LMFDB - Embedded newform 115.2.g.b.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.1
Root			$0.610271 - 1.33631i$ of defining polynomial
Character	$\chi$	$=$	115.6
Dual form			115.2.g.b.96.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.544078 + 1.19136i) q^{2} +(-1.40956 - 0.413883i) q^{3} +(0.186393 + 0.215109i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.25999 - 1.45411i) q^{6} +(-0.543517 + 3.78024i) q^{7} +(-2.87102 + 0.843008i) q^{8} +(-0.708209 - 0.455138i) q^{9} +O(q^{10})$	\(q+(-0.544078 + 1.19136i) q^{2} +(-1.40956 - 0.413883i) q^{3} +(0.186393 + 0.215109i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.25999 - 1.45411i) q^{6} +(-0.543517 + 3.78024i) q^{7} +(-2.87102 + 0.843008i) q^{8} +(-0.708209 - 0.455138i) q^{9} +(-0.186393 - 1.29639i) q^{10} +(0.175811 + 0.384973i) q^{11} +(-0.173701 - 0.380353i) q^{12} +(0.160369 + 1.11539i) q^{13} +(-4.20793 - 2.70427i) q^{14} +(1.40956 - 0.413883i) q^{15} +(0.476716 - 3.31563i) q^{16} +(1.29285 - 1.49203i) q^{17} +(0.927557 - 0.596105i) q^{18} +(4.12220 + 4.75727i) q^{19} +(-0.273100 - 0.0801894i) q^{20} +(2.33070 - 5.10351i) q^{21} -0.554298 q^{22} +(4.18490 - 2.34235i) q^{23} +4.39578 q^{24} +(0.415415 - 0.909632i) q^{25} +(-1.41609 - 0.415801i) q^{26} +(3.69598 + 4.26539i) q^{27} +(-0.914470 + 0.587694i) q^{28} +(-2.02505 + 2.33704i) q^{29} +(-0.273823 + 1.90448i) q^{30} +(3.19411 - 0.937877i) q^{31} +(-1.34369 - 0.863538i) q^{32} +(-0.0884821 - 0.615407i) q^{33} +(1.07414 + 2.35204i) q^{34} +(-1.58652 - 3.47399i) q^{35} +(-0.0341008 - 0.237177i) q^{36} +(-2.57746 - 1.65644i) q^{37} +(-7.91044 + 2.32271i) q^{38} +(0.235592 - 1.63858i) q^{39} +(1.95949 - 2.26138i) q^{40} +(4.88840 - 3.14158i) q^{41} +(4.81206 + 5.55342i) q^{42} +(7.59078 + 2.22886i) q^{43} +(-0.0500411 + 0.109575i) q^{44} +0.841850 q^{45} +(0.513680 + 6.26016i) q^{46} -12.4048 q^{47} +(-2.04424 + 4.47627i) q^{48} +(-7.27836 - 2.13712i) q^{49} +(0.857685 + 0.989821i) q^{50} +(-2.43987 + 1.56801i) q^{51} +(-0.210039 + 0.242397i) q^{52} +(0.607960 - 4.22845i) q^{53} +(-7.09254 + 2.08256i) q^{54} +(-0.356034 - 0.228809i) q^{55} +(-1.62633 - 11.3113i) q^{56} +(-3.84152 - 8.41175i) q^{57} +(-1.68248 - 3.68411i) q^{58} +(1.70110 + 11.8314i) q^{59} +(0.351761 + 0.226063i) q^{60} +(-12.6478 + 3.71373i) q^{61} +(-0.620494 + 4.31563i) q^{62} +(2.10546 - 2.42983i) q^{63} +(7.39580 - 4.75299i) q^{64} +(-0.737936 - 0.851624i) q^{65} +(0.781315 + 0.229415i) q^{66} +(3.10214 - 6.79273i) q^{67} +0.561926 q^{68} +(-6.86832 + 1.56962i) q^{69} +5.00198 q^{70} +(-4.47175 + 9.79176i) q^{71} +(2.41697 + 0.709686i) q^{72} +(6.13979 + 7.08570i) q^{73} +(3.37576 - 2.16947i) q^{74} +(-0.962033 + 1.11024i) q^{75} +(-0.254982 + 1.77344i) q^{76} +(-1.55085 + 0.455370i) q^{77} +(1.82397 + 1.17219i) q^{78} +(-0.588942 - 4.09618i) q^{79} +(1.39153 + 3.04702i) q^{80} +(-2.39517 - 5.24470i) q^{81} +(1.08310 + 7.53313i) q^{82} +(13.5415 + 8.70262i) q^{83} +(1.53224 - 0.449905i) q^{84} +(-0.280963 + 1.95414i) q^{85} +(-6.78536 + 7.83072i) q^{86} +(3.82169 - 2.45605i) q^{87} +(-0.829294 - 0.957056i) q^{88} +(-3.76366 - 1.10511i) q^{89} +(-0.458032 + 1.00295i) q^{90} -4.30361 q^{91} +(1.28390 + 0.463612i) q^{92} -4.89046 q^{93} +(6.74919 - 14.7787i) q^{94} +(-6.03979 - 1.77344i) q^{95} +(1.53660 + 1.77334i) q^{96} +(3.02202 - 1.94213i) q^{97} +(6.50608 - 7.50842i) q^{98} +(0.0507048 - 0.352660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	−0.544078	+	1.19136i	−0.384721	+	0.842422i	0.613872	+	0.789405i	$0.289611\pi$
$2$	−0.544078	+	1.19136i	−0.384721	+	0.842422i	−0.998594	+	0.0530167i	$0.983116\pi$
$3$	−1.40956	−	0.413883i	−0.813808	−	0.238956i	−0.151760	−	0.988417i	$-0.548494\pi$
$3$	−1.40956	−	0.413883i	−0.813808	−	0.238956i	−0.662048	+	0.749462i	$0.730312\pi$
$4$	0.186393	+	0.215109i	0.0931964	+	0.107554i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	1.25999	−	1.45411i	0.514391	−	0.593638i
$7$	−0.543517	+	3.78024i	−0.205430	+	1.42880i	0.582399	+	0.812903i	$0.302114\pi$
$7$	−0.543517	+	3.78024i	−0.205430	+	1.42880i	−0.787829	+	0.615894i	$0.788795\pi$
$8$	−2.87102	+	0.843008i	−1.01506	+	0.298048i
$9$	−0.708209	−	0.455138i	−0.236070	−	0.151713i
$10$	−0.186393	−	1.29639i	−0.0589426	−	0.409955i
$11$	0.175811	+	0.384973i	0.0530091	+	0.116074i	0.934283	−	0.356532i	$-0.116041\pi$
$11$	0.175811	+	0.384973i	0.0530091	+	0.116074i	−0.881274	+	0.472605i	$0.843314\pi$
$12$	−0.173701	−	0.380353i	−0.0501433	−	0.109798i
$13$	0.160369	+	1.11539i	0.0444783	+	0.309354i	0.999900	+	0.0141103i	$0.00449160\pi$
$13$	0.160369	+	1.11539i	0.0444783	+	0.309354i	−0.955422	+	0.295243i	$0.904599\pi$
$14$	−4.20793	−	2.70427i	−1.12462	−	0.722747i
$15$	1.40956	−	0.413883i	0.363946	−	0.106864i
$16$	0.476716	−	3.31563i	0.119179	−	0.828908i
$17$	1.29285	−	1.49203i	0.313562	−	0.361870i	−0.576990	−	0.816751i	$-0.695773\pi$
$17$	1.29285	−	1.49203i	0.313562	−	0.361870i	0.890552	+	0.454881i	$0.150318\pi$
$18$	0.927557	−	0.596105i	0.218627	−	0.140503i
$19$	4.12220	+	4.75727i	0.945697	+	1.09139i	0.995699	+	0.0926434i	$0.0295317\pi$
$19$	4.12220	+	4.75727i	0.945697	+	1.09139i	−0.0500024	+	0.998749i	$0.515923\pi$
$20$	−0.273100	−	0.0801894i	−0.0610671	−	0.0179309i
$21$	2.33070	−	5.10351i	0.508600	−	1.11368i
$22$	−0.554298			−0.118177
$23$	4.18490	−	2.34235i	0.872612	−	0.488414i
$23$	4.18490	−	2.34235i	0.872612	−	0.488414i
$24$	4.39578			0.897284
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−1.41609	−	0.415801i	−0.277718	−	0.0815454i
$27$	3.69598	+	4.26539i	0.711293	+	0.820875i
$28$	−0.914470	+	0.587694i	−0.172819	+	0.111064i
$29$	−2.02505	+	2.33704i	−0.376043	+	0.433977i	−0.911951	−	0.410300i	$-0.865424\pi$
$29$	−2.02505	+	2.33704i	−0.376043	+	0.433977i	0.535908	+	0.844277i	$0.319970\pi$
$30$	−0.273823	+	1.90448i	−0.0499930	+	0.347709i
$31$	3.19411	−	0.937877i	0.573680	−	0.168448i	0.0179913	−	0.999838i	$-0.494273\pi$
$31$	3.19411	−	0.937877i	0.573680	−	0.168448i	0.555689	+	0.831391i	$0.312455\pi$
$32$	−1.34369	−	0.863538i	−0.237533	−	0.152653i
$33$	−0.0884821	−	0.615407i	−0.0154028	−	0.107129i
$34$	1.07414	+	2.35204i	0.184213	+	0.403371i
$35$	−1.58652	−	3.47399i	−0.268170	−	0.587211i
$36$	−0.0341008	−	0.237177i	−0.00568347	−	0.0395294i
$37$	−2.57746	−	1.65644i	−0.423733	−	0.272316i	0.311348	−	0.950296i	$-0.399219\pi$
$37$	−2.57746	−	1.65644i	−0.423733	−	0.272316i	−0.735081	+	0.677979i	$0.762856\pi$
$38$	−7.91044	+	2.32271i	−1.28324	+	0.376794i
$39$	0.235592	−	1.63858i	0.0377249	−	0.262383i
$40$	1.95949	−	2.26138i	0.309823	−	0.357555i
$41$	4.88840	−	3.14158i	0.763440	−	0.490633i	−0.100060	−	0.994981i	$-0.531904\pi$
$41$	4.88840	−	3.14158i	0.763440	−	0.490633i	0.863500	+	0.504348i	$0.168267\pi$
$42$	4.81206	+	5.55342i	0.742517	+	0.856911i
$43$	7.59078	+	2.22886i	1.15758	+	0.339897i	0.803493	−	0.595314i	$-0.202972\pi$
$43$	7.59078	+	2.22886i	1.15758	+	0.339897i	0.354091	+	0.935211i	$0.384790\pi$
$44$	−0.0500411	+	0.109575i	−0.00754398	+	0.0165190i
$45$	0.841850			0.125496
$46$	0.513680	+	6.26016i	0.0757380	+	0.923011i
$47$	−12.4048			−1.80943			−0.904715	−	0.426018i	$-0.859916\pi$
$47$	−12.4048			−1.80943			−0.904715	+	0.426018i	$0.859916\pi$
$48$	−2.04424	+	4.47627i	−0.295061	+	0.646093i
$49$	−7.27836	−	2.13712i	−1.03977	−	0.305303i
$50$	0.857685	+	0.989821i	0.121295	+	0.139982i
$51$	−2.43987	+	1.56801i	−0.341650	+	0.219565i
$52$	−0.210039	+	0.242397i	−0.0291271	+	0.0336145i
$53$	0.607960	−	4.22845i	0.0835097	−	0.580823i	−0.904505	−	0.426463i	$-0.859759\pi$
$53$	0.607960	−	4.22845i	0.0835097	−	0.580823i	0.988015	−	0.154360i	$-0.0493315\pi$
$54$	−7.09254	+	2.08256i	−0.965173	+	0.283400i
$55$	−0.356034	−	0.228809i	−0.0480076	−	0.0308526i
$56$	−1.62633	−	11.3113i	−0.217327	−	1.51154i
$57$	−3.84152	−	8.41175i	−0.508821	−	1.11416i
$58$	−1.68248	−	3.68411i	−0.220920	−	0.483747i
$59$	1.70110	+	11.8314i	0.221464	+	1.54032i	0.732507	+	0.680760i	$0.238350\pi$
$59$	1.70110	+	11.8314i	0.221464	+	1.54032i	−0.511043	+	0.859555i	$0.670741\pi$
$60$	0.351761	+	0.226063i	0.0454122	+	0.0291846i
$61$	−12.6478	+	3.71373i	−1.61939	+	0.475494i	−0.960853	−	0.277058i	$-0.910640\pi$
$61$	−12.6478	+	3.71373i	−1.61939	+	0.475494i	−0.658532	+	0.752553i	$0.728822\pi$
$62$	−0.620494	+	4.31563i	−0.0788029	+	0.548086i
$63$	2.10546	−	2.42983i	0.265263	−	0.306129i
$64$	7.39580	−	4.75299i	0.924475	−	0.594124i
$65$	−0.737936	−	0.851624i	−0.0915297	−	0.105631i
$66$	0.781315	+	0.229415i	0.0961732	+	0.0282390i
$67$	3.10214	−	6.79273i	0.378986	−	0.829865i	−0.619989	−	0.784610i	$-0.712863\pi$
$67$	3.10214	−	6.79273i	0.378986	−	0.829865i	0.998976	−	0.0452542i	$-0.0144098\pi$
$68$	0.561926			0.0681436
$69$	−6.86832	+	1.56962i	−0.826848	+	0.188959i
$70$	5.00198			0.597850
$71$	−4.47175	+	9.79176i	−0.530699	+	1.16207i	0.434529	+	0.900658i	$0.356915\pi$
$71$	−4.47175	+	9.79176i	−0.530699	+	1.16207i	−0.965228	+	0.261410i	$0.915812\pi$
$72$	2.41697	+	0.709686i	0.284843	+	0.0836373i
$73$	6.13979	+	7.08570i	0.718608	+	0.829318i	0.991139	−	0.132829i	$-0.0424061\pi$
$73$	6.13979	+	7.08570i	0.718608	+	0.829318i	−0.272531	+	0.962147i	$0.587861\pi$
$74$	3.37576	−	2.16947i	0.392424	−	0.252196i
$75$	−0.962033	+	1.11024i	−0.111086	+	0.128200i
$76$	−0.254982	+	1.77344i	−0.0292485	+	0.203428i
$77$	−1.55085	+	0.455370i	−0.176735	+	0.0518942i
$78$	1.82397	+	1.17219i	0.206523	+	0.132725i
$79$	−0.588942	−	4.09618i	−0.0662611	−	0.460856i	−0.995757	−	0.0920234i	$-0.970667\pi$
$79$	−0.588942	−	4.09618i	−0.0662611	−	0.460856i	0.929496	−	0.368833i	$-0.120243\pi$
$80$	1.39153	+	3.04702i	0.155577	+	0.340667i
$81$	−2.39517	−	5.24470i	−0.266130	−	0.582745i
$82$	1.08310	+	7.53313i	0.119609	+	0.831895i
$83$	13.5415	+	8.70262i	1.48638	+	0.955236i	0.996513	+	0.0834376i	$0.0265899\pi$
$83$	13.5415	+	8.70262i	1.48638	+	0.955236i	0.489864	+	0.871799i	$0.337046\pi$
$84$	1.53224	−	0.449905i	0.167181	−	0.0490886i
$85$	−0.280963	+	1.95414i	−0.0304747	+	0.211956i
$86$	−6.78536	+	7.83072i	−0.731684	+	0.844408i
$87$	3.82169	−	2.45605i	0.409728	−	0.263316i
$88$	−0.829294	−	0.957056i	−0.0884030	−	0.102022i
$89$	−3.76366	−	1.10511i	−0.398948	−	0.117142i	0.0761032	−	0.997100i	$-0.475752\pi$
$89$	−3.76366	−	1.10511i	−0.398948	−	0.117142i	−0.475051	+	0.879958i	$0.657570\pi$
$90$	−0.458032	+	1.00295i	−0.0482808	+	0.105720i
$91$	−4.30361			−0.451141
$92$	1.28390	+	0.463612i	0.133855	+	0.0483349i
$93$	−4.89046			−0.507117
$94$	6.74919	−	14.7787i	0.696126	−	1.52430i
$95$	−6.03979	−	1.77344i	−0.619669	−	0.181951i
$96$	1.53660	+	1.77334i	0.156829	+	0.180990i
$97$	3.02202	−	1.94213i	0.306839	−	0.197194i	−0.378155	−	0.925742i	$-0.623441\pi$
$97$	3.02202	−	1.94213i	0.306839	−	0.197194i	0.684994	+	0.728549i	$0.259805\pi$
$98$	6.50608	−	7.50842i	0.657214	−	0.758465i
$99$	0.0507048	−	0.352660i	0.00509603	−	0.0354437i
$100$	0.273100	−	0.0801894i	0.0273100	−	0.00801894i
$101$	7.14035	+	4.58882i	0.710491	+	0.456605i	0.845317	−	0.534264i	$-0.179411\pi$
$101$	7.14035	+	4.58882i	0.710491	+	0.456605i	−0.134826	+	0.990869i	$0.543048\pi$
$102$	−0.540591	−	3.75990i	−0.0535265	−	0.372285i
$103$	−5.55918	−	12.1729i	−0.547762	−	1.19943i	−0.957819	−	0.287372i	$-0.907219\pi$
$103$	−5.55918	−	12.1729i	−0.547762	−	1.19943i	0.410057	−	0.912060i	$-0.365509\pi$
$104$	−1.40071	−	3.06712i	−0.137350	−	0.300756i
$105$	0.798461	+	5.55342i	0.0779218	+	0.541958i
$106$	4.70685	+	3.02491i	0.457170	+	0.293805i
$107$	−3.06888	+	0.901105i	−0.296680	+	0.0871131i	−0.426685	−	0.904400i	$-0.640319\pi$
$107$	−3.06888	+	0.901105i	−0.296680	+	0.0871131i	0.130005	+	0.991513i	$0.458501\pi$
$108$	−0.228619	+	1.59008i	−0.0219988	+	0.153005i
$109$	8.26394	−	9.53709i	0.791542	−	0.913488i	−0.206344	−	0.978479i	$-0.566157\pi$
$109$	8.26394	−	9.53709i	0.791542	−	0.913488i	0.997886	+	0.0649918i	$0.0207021\pi$
$110$	0.466305	−	0.299676i	0.0444605	−	0.0285730i
$111$	2.94751	+	3.40161i	0.279765	+	0.322867i
$112$	12.2748	+	3.60420i	1.15986	+	0.340565i
$113$	7.70799	−	16.8781i	0.725107	−	1.58776i	−0.0815002	−	0.996673i	$-0.525971\pi$
$113$	7.70799	−	16.8781i	0.725107	−	1.58776i	0.806607	−	0.591088i	$-0.201302\pi$
$114$	12.1115			1.13435
$115$	−2.25419	+	4.23304i	−0.210205	+	0.394733i
$116$	−0.880173			−0.0817220
$117$	0.394082	−	0.862920i	0.0364329	−	0.0797769i
$118$	−15.0210	−	4.41057i	−1.38280	−	0.406026i
$119$	4.93754	+	5.69823i	0.452624	+	0.522356i
$120$	−3.69796	+	2.37654i	−0.337576	+	0.216947i
$121$	7.08617	−	8.17788i	0.644198	−	0.743444i
$122$	2.45698	−	17.0887i	0.222445	−	1.54714i
$123$	−8.19073	+	2.40501i	−0.738533	+	0.216853i
$124$	0.797105	+	0.512269i	0.0715822	+	0.0460031i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	1.74928	+	3.83038i	0.155838	+	0.341237i
$127$	0.467028	+	1.02265i	0.0414420	+	0.0907454i	0.929221	−	0.369525i	$-0.120480\pi$
$127$	0.467028	+	1.02265i	0.0414420	+	0.0907454i	−0.887779	+	0.460271i	$0.847752\pi$
$128$	1.18403	+	8.23511i	0.104654	+	0.727888i
$129$	−9.77716	−	6.28340i	−0.860831	−	0.553222i
$130$	1.41609	−	0.415801i	0.124199	−	0.0364682i
$131$	0.170890	−	1.18857i	0.0149307	−	0.103846i	−0.980993	−	0.194042i	$-0.937840\pi$
$131$	0.170890	−	1.18857i	0.0149307	−	0.103846i	0.995924	+	0.0901961i	$0.0287494\pi$
$132$	0.115887	−	0.133741i	0.0100867	−	0.0116406i
$133$	−20.2241	+	12.9972i	−1.75365	+	1.12700i
$134$	6.40482	+	7.39155i	0.553292	+	0.638533i
$135$	−5.41531	−	1.59008i	−0.466075	−	0.136852i
$136$	−2.45401	+	5.37353i	−0.210430	+	0.460776i
$137$	1.21181			0.103532			0.0517661	−	0.998659i	$-0.483515\pi$
$137$	1.21181			0.103532			0.0517661	+	0.998659i	$0.483515\pi$
$138$	1.86692	−	9.03666i	0.158922	−	0.769252i
$139$	−19.8679			−1.68517			−0.842586	−	0.538562i	$-0.818968\pi$
$139$	−19.8679			−1.68517			−0.842586	+	0.538562i	$0.818968\pi$
$140$	0.451570	−	0.988800i	0.0381646	−	0.0835689i
$141$	17.4853	+	5.13415i	1.47253	+	0.432373i
$142$	−9.23258	−	10.6550i	−0.774781	−	0.894145i
$143$	−0.401200	+	0.257836i	−0.0335501	+	0.0215613i
$144$	−1.84669	+	2.13119i	−0.153890	+	0.177599i
$145$	0.440086	−	3.06087i	0.0365472	−	0.254191i
$146$	−11.7822	+	3.45956i	−0.975100	+	0.286315i
$147$	9.37474	+	6.02478i	0.773216	+	0.496916i
$148$	−0.124107	−	0.863183i	−0.0102015	−	0.0709532i
$149$	−0.193861	−	0.424496i	−0.0158817	−	0.0347761i	0.901525	−	0.432727i	$-0.142449\pi$
$149$	−0.193861	−	0.424496i	−0.0158817	−	0.0347761i	−0.917407	+	0.397951i	$0.869721\pi$
$150$	−0.799286	−	1.75019i	−0.0652614	−	0.142903i
$151$	−0.174870	−	1.21625i	−0.0142307	−	0.0989770i	0.981468	−	0.191625i	$-0.0613759\pi$
$151$	−0.174870	−	1.21625i	−0.0142307	−	0.0989770i	−0.995699	+	0.0926483i	$0.970467\pi$
$152$	−15.8453	−	10.1832i	−1.28523	−	0.825965i
$153$	−1.59469	+	0.468243i	−0.128923	+	0.0378552i
$154$	0.301270	−	2.09538i	0.0242771	−	0.168851i
$155$	−2.18001	+	2.51586i	−0.175102	+	0.202079i
$156$	0.396386	−	0.254742i	0.0317362	−	0.0203956i
$157$	9.42758	+	10.8800i	0.752403	+	0.868319i	0.994799	−	0.101858i	$-0.0324787\pi$
$157$	9.42758	+	10.8800i	0.752403	+	0.868319i	−0.242396	+	0.970177i	$0.577933\pi$
$158$	5.20047	+	1.52700i	0.413727	+	0.121481i
$159$	−2.60704	+	5.70862i	−0.206752	+	0.452723i
$160$	1.59725			0.126274
$161$	6.58008	+	17.0930i	0.518583	+	1.34712i
$162$	7.55151			0.593303
$163$	−5.40368	+	11.8324i	−0.423249	+	0.926785i	0.571126	+	0.820863i	$0.306507\pi$
$163$	−5.40368	+	11.8324i	−0.423249	+	0.926785i	−0.994374	+	0.105923i	$0.966220\pi$
$164$	1.58694	+	0.465969i	0.123920	+	0.0363861i
$165$	0.407150	+	0.469876i	0.0316966	+	0.0365798i
$166$	−17.7356	+	11.3980i	−1.37655	+	0.884657i
$167$	4.02759	−	4.64808i	0.311664	−	0.359680i	−0.578208	−	0.815889i	$-0.696248\pi$
$167$	4.02759	−	4.64808i	0.311664	−	0.359680i	0.889872	+	0.456210i	$0.150793\pi$
$168$	−2.38918	+	16.6171i	−0.184329	+	1.28204i
$169$	11.2550	−	3.30478i	0.865772	−	0.254213i
$170$	−2.17523	−	1.39794i	−0.166832	−	0.107217i
$171$	−0.754162	−	5.24531i	−0.0576722	−	0.401119i
$172$	0.935421	+	2.04829i	0.0713252	+	0.156180i
$173$	1.97653	+	4.32801i	0.150273	+	0.329052i	0.969766	−	0.244037i	$-0.0784720\pi$
$173$	1.97653	+	4.32801i	0.150273	+	0.329052i	−0.819493	+	0.573090i	$0.805745\pi$
$174$	0.846755	+	5.88931i	0.0641923	+	0.446467i
$175$	3.21284	+	2.06477i	0.242868	+	0.156082i
$176$	1.36024	−	0.399403i	0.102532	−	0.0301061i
$177$	2.49902	−	17.3811i	0.187838	−	1.30644i
$178$	3.36432	−	3.88263i	0.252166	−	0.291015i
$179$	1.02898	−	0.661288i	0.0769099	−	0.0494270i	−0.501621	−	0.865088i	$-0.667263\pi$
$179$	1.02898	−	0.661288i	0.0769099	−	0.0494270i	0.578531	+	0.815661i	$0.303626\pi$
$180$	0.156915	+	0.181089i	0.0116957	+	0.0134976i
$181$	−4.07157	−	1.19552i	−0.302638	−	0.0888624i	0.126888	−	0.991917i	$-0.459501\pi$
$181$	−4.07157	−	1.19552i	−0.302638	−	0.0888624i	−0.429526	+	0.903055i	$0.641319\pi$
$182$	2.34150	−	5.12716i	0.173563	−	0.380051i
$183$	19.3648			1.43149
$184$	−10.0403	+	10.2528i	−0.740182	+	0.755850i
$185$	3.06384			0.225258
$186$	2.66079	−	5.82632i	0.195099	−	0.427206i
$187$	0.801689	+	0.235397i	0.0586253	+	0.0172139i
$188$	−2.31217	−	2.66839i	−0.168632	−	0.194612i
$189$	−18.1330	+	11.6534i	−1.31898	+	0.847660i
$190$	5.39893	−	6.23070i	0.391680	−	0.452022i
$191$	1.11523	−	7.75659i	0.0806952	−	0.561247i	−0.908861	−	0.417099i	$-0.863047\pi$
$191$	1.11523	−	7.75659i	0.0806952	−	0.561247i	0.989556	−	0.144148i	$-0.0460442\pi$
$192$	−12.3920	+	3.63861i	−0.894314	+	0.262594i
$193$	−19.2693	−	12.3836i	−1.38704	−	0.891394i	−0.387501	−	0.921869i	$-0.626662\pi$
$193$	−19.2693	−	12.3836i	−1.38704	−	0.891394i	−0.999536	+	0.0304746i	$0.990298\pi$
$194$	0.669575	+	4.65700i	0.0480727	+	0.334353i
$195$	0.687690	+	1.50583i	0.0492465	+	0.107835i
$196$	−0.896921	−	1.96398i	−0.0640658	−	0.140284i
$197$	−0.547235	−	3.80610i	−0.0389889	−	0.271174i	0.960997	−	0.276560i	$-0.0891945\pi$
$197$	−0.547235	−	3.80610i	−0.0389889	−	0.271174i	−0.999985	+	0.00538648i	$0.998285\pi$
$198$	0.392559	+	0.252282i	0.0278980	+	0.0179289i
$199$	25.6082	−	7.51924i	1.81532	−	0.533025i	0.816311	−	0.577613i	$-0.196016\pi$
$199$	25.6082	−	7.51924i	1.81532	−	0.533025i	0.999005	+	0.0445878i	$0.0141974\pi$
$200$	−0.425839	+	2.96177i	−0.0301113	+	0.209429i
$201$	−7.18404	+	8.29082i	−0.506723	+	0.584790i
$202$	−9.35186	+	6.01008i	−0.657995	+	0.422868i
$203$	−7.73391	−	8.92541i	−0.542814	−	0.626441i
$204$	−0.792067	−	0.232572i	−0.0554558	−	0.0162833i
$205$	−2.41392	+	5.28574i	−0.168595	+	0.369172i
$206$	17.5270			1.22116
$207$	−4.02988	−	0.245835i	−0.280096	−	0.0170867i
$208$	3.77467			0.261726
$209$	−1.10669	+	2.42332i	−0.0765515	+	0.167624i
$210$	−7.05057	−	2.07023i	−0.486535	−	0.142860i
$211$	−16.5622	−	19.1138i	−1.14019	−	1.31585i	−0.941971	−	0.335693i	$-0.891029\pi$
$211$	−16.5622	−	19.1138i	−1.14019	−	1.31585i	−0.198220	−	0.980158i	$-0.563516\pi$
$212$	1.02290	−	0.657376i	0.0702528	−	0.0451487i
$213$	10.3558	−	11.9513i	0.709570	−	0.818887i
$214$	0.596167	−	4.14643i	0.0407531	−	0.283444i
$215$	−7.59078	+	2.22886i	−0.517687	+	0.152007i
$216$	−14.2070	−	9.13029i	−0.966665	−	0.621238i
$217$	1.80935	+	12.5843i	0.122826	+	0.854276i
$218$	6.86593	+	15.0343i	0.465019	+	1.01825i
$219$	−5.72174	−	12.5289i	−0.386639	−	0.846621i
$220$	−0.0171433	−	0.119234i	−0.00115580	−	0.00803878i
$221$	1.87153	+	1.20276i	0.125893	+	0.0809062i
$222$	−5.65623	+	1.66082i	−0.379622	+	0.111467i
$223$	−0.769616	+	5.35280i	−0.0515373	+	0.358450i	0.947692	+	0.319187i	$0.103410\pi$
$223$	−0.769616	+	5.35280i	−0.0515373	+	0.358450i	−0.999229	+	0.0392625i	$0.987499\pi$
$224$	3.99470	−	4.61013i	0.266907	−	0.308027i
$225$	−0.708209	+	0.455138i	−0.0472139	+	0.0303426i
$226$	15.9143	+	18.3660i	1.05860	+	1.22169i
$227$	10.0077	+	2.93853i	0.664235	+	0.195037i	0.596434	−	0.802662i	$-0.296584\pi$
$227$	10.0077	+	2.93853i	0.664235	+	0.195037i	0.0678007	+	0.997699i	$0.478402\pi$
$228$	1.09341	−	2.39423i	0.0724128	−	0.158562i
$229$	−2.55231			−0.168661			−0.0843307	−	0.996438i	$-0.526875\pi$
$229$	−2.55231			−0.168661			−0.0843307	+	0.996438i	$0.526875\pi$
$230$	−3.81664	−	4.98867i	−0.251661	−	0.328943i
$231$	2.37448			0.156229
$232$	3.84383	−	8.41682i	0.252360	−	0.552591i
$233$	12.0723	+	3.54474i	0.790881	+	0.232224i	0.652134	−	0.758104i	$-0.273874\pi$
$233$	12.0723	+	3.54474i	0.790881	+	0.232224i	0.138748	+	0.990328i	$0.455692\pi$
$234$	0.813640	+	0.938991i	0.0531893	+	0.0613838i
$235$	10.4356	−	6.70655i	0.680744	−	0.437487i
$236$	−2.22796	+	2.57121i	−0.145028	+	0.167371i
$237$	−0.865193	+	6.01755i	−0.0562003	+	0.390882i
$238$	−9.47507	+	2.78213i	−0.614178	+	0.180339i
$239$	13.9873	+	8.98906i	0.904760	+	0.581454i	0.908198	−	0.418540i	$-0.137458\pi$
$239$	13.9873	+	8.98906i	0.904760	+	0.581454i	−0.00343801	+	0.999994i	$0.501094\pi$
$240$	−0.700326	−	4.87088i	−0.0452059	−	0.314414i
$241$	−1.93484	−	4.23671i	−0.124634	−	0.272911i	0.837022	−	0.547170i	$-0.184295\pi$
$241$	−1.93484	−	4.23671i	−0.124634	−	0.272911i	−0.961656	+	0.274259i	$0.911567\pi$
$242$	5.88741	+	12.8916i	0.378457	+	0.828705i
$243$	−1.20420	−	8.37541i	−0.0772496	−	0.537283i
$244$	−3.15631	−	2.02844i	−0.202062	−	0.129858i
$245$	7.27836	−	2.13712i	0.464997	−	0.136536i
$246$	1.59115	−	11.0667i	0.101448	−	0.705584i
$247$	−4.64514	+	5.36078i	−0.295563	+	0.341098i
$248$	−8.37974	+	5.38533i	−0.532114	+	0.341969i
$249$	−15.4857	−	17.8715i	−0.981366	−	1.13256i
$250$	−1.25667	−	0.368991i	−0.0794787	−	0.0233371i
$251$	0.954125	−	2.08924i	0.0602239	−	0.131872i	−0.877127	−	0.480258i	$-0.840543\pi$
$251$	0.954125	−	2.08924i	0.0602239	−	0.131872i	0.937351	+	0.348386i	$0.113270\pi$
$252$	0.915119			0.0576471
$253$	1.63749	+	1.19926i	0.102948	+	0.0753970i
$254$	−1.47245			−0.0923895
$255$	1.20482	−	2.63819i	0.0754488	−	0.165210i
$256$	6.41536	+	1.88372i	0.400960	+	0.117732i
$257$	−1.07715	−	1.24310i	−0.0671907	−	0.0775422i	0.721159	−	0.692770i	$-0.243610\pi$
$257$	−1.07715	−	1.24310i	−0.0671907	−	0.0775422i	−0.788350	+	0.615227i	$0.789064\pi$
$258$	12.8054	−	8.22950i	0.797226	−	0.512346i
$259$	7.66262	−	8.84314i	0.476132	−	0.549486i
$260$	0.0456457	−	0.317473i	0.00283083	−	0.0196888i
$261$	2.49784	−	0.733431i	0.154612	−	0.0453983i
$262$	1.32304	+	0.850265i	0.0817376	+	0.0525296i
$263$	0.206228	+	1.43435i	0.0127166	+	0.0884456i	0.995191	−	0.0979499i	$-0.0312285\pi$
$263$	0.206228	+	1.43435i	0.0127166	+	0.0884456i	−0.982475	+	0.186396i	$0.940319\pi$
$264$	0.772827	+	1.69226i	0.0475642	+	0.104151i
$265$	1.77463	+	3.88589i	0.109014	+	0.238708i
$266$	−4.48097	−	31.1658i	−0.274746	−	1.91090i
$267$	4.84771	+	3.11544i	0.296675	+	0.190662i
$268$	2.03939	−	0.598820i	0.124576	−	0.0365787i
$269$	−1.91201	+	13.2984i	−0.116578	+	0.810815i	0.844701	+	0.535238i	$0.179778\pi$
$269$	−1.91201	+	13.2984i	−0.116578	+	0.810815i	−0.961279	+	0.275577i	$0.911131\pi$
$270$	4.84071	−	5.58648i	0.294596	−	0.339982i
$271$	11.5774	−	7.44034i	0.703277	−	0.451969i	−0.139507	−	0.990221i	$-0.544552\pi$
$271$	11.5774	−	7.44034i	0.703277	−	0.451969i	0.842784	+	0.538252i	$0.180915\pi$
$272$	−4.33069	−	4.99789i	−0.262587	−	0.303041i
$273$	6.06618	+	1.78119i	0.367142	+	0.107803i
$274$	−0.659322	+	1.44371i	−0.0398311	+	0.0872179i
$275$	0.423218			0.0255210
$276$	−1.61784	−	1.18487i	−0.0973827	−	0.0713208i
$277$	−19.3976			−1.16549			−0.582746	−	0.812654i	$-0.698022\pi$
$277$	−19.3976			−1.16549			−0.582746	+	0.812654i	$0.698022\pi$
$278$	10.8097	−	23.6699i	0.648321	−	1.41963i
$279$	−2.68896	−	0.789551i	−0.160984	−	0.0472692i
$280$	7.48353	+	8.63645i	0.447226	+	0.516127i
$281$	23.0439	−	14.8094i	1.37468	−	0.883454i	0.375620	−	0.926774i	$-0.377430\pi$
$281$	23.0439	−	14.8094i	1.37468	−	0.883454i	0.999061	+	0.0433200i	$0.0137935\pi$
$282$	−15.6300	+	18.0380i	−0.930754	+	1.07415i
$283$	−4.02029	+	27.9617i	−0.238981	+	1.66215i	0.418153	+	0.908377i	$0.362678\pi$
$283$	−4.02029	+	27.9617i	−0.238981	+	1.66215i	−0.657134	+	0.753774i	$0.728231\pi$
$284$	−2.93980	+	0.863202i	−0.174445	+	0.0512216i
$285$	7.77943	+	4.99953i	0.460813	+	0.296147i
$286$	−0.0888922	−	0.618259i	−0.00525631	−	0.0365584i
$287$	9.21902	+	20.1868i	0.544181	+	1.19159i
$288$	0.558585	+	1.22313i	0.0329149	+	0.0720737i
$289$	1.86466	+	12.9690i	0.109686	+	0.762884i
$290$	3.40717	+	2.18965i	0.200076	+	0.128581i
$291$	−5.06352	+	1.48678i	−0.296829	+	0.0871568i
$292$	−0.379783	+	2.64145i	−0.0222251	+	0.154579i
$293$	14.5296	−	16.7681i	0.848828	−	0.979600i	−0.151132	−	0.988514i	$-0.548292\pi$
$293$	14.5296	−	16.7681i	0.848828	−	0.979600i	0.999960	+	0.00891345i	$0.00283728\pi$
$294$	−12.2783	+	7.89079i	−0.716085	+	0.460200i
$295$	−7.82758	−	9.03351i	−0.455740	−	0.525951i
$296$	8.79635	+	2.58284i	0.511277	+	0.150125i
$297$	−0.992266	+	2.17276i	−0.0575771	+	0.126076i
$298$	0.611205			0.0354062
$299$	3.28376	+	4.29216i	0.189905	+	0.248222i
$300$	−0.418139			−0.0241413
$301$	−12.5513	+	27.4836i	−0.723446	+	1.58413i
$302$	1.54414	+	0.453400i	0.0888553	+	0.0260903i
$303$	−8.16549	−	9.42348i	−0.469095	−	0.541365i
$304$	17.7385	−	11.3998i	1.01737	−	0.653825i
$305$	8.63221	−	9.96211i	0.494279	−	0.570429i
$306$	0.309787	−	2.15462i	0.0177093	−	0.123171i
$307$	23.5469	−	6.91399i	1.34389	−	0.394602i	0.470836	−	0.882221i	$-0.343952\pi$
$307$	23.5469	−	6.91399i	1.34389	−	0.394602i	0.873057	+	0.487618i	$0.162134\pi$
$308$	−0.387021	−	0.248723i	−0.0220526	−	0.0141723i
$309$	2.79782	+	19.4592i	0.159162	+	1.10700i
$310$	−1.81121	−	3.96601i	−0.102870	−	0.225254i
$311$	−10.0537	−	22.0145i	−0.570092	−	1.24833i	−0.946748	−	0.321974i	$-0.895654\pi$
$311$	−10.0537	−	22.0145i	−0.570092	−	1.24833i	0.376656	−	0.926353i	$-0.377074\pi$
$312$	0.704946	+	4.90301i	0.0399097	+	0.277578i
$313$	19.3467	+	12.4333i	1.09354	+	0.702774i	0.957646	−	0.287949i	$-0.0929734\pi$
$313$	19.3467	+	12.4333i	1.09354	+	0.702774i	0.135893	+	0.990724i	$0.456610\pi$
$314$	−18.0914	+	5.31211i	−1.02096	+	0.299780i
$315$	−0.457559	+	3.18240i	−0.0257806	+	0.179308i
$316$	0.771350	−	0.890185i	0.0433918	−	0.0500768i
$317$	−17.4382	+	11.2068i	−0.979424	+	0.629438i	−0.929308	−	0.369306i	$-0.879596\pi$
$317$	−17.4382	+	11.2068i	−0.979424	+	0.629438i	−0.0501162	+	0.998743i	$0.515959\pi$
$318$	−5.38262	−	6.21187i	−0.301842	−	0.348344i
$319$	−1.25572	−	0.368714i	−0.0703070	−	0.0206440i
$320$	−3.65208	+	7.99694i	−0.204158	+	0.447043i
$321$	4.69872			0.262257
$322$	−23.9441	−	1.46067i	−1.33435	−	0.0813998i
$323$	12.4274			0.691477
$324$	0.681738	−	1.49280i	0.0378743	−	0.0829332i
$325$	1.08121	+	0.317473i	0.0599750	+	0.0176102i
$326$	−11.1567	−	12.8755i	−0.617911	−	0.713108i
$327$	−15.5957	+	10.0228i	−0.862446	+	0.554260i
$328$	−11.3863	+	13.1405i	−0.628705	+	0.725564i
$329$	6.74223	−	46.8932i	0.371711	−	2.58531i
$330$	−0.781315	+	0.229415i	−0.0430100	+	0.0126289i
$331$	−23.1157	−	14.8556i	−1.27056	−	0.816537i	−0.280864	−	0.959748i	$-0.590621\pi$
$331$	−23.1157	−	14.8556i	−1.27056	−	0.816537i	−0.989692	+	0.143211i	$0.954257\pi$
$332$	0.652036	+	4.53501i	0.0357851	+	0.248891i
$333$	1.07148	+	2.34621i	0.0587166	+	0.128571i
$334$	3.34624	+	7.32724i	0.183098	+	0.400929i
$335$	1.06275	+	7.39155i	0.0580640	+	0.403844i
$336$	−15.8103	−	10.1607i	−0.862522	−	0.554309i
$337$	−9.77447	+	2.87004i	−0.532449	+	0.156341i	−0.536895	−	0.843649i	$-0.680403\pi$
$337$	−9.77447	+	2.87004i	−0.532449	+	0.156341i	0.00444607	+	0.999990i	$0.498585\pi$
$338$	−2.18642	+	15.2069i	−0.118926	+	0.827146i
$339$	−17.8504	+	20.6005i	−0.969502	+	1.11887i
$340$	−0.472723	+	0.303800i	−0.0256370	+	0.0164759i
$341$	0.922619	+	1.06476i	0.0499626	+	0.0576599i
$342$	6.65940	+	1.95538i	0.360099	+	0.105735i
$343$	0.929113	−	2.03447i	0.0501674	−	0.109851i
$344$	−23.6723			−1.27632
$345$	4.92940	−	5.03374i	0.265390	−	0.271007i
$346$	−6.23162			−0.335014
$347$	−4.43163	+	9.70391i	−0.237902	+	0.520933i	−0.990494	−	0.137554i	$-0.956076\pi$
$347$	−4.43163	+	9.70391i	−0.237902	+	0.520933i	0.752592	+	0.658487i	$0.228803\pi$
$348$	1.24065	+	0.364289i	0.0665060	+	0.0195279i
$349$	2.99335	+	3.45451i	0.160230	+	0.184916i	0.830188	−	0.557484i	$-0.188233\pi$
$349$	2.99335	+	3.45451i	0.160230	+	0.184916i	−0.669957	+	0.742399i	$0.733688\pi$
$350$	−4.20793	+	2.70427i	−0.224923	+	0.144549i
$351$	−4.16486	+	4.80650i	−0.222304	+	0.256552i
$352$	0.0962027	−	0.669104i	0.00512762	−	0.0356634i
$353$	−28.1173	+	8.25599i	−1.49653	+	0.439422i	−0.924619	−	0.380892i	$-0.875617\pi$
$353$	−28.1173	+	8.25599i	−1.49653	+	0.439422i	−0.571914	+	0.820314i	$0.693799\pi$
$354$	19.3475	+	12.4339i	1.02831	+	0.660854i
$355$	−1.53195	−	10.6550i	−0.0813076	−	0.565507i
$356$	−0.463801	−	1.01558i	−0.0245814	−	0.0538257i
$357$	−4.60135	−	10.0755i	−0.243529	−	0.533254i
$358$	0.227987	+	1.58569i	0.0120495	+	0.0838061i
$359$	−2.87295	−	1.84634i	−0.151629	−	0.0974458i	0.462627	−	0.886553i	$-0.346907\pi$
$359$	−2.87295	−	1.84634i	−0.151629	−	0.0974458i	−0.614255	+	0.789107i	$0.710543\pi$
$360$	−2.41697	+	0.709686i	−0.127385	+	0.0374038i
$361$	−2.93512	+	20.4142i	−0.154480	+	1.07443i
$362$	3.63956	−	4.20027i	0.191291	−	0.220761i
$363$	−13.3731	+	8.59434i	−0.701903	+	0.451086i
$364$	−0.802161	−	0.925743i	−0.0420447	−	0.0485221i
$365$	−8.99594	−	2.64145i	−0.470869	−	0.138260i
$366$	−10.5360	+	23.0706i	−0.550725	+	1.20592i
$367$	3.99378			0.208474			0.104237	−	0.994553i	$-0.466760\pi$
$367$	3.99378			0.208474			0.104237	+	0.994553i	$0.466760\pi$
$368$	−5.77136	−	14.9922i	−0.300853	−	0.781524i
$369$	−4.89187			−0.254660
$370$	−1.66697	+	3.65015i	−0.0866615	+	0.189762i
$371$	15.6541	+	4.59647i	0.812722	+	0.238637i
$372$	−0.911546	−	1.05198i	−0.0472615	−	0.0545426i
$373$	16.7746	−	10.7804i	0.868555	−	0.558186i	−0.0287556	−	0.999586i	$-0.509154\pi$
$373$	16.7746	−	10.7804i	0.868555	−	0.558186i	0.897310	+	0.441400i	$0.145518\pi$
$374$	−0.716625	+	0.827029i	−0.0370558	+	0.0427646i
$375$	0.209070	−	1.45411i	0.0107963	−	0.0750900i
$376$	35.6145	−	10.4574i	1.83668	−	0.539298i
$377$	−2.93146	−	1.88394i	−0.150978	−	0.0970277i
$378$	−4.01766	−	27.9434i	−0.206646	−	1.43725i
$379$	−4.31428	−	9.44695i	−0.221610	−	0.485257i	0.765872	−	0.642993i	$-0.222308\pi$
$379$	−4.31428	−	9.44695i	−0.221610	−	0.485257i	−0.987481	+	0.157736i	$0.949581\pi$
$380$	−0.744290	−	1.62977i	−0.0381813	−	0.0836053i
$381$	−0.235045	−	1.63478i	−0.0120417	−	0.0837521i
$382$	8.63416	+	5.54884i	0.441762	+	0.283903i
$383$	−13.2289	+	3.88437i	−0.675968	+	0.198482i	−0.601659	−	0.798753i	$-0.705493\pi$
$383$	−13.2289	+	3.88437i	−0.675968	+	0.198482i	−0.0743089	+	0.997235i	$0.523675\pi$
$384$	1.73942	−	12.0979i	0.0887642	−	0.617369i
$385$	1.05846	−	1.22153i	0.0539443	−	0.0622551i
$386$	25.2375	−	16.2191i	1.28455	−	0.825532i
$387$	−4.36143	−	5.03335i	−0.221704	−	0.255860i
$388$	0.981052	+	0.288063i	0.0498054	+	0.0146242i
$389$	−10.5227	+	23.0415i	−0.533523	+	1.16825i	0.430539	+	0.902572i	$0.358324\pi$
$389$	−10.5227	+	23.0415i	−0.533523	+	1.16825i	−0.964061	+	0.265680i	$0.914404\pi$
$390$	−2.16815			−0.109789
$391$	1.91560	−	9.27230i	0.0968759	−	0.468920i
$392$	22.6979			1.14642
$393$	−0.732807	+	1.60462i	−0.0369652	+	0.0809426i
$394$	4.83220	+	1.41886i	0.243443	+	0.0714812i
$395$	2.71001	+	3.12752i	0.136355	+	0.157363i
$396$	0.0853113	−	0.0548262i	0.00428705	−	0.00275512i
$397$	−1.41722	+	1.63555i	−0.0711280	+	0.0820861i	−0.790198	−	0.612851i	$-0.790022\pi$
$397$	−1.41722	+	1.63555i	−0.0711280	+	0.0820861i	0.719070	+	0.694937i	$0.244568\pi$
$398$	−4.97469	+	34.5997i	−0.249359	+	1.73433i
$399$	33.8864	−	9.94994i	1.69644	−	0.498120i
$400$	−2.81797	−	1.81100i	−0.140898	−	0.0905499i
$401$	3.97444	+	27.6428i	0.198474	+	1.38042i	0.808715	+	0.588201i	$0.200164\pi$
$401$	3.97444	+	27.6428i	0.198474	+	1.38042i	−0.610241	+	0.792216i	$0.708927\pi$
$402$	−5.96872	−	13.0697i	−0.297692	−	0.651856i
$403$	1.55833	+	3.41228i	0.0776262	+	0.169978i
$404$	0.343813	+	2.39127i	0.0171054	+	0.118970i
$405$	4.85045	+	3.11719i	0.241021	+	0.154895i
$406$	14.8413	−	4.35779i	0.736560	−	0.216273i
$407$	0.184536	−	1.28347i	0.00914710	−	0.0636195i
$408$	5.68308	−	6.55862i	0.281354	−	0.324700i
$409$	20.1196	−	12.9301i	0.994851	−	0.639352i	0.0614211	−	0.998112i	$-0.480437\pi$
$409$	20.1196	−	12.9301i	0.994851	−	0.639352i	0.933430	+	0.358760i	$0.116800\pi$
$410$	−4.98388	−	5.75171i	−0.246136	−	0.284057i
$411$	−1.70812	−	0.501550i	−0.0842554	−	0.0247396i
$412$	1.58231	−	3.46477i	0.0779547	−	0.170697i
$413$	−45.6501			−2.24629
$414$	2.48545	−	4.66730i	0.122153	−	0.229385i
$415$	−16.0969			−0.790164
$416$	0.747695	−	1.63722i	0.0366588	−	0.0802715i
$417$	28.0049	+	8.22298i	1.37141	+	0.402681i
$418$	−2.28493	−	2.63695i	−0.111759	−	0.128977i
$419$	−8.28770	+	5.32618i	−0.404880	+	0.260201i	−0.727194	−	0.686432i	$-0.759176\pi$
$419$	−8.28770	+	5.32618i	−0.404880	+	0.260201i	0.322313	+	0.946633i	$0.395540\pi$
$420$	−1.04576	+	1.20687i	−0.0510279	+	0.0588894i
$421$	4.87164	−	33.8830i	0.237429	−	1.65136i	−0.427181	−	0.904166i	$-0.640493\pi$
$421$	4.87164	−	33.8830i	0.237429	−	1.65136i	0.664610	−	0.747190i	$-0.268598\pi$
$422$	31.7827	−	9.33224i	1.54716	−	0.454286i
$423$	8.78521	+	5.64591i	0.427152	+	0.274514i
$424$	1.81915	+	12.6525i	0.0883460	+	0.614460i
$425$	−0.820128	−	1.79583i	−0.0397820	−	0.0871105i
$426$	8.60393	+	18.8400i	0.416862	+	0.912800i
$427$	−7.16450	−	49.8302i	−0.346715	−	2.41145i
$428$	−0.765853	−	0.492184i	−0.0370189	−	0.0237906i
$429$	0.672229	−	0.197384i	0.0324555	−	0.00952980i
$430$	1.47460	−	10.2561i	0.0711115	−	0.494591i
$431$	−20.2173	+	23.3320i	−0.973834	+	1.12386i	0.0184439	+	0.999830i	$0.494129\pi$
$431$	−20.2173	+	23.3320i	−0.973834	+	1.12386i	−0.992278	+	0.124034i	$0.960417\pi$
$432$	15.9044	−	10.2211i	0.765201	−	0.491765i
$433$	−14.5416	−	16.7819i	−0.698826	−	0.806488i	0.289768	−	0.957097i	$-0.406422\pi$
$433$	−14.5416	−	16.7819i	−0.698826	−	0.806488i	−0.988593	+	0.150609i	$0.951876\pi$
$434$	−15.9769	−	4.69124i	−0.766915	−	0.225187i
$435$	−1.88717	+	4.13232i	−0.0904828	+	0.198130i
$436$	3.59185			0.172018
$437$	28.3942	+	10.2531i	1.35828	+	0.490471i
$438$	18.0395			0.861961
$439$	−7.71814	+	16.9004i	−0.368367	+	0.806611i	0.631154	+	0.775658i	$0.282582\pi$
$439$	−7.71814	+	16.9004i	−0.368367	+	0.806611i	−0.999521	+	0.0309535i	$0.990146\pi$
$440$	1.21507	+	0.356777i	0.0579262	+	0.0170087i
$441$	4.18192	+	4.82619i	0.199139	+	0.229819i
$442$	−2.45118	+	1.57528i	−0.116591	+	0.0749283i
$443$	8.01688	−	9.25197i	0.380893	−	0.439574i	−0.532638	−	0.846343i	$-0.678799\pi$
$443$	8.01688	−	9.25197i	0.380893	−	0.439574i	0.913531	+	0.406769i	$0.133345\pi$
$444$	−0.182321	+	1.26807i	−0.00865258	+	0.0601800i
$445$	3.76366	−	1.10511i	0.178415	−	0.0523873i
$446$	−5.95840	−	3.82923i	−0.282139	−	0.181319i
$447$	0.0975662	+	0.678588i	0.00461472	+	0.0320961i
$448$	13.9477	+	30.5412i	0.658968	+	1.44294i
$449$	3.93148	+	8.60874i	0.185538	+	0.406272i	0.979429	−	0.201788i	$-0.0646753\pi$
$449$	3.93148	+	8.60874i	0.185538	+	0.406272i	−0.793891	+	0.608060i	$0.791948\pi$
$450$	−0.156915	−	1.09137i	−0.00739703	−	0.0514475i
$451$	2.06886	+	1.32958i	0.0974189	+	0.0626073i
$452$	5.06735	−	1.48791i	0.238348	−	0.0699853i
$453$	−0.256896	+	1.78675i	−0.0120700	+	0.0839488i
$454$	−8.94583	+	10.3240i	−0.419849	+	0.484531i
$455$	3.62042	−	2.32671i	0.169728	−	0.109078i
$456$	18.1203	+	20.9119i	0.848559	+	0.979289i
$457$	−26.5220	−	7.78757i	−1.24065	−	0.364287i	−0.405389	−	0.914144i	$-0.632864\pi$
$457$	−26.5220	−	7.78757i	−1.24065	−	0.364287i	−0.835259	+	0.549857i	$0.814682\pi$
$458$	1.38866	−	3.04073i	0.0648876	−	0.142084i
$459$	11.1424			0.520085
$460$	−1.33073	+	0.304111i	−0.0620456	+	0.0141793i
$461$	29.7975			1.38781			0.693903	−	0.720069i	$-0.255890\pi$
$461$	29.7975			1.38781			0.693903	+	0.720069i	$0.255890\pi$
$462$	−1.29190	+	2.82887i	−0.0601047	+	0.131611i
$463$	−23.6267	−	6.93744i	−1.09803	−	0.322410i	−0.317959	−	0.948104i	$-0.602998\pi$
$463$	−23.6267	−	6.93744i	−1.09803	−	0.322410i	−0.780068	+	0.625694i	$0.784816\pi$
$464$	6.78338	+	7.82844i	0.314910	+	0.363426i
$465$	4.11411	−	2.64398i	0.190787	−	0.122612i
$466$	−10.7913	+	12.4539i	−0.499899	+	0.576914i
$467$	0.354341	−	2.46450i	0.0163970	−	0.114043i	−0.979979	−	0.199100i	$-0.936198\pi$
$467$	0.354341	−	2.46450i	0.0163970	−	0.114043i	0.996376	+	0.0850568i	$0.0271072\pi$
$468$	0.259076	−	0.0760715i	0.0119758	−	0.00351641i
$469$	23.9921	+	15.4188i	1.10785	+	0.711974i
$470$	2.31217	+	16.0815i	0.106652	+	0.741784i
$471$	−8.78566	−	19.2379i	−0.404822	−	0.886436i
$472$	−14.8578	−	32.5341i	−0.683888	−	1.49750i
$473$	0.476496	+	3.31411i	0.0219093	+	0.152383i
$474$	−6.69837	−	4.30478i	−0.307666	−	0.197725i
$475$	6.03979	−	1.77344i	0.277124	−	0.0813711i
$476$	−0.305416	+	2.12422i	−0.0139987	+	0.0973633i
$477$	−2.35509	+	2.71792i	−0.107832	+	0.124445i
$478$	−18.3194	+	11.7732i	−0.837910	+	0.538492i
$479$	−22.0790	−	25.4806i	−1.00882	−	1.16424i	−0.986379	−	0.164488i	$-0.947403\pi$
$479$	−22.0790	−	25.4806i	−1.00882	−	1.16424i	−0.0224375	−	0.999748i	$-0.507143\pi$
$480$	−2.25141	−	0.661074i	−0.102762	−	0.0301738i
$481$	1.43423	−	3.14052i	0.0653951	−	0.143195i
$482$	6.10018			0.277855
$483$	−2.20048	−	26.8170i	−0.100125	−	1.22022i
$484$	3.07995			0.139998
$485$	−1.49229	+	3.26765i	−0.0677612	+	0.148376i
$486$	10.6333	+	3.12223i	0.482338	+	0.141627i
$487$	17.9370	+	20.7004i	0.812801	+	0.938023i	0.999010	−	0.0444876i	$-0.0141655\pi$
$487$	17.9370	+	20.7004i	0.812801	+	0.938023i	−0.186209	+	0.982510i	$0.559620\pi$
$488$	33.1814	−	21.3244i	1.50205	−	0.965310i
$489$	12.5140	−	14.4419i	0.565904	−	0.653088i
$490$	−1.41391	+	9.83394i	−0.0638738	+	0.444252i
$491$	−16.2414	+	4.76890i	−0.732964	+	0.215218i	−0.626854	−	0.779137i	$-0.715658\pi$
$491$	−16.2414	+	4.76890i	−0.732964	+	0.215218i	−0.106110	+	0.994354i	$0.533840\pi$
$492$	−2.04403	−	1.31362i	−0.0921521	−	0.0592226i
$493$	0.868835	+	6.04288i	0.0391303	+	0.272158i
$494$	−3.85932	−	8.45073i	−0.173639	−	0.380217i
$495$	0.148007	+	0.324090i	0.00665241	+	0.0145667i
$496$	−1.58697	−	11.0376i	−0.0712570	−	0.495603i
$497$	−34.5847	−	22.2263i	−1.55134	−	0.996984i
$498$	29.7168	−	8.72565i	1.33164	−	0.391006i
$499$	5.62203	−	39.1021i	0.251677	−	1.75045i	−0.336468	−	0.941695i	$-0.609233\pi$
$499$	5.62203	−	39.1021i	0.251677	−	1.75045i	0.588145	−	0.808755i	$-0.299858\pi$
$500$	−0.186393	+	0.215109i	−0.00833574	+	0.00961996i
$501$	−7.60088	+	4.88479i	−0.339582	+	0.218236i
$502$	1.96993	+	2.27342i	0.0879224	+	0.101468i
$503$	−18.7720	−	5.51196i	−0.837003	−	0.245766i	−0.164980	−	0.986297i	$-0.552756\pi$
$503$	−18.7720	−	5.51196i	−0.837003	−	0.245766i	−0.672023	+	0.740531i	$0.734574\pi$
$504$	−3.99645	+	8.75100i	−0.178016	+	0.389801i
$505$	−8.48775			−0.377700
$506$	−2.31968	+	1.29836i	−0.103123	+	0.0577192i
$507$	−17.2324			−0.765318
$508$	−0.132930	+	0.291076i	−0.00589781	+	0.0129144i
$509$	−23.9070	−	7.01972i	−1.05966	−	0.311144i	−0.294945	−	0.955514i	$-0.595301\pi$
$509$	−23.9070	−	7.01972i	−1.05966	−	0.311144i	−0.764713	+	0.644371i	$0.777119\pi$
$510$	2.48753	+	2.87076i	0.110150	+	0.127119i
$511$	−30.1227	+	19.3587i	−1.33255	+	0.856378i
$512$	−16.6313	+	19.1935i	−0.735005	+	0.848241i
$513$	−5.05605	+	35.1656i	−0.223230	+	1.55260i
$514$	2.06703	−	0.606936i	0.0911729	−	0.0267708i
$515$	11.2578	+	7.23498i	0.496080	+	0.318811i
$516$	−0.470778	−	3.27433i	−0.0207248	−	0.144144i
$517$	−2.18091	−	4.77552i	−0.0959163	−	0.210027i
$518$	6.36634	+	13.9403i	0.279721	+	0.612503i
$519$	−0.994748	−	6.91863i	−0.0436646	−	0.303694i
$520$	2.83656	+	1.82294i	0.124391	+	0.0799414i
$521$	−12.8095	+	3.76121i	−0.561195	+	0.164782i	−0.550013	−	0.835156i	$-0.685377\pi$
$521$	−12.8095	+	3.76121i	−0.561195	+	0.164782i	−0.0111813	+	0.999937i	$0.503559\pi$
$522$	−0.485234	+	3.37488i	−0.0212381	+	0.147714i
$523$	12.4438	−	14.3609i	0.544128	−	0.627957i	−0.415377	−	0.909649i	$-0.636350\pi$
$523$	12.4438	−	14.3609i	0.544128	−	0.627957i	0.959505	+	0.281693i	$0.0908958\pi$
$524$	0.287524	−	0.184780i	0.0125605	−	0.00807217i
$525$	−3.67411	−	4.24015i	−0.160351	−	0.185055i
$526$	−1.82103	−	0.534704i	−0.0794009	−	0.0233142i
$527$	2.73017	−	5.97824i	0.118928	−	0.260416i
$528$	−2.08264			−0.0906354
$529$	12.0268	−	19.6050i	0.522904	−	0.852392i
$530$	−5.59505			−0.243033
$531$	4.18019	−	9.15333i	0.181405	−	0.397221i
$532$	−6.56545	−	1.92779i	−0.284648	−	0.0835803i
$533$	4.28804	+	4.94866i	0.185736	+	0.214350i
$534$	−6.34915	+	4.08035i	−0.274755	+	0.176574i
$535$	2.09453	−	2.41722i	0.0905546	−	0.104506i
$536$	−3.17998	+	22.1172i	−0.137354	+	0.955318i
$537$	−1.72411	+	0.506243i	−0.0744007	+	0.0218460i
$538$	−14.8029	−	9.51325i	−0.638198	−	0.410145i
$539$	−0.456885	−	3.17770i	−0.0196794	−	0.136873i
$540$	−0.667335	−	1.46126i	−0.0287175	−	0.0628826i
$541$	10.6735	+	23.3717i	0.458890	+	1.00483i	0.987739	+	0.156113i	$0.0498965\pi$
$541$	10.6735	+	23.3717i	0.458890	+	1.00483i	−0.528849	+	0.848716i	$0.677376\pi$
$542$	2.56515	+	17.8410i	0.110183	+	0.766338i
$543$	5.24431	+	3.37031i	0.225055	+	0.144634i
$544$	−3.02561	+	0.888400i	−0.129722	+	0.0380898i
$545$	−1.79593	+	12.4909i	−0.0769290	+	0.535053i
$546$	−5.42252	+	6.25792i	−0.232062	+	0.267814i
$547$	22.3599	−	14.3698i	0.956039	−	0.614409i	0.0331399	−	0.999451i	$-0.489449\pi$
$547$	22.3599	−	14.3698i	0.956039	−	0.614409i	0.922899	+	0.385042i	$0.125813\pi$
$548$	0.225873	+	0.260672i	0.00964884	+	0.0111354i
$549$	10.6476	+	3.12640i	0.454426	+	0.133432i
$550$	−0.230264	+	0.504207i	−0.00981848	+	0.0214995i
$551$	−19.4656			−0.829262
$552$	18.3959	−	10.2964i	0.782981	−	0.438246i
$553$	15.8046			0.672082
$554$	10.5538	−	23.1097i	0.448389	−	0.981836i
$555$	−4.31865	−	1.26807i	−0.183317	−	0.0538266i
$556$	−3.70323	−	4.27376i	−0.157052	−	0.181248i
$557$	3.31163	−	2.12826i	0.140318	−	0.0901771i	−0.468598	−	0.883411i	$-0.655241\pi$
$557$	3.31163	−	2.12826i	0.140318	−	0.0901771i	0.608917	+	0.793234i	$0.291604\pi$
$558$	2.40365	−	2.77396i	0.101755	−	0.117431i
$559$	−1.26872	+	8.82412i	−0.0536610	+	0.373221i
$560$	−12.2748	+	3.60420i	−0.518704	+	0.152305i
$561$	−1.03260	−	0.663611i	−0.0435964	−	0.0280177i
$562$	5.10572	+	35.5111i	0.215372	+	1.49794i
$563$	−0.442535	−	0.969017i	−0.0186506	−	0.0408392i	0.900077	−	0.435730i	$-0.143510\pi$
$563$	−0.442535	−	0.969017i	−0.0186506	−	0.0408392i	−0.918728	+	0.394891i	$0.870782\pi$
$564$	2.15473	+	4.71821i	0.0907307	+	0.198673i
$565$	2.64064	+	18.3660i	0.111093	+	0.772665i
$566$	−31.1252	−	20.0030i	−1.30829	−	0.840788i
$567$	21.1280	−	6.20375i	0.887295	−	0.260533i
$568$	4.58395	−	31.8821i	0.192338	−	1.33774i
$569$	8.68495	−	10.0230i	0.364092	−	0.420185i	−0.543915	−	0.839141i	$-0.683058\pi$
$569$	8.68495	−	10.0230i	0.364092	−	0.420185i	0.908006	+	0.418956i	$0.137604\pi$
$570$	−10.1889	+	6.54800i	−0.426765	+	0.274265i
$571$	−2.58417	−	2.98229i	−0.108144	−	0.124805i	0.699097	−	0.715027i	$-0.253586\pi$
$571$	−2.58417	−	2.98229i	−0.108144	−	0.124805i	−0.807241	+	0.590222i	$0.799040\pi$
$572$	−0.130244	−	0.0382430i	−0.00544576	−	0.00159902i
$573$	−4.78230	+	10.4718i	−0.199784	+	0.437465i
$574$	−29.0657			−1.21318
$575$	−0.392206	−	4.77977i	−0.0163561	−	0.199330i
$576$	−7.40104			−0.308377
$577$	2.14890	−	4.70544i	0.0894601	−	0.195890i	−0.859613	−	0.510945i	$-0.829296\pi$
$577$	2.14890	−	4.70544i	0.0894601	−	0.195890i	0.949074	+	0.315055i	$0.102023\pi$
$578$	−16.4654	−	4.83467i	−0.684869	−	0.201096i
$579$	22.0358	+	25.4307i	0.915778	+	1.05686i
$580$	0.740448	−	0.475857i	0.0307454	−	0.0197589i
$581$	−40.2580	+	46.4603i	−1.67019	+	1.92750i
$582$	0.983649	−	6.84143i	0.0407735	−	0.283586i
$583$	1.73473	−	0.509362i	0.0718450	−	0.0210956i
$584$	−23.6008	−	15.1673i	−0.976607	−	0.627627i
$585$	0.135007	+	0.938991i	0.00558183	+	0.0388225i
$586$	12.0716	+	26.4332i	0.498674	+	1.09194i
$587$	13.4633	+	29.4806i	0.555692	+	1.21680i	0.954073	+	0.299575i	$0.0968450\pi$
$587$	13.4633	+	29.4806i	0.555692	+	1.21680i	−0.398381	+	0.917220i	$0.630428\pi$
$588$	0.451401	+	3.13957i	0.0186155	+	0.129473i
$589$	17.6285	+	11.3292i	0.726370	+	0.466810i
$590$	15.0210	−	4.41057i	0.618406	−	0.181580i
$591$	−0.803924	+	5.59141i	−0.0330690	+	0.230000i
$592$	−6.72085	+	7.75627i	−0.276225	+	0.318781i
$593$	8.59593	−	5.52427i	0.352993	−	0.226855i	−0.352112	−	0.935958i	$-0.614536\pi$
$593$	8.59593	−	5.52427i	0.352993	−	0.226855i	0.705105	+	0.709103i	$0.250900\pi$
$594$	−2.04868	−	2.36430i	−0.0840583	−	0.0970084i
$595$	−7.23442	−	2.12422i	−0.296582	−	0.0870844i
$596$	0.0551786	−	0.120824i	0.00226020	−	0.00494915i
$597$	−39.2083			−1.60469
$598$	−6.90015	+	1.57689i	−0.282168	+	0.0644838i
$599$	10.0831			0.411986			0.205993	−	0.978553i	$-0.433958\pi$
$599$	10.0831			0.411986			0.205993	+	0.978553i	$0.433958\pi$
$600$	1.82607	−	3.99854i	0.0745491	−	0.163240i
$601$	3.92813	+	1.15340i	0.160232	+	0.0470483i	0.360865	−	0.932618i	$-0.382482\pi$
$601$	3.92813	+	1.15340i	0.160232	+	0.0470483i	−0.200633	+	0.979667i	$0.564300\pi$
$602$	−25.9141	−	29.9064i	−1.05618	−	1.21889i
$603$	−5.28860	+	3.39878i	−0.215368	+	0.138409i
$604$	0.229031	−	0.264316i	0.00931916	−	0.0107549i
$605$	−1.53997	+	10.7107i	−0.0626088	+	0.435454i
$606$	15.6695	−	4.60097i	0.636528	−	0.186902i
$607$	−3.48837	−	2.24184i	−0.141589	−	0.0909936i	0.467929	−	0.883766i	$-0.345000\pi$
$607$	−3.48837	−	2.24184i	−0.141589	−	0.0909936i	−0.609517	+	0.792773i	$0.708637\pi$
$608$	−1.43088	−	9.95197i	−0.0580297	−	0.403606i
$609$	7.20731	+	15.7818i	0.292055	+	0.639511i
$610$	7.17190	+	15.7043i	0.290382	+	0.635848i
$611$	−1.98935	−	13.8362i	−0.0804804	−	0.559754i
$612$	−0.397961	−	0.255754i	−0.0160866	−	0.0103383i
$613$	9.55412	−	2.80534i	0.385887	−	0.113307i	−0.0830339	−	0.996547i	$-0.526461\pi$
$613$	9.55412	−	2.80534i	0.385887	−	0.113307i	0.468921	+	0.883240i	$0.344643\pi$
$614$	−4.57426	+	31.8147i	−0.184602	+	1.28394i
$615$	5.59023	−	6.45147i	0.225420	−	0.260148i
$616$	4.06864	−	2.61475i	0.163930	−	0.105351i
$617$	−6.98592	−	8.06218i	−0.281243	−	0.324571i	0.597498	−	0.801870i	$-0.296161\pi$
$617$	−6.98592	−	8.06218i	−0.281243	−	0.324571i	−0.878741	+	0.477299i	$0.841616\pi$
$618$	−24.7053	−	7.25413i	−0.993792	−	0.291804i
$619$	−1.54355	+	3.37990i	−0.0620404	+	0.135850i	−0.938113	−	0.346330i	$-0.887428\pi$
$619$	−1.54355	+	3.37990i	−0.0620404	+	0.135850i	0.876072	+	0.482180i	$0.160155\pi$
$620$	−0.947521			−0.0380534
$621$	25.4584	+	9.19296i	1.02161	+	0.368901i
$622$	31.6973			1.27094
$623$	6.22320	−	13.6269i	0.249327	−	0.545951i
$624$	−5.32062	−	1.56227i	−0.212995	−	0.0625410i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−25.3387	+	16.2842i	−1.01274	+	0.650848i
$627$	2.56292	−	2.95776i	0.102353	−	0.118122i
$628$	−0.583152	+	4.05591i	−0.0232703	+	0.161848i
$629$	−5.80373	+	1.70413i	−0.231410	+	0.0679480i
$630$	−3.54245	−	2.27659i	−0.141134	−	0.0907016i
$631$	1.53442	+	10.6721i	0.0610843	+	0.424850i	0.997301	+	0.0734263i	$0.0233934\pi$
$631$	1.53442	+	10.6721i	0.0610843	+	0.424850i	−0.936216	+	0.351424i	$0.885698\pi$
$632$	5.14398	+	11.2637i	0.204616	+	0.448048i
$633$	15.4345	+	33.7969i	0.613467	+	1.34331i
$634$	−3.86369	−	26.8726i	−0.153447	−	1.06725i
$635$	−0.945774	−	0.607812i	−0.0375319	−	0.0241203i
$636$	−1.71391	+	0.503249i	−0.0679609	+	0.0199551i
$637$	1.21650	−	8.46094i	0.0481995	−	0.335235i
$638$	1.12248	−	1.29542i	0.0444396	−	0.0512860i
$639$	7.62354	−	4.89935i	0.301583	−	0.193815i
$640$	−5.44831	−	6.28768i	−0.215363	−	0.248542i
$641$	23.0001	+	6.75344i	0.908449	+	0.266745i	0.702388	−	0.711794i	$-0.252117\pi$
$641$	23.0001	+	6.75344i	0.908449	+	0.266745i	0.206061	+	0.978539i	$0.433935\pi$
$642$	−2.55647	+	5.59788i	−0.100896	+	0.220931i
$643$	−0.700632			−0.0276302			−0.0138151	−	0.999905i	$-0.504398\pi$
$643$	−0.700632			−0.0276302			−0.0138151	+	0.999905i	$0.504398\pi$
$644$	−2.45038	+	4.60145i	−0.0965586	+	0.181323i
$645$	11.6221			0.457621
$646$	−6.76146	+	14.8055i	−0.266026	+	0.582516i
$647$	7.03095	+	2.06447i	0.276415	+	0.0811628i	0.417002	−	0.908906i	$-0.363081\pi$
$647$	7.03095	+	2.06447i	0.276415	+	0.0811628i	−0.140587	+	0.990068i	$0.544899\pi$
$648$	11.2979	+	13.0385i	0.443824	+	0.512201i
$649$	−4.25569	+	2.73497i	−0.167051	+	0.107357i
$650$	−0.966491	+	1.11539i	−0.0379089	+	0.0437492i
$651$	2.65804	−	18.4871i	0.104177	−	0.724567i
$652$	−3.55246	+	1.04310i	−0.139125	+	0.0408508i
$653$	−1.62898	−	1.04688i	−0.0637468	−	0.0409676i	0.508379	−	0.861133i	$-0.330245\pi$
$653$	−1.62898	−	1.04688i	−0.0637468	−	0.0409676i	−0.572126	+	0.820166i	$0.693881\pi$
$654$	−3.45548	−	24.0334i	−0.135120	−	0.939779i
$655$	0.498826	+	1.09228i	0.0194907	+	0.0426788i
$656$	−8.08596	−	17.7058i	−0.315704	−	0.691294i
$657$	−1.12328	−	7.81261i	−0.0438235	−	0.304799i
$658$	52.1986	+	33.5460i	2.03491	+	1.30776i
$659$	30.7419	−	9.02664i	1.19753	−	0.351628i	0.378625	−	0.925550i	$-0.376397\pi$
$659$	30.7419	−	9.02664i	1.19753	−	0.351628i	0.818910	+	0.573922i	$0.194579\pi$
$660$	−0.0251846	+	0.175163i	−0.000980311	+	0.00681821i
$661$	6.93205	−	8.00001i	0.269625	−	0.311164i	−0.604749	−	0.796416i	$-0.706727\pi$
$661$	6.93205	−	8.00001i	0.269625	−	0.311164i	0.874374	+	0.485252i	$0.161272\pi$
$662$	30.2752	−	19.4567i	1.17668	−	0.756205i
$663$	−2.14022	−	2.46995i	−0.0831194	−	0.0959249i
$664$	−46.2144	−	13.5698i	−1.79347	−	0.526610i
$665$	9.98676	−	21.8680i	0.387270	−	0.848003i
$666$	−3.37815			−0.130901
$667$	−3.00049	+	14.5237i	−0.116180	+	0.562358i
$668$	1.75056			0.0677311
$669$	3.30025	−	7.22654i	0.127595	−	0.279394i
$670$	−9.38425	−	2.75547i	−0.362545	−	0.106453i
$671$	−3.65331	−	4.21615i	−0.141035	−	0.162763i
$672$	−7.53881	+	4.84490i	−0.290816	+	0.186896i
$673$	−3.95531	+	4.56467i	−0.152466	+	0.175955i	−0.826844	−	0.562431i	$-0.809866\pi$
$673$	−3.95531	+	4.56467i	−0.152466	+	0.175955i	0.674378	+	0.738386i	$0.264412\pi$
$674$	1.89881	−	13.2065i	0.0731392	−	0.508695i
$675$	5.41531	−	1.59008i	0.208435	−	0.0612021i
$676$	2.80874	+	1.80507i	0.108029	+	0.0694258i
$677$	−6.60154	−	45.9147i	−0.253718	−	1.76465i	−0.575471	−	0.817822i	$-0.695181\pi$
$677$	−6.60154	−	45.9147i	−0.253718	−	1.76465i	0.321753	−	0.946824i	$-0.395728\pi$
$678$	−14.8307	−	32.4746i	−0.569568	−	1.24718i
$679$	5.69921	+	12.4795i	0.218716	+	0.478921i
$680$	−0.840706	−	5.84724i	−0.0322396	−	0.224231i
$681$	−12.8902	−	8.28405i	−0.493955	−	0.317445i
$682$	−1.77049	+	0.519863i	−0.0677957	+	0.0199066i
$683$	−2.19587	+	15.2726i	−0.0840226	+	0.584390i	0.903699	+	0.428168i	$0.140841\pi$
$683$	−2.19587	+	15.2726i	−0.0840226	+	0.584390i	−0.987722	+	0.156223i	$0.950068\pi$
$684$	0.987742	−	1.13992i	0.0377673	−	0.0435858i
$685$	−1.01944	+	0.655156i	−0.0389509	+	0.0250322i
$686$	1.91829	+	2.21382i	0.0732406	+	0.0845242i
$687$	3.59763	+	1.05636i	0.137258	+	0.0403026i
$688$	11.0087	−	24.1057i	0.419703	−	0.919022i
$689$	4.81387			0.183394
$690$	3.31504	+	8.61145i	0.126201	+	0.327832i
$691$	−12.3705			−0.470596			−0.235298	−	0.971923i	$-0.575607\pi$
$691$	−12.3705			−0.470596			−0.235298	+	0.971923i	$0.575607\pi$
$692$	−0.562580	+	1.23188i	−0.0213861	+	0.0468290i
$693$	1.30558	+	0.383353i	0.0495949	+	0.0145624i
$694$	−9.14975	−	10.5594i	−0.347320	−	0.400828i
$695$	16.7139	−	10.7414i	0.633995	−	0.407444i
$696$	−8.90169	+	10.2731i	−0.337418	+	0.389401i
$697$	1.63264	−	11.3552i	0.0618405	−	0.430110i
$698$	−5.74420	+	1.68665i	−0.217421	+	0.0638406i
$699$	−15.5495	−	9.99303i	−0.588134	−	0.377971i
$700$	0.154701	+	1.07597i	0.00584715	+	0.0406678i
$701$	−9.68496	−	21.2071i	−0.365796	−	0.800981i	−0.999622	−	0.0275053i	$-0.991244\pi$
$701$	−9.68496	−	21.2071i	−0.365796	−	0.800981i	0.633826	−	0.773476i	$-0.281484\pi$
$702$	−3.46029	−	7.57697i	−0.130600	−	0.285974i
$703$	−2.74471	−	19.0899i	−0.103519	−	0.719987i
$704$	3.13004	+	2.01155i	0.117968	+	0.0758133i
$705$	−17.4853	+	5.13415i	−0.658535	+	0.193363i
$706$	5.46212	−	37.9899i	0.205569	−	1.42977i
$707$	−21.2277	+	24.4981i	−0.798352	+	0.921347i
$708$	4.20462	−	2.70214i	0.158019	−	0.101553i
$709$	28.4689	+	32.8549i	1.06917	+	1.23389i	0.971090	+	0.238712i	$0.0767252\pi$
$709$	28.4689	+	32.8549i	1.06917	+	1.23389i	0.0980816	+	0.995178i	$0.468729\pi$
$710$	13.5274	+	3.97202i	0.507676	+	0.149067i
$711$	−1.44723	+	3.16900i	−0.0542756	+	0.118847i
$712$	11.7372			0.439870
$713$	11.1702	−	11.4067i	0.418328	−	0.427183i
$714$	14.5071			0.542916
$715$	0.198115	−	0.433811i	0.00740907	−	0.0162236i
$716$	0.334044	+	0.0980841i	0.0124838	+	0.00366558i
$717$	−15.9954	−	18.4597i	−0.597360	−	0.689390i
$718$	3.76277	−	2.41818i	0.140425	−	0.0902459i
$719$	−32.3041	+	37.2810i	−1.20474	+	1.39035i	−0.305905	+	0.952062i	$0.598959\pi$
$719$	−32.3041	+	37.2810i	−1.20474	+	1.39035i	−0.898837	+	0.438283i	$0.855587\pi$
$720$	0.401323	−	2.79126i	0.0149564	−	0.104024i
$721$	49.0380	−	14.3989i	1.82627	−	0.536241i
$722$	−22.7238	−	14.6037i	−0.845693	−	0.543494i
$723$	0.973766	+	6.77269i	0.0362147	+	0.251879i
$724$	−0.501745	−	1.09867i	−0.0186472	−	0.0408317i
$725$	1.28461	+	2.81289i	0.0477091	+	0.104468i
$726$	−2.96301	−	20.6082i	−0.109968	−	0.764841i
$727$	22.5569	+	14.4964i	0.836588	+	0.537643i	0.887365	−	0.461067i	$-0.152533\pi$
$727$	22.5569	+	14.4964i	0.836588	+	0.537643i	−0.0507768	+	0.998710i	$0.516170\pi$
$728$	12.3557	−	3.62798i	0.457935	−	0.134462i
$729$	−4.23070	+	29.4252i	−0.156693	+	1.08982i
$730$	8.04142	−	9.28029i	0.297626	−	0.343479i
$731$	13.1393	−	8.44409i	0.485973	−	0.312316i
$732$	3.60947	+	4.16555i	0.133410	+	0.153963i
$733$	0.725158	+	0.212926i	0.0267843	+	0.00786458i	0.295097	−	0.955467i	$-0.404648\pi$
$733$	0.725158	+	0.212926i	0.0267843	+	0.00786458i	−0.268313	+	0.963332i	$0.586466\pi$
$734$	−2.17293	+	4.75805i	−0.0802043	+	0.175623i
$735$	−11.1438			−0.411044
$736$	−7.64592	−	0.466425i	−0.281832	−	0.0171927i
$737$	3.16041			0.116415
$738$	2.66156	−	5.82800i	0.0979732	−	0.214531i
$739$	6.38508	+	1.87483i	0.234879	+	0.0689667i	0.397054	−	0.917795i	$-0.370033\pi$
$739$	6.38508	+	1.87483i	0.234879	+	0.0689667i	−0.162175	+	0.986762i	$0.551851\pi$
$740$	0.571077	+	0.659058i	0.0209932	+	0.0242275i
$741$	8.76632	−	5.63377i	0.322039	−	0.206962i
$742$	−13.9931	+	16.1489i	−0.513704	+	0.592846i
$743$	−3.22405	+	22.4238i	−0.118279	+	0.822648i	0.841171	+	0.540769i	$0.181867\pi$
$743$	−3.22405	+	22.4238i	−0.118279	+	0.822648i	−0.959450	+	0.281879i	$0.909042\pi$
$744$	14.0406	−	4.12270i	0.514754	−	0.151145i
$745$	0.392586	+	0.252300i	0.0143832	+	0.00924355i
$746$	3.71667	+	25.8500i	0.136077	+	0.946436i
$747$	−5.62935	−	12.3265i	−0.205967	−	0.451005i
$748$	0.0987930	+	0.216327i	0.00361223	+	0.00790968i
$749$	−1.73841	−	12.0909i	−0.0635200	−	0.441791i
$750$	1.61863	+	1.04023i	0.0591039	+	0.0379838i
$751$	−26.6622	+	7.82874i	−0.972919	+	0.285675i	−0.729298	−	0.684196i	$-0.760153\pi$
$751$	−26.6622	+	7.82874i	−0.972919	+	0.285675i	−0.243621	+	0.969871i	$0.578335\pi$
$752$	−5.91358	+	41.1298i	−0.215646	+	1.49985i
$753$	−2.20960	+	2.55001i	−0.0805222	+	0.0929276i
$754$	3.83940	−	2.46743i	0.139823	−	0.0898586i
$755$	0.804665	+	0.928633i	0.0292847	+	0.0337964i
$756$	−5.88662	−	1.72847i	−0.214094	−	0.0628637i
$757$	−4.67170	+	10.2296i	−0.169796	+	0.371801i	−0.975331	−	0.220747i	$-0.929151\pi$
$757$	−4.67170	+	10.2296i	−0.169796	+	0.371801i	0.805535	+	0.592548i	$0.201878\pi$
$758$	13.6021			0.494049
$759$	−1.81179	−	2.36816i	−0.0657637	−	0.0859588i
$760$	18.8354			0.683231
$761$	20.6558	−	45.2299i	0.748772	−	1.63958i	−0.0197877	−	0.999804i	$-0.506299\pi$
$761$	20.6558	−	45.2299i	0.748772	−	1.63958i	0.768560	−	0.639778i	$-0.220974\pi$
$762$	2.07550	+	0.609421i	0.0751873	+	0.0220770i
$763$	31.5609	+	36.4232i	1.14258	+	1.31861i
$764$	1.87638	−	1.20588i	0.0678851	−	0.0436271i
$765$	1.08839	−	1.25606i	0.0393507	−	0.0454131i
$766$	2.56988	−	17.8739i	0.0928535	−	0.645810i
$767$	−12.9238	+	3.79477i	−0.466652	+	0.137021i
$768$	−8.26317	−	5.31042i	−0.298172	−	0.191623i
$769$	−0.564173	−	3.92391i	−0.0203446	−	0.141500i	0.977117	−	0.212701i	$-0.0682259\pi$
$769$	−0.564173	−	3.92391i	−0.0203446	−	0.141500i	−0.997462	+	0.0712010i	$0.977317\pi$
$770$	0.879404	+	1.92563i	0.0316915	+	0.0693947i
$771$	1.00381	+	2.19803i	0.0361512	+	0.0791600i
$772$	−0.927834	−	6.45322i	−0.0333935	−	0.232257i
$773$	0.590898	+	0.379747i	0.0212531	+	0.0136586i	0.551224	−	0.834357i	$-0.314161\pi$
$773$	0.590898	+	0.379747i	0.0212531	+	0.0136586i	−0.529971	+	0.848016i	$0.677797\pi$
$774$	8.36951	−	2.45751i	0.300836	−	0.0883334i
$775$	0.473760	−	3.29508i	0.0170180	−	0.118363i
$776$	−7.03905	+	8.12349i	−0.252687	+	0.291616i
$777$	−14.4609	+	9.29347i	−0.518783	+	0.333402i
$778$	−21.7257	−	25.0728i	−0.778904	−	0.898903i
$779$	35.0963	+	10.3052i	1.25746	+	0.369222i
$780$	−0.195737	+	0.428604i	−0.00700851	+	0.0153465i
$781$	−4.55575			−0.163017
$782$	10.0045	+	7.32703i	0.357759	+	0.262014i
$783$	−17.4530			−0.623718
$784$	−10.5556	+	23.1136i	−0.376986	+	0.825484i
$785$	−13.8132	−	4.05591i	−0.493013	−	0.144762i
$786$	−1.51299	−	1.74608i	−0.0539665	−	0.0622806i
$787$	12.5161	−	8.04359i	0.446150	−	0.286723i	−0.298212	−	0.954500i	$-0.596390\pi$
$787$	12.5161	−	8.04359i	0.446150	−	0.286723i	0.744362	+	0.667777i	$0.232754\pi$
$788$	0.716726	−	0.827145i	0.0255323	−	0.0294658i
$789$	0.302962	−	2.10715i	0.0107857	−	0.0750165i
$790$	−5.20047	+	1.52700i	−0.185025	+	0.0543281i
$791$	59.6140	+	38.3116i	2.11963	+	1.36220i
$792$	0.151720	+	1.05524i	0.00539115	+	0.0374963i
$793$	−6.17057	−	13.5117i	−0.219123	−	0.479813i
$794$	−1.17747	−	2.57829i	−0.0417867	−	0.0915001i
$795$	−0.893132	−	6.21187i	−0.0316761	−	0.220312i
$796$	6.39064	+	4.10701i	0.226510	+	0.145569i
$797$	0.962545	−	0.282629i	0.0340951	−	0.0100112i	−0.264641	−	0.964347i	$-0.585253\pi$
$797$	0.962545	−	0.282629i	0.0340951	−	0.0100112i	0.298736	+	0.954336i	$0.403435\pi$
$798$	−6.58283	+	45.7846i	−0.233030	+	1.62076i
$799$	−16.0376	+	18.5084i	−0.567369	+	0.654779i
$800$	−1.34369	+	0.863538i	−0.0475066	+	0.0305307i
$801$	2.16248	+	2.49564i	0.0764076	+	0.0881791i
$802$	−35.0951	−	10.3048i	−1.23925	−	0.363877i
$803$	−1.64836	+	3.60940i	−0.0581693	+	0.127373i
$804$	−3.12248			−0.110121
$805$	−14.7767	−	10.8221i	−0.520811	−	0.381430i
$806$	−4.91312			−0.173057
$807$	8.19906	−	17.9534i	0.288621	−	0.631991i
$808$	−24.3685	−	7.15524i	−0.857281	−	0.251720i
$809$	−31.6411	−	36.5158i	−1.11244	−	1.28383i	−0.955101	−	0.296281i	$-0.904253\pi$
$809$	−31.6411	−	36.5158i	−1.11244	−	1.28383i	−0.157341	−	0.987544i	$-0.550292\pi$
$810$	−6.35274	+	4.08266i	−0.223212	+	0.143450i
$811$	−17.2541	+	19.9123i	−0.605874	+	0.699216i	−0.972961	−	0.230971i	$-0.925810\pi$
$811$	−17.2541	+	19.9123i	−0.605874	+	0.699216i	0.367087	+	0.930187i	$0.380355\pi$
$812$	0.478388	−	3.32726i	0.0167881	−	0.116764i
$813$	−19.3984	+	5.69590i	−0.680333	+	0.199764i
$814$	1.42868	+	0.918160i	0.0500754	+	0.0321815i
$815$	−1.85122	−	12.8755i	−0.0648453	−	0.451009i
$816$	4.03582	+	8.83721i	0.141282	+	0.309364i
$817$	20.6874	+	45.2992i	0.723762	+	1.58482i
$818$	4.45781	+	31.0048i	0.155864	+	1.08406i
$819$	3.04785	+	1.95874i	0.106501	+	0.0684438i
$820$	−1.58694	+	0.465969i	−0.0554185	+	0.0162723i
$821$	2.88017	−	20.0320i	0.100518	−	0.699121i	−0.875783	−	0.482705i	$-0.839654\pi$
$821$	2.88017	−	20.0320i	0.100518	−	0.699121i	0.976301	−	0.216416i	$-0.0694367\pi$
$822$	1.52688	−	1.76211i	0.0532560	−	0.0614608i
$823$	−15.5657	+	10.0035i	−0.542588	+	0.348700i	−0.783050	−	0.621958i	$-0.786337\pi$
$823$	−15.5657	+	10.0035i	−0.542588	+	0.348700i	0.240462	+	0.970658i	$0.422701\pi$
$824$	26.2224	+	30.2622i	0.913500	+	1.05423i
$825$	−0.596551	−	0.175163i	−0.0207692	−	0.00609839i
$826$	24.8372	−	54.3859i	0.864196	−	1.89233i
$827$	−3.30850			−0.115048			−0.0575239	−	0.998344i	$-0.518321\pi$
$827$	−3.30850			−0.115048			−0.0575239	+	0.998344i	$0.518321\pi$
$828$	−0.698259	−	0.912684i	−0.0242662	−	0.0317180i
$829$	−30.9267			−1.07413			−0.537065	−	0.843541i	$-0.680467\pi$
$829$	−30.9267			−1.07413			−0.537065	+	0.843541i	$0.680467\pi$
$830$	8.75795	−	19.1772i	0.303993	−	0.665651i
$831$	27.3421	+	8.02836i	0.948487	+	0.278501i
$832$	6.48750	+	7.48697i	0.224913	+	0.259564i
$833$	−12.5985	+	8.09655i	−0.436511	+	0.280529i
$834$	−25.0334	+	28.8901i	−0.866837	+	1.00038i
$835$	−0.875278	+	6.08769i	−0.0302903	+	0.210673i
$836$	−0.727556	+	0.213630i	−0.0251631	+	0.00738854i
$837$	15.8058	+	10.1578i	0.546329	+	0.351104i
$838$	−1.83627	−	12.7715i	−0.0634328	−	0.441185i
$839$	−8.15272	−	17.8520i	−0.281463	−	0.616318i	0.715112	−	0.699010i	$-0.246376\pi$
$839$	−8.15272	−	17.8520i	−0.281463	−	0.616318i	−0.996575	+	0.0826917i	$0.973648\pi$
$840$	−6.97397	−	15.2709i	−0.240625	−	0.526895i
$841$	2.76623	+	19.2396i	0.0953873	+	0.663433i
$842$	37.7165	+	24.2389i	1.29979	+	0.835327i
$843$	−38.6110	+	11.3372i	−1.32983	+	0.390474i
$844$	1.02447	−	7.12536i	0.0352638	−	0.245265i
$845$	−7.68164	+	8.86508i	−0.264256	+	0.304968i
$846$	−11.5062	+	7.39457i	−0.395591	+	0.254231i
$847$	27.0629	+	31.2323i	0.929892	+	1.07315i
$848$	−13.7302	−	4.03154i	−0.471496	−	0.138444i
$849$	17.2397	−	37.7497i	0.591665	−	1.29557i
$850$	2.58570			0.0886888
$851$	−14.6664	−	0.894696i	−0.502757	−	0.0306698i
$852$	4.50107			0.154204
$853$	−3.72558	+	8.15787i	−0.127561	+	0.279320i	−0.962627	−	0.270829i	$-0.912702\pi$
$853$	−3.72558	+	8.15787i	−0.127561	+	0.279320i	0.835066	+	0.550150i	$0.185429\pi$
$854$	63.2640	+	18.5760i	2.16485	+	0.635657i
$855$	3.47027	+	4.00491i	0.118681	+	0.136965i
$856$	8.05119	−	5.17419i	0.275184	−	0.176850i
$857$	21.5467	−	24.8662i	0.736022	−	0.849414i	−0.257114	−	0.966381i	$-0.582772\pi$
$857$	21.5467	−	24.8662i	0.736022	−	0.849414i	0.993136	+	0.116967i	$0.0373171\pi$
$858$	−0.130588	+	0.908262i	−0.00445821	+	0.0310076i
$859$	−20.1264	+	5.90963i	−0.686703	+	0.201634i	−0.606428	−	0.795139i	$-0.707398\pi$
$859$	−20.1264	+	5.90963i	−0.686703	+	0.201634i	−0.0802751	+	0.996773i	$0.525580\pi$
$860$	−1.89431	−	1.21740i	−0.0645956	−	0.0415130i
$861$	−4.63974	−	32.2701i	−0.158122	−	1.09976i
$862$	−16.7972	−	36.7806i	−0.572113	−	1.25275i
$863$	−8.61685	−	18.8683i	−0.293321	−	0.642283i	0.704397	−	0.709806i	$-0.251218\pi$
$863$	−8.61685	−	18.8683i	−0.293321	−	0.642283i	−0.997718	+	0.0675231i	$0.978490\pi$
$864$	−1.28293	−	8.92299i	−0.0436463	−	0.303566i
$865$	−4.00266	−	2.57236i	−0.136095	−	0.0874627i
$866$	27.9052	−	8.19369i	0.948256	−	0.278433i
$867$	2.73931	−	19.0523i	0.0930319	−	0.647051i
$868$	−2.36974	+	2.73482i	−0.0804342	+	0.0928260i
$869$	1.47338	−	0.946881i	0.0499809	−	0.0321208i
$870$	−3.89634	−	4.49661i	−0.132098	−	0.152449i
$871$	8.07404	+	2.37075i	0.273578	+	0.0803298i
$872$	−15.6861	+	34.3478i	−0.531198	+	1.16316i
$873$	−3.02416			−0.102352
$874$	−27.6638	+	28.2493i	−0.935742	+	0.955548i
$875$	−3.81911			−0.129110
$876$	1.62858	−	3.56608i	0.0550245	−	0.120487i
$877$	−26.0160	−	7.63900i	−0.878499	−	0.257951i	−0.188773	−	0.982021i	$-0.560451\pi$
$877$	−26.0160	−	7.63900i	−0.878499	−	0.257951i	−0.689726	+	0.724070i	$0.742269\pi$
$878$	−15.9352	−	18.3902i	−0.537788	−	0.620641i
$879$	−27.4203	+	17.6220i	−0.924864	+	0.594374i
$880$	−0.928374	+	1.07140i	−0.0312955	+	0.0361169i
$881$	4.52337	−	31.4607i	0.152396	−	1.05994i	−0.759792	−	0.650166i	$-0.774699\pi$
$881$	4.52337	−	31.4607i	0.152396	−	1.05994i	0.912188	−	0.409772i	$-0.134392\pi$
$882$	−8.02504	+	2.35636i	−0.270217	+	0.0793429i
$883$	27.1375	+	17.4402i	0.913248	+	0.586909i	0.910691	−	0.413088i	$-0.135550\pi$
$883$	27.1375	+	17.4402i	0.913248	+	0.586909i	0.00255686	+	0.999997i	$0.499186\pi$
$884$	0.0901155	+	0.626767i	0.00303091	+	0.0210805i
$885$	7.29461	+	15.9730i	0.245205	+	0.536925i
$886$	6.66066	+	14.5848i	0.223769	+	0.489986i
$887$	2.58084	+	17.9502i	0.0866562	+	0.602707i	0.986160	+	0.165795i	$0.0530189\pi$
$887$	2.58084	+	17.9502i	0.0866562	+	0.602707i	−0.899504	+	0.436912i	$0.856072\pi$
$888$	−11.3300	−	7.28132i	−0.380209	−	0.244345i
$889$	−4.11969	+	1.20965i	−0.138170	+	0.0405704i
$890$	−0.731136	+	5.08516i	−0.0245077	+	0.170455i
$891$	1.59797	−	1.84416i	0.0535340	−	0.0617815i
$892$	−1.29488	+	0.832172i	−0.0433560	+	0.0278632i
$893$	−51.1351	−	59.0131i	−1.71117	−	1.97480i
$894$	−0.861529	−	0.252968i	−0.0288138	−	0.00846051i
$895$	−0.508117	+	1.11262i	−0.0169845	+	0.0371908i
$896$	−31.7742			−1.06150
$897$	−2.85220	−	7.40913i	−0.0952321	−	0.247384i
$898$	−12.3952			−0.413632
$899$	−4.27640	+	9.36401i	−0.142626	+	0.312307i
$900$	−0.229909	−	0.0675075i	−0.00766365	−	0.00225025i
$901$	−5.52297	−	6.37385i	−0.183997	−	0.212344i
$902$	−2.70963	+	1.74137i	−0.0902209	+	0.0579814i
$903$	29.0668	−	33.5449i	0.967283	−	1.11630i
$904$	−7.90140	+	54.9554i	−0.262797	+	1.82779i
$905$	4.07157	−	1.19552i	0.135344	−	0.0397405i
$906$	−1.98890	−	1.27819i	−0.0660767	−	0.0424649i
$907$	2.24994	+	15.6487i	0.0747081	+	0.519606i	0.992471	+	0.122478i	$0.0390841\pi$
$907$	2.24994	+	15.6487i	0.0747081	+	0.519606i	−0.917763	+	0.397128i	$0.870007\pi$
$908$	1.23326	+	2.70047i	0.0409272	+	0.0896181i
$909$	−2.96831	−	6.49969i	−0.0984526	−	0.215581i
$910$	0.802161	+	5.57915i	0.0265914	+	0.184947i
$911$	16.6811	+	10.7203i	0.552669	+	0.355179i	0.786976	−	0.616984i	$-0.211646\pi$
$911$	16.6811	+	10.7203i	0.552669	+	0.355179i	−0.234307	+	0.972163i	$0.575282\pi$
$912$	−29.7216	+	8.72704i	−0.984180	+	0.288981i
$913$	−0.969518	+	6.74315i	−0.0320864	+	0.223166i
$914$	23.7079	−	27.3603i	0.784187	−	0.905000i
$915$	−16.2907	+	10.4694i	−0.538555	+	0.346109i
$916$	−0.475732	−	0.549024i	−0.0157186	−	0.0181403i
$917$	4.40019	+	1.29201i	0.145307	+	0.0426660i
$918$	−6.06236	+	13.2747i	−0.200088	+	0.438131i
$919$	33.7542			1.11345			0.556725	−	0.830697i	$-0.312058\pi$
$919$	33.7542			1.11345			0.556725	+	0.830697i	$0.312058\pi$
$920$	2.90335	−	14.0535i	0.0957207	−	0.463329i
$921$	−36.0523			−1.18796
$922$	−16.2121	+	35.4996i	−0.533918	+	1.16912i
$923$	−11.6388	−	3.41745i	−0.383095	−	0.112487i
$924$	0.442585	+	0.510771i	0.0145600	+	0.0168031i
$925$	−2.57746	+	1.65644i	−0.0847465	+	0.0544633i
$926$	21.1198	−	24.3736i	0.694040	−	0.800965i
$927$	−1.60329	+	11.1512i	−0.0526591	+	0.366252i
$928$	4.73917	−	1.39154i	0.155571	−	0.0456797i
$929$	−29.7199	−	19.0998i	−0.975079	−	0.626645i	−0.0469475	−	0.998897i	$-0.514949\pi$
$929$	−29.7199	−	19.0998i	−0.975079	−	0.626645i	−0.928132	+	0.372252i	$0.878586\pi$
$930$	0.911546	+	6.33994i	0.0298908	+	0.207895i
$931$	−19.8360	−	43.4347i	−0.650098	−	1.42352i
$932$	1.48768	+	3.25757i	0.0487306	+	0.106705i
$933$	5.05981	+	35.1917i	0.165651	+	1.15213i
$934$	2.74332	+	1.76303i	0.0897643	+	0.0576880i
$935$	−0.801689	+	0.235397i	−0.0262180	+	0.00769830i
$936$	−0.403970	+	2.80968i	−0.0132042	+	0.0918371i
$937$	−17.4747	+	20.1669i	−0.570873	+	0.658823i	−0.965617	−	0.259968i	$-0.916288\pi$
$937$	−17.4747	+	20.1669i	−0.570873	+	0.658823i	0.394744	+	0.918791i	$0.370833\pi$
$938$	−31.4230	+	20.1943i	−1.02600	+	0.659368i
$939$	−22.1243	−	25.5328i	−0.721998	−	0.833231i
$940$	3.38776	+	0.994736i	0.110497	+	0.0324447i
$941$	13.2177	−	28.9427i	0.430885	−	0.943506i	−0.562298	−	0.826935i	$-0.690083\pi$
$941$	13.2177	−	28.9427i	0.430885	−	0.943506i	0.993182	−	0.116571i	$-0.0371902\pi$
$942$	27.6995			0.902497
$943$	13.0988	−	24.5976i	0.426555	−	0.801007i
$944$	40.0395			1.30317
$945$	8.95418	−	19.6069i	0.291280	−	0.637813i
$946$	−4.20756	−	1.23545i	−0.136800	−	0.0401680i
$947$	3.34031	+	3.85492i	0.108545	+	0.125268i	0.807422	−	0.589974i	$-0.200862\pi$
$947$	3.34031	+	3.85492i	0.108545	+	0.125268i	−0.698877	+	0.715242i	$0.746317\pi$
$948$	−1.45569	+	0.935518i	−0.0472787	+	0.0303842i
$949$	−6.91869	+	7.98459i	−0.224590	+	0.259191i
$950$	−1.17330	+	8.16048i	−0.0380669	+	0.264761i
$951$	29.2184	−	8.57929i	0.947471	−	0.278203i
$952$	−18.9794	−	12.1973i	−0.615127	−	0.395318i
$953$	0.899899	+	6.25894i	0.0291506	+	0.202747i	0.999192	−	0.0401931i	$-0.0127973\pi$
$953$	0.899899	+	6.25894i	0.0291506	+	0.202747i	−0.970041	+	0.242940i	$0.921888\pi$
$954$	−1.95668	−	4.28454i	−0.0633500	−	0.138717i
$955$	3.25534	+	7.12820i	0.105340	+	0.230663i
$956$	0.673498	+	4.68428i	0.0217825	+	0.151500i
$957$	1.61741	+	1.03945i	0.0522834	+	0.0336005i
$958$	42.3693	−	12.4408i	1.36889	−	0.401943i
$959$	−0.658641	+	4.58095i	−0.0212686	+	0.147927i
$960$	8.45762	−	9.76061i	0.272968	−	0.315022i
$961$	−16.7561	+	10.7685i	−0.540520	+	0.347371i
$962$	2.96117	+	3.41738i	0.0954720	+	0.110181i
$963$	2.58354	+	0.758595i	0.0832534	+	0.0244454i
$964$	0.550714	−	1.20589i	0.0177373	−	0.0388392i
$965$	22.9055			0.737354
$966$	33.1461	+	11.9690i	1.06646	+	0.385095i
$967$	−8.14868			−0.262044			−0.131022	−	0.991379i	$-0.541826\pi$
$967$	−8.14868			−0.262044			−0.131022	+	0.991379i	$0.541826\pi$
$968$	−13.4505	+	29.4526i	−0.432317	+	0.946642i
$969$	−17.5171	−	5.14348i	−0.562730	−	0.165232i
$970$	−3.08104	−	3.55571i	−0.0989264	−	0.114167i
$971$	−5.53369	+	3.55628i	−0.177584	+	0.114127i	−0.626413	−	0.779491i	$-0.715478\pi$
$971$	−5.53369	+	3.55628i	−0.177584	+	0.114127i	0.448829	+	0.893618i	$0.351841\pi$
$972$	1.57717	−	1.82015i	0.0505877	−	0.0583813i
$973$	10.7985	−	75.1054i	0.346185	−	2.40777i
$974$	−34.4208	+	10.1069i	−1.10291	+	0.323844i
$975$	−1.39264	−	0.894993i	−0.0446001	−	0.0286627i
$976$	6.28395	+	43.7058i	0.201144	+	1.39899i
$977$	7.08343	+	15.5105i	0.226619	+	0.496226i	0.988450	−	0.151550i	$-0.0484264\pi$
$977$	7.08343	+	15.5105i	0.226619	+	0.496226i	−0.761831	+	0.647776i	$0.775699\pi$
$978$	10.3970	+	22.7663i	0.332460	+	0.727986i
$979$	−0.236257	−	1.64320i	−0.00755079	−	0.0525169i
$980$	1.81635	+	1.16730i	0.0580211	+	0.0372879i
$981$	−10.1933	+	2.99302i	−0.325447	+	0.0955598i
$982$	3.15508	−	21.9441i	0.100683	−	0.700264i
$983$	10.4610	−	12.0726i	0.333654	−	0.385057i	−0.563988	−	0.825783i	$-0.690734\pi$
$983$	10.4610	−	12.0726i	0.333654	−	0.385057i	0.897642	+	0.440726i	$0.145279\pi$
$984$	21.4883	−	13.8097i	0.685022	−	0.440237i
$985$	2.51810	+	2.90604i	0.0802333	+	0.0925942i
$986$	−7.67198	−	2.25270i	−0.244326	−	0.0717405i
$987$	−28.9119	+	63.3082i	−0.920275	+	2.01512i
$988$	−2.01897			−0.0642320
$989$	36.9874	−	8.45273i	1.17613	−	0.268781i
$990$	−0.466636			−0.0148307
$991$	−1.07125	+	2.34571i	−0.0340293	+	0.0745138i	−0.925883	−	0.377810i	$-0.876677\pi$
$991$	−1.07125	+	2.34571i	−0.0340293	+	0.0745138i	0.891854	+	0.452323i	$0.149405\pi$
$992$	−5.10179	−	1.49802i	−0.161982	−	0.0475622i
$993$	26.4345	+	30.5070i	0.838873	+	0.968111i
$994$	45.2964	−	29.1102i	1.43671	−	0.923320i
$995$	−17.4778	+	20.1704i	−0.554083	+	0.639445i
$996$	0.957883	−	6.66222i	0.0303517	−	0.211101i
$997$	−18.7876	+	5.51653i	−0.595009	+	0.174710i	−0.565352	−	0.824850i	$-0.691260\pi$
$997$	−18.7876	+	5.51653i	−0.595009	+	0.174710i	−0.0296570	+	0.999560i	$0.509441\pi$
$998$	43.5260	+	27.9725i	1.37779	+	0.885453i
$999$	−2.46092	−	17.1161i	−0.0778600	−	0.541528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.6.1	✓	20
5.2	odd	4		575.2.p.c.374.1		40
5.3	odd	4		575.2.p.c.374.4		40
5.4	even	2		575.2.k.c.351.2		20
23.2	even	11		2645.2.a.t.1.4		10
23.4	even	11	inner	115.2.g.b.96.1	yes	20
23.21	odd	22		2645.2.a.u.1.4		10
115.4	even	22		575.2.k.c.326.2		20
115.27	odd	44		575.2.p.c.349.4		40
115.73	odd	44		575.2.p.c.349.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.6.1	✓	20	1.1	even	1	trivial
115.2.g.b.96.1	yes	20	23.4	even	11	inner
575.2.k.c.326.2		20	115.4	even	22
575.2.k.c.351.2		20	5.4	even	2
575.2.p.c.349.1		40	115.73	odd	44
575.2.p.c.349.4		40	115.27	odd	44
575.2.p.c.374.1		40	5.2	odd	4
575.2.p.c.374.4		40	5.3	odd	4
2645.2.a.t.1.4		10	23.2	even	11
2645.2.a.u.1.4		10	23.21	odd	22

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.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544078 + 1.19136i) q^{2} +(-1.40956 - 0.413883i) q^{3} +(0.186393 + 0.215109i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.25999 - 1.45411i) q^{6} +(-0.543517 + 3.78024i) q^{7} +(-2.87102 + 0.843008i) q^{8} +(-0.708209 - 0.455138i) q^{9} +O(q^{10})\)	\(q+(-0.544078 + 1.19136i) q^{2} +(-1.40956 - 0.413883i) q^{3} +(0.186393 + 0.215109i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.25999 - 1.45411i) q^{6} +(-0.543517 + 3.78024i) q^{7} +(-2.87102 + 0.843008i) q^{8} +(-0.708209 - 0.455138i) q^{9} +(-0.186393 - 1.29639i) q^{10} +(0.175811 + 0.384973i) q^{11} +(-0.173701 - 0.380353i) q^{12} +(0.160369 + 1.11539i) q^{13} +(-4.20793 - 2.70427i) q^{14} +(1.40956 - 0.413883i) q^{15} +(0.476716 - 3.31563i) q^{16} +(1.29285 - 1.49203i) q^{17} +(0.927557 - 0.596105i) q^{18} +(4.12220 + 4.75727i) q^{19} +(-0.273100 - 0.0801894i) q^{20} +(2.33070 - 5.10351i) q^{21} -0.554298 q^{22} +(4.18490 - 2.34235i) q^{23} +4.39578 q^{24} +(0.415415 - 0.909632i) q^{25} +(-1.41609 - 0.415801i) q^{26} +(3.69598 + 4.26539i) q^{27} +(-0.914470 + 0.587694i) q^{28} +(-2.02505 + 2.33704i) q^{29} +(-0.273823 + 1.90448i) q^{30} +(3.19411 - 0.937877i) q^{31} +(-1.34369 - 0.863538i) q^{32} +(-0.0884821 - 0.615407i) q^{33} +(1.07414 + 2.35204i) q^{34} +(-1.58652 - 3.47399i) q^{35} +(-0.0341008 - 0.237177i) q^{36} +(-2.57746 - 1.65644i) q^{37} +(-7.91044 + 2.32271i) q^{38} +(0.235592 - 1.63858i) q^{39} +(1.95949 - 2.26138i) q^{40} +(4.88840 - 3.14158i) q^{41} +(4.81206 + 5.55342i) q^{42} +(7.59078 + 2.22886i) q^{43} +(-0.0500411 + 0.109575i) q^{44} +0.841850 q^{45} +(0.513680 + 6.26016i) q^{46} -12.4048 q^{47} +(-2.04424 + 4.47627i) q^{48} +(-7.27836 - 2.13712i) q^{49} +(0.857685 + 0.989821i) q^{50} +(-2.43987 + 1.56801i) q^{51} +(-0.210039 + 0.242397i) q^{52} +(0.607960 - 4.22845i) q^{53} +(-7.09254 + 2.08256i) q^{54} +(-0.356034 - 0.228809i) q^{55} +(-1.62633 - 11.3113i) q^{56} +(-3.84152 - 8.41175i) q^{57} +(-1.68248 - 3.68411i) q^{58} +(1.70110 + 11.8314i) q^{59} +(0.351761 + 0.226063i) q^{60} +(-12.6478 + 3.71373i) q^{61} +(-0.620494 + 4.31563i) q^{62} +(2.10546 - 2.42983i) q^{63} +(7.39580 - 4.75299i) q^{64} +(-0.737936 - 0.851624i) q^{65} +(0.781315 + 0.229415i) q^{66} +(3.10214 - 6.79273i) q^{67} +0.561926 q^{68} +(-6.86832 + 1.56962i) q^{69} +5.00198 q^{70} +(-4.47175 + 9.79176i) q^{71} +(2.41697 + 0.709686i) q^{72} +(6.13979 + 7.08570i) q^{73} +(3.37576 - 2.16947i) q^{74} +(-0.962033 + 1.11024i) q^{75} +(-0.254982 + 1.77344i) q^{76} +(-1.55085 + 0.455370i) q^{77} +(1.82397 + 1.17219i) q^{78} +(-0.588942 - 4.09618i) q^{79} +(1.39153 + 3.04702i) q^{80} +(-2.39517 - 5.24470i) q^{81} +(1.08310 + 7.53313i) q^{82} +(13.5415 + 8.70262i) q^{83} +(1.53224 - 0.449905i) q^{84} +(-0.280963 + 1.95414i) q^{85} +(-6.78536 + 7.83072i) q^{86} +(3.82169 - 2.45605i) q^{87} +(-0.829294 - 0.957056i) q^{88} +(-3.76366 - 1.10511i) q^{89} +(-0.458032 + 1.00295i) q^{90} -4.30361 q^{91} +(1.28390 + 0.463612i) q^{92} -4.89046 q^{93} +(6.74919 - 14.7787i) q^{94} +(-6.03979 - 1.77344i) q^{95} +(1.53660 + 1.77334i) q^{96} +(3.02202 - 1.94213i) q^{97} +(6.50608 - 7.50842i) q^{98} +(0.0507048 - 0.352660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

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