LMFDB - Embedded newform 100.9.b.d.51.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(51,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.51"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{61}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.3
Root			$-4.16577 + 5.52698i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.d.51.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.5676 - 11.0540i) q^{2} +27.2434i q^{3} +(11.6196 + 255.736i) q^{4} +(301.148 - 315.141i) q^{6} -3325.58i q^{7} +(2692.49 - 3086.70i) q^{8} +5818.80 q^{9} +6361.21i q^{11} +(-6967.12 + 316.557i) q^{12} +30777.4 q^{13} +(-36760.8 + 38469.0i) q^{14} +(-65266.0 + 5943.09i) q^{16} -122375. q^{17} +(-67309.6 - 64320.8i) q^{18} -7554.43i q^{19} +90600.1 q^{21} +(70316.6 - 73584.1i) q^{22} +406311. i q^{23} +(84092.2 + 73352.6i) q^{24} +(-356021. - 340213. i) q^{26} +337268. i q^{27} +(850471. - 38641.8i) q^{28} +828838. q^{29} -1.39549e6i q^{31} +(820666. + 652701. i) q^{32} -173301. q^{33} +(1.41559e6 + 1.35273e6i) q^{34} +(67611.9 + 1.48808e6i) q^{36} +386059. q^{37} +(-83506.4 + 87386.8i) q^{38} +838482. i q^{39} -972335. q^{41} +(-1.04803e6 - 1.00149e6i) q^{42} -4.61450e6i q^{43} +(-1.62679e6 + 73914.5i) q^{44} +(4.49135e6 - 4.70005e6i) q^{46} -1.87219e6i q^{47} +(-161910. - 1.77807e6i) q^{48} -5.29467e6 q^{49} -3.33392e6i q^{51} +(357620. + 7.87090e6i) q^{52} +8.01944e6 q^{53} +(3.72815e6 - 3.90139e6i) q^{54} +(-1.02651e7 - 8.95408e6i) q^{56} +205808. q^{57} +(-9.58768e6 - 9.16195e6i) q^{58} -6.18263e6i q^{59} +9.79320e6 q^{61} +(-1.54257e7 + 1.61425e7i) q^{62} -1.93509e7i q^{63} +(-2.27822e6 - 1.66218e7i) q^{64} +(2.00468e6 + 1.91566e6i) q^{66} +1.19411e6i q^{67} +(-1.42195e6 - 3.12958e7i) q^{68} -1.10693e7 q^{69} -3.62332e7i q^{71} +(1.56670e7 - 1.79609e7i) q^{72} -3.35548e7 q^{73} +(-4.46578e6 - 4.26748e6i) q^{74} +(1.93194e6 - 87779.2i) q^{76} +2.11547e7 q^{77} +(9.26855e6 - 9.69923e6i) q^{78} +1.22874e6i q^{79} +2.89888e7 q^{81} +(1.12476e7 + 1.07482e7i) q^{82} -6.96923e7i q^{83} +(1.05273e6 + 2.31697e7i) q^{84} +(-5.10086e7 + 5.33788e7i) q^{86} +2.25804e7i q^{87} +(1.96352e7 + 1.71275e7i) q^{88} +5.58347e7 q^{89} -1.02353e8i q^{91} +(-1.03908e8 + 4.72116e6i) q^{92} +3.80180e7 q^{93} +(-2.06951e7 + 2.16567e7i) q^{94} +(-1.77818e7 + 2.23578e7i) q^{96} +5.97582e7 q^{97} +(6.12467e7 + 5.85271e7i) q^{98} +3.70146e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9} + 64040 q^{12} - 51392 q^{13} + 68472 q^{14} - 81424 q^{16} - 27552 q^{17} + 616994 q^{18} + 414496 q^{21} + 389120 q^{22} + 163792 q^{24}+ \cdots + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9 + 64040 * q^12 - 51392 * q^13 + 68472 * q^14 - 81424 * q^16 - 27552 * q^17 + 616994 * q^18 + 414496 * q^21 + 389120 * q^22 + 163792 * q^24 + 1037124 * q^26 - 1288520 * q^28 + 2764896 * q^29 + 4379904 * q^32 + 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 - 9009472 * q^37 + 3087360 * q^38 - 8576448 * q^41 + 4067400 * q^42 + 16921200 * q^44 - 7974152 * q^46 + 2696640 * q^48 - 32803600 * q^49 - 6679352 * q^52 - 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 - 11957760 * q^57 - 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 + 19358000 * q^66 - 16095192 * q^68 + 7527264 * q^69 + 42242664 * q^72 - 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 + 104032400 * q^78 + 140586672 * q^81 - 83921012 * q^82 + 69761824 * q^84 - 101724672 * q^86 - 44728480 * q^88 + 106647456 * q^89 + 13876200 * q^92 - 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 - 171851232 * q^97 + 285387714 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−11.5676	−	11.0540i	−0.722976	−	0.690873i
$2$	−11.5676	−	11.0540i	−0.722976	−	0.690873i
$3$			27.2434i			0.336338i	0.985758	+	0.168169i	$0.0537855\pi$
$3$			27.2434i			0.336338i	−0.985758	+	0.168169i	$0.946215\pi$
$4$	11.6196	+	255.736i	0.0453889	+	0.998969i
$5$		0			0
$5$		0			0
$6$	301.148	−	315.141i	0.232367	−	0.243165i
$7$		−	3325.58i		−	1.38508i	−0.721379	−	0.692540i	$-0.756492\pi$
$7$		−	3325.58i		−	1.38508i	0.721379	−	0.692540i	$-0.243508\pi$
$8$	2692.49	−	3086.70i	0.657346	−	0.753589i
$9$	5818.80			0.886877
$10$		0			0
$11$			6361.21i			0.434479i	0.976118	+	0.217240i	$0.0697053\pi$
$11$			6361.21i			0.434479i	−0.976118	+	0.217240i	$0.930295\pi$
$12$	−6967.12	+	316.557i	−0.335992	+	0.0152660i
$13$	30777.4			1.07760			0.538801	−	0.842433i	$-0.318877\pi$
$13$	30777.4			1.07760			0.538801	+	0.842433i	$0.318877\pi$
$14$	−36760.8	+	38469.0i	−0.956915	+	1.00138i
$15$		0			0
$16$	−65266.0	+	5943.09i	−0.995880	+	0.0906843i
$17$	−122375.			−1.46520			−0.732601	−	0.680658i	$-0.761694\pi$
$17$	−122375.			−1.46520			−0.732601	+	0.680658i	$0.761694\pi$
$18$	−67309.6	−	64320.8i	−0.641191	−	0.612719i
$19$		−	7554.43i		−	0.0579679i	−0.999580	−	0.0289839i	$-0.990773\pi$
$19$		−	7554.43i		−	0.0579679i	0.999580	−	0.0289839i	$-0.00922717\pi$
$20$		0			0
$21$	90600.1			0.465856
$22$	70316.6	−	73584.1i	0.300170	−	0.314118i
$23$			406311.i			1.45194i	0.687729	+	0.725968i	$0.258608\pi$
$23$			406311.i			1.45194i	−0.687729	+	0.725968i	$0.741392\pi$
$24$	84092.2	+	73352.6i	0.253461	+	0.221091i
$25$		0			0
$26$	−356021.	−	340213.i	−0.779081	−	0.744487i
$27$			337268.i			0.634629i
$28$	850471.	−	38641.8i	1.38365	−	0.0628673i
$29$	828838.			1.17187			0.585933	−	0.810360i	$-0.300728\pi$
$29$	828838.			1.17187			0.585933	+	0.810360i	$0.300728\pi$
$30$		0			0
$31$		−	1.39549e6i		−	1.51106i	−0.655116	−	0.755528i	$-0.727380\pi$
$31$		−	1.39549e6i		−	1.51106i	0.655116	−	0.755528i	$-0.272620\pi$
$32$	820666.	+	652701.i	0.782649	+	0.622464i
$33$	−173301.			−0.146132
$34$	1.41559e6	+	1.35273e6i	1.05931	+	1.01227i
$35$		0			0
$36$	67611.9	+	1.48808e6i	0.0402544	+	0.885962i
$37$	386059.			0.205990			0.102995	−	0.994682i	$-0.467157\pi$
$37$	386059.			0.205990			0.102995	+	0.994682i	$0.467157\pi$
$38$	−83506.4	+	87386.8i	−0.0400484	+	0.0419094i
$39$			838482.i			0.362439i
$40$		0			0
$41$	−972335.			−0.344097			−0.172048	−	0.985089i	$-0.555039\pi$
$41$	−972335.			−0.344097			−0.172048	+	0.985089i	$0.555039\pi$
$42$	−1.04803e6	−	1.00149e6i	−0.336803	−	0.321847i
$43$		−	4.61450e6i		−	1.34974i	−0.737935	−	0.674871i	$-0.764199\pi$
$43$		−	4.61450e6i		−	1.34974i	0.737935	−	0.674871i	$-0.235801\pi$
$44$	−1.62679e6	+	73914.5i	−0.434032	+	0.0197205i
$45$		0			0
$46$	4.49135e6	−	4.70005e6i	1.00310	−	1.04971i
$47$		−	1.87219e6i		−	0.383670i	−0.981427	−	0.191835i	$-0.938556\pi$
$47$		−	1.87219e6i		−	0.383670i	0.981427	−	0.191835i	$-0.0614438\pi$
$48$	−161910.	−	1.77807e6i	−0.0305006	−	0.334953i
$49$	−5.29467e6			−0.918447
$50$		0			0
$51$		−	3.33392e6i		−	0.492804i
$52$	357620.	+	7.87090e6i	0.0489112	+	1.07649i
$53$	8.01944e6			1.01634			0.508172	−	0.861256i	$-0.330322\pi$
$53$	8.01944e6			1.01634			0.508172	+	0.861256i	$0.330322\pi$
$54$	3.72815e6	−	3.90139e6i	0.438448	−	0.458822i
$55$		0			0
$56$	−1.02651e7	−	8.95408e6i	−1.04378	−	0.910477i
$57$	205808.			0.0194968
$58$	−9.58768e6	−	9.16195e6i	−0.847231	−	0.809610i
$59$		−	6.18263e6i		−	0.510229i	−0.966911	−	0.255115i	$-0.917887\pi$
$59$		−	6.18263e6i		−	0.510229i	0.966911	−	0.255115i	$-0.0821132\pi$
$60$		0			0
$61$	9.79320e6			0.707303			0.353651	−	0.935377i	$-0.384940\pi$
$61$	9.79320e6			0.707303			0.353651	+	0.935377i	$0.384940\pi$
$62$	−1.54257e7	+	1.61425e7i	−1.04395	+	1.09246i
$63$		−	1.93509e7i		−	1.22840i
$64$	−2.27822e6	−	1.66218e7i	−0.135793	−	0.990737i
$65$		0			0
$66$	2.00468e6	+	1.91566e6i	0.105650	+	0.100959i
$67$			1.19411e6i			0.0592579i	0.999561	+	0.0296290i	$0.00943257\pi$
$67$			1.19411e6i			0.0592579i	−0.999561	+	0.0296290i	$0.990567\pi$
$68$	−1.42195e6	−	3.12958e7i	−0.0665039	−	1.46369i
$69$	−1.10693e7			−0.488342
$70$		0			0
$71$		−	3.62332e7i		−	1.42585i	−0.701242	−	0.712923i	$-0.747371\pi$
$71$		−	3.62332e7i		−	1.42585i	0.701242	−	0.712923i	$-0.252629\pi$
$72$	1.56670e7	−	1.79609e7i	0.582985	−	0.668340i
$73$	−3.35548e7			−1.18158			−0.590790	−	0.806826i	$-0.701184\pi$
$73$	−3.35548e7			−1.18158			−0.590790	+	0.806826i	$0.701184\pi$
$74$	−4.46578e6	−	4.26748e6i	−0.148926	−	0.142313i
$75$		0			0
$76$	1.93194e6	−	87779.2i	0.0579081	−	0.00263110i
$77$	2.11547e7			0.601789
$78$	9.26855e6	−	9.69923e6i	0.250399	−	0.262035i
$79$			1.22874e6i			0.0315466i	0.999876	+	0.0157733i	$0.00502101\pi$
$79$			1.22874e6i			0.0315466i	−0.999876	+	0.0157733i	$0.994979\pi$
$80$		0			0
$81$	2.89888e7			0.673426
$82$	1.12476e7	+	1.07482e7i	0.248774	+	0.237727i
$83$		−	6.96923e7i		−	1.46849i	−0.678882	−	0.734247i	$-0.737535\pi$
$83$		−	6.96923e7i		−	1.46849i	0.678882	−	0.734247i	$-0.262465\pi$
$84$	1.05273e6	+	2.31697e7i	0.0211447	+	0.465376i
$85$		0			0
$86$	−5.10086e7	+	5.33788e7i	−0.932501	+	0.975832i
$87$			2.25804e7i			0.394143i
$88$	1.96352e7	+	1.71275e7i	0.327419	+	0.285603i
$89$	5.58347e7			0.889907			0.444953	−	0.895554i	$-0.353220\pi$
$89$	5.58347e7			0.889907			0.444953	+	0.895554i	$0.353220\pi$
$90$		0			0
$91$		−	1.02353e8i		−	1.49257i
$92$	−1.03908e8	+	4.72116e6i	−1.45044	+	0.0659018i
$93$	3.80180e7			0.508226
$94$	−2.06951e7	+	2.16567e7i	−0.265067	+	0.277384i
$95$		0			0
$96$	−1.77818e7	+	2.23578e7i	−0.209358	+	0.263235i
$97$	5.97582e7			0.675010			0.337505	−	0.941324i	$-0.390417\pi$
$97$	5.97582e7			0.675010			0.337505	+	0.941324i	$0.390417\pi$
$98$	6.12467e7	+	5.85271e7i	0.664016	+	0.634531i
$99$			3.70146e7i			0.385329i
$100$		0			0
$101$	9.62751e7			0.925185			0.462593	−	0.886571i	$-0.346919\pi$
$101$	9.62751e7			0.925185			0.462593	+	0.886571i	$0.346919\pi$
$102$	−3.68530e7	+	3.85655e7i	−0.340465	+	0.356285i
$103$			1.96312e8i			1.74421i	0.489320	+	0.872104i	$0.337245\pi$
$103$			1.96312e8i			1.74421i	−0.489320	+	0.872104i	$0.662755\pi$
$104$	8.28678e7	−	9.50006e7i	0.708358	−	0.812070i
$105$		0			0
$106$	−9.27658e7	−	8.86466e7i	−0.734792	−	0.702164i
$107$		−	1.64435e8i		−	1.25447i	−0.778832	−	0.627233i	$-0.784187\pi$
$107$		−	1.64435e8i		−	1.25447i	0.778832	−	0.627233i	$-0.215813\pi$
$108$	−8.62516e7	+	3.91891e6i	−0.633975	+	0.0288051i
$109$	−1.81680e8			−1.28707			−0.643534	−	0.765417i	$-0.722533\pi$
$109$	−1.81680e8			−1.28707			−0.643534	+	0.765417i	$0.722533\pi$
$110$		0			0
$111$			1.05176e7i			0.0692824i
$112$	1.97642e7	+	2.17047e8i	0.125605	+	1.37937i
$113$	1.30629e8			0.801172			0.400586	−	0.916259i	$-0.368807\pi$
$113$	1.30629e8			0.801172			0.400586	+	0.916259i	$0.368807\pi$
$114$	−2.38071e6	−	2.27500e6i	−0.0140957	−	0.0134698i
$115$		0			0
$116$	9.63074e6	+	2.11964e8i	0.0531897	+	1.17066i
$117$	1.79087e8			0.955700
$118$	−6.83426e7	+	7.15183e7i	−0.352504	+	0.368883i
$119$			4.06968e8i			2.02942i
$120$		0			0
$121$	1.73894e8			0.811228
$122$	−1.13284e8	−	1.08254e8i	−0.511363	−	0.488656i
$123$		−	2.64897e7i		−	0.115733i
$124$	3.56878e8	−	1.62150e7i	1.50950	−	0.0685852i
$125$		0			0
$126$	−2.13904e8	+	2.23843e8i	−0.848665	+	0.888100i
$127$		−	4.45982e8i		−	1.71436i	−0.515015	−	0.857181i	$-0.672214\pi$
$127$		−	4.45982e8i		−	1.71436i	0.515015	−	0.857181i	$-0.327786\pi$
$128$	−1.57383e8	+	2.17458e8i	−0.586299	+	0.810095i
$129$	1.25715e8			0.453970
$130$		0			0
$131$			1.31555e8i			0.446707i	0.974738	+	0.223353i	$0.0717004\pi$
$131$			1.31555e8i			0.446707i	−0.974738	+	0.223353i	$0.928300\pi$
$132$	−2.01368e6	−	4.43194e7i	−0.00663278	−	0.145981i
$133$	−2.51228e7			−0.0802902
$134$	1.31997e7	−	1.38130e7i	0.0409397	−	0.0428421i
$135$		0			0
$136$	−3.29494e8	+	3.77735e8i	−0.963145	+	1.10416i
$137$	3.26396e8			0.926536			0.463268	−	0.886218i	$-0.346677\pi$
$137$	3.26396e8			0.926536			0.463268	+	0.886218i	$0.346677\pi$
$138$	1.28045e8	+	1.22360e8i	0.353059	+	0.337382i
$139$		−	6.48927e8i		−	1.73835i	−0.494506	−	0.869174i	$-0.664651\pi$
$139$		−	6.48927e8i		−	1.73835i	0.494506	−	0.869174i	$-0.335349\pi$
$140$		0			0
$141$	5.10048e7			0.129043
$142$	−4.00520e8	+	4.19131e8i	−0.985079	+	1.03085i
$143$			1.95782e8i			0.468196i
$144$	−3.79769e8	+	3.45816e7i	−0.883222	+	0.0804258i
$145$		0			0
$146$	3.88149e8	+	3.70913e8i	0.854253	+	0.816321i
$147$		−	1.44245e8i		−	0.308909i
$148$	4.48584e6	+	9.87292e7i	0.00934968	+	0.205778i
$149$	−7.30660e8			−1.48242			−0.741208	−	0.671276i	$-0.765747\pi$
$149$	−7.30660e8			−1.48242			−0.741208	+	0.671276i	$0.765747\pi$
$150$		0			0
$151$		−	7.74114e8i		−	1.48901i	−0.667618	−	0.744504i	$-0.732686\pi$
$151$		−	7.74114e8i		−	1.48901i	0.667618	−	0.744504i	$-0.267314\pi$
$152$	−2.33183e7	−	2.03402e7i	−0.0436840	−	0.0381049i
$153$	−7.12076e8			−1.29945
$154$	−2.44710e8	−	2.33843e8i	−0.435079	−	0.415760i
$155$		0			0
$156$	−2.14430e8	+	9.74279e6i	−0.362066	+	0.0164507i
$157$	−3.17523e8			−0.522609			−0.261304	−	0.965256i	$-0.584153\pi$
$157$	−3.17523e8			−0.522609			−0.261304	+	0.965256i	$0.584153\pi$
$158$	1.35825e7	−	1.42136e7i	0.0217947	−	0.0228075i
$159$			2.18477e8i			0.341835i
$160$		0			0
$161$	1.35122e9			2.01105
$162$	−3.35331e8	−	3.20441e8i	−0.486871	−	0.465252i
$163$			2.02004e7i			0.0286161i	0.999898	+	0.0143081i	$0.00455455\pi$
$163$			2.02004e7i			0.0286161i	−0.999898	+	0.0143081i	$0.995445\pi$
$164$	−1.12981e7	−	2.48661e8i	−0.0156182	−	0.343742i
$165$		0			0
$166$	−7.70376e8	+	8.06174e8i	−1.01454	+	1.06169i
$167$			5.65743e7i			0.0727366i	0.999338	+	0.0363683i	$0.0115789\pi$
$167$			5.65743e7i			0.0727366i	−0.999338	+	0.0363683i	$0.988421\pi$
$168$	2.43940e8	−	2.79655e8i	0.306228	−	0.351064i
$169$	1.31518e8			0.161228
$170$		0			0
$171$		−	4.39577e7i		−	0.0514103i
$172$	1.18009e9	−	5.36185e7i	1.34835	−	0.0612634i
$173$	1.09785e9			1.22563			0.612813	−	0.790228i	$-0.290038\pi$
$173$	1.09785e9			1.22563			0.612813	+	0.790228i	$0.290038\pi$
$174$	2.49603e8	−	2.61201e8i	0.272303	−	0.284956i
$175$		0			0
$176$	−3.78052e7	−	4.15171e8i	−0.0394004	−	0.432689i
$177$	1.68436e8			0.171610
$178$	−6.45875e8	−	6.17196e8i	−0.643381	−	0.614813i
$179$			6.44793e8i			0.628070i	0.949411	+	0.314035i	$0.101681\pi$
$179$			6.44793e8i			0.628070i	−0.949411	+	0.314035i	$0.898319\pi$
$180$		0			0
$181$	−6.79018e8			−0.632655			−0.316328	−	0.948650i	$-0.602450\pi$
$181$	−6.79018e8			−0.632655			−0.316328	+	0.948650i	$0.602450\pi$
$182$	−1.13140e9	+	1.18398e9i	−1.03117	+	1.07909i
$183$			2.66800e8i			0.237893i
$184$	1.25416e9	+	1.09399e9i	1.09416	+	0.954424i
$185$		0			0
$186$	−4.39777e8	−	4.20250e8i	−0.367436	−	0.351120i
$187$		−	7.78454e8i		−	0.636600i
$188$	4.78786e8	−	2.17540e7i	0.383275	−	0.0174144i
$189$	1.12161e9			0.879012
$190$		0			0
$191$			1.53738e8i			0.115518i	0.998331	+	0.0577588i	$0.0183954\pi$
$191$			1.53738e8i			0.115518i	−0.998331	+	0.0577588i	$0.981605\pi$
$192$	4.52835e8	−	6.20666e7i	0.333223	−	0.0456723i
$193$	−9.67761e7			−0.0697491			−0.0348746	−	0.999392i	$-0.511103\pi$
$193$	−9.67761e7			−0.0697491			−0.0348746	+	0.999392i	$0.511103\pi$
$194$	−6.91259e8	−	6.60565e8i	−0.488016	−	0.466346i
$195$		0			0
$196$	−6.15217e7	−	1.35404e9i	−0.0416873	−	0.917501i
$197$	2.84766e9			1.89070			0.945352	−	0.326051i	$-0.105718\pi$
$197$	2.84766e9			1.89070			0.945352	+	0.326051i	$0.105718\pi$
$198$	4.09158e8	−	4.28171e8i	0.266214	−	0.278584i
$199$			8.71254e8i			0.555562i	0.960644	+	0.277781i	$0.0895990\pi$
$199$			8.71254e8i			0.555562i	−0.960644	+	0.277781i	$0.910401\pi$
$200$		0			0
$201$	−3.25317e7			−0.0199307
$202$	−1.11367e9	−	1.06422e9i	−0.668887	−	0.639185i
$203$		−	2.75637e9i		−	1.62313i
$204$	8.52603e8	−	3.87387e7i	0.492296	−	0.0223678i
$205$		0			0
$206$	2.17003e9	−	2.27087e9i	1.20503	−	1.26102i
$207$			2.36424e9i			1.28769i
$208$	−2.00872e9	+	1.82913e8i	−1.07316	+	0.0977216i
$209$	4.80553e7			0.0251858
$210$		0			0
$211$		−	2.22378e9i		−	1.12192i	−0.827843	−	0.560960i	$-0.810432\pi$
$211$		−	2.22378e9i		−	1.12192i	0.827843	−	0.560960i	$-0.189568\pi$
$212$	9.31824e7	+	2.05086e9i	0.0461307	+	1.01530i
$213$	9.87114e8			0.479567
$214$	−1.81766e9	+	1.90212e9i	−0.866676	+	0.906949i
$215$		0			0
$216$	1.04104e9	+	9.08090e8i	0.478249	+	0.417171i
$217$	−4.64082e9			−2.09293
$218$	2.10161e9	+	2.00829e9i	0.930520	+	0.889201i
$219$		−	9.14146e8i		−	0.397410i
$220$		0			0
$221$	−3.76639e9			−1.57891
$222$	1.16261e8	−	1.21663e8i	0.0478654	−	0.0500895i
$223$		−	1.76089e9i		−	0.712054i	−0.934476	−	0.356027i	$-0.884131\pi$
$223$		−	1.76089e9i		−	0.712054i	0.934476	−	0.356027i	$-0.115869\pi$
$224$	2.17061e9	−	2.72919e9i	0.862162	−	1.08403i
$225$		0			0
$226$	−1.51107e9	−	1.44397e9i	−0.579228	−	0.553508i
$227$			1.85447e9i			0.698418i	0.937045	+	0.349209i	$0.113550\pi$
$227$			1.85447e9i			0.698418i	−0.937045	+	0.349209i	$0.886450\pi$
$228$	2.39140e6	+	5.26327e7i	0.000884940	+	0.0194767i
$229$	−1.13087e9			−0.411218			−0.205609	−	0.978634i	$-0.565917\pi$
$229$	−1.13087e9			−0.411218			−0.205609	+	0.978634i	$0.565917\pi$
$230$		0			0
$231$			5.76326e8i			0.202405i
$232$	2.23164e9	−	2.55837e9i	0.770321	−	0.883105i
$233$	−2.24935e9			−0.763191			−0.381596	−	0.924329i	$-0.624625\pi$
$233$	−2.24935e9			−0.763191			−0.381596	+	0.924329i	$0.624625\pi$
$234$	−2.07162e9	−	1.97963e9i	−0.690949	−	0.660268i
$235$		0			0
$236$	1.58112e9	−	7.18395e7i	0.509703	−	0.0231587i
$237$	−3.34752e7			−0.0106103
$238$	4.49861e9	−	4.70765e9i	1.40207	−	1.46722i
$239$		−	2.77234e9i		−	0.849679i	−0.905269	−	0.424840i	$-0.860331\pi$
$239$		−	2.77234e9i		−	0.849679i	0.905269	−	0.424840i	$-0.139669\pi$
$240$		0			0
$241$	−1.60515e8			−0.0475826			−0.0237913	−	0.999717i	$-0.507574\pi$
$241$	−1.60515e8			−0.0475826			−0.0237913	+	0.999717i	$0.507574\pi$
$242$	−2.01154e9	−	1.92222e9i	−0.586498	−	0.560455i
$243$			3.00257e9i			0.861128i
$244$	1.13793e8	+	2.50448e9i	0.0321037	+	0.706574i
$245$		0			0
$246$	−2.92817e8	+	3.06423e8i	−0.0799568	+	0.0836721i
$247$		−	2.32506e8i		−	0.0624663i
$248$	−4.30747e9	−	3.75735e9i	−1.13872	−	0.993287i
$249$	1.89866e9			0.493911
$250$		0			0
$251$			5.77680e9i			1.45543i	0.685877	+	0.727717i	$0.259419\pi$
$251$			5.77680e9i			1.45543i	−0.685877	+	0.727717i	$0.740581\pi$
$252$	4.94871e9	−	2.24849e8i	1.22713	−	0.0557555i
$253$	−2.58463e9			−0.630836
$254$	−4.92987e9	+	5.15895e9i	−1.18441	+	1.23944i
$255$		0			0
$256$	4.22433e9	−	7.75762e8i	0.983553	−	0.180621i
$257$	−4.57743e9			−1.04928			−0.524638	−	0.851326i	$-0.675799\pi$
$257$	−4.57743e9			−1.04928			−0.524638	+	0.851326i	$0.675799\pi$
$258$	−1.45422e9	−	1.38965e9i	−0.328210	−	0.313636i
$259$		−	1.28387e9i		−	0.285313i
$260$		0			0
$261$	4.82284e9			1.03930
$262$	1.45421e9	−	1.52178e9i	0.308618	−	0.322958i
$263$			4.85941e8i			0.101569i	0.998710	+	0.0507844i	$0.0161721\pi$
$263$			4.85941e8i			0.101569i	−0.998710	+	0.0507844i	$0.983828\pi$
$264$	−4.66611e8	+	5.34929e8i	−0.0960593	+	0.110124i
$265$		0			0
$266$	2.90612e8	+	2.77707e8i	0.0580479	+	0.0554703i
$267$			1.52113e9i			0.299310i
$268$	−3.05378e8	+	1.38751e7i	−0.0591968	+	0.00268965i
$269$	−1.48731e9			−0.284049			−0.142024	−	0.989863i	$-0.545361\pi$
$269$	−1.48731e9			−0.284049			−0.142024	+	0.989863i	$0.545361\pi$
$270$		0			0
$271$			6.79398e9i			1.25964i	0.776740	+	0.629821i	$0.216872\pi$
$271$			6.79398e9i			1.25964i	−0.776740	+	0.629821i	$0.783128\pi$
$272$	7.98693e9	−	7.27286e8i	1.45917	−	0.132871i
$273$	2.78844e9			0.502007
$274$	−3.77562e9	−	3.60797e9i	−0.669863	−	0.640118i
$275$		0			0
$276$	−1.28620e8	−	2.83082e9i	−0.0221653	−	0.487838i
$277$	−1.54730e9			−0.262818			−0.131409	−	0.991328i	$-0.541950\pi$
$277$	−1.54730e9			−0.262818			−0.131409	+	0.991328i	$0.541950\pi$
$278$	−7.17322e9	+	7.50654e9i	−1.20098	+	1.25678i
$279$		−	8.12009e9i		−	1.34012i
$280$		0			0
$281$	−9.33090e9			−1.49657			−0.748287	−	0.663375i	$-0.769123\pi$
$281$	−9.33090e9			−1.49657			−0.748287	+	0.663375i	$0.769123\pi$
$282$	−5.90004e8	−	5.63805e8i	−0.0932950	−	0.0891523i
$283$			7.43824e9i			1.15964i	0.814743	+	0.579822i	$0.196878\pi$
$283$			7.43824e9i			1.15964i	−0.814743	+	0.579822i	$0.803122\pi$
$284$	9.26613e9	−	4.21013e8i	1.42438	−	0.0647176i
$285$		0			0
$286$	2.16416e9	−	2.26473e9i	0.323464	−	0.338495i
$287$			3.23358e9i			0.476602i
$288$	4.77529e9	+	3.79793e9i	0.694113	+	0.552049i
$289$	7.99992e9			1.14682
$290$		0			0
$291$			1.62802e9i			0.227032i
$292$	−3.89892e8	−	8.58117e9i	−0.0536306	−	1.18036i
$293$	1.59214e9			0.216028			0.108014	−	0.994149i	$-0.465551\pi$
$293$	1.59214e9			0.216028			0.108014	+	0.994149i	$0.465551\pi$
$294$	−1.59448e9	+	1.66857e9i	−0.213417	+	0.223334i
$295$		0			0
$296$	1.03946e9	−	1.19165e9i	0.135407	−	0.155232i
$297$	−2.14543e9			−0.275733
$298$	8.45199e9	+	8.07669e9i	1.07175	+	1.02416i
$299$			1.25052e10i			1.56461i
$300$		0			0
$301$	−1.53459e10			−1.86950
$302$	−8.55703e9	+	8.95465e9i	−1.02872	+	1.07652i
$303$			2.62286e9i			0.311175i
$304$	4.48966e7	+	4.93047e8i	0.00525678	+	0.0577290i
$305$		0			0
$306$	8.23702e9	+	7.87127e9i	0.939474	+	0.897757i
$307$		−	3.36362e9i		−	0.378663i	−0.981913	−	0.189332i	$-0.939368\pi$
$307$		−	3.36362e9i		−	0.378663i	0.981913	−	0.189332i	$-0.0606321\pi$
$308$	2.45808e8	+	5.41002e9i	0.0273145	+	0.601169i
$309$	−5.34821e9			−0.586644
$310$		0			0
$311$			1.23254e10i			1.31752i	0.752352	+	0.658761i	$0.228919\pi$
$311$			1.23254e10i			1.31752i	−0.752352	+	0.658761i	$0.771081\pi$
$312$	2.58814e9	+	2.25760e9i	0.273130	+	0.238248i
$313$	−2.77987e9			−0.289633			−0.144816	−	0.989459i	$-0.546259\pi$
$313$	−2.77987e9			−0.289633			−0.144816	+	0.989459i	$0.546259\pi$
$314$	3.67299e9	+	3.50989e9i	0.377834	+	0.361056i
$315$		0			0
$316$	−3.14234e8	+	1.42775e7i	−0.0315141	+	0.00143187i
$317$	5.40177e8			0.0534933			0.0267466	−	0.999642i	$-0.491485\pi$
$317$	5.40177e8			0.0534933			0.0267466	+	0.999642i	$0.491485\pi$
$318$	2.41504e9	−	2.52726e9i	0.236165	−	0.247139i
$319$			5.27241e9i			0.509151i
$320$		0			0
$321$	4.47977e9			0.421925
$322$	−1.56304e10	−	1.49363e10i	−1.45394	−	1.38938i
$323$			9.24475e8i			0.0849347i
$324$	3.36837e8	+	7.41348e9i	0.0305661	+	0.672732i
$325$		0			0
$326$	2.23295e8	−	2.33671e8i	0.0197701	−	0.0206888i
$327$		−	4.94959e9i		−	0.432891i
$328$	−2.61800e9	+	3.00131e9i	−0.226191	+	0.259307i
$329$	−6.22610e9			−0.531414
$330$		0			0
$331$		−	1.21115e10i		−	1.00899i	−0.863414	−	0.504495i	$-0.831679\pi$
$331$		−	1.21115e10i		−	1.00899i	0.863414	−	0.504495i	$-0.168321\pi$
$332$	1.78228e10	−	8.09794e8i	1.46698	−	0.0666534i
$333$	2.24640e9			0.182688
$334$	6.25370e8	−	6.54429e8i	0.0502518	−	0.0525868i
$335$		0			0
$336$	−5.91310e9	+	5.38444e8i	−0.463936	+	0.0422458i
$337$	9.48812e9			0.735632			0.367816	−	0.929899i	$-0.380106\pi$
$337$	9.48812e9			0.735632			0.367816	+	0.929899i	$0.380106\pi$
$338$	−1.52135e9	−	1.45380e9i	−0.116564	−	0.111388i
$339$			3.55878e9i			0.269465i
$340$		0			0
$341$	8.87702e9			0.656523
$342$	−4.85907e8	+	5.08486e8i	−0.0355180	+	0.0371685i
$343$		−	1.56347e9i		−	0.112957i
$344$	−1.42436e10	−	1.24245e10i	−1.01715	−	0.887248i
$345$		0			0
$346$	−1.26995e10	−	1.21356e10i	−0.886099	−	0.846752i
$347$			9.01032e9i			0.621473i	0.950496	+	0.310737i	$0.100576\pi$
$347$			9.01032e9i			0.621473i	−0.950496	+	0.310737i	$0.899424\pi$
$348$	−5.77462e9	+	2.62374e8i	−0.393737	+	0.0178897i
$349$	2.17409e10			1.46547			0.732733	−	0.680517i	$-0.238245\pi$
$349$	2.17409e10			1.46547			0.732733	+	0.680517i	$0.238245\pi$
$350$		0			0
$351$			1.03802e10i			0.683878i
$352$	−4.15197e9	+	5.22043e9i	−0.270448	+	0.340045i
$353$	5.60018e9			0.360664			0.180332	−	0.983606i	$-0.442283\pi$
$353$	5.60018e9			0.360664			0.180332	+	0.983606i	$0.442283\pi$
$354$	−1.94840e9	−	1.86189e9i	−0.124070	−	0.118560i
$355$		0			0
$356$	6.48775e8	+	1.42790e10i	0.0403919	+	0.888990i
$357$	−1.10872e10			−0.682573
$358$	7.12752e9	−	7.45872e9i	0.433917	−	0.454080i
$359$		−	1.31213e10i		−	0.789952i	−0.918692	−	0.394976i	$-0.870753\pi$
$359$		−	1.31213e10i		−	0.789952i	0.918692	−	0.394976i	$-0.129247\pi$
$360$		0			0
$361$	1.69265e10			0.996640
$362$	7.85462e9	+	7.50585e9i	0.457395	+	0.437085i
$363$			4.73746e9i			0.272847i
$364$	2.61753e10	−	1.18929e9i	1.49103	−	0.0677460i
$365$		0			0
$366$	2.94920e9	−	3.08624e9i	0.164354	−	0.171991i
$367$			9.89380e9i			0.545379i	0.962102	+	0.272690i	$0.0879132\pi$
$367$			9.89380e9i			0.545379i	−0.962102	+	0.272690i	$0.912087\pi$
$368$	−2.41474e9	−	2.65183e10i	−0.131668	−	1.44595i
$369$	−5.65782e9			−0.305171
$370$		0			0
$371$		−	2.66693e10i		−	1.40772i
$372$	4.41752e8	+	9.72257e9i	0.0230678	+	0.507703i
$373$	−1.01496e10			−0.524339			−0.262170	−	0.965022i	$-0.584438\pi$
$373$	−1.01496e10			−0.524339			−0.262170	+	0.965022i	$0.584438\pi$
$374$	−8.60501e9	+	9.00486e9i	−0.439810	+	0.460247i
$375$		0			0
$376$	−5.77888e9	−	5.04084e9i	−0.289129	−	0.252204i
$377$	2.55095e10			1.26281
$378$	−1.29744e10	−	1.23982e10i	−0.635505	−	0.607286i
$379$		−	1.39748e10i		−	0.677312i	−0.940910	−	0.338656i	$-0.890028\pi$
$379$		−	1.39748e10i		−	0.677312i	0.940910	−	0.338656i	$-0.109972\pi$
$380$		0			0
$381$	1.21501e10			0.576606
$382$	1.69942e9	−	1.77838e9i	0.0798080	−	0.0835165i
$383$		−	2.31617e10i		−	1.07640i	−0.842816	−	0.538201i	$-0.819104\pi$
$383$		−	2.31617e10i		−	1.07640i	0.842816	−	0.538201i	$-0.180896\pi$
$384$	−5.92430e9	−	4.28766e9i	−0.272466	−	0.197195i
$385$		0			0
$386$	1.11947e9	+	1.06976e9i	0.0504269	+	0.0481878i
$387$		−	2.68508e10i		−	1.19706i
$388$	6.94364e8	+	1.52823e10i	0.0306380	+	0.674314i
$389$	−1.13177e10			−0.494267			−0.247133	−	0.968981i	$-0.579489\pi$
$389$	−1.13177e10			−0.494267			−0.247133	+	0.968981i	$0.579489\pi$
$390$		0			0
$391$		−	4.97224e10i		−	2.12738i
$392$	−1.42558e10	+	1.63430e10i	−0.603738	+	0.692132i
$393$	−3.58401e9			−0.150245
$394$	−3.29407e10	−	3.14780e10i	−1.36693	−	1.30624i
$395$		0			0
$396$	−9.46597e9	+	4.30093e8i	−0.384932	+	0.0174897i
$397$	−1.01291e10			−0.407765			−0.203882	−	0.978995i	$-0.565356\pi$
$397$	−1.01291e10			−0.407765			−0.203882	+	0.978995i	$0.565356\pi$
$398$	9.63082e9	−	1.00783e10i	0.383823	−	0.401658i
$399$		−	6.84432e8i		−	0.0270047i
$400$		0			0
$401$	1.52259e10			0.588850			0.294425	−	0.955675i	$-0.404872\pi$
$401$	1.52259e10			0.588850			0.294425	+	0.955675i	$0.404872\pi$
$402$	3.76315e8	+	3.59605e8i	0.0144094	+	0.0137696i
$403$		−	4.29496e10i		−	1.62832i
$404$	1.11867e9	+	2.46210e10i	0.0419931	+	0.924232i
$405$		0			0
$406$	−3.04688e10	+	3.18846e10i	−1.12137	+	1.17348i
$407$			2.45580e9i			0.0894985i
$408$	−1.02908e10	−	8.97653e9i	−0.371371	−	0.323942i
$409$	−5.16482e10			−1.84570			−0.922851	−	0.385156i	$-0.874148\pi$
$409$	−5.16482e10			−1.84570			−0.922851	+	0.385156i	$0.874148\pi$
$410$		0			0
$411$			8.89213e9i			0.311629i
$412$	−5.02041e10	+	2.28106e9i	−1.74241	+	0.0791678i
$413$	−2.05608e10			−0.706708
$414$	2.61343e10	−	2.73487e10i	0.889629	−	0.930968i
$415$		0			0
$416$	2.52580e10	+	2.00884e10i	0.843384	+	0.670769i
$417$	1.76790e10			0.584673
$418$	−5.55886e8	−	5.31202e8i	−0.0182088	−	0.0174002i
$419$			2.90780e10i			0.943427i	0.881752	+	0.471714i	$0.156364\pi$
$419$			2.90780e10i			0.943427i	−0.881752	+	0.471714i	$0.843636\pi$
$420$		0			0
$421$	−2.02634e9			−0.0645037			−0.0322519	−	0.999480i	$-0.510268\pi$
$421$	−2.02634e9			−0.0645037			−0.0322519	+	0.999480i	$0.510268\pi$
$422$	−2.45816e10	+	2.57239e10i	−0.775105	+	0.811122i
$423$		−	1.08939e10i		−	0.340268i
$424$	2.15923e10	−	2.47536e10i	0.668089	−	0.765905i
$425$		0			0
$426$	−1.14186e10	−	1.09115e10i	−0.346715	−	0.331320i
$427$		−	3.25681e10i		−	0.979671i
$428$	4.20519e10	−	1.91066e9i	1.25317	−	0.0569388i
$429$	−5.33376e9			−0.157472
$430$		0			0
$431$		−	2.31188e10i		−	0.669972i	−0.942223	−	0.334986i	$-0.891268\pi$
$431$		−	2.31188e10i		−	0.669972i	0.942223	−	0.334986i	$-0.108732\pi$
$432$	−2.00441e9	−	2.20121e10i	−0.0575509	−	0.632014i
$433$	5.16117e10			1.46824			0.734119	−	0.679021i	$-0.237595\pi$
$433$	5.16117e10			1.46824			0.734119	+	0.679021i	$0.237595\pi$
$434$	5.36832e10	+	5.12995e10i	1.51314	+	1.44595i
$435$		0			0
$436$	−2.11105e9	−	4.64622e10i	−0.0584187	−	1.28574i
$437$	3.06945e9			0.0841656
$438$	−1.01049e10	+	1.05745e10i	−0.274560	+	0.287318i
$439$			4.07914e10i			1.09827i	0.835733	+	0.549137i	$0.185043\pi$
$439$			4.07914e10i			1.09827i	−0.835733	+	0.549137i	$0.814957\pi$
$440$		0			0
$441$	−3.08086e10			−0.814549
$442$	4.35682e10	+	4.16336e10i	1.14151	+	1.09082i
$443$			1.78192e9i			0.0462671i	0.999732	+	0.0231336i	$0.00736430\pi$
$443$			1.78192e9i			0.0462671i	−0.999732	+	0.0231336i	$0.992636\pi$
$444$	−2.68972e9	+	1.22209e8i	−0.0692110	+	0.00314466i
$445$		0			0
$446$	−1.94648e10	+	2.03693e10i	−0.491939	+	0.514798i
$447$		−	1.99057e10i		−	0.498593i
$448$	−5.52771e10	+	7.57641e9i	−1.37225	+	0.188084i
$449$	5.74811e10			1.41429			0.707147	−	0.707067i	$-0.249982\pi$
$449$	5.74811e10			1.41429			0.707147	+	0.707067i	$0.249982\pi$
$450$		0			0
$451$		−	6.18523e9i		−	0.149503i
$452$	1.51785e9	+	3.34066e10i	0.0363643	+	0.800347i
$453$	2.10895e10			0.500811
$454$	2.04992e10	−	2.14518e10i	0.482518	−	0.504940i
$455$		0			0
$456$	5.54137e8	−	6.35269e8i	0.0128162	−	0.0146926i
$457$	4.50957e10			1.03388			0.516941	−	0.856021i	$-0.327071\pi$
$457$	4.50957e10			1.03388			0.516941	+	0.856021i	$0.327071\pi$
$458$	1.30815e10	+	1.25006e10i	0.297301	+	0.284099i
$459$		−	4.12732e10i		−	0.929860i
$460$		0			0
$461$	7.73092e10			1.71170			0.855850	−	0.517225i	$-0.173035\pi$
$461$	7.73092e10			1.71170			0.855850	+	0.517225i	$0.173035\pi$
$462$	6.37069e9	−	6.66672e9i	0.139836	−	0.146334i
$463$			8.52854e10i			1.85588i	0.372726	+	0.927941i	$0.378423\pi$
$463$			8.52854e10i			1.85588i	−0.372726	+	0.927941i	$0.621577\pi$
$464$	−5.40949e10	+	4.92586e9i	−1.16704	+	0.106270i
$465$		0			0
$466$	2.60196e10	+	2.48643e10i	0.551769	+	0.527268i
$467$			3.20726e10i			0.674320i	0.941447	+	0.337160i	$0.109466\pi$
$467$			3.20726e10i			0.674320i	−0.941447	+	0.337160i	$0.890534\pi$
$468$	2.08092e9	+	4.57991e10i	0.0433782	+	0.954716i
$469$	3.97112e9			0.0820770
$470$		0			0
$471$		−	8.65041e9i		−	0.175773i
$472$	−1.90839e10	−	1.66467e10i	−0.384503	−	0.335397i
$473$	2.93538e10			0.586435
$474$	3.87228e8	+	3.70033e8i	0.00767102	+	0.00733040i
$475$		0			0
$476$	−1.04076e11	+	4.72879e9i	−2.02733	+	0.0921133i
$477$	4.66635e10			0.901371
$478$	−3.06454e10	+	3.20694e10i	−0.587020	+	0.614298i
$479$			3.58893e10i			0.681746i	0.940109	+	0.340873i	$0.110723\pi$
$479$			3.58893e10i			0.681746i	−0.940109	+	0.340873i	$0.889277\pi$
$480$		0			0
$481$	1.18819e10			0.221976
$482$	1.85678e9	+	1.77433e9i	0.0344010	+	0.0328735i
$483$			3.68118e10i			0.676393i
$484$	2.02057e9	+	4.44710e10i	0.0368208	+	0.810392i
$485$		0			0
$486$	3.31903e10	−	3.47326e10i	0.594930	−	0.622575i
$487$		−	5.98567e10i		−	1.06414i	−0.846702	−	0.532068i	$-0.821415\pi$
$487$		−	5.98567e10i		−	1.06414i	0.846702	−	0.532068i	$-0.178585\pi$
$488$	2.63681e10	−	3.02287e10i	0.464943	−	0.533016i
$489$	−5.50329e8			−0.00962470
$490$		0			0
$491$			3.00275e10i			0.516645i	0.966059	+	0.258323i	$0.0831698\pi$
$491$			3.00275e10i			0.516645i	−0.966059	+	0.258323i	$0.916830\pi$
$492$	6.77438e9	−	3.07799e8i	0.115614	−	0.00525299i
$493$	−1.01429e11			−1.71702
$494$	−2.57011e9	+	2.68954e9i	−0.0431563	+	0.0451617i
$495$		0			0
$496$	8.29353e9	+	9.10782e10i	0.137029	+	1.50483i
$497$	−1.20496e11			−1.97491
$498$	−2.19629e10	−	2.09877e10i	−0.357086	−	0.341230i
$499$		−	2.32602e10i		−	0.375156i	−0.982250	−	0.187578i	$-0.939936\pi$
$499$		−	2.32602e10i		−	0.375156i	0.982250	−	0.187578i	$-0.0600637\pi$
$500$		0			0
$501$	−1.54128e9			−0.0244641
$502$	6.38566e10	−	6.68238e10i	1.00552	−	1.05224i
$503$			2.16574e10i			0.338326i	0.985588	+	0.169163i	$0.0541064\pi$
$503$			2.16574e10i			0.338326i	−0.985588	+	0.169163i	$0.945894\pi$
$504$	−5.97303e10	−	5.21020e10i	−0.925705	−	0.807481i
$505$		0			0
$506$	2.98980e10	+	2.85704e10i	0.456079	+	0.435828i
$507$			3.58300e9i			0.0542270i
$508$	1.14054e11	−	5.18212e9i	1.71260	−	0.0778131i
$509$	1.21565e10			0.181108			0.0905541	−	0.995892i	$-0.471136\pi$
$509$	1.21565e10			0.181108			0.0905541	+	0.995892i	$0.471136\pi$
$510$		0			0
$511$			1.11589e11i			1.63658i
$512$	−5.74407e10	−	3.77219e10i	−0.835871	−	0.548925i
$513$	2.54787e9			0.0367881
$514$	5.29500e10	+	5.05988e10i	0.758601	+	0.724916i
$515$		0			0
$516$	1.46075e9	+	3.21498e10i	0.0206052	+	0.453502i
$517$	1.19094e10			0.166697
$518$	−1.41918e10	+	1.48513e10i	−0.197115	+	0.206275i
$519$			2.99091e10i			0.412225i
$520$		0			0
$521$	−5.20805e10			−0.706845			−0.353422	−	0.935464i	$-0.614982\pi$
$521$	−5.20805e10			−0.706845			−0.353422	+	0.935464i	$0.614982\pi$
$522$	−5.57888e10	−	5.33115e10i	−0.751389	−	0.718024i
$523$		−	2.42007e10i		−	0.323461i	−0.986835	−	0.161731i	$-0.948292\pi$
$523$		−	2.42007e10i		−	0.323461i	0.986835	−	0.161731i	$-0.0517075\pi$
$524$	−3.36434e10	+	1.52861e9i	−0.446246	+	0.0202755i
$525$		0			0
$526$	5.37158e9	−	5.62118e9i	0.0701712	−	0.0734319i
$527$			1.70774e11i			2.21400i
$528$	1.13107e10	−	1.02994e9i	0.145530	−	0.0132519i
$529$	−8.67778e10			−1.10812
$530$		0			0
$531$		−	3.59755e10i		−	0.452510i
$532$	−2.91917e8	−	6.42482e9i	−0.00364428	−	0.0802074i
$533$	−2.99260e10			−0.370800
$534$	1.68145e10	−	1.75958e10i	0.206785	−	0.216394i
$535$		0			0
$536$	3.68587e9	+	3.21514e9i	0.0446561	+	0.0389530i
$537$	−1.75664e10			−0.211244
$538$	1.72047e10	+	1.64407e10i	0.205361	+	0.196242i
$539$		−	3.36805e10i		−	0.399046i
$540$		0			0
$541$	−7.39316e10			−0.863060			−0.431530	−	0.902099i	$-0.642026\pi$
$541$	−7.39316e10			−0.863060			−0.431530	+	0.902099i	$0.642026\pi$
$542$	7.51005e10	−	7.85902e10i	0.870253	−	0.910692i
$543$		−	1.84988e10i		−	0.212786i
$544$	−1.00429e11	−	7.98743e10i	−1.14674	−	0.912035i
$545$		0			0
$546$	−3.22556e10	−	3.08233e10i	−0.362939	−	0.346823i
$547$		−	9.08736e10i		−	1.01505i	−0.861636	−	0.507526i	$-0.830560\pi$
$547$		−	9.08736e10i		−	1.01505i	0.861636	−	0.507526i	$-0.169440\pi$
$548$	3.79257e9	+	8.34712e10i	0.0420544	+	0.925581i
$549$	5.69847e10			0.627290
$550$		0			0
$551$		−	6.26140e9i		−	0.0679305i
$552$	−2.98040e10	+	3.41676e10i	−0.321009	+	0.368009i
$553$	4.08628e9			0.0436946
$554$	1.78985e10	+	1.71038e10i	0.190011	+	0.181574i
$555$		0			0
$556$	1.65954e11	−	7.54025e9i	1.73656	−	0.0789018i
$557$	7.25820e9			0.0754064			0.0377032	−	0.999289i	$-0.487996\pi$
$557$	7.25820e9			0.0754064			0.0377032	+	0.999289i	$0.487996\pi$
$558$	−8.97592e10	+	9.39301e10i	−0.925853	+	0.968875i
$559$		−	1.42022e11i		−	1.45449i
$560$		0			0
$561$	2.12077e10			0.214113
$562$	1.07936e11	+	1.03143e11i	1.08199	+	1.03394i
$563$		−	4.02851e10i		−	0.400969i	−0.979697	−	0.200485i	$-0.935748\pi$
$563$		−	4.02851e10i		−	0.400969i	0.979697	−	0.200485i	$-0.0642517\pi$
$564$	5.92653e8	+	1.30438e10i	0.00585712	+	0.128910i
$565$		0			0
$566$	8.22221e10	−	8.60427e10i	0.801166	−	0.838394i
$567$		−	9.64045e10i		−	0.932750i
$568$	−1.11841e11	−	9.75574e10i	−1.07450	−	0.937274i
$569$	4.42204e10			0.421866			0.210933	−	0.977501i	$-0.432350\pi$
$569$	4.42204e10			0.421866			0.210933	+	0.977501i	$0.432350\pi$
$570$		0			0
$571$			1.92416e11i			1.81008i	0.425327	+	0.905040i	$0.360159\pi$
$571$			1.92416e11i			1.81008i	−0.425327	+	0.905040i	$0.639841\pi$
$572$	−5.00684e10	+	2.27490e9i	−0.467714	+	0.0212509i
$573$	−4.18835e9			−0.0388530
$574$	3.57438e10	−	3.74048e10i	0.329271	−	0.344572i
$575$		0			0
$576$	−1.32565e10	−	9.67190e10i	−0.120431	−	0.878662i
$577$	−5.62180e10			−0.507192			−0.253596	−	0.967310i	$-0.581613\pi$
$577$	−5.62180e10			−0.507192			−0.253596	+	0.967310i	$0.581613\pi$
$578$	−9.25400e10	−	8.84309e10i	−0.829122	−	0.792305i
$579$		−	2.63651e9i		−	0.0234593i
$580$		0			0
$581$	−2.31767e11			−2.03398
$582$	1.79960e10	−	1.88323e10i	0.156850	−	0.164139i
$583$			5.10133e10i			0.441580i
$584$	−9.03458e10	+	1.03574e11i	−0.776706	+	0.890425i
$585$		0			0
$586$	−1.84172e10	−	1.75994e10i	−0.156183	−	0.149248i
$587$			2.12589e11i			1.79056i	0.445508	+	0.895278i	$0.353023\pi$
$587$			2.12589e11i			1.79056i	−0.445508	+	0.895278i	$0.646977\pi$
$588$	3.68886e10	−	1.67606e9i	0.308591	−	0.0140211i
$589$	−1.05422e10			−0.0875927
$590$		0			0
$591$			7.75800e10i			0.635916i
$592$	−2.51965e10	+	2.29438e9i	−0.205142	+	0.0186801i
$593$	3.64674e10			0.294908			0.147454	−	0.989069i	$-0.452892\pi$
$593$	3.64674e10			0.294908			0.147454	+	0.989069i	$0.452892\pi$
$594$	2.48175e10	+	2.37155e10i	0.199348	+	0.190497i
$595$		0			0
$596$	−8.48995e9	−	1.86856e11i	−0.0672853	−	1.48089i
$597$	−2.37359e10			−0.186857
$598$	1.38232e11	−	1.44655e11i	1.08095	−	1.13118i
$599$			1.54791e11i			1.20237i	0.799111	+	0.601184i	$0.205304\pi$
$599$			1.54791e11i			1.20237i	−0.799111	+	0.601184i	$0.794696\pi$
$600$		0			0
$601$	1.37850e11			1.05659			0.528297	−	0.849059i	$-0.322831\pi$
$601$	1.37850e11			1.05659			0.528297	+	0.849059i	$0.322831\pi$
$602$	1.77515e11	+	1.69633e11i	1.35161	+	1.29159i
$603$			6.94830e9i			0.0525545i
$604$	1.97969e11	−	8.99487e9i	1.48747	−	0.0675845i
$605$		0			0
$606$	2.89930e10	−	3.03403e10i	0.214983	−	0.224972i
$607$			4.21916e10i			0.310793i	0.987852	+	0.155396i	$0.0496655\pi$
$607$			4.21916e10i			0.310793i	−0.987852	+	0.155396i	$0.950335\pi$
$608$	4.93078e9	−	6.19967e9i	0.0360829	−	0.0453685i
$609$	7.50928e10			0.545920
$610$		0			0
$611$		−	5.76211e10i		−	0.413444i
$612$	−8.27401e9	−	1.82104e11i	−0.0589808	−	1.29811i
$613$	1.76436e11			1.24953			0.624763	−	0.780815i	$-0.285196\pi$
$613$	1.76436e11			1.24953			0.624763	+	0.780815i	$0.285196\pi$
$614$	−3.71813e10	+	3.89091e10i	−0.261608	+	0.273765i
$615$		0			0
$616$	5.69588e10	−	6.52982e10i	0.395583	−	0.453501i
$617$	−3.80722e10			−0.262705			−0.131352	−	0.991336i	$-0.541932\pi$
$617$	−3.80722e10			−0.262705			−0.131352	+	0.991336i	$0.541932\pi$
$618$	6.18661e10	+	5.91190e10i	0.424130	+	0.405297i
$619$			4.67363e10i			0.318340i	0.987251	+	0.159170i	$0.0508818\pi$
$619$			4.67363e10i			0.318340i	−0.987251	+	0.159170i	$0.949118\pi$
$620$		0			0
$621$	−1.37036e11			−0.921441
$622$	1.36244e11	−	1.42575e11i	0.910240	−	0.952537i
$623$		−	1.85683e11i		−	1.23259i
$624$	−4.98317e9	−	5.47243e10i	−0.0328675	−	0.360946i
$625$		0			0
$626$	3.21565e10	+	3.07286e10i	0.209398	+	0.200099i
$627$			1.30919e9i			0.00847096i
$628$	−3.68948e9	−	8.12021e10i	−0.0237206	−	0.522070i
$629$	−4.72440e10			−0.301817
$630$		0			0
$631$		−	1.82629e11i		−	1.15200i	−0.817450	−	0.576000i	$-0.804613\pi$
$631$		−	1.82629e11i		−	1.15200i	0.817450	−	0.576000i	$-0.195387\pi$
$632$	3.79276e9	+	3.30838e9i	0.0237732	+	0.0207370i
$633$	6.05834e10			0.377345
$634$	−6.24857e9	−	5.97110e9i	−0.0386744	−	0.0369571i
$635$		0			0
$636$	−5.58724e10	+	2.53861e9i	−0.341483	+	0.0155155i
$637$	−1.62956e11			−0.989721
$638$	5.82811e10	−	6.09893e10i	0.351759	−	0.368104i
$639$		−	2.10833e11i		−	1.26455i
$640$		0			0
$641$	1.05531e11			0.625100			0.312550	−	0.949901i	$-0.398817\pi$
$641$	1.05531e11			0.625100			0.312550	+	0.949901i	$0.398817\pi$
$642$	−5.18202e10	−	4.95192e10i	−0.305042	−	0.291497i
$643$			1.09834e11i			0.642528i	0.946990	+	0.321264i	$0.104108\pi$
$643$			1.09834e11i			0.642528i	−0.946990	+	0.321264i	$0.895892\pi$
$644$	1.57006e10	+	3.45556e11i	0.0912793	+	2.00898i
$645$		0			0
$646$	1.02191e10	−	1.06940e10i	0.0586791	−	0.0614057i
$647$			4.48807e9i			0.0256119i	0.999918	+	0.0128060i	$0.00407638\pi$
$647$			4.48807e9i			0.0256119i	−0.999918	+	0.0128060i	$0.995924\pi$
$648$	7.80520e10	−	8.94797e10i	0.442674	−	0.507487i
$649$	3.93290e10			0.221684
$650$		0			0
$651$		−	1.26432e11i		−	0.703934i
$652$	−5.16599e9	+	2.34720e8i	−0.0285866	+	0.00129885i
$653$	−2.96586e11			−1.63117			−0.815583	−	0.578640i	$-0.803584\pi$
$653$	−2.96586e11			−1.63117			−0.815583	+	0.578640i	$0.803584\pi$
$654$	−5.47126e10	+	5.72550e10i	−0.299072	+	0.312970i
$655$		0			0
$656$	6.34604e10	−	5.77867e9i	0.342679	−	0.0312042i
$657$	−1.95248e11			−1.04791
$658$	7.20212e10	+	6.88232e10i	0.384199	+	0.367139i
$659$			8.22505e10i			0.436111i	0.975936	+	0.218056i	$0.0699714\pi$
$659$			8.22505e10i			0.436111i	−0.975936	+	0.218056i	$0.930029\pi$
$660$		0			0
$661$	−1.54172e11			−0.807608			−0.403804	−	0.914845i	$-0.632312\pi$
$661$	−1.54172e11			−0.807608			−0.403804	+	0.914845i	$0.632312\pi$
$662$	−1.33881e11	+	1.40102e11i	−0.697085	+	0.729476i
$663$		−	1.02609e11i		−	0.531047i
$664$	−2.15119e11	−	1.87646e11i	−1.10664	−	0.965309i
$665$		0			0
$666$	−2.59855e10	−	2.48316e10i	−0.132079	−	0.126214i
$667$			3.36766e11i			1.70147i
$668$	−1.44681e10	+	6.57368e8i	−0.0726616	+	0.00330144i
$669$	4.79726e10			0.239491
$670$		0			0
$671$			6.22966e10i			0.307308i
$672$	7.43524e10	+	5.91347e10i	0.364601	+	0.289978i
$673$	−2.82157e11			−1.37541			−0.687703	−	0.725992i	$-0.741381\pi$
$673$	−2.82157e11			−1.37541			−0.687703	+	0.725992i	$0.741381\pi$
$674$	−1.09755e11	−	1.04881e11i	−0.531844	−	0.508228i
$675$		0			0
$676$	1.52818e9	+	3.36340e10i	0.00731794	+	0.161061i
$677$	2.70699e11			1.28864			0.644320	−	0.764756i	$-0.277140\pi$
$677$	2.70699e11			1.28864			0.644320	+	0.764756i	$0.277140\pi$
$678$	3.93386e10	−	4.11666e10i	0.186166	−	0.194817i
$679$		−	1.98730e11i		−	0.934943i
$680$		0			0
$681$	−5.05220e10			−0.234905
$682$	−1.02686e11	−	9.81263e10i	−0.474650	−	0.453574i
$683$		−	3.96155e10i		−	0.182046i	−0.995849	−	0.0910232i	$-0.970986\pi$
$683$		−	3.96155e10i		−	0.182046i	0.995849	−	0.0910232i	$-0.0290137\pi$
$684$	1.12416e10	−	5.10769e8i	0.0513574	−	0.00233346i
$685$		0			0
$686$	−1.72825e10	+	1.80856e10i	−0.0780389	+	0.0816651i
$687$		−	3.08088e10i		−	0.138308i
$688$	2.74244e10	+	3.01170e11i	0.122400	+	1.34418i
$689$	2.46818e11			1.09521
$690$		0			0
$691$		−	1.26869e11i		−	0.556472i	−0.960513	−	0.278236i	$-0.910250\pi$
$691$		−	1.26869e11i		−	0.556472i	0.960513	−	0.278236i	$-0.0897497\pi$
$692$	1.27565e10	+	2.80760e11i	0.0556299	+	1.22436i
$693$	1.23095e11			0.533712
$694$	9.95998e10	−	1.04228e11i	0.429359	−	0.449310i
$695$		0			0
$696$	6.96988e10	+	6.07974e10i	0.297022	+	0.259088i
$697$	1.18990e11			0.504171
$698$	−2.51490e11	−	2.40323e11i	−1.05950	−	1.01245i
$699$		−	6.12800e10i		−	0.256691i
$700$		0			0
$701$	−6.26836e10			−0.259587			−0.129793	−	0.991541i	$-0.541431\pi$
$701$	−6.26836e10			−0.259587			−0.129793	+	0.991541i	$0.541431\pi$
$702$	1.14743e11	−	1.20075e11i	0.472473	−	0.494427i
$703$		−	2.91646e9i		−	0.0119408i
$704$	1.05735e11	−	1.44923e10i	0.430455	−	0.0589991i
$705$		0			0
$706$	−6.47808e10	−	6.19042e10i	−0.260752	−	0.249173i
$707$		−	3.20170e11i		−	1.28146i
$708$	1.95715e9	+	4.30752e10i	0.00778918	+	0.171433i
$709$	−3.57762e11			−1.41582			−0.707912	−	0.706300i	$-0.750363\pi$
$709$	−3.57762e11			−1.41582			−0.707912	+	0.706300i	$0.750363\pi$
$710$		0			0
$711$			7.14981e9i			0.0279780i
$712$	1.50334e11	−	1.72345e11i	0.584977	−	0.670624i
$713$	5.67004e11			2.19396
$714$	1.28252e11	+	1.22558e11i	0.493484	+	0.471571i
$715$		0			0
$716$	−1.64897e11	+	7.49222e9i	−0.627423	+	0.0285074i
$717$	7.55280e10			0.285780
$718$	−1.45043e11	+	1.51783e11i	−0.545756	+	0.571116i
$719$			1.70342e11i			0.637392i	0.947857	+	0.318696i	$0.103245\pi$
$719$			1.70342e11i			0.637392i	−0.947857	+	0.318696i	$0.896755\pi$
$720$		0			0
$721$	6.52852e11			2.41587
$722$	−1.95799e11	−	1.87105e11i	−0.720547	−	0.688552i
$723$		−	4.37298e9i		−	0.0160038i
$724$	−7.88990e9	−	1.73650e11i	−0.0287155	−	0.632003i
$725$		0			0
$726$	5.23678e10	−	5.48011e10i	0.188503	−	0.197262i
$727$		−	6.56094e10i		−	0.234870i	−0.993081	−	0.117435i	$-0.962533\pi$
$727$		−	6.56094e10i		−	0.234870i	0.993081	−	0.117435i	$-0.0374672\pi$
$728$	−3.15932e11	−	2.75583e11i	−1.12478	−	0.981132i
$729$	1.08395e11			0.383796
$730$		0			0
$731$			5.64700e11i			1.97765i
$732$	−6.82305e10	+	3.10010e9i	−0.237648	+	0.0107977i
$733$	−2.60967e11			−0.904003			−0.452001	−	0.892017i	$-0.649290\pi$
$733$	−2.60967e11			−0.904003			−0.452001	+	0.892017i	$0.649290\pi$
$734$	1.09366e11	−	1.14448e11i	0.376788	−	0.394296i
$735$		0			0
$736$	−2.65200e11	+	3.33446e11i	−0.903778	+	1.13636i
$737$	−7.59601e9			−0.0257463
$738$	6.54475e10	+	6.25414e10i	0.220632	+	0.210835i
$739$			4.19763e11i			1.40743i	0.710483	+	0.703715i	$0.248477\pi$
$739$			4.19763e11i			1.40743i	−0.710483	+	0.703715i	$0.751523\pi$
$740$		0			0
$741$	6.33425e9			0.0210098
$742$	−2.94801e11	+	3.08500e11i	−0.972554	+	1.01775i
$743$		−	1.42604e11i		−	0.467925i	−0.972246	−	0.233962i	$-0.924831\pi$
$743$		−	1.42604e11i		−	0.467925i	0.972246	−	0.233962i	$-0.0751693\pi$
$744$	1.02363e11	−	1.17350e11i	0.334081	−	0.382994i
$745$		0			0
$746$	1.17406e11	+	1.12193e11i	0.379085	+	0.362252i
$747$		−	4.05525e11i		−	1.30237i
$748$	1.99079e11	−	9.04530e9i	0.635944	−	0.0288946i
$749$	−5.46841e11			−1.73754
$750$		0			0
$751$			3.26311e10i			0.102582i	0.998684	+	0.0512911i	$0.0163336\pi$
$751$			3.26311e10i			0.102582i	−0.998684	+	0.0512911i	$0.983666\pi$
$752$	1.11266e10	+	1.22190e11i	0.0347928	+	0.382089i
$753$	−1.57380e11			−0.489518
$754$	−2.95084e11	−	2.81981e11i	−0.912978	−	0.872438i
$755$		0			0
$756$	1.30326e10	+	2.86836e11i	0.0398974	+	0.878106i
$757$	4.36612e11			1.32957			0.664787	−	0.747033i	$-0.268522\pi$
$757$	4.36612e11			1.32957			0.664787	+	0.747033i	$0.268522\pi$
$758$	−1.54477e11	+	1.61655e11i	−0.467937	+	0.489680i
$759$		−	7.04142e10i		−	0.212174i
$760$		0			0
$761$	−1.98059e11			−0.590548			−0.295274	−	0.955413i	$-0.595411\pi$
$761$	−1.98059e11			−0.590548			−0.295274	+	0.955413i	$0.595411\pi$
$762$	−1.40547e11	−	1.34307e11i	−0.416872	−	0.398361i
$763$			6.04192e11i			1.78269i
$764$	−3.93164e10	+	1.78637e9i	−0.115399	+	0.00524322i
$765$		0			0
$766$	−2.56028e11	+	2.67925e11i	−0.743657	+	0.778213i
$767$		−	1.90285e11i		−	0.549824i
$768$	2.11344e10	+	1.15085e11i	0.0607499	+	0.330807i
$769$	−1.42097e10			−0.0406329			−0.0203165	−	0.999794i	$-0.506467\pi$
$769$	−1.42097e10			−0.0406329			−0.0203165	+	0.999794i	$0.506467\pi$
$770$		0			0
$771$		−	1.24705e11i		−	0.352912i
$772$	−1.12450e9	−	2.47491e10i	−0.00316584	−	0.0696772i
$773$	−6.62483e10			−0.185548			−0.0927741	−	0.995687i	$-0.529573\pi$
$773$	−6.62483e10			−0.185548			−0.0927741	+	0.995687i	$0.529573\pi$
$774$	−2.96808e11	+	3.10600e11i	−0.827013	+	0.865442i
$775$		0			0
$776$	1.60898e11	−	1.84456e11i	0.443715	−	0.508680i
$777$	3.49770e10			0.0959617
$778$	1.30919e11	+	1.25106e11i	0.357343	+	0.341476i
$779$			7.34544e9i			0.0199466i
$780$		0			0
$781$	2.30487e11			0.619501
$782$	−5.49630e11	+	5.75170e11i	−1.46975	+	1.53804i
$783$			2.79540e11i			0.743700i
$784$	3.45562e11	−	3.14667e10i	0.914663	−	0.0832887i
$785$		0			0
$786$	4.14584e10	+	3.96175e10i	0.108623	+	0.103800i
$787$		−	7.13437e10i		−	0.185976i	−0.995667	−	0.0929880i	$-0.970358\pi$
$787$		−	7.13437e10i		−	0.185976i	0.995667	−	0.0929880i	$-0.0296418\pi$
$788$	3.30886e10	+	7.28250e11i	0.0858170	+	1.88876i
$789$	−1.32387e10			−0.0341615
$790$		0			0
$791$		−	4.34417e11i		−	1.10969i
$792$	1.14253e11	+	9.96614e10i	0.290380	+	0.253295i
$793$	3.01409e11			0.762191
$794$	1.17170e11	+	1.11967e11i	0.294804	+	0.281714i
$795$		0			0
$796$	−2.22811e11	+	1.01236e10i	−0.554990	+	0.0252164i
$797$	−1.11980e11			−0.277527			−0.138764	−	0.990326i	$-0.544313\pi$
$797$	−1.11980e11			−0.277527			−0.138764	+	0.990326i	$0.544313\pi$
$798$	−7.56569e9	+	7.91725e9i	−0.0186568	+	0.0195237i
$799$			2.29109e11i			0.562154i
$800$		0			0
$801$	3.24891e11			0.789237
$802$	−1.76127e11	−	1.68306e11i	−0.425725	−	0.406821i
$803$		−	2.13449e11i		−	0.513372i
$804$	−3.78004e8	−	8.31954e9i	−0.000904634	−	0.0199102i
$805$		0			0
$806$	−4.74764e11	+	4.96825e11i	−1.12496	+	1.17724i
$807$		−	4.05195e10i		−	0.0955365i
$808$	2.59220e11	−	2.97172e11i	0.608167	−	0.697209i
$809$	5.57023e10			0.130041			0.0650203	−	0.997884i	$-0.479289\pi$
$809$	5.57023e10			0.130041			0.0650203	+	0.997884i	$0.479289\pi$
$810$		0			0
$811$		−	7.06448e11i		−	1.63304i	−0.577317	−	0.816520i	$-0.695900\pi$
$811$		−	7.06448e11i		−	1.63304i	0.577317	−	0.816520i	$-0.304100\pi$
$812$	7.04902e11	−	3.20278e10i	1.62145	−	0.0736720i
$813$	−1.85091e11			−0.423666
$814$	2.71464e10	−	2.84078e10i	0.0618321	−	0.0647053i
$815$		0			0
$816$	1.98137e10	+	2.17591e11i	0.0446896	+	0.490773i
$817$	−3.48599e10			−0.0782417
$818$	5.97446e11	+	5.70917e11i	1.33440	+	1.27515i
$819$		−	5.95569e11i		−	1.32372i
$820$		0			0
$821$	−8.39733e10			−0.184828			−0.0924142	−	0.995721i	$-0.529458\pi$
$821$	−8.39733e10			−0.184828			−0.0924142	+	0.995721i	$0.529458\pi$
$822$	9.82933e10	−	1.02861e11i	0.215296	−	0.225301i
$823$			1.90143e11i			0.414459i	0.978292	+	0.207229i	$0.0664446\pi$
$823$			1.90143e11i			0.414459i	−0.978292	+	0.207229i	$0.933555\pi$
$824$	6.05957e11	+	5.28569e11i	1.31442	+	1.14655i
$825$		0			0
$826$	2.37840e11	+	2.27279e11i	0.510933	+	0.488246i
$827$			3.98982e11i			0.852965i	0.904496	+	0.426483i	$0.140247\pi$
$827$			3.98982e11i			0.852965i	−0.904496	+	0.426483i	$0.859753\pi$
$828$	−6.04622e11	+	2.74715e10i	−1.28636	+	0.0584468i
$829$	9.18641e11			1.94504			0.972518	−	0.232827i	$-0.0747977\pi$
$829$	9.18641e11			1.94504			0.972518	+	0.232827i	$0.0747977\pi$
$830$		0			0
$831$		−	4.21536e10i		−	0.0883957i
$832$	−7.01178e10	−	5.11576e11i	−0.146331	−	1.06762i
$833$	6.47936e11			1.34571
$834$	−2.04504e11	−	1.95423e11i	−0.422705	−	0.403935i
$835$		0			0
$836$	5.58382e8	+	1.22895e10i	0.00114316	+	0.0251599i
$837$	4.70655e11			0.958960
$838$	3.21427e11	−	3.36363e11i	0.651789	−	0.682075i
$839$			4.31925e11i			0.871688i	0.900022	+	0.435844i	$0.143550\pi$
$839$			4.31925e11i			0.871688i	−0.900022	+	0.435844i	$0.856450\pi$
$840$		0			0
$841$	1.86726e11			0.373268
$842$	2.34400e10	+	2.23991e10i	0.0466347	+	0.0445639i
$843$		−	2.54205e11i		−	0.503355i
$844$	5.68701e11	−	2.58394e10i	1.12076	−	0.0509228i
$845$		0			0
$846$	−1.20421e11	+	1.26016e11i	−0.235082	+	0.246006i
$847$		−	5.78298e11i		−	1.12362i
$848$	−5.23396e11	+	4.76602e10i	−1.01216	+	0.0921664i
$849$	−2.02643e11			−0.390033
$850$		0			0
$851$			1.56860e11i			0.299085i
$852$	1.14698e10	+	2.52441e11i	0.0217670	+	0.479073i
$853$	−9.29871e11			−1.75641			−0.878206	−	0.478282i	$-0.841260\pi$
$853$	−9.29871e11			−1.75641			−0.878206	+	0.478282i	$0.841260\pi$
$854$	−3.60006e11	+	3.76735e11i	−0.676828	+	0.708279i
$855$		0			0
$856$	−5.07561e11	−	4.42739e11i	−0.945351	−	0.824618i
$857$	−1.19713e11			−0.221931			−0.110965	−	0.993824i	$-0.535394\pi$
$857$	−1.19713e11			−0.221931			−0.110965	+	0.993824i	$0.535394\pi$
$858$	6.16989e10	+	5.89592e10i	0.113849	+	0.108793i
$859$			4.22514e11i			0.776012i	0.921657	+	0.388006i	$0.126836\pi$
$859$			4.22514e11i			0.776012i	−0.921657	+	0.388006i	$0.873164\pi$
$860$		0			0
$861$	−8.80936e10			−0.160299
$862$	−2.55555e11	+	2.67430e11i	−0.462865	+	0.484374i
$863$			2.84698e11i			0.513264i	0.966509	+	0.256632i	$0.0826129\pi$
$863$			2.84698e11i			0.513264i	−0.966509	+	0.256632i	$0.917387\pi$
$864$	−2.20135e11	+	2.76784e11i	−0.395034	+	0.496691i
$865$		0			0
$866$	−5.97024e11	−	5.70514e11i	−1.06150	−	1.01437i
$867$			2.17945e11i			0.385719i
$868$	−5.39243e10	−	1.18683e12i	−0.0949961	−	2.09078i
$869$	−7.81630e9			−0.0137064
$870$		0			0
$871$			3.67517e10i			0.0638565i
$872$	−4.89172e11	+	5.60793e11i	−0.846049	+	0.969921i
$873$	3.47721e11			0.598651
$874$	−3.55062e10	−	3.39296e10i	−0.0608497	−	0.0581478i
$875$		0			0
$876$	2.33780e11	−	1.06220e10i	0.397001	−	0.0180380i
$877$	−1.94476e11			−0.328752			−0.164376	−	0.986398i	$-0.552561\pi$
$877$	−1.94476e11			−0.328752			−0.164376	+	0.986398i	$0.552561\pi$
$878$	4.50907e11	−	4.71859e11i	0.758767	−	0.794025i
$879$			4.33753e10i			0.0726585i
$880$		0			0
$881$	9.06691e11			1.50507			0.752533	−	0.658555i	$-0.228832\pi$
$881$	9.06691e11			1.50507			0.752533	+	0.658555i	$0.228832\pi$
$882$	3.56382e11	+	3.40557e11i	0.588900	+	0.562750i
$883$		−	2.26542e11i		−	0.372654i	−0.982488	−	0.186327i	$-0.940342\pi$
$883$		−	2.26542e11i		−	0.372654i	0.982488	−	0.186327i	$-0.0596584\pi$
$884$	−4.37638e10	−	9.63202e11i	−0.0716648	−	1.57728i
$885$		0			0
$886$	1.96973e10	−	2.06125e10i	0.0319647	−	0.0334500i
$887$		−	1.70744e11i		−	0.275837i	−0.990444	−	0.137918i	$-0.955959\pi$
$887$		−	1.70744e11i		−	0.275837i	0.990444	−	0.137918i	$-0.0440412\pi$
$888$	3.24646e10	+	2.83184e10i	0.0522105	+	0.0455425i
$889$	−1.48315e12			−2.37453
$890$		0			0
$891$			1.84404e11i			0.292590i
$892$	4.50323e11	−	2.04608e10i	0.711320	−	0.0323193i
$893$	−1.41433e10			−0.0222405
$894$	−2.20037e11	+	2.30261e11i	−0.344465	+	0.360471i
$895$		0			0
$896$	7.23174e11	+	5.23391e11i	1.12205	+	0.812071i
$897$	−3.40684e11			−0.526238
$898$	−6.64919e11	−	6.35394e11i	−1.02250	−	0.977097i
$899$		−	1.15664e12i		−	1.77075i
$900$		0			0
$901$	−9.81380e11			−1.48915
$902$	−6.83713e10	+	7.15484e10i	−0.103288	+	0.108087i
$903$		−	4.18074e11i		−	0.628785i
$904$	3.51717e11	−	4.03213e11i	0.526647	−	0.603755i
$905$		0			0
$906$	−2.43955e11	−	2.33123e11i	−0.362074	−	0.345997i
$907$		−	5.20431e11i		−	0.769013i	−0.923122	−	0.384507i	$-0.874372\pi$
$907$		−	5.20431e11i		−	0.769013i	0.923122	−	0.384507i	$-0.125628\pi$
$908$	−4.74254e11	+	2.15481e10i	−0.697698	+	0.0317004i
$909$	5.60205e11			0.820525
$910$		0			0
$911$		−	5.42499e11i		−	0.787635i	−0.919189	−	0.393818i	$-0.871154\pi$
$911$		−	5.42499e11i		−	0.787635i	0.919189	−	0.393818i	$-0.128846\pi$
$912$	−1.34323e10	+	1.22314e9i	−0.0194165	+	0.00176806i
$913$	4.43327e11			0.638030
$914$	−5.21650e11	−	4.98487e11i	−0.747472	−	0.714281i
$915$		0			0
$916$	−1.31403e10	−	2.89205e11i	−0.0186647	−	0.410794i
$917$	4.37497e11			0.618725
$918$	−4.56233e11	+	4.77433e11i	−0.642415	+	0.672266i
$919$			6.49225e11i			0.910192i	0.890442	+	0.455096i	$0.150395\pi$
$919$			6.49225e11i			0.910192i	−0.890442	+	0.455096i	$0.849605\pi$
$920$		0			0
$921$	9.16364e10			0.127359
$922$	−8.94283e11	−	8.54573e11i	−1.23752	−	1.18257i
$923$		−	1.11516e12i		−	1.53650i
$924$	−1.47387e11	+	6.69666e9i	−0.202196	+	0.00918693i
$925$		0			0
$926$	9.42742e11	−	9.86549e11i	1.28218	−	1.34176i
$927$			1.14230e12i			1.54690i
$928$	6.80200e11	+	5.40983e11i	0.917159	+	0.729444i
$929$	4.98636e11			0.669455			0.334727	−	0.942315i	$-0.391356\pi$
$929$	4.98636e11			0.669455			0.334727	+	0.942315i	$0.391356\pi$
$930$		0			0
$931$			3.99982e10i			0.0532404i
$932$	−2.61365e10	−	5.75240e11i	−0.0346404	−	0.762405i
$933$	−3.35785e11			−0.443133
$934$	3.54529e11	−	3.71003e11i	0.465870	−	0.487518i
$935$		0			0
$936$	4.82191e11	−	5.52789e11i	0.628226	−	0.720205i
$937$	−4.01408e11			−0.520748			−0.260374	−	0.965508i	$-0.583846\pi$
$937$	−4.01408e11			−0.520748			−0.260374	+	0.965508i	$0.583846\pi$
$938$	−4.59364e10	−	4.38966e10i	−0.0593397	−	0.0567048i
$939$		−	7.57332e10i		−	0.0974146i
$940$		0			0
$941$	−2.64682e10			−0.0337572			−0.0168786	−	0.999858i	$-0.505373\pi$
$941$	−2.64682e10			−0.0337572			−0.0168786	+	0.999858i	$0.505373\pi$
$942$	−9.56214e10	+	1.00065e11i	−0.121437	+	0.127080i
$943$		−	3.95071e11i		−	0.499606i
$944$	3.67439e10	+	4.03515e11i	0.0462698	+	0.508127i
$945$		0			0
$946$	−3.39554e11	−	3.24476e11i	−0.423979	−	0.405152i
$947$			5.71352e11i			0.710401i	0.934790	+	0.355201i	$0.115587\pi$
$947$			5.71352e11i			0.710401i	−0.934790	+	0.355201i	$0.884413\pi$
$948$	−3.88967e8	−	8.56081e9i	−0.000481592	−	0.0105994i
$949$	−1.03273e12			−1.27327
$950$		0			0
$951$			1.47163e10i			0.0179918i
$952$	1.25619e12	+	1.09576e12i	1.52935	+	1.33403i
$953$	1.09917e12			1.33258			0.666288	−	0.745694i	$-0.267882\pi$
$953$	1.09917e12			1.33258			0.666288	+	0.745694i	$0.267882\pi$
$954$	−5.39785e11	−	5.15817e11i	−0.651670	−	0.622733i
$955$		0			0
$956$	7.08988e11	−	3.22134e10i	0.848803	−	0.0385660i
$957$	−1.43639e11			−0.171247
$958$	3.96719e11	−	4.15153e11i	0.471000	−	0.492886i
$959$		−	1.08545e12i		−	1.28333i
$960$		0			0
$961$	−1.09451e12			−1.28329
$962$	−1.37445e11	−	1.31342e11i	−0.160483	−	0.153357i
$963$		−	9.56813e11i		−	1.11256i
$964$	−1.86512e9	−	4.10495e10i	−0.00215972	−	0.0475335i
$965$		0			0
$966$	4.06917e11	−	4.25825e11i	0.467301	−	0.489016i
$967$			8.78566e11i			1.00477i	0.864643	+	0.502387i	$0.167545\pi$
$967$			8.78566e11i			1.00477i	−0.864643	+	0.502387i	$0.832455\pi$
$968$	4.68207e11	−	5.36758e11i	0.533257	−	0.611332i
$969$	−2.51858e10			−0.0285668
$970$		0			0
$971$			7.91945e11i			0.890878i	0.895312	+	0.445439i	$0.146952\pi$
$971$			7.91945e11i			0.890878i	−0.895312	+	0.445439i	$0.853048\pi$
$972$	−7.67865e11	+	3.48885e10i	−0.860241	+	0.0390857i
$973$	−2.15806e12			−2.40775
$974$	−6.61654e11	+	6.92399e11i	−0.735182	+	0.769344i
$975$		0			0
$976$	−6.39163e11	+	5.82018e10i	−0.704389	+	0.0641413i
$977$	5.46919e11			0.600268			0.300134	−	0.953897i	$-0.402969\pi$
$977$	5.46919e11			0.600268			0.300134	+	0.953897i	$0.402969\pi$
$978$	6.36600e9	+	6.08332e9i	0.00695843	+	0.00664944i
$979$			3.55177e11i			0.386646i
$980$		0			0
$981$	−1.05716e12			−1.14147
$982$	3.31923e11	−	3.47346e11i	0.356936	−	0.373522i
$983$			7.38083e11i			0.790481i	0.918578	+	0.395240i	$0.129339\pi$
$983$			7.38083e11i			0.790481i	−0.918578	+	0.395240i	$0.870661\pi$
$984$	−8.17658e10	−	7.13233e10i	−0.0872151	−	0.0760766i
$985$		0			0
$986$	1.17329e12	+	1.12119e12i	1.24136	+	1.18624i
$987$		−	1.69620e11i		−	0.178735i
$988$	5.94601e10	−	2.70162e9i	0.0624020	−	0.00283528i
$989$	1.87492e12			1.95974
$990$		0			0
$991$			3.73877e11i			0.387645i	0.981037	+	0.193823i	$0.0620886\pi$
$991$			3.73877e11i			0.387645i	−0.981037	+	0.193823i	$0.937911\pi$
$992$	9.10839e11	−	1.14523e12i	0.940578	−	1.18263i
$993$	3.29959e11			0.339362
$994$	1.39385e12	+	1.33196e12i	1.42781	+	1.36441i
$995$		0			0
$996$	2.20615e10	+	4.85555e11i	0.0224181	+	0.493402i
$997$	−1.14224e12			−1.15605			−0.578025	−	0.816019i	$-0.696177\pi$
$997$	−1.14224e12			−1.15605			−0.578025	+	0.816019i	$0.696177\pi$
$998$	−2.57118e11	+	2.69066e11i	−0.259185	+	0.271229i
$999$			1.30205e11i			0.130727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.d.51.3		16
4.3	odd	2	inner	100.9.b.d.51.4		16
5.2	odd	4		100.9.d.c.99.23		32
5.3	odd	4		100.9.d.c.99.10		32
5.4	even	2		20.9.b.a.11.14	yes	16
15.14	odd	2		180.9.c.a.91.3		16
20.3	even	4		100.9.d.c.99.24		32
20.7	even	4		100.9.d.c.99.9		32
20.19	odd	2		20.9.b.a.11.13	✓	16
40.19	odd	2		320.9.b.d.191.7		16
40.29	even	2		320.9.b.d.191.10		16
60.59	even	2		180.9.c.a.91.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.13	✓	16	20.19	odd	2
20.9.b.a.11.14	yes	16	5.4	even	2
100.9.b.d.51.3		16	1.1	even	1	trivial
100.9.b.d.51.4		16	4.3	odd	2	inner
100.9.d.c.99.9		32	20.7	even	4
100.9.d.c.99.10		32	5.3	odd	4
100.9.d.c.99.23		32	5.2	odd	4
100.9.d.c.99.24		32	20.3	even	4
180.9.c.a.91.3		16	15.14	odd	2
180.9.c.a.91.4		16	60.59	even	2
320.9.b.d.191.7		16	40.19	odd	2
320.9.b.d.191.10		16	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.5676 - 11.0540i) q^{2} +27.2434i q^{3} +(11.6196 + 255.736i) q^{4} +(301.148 - 315.141i) q^{6} -3325.58i q^{7} +(2692.49 - 3086.70i) q^{8} +5818.80 q^{9} +6361.21i q^{11} +(-6967.12 + 316.557i) q^{12} +30777.4 q^{13} +(-36760.8 + 38469.0i) q^{14} +(-65266.0 + 5943.09i) q^{16} -122375. q^{17} +(-67309.6 - 64320.8i) q^{18} -7554.43i q^{19} +90600.1 q^{21} +(70316.6 - 73584.1i) q^{22} +406311. i q^{23} +(84092.2 + 73352.6i) q^{24} +(-356021. - 340213. i) q^{26} +337268. i q^{27} +(850471. - 38641.8i) q^{28} +828838. q^{29} -1.39549e6i q^{31} +(820666. + 652701. i) q^{32} -173301. q^{33} +(1.41559e6 + 1.35273e6i) q^{34} +(67611.9 + 1.48808e6i) q^{36} +386059. q^{37} +(-83506.4 + 87386.8i) q^{38} +838482. i q^{39} -972335. q^{41} +(-1.04803e6 - 1.00149e6i) q^{42} -4.61450e6i q^{43} +(-1.62679e6 + 73914.5i) q^{44} +(4.49135e6 - 4.70005e6i) q^{46} -1.87219e6i q^{47} +(-161910. - 1.77807e6i) q^{48} -5.29467e6 q^{49} -3.33392e6i q^{51} +(357620. + 7.87090e6i) q^{52} +8.01944e6 q^{53} +(3.72815e6 - 3.90139e6i) q^{54} +(-1.02651e7 - 8.95408e6i) q^{56} +205808. q^{57} +(-9.58768e6 - 9.16195e6i) q^{58} -6.18263e6i q^{59} +9.79320e6 q^{61} +(-1.54257e7 + 1.61425e7i) q^{62} -1.93509e7i q^{63} +(-2.27822e6 - 1.66218e7i) q^{64} +(2.00468e6 + 1.91566e6i) q^{66} +1.19411e6i q^{67} +(-1.42195e6 - 3.12958e7i) q^{68} -1.10693e7 q^{69} -3.62332e7i q^{71} +(1.56670e7 - 1.79609e7i) q^{72} -3.35548e7 q^{73} +(-4.46578e6 - 4.26748e6i) q^{74} +(1.93194e6 - 87779.2i) q^{76} +2.11547e7 q^{77} +(9.26855e6 - 9.69923e6i) q^{78} +1.22874e6i q^{79} +2.89888e7 q^{81} +(1.12476e7 + 1.07482e7i) q^{82} -6.96923e7i q^{83} +(1.05273e6 + 2.31697e7i) q^{84} +(-5.10086e7 + 5.33788e7i) q^{86} +2.25804e7i q^{87} +(1.96352e7 + 1.71275e7i) q^{88} +5.58347e7 q^{89} -1.02353e8i q^{91} +(-1.03908e8 + 4.72116e6i) q^{92} +3.80180e7 q^{93} +(-2.06951e7 + 2.16567e7i) q^{94} +(-1.77818e7 + 2.23578e7i) q^{96} +5.97582e7 q^{97} +(6.12467e7 + 5.85271e7i) q^{98} +3.70146e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9} + 64040 q^{12} - 51392 q^{13} + 68472 q^{14} - 81424 q^{16} - 27552 q^{17} + 616994 q^{18} + 414496 q^{21} + 389120 q^{22} + 163792 q^{24}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9 + 64040 * q^12 - 51392 * q^13 + 68472 * q^14 - 81424 * q^16 - 27552 * q^17 + 616994 * q^18 + 414496 * q^21 + 389120 * q^22 + 163792 * q^24 + 1037124 * q^26 - 1288520 * q^28 + 2764896 * q^29 + 4379904 * q^32 + 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 - 9009472 * q^37 + 3087360 * q^38 - 8576448 * q^41 + 4067400 * q^42 + 16921200 * q^44 - 7974152 * q^46 + 2696640 * q^48 - 32803600 * q^49 - 6679352 * q^52 - 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 - 11957760 * q^57 - 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 + 19358000 * q^66 - 16095192 * q^68 + 7527264 * q^69 + 42242664 * q^72 - 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 + 104032400 * q^78 + 140586672 * q^81 - 83921012 * q^82 + 69761824 * q^84 - 101724672 * q^86 - 44728480 * q^88 + 106647456 * q^89 + 13876200 * q^92 - 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 - 171851232 * q^97 + 285387714 * q^98

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