LMFDB - Embedded newform 15.10.b.a.4.4

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			4.4
Root			$-10.9137i$ of defining polynomial
Character	$\chi$	$=$	15.4
Dual form			15.10.b.a.4.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.3372i q^{2} -81.0000i q^{3} +306.446 q^{4} +(1380.00 + 220.717i) q^{5} -1161.31 q^{6} -2878.61i q^{7} -11734.2i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-14.3372i q^{2} -81.0000i q^{3} +306.446 q^{4} +(1380.00 + 220.717i) q^{5} -1161.31 q^{6} -2878.61i q^{7} -11734.2i q^{8} -6561.00 q^{9} +(3164.45 - 19785.3i) q^{10} -23286.0 q^{11} -24822.1i q^{12} -112501. i q^{13} -41271.2 q^{14} +(17878.0 - 111780. i) q^{15} -11335.0 q^{16} +115964. i q^{17} +94066.2i q^{18} +213578. q^{19} +(422896. + 67637.6i) q^{20} -233168. q^{21} +333855. i q^{22} +1.83629e6i q^{23} -950470. q^{24} +(1.85569e6 + 609179. i) q^{25} -1.61295e6 q^{26} +531441. i q^{27} -882139. i q^{28} -3.67540e6 q^{29} +(-1.60261e6 - 256321. i) q^{30} +8.85139e6 q^{31} -5.84540e6i q^{32} +1.88617e6i q^{33} +1.66259e6 q^{34} +(635358. - 3.97250e6i) q^{35} -2.01059e6 q^{36} -9.17921e6i q^{37} -3.06210e6i q^{38} -9.11258e6 q^{39} +(2.58993e6 - 1.61932e7i) q^{40} -1.17626e7 q^{41} +3.34297e6i q^{42} +3.93230e7i q^{43} -7.13589e6 q^{44} +(-9.05420e6 - 1.44812e6i) q^{45} +2.63272e7 q^{46} +3.26882e7i q^{47} +918134. i q^{48} +3.20672e7 q^{49} +(8.73391e6 - 2.66054e7i) q^{50} +9.39305e6 q^{51} -3.44754e7i q^{52} +1.04826e8i q^{53} +7.61936e6 q^{54} +(-3.21348e7 - 5.13961e6i) q^{55} -3.37782e7 q^{56} -1.72998e7i q^{57} +5.26948e7i q^{58} +1.02836e8 q^{59} +(5.47865e6 - 3.42546e7i) q^{60} -1.65686e8 q^{61} -1.26904e8i q^{62} +1.88866e7i q^{63} -8.96099e7 q^{64} +(2.48308e7 - 1.55252e8i) q^{65} +2.70423e7 q^{66} -1.76387e8i q^{67} +3.55365e7i q^{68} +1.48740e8 q^{69} +(-5.69544e7 - 9.10923e6i) q^{70} +1.30237e8 q^{71} +7.69880e7i q^{72} +2.35713e8i q^{73} -1.31604e8 q^{74} +(4.93435e7 - 1.50311e8i) q^{75} +6.54500e7 q^{76} +6.70314e7i q^{77} +1.30649e8i q^{78} -1.56763e8 q^{79} +(-1.56423e7 - 2.50182e6i) q^{80} +4.30467e7 q^{81} +1.68642e8i q^{82} +3.38241e7i q^{83} -7.14532e7 q^{84} +(-2.55951e7 + 1.60030e8i) q^{85} +5.63780e8 q^{86} +2.97707e8i q^{87} +2.73242e8i q^{88} -4.86766e8 q^{89} +(-2.07620e7 + 1.29812e8i) q^{90} -3.23847e8 q^{91} +5.62724e8i q^{92} -7.16963e8i q^{93} +4.68656e8 q^{94} +(2.94738e8 + 4.71402e7i) q^{95} -4.73477e8 q^{96} -1.40255e9i q^{97} -4.59753e8i q^{98} +1.52779e8 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 $

$2$		−	14.3372i		−	0.633619i	−0.948489	−	0.316810i	$-0.897388\pi$
$2$		−	14.3372i		−	0.633619i	0.948489	−	0.316810i	$-0.102612\pi$
$3$		−	81.0000i		−	0.577350i
$3$		−	81.0000i		−	0.577350i
$4$	306.446			0.598526
$5$	1380.00	+	220.717i	0.987450	+	0.157932i
$5$	1380.00	+	220.717i	0.987450	+	0.157932i
$6$	−1161.31			−0.365820
$7$		−	2878.61i		−	0.453150i	−0.973994	−	0.226575i	$-0.927247\pi$
$7$		−	2878.61i		−	0.453150i	0.973994	−	0.226575i	$-0.0727529\pi$
$8$		−	11734.2i		−	1.01286i
$9$	−6561.00			−0.333333
$10$	3164.45	−	19785.3i	0.100069	−	0.625667i
$11$	−23286.0			−0.479543			−0.239772	−	0.970829i	$-0.577073\pi$
$11$	−23286.0			−0.479543			−0.239772	+	0.970829i	$0.577073\pi$
$12$		−	24822.1i		−	0.345559i
$13$		−	112501.i		−	1.09247i	−0.837630	−	0.546237i	$-0.816060\pi$
$13$		−	112501.i		−	1.09247i	0.837630	−	0.546237i	$-0.183940\pi$
$14$	−41271.2			−0.287125
$15$	17878.0	−	111780.i	0.0911820	−	0.570105i
$16$	−11335.0			−0.0432396
$17$			115964.i			0.336745i	0.985723	+	0.168373i	$0.0538512\pi$
$17$			115964.i			0.336745i	−0.985723	+	0.168373i	$0.946149\pi$
$18$			94066.2i			0.211206i
$19$	213578.			0.375980			0.187990	−	0.982171i	$-0.439803\pi$
$19$	213578.			0.375980			0.187990	+	0.982171i	$0.439803\pi$
$20$	422896.	+	67637.6i	0.591015	+	0.0945264i
$21$	−233168.			−0.261627
$22$			333855.i			0.303848i
$23$			1.83629e6i			1.36825i	0.729363	+	0.684127i	$0.239816\pi$
$23$			1.83629e6i			1.36825i	−0.729363	+	0.684127i	$0.760184\pi$
$24$	−950470.			−0.584773
$25$	1.85569e6	+	609179.i	0.950115	+	0.311900i
$26$	−1.61295e6			−0.692213
$27$			531441.i			0.192450i
$28$		−	882139.i		−	0.271223i
$29$	−3.67540e6			−0.964969			−0.482485	−	0.875904i	$-0.660266\pi$
$29$	−3.67540e6			−0.964969			−0.482485	+	0.875904i	$0.660266\pi$
$30$	−1.60261e6	−	256321.i	−0.361229	−	0.0577747i
$31$	8.85139e6			1.72141			0.860704	−	0.509105i	$-0.170024\pi$
$31$	8.85139e6			1.72141			0.860704	+	0.509105i	$0.170024\pi$
$32$		−	5.84540e6i		−	0.985460i
$33$			1.88617e6i			0.276864i
$34$	1.66259e6			0.213368
$35$	635358.	−	3.97250e6i	0.0715669	−	0.447463i
$36$	−2.01059e6			−0.199509
$37$		−	9.17921e6i		−	0.805188i	−0.915379	−	0.402594i	$-0.868109\pi$
$37$		−	9.17921e6i		−	0.805188i	0.915379	−	0.402594i	$-0.131891\pi$
$38$		−	3.06210e6i		−	0.238228i
$39$	−9.11258e6			−0.630741
$40$	2.58993e6	−	1.61932e7i	0.159963	−	1.00015i
$41$	−1.17626e7			−0.650093			−0.325046	−	0.945698i	$-0.605380\pi$
$41$	−1.17626e7			−0.650093			−0.325046	+	0.945698i	$0.605380\pi$
$42$			3.34297e6i			0.165772i
$43$			3.93230e7i			1.75403i	0.480459	+	0.877017i	$0.340470\pi$
$43$			3.93230e7i			1.75403i	−0.480459	+	0.877017i	$0.659530\pi$
$44$	−7.13589e6			−0.287019
$45$	−9.05420e6	−	1.44812e6i	−0.329150	−	0.0526440i
$46$	2.63272e7			0.866952
$47$			3.26882e7i			0.977126i	0.872529	+	0.488563i	$0.162479\pi$
$47$			3.26882e7i			0.977126i	−0.872529	+	0.488563i	$0.837521\pi$
$48$			918134.i			0.0249644i
$49$	3.20672e7			0.794655
$50$	8.73391e6	−	2.66054e7i	0.197626	−	0.602011i
$51$	9.39305e6			0.194420
$52$		−	3.44754e7i		−	0.653875i
$53$			1.04826e8i			1.82486i	0.409238	+	0.912428i	$0.365794\pi$
$53$			1.04826e8i			1.82486i	−0.409238	+	0.912428i	$0.634206\pi$
$54$	7.61936e6			0.121940
$55$	−3.21348e7	−	5.13961e6i	−0.473525	−	0.0757352i
$56$	−3.37782e7			−0.458977
$57$		−	1.72998e7i		−	0.217072i
$58$			5.26948e7i			0.611423i
$59$	1.02836e8			1.10486			0.552432	−	0.833558i	$-0.313700\pi$
$59$	1.02836e8			1.10486			0.552432	+	0.833558i	$0.313700\pi$
$60$	5.47865e6	−	3.42546e7i	0.0545749	−	0.341223i
$61$	−1.65686e8			−1.53215			−0.766074	−	0.642752i	$-0.777792\pi$
$61$	−1.65686e8			−1.53215			−0.766074	+	0.642752i	$0.777792\pi$
$62$		−	1.26904e8i		−	1.09072i
$63$			1.88866e7i			0.151050i
$64$	−8.96099e7			−0.667646
$65$	2.48308e7	−	1.55252e8i	0.172537	−	1.07876i
$66$	2.70423e7			0.175427
$67$		−	1.76387e8i		−	1.06937i	−0.845051	−	0.534686i	$-0.820430\pi$
$67$		−	1.76387e8i		−	1.06937i	0.845051	−	0.534686i	$-0.179570\pi$
$68$			3.55365e7i			0.201551i
$69$	1.48740e8			0.789962
$70$	−5.69544e7	−	9.10923e6i	−0.283521	−	0.0453462i
$71$	1.30237e8			0.608234			0.304117	−	0.952635i	$-0.401639\pi$
$71$	1.30237e8			0.608234			0.304117	+	0.952635i	$0.401639\pi$
$72$			7.69880e7i			0.337619i
$73$			2.35713e8i			0.971474i	0.874105	+	0.485737i	$0.161449\pi$
$73$			2.35713e8i			0.971474i	−0.874105	+	0.485737i	$0.838551\pi$
$74$	−1.31604e8			−0.510183
$75$	4.93435e7	−	1.50311e8i	0.180075	−	0.548549i
$76$	6.54500e7			0.225034
$77$			6.70314e7i			0.217305i
$78$			1.30649e8i			0.399649i
$79$	−1.56763e8			−0.452815			−0.226407	−	0.974033i	$-0.572698\pi$
$79$	−1.56763e8			−0.452815			−0.226407	+	0.974033i	$0.572698\pi$
$80$	−1.56423e7	−	2.50182e6i	−0.0426969	−	0.00682891i
$81$	4.30467e7			0.111111
$82$			1.68642e8i			0.411911i
$83$			3.38241e7i			0.0782303i	0.999235	+	0.0391151i	$0.0124539\pi$
$83$			3.38241e7i			0.0782303i	−0.999235	+	0.0391151i	$0.987546\pi$
$84$	−7.14532e7			−0.156590
$85$	−2.55951e7	+	1.60030e8i	−0.0531828	+	0.332519i
$86$	5.63780e8			1.11139
$87$			2.97707e8i			0.557125i
$88$			2.73242e8i			0.485709i
$89$	−4.86766e8			−0.822366			−0.411183	−	0.911553i	$-0.634884\pi$
$89$	−4.86766e8			−0.822366			−0.411183	+	0.911553i	$0.634884\pi$
$90$	−2.07620e7	+	1.29812e8i	−0.0333562	+	0.208556i
$91$	−3.23847e8			−0.495055
$92$			5.62724e8i			0.818936i
$93$		−	7.16963e8i		−	0.993856i
$94$	4.68656e8			0.619126
$95$	2.94738e8	+	4.71402e7i	0.371262	+	0.0593793i
$96$	−4.73477e8			−0.568956
$97$		−	1.40255e9i		−	1.60859i	−0.594231	−	0.804294i	$-0.702544\pi$
$97$		−	1.40255e9i		−	1.60859i	0.594231	−	0.804294i	$-0.297456\pi$
$98$		−	4.59753e8i		−	0.503509i
$99$	1.52779e8			0.159848
$100$	5.68669e8	+	1.86680e8i	0.568669	+	0.186680i
$101$	−3.51675e8			−0.336276			−0.168138	−	0.985763i	$-0.553775\pi$
$101$	−3.51675e8			−0.336276			−0.168138	+	0.985763i	$0.553775\pi$
$102$		−	1.34670e8i		−	0.123188i
$103$		−	1.09902e9i		−	0.962137i	−0.876683	−	0.481069i	$-0.840249\pi$
$103$		−	1.09902e9i		−	0.962137i	0.876683	−	0.481069i	$-0.159751\pi$
$104$	−1.32011e9			−1.10652
$105$	−3.21772e8	−	5.14640e7i	−0.258343	−	0.0413192i
$106$	1.50291e9			1.15626
$107$			1.42345e8i			0.104982i	0.998621	+	0.0524910i	$0.0167161\pi$
$107$			1.42345e8i			0.104982i	−0.998621	+	0.0524910i	$0.983284\pi$
$108$			1.62858e8i			0.115186i
$109$	1.23981e9			0.841273			0.420637	−	0.907229i	$-0.361807\pi$
$109$	1.23981e9			0.841273			0.420637	+	0.907229i	$0.361807\pi$
$110$	−7.36874e7	+	4.60721e8i	−0.0479873	+	0.300035i
$111$	−7.43516e8			−0.464876
$112$			3.26291e7i			0.0195940i
$113$		−	1.73091e9i		−	0.998670i	−0.866409	−	0.499335i	$-0.833578\pi$
$113$		−	1.73091e9i		−	0.998670i	0.866409	−	0.499335i	$-0.166422\pi$
$114$	−2.48030e8			−0.137541
$115$	−4.05300e8	+	2.53409e9i	−0.216091	+	1.35108i
$116$	−1.12631e9			−0.577560
$117$			7.38119e8i			0.364158i
$118$		−	1.47437e9i		−	0.700064i
$119$	3.33814e8			0.152596
$120$	−1.31165e9	−	2.09784e8i	−0.577435	−	0.0923544i
$121$	−1.81571e9			−0.770038
$122$			2.37546e9i			0.970799i
$123$			9.52769e8i			0.375331i
$124$	2.71247e9			1.03031
$125$	2.42641e9	+	1.25025e9i	0.888932	+	0.458039i
$126$	2.70780e8			0.0957083
$127$			4.01797e9i			1.37053i	0.728292	+	0.685267i	$0.240315\pi$
$127$			4.01797e9i			1.37053i	−0.728292	+	0.685267i	$0.759685\pi$
$128$		−	1.70809e9i		−	0.562426i
$129$	3.18516e9			1.01269
$130$	−2.22587e9	−	3.56004e8i	−0.683526	−	0.109323i
$131$	1.65761e9			0.491768			0.245884	−	0.969299i	$-0.420922\pi$
$131$	1.65761e9			0.491768			0.245884	+	0.969299i	$0.420922\pi$
$132$			5.78007e8i			0.165711i
$133$		−	6.14808e8i		−	0.170376i
$134$	−2.52888e9			−0.677575
$135$	−1.17298e8	+	7.33390e8i	−0.0303940	+	0.190035i
$136$	1.36074e9			0.341075
$137$		−	3.50673e9i		−	0.850472i	−0.905083	−	0.425236i	$-0.860191\pi$
$137$		−	3.50673e9i		−	0.850472i	0.905083	−	0.425236i	$-0.139809\pi$
$138$		−	2.13251e9i		−	0.500535i
$139$	−2.92997e9			−0.665729			−0.332864	−	0.942975i	$-0.608015\pi$
$139$	−2.92997e9			−0.665729			−0.332864	+	0.942975i	$0.608015\pi$
$140$	1.94703e8	−	1.21735e9i	0.0428347	−	0.267819i
$141$	2.64774e9			0.564144
$142$		−	1.86722e9i		−	0.385389i
$143$			2.61970e9i			0.523889i
$144$	7.43689e7			0.0144132
$145$	−5.07206e9	−	8.11221e8i	−0.952859	−	0.152399i
$146$	3.37946e9			0.615545
$147$		−	2.59744e9i		−	0.458794i
$148$		−	2.81293e9i		−	0.481927i
$149$	−6.83881e9			−1.13669			−0.568345	−	0.822790i	$-0.692416\pi$
$149$	−6.83881e9			−1.13669			−0.568345	+	0.822790i	$0.692416\pi$
$150$	−2.15504e9	−	7.07446e8i	−0.347571	−	0.114099i
$151$	−7.68746e9			−1.20333			−0.601667	−	0.798747i	$-0.705497\pi$
$151$	−7.68746e9			−1.20333			−0.601667	+	0.798747i	$0.705497\pi$
$152$		−	2.50616e9i		−	0.380814i
$153$		−	7.60837e8i		−	0.112248i
$154$	9.61041e8			0.137689
$155$	1.22149e10	+	1.95365e9i	1.69980	+	0.271865i
$156$	−2.79251e9			−0.377515
$157$		−	2.91924e9i		−	0.383461i	−0.981448	−	0.191730i	$-0.938590\pi$
$157$		−	2.91924e9i		−	0.383461i	0.981448	−	0.191730i	$-0.0614099\pi$
$158$			2.24753e9i			0.286912i
$159$	8.49092e9			1.05358
$160$	1.29018e9	−	8.06666e9i	0.155636	−	0.973092i
$161$	5.28598e9			0.620025
$162$		−	6.17168e8i		−	0.0704022i
$163$			1.45510e10i			1.61454i	0.590181	+	0.807271i	$0.299057\pi$
$163$			1.45510e10i			1.61454i	−0.590181	+	0.807271i	$0.700943\pi$
$164$	−3.60459e9			−0.389098
$165$	−4.16308e8	+	2.60291e9i	−0.0437257	+	0.273390i
$166$	4.84942e8			0.0495682
$167$			3.12784e8i			0.0311186i	0.999879	+	0.0155593i	$0.00495289\pi$
$167$			3.12784e8i			0.0311186i	−0.999879	+	0.0155593i	$0.995047\pi$
$168$			2.73604e9i			0.264990i
$169$	−2.05198e9			−0.193501
$170$	2.29438e9	+	3.66961e8i	0.210690	+	0.0336977i
$171$	−1.40128e9			−0.125327
$172$			1.20503e10i			1.04984i
$173$			7.25178e9i			0.615513i	0.951465	+	0.307756i	$0.0995782\pi$
$173$			7.25178e9i			0.615513i	−0.951465	+	0.307756i	$0.900422\pi$
$174$	4.26828e9			0.353005
$175$	1.75359e9	−	5.34183e9i	0.141337	−	0.430545i
$176$	2.63947e8			0.0207352
$177$		−	8.32968e9i		−	0.637894i
$178$			6.97885e9i			0.521067i
$179$	−2.55227e10			−1.85818			−0.929091	−	0.369851i	$-0.879409\pi$
$179$	−2.55227e10			−1.85818			−0.929091	+	0.369851i	$0.879409\pi$
$180$	−2.77462e9	−	4.43770e8i	−0.197005	−	0.0315088i
$181$	−3.92246e9			−0.271647			−0.135823	−	0.990733i	$-0.543368\pi$
$181$	−3.92246e9			−0.271647			−0.135823	+	0.990733i	$0.543368\pi$
$182$			4.64305e9i			0.313677i
$183$			1.34205e10i			0.884586i
$184$	2.15474e10			1.38585
$185$	2.02600e9	−	1.26673e10i	0.127165	−	0.795083i
$186$	−1.02792e10			−0.629726
$187$		−	2.70033e9i		−	0.161484i
$188$			1.00171e10i			0.584836i
$189$	1.52981e9			0.0872088
$190$	6.75857e8	−	4.22571e9i	0.0376239	−	0.235239i
$191$	1.92925e10			1.04891			0.524456	−	0.851438i	$-0.324269\pi$
$191$	1.92925e10			1.04891			0.524456	+	0.851438i	$0.324269\pi$
$192$			7.25840e9i			0.385466i
$193$		−	2.10306e10i		−	1.09105i	−0.838095	−	0.545525i	$-0.816330\pi$
$193$		−	2.10306e10i		−	1.09105i	0.838095	−	0.545525i	$-0.183670\pi$
$194$	−2.01086e10			−1.01923
$195$	−1.25754e10	−	2.01130e9i	−0.622825	−	0.0996141i
$196$	9.82685e9			0.475622
$197$		−	4.12625e10i		−	1.95190i	−0.217991	−	0.975951i	$-0.569950\pi$
$197$		−	4.12625e10i		−	1.95190i	0.217991	−	0.975951i	$-0.430050\pi$
$198$		−	2.19042e9i		−	0.101283i
$199$	3.42528e10			1.54831			0.774154	−	0.632997i	$-0.218175\pi$
$199$	3.42528e10			1.54831			0.774154	+	0.632997i	$0.218175\pi$
$200$	7.14823e9	−	2.17751e10i	0.315910	−	0.962331i
$201$	−1.42873e10			−0.617402
$202$			5.04203e9i			0.213071i
$203$			1.05801e10i			0.437276i
$204$	2.87846e9			0.116365
$205$	−1.62324e10	−	2.59620e9i	−0.641934	−	0.102670i
$206$	−1.57568e10			−0.609629
$207$		−	1.20479e10i		−	0.456084i
$208$			1.27520e9i			0.0472381i
$209$	−4.97337e9			−0.180299
$210$	−7.37848e8	+	4.61330e9i	−0.0261806	+	0.163691i
$211$	8.11815e9			0.281959			0.140979	−	0.990013i	$-0.454975\pi$
$211$	8.11815e9			0.281959			0.140979	+	0.990013i	$0.454975\pi$
$212$			3.21235e10i			1.09222i
$213$		−	1.05492e10i		−	0.351164i
$214$	2.04082e9			0.0665187
$215$	−8.67923e9	+	5.42658e10i	−0.277018	+	1.73202i
$216$	6.23603e9			0.194924
$217$		−	2.54797e10i		−	0.780057i
$218$		−	1.77754e10i		−	0.533047i
$219$	1.90928e10			0.560881
$220$	−9.84755e9	−	1.57501e9i	−0.283417	−	0.0453295i
$221$	1.30460e10			0.367886
$222$			1.06599e10i			0.294554i
$223$			1.23274e10i			0.333811i	0.985973	+	0.166906i	$0.0533775\pi$
$223$			1.23274e10i			0.333811i	−0.985973	+	0.166906i	$0.946622\pi$
$224$	−1.68266e10			−0.446562
$225$	−1.21752e10	−	3.99682e9i	−0.316705	−	0.103967i
$226$	−2.48164e10			−0.632777
$227$			1.29830e10i			0.324532i	0.986747	+	0.162266i	$0.0518802\pi$
$227$			1.29830e10i			0.324532i	−0.986747	+	0.162266i	$0.948120\pi$
$228$		−	5.30145e9i		−	0.129924i
$229$	−1.23093e9			−0.0295784			−0.0147892	−	0.999891i	$-0.504708\pi$
$229$	−1.23093e9			−0.0295784			−0.0147892	+	0.999891i	$0.504708\pi$
$230$	3.63317e10	+	5.81086e9i	0.856072	+	0.136919i
$231$	5.42954e9			0.125461
$232$			4.31278e10i			0.977376i
$233$		−	1.54183e9i		−	0.0342716i	−0.999853	−	0.0171358i	$-0.994545\pi$
$233$		−	1.54183e9i		−	0.0342716i	0.999853	−	0.0171358i	$-0.00545476\pi$
$234$	1.05825e10			0.230738
$235$	−7.21482e9	+	4.51098e10i	−0.154319	+	0.964863i
$236$	3.15135e10			0.661291
$237$			1.26978e10i			0.261433i
$238$		−	4.78595e9i		−	0.0966879i
$239$	−6.33257e9			−0.125542			−0.0627711	−	0.998028i	$-0.519994\pi$
$239$	−6.33257e9			−0.125542			−0.0627711	+	0.998028i	$0.519994\pi$
$240$	−2.02647e8	+	1.26703e9i	−0.00394267	+	0.0246511i
$241$	−7.59959e7			−0.00145115			−0.000725577	−	1.00000i	$-0.500231\pi$
$241$	−7.59959e7			−0.00145115			−0.000725577		1.00000i	$0.500231\pi$
$242$			2.60321e10i			0.487911i
$243$		−	3.48678e9i		−	0.0641500i
$244$	−5.07736e10			−0.917031
$245$	4.42528e10	+	7.07776e9i	0.784682	+	0.125501i
$246$	1.36600e10			0.237817
$247$		−	2.40277e10i		−	0.410749i
$248$		−	1.03864e11i		−	1.74354i
$249$	2.73975e9			0.0451663
$250$	1.79251e10	−	3.47878e10i	0.290222	−	0.563245i
$251$	−6.53735e10			−1.03961			−0.519804	−	0.854285i	$-0.673995\pi$
$251$	−6.53735e10			−1.03961			−0.519804	+	0.854285i	$0.673995\pi$
$252$			5.78771e9i			0.0904075i
$253$		−	4.27599e10i		−	0.656137i
$254$	5.76063e10			0.868397
$255$	1.29624e10	+	2.07320e9i	0.191980	+	0.0307051i
$256$	−7.03695e10			−1.02401
$257$		−	1.09014e9i		−	0.0155878i	−0.999970	−	0.00779389i	$-0.997519\pi$
$257$		−	1.09014e9i		−	0.0155878i	0.999970	−	0.00779389i	$-0.00248090\pi$
$258$		−	4.56662e10i		−	0.641662i
$259$	−2.64234e10			−0.364871
$260$	7.60930e9	−	4.75762e10i	0.103268	−	0.645669i
$261$	2.41143e10			0.321656
$262$		−	2.37654e10i		−	0.311594i
$263$		−	3.67524e10i		−	0.473680i	−0.971549	−	0.236840i	$-0.923888\pi$
$263$		−	3.67524e10i		−	0.473680i	0.971549	−	0.236840i	$-0.0761117\pi$
$264$	2.21326e10			0.280424
$265$	−2.31369e10	+	1.44660e11i	−0.288203	+	1.80195i
$266$	−8.81461e9			−0.107953
$267$			3.94280e10i			0.474793i
$268$		−	5.40529e10i		−	0.640048i
$269$	−8.87738e10			−1.03371			−0.516856	−	0.856072i	$-0.672898\pi$
$269$	−8.87738e10			−1.03371			−0.516856	+	0.856072i	$0.672898\pi$
$270$	1.05147e10	+	1.68172e9i	0.120410	+	0.0192582i
$271$	5.79559e10			0.652733			0.326367	−	0.945243i	$-0.394176\pi$
$271$	5.79559e10			0.652733			0.326367	+	0.945243i	$0.394176\pi$
$272$		−	1.31445e9i		−	0.0145607i
$273$			2.62316e10i			0.285820i
$274$	−5.02766e10			−0.538875
$275$	−4.32117e10	−	1.41853e10i	−0.455621	−	0.149569i
$276$	4.55806e10			0.472813
$277$		−	4.41915e10i		−	0.451004i	−0.974243	−	0.225502i	$-0.927598\pi$
$277$		−	4.41915e10i		−	0.451004i	0.974243	−	0.225502i	$-0.0724022\pi$
$278$			4.20075e10i			0.421819i
$279$	−5.80740e10			−0.573803
$280$	−4.66141e10	−	7.45541e9i	−0.453217	−	0.0724871i
$281$	1.47398e11			1.41030			0.705151	−	0.709058i	$-0.250879\pi$
$281$	1.47398e11			1.41030			0.705151	+	0.709058i	$0.250879\pi$
$282$		−	3.79611e10i		−	0.357452i
$283$			1.63060e10i			0.151115i	0.997141	+	0.0755574i	$0.0240736\pi$
$283$			1.63060e10i			0.151115i	−0.997141	+	0.0755574i	$0.975926\pi$
$284$	3.99104e10			0.364044
$285$	3.81835e9	−	2.38738e10i	0.0342826	−	0.214348i
$286$	3.75591e10			0.331946
$287$			3.38599e10i			0.294590i
$288$			3.83516e10i			0.328487i
$289$	1.05140e11			0.886603
$290$	−1.16306e10	+	7.27190e10i	−0.0965632	+	0.603750i
$291$	−1.13606e11			−0.928719
$292$			7.22333e10i			0.581453i
$293$			1.20226e11i			0.952999i	0.879175	+	0.476499i	$0.158095\pi$
$293$			1.20226e11i			0.952999i	−0.879175	+	0.476499i	$0.841905\pi$
$294$	−3.72400e10			−0.290701
$295$	1.41913e11	+	2.26975e10i	1.09100	+	0.174493i
$296$	−1.07711e11			−0.815541
$297$		−	1.23751e10i		−	0.0922881i
$298$			9.80491e10i			0.720229i
$299$	2.06585e11			1.49478
$300$	1.51211e10	−	4.60622e10i	0.107780	−	0.328321i
$301$	1.13196e11			0.794842
$302$			1.10216e11i			0.762456i
$303$			2.84857e10i			0.194149i
$304$	−2.42090e9			−0.0162572
$305$	−2.28647e11	−	3.65696e10i	−1.51292	−	0.241975i
$306$	−1.09082e10			−0.0711227
$307$		−	1.80341e11i		−	1.15870i	−0.815078	−	0.579351i	$-0.803306\pi$
$307$		−	1.80341e11i		−	1.15870i	0.815078	−	0.579351i	$-0.196694\pi$
$308$			2.05415e10i			0.130063i
$309$	−8.90204e10			−0.555490
$310$	2.80098e10	−	1.75128e11i	0.172259	−	1.07703i
$311$	−2.27029e11			−1.37613			−0.688066	−	0.725648i	$-0.741540\pi$
$311$	−2.27029e11			−1.37613			−0.688066	+	0.725648i	$0.741540\pi$
$312$			1.06929e11i			0.638850i
$313$			1.04403e11i			0.614839i	0.951574	+	0.307420i	$0.0994655\pi$
$313$			1.04403e11i			0.614839i	−0.951574	+	0.307420i	$0.900534\pi$
$314$	−4.18536e10			−0.242968
$315$	−4.16858e9	+	2.60636e10i	−0.0238556	+	0.149154i
$316$	−4.80392e10			−0.271022
$317$		−	2.18268e11i		−	1.21401i	−0.794697	−	0.607006i	$-0.792370\pi$
$317$		−	2.18268e11i		−	1.21401i	0.794697	−	0.607006i	$-0.207630\pi$
$318$		−	1.21736e11i		−	0.667569i
$319$	8.55853e10			0.462744
$320$	−1.23662e11	−	1.97784e10i	−0.659267	−	0.105443i
$321$	1.15299e10			0.0606114
$322$		−	7.57860e10i		−	0.392860i
$323$			2.47672e10i			0.126610i
$324$	1.31915e10			0.0665029
$325$	6.85333e10	−	2.08767e11i	0.340743	−	1.03798i
$326$	2.08621e11			1.02301
$327$		−	1.00425e11i		−	0.485709i
$328$			1.38024e11i			0.658451i
$329$	9.40967e10			0.442785
$330$	3.73184e10	+	5.96868e9i	0.173225	+	0.0277055i
$331$	−2.79244e10			−0.127867			−0.0639334	−	0.997954i	$-0.520365\pi$
$331$	−2.79244e10			−0.127867			−0.0639334	+	0.997954i	$0.520365\pi$
$332$			1.03652e10i			0.0468229i
$333$			6.02248e10i			0.268396i
$334$	4.48444e9			0.0197174
$335$	3.89314e10	−	2.43414e11i	0.168888	−	1.05595i
$336$	2.64295e9			0.0113126
$337$			1.72048e11i			0.726631i	0.931666	+	0.363316i	$0.118355\pi$
$337$			1.72048e11i			0.726631i	−0.931666	+	0.363316i	$0.881645\pi$
$338$			2.94196e10i			0.122606i
$339$	−1.40204e11			−0.576583
$340$	−7.84350e9	+	4.90405e10i	−0.0318313	+	0.199021i
$341$	−2.06113e11			−0.825490
$342$			2.00905e10i			0.0794095i
$343$		−	2.08472e11i		−	0.813249i
$344$	4.61423e11			1.77659
$345$	2.05261e11	+	3.28293e10i	0.780047	+	0.124760i
$346$	1.03970e11			0.390001
$347$		−	2.86901e11i		−	1.06231i	−0.847276	−	0.531153i	$-0.821759\pi$
$347$		−	2.86901e11i		−	1.06231i	0.847276	−	0.531153i	$-0.178241\pi$
$348$			9.12311e10i			0.333454i
$349$	−4.90957e11			−1.77145			−0.885725	−	0.464210i	$-0.846338\pi$
$349$	−4.90957e11			−1.77145			−0.885725	+	0.464210i	$0.846338\pi$
$350$	−7.65867e10	−	2.51415e10i	−0.272802	−	0.0895542i
$351$	5.97877e10			0.210247
$352$			1.36116e11i			0.472571i
$353$			2.72119e11i			0.932765i	0.884583	+	0.466382i	$0.154443\pi$
$353$			2.72119e11i			0.932765i	−0.884583	+	0.466382i	$0.845557\pi$
$354$	−1.19424e11			−0.404182
$355$	1.79727e11	+	2.87454e10i	0.600600	+	0.0960595i
$356$	−1.49167e11			−0.492208
$357$		−	2.70390e10i		−	0.0881014i
$358$			3.65924e11i			1.17738i
$359$	−4.82246e10			−0.153230			−0.0766150	−	0.997061i	$-0.524411\pi$
$359$	−4.82246e10			−0.153230			−0.0766150	+	0.997061i	$0.524411\pi$
$360$	−1.69925e10	+	1.06244e11i	−0.0533208	+	0.333382i
$361$	−2.77072e11			−0.858639
$362$			5.62369e10i			0.172121i
$363$			1.47073e11i			0.444582i
$364$	−9.92415e10			−0.296304
$365$	−5.20258e10	+	3.25285e11i	−0.153427	+	0.959282i
$366$	1.92413e11			0.560491
$367$			1.87794e11i			0.540360i	0.962810	+	0.270180i	$0.0870832\pi$
$367$			1.87794e11i			0.540360i	−0.962810	+	0.270180i	$0.912917\pi$
$368$		−	2.08144e10i		−	0.0591627i
$369$	7.71743e10			0.216698
$370$	−1.81614e11	−	2.90472e10i	−0.503780	−	0.0805742i
$371$	3.01754e11			0.826934
$372$		−	2.19710e11i		−	0.594849i
$373$		−	7.83850e10i		−	0.209673i	−0.994489	−	0.104837i	$-0.966568\pi$
$373$		−	7.83850e10i		−	0.209673i	0.994489	−	0.104837i	$-0.0334320\pi$
$374$	−3.87150e10			−0.102319
$375$	1.01270e11	−	1.96539e11i	0.264449	−	0.513225i
$376$	3.83569e11			0.989689
$377$			4.13486e11i			1.05420i
$378$		−	2.19332e10i		−	0.0552572i
$379$	−2.25464e11			−0.561307			−0.280654	−	0.959809i	$-0.590551\pi$
$379$	−2.25464e11			−0.561307			−0.280654	+	0.959809i	$0.590551\pi$
$380$	9.03212e10	+	1.44459e10i	0.222210	+	0.0355401i
$381$	3.25456e11			0.791278
$382$		−	2.76600e11i		−	0.664611i
$383$		−	9.28094e10i		−	0.220393i	−0.993910	−	0.110196i	$-0.964852\pi$
$383$		−	9.28094e10i		−	0.220393i	0.993910	−	0.110196i	$-0.0351480\pi$
$384$	−1.38355e11			−0.324717
$385$	−1.47949e10	+	9.25036e10i	−0.0343194	+	0.214578i
$386$	−3.01520e11			−0.691310
$387$		−	2.57998e11i		−	0.584678i
$388$		−	4.29805e11i		−	0.962783i
$389$	8.47593e11			1.87678			0.938392	−	0.345573i	$-0.112316\pi$
$389$	8.47593e11			1.87678			0.938392	+	0.345573i	$0.112316\pi$
$390$	−2.88363e10	+	1.80296e11i	−0.0631174	+	0.394634i
$391$	−2.12943e11			−0.460753
$392$		−	3.76283e11i		−	0.804872i
$393$		−	1.34266e11i		−	0.283923i
$394$	−5.91588e11			−1.23676
$395$	−2.16333e11	−	3.46001e10i	−0.447132	−	0.0715139i
$396$	4.68186e10			0.0956731
$397$			7.37467e11i			1.49000i	0.667066	+	0.744999i	$0.267550\pi$
$397$			7.37467e11i			1.49000i	−0.667066	+	0.744999i	$0.732450\pi$
$398$		−	4.91089e11i		−	0.981038i
$399$	−4.97995e10			−0.0983664
$400$	−2.10343e10	−	6.90504e9i	−0.0410825	−	0.0134864i
$401$	2.85026e11			0.550471			0.275235	−	0.961377i	$-0.411244\pi$
$401$	2.85026e11			0.550471			0.275235	+	0.961377i	$0.411244\pi$
$402$			2.04840e11i			0.391198i
$403$		−	9.95791e11i		−	1.88060i
$404$	−1.07769e11			−0.201270
$405$	5.94046e10	+	9.50112e9i	0.109717	+	0.0175480i
$406$	1.51688e11			0.277067
$407$			2.13747e11i			0.386123i
$408$		−	1.10220e11i		−	0.196920i
$409$	−1.41255e11			−0.249603			−0.124801	−	0.992182i	$-0.539829\pi$
$409$	−1.41255e11			−0.249603			−0.124801	+	0.992182i	$0.539829\pi$
$410$	−3.72221e10	+	2.32727e11i	−0.0650540	+	0.406742i
$411$	−2.84045e11			−0.491020
$412$		−	3.36789e11i		−	0.575865i
$413$		−	2.96024e11i		−	0.500670i
$414$	−1.72733e11			−0.288984
$415$	−7.46554e9	+	4.66774e10i	−0.0123551	+	0.0772485i
$416$	−6.57613e11			−1.07659
$417$			2.37328e11i			0.384359i
$418$			7.13041e10i			0.114241i
$419$	6.90309e10			0.109416			0.0547080	−	0.998502i	$-0.482577\pi$
$419$	6.90309e10			0.109416			0.0547080	+	0.998502i	$0.482577\pi$
$420$	−9.86057e10	−	1.57709e10i	−0.154625	−	0.0247306i
$421$	−1.47198e11			−0.228367			−0.114184	−	0.993460i	$-0.536425\pi$
$421$	−1.47198e11			−0.228367			−0.114184	+	0.993460i	$0.536425\pi$
$422$		−	1.16391e11i		−	0.178655i
$423$		−	2.14467e11i		−	0.325709i
$424$	1.23005e12			1.84832
$425$	−7.06426e10	+	2.15193e11i	−0.105031	+	0.319947i
$426$	−1.51245e11			−0.222504
$427$			4.76945e11i			0.694294i
$428$			4.36210e10i			0.0628345i
$429$	2.12196e11			0.302467
$430$	7.78018e11	+	1.24436e11i	1.09744	+	0.175524i
$431$	−4.72940e11			−0.660173			−0.330087	−	0.943951i	$-0.607078\pi$
$431$	−4.72940e11			−0.660173			−0.330087	+	0.943951i	$0.607078\pi$
$432$		−	6.02388e9i		−	0.00832146i
$433$			6.97304e11i			0.953294i	0.879095	+	0.476647i	$0.158148\pi$
$433$			6.97304e11i			0.953294i	−0.879095	+	0.476647i	$0.841852\pi$
$434$	−3.65307e11			−0.494259
$435$	−6.57089e10	+	4.10837e11i	−0.0879879	+	0.550133i
$436$	3.79935e11			0.503524
$437$			3.92191e11i			0.514436i
$438$		−	2.73736e11i		−	0.355385i
$439$	9.99909e11			1.28490			0.642451	−	0.766327i	$-0.277918\pi$
$439$	9.99909e11			1.28490			0.642451	+	0.766327i	$0.277918\pi$
$440$	−6.03091e10	+	3.77075e11i	−0.0767089	+	0.479613i
$441$	−2.10393e11			−0.264885
$442$		−	1.87043e11i		−	0.233099i
$443$		−	2.04701e11i		−	0.252524i	−0.991997	−	0.126262i	$-0.959702\pi$
$443$		−	2.04701e11i		−	0.252524i	0.991997	−	0.126262i	$-0.0402980\pi$
$444$	−2.27847e11			−0.278240
$445$	−6.71739e11	−	1.07437e11i	−0.812045	−	0.129878i
$446$	1.76741e11			0.211509
$447$			5.53943e11i			0.656268i
$448$			2.57952e11i			0.302544i
$449$	−1.14845e11			−0.133354			−0.0666769	−	0.997775i	$-0.521240\pi$
$449$	−1.14845e11			−0.133354			−0.0666769	+	0.997775i	$0.521240\pi$
$450$	−5.73032e10	+	1.74558e11i	−0.0658752	+	0.200670i
$451$	2.73903e11			0.311748
$452$		−	5.30430e11i		−	0.597731i
$453$			6.22684e11i			0.694746i
$454$	1.86139e11			0.205630
$455$	−4.46910e11	−	7.14784e10i	−0.488842	−	0.0781850i
$456$	−2.02999e11			−0.219863
$457$		−	1.42783e11i		−	0.153128i	−0.997065	−	0.0765639i	$-0.975605\pi$
$457$		−	1.42783e11i		−	0.153128i	0.997065	−	0.0765639i	$-0.0243949\pi$
$458$			1.76481e10i			0.0187414i
$459$	−6.16278e10			−0.0648066
$460$	−1.24202e11	+	7.76560e11i	−0.129336	+	0.808658i
$461$	9.88626e11			1.01948			0.509739	−	0.860329i	$-0.329742\pi$
$461$	9.88626e11			1.01948			0.509739	+	0.860329i	$0.329742\pi$
$462$		−	7.78443e10i		−	0.0794947i
$463$		−	4.74513e11i		−	0.479881i	−0.970788	−	0.239940i	$-0.922872\pi$
$463$		−	4.74513e11i		−	0.479881i	0.970788	−	0.239940i	$-0.0771279\pi$
$464$	4.16606e10			0.0417248
$465$	1.58246e11	−	9.89411e11i	0.156962	−	0.981383i
$466$	−2.21054e10			−0.0217151
$467$			8.43343e11i			0.820499i	0.911973	+	0.410250i	$0.134558\pi$
$467$			8.43343e11i			0.820499i	−0.911973	+	0.410250i	$0.865442\pi$
$468$			2.26193e11i			0.217958i
$469$	−5.07749e11			−0.484587
$470$	6.46747e11	+	1.03440e11i	0.611356	+	0.0977797i
$471$	−2.36458e11			−0.221391
$472$		−	1.20669e12i		−	1.11907i
$473$		−	9.15674e11i		−	0.841135i
$474$	1.82050e11			0.165649
$475$	3.96335e11	+	1.30107e11i	0.357224	+	0.117268i
$476$	1.02296e11			0.0913329
$477$		−	6.87765e11i		−	0.608285i
$478$			9.07911e10i			0.0795459i
$479$	−2.16057e12			−1.87525			−0.937623	−	0.347655i	$-0.886978\pi$
$479$	−2.16057e12			−1.87525			−0.937623	+	0.347655i	$0.886978\pi$
$480$	−6.53400e11	−	1.04504e11i	−0.561815	−	0.0898562i
$481$	−1.03267e12			−0.879648
$482$			1.08957e9i			0.000919479i
$483$		−	4.28164e11i		−	0.357971i
$484$	−5.56416e11			−0.460888
$485$	3.09566e11	−	1.93552e12i	0.254047	−	1.58840i
$486$	−4.99906e10			−0.0406467
$487$		−	1.03201e12i		−	0.831387i	−0.909505	−	0.415694i	$-0.863539\pi$
$487$		−	1.03201e12i		−	0.831387i	0.909505	−	0.415694i	$-0.136461\pi$
$488$			1.94419e12i			1.55185i
$489$	1.17863e12			0.932157
$490$	1.01475e11	−	6.34460e11i	0.0795201	−	0.497190i
$491$	1.34186e12			1.04193			0.520966	−	0.853578i	$-0.325572\pi$
$491$	1.34186e12			1.04193			0.520966	+	0.853578i	$0.325572\pi$
$492$			2.91972e11i			0.224646i
$493$		−	4.26212e11i		−	0.324949i
$494$	−3.44490e11			−0.260258
$495$	2.10836e11	+	3.37209e10i	0.157842	+	0.0252451i
$496$	−1.00330e11			−0.0744329
$497$		−	3.74901e11i		−	0.275621i
$498$		−	3.92803e10i		−	0.0286182i
$499$	3.08677e11			0.222870			0.111435	−	0.993772i	$-0.464455\pi$
$499$	3.08677e11			0.222870			0.111435	+	0.993772i	$0.464455\pi$
$500$	7.43562e11	+	3.83134e11i	0.532049	+	0.274148i
$501$	2.53355e10			0.0179664
$502$			9.37271e11i			0.658716i
$503$			8.27354e11i			0.576283i	0.957588	+	0.288141i	$0.0930373\pi$
$503$			8.27354e11i			0.576283i	−0.957588	+	0.288141i	$0.906963\pi$
$504$	2.21619e11			0.152992
$505$	−4.85313e11	−	7.76206e10i	−0.332056	−	0.0531087i
$506$	−6.13056e11			−0.415741
$507$			1.66211e11i			0.111718i
$508$			1.23129e12i			0.820301i
$509$	−9.83765e11			−0.649623			−0.324812	−	0.945779i	$-0.605301\pi$
$509$	−9.83765e11			−0.649623			−0.324812	+	0.945779i	$0.605301\pi$
$510$	2.97238e10	−	1.85845e11i	0.0194553	−	0.121642i
$511$	6.78528e11			0.440224
$512$			1.34357e11i			0.0864063i
$513$			1.13504e11i			0.0723574i
$514$	−1.56296e10			−0.00987672
$515$	2.42571e11	−	1.51665e12i	0.151952	−	0.950062i
$516$	9.76078e11			0.606123
$517$		−	7.61177e11i		−	0.468574i
$518$			3.78837e11i			0.231190i
$519$	5.87394e11			0.355367
$520$	−1.82175e12	−	2.91370e11i	−1.09263	−	0.174755i
$521$	2.68426e12			1.59608			0.798041	−	0.602603i	$-0.205870\pi$
$521$	2.68426e12			1.59608			0.798041	+	0.602603i	$0.205870\pi$
$522$		−	3.45731e11i		−	0.203808i
$523$			2.53611e12i			1.48221i	0.671388	+	0.741106i	$0.265698\pi$
$523$			2.53611e12i			1.48221i	−0.671388	+	0.741106i	$0.734302\pi$
$524$	5.07966e11			0.294336
$525$	−4.32688e11	−	1.42041e11i	−0.248575	−	0.0816012i
$526$	−5.26925e11			−0.300133
$527$			1.02644e12i			0.579676i
$528$		−	2.13797e10i		−	0.0119715i
$529$	−1.57082e12			−0.872118
$530$	2.07402e12	+	3.31717e11i	1.14175	+	0.182611i
$531$	−6.74704e11			−0.368288
$532$		−	1.88405e11i		−	0.101974i
$533$			1.32330e12i			0.710210i
$534$	5.65287e11			0.300838
$535$	−3.14179e10	+	1.96437e11i	−0.0165800	+	0.103665i
$536$	−2.06975e12			−1.08312
$537$			2.06734e12i			1.07282i
$538$			1.27276e12i			0.654980i
$539$	−7.46716e11			−0.381071
$540$	−3.59454e10	+	2.24744e11i	−0.0181916	+	0.113741i
$541$	−3.13311e12			−1.57249			−0.786246	−	0.617914i	$-0.787978\pi$
$541$	−3.13311e12			−1.57249			−0.786246	+	0.617914i	$0.787978\pi$
$542$		−	8.30923e11i		−	0.413584i
$543$			3.17719e11i			0.156835i
$544$	6.77853e11			0.331849
$545$	1.71095e12	+	2.73647e11i	0.830715	+	0.132864i
$546$	3.76087e11			0.181101
$547$			9.13486e11i			0.436274i	0.975918	+	0.218137i	$0.0699979\pi$
$547$			9.13486e11i			0.436274i	−0.975918	+	0.218137i	$0.930002\pi$
$548$		−	1.07462e12i		−	0.509030i
$549$	1.08706e12			0.510716
$550$	−2.03378e11	+	6.19533e11i	−0.0947701	+	0.288690i
$551$	−7.84984e11			−0.362809
$552$		−	1.74534e12i		−	0.800118i
$553$			4.51259e11i			0.205193i
$554$	−6.33581e11			−0.285765
$555$	−1.02605e12	−	1.64106e11i	−0.459041	−	0.0734187i
$556$	−8.97878e11			−0.398456
$557$		−	3.59154e12i		−	1.58100i	−0.612461	−	0.790501i	$-0.709820\pi$
$557$		−	3.59154e12i		−	1.58100i	0.612461	−	0.790501i	$-0.290180\pi$
$558$			8.32616e11i			0.363573i
$559$	4.42387e12			1.91624
$560$	−7.20178e9	+	4.50282e10i	−0.00309452	+	0.0193481i
$561$	−2.18726e11			−0.0932327
$562$		−	2.11326e12i		−	0.893594i
$563$		−	2.56254e12i		−	1.07494i	−0.843284	−	0.537468i	$-0.819381\pi$
$563$		−	2.56254e12i		−	1.07494i	0.843284	−	0.537468i	$-0.180619\pi$
$564$	8.11389e11			0.337655
$565$	3.82041e11	−	2.38866e12i	0.157722	−	0.986137i
$566$	2.33781e11			0.0957493
$567$		−	1.23915e11i		−	0.0503500i
$568$		−	1.52822e12i		−	0.616054i
$569$	−3.17224e12			−1.26871			−0.634353	−	0.773043i	$-0.718733\pi$
$569$	−3.17224e12			−1.26871			−0.634353	+	0.773043i	$0.718733\pi$
$570$	−3.42283e11	−	5.47444e10i	−0.135815	−	0.0217221i
$571$	3.57733e12			1.40830			0.704152	−	0.710050i	$-0.251328\pi$
$571$	3.57733e12			1.40830			0.704152	+	0.710050i	$0.251328\pi$
$572$			8.02795e11i			0.313561i
$573$		−	1.56270e12i		−	0.605590i
$574$	4.85456e11			0.186658
$575$	−1.11863e12	+	3.40760e12i	−0.426758	+	1.30000i
$576$	5.87931e11			0.222549
$577$			7.07479e11i			0.265719i	0.991135	+	0.132859i	$0.0424159\pi$
$577$			7.07479e11i			0.265719i	−0.991135	+	0.132859i	$0.957584\pi$
$578$		−	1.50741e12i		−	0.561769i
$579$	−1.70348e12			−0.629918
$580$	−1.55431e12	−	2.48595e11i	−0.570311	−	0.0912151i
$581$	9.73665e10			0.0354501
$582$			1.62879e12i			0.588454i
$583$		−	2.44098e12i		−	0.875097i
$584$	2.76591e12			0.983965
$585$	−1.62915e11	+	1.01861e12i	−0.0575122	+	0.359588i
$586$	1.72369e12			0.603838
$587$			3.20959e12i			1.11578i	0.829916	+	0.557889i	$0.188388\pi$
$587$			3.20959e12i			1.11578i	−0.829916	+	0.557889i	$0.811612\pi$
$588$		−	7.95975e11i		−	0.274600i
$589$	1.89046e12			0.647216
$590$	3.25418e11	−	2.03464e12i	0.110562	−	0.691278i
$591$	−3.34227e12			−1.12693
$592$			1.04046e11i			0.0348160i
$593$			3.72506e12i			1.23705i	0.785765	+	0.618526i	$0.212270\pi$
$593$			3.72506e12i			1.23705i	−0.785765	+	0.618526i	$0.787730\pi$
$594$	−1.77424e11			−0.0584755
$595$	4.60665e11	+	7.36784e10i	0.150681	+	0.0240998i
$596$	−2.09572e12			−0.680339
$597$		−	2.77448e12i		−	0.893916i
$598$		−	2.96184e12i		−	0.947123i
$599$	−2.35643e12			−0.747883			−0.373942	−	0.927452i	$-0.621994\pi$
$599$	−2.35643e12			−0.747883			−0.373942	+	0.927452i	$0.621994\pi$
$600$	−1.76378e12	−	5.79006e11i	−0.555602	−	0.182391i
$601$	2.11495e10			0.00661250			0.00330625	−	0.999995i	$-0.498948\pi$
$601$	2.11495e10			0.00661250			0.00330625	+	0.999995i	$0.498948\pi$
$602$		−	1.62291e12i		−	0.503627i
$603$			1.15727e12i			0.356457i
$604$	−2.35579e12			−0.720228
$605$	−2.50569e12	−	4.00757e11i	−0.760374	−	0.121614i
$606$	4.08404e11			0.123017
$607$			5.85975e12i			1.75198i	0.482326	+	0.875992i	$0.339792\pi$
$607$			5.85975e12i			1.75198i	−0.482326	+	0.875992i	$0.660208\pi$
$608$		−	1.24845e12i		−	0.370513i
$609$	8.56985e11			0.252462
$610$	−5.24304e11	+	3.27815e12i	−0.153320	+	0.958615i
$611$	3.67745e12			1.06749
$612$		−	2.33155e11i		−	0.0671836i
$613$		−	3.39524e12i		−	0.971178i	−0.874187	−	0.485589i	$-0.838605\pi$
$613$		−	3.39524e12i		−	0.971178i	0.874187	−	0.485589i	$-0.161395\pi$
$614$	−2.58558e12			−0.734177
$615$	−2.10292e11	+	1.31482e12i	−0.0592768	+	0.370621i
$616$	7.86560e11			0.220099
$617$			2.99293e12i			0.831406i	0.909500	+	0.415703i	$0.136464\pi$
$617$			2.99293e12i			0.831406i	−0.909500	+	0.415703i	$0.863536\pi$
$618$			1.27630e12i			0.351969i
$619$	3.89410e12			1.06610			0.533052	−	0.846082i	$-0.321045\pi$
$619$	3.89410e12			1.06610			0.533052	+	0.846082i	$0.321045\pi$
$620$	3.74322e12	+	5.98687e11i	1.01738	+	0.162719i
$621$	−9.75881e11			−0.263321
$622$			3.25496e12i			0.871944i
$623$			1.40121e12i			0.372655i
$624$	1.03291e11			0.0272729
$625$	3.07250e12	+	2.26090e12i	0.805437	+	0.592681i
$626$	1.49684e12			0.389574
$627$			4.02843e11i			0.104096i
$628$		−	8.94587e11i		−	0.229511i
$629$	1.06445e12			0.271143
$630$	3.73678e11	+	5.97657e10i	0.0945072	+	0.0151154i
$631$	6.58750e11			0.165420			0.0827101	−	0.996574i	$-0.473642\pi$
$631$	6.58750e11			0.165420			0.0827101	+	0.996574i	$0.473642\pi$
$632$			1.83948e12i			0.458637i
$633$		−	6.57570e11i		−	0.162789i
$634$	−3.12934e12			−0.769222
$635$	−8.86832e11	+	5.54481e12i	−0.216451	+	1.35333i
$636$	2.60201e12			0.630596
$637$		−	3.60759e12i		−	0.868140i
$638$		−	1.22705e12i		−	0.293204i
$639$	−8.54482e11			−0.202745
$640$	3.77004e11	−	2.35717e12i	0.0888251	−	0.555368i
$641$	−2.24747e12			−0.525814			−0.262907	−	0.964821i	$-0.584681\pi$
$641$	−2.24747e12			−0.525814			−0.262907	+	0.964821i	$0.584681\pi$
$642$		−	1.65307e11i		−	0.0384046i
$643$		−	9.01721e11i		−	0.208028i	−0.994576	−	0.104014i	$-0.966831\pi$
$643$		−	9.01721e11i		−	0.208028i	0.994576	−	0.104014i	$-0.0331687\pi$
$644$	1.61986e12			0.371101
$645$	4.39553e12	+	7.03018e11i	0.999983	+	0.159936i
$646$	3.55092e11			0.0802222
$647$		−	3.78126e12i		−	0.848334i	−0.905584	−	0.424167i	$-0.860567\pi$
$647$		−	3.78126e12i		−	0.848334i	0.905584	−	0.424167i	$-0.139433\pi$
$648$		−	5.05119e11i		−	0.112540i
$649$	−2.39463e12			−0.529830
$650$	−2.99313e12	−	9.82573e11i	−0.657682	−	0.215901i
$651$	−2.06386e12			−0.450366
$652$			4.45910e12i			0.966347i
$653$		−	8.17889e12i		−	1.76029i	−0.474702	−	0.880146i	$-0.657444\pi$
$653$		−	8.17889e12i		−	1.76029i	0.474702	−	0.880146i	$-0.342556\pi$
$654$	−1.43981e12			−0.307755
$655$	2.28750e12	+	3.65861e11i	0.485597	+	0.0776659i
$656$	1.33329e11			0.0281097
$657$		−	1.54652e12i		−	0.323825i
$658$		−	1.34908e12i		−	0.280557i
$659$	−4.24425e12			−0.876631			−0.438315	−	0.898821i	$-0.644425\pi$
$659$	−4.24425e12			−0.876631			−0.438315	+	0.898821i	$0.644425\pi$
$660$	−1.27576e11	+	7.97652e11i	−0.0261710	+	0.163631i
$661$	−6.21151e12			−1.26558			−0.632791	−	0.774322i	$-0.718091\pi$
$661$	−6.21151e12			−1.26558			−0.632791	+	0.774322i	$0.718091\pi$
$662$			4.00357e11i			0.0810189i
$663$		−	1.05673e12i		−	0.212399i
$664$	3.96898e11			0.0792361
$665$	1.35698e11	−	8.48438e11i	0.0269077	−	0.168237i
$666$	8.63453e11			0.170061
$667$		−	6.74911e12i		−	1.32032i
$668$			9.58513e10i			0.0186253i
$669$	9.98523e11			0.192726
$670$	−3.48987e12	−	5.58167e11i	−0.669071	−	0.107011i
$671$	3.85816e12			0.734731
$672$			1.36296e12i			0.257822i
$673$			8.89347e12i			1.67110i	0.549412	+	0.835552i	$0.314852\pi$
$673$			8.89347e12i			1.67110i	−0.549412	+	0.835552i	$0.685148\pi$
$674$	2.46668e12			0.460408
$675$	−3.23743e11	+	9.86192e11i	−0.0600251	+	0.182850i
$676$	−6.28821e11			−0.115816
$677$		−	7.52635e12i		−	1.37700i	−0.725234	−	0.688502i	$-0.758268\pi$
$677$		−	7.52635e12i		−	1.37700i	0.725234	−	0.688502i	$-0.241732\pi$
$678$			2.01013e12i			0.365334i
$679$	−4.03740e12			−0.728933
$680$	1.87782e12	+	3.00338e11i	0.336794	+	0.0538666i
$681$	1.05162e12			0.187369
$682$			2.95508e12i			0.523046i
$683$		−	4.87406e12i		−	0.857034i	−0.903534	−	0.428517i	$-0.859036\pi$
$683$		−	4.87406e12i		−	0.857034i	0.903534	−	0.428517i	$-0.140964\pi$
$684$	−4.29417e11			−0.0750114
$685$	7.73994e11	−	4.83930e12i	0.134317	−	0.839798i
$686$	−2.98889e12			−0.515290
$687$			9.97055e10i			0.0170771i
$688$		−	4.45725e11i		−	0.0758437i
$689$	1.17931e13			1.99361
$690$	4.70679e11	−	2.94287e12i	0.0790504	−	0.494253i
$691$	−4.18834e12			−0.698861			−0.349430	−	0.936962i	$-0.613625\pi$
$691$	−4.18834e12			−0.698861			−0.349430	+	0.936962i	$0.613625\pi$
$692$			2.22228e12i			0.368401i
$693$		−	4.39793e11i		−	0.0724351i
$694$	−4.11335e12			−0.673098
$695$	−4.04337e12	−	6.46694e11i	−0.657374	−	0.105140i
$696$	3.49335e12			0.564288
$697$		−	1.36403e12i		−	0.218916i
$698$			7.03893e12i			1.12243i
$699$	−1.24888e11			−0.0197867
$700$	5.37381e11	−	1.63698e12i	0.0845942	−	0.257693i
$701$	2.63533e12			0.412195			0.206098	−	0.978531i	$-0.433924\pi$
$701$	2.63533e12			0.412195			0.206098	+	0.978531i	$0.433924\pi$
$702$		−	8.57186e11i		−	0.133216i
$703$		−	1.96048e12i		−	0.302735i
$704$	2.08666e12			0.320165
$705$	3.65389e12	+	5.84401e11i	0.557064	+	0.0890963i
$706$	3.90141e12			0.591018
$707$			1.01234e12i			0.152384i
$708$		−	2.55259e12i		−	0.381797i
$709$	−3.46943e12			−0.515644			−0.257822	−	0.966192i	$-0.583005\pi$
$709$	−3.46943e12			−0.515644			−0.257822	+	0.966192i	$0.583005\pi$
$710$	4.12127e11	−	2.57678e12i	0.0608652	−	0.380552i
$711$	1.02852e12			0.150938
$712$			5.71181e12i			0.832939i
$713$			1.62537e13i			2.35532i
$714$	−3.87662e11			−0.0558228
$715$	−5.78211e11	+	3.61519e12i	−0.0827388	+	0.517314i
$716$	−7.82132e12			−1.11217
$717$			5.12938e11i			0.0724818i
$718$			6.91405e11i			0.0970895i
$719$	8.98267e12			1.25350			0.626752	−	0.779219i	$-0.284384\pi$
$719$	8.98267e12			1.25350			0.626752	+	0.779219i	$0.284384\pi$
$720$	1.02629e11	+	1.64144e10i	0.0142323	+	0.00227630i
$721$	−3.16365e12			−0.435993
$722$			3.97243e12i			0.544050i
$723$			6.15567e9i			0.000837824i
$724$	−1.20202e12			−0.162588
$725$	−6.82041e12	−	2.23898e12i	−0.916832	−	0.300974i
$726$	2.10860e12			0.281696
$727$		−	5.78092e12i		−	0.767524i	−0.923432	−	0.383762i	$-0.874628\pi$
$727$		−	5.78092e12i		−	0.767524i	0.923432	−	0.383762i	$-0.125372\pi$
$728$			3.80008e12i			0.501420i
$729$	−2.82430e11			−0.0370370
$730$	4.66367e12	+	7.45903e11i	0.607820	+	0.0972142i
$731$	−4.56003e12			−0.590663
$732$			4.11267e12i			0.529448i
$733$			1.40487e13i			1.79749i	0.438469	+	0.898746i	$0.355521\pi$
$733$			1.40487e13i			1.79749i	−0.438469	+	0.898746i	$0.644479\pi$
$734$	2.69243e12			0.342383
$735$	5.73298e11	−	3.58448e12i	0.0724582	−	0.453036i
$736$	1.07339e13			1.34836
$737$			4.10734e12i			0.512810i
$738$		−	1.10646e12i		−	0.137304i
$739$	−3.93871e11			−0.0485796			−0.0242898	−	0.999705i	$-0.507732\pi$
$739$	−3.93871e11			−0.0485796			−0.0242898	+	0.999705i	$0.507732\pi$
$740$	6.20860e11	−	3.88185e12i	0.0761116	−	0.475878i
$741$	−1.94625e12			−0.237146
$742$		−	4.32630e12i		−	0.523961i
$743$		−	7.69778e12i		−	0.926651i	−0.886188	−	0.463325i	$-0.846656\pi$
$743$		−	7.69778e12i		−	0.926651i	0.886188	−	0.463325i	$-0.153344\pi$
$744$	−8.41298e12			−1.00663
$745$	−9.43758e12	−	1.50944e12i	−1.12242	−	0.179520i
$746$	−1.12382e12			−0.132853
$747$		−	2.21920e11i		−	0.0260768i
$748$		−	8.27503e11i		−	0.0966524i
$749$	4.09756e11			0.0475727
$750$	−2.81781e12	−	1.45193e12i	−0.325189	−	0.167560i
$751$	7.71512e12			0.885040			0.442520	−	0.896759i	$-0.354085\pi$
$751$	7.71512e12			0.885040			0.442520	+	0.896759i	$0.354085\pi$
$752$		−	3.70520e11i		−	0.0422505i
$753$			5.29525e12i			0.600219i
$754$	5.92822e12			0.667964
$755$	−1.06087e13	−	1.69675e12i	−1.18823	−	0.190045i
$756$	4.68805e11			0.0521968
$757$		−	5.54873e12i		−	0.614132i	−0.951688	−	0.307066i	$-0.900653\pi$
$757$		−	5.54873e12i		−	0.614132i	0.951688	−	0.307066i	$-0.0993473\pi$
$758$			3.23252e12i			0.355655i
$759$	−3.46355e12			−0.378821
$760$	5.53152e11	−	3.45851e12i	0.0601427	−	0.376035i
$761$	7.40605e12			0.800490			0.400245	−	0.916408i	$-0.368925\pi$
$761$	7.40605e12			0.800490			0.400245	+	0.916408i	$0.368925\pi$
$762$		−	4.66611e12i		−	0.501369i
$763$		−	3.56895e12i		−	0.381223i
$764$	5.91211e12			0.627802
$765$	1.67929e11	−	1.04996e12i	0.0177276	−	0.110840i
$766$	−1.33062e12			−0.139645
$767$		−	1.15691e13i		−	1.20704i
$768$			5.69993e12i			0.591213i
$769$	2.19820e12			0.226672			0.113336	−	0.993557i	$-0.463846\pi$
$769$	2.19820e12			0.226672			0.113336	+	0.993557i	$0.463846\pi$
$770$	1.32624e12	+	2.12118e11i	0.135961	+	0.0217455i
$771$	−8.83016e10			−0.00899961
$772$		−	6.44474e12i		−	0.653022i
$773$			4.88091e12i			0.491692i	0.969309	+	0.245846i	$0.0790658\pi$
$773$			4.88091e12i			0.491692i	−0.969309	+	0.245846i	$0.920934\pi$
$774$	−3.69896e12			−0.370463
$775$	1.64255e13	+	5.39208e12i	1.63554	+	0.536907i
$776$	−1.64578e13			−1.62927
$777$			2.14030e12i			0.210659i
$778$		−	1.21521e13i		−	1.18917i
$779$	−2.51223e12			−0.244422
$780$	−3.85367e12	−	6.16353e11i	−0.372777	−	0.0596217i
$781$	−3.03269e12			−0.291674
$782$			3.05300e12i			0.291942i
$783$		−	1.95326e12i		−	0.185708i
$784$	−3.63481e11			−0.0343605
$785$	6.44324e11	−	4.02856e12i	0.0605607	−	0.378648i
$786$	−1.92500e12			−0.179899
$787$		−	5.55849e12i		−	0.516500i	−0.966078	−	0.258250i	$-0.916854\pi$
$787$		−	5.55849e12i		−	0.516500i	0.966078	−	0.258250i	$-0.0831459\pi$
$788$		−	1.26447e13i		−	1.16826i
$789$	−2.97694e12			−0.273479
$790$	−4.96068e11	+	3.10160e12i	−0.0453126	+	0.283311i
$791$	−4.98263e12			−0.452548
$792$		−	1.79274e12i		−	0.161903i
$793$			1.86398e13i			1.67383i
$794$	1.05732e13			0.944091
$795$	1.17175e13	+	1.87409e12i	1.04036	+	0.166394i
$796$	1.04966e13			0.926704
$797$		−	4.50429e11i		−	0.0395425i	−0.999805	−	0.0197712i	$-0.993706\pi$
$797$		−	4.50429e11i		−	0.0395425i	0.999805	−	0.0197712i	$-0.00629379\pi$
$798$			7.13984e11i			0.0623269i
$799$	−3.79064e12			−0.329042
$800$	3.56089e12	−	1.08473e13i	0.307365	−	0.936300i
$801$	3.19367e12			0.274122
$802$		−	4.08646e12i		−	0.348789i
$803$		−	5.48882e12i		−	0.465864i
$804$	−4.37828e12			−0.369532
$805$	7.29467e12	+	1.16670e12i	0.612243	+	0.0979217i
$806$	−1.42768e13			−1.19158
$807$			7.19068e12i			0.596814i
$808$			4.12663e12i			0.340599i
$809$	−8.43581e12			−0.692402			−0.346201	−	0.938160i	$-0.612529\pi$
$809$	−8.43581e12			−0.692402			−0.346201	+	0.938160i	$0.612529\pi$
$810$	1.36219e11	−	8.51694e11i	0.0111187	−	0.0695186i
$811$	−1.79645e12			−0.145821			−0.0729106	−	0.997338i	$-0.523229\pi$
$811$	−1.79645e12			−0.145821			−0.0729106	+	0.997338i	$0.523229\pi$
$812$			3.24221e12i			0.261721i
$813$		−	4.69443e12i		−	0.376856i
$814$	3.06453e12			0.244655
$815$	−3.21165e12	+	2.00805e13i	−0.254988	+	1.59428i
$816$	−1.06470e11			−0.00840663
$817$			8.39851e12i			0.659482i
$818$			2.02520e12i			0.158153i
$819$	2.12476e12			0.165018
$820$	−4.97435e12	−	7.95593e11i	−0.384215	−	0.0614510i
$821$	2.37074e13			1.82112			0.910561	−	0.413374i	$-0.135650\pi$
$821$	2.37074e13			1.82112			0.910561	+	0.413374i	$0.135650\pi$
$822$			4.07240e12i			0.311120i
$823$		−	5.83064e12i		−	0.443013i	−0.975159	−	0.221507i	$-0.928903\pi$
$823$		−	5.83064e12i		−	0.443013i	0.975159	−	0.221507i	$-0.0710974\pi$
$824$	−1.28961e13			−0.974508
$825$	−1.14901e12	+	3.50015e12i	−0.0863539	+	0.263053i
$826$	−4.24415e12			−0.317234
$827$			1.53707e13i			1.14266i	0.820719	+	0.571332i	$0.193573\pi$
$827$			1.53707e13i			1.14266i	−0.820719	+	0.571332i	$0.806427\pi$
$828$		−	3.69203e12i		−	0.272979i
$829$	−1.38823e13			−1.02086			−0.510430	−	0.859920i	$-0.670514\pi$
$829$	−1.38823e13			−1.02086			−0.510430	+	0.859920i	$0.670514\pi$
$830$	6.69221e11	+	1.07035e11i	0.0489461	+	0.00782840i
$831$	−3.57951e12			−0.260387
$832$			1.00812e13i			0.729386i
$833$			3.71862e12i			0.267596i
$834$	3.40261e12			0.243537
$835$	−6.90367e10	+	4.31643e11i	−0.00491463	+	0.0307281i
$836$	−1.52407e12			−0.107914
$837$			4.70399e12i			0.331285i
$838$		−	9.89708e11i		−	0.0693281i
$839$	1.07137e13			0.746468			0.373234	−	0.927737i	$-0.378249\pi$
$839$	1.07137e13			0.746468			0.373234	+	0.927737i	$0.378249\pi$
$840$	−6.03888e11	+	3.77574e12i	−0.0418504	+	0.261665i
$841$	−9.98592e11			−0.0688345
$842$			2.11041e12i			0.144698i
$843$		−	1.19392e13i		−	0.814238i
$844$	2.48777e12			0.168760
$845$	−2.83174e12	−	4.52907e11i	−0.191073	−	0.0305600i
$846$	−3.07485e12			−0.206375
$847$			5.22673e12i			0.348943i
$848$		−	1.18820e12i		−	0.0789059i
$849$	1.32078e12			0.0872462
$850$	3.08526e12	+	1.01281e12i	0.202724	+	0.0665495i
$851$	1.68557e13			1.10170
$852$		−	3.23275e12i		−	0.210181i
$853$		−	1.35460e13i		−	0.876076i	−0.898956	−	0.438038i	$-0.855673\pi$
$853$		−	1.35460e13i		−	0.876076i	0.898956	−	0.438038i	$-0.144327\pi$
$854$	6.83805e12			0.439918
$855$	−1.93378e12	−	3.09287e11i	−0.123754	−	0.0197931i
$856$	1.67030e12			0.106332
$857$			5.74619e12i			0.363887i	0.983309	+	0.181943i	$0.0582387\pi$
$857$			5.74619e12i			0.363887i	−0.983309	+	0.181943i	$0.941761\pi$
$858$		−	3.04228e12i		−	0.191649i
$859$	−1.42325e13			−0.891890			−0.445945	−	0.895060i	$-0.647132\pi$
$859$	−1.42325e13			−0.891890			−0.445945	+	0.895060i	$0.647132\pi$
$860$	−2.65971e12	+	1.66295e13i	−0.165803	+	1.03666i
$861$	2.74266e12			0.170082
$862$			6.78062e12i			0.418299i
$863$		−	1.45815e13i		−	0.894859i	−0.894319	−	0.447429i	$-0.852340\pi$
$863$		−	1.45815e13i		−	0.894859i	0.894319	−	0.447429i	$-0.147660\pi$
$864$	3.10648e12			0.189652
$865$	−1.60059e12	+	1.00075e13i	−0.0972091	+	0.607788i
$866$	9.99737e12			0.604025
$867$		−	8.51637e12i		−	0.511880i
$868$		−	7.80815e12i		−	0.466885i
$869$	3.65037e12			0.217144
$870$	5.89024e12	+	9.42080e11i	0.348575	+	0.0557508i
$871$	−1.98437e13			−1.16826
$872$		−	1.45482e13i		−	0.852090i
$873$			9.20212e12i			0.536196i
$874$	5.62291e12			0.325957
$875$	3.59899e12	−	6.98469e12i	0.207561	−	0.402820i
$876$	5.85090e12			0.335702
$877$		−	1.38120e13i		−	0.788419i	−0.919021	−	0.394209i	$-0.871018\pi$
$877$		−	1.38120e13i		−	0.788419i	0.919021	−	0.394209i	$-0.128982\pi$
$878$		−	1.43359e13i		−	0.814139i
$879$	9.73827e12			0.550214
$880$	3.64247e11	+	5.82574e10i	0.0204750	+	0.00327476i
$881$	−9.98590e12			−0.558465			−0.279232	−	0.960224i	$-0.590080\pi$
$881$	−9.98590e12			−0.558465			−0.279232	+	0.960224i	$0.590080\pi$
$882$			3.01644e12i			0.167836i
$883$		−	2.46582e13i		−	1.36502i	−0.730878	−	0.682508i	$-0.760889\pi$
$883$		−	2.46582e13i		−	1.36502i	0.730878	−	0.682508i	$-0.239111\pi$
$884$	3.99789e12			0.220189
$885$	1.83850e12	−	1.14950e13i	0.100744	−	0.629889i
$886$	−2.93483e12			−0.160004
$887$		−	7.28183e12i		−	0.394988i	−0.980304	−	0.197494i	$-0.936720\pi$
$887$		−	7.28183e12i		−	0.394988i	0.980304	−	0.197494i	$-0.0632803\pi$
$888$			8.72456e12i			0.470853i
$889$	1.15662e13			0.621058
$890$	−1.54035e12	+	9.63083e12i	−0.0822931	+	0.514528i
$891$	−1.00239e12			−0.0532826
$892$			3.77769e12i			0.199795i
$893$			6.98147e12i			0.367380i
$894$	7.94198e12			0.415824
$895$	−3.52214e13	−	5.63329e12i	−1.83486	−	0.293466i
$896$	−4.91693e12			−0.254864
$897$		−	1.67334e13i		−	0.863013i
$898$			1.64656e12i			0.0844955i
$899$	−3.25324e13			−1.66111
$900$	−3.73104e12	−	1.22481e12i	−0.189556	−	0.0622268i
$901$	−1.21560e13			−0.614511
$902$		−	3.92700e12i		−	0.197529i
$903$		−	9.16885e12i		−	0.458902i
$904$	−2.03109e13			−1.01151
$905$	−5.41300e12	−	8.65751e11i	−0.268238	−	0.0429017i
$906$	8.92753e12			0.440204
$907$			2.90933e13i			1.42745i	0.700428	+	0.713723i	$0.252993\pi$
$907$			2.90933e13i			1.42745i	−0.700428	+	0.713723i	$0.747007\pi$
$908$			3.97857e12i			0.194241i
$909$	2.30734e12			0.112092
$910$	−1.02480e12	+	6.40743e12i	−0.0495396	+	0.309740i
$911$	2.72560e13			1.31108			0.655541	−	0.755160i	$-0.272441\pi$
$911$	2.72560e13			1.31108			0.655541	+	0.755160i	$0.272441\pi$
$912$			1.96093e11i			0.00938611i
$913$		−	7.87628e11i		−	0.0375148i
$914$	−2.04711e12			−0.0970247
$915$	−2.96214e12	+	1.85204e13i	−0.139704	+	0.873485i
$916$	−3.77214e11			−0.0177034
$917$		−	4.77161e12i		−	0.222845i
$918$			8.83568e11i			0.0410627i
$919$	2.72901e13			1.26208			0.631038	−	0.775752i	$-0.282629\pi$
$919$	2.72901e13			1.26208			0.631038	+	0.775752i	$0.282629\pi$
$920$	2.97355e13	+	4.75587e12i	1.36845	+	0.218869i
$921$	−1.46076e13			−0.668977
$922$		−	1.41741e13i		−	0.645961i
$923$		−	1.46518e13i		−	0.664480i
$924$	1.66386e12			0.0750919
$925$	5.59178e12	−	1.70338e13i	0.251138	−	0.765021i
$926$	−6.80317e12			−0.304062
$927$			7.21065e12i			0.320712i
$928$			2.14842e13i			0.950938i
$929$	2.46091e12			0.108399			0.0541994	−	0.998530i	$-0.482739\pi$
$929$	2.46091e12			0.108399			0.0541994	+	0.998530i	$0.482739\pi$
$930$	−1.41854e13	−	2.26879e12i	−0.621823	−	0.0994539i
$931$	6.84884e12			0.298774
$932$		−	4.72486e11i		−	0.0205125i
$933$			1.83894e13i			0.794510i
$934$	1.20911e13			0.519884
$935$	5.96007e11	−	3.72646e12i	0.0255035	−	0.159457i
$936$	8.66123e12			0.368840
$937$			1.99170e13i			0.844105i	0.906571	+	0.422052i	$0.138690\pi$
$937$			1.99170e13i			0.844105i	−0.906571	+	0.422052i	$0.861310\pi$
$938$			7.27968e12i			0.307043i
$939$	8.45661e12			0.354978
$940$	−2.21095e12	+	1.38237e13i	−0.0923642	+	0.577496i
$941$	−4.95810e12			−0.206140			−0.103070	−	0.994674i	$-0.532867\pi$
$941$	−4.95810e12			−0.206140			−0.103070	+	0.994674i	$0.532867\pi$
$942$			3.39014e12i			0.140278i
$943$		−	2.15995e13i		−	0.889492i
$944$	−1.16564e12			−0.0477739
$945$	2.11115e12	+	3.37655e11i	0.0861144	+	0.0137731i
$946$	−1.31282e13			−0.532960
$947$		−	1.51016e12i		−	0.0610165i	−0.999535	−	0.0305083i	$-0.990287\pi$
$947$		−	1.51016e12i		−	0.0610165i	0.999535	−	0.0305083i	$-0.00971259\pi$
$948$			3.89118e12i			0.156474i
$949$	2.65180e13			1.06131
$950$	1.86537e12	−	5.68232e12i	0.0743034	−	0.226344i
$951$	−1.76797e13			−0.700910
$952$		−	3.91704e12i		−	0.154558i
$953$			1.89236e13i			0.743167i	0.928399	+	0.371584i	$0.121185\pi$
$953$			1.89236e13i			0.743167i	−0.928399	+	0.371584i	$0.878815\pi$
$954$	−9.86060e12			−0.385421
$955$	2.66238e13	+	4.25818e12i	1.03575	+	0.165657i
$956$	−1.94059e12			−0.0751403
$957$		−	6.93241e12i		−	0.267166i
$958$			3.09764e13i			1.18819i
$959$	−1.00945e13			−0.385392
$960$	−1.60205e12	+	1.00166e13i	−0.0608773	+	0.380628i
$961$	5.19075e13			1.96325
$962$			1.48056e13i			0.557362i
$963$		−	9.33925e11i		−	0.0349940i
$964$	−2.32886e10			−0.000868554
$965$	4.64181e12	−	2.90223e13i	0.172311	−	1.07736i
$966$	−6.13866e12			−0.226818
$967$			2.37839e13i			0.874708i	0.899289	+	0.437354i	$0.144084\pi$
$967$			2.37839e13i			0.874708i	−0.899289	+	0.437354i	$0.855916\pi$
$968$			2.13059e13i			0.779939i
$969$	2.00615e12			0.0730980
$970$	−2.77499e13	−	4.43829e12i	−1.00644	−	0.160969i
$971$	−3.64444e13			−1.31566			−0.657831	−	0.753166i	$-0.728526\pi$
$971$	−3.64444e13			−1.31566			−0.657831	+	0.753166i	$0.728526\pi$
$972$		−	1.06851e12i		−	0.0383955i
$973$			8.43427e12i			0.301675i
$974$	−1.47961e13			−0.526783
$975$	−1.69102e13	−	5.55120e12i	−0.599276	−	0.196728i
$976$	1.87805e12			0.0662494
$977$			1.56031e13i			0.547878i	0.961747	+	0.273939i	$0.0883267\pi$
$977$			1.56031e13i			0.547878i	−0.961747	+	0.273939i	$0.911673\pi$
$978$		−	1.68983e13i		−	0.590632i
$979$	1.13348e13			0.394360
$980$	1.35611e13	+	2.16895e12i	0.469653	+	0.0751159i
$981$	−8.13442e12			−0.280424
$982$		−	1.92384e13i		−	0.660188i
$983$			3.08484e13i			1.05376i	0.849939	+	0.526881i	$0.176639\pi$
$983$			3.08484e13i			1.05376i	−0.849939	+	0.526881i	$0.823361\pi$
$984$	1.11800e13			0.380157
$985$	9.10733e12	−	5.69424e13i	0.308268	−	1.92741i
$986$	−6.11068e12			−0.205894
$987$		−	7.62183e12i		−	0.255642i
$988$		−	7.36319e12i		−	0.245844i
$989$	−7.22085e13			−2.39996
$990$	4.83463e11	−	3.02279e12i	0.0159958	−	0.100012i
$991$	−3.26910e13			−1.07671			−0.538353	−	0.842720i	$-0.680953\pi$
$991$	−3.26910e13			−1.07671			−0.538353	+	0.842720i	$0.680953\pi$
$992$		−	5.17399e13i		−	1.69638i
$993$			2.26188e12i			0.0738239i
$994$	−5.37502e12			−0.174639
$995$	4.72690e13	+	7.56017e12i	1.52888	+	0.244527i
$996$	8.39585e11			0.0270332
$997$		−	4.13191e13i		−	1.32441i	−0.749322	−	0.662206i	$-0.769621\pi$
$997$		−	4.13191e13i		−	1.32441i	0.749322	−	0.662206i	$-0.230379\pi$
$998$		−	4.42556e12i		−	0.141215i
$999$	4.87821e12			0.154959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.10.b.a.4.4	✓	8
3.2	odd	2		45.10.b.c.19.5		8
4.3	odd	2		240.10.f.c.49.8		8
5.2	odd	4		75.10.a.i.1.3		4
5.3	odd	4		75.10.a.l.1.2		4
5.4	even	2	inner	15.10.b.a.4.5	yes	8
15.2	even	4		225.10.a.u.1.2		4
15.8	even	4		225.10.a.q.1.3		4
15.14	odd	2		45.10.b.c.19.4		8
20.19	odd	2		240.10.f.c.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.b.a.4.4	✓	8	1.1	even	1	trivial
15.10.b.a.4.5	yes	8	5.4	even	2	inner
45.10.b.c.19.4		8	15.14	odd	2
45.10.b.c.19.5		8	3.2	odd	2
75.10.a.i.1.3		4	5.2	odd	4
75.10.a.l.1.2		4	5.3	odd	4
225.10.a.q.1.3		4	15.8	even	4
225.10.a.u.1.2		4	15.2	even	4
240.10.f.c.49.4		8	20.19	odd	2
240.10.f.c.49.8		8	4.3	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)

\(f(q)\)	\(=\)	\(q-14.3372i q^{2} -81.0000i q^{3} +306.446 q^{4} +(1380.00 + 220.717i) q^{5} -1161.31 q^{6} -2878.61i q^{7} -11734.2i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-14.3372i q^{2} -81.0000i q^{3} +306.446 q^{4} +(1380.00 + 220.717i) q^{5} -1161.31 q^{6} -2878.61i q^{7} -11734.2i q^{8} -6561.00 q^{9} +(3164.45 - 19785.3i) q^{10} -23286.0 q^{11} -24822.1i q^{12} -112501. i q^{13} -41271.2 q^{14} +(17878.0 - 111780. i) q^{15} -11335.0 q^{16} +115964. i q^{17} +94066.2i q^{18} +213578. q^{19} +(422896. + 67637.6i) q^{20} -233168. q^{21} +333855. i q^{22} +1.83629e6i q^{23} -950470. q^{24} +(1.85569e6 + 609179. i) q^{25} -1.61295e6 q^{26} +531441. i q^{27} -882139. i q^{28} -3.67540e6 q^{29} +(-1.60261e6 - 256321. i) q^{30} +8.85139e6 q^{31} -5.84540e6i q^{32} +1.88617e6i q^{33} +1.66259e6 q^{34} +(635358. - 3.97250e6i) q^{35} -2.01059e6 q^{36} -9.17921e6i q^{37} -3.06210e6i q^{38} -9.11258e6 q^{39} +(2.58993e6 - 1.61932e7i) q^{40} -1.17626e7 q^{41} +3.34297e6i q^{42} +3.93230e7i q^{43} -7.13589e6 q^{44} +(-9.05420e6 - 1.44812e6i) q^{45} +2.63272e7 q^{46} +3.26882e7i q^{47} +918134. i q^{48} +3.20672e7 q^{49} +(8.73391e6 - 2.66054e7i) q^{50} +9.39305e6 q^{51} -3.44754e7i q^{52} +1.04826e8i q^{53} +7.61936e6 q^{54} +(-3.21348e7 - 5.13961e6i) q^{55} -3.37782e7 q^{56} -1.72998e7i q^{57} +5.26948e7i q^{58} +1.02836e8 q^{59} +(5.47865e6 - 3.42546e7i) q^{60} -1.65686e8 q^{61} -1.26904e8i q^{62} +1.88866e7i q^{63} -8.96099e7 q^{64} +(2.48308e7 - 1.55252e8i) q^{65} +2.70423e7 q^{66} -1.76387e8i q^{67} +3.55365e7i q^{68} +1.48740e8 q^{69} +(-5.69544e7 - 9.10923e6i) q^{70} +1.30237e8 q^{71} +7.69880e7i q^{72} +2.35713e8i q^{73} -1.31604e8 q^{74} +(4.93435e7 - 1.50311e8i) q^{75} +6.54500e7 q^{76} +6.70314e7i q^{77} +1.30649e8i q^{78} -1.56763e8 q^{79} +(-1.56423e7 - 2.50182e6i) q^{80} +4.30467e7 q^{81} +1.68642e8i q^{82} +3.38241e7i q^{83} -7.14532e7 q^{84} +(-2.55951e7 + 1.60030e8i) q^{85} +5.63780e8 q^{86} +2.97707e8i q^{87} +2.73242e8i q^{88} -4.86766e8 q^{89} +(-2.07620e7 + 1.29812e8i) q^{90} -3.23847e8 q^{91} +5.62724e8i q^{92} -7.16963e8i q^{93} +4.68656e8 q^{94} +(2.94738e8 + 4.71402e7i) q^{95} -4.73477e8 q^{96} -1.40255e9i q^{97} -4.59753e8i q^{98} +1.52779e8 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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