LMFDB - Embedded newform 12.16.b.a.11.14

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			11.14
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-35.8416 + 177.436i) q^{2} +(-2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} -33476.6i q^{5} +(-453057. - 514708. i) q^{6} -694274. i q^{7} +(3.33920e6 - 4.90246e6i) q^{8} +(-3.84657e6 - 1.38237e7i) q^{9} +O(q^{10})$	\(q+(-35.8416 + 177.436i) q^{2} +(-2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} -33476.6i q^{5} +(-453057. - 514708. i) q^{6} -694274. i q^{7} +(3.33920e6 - 4.90246e6i) q^{8} +(-3.84657e6 - 1.38237e7i) q^{9} +(5.93994e6 + 1.19985e6i) q^{10} +5.49804e7 q^{11} +(1.07566e8 - 6.19404e7i) q^{12} -2.93342e8 q^{13} +(1.23189e8 + 2.48839e7i) q^{14} +(1.00974e8 + 7.67131e7i) q^{15} +(7.50189e8 + 7.68204e8i) q^{16} -1.09024e9i q^{17} +(2.59069e9 - 1.87054e8i) q^{18} +5.34556e9i q^{19} +(-4.25793e8 + 1.01095e9i) q^{20} +(2.09410e9 + 1.59096e9i) q^{21} +(-1.97058e9 + 9.75547e9i) q^{22} +1.46183e10 q^{23} +(7.13511e9 + 2.13060e10i) q^{24} +2.93969e10 q^{25} +(1.05138e10 - 5.20493e10i) q^{26} +(5.05103e10 + 2.00755e10i) q^{27} +(-8.83057e9 + 2.09662e10i) q^{28} -7.94865e10i q^{29} +(-1.72307e10 + 1.51668e10i) q^{30} -1.27900e11i q^{31} +(-1.63195e11 + 1.05577e11i) q^{32} +(-1.25990e11 + 1.65834e11i) q^{33} +(1.93447e11 + 3.90759e10i) q^{34} -2.32419e10 q^{35} +(-5.96641e10 + 4.66384e11i) q^{36} -4.22440e11 q^{37} +(-9.48493e11 - 1.91593e11i) q^{38} +(6.72206e11 - 8.84791e11i) q^{39} +(-1.64118e11 - 1.11785e11i) q^{40} -7.06327e11i q^{41} +(-3.57349e11 + 3.14546e11i) q^{42} -2.89245e12i q^{43} +(-1.66034e12 - 6.99303e11i) q^{44} +(-4.62771e11 + 1.28770e11i) q^{45} +(-5.23941e11 + 2.59380e12i) q^{46} +6.40017e12 q^{47} +(-4.03618e12 + 5.02381e11i) q^{48} +4.26554e12 q^{49} +(-1.05363e12 + 5.21606e12i) q^{50} +(3.28843e12 + 2.49833e12i) q^{51} +(8.85857e12 + 3.73106e12i) q^{52} +7.99661e11i q^{53} +(-5.37247e12 + 8.24279e12i) q^{54} -1.84055e12i q^{55} +(-3.40365e12 - 2.31832e12i) q^{56} +(-1.61235e13 - 1.22496e13i) q^{57} +(1.41037e13 + 2.84892e12i) q^{58} +1.39217e13 q^{59} +(-2.07355e12 - 3.60094e12i) q^{60} +9.62549e12 q^{61} +(2.26940e13 + 4.58413e12i) q^{62} +(-9.59745e12 + 2.67057e12i) q^{63} +(-1.28839e13 - 3.27406e13i) q^{64} +9.82009e12i q^{65} +(-2.49092e13 - 2.82988e13i) q^{66} -2.75795e13i q^{67} +(-1.38669e13 + 3.29239e13i) q^{68} +(-3.34984e13 + 4.40923e13i) q^{69} +(8.33027e11 - 4.12395e12i) q^{70} -1.40051e14 q^{71} +(-8.06147e13 - 2.73025e13i) q^{72} +1.33684e14 q^{73} +(1.51409e13 - 7.49559e13i) q^{74} +(-6.73643e13 + 8.86683e13i) q^{75} +(6.79909e13 - 1.61429e14i) q^{76} -3.81714e13i q^{77} +(1.32901e14 + 1.50986e14i) q^{78} +1.22264e14i q^{79} +(2.57169e13 - 2.51138e13i) q^{80} +(-1.76299e14 + 1.06348e14i) q^{81} +(1.25327e14 + 2.53158e13i) q^{82} -8.03046e13 q^{83} +(-4.30036e13 - 7.46802e13i) q^{84} -3.64975e13 q^{85} +(5.13224e14 + 1.03670e14i) q^{86} +(2.39751e14 + 1.82147e14i) q^{87} +(1.83590e14 - 2.69539e14i) q^{88} -4.85416e14i q^{89} +(-6.26194e12 - 8.67273e13i) q^{90} +2.03660e14i q^{91} +(-4.41454e14 - 1.85932e14i) q^{92} +(3.85777e14 + 2.93088e14i) q^{93} +(-2.29392e14 + 1.13562e15i) q^{94} +1.78951e14 q^{95} +(5.55228e13 - 7.34169e14i) q^{96} +1.97524e14 q^{97} +(-1.52884e14 + 7.56859e14i) q^{98} +(-2.11486e14 - 7.60033e14i) 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 $

$2$	−35.8416	+	177.436i	−0.197998	+	0.980202i
$2$	−35.8416	+	177.436i	−0.197998	+	0.980202i
$3$	−2291.54	+	3016.25i	−0.604949	+	0.796264i
$3$	−2291.54	+	3016.25i	−0.604949	+	0.796264i
$4$	−30198.8	−	12719.1i	−0.921593	−	0.388157i
$5$		−	33476.6i		−	0.191631i	−0.995399	−	0.0958156i	$-0.969454\pi$
$5$		−	33476.6i		−	0.191631i	0.995399	−	0.0958156i	$-0.0305459\pi$
$6$	−453057.	−	514708.i	−0.660721	−	0.750631i
$7$		−	694274.i		−	0.318637i	−0.987227	−	0.159318i	$-0.949070\pi$
$7$		−	694274.i		−	0.318637i	0.987227	−	0.159318i	$-0.0509296\pi$
$8$	3.33920e6	−	4.90246e6i	0.562947	−	0.826493i
$9$	−3.84657e6	−	1.38237e7i	−0.268074	−	0.963398i
$10$	5.93994e6	+	1.19985e6i	0.187837	+	0.0379427i
$11$	5.49804e7			0.850673			0.425336	−	0.905035i	$-0.360156\pi$
$11$	5.49804e7			0.850673			0.425336	+	0.905035i	$0.360156\pi$
$12$	1.07566e8	−	6.19404e7i	0.866592	−	0.499017i
$13$	−2.93342e8			−1.29658			−0.648290	−	0.761394i	$-0.724515\pi$
$13$	−2.93342e8			−1.29658			−0.648290	+	0.761394i	$0.724515\pi$
$14$	1.23189e8	+	2.48839e7i	0.312328	+	0.0630896i
$15$	1.00974e8	+	7.67131e7i	0.152589	+	0.115927i
$16$	7.50189e8	+	7.68204e8i	0.698668	+	0.715446i
$17$		−	1.09024e9i		−	0.644399i	−0.946672	−	0.322199i	$-0.895578\pi$
$17$		−	1.09024e9i		−	0.644399i	0.946672	−	0.322199i	$-0.104422\pi$
$18$	2.59069e9	−	1.87054e8i	0.997404	−	0.0720151i
$19$			5.34556e9i			1.37196i	0.727620	+	0.685980i	$0.240626\pi$
$19$			5.34556e9i			1.37196i	−0.727620	+	0.685980i	$0.759374\pi$
$20$	−4.25793e8	+	1.01095e9i	−0.0743830	+	0.176606i
$21$	2.09410e9	+	1.59096e9i	0.253719	+	0.192759i
$22$	−1.97058e9	+	9.75547e9i	−0.168432	+	0.833831i
$23$	1.46183e10			0.895235			0.447618	−	0.894225i	$-0.352273\pi$
$23$	1.46183e10			0.895235			0.447618	+	0.894225i	$0.352273\pi$
$24$	7.13511e9	+	2.13060e10i	0.317553	+	0.948240i
$25$	2.93969e10			0.963277
$26$	1.05138e10	−	5.20493e10i	0.256721	−	1.27091i
$27$	5.05103e10	+	2.00755e10i	0.929291	+	0.369349i
$28$	−8.83057e9	+	2.09662e10i	−0.123681	+	0.293653i
$29$		−	7.94865e10i		−	0.855674i	−0.903856	−	0.427837i	$-0.859276\pi$
$29$		−	7.94865e10i		−	0.855674i	0.903856	−	0.427837i	$-0.140724\pi$
$30$	−1.72307e10	+	1.51668e10i	−0.143844	+	0.126615i
$31$		−	1.27900e11i		−	0.834944i	−0.908690	−	0.417472i	$-0.862916\pi$
$31$		−	1.27900e11i		−	0.834944i	0.908690	−	0.417472i	$-0.137084\pi$
$32$	−1.63195e11	+	1.05577e11i	−0.839617	+	0.543179i
$33$	−1.25990e11	+	1.65834e11i	−0.514613	+	0.677360i
$34$	1.93447e11	+	3.90759e10i	0.631641	+	0.127590i
$35$	−2.32419e10			−0.0610607
$36$	−5.96641e10	+	4.66384e11i	−0.126895	+	0.991916i
$37$	−4.22440e11			−0.731564			−0.365782	−	0.930701i	$-0.619198\pi$
$37$	−4.22440e11			−0.731564			−0.365782	+	0.930701i	$0.619198\pi$
$38$	−9.48493e11	−	1.91593e11i	−1.34480	−	0.271646i
$39$	6.72206e11	−	8.84791e11i	0.784364	−	1.03242i
$40$	−1.64118e11	−	1.11785e11i	−0.158382	−	0.107878i
$41$		−	7.06327e11i		−	0.566405i	−0.959060	−	0.283202i	$-0.908603\pi$
$41$		−	7.06327e11i		−	0.566405i	0.959060	−	0.283202i	$-0.0913968\pi$
$42$	−3.57349e11	+	3.14546e11i	−0.239179	+	0.210530i
$43$		−	2.89245e12i		−	1.62275i	−0.584523	−	0.811377i	$-0.698718\pi$
$43$		−	2.89245e12i		−	1.62275i	0.584523	−	0.811377i	$-0.301282\pi$
$44$	−1.66034e12	−	6.99303e11i	−0.783974	−	0.330195i
$45$	−4.62771e11	+	1.28770e11i	−0.184617	+	0.0513713i
$46$	−5.23941e11	+	2.59380e12i	−0.177255	+	0.877512i
$47$	6.40017e12			1.84271			0.921357	−	0.388718i	$-0.127082\pi$
$47$	6.40017e12			1.84271			0.921357	+	0.388718i	$0.127082\pi$
$48$	−4.03618e12	+	5.02381e11i	−0.992343	+	0.123516i
$49$	4.26554e12			0.898471
$50$	−1.05363e12	+	5.21606e12i	−0.190727	+	0.944207i
$51$	3.28843e12	+	2.49833e12i	0.513112	+	0.389828i
$52$	8.85857e12	+	3.73106e12i	1.19492	+	0.503277i
$53$			7.99661e11i			0.0935055i	0.998906	+	0.0467527i	$0.0148873\pi$
$53$			7.99661e11i			0.0935055i	−0.998906	+	0.0467527i	$0.985113\pi$
$54$	−5.37247e12	+	8.24279e12i	−0.546035	+	0.837762i
$55$		−	1.84055e12i		−	0.163015i
$56$	−3.40365e12	−	2.31832e12i	−0.263351	−	0.179375i
$57$	−1.61235e13	−	1.22496e13i	−1.09244	−	0.829966i
$58$	1.41037e13	+	2.84892e12i	0.838733	+	0.169422i
$59$	1.39217e13			0.728289			0.364144	−	0.931343i	$-0.381361\pi$
$59$	1.39217e13			0.728289			0.364144	+	0.931343i	$0.381361\pi$
$60$	−2.07355e12	−	3.60094e12i	−0.0956271	−	0.166066i
$61$	9.62549e12			0.392147			0.196074	−	0.980589i	$-0.437181\pi$
$61$	9.62549e12			0.392147			0.196074	+	0.980589i	$0.437181\pi$
$62$	2.26940e13	+	4.58413e12i	0.818414	+	0.165318i
$63$	−9.59745e12	+	2.67057e12i	−0.306974	+	0.0854181i
$64$	−1.28839e13	−	3.27406e13i	−0.366182	−	0.930543i
$65$			9.82009e12i			0.248465i
$66$	−2.49092e13	−	2.82988e13i	−0.562057	−	0.638542i
$67$		−	2.75795e13i		−	0.555937i	−0.960590	−	0.277969i	$-0.910339\pi$
$67$		−	2.75795e13i		−	0.555937i	0.960590	−	0.277969i	$-0.0896611\pi$
$68$	−1.38669e13	+	3.29239e13i	−0.250128	+	0.593874i
$69$	−3.34984e13	+	4.40923e13i	−0.541572	+	0.712844i
$70$	8.33027e11	−	4.12395e12i	0.0120899	−	0.0598519i
$71$	−1.40051e14			−1.82746			−0.913732	−	0.406318i	$-0.866813\pi$
$71$	−1.40051e14			−1.82746			−0.913732	+	0.406318i	$0.866813\pi$
$72$	−8.06147e13	−	2.73025e13i	−0.947154	−	0.320781i
$73$	1.33684e14			1.41631			0.708153	−	0.706059i	$-0.249529\pi$
$73$	1.33684e14			1.41631			0.708153	+	0.706059i	$0.249529\pi$
$74$	1.51409e13	−	7.49559e13i	0.144849	−	0.717081i
$75$	−6.73643e13	+	8.86683e13i	−0.582734	+	0.767024i
$76$	6.79909e13	−	1.61429e14i	0.532536	−	1.26439i
$77$		−	3.81714e13i		−	0.271055i
$78$	1.32901e14	+	1.50986e14i	0.856677	+	0.973253i
$79$			1.22264e14i			0.716301i	0.933664	+	0.358150i	$0.116592\pi$
$79$			1.22264e14i			0.716301i	−0.933664	+	0.358150i	$0.883408\pi$
$80$	2.57169e13	−	2.51138e13i	0.137102	−	0.133887i
$81$	−1.76299e14	+	1.06348e14i	−0.856273	+	0.516524i
$82$	1.25327e14	+	2.53158e13i	0.555191	+	0.112147i
$83$	−8.03046e13			−0.324829			−0.162414	−	0.986723i	$-0.551928\pi$
$83$	−8.03046e13			−0.324829			−0.162414	+	0.986723i	$0.551928\pi$
$84$	−4.30036e13	−	7.46802e13i	−0.159005	−	0.276128i
$85$	−3.64975e13			−0.123487
$86$	5.13224e14	+	1.03670e14i	1.59063	+	0.321303i
$87$	2.39751e14	+	1.82147e14i	0.681342	+	0.517639i
$88$	1.83590e14	−	2.69539e14i	0.478883	−	0.703075i
$89$		−	4.85416e14i		−	1.16329i	−0.813442	−	0.581646i	$-0.802409\pi$
$89$		−	4.85416e14i		−	1.16329i	0.813442	−	0.581646i	$-0.197591\pi$
$90$	−6.26194e12	−	8.67273e13i	−0.0138003	−	0.191134i
$91$			2.03660e14i			0.413138i
$92$	−4.41454e14	−	1.85932e14i	−0.825043	−	0.347492i
$93$	3.85777e14	+	2.93088e14i	0.664836	+	0.505098i
$94$	−2.29392e14	+	1.13562e15i	−0.364854	+	1.80623i
$95$	1.78951e14			0.262910
$96$	5.55228e13	−	7.34169e14i	0.0754115	−	0.997153i
$97$	1.97524e14			0.248218			0.124109	−	0.992269i	$-0.460393\pi$
$97$	1.97524e14			0.248218			0.124109	+	0.992269i	$0.460393\pi$
$98$	−1.52884e14	+	7.56859e14i	−0.177896	+	0.880683i
$99$	−2.11486e14	−	7.60033e14i	−0.228043	−	0.819537i
$100$	−8.87750e14	−	3.73903e14i	−0.887750	−	0.373903i
$101$			7.20648e14i			0.668826i	0.942427	+	0.334413i	$0.108538\pi$
$101$			7.20648e14i			0.668826i	−0.942427	+	0.334413i	$0.891462\pi$
$102$	−5.61155e14	+	4.93940e14i	−0.483706	+	0.425768i
$103$		−	1.54207e15i		−	1.23545i	−0.786394	−	0.617725i	$-0.788055\pi$
$103$		−	1.54207e15i		−	1.23545i	0.786394	−	0.617725i	$-0.211945\pi$
$104$	−9.79527e14	+	1.43810e15i	−0.729905	+	1.07161i
$105$	5.32599e13	−	7.01034e13i	0.0369386	−	0.0486205i
$106$	−1.41888e14	−	2.86611e13i	−0.0916543	−	0.0185139i
$107$	1.67492e15			1.00836			0.504180	−	0.863599i	$-0.331795\pi$
$107$	1.67492e15			1.00836			0.504180	+	0.863599i	$0.331795\pi$
$108$	−1.27001e15	−	1.24870e15i	−0.713062	−	0.701100i
$109$	−2.64556e15			−1.38618			−0.693089	−	0.720852i	$-0.743751\pi$
$109$	−2.64556e15			−1.38618			−0.693089	+	0.720852i	$0.743751\pi$
$110$	3.26580e14	+	6.59684e13i	0.159788	+	0.0322768i
$111$	9.68040e14	−	1.27418e15i	0.442559	−	0.582519i
$112$	5.33344e14	−	5.20837e14i	0.227967	−	0.222621i
$113$		−	4.64724e15i		−	1.85826i	−0.369751	−	0.929131i	$-0.620557\pi$
$113$		−	4.64724e15i		−	1.85826i	0.369751	−	0.929131i	$-0.379443\pi$
$114$	2.75141e15	−	2.42184e15i	1.02984	−	0.906483i
$115$		−	4.89370e14i		−	0.171555i
$116$	−1.01100e15	+	2.40039e15i	−0.332136	+	0.788583i
$117$	1.12836e15	+	4.05508e15i	0.347579	+	1.24912i
$118$	−4.98977e14	+	2.47021e15i	−0.144200	+	0.713870i
$119$	−7.56925e14			−0.205329
$120$	7.13254e14	−	2.38859e14i	0.181712	−	0.0608531i
$121$	−1.15441e15			−0.276356
$122$	−3.44992e14	+	1.70790e15i	−0.0776445	+	0.384383i
$123$	2.13045e15	+	1.61858e15i	0.451008	+	0.342646i
$124$	−1.62677e15	+	3.86242e15i	−0.324089	+	0.769478i
$125$		−	2.00573e15i		−	0.376225i
$126$	−1.29867e14	−	1.79865e15i	−0.0229467	−	0.317809i
$127$			9.47528e15i			1.57784i	0.614494	+	0.788922i	$0.289360\pi$
$127$			9.47528e15i			1.57784i	−0.614494	+	0.788922i	$0.710640\pi$
$128$	6.27112e15	−	1.11259e15i	0.984624	−	0.174687i
$129$	8.72434e15	+	6.62818e15i	1.29214	+	0.981683i
$130$	−1.74243e15	−	3.51967e14i	−0.243546	−	0.0491957i
$131$	−6.95076e15			−0.917270			−0.458635	−	0.888625i	$-0.651661\pi$
$131$	−6.95076e15			−0.917270			−0.458635	+	0.888625i	$0.651661\pi$
$132$	5.91401e15	−	3.40551e15i	0.737186	−	0.424500i
$133$	3.71129e15			0.437157
$134$	4.89359e15	+	9.88493e14i	0.544931	+	0.110075i
$135$	6.72058e14	−	1.69091e15i	0.0707788	−	0.178081i
$136$	−5.34485e15	−	3.64052e15i	−0.532591	−	0.362762i
$137$		−	1.81089e16i		−	1.70800i	−0.520272	−	0.854001i	$-0.674169\pi$
$137$		−	1.81089e16i		−	1.70800i	0.520272	−	0.854001i	$-0.325831\pi$
$138$	−6.62291e15	−	7.52414e15i	−0.591501	−	0.671992i
$139$		−	1.37379e15i		−	0.116228i	−0.998310	−	0.0581140i	$-0.981491\pi$
$139$		−	1.37379e15i		−	0.116228i	0.998310	−	0.0581140i	$-0.0185087\pi$
$140$	7.01878e14	+	2.95617e14i	0.0562731	+	0.0237012i
$141$	−1.46663e16	+	1.93045e16i	−1.11475	+	1.46729i
$142$	5.01965e15	−	2.48500e16i	0.361835	−	1.79128i
$143$	−1.61280e16			−1.10296
$144$	7.73378e15	−	1.33253e16i	0.501965	−	0.864888i
$145$	−2.66094e15			−0.163974
$146$	−4.79143e15	+	2.37202e16i	−0.280426	+	1.38827i
$147$	−9.77468e15	+	1.28659e16i	−0.543529	+	0.715420i
$148$	1.27572e16	+	5.37308e15i	0.674205	+	0.283962i
$149$			6.04298e14i			0.0303637i	0.999885	+	0.0151818i	$0.00483271\pi$
$149$			6.04298e14i			0.0303637i	−0.999885	+	0.0151818i	$0.995167\pi$
$150$	−1.33185e16	−	1.51308e16i	−0.636458	−	0.723066i
$151$		−	1.35196e16i		−	0.614664i	−0.951602	−	0.307332i	$-0.900564\pi$
$151$		−	1.35196e16i		−	0.614664i	0.951602	−	0.307332i	$-0.0994362\pi$
$152$	2.62064e16	+	1.78499e16i	1.13392	+	0.772340i
$153$	−1.50711e16	+	4.19368e15i	−0.620813	+	0.172746i
$154$	6.77297e15	+	1.36812e15i	0.265689	+	0.0536686i
$155$	−4.28165e15			−0.160001
$156$	−3.15536e16	+	1.81697e16i	−1.12361	+	0.647015i
$157$	2.33116e16			0.791270			0.395635	−	0.918408i	$-0.370525\pi$
$157$	2.33116e16			0.791270			0.395635	+	0.918408i	$0.370525\pi$
$158$	−2.16940e16	−	4.38213e15i	−0.702120	−	0.141826i
$159$	−2.41198e15	−	1.83246e15i	−0.0744551	−	0.0565660i
$160$	3.53434e15	+	5.46320e15i	0.104090	+	0.160897i
$161$		−	1.01491e16i		−	0.285255i
$162$	−1.25510e16	−	3.50934e16i	−0.336757	−	0.941592i
$163$		−	1.11261e15i		−	0.0285060i	−0.999898	−	0.0142530i	$-0.995463\pi$
$163$		−	1.11261e15i		−	0.0285060i	0.999898	−	0.0142530i	$-0.00453702\pi$
$164$	−8.98386e15	+	2.13302e16i	−0.219854	+	0.521995i
$165$	5.55157e15	+	4.21771e15i	0.129803	+	0.0986160i
$166$	2.87824e15	−	1.42489e16i	0.0643156	−	0.318398i
$167$	7.24563e16			1.54776			0.773878	−	0.633334i	$-0.218314\pi$
$167$	7.24563e16			1.54776			0.773878	+	0.633334i	$0.218314\pi$
$168$	1.47922e16	−	4.95372e15i	0.302144	−	0.101184i
$169$	3.48636e16			0.681118
$170$	1.30813e15	−	6.47595e15i	0.0244502	−	0.121042i
$171$	7.38955e16	−	2.05621e16i	1.32174	−	0.367787i
$172$	−3.67895e16	+	8.73485e16i	−0.629884	+	1.49552i
$173$		−	6.62972e16i		−	1.08680i	−0.839474	−	0.543400i	$-0.817137\pi$
$173$		−	6.62972e16i		−	1.08680i	0.839474	−	0.543400i	$-0.182863\pi$
$174$	−4.09123e16	+	3.60119e16i	−0.642296	+	0.565362i
$175$		−	2.04095e16i		−	0.306935i
$176$	4.12457e16	+	4.22361e16i	0.594338	+	0.608610i
$177$	−3.19023e16	+	4.19914e16i	−0.440577	+	0.579910i
$178$	8.61301e16	+	1.73981e16i	1.14026	+	0.230330i
$179$	2.84284e16			0.360874			0.180437	−	0.983587i	$-0.442249\pi$
$179$	2.84284e16			0.360874			0.180437	+	0.983587i	$0.442249\pi$
$180$	1.56129e16	+	1.99735e15i	0.190082	+	0.0243170i
$181$	−5.40077e16			−0.630764			−0.315382	−	0.948965i	$-0.602133\pi$
$181$	−5.40077e16			−0.630764			−0.315382	+	0.948965i	$0.602133\pi$
$182$	−3.61365e16	−	7.29948e15i	−0.404959	−	0.0818006i
$183$	−2.20572e16	+	2.90328e16i	−0.237229	+	0.312253i
$184$	4.88133e16	−	7.16655e16i	0.503970	−	0.739906i
$185$			1.41419e16i			0.140191i
$186$	−6.58311e16	+	5.79459e16i	−0.626735	+	0.551665i
$187$		−	5.99417e16i		−	0.548172i
$188$	−1.93277e17	−	8.14047e16i	−1.69823	−	0.715262i
$189$	1.39379e16	−	3.50680e16i	0.117688	−	0.296106i
$190$	−6.41389e15	+	3.17523e16i	−0.0520559	+	0.257705i
$191$	−1.21047e17			−0.944506			−0.472253	−	0.881463i	$-0.656559\pi$
$191$	−1.21047e17			−0.944506			−0.472253	+	0.881463i	$0.656559\pi$
$192$	1.28278e17	+	3.61655e16i	0.962480	+	0.271353i
$193$	−5.51856e16			−0.398241			−0.199120	−	0.979975i	$-0.563808\pi$
$193$	−5.51856e16			−0.398241			−0.199120	+	0.979975i	$0.563808\pi$
$194$	−7.07958e15	+	3.50479e16i	−0.0491468	+	0.243304i
$195$	−2.96198e16	−	2.25032e16i	−0.197844	−	0.150309i
$196$	−1.28814e17	−	5.42540e16i	−0.828024	−	0.348748i
$197$			2.35075e16i			0.145449i	0.997352	+	0.0727244i	$0.0231694\pi$
$197$			2.35075e16i			0.145449i	−0.997352	+	0.0727244i	$0.976831\pi$
$198$	1.42437e17	−	1.02843e16i	0.848464	−	0.0612613i
$199$			3.43230e16i			0.196873i	0.995143	+	0.0984367i	$0.0313842\pi$
$199$			3.43230e16i			0.196873i	−0.995143	+	0.0984367i	$0.968616\pi$
$200$	9.81620e16	−	1.44117e17i	0.542274	−	0.796142i
$201$	8.31866e16	+	6.31997e16i	0.442673	+	0.336314i
$202$	−1.27869e17	−	2.58292e16i	−0.655585	−	0.132427i
$203$	−5.51854e16			−0.272649
$204$	−6.75299e16	−	1.17272e17i	−0.321566	−	0.558431i
$205$	−2.36454e16			−0.108541
$206$	2.73618e17	+	5.52702e16i	1.21099	+	0.244617i
$207$	−5.62301e16	−	2.02079e17i	−0.239989	−	0.862468i
$208$	−2.20062e17	−	2.25347e17i	−0.905879	−	0.927633i
$209$			2.93901e17i			1.16709i
$210$	1.05299e16	+	1.19628e16i	0.0403441	+	0.0458341i
$211$			3.73984e17i			1.38272i	0.722510	+	0.691360i	$0.242988\pi$
$211$			3.73984e17i			1.38272i	−0.722510	+	0.691360i	$0.757012\pi$
$212$	1.01710e16	−	2.41488e16i	0.0362948	−	0.0861740i
$213$	3.20933e17	−	4.22428e17i	1.10552	−	1.45514i
$214$	−6.00317e16	+	2.97190e17i	−0.199654	+	0.988396i
$215$	−9.68294e16			−0.310970
$216$	2.67083e17	−	1.80589e17i	0.828406	−	0.560129i
$217$	−8.87975e16			−0.266044
$218$	9.48210e16	−	4.69417e17i	0.274461	−	1.35873i
$219$	−3.06342e17	+	4.03223e17i	−0.856792	+	1.12775i
$220$	−2.34103e16	+	5.55825e16i	−0.0632756	+	0.150234i
$221$			3.19813e17i			0.835514i
$222$	1.91389e17	+	2.17434e17i	0.483360	+	0.549135i
$223$			2.16121e17i			0.527728i	0.964560	+	0.263864i	$0.0849969\pi$
$223$			2.16121e17i			0.527728i	−0.964560	+	0.263864i	$0.915003\pi$
$224$	7.32991e16	+	1.13302e17i	0.173077	+	0.267533i
$225$	−1.13077e17	−	4.06374e17i	−0.258229	−	0.928020i
$226$	8.24586e17	+	1.66564e17i	1.82147	+	0.367933i
$227$	2.86031e17			0.611250			0.305625	−	0.952152i	$-0.401135\pi$
$227$	2.86031e17			0.611250			0.305625	+	0.952152i	$0.401135\pi$
$228$	3.31107e17	+	5.75000e17i	0.684631	+	1.18893i
$229$	−6.84429e16			−0.136950			−0.0684751	−	0.997653i	$-0.521813\pi$
$229$	−6.84429e16			−0.136950			−0.0684751	+	0.997653i	$0.521813\pi$
$230$	8.68316e16	+	1.75398e16i	0.168159	+	0.0339676i
$231$	1.15134e17	+	8.74715e16i	0.215832	+	0.163975i
$232$	−3.89679e17	−	2.65421e17i	−0.707209	−	0.481699i
$233$			4.77935e17i			0.839846i	0.907560	+	0.419923i	$0.137943\pi$
$233$			4.77935e17i			0.839846i	−0.907560	+	0.419923i	$0.862057\pi$
$234$	−7.59957e17	+	5.48709e16i	−1.29321	+	0.0933733i
$235$		−	2.14256e17i		−	0.353121i
$236$	−4.20419e17	−	1.77073e17i	−0.671186	−	0.282690i
$237$	−3.68778e17	−	2.80173e17i	−0.570365	−	0.433325i
$238$	2.71294e16	−	1.34305e17i	0.0406548	−	0.201264i
$239$	2.45440e17			0.356419			0.178210	−	0.983993i	$-0.442970\pi$
$239$	2.45440e17			0.356419			0.178210	+	0.983993i	$0.442970\pi$
$240$	1.68180e16	+	1.35118e17i	0.0236696	+	0.190164i
$241$	2.59773e16			0.0354378			0.0177189	−	0.999843i	$-0.494360\pi$
$241$	2.59773e16			0.0354378			0.0177189	+	0.999843i	$0.494360\pi$
$242$	4.13758e16	−	2.04833e17i	0.0547181	−	0.270885i
$243$	8.32261e16	−	7.75461e17i	0.106712	−	0.994290i
$244$	−2.90678e17	−	1.22428e17i	−0.361400	−	0.152215i
$245$		−	1.42796e17i		−	0.172175i
$246$	−3.63552e17	+	3.20006e17i	−0.425161	+	0.374235i
$247$		−	1.56808e18i		−	1.77886i
$248$	−6.27024e17	−	4.27083e17i	−0.690075	−	0.470029i
$249$	1.84021e17	−	2.42218e17i	0.196505	−	0.258650i
$250$	3.55888e17	+	7.18886e16i	0.368777	+	0.0744920i
$251$	7.40843e17			0.745029			0.372514	−	0.928026i	$-0.378496\pi$
$251$	7.40843e17			0.745029			0.372514	+	0.928026i	$0.378496\pi$
$252$	3.23798e17	+	4.14233e16i	0.316061	+	0.0404334i
$253$	8.03718e17			0.761552
$254$	−1.68125e18	−	3.39609e17i	−1.54661	−	0.312411i
$255$	8.36355e16	−	1.10085e17i	0.0747033	−	0.0983282i
$256$	−2.73542e16	+	1.15260e18i	−0.0237260	+	0.999718i
$257$			2.57141e17i			0.216607i	0.994118	+	0.108304i	$0.0345419\pi$
$257$			2.57141e17i			0.216607i	−0.994118	+	0.108304i	$0.965458\pi$
$258$	−1.48877e18	+	1.31044e18i	−1.21809	+	1.07219i
$259$			2.93289e17i			0.233103i
$260$	1.24903e17	−	2.96555e17i	0.0964435	−	0.228984i
$261$	−1.09880e18	+	3.05750e17i	−0.824355	+	0.229384i
$262$	2.49126e17	−	1.23331e18i	0.181618	−	0.899110i
$263$	−1.13536e18			−0.804386			−0.402193	−	0.915555i	$-0.631752\pi$
$263$	−1.13536e18			−0.804386			−0.402193	+	0.915555i	$0.631752\pi$
$264$	3.92291e17	+	1.17141e18i	0.270134	+	0.806642i
$265$	2.67699e16			0.0179186
$266$	−1.33018e17	+	6.58514e17i	−0.0865564	+	0.428502i
$267$	1.46413e18	+	1.11235e18i	0.926288	+	0.703733i
$268$	−3.50788e17	+	8.32868e17i	−0.215791	+	0.512348i
$269$			8.06335e17i			0.482362i	0.970480	+	0.241181i	$0.0775348\pi$
$269$			8.06335e17i			0.482362i	−0.970480	+	0.241181i	$0.922465\pi$
$270$	2.75940e17	+	1.79852e17i	0.160541	+	0.104637i
$271$		−	7.28020e17i		−	0.411977i	−0.978554	−	0.205989i	$-0.933959\pi$
$271$		−	7.28020e17i		−	0.411977i	0.978554	−	0.205989i	$-0.0660410\pi$
$272$	8.37526e17	−	8.17885e17i	0.461033	−	0.450221i
$273$	−6.14288e17	−	4.66695e17i	−0.328967	−	0.249927i
$274$	3.21317e18	+	6.49052e17i	1.67419	+	0.338182i
$275$	1.61625e18			0.819434
$276$	1.57243e18	−	9.05462e17i	0.775804	−	0.446737i
$277$	3.30992e17			0.158935			0.0794673	−	0.996837i	$-0.474678\pi$
$277$	3.30992e17			0.158935			0.0794673	+	0.996837i	$0.474678\pi$
$278$	2.43760e17	+	4.92389e16i	0.113927	+	0.0230130i
$279$	−1.76805e18	+	4.91975e17i	−0.804383	+	0.223826i
$280$	−7.76094e16	+	1.13943e17i	−0.0343739	+	0.0504663i
$281$		−	4.26270e18i		−	1.83818i	−0.394053	−	0.919088i	$-0.628927\pi$
$281$		−	4.26270e18i		−	1.83818i	0.394053	−	0.919088i	$-0.371073\pi$
$282$	−2.89964e18	−	3.29422e18i	−1.21752	−	1.38320i
$283$			3.24968e18i			1.32875i	0.747401	+	0.664373i	$0.231301\pi$
$283$			3.24968e18i			1.32875i	−0.747401	+	0.664373i	$0.768699\pi$
$284$	4.22937e18	+	1.78133e18i	1.68418	+	0.709343i
$285$	−4.10075e17	+	5.39761e17i	−0.159047	+	0.209346i
$286$	5.78054e17	−	2.86169e18i	0.218385	−	1.08113i
$287$	−4.90384e17			−0.180477
$288$	2.08720e18	+	1.84985e18i	0.748377	+	0.663274i
$289$	1.67380e18			0.584750
$290$	9.53721e16	−	4.72145e17i	0.0324666	−	0.160727i
$291$	−4.52636e17	+	5.95782e17i	−0.150159	+	0.197647i
$292$	−4.03708e18	−	1.70034e18i	−1.30526	−	0.549749i
$293$			4.82189e18i			1.51953i	0.650195	+	0.759767i	$0.274687\pi$
$293$			4.82189e18i			1.51953i	−0.650195	+	0.759767i	$0.725313\pi$
$294$	−1.93253e18	−	2.19551e18i	−0.593639	−	0.674420i
$295$		−	4.66052e17i		−	0.139563i
$296$	−1.41061e18	+	2.07100e18i	−0.411832	+	0.604633i
$297$	2.77707e18	+	1.10376e18i	0.790522	+	0.314195i
$298$	−1.07224e17	−	2.16590e16i	−0.0297625	−	0.00601196i
$299$	−4.28815e18			−1.16074
$300$	3.16210e18	−	1.82086e18i	0.834769	−	0.480691i
$301$	−2.00815e18			−0.517069
$302$	2.39886e18	+	4.84565e17i	0.602495	+	0.121703i
$303$	−2.17365e18	−	1.65140e18i	−0.532562	−	0.404605i
$304$	−4.10649e18	+	4.01018e18i	−0.981563	+	0.958545i
$305$		−	3.22228e17i		−	0.0751476i
$306$	−2.03934e17	−	2.82447e18i	−0.0464065	−	0.642726i
$307$			2.84934e18i			0.632713i	0.948640	+	0.316357i	$0.102460\pi$
$307$			2.84934e18i			0.632713i	−0.948640	+	0.316357i	$0.897540\pi$
$308$	−4.85508e17	+	1.15273e18i	−0.105212	+	0.249803i
$309$	4.65126e18	+	3.53372e18i	0.983744	+	0.747384i
$310$	1.53461e17	−	7.59717e17i	0.0316800	−	0.156834i
$311$	−4.50890e18			−0.908589			−0.454295	−	0.890851i	$-0.650109\pi$
$311$	−4.50890e18			−0.908589			−0.454295	+	0.890851i	$0.650109\pi$
$312$	−2.09303e18	−	6.24996e18i	−0.411733	−	1.22947i
$313$	−3.78043e18			−0.726037			−0.363018	−	0.931782i	$-0.618254\pi$
$313$	−3.78043e18			−0.726037			−0.363018	+	0.931782i	$0.618254\pi$
$314$	−8.35524e17	+	4.13631e18i	−0.156670	+	0.775605i
$315$	8.94016e16	+	3.21290e17i	0.0163688	+	0.0588258i
$316$	1.55509e18	−	3.69222e18i	0.278037	−	0.660138i
$317$		−	1.09502e19i		−	1.91195i	−0.293440	−	0.955977i	$-0.594800\pi$
$317$		−	1.09502e19i		−	1.91195i	0.293440	−	0.955977i	$-0.405200\pi$
$318$	4.11592e17	−	3.62292e17i	0.0701882	−	0.0617811i
$319$		−	4.37019e18i		−	0.727898i
$320$	−1.09604e18	+	4.31309e17i	−0.178321	+	0.0701719i
$321$	−3.83815e18	+	5.05197e18i	−0.610006	+	0.802921i
$322$	1.80081e18	+	3.63759e17i	0.279607	+	0.0564800i
$323$	5.82794e18			0.884090
$324$	6.67666e18	−	9.69197e17i	0.989628	−	0.143656i
$325$	−8.62334e18			−1.24897
$326$	1.97417e17	+	3.98777e16i	0.0279416	+	0.00564414i
$327$	6.06242e18	−	7.97966e18i	0.838567	−	1.10376i
$328$	−3.46274e18	−	2.35856e18i	−0.468130	−	0.318856i
$329$		−	4.44348e18i		−	0.587156i
$330$	−9.47349e17	+	8.33876e17i	−0.122364	+	0.107708i
$331$			3.37469e18i			0.426112i	0.977040	+	0.213056i	$0.0683417\pi$
$331$			3.37469e18i			0.426112i	−0.977040	+	0.213056i	$0.931658\pi$
$332$	2.42510e18	+	1.02140e18i	0.299360	+	0.126085i
$333$	1.62494e18	+	5.83969e18i	0.196113	+	0.704788i
$334$	−2.59695e18	+	1.28563e19i	−0.306454	+	1.51711i
$335$	−9.23268e17			−0.106535
$336$	3.48790e17	+	2.80222e18i	0.0393568	+	0.316197i
$337$	8.45680e18			0.933215			0.466608	−	0.884464i	$-0.345476\pi$
$337$	8.45680e18			0.933215			0.466608	+	0.884464i	$0.345476\pi$
$338$	−1.24957e18	+	6.18605e18i	−0.134860	+	0.667633i
$339$	1.40172e19	+	1.06494e19i	1.47967	+	1.12415i
$340$	1.10218e18	+	4.64216e17i	0.113805	+	0.0479323i
$341$		−	7.03198e18i		−	0.710264i
$342$	9.99910e17	+	1.38487e19i	0.0988019	+	1.36840i
$343$		−	6.25757e18i		−	0.604922i
$344$	−1.41801e19	−	9.65847e18i	−1.34120	−	0.913524i
$345$	1.47606e18	+	1.12141e18i	0.136603	+	0.103782i
$346$	1.17635e19	+	2.37620e18i	1.06528	+	0.215185i
$347$	1.70796e19			1.51359			0.756793	−	0.653654i	$-0.226765\pi$
$347$	1.70796e19			1.51359			0.756793	+	0.653654i	$0.226765\pi$
$348$	−4.92343e18	−	8.55003e18i	−0.426995	−	0.741520i
$349$	1.14186e19			0.969222			0.484611	−	0.874730i	$-0.338961\pi$
$349$	1.14186e19			0.969222			0.484611	+	0.874730i	$0.338961\pi$
$350$	3.62137e18	+	7.31508e17i	0.300859	+	0.0607728i
$351$	−1.48168e19	−	5.88897e18i	−1.20490	−	0.478890i
$352$	−8.97250e18	+	5.80464e18i	−0.714239	+	0.462067i
$353$			4.25349e18i			0.331463i	0.986171	+	0.165731i	$0.0529985\pi$
$353$			4.25349e18i			0.331463i	−0.986171	+	0.165731i	$0.947002\pi$
$354$	−6.30734e18	−	7.16564e18i	−0.481196	−	0.546676i
$355$			4.68843e18i			0.350199i
$356$	−6.17407e18	+	1.46590e19i	−0.451540	+	1.07208i
$357$	1.73453e18	−	2.28307e18i	0.124214	−	0.163496i
$358$	−1.01892e18	+	5.04421e18i	−0.0714524	+	0.353729i
$359$	−8.34588e18			−0.573144			−0.286572	−	0.958059i	$-0.592516\pi$
$359$	−8.34588e18			−0.573144			−0.286572	+	0.958059i	$0.592516\pi$
$360$	−9.13994e17	+	2.69870e18i	−0.0614716	+	0.181504i
$361$	−1.33939e19			−0.882275
$362$	1.93572e18	−	9.58290e18i	0.124890	−	0.618276i
$363$	2.64538e18	−	3.48198e18i	0.167181	−	0.220053i
$364$	2.59038e18	−	6.15027e18i	0.160362	−	0.380745i
$365$		−	4.47527e18i		−	0.271408i
$366$	−4.36089e18	−	4.95432e18i	−0.259100	−	0.294358i
$367$		−	2.22875e19i		−	1.29737i	−0.761055	−	0.648687i	$-0.775318\pi$
$367$		−	2.22875e19i		−	1.29737i	0.761055	−	0.648687i	$-0.224682\pi$
$368$	1.09665e19	+	1.12298e19i	0.625472	+	0.640492i
$369$	−9.76406e18	+	2.71693e18i	−0.545673	+	0.151838i
$370$	−2.50927e18	−	5.06866e17i	−0.137415	−	0.0277575i
$371$	5.55184e17			0.0297943
$372$	−7.92217e18	−	1.37576e19i	−0.416651	−	0.723556i
$373$	6.53051e18			0.336613			0.168306	−	0.985735i	$-0.446170\pi$
$373$	6.53051e18			0.336613			0.168306	+	0.985735i	$0.446170\pi$
$374$	1.06358e19	+	2.14840e18i	0.537320	+	0.108537i
$375$	6.04978e18	+	4.59622e18i	0.299575	+	0.227597i
$376$	2.13714e19	−	3.13766e19i	1.03735	−	1.52299i
$377$			2.33167e19i			1.10945i
$378$	5.72275e18	+	3.72996e18i	0.266942	+	0.173987i
$379$			2.46209e19i			1.12592i	0.826482	+	0.562962i	$0.190338\pi$
$379$			2.46209e19i			1.12592i	−0.826482	+	0.562962i	$0.809662\pi$
$380$	−5.40411e18	−	2.27610e18i	−0.242296	−	0.102051i
$381$	−2.85798e19	−	2.17130e19i	−1.25638	−	0.954515i
$382$	4.33852e18	−	2.14781e19i	0.187011	−	0.925807i
$383$	−2.66962e19			−1.12839			−0.564195	−	0.825642i	$-0.690813\pi$
$383$	−2.66962e19			−1.12839			−0.564195	+	0.825642i	$0.690813\pi$
$384$	−1.10147e19	+	2.14648e19i	−0.456551	+	0.889697i
$385$	−1.27785e18			−0.0519427
$386$	1.97794e18	−	9.79188e18i	0.0788511	−	0.390356i
$387$	−3.99844e19	+	1.11260e19i	−1.56336	+	0.435018i
$388$	−5.96500e18	−	2.51234e18i	−0.228756	−	0.0963475i
$389$			1.39097e19i			0.523232i	0.965172	+	0.261616i	$0.0842555\pi$
$389$			1.39097e19i			0.523232i	−0.965172	+	0.261616i	$0.915745\pi$
$390$	5.05448e18	−	4.44906e18i	0.186506	−	0.164166i
$391$		−	1.59374e19i		−	0.576889i
$392$	1.42435e19	−	2.09117e19i	0.505791	−	0.742580i
$393$	1.59280e19	−	2.09652e19i	0.554902	−	0.730390i
$394$	−4.17107e18	−	8.42546e17i	−0.142569	−	0.0287986i
$395$	4.09298e18			0.137266
$396$	−3.28035e18	+	2.56420e19i	−0.107946	+	0.843796i
$397$	3.59590e19			1.16113			0.580563	−	0.814216i	$-0.302833\pi$
$397$	3.59590e19			1.16113			0.580563	+	0.814216i	$0.302833\pi$
$398$	−6.09012e18	−	1.23019e18i	−0.192976	−	0.0389806i
$399$	−8.50457e18	+	1.11942e19i	−0.264457	+	0.348092i
$400$	2.20532e19	+	2.25828e19i	0.673011	+	0.689173i
$401$			3.03739e19i			0.909742i	0.890557	+	0.454871i	$0.150315\pi$
$401$			3.03739e19i			0.909742i	−0.890557	+	0.454871i	$0.849685\pi$
$402$	−1.41954e19	+	1.24951e19i	−0.417304	+	0.367320i
$403$			3.75184e19i			1.08257i
$404$	9.16602e18	−	2.17627e19i	0.259610	−	0.616385i
$405$	3.56016e18	+	5.90189e18i	0.0989820	+	0.164089i
$406$	1.97793e18	−	9.79185e18i	0.0539841	−	0.267251i
$407$	−2.32259e19			−0.622322
$408$	2.32287e19	−	7.77898e18i	0.611045	−	0.204631i
$409$	3.50607e19			0.905515			0.452758	−	0.891634i	$-0.350440\pi$
$409$	3.50607e19			0.905515			0.452758	+	0.891634i	$0.350440\pi$
$410$	8.47488e17	−	4.19554e18i	0.0214909	−	0.106392i
$411$	5.46209e19	+	4.14974e19i	1.36002	+	1.03325i
$412$	−1.96138e19	+	4.65686e19i	−0.479549	+	1.13858i
$413$		−	9.66551e18i		−	0.232059i
$414$	3.78713e19	−	2.73441e18i	0.892911	−	0.0644705i
$415$			2.68832e18i			0.0622474i
$416$	4.78719e19	−	3.09700e19i	1.08863	−	0.704274i
$417$	4.14370e18	+	3.14811e18i	0.0925482	+	0.0703119i
$418$	−5.21485e19	−	1.05339e19i	−1.14398	−	0.231082i
$419$	6.29350e19			1.35609			0.678043	−	0.735022i	$-0.262828\pi$
$419$	6.29350e19			1.35609			0.678043	+	0.735022i	$0.262828\pi$
$420$	−2.50004e18	+	1.43962e18i	−0.0529148	+	0.0304703i
$421$	−6.75888e19			−1.40527			−0.702634	−	0.711551i	$-0.747993\pi$
$421$	−6.75888e19			−1.40527			−0.702634	+	0.711551i	$0.747993\pi$
$422$	−6.63580e19	−	1.34042e19i	−1.35535	−	0.273777i
$423$	−2.46187e19	−	8.84742e19i	−0.493983	−	1.77527i
$424$	3.92031e18	+	2.67023e18i	0.0772817	+	0.0526386i
$425$		−	3.20496e19i		−	0.620735i
$426$	6.34511e19	+	7.20854e19i	1.20744	+	1.37175i
$427$		−	6.68273e18i		−	0.124952i
$428$	−5.05805e19	−	2.13035e19i	−0.929297	−	0.391402i
$429$	3.69581e19	−	4.86462e19i	0.667237	−	0.878251i
$430$	3.47052e18	−	1.71810e19i	0.0615716	−	0.304814i
$431$	3.94732e18			0.0688213			0.0344106	−	0.999408i	$-0.489045\pi$
$431$	3.94732e18			0.0688213			0.0344106	+	0.999408i	$0.489045\pi$
$432$	2.24702e19	+	5.38626e19i	0.385016	+	0.922910i
$433$	−7.21093e19			−1.21432			−0.607159	−	0.794581i	$-0.707691\pi$
$433$	−7.21093e19			−1.21432			−0.607159	+	0.794581i	$0.707691\pi$
$434$	3.18264e18	−	1.57558e19i	0.0526762	−	0.260777i
$435$	6.09765e18	−	8.02604e18i	0.0991957	−	0.130566i
$436$	7.98927e19	+	3.36492e19i	1.27749	+	0.538055i
$437$			7.81429e19i			1.22823i
$438$	−6.05663e19	−	6.88081e19i	−0.935783	−	1.06312i
$439$		−	2.88017e19i		−	0.437455i	−0.975786	−	0.218728i	$-0.929809\pi$
$439$		−	2.88017e19i		−	0.437455i	0.975786	−	0.218728i	$-0.0701906\pi$
$440$	−9.02325e18	−	6.14598e18i	−0.134731	−	0.0917690i
$441$	−1.64077e19	−	5.89657e19i	−0.240856	−	0.865585i
$442$	−5.67462e19	−	1.14626e19i	−0.818973	−	0.165431i
$443$	1.56016e19			0.221381			0.110691	−	0.993855i	$-0.464694\pi$
$443$	1.56016e19			0.221381			0.110691	+	0.993855i	$0.464694\pi$
$444$	−4.54401e19	+	2.61661e19i	−0.633968	+	0.365063i
$445$	−1.62501e19			−0.222923
$446$	−3.83475e19	−	7.74610e18i	−0.517280	−	0.104489i
$447$	−1.82271e18	−	1.38478e18i	−0.0241775	−	0.0183685i
$448$	−2.27309e19	+	8.94495e18i	−0.296505	+	0.116679i
$449$			3.01854e19i			0.387213i	0.981079	+	0.193606i	$0.0620184\pi$
$449$			3.01854e19i			0.387213i	−0.981079	+	0.193606i	$0.937982\pi$
$450$	7.61581e19	−	5.49881e18i	0.960776	−	0.0693706i
$451$		−	3.88341e19i		−	0.481825i
$452$	−5.91089e19	+	1.40341e20i	−0.721298	+	1.71256i
$453$	4.07785e19	+	3.09808e19i	0.489435	+	0.371840i
$454$	−1.02518e19	+	5.07521e19i	−0.121027	+	0.599149i
$455$	6.81783e18			0.0791701
$456$	−1.13893e20	+	3.81412e19i	−1.30095	+	0.435670i
$457$	2.51719e19			0.282843			0.141421	−	0.989949i	$-0.454833\pi$
$457$	2.51719e19			0.282843			0.141421	+	0.989949i	$0.454833\pi$
$458$	2.45310e18	−	1.21442e19i	0.0271159	−	0.134239i
$459$	2.18870e19	−	5.50683e19i	0.238008	−	0.598834i
$460$	−6.22436e18	+	1.47784e19i	−0.0665903	+	0.158104i
$461$			6.57492e19i			0.692044i	0.938226	+	0.346022i	$0.112468\pi$
$461$			6.57492e19i			0.692044i	−0.938226	+	0.346022i	$0.887532\pi$
$462$	−1.96472e19	+	1.72938e19i	−0.203463	+	0.179092i
$463$		−	1.03671e20i		−	1.05633i	−0.849143	−	0.528163i	$-0.822881\pi$
$463$		−	1.03671e20i		−	1.05633i	0.849143	−	0.528163i	$-0.177119\pi$
$464$	6.10618e19	−	5.96299e19i	0.612188	−	0.597832i
$465$	9.81158e18	−	1.29145e19i	0.0967925	−	0.127403i
$466$	−8.48027e19	−	1.71299e19i	−0.823219	−	0.166288i
$467$	2.32853e19			0.222436			0.111218	−	0.993796i	$-0.464525\pi$
$467$	2.32853e19			0.222436			0.111218	+	0.993796i	$0.464525\pi$
$468$	1.75020e19	−	1.36810e20i	0.164529	−	1.28610i
$469$	−1.91478e19			−0.177142
$470$	3.80166e19	+	7.67927e18i	0.346130	+	0.0699175i
$471$	−5.34195e19	+	7.03135e19i	−0.478678	+	0.630060i
$472$	4.64875e19	−	6.82508e19i	0.409988	−	0.601926i
$473$		−	1.59028e20i		−	1.38043i
$474$	6.29303e19	−	5.53925e19i	0.537678	−	0.473275i
$475$			1.57143e20i			1.32158i
$476$	2.28582e19	+	9.62743e18i	0.189230	+	0.0796999i
$477$	1.10543e19	−	3.07595e18i	0.0900830	−	0.0250664i
$478$	−8.79695e18	+	4.35498e19i	−0.0705704	+	0.349363i
$479$	1.24139e20			0.980377			0.490188	−	0.871617i	$-0.336928\pi$
$479$	1.24139e20			0.980377			0.490188	+	0.871617i	$0.336928\pi$
$480$	−2.45775e19	−	1.85871e18i	−0.191086	−	0.0144512i
$481$	1.23920e20			0.948531
$482$	−9.31069e17	+	4.60931e18i	−0.00701663	+	0.0347362i
$483$	3.06121e19	+	2.32571e19i	0.227138	+	0.172565i
$484$	3.48617e19	+	1.46831e19i	0.254688	+	0.107270i
$485$		−	6.61245e18i		−	0.0475663i
$486$	1.34611e20	+	4.25610e19i	0.953477	+	0.301467i
$487$			1.13270e20i			0.790040i	0.918673	+	0.395020i	$0.129262\pi$
$487$			1.13270e20i			0.790040i	−0.918673	+	0.395020i	$0.870738\pi$
$488$	3.21414e19	−	4.71886e19i	0.220758	−	0.324107i
$489$	3.35591e18	+	2.54959e18i	0.0226983	+	0.0172447i
$490$	2.53371e19	+	5.11803e18i	0.168766	+	0.0340904i
$491$	−2.07059e20			−1.35826			−0.679130	−	0.734018i	$-0.737643\pi$
$491$	−2.07059e20			−1.35826			−0.679130	+	0.734018i	$0.737643\pi$
$492$	−4.37502e19	−	7.59766e19i	−0.282645	−	0.490842i
$493$	−8.66592e19			−0.551395
$494$	2.78233e20	+	5.62024e19i	1.74364	+	0.352211i
$495$	−2.54433e19	+	7.07982e18i	−0.157049	+	0.0437002i
$496$	9.82532e19	−	9.59490e19i	0.597357	−	0.583348i
$497$			9.72338e19i			0.582297i
$498$	3.63825e19	+	4.13334e19i	0.214621	+	0.243827i
$499$			1.45331e20i			0.844509i	0.906477	+	0.422255i	$0.138761\pi$
$499$			1.45331e20i			0.844509i	−0.906477	+	0.422255i	$0.861239\pi$
$500$	−2.55112e19	+	6.05706e19i	−0.146034	+	0.346727i
$501$	−1.66037e20	+	2.18546e20i	−0.936314	+	1.23242i
$502$	−2.65530e19	+	1.31452e20i	−0.147515	+	0.730279i
$503$	−2.35769e20			−1.29041			−0.645203	−	0.764011i	$-0.723227\pi$
$503$	−2.35769e20			−1.29041			−0.645203	+	0.764011i	$0.723227\pi$
$504$	−1.89554e19	+	5.59687e19i	−0.102212	+	0.301798i
$505$	2.41248e19			0.128168
$506$	−2.88065e19	+	1.42608e20i	−0.150786	+	0.746475i
$507$	−7.98915e19	+	1.05157e20i	−0.412042	+	0.542350i
$508$	1.20517e20	−	2.86142e20i	0.612451	−	1.45413i
$509$		−	3.29459e20i		−	1.64975i	−0.565314	−	0.824876i	$-0.691245\pi$
$509$		−	3.29459e20i		−	1.64975i	0.565314	−	0.824876i	$-0.308755\pi$
$510$	1.65354e19	+	1.87856e19i	0.0815904	+	0.0926931i
$511$		−	9.28131e19i		−	0.451287i
$512$	−2.03531e20	−	4.61645e19i	−0.975229	−	0.221199i
$513$	−1.07315e20	+	2.70006e20i	−0.506732	+	1.27495i
$514$	−4.56260e19	−	9.21634e18i	−0.212319	−	0.0428879i
$515$	−5.16232e19			−0.236751
$516$	−1.79160e20	−	3.11129e20i	−0.809781	−	1.40627i
$517$	3.51884e20			1.56755
$518$	−5.20400e19	−	1.05119e19i	−0.228488	−	0.0461541i
$519$	1.99969e20	+	1.51923e20i	0.865380	+	0.657458i
$520$	4.81426e19	+	3.27912e19i	0.205355	+	0.139873i
$521$		−	3.04901e20i		−	1.28197i	−0.767555	−	0.640983i	$-0.778527\pi$
$521$		−	3.04901e20i		−	1.28197i	0.767555	−	0.640983i	$-0.221473\pi$
$522$	−1.48683e19	−	2.05924e20i	−0.0616215	−	0.853452i
$523$		−	3.94730e20i		−	1.61264i	−0.591479	−	0.806320i	$-0.701456\pi$
$523$		−	3.94730e20i		−	1.61264i	0.591479	−	0.806320i	$-0.298544\pi$
$524$	2.09904e20	+	8.84076e19i	0.845350	+	0.356045i
$525$	6.15601e19	+	4.67693e19i	0.244402	+	0.185680i
$526$	4.06930e19	−	2.01453e20i	0.159267	−	0.788461i
$527$	−1.39441e20			−0.538037
$528$	−2.21911e20	+	2.76211e19i	−0.844159	+	0.105072i
$529$	−5.29415e19			−0.198554
$530$	−9.59476e17	+	4.74994e18i	−0.00354785	+	0.0175638i
$531$	−5.35509e19	−	1.92450e20i	−0.195235	−	0.701632i
$532$	−1.12076e20	−	4.72044e19i	−0.402881	−	0.169686i
$533$			2.07195e20i			0.734388i
$534$	−2.49848e20	+	2.19921e20i	−0.873204	+	0.768612i
$535$		−	5.60706e19i		−	0.193233i
$536$	−1.35208e20	−	9.20935e19i	−0.459478	−	0.312963i
$537$	−6.51450e19	+	8.57471e19i	−0.218310	+	0.287351i
$538$	−1.43072e20	−	2.89003e19i	−0.472813	−	0.0955070i
$539$	2.34521e20			0.764304
$540$	−4.18022e19	+	4.25155e19i	−0.134353	+	0.136645i
$541$	−1.95036e20			−0.618209			−0.309104	−	0.951028i	$-0.600029\pi$
$541$	−1.95036e20			−0.618209			−0.309104	+	0.951028i	$0.600029\pi$
$542$	1.29177e20	+	2.60934e19i	0.403821	+	0.0815709i
$543$	1.23761e20	−	1.62901e20i	0.381580	−	0.502255i
$544$	1.15104e20	+	1.77921e20i	0.350024	+	0.541048i
$545$			8.85643e19i			0.265635i
$546$	1.04825e20	−	9.22694e19i	0.310114	−	0.272969i
$547$		−	1.38572e20i		−	0.404363i	−0.979348	−	0.202182i	$-0.935197\pi$
$547$		−	1.38572e20i		−	0.404363i	0.979348	−	0.202182i	$-0.0648031\pi$
$548$	−2.30330e20	+	5.46867e20i	−0.662973	+	1.57408i
$549$	−3.70251e19	−	1.33060e20i	−0.105124	−	0.377794i
$550$	−5.79290e19	+	2.86781e20i	−0.162247	+	0.803211i
$551$	4.24900e20			1.17395
$552$	1.04303e20	+	3.11457e20i	0.284285	+	0.848898i
$553$	8.48847e19			0.228240
$554$	−1.18633e19	+	5.87297e19i	−0.0314688	+	0.155788i
$555$	−4.26553e19	−	3.24067e19i	−0.111629	−	0.0848081i
$556$	−1.74735e19	+	4.14869e19i	−0.0451147	+	0.107115i
$557$		−	4.79131e20i		−	1.22051i	−0.792206	−	0.610253i	$-0.791068\pi$
$557$		−	4.79131e20i		−	1.22051i	0.792206	−	0.610253i	$-0.208932\pi$
$558$	−2.39242e19	−	3.31348e20i	−0.0601286	−	0.832776i
$559$			8.48478e20i			2.10403i
$560$	−1.74358e19	−	1.78546e19i	−0.0426612	−	0.0436856i
$561$	1.80799e20	+	1.37359e20i	0.436490	+	0.331616i
$562$	7.56354e20	+	1.52782e20i	1.80178	+	0.363956i
$563$	1.00595e20			0.236463			0.118232	−	0.992986i	$-0.462277\pi$
$563$	1.00595e20			0.236463			0.118232	+	0.992986i	$0.462277\pi$
$564$	6.88440e20	−	3.96430e20i	1.59688	−	0.919545i
$565$	−1.55574e20			−0.356101
$566$	−5.76608e20	−	1.16473e20i	−1.30244	−	0.263090i
$567$	7.38344e19	+	1.22400e20i	0.164583	+	0.272840i
$568$	−4.67658e20	+	6.86595e20i	−1.02876	+	1.51039i
$569$			9.92056e19i			0.215375i	0.994185	+	0.107687i	$0.0343445\pi$
$569$			9.92056e19i			0.215375i	−0.994185	+	0.107687i	$0.965655\pi$
$570$	−8.10751e19	−	9.21077e19i	−0.173710	−	0.197349i
$571$		−	6.09538e20i		−	1.28893i	−0.764633	−	0.644466i	$-0.777080\pi$
$571$		−	6.09538e20i		−	1.28893i	0.764633	−	0.644466i	$-0.222920\pi$
$572$	4.87047e20	+	2.05135e20i	1.01648	+	0.428124i
$573$	2.77385e20	−	3.65108e20i	0.571378	−	0.752076i
$574$	1.75761e19	−	8.70116e19i	0.0357342	−	0.176904i
$575$	4.29732e20			0.862360
$576$	−4.03038e20	+	3.04042e20i	−0.798320	+	0.602234i
$577$	−8.52542e20			−1.66685			−0.833426	−	0.552630i	$-0.813624\pi$
$577$	−8.52542e20			−1.66685			−0.833426	+	0.552630i	$0.813624\pi$
$578$	−5.99917e19	+	2.96992e20i	−0.115780	+	0.573174i
$579$	1.26460e20	−	1.66453e20i	0.240915	−	0.317105i
$580$	8.03570e19	+	3.38448e19i	0.151117	+	0.0636476i
$581$			5.57534e19i			0.103502i
$582$	−8.94898e19	−	1.01667e20i	−0.164003	−	0.186320i
$583$			4.39657e19i			0.0795426i
$584$	4.46396e20	−	6.55379e20i	0.797304	−	1.17057i
$585$	1.35750e20	−	3.77736e19i	0.239371	−	0.0666070i
$586$	−8.55576e20	−	1.72824e20i	−1.48945	−	0.300866i
$587$	−2.43095e20			−0.417822			−0.208911	−	0.977935i	$-0.566992\pi$
$587$	−2.43095e20			−0.417822			−0.208911	+	0.977935i	$0.566992\pi$
$588$	4.58827e20	−	2.64210e20i	0.778608	−	0.448352i
$589$	6.83696e20			1.14551
$590$	8.26943e19	+	1.67040e19i	0.136800	+	0.0276332i
$591$	−7.09045e19	−	5.38685e19i	−0.115816	−	0.0879891i
$592$	−3.16910e20	−	3.24521e20i	−0.511121	−	0.523395i
$593$			6.80668e20i			1.08399i	0.840382	+	0.541995i	$0.182331\pi$
$593$			6.80668e20i			1.08399i	−0.840382	+	0.541995i	$0.817669\pi$
$594$	−2.95380e20	+	4.53191e20i	−0.464497	+	0.712661i
$595$			2.53393e19i			0.0393474i
$596$	7.68615e18	−	1.82491e19i	0.0117859	−	0.0279830i
$597$	−1.03527e20	−	7.86526e19i	−0.156763	−	0.119098i
$598$	1.53694e20	−	7.60871e20i	0.229825	−	1.13776i
$599$	3.33728e19			0.0492824			0.0246412	−	0.999696i	$-0.492156\pi$
$599$	3.33728e19			0.0492824			0.0246412	+	0.999696i	$0.492156\pi$
$600$	2.09750e20	+	6.26332e20i	0.305892	+	0.913419i
$601$	4.44009e20			0.639489			0.319744	−	0.947504i	$-0.396403\pi$
$601$	4.44009e20			0.639489			0.319744	+	0.947504i	$0.396403\pi$
$602$	7.19754e19	−	3.56318e20i	0.102379	−	0.506832i
$603$	−3.81251e20	+	1.06086e20i	−0.535589	+	0.149032i
$604$	−1.71958e20	+	4.08276e20i	−0.238586	+	0.566470i
$605$			3.86456e19i			0.0529585i
$606$	3.70924e20	−	3.26495e20i	0.502042	−	0.441907i
$607$		−	5.34672e19i		−	0.0714780i	−0.999361	−	0.0357390i	$-0.988621\pi$
$607$		−	5.34672e19i		−	0.0714780i	0.999361	−	0.0357390i	$-0.0113785\pi$
$608$	−5.64366e20	−	8.72368e20i	−0.745220	−	1.15192i
$609$	1.26460e20	−	1.66453e20i	0.164939	−	0.217101i
$610$	5.71748e19	+	1.15492e19i	0.0736598	+	0.0148791i
$611$	−1.87744e21			−2.38922
$612$	5.08470e20	+	6.50481e19i	0.639190	+	0.0817710i
$613$	−1.20047e21			−1.49072			−0.745361	−	0.666661i	$-0.767723\pi$
$613$	−1.20047e21			−1.49072			−0.745361	+	0.666661i	$0.767723\pi$
$614$	−5.05575e20	−	1.02125e20i	−0.620187	−	0.125276i
$615$	5.41845e19	−	7.13204e19i	0.0656616	−	0.0864271i
$616$	−1.87134e20	−	1.27462e20i	−0.224026	−	0.152590i
$617$			3.16260e20i			0.374030i	0.982357	+	0.187015i	$0.0598812\pi$
$617$			3.16260e20i			0.374030i	−0.982357	+	0.187015i	$0.940119\pi$
$618$	−7.93716e20	+	6.98645e20i	−0.927367	+	0.816288i
$619$			5.05346e20i			0.583322i	0.956522	+	0.291661i	$0.0942080\pi$
$619$			5.05346e20i			0.583322i	−0.956522	+	0.291661i	$0.905792\pi$
$620$	1.29300e20	+	5.44589e19i	0.147456	+	0.0621056i
$621$	7.38373e20	+	2.93468e20i	0.831934	+	0.330654i
$622$	1.61606e20	−	8.00039e20i	0.179899	−	0.890601i
$623$	−3.37012e20			−0.370668
$624$	1.18398e21	−	1.47369e20i	1.28665	−	0.160149i
$625$	8.29977e20			0.891181
$626$	1.35496e20	−	6.70783e20i	0.143754	−	0.711663i
$627$	−8.86478e20	−	6.73487e20i	−0.929311	−	0.706029i
$628$	−7.03982e20	−	2.96503e20i	−0.729229	−	0.307137i
$629$			4.60561e20i			0.471419i
$630$	−6.02125e19	+	4.34750e18i	−0.0609022	+	0.00439730i
$631$			1.43095e21i			1.43022i	0.699010	+	0.715112i	$0.253624\pi$
$631$			1.43095e21i			1.43022i	−0.699010	+	0.715112i	$0.746376\pi$
$632$	5.99394e20	+	4.08264e20i	0.592018	+	0.403239i
$633$	−1.12803e21	−	8.57000e20i	−1.10101	−	0.836475i
$634$	1.94296e21	+	3.92472e20i	1.87410	+	0.378564i
$635$	3.17200e20			0.302364
$636$	4.95314e19	+	8.60162e19i	0.0466608	+	0.0810312i
$637$	−1.25126e21			−1.16494
$638$	7.75428e20	+	1.56635e20i	0.713487	+	0.144123i
$639$	5.38716e20	+	1.93603e21i	0.489895	+	1.76058i
$640$	−3.72456e19	−	2.09936e20i	−0.0334754	−	0.188685i
$641$		−	2.62366e20i		−	0.233062i	−0.993187	−	0.116531i	$-0.962823\pi$
$641$		−	2.62366e20i		−	0.233062i	0.993187	−	0.116531i	$-0.0371775\pi$
$642$	−7.58833e20	−	8.62094e20i	−0.666244	−	0.756906i
$643$		−	1.31607e21i		−	1.14208i	−0.820923	−	0.571039i	$-0.806540\pi$
$643$		−	1.31607e21i		−	1.14208i	0.820923	−	0.571039i	$-0.193460\pi$
$644$	−1.29088e20	+	3.06490e20i	−0.110724	+	0.262889i
$645$	2.21889e20	−	2.92061e20i	0.188121	−	0.247615i
$646$	−2.08882e20	+	1.03408e21i	−0.175048	+	0.866587i
$647$	1.95960e21			1.62325			0.811625	−	0.584179i	$-0.198583\pi$
$647$	1.95960e21			1.62325			0.811625	+	0.584179i	$0.198583\pi$
$648$	−6.73319e19	+	1.21941e21i	−0.0551325	+	0.998479i
$649$	7.65422e20			0.619535
$650$	3.09074e20	−	1.53009e21i	0.247293	−	1.22424i
$651$	2.03483e20	−	2.67835e20i	0.160943	−	0.211841i
$652$	−1.41514e19	+	3.35995e19i	−0.0110648	+	0.0262709i
$653$			1.59848e21i			1.23555i	0.786356	+	0.617773i	$0.211965\pi$
$653$			1.59848e21i			1.23555i	−0.786356	+	0.617773i	$0.788035\pi$
$654$	1.19859e21	+	1.36169e21i	0.915877	+	1.04051i
$655$			2.32688e20i			0.175778i
$656$	5.42603e20	−	5.29879e20i	0.405232	−	0.395729i
$657$	−5.14223e20	−	1.84800e21i	−0.379674	−	1.36447i
$658$	7.88431e20	+	1.59261e20i	0.575532	+	0.116256i
$659$	4.07387e20			0.294013			0.147006	−	0.989136i	$-0.453036\pi$
$659$	4.07387e20			0.294013			0.147006	+	0.989136i	$0.453036\pi$
$660$	−1.14005e20	−	1.97981e20i	−0.0813474	−	0.141268i
$661$	2.34291e21			1.65289			0.826445	−	0.563017i	$-0.190359\pi$
$661$	2.34291e21			1.65289			0.826445	+	0.563017i	$0.190359\pi$
$662$	−5.98790e20	−	1.20954e20i	−0.417676	−	0.0843696i
$663$	−9.64634e20	−	7.32865e20i	−0.665290	−	0.505443i
$664$	−2.68153e20	+	3.93690e20i	−0.182861	+	0.268469i
$665$		−	1.24241e20i		−	0.0837729i
$666$	−1.09441e21	+	7.90193e19i	−0.729665	+	0.0526837i
$667$		−	1.16195e21i		−	0.766029i
$668$	−2.18809e21	−	9.21582e20i	−1.42640	−	0.600773i
$669$	−6.51873e20	−	4.95250e20i	−0.420211	−	0.319248i
$670$	3.30914e19	−	1.63821e20i	0.0210938	−	0.104426i
$671$	5.29213e20			0.333589
$672$	−5.09714e20	−	3.85481e19i	−0.317729	−	0.0240289i
$673$	1.04917e21			0.646746			0.323373	−	0.946272i	$-0.395183\pi$
$673$	1.04917e21			0.646746			0.323373	+	0.946272i	$0.395183\pi$
$674$	−3.03105e20	+	1.50054e21i	−0.184775	+	0.914740i
$675$	1.48485e21	+	5.90156e20i	0.895165	+	0.355786i
$676$	−1.05284e21	−	4.43435e20i	−0.627714	−	0.264381i
$677$			8.49037e20i			0.500624i	0.968165	+	0.250312i	$0.0805332\pi$
$677$			8.49037e20i			0.500624i	−0.968165	+	0.250312i	$0.919467\pi$
$678$	−2.39197e21	+	2.10546e21i	−1.39487	+	1.22779i
$679$		−	1.37136e20i		−	0.0790913i
$680$	−1.21872e20	+	1.78927e20i	−0.0695165	+	0.102061i
$681$	−6.55452e20	+	8.62739e20i	−0.369775	+	0.486717i
$682$	1.24772e21	+	2.52037e20i	0.696202	+	0.140631i
$683$	2.85892e20			0.157778			0.0788889	−	0.996883i	$-0.474863\pi$
$683$	2.85892e20			0.157778			0.0788889	+	0.996883i	$0.474863\pi$
$684$	−2.49309e21	−	3.18938e20i	−1.36087	−	0.174095i
$685$	−6.06225e20			−0.327306
$686$	1.11031e21	+	2.24281e20i	0.592946	+	0.119774i
$687$	1.56840e20	−	2.06441e20i	0.0828478	−	0.109049i
$688$	2.22199e21	−	2.16989e21i	1.16099	−	1.13377i
$689$		−	2.34574e20i		−	0.121237i
$690$	−2.51883e20	+	2.21712e20i	−0.128775	+	0.113350i
$691$		−	1.38315e21i		−	0.699496i	−0.936844	−	0.349748i	$-0.886267\pi$
$691$		−	1.38315e21i		−	0.699496i	0.936844	−	0.349748i	$-0.113733\pi$
$692$	−8.43243e20	+	2.00209e21i	−0.421849	+	1.00159i
$693$	−5.27671e20	+	1.46829e20i	−0.261134	+	0.0726629i
$694$	−6.12160e20	+	3.03053e21i	−0.299688	+	1.48362i
$695$	−4.59899e19			−0.0222729
$696$	1.69354e21	−	5.67145e20i	0.811384	−	0.271722i
$697$	−7.70065e20			−0.364990
$698$	−4.09261e20	+	2.02607e21i	−0.191904	+	0.950033i
$699$	−1.44157e21	−	1.09521e21i	−0.668740	−	0.508064i
$700$	−2.59591e20	+	6.16342e20i	−0.119139	+	0.282870i
$701$		−	5.12041e20i		−	0.232498i	−0.993220	−	0.116249i	$-0.962913\pi$
$701$		−	5.12041e20i		−	0.232498i	0.993220	−	0.116249i	$-0.0370871\pi$
$702$	1.57597e21	−	2.41796e21i	0.707978	−	1.08623i
$703$		−	2.25818e21i		−	1.00368i
$704$	−7.08361e20	−	1.80009e21i	−0.311501	−	0.791588i
$705$	6.46249e20	+	4.90977e20i	0.281178	+	0.213620i
$706$	−7.54720e20	−	1.52452e20i	−0.324901	−	0.0656292i
$707$	5.00328e20			0.213112
$708$	1.49750e21	−	8.62319e20i	0.631129	−	0.363428i
$709$	−3.47919e21			−1.45088			−0.725440	−	0.688285i	$-0.758364\pi$
$709$	−3.47919e21			−1.45088			−0.725440	+	0.688285i	$0.758364\pi$
$710$	−8.31895e20	−	1.68041e20i	−0.343266	−	0.0693389i
$711$	1.69014e21	−	4.70296e20i	0.690083	−	0.192021i
$712$	−2.37973e21	−	1.62090e21i	−0.961454	−	0.654872i
$713$		−	1.86967e21i		−	0.747471i
$714$	3.42930e20	+	3.89595e20i	0.135665	+	0.154126i
$715$			5.39912e20i			0.211362i
$716$	−8.58503e20	−	3.61585e20i	−0.332579	−	0.140076i
$717$	−5.62436e20	+	7.40307e20i	−0.215615	+	0.283804i
$718$	2.99129e20	−	1.48086e21i	0.113482	−	0.561797i
$719$	−8.54186e20			−0.320690			−0.160345	−	0.987061i	$-0.551261\pi$
$719$	−8.54186e20			−0.320690			−0.160345	+	0.987061i	$0.551261\pi$
$720$	−4.46087e20	−	2.58901e20i	−0.165739	−	0.0961921i
$721$	−1.07062e21			−0.393659
$722$	4.80059e20	−	2.37656e21i	0.174689	−	0.864808i
$723$	−5.95282e19	+	7.83541e19i	−0.0214381	+	0.0282179i
$724$	1.63097e21	+	6.86932e20i	0.581308	+	0.244835i
$725$		−	2.33666e21i		−	0.824251i
$726$	5.23012e20	+	5.94183e20i	0.182594	+	0.207442i
$727$			3.69552e21i			1.27693i	0.769651	+	0.638465i	$0.220430\pi$
$727$			3.69552e21i			1.27693i	−0.769651	+	0.638465i	$0.779570\pi$
$728$	9.98434e20	+	6.80060e20i	0.341456	+	0.232574i
$729$	2.14827e21	+	2.02803e21i	0.727162	+	0.686465i
$730$	7.94073e20	+	1.60401e20i	0.266035	+	0.0537384i
$731$	−3.15346e21			−1.04570
$732$	1.03537e21	−	5.96207e20i	0.339832	−	0.195688i
$733$	3.61825e21			1.17549			0.587745	−	0.809046i	$-0.300016\pi$
$733$	3.61825e21			1.17549			0.587745	+	0.809046i	$0.300016\pi$
$734$	3.95459e21	+	7.98817e20i	1.27169	+	0.256878i
$735$	4.30707e20	+	3.27223e20i	0.137097	+	0.104157i
$736$	−2.38562e21	+	1.54335e21i	−0.751655	+	0.486273i
$737$		−	1.51633e21i		−	0.472921i
$738$	−1.32121e20	−	1.82987e21i	−0.0407897	−	0.564934i
$739$			3.74316e21i			1.14395i	0.820273	+	0.571973i	$0.193822\pi$
$739$			3.74316e21i			1.14395i	−0.820273	+	0.571973i	$0.806178\pi$
$740$	1.79872e20	−	4.27067e20i	0.0544160	−	0.129199i
$741$	4.72971e21	+	3.59332e21i	1.41644	+	1.07612i
$742$	−1.98987e19	+	9.85094e19i	−0.00589922	+	0.0292044i
$743$	−6.23817e20			−0.183080			−0.0915401	−	0.995801i	$-0.529179\pi$
$743$	−6.23817e20			−0.183080			−0.0915401	+	0.995801i	$0.529179\pi$
$744$	2.72504e21	−	9.12579e20i	0.791727	−	0.265139i
$745$	2.02298e19			0.00581863
$746$	−2.34063e20	+	1.15874e21i	−0.0666488	+	0.329949i
$747$	3.08897e20	+	1.11011e21i	0.0870781	+	0.312940i
$748$	−7.62407e20	+	1.81017e21i	−0.212777	+	0.505192i
$749$		−	1.16285e21i		−	0.321300i
$750$	−1.03237e21	+	9.08711e20i	−0.282406	+	0.248580i
$751$			1.37628e21i			0.372741i	0.982479	+	0.186371i	$0.0596725\pi$
$751$			1.37628e21i			0.372741i	−0.982479	+	0.186371i	$0.940327\pi$
$752$	4.80134e21	+	4.91664e21i	1.28745	+	1.31836i
$753$	−1.69767e21	+	2.23456e21i	−0.450704	+	0.593240i
$754$	−4.13722e21	−	8.35707e20i	−1.08748	−	0.219669i
$755$	−4.52591e20			−0.117789
$756$	−8.66941e20	+	8.81732e20i	−0.223396	+	0.227208i
$757$	−5.99725e20			−0.153015			−0.0765073	−	0.997069i	$-0.524377\pi$
$757$	−5.99725e20			−0.153015			−0.0765073	+	0.997069i	$0.524377\pi$
$758$	−4.36862e21	−	8.82451e20i	−1.10363	−	0.222931i
$759$	−1.84175e21	+	2.42421e21i	−0.460700	+	0.606397i
$760$	5.97554e20	−	8.77302e20i	0.148004	−	0.217294i
$761$			2.91406e21i			0.714684i	0.933974	+	0.357342i	$0.116317\pi$
$761$			2.91406e21i			0.714684i	−0.933974	+	0.357342i	$0.883683\pi$
$762$	4.87700e21	−	4.29284e21i	1.18438	−	1.04251i
$763$			1.83674e21i			0.441687i
$764$	3.65548e21	+	1.53962e21i	0.870450	+	0.366617i
$765$	1.40390e20	+	5.04531e20i	0.0331036	+	0.118967i
$766$	9.56834e20	−	4.73686e21i	0.223419	−	1.10605i
$767$	−4.08383e21			−0.944284
$768$	−3.41383e21	−	2.72373e21i	−0.781687	−	0.623671i
$769$	1.79448e21			0.406904			0.203452	−	0.979085i	$-0.434784\pi$
$769$	1.79448e21			0.406904			0.203452	+	0.979085i	$0.434784\pi$
$770$	4.58001e19	−	2.26736e20i	0.0102846	−	0.0509143i
$771$	−7.75601e20	−	5.89250e20i	−0.172477	−	0.131036i
$772$	1.66654e21	+	7.01912e20i	0.367016	+	0.154580i
$773$		−	6.91323e21i		−	1.50777i	−0.657007	−	0.753885i	$-0.728178\pi$
$773$		−	6.91323e21i		−	1.50777i	0.657007	−	0.753885i	$-0.271822\pi$
$774$	−5.41045e20	−	7.49343e21i	−0.116863	−	1.61854i
$775$		−	3.75986e21i		−	0.804282i
$776$	6.59573e20	−	9.68356e20i	0.139733	−	0.205150i
$777$	−8.84633e20	−	6.72085e20i	−0.185612	−	0.141015i
$778$	−2.46807e21	−	4.98544e20i	−0.512874	−	0.103599i
$779$	3.77571e21			0.777084
$780$	6.08261e20	+	1.05631e21i	0.123988	+	0.215318i
$781$	−7.70006e21			−1.55457
$782$	2.82786e21	+	5.71221e20i	0.565467	+	0.114223i
$783$	1.59573e21	−	4.01488e21i	0.316042	−	0.795170i
$784$	3.19997e21	+	3.27681e21i	0.627733	+	0.642807i
$785$		−	7.80393e20i		−	0.151632i
$786$	3.14909e21	+	3.57761e21i	0.606060	+	0.688532i
$787$		−	5.42136e20i		−	0.103347i	−0.998664	−	0.0516735i	$-0.983544\pi$
$787$		−	5.42136e20i		−	0.103347i	0.998664	−	0.0516735i	$-0.0164555\pi$
$788$	2.98995e20	−	7.09898e20i	0.0564570	−	0.134045i
$789$	2.60172e21	−	3.42452e21i	0.486613	−	0.640504i
$790$	−1.46699e20	+	7.26240e20i	−0.0271784	+	0.134548i
$791$	−3.22646e21			−0.592110
$792$	−4.43222e21	−	1.50110e21i	−0.805718	−	0.272879i
$793$	−2.82356e21			−0.508450
$794$	−1.28883e21	+	6.38041e21i	−0.229901	+	1.13814i
$795$	−6.13445e19	+	8.07447e19i	−0.0108398	+	0.0142679i
$796$	4.36559e20	−	1.03651e21i	0.0764178	−	0.181437i
$797$			6.33610e21i			1.09871i	0.835588	+	0.549357i	$0.185127\pi$
$797$			6.33610e21i			1.09871i	−0.835588	+	0.549357i	$0.814873\pi$
$798$	−1.68142e21	−	1.91023e21i	−0.288839	−	0.328144i
$799$		−	6.97772e21i		−	1.18744i
$800$	−4.79742e21	+	3.10362e21i	−0.808784	+	0.523232i
$801$	−6.71025e21	+	1.86718e21i	−1.12071	+	0.311848i
$802$	−5.38941e21	−	1.08865e21i	−0.891731	−	0.180127i
$803$	7.34997e21			1.20481
$804$	−1.70829e21	−	2.96661e21i	−0.277422	−	0.481771i
$805$	−3.39757e20			−0.0546637
$806$	−6.65710e21	−	1.34472e21i	−1.06114	−	0.214347i
$807$	−2.43210e21	−	1.84775e21i	−0.384088	−	0.291804i
$808$	3.53295e21	+	2.40639e21i	0.552780	+	0.376513i
$809$			2.84009e21i			0.440270i	0.975469	+	0.220135i	$0.0706498\pi$
$809$			2.84009e21i			0.440270i	−0.975469	+	0.220135i	$0.929350\pi$
$810$	−1.17481e21	+	4.20166e20i	−0.180438	+	0.0645331i
$811$			6.32708e21i			0.962823i	0.876495	+	0.481412i	$0.159876\pi$
$811$			6.32708e21i			0.962823i	−0.876495	+	0.481412i	$0.840124\pi$
$812$	1.66653e21	+	7.01910e20i	0.251271	+	0.105831i
$813$	2.19589e21	+	1.66829e21i	0.328043	+	0.249225i
$814$	8.32453e20	−	4.12111e21i	0.123219	−	0.610001i
$815$	−3.72464e19			−0.00546264
$816$	5.47715e20	+	4.40040e21i	0.0795937	+	0.639464i
$817$	1.54618e22			2.22635
$818$	−1.25663e21	+	6.22102e21i	−0.179291	+	0.887588i
$819$	2.81533e21	−	7.83391e20i	0.398016	−	0.110751i
$820$	7.14062e20	+	3.00749e20i	0.100030	+	0.0421309i
$821$		−	6.53038e21i		−	0.906494i	−0.891385	−	0.453247i	$-0.850266\pi$
$821$		−	6.53038e21i		−	0.906494i	0.891385	−	0.453247i	$-0.149734\pi$
$822$	−9.32081e21	+	8.20437e21i	−1.28208	+	1.12851i
$823$		−	8.93559e21i		−	1.21794i	−0.793195	−	0.608968i	$-0.791584\pi$
$823$		−	8.93559e21i		−	1.21794i	0.793195	−	0.608968i	$-0.208416\pi$
$824$	−7.55994e21	−	5.14928e21i	−1.02109	−	0.695492i
$825$	−3.70371e21	+	4.87501e21i	−0.495716	+	0.652486i
$826$	1.71500e21	+	3.46427e20i	0.227465	+	0.0459474i
$827$	4.32274e21			0.568156			0.284078	−	0.958801i	$-0.408312\pi$
$827$	4.32274e21			0.568156			0.284078	+	0.958801i	$0.408312\pi$
$828$	−8.72186e20	+	6.81773e21i	−0.113601	+	0.887998i
$829$	1.52220e21			0.196478			0.0982389	−	0.995163i	$-0.468679\pi$
$829$	1.52220e21			0.196478			0.0982389	+	0.995163i	$0.468679\pi$
$830$	−4.77004e20	−	9.63537e19i	−0.0610150	−	0.0123249i
$831$	−7.58482e20	+	9.98352e20i	−0.0961474	+	0.126554i
$832$	3.77939e21	+	9.60419e21i	0.474784	+	1.20652i
$833$		−	4.65046e21i		−	0.578973i
$834$	−7.07103e20	+	6.22406e20i	−0.0872443	+	0.0767943i
$835$		−	2.42559e21i		−	0.296598i
$836$	3.73817e21	−	8.87545e21i	0.453014	−	1.07558i
$837$	2.56765e21	−	6.46025e21i	0.308386	−	0.775905i
$838$	−2.25569e21	+	1.11669e22i	−0.268503	+	1.32924i
$839$	5.83443e21			0.688309			0.344155	−	0.938913i	$-0.388166\pi$
$839$	5.83443e21			0.688309			0.344155	+	0.938913i	$0.388166\pi$
$840$	−1.65834e20	−	4.95194e20i	−0.0193900	−	0.0579002i
$841$	2.31109e21			0.267822
$842$	2.42249e21	−	1.19927e22i	0.278241	−	1.37745i
$843$	1.28573e22	+	9.76815e21i	1.46367	+	1.11200i
$844$	4.75675e21	−	1.12938e22i	0.536713	−	1.27431i
$845$		−	1.16712e21i		−	0.130523i
$846$	1.65808e22	−	1.19718e21i	1.83793	−	0.132703i
$847$			8.01476e20i			0.0880572i
$848$	−6.14303e20	+	5.99897e20i	−0.0668981	+	0.0653293i
$849$	−9.80182e21	−	7.44677e21i	−1.05803	−	0.803823i
$850$	5.68675e21	+	1.14871e21i	0.608446	+	0.122905i
$851$	−6.17535e21			−0.654922
$852$	−1.50647e22	+	8.67482e21i	−1.58367	+	0.911935i
$853$	−2.92759e21			−0.305065			−0.152532	−	0.988298i	$-0.548743\pi$
$853$	−2.92759e21			−0.305065			−0.152532	+	0.988298i	$0.548743\pi$
$854$	1.18575e21	+	2.39519e20i	0.122479	+	0.0247404i
$855$	−6.88348e20	−	2.47377e21i	−0.0704794	−	0.253287i
$856$	5.59288e21	−	8.21122e21i	0.567653	−	0.833402i
$857$			1.46480e22i			1.47374i	0.676033	+	0.736872i	$0.263698\pi$
$857$			1.46480e22i			1.47374i	−0.676033	+	0.736872i	$0.736302\pi$
$858$	7.30692e21	+	8.30124e21i	0.728752	+	0.827920i
$859$			4.53748e20i			0.0448607i	0.999748	+	0.0224303i	$0.00714040\pi$
$859$			4.53748e20i			0.0448607i	−0.999748	+	0.0224303i	$0.992860\pi$
$860$	2.92413e21	+	1.23159e21i	0.286588	+	0.120705i
$861$	1.12374e21	−	1.47912e21i	0.109179	−	0.143708i
$862$	−1.41478e20	+	7.00395e20i	−0.0136265	+	0.0674588i
$863$	4.59858e21			0.439080			0.219540	−	0.975604i	$-0.429544\pi$
$863$	4.59858e21			0.439080			0.219540	+	0.975604i	$0.429544\pi$
$864$	−1.03625e22	+	2.05650e21i	−0.980871	+	0.194659i
$865$	−2.21940e21			−0.208265
$866$	2.58451e21	−	1.27948e22i	0.240433	−	1.19028i
$867$	−3.83559e21	+	5.04860e21i	−0.353744	+	0.465616i
$868$	2.68158e21	+	1.12943e21i	0.245184	+	0.103267i
$869$			6.72212e21i			0.609337i
$870$	1.20555e21	+	1.36961e21i	0.108341	+	0.123084i
$871$			8.09023e21i			0.720817i
$872$	−8.83405e21	+	1.29698e22i	−0.780344	+	1.14567i
$873$	−7.59791e20	−	2.73052e21i	−0.0665407	−	0.239133i
$874$	−1.38653e22	−	2.80076e21i	−1.20391	−	0.243187i
$875$	−1.39253e21			−0.119879
$876$	1.43798e22	−	8.28042e21i	1.22736	−	0.706760i
$877$	−6.37888e21			−0.539818			−0.269909	−	0.962886i	$-0.586994\pi$
$877$	−6.37888e21			−0.539818			−0.269909	+	0.962886i	$0.586994\pi$
$878$	5.11044e21	+	1.03230e21i	0.428795	+	0.0866155i
$879$	−1.45440e22	−	1.10496e22i	−1.20995	−	0.919241i
$880$	1.41392e21	−	1.38076e21i	0.116629	−	0.113894i
$881$		−	1.56165e22i		−	1.27721i	−0.769533	−	0.638607i	$-0.779511\pi$
$881$		−	1.56165e22i		−	1.27721i	0.769533	−	0.638607i	$-0.220489\pi$
$882$	1.10507e22	−	7.97888e20i	0.896138	−	0.0647035i
$883$			7.64591e21i			0.614786i	0.951583	+	0.307393i	$0.0994566\pi$
$883$			7.64591e21i			0.614786i	−0.951583	+	0.307393i	$0.900543\pi$
$884$	4.06774e21	−	9.65795e21i	0.324311	−	0.770004i
$885$	1.40573e21	+	1.06798e21i	0.111129	+	0.0844284i
$886$	−5.59185e20	+	2.76828e21i	−0.0438332	+	0.216998i
$887$	−2.05677e22			−1.59867			−0.799334	−	0.600887i	$-0.794814\pi$
$887$	−2.05677e22			−1.59867			−0.799334	+	0.600887i	$0.794814\pi$
$888$	−3.01416e21	−	9.00053e21i	−0.232311	−	0.693699i
$889$	6.57844e21			0.502759
$890$	5.82428e20	−	2.88334e21i	0.0441384	−	0.218510i
$891$	−9.69298e21	+	5.84703e21i	−0.728408	+	0.439393i
$892$	2.74887e21	−	6.52658e21i	0.204841	−	0.486350i
$893$			3.42125e22i			2.52813i
$894$	3.11037e20	−	2.73781e20i	0.0227919	−	0.0200619i
$895$		−	9.51687e20i		−	0.0691546i
$896$	−7.72441e20	−	4.35388e21i	−0.0556615	−	0.313737i
$897$	9.82649e21	−	1.29341e22i	0.702190	−	0.924259i
$898$	−5.35596e21	−	1.08189e21i	−0.379547	−	0.0766675i
$899$	−1.01663e22			−0.714439
$900$	−1.75394e21	+	1.37102e22i	−0.122235	+	0.955491i
$901$	8.71822e20			0.0602548
$902$	6.89055e21	+	1.39187e21i	0.472286	+	0.0954006i
$903$	4.60177e21	−	6.05709e21i	0.312800	−	0.411723i
$904$	−2.27829e22	−	1.55181e22i	−1.53584	−	1.04610i
$905$			1.80800e21i			0.120874i
$906$	−6.95867e21	+	6.12516e21i	−0.461386	+	0.406122i
$907$			3.40756e21i			0.224073i	0.993704	+	0.112036i	$0.0357373\pi$
$907$			3.40756e21i			0.224073i	−0.993704	+	0.112036i	$0.964263\pi$
$908$	−8.63778e21	−	3.63807e21i	−0.563324	−	0.237261i
$909$	9.96204e21	−	2.77202e21i	0.644346	−	0.179295i
$910$	−2.44362e20	+	1.20973e21i	−0.0156756	+	0.0776027i
$911$	−7.32434e21			−0.465994			−0.232997	−	0.972477i	$-0.574853\pi$
$911$	−7.32434e21			−0.465994			−0.232997	+	0.972477i	$0.574853\pi$
$912$	−2.68551e21	−	2.15757e22i	−0.169459	−	1.36145i
$913$	−4.41518e21			−0.276323
$914$	−9.02202e20	+	4.46640e21i	−0.0560025	+	0.277243i
$915$	9.71920e20	+	7.38400e20i	0.0598373	+	0.0454604i
$916$	2.06689e21	+	8.70535e20i	0.126212	+	0.0531582i
$917$			4.82573e21i			0.292276i
$918$	8.98661e21	+	5.85727e21i	0.539853	+	0.351864i
$919$		−	1.70653e22i		−	1.01683i	−0.861113	−	0.508413i	$-0.830232\pi$
$919$		−	1.70653e22i		−	1.01683i	0.861113	−	0.508413i	$-0.169768\pi$
$920$	−2.39912e21	−	1.63410e21i	−0.141789	−	0.0965763i
$921$	−8.59432e21	−	6.52939e21i	−0.503807	−	0.382759i
$922$	−1.16663e22	−	2.35655e21i	−0.678343	−	0.137024i
$923$	4.10829e22			2.36945
$924$	−2.36436e21	−	4.10594e21i	−0.135261	−	0.234895i
$925$	−1.24184e22			−0.704699
$926$	1.83948e22	+	3.71571e21i	1.03541	+	0.209151i
$927$	−2.13171e22	+	5.93167e21i	−1.19023	+	0.331192i
$928$	8.39191e21	+	1.29718e22i	0.464784	+	0.718438i
$929$			2.27568e22i			1.25024i	0.780528	+	0.625121i	$0.214950\pi$
$929$			2.27568e22i			1.25024i	−0.780528	+	0.625121i	$0.785050\pi$
$930$	1.93983e21	+	2.20380e21i	0.105716	+	0.120102i
$931$			2.28017e22i			1.23267i
$932$	6.07892e21	−	1.44331e22i	0.325992	−	0.773997i
$933$	1.03323e22	−	1.35999e22i	0.549650	−	0.723477i
$934$	−8.34582e20	+	4.13164e21i	−0.0440420	+	0.218032i
$935$	−2.00664e21			−0.105047
$936$	2.36477e22	+	8.00896e21i	1.22806	+	0.415918i
$937$	1.82560e22			0.940502			0.470251	−	0.882533i	$-0.344163\pi$
$937$	1.82560e22			0.940502			0.470251	+	0.882533i	$0.344163\pi$
$938$	6.86285e20	−	3.39749e21i	0.0350738	−	0.173635i
$939$	8.66302e21	−	1.14027e22i	0.439215	−	0.578117i
$940$	−2.72515e21	+	6.47027e21i	−0.137067	+	0.325434i
$941$		−	1.47066e22i		−	0.733823i	−0.930256	−	0.366911i	$-0.880415\pi$
$941$		−	1.47066e22i		−	0.733823i	0.930256	−	0.366911i	$-0.119585\pi$
$942$	−1.05615e22	−	1.19987e22i	−0.522809	−	0.593952i
$943$		−	1.03253e22i		−	0.507065i
$944$	1.04439e22	+	1.06947e22i	0.508832	+	0.521051i
$945$	−1.17396e21	−	4.66592e20i	−0.0567432	−	0.0225527i
$946$	2.82172e22	+	5.69981e21i	1.35310	+	0.273324i
$947$	1.79636e22			0.854612			0.427306	−	0.904107i	$-0.359463\pi$
$947$	1.79636e22			0.854612			0.427306	+	0.904107i	$0.359463\pi$
$948$	7.57308e21	+	1.31514e22i	0.357446	+	0.620741i
$949$	−3.92150e22			−1.83635
$950$	−2.78828e22	−	5.63225e21i	−1.29541	−	0.261671i
$951$	3.30285e22	+	2.50929e22i	1.52242	+	1.15663i
$952$	−2.52752e21	+	3.71079e21i	−0.115589	+	0.169703i
$953$		−	4.21626e22i		−	1.91307i	−0.291616	−	0.956535i	$-0.594193\pi$
$953$		−	4.21626e22i		−	1.91307i	0.291616	−	0.956535i	$-0.405807\pi$
$954$	1.49580e20	+	2.07167e21i	0.00673381	+	0.0932627i
$955$			4.05225e21i			0.180997i
$956$	−7.41198e21	−	3.12178e21i	−0.328473	−	0.138347i
$957$	1.31816e22	+	1.00145e22i	0.579599	+	0.440341i
$958$	−4.44935e21	+	2.20267e22i	−0.194113	+	0.960968i
$959$	−1.25726e22			−0.544232
$960$	1.21070e21	−	4.29430e21i	0.0519997	−	0.184441i
$961$	7.10691e21			0.302869
$962$	−4.44147e21	+	2.19877e22i	−0.187808	+	0.929752i
$963$	−6.44269e21	−	2.31536e22i	−0.270315	−	0.971452i
$964$	−7.84484e20	−	3.30409e20i	−0.0326593	−	0.0137554i
$965$			1.84742e21i			0.0763153i
$966$	−5.22382e21	+	4.59811e21i	−0.214121	+	0.188474i
$967$			2.40261e22i			0.977202i	0.872507	+	0.488601i	$0.162493\pi$
$967$			2.40261e22i			0.977202i	−0.872507	+	0.488601i	$0.837507\pi$
$968$	−3.85480e21	+	5.65944e21i	−0.155574	+	0.228406i
$969$	−1.33550e22	+	1.75785e22i	−0.534829	+	0.703969i
$970$	1.17328e21	+	2.37000e20i	0.0466246	+	0.00941805i
$971$	−3.05559e22			−1.20490			−0.602450	−	0.798156i	$-0.705809\pi$
$971$	−3.05559e22			−1.20490			−0.602450	+	0.798156i	$0.705809\pi$
$972$	−1.23765e22	+	2.23594e22i	−0.484286	+	0.874910i
$973$	−9.53789e20			−0.0370345
$974$	−2.00982e22	−	4.05978e21i	−0.774399	−	0.156427i
$975$	1.97608e22	−	2.60101e22i	0.755560	−	0.994507i
$976$	7.22093e21	+	7.39434e21i	0.273981	+	0.280560i
$977$			1.20078e22i			0.452121i	0.974113	+	0.226061i	$0.0725847\pi$
$977$			1.20078e22i			0.452121i	−0.974113	+	0.226061i	$0.927415\pi$
$978$	−5.72670e20	+	5.04076e20i	−0.0213975	+	0.0188345i
$979$		−	2.66883e22i		−	0.989581i
$980$	−1.81624e21	+	4.31226e21i	−0.0668310	+	0.158675i
$981$	1.01763e22	+	3.65715e22i	0.371598	+	1.33544i
$982$	7.42132e21	−	3.67396e22i	0.268934	−	1.33137i
$983$	5.06817e22			1.82264			0.911318	−	0.411703i	$-0.135066\pi$
$983$	5.06817e22			1.82264			0.911318	+	0.411703i	$0.135066\pi$
$984$	1.50490e22	−	5.03972e21i	0.537088	−	0.179864i
$985$	7.86952e20			0.0278725
$986$	3.10600e21	−	1.53764e22i	0.109175	−	0.540479i
$987$	1.34026e22	+	1.01824e22i	0.467531	+	0.355199i
$988$	−1.99446e22	+	4.73540e22i	−0.690475	+	1.63938i
$989$		−	4.22826e22i		−	1.45275i
$990$	−3.44284e20	−	4.76830e21i	−0.0117396	−	0.162592i
$991$		−	3.51421e22i		−	1.18926i	−0.804001	−	0.594629i	$-0.797299\pi$
$991$		−	3.51421e22i		−	1.18926i	0.804001	−	0.594629i	$-0.202701\pi$
$992$	1.35032e22	+	2.08726e22i	0.453524	+	0.701033i
$993$	−1.01789e22	−	7.73325e21i	−0.339298	−	0.257776i
$994$	−1.72527e22	−	3.48501e21i	−0.570769	−	0.115294i
$995$	1.14902e21			0.0377271
$996$	−8.63803e21	+	4.97410e21i	−0.281494	+	0.162095i
$997$	1.88033e22			0.608165			0.304082	−	0.952646i	$-0.401650\pi$
$997$	1.88033e22			0.608165			0.304082	+	0.952646i	$0.401650\pi$
$998$	−2.57869e22	−	5.20889e21i	−0.827790	−	0.167212i
$999$	−2.13376e22	−	8.48068e21i	−0.679836	−	0.270203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.16.b.a.11.14	yes	28
3.2	odd	2	inner	12.16.b.a.11.15	yes	28
4.3	odd	2	inner	12.16.b.a.11.16	yes	28
12.11	even	2	inner	12.16.b.a.11.13	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.16.b.a.11.13	✓	28	12.11	even	2	inner
12.16.b.a.11.14	yes	28	1.1	even	1	trivial
12.16.b.a.11.15	yes	28	3.2	odd	2	inner
12.16.b.a.11.16	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)

\(f(q)\)	\(=\)	\(q+(-35.8416 + 177.436i) q^{2} +(-2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} -33476.6i q^{5} +(-453057. - 514708. i) q^{6} -694274. i q^{7} +(3.33920e6 - 4.90246e6i) q^{8} +(-3.84657e6 - 1.38237e7i) q^{9} +O(q^{10})\)	\(q+(-35.8416 + 177.436i) q^{2} +(-2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} -33476.6i q^{5} +(-453057. - 514708. i) q^{6} -694274. i q^{7} +(3.33920e6 - 4.90246e6i) q^{8} +(-3.84657e6 - 1.38237e7i) q^{9} +(5.93994e6 + 1.19985e6i) q^{10} +5.49804e7 q^{11} +(1.07566e8 - 6.19404e7i) q^{12} -2.93342e8 q^{13} +(1.23189e8 + 2.48839e7i) q^{14} +(1.00974e8 + 7.67131e7i) q^{15} +(7.50189e8 + 7.68204e8i) q^{16} -1.09024e9i q^{17} +(2.59069e9 - 1.87054e8i) q^{18} +5.34556e9i q^{19} +(-4.25793e8 + 1.01095e9i) q^{20} +(2.09410e9 + 1.59096e9i) q^{21} +(-1.97058e9 + 9.75547e9i) q^{22} +1.46183e10 q^{23} +(7.13511e9 + 2.13060e10i) q^{24} +2.93969e10 q^{25} +(1.05138e10 - 5.20493e10i) q^{26} +(5.05103e10 + 2.00755e10i) q^{27} +(-8.83057e9 + 2.09662e10i) q^{28} -7.94865e10i q^{29} +(-1.72307e10 + 1.51668e10i) q^{30} -1.27900e11i q^{31} +(-1.63195e11 + 1.05577e11i) q^{32} +(-1.25990e11 + 1.65834e11i) q^{33} +(1.93447e11 + 3.90759e10i) q^{34} -2.32419e10 q^{35} +(-5.96641e10 + 4.66384e11i) q^{36} -4.22440e11 q^{37} +(-9.48493e11 - 1.91593e11i) q^{38} +(6.72206e11 - 8.84791e11i) q^{39} +(-1.64118e11 - 1.11785e11i) q^{40} -7.06327e11i q^{41} +(-3.57349e11 + 3.14546e11i) q^{42} -2.89245e12i q^{43} +(-1.66034e12 - 6.99303e11i) q^{44} +(-4.62771e11 + 1.28770e11i) q^{45} +(-5.23941e11 + 2.59380e12i) q^{46} +6.40017e12 q^{47} +(-4.03618e12 + 5.02381e11i) q^{48} +4.26554e12 q^{49} +(-1.05363e12 + 5.21606e12i) q^{50} +(3.28843e12 + 2.49833e12i) q^{51} +(8.85857e12 + 3.73106e12i) q^{52} +7.99661e11i q^{53} +(-5.37247e12 + 8.24279e12i) q^{54} -1.84055e12i q^{55} +(-3.40365e12 - 2.31832e12i) q^{56} +(-1.61235e13 - 1.22496e13i) q^{57} +(1.41037e13 + 2.84892e12i) q^{58} +1.39217e13 q^{59} +(-2.07355e12 - 3.60094e12i) q^{60} +9.62549e12 q^{61} +(2.26940e13 + 4.58413e12i) q^{62} +(-9.59745e12 + 2.67057e12i) q^{63} +(-1.28839e13 - 3.27406e13i) q^{64} +9.82009e12i q^{65} +(-2.49092e13 - 2.82988e13i) q^{66} -2.75795e13i q^{67} +(-1.38669e13 + 3.29239e13i) q^{68} +(-3.34984e13 + 4.40923e13i) q^{69} +(8.33027e11 - 4.12395e12i) q^{70} -1.40051e14 q^{71} +(-8.06147e13 - 2.73025e13i) q^{72} +1.33684e14 q^{73} +(1.51409e13 - 7.49559e13i) q^{74} +(-6.73643e13 + 8.86683e13i) q^{75} +(6.79909e13 - 1.61429e14i) q^{76} -3.81714e13i q^{77} +(1.32901e14 + 1.50986e14i) q^{78} +1.22264e14i q^{79} +(2.57169e13 - 2.51138e13i) q^{80} +(-1.76299e14 + 1.06348e14i) q^{81} +(1.25327e14 + 2.53158e13i) q^{82} -8.03046e13 q^{83} +(-4.30036e13 - 7.46802e13i) q^{84} -3.64975e13 q^{85} +(5.13224e14 + 1.03670e14i) q^{86} +(2.39751e14 + 1.82147e14i) q^{87} +(1.83590e14 - 2.69539e14i) q^{88} -4.85416e14i q^{89} +(-6.26194e12 - 8.67273e13i) q^{90} +2.03660e14i q^{91} +(-4.41454e14 - 1.85932e14i) q^{92} +(3.85777e14 + 2.93088e14i) q^{93} +(-2.29392e14 + 1.13562e15i) q^{94} +1.78951e14 q^{95} +(5.55228e13 - 7.34169e14i) q^{96} +1.97524e14 q^{97} +(-1.52884e14 + 7.56859e14i) q^{98} +(-2.11486e14 - 7.60033e14i) 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

Introduction

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