LMFDB - Embedded newform 16.11.f.a.3.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,11,Mod(3,16)] 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("16.3"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, 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:	$10.1657160428$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	16.3
Dual form			16.11.f.a.11.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-19.3334 + 25.4994i) q^{2} +(-222.022 + 222.022i) q^{3} +(-276.439 - 985.981i) q^{4} +(-2711.76 + 2711.76i) q^{5} +(-1368.99 - 9953.89i) q^{6} -24891.4 q^{7} +(30486.4 + 12013.3i) q^{8} -39538.9i q^{9} +(-16720.7 - 121576. i) q^{10} +(158032. + 158032. i) q^{11} +(280285. + 157534. i) q^{12} +(-26357.8 - 26357.8i) q^{13} +(481236. - 634716. i) q^{14} -1.20414e6i q^{15} +(-895739. + 545126. i) q^{16} +1.46407e6 q^{17} +(1.00822e6 + 764422. i) q^{18} +(218956. - 218956. i) q^{19} +(3.42337e6 + 1.92410e6i) q^{20} +(5.52645e6 - 5.52645e6i) q^{21} +(-7.08500e6 + 974421. i) q^{22} -1.19227e7 q^{23} +(-9.43590e6 + 4.10144e6i) q^{24} -4.94162e6i q^{25} +(1.18169e6 - 162522. i) q^{26} +(-4.33167e6 - 4.33167e6i) q^{27} +(6.88095e6 + 2.45424e7i) q^{28} +(3.24715e6 + 3.24715e6i) q^{29} +(3.07049e7 + 2.32802e7i) q^{30} +1.71485e7i q^{31} +(3.41730e6 - 3.33800e7i) q^{32} -7.01731e7 q^{33} +(-2.83054e7 + 3.73329e7i) q^{34} +(6.74994e7 - 6.74994e7i) q^{35} +(-3.89846e7 + 1.09301e7i) q^{36} +(4.84002e7 - 4.84002e7i) q^{37} +(1.35008e6 + 9.81640e6i) q^{38} +1.17040e7 q^{39} +(-1.15249e8 + 5.00945e7i) q^{40} -2.01482e8i q^{41} +(3.40761e7 + 2.47766e8i) q^{42} +(-4.62694e7 - 4.62694e7i) q^{43} +(1.12130e8 - 1.99502e8i) q^{44} +(1.07220e8 + 1.07220e8i) q^{45} +(2.30507e8 - 3.04022e8i) q^{46} +3.80755e8i q^{47} +(7.78439e7 - 3.19905e8i) q^{48} +3.37107e8 q^{49} +(1.26008e8 + 9.55383e7i) q^{50} +(-3.25056e8 + 3.25056e8i) q^{51} +(-1.87019e7 + 3.32745e7i) q^{52} +(-1.53875e7 + 1.53875e7i) q^{53} +(1.94201e8 - 2.67091e7i) q^{54} -8.57086e8 q^{55} +(-7.58850e8 - 2.99029e8i) q^{56} +9.72262e7i q^{57} +(-1.45579e8 + 2.00219e7i) q^{58} +(3.55533e8 + 3.55533e8i) q^{59} +(-1.18726e9 + 3.32871e8i) q^{60} +(-6.17762e7 - 6.17762e7i) q^{61} +(-4.37275e8 - 3.31538e8i) q^{62} +9.84180e8i q^{63} +(7.85101e8 + 7.32488e8i) q^{64} +1.42952e8 q^{65} +(1.35668e9 - 1.78937e9i) q^{66} +(-8.03411e8 + 8.03411e8i) q^{67} +(-4.04725e8 - 1.44354e9i) q^{68} +(2.64711e9 - 2.64711e9i) q^{69} +(4.16201e8 + 3.02619e9i) q^{70} -3.60526e8 q^{71} +(4.74995e8 - 1.20540e9i) q^{72} +2.16123e9i q^{73} +(2.98435e8 + 2.16991e9i) q^{74} +(1.09715e9 + 1.09715e9i) q^{75} +(-2.76414e8 - 1.55358e8i) q^{76} +(-3.93363e9 - 3.93363e9i) q^{77} +(-2.26279e8 + 2.98446e8i) q^{78} -3.90441e9i q^{79} +(9.50777e8 - 3.90728e9i) q^{80} +4.25819e9 q^{81} +(5.13768e9 + 3.89534e9i) q^{82} +(1.64861e9 - 1.64861e9i) q^{83} +(-6.97670e9 - 3.92125e9i) q^{84} +(-3.97020e9 + 3.97020e9i) q^{85} +(2.07439e9 - 2.85297e8i) q^{86} -1.44188e9 q^{87} +(2.91933e9 + 6.71630e9i) q^{88} -4.00320e9i q^{89} +(-4.80697e9 + 6.61117e8i) q^{90} +(6.56082e8 + 6.56082e8i) q^{91} +(3.29590e9 + 1.17556e10i) q^{92} +(-3.80734e9 - 3.80734e9i) q^{93} +(-9.70903e9 - 7.36129e9i) q^{94} +1.18751e9i q^{95} +(6.65238e9 + 8.16982e9i) q^{96} +1.30440e9 q^{97} +(-6.51743e9 + 8.59603e9i) q^{98} +(6.24840e9 - 6.24840e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18}+ \cdots - 25616384098 q^{99}+O(q^{100}) $ 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8 - 147364 * q^10 - 45906 * q^11 - 10988 * q^12 - 2 * q^13 + 757836 * q^14 - 469032 * q^16 - 4 * q^17 + 2066926 * q^18 - 5107042 * q^19 + 5301516 * q^20 - 118100 * q^21 - 20568924 * q^22 - 8279748 * q^23 + 58519728 * q^24 - 18451512 * q^26 - 25871552 * q^27 - 36459784 * q^28 - 29652306 * q^29 + 132781252 * q^30 - 52661752 * q^32 - 4 * q^33 + 68474900 * q^34 + 14674460 * q^35 - 15810676 * q^36 - 94618130 * q^37 + 156046000 * q^38 - 279841732 * q^39 - 125381720 * q^40 + 107395416 * q^42 + 172486862 * q^43 + 73663988 * q^44 + 19649346 * q^45 - 437620836 * q^46 + 625190376 * q^48 + 1049193778 * q^49 - 875760314 * q^50 - 72924900 * q^51 - 771392444 * q^52 + 607072398 * q^53 + 913650464 * q^54 - 1427102468 * q^55 - 1385623464 * q^56 + 37561720 * q^58 + 1543683854 * q^59 + 318869600 * q^60 + 1673280158 * q^61 - 983062992 * q^62 - 867678656 * q^64 + 1098715212 * q^65 + 768197860 * q^66 - 4830427746 * q^67 - 855827792 * q^68 + 1698121420 * q^69 - 5103882496 * q^70 + 7572888316 * q^71 + 6888513460 * q^72 + 2513658844 * q^74 - 11656678318 * q^75 - 2250244316 * q^76 - 1336459028 * q^77 + 14243324268 * q^78 - 13115458328 * q^80 - 8523250762 * q^81 + 2724305648 * q^82 + 16141605438 * q^83 - 1633924184 * q^84 + 4779968748 * q^85 - 4025865500 * q^86 - 31832612676 * q^87 + 1023457912 * q^88 + 18960485240 * q^90 + 19874217404 * q^91 + 28060187160 * q^92 - 15001617056 * q^93 - 14829002256 * q^94 + 23525947312 * q^96 - 4 * q^97 - 43134832310 * q^98 - 25616384098 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−19.3334	+	25.4994i	−0.604169	+	0.796856i
$2$	−19.3334	+	25.4994i	−0.604169	+	0.796856i
$3$	−222.022	+	222.022i	−0.913673	+	0.913673i	−0.996559	−	0.0828864i	$-0.973586\pi$
$3$	−222.022	+	222.022i	−0.913673	+	0.913673i	0.0828864	+	0.996559i	$0.473586\pi$
$4$	−276.439	−	985.981i	−0.269960	−	0.962872i
$5$	−2711.76	+	2711.76i	−0.867762	+	0.867762i	−0.992224	−	0.124462i	$-0.960279\pi$
$5$	−2711.76	+	2711.76i	−0.867762	+	0.867762i	0.124462	+	0.992224i	$0.460279\pi$
$6$	−1368.99	−	9953.89i	−0.176053	−	1.28008i
$7$	−24891.4			−1.48101			−0.740507	−	0.672048i	$-0.765415\pi$
$7$	−24891.4			−1.48101			−0.740507	+	0.672048i	$0.765415\pi$
$8$	30486.4	+	12013.3i	0.930372	+	0.366618i
$9$		−	39538.9i		−	0.669595i
$10$	−16720.7	−	121576.i	−0.167207	−	1.21576i
$11$	158032.	+	158032.i	0.981251	+	0.981251i	0.999827	−	0.0185762i	$-0.00591332\pi$
$11$	158032.	+	158032.i	0.981251	+	0.981251i	−0.0185762	+	0.999827i	$0.505913\pi$
$12$	280285.	+	157534.i	1.12640	+	0.633095i
$13$	−26357.8	−	26357.8i	−0.0709891	−	0.0709891i	0.670721	−	0.741710i	$-0.265985\pi$
$13$	−26357.8	−	26357.8i	−0.0709891	−	0.0709891i	−0.741710	+	0.670721i	$0.765985\pi$
$14$	481236.	−	634716.i	0.894783	−	1.18016i
$15$		−	1.20414e6i		−	1.58570i
$16$	−895739.	+	545126.i	−0.854244	+	0.519873i
$17$	1.46407e6			1.03114			0.515569	−	0.856848i	$-0.327580\pi$
$17$	1.46407e6			1.03114			0.515569	+	0.856848i	$0.327580\pi$
$18$	1.00822e6	+	764422.i	0.533571	+	0.404549i
$19$	218956.	−	218956.i	0.0884277	−	0.0884277i	−0.661509	−	0.749937i	$-0.730084\pi$
$19$	218956.	−	218956.i	0.0884277	−	0.0884277i	0.749937	+	0.661509i	$0.230084\pi$
$20$	3.42337e6	+	1.92410e6i	1.06980	+	0.601283i
$21$	5.52645e6	−	5.52645e6i	1.35316	−	1.35316i
$22$	−7.08500e6	+	974421.i	−1.37476	+	0.189075i
$23$	−1.19227e7			−1.85240			−0.926202	−	0.377028i	$-0.876946\pi$
$23$	−1.19227e7			−1.85240			−0.926202	+	0.377028i	$0.876946\pi$
$24$	−9.43590e6	+	4.10144e6i	−1.18502	+	0.515086i
$25$		−	4.94162e6i		−	0.506022i
$26$	1.18169e6	−	162522.i	0.0994575	−	0.0136787i
$27$	−4.33167e6	−	4.33167e6i	−0.301882	−	0.301882i
$28$	6.88095e6	+	2.45424e7i	0.399814	+	1.42603i
$29$	3.24715e6	+	3.24715e6i	0.158312	+	0.158312i	0.781818	−	0.623507i	$-0.214293\pi$
$29$	3.24715e6	+	3.24715e6i	0.158312	+	0.158312i	−0.623507	+	0.781818i	$0.714293\pi$
$30$	3.07049e7	+	2.32802e7i	1.26358	+	0.958031i
$31$			1.71485e7i			0.598986i	0.954098	+	0.299493i	$0.0968175\pi$
$31$			1.71485e7i			0.598986i	−0.954098	+	0.299493i	$0.903182\pi$
$32$	3.41730e6	−	3.33800e7i	0.101843	−	0.994800i
$33$	−7.01731e7			−1.79308
$34$	−2.83054e7	+	3.73329e7i	−0.622982	+	0.821669i
$35$	6.74994e7	−	6.74994e7i	1.28517	−	1.28517i
$36$	−3.89846e7	+	1.09301e7i	−0.644734	+	0.180764i
$37$	4.84002e7	−	4.84002e7i	0.697972	−	0.697972i	−0.266001	−	0.963973i	$-0.585702\pi$
$37$	4.84002e7	−	4.84002e7i	0.697972	−	0.697972i	0.963973	+	0.266001i	$0.0857023\pi$
$38$	1.35008e6	+	9.81640e6i	0.0170389	+	0.123889i
$39$	1.17040e7			0.129722
$40$	−1.15249e8	+	5.00945e7i	−1.12548	+	0.489204i
$41$		−	2.01482e8i		−	1.73907i	−0.493868	−	0.869537i	$-0.664417\pi$
$41$		−	2.01482e8i		−	1.73907i	0.493868	−	0.869537i	$-0.335583\pi$
$42$	3.40761e7	+	2.47766e8i	0.260737	+	1.89581i
$43$	−4.62694e7	−	4.62694e7i	−0.314740	−	0.314740i	0.532003	−	0.846743i	$-0.321440\pi$
$43$	−4.62694e7	−	4.62694e7i	−0.314740	−	0.314740i	−0.846743	+	0.532003i	$0.821440\pi$
$44$	1.12130e8	−	1.99502e8i	0.679921	−	1.20972i
$45$	1.07220e8	+	1.07220e8i	0.581049	+	0.581049i
$46$	2.30507e8	−	3.04022e8i	1.11917	−	1.47610i
$47$			3.80755e8i			1.66018i	0.557626	+	0.830092i	$0.311712\pi$
$47$			3.80755e8i			1.66018i	−0.557626	+	0.830092i	$0.688288\pi$
$48$	7.78439e7	−	3.19905e8i	0.305505	−	1.25549i
$49$	3.37107e8			1.19340
$50$	1.26008e8	+	9.55383e7i	0.403227	+	0.305723i
$51$	−3.25056e8	+	3.25056e8i	−0.942123	+	0.942123i
$52$	−1.87019e7	+	3.32745e7i	−0.0491892	+	0.0875176i
$53$	−1.53875e7	+	1.53875e7i	−0.0367951	+	0.0367951i	−0.725265	−	0.688470i	$-0.758283\pi$
$53$	−1.53875e7	+	1.53875e7i	−0.0367951	+	0.0367951i	0.688470	+	0.725265i	$0.258283\pi$
$54$	1.94201e8	−	2.67091e7i	0.422944	−	0.0581688i
$55$	−8.57086e8			−1.70299
$56$	−7.58850e8	−	2.99029e8i	−1.37789	−	0.542967i
$57$			9.72262e7i			0.161588i
$58$	−1.45579e8	+	2.00219e7i	−0.221798	+	0.0305046i
$59$	3.55533e8	+	3.55533e8i	0.497301	+	0.497301i	0.910597	−	0.413296i	$-0.135622\pi$
$59$	3.55533e8	+	3.55533e8i	0.497301	+	0.497301i	−0.413296	+	0.910597i	$0.635622\pi$
$60$	−1.18726e9	+	3.32871e8i	−1.52683	+	0.428075i
$61$	−6.17762e7	−	6.17762e7i	−0.0731429	−	0.0731429i	0.669589	−	0.742732i	$-0.266470\pi$
$61$	−6.17762e7	−	6.17762e7i	−0.0731429	−	0.0731429i	−0.742732	+	0.669589i	$0.766470\pi$
$62$	−4.37275e8	−	3.31538e8i	−0.477306	−	0.361889i
$63$			9.84180e8i			0.991680i
$64$	7.85101e8	+	7.32488e8i	0.731182	+	0.682182i
$65$	1.42952e8			0.123203
$66$	1.35668e9	−	1.78937e9i	1.08333	−	1.42883i
$67$	−8.03411e8	+	8.03411e8i	−0.595064	+	0.595064i	−0.938995	−	0.343931i	$-0.888241\pi$
$67$	−8.03411e8	+	8.03411e8i	−0.595064	+	0.595064i	0.343931	+	0.938995i	$0.388241\pi$
$68$	−4.04725e8	−	1.44354e9i	−0.278366	−	0.992854i
$69$	2.64711e9	−	2.64711e9i	1.69249	−	1.69249i
$70$	4.16201e8	+	3.02619e9i	0.247635	+	1.80055i
$71$	−3.60526e8			−0.199823			−0.0999113	−	0.994996i	$-0.531856\pi$
$71$	−3.60526e8			−0.199823			−0.0999113	+	0.994996i	$0.531856\pi$
$72$	4.74995e8	−	1.20540e9i	0.245486	−	0.622972i
$73$			2.16123e9i			1.04252i	0.853397	+	0.521262i	$0.174539\pi$
$73$			2.16123e9i			1.04252i	−0.853397	+	0.521262i	$0.825461\pi$
$74$	2.98435e8	+	2.16991e9i	0.134490	+	0.977877i
$75$	1.09715e9	+	1.09715e9i	0.462338	+	0.462338i
$76$	−2.76414e8	−	1.55358e8i	−0.109016	−	0.0612726i
$77$	−3.93363e9	−	3.93363e9i	−1.45325	−	1.45325i
$78$	−2.26279e8	+	2.98446e8i	−0.0783738	+	0.103369i
$79$		−	3.90441e9i		−	1.26888i	−0.772973	−	0.634439i	$-0.781231\pi$
$79$		−	3.90441e9i		−	1.26888i	0.772973	−	0.634439i	$-0.218769\pi$
$80$	9.50777e8	−	3.90728e9i	0.290154	−	1.19241i
$81$	4.25819e9			1.22124
$82$	5.13768e9	+	3.89534e9i	1.38579	+	1.05069i
$83$	1.64861e9	−	1.64861e9i	0.418531	−	0.418531i	−0.466166	−	0.884697i	$-0.654365\pi$
$83$	1.64861e9	−	1.64861e9i	0.418531	−	0.418531i	0.884697	+	0.466166i	$0.154365\pi$
$84$	−6.97670e9	−	3.92125e9i	−1.66822	−	0.937622i
$85$	−3.97020e9	+	3.97020e9i	−0.894783	+	0.894783i
$86$	2.07439e9	−	2.85297e8i	0.440958	−	0.0606463i
$87$	−1.44188e9			−0.289290
$88$	2.91933e9	+	6.71630e9i	0.553184	+	1.27267i
$89$		−	4.00320e9i		−	0.716897i	−0.933549	−	0.358449i	$-0.883306\pi$
$89$		−	4.00320e9i		−	0.716897i	0.933549	−	0.358449i	$-0.116694\pi$
$90$	−4.80697e9	+	6.61117e8i	−0.814065	+	0.111961i
$91$	6.56082e8	+	6.56082e8i	0.105136	+	0.105136i
$92$	3.29590e9	+	1.17556e10i	0.500074	+	1.78363i
$93$	−3.80734e9	−	3.80734e9i	−0.547277	−	0.547277i
$94$	−9.70903e9	−	7.36129e9i	−1.32293	−	1.00303i
$95$			1.18751e9i			0.153468i
$96$	6.65238e9	+	8.16982e9i	0.815870	+	1.00197i
$97$	1.30440e9			0.151898			0.0759491	−	0.997112i	$-0.475801\pi$
$97$	1.30440e9			0.151898			0.0759491	+	0.997112i	$0.475801\pi$
$98$	−6.51743e9	+	8.59603e9i	−0.721018	+	0.950971i
$99$	6.24840e9	−	6.24840e9i	0.657041	−	0.657041i
$100$	−4.87234e9	+	1.36605e9i	−0.487234	+	0.136605i
$101$	6.72092e9	−	6.72092e9i	0.639472	−	0.639472i	−0.310953	−	0.950425i	$-0.600648\pi$
$101$	6.72092e9	−	6.72092e9i	0.639472	−	0.639472i	0.950425	+	0.310953i	$0.100648\pi$
$102$	−2.00429e9	−	1.45732e10i	−0.181535	−	1.31994i
$103$	−9.26277e9			−0.799014			−0.399507	−	0.916730i	$-0.630819\pi$
$103$	−9.26277e9			−0.799014			−0.399507	+	0.916730i	$0.630819\pi$
$104$	−4.86909e8	−	1.12020e9i	−0.0400204	−	0.0920721i
$105$			2.99728e10i			2.34845i
$106$	−9.48794e7	−	6.89866e8i	−0.00708994	−	0.0515508i
$107$	−7.28571e9	−	7.28571e9i	−0.519461	−	0.519461i	0.397947	−	0.917408i	$-0.369723\pi$
$107$	−7.28571e9	−	7.28571e9i	−0.519461	−	0.519461i	−0.917408	+	0.397947i	$0.869723\pi$
$108$	−3.07350e9	+	5.46839e9i	−0.209177	+	0.372169i
$109$	9.48438e9	+	9.48438e9i	0.616420	+	0.616420i	0.944611	−	0.328192i	$-0.106439\pi$
$109$	9.48438e9	+	9.48438e9i	0.616420	+	0.616420i	−0.328192	+	0.944611i	$0.606439\pi$
$110$	1.65704e10	−	2.18552e10i	1.02889	−	1.35703i
$111$			2.14918e10i			1.27544i
$112$	2.22962e10	−	1.35690e10i	1.26515	−	0.769939i
$113$	−3.03492e10			−1.64723			−0.823617	−	0.567147i	$-0.808047\pi$
$113$	−3.03492e10			−1.64723			−0.823617	+	0.567147i	$0.808047\pi$
$114$	−2.47921e9	−	1.87971e9i	−0.128762	−	0.0976264i
$115$	3.23315e10	−	3.23315e10i	1.60745	−	1.60745i
$116$	2.30399e9	−	4.09927e9i	0.109696	−	0.195171i
$117$	−1.04216e9	+	1.04216e9i	−0.0475340	+	0.0475340i
$118$	−1.59395e10	+	2.19221e9i	−0.696732	+	0.0958236i
$119$	−3.64427e10			−1.52713
$120$	1.44658e10	−	3.67100e10i	0.581347	−	1.47529i
$121$			2.40105e10i			0.925708i
$122$	2.76960e9	−	3.80912e8i	0.102475	−	0.0140937i
$123$	4.47336e10	+	4.47336e10i	1.58894	+	1.58894i
$124$	1.69081e10	−	4.74050e9i	0.576747	−	0.161702i
$125$	−1.30815e10	−	1.30815e10i	−0.428656	−	0.428656i
$126$	−2.50960e10	−	1.90275e10i	−0.790227	−	0.599142i
$127$		−	1.91705e10i		−	0.580249i	−0.956989	−	0.290125i	$-0.906303\pi$
$127$		−	1.91705e10i		−	0.580249i	0.956989	−	0.290125i	$-0.0936968\pi$
$128$	−3.38567e10	+	5.85812e9i	−0.985359	+	0.170494i
$129$	2.05457e10			0.575138
$130$	−2.76374e9	+	3.64518e9i	−0.0744356	+	0.0981753i
$131$	4.47215e10	−	4.47215e10i	1.15920	−	1.15920i	0.174558	−	0.984647i	$-0.444150\pi$
$131$	4.47215e10	−	4.47215e10i	1.15920	−	1.15920i	0.984647	−	0.174558i	$-0.0558496\pi$
$132$	1.93986e10	+	6.91893e10i	0.484061	+	1.72651i
$133$	−5.45012e9	+	5.45012e9i	−0.130963	+	0.130963i
$134$	−4.95382e9	−	3.60192e10i	−0.114661	−	0.833700i
$135$	2.34929e10			0.523923
$136$	4.46342e10	+	1.75884e10i	0.959342	+	0.378034i
$137$			6.73550e10i			1.39562i	0.716283	+	0.697810i	$0.245842\pi$
$137$			6.73550e10i			1.39562i	−0.716283	+	0.697810i	$0.754158\pi$
$138$	1.63220e10	+	1.18677e11i	0.326121	+	2.37122i
$139$	−4.41805e9	−	4.41805e9i	−0.0851444	−	0.0851444i	0.663252	−	0.748396i	$-0.269176\pi$
$139$	−4.41805e9	−	4.41805e9i	−0.0851444	−	0.0851444i	−0.748396	+	0.663252i	$0.769176\pi$
$140$	−8.52126e10	−	4.78937e10i	−1.58440	−	0.890508i
$141$	−8.45362e10	−	8.45362e10i	−1.51687	−	1.51687i
$142$	6.97019e9	−	9.19319e9i	0.120727	−	0.159230i
$143$		−	8.33071e9i		−	0.139316i
$144$	2.15537e10	+	3.54166e10i	0.348105	+	0.571997i
$145$	−1.76110e10			−0.274753
$146$	−5.51100e10	−	4.17839e10i	−0.830742	−	0.629861i
$147$	−7.48453e10	+	7.48453e10i	−1.09038	+	1.09038i
$148$	−6.11013e10	−	3.43419e10i	−0.860482	−	0.483633i
$149$	5.82764e9	−	5.82764e9i	0.0793526	−	0.0793526i	−0.666316	−	0.745669i	$-0.732130\pi$
$149$	5.82764e9	−	5.82764e9i	0.0793526	−	0.0793526i	0.745669	+	0.666316i	$0.232130\pi$
$150$	−4.91883e10	+	6.76502e9i	−0.647747	+	0.0890867i
$151$	−1.11118e11			−1.41547			−0.707735	−	0.706478i	$-0.750283\pi$
$151$	−1.11118e11			−1.41547			−0.707735	+	0.706478i	$0.750283\pi$
$152$	9.30557e9	−	4.04479e9i	0.114690	−	0.0498514i
$153$		−	5.78877e10i		−	0.690445i
$154$	1.76356e11	−	2.42547e10i	2.03604	−	0.280022i
$155$	−4.65025e10	−	4.65025e10i	−0.519777	−	0.519777i
$156$	−3.23545e9	−	1.15399e10i	−0.0350196	−	0.124905i
$157$	4.64779e10	+	4.64779e10i	0.487246	+	0.487246i	0.907436	−	0.420190i	$-0.138037\pi$
$157$	4.64779e10	+	4.64779e10i	0.487246	+	0.487246i	−0.420190	+	0.907436i	$0.638037\pi$
$158$	9.95601e10	+	7.54855e10i	1.01111	+	0.766617i
$159$		−	6.83275e9i		−	0.0672373i
$160$	8.12514e10	+	9.97852e10i	0.774874	+	0.951626i
$161$	2.96773e11			2.74344
$162$	−8.23254e10	+	1.08581e11i	−0.737834	+	0.973151i
$163$	−3.47669e8	+	3.47669e8i	−0.00302154	+	0.00302154i	−0.708616	−	0.705594i	$-0.750680\pi$
$163$	−3.47669e8	+	3.47669e8i	−0.00302154	+	0.00302154i	0.705594	+	0.708616i	$0.250680\pi$
$164$	−1.98658e11	+	5.56976e10i	−1.67450	+	0.469480i
$165$	1.90292e11	−	1.90292e11i	1.55597	−	1.55597i
$166$	1.01653e10	+	7.39118e10i	0.0806455	+	0.586372i
$167$	5.39356e10			0.415234			0.207617	−	0.978210i	$-0.433429\pi$
$167$	5.39356e10			0.415234			0.207617	+	0.978210i	$0.433429\pi$
$168$	2.34873e11	−	1.02091e11i	1.75504	−	0.762850i
$169$		−	1.36469e11i		−	0.989921i
$170$	−2.44802e10	−	1.77995e11i	−0.172413	−	1.25361i
$171$	−8.65728e9	−	8.65728e9i	−0.0592108	−	0.0592108i
$172$	−3.28301e10	+	5.84114e10i	−0.218087	+	0.388021i
$173$	−1.29518e11	−	1.29518e11i	−0.835795	−	0.835795i	0.152507	−	0.988302i	$-0.451265\pi$
$173$	−1.29518e11	−	1.29518e11i	−0.835795	−	0.835795i	−0.988302	+	0.152507i	$0.951265\pi$
$174$	2.78765e10	−	3.67671e10i	0.174780	−	0.230522i
$175$			1.23004e11i			0.749426i
$176$	−2.27702e11	−	5.54079e10i	−1.34835	−	0.328102i
$177$	−1.57872e11			−0.908741
$178$	1.02079e11	+	7.73954e10i	0.571264	+	0.433127i
$179$	−7.53414e10	+	7.53414e10i	−0.409985	+	0.409985i	−0.881733	−	0.471748i	$-0.843623\pi$
$179$	−7.53414e10	+	7.53414e10i	−0.409985	+	0.409985i	0.471748	+	0.881733i	$0.343623\pi$
$180$	7.60770e10	−	1.35357e11i	0.402616	−	0.716336i
$181$	−1.39253e11	+	1.39253e11i	−0.716822	+	0.716822i	−0.967953	−	0.251131i	$-0.919198\pi$
$181$	−1.39253e11	+	1.39253e11i	−0.716822	+	0.716822i	0.251131	+	0.967953i	$0.419198\pi$
$182$	−2.94140e10	+	4.04539e9i	−0.147298	+	0.0202583i
$183$	2.74314e10			0.133657
$184$	−3.63481e11	−	1.43232e11i	−1.72342	−	0.679125i
$185$			2.62499e11i			1.21135i
$186$	1.70694e11	−	2.34760e10i	0.766749	−	0.105453i
$187$	2.31369e11	+	2.31369e11i	1.01181	+	1.01181i
$188$	3.75417e11	−	1.05255e11i	1.59854	−	0.448183i
$189$	1.07821e11	+	1.07821e11i	0.447091	+	0.447091i
$190$	−3.02808e10	−	2.29586e10i	−0.122292	−	0.0927209i
$191$		−	7.62467e10i		−	0.299954i	−0.988690	−	0.149977i	$-0.952080\pi$
$191$		−	7.62467e10i		−	0.299954i	0.988690	−	0.149977i	$-0.0479199\pi$
$192$	−3.36939e11	+	1.16814e10i	−1.29135	+	0.0447701i
$193$	−3.32059e11			−1.24002			−0.620010	−	0.784594i	$-0.712871\pi$
$193$	−3.32059e11			−1.24002			−0.620010	+	0.784594i	$0.712871\pi$
$194$	−2.52185e10	+	3.32615e10i	−0.0917722	+	0.121041i
$195$	−3.17385e10	+	3.17385e10i	−0.112567	+	0.112567i
$196$	−9.31894e10	−	3.32381e11i	−0.322171	−	1.14909i
$197$	−1.14484e11	+	1.14484e11i	−0.385846	+	0.385846i	−0.873203	−	0.487357i	$-0.837961\pi$
$197$	−1.14484e11	+	1.14484e11i	−0.385846	+	0.385846i	0.487357	+	0.873203i	$0.337961\pi$
$198$	3.85276e10	+	2.80133e11i	0.126603	+	0.920531i
$199$	−1.76091e11			−0.564252			−0.282126	−	0.959377i	$-0.591040\pi$
$199$	−1.76091e11			−0.564252			−0.282126	+	0.959377i	$0.591040\pi$
$200$	5.93654e10	−	1.50652e11i	0.185517	−	0.470788i
$201$		−	3.56750e11i		−	1.08739i
$202$	4.14411e10	+	3.01317e11i	0.123218	+	0.895916i
$203$	−8.08262e10	−	8.08262e10i	−0.234462	−	0.234462i
$204$	4.10357e11	+	2.30641e11i	1.16148	+	0.652808i
$205$	5.46371e11	+	5.46371e11i	1.50910	+	1.50910i
$206$	1.79081e11	−	2.36195e11i	0.482740	−	0.636700i
$207$			4.71411e11i			1.24036i
$208$	3.79780e10	+	9.24137e9i	0.0975473	+	0.0237367i
$209$	6.92038e10			0.173540
$210$	−7.64288e11	−	5.79476e11i	−1.87137	−	1.41886i
$211$	−2.19478e11	+	2.19478e11i	−0.524782	+	0.524782i	−0.919012	−	0.394230i	$-0.871011\pi$
$211$	−2.19478e11	+	2.19478e11i	−0.524782	+	0.524782i	0.394230	+	0.919012i	$0.371011\pi$
$212$	1.94255e10	+	1.09181e10i	0.0453621	+	0.0254957i
$213$	8.00448e10	−	8.00448e10i	0.182572	−	0.182572i
$214$	3.26639e11	−	4.49236e10i	0.727778	−	0.100094i
$215$	2.50943e11			0.546238
$216$	−8.00193e10	−	1.84095e11i	−0.170187	−	0.391538i
$217$		−	4.26849e11i		−	0.887107i
$218$	−4.25211e11	+	5.84806e10i	−0.863619	+	0.118776i
$219$	−4.79841e11	−	4.79841e11i	−0.952526	−	0.952526i
$220$	2.36932e11	+	8.45070e11i	0.459737	+	1.63976i
$221$	−3.85896e10	−	3.85896e10i	−0.0731996	−	0.0731996i
$222$	−5.48029e11	−	4.15511e11i	−1.01634	−	0.770579i
$223$		−	7.21804e11i		−	1.30887i	−0.756120	−	0.654433i	$-0.772907\pi$
$223$		−	7.21804e11i		−	1.30887i	0.756120	−	0.654433i	$-0.227093\pi$
$224$	−8.50614e10	+	8.30874e11i	−0.150832	+	1.47331i
$225$	−1.95386e11			−0.338830
$226$	5.86754e11	−	7.73887e11i	0.995207	−	1.31261i
$227$	7.13411e11	−	7.13411e11i	1.18361	−	1.18361i	0.204814	−	0.978801i	$-0.434341\pi$
$227$	7.13411e11	−	7.13411e11i	1.18361	−	1.18361i	0.978801	−	0.204814i	$-0.0656590\pi$
$228$	9.58631e10	−	2.68771e10i	0.155588	−	0.0436222i
$229$	−3.01998e11	+	3.01998e11i	−0.479542	+	0.479542i	−0.904985	−	0.425443i	$-0.860118\pi$
$229$	−3.01998e11	+	3.01998e11i	−0.479542	+	0.479542i	0.425443	+	0.904985i	$0.360118\pi$
$230$	1.99356e11	+	1.44951e12i	0.309734	+	2.25207i
$231$	1.74671e12			2.65558
$232$	5.99848e10	+	1.38003e11i	0.0892486	+	0.205328i
$233$		−	7.09616e11i		−	1.03334i	−0.856184	−	0.516670i	$-0.827171\pi$
$233$		−	7.09616e11i		−	1.03334i	0.856184	−	0.516670i	$-0.172829\pi$
$234$	−6.42594e9	−	4.67229e10i	−0.00915919	−	0.0665963i
$235$	−1.03251e12	−	1.03251e12i	−1.44065	−	1.44065i
$236$	2.52265e11	−	4.48831e11i	0.344586	−	0.613088i
$237$	8.66867e11	+	8.66867e11i	1.15934	+	1.15934i
$238$	7.04563e11	−	9.29268e11i	0.922645	−	1.21690i
$239$		−	1.21693e11i		−	0.156054i	−0.996951	−	0.0780271i	$-0.975138\pi$
$239$		−	1.21693e11i		−	0.156054i	0.996951	−	0.0780271i	$-0.0248621\pi$
$240$	6.56409e11	+	1.07860e12i	0.824363	+	1.35457i
$241$	−4.41909e11			−0.543560			−0.271780	−	0.962359i	$-0.587612\pi$
$241$	−4.41909e11			−0.543560			−0.271780	+	0.962359i	$0.587612\pi$
$242$	−6.12253e11	−	4.64205e11i	−0.737656	−	0.559284i
$243$	−6.89633e11	+	6.89633e11i	−0.813929	+	0.813929i
$244$	−4.38328e10	+	7.79875e10i	−0.0506816	+	0.0901729i
$245$	−9.14152e11	+	9.14152e11i	−1.03559	+	1.03559i
$246$	−2.00553e12	+	2.75827e11i	−2.22615	+	0.306169i
$247$	−1.15424e10			−0.0125548
$248$	−2.06010e11	+	5.22795e11i	−0.219599	+	0.557280i
$249$			7.32057e11i			0.764800i
$250$	5.86482e11	−	8.06606e10i	0.600557	−	0.0825964i
$251$	1.15313e12	+	1.15313e12i	1.15747	+	1.15747i	0.985017	+	0.172455i	$0.0551699\pi$
$251$	1.15313e12	+	1.15313e12i	1.15747	+	1.15747i	0.172455	+	0.985017i	$0.444830\pi$
$252$	9.70382e11	−	2.72065e11i	0.954861	−	0.267714i
$253$	−1.88416e12	−	1.88416e12i	−1.81767	−	1.81767i
$254$	4.88836e11	+	3.70631e11i	0.462375	+	0.350569i
$255$		−	1.76295e12i		−	1.63508i
$256$	5.05186e11	−	9.76582e11i	0.459464	−	0.888196i
$257$	7.72934e11			0.689409			0.344704	−	0.938711i	$-0.387979\pi$
$257$	7.72934e11			0.689409			0.344704	+	0.938711i	$0.387979\pi$
$258$	−3.97218e11	+	5.23903e11i	−0.347481	+	0.458303i
$259$	−1.20475e12	+	1.20475e12i	−1.03371	+	1.03371i
$260$	−3.95174e10	−	1.40948e11i	−0.0332599	−	0.118629i
$261$	1.28389e11	−	1.28389e11i	0.106005	−	0.106005i
$262$	2.75753e11	+	2.00499e12i	0.223364	+	1.62408i
$263$	−7.99439e10			−0.0635341			−0.0317670	−	0.999495i	$-0.510113\pi$
$263$	−7.99439e10			−0.0635341			−0.0317670	+	0.999495i	$0.510113\pi$
$264$	−2.13933e12	−	8.43013e11i	−1.66824	−	0.657377i
$265$		−	8.34544e10i		−	0.0638587i
$266$	−3.36054e10	−	2.44344e11i	−0.0252348	−	0.183482i
$267$	8.88800e11	+	8.88800e11i	0.655009	+	0.655009i
$268$	1.01424e12	+	5.70054e11i	0.733613	+	0.412327i
$269$	1.13803e12	+	1.13803e12i	0.807963	+	0.807963i	0.984325	−	0.176362i	$-0.0564331\pi$
$269$	1.13803e12	+	1.13803e12i	0.807963	+	0.807963i	−0.176362	+	0.984325i	$0.556433\pi$
$270$	−4.54197e11	+	5.99054e11i	−0.316538	+	0.417491i
$271$		−	1.56451e12i		−	1.07036i	−0.844737	−	0.535182i	$-0.820243\pi$
$271$		−	1.56451e12i		−	1.07036i	0.844737	−	0.535182i	$-0.179757\pi$
$272$	−1.31142e12	+	7.98103e11i	−0.880843	+	0.536061i
$273$	−2.91330e11			−0.192120
$274$	−1.71751e12	−	1.30220e12i	−1.11211	−	0.843190i
$275$	7.80931e11	−	7.80931e11i	0.496534	−	0.496534i
$276$	−3.34176e12	−	1.87823e12i	−2.08656	−	1.17275i
$277$	−4.60406e11	+	4.60406e11i	−0.282320	+	0.282320i	−0.834034	−	0.551714i	$-0.813974\pi$
$277$	−4.60406e11	+	4.60406e11i	−0.282320	+	0.282320i	0.551714	+	0.834034i	$0.313974\pi$
$278$	1.98073e11	−	2.72416e10i	0.119290	−	0.0164062i
$279$	6.78032e11			0.401078
$280$	2.86871e12	−	1.24692e12i	1.66685	−	0.724518i
$281$			1.27548e12i			0.728018i	0.931396	+	0.364009i	$0.118592\pi$
$281$			1.27548e12i			0.728018i	−0.931396	+	0.364009i	$0.881408\pi$
$282$	3.78999e12	−	5.21249e11i	2.12517	−	0.292281i
$283$	−7.52464e11	−	7.52464e11i	−0.414528	−	0.414528i	0.468785	−	0.883312i	$-0.344692\pi$
$283$	−7.52464e11	−	7.52464e11i	−0.414528	−	0.414528i	−0.883312	+	0.468785i	$0.844692\pi$
$284$	9.96633e10	+	3.55471e11i	0.0539440	+	0.192404i
$285$	−2.63654e11	−	2.63654e11i	−0.140220	−	0.140220i
$286$	2.12428e11	+	1.61061e11i	0.111015	+	0.0841706i
$287$			5.01518e12i			2.57559i
$288$	−1.31981e12	−	1.35116e11i	−0.666114	−	0.0681939i
$289$	1.27505e11			0.0632466
$290$	3.40480e11	−	4.49069e11i	0.165997	−	0.218939i
$291$	−2.89607e11	+	2.89607e11i	−0.138785	+	0.138785i
$292$	2.13093e12	−	5.97447e11i	1.00382	−	0.281440i
$293$	2.17682e12	−	2.17682e12i	1.00806	−	1.00806i	0.00808970	−	0.999967i	$-0.497425\pi$
$293$	2.17682e12	−	2.17682e12i	1.00806	−	1.00806i	0.999967	−	0.00808970i	$-0.00257506\pi$
$294$	−4.61496e11	−	3.35553e12i	−0.210102	−	1.52765i
$295$	−1.92824e12			−0.863078
$296$	2.05699e12	−	8.94100e11i	0.905263	−	0.393484i
$297$		−	1.36908e12i		−	0.592444i
$298$	3.59332e10	+	2.61269e11i	0.0152902	+	0.111175i
$299$	3.14256e11	+	3.14256e11i	0.131501	+	0.131501i
$300$	7.78474e11	−	1.38506e12i	0.320360	−	0.569985i
$301$	1.15171e12	+	1.15171e12i	0.466134	+	0.466134i
$302$	2.14829e12	−	2.83345e12i	0.855183	−	1.12793i
$303$			2.98439e12i			1.16854i
$304$	−7.67687e10	+	3.15486e11i	−0.0295676	+	0.121510i
$305$	3.35044e11			0.126941
$306$	1.47610e12	+	1.11917e12i	0.550186	+	0.417146i
$307$	−3.88734e11	+	3.88734e11i	−0.142548	+	0.142548i	−0.774779	−	0.632232i	$-0.782139\pi$
$307$	−3.88734e11	+	3.88734e11i	−0.142548	+	0.142548i	0.632232	+	0.774779i	$0.282139\pi$
$308$	−2.79107e12	+	4.96589e12i	−1.00697	+	1.79161i
$309$	2.05654e12	−	2.05654e12i	0.730038	−	0.730038i
$310$	2.08484e12	−	2.86734e11i	0.728221	−	0.100154i
$311$	−3.01819e12			−1.03740			−0.518699	−	0.854957i	$-0.673583\pi$
$311$	−3.01819e12			−1.03740			−0.518699	+	0.854957i	$0.673583\pi$
$312$	3.56814e11	+	1.40605e11i	0.120689	+	0.0475583i
$313$			1.08558e12i			0.361360i	0.983542	+	0.180680i	$0.0578298\pi$
$313$			1.08558e12i			0.361360i	−0.983542	+	0.180680i	$0.942170\pi$
$314$	−2.08373e12	+	2.86582e11i	−0.682643	+	0.0938860i
$315$	−2.66886e12	−	2.66886e12i	−0.860542	−	0.860542i
$316$	−3.84967e12	+	1.07933e12i	−1.22177	+	0.342546i
$317$	−3.36479e11	−	3.36479e11i	−0.105114	−	0.105114i	0.652594	−	0.757708i	$-0.273681\pi$
$317$	−3.36479e11	−	3.36479e11i	−0.105114	−	0.105114i	−0.757708	+	0.652594i	$0.773681\pi$
$318$	1.74231e11	+	1.32100e11i	0.0535784	+	0.0406227i
$319$			1.02630e12i			0.310687i
$320$	−4.11533e12	+	1.42675e11i	−1.22646	+	0.0425204i
$321$	3.23518e12			0.949235
$322$	−5.73763e12	+	7.56753e12i	−1.65750	+	2.18613i
$323$	3.20566e11	−	3.20566e11i	0.0911812	−	0.0911812i
$324$	−1.17713e12	−	4.19849e12i	−0.329685	−	1.17589i
$325$	−1.30250e11	+	1.30250e11i	−0.0359220	+	0.0359220i
$326$	−2.14372e9	−	1.55870e10i	−0.000582211	−	0.00423325i
$327$	−4.21149e12			−1.12641
$328$	2.42048e12	−	6.14248e12i	0.637576	−	1.61798i
$329$		−	9.47753e12i		−	2.45876i
$330$	1.17334e12	+	8.53134e12i	0.299816	+	2.17995i
$331$	2.82809e12	+	2.82809e12i	0.711792	+	0.711792i	0.966910	−	0.255118i	$-0.0821142\pi$
$331$	2.82809e12	+	2.82809e12i	0.711792	+	0.711792i	−0.255118	+	0.966910i	$0.582114\pi$
$332$	−2.08124e12	−	1.16976e12i	−0.515978	−	0.290005i
$333$	−1.91369e12	−	1.91369e12i	−0.467359	−	0.467359i
$334$	−1.04276e12	+	1.37533e12i	−0.250872	+	0.330882i
$335$		−	4.35731e12i		−	1.03275i
$336$	−1.93765e12	+	7.96287e12i	−0.452458	+	1.85940i
$337$	−3.28584e12			−0.755958			−0.377979	−	0.925814i	$-0.623381\pi$
$337$	−3.28584e12			−0.755958			−0.377979	+	0.925814i	$0.623381\pi$
$338$	3.47988e12	+	2.63841e12i	0.788825	+	0.598080i
$339$	6.73821e12	−	6.73821e12i	1.50503	−	1.50503i
$340$	5.01206e12	+	2.81702e12i	1.10312	+	0.620006i
$341$	−2.71000e12	+	2.71000e12i	−0.587756	+	0.587756i
$342$	3.88130e11	−	5.33807e10i	0.0829558	−	0.0114092i
$343$	−1.35986e12			−0.286434
$344$	−8.54738e11	−	1.96644e12i	−0.177436	−	0.408214i
$345$			1.43566e13i			2.93736i
$346$	5.80666e12	−	7.98607e11i	1.17097	−	0.161047i
$347$	5.96113e12	+	5.96113e12i	1.18490	+	1.18490i	0.978459	+	0.206440i	$0.0661878\pi$
$347$	5.96113e12	+	5.96113e12i	1.18490	+	1.18490i	0.206440	+	0.978459i	$0.433812\pi$
$348$	3.98592e11	+	1.42167e12i	0.0780966	+	0.278549i
$349$	−4.73057e12	−	4.73057e12i	−0.913663	−	0.913663i	0.0828953	−	0.996558i	$-0.473583\pi$
$349$	−4.73057e12	−	4.73057e12i	−0.913663	−	0.913663i	−0.996558	+	0.0828953i	$0.973583\pi$
$350$	−3.13652e12	−	2.37808e12i	−0.597184	−	0.452780i
$351$			2.28346e11i			0.0428606i
$352$	5.81513e12	−	4.73504e12i	1.07608	−	0.876215i
$353$	1.06162e12			0.193684			0.0968422	−	0.995300i	$-0.469126\pi$
$353$	1.06162e12			0.193684			0.0968422	+	0.995300i	$0.469126\pi$
$354$	3.05221e12	−	4.02565e12i	0.549033	−	0.724136i
$355$	9.77658e11	−	9.77658e11i	0.173398	−	0.173398i
$356$	−3.94707e12	+	1.10664e12i	−0.690280	+	0.193533i
$357$	8.09111e12	−	8.09111e12i	1.39530	−	1.39530i
$358$	−4.64554e11	−	3.37776e12i	−0.0789989	−	0.574400i
$359$	1.84902e12			0.310076			0.155038	−	0.987909i	$-0.450450\pi$
$359$	1.84902e12			0.310076			0.155038	+	0.987909i	$0.450450\pi$
$360$	1.98068e12	+	4.55682e12i	0.327569	+	0.753615i
$361$			6.03518e12i			0.984361i
$362$	−8.58633e11	−	6.24310e12i	−0.138123	−	1.00429i
$363$	−5.33087e12	−	5.33087e12i	−0.845794	−	0.845794i
$364$	4.65518e11	−	8.28250e11i	0.0728499	−	0.129615i
$365$	−5.86072e12	−	5.86072e12i	−0.904663	−	0.904663i
$366$	−5.30343e11	+	6.99485e11i	−0.0807516	+	0.106506i
$367$			9.17814e11i			0.137856i	0.997622	+	0.0689278i	$0.0219578\pi$
$367$			9.17814e11i			0.137856i	−0.997622	+	0.0689278i	$0.978042\pi$
$368$	1.06796e13	−	6.49938e12i	1.58240	−	0.963015i
$369$	−7.96640e12			−1.16448
$370$	−6.69356e12	−	5.07500e12i	−0.965270	−	0.731859i
$371$	3.83017e11	−	3.83017e11i	0.0544940	−	0.0544940i
$372$	−2.70147e12	+	4.80646e12i	−0.379215	+	0.674700i
$373$	−4.07473e12	+	4.07473e12i	−0.564358	+	0.564358i	−0.930542	−	0.366184i	$-0.880664\pi$
$373$	−4.07473e12	+	4.07473e12i	−0.564358	+	0.564358i	0.366184	+	0.930542i	$0.380664\pi$
$374$	−1.03729e13	+	1.42662e12i	−1.41757	+	0.194962i
$375$	5.80879e12			0.783302
$376$	−4.57414e12	+	1.16079e13i	−0.608654	+	1.54459i
$377$		−	1.71175e11i		−	0.0224768i
$378$	−4.83394e12	+	6.64826e11i	−0.626386	+	0.0861488i
$379$	8.26161e11	+	8.26161e11i	0.105650	+	0.105650i	0.757956	−	0.652306i	$-0.226198\pi$
$379$	8.26161e11	+	8.26161e11i	0.105650	+	0.105650i	−0.652306	+	0.757956i	$0.726198\pi$
$380$	1.17086e12	−	3.28274e11i	0.147770	−	0.0414303i
$381$	4.25628e12	+	4.25628e12i	0.530158	+	0.530158i
$382$	1.94424e12	+	1.47411e12i	0.239020	+	0.181223i
$383$		−	7.98487e12i		−	0.968889i	−0.874822	−	0.484445i	$-0.839022\pi$
$383$		−	7.98487e12i		−	0.968889i	0.874822	−	0.484445i	$-0.160978\pi$
$384$	6.21631e12	−	8.81758e12i	0.744520	−	1.05607i
$385$	2.13341e13			2.52215
$386$	6.41983e12	−	8.46730e12i	0.749181	−	0.988117i
$387$	−1.82944e12	+	1.82944e12i	−0.210748	+	0.210748i
$388$	−3.60587e11	−	1.28611e12i	−0.0410064	−	0.146259i
$389$	−8.79978e11	+	8.79978e11i	−0.0987924	+	0.0987924i	−0.754776	−	0.655983i	$-0.772254\pi$
$389$	−8.79978e11	+	8.79978e11i	−0.0987924	+	0.0987924i	0.655983	+	0.754776i	$0.272254\pi$
$390$	−1.95699e11	−	1.42292e12i	−0.0216903	−	0.157710i
$391$	−1.74557e13			−1.91009
$392$	1.02772e13	+	4.04978e12i	1.11031	+	0.437524i
$393$			1.98584e13i			2.11827i
$394$	−7.05907e11	−	5.13264e12i	−0.0743475	−	0.540579i
$395$	1.05878e13	+	1.05878e13i	1.10108	+	1.10108i
$396$	−7.88810e12	−	4.43350e12i	−0.810021	−	0.455272i
$397$	8.00441e12	+	8.00441e12i	0.811665	+	0.811665i	0.984883	−	0.173218i	$-0.0554166\pi$
$397$	8.00441e12	+	8.00441e12i	0.811665	+	0.811665i	−0.173218	+	0.984883i	$0.555417\pi$
$398$	3.40445e12	−	4.49023e12i	0.340903	−	0.449627i
$399$		−	2.42010e12i		−	0.239314i
$400$	2.69381e12	+	4.42640e12i	0.263067	+	0.432266i
$401$	−1.19870e13			−1.15608			−0.578041	−	0.816008i	$-0.696183\pi$
$401$	−1.19870e13			−1.15608			−0.578041	+	0.816008i	$0.696183\pi$
$402$	9.09692e12	+	6.89720e12i	0.866491	+	0.656966i
$403$	4.51995e11	−	4.51995e11i	0.0425215	−	0.0425215i
$404$	−8.48461e12	−	4.76877e12i	−0.788361	−	0.443098i
$405$	−1.15472e13	+	1.15472e13i	−1.05974	+	1.05974i
$406$	3.62366e12	−	4.98373e11i	0.328487	−	0.0451778i
$407$	1.52975e13			1.36977
$408$	−1.38148e13	+	6.00479e12i	−1.22192	+	0.531125i
$409$		−	1.57002e13i		−	1.37179i	−0.727699	−	0.685897i	$-0.759410\pi$
$409$		−	1.57002e13i		−	1.37179i	0.727699	−	0.685897i	$-0.240590\pi$
$410$	−2.44954e13	+	3.36892e12i	−2.11429	+	0.290785i
$411$	−1.49543e13	−	1.49543e13i	−1.27514	−	1.27514i
$412$	2.56059e12	+	9.13291e12i	0.215702	+	0.769348i
$413$	−8.84971e12	−	8.84971e12i	−0.736510	−	0.736510i
$414$	−1.20207e13	−	9.11398e12i	−0.988389	−	0.749388i
$415$			8.94126e12i			0.726370i
$416$	−9.69893e11	+	7.89749e11i	−0.0778498	+	0.0633902i
$417$	1.96181e12			0.155588
$418$	−1.33795e12	+	1.76466e12i	−0.104847	+	0.138286i
$419$	−1.20675e13	+	1.20675e13i	−0.934432	+	0.934432i	−0.997979	−	0.0635472i	$-0.979759\pi$
$419$	−1.20675e13	+	1.20675e13i	−0.934432	+	0.934432i	0.0635472	+	0.997979i	$0.479759\pi$
$420$	2.95526e13	−	8.28564e12i	2.26125	−	0.633986i
$421$	−6.31654e12	+	6.31654e12i	−0.477605	+	0.477605i	−0.904365	−	0.426760i	$-0.859655\pi$
$421$	−6.31654e12	+	6.31654e12i	−0.477605	+	0.477605i	0.426760	+	0.904365i	$0.359655\pi$
$422$	−1.35330e12	−	9.83983e12i	−0.101119	−	0.735233i
$423$	1.50546e13			1.11165
$424$	−6.53966e11	+	2.84255e11i	−0.0477228	+	0.0207433i
$425$		−	7.23487e12i		−	0.521779i
$426$	4.93556e11	+	3.58863e12i	0.0351794	+	0.255789i
$427$	1.53770e12	+	1.53770e12i	0.108326	+	0.108326i
$428$	−5.16952e12	+	9.19762e12i	−0.359941	+	0.640408i
$429$	1.84961e12	+	1.84961e12i	0.127290	+	0.127290i
$430$	−4.85158e12	+	6.39889e12i	−0.330020	+	0.435274i
$431$		−	3.93371e12i		−	0.264494i	−0.991217	−	0.132247i	$-0.957781\pi$
$431$		−	3.93371e12i		−	0.264494i	0.991217	−	0.132247i	$-0.0422193\pi$
$432$	6.24136e12	+	1.51874e12i	0.414821	+	0.100940i
$433$	−5.09935e12			−0.335024			−0.167512	−	0.985870i	$-0.553573\pi$
$433$	−5.09935e12			−0.335024			−0.167512	+	0.985870i	$0.553573\pi$
$434$	1.08844e13	+	8.25245e12i	0.706897	+	0.535963i
$435$	3.91003e12	−	3.91003e12i	0.251035	−	0.251035i
$436$	6.72956e12	−	1.19733e13i	0.427125	−	0.759941i
$437$	−2.61055e12	+	2.61055e12i	−0.163804	+	0.163804i
$438$	2.15126e13	−	2.95870e12i	1.33451	−	0.183540i
$439$	5.35603e12			0.328489			0.164244	−	0.986420i	$-0.447481\pi$
$439$	5.35603e12			0.328489			0.164244	+	0.986420i	$0.447481\pi$
$440$	−2.61295e13	−	1.02965e13i	−1.58441	−	0.624345i
$441$		−	1.33289e13i		−	0.799098i
$442$	1.73008e12	−	2.37943e11i	0.102554	−	0.0141046i
$443$	−1.36681e12	−	1.36681e12i	−0.0801104	−	0.0801104i	0.665916	−	0.746027i	$-0.268041\pi$
$443$	−1.36681e12	−	1.36681e12i	−0.0801104	−	0.0801104i	−0.746027	+	0.665916i	$0.768041\pi$
$444$	2.11905e13	−	5.94118e12i	1.22808	−	0.344316i
$445$	1.08557e13	+	1.08557e13i	0.622096	+	0.622096i
$446$	1.84056e13	+	1.39549e13i	1.04298	+	0.790776i
$447$			2.58773e12i			0.145005i
$448$	−1.95423e13	−	1.82326e13i	−1.08289	−	1.01032i
$449$	−2.98013e13			−1.63306			−0.816532	−	0.577299i	$-0.804107\pi$
$449$	−2.98013e13			−1.63306			−0.816532	+	0.577299i	$0.804107\pi$
$450$	3.77748e12	−	4.98223e12i	0.204710	−	0.269999i
$451$	3.18406e13	−	3.18406e13i	1.70647	−	1.70647i
$452$	8.38970e12	+	2.99237e13i	0.444687	+	1.58607i
$453$	2.46707e13	−	2.46707e13i	1.29328	−	1.29328i
$454$	4.39889e12	+	3.19842e13i	0.228067	+	1.65827i
$455$	−3.55827e12			−0.182466
$456$	−1.16801e12	+	2.96408e12i	−0.0592411	+	0.150337i
$457$		−	3.59648e13i		−	1.80425i	−0.431477	−	0.902124i	$-0.642007\pi$
$457$		−	3.59648e13i		−	1.80425i	0.431477	−	0.902124i	$-0.357993\pi$
$458$	−1.86212e12	−	1.35394e13i	−0.0924016	−	0.671850i
$459$	−6.34187e12	−	6.34187e12i	−0.311282	−	0.311282i
$460$	−4.08159e13	−	2.29405e13i	−1.98171	−	1.11382i
$461$	2.06059e13	+	2.06059e13i	0.989661	+	0.989661i	0.999947	−	0.0102857i	$-0.00327409\pi$
$461$	2.06059e13	+	2.06059e13i	0.989661	+	0.989661i	−0.0102857	+	0.999947i	$0.503274\pi$
$462$	−3.37698e13	+	4.45400e13i	−1.60442	+	2.11612i
$463$			1.96699e12i			0.0924482i	0.998931	+	0.0462241i	$0.0147188\pi$
$463$			1.96699e12i			0.0924482i	−0.998931	+	0.0462241i	$0.985281\pi$
$464$	−4.67871e12	−	1.13849e12i	−0.217538	−	0.0529347i
$465$	2.06492e13			0.949813
$466$	1.80948e13	+	1.37193e13i	0.823424	+	0.624312i
$467$	−1.26406e13	+	1.26406e13i	−0.569093	+	0.569093i	−0.931874	−	0.362781i	$-0.881827\pi$
$467$	−1.26406e13	+	1.26406e13i	−0.569093	+	0.569093i	0.362781	+	0.931874i	$0.381827\pi$
$468$	1.31564e12	+	7.39455e11i	0.0586014	+	0.0329369i
$469$	1.99980e13	−	1.99980e13i	0.881298	−	0.881298i
$470$	4.62905e13	−	6.36648e12i	2.01838	−	0.277594i
$471$	−2.06383e13			−0.890366
$472$	6.56778e12	+	1.51101e13i	0.280355	+	0.644995i
$473$		−	1.46240e13i		−	0.617678i
$474$	−3.88641e13	+	5.34509e12i	−1.62426	+	0.223390i
$475$	−1.08200e12	−	1.08200e12i	−0.0447464	−	0.0447464i
$476$	1.00742e13	+	3.59318e13i	0.412264	+	1.47043i
$477$	6.08406e11	+	6.08406e11i	0.0246378	+	0.0246378i
$478$	3.10309e12	+	2.35274e12i	0.124353	+	0.0942831i
$479$			3.39675e12i			0.134706i	0.997729	+	0.0673529i	$0.0214554\pi$
$479$			3.39675e12i			0.134706i	−0.997729	+	0.0673529i	$0.978545\pi$
$480$	−4.01942e13	−	4.11491e12i	−1.57746	−	0.161493i
$481$	−2.55144e12			−0.0990969
$482$	8.54360e12	−	1.12684e13i	0.328402	−	0.433139i
$483$	−6.58903e13	+	6.58903e13i	−2.50660	+	2.50660i
$484$	2.36739e13	−	6.63743e12i	0.891338	−	0.249904i
$485$	−3.53722e12	+	3.53722e12i	−0.131812	+	0.131812i
$486$	−4.25227e12	−	3.09182e13i	−0.156834	−	1.14034i
$487$	−4.56052e12			−0.166483			−0.0832414	−	0.996529i	$-0.526527\pi$
$487$	−4.56052e12			−0.166483			−0.0832414	+	0.996529i	$0.526527\pi$
$488$	−1.14120e12	−	2.62547e12i	−0.0412346	−	0.0948656i
$489$		−	1.54381e11i		−	0.00552139i
$490$	−5.63665e12	−	4.09840e13i	−0.199545	−	1.45089i
$491$	−2.04666e13	−	2.04666e13i	−0.717195	−	0.717195i	0.250835	−	0.968030i	$-0.419295\pi$
$491$	−2.04666e13	−	2.04666e13i	−0.717195	−	0.717195i	−0.968030	+	0.250835i	$0.919295\pi$
$492$	3.17404e13	−	5.64726e13i	1.10100	−	1.95890i
$493$	4.75405e12	+	4.75405e12i	0.163241	+	0.163241i
$494$	2.23153e11	−	2.94323e11i	0.00758523	−	0.0100044i
$495$			3.38883e13i			1.14031i
$496$	−9.34808e12	−	1.53606e13i	−0.311397	−	0.511680i
$497$	8.97400e12			0.295940
$498$	−1.86670e13	−	1.41532e13i	−0.609436	−	0.462069i
$499$	−3.04333e13	+	3.04333e13i	−0.983662	+	0.983662i	−0.999869	−	0.0162066i	$-0.994841\pi$
$499$	−3.04333e13	+	3.04333e13i	−0.983662	+	0.983662i	0.0162066	+	0.999869i	$0.494841\pi$
$500$	−9.28189e12	+	1.65144e13i	−0.297021	+	0.528460i
$501$	−1.19749e13	+	1.19749e13i	−0.379388	+	0.379388i
$502$	−5.16982e13	+	7.11020e12i	−1.62165	+	0.223030i
$503$	1.82825e13			0.567800			0.283900	−	0.958854i	$-0.408372\pi$
$503$	1.82825e13			0.567800			0.283900	+	0.958854i	$0.408372\pi$
$504$	−1.18233e13	+	3.00041e13i	−0.363568	+	0.922631i
$505$			3.64510e13i			1.10982i
$506$	8.44723e13	−	1.16177e13i	2.54661	−	0.350243i
$507$	3.02992e13	+	3.02992e13i	0.904464	+	0.904464i
$508$	−1.89017e13	+	5.29947e12i	−0.558706	+	0.156644i
$509$	−4.24054e12	−	4.24054e12i	−0.124117	−	0.124117i	0.642320	−	0.766437i	$-0.277972\pi$
$509$	−4.24054e12	−	4.24054e12i	−0.124117	−	0.124117i	−0.766437	+	0.642320i	$0.777972\pi$
$510$	4.49541e13	+	3.40838e13i	1.30292	+	0.987863i
$511$		−	5.37960e13i		−	1.54399i
$512$	1.51353e13	+	3.17626e13i	0.430171	+	0.902748i
$513$	−1.89689e12			−0.0533894
$514$	−1.49434e13	+	1.97093e13i	−0.416519	+	0.549360i
$515$	2.51184e13	−	2.51184e13i	0.693354	−	0.693354i
$516$	−5.67962e12	−	2.02577e13i	−0.155264	−	0.553784i
$517$	−6.01713e13	+	6.01713e13i	−1.62906	+	1.62906i
$518$	−7.42847e12	−	5.40122e13i	−0.199182	−	1.44825i
$519$	5.75118e13			1.52729
$520$	4.35808e12	+	1.71733e12i	0.114625	+	0.0451686i
$521$		−	3.61842e13i		−	0.942606i	−0.881971	−	0.471303i	$-0.843784\pi$
$521$		−	3.61842e13i		−	0.942606i	0.881971	−	0.471303i	$-0.156216\pi$
$522$	7.91645e11	+	5.75603e12i	0.0204257	+	0.148515i
$523$	−1.99599e13	−	1.99599e13i	−0.510094	−	0.510094i	0.404461	−	0.914555i	$-0.367459\pi$
$523$	−1.99599e13	−	1.99599e13i	−0.510094	−	0.510094i	−0.914555	+	0.404461i	$0.867459\pi$
$524$	−5.64573e13	−	3.17318e13i	−1.42910	−	0.803227i
$525$	−2.73096e13	−	2.73096e13i	−0.684730	−	0.684730i
$526$	1.54559e12	−	2.03852e12i	0.0383853	−	0.0506275i
$527$			2.51065e13i			0.617638i
$528$	6.28568e13	−	3.82532e13i	1.53173	−	0.932176i
$529$	1.00724e14			2.43140
$530$	2.12804e12	+	1.61346e12i	0.0508862	+	0.0385814i
$531$	1.40574e13	−	1.40574e13i	0.332991	−	0.332991i
$532$	6.88034e12	+	3.86709e12i	0.161455	+	0.0907457i
$533$	−5.31063e12	+	5.31063e12i	−0.123455	+	0.123455i
$534$	−3.98474e13	+	5.48033e12i	−0.917685	+	0.126212i
$535$	3.95142e13			0.901537
$536$	−3.41448e13	+	1.48415e13i	−0.771792	+	0.335469i
$537$		−	3.34549e13i		−	0.749185i
$538$	−5.10210e13	+	7.01707e12i	−1.13198	+	0.155684i
$539$	5.32735e13	+	5.32735e13i	1.17103	+	1.17103i
$540$	−6.49434e12	−	2.31635e13i	−0.141438	−	0.504471i
$541$	3.38200e13	+	3.38200e13i	0.729773	+	0.729773i	0.970574	−	0.240802i	$-0.0774103\pi$
$541$	3.38200e13	+	3.38200e13i	0.729773	+	0.729773i	−0.240802	+	0.970574i	$0.577410\pi$
$542$	3.98941e13	+	3.02473e13i	0.852927	+	0.646681i
$543$		−	6.18346e13i		−	1.30988i
$544$	5.00316e12	−	4.88706e13i	0.105015	−	1.02578i
$545$	−5.14386e13			−1.06981
$546$	5.63240e12	−	7.42873e12i	0.116073	−	0.153092i
$547$	−7.91553e12	+	7.91553e12i	−0.161638	+	0.161638i	−0.783292	−	0.621654i	$-0.786461\pi$
$547$	−7.91553e12	+	7.91553e12i	−0.161638	+	0.161638i	0.621654	+	0.783292i	$0.286461\pi$
$548$	6.64107e13	−	1.86195e13i	1.34380	−	0.376761i
$549$	−2.44257e12	+	2.44257e12i	−0.0489761	+	0.0489761i
$550$	4.81522e12	+	3.50113e13i	0.0956759	+	0.695657i
$551$	1.42197e12			0.0279983
$552$	1.12501e14	−	4.89002e13i	2.19514	−	0.954147i
$553$			9.71863e13i			1.87923i
$554$	−2.83886e12	−	2.06413e13i	−0.0543995	−	0.395538i
$555$	−5.82806e13	−	5.82806e13i	−1.10678	−	1.10678i
$556$	−3.13479e12	+	5.57743e12i	−0.0589976	+	0.104969i
$557$	−5.05530e13	−	5.05530e13i	−0.942911	−	0.942911i	0.0555451	−	0.998456i	$-0.482310\pi$
$557$	−5.05530e13	−	5.05530e13i	−0.942911	−	0.942911i	−0.998456	+	0.0555451i	$0.982310\pi$
$558$	−1.31087e13	+	1.72894e13i	−0.242319	+	0.319602i
$559$			2.43912e12i			0.0446862i
$560$	−2.36662e13	+	9.72576e13i	−0.429722	+	1.76597i
$561$	−1.02738e14			−1.84892
$562$	−3.25240e13	−	2.46594e13i	−0.580125	−	0.439846i
$563$	2.24961e13	−	2.24961e13i	0.397709	−	0.397709i	−0.479715	−	0.877424i	$-0.659260\pi$
$563$	2.24961e13	−	2.24961e13i	0.397709	−	0.397709i	0.877424	+	0.479715i	$0.159260\pi$
$564$	−5.99820e13	+	1.06720e14i	−1.05105	+	1.87004i
$565$	8.22997e13	−	8.22997e13i	1.42941	−	1.42941i
$566$	3.37351e13	−	4.63968e12i	0.580764	−	0.0798742i
$567$	−1.05992e14			−1.80867
$568$	−1.09911e13	−	4.33112e12i	−0.185909	−	0.0732586i
$569$			6.75552e13i			1.13265i	0.824180	+	0.566327i	$0.191636\pi$
$569$			6.75552e13i			1.13265i	−0.824180	+	0.566327i	$0.808364\pi$
$570$	1.18203e13	−	1.62569e12i	0.196452	−	0.0270186i
$571$	−2.49940e13	−	2.49940e13i	−0.411771	−	0.411771i	0.470584	−	0.882355i	$-0.344043\pi$
$571$	−2.49940e13	−	2.49940e13i	−0.411771	−	0.411771i	−0.882355	+	0.470584i	$0.844043\pi$
$572$	−8.21392e12	+	2.30293e12i	−0.134144	+	0.0376098i
$573$	1.69285e13	+	1.69285e13i	0.274059	+	0.274059i
$574$	−1.27884e14	−	9.69606e13i	−2.05238	−	1.55609i
$575$			5.89175e13i			0.937357i
$576$	2.89618e13	−	3.10421e13i	0.456786	−	0.489596i
$577$	−2.53673e13			−0.396639			−0.198319	−	0.980137i	$-0.563548\pi$
$577$	−2.53673e13			−0.396639			−0.198319	+	0.980137i	$0.563548\pi$
$578$	−2.46510e12	+	3.25130e12i	−0.0382116	+	0.0503985i
$579$	7.37245e13	−	7.37245e13i	1.13297	−	1.13297i
$580$	4.86835e12	+	1.73641e13i	0.0741723	+	0.264552i
$581$	−4.10362e13	+	4.10362e13i	−0.619850	+	0.619850i
$582$	−1.78571e12	−	1.29839e13i	−0.0267421	−	0.194442i
$583$	−4.86343e12			−0.0722104
$584$	−2.59636e13	+	6.58881e13i	−0.382208	+	0.969935i
$585$		−	5.65216e12i		−	0.0824964i
$586$	1.34223e13	+	9.75931e13i	0.194240	+	1.41231i
$587$	6.97422e13	+	6.97422e13i	1.00070	+	1.00070i	1.00000		0.000703372i	$0.000223890\pi$
$587$	6.97422e13	+	6.97422e13i	1.00070	+	1.00070i	0.000703372		1.00000i	$0.499776\pi$
$588$	9.44862e13	+	5.31059e13i	1.34426	+	0.755538i
$589$	3.75476e12	+	3.75476e12i	0.0529670	+	0.0529670i
$590$	3.72794e13	−	4.91689e13i	0.521445	−	0.687749i
$591$		−	5.08360e13i		−	0.705073i
$592$	−1.69697e13	+	6.97381e13i	−0.233381	+	0.959095i
$593$	−1.62054e12			−0.0220996			−0.0110498	−	0.999939i	$-0.503517\pi$
$593$	−1.62054e12			−0.0220996			−0.0110498	+	0.999939i	$0.503517\pi$
$594$	3.49108e13	+	2.64690e13i	0.472092	+	0.357936i
$595$	9.88239e13	−	9.88239e13i	1.32519	−	1.32519i
$596$	−7.35692e12	−	4.13495e12i	−0.0978284	−	0.0549844i
$597$	3.90963e13	−	3.90963e13i	0.515541	−	0.515541i
$598$	−1.40890e13	+	1.93770e12i	−0.184236	+	0.0253385i
$599$	−3.44854e12			−0.0447199			−0.0223600	−	0.999750i	$-0.507118\pi$
$599$	−3.44854e12			−0.0447199			−0.0223600	+	0.999750i	$0.507118\pi$
$600$	2.02677e13	+	4.66286e13i	0.260645	+	0.599648i
$601$			5.27509e12i			0.0672756i	0.999434	+	0.0336378i	$0.0107093\pi$
$601$			5.27509e12i			0.0672756i	−0.999434	+	0.0336378i	$0.989291\pi$
$602$	−5.16344e13	+	7.10144e12i	−0.653066	+	0.0898181i
$603$	3.17660e13	+	3.17660e13i	0.398452	+	0.398452i
$604$	3.07174e13	+	1.09560e14i	0.382120	+	1.36292i
$605$	−6.51106e13	−	6.51106e13i	−0.803294	−	0.803294i
$606$	−7.61001e13	−	5.76984e13i	−0.931155	−	0.705993i
$607$		−	5.06420e13i		−	0.614565i	−0.951618	−	0.307282i	$-0.900580\pi$
$607$		−	5.06420e13i		−	0.614565i	0.951618	−	0.307282i	$-0.0994196\pi$
$608$	−6.56050e12	−	8.05697e12i	−0.0789622	−	0.0969737i
$609$	3.58904e13			0.428442
$610$	−6.47755e12	+	8.54342e12i	−0.0766940	+	0.101154i
$611$	1.00359e13	−	1.00359e13i	0.117855	−	0.117855i
$612$	−5.70762e13	+	1.60024e13i	−0.664810	+	0.186392i
$613$	−2.09438e13	+	2.09438e13i	−0.241966	+	0.241966i	−0.817663	−	0.575697i	$-0.804731\pi$
$613$	−2.09438e13	+	2.09438e13i	−0.241966	+	0.241966i	0.575697	+	0.817663i	$0.304731\pi$
$614$	−2.39693e12	−	1.74280e13i	−0.0274671	−	0.199713i
$615$	−2.42613e14			−2.75765
$616$	−7.26662e13	−	1.67178e14i	−0.819273	−	1.88485i
$617$			3.94745e13i			0.441459i	0.975335	+	0.220730i	$0.0708439\pi$
$617$			3.94745e13i			0.441459i	−0.975335	+	0.220730i	$0.929156\pi$
$618$	1.26806e13	+	9.22006e13i	0.140669	+	1.02280i
$619$	−7.60542e13	−	7.60542e13i	−0.836893	−	0.836893i	0.151556	−	0.988449i	$-0.451572\pi$
$619$	−7.60542e13	−	7.60542e13i	−0.836893	−	0.836893i	−0.988449	+	0.151556i	$0.951572\pi$
$620$	−3.29954e13	+	5.87056e13i	−0.360160	+	0.640798i
$621$	5.16453e13	+	5.16453e13i	0.559207	+	0.559207i
$622$	5.83520e13	−	7.69621e13i	0.626763	−	0.826656i
$623$			9.96452e13i			1.06174i
$624$	−1.04838e13	+	6.38017e12i	−0.110814	+	0.0674388i
$625$	1.19206e14			1.24996
$626$	−2.76816e13	−	2.09879e13i	−0.287952	−	0.218322i
$627$	−1.53648e13	+	1.53648e13i	−0.158558	+	0.158558i
$628$	3.29780e13	−	5.86745e13i	0.337618	−	0.600692i
$629$	7.08612e13	−	7.08612e13i	0.719706	−	0.719706i
$630$	1.19652e14	−	1.64561e13i	1.20564	−	0.165816i
$631$	6.65628e13			0.665403			0.332701	−	0.943032i	$-0.392040\pi$
$631$	6.65628e13			0.665403			0.332701	+	0.943032i	$0.392040\pi$
$632$	4.69050e13	−	1.19031e14i	0.465194	−	1.18053i
$633$		−	9.74582e13i		−	0.958959i
$634$	1.50853e13	−	2.07472e12i	0.147268	−	0.0202542i
$635$	5.19857e13	+	5.19857e13i	0.503518	+	0.503518i
$636$	−6.73696e12	+	1.88884e12i	−0.0647409	+	0.0181514i
$637$	−8.88539e12	−	8.88539e12i	−0.0847187	−	0.0847187i
$638$	−2.61701e13	−	1.98420e13i	−0.247573	−	0.187707i
$639$			1.42548e13i			0.133800i
$640$	7.59252e13	−	1.07697e14i	0.707109	−	1.00300i
$641$	−3.25100e13			−0.300419			−0.150210	−	0.988654i	$-0.547995\pi$
$641$	−3.25100e13			−0.300419			−0.150210	+	0.988654i	$0.547995\pi$
$642$	−6.25471e13	+	8.24952e13i	−0.573498	+	0.756404i
$643$	−7.17670e13	+	7.17670e13i	−0.652935	+	0.652935i	−0.953699	−	0.300763i	$-0.902759\pi$
$643$	−7.17670e13	+	7.17670e13i	−0.652935	+	0.652935i	0.300763	+	0.953699i	$0.402759\pi$
$644$	−8.20395e13	−	2.92612e14i	−0.740617	−	2.64158i
$645$	−5.57149e13	+	5.57149e13i	−0.499083	+	0.499083i
$646$	1.97661e12	+	1.43719e13i	0.0175695	+	0.127747i
$647$	8.38565e13			0.739632			0.369816	−	0.929105i	$-0.379421\pi$
$647$	8.38565e13			0.739632			0.369816	+	0.929105i	$0.379421\pi$
$648$	1.29817e14	+	5.11551e13i	1.13620	+	0.447728i
$649$			1.12371e14i			0.975955i
$650$	−8.03120e11	−	5.83947e12i	−0.00692172	−	0.0503277i
$651$	9.47702e13	+	9.47702e13i	0.810525	+	0.810525i
$652$	4.38904e11	+	2.46686e11i	0.00372504	+	0.00209366i
$653$	−1.23762e14	−	1.23762e14i	−1.04237	−	1.04237i	−0.999062	−	0.0433046i	$-0.986211\pi$
$653$	−1.23762e14	−	1.23762e14i	−1.04237	−	1.04237i	−0.0433046	−	0.999062i	$-0.513789\pi$
$654$	8.14225e13	−	1.07390e14i	0.680543	−	0.897588i
$655$			2.42548e14i			2.01183i
$656$	1.09833e14	+	1.80476e14i	0.904097	+	1.48559i
$657$	8.54527e13			0.698070
$658$	2.41671e14	+	1.83233e14i	1.95928	+	1.48551i
$659$	3.81389e13	−	3.81389e13i	0.306861	−	0.306861i	−0.536830	−	0.843690i	$-0.680378\pi$
$659$	3.81389e13	−	3.81389e13i	0.306861	−	0.306861i	0.843690	+	0.536830i	$0.180378\pi$
$660$	−2.40229e14	−	1.35020e14i	−1.91825	−	1.07815i
$661$	3.17204e12	−	3.17204e12i	0.0251381	−	0.0251381i	−0.694426	−	0.719564i	$-0.744342\pi$
$661$	3.17204e12	−	3.17204e12i	0.0251381	−	0.0251381i	0.719564	+	0.694426i	$0.244342\pi$
$662$	−1.26791e14	+	1.74380e13i	−0.997239	+	0.137153i
$663$	1.71355e13			0.133761
$664$	7.00655e13	−	3.04549e13i	0.542830	−	0.235948i
$665$		−	2.95588e13i		−	0.227289i
$666$	8.57961e13	−	1.17998e13i	0.654782	−	0.0900541i
$667$	−3.87148e13	−	3.87148e13i	−0.293257	−	0.293257i
$668$	−1.49099e13	−	5.31795e13i	−0.112097	−	0.399817i
$669$	1.60257e14	+	1.60257e14i	1.19588	+	1.19588i
$670$	1.11109e14	+	8.42416e13i	0.822951	+	0.623954i
$671$		−	1.95252e13i		−	0.143543i
$672$	−1.65587e14	−	2.03358e14i	−1.20832	−	1.48394i
$673$	−2.21404e14			−1.60365			−0.801825	−	0.597558i	$-0.796138\pi$
$673$	−2.21404e14			−1.60365			−0.801825	+	0.597558i	$0.796138\pi$
$674$	6.35266e13	−	8.37871e13i	0.456726	−	0.602390i
$675$	−2.14055e13	+	2.14055e13i	−0.152759	+	0.152759i
$676$	−1.34556e14	+	3.77253e13i	−0.953167	+	0.267239i
$677$	1.07660e14	−	1.07660e14i	0.757028	−	0.757028i	−0.218752	−	0.975780i	$-0.570199\pi$
$677$	1.07660e14	−	1.07660e14i	0.757028	−	0.757028i	0.975780	+	0.218752i	$0.0701987\pi$
$678$	4.15477e13	+	3.02093e14i	0.290000	+	2.10859i
$679$	−3.24684e13			−0.224964
$680$	−1.68732e14	+	7.33418e13i	−1.16052	+	0.504437i
$681$			3.16786e14i			2.16287i
$682$	−1.67098e13	−	1.21497e14i	−0.113253	−	0.823461i
$683$	−1.17203e14	−	1.17203e14i	−0.788562	−	0.788562i	0.192696	−	0.981258i	$-0.438277\pi$
$683$	−1.17203e14	−	1.17203e14i	−0.788562	−	0.788562i	−0.981258	+	0.192696i	$0.938277\pi$
$684$	−6.14270e12	+	1.09291e13i	−0.0410279	+	0.0729969i
$685$	−1.82650e14	−	1.82650e14i	−1.21107	−	1.21107i
$686$	2.62908e13	−	3.46757e13i	0.173055	−	0.228247i
$687$		−	1.34101e14i		−	0.876289i
$688$	6.66680e13	+	1.62227e13i	0.432489	+	0.105240i
$689$	8.11162e11			0.00522410
$690$	−3.66085e14	−	2.77563e14i	−2.34065	−	1.77466i
$691$	−1.65665e14	+	1.65665e14i	−1.05158	+	1.05158i	−0.0529810	+	0.998596i	$0.516872\pi$
$691$	−1.65665e14	+	1.65665e14i	−1.05158	+	1.05158i	−0.998596	+	0.0529810i	$0.983128\pi$
$692$	−9.18985e13	+	1.63506e14i	−0.579132	+	1.03039i
$693$	−1.55531e14	+	1.55531e14i	−0.973088	+	0.973088i
$694$	−2.67254e14	+	3.67563e13i	−1.66007	+	0.228315i
$695$	2.39613e13			0.147770
$696$	−4.39578e13	−	1.73218e13i	−0.269147	−	0.106059i
$697$		−	2.94984e14i		−	1.79323i
$698$	2.12085e14	−	2.91686e13i	1.28006	−	0.176051i
$699$	1.57551e14	+	1.57551e14i	0.944135	+	0.944135i
$700$	1.21279e14	−	3.40030e13i	0.721601	−	0.202315i
$701$	−7.24445e13	−	7.24445e13i	−0.427972	−	0.427972i	0.459965	−	0.887937i	$-0.347862\pi$
$701$	−7.24445e13	−	7.24445e13i	−0.427972	−	0.427972i	−0.887937	+	0.459965i	$0.847862\pi$
$702$	−5.82270e12	−	4.41471e12i	−0.0341538	−	0.0258951i
$703$		−	2.11950e13i		−	0.123440i
$704$	8.31458e12	+	2.39827e14i	0.0480814	+	1.38687i
$705$	4.58483e14			2.63256
$706$	−2.05247e13	+	2.70706e13i	−0.117018	+	0.154339i
$707$	−1.67293e14	+	1.67293e14i	−0.947067	+	0.947067i
$708$	4.36421e13	+	1.55659e14i	0.245323	+	0.875001i
$709$	2.20025e14	−	2.20025e14i	1.22812	−	1.22812i	0.263445	−	0.964674i	$-0.415141\pi$
$709$	2.20025e14	−	2.20025e14i	1.22812	−	1.22812i	0.964674	−	0.263445i	$-0.0848587\pi$
$710$	6.02823e12	+	4.38312e13i	0.0334117	+	0.242936i
$711$	−1.54376e14			−0.849635
$712$	4.80918e13	−	1.22043e14i	0.262828	−	0.666981i
$713$		−	2.04456e14i		−	1.10956i
$714$	4.98897e13	+	3.62747e14i	0.268856	+	1.95485i
$715$	2.25909e13	+	2.25909e13i	0.120893	+	0.120893i
$716$	9.51124e13	+	5.34579e13i	0.505443	+	0.284084i
$717$	2.70185e13	+	2.70185e13i	0.142582	+	0.142582i
$718$	−3.57478e13	+	4.71488e13i	−0.187338	+	0.247086i
$719$		−	9.91762e13i		−	0.516134i	−0.966127	−	0.258067i	$-0.916914\pi$
$719$		−	9.91762e13i		−	0.516134i	0.966127	−	0.258067i	$-0.0830856\pi$
$720$	−1.54490e14	−	3.75927e13i	−0.798430	−	0.194286i
$721$	2.30563e14			1.18335
$722$	−1.53894e14	−	1.16681e14i	−0.784394	−	0.594720i
$723$	9.81136e13	−	9.81136e13i	0.496636	−	0.496636i
$724$	1.75796e14	+	9.88058e13i	0.883721	+	0.496695i
$725$	1.60462e13	−	1.60462e13i	0.0801091	−	0.0801091i
$726$	2.38998e14	−	3.28701e13i	1.18498	−	0.162974i
$727$	2.52004e13			0.124089			0.0620447	−	0.998073i	$-0.480238\pi$
$727$	2.52004e13			0.124089			0.0620447	+	0.998073i	$0.480238\pi$
$728$	1.21198e13	+	2.78833e13i	0.0592707	+	0.136360i
$729$		−	5.47861e13i		−	0.266093i
$730$	2.62753e14	−	3.61372e13i	1.26746	−	0.174317i
$731$	−6.77416e13	−	6.77416e13i	−0.324540	−	0.324540i
$732$	−7.58311e12	−	2.70468e13i	−0.0360821	−	0.128695i
$733$	1.09106e14	+	1.09106e14i	0.515617	+	0.515617i	0.916242	−	0.400625i	$-0.131207\pi$
$733$	1.09106e14	+	1.09106e14i	0.515617	+	0.515617i	−0.400625	+	0.916242i	$0.631207\pi$
$734$	−2.34037e13	−	1.77445e13i	−0.109851	−	0.0832881i
$735$		−	4.05925e14i		−	1.89238i
$736$	−4.07435e13	+	3.97980e14i	−0.188655	+	1.84277i
$737$	−2.53928e14			−1.16781
$738$	1.54018e14	−	2.03138e14i	0.703540	−	0.927920i
$739$	−6.10889e13	+	6.10889e13i	−0.277166	+	0.277166i	−0.831977	−	0.554811i	$-0.812791\pi$
$739$	−6.10889e13	+	6.10889e13i	−0.277166	+	0.277166i	0.554811	+	0.831977i	$0.312791\pi$
$740$	2.58819e14	−	7.25648e13i	1.16637	−	0.327015i
$741$	2.56267e12	−	2.56267e12i	0.0114710	−	0.0114710i
$742$	2.36168e12	+	1.71717e13i	0.0105003	+	0.0763475i
$743$	−2.28971e14			−1.01120			−0.505598	−	0.862769i	$-0.668728\pi$
$743$	−2.28971e14			−1.01120			−0.505598	+	0.862769i	$0.668728\pi$
$744$	−7.03333e13	−	1.61811e14i	−0.308529	−	0.709813i
$745$			3.16063e13i			0.137718i
$746$	−2.51247e13	−	1.82682e14i	−0.108745	−	0.790680i
$747$	−6.51843e13	−	6.51843e13i	−0.280246	−	0.280246i
$748$	1.64166e14	−	2.92085e14i	0.701092	−	1.24739i
$749$	1.81352e14	+	1.81352e14i	0.769330	+	0.769330i
$750$	−1.12304e14	+	1.48121e14i	−0.473247	+	0.624179i
$751$			2.63501e14i			1.10302i	0.834169	+	0.551509i	$0.185948\pi$
$751$			2.63501e14i			1.10302i	−0.834169	+	0.551509i	$0.814052\pi$
$752$	−2.07560e14	−	3.41057e14i	−0.863085	−	1.41820i
$753$	−5.12043e14			−2.11510
$754$	4.36487e12	+	3.30940e12i	0.0179108	+	0.0135798i
$755$	3.01326e14	−	3.01326e14i	1.22829	−	1.22829i
$756$	7.65038e13	−	1.36116e14i	0.309795	−	0.551188i
$757$	−3.10544e14	+	3.10544e14i	−1.24923	+	1.24923i	−0.293174	+	0.956059i	$0.594712\pi$
$757$	−3.10544e14	+	3.10544e14i	−1.24923	+	1.24923i	−0.956059	+	0.293174i	$0.905288\pi$
$758$	−3.70391e13	+	5.09410e12i	−0.148018	+	0.0203574i
$759$	8.36653e14			3.32152
$760$	−1.42660e13	+	3.62029e13i	−0.0562643	+	0.142783i
$761$			6.89505e13i			0.270156i	0.990835	+	0.135078i	$0.0431285\pi$
$761$			6.89505e13i			0.270156i	−0.990835	+	0.135078i	$0.956872\pi$
$762$	−1.90821e14	+	2.62442e13i	−0.742765	+	0.102155i
$763$	−2.36080e14	−	2.36080e14i	−0.912926	−	0.912926i
$764$	−7.51777e13	+	2.10775e13i	−0.288817	+	0.0809754i
$765$	1.56977e14	+	1.56977e14i	0.599142	+	0.599142i
$766$	2.03609e14	+	1.54375e14i	0.772065	+	0.585373i
$767$		−	1.87421e13i		−	0.0706059i
$768$	1.04660e14	+	3.28986e14i	0.391721	+	1.23132i
$769$	−1.58927e14			−0.590971			−0.295486	−	0.955347i	$-0.595481\pi$
$769$	−1.58927e14			−0.590971			−0.295486	+	0.955347i	$0.595481\pi$
$770$	−4.12460e14	+	5.44006e14i	−1.52380	+	2.00979i
$771$	−1.71609e14	+	1.71609e14i	−0.629894	+	0.629894i
$772$	9.17939e13	+	3.27404e14i	0.334755	+	1.19398i
$773$	−8.02739e12	+	8.02739e12i	−0.0290855	+	0.0290855i	−0.721500	−	0.692414i	$-0.756547\pi$
$773$	−8.02739e12	+	8.02739e12i	−0.0290855	+	0.0290855i	0.692414	+	0.721500i	$0.256547\pi$
$774$	−1.12803e13	−	8.20191e13i	−0.0406085	−	0.295264i
$775$	8.47412e13			0.303100
$776$	3.97665e13	+	1.56702e13i	0.141322	+	0.0556887i
$777$		−	5.34962e14i		−	1.88894i
$778$	−5.42594e12	−	3.94519e13i	−0.0190360	−	0.138411i
$779$	−4.41158e13	−	4.41158e13i	−0.153782	−	0.153782i
$780$	4.00673e13	+	2.25198e13i	0.138777	+	0.0779994i
$781$	−5.69744e13	−	5.69744e13i	−0.196076	−	0.196076i
$782$	3.37478e14	−	4.45109e14i	1.15401	−	1.52206i
$783$		−	2.81312e13i		−	0.0955827i
$784$	−3.01960e14	+	1.83766e14i	−1.01946	+	0.620419i
$785$	−2.52073e14			−0.845626
$786$	−5.06376e14	−	3.83930e14i	−1.68795	−	1.27979i
$787$	4.20048e14	−	4.20048e14i	1.39131	−	1.39131i	0.568924	−	0.822390i	$-0.307360\pi$
$787$	4.20048e14	−	4.20048e14i	1.39131	−	1.39131i	0.822390	−	0.568924i	$-0.192640\pi$
$788$	1.44527e14	+	8.12312e13i	0.475682	+	0.267357i
$789$	1.77493e13	−	1.77493e13i	0.0580493	−	0.0580493i
$790$	−4.74681e14	+	6.52843e13i	−1.54265	+	0.212165i
$791$	7.55435e14			2.43958
$792$	2.65555e14	−	1.15427e14i	0.852176	−	0.370409i
$793$			3.25657e12i			0.0103847i
$794$	−3.58860e14	+	4.93551e13i	−1.13716	+	0.156398i
$795$	1.85288e13	+	1.85288e13i	0.0583459	+	0.0583459i
$796$	4.86785e13	+	1.73623e14i	0.152325	+	0.543302i
$797$	2.46612e14	+	2.46612e14i	0.766870	+	0.766870i	0.977554	−	0.210684i	$-0.0675691\pi$
$797$	2.46612e14	+	2.46612e14i	0.766870	+	0.766870i	−0.210684	+	0.977554i	$0.567569\pi$
$798$	6.17110e13	+	4.67887e13i	0.190699	+	0.144586i
$799$			5.57452e14i			1.71188i
$800$	−1.64951e14	−	1.68870e13i	−0.503391	−	0.0515350i
$801$	−1.58282e14			−0.480031
$802$	2.31750e14	−	3.05661e14i	0.698469	−	0.921231i
$803$	−3.41542e14	+	3.41542e14i	−1.02298	+	1.02298i
$804$	−3.51749e14	+	9.86196e13i	−1.04701	+	0.293551i
$805$	−8.04776e14	+	8.04776e14i	−2.38065	+	2.38065i
$806$	2.78700e12	+	2.02642e13i	0.00819335	+	0.0595737i
$807$	−5.05335e14			−1.47643
$808$	2.85637e14	−	1.24156e14i	0.829389	−	0.360505i
$809$			2.02869e14i			0.585426i	0.956200	+	0.292713i	$0.0945581\pi$
$809$			2.02869e14i			0.585426i	−0.956200	+	0.292713i	$0.905442\pi$
$810$	−7.11998e13	−	5.17692e14i	−0.204199	−	1.48473i
$811$	−1.87349e14	−	1.87349e14i	−0.534008	−	0.534008i	0.387755	−	0.921763i	$-0.373251\pi$
$811$	−1.87349e14	−	1.87349e14i	−0.534008	−	0.534008i	−0.921763	+	0.387755i	$0.873251\pi$
$812$	−5.73495e13	+	1.02037e14i	−0.162461	+	0.289052i
$813$	3.47356e14	+	3.47356e14i	0.977963	+	0.977963i
$814$	−2.95753e14	+	3.90077e14i	−0.827574	+	1.09151i
$815$		−	1.88559e12i		−	0.00524395i
$816$	1.13969e14	−	4.68362e14i	0.315018	−	1.29459i
$817$	−2.02619e13			−0.0556635
$818$	4.00346e14	+	3.03539e14i	1.09312	+	0.828795i
$819$	2.59408e13	−	2.59408e13i	0.0703985	−	0.0703985i
$820$	3.87673e14	−	6.89750e14i	1.04567	−	1.86047i
$821$	2.42188e14	−	2.42188e14i	0.649288	−	0.649288i	−0.303533	−	0.952821i	$-0.598166\pi$
$821$	2.42188e14	−	2.42188e14i	0.649288	−	0.649288i	0.952821	+	0.303533i	$0.0981662\pi$
$822$	6.70444e14	−	9.22082e13i	1.78650	−	0.245703i
$823$	−6.51837e14			−1.72639			−0.863197	−	0.504867i	$-0.831542\pi$
$823$	−6.51837e14			−1.72639			−0.863197	+	0.504867i	$0.831542\pi$
$824$	−2.82389e14	−	1.11277e14i	−0.743380	−	0.292933i
$825$			3.46769e14i			0.907340i
$826$	3.96757e14	−	5.45672e13i	1.03187	−	0.141916i
$827$	4.57277e14	+	4.57277e14i	1.18209	+	1.18209i	0.979201	+	0.202894i	$0.0650346\pi$
$827$	4.57277e14	+	4.57277e14i	1.18209	+	1.18209i	0.202894	+	0.979201i	$0.434965\pi$
$828$	4.64802e14	−	1.30316e14i	1.19431	−	0.334847i
$829$	−1.87604e14	−	1.87604e14i	−0.479148	−	0.479148i	0.425711	−	0.904859i	$-0.360024\pi$
$829$	−1.87604e14	−	1.87604e14i	−0.479148	−	0.479148i	−0.904859	+	0.425711i	$0.860024\pi$
$830$	−2.27997e14	−	1.72865e14i	−0.578813	−	0.438850i
$831$		−	2.04441e14i		−	0.515896i
$832$	−1.38677e12	−	4.00002e13i	−0.00347847	−	0.100333i
$833$	4.93548e14			1.23056
$834$	−3.79285e13	+	5.00250e13i	−0.0940016	+	0.123981i
$835$	−1.46260e14	+	1.46260e14i	−0.360325	+	0.360325i
$836$	−1.91306e13	−	6.82336e13i	−0.0468487	−	0.167096i
$837$	7.42815e13	−	7.42815e13i	0.180823	−	0.180823i
$838$	−7.44082e13	−	5.41020e14i	−0.180053	−	1.30916i
$839$	4.64839e14			1.11813			0.559066	−	0.829123i	$-0.311160\pi$
$839$	4.64839e14			1.11813			0.559066	+	0.829123i	$0.311160\pi$
$840$	−3.60073e14	+	9.13763e14i	−0.860983	+	2.18493i
$841$		−	3.99619e14i		−	0.949875i
$842$	−3.89477e13	−	2.83188e14i	−0.0920283	−	0.669136i
$843$	−2.83185e14	−	2.83185e14i	−0.665170	−	0.665170i
$844$	2.77074e14	+	1.55729e14i	0.646968	+	0.363628i
$845$	3.70071e14	+	3.70071e14i	0.859016	+	0.859016i
$846$	−2.91058e14	+	3.83884e14i	−0.671626	+	0.885827i
$847$		−	5.97655e14i		−	1.37099i
$848$	5.39507e12	−	2.21714e13i	0.0123032	−	0.0505607i
$849$	3.34128e14			0.757485
$850$	1.84485e14	+	1.39875e14i	0.415782	+	0.315242i
$851$	−5.77061e14	+	5.77061e14i	−1.29293	+	1.29293i
$852$	−1.01050e14	−	5.67952e13i	−0.225081	−	0.126507i
$853$	2.09739e14	−	2.09739e14i	0.464445	−	0.464445i	−0.435664	−	0.900109i	$-0.643486\pi$
$853$	2.09739e14	−	2.09739e14i	0.464445	−	0.464445i	0.900109	+	0.435664i	$0.143486\pi$
$854$	−6.89393e13	+	9.48143e12i	−0.151767	+	0.0208730i
$855$	4.69529e13			0.102762
$856$	−1.34589e14	−	3.09641e14i	−0.292848	−	0.673736i
$857$			3.03911e14i			0.657418i	0.944431	+	0.328709i	$0.106614\pi$
$857$			3.03911e14i			0.657418i	−0.944431	+	0.328709i	$0.893386\pi$
$858$	−8.29230e13	+	1.14046e13i	−0.178336	+	0.0245271i
$859$	−4.27977e12	−	4.27977e12i	−0.00915070	−	0.00915070i	0.702517	−	0.711667i	$-0.252060\pi$
$859$	−4.27977e12	−	4.27977e12i	−0.00915070	−	0.00915070i	−0.711667	+	0.702517i	$0.752060\pi$
$860$	−6.93703e13	−	2.47425e14i	−0.147462	−	0.525958i
$861$	−1.11348e15	−	1.11348e15i	−2.35325	−	2.35325i
$862$	1.00307e14	+	7.60521e13i	0.210764	+	0.159799i
$863$		−	7.72045e14i		−	1.61283i	−0.591351	−	0.806415i	$-0.701405\pi$
$863$		−	7.72045e14i		−	1.61283i	0.591351	−	0.806415i	$-0.298595\pi$
$864$	−1.59394e14	+	1.29788e14i	−0.331057	+	0.269567i
$865$	7.02443e14			1.45054
$866$	9.85878e13	−	1.30030e14i	0.202411	−	0.266966i
$867$	−2.83089e13	+	2.83089e13i	−0.0577867	+	0.0577867i
$868$	−4.20865e14	+	1.17998e14i	−0.854170	+	0.239483i
$869$	6.17020e14	−	6.17020e14i	1.24509	−	1.24509i
$870$	2.41092e13	+	1.75298e14i	0.0483712	+	0.351706i
$871$	4.23522e13			0.0844861
$872$	1.75206e14	+	4.03084e14i	0.347509	+	0.799490i
$873$		−	5.15747e13i		−	0.101710i
$874$	−1.60966e13	−	1.17038e14i	−0.0315629	−	0.229493i
$875$	3.25618e14	+	3.25618e14i	0.634845	+	0.634845i
$876$	−3.40467e14	+	6.05761e14i	−0.660017	+	1.17430i
$877$	−1.59298e14	−	1.59298e14i	−0.307053	−	0.307053i	0.536712	−	0.843765i	$-0.319666\pi$
$877$	−1.59298e14	−	1.59298e14i	−0.307053	−	0.307053i	−0.843765	+	0.536712i	$0.819666\pi$
$878$	−1.03550e14	+	1.36576e14i	−0.198463	+	0.261758i
$879$			9.66607e14i			1.84207i
$880$	7.67725e14	−	4.67220e14i	1.45476	−	0.885336i
$881$	−5.82082e14			−1.09674			−0.548371	−	0.836235i	$-0.684752\pi$
$881$	−5.82082e14			−1.09674			−0.548371	+	0.836235i	$0.684752\pi$
$882$	3.39878e14	+	2.57692e14i	0.636766	+	0.482790i
$883$	5.71494e14	−	5.71494e14i	1.06465	−	1.06465i	0.0668925	−	0.997760i	$-0.478692\pi$
$883$	5.71494e14	−	5.71494e14i	1.06465	−	1.06465i	0.997760	−	0.0668925i	$-0.0213085\pi$
$884$	−2.73809e13	+	4.87162e13i	−0.0507209	+	0.0902428i
$885$	4.28112e14	−	4.28112e14i	0.788571	−	0.788571i
$886$	6.12779e13	−	8.42773e12i	0.112237	−	0.0154363i
$887$	−6.09940e14			−1.11088			−0.555442	−	0.831555i	$-0.687451\pi$
$887$	−6.09940e14			−1.11088			−0.555442	+	0.831555i	$0.687451\pi$
$888$	−2.58189e14	+	6.55209e14i	−0.467598	+	1.18663i
$889$			4.77181e14i			0.859358i
$890$	−4.86691e14	+	6.69361e13i	−0.871573	+	0.119870i
$891$	6.72928e14	+	6.72928e14i	1.19834	+	1.19834i
$892$	−7.11685e14	+	1.99535e14i	−1.26027	+	0.353341i
$893$	8.33685e13	+	8.33685e13i	0.146806	+	0.146806i
$894$	−6.59856e13	−	5.00297e13i	−0.115548	−	0.0876073i
$895$		−	4.08615e14i		−	0.711539i
$896$	8.42740e14	−	1.45817e14i	1.45933	−	0.252504i
$897$	−1.39544e14			−0.240297
$898$	5.76161e14	−	7.59915e14i	0.986647	−	1.30132i
$899$	−5.56836e13	+	5.56836e13i	−0.0948264	+	0.0948264i
$900$	5.40123e13	+	1.92647e14i	0.0914704	+	0.326250i
$901$	−2.25284e13	+	2.25284e13i	−0.0379408	+	0.0379408i
$902$	1.96329e14	+	1.42750e15i	0.328815	+	2.39081i
$903$	−5.11411e14			−0.851788
$904$	−9.25238e14	−	3.64595e14i	−1.53254	−	0.603906i
$905$		−	7.55240e14i		−	1.24406i
$906$	1.52120e14	+	1.10606e15i	0.249198	+	1.81191i
$907$	−7.89105e14	−	7.89105e14i	−1.28558	−	1.28558i	−0.937446	−	0.348132i	$-0.886816\pi$
$907$	−7.89105e14	−	7.89105e14i	−1.28558	−	1.28558i	−0.348132	−	0.937446i	$-0.613184\pi$
$908$	−9.00624e14	−	5.06195e14i	−1.45920	−	0.820141i
$909$	−2.65738e14	−	2.65738e14i	−0.428187	−	0.428187i
$910$	6.87934e13	−	9.07337e13i	0.110240	−	0.145399i
$911$			2.95856e14i			0.471508i	0.971813	+	0.235754i	$0.0757559\pi$
$911$			2.95856e14i			0.471508i	−0.971813	+	0.235754i	$0.924244\pi$
$912$	−5.30006e13	−	8.70893e13i	−0.0840052	−	0.138035i
$913$	5.21065e14			0.821368
$914$	9.17080e14	+	6.95321e14i	1.43773	+	1.09007i
$915$	−7.43873e13	+	7.43873e13i	−0.115983	+	0.115983i
$916$	3.81248e14	+	2.14280e14i	0.591194	+	0.332280i
$917$	−1.11318e15	+	1.11318e15i	−1.71680	+	1.71680i
$918$	2.84324e14	−	3.91039e13i	0.436114	−	0.0599800i
$919$	9.08080e14			1.38531			0.692654	−	0.721270i	$-0.256441\pi$
$919$	9.08080e14			1.38531			0.692654	+	0.721270i	$0.256441\pi$
$920$	1.37408e15	−	5.97262e14i	2.08484	−	0.906203i
$921$		−	1.72615e14i		−	0.260484i
$922$	−9.23820e14	+	1.27056e14i	−1.38654	+	0.190695i
$923$	9.50265e12	+	9.50265e12i	0.0141852	+	0.0141852i
$924$	−4.82857e14	−	1.72222e15i	−0.716901	−	2.55699i
$925$	−2.39175e14	−	2.39175e14i	−0.353189	−	0.353189i
$926$	−5.01572e13	−	3.80287e13i	−0.0736679	−	0.0558543i
$927$			3.66240e14i			0.535016i
$928$	1.19486e14	−	9.72933e13i	0.173611	−	0.141365i
$929$	−1.53906e14			−0.222422			−0.111211	−	0.993797i	$-0.535473\pi$
$929$	−1.53906e14			−0.222422			−0.111211	+	0.993797i	$0.535473\pi$
$930$	−3.99219e14	+	5.26542e14i	−0.573847	+	0.756864i
$931$	7.38116e13	−	7.38116e13i	0.105530	−	0.105530i
$932$	−6.99667e14	+	1.96165e14i	−0.994975	+	0.278960i
$933$	6.70107e14	−	6.70107e14i	0.947841	−	0.947841i
$934$	−7.79418e13	−	5.66713e14i	−0.109657	−	0.797313i
$935$	−1.25483e15			−1.75601
$936$	−4.42914e13	+	1.92519e13i	−0.0616511	+	0.0267974i
$937$			3.45893e13i			0.0478899i	0.999713	+	0.0239450i	$0.00762265\pi$
$937$			3.45893e13i			0.0478899i	−0.999713	+	0.0239450i	$0.992377\pi$
$938$	1.23308e14	+	8.96568e14i	0.169815	+	1.23472i
$939$	−2.41023e14	−	2.41023e14i	−0.330165	−	0.330165i
$940$	−7.32613e14	+	1.30347e15i	−0.998240	+	1.77607i
$941$	2.07445e14	+	2.07445e14i	0.281160	+	0.281160i	0.833572	−	0.552411i	$-0.186292\pi$
$941$	2.07445e14	+	2.07445e14i	0.281160	+	0.281160i	−0.552411	+	0.833572i	$0.686292\pi$
$942$	3.99008e14	−	5.26263e14i	0.537931	−	0.709494i
$943$			2.40222e15i			3.22147i
$944$	−5.12275e14	−	1.24654e14i	−0.683350	−	0.166283i
$945$	−5.84771e14			−0.775938
$946$	3.72904e14	+	2.82733e14i	0.492200	+	0.373182i
$947$	5.13270e14	−	5.13270e14i	0.673901	−	0.673901i	−0.284712	−	0.958613i	$-0.591898\pi$
$947$	5.13270e14	−	5.13270e14i	0.673901	−	0.673901i	0.958613	+	0.284712i	$0.0918981\pi$
$948$	6.15078e14	−	1.09435e15i	0.803320	−	1.42927i
$949$	5.69651e13	−	5.69651e13i	0.0740079	−	0.0740079i
$950$	4.85089e13	−	6.67158e12i	0.0626908	−	0.00862205i
$951$	1.49412e14			0.192080
$952$	−1.11101e15	−	4.37799e14i	−1.42080	−	0.559874i
$953$			1.45400e15i			1.84969i	0.380345	+	0.924844i	$0.375805\pi$
$953$			1.45400e15i			1.84969i	−0.380345	+	0.924844i	$0.624195\pi$
$954$	−2.72766e13	+	3.75143e12i	−0.0345182	+	0.00474739i
$955$	2.06762e14	+	2.06762e14i	0.260288	+	0.260288i
$956$	−1.19987e14	+	3.36406e13i	−0.150260	+	0.0421283i
$957$	−2.27863e14	−	2.27863e14i	−0.283866	−	0.283866i
$958$	−8.66152e13	−	6.56708e13i	−0.107341	−	0.0813851i
$959$		−	1.67656e15i		−	2.06693i
$960$	8.82019e14	−	9.45373e14i	1.08174	−	1.15944i
$961$	5.25559e14			0.641216
$962$	4.93280e13	−	6.50602e13i	0.0598713	−	0.0789660i
$963$	−2.88069e14	+	2.88069e14i	−0.347829	+	0.347829i
$964$	1.22161e14	+	4.35713e14i	0.146739	+	0.523378i
$965$	9.00463e14	−	9.00463e14i	1.07604	−	1.07604i
$966$	−4.06279e14	−	2.95405e15i	−0.482990	−	3.51181i
$967$	−4.63065e14			−0.547658			−0.273829	−	0.961778i	$-0.588290\pi$
$967$	−4.63065e14			−0.547658			−0.273829	+	0.961778i	$0.588290\pi$
$968$	−2.88446e14	+	7.31994e14i	−0.339381	+	0.861252i
$969$			1.42346e14i			0.166620i
$970$	−2.18105e13	−	1.58584e14i	−0.0253984	−	0.184671i
$971$	−4.79989e14	−	4.79989e14i	−0.556077	−	0.556077i	0.372111	−	0.928188i	$-0.378634\pi$
$971$	−4.79989e14	−	4.79989e14i	−0.556077	−	0.556077i	−0.928188	+	0.372111i	$0.878634\pi$
$972$	8.70606e14	+	4.89324e14i	1.00344	+	0.563981i
$973$	1.09971e14	+	1.09971e14i	0.126100	+	0.126100i
$974$	8.81704e13	−	1.16290e14i	0.100584	−	0.132663i
$975$		−	5.78368e13i		−	0.0656420i
$976$	8.90113e13	+	2.16595e13i	0.100507	+	0.0244568i
$977$	1.56629e15			1.75955			0.879773	−	0.475394i	$-0.157695\pi$
$977$	1.56629e15			1.75955			0.879773	+	0.475394i	$0.157695\pi$
$978$	3.93661e12	+	2.98470e12i	0.00439975	+	0.00333585i
$979$	6.32631e14	−	6.32631e14i	0.703456	−	0.703456i
$980$	1.15404e15	+	6.48629e14i	1.27671	+	0.717573i
$981$	3.75002e14	−	3.75002e14i	0.412752	−	0.412752i
$982$	9.17573e14	−	1.26197e14i	1.00481	−	0.138194i
$983$	−8.23652e14			−0.897380			−0.448690	−	0.893687i	$-0.648109\pi$
$983$	−8.23652e14			−0.897380			−0.448690	+	0.893687i	$0.648109\pi$
$984$	8.26368e14	+	1.90117e15i	0.895773	+	2.06084i
$985$		−	6.20905e14i		−	0.669644i
$986$	−2.13138e14	+	2.93135e13i	−0.228705	+	0.0314545i
$987$	2.10422e15	+	2.10422e15i	2.24650	+	2.24650i
$988$	3.19076e12	+	1.13806e13i	0.00338929	+	0.0120887i
$989$	5.51657e14	+	5.51657e14i	0.583025	+	0.583025i
$990$	−8.64130e14	−	6.55175e14i	−0.908664	−	0.688940i
$991$			6.15292e14i			0.643744i	0.946783	+	0.321872i	$0.104312\pi$
$991$			6.15292e14i			0.643744i	−0.946783	+	0.321872i	$0.895688\pi$
$992$	5.72415e14	+	5.86014e13i	0.595872	+	0.0610028i
$993$	−1.25580e15			−1.30069
$994$	−1.73498e14	+	2.28832e14i	−0.178798	+	0.235822i
$995$	4.77517e14	−	4.77517e14i	0.489636	−	0.489636i
$996$	7.21794e14	−	2.02369e14i	0.736404	−	0.206465i
$997$	−8.84485e14	+	8.84485e14i	−0.897873	+	0.897873i	−0.995248	−	0.0973750i	$-0.968955\pi$
$997$	−8.84485e14	+	8.84485e14i	−0.897873	+	0.897873i	0.0973750	+	0.995248i	$0.468955\pi$
$998$	−1.87651e14	−	1.36441e15i	−0.189539	−	1.37814i
$999$	−4.19307e14			−0.421410

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.11.f.a.3.5	✓	38
4.3	odd	2		64.11.f.a.47.17		38
8.3	odd	2		128.11.f.a.95.3		38
8.5	even	2		128.11.f.b.95.17		38
16.3	odd	4		128.11.f.b.31.17		38
16.5	even	4		64.11.f.a.15.17		38
16.11	odd	4	inner	16.11.f.a.11.5	yes	38
16.13	even	4		128.11.f.a.31.3		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.11.f.a.3.5	✓	38	1.1	even	1	trivial
16.11.f.a.11.5	yes	38	16.11	odd	4	inner
64.11.f.a.15.17		38	16.5	even	4
64.11.f.a.47.17		38	4.3	odd	2
128.11.f.a.31.3		38	16.13	even	4
128.11.f.a.95.3		38	8.3	odd	2
128.11.f.b.31.17		38	16.3	odd	4
128.11.f.b.95.17		38	8.5	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.3334 + 25.4994i) q^{2} +(-222.022 + 222.022i) q^{3} +(-276.439 - 985.981i) q^{4} +(-2711.76 + 2711.76i) q^{5} +(-1368.99 - 9953.89i) q^{6} -24891.4 q^{7} +(30486.4 + 12013.3i) q^{8} -39538.9i q^{9} +(-16720.7 - 121576. i) q^{10} +(158032. + 158032. i) q^{11} +(280285. + 157534. i) q^{12} +(-26357.8 - 26357.8i) q^{13} +(481236. - 634716. i) q^{14} -1.20414e6i q^{15} +(-895739. + 545126. i) q^{16} +1.46407e6 q^{17} +(1.00822e6 + 764422. i) q^{18} +(218956. - 218956. i) q^{19} +(3.42337e6 + 1.92410e6i) q^{20} +(5.52645e6 - 5.52645e6i) q^{21} +(-7.08500e6 + 974421. i) q^{22} -1.19227e7 q^{23} +(-9.43590e6 + 4.10144e6i) q^{24} -4.94162e6i q^{25} +(1.18169e6 - 162522. i) q^{26} +(-4.33167e6 - 4.33167e6i) q^{27} +(6.88095e6 + 2.45424e7i) q^{28} +(3.24715e6 + 3.24715e6i) q^{29} +(3.07049e7 + 2.32802e7i) q^{30} +1.71485e7i q^{31} +(3.41730e6 - 3.33800e7i) q^{32} -7.01731e7 q^{33} +(-2.83054e7 + 3.73329e7i) q^{34} +(6.74994e7 - 6.74994e7i) q^{35} +(-3.89846e7 + 1.09301e7i) q^{36} +(4.84002e7 - 4.84002e7i) q^{37} +(1.35008e6 + 9.81640e6i) q^{38} +1.17040e7 q^{39} +(-1.15249e8 + 5.00945e7i) q^{40} -2.01482e8i q^{41} +(3.40761e7 + 2.47766e8i) q^{42} +(-4.62694e7 - 4.62694e7i) q^{43} +(1.12130e8 - 1.99502e8i) q^{44} +(1.07220e8 + 1.07220e8i) q^{45} +(2.30507e8 - 3.04022e8i) q^{46} +3.80755e8i q^{47} +(7.78439e7 - 3.19905e8i) q^{48} +3.37107e8 q^{49} +(1.26008e8 + 9.55383e7i) q^{50} +(-3.25056e8 + 3.25056e8i) q^{51} +(-1.87019e7 + 3.32745e7i) q^{52} +(-1.53875e7 + 1.53875e7i) q^{53} +(1.94201e8 - 2.67091e7i) q^{54} -8.57086e8 q^{55} +(-7.58850e8 - 2.99029e8i) q^{56} +9.72262e7i q^{57} +(-1.45579e8 + 2.00219e7i) q^{58} +(3.55533e8 + 3.55533e8i) q^{59} +(-1.18726e9 + 3.32871e8i) q^{60} +(-6.17762e7 - 6.17762e7i) q^{61} +(-4.37275e8 - 3.31538e8i) q^{62} +9.84180e8i q^{63} +(7.85101e8 + 7.32488e8i) q^{64} +1.42952e8 q^{65} +(1.35668e9 - 1.78937e9i) q^{66} +(-8.03411e8 + 8.03411e8i) q^{67} +(-4.04725e8 - 1.44354e9i) q^{68} +(2.64711e9 - 2.64711e9i) q^{69} +(4.16201e8 + 3.02619e9i) q^{70} -3.60526e8 q^{71} +(4.74995e8 - 1.20540e9i) q^{72} +2.16123e9i q^{73} +(2.98435e8 + 2.16991e9i) q^{74} +(1.09715e9 + 1.09715e9i) q^{75} +(-2.76414e8 - 1.55358e8i) q^{76} +(-3.93363e9 - 3.93363e9i) q^{77} +(-2.26279e8 + 2.98446e8i) q^{78} -3.90441e9i q^{79} +(9.50777e8 - 3.90728e9i) q^{80} +4.25819e9 q^{81} +(5.13768e9 + 3.89534e9i) q^{82} +(1.64861e9 - 1.64861e9i) q^{83} +(-6.97670e9 - 3.92125e9i) q^{84} +(-3.97020e9 + 3.97020e9i) q^{85} +(2.07439e9 - 2.85297e8i) q^{86} -1.44188e9 q^{87} +(2.91933e9 + 6.71630e9i) q^{88} -4.00320e9i q^{89} +(-4.80697e9 + 6.61117e8i) q^{90} +(6.56082e8 + 6.56082e8i) q^{91} +(3.29590e9 + 1.17556e10i) q^{92} +(-3.80734e9 - 3.80734e9i) q^{93} +(-9.70903e9 - 7.36129e9i) q^{94} +1.18751e9i q^{95} +(6.65238e9 + 8.16982e9i) q^{96} +1.30440e9 q^{97} +(-6.51743e9 + 8.59603e9i) q^{98} +(6.24840e9 - 6.24840e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18}+ \cdots - 25616384098 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8 - 147364 * q^10 - 45906 * q^11 - 10988 * q^12 - 2 * q^13 + 757836 * q^14 - 469032 * q^16 - 4 * q^17 + 2066926 * q^18 - 5107042 * q^19 + 5301516 * q^20 - 118100 * q^21 - 20568924 * q^22 - 8279748 * q^23 + 58519728 * q^24 - 18451512 * q^26 - 25871552 * q^27 - 36459784 * q^28 - 29652306 * q^29 + 132781252 * q^30 - 52661752 * q^32 - 4 * q^33 + 68474900 * q^34 + 14674460 * q^35 - 15810676 * q^36 - 94618130 * q^37 + 156046000 * q^38 - 279841732 * q^39 - 125381720 * q^40 + 107395416 * q^42 + 172486862 * q^43 + 73663988 * q^44 + 19649346 * q^45 - 437620836 * q^46 + 625190376 * q^48 + 1049193778 * q^49 - 875760314 * q^50 - 72924900 * q^51 - 771392444 * q^52 + 607072398 * q^53 + 913650464 * q^54 - 1427102468 * q^55 - 1385623464 * q^56 + 37561720 * q^58 + 1543683854 * q^59 + 318869600 * q^60 + 1673280158 * q^61 - 983062992 * q^62 - 867678656 * q^64 + 1098715212 * q^65 + 768197860 * q^66 - 4830427746 * q^67 - 855827792 * q^68 + 1698121420 * q^69 - 5103882496 * q^70 + 7572888316 * q^71 + 6888513460 * q^72 + 2513658844 * q^74 - 11656678318 * q^75 - 2250244316 * q^76 - 1336459028 * q^77 + 14243324268 * q^78 - 13115458328 * q^80 - 8523250762 * q^81 + 2724305648 * q^82 + 16141605438 * q^83 - 1633924184 * q^84 + 4779968748 * q^85 - 4025865500 * q^86 - 31832612676 * q^87 + 1023457912 * q^88 + 18960485240 * q^90 + 19874217404 * q^91 + 28060187160 * q^92 - 15001617056 * q^93 - 14829002256 * q^94 + 23525947312 * q^96 - 4 * q^97 - 43134832310 * q^98 - 25616384098 * q^99

Introduction

L-functions

Modular forms

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