LMFDB - Embedded newform 7.10.c.a.4.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,10,Mod(2,7)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7.2"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.60525085315$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 $ x^10 - x^9 + 430x^8 + 61x^7 + 146753x^6 + 23608x^5 + 16136944x^4 + 30575648x^3 + 1399072384x^2 + 1034227200x + 761760000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.5
Root			$8.80924 - 15.2580i$ of defining polynomial
Character	$\chi$	$=$	7.4
Dual form			7.10.c.a.2.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(15.6185 + 27.0520i) q^{2} +(-56.7670 + 98.3234i) q^{3} +(-231.874 + 401.617i) q^{4} +(-239.755 - 415.269i) q^{5} -3546.46 q^{6} +(1428.40 + 6189.77i) q^{7} +1507.26 q^{8} +(3396.51 + 5882.92i) q^{9} +(7489.23 - 12971.7i) q^{10} +(33637.5 - 58261.9i) q^{11} +(-26325.6 - 45597.2i) q^{12} +39620.0 q^{13} +(-145136. + 135316. i) q^{14} +54440.8 q^{15} +(142260. + 246402. i) q^{16} +(-106607. + 184649. i) q^{17} +(-106097. + 183765. i) q^{18} +(-566407. - 981046. i) q^{19} +222372. q^{20} +(-689686. - 210930. i) q^{21} +2.10147e6 q^{22} +(365109. + 632388. i) q^{23} +(-85562.8 + 148199. i) q^{24} +(861597. - 1.49233e6i) q^{25} +(618804. + 1.07180e6i) q^{26} -3.00593e6 q^{27} +(-2.81713e6 - 861574. i) q^{28} +383457. q^{29} +(850283. + 1.47273e6i) q^{30} +(2.73393e6 - 4.73530e6i) q^{31} +(-4.05793e6 + 7.02853e6i) q^{32} +(3.81901e6 + 6.61472e6i) q^{33} -6.66015e6 q^{34} +(2.22795e6 - 2.07720e6i) q^{35} -3.15024e6 q^{36} +(3.83476e6 + 6.64200e6i) q^{37} +(1.76928e7 - 3.06449e7i) q^{38} +(-2.24911e6 + 3.89557e6i) q^{39} +(-361374. - 625919. i) q^{40} +1.08865e6 q^{41} +(-5.06577e6 - 2.19518e7i) q^{42} -1.92137e7 q^{43} +(1.55993e7 + 2.70188e7i) q^{44} +(1.62866e6 - 2.82093e6i) q^{45} +(-1.14049e7 + 1.97539e7i) q^{46} +(2.11223e7 + 3.65850e7i) q^{47} -3.23028e7 q^{48} +(-3.62729e7 + 1.76830e7i) q^{49} +5.38273e7 q^{50} +(-1.21035e7 - 2.09639e7i) q^{51} +(-9.18684e6 + 1.59121e7i) q^{52} +(2.68028e7 - 4.64237e7i) q^{53} +(-4.69480e7 - 8.13164e7i) q^{54} -3.22591e7 q^{55} +(2.15298e6 + 9.32961e6i) q^{56} +1.28613e8 q^{57} +(5.98901e6 + 1.03733e7i) q^{58} +(-9.06495e6 + 1.57010e7i) q^{59} +(-1.26234e7 + 2.18644e7i) q^{60} +(-1.48303e7 - 2.56868e7i) q^{61} +1.70799e8 q^{62} +(-3.15624e7 + 2.94268e7i) q^{63} -1.07840e8 q^{64} +(-9.49911e6 - 1.64529e7i) q^{65} +(-1.19294e8 + 2.06624e8i) q^{66} +(8.34811e7 - 1.44594e8i) q^{67} +(-4.94387e7 - 8.56303e7i) q^{68} -8.29047e7 q^{69} +(9.09897e7 + 2.78278e7i) q^{70} -3.15617e8 q^{71} +(5.11942e6 + 8.86710e6i) q^{72} +(1.51081e7 - 2.61679e7i) q^{73} +(-1.19786e8 + 2.07476e8i) q^{74} +(9.78206e7 + 1.69430e8i) q^{75} +5.25340e8 q^{76} +(4.08676e8 + 1.24987e8i) q^{77} -1.40511e8 q^{78} +(-2.62085e8 - 4.53944e8i) q^{79} +(6.82155e7 - 1.18153e8i) q^{80} +(1.03784e8 - 1.79760e8i) q^{81} +(1.70030e7 + 2.94500e7i) q^{82} -6.01000e8 q^{83} +(2.44633e8 - 2.28081e8i) q^{84} +1.02238e8 q^{85} +(-3.00089e8 - 5.19769e8i) q^{86} +(-2.17677e7 + 3.77027e7i) q^{87} +(5.07006e7 - 8.78160e7i) q^{88} +(4.80628e8 + 8.32473e8i) q^{89} +1.01749e8 q^{90} +(5.65933e7 + 2.45239e8i) q^{91} -3.38637e8 q^{92} +(3.10394e8 + 5.37618e8i) q^{93} +(-6.59798e8 + 1.14280e9i) q^{94} +(-2.71598e8 + 4.70422e8i) q^{95} +(-4.60713e8 - 7.97978e8i) q^{96} +3.75562e8 q^{97} +(-1.04489e9 - 7.05074e8i) q^{98} +4.57001e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16}+ \cdots - 1900777180 q^{99}+O(q^{100}) $ 10 * q - 18 * q^2 + 161 * q^3 - 940 * q^4 + 1533 * q^5 - 8708 * q^6 - 1036 * q^7 + 34272 * q^8 - 35734 * q^9 + 4298 * q^10 + 42213 * q^11 + 135604 * q^12 - 319676 * q^13 - 39522 * q^14 + 151394 * q^15 + 322064 * q^16 + 324681 * q^17 - 1012868 * q^18 - 16121 * q^19 - 350616 * q^20 - 1557857 * q^21 - 62692 * q^22 + 2638863 * q^23 + 8449728 * q^24 - 1304092 * q^25 + 4179252 * q^26 - 18331558 * q^27 - 22156316 * q^28 + 15292500 * q^29 + 20557942 * q^30 + 19179237 * q^31 - 6263520 * q^32 + 1689359 * q^33 - 62909700 * q^34 - 43746759 * q^35 + 71476528 * q^36 + 39566985 * q^37 + 67365270 * q^38 - 44299486 * q^39 + 5721744 * q^40 - 53436852 * q^41 - 183129856 * q^42 + 101835992 * q^43 + 99704916 * q^44 + 85098230 * q^45 - 14489202 * q^46 + 32509659 * q^47 - 185141600 * q^48 - 49024598 * q^49 + 3328464 * q^50 + 44168403 * q^51 + 103893272 * q^52 - 25714707 * q^53 + 51200926 * q^54 - 144695222 * q^55 + 115352832 * q^56 - 121710346 * q^57 - 46645516 * q^58 + 46776513 * q^59 + 132391756 * q^60 - 113075039 * q^61 + 467465628 * q^62 + 318071530 * q^63 - 192008960 * q^64 - 338113566 * q^65 - 836682602 * q^66 - 126707879 * q^67 + 32262636 * q^68 + 1323616182 * q^69 + 697712470 * q^70 - 1188736032 * q^71 - 950557728 * q^72 - 859257651 * q^73 + 591757530 * q^74 - 169061732 * q^75 + 1101475592 * q^76 + 1911891891 * q^77 + 519432424 * q^78 - 527065417 * q^79 - 1257352656 * q^80 + 551662715 * q^81 - 1341703076 * q^82 - 144863208 * q^83 + 486452204 * q^84 - 1197360222 * q^85 - 678648216 * q^86 - 340781350 * q^87 + 903700608 * q^88 + 1661554797 * q^89 + 1967758744 * q^90 + 726641384 * q^91 - 1301840952 * q^92 - 423057489 * q^93 - 272580882 * q^94 - 1197123495 * q^95 - 1441922272 * q^96 + 869770188 * q^97 - 2404833858 * q^98 - 1900777180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	15.6185	+	27.0520i	0.690246	+	1.19554i	0.971757	+	0.235983i	$0.0758309\pi$
$2$	15.6185	+	27.0520i	0.690246	+	1.19554i	−0.281511	+	0.959558i	$0.590836\pi$
$3$	−56.7670	+	98.3234i	−0.404623	+	0.700828i	−0.994278	−	0.106828i	$-0.965931\pi$
$3$	−56.7670	+	98.3234i	−0.404623	+	0.700828i	0.589654	+	0.807656i	$0.299264\pi$
$4$	−231.874	+	401.617i	−0.452878	+	0.784408i
$5$	−239.755	−	415.269i	−0.171555	−	0.297142i	0.767409	−	0.641158i	$-0.221546\pi$
$5$	−239.755	−	415.269i	−0.171555	−	0.297142i	−0.938964	+	0.344016i	$0.888212\pi$
$6$	−3546.46			−1.11716
$7$	1428.40	+	6189.77i	0.224859	+	0.974391i
$7$	1428.40	+	6189.77i	0.224859	+	0.974391i
$8$	1507.26			0.130102
$9$	3396.51	+	5882.92i	0.172560	+	0.298883i
$10$	7489.23	−	12971.7i	0.236830	−	0.410202i
$11$	33637.5	−	58261.9i	0.692719	−	1.19982i	−0.278224	−	0.960516i	$-0.589746\pi$
$11$	33637.5	−	58261.9i	0.692719	−	1.19982i	0.970944	−	0.239309i	$-0.0769208\pi$
$12$	−26325.6	−	45597.2i	−0.366490	−	0.634779i
$13$	39620.0			0.384742			0.192371	−	0.981322i	$-0.438382\pi$
$13$	39620.0			0.384742			0.192371	+	0.981322i	$0.438382\pi$
$14$	−145136.	+	135316.i	−1.00972	+	0.941397i
$15$	54440.8			0.277661
$16$	142260.	+	246402.i	0.542681	+	0.939951i
$17$	−106607.	+	184649.i	−0.309575	+	0.536199i	−0.978269	−	0.207338i	$-0.933520\pi$
$17$	−106607.	+	184649.i	−0.309575	+	0.536199i	0.668695	+	0.743537i	$0.266853\pi$
$18$	−106097.	+	183765.i	−0.238218	+	0.412606i
$19$	−566407.	−	981046.i	−0.997097	−	1.72702i	−0.564485	−	0.825443i	$-0.690925\pi$
$19$	−566407.	−	981046.i	−0.997097	−	1.72702i	−0.432612	−	0.901580i	$-0.642408\pi$
$20$	222372.			0.310774
$21$	−689686.	−	210930.i	−0.773863	−	0.236674i
$22$	2.10147e6			1.91259
$23$	365109.	+	632388.i	0.272049	+	0.471203i	0.969386	−	0.245540i	$-0.0789652\pi$
$23$	365109.	+	632388.i	0.272049	+	0.471203i	−0.697337	+	0.716743i	$0.745632\pi$
$24$	−85562.8	+	148199.i	−0.0526422	+	0.0911790i
$25$	861597.	−	1.49233e6i	0.441138	−	0.764073i
$26$	618804.	+	1.07180e6i	0.265566	+	0.459974i
$27$	−3.00593e6			−1.08853
$28$	−2.81713e6	−	861574.i	−0.866154	−	0.264900i
$29$	383457.			0.100676			0.0503379	−	0.998732i	$-0.483970\pi$
$29$	383457.			0.100676			0.0503379	+	0.998732i	$0.483970\pi$
$30$	850283.	+	1.47273e6i	0.191654	+	0.331954i
$31$	2.73393e6	−	4.73530e6i	0.531691	−	0.920915i	−0.467625	−	0.883927i	$-0.654890\pi$
$31$	2.73393e6	−	4.73530e6i	0.531691	−	0.920915i	0.999316	−	0.0369885i	$-0.0117765\pi$
$32$	−4.05793e6	+	7.02853e6i	−0.684115	+	1.18492i
$33$	3.81901e6	+	6.61472e6i	0.560580	+	0.970954i
$34$	−6.66015e6			−0.854730
$35$	2.22795e6	−	2.07720e6i	0.250957	−	0.233977i
$36$	−3.15024e6			−0.312595
$37$	3.83476e6	+	6.64200e6i	0.336380	+	0.582627i	0.983749	−	0.179549i	$-0.0574640\pi$
$37$	3.83476e6	+	6.64200e6i	0.336380	+	0.582627i	−0.647369	+	0.762177i	$0.724131\pi$
$38$	1.76928e7	−	3.06449e7i	1.37648	−	2.38414i
$39$	−2.24911e6	+	3.89557e6i	−0.155675	+	0.269638i
$40$	−361374.	−	625919.i	−0.0223196	−	0.0386588i
$41$	1.08865e6			0.0601671			0.0300836	−	0.999547i	$-0.490423\pi$
$41$	1.08865e6			0.0601671			0.0300836	+	0.999547i	$0.490423\pi$
$42$	−5.06577e6	−	2.19518e7i	−0.251203	−	1.08855i
$43$	−1.92137e7			−0.857044			−0.428522	−	0.903531i	$-0.640965\pi$
$43$	−1.92137e7			−0.857044			−0.428522	+	0.903531i	$0.640965\pi$
$44$	1.55993e7	+	2.70188e7i	0.627435	+	1.08675i
$45$	1.62866e6	−	2.82093e6i	0.0592072	−	0.102550i
$46$	−1.14049e7	+	1.97539e7i	−0.375562	+	0.650492i
$47$	2.11223e7	+	3.65850e7i	0.631396	+	1.09361i	0.987267	+	0.159074i	$0.0508510\pi$
$47$	2.11223e7	+	3.65850e7i	0.631396	+	1.09361i	−0.355871	+	0.934535i	$0.615816\pi$
$48$	−3.23028e7			−0.878324
$49$	−3.62729e7	+	1.76830e7i	−0.898877	+	0.438201i
$50$	5.38273e7			1.21797
$51$	−1.21035e7	−	2.09639e7i	−0.250522	−	0.433917i
$52$	−9.18684e6	+	1.59121e7i	−0.174241	+	0.301795i
$53$	2.68028e7	−	4.64237e7i	0.466593	−	0.808163i	−0.532679	−	0.846317i	$-0.678815\pi$
$53$	2.68028e7	−	4.64237e7i	0.466593	−	0.808163i	0.999272	+	0.0381548i	$0.0121480\pi$
$54$	−4.69480e7	−	8.13164e7i	−0.751356	−	1.30139i
$55$	−3.22591e7			−0.475358
$56$	2.15298e6	+	9.32961e6i	0.0292545	+	0.126770i
$57$	1.28613e8			1.61379
$58$	5.98901e6	+	1.03733e7i	0.0694910	+	0.120362i
$59$	−9.06495e6	+	1.57010e7i	−0.0973938	+	0.168691i	−0.910605	−	0.413277i	$-0.864384\pi$
$59$	−9.06495e6	+	1.57010e7i	−0.0973938	+	0.168691i	0.813211	+	0.581968i	$0.197717\pi$
$60$	−1.26234e7	+	2.18644e7i	−0.125746	+	0.217799i
$61$	−1.48303e7	−	2.56868e7i	−0.137140	−	0.237534i	0.789273	−	0.614043i	$-0.210458\pi$
$61$	−1.48303e7	−	2.56868e7i	−0.137140	−	0.237534i	−0.926413	+	0.376509i	$0.877125\pi$
$62$	1.70799e8			1.46799
$63$	−3.15624e7	+	2.94268e7i	−0.252428	+	0.235348i
$64$	−1.07840e8			−0.803469
$65$	−9.49911e6	−	1.64529e7i	−0.0660044	−	0.114323i
$66$	−1.19294e8	+	2.06624e8i	−0.773876	+	1.34039i
$67$	8.34811e7	−	1.44594e8i	0.506118	−	0.876622i	−0.493857	−	0.869543i	$-0.664413\pi$
$67$	8.34811e7	−	1.44594e8i	0.506118	−	0.876622i	0.999975	−	0.00707865i	$-0.00225322\pi$
$68$	−4.94387e7	−	8.56303e7i	−0.280399	−	0.485666i
$69$	−8.29047e7			−0.440310
$70$	9.09897e7	+	2.78278e7i	0.452951	+	0.138528i
$71$	−3.15617e8			−1.47400			−0.737001	−	0.675892i	$-0.763759\pi$
$71$	−3.15617e8			−1.47400			−0.737001	+	0.675892i	$0.763759\pi$
$72$	5.11942e6	+	8.86710e6i	0.0224504	+	0.0388853i
$73$	1.51081e7	−	2.61679e7i	0.0622667	−	0.107849i	−0.833212	−	0.552954i	$-0.813500\pi$
$73$	1.51081e7	−	2.61679e7i	0.0622667	−	0.107849i	0.895478	+	0.445105i	$0.146834\pi$
$74$	−1.19786e8	+	2.07476e8i	−0.464370	+	0.804312i
$75$	9.78206e7	+	1.69430e8i	0.356989	+	0.618323i
$76$	5.25340e8			1.80626
$77$	4.08676e8	+	1.24987e8i	1.32486	+	0.405189i
$78$	−1.40511e8			−0.429817
$79$	−2.62085e8	−	4.53944e8i	−0.757041	−	1.31123i	−0.944353	−	0.328934i	$-0.893311\pi$
$79$	−2.62085e8	−	4.53944e8i	−0.757041	−	1.31123i	0.187312	−	0.982301i	$-0.440023\pi$
$80$	6.82155e7	−	1.18153e8i	0.186199	−	0.322507i
$81$	1.03784e8	−	1.79760e8i	0.267885	−	0.463991i
$82$	1.70030e7	+	2.94500e7i	0.0415301	+	0.0719323i
$83$	−6.01000e8			−1.39003			−0.695013	−	0.718997i	$-0.744601\pi$
$83$	−6.01000e8			−1.39003			−0.695013	+	0.718997i	$0.744601\pi$
$84$	2.44633e8	−	2.28081e8i	0.536115	−	0.499840i
$85$	1.02238e8			0.212436
$86$	−3.00089e8	−	5.19769e8i	−0.591571	−	1.02463i
$87$	−2.17677e7	+	3.77027e7i	−0.0407358	+	0.0705564i
$88$	5.07006e7	−	8.78160e7i	0.0901241	−	0.156100i
$89$	4.80628e8	+	8.32473e8i	0.811997	+	1.40642i	0.911464	+	0.411379i	$0.134953\pi$
$89$	4.80628e8	+	8.32473e8i	0.811997	+	1.40642i	−0.0994677	+	0.995041i	$0.531714\pi$
$90$	1.01749e8			0.163470
$91$	5.65933e7	+	2.45239e8i	0.0865125	+	0.374889i
$92$	−3.38637e8			−0.492821
$93$	3.10394e8	+	5.37618e8i	0.430269	+	0.745247i
$94$	−6.59798e8	+	1.14280e9i	−0.871636	+	1.50972i
$95$	−2.71598e8	+	4.70422e8i	−0.342114	+	0.592559i
$96$	−4.60713e8	−	7.97978e8i	−0.553618	−	0.958894i
$97$	3.75562e8			0.430734			0.215367	−	0.976533i	$-0.430905\pi$
$97$	3.75562e8			0.430734			0.215367	+	0.976533i	$0.430905\pi$
$98$	−1.04489e9	−	7.05074e8i	−1.14433	−	0.772178i
$99$	4.57001e8			0.478144
$100$	3.99563e8	+	6.92064e8i	0.399563	+	0.692064i
$101$	5.09386e8	−	8.82283e8i	0.487081	−	0.843649i	−0.512809	−	0.858503i	$-0.671395\pi$
$101$	5.09386e8	−	8.82283e8i	0.487081	−	0.843649i	0.999890	+	0.0148538i	$0.00472830\pi$
$102$	3.78077e8	−	6.54849e8i	0.345843	−	0.599019i
$103$	−5.41083e8	−	9.37183e8i	−0.473692	−	0.820459i	0.525854	−	0.850575i	$-0.323746\pi$
$103$	−5.41083e8	−	9.37183e8i	−0.473692	−	0.820459i	−0.999546	+	0.0301156i	$0.990412\pi$
$104$	5.97177e7			0.0500556
$105$	7.77635e7	+	3.36976e8i	0.0624344	+	0.270550i
$106$	1.67447e9			1.28825
$107$	−1.68779e8	−	2.92334e8i	−0.124478	−	0.215602i	0.797051	−	0.603912i	$-0.206392\pi$
$107$	−1.68779e8	−	2.92334e8i	−0.124478	−	0.215602i	−0.921529	+	0.388310i	$0.873059\pi$
$108$	6.96996e8	−	1.20723e9i	0.492973	−	0.853855i
$109$	−2.33360e8	+	4.04191e8i	−0.158346	+	0.274263i	−0.934272	−	0.356560i	$-0.883949\pi$
$109$	−2.33360e8	+	4.04191e8i	−0.158346	+	0.274263i	0.775926	+	0.630823i	$0.217283\pi$
$110$	−5.03839e8	−	8.72674e8i	−0.328114	−	0.568310i
$111$	−8.70752e8			−0.544429
$112$	−1.32197e9	+	1.23252e9i	−0.793853	+	0.740139i
$113$	2.80140e8			0.161630			0.0808150	−	0.996729i	$-0.474248\pi$
$113$	2.80140e8			0.161630			0.0808150	+	0.996729i	$0.474248\pi$
$114$	2.00874e9	+	3.47924e9i	1.11391	+	1.92936i
$115$	1.75074e8	−	3.03237e8i	0.0933429	−	0.161675i
$116$	−8.89135e7	+	1.54003e8i	−0.0455939	+	0.0789709i
$117$	1.34570e8	+	2.33081e8i	0.0663912	+	0.114993i
$118$	−5.66323e8			−0.268903
$119$	−1.29521e9	−	3.96120e8i	−0.592078	−	0.181078i
$120$	8.20566e7			0.0361242
$121$	−1.08400e9	−	1.87754e9i	−0.459720	−	0.796258i
$122$	4.63253e8	−	8.02379e8i	0.189321	−	0.327914i
$123$	−6.17992e7	+	1.07039e8i	−0.0243450	+	0.0421668i
$124$	1.26785e9	+	2.19598e9i	0.481583	+	0.834125i
$125$	−1.76284e9			−0.645828
$126$	−1.28901e9	−	3.94223e8i	−0.455605	−	0.139340i
$127$	−3.07172e9			−1.04777			−0.523883	−	0.851790i	$-0.675517\pi$
$127$	−3.07172e9			−1.04777			−0.523883	+	0.851790i	$0.675517\pi$
$128$	3.93365e8	+	6.81328e8i	0.129524	+	0.224342i
$129$	1.09070e9	−	1.88916e9i	0.346780	−	0.600640i
$130$	2.96723e8	−	5.13940e8i	0.0911185	−	0.157822i
$131$	2.35470e9	+	4.07846e9i	0.698577	+	1.20997i	0.968960	+	0.247219i	$0.0795165\pi$
$131$	2.35470e9	+	4.07846e9i	0.698577	+	1.20997i	−0.270382	+	0.962753i	$0.587150\pi$
$132$	−3.54211e9			−1.01550
$133$	5.26339e9	−	4.90726e9i	1.45859	−	1.35990i
$134$	5.21539e9			1.39738
$135$	7.20688e8	+	1.24827e9i	0.186743	+	0.323449i
$136$	−1.60685e8	+	2.78314e8i	−0.0402762	+	0.0697605i
$137$	−1.91105e9	+	3.31003e9i	−0.463477	+	0.802766i	−0.999131	−	0.0416712i	$-0.986732\pi$
$137$	−1.91105e9	+	3.31003e9i	−0.463477	+	0.802766i	0.535654	+	0.844438i	$0.320065\pi$
$138$	−1.29485e9	−	2.24274e9i	−0.303922	−	0.526408i
$139$	6.39628e9			1.45332			0.726659	−	0.686998i	$-0.241072\pi$
$139$	6.39628e9			1.45332			0.726659	+	0.686998i	$0.241072\pi$
$140$	3.17637e8	+	1.37643e9i	0.0698803	+	0.302816i
$141$	−4.79621e9			−1.02191
$142$	−4.92946e9	−	8.53807e9i	−1.01742	−	1.76223i
$143$	1.33272e9	−	2.30834e9i	0.266518	−	0.461623i
$144$	−9.66377e8	+	1.67381e9i	−0.187290	+	0.324396i
$145$	−9.19358e7	−	1.59237e8i	−0.0172714	−	0.0299150i
$146$	9.43860e8			0.171917
$147$	3.20457e8	−	4.57029e9i	0.0566032	−	0.807264i
$148$	−3.55672e9			−0.609357
$149$	3.00953e9	+	5.21266e9i	0.500220	+	0.866406i	1.00000		0.000253604i	$8.07246e-5\pi$
$149$	3.00953e9	+	5.21266e9i	0.500220	+	0.866406i	−0.499780	+	0.866152i	$0.666586\pi$
$150$	−3.05562e9	+	5.29249e9i	−0.492820	+	0.853590i
$151$	−1.33542e9	+	2.31302e9i	−0.209037	+	0.362063i	−0.951411	−	0.307923i	$-0.900366\pi$
$151$	−1.33542e9	+	2.31302e9i	−0.209037	+	0.362063i	0.742374	+	0.669985i	$0.233700\pi$
$152$	−8.53724e8	−	1.47869e9i	−0.129724	−	0.224689i
$153$	−1.44836e9			−0.213681
$154$	3.00175e9	+	1.30076e10i	0.430062	+	1.86361i
$155$	−2.62190e9			−0.364857
$156$	−1.04302e9	−	1.80656e9i	−0.141004	−	0.244226i
$157$	−5.82620e9	+	1.00913e10i	−0.765310	+	1.32556i	0.174773	+	0.984609i	$0.444081\pi$
$157$	−5.82620e9	+	1.00913e10i	−0.765310	+	1.32556i	−0.940083	+	0.340947i	$0.889252\pi$
$158$	8.18673e9	−	1.41798e10i	1.04509	−	1.81015i
$159$	3.04303e9	+	5.27068e9i	0.377588	+	0.654002i
$160$	3.89164e9			0.469454
$161$	−3.39281e9	+	3.16325e9i	−0.397964	+	0.371037i
$162$	6.48381e9			0.739627
$163$	−3.34534e9	−	5.79429e9i	−0.371189	−	0.642919i	0.618559	−	0.785738i	$-0.287717\pi$
$163$	−3.34534e9	−	5.79429e9i	−0.371189	−	0.642919i	−0.989749	+	0.142819i	$0.954383\pi$
$164$	−2.52428e8	+	4.37219e8i	−0.0272484	+	0.0471956i
$165$	1.83126e9	−	3.17183e9i	0.192341	−	0.333144i
$166$	−9.38670e9	−	1.62582e10i	−0.959459	−	1.66183i
$167$	8.67405e9			0.862975			0.431487	−	0.902119i	$-0.357989\pi$
$167$	8.67405e9			0.862975			0.431487	+	0.902119i	$0.357989\pi$
$168$	−1.03954e9	−	3.17926e8i	−0.100681	−	0.0307918i
$169$	−9.03476e9			−0.851974
$170$	1.59681e9	+	2.76575e9i	0.146633	+	0.253976i
$171$	3.84761e9	−	6.66426e9i	0.344119	−	0.596032i
$172$	4.45515e9	−	7.71655e9i	0.388137	−	0.672272i
$173$	−5.45393e9	−	9.44648e9i	−0.462916	−	0.801794i	0.536189	−	0.844098i	$-0.319863\pi$
$173$	−5.45393e9	−	9.44648e9i	−0.462916	−	0.801794i	−0.999105	+	0.0423043i	$0.986530\pi$
$174$	−1.35991e9			−0.112471
$175$	1.04679e10	+	3.20144e9i	0.843700	+	0.258032i
$176$	1.91412e10			1.50370
$177$	−1.02918e9	−	1.78259e9i	−0.0788155	−	0.136513i
$178$	−1.50134e10	+	2.60039e10i	−1.12095	+	1.94155i
$179$	−5.05123e9	+	8.74898e9i	−0.367755	+	0.636970i	−0.989214	−	0.146477i	$-0.953207\pi$
$179$	−5.05123e9	+	8.74898e9i	−0.367755	+	0.636970i	0.621459	+	0.783446i	$0.286540\pi$
$180$	7.55288e8	+	1.30820e9i	0.0536273	+	0.0928853i
$181$	7.43617e9			0.514986			0.257493	−	0.966280i	$-0.417104\pi$
$181$	7.43617e9			0.514986			0.257493	+	0.966280i	$0.417104\pi$
$182$	−5.75030e9	+	5.36122e9i	−0.388480	+	0.362195i
$183$	3.36749e9			0.221961
$184$	5.50316e8	+	9.53175e8i	0.0353942	+	0.0613045i
$185$	1.83881e9	−	3.18491e9i	0.115415	−	0.199905i
$186$	−9.69576e9	+	1.67935e10i	−0.593982	+	1.02881i
$187$	7.17199e9	+	1.24223e10i	0.428897	+	0.742871i
$188$	−1.95909e10			−1.14378
$189$	−4.29368e9	−	1.86060e10i	−0.244766	−	1.06066i
$190$	−1.69678e10			−0.944572
$191$	−6.09552e9	−	1.05578e10i	−0.331406	−	0.574013i	0.651381	−	0.758750i	$-0.274190\pi$
$191$	−6.09552e9	−	1.05578e10i	−0.331406	−	0.574013i	−0.982788	+	0.184738i	$0.940856\pi$
$192$	6.12174e9	−	1.06032e10i	0.325102	−	0.563093i
$193$	4.75728e8	−	8.23986e8i	0.0246803	−	0.0427476i	−0.853421	−	0.521222i	$-0.825477\pi$
$193$	4.75728e8	−	8.23986e8i	0.0246803	−	0.0427476i	0.878102	+	0.478474i	$0.158810\pi$
$194$	5.86571e9	+	1.01597e10i	0.297312	+	0.514960i
$195$	2.15695e9			0.106828
$196$	1.30895e9	−	1.86680e10i	0.0633537	−	0.903538i
$197$	−1.23046e10			−0.582061			−0.291031	−	0.956714i	$-0.593998\pi$
$197$	−1.23046e10			−0.582061			−0.291031	+	0.956714i	$0.593998\pi$
$198$	7.13765e9	+	1.23628e10i	0.330037	+	0.571640i
$199$	8.60008e9	−	1.48958e10i	0.388744	−	0.673324i	−0.603537	−	0.797335i	$-0.706242\pi$
$199$	8.60008e9	−	1.48958e10i	0.388744	−	0.673324i	0.992281	+	0.124011i	$0.0395758\pi$
$200$	1.29865e9	−	2.24933e9i	0.0573929	−	0.0994074i
$201$	9.47795e9	+	1.64163e10i	0.409574	+	0.709403i
$202$	3.18234e10			1.34482
$203$	5.47731e8	+	2.37351e9i	0.0226378	+	0.0980976i
$204$	1.12260e10			0.453824
$205$	−2.61009e8	−	4.52081e8i	−0.0103220	−	0.0178782i
$206$	1.69018e10	−	2.92748e10i	0.653928	−	1.13264i
$207$	−2.48019e9	+	4.29582e9i	−0.0938899	+	0.162622i
$208$	5.63636e9	+	9.76246e9i	0.208792	+	0.361638i
$209$	−7.62102e10			−2.76283
$210$	−7.90134e9	+	7.36672e9i	−0.280359	+	0.261389i
$211$	5.21321e9			0.181065			0.0905325	−	0.995894i	$-0.471143\pi$
$211$	5.21321e9			0.181065			0.0905325	+	0.995894i	$0.471143\pi$
$212$	1.24297e10	+	2.15289e10i	0.422620	+	0.731999i
$213$	1.79167e10	−	3.10326e10i	0.596415	−	1.03302i
$214$	5.27214e9	−	9.13162e9i	0.171840	−	0.297636i
$215$	4.60659e9	+	7.97885e9i	0.147030	+	0.254664i
$216$	−4.53072e9			−0.141620
$217$	3.32156e10	+	1.01585e10i	1.01689	+	0.310999i
$218$	−1.45789e10			−0.437190
$219$	1.71528e9	+	2.97095e9i	0.0503891	+	0.0872765i
$220$	7.48005e9	−	1.29558e10i	0.215279	−	0.372875i
$221$	−4.22377e9	+	7.31578e9i	−0.119106	+	0.206298i
$222$	−1.35998e10	−	2.35556e10i	−0.375789	−	0.650886i
$223$	−7.87749e9			−0.213312			−0.106656	−	0.994296i	$-0.534014\pi$
$223$	−7.87749e9			−0.213312			−0.106656	+	0.994296i	$0.534014\pi$
$224$	−4.93014e10	−	1.50781e10i	−1.30841	−	0.400156i
$225$	1.17057e10			0.304492
$226$	4.37536e9	+	7.57835e9i	0.111564	+	0.193235i
$227$	−1.10862e10	+	1.92018e10i	−0.277118	+	0.479982i	−0.970667	−	0.240427i	$-0.922713\pi$
$227$	−1.10862e10	+	1.92018e10i	−0.277118	+	0.479982i	0.693549	+	0.720409i	$0.256046\pi$
$228$	−2.98220e10	+	5.16532e10i	−0.730853	+	1.26587i
$229$	−6.79946e9	−	1.17770e10i	−0.163386	−	0.282993i	0.772695	−	0.634777i	$-0.218908\pi$
$229$	−6.79946e9	−	1.17770e10i	−0.163386	−	0.282993i	−0.936081	+	0.351785i	$0.885575\pi$
$230$	1.09376e10			0.257718
$231$	−3.54885e10	+	3.30873e10i	−0.820038	+	0.764552i
$232$	5.77969e8			0.0130981
$233$	2.19384e10	+	3.79983e10i	0.487644	+	0.844623i	0.999899	−	0.0142097i	$-0.00452325\pi$
$233$	2.19384e10	+	3.79983e10i	0.487644	+	0.844623i	−0.512256	+	0.858833i	$0.671190\pi$
$234$	−4.20354e9	+	7.28075e9i	−0.0916525	+	0.158747i
$235$	1.01284e10	−	1.75429e10i	0.216638	−	0.375229i
$236$	−4.20385e9	−	7.28128e9i	−0.0882151	−	0.152793i
$237$	5.95111e10			1.22527
$238$	−9.51338e9	−	4.12248e10i	−0.192193	−	0.832842i
$239$	6.21740e10			1.23259			0.616294	−	0.787516i	$-0.288633\pi$
$239$	6.21740e10			1.23259			0.616294	+	0.787516i	$0.288633\pi$
$240$	7.74478e9	+	1.34144e10i	0.150681	+	0.260987i
$241$	−3.11025e10	+	5.38711e10i	−0.593907	+	1.02868i	0.399793	+	0.916605i	$0.369082\pi$
$241$	−3.11025e10	+	5.38711e10i	−0.593907	+	1.02868i	−0.993700	+	0.112072i	$0.964251\pi$
$242$	3.38607e10	−	5.86485e10i	0.634639	−	1.09923i
$243$	−1.77998e10	−	3.08302e10i	−0.327482	−	0.567215i
$244$	1.37550e10			0.248432
$245$	1.60398e10	+	1.08234e10i	0.284415	+	0.191919i
$246$	−3.86084e9			−0.0672162
$247$	−2.24410e10	−	3.88690e10i	−0.383625	−	0.664458i
$248$	4.12074e9	−	7.13734e9i	0.0691740	−	0.119813i
$249$	3.41170e10	−	5.90923e10i	0.562436	−	0.974169i
$250$	−2.75328e10	−	4.76882e10i	−0.445780	−	0.772113i
$251$	−5.30329e10			−0.843362			−0.421681	−	0.906744i	$-0.638560\pi$
$251$	−5.30329e10			−0.843362			−0.421681	+	0.906744i	$0.638560\pi$
$252$	−4.49982e9	−	1.94993e10i	−0.0702898	−	0.304590i
$253$	4.91256e10			0.753816
$254$	−4.79756e10	−	8.30961e10i	−0.723217	−	1.25265i
$255$	−5.80377e9	+	1.00524e10i	−0.0859566	+	0.148881i
$256$	−3.98945e10	+	6.90993e10i	−0.580541	+	1.00553i
$257$	3.11245e10	+	5.39092e10i	0.445045	+	0.770840i	0.998055	−	0.0623343i	$-0.0198545\pi$
$257$	3.11245e10	+	5.39092e10i	0.445045	+	0.770840i	−0.553011	+	0.833174i	$0.686521\pi$
$258$	6.81406e10			0.957453
$259$	−3.56349e10	+	3.32237e10i	−0.492069	+	0.458775i
$260$	8.81038e9			0.119568
$261$	1.30241e9	+	2.25584e9i	0.0173727	+	0.0300903i
$262$	−7.35536e10	+	1.27399e11i	−0.964380	+	1.67036i
$263$	−9.16990e8	+	1.58827e9i	−0.0118185	+	0.0204703i	−0.871874	−	0.489730i	$-0.837095\pi$
$263$	−9.16990e8	+	1.58827e9i	−0.0118185	+	0.0204703i	0.860056	+	0.510200i	$0.170429\pi$
$264$	5.75625e9	+	9.97011e9i	0.0729326	+	0.126323i
$265$	−2.57044e10			−0.320185
$266$	2.14957e11	+	6.57414e10i	2.63260	+	0.805140i
$267$	−1.09135e11			−1.31421
$268$	3.87142e10	+	6.70549e10i	0.458420	+	0.794006i
$269$	2.04138e10	−	3.53577e10i	0.237705	−	0.411717i	−0.722350	−	0.691527i	$-0.756938\pi$
$269$	2.04138e10	−	3.53577e10i	0.237705	−	0.411717i	0.960055	+	0.279810i	$0.0902715\pi$
$270$	−2.25121e10	+	3.89921e10i	−0.257798	+	0.446519i
$271$	−2.76078e10	−	4.78182e10i	−0.310936	−	0.538557i	0.667629	−	0.744494i	$-0.267309\pi$
$271$	−2.76078e10	−	4.78182e10i	−0.310936	−	0.538557i	−0.978565	+	0.205937i	$0.933976\pi$
$272$	−6.06638e10			−0.672001
$273$	−2.73253e10	−	8.35703e9i	−0.297738	−	0.0910584i
$274$	−1.19391e11			−1.27965
$275$	−5.79640e10	−	1.00397e11i	−0.611169	−	1.05858i
$276$	1.92234e10	−	3.32960e10i	0.199407	−	0.345383i
$277$	2.32366e10	−	4.02469e10i	0.237145	−	0.410746i	−0.722749	−	0.691110i	$-0.757122\pi$
$277$	2.32366e10	−	4.02469e10i	0.237145	−	0.410746i	0.959894	+	0.280364i	$0.0904552\pi$
$278$	9.99001e10	+	1.73032e11i	1.00315	+	1.73750i
$279$	3.71432e10			0.366995
$280$	3.35811e9	−	3.13089e9i	0.0326500	−	0.0304408i
$281$	−4.61659e10			−0.441716			−0.220858	−	0.975306i	$-0.570886\pi$
$281$	−4.61659e10			−0.441716			−0.220858	+	0.975306i	$0.570886\pi$
$282$	−7.49095e10	−	1.29747e11i	−0.705368	−	1.22173i
$283$	4.11322e10	−	7.12430e10i	0.381191	−	0.660242i	−0.610042	−	0.792369i	$-0.708847\pi$
$283$	4.11322e10	−	7.12430e10i	0.381191	−	0.660242i	0.991233	+	0.132127i	$0.0421807\pi$
$284$	7.31833e10	−	1.26757e11i	0.667544	−	1.15622i
$285$	−3.08357e10	−	5.34090e10i	−0.276855	−	0.479526i
$286$	8.32602e10			0.735852
$287$	1.55503e9	+	6.73847e9i	0.0135291	+	0.0586263i
$288$	−5.51311e10			−0.472205
$289$	3.65639e10	+	6.33305e10i	0.308327	+	0.534038i
$290$	2.87179e9	−	4.97409e9i	0.0238431	−	0.0412974i
$291$	−2.13196e10	+	3.69265e10i	−0.174285	+	0.301870i
$292$	7.00633e9	+	1.21353e10i	0.0563985	+	0.0976851i
$293$	2.22523e11			1.76389			0.881945	−	0.471353i	$-0.156234\pi$
$293$	2.22523e11			1.76389			0.881945	+	0.471353i	$0.156234\pi$
$294$	1.28640e11	−	6.27120e10i	1.00419	−	0.489539i
$295$	8.69348e9			0.0668336
$296$	5.77999e9	+	1.00112e10i	0.0437637	+	0.0758010i
$297$	−1.01112e11	+	1.75131e11i	−0.754048	+	1.30605i
$298$	−9.40086e10	+	1.62828e11i	−0.690549	+	1.19607i
$299$	1.44656e10	+	2.50552e10i	0.104669	+	0.181292i
$300$	−9.07281e10			−0.646690
$301$	−2.74449e10	−	1.18928e11i	−0.192714	−	0.835096i
$302$	−8.34292e10			−0.577147
$303$	5.78327e10	+	1.00169e11i	0.394168	+	0.682720i
$304$	1.61155e11	−	2.79128e11i	1.08221	−	1.87444i
$305$	−7.11129e9	+	1.23171e10i	−0.0470543	+	0.0815004i
$306$	−2.26212e10	−	3.91811e10i	−0.147493	−	0.255465i
$307$	−3.25217e10			−0.208954			−0.104477	−	0.994527i	$-0.533317\pi$
$307$	−3.25217e10			−0.208954			−0.104477	+	0.994527i	$0.533317\pi$
$308$	−1.44958e11	+	1.35150e11i	−0.917835	+	0.855733i
$309$	1.22863e11			0.766667
$310$	−4.09500e10	−	7.09275e10i	−0.251841	−	0.436201i
$311$	−9.74749e10	+	1.68831e11i	−0.590841	+	1.02337i	0.403278	+	0.915078i	$0.367871\pi$
$311$	−9.74749e10	+	1.68831e11i	−0.590841	+	1.02337i	−0.994119	+	0.108290i	$0.965463\pi$
$312$	−3.39000e9	+	5.87165e9i	−0.0202537	+	0.0350804i
$313$	−9.62618e10	−	1.66730e11i	−0.566898	−	0.981896i	−0.996870	−	0.0790537i	$-0.974810\pi$
$313$	−9.62618e10	−	1.66730e11i	−0.566898	−	0.981896i	0.429973	−	0.902842i	$-0.358523\pi$
$314$	−3.63986e11			−2.11301
$315$	1.97873e10	+	6.05163e9i	0.113237	+	0.0346318i
$316$	2.43082e11			1.37139
$317$	2.36123e10	+	4.08978e10i	0.131333	+	0.227475i	0.924190	−	0.381932i	$-0.124741\pi$
$317$	2.36123e10	+	4.08978e10i	0.131333	+	0.227475i	−0.792858	+	0.609407i	$0.791408\pi$
$318$	−9.50549e10	+	1.64640e11i	−0.521258	+	0.902845i
$319$	1.28985e10	−	2.23409e10i	0.0697401	−	0.120793i
$320$	2.58552e10	+	4.47825e10i	0.137839	+	0.238744i
$321$	3.83243e10			0.201466
$322$	−1.38563e11	−	4.23773e10i	−0.718283	−	0.219675i
$323$	2.41532e11			1.23470
$324$	4.81297e10	+	8.33631e10i	0.242639	+	0.420263i
$325$	3.41365e10	−	5.91261e10i	0.169724	−	0.293971i
$326$	1.04498e11	−	1.80996e11i	0.512424	−	0.887544i
$327$	−2.64943e10	−	4.58895e10i	−0.128141	−	0.221946i
$328$	1.64087e9			0.00782786
$329$	−1.96281e11	+	1.83001e11i	−0.923629	+	0.861134i
$330$	1.14406e11			0.531050
$331$	1.71378e11	+	2.96835e11i	0.784746	+	1.35922i	0.929151	+	0.369701i	$0.120540\pi$
$331$	1.71378e11	+	2.96835e11i	0.784746	+	1.35922i	−0.144405	+	0.989519i	$0.546127\pi$
$332$	1.39356e11	−	2.41372e11i	0.629513	−	1.09035i
$333$	−2.60496e10	+	4.51192e10i	−0.116092	+	0.201077i
$334$	1.35476e11	+	2.34651e11i	0.595665	+	1.03172i
$335$	−8.00602e10			−0.347308
$336$	−4.61415e10	−	1.99947e11i	−0.197499	−	0.855832i
$337$	1.13211e9			0.00478138			0.00239069	−	0.999997i	$-0.499239\pi$
$337$	1.13211e9			0.00478138			0.00239069	+	0.999997i	$0.499239\pi$
$338$	−1.41109e11	−	2.44408e11i	−0.588071	−	1.01857i
$339$	−1.59027e10	+	2.75443e10i	−0.0653992	+	0.113275i
$340$	−2.37064e10	+	4.10607e10i	−0.0962078	+	0.166637i
$341$	−1.83925e11	−	3.18568e11i	−0.736625	−	1.27587i
$342$	2.40375e11			0.950107
$343$	−1.61266e11	−	1.99263e11i	−0.629099	−	0.777325i
$344$	−2.89601e10			−0.111503
$345$	1.98769e10	+	3.44277e10i	0.0755374	+	0.130835i
$346$	1.70364e11	−	2.95079e11i	0.639051	−	1.10687i
$347$	1.18578e11	−	2.05384e11i	0.439059	−	0.760473i	−0.558558	−	0.829466i	$-0.688645\pi$
$347$	1.18578e11	−	2.05384e11i	0.439059	−	0.760473i	0.997617	+	0.0689924i	$0.0219784\pi$
$348$	−1.00947e10	−	1.74846e10i	−0.0368967	−	0.0639069i
$349$	−2.73205e10			−0.0985767			−0.0492884	−	0.998785i	$-0.515695\pi$
$349$	−2.73205e10			−0.0985767			−0.0492884	+	0.998785i	$0.515695\pi$
$350$	7.68871e10	+	3.33179e11i	0.273872	+	1.18678i
$351$	−1.19095e11			−0.418804
$352$	2.72997e11	+	4.72845e11i	0.947799	+	1.64164i
$353$	4.35893e9	−	7.54989e9i	0.0149415	−	0.0258794i	−0.858458	−	0.512884i	$-0.828577\pi$
$353$	4.35893e9	−	7.54989e9i	0.0149415	−	0.0258794i	0.873399	+	0.487004i	$0.161910\pi$
$354$	3.21485e10	−	5.56828e10i	0.108804	−	0.188454i
$355$	7.56709e10	+	1.31066e11i	0.252872	+	0.437988i
$356$	−4.45780e11			−1.47094
$357$	1.12473e11	−	1.04863e11i	0.366473	−	0.341676i
$358$	−3.15570e11			−1.01536
$359$	−1.11440e11	−	1.93020e11i	−0.354093	−	0.613307i	0.632869	−	0.774259i	$-0.281877\pi$
$359$	−1.11440e11	−	1.93020e11i	−0.354093	−	0.613307i	−0.986962	+	0.160952i	$0.948544\pi$
$360$	2.45482e9	−	4.25187e9i	0.00770297	−	0.0133419i
$361$	−4.80290e11	+	8.31887e11i	−1.48841	+	2.57800i
$362$	1.16142e11	+	2.01163e11i	0.355467	+	0.615687i
$363$	2.46141e11			0.744053
$364$	−1.11615e11	−	3.41356e10i	−0.333246	−	0.101918i
$365$	−1.44890e10			−0.0427287
$366$	5.25951e10	+	9.10973e10i	0.153208	+	0.265363i
$367$	1.58342e11	−	2.74257e11i	0.455616	−	0.789150i	−0.543107	−	0.839663i	$-0.682752\pi$
$367$	1.58342e11	−	2.74257e11i	0.455616	−	0.789150i	0.998723	+	0.0505131i	$0.0160857\pi$
$368$	−1.03881e11	+	1.79928e11i	−0.295272	+	0.511426i
$369$	3.69759e9	+	6.40442e9i	0.0103825	+	0.0179830i
$370$	1.14878e11			0.318660
$371$	3.25637e11	+	9.95911e10i	0.892384	+	0.272922i
$372$	−2.87889e11			−0.779438
$373$	−1.26235e11	−	2.18645e11i	−0.337667	−	0.584857i	0.646326	−	0.763061i	$-0.276305\pi$
$373$	−1.26235e11	−	2.18645e11i	−0.337667	−	0.584857i	−0.983993	+	0.178204i	$0.942971\pi$
$374$	−2.24031e11	+	3.88033e11i	−0.592088	+	1.02553i
$375$	1.00071e11	−	1.73328e11i	0.261317	−	0.452614i
$376$	3.18369e10	+	5.51431e10i	0.0821458	+	0.142281i
$377$	1.51925e10			0.0387342
$378$	4.36269e11	−	4.06750e11i	1.09911	−	1.02474i
$379$	1.06974e11			0.266319			0.133160	−	0.991095i	$-0.457488\pi$
$379$	1.06974e11			0.266319			0.133160	+	0.991095i	$0.457488\pi$
$380$	−1.25953e11	−	2.18157e11i	−0.309872	−	0.536715i
$381$	1.74372e11	−	3.02022e11i	0.423951	−	0.734304i
$382$	1.90406e11	−	3.29792e11i	0.457504	−	0.792420i
$383$	2.70810e10	+	4.69057e10i	0.0643088	+	0.111386i	0.896387	−	0.443272i	$-0.146182\pi$
$383$	2.70810e10	+	4.69057e10i	0.0643088	+	0.111386i	−0.832078	+	0.554658i	$0.812849\pi$
$384$	−8.93207e10			−0.209634
$385$	−4.60791e10	−	1.99677e11i	−0.106888	−	0.463185i
$386$	2.97206e10			0.0681420
$387$	−6.52594e10	−	1.13033e11i	−0.147892	−	0.256156i
$388$	−8.70830e10	+	1.50832e11i	−0.195070	+	0.337871i
$389$	3.48418e11	−	6.03478e11i	0.771486	−	1.33625i	−0.165263	−	0.986250i	$-0.552847\pi$
$389$	3.48418e11	−	6.03478e11i	0.771486	−	1.33625i	0.936749	−	0.350003i	$-0.113819\pi$
$390$	3.36882e10	+	5.83497e10i	0.0737373	+	0.127717i
$391$	−1.55693e11			−0.336878
$392$	−5.46728e10	+	2.66529e10i	−0.116946	+	0.0570108i
$393$	−5.34677e11			−1.13064
$394$	−1.92179e11	−	3.32864e11i	−0.401765	−	0.695878i
$395$	−1.25672e11	+	2.17671e11i	−0.259749	+	0.449898i
$396$	−1.05966e11	+	1.83539e11i	−0.216541	+	0.375060i
$397$	2.25459e11	+	3.90507e11i	0.455524	+	0.788990i	0.998718	−	0.0506168i	$-0.0161187\pi$
$397$	2.25459e11	+	3.90507e11i	0.455524	+	0.788990i	−0.543194	+	0.839607i	$0.682785\pi$
$398$	5.37280e11			1.07331
$399$	1.83711e11	+	7.96085e11i	0.362876	+	1.57247i
$400$	4.90285e11			0.957588
$401$	−2.60191e11	−	4.50664e11i	−0.502508	−	0.870369i	−0.999996	−	0.00289840i	$-0.999077\pi$
$401$	−2.60191e11	−	4.50664e11i	−0.502508	−	0.870369i	0.497488	−	0.867471i	$-0.334256\pi$
$402$	−2.96062e11	+	5.12795e11i	−0.565413	+	0.979324i
$403$	1.08318e11	−	1.87612e11i	0.204564	−	0.354315i
$404$	2.36227e11	+	4.09157e11i	0.441177	+	0.764141i
$405$	−9.95314e10			−0.183828
$406$	−5.56534e10	+	5.18878e10i	−0.101654	+	0.0947759i
$407$	5.15968e11			0.932068
$408$	−1.82432e10	−	3.15981e10i	−0.0325934	−	0.0564534i
$409$	−3.17676e11	+	5.50231e11i	−0.561345	+	0.972277i	0.436035	+	0.899930i	$0.356382\pi$
$409$	−3.17676e11	+	5.50231e11i	−0.561345	+	0.972277i	−0.997379	+	0.0723477i	$0.976951\pi$
$410$	8.15312e9	−	1.41216e10i	0.0142494	−	0.0246807i
$411$	−2.16969e11	−	3.75801e11i	−0.375067	−	0.649636i
$412$	5.01852e11			0.858100
$413$	−1.10134e11	−	3.36827e10i	−0.186271	−	0.0569680i
$414$	−1.54947e11			−0.259228
$415$	1.44093e11	+	2.49576e11i	0.238466	+	0.413035i
$416$	−1.60775e11	+	2.78470e11i	−0.263208	+	0.455889i
$417$	−3.63098e11	+	6.28904e11i	−0.588046	+	1.01853i
$418$	−1.19029e12	−	2.06164e12i	−1.90703	−	3.30308i
$419$	−9.64396e11			−1.52860			−0.764298	−	0.644864i	$-0.776914\pi$
$419$	−9.64396e11			−1.52860			−0.764298	+	0.644864i	$0.776914\pi$
$420$	−1.53367e11	−	4.69048e10i	−0.240497	−	0.0735522i
$421$	−2.71303e11			−0.420906			−0.210453	−	0.977604i	$-0.567494\pi$
$421$	−2.71303e11			−0.420906			−0.210453	+	0.977604i	$0.567494\pi$
$422$	8.14224e10	+	1.41028e11i	0.124979	+	0.216470i
$423$	−1.43484e11	+	2.48522e11i	−0.217908	+	0.377427i
$424$	4.03988e10	−	6.99727e10i	0.0607046	−	0.105144i
$425$	1.83704e11	+	3.18185e11i	0.273130	+	0.473075i
$426$	1.11932e12			1.64669
$427$	1.37812e11	−	1.28487e11i	0.200614	−	0.187040i
$428$	1.56542e11			0.225493
$429$	1.51309e11	+	2.62075e11i	0.215679	+	0.373566i
$430$	−1.43896e11	+	2.49235e11i	−0.202974	+	0.351561i
$431$	4.13955e11	−	7.16991e11i	0.577837	−	1.00084i	−0.417890	−	0.908498i	$-0.637230\pi$
$431$	4.13955e11	−	7.16991e11i	0.577837	−	1.00084i	0.995727	−	0.0923452i	$-0.0294363\pi$
$432$	−4.27625e11	−	7.40668e11i	−0.590726	−	1.02317i
$433$	8.97674e11			1.22722			0.613611	−	0.789609i	$-0.289716\pi$
$433$	8.97674e11			1.22722			0.613611	+	0.789609i	$0.289716\pi$
$434$	2.43970e11	+	1.05721e12i	0.330090	+	1.43040i
$435$	2.08757e10			0.0279537
$436$	−1.08220e11	−	1.87443e11i	−0.143423	−	0.248416i
$437$	4.13601e11	−	7.16378e11i	0.542520	−	0.939671i
$438$	−5.35801e10	+	9.28035e10i	−0.0695617	+	0.120484i
$439$	6.72801e11	+	1.16533e12i	0.864562	+	1.49747i	0.867481	+	0.497470i	$0.165738\pi$
$439$	6.72801e11	+	1.16533e12i	0.864562	+	1.49747i	−0.00291881	+	0.999996i	$0.500929\pi$
$440$	−4.86230e10			−0.0618450
$441$	−2.27229e11	−	1.53330e11i	−0.286081	−	0.193043i
$442$	−2.63875e11			−0.328850
$443$	2.77134e11	+	4.80009e11i	0.341879	+	0.592152i	0.984782	−	0.173796i	$-0.0556034\pi$
$443$	2.77134e11	+	4.80009e11i	0.341879	+	0.592152i	−0.642903	+	0.765948i	$0.722270\pi$
$444$	2.01904e11	−	3.49709e11i	0.246560	−	0.427054i
$445$	2.30467e11	−	3.99180e11i	0.278604	−	0.482557i
$446$	−1.23034e11	−	2.13102e11i	−0.147238	−	0.255023i
$447$	−6.83369e11			−0.809602
$448$	−1.54039e11	−	6.67504e11i	−0.180667	−	0.782893i
$449$	3.21991e11			0.373882			0.186941	−	0.982371i	$-0.440143\pi$
$449$	3.21991e11			0.373882			0.186941	+	0.982371i	$0.440143\pi$
$450$	1.82825e11	+	3.16662e11i	0.210174	+	0.364032i
$451$	3.66194e10	−	6.34266e10i	0.0416789	−	0.0721900i
$452$	−6.49571e10	+	1.12509e11i	−0.0731988	+	0.126784i
$453$	−1.51616e11	−	2.62607e11i	−0.169162	−	0.292998i
$454$	−6.92595e11			−0.765118
$455$	8.82714e10	−	8.22988e10i	0.0965536	−	0.0900206i
$456$	1.93854e11			0.209958
$457$	−1.46014e11	−	2.52903e11i	−0.156592	−	0.271226i	0.777045	−	0.629445i	$-0.216718\pi$
$457$	−1.46014e11	−	2.52903e11i	−0.156592	−	0.271226i	−0.933638	+	0.358219i	$0.883384\pi$
$458$	2.12394e11	−	3.67878e11i	0.225553	−	0.390669i
$459$	3.20453e11	−	5.55041e11i	0.336982	−	0.583671i
$460$	8.11901e10	+	1.40625e11i	0.0845460	+	0.146438i
$461$	3.60855e11			0.372116			0.186058	−	0.982539i	$-0.440429\pi$
$461$	3.60855e11			0.372116			0.186058	+	0.982539i	$0.440429\pi$
$462$	−1.44935e12	−	4.43262e11i	−1.48008	−	0.452659i
$463$	−1.32086e12			−1.33580			−0.667901	−	0.744250i	$-0.732807\pi$
$463$	−1.32086e12			−1.33580			−0.667901	+	0.744250i	$0.732807\pi$
$464$	5.45507e10	+	9.44846e10i	0.0546348	+	0.0946303i
$465$	1.48837e11	−	2.57794e11i	0.147630	−	0.255702i
$466$	−6.85288e11	+	1.18695e12i	−0.673188	+	1.16600i
$467$	7.55544e11	+	1.30864e12i	0.735078	+	1.27319i	0.954689	+	0.297605i	$0.0961880\pi$
$467$	7.55544e11	+	1.30864e12i	0.735078	+	1.27319i	−0.219611	+	0.975588i	$0.570479\pi$
$468$	−1.24813e11			−0.120269
$469$	1.01425e12	+	3.10191e11i	0.967978	+	0.296041i
$470$	6.32760e11			0.598135
$471$	−6.61473e11	−	1.14570e12i	−0.619324	−	1.07270i
$472$	−1.36633e10	+	2.36654e10i	−0.0126711	+	0.0219470i
$473$	−6.46302e11	+	1.11943e12i	−0.593691	+	1.02830i
$474$	9.29472e11	+	1.60989e12i	0.845734	+	1.46485i
$475$	−1.95206e12			−1.75943
$476$	4.59414e11	−	4.28329e11i	0.410178	−	0.382425i
$477$	3.64143e11			0.322062
$478$	9.71063e11	+	1.68193e12i	0.850789	+	1.47361i
$479$	6.91809e11	−	1.19825e12i	0.600450	−	1.04001i	−0.392303	−	0.919836i	$-0.628322\pi$
$479$	6.91809e11	−	1.19825e12i	0.600450	−	1.04001i	0.992753	−	0.120173i	$-0.0383451\pi$
$480$	−2.20917e11	+	3.82639e11i	−0.189952	+	0.329006i
$481$	1.51933e11	+	2.63156e11i	0.129419	+	0.224161i
$482$	−1.94309e12			−1.63977
$483$	−1.18421e11	−	5.13161e11i	−0.0990075	−	0.429034i
$484$	1.00540e12			0.832789
$485$	−9.00431e10	−	1.55959e11i	−0.0738946	−	0.127989i
$486$	5.56012e11	−	9.63040e11i	0.452086	−	0.783035i
$487$	−3.53638e11	+	6.12519e11i	−0.284891	+	0.493445i	−0.972583	−	0.232557i	$-0.925291\pi$
$487$	−3.53638e11	+	6.12519e11i	−0.284891	+	0.493445i	0.687692	+	0.726003i	$0.258624\pi$
$488$	−2.23531e10	−	3.87168e10i	−0.0178422	−	0.0309037i
$489$	7.59619e11			0.600767
$490$	−4.22776e10	+	6.02955e11i	−0.0331305	+	0.472501i
$491$	−1.40786e12			−1.09318			−0.546592	−	0.837399i	$-0.684075\pi$
$491$	−1.40786e12			−1.09318			−0.546592	+	0.837399i	$0.684075\pi$
$492$	−2.86592e10	−	4.96392e10i	−0.0220507	−	0.0381929i
$493$	−4.08791e10	+	7.08047e10i	−0.0311667	+	0.0539823i
$494$	7.00990e11	−	1.21415e12i	0.529591	−	0.917279i
$495$	−1.09568e11	−	1.89778e11i	−0.0820280	−	0.142077i
$496$	1.55572e12			1.15415
$497$	−4.50829e11	−	1.95360e12i	−0.331442	−	1.43625i
$498$	2.13142e12			1.55288
$499$	−1.03159e12	−	1.78677e12i	−0.744827	−	1.29008i	−0.950275	−	0.311411i	$-0.899199\pi$
$499$	−1.03159e12	−	1.78677e12i	−0.744827	−	1.29008i	0.205448	−	0.978668i	$-0.434135\pi$
$500$	4.08755e11	−	7.07985e11i	0.292481	−	0.506593i
$501$	−4.92400e11	+	8.52863e11i	−0.349179	+	0.604797i
$502$	−8.28294e11	−	1.43465e12i	−0.582127	−	1.00827i
$503$	−1.01687e11			−0.0708289			−0.0354144	−	0.999373i	$-0.511275\pi$
$503$	−1.01687e11			−0.0708289			−0.0354144	+	0.999373i	$0.511275\pi$
$504$	−4.75727e10	+	4.43539e10i	−0.0328413	+	0.0306192i
$505$	−4.88513e11			−0.334245
$506$	7.67266e11	+	1.32894e12i	0.520318	+	0.901217i
$507$	5.12876e11	−	8.88328e11i	0.344728	−	0.597087i
$508$	7.12251e11	−	1.23365e12i	0.474511	−	0.821877i
$509$	−2.72912e11	−	4.72697e11i	−0.180215	−	0.312142i	0.761738	−	0.647885i	$-0.224346\pi$
$509$	−2.72912e11	−	4.72697e11i	−0.180215	−	0.312142i	−0.941954	+	0.335742i	$0.891013\pi$
$510$	−3.62584e11			−0.237325
$511$	1.83554e11	+	5.61371e10i	0.119088	+	0.0364214i
$512$	−2.08956e12			−1.34382
$513$	1.70258e12	+	2.94896e12i	1.08537	+	1.87992i
$514$	−9.72235e11	+	1.68396e12i	−0.614380	+	1.06414i
$515$	−2.59455e11	+	4.49390e11i	−0.162529	+	0.281508i
$516$	5.05812e11	+	8.76091e11i	0.314098	+	0.544034i
$517$	2.84201e12			1.74952
$518$	−1.45533e12	−	4.45090e11i	−0.888132	−	0.271621i
$519$	1.23841e12			0.749226
$520$	−1.43176e10	−	2.47989e10i	−0.00858730	−	0.0148736i
$521$	−4.99221e11	+	8.64676e11i	−0.296840	+	0.514143i	−0.975411	−	0.220392i	$-0.929266\pi$
$521$	−4.99221e11	+	8.64676e11i	−0.296840	+	0.514143i	0.678571	+	0.734535i	$0.262600\pi$
$522$	−4.06834e10	+	7.04657e10i	−0.0239828	+	0.0415394i
$523$	−4.40784e11	−	7.63460e11i	−0.257613	−	0.446199i	0.707989	−	0.706224i	$-0.249603\pi$
$523$	−4.40784e11	−	7.63460e11i	−0.257613	−	0.446199i	−0.965602	+	0.260025i	$0.916269\pi$
$524$	−2.18397e12			−1.26548
$525$	−9.09008e11	+	8.47502e11i	−0.522217	+	0.486882i
$526$	−5.72879e10			−0.0326308
$527$	5.82911e11	+	1.00963e12i	0.329196	+	0.570184i
$528$	−1.08659e12	+	1.88203e12i	−0.608432	+	1.05384i
$529$	6.33966e11	−	1.09806e12i	0.351978	−	0.609644i
$530$	−4.01464e11	−	6.95356e11i	−0.221007	−	0.382795i
$531$	−1.23157e11			−0.0672252
$532$	7.50397e11	+	3.25173e12i	0.406152	+	1.76000i
$533$	4.31321e10			0.0231488
$534$	−1.70453e12	−	2.95233e12i	−0.907128	−	1.57119i
$535$	−8.09314e10	+	1.40177e11i	−0.0427095	+	0.0739751i
$536$	1.25828e11	−	2.17940e11i	0.0658469	−	0.114050i
$537$	−5.73486e11	−	9.93308e11i	−0.297604	−	0.515465i
$538$	1.27533e12			0.656299
$539$	−1.89888e11	+	2.70814e12i	−0.0969054	+	1.38205i
$540$	−6.68435e11			−0.338288
$541$	−1.63782e11	−	2.83679e11i	−0.0822012	−	0.142377i	0.821994	−	0.569496i	$-0.192862\pi$
$541$	−1.63782e11	−	2.83679e11i	−0.0822012	−	0.142377i	−0.904195	+	0.427120i	$0.859528\pi$
$542$	8.62385e11	−	1.49369e12i	0.429244	−	0.743473i
$543$	−4.22129e11	+	7.31149e11i	−0.208375	+	0.360917i
$544$	−8.65206e11	−	1.49858e12i	−0.423569	−	0.733644i
$545$	2.23797e11			0.108660
$546$	−2.00706e11	−	8.69729e11i	−0.0966481	−	0.418810i
$547$	1.93653e12			0.924874			0.462437	−	0.886652i	$-0.346975\pi$
$547$	1.93653e12			0.924874			0.462437	+	0.886652i	$0.346975\pi$
$548$	−8.86243e11	−	1.53502e12i	−0.419798	−	0.727111i
$549$	1.00742e11	−	1.74491e11i	0.0473300	−	0.0819780i
$550$	1.81062e12	−	3.13609e12i	0.843714	−	1.46136i
$551$	−2.17193e11	−	3.76189e11i	−0.100384	−	0.173869i
$552$	−1.24959e11			−0.0572852
$553$	2.43545e12	−	2.27066e12i	1.10743	−	1.03250i
$554$	1.45168e12			0.654752
$555$	2.08767e11	+	3.61596e11i	0.0933995	+	0.161773i
$556$	−1.48313e12	+	2.56885e12i	−0.658176	+	1.14000i
$557$	−1.33279e12	+	2.30845e12i	−0.586695	+	1.01619i	0.407967	+	0.912997i	$0.366238\pi$
$557$	−1.33279e12	+	2.30845e12i	−0.586695	+	1.01619i	−0.994662	+	0.103189i	$0.967096\pi$
$558$	5.80120e11	+	1.00480e12i	0.253317	+	0.438758i
$559$	−7.61247e11			−0.329740
$560$	8.28777e11	+	2.53469e11i	0.356116	+	0.108913i
$561$	−1.62853e12			−0.694166
$562$	−7.21041e11	−	1.24888e12i	−0.304893	−	0.528089i
$563$	−1.87439e12	+	3.24654e12i	−0.786271	+	1.36186i	0.141966	+	0.989872i	$0.454658\pi$
$563$	−1.87439e12	+	3.24654e12i	−0.786271	+	1.36186i	−0.928237	+	0.371990i	$0.878676\pi$
$564$	1.11212e12	−	1.92624e12i	0.462801	−	0.801594i
$565$	−6.71651e10	−	1.16333e11i	−0.0277285	−	0.0480271i
$566$	2.56969e12			1.05246
$567$	1.26092e12	+	3.85632e11i	0.512345	+	0.156693i
$568$	−4.75718e11			−0.191770
$569$	2.61733e10	+	4.53336e10i	0.0104678	+	0.0181307i	0.871212	−	0.490907i	$-0.163335\pi$
$569$	2.61733e10	+	4.53336e10i	0.0104678	+	0.0181307i	−0.860744	+	0.509038i	$0.830001\pi$
$570$	9.63213e11	−	1.66833e12i	0.382195	−	0.661982i
$571$	5.39390e11	−	9.34251e11i	0.212344	−	0.367791i	−0.740104	−	0.672493i	$-0.765224\pi$
$571$	5.39390e11	−	9.34251e11i	0.212344	−	0.367791i	0.952448	+	0.304702i	$0.0985569\pi$
$572$	6.18045e11	+	1.07049e12i	0.241400	+	0.418118i
$573$	1.38410e12			0.536379
$574$	−1.58002e11	+	1.47311e11i	−0.0607518	+	0.0566412i
$575$	1.25831e12			0.480045
$576$	−3.66278e11	−	6.34413e11i	−0.138647	−	0.240143i
$577$	−7.01636e11	+	1.21527e12i	−0.263524	+	0.456437i	−0.967176	−	0.254108i	$-0.918218\pi$
$577$	−7.01636e11	+	1.21527e12i	−0.263524	+	0.456437i	0.703652	+	0.710545i	$0.251552\pi$
$578$	−1.14214e12	+	1.97825e12i	−0.425643	+	0.737235i
$579$	5.40114e10	+	9.35505e10i	0.0199725	+	0.0345933i
$580$	8.52700e10			0.0312875
$581$	−8.58470e11	−	3.72005e12i	−0.312559	−	1.35443i
$582$	−1.33192e12			−0.481197
$583$	−1.80316e12	−	3.12316e12i	−0.646436	−	1.11966i
$584$	2.27718e10	−	3.94419e10i	0.00810102	−	0.0140314i
$585$	6.45276e10	−	1.11765e11i	0.0227795	−	0.0394552i
$586$	3.47548e12	+	6.01970e12i	1.21752	+	2.10880i
$587$	1.12424e12			0.390829			0.195415	−	0.980721i	$-0.437395\pi$
$587$	1.12424e12			0.390829			0.195415	+	0.980721i	$0.437395\pi$
$588$	1.76120e12	+	1.18843e12i	0.607590	+	0.409993i
$589$	−6.19406e12			−2.12059
$590$	1.35779e11	+	2.35176e11i	0.0461316	+	0.0799023i
$591$	6.98495e11	−	1.20983e12i	0.235515	−	0.407925i
$592$	−1.09107e12	+	1.88979e12i	−0.365094	+	0.632361i
$593$	−2.20982e12	−	3.82752e12i	−0.733855	−	1.27107i	−0.955224	−	0.295884i	$-0.904386\pi$
$593$	−2.20982e12	−	3.82752e12i	−0.733855	−	1.27107i	0.221369	−	0.975190i	$-0.428948\pi$
$594$	−6.31687e12			−2.08191
$595$	1.46038e11	+	6.32832e11i	0.0477682	+	0.206996i
$596$	−2.79133e12			−0.906155
$597$	9.76402e11	+	1.69118e12i	0.314589	+	0.544885i
$598$	−4.51862e11	+	7.82649e11i	−0.144494	+	0.250272i
$599$	8.21099e11	−	1.42219e12i	0.260600	−	0.451373i	−0.705801	−	0.708410i	$-0.749413\pi$
$599$	8.21099e11	−	1.42219e12i	0.260600	−	0.451373i	0.966402	+	0.257037i	$0.0827462\pi$
$600$	1.47441e11	+	2.55376e11i	0.0464450	+	0.0804450i
$601$	−7.11098e11			−0.222328			−0.111164	−	0.993802i	$-0.535458\pi$
$601$	−7.11098e11			−0.222328			−0.111164	+	0.993802i	$0.535458\pi$
$602$	2.78860e12	−	2.59992e12i	0.865371	−	0.806819i
$603$	1.13418e12			0.349343
$604$	−6.19300e11	−	1.07266e12i	−0.189337	−	0.327941i
$605$	−5.19788e11	+	9.00299e11i	−0.157735	+	0.273204i
$606$	−1.80652e12	+	3.12898e12i	−0.544146	+	0.942489i
$607$	2.20303e12	+	3.81575e12i	0.658674	+	1.14086i	0.980959	+	0.194214i	$0.0622158\pi$
$607$	2.20303e12	+	3.81575e12i	0.658674	+	1.14086i	−0.322285	+	0.946643i	$0.604451\pi$
$608$	9.19375e12			2.72852
$609$	−2.64464e11	−	8.08823e10i	−0.0779093	−	0.0238274i
$610$	−4.44270e11			−0.129916
$611$	8.36867e11	+	1.44950e12i	0.242924	+	0.420757i
$612$	3.35838e11	−	5.81688e11i	0.0967716	−	0.167613i
$613$	−2.16617e12	+	3.75191e12i	−0.619612	+	1.07320i	0.369944	+	0.929054i	$0.379377\pi$
$613$	−2.16617e12	+	3.75191e12i	−0.619612	+	1.07320i	−0.989556	+	0.144146i	$0.953957\pi$
$614$	−5.07940e11	−	8.79777e11i	−0.144230	−	0.249813i
$615$	5.92668e10			0.0167060
$616$	6.15982e11	+	1.88388e11i	0.172367	+	0.0527158i
$617$	5.80005e12			1.61120			0.805598	−	0.592462i	$-0.201844\pi$
$617$	5.80005e12			1.61120			0.805598	+	0.592462i	$0.201844\pi$
$618$	1.91893e12	+	3.32368e12i	0.529189	+	0.916582i
$619$	3.36601e12	−	5.83010e12i	0.921526	−	1.59613i	0.124470	−	0.992223i	$-0.460277\pi$
$619$	3.36601e12	−	5.83010e12i	0.921526	−	1.59613i	0.797055	−	0.603906i	$-0.206390\pi$
$620$	6.07949e11	−	1.05300e12i	0.165236	−	0.286197i
$621$	−1.09749e12	−	1.90091e12i	−0.296135	−	0.512921i
$622$	−6.08964e12			−1.63130
$623$	−4.46628e12	+	4.16409e12i	−1.18782	+	1.10745i
$624$	−1.27984e12			−0.337928
$625$	−1.26016e12	−	2.18266e12i	−0.330343	−	0.572170i
$626$	3.00693e12	−	5.20815e12i	0.782597	−	1.35550i
$627$	4.32623e12	−	7.49325e12i	1.11791	−	1.93627i
$628$	−2.70189e12	−	4.67981e12i	−0.693185	−	1.20063i
$629$	−1.63525e12			−0.416539
$630$	1.45338e11	+	6.29802e11i	0.0367577	+	0.159284i
$631$	2.42752e12			0.609579			0.304790	−	0.952420i	$-0.401414\pi$
$631$	2.42752e12			0.609579			0.304790	+	0.952420i	$0.401414\pi$
$632$	−3.95030e11	−	6.84212e11i	−0.0984925	−	0.170594i
$633$	−2.95939e11	+	5.12581e11i	−0.0732630	+	0.126895i
$634$	−7.37578e11	+	1.27752e12i	−0.181303	+	0.314027i
$635$	7.36461e11	+	1.27559e12i	0.179750	+	0.311336i
$636$	−2.82239e12			−0.684007
$637$	−1.43713e12	+	7.00599e11i	−0.345836	+	0.168594i
$638$	8.05822e11			0.192551
$639$	−1.07200e12	−	1.85675e12i	−0.254354	−	0.440555i
$640$	1.88623e11	−	3.26704e11i	0.0444411	−	0.0769742i
$641$	8.09153e11	−	1.40149e12i	0.189308	−	0.327891i	−0.755712	−	0.654905i	$-0.772709\pi$
$641$	8.09153e11	−	1.40149e12i	0.189308	−	0.327891i	0.945020	+	0.327013i	$0.106042\pi$
$642$	5.98568e11	+	1.03675e12i	0.139061	+	0.240861i
$643$	−1.22787e12			−0.283271			−0.141636	−	0.989919i	$-0.545236\pi$
$643$	−1.22787e12			−0.283271			−0.141636	+	0.989919i	$0.545236\pi$
$644$	−4.83710e11	−	2.09609e12i	−0.110815	−	0.480201i
$645$	−1.04601e12			−0.237967
$646$	3.77236e12	+	6.53392e12i	0.852249	+	1.47614i
$647$	−2.03228e12	+	3.52001e12i	−0.455947	+	0.789723i	−0.998742	−	0.0501418i	$-0.984033\pi$
$647$	−2.03228e12	+	3.52001e12i	−0.455947	+	0.789723i	0.542795	+	0.839865i	$0.317366\pi$
$648$	1.56430e11	−	2.70945e11i	0.0348524	−	0.0603662i
$649$	6.09845e11	+	1.05628e12i	0.134933	+	0.233711i
$650$	2.13264e12			0.468605
$651$	−2.88436e12	+	2.68920e12i	−0.629413	+	0.586825i
$652$	3.10278e12			0.672415
$653$	3.93696e12	+	6.81901e12i	0.847327	+	1.46761i	0.883585	+	0.468271i	$0.155123\pi$
$653$	3.93696e12	+	6.81901e12i	0.847327	+	1.46761i	−0.0362576	+	0.999342i	$0.511544\pi$
$654$	8.27601e11	−	1.43345e12i	0.176897	−	0.306395i
$655$	1.12910e12	−	1.95567e12i	0.239689	−	0.415153i
$656$	1.54871e11	+	2.68245e11i	0.0326515	+	0.0565541i
$657$	2.05259e11			0.0429791
$658$	−8.01615e12	−	2.45161e12i	−1.66705	−	0.509842i
$659$	4.05662e12			0.837875			0.418938	−	0.908015i	$-0.362403\pi$
$659$	4.05662e12			0.837875			0.418938	+	0.908015i	$0.362403\pi$
$660$	8.49241e11	+	1.47093e12i	0.174214	+	0.301747i
$661$	−1.61565e12	+	2.79839e12i	−0.329186	+	0.570167i	−0.982351	−	0.187049i	$-0.940108\pi$
$661$	−1.61565e12	+	2.79839e12i	−0.329186	+	0.570167i	0.653165	+	0.757216i	$0.273441\pi$
$662$	−5.35333e12	+	9.27223e12i	−1.08333	+	1.87639i
$663$	−4.79541e11	−	8.30590e11i	−0.0963863	−	0.166946i
$664$	−9.05864e11			−0.180845
$665$	−3.29976e12	−	1.00918e12i	−0.654312	−	0.200111i
$666$	−1.62742e12			−0.320527
$667$	1.40004e11	+	2.42493e11i	0.0273888	+	0.0474388i
$668$	−2.01129e12	+	3.48365e12i	−0.390823	+	0.676925i
$669$	4.47182e11	−	7.74541e11i	0.0863111	−	0.149495i
$670$	−1.25042e12	−	2.16579e12i	−0.239728	−	0.415221i
$671$	−1.99542e12			−0.379999
$672$	4.28122e12	−	3.99154e12i	0.809852	−	0.755056i
$673$	4.73558e12			0.889827			0.444914	−	0.895573i	$-0.353234\pi$
$673$	4.73558e12			0.889827			0.444914	+	0.895573i	$0.353234\pi$
$674$	1.76818e10	+	3.06258e10i	0.00330033	+	0.00571634i
$675$	−2.58990e12	+	4.48584e12i	−0.480193	+	0.831719i
$676$	2.09492e12	−	3.62851e12i	0.385841	−	0.668295i
$677$	−5.07732e12	−	8.79417e12i	−0.928935	−	1.60896i	−0.785107	−	0.619360i	$-0.787392\pi$
$677$	−5.07732e12	−	8.79417e12i	−0.928935	−	1.60896i	−0.143829	−	0.989603i	$-0.545941\pi$
$678$	−9.93505e11			−0.180566
$679$	5.36454e11	+	2.32464e12i	0.0968542	+	0.419703i
$680$	1.54100e11			0.0276384
$681$	−1.25866e12	−	2.18006e12i	−0.224257	−	0.388424i
$682$	5.74526e12	−	9.95109e12i	1.01690	−	1.76133i
$683$	−7.11756e11	+	1.23280e12i	−0.125152	+	0.216770i	−0.921792	−	0.387684i	$-0.873275\pi$
$683$	−7.11756e11	+	1.23280e12i	−0.125152	+	0.216770i	0.796640	+	0.604454i	$0.206609\pi$
$684$	1.78432e12	+	3.09053e12i	0.311688	+	0.539860i
$685$	1.83273e12			0.318048
$686$	2.87173e12	−	7.47475e12i	0.495090	−	1.28866i
$687$	1.54394e12			0.264439
$688$	−2.73335e12	−	4.73430e12i	−0.465101	−	0.805579i
$689$	1.06193e12	−	1.83931e12i	0.179518	−	0.310934i
$690$	−6.20893e11	+	1.07542e12i	−0.104279	+	0.180616i
$691$	3.39648e12	+	5.88288e12i	0.566733	+	0.981610i	0.996886	+	0.0788540i	$0.0251261\pi$
$691$	3.39648e12	+	5.88288e12i	0.566733	+	0.981610i	−0.430154	+	0.902756i	$0.641541\pi$
$692$	5.05849e12			0.838578
$693$	6.52781e11	+	2.82873e12i	0.107515	+	0.465899i
$694$	7.40806e12			1.21224
$695$	−1.53354e12	−	2.65617e12i	−0.249324	−	0.431842i
$696$	−3.28096e10	+	5.68279e10i	−0.00529980	+	0.00917952i
$697$	−1.16057e11	+	2.01017e11i	−0.0186262	+	0.0322615i
$698$	−4.26705e11	−	7.39074e11i	−0.0680422	−	0.117852i
$699$	−4.98150e12			−0.789247
$700$	−3.71298e12	+	3.46175e12i	−0.584496	+	0.544948i
$701$	−1.00972e13			−1.57932			−0.789658	−	0.613548i	$-0.789742\pi$
$701$	−1.00972e13			−1.57932			−0.789658	+	0.613548i	$0.789742\pi$
$702$	−1.86008e12	−	3.22176e12i	−0.289078	−	0.500698i
$703$	4.34407e12	−	7.52415e12i	0.670807	−	1.16187i
$704$	−3.62747e12	+	6.28295e12i	−0.556578	+	0.964022i
$705$	1.14992e12	+	1.99172e12i	0.175314	+	0.303652i
$706$	2.72320e11			0.0412532
$707$	6.18874e12	+	1.89273e12i	0.931569	+	0.284906i
$708$	9.54560e11			0.142775
$709$	6.38534e12	+	1.10597e13i	0.949022	+	1.64375i	0.747491	+	0.664272i	$0.231258\pi$
$709$	6.38534e12	+	1.10597e13i	0.949022	+	1.64375i	0.201531	+	0.979482i	$0.435408\pi$
$710$	−2.36373e12	+	4.09410e12i	−0.349088	+	0.604639i
$711$	1.78034e12	−	3.08365e12i	0.261271	−	0.452534i
$712$	7.24433e11	+	1.25475e12i	0.105642	+	0.182978i
$713$	3.99273e12			0.578585
$714$	4.59341e12	+	1.40482e12i	0.661444	+	0.202292i
$715$	−1.27811e12			−0.182890
$716$	−2.34249e12	−	4.05732e12i	−0.333096	−	0.576940i
$717$	−3.52943e12	+	6.11316e12i	−0.498734	+	0.863832i
$718$	3.48106e12	−	6.02937e12i	0.488822	−	0.846665i
$719$	2.74890e12	+	4.76124e12i	0.383600	+	0.664415i	0.991574	−	0.129542i	$-0.0413507\pi$
$719$	2.74890e12	+	4.76124e12i	0.383600	+	0.664415i	−0.607974	+	0.793957i	$0.708017\pi$
$720$	9.26777e11			0.128522
$721$	5.02807e12	−	4.68786e12i	0.692935	−	0.646049i
$722$	−3.00056e13			−4.10946
$723$	−3.53119e12	−	6.11621e12i	−0.480617	−	0.832453i
$724$	−1.72425e12	+	2.98649e12i	−0.233226	+	0.403960i
$725$	3.30385e11	−	5.72244e11i	0.0444119	−	0.0769237i
$726$	3.84435e12	+	6.65860e12i	0.513580	+	0.889546i
$727$	−1.14873e13			−1.52515			−0.762575	−	0.646900i	$-0.776065\pi$
$727$	−1.14873e13			−1.52515			−0.762575	+	0.646900i	$0.776065\pi$
$728$	8.53010e10	+	3.69639e11i	0.0112554	+	0.0487738i
$729$	8.12734e12			1.06580
$730$	−2.26296e11	−	3.91956e11i	−0.0294933	−	0.0510839i
$731$	2.04831e12	−	3.54778e12i	0.265319	−	0.459546i
$732$	−7.80832e11	+	1.35244e12i	−0.100521	+	0.174108i
$733$	−6.26913e11	−	1.08585e12i	−0.0802120	−	0.138931i	0.823129	−	0.567855i	$-0.192226\pi$
$733$	−6.26913e11	−	1.08585e12i	−0.0802120	−	0.138931i	−0.903341	+	0.428923i	$0.858893\pi$
$734$	9.89225e12			1.25795
$735$	−1.97473e12	+	9.62676e11i	−0.249583	+	0.121671i
$736$	−5.92635e12			−0.744453
$737$	−5.61620e12	−	9.72754e12i	−0.701195	−	1.21451i
$738$	−1.15502e11	+	2.00055e11i	−0.0143329	+	0.0248253i
$739$	−2.45894e12	+	4.25902e12i	−0.303283	+	0.525302i	−0.976878	−	0.213799i	$-0.931416\pi$
$739$	−2.45894e12	+	4.25902e12i	−0.303283	+	0.525302i	0.673594	+	0.739101i	$0.264750\pi$
$740$	8.52743e11	+	1.47699e12i	0.104538	+	0.181066i
$741$	5.09565e12			0.620894
$742$	2.39182e12	+	1.03646e13i	0.289675	+	1.25526i
$743$	1.14947e11			0.0138372			0.00691860	−	0.999976i	$-0.497798\pi$
$743$	1.14947e11			0.0138372			0.00691860	+	0.999976i	$0.497798\pi$
$744$	4.67845e11	+	8.10331e11i	0.0559788	+	0.0969581i
$745$	1.44310e12	−	2.49953e12i	0.171630	−	0.297273i
$746$	3.94319e12	−	6.82980e12i	0.466147	−	0.807390i
$747$	−2.04130e12	−	3.53563e12i	−0.239863	−	0.415456i
$748$	−6.65199e12			−0.776952
$749$	1.56839e12	−	1.46227e12i	0.182090	−	0.169770i
$750$	6.25182e12			0.721491
$751$	4.65760e11	+	8.06720e11i	0.0534297	+	0.0925429i	0.891503	−	0.453014i	$-0.149651\pi$
$751$	4.65760e11	+	8.06720e11i	0.0534297	+	0.0925429i	−0.838074	+	0.545557i	$0.816318\pi$
$752$	−6.00975e12	+	1.04092e13i	−0.685293	+	1.18696i
$753$	3.01052e12	−	5.21438e12i	0.341244	−	0.591051i
$754$	2.37284e11	+	4.10989e11i	0.0267361	+	0.0463083i
$755$	1.28070e12			0.143445
$756$	8.46809e12	+	2.58983e12i	0.942838	+	0.288352i
$757$	−2.85730e12			−0.316246			−0.158123	−	0.987419i	$-0.550544\pi$
$757$	−2.85730e12			−0.316246			−0.158123	+	0.987419i	$0.550544\pi$
$758$	1.67077e12	+	2.89386e12i	0.183826	+	0.318395i
$759$	−2.78871e12	+	4.83019e12i	−0.305011	+	0.528295i
$760$	−4.09370e11	+	7.09050e11i	−0.0445097	+	0.0770931i
$761$	−3.85063e12	−	6.66949e12i	−0.416199	−	0.720878i	0.579354	−	0.815076i	$-0.303305\pi$
$761$	−3.85063e12	−	6.66949e12i	−0.416199	−	0.720878i	−0.995554	+	0.0941978i	$0.969971\pi$
$762$	1.08937e13			1.17052
$763$	−2.83518e12	−	8.67096e11i	−0.302845	−	0.0926204i
$764$	5.65357e12			0.600347
$765$	3.47253e11	+	6.01460e11i	0.0366581	+	0.0634937i
$766$	−8.45929e11	+	1.46519e12i	−0.0887778	+	0.153768i
$767$	−3.59153e11	+	6.22072e11i	−0.0374715	+	0.0649025i
$768$	−4.52939e12	−	7.84513e12i	−0.469801	−	0.813719i
$769$	9.37118e12			0.966331			0.483165	−	0.875529i	$-0.339487\pi$
$769$	9.37118e12			0.966331			0.483165	+	0.875529i	$0.339487\pi$
$770$	4.68197e12	−	4.36518e12i	0.479977	−	0.447501i
$771$	−7.06739e12			−0.720301
$772$	2.20618e11	+	3.82121e11i	0.0223544	+	0.0387189i
$773$	1.43217e12	−	2.48059e12i	0.144273	−	0.249889i	−0.784828	−	0.619713i	$-0.787249\pi$
$773$	1.43217e12	−	2.48059e12i	0.144273	−	0.249889i	0.929102	+	0.369824i	$0.120582\pi$
$774$	2.03851e12	−	3.53080e12i	0.204163	−	0.353621i
$775$	−4.71109e12	−	8.15984e12i	−0.469098	−	0.812501i
$776$	5.66070e11			0.0560393
$777$	−1.24378e12	−	5.38975e12i	−0.122419	−	0.530486i
$778$	2.17671e13			2.13006
$779$	−6.16617e11	−	1.06801e12i	−0.0599925	−	0.103910i
$780$	−5.00139e11	+	8.66266e11i	−0.0483799	+	0.0837965i
$781$	−1.06166e13	+	1.83885e13i	−1.02107	+	1.76854i
$782$	−2.43168e12	−	4.21180e12i	−0.232529	−	0.402752i
$783$	−1.15264e12			−0.109589
$784$	−9.51733e12	−	6.42215e12i	−0.899690	−	0.607097i
$785$	5.58746e12			0.525171
$786$	−8.35084e12	−	1.44641e13i	−0.780421	−	1.35173i
$787$	−2.89516e12	+	5.01456e12i	−0.269021	+	0.465958i	−0.968609	−	0.248588i	$-0.920033\pi$
$787$	−2.89516e12	+	5.01456e12i	−0.269021	+	0.465958i	0.699588	+	0.714546i	$0.253367\pi$
$788$	2.85311e12	−	4.94173e12i	0.263603	−	0.456574i
$789$	−1.04110e11	−	1.80323e11i	−0.00956410	−	0.0165655i
$790$	−7.85125e12			−0.717161
$791$	4.00153e11	+	1.73400e12i	0.0363439	+	0.157491i
$792$	6.88819e11			0.0622074
$793$	−5.87576e11	−	1.01771e12i	−0.0527637	−	0.0913894i
$794$	−7.04266e12	+	1.21983e13i	−0.628847	+	1.08919i
$795$	1.45916e12	−	2.52735e12i	0.129554	−	0.224395i
$796$	3.98826e12	+	6.90787e12i	0.352107	+	0.609868i
$797$	1.24776e13			1.09539			0.547696	−	0.836677i	$-0.315505\pi$
$797$	1.24776e13			1.09539			0.547696	+	0.836677i	$0.315505\pi$
$798$	−1.86664e13	+	1.74034e13i	−1.62948	+	1.51922i
$799$	−9.00715e12			−0.781856
$800$	6.99259e12	+	1.21115e13i	0.603578	+	1.04543i
$801$	−3.26491e12	+	5.65500e12i	−0.280237	+	0.485385i
$802$	8.12758e12	−	1.40774e13i	0.693708	−	1.20154i
$803$	−1.01640e12	−	1.76045e12i	−0.0862667	−	0.149418i
$804$	−8.79075e12			−0.741949
$805$	2.12704e12	+	6.50523e11i	0.178523	+	0.0545986i
$806$	6.76706e12			0.564797
$807$	2.31766e12	+	4.01430e12i	0.192362	+	0.333180i
$808$	7.67779e11	−	1.32983e12i	0.0633702	−	0.109760i
$809$	−6.53505e12	+	1.13190e13i	−0.536390	+	0.929055i	0.462704	+	0.886513i	$0.346879\pi$
$809$	−6.53505e12	+	1.13190e13i	−0.536390	+	0.929055i	−0.999095	+	0.0425425i	$0.986454\pi$
$810$	−1.55453e12	−	2.69252e12i	−0.126887	−	0.219774i
$811$	−1.06744e13			−0.866465			−0.433232	−	0.901282i	$-0.642627\pi$
$811$	−1.06744e13			−0.866465			−0.433232	+	0.901282i	$0.642627\pi$
$812$	−1.08025e12	−	3.30376e11i	−0.0872008	−	0.0266690i
$813$	6.26886e12			0.503247
$814$	8.05863e12	+	1.39580e13i	0.643356	+	1.11433i
$815$	−1.60413e12	+	2.77843e12i	−0.127359	+	0.220592i
$816$	3.44371e12	−	5.96467e12i	0.271907	−	0.470957i
$817$	1.08828e13	+	1.88495e13i	0.854556	+	1.48013i
$818$	−1.98465e13			−1.54986
$819$	−1.25050e12	+	1.16589e12i	−0.0971195	+	0.0905481i
$820$	2.42084e11			0.0186984
$821$	2.26982e12	+	3.93144e12i	0.174360	+	0.302001i	0.939940	−	0.341341i	$-0.110881\pi$
$821$	2.26982e12	+	3.93144e12i	0.174360	+	0.302001i	−0.765580	+	0.643341i	$0.777548\pi$
$822$	6.77745e12	−	1.17389e13i	0.517777	−	0.896816i
$823$	1.02569e13	−	1.77656e13i	0.779326	−	1.34983i	−0.153005	−	0.988225i	$-0.548895\pi$
$823$	1.02569e13	−	1.77656e13i	0.779326	−	1.34983i	0.932331	−	0.361606i	$-0.117771\pi$
$824$	−8.15554e11	−	1.41258e12i	−0.0616283	−	0.106743i
$825$	1.31618e13			0.989173
$826$	−8.08937e11	−	3.50541e12i	−0.0604651	−	0.262016i
$827$	1.04185e13			0.774513			0.387257	−	0.921972i	$-0.373423\pi$
$827$	1.04185e13			0.774513			0.387257	+	0.921972i	$0.373423\pi$
$828$	−1.15018e12	−	1.99218e12i	−0.0850414	−	0.147296i
$829$	9.54680e12	−	1.65355e13i	0.702041	−	1.21597i	−0.265708	−	0.964054i	$-0.585606\pi$
$829$	9.54680e12	−	1.65355e13i	0.702041	−	1.21597i	0.967749	−	0.251917i	$-0.0810610\pi$
$830$	−4.50103e12	+	7.79601e12i	−0.329200	+	0.570192i
$831$	2.63814e12	+	4.56940e12i	0.191908	+	0.332395i
$832$	−4.27261e12			−0.309128
$833$	6.01809e11	−	8.58287e12i	0.0433068	−	0.617633i
$834$	−2.26841e13			−1.62359
$835$	−2.07965e12	−	3.60206e12i	−0.148048	−	0.256426i
$836$	1.76711e13	−	3.06073e13i	1.25123	−	2.16719i
$837$	−8.21799e12	+	1.42340e13i	−0.578763	+	1.00245i
$838$	−1.50624e13	−	2.60889e13i	−1.05511	−	1.82750i
$839$	8.21859e12			0.572623			0.286311	−	0.958137i	$-0.407571\pi$
$839$	8.21859e12			0.572623			0.286311	+	0.958137i	$0.407571\pi$
$840$	1.17210e11	+	5.07912e11i	0.00812283	+	0.0351991i
$841$	−1.43601e13			−0.989864
$842$	−4.23734e12	−	7.33929e12i	−0.290529	−	0.503210i
$843$	2.62070e12	−	4.53919e12i	0.178728	−	0.309567i
$844$	−1.20881e12	+	2.09371e12i	−0.0820004	+	0.142029i
$845$	2.16613e12	+	3.75185e12i	0.146160	+	0.253157i
$846$	−8.96403e12			−0.601640
$847$	1.00731e13	−	9.39156e12i	0.672495	−	0.626993i
$848$	1.52519e13			1.01284
$849$	4.66990e12	+	8.08851e12i	0.308477	+	0.534299i
$850$	−5.73837e12	+	9.93914e12i	−0.377054	+	0.653076i
$851$	−2.80021e12	+	4.85011e12i	−0.183024	+	0.317007i
$852$	8.30880e12	+	1.43913e13i	0.540207	+	0.935666i
$853$	−9.72027e12			−0.628648			−0.314324	−	0.949316i	$-0.601778\pi$
$853$	−9.72027e12			−0.628648			−0.314324	+	0.949316i	$0.601778\pi$
$854$	5.62825e12	+	1.72131e12i	0.362087	+	0.110739i
$855$	−3.68994e12			−0.236141
$856$	−2.54394e11	−	4.40623e11i	−0.0161948	−	0.0280502i
$857$	8.46878e12	−	1.46684e13i	0.536299	−	0.928897i	−0.462800	−	0.886463i	$-0.653155\pi$
$857$	8.46878e12	−	1.46684e13i	0.536299	−	0.928897i	0.999099	−	0.0424348i	$-0.0135115\pi$
$858$	−4.72644e12	+	8.18643e12i	−0.297743	+	0.515705i
$859$	3.05776e12	+	5.29619e12i	0.191617	+	0.331890i	0.945786	−	0.324790i	$-0.105294\pi$
$859$	3.05776e12	+	5.29619e12i	0.191617	+	0.331890i	−0.754169	+	0.656680i	$0.771960\pi$
$860$	−4.27259e12			−0.266347
$861$	−7.50823e11	−	2.29628e11i	−0.0465611	−	0.0142400i
$862$	2.58614e13			1.59540
$863$	1.56664e13	+	2.71350e13i	0.961436	+	1.66526i	0.718899	+	0.695114i	$0.244646\pi$
$863$	1.56664e13	+	2.71350e13i	0.961436	+	1.66526i	0.242537	+	0.970142i	$0.422020\pi$
$864$	1.21978e13	−	2.11273e13i	0.744682	−	1.28983i
$865$	−2.61522e12	+	4.52969e12i	−0.158831	+	0.275104i
$866$	1.40203e13	+	2.42839e13i	0.847085	+	1.46719i
$867$	−8.30249e12			−0.499025
$868$	−1.17816e13	+	1.09845e13i	−0.704477	+	0.656810i
$869$	−3.52635e13			−2.09767
$870$	3.26047e11	+	5.64729e11i	0.0192949	+	0.0334198i
$871$	3.30752e12	−	5.72879e12i	0.194725	−	0.337273i
$872$	−3.51734e11	+	6.09222e11i	−0.0206011	+	0.0356822i
$873$	1.27560e12	+	2.20940e12i	0.0743276	+	0.128739i
$874$	2.58393e13			1.49789
$875$	−2.51804e12	−	1.09115e13i	−0.145220	−	0.629289i
$876$	−1.59091e12			−0.0912806
$877$	−9.69867e12	−	1.67986e13i	−0.553623	−	0.958903i	−0.998009	−	0.0630676i	$-0.979912\pi$
$877$	−9.69867e12	−	1.67986e13i	−0.553623	−	0.958903i	0.444386	−	0.895835i	$-0.353422\pi$
$878$	−2.10163e13	+	3.64012e13i	−1.19352	+	2.06724i
$879$	−1.26320e13	+	2.18793e13i	−0.713710	+	1.23618i
$880$	−4.58920e12	−	7.94873e12i	−0.257968	−	0.446813i
$881$	−1.54621e13			−0.864722			−0.432361	−	0.901701i	$-0.642319\pi$
$881$	−1.54621e13			−0.864722			−0.432361	+	0.901701i	$0.642319\pi$
$882$	5.98927e11	−	8.54178e12i	0.0333246	−	0.475269i
$883$	−2.28671e13			−1.26587			−0.632934	−	0.774206i	$-0.718150\pi$
$883$	−2.28671e13			−1.26587			−0.632934	+	0.774206i	$0.718150\pi$
$884$	−1.95876e12	−	3.39267e12i	−0.107881	−	0.186856i
$885$	−4.93503e11	+	8.54773e11i	−0.0270424	+	0.0468388i
$886$	−8.65681e12	+	1.49940e13i	−0.471961	+	0.817460i
$887$	4.90217e12	+	8.49080e12i	0.265908	+	0.460567i	0.967801	−	0.251716i	$-0.0809948\pi$
$887$	4.90217e12	+	8.49080e12i	0.265908	+	0.460567i	−0.701893	+	0.712283i	$0.747661\pi$
$888$	−1.31245e12			−0.0708312
$889$	−4.38765e12	−	1.90132e13i	−0.235599	−	1.02093i
$890$	1.43981e13			0.769222
$891$	−6.98210e12	−	1.20934e13i	−0.371139	−	0.642831i
$892$	1.82658e12	−	3.16373e12i	0.0966045	−	0.167324i
$893$	2.39277e13	−	4.14440e13i	1.25913	−	2.18087i
$894$	−1.06732e13	−	1.84865e13i	−0.558824	−	0.967912i
$895$	4.84424e12			0.252361
$896$	−3.65538e12	+	3.40805e12i	−0.189473	+	0.176653i
$897$	−3.28468e12			−0.169406
$898$	5.02901e12	+	8.71050e12i	0.258071	+	0.446992i
$899$	1.04834e12	−	1.81578e12i	0.0535284	−	0.0927139i
$900$	−2.71424e12	+	4.70120e12i	−0.137898	+	0.238846i
$901$	5.71472e12	+	9.89818e12i	0.288891	+	0.500373i
$902$	2.28776e12			0.115075
$903$	1.32514e13	+	4.05274e12i	0.663235	+	0.202840i
$904$	4.22244e11			0.0210284
$905$	−1.78286e12	−	3.08801e12i	−0.0883485	−	0.153024i
$906$	4.73603e12	−	8.20304e12i	0.233527	−	0.404481i
$907$	5.81619e12	−	1.00739e13i	0.285368	−	0.494273i	−0.687330	−	0.726345i	$-0.741217\pi$
$907$	5.81619e12	−	1.00739e13i	0.285368	−	0.494273i	0.972698	+	0.232073i	$0.0745507\pi$
$908$	−5.14118e12	−	8.90478e12i	−0.251001	−	0.434747i
$909$	6.92054e12			0.336204
$910$	3.60501e12	+	1.10254e12i	0.174269	+	0.0532975i
$911$	3.87840e13			1.86561			0.932804	−	0.360384i	$-0.117354\pi$
$911$	3.87840e13			1.86561			0.932804	+	0.360384i	$0.117354\pi$
$912$	1.82966e13	+	3.16906e13i	0.875775	+	1.51689i
$913$	−2.02162e13	+	3.50154e13i	−0.962898	+	1.66779i
$914$	4.56102e12	−	7.89992e12i	0.216174	−	0.374425i
$915$	−8.07374e11	−	1.39841e12i	−0.0380785	−	0.0659539i
$916$	6.30646e12			0.295976
$917$	−2.18813e13	+	2.04007e13i	−1.02190	+	0.952760i
$918$	2.00199e13			0.930403
$919$	−1.24097e13	−	2.14942e13i	−0.573906	−	0.994034i	−0.996160	−	0.0875565i	$-0.972094\pi$
$919$	−1.24097e13	−	2.14942e13i	−0.573906	−	0.994034i	0.422254	−	0.906478i	$-0.361239\pi$
$920$	2.63882e11	−	4.57058e11i	0.0121441	−	0.0210342i
$921$	1.84616e12	−	3.19764e12i	0.0845476	−	0.146441i
$922$	5.63601e12	+	9.76185e12i	0.256852	+	0.444880i
$923$	−1.25047e13			−0.567110
$924$	−5.05956e12	−	2.19249e13i	−0.228344	−	0.989493i
$925$	1.32161e13			0.593560
$926$	−2.06298e13	−	3.57319e13i	−0.922032	−	1.59701i
$927$	3.67558e12	−	6.36630e12i	0.163481	−	0.283158i
$928$	−1.55604e12	+	2.69514e12i	−0.0688738	+	0.119293i
$929$	−1.58675e13	−	2.74833e13i	−0.698936	−	1.21059i	−0.968836	−	0.247704i	$-0.920324\pi$
$929$	−1.58675e13	−	2.74833e13i	−0.698936	−	1.21059i	0.269900	−	0.962888i	$-0.413009\pi$
$930$	9.29844e12			0.407603
$931$	3.78931e13	+	2.55697e13i	1.65305	+	1.11545i
$932$	−2.03477e13			−0.883373
$933$	−1.10667e13	−	1.91681e13i	−0.478136	−	0.828156i
$934$	−2.36009e13	+	4.08779e13i	−1.01477	+	1.75763i
$935$	3.43905e12	−	5.95661e12i	0.147159	−	0.254886i
$936$	2.02832e11	+	3.51314e11i	0.00863762	+	0.0149608i
$937$	−6.07149e12			−0.257316			−0.128658	−	0.991689i	$-0.541067\pi$
$937$	−6.07149e12			−0.257316			−0.128658	+	0.991689i	$0.541067\pi$
$938$	7.44968e12	+	3.22821e13i	0.314214	+	1.36160i
$939$	2.18580e13			0.917519
$940$	4.69702e12	+	8.13547e12i	0.196222	+	0.339866i
$941$	1.14387e13	−	1.98124e13i	0.475579	−	0.823727i	−0.524030	−	0.851700i	$-0.675572\pi$
$941$	1.14387e13	−	1.98124e13i	0.475579	−	0.823727i	0.999609	+	0.0279729i	$0.00890520\pi$
$942$	2.06624e13	−	3.57883e13i	0.854971	−	1.48085i
$943$	3.97475e11	+	6.88447e11i	0.0163684	+	0.0283510i
$944$	−5.15834e12			−0.211415
$945$	−6.69706e12	+	6.24393e12i	−0.273175	+	0.254692i
$946$	−4.03770e13			−1.63917
$947$	1.33261e13	+	2.30814e13i	0.538428	+	0.932584i	0.998989	+	0.0449562i	$0.0143148\pi$
$947$	1.33261e13	+	2.30814e13i	0.538428	+	0.932584i	−0.460561	+	0.887628i	$0.652352\pi$
$948$	−1.37991e13	+	2.39007e13i	−0.554896	+	0.961109i
$949$	5.98582e11	−	1.03677e12i	0.0239566	−	0.0414941i
$950$	−3.04882e13	−	5.28071e13i	−1.21444	−	2.10347i
$951$	−5.36161e12			−0.212561
$952$	−1.95222e12	−	5.97056e11i	−0.0770305	−	0.0235586i
$953$	2.28306e13			0.896603			0.448302	−	0.893882i	$-0.352029\pi$
$953$	2.28306e13			0.896603			0.448302	+	0.893882i	$0.352029\pi$
$954$	5.68736e12	+	9.85079e12i	0.222302	+	0.385038i
$955$	−2.92287e12	+	5.06256e12i	−0.113709	+	0.196950i
$956$	−1.44165e13	+	2.49701e13i	−0.558213	+	0.966853i
$957$	1.46442e12	+	2.53646e12i	0.0564369	+	0.0977515i
$958$	4.32200e13			1.65783
$959$	−2.32181e13	−	7.10088e12i	−0.886426	−	0.271099i
$960$	−5.87089e12			−0.223092
$961$	−1.72889e12	−	2.99453e12i	−0.0653902	−	0.113259i
$962$	−4.74593e12	+	8.22019e12i	−0.178662	+	0.309452i
$963$	1.14652e12	−	1.98583e12i	0.0429598	−	0.0744086i
$964$	−1.44237e13	−	2.49826e13i	−0.537935	−	0.931731i
$965$	−4.56234e11			−0.0169362
$966$	1.20325e13	−	1.12183e13i	0.444588	−	0.414507i
$967$	−4.93714e13			−1.81575			−0.907875	−	0.419241i	$-0.862296\pi$
$967$	−4.93714e13			−1.81575			−0.907875	+	0.419241i	$0.862296\pi$
$968$	−1.63387e12	−	2.82994e12i	−0.0598105	−	0.103595i
$969$	−1.37110e13	+	2.37482e13i	−0.499590	+	0.865315i
$970$	2.81267e12	−	4.87169e12i	0.102011	−	0.176688i
$971$	1.97539e13	+	3.42148e13i	0.713128	+	1.23517i	0.963677	+	0.267070i	$0.0860554\pi$
$971$	1.97539e13	+	3.42148e13i	0.713128	+	1.23517i	−0.250550	+	0.968104i	$0.580611\pi$
$972$	1.65092e13			0.593237
$973$	9.13646e12	+	3.95915e13i	0.326791	+	1.41610i
$974$	−2.20931e13			−0.786579
$975$	3.87565e12	+	6.71283e12i	0.137349	+	0.237895i
$976$	4.21953e12	−	7.30844e12i	0.148847	−	0.257811i
$977$	−2.28523e13	+	3.95814e13i	−0.802425	+	1.38984i	0.115590	+	0.993297i	$0.463124\pi$
$977$	−2.28523e13	+	3.95814e13i	−0.802425	+	1.38984i	−0.918015	+	0.396545i	$0.870209\pi$
$978$	1.18641e13	+	2.05492e13i	0.414677	+	0.718242i
$979$	6.46686e13			2.24994
$980$	−8.06609e12	+	3.93220e12i	−0.279348	+	0.136182i
$981$	−3.17043e12			−0.109297
$982$	−2.19886e13	−	3.80854e13i	−0.754565	−	1.30694i
$983$	2.14849e12	−	3.72130e12i	0.0733911	−	0.127117i	−0.826994	−	0.562210i	$-0.809951\pi$
$983$	2.14849e12	−	3.72130e12i	0.0733911	−	0.127117i	0.900385	+	0.435093i	$0.143285\pi$
$984$	−9.31476e10	+	1.61336e11i	−0.00316733	+	0.00548598i
$985$	2.95009e12	+	5.10971e12i	0.0998556	+	0.172955i
$986$	−2.55388e12			−0.0860506
$987$	−6.85092e12	−	2.96874e13i	−0.229785	−	0.995739i
$988$	2.08140e13			0.694942
$989$	−7.01510e12	−	1.21505e13i	−0.233158	−	0.403842i
$990$	3.42258e12	−	5.92809e12i	0.113239	−	0.196136i
$991$	6.17990e12	−	1.07039e13i	0.203540	−	0.352542i	−0.746126	−	0.665804i	$-0.768089\pi$
$991$	6.17990e12	−	1.07039e13i	0.203540	−	0.352542i	0.949667	+	0.313262i	$0.101422\pi$
$992$	2.21881e13	+	3.84310e13i	0.727475	+	1.26002i
$993$	−3.89145e13			−1.27010
$994$	4.58075e13	−	4.27080e13i	1.48832	−	1.38762i
$995$	−8.24766e12			−0.266764
$996$	1.58217e13	+	2.74039e13i	0.509431	+	0.882360i
$997$	1.54242e13	−	2.67155e13i	0.494396	−	0.856319i	−0.505583	−	0.862778i	$-0.668723\pi$
$997$	1.54242e13	−	2.67155e13i	0.494396	−	0.856319i	0.999979	+	0.00645890i	$0.00205595\pi$
$998$	3.22238e13	−	5.58133e13i	1.02823	−	1.78094i
$999$	−1.15270e13	−	1.99654e13i	−0.366161	−	0.634210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.10.c.a.4.5	yes	10
3.2	odd	2		63.10.e.b.46.1		10
4.3	odd	2		112.10.i.c.81.4		10
7.2	even	3	inner	7.10.c.a.2.5	✓	10
7.3	odd	6		49.10.a.f.1.1		5
7.4	even	3		49.10.a.e.1.1		5
7.5	odd	6		49.10.c.g.30.5		10
7.6	odd	2		49.10.c.g.18.5		10
21.2	odd	6		63.10.e.b.37.1		10
28.23	odd	6		112.10.i.c.65.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.c.a.2.5	✓	10	7.2	even	3	inner
7.10.c.a.4.5	yes	10	1.1	even	1	trivial
49.10.a.e.1.1		5	7.4	even	3
49.10.a.f.1.1		5	7.3	odd	6
49.10.c.g.18.5		10	7.6	odd	2
49.10.c.g.30.5		10	7.5	odd	6
63.10.e.b.37.1		10	21.2	odd	6
63.10.e.b.46.1		10	3.2	odd	2
112.10.i.c.65.4		10	28.23	odd	6
112.10.i.c.81.4		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(15.6185 + 27.0520i) q^{2} +(-56.7670 + 98.3234i) q^{3} +(-231.874 + 401.617i) q^{4} +(-239.755 - 415.269i) q^{5} -3546.46 q^{6} +(1428.40 + 6189.77i) q^{7} +1507.26 q^{8} +(3396.51 + 5882.92i) q^{9} +(7489.23 - 12971.7i) q^{10} +(33637.5 - 58261.9i) q^{11} +(-26325.6 - 45597.2i) q^{12} +39620.0 q^{13} +(-145136. + 135316. i) q^{14} +54440.8 q^{15} +(142260. + 246402. i) q^{16} +(-106607. + 184649. i) q^{17} +(-106097. + 183765. i) q^{18} +(-566407. - 981046. i) q^{19} +222372. q^{20} +(-689686. - 210930. i) q^{21} +2.10147e6 q^{22} +(365109. + 632388. i) q^{23} +(-85562.8 + 148199. i) q^{24} +(861597. - 1.49233e6i) q^{25} +(618804. + 1.07180e6i) q^{26} -3.00593e6 q^{27} +(-2.81713e6 - 861574. i) q^{28} +383457. q^{29} +(850283. + 1.47273e6i) q^{30} +(2.73393e6 - 4.73530e6i) q^{31} +(-4.05793e6 + 7.02853e6i) q^{32} +(3.81901e6 + 6.61472e6i) q^{33} -6.66015e6 q^{34} +(2.22795e6 - 2.07720e6i) q^{35} -3.15024e6 q^{36} +(3.83476e6 + 6.64200e6i) q^{37} +(1.76928e7 - 3.06449e7i) q^{38} +(-2.24911e6 + 3.89557e6i) q^{39} +(-361374. - 625919. i) q^{40} +1.08865e6 q^{41} +(-5.06577e6 - 2.19518e7i) q^{42} -1.92137e7 q^{43} +(1.55993e7 + 2.70188e7i) q^{44} +(1.62866e6 - 2.82093e6i) q^{45} +(-1.14049e7 + 1.97539e7i) q^{46} +(2.11223e7 + 3.65850e7i) q^{47} -3.23028e7 q^{48} +(-3.62729e7 + 1.76830e7i) q^{49} +5.38273e7 q^{50} +(-1.21035e7 - 2.09639e7i) q^{51} +(-9.18684e6 + 1.59121e7i) q^{52} +(2.68028e7 - 4.64237e7i) q^{53} +(-4.69480e7 - 8.13164e7i) q^{54} -3.22591e7 q^{55} +(2.15298e6 + 9.32961e6i) q^{56} +1.28613e8 q^{57} +(5.98901e6 + 1.03733e7i) q^{58} +(-9.06495e6 + 1.57010e7i) q^{59} +(-1.26234e7 + 2.18644e7i) q^{60} +(-1.48303e7 - 2.56868e7i) q^{61} +1.70799e8 q^{62} +(-3.15624e7 + 2.94268e7i) q^{63} -1.07840e8 q^{64} +(-9.49911e6 - 1.64529e7i) q^{65} +(-1.19294e8 + 2.06624e8i) q^{66} +(8.34811e7 - 1.44594e8i) q^{67} +(-4.94387e7 - 8.56303e7i) q^{68} -8.29047e7 q^{69} +(9.09897e7 + 2.78278e7i) q^{70} -3.15617e8 q^{71} +(5.11942e6 + 8.86710e6i) q^{72} +(1.51081e7 - 2.61679e7i) q^{73} +(-1.19786e8 + 2.07476e8i) q^{74} +(9.78206e7 + 1.69430e8i) q^{75} +5.25340e8 q^{76} +(4.08676e8 + 1.24987e8i) q^{77} -1.40511e8 q^{78} +(-2.62085e8 - 4.53944e8i) q^{79} +(6.82155e7 - 1.18153e8i) q^{80} +(1.03784e8 - 1.79760e8i) q^{81} +(1.70030e7 + 2.94500e7i) q^{82} -6.01000e8 q^{83} +(2.44633e8 - 2.28081e8i) q^{84} +1.02238e8 q^{85} +(-3.00089e8 - 5.19769e8i) q^{86} +(-2.17677e7 + 3.77027e7i) q^{87} +(5.07006e7 - 8.78160e7i) q^{88} +(4.80628e8 + 8.32473e8i) q^{89} +1.01749e8 q^{90} +(5.65933e7 + 2.45239e8i) q^{91} -3.38637e8 q^{92} +(3.10394e8 + 5.37618e8i) q^{93} +(-6.59798e8 + 1.14280e9i) q^{94} +(-2.71598e8 + 4.70422e8i) q^{95} +(-4.60713e8 - 7.97978e8i) q^{96} +3.75562e8 q^{97} +(-1.04489e9 - 7.05074e8i) q^{98} +4.57001e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16}+ \cdots - 1900777180 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 + 161 * q^3 - 940 * q^4 + 1533 * q^5 - 8708 * q^6 - 1036 * q^7 + 34272 * q^8 - 35734 * q^9 + 4298 * q^10 + 42213 * q^11 + 135604 * q^12 - 319676 * q^13 - 39522 * q^14 + 151394 * q^15 + 322064 * q^16 + 324681 * q^17 - 1012868 * q^18 - 16121 * q^19 - 350616 * q^20 - 1557857 * q^21 - 62692 * q^22 + 2638863 * q^23 + 8449728 * q^24 - 1304092 * q^25 + 4179252 * q^26 - 18331558 * q^27 - 22156316 * q^28 + 15292500 * q^29 + 20557942 * q^30 + 19179237 * q^31 - 6263520 * q^32 + 1689359 * q^33 - 62909700 * q^34 - 43746759 * q^35 + 71476528 * q^36 + 39566985 * q^37 + 67365270 * q^38 - 44299486 * q^39 + 5721744 * q^40 - 53436852 * q^41 - 183129856 * q^42 + 101835992 * q^43 + 99704916 * q^44 + 85098230 * q^45 - 14489202 * q^46 + 32509659 * q^47 - 185141600 * q^48 - 49024598 * q^49 + 3328464 * q^50 + 44168403 * q^51 + 103893272 * q^52 - 25714707 * q^53 + 51200926 * q^54 - 144695222 * q^55 + 115352832 * q^56 - 121710346 * q^57 - 46645516 * q^58 + 46776513 * q^59 + 132391756 * q^60 - 113075039 * q^61 + 467465628 * q^62 + 318071530 * q^63 - 192008960 * q^64 - 338113566 * q^65 - 836682602 * q^66 - 126707879 * q^67 + 32262636 * q^68 + 1323616182 * q^69 + 697712470 * q^70 - 1188736032 * q^71 - 950557728 * q^72 - 859257651 * q^73 + 591757530 * q^74 - 169061732 * q^75 + 1101475592 * q^76 + 1911891891 * q^77 + 519432424 * q^78 - 527065417 * q^79 - 1257352656 * q^80 + 551662715 * q^81 - 1341703076 * q^82 - 144863208 * q^83 + 486452204 * q^84 - 1197360222 * q^85 - 678648216 * q^86 - 340781350 * q^87 + 903700608 * q^88 + 1661554797 * q^89 + 1967758744 * q^90 + 726641384 * q^91 - 1301840952 * q^92 - 423057489 * q^93 - 272580882 * q^94 - 1197123495 * q^95 - 1441922272 * q^96 + 869770188 * q^97 - 2404833858 * q^98 - 1900777180 * q^99

Introduction

L-functions

Modular forms

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