LMFDB - Embedded newform 10.12.b.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,12,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	10.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:	$7.68343180560$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 198x^{3} + 3568321x^{2} - 6762620x + 6408200 $ x^6 - 2x^5 + 2x^4 + 198x^3 + 3568321x^2 - 6762620*x + 6408200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{19}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.4
Root			$30.7598 + 30.7598i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.12.b.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.0000i q^{2} -697.195i q^{3} -1024.00 q^{4} +(-4156.64 + 5616.98i) q^{5} +22310.3 q^{6} +73603.8i q^{7} -32768.0i q^{8} -308934. q^{9} +O(q^{10})$	\(q+32.0000i q^{2} -697.195i q^{3} -1024.00 q^{4} +(-4156.64 + 5616.98i) q^{5} +22310.3 q^{6} +73603.8i q^{7} -32768.0i q^{8} -308934. q^{9} +(-179743. - 133012. i) q^{10} -276114. q^{11} +713928. i q^{12} +726988. i q^{13} -2.35532e6 q^{14} +(3.91613e6 + 2.89799e6i) q^{15} +1.04858e6 q^{16} -3.21222e6i q^{17} -9.88590e6i q^{18} -1.55879e7 q^{19} +(4.25640e6 - 5.75179e6i) q^{20} +5.13162e7 q^{21} -8.83564e6i q^{22} +3.25041e7i q^{23} -2.28457e7 q^{24} +(-1.42729e7 - 4.66955e7i) q^{25} -2.32636e7 q^{26} +9.18815e7i q^{27} -7.53703e7i q^{28} +4.53029e7 q^{29} +(-9.27356e7 + 1.25316e8i) q^{30} -1.06580e8 q^{31} +3.35544e7i q^{32} +1.92505e8i q^{33} +1.02791e8 q^{34} +(-4.13431e8 - 3.05944e8i) q^{35} +3.16349e8 q^{36} -1.65530e8i q^{37} -4.98812e8i q^{38} +5.06853e8 q^{39} +(1.84057e8 + 1.36205e8i) q^{40} +2.36566e8 q^{41} +1.64212e9i q^{42} -7.28874e8i q^{43} +2.82740e8 q^{44} +(1.28413e9 - 1.73528e9i) q^{45} -1.04013e9 q^{46} +1.41793e9i q^{47} -7.31062e8i q^{48} -3.44020e9 q^{49} +(1.49426e9 - 4.56731e8i) q^{50} -2.23954e9 q^{51} -7.44435e8i q^{52} +3.08706e9i q^{53} -2.94021e9 q^{54} +(1.14770e9 - 1.55093e9i) q^{55} +2.41185e9 q^{56} +1.08678e10i q^{57} +1.44969e9i q^{58} +7.61532e9 q^{59} +(-4.01012e9 - 2.96754e9i) q^{60} +1.45582e9 q^{61} -3.41054e9i q^{62} -2.27388e10i q^{63} -1.07374e9 q^{64} +(-4.08348e9 - 3.02182e9i) q^{65} -6.16017e9 q^{66} +1.32563e10i q^{67} +3.28931e9i q^{68} +2.26617e10 q^{69} +(9.79022e9 - 1.32298e10i) q^{70} +9.49012e8 q^{71} +1.01232e10i q^{72} +1.30829e10i q^{73} +5.29697e9 q^{74} +(-3.25559e10 + 9.95097e9i) q^{75} +1.59620e10 q^{76} -2.03230e10i q^{77} +1.62193e10i q^{78} -5.30163e10 q^{79} +(-4.35855e9 + 5.88983e9i) q^{80} +9.33259e9 q^{81} +7.57010e9i q^{82} -2.15490e10i q^{83} -5.25478e10 q^{84} +(1.80430e10 + 1.33520e10i) q^{85} +2.33240e10 q^{86} -3.15849e10i q^{87} +9.04769e9i q^{88} +5.64241e10 q^{89} +(5.55289e10 + 4.10921e10i) q^{90} -5.35091e10 q^{91} -3.32842e10i q^{92} +7.43067e10i q^{93} -4.53739e10 q^{94} +(6.47932e10 - 8.75569e10i) q^{95} +2.33940e10 q^{96} -4.40060e10i q^{97} -1.10086e11i q^{98} +8.53010e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6144 q^{4} + 530 q^{5} + 17024 q^{6} - 496022 q^{9}+O(q^{10}) $ 6 * q - 6144 * q^4 + 530 * q^5 + 17024 * q^6 - 496022 * q^9	\( 6 q - 6144 q^{4} + 530 q^{5} + 17024 q^{6} - 496022 q^{9} - 385920 q^{10} - 642728 q^{11} - 2125952 q^{14} - 698680 q^{15} + 6291456 q^{16} - 24109080 q^{19} - 542720 q^{20} + 125471192 q^{21} - 17432576 q^{24} - 181718850 q^{25} + 89251584 q^{26} - 256409820 q^{29} - 221514880 q^{30} + 458481792 q^{31} - 225288192 q^{34} - 697136360 q^{35} + 507926528 q^{36} + 1318797936 q^{39} + 395182080 q^{40} - 164768948 q^{41} + 658153472 q^{44} + 3174067390 q^{45} - 2956208256 q^{46} - 675514158 q^{49} + 3912262400 q^{50} - 13060087168 q^{51} - 6079189760 q^{54} + 3688644360 q^{55} + 2176974848 q^{56} + 17663962360 q^{59} + 715448320 q^{60} - 5020792428 q^{61} - 6442450944 q^{64} - 19996916880 q^{65} + 14496229888 q^{66} + 23117013976 q^{69} + 24956826240 q^{70} + 56788418832 q^{71} - 64135292672 q^{74} - 95499160400 q^{75} + 24687697920 q^{76} + 2602550880 q^{79} + 555745280 q^{80} - 7039907074 q^{81} - 128482500608 q^{84} - 85024210560 q^{85} + 111995790464 q^{86} + 249448412540 q^{89} + 225507463040 q^{90} - 184446766128 q^{91} - 337749482112 q^{94} + 104896380600 q^{95} + 17850957824 q^{96} + 520781125736 q^{99}+O(q^{100}) \) 6 * q - 6144 * q^4 + 530 * q^5 + 17024 * q^6 - 496022 * q^9 - 385920 * q^10 - 642728 * q^11 - 2125952 * q^14 - 698680 * q^15 + 6291456 * q^16 - 24109080 * q^19 - 542720 * q^20 + 125471192 * q^21 - 17432576 * q^24 - 181718850 * q^25 + 89251584 * q^26 - 256409820 * q^29 - 221514880 * q^30 + 458481792 * q^31 - 225288192 * q^34 - 697136360 * q^35 + 507926528 * q^36 + 1318797936 * q^39 + 395182080 * q^40 - 164768948 * q^41 + 658153472 * q^44 + 3174067390 * q^45 - 2956208256 * q^46 - 675514158 * q^49 + 3912262400 * q^50 - 13060087168 * q^51 - 6079189760 * q^54 + 3688644360 * q^55 + 2176974848 * q^56 + 17663962360 * q^59 + 715448320 * q^60 - 5020792428 * q^61 - 6442450944 * q^64 - 19996916880 * q^65 + 14496229888 * q^66 + 23117013976 * q^69 + 24956826240 * q^70 + 56788418832 * q^71 - 64135292672 * q^74 - 95499160400 * q^75 + 24687697920 * q^76 + 2602550880 * q^79 + 555745280 * q^80 - 7039907074 * q^81 - 128482500608 * q^84 - 85024210560 * q^85 + 111995790464 * q^86 + 249448412540 * q^89 + 225507463040 * q^90 - 184446766128 * q^91 - 337749482112 * q^94 + 104896380600 * q^95 + 17850957824 * q^96 + 520781125736 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

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 $

$2$			32.0000i			0.707107i
$2$			32.0000i			0.707107i
$3$		−	697.195i		−	1.65649i	−0.560370	−	0.828243i	$-0.689341\pi$
$3$		−	697.195i		−	1.65649i	0.560370	−	0.828243i	$-0.310659\pi$
$4$	−1024.00			−0.500000
$5$	−4156.64	+	5616.98i	−0.594850	+	0.803837i
$5$	−4156.64	+	5616.98i	−0.594850	+	0.803837i
$6$	22310.3			1.17131
$7$			73603.8i			1.65524i	0.561288	+	0.827620i	$0.310306\pi$
$7$			73603.8i			1.65524i	−0.561288	+	0.827620i	$0.689694\pi$
$8$		−	32768.0i		−	0.353553i
$9$	−308934.			−1.74394
$10$	−179743.	−	133012.i	−0.568399	−	0.420622i
$11$	−276114.			−0.516926			−0.258463	−	0.966021i	$-0.583216\pi$
$11$	−276114.			−0.516926			−0.258463	+	0.966021i	$0.583216\pi$
$12$			713928.i			0.828243i
$13$			726988.i			0.543049i	0.962432	+	0.271524i	$0.0875277\pi$
$13$			726988.i			0.543049i	−0.962432	+	0.271524i	$0.912472\pi$
$14$	−2.35532e6			−1.17043
$15$	3.91613e6	+	2.89799e6i	1.33154	+	0.985360i
$16$	1.04858e6			0.250000
$17$		−	3.21222e6i		−	0.548701i	−0.961630	−	0.274351i	$-0.911537\pi$
$17$		−	3.21222e6i		−	0.548701i	0.961630	−	0.274351i	$-0.0884629\pi$
$18$		−	9.88590e6i		−	1.23315i
$19$	−1.55879e7			−1.44425			−0.722125	−	0.691762i	$-0.756835\pi$
$19$	−1.55879e7			−1.44425			−0.722125	+	0.691762i	$0.756835\pi$
$20$	4.25640e6	−	5.75179e6i	0.297425	−	0.401919i
$21$	5.13162e7			2.74188
$22$		−	8.83564e6i		−	0.365522i
$23$			3.25041e7i			1.05302i	0.850170	+	0.526508i	$0.176499\pi$
$23$			3.25041e7i			1.05302i	−0.850170	+	0.526508i	$0.823501\pi$
$24$	−2.28457e7			−0.585656
$25$	−1.42729e7	−	4.66955e7i	−0.292308	−	0.956324i
$26$	−2.32636e7			−0.383993
$27$			9.18815e7i			1.23233i
$28$		−	7.53703e7i		−	0.827620i
$29$	4.53029e7			0.410144			0.205072	−	0.978747i	$-0.434257\pi$
$29$	4.53029e7			0.410144			0.205072	+	0.978747i	$0.434257\pi$
$30$	−9.27356e7	+	1.25316e8i	−0.696754	+	0.941544i
$31$	−1.06580e8			−0.668628			−0.334314	−	0.942462i	$-0.608505\pi$
$31$	−1.06580e8			−0.668628			−0.334314	+	0.942462i	$0.608505\pi$
$32$			3.35544e7i			0.176777i
$33$			1.92505e8i			0.856280i
$34$	1.02791e8			0.387990
$35$	−4.13431e8	−	3.05944e8i	−1.33054	−	0.984619i
$36$	3.16349e8			0.871972
$37$		−	1.65530e8i		−	0.392435i	−0.980560	−	0.196218i	$-0.937134\pi$
$37$		−	1.65530e8i		−	0.392435i	0.980560	−	0.196218i	$-0.0628659\pi$
$38$		−	4.98812e8i		−	1.02124i
$39$	5.06853e8			0.899552
$40$	1.84057e8	+	1.36205e8i	0.284199	+	0.210311i
$41$	2.36566e8			0.318890			0.159445	−	0.987207i	$-0.449030\pi$
$41$	2.36566e8			0.318890			0.159445	+	0.987207i	$0.449030\pi$
$42$			1.64212e9i			1.93880i
$43$		−	7.28874e8i		−	0.756095i	−0.925786	−	0.378047i	$-0.876596\pi$
$43$		−	7.28874e8i		−	0.756095i	0.925786	−	0.378047i	$-0.123404\pi$
$44$	2.82740e8			0.258463
$45$	1.28413e9	−	1.73528e9i	1.03738	−	1.40185i
$46$	−1.04013e9			−0.744595
$47$			1.41793e9i			0.901816i	0.892570	+	0.450908i	$0.148900\pi$
$47$			1.41793e9i			0.901816i	−0.892570	+	0.450908i	$0.851100\pi$
$48$		−	7.31062e8i		−	0.414121i
$49$	−3.44020e9			−1.73982
$50$	1.49426e9	−	4.56731e8i	0.676223	−	0.206693i
$51$	−2.23954e9			−0.908915
$52$		−	7.44435e8i		−	0.271524i
$53$			3.08706e9i			1.01397i	0.861953	+	0.506987i	$0.169241\pi$
$53$			3.08706e9i			1.01397i	−0.861953	+	0.506987i	$0.830759\pi$
$54$	−2.94021e9			−0.871390
$55$	1.14770e9	−	1.55093e9i	0.307493	−	0.415524i
$56$	2.41185e9			0.585216
$57$			1.08678e10i			2.39238i
$58$			1.44969e9i			0.290016i
$59$	7.61532e9			1.38676			0.693381	−	0.720571i	$-0.256120\pi$
$59$	7.61532e9			1.38676			0.693381	+	0.720571i	$0.256120\pi$
$60$	−4.01012e9	−	2.96754e9i	−0.665772	−	0.492680i
$61$	1.45582e9			0.220695			0.110347	−	0.993893i	$-0.464804\pi$
$61$	1.45582e9			0.220695			0.110347	+	0.993893i	$0.464804\pi$
$62$		−	3.41054e9i		−	0.472791i
$63$		−	2.27388e10i		−	2.88665i
$64$	−1.07374e9			−0.125000
$65$	−4.08348e9	−	3.02182e9i	−0.436523	−	0.323032i
$66$	−6.16017e9			−0.605481
$67$			1.32563e10i			1.19953i	0.800177	+	0.599764i	$0.204739\pi$
$67$			1.32563e10i			1.19953i	−0.800177	+	0.599764i	$0.795261\pi$
$68$			3.28931e9i			0.274351i
$69$	2.26617e10			1.74431
$70$	9.79022e9	−	1.32298e10i	0.696231	−	0.940837i
$71$	9.49012e8			0.0624239			0.0312119	−	0.999513i	$-0.490063\pi$
$71$	9.49012e8			0.0624239			0.0312119	+	0.999513i	$0.490063\pi$
$72$			1.01232e10i			0.616577i
$73$			1.30829e10i			0.738634i	0.929303	+	0.369317i	$0.120408\pi$
$73$			1.30829e10i			0.738634i	−0.929303	+	0.369317i	$0.879592\pi$
$74$	5.29697e9			0.277494
$75$	−3.25559e10	+	9.95097e9i	−1.58414	+	0.484204i
$76$	1.59620e10			0.722125
$77$		−	2.03230e10i		−	0.855637i
$78$			1.62193e10i			0.636079i
$79$	−5.30163e10			−1.93848			−0.969238	−	0.246124i	$-0.920843\pi$
$79$	−5.30163e10			−1.93848			−0.969238	+	0.246124i	$0.920843\pi$
$80$	−4.35855e9	+	5.88983e9i	−0.148712	+	0.200959i
$81$	9.33259e9			0.297396
$82$			7.57010e9i			0.225489i
$83$		−	2.15490e10i		−	0.600479i	−0.953864	−	0.300239i	$-0.902933\pi$
$83$		−	2.15490e10i		−	0.600479i	0.953864	−	0.300239i	$-0.0970666\pi$
$84$	−5.25478e10			−1.37094
$85$	1.80430e10	+	1.33520e10i	0.441066	+	0.326395i
$86$	2.33240e10			0.534640
$87$		−	3.15849e10i		−	0.679398i
$88$			9.04769e9i			0.182761i
$89$	5.64241e10			1.07107			0.535537	−	0.844511i	$-0.320109\pi$
$89$	5.64241e10			1.07107			0.535537	+	0.844511i	$0.320109\pi$
$90$	5.55289e10	+	4.10921e10i	0.991255	+	0.733541i
$91$	−5.35091e10			−0.898876
$92$		−	3.32842e10i		−	0.526508i
$93$			7.43067e10i			1.10757i
$94$	−4.53739e10			−0.637680
$95$	6.47932e10	−	8.75569e10i	0.859112	−	1.16094i
$96$	2.33940e10			0.292828
$97$		−	4.40060e10i		−	0.520316i	−0.965566	−	0.260158i	$-0.916225\pi$
$97$		−	4.40060e10i		−	0.520316i	0.965566	−	0.260158i	$-0.0837746\pi$
$98$		−	1.10086e11i		−	1.23024i
$99$	8.53010e10			0.901489
$100$	1.46154e10	+	4.78162e10i	0.146154	+	0.478162i
$101$	−9.78679e8			−0.00926558			−0.00463279	−	0.999989i	$-0.501475\pi$
$101$	−9.78679e8			−0.00926558			−0.00463279	+	0.999989i	$0.501475\pi$
$102$		−	7.16654e10i		−	0.642700i
$103$			9.00212e10i			0.765139i	0.923927	+	0.382569i	$0.124961\pi$
$103$			9.00212e10i			0.765139i	−0.923927	+	0.382569i	$0.875039\pi$
$104$	2.38219e10			0.191997
$105$	−2.13303e11	+	2.88242e11i	−1.63101	+	2.20403i
$106$	−9.87858e10			−0.716988
$107$		−	1.75119e11i		−	1.20705i	−0.797346	−	0.603523i	$-0.793763\pi$
$107$		−	1.75119e11i		−	1.20705i	0.797346	−	0.603523i	$-0.206237\pi$
$108$		−	9.40867e10i		−	0.616166i
$109$	2.69261e11			1.67620			0.838102	−	0.545513i	$-0.183665\pi$
$109$	2.69261e11			1.67620			0.838102	+	0.545513i	$0.183665\pi$
$110$	4.96296e10	+	3.67265e10i	0.293820	+	0.217430i
$111$	−1.15407e11			−0.650064
$112$			7.71792e10i			0.413810i
$113$			2.51799e11i			1.28565i	0.766013	+	0.642825i	$0.222238\pi$
$113$			2.51799e11i			1.28565i	−0.766013	+	0.642825i	$0.777762\pi$
$114$	−3.47770e11			−1.69167
$115$	−1.82575e11	−	1.35108e11i	−0.846454	−	0.626386i
$116$	−4.63901e10			−0.205072
$117$		−	2.24592e11i		−	0.947046i
$118$			2.43690e11i			0.980589i
$119$	2.36431e11			0.908232
$120$	9.49613e10	−	1.28324e11i	0.348377	−	0.470772i
$121$	−2.09073e11			−0.732788
$122$			4.65861e10i			0.156055i
$123$		−	1.64932e11i		−	0.528236i
$124$	1.09137e11			0.334314
$125$	3.21615e11	+	1.13926e11i	0.942608	+	0.333901i
$126$	7.27640e11			2.04117
$127$			5.68757e11i			1.52759i	0.645459	+	0.763795i	$0.276666\pi$
$127$			5.68757e11i			1.52759i	−0.645459	+	0.763795i	$0.723334\pi$
$128$		−	3.43597e10i		−	0.0883883i
$129$	−5.08168e11			−1.25246
$130$	9.66984e10	−	1.30671e11i	0.228418	−	0.308668i
$131$	3.29083e11			0.745270			0.372635	−	0.927978i	$-0.378454\pi$
$131$	3.29083e11			0.745270			0.372635	+	0.927978i	$0.378454\pi$
$132$		−	1.97125e11i		−	0.428140i
$133$		−	1.14733e12i		−	2.39058i
$134$	−4.24201e11			−0.848194
$135$	−5.16097e11	−	3.81918e11i	−0.990594	−	0.733052i
$136$	−1.05258e11			−0.193995
$137$		−	3.26164e11i		−	0.577394i	−0.957420	−	0.288697i	$-0.906778\pi$
$137$		−	3.26164e11i		−	0.577394i	0.957420	−	0.288697i	$-0.0932221\pi$
$138$			7.25175e11i			1.23341i
$139$	−2.17139e10			−0.0354942			−0.0177471	−	0.999843i	$-0.505649\pi$
$139$	−2.17139e10			−0.0354942			−0.0177471	+	0.999843i	$0.505649\pi$
$140$	4.23354e11	+	3.13287e11i	0.665272	+	0.492310i
$141$	9.88577e11			1.49384
$142$			3.03684e10i			0.0441403i
$143$		−	2.00731e11i		−	0.280716i
$144$	−3.23941e11			−0.435986
$145$	−1.88308e11	+	2.54465e11i	−0.243974	+	0.329689i
$146$	−4.18654e11			−0.522293
$147$			2.39849e12i			2.88199i
$148$			1.69503e11i			0.196218i
$149$	9.81939e10			0.109537			0.0547684	−	0.998499i	$-0.482558\pi$
$149$	9.81939e10			0.109537			0.0547684	+	0.998499i	$0.482558\pi$
$150$	−3.18431e11	−	1.04179e12i	−0.342384	−	1.12015i
$151$	−1.60820e12			−1.66712			−0.833558	−	0.552432i	$-0.813700\pi$
$151$	−1.60820e12			−1.66712			−0.833558	+	0.552432i	$0.813700\pi$
$152$			5.10784e11i			0.510620i
$153$			9.92364e11i			0.956904i
$154$	6.50337e11			0.605026
$155$	4.43012e11	−	5.98655e11i	0.397733	−	0.537468i
$156$	−5.19017e11			−0.449776
$157$		−	9.79921e11i		−	0.819867i	−0.912116	−	0.409933i	$-0.865552\pi$
$157$		−	9.79921e11i		−	0.819867i	0.912116	−	0.409933i	$-0.134448\pi$
$158$		−	1.69652e12i		−	1.37071i
$159$	2.15228e12			1.67963
$160$	−1.88475e11	−	1.39474e11i	−0.142100	−	0.105156i
$161$	−2.39243e12			−1.74300
$162$			2.98643e11i			0.210290i
$163$		−	8.12475e11i		−	0.553068i	−0.961004	−	0.276534i	$-0.910814\pi$
$163$		−	8.12475e11i		−	0.553068i	0.961004	−	0.276534i	$-0.0891858\pi$
$164$	−2.42243e11			−0.159445
$165$	−1.08130e12	−	8.00174e11i	−0.688310	−	0.509358i
$166$	6.89568e11			0.424603
$167$			2.27106e12i			1.35297i	0.736458	+	0.676484i	$0.236497\pi$
$167$			2.27106e12i			1.35297i	−0.736458	+	0.676484i	$0.763503\pi$
$168$		−	1.68153e12i		−	0.969402i
$169$	1.26365e12			0.705098
$170$	−4.27265e11	+	5.77375e11i	−0.230796	+	0.311881i
$171$	4.81563e12			2.51869
$172$			7.46367e11i			0.378047i
$173$			3.16932e12i			1.55494i	0.628921	+	0.777469i	$0.283497\pi$
$173$			3.16932e12i			1.55494i	−0.628921	+	0.777469i	$0.716503\pi$
$174$	1.01072e12			0.480407
$175$	3.43697e12	−	1.05054e12i	1.58295	−	0.483840i
$176$	−2.89526e11			−0.129231
$177$		−	5.30936e12i		−	2.29715i
$178$			1.80557e12i			0.757364i
$179$	−4.56681e12			−1.85747			−0.928734	−	0.370747i	$-0.879102\pi$
$179$	−4.56681e12			−1.85747			−0.928734	+	0.370747i	$0.879102\pi$
$180$	−1.31495e12	+	1.77693e12i	−0.518692	+	0.700923i
$181$	−1.55390e12			−0.594553			−0.297276	−	0.954791i	$-0.596078\pi$
$181$	−1.55390e12			−0.594553			−0.297276	+	0.954791i	$0.596078\pi$
$182$		−	1.71229e12i		−	0.635601i
$183$		−	1.01499e12i		−	0.365578i
$184$	1.06509e12			0.372297
$185$	9.29781e11	+	6.88050e11i	0.315454	+	0.233440i
$186$	−2.37782e12			−0.783172
$187$			8.86937e11i			0.283638i
$188$		−	1.45196e12i		−	0.450908i
$189$	−6.76283e12			−2.03981
$190$	2.80182e12	+	2.07338e12i	0.820910	+	0.607484i
$191$	−2.09841e12			−0.597319			−0.298659	−	0.954360i	$-0.596539\pi$
$191$	−2.09841e12			−0.597319			−0.298659	+	0.954360i	$0.596539\pi$
$192$			7.48608e11i			0.207061i
$193$		−	1.49038e12i		−	0.400620i	−0.979733	−	0.200310i	$-0.935805\pi$
$193$		−	1.49038e12i		−	0.400620i	0.979733	−	0.200310i	$-0.0641950\pi$
$194$	1.40819e12			0.367919
$195$	−2.10680e12	+	2.84698e12i	−0.535098	+	0.723093i
$196$	3.52276e12			0.869911
$197$			1.54638e12i			0.371322i	0.982614	+	0.185661i	$0.0594426\pi$
$197$			1.54638e12i			0.371322i	−0.982614	+	0.185661i	$0.940557\pi$
$198$			2.72963e12i			0.637449i
$199$	−3.26839e12			−0.742407			−0.371204	−	0.928552i	$-0.621055\pi$
$199$	−3.26839e12			−0.742407			−0.371204	+	0.928552i	$0.621055\pi$
$200$	−1.53012e12	+	4.67693e11i	−0.338112	+	0.103347i
$201$	9.24222e12			1.98700
$202$		−	3.13177e10i		−	0.00655176i
$203$			3.33446e12i			0.678888i
$204$	2.29329e12			0.454458
$205$	−9.83317e11	+	1.32878e12i	−0.189691	+	0.256335i
$206$	−2.88068e12			−0.541035
$207$		−	1.00416e13i		−	1.83640i
$208$			7.62302e11i			0.135762i
$209$	4.30403e12			0.746570
$210$	−9.22376e12	−	6.82570e12i	−1.55848	−	1.15330i
$211$	−2.09010e12			−0.344043			−0.172021	−	0.985093i	$-0.555030\pi$
$211$	−2.09010e12			−0.344043			−0.172021	+	0.985093i	$0.555030\pi$
$212$		−	3.16114e12i		−	0.506987i
$213$		−	6.61647e11i		−	0.103404i
$214$	5.60382e12			0.853510
$215$	4.09407e12	+	3.02967e12i	0.607777	+	0.449763i
$216$	3.01077e12			0.435695
$217$		−	7.84466e12i		−	1.10674i
$218$			8.61634e12i			1.18526i
$219$	9.12136e12			1.22354
$220$	−1.17525e12	+	1.58815e12i	−0.153747	+	0.207762i
$221$	2.33524e12			0.297971
$222$		−	3.69302e12i		−	0.459664i
$223$		−	1.89689e12i		−	0.230338i	−0.993346	−	0.115169i	$-0.963259\pi$
$223$		−	1.89689e12i		−	0.230338i	0.993346	−	0.115169i	$-0.0367409\pi$
$224$	−2.46973e12			−0.292608
$225$	4.40938e12	+	1.44259e13i	0.509769	+	1.66778i
$226$	−8.05757e12			−0.909092
$227$			2.22297e12i			0.244788i	0.992482	+	0.122394i	$0.0390572\pi$
$227$			2.22297e12i			0.244788i	−0.992482	+	0.122394i	$0.960943\pi$
$228$		−	1.11286e13i		−	1.19619i
$229$	−1.10056e12			−0.115483			−0.0577415	−	0.998332i	$-0.518390\pi$
$229$	−1.10056e12			−0.115483			−0.0577415	+	0.998332i	$0.518390\pi$
$230$	4.32345e12	−	5.84240e12i	0.442922	−	0.598533i
$231$	−1.41691e13			−1.41735
$232$		−	1.48448e12i		−	0.145008i
$233$		−	7.26117e12i		−	0.692706i	−0.938104	−	0.346353i	$-0.887420\pi$
$233$		−	7.26117e12i		−	0.692706i	0.938104	−	0.346353i	$-0.112580\pi$
$234$	7.18693e12			0.669663
$235$	−7.96451e12	−	5.89384e12i	−0.724913	−	0.536445i
$236$	−7.79808e12			−0.693381
$237$			3.69627e13i			3.21106i
$238$			7.56581e12i			0.642217i
$239$	−1.69859e13			−1.40896			−0.704482	−	0.709722i	$-0.748821\pi$
$239$	−1.69859e13			−1.40896			−0.704482	+	0.709722i	$0.748821\pi$
$240$	4.10636e12	+	3.03876e12i	0.332886	+	0.246340i
$241$	3.71937e12			0.294697			0.147349	−	0.989085i	$-0.452926\pi$
$241$	3.71937e12			0.294697			0.147349	+	0.989085i	$0.452926\pi$
$242$		−	6.69033e12i		−	0.518159i
$243$			9.76990e12i			0.739700i
$244$	−1.49076e12			−0.110347
$245$	1.42996e13	−	1.93235e13i	1.03493	−	1.39853i
$246$	5.27784e12			0.373519
$247$		−	1.13322e13i		−	0.784298i
$248$			3.49240e12i			0.236396i
$249$	−1.50239e13			−0.994685
$250$	−3.64563e12	+	1.02917e13i	−0.236104	+	0.666525i
$251$	1.95302e13			1.23737			0.618687	−	0.785637i	$-0.287665\pi$
$251$	1.95302e13			1.23737			0.618687	+	0.785637i	$0.287665\pi$
$252$			2.32845e13i			1.44332i
$253$		−	8.97483e12i		−	0.544331i
$254$	−1.82002e13			−1.08017
$255$	9.30897e12	−	1.25795e13i	0.540668	−	0.730620i
$256$	1.09951e12			0.0625000
$257$			9.96454e12i			0.554402i	0.960812	+	0.277201i	$0.0894068\pi$
$257$			9.96454e12i			0.554402i	−0.960812	+	0.277201i	$0.910593\pi$
$258$		−	1.62614e13i		−	0.885623i
$259$	1.21837e13			0.649575
$260$	4.18148e12	+	3.09435e12i	0.218261	+	0.161516i
$261$	−1.39956e13			−0.715269
$262$			1.05307e13i			0.526985i
$263$		−	1.85332e13i		−	0.908225i	−0.890944	−	0.454112i	$-0.849956\pi$
$263$		−	1.85332e13i		−	0.908225i	0.890944	−	0.454112i	$-0.150044\pi$
$264$	6.30801e12			0.302741
$265$	−1.73399e13	−	1.28318e13i	−0.815070	−	0.603162i
$266$	3.67145e13			1.69040
$267$		−	3.93386e13i		−	1.77422i
$268$		−	1.35744e13i		−	0.599764i
$269$	1.34102e13			0.580493			0.290247	−	0.956952i	$-0.406263\pi$
$269$	1.34102e13			0.580493			0.290247	+	0.956952i	$0.406263\pi$
$270$	1.22214e13	−	1.65151e13i	0.518346	−	0.700456i
$271$	−2.99278e13			−1.24378			−0.621890	−	0.783105i	$-0.713635\pi$
$271$	−2.99278e13			−1.24378			−0.621890	+	0.783105i	$0.713635\pi$
$272$		−	3.36825e12i		−	0.137175i
$273$			3.73063e13i			1.48897i
$274$	1.04372e13			0.408279
$275$	3.94093e12	+	1.28933e13i	0.151102	+	0.494349i
$276$	−2.32056e13			−0.872153
$277$			4.40434e13i			1.62271i	0.584551	+	0.811357i	$0.301271\pi$
$277$			4.40434e13i			1.62271i	−0.584551	+	0.811357i	$0.698729\pi$
$278$		−	6.94846e11i		−	0.0250982i
$279$	3.29261e13			1.16605
$280$	−1.00252e13	+	1.35473e13i	−0.348115	+	0.470418i
$281$	3.84310e13			1.30857			0.654286	−	0.756247i	$-0.272969\pi$
$281$	3.84310e13			1.30857			0.654286	+	0.756247i	$0.272969\pi$
$282$			3.16345e13i			1.05631i
$283$			1.73740e13i			0.568951i	0.958683	+	0.284475i	$0.0918194\pi$
$283$			1.73740e13i			0.568951i	−0.958683	+	0.284475i	$0.908181\pi$
$284$	−9.71788e11			−0.0312119
$285$	−6.10443e13	−	4.51735e13i	−1.92308	−	1.42311i
$286$	6.42340e12			0.198496
$287$			1.74121e13i			0.527839i
$288$		−	1.03661e13i		−	0.308289i
$289$	2.39536e13			0.698927
$290$	−8.14289e12	−	6.02584e12i	−0.233125	−	0.172516i
$291$	−3.06808e13			−0.861896
$292$		−	1.33969e13i		−	0.369317i
$293$		−	2.71688e13i		−	0.735019i	−0.930020	−	0.367510i	$-0.880210\pi$
$293$		−	2.71688e13i		−	0.735019i	0.930020	−	0.367510i	$-0.119790\pi$
$294$	−7.67516e13			−2.03787
$295$	−3.16541e13	+	4.27751e13i	−0.824915	+	1.11473i
$296$	−5.42410e12			−0.138747
$297$		−	2.53698e13i		−	0.637024i
$298$			3.14220e12i			0.0774542i
$299$	−2.36301e13			−0.571839
$300$	3.33372e13	−	1.01898e13i	0.792069	−	0.242102i
$301$	5.36479e13			1.25152
$302$		−	5.14623e13i		−	1.17883i
$303$			6.82331e11i			0.0153483i
$304$	−1.63451e13			−0.361063
$305$	−6.05130e12	+	8.17729e12i	−0.131280	+	0.177403i
$306$	−3.17557e13			−0.676633
$307$			7.68468e13i			1.60829i	0.594432	+	0.804146i	$0.297377\pi$
$307$			7.68468e13i			1.60829i	−0.594432	+	0.804146i	$0.702623\pi$
$308$			2.08108e13i			0.427818i
$309$	6.27624e13			1.26744
$310$	1.91570e13	+	1.41764e13i	0.380047	+	0.281240i
$311$	−4.58065e12			−0.0892781			−0.0446390	−	0.999003i	$-0.514214\pi$
$311$	−4.58065e12			−0.0892781			−0.0446390	+	0.999003i	$0.514214\pi$
$312$		−	1.66085e13i		−	0.318040i
$313$		−	6.56768e13i		−	1.23571i	−0.786290	−	0.617857i	$-0.788001\pi$
$313$		−	6.56768e13i		−	1.23571i	0.786290	−	0.617857i	$-0.211999\pi$
$314$	3.13575e13			0.579733
$315$	1.27723e14	+	9.45167e13i	2.32039	+	1.71712i
$316$	5.42887e13			0.969238
$317$		−	6.53941e13i		−	1.14739i	−0.819067	−	0.573697i	$-0.805509\pi$
$317$		−	6.53941e13i		−	1.14739i	0.819067	−	0.573697i	$-0.194491\pi$
$318$			6.88730e13i			1.18768i
$319$	−1.25087e13			−0.212014
$320$	4.46316e12	−	6.03119e12i	0.0743562	−	0.100480i
$321$	−1.22092e14			−1.99945
$322$		−	7.65576e13i		−	1.23248i
$323$			5.00717e13i			0.792462i
$324$	−9.55657e12			−0.148698
$325$	3.39471e13	−	1.03762e13i	0.519330	−	0.158737i
$326$	2.59992e13			0.391078
$327$		−	1.87727e14i		−	2.77661i
$328$		−	7.75178e12i		−	0.112744i
$329$	−1.04365e14			−1.49272
$330$	2.56056e13	−	3.46015e13i	0.360170	−	0.486708i
$331$	1.82867e13			0.252977			0.126488	−	0.991968i	$-0.459629\pi$
$331$	1.82867e13			0.252977			0.126488	+	0.991968i	$0.459629\pi$
$332$			2.20662e13i			0.300239i
$333$			5.11380e13i			0.684385i
$334$	−7.26738e13			−0.956693
$335$	−7.44603e13	−	5.51015e13i	−0.964225	−	0.713538i
$336$	5.38090e13			0.685470
$337$			6.32083e12i			0.0792155i	0.999215	+	0.0396077i	$0.0126108\pi$
$337$			6.32083e12i			0.0792155i	−0.999215	+	0.0396077i	$0.987389\pi$
$338$			4.04368e13i			0.498580i
$339$	1.75553e14			2.12966
$340$	−1.84760e13	−	1.36725e13i	−0.220533	−	0.163197i
$341$	2.94281e13			0.345631
$342$			1.54100e14i			1.78098i
$343$		−	1.07673e14i		−	1.22458i
$344$	−2.38838e13			−0.267320
$345$	−9.41965e13	+	1.27290e14i	−1.03760	+	1.40214i
$346$	−1.01418e14			−1.09951
$347$			9.38390e13i			1.00132i	0.865645	+	0.500658i	$0.166909\pi$
$347$			9.38390e13i			1.00132i	−0.865645	+	0.500658i	$0.833091\pi$
$348$			3.23430e13i			0.339699i
$349$	−1.24898e14			−1.29127			−0.645634	−	0.763647i	$-0.723407\pi$
$349$	−1.24898e14			−1.29127			−0.645634	+	0.763647i	$0.723407\pi$
$350$	3.36172e13	+	1.09983e14i	0.342127	+	1.11931i
$351$	−6.67968e13			−0.669216
$352$		−	9.26484e12i		−	0.0913804i
$353$			4.95093e13i			0.480757i	0.970679	+	0.240378i	$0.0772715\pi$
$353$			4.95093e13i			0.480757i	−0.970679	+	0.240378i	$0.922728\pi$
$354$	1.69900e14			1.62433
$355$	−3.94470e12	+	5.33058e12i	−0.0371328	+	0.0501786i
$356$	−5.77783e13			−0.535537
$357$		−	1.64839e14i		−	1.50447i
$358$		−	1.46138e14i		−	1.31343i
$359$	8.82048e13			0.780680			0.390340	−	0.920671i	$-0.372358\pi$
$359$	8.82048e13			0.780680			0.390340	+	0.920671i	$0.372358\pi$
$360$	−5.68616e13	−	4.20783e13i	−0.495628	−	0.366771i
$361$	1.26492e14			1.08586
$362$		−	4.97248e13i		−	0.420412i
$363$			1.45765e14i			1.21385i
$364$	5.47933e13			0.449438
$365$	−7.34866e13	−	5.43810e13i	−0.593742	−	0.439376i
$366$	3.24796e13			0.258503
$367$			9.89014e13i			0.775423i	0.921781	+	0.387712i	$0.126734\pi$
$367$			9.89014e13i			0.775423i	−0.921781	+	0.387712i	$0.873266\pi$
$368$			3.40830e13i			0.263254i
$369$	−7.30832e13			−0.556125
$370$	−2.20176e13	+	2.97530e13i	−0.165067	+	0.223060i
$371$	−2.27219e14			−1.67837
$372$		−	7.60901e13i		−	0.553786i
$373$		−	3.15437e13i		−	0.226211i	−0.993583	−	0.113105i	$-0.963920\pi$
$373$		−	3.15437e13i		−	0.226211i	0.993583	−	0.113105i	$-0.0360798\pi$
$374$	−2.83820e13			−0.200562
$375$	7.94287e13	−	2.24228e14i	0.553102	−	1.56142i
$376$	4.64629e13			0.318840
$377$			3.29346e13i			0.222728i
$378$		−	2.16411e14i		−	1.44236i
$379$	1.45966e14			0.958815			0.479408	−	0.877592i	$-0.340852\pi$
$379$	1.45966e14			0.958815			0.479408	+	0.877592i	$0.340852\pi$
$380$	−6.63482e13	+	8.96583e13i	−0.429556	+	0.580471i
$381$	3.96535e14			2.53043
$382$		−	6.71490e13i		−	0.422368i
$383$			9.39255e13i			0.582358i	0.956669	+	0.291179i	$0.0940476\pi$
$383$			9.39255e13i			0.582358i	−0.956669	+	0.291179i	$0.905952\pi$
$384$	−2.39555e13			−0.146414
$385$	1.14154e14	+	8.44754e13i	0.687792	+	0.508975i
$386$	4.76923e13			0.283281
$387$			2.25174e14i			1.31859i
$388$			4.50621e13i			0.260158i
$389$	−2.77248e13			−0.157814			−0.0789071	−	0.996882i	$-0.525143\pi$
$389$	−2.77248e13			−0.157814			−0.0789071	+	0.996882i	$0.525143\pi$
$390$	−9.11034e13	−	6.74177e13i	−0.511304	−	0.378371i
$391$	1.04410e14			0.577791
$392$			1.12728e14i			0.615120i
$393$		−	2.29435e14i		−	1.23453i
$394$	−4.94840e13			−0.262564
$395$	2.20370e14	−	2.97792e14i	1.15310	−	1.55822i
$396$	−8.73482e13			−0.450745
$397$			1.80795e14i			0.920106i	0.887892	+	0.460053i	$0.152170\pi$
$397$			1.80795e14i			0.920106i	−0.887892	+	0.460053i	$0.847830\pi$
$398$		−	1.04589e14i		−	0.524961i
$399$	−7.99912e14			−3.95996
$400$	−1.49662e13	−	4.89638e13i	−0.0730770	−	0.239081i
$401$	1.34767e14			0.649065			0.324533	−	0.945874i	$-0.394793\pi$
$401$	1.34767e14			0.649065			0.324533	+	0.945874i	$0.394793\pi$
$402$			2.95751e14i			1.40502i
$403$		−	7.74820e13i		−	0.363097i
$404$	1.00217e12			0.00463279
$405$	−3.87922e13	+	5.24210e13i	−0.176906	+	0.239058i
$406$	−1.06703e14			−0.480046
$407$			4.57052e13i			0.202860i
$408$			7.33854e13i			0.321350i
$409$	1.61853e14			0.699264			0.349632	−	0.936887i	$-0.386307\pi$
$409$	1.61853e14			0.699264			0.349632	+	0.936887i	$0.386307\pi$
$410$	−4.25211e13	−	3.14662e13i	−0.181256	−	0.134132i
$411$	−2.27400e14			−0.956445
$412$		−	9.21817e13i		−	0.382569i
$413$			5.60516e14i			2.29542i
$414$	3.21332e14			1.29853
$415$	1.21040e14	+	8.95714e13i	0.482687	+	0.357195i
$416$	−2.43937e13			−0.0959983
$417$			1.51389e13i			0.0587956i
$418$			1.37729e14i			0.527905i
$419$	4.46107e13			0.168757			0.0843785	−	0.996434i	$-0.473110\pi$
$419$	4.46107e13			0.168757			0.0843785	+	0.996434i	$0.473110\pi$
$420$	2.18422e14	−	2.95160e14i	0.815504	−	1.10201i
$421$	−3.96897e14			−1.46260			−0.731301	−	0.682055i	$-0.761086\pi$
$421$	−3.96897e14			−1.46260			−0.731301	+	0.682055i	$0.761086\pi$
$422$		−	6.68831e13i		−	0.243275i
$423$		−	4.38049e14i		−	1.57272i
$424$	1.01157e14			0.358494
$425$	−1.49996e14	+	4.58475e13i	−0.524736	+	0.160390i
$426$	2.11727e13			0.0731178
$427$			1.07154e14i			0.365303i
$428$			1.79322e14i			0.603523i
$429$	−1.39949e14			−0.465002
$430$	−9.69493e13	+	1.31010e14i	−0.318030	+	0.429763i
$431$	−4.73312e14			−1.53293			−0.766465	−	0.642286i	$-0.777986\pi$
$431$	−4.73312e14			−1.53293			−0.766465	+	0.642286i	$0.777986\pi$
$432$			9.63448e13i			0.308083i
$433$		−	6.09516e14i		−	1.92443i	−0.272297	−	0.962213i	$-0.587783\pi$
$433$		−	6.09516e14i		−	1.92443i	0.272297	−	0.962213i	$-0.412217\pi$
$434$	2.51029e14			0.782583
$435$	1.77412e14	+	1.31287e14i	0.546125	+	0.404140i
$436$	−2.75723e14			−0.838102
$437$		−	5.06670e14i		−	1.52082i
$438$			2.91884e14i			0.865171i
$439$	3.89020e14			1.13872			0.569360	−	0.822088i	$-0.307191\pi$
$439$	3.89020e14			1.13872			0.569360	+	0.822088i	$0.307191\pi$
$440$	−5.08207e13	−	3.76080e13i	−0.146910	−	0.108715i
$441$	1.06279e15			3.03415
$442$			7.47278e13i			0.210698i
$443$		−	6.78395e14i		−	1.88913i	−0.328322	−	0.944566i	$-0.606483\pi$
$443$		−	6.78395e14i		−	1.88913i	0.328322	−	0.944566i	$-0.393517\pi$
$444$	1.18177e14			0.325032
$445$	−2.34535e14	+	3.16933e14i	−0.637128	+	0.860970i
$446$	6.07005e13			0.162873
$447$		−	6.84603e13i		−	0.181446i
$448$		−	7.90315e13i		−	0.206905i
$449$	2.75571e14			0.712653			0.356327	−	0.934361i	$-0.384029\pi$
$449$	2.75571e14			0.712653			0.356327	+	0.934361i	$0.384029\pi$
$450$	−4.61627e14	+	1.41100e14i	−1.17930	+	0.360461i
$451$	−6.53190e13			−0.164842
$452$		−	2.57842e14i		−	0.642825i
$453$			1.12123e15i			2.76155i
$454$	−7.11349e13			−0.173091
$455$	2.22418e14	−	3.00560e14i	0.534696	−	0.722550i
$456$	3.56116e14			0.845834
$457$			5.15690e14i			1.21018i	0.796158	+	0.605089i	$0.206863\pi$
$457$			5.15690e14i			1.21018i	−0.796158	+	0.605089i	$0.793137\pi$
$458$		−	3.52179e13i		−	0.0816588i
$459$	2.95144e14			0.676182
$460$	1.86957e14	+	1.38350e14i	0.423227	+	0.313193i
$461$	−1.71680e14			−0.384030			−0.192015	−	0.981392i	$-0.561502\pi$
$461$	−1.71680e14			−0.384030			−0.192015	+	0.981392i	$0.561502\pi$
$462$		−	4.53412e14i		−	1.00222i
$463$		−	2.98973e14i		−	0.653034i	−0.945191	−	0.326517i	$-0.894125\pi$
$463$		−	2.98973e14i		−	0.653034i	0.945191	−	0.326517i	$-0.105875\pi$
$464$	4.75035e13			0.102536
$465$	−4.17380e14	−	3.08866e14i	−0.890307	−	0.658839i
$466$	2.32357e14			0.489817
$467$			9.49939e13i			0.197903i	0.995092	+	0.0989516i	$0.0315489\pi$
$467$			9.49939e13i			0.197903i	−0.995092	+	0.0989516i	$0.968451\pi$
$468$			2.29982e14i			0.473523i
$469$	−9.75713e14			−1.98551
$470$	1.88603e14	−	2.54864e14i	0.379324	−	0.512591i
$471$	−6.83197e14			−1.35810
$472$		−	2.49539e14i		−	0.490294i
$473$			2.01252e14i			0.390845i
$474$	−1.18281e15			−2.27056
$475$	2.22484e14	+	7.27885e14i	0.422166	+	1.38117i
$476$	−2.42106e14			−0.454116
$477$		−	9.53697e14i		−	1.76831i
$478$		−	5.43549e14i		−	0.996288i
$479$	3.78434e14			0.685717			0.342859	−	0.939387i	$-0.388605\pi$
$479$	3.78434e14			0.685717			0.342859	+	0.939387i	$0.388605\pi$
$480$	−9.72404e13	+	1.31404e14i	−0.174189	+	0.235386i
$481$	1.20339e14			0.213112
$482$			1.19020e14i			0.208382i
$483$			1.66799e15i			2.88725i
$484$	2.14091e14			0.366394
$485$	2.47181e14	+	1.82917e14i	0.418249	+	0.309510i
$486$	−3.12637e14			−0.523047
$487$		−	6.10112e14i		−	1.00925i	−0.863337	−	0.504627i	$-0.831630\pi$
$487$		−	6.10112e14i		−	1.00925i	0.863337	−	0.504627i	$-0.168370\pi$
$488$		−	4.77042e13i		−	0.0780274i
$489$	−5.66454e14			−0.916149
$490$	6.18353e14	+	4.57589e14i	0.988912	+	0.731808i
$491$	1.13713e15			1.79830			0.899152	−	0.437637i	$-0.144185\pi$
$491$	1.13713e15			1.79830			0.899152	+	0.437637i	$0.144185\pi$
$492$			1.68891e14i			0.264118i
$493$		−	1.45523e14i		−	0.225047i
$494$	3.62631e14			0.554583
$495$	−3.54565e14	+	4.79134e14i	−0.536251	+	0.724651i
$496$	−1.11757e14			−0.167157
$497$			6.98509e13i			0.103327i
$498$		−	4.80764e14i		−	0.703348i
$499$	−8.96225e14			−1.29677			−0.648387	−	0.761311i	$-0.724556\pi$
$499$	−8.96225e14			−1.29677			−0.648387	+	0.761311i	$0.724556\pi$
$500$	−3.29334e14	−	1.16660e14i	−0.471304	−	0.166950i
$501$	1.58337e15			2.24117
$502$			6.24966e14i			0.874956i
$503$			4.50342e14i			0.623618i	0.950145	+	0.311809i	$0.100935\pi$
$503$			4.50342e14i			0.623618i	−0.950145	+	0.311809i	$0.899065\pi$
$504$	−7.45103e14			−1.02058
$505$	4.06801e12	−	5.49722e12i	0.00551163	−	0.00744802i
$506$	2.87194e14			0.384900
$507$		−	8.81010e14i		−	1.16798i
$508$		−	5.82408e14i		−	0.763795i
$509$	1.35840e15			1.76230			0.881151	−	0.472834i	$-0.156769\pi$
$509$	1.35840e15			1.76230			0.881151	+	0.472834i	$0.156769\pi$
$510$	4.02543e14	+	2.97887e14i	0.516626	+	0.382310i
$511$	−9.62954e14			−1.22262
$512$			3.51844e13i			0.0441942i
$513$		−	1.43224e15i		−	1.77980i
$514$	−3.18865e14			−0.392022
$515$	−5.05648e14	−	3.74186e14i	−0.615047	−	0.455142i
$516$	5.20364e14			0.626230
$517$		−	3.91511e14i		−	0.466172i
$518$			3.89877e14i			0.459319i
$519$	2.20964e15			2.57573
$520$	−9.90192e13	+	1.33807e14i	−0.114209	+	0.154334i
$521$	−1.60516e15			−1.83194			−0.915970	−	0.401247i	$-0.868577\pi$
$521$	−1.60516e15			−1.83194			−0.915970	+	0.401247i	$0.868577\pi$
$522$		−	4.47860e14i		−	0.505771i
$523$		−	9.61728e13i		−	0.107471i	−0.998555	−	0.0537357i	$-0.982887\pi$
$523$		−	9.61728e13i		−	0.107471i	0.998555	−	0.0537357i	$-0.0171129\pi$
$524$	−3.36981e14			−0.372635
$525$	−7.32429e14	−	2.39624e15i	−0.801474	−	2.62213i
$526$	5.93062e14			0.642212
$527$			3.42357e14i			0.366877i
$528$			2.01856e14i			0.214070i
$529$	−1.03707e14			−0.108843
$530$	4.10617e14	−	5.54878e14i	0.426500	−	0.576342i
$531$	−2.35263e15			−2.41843
$532$			1.17486e15i			1.19529i
$533$			1.71980e14i			0.173173i
$534$	1.25884e15			1.25456
$535$	9.83643e14	+	7.27908e14i	0.970268	+	0.718010i
$536$	4.34382e14			0.424097
$537$			3.18396e15i			3.07687i
$538$			4.29126e14i			0.410471i
$539$	9.49885e14			0.899359
$540$	5.28483e14	+	3.91084e14i	0.495297	+	0.366526i
$541$	2.13640e14			0.198197			0.0990986	−	0.995078i	$-0.468404\pi$
$541$	2.13640e14			0.198197			0.0990986	+	0.995078i	$0.468404\pi$
$542$		−	9.57689e14i		−	0.879485i
$543$			1.08337e15i			0.984868i
$544$	1.07784e14			0.0969976
$545$	−1.11922e15	+	1.51243e15i	−0.997090	+	1.34740i
$546$	−1.19380e15			−1.05286
$547$		−	4.37872e13i		−	0.0382311i	−0.999817	−	0.0191156i	$-0.993915\pi$
$547$		−	4.37872e13i		−	0.0382311i	0.999817	−	0.0191156i	$-0.00608504\pi$
$548$			3.33992e14i			0.288697i
$549$	−4.49752e14			−0.384880
$550$	−4.12585e14	+	1.26110e14i	−0.349557	+	0.106845i
$551$	−7.06176e14			−0.592351
$552$		−	7.42579e14i		−	0.616705i
$553$		−	3.90220e15i		−	3.20865i
$554$	−1.40939e15			−1.14743
$555$	4.79705e14	−	6.48239e14i	0.386690	−	0.522545i
$556$	2.22351e13			0.0177471
$557$		−	1.57027e14i		−	0.124100i	−0.998073	−	0.0620500i	$-0.980236\pi$
$557$		−	1.57027e14i		−	0.124100i	0.998073	−	0.0620500i	$-0.0197638\pi$
$558$			1.05363e15i			0.824521i
$559$	5.29883e14			0.410596
$560$	−4.33514e14	−	3.20806e14i	−0.332636	−	0.246155i
$561$	6.18369e14			0.469842
$562$			1.22979e15i			0.925300i
$563$			4.81449e14i			0.358719i	0.983784	+	0.179359i	$0.0574025\pi$
$563$			4.81449e14i			0.358719i	−0.983784	+	0.179359i	$0.942598\pi$
$564$	−1.01230e15			−0.746922
$565$	−1.41435e15	−	1.04664e15i	−1.03345	−	0.764768i
$566$	−5.55968e14			−0.402309
$567$			6.86914e14i			0.492261i
$568$		−	3.10972e13i		−	0.0220702i
$569$	−1.74463e15			−1.22627			−0.613134	−	0.789979i	$-0.710092\pi$
$569$	−1.74463e15			−1.22627			−0.613134	+	0.789979i	$0.710092\pi$
$570$	1.44555e15	−	1.95342e15i	1.00629	−	1.35983i
$571$	2.52262e15			1.73921			0.869606	−	0.493747i	$-0.164373\pi$
$571$	2.52262e15			1.73921			0.869606	+	0.493747i	$0.164373\pi$
$572$			2.05549e14i			0.140358i
$573$			1.46300e15i			0.989449i
$574$	−5.57188e14			−0.373238
$575$	1.51780e15	−	4.63926e14i	1.00702	−	0.307805i
$576$	3.31716e14			0.217993
$577$			1.34881e15i			0.877978i	0.898492	+	0.438989i	$0.144663\pi$
$577$			1.34881e15i			0.877978i	−0.898492	+	0.438989i	$0.855337\pi$
$578$			7.66514e14i			0.494216i
$579$	−1.03909e15			−0.663622
$580$	1.92827e14	−	2.60573e14i	0.121987	−	0.164845i
$581$	1.58609e15			0.993937
$582$		−	9.81784e14i		−	0.609452i
$583$		−	8.52378e14i		−	0.524150i
$584$	4.28702e14			0.261147
$585$	1.26153e15	+	9.33545e14i	0.761271	+	0.563350i
$586$	8.69402e14			0.519737
$587$		−	7.29536e14i		−	0.432053i	−0.976387	−	0.216027i	$-0.930690\pi$
$587$		−	7.29536e14i		−	0.432053i	0.976387	−	0.216027i	$-0.0693098\pi$
$588$		−	2.45605e15i		−	1.44099i
$589$	1.66135e15			0.965666
$590$	−1.36880e15	−	1.01293e15i	−0.788234	−	0.583303i
$591$	1.07813e15			0.615090
$592$		−	1.73571e14i		−	0.0981089i
$593$			5.23392e14i			0.293107i	0.989203	+	0.146554i	$0.0468181\pi$
$593$			5.23392e14i			0.293107i	−0.989203	+	0.146554i	$0.953182\pi$
$594$	8.11832e14			0.450444
$595$	−9.82760e14	+	1.32803e15i	−0.540262	+	0.730071i
$596$	−1.00551e14			−0.0547684
$597$			2.27871e15i			1.22979i
$598$		−	7.56163e14i		−	0.404351i
$599$	−3.40071e15			−1.80186			−0.900932	−	0.433961i	$-0.857116\pi$
$599$	−3.40071e15			−1.80186			−0.900932	+	0.433961i	$0.857116\pi$
$600$	3.26073e14	+	1.06679e15i	0.171192	+	0.560077i
$601$	−6.34979e14			−0.330331			−0.165166	−	0.986266i	$-0.552816\pi$
$601$	−6.34979e14			−0.330331			−0.165166	+	0.986266i	$0.552816\pi$
$602$			1.71673e15i			0.884957i
$603$		−	4.09532e15i		−	2.09191i
$604$	1.64679e15			0.833558
$605$	8.69040e14	−	1.17436e15i	0.435898	−	0.589042i
$606$	−2.18346e13			−0.0108529
$607$		−	3.98915e14i		−	0.196491i	−0.995162	−	0.0982455i	$-0.968677\pi$
$607$		−	3.98915e14i		−	0.196491i	0.995162	−	0.0982455i	$-0.0313230\pi$
$608$		−	5.23043e14i		−	0.255310i
$609$	2.32477e15			1.12457
$610$	−2.61673e14	−	1.93642e14i	−0.125443	−	0.0928292i
$611$	−1.03082e15			−0.489730
$612$		−	1.01618e15i		−	0.478452i
$613$			2.02942e15i			0.946977i	0.880800	+	0.473489i	$0.157006\pi$
$613$			2.02942e15i			0.946977i	−0.880800	+	0.473489i	$0.842994\pi$
$614$	−2.45910e15			−1.13723
$615$	9.26422e14	+	6.85564e14i	0.424616	+	0.314221i
$616$	−6.65945e14			−0.302513
$617$		−	2.44138e15i		−	1.09917i	−0.835436	−	0.549587i	$-0.814785\pi$
$617$		−	2.44138e15i		−	1.09917i	0.835436	−	0.549587i	$-0.185215\pi$
$618$			2.00840e15i			0.896216i
$619$	5.08622e14			0.224955			0.112478	−	0.993654i	$-0.464121\pi$
$619$	5.08622e14			0.224955			0.112478	+	0.993654i	$0.464121\pi$
$620$	−4.53645e14	+	6.13023e14i	−0.198866	+	0.268734i
$621$	−2.98653e15			−1.29767
$622$		−	1.46581e14i		−	0.0631291i
$623$			4.15303e15i			1.77289i
$624$	5.31473e14			0.224888
$625$	−1.97676e15	+	1.33296e15i	−0.829112	+	0.559083i
$626$	2.10166e15			0.873782
$627$		−	3.00075e15i		−	1.23668i
$628$			1.00344e15i			0.409933i
$629$	−5.31720e14			−0.215330
$630$	−3.02454e15	+	4.08714e15i	−1.21419	+	1.64077i
$631$	5.49054e14			0.218501			0.109251	−	0.994014i	$-0.465155\pi$
$631$	5.49054e14			0.218501			0.109251	+	0.994014i	$0.465155\pi$
$632$			1.73724e15i			0.685355i
$633$			1.45721e15i			0.569902i
$634$	2.09261e15			0.811330
$635$	−3.19470e15	−	2.36412e15i	−1.22793	−	0.908686i
$636$	−2.20394e15			−0.839817
$637$		−	2.50098e15i		−	0.944808i
$638$		−	4.00280e14i		−	0.149917i
$639$	−2.93182e14			−0.108864
$640$	1.92998e14	+	1.42821e14i	0.0710498	+	0.0525778i
$641$	4.07205e15			1.48626			0.743129	−	0.669149i	$-0.233341\pi$
$641$	4.07205e15			1.48626			0.743129	+	0.669149i	$0.233341\pi$
$642$		−	3.90696e15i		−	1.41383i
$643$		−	1.05002e15i		−	0.376738i	−0.982098	−	0.188369i	$-0.939680\pi$
$643$		−	1.05002e15i		−	0.376738i	0.982098	−	0.188369i	$-0.0603200\pi$
$644$	2.44984e15			0.871498
$645$	2.11227e15	−	2.85437e15i	0.745025	−	1.00677i
$646$	−1.60229e15			−0.560355
$647$			1.33847e15i			0.464125i	0.972701	+	0.232063i	$0.0745475\pi$
$647$			1.33847e15i			0.464125i	−0.972701	+	0.232063i	$0.925453\pi$
$648$		−	3.05810e14i		−	0.105145i
$649$	−2.10269e15			−0.716853
$650$	3.32038e14	+	1.08631e15i	0.112244	+	0.367222i
$651$	−5.46926e15			−1.83330
$652$			8.31975e14i			0.276534i
$653$			5.09952e15i			1.68076i	0.541995	+	0.840382i	$0.317669\pi$
$653$			5.09952e15i			1.68076i	−0.541995	+	0.840382i	$0.682331\pi$
$654$	6.00727e15			1.96336
$655$	−1.36788e15	+	1.84845e15i	−0.443323	+	0.599075i
$656$	2.48057e14			0.0797224
$657$		−	4.04177e15i		−	1.28814i
$658$		−	3.33969e15i		−	1.05551i
$659$	−1.69518e15			−0.531307			−0.265654	−	0.964069i	$-0.585588\pi$
$659$	−1.69518e15			−0.531307			−0.265654	+	0.964069i	$0.585588\pi$
$660$	1.10725e15	+	8.19378e14i	0.344155	+	0.254679i
$661$	2.86480e15			0.883051			0.441526	−	0.897249i	$-0.354437\pi$
$661$	2.86480e15			0.883051			0.441526	+	0.897249i	$0.354437\pi$
$662$			5.85173e14i			0.178881i
$663$		−	1.62812e15i		−	0.493585i
$664$	−7.06118e14			−0.212301
$665$	6.44452e15	+	4.76903e15i	1.92164	+	1.42204i
$666$	−1.63642e15			−0.483934
$667$			1.47253e15i			0.431889i
$668$		−	2.32556e15i		−	0.676484i
$669$	−1.32250e15			−0.381551
$670$	1.76325e15	−	2.38273e15i	0.504548	−	0.681810i
$671$	−4.01971e14			−0.114083
$672$			1.72189e15i			0.484701i
$673$		−	2.65808e15i		−	0.742139i	−0.928605	−	0.371070i	$-0.878991\pi$
$673$		−	2.65808e15i		−	0.742139i	0.928605	−	0.371070i	$-0.121009\pi$
$674$	−2.02267e14			−0.0560138
$675$	4.29046e15	−	1.31141e15i	1.17851	−	0.360220i
$676$	−1.29398e15			−0.352549
$677$		−	4.00056e15i		−	1.08114i	−0.841298	−	0.540572i	$-0.818208\pi$
$677$		−	4.00056e15i		−	1.08114i	0.841298	−	0.540572i	$-0.181792\pi$
$678$			5.61770e15i			1.50590i
$679$	3.23901e15			0.861248
$680$	4.37519e14	−	5.91232e14i	0.115398	−	0.155941i
$681$	1.54984e15			0.405488
$682$			9.41698e14i			0.244398i
$683$		−	4.87594e15i		−	1.25529i	−0.778499	−	0.627646i	$-0.784019\pi$
$683$		−	4.87594e15i		−	1.25529i	0.778499	−	0.627646i	$-0.215981\pi$
$684$	−4.93121e15			−1.25935
$685$	1.83206e15	+	1.35574e15i	0.464131	+	0.343463i
$686$	3.44553e15			0.865911
$687$			7.67304e14i			0.191296i
$688$		−	7.64280e14i		−	0.189024i
$689$	−2.24425e15			−0.550638
$690$	−4.07329e15	−	3.01429e15i	−0.991461	−	0.733694i
$691$	9.81621e14			0.237036			0.118518	−	0.992952i	$-0.462186\pi$
$691$	9.81621e14			0.237036			0.118518	+	0.992952i	$0.462186\pi$
$692$		−	3.24539e15i		−	0.777469i
$693$			6.27848e15i			1.49218i
$694$	−3.00285e15			−0.708038
$695$	9.02570e13	−	1.21967e14i	0.0211137	−	0.0285315i
$696$	−1.03498e15			−0.240203
$697$		−	7.59900e14i		−	0.174975i
$698$		−	3.99675e15i		−	0.913065i
$699$	−5.06245e15			−1.14746
$700$	−3.51946e15	+	1.07575e15i	−0.791473	+	0.241920i
$701$	−5.96272e15			−1.33044			−0.665220	−	0.746648i	$-0.731662\pi$
$701$	−5.96272e15			−1.33044			−0.665220	+	0.746648i	$0.731662\pi$
$702$		−	2.13750e15i		−	0.473207i
$703$			2.58027e15i			0.566775i
$704$	2.96475e14			0.0646157
$705$	−4.10916e15	+	5.55282e15i	−0.888613	+	1.20081i
$706$	−1.58430e15			−0.339946
$707$		−	7.20345e13i		−	0.0153368i
$708$			5.43679e15i			1.14858i
$709$	−7.33103e15			−1.53678			−0.768388	−	0.639984i	$-0.778941\pi$
$709$	−7.33103e15			−1.53678			−0.768388	+	0.639984i	$0.778941\pi$
$710$	−1.70579e14	−	1.26230e14i	−0.0354816	−	0.0262569i
$711$	1.63786e16			3.38059
$712$		−	1.84891e15i		−	0.378682i
$713$		−	3.46427e15i		−	0.704076i
$714$	5.27485e15			1.06382
$715$	1.12750e15	+	8.34367e14i	0.225650	+	0.166984i
$716$	4.67641e15			0.928734
$717$			1.18425e16i			2.33393i
$718$			2.82255e15i			0.552024i
$719$	5.64957e15			1.09649			0.548247	−	0.836317i	$-0.315295\pi$
$719$	5.64957e15			1.09649			0.548247	+	0.836317i	$0.315295\pi$
$720$	1.34651e15	−	1.81957e15i	0.259346	−	0.350462i
$721$	−6.62591e15			−1.26649
$722$			4.04774e15i			0.767818i
$723$		−	2.59313e15i		−	0.488161i
$724$	1.59119e15			0.297276
$725$	−6.46601e14	−	2.11544e15i	−0.119888	−	0.392231i
$726$	−4.66447e15			−0.858323
$727$			1.03387e16i			1.88811i	0.329790	+	0.944054i	$0.393022\pi$
$727$			1.03387e16i			1.88811i	−0.329790	+	0.944054i	$0.606978\pi$
$728$			1.75339e15i			0.317801i
$729$	8.46477e15			1.52270
$730$	1.74019e15	−	2.35157e15i	0.310686	−	0.419839i
$731$	−2.34130e15			−0.414870
$732$			1.03935e15i			0.182789i
$733$		−	4.98348e15i		−	0.869883i	−0.900459	−	0.434942i	$-0.856769\pi$
$733$		−	4.98348e15i		−	0.869883i	0.900459	−	0.434942i	$-0.143231\pi$
$734$	−3.16484e15			−0.548307
$735$	−1.34723e16	−	9.96965e15i	−2.31665	−	1.71435i
$736$	−1.09066e15			−0.186149
$737$		−	3.66024e15i		−	0.620067i
$738$		−	2.33866e15i		−	0.393240i
$739$	−2.94537e15			−0.491582			−0.245791	−	0.969323i	$-0.579048\pi$
$739$	−2.94537e15			−0.491582			−0.245791	+	0.969323i	$0.579048\pi$
$740$	−9.52096e14	−	7.04563e14i	−0.157727	−	0.116720i
$741$	−7.90076e15			−1.29918
$742$		−	7.27101e15i		−	1.18679i
$743$		−	5.61294e15i		−	0.909393i	−0.890646	−	0.454697i	$-0.849748\pi$
$743$		−	5.61294e15i		−	0.909393i	0.890646	−	0.454697i	$-0.150252\pi$
$744$	2.43488e15			0.391586
$745$	−4.08156e14	+	5.51553e14i	−0.0651579	+	0.0880497i
$746$	1.00940e15			0.159955
$747$			6.65723e15i			1.04720i
$748$		−	9.08224e14i		−	0.141819i
$749$	1.28895e16			1.99795
$750$	7.17531e15	+	2.54172e15i	1.10409	+	0.391102i
$751$	5.13668e15			0.784626			0.392313	−	0.919832i	$-0.371675\pi$
$751$	5.13668e15			0.784626			0.392313	+	0.919832i	$0.371675\pi$
$752$			1.48681e15i			0.225454i
$753$		−	1.36164e16i		−	2.04969i
$754$	−1.05391e15			−0.157493
$755$	6.68469e15	−	9.03321e15i	0.991683	−	1.34009i
$756$	6.92514e15			1.01990
$757$		−	9.14554e15i		−	1.33716i	−0.743642	−	0.668578i	$-0.766903\pi$
$757$		−	9.14554e15i		−	1.33716i	0.743642	−	0.668578i	$-0.233097\pi$
$758$			4.67090e15i			0.677985i
$759$	−6.25721e15			−0.901677
$760$	−2.86906e15	−	2.12314e15i	−0.410455	−	0.303742i
$761$	2.23954e15			0.318084			0.159042	−	0.987272i	$-0.449159\pi$
$761$	2.23954e15			0.318084			0.159042	+	0.987272i	$0.449159\pi$
$762$			1.26891e16i			1.78928i
$763$			1.98186e16i			2.77452i
$764$	2.14877e15			0.298659
$765$	−5.57409e15	−	4.12490e15i	−0.769195	−	0.569214i
$766$	−3.00562e15			−0.411789
$767$			5.53624e15i			0.753079i
$768$		−	7.66574e14i		−	0.103530i
$769$	1.08968e16			1.46118			0.730588	−	0.682819i	$-0.239246\pi$
$769$	1.08968e16			1.46118			0.730588	+	0.682819i	$0.239246\pi$
$770$	−2.70321e15	+	3.65293e15i	−0.359900	+	0.486343i
$771$	6.94723e15			0.918359
$772$			1.52615e15i			0.200310i
$773$		−	4.35156e15i		−	0.567098i	−0.958958	−	0.283549i	$-0.908488\pi$
$773$		−	4.35156e15i		−	0.567098i	0.958958	−	0.283549i	$-0.0915119\pi$
$774$	−7.20558e15			−0.932382
$775$	1.52119e15	+	4.97679e15i	0.195445	+	0.639425i
$776$	−1.44199e15			−0.183959
$777$		−	8.49440e15i		−	1.07601i
$778$		−	8.87195e14i		−	0.111592i
$779$	−3.68756e15			−0.460556
$780$	2.15737e15	−	2.91531e15i	0.267549	−	0.361547i
$781$	−2.62035e14			−0.0322685
$782$			3.34113e15i			0.408560i
$783$			4.16250e15i			0.505434i
$784$	−3.60731e15			−0.434955
$785$	5.50420e15	+	4.07318e15i	0.659039	+	0.487697i
$786$	7.34193e15			0.872943
$787$		−	1.61926e15i		−	0.191186i	−0.995420	−	0.0955930i	$-0.969525\pi$
$787$		−	1.61926e15i		−	0.191186i	0.995420	−	0.0955930i	$-0.0304747\pi$
$788$		−	1.58349e15i		−	0.185661i
$789$	−1.29212e16			−1.50446
$790$	9.52933e15	+	7.05183e15i	1.10183	+	0.815366i
$791$	−1.85334e16			−2.12806
$792$		−	2.79514e15i		−	0.318725i
$793$			1.05836e15i			0.119848i
$794$	−5.78543e15			−0.650613
$795$	−8.94625e15	+	1.20893e16i	−0.999130	+	1.35015i
$796$	3.34683e15			0.371204
$797$			8.03974e15i			0.885567i	0.896629	+	0.442783i	$0.146009\pi$
$797$			8.03974e15i			0.885567i	−0.896629	+	0.442783i	$0.853991\pi$
$798$		−	2.55972e16i		−	2.80012i
$799$	4.55471e15			0.494827
$800$	1.56684e15	−	4.78918e14i	0.169056	−	0.0516733i
$801$	−1.74314e16			−1.86789
$802$			4.31253e15i			0.458959i
$803$		−	3.61238e15i		−	0.381819i
$804$	−9.46403e15			−0.993500
$805$	9.94445e15	−	1.34382e16i	1.03682	−	1.40108i
$806$	2.47942e15			0.256749
$807$		−	9.34952e15i		−	0.961579i
$808$			3.20694e13i			0.00327588i
$809$	−1.14828e16			−1.16501			−0.582506	−	0.812826i	$-0.697928\pi$
$809$	−1.14828e16			−1.16501			−0.582506	+	0.812826i	$0.697928\pi$
$810$	−1.67747e15	−	1.24135e15i	−0.169039	−	0.125091i
$811$	5.96668e15			0.597198			0.298599	−	0.954379i	$-0.403481\pi$
$811$	5.96668e15			0.597198			0.298599	+	0.954379i	$0.403481\pi$
$812$		−	3.41449e15i		−	0.339444i
$813$			2.08655e16i			2.06030i
$814$	−1.46257e15			−0.143444
$815$	4.56366e15	+	3.37717e15i	0.444576	+	0.328992i
$816$	−2.34833e15			−0.227229
$817$			1.13616e16i			1.09199i
$818$			5.17928e15i			0.494454i
$819$	1.65308e16			1.56759
$820$	1.00692e15	−	1.36068e15i	0.0948456	−	0.128168i
$821$	−1.58047e15			−0.147876			−0.0739381	−	0.997263i	$-0.523557\pi$
$821$	−1.58047e15			−0.147876			−0.0739381	+	0.997263i	$0.523557\pi$
$822$		−	7.27679e15i		−	0.676309i
$823$			1.03090e16i			0.951734i	0.879517	+	0.475867i	$0.157866\pi$
$823$			1.03090e16i			0.951734i	−0.879517	+	0.475867i	$0.842134\pi$
$824$	2.94982e15			0.270517
$825$	8.98913e15	−	2.74760e15i	0.818881	−	0.250298i
$826$	−1.79365e16			−1.62311
$827$		−	1.03944e16i		−	0.934374i	−0.884158	−	0.467187i	$-0.845267\pi$
$827$		−	1.03944e16i		−	0.934374i	0.884158	−	0.467187i	$-0.154733\pi$
$828$			1.02826e16i			0.918200i
$829$	1.52772e16			1.35517			0.677584	−	0.735445i	$-0.263027\pi$
$829$	1.52772e16			1.35517			0.677584	+	0.735445i	$0.263027\pi$
$830$	−2.86629e15	+	3.87329e15i	−0.252575	+	0.341311i
$831$	3.07068e16			2.68800
$832$		−	7.80597e14i		−	0.0678811i
$833$			1.10507e16i			0.954642i
$834$	−4.84443e14			−0.0415748
$835$	−1.27565e16	−	9.43996e15i	−1.08757	−	0.804812i
$836$	−4.40733e15			−0.373285
$837$		−	9.79269e15i		−	0.823971i
$838$			1.42754e15i			0.119329i
$839$	−4.62607e13			−0.00384168			−0.00192084	−	0.999998i	$-0.500611\pi$
$839$	−4.62607e13			−0.00384168			−0.00192084	+	0.999998i	$0.500611\pi$
$840$	9.44513e15	+	6.98951e15i	0.779241	+	0.576648i
$841$	−1.01482e16			−0.831782
$842$		−	1.27007e16i		−	1.03422i
$843$		−	2.67939e16i		−	2.16763i
$844$	2.14026e15			0.172021
$845$	−5.25253e15	+	7.09789e15i	−0.419427	+	0.566784i
$846$	1.40176e16			1.11208
$847$		−	1.53886e16i		−	1.21294i
$848$			3.23701e15i			0.253494i
$849$	1.21131e16			0.942458
$850$	−1.46712e15	−	4.79988e15i	−0.113413	−	0.371045i
$851$	5.38042e15			0.413241
$852$			6.77526e14i			0.0517021i
$853$		−	1.39374e16i		−	1.05672i	−0.849019	−	0.528362i	$-0.822806\pi$
$853$		−	1.39374e16i		−	1.05672i	0.849019	−	0.528362i	$-0.177194\pi$
$854$	−3.42892e15			−0.258308
$855$	−2.00168e16	+	2.70493e16i	−1.49824	+	2.02462i
$856$	−5.73831e15			−0.426755
$857$			2.60789e16i			1.92706i	0.267605	+	0.963529i	$0.413768\pi$
$857$			2.60789e16i			1.92706i	−0.267605	+	0.963529i	$0.586232\pi$
$858$		−	4.47837e15i		−	0.328806i
$859$	4.60719e15			0.336104			0.168052	−	0.985778i	$-0.446252\pi$
$859$	4.60719e15			0.336104			0.168052	+	0.985778i	$0.446252\pi$
$860$	−4.19233e15	−	3.10238e15i	−0.303889	−	0.224881i
$861$	1.21397e16			0.874357
$862$		−	1.51460e16i		−	1.08395i
$863$		−	5.99532e15i		−	0.426337i	−0.977015	−	0.213169i	$-0.931622\pi$
$863$		−	5.99532e15i		−	0.426337i	0.977015	−	0.213169i	$-0.0683784\pi$
$864$	−3.08303e15			−0.217847
$865$	−1.78020e16	−	1.31737e16i	−1.24992	−	0.924954i
$866$	1.95045e16			1.36078
$867$		−	1.67003e16i		−	1.15776i
$868$			8.03293e15i			0.553370i
$869$	1.46385e16			1.00205
$870$	−4.20119e15	+	5.67719e15i	−0.285770	+	0.386169i
$871$	−9.63715e15			−0.651402
$872$		−	8.82313e15i		−	0.592628i
$873$			1.35950e16i			0.907402i
$874$	1.62135e16			1.07538
$875$	−8.38539e15	+	2.36721e16i	−0.552686	+	1.56024i
$876$	−9.34028e15			−0.611769
$877$		−	2.57912e16i		−	1.67870i	−0.543592	−	0.839350i	$-0.682936\pi$
$877$		−	2.57912e16i		−	1.67870i	0.543592	−	0.839350i	$-0.317064\pi$
$878$			1.24486e16i			0.805197i
$879$	−1.89420e16			−1.21755
$880$	1.20346e15	−	1.62626e15i	0.0768733	−	0.103881i
$881$	−2.80787e16			−1.78242			−0.891209	−	0.453592i	$-0.850142\pi$
$881$	−2.80787e16			−1.78242			−0.891209	+	0.453592i	$0.850142\pi$
$882$			3.40094e16i			2.14547i
$883$			2.68062e16i			1.68055i	0.542162	+	0.840274i	$0.317606\pi$
$883$			2.68062e16i			1.68055i	−0.542162	+	0.840274i	$0.682394\pi$
$884$	−2.39129e15			−0.148986
$885$	2.98226e16	+	2.20691e16i	1.84653	+	1.36646i
$886$	2.17086e16			1.33582
$887$		−	7.52556e15i		−	0.460213i	−0.973165	−	0.230106i	$-0.926093\pi$
$887$		−	7.52556e15i		−	0.460213i	0.973165	−	0.230106i	$-0.0739074\pi$
$888$			3.78166e15i			0.229832i
$889$	−4.18627e16			−2.52853
$890$	−1.01419e16	−	7.50511e15i	−0.608798	−	0.450518i
$891$	−2.57686e15			−0.153731
$892$			1.94241e15i			0.115169i
$893$		−	2.21026e16i		−	1.30245i
$894$	2.19073e15			0.128302
$895$	1.89826e16	−	2.56517e16i	1.10491	−	1.49310i
$896$	2.52901e15			0.146304
$897$			1.64748e16i			0.947243i
$898$			8.81827e15i			0.503922i
$899$	−4.82836e15			−0.274234
$900$	−4.51520e15	−	1.47721e16i	−0.254884	−	0.833888i
$901$	9.91629e15			0.556369
$902$		−	2.09021e15i		−	0.116561i
$903$		−	3.74031e16i		−	2.07312i
$904$	8.25095e15			0.454546
$905$	6.45899e15	−	8.72822e15i	0.353670	−	0.477924i
$906$	−3.58793e16			−1.95271
$907$			1.54682e16i			0.836756i	0.908273	+	0.418378i	$0.137401\pi$
$907$			1.54682e16i			0.836756i	−0.908273	+	0.418378i	$0.862599\pi$
$908$		−	2.27632e15i		−	0.122394i
$909$	3.02348e14			0.0161587
$910$	9.61791e15	+	7.11737e15i	0.510920	+	0.378087i
$911$	−2.54945e16			−1.34616			−0.673079	−	0.739570i	$-0.735029\pi$
$911$	−2.54945e16			−1.34616			−0.673079	+	0.739570i	$0.735029\pi$
$912$			1.13957e16i			0.598095i
$913$			5.94998e15i			0.310403i
$914$	−1.65021e16			−0.855725
$915$	5.70117e15	+	4.21894e15i	0.293865	+	0.217464i
$916$	1.12697e15			0.0577415
$917$			2.42218e16i			1.23360i
$918$			9.44459e15i			0.478133i
$919$	−1.50582e16			−0.757771			−0.378885	−	0.925444i	$-0.623693\pi$
$919$	−1.50582e16			−0.757771			−0.378885	+	0.925444i	$0.623693\pi$
$920$	−4.42721e15	+	5.98262e15i	−0.221461	+	0.299267i
$921$	5.35772e16			2.66411
$922$		−	5.49376e15i		−	0.271550i
$923$			6.89920e14i			0.0338992i
$924$	1.45092e16			0.708675
$925$	−7.72953e15	+	2.36259e15i	−0.375296	+	0.114712i
$926$	9.56712e15			0.461765
$927$		−	2.78106e16i		−	1.33436i
$928$			1.52011e15i			0.0725040i
$929$	2.90569e16			1.37773			0.688864	−	0.724891i	$-0.258110\pi$
$929$	2.90569e16			1.37773			0.688864	+	0.724891i	$0.258110\pi$
$930$	9.88372e15	−	1.33561e16i	0.465869	−	0.629542i
$931$	5.36254e16			2.51274
$932$			7.43544e15i			0.346353i
$933$			3.19361e15i			0.147888i
$934$	−3.03981e15			−0.139939
$935$	−4.98191e15	−	3.68668e15i	−0.227999	−	0.168722i
$936$	−7.35941e15			−0.334831
$937$			1.97723e16i			0.894313i	0.894456	+	0.447156i	$0.147563\pi$
$937$			1.97723e16i			0.894313i	−0.894456	+	0.447156i	$0.852437\pi$
$938$		−	3.12228e16i		−	1.40397i
$939$	−4.57896e16			−2.04694
$940$	8.15566e15	+	6.03529e15i	0.362456	+	0.268222i
$941$	−1.84496e16			−0.815160			−0.407580	−	0.913169i	$-0.633627\pi$
$941$	−1.84496e16			−0.815160			−0.407580	+	0.913169i	$0.633627\pi$
$942$		−	2.18623e16i		−	0.960320i
$943$			7.68935e15i			0.335796i
$944$	7.98524e15			0.346690
$945$	2.81106e16	−	3.79867e16i	1.21338	−	1.63967i
$946$	−6.44007e15			−0.276369
$947$			1.21152e16i			0.516897i	0.966025	+	0.258449i	$0.0832113\pi$
$947$			1.21152e16i			0.516897i	−0.966025	+	0.258449i	$0.916789\pi$
$948$		−	3.78498e16i		−	1.60553i
$949$	−9.51114e15			−0.401114
$950$	−2.32923e16	+	7.11948e15i	−0.976636	+	0.298516i
$951$	−4.55925e16			−1.90064
$952$		−	7.74739e15i		−	0.321109i
$953$		−	1.02683e16i		−	0.423143i	−0.977362	−	0.211572i	$-0.932142\pi$
$953$		−	1.02683e16i		−	0.423143i	0.977362	−	0.211572i	$-0.0678582\pi$
$954$	3.05183e16			1.25039
$955$	8.72231e15	−	1.17867e16i	0.355315	−	0.480147i
$956$	1.73936e16			0.704482
$957$			8.72104e15i			0.351198i
$958$			1.21099e16i			0.484875i
$959$	2.40069e16			0.955726
$960$	−4.20492e15	−	3.11169e15i	−0.166443	−	0.123170i
$961$	−1.40493e16			−0.552937
$962$			3.85083e15i			0.150693i
$963$			5.41004e16i			2.10502i
$964$	−3.80864e15			−0.147349
$965$	8.37146e15	+	6.19499e15i	0.322034	+	0.238309i
$966$	−5.33756e16			−2.04159
$967$			6.61638e15i			0.251637i	0.992053	+	0.125819i	$0.0401557\pi$
$967$			6.61638e15i			0.251637i	−0.992053	+	0.125819i	$0.959844\pi$
$968$			6.85090e15i			0.259080i
$969$	3.49098e16			1.31270
$970$	−5.85334e15	+	7.90979e15i	−0.218856	+	0.295747i
$971$	4.23912e16			1.57605			0.788024	−	0.615644i	$-0.211104\pi$
$971$	4.23912e16			1.57605			0.788024	+	0.615644i	$0.211104\pi$
$972$		−	1.00044e16i		−	0.369850i
$973$		−	1.59823e15i		−	0.0587514i
$974$	1.95236e16			0.713650
$975$	−7.23423e15	−	2.36677e16i	−0.262946	−	0.860263i
$976$	1.52653e15			0.0551737
$977$			3.85191e15i			0.138438i	0.997601	+	0.0692191i	$0.0220507\pi$
$977$			3.85191e15i			0.138438i	−0.997601	+	0.0692191i	$0.977949\pi$
$978$		−	1.81265e16i		−	0.647815i
$979$	−1.55795e16			−0.553666
$980$	−1.46428e16	+	1.97873e16i	−0.517466	+	0.699267i
$981$	−8.31838e16			−2.92321
$982$			3.63882e16i			1.27159i
$983$			1.22656e16i			0.426230i	0.977027	+	0.213115i	$0.0683610\pi$
$983$			1.22656e16i			0.426230i	−0.977027	+	0.213115i	$0.931639\pi$
$984$	−5.40450e15			−0.186760
$985$	−8.68597e15	−	6.42772e15i	−0.298483	−	0.220881i
$986$	4.65673e15			0.159132
$987$			7.27630e16i			2.47267i
$988$			1.16042e16i			0.392149i
$989$	2.36914e16			0.796180
$990$	−1.53323e16	−	1.13461e16i	−0.512405	−	0.379186i
$991$	1.86075e16			0.618420			0.309210	−	0.950994i	$-0.399935\pi$
$991$	1.86075e16			0.618420			0.309210	+	0.950994i	$0.399935\pi$
$992$		−	3.57621e15i		−	0.118198i
$993$		−	1.27494e16i		−	0.419052i
$994$	−2.23523e15			−0.0730629
$995$	1.35855e16	−	1.83585e16i	0.441621	−	0.596774i
$996$	1.53844e16			0.497342
$997$			1.75336e16i			0.563701i	0.959458	+	0.281850i	$0.0909482\pi$
$997$			1.75336e16i			0.563701i	−0.959458	+	0.281850i	$0.909052\pi$
$998$		−	2.86792e16i		−	0.916957i
$999$	1.52092e16			0.483611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.b.a.9.4	yes	6
3.2	odd	2		90.12.c.b.19.3		6
4.3	odd	2		80.12.c.c.49.6		6
5.2	odd	4		50.12.a.i.1.1		3
5.3	odd	4		50.12.a.j.1.3		3
5.4	even	2	inner	10.12.b.a.9.3	✓	6
15.14	odd	2		90.12.c.b.19.6		6
20.19	odd	2		80.12.c.c.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.b.a.9.3	✓	6	5.4	even	2	inner
10.12.b.a.9.4	yes	6	1.1	even	1	trivial
50.12.a.i.1.1		3	5.2	odd	4
50.12.a.j.1.3		3	5.3	odd	4
80.12.c.c.49.1		6	20.19	odd	2
80.12.c.c.49.6		6	4.3	odd	2
90.12.c.b.19.3		6	3.2	odd	2
90.12.c.b.19.6		6	15.14	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+32.0000i q^{2} -697.195i q^{3} -1024.00 q^{4} +(-4156.64 + 5616.98i) q^{5} +22310.3 q^{6} +73603.8i q^{7} -32768.0i q^{8} -308934. q^{9} +O(q^{10})\)	\(q+32.0000i q^{2} -697.195i q^{3} -1024.00 q^{4} +(-4156.64 + 5616.98i) q^{5} +22310.3 q^{6} +73603.8i q^{7} -32768.0i q^{8} -308934. q^{9} +(-179743. - 133012. i) q^{10} -276114. q^{11} +713928. i q^{12} +726988. i q^{13} -2.35532e6 q^{14} +(3.91613e6 + 2.89799e6i) q^{15} +1.04858e6 q^{16} -3.21222e6i q^{17} -9.88590e6i q^{18} -1.55879e7 q^{19} +(4.25640e6 - 5.75179e6i) q^{20} +5.13162e7 q^{21} -8.83564e6i q^{22} +3.25041e7i q^{23} -2.28457e7 q^{24} +(-1.42729e7 - 4.66955e7i) q^{25} -2.32636e7 q^{26} +9.18815e7i q^{27} -7.53703e7i q^{28} +4.53029e7 q^{29} +(-9.27356e7 + 1.25316e8i) q^{30} -1.06580e8 q^{31} +3.35544e7i q^{32} +1.92505e8i q^{33} +1.02791e8 q^{34} +(-4.13431e8 - 3.05944e8i) q^{35} +3.16349e8 q^{36} -1.65530e8i q^{37} -4.98812e8i q^{38} +5.06853e8 q^{39} +(1.84057e8 + 1.36205e8i) q^{40} +2.36566e8 q^{41} +1.64212e9i q^{42} -7.28874e8i q^{43} +2.82740e8 q^{44} +(1.28413e9 - 1.73528e9i) q^{45} -1.04013e9 q^{46} +1.41793e9i q^{47} -7.31062e8i q^{48} -3.44020e9 q^{49} +(1.49426e9 - 4.56731e8i) q^{50} -2.23954e9 q^{51} -7.44435e8i q^{52} +3.08706e9i q^{53} -2.94021e9 q^{54} +(1.14770e9 - 1.55093e9i) q^{55} +2.41185e9 q^{56} +1.08678e10i q^{57} +1.44969e9i q^{58} +7.61532e9 q^{59} +(-4.01012e9 - 2.96754e9i) q^{60} +1.45582e9 q^{61} -3.41054e9i q^{62} -2.27388e10i q^{63} -1.07374e9 q^{64} +(-4.08348e9 - 3.02182e9i) q^{65} -6.16017e9 q^{66} +1.32563e10i q^{67} +3.28931e9i q^{68} +2.26617e10 q^{69} +(9.79022e9 - 1.32298e10i) q^{70} +9.49012e8 q^{71} +1.01232e10i q^{72} +1.30829e10i q^{73} +5.29697e9 q^{74} +(-3.25559e10 + 9.95097e9i) q^{75} +1.59620e10 q^{76} -2.03230e10i q^{77} +1.62193e10i q^{78} -5.30163e10 q^{79} +(-4.35855e9 + 5.88983e9i) q^{80} +9.33259e9 q^{81} +7.57010e9i q^{82} -2.15490e10i q^{83} -5.25478e10 q^{84} +(1.80430e10 + 1.33520e10i) q^{85} +2.33240e10 q^{86} -3.15849e10i q^{87} +9.04769e9i q^{88} +5.64241e10 q^{89} +(5.55289e10 + 4.10921e10i) q^{90} -5.35091e10 q^{91} -3.32842e10i q^{92} +7.43067e10i q^{93} -4.53739e10 q^{94} +(6.47932e10 - 8.75569e10i) q^{95} +2.33940e10 q^{96} -4.40060e10i q^{97} -1.10086e11i q^{98} +8.53010e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6144 q^{4} + 530 q^{5} + 17024 q^{6} - 496022 q^{9}+O(q^{10}) \) 6 * q - 6144 * q^4 + 530 * q^5 + 17024 * q^6 - 496022 * q^9	\( 6 q - 6144 q^{4} + 530 q^{5} + 17024 q^{6} - 496022 q^{9} - 385920 q^{10} - 642728 q^{11} - 2125952 q^{14} - 698680 q^{15} + 6291456 q^{16} - 24109080 q^{19} - 542720 q^{20} + 125471192 q^{21} - 17432576 q^{24} - 181718850 q^{25} + 89251584 q^{26} - 256409820 q^{29} - 221514880 q^{30} + 458481792 q^{31} - 225288192 q^{34} - 697136360 q^{35} + 507926528 q^{36} + 1318797936 q^{39} + 395182080 q^{40} - 164768948 q^{41} + 658153472 q^{44} + 3174067390 q^{45} - 2956208256 q^{46} - 675514158 q^{49} + 3912262400 q^{50} - 13060087168 q^{51} - 6079189760 q^{54} + 3688644360 q^{55} + 2176974848 q^{56} + 17663962360 q^{59} + 715448320 q^{60} - 5020792428 q^{61} - 6442450944 q^{64} - 19996916880 q^{65} + 14496229888 q^{66} + 23117013976 q^{69} + 24956826240 q^{70} + 56788418832 q^{71} - 64135292672 q^{74} - 95499160400 q^{75} + 24687697920 q^{76} + 2602550880 q^{79} + 555745280 q^{80} - 7039907074 q^{81} - 128482500608 q^{84} - 85024210560 q^{85} + 111995790464 q^{86} + 249448412540 q^{89} + 225507463040 q^{90} - 184446766128 q^{91} - 337749482112 q^{94} + 104896380600 q^{95} + 17850957824 q^{96} + 520781125736 q^{99}+O(q^{100}) \) 6 * q - 6144 * q^4 + 530 * q^5 + 17024 * q^6 - 496022 * q^9 - 385920 * q^10 - 642728 * q^11 - 2125952 * q^14 - 698680 * q^15 + 6291456 * q^16 - 24109080 * q^19 - 542720 * q^20 + 125471192 * q^21 - 17432576 * q^24 - 181718850 * q^25 + 89251584 * q^26 - 256409820 * q^29 - 221514880 * q^30 + 458481792 * q^31 - 225288192 * q^34 - 697136360 * q^35 + 507926528 * q^36 + 1318797936 * q^39 + 395182080 * q^40 - 164768948 * q^41 + 658153472 * q^44 + 3174067390 * q^45 - 2956208256 * q^46 - 675514158 * q^49 + 3912262400 * q^50 - 13060087168 * q^51 - 6079189760 * q^54 + 3688644360 * q^55 + 2176974848 * q^56 + 17663962360 * q^59 + 715448320 * q^60 - 5020792428 * q^61 - 6442450944 * q^64 - 19996916880 * q^65 + 14496229888 * q^66 + 23117013976 * q^69 + 24956826240 * q^70 + 56788418832 * q^71 - 64135292672 * q^74 - 95499160400 * q^75 + 24687697920 * q^76 + 2602550880 * q^79 + 555745280 * q^80 - 7039907074 * q^81 - 128482500608 * q^84 - 85024210560 * q^85 + 111995790464 * q^86 + 249448412540 * q^89 + 225507463040 * q^90 - 184446766128 * q^91 - 337749482112 * q^94 + 104896380600 * q^95 + 17850957824 * q^96 + 520781125736 * q^99

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