LMFDB - Embedded newform 12.16.b.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,16,Mod(11,12)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 16, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.1232206120$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-80.5973 + 162.087i) q^{2} +(-2767.36 - 2586.62i) q^{3} +(-19776.2 - 26127.5i) q^{4} +332581. i q^{5} +(642299. - 240078. i) q^{6} +2.13481e6i q^{7} +(5.82882e6 - 1.09965e6i) q^{8} +(967701. + 1.43162e7i) q^{9} +O(q^{10})$	\(q+(-80.5973 + 162.087i) q^{2} +(-2767.36 - 2586.62i) q^{3} +(-19776.2 - 26127.5i) q^{4} +332581. i q^{5} +(642299. - 240078. i) q^{6} +2.13481e6i q^{7} +(5.82882e6 - 1.09965e6i) q^{8} +(967701. + 1.43162e7i) q^{9} +(-5.39069e7 - 2.68051e7i) q^{10} -7.24202e7 q^{11} +(-1.28540e7 + 1.23458e8i) q^{12} +5.97405e7 q^{13} +(-3.46024e8 - 1.72060e8i) q^{14} +(8.60260e8 - 9.20372e8i) q^{15} +(-2.91549e8 + 1.03340e9i) q^{16} -9.88823e8i q^{17} +(-2.39847e9 - 9.96998e8i) q^{18} -6.22690e7i q^{19} +(8.68950e9 - 6.57717e9i) q^{20} +(5.52194e9 - 5.90779e9i) q^{21} +(5.83687e9 - 1.17383e10i) q^{22} -2.88688e9 q^{23} +(-1.89748e10 - 1.20338e10i) q^{24} -8.00924e10 q^{25} +(-4.81493e9 + 9.68315e9i) q^{26} +(3.43527e10 - 4.21213e10i) q^{27} +(5.57772e10 - 4.22183e10i) q^{28} -3.09233e10i q^{29} +(7.98454e10 + 2.13616e11i) q^{30} -4.97193e10i q^{31} +(-1.44003e11 - 1.30546e11i) q^{32} +(2.00413e11 + 1.87324e11i) q^{33} +(1.60275e11 + 7.96964e10i) q^{34} -7.09996e11 q^{35} +(3.54910e11 - 3.08404e11i) q^{36} +2.95345e11 q^{37} +(1.00930e10 + 5.01871e9i) q^{38} +(-1.65324e11 - 1.54526e11i) q^{39} +(3.65722e11 + 1.93855e12i) q^{40} +1.49988e12i q^{41} +(5.12521e11 + 1.37118e12i) q^{42} -2.69129e12i q^{43} +(1.43219e12 + 1.89216e12i) q^{44} +(-4.76131e12 + 3.21839e11i) q^{45} +(2.32675e11 - 4.67925e11i) q^{46} -4.45404e12 q^{47} +(3.47984e12 - 2.10568e12i) q^{48} +1.90153e11 q^{49} +(6.45523e12 - 1.29819e13i) q^{50} +(-2.55771e12 + 2.73643e12i) q^{51} +(-1.18144e12 - 1.56087e12i) q^{52} -3.63427e12i q^{53} +(4.05857e12 + 8.96298e12i) q^{54} -2.40856e13i q^{55} +(2.34754e12 + 1.24434e13i) q^{56} +(-1.61066e11 + 1.72321e11i) q^{57} +(5.01226e12 + 2.49234e12i) q^{58} +2.17253e13 q^{59} +(-4.10596e13 - 4.27500e12i) q^{60} -3.26526e12 q^{61} +(8.05883e12 + 4.00724e12i) q^{62} +(-3.05624e13 + 2.06586e12i) q^{63} +(3.27659e13 - 1.28193e13i) q^{64} +1.98686e13i q^{65} +(-4.65154e13 + 1.73865e13i) q^{66} +7.11776e13i q^{67} +(-2.58355e13 + 1.95551e13i) q^{68} +(7.98905e12 + 7.46727e12i) q^{69} +(5.72238e13 - 1.15081e14i) q^{70} -4.18952e13 q^{71} +(2.13834e13 + 8.23827e13i) q^{72} +1.11208e14 q^{73} +(-2.38040e13 + 4.78715e13i) q^{74} +(2.21645e14 + 2.07169e14i) q^{75} +(-1.62693e12 + 1.23144e12i) q^{76} -1.54603e14i q^{77} +(3.83713e13 - 1.43424e13i) q^{78} -1.98903e14i q^{79} +(-3.43690e14 - 9.69635e13i) q^{80} +(-2.04018e14 + 2.77077e13i) q^{81} +(-2.43111e14 - 1.20886e14i) q^{82} +1.29134e14 q^{83} +(-2.63559e14 - 2.74409e13i) q^{84} +3.28864e14 q^{85} +(4.36222e14 + 2.16910e14i) q^{86} +(-7.99869e13 + 8.55761e13i) q^{87} +(-4.22124e14 + 7.96367e13i) q^{88} -1.60087e14i q^{89} +(3.31582e14 - 7.97683e14i) q^{90} +1.27535e14i q^{91} +(5.70914e13 + 7.54270e13i) q^{92} +(-1.28605e14 + 1.37591e14i) q^{93} +(3.58983e14 - 7.21940e14i) q^{94} +2.07095e13 q^{95} +(6.08361e13 + 7.33747e14i) q^{96} -1.03196e15 q^{97} +(-1.53258e13 + 3.08212e13i) q^{98} +(-7.00811e13 - 1.03678e15i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) $ 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−80.5973	+	162.087i	−0.445241	+	0.895411i
$2$	−80.5973	+	162.087i	−0.445241	+	0.895411i
$3$	−2767.36	−	2586.62i	−0.730562	−	0.682847i
$3$	−2767.36	−	2586.62i	−0.730562	−	0.682847i
$4$	−19776.2	−	26127.5i	−0.603521	−	0.797347i
$5$			332581.i			1.90380i	0.306404	+	0.951902i	$0.400874\pi$
$5$			332581.i			1.90380i	−0.306404	+	0.951902i	$0.599126\pi$
$6$	642299.	−	240078.i	0.936704	−	0.350121i
$7$			2.13481e6i			0.979769i	0.871787	+	0.489884i	$0.162961\pi$
$7$			2.13481e6i			0.979769i	−0.871787	+	0.489884i	$0.837039\pi$
$8$	5.82882e6	−	1.09965e6i	0.982666	−	0.185387i
$9$	967701.	+	1.43162e7i	0.0674407	+	0.997723i
$10$	−5.39069e7	−	2.68051e7i	−1.70469	−	0.847652i
$11$	−7.24202e7			−1.12051			−0.560253	−	0.828321i	$-0.689296\pi$
$11$	−7.24202e7			−1.12051			−0.560253	+	0.828321i	$0.689296\pi$
$12$	−1.28540e7	+	1.23458e8i	−0.103557	+	0.994624i
$13$	5.97405e7			0.264055			0.132027	−	0.991246i	$-0.457851\pi$
$13$	5.97405e7			0.264055			0.132027	+	0.991246i	$0.457851\pi$
$14$	−3.46024e8	−	1.72060e8i	−0.877296	−	0.436234i
$15$	8.60260e8	−	9.20372e8i	1.30001	−	1.39085i
$16$	−2.91549e8	+	1.03340e9i	−0.271526	+	0.962431i
$17$		−	9.88823e8i		−	0.584456i	−0.956349	−	0.292228i	$-0.905603\pi$
$17$		−	9.88823e8i		−	0.584456i	0.956349	−	0.292228i	$-0.0943966\pi$
$18$	−2.39847e9	−	9.96998e8i	−0.923399	−	0.383840i
$19$		−	6.22690e7i		−	0.0159816i	−0.999968	−	0.00799079i	$-0.997456\pi$
$19$		−	6.22690e7i		−	0.0159816i	0.999968	−	0.00799079i	$-0.00254357\pi$
$20$	8.68950e9	−	6.57717e9i	1.51799	−	1.14898i
$21$	5.52194e9	−	5.90779e9i	0.669032	−	0.715782i
$22$	5.83687e9	−	1.17383e10i	0.498896	−	1.00331i
$23$	−2.88688e9			−0.176795			−0.0883976	−	0.996085i	$-0.528175\pi$
$23$	−2.88688e9			−0.176795			−0.0883976	+	0.996085i	$0.528175\pi$
$24$	−1.89748e10	−	1.20338e10i	−0.844489	−	0.535574i
$25$	−8.00924e10			−2.62447
$26$	−4.81493e9	+	9.68315e9i	−0.117568	+	0.236437i
$27$	3.43527e10	−	4.21213e10i	0.632022	−	0.774950i
$28$	5.57772e10	−	4.22183e10i	0.781216	−	0.591311i
$29$		−	3.09233e10i		−	0.332890i	−0.986051	−	0.166445i	$-0.946771\pi$
$29$		−	3.09233e10i		−	0.332890i	0.986051	−	0.166445i	$-0.0532289\pi$
$30$	7.98454e10	+	2.13616e11i	0.666562	+	1.78330i
$31$		−	4.97193e10i		−	0.324573i	−0.986744	−	0.162286i	$-0.948113\pi$
$31$		−	4.97193e10i		−	0.324573i	0.986744	−	0.162286i	$-0.0518868\pi$
$32$	−1.44003e11	−	1.30546e11i	−0.740877	−	0.671641i
$33$	2.00413e11	+	1.87324e11i	0.818599	+	0.765134i
$34$	1.60275e11	+	7.96964e10i	0.523328	+	0.260224i
$35$	−7.09996e11			−1.86529
$36$	3.54910e11	−	3.08404e11i	0.754830	−	0.655920i
$37$	2.95345e11			0.511466			0.255733	−	0.966747i	$-0.417683\pi$
$37$	2.95345e11			0.511466			0.255733	+	0.966747i	$0.417683\pi$
$38$	1.00930e10	+	5.01871e9i	0.0143101	+	0.00711566i
$39$	−1.65324e11	−	1.54526e11i	−0.192908	−	0.180309i
$40$	3.65722e11	+	1.93855e12i	0.352940	+	1.87080i
$41$			1.49988e12i			1.20276i	0.798964	+	0.601379i	$0.205382\pi$
$41$			1.49988e12i			1.20276i	−0.798964	+	0.601379i	$0.794618\pi$
$42$	5.12521e11	+	1.37118e12i	0.343038	+	0.917754i
$43$		−	2.69129e12i		−	1.50990i	−0.655785	−	0.754948i	$-0.727662\pi$
$43$		−	2.69129e12i		−	1.50990i	0.655785	−	0.754948i	$-0.272338\pi$
$44$	1.43219e12	+	1.89216e12i	0.676249	+	0.893433i
$45$	−4.76131e12	+	3.21839e11i	−1.89947	+	0.128394i
$46$	2.32675e11	−	4.67925e11i	0.0787165	−	0.158304i
$47$	−4.45404e12			−1.28239			−0.641194	−	0.767378i	$-0.721561\pi$
$47$	−4.45404e12			−1.28239			−0.641194	+	0.767378i	$0.721561\pi$
$48$	3.47984e12	−	2.10568e12i	0.855559	−	0.517705i
$49$	1.90153e11			0.0400527
$50$	6.45523e12	−	1.29819e13i	1.16852	−	2.34998i
$51$	−2.55771e12	+	2.73643e12i	−0.399094	+	0.426981i
$52$	−1.18144e12	−	1.56087e12i	−0.159362	−	0.210543i
$53$		−	3.63427e12i		−	0.424960i	−0.977165	−	0.212480i	$-0.931846\pi$
$53$		−	3.63427e12i		−	0.424960i	0.977165	−	0.212480i	$-0.0681541\pi$
$54$	4.05857e12	+	8.96298e12i	0.412496	+	0.910959i
$55$		−	2.40856e13i		−	2.13322i
$56$	2.34754e12	+	1.24434e13i	0.181636	+	0.962785i
$57$	−1.61066e11	+	1.72321e11i	−0.0109130	+	0.0116755i
$58$	5.01226e12	+	2.49234e12i	0.298074	+	0.148217i
$59$	2.17253e13			1.13652			0.568259	−	0.822850i	$-0.307617\pi$
$59$	2.17253e13			1.13652			0.568259	+	0.822850i	$0.307617\pi$
$60$	−4.10596e13	−	4.27500e12i	−1.89357	−	0.197152i
$61$	−3.26526e12			−0.133028			−0.0665142	−	0.997785i	$-0.521188\pi$
$61$	−3.26526e12			−0.133028			−0.0665142	+	0.997785i	$0.521188\pi$
$62$	8.05883e12	+	4.00724e12i	0.290626	+	0.144513i
$63$	−3.05624e13	+	2.06586e12i	−0.977538	+	0.0660763i
$64$	3.27659e13	−	1.28193e13i	0.931263	−	0.364346i
$65$			1.98686e13i			0.502708i
$66$	−4.65154e13	+	1.73865e13i	−1.04958	+	0.392313i
$67$			7.11776e13i			1.43477i	0.696677	+	0.717385i	$0.254661\pi$
$67$			7.11776e13i			1.43477i	−0.696677	+	0.717385i	$0.745339\pi$
$68$	−2.58355e13	+	1.95551e13i	−0.466014	+	0.352731i
$69$	7.98905e12	+	7.46727e12i	0.129160	+	0.120724i
$70$	5.72238e13	−	1.15081e14i	0.830503	−	1.67020i
$71$	−4.18952e13			−0.546672			−0.273336	−	0.961919i	$-0.588127\pi$
$71$	−4.18952e13			−0.546672			−0.273336	+	0.961919i	$0.588127\pi$
$72$	2.13834e13	+	8.23827e13i	0.251236	+	0.967926i
$73$	1.11208e14			1.17819			0.589093	−	0.808065i	$-0.299485\pi$
$73$	1.11208e14			1.17819			0.589093	+	0.808065i	$0.299485\pi$
$74$	−2.38040e13	+	4.78715e13i	−0.227726	+	0.457972i
$75$	2.21645e14	+	2.07169e14i	1.91734	+	1.79211i
$76$	−1.62693e12	+	1.23144e12i	−0.0127429	+	0.00964521i
$77$		−	1.54603e14i		−	1.09784i
$78$	3.83713e13	−	1.43424e13i	0.247341	−	0.0924512i
$79$		−	1.98903e14i		−	1.16530i	−0.812722	−	0.582651i	$-0.802015\pi$
$79$		−	1.98903e14i		−	1.16530i	0.812722	−	0.582651i	$-0.197985\pi$
$80$	−3.43690e14	−	9.69635e13i	−1.83228	−	0.516932i
$81$	−2.04018e14	+	2.77077e13i	−0.990903	+	0.134574i
$82$	−2.43111e14	−	1.20886e14i	−1.07696	−	0.535518i
$83$	1.29134e14			0.522344			0.261172	−	0.965292i	$-0.415891\pi$
$83$	1.29134e14			0.522344			0.261172	+	0.965292i	$0.415891\pi$
$84$	−2.63559e14	−	2.74409e13i	−0.974501	−	0.101462i
$85$	3.28864e14			1.11269
$86$	4.36222e14	+	2.16910e14i	1.35198	+	0.672268i
$87$	−7.99869e13	+	8.55761e13i	−0.227313	+	0.243197i
$88$	−4.22124e14	+	7.96367e13i	−1.10108	+	0.207727i
$89$		−	1.60087e14i		−	0.383646i	−0.981430	−	0.191823i	$-0.938560\pi$
$89$		−	1.60087e14i		−	0.383646i	0.981430	−	0.191823i	$-0.0614399\pi$
$90$	3.31582e14	−	7.97683e14i	0.730757	−	1.75797i
$91$			1.27535e14i			0.258713i
$92$	5.70914e13	+	7.54270e13i	0.106699	+	0.140967i
$93$	−1.28605e14	+	1.37591e14i	−0.221633	+	0.237120i
$94$	3.58983e14	−	7.21940e14i	0.570972	−	1.14826i
$95$	2.07095e13			0.0304258
$96$	6.08361e13	+	7.33747e14i	0.0826280	+	0.996580i
$97$	−1.03196e15			−1.29681			−0.648405	−	0.761296i	$-0.724563\pi$
$97$	−1.03196e15			−1.29681			−0.648405	+	0.761296i	$0.724563\pi$
$98$	−1.53258e13	+	3.08212e13i	−0.0178331	+	0.0358636i
$99$	−7.00811e13	−	1.03678e15i	−0.0755678	−	1.11796i
$100$	1.58392e15	+	2.09261e15i	1.58392	+	2.09261i
$101$		−	5.16077e14i		−	0.478965i	−0.970901	−	0.239483i	$-0.923022\pi$
$101$		−	5.16077e14i		−	0.478965i	0.970901	−	0.239483i	$-0.0769779\pi$
$102$	−2.37395e14	−	6.35120e14i	−0.204630	−	0.547462i
$103$			3.00999e14i			0.241149i	0.992704	+	0.120574i	$0.0384736\pi$
$103$			3.00999e14i			0.241149i	−0.992704	+	0.120574i	$0.961526\pi$
$104$	3.48217e14	−	6.56936e13i	0.259478	−	0.0489523i
$105$	1.96482e15	+	1.83649e15i	1.36271	+	1.27371i
$106$	5.89067e14	+	2.92912e14i	0.380514	+	0.189210i
$107$	−3.15916e15			−1.90192			−0.950961	−	0.309310i	$-0.899902\pi$
$107$	−3.15916e15			−1.90192			−0.950961	+	0.309310i	$0.899902\pi$
$108$	−1.77989e15	−	6.45513e13i	−0.999343	−	0.0362432i
$109$	−1.49688e15			−0.784313			−0.392156	−	0.919899i	$-0.628271\pi$
$109$	−1.49688e15			−0.784313			−0.392156	+	0.919899i	$0.628271\pi$
$110$	3.90395e15	+	1.94123e15i	1.91011	+	0.949800i
$111$	−8.17327e14	−	7.63945e14i	−0.373657	−	0.349253i
$112$	−2.20612e15	−	6.22401e14i	−0.942960	−	0.266033i
$113$			2.24823e15i			0.898987i	0.893284	+	0.449493i	$0.148395\pi$
$113$			2.24823e15i			0.898987i	−0.893284	+	0.449493i	$0.851605\pi$
$114$	−1.49494e13	−	3.99953e13i	−0.00559549	−	0.0149700i
$115$		−	9.60121e14i		−	0.336583i
$116$	−8.07949e14	+	6.11545e14i	−0.265429	+	0.200906i
$117$	5.78110e13	+	8.55260e14i	0.0178080	+	0.263454i
$118$	−1.75100e15	+	3.52139e15i	−0.506025	+	1.01765i
$119$	2.11095e15			0.572632
$120$	4.00222e15	−	6.31067e15i	1.01963	−	1.60774i
$121$	1.06744e15			0.255536
$122$	2.63171e14	−	5.29256e14i	0.0592297	−	0.119115i
$123$	3.87963e15	−	4.15072e15i	0.821300	−	0.878689i
$124$	−1.29904e15	+	9.83256e14i	−0.258797	+	0.195886i
$125$		−	1.64876e16i		−	3.09267i
$126$	2.12840e15	−	5.12026e15i	0.376075	−	0.904718i
$127$			3.71906e15i			0.619305i	0.950850	+	0.309653i	$0.100213\pi$
$127$			3.71906e15i			0.619305i	−0.950850	+	0.309653i	$0.899787\pi$
$128$	−5.63006e14	+	6.34412e15i	−0.0883972	+	0.996085i
$129$	−6.96134e15	+	7.44777e15i	−1.03103	+	1.10307i
$130$	−3.22043e15	−	1.60135e15i	−0.450130	−	0.223827i
$131$	−4.77701e15			−0.630407			−0.315204	−	0.949024i	$-0.602073\pi$
$131$	−4.77701e15			−0.630407			−0.315204	+	0.949024i	$0.602073\pi$
$132$	9.30891e14	−	8.94083e15i	0.116036	−	1.11448i
$133$	1.32932e14			0.0156583
$134$	−1.15369e16	−	5.73672e15i	−1.28471	−	0.638818i
$135$	1.40087e16	+	1.14250e16i	1.47535	+	1.20325i
$136$	−1.08736e15	−	5.76367e15i	−0.108350	−	0.574325i
$137$			5.77103e14i			0.0544313i	0.999630	+	0.0272157i	$0.00866409\pi$
$137$			5.77103e14i			0.0544313i	−0.999630	+	0.0272157i	$0.991336\pi$
$138$	−1.85424e15	+	6.93078e14i	−0.165605	+	0.0618997i
$139$			8.39263e15i			0.710047i	0.934857	+	0.355023i	$0.115527\pi$
$139$			8.39263e15i			0.710047i	−0.934857	+	0.355023i	$0.884473\pi$
$140$	1.40410e16	+	1.85504e16i	1.12574	+	1.48728i
$141$	1.23259e16	+	1.15209e16i	0.936864	+	0.875675i
$142$	3.37664e15	−	6.79066e15i	0.243401	−	0.489496i
$143$	−4.32642e15			−0.295875
$144$	−1.50766e16	−	3.17386e15i	−0.978552	−	0.206001i
$145$	1.02845e16			0.633758
$146$	−8.96305e15	+	1.80253e16i	−0.524577	+	1.05496i
$147$	−5.26222e14	−	4.91853e14i	−0.0292610	−	0.0273499i
$148$	−5.84079e15	−	7.71662e15i	−0.308680	−	0.407816i
$149$		−	1.81929e16i		−	0.914122i	−0.889435	−	0.457061i	$-0.848902\pi$
$149$		−	1.81929e16i		−	0.914122i	0.889435	−	0.457061i	$-0.151098\pi$
$150$	−5.14432e16	+	1.92284e16i	−2.45835	+	0.918882i
$151$		−	9.74788e15i		−	0.443183i	−0.975140	−	0.221591i	$-0.928875\pi$
$151$		−	9.74788e15i		−	0.443183i	0.975140	−	0.221591i	$-0.0711251\pi$
$152$	−6.84739e13	−	3.62955e14i	−0.00296277	−	0.0157045i
$153$	1.41562e16	−	9.56885e14i	0.583125	−	0.0394161i
$154$	2.50591e16	+	1.24606e16i	0.983016	+	0.488803i
$155$	1.65357e16			0.617922
$156$	−7.67907e14	+	7.37543e15i	−0.0273448	+	0.262635i
$157$	5.74704e15			0.195073			0.0975364	−	0.995232i	$-0.468904\pi$
$157$	5.74704e15			0.195073			0.0975364	+	0.995232i	$0.468904\pi$
$158$	3.22396e16	+	1.60311e16i	1.04342	+	0.518841i
$159$	−9.40048e15	+	1.00574e16i	−0.290183	+	0.310460i
$160$	4.34169e16	−	4.78925e16i	1.27867	−	1.41048i
$161$		−	6.16294e15i		−	0.173218i
$162$	1.19523e16	−	3.53018e16i	0.320692	−	0.947184i
$163$			3.06599e15i			0.0785533i	0.999228	+	0.0392766i	$0.0125054\pi$
$163$			3.06599e15i			0.0785533i	−0.999228	+	0.0392766i	$0.987495\pi$
$164$	3.91882e16	−	2.96619e16i	0.959016	−	0.725889i
$165$	−6.23002e16	+	6.66535e16i	−1.45667	+	1.55845i
$166$	−1.04079e16	+	2.09310e16i	−0.232569	+	0.467712i
$167$	−6.03839e16			−1.28987			−0.644937	−	0.764236i	$-0.723116\pi$
$167$	−6.03839e16			−1.28987			−0.644937	+	0.764236i	$0.723116\pi$
$168$	2.56899e16	−	4.05077e16i	0.524738	−	0.827404i
$169$	−4.76170e16			−0.930275
$170$	−2.65055e16	+	5.33044e16i	−0.495415	+	0.996314i
$171$	8.91457e14	−	6.02577e13i	0.0159452	−	0.00107781i
$172$	−7.03166e16	+	5.32234e16i	−1.20391	+	0.911253i
$173$		−	5.54209e16i		−	0.908506i	−0.890873	−	0.454253i	$-0.849906\pi$
$173$		−	5.54209e16i		−	0.908506i	0.890873	−	0.454253i	$-0.150094\pi$
$174$	−7.42402e15	−	1.98620e16i	−0.116552	−	0.311820i
$175$		−	1.70982e17i		−	2.57137i
$176$	2.11140e16	−	7.48392e16i	0.304247	−	1.07841i
$177$	−6.01219e16	−	5.61952e16i	−0.830297	−	0.776068i
$178$	2.59479e16	+	1.29026e16i	0.343520	+	0.170815i
$179$	3.27220e16			0.415377			0.207688	−	0.978195i	$-0.433406\pi$
$179$	3.27220e16			0.415377			0.207688	+	0.978195i	$0.433406\pi$
$180$	1.02569e17	+	1.18036e17i	1.24874	+	1.43705i
$181$	8.38904e16			0.979767			0.489884	−	0.871788i	$-0.337039\pi$
$181$	8.38904e16			0.979767			0.489884	+	0.871788i	$0.337039\pi$
$182$	−2.06717e16	−	1.02789e16i	−0.231654	−	0.115190i
$183$	9.03617e15	+	8.44599e15i	0.0971855	+	0.0908380i
$184$	−1.68271e16	+	3.17455e15i	−0.173730	+	0.0327755i
$185$			9.82260e16i			0.973730i
$186$	−1.19365e16	−	3.19346e16i	−0.113640	−	0.304029i
$187$			7.16108e16i			0.654887i
$188$	8.80837e16	+	1.16373e17i	0.773948	+	1.02251i
$189$	8.99210e16	+	7.33364e16i	0.759272	+	0.619236i
$190$	−1.66913e15	+	3.35673e15i	−0.0135468	+	0.0272436i
$191$	−1.70177e17			−1.32786			−0.663929	−	0.747795i	$-0.731112\pi$
$191$	−1.70177e17			−1.32786			−0.663929	+	0.747795i	$0.731112\pi$
$192$	−1.23834e17	−	4.92773e16i	−0.929138	−	0.369733i
$193$	8.40790e16			0.606747			0.303374	−	0.952872i	$-0.401887\pi$
$193$	8.40790e16			0.606747			0.303374	+	0.952872i	$0.401887\pi$
$194$	8.31734e16	−	1.67267e17i	0.577393	−	1.16118i
$195$	5.13924e16	−	5.49835e16i	0.343273	−	0.367260i
$196$	−3.76049e15	−	4.96821e15i	−0.0241726	−	0.0319359i
$197$			5.07424e16i			0.313960i	0.987602	+	0.156980i	$0.0501758\pi$
$197$			5.07424e16i			0.313960i	−0.987602	+	0.156980i	$0.949824\pi$
$198$	1.73697e17	+	7.22028e16i	1.03468	+	0.430096i
$199$			3.13880e17i			1.80039i	0.435490	+	0.900193i	$0.356575\pi$
$199$			3.13880e17i			1.80039i	−0.435490	+	0.900193i	$0.643425\pi$
$200$	−4.66844e17	+	8.80734e16i	−2.57897	+	0.486541i
$201$	1.84109e17	−	1.96974e17i	0.979727	−	1.04819i
$202$	8.36492e16	+	4.15944e16i	0.428871	+	0.213255i
$203$	6.60154e16			0.326156
$204$	1.22078e17	+	1.27104e16i	0.581314	+	0.0605246i
$205$	−4.98832e17			−2.28982
$206$	−4.87878e16	−	2.42597e16i	−0.215927	−	0.107369i
$207$	−2.79364e15	−	4.13293e16i	−0.0119232	−	0.176393i
$208$	−1.74173e16	+	6.17360e16i	−0.0716977	+	0.254135i
$209$			4.50953e15i			0.0179075i
$210$	−4.56030e17	+	1.70455e17i	−1.74722	+	0.653077i
$211$			9.66301e16i			0.357268i	0.983916	+	0.178634i	$0.0571678\pi$
$211$			9.66301e16i			0.357268i	−0.983916	+	0.178634i	$0.942832\pi$
$212$	−9.49544e16	+	7.18720e16i	−0.338841	+	0.256472i
$213$	1.15939e17	+	1.08367e17i	0.399378	+	0.373293i
$214$	2.54619e17	−	5.12057e17i	0.846814	−	1.70300i
$215$	8.95071e17			2.87454
$216$	1.53917e17	−	2.83293e17i	0.477401	−	0.878685i
$217$	1.06141e17			0.318006
$218$	1.20645e17	−	2.42625e17i	0.349208	−	0.702282i
$219$	−3.07753e17	−	2.87652e17i	−0.860738	−	0.804521i
$220$	−6.29295e17	+	4.76320e17i	−1.70092	+	1.28744i
$221$		−	5.90728e16i		−	0.154328i
$222$	1.89700e17	−	7.09059e16i	0.479092	−	0.179075i
$223$			5.01664e17i			1.22497i	0.790481	+	0.612487i	$0.209831\pi$
$223$			5.01664e17i			1.22497i	−0.790481	+	0.612487i	$0.790169\pi$
$224$	2.78690e17	−	3.07418e17i	0.658053	−	0.725888i
$225$	−7.75055e16	−	1.14662e18i	−0.176996	−	2.61849i
$226$	−3.64409e17	−	1.81202e17i	−0.804962	−	0.400266i
$227$	−4.52676e16			−0.0967371			−0.0483686	−	0.998830i	$-0.515402\pi$
$227$	−4.52676e16			−0.0967371			−0.0483686	+	0.998830i	$0.515402\pi$
$228$	7.68758e15	+	8.00407e14i	0.0158957	+	0.00165501i
$229$	8.67256e17			1.73533			0.867663	−	0.497153i	$-0.165621\pi$
$229$	8.67256e17			1.73533			0.867663	+	0.497153i	$0.165621\pi$
$230$	1.55623e17	+	7.73832e16i	0.301380	+	0.149861i
$231$	−3.99900e17	+	4.27844e17i	−0.749655	+	0.802038i
$232$	−3.40048e16	−	1.80247e17i	−0.0617135	−	0.327120i
$233$			9.66442e17i			1.69827i	0.528178	+	0.849134i	$0.322876\pi$
$233$			9.66442e17i			1.69827i	−0.528178	+	0.849134i	$0.677124\pi$
$234$	−1.43286e17	−	5.95612e16i	−0.243828	−	0.101355i
$235$		−	1.48133e18i		−	2.44142i
$236$	−4.29644e17	−	5.67628e17i	−0.685912	−	0.906200i
$237$	−5.14487e17	+	5.50438e17i	−0.795723	+	0.851325i
$238$	−1.70137e17	+	3.42157e17i	−0.254959	+	0.512741i
$239$	−3.69115e17			−0.536015			−0.268008	−	0.963417i	$-0.586365\pi$
$239$	−3.69115e17			−0.536015			−0.268008	+	0.963417i	$0.586365\pi$
$240$	7.00307e17	+	1.15733e18i	0.985608	+	1.62882i
$241$	−8.78718e17			−1.19873			−0.599365	−	0.800475i	$-0.704580\pi$
$241$	−8.78718e17			−1.19873			−0.599365	+	0.800475i	$0.704580\pi$
$242$	−8.60324e16	+	1.73017e17i	−0.113775	+	0.228809i
$243$	6.36262e17	+	4.51040e17i	0.815810	+	0.578320i
$244$	6.45744e16	+	8.53131e16i	0.0802854	+	0.106070i
$245$			6.32412e16i			0.0762525i
$246$	3.60089e17	+	9.63373e17i	0.421111	+	1.12663i
$247$		−	3.71998e15i		−	0.00422001i
$248$	−5.46737e16	−	2.89805e17i	−0.0601715	−	0.318946i
$249$	−3.57362e17	−	3.34022e17i	−0.381604	−	0.356681i
$250$	2.67242e18	+	1.32886e18i	2.76921	+	1.37698i
$251$	−7.88585e17			−0.793041			−0.396521	−	0.918026i	$-0.629782\pi$
$251$	−7.88585e17			−0.793041			−0.396521	+	0.918026i	$0.629782\pi$
$252$	6.58383e17	+	7.57665e17i	0.642650	+	0.739559i
$253$	2.09069e17			0.198100
$254$	−6.02809e17	−	2.99746e17i	−0.554533	−	0.275740i
$255$	−9.10085e17	−	8.50645e17i	−0.812888	−	0.759796i
$256$	−9.82920e17	−	6.02574e17i	−0.852547	−	0.522650i
$257$			1.65283e18i			1.39229i	0.717902	+	0.696144i	$0.245102\pi$
$257$			1.65283e18i			1.39229i	−0.717902	+	0.696144i	$0.754898\pi$
$258$	−6.46120e17	−	1.72861e18i	−0.528646	−	1.41433i
$259$			6.30505e17i			0.501118i
$260$	5.19115e17	−	3.92924e17i	0.400833	−	0.303395i
$261$	4.42706e17	−	2.99245e16i	0.332133	−	0.0224504i
$262$	3.85014e17	−	7.74289e17i	0.280683	−	0.564474i
$263$	−1.84436e18			−1.30670			−0.653352	−	0.757055i	$-0.726638\pi$
$263$	−1.84436e18			−1.30670			−0.653352	+	0.757055i	$0.726638\pi$
$264$	1.37416e18	+	8.71491e17i	0.946255	+	0.600114i
$265$	1.20869e18			0.809041
$266$	−1.07140e16	+	2.15466e16i	−0.00697170	+	0.0140206i
$267$	−4.14084e17	+	4.43018e17i	−0.261971	+	0.280277i
$268$	1.85969e18	−	1.40762e18i	1.14401	−	0.865913i
$269$		−	2.08695e18i		−	1.24844i	−0.781247	−	0.624222i	$-0.785416\pi$
$269$		−	2.08695e18i		−	1.24844i	0.781247	−	0.624222i	$-0.214584\pi$
$270$	−2.98091e18	+	1.34980e18i	−1.73429	+	0.785312i
$271$		−	1.61672e18i		−	0.914881i	−0.889240	−	0.457441i	$-0.848766\pi$
$271$		−	1.61672e18i		−	0.914881i	0.889240	−	0.457441i	$-0.151234\pi$
$272$	1.02185e18	+	2.88290e17i	0.562499	+	0.158695i
$273$	3.29884e17	−	3.52935e17i	0.176661	−	0.189006i
$274$	−9.35407e16	−	4.65129e16i	−0.0487384	−	0.0242351i
$275$	5.80031e18			2.94073
$276$	3.71081e16	−	3.56408e17i	0.0183084	−	0.175845i
$277$	−3.16017e18			−1.51744			−0.758720	−	0.651416i	$-0.774175\pi$
$277$	−3.16017e18			−1.51744			−0.758720	+	0.651416i	$0.774175\pi$
$278$	−1.36033e18	−	6.76423e17i	−0.635783	−	0.316142i
$279$	7.11793e17	−	4.81134e16i	0.323834	−	0.0218894i
$280$	−4.13844e18	+	7.80746e17i	−1.83295	+	0.345800i
$281$			5.35688e17i			0.231001i	0.993307	+	0.115501i	$0.0368472\pi$
$281$			5.35688e17i			0.231001i	−0.993307	+	0.115501i	$0.963153\pi$
$282$	−2.86082e18	+	1.06932e18i	−1.20122	+	0.448992i
$283$		−	2.43367e18i		−	0.995094i	−0.867437	−	0.497547i	$-0.834234\pi$
$283$		−	2.43367e18i		−	0.995094i	0.867437	−	0.497547i	$-0.165766\pi$
$284$	8.28527e17	+	1.09462e18i	0.329928	+	0.435888i
$285$	−5.73106e16	−	5.35675e16i	−0.0222279	−	0.0207761i
$286$	3.48698e17	−	7.01255e17i	0.131736	−	0.264930i
$287$	−3.20196e18			−1.17843
$288$	1.72957e18	−	2.18791e18i	0.620147	−	0.784486i
$289$	1.88465e18			0.658411
$290$	−8.28903e17	+	1.66698e18i	−0.282175	+	0.567474i
$291$	2.85582e18	+	2.66930e18i	0.947399	+	0.885522i
$292$	−2.19926e18	−	2.90558e18i	−0.711060	−	0.939424i
$293$		−	3.69904e18i		−	1.16569i	−0.812585	−	0.582843i	$-0.801940\pi$
$293$		−	3.69904e18i		−	1.16569i	0.812585	−	0.582843i	$-0.198060\pi$
$294$	1.22135e17	−	4.56516e16i	0.0375176	−	0.0140233i
$295$			7.22543e18i			2.16371i
$296$	1.72151e18	−	3.24775e17i	0.502600	−	0.0948190i
$297$	−2.48783e18	+	3.05043e18i	−0.708186	+	0.868337i
$298$	2.94882e18	+	1.46629e18i	0.818514	+	0.407005i
$299$	−1.72464e17			−0.0466836
$300$	1.02951e18	−	9.88802e18i	0.271782	−	2.61036i
$301$	5.74539e18			1.47935
$302$	1.58000e18	+	7.85652e17i	0.396831	+	0.197323i
$303$	−1.33490e18	+	1.42817e18i	−0.327060	+	0.349914i
$304$	6.43489e16	+	1.81544e16i	0.0153812	+	0.00433941i
$305$		−	1.08596e18i		−	0.253260i
$306$	−9.85855e17	+	2.37166e18i	−0.224338	+	0.539686i
$307$			2.87107e18i			0.637537i	0.947833	+	0.318769i	$0.103269\pi$
$307$			2.87107e18i			0.637537i	−0.947833	+	0.318769i	$0.896731\pi$
$308$	−4.03939e18	+	3.05746e18i	−0.875358	+	0.662568i
$309$	7.78569e17	−	8.32973e17i	0.164668	−	0.176174i
$310$	−1.33273e18	+	2.68021e18i	−0.275125	+	0.553294i
$311$	2.84259e18			0.572812			0.286406	−	0.958108i	$-0.407539\pi$
$311$	2.84259e18			0.572812			0.286406	+	0.958108i	$0.407539\pi$
$312$	−1.13357e18	−	7.18907e17i	−0.222991	−	0.141421i
$313$	−2.40172e18			−0.461254			−0.230627	−	0.973042i	$-0.574078\pi$
$313$	−2.40172e18			−0.461254			−0.230627	+	0.973042i	$0.574078\pi$
$314$	−4.63196e17	+	9.31518e17i	−0.0868545	+	0.174670i
$315$	−6.87064e17	−	1.01645e19i	−0.125796	−	1.86104i
$316$	−5.19684e18	+	3.93354e18i	−0.929151	+	0.703284i
$317$			9.18122e17i			0.160308i	0.996782	+	0.0801541i	$0.0255412\pi$
$317$			9.18122e17i			0.160308i	−0.996782	+	0.0801541i	$0.974459\pi$
$318$	−8.72510e17	−	2.33429e18i	−0.148788	−	0.398062i
$319$			2.23947e18i			0.373006i
$320$	4.26345e18	+	1.08973e19i	0.693644	+	1.77294i
$321$	8.74254e18	+	8.17154e18i	1.38947	+	1.29872i
$322$	9.98930e17	+	4.96716e17i	0.155102	+	0.0771240i
$323$	−6.15730e16			−0.00934053
$324$	4.75863e18	+	4.78253e18i	0.705333	+	0.708876i
$325$	−4.78476e18			−0.693003
$326$	−4.96957e17	−	2.47111e17i	−0.0703374	−	0.0349752i
$327$	4.14242e18	+	3.87187e18i	0.572989	+	0.535565i
$328$	1.64934e18	+	8.74255e18i	0.222976	+	1.18191i
$329$		−	9.50851e18i		−	1.25644i
$330$	−5.78242e18	−	1.54701e19i	−0.746887	−	1.99820i
$331$		−	1.34144e19i		−	1.69380i	−0.531750	−	0.846902i	$-0.678465\pi$
$331$		−	1.34144e19i		−	1.69380i	0.531750	−	0.846902i	$-0.321535\pi$
$332$	−2.55378e18	−	3.37396e18i	−0.315245	−	0.416490i
$333$	2.85805e17	+	4.22823e18i	0.0344936	+	0.510301i
$334$	4.86677e18	−	9.78742e18i	0.574305	−	1.15497i
$335$	−2.36723e19			−2.73152
$336$	4.49521e18	+	7.42880e18i	0.507231	+	0.838251i
$337$	−1.44132e19			−1.59051			−0.795255	−	0.606275i	$-0.792663\pi$
$337$	−1.44132e19			−1.59051			−0.795255	+	0.606275i	$0.792663\pi$
$338$	3.83780e18	−	7.71807e18i	0.414197	−	0.832978i
$339$	5.81533e18	−	6.22168e18i	0.613870	−	0.656765i
$340$	−6.50366e18	−	8.59238e18i	−0.671531	−	0.887200i
$341$			3.60068e18i			0.363686i
$342$	−6.20821e16	+	1.49350e17i	−0.00613437	+	0.0147574i
$343$			1.05411e19i			1.01901i
$344$	−2.95947e18	−	1.56870e19i	−0.279915	−	1.48372i
$345$	−2.48347e18	+	2.65701e18i	−0.229835	+	0.245895i
$346$	8.98298e18	+	4.46677e18i	0.813486	+	0.404504i
$347$	5.85580e17			0.0518937			0.0259469	−	0.999663i	$-0.491740\pi$
$347$	5.85580e17			0.0518937			0.0259469	+	0.999663i	$0.491740\pi$
$348$	3.81772e18	+	3.97489e17i	0.331101	+	0.0344732i
$349$	−2.20097e18			−0.186820			−0.0934100	−	0.995628i	$-0.529777\pi$
$349$	−2.20097e18			−0.186820			−0.0934100	+	0.995628i	$0.529777\pi$
$350$	2.77139e19	+	1.37807e19i	2.30243	+	1.14488i
$351$	2.05225e18	−	2.51635e18i	0.166889	−	0.204629i
$352$	1.04287e19	+	9.45414e18i	0.830157	+	0.752579i
$353$		−	2.05266e19i		−	1.59958i	−0.600280	−	0.799790i	$-0.704944\pi$
$353$		−	2.05266e19i		−	1.59958i	0.600280	−	0.799790i	$-0.295056\pi$
$354$	1.39542e19	−	5.21578e18i	1.06458	−	0.397919i
$355$		−	1.39335e19i		−	1.04076i
$356$	−4.18266e18	+	3.16590e18i	−0.305899	+	0.231538i
$357$	−5.84176e18	−	5.46022e18i	−0.418343	−	0.391020i
$358$	−2.63731e18	+	5.30380e18i	−0.184943	+	0.371933i
$359$	1.21071e19			0.831440			0.415720	−	0.909493i	$-0.363530\pi$
$359$	1.21071e19			0.831440			0.415720	+	0.909493i	$0.363530\pi$
$360$	−2.73989e19	+	7.11170e18i	−1.84274	+	0.478305i
$361$	1.51772e19			0.999745
$362$	−6.76134e18	+	1.35975e19i	−0.436233	+	0.877294i
$363$	−2.95398e18	−	2.76105e18i	−0.186685	−	0.174492i
$364$	3.33216e18	−	2.52215e18i	0.206284	−	0.156138i
$365$			3.69856e19i			2.24304i
$366$	−2.09727e18	+	7.83919e17i	−0.124608	+	0.0465761i
$367$		−	6.43775e18i		−	0.374747i	−0.982289	−	0.187374i	$-0.940002\pi$
$367$		−	6.43775e18i		−	0.374747i	0.982289	−	0.187374i	$-0.0599975\pi$
$368$	8.41667e17	−	2.98331e18i	0.0480045	−	0.170153i
$369$	−2.14727e19	+	1.45144e18i	−1.20002	+	0.0811149i
$370$	−1.59211e19	−	7.91675e18i	−0.871888	−	0.433545i
$371$	7.75848e18			0.416363
$372$	6.13822e18	+	6.39093e17i	0.322828	+	0.0336118i
$373$	1.96745e19			1.01412			0.507058	−	0.861912i	$-0.330733\pi$
$373$	1.96745e19			1.01412			0.507058	+	0.861912i	$0.330733\pi$
$374$	−1.16071e19	−	5.77163e18i	−0.586393	−	0.291583i
$375$	−4.26472e19	+	4.56273e19i	−2.11182	+	2.25938i
$376$	−2.59618e19	+	4.89787e18i	−1.26016	+	0.237738i
$377$		−	1.84738e18i		−	0.0879013i
$378$	−1.91342e19	+	8.66427e18i	−0.892530	+	0.404151i
$379$			8.39709e18i			0.384003i	0.981395	+	0.192002i	$0.0614979\pi$
$379$			8.39709e18i			0.384003i	−0.981395	+	0.192002i	$0.938502\pi$
$380$	−4.09554e17	−	5.41086e17i	−0.0183626	−	0.0242599i
$381$	9.61978e18	−	1.02920e19i	0.422891	−	0.452441i
$382$	1.37158e19	−	2.75835e19i	0.591217	−	1.18898i
$383$	−7.98322e18			−0.337433			−0.168716	−	0.985665i	$-0.553962\pi$
$383$	−7.98322e18			−0.337433			−0.168716	+	0.985665i	$0.553962\pi$
$384$	1.79679e19	−	1.61002e19i	0.744753	−	0.667340i
$385$	5.14181e19			2.09007
$386$	−6.77654e18	+	1.36281e19i	−0.270149	+	0.543288i
$387$	3.85291e19	−	2.60436e18i	1.50646	−	0.101828i
$388$	2.04083e19	+	2.69626e19i	0.782651	+	1.03401i
$389$		−	2.98387e18i		−	0.112242i	−0.998424	−	0.0561212i	$-0.982127\pi$
$389$		−	2.98387e18i		−	0.112242i	0.998424	−	0.0561212i	$-0.0178733\pi$
$390$	4.77001e18	+	1.27615e19i	0.176009	+	0.470889i
$391$			2.85462e18i			0.103329i
$392$	1.10837e18	−	2.09101e17i	0.0393584	−	0.00742525i
$393$	1.32197e19	+	1.23563e19i	0.460552	+	0.430472i
$394$	−8.22466e18	−	4.08970e18i	−0.281123	−	0.139788i
$395$	6.61514e19			2.21851
$396$	−2.57026e19	+	2.23347e19i	−0.845793	+	0.734963i
$397$	−4.83928e19			−1.56262			−0.781308	−	0.624146i	$-0.785447\pi$
$397$	−4.83928e19			−1.56262			−0.781308	+	0.624146i	$0.785447\pi$
$398$	−5.08758e19	−	2.52979e19i	−1.61209	−	0.801606i
$399$	−3.67872e17	−	3.43845e17i	−0.0114393	−	0.0106922i
$400$	2.33508e19	−	8.27677e19i	0.712611	−	2.52587i
$401$		−	2.99456e19i		−	0.896912i	−0.893805	−	0.448456i	$-0.851974\pi$
$401$		−	2.99456e19i		−	0.896912i	0.893805	−	0.448456i	$-0.148026\pi$
$402$	1.70882e19	+	4.57172e19i	0.502343	+	1.34395i
$403$		−	2.97026e18i		−	0.0857050i
$404$	−1.34838e19	+	1.02060e19i	−0.381902	+	0.289065i
$405$	−9.21504e18	−	6.78525e19i	−0.256203	−	1.88649i
$406$	−5.32066e18	+	1.07002e19i	−0.145218	+	0.292043i
$407$	−2.13889e19			−0.573101
$408$	−1.18993e19	+	1.87628e19i	−0.313019	+	0.493566i
$409$	−7.20143e19			−1.85992			−0.929960	−	0.367662i	$-0.880158\pi$
$409$	−7.20143e19			−1.85992			−0.929960	+	0.367662i	$0.880158\pi$
$410$	4.02045e19	−	8.08540e19i	1.01952	−	2.05033i
$411$	1.49275e18	−	1.59705e18i	0.0371683	−	0.0397655i
$412$	7.86433e18	−	5.95260e18i	0.192279	−	0.145538i
$413$			4.63795e19i			1.11353i
$414$	6.92409e18	+	2.87822e18i	0.163253	+	0.0678611i
$415$			4.29476e19i			0.994440i
$416$	−8.60280e18	−	7.79886e18i	−0.195632	−	0.177350i
$417$	2.17085e19	−	2.32255e19i	0.484853	−	0.518733i
$418$	−7.30935e17	−	3.63456e17i	−0.0160345	−	0.00797314i
$419$	−3.80628e17			−0.00820153			−0.00410077	−	0.999992i	$-0.501305\pi$
$419$	−3.80628e17			−0.00820153			−0.00410077	+	0.999992i	$0.501305\pi$
$420$	9.12631e18	−	8.76545e19i	0.193164	−	1.85526i
$421$	4.05803e19			0.843723			0.421861	−	0.906660i	$-0.361377\pi$
$421$	4.05803e19			0.843723			0.421861	+	0.906660i	$0.361377\pi$
$422$	−1.56625e19	−	7.78812e18i	−0.319902	−	0.159070i
$423$	−4.31017e18	−	6.37650e19i	−0.0864852	−	1.27947i
$424$	−3.99642e18	−	2.11835e19i	−0.0787821	−	0.417594i
$425$			7.91972e19i			1.53389i
$426$	−2.69092e19	+	1.00581e19i	−0.512070	+	0.191401i
$427$		−	6.97071e18i		−	0.130337i
$428$	6.24760e19	+	8.25408e19i	1.14785	+	1.51649i
$429$	1.19728e19	+	1.11908e19i	0.216155	+	0.202037i
$430$	−7.21403e19	+	1.45079e20i	−1.27987	+	2.57390i
$431$	−7.50201e19			−1.30797			−0.653985	−	0.756507i	$-0.726904\pi$
$431$	−7.50201e19			−1.30797			−0.653985	+	0.756507i	$0.726904\pi$
$432$	3.35128e19	+	4.77806e19i	0.574226	+	0.818697i
$433$	−2.37173e19			−0.399398			−0.199699	−	0.979857i	$-0.563996\pi$
$433$	−2.37173e19			−0.399398			−0.199699	+	0.979857i	$0.563996\pi$
$434$	−8.55468e18	+	1.72041e19i	−0.141589	+	0.284746i
$435$	−2.84610e19	−	2.66021e19i	−0.462999	−	0.432760i
$436$	2.96026e19	+	3.91098e19i	0.473349	+	0.625370i
$437$			1.79763e17i			0.00282546i
$438$	7.14286e19	−	2.66986e19i	1.10361	−	0.412508i
$439$		−	2.67499e19i		−	0.406292i	−0.979148	−	0.203146i	$-0.934883\pi$
$439$		−	2.67499e19i		−	0.406292i	0.979148	−	0.203146i	$-0.0651166\pi$
$440$	−2.64856e19	−	1.40390e20i	−0.395472	−	2.09625i
$441$	1.84011e17	+	2.72227e18i	0.00270119	+	0.0399615i
$442$	9.57492e18	+	4.76111e18i	0.138187	+	0.0687134i
$443$	7.12928e19			1.01162			0.505810	−	0.862645i	$-0.331194\pi$
$443$	7.12928e19			1.01162			0.505810	+	0.862645i	$0.331194\pi$
$444$	−3.79637e18	+	3.64626e19i	−0.0529659	+	0.508716i
$445$	5.32418e19			0.730386
$446$	−8.13131e19	−	4.04328e19i	−1.09685	−	0.545409i
$447$	−4.70580e19	+	5.03463e19i	−0.624205	+	0.667822i
$448$	2.73668e19	+	6.99490e19i	0.356975	+	0.912423i
$449$		−	1.27554e19i		−	0.163623i	−0.996648	−	0.0818117i	$-0.973929\pi$
$449$		−	1.27554e19i		−	0.163623i	0.996648	−	0.0818117i	$-0.0260706\pi$
$450$	1.92099e20	+	7.98520e19i	2.42343	+	1.00738i
$451$		−	1.08622e20i		−	1.34770i
$452$	5.87407e19	−	4.44614e19i	0.716805	−	0.542557i
$453$	−2.52141e19	+	2.69759e19i	−0.302626	+	0.323772i
$454$	3.64844e18	−	7.33727e18i	0.0430714	−	0.0866195i
$455$	−4.24156e19			−0.492538
$456$	−7.49333e17	+	1.18154e18i	−0.00855931	+	0.0134963i
$457$	2.66760e19			0.299743			0.149871	−	0.988705i	$-0.452114\pi$
$457$	2.66760e19			0.299743			0.149871	+	0.988705i	$0.452114\pi$
$458$	−6.98985e19	+	1.40571e20i	−0.772639	+	1.55383i
$459$	−4.16505e19	−	3.39687e19i	−0.452924	−	0.369389i
$460$	−2.50856e19	+	1.89875e19i	−0.268374	+	0.203135i
$461$			1.34446e18i			0.0141511i	0.999975	+	0.00707554i	$0.00225223\pi$
$461$			1.34446e18i			0.0141511i	−0.999975	+	0.00707554i	$0.997748\pi$
$462$	−3.71169e19	−	9.93015e19i	−0.384376	−	1.02835i
$463$			1.41938e20i			1.44624i	0.690722	+	0.723121i	$0.257293\pi$
$463$			1.41938e20i			1.44624i	−0.690722	+	0.723121i	$0.742707\pi$
$464$	3.19563e19	+	9.01566e18i	0.320384	+	0.0903884i
$465$	−4.57602e19	−	4.27715e19i	−0.451430	−	0.421946i
$466$	−1.56647e20	−	7.78926e19i	−1.52065	−	0.756139i
$467$	−6.40618e19			−0.611959			−0.305980	−	0.952038i	$-0.598984\pi$
$467$	−6.40618e19			−0.611959			−0.305980	+	0.952038i	$0.598984\pi$
$468$	2.12025e19	−	1.84242e19i	0.199317	−	0.173199i
$469$	−1.51950e20			−1.40574
$470$	2.40103e20	+	1.19391e20i	2.18607	+	1.08702i
$471$	−1.59042e19	−	1.48654e19i	−0.142513	−	0.133205i
$472$	1.26633e20	−	2.38902e19i	1.11682	−	0.210696i
$473$			1.94904e20i			1.69185i
$474$	−4.77523e19	−	1.27755e20i	−0.407997	−	1.09154i
$475$			4.98727e18i			0.0419431i
$476$	−4.17465e19	−	5.51538e19i	−0.345595	−	0.456586i
$477$	5.20291e19	−	3.51689e18i	0.423993	−	0.0286596i
$478$	2.97497e19	−	5.98286e19i	0.238656	−	0.479954i
$479$	2.46473e20			1.94649			0.973245	−	0.229770i	$-0.0737973\pi$
$479$	2.46473e20			1.94649			0.973245	+	0.229770i	$0.0737973\pi$
$480$	−2.44030e20	+	2.02329e19i	−1.89729	+	0.157307i
$481$	1.76441e19			0.135055
$482$	7.08223e19	−	1.42428e20i	0.533724	−	1.07336i
$483$	−1.59412e19	+	1.70551e19i	−0.118282	+	0.126547i
$484$	−2.11098e19	−	2.78894e19i	−0.154221	−	0.203751i
$485$		−	3.43211e20i		−	2.46887i
$486$	−1.24389e20	+	6.67769e19i	−0.881066	+	0.472993i
$487$			8.61209e19i			0.600677i	0.953833	+	0.300339i	$0.0970997\pi$
$487$			8.61209e19i			0.600677i	−0.953833	+	0.300339i	$0.902900\pi$
$488$	−1.90326e19	+	3.59064e18i	−0.130722	+	0.0246617i
$489$	7.93056e18	−	8.48472e18i	0.0536398	−	0.0573880i
$490$	−1.02505e19	−	5.09707e18i	−0.0682773	−	0.0339508i
$491$	−6.12023e18			−0.0401473			−0.0200737	−	0.999799i	$-0.506390\pi$
$491$	−6.12023e18			−0.0401473			−0.0200737	+	0.999799i	$0.506390\pi$
$492$	−1.85172e20	−	1.92795e19i	−1.19629	−	0.124554i
$493$	−3.05777e19			−0.194560
$494$	6.02959e17	+	2.99820e17i	0.00377864	+	0.00187892i
$495$	3.44815e20	−	2.33076e19i	2.12837	−	0.143866i
$496$	5.13800e19	+	1.44956e19i	0.312379	+	0.0881299i
$497$		−	8.94383e19i		−	0.535612i
$498$	8.29429e19	−	3.10024e19i	0.489282	−	0.182884i
$499$		−	2.61288e20i		−	1.51832i	−0.650901	−	0.759162i	$-0.725609\pi$
$499$		−	2.61288e20i		−	1.51832i	0.650901	−	0.759162i	$-0.274391\pi$
$500$	−4.30780e20	+	3.26062e20i	−2.46593	+	1.86649i
$501$	1.67104e20	+	1.56190e20i	0.942333	+	0.880786i
$502$	6.35578e19	−	1.27819e20i	0.353095	−	0.710098i
$503$	−1.88131e20			−1.02968			−0.514839	−	0.857287i	$-0.672148\pi$
$503$	−1.88131e20			−1.02968			−0.514839	+	0.857287i	$0.672148\pi$
$504$	−1.75871e20	+	4.56494e19i	−0.948344	+	0.246154i
$505$	1.71637e20			0.911856
$506$	−1.68504e19	+	3.38872e19i	−0.0882023	+	0.177381i
$507$	1.31773e20	+	1.23167e20i	0.679623	+	0.635235i
$508$	9.71696e19	−	7.35486e19i	0.493802	−	0.373763i
$509$		−	2.95767e20i		−	1.48104i	−0.672035	−	0.740520i	$-0.734579\pi$
$509$		−	2.95767e20i		−	1.48104i	0.672035	−	0.740520i	$-0.265421\pi$
$510$	2.11229e20	−	7.89530e19i	1.04226	−	0.389576i
$511$			2.37408e20i			1.15435i
$512$	1.76890e20	−	1.10752e20i	0.847576	−	0.530675i
$513$	−2.62285e18	−	2.13911e18i	−0.0123849	−	0.0101007i
$514$	−2.67901e20	−	1.33213e20i	−1.24667	−	0.619904i
$515$	−1.00106e20			−0.459100
$516$	3.32260e20	+	3.45939e19i	1.50178	+	0.156360i
$517$	3.22562e20			1.43693
$518$	−1.02196e20	−	5.08170e19i	−0.448707	−	0.223118i
$519$	−1.43353e20	+	1.53370e20i	−0.620370	+	0.663719i
$520$	2.18484e19	+	1.15810e20i	0.0931955	+	0.493994i
$521$			2.63757e20i			1.10897i	0.832193	+	0.554486i	$0.187085\pi$
$521$			2.63757e20i			1.10897i	−0.832193	+	0.554486i	$0.812915\pi$
$522$	−3.08305e19	+	7.41685e19i	−0.127777	+	0.307391i
$523$			3.90384e20i			1.59489i	0.603395	+	0.797443i	$0.293814\pi$
$523$			3.90384e20i			1.59489i	−0.603395	+	0.797443i	$0.706186\pi$
$524$	9.44709e19	+	1.24811e20i	0.380464	+	0.502654i
$525$	−4.42265e20	+	4.73169e20i	−1.75585	+	1.87855i
$526$	1.48650e20	−	2.98946e20i	0.581798	−	1.17004i
$527$	−4.91635e19			−0.189698
$528$	−2.52011e20	+	1.52493e20i	−0.958660	+	0.580092i
$529$	−2.58301e20			−0.968743
$530$	−9.74171e19	+	1.95912e20i	−0.360218	+	0.724424i
$531$	2.10236e19	+	3.11025e20i	0.0766476	+	1.13393i
$532$	−2.62889e18	−	3.47319e18i	−0.00945008	−	0.0124851i
$533$			8.96038e19i			0.317594i
$534$	−3.84333e19	−	1.02823e20i	−0.134322	−	0.359363i
$535$		−	1.05067e21i		−	3.62089i
$536$	7.82703e19	+	4.14881e20i	0.265987	+	1.40990i
$537$	−9.05537e19	−	8.46394e19i	−0.303458	−	0.283639i
$538$	3.38266e20	+	1.68202e20i	1.11787	+	0.555859i
$539$	−1.37709e19			−0.0448794
$540$	2.14685e19	−	5.91957e20i	0.0690000	−	1.90255i
$541$	2.16728e19			0.0686968			0.0343484	−	0.999410i	$-0.489064\pi$
$541$	2.16728e19			0.0686968			0.0343484	+	0.999410i	$0.489064\pi$
$542$	2.62048e20	+	1.30303e20i	0.819194	+	0.407343i
$543$	−2.32155e20	−	2.16993e20i	−0.715781	−	0.669031i
$544$	−1.29087e20	+	1.42393e20i	−0.392545	+	0.433010i
$545$		−	4.97835e20i		−	1.49318i
$546$	3.06183e19	+	8.19153e19i	0.0905808	+	0.242337i
$547$			2.18502e20i			0.637604i	0.947821	+	0.318802i	$0.103281\pi$
$547$			2.18502e20i			0.637604i	−0.947821	+	0.318802i	$0.896719\pi$
$548$	1.50782e19	−	1.14129e19i	0.0434007	−	0.0328504i
$549$	−3.15980e18	−	4.67463e19i	−0.00897153	−	0.132726i
$550$	−4.67489e20	+	9.40152e20i	−1.30934	+	2.63316i
$551$	−1.92556e18			−0.00532011
$552$	5.47781e19	+	3.47402e19i	0.149301	+	0.0946868i
$553$	4.24620e20			1.14173
$554$	2.54701e20	−	5.12221e20i	0.675627	−	1.35873i
$555$	2.54073e20	−	2.71827e20i	0.664908	−	0.711370i
$556$	2.19278e20	−	1.65974e20i	0.566154	−	0.428528i
$557$			2.73010e20i			0.695448i	0.937597	+	0.347724i	$0.113045\pi$
$557$			2.73010e20i			0.695448i	−0.937597	+	0.347724i	$0.886955\pi$
$558$	−4.95700e19	+	1.19250e20i	−0.124584	+	0.299710i
$559$		−	1.60779e20i		−	0.398695i
$560$	2.06999e20	−	7.33712e20i	0.506474	−	1.79521i
$561$	1.85230e20	−	1.98173e20i	0.447187	−	0.478435i
$562$	−8.68279e19	−	4.31750e19i	−0.206841	−	0.102851i
$563$	−4.23158e20			−0.994695			−0.497348	−	0.867551i	$-0.665693\pi$
$563$	−4.23158e20			−0.994695			−0.497348	+	0.867551i	$0.665693\pi$
$564$	5.72523e19	−	5.49885e20i	0.132800	−	1.27549i
$565$	−7.47719e20			−1.71149
$566$	3.94466e20	+	1.96147e20i	0.891018	+	0.443057i
$567$	−5.91506e19	−	4.35540e20i	−0.131852	−	0.970857i
$568$	−2.44200e20	+	4.60700e19i	−0.537196	+	0.101346i
$569$		−	1.62716e20i		−	0.353254i	−0.984278	−	0.176627i	$-0.943481\pi$
$569$		−	1.62716e20i		−	0.353254i	0.984278	−	0.176627i	$-0.0565187\pi$
$570$	1.33017e19	−	4.97189e18i	0.0285000	−	0.0106527i
$571$			2.41399e20i			0.510463i	0.966880	+	0.255231i	$0.0821517\pi$
$571$			2.41399e20i			0.510463i	−0.966880	+	0.255231i	$0.917848\pi$
$572$	8.55600e19	+	1.13039e20i	0.178567	+	0.235915i
$573$	4.70943e20	+	4.40184e20i	0.970083	+	0.906724i
$574$	2.58069e20	−	5.18995e20i	0.524684	−	1.05517i
$575$	2.31217e20			0.463993
$576$	2.15232e20	+	4.56679e20i	0.426322	+	0.904571i
$577$	−4.25822e20			−0.832549			−0.416275	−	0.909239i	$-0.636664\pi$
$577$	−4.25822e20			−0.832549			−0.416275	+	0.909239i	$0.636664\pi$
$578$	−1.51898e20	+	3.05477e20i	−0.293152	+	0.589549i
$579$	−2.32677e20	−	2.17480e20i	−0.443266	−	0.414315i
$580$	−2.03388e20	−	2.68708e20i	−0.382486	−	0.505325i
$581$			2.75677e20i			0.511776i
$582$	−6.62828e20	+	2.47752e20i	−1.21473	+	0.454040i
$583$			2.63195e20i			0.476171i
$584$	6.48211e20	−	1.22289e20i	1.15776	−	0.218420i
$585$	−2.84443e20	+	1.92268e19i	−0.501564	+	0.0339030i
$586$	5.99564e20	+	2.98132e20i	1.04377	+	0.519011i
$587$	−1.12071e20			−0.192622			−0.0963110	−	0.995351i	$-0.530704\pi$
$587$	−1.12071e20			−0.192622			−0.0963110	+	0.995351i	$0.530704\pi$
$588$	−2.44423e18	+	2.34758e19i	−0.00414775	+	0.0398374i
$589$	−3.09597e18			−0.00518718
$590$	−1.17115e21	−	5.82350e20i	−1.93741	−	0.963372i
$591$	1.31251e20	−	1.40423e20i	0.214386	−	0.229367i
$592$	−8.61074e19	+	3.05210e20i	−0.138876	+	0.492250i
$593$		−	6.72168e19i		−	0.107045i	−0.998567	−	0.0535226i	$-0.982955\pi$
$593$		−	6.72168e19i		−	0.107045i	0.998567	−	0.0535226i	$-0.0170449\pi$
$594$	−2.93922e20	−	6.49100e20i	−0.462205	−	1.02074i
$595$			7.02061e20i			1.09018i
$596$	−4.75334e20	+	3.59785e20i	−0.728873	+	0.551691i
$597$	8.11889e20	−	8.68621e20i	1.22939	−	1.31529i
$598$	1.39001e19	−	2.79541e19i	0.0207855	−	0.0418010i
$599$	1.09204e21			1.61264			0.806320	−	0.591480i	$-0.201456\pi$
$599$	1.09204e21			1.61264			0.806320	+	0.591480i	$0.201456\pi$
$600$	1.51974e21	+	9.63817e20i	2.21633	+	1.40560i
$601$	−8.56160e20			−1.23310			−0.616548	−	0.787318i	$-0.711469\pi$
$601$	−8.56160e20			−1.23310			−0.616548	+	0.787318i	$0.711469\pi$
$602$	−4.63062e20	+	9.31250e20i	−0.658667	+	1.32462i
$603$	−1.01899e21	+	6.88786e19i	−1.43150	+	0.0967619i
$604$	−2.54688e20	+	1.92776e20i	−0.353371	+	0.267470i
$605$			3.55009e20i			0.486490i
$606$	−1.23899e20	−	3.31476e20i	−0.167696	−	0.448649i
$607$		−	3.48456e20i		−	0.465836i	−0.972496	−	0.232918i	$-0.925173\pi$
$607$		−	3.48456e20i		−	0.465836i	0.972496	−	0.232918i	$-0.0748274\pi$
$608$	−8.12894e18	+	8.96690e18i	−0.0107339	+	0.0118404i
$609$	−1.82689e20	−	1.70757e20i	−0.238277	−	0.222714i
$610$	1.76020e20	+	8.75257e19i	0.226772	+	0.112762i
$611$	−2.66087e20			−0.338621
$612$	−3.04957e20	−	3.50943e20i	−0.383356	−	0.441165i
$613$	5.58125e20			0.693071			0.346536	−	0.938037i	$-0.387358\pi$
$613$	5.58125e20			0.693071			0.346536	+	0.938037i	$0.387358\pi$
$614$	−4.65362e20	−	2.31400e20i	−0.570858	−	0.283858i
$615$	1.38045e21	+	1.29029e21i	1.67285	+	1.56359i
$616$	−1.70009e20	−	9.01155e20i	−0.203525	−	1.07881i
$617$			7.94207e20i			0.939280i	0.882858	+	0.469640i	$0.155616\pi$
$617$			7.94207e20i			0.939280i	−0.882858	+	0.469640i	$0.844384\pi$
$618$	7.22632e19	+	1.93331e20i	0.0844313	+	0.225885i
$619$			7.63690e20i			0.881530i	0.897623	+	0.440765i	$0.145293\pi$
$619$			7.63690e20i			0.881530i	−0.897623	+	0.440765i	$0.854707\pi$
$620$	−3.27012e20	−	4.32035e20i	−0.372929	−	0.492699i
$621$	−9.91722e19	+	1.21599e20i	−0.111738	+	0.137007i
$622$	−2.29105e20	+	4.60747e20i	−0.255039	+	0.512902i
$623$	3.41755e20			0.375884
$624$	2.07888e20	−	1.25794e20i	0.225915	−	0.136702i
$625$	3.03924e21			3.26336
$626$	1.93572e20	−	3.89287e20i	0.205369	−	0.413012i
$627$	1.16644e19	−	1.24795e19i	0.0122281	−	0.0130825i
$628$	−1.13654e20	−	1.50156e20i	−0.117730	−	0.155541i
$629$		−	2.92044e20i		−	0.298929i
$630$	1.70290e21	+	7.07865e20i	1.72241	+	0.715973i
$631$			6.83396e20i			0.683049i	0.939873	+	0.341525i	$0.110943\pi$
$631$			6.83396e20i			0.683049i	−0.939873	+	0.341525i	$0.889057\pi$
$632$	−2.18724e20	−	1.15937e21i	−0.216032	−	1.14510i
$633$	2.49945e20	−	2.67411e20i	0.243959	−	0.261006i
$634$	−1.48815e20	−	7.39981e19i	−0.143542	−	0.0713758i
$635$	−1.23689e21			−1.17904
$636$	4.48679e20	+	4.67151e19i	0.422676	+	0.0440077i
$637$	1.13598e19			0.0105761
$638$	−3.62989e20	−	1.80495e20i	−0.333994	−	0.166078i
$639$	−4.05420e19	−	5.99782e20i	−0.0368680	−	0.545427i
$640$	−2.10993e21	−	1.87245e20i	−1.89635	−	0.168291i
$641$		−	1.62888e20i		−	0.144695i	−0.997379	−	0.0723477i	$-0.976951\pi$
$641$		−	1.62888e20i		−	0.144695i	0.997379	−	0.0723477i	$-0.0230491\pi$
$642$	−2.02912e21	+	7.58445e20i	−1.78154	+	0.665903i
$643$		−	1.30635e21i		−	1.13364i	−0.823840	−	0.566822i	$-0.808173\pi$
$643$		−	1.30635e21i		−	1.13364i	0.823840	−	0.566822i	$-0.191827\pi$
$644$	−1.61022e20	+	1.21879e20i	−0.138115	+	0.104541i
$645$	−2.47699e21	−	2.31521e21i	−2.10003	−	1.96287i
$646$	4.96262e18	−	9.98016e18i	0.00415879	−	0.00836361i
$647$	1.40255e21			1.16182			0.580908	−	0.813970i	$-0.302698\pi$
$647$	1.40255e21			1.16182			0.580908	+	0.813970i	$0.302698\pi$
$648$	−1.15872e21	+	3.85851e20i	−0.948779	+	0.315942i
$649$	−1.57335e21			−1.27348
$650$	3.85639e20	−	7.75546e20i	0.308554	−	0.620522i
$651$	−2.93731e20	−	2.74547e20i	−0.232323	−	0.217149i
$652$	8.01067e19	−	6.06336e19i	0.0626343	−	0.0474085i
$653$			8.06788e20i			0.623606i	0.950147	+	0.311803i	$0.100933\pi$
$653$			8.06788e20i			0.623606i	−0.950147	+	0.311803i	$0.899067\pi$
$654$	−9.61446e20	+	3.59369e20i	−0.734669	+	0.274605i
$655$		−	1.58874e21i		−	1.20017i
$656$	−1.54998e21	−	4.37289e20i	−1.15757	−	0.326580i
$657$	1.07616e20	+	1.59208e21i	0.0794578	+	1.17550i
$658$	1.54120e21	+	7.66360e20i	1.12503	+	0.559421i
$659$	1.61103e21			1.16268			0.581342	−	0.813659i	$-0.302528\pi$
$659$	1.61103e21			1.16268			0.581342	+	0.813659i	$0.302528\pi$
$660$	2.97355e21	+	3.09597e20i	2.12176	+	0.220911i
$661$	−1.02959e21			−0.726360			−0.363180	−	0.931719i	$-0.618309\pi$
$661$	−1.02959e21			−0.726360			−0.363180	+	0.931719i	$0.618309\pi$
$662$	2.17430e21	+	1.08117e21i	1.51665	+	0.754151i
$663$	−1.52799e20	+	1.63476e20i	−0.105383	+	0.112746i
$664$	7.52702e20	−	1.42002e20i	0.513289	−	0.0968357i
$665$			4.42107e19i			0.0298102i
$666$	−7.08374e20	−	2.94458e20i	−0.472287	−	0.196321i
$667$			8.92720e19i			0.0588534i
$668$	1.19416e21	+	1.57768e21i	0.778466	+	1.02848i
$669$	1.29761e21	−	1.38829e21i	0.836469	−	0.894919i
$670$	1.90792e21	−	3.83696e21i	1.21618	−	2.44583i
$671$	2.36471e20			0.149059
$672$	−1.56641e21	+	1.29873e20i	−0.976419	+	0.0809564i
$673$	−9.10146e20			−0.561046			−0.280523	−	0.959847i	$-0.590508\pi$
$673$	−9.10146e20			−0.561046			−0.280523	+	0.959847i	$0.590508\pi$
$674$	1.16167e21	−	2.33619e21i	0.708161	−	1.42416i
$675$	−2.75139e21	+	3.37360e21i	−1.65872	+	2.03383i
$676$	9.41681e20	+	1.24411e21i	0.561440	+	0.741752i
$677$			2.21185e21i			1.30419i	0.758136	+	0.652096i	$0.226110\pi$
$677$			2.21185e21i			1.30419i	−0.758136	+	0.652096i	$0.773890\pi$
$678$	5.39752e20	+	1.44404e21i	0.314754	+	0.842085i
$679$		−	2.20304e21i		−	1.27057i
$680$	1.91689e21	−	3.61634e20i	1.09340	−	0.206278i
$681$	1.25272e20	+	1.17090e20i	0.0706725	+	0.0660566i
$682$	−5.83622e20	−	2.90205e20i	−0.325648	−	0.161928i
$683$	−1.46098e21			−0.806284			−0.403142	−	0.915137i	$-0.632082\pi$
$683$	−1.46098e21			−0.806284			−0.403142	+	0.915137i	$0.632082\pi$
$684$	−1.92040e19	−	2.20999e19i	−0.0104826	−	0.0120634i
$685$	−1.91933e20			−0.103627
$686$	−1.70857e21	−	8.49582e20i	−0.912434	−	0.453706i
$687$	−2.40001e21	−	2.24326e21i	−1.26776	−	1.18496i
$688$	2.78118e21	+	7.84642e20i	1.45317	+	0.409976i
$689$		−	2.17113e20i		−	0.112213i
$690$	−2.30504e20	−	6.16685e20i	−0.117845	−	0.315279i
$691$			2.20684e21i			1.11606i	0.829822	+	0.558028i	$0.188442\pi$
$691$			2.20684e21i			1.11606i	−0.829822	+	0.558028i	$0.811558\pi$
$692$	−1.44801e21	+	1.09601e21i	−0.724395	+	0.548302i
$693$	2.21334e21	−	1.49610e20i	1.09534	−	0.0740390i
$694$	−4.71961e19	+	9.49146e19i	−0.0231052	+	0.0464662i
$695$	−2.79123e21			−1.35179
$696$	−3.72126e20	+	5.86765e20i	−0.178287	+	0.281122i
$697$	1.48312e21			0.702959
$698$	1.77392e20	−	3.56748e20i	0.0831800	−	0.167281i
$699$	2.49982e21	−	2.67450e21i	1.15966	−	1.24069i
$700$	−4.46733e21	+	3.38137e21i	−2.05028	+	1.55188i
$701$		−	2.09798e21i		−	0.952614i	−0.879279	−	0.476307i	$-0.841975\pi$
$701$		−	2.09798e21i		−	0.952614i	0.879279	−	0.476307i	$-0.158025\pi$
$702$	2.42461e20	+	5.35453e20i	0.108922	+	0.240543i
$703$		−	1.83908e19i		−	0.00817403i
$704$	−2.37291e21	+	9.28376e20i	−1.04349	+	0.408253i
$705$	−3.83163e21	+	4.09937e21i	−1.66711	+	1.78361i
$706$	3.32708e21	+	1.65438e21i	1.43228	+	0.712199i
$707$	1.10173e21			0.469276
$708$	−2.79258e20	+	2.68216e21i	−0.117695	+	1.13041i
$709$	2.58297e21			1.07714			0.538570	−	0.842581i	$-0.318965\pi$
$709$	2.58297e21			1.07714			0.538570	+	0.842581i	$0.318965\pi$
$710$	2.25844e21	+	1.12301e21i	0.931904	+	0.463387i
$711$	2.84755e21	−	1.92479e20i	1.16265	−	0.0785888i
$712$	−1.76039e20	−	9.33117e20i	−0.0711228	−	0.376995i
$713$			1.43534e20i			0.0573828i
$714$	1.35586e21	−	5.06793e20i	0.536387	−	0.200491i
$715$		−	1.43888e21i		−	0.563288i
$716$	−6.47116e20	−	8.54944e20i	−0.250689	−	0.331200i
$717$	1.02148e21	+	9.54760e20i	0.391592	+	0.366016i
$718$	−9.75798e20	+	1.96240e21i	−0.370192	+	0.744481i
$719$	−1.59796e21			−0.599930			−0.299965	−	0.953950i	$-0.596975\pi$
$719$	−1.59796e21			−0.599930			−0.299965	+	0.953950i	$0.596975\pi$
$720$	1.05556e21	−	5.01418e21i	0.392185	−	1.86297i
$721$	−6.42574e20			−0.236270
$722$	−1.22324e21	+	2.46003e21i	−0.445127	+	0.895182i
$723$	2.43173e21	+	2.27291e21i	0.875747	+	0.818550i
$724$	−1.65903e21	−	2.19185e21i	−0.591310	−	0.781215i
$725$			2.47672e21i			0.873660i
$726$	6.85613e20	−	2.56268e20i	0.239361	−	0.0894685i
$727$			1.15585e21i			0.399387i	0.979858	+	0.199693i	$0.0639946\pi$
$727$			1.15585e21i			0.399387i	−0.979858	+	0.199693i	$0.936005\pi$
$728$	1.40243e20	+	7.43377e20i	0.0479619	+	0.254228i
$729$	−5.94098e20	−	2.89396e21i	−0.201095	−	0.979572i
$730$	−5.99487e21	−	2.98094e21i	−2.00844	−	0.998692i
$731$	−2.66121e21			−0.882467
$732$	4.19718e19	−	4.03122e20i	0.0137760	−	0.132313i
$733$	−4.08602e21			−1.32746			−0.663729	−	0.747974i	$-0.731027\pi$
$733$	−4.08602e21			−1.32746			−0.663729	+	0.747974i	$0.731027\pi$
$734$	1.04347e21	+	5.18865e20i	0.335553	+	0.166853i
$735$	1.63581e20	−	1.75011e20i	0.0520688	−	0.0557072i
$736$	4.15719e20	+	3.76870e20i	0.130983	+	0.118743i
$737$		−	5.15469e21i		−	1.60767i
$738$	1.49538e21	−	3.59742e21i	0.461667	−	1.11063i
$739$			2.04155e21i			0.623916i	0.950096	+	0.311958i	$0.100985\pi$
$739$			2.04155e21i			0.623916i	−0.950096	+	0.311958i	$0.899015\pi$
$740$	2.56640e21	−	1.94253e21i	0.776401	−	0.587666i
$741$	−9.62218e18	+	1.02945e19i	−0.00288162	+	0.00308298i
$742$	−6.25312e20	+	1.25755e21i	−0.185382	+	0.372816i
$743$	3.65827e21			1.07364			0.536822	−	0.843696i	$-0.319625\pi$
$743$	3.65827e21			1.07364			0.536822	+	0.843696i	$0.319625\pi$
$744$	−5.98312e20	+	9.43415e20i	−0.173833	+	0.274098i
$745$	6.05060e21			1.74031
$746$	−1.58571e21	+	3.18898e21i	−0.451527	+	0.908051i
$747$	1.24964e20	+	1.84872e21i	0.0352273	+	0.521155i
$748$	1.87101e21	−	1.41619e21i	0.522172	−	0.395238i
$749$		−	6.74420e21i		−	1.86344i
$750$	−3.95832e21	−	1.05900e22i	−1.08281	−	2.89691i
$751$			4.71333e21i			1.27652i	0.769820	+	0.638261i	$0.220346\pi$
$751$			4.71333e21i			1.27652i	−0.769820	+	0.638261i	$0.779654\pi$
$752$	1.29857e21	−	4.60281e21i	0.348202	−	1.23421i
$753$	2.18230e21	+	2.03977e21i	0.579366	+	0.541526i
$754$	2.99435e20	+	1.48894e20i	0.0787078	+	0.0391373i
$755$	3.24196e21			0.843733
$756$	1.37805e20	−	3.79972e21i	0.0355100	−	0.979125i
$757$	−5.48524e21			−1.39951			−0.699756	−	0.714382i	$-0.746708\pi$
$757$	−5.48524e21			−1.39951			−0.699756	+	0.714382i	$0.746708\pi$
$758$	−1.36106e21	−	6.76782e20i	−0.343840	−	0.170974i
$759$	−5.78569e20	−	5.40781e20i	−0.144724	−	0.135272i
$760$	1.20712e20	−	2.27731e19i	0.0298984	−	0.00564054i
$761$		−	2.76565e21i		−	0.678286i	−0.940735	−	0.339143i	$-0.889863\pi$
$761$		−	2.76565e21i		−	0.678286i	0.940735	−	0.339143i	$-0.110137\pi$
$762$	8.92864e20	+	2.38874e21i	0.216832	+	0.580106i
$763$		−	3.19556e21i		−	0.768445i
$764$	3.36546e21	+	4.44631e21i	0.801390	+	1.05876i
$765$	3.18242e20	+	4.70809e21i	0.0750406	+	1.11016i
$766$	6.43425e20	−	1.29397e21i	0.150239	−	0.302141i
$767$	1.29788e21			0.300103
$768$	1.16147e21	+	4.20998e21i	0.265949	+	0.963987i
$769$	−3.02478e21			−0.685877			−0.342939	−	0.939358i	$-0.611422\pi$
$769$	−3.02478e21			−0.685877			−0.342939	+	0.939358i	$0.611422\pi$
$770$	−4.14416e21	+	8.33418e21i	−0.930584	+	1.87147i
$771$	4.27524e21	−	4.57397e21i	0.950719	−	1.01715i
$772$	−1.66276e21	−	2.19677e21i	−0.366184	−	0.483788i
$773$			4.25049e21i			0.927028i	0.886090	+	0.463514i	$0.153412\pi$
$773$			4.25049e21i			0.927028i	−0.886090	+	0.463514i	$0.846588\pi$
$774$	−2.68321e21	+	6.45496e21i	−0.579559	+	1.39424i
$775$			3.98213e21i			0.851830i
$776$	−6.01513e21	+	1.13480e21i	−1.27433	+	0.240411i
$777$	1.63088e21	−	1.74484e21i	0.342187	−	0.366098i
$778$	4.83645e20	+	2.40491e20i	0.100503	+	0.0499750i
$779$	9.33962e19			0.0192220
$780$	−2.45293e21	−	2.55391e20i	−0.500006	−	0.0520590i
$781$	3.03406e21			0.612550
$782$	−4.62695e20	−	2.30074e20i	−0.0925218	−	0.0460063i
$783$	−1.30253e21	−	1.06230e21i	−0.257973	−	0.210394i
$784$	−5.54388e19	+	1.96504e20i	−0.0108754	+	0.0385480i
$785$			1.91135e21i			0.371380i
$786$	−3.06827e21	+	1.14686e21i	−0.590505	+	0.220719i
$787$		−	7.52080e20i		−	0.143368i	−0.997427	−	0.0716842i	$-0.977163\pi$
$787$		−	7.52080e20i		−	0.143368i	0.997427	−	0.0716842i	$-0.0228374\pi$
$788$	1.32577e21	−	1.00349e21i	0.250335	−	0.189481i
$789$	5.10401e21	+	4.77065e21i	0.954627	+	0.892278i
$790$	−5.33162e21	+	1.07223e22i	−0.987771	+	1.98647i
$791$	−4.79955e21			−0.880799
$792$	−1.54859e21	−	5.96617e21i	−0.281512	−	1.08457i
$793$	−1.95069e20			−0.0351268
$794$	3.90033e21	−	7.84383e21i	0.695741	−	1.39918i
$795$	−3.34488e21	−	3.12642e21i	−0.591054	−	0.552451i
$796$	8.20090e21	−	6.20735e21i	1.43553	−	1.08657i
$797$		−	6.45738e21i		−	1.11974i	−0.828579	−	0.559872i	$-0.810850\pi$
$797$		−	6.45738e21i		−	1.11974i	0.828579	−	0.559872i	$-0.189150\pi$
$798$	8.53822e19	−	3.19142e19i	0.0146672	−	0.00548229i
$799$			4.40425e21i			0.749500i
$800$	1.15335e22	+	1.04557e22i	1.94441	+	1.76270i
$801$	2.29184e21	−	1.54916e20i	0.382772	−	0.0258733i
$802$	4.85378e21	+	2.41353e21i	0.803104	+	0.399342i
$803$	−8.05369e21			−1.32017
$804$	−8.78742e21	−	9.14919e20i	−1.42706	−	0.148581i
$805$	2.04968e21			0.329774
$806$	4.81439e20	+	2.39394e20i	0.0767411	+	0.0381594i
$807$	−5.39814e21	+	5.77534e21i	−0.852496	+	0.912065i
$808$	−5.67503e20	−	3.00812e21i	−0.0887939	−	0.470663i
$809$			7.64146e21i			1.18457i	0.805727	+	0.592287i	$0.201775\pi$
$809$			7.64146e21i			1.18457i	−0.805727	+	0.592287i	$0.798225\pi$
$810$	1.17407e22	+	3.97509e21i	1.80325	+	0.610534i
$811$		−	3.94043e21i		−	0.599635i	−0.953997	−	0.299817i	$-0.903074\pi$
$811$		−	3.94043e21i		−	0.599635i	0.953997	−	0.299817i	$-0.0969257\pi$
$812$	−1.30553e21	−	1.72482e21i	−0.196842	−	0.260059i
$813$	−4.18184e21	+	4.47405e21i	−0.624724	+	0.668377i
$814$	1.72389e21	−	3.46686e21i	0.255168	−	0.513161i
$815$	−1.01969e21			−0.149550
$816$	−2.08214e21	−	3.44095e21i	−0.302576	−	0.500037i
$817$	−1.67584e20			−0.0241305
$818$	5.80416e21	−	1.16726e22i	0.828113	−	1.66539i
$819$	−1.82582e21	+	1.23415e20i	−0.258124	+	0.0174478i
$820$	9.86499e21	+	1.30332e22i	1.38195	+	1.82578i
$821$			6.95621e21i			0.965603i	0.875730	+	0.482802i	$0.160381\pi$
$821$			6.95621e21i			0.965603i	−0.875730	+	0.482802i	$0.839619\pi$
$822$	1.38550e20	+	3.70672e20i	0.0190576	+	0.0509861i
$823$		−	1.06829e22i		−	1.45610i	−0.685526	−	0.728048i	$-0.740428\pi$
$823$		−	1.06829e22i		−	1.45610i	0.685526	−	0.728048i	$-0.259572\pi$
$824$	3.30992e20	+	1.75447e21i	0.0447058	+	0.236969i
$825$	−1.60516e22	−	1.50032e22i	−2.14839	−	2.00807i
$826$	−7.51749e21	−	3.73806e21i	−0.997063	−	0.495787i
$827$	1.10778e22			1.45600			0.727999	−	0.685579i	$-0.240451\pi$
$827$	1.10778e22			1.45600			0.727999	+	0.685579i	$0.240451\pi$
$828$	−1.02458e21	+	8.90325e20i	−0.133450	+	0.115963i
$829$	−3.20437e21			−0.413603			−0.206802	−	0.978383i	$-0.566305\pi$
$829$	−3.20437e21			−0.413603			−0.206802	+	0.978383i	$0.566305\pi$
$830$	−6.96124e21	−	3.46146e21i	−0.890432	−	0.442766i
$831$	8.74533e21	+	8.17415e21i	1.10858	+	1.03618i
$832$	1.95745e21	−	7.65832e20i	0.245905	−	0.0962074i
$833$		−	1.88028e20i		−	0.0234091i
$834$	2.01489e21	+	5.39057e21i	0.248602	+	0.665104i
$835$		−	2.00825e22i		−	2.45567i
$836$	1.17823e20	−	8.91812e19i	0.0142785	−	0.0108075i
$837$	−2.09424e21	−	1.70799e21i	−0.251528	−	0.205137i
$838$	3.06775e19	−	6.16947e19i	0.00365166	−	0.00734374i
$839$	−5.66865e21			−0.668752			−0.334376	−	0.942440i	$-0.608525\pi$
$839$	−5.66865e21			−0.668752			−0.334376	+	0.942440i	$0.608525\pi$
$840$	1.34721e22	+	8.54397e21i	1.57521	+	0.998999i
$841$	7.67294e21			0.889184
$842$	−3.27066e21	+	6.57753e21i	−0.375660	+	0.755478i
$843$	1.38562e21	−	1.48244e21i	0.157739	−	0.168761i
$844$	2.52470e21	−	1.91097e21i	0.284867	−	0.215619i
$845$		−	1.58365e22i		−	1.77106i
$846$	1.06828e22	+	4.44067e21i	1.18416	+	0.492233i
$847$			2.27877e21i			0.250366i
$848$	3.75567e21	+	1.05957e21i	0.408995	+	0.115388i
$849$	−6.29499e21	+	6.73486e21i	−0.679497	+	0.726978i
$850$	−1.28368e22	−	6.38308e21i	−1.37346	−	0.682949i
$851$	−8.52626e20			−0.0904246
$852$	5.38522e20	−	5.17229e21i	0.0566118	−	0.543733i
$853$	−1.03216e22			−1.07554			−0.537771	−	0.843091i	$-0.680734\pi$
$853$	−1.03216e22			−1.07554			−0.537771	+	0.843091i	$0.680734\pi$
$854$	1.12986e21	+	5.61820e20i	0.116705	+	0.0580315i
$855$	2.00406e19	+	2.96482e20i	0.00205194	+	0.0303565i
$856$	−1.84142e22	+	3.47396e21i	−1.86895	+	0.352591i
$857$			9.79087e21i			0.985065i	0.870294	+	0.492533i	$0.163929\pi$
$857$			9.79087e21i			0.985065i	−0.870294	+	0.492533i	$0.836071\pi$
$858$	−2.77885e21	+	1.03868e21i	−0.277148	+	0.103592i
$859$			9.48727e21i			0.937978i	0.883204	+	0.468989i	$0.155382\pi$
$859$			9.48727e21i			0.937978i	−0.883204	+	0.468989i	$0.844618\pi$
$860$	−1.77011e22	−	2.33859e22i	−1.73485	−	2.29201i
$861$	8.86100e21	+	8.28226e21i	0.860912	+	0.804684i
$862$	6.04641e21	−	1.21598e22i	0.582362	−	1.17117i
$863$	−2.00678e22			−1.91610			−0.958050	−	0.286602i	$-0.907474\pi$
$863$	−2.00678e22			−1.91610			−0.958050	+	0.286602i	$0.907474\pi$
$864$	−1.04456e22	+	1.58099e21i	−0.988739	+	0.149650i
$865$	1.84319e22			1.72962
$866$	1.91155e21	−	3.84425e21i	0.177828	−	0.357625i
$867$	−5.21552e21	−	4.87488e21i	−0.481010	−	0.449594i
$868$	−2.09906e21	−	2.77320e21i	−0.191923	−	0.253561i
$869$			1.44046e22i			1.30573i
$870$	6.60572e21	−	2.46909e21i	0.593644	−	0.221892i
$871$			4.25219e21i			0.378858i
$872$	−8.72507e21	+	1.64605e21i	−0.770717	+	0.145401i
$873$	−9.98631e20	−	1.47738e22i	−0.0874578	−	1.29386i
$874$	−2.91372e19	−	1.44884e19i	−0.00252995	−	0.00125801i
$875$	3.51979e22			3.03010
$876$	−1.42947e21	+	1.37295e22i	−0.122010	+	1.17185i
$877$	2.66187e21			0.225263			0.112631	−	0.993637i	$-0.464072\pi$
$877$	2.66187e21			0.225263			0.112631	+	0.993637i	$0.464072\pi$
$878$	4.33580e21	+	2.15597e21i	0.363798	+	0.180898i
$879$	−9.56800e21	+	1.02366e22i	−0.795984	+	0.851605i
$880$	2.48901e22	+	7.02212e21i	2.05308	+	0.579226i
$881$		−	6.89696e21i		−	0.564077i	−0.959403	−	0.282039i	$-0.908989\pi$
$881$		−	6.89696e21i		−	0.564077i	0.959403	−	0.282039i	$-0.0910106\pi$
$882$	−4.56075e20	−	1.89582e20i	−0.0369847	−	0.0153739i
$883$			6.26394e21i			0.503666i	0.967771	+	0.251833i	$0.0810333\pi$
$883$			6.26394e21i			0.503666i	−0.967771	+	0.251833i	$0.918967\pi$
$884$	−1.54342e21	+	1.16823e21i	−0.123053	+	0.0931403i
$885$	1.86894e22	−	1.99954e22i	1.47748	−	1.58072i
$886$	−5.74600e21	+	1.15556e22i	−0.450415	+	0.905816i
$887$	1.02327e22			0.795361			0.397680	−	0.917524i	$-0.369815\pi$
$887$	1.02327e22			0.795361			0.397680	+	0.917524i	$0.369815\pi$
$888$	−5.60412e21	−	3.55413e21i	−0.431927	−	0.273927i
$889$	−7.93947e21			−0.606776
$890$	−4.29114e21	+	8.62978e21i	−0.325198	+	0.653995i
$891$	1.47750e22	−	2.00659e21i	1.11031	−	0.150792i
$892$	1.31072e22	−	9.92099e21i	0.976729	−	0.739297i
$893$			2.77348e20i			0.0204946i
$894$	−4.36771e21	−	1.16852e22i	−0.320053	−	0.856262i
$895$			1.08827e22i			0.790796i
$896$	−1.35435e22	−	1.20191e21i	−0.975933	−	0.0866089i
$897$	4.77270e20	+	4.46099e20i	0.0341052	+	0.0318777i
$898$	2.06747e21	+	1.02805e21i	0.146510	+	0.0728519i
$899$	−1.53748e21			−0.108047
$900$	−2.84256e22	+	2.47008e22i	−1.98103	+	1.72144i
$901$	−3.59365e21			−0.248371
$902$	1.76061e22	+	8.75462e21i	1.20674	+	0.600051i
$903$	−1.58996e22	−	1.48611e22i	−1.08076	−	1.01017i
$904$	2.47227e21	+	1.31046e22i	0.166660	+	0.883403i
$905$			2.79003e22i			1.86528i
$906$	−2.34025e21	−	6.26105e21i	−0.155168	−	0.415131i
$907$			2.53200e22i			1.66498i	0.554042	+	0.832489i	$0.313085\pi$
$907$			2.53200e22i			1.66498i	−0.554042	+	0.832489i	$0.686915\pi$
$908$	8.95219e20	+	1.18273e21i	0.0583829	+	0.0771331i
$909$	7.38828e21	−	4.99408e20i	0.477875	−	0.0323018i
$910$	3.41858e21	−	6.87500e21i	0.219298	−	0.441024i
$911$	1.24018e22			0.789039			0.394519	−	0.918888i	$-0.370911\pi$
$911$	1.24018e22			0.789039			0.394519	+	0.918888i	$0.370911\pi$
$912$	−1.31118e20	−	2.16686e20i	−0.00827374	−	0.0136732i
$913$	−9.35195e21			−0.585290
$914$	−2.15001e21	+	4.32382e21i	−0.133458	+	0.268393i
$915$	−2.80898e21	+	3.00526e21i	−0.172938	+	0.185022i
$916$	−1.71510e22	−	2.26592e22i	−1.04731	−	1.38366i
$917$		−	1.01980e22i		−	0.617654i
$918$	8.86280e21	−	4.01321e21i	0.532416	−	0.241086i
$919$		−	4.00707e21i		−	0.238759i	−0.992849	−	0.119380i	$-0.961909\pi$
$919$		−	4.00707e21i		−	0.238759i	0.992849	−	0.119380i	$-0.0380906\pi$
$920$	−1.05580e21	−	5.59637e21i	−0.0623981	−	0.330749i
$921$	7.42636e21	−	7.94529e21i	0.435340	−	0.465760i
$922$	−2.17918e20	−	1.08360e20i	−0.0126710	−	0.00630065i
$923$	−2.50284e21			−0.144351
$924$	1.90870e22	+	1.98728e21i	1.09194	+	0.113689i
$925$	−2.36549e22			−1.34232
$926$	−2.30062e22	−	1.14398e22i	−1.29498	−	0.643926i
$927$	−4.30917e21	+	2.91277e20i	−0.240600	+	0.0162633i
$928$	−4.03690e21	+	4.45304e21i	−0.223583	+	0.246631i
$929$			2.01199e22i			1.10537i	0.833391	+	0.552684i	$0.186396\pi$
$929$			2.01199e22i			1.10537i	−0.833391	+	0.552684i	$0.813604\pi$
$930$	1.06208e22	−	3.96985e21i	0.578811	−	0.216348i
$931$		−	1.18406e19i		−	0.000640106i
$932$	2.52507e22	−	1.91125e22i	1.35411	−	1.02494i
$933$	−7.86650e21	−	7.35271e21i	−0.418474	−	0.391143i
$934$	5.16321e21	−	1.03836e22i	0.272470	−	0.547955i
$935$	−2.38164e22			−1.24678
$936$	1.27745e21	+	4.92158e21i	0.0663402	+	0.255585i
$937$	2.11836e22			1.09132			0.545661	−	0.838006i	$-0.316279\pi$
$937$	2.11836e22			1.09132			0.545661	+	0.838006i	$0.316279\pi$
$938$	1.22468e22	−	2.46291e22i	0.625894	−	1.25872i
$939$	6.64644e21	+	6.21235e21i	0.336975	+	0.314966i
$940$	−3.87033e22	+	2.92950e22i	−1.94666	+	1.47344i
$941$		−	2.51963e22i		−	1.25723i	−0.777717	−	0.628615i	$-0.783622\pi$
$941$		−	2.51963e22i		−	1.25723i	0.777717	−	0.628615i	$-0.216378\pi$
$942$	3.69132e21	−	1.37974e21i	0.182726	−	0.0682991i
$943$		−	4.32998e21i		−	0.212642i
$944$	−6.33400e21	+	2.24510e22i	−0.308594	+	1.09382i
$945$	−2.43903e22	+	2.99060e22i	−1.17890	+	1.44550i
$946$	−3.15913e22	−	1.57087e22i	−1.51490	−	0.753280i
$947$	1.86383e22			0.886710			0.443355	−	0.896346i	$-0.353788\pi$
$947$	1.86383e22			0.886710			0.443355	+	0.896346i	$0.353788\pi$
$948$	2.45561e22	+	2.55671e21i	1.15904	+	0.120675i
$949$	6.64362e21			0.311106
$950$	−8.08370e20	−	4.01960e20i	−0.0375563	−	0.0186748i
$951$	2.37483e21	−	2.54078e21i	0.109466	−	0.117115i
$952$	1.23043e22	−	2.32130e21i	0.562706	−	0.106158i
$953$		−	2.79776e22i		−	1.26945i	−0.772740	−	0.634723i	$-0.781114\pi$
$953$		−	2.79776e22i		−	1.26945i	0.772740	−	0.634723i	$-0.218886\pi$
$954$	−3.62336e21	+	8.71668e21i	−0.163117	+	0.392408i
$955$		−	5.65978e22i		−	2.52798i
$956$	7.29968e21	+	9.64404e21i	0.323496	+	0.427391i
$957$	5.79267e21	−	6.19744e21i	0.254706	−	0.272504i
$958$	−1.98650e22	+	3.99499e22i	−0.866658	+	1.74291i
$959$	−1.23200e21			−0.0533301
$960$	1.63887e22	−	4.11848e22i	0.703898	−	1.76890i
$961$	2.09933e22			0.894653
$962$	−1.42206e21	+	2.85987e21i	−0.0601320	+	0.120930i
$963$	−3.05712e21	−	4.52272e22i	−0.128267	−	1.89759i
$964$	1.73777e22	+	2.29587e22i	0.723459	+	0.955805i
$965$			2.79631e22i			1.15513i
$966$	−1.47959e21	−	3.95845e21i	−0.0606474	−	0.162254i
$967$			3.09934e21i			0.126058i	0.998012	+	0.0630291i	$0.0200761\pi$
$967$			3.09934e21i			0.126058i	−0.998012	+	0.0630291i	$0.979924\pi$
$968$	6.22189e21	−	1.17380e21i	0.251106	−	0.0473729i
$969$	1.70395e20	+	1.59266e20i	0.00682383	+	0.00637815i
$970$	5.56299e22	+	2.76619e22i	2.21065	+	1.09924i
$971$	−1.79148e22			−0.706429			−0.353214	−	0.935542i	$-0.614911\pi$
$971$	−1.79148e22			−0.706429			−0.353214	+	0.935542i	$0.614911\pi$
$972$	−7.98268e20	−	2.55438e22i	−0.0312357	−	0.999512i
$973$	−1.79167e22			−0.695682
$974$	−1.39590e22	−	6.94111e21i	−0.537853	−	0.267446i
$975$	1.32412e22	+	1.23764e22i	0.506282	+	0.473215i
$976$	9.51983e20	−	3.37433e21i	0.0361207	−	0.128031i
$977$		−	1.13585e22i		−	0.427673i	−0.976869	−	0.213836i	$-0.931404\pi$
$977$		−	1.13585e22i		−	0.427673i	0.976869	−	0.213836i	$-0.0685959\pi$
$978$	7.36079e20	+	1.96928e21i	0.0275032	+	0.0735812i
$979$			1.15935e22i			0.429878i
$980$	1.65233e21	−	1.25067e21i	0.0607998	−	0.0460200i
$981$	−1.44854e21	−	2.14297e22i	−0.0528946	−	0.782527i
$982$	4.93274e20	−	9.92008e20i	0.0178752	−	0.0359483i
$983$	1.87521e22			0.674370			0.337185	−	0.941438i	$-0.390525\pi$
$983$	1.87521e22			0.674370			0.337185	+	0.941438i	$0.390525\pi$
$984$	1.80493e22	−	2.84600e22i	0.644166	−	1.01572i
$985$	−1.68759e22			−0.597718
$986$	2.46448e21	−	4.95624e21i	0.0866260	−	0.174211i
$987$	−2.45949e22	+	2.63135e22i	−0.857959	+	0.917910i
$988$	−9.71938e19	+	7.35670e19i	−0.00336482	+	0.00254686i
$989$			7.76943e21i			0.266942i
$990$	−2.40133e22	+	5.77684e22i	−0.818818	+	1.96982i
$991$			2.20373e22i			0.745771i	0.927877	+	0.372885i	$0.121632\pi$
$991$			2.20373e22i			0.745771i	−0.927877	+	0.372885i	$0.878368\pi$
$992$	−6.49063e21	+	7.15971e21i	−0.217996	+	0.240468i
$993$	−3.46981e22	+	3.71227e22i	−1.15661	+	1.23743i
$994$	1.44968e22	+	7.20848e21i	0.479593	+	0.238477i
$995$	−1.04391e23			−3.42758
$996$	−1.65990e21	+	1.59426e22i	−0.0540924	+	0.519536i
$997$	−3.24585e22			−1.04982			−0.524910	−	0.851157i	$-0.675901\pi$
$997$	−3.24585e22			−1.04982			−0.524910	+	0.851157i	$0.675901\pi$
$998$	4.23512e22	+	2.10591e22i	1.35952	+	0.676021i
$999$	1.01459e22	−	1.24403e22i	0.323258	−	0.396360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.16.b.a.11.12	yes	28
3.2	odd	2	inner	12.16.b.a.11.17	yes	28
4.3	odd	2	inner	12.16.b.a.11.18	yes	28
12.11	even	2	inner	12.16.b.a.11.11	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.16.b.a.11.11	✓	28	12.11	even	2	inner
12.16.b.a.11.12	yes	28	1.1	even	1	trivial
12.16.b.a.11.17	yes	28	3.2	odd	2	inner
12.16.b.a.11.18	yes	28	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-80.5973 + 162.087i) q^{2} +(-2767.36 - 2586.62i) q^{3} +(-19776.2 - 26127.5i) q^{4} +332581. i q^{5} +(642299. - 240078. i) q^{6} +2.13481e6i q^{7} +(5.82882e6 - 1.09965e6i) q^{8} +(967701. + 1.43162e7i) q^{9} +O(q^{10})\)	\(q+(-80.5973 + 162.087i) q^{2} +(-2767.36 - 2586.62i) q^{3} +(-19776.2 - 26127.5i) q^{4} +332581. i q^{5} +(642299. - 240078. i) q^{6} +2.13481e6i q^{7} +(5.82882e6 - 1.09965e6i) q^{8} +(967701. + 1.43162e7i) q^{9} +(-5.39069e7 - 2.68051e7i) q^{10} -7.24202e7 q^{11} +(-1.28540e7 + 1.23458e8i) q^{12} +5.97405e7 q^{13} +(-3.46024e8 - 1.72060e8i) q^{14} +(8.60260e8 - 9.20372e8i) q^{15} +(-2.91549e8 + 1.03340e9i) q^{16} -9.88823e8i q^{17} +(-2.39847e9 - 9.96998e8i) q^{18} -6.22690e7i q^{19} +(8.68950e9 - 6.57717e9i) q^{20} +(5.52194e9 - 5.90779e9i) q^{21} +(5.83687e9 - 1.17383e10i) q^{22} -2.88688e9 q^{23} +(-1.89748e10 - 1.20338e10i) q^{24} -8.00924e10 q^{25} +(-4.81493e9 + 9.68315e9i) q^{26} +(3.43527e10 - 4.21213e10i) q^{27} +(5.57772e10 - 4.22183e10i) q^{28} -3.09233e10i q^{29} +(7.98454e10 + 2.13616e11i) q^{30} -4.97193e10i q^{31} +(-1.44003e11 - 1.30546e11i) q^{32} +(2.00413e11 + 1.87324e11i) q^{33} +(1.60275e11 + 7.96964e10i) q^{34} -7.09996e11 q^{35} +(3.54910e11 - 3.08404e11i) q^{36} +2.95345e11 q^{37} +(1.00930e10 + 5.01871e9i) q^{38} +(-1.65324e11 - 1.54526e11i) q^{39} +(3.65722e11 + 1.93855e12i) q^{40} +1.49988e12i q^{41} +(5.12521e11 + 1.37118e12i) q^{42} -2.69129e12i q^{43} +(1.43219e12 + 1.89216e12i) q^{44} +(-4.76131e12 + 3.21839e11i) q^{45} +(2.32675e11 - 4.67925e11i) q^{46} -4.45404e12 q^{47} +(3.47984e12 - 2.10568e12i) q^{48} +1.90153e11 q^{49} +(6.45523e12 - 1.29819e13i) q^{50} +(-2.55771e12 + 2.73643e12i) q^{51} +(-1.18144e12 - 1.56087e12i) q^{52} -3.63427e12i q^{53} +(4.05857e12 + 8.96298e12i) q^{54} -2.40856e13i q^{55} +(2.34754e12 + 1.24434e13i) q^{56} +(-1.61066e11 + 1.72321e11i) q^{57} +(5.01226e12 + 2.49234e12i) q^{58} +2.17253e13 q^{59} +(-4.10596e13 - 4.27500e12i) q^{60} -3.26526e12 q^{61} +(8.05883e12 + 4.00724e12i) q^{62} +(-3.05624e13 + 2.06586e12i) q^{63} +(3.27659e13 - 1.28193e13i) q^{64} +1.98686e13i q^{65} +(-4.65154e13 + 1.73865e13i) q^{66} +7.11776e13i q^{67} +(-2.58355e13 + 1.95551e13i) q^{68} +(7.98905e12 + 7.46727e12i) q^{69} +(5.72238e13 - 1.15081e14i) q^{70} -4.18952e13 q^{71} +(2.13834e13 + 8.23827e13i) q^{72} +1.11208e14 q^{73} +(-2.38040e13 + 4.78715e13i) q^{74} +(2.21645e14 + 2.07169e14i) q^{75} +(-1.62693e12 + 1.23144e12i) q^{76} -1.54603e14i q^{77} +(3.83713e13 - 1.43424e13i) q^{78} -1.98903e14i q^{79} +(-3.43690e14 - 9.69635e13i) q^{80} +(-2.04018e14 + 2.77077e13i) q^{81} +(-2.43111e14 - 1.20886e14i) q^{82} +1.29134e14 q^{83} +(-2.63559e14 - 2.74409e13i) q^{84} +3.28864e14 q^{85} +(4.36222e14 + 2.16910e14i) q^{86} +(-7.99869e13 + 8.55761e13i) q^{87} +(-4.22124e14 + 7.96367e13i) q^{88} -1.60087e14i q^{89} +(3.31582e14 - 7.97683e14i) q^{90} +1.27535e14i q^{91} +(5.70914e13 + 7.54270e13i) q^{92} +(-1.28605e14 + 1.37591e14i) q^{93} +(3.58983e14 - 7.21940e14i) q^{94} +2.07095e13 q^{95} +(6.08361e13 + 7.33747e14i) q^{96} -1.03196e15 q^{97} +(-1.53258e13 + 3.08212e13i) q^{98} +(-7.00811e13 - 1.03678e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

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