LMFDB - Embedded newform 16.11.f.a.3.7

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			3.7
Character	$\chi$	$=$	16.3
Dual form			16.11.f.a.11.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-16.8116 - 27.2281i) q^{2} +(183.793 - 183.793i) q^{3} +(-458.741 + 915.496i) q^{4} +(3496.01 - 3496.01i) q^{5} +(-8094.18 - 1914.49i) q^{6} +26135.6 q^{7} +(32639.4 - 2900.27i) q^{8} -8510.59i q^{9} +(-153963. - 36416.3i) q^{10} +(-23602.7 - 23602.7i) q^{11} +(83948.2 + 252575. i) q^{12} +(-198530. - 198530. i) q^{13} +(-439381. - 711623. i) q^{14} -1.28508e6i q^{15} +(-627689. - 839951. i) q^{16} -37124.7 q^{17} +(-231727. + 143076. i) q^{18} +(-2.46575e6 + 2.46575e6i) q^{19} +(1.59682e6 + 4.80434e6i) q^{20} +(4.80353e6 - 4.80353e6i) q^{21} +(-245858. + 1.03946e6i) q^{22} -928760. q^{23} +(5.46584e6 - 6.53193e6i) q^{24} -1.46785e7i q^{25} +(-2.06800e6 + 8.74322e6i) q^{26} +(9.28860e6 + 9.28860e6i) q^{27} +(-1.19895e7 + 2.39270e7i) q^{28} +(2.31954e7 + 2.31954e7i) q^{29} +(-3.49904e7 + 2.16043e7i) q^{30} -4.20509e7i q^{31} +(-1.23179e7 + 3.12117e7i) q^{32} -8.67601e6 q^{33} +(624126. + 1.01084e6i) q^{34} +(9.13702e7 - 9.13702e7i) q^{35} +(7.79141e6 + 3.90416e6i) q^{36} +(-7.15654e7 + 7.15654e7i) q^{37} +(1.08591e8 + 2.56846e7i) q^{38} -7.29769e7 q^{39} +(1.03968e8 - 1.24247e8i) q^{40} -3.19196e7i q^{41} +(-2.11546e8 - 5.00362e7i) q^{42} +(-7.38726e7 - 7.38726e7i) q^{43} +(3.24357e7 - 1.07806e7i) q^{44} +(-2.97531e7 - 2.97531e7i) q^{45} +(1.56139e7 + 2.52884e7i) q^{46} -4.97800e6i q^{47} +(-2.69742e8 - 3.90124e7i) q^{48} +4.00594e8 q^{49} +(-3.99668e8 + 2.46769e8i) q^{50} +(-6.82326e6 + 6.82326e6i) q^{51} +(2.72828e8 - 9.06796e7i) q^{52} +(-4.22772e8 + 4.22772e8i) q^{53} +(9.67550e7 - 4.09067e8i) q^{54} -1.65030e8 q^{55} +(8.53050e8 - 7.58002e7i) q^{56} +9.06373e8i q^{57} +(2.41616e8 - 1.02152e9i) q^{58} +(-2.04599e8 - 2.04599e8i) q^{59} +(1.17649e9 + 5.89520e8i) q^{60} +(9.65784e8 + 9.65784e8i) q^{61} +(-1.14497e9 + 7.06942e8i) q^{62} -2.22429e8i q^{63} +(1.05692e9 - 1.89326e8i) q^{64} -1.38813e9 q^{65} +(1.45857e8 + 2.36231e8i) q^{66} +(-4.22476e7 + 4.22476e7i) q^{67} +(1.70307e7 - 3.39875e7i) q^{68} +(-1.70699e8 + 1.70699e8i) q^{69} +(-4.02392e9 - 9.51762e8i) q^{70} +1.24987e9 q^{71} +(-2.46830e7 - 2.77780e8i) q^{72} +1.86037e8i q^{73} +(3.15172e9 + 7.45464e8i) q^{74} +(-2.69781e9 - 2.69781e9i) q^{75} +(-1.12624e9 - 3.38852e9i) q^{76} +(-6.16870e8 - 6.16870e8i) q^{77} +(1.22686e9 + 1.98702e9i) q^{78} -3.24767e9i q^{79} +(-5.13088e9 - 7.42072e8i) q^{80} +3.91690e9 q^{81} +(-8.69110e8 + 5.36618e8i) q^{82} +(1.80568e9 - 1.80568e9i) q^{83} +(2.19403e9 + 6.60119e9i) q^{84} +(-1.29788e8 + 1.29788e8i) q^{85} +(-7.69497e8 + 3.25333e9i) q^{86} +8.52631e9 q^{87} +(-8.38832e8 - 7.01923e8i) q^{88} +1.74176e9i q^{89} +(-3.09924e8 + 1.31032e9i) q^{90} +(-5.18871e9 - 5.18871e9i) q^{91} +(4.26060e8 - 8.50275e8i) q^{92} +(-7.72865e9 - 7.72865e9i) q^{93} +(-1.35542e8 + 8.36880e7i) q^{94} +1.72405e10i q^{95} +(3.47255e9 + 8.00042e9i) q^{96} +1.21698e10 q^{97} +(-6.73462e9 - 1.09074e10i) q^{98} +(-2.00873e8 + 2.00873e8i) 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 $

$2$	−16.8116	−	27.2281i	−0.525362	−	0.850879i
$2$	−16.8116	−	27.2281i	−0.525362	−	0.850879i
$3$	183.793	−	183.793i	0.756349	−	0.756349i	−0.219307	−	0.975656i	$-0.570380\pi$
$3$	183.793	−	183.793i	0.756349	−	0.756349i	0.975656	+	0.219307i	$0.0703796\pi$
$4$	−458.741	+	915.496i	−0.447990	+	0.894039i
$5$	3496.01	−	3496.01i	1.11872	−	1.11872i	0.126793	−	0.991929i	$-0.459531\pi$
$5$	3496.01	−	3496.01i	1.11872	−	1.11872i	0.991929	−	0.126793i	$-0.0404685\pi$
$6$	−8094.18	−	1914.49i	−1.04092	−	0.246204i
$7$	26135.6			1.55504			0.777521	−	0.628857i	$-0.216477\pi$
$7$	26135.6			1.55504			0.777521	+	0.628857i	$0.216477\pi$
$8$	32639.4	−	2900.27i	0.996075	−	0.0885091i
$9$		−	8510.59i		−	0.144128i
$10$	−153963.	−	36416.3i	−1.53963	−	0.364163i
$11$	−23602.7	−	23602.7i	−0.146554	−	0.146554i	0.630023	−	0.776577i	$-0.283046\pi$
$11$	−23602.7	−	23602.7i	−0.146554	−	0.146554i	−0.776577	+	0.630023i	$0.783046\pi$
$12$	83948.2	+	252575.i	0.337369	+	1.01504i
$13$	−198530.	−	198530.i	−0.534700	−	0.534700i	0.387268	−	0.921967i	$-0.373419\pi$
$13$	−198530.	−	198530.i	−0.534700	−	0.534700i	−0.921967	+	0.387268i	$0.873419\pi$
$14$	−439381.	−	711623.i	−0.816960	−	1.32315i
$15$		−	1.28508e6i		−	1.69229i
$16$	−627689.	−	839951.i	−0.598611	−	0.801040i
$17$	−37124.7			−0.0261468			−0.0130734	−	0.999915i	$-0.504162\pi$
$17$	−37124.7			−0.0261468			−0.0130734	+	0.999915i	$0.504162\pi$
$18$	−231727.	+	143076.i	−0.122635	+	0.0757191i
$19$	−2.46575e6	+	2.46575e6i	−0.995819	+	0.995819i	−0.999991	−	0.00417198i	$-0.998672\pi$
$19$	−2.46575e6	+	2.46575e6i	−0.995819	+	0.995819i	0.00417198	+	0.999991i	$0.498672\pi$
$20$	1.59682e6	+	4.80434e6i	0.499005	+	1.50136i
$21$	4.80353e6	−	4.80353e6i	1.17615	−	1.17615i
$22$	−245858.	+	1.03946e6i	−0.0477058	+	0.201694i
$23$	−928760.			−0.144299			−0.0721496	−	0.997394i	$-0.522986\pi$
$23$	−928760.			−0.144299			−0.0721496	+	0.997394i	$0.522986\pi$
$24$	5.46584e6	−	6.53193e6i	0.686437	−	0.820324i
$25$		−	1.46785e7i		−	1.50308i
$26$	−2.06800e6	+	8.74322e6i	−0.174054	+	0.735876i
$27$	9.28860e6	+	9.28860e6i	0.647338	+	0.647338i
$28$	−1.19895e7	+	2.39270e7i	−0.696643	+	1.39027i
$29$	2.31954e7	+	2.31954e7i	1.13087	+	1.13087i	0.990033	+	0.140837i	$0.0449794\pi$
$29$	2.31954e7	+	2.31954e7i	1.13087	+	1.13087i	0.140837	+	0.990033i	$0.455021\pi$
$30$	−3.49904e7	+	2.16043e7i	−1.43993	+	0.889064i
$31$		−	4.20509e7i		−	1.46881i	−0.678710	−	0.734407i	$-0.737461\pi$
$31$		−	4.20509e7i		−	1.46881i	0.678710	−	0.734407i	$-0.262539\pi$
$32$	−1.23179e7	+	3.12117e7i	−0.367101	+	0.930181i
$33$	−8.67601e6			−0.221692
$34$	624126.	+	1.01084e6i	0.0137365	+	0.0222478i
$35$	9.13702e7	−	9.13702e7i	1.73966	−	1.73966i
$36$	7.79141e6	+	3.90416e6i	0.128856	+	0.0645676i
$37$	−7.15654e7	+	7.15654e7i	−1.03203	+	1.03203i	−0.0325652	+	0.999470i	$0.510368\pi$
$37$	−7.15654e7	+	7.15654e7i	−1.03203	+	1.03203i	−0.999470	+	0.0325652i	$0.989632\pi$
$38$	1.08591e8	+	2.56846e7i	1.37049	+	0.324156i
$39$	−7.29769e7			−0.808839
$40$	1.03968e8	−	1.24247e8i	1.01531	−	1.21335i
$41$		−	3.19196e7i		−	0.275510i	−0.990466	−	0.137755i	$-0.956011\pi$
$41$		−	3.19196e7i		−	0.275510i	0.990466	−	0.137755i	$-0.0439887\pi$
$42$	−2.11546e8	−	5.00362e7i	−1.61867	−	0.382858i
$43$	−7.38726e7	−	7.38726e7i	−0.502506	−	0.502506i	0.409710	−	0.912216i	$-0.365630\pi$
$43$	−7.38726e7	−	7.38726e7i	−0.502506	−	0.502506i	−0.912216	+	0.409710i	$0.865630\pi$
$44$	3.24357e7	−	1.07806e7i	0.196680	−	0.0653703i
$45$	−2.97531e7	−	2.97531e7i	−0.161239	−	0.161239i
$46$	1.56139e7	+	2.52884e7i	0.0758094	+	0.122781i
$47$		−	4.97800e6i		−	0.0217053i	−0.999941	−	0.0108526i	$-0.996545\pi$
$47$		−	4.97800e6i		−	0.0217053i	0.999941	−	0.0108526i	$-0.00345457\pi$
$48$	−2.69742e8	−	3.90124e7i	−1.05862	−	0.153107i
$49$	4.00594e8			1.41816
$50$	−3.99668e8	+	2.46769e8i	−1.27894	+	0.789661i
$51$	−6.82326e6	+	6.82326e6i	−0.0197761	+	0.0197761i
$52$	2.72828e8	−	9.06796e7i	0.717582	−	0.238502i
$53$	−4.22772e8	+	4.22772e8i	−1.01094	+	1.01094i	−0.0110035	+	0.999939i	$0.503503\pi$
$53$	−4.22772e8	+	4.22772e8i	−1.01094	+	1.01094i	−0.999939	+	0.0110035i	$0.996497\pi$
$54$	9.67550e7	−	4.09067e8i	0.210720	−	0.890893i
$55$	−1.65030e8			−0.327907
$56$	8.53050e8	−	7.58002e7i	1.54894	−	0.137635i
$57$			9.06373e8i			1.50637i
$58$	2.41616e8	−	1.02152e9i	0.368117	−	1.55635i
$59$	−2.04599e8	−	2.04599e8i	−0.286183	−	0.286183i	0.549386	−	0.835569i	$-0.314862\pi$
$59$	−2.04599e8	−	2.04599e8i	−0.286183	−	0.286183i	−0.835569	+	0.549386i	$0.814862\pi$
$60$	1.17649e9	+	5.89520e8i	1.51297	+	0.758128i
$61$	9.65784e8	+	9.65784e8i	1.14349	+	1.14349i	0.987808	+	0.155678i	$0.0497563\pi$
$61$	9.65784e8	+	9.65784e8i	1.14349	+	1.14349i	0.155678	+	0.987808i	$0.450244\pi$
$62$	−1.14497e9	+	7.06942e8i	−1.24978	+	0.771659i
$63$		−	2.22429e8i		−	0.224124i
$64$	1.05692e9	−	1.89326e8i	0.984332	−	0.176323i
$65$	−1.38813e9			−1.19636
$66$	1.45857e8	+	2.36231e8i	0.116469	+	0.188633i
$67$	−4.22476e7	+	4.22476e7i	−0.0312916	+	0.0312916i	−0.722579	−	0.691288i	$-0.757044\pi$
$67$	−4.22476e7	+	4.22476e7i	−0.0312916	+	0.0312916i	0.691288	+	0.722579i	$0.257044\pi$
$68$	1.70307e7	−	3.39875e7i	0.0117135	−	0.0233763i
$69$	−1.70699e8	+	1.70699e8i	−0.109141	+	0.109141i
$70$	−4.02392e9	−	9.51762e8i	−2.39419	−	0.566289i
$71$	1.24987e9			0.692747			0.346373	−	0.938097i	$-0.387413\pi$
$71$	1.24987e9			0.692747			0.346373	+	0.938097i	$0.387413\pi$
$72$	−2.46830e7	−	2.77780e8i	−0.0127566	−	0.143562i
$73$			1.86037e8i			0.0897399i	0.998993	+	0.0448700i	$0.0142873\pi$
$73$			1.86037e8i			0.0897399i	−0.998993	+	0.0448700i	$0.985713\pi$
$74$	3.15172e9	+	7.45464e8i	1.42033	+	0.335945i
$75$	−2.69781e9	−	2.69781e9i	−1.13685	−	1.13685i
$76$	−1.12624e9	−	3.38852e9i	−0.444184	−	1.33642i
$77$	−6.16870e8	−	6.16870e8i	−0.227898	−	0.227898i
$78$	1.22686e9	+	1.98702e9i	0.424933	+	0.688224i
$79$		−	3.24767e9i		−	1.05545i	−0.849417	−	0.527723i	$-0.823046\pi$
$79$		−	3.24767e9i		−	1.05545i	0.849417	−	0.527723i	$-0.176954\pi$
$80$	−5.13088e9	−	7.42072e8i	−1.56582	−	0.226463i
$81$	3.91690e9			1.12335
$82$	−8.69110e8	+	5.36618e8i	−0.234426	+	0.144743i
$83$	1.80568e9	−	1.80568e9i	0.458407	−	0.458407i	−0.439725	−	0.898132i	$-0.644924\pi$
$83$	1.80568e9	−	1.80568e9i	0.458407	−	0.458407i	0.898132	+	0.439725i	$0.144924\pi$
$84$	2.19403e9	+	6.60119e9i	0.524623	+	1.57843i
$85$	−1.29788e8	+	1.29788e8i	−0.0292510	+	0.0292510i
$86$	−7.69497e8	+	3.25333e9i	−0.163574	+	0.691569i
$87$	8.52631e9			1.71066
$88$	−8.38832e8	−	7.01923e8i	−0.158950	−	0.133008i
$89$			1.74176e9i			0.311916i	0.987764	+	0.155958i	$0.0498465\pi$
$89$			1.74176e9i			0.311916i	−0.987764	+	0.155958i	$0.950154\pi$
$90$	−3.09924e8	+	1.31032e9i	−0.0524859	+	0.221903i
$91$	−5.18871e9	−	5.18871e9i	−0.831481	−	0.831481i
$92$	4.26060e8	−	8.50275e8i	0.0646446	−	0.129009i
$93$	−7.72865e9	−	7.72865e9i	−1.11094	−	1.11094i
$94$	−1.35542e8	+	8.36880e7i	−0.0184686	+	0.0114031i
$95$			1.72405e10i			2.22809i
$96$	3.47255e9	+	8.00042e9i	0.425885	+	0.981198i
$97$	1.21698e10			1.41718			0.708588	−	0.705622i	$-0.249332\pi$
$97$	1.21698e10			1.41718			0.708588	+	0.705622i	$0.249332\pi$
$98$	−6.73462e9	−	1.09074e10i	−0.745045	−	1.20668i
$99$	−2.00873e8	+	2.00873e8i	−0.0211225	+	0.0211225i
$100$	1.34381e10	+	6.73364e9i	1.34381	+	0.673364i
$101$	−1.09920e10	+	1.09920e10i	−1.04585	+	1.04585i	−0.0469532	+	0.998897i	$0.514951\pi$
$101$	−1.09920e10	+	1.09920e10i	−1.04585	+	1.04585i	−0.998897	+	0.0469532i	$0.985049\pi$
$102$	3.00494e8	+	7.10747e7i	0.0272167	+	0.00643746i
$103$	−1.00075e10			−0.863258			−0.431629	−	0.902051i	$-0.642061\pi$
$103$	−1.00075e10			−0.863258			−0.431629	+	0.902051i	$0.642061\pi$
$104$	−7.05570e9	−	5.90412e9i	−0.579927	−	0.485276i
$105$		−	3.35864e10i		−	2.63158i
$106$	1.86187e10	+	4.40382e9i	1.39130	+	0.329079i
$107$	5.65526e9	+	5.65526e9i	0.403212	+	0.403212i	0.879363	−	0.476151i	$-0.157969\pi$
$107$	5.65526e9	+	5.65526e9i	0.403212	+	0.403212i	−0.476151	+	0.879363i	$0.657969\pi$
$108$	−1.27647e10	+	4.24261e9i	−0.868746	+	0.288745i
$109$	1.19223e10	+	1.19223e10i	0.774870	+	0.774870i	0.978954	−	0.204083i	$-0.0654213\pi$
$109$	1.19223e10	+	1.19223e10i	0.774870	+	0.774870i	−0.204083	+	0.978954i	$0.565421\pi$
$110$	2.77442e9	+	4.49347e9i	0.172270	+	0.279009i
$111$			2.63064e10i			1.56116i
$112$	−1.64050e10	−	2.19526e10i	−0.930865	−	1.24565i
$113$	5.34527e9			0.290120			0.145060	−	0.989423i	$-0.453662\pi$
$113$	5.34527e9			0.290120			0.145060	+	0.989423i	$0.453662\pi$
$114$	2.46788e10	−	1.52376e10i	1.28174	−	0.791392i
$115$	−3.24695e9	+	3.24695e9i	−0.161431	+	0.161431i
$116$	−3.18760e10	+	1.05946e10i	−1.51766	+	0.504424i
$117$	−1.68961e9	+	1.68961e9i	−0.0770650	+	0.0770650i
$118$	−2.13122e9	+	9.01049e9i	−0.0931574	+	0.393857i
$119$	−9.70277e8			−0.0406594
$120$	−3.72708e9	−	4.19443e10i	−0.149783	−	1.68565i
$121$		−	2.48233e10i		−	0.957044i
$122$	1.00601e10	−	4.25328e10i	0.372224	−	1.57371i
$123$	−5.86658e9	−	5.86658e9i	−0.208382	−	0.208382i
$124$	3.84974e10	+	1.92905e10i	1.31318	+	0.658013i
$125$	−1.71755e10	−	1.71755e10i	−0.562807	−	0.562807i
$126$	−6.05633e9	+	3.73939e9i	−0.190703	+	0.117746i
$127$			6.34853e9i			0.192156i	0.995374	+	0.0960781i	$0.0306299\pi$
$127$			6.34853e9i			0.192156i	−0.995374	+	0.0960781i	$0.969370\pi$
$128$	−2.29235e10	−	2.55950e10i	−0.667161	−	0.744914i
$129$	−2.71545e10			−0.760140
$130$	2.33366e10	+	3.77961e10i	0.628523	+	1.01796i
$131$	−2.58385e10	+	2.58385e10i	−0.669746	+	0.669746i	−0.957657	−	0.287911i	$-0.907039\pi$
$131$	−2.58385e10	+	2.58385e10i	−0.669746	+	0.669746i	0.287911	+	0.957657i	$0.407039\pi$
$132$	3.98004e9	−	7.94285e9i	0.0993158	−	0.198201i
$133$	−6.44438e10	+	6.44438e10i	−1.54854	+	1.54854i
$134$	1.86057e9	+	4.40074e8i	0.0430648	+	0.0101859i
$135$	6.49460e10			1.44838
$136$	−1.21173e9	+	1.07672e8i	−0.0260442	+	0.00231423i
$137$			1.89659e10i			0.392980i	0.980506	+	0.196490i	$0.0629543\pi$
$137$			1.89659e10i			0.392980i	−0.980506	+	0.196490i	$0.937046\pi$
$138$	7.51755e9	+	1.77810e9i	0.150204	+	0.0355271i
$139$	−1.93924e10	−	1.93924e10i	−0.373729	−	0.373729i	0.495104	−	0.868834i	$-0.335130\pi$
$139$	−1.93924e10	−	1.93924e10i	−0.373729	−	0.373729i	−0.868834	+	0.495104i	$0.835130\pi$
$140$	4.17338e10	+	1.25564e11i	0.775974	+	2.33467i
$141$	−9.14920e8	−	9.14920e8i	−0.0164168	−	0.0164168i
$142$	−2.10124e10	−	3.40317e10i	−0.363943	−	0.589443i
$143$			9.37170e9i			0.156725i
$144$	−7.14848e9	+	5.34200e9i	−0.115452	+	0.0862763i
$145$	1.62183e11			2.53026
$146$	5.06545e9	−	3.12758e9i	0.0763578	−	0.0471459i
$147$	7.36263e10	−	7.36263e10i	1.07262	−	1.07262i
$148$	−3.26878e10	−	9.83478e10i	−0.460338	−	1.38502i
$149$	6.82578e10	−	6.82578e10i	0.929439	−	0.929439i	−0.0682304	−	0.997670i	$-0.521735\pi$
$149$	6.82578e10	−	6.82578e10i	0.929439	−	0.929439i	0.997670	+	0.0682304i	$0.0217353\pi$
$150$	−2.81018e10	+	1.18811e11i	−0.370065	+	1.56458i
$151$	6.53650e10			0.832646			0.416323	−	0.909217i	$-0.363319\pi$
$151$	6.53650e10			0.832646			0.416323	+	0.909217i	$0.363319\pi$
$152$	−7.33292e10	+	8.76318e10i	−0.903772	+	1.08005i
$153$			3.15953e8i			0.00376848i
$154$	−6.42565e9	+	2.71668e10i	−0.0741846	+	0.313642i
$155$	−1.47010e11	−	1.47010e11i	−1.64319	−	1.64319i
$156$	3.34775e10	−	6.68100e10i	0.362352	−	0.723134i
$157$	−4.64668e10	−	4.64668e10i	−0.487130	−	0.487130i	0.420270	−	0.907399i	$-0.361936\pi$
$157$	−4.64668e10	−	4.64668e10i	−0.487130	−	0.487130i	−0.907399	+	0.420270i	$0.861936\pi$
$158$	−8.84278e10	+	5.45984e10i	−0.898056	+	0.554491i
$159$			1.55405e11i			1.52925i
$160$	6.60530e10	+	1.52180e11i	0.629931	+	1.45130i
$161$	−2.42737e10			−0.224391
$162$	−6.58492e10	−	1.06650e11i	−0.590168	−	0.955839i
$163$	−1.94881e10	+	1.94881e10i	−0.169368	+	0.169368i	−0.786701	−	0.617334i	$-0.788213\pi$
$163$	−1.94881e10	+	1.94881e10i	−0.169368	+	0.169368i	0.617334	+	0.786701i	$0.288213\pi$
$164$	2.92222e10	+	1.46428e10i	0.246317	+	0.123426i
$165$	−3.03314e10	+	3.03314e10i	−0.248012	+	0.248012i
$166$	−7.95218e10	−	1.88090e10i	−0.630879	−	0.149219i
$167$	−1.78588e11			−1.37490			−0.687450	−	0.726232i	$-0.741270\pi$
$167$	−1.78588e11			−1.37490			−0.687450	+	0.726232i	$0.741270\pi$
$168$	1.42853e11	−	1.70716e11i	1.06744	−	1.27564i
$169$		−	5.90299e10i		−	0.428192i
$170$	5.71584e9	+	1.35195e9i	0.0402565	+	0.00952170i
$171$	2.09850e10	+	2.09850e10i	0.143525	+	0.143525i
$172$	1.01518e11	−	3.37416e10i	0.674377	−	0.224142i
$173$	5.79481e10	+	5.79481e10i	0.373946	+	0.373946i	0.868912	−	0.494966i	$-0.164820\pi$
$173$	5.79481e10	+	5.79481e10i	0.373946	+	0.373946i	−0.494966	+	0.868912i	$0.664820\pi$
$174$	−1.43341e11	−	2.32155e11i	−0.898718	−	1.45557i
$175$		−	3.83632e11i		−	2.33735i
$176$	−5.00997e9	+	3.46403e10i	−0.0296669	+	0.205125i
$177$	−7.52077e10			−0.432909
$178$	4.74248e10	−	2.92817e10i	0.265403	−	0.163869i
$179$	9.96053e10	−	9.96053e10i	0.542023	−	0.542023i	−0.382099	−	0.924121i	$-0.624799\pi$
$179$	9.96053e10	−	9.96053e10i	0.542023	−	0.542023i	0.924121	+	0.382099i	$0.124799\pi$
$180$	4.08878e10	−	1.35898e10i	0.216387	−	0.0719204i
$181$	−1.43128e11	+	1.43128e11i	−0.736770	+	0.736770i	−0.971952	−	0.235181i	$-0.924432\pi$
$181$	−1.43128e11	+	1.43128e11i	−0.736770	+	0.736770i	0.235181	+	0.971952i	$0.424432\pi$
$182$	−5.40484e10	+	2.28509e11i	−0.270661	+	1.14432i
$183$	3.55008e11			1.72975
$184$	−3.03142e10	+	2.69365e9i	−0.143733	+	0.0127718i
$185$			5.00386e11i			2.30912i
$186$	−8.05058e10	+	3.40367e11i	−0.361628	+	1.52891i
$187$	8.76244e8	+	8.76244e8i	0.00383192	+	0.00383192i
$188$	4.55734e9	+	2.28361e9i	0.0194054	+	0.00972374i
$189$	2.42763e11	+	2.42763e11i	1.00664	+	1.00664i
$190$	4.69428e11	−	2.89841e11i	1.89584	−	1.17055i
$191$		−	1.17738e11i		−	0.463180i	−0.972813	−	0.231590i	$-0.925607\pi$
$191$		−	1.17738e11i		−	0.463180i	0.972813	−	0.231590i	$-0.0743928\pi$
$192$	1.59457e11	−	2.29051e11i	0.611137	−	0.877861i
$193$	−3.28289e11			−1.22594			−0.612970	−	0.790106i	$-0.710025\pi$
$193$	−3.28289e11			−1.22594			−0.612970	+	0.790106i	$0.710025\pi$
$194$	−2.04593e11	−	3.31360e11i	−0.744531	−	1.20585i
$195$	−2.55128e11	+	2.55128e11i	−0.904867	+	0.904867i
$196$	−1.83769e11	+	3.66742e11i	−0.635319	+	1.26789i
$197$	1.07459e11	−	1.07459e11i	0.362169	−	0.362169i	−0.502442	−	0.864611i	$-0.667565\pi$
$197$	1.07459e11	−	1.07459e11i	0.362169	−	0.362169i	0.864611	+	0.502442i	$0.167565\pi$
$198$	8.84638e9	+	2.09240e9i	0.0290696	+	0.00687573i
$199$	−5.25486e11			−1.68382			−0.841911	−	0.539617i	$-0.818569\pi$
$199$	−5.25486e11			−1.68382			−0.841911	+	0.539617i	$0.818569\pi$
$200$	−4.25716e10	−	4.79098e11i	−0.133036	−	1.49718i
$201$			1.55296e10i			0.0473348i
$202$	4.84084e11	+	1.14499e11i	1.43934	+	0.340442i
$203$	6.06227e11	+	6.06227e11i	1.75855	+	1.75855i
$204$	−3.11655e9	−	9.37678e9i	−0.00882112	−	0.0265401i
$205$	−1.11591e11	−	1.11591e11i	−0.308219	−	0.308219i
$206$	1.68242e11	+	2.72486e11i	0.453523	+	0.734528i
$207$			7.90429e9i			0.0207975i
$208$	−4.21406e10	+	2.91371e11i	−0.108239	+	0.748393i
$209$	1.16397e11			0.291883
$210$	−9.14494e11	+	5.64640e11i	−2.23916	+	1.38253i
$211$	2.23137e9	−	2.23137e9i	0.00533531	−	0.00533531i	−0.704434	−	0.709769i	$-0.748799\pi$
$211$	2.23137e9	−	2.23137e9i	0.00533531	−	0.00533531i	0.709769	+	0.704434i	$0.248799\pi$
$212$	−1.93103e11	−	5.80989e11i	−0.450930	−	1.35671i
$213$	2.29718e11	−	2.29718e11i	0.523958	−	0.523958i
$214$	5.89082e10	−	2.49056e11i	0.131252	−	0.554917i
$215$	−5.16518e11			−1.12433
$216$	3.30114e11	+	2.76235e11i	0.702093	+	0.587502i
$217$		−	1.09902e12i		−	2.28407i
$218$	1.24190e11	−	5.25056e11i	0.252233	−	1.06641i
$219$	3.41923e10	+	3.41923e10i	0.0678747	+	0.0678747i
$220$	7.57063e10	−	1.51085e11i	0.146899	−	0.293161i
$221$	7.37039e9	+	7.37039e9i	0.0139807	+	0.0139807i
$222$	7.16274e11	−	4.42252e11i	1.32836	−	0.820172i
$223$			4.18867e11i			0.759542i	0.925081	+	0.379771i	$0.123997\pi$
$223$			4.18867e11i			0.759542i	−0.925081	+	0.379771i	$0.876003\pi$
$224$	−3.21935e11	+	8.15736e11i	−0.570857	+	1.44647i
$225$	−1.24923e11			−0.216635
$226$	−8.98625e10	−	1.45542e11i	−0.152418	−	0.246857i
$227$	3.41296e11	−	3.41296e11i	0.566241	−	0.566241i	−0.364832	−	0.931073i	$-0.618874\pi$
$227$	3.41296e11	−	3.41296e11i	0.566241	−	0.566241i	0.931073	+	0.364832i	$0.118874\pi$
$228$	−8.29781e11	−	4.15791e11i	−1.34676	−	0.674840i
$229$	2.37059e11	−	2.37059e11i	0.376426	−	0.376426i	−0.493385	−	0.869811i	$-0.664241\pi$
$229$	2.37059e11	−	2.37059e11i	0.376426	−	0.376426i	0.869811	+	0.493385i	$0.164241\pi$
$230$	1.42995e11	+	3.38220e10i	0.222168	+	0.0525485i
$231$	−2.26753e11			−0.344741
$232$	8.24358e11	+	6.89812e11i	1.22652	+	1.02634i
$233$			7.99650e11i			1.16445i	0.813028	+	0.582224i	$0.197817\pi$
$233$			7.99650e11i			1.16445i	−0.813028	+	0.582224i	$0.802183\pi$
$234$	7.44099e10	+	1.75999e10i	0.106060	+	0.0250860i
$235$	−1.74031e10	−	1.74031e10i	−0.0242822	−	0.0242822i
$236$	2.81168e11	−	9.34516e10i	0.384066	−	0.127652i
$237$	−5.96897e11	−	5.96897e11i	−0.798285	−	0.798285i
$238$	1.63119e10	+	2.64188e10i	0.0213609	+	0.0345962i
$239$		−	6.33692e11i		−	0.812622i	−0.913735	−	0.406311i	$-0.866815\pi$
$239$		−	6.33692e11i		−	0.812622i	0.913735	−	0.406311i	$-0.133185\pi$
$240$	−1.07941e12	+	8.06632e11i	−1.35559	+	1.01302i
$241$	−6.63015e11			−0.815527			−0.407763	−	0.913088i	$-0.633691\pi$
$241$	−6.63015e11			−0.815527			−0.407763	+	0.913088i	$0.633691\pi$
$242$	−6.75891e11	+	4.17318e11i	−0.814328	+	0.502794i
$243$	1.71415e11	−	1.71415e11i	0.202310	−	0.202310i
$244$	−1.32722e12	+	4.41126e11i	−1.53459	+	0.510051i
$245$	1.40048e12	−	1.40048e12i	1.58652	−	1.58652i
$246$	−6.11095e10	+	2.58363e11i	−0.0678318	+	0.286784i
$247$	9.79051e11			1.06493
$248$	−1.21959e11	−	1.37252e12i	−0.130003	−	1.46305i
$249$		−	6.63744e11i		−	0.693432i
$250$	−1.78909e11	+	7.56405e11i	−0.183203	+	0.774558i
$251$	8.91650e11	+	8.91650e11i	0.895006	+	0.895006i	0.994989	−	0.0999833i	$-0.0318789\pi$
$251$	8.91650e11	+	8.91650e11i	0.895006	+	0.895006i	−0.0999833	+	0.994989i	$0.531879\pi$
$252$	2.03633e11	+	1.02037e11i	0.200376	+	0.100405i
$253$	2.19212e10	+	2.19212e10i	0.0211477	+	0.0211477i
$254$	1.72859e11	−	1.06729e11i	0.163502	−	0.100952i
$255$			4.77083e10i			0.0442480i
$256$	−3.11525e11	+	1.05446e12i	−0.283331	+	0.959022i
$257$	5.26674e11			0.469760			0.234880	−	0.972024i	$-0.424530\pi$
$257$	5.26674e11			0.469760			0.234880	+	0.972024i	$0.424530\pi$
$258$	4.56510e11	+	7.39366e11i	0.399348	+	0.646787i
$259$	−1.87040e12	+	1.87040e12i	−1.60486	+	1.60486i
$260$	6.36791e11	−	1.27082e12i	0.535958	−	1.06959i
$261$	1.97407e11	−	1.97407e11i	0.162989	−	0.162989i
$262$	1.13792e12	+	2.69147e11i	0.921732	+	0.218014i
$263$	4.72112e11			0.375203			0.187601	−	0.982245i	$-0.439929\pi$
$263$	4.72112e11			0.375203			0.187601	+	0.982245i	$0.439929\pi$
$264$	−2.83180e11	+	2.51627e10i	−0.220822	+	0.0196218i
$265$			2.95603e12i			2.26193i
$266$	2.83808e12	+	6.71281e11i	2.13117	+	0.504076i
$267$	3.20122e11	+	3.20122e11i	0.235917	+	0.235917i
$268$	−1.92968e10	−	5.80582e10i	−0.0139576	−	0.0419942i
$269$	−6.07912e11	−	6.07912e11i	−0.431598	−	0.431598i	0.457574	−	0.889172i	$-0.348719\pi$
$269$	−6.07912e11	−	6.07912e11i	−0.431598	−	0.431598i	−0.889172	+	0.457574i	$0.848719\pi$
$270$	−1.09185e12	−	1.76836e12i	−0.760926	−	1.23240i
$271$		−	1.05806e12i		−	0.723874i	−0.932202	−	0.361937i	$-0.882115\pi$
$271$		−	1.05806e12i		−	0.723874i	0.932202	−	0.361937i	$-0.117885\pi$
$272$	2.33028e10	+	3.11830e10i	0.0156518	+	0.0209446i
$273$	−1.90729e12			−1.25778
$274$	5.16405e11	−	3.18846e11i	0.334378	−	0.206457i
$275$	−3.46452e11	+	3.46452e11i	−0.220283	+	0.220283i
$276$	−7.79677e10	−	2.34581e11i	−0.0486821	−	0.146470i
$277$	−6.11243e11	+	6.11243e11i	−0.374813	+	0.374813i	−0.869227	−	0.494413i	$-0.835383\pi$
$277$	−6.11243e11	+	6.11243e11i	−0.374813	+	0.374813i	0.494413	+	0.869227i	$0.335383\pi$
$278$	−2.02001e11	+	8.54035e11i	−0.121655	+	0.514341i
$279$	−3.57878e11			−0.211696
$280$	2.71727e12	−	3.24727e12i	1.57886	−	1.88681i
$281$		−	8.13166e11i		−	0.464139i	−0.972699	−	0.232069i	$-0.925450\pi$
$281$		−	8.13166e11i		−	0.464139i	0.972699	−	0.232069i	$-0.0745496\pi$
$282$	−9.53031e9	+	4.02928e10i	−0.00534394	+	0.0225934i
$283$	−1.65712e12	−	1.65712e12i	−0.912895	−	0.912895i	0.0836044	−	0.996499i	$-0.473357\pi$
$283$	−1.65712e12	−	1.65712e12i	−0.912895	−	0.912895i	−0.996499	+	0.0836044i	$0.973357\pi$
$284$	−5.73369e11	+	1.14425e12i	−0.310343	+	0.619342i
$285$	3.16869e12	+	3.16869e12i	1.68521	+	1.68521i
$286$	2.55174e11	−	1.57553e11i	0.133354	−	0.0823373i
$287$		−	8.34237e11i		−	0.428430i
$288$	2.65630e11	+	1.04832e11i	0.134065	+	0.0529093i
$289$	−2.01462e12			−0.999316
$290$	−2.72655e12	−	4.41594e12i	−1.32930	−	2.15294i
$291$	2.23672e12	−	2.23672e12i	1.07188	−	1.07188i
$292$	−1.70316e11	−	8.53430e10i	−0.0802310	−	0.0402025i
$293$	−1.41632e12	+	1.41632e12i	−0.655877	+	0.655877i	−0.954402	−	0.298525i	$-0.903506\pi$
$293$	−1.41632e12	+	1.41632e12i	−0.655877	+	0.655877i	0.298525	+	0.954402i	$0.403506\pi$
$294$	−3.24248e12	−	7.66931e11i	−1.47618	−	0.349156i
$295$	−1.43056e12			−0.640319
$296$	−2.12829e12	+	2.54341e12i	−0.936640	+	1.11933i
$297$		−	4.38472e11i		−	0.189740i
$298$	−3.00605e12	−	7.11010e11i	−1.27913	−	0.302548i
$299$	1.84387e11	+	1.84387e11i	0.0771568	+	0.0771568i
$300$	3.70742e12	−	1.23223e12i	1.52569	−	0.507092i
$301$	−1.93070e12	−	1.93070e12i	−0.781418	−	0.781418i
$302$	−1.09889e12	−	1.77977e12i	−0.437440	−	0.708481i
$303$			4.04050e12i			1.58206i
$304$	3.61883e12	+	5.23386e11i	1.39380	+	0.201583i
$305$	6.75278e12			2.55849
$306$	8.60281e9	−	5.31167e9i	0.00320652	−	0.00197981i
$307$	1.31036e12	−	1.31036e12i	0.480505	−	0.480505i	−0.424788	−	0.905293i	$-0.639651\pi$
$307$	1.31036e12	−	1.31036e12i	0.480505	−	0.480505i	0.905293	+	0.424788i	$0.139651\pi$
$308$	8.47726e11	−	2.81758e11i	0.305845	−	0.101654i
$309$	−1.83931e12	+	1.83931e12i	−0.652924	+	0.652924i
$310$	−1.53134e12	+	6.47429e12i	−0.534887	+	2.26143i
$311$	−2.51450e12			−0.864270			−0.432135	−	0.901809i	$-0.642240\pi$
$311$	−2.51450e12			−0.864270			−0.432135	+	0.901809i	$0.642240\pi$
$312$	−2.38192e12	+	2.11652e11i	−0.805665	+	0.0715896i
$313$		−	2.07780e12i		−	0.691644i	−0.938300	−	0.345822i	$-0.887600\pi$
$313$		−	2.07780e12i		−	0.691644i	0.938300	−	0.345822i	$-0.112400\pi$
$314$	−4.84023e11	+	2.04638e12i	−0.158569	+	0.670408i
$315$	−7.77614e11	−	7.77614e11i	−0.250733	−	0.250733i
$316$	2.97322e12	+	1.48984e12i	0.943609	+	0.472829i
$317$	7.27815e11	+	7.27815e11i	0.227366	+	0.227366i	0.811591	−	0.584226i	$-0.198602\pi$
$317$	7.27815e11	+	7.27815e11i	0.227366	+	0.227366i	−0.584226	+	0.811591i	$0.698602\pi$
$318$	4.23138e12	−	2.61260e12i	1.30121	−	0.803410i
$319$		−	1.09495e12i		−	0.331467i
$320$	3.03311e12	−	4.35688e12i	0.903938	−	1.29845i
$321$	2.07879e12			0.609938
$322$	4.08079e11	+	6.60927e11i	0.117887	+	0.190930i
$323$	9.15402e10	−	9.15402e10i	0.0260375	−	0.0260375i
$324$	−1.79684e12	+	3.58590e12i	−0.503251	+	1.00432i
$325$	−2.91413e12	+	2.91413e12i	−0.803697	+	0.803697i
$326$	8.58249e11	+	2.02998e11i	0.233091	+	0.0551321i
$327$	4.38248e12			1.17214
$328$	−9.25752e10	−	1.04184e12i	−0.0243851	−	0.274429i
$329$		−	1.30103e11i		−	0.0337526i
$330$	1.33579e12	+	3.15948e11i	0.341324	+	0.0807321i
$331$	−4.79981e12	−	4.79981e12i	−1.20805	−	1.20805i	−0.971658	−	0.236390i	$-0.924036\pi$
$331$	−4.79981e12	−	4.79981e12i	−1.20805	−	1.20805i	−0.236390	−	0.971658i	$-0.575964\pi$
$332$	8.24754e11	+	2.48144e12i	0.204472	+	0.615196i
$333$	6.09063e11	+	6.09063e11i	0.148745	+	0.148745i
$334$	3.00235e12	+	4.86263e12i	0.722320	+	1.16987i
$335$			2.95396e11i			0.0700133i
$336$	−7.04986e12	−	1.01961e12i	−1.64621	−	0.238088i
$337$	4.02759e12			0.926607			0.463304	−	0.886200i	$-0.346664\pi$
$337$	4.02759e12			0.926607			0.463304	+	0.886200i	$0.346664\pi$
$338$	−1.60727e12	+	9.92386e11i	−0.364340	+	0.224956i
$339$	9.82423e11	−	9.82423e11i	0.219432	−	0.219432i
$340$	−5.92814e10	−	1.78360e11i	−0.0130474	−	0.0392557i
$341$	−9.92514e11	+	9.92514e11i	−0.215261	+	0.215261i
$342$	2.18591e11	−	9.24171e11i	0.0467198	−	0.197525i
$343$	3.08710e12			0.650250
$344$	−2.62541e12	−	2.19691e12i	−0.545010	−	0.456057i
$345$			1.19353e12i			0.244196i
$346$	6.03619e11	−	2.55202e12i	0.121726	−	0.514639i
$347$	1.80948e12	+	1.80948e12i	0.359671	+	0.359671i	0.863692	−	0.504021i	$-0.168146\pi$
$347$	1.80948e12	+	1.80948e12i	0.359671	+	0.359671i	−0.504021	+	0.863692i	$0.668146\pi$
$348$	−3.91137e12	+	7.80580e12i	−0.766360	+	1.52940i
$349$	−2.56712e12	−	2.56712e12i	−0.495815	−	0.495815i	0.414317	−	0.910133i	$-0.364020\pi$
$349$	−2.56712e12	−	2.56712e12i	−0.495815	−	0.495815i	−0.910133	+	0.414317i	$0.864020\pi$
$350$	−1.04456e13	+	6.44946e12i	−1.98880	+	1.22796i
$351$		−	3.68814e12i		−	0.692263i
$352$	1.02741e12	−	4.45945e11i	0.190122	−	0.0825217i
$353$	−5.57531e12			−1.01717			−0.508587	−	0.861011i	$-0.669832\pi$
$353$	−5.57531e12			−1.01717			−0.508587	+	0.861011i	$0.669832\pi$
$354$	1.26436e12	+	2.04777e12i	0.227434	+	0.368353i
$355$	4.36957e12	−	4.36957e12i	0.774991	−	0.774991i
$356$	−1.59457e12	−	7.99016e11i	−0.278865	−	0.139735i
$357$	−1.78330e11	+	1.78330e11i	−0.0307527	+	0.0307527i
$358$	−4.38659e12	−	1.03754e12i	−0.745954	−	0.176437i
$359$	7.28553e12			1.22177			0.610884	−	0.791720i	$-0.290814\pi$
$359$	7.28553e12			1.22177			0.610884	+	0.791720i	$0.290814\pi$
$360$	−1.05741e12	−	8.84831e11i	−0.174877	−	0.146335i
$361$		−	6.02875e12i		−	0.983312i
$362$	6.30332e12	+	1.49090e12i	1.01397	+	0.239831i
$363$	−4.56233e12	−	4.56233e12i	−0.723859	−	0.723859i
$364$	7.13051e12	−	2.36996e12i	1.11587	−	0.370881i
$365$	6.50388e11	+	6.50388e11i	0.100394	+	0.100394i
$366$	−5.96825e12	−	9.66621e12i	−0.908744	−	1.47181i
$367$			3.99828e12i			0.600542i	0.953854	+	0.300271i	$0.0970771\pi$
$367$			3.99828e12i			0.600542i	−0.953854	+	0.300271i	$0.902923\pi$
$368$	5.82972e11	+	7.80113e11i	0.0863791	+	0.115590i
$369$	−2.71654e11			−0.0397086
$370$	1.36246e13	−	8.41228e12i	1.96478	−	1.21312i
$371$	−1.10494e13	+	1.10494e13i	−1.57206	+	1.57206i
$372$	1.06210e13	−	3.53009e12i	1.49091	−	0.495532i
$373$	6.58369e12	−	6.58369e12i	0.911854	−	0.911854i	−0.0845641	−	0.996418i	$-0.526950\pi$
$373$	6.58369e12	−	6.58369e12i	0.911854	−	0.911854i	0.996418	+	0.0845641i	$0.0269498\pi$
$374$	9.12743e9	−	3.85895e10i	0.00124736	−	0.00527365i
$375$	−6.31347e12			−0.851357
$376$	−1.44375e10	−	1.62479e11i	−0.00192111	−	0.0216201i
$377$		−	9.21000e12i		−	1.20935i
$378$	2.52875e12	−	1.06912e13i	0.327678	−	1.38538i
$379$	7.91355e12	+	7.91355e12i	1.01199	+	1.01199i	0.999927	+	0.0120604i	$0.00383903\pi$
$379$	7.91355e12	+	7.91355e12i	1.01199	+	1.01199i	0.0120604	+	0.999927i	$0.496161\pi$
$380$	−1.57836e13	−	7.90895e12i	−1.99200	−	0.998162i
$381$	1.16681e12	+	1.16681e12i	0.145337	+	0.145337i
$382$	−3.20579e12	+	1.97936e12i	−0.394110	+	0.243337i
$383$			1.20215e13i			1.45870i	0.684142	+	0.729349i	$0.260177\pi$
$383$			1.20215e13i			1.45870i	−0.684142	+	0.729349i	$0.739823\pi$
$384$	−8.91735e12	−	4.91018e11i	−1.06802	−	0.0588086i
$385$	−4.31317e12			−0.509909
$386$	5.51905e12	+	8.93868e12i	0.644062	+	1.04313i
$387$	−6.28699e11	+	6.28699e11i	−0.0724249	+	0.0724249i
$388$	−5.58278e12	+	1.11414e13i	−0.634880	+	1.26701i
$389$	−7.67209e12	+	7.67209e12i	−0.861322	+	0.861322i	−0.991492	−	0.130169i	$-0.958448\pi$
$389$	−7.67209e12	+	7.67209e12i	−0.861322	+	0.861322i	0.130169	+	0.991492i	$0.458448\pi$
$390$	1.12358e13	+	2.65755e12i	1.24531	+	0.294549i
$391$	3.44800e10			0.00377297
$392$	1.30751e13	−	1.16183e12i	1.41259	−	0.125520i
$393$			9.49784e12i			1.01312i
$394$	−4.73246e12	−	1.11935e12i	−0.498432	−	0.117892i
$395$	−1.13539e13	−	1.13539e13i	−1.18075	−	1.18075i
$396$	−9.17495e10	−	2.76047e11i	−0.00942167	−	0.0283470i
$397$	−7.80668e12	−	7.80668e12i	−0.791615	−	0.791615i	0.190142	−	0.981757i	$-0.439105\pi$
$397$	−7.80668e12	−	7.80668e12i	−0.791615	−	0.791615i	−0.981757	+	0.190142i	$0.939105\pi$
$398$	8.83426e12	+	1.43080e13i	0.884616	+	1.43273i
$399$			2.36886e13i			2.34247i
$400$	−1.23292e13	+	9.21354e12i	−1.20403	+	0.899760i
$401$	1.81263e13			1.74818			0.874090	−	0.485763i	$-0.161458\pi$
$401$	1.81263e13			1.74818			0.874090	+	0.485763i	$0.161458\pi$
$402$	4.22842e11	−	2.61077e11i	0.0402761	−	0.0248679i
$403$	−8.34837e12	+	8.34837e12i	−0.785374	+	0.785374i
$404$	−5.02064e12	−	1.51056e13i	−0.466501	−	1.40356i
$405$	1.36935e13	−	1.36935e13i	1.25672	−	1.25672i
$406$	6.31478e12	−	2.66980e13i	0.572438	−	2.42019i
$407$	3.37827e12			0.302498
$408$	−2.02918e11	+	2.42496e11i	−0.0179481	+	0.0214489i
$409$			5.55158e12i			0.485065i	0.970143	+	0.242533i	$0.0779782\pi$
$409$			5.55158e12i			0.485065i	−0.970143	+	0.242533i	$0.922022\pi$
$410$	−1.16239e12	+	4.91444e12i	−0.100331	+	0.424184i
$411$	3.48579e12	+	3.48579e12i	0.297230	+	0.297230i
$412$	4.59087e12	−	9.16185e12i	0.386731	−	0.771786i
$413$	−5.34732e12	−	5.34732e12i	−0.445027	−	0.445027i
$414$	2.15219e11	−	1.32884e11i	0.0176962	−	0.0109262i
$415$		−	1.26254e13i		−	1.02566i
$416$	8.64194e12	−	3.75100e12i	0.693657	−	0.301079i
$417$	−7.12836e12			−0.565339
$418$	−1.95681e12	−	3.16926e12i	−0.153344	−	0.248357i
$419$	−1.20736e11	+	1.20736e11i	−0.00934904	+	0.00934904i	−0.711766	−	0.702417i	$-0.752104\pi$
$419$	−1.20736e11	+	1.20736e11i	−0.00934904	+	0.00934904i	0.702417	+	0.711766i	$0.252104\pi$
$420$	3.07482e13	+	1.54075e13i	2.35274	+	1.17892i
$421$	−1.42648e13	+	1.42648e13i	−1.07858	+	1.07858i	−0.0819482	+	0.996637i	$0.526114\pi$
$421$	−1.42648e13	+	1.42648e13i	−1.07858	+	1.07858i	−0.996637	+	0.0819482i	$0.973886\pi$
$422$	−9.82689e10	−	2.32432e10i	−0.00734267	−	0.00173673i
$423$	−4.23657e10			−0.00312833
$424$	−1.25729e13	+	1.50252e13i	−0.917498	+	1.09645i
$425$			5.44936e11i			0.0393008i
$426$	−1.01167e13	−	2.39286e12i	−0.721093	−	0.170557i
$427$	2.52413e13	+	2.52413e13i	1.77817	+	1.77817i
$428$	−7.77167e12	+	2.58306e12i	−0.541122	+	0.179852i
$429$	1.72245e12	+	1.72245e12i	0.118539	+	0.118539i
$430$	8.68349e12	+	1.40638e13i	0.590680	+	0.956668i
$431$		−	2.03574e13i		−	1.36879i	−0.729112	−	0.684395i	$-0.760067\pi$
$431$		−	2.03574e13i		−	1.36879i	0.729112	−	0.684395i	$-0.239933\pi$
$432$	1.97162e12	−	1.36323e13i	0.131040	−	0.906047i
$433$	−1.41241e12			−0.0927942			−0.0463971	−	0.998923i	$-0.514774\pi$
$433$	−1.41241e12			−0.0927942			−0.0463971	+	0.998923i	$0.514774\pi$
$434$	−2.99244e13	+	1.84763e13i	−1.94346	+	1.19996i
$435$	2.98080e13	−	2.98080e13i	1.91376	−	1.91376i
$436$	−1.63841e13	+	5.44558e12i	−1.03990	+	0.345630i
$437$	2.29009e12	−	2.29009e12i	0.143696	−	0.143696i
$438$	3.56166e11	−	1.50582e12i	0.0220944	−	0.0934119i
$439$	2.38960e12			0.146555			0.0732777	−	0.997312i	$-0.476654\pi$
$439$	2.38960e12			0.146555			0.0732777	+	0.997312i	$0.476654\pi$
$440$	−5.38649e12	+	4.78632e11i	−0.326620	+	0.0290227i
$441$		−	3.40929e12i		−	0.204395i
$442$	7.67739e10	−	3.24590e11i	0.00455095	−	0.0192408i
$443$	−1.86600e13	−	1.86600e13i	−1.09369	−	1.09369i	−0.995131	−	0.0985578i	$-0.968577\pi$
$443$	−1.86600e13	−	1.86600e13i	−1.09369	−	1.09369i	−0.0985578	−	0.995131i	$-0.531423\pi$
$444$	−2.40834e13	−	1.20678e13i	−1.39573	−	0.699382i
$445$	6.08920e12	+	6.08920e12i	0.348947	+	0.348947i
$446$	1.14050e13	−	7.04182e12i	0.646278	−	0.399035i
$447$		−	2.50906e13i		−	1.40596i
$448$	2.76232e13	−	4.94814e12i	1.53068	−	0.274190i
$449$	−9.36693e12			−0.513293			−0.256647	−	0.966505i	$-0.582618\pi$
$449$	−9.36693e12			−0.513293			−0.256647	+	0.966505i	$0.582618\pi$
$450$	2.10015e12	+	3.40141e12i	0.113812	+	0.184330i
$451$	−7.53387e11	+	7.53387e11i	−0.0403771	+	0.0403771i
$452$	−2.45210e12	+	4.89357e12i	−0.129971	+	0.259378i
$453$	1.20136e13	−	1.20136e13i	0.629771	−	0.629771i
$454$	−1.50306e13	−	3.55512e12i	−0.779284	−	0.184321i
$455$	−3.62795e13			−1.86039
$456$	2.62872e12	+	2.95835e13i	0.133328	+	1.50046i
$457$		−	4.79735e12i		−	0.240669i	−0.992733	−	0.120334i	$-0.961603\pi$
$457$		−	4.79735e12i		−	0.240669i	0.992733	−	0.120334i	$-0.0383967\pi$
$458$	−1.04400e13	−	2.46934e12i	−0.518053	−	0.122533i
$459$	−3.44837e11	−	3.44837e11i	−0.0169258	−	0.0169258i
$460$	−1.48306e12	−	4.46208e12i	−0.0720061	−	0.216645i
$461$	2.85615e13	+	2.85615e13i	1.37176	+	1.37176i	0.857842	+	0.513914i	$0.171805\pi$
$461$	2.85615e13	+	2.85615e13i	1.37176	+	1.37176i	0.513914	+	0.857842i	$0.328195\pi$
$462$	3.81207e12	+	6.17405e12i	0.181114	+	0.293332i
$463$		−	2.53353e13i		−	1.19075i	−0.803447	−	0.595376i	$-0.797003\pi$
$463$		−	2.53353e13i		−	1.19075i	0.803447	−	0.595376i	$-0.202997\pi$
$464$	4.92353e12	−	3.40426e13i	0.228921	−	1.58282i
$465$	−5.40388e13			−2.48566
$466$	2.17730e13	−	1.34434e13i	0.990804	−	0.611757i
$467$	−1.32024e13	+	1.32024e13i	−0.594384	+	0.594384i	−0.938813	−	0.344428i	$-0.888073\pi$
$467$	−1.32024e13	+	1.32024e13i	−0.594384	+	0.594384i	0.344428	+	0.938813i	$0.388073\pi$
$468$	−7.71736e11	−	2.32192e12i	−0.0343748	−	0.103423i
$469$	−1.10417e12	+	1.10417e12i	−0.0486598	+	0.0486598i
$470$	−1.81280e11	+	7.66429e11i	−0.00790426	+	0.0334181i
$471$	−1.70805e13			−0.736880
$472$	−7.27139e12	−	6.08460e12i	−0.310390	−	0.259730i
$473$			3.48718e12i			0.147289i
$474$	−6.21761e12	+	2.62872e13i	−0.259855	+	1.09863i
$475$	3.61935e13	+	3.61935e13i	1.49680	+	1.49680i
$476$	4.45106e11	−	8.88284e11i	0.0182150	−	0.0363511i
$477$	3.59804e12	+	3.59804e12i	0.145705	+	0.145705i
$478$	−1.72542e13	+	1.06534e13i	−0.691443	+	0.426921i
$479$		−	8.30840e12i		−	0.329488i	−0.986336	−	0.164744i	$-0.947320\pi$
$479$		−	8.30840e12i		−	0.329488i	0.986336	−	0.164744i	$-0.0526798\pi$
$480$	4.01096e13	+	1.58295e13i	1.57414	+	0.621241i
$481$	2.84158e13			1.10366
$482$	1.11463e13	+	1.80527e13i	0.428447	+	0.693914i
$483$	−4.46133e12	+	4.46133e12i	−0.169718	+	0.169718i
$484$	2.27256e13	+	1.13875e13i	0.855634	+	0.428746i
$485$	4.25456e13	−	4.25456e13i	1.58543	−	1.58543i
$486$	−7.54906e12	−	1.78555e12i	−0.278427	−	0.0658553i
$487$	1.06812e13			0.389921			0.194960	−	0.980811i	$-0.437542\pi$
$487$	1.06812e13			0.389921			0.194960	+	0.980811i	$0.437542\pi$
$488$	3.43236e13	+	2.87216e13i	1.24021	+	1.03779i
$489$			7.16353e12i			0.256202i
$490$	−6.16767e13	−	1.45882e13i	−2.18344	−	0.516440i
$491$	7.67425e12	+	7.67425e12i	0.268923	+	0.268923i	0.828666	−	0.559743i	$-0.189100\pi$
$491$	7.67425e12	+	7.67425e12i	0.268923	+	0.268923i	−0.559743	+	0.828666i	$0.689100\pi$
$492$	8.06208e12	−	2.67959e12i	0.279654	−	0.0929485i
$493$	−8.61125e11	−	8.61125e11i	−0.0295686	−	0.0295686i
$494$	−1.64594e13	−	2.66577e13i	−0.559473	−	0.906126i
$495$			1.40451e12i			0.0472604i
$496$	−3.53207e13	+	2.63949e13i	−1.17658	+	0.879247i
$497$	3.26662e13			1.07725
$498$	−1.80725e13	+	1.11586e13i	−0.590026	+	0.364303i
$499$	1.62221e13	−	1.62221e13i	0.524331	−	0.524331i	−0.394546	−	0.918876i	$-0.629098\pi$
$499$	1.62221e13	−	1.62221e13i	0.524331	−	0.524331i	0.918876	+	0.394546i	$0.129098\pi$
$500$	2.36032e13	−	7.84499e12i	0.755303	−	0.251040i
$501$	−3.28233e13	+	3.28233e13i	−1.03990	+	1.03990i
$502$	9.28791e12	−	3.92680e13i	0.291340	−	1.23174i
$503$	6.29489e12			0.195501			0.0977504	−	0.995211i	$-0.468835\pi$
$503$	6.29489e12			0.195501			0.0977504	+	0.995211i	$0.468835\pi$
$504$	−6.45104e11	−	7.25996e12i	−0.0198370	−	0.223245i
$505$			7.68562e13i			2.34003i
$506$	2.28343e11	−	9.65404e11i	0.00688392	−	0.0291043i
$507$	−1.08493e13	−	1.08493e13i	−0.323863	−	0.323863i
$508$	−5.81205e12	−	2.91233e12i	−0.171795	−	0.0860840i
$509$	3.34514e12	+	3.34514e12i	0.0979098	+	0.0979098i	0.754365	−	0.656455i	$-0.227945\pi$
$509$	3.34514e12	+	3.34514e12i	0.0979098	+	0.0979098i	−0.656455	+	0.754365i	$0.727945\pi$
$510$	1.29901e12	−	8.02053e11i	0.0376497	−	0.0232462i
$511$			4.86219e12i			0.139549i
$512$	3.39481e13	−	9.24483e12i	0.964863	−	0.262754i
$513$	−4.58067e13			−1.28926
$514$	−8.85422e12	−	1.43403e13i	−0.246794	−	0.399709i
$515$	−3.49864e13	+	3.49864e13i	−0.965746	+	0.965746i
$516$	1.24569e13	−	2.48598e13i	0.340535	−	0.679594i
$517$	−1.17494e11	+	1.17494e11i	−0.00318100	+	0.00318100i
$518$	8.23720e13	+	1.94831e13i	2.20867	+	0.522408i
$519$	2.13009e13			0.565667
$520$	−4.53076e13	+	4.02594e12i	−1.19167	+	0.105889i
$521$			5.14980e13i			1.34153i	0.741668	+	0.670767i	$0.234035\pi$
$521$			5.14980e13i			1.34153i	−0.741668	+	0.670767i	$0.765965\pi$
$522$	−8.69374e12	−	2.05630e12i	−0.224313	−	0.0530558i
$523$	−5.38368e13	−	5.38368e13i	−1.37585	−	1.37585i	−0.851507	−	0.524343i	$-0.824311\pi$
$523$	−5.38368e13	−	5.38368e13i	−1.37585	−	1.37585i	−0.524343	−	0.851507i	$-0.675689\pi$
$524$	−1.18018e13	−	3.55082e13i	−0.298740	−	0.898818i
$525$	−7.05088e13	−	7.05088e13i	−1.76785	−	1.76785i
$526$	−7.93695e12	−	1.28547e13i	−0.197117	−	0.319252i
$527$			1.56113e12i			0.0384048i
$528$	5.44583e12	+	7.28743e12i	0.132707	+	0.177584i
$529$	−4.05639e13			−0.979178
$530$	8.04871e13	−	4.96955e13i	1.92463	−	1.18833i
$531$	−1.74126e12	+	1.74126e12i	−0.0412469	+	0.0412469i
$532$	−2.94350e13	−	8.85610e13i	−0.690725	−	2.07819i
$533$	−6.33700e12	+	6.33700e12i	−0.147315	+	0.147315i
$534$	3.33457e12	−	1.40981e13i	0.0767951	−	0.324679i
$535$	3.95417e13			0.902165
$536$	−1.25641e12	+	1.50147e12i	−0.0283992	+	0.0339384i
$537$		−	3.66135e13i		−	0.819916i
$538$	−6.33234e12	+	2.67723e13i	−0.140492	+	0.593983i
$539$	−9.45510e12	−	9.45510e12i	−0.207837	−	0.207837i
$540$	−2.97934e13	+	5.94578e13i	−0.648861	+	1.29491i
$541$	2.48695e13	+	2.48695e13i	0.536636	+	0.536636i	0.922539	−	0.385903i	$-0.126110\pi$
$541$	2.48695e13	+	2.48695e13i	0.536636	+	0.536636i	−0.385903	+	0.922539i	$0.626110\pi$
$542$	−2.88089e13	+	1.77876e13i	−0.615929	+	0.380296i
$543$			5.26118e13i			1.11451i
$544$	4.57297e11	−	1.15873e12i	0.00959852	−	0.0243213i
$545$	8.33612e13			1.73373
$546$	3.20646e13	+	5.19320e13i	0.660789	+	1.07022i
$547$	1.57563e12	−	1.57563e12i	0.0321749	−	0.0321749i	−0.690836	−	0.723011i	$-0.742757\pi$
$547$	1.57563e12	−	1.57563e12i	0.0321749	−	0.0321749i	0.723011	+	0.690836i	$0.242757\pi$
$548$	−1.73632e13	−	8.70043e12i	−0.351339	−	0.176051i
$549$	8.21939e12	−	8.21939e12i	0.164808	−	0.164808i
$550$	1.52577e13	+	3.60884e12i	0.303162	+	0.0717057i
$551$	−1.14388e14			−2.25228
$552$	−5.07645e12	+	6.06660e12i	−0.0990523	+	0.118372i
$553$		−	8.48797e13i		−	1.64126i
$554$	2.69190e13	+	6.36704e12i	0.515833	+	0.122008i
$555$	9.19674e13	+	9.19674e13i	1.74650	+	1.74650i
$556$	2.66497e13	−	8.85755e12i	0.501555	−	0.166702i
$557$	−1.01553e12	−	1.01553e12i	−0.0189416	−	0.0189416i	0.697573	−	0.716514i	$-0.254263\pi$
$557$	−1.01553e12	−	1.01553e12i	−0.0189416	−	0.0189416i	−0.716514	+	0.697573i	$0.754263\pi$
$558$	6.01649e12	+	9.74434e12i	0.111217	+	0.180128i
$559$			2.93319e13i			0.537380i
$560$	−1.34099e14	−	1.93945e13i	−2.43492	−	0.352159i
$561$	3.22095e11			0.00579654
$562$	−2.21410e13	+	1.36706e13i	−0.394926	+	0.243841i
$563$	5.85163e13	−	5.85163e13i	1.03451	−	1.03451i	0.0351281	−	0.999383i	$-0.488816\pi$
$563$	5.85163e13	−	5.85163e13i	1.03451	−	1.03451i	0.999383	−	0.0351281i	$-0.0111839\pi$
$564$	1.25732e12	−	4.17894e11i	0.0220318	−	0.00732269i
$565$	1.86871e13	−	1.86871e13i	0.324564	−	0.324564i
$566$	−1.72614e13	+	7.29789e13i	−0.297163	+	1.25636i
$567$	1.02370e14			1.74686
$568$	4.07951e13	−	3.62497e12i	0.690028	−	0.0613144i
$569$		−	9.64364e13i		−	1.61689i	−0.588574	−	0.808443i	$-0.700311\pi$
$569$		−	9.64364e13i		−	1.61689i	0.588574	−	0.808443i	$-0.299689\pi$
$570$	3.30068e13	−	1.39548e14i	0.548566	−	2.31926i
$571$	−2.96530e13	−	2.96530e13i	−0.488526	−	0.488526i	0.419315	−	0.907841i	$-0.362270\pi$
$571$	−2.96530e13	−	2.96530e13i	−0.488526	−	0.488526i	−0.907841	+	0.419315i	$0.862270\pi$
$572$	−8.57975e12	−	4.29919e12i	−0.140118	−	0.0702111i
$573$	−2.16394e13	−	2.16394e13i	−0.350326	−	0.350326i
$574$	−2.27147e13	+	1.40248e13i	−0.364542	+	0.225081i
$575$			1.36328e13i			0.216893i
$576$	−1.61127e12	−	8.99500e12i	−0.0254131	−	0.141869i
$577$	−2.17271e13			−0.339721			−0.169861	−	0.985468i	$-0.554332\pi$
$577$	−2.17271e13			−0.339721			−0.169861	+	0.985468i	$0.554332\pi$
$578$	3.38689e13	+	5.48542e13i	0.525003	+	0.850297i
$579$	−6.03371e13	+	6.03371e13i	−0.927238	+	0.927238i
$580$	−7.44000e13	+	1.48478e14i	−1.13353	+	2.26215i
$581$	4.71926e13	−	4.71926e13i	0.712843	−	0.712843i
$582$	−9.85044e13	−	2.32989e13i	−1.47517	−	0.348915i
$583$	1.99571e13			0.296316
$584$	5.39557e11	+	6.07214e12i	0.00794280	+	0.0893877i
$585$			1.18138e13i			0.172429i
$586$	6.23742e13	+	1.47531e13i	0.902645	+	0.213499i
$587$	−1.69648e13	−	1.69648e13i	−0.243422	−	0.243422i	0.574843	−	0.818264i	$-0.305063\pi$
$587$	−1.69648e13	−	1.69648e13i	−0.243422	−	0.243422i	−0.818264	+	0.574843i	$0.805063\pi$
$588$	3.36291e13	+	1.01180e14i	0.478442	+	1.43949i
$589$	1.03687e14	+	1.03687e14i	1.46267	+	1.46267i
$590$	2.40500e13	+	3.89515e13i	0.336399	+	0.544834i
$591$		−	3.95004e13i		−	0.547853i
$592$	1.05032e14	+	1.51907e13i	1.44449	+	0.208914i
$593$	−6.94902e13			−0.947654			−0.473827	−	0.880618i	$-0.657128\pi$
$593$	−6.94902e13			−0.947654			−0.473827	+	0.880618i	$0.657128\pi$
$594$	−1.19388e13	+	7.37140e12i	−0.161446	+	0.0996823i
$595$	−3.39210e12	+	3.39210e12i	−0.0454866	+	0.0454866i
$596$	3.11770e13	+	9.38024e13i	0.414576	+	1.24733i
$597$	−9.65806e13	+	9.65806e13i	−1.27356	+	1.27356i
$598$	1.92067e12	−	8.12035e12i	0.0251158	−	0.106186i
$599$	−5.76484e12			−0.0747572			−0.0373786	−	0.999301i	$-0.511901\pi$
$599$	−5.76484e12			−0.0747572			−0.0373786	+	0.999301i	$0.511901\pi$
$600$	−9.58791e13	−	8.02304e13i	−1.23301	−	1.03177i
$601$		−	5.22266e13i		−	0.666069i	−0.942915	−	0.333035i	$-0.891927\pi$
$601$		−	5.22266e13i		−	0.666069i	0.942915	−	0.333035i	$-0.108073\pi$
$602$	−2.01113e13	+	8.50276e13i	−0.254365	+	1.07542i
$603$	3.59552e11	+	3.59552e11i	0.00450998	+	0.00450998i
$604$	−2.99856e13	+	5.98414e13i	−0.373017	+	0.744418i
$605$	−8.67823e13	−	8.67823e13i	−1.07067	−	1.07067i
$606$	1.10015e14	−	6.79272e13i	1.34614	−	0.831152i
$607$			4.76946e13i			0.578796i	0.957209	+	0.289398i	$0.0934551\pi$
$607$			4.76946e13i			0.578796i	−0.957209	+	0.289398i	$0.906545\pi$
$608$	−4.65874e13	−	1.07333e14i	−0.560726	−	1.29186i
$609$	2.22840e14			2.66016
$610$	−1.13525e14	−	1.83865e14i	−1.34413	−	2.17696i
$611$	−9.88284e11	+	9.88284e11i	−0.0116058	+	0.0116058i
$612$	−2.89254e11	−	1.44941e11i	−0.00336916	−	0.00168824i
$613$	−4.11673e13	+	4.11673e13i	−0.475609	+	0.475609i	−0.903724	−	0.428115i	$-0.859178\pi$
$613$	−4.11673e13	+	4.11673e13i	−0.475609	+	0.475609i	0.428115	+	0.903724i	$0.359178\pi$
$614$	−5.77078e13	−	1.36494e13i	−0.661291	−	0.156412i
$615$	−4.10193e13			−0.466243
$616$	−2.19234e13	−	1.83452e13i	−0.247174	−	0.206832i
$617$		−	8.85732e13i		−	0.990551i	−0.868736	−	0.495275i	$-0.835067\pi$
$617$		−	8.85732e13i		−	0.990551i	0.868736	−	0.495275i	$-0.164933\pi$
$618$	8.10027e13	+	1.91593e13i	0.898581	+	0.212538i
$619$	−3.06918e13	−	3.06918e13i	−0.337729	−	0.337729i	0.517783	−	0.855512i	$-0.326758\pi$
$619$	−3.06918e13	−	3.06918e13i	−0.337729	−	0.337729i	−0.855512	+	0.517783i	$0.826758\pi$
$620$	2.02027e14	−	6.71475e13i	2.20521	−	0.732945i
$621$	−8.62687e12	−	8.62687e12i	−0.0934104	−	0.0934104i
$622$	4.22727e13	+	6.84651e13i	0.454055	+	0.735389i
$623$			4.55219e13i			0.485043i
$624$	4.58068e13	+	6.12970e13i	0.484180	+	0.647913i
$625$	2.32534e13			0.243830
$626$	−5.65747e13	+	3.49312e13i	−0.588505	+	0.363363i
$627$	2.13928e13	−	2.13928e13i	0.220765	−	0.220765i
$628$	6.38564e13	−	2.12239e13i	0.653742	−	0.217284i
$629$	2.65685e12	−	2.65685e12i	0.0269844	−	0.0269844i
$630$	−8.10005e12	+	3.42459e13i	−0.0816178	+	0.345069i
$631$	1.20174e14			1.20133			0.600666	−	0.799500i	$-0.294902\pi$
$631$	1.20174e14			1.20133			0.600666	+	0.799500i	$0.294902\pi$
$632$	−9.41909e12	−	1.06002e14i	−0.0934165	−	1.05130i
$633$		−	8.20220e11i		−	0.00807071i
$634$	7.58131e12	−	3.20528e13i	0.0740113	−	0.312910i
$635$	2.21945e13	+	2.21945e13i	0.214970	+	0.214970i
$636$	−1.42272e14	−	7.12906e13i	−1.36721	−	0.685089i
$637$	−7.95301e13	−	7.95301e13i	−0.758288	−	0.758288i
$638$	−2.98134e13	+	1.84078e13i	−0.282039	+	0.174140i
$639$		−	1.06372e13i		−	0.0998439i
$640$	−1.69621e14	−	9.33988e12i	−1.57972	−	0.0869844i
$641$	3.91790e13			0.362046			0.181023	−	0.983479i	$-0.442059\pi$
$641$	3.91790e13			0.362046			0.181023	+	0.983479i	$0.442059\pi$
$642$	−3.49478e13	−	5.66016e13i	−0.320438	−	0.518983i
$643$	−1.77735e13	+	1.77735e13i	−0.161703	+	0.161703i	−0.783321	−	0.621618i	$-0.786476\pi$
$643$	−1.77735e13	+	1.77735e13i	−0.161703	+	0.161703i	0.621618	+	0.783321i	$0.286476\pi$
$644$	1.11353e13	−	2.22225e13i	0.100525	−	0.200615i
$645$	−9.49324e13	+	9.49324e13i	−0.850385	+	0.850385i
$646$	−4.03140e12	−	9.53532e11i	−0.0358339	−	0.00847565i
$647$	−1.55422e14			−1.37086			−0.685428	−	0.728140i	$-0.740385\pi$
$647$	−1.55422e14			−1.37086			−0.685428	+	0.728140i	$0.740385\pi$
$648$	1.27845e14	−	1.13600e13i	1.11895	−	0.0994271i
$649$			9.65818e12i			0.0838826i
$650$	1.28337e14	+	3.03552e13i	1.10608	+	0.261617i
$651$	−2.01993e14	−	2.01993e14i	−1.72755	−	1.72755i
$652$	−8.90126e12	−	2.67812e13i	−0.0755463	−	0.227296i
$653$	7.37037e13	+	7.37037e13i	0.620759	+	0.620759i	0.945726	−	0.324966i	$-0.105353\pi$
$653$	7.37037e13	+	7.37037e13i	0.620759	+	0.620759i	−0.324966	+	0.945726i	$0.605353\pi$
$654$	−7.36765e13	−	1.19327e14i	−0.615800	−	0.997353i
$655$			1.80663e14i			1.49852i
$656$	−2.68109e13	+	2.00355e13i	−0.220695	+	0.164923i
$657$	1.58329e12			0.0129340
$658$	−3.54246e12	+	2.18724e12i	−0.0287194	+	0.0177324i
$659$	1.11511e14	−	1.11511e14i	0.897203	−	0.897203i	−0.0979852	−	0.995188i	$-0.531240\pi$
$659$	1.11511e14	−	1.11511e14i	0.897203	−	0.897203i	0.995188	+	0.0979852i	$0.0312398\pi$
$660$	−1.38540e13	−	4.16825e13i	−0.110626	−	0.332839i
$661$	−9.52850e13	+	9.52850e13i	−0.755122	+	0.755122i	−0.975430	−	0.220308i	$-0.929294\pi$
$661$	−9.52850e13	+	9.52850e13i	−0.755122	+	0.755122i	0.220308	+	0.975430i	$0.429294\pi$
$662$	−4.99974e13	+	2.11382e14i	−0.393240	+	1.66257i
$663$	2.70925e12			0.0211486
$664$	5.36995e13	−	6.41734e13i	0.416035	−	0.497181i
$665$			4.50592e14i			3.46478i
$666$	6.34433e12	−	2.68230e13i	0.0484189	−	0.204708i
$667$	−2.15430e13	−	2.15430e13i	−0.163184	−	0.163184i
$668$	8.19259e13	−	1.63497e14i	0.615941	−	1.22921i
$669$	7.69847e13	+	7.69847e13i	0.574479	+	0.574479i
$670$	8.04307e12	−	4.96607e12i	0.0595728	−	0.0367823i
$671$		−	4.55902e13i		−	0.335165i
$672$	9.07572e13	+	2.09096e14i	0.662269	+	1.52580i
$673$	−2.09843e14			−1.51991			−0.759956	−	0.649975i	$-0.774779\pi$
$673$	−2.09843e14			−1.51991			−0.759956	+	0.649975i	$0.774779\pi$
$674$	−6.77102e13	−	1.09664e14i	−0.486804	−	0.788431i
$675$	1.36343e14	−	1.36343e14i	0.973001	−	0.973001i
$676$	5.40416e13	+	2.70795e13i	0.382820	+	0.191826i
$677$	−4.07331e13	+	4.07331e13i	−0.286420	+	0.286420i	−0.835663	−	0.549243i	$-0.814916\pi$
$677$	−4.07331e13	+	4.07331e13i	−0.286420	+	0.286420i	0.549243	+	0.835663i	$0.314916\pi$
$678$	−4.32656e13	−	1.02334e13i	−0.301991	−	0.0714288i
$679$	3.18064e14			2.20377
$680$	−3.85979e12	+	4.61263e12i	−0.0265472	+	0.0317252i
$681$		−	1.25455e14i		−	0.856552i
$682$	4.37100e13	+	1.03386e13i	0.296250	+	0.0700710i
$683$	−5.74561e13	−	5.74561e13i	−0.386574	−	0.386574i	0.486889	−	0.873464i	$-0.338131\pi$
$683$	−5.74561e13	−	5.74561e13i	−0.386574	−	0.386574i	−0.873464	+	0.486889i	$0.838131\pi$
$684$	−2.88383e13	+	9.58497e12i	−0.192615	+	0.0640192i
$685$	6.63049e13	+	6.63049e13i	0.439635	+	0.439635i
$686$	−5.18991e13	−	8.40560e13i	−0.341617	−	0.553284i
$687$		−	8.71395e13i		−	0.569418i
$688$	−1.56804e13	+	1.08418e14i	−0.101722	+	0.703333i
$689$	1.67866e14			1.08110
$690$	3.24976e13	−	2.00652e13i	0.207781	−	0.128291i
$691$	−6.51646e13	+	6.51646e13i	−0.413639	+	0.413639i	−0.883004	−	0.469365i	$-0.844483\pi$
$691$	−6.51646e13	+	6.51646e13i	−0.413639	+	0.413639i	0.469365	+	0.883004i	$0.344483\pi$
$692$	−7.96344e13	+	2.64680e13i	−0.501846	+	0.166798i
$693$	−5.24993e12	+	5.24993e12i	−0.0328464	+	0.0328464i
$694$	1.88485e13	−	7.96888e13i	0.117079	−	0.494994i
$695$	−1.35592e14			−0.836199
$696$	2.78294e14	−	2.47286e13i	1.70395	−	0.151409i
$697$			1.18501e12i			0.00720371i
$698$	−2.67406e13	+	1.13055e14i	−0.161396	+	0.682361i
$699$	1.46970e14	+	1.46970e14i	0.880729	+	0.880729i
$700$	3.51213e14	+	1.75988e14i	2.08968	+	1.04711i
$701$	6.77411e12	+	6.77411e12i	0.0400186	+	0.0400186i	0.726833	−	0.686814i	$-0.240991\pi$
$701$	6.77411e12	+	6.77411e12i	0.0400186	+	0.0400186i	−0.686814	+	0.726833i	$0.740991\pi$
$702$	−1.00421e14	+	6.20034e13i	−0.589032	+	0.363689i
$703$		−	3.52924e14i		−	2.05544i
$704$	−2.94147e13	−	2.04775e13i	−0.170099	−	0.118417i
$705$	−6.39714e12			−0.0367316
$706$	9.37297e13	+	1.51805e14i	0.534385	+	0.865492i
$707$	−2.87282e14	+	2.87282e14i	−1.62634	+	1.62634i
$708$	3.45009e13	−	6.88524e13i	0.193939	−	0.387037i
$709$	1.98902e14	−	1.98902e14i	1.11022	−	1.11022i	0.117098	−	0.993120i	$-0.462641\pi$
$709$	1.98902e14	−	1.98902e14i	1.11022	−	1.11022i	0.993120	−	0.117098i	$-0.0373593\pi$
$710$	−1.92435e14	−	4.55158e13i	−1.06657	−	0.252273i
$711$	−2.76395e13			−0.152119
$712$	5.05156e12	+	5.68499e13i	0.0276074	+	0.310692i
$713$			3.90552e13i			0.211949i
$714$	7.85360e12	+	1.85758e12i	0.0423231	+	0.0100105i
$715$	3.27635e13	+	3.27635e13i	0.175332	+	0.175332i
$716$	4.54952e13	+	1.36881e14i	0.241769	+	0.727410i
$717$	−1.16468e14	−	1.16468e14i	−0.614626	−	0.614626i
$718$	−1.22481e14	−	1.98371e14i	−0.641871	−	1.03958i
$719$			3.08820e14i			1.60717i	0.595193	+	0.803583i	$0.297076\pi$
$719$			3.08820e14i			1.60717i	−0.595193	+	0.803583i	$0.702924\pi$
$720$	−6.31547e12	+	4.36668e13i	−0.0326395	+	0.225678i
$721$	−2.61553e14			−1.34240
$722$	−1.64152e14	+	1.01353e14i	−0.836680	+	0.516595i
$723$	−1.21857e14	+	1.21857e14i	−0.616823	+	0.616823i
$724$	−6.53744e13	−	1.96692e14i	−0.328636	−	0.988767i
$725$	3.40475e14	−	3.40475e14i	1.69979	−	1.69979i
$726$	−4.75237e13	+	2.00924e14i	−0.235628	+	0.996204i
$727$	−2.19937e12			−0.0108299			−0.00541497	−	0.999985i	$-0.501724\pi$
$727$	−2.19937e12			−0.0108299			−0.00541497	+	0.999985i	$0.501724\pi$
$728$	−1.84405e14	−	1.54308e14i	−0.901811	−	0.754624i
$729$			1.68279e14i			0.817321i
$730$	6.77479e12	−	2.86429e13i	0.0326800	−	0.138166i
$731$	2.74250e12	+	2.74250e12i	0.0131389	+	0.0131389i
$732$	−1.62857e14	+	3.25009e14i	−0.774910	+	1.54646i
$733$	−1.10887e14	−	1.10887e14i	−0.524037	−	0.524037i	0.394751	−	0.918788i	$-0.370831\pi$
$733$	−1.10887e14	−	1.10887e14i	−0.524037	−	0.524037i	−0.918788	+	0.394751i	$0.870831\pi$
$734$	1.08866e14	−	6.72174e13i	0.510988	−	0.315502i
$735$		−	5.14796e14i		−	2.39993i
$736$	1.14403e13	−	2.89882e13i	0.0529724	−	0.134224i
$737$	1.99431e12			0.00917183
$738$	4.56694e12	+	7.39663e12i	0.0208614	+	0.0337872i
$739$	1.16552e14	−	1.16552e14i	0.528807	−	0.528807i	−0.391410	−	0.920216i	$-0.628013\pi$
$739$	1.16552e14	−	1.16552e14i	0.528807	−	0.528807i	0.920216	+	0.391410i	$0.128013\pi$
$740$	−4.58101e14	−	2.29548e14i	−2.06444	−	1.03446i
$741$	1.79943e14	−	1.79943e14i	0.805458	−	0.805458i
$742$	4.86612e14	+	1.15096e14i	2.16353	+	0.511732i
$743$	−2.56883e13			−0.113447			−0.0567233	−	0.998390i	$-0.518065\pi$
$743$	−2.56883e13			−0.113447			−0.0567233	+	0.998390i	$0.518065\pi$
$744$	−2.74674e14	−	2.29843e14i	−1.20490	−	1.00825i
$745$		−	4.77260e14i		−	2.07957i
$746$	−2.89944e14	−	6.85793e13i	−1.25493	−	0.296824i
$747$	−1.53674e13	−	1.53674e13i	−0.0660691	−	0.0660691i
$748$	−1.20417e12	+	4.00228e11i	−0.00514255	+	0.00170923i
$749$	1.47804e14	+	1.47804e14i	0.627012	+	0.627012i
$750$	1.06139e14	+	1.71904e14i	0.447271	+	0.724402i
$751$		−	1.52208e13i		−	0.0637142i	−0.999492	−	0.0318571i	$-0.989858\pi$
$751$		−	1.52208e13i		−	0.0637142i	0.999492	−	0.0318571i	$-0.0101422\pi$
$752$	−4.18128e12	+	3.12463e12i	−0.0173868	+	0.0129930i
$753$	3.27758e14			1.35387
$754$	−2.50771e14	+	1.54835e14i	−1.02901	+	0.635348i
$755$	2.28516e14	−	2.28516e14i	0.931500	−	0.931500i
$756$	−3.33614e14	+	1.10883e14i	−1.35094	+	0.449010i
$757$	−1.46843e14	+	1.46843e14i	−0.590711	+	0.590711i	−0.937823	−	0.347113i	$-0.887162\pi$
$757$	−1.46843e14	+	1.46843e14i	−0.590711	+	0.590711i	0.347113	+	0.937823i	$0.387162\pi$
$758$	8.24318e13	−	3.48510e14i	0.329419	−	1.39274i
$759$	8.05793e12			0.0319900
$760$	5.00021e13	+	5.62721e14i	0.197206	+	2.21935i
$761$		−	2.31998e14i		−	0.908992i	−0.890749	−	0.454496i	$-0.849819\pi$
$761$		−	2.31998e14i		−	0.908992i	0.890749	−	0.454496i	$-0.150181\pi$
$762$	1.21542e13	−	5.13862e13i	0.0473097	−	0.200019i
$763$	3.11598e14	+	3.11598e14i	1.20496	+	1.20496i
$764$	1.07789e14	+	5.40113e13i	0.414101	+	0.207500i
$765$	1.10458e12	+	1.10458e12i	0.00421588	+	0.00421588i
$766$	3.27323e14	−	2.02101e14i	1.24118	−	0.766345i
$767$			8.12383e13i			0.306044i
$768$	1.36545e14	+	2.51058e14i	0.511059	+	0.939652i
$769$	−4.30370e14			−1.60033			−0.800166	−	0.599779i	$-0.795255\pi$
$769$	−4.30370e14			−1.60033			−0.800166	+	0.599779i	$0.795255\pi$
$770$	7.25112e13	+	1.17439e14i	0.267887	+	0.433871i
$771$	9.67989e13	−	9.67989e13i	0.355303	−	0.355303i
$772$	1.50600e14	−	3.00547e14i	0.549208	−	1.09604i
$773$	−3.24190e14	+	3.24190e14i	−1.17463	+	1.17463i	−0.193540	+	0.981092i	$0.561997\pi$
$773$	−3.24190e14	+	3.24190e14i	−1.17463	+	1.17463i	−0.981092	+	0.193540i	$0.938003\pi$
$774$	2.76877e13	+	6.54887e12i	0.0996741	+	0.0235755i
$775$	−6.17244e14			−2.20774
$776$	3.97214e14	−	3.52956e13i	1.41161	−	0.125433i
$777$			6.87533e14i			2.42766i
$778$	3.37877e14	+	7.99166e13i	1.18539	+	0.280375i
$779$	7.87056e13	+	7.87056e13i	0.274358	+	0.274358i
$780$	−1.16531e14	−	3.50606e14i	−0.403615	−	1.21436i
$781$	−2.95004e13	−	2.95004e13i	−0.101525	−	0.101525i
$782$	−5.79663e11	−	9.38824e11i	−0.00198217	−	0.00321034i
$783$			4.30906e14i			1.46411i
$784$	−2.51448e14	−	3.36480e14i	−0.848923	−	1.13600i
$785$	−3.24897e14			−1.08993
$786$	2.58608e14	−	1.59674e14i	0.862045	−	0.532256i
$787$	−7.68397e13	+	7.68397e13i	−0.254514	+	0.254514i	−0.822818	−	0.568304i	$-0.807600\pi$
$787$	−7.68397e13	+	7.68397e13i	−0.254514	+	0.254514i	0.568304	+	0.822818i	$0.307600\pi$
$788$	4.90824e13	+	1.47674e14i	0.161545	+	0.486042i
$789$	8.67707e13	−	8.67707e13i	0.283784	−	0.283784i
$790$	−1.18268e14	+	5.00021e14i	−0.384354	+	1.62500i
$791$	1.39702e14			0.451149
$792$	−5.97378e12	+	7.13895e12i	−0.0191701	+	0.0229091i
$793$		−	3.83475e14i		−	1.22284i
$794$	−8.13186e13	+	3.43804e14i	−0.257684	+	1.08945i
$795$	5.43296e14	+	5.43296e14i	1.71081	+	1.71081i
$796$	2.41062e14	−	4.81080e14i	0.754335	−	1.50540i
$797$	2.08719e13	+	2.08719e13i	0.0649037	+	0.0649037i	0.738814	−	0.673910i	$-0.235386\pi$
$797$	2.08719e13	+	2.08719e13i	0.0649037	+	0.0649037i	−0.673910	+	0.738814i	$0.735386\pi$
$798$	6.44996e14	−	3.98243e14i	1.99316	−	1.23065i
$799$			1.84807e11i			0.000567524i
$800$	4.58141e14	+	1.80808e14i	1.39814	+	0.551782i
$801$	1.48234e13			0.0449557
$802$	−3.04731e14	−	4.93544e14i	−0.918428	−	1.48749i
$803$	4.39098e12	−	4.39098e12i	0.0131518	−	0.0131518i
$804$	−1.42173e13	−	7.12407e12i	−0.0423191	−	0.0212055i
$805$	−8.48610e13	+	8.48610e13i	−0.251032	+	0.251032i
$806$	3.67660e14	+	8.69612e13i	1.08086	+	0.255653i
$807$	−2.23460e14			−0.652877
$808$	−3.26892e14	+	3.90652e14i	−0.949179	+	1.13431i
$809$		−	1.47836e14i		−	0.426616i	−0.976985	−	0.213308i	$-0.931576\pi$
$809$		−	1.47836e14i		−	0.426616i	0.976985	−	0.213308i	$-0.0684238\pi$
$810$	−6.03058e14	−	1.42639e14i	−1.72955	−	0.409084i
$811$	−2.86313e14	−	2.86313e14i	−0.816088	−	0.816088i	0.169450	−	0.985539i	$-0.445801\pi$
$811$	−2.86313e14	−	2.86313e14i	−0.816088	−	0.816088i	−0.985539	+	0.169450i	$0.945801\pi$
$812$	−8.33099e14	+	2.76897e14i	−2.36002	+	0.784400i
$813$	−1.94464e14	−	1.94464e14i	−0.547502	−	0.547502i
$814$	−5.67941e13	−	9.19840e13i	−0.158921	−	0.257389i
$815$			1.36261e14i			0.378951i
$816$	1.00141e13	+	1.44832e12i	0.0276797	+	0.00400327i
$817$	3.64302e14			1.00081
$818$	1.51159e14	−	9.33309e13i	0.412732	−	0.254835i
$819$	−4.41589e13	+	4.41589e13i	−0.119839	+	0.119839i
$820$	1.53353e14	−	5.09697e13i	0.413639	−	0.137481i
$821$	3.34949e14	−	3.34949e14i	0.897971	−	0.897971i	−0.0972851	−	0.995257i	$-0.531016\pi$
$821$	3.34949e14	−	3.34949e14i	0.897971	−	0.897971i	0.995257	+	0.0972851i	$0.0310159\pi$
$822$	3.63099e13	−	1.53513e14i	0.0967533	−	0.409060i
$823$	−1.27724e14			−0.338277			−0.169138	−	0.985592i	$-0.554098\pi$
$823$	−1.27724e14			−0.338277			−0.169138	+	0.985592i	$0.554098\pi$
$824$	−3.26640e14	+	2.90245e13i	−0.859870	+	0.0764062i
$825$			1.27351e14i			0.333221i
$826$	−5.57006e13	+	2.35495e14i	−0.144864	+	0.612464i
$827$	1.89702e14	+	1.89702e14i	0.490392	+	0.490392i	0.908430	−	0.418037i	$-0.137282\pi$
$827$	1.89702e14	+	1.89702e14i	0.490392	+	0.490392i	−0.418037	+	0.908430i	$0.637282\pi$
$828$	−7.23634e12	−	3.62602e12i	−0.0185938	−	0.00931706i
$829$	3.38586e14	+	3.38586e14i	0.864761	+	0.864761i	0.991887	−	0.127126i	$-0.0405752\pi$
$829$	3.38586e14	+	3.38586e14i	0.864761	+	0.864761i	−0.127126	+	0.991887i	$0.540575\pi$
$830$	−3.43765e14	+	2.12253e14i	−0.872713	+	0.538843i
$831$			2.24684e14i			0.566979i
$832$	−2.47417e14	−	1.72244e14i	−0.620602	−	0.432042i
$833$	−1.48719e13			−0.0370803
$834$	1.19839e14	+	1.94092e14i	0.297008	+	0.481035i
$835$	−6.24347e14	+	6.24347e14i	−1.53813	+	1.53813i
$836$	−5.33959e13	+	1.06561e14i	−0.130760	+	0.260955i
$837$	3.90594e14	−	3.90594e14i	0.950819	−	0.950819i
$838$	5.31718e12	+	1.25765e12i	0.0128665	+	0.00304327i
$839$	3.59634e14			0.865070			0.432535	−	0.901617i	$-0.357619\pi$
$839$	3.59634e14			0.865070			0.432535	+	0.901617i	$0.357619\pi$
$840$	−9.74094e13	−	1.09624e15i	−0.232919	−	2.62125i
$841$			6.55350e14i			1.55773i
$842$	6.28216e14	+	1.48590e14i	1.48439	+	0.351098i
$843$	−1.49454e14	−	1.49454e14i	−0.351051	−	0.351051i
$844$	1.01919e12	+	3.06643e12i	0.00237981	+	0.00716013i
$845$	−2.06369e14	−	2.06369e14i	−0.479028	−	0.479028i
$846$	7.12234e11	+	1.15354e12i	0.00164351	+	0.00266183i
$847$		−	6.48770e14i		−	1.48824i
$848$	6.20477e14	+	8.97387e13i	1.41497	+	0.204645i
$849$	−6.09132e14			−1.38093
$850$	1.48376e13	−	9.16124e12i	0.0334402	−	0.0206471i
$851$	6.64670e13	−	6.64670e13i	0.148922	−	0.148922i
$852$	1.04925e14	+	3.15687e14i	0.233711	+	0.703167i
$853$	3.10861e13	−	3.10861e13i	0.0688368	−	0.0688368i	−0.671850	−	0.740687i	$-0.734500\pi$
$853$	3.10861e13	−	3.10861e13i	0.0688368	−	0.0688368i	0.740687	+	0.671850i	$0.234500\pi$
$854$	2.62927e14	−	1.11162e15i	0.578824	−	2.44719i
$855$	1.46727e14			0.321129
$856$	2.00986e14	+	1.68182e14i	0.437318	+	0.365942i
$857$		−	4.02231e14i		−	0.870104i	−0.900405	−	0.435052i	$-0.856730\pi$
$857$		−	4.02231e14i		−	0.870104i	0.900405	−	0.435052i	$-0.143270\pi$
$858$	1.79420e13	−	7.58562e13i	0.0385864	−	0.163138i
$859$	−1.16040e14	−	1.16040e14i	−0.248109	−	0.248109i	0.572085	−	0.820194i	$-0.306135\pi$
$859$	−1.16040e14	−	1.16040e14i	−0.248109	−	0.248109i	−0.820194	+	0.572085i	$0.806135\pi$
$860$	2.36948e14	−	4.72870e14i	0.503688	−	1.00519i
$861$	−1.53327e14	−	1.53327e14i	−0.324043	−	0.324043i
$862$	−5.54295e14	+	3.42241e14i	−1.16467	+	0.719110i
$863$		−	8.01235e14i		−	1.67381i	−0.547348	−	0.836905i	$-0.684363\pi$
$863$		−	8.01235e14i		−	1.67381i	0.547348	−	0.836905i	$-0.315637\pi$
$864$	−4.04329e14	+	1.75497e14i	−0.839780	+	0.364503i
$865$	4.05174e14			0.836683
$866$	2.37448e13	+	3.84573e13i	0.0487506	+	0.0789567i
$867$	−3.70272e14	+	3.70272e14i	−0.755832	+	0.755832i
$868$	1.00615e15	+	5.04168e14i	2.04204	+	1.02324i
$869$	−7.66536e13	+	7.66536e13i	−0.154680	+	0.154680i
$870$	−1.31274e15	−	3.10497e14i	−2.63379	−	0.622961i
$871$	1.67749e13			0.0334632
$872$	4.23716e14	+	3.54560e14i	0.840412	+	0.703246i
$873$		−	1.03572e14i		−	0.204254i
$874$	−1.00855e14	−	2.38548e13i	−0.197760	−	0.0467755i
$875$	−4.48892e14	−	4.48892e14i	−0.875189	−	0.875189i
$876$	−4.69883e13	+	1.56175e13i	−0.0910898	+	0.0302754i
$877$	9.24183e13	+	9.24183e13i	0.178139	+	0.178139i	0.790544	−	0.612405i	$-0.209798\pi$
$877$	9.24183e13	+	9.24183e13i	0.178139	+	0.178139i	−0.612405	+	0.790544i	$0.709798\pi$
$878$	−4.01729e13	−	6.50642e13i	−0.0769947	−	0.124701i
$879$			5.20618e14i			0.992144i
$880$	1.03588e14	+	1.38618e14i	0.196288	+	0.262667i
$881$	−1.31735e14			−0.248212			−0.124106	−	0.992269i	$-0.539606\pi$
$881$	−1.31735e14			−0.248212			−0.124106	+	0.992269i	$0.539606\pi$
$882$	−9.28286e13	+	5.73156e13i	−0.173916	+	0.107382i
$883$	1.99062e14	−	1.99062e14i	0.370839	−	0.370839i	−0.496944	−	0.867783i	$-0.665544\pi$
$883$	1.99062e14	−	1.99062e14i	0.370839	−	0.370839i	0.867783	+	0.496944i	$0.165544\pi$
$884$	−1.01287e13	+	3.36646e12i	−0.0187625	+	0.00623608i
$885$	−2.62927e14	+	2.62927e14i	−0.484305	+	0.484305i
$886$	−1.94373e14	+	8.21783e14i	−0.356014	+	1.50518i
$887$	1.00259e15			1.82602			0.913012	−	0.407932i	$-0.133750\pi$
$887$	1.00259e15			1.82602			0.913012	+	0.407932i	$0.133750\pi$
$888$	7.62955e13	+	8.58625e14i	0.138177	+	1.55503i
$889$			1.65923e14i			0.298811i
$890$	6.34284e13	−	2.68166e14i	0.113588	−	0.480236i
$891$	−9.24493e13	−	9.24493e13i	−0.164632	−	0.164632i
$892$	−3.83471e14	−	1.92152e14i	−0.679060	−	0.340267i
$893$	1.22745e13	+	1.22745e13i	0.0216145	+	0.0216145i
$894$	−6.83170e14	+	4.21812e14i	−1.19630	+	0.738638i
$895$		−	6.96442e14i		−	1.21275i
$896$	−5.99118e14	−	6.68942e14i	−1.03746	−	1.15837i
$897$	6.77780e13			0.116715
$898$	1.57473e14	+	2.55044e14i	0.269665	+	0.436751i
$899$	9.75389e14	−	9.75389e14i	1.66104	−	1.66104i
$900$	5.73073e13	−	1.14366e14i	0.0970503	−	0.193680i
$901$	1.56953e13	−	1.56953e13i	0.0264329	−	0.0264329i
$902$	3.31790e13	+	7.84769e12i	0.0555687	+	0.0131434i
$903$	−7.09699e14			−1.18205
$904$	1.74466e14	−	1.55027e13i	0.288981	−	0.0256782i
$905$			1.00075e15i			1.64848i
$906$	−5.29076e14	−	1.25140e14i	−0.866716	−	0.205001i
$907$	−3.68117e14	−	3.68117e14i	−0.599720	−	0.599720i	0.340518	−	0.940238i	$-0.389398\pi$
$907$	−3.68117e14	−	3.68117e14i	−0.599720	−	0.599720i	−0.940238	+	0.340518i	$0.889398\pi$
$908$	1.55888e14	+	4.69021e14i	0.252571	+	0.759912i
$909$	9.35483e13	+	9.35483e13i	0.150736	+	0.150736i
$910$	6.09916e14	+	9.87823e14i	0.977380	+	1.58297i
$911$			1.03238e15i			1.64530i	0.568545	+	0.822652i	$0.307506\pi$
$911$			1.03238e15i			1.64530i	−0.568545	+	0.822652i	$0.692494\pi$
$912$	7.61309e14	−	5.68920e14i	1.20667	−	0.901731i
$913$	−8.52380e13			−0.134363
$914$	−1.30623e14	+	8.06510e13i	−0.204780	+	0.126438i
$915$	1.24111e15	−	1.24111e15i	1.93511	−	1.93511i
$916$	1.08278e14	+	3.25775e14i	0.167904	+	0.505174i
$917$	−6.75303e14	+	6.75303e14i	−1.04148	+	1.04148i
$918$	−3.59201e12	+	1.51865e13i	−0.00550964	+	0.0232940i
$919$	5.76490e14			0.879456			0.439728	−	0.898131i	$-0.355075\pi$
$919$	5.76490e14			0.879456			0.439728	+	0.898131i	$0.355075\pi$
$920$	−9.65615e13	+	1.15396e14i	−0.146509	+	0.175085i
$921$		−	4.81669e14i		−	0.726859i
$922$	2.97512e14	−	1.25784e15i	0.446530	−	1.88787i
$923$	−2.48138e14	−	2.48138e14i	−0.370412	−	0.370412i
$924$	1.04021e14	−	2.07591e14i	0.154440	−	0.308211i
$925$	1.05047e15	+	1.05047e15i	1.55123	+	1.55123i
$926$	−6.89833e14	+	4.25927e14i	−1.01319	+	0.625576i
$927$			8.51699e13i			0.124419i
$928$	−1.00969e15	+	4.38251e14i	−1.46706	+	0.636771i
$929$	1.00771e15			1.45633			0.728163	−	0.685404i	$-0.240374\pi$
$929$	1.00771e15			1.45633			0.728163	+	0.685404i	$0.240374\pi$
$930$	9.08478e14	+	1.47138e15i	1.30587	+	2.11499i
$931$	−9.87764e14	+	9.87764e14i	−1.41223	+	1.41223i
$932$	−7.32076e14	−	3.66832e14i	−1.04106	−	0.521661i
$933$	−4.62147e14	+	4.62147e14i	−0.653690	+	0.653690i
$934$	5.81428e14	+	1.37523e14i	0.818016	+	0.193482i
$935$	6.12671e12			0.00857372
$936$	−5.02475e13	+	6.00482e13i	−0.0699416	+	0.0835835i
$937$		−	5.50566e14i		−	0.762274i	−0.924519	−	0.381137i	$-0.875533\pi$
$937$		−	5.50566e14i		−	0.762274i	0.924519	−	0.381137i	$-0.124467\pi$
$938$	4.86271e13	+	1.15016e13i	0.0669676	+	0.0158396i
$939$	−3.81885e14	−	3.81885e14i	−0.523124	−	0.523124i
$940$	2.39160e13	−	7.94895e12i	0.0325874	−	0.0108311i
$941$	−8.84842e14	−	8.84842e14i	−1.19927	−	1.19927i	−0.974385	−	0.224887i	$-0.927799\pi$
$941$	−8.84842e14	−	8.84842e14i	−1.19927	−	1.19927i	−0.224887	−	0.974385i	$-0.572201\pi$
$942$	2.87151e14	+	4.65071e14i	0.387129	+	0.626996i
$943$			2.96456e13i			0.0397559i
$944$	−4.34288e13	+	3.00278e14i	−0.0579319	+	0.400556i
$945$	1.69740e15			2.25230
$946$	9.49495e13	−	5.86251e13i	0.125325	−	0.0773798i
$947$	5.25029e13	−	5.25029e13i	0.0689340	−	0.0689340i	−0.671799	−	0.740733i	$-0.734478\pi$
$947$	5.25029e13	−	5.25029e13i	0.0689340	−	0.0689340i	0.740733	+	0.671799i	$0.234478\pi$
$948$	8.20279e14	−	2.72635e14i	1.07132	−	0.356074i
$949$	3.69340e13	−	3.69340e13i	0.0479839	−	0.0479839i
$950$	3.77011e14	−	1.59395e15i	0.487232	−	2.05995i
$951$	2.67534e14			0.343935
$952$	−3.16693e13	+	2.81406e12i	−0.0404998	+	0.00359873i
$953$		−	5.38588e14i		−	0.685160i	−0.939489	−	0.342580i	$-0.888699\pi$
$953$		−	5.38588e14i		−	0.685160i	0.939489	−	0.342580i	$-0.111301\pi$
$954$	3.74791e13	−	1.58456e14i	0.0474293	−	0.200525i
$955$	−4.11613e14	−	4.11613e14i	−0.518170	−	0.518170i
$956$	5.80142e14	+	2.90701e14i	0.726516	+	0.364046i
$957$	−2.01244e14	−	2.01244e14i	−0.250705	−	0.250705i
$958$	−2.26222e14	+	1.39677e14i	−0.280354	+	0.173100i
$959$			4.95685e14i			0.611100i
$960$	−2.43299e14	−	1.35823e15i	−0.298390	−	1.66577i
$961$	−9.48648e14			−1.15741
$962$	−4.77714e14	−	7.73709e14i	−0.579820	−	0.939079i
$963$	4.81296e13	−	4.81296e13i	0.0581140	−	0.0581140i
$964$	3.04152e14	−	6.06987e14i	0.365348	−	0.729113i
$965$	−1.14770e15	+	1.14770e15i	−1.37149	+	1.37149i
$966$	1.96476e14	+	4.64716e13i	0.233573	+	0.0552462i
$967$	−9.06728e14			−1.07237			−0.536185	−	0.844100i	$-0.680135\pi$
$967$	−9.06728e14			−1.07237			−0.536185	+	0.844100i	$0.680135\pi$
$968$	−7.19940e13	−	8.10216e14i	−0.0847071	−	0.953288i
$969$		−	3.36489e13i		−	0.0393869i
$970$	−1.87370e15	−	4.43178e14i	−2.18193	−	0.516083i
$971$	6.50122e14	+	6.50122e14i	0.753180	+	0.753180i	0.975071	−	0.221892i	$-0.0712231\pi$
$971$	6.50122e14	+	6.50122e14i	0.753180	+	0.753180i	−0.221892	+	0.975071i	$0.571223\pi$
$972$	7.82945e13	+	2.35565e14i	0.0902402	+	0.271506i
$973$	−5.06831e14	−	5.06831e14i	−0.581165	−	0.581165i
$974$	−1.79568e14	−	2.90830e14i	−0.204849	−	0.331775i
$975$			1.07119e15i			1.21575i
$976$	2.05000e14	−	1.41742e15i	0.231475	−	1.60048i
$977$	1.05626e15			1.18658			0.593291	−	0.804988i	$-0.297829\pi$
$977$	1.05626e15			1.18658			0.593291	+	0.804988i	$0.297829\pi$
$978$	1.95050e14	−	1.20430e14i	0.217997	−	0.134599i
$979$	4.11102e13	−	4.11102e13i	0.0457126	−	0.0457126i
$980$	6.39675e14	+	1.92459e15i	0.707667	+	2.12916i
$981$	1.01466e14	−	1.01466e14i	0.111680	−	0.111680i
$982$	7.99391e13	−	3.37972e14i	0.0875391	−	0.370103i
$983$	−3.10571e14			−0.338372			−0.169186	−	0.985584i	$-0.554114\pi$
$983$	−3.10571e14			−0.338372			−0.169186	+	0.985584i	$0.554114\pi$
$984$	−2.08496e14	−	1.74467e14i	−0.226008	−	0.189120i
$985$		−	7.51355e14i		−	0.810334i
$986$	−8.96994e12	+	3.79237e13i	−0.00962509	+	0.0406936i
$987$	−2.39120e13	−	2.39120e13i	−0.0255288	−	0.0255288i
$988$	−4.49131e14	+	8.96317e14i	−0.477077	+	0.952088i
$989$	6.86099e13	+	6.86099e13i	0.0725112	+	0.0725112i
$990$	3.82420e13	−	2.36120e13i	0.0402129	−	0.0248288i
$991$			7.42475e14i			0.776808i	0.921489	+	0.388404i	$0.126973\pi$
$991$			7.42475e14i			0.776808i	−0.921489	+	0.388404i	$0.873027\pi$
$992$	1.31248e15	+	5.17977e14i	1.36626	+	0.539203i
$993$	−1.76434e15			−1.82741
$994$	−5.49170e14	−	8.89439e14i	−0.565946	−	0.916609i
$995$	−1.83710e15	+	1.83710e15i	−1.88373	+	1.88373i
$996$	6.07655e14	+	3.04487e14i	0.619955	+	0.310650i
$997$	1.23860e14	−	1.23860e14i	0.125735	−	0.125735i	−0.641439	−	0.767174i	$-0.721662\pi$
$997$	1.23860e14	−	1.23860e14i	0.125735	−	0.125735i	0.767174	+	0.641439i	$0.221662\pi$
$998$	−7.14418e14	−	1.68979e14i	−0.721606	−	0.170679i
$999$	−1.32948e15			−1.33615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.11.f.a.3.7	✓	38
4.3	odd	2		64.11.f.a.47.5		38
8.3	odd	2		128.11.f.a.95.15		38
8.5	even	2		128.11.f.b.95.5		38
16.3	odd	4		128.11.f.b.31.5		38
16.5	even	4		64.11.f.a.15.5		38
16.11	odd	4	inner	16.11.f.a.11.7	yes	38
16.13	even	4		128.11.f.a.31.15		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.11.f.a.3.7	✓	38	1.1	even	1	trivial
16.11.f.a.11.7	yes	38	16.11	odd	4	inner
64.11.f.a.15.5		38	16.5	even	4
64.11.f.a.47.5		38	4.3	odd	2
128.11.f.a.31.15		38	16.13	even	4
128.11.f.a.95.15		38	8.3	odd	2
128.11.f.b.31.5		38	16.3	odd	4
128.11.f.b.95.5		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+(-16.8116 - 27.2281i) q^{2} +(183.793 - 183.793i) q^{3} +(-458.741 + 915.496i) q^{4} +(3496.01 - 3496.01i) q^{5} +(-8094.18 - 1914.49i) q^{6} +26135.6 q^{7} +(32639.4 - 2900.27i) q^{8} -8510.59i q^{9} +(-153963. - 36416.3i) q^{10} +(-23602.7 - 23602.7i) q^{11} +(83948.2 + 252575. i) q^{12} +(-198530. - 198530. i) q^{13} +(-439381. - 711623. i) q^{14} -1.28508e6i q^{15} +(-627689. - 839951. i) q^{16} -37124.7 q^{17} +(-231727. + 143076. i) q^{18} +(-2.46575e6 + 2.46575e6i) q^{19} +(1.59682e6 + 4.80434e6i) q^{20} +(4.80353e6 - 4.80353e6i) q^{21} +(-245858. + 1.03946e6i) q^{22} -928760. q^{23} +(5.46584e6 - 6.53193e6i) q^{24} -1.46785e7i q^{25} +(-2.06800e6 + 8.74322e6i) q^{26} +(9.28860e6 + 9.28860e6i) q^{27} +(-1.19895e7 + 2.39270e7i) q^{28} +(2.31954e7 + 2.31954e7i) q^{29} +(-3.49904e7 + 2.16043e7i) q^{30} -4.20509e7i q^{31} +(-1.23179e7 + 3.12117e7i) q^{32} -8.67601e6 q^{33} +(624126. + 1.01084e6i) q^{34} +(9.13702e7 - 9.13702e7i) q^{35} +(7.79141e6 + 3.90416e6i) q^{36} +(-7.15654e7 + 7.15654e7i) q^{37} +(1.08591e8 + 2.56846e7i) q^{38} -7.29769e7 q^{39} +(1.03968e8 - 1.24247e8i) q^{40} -3.19196e7i q^{41} +(-2.11546e8 - 5.00362e7i) q^{42} +(-7.38726e7 - 7.38726e7i) q^{43} +(3.24357e7 - 1.07806e7i) q^{44} +(-2.97531e7 - 2.97531e7i) q^{45} +(1.56139e7 + 2.52884e7i) q^{46} -4.97800e6i q^{47} +(-2.69742e8 - 3.90124e7i) q^{48} +4.00594e8 q^{49} +(-3.99668e8 + 2.46769e8i) q^{50} +(-6.82326e6 + 6.82326e6i) q^{51} +(2.72828e8 - 9.06796e7i) q^{52} +(-4.22772e8 + 4.22772e8i) q^{53} +(9.67550e7 - 4.09067e8i) q^{54} -1.65030e8 q^{55} +(8.53050e8 - 7.58002e7i) q^{56} +9.06373e8i q^{57} +(2.41616e8 - 1.02152e9i) q^{58} +(-2.04599e8 - 2.04599e8i) q^{59} +(1.17649e9 + 5.89520e8i) q^{60} +(9.65784e8 + 9.65784e8i) q^{61} +(-1.14497e9 + 7.06942e8i) q^{62} -2.22429e8i q^{63} +(1.05692e9 - 1.89326e8i) q^{64} -1.38813e9 q^{65} +(1.45857e8 + 2.36231e8i) q^{66} +(-4.22476e7 + 4.22476e7i) q^{67} +(1.70307e7 - 3.39875e7i) q^{68} +(-1.70699e8 + 1.70699e8i) q^{69} +(-4.02392e9 - 9.51762e8i) q^{70} +1.24987e9 q^{71} +(-2.46830e7 - 2.77780e8i) q^{72} +1.86037e8i q^{73} +(3.15172e9 + 7.45464e8i) q^{74} +(-2.69781e9 - 2.69781e9i) q^{75} +(-1.12624e9 - 3.38852e9i) q^{76} +(-6.16870e8 - 6.16870e8i) q^{77} +(1.22686e9 + 1.98702e9i) q^{78} -3.24767e9i q^{79} +(-5.13088e9 - 7.42072e8i) q^{80} +3.91690e9 q^{81} +(-8.69110e8 + 5.36618e8i) q^{82} +(1.80568e9 - 1.80568e9i) q^{83} +(2.19403e9 + 6.60119e9i) q^{84} +(-1.29788e8 + 1.29788e8i) q^{85} +(-7.69497e8 + 3.25333e9i) q^{86} +8.52631e9 q^{87} +(-8.38832e8 - 7.01923e8i) q^{88} +1.74176e9i q^{89} +(-3.09924e8 + 1.31032e9i) q^{90} +(-5.18871e9 - 5.18871e9i) q^{91} +(4.26060e8 - 8.50275e8i) q^{92} +(-7.72865e9 - 7.72865e9i) q^{93} +(-1.35542e8 + 8.36880e7i) q^{94} +1.72405e10i q^{95} +(3.47255e9 + 8.00042e9i) q^{96} +1.21698e10 q^{97} +(-6.73462e9 - 1.09074e10i) q^{98} +(-2.00873e8 + 2.00873e8i) 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

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