LMFDB - Embedded newform 60.3.c.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.1
Root			$-1.34966 + 0.422403i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.3.c.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 + 0.675358i) q^{4} -2.23607 q^{5} +(-0.293494 + 3.45165i) q^{6} -12.3959i q^{7} +(-7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 + 0.675358i) q^{4} -2.23607 q^{5} +(-0.293494 + 3.45165i) q^{6} -12.3959i q^{7} +(-7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +(4.45606 + 0.378899i) q^{10} -11.0403i q^{11} +(1.16975 - 6.82874i) q^{12} +2.82009 q^{13} +(-2.10047 + 24.7027i) q^{14} +3.87298i q^{15} +(15.0878 + 5.32529i) q^{16} +6.52606 q^{17} +(5.97843 + 0.508346i) q^{18} +27.9928i q^{19} +(-8.81586 - 1.51015i) q^{20} -21.4703 q^{21} +(-1.87077 + 22.0012i) q^{22} +7.90421i q^{23} +(-3.48822 + 13.4102i) q^{24} +5.00000 q^{25} +(-5.61989 - 0.477860i) q^{26} +5.19615i q^{27} +(8.37167 - 48.8718i) q^{28} +50.7169 q^{29} +(0.656272 - 7.71812i) q^{30} -36.3467i q^{31} +(-29.1647 - 13.1689i) q^{32} -19.1224 q^{33} +(-13.0052 - 1.10583i) q^{34} +27.7181i q^{35} +(-11.8277 - 2.02607i) q^{36} -18.9279 q^{37} +(4.74333 - 55.7842i) q^{38} -4.88453i q^{39} +(17.3124 + 4.50327i) q^{40} +5.30410 q^{41} +(42.7863 + 3.63812i) q^{42} +45.5870i q^{43} +(7.45616 - 43.5273i) q^{44} +6.70820 q^{45} +(1.33936 - 15.7516i) q^{46} -11.7246i q^{47} +(9.22368 - 26.1328i) q^{48} -104.658 q^{49} +(-9.96404 - 0.847243i) q^{50} -11.3035i q^{51} +(11.1184 + 1.90457i) q^{52} +41.1680 q^{53} +(0.880481 - 10.3549i) q^{54} +24.6869i q^{55} +(-24.9644 + 95.9735i) q^{56} +48.4849 q^{57} +(-101.069 - 8.59391i) q^{58} -10.7008i q^{59} +(-2.61565 + 15.2695i) q^{60} +56.1297 q^{61} +(-6.15889 + 72.4319i) q^{62} +37.1877i q^{63} +(55.8882 + 31.1850i) q^{64} -6.30590 q^{65} +(38.1073 + 3.24026i) q^{66} +16.1709i q^{67} +(25.7295 + 4.40743i) q^{68} +13.6905 q^{69} +(4.69679 - 55.2368i) q^{70} -66.1617i q^{71} +(23.2271 + 6.04177i) q^{72} +15.6330 q^{73} +(37.7198 + 3.20731i) q^{74} -8.66025i q^{75} +(-18.9051 + 110.363i) q^{76} -136.855 q^{77} +(-0.827677 + 9.73394i) q^{78} -123.057i q^{79} +(-33.7373 - 11.9077i) q^{80} +9.00000 q^{81} +(-10.5701 - 0.898773i) q^{82} +99.6700i q^{83} +(-84.6484 - 14.5002i) q^{84} -14.5927 q^{85} +(7.72465 - 90.8461i) q^{86} -87.8443i q^{87} +(-22.2343 + 85.4781i) q^{88} +101.083 q^{89} +(-13.3682 - 1.13670i) q^{90} -34.9575i q^{91} +(-5.33817 + 31.1629i) q^{92} -62.9543 q^{93} +(-1.98672 + 23.3649i) q^{94} -62.5937i q^{95} +(-22.8092 + 50.5148i) q^{96} +127.293 q^{97} +(208.564 + 17.7342i) q^{98} +33.1209i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	$ 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 34 q^{16} - 12 q^{18} - 40 q^{20} - 48 q^{21} + 68 q^{22} + 18 q^{24} + 40 q^{25} - 36 q^{26} + 28 q^{28} + 64 q^{29} - 76 q^{32} - 92 q^{34} - 30 q^{36} - 112 q^{37} - 40 q^{38} - 10 q^{40} - 16 q^{41} + 108 q^{42} + 172 q^{44} + 152 q^{46} + 48 q^{48} - 56 q^{49} + 20 q^{50} - 128 q^{52} + 352 q^{53} + 18 q^{54} + 116 q^{56} + 144 q^{57} - 204 q^{58} + 30 q^{60} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 80 q^{65} + 108 q^{66} - 184 q^{68} - 96 q^{69} - 60 q^{70} + 60 q^{72} - 240 q^{73} + 132 q^{74} - 24 q^{76} - 288 q^{77} - 240 q^{78} - 80 q^{80} + 72 q^{81} + 40 q^{82} - 36 q^{84} + 160 q^{85} - 200 q^{86} + 140 q^{88} + 80 q^{89} - 30 q^{90} + 144 q^{92} + 144 q^{93} - 96 q^{94} - 174 q^{96} + 432 q^{97} + 660 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 + 10 * q^10 + 16 * q^13 - 20 * q^14 + 34 * q^16 - 12 * q^18 - 40 * q^20 - 48 * q^21 + 68 * q^22 + 18 * q^24 + 40 * q^25 - 36 * q^26 + 28 * q^28 + 64 * q^29 - 76 * q^32 - 92 * q^34 - 30 * q^36 - 112 * q^37 - 40 * q^38 - 10 * q^40 - 16 * q^41 + 108 * q^42 + 172 * q^44 + 152 * q^46 + 48 * q^48 - 56 * q^49 + 20 * q^50 - 128 * q^52 + 352 * q^53 + 18 * q^54 + 116 * q^56 + 144 * q^57 - 204 * q^58 + 30 * q^60 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 80 * q^65 + 108 * q^66 - 184 * q^68 - 96 * q^69 - 60 * q^70 + 60 * q^72 - 240 * q^73 + 132 * q^74 - 24 * q^76 - 288 * q^77 - 240 * q^78 - 80 * q^80 + 72 * q^81 + 40 * q^82 - 36 * q^84 + 160 * q^85 - 200 * q^86 + 140 * q^88 + 80 * q^89 - 30 * q^90 + 144 * q^92 + 144 * q^93 - 96 * q^94 - 174 * q^96 + 432 * q^97 + 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.99281	−	0.169449i	−0.996404	−	0.0847243i
$2$	−1.99281	−	0.169449i	−0.996404	−	0.0847243i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.94257	+	0.675358i	0.985644	+	0.168839i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	−0.293494	+	3.45165i	−0.0489156	+	0.575274i
$7$		−	12.3959i		−	1.77084i	−0.464789	−	0.885422i	$-0.653870\pi$
$7$		−	12.3959i		−	1.77084i	0.464789	−	0.885422i	$-0.346130\pi$
$8$	−7.74236	−	2.01392i	−0.967795	−	0.251740i
$9$	−3.00000			−0.333333
$10$	4.45606	+	0.378899i	0.445606	+	0.0378899i
$11$		−	11.0403i		−	1.00366i	−0.864965	−	0.501832i	$-0.832659\pi$
$11$		−	11.0403i		−	1.00366i	0.864965	−	0.501832i	$-0.167341\pi$
$12$	1.16975	−	6.82874i	0.0974795	−	0.569062i
$13$	2.82009			0.216930			0.108465	−	0.994100i	$-0.465407\pi$
$13$	2.82009			0.216930			0.108465	+	0.994100i	$0.465407\pi$
$14$	−2.10047	+	24.7027i	−0.150034	+	1.76448i
$15$			3.87298i			0.258199i
$16$	15.0878	+	5.32529i	0.942987	+	0.332831i
$17$	6.52606			0.383886			0.191943	−	0.981406i	$-0.438521\pi$
$17$	6.52606			0.383886			0.191943	+	0.981406i	$0.438521\pi$
$18$	5.97843	+	0.508346i	0.332135	+	0.0282414i
$19$			27.9928i			1.47330i	0.676273	+	0.736651i	$0.263594\pi$
$19$			27.9928i			1.47330i	−0.676273	+	0.736651i	$0.736406\pi$
$20$	−8.81586	−	1.51015i	−0.440793	−	0.0755073i
$21$	−21.4703			−1.02240
$22$	−1.87077	+	22.0012i	−0.0850348	+	1.00006i
$23$			7.90421i			0.343661i	0.985126	+	0.171831i	$0.0549682\pi$
$23$			7.90421i			0.343661i	−0.985126	+	0.171831i	$0.945032\pi$
$24$	−3.48822	+	13.4102i	−0.145342	+	0.558757i
$25$	5.00000			0.200000
$26$	−5.61989	−	0.477860i	−0.216150	−	0.0183792i
$27$			5.19615i			0.192450i
$28$	8.37167	−	48.8718i	0.298988	−	1.74542i
$29$	50.7169			1.74886			0.874429	−	0.485153i	$-0.161236\pi$
$29$	50.7169			1.74886			0.874429	+	0.485153i	$0.161236\pi$
$30$	0.656272	−	7.71812i	0.0218757	−	0.257271i
$31$		−	36.3467i		−	1.17247i	−0.810140	−	0.586236i	$-0.800609\pi$
$31$		−	36.3467i		−	1.17247i	0.810140	−	0.586236i	$-0.199391\pi$
$32$	−29.1647	−	13.1689i	−0.911397	−	0.411528i
$33$	−19.1224			−0.579466
$34$	−13.0052	−	1.10583i	−0.382506	−	0.0325245i
$35$			27.7181i			0.791945i
$36$	−11.8277	−	2.02607i	−0.328548	−	0.0562798i
$37$	−18.9279			−0.511566			−0.255783	−	0.966734i	$-0.582333\pi$
$37$	−18.9279			−0.511566			−0.255783	+	0.966734i	$0.582333\pi$
$38$	4.74333	−	55.7842i	0.124825	−	1.46801i
$39$		−	4.88453i		−	0.125244i
$40$	17.3124	+	4.50327i	0.432811	+	0.112582i
$41$	5.30410			0.129368			0.0646842	−	0.997906i	$-0.479396\pi$
$41$	5.30410			0.129368			0.0646842	+	0.997906i	$0.479396\pi$
$42$	42.7863	+	3.63812i	1.01872	+	0.0866219i
$43$			45.5870i			1.06016i	0.847947	+	0.530081i	$0.177838\pi$
$43$			45.5870i			1.06016i	−0.847947	+	0.530081i	$0.822162\pi$
$44$	7.45616	−	43.5273i	0.169458	−	0.989256i
$45$	6.70820			0.149071
$46$	1.33936	−	15.7516i	0.0291165	−	0.342426i
$47$		−	11.7246i		−	0.249460i	−0.992191	−	0.124730i	$-0.960194\pi$
$47$		−	11.7246i		−	0.249460i	0.992191	−	0.124730i	$-0.0398064\pi$
$48$	9.22368	−	26.1328i	0.192160	−	0.544434i
$49$	−104.658			−2.13589
$50$	−9.96404	−	0.847243i	−0.199281	−	0.0169449i
$51$		−	11.3035i		−	0.221637i
$52$	11.1184	+	1.90457i	0.213815	+	0.0366263i
$53$	41.1680			0.776755			0.388378	−	0.921500i	$-0.373036\pi$
$53$	41.1680			0.776755			0.388378	+	0.921500i	$0.373036\pi$
$54$	0.880481	−	10.3549i	0.0163052	−	0.191758i
$55$			24.6869i			0.448853i
$56$	−24.9644	+	95.9735i	−0.445793	+	1.71381i
$57$	48.4849			0.850612
$58$	−101.069	−	8.59391i	−1.74257	−	0.148171i
$59$		−	10.7008i		−	0.181370i	−0.995880	−	0.0906848i	$-0.971094\pi$
$59$		−	10.7008i		−	0.181370i	0.995880	−	0.0906848i	$-0.0289056\pi$
$60$	−2.61565	+	15.2695i	−0.0435941	+	0.254492i
$61$	56.1297			0.920159			0.460080	−	0.887878i	$-0.347821\pi$
$61$	56.1297			0.920159			0.460080	+	0.887878i	$0.347821\pi$
$62$	−6.15889	+	72.4319i	−0.0993370	+	1.16826i
$63$			37.1877i			0.590281i
$64$	55.8882	+	31.1850i	0.873254	+	0.487266i
$65$	−6.30590			−0.0970139
$66$	38.1073	+	3.24026i	0.577383	+	0.0490949i
$67$			16.1709i			0.241357i	0.992692	+	0.120679i	$0.0385071\pi$
$67$			16.1709i			0.241357i	−0.992692	+	0.120679i	$0.961493\pi$
$68$	25.7295	+	4.40743i	0.378375	+	0.0648151i
$69$	13.6905			0.198413
$70$	4.69679	−	55.2368i	0.0670970	−	0.789098i
$71$		−	66.1617i		−	0.931855i	−0.884823	−	0.465928i	$-0.845721\pi$
$71$		−	66.1617i		−	0.931855i	0.884823	−	0.465928i	$-0.154279\pi$
$72$	23.2271	+	6.04177i	0.322598	+	0.0839134i
$73$	15.6330			0.214150			0.107075	−	0.994251i	$-0.465851\pi$
$73$	15.6330			0.214150			0.107075	+	0.994251i	$0.465851\pi$
$74$	37.7198	+	3.20731i	0.509727	+	0.0433421i
$75$		−	8.66025i		−	0.115470i
$76$	−18.9051	+	110.363i	−0.248752	+	1.45215i
$77$	−136.855			−1.77733
$78$	−0.827677	+	9.73394i	−0.0106112	+	0.124794i
$79$		−	123.057i		−	1.55768i	−0.627223	−	0.778840i	$-0.715809\pi$
$79$		−	123.057i		−	1.55768i	0.627223	−	0.778840i	$-0.284191\pi$
$80$	−33.7373	−	11.9077i	−0.421716	−	0.148847i
$81$	9.00000			0.111111
$82$	−10.5701	−	0.898773i	−0.128903	−	0.0109606i
$83$			99.6700i			1.20084i	0.799684	+	0.600422i	$0.205001\pi$
$83$			99.6700i			1.20084i	−0.799684	+	0.600422i	$0.794999\pi$
$84$	−84.6484	−	14.5002i	−1.00772	−	0.172621i
$85$	−14.5927			−0.171679
$86$	7.72465	−	90.8461i	0.0898215	−	1.05635i
$87$		−	87.8443i		−	1.00970i
$88$	−22.2343	+	85.4781i	−0.252663	+	0.971342i
$89$	101.083			1.13576			0.567881	−	0.823110i	$-0.307763\pi$
$89$	101.083			1.13576			0.567881	+	0.823110i	$0.307763\pi$
$90$	−13.3682	−	1.13670i	−0.148535	−	0.0126300i
$91$		−	34.9575i		−	0.384148i
$92$	−5.33817	+	31.1629i	−0.0580236	+	0.338728i
$93$	−62.9543			−0.676927
$94$	−1.98672	+	23.3649i	−0.0211353	+	0.248563i
$95$		−	62.5937i		−	0.658881i
$96$	−22.8092	+	50.5148i	−0.237596	+	0.526195i
$97$	127.293			1.31230			0.656151	−	0.754630i	$-0.272183\pi$
$97$	127.293			1.31230			0.656151	+	0.754630i	$0.272183\pi$
$98$	208.564	+	17.7342i	2.12821	+	0.180962i
$99$			33.1209i			0.334555i
$100$	19.7129	+	3.37679i	0.197129	+	0.0337679i
$101$	−94.3535			−0.934193			−0.467096	−	0.884206i	$-0.654700\pi$
$101$	−94.3535			−0.934193			−0.467096	+	0.884206i	$0.654700\pi$
$102$	−1.91536	+	22.5257i	−0.0187780	+	0.220840i
$103$			31.8455i			0.309180i	0.987979	+	0.154590i	$0.0494056\pi$
$103$			31.8455i			0.309180i	−0.987979	+	0.154590i	$0.950594\pi$
$104$	−21.8341	−	5.67943i	−0.209943	−	0.0546099i
$105$	48.0091			0.457230
$106$	−82.0400	−	6.97587i	−0.773962	−	0.0658101i
$107$		−	33.7912i		−	0.315805i	−0.987455	−	0.157903i	$-0.949527\pi$
$107$		−	33.7912i		−	0.315805i	0.987455	−	0.157903i	$-0.0504732\pi$
$108$	−3.50926	+	20.4862i	−0.0324932	+	0.189687i
$109$	−83.4266			−0.765382			−0.382691	−	0.923876i	$-0.625003\pi$
$109$	−83.4266			−0.765382			−0.382691	+	0.923876i	$0.625003\pi$
$110$	4.18316	−	49.1963i	0.0380287	−	0.447239i
$111$			32.7842i			0.295353i
$112$	66.0118	−	187.027i	0.589391	−	1.66988i
$113$	−111.796			−0.989342			−0.494671	−	0.869080i	$-0.664711\pi$
$113$	−111.796			−0.989342			−0.494671	+	0.869080i	$0.664711\pi$
$114$	−96.6211	−	8.21569i	−0.847553	−	0.0720675i
$115$		−	17.6744i		−	0.153690i
$116$	199.955	+	34.2520i	1.72375	+	0.295276i
$117$	−8.46026			−0.0723099
$118$	−1.81324	+	21.3247i	−0.0153664	+	0.180717i
$119$		−	80.8964i		−	0.679802i
$120$	7.79989	−	29.9860i	0.0649991	−	0.249884i
$121$	−0.888544			−0.00734334
$122$	−111.856	−	9.51110i	−0.916851	−	0.0779599i
$123$		−	9.18697i		−	0.0746908i
$124$	24.5470	−	143.299i	0.197960	−	1.15564i
$125$	−11.1803			−0.0894427
$126$	6.30141	−	74.1080i	0.0500112	−	0.588159i
$127$		−	16.6855i		−	0.131382i	−0.997840	−	0.0656909i	$-0.979075\pi$
$127$		−	16.6855i		−	0.131382i	0.997840	−	0.0656909i	$-0.0209251\pi$
$128$	−106.090	−	71.6160i	−0.828831	−	0.559500i
$129$	78.9589			0.612085
$130$	12.5665	+	1.06853i	0.0966651	+	0.00821944i
$131$			196.418i			1.49937i	0.661794	+	0.749686i	$0.269796\pi$
$131$			196.418i			1.49937i	−0.661794	+	0.749686i	$0.730204\pi$
$132$	−75.3914	−	12.9144i	−0.571147	−	0.0978367i
$133$	346.995			2.60899
$134$	2.74015	−	32.2256i	0.0204488	−	0.240490i
$135$		−	11.6190i		−	0.0860663i
$136$	−50.5271	−	13.1430i	−0.371523	−	0.0966396i
$137$	−117.127			−0.854942			−0.427471	−	0.904029i	$-0.640595\pi$
$137$	−117.127			−0.854942			−0.427471	+	0.904029i	$0.640595\pi$
$138$	−27.2825	−	2.31984i	−0.197700	−	0.0168104i
$139$			187.238i			1.34704i	0.739170	+	0.673519i	$0.235218\pi$
$139$			187.238i			1.34704i	−0.739170	+	0.673519i	$0.764782\pi$
$140$	−18.7196	+	109.281i	−0.133712	+	0.780576i
$141$	−20.3076			−0.144026
$142$	−11.2110	+	131.848i	−0.0789508	+	0.928505i
$143$		−	31.1346i		−	0.217725i
$144$	−45.2634	−	15.9759i	−0.314329	−	0.110944i
$145$	−113.406			−0.782113
$146$	−31.1535	−	2.64899i	−0.213380	−	0.0181437i
$147$			181.274i			1.23315i
$148$	−74.6248	−	12.7831i	−0.504222	−	0.0863725i
$149$	−50.2274			−0.337096			−0.168548	−	0.985693i	$-0.553908\pi$
$149$	−50.2274			−0.337096			−0.168548	+	0.985693i	$0.553908\pi$
$150$	−1.46747	+	17.2582i	−0.00978312	+	0.115055i
$151$			213.160i			1.41166i	0.708382	+	0.705829i	$0.249425\pi$
$151$			213.160i			1.41166i	−0.708382	+	0.705829i	$0.750575\pi$
$152$	56.3752	−	216.730i	0.370890	−	1.42585i
$153$	−19.5782			−0.127962
$154$	272.725	+	23.1898i	1.77094	+	0.150583i
$155$			81.2736i			0.524346i
$156$	3.29880	−	19.2576i	0.0211462	−	0.123446i
$157$	203.918			1.29884			0.649419	−	0.760431i	$-0.275012\pi$
$157$	203.918			1.29884			0.649419	+	0.760431i	$0.275012\pi$
$158$	−20.8518	+	245.228i	−0.131973	+	1.55208i
$159$		−	71.3051i		−	0.448460i
$160$	65.2143	+	29.4466i	0.407589	+	0.184041i
$161$	97.9798			0.608570
$162$	−17.9353	−	1.52504i	−0.110712	−	0.00941381i
$163$		−	215.898i		−	1.32452i	−0.749272	−	0.662262i	$-0.769596\pi$
$163$		−	215.898i		−	1.32452i	0.749272	−	0.662262i	$-0.230404\pi$
$164$	20.9118	+	3.58216i	0.127511	+	0.0218425i
$165$	42.7590			0.259145
$166$	16.8889	−	198.623i	0.101741	−	1.19653i
$167$			255.029i			1.52712i	0.645737	+	0.763560i	$0.276550\pi$
$167$			255.029i			1.52712i	−0.645737	+	0.763560i	$0.723450\pi$
$168$	166.231	+	43.2396i	0.989470	+	0.257378i
$169$	−161.047			−0.952942
$170$	29.0805	+	2.47272i	0.171062	+	0.0145454i
$171$		−	83.9783i		−	0.491101i
$172$	−30.7875	+	179.730i	−0.178997	+	1.04494i
$173$	−235.426			−1.36084			−0.680421	−	0.732822i	$-0.738203\pi$
$173$	−235.426			−1.36084			−0.680421	+	0.732822i	$0.738203\pi$
$174$	−14.8851	+	175.057i	−0.0855465	+	1.00607i
$175$		−	61.9795i		−	0.354169i
$176$	58.7929	−	166.574i	0.334051	−	0.946443i
$177$	−18.5343			−0.104714
$178$	−201.439	−	17.1284i	−1.13168	−	0.0962267i
$179$			102.669i			0.573572i	0.957995	+	0.286786i	$0.0925869\pi$
$179$			102.669i			0.573572i	−0.957995	+	0.286786i	$0.907413\pi$
$180$	26.4476	+	4.53044i	0.146931	+	0.0251691i
$181$	−56.8222			−0.313935			−0.156967	−	0.987604i	$-0.550172\pi$
$181$	−56.8222			−0.313935			−0.156967	+	0.987604i	$0.550172\pi$
$182$	−5.92350	+	69.6636i	−0.0325467	+	0.382767i
$183$		−	97.2195i		−	0.531254i
$184$	15.9185	−	61.1972i	0.0865134	−	0.332594i
$185$	42.3242			0.228779
$186$	125.456	+	10.6675i	0.674493	+	0.0573522i
$187$		−	72.0498i		−	0.385293i
$188$	7.91830	−	46.2251i	0.0421186	−	0.245878i
$189$	64.4110			0.340799
$190$	−10.6064	+	124.737i	−0.0558232	+	0.656512i
$191$		−	158.493i		−	0.829808i	−0.909865	−	0.414904i	$-0.863815\pi$
$191$		−	158.493i		−	0.829808i	0.909865	−	0.414904i	$-0.136185\pi$
$192$	54.0140	−	96.8013i	0.281323	−	0.504173i
$193$	−156.732			−0.812084			−0.406042	−	0.913854i	$-0.633091\pi$
$193$	−156.732			−0.812084			−0.406042	+	0.913854i	$0.633091\pi$
$194$	−253.671	−	21.5697i	−1.30758	−	0.111184i
$195$			10.9221i			0.0560110i
$196$	−412.624	−	70.6819i	−2.10522	−	0.360622i
$197$	260.127			1.32044			0.660221	−	0.751072i	$-0.270463\pi$
$197$	260.127			1.32044			0.660221	+	0.751072i	$0.270463\pi$
$198$	5.61230	−	66.0037i	0.0283449	−	0.333352i
$199$			14.0326i			0.0705157i	0.999378	+	0.0352579i	$0.0112253\pi$
$199$			14.0326i			0.0705157i	−0.999378	+	0.0352579i	$0.988775\pi$
$200$	−38.7118	−	10.0696i	−0.193559	−	0.0503481i
$201$	28.0089			0.139348
$202$	188.028	+	15.9881i	0.930834	+	0.0791489i
$203$		−	628.682i		−	3.09696i
$204$	7.63389	−	44.5648i	0.0374210	−	0.218455i
$205$	−11.8603			−0.0578553
$206$	5.39618	−	63.4620i	0.0261950	−	0.308068i
$207$		−	23.7126i		−	0.114554i
$208$	42.5488	+	15.0178i	0.204562	+	0.0722009i
$209$	309.049			1.47870
$210$	−95.6730	−	8.13508i	−0.455586	−	0.0387385i
$211$		−	74.4941i		−	0.353052i	−0.984296	−	0.176526i	$-0.943514\pi$
$211$		−	74.4941i		−	0.353052i	0.984296	−	0.176526i	$-0.0564860\pi$
$212$	162.308	+	27.8031i	0.765604	+	0.131147i
$213$	−114.595			−0.538007
$214$	−5.72587	+	67.3393i	−0.0267564	+	0.314670i
$215$		−	101.936i		−	0.474119i
$216$	10.4646	−	40.2305i	0.0484474	−	0.186252i
$217$	−450.550			−2.07627
$218$	166.253	+	14.1365i	0.762630	+	0.0648465i
$219$		−	27.0771i		−	0.123640i
$220$	−16.6725	+	97.3299i	−0.0757840	+	0.442409i
$221$	18.4041			0.0832763
$222$	5.55523	−	65.3326i	0.0250236	−	0.294291i
$223$		−	159.996i		−	0.717471i	−0.933439	−	0.358736i	$-0.883208\pi$
$223$		−	159.996i		−	0.717471i	0.933439	−	0.358736i	$-0.116792\pi$
$224$	−163.240	+	361.523i	−0.728752	+	1.61394i
$225$	−15.0000			−0.0666667
$226$	222.787	+	18.9436i	0.985784	+	0.0838213i
$227$		−	175.978i		−	0.775236i	−0.921820	−	0.387618i	$-0.873298\pi$
$227$		−	175.978i		−	0.775236i	0.921820	−	0.387618i	$-0.126702\pi$
$228$	191.155	+	32.7446i	0.838400	+	0.143617i
$229$	−114.170			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$229$	−114.170			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$230$	−2.99490	+	35.2216i	−0.0130213	+	0.153137i
$231$			237.039i			1.02614i
$232$	−392.668	−	102.140i	−1.69254	−	0.440258i
$233$	260.062			1.11615			0.558073	−	0.829792i	$-0.311541\pi$
$233$	260.062			1.11615			0.558073	+	0.829792i	$0.311541\pi$
$234$	16.8597	+	1.43358i	0.0720499	+	0.00612641i
$235$			26.2170i			0.111562i
$236$	7.22687	−	42.1887i	0.0306223	−	0.178766i
$237$	−213.140			−0.899327
$238$	−13.7078	+	161.211i	−0.0575958	+	0.677358i
$239$			140.089i			0.586147i	0.956090	+	0.293073i	$0.0946780\pi$
$239$			140.089i			0.586147i	−0.956090	+	0.293073i	$0.905322\pi$
$240$	−20.6248	+	58.4347i	−0.0859366	+	0.243478i
$241$	105.920			0.439503			0.219752	−	0.975556i	$-0.429475\pi$
$241$	105.920			0.439503			0.219752	+	0.975556i	$0.429475\pi$
$242$	1.77070	+	0.150563i	0.00731693	+	0.000622159i
$243$		−	15.5885i		−	0.0641500i
$244$	221.296	+	37.9076i	0.906949	+	0.155359i
$245$	234.023			0.955197
$246$	−1.55672	+	18.3079i	−0.00632813	+	0.0744223i
$247$			78.9419i			0.319603i
$248$	−73.1993	+	281.409i	−0.295159	+	1.13471i
$249$	172.633			0.693307
$250$	22.2803	+	1.89449i	0.0891211	+	0.00757797i
$251$			167.879i			0.668839i	0.942424	+	0.334420i	$0.108540\pi$
$251$			167.879i			0.668839i	−0.942424	+	0.334420i	$0.891460\pi$
$252$	−25.1150	+	146.615i	−0.0996627	+	0.581807i
$253$	87.2650			0.344921
$254$	−2.82733	+	33.2510i	−0.0111312	+	0.130909i
$255$			25.2753i			0.0991190i
$256$	199.282	+	160.694i	0.778447	+	0.627710i
$257$	198.849			0.773732			0.386866	−	0.922136i	$-0.373558\pi$
$257$	198.849			0.773732			0.386866	+	0.922136i	$0.373558\pi$
$258$	−157.350	−	13.3795i	−0.609884	−	0.0518585i
$259$			234.629i			0.905903i
$260$	−24.8615	−	4.25874i	−0.0956211	−	0.0163798i
$261$	−152.151			−0.582953
$262$	33.2827	−	391.423i	0.127033	−	1.49398i
$263$			480.528i			1.82710i	0.406722	+	0.913552i	$0.366672\pi$
$263$			480.528i			1.82710i	−0.406722	+	0.913552i	$0.633328\pi$
$264$	148.052	+	38.5110i	0.560804	+	0.145875i
$265$	−92.0545			−0.347376
$266$	−691.496	−	58.7979i	−2.59961	−	0.221045i
$267$		−	175.081i		−	0.655733i
$268$	−10.9212	+	63.7552i	−0.0407506	+	0.237892i
$269$	−291.496			−1.08363			−0.541815	−	0.840498i	$-0.682263\pi$
$269$	−291.496			−1.08363			−0.541815	+	0.840498i	$0.682263\pi$
$270$	−1.96882	+	23.1543i	−0.00729191	+	0.0857568i
$271$			174.063i			0.642299i	0.947029	+	0.321150i	$0.104069\pi$
$271$			174.063i			0.642299i	−0.947029	+	0.321150i	$0.895931\pi$
$272$	98.4638	+	34.7532i	0.361999	+	0.127769i
$273$	−60.5482			−0.221788
$274$	233.412	+	19.8470i	0.851868	+	0.0724344i
$275$		−	55.2016i		−	0.200733i
$276$	53.9758	+	9.24598i	0.195564	+	0.0334999i
$277$	−50.5203			−0.182384			−0.0911918	−	0.995833i	$-0.529068\pi$
$277$	−50.5203			−0.182384			−0.0911918	+	0.995833i	$0.529068\pi$
$278$	31.7273	−	373.130i	0.114127	−	1.34219i
$279$			109.040i			0.390824i
$280$	55.8221	−	214.603i	0.199365	−	0.766441i
$281$	−66.0514			−0.235058			−0.117529	−	0.993069i	$-0.537497\pi$
$281$	−66.0514			−0.235058			−0.117529	+	0.993069i	$0.537497\pi$
$282$	40.4692	+	3.44110i	0.143508	+	0.0122025i
$283$		−	116.934i		−	0.413196i	−0.978426	−	0.206598i	$-0.933761\pi$
$283$		−	116.934i		−	0.413196i	0.978426	−	0.206598i	$-0.0662392\pi$
$284$	44.6828	−	260.848i	0.157334	−	0.918477i
$285$	−108.415			−0.380405
$286$	−5.27572	+	62.0454i	−0.0184466	+	0.216942i
$287$		−	65.7491i		−	0.229091i
$288$	87.4941	+	39.5067i	0.303799	+	0.137176i
$289$	−246.411			−0.852631
$290$	225.997	+	19.2166i	0.779301	+	0.0662640i
$291$		−	220.478i		−	0.757658i
$292$	61.6341	+	10.5578i	0.211076	+	0.0361570i
$293$	−68.3732			−0.233356			−0.116678	−	0.993170i	$-0.537224\pi$
$293$	−68.3732			−0.233356			−0.116678	+	0.993170i	$0.537224\pi$
$294$	30.7166	−	361.244i	0.104478	−	1.22872i
$295$			23.9277i			0.0811110i
$296$	146.547	+	38.1194i	0.495091	+	0.128782i
$297$	57.3672			0.193155
$298$	100.094	+	8.51096i	0.335884	+	0.0285603i
$299$			22.2905i			0.0745503i
$300$	5.84877	−	34.1437i	0.0194959	−	0.113812i
$301$	565.092			1.87738
$302$	36.1197	−	424.788i	0.119602	−	1.40658i
$303$			163.425i			0.539356i
$304$	−149.070	+	422.349i	−0.490361	+	1.38930i
$305$	−125.510			−0.411508
$306$	39.0156	+	3.31750i	0.127502	+	0.0108415i
$307$			369.497i			1.20357i	0.798657	+	0.601786i	$0.205544\pi$
$307$			369.497i			1.20357i	−0.798657	+	0.601786i	$0.794456\pi$
$308$	−539.560	−	92.4258i	−1.75182	−	0.300084i
$309$	55.1580			0.178505
$310$	13.7717	−	161.963i	0.0444248	−	0.522460i
$311$			303.446i			0.975712i	0.872924	+	0.487856i	$0.162221\pi$
$311$			303.446i			0.975712i	−0.872924	+	0.487856i	$0.837779\pi$
$312$	−9.83707	+	37.8178i	−0.0315291	+	0.121211i
$313$	297.693			0.951097			0.475549	−	0.879689i	$-0.342250\pi$
$313$	297.693			0.951097			0.475549	+	0.879689i	$0.342250\pi$
$314$	−406.369	−	34.5536i	−1.29417	−	0.110043i
$315$		−	83.1542i		−	0.263982i
$316$	83.1072	−	485.160i	0.262998	−	1.53532i
$317$	264.678			0.834948			0.417474	−	0.908689i	$-0.362916\pi$
$317$	264.678			0.834948			0.417474	+	0.908689i	$0.362916\pi$
$318$	−12.0826	+	142.097i	−0.0379955	+	0.446847i
$319$		−	559.931i		−	1.75527i
$320$	−124.970	−	69.7318i	−0.390531	−	0.217912i
$321$	−58.5280			−0.182330
$322$	−195.255	−	16.6026i	−0.606382	−	0.0515607i
$323$			182.682i			0.565580i
$324$	35.4832	+	6.07822i	0.109516	+	0.0187599i
$325$	14.1004			0.0433859
$326$	−36.5835	+	430.243i	−0.112219	+	1.31976i
$327$			144.499i			0.441893i
$328$	−41.0663	−	10.6820i	−0.125202	−	0.0325672i
$329$	−145.337			−0.441754
$330$	−85.2104	−	7.24545i	−0.258213	−	0.0219559i
$331$		−	473.426i		−	1.43029i	−0.698976	−	0.715145i	$-0.746361\pi$
$331$		−	473.426i		−	1.43029i	0.698976	−	0.715145i	$-0.253639\pi$
$332$	−67.3129	+	392.956i	−0.202750	+	1.18360i
$333$	56.7838			0.170522
$334$	43.2143	−	508.224i	0.129384	−	1.52163i
$335$		−	36.1593i		−	0.107938i
$336$	−323.940	−	114.336i	−0.964107	−	0.340285i
$337$	29.7588			0.0883051			0.0441526	−	0.999025i	$-0.485941\pi$
$337$	29.7588			0.0883051			0.0441526	+	0.999025i	$0.485941\pi$
$338$	320.936	+	27.2892i	0.949515	+	0.0807373i
$339$			193.636i			0.571197i
$340$	−57.5329	−	9.85530i	−0.169214	−	0.0289862i
$341$	−401.278			−1.17677
$342$	−14.2300	+	167.353i	−0.0416082	+	0.489335i
$343$			689.937i			2.01148i
$344$	91.8086	−	352.951i	0.266885	−	1.02602i
$345$	−30.6129			−0.0887330
$346$	469.158	+	39.8925i	1.35595	+	0.115296i
$347$		−	306.190i		−	0.882391i	−0.897411	−	0.441195i	$-0.854555\pi$
$347$		−	306.190i		−	0.882391i	0.897411	−	0.441195i	$-0.145445\pi$
$348$	59.3263	−	346.333i	0.170478	−	0.995208i
$349$	649.149			1.86002			0.930012	−	0.367528i	$-0.119796\pi$
$349$	649.149			1.86002			0.930012	+	0.367528i	$0.119796\pi$
$350$	−10.5023	+	123.513i	−0.0300067	+	0.352895i
$351$			14.6536i			0.0417481i
$352$	−145.389	+	321.988i	−0.413036	+	0.914737i
$353$	−275.547			−0.780587			−0.390293	−	0.920691i	$-0.627626\pi$
$353$	−275.547			−0.780587			−0.390293	+	0.920691i	$0.627626\pi$
$354$	36.9354	+	3.14062i	0.104337	+	0.00887181i
$355$			147.942i			0.416738i
$356$	398.527	+	68.2671i	1.11946	+	0.191761i
$357$	−140.117			−0.392484
$358$	17.3972	−	204.600i	0.0485955	−	0.571510i
$359$		−	507.672i		−	1.41413i	−0.707149	−	0.707065i	$-0.750019\pi$
$359$		−	507.672i		−	1.41413i	0.707149	−	0.707065i	$-0.249981\pi$
$360$	−51.9373	−	13.5098i	−0.144270	−	0.0375272i
$361$	−422.594			−1.17062
$362$	113.236	+	9.62845i	0.312806	+	0.0265979i
$363$			1.53900i			0.00423968i
$364$	23.6088	−	137.823i	0.0648594	−	0.378633i
$365$	−34.9564			−0.0957709
$366$	−16.4737	+	193.740i	−0.0450102	+	0.529344i
$367$			62.7671i			0.171028i	0.996337	+	0.0855138i	$0.0272532\pi$
$367$			62.7671i			0.171028i	−0.996337	+	0.0855138i	$0.972747\pi$
$368$	−42.0923	+	119.257i	−0.114381	+	0.324068i
$369$	−15.9123			−0.0431228
$370$	−84.3440	−	7.17177i	−0.227957	−	0.0193832i
$371$		−	510.315i		−	1.37551i
$372$	−248.202	−	42.5166i	−0.667209	−	0.114292i
$373$	−272.776			−0.731302			−0.365651	−	0.930752i	$-0.619154\pi$
$373$	−272.776			−0.731302			−0.365651	+	0.930752i	$0.619154\pi$
$374$	−12.2087	+	143.581i	−0.0326437	+	0.383908i
$375$			19.3649i			0.0516398i
$376$	−23.6124	+	90.7761i	−0.0627990	+	0.241426i
$377$	143.026			0.379379
$378$	−128.359	−	10.9144i	−0.339574	−	0.0288740i
$379$		−	376.828i		−	0.994270i	−0.867673	−	0.497135i	$-0.834385\pi$
$379$		−	376.828i		−	0.994270i	0.867673	−	0.497135i	$-0.165615\pi$
$380$	42.2731	−	246.780i	0.111245	−	0.649422i
$381$	−28.9001			−0.0758533
$382$	−26.8565	+	315.847i	−0.0703049	+	0.826825i
$383$			412.206i			1.07625i	0.842864	+	0.538127i	$0.180868\pi$
$383$			412.206i			1.07625i	−0.842864	+	0.538127i	$0.819132\pi$
$384$	−124.042	+	183.754i	−0.323027	+	0.478526i
$385$	306.016			0.794848
$386$	312.337	+	26.5581i	0.809164	+	0.0688032i
$387$		−	136.761i		−	0.353387i
$388$	501.863	+	85.9685i	1.29346	+	0.221568i
$389$	−161.289			−0.414623			−0.207312	−	0.978275i	$-0.566471\pi$
$389$	−161.289			−0.414623			−0.207312	+	0.978275i	$0.566471\pi$
$390$	1.85074	−	21.7657i	0.00474549	−	0.0558096i
$391$			51.5834i			0.131927i
$392$	810.303	+	210.774i	2.06710	+	0.537689i
$393$	340.206			0.865663
$394$	−518.383	−	44.0782i	−1.31569	−	0.111874i
$395$			275.163i			0.696615i
$396$	−22.3685	+	130.582i	−0.0564861	+	0.329752i
$397$	−186.505			−0.469785			−0.234893	−	0.972021i	$-0.575474\pi$
$397$	−186.505			−0.469785			−0.234893	+	0.972021i	$0.575474\pi$
$398$	2.37781	−	27.9643i	0.00597440	−	0.0702622i
$399$		−	601.014i		−	1.50630i
$400$	75.4389	+	26.6265i	0.188597	+	0.0665662i
$401$	239.061			0.596162			0.298081	−	0.954541i	$-0.403653\pi$
$401$	239.061			0.596162			0.298081	+	0.954541i	$0.403653\pi$
$402$	−55.8164	−	4.74607i	−0.138847	−	0.0118061i
$403$		−	102.501i		−	0.254344i
$404$	−371.996	−	63.7223i	−0.920781	−	0.157729i
$405$	−20.1246			−0.0496904
$406$	−106.529	+	1252.84i	−0.262387	+	3.08582i
$407$			208.970i			0.513441i
$408$	−22.7643	+	87.5155i	−0.0557949	+	0.214499i
$409$	47.8016			0.116874			0.0584372	−	0.998291i	$-0.481388\pi$
$409$	47.8016			0.116874			0.0584372	+	0.998291i	$0.481388\pi$
$410$	23.6354	+	2.00972i	0.0576473	+	0.00490175i
$411$			202.870i			0.493601i
$412$	−21.5071	+	125.553i	−0.0522017	+	0.304741i
$413$	−132.646			−0.321177
$414$	−4.01807	+	47.2547i	−0.00970549	+	0.114142i
$415$		−	222.869i		−	0.537033i
$416$	−82.2470	−	37.1374i	−0.197709	−	0.0892726i
$417$	324.306			0.777713
$418$	−615.875	−	52.3679i	−1.47339	−	0.125282i
$419$			239.009i			0.570428i	0.958464	+	0.285214i	$0.0920647\pi$
$419$			239.009i			0.570428i	−0.958464	+	0.285214i	$0.907935\pi$
$420$	189.280	+	32.4233i	0.450666	+	0.0771984i
$421$	−257.592			−0.611857			−0.305929	−	0.952054i	$-0.598967\pi$
$421$	−257.592			−0.611857			−0.305929	+	0.952054i	$0.598967\pi$
$422$	−12.6229	+	148.452i	−0.0299121	+	0.351783i
$423$			35.1738i			0.0831532i
$424$	−318.738	−	82.9092i	−0.751740	−	0.195541i
$425$	32.6303			0.0767772
$426$	228.367	+	19.4181i	0.536073	+	0.0455823i
$427$		−	695.779i		−	1.62946i
$428$	22.8211	−	133.224i	0.0533204	−	0.311271i
$429$	−53.9268			−0.125703
$430$	−17.2728	+	203.138i	−0.0401694	+	0.472414i
$431$		−	343.164i		−	0.796205i	−0.917341	−	0.398103i	$-0.869669\pi$
$431$		−	343.164i		−	0.796205i	0.917341	−	0.398103i	$-0.130331\pi$
$432$	−27.6710	+	78.3984i	−0.0640533	+	0.181478i
$433$	−234.760			−0.542171			−0.271085	−	0.962555i	$-0.587383\pi$
$433$	−234.760			−0.542171			−0.271085	+	0.962555i	$0.587383\pi$
$434$	897.859	+	76.3450i	2.06880	+	0.175910i
$435$			196.426i			0.451553i
$436$	−328.916	−	56.3428i	−0.754394	−	0.129227i
$437$	−221.261			−0.506317
$438$	−4.58818	+	53.9595i	−0.0104753	+	0.123195i
$439$			374.473i			0.853013i	0.904484	+	0.426507i	$0.140256\pi$
$439$			374.473i			0.853013i	−0.904484	+	0.426507i	$0.859744\pi$
$440$	49.7175	−	191.135i	0.112994	−	0.434397i
$441$	313.975			0.711962
$442$	−36.6758	−	3.11854i	−0.0829768	−	0.00705553i
$443$		−	108.557i		−	0.245050i	−0.992465	−	0.122525i	$-0.960901\pi$
$443$		−	108.557i		−	0.245050i	0.992465	−	0.122525i	$-0.0390992\pi$
$444$	−22.1410	+	129.254i	−0.0498672	+	0.291113i
$445$	−226.028			−0.507929
$446$	−27.1111	+	318.842i	−0.0607873	+	0.714891i
$447$			86.9963i			0.194623i
$448$	386.566	−	692.785i	0.862872	−	1.54640i
$449$	−431.511			−0.961050			−0.480525	−	0.876981i	$-0.659554\pi$
$449$	−431.511			−0.961050			−0.480525	+	0.876981i	$0.659554\pi$
$450$	29.8921	+	2.54173i	0.0664270	+	0.00564829i
$451$		−	58.5589i		−	0.129842i
$452$	−440.762	−	75.5020i	−0.975138	−	0.167040i
$453$	369.205			0.815021
$454$	−29.8193	+	350.692i	−0.0656813	+	0.772448i
$455$			78.1674i			0.171796i
$456$	−375.387	−	97.6448i	−0.823218	−	0.214133i
$457$	219.747			0.480847			0.240424	−	0.970668i	$-0.422714\pi$
$457$	219.747			0.480847			0.240424	+	0.970668i	$0.422714\pi$
$458$	227.520	+	19.3460i	0.496768	+	0.0422402i
$459$			33.9104i			0.0738789i
$460$	11.9365	−	69.6825i	0.0259489	−	0.151484i
$461$	223.434			0.484673			0.242337	−	0.970192i	$-0.422086\pi$
$461$	223.434			0.484673			0.242337	+	0.970192i	$0.422086\pi$
$462$	40.1660	−	472.374i	0.0869394	−	1.02245i
$463$			740.855i			1.60012i	0.599921	+	0.800059i	$0.295198\pi$
$463$			740.855i			1.60012i	−0.599921	+	0.800059i	$0.704802\pi$
$464$	765.206	+	270.082i	1.64915	+	0.582074i
$465$	140.770			0.302731
$466$	−518.254	−	44.0672i	−1.11213	−	0.0945648i
$467$			249.381i			0.534007i	0.963696	+	0.267004i	$0.0860336\pi$
$467$			249.381i			0.534007i	−0.963696	+	0.267004i	$0.913966\pi$
$468$	−33.3552	−	5.71370i	−0.0712718	−	0.0122088i
$469$	200.454			0.427406
$470$	4.44244	−	52.2455i	0.00945199	−	0.111161i
$471$		−	353.196i		−	0.749885i
$472$	−21.5506	+	82.8495i	−0.0456580	+	0.175529i
$473$	503.294			1.06405
$474$	424.748	+	36.1164i	0.896093	+	0.0761948i
$475$			139.964i			0.294661i
$476$	54.6340	−	318.940i	0.114777	−	0.670043i
$477$	−123.504			−0.258918
$478$	23.7379	−	279.171i	0.0496609	−	0.584039i
$479$		−	210.915i		−	0.440324i	−0.975463	−	0.220162i	$-0.929341\pi$
$479$		−	210.915i		−	0.440324i	0.975463	−	0.220162i	$-0.0706587\pi$
$480$	51.0029	−	112.954i	0.106256	−	0.235322i
$481$	−53.3784			−0.110974
$482$	−211.079	−	17.9480i	−0.437923	−	0.0372366i
$483$		−	169.706i		−	0.351358i
$484$	−3.50315	−	0.600085i	−0.00723791	−	0.00123984i
$485$	−284.636			−0.586879
$486$	−2.64144	+	31.0648i	−0.00543507	+	0.0639194i
$487$		−	710.541i		−	1.45902i	−0.683972	−	0.729508i	$-0.739749\pi$
$487$		−	710.541i		−	1.45902i	0.683972	−	0.729508i	$-0.260251\pi$
$488$	−434.576	−	113.041i	−0.890525	−	0.231641i
$489$	−373.946			−0.764715
$490$	−466.364	−	39.6549i	−0.951763	−	0.0809285i
$491$		−	697.876i		−	1.42134i	−0.703528	−	0.710668i	$-0.748393\pi$
$491$		−	697.876i		−	1.42134i	0.703528	−	0.710668i	$-0.251607\pi$
$492$	6.20449	−	36.2203i	0.0126108	−	0.0736185i
$493$	330.982			0.671363
$494$	13.3766	−	157.316i	0.0270781	−	0.318454i
$495$		−	74.0607i		−	0.149618i
$496$	193.557	−	548.390i	0.390235	−	1.10563i
$497$	−820.135			−1.65017
$498$	−344.025	−	29.2525i	−0.690814	−	0.0587400i
$499$			875.602i			1.75471i	0.479838	+	0.877357i	$0.340695\pi$
$499$			875.602i			1.75471i	−0.479838	+	0.877357i	$0.659305\pi$
$500$	−44.0793	−	7.55073i	−0.0881586	−	0.0151015i
$501$	441.723			0.881683
$502$	28.4468	−	334.550i	0.0566670	−	0.666434i
$503$		−	142.849i		−	0.283995i	−0.989867	−	0.141997i	$-0.954648\pi$
$503$		−	142.849i		−	0.283995i	0.989867	−	0.141997i	$-0.0453524\pi$
$504$	74.8932	−	287.921i	0.148598	−	0.571271i
$505$	210.981			0.417784
$506$	−173.902	−	14.7869i	−0.343681	−	0.0292232i
$507$			278.942i			0.550181i
$508$	11.2687	−	65.7837i	0.0221824	−	0.129496i
$509$	−147.662			−0.290102			−0.145051	−	0.989424i	$-0.546335\pi$
$509$	−147.662			−0.290102			−0.145051	+	0.989424i	$0.546335\pi$
$510$	4.28287	−	50.3689i	0.00839779	−	0.0987626i
$511$		−	193.785i		−	0.379227i
$512$	−369.903	−	354.000i	−0.722466	−	0.691407i
$513$	−145.455			−0.283537
$514$	−396.268	−	33.6947i	−0.770950	−	0.0655539i
$515$		−	71.2087i		−	0.138269i
$516$	311.301	+	53.3255i	0.603297	+	0.103344i
$517$	−129.443			−0.250374
$518$	39.7576	−	467.571i	0.0767520	−	0.902646i
$519$			407.769i			0.785682i
$520$	48.8226	+	12.6996i	0.0938895	+	0.0244223i
$521$	−348.592			−0.669082			−0.334541	−	0.942381i	$-0.608581\pi$
$521$	−348.592			−0.669082			−0.334541	+	0.942381i	$0.608581\pi$
$522$	303.207	+	25.7817i	0.580857	+	0.0493903i
$523$		−	370.317i		−	0.708063i	−0.935233	−	0.354032i	$-0.884811\pi$
$523$		−	370.317i		−	0.708063i	0.935233	−	0.354032i	$-0.115189\pi$
$524$	−132.652	+	774.392i	−0.253153	+	1.47785i
$525$	−107.352			−0.204479
$526$	81.4249	−	957.601i	0.154800	−	1.82053i
$527$		−	237.201i		−	0.450096i
$528$	−288.514	−	101.832i	−0.546429	−	0.192864i
$529$	466.523			0.881897
$530$	183.447	+	15.5985i	0.346127	+	0.0294312i
$531$			32.1024i			0.0604565i
$532$	1368.06	+	234.346i	2.57153	+	0.440500i
$533$	14.9580			0.0280638
$534$	−29.6672	+	348.902i	−0.0555565	+	0.653375i
$535$			75.5593i			0.141232i
$536$	32.5670	−	125.201i	0.0607594	−	0.233584i
$537$	177.829			0.331152
$538$	580.897	+	49.3937i	1.07973	+	0.0918098i
$539$			1155.46i			2.14371i
$540$	7.84695	−	45.8086i	0.0145314	−	0.0848307i
$541$	−279.719			−0.517041			−0.258520	−	0.966006i	$-0.583235\pi$
$541$	−279.719			−0.517041			−0.258520	+	0.966006i	$0.583235\pi$
$542$	29.4947	−	346.874i	0.0544183	−	0.639990i
$543$			98.4190i			0.181250i
$544$	−190.331	−	85.9411i	−0.349873	−	0.157980i
$545$	186.548			0.342289
$546$	120.661	+	10.2598i	0.220991	+	0.0187909i
$547$			387.716i			0.708804i	0.935093	+	0.354402i	$0.115315\pi$
$547$			387.716i			0.708804i	−0.935093	+	0.354402i	$0.884685\pi$
$548$	−461.782	−	79.1026i	−0.842668	−	0.144348i
$549$	−168.389			−0.306720
$550$	−9.35383	+	110.006i	−0.0170070	+	0.200011i
$551$			1419.71i			2.57660i
$552$	−105.997	−	27.5716i	−0.192023	−	0.0499485i
$553$	−1525.40			−2.75841
$554$	100.677	+	8.56059i	0.181728	+	0.0154523i
$555$		−	73.3076i		−	0.132086i
$556$	−126.453	+	738.201i	−0.227433	+	1.32770i
$557$	43.5564			0.0781983			0.0390991	−	0.999235i	$-0.487551\pi$
$557$	43.5564			0.0781983			0.0390991	+	0.999235i	$0.487551\pi$
$558$	18.4767	−	217.296i	0.0331123	−	0.389419i
$559$			128.559i			0.229981i
$560$	−147.607	+	418.204i	−0.263584	+	0.746794i
$561$	−124.794			−0.222449
$562$	131.628	+	11.1923i	0.234213	+	0.0199152i
$563$			361.646i			0.642355i	0.947019	+	0.321178i	$0.104079\pi$
$563$			361.646i			0.642355i	−0.947019	+	0.321178i	$0.895921\pi$
$564$	−80.0642	−	13.7149i	−0.141958	−	0.0243172i
$565$	249.983			0.442447
$566$	−19.8144	+	233.028i	−0.0350078	+	0.411710i
$567$		−	111.563i		−	0.196760i
$568$	−133.245	+	512.248i	−0.234586	+	0.901845i
$569$	888.559			1.56161			0.780807	−	0.624772i	$-0.214808\pi$
$569$	888.559			1.56161			0.780807	+	0.624772i	$0.214808\pi$
$570$	216.051	+	18.3709i	0.379037	+	0.0322296i
$571$			447.745i			0.784142i	0.919935	+	0.392071i	$0.128241\pi$
$571$			447.745i			0.784142i	−0.919935	+	0.392071i	$0.871759\pi$
$572$	21.0270	−	122.751i	0.0367605	−	0.214599i
$573$	−274.519			−0.479090
$574$	−11.1411	+	131.025i	−0.0194096	+	0.228267i
$575$			39.5211i			0.0687323i
$576$	−167.665	−	93.5551i	−0.291085	−	0.162422i
$577$	1069.90			1.85425			0.927124	−	0.374756i	$-0.122273\pi$
$577$	1069.90			1.85425			0.927124	+	0.374756i	$0.122273\pi$
$578$	491.049	+	41.7539i	0.849566	+	0.0722386i
$579$			271.468i			0.468857i
$580$	−447.113	−	76.5899i	−0.770885	−	0.132052i
$581$	1235.50			2.12651
$582$	−37.3598	+	439.371i	−0.0641921	+	0.754934i
$583$		−	454.508i		−	0.779602i
$584$	−121.036	−	31.4836i	−0.207253	−	0.0539102i
$585$	18.9177			0.0323380
$586$	136.255	+	11.5857i	0.232517	+	0.0197709i
$587$			129.637i			0.220847i	0.993885	+	0.110424i	$0.0352208\pi$
$587$			129.637i			0.220847i	−0.993885	+	0.110424i	$0.964779\pi$
$588$	−122.425	+	714.685i	−0.208205	+	1.21545i
$589$	1017.44			1.72741
$590$	4.05452	−	47.6834i	0.00687207	−	0.0808193i
$591$		−	450.553i		−	0.762357i
$592$	−285.581	−	100.797i	−0.482400	−	0.170265i
$593$	892.757			1.50549			0.752746	−	0.658311i	$-0.228729\pi$
$593$	892.757			1.50549			0.752746	+	0.658311i	$0.228729\pi$
$594$	−114.322	−	9.72079i	−0.192461	−	0.0163650i
$595$			180.890i			0.304017i
$596$	−198.025	−	33.9214i	−0.332257	−	0.0569151i
$597$	24.3052			0.0407123
$598$	3.77710	−	44.4208i	0.00631623	−	0.0742823i
$599$		−	1030.62i		−	1.72057i	−0.509816	−	0.860284i	$-0.670286\pi$
$599$		−	1030.62i		−	1.72057i	0.509816	−	0.860284i	$-0.329714\pi$
$600$	−17.4411	+	67.0508i	−0.0290685	+	0.111751i
$601$	−815.961			−1.35767			−0.678836	−	0.734289i	$-0.737515\pi$
$601$	−815.961			−1.35767			−0.678836	+	0.734289i	$0.737515\pi$
$602$	−1126.12	−	95.7540i	−1.87063	−	0.159060i
$603$		−	48.5128i		−	0.0804525i
$604$	−143.959	+	840.401i	−0.238343	+	1.39139i
$605$	1.98684			0.00328404
$606$	27.6921	−	325.675i	0.0456966	−	0.537417i
$607$			842.678i			1.38827i	0.719847	+	0.694133i	$0.244212\pi$
$607$			842.678i			1.38827i	−0.719847	+	0.694133i	$0.755788\pi$
$608$	368.634	−	816.400i	0.606305	−	1.34276i
$609$	−1088.91			−1.78803
$610$	250.117	+	21.2675i	0.410028	+	0.0348647i
$611$		−	33.0644i		−	0.0541152i
$612$	−77.1885	−	13.2223i	−0.126125	−	0.0216050i
$613$	−731.088			−1.19264			−0.596320	−	0.802747i	$-0.703371\pi$
$613$	−731.088			−1.19264			−0.596320	+	0.802747i	$0.703371\pi$
$614$	62.6107	−	736.336i	0.101972	−	1.19924i
$615$			20.5427i			0.0334028i
$616$	1059.58	+	275.615i	1.72009	+	0.447426i
$617$	−919.609			−1.49045			−0.745226	−	0.666812i	$-0.767658\pi$
$617$	−919.609			−1.49045			−0.745226	+	0.666812i	$0.767658\pi$
$618$	−109.919	−	9.34645i	−0.177863	−	0.0151237i
$619$		−	688.974i		−	1.11304i	−0.830833	−	0.556522i	$-0.812135\pi$
$619$		−	688.974i		−	1.11304i	0.830833	−	0.556522i	$-0.187865\pi$
$620$	−54.8887	+	320.427i	−0.0885302	+	0.516818i
$621$	−41.0715			−0.0661377
$622$	51.4186	−	604.711i	0.0826665	−	0.972203i
$623$		−	1253.01i		−	2.01126i
$624$	26.0116	−	73.6968i	0.0416852	−	0.118104i
$625$	25.0000			0.0400000
$626$	−593.246	−	50.4438i	−0.947678	−	0.0805811i
$627$		−	535.288i		−	0.853729i
$628$	803.960	+	137.717i	1.28019	+	0.219295i
$629$	−123.525			−0.196383
$630$	−14.0904	+	165.711i	−0.0223657	+	0.263033i
$631$		−	418.968i		−	0.663975i	−0.943284	−	0.331987i	$-0.892281\pi$
$631$		−	418.968i		−	0.663975i	0.943284	−	0.331987i	$-0.107719\pi$
$632$	−247.827	+	952.749i	−0.392131	+	1.50751i
$633$	−129.027			−0.203835
$634$	−527.454	−	44.8494i	−0.831946	−	0.0707404i
$635$			37.3099i			0.0587557i
$636$	48.1565	−	281.126i	0.0757177	−	0.442022i
$637$	−295.146			−0.463337
$638$	−94.8795	+	1115.83i	−0.148714	+	1.74896i
$639$			198.485i			0.310618i
$640$	237.225	+	160.138i	0.370664	+	0.250216i
$641$	−47.2426			−0.0737014			−0.0368507	−	0.999321i	$-0.511733\pi$
$641$	−47.2426			−0.0737014			−0.0368507	+	0.999321i	$0.511733\pi$
$642$	116.635	+	9.91749i	0.181675	+	0.0154478i
$643$		−	710.880i		−	1.10557i	−0.833325	−	0.552784i	$-0.813565\pi$
$643$		−	710.880i		−	1.10557i	0.833325	−	0.552784i	$-0.186435\pi$
$644$	386.293	+	66.1714i	0.599834	+	0.102751i
$645$	−176.558			−0.273733
$646$	30.9553	−	364.051i	0.0479184	−	0.563547i
$647$		−	468.195i		−	0.723641i	−0.932248	−	0.361820i	$-0.882155\pi$
$647$		−	468.195i		−	0.723641i	0.932248	−	0.361820i	$-0.117845\pi$
$648$	−69.6812	−	18.1253i	−0.107533	−	0.0279711i
$649$	−118.140			−0.182034
$650$	−28.0995	−	2.38930i	−0.0432299	−	0.00367584i
$651$			780.375i			1.19873i
$652$	145.808	−	851.192i	0.223632	−	1.30551i
$653$	551.066			0.843900			0.421950	−	0.906619i	$-0.361346\pi$
$653$	551.066			0.843900			0.421950	+	0.906619i	$0.361346\pi$
$654$	24.4852	−	287.959i	0.0374391	−	0.440304i
$655$		−	439.203i		−	0.670540i
$656$	80.0271	+	28.2459i	0.121993	+	0.0430578i
$657$	−46.8989			−0.0713834
$658$	289.629	+	24.6272i	0.440165	+	0.0374273i
$659$			158.259i			0.240151i	0.992765	+	0.120075i	$0.0383136\pi$
$659$			158.259i			0.240151i	−0.992765	+	0.120075i	$0.961686\pi$
$660$	168.580	+	28.8776i	0.255425	+	0.0437539i
$661$	92.4953			0.139932			0.0699662	−	0.997549i	$-0.477711\pi$
$661$	92.4953			0.139932			0.0699662	+	0.997549i	$0.477711\pi$
$662$	−80.2214	+	943.447i	−0.121180	+	1.42515i
$663$		−	31.8768i		−	0.0480796i
$664$	200.728	−	771.681i	0.302301	−	1.16217i
$665$	−775.905			−1.16678
$666$	−113.159	−	9.62194i	−0.169909	−	0.0144474i
$667$			400.877i			0.601015i
$668$	−172.236	+	1005.47i	−0.257838	+	1.50520i
$669$	−277.121			−0.414232
$670$	−6.12715	+	72.0587i	−0.00914500	+	0.107550i
$671$		−	619.690i		−	0.923532i
$672$	626.176	+	282.741i	0.931810	+	0.420745i
$673$	956.062			1.42060			0.710299	−	0.703900i	$-0.248560\pi$
$673$	956.062			1.42060			0.710299	+	0.703900i	$0.248560\pi$
$674$	−59.3037	−	5.04259i	−0.0879876	−	0.00748159i
$675$			25.9808i			0.0384900i
$676$	−634.940	−	108.764i	−0.939261	−	0.160894i
$677$	1116.67			1.64944			0.824719	−	0.565543i	$-0.191333\pi$
$677$	1116.67			1.64944			0.824719	+	0.565543i	$0.191333\pi$
$678$	32.8113	−	385.879i	0.0483942	−	0.569143i
$679$		−	1577.92i		−	2.32388i
$680$	112.982	+	29.3886i	0.166150	+	0.0432185i
$681$	−304.804			−0.447583
$682$	799.671	+	67.9961i	1.17254	+	0.0997010i
$683$		−	826.776i		−	1.21051i	−0.796033	−	0.605254i	$-0.793072\pi$
$683$		−	826.776i		−	1.21051i	0.796033	−	0.605254i	$-0.206928\pi$
$684$	56.7153	−	331.090i	0.0829172	−	0.484050i
$685$	261.904			0.382342
$686$	116.909	−	1374.91i	0.170421	−	2.00424i
$687$			197.749i			0.287844i
$688$	−242.764	+	687.806i	−0.352855	+	0.999718i
$689$	116.097			0.168501
$690$	61.0056	+	5.18731i	0.0884139	+	0.00751784i
$691$			965.432i			1.39715i	0.715536	+	0.698576i	$0.246182\pi$
$691$			965.432i			1.39715i	−0.715536	+	0.698576i	$0.753818\pi$
$692$	−928.183	−	158.996i	−1.34130	−	0.229764i
$693$	410.564			0.592444
$694$	−51.8834	+	610.177i	−0.0747600	+	0.879218i
$695$		−	418.677i		−	0.602414i
$696$	−176.912	+	680.122i	−0.254183	+	0.977186i
$697$	34.6149			0.0496627
$698$	−1293.63	−	109.997i	−1.85334	−	0.157589i
$699$		−	450.441i		−	0.644408i
$700$	41.8583	−	244.359i	0.0597976	−	0.349084i
$701$	−1109.94			−1.58337			−0.791686	−	0.610928i	$-0.790797\pi$
$701$	−1109.94			−1.58337			−0.791686	+	0.610928i	$0.790797\pi$
$702$	2.48303	−	29.2018i	0.00353708	−	0.0415980i
$703$		−	529.845i		−	0.753691i
$704$	344.292	−	617.024i	0.489052	−	0.876454i
$705$	45.4092			0.0644102
$706$	549.113	+	46.6911i	0.777780	+	0.0661347i
$707$			1169.60i			1.65431i
$708$	−73.0730	−	12.5173i	−0.103210	−	0.0176798i
$709$	−964.244			−1.36001			−0.680003	−	0.733210i	$-0.738021\pi$
$709$	−964.244			−1.36001			−0.680003	+	0.733210i	$0.738021\pi$
$710$	25.0686	−	294.820i	0.0353079	−	0.415240i
$711$			369.170i			0.519226i
$712$	−782.620	−	203.573i	−1.09919	−	0.285917i
$713$	287.292			0.402934
$714$	279.226	+	23.7426i	0.391073	+	0.0332529i
$715$			69.6191i			0.0973694i
$716$	−69.3385	+	404.782i	−0.0968415	+	0.565338i
$717$	242.641			0.338412
$718$	−86.0244	+	1011.69i	−0.119811	+	1.40904i
$719$			190.820i			0.265396i	0.991157	+	0.132698i	$0.0423641\pi$
$719$			190.820i			0.265396i	−0.991157	+	0.132698i	$0.957636\pi$
$720$	101.212	+	35.7232i	0.140572	+	0.0496155i
$721$	394.754			0.547509
$722$	842.149	+	71.6080i	1.16641	+	0.0991801i
$723$		−	183.459i		−	0.253747i
$724$	−224.026	−	38.3753i	−0.309428	−	0.0530046i
$725$	253.585			0.349772
$726$	0.260782	−	3.06694i	0.000359204	−	0.00422443i
$727$			202.134i			0.278039i	0.990290	+	0.139019i	$0.0443951\pi$
$727$			202.134i			0.278039i	−0.990290	+	0.139019i	$0.955605\pi$
$728$	−70.4017	+	270.654i	−0.0967056	+	0.371777i
$729$	−27.0000			−0.0370370
$730$	69.6614	+	5.92331i	0.0954265	+	0.00811412i
$731$			297.503i			0.406981i
$732$	65.6579	−	383.295i	0.0896966	−	0.523627i
$733$	−962.435			−1.31301			−0.656504	−	0.754322i	$-0.727966\pi$
$733$	−962.435			−1.31301			−0.656504	+	0.754322i	$0.727966\pi$
$734$	10.6358	−	125.083i	0.0144902	−	0.170413i
$735$		−	405.340i		−	0.551483i
$736$	104.090	−	230.524i	0.141426	−	0.313212i
$737$	178.532			0.242242
$738$	31.7102	+	2.69632i	0.0429677	+	0.00365355i
$739$			932.112i			1.26132i	0.776061	+	0.630658i	$0.217215\pi$
$739$			932.112i			1.26132i	−0.776061	+	0.630658i	$0.782785\pi$
$740$	166.866	+	28.5839i	0.225495	+	0.0386269i
$741$	136.731			0.184523
$742$	−86.4722	+	1016.96i	−0.116539	+	1.37057i
$743$			1153.70i			1.55276i	0.630266	+	0.776379i	$0.282946\pi$
$743$			1153.70i			1.55276i	−0.630266	+	0.776379i	$0.717054\pi$
$744$	487.414	+	126.785i	0.655127	+	0.170410i
$745$	112.312			0.150754
$746$	543.590	+	46.2215i	0.728672	+	0.0619591i
$747$		−	299.010i		−	0.400281i
$748$	48.6594	−	284.062i	0.0650526	−	0.379762i
$749$	−418.872			−0.559242
$750$	3.28136	−	38.5906i	0.00437515	−	0.0514541i
$751$			204.359i			0.272116i	0.990701	+	0.136058i	$0.0434434\pi$
$751$			204.359i			0.272116i	−0.990701	+	0.136058i	$0.956557\pi$
$752$	62.4369	−	176.898i	0.0830279	−	0.235237i
$753$	290.774			0.386155
$754$	−285.023	−	24.2356i	−0.378015	−	0.0321427i
$755$		−	476.641i		−	0.631313i
$756$	253.945	+	43.5005i	0.335906	+	0.0575403i
$757$	−216.739			−0.286314			−0.143157	−	0.989700i	$-0.545725\pi$
$757$	−216.739			−0.286314			−0.143157	+	0.989700i	$0.545725\pi$
$758$	−63.8530	+	750.947i	−0.0842388	+	0.990695i
$759$		−	151.147i		−	0.199140i
$760$	−126.059	+	484.623i	−0.165867	+	0.637662i
$761$	1324.78			1.74085			0.870424	−	0.492303i	$-0.163845\pi$
$761$	1324.78			1.74085			0.870424	+	0.492303i	$0.163845\pi$
$762$	57.5924	+	4.89708i	0.0755805	+	0.00642662i
$763$			1034.15i			1.35537i
$764$	107.040	−	624.872i	0.140104	−	0.817895i
$765$	43.7782			0.0572264
$766$	69.8477	−	821.447i	0.0911849	−	1.07238i
$767$		−	30.1772i		−	0.0393444i
$768$	278.330	−	345.167i	0.362409	−	0.449437i
$769$	444.088			0.577488			0.288744	−	0.957406i	$-0.406762\pi$
$769$	444.088			0.577488			0.288744	+	0.957406i	$0.406762\pi$
$770$	−609.832	−	51.8541i	−0.791990	−	0.0673429i
$771$		−	344.417i		−	0.446714i
$772$	−617.928	−	105.850i	−0.800425	−	0.137112i
$773$	−751.987			−0.972817			−0.486408	−	0.873732i	$-0.661693\pi$
$773$	−751.987			−0.972817			−0.486408	+	0.873732i	$0.661693\pi$
$774$	−23.1739	+	272.538i	−0.0299405	+	0.352117i
$775$		−	181.733i		−	0.234495i
$776$	−985.550	−	256.359i	−1.27004	−	0.330359i
$777$	406.389			0.523023
$778$	321.417	+	27.3301i	0.413133	+	0.0351287i
$779$			148.476i			0.190599i
$780$	−7.37635	+	43.0614i	−0.00945686	+	0.0552069i
$781$	−730.446			−0.935271
$782$	8.74073	−	102.796i	0.0111774	−	0.131452i
$783$			263.533i			0.336568i
$784$	−1579.06	−	557.337i	−2.01411	−	0.710889i
$785$	−455.974			−0.580858
$786$	−677.965	−	57.6474i	−0.862550	−	0.0733427i
$787$		−	442.296i		−	0.562002i	−0.959707	−	0.281001i	$-0.909334\pi$
$787$		−	442.296i		−	0.562002i	0.959707	−	0.281001i	$-0.0906665\pi$
$788$	1025.57	+	175.679i	1.30148	+	0.222943i
$789$	832.299			1.05488
$790$	46.6260	−	548.347i	0.0590203	−	0.694111i
$791$			1385.81i			1.75197i
$792$	66.7030	−	256.434i	0.0842210	−	0.323781i
$793$	158.291			0.199610
$794$	371.668	+	31.6030i	0.468096	+	0.0398022i
$795$			159.443i			0.200557i
$796$	−9.47704	+	55.3247i	−0.0119058	+	0.0695034i
$797$	−56.2072			−0.0705235			−0.0352618	−	0.999378i	$-0.511226\pi$
$797$	−56.2072			−0.0705235			−0.0352618	+	0.999378i	$0.511226\pi$
$798$	−101.841	+	1197.71i	−0.127620	+	1.50088i
$799$		−	76.5155i		−	0.0957641i
$800$	−145.824	−	65.8445i	−0.182279	−	0.0823056i
$801$	−303.249			−0.378588
$802$	−476.403	−	40.5086i	−0.594019	−	0.0505094i
$803$		−	172.593i		−	0.214935i
$804$	110.427	+	18.9160i	0.137347	+	0.0235274i
$805$	−219.090			−0.272161
$806$	−17.3686	+	204.264i	−0.0215491	+	0.253430i
$807$			504.887i			0.625634i
$808$	730.518	+	190.021i	0.904107	+	0.235174i
$809$	1522.16			1.88153			0.940765	−	0.339060i	$-0.110109\pi$
$809$	1522.16			1.88153			0.940765	+	0.339060i	$0.110109\pi$
$810$	40.1045	+	3.41009i	0.0495117	+	0.00420999i
$811$			930.734i			1.14764i	0.818982	+	0.573819i	$0.194539\pi$
$811$			930.734i			1.14764i	−0.818982	+	0.573819i	$0.805461\pi$
$812$	424.585	−	2478.63i	0.522888	−	3.05249i
$813$	301.486			0.370832
$814$	35.4098	−	416.438i	0.0435009	−	0.511595i
$815$			482.762i			0.592346i
$816$	60.1943	−	170.544i	0.0737676	−	0.209000i
$817$	−1276.10			−1.56194
$818$	−95.2595	−	8.09992i	−0.116454	−	0.00990210i
$819$			104.873i			0.128049i
$820$	−46.7602	−	8.00996i	−0.0570247	−	0.00976825i
$821$	349.814			0.426083			0.213041	−	0.977043i	$-0.431663\pi$
$821$	349.814			0.426083			0.213041	+	0.977043i	$0.431663\pi$
$822$	34.3761	−	404.281i	0.0418200	−	0.491826i
$823$			61.2187i			0.0743849i	0.999308	+	0.0371924i	$0.0118414\pi$
$823$			61.2187i			0.0743849i	−0.999308	+	0.0371924i	$0.988159\pi$
$824$	64.1344	−	246.559i	0.0778330	−	0.299222i
$825$	−95.6119			−0.115893
$826$	264.338	+	22.4767i	0.320022	+	0.0272115i
$827$			46.2063i			0.0558721i	0.999610	+	0.0279361i	$0.00889348\pi$
$827$			46.2063i			0.0558721i	−0.999610	+	0.0279361i	$0.991107\pi$
$828$	16.0145	−	93.4888i	0.0193412	−	0.112909i
$829$	223.832			0.270002			0.135001	−	0.990845i	$-0.456896\pi$
$829$	223.832			0.270002			0.135001	+	0.990845i	$0.456896\pi$
$830$	−37.7648	+	444.135i	−0.0454998	+	0.535102i
$831$			87.5037i			0.105299i
$832$	157.610	+	87.9444i	0.189435	+	0.105702i
$833$	−683.007			−0.819937
$834$	−646.280	−	54.9532i	−0.774916	−	0.0658912i
$835$		−	570.262i		−	0.682949i
$836$	1218.45	+	208.718i	1.45747	+	0.249663i
$837$	188.863			0.225642
$838$	40.4998	−	476.300i	0.0483291	−	0.568377i
$839$		−	361.794i		−	0.431220i	−0.976480	−	0.215610i	$-0.930826\pi$
$839$		−	361.794i		−	0.431220i	0.976480	−	0.215610i	$-0.0691740\pi$
$840$	−371.704	−	96.6867i	−0.442505	−	0.115103i
$841$	1731.20			2.05851
$842$	513.332	+	43.6486i	0.609657	+	0.0518392i
$843$			114.404i			0.135711i
$844$	50.3101	−	293.698i	0.0596092	−	0.347984i
$845$	360.112			0.426168
$846$	5.96015	−	70.0947i	0.00704510	−	0.0828542i
$847$			11.0143i			0.0130039i
$848$	621.134	+	219.232i	0.732470	+	0.258528i
$849$	−202.536			−0.238559
$850$	−65.0260	−	5.52916i	−0.0765012	−	0.00650490i
$851$		−	149.610i		−	0.175805i
$852$	−451.801	−	77.3929i	−0.530283	−	0.0908368i
$853$	−844.503			−0.990039			−0.495019	−	0.868882i	$-0.664839\pi$
$853$	−844.503			−0.990039			−0.495019	+	0.868882i	$0.664839\pi$
$854$	−117.899	+	1386.55i	−0.138055	+	1.62360i
$855$			187.781i			0.219627i
$856$	−68.0528	+	261.623i	−0.0795009	+	0.305635i
$857$	−1389.51			−1.62137			−0.810685	−	0.585482i	$-0.800905\pi$
$857$	−1389.51			−1.62137			−0.810685	+	0.585482i	$0.800905\pi$
$858$	107.466	+	9.13782i	0.125251	+	0.0106501i
$859$			1205.45i			1.40332i	0.712512	+	0.701660i	$0.247558\pi$
$859$			1205.45i			1.40332i	−0.712512	+	0.701660i	$0.752442\pi$
$860$	68.8429	−	401.888i	0.0800499	−	0.467312i
$861$	−113.881			−0.132266
$862$	−58.1487	+	683.861i	−0.0674579	+	0.793342i
$863$			258.868i			0.299963i	0.988689	+	0.149981i	$0.0479214\pi$
$863$			258.868i			0.299963i	−0.988689	+	0.149981i	$0.952079\pi$
$864$	68.4276	−	151.544i	0.0791986	−	0.175398i
$865$	526.428			0.608587
$866$	467.832	+	39.7798i	0.540222	+	0.0459351i
$867$			426.796i			0.492267i
$868$	−1776.33	−	304.282i	−2.04646	−	0.350555i
$869$	−1358.58			−1.56339
$870$	33.2841	−	391.439i	0.0382576	−	0.449930i
$871$			45.6035i			0.0523576i
$872$	645.919	+	168.015i	0.740732	+	0.192677i
$873$	−381.880			−0.437434
$874$	440.930	+	37.4923i	0.504497	+	0.0428974i
$875$			138.590i			0.158389i
$876$	18.2867	−	106.753i	0.0208752	−	0.121865i
$877$	−156.268			−0.178185			−0.0890926	−	0.996023i	$-0.528397\pi$
$877$	−156.268			−0.178185			−0.0890926	+	0.996023i	$0.528397\pi$
$878$	63.4539	−	746.253i	0.0722710	−	0.849946i
$879$			118.426i			0.134728i
$880$	−131.465	+	372.471i	−0.149392	+	0.423262i
$881$	−1343.58			−1.52507			−0.762533	−	0.646950i	$-0.776044\pi$
$881$	−1343.58			−1.52507			−0.762533	+	0.646950i	$0.776044\pi$
$882$	−625.693	−	53.2027i	−0.709402	−	0.0603205i
$883$			149.478i			0.169284i	0.996411	+	0.0846420i	$0.0269747\pi$
$883$			149.478i			0.169284i	−0.996411	+	0.0846420i	$0.973025\pi$
$884$	72.5594	+	12.4293i	0.0820807	+	0.0140603i
$885$	41.4440			0.0468294
$886$	−18.3949	+	216.334i	−0.0207617	+	0.244169i
$887$		−	1532.07i		−	1.72725i	−0.504134	−	0.863626i	$-0.668188\pi$
$887$		−	1532.07i		−	1.72725i	0.504134	−	0.863626i	$-0.331812\pi$
$888$	66.0247	−	253.827i	0.0743522	−	0.285841i
$889$	−206.832			−0.232656
$890$	450.431	+	38.3002i	0.506102	+	0.0430339i
$891$		−	99.3628i		−	0.111518i
$892$	108.055	−	630.796i	0.121137	−	0.707171i
$893$	328.204			0.367529
$894$	14.7414	−	173.367i	0.0164893	−	0.193923i
$895$		−	229.576i		−	0.256509i
$896$	−887.745	+	1315.09i	−0.990786	+	1.46773i
$897$	38.6084			0.0430417
$898$	859.919	+	73.1190i	0.957594	+	0.0814243i
$899$		−	1843.39i		−	2.05049i
$900$	−59.1386	−	10.1304i	−0.0657096	−	0.0112560i
$901$	268.665			0.298186
$902$	−9.92273	+	116.697i	−0.0110008	+	0.129376i
$903$		−	978.767i		−	1.08391i
$904$	865.562	+	225.148i	0.957480	+	0.249057i
$905$	127.058			0.140396
$906$	−735.754	−	62.5612i	−0.812091	−	0.0690521i
$907$		−	1245.02i		−	1.37268i	−0.727280	−	0.686341i	$-0.759216\pi$
$907$		−	1245.02i		−	1.37268i	0.727280	−	0.686341i	$-0.240784\pi$
$908$	118.848	−	693.808i	0.130890	−	0.764106i
$909$	283.060			0.311398
$910$	13.2454	−	155.773i	0.0145553	−	0.171179i
$911$		−	173.681i		−	0.190649i	−0.995446	−	0.0953245i	$-0.969611\pi$
$911$		−	173.681i		−	0.190649i	0.995446	−	0.0953245i	$-0.0303889\pi$
$912$	731.529	+	258.196i	0.802115	+	0.283110i
$913$	1100.39			1.20524
$914$	−437.914	−	37.2359i	−0.479118	−	0.0407395i
$915$			217.389i			0.237584i
$916$	−450.125	−	77.1058i	−0.491403	−	0.0841766i
$917$	2434.78			2.65515
$918$	5.74607	−	67.5770i	0.00625934	−	0.0736133i
$919$			874.426i			0.951498i	0.879581	+	0.475749i	$0.157823\pi$
$919$			874.426i			0.951498i	−0.879581	+	0.475749i	$0.842177\pi$
$920$	−35.5948	+	136.841i	−0.0386900	+	0.148740i
$921$	639.987			0.694882
$922$	−445.262	−	37.8607i	−0.482931	−	0.0410636i
$923$		−	186.582i		−	0.202147i
$924$	−160.086	+	934.545i	−0.173254	+	1.01141i
$925$	−94.6397			−0.102313
$926$	125.537	−	1476.38i	0.135569	−	1.59436i
$927$		−	95.5365i		−	0.103060i
$928$	−1479.14	−	667.886i	−1.59390	−	0.719705i
$929$	−1564.05			−1.68358			−0.841792	−	0.539803i	$-0.818499\pi$
$929$	−1564.05			−1.68358			−0.841792	+	0.539803i	$0.818499\pi$
$930$	−280.528	−	23.8533i	−0.301643	−	0.0256487i
$931$		−	2929.68i		−	3.14681i
$932$	1025.31	+	175.635i	1.10012	+	0.188450i
$933$	525.584			0.563327
$934$	42.2573	−	496.970i	0.0452434	−	0.532087i
$935$			161.108i			0.172308i
$936$	65.5023	+	17.0383i	0.0699811	+	0.0182033i
$937$	958.621			1.02308			0.511538	−	0.859261i	$-0.329076\pi$
$937$	958.621			1.02308			0.511538	+	0.859261i	$0.329076\pi$
$938$	−399.466	−	33.9666i	−0.425869	−	0.0362117i
$939$		−	515.620i		−	0.549116i
$940$	−17.7059	+	103.362i	−0.0188360	+	0.109960i
$941$	−752.357			−0.799529			−0.399765	−	0.916618i	$-0.630908\pi$
$941$	−752.357			−0.799529			−0.399765	+	0.916618i	$0.630908\pi$
$942$	−59.8485	+	703.852i	−0.0635335	+	0.747188i
$943$			41.9247i			0.0444589i
$944$	56.9849	−	161.451i	0.0603654	−	0.171029i
$945$	−144.027			−0.152410
$946$	−1002.97	−	85.2825i	−1.06022	−	0.0901507i
$947$			1013.16i			1.06986i	0.844895	+	0.534932i	$0.179663\pi$
$947$			1013.16i			1.06986i	−0.844895	+	0.534932i	$0.820337\pi$
$948$	−840.322	−	143.946i	−0.886415	−	0.151842i
$949$	44.0863			0.0464555
$950$	23.7167	−	278.921i	0.0249649	−	0.293601i
$951$		−	458.436i		−	0.482057i
$952$	−162.919	+	626.329i	−0.171134	+	0.657909i
$953$	−21.5482			−0.0226109			−0.0113054	−	0.999936i	$-0.503599\pi$
$953$	−21.5482			−0.0226109			−0.0113054	+	0.999936i	$0.503599\pi$
$954$	246.120	+	20.9276i	0.257987	+	0.0219367i
$955$			354.402i			0.371102i
$956$	−94.6102	+	552.312i	−0.0989646	+	0.577732i
$957$	−969.828			−1.01340
$958$	−35.7393	+	420.314i	−0.0373062	+	0.438741i
$959$			1451.90i			1.51397i
$960$	−120.779	+	216.454i	−0.125812	+	0.225473i
$961$	−360.079			−0.374692
$962$	106.373	+	9.04490i	0.110575	+	0.00940218i
$963$			101.373i			0.105268i
$964$	417.599	+	71.5340i	0.433193	+	0.0742054i
$965$	350.464			0.363175
$966$	−28.7565	+	338.192i	−0.0297686	+	0.350095i
$967$			303.965i			0.314338i	0.987572	+	0.157169i	$0.0502367\pi$
$967$			303.965i			0.314338i	−0.987572	+	0.157169i	$0.949763\pi$
$968$	6.87942	+	1.78946i	0.00710684	+	0.00184861i
$969$	316.415			0.326538
$970$	567.226	+	48.2313i	0.584769	+	0.0497230i
$971$		−	356.162i		−	0.366799i	−0.983038	−	0.183399i	$-0.941290\pi$
$971$		−	356.162i		−	0.366799i	0.983038	−	0.183399i	$-0.0587101\pi$
$972$	10.5278	−	61.4587i	0.0108311	−	0.0632291i
$973$	2320.99			2.38539
$974$	−120.400	+	1415.97i	−0.123614	+	1.45377i
$975$		−	24.4227i		−	0.0250489i
$976$	846.873	+	298.907i	0.867698	+	0.306257i
$977$	−1845.09			−1.88852			−0.944262	−	0.329194i	$-0.893223\pi$
$977$	−1845.09			−1.88852			−0.944262	+	0.329194i	$0.893223\pi$
$978$	745.202	+	63.3646i	0.761965	+	0.0647899i
$979$		−	1115.99i		−	1.13993i
$980$	922.654	+	158.049i	0.941484	+	0.161275i
$981$	250.280			0.255127
$982$	−118.254	+	1390.73i	−0.120422	+	1.41623i
$983$		−	289.444i		−	0.294449i	−0.989103	−	0.147225i	$-0.952966\pi$
$983$		−	289.444i		−	0.294449i	0.989103	−	0.147225i	$-0.0470340\pi$
$984$	−18.5019	+	71.1288i	−0.0188027	+	0.0722854i
$985$	−581.662			−0.590519
$986$	−659.583	−	56.0844i	−0.668949	−	0.0568807i
$987$			251.731i			0.255047i
$988$	−53.3140	+	311.234i	−0.0539616	+	0.315015i
$989$	−360.329			−0.364337
$990$	−12.5495	+	147.589i	−0.0126762	+	0.149080i
$991$		−	441.980i		−	0.445994i	−0.974819	−	0.222997i	$-0.928416\pi$
$991$		−	441.980i		−	0.445994i	0.974819	−	0.222997i	$-0.0715840\pi$
$992$	−478.645	+	1060.04i	−0.482505	+	1.06859i
$993$	−819.998			−0.825778
$994$	1634.37	+	138.971i	1.64424	+	0.139810i
$995$		−	31.3779i		−	0.0315356i
$996$	680.620	+	116.589i	0.683354	+	0.117058i
$997$	−1045.42			−1.04856			−0.524282	−	0.851545i	$-0.675666\pi$
$997$	−1045.42			−1.04856			−0.524282	+	0.851545i	$0.675666\pi$
$998$	148.370	−	1744.91i	0.148667	−	1.74841i
$999$		−	98.3525i		−	0.0984509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.c.a.31.1	✓	8
3.2	odd	2		180.3.c.b.91.8		8
4.3	odd	2	inner	60.3.c.a.31.2	yes	8
5.2	odd	4		300.3.f.b.199.9		16
5.3	odd	4		300.3.f.b.199.8		16
5.4	even	2		300.3.c.d.151.8		8
8.3	odd	2		960.3.e.c.511.4		8
8.5	even	2		960.3.e.c.511.7		8
12.11	even	2		180.3.c.b.91.7		8
15.2	even	4		900.3.f.f.199.8		16
15.8	even	4		900.3.f.f.199.9		16
15.14	odd	2		900.3.c.u.451.1		8
20.3	even	4		300.3.f.b.199.10		16
20.7	even	4		300.3.f.b.199.7		16
20.19	odd	2		300.3.c.d.151.7		8
24.5	odd	2		2880.3.e.j.2431.1		8
24.11	even	2		2880.3.e.j.2431.4		8
60.23	odd	4		900.3.f.f.199.7		16
60.47	odd	4		900.3.f.f.199.10		16
60.59	even	2		900.3.c.u.451.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.1	✓	8	1.1	even	1	trivial
60.3.c.a.31.2	yes	8	4.3	odd	2	inner
180.3.c.b.91.7		8	12.11	even	2
180.3.c.b.91.8		8	3.2	odd	2
300.3.c.d.151.7		8	20.19	odd	2
300.3.c.d.151.8		8	5.4	even	2
300.3.f.b.199.7		16	20.7	even	4
300.3.f.b.199.8		16	5.3	odd	4
300.3.f.b.199.9		16	5.2	odd	4
300.3.f.b.199.10		16	20.3	even	4
900.3.c.u.451.1		8	15.14	odd	2
900.3.c.u.451.2		8	60.59	even	2
900.3.f.f.199.7		16	60.23	odd	4
900.3.f.f.199.8		16	15.2	even	4
900.3.f.f.199.9		16	15.8	even	4
900.3.f.f.199.10		16	60.47	odd	4
960.3.e.c.511.4		8	8.3	odd	2
960.3.e.c.511.7		8	8.5	even	2
2880.3.e.j.2431.1		8	24.5	odd	2
2880.3.e.j.2431.4		8	24.11	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 + 0.675358i) q^{4} -2.23607 q^{5} +(-0.293494 + 3.45165i) q^{6} -12.3959i q^{7} +(-7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 + 0.675358i) q^{4} -2.23607 q^{5} +(-0.293494 + 3.45165i) q^{6} -12.3959i q^{7} +(-7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +(4.45606 + 0.378899i) q^{10} -11.0403i q^{11} +(1.16975 - 6.82874i) q^{12} +2.82009 q^{13} +(-2.10047 + 24.7027i) q^{14} +3.87298i q^{15} +(15.0878 + 5.32529i) q^{16} +6.52606 q^{17} +(5.97843 + 0.508346i) q^{18} +27.9928i q^{19} +(-8.81586 - 1.51015i) q^{20} -21.4703 q^{21} +(-1.87077 + 22.0012i) q^{22} +7.90421i q^{23} +(-3.48822 + 13.4102i) q^{24} +5.00000 q^{25} +(-5.61989 - 0.477860i) q^{26} +5.19615i q^{27} +(8.37167 - 48.8718i) q^{28} +50.7169 q^{29} +(0.656272 - 7.71812i) q^{30} -36.3467i q^{31} +(-29.1647 - 13.1689i) q^{32} -19.1224 q^{33} +(-13.0052 - 1.10583i) q^{34} +27.7181i q^{35} +(-11.8277 - 2.02607i) q^{36} -18.9279 q^{37} +(4.74333 - 55.7842i) q^{38} -4.88453i q^{39} +(17.3124 + 4.50327i) q^{40} +5.30410 q^{41} +(42.7863 + 3.63812i) q^{42} +45.5870i q^{43} +(7.45616 - 43.5273i) q^{44} +6.70820 q^{45} +(1.33936 - 15.7516i) q^{46} -11.7246i q^{47} +(9.22368 - 26.1328i) q^{48} -104.658 q^{49} +(-9.96404 - 0.847243i) q^{50} -11.3035i q^{51} +(11.1184 + 1.90457i) q^{52} +41.1680 q^{53} +(0.880481 - 10.3549i) q^{54} +24.6869i q^{55} +(-24.9644 + 95.9735i) q^{56} +48.4849 q^{57} +(-101.069 - 8.59391i) q^{58} -10.7008i q^{59} +(-2.61565 + 15.2695i) q^{60} +56.1297 q^{61} +(-6.15889 + 72.4319i) q^{62} +37.1877i q^{63} +(55.8882 + 31.1850i) q^{64} -6.30590 q^{65} +(38.1073 + 3.24026i) q^{66} +16.1709i q^{67} +(25.7295 + 4.40743i) q^{68} +13.6905 q^{69} +(4.69679 - 55.2368i) q^{70} -66.1617i q^{71} +(23.2271 + 6.04177i) q^{72} +15.6330 q^{73} +(37.7198 + 3.20731i) q^{74} -8.66025i q^{75} +(-18.9051 + 110.363i) q^{76} -136.855 q^{77} +(-0.827677 + 9.73394i) q^{78} -123.057i q^{79} +(-33.7373 - 11.9077i) q^{80} +9.00000 q^{81} +(-10.5701 - 0.898773i) q^{82} +99.6700i q^{83} +(-84.6484 - 14.5002i) q^{84} -14.5927 q^{85} +(7.72465 - 90.8461i) q^{86} -87.8443i q^{87} +(-22.2343 + 85.4781i) q^{88} +101.083 q^{89} +(-13.3682 - 1.13670i) q^{90} -34.9575i q^{91} +(-5.33817 + 31.1629i) q^{92} -62.9543 q^{93} +(-1.98672 + 23.3649i) q^{94} -62.5937i q^{95} +(-22.8092 + 50.5148i) q^{96} +127.293 q^{97} +(208.564 + 17.7342i) q^{98} +33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	\( 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 34 q^{16} - 12 q^{18} - 40 q^{20} - 48 q^{21} + 68 q^{22} + 18 q^{24} + 40 q^{25} - 36 q^{26} + 28 q^{28} + 64 q^{29} - 76 q^{32} - 92 q^{34} - 30 q^{36} - 112 q^{37} - 40 q^{38} - 10 q^{40} - 16 q^{41} + 108 q^{42} + 172 q^{44} + 152 q^{46} + 48 q^{48} - 56 q^{49} + 20 q^{50} - 128 q^{52} + 352 q^{53} + 18 q^{54} + 116 q^{56} + 144 q^{57} - 204 q^{58} + 30 q^{60} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 80 q^{65} + 108 q^{66} - 184 q^{68} - 96 q^{69} - 60 q^{70} + 60 q^{72} - 240 q^{73} + 132 q^{74} - 24 q^{76} - 288 q^{77} - 240 q^{78} - 80 q^{80} + 72 q^{81} + 40 q^{82} - 36 q^{84} + 160 q^{85} - 200 q^{86} + 140 q^{88} + 80 q^{89} - 30 q^{90} + 144 q^{92} + 144 q^{93} - 96 q^{94} - 174 q^{96} + 432 q^{97} + 660 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 + 10 * q^10 + 16 * q^13 - 20 * q^14 + 34 * q^16 - 12 * q^18 - 40 * q^20 - 48 * q^21 + 68 * q^22 + 18 * q^24 + 40 * q^25 - 36 * q^26 + 28 * q^28 + 64 * q^29 - 76 * q^32 - 92 * q^34 - 30 * q^36 - 112 * q^37 - 40 * q^38 - 10 * q^40 - 16 * q^41 + 108 * q^42 + 172 * q^44 + 152 * q^46 + 48 * q^48 - 56 * q^49 + 20 * q^50 - 128 * q^52 + 352 * q^53 + 18 * q^54 + 116 * q^56 + 144 * q^57 - 204 * q^58 + 30 * q^60 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 80 * q^65 + 108 * q^66 - 184 * q^68 - 96 * q^69 - 60 * q^70 + 60 * q^72 - 240 * q^73 + 132 * q^74 - 24 * q^76 - 288 * q^77 - 240 * q^78 - 80 * q^80 + 72 * q^81 + 40 * q^82 - 36 * q^84 + 160 * q^85 - 200 * q^86 + 140 * q^88 + 80 * q^89 - 30 * q^90 + 144 * q^92 + 144 * q^93 - 96 * q^94 - 174 * q^96 + 432 * q^97 + 660 * q^98

Introduction

L-functions

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