LMFDB - Embedded newform 10.12.b.a.9.5

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			9.5
Root			$0.947541 + 0.947541i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.12.b.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.0000i q^{2} -100.951i q^{3} -1024.00 q^{4} +(2827.02 - 6390.31i) q^{5} +3230.43 q^{6} -15908.8i q^{7} -32768.0i q^{8} +166956. q^{9} +O(q^{10})$	\(q+32.0000i q^{2} -100.951i q^{3} -1024.00 q^{4} +(2827.02 - 6390.31i) q^{5} +3230.43 q^{6} -15908.8i q^{7} -32768.0i q^{8} +166956. q^{9} +(204490. + 90464.5i) q^{10} +623805. q^{11} +103374. i q^{12} -1.54230e6i q^{13} +509081. q^{14} +(-645107. - 285390. i) q^{15} +1.04858e6 q^{16} -1.11817e6i q^{17} +5.34259e6i q^{18} -1.45889e7 q^{19} +(-2.89487e6 + 6.54368e6i) q^{20} -1.60601e6 q^{21} +1.99618e7i q^{22} -6.03368e6i q^{23} -3.30796e6 q^{24} +(-3.28441e7 - 3.61310e7i) q^{25} +4.93536e7 q^{26} -3.47375e7i q^{27} +1.62906e7i q^{28} +2.91997e7 q^{29} +(9.13247e6 - 2.06434e7i) q^{30} +2.33031e8 q^{31} +3.35544e7i q^{32} -6.29736e7i q^{33} +3.57814e7 q^{34} +(-1.01662e8 - 4.49744e7i) q^{35} -1.70963e8 q^{36} +6.65053e8i q^{37} -4.66846e8i q^{38} -1.55696e8 q^{39} +(-2.09398e8 - 9.26357e7i) q^{40} -6.63914e8 q^{41} -5.13922e7i q^{42} +4.11150e8i q^{43} -6.38776e8 q^{44} +(4.71987e8 - 1.06690e9i) q^{45} +1.93078e8 q^{46} +2.47761e9i q^{47} -1.05855e8i q^{48} +1.72424e9 q^{49} +(1.15619e9 - 1.05101e9i) q^{50} -1.12880e8 q^{51} +1.57931e9i q^{52} -3.69178e9i q^{53} +1.11160e9 q^{54} +(1.76351e9 - 3.98631e9i) q^{55} -5.21299e8 q^{56} +1.47277e9i q^{57} +9.34390e8i q^{58} -1.25820e9 q^{59} +(6.60590e8 + 2.92239e8i) q^{60} -4.05784e9 q^{61} +7.45700e9i q^{62} -2.65607e9i q^{63} -1.07374e9 q^{64} +(-9.85577e9 - 4.36011e9i) q^{65} +2.01516e9 q^{66} +1.84180e10i q^{67} +1.14500e9i q^{68} -6.09105e8 q^{69} +(1.43918e9 - 3.25319e9i) q^{70} +3.19489e9 q^{71} -5.47081e9i q^{72} -1.51712e10i q^{73} -2.12817e10 q^{74} +(-3.64746e9 + 3.31564e9i) q^{75} +1.49391e10 q^{76} -9.92398e9i q^{77} -4.98228e9i q^{78} +4.26826e10 q^{79} +(2.96434e9 - 6.70073e9i) q^{80} +2.60690e10 q^{81} -2.12453e10i q^{82} +5.86787e10i q^{83} +1.64455e9 q^{84} +(-7.14544e9 - 3.16108e9i) q^{85} -1.31568e10 q^{86} -2.94773e9i q^{87} -2.04408e10i q^{88} -3.40792e10 q^{89} +(3.41408e10 + 1.51036e10i) q^{90} -2.45361e10 q^{91} +6.17849e9i q^{92} -2.35247e10i q^{93} -7.92835e10 q^{94} +(-4.12432e10 + 9.32279e10i) q^{95} +3.38735e9 q^{96} -1.37873e11i q^{97} +5.51756e10i q^{98} +1.04148e11 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
$3$		−	100.951i		−	0.239852i	−0.992783	−	0.119926i	$-0.961734\pi$
$3$		−	100.951i		−	0.239852i	0.992783	−	0.119926i	$-0.0382657\pi$
$4$	−1024.00			−0.500000
$5$	2827.02	−	6390.31i	0.404570	−	0.914507i
$5$	2827.02	−	6390.31i	0.404570	−	0.914507i
$6$	3230.43			0.169601
$7$		−	15908.8i		−	0.357765i	−0.983870	−	0.178883i	$-0.942752\pi$
$7$		−	15908.8i		−	0.357765i	0.983870	−	0.178883i	$-0.0572482\pi$
$8$		−	32768.0i		−	0.353553i
$9$	166956.			0.942471
$10$	204490.	+	90464.5i	0.646654	+	0.286074i
$11$	623805.			1.16786			0.583928	−	0.811806i	$-0.301515\pi$
$11$	623805.			1.16786			0.583928	+	0.811806i	$0.301515\pi$
$12$			103374.i			0.119926i
$13$		−	1.54230e6i		−	1.15207i	−0.817424	−	0.576037i	$-0.804599\pi$
$13$		−	1.54230e6i		−	1.15207i	0.817424	−	0.576037i	$-0.195401\pi$
$14$	509081.			0.252978
$15$	−645107.	−	285390.i	−0.219346	−	0.0970368i
$16$	1.04858e6			0.250000
$17$		−	1.11817e6i		−	0.191002i	−0.995429	−	0.0955010i	$-0.969555\pi$
$17$		−	1.11817e6i		−	0.191002i	0.995429	−	0.0955010i	$-0.0304453\pi$
$18$			5.34259e6i			0.666428i
$19$	−1.45889e7			−1.35170			−0.675848	−	0.737041i	$-0.736223\pi$
$19$	−1.45889e7			−1.35170			−0.675848	+	0.737041i	$0.736223\pi$
$20$	−2.89487e6	+	6.54368e6i	−0.202285	+	0.457254i
$21$	−1.60601e6			−0.0858106
$22$			1.99618e7i			0.825798i
$23$		−	6.03368e6i		−	0.195470i	−0.995212	−	0.0977348i	$-0.968840\pi$
$23$		−	6.03368e6i		−	0.195470i	0.995212	−	0.0977348i	$-0.0311597\pi$
$24$	−3.30796e6			−0.0848004
$25$	−3.28441e7	−	3.61310e7i	−0.672647	−	0.739964i
$26$	4.93536e7			0.814639
$27$		−	3.47375e7i		−	0.465905i
$28$			1.62906e7i			0.178883i
$29$	2.91997e7			0.264356			0.132178	−	0.991226i	$-0.457803\pi$
$29$	2.91997e7			0.264356			0.132178	+	0.991226i	$0.457803\pi$
$30$	9.13247e6	−	2.06434e7i	0.0686154	−	0.155101i
$31$	2.33031e8			1.46192			0.730962	−	0.682418i	$-0.239072\pi$
$31$	2.33031e8			1.46192			0.730962	+	0.682418i	$0.239072\pi$
$32$			3.35544e7i			0.176777i
$33$		−	6.29736e7i		−	0.280112i
$34$	3.57814e7			0.135059
$35$	−1.01662e8	−	4.49744e7i	−0.327179	−	0.144741i
$36$	−1.70963e8			−0.471236
$37$			6.65053e8i			1.57669i	0.615232	+	0.788346i	$0.289062\pi$
$37$			6.65053e8i			1.57669i	−0.615232	+	0.788346i	$0.710938\pi$
$38$		−	4.66846e8i		−	0.955794i
$39$	−1.55696e8			−0.276327
$40$	−2.09398e8	−	9.26357e7i	−0.323327	−	0.143037i
$41$	−6.63914e8			−0.894954			−0.447477	−	0.894295i	$-0.647677\pi$
$41$	−6.63914e8			−0.894954			−0.447477	+	0.894295i	$0.647677\pi$
$42$		−	5.13922e7i		−	0.0606773i
$43$			4.11150e8i			0.426505i	0.976997	+	0.213252i	$0.0684057\pi$
$43$			4.11150e8i			0.426505i	−0.976997	+	0.213252i	$0.931594\pi$
$44$	−6.38776e8			−0.583928
$45$	4.71987e8	−	1.06690e9i	0.381295	−	0.861897i
$46$	1.93078e8			0.138218
$47$			2.47761e9i			1.57578i	0.615818	+	0.787888i	$0.288825\pi$
$47$			2.47761e9i			1.57578i	−0.615818	+	0.787888i	$0.711175\pi$
$48$		−	1.05855e8i		−	0.0599630i
$49$	1.72424e9			0.872004
$50$	1.15619e9	−	1.05101e9i	0.523233	−	0.475633i
$51$	−1.12880e8			−0.0458122
$52$			1.57931e9i			0.576037i
$53$		−	3.69178e9i		−	1.21260i	−0.795235	−	0.606302i	$-0.792652\pi$
$53$		−	3.69178e9i		−	1.21260i	0.795235	−	0.606302i	$-0.207348\pi$
$54$	1.11160e9			0.329445
$55$	1.76351e9	−	3.98631e9i	0.472479	−	1.06801i
$56$	−5.21299e8			−0.126489
$57$			1.47277e9i			0.324207i
$58$			9.34390e8i			0.186928i
$59$	−1.25820e9			−0.229121			−0.114561	−	0.993416i	$-0.536546\pi$
$59$	−1.25820e9			−0.229121			−0.114561	+	0.993416i	$0.536546\pi$
$60$	6.60590e8	+	2.92239e8i	0.109673	+	0.0485184i
$61$	−4.05784e9			−0.615150			−0.307575	−	0.951524i	$-0.599517\pi$
$61$	−4.05784e9			−0.615150			−0.307575	+	0.951524i	$0.599517\pi$
$62$			7.45700e9i			1.03374i
$63$		−	2.65607e9i		−	0.337183i
$64$	−1.07374e9			−0.125000
$65$	−9.85577e9	−	4.36011e9i	−1.05358	−	0.466094i
$66$	2.01516e9			0.198069
$67$			1.84180e10i			1.66660i	0.552821	+	0.833300i	$0.313551\pi$
$67$			1.84180e10i			1.66660i	−0.552821	+	0.833300i	$0.686449\pi$
$68$			1.14500e9i			0.0955010i
$69$	−6.09105e8			−0.0468837
$70$	1.43918e9	−	3.25319e9i	0.102347	−	0.231350i
$71$	3.19489e9			0.210153			0.105076	−	0.994464i	$-0.466491\pi$
$71$	3.19489e9			0.210153			0.105076	+	0.994464i	$0.466491\pi$
$72$		−	5.47081e9i		−	0.333214i
$73$		−	1.51712e10i		−	0.856535i	−0.903652	−	0.428267i	$-0.859124\pi$
$73$		−	1.51712e10i		−	0.856535i	0.903652	−	0.428267i	$-0.140876\pi$
$74$	−2.12817e10			−1.11489
$75$	−3.64746e9	+	3.31564e9i	−0.177482	+	0.161336i
$76$	1.49391e10			0.675848
$77$		−	9.92398e9i		−	0.417818i
$78$		−	4.98228e9i		−	0.195393i
$79$	4.26826e10			1.56064			0.780319	−	0.625382i	$-0.215057\pi$
$79$	4.26826e10			1.56064			0.780319	+	0.625382i	$0.215057\pi$
$80$	2.96434e9	−	6.70073e9i	0.101142	−	0.228627i
$81$	2.60690e10			0.830723
$82$		−	2.12453e10i		−	0.632828i
$83$			5.86787e10i			1.63512i	0.575840	+	0.817562i	$0.304675\pi$
$83$			5.86787e10i			1.63512i	−0.575840	+	0.817562i	$0.695325\pi$
$84$	1.64455e9			0.0429053
$85$	−7.14544e9	−	3.16108e9i	−0.174673	−	0.0772736i
$86$	−1.31568e10			−0.301584
$87$		−	2.94773e9i		−	0.0634063i
$88$		−	2.04408e10i		−	0.412899i
$89$	−3.40792e10			−0.646910			−0.323455	−	0.946244i	$-0.604844\pi$
$89$	−3.40792e10			−0.646910			−0.323455	+	0.946244i	$0.604844\pi$
$90$	3.41408e10	+	1.51036e10i	0.609453	+	0.269616i
$91$	−2.45361e10			−0.412172
$92$			6.17849e9i			0.0977348i
$93$		−	2.35247e10i		−	0.350645i
$94$	−7.92835e10			−1.11424
$95$	−4.12432e10	+	9.32279e10i	−0.546855	+	1.23614i
$96$	3.38735e9			0.0424002
$97$		−	1.37873e11i		−	1.63017i	−0.579339	−	0.815087i	$-0.696689\pi$
$97$		−	1.37873e11i		−	1.63017i	0.579339	−	0.815087i	$-0.303311\pi$
$98$			5.51756e10i			0.616600i
$99$	1.04148e11			1.10067
$100$	3.36323e10	+	3.69982e10i	0.336323	+	0.369982i
$101$	−2.07552e11			−1.96499			−0.982493	−	0.186302i	$-0.940350\pi$
$101$	−2.07552e11			−1.96499			−0.982493	+	0.186302i	$0.940350\pi$
$102$		−	3.61216e9i		−	0.0323941i
$103$			2.57852e10i			0.219162i	0.993978	+	0.109581i	$0.0349509\pi$
$103$			2.57852e10i			0.219162i	−0.993978	+	0.109581i	$0.965049\pi$
$104$	−5.05381e10			−0.407319
$105$	−4.54021e9	+	1.02629e10i	−0.0347164	+	0.0784744i
$106$	1.18137e11			0.857440
$107$		−	1.05201e11i		−	0.725119i	−0.931961	−	0.362559i	$-0.881903\pi$
$107$		−	1.05201e11i		−	0.725119i	0.931961	−	0.362559i	$-0.118097\pi$
$108$			3.55712e10i			0.232953i
$109$	2.37343e11			1.47751			0.738757	−	0.673972i	$-0.235413\pi$
$109$	2.37343e11			1.47751			0.738757	+	0.673972i	$0.235413\pi$
$110$	1.27562e11	+	5.64322e10i	0.755198	+	0.334093i
$111$	6.71377e10			0.378172
$112$		−	1.66816e10i		−	0.0894413i
$113$			1.77970e10i			0.0908689i	0.998967	+	0.0454344i	$0.0144672\pi$
$113$			1.77970e10i			0.0908689i	−0.998967	+	0.0454344i	$0.985533\pi$
$114$	−4.71285e10			−0.229249
$115$	−3.85571e10	−	1.70573e10i	−0.178758	−	0.0790811i
$116$	−2.99005e10			−0.132178
$117$		−	2.57496e11i		−	1.08580i
$118$		−	4.02625e10i		−	0.162013i
$119$	−1.77887e10			−0.0683338
$120$	−9.35165e9	+	2.11389e10i	−0.0343077	+	0.0775506i
$121$	1.03821e11			0.363886
$122$		−	1.29851e11i		−	0.434977i
$123$			6.70227e10i			0.214656i
$124$	−2.38624e11			−0.730962
$125$	−3.23739e11	+	1.07741e11i	−0.948835	+	0.315773i
$126$	8.49941e10			0.238425
$127$			5.56375e11i			1.49433i	0.664637	+	0.747167i	$0.268586\pi$
$127$			5.56375e11i			1.49433i	−0.664637	+	0.747167i	$0.731414\pi$
$128$		−	3.43597e10i		−	0.0883883i
$129$	4.15059e10			0.102298
$130$	1.39523e11	−	3.15385e11i	0.329578	−	0.744993i
$131$	−7.67575e10			−0.173832			−0.0869158	−	0.996216i	$-0.527701\pi$
$131$	−7.67575e10			−0.173832			−0.0869158	+	0.996216i	$0.527701\pi$
$132$			6.44850e10i			0.140056i
$133$			2.32093e11i			0.483590i
$134$	−5.89377e11			−1.17846
$135$	−2.21983e11	−	9.82034e10i	−0.426074	−	0.188491i
$136$	−3.66401e10			−0.0675294
$137$			5.87391e11i			1.03983i	0.854217	+	0.519917i	$0.174037\pi$
$137$			5.87391e11i			1.03983i	−0.854217	+	0.519917i	$0.825963\pi$
$138$		−	1.94914e10i		−	0.0331518i
$139$	2.71414e11			0.443660			0.221830	−	0.975085i	$-0.428797\pi$
$139$	2.71414e11			0.443660			0.221830	+	0.975085i	$0.428797\pi$
$140$	1.04102e11	+	4.60538e10i	0.163589	+	0.0723705i
$141$	2.50117e11			0.377953
$142$			1.02237e11i			0.148601i
$143$		−	9.62094e11i		−	1.34545i
$144$	1.75066e11			0.235618
$145$	8.25481e10	−	1.86595e11i	0.106951	−	0.241756i
$146$	4.85479e11			0.605662
$147$		−	1.74063e11i		−	0.209152i
$148$		−	6.81014e11i		−	0.788346i
$149$	4.91446e11			0.548215			0.274108	−	0.961699i	$-0.411618\pi$
$149$	4.91446e11			0.548215			0.274108	+	0.961699i	$0.411618\pi$
$150$	−1.06100e11	−	1.16719e11i	−0.114081	−	0.125498i
$151$	−3.53354e11			−0.366300			−0.183150	−	0.983085i	$-0.558629\pi$
$151$	−3.53354e11			−0.366300			−0.183150	+	0.983085i	$0.558629\pi$
$152$			4.78051e11i			0.477897i
$153$		−	1.86685e11i		−	0.180014i
$154$	3.17567e11			0.295442
$155$	6.58783e11	−	1.48914e12i	0.591450	−	1.33694i
$156$	1.59433e11			0.138163
$157$			1.61767e12i			1.35345i	0.736236	+	0.676725i	$0.236601\pi$
$157$			1.61767e12i			1.35345i	−0.736236	+	0.676725i	$0.763399\pi$
$158$			1.36584e12i			1.10354i
$159$	−3.72688e11			−0.290845
$160$	2.14423e11	+	9.48589e10i	0.161664	+	0.0715185i
$161$	−9.59885e10			−0.0699322
$162$			8.34207e11i			0.587410i
$163$		−	2.86025e11i		−	0.194703i	−0.995250	−	0.0973513i	$-0.968963\pi$
$163$		−	2.86025e11i		−	0.194703i	0.995250	−	0.0973513i	$-0.0310370\pi$
$164$	6.79848e11			0.447477
$165$	−4.02421e11	−	1.78027e11i	−0.256165	−	0.113325i
$166$	−1.87772e12			−1.15621
$167$		−	8.22338e11i		−	0.489903i	−0.969535	−	0.244951i	$-0.921228\pi$
$167$		−	8.22338e11i		−	0.489903i	0.969535	−	0.244951i	$-0.0787720\pi$
$168$			5.26256e10i			0.0303386i
$169$	−5.86526e11			−0.327273
$170$	1.01154e11	−	2.28654e11i	0.0546407	−	0.123512i
$171$	−2.43571e12			−1.27393
$172$		−	4.21018e11i		−	0.213252i
$173$			5.03556e11i			0.247055i	0.992341	+	0.123528i	$0.0394208\pi$
$173$			5.03556e11i			0.247055i	−0.992341	+	0.123528i	$0.960579\pi$
$174$	9.43275e10			0.0448350
$175$	−5.74801e11	+	5.22510e11i	−0.264733	+	0.240650i
$176$	6.54107e11			0.291964
$177$			1.27017e11i			0.0549551i
$178$		−	1.09053e12i		−	0.457435i
$179$	−1.28718e12			−0.523536			−0.261768	−	0.965131i	$-0.584306\pi$
$179$	−1.28718e12			−0.523536			−0.261768	+	0.965131i	$0.584306\pi$
$180$	−4.83315e11	+	1.09251e12i	−0.190648	+	0.430948i
$181$	1.43456e12			0.548890			0.274445	−	0.961603i	$-0.411506\pi$
$181$	1.43456e12			0.548890			0.274445	+	0.961603i	$0.411506\pi$
$182$		−	7.85156e11i		−	0.291449i
$183$			4.09642e11i			0.147545i
$184$	−1.97712e11			−0.0691089
$185$	4.24990e12	+	1.88012e12i	1.44190	+	0.637882i
$186$	7.52790e11			0.247943
$187$		−	6.97518e11i		−	0.223063i
$188$		−	2.53707e12i		−	0.787888i
$189$	−5.52631e11			−0.166685
$190$	−2.98329e12	−	1.31978e12i	−0.874080	−	0.386685i
$191$	6.04865e12			1.72177			0.860885	−	0.508800i	$-0.169911\pi$
$191$	6.04865e12			1.72177			0.860885	+	0.508800i	$0.169911\pi$
$192$			1.08395e11i			0.0299815i
$193$			3.02913e12i			0.814241i	0.913375	+	0.407120i	$0.133467\pi$
$193$			3.02913e12i			0.814241i	−0.913375	+	0.407120i	$0.866533\pi$
$194$	4.41193e12			1.15271
$195$	−4.40156e11	+	9.94949e11i	−0.111793	+	0.252703i
$196$	−1.76562e12			−0.436002
$197$		−	5.19664e12i		−	1.24784i	−0.781489	−	0.623920i	$-0.785539\pi$
$197$		−	5.19664e12i		−	1.24784i	0.781489	−	0.623920i	$-0.214461\pi$
$198$			3.33273e12i			0.778291i
$199$	−5.20023e11			−0.118122			−0.0590610	−	0.998254i	$-0.518811\pi$
$199$	−5.20023e11			−0.118122			−0.0590610	+	0.998254i	$0.518811\pi$
$200$	−1.18394e12	+	1.07623e12i	−0.261617	+	0.237817i
$201$	1.85931e12			0.399737
$202$		−	6.64166e12i		−	1.38945i
$203$		−	4.64532e11i		−	0.0945774i
$204$	1.15589e11			0.0229061
$205$	−1.87690e12	+	4.24262e12i	−0.362071	+	0.818442i
$206$	−8.25126e11			−0.154971
$207$		−	1.00736e12i		−	0.184224i
$208$		−	1.61722e12i		−	0.288018i
$209$	−9.10066e12			−1.57859
$210$	−3.28412e11	−	1.45287e11i	−0.0554898	−	0.0245482i
$211$	−2.82884e12			−0.465645			−0.232822	−	0.972519i	$-0.574796\pi$
$211$	−2.82884e12			−0.465645			−0.232822	+	0.972519i	$0.574796\pi$
$212$			3.78038e12i			0.606302i
$213$		−	3.22527e11i		−	0.0504056i
$214$	3.36643e12			0.512736
$215$	2.62738e12	+	1.16233e12i	0.390042	+	0.172551i
$216$	−1.13828e12			−0.164722
$217$		−	3.70724e12i		−	0.523025i
$218$			7.59499e12i			1.04476i
$219$	−1.53155e12			−0.205441
$220$	−1.80583e12	+	4.08198e12i	−0.236239	+	0.534006i
$221$	−1.72455e12			−0.220048
$222$			2.14841e12i			0.267408i
$223$			6.97675e12i			0.847182i	0.905854	+	0.423591i	$0.139231\pi$
$223$			6.97675e12i			0.847182i	−0.905854	+	0.423591i	$0.860769\pi$
$224$	5.33810e11			0.0632445
$225$	−5.48351e12	−	6.03229e12i	−0.633950	−	0.697395i
$226$	−5.69504e11			−0.0642540
$227$		−	3.33075e12i		−	0.366775i	−0.983041	−	0.183388i	$-0.941294\pi$
$227$		−	3.33075e12i		−	0.366775i	0.983041	−	0.183388i	$-0.0587063\pi$
$228$		−	1.50811e12i		−	0.162103i
$229$	4.95393e12			0.519822			0.259911	−	0.965633i	$-0.416307\pi$
$229$	4.95393e12			0.519822			0.259911	+	0.965633i	$0.416307\pi$
$230$	5.45834e11	−	1.23383e12i	0.0559188	−	0.126401i
$231$	−1.00183e12			−0.100214
$232$		−	9.56816e11i		−	0.0934640i
$233$		−	1.20602e13i		−	1.15053i	−0.817968	−	0.575264i	$-0.804899\pi$
$233$		−	1.20602e13i		−	1.15053i	0.817968	−	0.575264i	$-0.195101\pi$
$234$	8.23987e12			0.767774
$235$	1.58327e13	+	7.00424e12i	1.44106	+	0.637511i
$236$	1.28840e12			0.114561
$237$		−	4.30885e12i		−	0.374322i
$238$		−	5.69238e11i		−	0.0483193i
$239$	−4.41187e12			−0.365961			−0.182980	−	0.983117i	$-0.558574\pi$
$239$	−4.41187e12			−0.365961			−0.182980	+	0.983117i	$0.558574\pi$
$240$	−6.76444e11	−	2.99253e11i	−0.0548365	−	0.0242592i
$241$	2.16312e12			0.171390			0.0856952	−	0.996321i	$-0.472689\pi$
$241$	2.16312e12			0.171390			0.0856952	+	0.996321i	$0.472689\pi$
$242$			3.32227e12i			0.257306i
$243$		−	8.78532e12i		−	0.665156i
$244$	4.15523e12			0.307575
$245$	4.87445e12	−	1.10184e13i	0.352786	−	0.797454i
$246$	−2.14473e12			−0.151785
$247$			2.25005e13i			1.55725i
$248$		−	7.63596e12i		−	0.516868i
$249$	5.92366e12			0.392188
$250$	−3.44771e12	−	1.03597e13i	−0.223285	−	0.670927i
$251$	−1.06811e13			−0.676723			−0.338361	−	0.941016i	$-0.609873\pi$
$251$	−1.06811e13			−0.676723			−0.338361	+	0.941016i	$0.609873\pi$
$252$			2.71981e12i			0.168592i
$253$		−	3.76384e12i		−	0.228280i
$254$	−1.78040e13			−1.05665
$255$	−3.19113e11	+	7.21338e11i	−0.0185342	+	0.0418955i
$256$	1.09951e12			0.0625000
$257$			2.32150e13i			1.29162i	0.763496	+	0.645812i	$0.223481\pi$
$257$			2.32150e13i			1.29162i	−0.763496	+	0.645812i	$0.776519\pi$
$258$			1.32819e12i			0.0723356i
$259$	1.05802e13			0.564085
$260$	1.00923e13	+	4.46475e12i	0.526790	+	0.233047i
$261$	4.87506e12			0.249148
$262$		−	2.45624e12i		−	0.122917i
$263$			3.54305e13i			1.73628i	0.496317	+	0.868141i	$0.334685\pi$
$263$			3.54305e13i			1.73628i	−0.496317	+	0.868141i	$0.665315\pi$
$264$	−2.06352e12			−0.0990346
$265$	−2.35916e13	−	1.04367e13i	−1.10893	−	0.490583i
$266$	−7.42696e12			−0.341950
$267$			3.44032e12i			0.155163i
$268$		−	1.88601e13i		−	0.833300i
$269$	−2.98211e13			−1.29088			−0.645441	−	0.763810i	$-0.723326\pi$
$269$	−2.98211e13			−1.29088			−0.645441	+	0.763810i	$0.723326\pi$
$270$	3.14251e12	−	7.10347e12i	0.133283	−	0.301280i
$271$	5.87087e12			0.243989			0.121995	−	0.992531i	$-0.461071\pi$
$271$	5.87087e12			0.243989			0.121995	+	0.992531i	$0.461071\pi$
$272$		−	1.17248e12i		−	0.0477505i
$273$			2.47694e12i			0.0988601i
$274$	−1.87965e13			−0.735274
$275$	−2.04883e13	−	2.25387e13i	−0.785554	−	0.864171i
$276$	6.23723e11			0.0234419
$277$			1.03428e13i			0.381066i	0.981681	+	0.190533i	$0.0610215\pi$
$277$			1.03428e13i			0.381066i	−0.981681	+	0.190533i	$0.938978\pi$
$278$			8.68524e12i			0.313715i
$279$	3.89059e13			1.37782
$280$	−1.47372e12	+	3.33127e12i	−0.0511736	+	0.115675i
$281$	1.50495e13			0.512432			0.256216	−	0.966620i	$-0.417524\pi$
$281$	1.50495e13			0.512432			0.256216	+	0.966620i	$0.417524\pi$
$282$			8.00373e12i			0.267253i
$283$		−	5.55117e13i		−	1.81785i	−0.416955	−	0.908927i	$-0.636903\pi$
$283$		−	5.55117e13i		−	1.81785i	0.416955	−	0.908927i	$-0.363097\pi$
$284$	−3.27157e12			−0.105076
$285$	9.41144e12	+	4.16354e12i	0.296489	+	0.131164i
$286$	3.07870e13			0.951380
$287$			1.05621e13i			0.320183i
$288$			5.60211e12i			0.166607i
$289$	3.30216e13			0.963518
$290$	5.97105e12	+	2.64154e12i	0.170947	+	0.0756254i
$291$	−1.39184e13			−0.391000
$292$			1.55353e13i			0.428267i
$293$		−	5.82419e12i		−	0.157566i	−0.996892	−	0.0787832i	$-0.974897\pi$
$293$		−	5.82419e12i		−	0.157566i	0.996892	−	0.0787832i	$-0.0251035\pi$
$294$	5.57002e12			0.147893
$295$	−3.55696e12	+	8.04032e12i	−0.0926954	+	0.209533i
$296$	2.17925e13			0.557445
$297$		−	2.16694e13i		−	0.544110i
$298$			1.57263e13i			0.387647i
$299$	−9.30574e12			−0.225195
$300$	3.73500e12	−	3.39521e12i	0.0887408	−	0.0806678i
$301$	6.54090e12			0.152589
$302$		−	1.13073e13i		−	0.259013i
$303$			2.09525e13i			0.471305i
$304$	−1.52976e13			−0.337924
$305$	−1.14716e13	+	2.59309e13i	−0.248871	+	0.562559i
$306$	5.97391e12			0.127289
$307$		−	7.34987e13i		−	1.53822i	−0.639117	−	0.769110i	$-0.720700\pi$
$307$		−	7.34987e13i		−	1.53822i	0.639117	−	0.769110i	$-0.279300\pi$
$308$			1.01622e13i			0.208909i
$309$	2.60304e12			0.0525664
$310$	4.76525e13	+	2.10811e13i	0.945359	+	0.418218i
$311$	−5.27276e13			−1.02768			−0.513838	−	0.857887i	$-0.671777\pi$
$311$	−5.27276e13			−1.02768			−0.513838	+	0.857887i	$0.671777\pi$
$312$			5.10186e12i			0.0976963i
$313$			1.10252e12i			0.0207440i	0.999946	+	0.0103720i	$0.00330157\pi$
$313$			1.10252e12i			0.0207440i	−0.999946	+	0.0103720i	$0.996698\pi$
$314$	−5.17655e13			−0.957033
$315$	−1.69731e13	−	7.50875e12i	−0.308357	−	0.136414i
$316$	−4.37070e13			−0.780319
$317$		−	9.68269e12i		−	0.169891i	−0.996386	−	0.0849455i	$-0.972928\pi$
$317$		−	9.68269e12i		−	0.169891i	0.996386	−	0.0849455i	$-0.0270716\pi$
$318$		−	1.19260e13i		−	0.205659i
$319$	1.82149e13			0.308730
$320$	−3.03549e12	+	6.86155e12i	−0.0505712	+	0.114313i
$321$	−1.06201e13			−0.173921
$322$		−	3.07163e12i		−	0.0494495i
$323$			1.63129e13i			0.258177i
$324$	−2.66946e13			−0.415361
$325$	−5.57249e13	+	5.06554e13i	−0.852493	+	0.774938i
$326$	9.15279e12			0.137676
$327$		−	2.39600e13i		−	0.354384i
$328$			2.17551e13i			0.316414i
$329$	3.94158e13			0.563758
$330$	5.69688e12	−	1.28775e13i	0.0801328	−	0.181136i
$331$	−8.90833e13			−1.23237			−0.616187	−	0.787600i	$-0.711323\pi$
$331$	−8.90833e13			−1.23237			−0.616187	+	0.787600i	$0.711323\pi$
$332$		−	6.00870e13i		−	0.817562i
$333$			1.11035e14i			1.48599i
$334$	2.63148e13			0.346414
$335$	1.17697e14	+	5.20681e13i	1.52412	+	0.674256i
$336$	−1.68402e12			−0.0214527
$337$			4.89653e13i			0.613655i	0.951765	+	0.306827i	$0.0992674\pi$
$337$			4.89653e13i			0.613655i	−0.951765	+	0.306827i	$0.900733\pi$
$338$		−	1.87688e13i		−	0.231417i
$339$	1.79662e12			0.0217951
$340$	7.31693e12	+	3.23694e12i	0.0873363	+	0.0386368i
$341$	1.45366e14			1.70731
$342$		−	7.79428e13i		−	0.900808i
$343$		−	5.88874e13i		−	0.669738i
$344$	1.34726e13			0.150792
$345$	−1.72195e12	+	3.89237e12i	−0.0189677	+	0.0428755i
$346$	−1.61138e13			−0.174694
$347$		−	1.41507e14i		−	1.50997i	−0.655744	−	0.754983i	$-0.727645\pi$
$347$		−	1.41507e14i		−	1.50997i	0.655744	−	0.754983i	$-0.272355\pi$
$348$			3.01848e12i			0.0317032i
$349$	−1.17661e13			−0.121645			−0.0608223	−	0.998149i	$-0.519372\pi$
$349$	−1.17661e13			−0.121645			−0.0608223	+	0.998149i	$0.519372\pi$
$350$	−1.67203e13	−	1.83936e13i	−0.170165	−	0.187195i
$351$	−5.35756e13			−0.536757
$352$			2.09314e13i			0.206450i
$353$			2.34718e13i			0.227921i	0.993485	+	0.113961i	$0.0363538\pi$
$353$			2.34718e13i			0.227921i	−0.993485	+	0.113961i	$0.963646\pi$
$354$	−4.06454e12			−0.0388591
$355$	9.03202e12	−	2.04164e13i	0.0850215	−	0.192186i
$356$	3.48971e13			0.323455
$357$			1.79578e12i			0.0163900i
$358$		−	4.11897e13i		−	0.370196i
$359$	1.12805e14			0.998413			0.499207	−	0.866483i	$-0.333625\pi$
$359$	1.12805e14			0.998413			0.499207	+	0.866483i	$0.333625\pi$
$360$	−3.49602e13	−	1.54661e13i	−0.304726	−	0.134808i
$361$	9.63471e13			0.827083
$362$			4.59058e13i			0.388124i
$363$		−	1.04808e13i		−	0.0872786i
$364$	2.51250e13			0.206086
$365$	−9.69489e13	−	4.28893e13i	−0.783307	−	0.346528i
$366$	−1.31086e13			−0.104330
$367$			1.66738e14i			1.30729i	0.756802	+	0.653645i	$0.226761\pi$
$367$			1.66738e14i			1.30729i	−0.756802	+	0.653645i	$0.773239\pi$
$368$		−	6.32677e12i		−	0.0488674i
$369$	−1.10844e14			−0.843469
$370$	−6.01637e13	+	1.35997e14i	−0.451051	+	1.01957i
$371$	−5.87318e13			−0.433827
$372$			2.40893e13i			0.175323i
$373$		−	1.39847e14i		−	1.00290i	−0.865188	−	0.501448i	$-0.832801\pi$
$373$		−	1.39847e14i		−	1.00290i	0.865188	−	0.501448i	$-0.167199\pi$
$374$	2.23206e13			0.157729
$375$	1.08765e13	+	3.26818e13i	0.0757388	+	0.227580i
$376$	8.11863e13			0.557121
$377$		−	4.50347e13i		−	0.304558i
$378$		−	1.76842e13i		−	0.117864i
$379$	−2.46176e14			−1.61708			−0.808539	−	0.588443i	$-0.799741\pi$
$379$	−2.46176e14			−1.61708			−0.808539	+	0.588443i	$0.799741\pi$
$380$	4.22330e13	−	9.54654e13i	0.273428	−	0.618068i
$381$	5.61666e13			0.358419
$382$			1.93557e14i			1.21748i
$383$			1.19986e14i			0.743941i	0.928245	+	0.371970i	$0.121318\pi$
$383$			1.19986e14i			0.743941i	−0.928245	+	0.371970i	$0.878682\pi$
$384$	−3.46864e12			−0.0212001
$385$	−6.34173e13	−	2.80553e13i	−0.382097	−	0.169036i
$386$	−9.69322e13			−0.575755
$387$			6.86439e13i			0.401968i
$388$			1.41182e14i			0.815087i
$389$	−9.66133e13			−0.549939			−0.274969	−	0.961453i	$-0.588668\pi$
$389$	−9.66133e13			−0.549939			−0.274969	+	0.961453i	$0.588668\pi$
$390$	−3.18384e13	−	1.40850e13i	−0.178688	−	0.0790499i
$391$	−6.74666e12			−0.0373351
$392$		−	5.64998e13i		−	0.308300i
$393$			7.74873e12i			0.0416938i
$394$	1.66293e14			0.882355
$395$	1.20664e14	−	2.72755e14i	0.631387	−	1.42721i
$396$	−1.06647e14			−0.550335
$397$		−	3.07115e13i		−	0.156298i	−0.996942	−	0.0781489i	$-0.975099\pi$
$397$		−	3.07115e13i		−	0.156298i	0.996942	−	0.0781489i	$-0.0249010\pi$
$398$		−	1.66407e13i		−	0.0835249i
$399$	2.34299e13			0.115990
$400$	−3.44395e13	−	3.78861e13i	−0.168162	−	0.184991i
$401$	1.38014e14			0.664707			0.332354	−	0.943155i	$-0.392157\pi$
$401$	1.38014e14			0.664707			0.332354	+	0.943155i	$0.392157\pi$
$402$			5.94981e13i			0.282657i
$403$		−	3.59404e14i		−	1.68424i
$404$	2.12533e14			0.982493
$405$	7.36974e13	−	1.66589e14i	0.336085	−	0.759702i
$406$	1.48650e13			0.0668763
$407$			4.14863e14i			1.84135i
$408$			3.69885e12i			0.0161970i
$409$	−1.98577e14			−0.857927			−0.428963	−	0.903322i	$-0.641121\pi$
$409$	−1.98577e14			−0.857927			−0.428963	+	0.903322i	$0.641121\pi$
$410$	−1.35764e14	−	6.00607e13i	−0.578726	−	0.256023i
$411$	5.92976e13			0.249406
$412$		−	2.64040e13i		−	0.109581i
$413$			2.00165e13i			0.0819715i
$414$	3.22355e13			0.130266
$415$	3.74975e14	+	1.65886e14i	1.49533	+	0.661522i
$416$	5.17510e13			0.203660
$417$		−	2.73995e13i		−	0.106413i
$418$		−	2.91221e14i		−	1.11623i
$419$	3.42176e14			1.29441			0.647205	−	0.762316i	$-0.275938\pi$
$419$	3.42176e14			1.29441			0.647205	+	0.762316i	$0.275938\pi$
$420$	4.64917e12	−	1.05092e13i	0.0173582	−	0.0392372i
$421$	−3.12187e13			−0.115044			−0.0575219	−	0.998344i	$-0.518320\pi$
$421$	−3.12187e13			−0.115044			−0.0575219	+	0.998344i	$0.518320\pi$
$422$		−	9.05229e13i		−	0.329261i
$423$			4.13652e14i			1.48512i
$424$	−1.20972e14			−0.428720
$425$	−4.04006e13	+	3.67252e13i	−0.141334	+	0.128477i
$426$	1.03209e13			0.0356421
$427$			6.45553e13i			0.220079i
$428$			1.07726e14i			0.362559i
$429$	−9.71242e13			−0.322710
$430$	−3.71945e13	+	8.40761e13i	−0.122012	+	0.275801i
$431$	−4.22057e14			−1.36693			−0.683465	−	0.729983i	$-0.739528\pi$
$431$	−4.22057e14			−1.36693			−0.683465	+	0.729983i	$0.739528\pi$
$432$		−	3.64249e13i		−	0.116476i
$433$		−	3.63091e14i		−	1.14639i	−0.819419	−	0.573194i	$-0.805704\pi$
$433$		−	3.63091e14i		−	1.14639i	0.819419	−	0.573194i	$-0.194296\pi$
$434$	1.18632e14			0.369835
$435$	−1.88369e13	−	8.33329e12i	−0.0579855	−	0.0256523i
$436$	−2.43040e14			−0.738757
$437$			8.80250e13i			0.264215i
$438$		−	4.90095e13i		−	0.145269i
$439$	8.98176e13			0.262910			0.131455	−	0.991322i	$-0.458035\pi$
$439$	8.98176e13			0.262910			0.131455	+	0.991322i	$0.458035\pi$
$440$	−1.30623e14	−	5.77866e13i	−0.377599	−	0.167046i
$441$	2.87872e14			0.821839
$442$		−	5.51855e13i		−	0.155598i
$443$			2.31585e14i			0.644895i	0.946587	+	0.322448i	$0.104506\pi$
$443$			2.31585e14i			0.644895i	−0.946587	+	0.322448i	$0.895494\pi$
$444$	−6.87490e13			−0.189086
$445$	−9.63424e13	+	2.17777e14i	−0.261720	+	0.591604i
$446$	−2.23256e14			−0.599048
$447$		−	4.96118e13i		−	0.131490i
$448$			1.70819e13i			0.0447206i
$449$	−5.36475e14			−1.38738			−0.693689	−	0.720275i	$-0.744016\pi$
$449$	−5.36475e14			−1.38738			−0.693689	+	0.720275i	$0.744016\pi$
$450$	1.93033e14	−	1.75472e14i	0.493132	−	0.448270i
$451$	−4.14153e14			−1.04518
$452$		−	1.82241e13i		−	0.0454344i
$453$			3.56714e13i			0.0878578i
$454$	1.06584e14			0.259349
$455$	−6.93640e13	+	1.56793e14i	−0.166752	+	0.376934i
$456$	4.82596e13			0.114624
$457$		−	1.86645e14i		−	0.438002i	−0.975725	−	0.219001i	$-0.929720\pi$
$457$		−	1.86645e14i		−	0.438002i	0.975725	−	0.219001i	$-0.0702799\pi$
$458$			1.58526e14i			0.367569i
$459$	−3.88423e13			−0.0889888
$460$	3.94825e13	+	1.74667e13i	0.0893791	+	0.0395405i
$461$	4.16181e14			0.930951			0.465476	−	0.885061i	$-0.345883\pi$
$461$	4.16181e14			0.930951			0.465476	+	0.885061i	$0.345883\pi$
$462$		−	3.20587e13i		−	0.0708623i
$463$		−	9.23323e13i		−	0.201678i	−0.994903	−	0.100839i	$-0.967847\pi$
$463$		−	9.23323e13i		−	0.201678i	0.994903	−	0.100839i	$-0.0321527\pi$
$464$	3.06181e13			0.0660890
$465$	−1.50330e14	−	6.65047e13i	−0.320667	−	0.141860i
$466$	3.85927e14			0.813546
$467$		−	6.81230e14i		−	1.41922i	−0.704592	−	0.709612i	$-0.748870\pi$
$467$		−	6.81230e14i		−	1.41922i	0.704592	−	0.709612i	$-0.251130\pi$
$468$			2.63676e14i			0.542898i
$469$	2.93008e14			0.596252
$470$	−2.24136e14	+	5.06646e14i	−0.450789	+	1.01898i
$471$	1.63305e14			0.324627
$472$			4.12288e13i			0.0810065i
$473$			2.56477e14i			0.498096i
$474$	1.37883e14			0.264685
$475$	4.79161e14	+	5.27114e14i	0.909214	+	1.00021i
$476$	1.82156e13			0.0341669
$477$		−	6.16365e14i		−	1.14284i
$478$		−	1.41180e14i		−	0.258773i
$479$	2.62125e14			0.474966			0.237483	−	0.971392i	$-0.423678\pi$
$479$	2.62125e14			0.474966			0.237483	+	0.971392i	$0.423678\pi$
$480$	9.57609e12	−	2.16462e13i	0.0171538	−	0.0387753i
$481$	1.02571e15			1.81647
$482$			6.92198e13i			0.121191i
$483$			9.69012e12i			0.0167734i
$484$	−1.06313e14			−0.181943
$485$	−8.81050e14	−	3.89769e14i	−1.49081	−	0.659519i
$486$	2.81130e14			0.470336
$487$		−	5.11692e14i		−	0.846446i	−0.906025	−	0.423223i	$-0.860899\pi$
$487$		−	5.11692e14i		−	0.846446i	0.906025	−	0.423223i	$-0.139101\pi$
$488$			1.32967e14i			0.217488i
$489$	−2.88744e13			−0.0466998
$490$	3.52589e14	+	1.55982e14i	0.563885	+	0.249458i
$491$	−1.06861e15			−1.68994			−0.844971	−	0.534812i	$-0.820382\pi$
$491$	−1.06861e15			−1.68994			−0.844971	+	0.534812i	$0.820382\pi$
$492$		−	6.86313e13i		−	0.107328i
$493$		−	3.26502e13i		−	0.0504925i
$494$	−7.20017e14			−1.10114
$495$	2.94428e14	−	6.65538e14i	0.445298	−	1.00657i
$496$	2.44351e14			0.365481
$497$		−	5.08269e13i		−	0.0751854i
$498$			1.89557e14i			0.277318i
$499$	−1.64668e14			−0.238263			−0.119132	−	0.992878i	$-0.538011\pi$
$499$	−1.64668e14			−0.238263			−0.119132	+	0.992878i	$0.538011\pi$
$500$	3.31509e14	−	1.10327e14i	0.474417	−	0.157887i
$501$	−8.30157e13			−0.117504
$502$		−	3.41796e14i		−	0.478515i
$503$			1.55884e14i			0.215862i	0.994158	+	0.107931i	$0.0344226\pi$
$503$			1.55884e14i			0.215862i	−0.994158	+	0.107931i	$0.965577\pi$
$504$	−8.70340e13			−0.119212
$505$	−5.86753e14	+	1.32632e15i	−0.794973	+	1.79699i
$506$	1.20443e14			0.161418
$507$			5.92103e13i			0.0784971i
$508$		−	5.69728e14i		−	0.747167i
$509$	5.27594e14			0.684466			0.342233	−	0.939615i	$-0.388817\pi$
$509$	5.27594e14			0.684466			0.342233	+	0.939615i	$0.388817\pi$
$510$	−2.30828e13	−	1.02116e13i	−0.0296246	−	0.0131057i
$511$	−2.41356e14			−0.306438
$512$			3.51844e13i			0.0441942i
$513$			5.06783e14i			0.629762i
$514$	−7.42879e14			−0.913316
$515$	1.64775e14	+	7.28952e13i	0.200425	+	0.0886664i
$516$	−4.25021e13			−0.0511490
$517$			1.54554e15i			1.84028i
$518$			3.38566e14i			0.398869i
$519$	5.08344e13			0.0592567
$520$	−1.42872e14	+	3.22954e14i	−0.164789	+	0.372497i
$521$	−8.60186e14			−0.981713			−0.490857	−	0.871240i	$-0.663316\pi$
$521$	−8.60186e14			−0.981713			−0.490857	+	0.871240i	$0.663316\pi$
$522$			1.56002e14i			0.176174i
$523$		−	1.14697e15i		−	1.28171i	−0.767661	−	0.640857i	$-0.778579\pi$
$523$		−	1.14697e15i		−	1.28171i	0.767661	−	0.640857i	$-0.221421\pi$
$524$	7.85997e13			0.0869158
$525$	5.27478e13	+	5.80267e13i	0.0577202	+	0.0634967i
$526$	−1.13378e15			−1.22774
$527$		−	2.60568e14i		−	0.279230i
$528$		−	6.60326e13i		−	0.0700280i
$529$	9.16404e14			0.961792
$530$	3.33975e14	−	7.54932e14i	0.346894	−	0.784135i
$531$	−2.10065e14			−0.215940
$532$		−	2.37663e14i		−	0.241795i
$533$			1.02395e15i			1.03105i
$534$	−1.10090e14			−0.109717
$535$	−6.72267e14	−	2.97405e14i	−0.663126	−	0.293361i
$536$	6.03522e14			0.589232
$537$			1.29942e14i			0.125571i
$538$		−	9.54276e14i		−	0.912791i
$539$	1.07559e15			1.01837
$540$	2.27311e14	+	1.00560e14i	0.213037	+	0.0942456i
$541$	1.24370e15			1.15380			0.576898	−	0.816816i	$-0.304263\pi$
$541$	1.24370e15			1.15380			0.576898	+	0.816816i	$0.304263\pi$
$542$			1.87868e14i			0.172527i
$543$		−	1.44820e14i		−	0.131652i
$544$	3.75195e13			0.0337647
$545$	6.70974e14	−	1.51670e15i	0.597757	−	1.35120i
$546$	−7.92621e13			−0.0699047
$547$			1.40219e15i			1.22427i	0.790755	+	0.612133i	$0.209688\pi$
$547$			1.40219e15i			1.22427i	−0.790755	+	0.612133i	$0.790312\pi$
$548$		−	6.01488e14i		−	0.519917i
$549$	−6.77481e14			−0.579761
$550$	7.21239e14	−	6.55625e14i	0.611061	−	0.555470i
$551$	−4.25993e14			−0.357329
$552$			1.99591e13i			0.0165759i
$553$		−	6.79029e14i		−	0.558342i
$554$	−3.30970e14			−0.269454
$555$	1.89799e14	−	4.29031e14i	0.152997	−	0.345841i
$556$	−2.77928e14			−0.221830
$557$		−	4.54370e14i		−	0.359092i	−0.983750	−	0.179546i	$-0.942537\pi$
$557$		−	4.54370e14i		−	0.359092i	0.983750	−	0.179546i	$-0.0574629\pi$
$558$			1.24499e15i			0.974266i
$559$	6.34116e14			0.491365
$560$	−1.06600e14	−	4.71591e13i	−0.0817947	−	0.0361852i
$561$	−7.04150e13			−0.0535020
$562$			4.81583e14i			0.362344i
$563$			3.40271e14i			0.253530i	0.991933	+	0.126765i	$0.0404594\pi$
$563$			3.40271e14i			0.253530i	−0.991933	+	0.126765i	$0.959541\pi$
$564$	−2.56119e14			−0.188976
$565$	1.13728e14	+	5.03124e13i	0.0831002	+	0.0367628i
$566$	1.77637e15			1.28542
$567$		−	4.14726e14i		−	0.297204i
$568$		−	1.04690e14i		−	0.0743003i
$569$	1.02622e15			0.721311			0.360656	−	0.932699i	$-0.382553\pi$
$569$	1.02622e15			0.721311			0.360656	+	0.932699i	$0.382553\pi$
$570$	−1.33233e14	+	3.01166e14i	−0.0927471	+	0.209650i
$571$	−1.81645e15			−1.25235			−0.626174	−	0.779683i	$-0.715380\pi$
$571$	−1.81645e15			−1.25235			−0.626174	+	0.779683i	$0.715380\pi$
$572$			9.85184e14i			0.672727i
$573$		−	6.10616e14i		−	0.412970i
$574$	−3.37986e14			−0.226404
$575$	−2.18003e14	+	1.98171e14i	−0.144640	+	0.131482i
$576$	−1.79268e14			−0.117809
$577$			2.60905e15i			1.69830i	0.528148	+	0.849152i	$0.322887\pi$
$577$			2.60905e15i			1.69830i	−0.528148	+	0.849152i	$0.677113\pi$
$578$			1.05669e15i			0.681310i
$579$	3.05793e14			0.195297
$580$	−8.45292e13	+	1.91074e14i	−0.0534753	+	0.120878i
$581$	9.33507e14			0.584990
$582$		−	4.45388e14i		−	0.276479i
$583$		−	2.30295e15i		−	1.41614i
$584$	−4.97131e14			−0.302831
$585$	−1.64548e15	−	7.27945e14i	−0.992968	−	0.439280i
$586$	1.86374e14			0.111416
$587$			2.46315e14i			0.145875i	0.997337	+	0.0729375i	$0.0232374\pi$
$587$			2.46315e14i			0.145875i	−0.997337	+	0.0729375i	$0.976763\pi$
$588$			1.78241e14i			0.104576i
$589$	−3.39968e15			−1.97608
$590$	−2.57290e14	−	1.13823e14i	−0.148162	−	0.0655456i
$591$	−5.24605e14			−0.299296
$592$			6.97359e14i			0.394173i
$593$		−	1.31447e15i		−	0.736121i	−0.929802	−	0.368060i	$-0.880022\pi$
$593$		−	1.31447e15i		−	0.736121i	0.929802	−	0.368060i	$-0.119978\pi$
$594$	6.93421e14			0.384744
$595$	−5.02889e13	+	1.13675e14i	−0.0276458	+	0.0624918i
$596$	−5.03240e14			−0.274108
$597$			5.24968e13i			0.0283318i
$598$		−	2.97784e14i		−	0.159237i
$599$	−2.18539e15			−1.15793			−0.578963	−	0.815354i	$-0.696542\pi$
$599$	−2.18539e15			−1.15793			−0.578963	+	0.815354i	$0.696542\pi$
$600$	1.08647e14	+	1.19520e14i	0.0570407	+	0.0627492i
$601$	9.81120e14			0.510402			0.255201	−	0.966888i	$-0.417858\pi$
$601$	9.81120e14			0.510402			0.255201	+	0.966888i	$0.417858\pi$
$602$			2.09309e14i			0.107896i
$603$			3.07500e15i			1.57072i
$604$	3.61835e14			0.183150
$605$	2.93503e14	−	6.63448e14i	0.147217	−	0.332776i
$606$	−6.70481e14			−0.333263
$607$		−	1.08458e15i		−	0.534225i	−0.963665	−	0.267112i	$-0.913930\pi$
$607$		−	1.08458e15i		−	0.534225i	0.963665	−	0.267112i	$-0.0860695\pi$
$608$		−	4.89524e14i		−	0.238948i
$609$	−4.68949e13			−0.0226846
$610$	−8.29788e14	−	3.67091e14i	−0.397789	−	0.175978i
$611$	3.82121e15			1.81541
$612$			1.91165e14i			0.0900069i
$613$			7.52110e13i			0.0350953i	0.999846	+	0.0175476i	$0.00558588\pi$
$613$			7.52110e13i			0.0350953i	−0.999846	+	0.0175476i	$0.994414\pi$
$614$	2.35196e15			1.08769
$615$	4.28296e14	+	1.89474e14i	0.196305	+	0.0868435i
$616$	−3.25189e14			−0.147721
$617$		−	2.63722e15i		−	1.18735i	−0.804705	−	0.593675i	$-0.797677\pi$
$617$		−	2.63722e15i		−	1.18735i	0.804705	−	0.593675i	$-0.202323\pi$
$618$			8.32972e13i			0.0371701i
$619$	1.97316e15			0.872696			0.436348	−	0.899778i	$-0.356272\pi$
$619$	1.97316e15			0.872696			0.436348	+	0.899778i	$0.356272\pi$
$620$	−6.74594e14	+	1.52488e15i	−0.295725	+	0.668470i
$621$	−2.09595e14			−0.0910703
$622$		−	1.68728e15i		−	0.726676i
$623$			5.42158e14i			0.231442i
$624$	−1.63259e14			−0.0690817
$625$	−2.26719e14	+	2.37338e15i	−0.0950929	+	0.995468i
$626$	−3.52807e13			−0.0146682
$627$			9.18719e14i			0.378627i
$628$		−	1.65650e15i		−	0.676725i
$629$	7.43641e14			0.301151
$630$	2.40280e14	−	5.43139e14i	0.0964594	−	0.218041i
$631$	−4.42271e14			−0.176006			−0.0880028	−	0.996120i	$-0.528048\pi$
$631$	−4.42271e14			−0.176006			−0.0880028	+	0.996120i	$0.528048\pi$
$632$		−	1.39862e15i		−	0.551769i
$633$			2.85574e14i			0.111686i
$634$	3.09846e14			0.120131
$635$	3.55541e15	+	1.57288e15i	1.36658	+	0.604562i
$636$	3.81633e14			0.145423
$637$		−	2.65929e15i		−	1.00461i
$638$			5.82877e14i			0.218305i
$639$	5.33406e14			0.198063
$640$	−2.19569e14	−	9.71356e13i	−0.0808318	−	0.0357592i
$641$	−6.82035e14			−0.248936			−0.124468	−	0.992224i	$-0.539722\pi$
$641$	−6.82035e14			−0.248936			−0.124468	+	0.992224i	$0.539722\pi$
$642$		−	3.39844e14i		−	0.122981i
$643$			2.75748e15i			0.989356i	0.869076	+	0.494678i	$0.164714\pi$
$643$			2.75748e15i			0.989356i	−0.869076	+	0.494678i	$0.835286\pi$
$644$	9.82923e13			0.0349661
$645$	1.17338e14	−	2.65236e14i	0.0413866	−	0.0935522i
$646$	−5.22012e14			−0.182558
$647$			6.27496e14i			0.217589i	0.994064	+	0.108795i	$0.0346991\pi$
$647$			6.27496e14i			0.217589i	−0.994064	+	0.108795i	$0.965301\pi$
$648$		−	8.54228e14i		−	0.293705i
$649$	−7.84874e14			−0.267580
$650$	−1.62097e15	−	1.78320e15i	−0.547964	−	0.602803i
$651$	−3.74249e14			−0.125449
$652$			2.92889e14i			0.0973513i
$653$			8.70491e14i			0.286908i	0.989657	+	0.143454i	$0.0458208\pi$
$653$			8.70491e14i			0.286908i	−0.989657	+	0.143454i	$0.954179\pi$
$654$	7.66720e14			0.250587
$655$	−2.16995e14	+	4.90504e14i	−0.0703270	+	0.158970i
$656$	−6.96165e14			−0.223739
$657$		−	2.53293e15i		−	0.807259i
$658$			1.26130e15i			0.398637i
$659$	−3.46426e15			−1.08578			−0.542889	−	0.839805i	$-0.682670\pi$
$659$	−3.46426e15			−1.08578			−0.542889	+	0.839805i	$0.682670\pi$
$660$	4.12079e14	+	1.82300e14i	0.128082	+	0.0566625i
$661$	−1.96770e15			−0.606528			−0.303264	−	0.952907i	$-0.598076\pi$
$661$	−1.96770e15			−0.606528			−0.303264	+	0.952907i	$0.598076\pi$
$662$		−	2.85067e15i		−	0.871420i
$663$			1.74095e14i			0.0527790i
$664$	1.92278e15			0.578104
$665$	1.48314e15	+	6.56129e14i	0.442246	+	0.195646i
$666$	−3.55311e15			−1.05075
$667$		−	1.76182e14i		−	0.0516736i
$668$			8.42074e14i			0.244951i
$669$	7.04309e14			0.203198
$670$	−1.66618e15	+	3.76630e15i	−0.476771	+	1.07771i
$671$	−2.53130e15			−0.718406
$672$		−	5.38886e13i		−	0.0151693i
$673$		−	8.57604e14i		−	0.239444i	−0.992807	−	0.119722i	$-0.961800\pi$
$673$		−	8.57604e14i		−	0.239444i	0.992807	−	0.119722i	$-0.0382003\pi$
$674$	−1.56689e15			−0.433919
$675$	−1.25510e15	+	1.14092e15i	−0.344753	+	0.313390i
$676$	6.00603e14			0.163637
$677$		−	2.11042e15i		−	0.570336i	−0.958478	−	0.285168i	$-0.907951\pi$
$677$		−	2.11042e15i		−	0.570336i	0.958478	−	0.285168i	$-0.0920494\pi$
$678$			5.74919e13i			0.0154114i
$679$	−2.19339e15			−0.583219
$680$	−1.03582e14	+	2.34142e14i	−0.0273203	+	0.0617561i
$681$	−3.36242e14			−0.0879717
$682$			4.65171e15i			1.20725i
$683$			3.30397e15i			0.850593i	0.905054	+	0.425296i	$0.139830\pi$
$683$			3.30397e15i			0.850593i	−0.905054	+	0.425296i	$0.860170\pi$
$684$	2.49417e15			0.636967
$685$	3.75361e15	+	1.66056e15i	0.950936	+	0.420685i
$686$	1.88440e15			0.473576
$687$		−	5.00103e14i		−	0.124680i
$688$			4.31122e14i			0.106626i
$689$	−5.69383e15			−1.39701
$690$	−1.24556e14	−	5.51024e13i	−0.0303176	−	0.0134122i
$691$	7.09703e15			1.71375			0.856875	−	0.515524i	$-0.172403\pi$
$691$	7.09703e15			1.71375			0.856875	+	0.515524i	$0.172403\pi$
$692$		−	5.15641e14i		−	0.123528i
$693$		−	1.65687e15i		−	0.393781i
$694$	4.52824e15			1.06771
$695$	7.67292e14	−	1.73442e15i	0.179492	−	0.405731i
$696$	−9.65914e13			−0.0224175
$697$			7.42367e14i			0.170938i
$698$		−	3.76516e14i		−	0.0860158i
$699$	−1.21749e15			−0.275956
$700$	5.88596e14	−	5.35050e14i	0.132367	−	0.120325i
$701$	−5.37565e15			−1.19945			−0.599725	−	0.800206i	$-0.704723\pi$
$701$	−5.37565e15			−1.19945			−0.599725	+	0.800206i	$0.704723\pi$
$702$		−	1.71442e15i		−	0.379545i
$703$		−	9.70243e15i		−	2.13121i
$704$	−6.69805e14			−0.145982
$705$	7.07084e14	−	1.59832e15i	0.152908	−	0.345641i
$706$	−7.51097e14			−0.161165
$707$			3.30190e15i			0.703003i
$708$		−	1.30065e14i		−	0.0274776i
$709$	6.48992e15			1.36046			0.680229	−	0.733000i	$-0.261880\pi$
$709$	6.48992e15			1.36046			0.680229	+	0.733000i	$0.261880\pi$
$710$	6.53324e14	+	2.89025e14i	0.135896	+	0.0601193i
$711$	7.12612e15			1.47086
$712$			1.11671e15i			0.228717i
$713$		−	1.40604e15i		−	0.285762i
$714$	−5.74651e13			−0.0115895
$715$	−6.14808e15	−	2.71986e15i	−1.23043	−	0.544330i
$716$	1.31807e15			0.261768
$717$			4.45382e14i			0.0877763i
$718$			3.60977e15i			0.705985i
$719$	1.27151e15			0.246781			0.123391	−	0.992358i	$-0.460623\pi$
$719$	1.27151e15			0.246781			0.123391	+	0.992358i	$0.460623\pi$
$720$	4.94914e14	−	1.11873e15i	0.0953238	−	0.215474i
$721$	4.10211e14			0.0784086
$722$			3.08311e15i			0.584836i
$723$		−	2.18368e14i		−	0.0411083i
$724$	−1.46899e15			−0.274445
$725$	−9.59037e14	−	1.05502e15i	−0.177818	−	0.195614i
$726$	3.35386e14			0.0617153
$727$		−	8.04231e15i		−	1.46873i	−0.678755	−	0.734364i	$-0.737480\pi$
$727$		−	8.04231e15i		−	1.46873i	0.678755	−	0.734364i	$-0.262520\pi$
$728$			8.03999e14i			0.145725i
$729$	3.73115e15			0.671184
$730$	1.37246e15	−	3.10236e15i	0.245032	−	0.553882i
$731$	4.59735e14			0.0814632
$732$		−	4.19474e14i		−	0.0737724i
$733$			6.66245e15i			1.16295i	0.813563	+	0.581477i	$0.197525\pi$
$733$			6.66245e15i			1.16295i	−0.813563	+	0.581477i	$0.802475\pi$
$734$	−5.33562e15			−0.924393
$735$	−1.11232e15	−	4.92080e14i	−0.191271	−	0.0846165i
$736$	2.02457e14			0.0345545
$737$			1.14893e16i			1.94635i
$738$		−	3.54702e15i		−	0.596422i
$739$	−4.29592e15			−0.716989			−0.358494	−	0.933532i	$-0.616710\pi$
$739$	−4.29592e15			−0.716989			−0.358494	+	0.933532i	$0.616710\pi$
$740$	−4.35190e15	−	1.92524e15i	−0.720948	−	0.318941i
$741$	2.27145e15			0.373510
$742$		−	1.87942e15i		−	0.306762i
$743$			1.83929e15i			0.297998i	0.988837	+	0.148999i	$0.0476051\pi$
$743$			1.83929e15i			0.297998i	−0.988837	+	0.148999i	$0.952395\pi$
$744$	−7.70857e14			−0.123972
$745$	1.38933e15	−	3.14049e15i	0.221791	−	0.501347i
$746$	4.47512e15			0.709155
$747$			9.79675e15i			1.54106i
$748$			7.14259e14i			0.111531i
$749$	−1.67362e15			−0.259422
$750$	−1.04582e15	+	3.48049e14i	−0.160923	+	0.0535554i
$751$	−7.02545e15			−1.07314			−0.536568	−	0.843857i	$-0.680279\pi$
$751$	−7.02545e15			−1.07314			−0.536568	+	0.843857i	$0.680279\pi$
$752$			2.59796e15i			0.393944i
$753$			1.07827e15i			0.162313i
$754$	1.44111e15			0.215355
$755$	−9.98939e14	+	2.25805e15i	−0.148194	+	0.334984i
$756$	5.65894e14			0.0833423
$757$			6.85179e15i			1.00179i	0.865508	+	0.500895i	$0.166996\pi$
$757$			6.85179e15i			1.00179i	−0.865508	+	0.500895i	$0.833004\pi$
$758$		−	7.87765e15i		−	1.14345i
$759$	−3.79963e14			−0.0547534
$760$	3.05489e15	+	1.35146e15i	0.437040	+	0.193343i
$761$	−4.99642e15			−0.709649			−0.354824	−	0.934933i	$-0.615459\pi$
$761$	−4.99642e15			−0.709649			−0.354824	+	0.934933i	$0.615459\pi$
$762$			1.79733e15i			0.253440i
$763$		−	3.77585e15i		−	0.528603i
$764$	−6.19382e15			−0.860885
$765$	−1.19297e15	−	5.27761e14i	−0.164624	−	0.0728281i
$766$	−3.83956e15			−0.526046
$767$			1.94053e15i			0.263964i
$768$		−	1.10997e14i		−	0.0149907i
$769$	2.45456e15			0.329138			0.164569	−	0.986366i	$-0.447377\pi$
$769$	2.45456e15			0.329138			0.164569	+	0.986366i	$0.447377\pi$
$770$	8.97768e14	−	2.02936e15i	0.119527	−	0.270184i
$771$	2.34357e15			0.309798
$772$		−	3.10183e15i		−	0.407120i
$773$		−	3.34228e15i		−	0.435568i	−0.975997	−	0.217784i	$-0.930117\pi$
$773$		−	3.34228e15i		−	0.435568i	0.975997	−	0.217784i	$-0.0698829\pi$
$774$	−2.19661e15			−0.284235
$775$	−7.65369e15	−	8.41966e15i	−0.983358	−	1.08177i
$776$	−4.51781e15			−0.576353
$777$		−	1.06808e15i		−	0.135297i
$778$		−	3.09163e15i		−	0.388865i
$779$	9.68581e15			1.20971
$780$	4.50720e14	−	1.01883e15i	0.0558967	−	0.126351i
$781$	1.99299e15			0.245428
$782$		−	2.15893e14i		−	0.0263999i
$783$		−	1.01432e15i		−	0.123165i
$784$	1.80799e15			0.218001
$785$	1.03374e16	+	4.57318e15i	1.23774	+	0.547565i
$786$	−2.47959e14			−0.0294820
$787$		−	6.92298e15i		−	0.817395i	−0.912670	−	0.408698i	$-0.865983\pi$
$787$		−	6.92298e15i		−	0.817395i	0.912670	−	0.408698i	$-0.134017\pi$
$788$			5.32136e15i			0.623920i
$789$	3.57674e15			0.416451
$790$	8.72817e15	+	3.86126e15i	1.00919	+	0.446458i
$791$	2.83129e14			0.0325097
$792$		−	3.41272e15i		−	0.389146i
$793$			6.25840e15i			0.708698i
$794$	9.82767e14			0.110519
$795$	−1.05360e15	+	2.38160e15i	−0.117667	+	0.265980i
$796$	5.32504e14			0.0590610
$797$		−	1.92200e15i		−	0.211706i	−0.994382	−	0.105853i	$-0.966243\pi$
$797$		−	1.92200e15i		−	0.211706i	0.994382	−	0.105853i	$-0.0337573\pi$
$798$			7.49758e14i			0.0820172i
$799$	2.77038e15			0.300976
$800$	1.21236e15	−	1.10206e15i	0.130808	−	0.118908i
$801$	−5.68972e15			−0.609694
$802$			4.41646e15i			0.470019i
$803$		−	9.46388e15i		−	1.00031i
$804$	−1.90394e15			−0.199869
$805$	−2.71361e14	+	6.13397e14i	−0.0282924	+	0.0639535i
$806$	1.15009e16			1.19094
$807$			3.01047e15i			0.309620i
$808$			6.80106e15i			0.694727i
$809$	9.00708e15			0.913834			0.456917	−	0.889509i	$-0.348954\pi$
$809$	9.00708e15			0.913834			0.456917	+	0.889509i	$0.348954\pi$
$810$	5.33084e15	+	2.35832e15i	0.537190	+	0.237648i
$811$	6.65720e15			0.666311			0.333156	−	0.942872i	$-0.391887\pi$
$811$	6.65720e15			0.666311			0.333156	+	0.942872i	$0.391887\pi$
$812$			4.75681e14i			0.0472887i
$813$		−	5.92669e14i		−	0.0585213i
$814$	−1.32756e16			−1.30203
$815$	−1.82779e15	−	8.08597e14i	−0.178057	−	0.0787708i
$816$	−1.18363e14			−0.0114530
$817$		−	5.99825e15i		−	0.576505i
$818$		−	6.35446e15i		−	0.606646i
$819$	−4.09645e15			−0.388460
$820$	1.92194e15	−	4.34444e15i	0.181036	−	0.409221i
$821$	−1.71399e16			−1.60369			−0.801847	−	0.597530i	$-0.796149\pi$
$821$	−1.71399e16			−1.60369			−0.801847	+	0.597530i	$0.796149\pi$
$822$			1.89752e15i			0.176357i
$823$			8.06228e15i			0.744318i	0.928169	+	0.372159i	$0.121382\pi$
$823$			8.06228e15i			0.744318i	−0.928169	+	0.372159i	$0.878618\pi$
$824$	8.44929e14			0.0774855
$825$	−2.27530e15	+	2.06831e15i	−0.207273	+	0.188417i
$826$	−6.40528e14			−0.0579626
$827$		−	1.42703e16i		−	1.28279i	−0.767213	−	0.641393i	$-0.778357\pi$
$827$		−	1.42703e16i		−	1.28279i	0.767213	−	0.641393i	$-0.221643\pi$
$828$			1.03154e15i			0.0921122i
$829$	1.25323e15			0.111168			0.0555842	−	0.998454i	$-0.482298\pi$
$829$	1.25323e15			0.111168			0.0555842	+	0.998454i	$0.482298\pi$
$830$	−5.30834e15	+	1.19992e16i	−0.467767	+	1.05736i
$831$	1.04412e15			0.0913993
$832$			1.65603e15i			0.144009i
$833$		−	1.92799e15i		−	0.166554i
$834$	8.76783e14			0.0752452
$835$	−5.25500e15	−	2.32476e15i	−0.448020	−	0.198200i
$836$	9.31907e15			0.789293
$837$		−	8.09491e15i		−	0.681118i
$838$			1.09496e16i			0.915287i
$839$	1.10625e15			0.0918678			0.0459339	−	0.998944i	$-0.485374\pi$
$839$	1.10625e15			0.0918678			0.0459339	+	0.998944i	$0.485374\pi$
$840$	3.36294e14	+	1.48773e14i	0.0277449	+	0.0122741i
$841$	−1.13479e16			−0.930116
$842$		−	9.98997e14i		−	0.0813482i
$843$		−	1.51926e15i		−	0.122908i
$844$	2.89673e15			0.232822
$845$	−1.65812e15	+	3.74809e15i	−0.132405	+	0.299294i
$846$	−1.32368e16			−1.05014
$847$		−	1.65166e15i		−	0.130186i
$848$		−	3.87111e15i		−	0.303151i
$849$	−5.60395e15			−0.436016
$850$	−1.17521e15	−	1.29282e15i	−0.0908468	−	0.0999386i
$851$	4.01272e15			0.308195
$852$			3.30268e14i			0.0252028i
$853$			1.53821e16i			1.16626i	0.812378	+	0.583131i	$0.198173\pi$
$853$			1.53821e16i			1.16626i	−0.812378	+	0.583131i	$0.801827\pi$
$854$	−2.06577e15			−0.155619
$855$	−6.88580e15	+	1.55650e16i	−0.515395	+	1.16502i
$856$	−3.44723e15			−0.256368
$857$		−	1.34229e16i		−	0.991862i	−0.868362	−	0.495931i	$-0.834827\pi$
$857$		−	1.34229e16i		−	0.991862i	0.868362	−	0.495931i	$-0.165173\pi$
$858$		−	3.10797e15i		−	0.228190i
$859$	−2.30497e16			−1.68152			−0.840760	−	0.541408i	$-0.817891\pi$
$859$	−2.30497e16			−1.68152			−0.840760	+	0.541408i	$0.817891\pi$
$860$	−2.69043e15	−	1.19022e15i	−0.195021	−	0.0862754i
$861$	1.06625e15			0.0767966
$862$		−	1.35058e16i		−	0.966566i
$863$			2.37761e16i			1.69076i	0.534166	+	0.845379i	$0.320626\pi$
$863$			2.37761e16i			1.69076i	−0.534166	+	0.845379i	$0.679374\pi$
$864$	1.16560e15			0.0823612
$865$	3.21788e15	+	1.42356e15i	0.225934	+	0.0999511i
$866$	1.16189e16			0.810619
$867$		−	3.33356e15i		−	0.231102i
$868$			3.79622e15i			0.261513i
$869$	2.66256e16			1.82260
$870$	2.66665e14	−	6.02782e14i	0.0181389	−	0.0410020i
$871$	2.84061e16			1.92005
$872$		−	7.77727e15i		−	0.522380i
$873$		−	2.30187e16i		−	1.53639i
$874$	−2.81680e15			−0.186829
$875$	1.71403e15	+	5.15030e15i	0.112973	+	0.339460i
$876$	1.56831e15			0.102721
$877$			7.60940e15i			0.495282i	0.968852	+	0.247641i	$0.0796553\pi$
$877$			7.60940e15i			0.495282i	−0.968852	+	0.247641i	$0.920345\pi$
$878$			2.87416e15i			0.185905i
$879$	−5.87957e14			−0.0377926
$880$	1.84917e15	−	4.17995e15i	0.118120	−	0.267003i
$881$	−1.17608e15			−0.0746565			−0.0373282	−	0.999303i	$-0.511885\pi$
$881$	−1.17608e15			−0.0746565			−0.0373282	+	0.999303i	$0.511885\pi$
$882$			9.21189e15i			0.581128i
$883$			6.74481e15i			0.422849i	0.977394	+	0.211425i	$0.0678103\pi$
$883$			6.74481e15i			0.422849i	−0.977394	+	0.211425i	$0.932190\pi$
$884$	1.76594e15			0.110024
$885$	8.11677e14	+	3.59078e14i	0.0502568	+	0.0222332i
$886$	−7.41070e15			−0.456010
$887$			1.45784e16i			0.891519i	0.895153	+	0.445759i	$0.147066\pi$
$887$			1.45784e16i			0.891519i	−0.895153	+	0.445759i	$0.852934\pi$
$888$		−	2.19997e15i		−	0.133704i
$889$	8.85126e15			0.534620
$890$	−6.96885e15	−	3.08296e15i	−0.418327	−	0.185064i
$891$	1.62619e16			0.970164
$892$		−	7.14420e15i		−	0.423591i
$893$		−	3.61457e16i		−	2.12997i
$894$	1.58758e15			0.0929777
$895$	−3.63887e15	+	8.22546e15i	−0.211807	+	0.478778i
$896$	−5.46622e14			−0.0316223
$897$			9.39422e14i			0.0540135i
$898$		−	1.71672e16i		−	0.981024i
$899$	6.80444e15			0.386469
$900$	5.61512e15	+	6.17707e15i	0.316975	+	0.348697i
$901$	−4.12803e15			−0.231610
$902$		−	1.32529e16i		−	0.739052i
$903$		−	6.60309e14i		−	0.0365986i
$904$	5.83172e14			0.0321270
$905$	4.05551e15	−	9.16726e15i	0.222064	−	0.501964i
$906$	−1.14149e15			−0.0621248
$907$		−	5.14712e15i		−	0.278435i	−0.990262	−	0.139218i	$-0.955541\pi$
$907$		−	5.14712e15i		−	0.278435i	0.990262	−	0.139218i	$-0.0444588\pi$
$908$			3.41069e15i			0.183388i
$909$	−3.46520e16			−1.85194
$910$	−5.01739e15	−	2.21965e15i	−0.266533	−	0.117912i
$911$	1.22053e16			0.644462			0.322231	−	0.946661i	$-0.395567\pi$
$911$	1.22053e16			0.644462			0.322231	+	0.946661i	$0.395567\pi$
$912$			1.54431e15i			0.0810517i
$913$			3.66040e16i			1.90959i
$914$	5.97263e15			0.309715
$915$	2.61774e15	+	1.15807e15i	0.134931	+	0.0596922i
$916$	−5.07282e15			−0.259911
$917$			1.22112e15i			0.0621909i
$918$		−	1.24295e15i		−	0.0629246i
$919$	1.21787e15			0.0612864			0.0306432	−	0.999530i	$-0.490244\pi$
$919$	1.21787e15			0.0612864			0.0306432	+	0.999530i	$0.490244\pi$
$920$	−5.58934e14	+	1.26344e15i	−0.0279594	+	0.0632006i
$921$	−7.41975e15			−0.368945
$922$			1.33178e16i			0.658282i
$923$		−	4.92748e15i		−	0.242112i
$924$	1.02588e15			0.0501072
$925$	2.40291e16	−	2.18431e16i	1.16670	−	1.06056i
$926$	2.95463e15			0.142608
$927$			4.30499e15i			0.206554i
$928$			9.79779e14i			0.0467320i
$929$	−1.51088e16			−0.716380			−0.358190	−	0.933649i	$-0.616606\pi$
$929$	−1.51088e16			−0.716380			−0.358190	+	0.933649i	$0.616606\pi$
$930$	2.12815e15	−	4.81056e15i	0.100310	−	0.226746i
$931$	−2.51548e16			−1.17868
$932$			1.23497e16i			0.575264i
$933$			5.32290e15i			0.246490i
$934$	2.17994e16			1.00354
$935$	−4.45736e15	−	1.97190e15i	−0.203992	−	0.0902444i
$936$	−8.43763e15			−0.383887
$937$			1.74345e16i			0.788572i	0.918988	+	0.394286i	$0.129008\pi$
$937$			1.74345e16i			0.788572i	−0.918988	+	0.394286i	$0.870992\pi$
$938$			9.37627e15i			0.421613i
$939$	1.11300e14			0.00497549
$940$	−1.62127e16	−	7.17234e15i	−0.720529	−	0.318756i
$941$	−3.26895e16			−1.44433			−0.722164	−	0.691722i	$-0.756853\pi$
$941$	−3.26895e16			−1.44433			−0.722164	+	0.691722i	$0.756853\pi$
$942$			5.22577e15i			0.229546i
$943$			4.00585e15i			0.174936i
$944$	−1.31932e15			−0.0572803
$945$	−1.56230e15	+	3.53149e15i	−0.0674355	+	0.152434i
$946$	−8.20728e15			−0.352207
$947$			2.42336e16i			1.03393i	0.856005	+	0.516967i	$0.172939\pi$
$947$			2.42336e16i			1.03393i	−0.856005	+	0.516967i	$0.827061\pi$
$948$			4.41226e15i			0.187161i
$949$	−2.33986e16			−0.986791
$950$	−1.68676e16	+	1.53331e16i	−0.707253	+	0.642911i
$951$	−9.77476e14			−0.0407486
$952$			5.82900e14i			0.0241597i
$953$		−	3.07149e16i		−	1.26572i	−0.774266	−	0.632860i	$-0.781881\pi$
$953$		−	3.07149e16i		−	1.26572i	0.774266	−	0.632860i	$-0.218119\pi$
$954$	1.97237e16			0.808112
$955$	1.70996e16	−	3.86528e16i	0.696576	−	1.57457i
$956$	4.51775e15			0.182980
$957$		−	1.83881e15i		−	0.0740494i
$958$			8.38799e15i			0.335852i
$959$	9.34468e15			0.372016
$960$	6.92679e14	+	3.06435e14i	0.0274183	+	0.0121296i
$961$	2.88950e16			1.13722
$962$			3.28227e16i			1.28443i
$963$		−	1.75639e16i		−	0.683404i
$964$	−2.21503e15			−0.0856952
$965$	1.93571e16	+	8.56340e15i	0.744629	+	0.329417i
$966$	−3.10084e14			−0.0118606
$967$			2.20548e15i			0.0838799i	0.999120	+	0.0419399i	$0.0133538\pi$
$967$			2.20548e15i			0.0838799i	−0.999120	+	0.0419399i	$0.986646\pi$
$968$		−	3.40200e15i		−	0.128653i
$969$	1.64680e15			0.0619241
$970$	1.24726e16	−	2.81936e16i	0.466350	−	1.05416i
$971$	−2.99429e16			−1.11324			−0.556619	−	0.830768i	$-0.687902\pi$
$971$	−2.99429e16			−1.11324			−0.556619	+	0.830768i	$0.687902\pi$
$972$			8.99617e15i			0.332578i
$973$		−	4.31787e15i		−	0.158726i
$974$	1.63742e16			0.598528
$975$	5.11370e15	+	5.62547e15i	0.185870	+	0.204472i
$976$	−4.25495e15			−0.153787
$977$		−	1.87713e16i		−	0.674644i	−0.941389	−	0.337322i	$-0.890479\pi$
$977$		−	1.87713e16i		−	0.674644i	0.941389	−	0.337322i	$-0.109521\pi$
$978$		−	9.23982e14i		−	0.0330217i
$979$	−2.12588e16			−0.755497
$980$	−4.99143e15	+	1.12829e16i	−0.176393	+	0.398727i
$981$	3.96259e16			1.39251
$982$		−	3.41956e16i		−	1.19497i
$983$		−	1.90327e16i		−	0.661388i	−0.943738	−	0.330694i	$-0.892717\pi$
$983$		−	1.90327e16i		−	0.661388i	0.943738	−	0.330694i	$-0.107283\pi$
$984$	2.19620e15			0.0758925
$985$	−3.32082e16	−	1.46910e16i	−1.14116	−	0.504838i
$986$	1.04480e15			0.0357036
$987$		−	3.97905e15i		−	0.135218i
$988$		−	2.30405e16i		−	0.778627i
$989$	2.48075e15			0.0833687
$990$	2.12972e16	+	9.42169e15i	0.711753	+	0.314873i
$991$	3.63443e16			1.20790			0.603950	−	0.797023i	$-0.293593\pi$
$991$	3.63443e16			1.20790			0.603950	+	0.797023i	$0.293593\pi$
$992$			7.81923e15i			0.258434i
$993$			8.99303e15i			0.295587i
$994$	1.62646e15			0.0531641
$995$	−1.47011e15	+	3.32311e15i	−0.0477886	+	0.108023i
$996$	−6.06583e15			−0.196094
$997$			2.46615e16i			0.792858i	0.918065	+	0.396429i	$0.129751\pi$
$997$			2.46615e16i			0.792858i	−0.918065	+	0.396429i	$0.870249\pi$
$998$		−	5.26939e15i		−	0.168478i
$999$	2.31023e16			0.734589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.b.a.9.5	yes	6
3.2	odd	2		90.12.c.b.19.1		6
4.3	odd	2		80.12.c.c.49.4		6
5.2	odd	4		50.12.a.i.1.2		3
5.3	odd	4		50.12.a.j.1.2		3
5.4	even	2	inner	10.12.b.a.9.2	✓	6
15.14	odd	2		90.12.c.b.19.4		6
20.19	odd	2		80.12.c.c.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.b.a.9.2	✓	6	5.4	even	2	inner
10.12.b.a.9.5	yes	6	1.1	even	1	trivial
50.12.a.i.1.2		3	5.2	odd	4
50.12.a.j.1.2		3	5.3	odd	4
80.12.c.c.49.3		6	20.19	odd	2
80.12.c.c.49.4		6	4.3	odd	2
90.12.c.b.19.1		6	3.2	odd	2
90.12.c.b.19.4		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)

\(f(q)\)	\(=\)	\(q+32.0000i q^{2} -100.951i q^{3} -1024.00 q^{4} +(2827.02 - 6390.31i) q^{5} +3230.43 q^{6} -15908.8i q^{7} -32768.0i q^{8} +166956. q^{9} +O(q^{10})\)	\(q+32.0000i q^{2} -100.951i q^{3} -1024.00 q^{4} +(2827.02 - 6390.31i) q^{5} +3230.43 q^{6} -15908.8i q^{7} -32768.0i q^{8} +166956. q^{9} +(204490. + 90464.5i) q^{10} +623805. q^{11} +103374. i q^{12} -1.54230e6i q^{13} +509081. q^{14} +(-645107. - 285390. i) q^{15} +1.04858e6 q^{16} -1.11817e6i q^{17} +5.34259e6i q^{18} -1.45889e7 q^{19} +(-2.89487e6 + 6.54368e6i) q^{20} -1.60601e6 q^{21} +1.99618e7i q^{22} -6.03368e6i q^{23} -3.30796e6 q^{24} +(-3.28441e7 - 3.61310e7i) q^{25} +4.93536e7 q^{26} -3.47375e7i q^{27} +1.62906e7i q^{28} +2.91997e7 q^{29} +(9.13247e6 - 2.06434e7i) q^{30} +2.33031e8 q^{31} +3.35544e7i q^{32} -6.29736e7i q^{33} +3.57814e7 q^{34} +(-1.01662e8 - 4.49744e7i) q^{35} -1.70963e8 q^{36} +6.65053e8i q^{37} -4.66846e8i q^{38} -1.55696e8 q^{39} +(-2.09398e8 - 9.26357e7i) q^{40} -6.63914e8 q^{41} -5.13922e7i q^{42} +4.11150e8i q^{43} -6.38776e8 q^{44} +(4.71987e8 - 1.06690e9i) q^{45} +1.93078e8 q^{46} +2.47761e9i q^{47} -1.05855e8i q^{48} +1.72424e9 q^{49} +(1.15619e9 - 1.05101e9i) q^{50} -1.12880e8 q^{51} +1.57931e9i q^{52} -3.69178e9i q^{53} +1.11160e9 q^{54} +(1.76351e9 - 3.98631e9i) q^{55} -5.21299e8 q^{56} +1.47277e9i q^{57} +9.34390e8i q^{58} -1.25820e9 q^{59} +(6.60590e8 + 2.92239e8i) q^{60} -4.05784e9 q^{61} +7.45700e9i q^{62} -2.65607e9i q^{63} -1.07374e9 q^{64} +(-9.85577e9 - 4.36011e9i) q^{65} +2.01516e9 q^{66} +1.84180e10i q^{67} +1.14500e9i q^{68} -6.09105e8 q^{69} +(1.43918e9 - 3.25319e9i) q^{70} +3.19489e9 q^{71} -5.47081e9i q^{72} -1.51712e10i q^{73} -2.12817e10 q^{74} +(-3.64746e9 + 3.31564e9i) q^{75} +1.49391e10 q^{76} -9.92398e9i q^{77} -4.98228e9i q^{78} +4.26826e10 q^{79} +(2.96434e9 - 6.70073e9i) q^{80} +2.60690e10 q^{81} -2.12453e10i q^{82} +5.86787e10i q^{83} +1.64455e9 q^{84} +(-7.14544e9 - 3.16108e9i) q^{85} -1.31568e10 q^{86} -2.94773e9i q^{87} -2.04408e10i q^{88} -3.40792e10 q^{89} +(3.41408e10 + 1.51036e10i) q^{90} -2.45361e10 q^{91} +6.17849e9i q^{92} -2.35247e10i q^{93} -7.92835e10 q^{94} +(-4.12432e10 + 9.32279e10i) q^{95} +3.38735e9 q^{96} -1.37873e11i q^{97} +5.51756e10i q^{98} +1.04148e11 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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