LMFDB - Embedded newform 15.10.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,10,Mod(4,15)]

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([0, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("15.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	15.b (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:	$7.72553754246$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 939x^{6} + 217699x^{4} + 14559561x^{2} + 31136400 $ x^8 + 939x^6 + 217699x^4 + 14559561*x^2 + 31136400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{12}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$13.6993i$ of defining polynomial
Character	$\chi$	$=$	15.4
Dual form			15.10.b.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.9703i q^{2} +81.0000i q^{3} +72.2477 q^{4} +(-743.946 - 1183.08i) q^{5} +1698.59 q^{6} -3575.78i q^{7} -12251.8i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-20.9703i q^{2} +81.0000i q^{3} +72.2477 q^{4} +(-743.946 - 1183.08i) q^{5} +1698.59 q^{6} -3575.78i q^{7} -12251.8i q^{8} -6561.00 q^{9} +(-24809.4 + 15600.8i) q^{10} -74517.5 q^{11} +5852.07i q^{12} -34478.5i q^{13} -74985.1 q^{14} +(95829.2 - 60259.7i) q^{15} -219933. q^{16} -372733. i q^{17} +137586. i q^{18} +835114. q^{19} +(-53748.4 - 85474.5i) q^{20} +289638. q^{21} +1.56265e6i q^{22} +31807.7i q^{23} +992398. q^{24} +(-846213. + 1.76029e6i) q^{25} -723024. q^{26} -531441. i q^{27} -258342. i q^{28} +6.73894e6 q^{29} +(-1.26366e6 - 2.00956e6i) q^{30} -4.04277e6 q^{31} -1.66087e6i q^{32} -6.03591e6i q^{33} -7.81631e6 q^{34} +(-4.23042e6 + 2.66019e6i) q^{35} -474017. q^{36} +6.29831e6i q^{37} -1.75126e7i q^{38} +2.79276e6 q^{39} +(-1.44948e7 + 9.11471e6i) q^{40} +1.10746e7 q^{41} -6.07379e6i q^{42} +1.42409e7i q^{43} -5.38372e6 q^{44} +(4.88103e6 + 7.76216e6i) q^{45} +667017. q^{46} +2.76408e7i q^{47} -1.78146e7i q^{48} +2.75674e7 q^{49} +(3.69138e7 + 1.77453e7i) q^{50} +3.01914e7 q^{51} -2.49100e6i q^{52} -8.30946e7i q^{53} -1.11445e7 q^{54} +(5.54370e7 + 8.81598e7i) q^{55} -4.38099e7 q^{56} +6.76443e7i q^{57} -1.41317e8i q^{58} -1.04437e8 q^{59} +(6.92344e6 - 4.35362e6i) q^{60} +3.99467e7 q^{61} +8.47779e7i q^{62} +2.34607e7i q^{63} -1.47435e8 q^{64} +(-4.07907e7 + 2.56502e7i) q^{65} -1.26575e8 q^{66} -1.98351e8i q^{67} -2.69291e7i q^{68} -2.57643e6 q^{69} +(5.57849e7 + 8.87131e7i) q^{70} +4.52976e7 q^{71} +8.03843e7i q^{72} -3.64162e8i q^{73} +1.32077e8 q^{74} +(-1.42584e8 - 6.85432e7i) q^{75} +6.03351e7 q^{76} +2.66458e8i q^{77} -5.85650e7i q^{78} +4.55156e8 q^{79} +(1.63619e8 + 2.60198e8i) q^{80} +4.30467e7 q^{81} -2.32238e8i q^{82} -3.16569e7i q^{83} +2.09257e7 q^{84} +(-4.40971e8 + 2.77293e8i) q^{85} +2.98635e8 q^{86} +5.45854e8i q^{87} +9.12975e8i q^{88} -2.77919e8 q^{89} +(1.62775e8 - 1.02357e8i) q^{90} -1.23288e8 q^{91} +2.29804e6i q^{92} -3.27464e8i q^{93} +5.79636e8 q^{94} +(-6.21280e8 - 9.88004e8i) q^{95} +1.34531e8 q^{96} -1.06978e9i q^{97} -5.78096e8i q^{98} +4.88909e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9}+O(q^{10}) $ 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9	\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9} + 67090 q^{10} - 71988 q^{11} + 416364 q^{14} + 80190 q^{15} - 1505630 q^{16} + 851584 q^{19} + 2078100 q^{20} - 1593108 q^{21} + 1242702 q^{24} + 1695500 q^{25} - 877524 q^{26} - 73572 q^{29} + 3086100 q^{30} + 474088 q^{31} - 8124388 q^{34} - 36357180 q^{35} + 7833834 q^{36} + 12959676 q^{39} - 15313390 q^{40} + 93320088 q^{41} - 74555892 q^{44} + 4527090 q^{45} - 9664072 q^{46} + 51329600 q^{49} + 67798200 q^{50} - 108196236 q^{51} - 3188646 q^{54} + 64428480 q^{55} - 67781220 q^{56} + 236526036 q^{59} + 63172710 q^{60} - 357427760 q^{61} - 12137026 q^{64} + 19848300 q^{65} + 23317308 q^{66} + 167059584 q^{69} + 200900520 q^{70} - 156890664 q^{71} - 1523381796 q^{74} - 528573600 q^{75} + 1098697344 q^{76} + 863922280 q^{79} + 630213180 q^{80} + 344373768 q^{81} + 529023636 q^{84} - 2223350420 q^{85} + 997642392 q^{86} + 357382224 q^{89} - 440177490 q^{90} + 214754328 q^{91} - 721679824 q^{94} + 1698584640 q^{95} - 475022718 q^{96} + 472313268 q^{99}+O(q^{100}) \) 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9 + 67090 * q^10 - 71988 * q^11 + 416364 * q^14 + 80190 * q^15 - 1505630 * q^16 + 851584 * q^19 + 2078100 * q^20 - 1593108 * q^21 + 1242702 * q^24 + 1695500 * q^25 - 877524 * q^26 - 73572 * q^29 + 3086100 * q^30 + 474088 * q^31 - 8124388 * q^34 - 36357180 * q^35 + 7833834 * q^36 + 12959676 * q^39 - 15313390 * q^40 + 93320088 * q^41 - 74555892 * q^44 + 4527090 * q^45 - 9664072 * q^46 + 51329600 * q^49 + 67798200 * q^50 - 108196236 * q^51 - 3188646 * q^54 + 64428480 * q^55 - 67781220 * q^56 + 236526036 * q^59 + 63172710 * q^60 - 357427760 * q^61 - 12137026 * q^64 + 19848300 * q^65 + 23317308 * q^66 + 167059584 * q^69 + 200900520 * q^70 - 156890664 * q^71 - 1523381796 * q^74 - 528573600 * q^75 + 1098697344 * q^76 + 863922280 * q^79 + 630213180 * q^80 + 344373768 * q^81 + 529023636 * q^84 - 2223350420 * q^85 + 997642392 * q^86 + 357382224 * q^89 - 440177490 * q^90 + 214754328 * q^91 - 721679824 * q^94 + 1698584640 * q^95 - 475022718 * q^96 + 472313268 * 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 $

$2$		−	20.9703i		−	0.926764i	−0.886159	−	0.463382i	$-0.846636\pi$
$2$		−	20.9703i		−	0.926764i	0.886159	−	0.463382i	$-0.153364\pi$
$3$			81.0000i			0.577350i
$3$			81.0000i			0.577350i
$4$	72.2477			0.141109
$5$	−743.946	−	1183.08i	−0.532325	−	0.846540i
$5$	−743.946	−	1183.08i	−0.532325	−	0.846540i
$6$	1698.59			0.535067
$7$		−	3575.78i		−	0.562898i	−0.959576	−	0.281449i	$-0.909185\pi$
$7$		−	3575.78i		−	0.562898i	0.959576	−	0.281449i	$-0.0908151\pi$
$8$		−	12251.8i		−	1.05754i
$9$	−6561.00			−0.333333
$10$	−24809.4	+	15600.8i	−0.784543	+	0.493339i
$11$	−74517.5			−1.53458			−0.767292	−	0.641297i	$-0.778397\pi$
$11$	−74517.5			−1.53458			−0.767292	+	0.641297i	$0.778397\pi$
$12$			5852.07i			0.0814692i
$13$		−	34478.5i		−	0.334814i	−0.985888	−	0.167407i	$-0.946461\pi$
$13$		−	34478.5i		−	0.334814i	0.985888	−	0.167407i	$-0.0535394\pi$
$14$	−74985.1			−0.521674
$15$	95829.2	−	60259.7i	0.488750	−	0.307338i
$16$	−219933.			−0.838979
$17$		−	372733.i		−	1.08237i	−0.840902	−	0.541187i	$-0.817975\pi$
$17$		−	372733.i		−	1.08237i	0.840902	−	0.541187i	$-0.182025\pi$
$18$			137586.i			0.308921i
$19$	835114.			1.47013			0.735063	−	0.677998i	$-0.237152\pi$
$19$	835114.			1.47013			0.735063	+	0.677998i	$0.237152\pi$
$20$	−53748.4	−	85474.5i	−0.0751157	−	0.119454i
$21$	289638.			0.324989
$22$			1.56265e6i			1.42220i
$23$			31807.7i			0.0237005i	0.999930	+	0.0118503i	$0.00377214\pi$
$23$			31807.7i			0.0237005i	−0.999930	+	0.0118503i	$0.996228\pi$
$24$	992398.			0.610570
$25$	−846213.	+	1.76029e6i	−0.433261	+	0.901269i
$26$	−723024.			−0.310294
$27$		−	531441.i		−	0.192450i
$28$		−	258342.i		−	0.0794299i
$29$	6.73894e6			1.76930			0.884649	−	0.466258i	$-0.154398\pi$
$29$	6.73894e6			1.76930			0.884649	+	0.466258i	$0.154398\pi$
$30$	−1.26366e6	−	2.00956e6i	−0.284830	−	0.452956i
$31$	−4.04277e6			−0.786232			−0.393116	−	0.919489i	$-0.628603\pi$
$31$	−4.04277e6			−0.786232			−0.393116	+	0.919489i	$0.628603\pi$
$32$		−	1.66087e6i		−	0.280003i
$33$		−	6.03591e6i		−	0.885993i
$34$	−7.81631e6			−1.00311
$35$	−4.23042e6	+	2.66019e6i	−0.476516	+	0.299645i
$36$	−474017.			−0.0470363
$37$			6.29831e6i			0.552480i	0.961089	+	0.276240i	$0.0890884\pi$
$37$			6.29831e6i			0.552480i	−0.961089	+	0.276240i	$0.910912\pi$
$38$		−	1.75126e7i		−	1.36246i
$39$	2.79276e6			0.193305
$40$	−1.44948e7	+	9.11471e6i	−0.895249	+	0.562954i
$41$	1.10746e7			0.612072			0.306036	−	0.952020i	$-0.400997\pi$
$41$	1.10746e7			0.612072			0.306036	+	0.952020i	$0.400997\pi$
$42$		−	6.07379e6i		−	0.301188i
$43$			1.42409e7i			0.635226i	0.948220	+	0.317613i	$0.102881\pi$
$43$			1.42409e7i			0.635226i	−0.948220	+	0.317613i	$0.897119\pi$
$44$	−5.38372e6			−0.216543
$45$	4.88103e6	+	7.76216e6i	0.177442	+	0.282180i
$46$	667017.			0.0219648
$47$			2.76408e7i			0.826249i	0.910675	+	0.413124i	$0.135563\pi$
$47$			2.76408e7i			0.826249i	−0.910675	+	0.413124i	$0.864437\pi$
$48$		−	1.78146e7i		−	0.484385i
$49$	2.75674e7			0.683146
$50$	3.69138e7	+	1.77453e7i	0.835263	+	0.401530i
$51$	3.01914e7			0.624909
$52$		−	2.49100e6i		−	0.0472452i
$53$		−	8.30946e7i		−	1.44654i	−0.690564	−	0.723272i	$-0.742637\pi$
$53$		−	8.30946e7i		−	1.44654i	0.690564	−	0.723272i	$-0.257363\pi$
$54$	−1.11445e7			−0.178356
$55$	5.54370e7	+	8.81598e7i	0.816897	+	1.29909i
$56$	−4.38099e7			−0.595286
$57$			6.76443e7i			0.848778i
$58$		−	1.41317e8i		−	1.63972i
$59$	−1.04437e8			−1.12207			−0.561034	−	0.827793i	$-0.689596\pi$
$59$	−1.04437e8			−1.12207			−0.561034	+	0.827793i	$0.689596\pi$
$60$	6.92344e6	−	4.35362e6i	0.0689670	−	0.0433681i
$61$	3.99467e7			0.369400			0.184700	−	0.982795i	$-0.440869\pi$
$61$	3.99467e7			0.369400			0.184700	+	0.982795i	$0.440869\pi$
$62$			8.47779e7i			0.728652i
$63$			2.34607e7i			0.187633i
$64$	−1.47435e8			−1.09848
$65$	−4.07907e7	+	2.56502e7i	−0.283434	+	0.178230i
$66$	−1.26575e8			−0.821106
$67$		−	1.98351e8i		−	1.20254i	−0.799047	−	0.601268i	$-0.794662\pi$
$67$		−	1.98351e8i		−	1.20254i	0.799047	−	0.601268i	$-0.205338\pi$
$68$		−	2.69291e7i		−	0.152733i
$69$	−2.57643e6			−0.0136835
$70$	5.57849e7	+	8.87131e7i	0.277700	+	0.441618i
$71$	4.52976e7			0.211550			0.105775	−	0.994390i	$-0.466268\pi$
$71$	4.52976e7			0.211550			0.105775	+	0.994390i	$0.466268\pi$
$72$			8.03843e7i			0.352513i
$73$		−	3.64162e8i		−	1.50087i	−0.660947	−	0.750433i	$-0.729845\pi$
$73$		−	3.64162e8i		−	1.50087i	0.660947	−	0.750433i	$-0.270155\pi$
$74$	1.32077e8			0.512018
$75$	−1.42584e8	−	6.85432e7i	−0.520348	−	0.250143i
$76$	6.03351e7			0.207448
$77$			2.66458e8i			0.863815i
$78$		−	5.85650e7i		−	0.179148i
$79$	4.55156e8			1.31473			0.657367	−	0.753570i	$-0.271670\pi$
$79$	4.55156e8			1.31473			0.657367	+	0.753570i	$0.271670\pi$
$80$	1.63619e8	+	2.60198e8i	0.446609	+	0.710230i
$81$	4.30467e7			0.111111
$82$		−	2.32238e8i		−	0.567246i
$83$		−	3.16569e7i		−	0.0732178i	−0.999330	−	0.0366089i	$-0.988344\pi$
$83$		−	3.16569e7i		−	0.0732178i	0.999330	−	0.0366089i	$-0.0116556\pi$
$84$	2.09257e7			0.0458589
$85$	−4.40971e8	+	2.77293e8i	−0.916274	+	0.576175i
$86$	2.98635e8			0.588704
$87$			5.45854e8i			1.02150i
$88$			9.12975e8i			1.62288i
$89$	−2.77919e8			−0.469530			−0.234765	−	0.972052i	$-0.575432\pi$
$89$	−2.77919e8			−0.469530			−0.234765	+	0.972052i	$0.575432\pi$
$90$	1.62775e8	−	1.02357e8i	0.261514	−	0.164446i
$91$	−1.23288e8			−0.188466
$92$			2.29804e6i			0.00334435i
$93$		−	3.27464e8i		−	0.453932i
$94$	5.79636e8			0.765737
$95$	−6.21280e8	−	9.88004e8i	−0.782585	−	1.24452i
$96$	1.34531e8			0.161660
$97$		−	1.06978e9i		−	1.22694i	−0.789720	−	0.613468i	$-0.789774\pi$
$97$		−	1.06978e9i		−	1.22694i	0.789720	−	0.613468i	$-0.210226\pi$
$98$		−	5.78096e8i		−	0.633115i
$99$	4.88909e8			0.511528
$100$	−6.11369e7	+	1.27177e8i	−0.0611369	+	0.127177i
$101$	−5.28777e8			−0.505623			−0.252811	−	0.967516i	$-0.581355\pi$
$101$	−5.28777e8			−0.505623			−0.252811	+	0.967516i	$0.581355\pi$
$102$		−	6.33121e8i		−	0.579143i
$103$			1.45019e9i			1.26957i	0.772688	+	0.634786i	$0.218912\pi$
$103$			1.45019e9i			1.26957i	−0.772688	+	0.634786i	$0.781088\pi$
$104$	−4.22425e8			−0.354079
$105$	−2.15475e8	−	3.42664e8i	−0.173000	−	0.275117i
$106$	−1.74252e9			−1.34060
$107$		−	1.18511e8i		−	0.0874043i	−0.999045	−	0.0437021i	$-0.986085\pi$
$107$		−	1.18511e8i		−	0.0874043i	0.999045	−	0.0437021i	$-0.0139153\pi$
$108$		−	3.83954e7i		−	0.0271564i
$109$	−1.47459e9			−1.00058			−0.500289	−	0.865859i	$-0.666773\pi$
$109$	−1.47459e9			−1.00058			−0.500289	+	0.865859i	$0.666773\pi$
$110$	1.84874e9	−	1.16253e9i	1.20395	−	0.757071i
$111$	−5.10163e8			−0.318974
$112$			7.86434e8i			0.472260i
$113$			1.73649e9i			1.00189i	0.865480	+	0.500943i	$0.167013\pi$
$113$			1.73649e9i			1.00189i	−0.865480	+	0.500943i	$0.832987\pi$
$114$	1.41852e9			0.786617
$115$	3.76310e7	−	2.36633e7i	0.0200634	−	0.0126164i
$116$	4.86873e8			0.249663
$117$			2.26214e8i			0.111605i
$118$			2.19006e9i			1.03989i
$119$	−1.33281e9			−0.609267
$120$	−7.38291e8	−	1.17408e9i	−0.325022	−	0.516872i
$121$	3.19490e9			1.35495
$122$		−	8.37694e8i		−	0.342347i
$123$			8.97046e8i			0.353380i
$124$	−2.92081e8			−0.110944
$125$	2.71209e9	−	3.08428e8i	0.993596	−	0.112995i
$126$	4.91977e8			0.173891
$127$		−	2.07925e9i		−	0.709235i	−0.935011	−	0.354618i	$-0.884611\pi$
$127$		−	2.07925e9i		−	0.709235i	0.935011	−	0.354618i	$-0.115389\pi$
$128$			2.24138e9i			0.738025i
$129$	−1.15351e9			−0.366748
$130$	5.37891e8	+	8.55393e8i	0.165177	+	0.262676i
$131$	6.49740e9			1.92761			0.963804	−	0.266612i	$-0.0859043\pi$
$131$	6.49740e9			1.92761			0.963804	+	0.266612i	$0.0859043\pi$
$132$		−	4.36081e8i		−	0.125021i
$133$		−	2.98619e9i		−	0.827532i
$134$	−4.15948e9			−1.11447
$135$	−6.28735e8	+	3.95364e8i	−0.162917	+	0.102446i
$136$	−4.56666e9			−1.14465
$137$			2.45780e9i			0.596080i	0.954553	+	0.298040i	$0.0963329\pi$
$137$			2.45780e9i			0.596080i	−0.954553	+	0.298040i	$0.903667\pi$
$138$			5.40284e7i			0.0126814i
$139$	5.53229e9			1.25701			0.628505	−	0.777806i	$-0.283667\pi$
$139$	5.53229e9			1.25701			0.628505	+	0.777806i	$0.283667\pi$
$140$	−3.05638e8	+	1.92193e8i	−0.0672406	+	0.0422825i
$141$	−2.23891e9			−0.477035
$142$		−	9.49903e8i		−	0.196057i
$143$			2.56925e9i			0.513801i
$144$	1.44298e9			0.279660
$145$	−5.01341e9	−	7.97268e9i	−0.941840	−	1.49778i
$146$	−7.63657e9			−1.39095
$147$			2.23296e9i			0.394414i
$148$			4.55038e8i			0.0779597i
$149$	−1.06402e10			−1.76852			−0.884261	−	0.466994i	$-0.845337\pi$
$149$	−1.06402e10			−1.76852			−0.884261	+	0.466994i	$0.845337\pi$
$150$	−1.43737e9	+	2.99001e9i	−0.231824	+	0.482239i
$151$	5.40470e9			0.846009			0.423005	−	0.906128i	$-0.360975\pi$
$151$	5.40470e9			0.846009			0.423005	+	0.906128i	$0.360975\pi$
$152$		−	1.02317e10i		−	1.55472i
$153$			2.44550e9i			0.360792i
$154$	5.58770e9			0.800553
$155$	3.00760e9	+	4.78290e9i	0.418531	+	0.665577i
$156$	2.01771e8			0.0272770
$157$			7.89002e9i			1.03641i	0.855258	+	0.518203i	$0.173399\pi$
$157$			7.89002e9i			1.03641i	−0.855258	+	0.518203i	$0.826601\pi$
$158$		−	9.54474e9i		−	1.21845i
$159$	6.73066e9			0.835162
$160$	−1.96494e9	+	1.23560e9i	−0.237033	+	0.149052i
$161$	1.13738e8			0.0133410
$162$		−	9.02701e8i		−	0.102974i
$163$		−	1.43411e10i		−	1.59125i	−0.605787	−	0.795627i	$-0.707142\pi$
$163$		−	1.43411e10i		−	1.59125i	0.605787	−	0.795627i	$-0.292858\pi$
$164$	8.00118e8			0.0863688
$165$	−7.14094e9	+	4.49040e9i	−0.750029	+	0.471636i
$166$	−6.63853e8			−0.0678556
$167$			1.43038e10i			1.42308i	0.702647	+	0.711539i	$0.252001\pi$
$167$			1.43038e10i			1.42308i	−0.702647	+	0.711539i	$0.747999\pi$
$168$		−	3.54860e9i		−	0.343689i
$169$	9.41573e9			0.887900
$170$	5.81492e9	+	9.24729e9i	0.533978	+	0.849169i
$171$	−5.47919e9			−0.490042
$172$			1.02887e9i			0.0896360i
$173$		−	3.74604e9i		−	0.317955i	−0.987282	−	0.158977i	$-0.949180\pi$
$173$		−	3.74604e9i		−	0.317955i	0.987282	−	0.158977i	$-0.0508197\pi$
$174$	1.14467e10			0.946693
$175$	6.29441e9	+	3.02587e9i	0.507322	+	0.243882i
$176$	1.63889e10			1.28749
$177$		−	8.45937e9i		−	0.647826i
$178$			5.82804e9i			0.435144i
$179$	−2.22667e9			−0.162113			−0.0810565	−	0.996710i	$-0.525829\pi$
$179$	−2.22667e9			−0.162113			−0.0810565	+	0.996710i	$0.525829\pi$
$180$	3.52643e8	+	5.60798e8i	0.0250386	+	0.0398181i
$181$	−2.08908e10			−1.44678			−0.723388	−	0.690442i	$-0.757416\pi$
$181$	−2.08908e10			−1.44678			−0.723388	+	0.690442i	$0.757416\pi$
$182$			2.58538e9i			0.174664i
$183$			3.23569e9i			0.213273i
$184$	3.89703e8			0.0250642
$185$	7.45138e9	−	4.68560e9i	0.467696	−	0.294098i
$186$	−6.86701e9			−0.420687
$187$			2.77751e10i			1.66100i
$188$			1.99699e9i			0.116591i
$189$	−1.90032e9			−0.108330
$190$	−2.07187e10	+	1.30284e10i	−1.15338	+	0.725271i
$191$	1.10380e9			0.0600125			0.0300062	−	0.999550i	$-0.490447\pi$
$191$	1.10380e9			0.0600125			0.0300062	+	0.999550i	$0.490447\pi$
$192$		−	1.19422e10i		−	0.634205i
$193$		−	2.76093e10i		−	1.43234i	−0.697925	−	0.716171i	$-0.745893\pi$
$193$		−	2.76093e10i		−	1.43234i	0.697925	−	0.716171i	$-0.254107\pi$
$194$	−2.24336e10			−1.13708
$195$	−2.07766e9	−	3.30405e9i	−0.102901	−	0.163640i
$196$	1.99168e9			0.0963979
$197$		−	3.05799e10i		−	1.44656i	−0.690553	−	0.723282i	$-0.742633\pi$
$197$		−	3.05799e10i		−	1.44656i	0.690553	−	0.723282i	$-0.257367\pi$
$198$		−	1.02526e10i		−	0.474066i
$199$	−7.92786e9			−0.358358			−0.179179	−	0.983816i	$-0.557344\pi$
$199$	−7.92786e9			−0.358358			−0.179179	+	0.983816i	$0.557344\pi$
$200$	2.15668e10	+	1.03677e10i	0.953126	+	0.458190i
$201$	1.60664e10			0.694285
$202$			1.10886e10i			0.468593i
$203$		−	2.40970e10i		−	0.995934i
$204$	2.18126e9			0.0881802
$205$	−8.23894e9	−	1.31021e10i	−0.325821	−	0.518144i
$206$	3.04109e10			1.17659
$207$		−	2.08691e8i		−	0.00790017i
$208$			7.58298e9i			0.280902i
$209$	−6.22306e10			−2.25603
$210$	−7.18576e9	+	4.51858e9i	−0.254968	+	0.160330i
$211$	−3.97409e9			−0.138028			−0.0690139	−	0.997616i	$-0.521985\pi$
$211$	−3.97409e9			−0.138028			−0.0690139	+	0.997616i	$0.521985\pi$
$212$		−	6.00340e9i		−	0.204120i
$213$			3.66911e9i			0.122138i
$214$	−2.48521e9			−0.0810031
$215$	1.68480e10	−	1.05944e10i	0.537744	−	0.338146i
$216$	−6.51113e9			−0.203523
$217$			1.44561e10i			0.442569i
$218$			3.09225e10i			0.927299i
$219$	2.94971e10			0.866525
$220$	4.00520e9	+	6.36935e9i	0.115271	+	0.183313i
$221$	−1.28513e10			−0.362394
$222$			1.06983e10i			0.295614i
$223$			4.90677e10i			1.32869i	0.747426	+	0.664345i	$0.231289\pi$
$223$			4.90677e10i			1.32869i	−0.747426	+	0.664345i	$0.768711\pi$
$224$	−5.93893e9			−0.157613
$225$	5.55200e9	−	1.15493e10i	0.144420	−	0.300423i
$226$	3.64146e10			0.928512
$227$			4.97991e10i			1.24482i	0.782693	+	0.622408i	$0.213846\pi$
$227$			4.97991e10i			1.24482i	−0.782693	+	0.622408i	$0.786154\pi$
$228$			4.88714e9i			0.119770i
$229$	3.84531e10			0.923999			0.462000	−	0.886880i	$-0.347132\pi$
$229$	3.84531e10			0.923999			0.462000	+	0.886880i	$0.347132\pi$
$230$	−4.96225e8	−	7.89132e8i	−0.0116924	−	0.0185941i
$231$	−2.15831e10			−0.498724
$232$		−	8.25644e10i		−	1.87110i
$233$		−	5.45563e9i		−	0.121267i	−0.998160	−	0.0606336i	$-0.980688\pi$
$233$		−	5.45563e9i		−	0.121267i	0.998160	−	0.0606336i	$-0.0193121\pi$
$234$	4.74376e9			0.103431
$235$	3.27012e10	−	2.05633e10i	0.699453	−	0.439833i
$236$	−7.54531e9			−0.158334
$237$			3.68676e10i			0.759062i
$238$			2.79494e10i			0.564646i
$239$	5.86338e10			1.16240			0.581202	−	0.813759i	$-0.302582\pi$
$239$	5.86338e10			1.16240			0.581202	+	0.813759i	$0.302582\pi$
$240$	−2.10760e10	+	1.32531e10i	−0.410051	+	0.257850i
$241$	−2.28707e10			−0.436719			−0.218360	−	0.975868i	$-0.570071\pi$
$241$	−2.28707e10			−0.436719			−0.218360	+	0.975868i	$0.570071\pi$
$242$		−	6.69980e10i		−	1.25572i
$243$			3.48678e9i			0.0641500i
$244$	2.88606e9			0.0521256
$245$	−2.05087e10	−	3.26143e10i	−0.363655	−	0.578310i
$246$	1.88113e10			0.327500
$247$		−	2.87935e10i		−	0.492219i
$248$			4.95313e10i			0.831471i
$249$	2.56421e9			0.0422723
$250$	−6.46781e9	−	5.68733e10i	−0.104719	−	0.920828i
$251$	−1.14619e10			−0.182275			−0.0911374	−	0.995838i	$-0.529050\pi$
$251$	−1.14619e10			−0.182275			−0.0911374	+	0.995838i	$0.529050\pi$
$252$			1.69498e9i			0.0264766i
$253$		−	2.37023e9i		−	0.0363704i
$254$	−4.36025e10			−0.657293
$255$	−2.24608e10	−	3.57187e10i	−0.332655	−	0.529011i
$256$	−2.84843e10			−0.414501
$257$			7.03335e10i			1.00569i	0.864377	+	0.502844i	$0.167713\pi$
$257$			7.03335e10i			1.00569i	−0.864377	+	0.502844i	$0.832287\pi$
$258$			2.41894e10i			0.339889i
$259$	2.25214e10			0.310990
$260$	−2.94704e9	+	1.85317e9i	−0.0399950	+	0.0251498i
$261$	−4.42142e10			−0.589766
$262$		−	1.36252e11i		−	1.78644i
$263$			1.11602e11i			1.43838i	0.694815	+	0.719188i	$0.255486\pi$
$263$			1.11602e11i			1.43838i	−0.694815	+	0.719188i	$0.744514\pi$
$264$	−7.39510e10			−0.936972
$265$	−9.83072e10	+	6.18179e10i	−1.22456	+	0.770031i
$266$	−6.26212e10			−0.766926
$267$		−	2.25115e10i		−	0.271083i
$268$		−	1.43304e10i		−	0.169688i
$269$	6.35228e10			0.739680			0.369840	−	0.929095i	$-0.379412\pi$
$269$	6.35228e10			0.739680			0.369840	+	0.929095i	$0.379412\pi$
$270$	8.29088e9	+	1.31847e10i	0.0949432	+	0.150985i
$271$	−7.97056e8			−0.00897691			−0.00448845	−	0.999990i	$-0.501429\pi$
$271$	−7.97056e8			−0.00897691			−0.00448845	+	0.999990i	$0.501429\pi$
$272$			8.19764e10i			0.908090i
$273$		−	9.98631e9i		−	0.108811i
$274$	5.15408e10			0.552425
$275$	6.30576e10	−	1.31172e11i	0.664876	−	1.38307i
$276$	−1.86141e8			−0.00193086
$277$			3.68479e10i			0.376057i	0.982164	+	0.188029i	$0.0602098\pi$
$277$			3.68479e10i			0.376057i	−0.982164	+	0.188029i	$0.939790\pi$
$278$		−	1.16014e11i		−	1.16495i
$279$	2.65246e10			0.262077
$280$	3.25922e10	+	5.18304e10i	0.316886	+	0.503934i
$281$	7.86433e10			0.752460			0.376230	−	0.926526i	$-0.377220\pi$
$281$	7.86433e10			0.752460			0.376230	+	0.926526i	$0.377220\pi$
$282$			4.69505e10i			0.442099i
$283$		−	3.08266e10i		−	0.285685i	−0.989745	−	0.142842i	$-0.954376\pi$
$283$		−	3.08266e10i		−	0.285685i	0.989745	−	0.142842i	$-0.0456242\pi$
$284$	3.27265e9			0.0298515
$285$	8.00283e10	−	5.03237e10i	0.718525	−	0.451826i
$286$	5.38779e10			0.476172
$287$		−	3.96005e10i		−	0.344534i
$288$			1.08970e10i			0.0933342i
$289$	−2.03420e10			−0.171535
$290$	−1.67189e11	+	1.05133e11i	−1.38809	+	0.872864i
$291$	8.66522e10			0.708372
$292$		−	2.63099e10i		−	0.211785i
$293$		−	6.04362e10i		−	0.479064i	−0.970889	−	0.239532i	$-0.923006\pi$
$293$		−	6.04362e10i		−	0.479064i	0.970889	−	0.239532i	$-0.0769939\pi$
$294$	4.68257e10			0.365529
$295$	7.76953e10	+	1.23556e11i	0.597304	+	0.949875i
$296$	7.71658e10			0.584268
$297$			3.96016e10i			0.295331i
$298$			2.23127e11i			1.63900i
$299$	1.09668e9			0.00793526
$300$	−1.03013e10	−	4.95209e9i	−0.0734256	−	0.0352974i
$301$	5.09222e10			0.357568
$302$		−	1.13338e11i		−	0.784051i
$303$		−	4.28309e10i		−	0.291921i
$304$	−1.83670e11			−1.23341
$305$	−2.97182e10	−	4.72600e10i	−0.196641	−	0.312712i
$306$	5.12828e10			0.334369
$307$			2.37829e11i			1.52807i	0.645176	+	0.764034i	$0.276784\pi$
$307$			2.37829e11i			1.52807i	−0.645176	+	0.764034i	$0.723216\pi$
$308$			1.92510e10i			0.121892i
$309$	−1.17465e11			−0.732988
$310$	1.00299e11	−	6.30702e10i	0.616833	−	0.387879i
$311$	−1.05237e11			−0.637892			−0.318946	−	0.947773i	$-0.603329\pi$
$311$	−1.05237e11			−0.637892			−0.318946	+	0.947773i	$0.603329\pi$
$312$		−	3.42164e10i		−	0.204427i
$313$		−	1.21699e11i		−	0.716702i	−0.933587	−	0.358351i	$-0.883339\pi$
$313$		−	1.21699e11i		−	0.716702i	0.933587	−	0.358351i	$-0.116661\pi$
$314$	1.65456e11			0.960504
$315$	2.77558e10	−	1.74535e10i	0.158839	−	0.0998815i
$316$	3.28840e10			0.185521
$317$			8.05511e10i			0.448028i	0.974586	+	0.224014i	$0.0719161\pi$
$317$			8.05511e10i			0.448028i	−0.974586	+	0.224014i	$0.928084\pi$
$318$		−	1.41144e11i		−	0.773998i
$319$	−5.02169e11			−2.71514
$320$	1.09684e11	+	1.74427e11i	0.584746	+	0.929904i
$321$	9.59941e9			0.0504629
$322$		−	2.38511e9i		−	0.0123639i
$323$		−	3.11275e11i		−	1.59123i
$324$	3.11003e9			0.0156788
$325$	6.06922e10	+	2.91762e10i	0.301757	+	0.145062i
$326$	−3.00738e11			−1.47472
$327$		−	1.19441e11i		−	0.577684i
$328$		−	1.35685e11i		−	0.647290i
$329$	9.88376e10			0.465094
$330$	9.41648e10	+	1.49748e11i	0.437095	+	0.695100i
$331$	−2.15934e11			−0.988769			−0.494385	−	0.869243i	$-0.664607\pi$
$331$	−2.15934e11			−0.988769			−0.494385	+	0.869243i	$0.664607\pi$
$332$		−	2.28714e9i		−	0.0103317i
$333$		−	4.13232e10i		−	0.184160i
$334$	2.99955e11			1.31886
$335$	−2.34665e11	+	1.47563e11i	−1.01800	+	0.640140i
$336$	−6.37012e10			−0.272659
$337$			1.13654e10i			0.0480010i	0.999712	+	0.0240005i	$0.00764034\pi$
$337$			1.13654e10i			0.0480010i	−0.999712	+	0.0240005i	$0.992360\pi$
$338$		−	1.97450e11i		−	0.822873i
$339$	−1.40655e11			−0.578439
$340$	−3.18592e10	+	2.00338e10i	−0.129294	+	0.0813033i
$341$	3.01257e11			1.20654
$342$			1.14900e11i			0.454153i
$343$		−	2.42871e11i		−	0.947440i
$344$	1.74477e11			0.671776
$345$	1.91672e9	+	3.04811e9i	0.00728406	+	0.0115836i
$346$	−7.85555e10			−0.294669
$347$		−	1.23817e11i		−	0.458455i	−0.973373	−	0.229228i	$-0.926380\pi$
$347$		−	1.23817e11i		−	0.458455i	0.973373	−	0.229228i	$-0.0736200\pi$
$348$			3.94367e10i			0.144143i
$349$	1.76035e11			0.635161			0.317580	−	0.948231i	$-0.397130\pi$
$349$	1.76035e11			0.635161			0.317580	+	0.948231i	$0.397130\pi$
$350$	6.34534e10	−	1.31996e11i	0.226021	−	0.470168i
$351$	−1.83233e10			−0.0644350
$352$			1.23764e11i			0.429688i
$353$			5.17450e11i			1.77371i	0.462051	+	0.886853i	$0.347114\pi$
$353$			5.17450e11i			1.77371i	−0.462051	+	0.886853i	$0.652886\pi$
$354$	−1.77395e11			−0.600381
$355$	−3.36990e10	−	5.35905e10i	−0.112613	−	0.179085i
$356$	−2.00790e10			−0.0662549
$357$		−	1.07958e11i		−	0.351760i
$358$			4.66939e10i			0.150240i
$359$	2.86436e11			0.910128			0.455064	−	0.890459i	$-0.349616\pi$
$359$	2.86436e11			0.910128			0.455064	+	0.890459i	$0.349616\pi$
$360$	9.51007e10	−	5.98016e10i	0.298416	−	0.187651i
$361$	3.74728e11			1.16127
$362$			4.38086e11i			1.34082i
$363$			2.58787e11i			0.782281i
$364$	−8.90726e9			−0.0265943
$365$	−4.30831e11	+	2.70917e11i	−1.27054	+	0.798948i
$366$	6.78532e10			0.197654
$367$			1.20491e11i			0.346704i	0.984860	+	0.173352i	$0.0554598\pi$
$367$			1.20491e11i			0.346704i	−0.984860	+	0.173352i	$0.944540\pi$
$368$		−	6.99559e9i		−	0.0198842i
$369$	−7.26607e10			−0.204024
$370$	−9.82584e10	−	1.56257e11i	−0.272560	−	0.433444i
$371$	−2.97128e11			−0.814257
$372$		−	2.36585e10i		−	0.0640537i
$373$		−	4.05791e11i		−	1.08546i	−0.839909	−	0.542728i	$-0.817391\pi$
$373$		−	4.05791e11i		−	1.08546i	0.839909	−	0.542728i	$-0.182609\pi$
$374$	5.82452e11			1.53935
$375$	2.49826e10	+	2.19680e11i	0.0652375	+	0.573653i
$376$	3.38651e11			0.873790
$377$		−	2.32349e11i		−	0.592386i
$378$			3.98502e10i			0.100396i
$379$	2.12253e11			0.528418			0.264209	−	0.964465i	$-0.414889\pi$
$379$	2.12253e11			0.528418			0.264209	+	0.964465i	$0.414889\pi$
$380$	−4.48861e10	−	7.13810e10i	−0.110430	−	0.175613i
$381$	1.68419e11			0.409477
$382$		−	2.31470e10i		−	0.0556174i
$383$			4.96937e10i			0.118007i	0.998258	+	0.0590034i	$0.0187923\pi$
$383$			4.96937e10i			0.118007i	−0.998258	+	0.0590034i	$0.981208\pi$
$384$	−1.81552e11			−0.426099
$385$	3.15240e11	−	1.98231e11i	0.731254	−	0.459830i
$386$	−5.78974e11			−1.32744
$387$		−	9.34343e10i		−	0.211742i
$388$		−	7.72892e10i		−	0.173131i
$389$	−2.74472e11			−0.607750			−0.303875	−	0.952712i	$-0.598280\pi$
$389$	−2.74472e11			−0.607750			−0.303875	+	0.952712i	$0.598280\pi$
$390$	−6.92868e10	+	4.35692e10i	−0.151656	+	0.0953649i
$391$	1.18558e10			0.0256528
$392$		−	3.37751e11i		−	0.722453i
$393$			5.26289e11i			1.11290i
$394$	−6.41268e11			−1.34062
$395$	−3.38611e11	−	5.38484e11i	−0.699866	−	1.11298i
$396$	3.53226e10			0.0721812
$397$		−	2.17106e10i		−	0.0438646i	−0.999759	−	0.0219323i	$-0.993018\pi$
$397$		−	2.17106e10i		−	0.0438646i	0.999759	−	0.0219323i	$-0.00698183\pi$
$398$			1.66249e11i			0.332113i
$399$	2.41881e11			0.477776
$400$	1.86110e11	−	3.87147e11i	0.363497	−	0.756146i
$401$	2.16300e11			0.417741			0.208871	−	0.977943i	$-0.433021\pi$
$401$	2.16300e11			0.417741			0.208871	+	0.977943i	$0.433021\pi$
$402$		−	3.36918e11i		−	0.643438i
$403$			1.39389e11i			0.263242i
$404$	−3.82029e10			−0.0713478
$405$	−3.20245e10	−	5.09275e10i	−0.0591472	−	0.0940600i
$406$	−5.05320e11			−0.922996
$407$		−	4.69334e11i		−	0.847827i
$408$		−	3.69900e11i		−	0.660866i
$409$	2.30916e11			0.408037			0.204019	−	0.978967i	$-0.434600\pi$
$409$	2.30916e11			0.408037			0.204019	+	0.978967i	$0.434600\pi$
$410$	−2.74756e11	+	1.72773e11i	−0.480197	+	0.301959i
$411$	−1.99082e11			−0.344147
$412$			1.04773e11i			0.179148i
$413$			3.73443e11i			0.631610i
$414$	−4.37630e9			−0.00732159
$415$	−3.74525e10	+	2.35510e10i	−0.0619818	+	0.0389756i
$416$	−5.72645e10			−0.0937488
$417$			4.48116e11i			0.725735i
$418$			1.30499e12i			2.09081i
$419$	−2.38946e11			−0.378736			−0.189368	−	0.981906i	$-0.560644\pi$
$419$	−2.38946e11			−0.378736			−0.189368	+	0.981906i	$0.560644\pi$
$420$	−1.55676e10	−	2.47567e10i	−0.0244118	−	0.0388214i
$421$	4.09581e11			0.635434			0.317717	−	0.948186i	$-0.397084\pi$
$421$	4.09581e11			0.635434			0.317717	+	0.948186i	$0.397084\pi$
$422$			8.33377e10i			0.127919i
$423$		−	1.81352e11i		−	0.275416i
$424$	−1.01806e12			−1.52977
$425$	6.56118e11	+	3.15411e11i	0.975510	+	0.468951i
$426$	7.69421e10			0.113193
$427$		−	1.42841e11i		−	0.207935i
$428$		−	8.56217e9i		−	0.0123335i
$429$	−2.08109e11			−0.296643
$430$	−2.22168e11	−	3.53308e11i	−0.313382	−	0.498362i
$431$	5.29879e11			0.739655			0.369828	−	0.929100i	$-0.379417\pi$
$431$	5.29879e11			0.739655			0.369828	+	0.929100i	$0.379417\pi$
$432$			1.16882e11i			0.161462i
$433$			1.70997e11i			0.233772i	0.993145	+	0.116886i	$0.0372912\pi$
$433$			1.70997e11i			0.233772i	−0.993145	+	0.116886i	$0.962709\pi$
$434$	3.03147e11			0.410157
$435$	6.45787e11	−	4.06086e11i	0.864744	−	0.543772i
$436$	−1.06535e11			−0.141190
$437$			2.65631e10i			0.0348427i
$438$		−	6.18563e11i		−	0.803064i
$439$	2.23652e11			0.287398			0.143699	−	0.989621i	$-0.454100\pi$
$439$	2.23652e11			0.287398			0.143699	+	0.989621i	$0.454100\pi$
$440$	1.08012e12	−	6.79205e11i	1.37384	−	0.863900i
$441$	−1.80870e11			−0.227715
$442$			2.69495e11i			0.335854i
$443$			8.32773e11i			1.02733i	0.857991	+	0.513665i	$0.171712\pi$
$443$			8.32773e11i			1.02733i	−0.857991	+	0.513665i	$0.828288\pi$
$444$	−3.68581e10			−0.0450101
$445$	2.06757e11	+	3.28800e11i	0.249943	+	0.397476i
$446$	1.02896e12			1.23138
$447$		−	8.61854e11i		−	1.02106i
$448$			5.27195e11i			0.618330i
$449$	5.62842e11			0.653549			0.326774	−	0.945102i	$-0.394038\pi$
$449$	5.62842e11			0.653549			0.326774	+	0.945102i	$0.394038\pi$
$450$	−2.42191e11	−	1.16427e11i	−0.278421	−	0.133843i
$451$	−8.25254e11			−0.939276
$452$			1.25457e11i			0.141375i
$453$			4.37780e11i			0.488444i
$454$	1.04430e12			1.15365
$455$	9.17195e10	+	1.45859e11i	0.100325	+	0.159544i
$456$	8.28766e11			0.897615
$457$		−	7.43811e11i		−	0.797700i	−0.917016	−	0.398850i	$-0.869409\pi$
$457$		−	7.43811e11i		−	0.797700i	0.917016	−	0.398850i	$-0.130591\pi$
$458$		−	8.06372e11i		−	0.856329i
$459$	−1.98086e11			−0.208303
$460$	2.71875e9	−	1.70962e9i	0.00283113	−	0.00178028i
$461$	−9.90060e11			−1.02096			−0.510478	−	0.859891i	$-0.670532\pi$
$461$	−9.90060e11			−1.02096			−0.510478	+	0.859891i	$0.670532\pi$
$462$			4.52604e11i			0.462199i
$463$			7.40358e11i			0.748734i	0.927281	+	0.374367i	$0.122140\pi$
$463$			7.40358e11i			0.748734i	−0.927281	+	0.374367i	$0.877860\pi$
$464$	−1.48212e12			−1.48440
$465$	−3.87415e11	+	2.43616e11i	−0.384271	+	0.241639i
$466$	−1.14406e11			−0.112386
$467$			1.86063e11i			0.181023i	0.995895	+	0.0905114i	$0.0288502\pi$
$467$			1.86063e11i			0.181023i	−0.995895	+	0.0905114i	$0.971150\pi$
$468$			1.63434e10i			0.0157484i
$469$	−7.09261e11			−0.676906
$470$	−4.31218e11	−	6.85753e11i	−0.407621	−	0.648228i
$471$	−6.39092e11			−0.598369
$472$			1.27954e12i			1.18663i
$473$		−	1.06119e12i		−	0.974808i
$474$	7.73124e11			0.703472
$475$	−7.06684e11	+	1.47004e12i	−0.636948	+	1.32498i
$476$	−9.62926e10			−0.0859729
$477$			5.45184e11i			0.482181i
$478$		−	1.22957e12i		−	1.07727i
$479$	−5.77280e11			−0.501045			−0.250522	−	0.968111i	$-0.580602\pi$
$479$	−5.77280e11			−0.501045			−0.250522	+	0.968111i	$0.580602\pi$
$480$	−1.00084e11	−	1.59160e11i	−0.0860554	−	0.136851i
$481$	2.17156e11			0.184978
$482$			4.79604e11i			0.404736i
$483$			9.21274e9i			0.00770241i
$484$	2.30824e11			0.191196
$485$	−1.26563e12	+	7.95859e11i	−1.03865	+	0.653128i
$486$	7.31188e10			0.0594519
$487$		−	2.33534e12i		−	1.88135i	−0.339310	−	0.940675i	$-0.610194\pi$
$487$		−	2.33534e12i		−	1.88135i	0.339310	−	0.940675i	$-0.389806\pi$
$488$		−	4.89421e11i		−	0.390655i
$489$	1.16163e12			0.918711
$490$	−6.83931e11	+	4.30072e11i	−0.535957	+	0.337023i
$491$	9.07091e11			0.704343			0.352171	−	0.935936i	$-0.385443\pi$
$491$	9.07091e11			0.704343			0.352171	+	0.935936i	$0.385443\pi$
$492$			6.48095e10i			0.0498650i
$493$		−	2.51183e12i		−	1.91504i
$494$	−6.03808e11			−0.456171
$495$	−3.63722e11	−	5.78417e11i	−0.272299	−	0.433029i
$496$	8.89139e11			0.659633
$497$		−	1.61974e11i		−	0.119081i
$498$		−	5.37721e10i		−	0.0391764i
$499$	1.13701e12			0.820937			0.410469	−	0.911875i	$-0.365365\pi$
$499$	1.13701e12			0.820937			0.410469	+	0.911875i	$0.365365\pi$
$500$	1.95943e11	−	2.22832e10i	0.140205	−	0.0159446i
$501$	−1.15861e12			−0.821614
$502$			2.40360e11i			0.168926i
$503$			1.85806e11i			0.129421i	0.997904	+	0.0647103i	$0.0206123\pi$
$503$			1.85806e11i			0.129421i	−0.997904	+	0.0647103i	$0.979388\pi$
$504$	2.87437e11			0.198429
$505$	3.93382e11	+	6.25583e11i	0.269155	+	0.428030i
$506$	−4.97044e10			−0.0337068
$507$			7.62674e11i			0.512629i
$508$		−	1.50221e11i		−	0.100079i
$509$	−7.38201e11			−0.487466			−0.243733	−	0.969842i	$-0.578372\pi$
$509$	−7.38201e11			−0.487466			−0.243733	+	0.969842i	$0.578372\pi$
$510$	−7.49030e11	+	4.71008e11i	−0.490268	+	0.308292i
$511$	−1.30216e12			−0.844834
$512$			1.74491e12i			1.12217i
$513$		−	4.43814e11i		−	0.282926i
$514$	1.47491e12			0.932035
$515$	1.71568e12	−	1.07886e12i	1.07474	−	0.675824i
$516$	−8.33384e10			−0.0517514
$517$		−	2.05972e12i		−	1.26795i
$518$		−	4.72279e11i		−	0.288214i
$519$	3.03429e11			0.183571
$520$	3.14262e11	+	4.99761e11i	0.188485	+	0.299742i
$521$	−1.17044e11			−0.0695955			−0.0347977	−	0.999394i	$-0.511079\pi$
$521$	−1.17044e11			−0.0695955			−0.0347977	+	0.999394i	$0.511079\pi$
$522$			9.27184e11i			0.546573i
$523$			1.53771e12i			0.898707i	0.893354	+	0.449354i	$0.148346\pi$
$523$			1.53771e12i			0.898707i	−0.893354	+	0.449354i	$0.851654\pi$
$524$	4.69422e11			0.272002
$525$	−2.45096e11	+	5.09848e11i	−0.140805	+	0.292903i
$526$	2.34033e12			1.33304
$527$			1.50687e12i			0.850998i
$528$			1.32750e12i			0.743330i
$529$	1.80014e12			0.999438
$530$	1.29634e12	+	2.06153e12i	0.713637	+	1.13488i
$531$	6.85209e11			0.374022
$532$		−	2.15745e11i		−	0.116772i
$533$		−	3.81838e11i		−	0.204930i
$534$	−4.72072e11			−0.251230
$535$	−1.40208e11	+	8.81660e10i	−0.0739912	+	0.0465274i
$536$	−2.43017e12			−1.27173
$537$		−	1.80360e11i		−	0.0935960i
$538$		−	1.33209e12i		−	0.685509i
$539$	−2.05425e12			−1.04834
$540$	−4.54247e10	+	2.85641e10i	−0.0229890	+	0.0144560i
$541$	−2.24717e12			−1.12784			−0.563922	−	0.825828i	$-0.690708\pi$
$541$	−2.24717e12			−1.12784			−0.563922	+	0.825828i	$0.690708\pi$
$542$			1.67145e10i			0.00831947i
$543$		−	1.69215e12i		−	0.835297i
$544$	−6.19063e11			−0.303068
$545$	1.09701e12	+	1.74455e12i	0.532632	+	0.847029i
$546$	−2.09416e11			−0.100842
$547$			2.72880e12i			1.30325i	0.758541	+	0.651625i	$0.225913\pi$
$547$			2.72880e12i			1.30325i	−0.758541	+	0.651625i	$0.774087\pi$
$548$			1.77571e11i			0.0841122i
$549$	−2.62091e11			−0.123133
$550$	−2.75072e12	−	1.32234e12i	−1.28178	−	0.616183i
$551$	5.62779e12			2.60109
$552$			3.15660e10i			0.0144708i
$553$		−	1.62754e12i		−	0.740062i
$554$	7.72711e11			0.348516
$555$	3.79534e11	+	6.03562e11i	0.169798	+	0.270025i
$556$	3.99695e11			0.177375
$557$		−	1.50494e12i		−	0.662477i	−0.943547	−	0.331238i	$-0.892534\pi$
$557$		−	1.50494e12i		−	0.662477i	0.943547	−	0.331238i	$-0.107466\pi$
$558$		−	5.56228e11i		−	0.242884i
$559$	4.91004e11			0.212683
$560$	9.30411e11	−	5.85065e11i	0.399787	−	0.251396i
$561$	−2.24978e12			−0.958976
$562$		−	1.64917e12i		−	0.697353i
$563$		−	1.28466e12i		−	0.538892i	−0.963015	−	0.269446i	$-0.913159\pi$
$563$		−	1.28466e12i		−	0.538892i	0.963015	−	0.269446i	$-0.0868406\pi$
$564$	−1.61756e11			−0.0673138
$565$	2.05440e12	−	1.29185e12i	0.848137	−	0.533329i
$566$	−6.46443e11			−0.264762
$567$		−	1.53926e11i		−	0.0625442i
$568$		−	5.54979e11i		−	0.223722i
$569$	−4.36230e12			−1.74466			−0.872329	−	0.488920i	$-0.837391\pi$
$569$	−4.36230e12			−1.74466			−0.872329	+	0.488920i	$0.837391\pi$
$570$	−1.05530e12	−	1.67822e12i	−0.418736	−	0.665903i
$571$	−2.22894e12			−0.877475			−0.438738	−	0.898615i	$-0.644574\pi$
$571$	−2.22894e12			−0.877475			−0.438738	+	0.898615i	$0.644574\pi$
$572$			1.85623e11i			0.0725018i
$573$			8.94080e10i			0.0346482i
$574$	−8.30434e11			−0.319302
$575$	−5.59909e10	−	2.69161e10i	−0.0213605	−	0.0102685i
$576$	9.67320e11			0.366159
$577$			2.37578e12i			0.892307i	0.894956	+	0.446153i	$0.147206\pi$
$577$			2.37578e12i			0.892307i	−0.894956	+	0.446153i	$0.852794\pi$
$578$			4.26576e11i			0.158972i
$579$	2.23635e12			0.826963
$580$	−3.62208e11	−	5.76008e11i	−0.132902	−	0.211350i
$581$	−1.13198e11			−0.0412142
$582$		−	1.81712e12i		−	0.656493i
$583$			6.19200e12i			2.21984i
$584$	−4.46165e12			−1.58722
$585$	2.67628e11	−	1.68291e11i	0.0944779	−	0.0594099i
$586$	−1.26736e12			−0.443979
$587$		−	4.85338e12i		−	1.68722i	−0.536954	−	0.843612i	$-0.680425\pi$
$587$		−	4.85338e12i		−	1.68722i	0.536954	−	0.843612i	$-0.319575\pi$
$588$			1.61326e11i			0.0556553i
$589$	−3.37617e12			−1.15586
$590$	2.59101e12	−	1.62929e12i	0.880310	−	0.553560i
$591$	2.47697e12			0.835174
$592$		−	1.38521e12i		−	0.463519i
$593$			3.40807e12i			1.13178i	0.824480	+	0.565891i	$0.191468\pi$
$593$			3.40807e12i			1.13178i	−0.824480	+	0.565891i	$0.808532\pi$
$594$	8.30457e11			0.273702
$595$	9.91540e11	+	1.57682e12i	0.324328	+	0.515769i
$596$	−7.68728e11			−0.249554
$597$		−	6.42157e11i		−	0.206898i
$598$		−	2.29978e10i		−	0.00735412i
$599$	9.36596e11			0.297257			0.148628	−	0.988893i	$-0.452514\pi$
$599$	9.36596e11			0.297257			0.148628	+	0.988893i	$0.452514\pi$
$600$	−8.39780e11	+	1.74691e12i	−0.264536	+	0.550288i
$601$	2.48082e12			0.775639			0.387820	−	0.921735i	$-0.373228\pi$
$601$	2.48082e12			0.775639			0.387820	+	0.921735i	$0.373228\pi$
$602$		−	1.06785e12i		−	0.331381i
$603$			1.30138e12i			0.400845i
$604$	3.90477e11			0.119379
$605$	−2.37684e12	−	3.77981e12i	−0.721274	−	1.14702i
$606$	−8.98176e11			−0.270542
$607$			5.87176e12i			1.75557i	0.479052	+	0.877787i	$0.340981\pi$
$607$			5.87176e12i			1.75557i	−0.479052	+	0.877787i	$0.659019\pi$
$608$		−	1.38702e12i		−	0.411639i
$609$	1.95186e12			0.575003
$610$	−9.91056e11	+	6.23199e11i	−0.289810	+	0.182240i
$611$	9.53015e11			0.276640
$612$			1.76682e11i			0.0509109i
$613$			3.44781e11i			0.0986215i	0.998783	+	0.0493108i	$0.0157025\pi$
$613$			3.44781e11i			0.0986215i	−0.998783	+	0.0493108i	$0.984298\pi$
$614$	4.98734e12			1.41616
$615$	1.06127e12	−	6.67354e11i	0.299150	−	0.188113i
$616$	3.26460e12			0.913518
$617$			3.81915e12i			1.06092i	0.847709	+	0.530461i	$0.177981\pi$
$617$			3.81915e12i			1.06092i	−0.847709	+	0.530461i	$0.822019\pi$
$618$			2.46328e12i			0.679306i
$619$	−8.91644e11			−0.244109			−0.122055	−	0.992523i	$-0.538948\pi$
$619$	−8.91644e11			−0.244109			−0.122055	+	0.992523i	$0.538948\pi$
$620$	2.17292e11	+	3.45554e11i	0.0590584	+	0.0939189i
$621$	1.69039e10			0.00456116
$622$			2.20685e12i			0.591176i
$623$			9.93779e11i			0.264298i
$624$	−6.14222e11			−0.162179
$625$	−2.38255e12	−	2.97916e12i	−0.624570	−	0.780969i
$626$	−2.55207e12			−0.664213
$627$		−	5.04068e12i		−	1.30252i
$628$			5.70036e11i			0.146246i
$629$	2.34759e12			0.597990
$630$	−3.66005e11	−	5.82047e11i	−0.0925666	−	0.147206i
$631$	2.72749e12			0.684907			0.342453	−	0.939535i	$-0.388742\pi$
$631$	2.72749e12			0.684907			0.342453	+	0.939535i	$0.388742\pi$
$632$		−	5.57649e12i		−	1.39038i
$633$		−	3.21901e11i		−	0.0796904i
$634$	1.68918e12			0.415216
$635$	−2.45991e12	+	1.54685e12i	−0.600396	+	0.377543i
$636$	4.86275e11			0.117849
$637$		−	9.50483e11i		−	0.228727i
$638$			1.05306e13i			2.51629i
$639$	−2.97198e11			−0.0705166
$640$	2.65173e12	−	1.66747e12i	0.624768	−	0.392869i
$641$	5.88474e12			1.37678			0.688392	−	0.725339i	$-0.258317\pi$
$641$	5.88474e12			1.37678			0.688392	+	0.725339i	$0.258317\pi$
$642$		−	2.01302e11i		−	0.0467672i
$643$			8.44268e11i			0.194774i	0.995247	+	0.0973870i	$0.0310485\pi$
$643$			8.44268e11i			0.194774i	−0.995247	+	0.0973870i	$0.968952\pi$
$644$	8.21728e9			0.00188253
$645$	8.58149e11	+	1.36469e12i	0.195229	+	0.310467i
$646$	−6.52751e12			−1.47469
$647$		−	1.54662e12i		−	0.346988i	−0.984835	−	0.173494i	$-0.944494\pi$
$647$		−	1.54662e12i		−	0.346988i	0.984835	−	0.173494i	$-0.0555057\pi$
$648$		−	5.27401e11i		−	0.117504i
$649$	7.78235e12			1.72191
$650$	6.11832e11	−	1.27273e12i	0.134438	−	0.279658i
$651$	−1.17094e12			−0.255517
$652$		−	1.03611e12i		−	0.224540i
$653$		−	7.20565e12i		−	1.55083i	−0.631453	−	0.775414i	$-0.717541\pi$
$653$		−	7.20565e12i		−	1.55083i	0.631453	−	0.775414i	$-0.282459\pi$
$654$	−2.50472e12			−0.535376
$655$	−4.83372e12	−	7.68692e12i	−1.02611	−	1.63180i
$656$	−2.43568e12			−0.513516
$657$			2.38927e12i			0.500288i
$658$		−	2.07265e12i		−	0.431032i
$659$	1.96856e12			0.406597			0.203299	−	0.979117i	$-0.434834\pi$
$659$	1.96856e12			0.406597			0.203299	+	0.979117i	$0.434834\pi$
$660$	−5.15917e11	+	3.24421e11i	−0.105836	+	0.0665520i
$661$	−8.75497e12			−1.78381			−0.891904	−	0.452225i	$-0.850630\pi$
$661$	−8.75497e12			−1.78381			−0.891904	+	0.452225i	$0.850630\pi$
$662$			4.52819e12i			0.916356i
$663$		−	1.04095e12i		−	0.209228i
$664$	−3.87855e11			−0.0774306
$665$	−3.53289e12	+	2.22156e12i	−0.700539	+	0.440516i
$666$	−8.66559e11			−0.170673
$667$			2.14351e11i			0.0419332i
$668$			1.03342e12i			0.200809i
$669$	−3.97448e12			−0.767119
$670$	3.09443e12	+	4.92098e12i	0.593258	+	0.943441i
$671$	−2.97673e12			−0.566876
$672$		−	4.81053e11i		−	0.0909979i
$673$		−	1.73755e12i		−	0.326489i	−0.986586	−	0.163244i	$-0.947804\pi$
$673$		−	1.73755e12i		−	0.326489i	0.986586	−	0.163244i	$-0.0521959\pi$
$674$	2.38336e11			0.0444856
$675$	9.35490e11	+	4.49712e11i	0.173449	+	0.0833811i
$676$	6.80265e11			0.125290
$677$			1.87762e12i			0.343526i	0.985138	+	0.171763i	$0.0549463\pi$
$677$			1.87762e12i			0.343526i	−0.985138	+	0.171763i	$0.945054\pi$
$678$			2.94958e12i			0.536077i
$679$	−3.82530e12			−0.690640
$680$	3.39735e12	+	5.40271e12i	0.609327	+	0.968995i
$681$	−4.03373e12			−0.718695
$682$		−	6.31743e12i		−	1.11818i
$683$			3.03387e11i			0.0533463i	0.999644	+	0.0266731i	$0.00849133\pi$
$683$			3.03387e11i			0.0533463i	−0.999644	+	0.0266731i	$0.991509\pi$
$684$	−3.95859e11			−0.0691493
$685$	2.90777e12	−	1.82847e12i	0.504606	−	0.317308i
$686$	−5.09306e12			−0.878053
$687$			3.11470e12i			0.533471i
$688$		−	3.13204e12i		−	0.532941i
$689$	−2.86498e12			−0.484323
$690$	6.39197e10	−	4.01942e10i	0.0107353	−	0.00675061i
$691$	7.73855e12			1.29124			0.645622	−	0.763657i	$-0.276598\pi$
$691$	7.73855e12			1.29124			0.645622	+	0.763657i	$0.276598\pi$
$692$		−	2.70643e11i		−	0.0448662i
$693$		−	1.74823e12i		−	0.287938i
$694$	−2.59647e12			−0.424880
$695$	−4.11573e12	−	6.54512e12i	−0.669137	−	1.06411i
$696$	6.68772e12			1.08028
$697$		−	4.12789e12i		−	0.662491i
$698$		−	3.69149e12i		−	0.588644i
$699$	4.41906e11			0.0700137
$700$	4.54757e11	+	2.18612e11i	0.0715877	+	0.0344139i
$701$	−1.29003e12			−0.201776			−0.100888	−	0.994898i	$-0.532168\pi$
$701$	−1.29003e12			−0.201776			−0.100888	+	0.994898i	$0.532168\pi$
$702$			3.84245e11i			0.0597160i
$703$			5.25981e12i			0.812215i
$704$	1.09865e13			1.68570
$705$	1.66563e12	+	2.64880e12i	0.253937	+	0.403829i
$706$	1.08511e13			1.64381
$707$			1.89079e12i			0.284614i
$708$		−	6.11170e11i		−	0.0914139i
$709$	−1.80911e12			−0.268879			−0.134440	−	0.990922i	$-0.542923\pi$
$709$	−1.80911e12			−0.268879			−0.134440	+	0.990922i	$0.542923\pi$
$710$	−1.12381e12	+	7.06677e11i	−0.165970	+	0.104366i
$711$	−2.98628e12			−0.438245
$712$			3.40502e12i			0.496546i
$713$		−	1.28591e11i		−	0.0186341i
$714$	−2.26390e12			−0.325999
$715$	3.03962e12	−	1.91139e12i	0.434953	−	0.273509i
$716$	−1.60872e11			−0.0228756
$717$			4.74934e12i			0.671115i
$718$		−	6.00664e12i		−	0.843473i
$719$	8.24498e11			0.115056			0.0575280	−	0.998344i	$-0.481678\pi$
$719$	8.24498e11			0.115056			0.0575280	+	0.998344i	$0.481678\pi$
$720$	−1.07350e12	−	1.70716e12i	−0.148870	−	0.236743i
$721$	5.18556e12			0.714640
$722$		−	7.85816e12i		−	1.07623i
$723$		−	1.85252e12i		−	0.252140i
$724$	−1.50931e12			−0.204153
$725$	−5.70258e12	+	1.18625e13i	−0.766567	+	1.59461i
$726$	5.42684e12			0.724990
$727$			4.26121e12i			0.565754i	0.959156	+	0.282877i	$0.0912889\pi$
$727$			4.26121e12i			0.565754i	−0.959156	+	0.282877i	$0.908711\pi$
$728$			1.51050e12i			0.199310i
$729$	−2.82430e11			−0.0370370
$730$	5.68120e12	+	9.03465e12i	0.740436	+	1.17749i
$731$	5.30804e12			0.687552
$732$			2.33771e11i			0.0300947i
$733$		−	1.17006e13i		−	1.49707i	−0.663095	−	0.748535i	$-0.730758\pi$
$733$		−	1.17006e13i		−	1.49707i	0.663095	−	0.748535i	$-0.269242\pi$
$734$	2.52674e12			0.321313
$735$	2.64176e12	−	1.66120e12i	0.333888	−	0.209956i
$736$	5.28287e10			0.00663620
$737$			1.47806e13i			1.84539i
$738$			1.52372e12i			0.189082i
$739$	−1.30351e13			−1.60773			−0.803866	−	0.594811i	$-0.797227\pi$
$739$	−1.30351e13			−1.60773			−0.803866	+	0.594811i	$0.797227\pi$
$740$	5.38345e11	−	3.38524e11i	0.0659961	−	0.0414999i
$741$	2.33228e12			0.284183
$742$			6.23086e12i			0.754624i
$743$		−	8.72982e12i		−	1.05089i	−0.850829	−	0.525443i	$-0.823900\pi$
$743$		−	8.72982e12i		−	1.05089i	0.850829	−	0.525443i	$-0.176100\pi$
$744$	−4.01203e12			−0.480050
$745$	7.91571e12	+	1.25881e13i	0.941428	+	1.49712i
$746$	−8.50954e12			−1.00596
$747$			2.07701e11i			0.0244059i
$748$			2.00669e12i			0.234381i
$749$	−4.23770e11			−0.0491997
$750$	4.60674e12	−	5.23893e11i	0.531641	−	0.0604598i
$751$	−1.03083e13			−1.18252			−0.591259	−	0.806482i	$-0.701369\pi$
$751$	−1.03083e13			−1.18252			−0.591259	+	0.806482i	$0.701369\pi$
$752$		−	6.07914e12i		−	0.693206i
$753$		−	9.28418e11i		−	0.105236i
$754$	−4.87242e12			−0.549001
$755$	−4.02081e12	−	6.39417e12i	−0.450352	−	0.716181i
$756$	−1.37294e11			−0.0152863
$757$		−	5.42609e12i		−	0.600559i	−0.953851	−	0.300280i	$-0.902920\pi$
$757$		−	5.42609e12i		−	0.600559i	0.953851	−	0.300280i	$-0.0970800\pi$
$758$		−	4.45101e12i		−	0.489719i
$759$	1.91989e11			0.0209985
$760$	−1.21049e13	+	7.61182e12i	−1.31613	+	0.827613i
$761$	9.12828e12			0.986639			0.493319	−	0.869848i	$-0.335783\pi$
$761$	9.12828e12			0.986639			0.493319	+	0.869848i	$0.335783\pi$
$762$		−	3.53180e12i		−	0.379489i
$763$			5.27280e12i			0.563223i
$764$	7.97473e10			0.00846829
$765$	2.89321e12	−	1.81932e12i	0.305425	−	0.192058i
$766$	1.04209e12			0.109364
$767$			3.60082e12i			0.375684i
$768$		−	2.30723e12i		−	0.239312i
$769$	5.29627e12			0.546137			0.273069	−	0.961995i	$-0.411961\pi$
$769$	5.29627e12			0.546137			0.273069	+	0.961995i	$0.411961\pi$
$770$	−4.15695e12	−	6.61067e12i	−0.426154	−	0.677700i
$771$	−5.69701e12			−0.580634
$772$		−	1.99471e12i		−	0.202116i
$773$		−	1.45554e13i		−	1.46628i	−0.680080	−	0.733138i	$-0.738055\pi$
$773$		−	1.45554e13i		−	1.46628i	0.680080	−	0.733138i	$-0.261945\pi$
$774$	−1.95934e12			−0.196235
$775$	3.42104e12	−	7.11644e12i	0.340644	−	0.708607i
$776$	−1.31068e13			−1.29753
$777$			1.82423e12i			0.179550i
$778$			5.75575e12i			0.563240i
$779$	9.24860e12			0.899823
$780$	−1.50107e11	−	2.38710e11i	−0.0145202	−	0.0230911i
$781$	−3.37546e12			−0.324641
$782$		−	2.48619e11i		−	0.0237741i
$783$		−	3.58135e12i		−	0.340501i
$784$	−6.06299e12			−0.573145
$785$	9.33450e12	−	5.86975e12i	0.877359	−	0.551704i
$786$	1.10364e13			1.03140
$787$		−	1.36878e13i		−	1.27188i	−0.771737	−	0.635941i	$-0.780612\pi$
$787$		−	1.36878e13i		−	1.27188i	0.771737	−	0.635941i	$-0.219388\pi$
$788$		−	2.20932e12i		−	0.204123i
$789$	−9.03979e12			−0.830447
$790$	−1.12922e13	+	7.10077e12i	−1.03147	+	0.648610i
$791$	6.20930e12			0.563960
$792$		−	5.99003e12i		−	0.540961i
$793$		−	1.37730e12i		−	0.123680i
$794$	−4.55277e11			−0.0406522
$795$	−5.00725e12	−	7.96289e12i	−0.444577	−	0.706998i
$796$	−5.72770e11			−0.0505675
$797$			1.44438e13i			1.26800i	0.773334	+	0.633999i	$0.218587\pi$
$797$			1.44438e13i			1.26800i	−0.773334	+	0.633999i	$0.781413\pi$
$798$		−	5.07231e12i		−	0.442785i
$799$	1.03026e13			0.894311
$800$	2.92362e12	+	1.40545e12i	0.252358	+	0.121314i
$801$	1.82343e12			0.156510
$802$		−	4.53588e12i		−	0.387147i
$803$			2.71364e13i			2.30321i
$804$	1.16076e12			0.0979697
$805$	−8.46147e10	−	1.34560e11i	−0.00710173	−	0.0112937i
$806$	2.92302e12			0.243963
$807$			5.14534e12i			0.427055i
$808$			6.47849e12i			0.534715i
$809$	2.28499e13			1.87550			0.937749	−	0.347314i	$-0.112906\pi$
$809$	2.28499e13			1.87550			0.937749	+	0.347314i	$0.112906\pi$
$810$	−1.06796e12	+	6.71561e11i	−0.0871714	+	0.0548155i
$811$	−2.16202e13			−1.75495			−0.877477	−	0.479618i	$-0.840775\pi$
$811$	−2.16202e13			−1.75495			−0.877477	+	0.479618i	$0.840775\pi$
$812$		−	1.74095e12i		−	0.140535i
$813$		−	6.45615e10i		−	0.00518282i
$814$	−9.84206e12			−0.785735
$815$	−1.69667e13	+	1.06690e13i	−1.34706	+	0.847063i
$816$	−6.64009e12			−0.524286
$817$			1.18927e13i			0.933863i
$818$		−	4.84238e12i		−	0.378154i
$819$	8.08891e11			0.0628221
$820$	−5.95245e11	−	9.46600e11i	−0.0459762	−	0.0731146i
$821$	−9.90438e12			−0.760822			−0.380411	−	0.924817i	$-0.624218\pi$
$821$	−9.90438e12			−0.760822			−0.380411	+	0.924817i	$0.624218\pi$
$822$			4.17480e12i			0.318943i
$823$			1.33090e13i			1.01122i	0.862762	+	0.505610i	$0.168733\pi$
$823$			1.33090e13i			1.01122i	−0.862762	+	0.505610i	$0.831267\pi$
$824$	1.77675e13			1.34262
$825$	1.06250e13	+	5.10767e12i	0.798518	+	0.383866i
$826$	7.83119e12			0.585353
$827$		−	9.27779e12i		−	0.689715i	−0.938655	−	0.344858i	$-0.887927\pi$
$827$		−	9.27779e12i		−	0.689715i	0.938655	−	0.344858i	$-0.112073\pi$
$828$		−	1.50774e10i		−	0.00111478i
$829$	1.67554e13			1.23214			0.616071	−	0.787691i	$-0.288724\pi$
$829$	1.67554e13			1.23214			0.616071	+	0.787691i	$0.288724\pi$
$830$	4.93871e11	+	7.85389e11i	0.0361212	+	0.0574425i
$831$	−2.98468e12			−0.217117
$832$			5.08334e12i			0.367785i
$833$		−	1.02753e13i		−	0.739419i
$834$	9.39711e12			0.672585
$835$	1.69225e13	−	1.06413e13i	1.20469	−	0.757539i
$836$	−4.49602e12			−0.318346
$837$			2.14849e12i			0.151311i
$838$			5.01076e12i			0.350998i
$839$	−1.08548e13			−0.756295			−0.378147	−	0.925745i	$-0.623439\pi$
$839$	−1.08548e13			−0.756295			−0.378147	+	0.925745i	$0.623439\pi$
$840$	−4.19826e12	+	2.63997e12i	−0.290946	+	0.182954i
$841$	3.09062e13			2.13041
$842$		−	8.58902e12i		−	0.588897i
$843$			6.37011e12i			0.434433i
$844$	−2.87119e11			−0.0194769
$845$	−7.00480e12	−	1.11395e13i	−0.472651	−	0.751643i
$846$	−3.80299e12			−0.255246
$847$		−	1.14243e13i		−	0.762699i
$848$			1.82753e13i			1.21362i
$849$	2.49696e12			0.164940
$850$	6.61426e12	−	1.37590e13i	0.434606	−	0.904068i
$851$	−2.00335e11			−0.0130940
$852$			2.65085e11i			0.0172348i
$853$			1.55815e12i			0.100772i	0.998730	+	0.0503858i	$0.0160451\pi$
$853$			1.55815e12i			0.100772i	−0.998730	+	0.0503858i	$0.983955\pi$
$854$	−2.99541e12			−0.192706
$855$	4.07622e12	+	6.48229e12i	0.260862	+	0.414840i
$856$	−1.45198e12			−0.0924334
$857$		−	1.18714e13i		−	0.751778i	−0.926665	−	0.375889i	$-0.877337\pi$
$857$		−	1.18714e13i		−	0.751778i	0.926665	−	0.375889i	$-0.122663\pi$
$858$			4.36411e12i			0.274918i
$859$	−8.41923e12			−0.527598			−0.263799	−	0.964578i	$-0.584976\pi$
$859$	−8.41923e12			−0.527598			−0.263799	+	0.964578i	$0.584976\pi$
$860$	1.21723e12	−	7.65424e11i	0.0758805	−	0.0477154i
$861$	3.20764e12			0.198917
$862$		−	1.11117e13i		−	0.685486i
$863$			1.09630e13i			0.672790i	0.941721	+	0.336395i	$0.109208\pi$
$863$			1.09630e13i			0.672790i	−0.941721	+	0.336395i	$0.890792\pi$
$864$	−8.82657e11			−0.0538865
$865$	−4.43185e12	+	2.78685e12i	−0.269161	+	0.169255i
$866$	3.58585e12			0.216651
$867$		−	1.64770e12i		−	0.0990357i
$868$			1.04442e12i			0.0624504i
$869$	−3.39170e13			−2.01757
$870$	−8.51574e12	−	1.35423e13i	−0.503948	−	0.801414i
$871$	−6.83886e12			−0.402626
$872$			1.80664e13i			1.05815i
$873$			7.01883e12i			0.408979i
$874$	5.57036e11			0.0322910
$875$	−1.10287e12	−	9.69786e12i	−0.0636045	−	0.559293i
$876$	2.13110e12			0.122274
$877$		−	1.49209e12i		−	0.0851723i	−0.999093	−	0.0425861i	$-0.986440\pi$
$877$		−	1.49209e12i		−	0.0851723i	0.999093	−	0.0425861i	$-0.0135597\pi$
$878$		−	4.69005e12i		−	0.266350i
$879$	4.89533e12			0.276587
$880$	−1.21924e13	−	1.93893e13i	−0.685360	−	1.08991i
$881$	5.94363e12			0.332399			0.166200	−	0.986092i	$-0.446850\pi$
$881$	5.94363e12			0.332399			0.166200	+	0.986092i	$0.446850\pi$
$882$			3.79289e12i			0.211038i
$883$		−	1.57021e13i		−	0.869230i	−0.900616	−	0.434615i	$-0.856884\pi$
$883$		−	1.57021e13i		−	0.869230i	0.900616	−	0.434615i	$-0.143116\pi$
$884$	−9.28476e11			−0.0511370
$885$	−1.00081e13	+	6.29332e12i	−0.548411	+	0.344854i
$886$	1.74635e13			0.952092
$887$		−	2.07953e13i		−	1.12800i	−0.825774	−	0.564001i	$-0.809262\pi$
$887$		−	2.07953e13i		−	1.12800i	0.825774	−	0.564001i	$-0.190738\pi$
$888$			6.25043e12i			0.337327i
$889$	−7.43495e12			−0.399227
$890$	6.89502e12	−	4.33575e12i	0.368367	−	0.231638i
$891$	−3.20773e12			−0.170509
$892$			3.54503e12i			0.187490i
$893$			2.30833e13i			1.21469i
$894$	−1.80733e13			−0.946278
$895$	1.65652e12	+	2.63432e12i	0.0862967	+	0.137235i
$896$	8.01469e12			0.415433
$897$			8.88314e10i			0.00458143i
$898$		−	1.18029e13i		−	0.605685i
$899$	−2.72440e13			−1.39108
$900$	4.01119e11	−	8.34408e11i	0.0203790	−	0.0423923i
$901$	−3.09721e13			−1.56570
$902$			1.73058e13i			0.870487i
$903$			4.12470e12i			0.206442i
$904$	2.12751e13			1.05953
$905$	1.55416e13	+	2.47154e13i	0.770155	+	1.22475i
$906$	9.18038e12			0.452672
$907$		−	5.16199e12i		−	0.253270i	−0.991949	−	0.126635i	$-0.959582\pi$
$907$		−	5.16199e12i		−	0.253270i	0.991949	−	0.126635i	$-0.0404177\pi$
$908$			3.59787e12i			0.175655i
$909$	3.46931e12			0.168541
$910$	3.05870e12	−	1.92338e12i	0.147860	−	0.0929778i
$911$	−1.23036e13			−0.591834			−0.295917	−	0.955214i	$-0.595625\pi$
$911$	−1.23036e13			−0.591834			−0.295917	+	0.955214i	$0.595625\pi$
$912$		−	1.48772e13i		−	0.712107i
$913$			2.35899e12i			0.112359i
$914$	−1.55979e13			−0.739280
$915$	3.82806e12	−	2.40718e12i	0.180544	−	0.113531i
$916$	2.77815e12			0.130384
$917$		−	2.32333e13i		−	1.08505i
$918$			4.15391e12i			0.193048i
$919$	6.62689e12			0.306471			0.153236	−	0.988190i	$-0.451031\pi$
$919$	6.62689e12			0.306471			0.153236	+	0.988190i	$0.451031\pi$
$920$	−2.89918e11	−	4.61049e11i	−0.0133423	−	0.0212179i
$921$	−1.92642e13			−0.882230
$922$			2.07618e13i			0.946185i
$923$		−	1.56179e12i		−	0.0708299i
$924$	−1.55933e12			−0.0703743
$925$	−1.10869e13	−	5.32971e12i	−0.497932	−	0.239368i
$926$	1.55255e13			0.693900
$927$		−	9.51469e12i		−	0.423191i
$928$		−	1.11925e13i		−	0.495408i
$929$	1.50849e12			0.0664466			0.0332233	−	0.999448i	$-0.489423\pi$
$929$	1.50849e12			0.0664466			0.0332233	+	0.999448i	$0.489423\pi$
$930$	5.10869e12	+	8.12419e12i	0.223942	+	0.356129i
$931$	2.30219e13			1.00431
$932$		−	3.94157e11i		−	0.0171119i
$933$		−	8.52421e12i		−	0.368287i
$934$	3.90179e12			0.167765
$935$	3.28601e13	−	2.06632e13i	1.40610	−	0.884189i
$936$	2.77153e12			0.118026
$937$			2.83761e13i			1.20261i	0.799019	+	0.601305i	$0.205352\pi$
$937$			2.83761e13i			1.20261i	−0.799019	+	0.601305i	$0.794648\pi$
$938$			1.48734e13i			0.627332i
$939$	9.85764e12			0.413788
$940$	2.36259e12	−	1.48565e12i	0.0986990	−	0.0620643i
$941$	2.17067e13			0.902488			0.451244	−	0.892401i	$-0.350980\pi$
$941$	2.17067e13			0.902488			0.451244	+	0.892401i	$0.350980\pi$
$942$			1.34019e13i			0.554547i
$943$			3.52260e11i			0.0145064i
$944$	2.29691e13			0.941391
$945$	1.41373e12	+	2.24822e12i	0.0576666	+	0.0917055i
$946$	−2.22535e13			−0.903417
$947$			1.50628e13i			0.608600i	0.952576	+	0.304300i	$0.0984225\pi$
$947$			1.50628e13i			0.608600i	−0.952576	+	0.304300i	$0.901578\pi$
$948$			2.66360e12i			0.107110i
$949$	−1.25558e13			−0.502511
$950$	3.08272e13	+	1.48194e13i	1.22794	+	0.590301i
$951$	−6.52464e12			−0.258669
$952$			1.63294e13i			0.644323i
$953$		−	3.10734e13i		−	1.22031i	−0.792281	−	0.610156i	$-0.791107\pi$
$953$		−	3.10734e13i		−	1.22031i	0.792281	−	0.610156i	$-0.208893\pi$
$954$	1.14326e13			0.446868
$955$	−8.21170e11	−	1.30588e12i	−0.0319461	−	0.0508030i
$956$	4.23616e12			0.164026
$957$		−	4.06757e13i		−	1.56758i
$958$			1.21057e13i			0.464350i
$959$	8.78857e12			0.335532
$960$	−1.41286e13	+	8.88438e12i	−0.536880	+	0.337603i
$961$	−1.00957e13			−0.381839
$962$		−	4.55383e12i		−	0.171431i
$963$			7.77552e11i			0.0291348i
$964$	−1.65235e12			−0.0616249
$965$	−3.26638e13	+	2.05398e13i	−1.21254	+	0.762471i
$966$	1.93194e11			0.00713832
$967$			1.56729e13i			0.576408i	0.957569	+	0.288204i	$0.0930581\pi$
$967$			1.56729e13i			0.576408i	−0.957569	+	0.288204i	$0.906942\pi$
$968$		−	3.91434e13i		−	1.43291i
$969$	2.52132e13			0.918696
$970$	1.66894e13	+	2.65406e13i	0.605296	+	0.962584i
$971$	2.46434e13			0.889641			0.444820	−	0.895620i	$-0.353267\pi$
$971$	2.46434e13			0.889641			0.444820	+	0.895620i	$0.353267\pi$
$972$			2.51912e11i			0.00905214i
$973$		−	1.97823e13i		−	0.707568i
$974$	−4.89727e13			−1.74357
$975$	−2.36327e12	+	4.91607e12i	−0.0837515	+	0.174220i
$976$	−8.78562e12			−0.309919
$977$			1.86706e13i			0.655591i	0.944749	+	0.327796i	$0.106306\pi$
$977$			1.86706e13i			0.655591i	−0.944749	+	0.327796i	$0.893694\pi$
$978$		−	2.43597e13i		−	0.851428i
$979$	2.07098e13			0.720534
$980$	−1.48170e12	−	2.35631e12i	−0.0513150	−	0.0816047i
$981$	9.67476e12			0.333526
$982$		−	1.90219e13i		−	0.652759i
$983$			2.04996e13i			0.700252i	0.936703	+	0.350126i	$0.113861\pi$
$983$			2.04996e13i			0.700252i	−0.936703	+	0.350126i	$0.886139\pi$
$984$	1.09905e13			0.373713
$985$	−3.61783e13	+	2.27498e13i	−1.22457	+	0.770041i
$986$	−5.26737e13			−1.77479
$987$			8.00585e12i			0.268522i
$988$		−	2.08027e12i		−	0.0694565i
$989$	−4.52970e11			−0.0150552
$990$	−1.21296e13	+	7.62735e12i	−0.401316	+	0.252357i
$991$	−6.90837e12			−0.227533			−0.113766	−	0.993508i	$-0.536292\pi$
$991$	−6.90837e12			−0.227533			−0.113766	+	0.993508i	$0.536292\pi$
$992$			6.71453e12i			0.220147i
$993$		−	1.74907e13i		−	0.570866i
$994$	−3.39665e12			−0.110360
$995$	5.89790e12	+	9.37926e12i	0.190763	+	0.303365i
$996$	1.85258e11			0.00596500
$997$			2.80773e13i			0.899969i	0.893036	+	0.449984i	$0.148570\pi$
$997$			2.80773e13i			0.899969i	−0.893036	+	0.449984i	$0.851430\pi$
$998$		−	2.38433e13i		−	0.760815i
$999$	3.34718e12			0.106325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.10.b.a.4.3	✓	8
3.2	odd	2		45.10.b.c.19.6		8
4.3	odd	2		240.10.f.c.49.2		8
5.2	odd	4		75.10.a.l.1.3		4
5.3	odd	4		75.10.a.i.1.2		4
5.4	even	2	inner	15.10.b.a.4.6	yes	8
15.2	even	4		225.10.a.q.1.2		4
15.8	even	4		225.10.a.u.1.3		4
15.14	odd	2		45.10.b.c.19.3		8
20.19	odd	2		240.10.f.c.49.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.b.a.4.3	✓	8	1.1	even	1	trivial
15.10.b.a.4.6	yes	8	5.4	even	2	inner
45.10.b.c.19.3		8	15.14	odd	2
45.10.b.c.19.6		8	3.2	odd	2
75.10.a.i.1.2		4	5.3	odd	4
75.10.a.l.1.3		4	5.2	odd	4
225.10.a.q.1.2		4	15.2	even	4
225.10.a.u.1.3		4	15.8	even	4
240.10.f.c.49.2		8	4.3	odd	2
240.10.f.c.49.6		8	20.19	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	15.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-20.9703i q^{2} +81.0000i q^{3} +72.2477 q^{4} +(-743.946 - 1183.08i) q^{5} +1698.59 q^{6} -3575.78i q^{7} -12251.8i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-20.9703i q^{2} +81.0000i q^{3} +72.2477 q^{4} +(-743.946 - 1183.08i) q^{5} +1698.59 q^{6} -3575.78i q^{7} -12251.8i q^{8} -6561.00 q^{9} +(-24809.4 + 15600.8i) q^{10} -74517.5 q^{11} +5852.07i q^{12} -34478.5i q^{13} -74985.1 q^{14} +(95829.2 - 60259.7i) q^{15} -219933. q^{16} -372733. i q^{17} +137586. i q^{18} +835114. q^{19} +(-53748.4 - 85474.5i) q^{20} +289638. q^{21} +1.56265e6i q^{22} +31807.7i q^{23} +992398. q^{24} +(-846213. + 1.76029e6i) q^{25} -723024. q^{26} -531441. i q^{27} -258342. i q^{28} +6.73894e6 q^{29} +(-1.26366e6 - 2.00956e6i) q^{30} -4.04277e6 q^{31} -1.66087e6i q^{32} -6.03591e6i q^{33} -7.81631e6 q^{34} +(-4.23042e6 + 2.66019e6i) q^{35} -474017. q^{36} +6.29831e6i q^{37} -1.75126e7i q^{38} +2.79276e6 q^{39} +(-1.44948e7 + 9.11471e6i) q^{40} +1.10746e7 q^{41} -6.07379e6i q^{42} +1.42409e7i q^{43} -5.38372e6 q^{44} +(4.88103e6 + 7.76216e6i) q^{45} +667017. q^{46} +2.76408e7i q^{47} -1.78146e7i q^{48} +2.75674e7 q^{49} +(3.69138e7 + 1.77453e7i) q^{50} +3.01914e7 q^{51} -2.49100e6i q^{52} -8.30946e7i q^{53} -1.11445e7 q^{54} +(5.54370e7 + 8.81598e7i) q^{55} -4.38099e7 q^{56} +6.76443e7i q^{57} -1.41317e8i q^{58} -1.04437e8 q^{59} +(6.92344e6 - 4.35362e6i) q^{60} +3.99467e7 q^{61} +8.47779e7i q^{62} +2.34607e7i q^{63} -1.47435e8 q^{64} +(-4.07907e7 + 2.56502e7i) q^{65} -1.26575e8 q^{66} -1.98351e8i q^{67} -2.69291e7i q^{68} -2.57643e6 q^{69} +(5.57849e7 + 8.87131e7i) q^{70} +4.52976e7 q^{71} +8.03843e7i q^{72} -3.64162e8i q^{73} +1.32077e8 q^{74} +(-1.42584e8 - 6.85432e7i) q^{75} +6.03351e7 q^{76} +2.66458e8i q^{77} -5.85650e7i q^{78} +4.55156e8 q^{79} +(1.63619e8 + 2.60198e8i) q^{80} +4.30467e7 q^{81} -2.32238e8i q^{82} -3.16569e7i q^{83} +2.09257e7 q^{84} +(-4.40971e8 + 2.77293e8i) q^{85} +2.98635e8 q^{86} +5.45854e8i q^{87} +9.12975e8i q^{88} -2.77919e8 q^{89} +(1.62775e8 - 1.02357e8i) q^{90} -1.23288e8 q^{91} +2.29804e6i q^{92} -3.27464e8i q^{93} +5.79636e8 q^{94} +(-6.21280e8 - 9.88004e8i) q^{95} +1.34531e8 q^{96} -1.06978e9i q^{97} -5.78096e8i q^{98} +4.88909e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9}+O(q^{10}) \) 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9	\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9} + 67090 q^{10} - 71988 q^{11} + 416364 q^{14} + 80190 q^{15} - 1505630 q^{16} + 851584 q^{19} + 2078100 q^{20} - 1593108 q^{21} + 1242702 q^{24} + 1695500 q^{25} - 877524 q^{26} - 73572 q^{29} + 3086100 q^{30} + 474088 q^{31} - 8124388 q^{34} - 36357180 q^{35} + 7833834 q^{36} + 12959676 q^{39} - 15313390 q^{40} + 93320088 q^{41} - 74555892 q^{44} + 4527090 q^{45} - 9664072 q^{46} + 51329600 q^{49} + 67798200 q^{50} - 108196236 q^{51} - 3188646 q^{54} + 64428480 q^{55} - 67781220 q^{56} + 236526036 q^{59} + 63172710 q^{60} - 357427760 q^{61} - 12137026 q^{64} + 19848300 q^{65} + 23317308 q^{66} + 167059584 q^{69} + 200900520 q^{70} - 156890664 q^{71} - 1523381796 q^{74} - 528573600 q^{75} + 1098697344 q^{76} + 863922280 q^{79} + 630213180 q^{80} + 344373768 q^{81} + 529023636 q^{84} - 2223350420 q^{85} + 997642392 q^{86} + 357382224 q^{89} - 440177490 q^{90} + 214754328 q^{91} - 721679824 q^{94} + 1698584640 q^{95} - 475022718 q^{96} + 472313268 q^{99}+O(q^{100}) \) 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9 + 67090 * q^10 - 71988 * q^11 + 416364 * q^14 + 80190 * q^15 - 1505630 * q^16 + 851584 * q^19 + 2078100 * q^20 - 1593108 * q^21 + 1242702 * q^24 + 1695500 * q^25 - 877524 * q^26 - 73572 * q^29 + 3086100 * q^30 + 474088 * q^31 - 8124388 * q^34 - 36357180 * q^35 + 7833834 * q^36 + 12959676 * q^39 - 15313390 * q^40 + 93320088 * q^41 - 74555892 * q^44 + 4527090 * q^45 - 9664072 * q^46 + 51329600 * q^49 + 67798200 * q^50 - 108196236 * q^51 - 3188646 * q^54 + 64428480 * q^55 - 67781220 * q^56 + 236526036 * q^59 + 63172710 * q^60 - 357427760 * q^61 - 12137026 * q^64 + 19848300 * q^65 + 23317308 * q^66 + 167059584 * q^69 + 200900520 * q^70 - 156890664 * q^71 - 1523381796 * q^74 - 528573600 * q^75 + 1098697344 * q^76 + 863922280 * q^79 + 630213180 * q^80 + 344373768 * q^81 + 529023636 * q^84 - 2223350420 * q^85 + 997642392 * q^86 + 357382224 * q^89 - 440177490 * q^90 + 214754328 * q^91 - 721679824 * q^94 + 1698584640 * q^95 - 475022718 * q^96 + 472313268 * q^99

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