LMFDB - Embedded newform 60.3.c.a.31.7

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			31.7
Root			$1.04064 - 0.957636i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.3.c.a.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 - 2.61185i) q^{4} -2.23607 q^{5} +(-1.20651 - 3.24721i) q^{6} +5.46770i q^{7} +(3.86039 - 7.00695i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 - 2.61185i) q^{4} -2.23607 q^{5} +(-1.20651 - 3.24721i) q^{6} +5.46770i q^{7} +(3.86039 - 7.00695i) q^{8} -3.00000 q^{9} +(-4.19212 + 1.55759i) q^{10} +11.0403i q^{11} +(-4.52386 - 5.24735i) q^{12} +10.1242 q^{13} +(3.80867 + 10.2507i) q^{14} +3.87298i q^{15} +(2.35649 - 15.8255i) q^{16} -24.4146 q^{17} +(-5.62432 + 2.08973i) q^{18} +23.7757i q^{19} +(-6.77431 + 5.84027i) q^{20} +9.47033 q^{21} +(7.69043 + 20.6981i) q^{22} -37.2526i q^{23} +(-12.1364 - 6.68640i) q^{24} +5.00000 q^{25} +(18.9806 - 7.05227i) q^{26} +5.19615i q^{27} +(14.2808 + 16.5647i) q^{28} -25.7726 q^{29} +(2.69783 + 7.26097i) q^{30} -4.83647i q^{31} +(-6.60580 - 31.3108i) q^{32} +19.1224 q^{33} +(-45.7719 + 17.0066i) q^{34} -12.2261i q^{35} +(-9.08868 + 7.83555i) q^{36} +35.6493 q^{37} +(16.5616 + 44.5741i) q^{38} -17.5356i q^{39} +(-8.63210 + 15.6680i) q^{40} -9.30410 q^{41} +(17.7547 - 6.59682i) q^{42} -70.0287i q^{43} +(28.8356 + 33.4473i) q^{44} +6.70820 q^{45} +(-25.9493 - 69.8401i) q^{46} -38.0223i q^{47} +(-27.4106 - 4.08156i) q^{48} +19.1043 q^{49} +(9.37387 - 3.48288i) q^{50} +42.2873i q^{51} +(30.6718 - 26.4428i) q^{52} +55.7762 q^{53} +(3.61952 + 9.74162i) q^{54} -24.6869i q^{55} +(38.3119 + 21.1075i) q^{56} +41.1808 q^{57} +(-48.3179 + 17.9526i) q^{58} +55.5411i q^{59} +(10.1156 + 11.7334i) q^{60} -82.2412 q^{61} +(-3.36897 - 9.06729i) q^{62} -16.4031i q^{63} +(-34.1947 - 54.0992i) q^{64} -22.6384 q^{65} +(35.8502 - 13.3202i) q^{66} +104.493i q^{67} +(-73.9656 + 63.7673i) q^{68} -64.5233 q^{69} +(-8.51645 - 22.9213i) q^{70} +76.7471i q^{71} +(-11.5812 + 21.0209i) q^{72} -93.5215 q^{73} +(66.8344 - 24.8325i) q^{74} -8.66025i q^{75} +(62.0986 + 72.0300i) q^{76} -60.3651 q^{77} +(-12.2149 - 32.8753i) q^{78} -49.3762i q^{79} +(-5.26927 + 35.3869i) q^{80} +9.00000 q^{81} +(-17.4431 + 6.48102i) q^{82} +72.3768i q^{83} +(28.6910 - 24.7351i) q^{84} +54.5927 q^{85} +(-48.7804 - 131.288i) q^{86} +44.6395i q^{87} +(77.3589 + 42.6199i) q^{88} +115.691 q^{89} +(12.5764 - 4.67278i) q^{90} +55.3560i q^{91} +(-97.2980 - 112.859i) q^{92} -8.37701 q^{93} +(-26.4854 - 71.2832i) q^{94} -53.1641i q^{95} +(-54.2318 + 11.4416i) q^{96} -72.9589 q^{97} +(35.8162 - 13.3076i) 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 $

$2$	1.87477	−	0.696577i	0.937387	−	0.348288i
$2$	1.87477	−	0.696577i	0.937387	−	0.348288i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.02956	−	2.61185i	0.757390	−	0.652962i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	−1.20651	−	3.24721i	−0.201084	−	0.541201i
$7$			5.46770i			0.781100i	0.920582	+	0.390550i	$0.127715\pi$
$7$			5.46770i			0.781100i	−0.920582	+	0.390550i	$0.872285\pi$
$8$	3.86039	−	7.00695i	0.482549	−	0.875869i
$9$	−3.00000			−0.333333
$10$	−4.19212	+	1.55759i	−0.419212	+	0.155759i
$11$			11.0403i			1.00366i	0.864965	+	0.501832i	$0.167341\pi$
$11$			11.0403i			1.00366i	−0.864965	+	0.501832i	$0.832659\pi$
$12$	−4.52386	−	5.24735i	−0.376988	−	0.437280i
$13$	10.1242			0.778784			0.389392	−	0.921072i	$-0.372685\pi$
$13$	10.1242			0.778784			0.389392	+	0.921072i	$0.372685\pi$
$14$	3.80867	+	10.2507i	0.272048	+	0.732193i
$15$			3.87298i			0.258199i
$16$	2.35649	−	15.8255i	0.147280	−	0.989095i
$17$	−24.4146			−1.43615			−0.718077	−	0.695964i	$-0.754977\pi$
$17$	−24.4146			−1.43615			−0.718077	+	0.695964i	$0.754977\pi$
$18$	−5.62432	+	2.08973i	−0.312462	+	0.116096i
$19$			23.7757i			1.25135i	0.780082	+	0.625677i	$0.215177\pi$
$19$			23.7757i			1.25135i	−0.780082	+	0.625677i	$0.784823\pi$
$20$	−6.77431	+	5.84027i	−0.338715	+	0.292014i
$21$	9.47033			0.450968
$22$	7.69043	+	20.6981i	0.349565	+	0.940823i
$23$		−	37.2526i		−	1.61968i	−0.586653	−	0.809838i	$-0.699555\pi$
$23$		−	37.2526i		−	1.61968i	0.586653	−	0.809838i	$-0.300445\pi$
$24$	−12.1364	−	6.68640i	−0.505683	−	0.278600i
$25$	5.00000			0.200000
$26$	18.9806	−	7.05227i	0.730022	−	0.271241i
$27$			5.19615i			0.192450i
$28$	14.2808	+	16.5647i	0.510029	+	0.591598i
$29$	−25.7726			−0.888712			−0.444356	−	0.895850i	$-0.646567\pi$
$29$	−25.7726			−0.888712			−0.444356	+	0.895850i	$0.646567\pi$
$30$	2.69783	+	7.26097i	0.0899277	+	0.242032i
$31$		−	4.83647i		−	0.156015i	−0.996953	−	0.0780076i	$-0.975144\pi$
$31$		−	4.83647i		−	0.156015i	0.996953	−	0.0780076i	$-0.0248558\pi$
$32$	−6.60580	−	31.3108i	−0.206431	−	0.978461i
$33$	19.1224			0.579466
$34$	−45.7719	+	17.0066i	−1.34623	+	0.500196i
$35$		−	12.2261i		−	0.349319i
$36$	−9.08868	+	7.83555i	−0.252463	+	0.217654i
$37$	35.6493			0.963495			0.481747	−	0.876310i	$-0.340002\pi$
$37$	35.6493			0.963495			0.481747	+	0.876310i	$0.340002\pi$
$38$	16.5616	+	44.5741i	0.435832	+	1.17300i
$39$		−	17.5356i		−	0.449631i
$40$	−8.63210	+	15.6680i	−0.215803	+	0.391700i
$41$	−9.30410			−0.226929			−0.113465	−	0.993542i	$-0.536195\pi$
$41$	−9.30410			−0.226929			−0.113465	+	0.993542i	$0.536195\pi$
$42$	17.7547	−	6.59682i	0.422732	−	0.157067i
$43$		−	70.0287i		−	1.62857i	−0.580462	−	0.814287i	$-0.697128\pi$
$43$		−	70.0287i		−	1.62857i	0.580462	−	0.814287i	$-0.302872\pi$
$44$	28.8356	+	33.4473i	0.655355	+	0.760166i
$45$	6.70820			0.149071
$46$	−25.9493	−	69.8401i	−0.564114	−	1.51826i
$47$		−	38.0223i		−	0.808984i	−0.914542	−	0.404492i	$-0.867448\pi$
$47$		−	38.0223i		−	0.808984i	0.914542	−	0.404492i	$-0.132552\pi$
$48$	−27.4106	−	4.08156i	−0.571054	−	0.0850324i
$49$	19.1043			0.389883
$50$	9.37387	−	3.48288i	0.187477	−	0.0696577i
$51$			42.2873i			0.829164i
$52$	30.6718	−	26.4428i	0.589843	−	0.508516i
$53$	55.7762			1.05238			0.526191	−	0.850366i	$-0.323620\pi$
$53$	55.7762			1.05238			0.526191	+	0.850366i	$0.323620\pi$
$54$	3.61952	+	9.74162i	0.0670281	+	0.180400i
$55$		−	24.6869i		−	0.448853i
$56$	38.3119	+	21.1075i	0.684141	+	0.376919i
$57$	41.1808			0.722470
$58$	−48.3179	+	17.9526i	−0.833067	+	0.309528i
$59$			55.5411i			0.941374i	0.882300	+	0.470687i	$0.155994\pi$
$59$			55.5411i			0.941374i	−0.882300	+	0.470687i	$0.844006\pi$
$60$	10.1156	+	11.7334i	0.168594	+	0.195557i
$61$	−82.2412			−1.34822			−0.674108	−	0.738633i	$-0.735472\pi$
$61$	−82.2412			−1.34822			−0.674108	+	0.738633i	$0.735472\pi$
$62$	−3.36897	−	9.06729i	−0.0543383	−	0.146247i
$63$		−	16.4031i		−	0.260367i
$64$	−34.1947	−	54.0992i	−0.534293	−	0.845299i
$65$	−22.6384			−0.348283
$66$	35.8502	−	13.3202i	0.543184	−	0.201821i
$67$			104.493i			1.55960i	0.626026	+	0.779802i	$0.284680\pi$
$67$			104.493i			1.55960i	−0.626026	+	0.779802i	$0.715320\pi$
$68$	−73.9656	+	63.7673i	−1.08773	+	0.937754i
$69$	−64.5233			−0.935120
$70$	−8.51645	−	22.9213i	−0.121664	−	0.327447i
$71$			76.7471i			1.08094i	0.841362	+	0.540472i	$0.181754\pi$
$71$			76.7471i			1.08094i	−0.841362	+	0.540472i	$0.818246\pi$
$72$	−11.5812	+	21.0209i	−0.160850	+	0.291956i
$73$	−93.5215			−1.28112			−0.640558	−	0.767910i	$-0.721297\pi$
$73$	−93.5215			−1.28112			−0.640558	+	0.767910i	$0.721297\pi$
$74$	66.8344	−	24.8325i	0.903168	−	0.335574i
$75$		−	8.66025i		−	0.115470i
$76$	62.0986	+	72.0300i	0.817087	+	0.947764i
$77$	−60.3651			−0.783963
$78$	−12.2149	−	32.8753i	−0.156601	−	0.421478i
$79$		−	49.3762i		−	0.625016i	−0.949915	−	0.312508i	$-0.898831\pi$
$79$		−	49.3762i		−	0.625016i	0.949915	−	0.312508i	$-0.101169\pi$
$80$	−5.26927	+	35.3869i	−0.0658658	+	0.442337i
$81$	9.00000			0.111111
$82$	−17.4431	+	6.48102i	−0.212721	+	0.0790368i
$83$			72.3768i			0.872010i	0.899944	+	0.436005i	$0.143607\pi$
$83$			72.3768i			0.872010i	−0.899944	+	0.436005i	$0.856393\pi$
$84$	28.6910	−	24.7351i	0.341559	−	0.294465i
$85$	54.5927			0.642267
$86$	−48.7804	−	131.288i	−0.567214	−	1.52661i
$87$			44.6395i			0.513098i
$88$	77.3589	+	42.6199i	0.879079	+	0.484318i
$89$	115.691			1.29990			0.649950	−	0.759977i	$-0.274790\pi$
$89$	115.691			1.29990			0.649950	+	0.759977i	$0.274790\pi$
$90$	12.5764	−	4.67278i	0.139737	−	0.0519198i
$91$			55.3560i			0.608308i
$92$	−97.2980	−	112.859i	−1.05759	−	1.22673i
$93$	−8.37701			−0.0900754
$94$	−26.4854	−	71.2832i	−0.281760	−	0.758332i
$95$		−	53.1641i		−	0.559623i
$96$	−54.2318	+	11.4416i	−0.564915	+	0.119183i
$97$	−72.9589			−0.752154			−0.376077	−	0.926588i	$-0.622727\pi$
$97$	−72.9589			−0.752154			−0.376077	+	0.926588i	$0.622727\pi$
$98$	35.8162	−	13.3076i	0.365471	−	0.135792i
$99$		−	33.1209i		−	0.334555i
$100$	15.1478	−	13.0592i	0.151478	−	0.130592i
$101$	29.4092			0.291180			0.145590	−	0.989345i	$-0.453492\pi$
$101$	29.4092			0.291180			0.145590	+	0.989345i	$0.453492\pi$
$102$	29.4564	+	79.2792i	0.288788	+	0.777247i
$103$		−	28.1884i		−	0.273673i	−0.990594	−	0.136837i	$-0.956306\pi$
$103$		−	28.1884i		−	0.273673i	0.990594	−	0.136837i	$-0.0436935\pi$
$104$	39.0833	−	70.9397i	0.375801	−	0.682112i
$105$	−21.1763			−0.201679
$106$	104.568	−	38.8524i	0.986490	−	0.366532i
$107$		−	4.50700i		−	0.0421215i	−0.999778	−	0.0210607i	$-0.993296\pi$
$107$		−	4.50700i		−	0.0421215i	0.999778	−	0.0210607i	$-0.00670434\pi$
$108$	13.5716	+	15.7421i	0.125663	+	0.145760i
$109$	193.315			1.77353			0.886767	−	0.462217i	$-0.152946\pi$
$109$	193.315			1.77353			0.886767	+	0.462217i	$0.152946\pi$
$110$	−17.1963	−	46.2824i	−0.156330	−	0.420749i
$111$		−	61.7464i		−	0.556274i
$112$	86.5292	+	12.8846i	0.772582	+	0.115041i
$113$	75.5727			0.668785			0.334392	−	0.942434i	$-0.391469\pi$
$113$	75.5727			0.668785			0.334392	+	0.942434i	$0.391469\pi$
$114$	77.2047	−	28.6856i	0.677234	−	0.251628i
$115$			83.2992i			0.724341i
$116$	−78.0798	+	67.3142i	−0.673102	+	0.580295i
$117$	−30.3726			−0.259595
$118$	38.6886	+	104.127i	0.327870	+	0.882432i
$119$		−	133.492i		−	1.12178i
$120$	27.1378	+	14.9512i	0.226148	+	0.124594i
$121$	−0.888544			−0.00734334
$122$	−154.184	+	57.2873i	−1.26380	+	0.469568i
$123$			16.1152i			0.131018i
$124$	−12.6321	−	14.6524i	−0.101872	−	0.118164i
$125$	−11.1803			−0.0894427
$126$	−11.4260	−	30.7521i	−0.0906827	−	0.244064i
$127$		−	131.306i		−	1.03390i	−0.856015	−	0.516951i	$-0.827067\pi$
$127$		−	131.306i		−	1.03390i	0.856015	−	0.516951i	$-0.172933\pi$
$128$	−101.792	−	77.6045i	−0.795247	−	0.606285i
$129$	−121.293			−0.940258
$130$	−42.4418	+	15.7694i	−0.326476	+	0.121303i
$131$		−	75.7533i		−	0.578270i	−0.957288	−	0.289135i	$-0.906632\pi$
$131$		−	75.7533i		−	0.578270i	0.957288	−	0.289135i	$-0.0933676\pi$
$132$	57.9324	−	49.9448i	0.438882	−	0.378370i
$133$	−129.999			−0.977433
$134$	72.7877	+	195.902i	0.543192	+	1.46195i
$135$		−	11.6190i		−	0.0860663i
$136$	−94.2500	+	171.072i	−0.693014	+	1.25788i
$137$	66.7927			0.487538			0.243769	−	0.969833i	$-0.421616\pi$
$137$	66.7927			0.487538			0.243769	+	0.969833i	$0.421616\pi$
$138$	−120.967	+	44.9454i	−0.876570	+	0.325692i
$139$			38.1214i			0.274255i	0.990553	+	0.137127i	$0.0437869\pi$
$139$			38.1214i			0.274255i	−0.990553	+	0.137127i	$0.956213\pi$
$140$	−31.9329	−	37.0399i	−0.228092	−	0.264571i
$141$	−65.8565			−0.467067
$142$	53.4602	+	143.884i	0.376481	+	1.01326i
$143$			111.774i			0.781638i
$144$	−7.06946	+	47.4765i	−0.0490935	+	0.329698i
$145$	57.6294			0.397444
$146$	−175.332	+	65.1449i	−1.20090	+	0.446198i
$147$		−	33.0895i		−	0.225099i
$148$	108.002	−	93.1106i	0.729742	−	0.629126i
$149$	−126.717			−0.850449			−0.425225	−	0.905088i	$-0.639805\pi$
$149$	−126.717			−0.850449			−0.425225	+	0.905088i	$0.639805\pi$
$150$	−6.03253	−	16.2360i	−0.0402169	−	0.108240i
$151$		−	68.4403i		−	0.453247i	−0.973982	−	0.226623i	$-0.927231\pi$
$151$		−	68.4403i		−	0.453247i	0.973982	−	0.226623i	$-0.0727687\pi$
$152$	166.595	+	91.7836i	1.09602	+	0.603840i
$153$	73.2438			0.478718
$154$	−113.171	+	42.0489i	−0.734877	+	0.273045i
$155$			10.8147i			0.0697721i
$156$	−45.8004	−	53.1252i	−0.293592	−	0.340546i
$157$	25.5777			0.162915			0.0814577	−	0.996677i	$-0.474042\pi$
$157$	25.5777			0.162915			0.0814577	+	0.996677i	$0.474042\pi$
$158$	−34.3943	−	92.5693i	−0.217686	−	0.585882i
$159$		−	96.6073i		−	0.607593i
$160$	14.7710	+	70.0130i	0.0923189	+	0.437581i
$161$	203.686			1.26513
$162$	16.8730	−	6.26919i	0.104154	−	0.0386987i
$163$			63.4771i			0.389430i	0.980860	+	0.194715i	$0.0623782\pi$
$163$			63.4771i			0.389430i	−0.980860	+	0.194715i	$0.937622\pi$
$164$	−28.1873	+	24.3009i	−0.171874	+	0.148176i
$165$	−42.7590			−0.259145
$166$	50.4160	+	135.690i	0.303711	+	0.817411i
$167$			12.3771i			0.0741144i	0.999313	+	0.0370572i	$0.0117984\pi$
$167$			12.3771i			0.0741144i	−0.999313	+	0.0370572i	$0.988202\pi$
$168$	36.5592	−	66.3582i	0.217614	−	0.394989i
$169$	−66.5008			−0.393496
$170$	102.349	−	38.0280i	0.602053	−	0.223694i
$171$		−	71.3272i		−	0.417118i
$172$	−182.904	−	212.156i	−1.06340	−	1.23347i
$173$	59.3729			0.343196			0.171598	−	0.985167i	$-0.445107\pi$
$173$	59.3729			0.343196			0.171598	+	0.985167i	$0.445107\pi$
$174$	31.0948	+	83.6890i	0.178706	+	0.480971i
$175$			27.3385i			0.156220i
$176$	174.719	+	26.0164i	0.992720	+	0.147820i
$177$	96.2000			0.543503
$178$	216.895	−	80.5877i	1.21851	−	0.452740i
$179$			252.782i			1.41219i	0.708118	+	0.706094i	$0.249545\pi$
$179$			252.782i			1.41219i	−0.708118	+	0.706094i	$0.750455\pi$
$180$	20.3229	−	17.5208i	0.112905	−	0.0973379i
$181$	125.373			0.692670			0.346335	−	0.938111i	$-0.387426\pi$
$181$	125.373			0.692670			0.346335	+	0.938111i	$0.387426\pi$
$182$	38.5597	+	103.780i	0.211867	+	0.570220i
$183$			142.446i			0.778393i
$184$	−261.027	−	143.809i	−1.41862	−	0.781573i
$185$	−79.7143			−0.430888
$186$	−15.7050	+	5.83523i	−0.0844355	+	0.0313722i
$187$		−	269.545i		−	1.44142i
$188$	−99.3084	−	115.191i	−0.528236	−	0.612717i
$189$	−28.4110			−0.150323
$190$	−37.0329	−	99.6708i	−0.194910	−	0.524583i
$191$		−	97.4640i		−	0.510283i	−0.966904	−	0.255141i	$-0.917878\pi$
$191$		−	97.4640i		−	0.510283i	0.966904	−	0.255141i	$-0.0821220\pi$
$192$	−93.7025	+	59.2270i	−0.488034	+	0.308474i
$193$	−342.376			−1.77397			−0.886985	−	0.461798i	$-0.847204\pi$
$193$	−342.376			−1.77397			−0.886985	+	0.461798i	$0.847204\pi$
$194$	−136.782	+	50.8215i	−0.705060	+	0.261966i
$195$			39.2108i			0.201081i
$196$	57.8775	−	49.8974i	0.295293	−	0.254579i
$197$	74.4829			0.378086			0.189043	−	0.981969i	$-0.439461\pi$
$197$	74.4829			0.378086			0.189043	+	0.981969i	$0.439461\pi$
$198$	−23.0713	−	62.0943i	−0.116522	−	0.313608i
$199$			178.027i			0.894606i	0.894382	+	0.447303i	$0.147615\pi$
$199$			178.027i			0.894606i	−0.894382	+	0.447303i	$0.852385\pi$
$200$	19.3020	−	35.0348i	0.0965098	−	0.175174i
$201$	180.988			0.900438
$202$	55.1356	−	20.4858i	0.272949	−	0.101415i
$203$		−	140.917i		−	0.694173i
$204$	110.448	+	128.112i	0.541413	+	0.628000i
$205$	20.8046			0.101486
$206$	−19.6354	−	52.8468i	−0.0953172	−	0.256538i
$207$			111.758i			0.539892i
$208$	23.8575	−	160.220i	0.114700	−	0.770291i
$209$	−262.491			−1.25594
$210$	−39.7008	+	14.7509i	−0.189052	+	0.0702425i
$211$		−	185.893i		−	0.881008i	−0.897751	−	0.440504i	$-0.854800\pi$
$211$		−	185.893i		−	0.881008i	0.897751	−	0.440504i	$-0.145200\pi$
$212$	168.978	−	145.679i	0.797064	−	0.687166i
$213$	132.930			0.624084
$214$	−3.13947	−	8.44961i	−0.0146704	−	0.0394842i
$215$			156.589i			0.728321i
$216$	36.4092	+	20.0592i	0.168561	+	0.0928666i
$217$	26.4444			0.121863
$218$	362.422	−	134.659i	1.66249	−	0.617701i
$219$			161.984i			0.739653i
$220$	−64.4784	−	74.7905i	−0.293084	−	0.339957i
$221$	−247.178			−1.11845
$222$	−43.0111	−	115.761i	−0.193744	−	0.521444i
$223$			202.724i			0.909074i	0.890728	+	0.454537i	$0.150195\pi$
$223$			202.724i			0.909074i	−0.890728	+	0.454537i	$0.849805\pi$
$224$	171.198	−	36.1186i	0.764276	−	0.161244i
$225$	−15.0000			−0.0666667
$226$	141.682	−	52.6422i	0.626910	−	0.232930i
$227$			51.2708i			0.225863i	0.993603	+	0.112931i	$0.0360240\pi$
$227$			51.2708i			0.225863i	−0.993603	+	0.112931i	$0.963976\pi$
$228$	124.760	−	107.558i	0.547192	−	0.471745i
$229$	337.056			1.47186			0.735930	−	0.677058i	$-0.236745\pi$
$229$	337.056			1.47186			0.735930	+	0.677058i	$0.236745\pi$
$230$	58.0243	+	156.167i	0.252280	+	0.678988i
$231$			104.555i			0.452621i
$232$	−99.4925	+	180.588i	−0.428847	+	0.778395i
$233$	−80.2851			−0.344571			−0.172286	−	0.985047i	$-0.555115\pi$
$233$	−80.2851			−0.344571			−0.172286	+	0.985047i	$0.555115\pi$
$234$	−56.9417	+	21.1568i	−0.243341	+	0.0904138i
$235$			85.0203i			0.361789i
$236$	145.065	+	168.265i	0.614682	+	0.712988i
$237$	−85.5221			−0.360853
$238$	−92.9873	−	250.267i	−0.390703	−	1.05154i
$239$		−	330.808i		−	1.38413i	−0.721834	−	0.692066i	$-0.756701\pi$
$239$		−	330.808i		−	1.38413i	0.721834	−	0.692066i	$-0.243299\pi$
$240$	61.2920	+	9.12664i	0.255383	+	0.0380277i
$241$	−359.914			−1.49342			−0.746710	−	0.665150i	$-0.768368\pi$
$241$	−359.914			−1.49342			−0.746710	+	0.665150i	$0.768368\pi$
$242$	−1.66582	+	0.618939i	−0.00688355	+	0.00255760i
$243$		−	15.5885i		−	0.0641500i
$244$	−249.155	+	214.802i	−1.02113	+	0.880334i
$245$	−42.7184			−0.174361
$246$	11.2255	+	30.2123i	0.0456319	+	0.122814i
$247$			240.710i			0.974534i
$248$	−33.8889	−	18.6707i	−0.136649	−	0.0752850i
$249$	125.360			0.503455
$250$	−20.9606	+	7.78796i	−0.0838425	+	0.0311519i
$251$		−	312.213i		−	1.24388i	−0.783067	−	0.621938i	$-0.786346\pi$
$251$		−	312.213i		−	1.24388i	0.783067	−	0.621938i	$-0.213654\pi$
$252$	−42.8424	−	49.6942i	−0.170010	−	0.197199i
$253$	411.280			1.62561
$254$	−91.4645	−	246.169i	−0.360096	−	0.969167i
$255$		−	94.5574i		−	0.370813i
$256$	−244.894	−	74.5853i	−0.956617	−	0.291349i
$257$	80.2592			0.312293			0.156146	−	0.987734i	$-0.450093\pi$
$257$	80.2592			0.312293			0.156146	+	0.987734i	$0.450093\pi$
$258$	−227.398	+	84.4901i	−0.881386	+	0.327481i
$259$			194.920i			0.752586i
$260$	−68.5843	+	59.1280i	−0.263786	+	0.227415i
$261$	77.3179			0.296237
$262$	−52.7680	−	142.020i	−0.201405	−	0.542063i
$263$			487.967i			1.85539i	0.373342	+	0.927694i	$0.378212\pi$
$263$			487.967i			1.85539i	−0.373342	+	0.927694i	$0.621788\pi$
$264$	73.8199	−	133.990i	0.279621	−	0.507536i
$265$	−124.719			−0.470639
$266$	−243.718	+	90.5540i	−0.916233	+	0.340428i
$267$		−	200.383i		−	0.750498i
$268$	272.921	+	316.569i	1.01836	+	1.18123i
$269$	−309.553			−1.15076			−0.575378	−	0.817888i	$-0.695145\pi$
$269$	−309.553			−1.15076			−0.575378	+	0.817888i	$0.695145\pi$
$270$	−8.09349	−	21.7829i	−0.0299759	−	0.0806775i
$271$		−	48.9693i		−	0.180698i	−0.995910	−	0.0903492i	$-0.971202\pi$
$271$		−	48.9693i		−	0.180698i	0.995910	−	0.0903492i	$-0.0287983\pi$
$272$	−57.5327	+	386.374i	−0.211517	+	1.42049i
$273$	95.8794			0.351207
$274$	125.221	−	46.5262i	0.457012	−	0.169804i
$275$			55.2016i			0.200733i
$276$	−195.477	+	168.525i	−0.708251	+	0.610598i
$277$	−199.644			−0.720736			−0.360368	−	0.932810i	$-0.617349\pi$
$277$	−199.644			−0.720736			−0.360368	+	0.932810i	$0.617349\pi$
$278$	26.5545	+	71.4690i	0.0955197	+	0.257083i
$279$			14.5094i			0.0520051i
$280$	−85.6680	−	47.1977i	−0.305957	−	0.168563i
$281$	61.1598			0.217650			0.108825	−	0.994061i	$-0.465291\pi$
$281$	61.1598			0.217650			0.108825	+	0.994061i	$0.465291\pi$
$282$	−123.466	+	45.8741i	−0.437823	+	0.162674i
$283$		−	432.506i		−	1.52829i	−0.645044	−	0.764145i	$-0.723161\pi$
$283$		−	432.506i		−	1.52829i	0.645044	−	0.764145i	$-0.276839\pi$
$284$	200.452	+	232.510i	0.705816	+	0.818697i
$285$	−92.0830			−0.323098
$286$	77.8593	+	209.551i	0.272235	+	0.732697i
$287$		−	50.8720i		−	0.177254i
$288$	19.8174	+	93.9323i	0.0688105	+	0.326154i
$289$	307.073			1.06254
$290$	108.042	−	40.1433i	0.372559	−	0.138425i
$291$			126.369i			0.434256i
$292$	−283.329	+	244.264i	−0.970305	+	0.836521i
$293$	−283.234			−0.966668			−0.483334	−	0.875436i	$-0.660574\pi$
$293$	−283.234			−0.966668			−0.483334	+	0.875436i	$0.660574\pi$
$294$	−23.0494	−	62.0354i	−0.0783993	−	0.211005i
$295$		−	124.194i		−	0.420995i
$296$	137.620	−	249.793i	0.464933	−	0.843895i
$297$	−57.3672			−0.193155
$298$	−237.566	+	88.2681i	−0.797200	+	0.296202i
$299$		−	377.152i		−	1.26138i
$300$	−22.6193	−	26.2368i	−0.0753976	−	0.0874559i
$301$	382.896			1.27208
$302$	−47.6739	−	128.310i	−0.157861	−	0.424868i
$303$		−	50.9382i		−	0.168113i
$304$	376.263	+	56.0272i	1.23771	+	0.184300i
$305$	183.897			0.602940
$306$	137.316	−	51.0199i	0.448744	−	0.166732i
$307$			100.077i			0.325983i	0.986627	+	0.162992i	$0.0521144\pi$
$307$			100.077i			0.325983i	−0.986627	+	0.162992i	$0.947886\pi$
$308$	−182.880	+	157.665i	−0.593766	+	0.511898i
$309$	−48.8237			−0.158005
$310$	7.53325	+	20.2751i	0.0243008	+	0.0654035i
$311$			404.185i			1.29963i	0.760092	+	0.649815i	$0.225154\pi$
$311$			404.185i			1.29963i	−0.760092	+	0.649815i	$0.774846\pi$
$312$	−122.871	−	67.6943i	−0.393818	−	0.216969i
$313$	−128.579			−0.410795			−0.205398	−	0.978679i	$-0.565849\pi$
$313$	−128.579			−0.410795			−0.205398	+	0.978679i	$0.565849\pi$
$314$	47.9525	−	17.8168i	0.152715	−	0.0567415i
$315$			36.6784i			0.116440i
$316$	−128.963	−	149.588i	−0.408112	−	0.473381i
$317$	85.9315			0.271077			0.135539	−	0.990772i	$-0.456724\pi$
$317$	85.9315			0.271077			0.135539	+	0.990772i	$0.456724\pi$
$318$	−67.2944	−	181.117i	−0.211618	−	0.569550i
$319$		−	284.538i		−	0.891969i
$320$	76.4618	+	120.969i	0.238943	+	0.378029i
$321$	−7.80635			−0.0243189
$322$	381.865	−	141.883i	1.18592	−	0.440630i
$323$		−	580.475i		−	1.79714i
$324$	27.2661	−	23.5066i	0.0841545	−	0.0725514i
$325$	50.6209			0.155757
$326$	44.2167	+	119.005i	0.135634	+	0.365047i
$327$		−	334.832i		−	1.02395i
$328$	−35.9175	+	65.1934i	−0.109505	+	0.198760i
$329$	207.894			0.631898
$330$	−80.1634	+	29.7849i	−0.242919	+	0.0902573i
$331$		−	183.391i		−	0.554052i	−0.960862	−	0.277026i	$-0.910651\pi$
$331$		−	183.391i		−	0.554052i	0.960862	−	0.277026i	$-0.0893488\pi$
$332$	189.037	+	219.270i	0.569390	+	0.660452i
$333$	−106.948			−0.321165
$334$	8.62160	+	23.2043i	0.0258132	+	0.0694739i
$335$		−	233.654i		−	0.697476i
$336$	22.3167	−	149.873i	0.0664188	−	0.446050i
$337$	168.130			0.498901			0.249451	−	0.968388i	$-0.419750\pi$
$337$	168.130			0.498901			0.249451	+	0.968388i	$0.419750\pi$
$338$	−124.674	+	46.3229i	−0.368858	+	0.137050i
$339$		−	130.896i		−	0.386123i
$340$	165.392	−	142.588i	0.486447	−	0.419376i
$341$	53.3962			0.156587
$342$	−49.6849	−	133.722i	−0.145277	−	0.391001i
$343$			372.374i			1.08564i
$344$	−490.688	−	270.338i	−1.42642	−	0.785867i
$345$	144.279			0.418199
$346$	111.311	−	41.3578i	0.321708	−	0.119531i
$347$			137.414i			0.396006i	0.980201	+	0.198003i	$0.0634455\pi$
$347$			137.414i			0.396006i	−0.980201	+	0.198003i	$0.936554\pi$
$348$	116.592	+	135.238i	0.335034	+	0.388615i
$349$	−13.4893			−0.0386513			−0.0193256	−	0.999813i	$-0.506152\pi$
$349$	−13.4893			−0.0386513			−0.0193256	+	0.999813i	$0.506152\pi$
$350$	19.0434	+	51.2535i	0.0544096	+	0.146439i
$351$			52.6068i			0.149877i
$352$	345.681	−	72.9301i	0.982047	−	0.207188i
$353$	243.547			0.689935			0.344968	−	0.938615i	$-0.387890\pi$
$353$	243.547			0.689935			0.344968	+	0.938615i	$0.387890\pi$
$354$	180.353	−	67.0107i	0.509473	−	0.189296i
$355$		−	171.612i		−	0.483413i
$356$	350.493	−	302.168i	0.984532	−	0.848786i
$357$	−231.215			−0.647660
$358$	176.082	+	473.909i	0.491849	+	1.32377i
$359$		−	17.9166i		−	0.0499068i	−0.999689	−	0.0249534i	$-0.992056\pi$
$359$		−	17.9166i		−	0.0499068i	0.999689	−	0.0249534i	$-0.00794374\pi$
$360$	25.8963	−	47.0041i	0.0719342	−	0.130567i
$361$	−204.285			−0.565887
$362$	235.047	−	87.3321i	0.649300	−	0.241249i
$363$			1.53900i			0.00423968i
$364$	144.582	+	167.704i	0.397202	+	0.460727i
$365$	209.120			0.572933
$366$	99.2245	+	267.054i	0.271105	+	0.729656i
$367$			238.417i			0.649637i	0.945776	+	0.324818i	$0.105303\pi$
$367$			238.417i			0.649637i	−0.945776	+	0.324818i	$0.894697\pi$
$368$	−589.541	−	87.7852i	−1.60201	−	0.238547i
$369$	27.9123			0.0756431
$370$	−149.446	+	55.5271i	−0.403909	+	0.150073i
$371$			304.968i			0.822016i
$372$	−25.3787	+	21.8795i	−0.0682222	+	0.0588158i
$373$	−181.271			−0.485981			−0.242990	−	0.970029i	$-0.578128\pi$
$373$	−181.271			−0.485981			−0.242990	+	0.970029i	$0.578128\pi$
$374$	−187.759	−	505.336i	−0.502029	−	1.35117i
$375$			19.3649i			0.0516398i
$376$	−266.420	−	146.781i	−0.708564	−	0.390375i
$377$	−260.927			−0.692114
$378$	−53.2642	+	19.7904i	−0.140911	+	0.0523557i
$379$			306.206i			0.807931i	0.914774	+	0.403965i	$0.132368\pi$
$379$			306.206i			0.807931i	−0.914774	+	0.403965i	$0.867632\pi$
$380$	−138.857	−	161.064i	−0.365412	−	0.423853i
$381$	−227.428			−0.596924
$382$	−67.8912	−	182.723i	−0.177726	−	0.478333i
$383$		−	144.027i		−	0.376050i	−0.982164	−	0.188025i	$-0.939791\pi$
$383$		−	144.027i		−	0.376050i	0.982164	−	0.188025i	$-0.0602086\pi$
$384$	−134.415	+	176.308i	−0.350039	+	0.459136i
$385$	134.981			0.350599
$386$	−641.878	+	238.491i	−1.66290	+	0.617853i
$387$			210.086i			0.542858i
$388$	−221.034	+	190.558i	−0.569674	+	0.491128i
$389$	14.0099			0.0360152			0.0180076	−	0.999838i	$-0.494268\pi$
$389$	14.0099			0.0360152			0.0180076	+	0.999838i	$0.494268\pi$
$390$	27.3133	+	73.5114i	0.0700342	+	0.188491i
$391$			909.506i			2.32610i
$392$	73.7499	−	133.863i	0.188138	−	0.341486i
$393$	−131.209			−0.333864
$394$	139.639	−	51.8831i	0.354413	−	0.131683i
$395$			110.409i			0.279515i
$396$	−86.5069	−	100.342i	−0.218452	−	0.253389i
$397$	39.1084			0.0985098			0.0492549	−	0.998786i	$-0.484315\pi$
$397$	39.1084			0.0985098			0.0492549	+	0.998786i	$0.484315\pi$
$398$	124.009	+	333.760i	0.311581	+	0.838592i
$399$			225.164i			0.564321i
$400$	11.7824	−	79.1276i	0.0294561	−	0.197819i
$401$	−121.067			−0.301913			−0.150957	−	0.988540i	$-0.548235\pi$
$401$	−121.067			−0.301913			−0.150957	+	0.988540i	$0.548235\pi$
$402$	339.312	−	126.072i	0.844059	−	0.313612i
$403$		−	48.9653i		−	0.121502i
$404$	89.0970	−	76.8124i	0.220537	−	0.190130i
$405$	−20.1246			−0.0496904
$406$	−98.1595	−	264.188i	−0.241772	−	0.650709i
$407$			393.579i			0.967026i
$408$	296.305	+	163.246i	0.726239	+	0.400112i
$409$	−541.795			−1.32468			−0.662342	−	0.749202i	$-0.730437\pi$
$409$	−541.795			−1.32468			−0.662342	+	0.749202i	$0.730437\pi$
$410$	39.0039	−	14.4920i	0.0951316	−	0.0353463i
$411$		−	115.688i		−	0.281480i
$412$	−73.6237	−	85.3983i	−0.178698	−	0.207278i
$413$	−303.682			−0.735307
$414$	77.8478	+	209.520i	0.188038	+	0.506088i
$415$		−	161.839i		−	0.389975i
$416$	−66.8784	−	316.996i	−0.160765	−	0.762009i
$417$	66.0282			0.158341
$418$	−492.112	+	182.845i	−1.17730	+	0.437429i
$419$			687.825i			1.64159i	0.571224	+	0.820794i	$0.306469\pi$
$419$			687.825i			1.64159i	−0.571224	+	0.820794i	$0.693531\pi$
$420$	−64.1549	+	55.3093i	−0.152750	+	0.131689i
$421$	−454.396			−1.07932			−0.539662	−	0.841882i	$-0.681448\pi$
$421$	−454.396			−1.07932			−0.539662	+	0.841882i	$0.681448\pi$
$422$	−129.489	−	348.507i	−0.306845	−	0.825846i
$423$			114.067i			0.269661i
$424$	215.318	−	390.821i	0.507826	−	0.921749i
$425$	−122.073			−0.287231
$426$	249.214	−	92.5959i	0.585008	−	0.217361i
$427$		−	449.670i		−	1.05309i
$428$	−11.7716	−	13.6542i	−0.0275037	−	0.0319024i
$429$	193.599			0.451279
$430$	109.076	+	293.569i	0.253666	+	0.682719i
$431$			466.145i			1.08154i	0.841169	+	0.540772i	$0.181868\pi$
$431$			466.145i			1.08154i	−0.841169	+	0.540772i	$0.818132\pi$
$432$	82.2318	+	12.2447i	0.190351	+	0.0283441i
$433$	457.094			1.05565			0.527823	−	0.849355i	$-0.323009\pi$
$433$	457.094			1.05565			0.527823	+	0.849355i	$0.323009\pi$
$434$	49.5772	−	18.4205i	0.114233	−	0.0424436i
$435$		−	99.8170i		−	0.229464i
$436$	585.660	−	504.910i	1.34326	−	1.15805i
$437$	885.706			2.02679
$438$	112.834	+	303.684i	0.257613	+	0.693341i
$439$		−	777.467i		−	1.77100i	−0.464644	−	0.885498i	$-0.653818\pi$
$439$		−	777.467i		−	1.77100i	0.464644	−	0.885498i	$-0.346182\pi$
$440$	−172.980	−	95.3011i	−0.393136	−	0.216593i
$441$	−57.3128			−0.129961
$442$	−463.403	+	172.178i	−1.04842	+	0.389544i
$443$		−	247.484i		−	0.558654i	−0.960196	−	0.279327i	$-0.909889\pi$
$443$		−	247.484i		−	0.558654i	0.960196	−	0.279327i	$-0.0901114\pi$
$444$	−161.272	−	187.065i	−0.363226	−	0.421316i
$445$	−258.693			−0.581333
$446$	141.213	+	380.061i	0.316620	+	0.852155i
$447$			219.480i			0.491007i
$448$	295.798	−	186.967i	0.660263	−	0.417336i
$449$	412.508			0.918726			0.459363	−	0.888249i	$-0.348078\pi$
$449$	412.508			0.918726			0.459363	+	0.888249i	$0.348078\pi$
$450$	−28.1216	+	10.4487i	−0.0624925	+	0.0232192i
$451$		−	102.720i		−	0.227761i
$452$	228.952	−	197.384i	0.506531	−	0.436691i
$453$	−118.542			−0.261682
$454$	35.7141	+	96.1213i	0.0786654	+	0.211721i
$455$		−	123.780i		−	0.272044i
$456$	158.974	−	288.552i	0.348627	−	0.632789i
$457$	−745.400			−1.63107			−0.815537	−	0.578706i	$-0.803558\pi$
$457$	−745.400			−1.63107			−0.815537	+	0.578706i	$0.803558\pi$
$458$	631.904	−	234.785i	1.37970	−	0.512631i
$459$		−	126.862i		−	0.276388i
$460$	217.565	+	252.360i	0.472967	+	0.548609i
$461$	81.6151			0.177039			0.0885196	−	0.996074i	$-0.471786\pi$
$461$	81.6151			0.177039			0.0885196	+	0.996074i	$0.471786\pi$
$462$	72.8309	+	196.018i	0.157643	+	0.424281i
$463$		−	292.248i		−	0.631205i	−0.948891	−	0.315603i	$-0.897793\pi$
$463$		−	292.248i		−	0.631205i	0.948891	−	0.315603i	$-0.102207\pi$
$464$	−60.7329	+	407.865i	−0.130890	+	0.879020i
$465$	18.7316			0.0402829
$466$	−150.517	+	55.9248i	−0.322997	+	0.120010i
$467$			51.4163i			0.110099i	0.998484	+	0.0550495i	$0.0175317\pi$
$467$			51.4163i			0.110099i	−0.998484	+	0.0550495i	$0.982468\pi$
$468$	−92.0155	+	79.3285i	−0.196614	+	0.169505i
$469$	−571.339			−1.21821
$470$	59.2232	+	159.394i	0.126007	+	0.339136i
$471$		−	44.3019i		−	0.0940592i
$472$	389.174	+	214.410i	0.824520	+	0.454259i
$473$	773.139			1.63454
$474$	−160.335	+	59.5727i	−0.338259	+	0.125681i
$475$			118.879i			0.250271i
$476$	−348.660	−	404.422i	−0.732480	−	0.849625i
$477$	−167.329			−0.350794
$478$	−230.433	−	620.190i	−0.482077	−	1.29747i
$479$		−	122.593i		−	0.255935i	−0.991778	−	0.127967i	$-0.959155\pi$
$479$		−	122.593i		−	0.255935i	0.991778	−	0.127967i	$-0.0408453\pi$
$480$	121.266	−	25.5842i	0.252638	−	0.0533003i
$481$	360.920			0.750354
$482$	−674.758	+	250.708i	−1.39991	+	0.520141i
$483$		−	352.794i		−	0.730423i
$484$	−2.69190	+	2.32074i	−0.00556177	+	0.00479492i
$485$	163.141			0.336373
$486$	−10.8586	−	29.2248i	−0.0223427	−	0.0601334i
$487$		−	65.9859i		−	0.135495i	−0.997703	−	0.0677474i	$-0.978419\pi$
$487$		−	65.9859i		−	0.135495i	0.997703	−	0.0677474i	$-0.0215812\pi$
$488$	−317.483	+	576.260i	−0.650580	+	1.18086i
$489$	109.946			0.224837
$490$	−80.0874	+	29.7566i	−0.163444	+	0.0607279i
$491$		−	361.163i		−	0.735567i	−0.929911	−	0.367783i	$-0.880117\pi$
$491$		−	361.163i		−	0.735567i	0.929911	−	0.367783i	$-0.119883\pi$
$492$	42.0904	+	48.8219i	0.0855496	+	0.0992315i
$493$	629.229			1.27633
$494$	167.673	+	451.277i	0.339419	+	0.913516i
$495$			74.0607i			0.149618i
$496$	−76.5396	−	11.3971i	−0.154314	−	0.0229780i
$497$	−419.630			−0.844326
$498$	235.022	−	87.3231i	0.471933	−	0.175348i
$499$			711.138i			1.42513i	0.701608	+	0.712564i	$0.252466\pi$
$499$			711.138i			1.42513i	−0.701608	+	0.712564i	$0.747534\pi$
$500$	−33.8715	+	29.2014i	−0.0677431	+	0.0584027i
$501$	21.4378			0.0427900
$502$	−217.480	−	585.328i	−0.433227	−	1.16599i
$503$		−	353.756i		−	0.703292i	−0.936133	−	0.351646i	$-0.885622\pi$
$503$		−	353.756i		−	0.703292i	0.936133	−	0.351646i	$-0.114378\pi$
$504$	−114.936	−	63.3224i	−0.228047	−	0.125640i
$505$	−65.7610			−0.130220
$506$	771.057	−	286.488i	1.52383	−	0.566182i
$507$			115.183i			0.227185i
$508$	−342.951	−	397.799i	−0.675100	−	0.783068i
$509$	478.049			0.939192			0.469596	−	0.882881i	$-0.344400\pi$
$509$	478.049			0.939192			0.469596	+	0.882881i	$0.344400\pi$
$510$	−65.8665	−	177.274i	−0.129150	−	0.347596i
$511$		−	511.348i		−	1.00068i
$512$	−511.075	+	30.7568i	−0.998194	+	0.0600720i
$513$	−123.542			−0.240823
$514$	150.468	−	55.9067i	0.292739	−	0.108768i
$515$			63.0311i			0.122390i
$516$	−367.466	+	316.800i	−0.712142	+	0.613953i
$517$	419.778			0.811949
$518$	135.777	+	365.431i	0.262117	+	0.705464i
$519$		−	102.837i		−	0.198144i
$520$	−87.3930	+	158.626i	−0.168063	+	0.305050i
$521$	−35.7365			−0.0685921			−0.0342960	−	0.999412i	$-0.510919\pi$
$521$	−35.7365			−0.0685921			−0.0342960	+	0.999412i	$0.510919\pi$
$522$	144.954	−	53.8579i	0.277689	−	0.103176i
$523$		−	733.562i		−	1.40260i	−0.712864	−	0.701302i	$-0.752602\pi$
$523$		−	733.562i		−	1.40260i	0.712864	−	0.701302i	$-0.247398\pi$
$524$	−197.856	−	229.499i	−0.377588	−	0.437976i
$525$	47.3517			0.0901937
$526$	339.906	+	914.828i	0.646210	+	1.73922i
$527$			118.081i			0.224062i
$528$	45.0617	−	302.622i	0.0853441	−	0.573147i
$529$	−858.753			−1.62335
$530$	−233.821	+	86.8767i	−0.441172	+	0.163918i
$531$		−	166.623i		−	0.313791i
$532$	−393.839	+	339.537i	−0.740298	+	0.638227i
$533$	−94.1965			−0.176729
$534$	−139.582	−	375.673i	−0.261390	−	0.703507i
$535$			10.0780i			0.0188373i
$536$	732.181	+	403.386i	1.36601	+	0.752585i
$537$	437.831			0.815327
$538$	−580.342	+	215.628i	−1.07870	+	0.400795i
$539$			210.917i			0.391312i
$540$	−30.3469	−	35.2003i	−0.0561980	−	0.0651858i
$541$	608.939			1.12558			0.562790	−	0.826600i	$-0.309728\pi$
$541$	608.939			1.12558			0.562790	+	0.826600i	$0.309728\pi$
$542$	−34.1109	−	91.8064i	−0.0629352	−	0.169384i
$543$		−	217.153i		−	0.399913i
$544$	161.278	+	764.440i	0.296467	+	1.40522i
$545$	−432.266			−0.793148
$546$	179.752	−	66.7874i	0.329217	−	0.122321i
$547$			78.5868i			0.143669i	0.997417	+	0.0718344i	$0.0228853\pi$
$547$			78.5868i			0.143669i	−0.997417	+	0.0718344i	$0.977115\pi$
$548$	202.353	−	174.452i	0.369257	−	0.318344i
$549$	246.724			0.449405
$550$	38.4521	+	103.491i	0.0699130	+	0.188165i
$551$		−	612.763i		−	1.11209i
$552$	−249.085	+	452.112i	−0.451242	+	0.819043i
$553$	269.974			0.488200
$554$	−374.287	+	139.067i	−0.675609	+	0.251024i
$555$			138.069i			0.248773i
$556$	99.5673	+	115.491i	0.179078	+	0.207718i
$557$	−928.488			−1.66694			−0.833472	−	0.552561i	$-0.813651\pi$
$557$	−928.488			−1.66694			−0.833472	+	0.552561i	$0.813651\pi$
$558$	10.1069	+	27.2019i	0.0181128	+	0.0487489i
$559$		−	708.984i		−	1.26831i
$560$	−193.485	−	28.8108i	−0.345509	−	0.0514478i
$561$	−466.866			−0.832202
$562$	114.661	−	42.6025i	0.204023	−	0.0758051i
$563$			447.978i			0.795697i	0.917451	+	0.397849i	$0.130243\pi$
$563$			447.978i			0.795697i	−0.917451	+	0.397849i	$0.869757\pi$
$564$	−199.516	+	172.007i	−0.353752	+	0.304977i
$565$	−168.986			−0.299090
$566$	−301.274	−	810.852i	−0.532286	−	1.43260i
$567$			49.2093i			0.0867889i
$568$	537.763	+	296.274i	0.946766	+	0.521609i
$569$	571.441			1.00429			0.502145	−	0.864783i	$-0.332544\pi$
$569$	571.441			1.00429			0.502145	+	0.864783i	$0.332544\pi$
$570$	−172.635	+	64.1429i	−0.302868	+	0.112531i
$571$			990.801i			1.73520i	0.497260	+	0.867602i	$0.334340\pi$
$571$			990.801i			1.73520i	−0.497260	+	0.867602i	$0.665660\pi$
$572$	291.937	+	338.627i	0.510380	+	0.592005i
$573$	−168.813			−0.294612
$574$	−35.4363	−	95.3736i	−0.0617357	−	0.166156i
$575$		−	186.263i		−	0.323935i
$576$	102.584	+	162.298i	0.178098	+	0.281766i
$577$	826.638			1.43265			0.716324	−	0.697768i	$-0.245823\pi$
$577$	826.638			1.43265			0.716324	+	0.697768i	$0.245823\pi$
$578$	575.693	−	213.900i	0.996008	−	0.370069i
$579$			593.013i			1.02420i
$580$	174.592	−	150.519i	0.301020	−	0.259516i
$581$	−395.735			−0.681127
$582$	88.0254	+	236.913i	0.151246	+	0.407066i
$583$			615.787i			1.05624i
$584$	−361.030	+	655.301i	−0.618202	+	1.12209i
$585$	67.9151			0.116094
$586$	−530.999	+	197.294i	−0.906142	+	0.336679i
$587$		−	900.009i		−	1.53323i	−0.642104	−	0.766617i	$-0.721938\pi$
$587$		−	900.009i		−	1.53323i	0.642104	−	0.766617i	$-0.278062\pi$
$588$	−86.4249	−	100.247i	−0.146981	−	0.170488i
$589$	114.991			0.195230
$590$	−86.5104	−	232.835i	−0.146628	−	0.394636i
$591$		−	129.008i		−	0.218288i
$592$	84.0071	−	564.169i	0.141904	−	0.952987i
$593$	−704.088			−1.18733			−0.593666	−	0.804711i	$-0.702320\pi$
$593$	−704.088			−1.18733			−0.593666	+	0.804711i	$0.702320\pi$
$594$	−107.551	+	39.9606i	−0.181061	+	0.0672738i
$595$			298.497i			0.501675i
$596$	−383.897	+	330.965i	−0.644122	+	0.555311i
$597$	308.351			0.516501
$598$	−262.715	−	707.075i	−0.439323	−	1.18240i
$599$			376.098i			0.627876i	0.949444	+	0.313938i	$0.101648\pi$
$599$			376.098i			0.627876i	−0.949444	+	0.313938i	$0.898352\pi$
$600$	−60.6820	−	33.4320i	−0.101137	−	0.0557200i
$601$	430.191			0.715791			0.357896	−	0.933762i	$-0.383494\pi$
$601$	430.191			0.715791			0.357896	+	0.933762i	$0.383494\pi$
$602$	717.844	−	266.716i	1.19243	−	0.443051i
$603$		−	313.480i		−	0.519868i
$604$	−178.756	−	207.344i	−0.295953	−	0.343285i
$605$	1.98684			0.00328404
$606$	−35.4824	−	95.4977i	−0.0585518	−	0.157587i
$607$			93.4019i			0.153875i	0.997036	+	0.0769373i	$0.0245141\pi$
$607$			93.4019i			0.153875i	−0.997036	+	0.0769373i	$0.975486\pi$
$608$	744.436	−	157.058i	1.22440	−	0.258319i
$609$	−244.075			−0.400781
$610$	344.765	−	128.098i	0.565189	−	0.209997i
$611$		−	384.944i		−	0.630024i
$612$	221.897	−	191.302i	0.362576	−	0.312585i
$613$	−156.506			−0.255312			−0.127656	−	0.991818i	$-0.540745\pi$
$613$	−156.506			−0.255312			−0.127656	+	0.991818i	$0.540745\pi$
$614$	69.7113	+	187.622i	0.113536	+	0.305573i
$615$		−	36.0346i		−	0.0585929i
$616$	−233.033	+	422.976i	−0.378301	+	0.686649i
$617$	−553.493			−0.897072			−0.448536	−	0.893765i	$-0.648054\pi$
$617$	−553.493			−0.897072			−0.448536	+	0.893765i	$0.648054\pi$
$618$	−91.5334	+	34.0094i	−0.148112	+	0.0550314i
$619$			14.4398i			0.0233276i	0.999932	+	0.0116638i	$0.00371278\pi$
$619$			14.4398i			0.0233276i	−0.999932	+	0.0116638i	$0.996287\pi$
$620$	28.2463	+	32.7637i	0.0455586	+	0.0528447i
$621$	193.570			0.311707
$622$	281.546	+	757.756i	0.452646	+	1.21826i
$623$			632.564i			1.01535i
$624$	−277.510	−	41.3224i	−0.444728	−	0.0662219i
$625$	25.0000			0.0400000
$626$	−241.056	+	89.5651i	−0.385074	+	0.143075i
$627$			454.649i			0.725117i
$628$	77.4893	−	66.8051i	0.123391	−	0.106378i
$629$	−870.364			−1.38373
$630$	25.5494	+	68.7638i	0.0405545	+	0.109149i
$631$			352.389i			0.558460i	0.960224	+	0.279230i	$0.0900793\pi$
$631$			352.389i			0.558460i	−0.960224	+	0.279230i	$0.909921\pi$
$632$	−345.977	−	190.612i	−0.547432	−	0.301601i
$633$	−321.976			−0.508650
$634$	161.102	−	59.8579i	0.254104	−	0.0944130i
$635$			293.608i			0.462375i
$636$	−252.324	−	292.678i	−0.396735	−	0.460185i
$637$	193.415			0.303634
$638$	−198.203	−	533.445i	−0.310662	−	0.836120i
$639$		−	230.241i		−	0.360315i
$640$	227.613	+	173.529i	0.355645	+	0.271139i
$641$	−545.742			−0.851391			−0.425696	−	0.904866i	$-0.639971\pi$
$641$	−545.742			−0.851391			−0.425696	+	0.904866i	$0.639971\pi$
$642$	−14.6352	+	5.43772i	−0.0227962	+	0.00846997i
$643$			757.447i			1.17799i	0.808137	+	0.588995i	$0.200476\pi$
$643$			757.447i			1.17799i	−0.808137	+	0.588995i	$0.799524\pi$
$644$	617.079	−	531.997i	0.958197	−	0.826082i
$645$	271.220			0.420496
$646$	−404.345	−	1088.26i	−0.625922	−	1.68461i
$647$		−	1161.36i		−	1.79500i	−0.441016	−	0.897499i	$-0.645382\pi$
$647$		−	1161.36i		−	1.79500i	0.441016	−	0.897499i	$-0.354618\pi$
$648$	34.7435	−	63.0626i	0.0536166	−	0.0973188i
$649$	−613.191			−0.944824
$650$	94.9029	−	35.2614i	0.146004	−	0.0542483i
$651$		−	45.8030i		−	0.0703579i
$652$	165.793	+	192.308i	0.254283	+	0.294950i
$653$	−621.231			−0.951348			−0.475674	−	0.879622i	$-0.657796\pi$
$653$	−621.231			−0.951348			−0.475674	+	0.879622i	$0.657796\pi$
$654$	−233.236	−	627.734i	−0.356630	−	0.959838i
$655$			169.390i			0.258610i
$656$	−21.9250	+	147.242i	−0.0334223	+	0.224455i
$657$	280.565			0.427039
$658$	389.755	−	144.814i	0.592333	−	0.220083i
$659$			736.047i			1.11692i	0.829533	+	0.558458i	$0.188607\pi$
$659$			736.047i			1.11692i	−0.829533	+	0.558458i	$0.811393\pi$
$660$	−129.541	+	111.680i	−0.196274	+	0.169212i
$661$	383.845			0.580704			0.290352	−	0.956920i	$-0.406228\pi$
$661$	383.845			0.580704			0.290352	+	0.956920i	$0.406228\pi$
$662$	−127.746	−	343.817i	−0.192970	−	0.519362i
$663$			428.125i			0.645739i
$664$	507.141	+	279.403i	0.763766	+	0.420788i
$665$	290.686			0.437121
$666$	−200.503	+	74.4974i	−0.301056	+	0.111858i
$667$			960.096i			1.43942i
$668$	32.3271	+	37.4972i	0.0483939	+	0.0561335i
$669$	351.128			0.524854
$670$	−162.758	−	438.050i	−0.242923	−	0.653805i
$671$		−	907.968i		−	1.35316i
$672$	−62.5592	−	296.523i	−0.0930940	−	0.441255i
$673$	984.464			1.46280			0.731400	−	0.681949i	$-0.238867\pi$
$673$	984.464			1.46280			0.731400	+	0.681949i	$0.238867\pi$
$674$	315.205	−	117.115i	0.467664	−	0.173761i
$675$			25.9808i			0.0384900i
$676$	−201.468	+	173.690i	−0.298030	+	0.256938i
$677$	673.154			0.994319			0.497160	−	0.867659i	$-0.334376\pi$
$677$	673.154			0.994319			0.497160	+	0.867659i	$0.334376\pi$
$678$	−91.1789	−	245.400i	−0.134482	−	0.361947i
$679$		−	398.918i		−	0.587507i
$680$	210.749	−	382.529i	0.309925	−	0.562542i
$681$	88.8037			0.130402
$682$	100.106	−	37.1945i	0.146783	−	0.0545374i
$683$			291.192i			0.426343i	0.977015	+	0.213171i	$0.0683793\pi$
$683$			291.192i			0.426343i	−0.977015	+	0.213171i	$0.931621\pi$
$684$	−186.296	−	216.090i	−0.272362	−	0.315921i
$685$	−149.353			−0.218034
$686$	259.387	+	698.117i	0.378115	+	1.01766i
$687$		−	583.798i		−	0.849778i
$688$	−1108.24	−	165.022i	−1.61081	−	0.239857i
$689$	564.689			0.819578
$690$	270.490	−	100.501i	0.392014	−	0.145654i
$691$		−	943.693i		−	1.36569i	−0.730563	−	0.682846i	$-0.760742\pi$
$691$		−	943.693i		−	1.36569i	0.730563	−	0.682846i	$-0.239258\pi$
$692$	179.874	−	155.073i	0.259933	−	0.224094i
$693$	181.095			0.261321
$694$	95.7193	+	257.620i	0.137924	+	0.371211i
$695$		−	85.2420i		−	0.122650i
$696$	312.787	+	172.326i	0.449406	+	0.247595i
$697$	227.156			0.325905
$698$	−25.2894	+	9.39633i	−0.0362312	+	0.0134618i
$699$			139.058i			0.198938i
$700$	71.4040	+	82.8237i	0.102006	+	0.118320i
$701$	885.681			1.26345			0.631727	−	0.775191i	$-0.282346\pi$
$701$	885.681			1.26345			0.631727	+	0.775191i	$0.282346\pi$
$702$	36.6447	+	98.6259i	0.0522004	+	0.140493i
$703$			847.588i			1.20567i
$704$	597.272	−	377.521i	0.848397	−	0.536251i
$705$	147.260			0.208879
$706$	456.596	−	169.649i	0.646737	−	0.240296i
$707$			160.801i			0.227441i
$708$	291.444	−	251.260i	0.411644	−	0.354887i
$709$	−286.183			−0.403644			−0.201822	−	0.979422i	$-0.564686\pi$
$709$	−286.183			−0.403644			−0.201822	+	0.979422i	$0.564686\pi$
$710$	−119.541	−	321.733i	−0.168367	−	0.453146i
$711$			148.129i			0.208339i
$712$	446.613	−	810.642i	0.627266	−	1.13854i
$713$	−180.171			−0.252694
$714$	−433.475	+	161.059i	−0.607108	+	0.225572i
$715$		−	249.935i		−	0.349559i
$716$	660.228	+	765.818i	0.922106	+	1.06958i
$717$	−572.976			−0.799129
$718$	−12.4803	−	33.5895i	−0.0173820	−	0.0467820i
$719$		−	666.163i		−	0.926513i	−0.886224	−	0.463257i	$-0.846681\pi$
$719$		−	666.163i		−	0.926513i	0.886224	−	0.463257i	$-0.153319\pi$
$720$	15.8078	−	106.161i	0.0219553	−	0.147446i
$721$	154.125			0.213766
$722$	−382.989	+	142.300i	−0.530455	+	0.197092i
$723$			623.389i			0.862226i
$724$	379.826	−	327.456i	0.524622	−	0.452287i
$725$	−128.863			−0.177742
$726$	1.07203	+	2.88528i	0.00147663	+	0.00397422i
$727$		−	856.270i		−	1.17781i	−0.808201	−	0.588907i	$-0.799559\pi$
$727$		−	856.270i		−	1.17781i	0.808201	−	0.588907i	$-0.200441\pi$
$728$	387.877	+	213.696i	0.532798	+	0.293538i
$729$	−27.0000			−0.0370370
$730$	392.054	−	145.668i	0.537060	−	0.199546i
$731$			1709.72i			2.33888i
$732$	372.047	+	431.549i	0.508261	+	0.589547i
$733$	−769.487			−1.04978			−0.524889	−	0.851171i	$-0.675893\pi$
$733$	−769.487			−1.04978			−0.524889	+	0.851171i	$0.675893\pi$
$734$	166.076	+	446.978i	0.226261	+	0.608961i
$735$			73.9905i			0.100667i
$736$	−1166.41	+	246.083i	−1.58479	+	0.334352i
$737$	−1153.64			−1.56532
$738$	52.3293	−	19.4431i	0.0709069	−	0.0263456i
$739$		−	1156.70i		−	1.56522i	−0.622511	−	0.782611i	$-0.713887\pi$
$739$		−	1156.70i		−	1.56522i	0.622511	−	0.782611i	$-0.286113\pi$
$740$	−241.499	+	208.202i	−0.326350	+	0.281354i
$741$	416.922			0.562647
$742$	212.433	+	571.746i	0.286298	+	0.770547i
$743$			426.794i			0.574421i	0.957868	+	0.287210i	$0.0927278\pi$
$743$			426.794i			0.574421i	−0.957868	+	0.287210i	$0.907272\pi$
$744$	−32.3386	+	58.6973i	−0.0434658	+	0.0788942i
$745$	283.348			0.380332
$746$	−339.842	+	126.269i	−0.455552	+	0.169261i
$747$		−	217.130i		−	0.290670i
$748$	−704.011	−	816.603i	−0.941191	−	1.09172i
$749$	24.6429			0.0329011
$750$	13.4892	+	36.3049i	0.0179855	+	0.0484065i
$751$		−	1222.03i		−	1.62721i	−0.581420	−	0.813604i	$-0.697503\pi$
$751$		−	1222.03i		−	1.62721i	0.581420	−	0.813604i	$-0.302497\pi$
$752$	−601.722	−	89.5990i	−0.800162	−	0.119148i
$753$	−540.768			−0.718152
$754$	−489.179	+	181.756i	−0.648779	+	0.241055i
$755$			153.037i			0.202698i
$756$	−86.0729	+	74.2053i	−0.113853	+	0.0981551i
$757$	−1312.95			−1.73442			−0.867209	−	0.497945i	$-0.834088\pi$
$757$	−1312.95			−1.73442			−0.867209	+	0.497945i	$0.834088\pi$
$758$	213.296	+	574.067i	0.281393	+	0.757344i
$759$		−	712.358i		−	0.938548i
$760$	−372.519	−	205.234i	−0.490156	−	0.270045i
$761$	−189.584			−0.249124			−0.124562	−	0.992212i	$-0.539753\pi$
$761$	−189.584			−0.249124			−0.124562	+	0.992212i	$0.539753\pi$
$762$	−426.376	+	158.421i	−0.559549	+	0.207902i
$763$			1056.99i			1.38531i
$764$	−254.561	−	295.273i	−0.333195	−	0.386483i
$765$	−163.778			−0.214089
$766$	−100.326	−	270.019i	−0.130974	−	0.352505i
$767$			562.308i			0.733127i
$768$	−129.185	+	424.169i	−0.168210	+	0.552303i
$769$	254.995			0.331594			0.165797	−	0.986160i	$-0.446980\pi$
$769$	254.995			0.331594			0.165797	+	0.986160i	$0.446980\pi$
$770$	253.058	−	94.0243i	0.328647	−	0.122109i
$771$		−	139.013i		−	0.180302i
$772$	−1037.25	+	894.235i	−1.34359	+	1.15834i
$773$	23.2536			0.0300823			0.0150411	−	0.999887i	$-0.495212\pi$
$773$	23.2536			0.0300823			0.0150411	+	0.999887i	$0.495212\pi$
$774$	146.341	+	393.864i	0.189071	+	0.508869i
$775$		−	24.1824i		−	0.0312030i
$776$	−281.650	+	511.220i	−0.362951	+	0.658788i
$777$	337.611			0.434506
$778$	26.2654	−	9.75897i	0.0337602	−	0.0125437i
$779$		−	221.212i		−	0.283969i
$780$	102.413	+	118.792i	0.131298	+	0.152297i
$781$	−847.312			−1.08491
$782$	633.541	+	1705.12i	0.810155	+	2.18046i
$783$		−	133.919i		−	0.171033i
$784$	45.0189	−	302.335i	0.0574221	−	0.385631i
$785$	−57.1935			−0.0728580
$786$	−245.987	+	91.3969i	−0.312960	+	0.116281i
$787$			220.593i			0.280296i	0.990131	+	0.140148i	$0.0447579\pi$
$787$			220.593i			0.280296i	−0.990131	+	0.140148i	$0.955242\pi$
$788$	225.651	−	194.538i	0.286359	−	0.246876i
$789$	845.183			1.07121
$790$	76.9081	+	206.991i	0.0973520	+	0.262014i
$791$			413.209i			0.522388i
$792$	−232.077	−	127.860i	−0.293026	−	0.161439i
$793$	−832.625			−1.04997
$794$	73.3194	−	27.2420i	0.0923418	−	0.0343098i
$795$			216.020i			0.271724i
$796$	464.979	+	539.343i	0.584144	+	0.677566i
$797$	1010.38			1.26773			0.633867	−	0.773442i	$-0.281467\pi$
$797$	1010.38			1.26773			0.633867	+	0.773442i	$0.281467\pi$
$798$	156.844	+	422.132i	0.196546	+	0.528987i
$799$			928.298i			1.16183i
$800$	−33.0290	−	156.554i	−0.0412863	−	0.195692i
$801$	−347.073			−0.433300
$802$	−226.974	+	84.3327i	−0.283010	+	0.105153i
$803$		−	1032.51i		−	1.28581i
$804$	548.314	−	472.713i	0.681983	−	0.587952i
$805$	−455.455			−0.565783
$806$	−34.1081	−	91.7990i	−0.0423178	−	0.113894i
$807$			536.162i			0.664389i
$808$	113.531	−	206.069i	0.140509	−	0.255036i
$809$	1410.37			1.74335			0.871674	−	0.490086i	$-0.163035\pi$
$809$	1410.37			1.74335			0.871674	+	0.490086i	$0.163035\pi$
$810$	−37.7291	+	14.0183i	−0.0465792	+	0.0173066i
$811$		−	950.157i		−	1.17159i	−0.810460	−	0.585793i	$-0.800783\pi$
$811$		−	950.157i		−	1.17159i	0.810460	−	0.585793i	$-0.199217\pi$
$812$	−368.054	−	426.917i	−0.453269	−	0.525760i
$813$	−84.8173			−0.104326
$814$	274.158	+	737.873i	0.336804	+	0.906478i
$815$		−	141.939i		−	0.174158i
$816$	669.219	+	99.6496i	0.820121	+	0.122120i
$817$	1664.98			2.03792
$818$	−1015.74	+	377.402i	−1.24174	+	0.461372i
$819$		−	166.068i		−	0.202769i
$820$	63.0288	−	54.3385i	0.0768644	−	0.0662664i
$821$	77.3347			0.0941957			0.0470979	−	0.998890i	$-0.485003\pi$
$821$	77.3347			0.0941957			0.0470979	+	0.998890i	$0.485003\pi$
$822$	−80.5858	−	216.890i	−0.0980363	−	0.263856i
$823$		−	1260.16i		−	1.53118i	−0.643328	−	0.765591i	$-0.722447\pi$
$823$		−	1260.16i		−	1.53118i	0.643328	−	0.765591i	$-0.277553\pi$
$824$	−197.514	−	108.818i	−0.239702	−	0.132061i
$825$	95.6119			0.115893
$826$	−569.335	+	211.538i	−0.689268	+	0.256099i
$827$		−	438.047i		−	0.529681i	−0.964292	−	0.264841i	$-0.914681\pi$
$827$		−	438.047i		−	0.529681i	0.964292	−	0.264841i	$-0.0853194\pi$
$828$	291.894	+	338.577i	0.352529	+	0.408909i
$829$	361.388			0.435933			0.217966	−	0.975956i	$-0.430058\pi$
$829$	361.388			0.435933			0.217966	+	0.975956i	$0.430058\pi$
$830$	−112.734	−	303.413i	−0.135824	−	0.365557i
$831$			345.793i			0.416117i
$832$	−346.194	−	547.710i	−0.416098	−	0.658305i
$833$	−466.423			−0.559931
$834$	123.788	−	45.9937i	0.148427	−	0.0551483i
$835$		−	27.6760i		−	0.0331450i
$836$	−795.234	+	685.588i	−0.951237	+	0.820082i
$837$	25.1310			0.0300251
$838$	479.123	+	1289.52i	0.571746	+	1.53880i
$839$		−	785.017i		−	0.935658i	−0.883819	−	0.467829i	$-0.845036\pi$
$839$		−	785.017i		−	0.935658i	0.883819	−	0.467829i	$-0.154964\pi$
$840$	−81.7489	+	148.381i	−0.0973201	+	0.176645i
$841$	−176.771			−0.210192
$842$	−851.890	+	316.521i	−1.01175	+	0.375916i
$843$		−	105.932i		−	0.125661i
$844$	−485.524	−	563.173i	−0.575265	−	0.667267i
$845$	148.700			0.175977
$846$	79.4563	+	213.849i	0.0939199	+	0.252777i
$847$		−	4.85829i		−	0.00573588i
$848$	131.436	−	882.688i	0.154995	−	1.04091i
$849$	−749.123			−0.882359
$850$	−228.859	+	85.0332i	−0.269246	+	0.100039i
$851$		−	1328.03i		−	1.56055i
$852$	402.719	−	347.193i	0.472675	−	0.407503i
$853$	1113.79			1.30573			0.652865	−	0.757474i	$-0.273567\pi$
$853$	1113.79			1.30573			0.652865	+	0.757474i	$0.273567\pi$
$854$	−313.230	−	843.030i	−0.366780	−	0.987155i
$855$			159.492i			0.186541i
$856$	−31.5803	−	17.3988i	−0.0368929	−	0.0203257i
$857$	−306.591			−0.357749			−0.178875	−	0.983872i	$-0.557246\pi$
$857$	−306.591			−0.357749			−0.178875	+	0.983872i	$0.557246\pi$
$858$	362.954	−	134.856i	0.423023	−	0.157175i
$859$		−	204.542i		−	0.238116i	−0.992887	−	0.119058i	$-0.962013\pi$
$859$		−	204.542i		−	0.238116i	0.992887	−	0.119058i	$-0.0379875\pi$
$860$	408.987	+	474.396i	0.475566	+	0.551623i
$861$	−88.1130			−0.102338
$862$	324.706	+	873.918i	0.376689	+	1.01383i
$863$			654.384i			0.758266i	0.925342	+	0.379133i	$0.123778\pi$
$863$			654.384i			0.758266i	−0.925342	+	0.379133i	$0.876222\pi$
$864$	162.695	−	34.3248i	0.188305	−	0.0397277i
$865$	−132.762			−0.153482
$866$	856.949	−	318.401i	0.989549	−	0.367669i
$867$		−	531.866i		−	0.613456i
$868$	80.1149	−	69.0687i	0.0922982	−	0.0795722i
$869$	545.129			0.627306
$870$	−69.5302	−	187.134i	−0.0799198	−	0.215097i
$871$			1057.91i			1.21459i
$872$	746.272	−	1354.55i	0.855817	−	1.55338i
$873$	218.877			0.250718
$874$	1660.50	−	616.963i	1.89989	−	0.705907i
$875$		−	61.1307i		−	0.0698637i
$876$	423.078	+	490.741i	0.482966	+	0.560206i
$877$	−604.453			−0.689228			−0.344614	−	0.938744i	$-0.611990\pi$
$877$	−604.453			−0.689228			−0.344614	+	0.938744i	$0.611990\pi$
$878$	−541.565	−	1457.58i	−0.616817	−	1.66011i
$879$			490.575i			0.558106i
$880$	−390.683	−	58.1744i	−0.443958	−	0.0661072i
$881$	1436.81			1.63089			0.815445	−	0.578834i	$-0.196492\pi$
$881$	1436.81			1.63089			0.815445	+	0.578834i	$0.196492\pi$
$882$	−107.449	+	39.9227i	−0.121824	+	0.0452639i
$883$		−	120.993i		−	0.137025i	−0.997650	−	0.0685123i	$-0.978175\pi$
$883$		−	120.993i		−	0.137025i	0.997650	−	0.0685123i	$-0.0218252\pi$
$884$	−748.841	+	645.592i	−0.847105	+	0.730307i
$885$	−215.110			−0.243062
$886$	−172.392	−	463.977i	−0.194573	−	0.523676i
$887$			286.448i			0.322941i	0.986878	+	0.161470i	$0.0516236\pi$
$887$			286.448i			0.322941i	−0.986878	+	0.161470i	$0.948376\pi$
$888$	−432.654	−	238.365i	−0.487223	−	0.268429i
$889$	717.940			0.807582
$890$	−484.991	+	180.200i	−0.544934	+	0.202471i
$891$			99.3628i			0.111518i
$892$	529.483	+	614.164i	0.593591	+	0.688524i
$893$	904.007			1.01233
$894$	152.885	+	411.476i	0.171012	+	0.460264i
$895$		−	565.237i		−	0.631550i
$896$	424.318	−	556.566i	0.473569	−	0.621168i
$897$	−653.246			−0.728256
$898$	773.360	−	287.344i	0.861203	−	0.319982i
$899$			124.649i			0.138652i
$900$	−45.4434	+	39.1777i	−0.0504927	+	0.0435308i
$901$	−1361.75			−1.51138
$902$	−71.5525	−	192.577i	−0.0793265	−	0.213500i
$903$		−	663.195i		−	0.734436i
$904$	291.740	−	529.534i	0.322721	−	0.585768i
$905$	−280.343			−0.309771
$906$	−222.240	+	82.5736i	−0.245298	+	0.0911409i
$907$		−	234.706i		−	0.258772i	−0.991594	−	0.129386i	$-0.958699\pi$
$907$		−	234.706i		−	0.258772i	0.991594	−	0.129386i	$-0.0413006\pi$
$908$	133.912	+	155.328i	0.147480	+	0.171066i
$909$	−88.2276			−0.0970601
$910$	−86.2221	−	232.059i	−0.0947496	−	0.255010i
$911$		−	491.244i		−	0.539236i	−0.962967	−	0.269618i	$-0.913103\pi$
$911$		−	491.244i		−	0.539236i	0.962967	−	0.269618i	$-0.0868974\pi$
$912$	97.0420	−	651.707i	0.106406	−	0.714591i
$913$	−799.063			−0.875206
$914$	−1397.46	+	519.229i	−1.52895	+	0.568084i
$915$		−	318.519i		−	0.348108i
$916$	1021.13	−	880.339i	1.11477	−	0.961069i
$917$	414.197			0.451687
$918$	−88.3691	−	237.838i	−0.0962627	−	0.259082i
$919$			356.091i			0.387477i	0.981053	+	0.193738i	$0.0620613\pi$
$919$			356.091i			0.387477i	−0.981053	+	0.193738i	$0.937939\pi$
$920$	583.674	+	321.568i	0.634428	+	0.349530i
$921$	173.338			0.188207
$922$	153.010	−	56.8511i	0.165954	−	0.0616607i
$923$			777.002i			0.841822i
$924$	273.083	+	316.757i	0.295545	+	0.342811i
$925$	178.246			0.192699
$926$	−203.573	−	547.899i	−0.219841	−	0.591684i
$927$			84.5651i			0.0912244i
$928$	170.249	+	806.961i	0.183458	+	0.869570i
$929$	−916.019			−0.986027			−0.493014	−	0.870022i	$-0.664105\pi$
$929$	−916.019			−0.986027			−0.493014	+	0.870022i	$0.664105\pi$
$930$	35.1175	−	13.0480i	0.0377607	−	0.0140301i
$931$			454.217i			0.487881i
$932$	−243.229	+	209.693i	−0.260975	+	0.224992i
$933$	700.069			0.750342
$934$	35.8154	+	96.3939i	0.0383462	+	0.103205i
$935$			602.721i			0.644621i
$936$	−117.250	+	212.819i	−0.125267	+	0.227371i
$937$	143.818			0.153488			0.0767440	−	0.997051i	$-0.475548\pi$
$937$	143.818			0.153488			0.0767440	+	0.997051i	$0.475548\pi$
$938$	−1071.13	+	397.981i	−1.14193	+	0.424287i
$939$			222.705i			0.237173i
$940$	222.060	+	257.574i	0.236234	+	0.274015i
$941$	−1488.04			−1.58133			−0.790667	−	0.612246i	$-0.790266\pi$
$941$	−1488.04			−1.58133			−0.790667	+	0.612246i	$0.790266\pi$
$942$	−30.8597	−	83.0561i	−0.0327597	−	0.0881699i
$943$			346.602i			0.367552i
$944$	878.966	+	130.882i	0.931108	+	0.138646i
$945$	63.5289			0.0672264
$946$	1449.46	−	538.551i	1.53220	−	0.569292i
$947$			1095.51i			1.15682i	0.815745	+	0.578411i	$0.196327\pi$
$947$			1095.51i			1.15682i	−0.815745	+	0.578411i	$0.803673\pi$
$948$	−259.095	+	223.371i	−0.273307	+	0.235623i
$949$	−946.829			−0.997713
$950$	82.8081	+	222.871i	0.0871664	+	0.234601i
$951$		−	148.838i		−	0.156506i
$952$	−935.370	−	515.331i	−0.982532	−	0.541314i
$953$	1277.86			1.34089			0.670443	−	0.741961i	$-0.266104\pi$
$953$	1277.86			1.34089			0.670443	+	0.741961i	$0.266104\pi$
$954$	−313.704	+	116.557i	−0.328830	+	0.122177i
$955$			217.936i			0.228205i
$956$	−864.020	−	1002.20i	−0.903786	−	1.04833i
$957$	−492.834			−0.514978
$958$	−85.3953	−	229.834i	−0.0891392	−	0.239910i
$959$			365.202i			0.380816i
$960$	209.525	−	132.436i	0.218255	−	0.137954i
$961$	937.609			0.975659
$962$	676.644	−	251.409i	0.703372	−	0.261339i
$963$			13.5210i			0.0140405i
$964$	−1090.38	+	940.041i	−1.13110	+	0.975146i
$965$	765.576			0.793343
$966$	−245.748	−	661.410i	−0.254398	−	0.684689i
$967$			237.958i			0.246079i	0.992402	+	0.123039i	$0.0392641\pi$
$967$			237.958i			0.246079i	−0.992402	+	0.123039i	$0.960736\pi$
$968$	−3.43013	+	6.22598i	−0.00354352	+	0.00643180i
$969$	−1005.41			−1.03758
$970$	305.853	−	113.640i	0.315312	−	0.117155i
$971$			1602.10i			1.64995i	0.565169	+	0.824975i	$0.308811\pi$
$971$			1602.10i			1.64995i	−0.565169	+	0.824975i	$0.691189\pi$
$972$	−40.7147	−	47.2262i	−0.0418876	−	0.0485866i
$973$	−208.436			−0.214220
$974$	−45.9643	−	123.709i	−0.0471912	−	0.127011i
$975$		−	87.6780i		−	0.0899262i
$976$	−193.800	+	1301.51i	−0.198566	+	1.33351i
$977$	918.977			0.940611			0.470305	−	0.882504i	$-0.344144\pi$
$977$	918.977			0.940611			0.470305	+	0.882504i	$0.344144\pi$
$978$	206.123	−	76.5855i	0.210760	−	0.0783083i
$979$			1277.27i			1.30466i
$980$	−129.418	+	111.574i	−0.132059	+	0.113851i
$981$	−579.945			−0.591178
$982$	−251.578	−	677.100i	−0.256189	−	0.689511i
$983$		−	1162.30i		−	1.18240i	−0.806525	−	0.591200i	$-0.798654\pi$
$983$		−	1162.30i		−	1.18240i	0.806525	−	0.591200i	$-0.201346\pi$
$984$	112.918	+	62.2109i	0.114754	+	0.0632225i
$985$	−166.549			−0.169085
$986$	1179.66	−	438.306i	1.19641	−	0.444530i
$987$		−	360.083i		−	0.364826i
$988$	628.698	+	729.245i	0.636334	+	0.738103i
$989$	−2608.75			−2.63776
$990$	51.5889	+	138.847i	0.0521100	+	0.140250i
$991$			491.614i			0.496079i	0.968750	+	0.248040i	$0.0797863\pi$
$991$			491.614i			0.496079i	−0.968750	+	0.248040i	$0.920214\pi$
$992$	−151.434	+	31.9488i	−0.152655	+	0.0322064i
$993$	−317.643			−0.319882
$994$	−786.712	+	292.305i	−0.791461	+	0.294069i
$995$		−	398.080i		−	0.400080i
$996$	379.787	−	327.422i	0.381312	−	0.328737i
$997$	−1262.51			−1.26630			−0.633152	−	0.774027i	$-0.718239\pi$
$997$	−1262.51			−1.26630			−0.633152	+	0.774027i	$0.718239\pi$
$998$	495.363	+	1333.22i	0.496355	+	1.33590i
$999$			185.239i			0.185425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.c.a.31.7	✓	8
3.2	odd	2		180.3.c.b.91.2		8
4.3	odd	2	inner	60.3.c.a.31.8	yes	8
5.2	odd	4		300.3.f.b.199.12		16
5.3	odd	4		300.3.f.b.199.5		16
5.4	even	2		300.3.c.d.151.2		8
8.3	odd	2		960.3.e.c.511.3		8
8.5	even	2		960.3.e.c.511.8		8
12.11	even	2		180.3.c.b.91.1		8
15.2	even	4		900.3.f.f.199.5		16
15.8	even	4		900.3.f.f.199.12		16
15.14	odd	2		900.3.c.u.451.7		8
20.3	even	4		300.3.f.b.199.11		16
20.7	even	4		300.3.f.b.199.6		16
20.19	odd	2		300.3.c.d.151.1		8
24.5	odd	2		2880.3.e.j.2431.3		8
24.11	even	2		2880.3.e.j.2431.2		8
60.23	odd	4		900.3.f.f.199.6		16
60.47	odd	4		900.3.f.f.199.11		16
60.59	even	2		900.3.c.u.451.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.7	✓	8	1.1	even	1	trivial
60.3.c.a.31.8	yes	8	4.3	odd	2	inner
180.3.c.b.91.1		8	12.11	even	2
180.3.c.b.91.2		8	3.2	odd	2
300.3.c.d.151.1		8	20.19	odd	2
300.3.c.d.151.2		8	5.4	even	2
300.3.f.b.199.5		16	5.3	odd	4
300.3.f.b.199.6		16	20.7	even	4
300.3.f.b.199.11		16	20.3	even	4
300.3.f.b.199.12		16	5.2	odd	4
900.3.c.u.451.7		8	15.14	odd	2
900.3.c.u.451.8		8	60.59	even	2
900.3.f.f.199.5		16	15.2	even	4
900.3.f.f.199.6		16	60.23	odd	4
900.3.f.f.199.11		16	60.47	odd	4
900.3.f.f.199.12		16	15.8	even	4
960.3.e.c.511.3		8	8.3	odd	2
960.3.e.c.511.8		8	8.5	even	2
2880.3.e.j.2431.2		8	24.11	even	2
2880.3.e.j.2431.3		8	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 - 2.61185i) q^{4} -2.23607 q^{5} +(-1.20651 - 3.24721i) q^{6} +5.46770i q^{7} +(3.86039 - 7.00695i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 - 2.61185i) q^{4} -2.23607 q^{5} +(-1.20651 - 3.24721i) q^{6} +5.46770i q^{7} +(3.86039 - 7.00695i) q^{8} -3.00000 q^{9} +(-4.19212 + 1.55759i) q^{10} +11.0403i q^{11} +(-4.52386 - 5.24735i) q^{12} +10.1242 q^{13} +(3.80867 + 10.2507i) q^{14} +3.87298i q^{15} +(2.35649 - 15.8255i) q^{16} -24.4146 q^{17} +(-5.62432 + 2.08973i) q^{18} +23.7757i q^{19} +(-6.77431 + 5.84027i) q^{20} +9.47033 q^{21} +(7.69043 + 20.6981i) q^{22} -37.2526i q^{23} +(-12.1364 - 6.68640i) q^{24} +5.00000 q^{25} +(18.9806 - 7.05227i) q^{26} +5.19615i q^{27} +(14.2808 + 16.5647i) q^{28} -25.7726 q^{29} +(2.69783 + 7.26097i) q^{30} -4.83647i q^{31} +(-6.60580 - 31.3108i) q^{32} +19.1224 q^{33} +(-45.7719 + 17.0066i) q^{34} -12.2261i q^{35} +(-9.08868 + 7.83555i) q^{36} +35.6493 q^{37} +(16.5616 + 44.5741i) q^{38} -17.5356i q^{39} +(-8.63210 + 15.6680i) q^{40} -9.30410 q^{41} +(17.7547 - 6.59682i) q^{42} -70.0287i q^{43} +(28.8356 + 33.4473i) q^{44} +6.70820 q^{45} +(-25.9493 - 69.8401i) q^{46} -38.0223i q^{47} +(-27.4106 - 4.08156i) q^{48} +19.1043 q^{49} +(9.37387 - 3.48288i) q^{50} +42.2873i q^{51} +(30.6718 - 26.4428i) q^{52} +55.7762 q^{53} +(3.61952 + 9.74162i) q^{54} -24.6869i q^{55} +(38.3119 + 21.1075i) q^{56} +41.1808 q^{57} +(-48.3179 + 17.9526i) q^{58} +55.5411i q^{59} +(10.1156 + 11.7334i) q^{60} -82.2412 q^{61} +(-3.36897 - 9.06729i) q^{62} -16.4031i q^{63} +(-34.1947 - 54.0992i) q^{64} -22.6384 q^{65} +(35.8502 - 13.3202i) q^{66} +104.493i q^{67} +(-73.9656 + 63.7673i) q^{68} -64.5233 q^{69} +(-8.51645 - 22.9213i) q^{70} +76.7471i q^{71} +(-11.5812 + 21.0209i) q^{72} -93.5215 q^{73} +(66.8344 - 24.8325i) q^{74} -8.66025i q^{75} +(62.0986 + 72.0300i) q^{76} -60.3651 q^{77} +(-12.2149 - 32.8753i) q^{78} -49.3762i q^{79} +(-5.26927 + 35.3869i) q^{80} +9.00000 q^{81} +(-17.4431 + 6.48102i) q^{82} +72.3768i q^{83} +(28.6910 - 24.7351i) q^{84} +54.5927 q^{85} +(-48.7804 - 131.288i) q^{86} +44.6395i q^{87} +(77.3589 + 42.6199i) q^{88} +115.691 q^{89} +(12.5764 - 4.67278i) q^{90} +55.3560i q^{91} +(-97.2980 - 112.859i) q^{92} -8.37701 q^{93} +(-26.4854 - 71.2832i) q^{94} -53.1641i q^{95} +(-54.2318 + 11.4416i) q^{96} -72.9589 q^{97} +(35.8162 - 13.3076i) 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

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