LMFDB - Embedded newform 12.16.b.a.11.15

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			11.15
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(35.8416 - 177.436i) q^{2} +(2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} +33476.6i q^{5} +(617322. - 298494. i) q^{6} -694274. i q^{7} +(-3.33920e6 + 4.90246e6i) q^{8} +(-3.84657e6 + 1.38237e7i) q^{9} +O(q^{10})$	\(q+(35.8416 - 177.436i) q^{2} +(2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} +33476.6i q^{5} +(617322. - 298494. 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} +(-3.08377e7 - 1.20233e8i) 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} +(2.31495e9 + 1.17798e9i) 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} +(-2.24389e10 + 1.16236e9i) 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} +(9.99257e9 + 2.06658e10i) 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} +(2.91987e11 - 3.68534e11i) 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} +(-2.07237e11 - 4.28591e11i) 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} +(-5.98002e11 + 4.02313e12i) 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} +(1.75173e12 + 9.68186e12i) 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} +(4.02500e12 - 1.03234e12i) 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} +(-3.39406e13 + 1.64113e13i) 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} +(-5.49258e13 - 6.50178e13i) 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} +(-1.81086e14 + 8.75609e13i) 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} +(-8.34749e13 + 2.14099e13i) 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} +(-3.94348e13 + 7.74967e13i) 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} +(6.92413e14 + 2.50302e14i) 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	$0.0305459\pi$
$5$			33476.6i			0.191631i	−0.995399	+	0.0958156i	$0.969454\pi$
$6$	617322.	−	298494.i	0.900279	−	0.435313i
$7$		−	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	$-0.639844\pi$
$11$	−5.49804e7			−0.850673			−0.425336	+	0.905035i	$0.639844\pi$
$12$	−3.08377e7	−	1.20233e8i	−0.248441	−	0.968647i
$13$	−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	$0.104422\pi$
$17$			1.09024e9i			0.644399i	−0.946672	+	0.322199i	$0.895578\pi$
$18$	2.31495e9	+	1.17798e9i	0.891247	+	0.453518i
$19$			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	$-0.647727\pi$
$23$	−1.46183e10			−0.895235			−0.447618	+	0.894225i	$0.647727\pi$
$24$	−2.24389e10	+	1.16236e9i	−0.998661	+	0.0517318i
$25$	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	$0.140724\pi$
$29$			7.94865e10i			0.855674i	−0.903856	+	0.427837i	$0.859276\pi$
$30$	9.99257e9	+	2.06658e10i	0.0834196	+	0.172522i
$31$		−	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
$36$	2.91987e11	−	3.68534e11i	0.621005	−	0.783807i
$37$	−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	$0.0913968\pi$
$41$			7.06327e11i			0.566405i	−0.959060	+	0.283202i	$0.908603\pi$
$42$	−2.07237e11	−	4.28591e11i	−0.138707	−	0.286862i
$43$		−	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	$-0.872918\pi$
$47$	−6.40017e12			−1.84271			−0.921357	+	0.388718i	$0.872918\pi$
$48$	−5.98002e11	+	4.02313e12i	−0.147026	+	0.989133i
$49$	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	$-0.985113\pi$
$53$		−	7.99661e11i		−	0.0935055i	0.998906	−	0.0467527i	$-0.0148873\pi$
$54$	1.75173e12	+	9.68186e12i	0.178039	+	0.984023i
$55$		−	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	$-0.618639\pi$
$59$	−1.39217e13			−0.728289			−0.364144	+	0.931343i	$0.618639\pi$
$60$	4.02500e12	−	1.03234e12i	0.185623	−	0.0476090i
$61$	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
$66$	−3.39406e13	+	1.64113e13i	−0.765843	+	0.370309i
$67$		−	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	$-0.133187\pi$
$71$	1.40051e14			1.82746			0.913732	+	0.406318i	$0.133187\pi$
$72$	−5.49258e13	−	6.50178e13i	−0.645331	−	0.763903i
$73$	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
$78$	−1.81086e14	+	8.75609e13i	−1.16728	+	0.564418i
$79$			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	$-0.448072\pi$
$83$	8.03046e13			0.324829			0.162414	+	0.986723i	$0.448072\pi$
$84$	−8.34749e13	+	2.14099e13i	−0.308646	+	0.0791624i
$85$	−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	$0.197591\pi$
$89$			4.85416e14i			1.16329i	−0.813442	+	0.581646i	$0.802409\pi$
$90$	−3.94348e13	+	7.74967e13i	−0.0869082	+	0.170791i
$91$			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
$96$	6.92413e14	+	2.50302e14i	0.940439	+	0.339962i
$97$	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	$-0.891462\pi$
$101$		−	7.20648e14i		−	0.668826i	0.942427	−	0.334413i	$-0.108538\pi$
$102$	3.25430e14	+	6.73028e14i	0.280515	+	0.580139i
$103$		−	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	$-0.668205\pi$
$107$	−1.67492e15			−1.00836			−0.504180	+	0.863599i	$0.668205\pi$
$108$	1.78069e15	+	3.61933e13i	0.999794	+	0.0203212i
$109$	−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	$0.379443\pi$
$113$			4.64724e15i			1.85826i	−0.369751	+	0.929131i	$0.620557\pi$
$114$	1.59562e15	+	3.29993e15i	0.597232	+	1.23515i
$115$		−	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
$120$	−3.89120e13	−	7.51179e14i	−0.00991343	−	0.191375i
$121$	−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
$126$	8.17842e14	−	1.60721e15i	0.144507	−	0.283984i
$127$			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	$-0.348339\pi$
$131$	6.95076e15			0.917270			0.458635	+	0.888625i	$0.348339\pi$
$132$	1.69547e15	+	6.61047e15i	0.211342	+	0.824001i
$133$	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	$0.325831\pi$
$137$			1.81089e16i			1.70800i	−0.520272	+	0.854001i	$0.674169\pi$
$138$	−9.02417e15	+	4.36347e15i	−0.805962	+	0.389708i
$139$		−	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
$144$	−1.35051e16	+	7.41545e15i	−0.876554	+	0.481303i
$145$	−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	$-0.995167\pi$
$149$		−	6.04298e14i		−	0.0303637i	0.999885	−	0.0151818i	$-0.00483271\pi$
$150$	1.81473e16	−	8.77481e15i	0.867219	−	0.419327i
$151$		−	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
$156$	9.04601e15	+	3.52695e16i	0.322124	+	1.25593i
$157$	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
$162$	−2.51887e16	+	2.74700e16i	−0.675838	+	0.737050i
$163$		−	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	$-0.781686\pi$
$167$	−7.24563e16			−1.54776			−0.773878	+	0.633334i	$0.781686\pi$
$168$	8.06999e14	+	1.55788e16i	0.0164837	+	0.318210i
$169$	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	$0.182863\pi$
$173$			6.62972e16i			1.08680i	−0.839474	+	0.543400i	$0.817137\pi$
$174$	2.37263e16	+	4.90687e16i	0.372486	+	0.770345i
$175$		−	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	$-0.557751\pi$
$179$	−2.84284e16			−0.360874			−0.180437	+	0.983587i	$0.557751\pi$
$180$	1.23373e16	+	9.77474e15i	0.150202	+	0.119004i
$181$	−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
$186$	−3.81774e16	−	7.89553e16i	−0.363462	−	0.751682i
$187$		−	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	$-0.343441\pi$
$191$	1.21047e17			0.944506			0.472253	+	0.881463i	$0.343441\pi$
$192$	6.92296e16	−	1.13887e17i	0.519437	−	0.854509i
$193$	−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	$-0.976831\pi$
$197$		−	2.35075e16i		−	0.145449i	0.997352	−	0.0727244i	$-0.0231694\pi$
$198$	−1.27277e17	−	6.47658e16i	−0.758160	−	0.385795i
$199$			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
$204$	1.31083e17	−	3.36205e16i	0.624195	−	0.160095i
$205$	−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
$210$	1.43477e16	−	6.93759e15i	0.0549717	−	0.0265805i
$211$			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
$216$	7.02447e16	−	3.14661e17i	0.217876	−	0.975976i
$217$	−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
$222$	−2.60782e17	+	1.26096e17i	−0.658612	+	0.318460i
$223$			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	$-0.598865\pi$
$227$	−2.86031e17			−0.611250			−0.305625	+	0.952152i	$0.598865\pi$
$228$	6.42715e17	−	1.64845e17i	1.32895	−	0.340851i
$229$	−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	$-0.862057\pi$
$233$		−	4.77935e17i		−	0.839846i	0.907560	−	0.419923i	$-0.137943\pi$
$234$	−6.79073e17	−	3.45551e17i	−1.15557	−	0.588022i
$235$		−	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	$-0.557030\pi$
$239$	−2.45440e17			−0.356419			−0.178210	+	0.983993i	$0.557030\pi$
$240$	−1.34681e17	−	2.00191e16i	−0.189549	−	0.0281747i
$241$	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
$246$	2.10835e17	+	4.36031e17i	0.246563	+	0.509922i
$247$		−	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	$-0.621504\pi$
$251$	−7.40843e17			−0.745029			−0.372514	+	0.928026i	$0.621504\pi$
$252$	−2.55864e17	−	2.02719e17i	−0.249750	−	0.197875i
$253$	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	$-0.965458\pi$
$257$		−	2.57141e17i		−	0.216607i	0.994118	−	0.108304i	$-0.0345419\pi$
$258$	−8.63380e17	−	1.78557e18i	−0.706406	−	1.46093i
$259$			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	$-0.368248\pi$
$263$	1.13536e18			0.804386			0.402193	+	0.915555i	$0.368248\pi$
$264$	1.23370e18	−	6.39072e16i	0.849534	−	0.0440068i
$265$	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	$-0.922465\pi$
$269$		−	8.06335e17i		−	0.482362i	0.970480	−	0.241181i	$-0.0775348\pi$
$270$	−3.24116e17	+	5.86420e16i	−0.188570	+	0.0341178i
$271$		−	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
$276$	4.50794e17	+	1.75760e18i	0.222413	+	0.867167i
$277$	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	$0.371073\pi$
$281$			4.26270e18i			1.83818i	−0.394053	+	0.919088i	$0.628927\pi$
$282$	−3.95097e18	+	1.91042e18i	−1.65896	+	0.802157i
$283$			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
$288$	8.31721e17	+	2.66206e18i	0.298218	+	0.954498i
$289$	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	$-0.725313\pi$
$293$		−	4.82189e18i		−	1.51953i	0.650195	−	0.759767i	$-0.274687\pi$
$294$	2.63321e18	−	1.27324e18i	0.808874	−	0.391116i
$295$		−	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
$300$	−9.06534e17	−	3.53449e18i	−0.239318	−	0.933076i
$301$	−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
$306$	−1.28428e18	+	2.52385e18i	−0.292246	+	0.574319i
$307$			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	$-0.349891\pi$
$311$	4.50890e18			0.908589			0.454295	+	0.890851i	$0.349891\pi$
$312$	6.58228e18	−	3.40970e17i	1.29484	−	0.0670744i
$313$	−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	$0.405200\pi$
$317$			1.09502e19i			1.91195i	−0.293440	+	0.955977i	$0.594800\pi$
$318$	−2.38694e17	−	4.93648e17i	−0.0407042	−	0.0841810i
$319$		−	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
$324$	3.97136e18	+	5.45394e18i	0.588643	+	0.808393i
$325$	−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
$330$	−5.49395e17	−	1.13621e18i	−0.0709627	−	0.146759i
$331$			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
$336$	2.79315e18	+	4.15177e17i	0.315174	+	0.0468478i
$337$	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
$342$	−6.29697e18	+	1.23747e19i	−0.622209	+	1.22276i
$343$		−	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	$-0.773235\pi$
$347$	−1.70796e19			−1.51359			−0.756793	+	0.653654i	$0.773235\pi$
$348$	9.55692e18	−	2.45118e18i	0.828846	−	0.212584i
$349$	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	$-0.947002\pi$
$353$		−	4.25349e18i		−	0.331463i	0.986171	−	0.165731i	$-0.0529985\pi$
$354$	−8.59419e18	+	4.15556e18i	−0.655663	+	0.317034i
$355$			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	$-0.407484\pi$
$359$	8.34588e18			0.573144			0.286572	+	0.958059i	$0.407484\pi$
$360$	2.17657e18	−	1.83873e18i	0.146388	−	0.123666i
$361$	−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
$366$	5.94202e18	−	2.87315e18i	0.353042	−	0.170707i
$367$		−	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
$372$	−1.53778e19	+	3.94414e18i	−0.808766	+	0.207434i
$373$	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
$378$	6.72186e18	−	1.21618e18i	0.313546	−	0.0567297i
$379$			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	$-0.309187\pi$
$383$	2.66962e19			1.12839			0.564195	+	0.825642i	$0.309187\pi$
$384$	−1.77264e19	−	1.63657e19i	−0.734744	−	0.678345i
$385$	−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	$-0.915745\pi$
$389$		−	1.39097e19i		−	0.523232i	0.965172	−	0.261616i	$-0.0842555\pi$
$390$	−2.93124e18	−	6.06215e18i	−0.108160	−	0.223688i
$391$		−	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
$396$	−1.60536e19	+	2.02621e19i	−0.528272	+	0.666763i
$397$	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	$-0.849685\pi$
$401$		−	3.03739e19i		−	0.909742i	0.890557	−	0.454871i	$-0.150315\pi$
$402$	−8.23233e18	−	1.70254e19i	−0.242007	−	0.500499i
$403$			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
$408$	−1.26725e18	−	2.44638e19i	−0.0333359	−	0.643536i
$409$	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
$414$	−3.38406e19	−	1.72200e19i	−0.797876	−	0.406005i
$415$			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	$-0.737172\pi$
$419$	−6.29350e19			−1.35609			−0.678043	+	0.735022i	$0.737172\pi$
$420$	−7.16729e17	−	2.79445e18i	−0.0151700	−	0.0591463i
$421$	−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
$426$	8.64566e19	−	4.18045e19i	1.64523	−	0.795519i
$427$		−	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	$-0.510955\pi$
$431$	−3.94732e18			−0.0688213			−0.0344106	+	0.999408i	$0.510955\pi$
$432$	−5.33143e19	−	2.37418e19i	−0.913515	−	0.406805i
$433$	−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
$438$	8.25258e19	−	3.99038e19i	1.27507	−	0.616536i
$439$		−	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	$-0.535306\pi$
$443$	−1.56016e19			−0.221381			−0.110691	+	0.993855i	$0.535306\pi$
$444$	1.30271e19	+	5.07914e19i	0.181751	+	0.708628i
$445$	−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	$-0.937982\pi$
$449$		−	3.01854e19i		−	0.387213i	0.981079	−	0.193606i	$-0.0620184\pi$
$450$	6.80524e19	+	3.46290e19i	0.858518	+	0.436864i
$451$		−	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
$456$	−6.21349e18	−	1.19949e20i	−0.0709740	−	1.37012i
$457$	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	$-0.887532\pi$
$461$		−	6.57492e19i		−	0.692044i	0.938226	−	0.346022i	$-0.112468\pi$
$462$	1.13940e19	+	2.35641e19i	0.117994	+	0.244026i
$463$		−	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	$-0.535475\pi$
$467$	−2.32853e19			−0.222436			−0.111218	+	0.993796i	$0.535475\pi$
$468$	−8.56521e19	+	1.08107e20i	−0.805182	+	1.01627i
$469$	−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
$474$	3.64951e19	+	7.54762e19i	0.311815	+	0.644870i
$475$			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	$-0.663072\pi$
$479$	−1.24139e20			−0.980377			−0.490188	+	0.871617i	$0.663072\pi$
$480$	−8.37926e18	+	2.31796e19i	−0.0651473	+	0.180217i
$481$	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
$486$	−1.40577e20	−	1.30265e19i	−0.995734	−	0.0922687i
$487$			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	$-0.262357\pi$
$491$	2.07059e20			1.35826			0.679130	+	0.734018i	$0.262357\pi$
$492$	8.49240e19	−	2.17815e19i	0.548646	−	0.140718i
$493$	−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
$498$	4.95738e19	−	2.39705e19i	0.292437	−	0.141402i
$499$			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	$-0.276773\pi$
$503$	2.35769e20			1.29041			0.645203	+	0.764011i	$0.276773\pi$
$504$	−4.51401e19	+	3.81336e19i	−0.243407	+	0.205626i
$505$	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	$0.308755\pi$
$509$			3.29459e20i			1.64975i	−0.565314	+	0.824876i	$0.691245\pi$
$510$	−2.25307e19	+	1.08943e19i	−0.111173	+	0.0537555i
$511$		−	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
$516$	−3.47769e20	+	8.91967e19i	−1.57188	+	0.403159i
$517$	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	$0.221473\pi$
$521$			3.04901e20i			1.28197i	−0.767555	+	0.640983i	$0.778527\pi$
$522$	−9.36335e19	+	1.84007e20i	−0.388063	+	0.762617i
$523$		−	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
$528$	3.28784e19	−	2.21193e20i	0.125071	−	0.841428i
$529$	−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
$534$	1.44894e20	+	2.99658e20i	0.506397	+	1.04729i
$535$		−	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
$540$	−1.21163e18	+	5.96114e19i	−0.00389418	+	0.191592i
$541$	−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
$546$	6.07913e19	+	1.25724e20i	0.179844	+	0.371939i
$547$		−	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
$552$	3.28019e20	−	1.69917e19i	0.894037	−	0.0463121i
$553$	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	$0.208932\pi$
$557$			4.79131e20i			1.22051i	−0.792206	+	0.610253i	$0.791068\pi$
$558$	1.50664e20	−	2.96082e20i	0.378662	−	0.744141i
$559$			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	$-0.537723\pi$
$563$	−1.00595e20			−0.236463			−0.118232	+	0.992986i	$0.537723\pi$
$564$	1.97367e20	+	7.69514e20i	0.457806	+	1.78494i
$565$	−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	$-0.965655\pi$
$569$		−	9.92056e19i		−	0.215375i	0.994185	−	0.107687i	$-0.0343445\pi$
$570$	−1.10470e20	+	5.34159e19i	−0.236693	+	0.114448i
$571$		−	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
$576$	5.02155e20	−	5.21644e19i	0.994648	−	0.103325i
$577$	−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
$582$	1.21936e20	−	5.89599e19i	0.223465	−	0.108052i
$583$			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	$-0.433008\pi$
$587$	2.43095e20			0.417822			0.208911	+	0.977935i	$0.433008\pi$
$588$	−1.31540e20	−	5.12861e20i	−0.223217	−	0.870301i
$589$	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	$-0.817669\pi$
$593$		−	6.80668e20i		−	1.08399i	0.840382	−	0.541995i	$-0.182331\pi$
$594$	−9.63109e19	−	5.32312e20i	−0.151453	−	0.837082i
$595$			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	$-0.507844\pi$
$599$	−3.33728e19			−0.0492824			−0.0246412	+	0.999696i	$0.507844\pi$
$600$	−6.59635e20	+	3.41699e19i	−0.961988	+	0.0498321i
$601$	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
$606$	−2.15109e20	−	4.44872e20i	−0.291149	−	0.602130i
$607$		−	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
$612$	4.01790e20	+	3.18336e20i	0.505084	+	0.400175i
$613$	−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	$-0.940119\pi$
$617$		−	3.16260e20i		−	0.374030i	0.982357	−	0.187015i	$-0.0598812\pi$
$618$	−4.60299e20	−	9.51953e20i	−0.537807	−	1.11225i
$619$			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
$624$	1.75419e20	−	1.18015e21i	0.190631	−	1.28249i
$625$	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
$630$	5.38039e19	+	2.73786e19i	0.0544202	+	0.0276921i
$631$			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
$636$	−9.61460e19	+	2.46598e19i	−0.0905738	+	0.0232306i
$637$	−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	$0.0371775\pi$
$641$			2.62366e20i			0.233062i	−0.993187	+	0.116531i	$0.962823\pi$
$642$	−1.03396e21	+	4.99954e20i	−0.907805	+	0.438952i
$643$		−	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	$-0.801417\pi$
$647$	−1.95960e21			−1.62325			−0.811625	+	0.584179i	$0.801417\pi$
$648$	1.11006e21	−	5.09183e20i	0.908939	−	0.416928i
$649$	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	$-0.788035\pi$
$653$		−	1.59848e21i		−	1.23555i	0.786356	−	0.617773i	$-0.211965\pi$
$654$	−1.63316e21	+	7.89685e20i	−1.24795	+	0.603421i
$655$			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	$-0.546964\pi$
$659$	−4.07387e20			−0.294013			−0.147006	+	0.989136i	$0.546964\pi$
$660$	−2.21296e20	+	5.67586e19i	−0.157904	+	0.0404997i
$661$	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
$666$	−9.77929e20	−	4.97627e20i	−0.652005	−	0.331778i
$667$		−	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
$672$	1.73778e20	−	4.80724e20i	0.108324	−	0.299658i
$673$	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	$-0.919467\pi$
$677$		−	8.49037e20i		−	0.500624i	0.968165	−	0.250312i	$-0.0805332\pi$
$678$	1.38718e21	+	2.86884e21i	0.808926	+	1.67295i
$679$		−	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	$-0.525137\pi$
$683$	−2.85892e20			−0.157778			−0.0788889	+	0.996883i	$0.525137\pi$
$684$	1.97002e21	+	1.56084e21i	1.07535	+	0.851994i
$685$	−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
$690$	−1.46074e20	−	3.02099e20i	−0.0746801	−	0.154447i
$691$		−	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
$696$	−9.23922e19	−	1.78359e21i	−0.0442656	−	0.854528i
$697$	−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	$0.0370871\pi$
$701$			5.12041e20i			0.232498i	−0.993220	+	0.116249i	$0.962913\pi$
$702$	−5.13857e20	−	2.84010e21i	−0.230841	−	1.27586i
$703$		−	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
$708$	4.29315e20	+	1.67386e21i	0.180937	+	0.705455i
$709$	−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
$714$	4.67266e20	−	2.25938e20i	0.184853	−	0.0893824i
$715$			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	$-0.448739\pi$
$719$	8.54186e20			0.320690			0.160345	+	0.987061i	$0.448739\pi$
$720$	−2.48244e20	−	4.52104e20i	−0.0922327	−	0.167975i
$721$	−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
$726$	−7.12641e20	+	3.44584e20i	−0.248798	+	0.120301i
$727$			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
$732$	−2.96828e20	−	1.15730e21i	−0.0974254	−	0.379852i
$733$	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
$738$	−8.32039e20	+	1.63511e21i	−0.256875	+	0.504806i
$739$			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	$-0.470821\pi$
$743$	6.23817e20			0.183080			0.0915401	+	0.995801i	$0.470821\pi$
$744$	1.48666e20	+	2.86994e21i	0.0431931	+	0.833826i
$745$	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
$750$	5.98700e20	+	1.23818e21i	0.163776	+	0.338708i
$751$			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
$756$	2.51280e19	−	1.23629e21i	0.00647508	−	0.318571i
$757$	−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	$-0.883683\pi$
$761$		−	2.91406e21i		−	0.714684i	0.933974	−	0.357342i	$-0.116317\pi$
$762$	2.82832e21	+	5.84929e21i	0.686856	+	1.42050i
$763$			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
$768$	−3.53920e21	+	2.55872e21i	−0.810393	+	0.585886i
$769$	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	$0.271822\pi$
$773$			6.91323e21i			1.50777i	−0.657007	+	0.753885i	$0.728178\pi$
$774$	3.40725e21	−	6.69589e21i	0.735948	−	1.44627i
$775$		−	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
$780$	−1.18070e21	+	3.02829e20i	−0.240675	+	0.0617289i
$781$	−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
$786$	4.29085e21	−	2.07476e21i	0.825799	−	0.399300i
$787$		−	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
$792$	3.01984e21	+	3.57470e21i	0.548965	+	0.649831i
$793$	−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	$-0.814873\pi$
$797$		−	6.33610e21i		−	1.09871i	0.835588	−	0.549357i	$-0.185127\pi$
$798$	2.29106e21	−	1.10780e21i	0.393563	−	0.190300i
$799$		−	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
$804$	−3.31598e21	+	8.50490e20i	−0.538507	+	0.138118i
$805$	−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	$-0.929350\pi$
$809$		−	2.84009e21i		−	0.440270i	0.975469	−	0.220135i	$-0.0706498\pi$
$810$	−9.19603e20	−	8.43231e20i	−0.141242	−	0.129512i
$811$			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
$816$	−4.38617e21	−	6.51965e20i	−0.637396	−	0.0947432i
$817$	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	$0.149734\pi$
$821$			6.53038e21i			0.906494i	−0.891385	+	0.453247i	$0.850266\pi$
$822$	5.40541e21	+	1.11790e22i	0.743515	+	1.53768i
$823$		−	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	$-0.591688\pi$
$827$	−4.32274e21			−0.568156			−0.284078	+	0.958801i	$0.591688\pi$
$828$	−4.26835e21	+	5.38733e21i	−0.555946	+	0.701691i
$829$	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
$834$	−4.10070e20	−	8.48073e20i	−0.0505955	−	0.104638i
$835$		−	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	$-0.611834\pi$
$839$	−5.83443e21			−0.688309			−0.344155	+	0.938913i	$0.611834\pi$
$840$	−5.21524e20	+	2.70156e19i	−0.0609790	+	0.00315878i
$841$	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
$846$	−1.48161e22	−	7.53928e21i	−1.64231	−	0.835704i
$847$			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
$852$	−4.31886e21	−	1.68388e22i	−0.454017	−	1.77017i
$853$	−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	$-0.736302\pi$
$857$		−	1.46480e22i		−	1.47374i	0.676033	−	0.736872i	$-0.263698\pi$
$858$	9.95619e21	−	4.81413e21i	0.992976	−	0.480135i
$859$			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	$-0.570456\pi$
$863$	−4.59858e21			−0.439080			−0.219540	+	0.975604i	$0.570456\pi$
$864$	−6.12351e21	+	8.60891e21i	−0.579626	+	0.814883i
$865$	−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
$870$	−1.64265e21	+	7.94274e20i	−0.147622	+	0.0713799i
$871$			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
$876$	−4.12250e21	−	1.60732e22i	−0.351868	−	1.37190i
$877$	−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	$0.220489\pi$
$881$			1.56165e22i			1.27721i	−0.769533	+	0.638607i	$0.779511\pi$
$882$	9.87453e21	+	5.02473e21i	0.800759	+	0.407473i
$883$			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	$-0.205186\pi$
$887$	2.05677e22			1.59867			0.799334	+	0.600887i	$0.205186\pi$
$888$	9.47912e21	−	4.91029e20i	0.730585	−	0.0378451i
$889$	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
$894$	−1.80380e20	−	3.73046e20i	−0.0132177	−	0.0273358i
$895$		−	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
$900$	8.58352e21	−	1.08338e22i	0.598200	−	0.755023i
$901$	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
$906$	−4.03554e21	−	8.34597e21i	−0.267571	−	0.553369i
$907$			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	$-0.425147\pi$
$911$	7.32434e21			0.465994			0.232997	+	0.972477i	$0.425147\pi$
$912$	−2.15059e22	−	3.19666e21i	−1.35705	−	0.201713i
$913$	−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
$918$	−1.05555e22	+	1.90981e21i	−0.634104	+	0.114728i
$919$		−	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
$924$	4.58948e21	−	1.17712e21i	0.262557	−	0.0673413i
$925$	−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	$-0.785050\pi$
$929$		−	2.27568e22i		−	1.25024i	0.780528	−	0.625121i	$-0.214950\pi$
$930$	2.64315e21	−	1.27805e21i	0.144046	−	0.0696506i
$931$			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
$936$	1.61120e22	+	1.90724e22i	0.836723	+	0.990461i
$937$	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	$0.119585\pi$
$941$			1.47066e22i			0.733823i	−0.930256	+	0.366911i	$0.880415\pi$
$942$	1.43908e22	−	6.95838e21i	0.712364	−	0.344450i
$943$		−	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	$-0.640537\pi$
$947$	−1.79636e22			−0.854612			−0.427306	+	0.904107i	$0.640537\pi$
$948$	1.47002e22	−	3.77035e21i	0.693842	−	0.177958i
$949$	−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	$0.405807\pi$
$953$			4.21626e22i			1.91307i	−0.291616	+	0.956535i	$0.594193\pi$
$954$	9.41986e20	−	1.85118e21i	0.0424064	−	0.0833365i
$955$			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
$960$	3.81256e21	+	2.31757e21i	0.163751	+	0.0995403i
$961$	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
$966$	3.02945e21	+	6.26525e21i	0.124175	+	0.256809i
$967$			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	$-0.294191\pi$
$971$	3.05559e22			1.20490			0.602450	+	0.798156i	$0.294191\pi$
$972$	−7.34987e21	+	2.44765e22i	−0.287596	+	0.957752i
$973$	−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	$-0.927415\pi$
$977$		−	1.20078e22i		−	0.452121i	0.974113	−	0.226061i	$-0.0725847\pi$
$978$	−3.32108e20	−	6.86838e20i	−0.0124090	−	0.0256633i
$979$		−	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	$-0.864934\pi$
$983$	−5.06817e22			−1.82264			−0.911318	+	0.411703i	$0.864934\pi$
$984$	−8.21009e20	−	1.58492e22i	−0.0293011	−	0.565646i
$985$	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
$990$	2.16814e21	−	4.26080e21i	0.0739304	−	0.145287i
$991$		−	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
$996$	−2.47641e21	−	9.65529e21i	−0.0807008	−	0.314645i
$997$	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.11.15	yes	28
3.2	odd	2	inner	12.16.b.a.11.14	yes	28
4.3	odd	2	inner	12.16.b.a.11.13	✓	28
12.11	even	2	inner	12.16.b.a.11.16	yes	28

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

\(f(q)\)	\(=\)	\(q+(35.8416 - 177.436i) q^{2} +(2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} +33476.6i q^{5} +(617322. - 298494. i) q^{6} -694274. i q^{7} +(-3.33920e6 + 4.90246e6i) q^{8} +(-3.84657e6 + 1.38237e7i) q^{9} +O(q^{10})\)	\(q+(35.8416 - 177.436i) q^{2} +(2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} +33476.6i q^{5} +(617322. - 298494. 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} +(-3.08377e7 - 1.20233e8i) 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} +(2.31495e9 + 1.17798e9i) 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} +(-2.24389e10 + 1.16236e9i) 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} +(9.99257e9 + 2.06658e10i) 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} +(2.91987e11 - 3.68534e11i) 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} +(-2.07237e11 - 4.28591e11i) 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} +(-5.98002e11 + 4.02313e12i) 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} +(1.75173e12 + 9.68186e12i) 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} +(4.02500e12 - 1.03234e12i) 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} +(-3.39406e13 + 1.64113e13i) 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} +(-5.49258e13 - 6.50178e13i) 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} +(-1.81086e14 + 8.75609e13i) 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} +(-8.34749e13 + 2.14099e13i) 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} +(-3.94348e13 + 7.74967e13i) 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} +(6.92413e14 + 2.50302e14i) 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

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