LMFDB - Embedded newform 15.9.c.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,9,Mod(11,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	15.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:	$6.11067915092$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 433 x^{8} - 2220 x^{7} + 49747 x^{6} + 744964 x^{5} + 4580249 x^{4} + 16418988 x^{3} + \cdots + 53656344 $ x^10 - 4x^9 - 433x^8 - 2220x^7 + 49747x^6 + 744964x^5 + 4580249x^4 + 16418988x^3 + 38943804x^2 + 57910464*x + 53656344
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{10}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.6
Root			$-6.39402 + 2.23607i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.9.c.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.97572i q^{2} +(-29.8424 + 75.3023i) q^{3} +192.388 q^{4} +279.508i q^{5} +(-600.590 - 238.014i) q^{6} -3211.86 q^{7} +3576.22i q^{8} +(-4779.87 - 4494.40i) q^{9} +O(q^{10})$	\(q+7.97572i q^{2} +(-29.8424 + 75.3023i) q^{3} +192.388 q^{4} +279.508i q^{5} +(-600.590 - 238.014i) q^{6} -3211.86 q^{7} +3576.22i q^{8} +(-4779.87 - 4494.40i) q^{9} -2229.28 q^{10} +6481.82i q^{11} +(-5741.31 + 14487.3i) q^{12} -10510.3 q^{13} -25616.9i q^{14} +(-21047.6 - 8341.19i) q^{15} +20728.4 q^{16} +57738.3i q^{17} +(35846.0 - 38122.9i) q^{18} +228667. q^{19} +53774.1i q^{20} +(95849.5 - 241860. i) q^{21} -51697.1 q^{22} +113904. i q^{23} +(-269297. - 106723. i) q^{24} -78125.0 q^{25} -83827.4i q^{26} +(481081. - 225811. i) q^{27} -617923. q^{28} +1.11666e6i q^{29} +(66527.0 - 167870. i) q^{30} -304758. q^{31} +1.08084e6i q^{32} +(-488096. - 193433. i) q^{33} -460504. q^{34} -897742. i q^{35} +(-919589. - 864668. i) q^{36} +630294. q^{37} +1.82379e6i q^{38} +(313653. - 791452. i) q^{39} -999583. q^{40} -4.62696e6i q^{41} +(1.92901e6 + 764469. i) q^{42} +5.44386e6 q^{43} +1.24702e6i q^{44} +(1.25622e6 - 1.33601e6i) q^{45} -908469. q^{46} +6.69692e6i q^{47} +(-618586. + 1.56090e6i) q^{48} +4.55125e6 q^{49} -623103. i q^{50} +(-4.34782e6 - 1.72305e6i) q^{51} -2.02206e6 q^{52} -1.25196e7i q^{53} +(1.80101e6 + 3.83696e6i) q^{54} -1.81172e6 q^{55} -1.14863e7i q^{56} +(-6.82398e6 + 1.72192e7i) q^{57} -8.90615e6 q^{58} +5.55982e6i q^{59} +(-4.04931e6 - 1.60475e6i) q^{60} -1.31704e7 q^{61} -2.43067e6i q^{62} +(1.53523e7 + 1.44354e7i) q^{63} -3.31396e6 q^{64} -2.93773e6i q^{65} +(1.54276e6 - 3.89291e6i) q^{66} +1.70044e7 q^{67} +1.11081e7i q^{68} +(-8.57726e6 - 3.39918e6i) q^{69} +7.16014e6 q^{70} -1.08797e7i q^{71} +(1.60729e7 - 1.70938e7i) q^{72} -2.67184e7 q^{73} +5.02705e6i q^{74} +(2.33143e6 - 5.88299e6i) q^{75} +4.39928e7 q^{76} -2.08187e7i q^{77} +(6.31239e6 + 2.50161e6i) q^{78} -3.07855e6 q^{79} +5.79377e6i q^{80} +(2.64753e6 + 4.29652e7i) q^{81} +3.69033e7 q^{82} -2.32739e7i q^{83} +(1.84403e7 - 4.65310e7i) q^{84} -1.61383e7 q^{85} +4.34187e7i q^{86} +(-8.40869e7 - 3.33237e7i) q^{87} -2.31804e7 q^{88} +3.21685e7i q^{89} +(1.06557e7 + 1.00193e7i) q^{90} +3.37577e7 q^{91} +2.19138e7i q^{92} +(9.09471e6 - 2.29490e7i) q^{93} -5.34128e7 q^{94} +6.39145e7i q^{95} +(-8.13894e7 - 3.22547e7i) q^{96} -9.03610e7 q^{97} +3.62994e7i q^{98} +(2.91319e7 - 3.09822e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9}+O(q^{10}) $ 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9 - 8750 * q^10 - 3812 * q^12 - 55464 * q^13 - 21250 * q^15 + 280386 * q^16 - 419800 * q^18 - 231516 * q^19 + 289572 * q^21 + 1129940 * q^22 + 1136334 * q^24 - 781250 * q^25 - 335512 * q^27 - 3340724 * q^28 - 965000 * q^30 + 881620 * q^31 + 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 + 4672616 * q^37 + 1826792 * q^39 + 2913750 * q^40 - 5392860 * q^42 + 7731336 * q^43 - 2142500 * q^45 - 25424604 * q^46 + 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 + 21064016 * q^52 - 7979798 * q^54 - 4377500 * q^55 - 2856304 * q^57 - 4351100 * q^58 + 23016250 * q^60 + 22417020 * q^61 + 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 - 46646024 * q^67 + 33562632 * q^69 - 62992500 * q^70 + 54175560 * q^72 - 129964884 * q^73 + 8750000 * q^75 + 198922436 * q^76 + 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 + 202877560 * q^82 - 197346768 * q^84 - 110682500 * q^85 - 168322540 * q^87 - 484775700 * q^88 + 171878750 * q^90 + 444288464 * q^91 + 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 - 258825724 * q^97 - 33965200 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$			7.97572i			0.498482i	0.968441	+	0.249241i	$0.0801812\pi$
$2$			7.97572i			0.498482i	−0.968441	+	0.249241i	$0.919819\pi$
$3$	−29.8424	+	75.3023i	−0.368424	+	0.929658i
$3$	−29.8424	+	75.3023i	−0.368424	+	0.929658i
$4$	192.388			0.751515
$5$			279.508i			0.447214i
$5$			279.508i			0.447214i
$6$	−600.590	−	238.014i	−0.463418	−	0.183653i
$7$	−3211.86			−1.33772			−0.668859	−	0.743389i	$-0.733217\pi$
$7$	−3211.86			−1.33772			−0.668859	+	0.743389i	$0.733217\pi$
$8$			3576.22i			0.873099i
$9$	−4779.87	−	4494.40i	−0.728527	−	0.685017i
$10$	−2229.28			−0.222928
$11$			6481.82i			0.442717i	0.975193	+	0.221358i	$0.0710491\pi$
$11$			6481.82i			0.442717i	−0.975193	+	0.221358i	$0.928951\pi$
$12$	−5741.31	+	14487.3i	−0.276877	+	0.698652i
$13$	−10510.3			−0.367996			−0.183998	−	0.982927i	$-0.558904\pi$
$13$	−10510.3			−0.367996			−0.183998	+	0.982927i	$0.558904\pi$
$14$		−	25616.9i		−	0.666829i
$15$	−21047.6	−	8341.19i	−0.415756	−	0.164764i
$16$	20728.4			0.316291
$17$			57738.3i			0.691302i	0.938363	+	0.345651i	$0.112342\pi$
$17$			57738.3i			0.691302i	−0.938363	+	0.345651i	$0.887658\pi$
$18$	35846.0	−	38122.9i	0.341469	−	0.363158i
$19$	228667.			1.75465			0.877324	−	0.479899i	$-0.159327\pi$
$19$	228667.			1.75465			0.877324	+	0.479899i	$0.159327\pi$
$20$			53774.1i			0.336088i
$21$	95849.5	−	241860.i	0.492848	−	1.24362i
$22$	−51697.1			−0.220686
$23$			113904.i			0.407033i	0.979072	+	0.203516i	$0.0652370\pi$
$23$			113904.i			0.407033i	−0.979072	+	0.203516i	$0.934763\pi$
$24$	−269297.	−	106723.i	−0.811684	−	0.321671i
$25$	−78125.0			−0.200000
$26$		−	83827.4i		−	0.183439i
$27$	481081.	−	225811.i	0.905238	−	0.424904i
$28$	−617923.			−1.00532
$29$			1.11666e6i			1.57880i	0.613876	+	0.789402i	$0.289609\pi$
$29$			1.11666e6i			1.57880i	−0.613876	+	0.789402i	$0.710391\pi$
$30$	66527.0	−	167870.i	0.0821321	−	0.207247i
$31$	−304758.			−0.329996			−0.164998	−	0.986294i	$-0.552762\pi$
$31$	−304758.			−0.329996			−0.164998	+	0.986294i	$0.552762\pi$
$32$			1.08084e6i			1.03076i
$33$	−488096.	−	193433.i	−0.411575	−	0.163108i
$34$	−460504.			−0.344602
$35$		−	897742.i		−	0.598246i
$36$	−919589.	−	864668.i	−0.547499	−	0.514801i
$37$	630294.			0.336307			0.168154	−	0.985761i	$-0.446220\pi$
$37$	630294.			0.336307			0.168154	+	0.985761i	$0.446220\pi$
$38$			1.82379e6i			0.874661i
$39$	313653.	−	791452.i	0.135579	−	0.342110i
$40$	−999583.			−0.390462
$41$		−	4.62696e6i		−	1.63742i	−0.574207	−	0.818710i	$-0.694690\pi$
$41$		−	4.62696e6i		−	1.63742i	0.574207	−	0.818710i	$-0.305310\pi$
$42$	1.92901e6	+	764469.i	0.619922	+	0.245676i
$43$	5.44386e6			1.59233			0.796165	−	0.605080i	$-0.206859\pi$
$43$	5.44386e6			1.59233			0.796165	+	0.605080i	$0.206859\pi$
$44$			1.24702e6i			0.332709i
$45$	1.25622e6	−	1.33601e6i	0.306349	−	0.325807i
$46$	−908469.			−0.202898
$47$			6.69692e6i			1.37241i	0.727408	+	0.686205i	$0.240725\pi$
$47$			6.69692e6i			1.37241i	−0.727408	+	0.686205i	$0.759275\pi$
$48$	−618586.	+	1.56090e6i	−0.116529	+	0.294042i
$49$	4.55125e6			0.789489
$50$		−	623103.i		−	0.0996965i
$51$	−4.34782e6	−	1.72305e6i	−0.642675	−	0.254693i
$52$	−2.02206e6			−0.276554
$53$		−	1.25196e7i		−	1.58667i	−0.608786	−	0.793335i	$-0.708343\pi$
$53$		−	1.25196e7i		−	1.58667i	0.608786	−	0.793335i	$-0.291657\pi$
$54$	1.80101e6	+	3.83696e6i	0.211807	+	0.451245i
$55$	−1.81172e6			−0.197989
$56$		−	1.14863e7i		−	1.16796i
$57$	−6.82398e6	+	1.72192e7i	−0.646455	+	1.63122i
$58$	−8.90615e6			−0.787006
$59$			5.55982e6i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$59$			5.55982e6i			0.458831i	−0.973329	+	0.229416i	$0.926319\pi$
$60$	−4.04931e6	−	1.60475e6i	−0.312447	−	0.123823i
$61$	−1.31704e7			−0.951219			−0.475610	−	0.879656i	$-0.657773\pi$
$61$	−1.31704e7			−0.951219			−0.475610	+	0.879656i	$0.657773\pi$
$62$		−	2.43067e6i		−	0.164497i
$63$	1.53523e7	+	1.44354e7i	0.974564	+	0.916359i
$64$	−3.31396e6			−0.197527
$65$		−	2.93773e6i		−	0.164573i
$66$	1.54276e6	−	3.89291e6i	0.0813063	−	0.205163i
$67$	1.70044e7			0.843841			0.421921	−	0.906633i	$-0.361356\pi$
$67$	1.70044e7			0.843841			0.421921	+	0.906633i	$0.361356\pi$
$68$			1.11081e7i			0.519524i
$69$	−8.57726e6	−	3.39918e6i	−0.378401	−	0.149961i
$70$	7.16014e6			0.298215
$71$		−	1.08797e7i		−	0.428137i	−0.976819	−	0.214068i	$-0.931328\pi$
$71$		−	1.08797e7i		−	0.428137i	0.976819	−	0.214068i	$-0.0686715\pi$
$72$	1.60729e7	−	1.70938e7i	0.598088	−	0.636077i
$73$	−2.67184e7			−0.940847			−0.470424	−	0.882441i	$-0.655899\pi$
$73$	−2.67184e7			−0.940847			−0.470424	+	0.882441i	$0.655899\pi$
$74$			5.02705e6i			0.167643i
$75$	2.33143e6	−	5.88299e6i	0.0736849	−	0.185932i
$76$	4.39928e7			1.31864
$77$		−	2.08187e7i		−	0.592230i
$78$	6.31239e6	+	2.50161e6i	0.170536	+	0.0675835i
$79$	−3.07855e6			−0.0790383			−0.0395192	−	0.999219i	$-0.512583\pi$
$79$	−3.07855e6			−0.0790383			−0.0395192	+	0.999219i	$0.512583\pi$
$80$			5.79377e6i			0.141450i
$81$	2.64753e6	+	4.29652e7i	0.0615035	+	0.998107i
$82$	3.69033e7			0.816225
$83$		−	2.32739e7i		−	0.490407i	−0.969472	−	0.245203i	$-0.921145\pi$
$83$		−	2.32739e7i		−	0.490407i	0.969472	−	0.245203i	$-0.0788548\pi$
$84$	1.84403e7	−	4.65310e7i	0.370383	−	0.934599i
$85$	−1.61383e7			−0.309160
$86$			4.34187e7i			0.793748i
$87$	−8.40869e7	−	3.33237e7i	−1.46775	−	0.581670i
$88$	−2.31804e7			−0.386536
$89$			3.21685e7i			0.512709i	0.966583	+	0.256354i	$0.0825214\pi$
$89$			3.21685e7i			0.512709i	−0.966583	+	0.256354i	$0.917479\pi$
$90$	1.06557e7	+	1.00193e7i	0.162409	+	0.152709i
$91$	3.37577e7			0.492274
$92$			2.19138e7i			0.305891i
$93$	9.09471e6	−	2.29490e7i	0.121579	−	0.306784i
$94$	−5.34128e7			−0.684122
$95$			6.39145e7i			0.784702i
$96$	−8.13894e7	−	3.22547e7i	−0.958258	−	0.379759i
$97$	−9.03610e7			−1.02069			−0.510345	−	0.859970i	$-0.670482\pi$
$97$	−9.03610e7			−1.02069			−0.510345	+	0.859970i	$0.670482\pi$
$98$			3.62994e7i			0.393546i
$99$	2.91319e7	−	3.09822e7i	0.303269	−	0.322531i
$100$	−1.50303e7			−0.150303
$101$			1.24539e8i			1.19679i	0.801201	+	0.598395i	$0.204195\pi$
$101$			1.24539e8i			1.19679i	−0.801201	+	0.598395i	$0.795805\pi$
$102$	1.37425e7	−	3.46770e7i	0.126960	−	0.320362i
$103$	−9.24945e6			−0.0821802			−0.0410901	−	0.999155i	$-0.513083\pi$
$103$	−9.24945e6			−0.0821802			−0.0410901	+	0.999155i	$0.513083\pi$
$104$		−	3.75872e7i		−	0.321297i
$105$	6.76020e7	+	2.67908e7i	0.556164	+	0.220408i
$106$	9.98527e7			0.790927
$107$		−	1.21294e8i		−	0.925348i	−0.886528	−	0.462674i	$-0.846890\pi$
$107$		−	1.21294e8i		−	0.925348i	0.886528	−	0.462674i	$-0.153110\pi$
$108$	9.25541e7	−	4.34434e7i	0.680301	−	0.319322i
$109$	1.29780e8			0.919394			0.459697	−	0.888076i	$-0.347958\pi$
$109$	1.29780e8			0.919394			0.459697	+	0.888076i	$0.347958\pi$
$110$		−	1.44498e7i		−	0.0986940i
$111$	−1.88095e7	+	4.74626e7i	−0.123904	+	0.312651i
$112$	−6.65768e7			−0.423108
$113$		−	1.54559e8i		−	0.947942i	−0.880541	−	0.473971i	$-0.842820\pi$
$113$		−	1.54559e8i		−	0.947942i	0.880541	−	0.473971i	$-0.157180\pi$
$114$	−1.37335e8	−	5.44261e7i	−0.813135	−	0.322246i
$115$	−3.18372e7			−0.182030
$116$			2.14832e8i			1.18650i
$117$	5.02380e7	+	4.72376e7i	0.268095	+	0.252083i
$118$	−4.43436e7			−0.228719
$119$		−	1.85447e8i		−	0.924767i
$120$	2.98299e7	−	7.52708e7i	0.143856	−	0.362996i
$121$	1.72345e8			0.804002
$122$		−	1.05044e8i		−	0.474166i
$123$	3.48420e8	+	1.38079e8i	1.52224	+	0.603265i
$124$	−5.86319e7			−0.247997
$125$		−	2.18366e7i		−	0.0894427i
$126$	−1.15132e8	+	1.22445e8i	−0.456789	+	0.485803i
$127$	2.78135e8			1.06916			0.534578	−	0.845119i	$-0.320470\pi$
$127$	2.78135e8			1.06916			0.534578	+	0.845119i	$0.320470\pi$
$128$			2.50263e8i			0.932301i
$129$	−1.62458e8	+	4.09935e8i	−0.586653	+	1.48032i
$130$	2.34305e7			0.0820366
$131$		−	5.54604e8i		−	1.88321i	−0.336723	−	0.941604i	$-0.609319\pi$
$131$		−	5.54604e8i		−	1.88321i	0.336723	−	0.941604i	$-0.390681\pi$
$132$	−9.39037e7	−	3.72141e7i	−0.309305	−	0.122578i
$133$	−7.34448e8			−2.34722
$134$			1.35622e8i			0.420640i
$135$	6.31162e7	+	1.34466e8i	0.190023	+	0.404835i
$136$	−2.06484e8			−0.603576
$137$			5.75001e7i			0.163225i	0.996664	+	0.0816124i	$0.0260070\pi$
$137$			5.75001e7i			0.163225i	−0.996664	+	0.0816124i	$0.973993\pi$
$138$	2.71109e7	−	6.84098e7i	0.0747527	−	0.188626i
$139$	2.24212e8			0.600620			0.300310	−	0.953842i	$-0.402910\pi$
$139$	2.24212e8			0.600620			0.300310	+	0.953842i	$0.402910\pi$
$140$		−	1.72715e8i		−	0.449591i
$141$	−5.04294e8	−	1.99852e8i	−1.27587	−	0.505629i
$142$	8.67732e7			0.213419
$143$		−	6.81260e7i		−	0.162918i
$144$	−9.90792e7	−	9.31618e7i	−0.230426	−	0.216665i
$145$	−3.12116e8			−0.706063
$146$		−	2.13098e8i		−	0.468996i
$147$	−1.35820e8	+	3.42719e8i	−0.290867	+	0.733954i
$148$	1.21261e8			0.252740
$149$			1.53808e8i			0.312057i	0.987753	+	0.156028i	$0.0498691\pi$
$149$			1.53808e8i			0.312057i	−0.987753	+	0.156028i	$0.950131\pi$
$150$	4.69211e7	+	1.85949e7i	0.0926836	+	0.0367306i
$151$	8.78222e8			1.68926			0.844630	−	0.535351i	$-0.179821\pi$
$151$	8.78222e8			1.68926			0.844630	+	0.535351i	$0.179821\pi$
$152$			8.17764e8i			1.53198i
$153$	2.59499e8	−	2.75981e8i	0.473554	−	0.503633i
$154$	1.66044e8			0.295216
$155$		−	8.51826e7i		−	0.147579i
$156$	6.03431e7	−	1.52266e8i	0.101889	−	0.257101i
$157$	2.80886e8			0.462308			0.231154	−	0.972917i	$-0.425750\pi$
$157$	2.80886e8			0.462308			0.231154	+	0.972917i	$0.425750\pi$
$158$		−	2.45536e7i		−	0.0393992i
$159$	9.42753e8	+	3.73614e8i	1.47506	+	0.584568i
$160$	−3.02103e8			−0.460972
$161$		−	3.65845e8i		−	0.544495i
$162$	−3.42678e8	+	2.11159e7i	−0.497539	+	0.0306584i
$163$	−5.02070e8			−0.711237			−0.355618	−	0.934631i	$-0.615730\pi$
$163$	−5.02070e8			−0.711237			−0.355618	+	0.934631i	$0.615730\pi$
$164$		−	8.90171e8i		−	1.23055i
$165$	5.40661e7	−	1.36427e8i	0.0729439	−	0.184062i
$166$	1.85626e8			0.244459
$167$			2.33934e8i			0.300765i	0.988628	+	0.150383i	$0.0480505\pi$
$167$			2.33934e8i			0.300765i	−0.988628	+	0.150383i	$0.951949\pi$
$168$	8.64945e8	+	3.42778e8i	1.08580	+	0.430305i
$169$	−7.05264e8			−0.864579
$170$		−	1.28715e8i		−	0.154111i
$171$	−1.09300e9	−	1.02772e9i	−1.27831	−	1.20196i
$172$	1.04733e9			1.19666
$173$			6.37704e8i			0.711925i	0.934500	+	0.355963i	$0.115847\pi$
$173$			6.37704e8i			0.711925i	−0.934500	+	0.355963i	$0.884153\pi$
$174$	2.65781e8	−	6.70654e8i	0.289952	−	0.731646i
$175$	2.50927e8			0.267544
$176$			1.34358e8i			0.140027i
$177$	−4.18667e8	−	1.65918e8i	−0.426556	−	0.169045i
$178$	−2.56567e8			−0.255576
$179$			1.57028e9i			1.52955i	0.644297	+	0.764775i	$0.277150\pi$
$179$			1.57028e9i			1.52955i	−0.644297	+	0.764775i	$0.722850\pi$
$180$	2.41682e8	−	2.57033e8i	0.230226	−	0.244849i
$181$	−9.00318e8			−0.838845			−0.419423	−	0.907791i	$-0.637767\pi$
$181$	−9.00318e8			−0.838845			−0.419423	+	0.907791i	$0.637767\pi$
$182$			2.69242e8i			0.245390i
$183$	3.93037e8	−	9.91763e8i	0.350452	−	0.884308i
$184$	−4.07347e8			−0.355380
$185$			1.76173e8i			0.150401i
$186$	1.83035e8	+	7.25369e7i	0.152926	+	0.0606048i
$187$	−3.74249e8			−0.306051
$188$			1.28841e9i			1.03139i
$189$	−1.54516e9	+	7.25275e8i	−1.21095	+	0.568402i
$190$	−5.09764e8			−0.391160
$191$			1.56461e9i			1.17564i	0.808993	+	0.587819i	$0.200013\pi$
$191$			1.56461e9i			1.17564i	−0.808993	+	0.587819i	$0.799987\pi$
$192$	9.88963e7	−	2.49548e8i	0.0727738	−	0.183633i
$193$	−8.89688e8			−0.641222			−0.320611	−	0.947211i	$-0.603888\pi$
$193$	−8.89688e8			−0.641222			−0.320611	+	0.947211i	$0.603888\pi$
$194$		−	7.20694e8i		−	0.508796i
$195$	2.21217e8	+	8.76687e7i	0.152996	+	0.0606326i
$196$	8.75605e8			0.593313
$197$		−	9.87151e8i		−	0.655418i	−0.944779	−	0.327709i	$-0.893723\pi$
$197$		−	9.87151e8i		−	0.655418i	0.944779	−	0.327709i	$-0.106277\pi$
$198$	2.47105e8	+	2.32347e8i	0.160776	+	0.151174i
$199$	1.36346e9			0.869418			0.434709	−	0.900571i	$-0.356851\pi$
$199$	1.36346e9			0.869418			0.434709	+	0.900571i	$0.356851\pi$
$200$		−	2.79392e8i		−	0.174620i
$201$	−5.07450e8	+	1.28047e9i	−0.310892	+	0.784484i
$202$	−9.93284e8			−0.596579
$203$		−	3.58655e9i		−	2.11199i
$204$	−8.36469e8	−	3.31493e8i	−0.482980	−	0.191405i
$205$	1.29327e9			0.732276
$206$		−	7.37710e7i		−	0.0409654i
$207$	5.11931e8	−	5.44448e8i	0.278824	−	0.296534i
$208$	−2.17863e8			−0.116394
$209$			1.48218e9i			0.776812i
$210$	−2.13675e8	+	5.39175e8i	−0.109870	+	0.277238i
$211$	9.47762e8			0.478156			0.239078	−	0.971000i	$-0.423155\pi$
$211$	9.47762e8			0.478156			0.239078	+	0.971000i	$0.423155\pi$
$212$		−	2.40862e9i		−	1.19241i
$213$	8.19264e8	+	3.24675e8i	0.398021	+	0.157736i
$214$	9.67409e8			0.461270
$215$			1.52160e9i			0.712111i
$216$	8.07550e8	+	1.72045e9i	0.370983	+	0.790363i
$217$	9.78842e8			0.441442
$218$			1.03509e9i			0.458302i
$219$	7.97340e8	−	2.01196e9i	0.346631	−	0.874666i
$220$	−3.48554e8			−0.148792
$221$		−	6.06848e8i		−	0.254396i
$222$	−3.78548e8	−	1.50019e8i	−0.155851	−	0.0617638i
$223$	1.01919e9			0.412130			0.206065	−	0.978538i	$-0.433934\pi$
$223$	1.01919e9			0.412130			0.206065	+	0.978538i	$0.433934\pi$
$224$		−	3.47149e9i		−	1.37887i
$225$	3.73427e8	+	3.51125e8i	0.145705	+	0.137003i
$226$	1.23272e9			0.472532
$227$			1.43749e8i			0.0541377i	0.999634	+	0.0270689i	$0.00861734\pi$
$227$			1.43749e8i			0.0541377i	−0.999634	+	0.0270689i	$0.991383\pi$
$228$	−1.31285e9	+	3.31276e9i	−0.485821	+	1.22589i
$229$	−6.14128e7			−0.0223314			−0.0111657	−	0.999938i	$-0.503554\pi$
$229$	−6.14128e7			−0.0223314			−0.0111657	+	0.999938i	$0.503554\pi$
$230$		−	2.53925e8i		−	0.0907390i
$231$	1.56769e9	+	6.21279e8i	0.550571	+	0.218192i
$232$	−3.99341e9			−1.37845
$233$		−	1.11728e9i		−	0.379087i	−0.981872	−	0.189543i	$-0.939299\pi$
$233$		−	1.11728e9i		−	0.379087i	0.981872	−	0.189543i	$-0.0607008\pi$
$234$	−3.76754e8	+	4.00684e8i	−0.125659	+	0.133641i
$235$	−1.87185e9			−0.613760
$236$			1.06964e9i			0.344819i
$237$	9.18712e7	−	2.31822e8i	0.0291196	−	0.0734786i
$238$	1.47907e9			0.460980
$239$		−	1.81745e9i		−	0.557021i	−0.960433	−	0.278511i	$-0.910159\pi$
$239$		−	1.81745e9i		−	0.557021i	0.960433	−	0.278511i	$-0.0898407\pi$
$240$	−4.36284e8	−	1.72900e8i	−0.131500	−	0.0521135i
$241$	2.33083e8			0.0690942			0.0345471	−	0.999403i	$-0.489001\pi$
$241$	2.33083e8			0.0690942			0.0345471	+	0.999403i	$0.489001\pi$
$242$			1.37457e9i			0.400781i
$243$	−3.31439e9	−	1.08282e9i	−0.950557	−	0.310550i
$244$	−2.53383e9			−0.714856
$245$			1.27211e9i			0.353070i
$246$	−1.10128e9	+	2.77890e9i	−0.300717	+	0.758810i
$247$	−2.40337e9			−0.645703
$248$		−	1.08988e9i		−	0.288120i
$249$	1.75258e9	+	6.94548e8i	0.455911	+	0.180678i
$250$	1.74163e8			0.0445856
$251$			4.09933e9i			1.03280i	0.856346	+	0.516402i	$0.172729\pi$
$251$			4.09933e9i			1.03280i	−0.856346	+	0.516402i	$0.827271\pi$
$252$	2.95359e9	+	2.77719e9i	0.732400	+	0.688658i
$253$	−7.38307e8			−0.180200
$254$			2.21833e9i			0.532956i
$255$	4.81606e8	−	1.21525e9i	0.113902	−	0.287413i
$256$	−2.84440e9			−0.662263
$257$		−	6.47154e9i		−	1.48346i	−0.670700	−	0.741729i	$-0.734006\pi$
$257$		−	6.47154e9i		−	1.48346i	0.670700	−	0.741729i	$-0.265994\pi$
$258$	−3.26952e9	−	1.29572e9i	−0.737914	−	0.292436i
$259$	−2.02442e9			−0.449884
$260$		−	5.65183e8i		−	0.123679i
$261$	5.01871e9	−	5.33748e9i	1.08151	−	1.15020i
$262$	4.42337e9			0.938746
$263$			1.19014e9i			0.248757i	0.992235	+	0.124379i	$0.0396937\pi$
$263$			1.19014e9i			0.248757i	−0.992235	+	0.124379i	$0.960306\pi$
$264$	6.91757e8	−	1.74553e9i	0.142409	−	0.359346i
$265$	3.49933e9			0.709580
$266$		−	5.85775e9i		−	1.17005i
$267$	−2.42236e9	−	9.59984e8i	−0.476644	−	0.188894i
$268$	3.27143e9			0.634160
$269$			9.23705e9i			1.76410i	0.471153	+	0.882052i	$0.343838\pi$
$269$			9.23705e9i			1.76410i	−0.471153	+	0.882052i	$0.656162\pi$
$270$	−1.07246e9	+	5.03397e8i	−0.201803	+	0.0947230i
$271$	−5.47412e9			−1.01493			−0.507466	−	0.861672i	$-0.669418\pi$
$271$	−5.47412e9			−1.01493			−0.507466	+	0.861672i	$0.669418\pi$
$272$			1.19682e9i			0.218653i
$273$	−1.00741e9	+	2.54203e9i	−0.181366	+	0.457647i
$274$	−4.58604e8			−0.0813647
$275$		−	5.06392e8i		−	0.0885434i
$276$	−1.65016e9	−	6.53961e8i	−0.284374	−	0.112698i
$277$	7.77657e9			1.32090			0.660449	−	0.750871i	$-0.270366\pi$
$277$	7.77657e9			1.32090			0.660449	+	0.750871i	$0.270366\pi$
$278$			1.78825e9i			0.299398i
$279$	1.45670e9	+	1.36971e9i	0.240411	+	0.226053i
$280$	3.21052e9			0.522328
$281$		−	3.41673e9i		−	0.548006i	−0.961729	−	0.274003i	$-0.911652\pi$
$281$		−	3.41673e9i		−	0.548006i	0.961729	−	0.274003i	$-0.0883478\pi$
$282$	1.59396e9	−	4.02210e9i	0.252047	−	0.635999i
$283$	9.09925e9			1.41860			0.709300	−	0.704907i	$-0.249011\pi$
$283$	9.09925e9			1.41860			0.709300	+	0.704907i	$0.249011\pi$
$284$		−	2.09312e9i		−	0.321751i
$285$	−4.81291e9	−	1.90736e9i	−0.729504	−	0.289103i
$286$	5.43354e8			0.0812117
$287$			1.48611e10i			2.19041i
$288$	4.85770e9	−	5.16625e9i	0.706091	−	0.750940i
$289$	3.64205e9			0.522101
$290$		−	2.48935e9i		−	0.351960i
$291$	2.69659e9	−	6.80439e9i	0.376047	−	0.948893i
$292$	−5.14030e9			−0.707061
$293$			2.26766e9i			0.307686i	0.988095	+	0.153843i	$0.0491650\pi$
$293$			2.26766e9i			0.307686i	−0.988095	+	0.153843i	$0.950835\pi$
$294$	−2.73343e9	−	1.08326e9i	−0.365863	−	0.144992i
$295$	−1.55402e9			−0.205196
$296$			2.25407e9i			0.293630i
$297$	1.46367e9	+	3.11828e9i	0.188112	+	0.400764i
$298$	−1.22673e9			−0.155555
$299$		−	1.19717e9i		−	0.149786i
$300$	4.48540e8	−	1.13182e9i	0.0553753	−	0.139730i
$301$	−1.74849e10			−2.13009
$302$			7.00445e9i			0.842066i
$303$	−9.37803e9	−	3.71652e9i	−1.11261	−	0.440927i
$304$	4.73992e9			0.554979
$305$		−	3.68125e9i		−	0.425398i
$306$	2.20115e9	+	2.06969e9i	0.251052	+	0.236058i
$307$	−1.05438e10			−1.18698			−0.593489	−	0.804842i	$-0.702250\pi$
$307$	−1.05438e10			−1.18698			−0.593489	+	0.804842i	$0.702250\pi$
$308$		−	4.00527e9i		−	0.445070i
$309$	2.76025e8	−	6.96505e8i	0.0302772	−	0.0763994i
$310$	6.79392e8			0.0735654
$311$		−	7.20415e9i		−	0.770089i	−0.922898	−	0.385045i	$-0.874186\pi$
$311$		−	7.20415e9i		−	0.770089i	0.922898	−	0.385045i	$-0.125814\pi$
$312$	2.83040e9	+	1.12169e9i	0.298696	+	0.118374i
$313$	−2.32153e9			−0.241878			−0.120939	−	0.992660i	$-0.538591\pi$
$313$	−2.32153e9			−0.241878			−0.120939	+	0.992660i	$0.538591\pi$
$314$			2.24026e9i			0.230452i
$315$	−4.03481e9	+	4.29109e9i	−0.409808	+	0.435838i
$316$	−5.92276e8			−0.0593985
$317$			1.17812e9i			0.116668i	0.998297	+	0.0583340i	$0.0185788\pi$
$317$			1.17812e9i			0.116668i	−0.998297	+	0.0583340i	$0.981421\pi$
$318$	−2.97984e9	+	7.51913e9i	−0.291397	+	0.735291i
$319$	−7.23798e9			−0.698963
$320$		−	9.26279e8i		−	0.0883368i
$321$	9.13374e9	+	3.61971e9i	0.860257	+	0.340921i
$322$	2.91788e9			0.271421
$323$			1.32029e10i			1.21299i
$324$	5.09352e8	+	8.26599e9i	0.0462209	+	0.750093i
$325$	8.21119e8			0.0735992
$326$		−	4.00437e9i		−	0.354539i
$327$	−3.87294e9	+	9.77273e9i	−0.338727	+	0.854722i
$328$	1.65470e10			1.42963
$329$		−	2.15096e10i		−	1.83590i
$330$	1.08810e9	+	4.31216e8i	0.0917516	+	0.0363613i
$331$	3.67861e9			0.306458			0.153229	−	0.988191i	$-0.451033\pi$
$331$	3.67861e9			0.306458			0.153229	+	0.988191i	$0.451033\pi$
$332$		−	4.47762e9i		−	0.368548i
$333$	−3.01272e9	−	2.83279e9i	−0.245009	−	0.230376i
$334$	−1.86579e9			−0.149926
$335$			4.75286e9i			0.377377i
$336$	1.98681e9	−	5.01339e9i	0.155883	−	0.393346i
$337$	3.59368e9			0.278625			0.139312	−	0.990248i	$-0.455511\pi$
$337$	3.59368e9			0.278625			0.139312	+	0.990248i	$0.455511\pi$
$338$		−	5.62498e9i		−	0.430977i
$339$	1.16387e10	+	4.61242e9i	0.881261	+	0.349245i
$340$	−3.10482e9			−0.232338
$341$		−	1.97539e9i		−	0.146095i
$342$	8.19682e9	−	8.71745e9i	0.599157	−	0.637214i
$343$	3.89777e9			0.281605
$344$			1.94684e10i			1.39026i
$345$	9.50099e8	−	2.39742e9i	0.0670644	−	0.169226i
$346$	−5.08614e9			−0.354882
$347$		−	2.36195e10i		−	1.62912i	−0.580078	−	0.814561i	$-0.696978\pi$
$347$		−	2.36195e10i		−	1.62912i	0.580078	−	0.814561i	$-0.303022\pi$
$348$	−1.61773e10	−	6.41108e9i	−1.10304	−	0.437134i
$349$	2.24057e9			0.151028			0.0755139	−	0.997145i	$-0.475940\pi$
$349$	2.24057e9			0.151028			0.0755139	+	0.997145i	$0.475940\pi$
$350$			2.00132e9i			0.133366i
$351$	−5.05632e9	+	2.37335e9i	−0.333124	+	0.156363i
$352$	−7.00578e9			−0.456337
$353$		−	1.21859e10i		−	0.784797i	−0.919795	−	0.392399i	$-0.871645\pi$
$353$		−	1.21859e10i		−	0.784797i	0.919795	−	0.392399i	$-0.128355\pi$
$354$	1.32332e9	−	3.33917e9i	0.0842657	−	0.212631i
$355$	3.04096e9			0.191469
$356$			6.18883e9i			0.385309i
$357$	1.39646e10	+	5.53418e9i	0.859717	+	0.340707i
$358$	−1.25241e10			−0.762454
$359$		−	1.53929e10i		−	0.926706i	−0.886174	−	0.463353i	$-0.846646\pi$
$359$		−	1.53929e10i		−	0.926706i	0.886174	−	0.463353i	$-0.153354\pi$
$360$	4.77787e9	+	4.49252e9i	0.284462	+	0.267473i
$361$	3.53052e10			2.07879
$362$		−	7.18068e9i		−	0.418149i
$363$	−5.14318e9	+	1.29780e10i	−0.296214	+	0.747447i
$364$	6.49457e9			0.369952
$365$		−	7.46802e9i		−	0.420760i
$366$	7.91002e9	+	3.13475e9i	0.440812	+	0.174694i
$367$	3.67051e9			0.202331			0.101165	−	0.994870i	$-0.467743\pi$
$367$	3.67051e9			0.202331			0.101165	+	0.994870i	$0.467743\pi$
$368$			2.36106e9i			0.128741i
$369$	−2.07954e10	+	2.21162e10i	−1.12166	+	1.19290i
$370$	−1.40510e9			−0.0749723
$371$			4.02112e10i			2.12252i
$372$	1.74971e9	−	4.41511e9i	0.0913682	−	0.230553i
$373$	1.40817e10			0.727478			0.363739	−	0.931501i	$-0.381500\pi$
$373$	1.40817e10			0.727478			0.363739	+	0.931501i	$0.381500\pi$
$374$		−	2.98490e9i		−	0.152561i
$375$	1.64435e9	+	6.51656e8i	0.0831511	+	0.0329529i
$376$	−2.39496e10			−1.19825
$377$		−	1.17364e10i		−	0.580993i
$378$	−5.78459e9	−	1.23238e10i	−0.283338	−	0.603639i
$379$	−2.08709e10			−1.01154			−0.505770	−	0.862668i	$-0.668792\pi$
$379$	−2.08709e10			−1.01154			−0.505770	+	0.862668i	$0.668792\pi$
$380$			1.22964e10i			0.589716i
$381$	−8.30022e9	+	2.09442e10i	−0.393903	+	0.993950i
$382$	−1.24789e10			−0.586034
$383$			9.93413e9i			0.461673i	0.972993	+	0.230837i	$0.0741463\pi$
$383$			9.93413e9i			0.461673i	−0.972993	+	0.230837i	$0.925854\pi$
$384$	−1.88453e10	−	7.46843e9i	−0.866721	−	0.343482i
$385$	5.81900e9			0.264853
$386$		−	7.09590e9i		−	0.319638i
$387$	−2.60209e10	−	2.44669e10i	−1.16006	−	1.09077i
$388$	−1.73844e10			−0.767065
$389$		−	2.35323e10i		−	1.02770i	−0.857881	−	0.513849i	$-0.828219\pi$
$389$		−	2.35323e10i		−	1.02770i	0.857881	−	0.513849i	$-0.171781\pi$
$390$	−6.99221e8	+	1.76437e9i	−0.0302243	+	0.0762659i
$391$	−6.57664e9			−0.281383
$392$			1.62762e10i			0.689302i
$393$	4.17630e10	+	1.65507e10i	1.75074	+	0.693819i
$394$	7.87324e9			0.326714
$395$		−	8.60481e8i		−	0.0353470i
$396$	5.60462e9	−	5.96061e9i	0.227911	−	0.242387i
$397$	−1.45076e10			−0.584027			−0.292014	−	0.956414i	$-0.594325\pi$
$397$	−1.45076e10			−0.584027			−0.292014	+	0.956414i	$0.594325\pi$
$398$			1.08745e10i			0.433390i
$399$	2.19177e10	−	5.53056e10i	0.864774	−	2.18211i
$400$	−1.61941e9			−0.0632582
$401$			1.72695e10i			0.667887i	0.942593	+	0.333943i	$0.108379\pi$
$401$			1.72695e10i			0.667887i	−0.942593	+	0.333943i	$0.891621\pi$
$402$	−1.02126e10	−	4.04728e9i	−0.391051	−	0.154974i
$403$	3.20311e9			0.121437
$404$			2.39597e10i			0.899407i
$405$	−1.20091e10	+	7.40006e8i	−0.446367	+	0.0275052i
$406$	2.86053e10			1.05279
$407$			4.08545e9i			0.148889i
$408$	6.16198e9	−	1.55487e10i	0.222372	−	0.561119i
$409$	1.11042e10			0.396819			0.198409	−	0.980119i	$-0.436422\pi$
$409$	1.11042e10			0.396819			0.198409	+	0.980119i	$0.436422\pi$
$410$			1.03148e10i			0.365027i
$411$	−4.32989e9	−	1.71594e9i	−0.151743	−	0.0601360i
$412$	−1.77948e9			−0.0617597
$413$		−	1.78574e10i		−	0.613787i
$414$	4.34236e9	+	4.08302e9i	0.147817	+	0.138989i
$415$	6.50525e9			0.219317
$416$		−	1.13599e10i		−	0.379317i
$417$	−6.69102e9	+	1.68837e10i	−0.221283	+	0.558371i
$418$	−1.18214e10			−0.387227
$419$			2.66208e10i			0.863705i	0.901944	+	0.431852i	$0.142140\pi$
$419$			2.66208e10i			0.863705i	−0.901944	+	0.431852i	$0.857860\pi$
$420$	1.30058e10	+	5.15422e9i	0.417966	+	0.165640i
$421$	−2.03614e10			−0.648155			−0.324078	−	0.946031i	$-0.605054\pi$
$421$	−2.03614e10			−0.648155			−0.324078	+	0.946031i	$0.605054\pi$
$422$			7.55908e9i			0.238352i
$423$	3.00986e10	−	3.20104e10i	0.940124	−	0.999838i
$424$	4.47727e10			1.38532
$425$		−	4.51080e9i		−	0.138260i
$426$	−2.58952e9	+	6.53422e9i	−0.0786286	+	0.198406i
$427$	4.23016e10			1.27246
$428$		−	2.33356e10i		−	0.695414i
$429$	5.13004e9	+	2.03304e9i	0.151458	+	0.0600229i
$430$	−1.21359e10			−0.354975
$431$		−	1.26533e10i		−	0.366687i	−0.983049	−	0.183343i	$-0.941308\pi$
$431$		−	1.26533e10i		−	0.366687i	0.983049	−	0.183343i	$-0.0586920\pi$
$432$	9.97205e9	−	4.68072e9i	0.286319	−	0.134393i
$433$	−3.63896e10			−1.03520			−0.517601	−	0.855622i	$-0.673175\pi$
$433$	−3.63896e10			−1.03520			−0.517601	+	0.855622i	$0.673175\pi$
$434$			7.80696e9i			0.220051i
$435$	9.31427e9	−	2.35030e10i	0.260131	−	0.656397i
$436$	2.49681e10			0.690939
$437$			2.60462e10i			0.714198i
$438$	1.60468e10	+	6.35936e9i	0.436005	+	0.172789i
$439$	−5.90206e10			−1.58908			−0.794539	−	0.607213i	$-0.792287\pi$
$439$	−5.90206e10			−1.58908			−0.794539	+	0.607213i	$0.792287\pi$
$440$		−	6.47911e9i		−	0.172864i
$441$	−2.17543e10	−	2.04551e10i	−0.575164	−	0.540813i
$442$	4.84005e9			0.126812
$443$			1.59909e10i			0.415200i	0.978214	+	0.207600i	$0.0665652\pi$
$443$			1.59909e10i			0.415200i	−0.978214	+	0.207600i	$0.933435\pi$
$444$	−3.61872e9	+	9.13123e9i	−0.0931156	+	0.234962i
$445$	−8.99137e9			−0.229290
$446$			8.12874e9i			0.205439i
$447$	−1.15821e10	−	4.58999e9i	−0.290106	−	0.114969i
$448$	1.06440e10			0.264236
$449$		−	1.61660e9i		−	0.0397756i	−0.999802	−	0.0198878i	$-0.993669\pi$
$449$		−	1.61660e9i		−	0.0397756i	0.999802	−	0.0198878i	$-0.00633090\pi$
$450$	−2.80047e9	+	2.97835e9i	−0.0682938	+	0.0726316i
$451$	2.99911e10			0.724913
$452$		−	2.97354e10i		−	0.712393i
$453$	−2.62082e10	+	6.61321e10i	−0.622364	+	1.57043i
$454$	−1.14650e9			−0.0269867
$455$			9.43556e9i			0.220152i
$456$	−6.15795e10	−	2.44040e10i	−1.42422	−	0.564419i
$457$	5.01622e10			1.15004			0.575019	−	0.818140i	$-0.304995\pi$
$457$	5.01622e10			1.15004			0.575019	+	0.818140i	$0.304995\pi$
$458$		−	4.89811e8i		−	0.0111318i
$459$	1.30380e10	+	2.77768e10i	0.293737	+	0.625793i
$460$	−6.12510e9			−0.136799
$461$		−	7.19471e10i		−	1.59298i	−0.604654	−	0.796488i	$-0.706689\pi$
$461$		−	7.19471e10i		−	1.59298i	0.604654	−	0.796488i	$-0.293311\pi$
$462$	−4.95514e9	+	1.25035e10i	−0.108765	+	0.274450i
$463$	−6.19020e10			−1.34704			−0.673521	−	0.739168i	$-0.735219\pi$
$463$	−6.19020e10			−1.34704			−0.673521	+	0.739168i	$0.735219\pi$
$464$			2.31466e10i			0.499361i
$465$	6.41444e9	+	2.54205e9i	0.137198	+	0.0543716i
$466$	8.91112e9			0.188968
$467$			4.98272e9i			0.104761i	0.998627	+	0.0523804i	$0.0166808\pi$
$467$			4.98272e9i			0.104761i	−0.998627	+	0.0523804i	$0.983319\pi$
$468$	9.66518e9	+	9.08794e9i	0.201477	+	0.189445i
$469$	−5.46156e10			−1.12882
$470$		−	1.49293e10i		−	0.305949i
$471$	−8.38229e9	+	2.11513e10i	−0.170325	+	0.429788i
$472$	−1.98831e10			−0.400605
$473$			3.52861e10i			0.704951i
$474$	1.84895e9	+	7.32739e8i	0.0366278	+	0.0145156i
$475$	−1.78646e10			−0.350929
$476$		−	3.56778e10i		−	0.694977i
$477$	−5.62680e10	+	5.98419e10i	−1.08690	+	1.15593i
$478$	1.44955e10			0.277665
$479$		−	1.00172e9i		−	0.0190284i	−0.999955	−	0.00951420i	$-0.996971\pi$
$479$		−	1.00172e9i		−	0.0190284i	0.999955	−	0.00951420i	$-0.00302851\pi$
$480$	9.01546e9	−	2.27490e10i	0.169833	−	0.428546i
$481$	−6.62460e9			−0.123760
$482$			1.85900e9i			0.0344422i
$483$	2.75490e10	+	1.09177e10i	0.506194	+	0.200605i
$484$	3.31571e10			0.604220
$485$		−	2.52567e10i		−	0.456467i
$486$	8.63626e9	−	2.64346e10i	0.154803	−	0.473836i
$487$	8.29709e10			1.47506			0.737530	−	0.675314i	$-0.235992\pi$
$487$	8.29709e10			1.47506			0.737530	+	0.675314i	$0.235992\pi$
$488$		−	4.71003e10i		−	0.830509i
$489$	1.49830e10	−	3.78070e10i	0.262037	−	0.661207i
$490$	−1.01460e10			−0.175999
$491$			1.72161e10i			0.296216i	0.988971	+	0.148108i	$0.0473183\pi$
$491$			1.72161e10i			0.296216i	−0.988971	+	0.148108i	$0.952682\pi$
$492$	6.70319e10	+	2.65648e10i	1.14399	+	0.453363i
$493$	−6.44739e10			−1.09143
$494$		−	1.91686e10i		−	0.321871i
$495$	8.65979e9	+	8.14260e9i	0.144240	+	0.135626i
$496$	−6.31717e9			−0.104375
$497$			3.49440e10i			0.572726i
$498$	−5.53952e9	+	1.39781e10i	−0.0900647	+	0.227263i
$499$	7.02839e10			1.13358			0.566792	−	0.823861i	$-0.308184\pi$
$499$	7.02839e10			1.13358			0.566792	+	0.823861i	$0.308184\pi$
$500$		−	4.20110e9i		−	0.0672176i
$501$	−1.76158e10	−	6.98114e9i	−0.279609	−	0.110809i
$502$	−3.26951e10			−0.514834
$503$		−	2.10506e10i		−	0.328846i	−0.986390	−	0.164423i	$-0.947424\pi$
$503$		−	2.10506e10i		−	0.328846i	0.986390	−	0.164423i	$-0.0525762\pi$
$504$	−5.16240e10	+	5.49030e10i	−0.800073	+	0.850891i
$505$	−3.48096e10			−0.535221
$506$		−	5.88853e9i		−	0.0898266i
$507$	2.10467e10	−	5.31080e10i	0.318532	−	0.803763i
$508$	5.35099e10			0.803488
$509$			3.73005e10i			0.555704i	0.960624	+	0.277852i	$0.0896224\pi$
$509$			3.73005e10i			0.555704i	−0.960624	+	0.277852i	$0.910378\pi$
$510$	9.69252e9	+	3.84115e9i	0.143270	+	0.0567781i
$511$	8.58158e10			1.25859
$512$			4.13811e10i			0.602175i
$513$	1.10007e11	−	5.16357e10i	1.58837	−	0.745557i
$514$	5.16152e10			0.739477
$515$		−	2.58530e9i		−	0.0367521i
$516$	−3.12549e10	+	7.88665e10i	−0.440879	+	1.11248i
$517$	−4.34082e10			−0.607589
$518$		−	1.61462e10i		−	0.224259i
$519$	−4.80205e10	−	1.90306e10i	−0.661847	−	0.262291i
$520$	1.05059e10			0.143688
$521$		−	1.35295e11i		−	1.83625i	−0.396288	−	0.918126i	$-0.629702\pi$
$521$		−	1.35295e11i		−	1.83625i	0.396288	−	0.918126i	$-0.370298\pi$
$522$	4.25702e10	+	4.00278e10i	0.573355	+	0.539113i
$523$	−4.33058e9			−0.0578815			−0.0289407	−	0.999581i	$-0.509213\pi$
$523$	−4.33058e9			−0.0578815			−0.0289407	+	0.999581i	$0.509213\pi$
$524$		−	1.06699e11i		−	1.41526i
$525$	−7.48824e9	+	1.88953e10i	−0.0985695	+	0.248724i
$526$	−9.49223e9			−0.124001
$527$		−	1.75962e10i		−	0.228127i
$528$	−1.01175e10	−	4.00956e9i	−0.130177	−	0.0515894i
$529$	6.53368e10			0.834325
$530$			2.79097e10i			0.353713i
$531$	2.49880e10	−	2.65752e10i	0.314307	−	0.334271i
$532$	−1.41299e11			−1.76397
$533$			4.86308e10i			0.602564i
$534$	7.65656e9	−	1.93201e10i	0.0941605	−	0.237598i
$535$	3.39028e10			0.413828
$536$			6.08112e10i			0.736757i
$537$	−1.18245e11	−	4.68607e10i	−1.42196	−	0.563523i
$538$	−7.36721e10			−0.879374
$539$			2.95003e10i			0.349520i
$540$	1.21428e10	+	2.58697e10i	0.142805	+	0.304240i
$541$	−1.24450e11			−1.45280			−0.726402	−	0.687270i	$-0.758809\pi$
$541$	−1.24450e11			−1.45280			−0.726402	+	0.687270i	$0.758809\pi$
$542$		−	4.36600e10i		−	0.505926i
$543$	2.68676e10	−	6.77960e10i	0.309051	−	0.779839i
$544$	−6.24055e10			−0.712570
$545$			3.62746e10i			0.411166i
$546$	−2.02745e10	−	8.03481e9i	−0.228129	−	0.0904077i
$547$	3.16725e10			0.353780			0.176890	−	0.984231i	$-0.443396\pi$
$547$	3.16725e10			0.353780			0.176890	+	0.984231i	$0.443396\pi$
$548$			1.10623e10i			0.122666i
$549$	6.29529e10	+	5.91931e10i	0.692989	+	0.651601i
$550$	4.03884e9			0.0441373
$551$			2.55343e11i			2.77025i
$552$	1.21562e10	−	3.06741e10i	0.130931	−	0.330382i
$553$	9.88787e9			0.105731
$554$			6.20237e10i			0.658444i
$555$	−1.32662e10	−	5.25741e9i	−0.139822	−	0.0554115i
$556$	4.31357e10			0.451375
$557$			3.02144e10i			0.313902i	0.987606	+	0.156951i	$0.0501664\pi$
$557$			3.02144e10i			0.313902i	−0.987606	+	0.156951i	$0.949834\pi$
$558$	−1.09244e10	+	1.16183e10i	−0.112683	+	0.119841i
$559$	−5.72167e10			−0.585971
$560$		−	1.86088e10i		−	0.189220i
$561$	1.11685e10	−	2.81818e10i	0.112757	−	0.284523i
$562$	2.72508e10			0.273171
$563$			6.11519e10i			0.608662i	0.952566	+	0.304331i	$0.0984329\pi$
$563$			6.11519e10i			0.608662i	−0.952566	+	0.304331i	$0.901567\pi$
$564$	−9.70200e10	−	3.84491e10i	−0.958837	−	0.379988i
$565$	4.32007e10			0.423932
$566$			7.25730e10i			0.707147i
$567$	−8.50348e9	−	1.37998e11i	−0.0822744	−	1.33519i
$568$	3.89081e10			0.373806
$569$		−	3.99163e10i		−	0.380804i	−0.981706	−	0.190402i	$-0.939021\pi$
$569$		−	3.99163e10i		−	0.380804i	0.981706	−	0.190402i	$-0.0609791\pi$
$570$	1.52126e10	−	3.83864e10i	0.144113	−	0.363645i
$571$	9.07730e10			0.853911			0.426955	−	0.904273i	$-0.359586\pi$
$571$	9.07730e10			0.853911			0.426955	+	0.904273i	$0.359586\pi$
$572$		−	1.31066e10i		−	0.122435i
$573$	−1.17819e11	−	4.66917e10i	−1.09294	−	0.433133i
$574$	−1.18528e11			−1.09188
$575$		−	8.89878e9i		−	0.0814065i
$576$	1.58403e10	+	1.48942e10i	0.143904	+	0.135309i
$577$	1.33041e11			1.20028			0.600141	−	0.799894i	$-0.295111\pi$
$577$	1.33041e11			1.20028			0.600141	+	0.799894i	$0.295111\pi$
$578$			2.90480e10i			0.260258i
$579$	2.65504e10	−	6.69956e10i	0.236242	−	0.596117i
$580$	−6.00473e10			−0.530617
$581$			7.47525e10i			0.656026i
$582$	5.42699e10	+	2.15072e10i	0.473006	+	0.187453i
$583$	8.11497e10			0.702445
$584$		−	9.55508e10i		−	0.821453i
$585$	−1.32033e10	+	1.40419e10i	−0.112735	+	0.119896i
$586$	−1.80862e10			−0.153376
$587$		−	1.98669e11i		−	1.67331i	−0.547728	−	0.836657i	$-0.684507\pi$
$587$		−	1.98669e11i		−	1.67331i	0.547728	−	0.836657i	$-0.315493\pi$
$588$	−2.61301e10	+	6.59350e10i	−0.218591	+	0.551578i
$589$	−6.96883e10			−0.579027
$590$		−	1.23944e10i		−	0.102286i
$591$	7.43347e10	+	2.94589e10i	0.609315	+	0.241472i
$592$	1.30650e10			0.106371
$593$		−	1.33920e11i		−	1.08300i	−0.840702	−	0.541498i	$-0.817857\pi$
$593$		−	1.33920e11i		−	1.08300i	0.840702	−	0.541498i	$-0.182143\pi$
$594$	−2.48705e10	+	1.16738e10i	−0.199774	+	0.0937706i
$595$	5.18341e10			0.413569
$596$			2.95908e10i			0.234515i
$597$	−4.06887e10	+	1.02671e11i	−0.320315	+	0.808261i
$598$	9.54831e9			0.0746658
$599$			1.14673e10i			0.0890745i	0.999008	+	0.0445372i	$0.0141813\pi$
$599$			1.14673e10i			0.0890745i	−0.999008	+	0.0445372i	$0.985819\pi$
$600$	2.10388e10	+	8.33771e9i	0.162337	+	0.0643342i
$601$	4.71067e10			0.361065			0.180532	−	0.983569i	$-0.442218\pi$
$601$	4.71067e10			0.361065			0.180532	+	0.983569i	$0.442218\pi$
$602$		−	1.39455e11i		−	1.06181i
$603$	−8.12785e10	−	7.64243e10i	−0.614761	−	0.578046i
$604$	1.68959e11			1.26950
$605$			4.81719e10i			0.359561i
$606$	2.96419e10	−	7.47965e10i	0.219794	−	0.554614i
$607$	−1.36835e11			−1.00796			−0.503979	−	0.863716i	$-0.668131\pi$
$607$	−1.36835e11			−1.00796			−0.503979	+	0.863716i	$0.668131\pi$
$608$			2.47152e11i			1.80863i
$609$	2.70075e11	+	1.07031e11i	1.96343	+	0.778110i
$610$	2.93606e10			0.212053
$611$		−	7.03868e10i		−	0.505041i
$612$	4.99244e10	−	5.30955e10i	0.355883	−	0.378488i
$613$	8.50169e10			0.602093			0.301046	−	0.953610i	$-0.402664\pi$
$613$	8.50169e10			0.602093			0.301046	+	0.953610i	$0.402664\pi$
$614$		−	8.40942e10i		−	0.591688i
$615$	−3.85944e10	+	9.73865e10i	−0.269788	+	0.680767i
$616$	7.44521e10			0.517076
$617$			1.76659e11i			1.21898i	0.792795	+	0.609489i	$0.208625\pi$
$617$			1.76659e11i			1.21898i	−0.792795	+	0.609489i	$0.791375\pi$
$618$	5.55512e9	+	2.20150e9i	0.0380838	+	0.0150926i
$619$	−1.22476e11			−0.834234			−0.417117	−	0.908853i	$-0.636960\pi$
$619$	−1.22476e11			−0.834234			−0.417117	+	0.908853i	$0.636960\pi$
$620$		−	1.63881e10i		−	0.110908i
$621$	2.57209e10	+	5.47972e10i	0.172950	+	0.368461i
$622$	5.74582e10			0.383876
$623$		−	1.03321e11i		−	0.685860i
$624$	6.50154e9	−	1.64056e10i	0.0428823	−	0.108206i
$625$	6.10352e9			0.0400000
$626$		−	1.85159e10i		−	0.120572i
$627$	−1.11612e11	−	4.42318e10i	−0.722169	−	0.286196i
$628$	5.40390e10			0.347431
$629$			3.63921e10i			0.232490i
$630$	−3.42245e10	−	3.21805e10i	−0.217258	−	0.204282i
$631$	−2.62046e11			−1.65295			−0.826475	−	0.562974i	$-0.809657\pi$
$631$	−2.62046e11			−1.65295			−0.826475	+	0.562974i	$0.809657\pi$
$632$		−	1.10096e10i		−	0.0690083i
$633$	−2.82835e10	+	7.13686e10i	−0.176164	+	0.444521i
$634$	−9.39633e9			−0.0581569
$635$			7.77412e10i			0.478141i
$636$	1.81374e11	+	7.18788e10i	1.10853	+	0.439312i
$637$	−4.78351e10			−0.290529
$638$		−	5.77280e10i		−	0.348421i
$639$	−4.88976e10	+	5.20034e10i	−0.293281	+	0.311909i
$640$	−6.99505e10			−0.416938
$641$		−	2.31601e11i		−	1.37185i	−0.727671	−	0.685926i	$-0.759397\pi$
$641$		−	2.31601e11i		−	1.37185i	0.727671	−	0.685926i	$-0.240603\pi$
$642$	−2.88698e10	+	7.28481e10i	−0.169943	+	0.428823i
$643$	−2.66842e11			−1.56103			−0.780515	−	0.625138i	$-0.785043\pi$
$643$	−2.66842e11			−1.56103			−0.780515	+	0.625138i	$0.785043\pi$
$644$		−	7.03842e10i		−	0.409196i
$645$	−1.14580e11	−	4.54083e10i	−0.662020	−	0.262359i
$646$	−1.05302e11			−0.604655
$647$			1.98677e11i			1.13378i	0.823792	+	0.566892i	$0.191854\pi$
$647$			1.98677e11i			1.13378i	−0.823792	+	0.566892i	$0.808146\pi$
$648$	−1.53653e11	+	9.46812e9i	−0.871447	+	0.0536987i
$649$	−3.60378e10			−0.203132
$650$			6.54901e9i			0.0366879i
$651$	−2.92109e10	+	7.37090e10i	−0.162638	+	0.410390i
$652$	−9.65923e10			−0.534505
$653$		−	2.49774e11i		−	1.37371i	−0.726795	−	0.686855i	$-0.758991\pi$
$653$		−	2.49774e11i		−	1.37371i	0.726795	−	0.686855i	$-0.241009\pi$
$654$	−7.79445e10	−	3.08895e10i	−0.426064	−	0.168850i
$655$	1.55017e11			0.842196
$656$		−	9.59096e10i		−	0.517901i
$657$	1.27710e11	+	1.20083e11i	0.685433	+	0.644496i
$658$	1.71554e11			0.915162
$659$			1.55774e11i			0.825947i	0.910743	+	0.412974i	$0.135510\pi$
$659$			1.55774e11i			0.825947i	−0.910743	+	0.412974i	$0.864490\pi$
$660$	1.04017e10	−	2.62469e10i	0.0548185	−	0.138325i
$661$	−7.07460e10			−0.370592			−0.185296	−	0.982683i	$-0.559324\pi$
$661$	−7.07460e10			−0.370592			−0.185296	+	0.982683i	$0.559324\pi$
$662$			2.93395e10i			0.152764i
$663$	4.56970e10	+	1.81098e10i	0.236502	+	0.0937258i
$664$	8.32324e10			0.428174
$665$		−	2.05284e11i		−	1.04971i
$666$	2.25935e10	−	2.40286e10i	0.114838	−	0.122133i
$667$	−1.27192e11			−0.642625
$668$			4.50061e10i			0.226030i
$669$	−3.04149e10	+	7.67471e10i	−0.151839	+	0.383140i
$670$	−3.79075e10			−0.188116
$671$		−	8.53683e10i		−	0.421121i
$672$	2.61411e11	+	1.03598e11i	1.28188	+	0.508010i
$673$	3.05166e11			1.48757			0.743783	−	0.668421i	$-0.233029\pi$
$673$	3.05166e11			1.48757			0.743783	+	0.668421i	$0.233029\pi$
$674$			2.86622e10i			0.138890i
$675$	−3.75844e10	+	1.76415e10i	−0.181048	+	0.0849808i
$676$	−1.35684e11			−0.649745
$677$			6.05189e10i			0.288095i	0.989571	+	0.144048i	$0.0460119\pi$
$677$			6.05189e10i			0.288095i	−0.989571	+	0.144048i	$0.953988\pi$
$678$	−3.67873e10	+	9.28268e10i	−0.174092	+	0.439293i
$679$	2.90227e11			1.36540
$680$		−	5.77142e10i		−	0.269927i
$681$	−1.08246e10	−	4.28980e9i	−0.0503296	−	0.0199457i
$682$	1.57551e10			0.0728257
$683$			1.55016e11i			0.712352i	0.934419	+	0.356176i	$0.115920\pi$
$683$			1.55016e11i			0.712352i	−0.934419	+	0.356176i	$0.884080\pi$
$684$	−2.10280e11	−	1.97721e11i	−0.960668	−	0.903294i
$685$	−1.60718e10			−0.0729964
$686$			3.10875e10i			0.140375i
$687$	1.83270e9	−	4.62452e9i	0.00822744	−	0.0207606i
$688$	1.12843e11			0.503639
$689$			1.31585e11i			0.583888i
$690$	1.91211e10	+	7.57772e9i	0.0843562	+	0.0334304i
$691$	−2.65978e11			−1.16663			−0.583315	−	0.812246i	$-0.698245\pi$
$691$	−2.65978e11			−1.16663			−0.583315	+	0.812246i	$0.698245\pi$
$692$			1.22686e11i			0.535023i
$693$	−9.35674e10	+	9.95106e10i	−0.405688	+	0.431456i
$694$	1.88383e11			0.812088
$695$			6.26691e10i			0.268605i
$696$	1.19173e11	−	3.00713e11i	0.507856	−	1.28149i
$697$	2.67152e11			1.13195
$698$			1.78702e10i			0.0752847i
$699$	8.41338e10	+	3.33423e10i	0.352421	+	0.139665i
$700$	4.82753e10			0.201063
$701$		−	4.58950e11i		−	1.90061i	−0.311319	−	0.950306i	$-0.600771\pi$
$701$		−	4.58950e11i		−	1.90061i	0.311319	−	0.950306i	$-0.399229\pi$
$702$	−1.89292e10	−	4.03277e10i	−0.0779441	−	0.166056i
$703$	1.44128e11			0.590101
$704$		−	2.14805e10i		−	0.0874486i
$705$	5.58603e10	−	1.40954e11i	0.226124	−	0.570587i
$706$	9.71910e10			0.391208
$707$		−	4.00000e11i		−	1.60097i
$708$	−8.05466e10	−	3.19207e10i	−0.320563	−	0.127040i
$709$	−3.22572e11			−1.27656			−0.638280	−	0.769804i	$-0.720354\pi$
$709$	−3.22572e11			−1.27656			−0.638280	+	0.769804i	$0.720354\pi$
$710$			2.42538e10i			0.0954437i
$711$	1.47151e10	+	1.38362e10i	0.0575816	+	0.0541426i
$712$	−1.15041e11			−0.447646
$713$		−	3.47133e10i		−	0.134319i
$714$	−4.41391e10	+	1.11378e11i	−0.169836	+	0.428554i
$715$	1.90418e10			0.0728591
$716$			3.02102e11i			1.14948i
$717$	1.36858e11	+	5.42371e10i	0.517839	+	0.205220i
$718$	1.22769e11			0.461946
$719$			1.31701e11i			0.492805i	0.969168	+	0.246402i	$0.0792485\pi$
$719$			1.31701e11i			0.492805i	−0.969168	+	0.246402i	$0.920752\pi$
$720$	2.60395e10	−	2.76935e10i	0.0968953	−	0.103050i
$721$	2.97079e10			0.109934
$722$			2.81584e11i			1.03624i
$723$	−6.95574e9	+	1.75516e10i	−0.0254560	+	0.0642340i
$724$	−1.73210e11			−0.630405
$725$		−	8.72389e10i		−	0.315761i
$726$	−1.03509e11	−	4.10205e10i	−0.372589	−	0.147657i
$727$	1.82998e11			0.655102			0.327551	−	0.944834i	$-0.393777\pi$
$727$	1.82998e11			0.655102			0.327551	+	0.944834i	$0.393777\pi$
$728$			1.20725e11i			0.429805i
$729$	1.80448e11	−	2.17267e11i	0.638913	−	0.769279i
$730$	5.95628e10			0.209741
$731$			3.14319e11i			1.10078i
$732$	7.56155e10	−	1.90803e11i	0.263370	−	0.664571i
$733$	1.52831e10			0.0529413			0.0264707	−	0.999650i	$-0.491573\pi$
$733$	1.52831e10			0.0529413			0.0264707	+	0.999650i	$0.491573\pi$
$734$			2.92750e10i			0.100858i
$735$	−9.57929e10	−	3.79628e10i	−0.328234	−	0.130080i
$736$	−1.23112e11			−0.419555
$737$			1.10219e11i			0.373583i
$738$	−1.76393e11	−	1.65858e11i	−0.594642	−	0.559128i
$739$	−2.80725e11			−0.941245			−0.470623	−	0.882335i	$-0.655971\pi$
$739$	−2.80725e11			−0.941245			−0.470623	+	0.882335i	$0.655971\pi$
$740$			3.38935e10i			0.113029i
$741$	7.17222e10	−	1.80979e11i	0.237893	−	0.600283i
$742$	−3.20713e11			−1.05804
$743$		−	2.05247e11i		−	0.673475i	−0.941599	−	0.336737i	$-0.890677\pi$
$743$		−	2.05247e11i		−	0.673475i	0.941599	−	0.336737i	$-0.109323\pi$
$744$	8.20706e10	+	3.25247e10i	0.267853	+	0.106150i
$745$	−4.29906e10			−0.139556
$746$			1.12312e11i			0.362635i
$747$	−1.04602e11	+	1.11246e11i	−0.335937	+	0.357275i
$748$	−7.20010e10			−0.230002
$749$			3.89580e11i			1.23785i
$750$	−5.19742e9	+	1.31148e10i	−0.0164264	+	0.0414494i
$751$	1.85798e11			0.584094			0.292047	−	0.956404i	$-0.405664\pi$
$751$	1.85798e11			0.584094			0.292047	+	0.956404i	$0.405664\pi$
$752$			1.38817e11i			0.434081i
$753$	−3.08689e11	−	1.22334e11i	−0.960154	−	0.380510i
$754$	9.36066e10			0.289615
$755$			2.45470e11i			0.755460i
$756$	−2.97271e11	+	1.39534e11i	−0.910050	+	0.427163i
$757$	−1.02442e11			−0.311956			−0.155978	−	0.987761i	$-0.549853\pi$
$757$	−1.02442e11			−0.311956			−0.155978	+	0.987761i	$0.549853\pi$
$758$		−	1.66460e11i		−	0.504235i
$759$	2.20328e10	−	5.55962e10i	0.0663901	−	0.167524i
$760$	−2.28572e11			−0.685123
$761$		−	2.07040e11i		−	0.617327i	−0.951171	−	0.308664i	$-0.900118\pi$
$761$		−	2.07040e11i		−	0.617327i	0.951171	−	0.308664i	$-0.0998817\pi$
$762$	−1.67045e11	−	6.62002e10i	−0.495466	−	0.196354i
$763$	−4.16835e11			−1.22989
$764$			3.01013e11i			0.883509i
$765$	7.71391e10	+	7.25321e10i	0.225231	+	0.211780i
$766$	−7.92318e10			−0.230136
$767$		−	5.84356e10i		−	0.168848i
$768$	8.48835e10	−	2.14190e11i	0.243994	−	0.615678i
$769$	4.39556e11			1.25692			0.628462	−	0.777841i	$-0.283685\pi$
$769$	4.39556e11			1.25692			0.628462	+	0.777841i	$0.283685\pi$
$770$			4.64107e10i			0.132025i
$771$	4.87322e11	+	1.93126e11i	1.37911	+	0.546542i
$772$	−1.71165e11			−0.481888
$773$			4.81386e11i			1.34827i	0.738610	+	0.674133i	$0.235482\pi$
$773$			4.81386e11i			1.34827i	−0.738610	+	0.674133i	$0.764518\pi$
$774$	1.95141e11	−	2.07535e11i	0.543731	−	0.578267i
$775$	2.38093e10			0.0659992
$776$		−	3.23150e11i		−	0.891164i
$777$	6.04134e10	−	1.52443e11i	0.165748	−	0.418238i
$778$	1.87687e11			0.512289
$779$		−	1.05803e12i		−	2.87309i
$780$	4.25596e10	+	1.68664e10i	0.114979	+	0.0455663i
$781$	7.05201e10			0.189543
$782$		−	5.24534e10i		−	0.140264i
$783$	2.52154e11	+	5.37203e11i	0.670840	+	1.42919i
$784$	9.43402e10			0.249708
$785$			7.85099e10i			0.206750i
$786$	−1.32004e11	+	3.33090e11i	−0.345857	+	0.872712i
$787$	1.76591e10			0.0460331			0.0230166	−	0.999735i	$-0.492673\pi$
$787$	1.76591e10			0.0460331			0.0230166	+	0.999735i	$0.492673\pi$
$788$		−	1.89916e11i		−	0.492557i
$789$	−8.96203e10	−	3.55166e10i	−0.231259	−	0.0916481i
$790$	6.86295e9			0.0176199
$791$			4.96423e11i			1.26808i
$792$	1.10799e11	+	1.04182e11i	0.281602	+	0.264784i
$793$	1.38426e11			0.350045
$794$		−	1.15708e11i		−	0.291127i
$795$	−1.04428e11	+	2.63508e11i	−0.261427	+	0.659667i
$796$	2.62312e11			0.653381
$797$		−	2.22982e11i		−	0.552633i	−0.961067	−	0.276317i	$-0.910886\pi$
$797$		−	2.22982e11i		−	0.552633i	0.961067	−	0.276317i	$-0.0891139\pi$
$798$	4.41102e11	+	1.74809e11i	1.08775	+	0.431074i
$799$	−3.86669e11			−0.948750
$800$		−	8.44403e10i		−	0.206153i
$801$	1.44578e11	−	1.53761e11i	0.351214	−	0.373522i
$802$	−1.37737e11			−0.332930
$803$		−	1.73184e11i		−	0.416529i
$804$	−9.76273e10	+	2.46346e11i	−0.233640	+	0.589552i
$805$	1.02257e11			0.243505
$806$			2.55471e10i			0.0605343i
$807$	−6.95571e11	−	2.75655e11i	−1.64001	−	0.649938i
$808$	−4.45377e11			−1.04492
$809$		−	1.32706e11i		−	0.309810i	−0.987929	−	0.154905i	$-0.950493\pi$
$809$		−	1.32706e11i		−	0.309810i	0.987929	−	0.154905i	$-0.0495072\pi$
$810$	−5.90208e9	−	9.57815e10i	−0.0137109	−	0.222506i
$811$	7.48071e11			1.72926			0.864628	−	0.502412i	$-0.167554\pi$
$811$	7.48071e11			1.72926			0.864628	+	0.502412i	$0.167554\pi$
$812$		−	6.90009e11i		−	1.58720i
$813$	1.63361e11	−	4.12214e11i	0.373926	−	0.943540i
$814$	−3.25844e10			−0.0742185
$815$		−	1.40333e11i		−	0.318075i
$816$	−9.01236e10	−	3.57161e10i	−0.203272	−	0.0805569i
$817$	1.24483e12			2.79398
$818$			8.85636e10i			0.197807i
$819$	−1.61357e11	−	1.51720e11i	−0.358635	−	0.337216i
$820$	2.48810e11			0.550317
$821$			4.86613e11i			1.07105i	0.844519	+	0.535526i	$0.179887\pi$
$821$			4.86613e11i			1.07105i	−0.844519	+	0.535526i	$0.820113\pi$
$822$	1.36858e10	−	3.45339e10i	0.0299767	−	0.0756413i
$823$	−2.67253e11			−0.582537			−0.291269	−	0.956641i	$-0.594077\pi$
$823$	−2.67253e11			−0.582537			−0.291269	+	0.956641i	$0.594077\pi$
$824$		−	3.30780e10i		−	0.0717515i
$825$	3.81325e10	+	1.51119e10i	0.0823150	+	0.0326215i
$826$	1.42425e11			0.305962
$827$		−	9.99227e10i		−	0.213620i	−0.994279	−	0.106810i	$-0.965936\pi$
$827$		−	9.99227e10i		−	0.213620i	0.994279	−	0.106810i	$-0.0340637\pi$
$828$	9.84894e10	−	1.04745e11i	0.209541	−	0.222850i
$829$	−1.37202e11			−0.290497			−0.145249	−	0.989395i	$-0.546398\pi$
$829$	−1.37202e11			−0.290497			−0.145249	+	0.989395i	$0.546398\pi$
$830$			5.18840e10i			0.109325i
$831$	−2.32071e11	+	5.85594e11i	−0.486651	+	1.22798i
$832$	3.48308e10			0.0726892
$833$			2.62781e11i			0.545775i
$834$	−1.34659e11	−	5.33656e10i	−0.278338	−	0.110306i
$835$	−6.53865e10			−0.134506
$836$			2.85154e11i			0.583786i
$837$	−1.46613e11	+	6.88179e10i	−0.298725	+	0.140217i
$838$	−2.12320e11			−0.430542
$839$		−	2.29368e11i		−	0.462899i	−0.972847	−	0.231449i	$-0.925653\pi$
$839$		−	2.29368e11i		−	0.462899i	0.972847	−	0.231449i	$-0.0743467\pi$
$840$	−9.58095e10	+	2.41759e11i	−0.192438	+	0.485586i
$841$	−7.46680e11			−1.49262
$842$		−	1.62397e11i		−	0.323094i
$843$	2.57287e11	+	1.01963e11i	0.509458	+	0.201899i
$844$	1.82338e11			0.359341
$845$		−	1.97127e11i		−	0.386652i
$846$	2.55306e11	+	2.40058e11i	0.498401	+	0.468635i
$847$	−5.53548e11			−1.07553
$848$		−	2.59511e11i		−	0.501849i
$849$	−2.71543e11	+	6.85194e11i	−0.522646	+	1.31881i
$850$	3.59769e10			0.0689204
$851$			7.17933e10i			0.136888i
$852$	1.57617e11	+	6.24636e10i	0.299119	+	0.118541i
$853$	−7.54864e11			−1.42585			−0.712923	−	0.701242i	$-0.752629\pi$
$853$	−7.54864e11			−1.42585			−0.712923	+	0.701242i	$0.752629\pi$
$854$			3.37385e11i			0.634300i
$855$	2.87257e11	−	3.05503e11i	0.537534	−	0.571677i
$856$	4.33774e11			0.807921
$857$			9.33249e9i			0.0173011i	0.999963	+	0.00865056i	$0.00275359\pi$
$857$			9.33249e9i			0.0173011i	−0.999963	+	0.00865056i	$0.997246\pi$
$858$	−1.62150e10	+	4.09158e10i	−0.0299204	+	0.0754991i
$859$	3.51970e11			0.646447			0.323224	−	0.946323i	$-0.395233\pi$
$859$	3.51970e11			0.646447			0.323224	+	0.946323i	$0.395233\pi$
$860$			2.92738e11i			0.535163i
$861$	−1.11908e12	−	4.43492e11i	−2.03633	−	0.806999i
$862$	1.00919e11			0.182787
$863$		−	4.14848e11i		−	0.747905i	−0.927448	−	0.373952i	$-0.878002\pi$
$863$		−	4.14848e11i		−	0.747905i	0.927448	−	0.373952i	$-0.121998\pi$
$864$	2.44065e11	+	5.19969e11i	0.437976	+	0.933088i
$865$	−1.78244e11			−0.318383
$866$		−	2.90233e11i		−	0.516030i
$867$	−1.08687e11	+	2.74255e11i	−0.192355	+	0.485375i
$868$	1.88317e11			0.331750
$869$		−	1.99546e10i		−	0.0349916i
$870$	1.87453e11	+	7.42879e10i	0.327202	+	0.129671i
$871$	−1.78721e11			−0.310530
$872$			4.64121e11i			0.802723i
$873$	4.31913e11	+	4.06118e11i	0.743601	+	0.699190i
$874$	−2.07737e11			−0.356015
$875$			7.01361e10i			0.119649i
$876$	1.53399e11	−	3.87076e11i	0.260498	−	0.657325i
$877$	−6.49541e11			−1.09801			−0.549007	−	0.835818i	$-0.684994\pi$
$877$	−6.49541e11			−1.09801			−0.549007	+	0.835818i	$0.684994\pi$
$878$		−	4.70731e11i		−	0.792127i
$879$	−1.70760e11	−	6.76724e10i	−0.286043	−	0.113359i
$880$	−3.75542e10			−0.0626221
$881$		−	2.43386e11i		−	0.404010i	−0.979384	−	0.202005i	$-0.935254\pi$
$881$		−	2.43386e11i		−	0.404010i	0.979384	−	0.202005i	$-0.0647458\pi$
$882$	1.63144e11	−	1.73506e11i	0.269586	−	0.286709i
$883$	5.16877e11			0.850245			0.425122	−	0.905136i	$-0.360231\pi$
$883$	5.16877e11			0.850245			0.425122	+	0.905136i	$0.360231\pi$
$884$		−	1.16750e11i		−	0.191183i
$885$	4.63756e10	−	1.17021e11i	0.0755990	−	0.190762i
$886$	−1.27539e11			−0.206970
$887$		−	6.37860e11i		−	1.03046i	−0.857052	−	0.515229i	$-0.827707\pi$
$887$		−	6.37860e11i		−	1.03046i	0.857052	−	0.515229i	$-0.172293\pi$
$888$	−1.69736e11	−	6.72667e10i	−0.272975	−	0.108180i
$889$	−8.93332e11			−1.43023
$890$		−	7.17126e10i		−	0.114297i
$891$	−2.78493e11	+	1.71608e10i	−0.441879	+	0.0272286i
$892$	1.96079e11			0.309722
$893$			1.53137e12i			2.40810i
$894$	3.66085e10	−	9.23754e10i	0.0573101	−	0.144613i
$895$	−4.38905e11			−0.684036
$896$		−	8.03809e11i		−	1.24716i
$897$	9.01498e10	+	3.57265e10i	0.139250	+	0.0551849i
$898$	1.28935e10			0.0198274
$899$		−	3.40311e11i		−	0.521000i
$900$	7.18429e10	+	6.75522e10i	0.109500	+	0.102960i
$901$	7.22859e11			1.09687
$902$			2.39200e11i			0.361356i
$903$	5.21791e11	−	1.31665e12i	0.784776	−	1.98025i
$904$	5.52738e11			0.827647
$905$		−	2.51647e11i		−	0.375143i
$906$	−5.27451e11	−	2.09029e11i	−0.782833	−	0.310238i
$907$	5.28792e11			0.781368			0.390684	−	0.920525i	$-0.372239\pi$
$907$	5.28792e11			0.781368			0.390684	+	0.920525i	$0.372239\pi$
$908$			2.76555e10i			0.0406853i
$909$	5.59725e11	−	5.95277e11i	0.819822	−	0.871894i
$910$	−7.52554e10			−0.109742
$911$			1.10395e12i			1.60279i	0.598137	+	0.801394i	$0.295908\pi$
$911$			1.10395e12i			1.60279i	−0.598137	+	0.801394i	$0.704092\pi$
$912$	−1.41450e11	+	3.56927e11i	−0.204468	+	0.515940i
$913$	1.50857e11			0.217111
$914$			4.00080e11i			0.573273i
$915$	2.77206e11	+	1.09857e11i	0.395475	+	0.156727i
$916$	−1.18151e10			−0.0167824
$917$			1.78131e12i			2.51920i
$918$	−2.21540e11	+	1.03987e11i	−0.311947	+	0.146423i
$919$	8.75563e11			1.22751			0.613756	−	0.789496i	$-0.289658\pi$
$919$	8.75563e11			1.22751			0.613756	+	0.789496i	$0.289658\pi$
$920$		−	1.13857e11i		−	0.158931i
$921$	3.14651e11	−	7.93971e11i	0.437312	−	1.10348i
$922$	5.73829e11			0.794070
$923$			1.14349e11i			0.157553i
$924$	3.01606e11	+	1.19527e11i	0.413763	+	0.163975i
$925$	−4.92417e10			−0.0672615
$926$		−	4.93713e11i		−	0.671476i
$927$	4.42111e10	+	4.15707e10i	0.0598705	+	0.0562948i
$928$	−1.20692e12			−1.62738
$929$			2.94492e11i			0.395377i	0.980265	+	0.197688i	$0.0633434\pi$
$929$			2.94492e11i			0.395377i	−0.980265	+	0.197688i	$0.936657\pi$
$930$	−2.02747e10	+	5.11598e10i	−0.0271033	+	0.0683907i
$931$	1.04072e12			1.38527
$932$		−	2.14951e11i		−	0.284890i
$933$	5.42489e11	+	2.14989e11i	0.715919	+	0.283720i
$934$	−3.97407e10			−0.0522214
$935$		−	1.04606e11i		−	0.136870i
$936$	−1.68932e11	+	1.79662e11i	−0.220094	+	0.234073i
$937$	−6.27494e11			−0.814050			−0.407025	−	0.913417i	$-0.633434\pi$
$937$	−6.27494e11			−0.814050			−0.407025	+	0.913417i	$0.633434\pi$
$938$		−	4.35599e11i		−	0.562698i
$939$	6.92799e10	−	1.74816e11i	0.0891138	−	0.224864i
$940$	−3.60121e11			−0.461250
$941$		−	4.89291e11i		−	0.624035i	−0.950076	−	0.312017i	$-0.898995\pi$
$941$		−	4.89291e11i		−	0.624035i	0.950076	−	0.312017i	$-0.101005\pi$
$942$	−1.68697e11	−	6.68548e10i	−0.214242	−	0.0849042i
$943$	5.27031e11			0.666483
$944$			1.15246e11i			0.145124i
$945$	−2.02720e11	−	4.31887e11i	−0.254197	−	0.541555i
$946$	−2.81432e11			−0.351406
$947$			1.12362e12i			1.39708i	0.715571	+	0.698540i	$0.246166\pi$
$947$			1.12362e12i			1.39708i	−0.715571	+	0.698540i	$0.753834\pi$
$948$	1.76749e10	−	4.45997e10i	0.0218839	−	0.0552203i
$949$	2.80819e11			0.346228
$950$		−	1.42483e11i		−	0.174932i
$951$	−8.87149e10	−	3.51578e10i	−0.108461	−	0.0429833i
$952$	6.63199e11			0.807414
$953$		−	2.38597e11i		−	0.289263i	−0.989486	−	0.144632i	$-0.953800\pi$
$953$		−	2.38597e11i		−	0.289263i	0.989486	−	0.144632i	$-0.0461997\pi$
$954$	−4.77282e11	−	4.48777e11i	−0.576211	−	0.541798i
$955$	−4.37322e11			−0.525761
$956$		−	3.49656e11i		−	0.418610i
$957$	2.15998e11	−	5.45036e11i	0.257515	−	0.649797i
$958$	7.98940e9			0.00948532
$959$		−	1.84682e11i		−	0.218349i
$960$	6.97509e10	+	2.76423e10i	0.0821230	+	0.0325454i
$961$	−7.60013e11			−0.891102
$962$		−	5.28359e10i		−	0.0616920i
$963$	−5.45145e11	+	5.79770e11i	−0.633879	+	0.674141i
$964$	4.48423e10			0.0519254
$965$		−	2.48675e11i		−	0.286763i
$966$	−8.70763e10	+	2.19723e11i	−0.0999981	+	0.252329i
$967$	−7.79476e11			−0.891450			−0.445725	−	0.895170i	$-0.647054\pi$
$967$	−7.79476e11			−0.891450			−0.445725	+	0.895170i	$0.647054\pi$
$968$			6.16343e11i			0.701974i
$969$	−9.94205e11	−	3.94004e11i	−1.12767	−	0.446896i
$970$	2.01440e11			0.227541
$971$		−	8.66546e11i		−	0.974798i	−0.873179	−	0.487399i	$-0.837946\pi$
$971$		−	8.66546e11i		−	0.974798i	0.873179	−	0.487399i	$-0.162054\pi$
$972$	−6.37648e11	−	2.08321e11i	−0.714358	−	0.233383i
$973$	−7.20137e11			−0.803460
$974$			6.61752e11i			0.735291i
$975$	−2.45041e10	+	6.18322e10i	−0.0271157	+	0.0684220i
$976$	−2.73002e11			−0.300862
$977$			4.89741e11i			0.537512i	0.963208	+	0.268756i	$0.0866125\pi$
$977$			4.89741e11i			0.537512i	−0.963208	+	0.268756i	$0.913388\pi$
$978$	3.01538e11	+	1.19500e11i	0.329600	+	0.130621i
$979$	−2.08510e11			−0.226985
$980$			2.44739e11i			0.265338i
$981$	−6.20331e11	−	5.83283e11i	−0.669804	−	0.629801i
$982$	−1.37311e11			−0.147659
$983$			6.13109e11i			0.656635i	0.944567	+	0.328317i	$0.106482\pi$
$983$			6.13109e11i			0.656635i	−0.944567	+	0.328317i	$0.893518\pi$
$984$	−4.93802e11	+	1.24603e12i	−0.526711	+	1.32907i
$985$	2.75917e11			0.293112
$986$		−	5.14226e11i		−	0.544059i
$987$	1.61972e12	+	6.41897e11i	1.70676	+	0.676389i
$988$	−4.62379e11			−0.485256
$989$			6.20079e11i			0.648130i
$990$	−6.49431e10	+	6.90681e10i	−0.0676071	+	0.0719013i
$991$	3.85928e11			0.400140			0.200070	−	0.979782i	$-0.435883\pi$
$991$	3.85928e11			0.400140			0.200070	+	0.979782i	$0.435883\pi$
$992$		−	3.29394e11i		−	0.340148i
$993$	−1.09778e11	+	2.77008e11i	−0.112907	+	0.284901i
$994$	−2.78703e11			−0.285494
$995$			3.81097e11i			0.388816i
$996$	3.37175e11	+	1.33623e11i	0.342624	+	0.135782i
$997$	1.56419e12			1.58310			0.791551	−	0.611104i	$-0.209274\pi$
$997$	1.56419e12			1.58310			0.791551	+	0.611104i	$0.209274\pi$
$998$			5.60565e11i			0.565072i
$999$	3.03222e11	−	1.42328e11i	0.304438	−	0.142898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.c.a.11.6	yes	10
3.2	odd	2	inner	15.9.c.a.11.5	✓	10
4.3	odd	2		240.9.l.b.161.5		10
5.2	odd	4		75.9.d.c.74.10		20
5.3	odd	4		75.9.d.c.74.11		20
5.4	even	2		75.9.c.g.26.5		10
12.11	even	2		240.9.l.b.161.6		10
15.2	even	4		75.9.d.c.74.12		20
15.8	even	4		75.9.d.c.74.9		20
15.14	odd	2		75.9.c.g.26.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.5	✓	10	3.2	odd	2	inner
15.9.c.a.11.6	yes	10	1.1	even	1	trivial
75.9.c.g.26.5		10	5.4	even	2
75.9.c.g.26.6		10	15.14	odd	2
75.9.d.c.74.9		20	15.8	even	4
75.9.d.c.74.10		20	5.2	odd	4
75.9.d.c.74.11		20	5.3	odd	4
75.9.d.c.74.12		20	15.2	even	4
240.9.l.b.161.5		10	4.3	odd	2
240.9.l.b.161.6		10	12.11	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+7.97572i q^{2} +(-29.8424 + 75.3023i) q^{3} +192.388 q^{4} +279.508i q^{5} +(-600.590 - 238.014i) q^{6} -3211.86 q^{7} +3576.22i q^{8} +(-4779.87 - 4494.40i) q^{9} +O(q^{10})\)	\(q+7.97572i q^{2} +(-29.8424 + 75.3023i) q^{3} +192.388 q^{4} +279.508i q^{5} +(-600.590 - 238.014i) q^{6} -3211.86 q^{7} +3576.22i q^{8} +(-4779.87 - 4494.40i) q^{9} -2229.28 q^{10} +6481.82i q^{11} +(-5741.31 + 14487.3i) q^{12} -10510.3 q^{13} -25616.9i q^{14} +(-21047.6 - 8341.19i) q^{15} +20728.4 q^{16} +57738.3i q^{17} +(35846.0 - 38122.9i) q^{18} +228667. q^{19} +53774.1i q^{20} +(95849.5 - 241860. i) q^{21} -51697.1 q^{22} +113904. i q^{23} +(-269297. - 106723. i) q^{24} -78125.0 q^{25} -83827.4i q^{26} +(481081. - 225811. i) q^{27} -617923. q^{28} +1.11666e6i q^{29} +(66527.0 - 167870. i) q^{30} -304758. q^{31} +1.08084e6i q^{32} +(-488096. - 193433. i) q^{33} -460504. q^{34} -897742. i q^{35} +(-919589. - 864668. i) q^{36} +630294. q^{37} +1.82379e6i q^{38} +(313653. - 791452. i) q^{39} -999583. q^{40} -4.62696e6i q^{41} +(1.92901e6 + 764469. i) q^{42} +5.44386e6 q^{43} +1.24702e6i q^{44} +(1.25622e6 - 1.33601e6i) q^{45} -908469. q^{46} +6.69692e6i q^{47} +(-618586. + 1.56090e6i) q^{48} +4.55125e6 q^{49} -623103. i q^{50} +(-4.34782e6 - 1.72305e6i) q^{51} -2.02206e6 q^{52} -1.25196e7i q^{53} +(1.80101e6 + 3.83696e6i) q^{54} -1.81172e6 q^{55} -1.14863e7i q^{56} +(-6.82398e6 + 1.72192e7i) q^{57} -8.90615e6 q^{58} +5.55982e6i q^{59} +(-4.04931e6 - 1.60475e6i) q^{60} -1.31704e7 q^{61} -2.43067e6i q^{62} +(1.53523e7 + 1.44354e7i) q^{63} -3.31396e6 q^{64} -2.93773e6i q^{65} +(1.54276e6 - 3.89291e6i) q^{66} +1.70044e7 q^{67} +1.11081e7i q^{68} +(-8.57726e6 - 3.39918e6i) q^{69} +7.16014e6 q^{70} -1.08797e7i q^{71} +(1.60729e7 - 1.70938e7i) q^{72} -2.67184e7 q^{73} +5.02705e6i q^{74} +(2.33143e6 - 5.88299e6i) q^{75} +4.39928e7 q^{76} -2.08187e7i q^{77} +(6.31239e6 + 2.50161e6i) q^{78} -3.07855e6 q^{79} +5.79377e6i q^{80} +(2.64753e6 + 4.29652e7i) q^{81} +3.69033e7 q^{82} -2.32739e7i q^{83} +(1.84403e7 - 4.65310e7i) q^{84} -1.61383e7 q^{85} +4.34187e7i q^{86} +(-8.40869e7 - 3.33237e7i) q^{87} -2.31804e7 q^{88} +3.21685e7i q^{89} +(1.06557e7 + 1.00193e7i) q^{90} +3.37577e7 q^{91} +2.19138e7i q^{92} +(9.09471e6 - 2.29490e7i) q^{93} -5.34128e7 q^{94} +6.39145e7i q^{95} +(-8.13894e7 - 3.22547e7i) q^{96} -9.03610e7 q^{97} +3.62994e7i q^{98} +(2.91319e7 - 3.09822e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9}+O(q^{10}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9 - 8750 * q^10 - 3812 * q^12 - 55464 * q^13 - 21250 * q^15 + 280386 * q^16 - 419800 * q^18 - 231516 * q^19 + 289572 * q^21 + 1129940 * q^22 + 1136334 * q^24 - 781250 * q^25 - 335512 * q^27 - 3340724 * q^28 - 965000 * q^30 + 881620 * q^31 + 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 + 4672616 * q^37 + 1826792 * q^39 + 2913750 * q^40 - 5392860 * q^42 + 7731336 * q^43 - 2142500 * q^45 - 25424604 * q^46 + 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 + 21064016 * q^52 - 7979798 * q^54 - 4377500 * q^55 - 2856304 * q^57 - 4351100 * q^58 + 23016250 * q^60 + 22417020 * q^61 + 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 - 46646024 * q^67 + 33562632 * q^69 - 62992500 * q^70 + 54175560 * q^72 - 129964884 * q^73 + 8750000 * q^75 + 198922436 * q^76 + 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 + 202877560 * q^82 - 197346768 * q^84 - 110682500 * q^85 - 168322540 * q^87 - 484775700 * q^88 + 171878750 * q^90 + 444288464 * q^91 + 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 - 258825724 * q^97 - 33965200 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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