LMFDB - Embedded newform 115.2.l.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	115.7
Dual form			115.2.l.a.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30561 + 0.0933793i) q^{2} +(0.136266 - 0.626406i) q^{3} +(-0.283736 + 0.0407951i) q^{4} +(-1.37401 + 1.76411i) q^{5} +(-0.119418 + 0.830568i) q^{6} +(-2.05467 + 3.76286i) q^{7} +(2.92471 - 0.636232i) q^{8} +(2.35508 + 1.07553i) q^{9} +O(q^{10})$	\(q+(-1.30561 + 0.0933793i) q^{2} +(0.136266 - 0.626406i) q^{3} +(-0.283736 + 0.0407951i) q^{4} +(-1.37401 + 1.76411i) q^{5} +(-0.119418 + 0.830568i) q^{6} +(-2.05467 + 3.76286i) q^{7} +(2.92471 - 0.636232i) q^{8} +(2.35508 + 1.07553i) q^{9} +(1.62920 - 2.43155i) q^{10} +(0.410379 - 0.355596i) q^{11} +(-0.0131094 + 0.183293i) q^{12} +(-5.09550 + 2.78235i) q^{13} +(2.33124 - 5.10470i) q^{14} +(0.917818 + 1.10108i) q^{15} +(-3.20905 + 0.942261i) q^{16} +(0.258417 + 0.345204i) q^{17} +(-3.17526 - 1.18431i) q^{18} +(0.232168 + 1.61476i) q^{19} +(0.317890 - 0.556595i) q^{20} +(2.07709 + 1.79981i) q^{21} +(-0.502591 + 0.502591i) q^{22} +(-2.24548 - 4.23767i) q^{23} -1.91875i q^{24} +(-1.22418 - 4.84782i) q^{25} +(6.39294 - 4.10849i) q^{26} +(2.14715 - 2.86825i) q^{27} +(0.429479 - 1.15148i) q^{28} +(8.41206 + 1.20947i) q^{29} +(-1.30113 - 1.35188i) q^{30} +(-2.54336 - 1.63452i) q^{31} +(-1.50700 + 0.562084i) q^{32} +(-0.166826 - 0.305519i) q^{33} +(-0.369628 - 0.426573i) q^{34} +(-3.81495 - 8.79488i) q^{35} +(-0.712097 - 0.209091i) q^{36} +(3.09715 + 8.30378i) q^{37} +(-0.453907 - 2.08658i) q^{38} +(1.04854 + 3.57099i) q^{39} +(-2.89620 + 6.03371i) q^{40} +(0.0749684 + 0.164158i) q^{41} +(-2.87994 - 2.15590i) q^{42} +(9.17525 + 1.99595i) q^{43} +(-0.101933 + 0.117637i) q^{44} +(-5.13326 + 2.67683i) q^{45} +(3.32744 + 5.32307i) q^{46} +(-3.18076 - 3.18076i) q^{47} +(0.152953 + 2.13856i) q^{48} +(-6.15291 - 9.57411i) q^{49} +(2.05099 + 6.21507i) q^{50} +(0.251452 - 0.114834i) q^{51} +(1.33227 - 0.997324i) q^{52} +(6.18111 + 3.37514i) q^{53} +(-2.53551 + 3.94533i) q^{54} +(0.0634443 + 1.21255i) q^{55} +(-3.61528 + 12.3125i) q^{56} +(1.04313 + 0.0746063i) q^{57} +(-11.0958 - 0.793590i) q^{58} +(-1.89837 + 6.46526i) q^{59} +(-0.305336 - 0.274973i) q^{60} +(-4.72595 + 7.35372i) q^{61} +(3.47328 + 1.89656i) q^{62} +(-8.88598 + 6.65196i) q^{63} +(7.99965 - 3.65332i) q^{64} +(2.09290 - 12.8120i) q^{65} +(0.246340 + 0.383312i) q^{66} +(-0.323924 - 4.52905i) q^{67} +(-0.0874048 - 0.0874048i) q^{68} +(-2.96048 + 0.829132i) q^{69} +(5.80211 + 11.1265i) q^{70} +(1.91222 - 2.20682i) q^{71} +(7.57221 + 1.64723i) q^{72} +(6.38913 + 4.78284i) q^{73} +(-4.81908 - 10.5523i) q^{74} +(-3.20352 + 0.106239i) q^{75} +(-0.131749 - 0.448694i) q^{76} +(0.494859 + 2.27483i) q^{77} +(-1.70244 - 4.56442i) q^{78} +(-2.33510 - 0.685646i) q^{79} +(2.74702 - 6.95579i) q^{80} +(3.58229 + 4.13418i) q^{81} +(-0.113209 - 0.207326i) q^{82} +(8.67329 - 3.23497i) q^{83} +(-0.662768 - 0.425935i) q^{84} +(-0.964047 - 0.0184391i) q^{85} +(-12.1657 - 1.74917i) q^{86} +(1.90390 - 5.10455i) q^{87} +(0.973999 - 1.30111i) q^{88} +(-5.65876 + 3.63667i) q^{89} +(6.45210 - 3.97425i) q^{90} -24.8904i q^{91} +(0.810000 + 1.11077i) q^{92} +(-1.37045 + 1.37045i) q^{93} +(4.44986 + 3.85582i) q^{94} +(-3.16762 - 1.80913i) q^{95} +(0.146739 + 1.02059i) q^{96} +(2.62729 + 0.979928i) q^{97} +(8.92734 + 11.9255i) q^{98} +(1.34893 - 0.396081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−1.30561	+	0.0933793i	−0.923208	+	0.0660292i	−0.524844	−	0.851198i	$-0.675876\pi$
$2$	−1.30561	+	0.0933793i	−0.923208	+	0.0660292i	−0.398364	+	0.917227i	$0.630422\pi$
$3$	0.136266	−	0.626406i	0.0786733	−	0.361655i	−0.920933	−	0.389722i	$-0.872571\pi$
$3$	0.136266	−	0.626406i	0.0786733	−	0.361655i	0.999606	+	0.0280661i	$0.00893489\pi$
$4$	−0.283736	+	0.0407951i	−0.141868	+	0.0203975i
$5$	−1.37401	+	1.76411i	−0.614477	+	0.788935i
$5$	−1.37401	+	1.76411i	−0.614477	+	0.788935i
$6$	−0.119418	+	0.830568i	−0.0487521	+	0.339078i
$7$	−2.05467	+	3.76286i	−0.776594	+	1.42223i	0.126134	+	0.992013i	$0.459743\pi$
$7$	−2.05467	+	3.76286i	−0.776594	+	1.42223i	−0.902728	+	0.430212i	$0.858439\pi$
$8$	2.92471	−	0.636232i	1.03404	−	0.224942i
$9$	2.35508	+	1.07553i	0.785027	+	0.358510i
$10$	1.62920	−	2.43155i	0.515198	−	0.768924i
$11$	0.410379	−	0.355596i	0.123734	−	0.107216i	−0.590796	−	0.806821i	$-0.701186\pi$
$11$	0.410379	−	0.355596i	0.123734	−	0.107216i	0.714530	+	0.699605i	$0.246641\pi$
$12$	−0.0131094	+	0.183293i	−0.00378434	+	0.0529120i
$13$	−5.09550	+	2.78235i	−1.41324	+	0.771686i	−0.990880	−	0.134744i	$-0.956979\pi$
$13$	−5.09550	+	2.78235i	−1.41324	+	0.771686i	−0.422356	+	0.906430i	$0.638797\pi$
$14$	2.33124	−	5.10470i	0.623050	−	1.36429i
$15$	0.917818	+	1.10108i	0.236980	+	0.284297i
$16$	−3.20905	+	0.942261i	−0.802261	+	0.235565i
$17$	0.258417	+	0.345204i	0.0626753	+	0.0837244i	0.830784	−	0.556596i	$-0.187893\pi$
$17$	0.258417	+	0.345204i	0.0626753	+	0.0837244i	−0.768108	+	0.640320i	$0.778802\pi$
$18$	−3.17526	−	1.18431i	−0.748415	−	0.279144i
$19$	0.232168	+	1.61476i	0.0532629	+	0.370452i	0.998968	+	0.0454250i	$0.0144642\pi$
$19$	0.232168	+	1.61476i	0.0532629	+	0.370452i	−0.945705	+	0.325027i	$0.894627\pi$
$20$	0.317890	−	0.556595i	0.0710823	−	0.124458i
$21$	2.07709	+	1.79981i	0.453258	+	0.392751i
$22$	−0.502591	+	0.502591i	−0.107153	+	0.107153i
$23$	−2.24548	−	4.23767i	−0.468215	−	0.883614i
$23$	−2.24548	−	4.23767i	−0.468215	−	0.883614i
$24$		−	1.91875i		−	0.391664i
$25$	−1.22418	−	4.84782i	−0.244836	−	0.969564i
$26$	6.39294	−	4.10849i	1.25376	−	0.805741i
$27$	2.14715	−	2.86825i	0.413219	−	0.551995i
$28$	0.429479	−	1.15148i	0.0811639	−	0.217609i
$29$	8.41206	+	1.20947i	1.56208	+	0.224593i	0.868464	−	0.495752i	$-0.165108\pi$
$29$	8.41206	+	1.20947i	1.56208	+	0.224593i	0.693615	+	0.720345i	$0.256017\pi$
$30$	−1.30113	−	1.35188i	−0.237553	−	0.246818i
$31$	−2.54336	−	1.63452i	−0.456802	−	0.293569i	0.291932	−	0.956439i	$-0.405702\pi$
$31$	−2.54336	−	1.63452i	−0.456802	−	0.293569i	−0.748734	+	0.662870i	$0.769338\pi$
$32$	−1.50700	+	0.562084i	−0.266403	+	0.0993633i
$33$	−0.166826	−	0.305519i	−0.0290407	−	0.0531841i
$34$	−0.369628	−	0.426573i	−0.0633906	−	0.0731566i
$35$	−3.81495	−	8.79488i	−0.644844	−	1.48661i
$36$	−0.712097	−	0.209091i	−0.118683	−	0.0348484i
$37$	3.09715	+	8.30378i	0.509168	+	1.36513i	0.896439	+	0.443167i	$0.146145\pi$
$37$	3.09715	+	8.30378i	0.509168	+	1.36513i	−0.387270	+	0.921966i	$0.626582\pi$
$38$	−0.453907	−	2.08658i	−0.0736334	−	0.338487i
$39$	1.04854	+	3.57099i	0.167900	+	0.571816i
$40$	−2.89620	+	6.03371i	−0.457930	+	0.954013i
$41$	0.0749684	+	0.164158i	0.0117081	+	0.0256372i	0.915396	−	0.402555i	$-0.131878\pi$
$41$	0.0749684	+	0.164158i	0.0117081	+	0.0256372i	−0.903688	+	0.428192i	$0.859151\pi$
$42$	−2.87994	−	2.15590i	−0.444385	−	0.332662i
$43$	9.17525	+	1.99595i	1.39921	+	0.304380i	0.848005	−	0.529988i	$-0.177804\pi$
$43$	9.17525	+	1.99595i	1.39921	+	0.304380i	0.551208	+	0.834368i	$0.314167\pi$
$44$	−0.101933	+	0.117637i	−0.0153669	+	0.0177344i
$45$	−5.13326	+	2.67683i	−0.765222	+	0.399039i
$46$	3.32744	+	5.32307i	0.490605	+	0.784844i
$47$	−3.18076	−	3.18076i	−0.463961	−	0.463961i	0.435990	−	0.899951i	$-0.356398\pi$
$47$	−3.18076	−	3.18076i	−0.463961	−	0.463961i	−0.899951	+	0.435990i	$0.856398\pi$
$48$	0.152953	+	2.13856i	0.0220769	+	0.308675i
$49$	−6.15291	−	9.57411i	−0.878987	−	1.36773i
$50$	2.05099	+	6.21507i	0.290054	+	0.878944i
$51$	0.251452	−	0.114834i	0.0352103	−	0.0160800i
$52$	1.33227	−	0.997324i	0.184752	−	0.138304i
$53$	6.18111	+	3.37514i	0.849041	+	0.463611i	0.843979	−	0.536376i	$-0.180207\pi$
$53$	6.18111	+	3.37514i	0.849041	+	0.463611i	0.00506170	+	0.999987i	$0.498389\pi$
$54$	−2.53551	+	3.94533i	−0.345039	+	0.536891i
$55$	0.0634443	+	1.21255i	0.00855482	+	0.163500i
$56$	−3.61528	+	12.3125i	−0.483112	+	1.64533i
$57$	1.04313	+	0.0746063i	0.138166	+	0.00988185i
$58$	−11.0958	−	0.793590i	−1.45695	−	0.104203i
$59$	−1.89837	+	6.46526i	−0.247147	+	0.841705i	0.738697	+	0.674038i	$0.235442\pi$
$59$	−1.89837	+	6.46526i	−0.247147	+	0.841705i	−0.985844	+	0.167667i	$0.946377\pi$
$60$	−0.305336	−	0.274973i	−0.0394188	−	0.0354988i
$61$	−4.72595	+	7.35372i	−0.605096	+	0.941548i	0.394646	+	0.918833i	$0.370867\pi$
$61$	−4.72595	+	7.35372i	−0.605096	+	0.941548i	−0.999742	+	0.0227144i	$0.992769\pi$
$62$	3.47328	+	1.89656i	0.441107	+	0.240863i
$63$	−8.88598	+	6.65196i	−1.11953	+	0.838069i
$64$	7.99965	−	3.65332i	0.999956	−	0.456665i
$65$	2.09290	−	12.8120i	0.259592	−	1.58913i
$66$	0.246340	+	0.383312i	0.0303223	+	0.0471825i
$67$	−0.323924	−	4.52905i	−0.0395736	−	0.553312i	−0.978104	−	0.208116i	$-0.933267\pi$
$67$	−0.323924	−	4.52905i	−0.0395736	−	0.553312i	0.938531	−	0.345196i	$-0.112188\pi$
$68$	−0.0874048	−	0.0874048i	−0.0105994	−	0.0105994i
$69$	−2.96048	+	0.829132i	−0.356400	+	0.0998158i
$70$	5.80211	+	11.1265i	0.693485	+	1.32987i
$71$	1.91222	−	2.20682i	0.226939	−	0.261901i	−0.630849	−	0.775906i	$-0.717293\pi$
$71$	1.91222	−	2.20682i	0.226939	−	0.261901i	0.857787	+	0.514005i	$0.171839\pi$
$72$	7.57221	+	1.64723i	0.892394	+	0.194128i
$73$	6.38913	+	4.78284i	0.747791	+	0.559789i	0.903794	−	0.427967i	$-0.140770\pi$
$73$	6.38913	+	4.78284i	0.747791	+	0.559789i	−0.156004	+	0.987756i	$0.549861\pi$
$74$	−4.81908	−	10.5523i	−0.560207	−	1.22668i
$75$	−3.20352	+	0.106239i	−0.369910	+	0.0122674i
$76$	−0.131749	−	0.448694i	−0.0151126	−	0.0514688i
$77$	0.494859	+	2.27483i	0.0563944	+	0.259241i
$78$	−1.70244	−	4.56442i	−0.192763	−	0.516819i
$79$	−2.33510	−	0.685646i	−0.262719	−	0.0771412i	0.147720	−	0.989029i	$-0.452806\pi$
$79$	−2.33510	−	0.685646i	−0.262719	−	0.0771412i	−0.410439	+	0.911888i	$0.634625\pi$
$80$	2.74702	−	6.95579i	0.307126	−	0.777681i
$81$	3.58229	+	4.13418i	0.398032	+	0.459354i
$82$	−0.113209	−	0.207326i	−0.0125018	−	0.0228954i
$83$	8.67329	−	3.23497i	0.952017	−	0.355084i	0.175004	−	0.984568i	$-0.444006\pi$
$83$	8.67329	−	3.23497i	0.952017	−	0.355084i	0.777014	+	0.629484i	$0.216734\pi$
$84$	−0.662768	−	0.425935i	−0.0723140	−	0.0464734i
$85$	−0.964047	−	0.0184391i	−0.104566	−	0.00200000i
$86$	−12.1657	−	1.74917i	−1.31186	−	0.188617i
$87$	1.90390	−	5.10455i	0.204119	−	0.547265i
$88$	0.973999	−	1.30111i	0.103829	−	0.138699i
$89$	−5.65876	+	3.63667i	−0.599828	+	0.385486i	−0.805030	−	0.593234i	$-0.797851\pi$
$89$	−5.65876	+	3.63667i	−0.599828	+	0.385486i	0.205203	+	0.978720i	$0.434215\pi$
$90$	6.45210	−	3.97425i	0.680111	−	0.418923i
$91$		−	24.8904i		−	2.60923i
$92$	0.810000	+	1.11077i	0.0844483	+	0.115806i
$93$	−1.37045	+	1.37045i	−0.142109	+	0.142109i
$94$	4.44986	+	3.85582i	0.458968	+	0.397698i
$95$	−3.16762	−	1.80913i	−0.324991	−	0.185613i
$96$	0.146739	+	1.02059i	0.0149764	+	0.104163i
$97$	2.62729	+	0.979928i	0.266761	+	0.0994966i	0.479285	−	0.877659i	$-0.340896\pi$
$97$	2.62729	+	0.979928i	0.266761	+	0.0994966i	−0.212525	+	0.977156i	$0.568169\pi$
$98$	8.92734	+	11.9255i	0.901798	+	1.20466i
$99$	1.34893	−	0.396081i	0.135573	−	0.0398077i
$100$	0.545111	+	1.32556i	0.0545111	+	0.132556i
$101$	5.30810	−	11.6231i	0.528176	−	1.15654i	−0.438074	−	0.898939i	$-0.644339\pi$
$101$	5.30810	−	11.6231i	0.528176	−	1.15654i	0.966250	−	0.257605i	$-0.0829334\pi$
$102$	−0.317575	+	0.173409i	−0.0314446	+	0.0171701i
$103$	0.689015	−	9.63369i	0.0678907	−	0.949236i	−0.843351	−	0.537363i	$-0.819420\pi$
$103$	0.689015	−	9.63369i	0.0678907	−	0.949236i	0.911241	−	0.411873i	$-0.135125\pi$
$104$	−13.1326	+	11.3795i	−1.28776	+	1.11585i
$105$	−6.02901	+	1.19126i	−0.588371	+	0.116255i
$106$	−8.38531	−	3.82944i	−0.814453	−	0.371948i
$107$	−2.01561	+	0.438470i	−0.194857	+	0.0423885i	−0.308934	−	0.951083i	$-0.599972\pi$
$107$	−2.01561	+	0.438470i	−0.194857	+	0.0423885i	0.114078	+	0.993472i	$0.463609\pi$
$108$	−0.492212	+	0.901419i	−0.0473631	+	0.0867391i
$109$	−1.22405	+	8.51344i	−0.117243	+	0.815440i	0.843327	+	0.537400i	$0.180594\pi$
$109$	−1.22405	+	8.51344i	−0.117243	+	0.815440i	−0.960570	+	0.278039i	$0.910315\pi$
$110$	−0.196061	−	1.57719i	−0.0186936	−	0.150380i
$111$	5.62357	−	0.808548i	0.533766	−	0.0767440i
$112$	3.04795	−	14.0112i	0.288004	−	1.32394i
$113$	1.84399	−	0.131885i	0.173468	−	0.0124067i	0.0156650	−	0.999877i	$-0.495013\pi$
$113$	1.84399	−	0.131885i	0.173468	−	0.0124067i	0.157803	+	0.987471i	$0.449559\pi$
$114$	−1.36889			−0.128209
$115$	10.5610	+	1.86132i	0.984822	+	0.173569i
$116$	−2.43614			−0.226190
$117$	−14.9928	+	1.07231i	−1.38609	+	0.0991348i
$118$	1.87482	−	8.61840i	0.172591	−	0.793388i
$119$	−1.82992	+	0.263102i	−0.167748	+	0.0241186i
$120$	3.38489	+	2.63639i	0.308997	+	0.240668i
$121$	−1.52350	+	10.5962i	−0.138500	+	0.963289i
$122$	5.48358	−	10.0424i	0.496460	−	0.909198i
$123$	0.113045	−	0.0245915i	0.0101929	−	0.00221734i
$124$	0.788324	+	0.360016i	0.0707936	+	0.0323304i
$125$	10.2341	+	4.50138i	0.915369	+	0.402615i
$126$	10.9805	−	9.51466i	0.978221	−	0.847633i
$127$	0.851470	−	11.9051i	0.0755558	−	1.05641i	−0.808338	−	0.588719i	$-0.799632\pi$
$127$	0.851470	−	11.9051i	0.0755558	−	1.05641i	0.883893	−	0.467688i	$-0.154913\pi$
$128$	−7.27996	+	3.97516i	−0.643464	+	0.351358i
$129$	2.50055	−	5.47545i	0.220161	−	0.482086i
$130$	−1.53614	+	16.9230i	−0.134728	+	1.48424i
$131$	4.62538	−	1.35813i	0.404121	−	0.118661i	−0.0733538	−	0.997306i	$-0.523370\pi$
$131$	4.62538	−	1.35813i	0.404121	−	0.118661i	0.477475	+	0.878645i	$0.341552\pi$
$132$	0.0597983	+	0.0798811i	0.00520477	+	0.00695276i
$133$	−6.55314	−	2.44420i	−0.568230	−	0.211939i
$134$	0.845840	+	5.88294i	0.0730694	+	0.508209i
$135$	2.10971	+	7.72882i	0.181575	+	0.665191i
$136$	0.975424	+	0.845210i	0.0836420	+	0.0724762i
$137$	−8.16753	+	8.16753i	−0.697799	+	0.697799i	−0.963935	−	0.266136i	$-0.914253\pi$
$137$	−8.16753	+	8.16753i	−0.697799	+	0.697799i	0.266136	+	0.963935i	$0.414253\pi$
$138$	3.78782	−	1.35897i	0.322441	−	0.115684i
$139$		−	0.555818i		−	0.0471439i	−0.999722	−	0.0235720i	$-0.992496\pi$
$139$		−	0.555818i		−	0.0471439i	0.999722	−	0.0235720i	$-0.00750388\pi$
$140$	1.44123	+	2.33979i	0.121806	+	0.197749i
$141$	−2.42587	+	1.55901i	−0.204295	+	0.131293i
$142$	−2.29055	+	3.05981i	−0.192219	+	0.256774i
$143$	−1.10169	+	2.95376i	−0.0921283	+	0.247005i
$144$	−8.57099	−	1.23232i	−0.714249	−	0.102694i
$145$	−13.6919	+	13.1780i	−1.13705	+	1.09437i
$146$	−8.78835	−	5.64793i	−0.727329	−	0.467426i
$147$	−6.83571	+	2.54959i	−0.563800	+	0.210286i
$148$	−1.21753	−	2.22973i	−0.100080	−	0.183283i
$149$	4.29837	+	4.96059i	0.352137	+	0.406387i	0.903990	−	0.427554i	$-0.140625\pi$
$149$	4.29837	+	4.96059i	0.352137	+	0.406387i	−0.551853	+	0.833941i	$0.686079\pi$
$150$	4.17264	−	0.437849i	0.340694	−	0.0357502i
$151$	−6.29276	−	1.84772i	−0.512097	−	0.150365i	0.0154670	−	0.999880i	$-0.495076\pi$
$151$	−6.29276	−	1.84772i	−0.512097	−	0.150365i	−0.527564	+	0.849515i	$0.676895\pi$
$152$	1.70639	+	4.57500i	0.138406	+	0.371081i
$153$	0.237315	+	1.09092i	0.0191858	+	0.0881956i
$154$	−0.858517	−	2.92384i	−0.0691813	−	0.235610i
$155$	6.37809	−	2.24093i	0.512301	−	0.179996i
$156$	−0.443186	−	0.970442i	−0.0354833	−	0.0776976i
$157$	4.69119	+	3.51178i	0.374398	+	0.280271i	0.769862	−	0.638211i	$-0.220325\pi$
$157$	4.69119	+	3.51178i	0.374398	+	0.280271i	−0.395464	+	0.918482i	$0.629416\pi$
$158$	3.11276	+	0.677139i	0.247638	+	0.0538703i
$159$	2.95648	−	3.41197i	0.234465	−	0.270586i
$160$	1.07906	−	3.43083i	0.0853075	−	0.271231i
$161$	20.5595	+	0.257596i	1.62031	+	0.0203014i
$162$	−5.06313	−	5.06313i	−0.397797	−	0.397797i
$163$	−0.433158	−	6.05634i	−0.0339276	−	0.474369i	−0.985805	−	0.167892i	$-0.946304\pi$
$163$	−0.433158	−	6.05634i	−0.0339276	−	0.474369i	0.951878	−	0.306478i	$-0.0991504\pi$
$164$	−0.0279680	−	0.0435191i	−0.00218394	−	0.00339827i
$165$	0.768192	+	0.125487i	0.0598037	+	0.00976918i
$166$	−11.0219	+	5.03353i	−0.855464	+	0.390677i
$167$	7.25483	−	5.43090i	0.561396	−	0.420255i	−0.280533	−	0.959844i	$-0.590511\pi$
$167$	7.25483	−	5.43090i	0.561396	−	0.420255i	0.841929	+	0.539589i	$0.181420\pi$
$168$	7.21998	+	3.94241i	0.557034	+	0.304164i
$169$	11.1943	−	17.4186i	0.861099	−	1.33990i
$170$	1.26039	−	0.0659478i	0.0966679	−	0.00505797i
$171$	−1.18995	+	4.05260i	−0.0909977	+	0.309910i
$172$	−2.68477	−	0.192019i	−0.204712	−	0.0146413i
$173$	−6.24169	−	0.446415i	−0.474547	−	0.0339403i	−0.167982	−	0.985790i	$-0.553725\pi$
$173$	−6.24169	−	0.446415i	−0.474547	−	0.0339403i	−0.306565	+	0.951850i	$0.599180\pi$
$174$	−2.00910	+	6.84235i	−0.152309	+	0.518717i
$175$	20.7569	+	5.35428i	1.56908	+	0.404746i
$176$	−0.981862	+	1.52781i	−0.0740106	+	0.115163i
$177$	3.79119	+	2.07015i	0.284963	+	0.155602i
$178$	7.04857	−	5.27649i	0.528313	−	0.395490i
$179$	−21.2881	+	9.72196i	−1.59115	+	0.726653i	−0.996978	−	0.0776856i	$-0.975247\pi$
$179$	−21.2881	+	9.72196i	−1.59115	+	0.726653i	−0.594171	+	0.804339i	$0.702520\pi$
$180$	1.34729	−	0.968926i	0.100421	−	0.0722195i
$181$	−4.23432	−	6.58872i	−0.314734	−	0.489736i	0.647460	−	0.762099i	$-0.275831\pi$
$181$	−4.23432	−	6.58872i	−0.314734	−	0.489736i	−0.962195	+	0.272363i	$0.912195\pi$
$182$	2.32425	+	32.4973i	0.172285	+	2.40886i
$183$	3.96243	+	3.96243i	0.292911	+	0.292911i
$184$	−9.26352	−	10.9653i	−0.682916	−	0.808372i
$185$	−18.9043	−	5.94578i	−1.38987	−	0.437142i
$186$	1.66130	−	1.91725i	0.121813	−	0.140579i
$187$	0.228802	+	0.0497728i	0.0167317	+	0.00363975i
$188$	1.03225	+	0.772736i	0.0752849	+	0.0563576i
$189$	6.38113	+	13.9727i	0.464159	+	1.01637i
$190$	4.30463	+	2.06624i	0.312290	+	0.149901i
$191$	−1.33899	−	4.56019i	−0.0968861	−	0.329964i	0.896759	−	0.442518i	$-0.145915\pi$
$191$	−1.33899	−	4.56019i	−0.0968861	−	0.329964i	−0.993646	+	0.112555i	$0.964097\pi$
$192$	−1.19838	−	5.50885i	−0.0864854	−	0.397567i
$193$	−2.59138	−	6.94777i	−0.186532	−	0.500111i	0.809700	−	0.586844i	$-0.199630\pi$
$193$	−2.59138	−	6.94777i	−0.186532	−	0.500111i	−0.996232	+	0.0867330i	$0.972357\pi$
$194$	−3.52173	−	1.03407i	−0.252845	−	0.0742421i
$195$	−7.74033	−	3.05685i	−0.554296	−	0.218905i
$196$	2.13638	+	2.46551i	0.152598	+	0.176108i
$197$	−7.60125	−	13.9206i	−0.541567	−	0.991805i	−0.994939	−	0.100484i	$-0.967961\pi$
$197$	−7.60125	−	13.9206i	−0.541567	−	0.991805i	0.453372	−	0.891321i	$-0.350221\pi$
$198$	−1.72419	+	0.643091i	−0.122533	+	0.0457025i
$199$	10.9496	+	7.03690i	0.776199	+	0.498833i	0.867770	−	0.496966i	$-0.165553\pi$
$199$	10.9496	+	7.03690i	0.776199	+	0.498833i	−0.0915713	+	0.995799i	$0.529189\pi$
$200$	−6.66471	−	13.3996i	−0.471266	−	0.947496i
$201$	−2.88116	−	0.414249i	−0.203222	−	0.0292189i
$202$	−5.84497	+	15.6710i	−0.411251	+	1.10261i
$203$	−21.8351	+	29.1683i	−1.53252	+	2.04721i
$204$	−0.0666611	+	0.0428405i	−0.00466721	+	0.00299944i
$205$	−0.392600	−	0.0933023i	−0.0274204	−	0.00651652i
$206$			12.6422i			0.880825i
$207$	−0.730559	−	12.3951i	−0.0507774	−	0.861521i
$208$	13.7300	−	13.7300i	0.952003	−	0.952003i
$209$	0.669479	+	0.580107i	0.0463088	+	0.0401268i
$210$	7.76032	−	2.11831i	0.535513	−	0.146177i
$211$	3.42270	+	23.8054i	0.235628	+	1.63883i	0.673066	+	0.739583i	$0.264977\pi$
$211$	3.42270	+	23.8054i	0.235628	+	1.63883i	−0.437437	+	0.899249i	$0.644114\pi$
$212$	−1.89149	−	0.705490i	−0.129908	−	0.0484533i
$213$	−1.12179	−	1.49854i	−0.0768640	−	0.102678i
$214$	2.59067	−	0.760689i	0.177095	−	0.0519996i
$215$	−16.1280	+	13.4437i	−1.09992	+	0.916853i
$216$	4.45491	−	9.75489i	0.303118	−	0.663736i
$217$	11.3763	−	6.21190i	0.772270	−	0.421692i
$218$	0.803154	−	11.2296i	0.0543965	−	0.760562i
$219$	3.86662	−	3.35044i	0.261282	−	0.226402i
$220$	−0.0674673	−	0.341455i	−0.00454865	−	0.0230209i
$221$	−2.27724	−	1.03998i	−0.153184	−	0.0699568i
$222$	−7.26671	+	1.58078i	−0.487710	+	0.106095i
$223$	−7.29643	+	13.3624i	−0.488605	+	0.894813i	0.510779	+	0.859712i	$0.329357\pi$
$223$	−7.29643	+	13.3624i	−0.488605	+	0.894813i	−0.999384	+	0.0351010i	$0.988825\pi$
$224$	0.981364	−	6.82554i	0.0655702	−	0.456051i
$225$	2.33093	−	12.7337i	0.155395	−	0.848910i
$226$	−2.39522	+	0.344381i	−0.159328	+	0.0229079i
$227$	−1.60723	+	7.38830i	−0.106675	+	0.490379i	0.892547	+	0.450954i	$0.148916\pi$
$227$	−1.60723	+	7.38830i	−0.106675	+	0.490379i	−0.999223	+	0.0394248i	$0.987447\pi$
$228$	−0.299018	+	0.0213862i	−0.0198029	+	0.00141633i
$229$	12.3914			0.818845			0.409423	−	0.912345i	$-0.365730\pi$
$229$	12.3914			0.818845			0.409423	+	0.912345i	$0.365730\pi$
$230$	−13.9624	−	1.44399i	−0.920656	−	0.0952136i
$231$	1.49240			0.0981927
$232$	25.3723	−	1.81466i	1.66577	−	0.119139i
$233$	2.49649	−	11.4762i	0.163550	−	0.751829i	−0.820170	−	0.572120i	$-0.806121\pi$
$233$	2.49649	−	11.4762i	0.163550	−	0.751829i	0.983720	−	0.179708i	$-0.0575154\pi$
$234$	19.4747	−	2.80004i	1.27310	−	0.183044i
$235$	9.98161	−	1.24081i	0.651129	−	0.0809416i
$236$	0.274885	−	1.91187i	0.0178935	−	0.124452i
$237$	−0.747687	+	1.36929i	−0.0485675	+	0.0889447i
$238$	2.36460	−	0.514386i	0.153274	−	0.0333427i
$239$	7.89157	+	3.60396i	0.510463	+	0.233121i	0.653959	−	0.756530i	$-0.273107\pi$
$239$	7.89157	+	3.60396i	0.510463	+	0.233121i	−0.143496	+	0.989651i	$0.545834\pi$
$240$	−3.98282	−	2.66859i	−0.257090	−	0.172256i
$241$	−0.183056	+	0.158619i	−0.0117917	+	0.0102176i	−0.660737	−	0.750618i	$-0.729756\pi$
$241$	−0.183056	+	0.158619i	−0.0117917	+	0.0102176i	0.648945	+	0.760835i	$0.275211\pi$
$242$	0.999639	−	13.9768i	0.0642592	−	0.898461i
$243$	12.5117	−	6.83191i	0.802626	−	0.438267i
$244$	1.04093	−	2.27931i	0.0666385	−	0.145918i
$245$	25.3440	+	2.30053i	1.61917	+	0.146975i
$246$	−0.145297	+	0.0426630i	−0.00926379	+	0.00272009i
$247$	−5.67585	−	7.58204i	−0.361145	−	0.482434i
$248$	−8.47854	−	3.16233i	−0.538388	−	0.200808i
$249$	−0.844527	−	5.87381i	−0.0535197	−	0.372238i
$250$	−13.7822	−	4.92140i	−0.871661	−	0.311257i
$251$	−19.2265	−	16.6599i	−1.21357	−	1.05156i	−0.997164	−	0.0752560i	$-0.976023\pi$
$251$	−19.2265	−	16.6599i	−1.21357	−	1.05156i	−0.216401	−	0.976305i	$-0.569432\pi$
$252$	2.24990	−	2.24990i	0.141731	−	0.141731i
$253$	−2.42839	−	0.940566i	−0.152672	−	0.0591329i
$254$			15.6230i			0.980273i
$255$	−0.142917	+	0.601372i	−0.00894983	+	0.0376594i
$256$	−5.66299	+	3.63938i	−0.353937	+	0.227461i
$257$	−0.0999564	+	0.133526i	−0.00623511	+	0.00832913i	−0.803648	−	0.595105i	$-0.797110\pi$
$257$	−0.0999564	+	0.133526i	−0.00623511	+	0.00832913i	0.797413	+	0.603434i	$0.206201\pi$
$258$	−2.75346	+	7.38232i	−0.171423	+	0.459603i
$259$	−37.6096	−	5.40744i	−2.33694	−	0.336002i
$260$	−0.0711630	+	3.72061i	−0.00441334	+	0.230742i
$261$	18.5102	+	11.8958i	1.14576	+	0.736332i
$262$	−5.91214	+	2.20511i	−0.365253	+	0.136232i
$263$	2.03487	+	3.72658i	0.125475	+	0.229791i	0.932864	−	0.360229i	$-0.117302\pi$
$263$	2.03487	+	3.72658i	0.125475	+	0.229791i	−0.807388	+	0.590020i	$0.799120\pi$
$264$	−0.682300	−	0.787416i	−0.0419926	−	0.0484621i
$265$	−14.4471	+	6.26668i	−0.887475	+	0.384959i
$266$	8.78411	+	2.57925i	0.538588	+	0.158144i
$267$	1.50693	+	4.04024i	0.0922226	+	0.247258i
$268$	0.276672	+	1.27184i	0.0169004	+	0.0776900i
$269$	−2.24088	−	7.63175i	−0.136629	−	0.465316i	0.862544	−	0.505983i	$-0.168870\pi$
$269$	−2.24088	−	7.63175i	−0.136629	−	0.465316i	−0.999173	+	0.0406666i	$0.987052\pi$
$270$	−3.47618	−	9.89385i	−0.211554	−	0.602120i
$271$	−3.74193	−	8.19368i	−0.227306	−	0.497731i	0.761273	−	0.648431i	$-0.224574\pi$
$271$	−3.74193	−	8.19368i	−0.227306	−	0.497731i	−0.988580	+	0.150700i	$0.951847\pi$
$272$	−1.15454	−	0.864281i	−0.0700045	−	0.0524047i
$273$	−15.5915	−	3.39173i	−0.943641	−	0.205277i
$274$	9.90096	−	11.4263i	0.598139	−	0.690289i
$275$	−2.22624	−	1.55413i	−0.134247	−	0.0937177i
$276$	0.806170	−	0.356028i	0.0485257	−	0.0214303i
$277$	12.8413	+	12.8413i	0.771558	+	0.771558i	0.978379	−	0.206821i	$-0.0663117\pi$
$277$	12.8413	+	12.8413i	0.771558	+	0.771558i	−0.206821	+	0.978379i	$0.566312\pi$
$278$	0.0519020	+	0.725684i	0.00311287	+	0.0435236i
$279$	−4.23185	−	6.58489i	−0.253354	−	0.394227i
$280$	−16.7532	−	23.2953i	−1.00120	−	1.39216i
$281$	20.2929	−	9.26746i	1.21057	−	0.552850i	0.295192	−	0.955438i	$-0.404616\pi$
$281$	20.2929	−	9.26746i	1.21057	−	0.552850i	0.915381	+	0.402588i	$0.131889\pi$
$282$	3.02167	−	2.26200i	0.179938	−	0.134700i
$283$	23.6819	+	12.9313i	1.40775	+	0.768687i	0.990159	−	0.139950i	$-0.0446940\pi$
$283$	23.6819	+	12.9313i	1.40775	+	0.768687i	0.417587	+	0.908637i	$0.362876\pi$
$284$	−0.452538	+	0.704163i	−0.0268532	+	0.0417844i
$285$	−1.56489	+	1.73769i	−0.0926961	+	0.102932i
$286$	1.16257	−	3.95934i	0.0687440	−	0.234121i
$287$	−0.771738	−	0.0551958i	−0.0455543	−	0.00325810i
$288$	−4.15365	−	0.297075i	−0.244756	−	0.0175053i
$289$	4.73707	−	16.1330i	0.278651	−	0.948998i
$290$	16.6458	−	18.4839i	0.977475	−	1.08541i
$291$	0.971843	−	1.51222i	0.0569705	−	0.0886478i
$292$	−2.00794	−	1.09642i	−0.117506	−	0.0641630i
$293$	6.89923	−	5.16470i	0.403058	−	0.301725i	−0.378449	−	0.925622i	$-0.623542\pi$
$293$	6.89923	−	5.16470i	0.403058	−	0.301725i	0.781507	+	0.623897i	$0.214452\pi$
$294$	8.68672	−	3.96709i	0.506620	−	0.231365i
$295$	−8.79705	−	12.2323i	−0.512184	−	0.712191i
$296$	14.3414	+	22.3157i	0.833577	+	1.29707i
$297$	−0.138793	−	1.94059i	−0.00805362	−	0.112604i
$298$	−6.07523	−	6.07523i	−0.351929	−	0.351929i
$299$	23.2325	+	15.3453i	1.34357	+	0.887441i
$300$	0.904619	−	0.160831i	0.0522282	−	0.00928561i
$301$	−26.3626	+	30.4241i	−1.51952	+	1.75362i
$302$	8.38845	+	1.82480i	0.482701	+	0.105005i
$303$	−6.55748	−	4.90886i	−0.376717	−	0.282007i
$304$	−2.26656	−	4.96308i	−0.129996	−	0.284652i
$305$	−6.47927	−	18.4412i	−0.371002	−	1.05594i
$306$	−0.411711	−	1.40216i	−0.0235359	−	0.0801561i
$307$	6.49690	+	29.8658i	0.370798	+	1.70453i	0.663375	+	0.748287i	$0.269124\pi$
$307$	6.49690	+	29.8658i	0.370798	+	1.70453i	−0.292577	+	0.956242i	$0.594513\pi$
$308$	−0.233211	−	0.625263i	−0.0132884	−	0.0356277i
$309$	−5.94071	−	1.74435i	−0.337955	−	0.0992326i
$310$	−8.11807	+	3.52137i	−0.461075	+	0.200000i
$311$	3.82715	+	4.41677i	0.217018	+	0.250452i	0.853811	−	0.520582i	$-0.174285\pi$
$311$	3.82715	+	4.41677i	0.217018	+	0.250452i	−0.636794	+	0.771034i	$0.719740\pi$
$312$	5.33864	+	9.77699i	0.302241	+	0.553513i
$313$	−32.0118	+	11.9398i	−1.80942	+	0.674877i	−0.813821	+	0.581116i	$0.802616\pi$
$313$	−32.0118	+	11.9398i	−1.80942	+	0.674877i	−0.995595	+	0.0937614i	$0.970111\pi$
$314$	−6.45281	−	4.14697i	−0.364153	−	0.234027i
$315$	0.474644	−	24.8157i	0.0267431	−	1.39821i
$316$	0.690521	+	0.0992820i	0.0388449	+	0.00558505i
$317$	2.31565	−	6.20850i	0.130060	−	0.348704i	−0.855555	−	0.517712i	$-0.826784\pi$
$317$	2.31565	−	6.20850i	0.130060	−	0.348704i	0.985615	+	0.169008i	$0.0540565\pi$
$318$	−3.54142	+	4.73078i	−0.198593	+	0.265289i
$319$	3.88221	−	2.49495i	0.217362	−	0.139690i
$320$	−4.54676	+	19.1320i	−0.254171	+	1.06951i
$321$			1.32234i			0.0738059i
$322$	−26.8668	+	1.58351i	−1.49723	+	0.0882454i
$323$	−0.497427	+	0.497427i	−0.0276776	+	0.0276776i
$324$	−1.18508	−	1.02688i	−0.0658377	−	0.0570487i
$325$	19.7262	+	21.2960i	1.09421	+	1.18129i
$326$	1.13107	+	7.86679i	0.0626444	+	0.435701i
$327$	5.16607	+	1.92684i	0.285684	+	0.106555i
$328$	0.323703	+	0.432417i	0.0178735	+	0.0238762i
$329$	18.5042	−	5.43331i	1.02017	−	0.299548i
$330$	−1.01468	−	0.0921048i	−0.0558563	−	0.00507020i
$331$	0.461152	−	1.00978i	0.0253472	−	0.0555026i	−0.896535	−	0.442973i	$-0.853924\pi$
$331$	0.461152	−	1.00978i	0.0253472	−	0.0555026i	0.921882	+	0.387470i	$0.126651\pi$
$332$	−2.32895	+	1.27170i	−0.127818	+	0.0697938i
$333$	−1.63692	+	22.8872i	−0.0897027	+	1.25421i
$334$	−8.96487	+	7.76810i	−0.490536	+	0.425052i
$335$	8.43483	+	5.65153i	0.460844	+	0.308776i
$336$	−8.36137	−	3.81851i	−0.456150	−	0.208317i
$337$	−17.2106	+	3.74393i	−0.937519	+	0.203945i	−0.655269	−	0.755396i	$-0.727445\pi$
$337$	−17.2106	+	3.74393i	−0.937519	+	0.203945i	−0.282251	+	0.959341i	$0.591081\pi$
$338$	−12.9889	+	23.7873i	−0.706501	+	1.29386i
$339$	0.168660	−	1.17306i	0.00916036	−	0.0637117i
$340$	0.274287	−	0.0340965i	0.0148753	−	0.00184914i
$341$	−1.62497	+	0.233636i	−0.0879972	+	0.0126521i
$342$	1.17519	−	5.40224i	0.0635468	−	0.292120i
$343$	18.7337	−	1.33986i	1.01153	−	0.0723457i
$344$	28.1048			1.51531
$345$	2.60506	−	6.36186i	0.140251	−	0.342511i
$346$	8.19092			0.440347
$347$	14.9639	−	1.07024i	0.803305	−	0.0574535i	0.336353	−	0.941736i	$-0.390806\pi$
$347$	14.9639	−	1.07024i	0.803305	−	0.0574535i	0.466952	+	0.884282i	$0.345352\pi$
$348$	−0.331964	+	1.52601i	−0.0177951	+	0.0818029i
$349$	−8.16540	+	1.17401i	−0.437084	+	0.0628432i	−0.357345	−	0.933973i	$-0.616318\pi$
$349$	−8.16540	+	1.17401i	−0.437084	+	0.0628432i	−0.0797393	+	0.996816i	$0.525409\pi$
$350$	−27.6005	−	5.05236i	−1.47531	−	0.270060i
$351$	−2.96029	+	20.5893i	−0.158009	+	1.09898i
$352$	−0.418569	+	0.766552i	−0.0223098	+	0.0408573i
$353$	6.96045	−	1.51415i	0.370467	−	0.0805903i	−0.0234773	−	0.999724i	$-0.507474\pi$
$353$	6.96045	−	1.51415i	0.370467	−	0.0805903i	0.393945	+	0.919134i	$0.371110\pi$
$354$	−5.14314	−	2.34879i	−0.273355	−	0.124837i
$355$	1.26566	+	6.40556i	0.0671744	+	0.339972i
$356$	1.45724	−	1.26270i	0.0772333	−	0.0669231i
$357$	−0.0845471	+	1.18212i	−0.00447470	+	0.0625645i
$358$	26.8862	−	14.6810i	1.42098	−	0.775914i
$359$	−8.16532	+	17.8796i	−0.430949	+	0.943647i	0.562223	+	0.826986i	$0.309946\pi$
$359$	−8.16532	+	17.8796i	−0.430949	+	0.943647i	−0.993172	+	0.116661i	$0.962781\pi$
$360$	−13.3102	+	11.0949i	−0.701510	+	0.584753i
$361$	15.6768	−	4.60313i	0.825095	−	0.242270i
$362$	6.14363	+	8.20693i	0.322902	+	0.431347i
$363$	6.42990	+	2.39823i	0.337482	+	0.125874i
$364$	1.01541	+	7.06231i	0.0532218	+	0.370166i
$365$	−17.2162	+	4.69945i	−0.901137	+	0.245980i
$366$	−5.54341	−	4.80339i	−0.289758	−	0.251077i
$367$	−16.7405	+	16.7405i	−0.873845	+	0.873845i	−0.992889	−	0.119044i	$-0.962017\pi$
$367$	−16.7405	+	16.7405i	−0.873845	+	0.873845i	0.119044	+	0.992889i	$0.462017\pi$
$368$	11.1988	+	11.4830i	0.583780	+	0.598594i
$369$			0.467236i			0.0243233i
$370$	25.2370	+	5.99762i	1.31201	+	0.311801i
$371$	−25.4003	+	16.3238i	−1.31872	+	0.847490i
$372$	0.332938	−	0.444753i	0.0172620	−	0.0230594i
$373$	4.05572	−	10.8738i	0.209997	−	0.563024i	−0.788660	−	0.614829i	$-0.789225\pi$
$373$	4.05572	−	10.8738i	0.209997	−	0.563024i	0.998657	+	0.0518055i	$0.0164976\pi$
$374$	−0.303375	−	0.0436187i	−0.0156871	−	0.00225547i
$375$	4.21426	−	5.79734i	0.217623	−	0.299373i
$376$	−11.3265	−	7.27910i	−0.584119	−	0.375391i
$377$	−46.2288	+	17.2424i	−2.38090	+	0.888031i
$378$	−9.63605	−	17.6471i	−0.495625	−	0.907670i
$379$	−15.0147	−	17.3278i	−0.771252	−	0.890072i	0.225194	−	0.974314i	$-0.427699\pi$
$379$	−15.0147	−	17.3278i	−0.771252	−	0.890072i	−0.996445	+	0.0842422i	$0.973153\pi$
$380$	0.972571	+	0.384093i	0.0498919	+	0.0197035i
$381$	−7.34140	−	2.15563i	−0.376111	−	0.110436i
$382$	2.17404	+	5.82881i	0.111233	+	0.298228i
$383$	−6.45342	−	29.6659i	−0.329754	−	1.51586i	−0.781611	−	0.623766i	$-0.785602\pi$
$383$	−6.45342	−	29.6659i	−0.329754	−	1.51586i	0.451857	−	0.892090i	$-0.350762\pi$
$384$	1.49805	+	5.10189i	0.0764470	+	0.260355i
$385$	−4.69300	−	2.25266i	−0.239177	−	0.114806i
$386$	4.03212	+	8.82912i	0.205230	+	0.449390i
$387$	19.4618	+	14.5689i	0.989296	+	0.740578i
$388$	−0.785432	−	0.170860i	−0.0398743	−	0.00867412i
$389$	15.1708	−	17.5081i	0.769191	−	0.887693i	−0.227089	−	0.973874i	$-0.572921\pi$
$389$	15.1708	−	17.5081i	0.769191	−	0.887693i	0.996280	+	0.0861807i	$0.0274662\pi$
$390$	10.3913	+	3.26827i	0.526185	+	0.165495i
$391$	0.882591	−	1.87023i	0.0446345	−	0.0945818i
$392$	−24.0868	−	24.0868i	−1.21657	−	1.21657i
$393$	−0.220460	−	3.08243i	−0.0111207	−	0.155488i
$394$	11.2242	+	17.4652i	0.565467	+	0.879883i
$395$	4.41801	−	3.17728i	0.222294	−	0.159867i
$396$	−0.366581	+	0.167412i	−0.0184214	+	0.00841278i
$397$	22.7911	−	17.0612i	1.14385	−	0.856276i	0.152602	−	0.988288i	$-0.451235\pi$
$397$	22.7911	−	17.0612i	1.14385	−	0.856276i	0.991248	+	0.132012i	$0.0421437\pi$
$398$	−14.9531	−	8.16500i	−0.749531	−	0.409275i
$399$	−2.42403	+	3.77186i	−0.121353	+	0.188829i
$400$	8.49636	+	14.4034i	0.424818	+	0.720169i
$401$	−1.20037	+	4.08807i	−0.0599434	+	0.204148i	−0.984020	−	0.178060i	$-0.943018\pi$
$401$	−1.20037	+	4.08807i	−0.0599434	+	0.204148i	0.924076	+	0.382208i	$0.124836\pi$
$402$	3.80037	+	0.271808i	0.189545	+	0.0135565i
$403$	17.5075	+	1.25216i	0.872112	+	0.0623747i
$404$	−1.03193	+	3.51444i	−0.0513406	+	0.174850i
$405$	−12.2153	+	0.639141i	−0.606982	+	0.0317592i
$406$	25.7845	−	40.1214i	1.27966	−	1.99119i
$407$	4.22379	+	2.30637i	0.209366	+	0.114322i
$408$	0.662362	−	0.495838i	0.0327918	−	0.0245476i
$409$	−5.53849	+	2.52934i	−0.273861	+	0.125068i	−0.547612	−	0.836733i	$-0.684463\pi$
$409$	−5.53849	+	2.52934i	−0.273861	+	0.125068i	0.273751	+	0.961801i	$0.411736\pi$
$410$	0.521297	+	0.0851560i	0.0257450	+	0.00420556i
$411$	4.00323	+	6.22914i	0.197465	+	0.307261i
$412$	0.197509	+	2.76153i	0.00973055	+	0.136051i
$413$	−20.4273	−	20.4273i	−1.00516	−	1.00516i
$414$	2.11128	+	16.1150i	0.103764	+	0.792010i
$415$	−6.21036	+	19.7455i	−0.304855	+	0.969270i
$416$	6.11502	−	7.05711i	0.299814	−	0.346003i
$417$	−0.348168	−	0.0757393i	−0.0170499	−	0.00370897i
$418$	−0.928251	−	0.694880i	−0.0454022	−	0.0339877i
$419$	−0.940522	−	2.05946i	−0.0459475	−	0.100611i	0.885266	−	0.465085i	$-0.153976\pi$
$419$	−0.940522	−	2.05946i	−0.0459475	−	0.100611i	−0.931214	+	0.364474i	$0.881249\pi$
$420$	1.66205	−	0.583957i	0.0810997	−	0.0284942i
$421$	−3.93462	−	13.4001i	−0.191762	−	0.653080i	−0.998099	−	0.0616248i	$-0.980372\pi$
$421$	−3.93462	−	13.4001i	−0.191762	−	0.653080i	0.806338	−	0.591455i	$-0.201446\pi$
$422$	−6.69166	−	30.7610i	−0.325745	−	1.49742i
$423$	−4.06994	−	10.9119i	−0.197887	−	0.530557i
$424$	20.2253	+	5.93869i	0.982229	+	0.288408i
$425$	1.35714	−	1.67535i	0.0658310	−	0.0812665i
$426$	1.60456	+	1.85176i	0.0777412	+	0.0897181i
$427$	−17.9607	−	32.8926i	−0.869179	−	1.59178i
$428$	0.554015	−	0.206637i	0.0267793	−	0.00998817i
$429$	1.70013	+	1.09260i	0.0820828	+	0.0527514i
$430$	19.8016	−	19.0583i	0.954916	−	0.919073i
$431$	30.1975	+	4.34175i	1.45456	+	0.209135i	0.823818	−	0.566854i	$-0.191840\pi$
$431$	30.1975	+	4.34175i	1.45456	+	0.209135i	0.630746	+	0.775989i	$0.282749\pi$
$432$	−4.18765	+	11.2275i	−0.201478	+	0.540185i
$433$	7.51949	−	10.0449i	0.361364	−	0.482725i	−0.582607	−	0.812754i	$-0.697967\pi$
$433$	7.51949	−	10.0449i	0.361364	−	0.482725i	0.943971	+	0.330028i	$0.107058\pi$
$434$	−14.2729	+	9.17265i	−0.685122	+	0.440301i
$435$	6.38901	+	10.3724i	0.306330	+	0.497319i
$436$		−	2.46550i		−	0.118076i
$437$	6.32149	−	4.60977i	0.302398	−	0.220515i
$438$	−4.73545	+	4.73545i	−0.226268	+	0.226268i
$439$	−19.7301	−	17.0962i	−0.941667	−	0.815959i	0.0414117	−	0.999142i	$-0.486814\pi$
$439$	−19.7301	−	17.0962i	−0.941667	−	0.815959i	−0.983079	+	0.183183i	$0.941360\pi$
$440$	0.957017	+	3.50598i	0.0456240	+	0.167141i
$441$	−4.19336	−	29.1654i	−0.199684	−	1.38883i
$442$	3.07031	+	1.14517i	0.146040	+	0.0544700i
$443$	−22.1164	−	29.5440i	−1.05078	−	1.40368i	−0.910471	−	0.413572i	$-0.864281\pi$
$443$	−22.1164	−	29.5440i	−1.05078	−	1.40368i	−0.140310	−	0.990108i	$-0.544810\pi$
$444$	−1.56262	+	0.458828i	−0.0741589	+	0.0217750i
$445$	1.35972	−	14.9795i	0.0644571	−	0.710097i
$446$	8.27854	−	18.1275i	0.392000	−	0.858361i
$447$	3.69306	−	2.01657i	0.174676	−	0.0953803i
$448$	−2.68977	+	37.6079i	−0.127080	+	1.77681i
$449$	23.0284	−	19.9542i	1.08678	−	0.941698i	0.0882587	−	0.996098i	$-0.471870\pi$
$449$	23.0284	−	19.9542i	1.08678	−	0.941698i	0.998519	+	0.0543992i	$0.0173243\pi$
$450$	−1.85424	+	16.8429i	−0.0874095	+	0.793982i
$451$	0.0891393	+	0.0407085i	0.00419740	+	0.00191689i
$452$	−0.517826	+	0.112646i	−0.0243565	+	0.00529843i
$453$	−2.01491	+	3.69004i	−0.0946689	+	0.173373i
$454$	1.40850	−	9.79635i	0.0661043	−	0.459766i
$455$	43.9095	+	34.1998i	2.05851	+	1.60331i
$456$	3.09833	−	0.445472i	0.145092	−	0.0208611i
$457$	6.73901	−	30.9787i	0.315238	−	1.44912i	−0.497992	−	0.867181i	$-0.665929\pi$
$457$	6.73901	−	30.9787i	0.315238	−	1.44912i	0.813230	−	0.581942i	$-0.197707\pi$
$458$	−16.1784	+	1.15710i	−0.755965	+	0.0540677i
$459$	1.54499			0.0721141
$460$	−3.07248	−	0.0972858i	−0.143255	−	0.00453597i
$461$	16.6266			0.774376			0.387188	−	0.922001i	$-0.373446\pi$
$461$	16.6266			0.774376			0.387188	+	0.922001i	$0.373446\pi$
$462$	−1.94850	+	0.139359i	−0.0906523	+	0.00648358i
$463$	−2.69487	+	12.3881i	−0.125241	+	0.575725i	0.871163	+	0.490995i	$0.163367\pi$
$463$	−2.69487	+	12.3881i	−0.125241	+	0.575725i	−0.996404	+	0.0847304i	$0.972997\pi$
$464$	−28.1343	+	4.04510i	−1.30610	+	0.187789i
$465$	−0.534611	−	4.30064i	−0.0247920	−	0.199437i
$466$	−2.18781	+	15.2166i	−0.101348	+	0.704894i
$467$	2.33467	−	4.27563i	0.108036	−	0.197852i	−0.818068	−	0.575121i	$-0.804955\pi$
$467$	2.33467	−	4.27563i	0.108036	−	0.197852i	0.926104	+	0.377269i	$0.123137\pi$
$468$	4.21025	−	0.915884i	0.194619	−	0.0423368i
$469$	17.7077	+	8.08685i	0.817667	+	0.373416i
$470$	−12.9163	+	2.55210i	−0.595783	+	0.117719i
$471$	2.83905	−	2.46005i	0.130816	−	0.113353i
$472$	−1.43878	+	20.1168i	−0.0662254	+	0.925951i
$473$	4.47508	−	2.44358i	0.205765	−	0.112356i
$474$	0.848327	−	1.85758i	0.0389650	−	0.0853214i
$475$	7.54386	−	3.10227i	0.346136	−	0.142342i
$476$	0.508480	−	0.149303i	0.0233061	−	0.00684330i
$477$	10.9270	+	14.5967i	0.500311	+	0.668337i
$478$	−10.6399	−	3.96847i	−0.486657	−	0.181514i
$479$	−2.58163	−	17.9557i	−0.117958	−	0.820415i	−0.959799	−	0.280689i	$-0.909437\pi$
$479$	−2.58163	−	17.9557i	−0.117958	−	0.820415i	0.841841	−	0.539726i	$-0.181472\pi$
$480$	−2.00205	−	1.14344i	−0.0913808	−	0.0521906i
$481$	−38.8856	−	33.6945i	−1.77303	−	1.53634i
$482$	0.224189	−	0.224189i	0.0102115	−	0.0102115i
$483$	2.96292	−	12.8435i	0.134817	−	0.584398i
$484$		−	3.06867i		−	0.139485i
$485$	−5.33863	+	3.28840i	−0.242415	+	0.149318i
$486$	−15.6975	+	10.0882i	−0.712053	+	0.457609i
$487$	6.82459	−	9.11658i	0.309252	−	0.413112i	−0.618809	−	0.785542i	$-0.712384\pi$
$487$	6.82459	−	9.11658i	0.309252	−	0.413112i	0.928060	+	0.372430i	$0.121475\pi$
$488$	−9.14336	+	24.5143i	−0.413901	+	1.10971i
$489$	−3.85275	−	0.553942i	−0.174227	−	0.0250501i
$490$	−33.3042	−	0.637001i	−1.50453	−	0.0287768i
$491$	−32.3069	−	20.7624i	−1.45799	−	0.936992i	−0.998816	−	0.0486443i	$-0.984510\pi$
$491$	−32.3069	−	20.7624i	−1.45799	−	0.936992i	−0.459172	−	0.888348i	$-0.651854\pi$
$492$	−0.0310717	+	0.0115892i	−0.00140082	+	0.000522479i
$493$	1.75630	+	3.21643i	0.0790999	+	0.144861i
$494$	8.11847	+	9.36921i	0.365267	+	0.421541i
$495$	−1.15471	+	2.92388i	−0.0519005	+	0.131419i
$496$	9.70192	+	2.84874i	0.435629	+	0.127912i
$497$	4.37495	+	11.7297i	0.196243	+	0.526149i
$498$	1.65112	+	7.59007i	0.0739884	+	0.340119i
$499$	11.7394	+	39.9809i	0.525530	+	1.78979i	0.608872	+	0.793268i	$0.291622\pi$
$499$	11.7394	+	39.9809i	0.525530	+	1.78979i	−0.0833427	+	0.996521i	$0.526560\pi$
$500$	−3.08743	−	0.859700i	−0.138074	−	0.0384469i
$501$	−2.41336	−	5.28451i	−0.107821	−	0.236095i
$502$	26.6581	+	19.9560i	1.18981	+	0.890679i
$503$	34.1466	+	7.42815i	1.52252	+	0.331205i	0.894528	−	0.447012i	$-0.147512\pi$
$503$	34.1466	+	7.42815i	1.52252	+	0.331205i	0.627996	+	0.778217i	$0.283876\pi$
$504$	−21.7567	+	25.1086i	−0.969122	+	1.11843i
$505$	13.2111	+	25.3344i	0.587886	+	1.12737i
$506$	3.25837	+	1.00125i	0.144852	+	0.0445112i
$507$	−9.38573	−	9.38573i	−0.416835	−	0.416835i
$508$	0.244077	+	3.41264i	0.0108292	+	0.151412i
$509$	−18.7488	−	29.1737i	−0.831026	−	1.29310i	−0.953732	−	0.300659i	$-0.902793\pi$
$509$	−18.7488	−	29.1737i	−0.831026	−	1.29310i	0.122706	−	0.992443i	$-0.460843\pi$
$510$	0.130439	−	0.798505i	0.00577594	−	0.0353584i
$511$	−31.1247	+	14.2142i	−1.37688	+	0.628798i
$512$	20.3341	−	15.2219i	0.898649	−	0.672720i
$513$	5.13004	+	2.80121i	0.226497	+	0.123677i
$514$	0.118036	−	0.183667i	0.00520634	−	0.00810122i
$515$	16.0482	+	14.4523i	0.707168	+	0.636845i
$516$	−0.486125	+	1.65559i	−0.0214005	+	0.0728833i
$517$	−2.43638	−	0.174253i	−0.107152	−	0.00766365i
$518$	49.6085	+	3.54807i	2.17967	+	0.155893i
$519$	−1.13017	+	3.84900i	−0.0496089	+	0.168952i
$520$	−2.03029	−	38.8030i	−0.0890343	−	1.70162i
$521$	4.68933	−	7.29674i	0.205443	−	0.319676i	−0.723208	−	0.690631i	$-0.757333\pi$
$521$	4.68933	−	7.29674i	0.205443	−	0.319676i	0.928651	+	0.370955i	$0.120969\pi$
$522$	−25.2781	−	13.8029i	−1.10639	−	0.604135i
$523$	3.87997	−	2.90451i	0.169659	−	0.127005i	−0.511074	−	0.859537i	$-0.670752\pi$
$523$	3.87997	−	2.90451i	0.169659	−	0.127005i	0.680733	+	0.732531i	$0.261661\pi$
$524$	−1.25698	+	0.574044i	−0.0549115	+	0.0250772i
$525$	6.18242	−	12.2727i	0.269823	−	0.535623i
$526$	−3.00474	−	4.67546i	−0.131013	−	0.203860i
$527$	−0.0930042	−	1.30037i	−0.00405133	−	0.0566450i
$528$	0.823232	+	0.823232i	0.0358266	+	0.0358266i
$529$	−12.9156	+	19.0312i	−0.561548	+	0.827444i
$530$	18.2771	−	9.53092i	0.793906	−	0.413997i
$531$	−11.4244	+	13.1845i	−0.495776	+	0.572157i
$532$	1.95907	+	0.426170i	0.0849366	+	0.0184768i
$533$	−0.838746	−	0.627878i	−0.0363301	−	0.0271964i
$534$	−2.34474	−	5.13427i	−0.101467	−	0.222182i
$535$	1.99597	−	4.15823i	0.0862933	−	0.179776i
$536$	−3.82891	−	13.0401i	−0.165384	−	0.563245i
$537$	3.18904	+	14.6598i	0.137617	+	0.632616i
$538$	3.63838	+	9.75487i	0.156862	+	0.420562i
$539$	−5.92954	−	1.74107i	−0.255403	−	0.0749931i
$540$	−0.913898	−	2.10688i	−0.0393279	−	0.0906656i
$541$	22.1669	+	25.5820i	0.953029	+	1.09985i	0.994914	+	0.100732i	$0.0321185\pi$
$541$	22.1669	+	25.5820i	0.953029	+	1.09985i	−0.0418841	+	0.999122i	$0.513336\pi$
$542$	5.65063	+	10.3484i	0.242716	+	0.444500i
$543$	−4.70421	+	1.75458i	−0.201877	+	0.0752962i
$544$	−0.583469	−	0.374973i	−0.0250160	−	0.0160768i
$545$	−13.3368	−	13.8569i	−0.571286	−	0.593566i
$546$	20.6732	+	2.97236i	0.884732	+	0.127205i
$547$	1.41513	−	3.79410i	0.0605064	−	0.162224i	−0.903179	−	0.429264i	$-0.858773\pi$
$547$	1.41513	−	3.79410i	0.0605064	−	0.162224i	0.963685	+	0.267040i	$0.0860456\pi$
$548$	1.98423	−	2.65062i	0.0847619	−	0.113229i
$549$	−19.0391	+	12.2357i	−0.812570	+	0.522207i
$550$	3.05174	+	1.82121i	0.130126	+	0.0776567i
$551$			13.8643i			0.590638i
$552$	−8.13103	+	4.30852i	−0.346080	+	0.183383i
$553$	7.37785	−	7.37785i	0.313738	−	0.313738i
$554$	−17.9649	−	15.5666i	−0.763254	−	0.661363i
$555$	−6.30049	+	11.0316i	−0.267441	+	0.468264i
$556$	0.0226746	+	0.157706i	0.000961619	+	0.00668821i
$557$	17.4379	+	6.50402i	0.738870	+	0.275584i	0.690587	−	0.723250i	$-0.257352\pi$
$557$	17.4379	+	6.50402i	0.738870	+	0.275584i	0.0482828	+	0.998834i	$0.484625\pi$
$558$	6.14006	+	8.20216i	0.259929	+	0.347225i
$559$	−52.3059	+	15.3584i	−2.21230	+	0.649591i
$560$	20.5294	+	24.6285i	0.867526	+	1.04074i
$561$	0.0623560	−	0.136541i	0.00263267	−	0.00576475i
$562$	−25.6293	+	13.9947i	−1.08111	+	0.590329i
$563$	−1.66498	+	23.2794i	−0.0701705	+	0.981111i	0.833400	+	0.552671i	$0.186391\pi$
$563$	−1.66498	+	23.2794i	−0.0701705	+	0.981111i	−0.903570	+	0.428440i	$0.859063\pi$
$564$	0.624707	−	0.541312i	0.0263049	−	0.0227934i
$565$	−2.30101	+	3.43422i	−0.0968041	+	0.144479i
$566$	−32.1270	−	14.6719i	−1.35040	−	0.616706i
$567$	−22.9168	+	4.98524i	−0.962414	+	0.209360i
$568$	4.18864	−	7.67092i	0.175751	−	0.321865i
$569$	1.28256	−	8.92040i	0.0537677	−	0.373963i	−0.945116	−	0.326734i	$-0.894052\pi$
$569$	1.28256	−	8.92040i	0.0537677	−	0.373963i	0.998884	−	0.0472287i	$-0.0150390\pi$
$570$	1.88088	−	2.41488i	0.0787813	−	0.101148i
$571$	10.2046	−	1.46719i	0.427048	−	0.0614002i	0.0745597	−	0.997217i	$-0.476245\pi$
$571$	10.2046	−	1.46719i	0.427048	−	0.0614002i	0.352488	+	0.935816i	$0.385336\pi$
$572$	0.192091	−	0.883030i	0.00803175	−	0.0369213i
$573$	−3.03899	+	0.217353i	−0.126956	+	0.00908004i
$574$	1.01275			0.0422712
$575$	−17.7946	+	16.0734i	−0.742085	+	0.670306i
$576$	22.7691			0.948711
$577$	−2.89672	+	0.207177i	−0.120592	+	0.00862490i	−0.131505	−	0.991316i	$-0.541981\pi$
$577$	−2.89672	+	0.207177i	−0.120592	+	0.00862490i	0.0109128	+	0.999940i	$0.496526\pi$
$578$	−4.67829	+	21.5058i	−0.194591	+	0.894522i
$579$	−4.70524	+	0.676511i	−0.195543	+	0.0281149i
$580$	3.34729	−	4.29763i	0.138989	−	0.178449i
$581$	−5.64806	+	39.2831i	−0.234321	+	1.62974i
$582$	−1.12764	+	2.06512i	−0.0467423	+	0.0856021i
$583$	3.73679	−	0.812888i	0.154762	−	0.0336664i
$584$	21.7293	+	9.92345i	0.899166	+	0.410635i
$585$	18.7086	−	27.9224i	0.773507	−	1.15445i
$586$	−8.52546	+	7.38735i	−0.352183	+	0.305169i
$587$	1.52320	−	21.2971i	0.0628691	−	0.879025i	−0.863965	−	0.503553i	$-0.832026\pi$
$587$	1.52320	−	21.2971i	0.0628691	−	0.879025i	0.926834	−	0.375472i	$-0.122519\pi$
$588$	1.83553	−	1.00227i	0.0756958	−	0.0413330i
$589$	2.04888	−	4.48641i	0.0844224	−	0.184859i
$590$	12.6278	+	15.1492i	0.519878	+	0.623682i
$591$	−9.75576	+	2.86455i	−0.401299	+	0.117832i
$592$	−17.7632	−	23.7289i	−0.730064	−	0.975252i
$593$	13.5558	+	5.05603i	0.556668	+	0.207626i	0.612023	−	0.790840i	$-0.290356\pi$
$593$	13.5558	+	5.05603i	0.556668	+	0.207626i	−0.0553545	+	0.998467i	$0.517629\pi$
$594$	0.362421	+	2.52070i	0.0148703	+	0.103425i
$595$	2.05019	−	3.58968i	0.0840495	−	0.147163i
$596$	−1.42197	−	1.23214i	−0.0582462	−	0.0504706i
$597$	5.90002	−	5.90002i	0.241472	−	0.241472i
$598$	−31.7656	−	17.8656i	−1.29899	−	0.730578i
$599$			11.2046i			0.457807i	0.973449	+	0.228904i	$0.0735140\pi$
$599$			11.2046i			0.457807i	−0.973449	+	0.228904i	$0.926486\pi$
$600$	−9.30177	+	2.34890i	−0.379743	+	0.0958933i
$601$	−2.96372	+	1.90467i	−0.120893	+	0.0776931i	−0.599690	−	0.800233i	$-0.704709\pi$
$601$	−2.96372	+	1.90467i	−0.120893	+	0.0776931i	0.478797	+	0.877926i	$0.341073\pi$
$602$	31.5784	−	42.1839i	1.28704	−	1.71929i
$603$	4.10826	−	11.0147i	0.167301	−	0.448552i
$604$	1.86086	+	0.267551i	0.0757173	+	0.0108865i
$605$	−16.5995	−	17.2469i	−0.674867	−	0.701186i
$606$	9.01991	+	5.79675i	0.366409	+	0.235477i
$607$	19.6847	−	7.34201i	0.798977	−	0.298003i	0.0833814	−	0.996518i	$-0.473428\pi$
$607$	19.6847	−	7.34201i	0.798977	−	0.298003i	0.715596	+	0.698515i	$0.246155\pi$
$608$	−1.25751	−	2.30296i	−0.0509987	−	0.0933972i
$609$	15.2958	+	17.6523i	0.619817	+	0.715306i
$610$	10.1815	+	23.4721i	0.412235	+	0.950356i
$611$	25.0575	+	7.35756i	1.01372	+	0.297655i
$612$	−0.111839	−	0.299852i	−0.00452082	−	0.0121208i
$613$	−3.74991	−	17.2381i	−0.151458	−	0.696240i	−0.988761	−	0.149502i	$-0.952233\pi$
$613$	−3.74991	−	17.2381i	−0.151458	−	0.696240i	0.837304	−	0.546738i	$-0.184131\pi$
$614$	−11.2713	−	38.3865i	−0.454872	−	1.54915i
$615$	−0.111943	+	0.233213i	−0.00451399	+	0.00940406i
$616$	2.89464	+	6.33837i	0.116628	+	0.255380i
$617$	−18.1499	−	13.5868i	−0.730687	−	0.546985i	0.167888	−	0.985806i	$-0.446305\pi$
$617$	−18.1499	−	13.5868i	−0.730687	−	0.546985i	−0.898575	+	0.438821i	$0.855396\pi$
$618$	7.91916	+	1.72271i	0.318555	+	0.0692975i
$619$	−2.83621	+	3.27317i	−0.113997	+	0.131560i	−0.809880	−	0.586596i	$-0.800468\pi$
$619$	−2.83621	+	3.27317i	−0.113997	+	0.131560i	0.695883	+	0.718155i	$0.255013\pi$
$620$	−1.71827	+	0.896026i	−0.0690076	+	0.0359853i
$621$	−16.9761	−	2.65828i	−0.681226	−	0.106673i
$622$	−5.40922	−	5.40922i	−0.216890	−	0.216890i
$623$	−2.05733	−	28.7653i	−0.0824253	−	1.15246i
$624$	−6.72961	−	10.4715i	−0.269400	−	0.419194i
$625$	−22.0028	+	11.8692i	−0.880111	+	0.474769i
$626$	40.6801	−	18.5780i	1.62591	−	0.742526i
$627$	0.454610	−	0.340316i	0.0181554	−	0.0135909i
$628$	−1.47432	−	0.805041i	−0.0588318	−	0.0321246i
$629$	−2.06615	+	3.21499i	−0.0823827	+	0.128190i
$630$	1.69758	+	32.4441i	0.0676331	+	1.29260i
$631$	8.28511	−	28.2165i	0.329825	−	1.12328i	−0.613025	−	0.790063i	$-0.710048\pi$
$631$	8.28511	−	28.2165i	0.329825	−	1.12328i	0.942850	−	0.333217i	$-0.108134\pi$
$632$	−7.26571	−	0.519654i	−0.289014	−	0.0206707i
$633$	15.3782	+	1.09987i	0.611230	+	0.0437160i
$634$	−2.44360	+	8.32213i	−0.0970477	+	0.330514i
$635$	19.8320	+	17.8599i	0.787009	+	0.708747i
$636$	−0.699669	+	1.08871i	−0.0277437	+	0.0431700i
$637$	57.9907	+	31.6653i	2.29767	+	1.25462i
$638$	−4.83570	+	3.61996i	−0.191447	+	0.143315i
$639$	6.87693	−	3.14059i	0.272047	−	0.124240i
$640$	2.99013	−	18.3046i	0.118195	−	0.723552i
$641$	−0.422023	−	0.656681i	−0.0166689	−	0.0259373i	0.832819	−	0.553545i	$-0.186725\pi$
$641$	−0.422023	−	0.656681i	−0.0166689	−	0.0259373i	−0.849488	+	0.527608i	$0.823089\pi$
$642$	−0.123479	−	1.72647i	−0.00487334	−	0.0681382i
$643$	14.8253	+	14.8253i	0.584652	+	0.584652i	0.936178	−	0.351526i	$-0.114337\pi$
$643$	14.8253	+	14.8253i	0.584652	+	0.584652i	−0.351526	+	0.936178i	$0.614337\pi$
$644$	−5.84396	+	0.765635i	−0.230284	+	0.0301702i
$645$	6.22351	+	11.9346i	0.245051	+	0.469924i
$646$	0.602998	−	0.695897i	0.0237246	−	0.0273797i
$647$	−14.5633	−	3.16805i	−0.572542	−	0.124549i	−0.0830327	−	0.996547i	$-0.526461\pi$
$647$	−14.5633	−	3.16805i	−0.572542	−	0.124549i	−0.489510	+	0.871998i	$0.662824\pi$
$648$	13.1075	+	9.81212i	0.514910	+	0.385457i
$649$	1.51997	+	3.32826i	0.0596639	+	0.130646i
$650$	−27.7433	−	25.9623i	−1.08818	−	1.01832i
$651$	−2.34097	−	7.97262i	−0.0917500	−	0.312472i
$652$	0.369971	+	1.70073i	0.0144892	+	0.0666057i
$653$	4.68572	+	12.5629i	0.183366	+	0.491624i	0.995813	−	0.0914110i	$-0.0291377\pi$
$653$	4.68572	+	12.5629i	0.183366	+	0.491624i	−0.812447	+	0.583035i	$0.801865\pi$
$654$	−6.92482	−	2.03331i	−0.270782	−	0.0795087i
$655$	−3.95943	+	10.0258i	−0.154708	+	0.391740i
$656$	−0.395257	−	0.456150i	−0.0154322	−	0.0178097i
$657$	9.90282	+	18.1357i	0.386346	+	0.707540i
$658$	−23.6519	+	8.82171i	−0.922048	+	0.343906i
$659$	5.18863	+	3.33453i	0.202120	+	0.129895i	0.637786	−	0.770214i	$-0.279851\pi$
$659$	5.18863	+	3.33453i	0.202120	+	0.129895i	−0.435665	+	0.900109i	$0.643487\pi$
$660$	−0.223083	−	0.00426684i	−0.00868349	−	0.000166087i
$661$	−29.5105	−	4.24296i	−1.14782	−	0.165032i	−0.457961	−	0.888972i	$-0.651420\pi$
$661$	−29.5105	−	4.24296i	−1.14782	−	0.165032i	−0.689863	+	0.723940i	$0.742329\pi$
$662$	−0.507793	+	1.36145i	−0.0197360	+	0.0529141i
$663$	−0.961762	+	1.28476i	−0.0373517	+	0.0498961i
$664$	23.3087	−	14.9796i	0.904552	−	0.581320i
$665$	13.3159	−	8.20212i	0.516370	−	0.318065i
$666$		−	30.0346i		−	1.16382i
$667$	−13.7638	−	38.3633i	−0.532936	−	1.48543i
$668$	−1.83690	+	1.83690i	−0.0710718	+	0.0710718i
$669$	7.37603	+	6.39137i	0.285174	+	0.247105i
$670$	−11.5404	−	6.59108i	−0.445843	−	0.254636i
$671$	0.675519	+	4.69834i	0.0260781	+	0.181377i
$672$	−4.14183	−	1.54482i	−0.159775	−	0.0595928i
$673$	18.1689	+	24.2709i	0.700362	+	0.935573i	0.999828	−	0.0185333i	$-0.00589966\pi$
$673$	18.1689	+	24.2709i	0.700362	+	0.935573i	−0.299467	+	0.954107i	$0.596809\pi$
$674$	22.1207	−	6.49524i	0.852059	−	0.250187i
$675$	−16.5333	−	6.89773i	−0.636366	−	0.265494i
$676$	−2.46562	+	5.39896i	−0.0948317	+	0.207652i
$677$	5.12281	−	2.79726i	0.196885	−	0.107508i	−0.377782	−	0.925895i	$-0.623313\pi$
$677$	5.12281	−	2.79726i	0.196885	−	0.107508i	0.574668	+	0.818387i	$0.305131\pi$
$678$	−0.110666	+	1.54731i	−0.00425009	+	0.0594240i
$679$	−9.08555	+	7.87267i	−0.348671	+	0.302126i
$680$	−2.83129	+	0.559429i	−0.108575	+	0.0214531i
$681$	4.40906	+	2.01355i	0.168956	+	0.0771595i
$682$	2.09977	−	0.456777i	0.0804043	−	0.0174909i
$683$	−9.43546	+	17.2797i	−0.361038	+	0.661191i	−0.993554	−	0.113356i	$-0.963840\pi$
$683$	−9.43546	+	17.2797i	−0.361038	+	0.661191i	0.632517	+	0.774547i	$0.282022\pi$
$684$	0.172306	−	1.19841i	0.00658827	−	0.0458224i
$685$	−3.18615	−	25.6307i	−0.121736	−	0.979299i
$686$	−24.3339	+	3.49868i	−0.929072	+	0.133580i
$687$	1.68853	−	7.76203i	0.0644213	−	0.296140i
$688$	−31.3245	+	2.24037i	−1.19424	+	0.0854134i
$689$	−40.8867			−1.55766
$690$	−2.80713	+	8.54939i	−0.106866	+	0.325470i
$691$	−13.5920			−0.517062			−0.258531	−	0.966003i	$-0.583238\pi$
$691$	−13.5920			−0.517062			−0.258531	+	0.966003i	$0.583238\pi$
$692$	1.78920	−	0.127966i	0.0680153	−	0.00486455i
$693$	−1.28121	+	5.88964i	−0.0486693	+	0.223729i
$694$	−19.4372	+	2.79464i	−0.737824	+	0.106083i
$695$	0.980526	+	0.763701i	0.0371935	+	0.0289688i
$696$	2.32067	−	16.1406i	0.0879649	−	0.611810i
$697$	−0.0372949	+	0.0683006i	−0.00141265	+	0.00258707i
$698$	10.5512	−	2.29528i	0.399370	−	0.0868777i
$699$	−6.84855	−	3.12763i	−0.259036	−	0.118298i
$700$	−6.10792	−	0.672422i	−0.230858	−	0.0254151i
$701$	−38.7890	+	33.6108i	−1.46504	+	1.26946i	−0.571405	+	0.820668i	$0.693601\pi$
$701$	−38.7890	+	33.6108i	−1.46504	+	1.26946i	−0.893634	+	0.448796i	$0.851853\pi$
$702$	1.94238	−	27.1581i	0.0733106	−	1.02502i
$703$	−12.6896	+	6.92903i	−0.478596	+	0.261333i
$704$	1.98379	−	4.34388i	0.0747667	−	0.163716i
$705$	0.582905	−	6.42162i	0.0219535	−	0.241852i
$706$	−8.94627	+	2.62686i	−0.336697	+	0.0988632i
$707$	32.8297	+	43.8554i	1.23469	+	1.64935i
$708$	−1.16015	−	0.432713i	−0.0436011	−	0.0162624i
$709$	−0.959848	−	6.67589i	−0.0360479	−	0.250718i	0.963827	−	0.266528i	$-0.0858765\pi$
$709$	−0.959848	−	6.67589i	−0.0360479	−	0.250718i	−0.999875	+	0.0158097i	$0.994967\pi$
$710$	−2.25061	−	8.24501i	−0.0844640	−	0.309430i
$711$	−4.76191	−	4.12622i	−0.178585	−	0.154745i
$712$	−14.2365	+	14.2365i	−0.533535	+	0.533535i
$713$	−1.21547	+	14.4482i	−0.0455198	+	0.541090i
$714$		−	1.55129i		−	0.0580556i
$715$	−3.69701	−	6.00201i	−0.138260	−	0.224462i
$716$	5.64359	−	3.62692i	0.210911	−	0.135544i
$717$	3.33289	−	4.45223i	0.124469	−	0.166271i
$718$	8.99117	−	24.1063i	0.335548	−	0.899638i
$719$	42.1580	+	6.06140i	1.57223	+	0.226052i	0.872593	−	0.488449i	$-0.162437\pi$
$719$	42.1580	+	6.06140i	1.57223	+	0.226052i	0.699635	+	0.714501i	$0.253346\pi$
$720$	13.9506	−	13.4270i	0.519908	−	0.500393i
$721$	34.8345	+	22.3868i	1.29730	+	0.833727i
$722$	−20.0380	+	7.47380i	−0.745738	+	0.278146i
$723$	0.0744155	+	0.136282i	0.00276754	+	0.00506838i
$724$	1.47021	+	1.69672i	0.0546401	+	0.0630580i
$725$	−4.43457	−	42.2608i	−0.164696	−	1.56953i
$726$	−8.61891	−	2.53074i	−0.319878	−	0.0939246i
$727$	15.5681	+	41.7398i	0.577390	+	1.54804i	0.816678	+	0.577094i	$0.195813\pi$
$727$	15.5681	+	41.7398i	0.577390	+	1.54804i	−0.239288	+	0.970949i	$0.576914\pi$
$728$	−15.8361	−	72.7973i	−0.586925	−	2.69805i
$729$	2.04887	+	6.97781i	0.0758841	+	0.258437i
$730$	22.0389	−	7.74330i	0.815695	−	0.286593i
$731$	1.68203	+	3.68313i	0.0622120	+	0.136225i
$732$	−1.28593	−	0.962635i	−0.0475293	−	0.0355800i
$733$	18.0224	+	3.92052i	0.665671	+	0.144808i	0.532689	−	0.846311i	$-0.321181\pi$
$733$	18.0224	+	3.92052i	0.665671	+	0.144808i	0.132981	+	0.991119i	$0.457545\pi$
$734$	20.2934	−	23.4198i	0.749042	−	0.864440i
$735$	4.89459	−	15.5621i	0.180540	−	0.574017i
$736$	5.76588	+	5.12403i	0.212533	+	0.188874i
$737$	−1.74344	−	1.74344i	−0.0642205	−	0.0642205i
$738$	−0.0436302	−	0.610029i	−0.00160605	−	0.0224555i
$739$	15.6066	+	24.2843i	0.574097	+	0.893313i	0.999934	−	0.0114871i	$-0.00365654\pi$
$739$	15.6066	+	24.2843i	0.574097	+	0.893313i	−0.425837	+	0.904800i	$0.640020\pi$
$740$	5.60639	+	0.915828i	0.206095	+	0.0336665i
$741$	−5.52286	+	2.52221i	−0.202887	+	0.0926555i
$742$	31.6387	−	23.6845i	1.16149	−	0.869484i
$743$	−19.1727	−	10.4691i	−0.703379	−	0.384074i	0.0874021	−	0.996173i	$-0.472144\pi$
$743$	−19.1727	−	10.4691i	−0.703379	−	0.384074i	−0.790781	+	0.612099i	$0.790325\pi$
$744$	−3.13624	+	4.88009i	−0.114980	+	0.178913i
$745$	−14.6571	+	0.766903i	−0.536993	+	0.0280971i
$746$	−4.27981	+	14.5757i	−0.156695	+	0.533654i
$747$	23.9056	+	1.70976i	0.874660	+	0.0625569i
$748$	−0.0669498	−	0.00478835i	−0.00244793	−	0.000175079i
$749$	2.49153	−	8.48538i	0.0910386	−	0.310049i
$750$	−4.96084	+	7.96261i	−0.181144	+	0.290753i
$751$	21.6291	−	33.6555i	0.789257	−	1.22811i	−0.180390	−	0.983595i	$-0.557736\pi$
$751$	21.6291	−	33.6555i	0.789257	−	1.22811i	0.969646	−	0.244512i	$-0.0786278\pi$
$752$	13.2043	+	7.21009i	0.481511	+	0.262925i
$753$	−13.0557	+	9.77341i	−0.475778	+	0.356163i
$754$	58.7468	−	26.8288i	2.13943	−	0.977047i
$755$	11.9059	−	8.56234i	0.433301	−	0.311615i
$756$	−2.38057	−	3.70424i	−0.0865806	−	0.134722i
$757$	2.49347	+	34.8633i	0.0906268	+	1.26713i	0.815708	+	0.578464i	$0.196348\pi$
$757$	2.49347	+	34.8633i	0.0906268	+	1.26713i	−0.725081	+	0.688664i	$0.758198\pi$
$758$	21.2214	+	21.2214i	0.770797	+	0.770797i
$759$	−0.920084	+	1.39299i	−0.0333969	+	0.0505624i
$760$	−10.4154	−	3.27585i	−0.377806	−	0.118827i
$761$	25.2703	−	29.1635i	0.916048	−	1.05718i	−0.0821170	−	0.996623i	$-0.526168\pi$
$761$	25.2703	−	29.1635i	0.916048	−	1.05718i	0.998165	−	0.0605530i	$-0.0192864\pi$
$762$	9.78632	+	2.12888i	0.354521	+	0.0771213i
$763$	−29.5198	−	22.0983i	−1.06869	−	0.800011i
$764$	0.565954	+	1.23927i	0.0204755	+	0.0448351i
$765$	−2.25058	−	1.08029i	−0.0813698	−	0.0390578i
$766$	11.1959	+	38.1296i	0.404523	+	1.37768i
$767$	−8.31548	−	38.2257i	−0.300255	−	1.38025i
$768$	1.50806	+	4.04325i	0.0544173	+	0.145898i
$769$	−28.9204	−	8.49181i	−1.04290	−	0.306222i	−0.284953	−	0.958541i	$-0.591978\pi$
$769$	−28.9204	−	8.49181i	−1.04290	−	0.306222i	−0.757944	+	0.652319i	$0.773796\pi$
$770$	6.33759	+	2.50287i	0.228391	+	0.0901973i
$771$	0.0700208	+	0.0808084i	0.00252174	+	0.00291024i
$772$	1.01870	+	1.86562i	0.0366639	+	0.0671450i
$773$	−36.4706	+	13.6028i	−1.31176	+	0.489260i	−0.905440	−	0.424473i	$-0.860459\pi$
$773$	−36.4706	+	13.6028i	−1.31176	+	0.489260i	−0.406315	+	0.913733i	$0.633187\pi$
$774$	−26.7700	−	17.2040i	−0.962226	−	0.618385i
$775$	−4.81033	+	14.3307i	−0.172792	+	0.514775i
$776$	8.30752	+	1.19444i	0.298223	+	0.0428779i
$777$	−8.51216	+	22.8220i	−0.305372	+	0.818735i
$778$	−18.1723	+	24.2754i	−0.651510	+	0.870315i
$779$	−0.247671	+	0.159168i	−0.00887372	+	0.00570279i
$780$	2.32091	+	0.551570i	0.0831020	+	0.0197494i
$781$		−	1.58561i		−	0.0567376i
$782$	−0.977681	+	2.52422i	−0.0349618	+	0.0902659i
$783$	21.5310	−	21.5310i	0.769455	−	0.769455i
$784$	28.7663	+	24.9261i	1.02737	+	0.890218i
$785$	−12.6409	+	3.45055i	−0.451174	+	0.123155i
$786$	0.575671	+	4.00388i	0.0205335	+	0.142814i
$787$	−36.4415	−	13.5920i	−1.29900	−	0.484501i	−0.397627	−	0.917547i	$-0.630166\pi$
$787$	−36.4415	−	13.5920i	−1.29900	−	0.484501i	−0.901372	+	0.433046i	$0.857439\pi$
$788$	2.72464	+	3.63969i	0.0970613	+	0.129659i
$789$	2.61164	−	0.766846i	0.0929768	−	0.0273004i
$790$	−5.47152	+	4.56086i	−0.194668	+	0.162268i
$791$	−3.29254	+	7.20965i	−0.117069	+	0.256346i
$792$	3.69323	−	2.01665i	0.131233	−	0.0716587i
$793$	3.62042	−	50.6201i	0.128565	−	1.79757i
$794$	−28.1632	+	24.4035i	−0.999473	+	0.866048i
$795$	1.95684	+	9.90365i	0.0694020	+	0.351246i
$796$	−3.39387	−	1.54993i	−0.120293	−	0.0549358i
$797$	−30.6565	+	6.66890i	−1.08591	+	0.236225i	−0.719684	−	0.694302i	$-0.755713\pi$
$797$	−30.6565	+	6.66890i	−1.08591	+	0.236225i	−0.366224	+	0.930527i	$0.619350\pi$
$798$	2.81263	−	5.15095i	0.0995661	−	0.182342i
$799$	0.276051	−	1.91997i	0.00976596	−	0.0679238i
$800$	4.56973	+	6.61760i	0.161564	+	0.233967i
$801$	−17.2382	+	2.47848i	−0.609081	+	0.0875727i
$802$	1.18547	−	5.44953i	0.0418605	−	0.192430i
$803$	4.32272	−	0.309167i	0.152545	−	0.0109103i
$804$	0.834389			0.0294266
$805$	−28.7034	+	35.9152i	−1.01166	+	1.26585i
$806$	−22.9750			−0.809259
$807$	−5.08593	+	0.363753i	−0.179033	+	0.0128047i
$808$	8.12966	−	37.3714i	0.286000	−	1.31472i
$809$	7.19191	−	1.03404i	0.252854	−	0.0363549i	−0.0147222	−	0.999892i	$-0.504686\pi$
$809$	7.19191	−	1.03404i	0.252854	−	0.0363549i	0.267576	+	0.963537i	$0.413777\pi$
$810$	15.8887	−	1.97513i	0.558274	−	0.0693988i
$811$	3.03093	−	21.0806i	0.106430	−	0.740240i	−0.864803	−	0.502111i	$-0.832557\pi$
$811$	3.03093	−	21.0806i	0.106430	−	0.740240i	0.971234	−	0.238129i	$-0.0765340\pi$
$812$	5.00548	−	9.16685i	0.175658	−	0.321693i
$813$	−5.64247	+	1.22744i	−0.197890	+	0.0430483i
$814$	−5.73001	−	2.61681i	−0.200837	−	0.0917191i
$815$	11.2792	+	7.55735i	0.395094	+	0.264722i
$816$	−0.698716	+	0.605441i	−0.0244599	+	0.0211947i
$817$	−1.09279	+	15.2792i	−0.0382320	+	0.534553i
$818$	6.99494	−	3.81953i	0.244572	−	0.133547i
$819$	26.7704	−	58.6190i	0.935434	−	2.04831i
$820$	0.115201	+	0.0104571i	0.00402300	+	0.000365177i
$821$	−25.1028	+	7.37084i	−0.876092	+	0.257244i	−0.688705	−	0.725042i	$-0.741820\pi$
$821$	−25.1028	+	7.37084i	−0.876092	+	0.257244i	−0.187388	+	0.982286i	$0.560002\pi$
$822$	−5.80834	−	7.75904i	−0.202589	−	0.270627i
$823$	29.1297	+	10.8648i	1.01540	+	0.378724i	0.801412	−	0.598113i	$-0.204083\pi$
$823$	29.1297	+	10.8648i	1.01540	+	0.378724i	0.213986	+	0.976837i	$0.431355\pi$
$824$	−4.11409	−	28.6141i	−0.143321	−	0.996820i
$825$	−1.27688	+	1.18275i	−0.0444552	+	0.0411782i
$826$	28.5776	+	24.7627i	0.994344	+	0.861604i
$827$	−16.3042	+	16.3042i	−0.566952	+	0.566952i	−0.931273	−	0.364321i	$-0.881301\pi$
$827$	−16.3042	+	16.3042i	−0.566952	+	0.566952i	0.364321	+	0.931273i	$0.381301\pi$
$828$	0.712946	+	3.48714i	0.0247766	+	0.121186i
$829$		−	1.25894i		−	0.0437247i	−0.999761	−	0.0218623i	$-0.993040\pi$
$829$		−	1.25894i		−	0.0437247i	0.999761	−	0.0218623i	$-0.00695955\pi$
$830$	6.26450	−	26.3600i	0.217444	−	0.914968i
$831$	9.79368	−	6.29402i	0.339739	−	0.218337i
$832$	−30.5974	+	40.8733i	−1.06077	+	1.41703i
$833$	1.71501	−	4.59812i	0.0594216	−	0.159315i
$834$	0.461645	+	0.0663745i	0.0159855	+	0.00229836i
$835$	−0.387516	+	20.2604i	−0.0134105	+	0.701142i
$836$	−0.213621	−	0.137286i	−0.00738822	−	0.00474812i
$837$	−10.1492	+	3.78545i	−0.350808	+	0.130844i
$838$	1.42027	+	2.60103i	0.0490624	+	0.0898510i
$839$	33.1276	+	38.2312i	1.14369	+	1.31989i	0.940126	+	0.340828i	$0.110707\pi$
$839$	33.1276	+	38.2312i	1.14369	+	1.31989i	0.203565	+	0.979062i	$0.434747\pi$
$840$	−16.8752	+	7.31994i	−0.582250	+	0.252562i
$841$	41.4746	+	12.1780i	1.43016	+	0.419932i
$842$	6.38838	+	17.1279i	0.220158	+	0.590267i
$843$	−3.03995	−	13.9744i	−0.104702	−	0.481305i
$844$	−1.94229	−	6.61482i	−0.0668562	−	0.227691i
$845$	15.3473	+	43.6814i	0.527965	+	1.50269i
$846$	6.33272	+	13.8667i	0.217723	+	0.476748i
$847$	−36.7416	−	27.5044i	−1.26246	−	0.945063i
$848$	−23.0157	−	5.00677i	−0.790364	−	0.171933i
$849$	11.3273	−	13.0724i	0.388752	−	0.448644i
$850$	−1.61546	+	2.31409i	−0.0554098	+	0.0793727i
$851$	28.2341	−	31.7707i	0.967851	−	1.08909i
$852$	0.379426	+	0.379426i	0.0129989	+	0.0129989i
$853$	2.54972	+	35.6497i	0.0873008	+	1.22062i	0.832593	+	0.553886i	$0.186856\pi$
$853$	2.54972	+	35.6497i	0.0873008	+	1.22062i	−0.745292	+	0.666738i	$0.767690\pi$
$854$	26.5212	+	41.2678i	0.907538	+	1.41216i
$855$	−5.51423	−	7.66752i	−0.188583	−	0.262224i
$856$	−5.61612	+	2.56480i	−0.191955	+	0.0876629i
$857$	−38.3258	+	28.6903i	−1.30918	+	0.980042i	−0.309609	+	0.950864i	$0.600198\pi$
$857$	−38.3258	+	28.6903i	−1.30918	+	0.980042i	−0.999574	+	0.0291779i	$0.990711\pi$
$858$	−2.32173	−	1.26776i	−0.0792627	−	0.0432807i
$859$	11.5425	−	17.9604i	0.393824	−	0.612802i	−0.586558	−	0.809907i	$-0.699518\pi$
$859$	11.5425	−	17.9604i	0.393824	−	0.612802i	0.980382	+	0.197105i	$0.0631539\pi$
$860$	4.02765	−	4.47240i	0.137342	−	0.152508i
$861$	−0.139737	+	0.475900i	−0.00476222	+	0.0162186i
$862$	−39.8317	−	2.84882i	−1.35667	−	0.0970313i
$863$	−35.8068	−	2.56095i	−1.21888	−	0.0871757i	−0.552963	−	0.833205i	$-0.686503\pi$
$863$	−35.8068	−	2.56095i	−1.21888	−	0.0871757i	−0.665913	+	0.746030i	$0.731958\pi$
$864$	−1.62356	+	5.52935i	−0.0552347	+	0.188112i
$865$	9.36369	−	10.3977i	0.318375	−	0.353531i
$866$	−8.87956	+	13.8169i	−0.301740	+	0.469516i
$867$	−9.46028	−	5.16570i	−0.321288	−	0.175436i
$868$	−2.97444	+	2.22663i	−0.100959	+	0.0755769i
$869$	−1.20209	+	0.548975i	−0.0407780	+	0.0186227i
$870$	−9.31015	−	12.9457i	−0.315644	−	0.438902i
$871$	14.2520	+	22.1765i	0.482910	+	0.751422i
$872$	1.83654	+	25.6781i	0.0621929	+	0.869571i
$873$	5.13354	+	5.13354i	0.173744	+	0.173744i
$874$	−7.82297	+	6.60887i	−0.264616	+	0.223548i
$875$	−37.9659	+	29.2607i	−1.28348	+	0.989193i
$876$	−0.960417	+	1.10838i	−0.0324495	+	0.0374487i
$877$	−12.5552	−	2.73122i	−0.423960	−	0.0922269i	−0.00447696	−	0.999990i	$-0.501425\pi$
$877$	−12.5552	−	2.73122i	−0.423960	−	0.0922269i	−0.419483	+	0.907763i	$0.637789\pi$
$878$	27.3563	+	20.4787i	0.923232	+	0.691123i
$879$	−2.29507	−	5.02549i	−0.0774107	−	0.169506i
$880$	−1.34613	−	3.83134i	−0.0453781	−	0.129154i
$881$	6.93386	+	23.6146i	0.233608	+	0.795595i	0.989950	+	0.141419i	$0.0451664\pi$
$881$	6.93386	+	23.6146i	0.233608	+	0.795595i	−0.756342	+	0.654176i	$0.773015\pi$
$882$	8.19835	+	37.6872i	0.276053	+	1.26899i
$883$	−10.0830	−	27.0337i	−0.339321	−	0.909756i	−0.988783	−	0.149361i	$-0.952278\pi$
$883$	−10.0830	−	27.0337i	−0.339321	−	0.909756i	0.649461	−	0.760395i	$-0.274994\pi$
$884$	0.688562	+	0.202180i	0.0231588	+	0.00680005i
$885$	−8.86111	+	3.84368i	−0.297863	+	0.129204i
$886$	31.6343	+	36.5079i	1.06277	+	1.22651i
$887$	−2.73357	−	5.00615i	−0.0917842	−	0.168090i	0.827754	−	0.561092i	$-0.189619\pi$
$887$	−2.73357	−	5.00615i	−0.0917842	−	0.168090i	−0.919538	+	0.393002i	$0.871437\pi$
$888$	15.9329	−	5.94266i	0.534673	−	0.199423i
$889$	43.0477	+	27.6651i	1.44377	+	0.927857i
$890$	−0.376498	+	19.6844i	−0.0126203	+	0.659823i
$891$	2.94020	+	0.422736i	0.0985002	+	0.0141622i
$892$	1.52514	−	4.08905i	0.0510654	−	0.136912i
$893$	4.39770	−	5.87464i	0.147163	−	0.196587i
$894$	−4.63341	+	2.97771i	−0.154964	+	0.0995895i
$895$	12.0995	−	50.9127i	0.404442	−	1.70182i
$896$		−	35.5611i		−	1.18801i
$897$	12.7782	−	12.4619i	0.426651	−	0.416092i
$898$	−28.2029	+	28.2029i	−0.941143	+	0.941143i
$899$	−19.4180	−	16.8258i	−0.647627	−	0.561172i
$900$	−0.141899	+	3.70808i	−0.00472996	+	0.123603i
$901$	0.432189	+	3.00594i	0.0143983	+	0.100142i
$902$	−0.120183	−	0.0448259i	−0.00400165	−	0.00149254i
$903$	15.4655	+	20.6595i	0.514660	+	0.687505i
$904$	5.30923	−	1.55893i	0.176582	−	0.0518492i
$905$	17.4412	+	1.58318i	0.579767	+	0.0526268i
$906$	2.28612	−	5.00591i	0.0759514	−	0.166310i
$907$	13.2615	−	7.24132i	0.440340	−	0.240444i	−0.243755	−	0.969837i	$-0.578379\pi$
$907$	13.2615	−	7.24132i	0.440340	−	0.240444i	0.684095	+	0.729393i	$0.260197\pi$
$908$	0.154622	−	2.16189i	0.00513130	−	0.0717450i
$909$	25.0020	−	21.6644i	0.829265	−	0.718562i
$910$	−60.5224	−	40.5515i	−2.00630	−	1.34427i
$911$	−38.6210	−	17.6376i	−1.27957	−	0.584360i	−0.344488	−	0.938791i	$-0.611948\pi$
$911$	−38.6210	−	17.6376i	−1.27957	−	0.584360i	−0.935082	+	0.354430i	$0.884675\pi$
$912$	−3.41776	+	0.743488i	−0.113173	+	0.0246193i
$913$	2.40900	−	4.41175i	0.0797261	−	0.146008i
$914$	−5.90577	+	41.0755i	−0.195345	+	1.35866i
$915$	−12.4346	+	1.54574i	−0.411075	+	0.0511006i
$916$	−3.51588	+	0.505507i	−0.116168	+	0.0167024i
$917$	−4.39319	+	20.1952i	−0.145076	+	0.666903i
$918$	−2.01716	+	0.144270i	−0.0665763	+	0.00476163i
$919$	−0.266970			−0.00880653			−0.00440327	−	0.999990i	$-0.501402\pi$
$919$	−0.266970			−0.00880653			−0.00440327	+	0.999990i	$0.501402\pi$
$920$	32.0722	−	1.27544i	1.05739	−	0.0420499i
$921$	19.5934			0.645624
$922$	−21.7079	+	1.55258i	−0.714910	+	0.0511314i
$923$	−3.60356	+	16.5653i	−0.118613	+	0.545254i
$924$	−0.423447	+	0.0608825i	−0.0139304	+	0.00200289i
$925$	36.4638	−	25.1798i	1.19892	−	0.827906i
$926$	2.36167	−	16.4258i	0.0776092	−	0.539784i
$927$	11.9840	−	21.9471i	0.393606	−	0.720836i
$928$	−13.3568	+	2.90560i	−0.438459	+	0.0953810i
$929$	39.0156	+	17.8178i	1.28006	+	0.584585i	0.935217	−	0.354075i	$-0.115204\pi$
$929$	39.0156	+	17.8178i	1.28006	+	0.584585i	0.344845	+	0.938660i	$0.387932\pi$
$930$	1.09959	+	5.56505i	0.0360568	+	0.182485i
$931$	14.0314	−	12.1583i	0.459861	−	0.398471i
$932$	−0.240172	+	3.35804i	−0.00786710	+	0.109996i
$933$	3.28820	−	1.79549i	0.107651	−	0.0587818i
$934$	−2.64892	+	5.80033i	−0.0866753	+	0.189792i
$935$	−0.402182	+	0.335244i	−0.0131527	+	0.0109636i
$936$	−43.1674	+	12.6751i	−1.41097	+	0.414298i
$937$	−27.0746	−	36.1675i	−0.884489	−	1.18154i	−0.982483	−	0.186352i	$-0.940333\pi$
$937$	−27.0746	−	36.1675i	−0.884489	−	1.18154i	0.0979936	−	0.995187i	$-0.468758\pi$
$938$	−23.8746	−	8.90476i	−0.779533	−	0.290751i
$939$	3.11702	+	21.6794i	0.101720	+	0.707480i
$940$	−2.78152	+	0.759263i	−0.0907233	+	0.0247644i
$941$	40.5826	+	35.1650i	1.32295	+	1.14635i	0.978202	+	0.207653i	$0.0665826\pi$
$941$	40.5826	+	35.1650i	1.32295	+	1.14635i	0.344752	+	0.938694i	$0.387963\pi$
$942$	−3.47698	+	3.47698i	−0.113286	+	0.113286i
$943$	0.527306	−	0.686305i	0.0171714	−	0.0223492i
$944$		−	22.5361i		−	0.733487i
$945$	−33.4172	−	7.94167i	−1.08706	−	0.258343i
$946$	−5.61455	+	3.60825i	−0.182545	+	0.117314i
$947$	1.08460	−	1.44886i	0.0352448	−	0.0470815i	−0.782573	−	0.622559i	$-0.786093\pi$
$947$	1.08460	−	1.44886i	0.0352448	−	0.0470815i	0.817817	+	0.575478i	$0.195184\pi$
$948$	0.156286	−	0.419018i	0.00507592	−	0.0136091i
$949$	−45.8633	−	6.59415i	−1.48879	−	0.214055i
$950$	−9.55968	+	4.75480i	−0.310157	+	0.154266i
$951$	−3.57349	−	2.29654i	−0.115878	−	0.0744705i
$952$	−5.18458	+	1.93375i	−0.168033	+	0.0626732i
$953$	−10.4568	−	19.1502i	−0.338728	−	0.620334i	0.651682	−	0.758492i	$-0.274064\pi$
$953$	−10.4568	−	19.1502i	−0.338728	−	0.620334i	−0.990410	+	0.138158i	$0.955882\pi$
$954$	−15.6294	−	18.0373i	−0.506021	−	0.583979i
$955$	9.88448	+	3.90363i	0.319854	+	0.126318i
$956$	−2.38614	−	0.700635i	−0.0771734	−	0.0226602i
$957$	−1.03383	−	2.77182i	−0.0334191	−	0.0896002i
$958$	5.04730	+	23.2021i	0.163071	+	0.749625i
$959$	−13.9516	−	47.5148i	−0.450521	−	1.53433i
$960$	11.3648	+	5.45516i	0.366798	+	0.176064i
$961$	−9.08082	−	19.8842i	−0.292930	−	0.641427i
$962$	53.9159	+	40.3609i	1.73832	+	1.30129i
$963$	−5.21852	−	1.13522i	−0.168164	−	0.0365819i
$964$	0.0454687	−	0.0524737i	0.00146445	−	0.00169006i
$965$	15.8172	+	4.97483i	0.509175	+	0.160145i
$966$	−2.66911	+	17.0453i	−0.0858773	+	0.548422i
$967$	27.8956	+	27.8956i	0.897061	+	0.897061i	0.995175	−	0.0981139i	$-0.0312810\pi$
$967$	27.8956	+	27.8956i	0.897061	+	0.897061i	−0.0981139	+	0.995175i	$0.531281\pi$
$968$	2.28583	+	31.9600i	0.0734693	+	1.02723i
$969$	0.243809	+	0.379374i	0.00783226	+	0.0121872i
$970$	6.66312	−	4.79189i	0.213940	−	0.153858i
$971$	−40.7544	+	18.6119i	−1.30787	+	0.597284i	−0.942695	−	0.333655i	$-0.891718\pi$
$971$	−40.7544	+	18.6119i	−1.30787	+	0.597284i	−0.365174	+	0.930939i	$0.618991\pi$
$972$	−3.27131	+	2.44887i	−0.104927	+	0.0785476i
$973$	2.09146	+	1.14203i	0.0670493	+	0.0366117i
$974$	−8.05897	+	12.5400i	−0.258226	+	0.401808i
$975$	16.0279	−	9.45465i	0.513304	−	0.302791i
$976$	8.23667	−	28.0515i	0.263649	−	0.897907i
$977$	19.2851	+	1.37930i	0.616986	+	0.0441277i	0.376334	−	0.926484i	$-0.377184\pi$
$977$	19.2851	+	1.37930i	0.616986	+	0.0441277i	0.240651	+	0.970612i	$0.422639\pi$
$978$	5.08193	+	0.363467i	0.162502	+	0.0116224i
$979$	−1.02906	+	3.50464i	−0.0328888	+	0.112009i
$980$	−7.28484	+	0.381166i	−0.232706	+	0.0121759i
$981$	−12.0392	+	18.7333i	−0.384382	+	0.598109i
$982$	44.1190	+	24.0908i	1.40790	+	0.768769i
$983$	6.10538	−	4.57043i	0.194731	−	0.145774i	−0.497463	−	0.867485i	$-0.665735\pi$
$983$	6.10538	−	4.57043i	0.194731	−	0.145774i	0.692194	+	0.721711i	$0.256644\pi$
$984$	0.314978	−	0.143846i	0.0100411	−	0.00458563i
$985$	35.0018	+	5.71769i	1.11525	+	0.182181i
$986$	−2.59340	−	4.03541i	−0.0825907	−	0.128514i
$987$	−0.881965	−	12.3315i	−0.0280733	−	0.392515i
$988$	1.91975	+	1.91975i	0.0610754	+	0.0610754i
$989$	−12.1447	−	43.3635i	−0.386179	−	1.37888i
$990$	1.23458	−	3.92529i	0.0392375	−	0.124754i
$991$	26.7961	−	30.9243i	0.851205	−	0.982343i	−0.148774	−	0.988871i	$-0.547533\pi$
$991$	26.7961	−	30.9243i	0.851205	−	0.982343i	0.999979	+	0.00652832i	$0.00207804\pi$
$992$	4.75160	+	1.03365i	0.150863	+	0.0328183i
$993$	−0.569694	−	0.426467i	−0.0180787	−	0.0135335i
$994$	−6.80731	−	14.9059i	−0.215915	−	0.472787i
$995$	−27.4588	+	9.64758i	−0.870503	+	0.305849i
$996$	0.479245	+	1.63216i	0.0151855	+	0.0517169i
$997$	−9.39513	−	43.1887i	−0.297547	−	1.36780i	−0.846697	−	0.532076i	$-0.821412\pi$
$997$	−9.39513	−	43.1887i	−0.297547	−	1.36780i	0.549150	−	0.835724i	$-0.314952\pi$
$998$	−19.0606	−	51.1033i	−0.603351	−	1.61765i
$999$	30.4674	+	8.94603i	0.963945	+	0.283040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.7.3	✓	200
5.2	odd	4		575.2.r.b.168.3		200
5.3	odd	4	inner	115.2.l.a.53.8	yes	200
5.4	even	2		575.2.r.b.7.8		200
23.10	odd	22	inner	115.2.l.a.102.8	yes	200
115.33	even	44	inner	115.2.l.a.33.3	yes	200
115.79	odd	22		575.2.r.b.332.3		200
115.102	even	44		575.2.r.b.493.8		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.3	✓	200	1.1	even	1	trivial
115.2.l.a.33.3	yes	200	115.33	even	44	inner
115.2.l.a.53.8	yes	200	5.3	odd	4	inner
115.2.l.a.102.8	yes	200	23.10	odd	22	inner
575.2.r.b.7.8		200	5.4	even	2
575.2.r.b.168.3		200	5.2	odd	4
575.2.r.b.332.3		200	115.79	odd	22
575.2.r.b.493.8		200	115.102	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30561 + 0.0933793i) q^{2} +(0.136266 - 0.626406i) q^{3} +(-0.283736 + 0.0407951i) q^{4} +(-1.37401 + 1.76411i) q^{5} +(-0.119418 + 0.830568i) q^{6} +(-2.05467 + 3.76286i) q^{7} +(2.92471 - 0.636232i) q^{8} +(2.35508 + 1.07553i) q^{9} +O(q^{10})\)	\(q+(-1.30561 + 0.0933793i) q^{2} +(0.136266 - 0.626406i) q^{3} +(-0.283736 + 0.0407951i) q^{4} +(-1.37401 + 1.76411i) q^{5} +(-0.119418 + 0.830568i) q^{6} +(-2.05467 + 3.76286i) q^{7} +(2.92471 - 0.636232i) q^{8} +(2.35508 + 1.07553i) q^{9} +(1.62920 - 2.43155i) q^{10} +(0.410379 - 0.355596i) q^{11} +(-0.0131094 + 0.183293i) q^{12} +(-5.09550 + 2.78235i) q^{13} +(2.33124 - 5.10470i) q^{14} +(0.917818 + 1.10108i) q^{15} +(-3.20905 + 0.942261i) q^{16} +(0.258417 + 0.345204i) q^{17} +(-3.17526 - 1.18431i) q^{18} +(0.232168 + 1.61476i) q^{19} +(0.317890 - 0.556595i) q^{20} +(2.07709 + 1.79981i) q^{21} +(-0.502591 + 0.502591i) q^{22} +(-2.24548 - 4.23767i) q^{23} -1.91875i q^{24} +(-1.22418 - 4.84782i) q^{25} +(6.39294 - 4.10849i) q^{26} +(2.14715 - 2.86825i) q^{27} +(0.429479 - 1.15148i) q^{28} +(8.41206 + 1.20947i) q^{29} +(-1.30113 - 1.35188i) q^{30} +(-2.54336 - 1.63452i) q^{31} +(-1.50700 + 0.562084i) q^{32} +(-0.166826 - 0.305519i) q^{33} +(-0.369628 - 0.426573i) q^{34} +(-3.81495 - 8.79488i) q^{35} +(-0.712097 - 0.209091i) q^{36} +(3.09715 + 8.30378i) q^{37} +(-0.453907 - 2.08658i) q^{38} +(1.04854 + 3.57099i) q^{39} +(-2.89620 + 6.03371i) q^{40} +(0.0749684 + 0.164158i) q^{41} +(-2.87994 - 2.15590i) q^{42} +(9.17525 + 1.99595i) q^{43} +(-0.101933 + 0.117637i) q^{44} +(-5.13326 + 2.67683i) q^{45} +(3.32744 + 5.32307i) q^{46} +(-3.18076 - 3.18076i) q^{47} +(0.152953 + 2.13856i) q^{48} +(-6.15291 - 9.57411i) q^{49} +(2.05099 + 6.21507i) q^{50} +(0.251452 - 0.114834i) q^{51} +(1.33227 - 0.997324i) q^{52} +(6.18111 + 3.37514i) q^{53} +(-2.53551 + 3.94533i) q^{54} +(0.0634443 + 1.21255i) q^{55} +(-3.61528 + 12.3125i) q^{56} +(1.04313 + 0.0746063i) q^{57} +(-11.0958 - 0.793590i) q^{58} +(-1.89837 + 6.46526i) q^{59} +(-0.305336 - 0.274973i) q^{60} +(-4.72595 + 7.35372i) q^{61} +(3.47328 + 1.89656i) q^{62} +(-8.88598 + 6.65196i) q^{63} +(7.99965 - 3.65332i) q^{64} +(2.09290 - 12.8120i) q^{65} +(0.246340 + 0.383312i) q^{66} +(-0.323924 - 4.52905i) q^{67} +(-0.0874048 - 0.0874048i) q^{68} +(-2.96048 + 0.829132i) q^{69} +(5.80211 + 11.1265i) q^{70} +(1.91222 - 2.20682i) q^{71} +(7.57221 + 1.64723i) q^{72} +(6.38913 + 4.78284i) q^{73} +(-4.81908 - 10.5523i) q^{74} +(-3.20352 + 0.106239i) q^{75} +(-0.131749 - 0.448694i) q^{76} +(0.494859 + 2.27483i) q^{77} +(-1.70244 - 4.56442i) q^{78} +(-2.33510 - 0.685646i) q^{79} +(2.74702 - 6.95579i) q^{80} +(3.58229 + 4.13418i) q^{81} +(-0.113209 - 0.207326i) q^{82} +(8.67329 - 3.23497i) q^{83} +(-0.662768 - 0.425935i) q^{84} +(-0.964047 - 0.0184391i) q^{85} +(-12.1657 - 1.74917i) q^{86} +(1.90390 - 5.10455i) q^{87} +(0.973999 - 1.30111i) q^{88} +(-5.65876 + 3.63667i) q^{89} +(6.45210 - 3.97425i) q^{90} -24.8904i q^{91} +(0.810000 + 1.11077i) q^{92} +(-1.37045 + 1.37045i) q^{93} +(4.44986 + 3.85582i) q^{94} +(-3.16762 - 1.80913i) q^{95} +(0.146739 + 1.02059i) q^{96} +(2.62729 + 0.979928i) q^{97} +(8.92734 + 11.9255i) q^{98} +(1.34893 - 0.396081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

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