LMFDB - Embedded newform 12.16.b.a.11.7

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			11.7
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-127.986 - 128.014i) q^{2} +(-692.213 + 3724.21i) q^{3} +(-7.18349 + 32768.0i) q^{4} +230590. i q^{5} +(565345. - 388034. i) q^{6} +3.60781e6i q^{7} +(4.19568e6 - 4.19292e6i) q^{8} +(-1.33906e7 - 5.15589e6i) q^{9} +O(q^{10})$	\(q+(-127.986 - 128.014i) q^{2} +(-692.213 + 3724.21i) q^{3} +(-7.18349 + 32768.0i) q^{4} +230590. i q^{5} +(565345. - 388034. i) q^{6} +3.60781e6i q^{7} +(4.19568e6 - 4.19292e6i) q^{8} +(-1.33906e7 - 5.15589e6i) q^{9} +(2.95188e7 - 2.95123e7i) q^{10} +5.00101e7 q^{11} +(-1.22030e8 - 2.27092e7i) q^{12} +3.24482e7 q^{13} +(4.61850e8 - 4.61749e8i) q^{14} +(-8.58766e8 - 1.59617e8i) q^{15} +(-1.07374e9 - 470777. i) q^{16} +2.12956e9i q^{17} +(1.05378e9 + 2.37407e9i) q^{18} +2.21302e9i q^{19} +(-7.55598e9 - 1.65644e6i) q^{20} +(-1.34362e10 - 2.49737e9i) q^{21} +(-6.40059e9 - 6.40199e9i) q^{22} -1.70156e9 q^{23} +(1.27110e10 + 1.85280e10i) q^{24} -2.26542e10 q^{25} +(-4.15291e9 - 4.15382e9i) q^{26} +(2.84708e10 - 4.63004e10i) q^{27} +(-1.18221e11 - 2.59167e7i) q^{28} -1.34796e11i q^{29} +(8.94768e10 + 1.30363e11i) q^{30} +1.31549e11i q^{31} +(1.37364e11 + 1.37514e11i) q^{32} +(-3.46176e10 + 1.86248e11i) q^{33} +(2.72614e11 - 2.72554e11i) q^{34} -8.31925e11 q^{35} +(1.69044e11 - 4.38746e11i) q^{36} +6.49189e11 q^{37} +(2.83298e11 - 2.83236e11i) q^{38} +(-2.24610e10 + 1.20844e11i) q^{39} +(9.66847e11 + 9.67483e11i) q^{40} -2.08594e12i q^{41} +(1.39995e12 + 2.03965e12i) q^{42} +9.33060e9i q^{43} +(-3.59247e8 + 1.63873e12i) q^{44} +(1.18890e12 - 3.08774e12i) q^{45} +(2.17776e11 + 2.17824e11i) q^{46} -1.60059e12 q^{47} +(7.45011e11 - 3.99852e12i) q^{48} -8.26871e12 q^{49} +(2.89942e12 + 2.90006e12i) q^{50} +(-7.93093e12 - 1.47411e12i) q^{51} +(-2.33091e8 + 1.06326e12i) q^{52} -1.07105e12i q^{53} +(-9.57096e12 + 2.28115e12i) q^{54} +1.15318e13i q^{55} +(1.51273e13 + 1.51372e13i) q^{56} +(-8.24177e12 - 1.53188e12i) q^{57} +(-1.72558e13 + 1.72520e13i) q^{58} -1.36526e13 q^{59} +(5.23651e12 - 2.81389e13i) q^{60} +2.10077e13 q^{61} +(1.68402e13 - 1.68365e13i) q^{62} +(1.86015e13 - 4.83107e13i) q^{63} +(2.31397e10 - 3.51844e13i) q^{64} +7.48222e12i q^{65} +(2.82729e13 - 1.94056e13i) q^{66} +6.54581e13i q^{67} +(-6.97814e13 - 1.52977e10i) q^{68} +(1.17784e12 - 6.33698e12i) q^{69} +(1.06475e14 + 1.06498e14i) q^{70} +1.13149e14 q^{71} +(-7.78009e13 + 3.45133e13i) q^{72} +7.40026e13 q^{73} +(-8.30871e13 - 8.31053e13i) q^{74} +(1.56815e13 - 8.43692e13i) q^{75} +(-7.25163e13 - 1.58972e10i) q^{76} +1.80427e14i q^{77} +(1.83444e13 - 1.25910e13i) q^{78} -2.01713e13i q^{79} +(1.08557e11 - 2.47594e14i) q^{80} +(1.52725e14 + 1.38081e14i) q^{81} +(-2.67029e14 + 2.66971e14i) q^{82} -1.31804e14 q^{83} +(8.19303e13 - 4.40261e14i) q^{84} -4.91056e14 q^{85} +(1.19445e12 - 1.19419e12i) q^{86} +(5.02009e14 + 9.33075e13i) q^{87} +(2.09826e14 - 2.09688e14i) q^{88} -4.75996e13i q^{89} +(-5.47436e14 + 2.42992e14i) q^{90} +1.17067e14i q^{91} +(1.22232e10 - 5.57568e13i) q^{92} +(-4.89918e14 - 9.10602e13i) q^{93} +(2.04852e14 + 2.04897e14i) q^{94} -5.10301e14 q^{95} +(-6.07217e14 + 4.16382e14i) q^{96} +9.60484e14 q^{97} +(1.05828e15 + 1.05851e15i) q^{98} +(-6.69664e14 - 2.57846e14i) 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 $

$2$	−127.986	−	128.014i	−0.707029	−	0.707184i
$2$	−127.986	−	128.014i	−0.707029	−	0.707184i
$3$	−692.213	+	3724.21i	−0.182738	+	0.983162i
$3$	−692.213	+	3724.21i	−0.182738	+	0.983162i
$4$	−7.18349	+	32768.0i	−0.000219223	+	1.00000i
$5$			230590.i			1.31998i	0.751277	+	0.659988i	$0.229438\pi$
$5$			230590.i			1.31998i	−0.751277	+	0.659988i	$0.770562\pi$
$6$	565345.	−	388034.i	0.824478	−	0.565894i
$7$			3.60781e6i			1.65580i	0.560876	+	0.827900i	$0.310465\pi$
$7$			3.60781e6i			1.65580i	−0.560876	+	0.827900i	$0.689535\pi$
$8$	4.19568e6	−	4.19292e6i	0.707339	−	0.706874i
$9$	−1.33906e7	−	5.15589e6i	−0.933213	−	0.359323i
$10$	2.95188e7	−	2.95123e7i	0.933466	−	0.933261i
$11$	5.00101e7			0.773771			0.386885	−	0.922128i	$-0.373551\pi$
$11$	5.00101e7			0.773771			0.386885	+	0.922128i	$0.373551\pi$
$12$	−1.22030e8	−	2.27092e7i	−0.983121	−	0.182954i
$13$	3.24482e7			0.143422			0.0717108	−	0.997425i	$-0.477154\pi$
$13$	3.24482e7			0.143422			0.0717108	+	0.997425i	$0.477154\pi$
$14$	4.61850e8	−	4.61749e8i	1.17096	−	1.17070i
$15$	−8.58766e8	−	1.59617e8i	−1.29775	−	0.241210i
$16$	−1.07374e9	−	470777.i	−1.00000	−	0.000438446i
$17$			2.12956e9i			1.25870i	0.777121	+	0.629351i	$0.216679\pi$
$17$			2.12956e9i			1.25870i	−0.777121	+	0.629351i	$0.783321\pi$
$18$	1.05378e9	+	2.37407e9i	0.405702	+	0.914006i
$19$			2.21302e9i			0.567981i	0.958827	+	0.283991i	$0.0916585\pi$
$19$			2.21302e9i			0.567981i	−0.958827	+	0.283991i	$0.908342\pi$
$20$	−7.55598e9	−	1.65644e6i	−1.31998	−	0.000289369i
$21$	−1.34362e10	−	2.49737e9i	−1.62792	−	0.302578i
$22$	−6.40059e9	−	6.40199e9i	−0.547079	−	0.547198i
$23$	−1.70156e9			−0.104205			−0.0521026	−	0.998642i	$-0.516592\pi$
$23$	−1.70156e9			−0.104205			−0.0521026	+	0.998642i	$0.516592\pi$
$24$	1.27110e10	+	1.85280e10i	0.565713	+	0.824602i
$25$	−2.26542e10			−0.742334
$26$	−4.15291e9	−	4.15382e9i	−0.101403	−	0.101426i
$27$	2.84708e10	−	4.63004e10i	0.523806	−	0.851837i
$28$	−1.18221e11	−	2.59167e7i	−1.65580	−	0.000362989i
$29$		−	1.34796e11i		−	1.45108i	−0.688179	−	0.725541i	$-0.741589\pi$
$29$		−	1.34796e11i		−	1.45108i	0.688179	−	0.725541i	$-0.258411\pi$
$30$	8.94768e10	+	1.30363e11i	0.746966	+	1.08829i
$31$			1.31549e11i			0.858769i	0.903122	+	0.429385i	$0.141269\pi$
$31$			1.31549e11i			0.858769i	−0.903122	+	0.429385i	$0.858731\pi$
$32$	1.37364e11	+	1.37514e11i	0.706719	+	0.707494i
$33$	−3.46176e10	+	1.86248e11i	−0.141398	+	0.760742i
$34$	2.72614e11	−	2.72554e11i	0.890134	−	0.889939i
$35$	−8.31925e11			−2.18561
$36$	1.69044e11	−	4.38746e11i	0.359527	−	0.933134i
$37$	6.49189e11			1.12424			0.562119	−	0.827056i	$-0.309986\pi$
$37$	6.49189e11			1.12424			0.562119	+	0.827056i	$0.309986\pi$
$38$	2.83298e11	−	2.83236e11i	0.401667	−	0.401579i
$39$	−2.24610e10	+	1.20844e11i	−0.0262087	+	0.141007i
$40$	9.66847e11	+	9.67483e11i	0.933056	+	0.933670i
$41$		−	2.08594e12i		−	1.67272i	−0.548184	−	0.836358i	$-0.684681\pi$
$41$		−	2.08594e12i		−	1.67272i	0.548184	−	0.836358i	$-0.315319\pi$
$42$	1.39995e12	+	2.03965e12i	0.937008	+	1.36517i
$43$			9.33060e9i			0.00523475i	0.999997	+	0.00261738i	$0.000833138\pi$
$43$			9.33060e9i			0.00523475i	−0.999997	+	0.00261738i	$0.999167\pi$
$44$	−3.59247e8	+	1.63873e12i	−0.000169628	+	0.773771i
$45$	1.18890e12	−	3.08774e12i	0.474297	−	1.23182i
$46$	2.17776e11	+	2.17824e11i	0.0736761	+	0.0736923i
$47$	−1.60059e12			−0.460834			−0.230417	−	0.973092i	$-0.574009\pi$
$47$	−1.60059e12			−0.460834			−0.230417	+	0.973092i	$0.574009\pi$
$48$	7.45011e11	−	3.99852e12i	0.183170	−	0.983081i
$49$	−8.26871e12			−1.74167
$50$	2.89942e12	+	2.90006e12i	0.524852	+	0.524967i
$51$	−7.93093e12	−	1.47411e12i	−1.23751	−	0.230013i
$52$	−2.33091e8	+	1.06326e12i	−3.14413e−5	+	0.143422i
$53$		−	1.07105e12i		−	0.125239i	−0.998037	−	0.0626195i	$-0.980055\pi$
$53$		−	1.07105e12i		−	0.125239i	0.998037	−	0.0626195i	$-0.0199455\pi$
$54$	−9.57096e12	+	2.28115e12i	−0.972752	+	0.231846i
$55$			1.15318e13i			1.02136i
$56$	1.51273e13	+	1.51372e13i	1.17044	+	1.17121i
$57$	−8.24177e12	−	1.53188e12i	−0.558417	−	0.103792i
$58$	−1.72558e13	+	1.72520e13i	−1.02618	+	1.02596i
$59$	−1.36526e13			−0.714208			−0.357104	−	0.934065i	$-0.616236\pi$
$59$	−1.36526e13			−0.714208			−0.357104	+	0.934065i	$0.616236\pi$
$60$	5.23651e12	−	2.81389e13i	0.241495	−	1.29770i
$61$	2.10077e13			0.855864			0.427932	−	0.903811i	$-0.359242\pi$
$61$	2.10077e13			0.855864			0.427932	+	0.903811i	$0.359242\pi$
$62$	1.68402e13	−	1.68365e13i	0.607308	−	0.607175i
$63$	1.86015e13	−	4.83107e13i	0.594967	−	1.54521i
$64$	2.31397e10	−	3.51844e13i	0.000657669	−	1.00000i
$65$			7.48222e12i			0.189313i
$66$	2.82729e13	−	1.94056e13i	0.637957	−	0.437872i
$67$			6.54581e13i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$67$			6.54581e13i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$68$	−6.97814e13	−	1.52977e10i	−1.25870	−	0.000275936i
$69$	1.17784e12	−	6.33698e12i	0.0190423	−	0.102451i
$70$	1.06475e14	+	1.06498e14i	1.54529	+	1.54563i
$71$	1.13149e14			1.47643			0.738217	−	0.674563i	$-0.235668\pi$
$71$	1.13149e14			1.47643			0.738217	+	0.674563i	$0.235668\pi$
$72$	−7.78009e13	+	3.45133e13i	−0.914095	+	0.405501i
$73$	7.40026e13			0.784017			0.392009	−	0.919962i	$-0.371780\pi$
$73$	7.40026e13			0.784017			0.392009	+	0.919962i	$0.371780\pi$
$74$	−8.30871e13	−	8.31053e13i	−0.794869	−	0.795043i
$75$	1.56815e13	−	8.43692e13i	0.135653	−	0.729834i
$76$	−7.25163e13	−	1.58972e10i	−0.567981	−	0.000124514i
$77$			1.80427e14i			1.28121i
$78$	1.83444e13	−	1.25910e13i	0.118248	−	0.0811615i
$79$		−	2.01713e13i		−	0.118176i	−0.998253	−	0.0590882i	$-0.981181\pi$
$79$		−	2.01713e13i		−	0.118176i	0.998253	−	0.0590882i	$-0.0188193\pi$
$80$	1.08557e11	−	2.47594e14i	0.000578737	−	1.31997i
$81$	1.52725e14	+	1.38081e14i	0.741774	+	0.670650i
$82$	−2.67029e14	+	2.66971e14i	−1.18292	+	1.18266i
$83$	−1.31804e14			−0.533141			−0.266570	−	0.963815i	$-0.585890\pi$
$83$	−1.31804e14			−0.533141			−0.266570	+	0.963815i	$0.585890\pi$
$84$	8.19303e13	−	4.40261e14i	0.302935	−	1.62785i
$85$	−4.91056e14			−1.66146
$86$	1.19445e12	−	1.19419e12i	0.00370194	−	0.00370112i
$87$	5.02009e14	+	9.33075e13i	1.42665	+	0.265169i
$88$	2.09826e14	−	2.09688e14i	0.547318	−	0.546959i
$89$		−	4.75996e13i		−	0.114072i	−0.998372	−	0.0570359i	$-0.981835\pi$
$89$		−	4.75996e13i		−	0.114072i	0.998372	−	0.0570359i	$-0.0181649\pi$
$90$	−5.47436e14	+	2.42992e14i	−1.20646	+	0.535516i
$91$			1.17067e14i			0.237478i
$92$	1.22232e10	−	5.57568e13i	2.28442e−5	−	0.104205i
$93$	−4.89918e14	−	9.10602e13i	−0.844309	−	0.156930i
$94$	2.04852e14	+	2.04897e14i	0.325823	+	0.325895i
$95$	−5.10301e14			−0.749721
$96$	−6.07217e14	+	4.16382e14i	−0.824726	+	0.565533i
$97$	9.60484e14			1.20699			0.603493	−	0.797368i	$-0.293775\pi$
$97$	9.60484e14			1.20699			0.603493	+	0.797368i	$0.293775\pi$
$98$	1.05828e15	+	1.05851e15i	1.23141	+	1.23168i
$99$	−6.69664e14	−	2.57846e14i	−0.722093	−	0.278034i
$100$	1.62737e11	−	7.42334e14i	0.000162737	−	0.742334i
$101$		−	3.73790e12i		−	0.00346911i	−0.999998	−	0.00173455i	$-0.999448\pi$
$101$		−	3.73790e12i		−	0.00346911i	0.999998	−	0.00173455i	$-0.000552126\pi$
$102$	8.26341e14	+	1.20394e15i	0.712292	+	1.03777i
$103$		−	4.51210e14i		−	0.361492i	−0.983530	−	0.180746i	$-0.942149\pi$
$103$		−	4.51210e14i		−	0.361492i	0.983530	−	0.180746i	$-0.0578513\pi$
$104$	1.36142e14	−	1.36053e14i	0.101448	−	0.101381i
$105$	5.75869e14	−	3.09826e15i	0.399396	−	2.14881i
$106$	−1.37109e14	+	1.37079e14i	−0.0885670	+	0.0885476i
$107$	−2.28317e14			−0.137455			−0.0687275	−	0.997635i	$-0.521894\pi$
$107$	−2.28317e14			−0.137455			−0.0687275	+	0.997635i	$0.521894\pi$
$108$	1.51697e15	+	9.33262e14i	0.851722	+	0.523993i
$109$	−1.64664e13			−0.00862781			−0.00431391	−	0.999991i	$-0.501373\pi$
$109$	−1.64664e13			−0.00862781			−0.00431391	+	0.999991i	$0.501373\pi$
$110$	1.47624e15	−	1.47591e15i	0.722288	−	0.722130i
$111$	−4.49377e14	+	2.41772e15i	−0.205442	+	1.10531i
$112$	1.69847e12	−	3.87385e15i	0.000725978	−	1.65580i
$113$			1.34829e15i			0.539131i	0.962982	+	0.269566i	$0.0868801\pi$
$113$			1.34829e15i			0.539131i	−0.962982	+	0.269566i	$0.913120\pi$
$114$	8.58728e14	+	1.25112e15i	0.321417	+	0.468288i
$115$		−	3.92364e14i		−	0.137548i
$116$	4.41700e15	+	9.68307e11i	1.45108	+	0.000318110i
$117$	−4.34500e14	−	1.67299e14i	−0.133843	−	0.0515347i
$118$	1.74734e15	+	1.74772e15i	0.504966	+	0.505077i
$119$	−7.68304e15			−2.08416
$120$	−4.27238e15	+	2.93104e15i	−1.08845	+	0.746728i
$121$	−1.67624e15			−0.401279
$122$	−2.68869e15	−	2.68928e15i	−0.605121	−	0.605254i
$123$	7.76847e15	+	1.44391e15i	1.64455	+	0.305669i
$124$	−4.31061e15	−	9.44985e11i	−0.858769	−	0.000188262i
$125$			1.81321e15i			0.340113i
$126$	−8.56517e15	+	3.80184e15i	−1.51341	+	0.671761i
$127$		−	9.11858e15i		−	1.51845i	−0.650831	−	0.759223i	$-0.725579\pi$
$127$		−	9.11858e15i		−	1.51845i	0.650831	−	0.759223i	$-0.274421\pi$
$128$	−4.50705e15	+	4.50014e15i	−0.707649	+	0.706564i
$129$	−3.47491e13	−	6.45876e12i	−0.00514661	−	0.000956591i
$130$	9.57830e14	−	9.57620e14i	0.133879	−	0.133850i
$131$	3.30193e15			0.435745			0.217873	−	0.975977i	$-0.430088\pi$
$131$	3.30193e15			0.435745			0.217873	+	0.975977i	$0.430088\pi$
$132$	−6.10273e15	−	1.13569e15i	−0.760711	−	0.141564i
$133$	−7.98416e15			−0.940463
$134$	8.37955e15	−	8.37772e15i	0.933114	−	0.932910i
$135$	1.06764e16	+	6.56508e15i	1.12440	+	0.691411i
$136$	8.92908e15	+	8.93496e15i	0.889744	+	0.890329i
$137$			1.08435e16i			1.02274i	0.859361	+	0.511370i	$0.170862\pi$
$137$			1.08435e16i			1.02274i	−0.859361	+	0.511370i	$0.829138\pi$
$138$	−9.61970e14	+	6.60264e14i	−0.0859149	+	0.0589691i
$139$			9.56396e15i			0.809146i	0.914506	+	0.404573i	$0.132580\pi$
$139$			9.56396e15i			0.809146i	−0.914506	+	0.404573i	$0.867420\pi$
$140$	5.97613e12	−	2.72605e16i	0.000479137	−	2.18561i
$141$	1.10795e15	−	5.96092e15i	0.0842122	−	0.453075i
$142$	−1.44815e16	−	1.44847e16i	−1.04388	−	1.04411i
$143$	1.62273e15			0.110976
$144$	1.43756e16	+	5.54240e15i	0.933056	+	0.359732i
$145$	3.10826e16			1.91539
$146$	−9.47130e15	−	9.47337e15i	−0.554323	−	0.554445i
$147$	5.72370e15	−	3.07944e16i	0.318271	−	1.71235i
$148$	−4.66344e12	+	2.12726e16i	−0.000246459	+	1.12424i
$149$			3.88677e16i			1.95296i	0.215619	+	0.976478i	$0.430823\pi$
$149$			3.88677e16i			1.95296i	−0.215619	+	0.976478i	$0.569177\pi$
$150$	−1.28075e16	+	8.79061e15i	−0.612038	+	0.420083i
$151$			9.17970e15i			0.417351i	0.977985	+	0.208675i	$0.0669152\pi$
$151$			9.17970e15i			0.417351i	−0.977985	+	0.208675i	$0.933085\pi$
$152$	9.27904e15	+	9.28514e15i	0.401491	+	0.401755i
$153$	1.09798e16	−	2.85161e16i	0.452281	−	1.17464i
$154$	2.30971e16	−	2.30921e16i	0.906051	−	0.905853i
$155$	−3.03340e16			−1.13355
$156$	−3.95965e15	−	7.36871e14i	−0.141001	−	0.0262396i
$157$	−1.09692e16			−0.372328			−0.186164	−	0.982519i	$-0.559606\pi$
$157$	−1.09692e16			−0.372328			−0.186164	+	0.982519i	$0.559606\pi$
$158$	−2.58221e15	+	2.58164e15i	−0.0835724	+	0.0835541i
$159$	3.98881e15	+	7.41392e14i	0.123130	+	0.0228860i
$160$	−3.17094e16	+	3.16747e16i	−0.933875	+	0.932852i
$161$		−	6.13891e15i		−	0.172543i
$162$	−1.87033e15	−	3.72233e16i	−0.0501830	−	0.998740i
$163$			5.22199e16i			1.33792i	0.743300	+	0.668959i	$0.233260\pi$
$163$			5.22199e16i			1.33792i	−0.743300	+	0.668959i	$0.766740\pi$
$164$	6.83519e16	+	1.49843e13i	1.67272	+	0.000366697i
$165$	−4.29470e16	−	7.98248e15i	−1.00416	−	0.186641i
$166$	1.68690e16	+	1.68727e16i	0.376946	+	0.377029i
$167$	1.59105e16			0.339867			0.169934	−	0.985456i	$-0.445645\pi$
$167$	1.59105e16			0.339867			0.169934	+	0.985456i	$0.445645\pi$
$168$	−6.68455e16	+	4.58589e16i	−1.36538	+	0.936708i
$169$	−5.01330e16			−0.979430
$170$	6.28482e16	+	6.28620e16i	1.17470	+	1.17496i
$171$	1.14101e16	−	2.96337e16i	0.204089	−	0.530048i
$172$	−3.05745e14	−	6.70263e10i	−0.00523475	−	1.14758e-6i
$173$		−	1.02199e17i		−	1.67533i	−0.546181	−	0.837667i	$-0.683919\pi$
$173$		−	1.02199e17i		−	1.67533i	0.546181	−	0.837667i	$-0.316081\pi$
$174$	−5.23054e16	−	7.62062e16i	−0.821159	−	1.19639i
$175$		−	8.17321e16i		−	1.22916i
$176$	−5.36979e16	−	2.35436e13i	−0.773771	−	0.000339256i
$177$	9.45049e15	−	5.08451e16i	0.130513	−	0.702182i
$178$	−6.09342e15	+	6.09208e15i	−0.0806698	+	0.0806521i
$179$	−1.49145e17			−1.89327			−0.946633	−	0.322313i	$-0.895540\pi$
$179$	−1.49145e17			−1.89327			−0.946633	+	0.322313i	$0.895540\pi$
$180$	1.01170e17	+	3.89800e16i	1.23171	+	0.474567i
$181$	3.50317e15			0.0409140			0.0204570	−	0.999791i	$-0.493488\pi$
$181$	3.50317e15			0.0409140			0.0204570	+	0.999791i	$0.493488\pi$
$182$	1.49862e16	−	1.49829e16i	0.167940	−	0.167904i
$183$	−1.45418e16	+	7.82371e16i	−0.156399	+	0.841453i
$184$	−7.13922e15	+	7.13453e15i	−0.0737084	+	0.0736600i
$185$			1.49697e17i			1.48397i
$186$	5.10456e16	+	7.43708e16i	0.485972	+	0.708036i
$187$			1.06499e17i			0.973947i
$188$	1.14978e13	−	5.24480e16i	0.000101025	−	0.460834i
$189$	1.67043e17	+	1.02717e17i	1.41047	+	0.867319i
$190$	6.53114e16	+	6.53257e16i	0.530075	+	0.530191i
$191$	−1.66729e15			−0.0130095			−0.00650477	−	0.999979i	$-0.502071\pi$
$191$	−1.66729e15			−0.0130095			−0.00650477	+	0.999979i	$0.502071\pi$
$192$	1.31018e17	+	2.44412e16i	0.983041	+	0.183385i
$193$	−3.73696e16			−0.269673			−0.134837	−	0.990868i	$-0.543051\pi$
$193$	−3.73696e16			−0.269673			−0.134837	+	0.990868i	$0.543051\pi$
$194$	−1.22928e17	−	1.22955e17i	−0.853374	−	0.853561i
$195$	−2.78654e16	−	5.17929e15i	−0.186125	−	0.0345948i
$196$	5.93982e13	−	2.70949e17i	0.000381815	−	1.74167i
$197$		−	2.22270e17i		−	1.37525i	−0.726064	−	0.687627i	$-0.758652\pi$
$197$		−	2.22270e17i		−	1.37525i	0.726064	−	0.687627i	$-0.241348\pi$
$198$	5.26997e16	+	1.18727e17i	0.313920	+	0.707231i
$199$		−	1.65557e17i		−	0.949618i	−0.880089	−	0.474809i	$-0.842517\pi$
$199$		−	1.65557e17i		−	0.949618i	0.880089	−	0.474809i	$-0.157483\pi$
$200$	−9.50500e16	+	9.49875e16i	−0.525082	+	0.524737i
$201$	−2.43780e17	−	4.53109e16i	−1.29726	−	0.241119i
$202$	−4.78504e14	+	4.78399e14i	−0.00245330	+	0.00245276i
$203$	4.86318e17			2.40270
$204$	4.83605e16	−	2.59870e17i	0.230285	−	1.23746i
$205$	4.80996e17			2.20794
$206$	−5.77612e16	+	5.77485e16i	−0.255642	+	0.255586i
$207$	2.27849e16	+	8.77307e15i	0.0972457	+	0.0374433i
$208$	−3.48409e16	−	1.52759e13i	−0.143422	−	6.28826e-5i
$209$			1.10673e17i			0.439487i
$210$	−4.70324e17	+	3.22815e17i	−1.80199	+	1.23683i
$211$		−	2.09971e17i		−	0.776321i	−0.921592	−	0.388161i	$-0.873111\pi$
$211$		−	2.09971e17i		−	0.776321i	0.921592	−	0.388161i	$-0.126889\pi$
$212$	3.50961e16	+	7.69386e12i	0.125239	+	2.74552e-5i
$213$	−7.83233e16	+	4.21392e17i	−0.269801	+	1.45157i
$214$	2.92214e16	+	2.92278e16i	0.0971848	+	0.0972061i
$215$	−2.15155e15			−0.00690974
$216$	−7.46799e16	−	3.13638e17i	−0.231633	−	0.972803i
$217$	−4.74605e17			−1.42195
$218$	2.10747e15	+	2.10793e15i	0.00610012	+	0.00610145i
$219$	−5.12255e16	+	2.75601e17i	−0.143270	+	0.770816i
$220$	−3.77875e17	−	8.28388e13i	−1.02136	−	0.000223905i
$221$			6.91003e16i			0.180525i
$222$	3.67016e17	−	2.51907e17i	0.926909	−	0.636200i
$223$			1.89473e17i			0.462660i	0.972875	+	0.231330i	$0.0743076\pi$
$223$			1.89473e17i			0.462660i	−0.972875	+	0.231330i	$0.925692\pi$
$224$	−4.96125e17	+	4.95581e17i	−1.17147	+	1.17019i
$225$	3.03354e17	+	1.16803e17i	0.692756	+	0.266738i
$226$	1.72600e17	−	1.72562e17i	0.381265	−	0.381182i
$227$	2.88628e17			0.616801			0.308400	−	0.951257i	$-0.400206\pi$
$227$	2.88628e17			0.616801			0.308400	+	0.951257i	$0.400206\pi$
$228$	5.02559e16	−	2.70055e17i	0.103914	−	0.558395i
$229$	−6.29239e17			−1.25907			−0.629535	−	0.776973i	$-0.716754\pi$
$229$	−6.29239e17			−1.25907			−0.629535	+	0.776973i	$0.716754\pi$
$230$	−5.02281e16	+	5.02171e16i	−0.0972720	+	0.0972506i
$231$	−6.71947e17	−	1.24894e17i	−1.25964	−	0.234126i
$232$	−5.65190e17	−	5.65561e17i	−1.02573	−	1.02641i
$233$			1.93811e17i			0.340572i	0.985395	+	0.170286i	$0.0544692\pi$
$233$			1.93811e17i			0.340572i	−0.985395	+	0.170286i	$0.945531\pi$
$234$	3.41933e16	+	7.70340e16i	0.0581864	+	0.131088i
$235$		−	3.69079e17i		−	0.608290i
$236$	9.80732e13	−	4.47368e17i	0.000156571	−	0.714208i
$237$	7.51221e16	+	1.39628e16i	0.116186	+	0.0215954i
$238$	9.83321e17	+	9.83537e17i	1.47356	+	1.47388i
$239$	3.34883e17			0.486305			0.243153	−	0.969988i	$-0.421818\pi$
$239$	3.34883e17			0.486305			0.243153	+	0.969988i	$0.421818\pi$
$240$	9.22018e17	+	1.71792e17i	1.29764	+	0.241779i
$241$	1.03195e18			1.40777			0.703887	−	0.710312i	$-0.251446\pi$
$241$	1.03195e18			1.40777			0.703887	+	0.710312i	$0.251446\pi$
$242$	2.14535e17	+	2.14582e17i	0.283716	+	0.283778i
$243$	−6.19960e17	+	4.73198e17i	−0.794908	+	0.606730i
$244$	−1.50909e14	+	6.88380e17i	−0.000187625	+	0.855864i
$245$		−	1.90668e18i		−	2.29897i
$246$	−8.09414e17	−	1.17927e18i	−0.946580	−	1.37912i
$247$			7.18085e16i			0.0814608i
$248$	5.51577e17	+	5.51940e17i	0.607042	+	0.607441i
$249$	9.12362e16	−	4.90865e17i	0.0974254	−	0.524164i
$250$	2.32116e17	−	2.32065e17i	0.240522	−	0.240470i
$251$	1.25407e17			0.126115			0.0630577	−	0.998010i	$-0.479915\pi$
$251$	1.25407e17			0.126115			0.0630577	+	0.998010i	$0.479915\pi$
$252$	1.58291e18	+	6.09880e17i	1.54508	+	0.595306i
$253$	−8.50953e16			−0.0806309
$254$	−1.16731e18	+	1.16705e18i	−1.07382	+	1.07359i
$255$	3.39915e17	−	1.82879e18i	0.303612	−	1.63348i
$256$	1.15292e18	+	1.01099e15i	1.00000	+	0.000876891i
$257$		−	1.24842e18i		−	1.05163i	−0.850599	−	0.525815i	$-0.823761\pi$
$257$		−	1.24842e18i		−	1.05163i	0.850599	−	0.525815i	$-0.176239\pi$
$258$	3.62059e15	+	5.27501e15i	0.00296232	+	0.00431594i
$259$			2.34215e18i			1.86151i
$260$	−2.45178e17	−	5.37485e13i	−0.189313	−	4.15017e-5i
$261$	−6.94994e17	+	1.80500e18i	−0.521407	+	1.35417i
$262$	−4.22600e17	−	4.22693e17i	−0.308085	−	0.308152i
$263$	−2.36889e18			−1.67833			−0.839165	−	0.543877i	$-0.816956\pi$
$263$	−2.36889e18			−1.67833			−0.839165	+	0.543877i	$0.816956\pi$
$264$	6.35680e17	+	9.26587e17i	0.437732	+	0.638053i
$265$	2.46973e17			0.165312
$266$	1.02186e18	+	1.02208e18i	0.664935	+	0.665081i
$267$	1.77271e17	+	3.29490e16i	0.112151	+	0.0208453i
$268$	−2.14493e18	−	4.70218e14i	−1.31948	−	0.000289260i
$269$			7.72361e17i			0.462039i	0.972949	+	0.231019i	$0.0742061\pi$
$269$			7.72361e17i			0.462039i	−0.972949	+	0.231019i	$0.925794\pi$
$270$	−5.26010e17	−	2.20697e18i	−0.306031	−	1.28401i
$271$			1.73967e17i			0.0984459i	0.998788	+	0.0492230i	$0.0156745\pi$
$271$			1.73967e17i			0.0984459i	−0.998788	+	0.0492230i	$0.984326\pi$
$272$	1.00255e15	−	2.28660e18i	0.000551873	−	1.25870i
$273$	−4.35981e17	−	8.10350e16i	−0.233479	−	0.0433963i
$274$	1.38812e18	−	1.38782e18i	0.723266	−	0.723107i
$275$	−1.13294e18			−0.574396
$276$	2.07642e17	+	3.86411e16i	0.102446	+	0.0190648i
$277$	−6.52779e17			−0.313450			−0.156725	−	0.987642i	$-0.550094\pi$
$277$	−6.52779e17			−0.313450			−0.156725	+	0.987642i	$0.550094\pi$
$278$	1.22432e18	−	1.22405e18i	0.572215	−	0.572090i
$279$	6.78255e17	−	1.76153e18i	0.308575	−	0.801415i
$280$	−3.49049e18	+	3.48820e18i	−1.54597	+	1.54495i
$281$			1.74081e18i			0.750681i	0.926887	+	0.375340i	$0.122474\pi$
$281$			1.74081e18i			0.750681i	−0.926887	+	0.375340i	$0.877526\pi$
$282$	−9.04882e17	+	6.21081e17i	−0.379948	+	0.260783i
$283$		−	5.03165e17i		−	0.205737i	−0.994695	−	0.102868i	$-0.967198\pi$
$283$		−	5.03165e17i		−	0.205737i	0.994695	−	0.102868i	$-0.0328020\pi$
$284$	−8.12807e14	+	3.70768e18i	−0.000323668	+	1.47643i
$285$	3.53237e17	−	1.90047e18i	0.137003	−	0.737097i
$286$	−2.07687e17	−	2.07733e17i	−0.0784629	−	0.0784801i
$287$	7.52565e18			2.76968
$288$	−1.13037e18	−	2.54963e18i	−0.405301	−	0.914183i
$289$	−1.67260e18			−0.584331
$290$	−3.97814e18	−	3.97901e18i	−1.35424	−	1.35454i
$291$	−6.64859e17	+	3.57705e18i	−0.220563	+	1.18666i
$292$	−5.31597e14	+	2.42492e18i	−0.000171875	+	0.784017i
$293$			4.05786e18i			1.27876i	0.768890	+	0.639381i	$0.220809\pi$
$293$			4.05786e18i			1.27876i	−0.768890	+	0.639381i	$0.779191\pi$
$294$	−4.67467e18	+	3.20854e18i	−1.43597	+	0.985603i
$295$		−	3.14815e18i		−	0.942737i
$296$	2.72379e18	−	2.72200e18i	0.795218	−	0.794695i
$297$	1.42382e18	−	2.31549e18i	0.405306	−	0.659127i
$298$	4.97562e18	−	4.97453e18i	1.38110	−	1.38080i
$299$	−5.52126e16			−0.0149453
$300$	2.76450e18	+	5.14459e17i	0.729805	+	0.135813i
$301$	−3.36630e16			−0.00866771
$302$	1.17513e18	−	1.17487e18i	0.295144	−	0.295079i
$303$	1.39207e16	+	2.58742e15i	0.00341069	+	0.000633939i
$304$	1.04184e15	−	2.37622e18i	0.000249029	−	0.567981i
$305$			4.84417e18i			1.12972i
$306$	−5.05571e18	+	2.24409e18i	−1.15046	+	0.510657i
$307$		−	6.68813e17i		−	0.148514i	−0.997239	−	0.0742569i	$-0.976342\pi$
$307$		−	6.68813e17i		−	0.148514i	0.997239	−	0.0742569i	$-0.0236585\pi$
$308$	−5.91222e18	−	1.29609e15i	−1.28121	−	0.000280870i
$309$	1.68040e18	+	3.12333e17i	0.355405	+	0.0660586i
$310$	3.88233e18	+	3.88318e18i	0.801456	+	0.801631i
$311$	−7.17446e18			−1.44573			−0.722863	−	0.690991i	$-0.757174\pi$
$311$	−7.17446e18			−1.44573			−0.722863	+	0.690991i	$0.757174\pi$
$312$	4.12450e17	+	6.01200e17i	0.0811356	+	0.118266i
$313$	7.65538e18			1.47023			0.735114	−	0.677944i	$-0.237129\pi$
$313$	7.65538e18			1.47023			0.735114	+	0.677944i	$0.237129\pi$
$314$	1.40390e18	+	1.40421e18i	0.263247	+	0.263305i
$315$	1.11400e19	+	4.28931e18i	2.03964	+	0.785342i
$316$	6.60973e17	+	1.44900e14i	0.118176	+	2.59069e-5i
$317$		−	2.51712e18i		−	0.439500i	−0.975556	−	0.219750i	$-0.929476\pi$
$317$		−	2.51712e18i		−	0.439500i	0.975556	−	0.219750i	$-0.0705242\pi$
$318$	−4.15603e17	−	6.05511e17i	−0.0708720	−	0.103257i
$319$		−	6.74116e18i		−	1.12281i
$320$	8.11317e18	+	5.33578e15i	1.31997	+	0.000868106i
$321$	1.58044e17	−	8.50303e17i	0.0251183	−	0.135141i
$322$	−7.85867e17	+	7.85694e17i	−0.122020	+	0.121993i
$323$	−4.71277e18			−0.714919
$324$	−4.52573e18	+	5.00349e18i	−0.670812	+	0.741627i
$325$	−7.35088e17			−0.106467
$326$	6.68488e18	−	6.68342e18i	0.946154	−	0.945947i
$327$	1.13983e16	−	6.13245e16i	0.00157663	−	0.00848253i
$328$	−8.74617e18	−	8.75193e18i	−1.18240	−	1.18318i
$329$		−	5.77460e18i		−	0.763050i
$330$	4.47474e18	+	6.51946e18i	0.577981	+	0.842087i
$331$			1.13410e19i			1.43200i	0.698102	+	0.715998i	$0.254028\pi$
$331$			1.13410e19i			1.43200i	−0.698102	+	0.715998i	$0.745972\pi$
$332$	9.46811e14	−	4.31894e18i	0.000116877	−	0.533141i
$333$	−8.69302e18	−	3.34715e18i	−1.04915	−	0.403964i
$334$	−2.03632e18	−	2.03676e18i	−0.240296	−	0.240349i
$335$	−1.50940e19			−1.74168
$336$	1.44259e19	+	2.68785e18i	1.62779	+	0.303292i
$337$	−1.08624e19			−1.19867			−0.599336	−	0.800497i	$-0.704569\pi$
$337$	−1.08624e19			−1.19867			−0.599336	+	0.800497i	$0.704569\pi$
$338$	6.41632e18	+	6.41773e18i	0.692486	+	0.692638i
$339$	−5.02131e18	−	9.33302e17i	−0.530053	−	0.0985201i
$340$	3.52749e15	−	1.60909e19i	0.000364229	−	1.66146i
$341$			6.57880e18i			0.664490i
$342$	−5.25386e18	+	2.33204e18i	−0.519138	+	0.230431i
$343$		−	1.27036e19i		−	1.22806i
$344$	3.91225e16	+	3.91483e16i	0.00370031	+	0.00370275i
$345$	1.46125e18	+	2.71599e17i	0.135232	+	0.0251354i
$346$	−1.30829e19	+	1.30801e19i	−1.18477	+	1.18451i
$347$	1.19354e19			1.05771			0.528855	−	0.848712i	$-0.322622\pi$
$347$	1.19354e19			1.05771			0.528855	+	0.848712i	$0.322622\pi$
$348$	−3.06111e18	+	1.64492e19i	−0.265481	+	1.42659i
$349$	−6.22554e18			−0.528429			−0.264214	−	0.964464i	$-0.585113\pi$
$349$	−6.22554e18			−0.528429			−0.264214	+	0.964464i	$0.585113\pi$
$350$	−1.04629e19	+	1.04606e19i	−0.869240	+	0.869050i
$351$	9.23824e17	−	1.50236e18i	0.0751252	−	0.122172i
$352$	6.86956e18	+	6.87710e18i	0.546839	+	0.547438i
$353$		−	1.13953e19i		−	0.888002i	−0.896026	−	0.444001i	$-0.853559\pi$
$353$		−	1.13953e19i		−	0.888002i	0.896026	−	0.444001i	$-0.146441\pi$
$354$	−7.71841e18	+	5.29766e18i	−0.588849	+	0.404166i
$355$			2.60911e19i			1.94886i
$356$	1.55974e18	+	3.41931e14i	0.114072	+	2.50071e-5i
$357$	5.31830e18	−	2.86133e19i	0.380856	−	2.04907i
$358$	1.90885e19	+	1.90927e19i	1.33859	+	1.33889i
$359$	−1.11358e19			−0.764742			−0.382371	−	0.924009i	$-0.624892\pi$
$359$	−1.11358e19			−0.764742			−0.382371	+	0.924009i	$0.624892\pi$
$360$	−7.95842e18	−	1.79401e19i	−0.535251	−	1.20658i
$361$	1.02837e19			0.677397
$362$	−4.48357e17	−	4.48455e17i	−0.0289274	−	0.0289338i
$363$	1.16032e18	−	6.24268e18i	0.0733291	−	0.394522i
$364$	−3.83604e18	−	8.40948e14i	−0.237478	−	5.20605e-5i
$365$			1.70643e19i			1.03488i
$366$	1.18766e19	−	8.15170e18i	0.705641	−	0.484329i
$367$		−	3.20105e19i		−	1.86336i	−0.363280	−	0.931680i	$-0.618343\pi$
$367$		−	3.20105e19i		−	1.86336i	0.363280	−	0.931680i	$-0.381657\pi$
$368$	1.82704e18	+	8.01058e14i	0.104205	+	4.56883e-5i
$369$	−1.07549e19	+	2.79319e19i	−0.601045	+	1.56100i
$370$	1.91633e19	−	1.91591e19i	1.04944	−	1.04921i
$371$	3.86413e18			0.207371
$372$	2.98738e18	−	1.60530e19i	0.157115	−	0.844274i
$373$	2.66646e19			1.37442			0.687208	−	0.726460i	$-0.258836\pi$
$373$	2.66646e19			1.37442			0.687208	+	0.726460i	$0.258836\pi$
$374$	1.36334e19	−	1.36304e19i	0.688760	−	0.688609i
$375$	−6.75277e18	−	1.25513e18i	−0.334386	−	0.0621516i
$376$	−6.71555e18	+	6.71113e18i	−0.325966	+	0.325752i
$377$		−	4.37388e18i		−	0.208117i
$378$	−8.22994e18	−	3.45302e19i	−0.383891	−	1.61068i
$379$			3.72652e19i			1.70416i	0.523414	+	0.852078i	$0.324658\pi$
$379$			3.72652e19i			1.70416i	−0.523414	+	0.852078i	$0.675342\pi$
$380$	3.66575e15	−	1.67216e19i	0.000164356	−	0.749721i
$381$	3.39595e19	+	6.31199e18i	1.49288	+	0.277478i
$382$	2.13390e17	+	2.13437e17i	0.00919813	+	0.00920014i
$383$	3.64339e19			1.53998			0.769991	−	0.638055i	$-0.220261\pi$
$383$	3.64339e19			1.53998			0.769991	+	0.638055i	$0.220261\pi$
$384$	−1.36396e19	−	1.99003e19i	−0.565352	−	0.824850i
$385$	−4.16046e19			−1.69116
$386$	4.78278e18	+	4.78383e18i	0.190667	+	0.190709i
$387$	4.81076e16	−	1.24942e17i	0.00188097	−	0.00488514i
$388$	−6.89963e15	+	3.14731e19i	−0.000264599	+	1.20699i
$389$		−	1.65885e17i		−	0.00624000i	−0.999995	−	0.00312000i	$-0.999007\pi$
$389$		−	1.65885e17i		−	0.00624000i	0.999995	−	0.00312000i	$-0.000993128\pi$
$390$	2.90336e18	+	4.23004e18i	0.107131	+	0.156084i
$391$		−	3.62358e18i		−	0.131163i
$392$	−3.46929e19	+	3.46701e19i	−1.23195	+	1.23114i
$393$	−2.28563e18	+	1.22971e19i	−0.0796274	+	0.428408i
$394$	−2.84536e19	+	2.84474e19i	−0.972559	+	0.972345i
$395$	4.65130e18			0.155990
$396$	8.45392e18	−	2.19417e19i	0.278192	−	0.722032i
$397$	2.28171e19			0.736771			0.368385	−	0.929673i	$-0.379911\pi$
$397$	2.28171e19			0.736771			0.368385	+	0.929673i	$0.379911\pi$
$398$	−2.11936e19	+	2.11890e19i	−0.671555	+	0.671408i
$399$	5.52674e18	−	2.97347e19i	0.171859	−	0.924628i
$400$	2.43248e19	+	1.06651e16i	0.742334	+	0.000325473i
$401$			2.16175e19i			0.647474i	0.946147	+	0.323737i	$0.104939\pi$
$401$			2.16175e19i			0.647474i	−0.946147	+	0.323737i	$0.895061\pi$
$402$	2.54000e19	+	3.70064e19i	0.746685	+	1.08788i
$403$			4.26854e18i			0.123166i
$404$	1.22484e17	+	2.68512e13i	0.00346911	+	7.60508e-7i
$405$	−3.18401e19	+	3.52168e19i	−0.885241	+	0.979123i
$406$	−6.22419e19	−	6.22555e19i	−1.69878	−	1.69915i
$407$	3.24660e19			0.869902
$408$	−3.94565e19	+	2.70689e19i	−1.03793	+	0.712065i
$409$	1.02772e19			0.265430			0.132715	−	0.991154i	$-0.457631\pi$
$409$	1.02772e19			0.265430			0.132715	+	0.991154i	$0.457631\pi$
$410$	−6.15608e19	−	6.15743e19i	−1.56108	−	1.56142i
$411$	−4.03835e19	−	7.50601e18i	−1.00552	−	0.186894i
$412$	1.47852e19	+	3.24126e15i	0.361492	+	7.92474e-5i
$413$		−	4.92559e19i		−	1.18259i
$414$	−1.79308e18	−	4.03962e18i	−0.0422762	−	0.0952441i
$415$		−	3.03926e19i		−	0.703733i
$416$	4.45720e18	+	4.46208e18i	0.101359	+	0.101470i
$417$	−3.56182e19	−	6.62029e18i	−0.795521	−	0.147862i
$418$	1.41678e19	−	1.41646e19i	0.310798	−	0.310730i
$419$	2.39246e19			0.515514			0.257757	−	0.966210i	$-0.417017\pi$
$419$	2.39246e19			0.515514			0.257757	+	0.966210i	$0.417017\pi$
$420$	1.01520e20	+	1.88923e19i	2.14872	+	0.399867i
$421$	−5.43020e19			−1.12902			−0.564508	−	0.825428i	$-0.690934\pi$
$421$	−5.43020e19			−1.12902			−0.564508	+	0.825428i	$0.690934\pi$
$422$	−2.68793e19	+	2.68734e19i	−0.549002	+	0.548882i
$423$	2.14328e19	+	8.25244e18i	0.430057	+	0.165588i
$424$	−4.49082e18	−	4.49377e18i	−0.0885282	−	0.0885865i
$425$		−	4.82436e19i		−	0.934378i
$426$	6.39683e19	−	4.39057e19i	1.21729	−	0.835506i
$427$			7.57917e19i			1.41714i
$428$	1.64012e15	−	7.48151e18i	3.01333e−5	−	0.137455i
$429$	−1.12328e18	+	6.04341e18i	−0.0202795	+	0.109107i
$430$	2.75368e17	+	2.75428e17i	0.00488539	+	0.00488646i
$431$	−5.18781e19			−0.904492			−0.452246	−	0.891893i	$-0.649377\pi$
$431$	−5.18781e19			−0.904492			−0.452246	+	0.891893i	$0.649377\pi$
$432$	−3.05920e19	+	4.97013e19i	−0.524180	+	0.851608i
$433$	5.01390e19			0.844338			0.422169	−	0.906517i	$-0.361269\pi$
$433$	5.01390e19			0.844338			0.422169	+	0.906517i	$0.361269\pi$
$434$	6.07428e19	+	6.07561e19i	1.00536	+	1.00558i
$435$	−2.15158e19	+	1.15758e20i	−0.350016	+	1.88314i
$436$	1.18287e14	−	5.39572e17i	1.89141e−6	−	0.00862781i
$437$		−	3.76560e18i		−	0.0591866i
$438$	4.18370e19	−	2.87155e19i	0.646405	−	0.443671i
$439$		−	1.18283e20i		−	1.79655i	−0.439436	−	0.898274i	$-0.644822\pi$
$439$		−	1.18283e20i		−	1.79655i	0.439436	−	0.898274i	$-0.355178\pi$
$440$	4.83521e19	+	4.83839e19i	0.721972	+	0.722447i
$441$	1.10723e20	+	4.26325e19i	1.62535	+	0.625823i
$442$	8.84581e18	−	8.84387e18i	0.127665	−	0.127637i
$443$	−5.06788e19			−0.719115			−0.359558	−	0.933123i	$-0.617072\pi$
$443$	−5.06788e19			−0.719115			−0.359558	+	0.933123i	$0.617072\pi$
$444$	−7.92205e19	−	1.47425e19i	−1.10526	−	0.205684i
$445$	1.09760e19			0.150572
$446$	2.42552e19	−	2.42499e19i	0.327186	−	0.327114i
$447$	−1.44752e20	−	2.69047e19i	−1.92007	−	0.356880i
$448$	1.26938e20	+	8.34834e16i	1.65580	+	0.00108897i
$449$		−	7.96167e19i		−	1.02131i	−0.859787	−	0.510654i	$-0.829403\pi$
$449$		−	7.96167e19i		−	1.02131i	0.859787	−	0.510654i	$-0.170597\pi$
$450$	−2.38726e19	−	5.37826e19i	−0.301166	−	0.678498i
$451$		−	1.04318e20i		−	1.29430i
$452$	−4.41807e19	−	9.68543e15i	−0.539131	−	0.000118190i
$453$	−3.41871e19	−	6.35430e18i	−0.410323	−	0.0762661i
$454$	−3.69404e19	−	3.69485e19i	−0.436096	−	0.436192i
$455$	−2.69944e19			−0.313465
$456$	−4.10029e19	+	2.81298e19i	−0.468358	+	0.321315i
$457$	5.70521e19			0.641062			0.320531	−	0.947238i	$-0.396139\pi$
$457$	5.70521e19			0.641062			0.320531	+	0.947238i	$0.396139\pi$
$458$	8.05338e19	+	8.05514e19i	0.890199	+	0.890394i
$459$	9.85995e19	+	6.06302e19i	1.07221	+	0.659316i
$460$	1.28570e19	+	2.81854e15i	0.137548	+	3.01537e-5i
$461$		−	1.15240e19i		−	0.121296i	−0.998159	−	0.0606480i	$-0.980683\pi$
$461$		−	1.15240e19i		−	0.121296i	0.998159	−	0.0606480i	$-0.0193167\pi$
$462$	7.00116e19	+	1.02003e20i	0.725029	+	1.05633i
$463$			1.40236e20i			1.42890i	0.699686	+	0.714450i	$0.253323\pi$
$463$			1.40236e20i			1.42890i	−0.699686	+	0.714450i	$0.746677\pi$
$464$	−6.34589e16	+	1.44736e20i	−0.000636221	+	1.45108i
$465$	2.09976e19	−	1.12970e20i	0.207144	−	1.11447i
$466$	2.48105e19	−	2.48051e19i	0.240847	−	0.240795i
$467$	1.53342e20			1.46482			0.732409	−	0.680865i	$-0.238396\pi$
$467$	1.53342e20			1.46482			0.732409	+	0.680865i	$0.238396\pi$
$468$	5.48518e18	−	1.42365e19i	0.0515640	−	0.133832i
$469$	−2.36160e20			−2.18479
$470$	−4.72473e19	+	4.72370e19i	−0.430173	+	0.430079i
$471$	7.59299e18	−	4.08514e19i	0.0680387	−	0.366059i
$472$	−5.72819e19	+	5.72442e19i	−0.505187	+	0.504855i
$473$			4.66624e17i			0.00405050i
$474$	−7.82714e18	−	1.14037e19i	−0.0668753	−	0.0974338i
$475$		−	5.01344e19i		−	0.421632i
$476$	5.51911e16	−	2.51758e20i	0.000456895	−	2.08416i
$477$	−5.52220e18	+	1.43420e19i	−0.0450012	+	0.116875i
$478$	−4.28603e19	−	4.28697e19i	−0.343832	−	0.343907i
$479$	4.22260e19			0.333475			0.166738	−	0.986001i	$-0.446677\pi$
$479$	4.22260e19			0.333475			0.166738	+	0.986001i	$0.446677\pi$
$480$	−9.60136e19	−	1.40018e20i	−0.746489	−	1.08862i
$481$	2.10650e19			0.161240
$482$	−1.32076e20	−	1.32105e20i	−0.995337	−	0.995555i
$483$	2.28626e19	+	4.24943e18i	0.169638	+	0.0315302i
$484$	1.20413e16	−	5.49271e19i	8.79695e−5	−	0.401279i
$485$			2.21478e20i			1.59319i
$486$	1.39922e20	+	1.88009e19i	0.991093	+	0.133170i
$487$			7.52066e18i			0.0524552i	0.999656	+	0.0262276i	$0.00834946\pi$
$487$			7.52066e18i			0.0524552i	−0.999656	+	0.0262276i	$0.991651\pi$
$488$	8.81417e19	−	8.80837e19i	0.605386	−	0.604988i
$489$	−1.94478e20	−	3.61473e19i	−1.31539	−	0.244489i
$490$	−2.44082e20	+	2.44029e20i	−1.62579	+	1.62544i
$491$	−1.46276e20			−0.959539			−0.479769	−	0.877395i	$-0.659280\pi$
$491$	−1.46276e20			−0.959539			−0.479769	+	0.877395i	$0.659280\pi$
$492$	−4.73699e19	+	2.54547e20i	−0.306030	+	1.64448i
$493$	2.87056e20			1.82648
$494$	9.19250e18	−	9.19048e18i	0.0576078	−	0.0575952i
$495$	5.94569e19	−	1.54418e20i	0.366997	−	0.953145i
$496$	6.19305e16	−	1.41250e20i	0.000376524	−	0.858769i
$497$			4.08221e20i			2.44468i
$498$	−7.45145e19	+	5.11443e19i	−0.439563	+	0.301701i
$499$			9.08565e19i			0.527961i	0.964528	+	0.263981i	$0.0850355\pi$
$499$			9.08565e19i			0.527961i	−0.964528	+	0.263981i	$0.914965\pi$
$500$	−5.94152e19	−	1.30252e16i	−0.340113	−	7.45604e-5i
$501$	−1.10134e19	+	5.92539e19i	−0.0621068	+	0.334144i
$502$	−1.60503e19	−	1.60538e19i	−0.0891673	−	0.0891868i
$503$	−1.71643e19			−0.0939432			−0.0469716	−	0.998896i	$-0.514957\pi$
$503$	−1.71643e19			−0.0939432			−0.0469716	+	0.998896i	$0.514957\pi$
$504$	−1.24517e20	−	2.80691e20i	−0.671429	−	1.51356i
$505$	8.61924e17			0.00457913
$506$	1.08910e19	+	1.08934e19i	0.0570084	+	0.0570209i
$507$	3.47027e19	−	1.86706e20i	0.178980	−	0.962938i
$508$	2.98798e20	+	6.55033e16i	1.51845	+	0.000332878i
$509$		−	3.17763e20i		−	1.59118i	−0.605835	−	0.795590i	$-0.707161\pi$
$509$		−	3.17763e20i		−	1.59118i	0.605835	−	0.795590i	$-0.292839\pi$
$510$	−2.77616e20	+	1.90546e20i	−1.36983	+	0.940208i
$511$			2.66987e20i			1.29818i
$512$	−1.47428e20	−	1.47719e20i	−0.706409	−	0.707804i
$513$	1.02464e20	+	6.30065e19i	0.483828	+	0.297512i
$514$	−1.59815e20	+	1.59780e20i	−0.743696	+	0.743533i
$515$	1.04044e20			0.477161
$516$	2.11890e17	−	1.13861e18i	0.000957719	−	0.00514640i
$517$	−8.00454e19			−0.356580
$518$	2.99828e20	−	2.99762e20i	1.31643	−	1.31614i
$519$	3.80611e20	+	7.07435e19i	1.64712	+	0.306148i
$520$	3.13724e19	+	3.13930e19i	0.133821	+	0.133909i
$521$			1.76873e19i			0.0743668i	0.999308	+	0.0371834i	$0.0118386\pi$
$521$			1.76873e19i			0.0743668i	−0.999308	+	0.0371834i	$0.988161\pi$
$522$	3.20015e20	−	1.42046e20i	1.32630	−	0.588707i
$523$		−	1.26638e20i		−	0.517371i	−0.965962	−	0.258685i	$-0.916711\pi$
$523$		−	1.26638e20i		−	0.517371i	0.965962	−	0.258685i	$-0.0832893\pi$
$524$	−2.37194e16	+	1.08197e20i	−9.55253e−5	+	0.435745i
$525$	3.04388e20	+	5.65760e19i	1.20846	+	0.224614i
$526$	3.03185e20	+	3.03252e20i	1.18663	+	1.18689i
$527$	−2.80142e20			−1.08093
$528$	3.72580e19	−	1.99966e20i	0.141731	−	0.760680i
$529$	−2.63740e20			−0.989141
$530$	−3.16091e19	−	3.16160e19i	−0.116881	−	0.116906i
$531$	1.82816e20	+	7.03912e19i	0.666508	+	0.256631i
$532$	5.73542e16	−	2.61625e20i	0.000206171	−	0.940463i
$533$		−	6.76848e19i		−	0.239904i
$534$	−1.84703e19	−	2.69102e19i	−0.0645525	−	0.0940496i
$535$		−	5.26478e19i		−	0.181437i
$536$	2.74461e20	+	2.74641e20i	0.932705	+	0.933319i
$537$	1.03240e20	−	5.55448e20i	0.345973	−	1.86139i
$538$	9.88731e19	−	9.88514e19i	0.326746	−	0.326675i
$539$	−4.13519e20			−1.34766
$540$	−2.15201e20	+	3.49798e20i	−0.691658	+	1.12425i
$541$	2.51947e20			0.798602			0.399301	−	0.916820i	$-0.369253\pi$
$541$	2.51947e20			0.798602			0.399301	+	0.916820i	$0.369253\pi$
$542$	2.22702e19	−	2.22654e19i	0.0696194	−	0.0696042i
$543$	−2.42494e18	+	1.30466e19i	−0.00747657	+	0.0402251i
$544$	−2.92845e20	+	2.92524e20i	−0.890524	+	0.889549i
$545$		−	3.79700e18i		−	0.0113885i
$546$	4.54258e19	+	6.61830e19i	0.134387	+	0.195795i
$547$		−	2.00954e20i		−	0.586398i	−0.956051	−	0.293199i	$-0.905280\pi$
$547$		−	2.00954e20i		−	0.586398i	0.956051	−	0.293199i	$-0.0947198\pi$
$548$	−3.55320e20	−	7.78942e16i	−1.02274	−	0.000224208i
$549$	−2.81306e20	−	1.08313e20i	−0.798704	−	0.307532i
$550$	1.45000e20	+	1.45032e20i	0.406115	+	0.406204i
$551$	2.98307e20			0.824188
$552$	−2.16286e19	−	3.15266e19i	−0.0589503	−	0.0859278i
$553$	7.27741e19			0.195676
$554$	8.35466e19	+	8.35649e19i	0.221618	+	0.221667i
$555$	−5.57502e20	−	1.03622e20i	−1.45898	−	0.271178i
$556$	−3.13392e20	−	6.87027e16i	−0.809146	−	0.000177383i
$557$			2.20951e20i			0.562837i	0.959585	+	0.281419i	$0.0908049\pi$
$557$			2.20951e20i			0.562837i	−0.959585	+	0.281419i	$0.909195\pi$
$558$	−3.12307e20	+	1.38624e20i	−0.784920	+	0.348404i
$559$			3.02761e17i			0.000750777i
$560$	8.93272e20	+	3.91651e17i	2.18561	+	0.000958273i
$561$	−3.96626e20	−	7.37202e19i	−0.957547	−	0.177978i
$562$	2.22849e20	−	2.22800e20i	0.530870	−	0.530753i
$563$	−3.72267e20			−0.875068			−0.437534	−	0.899202i	$-0.644148\pi$
$563$	−3.72267e20			−0.875068			−0.437534	+	0.899202i	$0.644148\pi$
$564$	1.95319e20	+	3.63480e19i	0.453056	+	0.0843115i
$565$	−3.10902e20			−0.711640
$566$	−6.44121e19	+	6.43980e19i	−0.145494	+	0.145462i
$567$	−4.98169e20	+	5.51001e20i	−1.11046	+	1.22823i
$568$	4.74738e20	−	4.74426e20i	1.04434	−	1.04365i
$569$			4.83794e20i			1.05031i	0.851006	+	0.525157i	$0.175993\pi$
$569$			4.83794e20i			1.05031i	−0.851006	+	0.525157i	$0.824007\pi$
$570$	−2.88496e20	+	1.98014e20i	−0.618128	+	0.424263i
$571$			5.28333e20i			1.11722i	0.829432	+	0.558608i	$0.188664\pi$
$571$			5.28333e20i			1.11722i	−0.829432	+	0.558608i	$0.811336\pi$
$572$	−1.16569e16	+	5.31738e19i	−2.43284e−5	+	0.110976i
$573$	1.15412e18	−	6.20936e18i	0.00237734	−	0.0127905i
$574$	−9.63178e20	−	9.63389e20i	−1.95825	−	1.95868i
$575$	3.85476e19			0.0773551
$576$	−1.81717e20	+	4.71020e20i	−0.359937	+	0.932977i
$577$	−1.32135e20			−0.258345			−0.129172	−	0.991622i	$-0.541232\pi$
$577$	−1.32135e20			−0.258345			−0.129172	+	0.991622i	$0.541232\pi$
$578$	2.14070e20	+	2.14117e20i	0.413139	+	0.413230i
$579$	2.58677e19	−	1.39172e20i	0.0492797	−	0.265133i
$580$	−2.23282e17	+	1.01852e21i	−0.000419898	+	1.91539i
$581$		−	4.75522e20i		−	0.882775i
$582$	5.43005e20	−	3.72700e20i	0.995133	−	0.683026i
$583$		−	5.35631e19i		−	0.0969063i
$584$	3.10492e20	−	3.10287e20i	0.554566	−	0.554202i
$585$	3.85775e19	−	1.00191e20i	0.0680245	−	0.176669i
$586$	5.19463e20	−	5.19349e20i	0.904320	−	0.904122i
$587$	5.66505e20			0.973684			0.486842	−	0.873490i	$-0.338149\pi$
$587$	5.66505e20			0.973684			0.486842	+	0.873490i	$0.338149\pi$
$588$	1.00903e21	+	1.87775e20i	1.71228	+	0.318646i
$589$	−2.91122e20			−0.487765
$590$	−4.03007e20	+	4.02919e20i	−0.666688	+	0.666542i
$591$	8.27779e20	+	1.53858e20i	1.35210	+	0.251312i
$592$	−6.97061e20	−	3.05624e17i	−1.12424	−	0.000492917i
$593$		−	8.41762e20i		−	1.34054i	−0.742118	−	0.670269i	$-0.766179\pi$
$593$		−	8.41762e20i		−	1.34054i	0.742118	−	0.670269i	$-0.233821\pi$
$594$	−4.78644e20	+	1.14080e20i	−0.752687	+	0.179396i
$595$		−	1.77163e21i		−	2.75104i
$596$	−1.27362e21	−	2.79206e17i	−1.95296	−	0.000428132i
$597$	6.16569e20	+	1.14601e20i	0.933628	+	0.173532i
$598$	7.06644e18	+	7.06799e18i	0.0105668	+	0.0105691i
$599$	5.44591e19			0.0804210			0.0402105	−	0.999191i	$-0.487197\pi$
$599$	5.44591e19			0.0804210			0.0402105	+	0.999191i	$0.487197\pi$
$600$	−2.87959e20	−	4.19738e20i	−0.419948	−	0.612130i
$601$	1.03672e21			1.49315			0.746577	−	0.665300i	$-0.231696\pi$
$601$	1.03672e21			1.49315			0.746577	+	0.665300i	$0.231696\pi$
$602$	4.30839e18	+	4.30934e18i	0.00612832	+	0.00612967i
$603$	3.37495e20	−	8.76522e20i	0.474119	−	1.23135i
$604$	−3.00800e20	−	6.59423e16i	−0.417351	−	9.14929e-5i
$605$		−	3.86525e20i		−	0.529678i
$606$	−1.45043e18	−	2.11320e18i	−0.00196315	−	0.00286020i
$607$			1.03494e21i			1.38357i	0.722103	+	0.691785i	$0.243175\pi$
$607$			1.03494e21i			1.38357i	−0.722103	+	0.691785i	$0.756825\pi$
$608$	−3.04322e20	+	3.03989e20i	−0.401843	+	0.401403i
$609$	−3.36635e20	+	1.81115e21i	−0.439066	+	2.36225i
$610$	6.20122e20	−	6.19986e20i	0.798920	−	0.798745i
$611$	−5.19360e19			−0.0660936
$612$	9.34336e20	+	3.59990e20i	1.17454	+	0.452538i
$613$	8.49571e20			1.05498			0.527492	−	0.849560i	$-0.323132\pi$
$613$	8.49571e20			1.05498			0.527492	+	0.849560i	$0.323132\pi$
$614$	−8.56175e19	+	8.55987e19i	−0.105027	+	0.105004i
$615$	−3.32952e20	+	1.79133e21i	−0.403476	+	2.17076i
$616$	7.56515e20	+	7.57013e20i	0.905654	+	0.906250i
$617$			5.74819e20i			0.679818i	0.940458	+	0.339909i	$0.110396\pi$
$617$			5.74819e20i			0.679818i	−0.940458	+	0.339909i	$0.889604\pi$
$618$	−1.75085e20	−	2.55089e20i	−0.204566	−	0.298042i
$619$		−	1.58570e19i		−	0.0183038i	−0.999958	−	0.00915189i	$-0.997087\pi$
$619$		−	1.58570e19i		−	0.0183038i	0.999958	−	0.00915189i	$-0.00291318\pi$
$620$	2.17904e17	−	9.93985e20i	0.000248501	−	1.13355i
$621$	−4.84448e19	+	7.87831e19i	−0.0545834	+	0.0887659i
$622$	9.18230e20	+	9.18431e20i	1.02217	+	1.02239i
$623$	1.71730e20			0.188880
$624$	2.41742e19	−	1.29744e20i	0.0262705	−	0.140995i
$625$	−1.10946e21			−1.19127
$626$	−9.79782e20	−	9.79997e20i	−1.03949	−	1.03972i
$627$	−4.12171e20	−	7.66095e19i	−0.432087	−	0.0803112i
$628$	7.87969e16	−	3.59437e20i	8.16228e−5	−	0.372328i
$629$			1.38249e21i			1.41508i
$630$	−8.76667e20	−	1.97504e21i	−0.886707	−	1.99766i
$631$		−	6.76245e20i		−	0.675903i	−0.941164	−	0.337951i	$-0.890266\pi$
$631$		−	6.76245e20i		−	0.675903i	0.941164	−	0.337951i	$-0.109734\pi$
$632$	−8.45767e19	−	8.46323e19i	−0.0835358	−	0.0835907i
$633$	7.81977e20	+	1.45345e20i	0.763249	+	0.141864i
$634$	−3.22226e20	+	3.22156e20i	−0.310808	+	0.310739i
$635$	2.10265e21			2.00431
$636$	−2.43226e19	+	1.30700e20i	−0.0229130	+	0.123125i
$637$	−2.68304e20			−0.249794
$638$	−8.62963e20	+	8.62774e20i	−0.794030	+	0.793856i
$639$	−1.51514e21	−	5.83385e20i	−1.37783	−	0.530517i
$640$	−1.03769e21	−	1.03928e21i	−0.932647	−	0.934079i
$641$		−	1.56301e21i		−	1.38843i	−0.719765	−	0.694217i	$-0.755751\pi$
$641$		−	1.56301e21i		−	1.38843i	0.719765	−	0.694217i	$-0.244249\pi$
$642$	−1.29078e20	+	8.85949e19i	−0.113329	+	0.0777850i
$643$			4.68376e20i			0.406455i	0.979132	+	0.203228i	$0.0651431\pi$
$643$			4.68376e20i			0.406455i	−0.979132	+	0.203228i	$0.934857\pi$
$644$	2.01160e20	+	4.40988e16i	0.172543	+	3.78254e-5i
$645$	1.48933e18	−	8.01281e18i	0.00126268	−	0.00679340i
$646$	6.03168e20	+	6.03300e20i	0.505469	+	0.505580i
$647$	7.81258e20			0.647161			0.323580	−	0.946201i	$-0.395113\pi$
$647$	7.81258e20			0.647161			0.323580	+	0.946201i	$0.395113\pi$
$648$	1.21975e21	−	6.10197e19i	0.998751	−	0.0499640i
$649$	−6.82766e20			−0.552633
$650$	9.40810e19	+	9.41016e19i	0.0752752	+	0.0752917i
$651$	3.28528e20	−	1.76753e21i	0.259845	−	1.39801i
$652$	−1.71114e21	−	3.75122e17i	−1.33792	−	0.000293302i
$653$			5.57953e20i			0.431269i	0.976474	+	0.215635i	$0.0691820\pi$
$653$			5.57953e20i			0.431269i	−0.976474	+	0.215635i	$0.930818\pi$
$654$	−9.30921e18	+	6.38953e18i	−0.00711344	+	0.00488243i
$655$			7.61391e20i			0.575173i
$656$	−9.82012e17	+	2.23976e21i	−0.000733395	+	1.67272i
$657$	−9.90939e20	−	3.81549e20i	−0.731655	−	0.281715i
$658$	−7.39230e20	+	7.39068e20i	−0.539617	+	0.539498i
$659$	−1.68829e21			−1.21845			−0.609224	−	0.792999i	$-0.708519\pi$
$659$	−1.68829e21			−1.21845			−0.609224	+	0.792999i	$0.708519\pi$
$660$	2.61878e20	−	1.40723e21i	0.186862	−	1.00412i
$661$	−4.74584e20			−0.334813			−0.167406	−	0.985888i	$-0.553539\pi$
$661$	−4.74584e20			−0.334813			−0.167406	+	0.985888i	$0.553539\pi$
$662$	1.45181e21	−	1.45149e21i	1.01269	−	1.01246i
$663$	−2.57344e20	−	4.78321e19i	−0.177485	−	0.0329889i
$664$	−5.53007e20	+	5.52643e20i	−0.377111	+	0.376864i
$665$		−	1.84107e21i		−	1.24139i
$666$	6.84103e20	+	1.54122e21i	0.456105	+	1.02756i
$667$			2.29364e20i			0.151210i
$668$	−1.14293e17	+	5.21354e20i	−7.45066e−5	+	0.339867i
$669$	−7.05639e20	−	1.31156e20i	−0.454869	−	0.0845457i
$670$	1.93182e21	+	1.93224e21i	1.23142	+	1.23169i
$671$	1.05060e21			0.662243
$672$	−1.50223e21	−	2.19072e21i	−0.936409	−	1.36558i
$673$	1.79144e21			1.10431			0.552154	−	0.833742i	$-0.313806\pi$
$673$	1.79144e21			1.10431			0.552154	+	0.833742i	$0.313806\pi$
$674$	1.39023e21	+	1.39054e21i	0.847497	+	0.847682i
$675$	−6.44983e20	+	1.04890e21i	−0.388839	+	0.632348i
$676$	3.60130e17	−	1.64276e21i	0.000214713	−	0.979430i
$677$		−	9.72443e20i		−	0.573388i	−0.958022	−	0.286694i	$-0.907444\pi$
$677$		−	9.72443e20i		−	0.573388i	0.958022	−	0.286694i	$-0.0925564\pi$
$678$	5.23182e20	+	7.62248e20i	0.305091	+	0.444502i
$679$			3.46524e21i			1.99853i
$680$	−2.06031e21	+	2.05896e21i	−1.17521	+	1.17444i
$681$	−1.99792e20	+	1.07491e21i	−0.112713	+	0.606415i
$682$	8.42178e20	−	8.41994e20i	0.469917	−	0.469814i
$683$	−1.76728e21			−0.975327			−0.487664	−	0.873032i	$-0.662151\pi$
$683$	−1.76728e21			−0.975327			−0.487664	+	0.873032i	$0.662151\pi$
$684$	9.70955e20	+	3.74099e20i	0.530003	+	0.204205i
$685$	−2.50040e21			−1.34999
$686$	−1.62624e21	+	1.62588e21i	−0.868468	+	0.868277i
$687$	4.35567e20	−	2.34342e21i	0.230080	−	1.23787i
$688$	4.39264e15	−	1.00187e19i	2.29516e−6	−	0.00523475i
$689$		−	3.47535e19i		−	0.0179620i
$690$	−1.52250e20	−	2.21821e20i	−0.0778378	−	0.113405i
$691$		−	2.77934e21i		−	1.40558i	−0.711395	−	0.702792i	$-0.751936\pi$
$691$		−	2.77934e21i		−	1.40558i	0.711395	−	0.702792i	$-0.248064\pi$
$692$	3.34886e21	+	7.34147e17i	1.67533	+	0.000367272i
$693$	9.30260e20	−	2.41602e21i	0.460368	−	1.19564i
$694$	−1.52757e21	−	1.52790e21i	−0.747831	−	0.747995i
$695$	−2.20536e21			−1.06805
$696$	2.49750e21	−	1.71340e21i	1.19657	−	0.820897i
$697$	4.44213e21			2.10545
$698$	7.96782e20	+	7.96957e20i	0.373615	+	0.373697i
$699$	−7.21793e20	−	1.34158e20i	−0.334838	−	0.0622357i
$700$	2.67820e21	+	5.87122e17i	1.22916	+	0.000269459i
$701$		−	9.06379e19i		−	0.0411552i	−0.999788	−	0.0205776i	$-0.993449\pi$
$701$		−	9.06379e19i		−	0.0411552i	0.999788	−	0.0205776i	$-0.00655052\pi$
$702$	−3.10560e20	+	7.40190e19i	−0.139514	+	0.0332518i
$703$			1.43667e21i			0.638546i
$704$	1.15722e18	−	1.75957e21i	0.000508885	−	0.773771i
$705$	1.37453e21	+	2.55481e20i	0.598047	+	0.111158i
$706$	−1.45875e21	+	1.45843e21i	−0.627981	+	0.627844i
$707$	1.34856e19			0.00574415
$708$	1.66602e21	+	3.10039e20i	0.702153	+	0.130667i
$709$	−1.26617e21			−0.528016			−0.264008	−	0.964521i	$-0.585044\pi$
$709$	−1.26617e21			−0.528016			−0.264008	+	0.964521i	$0.585044\pi$
$710$	3.34003e21	−	3.33930e21i	1.37820	−	1.37790i
$711$	−1.04001e20	+	2.70105e20i	−0.0424635	+	0.110284i
$712$	−1.99581e20	−	1.99713e20i	−0.0806344	−	0.0806874i
$713$		−	2.23840e20i		−	0.0894882i
$714$	−4.34357e21	+	2.98128e21i	−1.71834	+	1.17941i
$715$			3.74187e20i			0.146485i
$716$	1.07138e18	−	4.88719e21i	0.000415047	−	1.89327i
$717$	−2.31810e20	+	1.24718e21i	−0.0888667	+	0.478117i
$718$	1.42523e21	+	1.42554e21i	0.540695	+	0.540813i
$719$	1.96057e21			0.736065			0.368033	−	0.929813i	$-0.380032\pi$
$719$	1.96057e21			0.736065			0.368033	+	0.929813i	$0.380032\pi$
$720$	−1.27802e21	+	3.31487e21i	−0.474837	+	1.23161i
$721$	1.62788e21			0.598559
$722$	−1.31616e21	−	1.31645e21i	−0.478940	−	0.479045i
$723$	−7.14332e20	+	3.84322e21i	−0.257254	+	1.38407i
$724$	−2.51650e16	+	1.14792e20i	−8.96929e−6	+	0.0409140i
$725$			3.05370e21i			1.07719i
$726$	−9.47654e20	+	6.50438e20i	−0.330846	+	0.227081i
$727$		−	3.72985e21i		−	1.28879i	−0.764691	−	0.644397i	$-0.777108\pi$
$727$		−	3.72985e21i		−	1.28879i	0.764691	−	0.644397i	$-0.222892\pi$
$728$	4.90852e20	+	4.91175e20i	0.167867	+	0.167977i
$729$	−1.33314e21	−	2.63642e21i	−0.451254	−	0.892396i
$730$	2.18447e21	−	2.18399e21i	0.731853	−	0.731693i
$731$	−1.98701e19			−0.00658900
$732$	−2.56357e21	−	4.77068e20i	−0.841418	−	0.156584i
$733$	−1.50329e21			−0.488386			−0.244193	−	0.969727i	$-0.578523\pi$
$733$	−1.50329e21			−0.488386			−0.244193	+	0.969727i	$0.578523\pi$
$734$	−4.09779e21	+	4.09689e21i	−1.31774	+	1.31745i
$735$	7.10089e21	+	1.31983e21i	2.26026	+	0.420110i
$736$	−2.33733e20	−	2.33989e20i	−0.0736438	−	0.0737246i
$737$			3.27356e21i			1.02097i
$738$	4.95215e21	−	2.19812e21i	1.52887	−	0.678623i
$739$		−	4.42592e21i		−	1.35260i	−0.736625	−	0.676302i	$-0.763582\pi$
$739$		−	4.42592e21i		−	1.35260i	0.736625	−	0.676302i	$-0.236418\pi$
$740$	−4.90526e21	−	1.07534e18i	−1.48397	−	0.000325319i
$741$	−2.67430e20	−	4.97068e19i	−0.0800892	−	0.0148860i
$742$	−4.94555e20	−	4.94663e20i	−0.146617	−	0.146649i
$743$	−1.12113e21			−0.329034			−0.164517	−	0.986374i	$-0.552607\pi$
$743$	−1.12113e21			−0.329034			−0.164517	+	0.986374i	$0.552607\pi$
$744$	−2.43735e21	+	1.67213e21i	−0.708143	+	0.485817i
$745$	−8.96252e21			−2.57785
$746$	−3.41269e21	−	3.41344e21i	−0.971753	−	0.971966i
$747$	1.76493e21	+	6.79566e20i	0.497534	+	0.191570i
$748$	−3.48977e21	−	7.65038e17i	−0.973947	−	0.000213511i
$749$		−	8.23725e20i		−	0.227598i
$750$	7.03586e20	+	1.02509e21i	0.192468	+	0.280415i
$751$			1.43822e21i			0.389517i	0.980851	+	0.194759i	$0.0623923\pi$
$751$			1.43822e21i			0.389517i	−0.980851	+	0.194759i	$0.937608\pi$
$752$	1.71862e21	+	7.53519e17i	0.460834	+	0.000202051i
$753$	−8.68081e19	+	4.67041e20i	−0.0230461	+	0.123992i
$754$	−5.59918e20	+	5.59796e20i	−0.147177	+	0.147145i
$755$	−2.11675e21			−0.550893
$756$	−3.36703e21	+	5.47292e21i	−0.867628	+	1.41028i
$757$	2.33466e21			0.595669			0.297835	−	0.954617i	$-0.403736\pi$
$757$	2.33466e21			0.595669			0.297835	+	0.954617i	$0.403736\pi$
$758$	4.77047e21	−	4.76942e21i	1.20515	−	1.20489i
$759$	5.89040e19	−	3.16913e20i	0.0147344	−	0.0792732i
$760$	−2.14106e21	+	2.13966e21i	−0.530307	+	0.529959i
$761$			3.80463e21i			0.933100i	0.884495	+	0.466550i	$0.154503\pi$
$761$			3.80463e21i			0.933100i	−0.884495	+	0.466550i	$0.845497\pi$
$762$	−3.53832e21	−	5.15514e21i	−0.859280	−	1.25192i
$763$		−	5.94077e19i		−	0.0142859i
$764$	1.19770e16	−	5.46339e19i	2.85199e−6	−	0.0130095i
$765$	6.57552e21	+	2.53183e21i	1.55049	+	0.596999i
$766$	−4.66303e21	−	4.66406e21i	−1.08881	−	1.08905i
$767$	−4.43001e20			−0.102433
$768$	−8.01832e20	+	4.29302e21i	−0.183601	+	0.983001i
$769$	4.62042e21			1.04769			0.523846	−	0.851813i	$-0.324497\pi$
$769$	4.62042e21			1.04769			0.523846	+	0.851813i	$0.324497\pi$
$770$	5.32481e21	+	5.32597e21i	1.19570	+	1.19597i
$771$	4.64938e21	+	8.64173e20i	1.03392	+	0.192173i
$772$	2.68444e17	−	1.22453e21i	5.91186e−5	−	0.269673i
$773$			4.30342e21i			0.938571i	0.883046	+	0.469286i	$0.155489\pi$
$773$			4.30342e21i			0.938571i	−0.883046	+	0.469286i	$0.844511\pi$
$774$	−2.21515e19	+	9.83242e18i	−0.00478459	+	0.00212375i
$775$		−	2.98015e21i		−	0.637494i
$776$	4.02989e21	−	4.02724e21i	0.853748	−	0.853187i
$777$	−8.72265e21	−	1.62126e21i	−1.83017	−	0.340170i
$778$	−2.12356e19	+	2.12309e19i	−0.00441283	+	0.00441186i
$779$	4.61623e21			0.950071
$780$	1.69915e20	−	9.13056e20i	0.0346356	−	0.186118i
$781$	5.65860e21			1.14242
$782$	−4.63869e20	+	4.63768e20i	−0.0927566	+	0.0927363i
$783$	−6.24111e21	−	3.83775e21i	−1.23609	−	0.760087i
$784$	8.87845e21	+	3.89272e18i	1.74167	+	0.000763630i
$785$		−	2.52938e21i		−	0.491464i
$786$	1.86673e21	−	1.28126e21i	0.359262	−	0.246586i
$787$			8.06412e21i			1.53726i	0.639695	+	0.768629i	$0.279061\pi$
$787$			8.06412e21i			1.53726i	−0.639695	+	0.768629i	$0.720939\pi$
$788$	7.28333e21	+	1.59667e18i	1.37525	+	0.000301487i
$789$	1.63978e21	−	8.82226e21i	0.306695	−	1.65007i
$790$	−5.95301e20	−	5.95432e20i	−0.110289	−	0.110314i
$791$	−4.86437e21			−0.892694
$792$	−3.89083e21	+	1.72601e21i	−0.707300	+	0.313765i
$793$	6.81661e20			0.122749
$794$	−2.92027e21	−	2.92091e21i	−0.520919	−	0.521033i
$795$	−1.70958e20	+	9.19779e20i	−0.0302089	+	0.162529i
$796$	5.42497e21	+	1.18928e18i	0.949618	+	0.000208178i
$797$		−	5.97458e21i		−	1.03603i	−0.855373	−	0.518013i	$-0.826672\pi$
$797$		−	5.97458e21i		−	1.03603i	0.855373	−	0.518013i	$-0.173328\pi$
$798$	−4.51380e21	+	3.09812e21i	−0.775391	+	0.532203i
$799$		−	3.40854e21i		−	0.580053i
$800$	−3.11187e21	−	3.11528e21i	−0.524622	−	0.525197i
$801$	−2.45418e20	+	6.37387e20i	−0.0409886	+	0.106453i
$802$	2.76734e21	−	2.76673e21i	0.457883	−	0.457783i
$803$	3.70088e21			0.606650
$804$	1.48650e21	−	7.98785e21i	0.241404	−	1.29721i
$805$	1.41557e21			0.227752
$806$	5.46433e20	−	5.46313e20i	0.0871011	−	0.0870820i
$807$	−2.87644e21	−	5.34638e20i	−0.454259	−	0.0844322i
$808$	−1.56727e19	−	1.56831e19i	−0.00245222	−	0.00245384i
$809$			1.12658e22i			1.74641i	0.487351	+	0.873206i	$0.337963\pi$
$809$			1.12658e22i			1.74641i	−0.487351	+	0.873206i	$0.662037\pi$
$810$	8.58333e21	−	4.31280e20i	1.31831	−	0.0662403i
$811$			7.78307e21i			1.18439i	0.805795	+	0.592195i	$0.201738\pi$
$811$			7.78307e21i			1.18439i	−0.805795	+	0.592195i	$0.798262\pi$
$812$	−3.49346e18	+	1.59357e22i	−0.000526727	+	2.40270i
$813$	−6.47891e20	−	1.20422e20i	−0.0967883	−	0.0179899i
$814$	−4.15519e21	−	4.15610e21i	−0.615046	−	0.615181i
$815$	−1.20414e22			−1.76602
$816$	8.51508e21	+	1.58655e21i	1.23741	+	0.230556i
$817$	−2.06488e19			−0.00297324
$818$	−1.31534e21	−	1.31562e21i	−0.187666	−	0.187708i
$819$	6.03583e20	−	1.56759e21i	0.0853312	−	0.221617i
$820$	−3.45523e18	+	1.57613e22i	−0.000484031	+	2.20794i
$821$		−	2.90364e21i		−	0.403059i	−0.979482	−	0.201530i	$-0.935409\pi$
$821$		−	2.90364e21i		−	0.403059i	0.979482	−	0.201530i	$-0.0645912\pi$
$822$	4.20765e21	+	6.13032e21i	0.578763	+	0.843226i
$823$		−	4.60753e21i		−	0.628014i	−0.949421	−	0.314007i	$-0.898328\pi$
$823$		−	4.60753e21i		−	0.628014i	0.949421	−	0.314007i	$-0.101672\pi$
$824$	−1.89189e21	−	1.89313e21i	−0.255530	−	0.255698i
$825$	7.84235e20	−	4.21931e21i	0.104964	−	0.564724i
$826$	−6.30544e21	+	6.30406e21i	−0.836306	+	0.836123i
$827$	−3.27566e21			−0.430535			−0.215267	−	0.976555i	$-0.569062\pi$
$827$	−3.27566e21			−0.430535			−0.215267	+	0.976555i	$0.569062\pi$
$828$	−2.87640e20	+	7.46554e20i	−0.0374646	+	0.0972375i
$829$	−9.59056e21			−1.23790			−0.618949	−	0.785431i	$-0.712441\pi$
$829$	−9.59056e21			−1.23790			−0.618949	+	0.785431i	$0.712441\pi$
$830$	−3.89068e21	+	3.88983e21i	−0.497669	+	0.497560i
$831$	4.51862e20	−	2.43109e21i	0.0572794	−	0.308172i
$832$	7.50839e17	−	1.14167e21i	9.43239e−5	−	0.143422i
$833$		−	1.76087e22i		−	2.19225i
$834$	3.71114e21	+	5.40694e21i	0.457891	+	0.667123i
$835$			3.66880e21i			0.448616i
$836$	−3.62655e21	−	7.95022e17i	−0.439487	−	9.63456e-5i
$837$	6.09079e21	+	3.74531e21i	0.731531	+	0.449829i
$838$	−3.06202e21	−	3.06269e21i	−0.364483	−	0.364563i
$839$	1.30050e22			1.53425			0.767126	−	0.641496i	$-0.221686\pi$
$839$	1.30050e22			1.53425			0.767126	+	0.641496i	$0.221686\pi$
$840$	−1.05746e22	−	1.54139e22i	−1.23643	−	1.80226i
$841$	−9.54079e21			−1.10564
$842$	6.94989e21	+	6.95141e21i	0.798247	+	0.798422i
$843$	−6.48316e21	−	1.20501e21i	−0.738040	−	0.137178i
$844$	6.88034e21	+	1.50833e18i	0.776321	+	0.000170187i
$845$		−	1.15602e22i		−	1.29282i
$846$	−1.68667e21	−	3.79989e21i	−0.186961	−	0.421205i
$847$		−	6.04756e21i		−	0.664438i
$848$	−5.04225e17	+	1.15003e21i	−5.49105e−5	+	0.125239i
$849$	1.87389e21	+	3.48297e20i	0.202272	+	0.0375960i
$850$	−6.17585e21	+	6.17450e21i	−0.660777	+	0.660632i
$851$	−1.10464e21			−0.117151
$852$	−1.38076e22	−	2.56953e21i	−1.45151	−	0.270120i
$853$	−1.20891e22			−1.25973			−0.629863	−	0.776706i	$-0.716889\pi$
$853$	−1.20891e22			−1.25973			−0.629863	+	0.776706i	$0.716889\pi$
$854$	9.70241e21	−	9.70028e21i	1.00218	−	1.00196i
$855$	6.83324e21	+	2.63106e21i	0.699650	+	0.269392i
$856$	−9.57948e20	+	9.57318e20i	−0.0972274	+	0.0971635i
$857$			9.59428e21i			0.965287i	0.875817	+	0.482643i	$0.160323\pi$
$857$			9.59428e21i			0.965287i	−0.875817	+	0.482643i	$0.839677\pi$
$858$	9.17404e20	−	6.29676e20i	0.0914968	−	0.0628004i
$859$			1.11271e22i			1.10010i	0.835130	+	0.550052i	$0.185392\pi$
$859$			1.11271e22i			1.10010i	−0.835130	+	0.550052i	$0.814608\pi$
$860$	1.54556e16	−	7.05018e19i	1.51477e−6	−	0.00690974i
$861$	−5.20935e21	+	2.80271e22i	−0.506128	+	2.72305i
$862$	6.63968e21	+	6.64113e21i	0.639503	+	0.639643i
$863$	−2.70420e21			−0.258201			−0.129101	−	0.991632i	$-0.541209\pi$
$863$	−2.70420e21			−0.258201			−0.129101	+	0.991632i	$0.541209\pi$
$864$	1.02778e22	−	2.44486e21i	0.972854	−	0.231420i
$865$	2.35661e22			2.21140
$866$	−6.41708e21	−	6.41849e21i	−0.596971	−	0.597102i
$867$	1.15780e21	−	6.22912e21i	0.106780	−	0.574492i
$868$	3.40932e18	−	1.55519e22i	0.000311724	−	1.42195i
$869$		−	1.00877e21i		−	0.0914414i
$870$	1.75724e22	−	1.20611e22i	1.57920	−	1.08391i
$871$			2.12399e21i			0.189242i
$872$	−6.90879e19	+	6.90425e19i	−0.00610279	+	0.00609878i
$873$	−1.28614e22	−	4.95215e21i	−1.12638	−	0.433698i
$874$	−4.82050e20	+	4.81944e20i	−0.0418558	+	0.0418467i
$875$	−6.54170e21			−0.563158
$876$	−9.03054e21	−	1.68054e21i	−0.770784	−	0.143439i
$877$	−8.97769e21			−0.759745			−0.379872	−	0.925039i	$-0.624032\pi$
$877$	−8.97769e21			−0.759745			−0.379872	+	0.925039i	$0.624032\pi$
$878$	−1.51419e22	+	1.51386e22i	−1.27049	+	1.27021i
$879$	−1.51123e22	−	2.80890e21i	−1.25723	−	0.233679i
$880$	5.42893e18	−	1.23822e22i	0.000447810	−	1.02136i
$881$			8.19209e21i			0.670001i	0.942218	+	0.335000i	$0.108736\pi$
$881$			8.19209e21i			0.670001i	−0.942218	+	0.335000i	$0.891264\pi$
$882$	−8.71341e21	−	1.96304e22i	−0.706600	−	1.59190i
$883$			9.78525e21i			0.786804i	0.919367	+	0.393402i	$0.128702\pi$
$883$			9.78525e21i			0.786804i	−0.919367	+	0.393402i	$0.871298\pi$
$884$	−2.26428e21	−	4.96382e17i	−0.180525	−	3.95752e-5i
$885$	1.17244e22	+	2.17919e21i	0.926862	+	0.172274i
$886$	6.48618e21	+	6.48760e21i	0.508435	+	0.508547i
$887$	2.10021e22			1.63243			0.816216	−	0.577746i	$-0.196068\pi$
$887$	2.10021e22			1.63243			0.816216	+	0.577746i	$0.196068\pi$
$888$	8.25186e21	+	1.20282e22i	0.635996	+	0.927049i
$889$	3.28981e22			2.51424
$890$	−1.40477e21	−	1.40508e21i	−0.106459	−	0.106482i
$891$	7.63777e21	+	6.90543e21i	0.573963	+	0.518929i
$892$	−6.20866e21	−	1.36108e18i	−0.462660	−	0.000101426i
$893$		−	3.54213e21i		−	0.261745i
$894$	1.50820e22	+	2.19737e22i	1.10517	+	1.61017i
$895$		−	3.43914e22i		−	2.49906i
$896$	−1.62356e22	−	1.62606e22i	−1.16993	−	1.17173i
$897$	3.82188e19	−	2.05623e20i	0.00273108	−	0.0146936i
$898$	−1.01921e22	+	1.01898e22i	−0.722252	+	0.722094i
$899$	1.77323e22			1.24614
$900$	−3.82957e21	+	9.93945e21i	−0.266890	+	0.692698i
$901$	2.28086e21			0.157639
$902$	−1.33541e22	+	1.33512e22i	−0.915307	+	0.915107i
$903$	2.33020e19	−	1.25368e20i	0.00158392	−	0.00852176i
$904$	5.65327e21	+	5.65699e21i	0.381098	+	0.381349i
$905$			8.07797e20i			0.0540055i
$906$	3.56203e21	+	5.18970e21i	0.236176	+	0.344097i
$907$			1.50029e22i			0.986556i	0.869872	+	0.493278i	$0.164201\pi$
$907$			1.50029e22i			0.986556i	−0.869872	+	0.493278i	$0.835799\pi$
$908$	−2.07336e18	+	9.45777e21i	−0.000135217	+	0.616801i
$909$	−1.92722e19	+	5.00527e19i	−0.00124653	+	0.00323742i
$910$	3.45491e21	+	3.45566e21i	0.221629	+	0.221677i
$911$	2.59251e22			1.64943			0.824713	−	0.565551i	$-0.191336\pi$
$911$	2.59251e22			1.64943			0.824713	+	0.565551i	$0.191336\pi$
$912$	8.84881e21	+	1.64873e21i	0.558372	+	0.104037i
$913$	−6.59151e21			−0.412529
$914$	−7.30186e21	−	7.30346e21i	−0.453249	−	0.453349i
$915$	−1.80407e22	−	3.35320e21i	−1.11070	−	0.206443i
$916$	4.52014e18	−	2.06189e22i	0.000276017	−	1.25907i
$917$			1.19127e22i			0.721507i
$918$	−4.85784e21	−	2.03819e22i	−0.291825	−	1.22441i
$919$		−	4.08478e21i		−	0.243390i	−0.992568	−	0.121695i	$-0.961167\pi$
$919$		−	4.08478e21i		−	0.243390i	0.992568	−	0.121695i	$-0.0388330\pi$
$920$	−1.64515e21	−	1.64623e21i	−0.0972293	−	0.0972933i
$921$	2.49080e21	+	4.62961e20i	0.146013	+	0.0271392i
$922$	−1.47523e21	+	1.47491e21i	−0.0857787	+	0.0857599i
$923$	3.67148e21			0.211753
$924$	4.09734e21	−	2.20175e22i	0.234402	−	1.25958i
$925$	−1.47069e22			−0.834560
$926$	1.79522e22	−	1.79482e22i	1.01050	−	1.01027i
$927$	−2.32639e21	+	6.04196e21i	−0.129892	+	0.337349i
$928$	1.85364e22	−	1.85161e22i	1.02663	−	1.02551i
$929$		−	1.71020e22i		−	0.939572i	−0.882780	−	0.469786i	$-0.844331\pi$
$929$		−	1.71020e22i		−	0.939572i	0.882780	−	0.469786i	$-0.155669\pi$
$930$	−1.71492e22	+	1.17706e22i	−0.934590	+	0.641471i
$931$		−	1.82988e22i		−	0.989238i
$932$	−6.35080e21	−	1.39224e18i	−0.340572	−	7.46612e-5i
$933$	4.96625e21	−	2.67192e22i	0.264190	−	1.42138i
$934$	−1.96256e22	−	1.96299e22i	−1.03567	−	1.03590i
$935$	−2.45577e22			−1.28559
$936$	−2.52450e21	+	1.11989e21i	−0.131101	+	0.0581577i
$937$	−2.35031e22			−1.21082			−0.605408	−	0.795915i	$-0.706990\pi$
$937$	−2.35031e22			−1.21082			−0.605408	+	0.795915i	$0.706990\pi$
$938$	3.02252e22	+	3.02318e22i	1.54471	+	1.54505i
$939$	−5.29915e21	+	2.85103e22i	−0.268667	+	1.44547i
$940$	1.20940e22	+	2.65128e18i	0.608290	+	0.000133351i
$941$			1.09694e22i			0.547346i	0.961823	+	0.273673i	$0.0882386\pi$
$941$			1.09694e22i			0.547346i	−0.961823	+	0.273673i	$0.911761\pi$
$942$	−6.20135e21	+	4.25640e21i	−0.306976	+	0.210698i
$943$			3.54935e21i			0.174306i
$944$	1.46593e22	+	6.42733e18i	0.714208	+	0.000313141i
$945$	−2.36855e22	+	3.85185e22i	−1.14484	+	1.86179i
$946$	5.97344e19	−	5.97213e19i	0.00286445	−	0.00286382i
$947$	1.04407e22			0.496714			0.248357	−	0.968669i	$-0.420109\pi$
$947$	1.04407e22			0.496714			0.248357	+	0.968669i	$0.420109\pi$
$948$	−4.58073e20	+	2.46150e21i	−0.0216208	+	0.116182i
$949$	2.40125e21			0.112445
$950$	−6.41790e21	+	6.41649e21i	−0.298171	+	0.298106i
$951$	9.37428e21	+	1.74238e21i	0.432100	+	0.0803136i
$952$	−3.22356e22	+	3.22144e22i	−1.47421	+	1.47324i
$953$		−	1.55371e22i		−	0.704974i	−0.935817	−	0.352487i	$-0.885336\pi$
$953$		−	1.55371e22i		−	0.704974i	0.935817	−	0.352487i	$-0.114664\pi$
$954$	2.54274e21	−	1.12865e21i	0.114469	−	0.0508097i
$955$		−	3.84462e20i		−	0.0171723i
$956$	−2.40563e18	+	1.09734e22i	−0.000106609	+	0.486305i
$957$	2.51055e22	+	4.66631e21i	1.10390	+	0.205180i
$958$	−5.40434e21	−	5.40552e21i	−0.235777	−	0.235829i
$959$	−3.91212e22			−1.69345
$960$	−5.63591e21	+	3.02115e22i	−0.242064	+	1.29759i
$961$	6.16000e21			0.262516
$962$	−2.69602e21	−	2.69661e21i	−0.114001	−	0.114026i
$963$	3.05731e21	+	1.17718e21i	0.128275	+	0.0493908i
$964$	−7.41304e18	+	3.38151e22i	−0.000308616	+	1.40777i
$965$		−	8.61705e21i		−	0.355962i
$966$	−2.38211e21	−	3.47060e21i	−0.0976411	−	0.142258i
$967$		−	1.22020e22i		−	0.496288i	−0.968723	−	0.248144i	$-0.920179\pi$
$967$		−	1.22020e22i		−	0.496288i	0.968723	−	0.248144i	$-0.0798205\pi$
$968$	−7.03298e21	+	7.02835e21i	−0.283840	+	0.283654i
$969$	3.26224e21	−	1.75513e22i	0.130643	−	0.702881i
$970$	2.83523e22	−	2.83461e22i	1.12668	−	1.12643i
$971$	−4.37020e22			−1.72329			−0.861643	−	0.507515i	$-0.830564\pi$
$971$	−4.37020e22			−1.72329			−0.861643	+	0.507515i	$0.830564\pi$
$972$	−1.55013e22	−	2.03183e22i	−0.606556	−	0.795041i
$973$	−3.45049e22			−1.33978
$974$	9.62750e20	−	9.62539e20i	0.0370955	−	0.0370874i
$975$	5.08837e20	−	2.73762e21i	0.0194556	−	0.104674i
$976$	−2.25569e22	−	9.88995e18i	−0.855864	−	0.000375250i
$977$		−	2.08948e22i		−	0.786735i	−0.919381	−	0.393367i	$-0.871310\pi$
$977$		−	2.08948e22i		−	0.786735i	0.919381	−	0.393367i	$-0.128690\pi$
$978$	2.02631e22	+	2.95223e22i	0.757120	+	1.10308i
$979$		−	2.38046e21i		−	0.0882654i
$980$	6.24782e22	+	1.36966e19i	2.29897	+	0.000503986i
$981$	2.20495e20	+	8.48991e19i	0.00805159	+	0.00310017i
$982$	1.87213e22	+	1.87254e22i	0.678422	+	0.678571i
$983$	−2.99930e22			−1.07862			−0.539310	−	0.842108i	$-0.681315\pi$
$983$	−2.99930e22			−1.07862			−0.539310	+	0.842108i	$0.681315\pi$
$984$	3.86482e22	−	2.65144e22i	1.37932	−	0.946278i
$985$	5.12532e22			1.81530
$986$	−3.67392e22	−	3.67472e22i	−1.29138	−	1.29166i
$987$	2.15058e22	+	3.99725e21i	0.750201	+	0.139439i
$988$	−2.35302e21	−	5.15836e17i	−0.0814608	−	1.78581e-5i
$989$		−	1.58766e19i		−	0.000545489i
$990$	−2.73773e22	+	1.21520e22i	−0.933527	+	0.414367i
$991$			3.08407e22i			1.04369i	0.853040	+	0.521846i	$0.174756\pi$
$991$			3.08407e22i			1.04369i	−0.853040	+	0.521846i	$0.825244\pi$
$992$	−1.80899e22	+	1.80701e22i	−0.607574	+	0.606909i
$993$	−4.22363e22	−	7.85039e21i	−1.40788	−	0.261681i
$994$	5.22580e22	−	5.22465e22i	1.72884	−	1.72846i
$995$	3.81758e22			1.25347
$996$	1.60840e22	+	2.99315e21i	0.524142	+	0.0975403i
$997$	7.72383e21			0.249815			0.124908	−	0.992168i	$-0.460137\pi$
$997$	7.72383e21			0.249815			0.124908	+	0.992168i	$0.460137\pi$
$998$	1.16309e22	−	1.16284e22i	0.373366	−	0.373284i
$999$	1.84829e22	−	3.00577e22i	0.588883	−	0.957668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.16.b.a.11.7	✓	28
3.2	odd	2	inner	12.16.b.a.11.22	yes	28
4.3	odd	2	inner	12.16.b.a.11.21	yes	28
12.11	even	2	inner	12.16.b.a.11.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.16.b.a.11.7	✓	28	1.1	even	1	trivial
12.16.b.a.11.8	yes	28	12.11	even	2	inner
12.16.b.a.11.21	yes	28	4.3	odd	2	inner
12.16.b.a.11.22	yes	28	3.2	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)

\(f(q)\)	\(=\)	\(q+(-127.986 - 128.014i) q^{2} +(-692.213 + 3724.21i) q^{3} +(-7.18349 + 32768.0i) q^{4} +230590. i q^{5} +(565345. - 388034. i) q^{6} +3.60781e6i q^{7} +(4.19568e6 - 4.19292e6i) q^{8} +(-1.33906e7 - 5.15589e6i) q^{9} +O(q^{10})\)	\(q+(-127.986 - 128.014i) q^{2} +(-692.213 + 3724.21i) q^{3} +(-7.18349 + 32768.0i) q^{4} +230590. i q^{5} +(565345. - 388034. i) q^{6} +3.60781e6i q^{7} +(4.19568e6 - 4.19292e6i) q^{8} +(-1.33906e7 - 5.15589e6i) q^{9} +(2.95188e7 - 2.95123e7i) q^{10} +5.00101e7 q^{11} +(-1.22030e8 - 2.27092e7i) q^{12} +3.24482e7 q^{13} +(4.61850e8 - 4.61749e8i) q^{14} +(-8.58766e8 - 1.59617e8i) q^{15} +(-1.07374e9 - 470777. i) q^{16} +2.12956e9i q^{17} +(1.05378e9 + 2.37407e9i) q^{18} +2.21302e9i q^{19} +(-7.55598e9 - 1.65644e6i) q^{20} +(-1.34362e10 - 2.49737e9i) q^{21} +(-6.40059e9 - 6.40199e9i) q^{22} -1.70156e9 q^{23} +(1.27110e10 + 1.85280e10i) q^{24} -2.26542e10 q^{25} +(-4.15291e9 - 4.15382e9i) q^{26} +(2.84708e10 - 4.63004e10i) q^{27} +(-1.18221e11 - 2.59167e7i) q^{28} -1.34796e11i q^{29} +(8.94768e10 + 1.30363e11i) q^{30} +1.31549e11i q^{31} +(1.37364e11 + 1.37514e11i) q^{32} +(-3.46176e10 + 1.86248e11i) q^{33} +(2.72614e11 - 2.72554e11i) q^{34} -8.31925e11 q^{35} +(1.69044e11 - 4.38746e11i) q^{36} +6.49189e11 q^{37} +(2.83298e11 - 2.83236e11i) q^{38} +(-2.24610e10 + 1.20844e11i) q^{39} +(9.66847e11 + 9.67483e11i) q^{40} -2.08594e12i q^{41} +(1.39995e12 + 2.03965e12i) q^{42} +9.33060e9i q^{43} +(-3.59247e8 + 1.63873e12i) q^{44} +(1.18890e12 - 3.08774e12i) q^{45} +(2.17776e11 + 2.17824e11i) q^{46} -1.60059e12 q^{47} +(7.45011e11 - 3.99852e12i) q^{48} -8.26871e12 q^{49} +(2.89942e12 + 2.90006e12i) q^{50} +(-7.93093e12 - 1.47411e12i) q^{51} +(-2.33091e8 + 1.06326e12i) q^{52} -1.07105e12i q^{53} +(-9.57096e12 + 2.28115e12i) q^{54} +1.15318e13i q^{55} +(1.51273e13 + 1.51372e13i) q^{56} +(-8.24177e12 - 1.53188e12i) q^{57} +(-1.72558e13 + 1.72520e13i) q^{58} -1.36526e13 q^{59} +(5.23651e12 - 2.81389e13i) q^{60} +2.10077e13 q^{61} +(1.68402e13 - 1.68365e13i) q^{62} +(1.86015e13 - 4.83107e13i) q^{63} +(2.31397e10 - 3.51844e13i) q^{64} +7.48222e12i q^{65} +(2.82729e13 - 1.94056e13i) q^{66} +6.54581e13i q^{67} +(-6.97814e13 - 1.52977e10i) q^{68} +(1.17784e12 - 6.33698e12i) q^{69} +(1.06475e14 + 1.06498e14i) q^{70} +1.13149e14 q^{71} +(-7.78009e13 + 3.45133e13i) q^{72} +7.40026e13 q^{73} +(-8.30871e13 - 8.31053e13i) q^{74} +(1.56815e13 - 8.43692e13i) q^{75} +(-7.25163e13 - 1.58972e10i) q^{76} +1.80427e14i q^{77} +(1.83444e13 - 1.25910e13i) q^{78} -2.01713e13i q^{79} +(1.08557e11 - 2.47594e14i) q^{80} +(1.52725e14 + 1.38081e14i) q^{81} +(-2.67029e14 + 2.66971e14i) q^{82} -1.31804e14 q^{83} +(8.19303e13 - 4.40261e14i) q^{84} -4.91056e14 q^{85} +(1.19445e12 - 1.19419e12i) q^{86} +(5.02009e14 + 9.33075e13i) q^{87} +(2.09826e14 - 2.09688e14i) q^{88} -4.75996e13i q^{89} +(-5.47436e14 + 2.42992e14i) q^{90} +1.17067e14i q^{91} +(1.22232e10 - 5.57568e13i) q^{92} +(-4.89918e14 - 9.10602e13i) q^{93} +(2.04852e14 + 2.04897e14i) q^{94} -5.10301e14 q^{95} +(-6.07217e14 + 4.16382e14i) q^{96} +9.60484e14 q^{97} +(1.05828e15 + 1.05851e15i) q^{98} +(-6.69664e14 - 2.57846e14i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more