LMFDB - Embedded newform 8.18.b.a.5.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,18,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	8.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:	$14.6577669876$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} + \cdots + 12\!\cdots\!00 $ x^16 - 7x^15 + 4022x^14 - 1102776x^13 - 373411968x^12 + 2100004864x^11 - 3763915816960x^10 + 7317489121656832x^9 - 1108241988138827776x^8 + 163121042717484777472x^7 + 5699397839986467274752x^6 + 1127435088957285706235904x^5 - 217909345031306501735579648x^4 - 78950720850572326734309359616x^3 + 13720647095471028734661620662272x^2 - 5242030267748791654842336509165568*x + 1286374137827816254118965326485913600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{14}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.16
Root			$167.908 - 42.7144i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.18.b.a.5.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(351.815 + 85.4288i) q^{2} +21682.7i q^{3} +(116476. + 60110.3i) q^{4} +465248. i q^{5} +(-1.85232e6 + 7.62829e6i) q^{6} +2.24795e7 q^{7} +(3.58428e7 + 3.10981e7i) q^{8} -3.40998e8 q^{9} +O(q^{10})$	\(q+(351.815 + 85.4288i) q^{2} +21682.7i q^{3} +(116476. + 60110.3i) q^{4} +465248. i q^{5} +(-1.85232e6 + 7.62829e6i) q^{6} +2.24795e7 q^{7} +(3.58428e7 + 3.10981e7i) q^{8} -3.40998e8 q^{9} +(-3.97456e7 + 1.63681e8i) q^{10} -6.06148e8i q^{11} +(-1.30335e9 + 2.52551e9i) q^{12} -2.12768e9i q^{13} +(7.90864e9 + 1.92040e9i) q^{14} -1.00878e10 q^{15} +(9.95338e9 + 1.40028e10i) q^{16} -5.45139e9 q^{17} +(-1.19968e11 - 2.91311e10i) q^{18} -5.72346e9i q^{19} +(-2.79662e10 + 5.41902e10i) q^{20} +4.87417e11i q^{21} +(5.17825e10 - 2.13252e11i) q^{22} -1.30247e11 q^{23} +(-6.74290e11 + 7.77168e11i) q^{24} +5.46483e11 q^{25} +(1.81765e11 - 7.48551e11i) q^{26} -4.59365e12i q^{27} +(2.61832e12 + 1.35125e12i) q^{28} +4.23568e11i q^{29} +(-3.54905e12 - 8.61791e11i) q^{30} +3.83783e12 q^{31} +(2.30551e12 + 5.77670e12i) q^{32} +1.31429e13 q^{33} +(-1.91788e12 - 4.65706e11i) q^{34} +1.04586e13i q^{35} +(-3.97181e13 - 2.04975e13i) q^{36} -2.39674e13i q^{37} +(4.88948e11 - 2.01360e12i) q^{38} +4.61339e13 q^{39} +(-1.44683e13 + 1.66758e13i) q^{40} -5.79528e12 q^{41} +(-4.16394e13 + 1.71481e14i) q^{42} +4.00069e13i q^{43} +(3.64357e13 - 7.06016e13i) q^{44} -1.58649e14i q^{45} +(-4.58229e13 - 1.11268e13i) q^{46} -1.56837e14 q^{47} +(-3.03618e14 + 2.15816e14i) q^{48} +2.72699e14 q^{49} +(1.92261e14 + 4.66854e13i) q^{50} -1.18201e14i q^{51} +(1.27896e14 - 2.47824e14i) q^{52} +6.45318e14i q^{53} +(3.92430e14 - 1.61612e15i) q^{54} +2.82010e14 q^{55} +(8.05730e14 + 6.99071e14i) q^{56} +1.24100e14 q^{57} +(-3.61849e13 + 1.49018e14i) q^{58} -8.37680e14i q^{59} +(-1.17499e15 - 6.06382e14i) q^{60} +3.98624e14i q^{61} +(1.35021e15 + 3.27862e14i) q^{62} -7.66548e15 q^{63} +(3.17616e14 + 2.22929e15i) q^{64} +9.89901e14 q^{65} +(4.62388e15 + 1.12278e15i) q^{66} +5.22273e15i q^{67} +(-6.34956e14 - 3.27685e14i) q^{68} -2.82410e15i q^{69} +(-8.93463e14 + 3.67948e15i) q^{70} +5.50116e15 q^{71} +(-1.22223e16 - 1.06044e16i) q^{72} +1.47400e15 q^{73} +(2.04751e15 - 8.43211e15i) q^{74} +1.18492e16i q^{75} +(3.44039e14 - 6.66645e14i) q^{76} -1.36259e16i q^{77} +(1.62306e16 + 3.94116e15i) q^{78} -1.94988e16 q^{79} +(-6.51478e15 + 4.63079e15i) q^{80} +5.55660e16 q^{81} +(-2.03887e15 - 4.95084e14i) q^{82} -3.36599e16i q^{83} +(-2.92987e16 + 5.67723e16i) q^{84} -2.53625e15i q^{85} +(-3.41774e15 + 1.40750e16i) q^{86} -9.18409e15 q^{87} +(1.88501e16 - 2.17261e16i) q^{88} -1.09831e16 q^{89} +(1.35532e16 - 5.58151e16i) q^{90} -4.78293e16i q^{91} +(-1.51706e16 - 7.82918e15i) q^{92} +8.32145e16i q^{93} +(-5.51777e16 - 1.33984e16i) q^{94} +2.66283e15 q^{95} +(-1.25254e17 + 4.99896e16i) q^{96} +6.57395e16 q^{97} +(9.59397e16 + 2.32964e16i) q^{98} +2.06695e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9}+O(q^{10}) $ 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9	$ 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + 131002712 q^{10} - 2795125400 q^{12} + 16363788528 q^{14} - 9993282176 q^{15} + 26500434192 q^{16} - 7489125600 q^{17} - 113450563870 q^{18} - 209445719856 q^{20} + 223126527100 q^{22} + 746845345920 q^{23} - 1099415493232 q^{24} - 1809682431664 q^{25} + 2467726531080 q^{26} + 3220542267040 q^{28} - 1188624268048 q^{30} - 318979758592 q^{31} + 1455647316000 q^{32} + 5633526177600 q^{33} - 4461251980292 q^{34} - 33088278002484 q^{36} + 24076283913900 q^{38} - 18457706051456 q^{39} + 60626292962592 q^{40} + 7482251536032 q^{41} - 51630378688160 q^{42} + 193654716236040 q^{44} - 195097141003568 q^{46} - 376698804821760 q^{47} - 329350060416480 q^{48} + 127691292101520 q^{49} + 474997408872102 q^{50} - 272251877663120 q^{52} + 735354219382520 q^{54} + 22\!\cdots\!52 q^{55}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9 + 131002712 * q^10 - 2795125400 * q^12 + 16363788528 * q^14 - 9993282176 * q^15 + 26500434192 * q^16 - 7489125600 * q^17 - 113450563870 * q^18 - 209445719856 * q^20 + 223126527100 * q^22 + 746845345920 * q^23 - 1099415493232 * q^24 - 1809682431664 * q^25 + 2467726531080 * q^26 + 3220542267040 * q^28 - 1188624268048 * q^30 - 318979758592 * q^31 + 1455647316000 * q^32 + 5633526177600 * q^33 - 4461251980292 * q^34 - 33088278002484 * q^36 + 24076283913900 * q^38 - 18457706051456 * q^39 + 60626292962592 * q^40 + 7482251536032 * q^41 - 51630378688160 * q^42 + 193654716236040 * q^44 - 195097141003568 * q^46 - 376698804821760 * q^47 - 329350060416480 * q^48 + 127691292101520 * q^49 + 474997408872102 * q^50 - 272251877663120 * q^52 + 735354219382520 * q^54 + 2209036687713152 * q^55 - 162767516076480 * q^56 - 190521298294720 * q^57 - 623262610679960 * q^58 - 1973616194963808 * q^60 + 695695648144320 * q^62 - 8131096607338880 * q^63 + 1111931745501248 * q^64 + 2385987975356160 * q^65 + 3598826202828312 * q^66 + 5981109959771880 * q^68 - 10044559836180288 * q^70 + 9025926285576576 * q^71 - 19918679666289160 * q^72 + 11332002046118560 * q^73 + 11098735408189464 * q^74 + 5959440926938280 * q^76 + 4184252259031760 * q^78 - 45299671392008448 * q^79 + 1337342539452480 * q^80 + 20101901999290832 * q^81 + 15639739637081420 * q^82 + 19796542864700224 * q^84 - 14252032276026564 * q^86 + 25965768920837760 * q^87 - 66964872768837680 * q^88 - 69879174608766048 * q^89 + 136151511125051240 * q^90 + 57336249810701280 * q^92 - 192318922166254176 * q^94 + 93790444358203776 * q^95 - 342799224184788928 * q^96 + 95593398602180640 * q^97 + 339641261743253790 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

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

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 $

$2$	351.815	+	85.4288i	0.971761	+	0.235966i
$2$	351.815	+	85.4288i	0.971761	+	0.235966i
$3$			21682.7i			1.90802i	0.299780	+	0.954008i	$0.403087\pi$
$3$			21682.7i			1.90802i	−0.299780	+	0.954008i	$0.596913\pi$
$4$	116476.	+	60110.3i	0.888640	+	0.458605i
$5$			465248.i			0.532647i	0.963884	+	0.266324i	$0.0858090\pi$
$5$			465248.i			0.532647i	−0.963884	+	0.266324i	$0.914191\pi$
$6$	−1.85232e6	+	7.62829e6i	−0.450227	+	1.85414i
$7$	2.24795e7			1.47385			0.736926	−	0.675973i	$-0.236276\pi$
$7$	2.24795e7			1.47385			0.736926	+	0.675973i	$0.236276\pi$
$8$	3.58428e7	+	3.10981e7i	0.755331	+	0.655343i
$9$	−3.40998e8			−2.64053
$10$	−3.97456e7	+	1.63681e8i	−0.125687	+	0.517606i
$11$		−	6.06148e8i		−	0.852592i	−0.904584	−	0.426296i	$-0.859818\pi$
$11$		−	6.06148e8i		−	0.852592i	0.904584	−	0.426296i	$-0.140182\pi$
$12$	−1.30335e9	+	2.52551e9i	−0.875026	+	1.69554i
$13$		−	2.12768e9i		−	0.723417i	−0.932291	−	0.361708i	$-0.882194\pi$
$13$		−	2.12768e9i		−	0.723417i	0.932291	−	0.361708i	$-0.117806\pi$
$14$	7.90864e9	+	1.92040e9i	1.43223	+	0.347779i
$15$	−1.00878e10			−1.01630
$16$	9.95338e9	+	1.40028e10i	0.579363	+	0.815070i
$17$	−5.45139e9			−0.189536			−0.0947680	−	0.995499i	$-0.530211\pi$
$17$	−5.45139e9			−0.189536			−0.0947680	+	0.995499i	$0.530211\pi$
$18$	−1.19968e11	−	2.91311e10i	−2.56596	−	0.623075i
$19$		−	5.72346e9i		−	0.0773131i	−0.999253	−	0.0386565i	$-0.987692\pi$
$19$		−	5.72346e9i		−	0.0773131i	0.999253	−	0.0386565i	$-0.0123078\pi$
$20$	−2.79662e10	+	5.41902e10i	−0.244275	+	0.473332i
$21$			4.87417e11i			2.81214i
$22$	5.17825e10	−	2.13252e11i	0.201183	−	0.828515i
$23$	−1.30247e11			−0.346802			−0.173401	−	0.984851i	$-0.555476\pi$
$23$	−1.30247e11			−0.346802			−0.173401	+	0.984851i	$0.555476\pi$
$24$	−6.74290e11	+	7.77168e11i	−1.25041	+	1.44118i
$25$	5.46483e11			0.716287
$26$	1.81765e11	−	7.48551e11i	0.170702	−	0.702988i
$27$		−	4.59365e12i		−	3.13016i
$28$	2.61832e12	+	1.35125e12i	1.30972	+	0.675916i
$29$			4.23568e11i			0.157232i	0.996905	+	0.0786159i	$0.0250501\pi$
$29$			4.23568e11i			0.157232i	−0.996905	+	0.0786159i	$0.974950\pi$
$30$	−3.54905e12	−	8.61791e11i	−0.987601	−	0.239812i
$31$	3.83783e12			0.808187			0.404093	−	0.914718i	$-0.367587\pi$
$31$	3.83783e12			0.808187			0.404093	+	0.914718i	$0.367587\pi$
$32$	2.30551e12	+	5.77670e12i	0.370674	+	0.928763i
$33$	1.31429e13			1.62676
$34$	−1.91788e12	−	4.65706e11i	−0.184184	−	0.0447240i
$35$			1.04586e13i			0.785044i
$36$	−3.97181e13	−	2.04975e13i	−2.34648	−	1.21096i
$37$		−	2.39674e13i		−	1.12178i	−0.827891	−	0.560889i	$-0.810459\pi$
$37$		−	2.39674e13i		−	1.12178i	0.827891	−	0.560889i	$-0.189541\pi$
$38$	4.88948e11	−	2.01360e12i	0.0182432	−	0.0751299i
$39$	4.61339e13			1.38029
$40$	−1.44683e13	+	1.66758e13i	−0.349067	+	0.402325i
$41$	−5.79528e12			−0.113347			−0.0566737	−	0.998393i	$-0.518049\pi$
$41$	−5.79528e12			−0.113347			−0.0566737	+	0.998393i	$0.518049\pi$
$42$	−4.16394e13	+	1.71481e14i	−0.663568	+	2.73272i
$43$			4.00069e13i			0.521979i	0.965342	+	0.260989i	$0.0840488\pi$
$43$			4.00069e13i			0.521979i	−0.965342	+	0.260989i	$0.915951\pi$
$44$	3.64357e13	−	7.06016e13i	0.391003	−	0.757647i
$45$		−	1.58649e14i		−	1.40647i
$46$	−4.58229e13	−	1.11268e13i	−0.337008	−	0.0818333i
$47$	−1.56837e14			−0.960765			−0.480382	−	0.877059i	$-0.659502\pi$
$47$	−1.56837e14			−0.960765			−0.480382	+	0.877059i	$0.659502\pi$
$48$	−3.03618e14	+	2.15816e14i	−1.55517	+	1.10543i
$49$	2.72699e14			1.17224
$50$	1.92261e14	+	4.66854e13i	0.696060	+	0.169019i
$51$		−	1.18201e14i		−	0.361638i
$52$	1.27896e14	−	2.47824e14i	0.331763	−	0.642857i
$53$			6.45318e14i			1.42374i	0.702314	+	0.711868i	$0.252150\pi$
$53$			6.45318e14i			1.42374i	−0.702314	+	0.711868i	$0.747850\pi$
$54$	3.92430e14	−	1.61612e15i	0.738610	−	3.04176i
$55$	2.82010e14			0.454131
$56$	8.05730e14	+	6.99071e14i	1.11325	+	0.965880i
$57$	1.24100e14			0.147515
$58$	−3.61849e13	+	1.49018e14i	−0.0371013	+	0.152792i
$59$		−	8.37680e14i		−	0.742739i	−0.928485	−	0.371369i	$-0.878888\pi$
$59$		−	8.37680e14i		−	0.742739i	0.928485	−	0.371369i	$-0.121112\pi$
$60$	−1.17499e15	−	6.06382e14i	−0.903125	−	0.466081i
$61$			3.98624e14i			0.266232i	0.991100	+	0.133116i	$0.0424983\pi$
$61$			3.98624e14i			0.266232i	−0.991100	+	0.133116i	$0.957502\pi$
$62$	1.35021e15	+	3.27862e14i	0.785365	+	0.190705i
$63$	−7.66548e15			−3.89175
$64$	3.17616e14	+	2.22929e15i	0.141050	+	0.990002i
$65$	9.89901e14			0.385326
$66$	4.62388e15	+	1.12278e15i	1.58082	+	0.383860i
$67$			5.22273e15i			1.57131i	0.618665	+	0.785655i	$0.287674\pi$
$67$			5.22273e15i			1.57131i	−0.618665	+	0.785655i	$0.712326\pi$
$68$	−6.34956e14	−	3.27685e14i	−0.168429	−	0.0869222i
$69$		−	2.82410e15i		−	0.661703i
$70$	−8.93463e14	+	3.67948e15i	−0.185244	+	0.762875i
$71$	5.50116e15			1.01102			0.505508	−	0.862822i	$-0.331305\pi$
$71$	5.50116e15			1.01102			0.505508	+	0.862822i	$0.331305\pi$
$72$	−1.22223e16	−	1.06044e16i	−1.99447	−	1.73045i
$73$	1.47400e15			0.213921			0.106960	−	0.994263i	$-0.465888\pi$
$73$	1.47400e15			0.213921			0.106960	+	0.994263i	$0.465888\pi$
$74$	2.04751e15	−	8.43211e15i	0.264701	−	1.09010i
$75$			1.18492e16i			1.36669i
$76$	3.44039e14	−	6.66645e14i	0.0354562	−	0.0687035i
$77$		−	1.36259e16i		−	1.25659i
$78$	1.62306e16	+	3.94116e15i	1.34131	+	0.325702i
$79$	−1.94988e16			−1.44603			−0.723015	−	0.690833i	$-0.757244\pi$
$79$	−1.94988e16			−1.44603			−0.723015	+	0.690833i	$0.757244\pi$
$80$	−6.51478e15	+	4.63079e15i	−0.434145	+	0.308596i
$81$	5.55660e16			3.33186
$82$	−2.03887e15	−	4.95084e14i	−0.110147	−	0.0267461i
$83$		−	3.36599e16i		−	1.64040i	−0.572078	−	0.820199i	$-0.693862\pi$
$83$		−	3.36599e16i		−	1.64040i	0.572078	−	0.820199i	$-0.306138\pi$
$84$	−2.92987e16	+	5.67723e16i	−1.28966	+	2.49898i
$85$		−	2.53625e15i		−	0.100956i
$86$	−3.41774e15	+	1.40750e16i	−0.123169	+	0.507239i
$87$	−9.18409e15			−0.300001
$88$	1.88501e16	−	2.17261e16i	0.558740	−	0.643989i
$89$	−1.09831e16			−0.295740			−0.147870	−	0.989007i	$-0.547242\pi$
$89$	−1.09831e16			−0.295740			−0.147870	+	0.989007i	$0.547242\pi$
$90$	1.35532e16	−	5.58151e16i	0.331879	−	1.36675i
$91$		−	4.78293e16i		−	1.06621i
$92$	−1.51706e16	−	7.82918e15i	−0.308182	−	0.159045i
$93$			8.32145e16i			1.54203i
$94$	−5.51777e16	−	1.33984e16i	−0.933634	−	0.226708i
$95$	2.66283e15			0.0411806
$96$	−1.25254e17	+	4.99896e16i	−1.77210	+	0.707251i
$97$	6.57395e16			0.851660			0.425830	−	0.904803i	$-0.359982\pi$
$97$	6.57395e16			0.851660			0.425830	+	0.904803i	$0.359982\pi$
$98$	9.59397e16	+	2.32964e16i	1.13914	+	0.276609i
$99$			2.06695e17i			2.25129i
$100$	6.36521e16	+	3.28493e16i	0.636521	+	0.328493i
$101$		−	7.10748e16i		−	0.653106i	−0.945179	−	0.326553i	$-0.894113\pi$
$101$		−	7.10748e16i		−	0.653106i	0.945179	−	0.326553i	$-0.105887\pi$
$102$	1.00977e16	−	4.15848e16i	0.0853342	−	0.351426i
$103$	−1.91977e17			−1.49325			−0.746624	−	0.665246i	$-0.768327\pi$
$103$	−1.91977e17			−1.49325			−0.746624	+	0.665246i	$0.768327\pi$
$104$	6.61669e16	−	7.62622e16i	0.474086	−	0.546419i
$105$	−2.26770e17			−1.49788
$106$	−5.51288e16	+	2.27033e17i	−0.335953	+	1.38353i
$107$		−	5.53132e16i		−	0.311220i	−0.987819	−	0.155610i	$-0.950266\pi$
$107$		−	5.53132e16i		−	0.311220i	0.987819	−	0.155610i	$-0.0497342\pi$
$108$	2.76126e17	−	5.35049e17i	1.43551	−	2.78158i
$109$		−	3.67908e17i		−	1.76854i	−0.466978	−	0.884269i	$-0.654657\pi$
$109$		−	3.67908e17i		−	1.76854i	0.466978	−	0.884269i	$-0.345343\pi$
$110$	9.92152e16	+	2.40917e16i	0.441307	+	0.107159i
$111$	5.19678e17			2.14037
$112$	2.23747e17	+	3.14776e17i	0.853895	+	1.20129i
$113$	−3.48457e17			−1.23306			−0.616528	−	0.787333i	$-0.711461\pi$
$113$	−3.48457e17			−1.23306			−0.616528	+	0.787333i	$0.711461\pi$
$114$	4.36602e16	+	1.06017e16i	0.143349	+	0.0348084i
$115$		−	6.05972e16i		−	0.184723i
$116$	−2.54608e16	+	4.93355e16i	−0.0721073	+	0.139723i
$117$			7.25536e17i			1.91020i
$118$	7.15620e16	−	2.94708e17i	0.175261	−	0.721765i
$119$	−1.22545e17			−0.279348
$120$	−3.61576e17	−	3.13712e17i	−0.767643	−	0.666026i
$121$	1.38031e17			0.273088
$122$	−3.40540e16	+	1.40242e17i	−0.0628217	+	0.258714i
$123$		−	1.25657e17i		−	0.216269i
$124$	4.47015e17	+	2.30693e17i	0.718187	+	0.370639i
$125$			6.09207e17i			0.914176i
$126$	−2.69683e18	−	6.54853e17i	−3.78185	−	0.918320i
$127$	5.29745e17			0.694600			0.347300	−	0.937754i	$-0.387099\pi$
$127$	5.29745e17			0.694600			0.347300	+	0.937754i	$0.387099\pi$
$128$	−7.87032e16	+	8.11431e17i	−0.0965401	+	0.995329i
$129$	−8.67456e17			−0.995944
$130$	3.48262e17	+	8.45661e16i	0.374445	+	0.0909238i
$131$		−	1.11774e18i		−	1.12599i	−0.826459	−	0.562996i	$-0.809649\pi$
$131$		−	1.11774e18i		−	1.12599i	0.826459	−	0.562996i	$-0.190351\pi$
$132$	1.53083e18	+	7.90024e17i	1.44560	+	0.746040i
$133$		−	1.28661e17i		−	0.113948i
$134$	−4.46171e17	+	1.83744e18i	−0.370775	+	1.52694i
$135$	2.13719e18			1.66727
$136$	−1.95393e17	−	1.69528e17i	−0.143162	−	0.124211i
$137$	6.75639e17			0.465146			0.232573	−	0.972579i	$-0.425285\pi$
$137$	6.75639e17			0.465146			0.232573	+	0.972579i	$0.425285\pi$
$138$	2.41260e17	−	9.93562e17i	0.156139	−	0.643018i
$139$		−	1.43378e18i		−	0.872686i	−0.899780	−	0.436343i	$-0.856273\pi$
$139$		−	1.43378e18i		−	0.872686i	0.899780	−	0.436343i	$-0.143727\pi$
$140$	−6.28668e17	+	1.21817e18i	−0.360025	+	0.697622i
$141$		−	3.40065e18i		−	1.83316i
$142$	1.93539e18	+	4.69957e17i	0.982467	+	0.238565i
$143$	−1.28969e18			−0.616779
$144$	−3.39408e18	−	4.77493e18i	−1.52982	−	2.15221i
$145$	−1.97064e17			−0.0837491
$146$	5.18575e17	+	1.25922e17i	0.207880	+	0.0504780i
$147$			5.91285e18i			2.23666i
$148$	1.44069e18	−	2.79163e18i	0.514453	−	0.996857i
$149$			2.92569e18i			0.986608i	0.869857	+	0.493304i	$0.164211\pi$
$149$			2.92569e18i			0.986608i	−0.869857	+	0.493304i	$0.835789\pi$
$150$	−1.01226e18	+	4.16874e18i	−0.322492	+	1.32809i
$151$	3.38847e18			1.02023			0.510117	−	0.860105i	$-0.329602\pi$
$151$	3.38847e18			1.02023			0.510117	+	0.860105i	$0.329602\pi$
$152$	1.77989e17	−	2.05145e17i	0.0506666	−	0.0583970i
$153$	1.85892e18			0.500475
$154$	1.16405e18	−	4.79381e18i	0.296513	−	1.22111i
$155$			1.78555e18i			0.430479i
$156$	5.37348e18	+	2.77312e18i	1.22658	+	0.633009i
$157$		−	3.55208e18i		−	0.767954i	−0.923343	−	0.383977i	$-0.874554\pi$
$157$		−	3.55208e18i		−	0.767954i	0.923343	−	0.383977i	$-0.125446\pi$
$158$	−6.85997e18	−	1.66576e18i	−1.40520	−	0.341214i
$159$	−1.39922e19			−2.71651
$160$	−2.68760e18	+	1.07263e18i	−0.494703	+	0.197438i
$161$	−2.92789e18			−0.511134
$162$	1.95490e19	+	4.74694e18i	3.23777	+	0.786205i
$163$		−	6.81975e18i		−	1.07195i	−0.844234	−	0.535974i	$-0.819944\pi$
$163$		−	6.81975e18i		−	1.07195i	0.844234	−	0.535974i	$-0.180056\pi$
$164$	−6.75010e17	−	3.48356e17i	−0.100725	−	0.0519817i
$165$			6.11472e18i			0.866489i
$166$	2.87553e18	−	1.18421e19i	0.387078	−	1.59408i
$167$	−1.29136e19			−1.65180			−0.825899	−	0.563819i	$-0.809332\pi$
$167$	−1.29136e19			−1.65180			−0.825899	+	0.563819i	$0.809332\pi$
$168$	−1.51577e19	+	1.74704e19i	−1.84291	+	2.12409i
$169$	4.12338e18			0.476668
$170$	2.16669e17	−	8.92292e17i	0.0238221	−	0.0981050i
$171$			1.95169e18i			0.204147i
$172$	−2.40483e18	+	4.65984e18i	−0.239382	+	0.463851i
$173$			2.98078e18i			0.282448i	0.989978	+	0.141224i	$0.0451037\pi$
$173$			2.98078e18i			0.282448i	−0.989978	+	0.141224i	$0.954896\pi$
$174$	−3.23110e18	−	7.84586e17i	−0.291529	−	0.0707900i
$175$	1.22847e19			1.05570
$176$	8.48777e18	−	6.03322e18i	0.694922	−	0.493960i
$177$	1.81631e19			1.41716
$178$	−3.86403e18	−	9.38274e17i	−0.287389	−	0.0697846i
$179$		−	4.00351e18i		−	0.283916i	−0.989873	−	0.141958i	$-0.954660\pi$
$179$		−	4.00351e18i		−	0.283916i	0.989873	−	0.141958i	$-0.0453398\pi$
$180$	9.53643e18	−	1.84788e19i	0.645015	−	1.24985i
$181$			2.28445e19i			1.47406i	0.675861	+	0.737029i	$0.263772\pi$
$181$			2.28445e19i			1.47406i	−0.675861	+	0.737029i	$0.736228\pi$
$182$	4.08600e18	−	1.68271e19i	0.251589	−	1.03610i
$183$	−8.64324e18			−0.507975
$184$	−4.66842e18	−	4.05043e18i	−0.261950	−	0.227274i
$185$	1.11508e19			0.597512
$186$	−7.10891e18	+	2.92761e19i	−0.363867	+	1.49849i
$187$			3.30435e18i			0.161597i
$188$	−1.82677e19	−	9.42753e18i	−0.853774	−	0.440612i
$189$		−	1.03263e20i		−	4.61339i
$190$	9.36824e17	+	2.27482e17i	0.0400177	+	0.00971722i
$191$	3.05570e19			1.24832			0.624162	−	0.781295i	$-0.285441\pi$
$191$	3.05570e19			1.24832			0.624162	+	0.781295i	$0.285441\pi$
$192$	−4.83369e19	+	6.88676e18i	−1.88894	+	0.269125i
$193$	2.24801e19			0.840547			0.420274	−	0.907397i	$-0.361934\pi$
$193$	2.24801e19			0.840547			0.420274	+	0.907397i	$0.361934\pi$
$194$	2.31281e19	+	5.61604e18i	0.827611	+	0.200963i
$195$			2.14637e19i			0.735209i
$196$	3.17629e19	+	1.63920e19i	1.04170	+	0.537596i
$197$			5.40141e19i			1.69646i	0.529625	+	0.848232i	$0.322333\pi$
$197$			5.40141e19i			1.69646i	−0.529625	+	0.848232i	$0.677667\pi$
$198$	−1.76577e19	+	7.27186e19i	−0.531228	+	2.18772i
$199$	−3.30197e18			−0.0951747			−0.0475874	−	0.998867i	$-0.515153\pi$
$199$	−3.30197e18			−0.0951747			−0.0475874	+	0.998867i	$0.515153\pi$
$200$	1.95875e19	+	1.69946e19i	0.541034	+	0.469414i
$201$	−1.13243e20			−2.99808
$202$	6.07183e18	−	2.50052e19i	0.154111	−	0.634663i
$203$			9.52162e18i			0.231737i
$204$	7.10508e18	−	1.37675e19i	0.165849	−	0.321366i
$205$		−	2.69624e18i		−	0.0603742i
$206$	−6.75403e19	−	1.64003e19i	−1.45108	−	0.352356i
$207$	4.44140e19			0.915739
$208$	2.97935e19	−	2.11776e19i	0.589635	−	0.419121i
$209$	−3.46926e18			−0.0659165
$210$	−7.97811e19	−	1.93727e19i	−1.45558	−	0.353448i
$211$		−	7.95957e19i		−	1.39473i	−0.716718	−	0.697363i	$-0.754357\pi$
$211$		−	7.95957e19i		−	1.39473i	0.716718	−	0.697363i	$-0.245643\pi$
$212$	−3.87903e19	+	7.51640e19i	−0.652932	+	1.26519i
$213$			1.19280e20i			1.92904i
$214$	4.72534e18	−	1.94600e19i	0.0734372	−	0.302431i
$215$	−1.86131e19			−0.278031
$216$	1.42854e20	−	1.64649e20i	2.05133	−	2.36430i
$217$	8.62727e19			1.19115
$218$	3.14300e19	−	1.29436e20i	0.417315	−	1.71860i
$219$			3.19603e19i			0.408164i
$220$	3.28473e19	+	1.69517e19i	0.403559	+	0.208267i
$221$			1.15988e19i			0.137113i
$222$	1.82831e20	+	4.43955e19i	2.07993	+	0.505055i
$223$	−7.18745e19			−0.787015			−0.393508	−	0.919321i	$-0.628739\pi$
$223$	−7.18745e19			−0.787015			−0.393508	+	0.919321i	$0.628739\pi$
$224$	5.18267e19	+	1.29858e20i	0.546318	+	1.36886i
$225$	−1.86350e20			−1.89138
$226$	−1.22593e20	−	2.97683e19i	−1.19824	−	0.290959i
$227$		−	1.07253e20i		−	1.00969i	−0.863210	−	0.504845i	$-0.831550\pi$
$227$		−	1.07253e20i		−	1.00969i	0.863210	−	0.504845i	$-0.168450\pi$
$228$	1.44546e19	+	7.45968e18i	0.131087	+	0.0676510i
$229$			8.55186e19i			0.747238i	0.927582	+	0.373619i	$0.121883\pi$
$229$			8.55186e19i			0.747238i	−0.927582	+	0.373619i	$0.878117\pi$
$230$	5.17674e18	−	2.13190e19i	0.0435883	−	0.179507i
$231$	2.95447e20			2.39760
$232$	−1.31722e19	+	1.51819e19i	−0.103041	+	0.118762i
$233$	−1.65020e20			−1.24455			−0.622273	−	0.782801i	$-0.713790\pi$
$233$	−1.65020e20			−1.24455			−0.622273	+	0.782801i	$0.713790\pi$
$234$	−6.19817e19	+	2.55255e20i	−0.450743	+	1.85626i
$235$		−	7.29682e19i		−	0.511749i
$236$	5.03532e19	−	9.75695e19i	0.340624	−	0.660027i
$237$		−	4.22786e20i		−	2.75905i
$238$	−4.31131e19	−	1.04689e19i	−0.271460	−	0.0659166i
$239$	−2.20002e20			−1.33673			−0.668367	−	0.743832i	$-0.733006\pi$
$239$	−2.20002e20			−1.33673			−0.668367	+	0.743832i	$0.733006\pi$
$240$	−1.00408e20	−	1.41258e20i	−0.588807	−	0.828356i
$241$	1.65734e19			0.0938137			0.0469069	−	0.998899i	$-0.485064\pi$
$241$	1.65734e19			0.0938137			0.0469069	+	0.998899i	$0.485064\pi$
$242$	4.85615e19	+	1.17919e19i	0.265376	+	0.0644394i
$243$			6.11596e20i			3.22709i
$244$	−2.39614e19	+	4.64301e19i	−0.122095	+	0.236584i
$245$			1.26873e20i			0.624392i
$246$	1.07347e19	−	4.42081e19i	0.0510320	−	0.210162i
$247$	−1.21777e19			−0.0559296
$248$	1.37559e20	+	1.19349e20i	0.610449	+	0.529640i
$249$	7.29837e20			3.12991
$250$	−5.20438e19	+	2.14328e20i	−0.215714	+	0.888361i
$251$		−	5.13762e19i		−	0.205843i	−0.994690	−	0.102921i	$-0.967181\pi$
$251$		−	5.13762e19i		−	0.205843i	0.994690	−	0.102921i	$-0.0328190\pi$
$252$	−8.92844e20	−	4.60774e20i	−3.45836	−	1.78478i
$253$			7.89490e19i			0.295680i
$254$	1.86372e20	+	4.52554e19i	0.674986	+	0.163902i
$255$	5.49927e19			0.192625
$256$	−9.70085e19	+	2.78750e20i	−0.328678	+	0.944442i
$257$	−9.03372e19			−0.296098			−0.148049	−	0.988980i	$-0.547299\pi$
$257$	−9.03372e19			−0.296098			−0.148049	+	0.988980i	$0.547299\pi$
$258$	−3.05184e20	−	7.41057e19i	−0.967820	−	0.235009i
$259$		−	5.38777e20i		−	1.65334i
$260$	1.15300e20	+	5.95033e19i	0.342416	+	0.176713i
$261$		−	1.44436e20i		−	0.415175i
$262$	9.54873e19	−	3.93239e20i	0.265696	−	1.09420i
$263$	−1.92468e20			−0.518484			−0.259242	−	0.965812i	$-0.583473\pi$
$263$	−1.92468e20			−0.518484			−0.259242	+	0.965812i	$0.583473\pi$
$264$	4.71079e20	+	4.08720e20i	1.22874	+	1.06609i
$265$	−3.00233e20			−0.758349
$266$	1.09913e19	−	4.52648e19i	0.0268879	−	0.110730i
$267$		−	2.38143e20i		−	0.564277i
$268$	−3.13940e20	+	6.08322e20i	−0.720611	+	1.39633i
$269$			5.40117e19i			0.120114i	0.998195	+	0.0600569i	$0.0191282\pi$
$269$			5.40117e19i			0.120114i	−0.998195	+	0.0600569i	$0.980872\pi$
$270$	7.51895e20	+	1.82577e20i	1.62019	+	0.393419i
$271$	6.53682e19			0.136498			0.0682492	−	0.997668i	$-0.478259\pi$
$271$	6.53682e19			0.136498			0.0682492	+	0.997668i	$0.478259\pi$
$272$	−5.42598e19	−	7.63347e19i	−0.109810	−	0.154485i
$273$	1.03707e21			2.03435
$274$	2.37700e20	+	5.77190e19i	0.452011	+	0.109759i
$275$		−	3.31250e20i		−	0.610700i
$276$	1.69758e20	−	3.28940e20i	0.303460	−	0.588016i
$277$			1.79771e20i			0.311632i	0.987786	+	0.155816i	$0.0498007\pi$
$277$			1.79771e20i			0.311632i	−0.987786	+	0.155816i	$0.950199\pi$
$278$	1.22486e20	−	5.04427e20i	0.205924	−	0.848043i
$279$	−1.30869e21			−2.13404
$280$	−3.25242e20	+	3.74865e20i	−0.514473	+	0.592968i
$281$	5.43168e20			0.833547			0.416774	−	0.909010i	$-0.363161\pi$
$281$	5.43168e20			0.833547			0.416774	+	0.909010i	$0.363161\pi$
$282$	2.90513e20	−	1.19640e21i	0.432562	−	1.78139i
$283$			7.08836e20i			1.02414i	0.858943	+	0.512072i	$0.171122\pi$
$283$			7.08836e20i			1.02414i	−0.858943	+	0.512072i	$0.828878\pi$
$284$	6.40752e20	+	3.30676e20i	0.898430	+	0.463657i
$285$			5.77373e19i			0.0785733i
$286$	−4.53733e20	−	1.10177e20i	−0.599362	−	0.145539i
$287$	−1.30275e20			−0.167057
$288$	−7.86174e20	−	1.96984e21i	−0.978774	−	2.45243i
$289$	−7.97523e20			−0.964076
$290$	−6.93303e19	−	1.68350e19i	−0.0813842	−	0.0197619i
$291$			1.42541e21i			1.62498i
$292$	1.71685e20	+	8.86025e19i	0.190099	+	0.0981052i
$293$			1.02708e20i			0.110467i	0.998473	+	0.0552334i	$0.0175903\pi$
$293$			1.02708e20i			0.110467i	−0.998473	+	0.0552334i	$0.982410\pi$
$294$	−5.05127e20	+	2.08023e21i	−0.527775	+	2.17350i
$295$	3.89729e20			0.395618
$296$	7.45342e20	−	8.59060e20i	0.735150	−	0.847314i
$297$	−2.78443e21			−2.66874
$298$	−2.49938e20	+	1.02930e21i	−0.232806	+	0.958747i
$299$			2.77124e20i			0.250882i
$300$	−7.12260e20	+	1.38015e21i	−0.626770	+	1.21449i
$301$			8.99336e20i			0.769320i
$302$	1.19211e21	+	2.89473e20i	0.991423	+	0.240740i
$303$	1.54109e21			1.24614
$304$	8.01444e19	−	5.69677e19i	0.0630156	−	0.0447923i
$305$	−1.85459e20			−0.141808
$306$	6.53995e20	+	1.58805e20i	0.486342	+	0.118095i
$307$		−	6.24758e19i		−	0.0451893i	−0.999745	−	0.0225946i	$-0.992807\pi$
$307$		−	6.24758e19i		−	0.0451893i	0.999745	−	0.0225946i	$-0.00719271\pi$
$308$	8.19059e20	−	1.58709e21i	0.576281	−	1.11666i
$309$		−	4.16257e21i		−	2.84914i
$310$	−1.52537e20	+	6.28182e20i	−0.101578	+	0.418323i
$311$	−6.19747e20			−0.401561			−0.200780	−	0.979636i	$-0.564348\pi$
$311$	−6.19747e20			−0.401561			−0.200780	+	0.979636i	$0.564348\pi$
$312$	1.65357e21	+	1.43468e21i	1.04258	+	0.904565i
$313$	2.05658e21			1.26188			0.630942	−	0.775830i	$-0.282669\pi$
$313$	2.05658e21			1.26188			0.630942	+	0.775830i	$0.282669\pi$
$314$	3.03450e20	−	1.24967e21i	0.181211	−	0.746268i
$315$		−	3.56635e21i		−	2.07293i
$316$	−2.27114e21	−	1.17208e21i	−1.28500	−	0.663156i
$317$			2.76754e21i			1.52437i	0.647361	+	0.762184i	$0.275873\pi$
$317$			2.76754e21i			1.52437i	−0.647361	+	0.762184i	$0.724127\pi$
$318$	−4.92268e21	−	1.19534e21i	−2.63980	−	0.641004i
$319$	2.56745e20			0.134055
$320$	−1.03717e21	+	1.47770e20i	−0.527322	+	0.0751298i
$321$	1.19934e21			0.593812
$322$	−1.03008e21	−	2.50126e20i	−0.496701	−	0.120610i
$323$			3.12008e19i			0.0146536i
$324$	6.47210e21	+	3.34009e21i	2.96083	+	1.52801i
$325$		−	1.16274e21i		−	0.518174i
$326$	5.82603e20	−	2.39929e21i	0.252943	−	1.04168i
$327$	7.97723e21			3.37440
$328$	−2.07719e20	−	1.80222e20i	−0.0856148	−	0.0742815i
$329$	−3.52563e21			−1.41603
$330$	−5.22373e20	+	2.15125e21i	−0.204462	+	0.842021i
$331$			1.62038e21i			0.618128i	0.951041	+	0.309064i	$0.100016\pi$
$331$			1.62038e21i			0.618128i	−0.951041	+	0.309064i	$0.899984\pi$
$332$	2.02331e21	−	3.92057e21i	0.752295	−	1.45772i
$333$			8.17285e21i			2.96209i
$334$	−4.54319e21	−	1.10319e21i	−1.60515	−	0.389768i
$335$	−2.42987e21			−0.836954
$336$	−6.82519e21	+	4.85144e21i	−2.29209	+	1.62925i
$337$	7.17480e20			0.234939			0.117470	−	0.993076i	$-0.462522\pi$
$337$	7.17480e20			0.234939			0.117470	+	0.993076i	$0.462522\pi$
$338$	1.45067e21	+	3.52255e20i	0.463208	+	0.112477i
$339$		−	7.55549e21i		−	2.35269i
$340$	1.52455e20	−	2.95412e20i	0.0462989	−	0.0897134i
$341$		−	2.32630e21i		−	0.689053i
$342$	−1.66730e20	+	6.86634e20i	−0.0481718	+	0.198382i
$343$	9.00726e20			0.253859
$344$	−1.24414e21	+	1.43396e21i	−0.342075	+	0.394267i
$345$	1.31391e21			0.352455
$346$	−2.54644e20	+	1.04868e21i	−0.0666480	+	0.274472i
$347$			6.16195e21i			1.57369i	0.617154	+	0.786843i	$0.288286\pi$
$347$			6.16195e21i			1.57369i	−0.617154	+	0.786843i	$0.711714\pi$
$348$	−1.06972e21	−	5.52058e20i	−0.266593	−	0.137582i
$349$		−	5.73892e21i		−	1.39577i	−0.716210	−	0.697885i	$-0.754125\pi$
$349$		−	5.73892e21i		−	1.39577i	0.716210	−	0.697885i	$-0.245875\pi$
$350$	4.32194e21	+	1.04947e21i	1.02589	+	0.249109i
$351$	−9.77383e21			−2.26441
$352$	3.50154e21	−	1.39748e21i	0.791856	−	0.316033i
$353$	−7.35535e21			−1.62375			−0.811873	−	0.583834i	$-0.801552\pi$
$353$	−7.35535e21			−1.62375			−0.811873	+	0.583834i	$0.801552\pi$
$354$	6.39007e21	+	1.55165e21i	1.37714	+	0.334401i
$355$			2.55941e21i			0.538515i
$356$	−1.27927e21	−	6.60198e20i	−0.262807	−	0.135628i
$357$		−	2.65710e21i		−	0.533001i
$358$	3.42015e20	−	1.40849e21i	0.0669945	−	0.275898i
$359$	−1.38050e21			−0.264079			−0.132040	−	0.991244i	$-0.542153\pi$
$359$	−1.38050e21			−0.264079			−0.132040	+	0.991244i	$0.542153\pi$
$360$	4.93368e21	−	5.68642e21i	0.921721	−	1.06235i
$361$	5.44763e21			0.994023
$362$	−1.95158e21	+	8.03706e21i	−0.347827	+	1.43243i
$363$			2.99289e21i			0.521056i
$364$	2.87504e21	−	5.57096e21i	0.488969	−	0.947477i
$365$			6.85776e20i			0.113944i
$366$	−3.04082e21	−	7.38381e20i	−0.493630	−	0.119865i
$367$	9.17912e21			1.45593			0.727963	−	0.685616i	$-0.240467\pi$
$367$	9.17912e21			1.45593			0.727963	+	0.685616i	$0.240467\pi$
$368$	−1.29640e21	−	1.82382e21i	−0.200924	−	0.282667i
$369$	1.97618e21			0.299297
$370$	3.92302e21	+	9.52600e20i	0.580639	+	0.140993i
$371$			1.45065e22i			2.09838i
$372$	−5.00205e21	+	9.69248e21i	−0.707185	+	1.37031i
$373$		−	3.68573e21i		−	0.509329i	−0.967029	−	0.254665i	$-0.918035\pi$
$373$		−	3.68573e21i		−	0.509329i	0.967029	−	0.254665i	$-0.0819651\pi$
$374$	−2.82287e20	+	1.16252e21i	−0.0381313	+	0.157033i
$375$	−1.32092e22			−1.74426
$376$	−5.62149e21	−	4.87734e21i	−0.725696	−	0.629631i
$377$	9.01219e20			0.113744
$378$	8.82164e21	−	3.63295e22i	1.08860	−	4.48311i
$379$		−	9.17543e21i		−	1.10712i	−0.832810	−	0.553558i	$-0.813270\pi$
$379$		−	9.17543e21i		−	1.10712i	0.832810	−	0.553558i	$-0.186730\pi$
$380$	3.10155e20	+	1.60063e20i	0.0365947	+	0.0188856i
$381$			1.14863e22i			1.32531i
$382$	1.07504e22	+	2.61045e21i	1.21307	+	0.294562i
$383$	−7.23389e21			−0.798329			−0.399165	−	0.916879i	$-0.630700\pi$
$383$	−7.23389e21			−0.798329			−0.399165	+	0.916879i	$0.630700\pi$
$384$	−1.75940e22	−	1.70650e21i	−1.89910	−	0.184200i
$385$	6.33944e21			0.669322
$386$	7.90886e21	+	1.92045e21i	0.816811	+	0.198340i
$387$		−	1.36423e22i		−	1.37830i
$388$	7.65706e21	+	3.95162e21i	0.756820	+	0.390576i
$389$		−	1.25731e21i		−	0.121583i	−0.998150	−	0.0607914i	$-0.980638\pi$
$389$		−	1.25731e21i		−	0.121583i	0.998150	−	0.0607914i	$-0.0193624\pi$
$390$	−1.83362e21	+	7.55126e21i	−0.173484	+	0.714447i
$391$	7.10027e20			0.0657314
$392$	9.77431e21	+	8.48043e21i	0.885431	+	0.768221i
$393$	2.42356e22			2.14841
$394$	−4.61436e21	+	1.90030e22i	−0.400308	+	1.64856i
$395$		−	9.07178e21i		−	0.770224i
$396$	−1.24245e22	+	2.40750e22i	−1.03245	+	2.00059i
$397$		−	1.07820e22i		−	0.876957i	−0.898742	−	0.438478i	$-0.855518\pi$
$397$		−	1.07820e22i		−	0.876957i	0.898742	−	0.438478i	$-0.144482\pi$
$398$	−1.16168e21	−	2.82083e20i	−0.0924871	−	0.0224580i
$399$	2.78971e21			0.217415
$400$	5.43935e21	+	7.65229e21i	0.414990	+	0.583824i
$401$	−1.08434e22			−0.809915			−0.404957	−	0.914336i	$-0.632714\pi$
$401$	−1.08434e22			−0.809915			−0.404957	+	0.914336i	$0.632714\pi$
$402$	−3.98405e22	−	9.67419e21i	−2.91342	−	0.707446i
$403$		−	8.16570e21i		−	0.584656i
$404$	4.27233e21	−	8.27850e21i	0.299518	−	0.580377i
$405$			2.58520e22i			1.77471i
$406$	−8.13420e20	+	3.34985e21i	−0.0546819	+	0.225193i
$407$	−1.45278e22			−0.956418
$408$	3.67582e21	−	4.23665e21i	0.236997	−	0.273156i
$409$	−2.32714e22			−1.46951			−0.734757	−	0.678330i	$-0.762704\pi$
$409$	−2.32714e22			−1.46951			−0.734757	+	0.678330i	$0.762704\pi$
$410$	2.30337e20	−	9.48580e20i	0.0142463	−	0.0586693i
$411$			1.46497e22i			0.887507i
$412$	−2.23606e22	−	1.15398e22i	−1.32696	−	0.684811i
$413$		−	1.88307e22i		−	1.09469i
$414$	1.56255e22	+	3.79423e21i	0.889880	+	0.216083i
$415$	1.56602e22			0.873754
$416$	1.22910e22	−	4.90539e21i	0.671883	−	0.268151i
$417$	3.10883e22			1.66510
$418$	−1.22054e21	−	2.96375e20i	−0.0640551	−	0.0155540i
$419$			2.64974e22i			1.36265i	0.731980	+	0.681326i	$0.238596\pi$
$419$			2.64974e22i			1.36265i	−0.731980	+	0.681326i	$0.761404\pi$
$420$	−2.64132e22	−	1.36312e22i	−1.33107	−	0.686934i
$421$		−	3.52910e21i		−	0.174288i	−0.996196	−	0.0871438i	$-0.972226\pi$
$421$		−	3.52910e21i		−	0.174288i	0.996196	−	0.0871438i	$-0.0277739\pi$
$422$	6.79976e21	−	2.80030e22i	0.329108	−	1.35534i
$423$	5.34812e22			2.53693
$424$	−2.00682e22	+	2.31300e22i	−0.933036	+	1.07539i
$425$	−2.97910e21			−0.135762
$426$	−1.01899e22	+	4.19645e22i	−0.455187	+	1.87456i
$427$			8.96089e21i			0.392387i
$428$	3.32489e21	−	6.44266e21i	0.142727	−	0.276562i
$429$		−	2.79640e22i		−	1.17682i
$430$	−6.54839e21	−	1.59010e21i	−0.270179	−	0.0656058i
$431$	−1.62468e22			−0.657220			−0.328610	−	0.944466i	$-0.606580\pi$
$431$	−1.62468e22			−0.657220			−0.328610	+	0.944466i	$0.606580\pi$
$432$	6.43239e22	−	4.57223e22i	2.55129	−	1.81350i
$433$	−2.11243e22			−0.821553			−0.410776	−	0.911736i	$-0.634742\pi$
$433$	−2.11243e22			−0.821553			−0.410776	+	0.911736i	$0.634742\pi$
$434$	3.03521e22	+	7.37018e21i	1.15751	+	0.281070i
$435$		−	4.27288e21i		−	0.159795i
$436$	2.21151e22	−	4.28524e22i	0.811060	−	1.57159i
$437$			7.45463e20i			0.0268123i
$438$	−2.73033e21	+	1.12441e22i	−0.0963129	+	0.396638i
$439$	3.57810e22			1.23795			0.618977	−	0.785409i	$-0.287548\pi$
$439$	3.57810e22			1.23795			0.618977	+	0.785409i	$0.287548\pi$
$440$	1.01080e22	+	8.76996e21i	0.343019	+	0.297612i
$441$	−9.29899e22			−3.09534
$442$	−9.90875e20	+	4.08065e21i	−0.0323541	+	0.133242i
$443$		−	5.46996e22i		−	1.75207i	−0.482245	−	0.876036i	$-0.660178\pi$
$443$		−	5.46996e22i		−	1.75207i	0.482245	−	0.876036i	$-0.339822\pi$
$444$	6.05299e22	+	3.12380e22i	1.90202	+	0.981585i
$445$		−	5.10988e21i		−	0.157525i
$446$	−2.52865e22	−	6.14015e21i	−0.764791	−	0.185709i
$447$	−6.34367e22			−1.88246
$448$	7.13986e21	+	5.01134e22i	0.207887	+	1.45912i
$449$	1.84591e22			0.527371			0.263686	−	0.964609i	$-0.415062\pi$
$449$	1.84591e22			0.527371			0.263686	+	0.964609i	$0.415062\pi$
$450$	−6.55607e22	−	1.59196e22i	−1.83797	−	0.446300i
$451$			3.51280e21i			0.0966390i
$452$	−4.05869e22	−	2.09459e22i	−1.09574	−	0.565486i
$453$			7.34711e22i			1.94662i
$454$	9.16246e21	−	3.77331e22i	0.238252	−	0.981177i
$455$	2.22525e22			0.567914
$456$	4.44809e21	+	3.85927e21i	0.111422	+	0.0966728i
$457$	2.92054e22			0.718085			0.359042	−	0.933321i	$-0.383103\pi$
$457$	2.92054e22			0.718085			0.359042	+	0.933321i	$0.383103\pi$
$458$	−7.30575e21	+	3.00867e22i	−0.176323	+	0.726137i
$459$			2.50418e22i			0.593277i
$460$	3.64251e21	−	7.05811e21i	0.0847149	−	0.164152i
$461$			4.03608e22i			0.921513i	0.887527	+	0.460756i	$0.152422\pi$
$461$			4.03608e22i			0.921513i	−0.887527	+	0.460756i	$0.847578\pi$
$462$	1.03943e23	+	2.52397e22i	2.32990	+	0.565753i
$463$	−6.51927e22			−1.43470			−0.717349	−	0.696714i	$-0.754644\pi$
$463$	−6.51927e22			−1.43470			−0.717349	+	0.696714i	$0.754644\pi$
$464$	−5.93114e21	+	4.21593e21i	−0.128155	+	0.0910943i
$465$	−3.87154e22			−0.821361
$466$	−5.80565e22	−	1.40974e22i	−1.20940	−	0.293670i
$467$		−	3.14842e21i		−	0.0644021i	−0.999481	−	0.0322010i	$-0.989748\pi$
$467$		−	3.14842e21i		−	0.0644021i	0.999481	−	0.0322010i	$-0.0102517\pi$
$468$	−4.36122e22	+	8.45075e22i	−0.876028	+	1.69748i
$469$			1.17405e23i			2.31588i
$470$	6.23359e21	−	2.56713e22i	0.120755	−	0.497298i
$471$	7.70185e22			1.46527
$472$	2.60503e22	−	3.00248e22i	0.486749	−	0.561013i
$473$	2.42501e22			0.445035
$474$	3.61181e22	−	1.48742e23i	0.651041	−	2.68114i
$475$		−	3.12777e21i		−	0.0553783i
$476$	−1.42735e22	−	7.36620e21i	−0.248240	−	0.128110i
$477$		−	2.20052e23i		−	3.75941i
$478$	−7.74001e22	−	1.87945e22i	−1.29899	−	0.315423i
$479$	5.37771e22			0.886637			0.443318	−	0.896364i	$-0.353801\pi$
$479$	5.37771e22			0.886637			0.443318	+	0.896364i	$0.353801\pi$
$480$	−2.32576e22	−	5.82744e22i	−0.376716	−	0.943902i
$481$	−5.09951e22			−0.811513
$482$	5.83077e21	+	1.41584e21i	0.0911645	+	0.0221368i
$483$		−	6.34845e22i		−	0.975253i
$484$	1.60773e22	+	8.29710e21i	0.242677	+	0.125239i
$485$			3.05852e22i			0.453635i
$486$	−5.22479e22	+	2.15169e23i	−0.761483	+	3.13596i
$487$	−1.62097e22			−0.232155			−0.116078	−	0.993240i	$-0.537032\pi$
$487$	−1.62097e22			−0.232155			−0.116078	+	0.993240i	$0.537032\pi$
$488$	−1.23965e22	+	1.42878e22i	−0.174473	+	0.201093i
$489$	1.47870e23			2.04530
$490$	−1.08386e22	+	4.46358e22i	−0.147335	+	0.606760i
$491$			3.89242e22i			0.520028i	0.965605	+	0.260014i	$0.0837273\pi$
$491$			3.89242e22i			0.520028i	−0.965605	+	0.260014i	$0.916273\pi$
$492$	7.55329e21	−	1.46360e22i	0.0991819	−	0.192185i
$493$		−	2.30904e21i		−	0.0298011i
$494$	−4.28430e21	−	1.04033e21i	−0.0543502	−	0.0131975i
$495$	−9.61647e22			−1.19914
$496$	3.81994e22	+	5.37404e22i	0.468233	+	0.658729i
$497$	1.23664e23			1.49009
$498$	2.56768e23	+	6.23491e22i	3.04152	+	0.738552i
$499$			6.70841e22i			0.781205i	0.920560	+	0.390602i	$0.127733\pi$
$499$			6.70841e22i			0.781205i	−0.920560	+	0.390602i	$0.872267\pi$
$500$	−3.66196e22	+	7.09579e22i	−0.419246	+	0.812373i
$501$		−	2.80001e23i		−	3.15166i
$502$	4.38901e21	−	1.80749e22i	0.0485718	−	0.200030i
$503$	−2.47633e22			−0.269452			−0.134726	−	0.990883i	$-0.543015\pi$
$503$	−2.47633e22			−0.269452			−0.134726	+	0.990883i	$0.543015\pi$
$504$	−2.74753e23	−	2.38382e23i	−2.93956	−	2.55043i
$505$	3.30674e22			0.347875
$506$	−6.74451e21	+	2.77754e22i	−0.0697704	+	0.287330i
$507$			8.94059e22i			0.909491i
$508$	6.17024e22	+	3.18431e22i	0.617250	+	0.318547i
$509$			5.33536e22i			0.524883i	0.964948	+	0.262441i	$0.0845276\pi$
$509$			5.33536e22i			0.524883i	−0.964948	+	0.262441i	$0.915472\pi$
$510$	1.93473e22	+	4.69796e21i	0.187186	+	0.0454530i
$511$	3.31348e22			0.315288
$512$	−5.79424e22	+	8.97812e22i	−0.542252	+	0.840216i
$513$	−2.62916e22			−0.242002
$514$	−3.17820e22	−	7.71740e21i	−0.287736	−	0.0698690i
$515$		−	8.93169e22i		−	0.795375i
$516$	−1.01038e23	−	5.21430e22i	−0.885036	−	0.456745i
$517$			9.50666e22i			0.819140i
$518$	4.60271e22	−	1.89550e23i	0.390131	−	1.60665i
$519$	−6.46312e22			−0.538915
$520$	3.54809e22	+	3.07841e22i	0.291049	+	0.252521i
$521$	−2.10097e22			−0.169551			−0.0847754	−	0.996400i	$-0.527017\pi$
$521$	−2.10097e22			−0.169551			−0.0847754	+	0.996400i	$0.527017\pi$
$522$	1.23390e22	−	5.08148e22i	0.0979671	−	0.403451i
$523$		−	7.86323e22i		−	0.614238i	−0.951671	−	0.307119i	$-0.900635\pi$
$523$		−	7.86323e22i		−	0.614238i	0.951671	−	0.307119i	$-0.0993650\pi$
$524$	6.71878e22	−	1.30190e23i	0.516386	−	1.00060i
$525$			2.66365e23i			2.01430i
$526$	−6.77132e22	−	1.64423e22i	−0.503842	−	0.122344i
$527$	−2.09215e22			−0.153180
$528$	1.30816e23	+	1.84038e23i	0.942484	+	1.32592i
$529$	−1.24086e23			−0.879729
$530$	−1.05627e23	−	2.56486e22i	−0.736934	−	0.178944i
$531$			2.85647e23i			1.96122i
$532$	7.73383e21	−	1.49859e22i	0.0522572	−	0.101259i
$533$			1.23305e22i			0.0819974i
$534$	2.03443e22	−	8.37824e22i	0.133150	−	0.548343i
$535$	2.57344e22			0.165770
$536$	−1.62417e23	+	1.87197e23i	−1.02975	+	1.18686i
$537$	8.68067e22			0.541716
$538$	−4.61415e21	+	1.90021e22i	−0.0283428	+	0.116722i
$539$		−	1.65296e23i		−	0.999443i
$540$	2.48931e23	+	1.28467e23i	1.48160	+	0.764618i
$541$			8.46969e22i			0.496239i	0.968729	+	0.248120i	$0.0798126\pi$
$541$			8.46969e22i			0.496239i	−0.968729	+	0.248120i	$0.920187\pi$
$542$	2.29975e22	+	5.58433e21i	0.132644	+	0.0322090i
$543$	−4.95331e23			−2.81253
$544$	−1.25682e22	−	3.14911e22i	−0.0702560	−	0.176034i
$545$	1.71169e23			0.942007
$546$	3.64856e23	+	8.85955e22i	1.97690	+	0.480036i
$547$		−	3.22585e23i		−	1.72088i	−0.509548	−	0.860442i	$-0.670187\pi$
$547$		−	3.22585e23i		−	1.72088i	0.509548	−	0.860442i	$-0.329813\pi$
$548$	7.86956e22	+	4.06128e22i	0.413348	+	0.213318i
$549$		−	1.35930e23i		−	0.702993i
$550$	2.82983e22	−	1.16539e23i	0.144104	−	0.593455i
$551$	2.42428e21			0.0121561
$552$	8.78242e22	−	1.01224e23i	0.433643	−	0.499805i
$553$	−4.38324e23			−2.13123
$554$	−1.53576e22	+	6.32462e22i	−0.0735345	+	0.302832i
$555$			2.41779e23i			1.14006i
$556$	8.61852e22	−	1.67001e23i	0.400218	−	0.775504i
$557$		−	1.27684e23i		−	0.583937i	−0.956428	−	0.291968i	$-0.905690\pi$
$557$		−	1.27684e23i		−	0.583937i	0.956428	−	0.291968i	$-0.0943102\pi$
$558$	−4.60419e23	−	1.11800e23i	−2.07378	−	0.503561i
$559$	8.51220e22			0.377608
$560$	−1.46449e23	+	1.04098e23i	−0.639866	+	0.454825i
$561$	−7.16472e22			−0.308329
$562$	1.91095e23	+	4.64022e22i	0.810009	+	0.196689i
$563$		−	3.00272e23i		−	1.25370i	−0.779141	−	0.626849i	$-0.784344\pi$
$563$		−	3.00272e23i		−	1.25370i	0.779141	−	0.626849i	$-0.215656\pi$
$564$	2.04414e23	−	3.96093e23i	0.840694	−	1.62902i
$565$		−	1.62119e23i		−	0.656785i
$566$	−6.05550e22	+	2.49379e23i	−0.241663	+	0.995223i
$567$	1.24910e24			4.91067
$568$	1.97177e23	+	1.71076e23i	0.763652	+	0.662563i
$569$	1.90009e23			0.724969			0.362485	−	0.931990i	$-0.381929\pi$
$569$	1.90009e23			0.724969			0.362485	+	0.931990i	$0.381929\pi$
$570$	−4.93243e21	+	2.03129e22i	−0.0185406	+	0.0763545i
$571$			1.14724e23i			0.424862i	0.977176	+	0.212431i	$0.0681381\pi$
$571$			1.14724e23i			0.424862i	−0.977176	+	0.212431i	$0.931862\pi$
$572$	−1.50218e23	−	7.75237e22i	−0.548095	−	0.282858i
$573$			6.62557e23i			2.38182i
$574$	−4.58328e22	−	1.11293e22i	−0.162340	−	0.0394198i
$575$	−7.11778e22			−0.248409
$576$	−1.08306e23	−	7.60183e23i	−0.372446	−	2.61413i
$577$	−3.30120e23			−1.11861			−0.559303	−	0.828963i	$-0.688931\pi$
$577$	−3.30120e23			−1.11861			−0.559303	+	0.828963i	$0.688931\pi$
$578$	−2.80581e23	−	6.81314e22i	−0.936852	−	0.227489i
$579$			4.87430e23i			1.60378i
$580$	−2.29533e22	−	1.18456e22i	−0.0744228	−	0.0384078i
$581$		−	7.56660e23i		−	2.41771i
$582$	−1.21771e23	+	5.01480e23i	−0.383440	+	1.57909i
$583$	3.91159e23			1.21386
$584$	5.28323e22	+	4.58386e22i	0.161581	+	0.140192i
$585$	−3.37555e23			−1.01746
$586$	−8.77426e21	+	3.61344e22i	−0.0260664	+	0.107347i
$587$			4.63905e23i			1.35833i	0.733985	+	0.679166i	$0.237658\pi$
$587$			4.63905e23i			1.35833i	−0.733985	+	0.679166i	$0.762342\pi$
$588$	−3.55423e23	+	6.88704e23i	−1.02574	+	1.98758i
$589$		−	2.19657e22i		−	0.0624834i
$590$	1.37113e23	+	3.32941e22i	0.384446	+	0.0933523i
$591$	−1.17117e24			−3.23688
$592$	3.35611e23	−	2.38557e23i	0.914327	−	0.649916i
$593$	6.61931e23			1.77766			0.888829	−	0.458240i	$-0.151520\pi$
$593$	6.61931e23			1.77766			0.888829	+	0.458240i	$0.151520\pi$
$594$	−9.79606e23	−	2.37871e23i	−2.59338	−	0.629733i
$595$		−	5.70138e22i		−	0.148794i
$596$	−1.75864e23	+	3.40772e23i	−0.452463	+	0.876739i
$597$		−	7.15955e22i		−	0.181595i
$598$	−2.36744e22	+	9.74965e22i	−0.0591996	+	0.243797i
$599$	3.11969e23			0.769102			0.384551	−	0.923104i	$-0.374356\pi$
$599$	3.11969e23			0.769102			0.384551	+	0.923104i	$0.374356\pi$
$600$	−3.68488e23	+	4.24710e23i	−0.895649	+	1.03230i
$601$	−2.76234e22			−0.0661978			−0.0330989	−	0.999452i	$-0.510538\pi$
$601$	−2.76234e22			−0.0661978			−0.0330989	+	0.999452i	$0.510538\pi$
$602$	−7.68292e22	+	3.16400e23i	−0.181533	+	0.747595i
$603$		−	1.78094e24i		−	4.14909i
$604$	3.94675e23	+	2.03682e23i	0.906620	+	0.467884i
$605$			6.42189e22i			0.145459i
$606$	5.42179e23	+	1.31654e23i	1.21095	+	0.294046i
$607$	5.72816e23			1.26157			0.630785	−	0.775958i	$-0.282733\pi$
$607$	5.72816e23			1.26157			0.630785	+	0.775958i	$0.282733\pi$
$608$	3.30627e22	−	1.31955e22i	0.0718055	−	0.0286579i
$609$	−2.06454e23			−0.442157
$610$	−6.52474e22	−	1.58436e22i	−0.137803	−	0.0334618i
$611$			3.33700e23i			0.695033i
$612$	2.16519e23	+	1.11740e23i	0.444742	+	0.229520i
$613$			5.83184e23i			1.18139i	0.806896	+	0.590693i	$0.201146\pi$
$613$			5.83184e23i			1.18139i	−0.806896	+	0.590693i	$0.798854\pi$
$614$	5.33723e21	−	2.19799e22i	0.0106631	−	0.0439132i
$615$	5.84618e22			0.115195
$616$	4.23741e23	−	4.88392e23i	0.823501	−	0.949145i
$617$	−5.87532e23			−1.12618			−0.563090	−	0.826396i	$-0.690388\pi$
$617$	−5.87532e23			−1.12618			−0.563090	+	0.826396i	$0.690388\pi$
$618$	3.55603e23	−	1.46445e24i	0.672301	−	2.76869i
$619$			1.26636e23i			0.236150i	0.993005	+	0.118075i	$0.0376723\pi$
$619$			1.26636e23i			0.236150i	−0.993005	+	0.118075i	$0.962328\pi$
$620$	−1.07330e23	+	2.07973e23i	−0.197420	+	0.382541i
$621$			5.98309e23i			1.08554i
$622$	−2.18037e23	−	5.29443e22i	−0.390221	−	0.0947547i
$623$	−2.46895e23			−0.435878
$624$	4.59188e23	+	6.46003e23i	0.799689	+	1.12503i
$625$	1.33501e23			0.229353
$626$	7.23537e23	+	1.75691e23i	1.22625	+	0.297762i
$627$		−	7.52229e22i		−	0.125770i
$628$	2.13516e23	−	4.13731e23i	0.352188	−	0.682435i
$629$			1.30656e23i			0.212617i
$630$	3.04669e23	−	1.25470e24i	0.489141	−	2.01439i
$631$	9.95923e22			0.157753			0.0788763	−	0.996884i	$-0.474867\pi$
$631$	9.95923e22			0.157753			0.0788763	+	0.996884i	$0.474867\pi$
$632$	−6.98891e23	−	6.06375e23i	−1.09223	−	0.947646i
$633$	1.72585e24			2.66116
$634$	−2.36427e23	+	9.73661e23i	−0.359699	+	1.48132i
$635$			2.46463e23i			0.369977i
$636$	−1.62976e24	−	8.41077e23i	−2.41400	−	1.24581i
$637$		−	5.80218e23i		−	0.848019i
$638$	9.03268e22	+	2.19334e22i	0.130269	+	0.0316323i
$639$	−1.87589e24			−2.66962
$640$	−3.77517e23	−	3.66165e22i	−0.530160	−	0.0514218i
$641$	8.64785e22			0.119844			0.0599218	−	0.998203i	$-0.480915\pi$
$641$	8.64785e22			0.119844			0.0599218	+	0.998203i	$0.480915\pi$
$642$	4.21946e23	+	1.02458e23i	0.577044	+	0.140119i
$643$			5.63561e22i			0.0760585i	0.999277	+	0.0380292i	$0.0121080\pi$
$643$			5.63561e22i			0.0760585i	−0.999277	+	0.0380292i	$0.987892\pi$
$644$	−3.41029e23	−	1.75996e23i	−0.454215	−	0.234409i
$645$		−	4.03583e23i		−	0.530487i
$646$	−2.66545e21	+	1.09769e22i	−0.00345775	+	0.0142398i
$647$	−8.85704e23			−1.13397			−0.566986	−	0.823728i	$-0.691890\pi$
$647$	−8.85704e23			−1.13397			−0.566986	+	0.823728i	$0.691890\pi$
$648$	1.99164e24	+	1.72800e24i	2.51666	+	2.18351i
$649$	−5.07758e23			−0.633253
$650$	9.93318e22	−	4.09071e23i	0.122271	−	0.503541i
$651$			1.87062e24i			2.27273i
$652$	4.09937e23	−	7.94337e23i	0.491601	−	0.952577i
$653$			3.56939e23i			0.422505i	0.977432	+	0.211252i	$0.0677542\pi$
$653$			3.56939e23i			0.422505i	−0.977432	+	0.211252i	$0.932246\pi$
$654$	2.80651e24	+	6.81485e23i	3.27911	+	0.796243i
$655$	5.20028e23			0.599757
$656$	−5.76826e22	−	8.11501e22i	−0.0656693	−	0.0923860i
$657$	−5.02631e23			−0.564864
$658$	−1.24037e24	−	3.01190e23i	−1.37604	−	0.334134i
$659$			6.90655e23i			0.756372i	0.925730	+	0.378186i	$0.123452\pi$
$659$			6.90655e23i			0.756372i	−0.925730	+	0.378186i	$0.876548\pi$
$660$	−3.67558e23	+	7.12217e23i	−0.397376	+	0.769997i
$661$		−	1.43884e24i		−	1.53567i	−0.640645	−	0.767837i	$-0.721333\pi$
$661$		−	1.43884e24i		−	1.53567i	0.640645	−	0.767837i	$-0.278667\pi$
$662$	−1.38427e23	+	5.70074e23i	−0.145857	+	0.600673i
$663$	−2.51494e23			−0.261615
$664$	1.04676e24	−	1.20647e24i	1.07502	−	1.23904i
$665$	5.98592e22			0.0606942
$666$	−6.98197e23	+	2.87533e24i	−0.698951	+	2.87844i
$667$		−	5.51685e22i		−	0.0545282i
$668$	−1.50412e24	−	7.76239e23i	−1.46785	−	0.757523i
$669$		−	1.55843e24i		−	1.50164i
$670$	−8.54864e23	−	2.07581e23i	−0.813320	−	0.197493i
$671$	2.41625e23			0.226987
$672$	−2.81566e24	+	1.12374e24i	−2.61181	+	1.04238i
$673$	−1.28567e24			−1.17761			−0.588806	−	0.808275i	$-0.700402\pi$
$673$	−1.28567e24			−1.17761			−0.588806	+	0.808275i	$0.700402\pi$
$674$	2.52420e23	+	6.12935e22i	0.228305	+	0.0554377i
$675$		−	2.51035e24i		−	2.24209i
$676$	4.80274e23	+	2.47858e23i	0.423587	+	0.218603i
$677$			7.83643e23i			0.682519i	0.939969	+	0.341259i	$0.110853\pi$
$677$			7.83643e23i			0.682519i	−0.939969	+	0.341259i	$0.889147\pi$
$678$	6.45456e23	−	2.65814e24i	0.555155	−	2.28626i
$679$	1.47779e24			1.25522
$680$	7.88726e22	−	9.09064e22i	0.0661608	−	0.0762551i
$681$	2.32552e24			1.92650
$682$	1.98733e23	−	8.18426e23i	0.162593	−	0.669595i
$683$			7.52256e23i			0.607841i	0.952697	+	0.303920i	$0.0982957\pi$
$683$			7.52256e23i			0.607841i	−0.952697	+	0.303920i	$0.901704\pi$
$684$	−1.17317e23	+	2.27325e23i	−0.0936230	+	0.181414i
$685$			3.14340e23i			0.247759i
$686$	3.16889e23	+	7.69479e22i	0.246690	+	0.0599021i
$687$	−1.85427e24			−1.42574
$688$	−5.60208e23	+	3.98204e23i	−0.425449	+	0.302415i
$689$	1.37303e24			1.02995
$690$	4.62253e23	+	1.12246e23i	0.342502	+	0.0831672i
$691$			1.95452e24i			1.43046i	0.698888	+	0.715231i	$0.253679\pi$
$691$			1.95452e24i			1.43046i	−0.698888	+	0.715231i	$0.746321\pi$
$692$	−1.79175e23	+	3.47189e23i	−0.129532	+	0.250994i
$693$			4.64642e24i			3.31807i
$694$	−5.26408e23	+	2.16787e24i	−0.371336	+	1.52925i
$695$	6.67066e23			0.464834
$696$	−3.29184e23	−	2.85608e23i	−0.226600	−	0.196604i
$697$	3.15923e22			0.0214834
$698$	4.90269e23	−	2.01904e24i	0.329354	−	1.35636i
$699$		−	3.57807e24i		−	2.37461i
$700$	1.43087e24	+	7.38437e23i	0.938138	+	0.484150i
$701$		−	2.08668e24i		−	1.35162i	−0.737078	−	0.675808i	$-0.763795\pi$
$701$		−	2.08668e24i		−	1.35162i	0.737078	−	0.675808i	$-0.236205\pi$
$702$	−3.43858e24	−	8.34967e23i	−2.20046	−	0.534323i
$703$	−1.37177e23			−0.0867281
$704$	1.35128e24	−	1.92522e23i	0.844068	−	0.120258i
$705$	1.58215e24			0.976426
$706$	−2.58772e24	−	6.28358e23i	−1.57789	−	0.383149i
$707$		−	1.59773e24i		−	0.962583i
$708$	2.11557e24	+	1.09179e24i	1.25934	+	0.649916i
$709$			1.76067e24i			1.03558i	0.855508	+	0.517790i	$0.173245\pi$
$709$			1.76067e24i			1.03558i	−0.855508	+	0.517790i	$0.826755\pi$
$710$	−2.18647e23	+	9.00438e23i	−0.127071	+	0.523308i
$711$	6.64905e24			3.81828
$712$	−3.93666e23	−	3.41554e23i	−0.223382	−	0.193811i
$713$	−4.99866e23			−0.280280
$714$	2.26993e23	−	9.34808e23i	0.125770	−	0.517950i
$715$		−	6.00027e23i		−	0.328526i
$716$	2.40652e23	−	4.66312e23i	0.130205	−	0.252299i
$717$		−	4.77023e24i		−	2.55051i
$718$	−4.85682e23	−	1.17935e23i	−0.256622	−	0.0623137i
$719$	−3.64140e24			−1.90140			−0.950698	−	0.310118i	$-0.899631\pi$
$719$	−3.64140e24			−1.90140			−0.950698	+	0.310118i	$0.899631\pi$
$720$	2.22153e24	−	1.57909e24i	1.14637	−	0.814857i
$721$	−4.31555e24			−2.20083
$722$	1.91656e24	+	4.65384e23i	0.965953	+	0.234555i
$723$			3.59355e23i			0.178998i
$724$	−1.37319e24	+	2.66084e24i	−0.676010	+	1.30991i
$725$			2.31473e23i			0.112623i
$726$	−2.55679e23	+	1.05294e24i	−0.122951	+	0.506342i
$727$	2.16795e24			1.03040			0.515201	−	0.857069i	$-0.327717\pi$
$727$	2.16795e24			1.03040			0.515201	+	0.857069i	$0.327717\pi$
$728$	1.48740e24	−	1.71434e24i	0.698734	−	0.805341i
$729$	−6.08522e24			−2.82548
$730$	−5.85850e22	+	2.41266e23i	−0.0268870	+	0.110727i
$731$		−	2.18093e23i		−	0.0989338i
$732$	−1.00673e24	−	5.19548e23i	−0.451407	−	0.232960i
$733$			2.91223e24i			1.29075i	0.763866	+	0.645375i	$0.223299\pi$
$733$			2.91223e24i			1.29075i	−0.763866	+	0.645375i	$0.776701\pi$
$734$	3.22935e24	+	7.84161e23i	1.41481	+	0.343549i
$735$	−2.75094e24			−1.19135
$736$	−3.00285e23	−	7.52398e23i	−0.128550	−	0.322096i
$737$	3.16575e24			1.33969
$738$	6.95250e23	+	1.68823e23i	0.290845	+	0.0706239i
$739$			2.56079e23i			0.105900i	0.998597	+	0.0529500i	$0.0168624\pi$
$739$			2.56079e23i			0.105900i	−0.998597	+	0.0529500i	$0.983138\pi$
$740$	1.29880e24	+	6.70278e23i	0.530973	+	0.274022i
$741$		−	2.64045e23i		−	0.106715i
$742$	−1.23927e24	+	5.10359e24i	−0.495145	+	2.03912i
$743$	−1.24281e24			−0.490907			−0.245453	−	0.969408i	$-0.578937\pi$
$743$	−1.24281e24			−0.490907			−0.245453	+	0.969408i	$0.578937\pi$
$744$	−2.58781e24	+	2.98264e24i	−1.01056	+	1.16475i
$745$	−1.36117e24			−0.525514
$746$	3.14868e23	−	1.29670e24i	0.120184	−	0.494947i
$747$			1.14780e25i			4.33152i
$748$	−1.98626e23	+	3.84877e23i	−0.0741091	+	0.143601i
$749$		−	1.24342e24i		−	0.458692i
$750$	−4.64721e24	−	1.12845e24i	−1.69501	−	0.411587i
$751$	4.22804e24			1.52475			0.762376	−	0.647134i	$-0.224032\pi$
$751$	4.22804e24			1.52475			0.762376	+	0.647134i	$0.224032\pi$
$752$	−1.56106e24	−	2.19616e24i	−0.556631	−	0.783090i
$753$	1.11397e24			0.392751
$754$	3.17063e23	+	7.69901e22i	0.110532	+	0.0268397i
$755$			1.57648e24i			0.543425i
$756$	6.20718e24	−	1.20277e25i	2.11572	−	4.09964i
$757$			1.18946e24i			0.400899i	0.979704	+	0.200449i	$0.0642402\pi$
$757$			1.18946e24i			0.400899i	−0.979704	+	0.200449i	$0.935760\pi$
$758$	7.83846e23	−	3.22806e24i	0.261242	−	1.07585i
$759$	−1.71182e24			−0.564162
$760$	9.54433e22	+	8.28090e22i	0.0311050	+	0.0269874i
$761$	−5.41223e24			−1.74424			−0.872120	−	0.489291i	$-0.837255\pi$
$761$	−5.41223e24			−1.74424			−0.872120	+	0.489291i	$0.837255\pi$
$762$	−9.81259e23	+	4.04105e24i	−0.312728	+	1.28788i
$763$		−	8.27041e24i		−	2.60656i
$764$	3.55915e24	+	1.83679e24i	1.10931	+	0.572487i
$765$			8.64857e23i			0.266577i
$766$	−2.54499e24	−	6.17982e23i	−0.775785	−	0.188378i
$767$	−1.78232e24			−0.537309
$768$	−6.04405e24	−	2.10340e24i	−1.80201	−	0.627122i
$769$	−2.19062e24			−0.645942			−0.322971	−	0.946409i	$-0.604682\pi$
$769$	−2.19062e24			−0.645942			−0.322971	+	0.946409i	$0.604682\pi$
$770$	2.23031e24	+	5.41571e23i	0.650421	+	0.157937i
$771$		−	1.95875e24i		−	0.564959i
$772$	2.61839e24	+	1.35129e24i	0.746944	+	0.385479i
$773$			1.32708e24i			0.374431i	0.982319	+	0.187216i	$0.0599463\pi$
$773$			1.32708e24i			0.374431i	−0.982319	+	0.187216i	$0.940054\pi$
$774$	1.16544e24	−	4.79956e24i	0.325232	−	1.33938i
$775$	2.09731e24			0.578893
$776$	2.35629e24	+	2.04437e24i	0.643285	+	0.558130i
$777$	1.16821e25			3.15459
$778$	1.07411e23	−	4.42342e23i	0.0286894	−	0.118149i
$779$			3.31690e22i			0.00876324i
$780$	−1.29019e24	+	2.50000e24i	−0.337170	+	0.653336i
$781$		−	3.33452e24i		−	0.861984i
$782$	2.49798e23	+	6.06568e22i	0.0638752	+	0.0155104i
$783$	1.94572e24			0.492160
$784$	2.71428e24	+	3.81855e24i	0.679153	+	0.955459i
$785$	1.65260e24			0.409049
$786$	8.52646e24	+	2.07042e24i	2.08774	+	0.506952i
$787$		−	2.81620e24i		−	0.682146i	−0.940037	−	0.341073i	$-0.889210\pi$
$787$		−	2.81620e24i		−	0.682146i	0.940037	−	0.341073i	$-0.110790\pi$
$788$	−3.24681e24	+	6.29134e24i	−0.778007	+	1.50755i
$789$		−	4.17322e24i		−	0.989276i
$790$	7.74991e23	−	3.19159e24i	0.181747	−	0.748474i
$791$	−7.83316e24			−1.81734
$792$	−6.42784e24	+	7.40855e24i	−1.47537	+	1.70047i
$793$	8.48146e23			0.192597
$794$	9.21089e23	−	3.79326e24i	0.206932	−	0.852193i
$795$		−	6.50986e24i		−	1.44694i
$796$	−3.84600e23	−	1.98482e23i	−0.0845761	−	0.0436476i
$797$			6.52060e24i			1.41870i	0.704854	+	0.709352i	$0.251012\pi$
$797$			6.52060e24i			1.41870i	−0.704854	+	0.709352i	$0.748988\pi$
$798$	9.81462e23	+	2.38321e23i	0.211275	+	0.0513025i
$799$	8.54981e23			0.182100
$800$	1.25992e24	+	3.15687e24i	0.265509	+	0.665261i
$801$	3.74522e24			0.780910
$802$	−3.81488e24	−	9.26340e23i	−0.787044	−	0.191112i
$803$		−	8.93462e23i		−	0.182387i
$804$	−1.31900e25	−	6.80705e24i	−2.66422	−	1.37494i
$805$		−	1.36220e24i		−	0.272254i
$806$	6.97585e23	−	2.87282e24i	0.137959	−	0.568146i
$807$	−1.17112e24			−0.229179
$808$	2.21029e24	−	2.54752e24i	0.428009	−	0.493311i
$809$	8.81198e23			0.168854			0.0844269	−	0.996430i	$-0.473094\pi$
$809$	8.81198e23			0.168854			0.0844269	+	0.996430i	$0.473094\pi$
$810$	−2.20851e24	+	9.09513e24i	−0.418770	+	1.72459i
$811$			3.57272e24i			0.670381i	0.942150	+	0.335191i	$0.108801\pi$
$811$			3.57272e24i			0.670381i	−0.942150	+	0.335191i	$0.891199\pi$
$812$	−5.72347e23	+	1.10904e24i	−0.106276	+	0.205930i
$813$			1.41736e24i			0.260441i
$814$	−5.11111e24	−	1.24109e24i	−0.929410	−	0.225682i
$815$	3.17288e24			0.570971
$816$	1.65514e24	−	1.17650e24i	0.294760	−	0.209519i
$817$	2.28978e23			0.0403558
$818$	−8.18722e24	−	1.98804e24i	−1.42802	−	0.346755i
$819$			1.63097e25i			2.81536i
$820$	1.62072e23	−	3.14047e23i	0.0276879	−	0.0536509i
$821$		−	1.46618e24i		−	0.247896i	−0.992289	−	0.123948i	$-0.960444\pi$
$821$		−	1.46618e24i		−	0.247896i	0.992289	−	0.123948i	$-0.0395556\pi$
$822$	−1.25150e24	+	5.15397e24i	−0.209421	+	0.862445i
$823$	−2.89883e24			−0.480091			−0.240046	−	0.970762i	$-0.577162\pi$
$823$	−2.89883e24			−0.480091			−0.240046	+	0.970762i	$0.577162\pi$
$824$	−6.88099e24	−	5.97011e24i	−1.12790	−	0.978591i
$825$	7.18238e24			1.16523
$826$	1.60868e24	−	6.62491e24i	0.258309	−	1.06377i
$827$		−	4.06842e24i		−	0.646590i	−0.946298	−	0.323295i	$-0.895209\pi$
$827$		−	4.06842e24i		−	0.646590i	0.946298	−	0.323295i	$-0.104791\pi$
$828$	5.17316e24	+	2.66974e24i	0.813763	+	0.419963i
$829$			7.02644e24i			1.09401i	0.837129	+	0.547005i	$0.184232\pi$
$829$			7.02644e24i			1.09401i	−0.837129	+	0.547005i	$0.815768\pi$
$830$	5.50951e24	+	1.33783e24i	0.849081	+	0.206176i
$831$	−3.89792e24			−0.594599
$832$	4.74322e24	−	6.75786e23i	0.716184	−	0.102038i
$833$	−1.48659e24			−0.222182
$834$	1.09373e25	+	2.65583e24i	1.61808	+	0.392907i
$835$		−	6.00802e24i		−	0.879826i
$836$	−4.04085e23	−	2.08538e23i	−0.0585760	−	0.0302296i
$837$		−	1.76297e25i		−	2.52975i
$838$	−2.26364e24	+	9.32220e24i	−0.321539	+	1.32417i
$839$	−3.75744e24			−0.528342			−0.264171	−	0.964476i	$-0.585098\pi$
$839$	−3.75744e24			−0.528342			−0.264171	+	0.964476i	$0.585098\pi$
$840$	−8.12807e24	−	7.05211e24i	−1.13139	−	0.981624i
$841$	7.07774e24			0.975278
$842$	3.01487e23	−	1.24159e24i	0.0411259	−	0.169366i
$843$			1.17773e25i			1.59042i
$844$	4.78452e24	−	9.27097e24i	0.639628	−	1.23941i
$845$			1.91840e24i			0.253896i
$846$	1.88155e25	+	4.56883e24i	2.46529	+	0.598628i
$847$	3.10288e24			0.402491
$848$	−9.03626e24	+	6.42310e24i	−1.16044	+	0.824859i
$849$	−1.53695e25			−1.95408
$850$	−1.04809e24	−	2.54500e23i	−0.131928	−	0.0320352i
$851$			3.12169e24i			0.389034i
$852$	−7.16994e24	+	1.38932e25i	−0.884666	+	1.71422i
$853$		−	8.76545e24i		−	1.07080i	−0.844599	−	0.535399i	$-0.820161\pi$
$853$		−	8.76545e24i		−	1.07080i	0.844599	−	0.535399i	$-0.179839\pi$
$854$	−7.65518e23	+	3.15258e24i	−0.0925899	+	0.381306i
$855$	−9.08020e23			−0.108739
$856$	1.72014e24	−	1.98258e24i	0.203956	−	0.235074i
$857$	−7.03954e24			−0.826432			−0.413216	−	0.910633i	$-0.635595\pi$
$857$	−7.03954e24			−0.826432			−0.413216	+	0.910633i	$0.635595\pi$
$858$	2.38893e24	−	9.83815e24i	0.277690	−	1.14359i
$859$		−	5.42420e24i		−	0.624301i	−0.950033	−	0.312151i	$-0.898951\pi$
$859$		−	5.42420e24i		−	0.624301i	0.950033	−	0.312151i	$-0.101049\pi$
$860$	−2.16798e24	−	1.11884e24i	−0.247069	−	0.127506i
$861$		−	2.82471e24i		−	0.318748i
$862$	−5.71587e24	−	1.38794e24i	−0.638661	−	0.155082i
$863$	−4.27768e24			−0.473278			−0.236639	−	0.971598i	$-0.576046\pi$
$863$	−4.27768e24			−0.473278			−0.236639	+	0.971598i	$0.576046\pi$
$864$	2.65361e25	−	1.05907e25i	2.90717	−	1.16027i
$865$	−1.38680e24			−0.150445
$866$	−7.43186e24	−	1.80462e24i	−0.798353	−	0.193858i
$867$		−	1.72924e25i		−	1.83947i
$868$	1.00487e25	+	5.18588e24i	1.05850	+	0.546267i
$869$			1.18192e25i			1.23287i
$870$	3.65027e23	−	1.50327e24i	0.0377061	−	0.155282i
$871$	1.11123e25			1.13671
$872$	1.14412e25	−	1.31869e25i	1.15900	−	1.33583i
$873$	−2.24170e25			−2.24883
$874$	−6.36840e22	+	2.62265e23i	−0.00632679	+	0.0260551i
$875$			1.36947e25i			1.34736i
$876$	−1.92114e24	+	3.72260e24i	−0.187186	+	0.362711i
$877$			1.78456e25i			1.72201i	0.508597	+	0.861005i	$0.330164\pi$
$877$			1.78456e25i			1.72201i	−0.508597	+	0.861005i	$0.669836\pi$
$878$	1.25883e25	+	3.05673e24i	1.20300	+	0.292115i
$879$	−2.22699e24			−0.210772
$880$	2.80695e24	+	3.94892e24i	0.263106	+	0.370148i
$881$	2.01186e25			1.86768			0.933841	−	0.357688i	$-0.116435\pi$
$881$	2.01186e25			1.86768			0.933841	+	0.357688i	$0.116435\pi$
$882$	−3.27153e25	−	7.94402e24i	−3.00793	−	0.730394i
$883$			9.33262e24i			0.849841i	0.905231	+	0.424921i	$0.139698\pi$
$883$			9.33262e24i			0.849841i	−0.905231	+	0.424921i	$0.860302\pi$
$884$	−6.97209e23	+	1.35098e24i	−0.0628809	+	0.121845i
$885$			8.45037e24i			0.754845i
$886$	4.67292e24	−	1.92441e25i	0.413429	−	1.70260i
$887$	1.53656e25			1.34647			0.673237	−	0.739426i	$-0.264903\pi$
$887$	1.53656e25			1.34647			0.673237	+	0.739426i	$0.264903\pi$
$888$	1.86267e25	+	1.61610e25i	1.61669	+	1.40268i
$889$	1.19084e25			1.02374
$890$	4.36531e23	−	1.79773e24i	0.0371706	−	0.153077i
$891$		−	3.36813e25i		−	2.84072i
$892$	−8.37164e24	−	4.32039e24i	−0.699373	−	0.360929i
$893$			8.97651e23i			0.0742797i
$894$	−2.23180e25	−	5.41932e24i	−1.82931	−	0.444197i
$895$	1.86262e24			0.151227
$896$	−1.76921e24	+	1.82406e25i	−0.142286	+	1.46697i
$897$	−6.00880e24			−0.478687
$898$	6.49419e24	+	1.57694e24i	0.512479	+	0.124442i
$899$			1.62558e24i			0.127073i
$900$	−2.17053e25	−	1.12015e25i	−1.68075	−	0.867394i
$901$		−	3.51788e24i		−	0.269849i
$902$	−3.00094e23	+	1.23586e24i	−0.0228035	+	0.0939101i
$903$	−1.95000e25			−1.46788
$904$	−1.24897e25	−	1.08364e25i	−0.931366	−	0.808076i
$905$	−1.06284e25			−0.785153
$906$	−6.27654e24	+	2.58482e25i	−0.459336	+	1.89165i
$907$			1.19285e25i			0.864818i	0.901678	+	0.432409i	$0.142336\pi$
$907$			1.19285e25i			0.864818i	−0.901678	+	0.432409i	$0.857664\pi$
$908$	6.44698e24	−	1.24923e25i	0.463049	−	0.897251i
$909$			2.42364e25i			1.72455i
$910$	7.82878e24	+	1.90101e24i	0.551877	+	0.134008i
$911$	2.47178e24			0.172625			0.0863124	−	0.996268i	$-0.472492\pi$
$911$	2.47178e24			0.172625			0.0863124	+	0.996268i	$0.472492\pi$
$912$	1.23521e24	+	1.73775e24i	0.0854645	+	0.120235i
$913$	−2.04029e25			−1.39859
$914$	1.02749e25	+	2.49498e24i	0.697807	+	0.169443i
$915$		−	4.02125e24i		−	0.270572i
$916$	−5.14054e24	+	9.96085e24i	−0.342687	+	0.664025i
$917$		−	2.51263e25i		−	1.65955i
$918$	−2.13929e24	+	8.81008e24i	−0.139993	+	0.576524i
$919$	2.69765e24			0.174905			0.0874527	−	0.996169i	$-0.472127\pi$
$919$	2.69765e24			0.174905			0.0874527	+	0.996169i	$0.472127\pi$
$920$	1.88446e24	−	2.17197e24i	0.121057	−	0.139527i
$921$	1.35464e24			0.0862219
$922$	−3.44797e24	+	1.41995e25i	−0.217446	+	0.895491i
$923$		−	1.17047e25i		−	0.731386i
$924$	3.44124e25	+	1.77594e25i	2.13061	+	1.09955i
$925$		−	1.30978e25i		−	0.803515i
$926$	−2.29358e25	−	5.56933e24i	−1.39418	−	0.338540i
$927$	6.54637e25			3.94296
$928$	−2.44683e24	+	9.76540e23i	−0.146031	+	0.0582817i
$929$	1.73143e24			0.102393			0.0511967	−	0.998689i	$-0.483696\pi$
$929$	1.73143e24			0.102393			0.0511967	+	0.998689i	$0.483696\pi$
$930$	−1.36207e25	−	3.30741e24i	−0.798167	−	0.193813i
$931$		−	1.56078e24i		−	0.0906296i
$932$	−1.92208e25	−	9.91939e24i	−1.10595	−	0.570755i
$933$		−	1.34378e25i		−	0.766185i
$934$	2.68966e23	−	1.10766e24i	0.0151967	−	0.0625834i
$935$	−1.53734e24			−0.0860741
$936$	−2.25628e25	+	2.60053e25i	−1.25184	+	1.44283i
$937$	−1.92274e25			−1.05714			−0.528572	−	0.848888i	$-0.677272\pi$
$937$	−1.92274e25			−1.05714			−0.528572	+	0.848888i	$0.677272\pi$
$938$	−1.00297e25	+	4.13047e25i	−0.546468	+	2.25048i
$939$			4.45922e25i			2.40770i
$940$	4.38614e24	−	8.49904e24i	0.234691	−	0.454761i
$941$		−	2.50201e25i		−	1.32671i	−0.748303	−	0.663357i	$-0.769131\pi$
$941$		−	2.50201e25i		−	1.32671i	0.748303	−	0.663357i	$-0.230869\pi$
$942$	2.70963e25	+	6.57960e24i	1.42389	+	0.345754i
$943$	7.54817e23			0.0393090
$944$	1.17299e25	−	8.33774e24i	0.605384	−	0.430315i
$945$	4.80430e25			2.45731
$946$	8.53155e24	+	2.07166e24i	0.432468	+	0.105013i
$947$		−	2.84634e25i		−	1.42992i	−0.699165	−	0.714961i	$-0.746445\pi$
$947$		−	2.84634e25i		−	1.42992i	0.699165	−	0.714961i	$-0.253555\pi$
$948$	2.54138e25	−	4.92443e25i	1.26531	−	2.45180i
$949$		−	3.13620e24i		−	0.154754i
$950$	2.67202e23	−	1.10040e24i	0.0130674	−	0.0538145i
$951$	−6.00076e25			−2.90852
$952$	−4.39235e24	−	3.81091e24i	−0.211000	−	0.183069i
$953$	3.20703e25			1.52691			0.763455	−	0.645862i	$-0.223502\pi$
$953$	3.20703e25			1.52691			0.763455	+	0.645862i	$0.223502\pi$
$954$	1.87988e25	−	7.74178e25i	0.887093	−	3.65325i
$955$			1.42166e25i			0.664916i
$956$	−2.56249e25	−	1.32244e25i	−1.18787	−	0.613033i
$957$			5.56692e24i			0.255778i
$958$	1.89196e25	+	4.59412e24i	0.861599	+	0.209216i
$959$	1.51880e25			0.685557
$960$	−3.20406e24	−	2.24887e25i	−0.143349	−	1.00614i
$961$	−7.82115e24			−0.346834
$962$	−1.79409e25	−	4.35645e24i	−0.788597	−	0.191489i
$963$			1.88617e25i			0.821784i
$964$	1.93040e24	+	9.96231e23i	0.0833666	+	0.0430234i
$965$			1.04589e25i			0.447715i
$966$	5.42341e24	−	2.23348e25i	0.230126	−	0.947713i
$967$	−4.41829e25			−1.85836			−0.929178	−	0.369633i	$-0.879483\pi$
$967$	−4.41829e25			−1.85836			−0.929178	+	0.369633i	$0.879483\pi$
$968$	4.94743e24	+	4.29251e24i	0.206272	+	0.178966i
$969$	−6.76517e23			−0.0279593
$970$	−2.61286e24	+	1.07603e25i	−0.107042	+	0.440825i
$971$			5.97199e24i			0.242524i	0.992621	+	0.121262i	$0.0386942\pi$
$971$			5.97199e24i			0.242524i	−0.992621	+	0.121262i	$0.961306\pi$
$972$	−3.67632e25	+	7.12361e25i	−1.47996	+	2.86772i
$973$		−	3.22308e25i		−	1.28621i
$974$	−5.70281e24	−	1.38477e24i	−0.225599	−	0.0547807i
$975$	2.52114e25			0.988684
$976$	−5.58185e24	+	3.96766e24i	−0.216998	+	0.154245i
$977$	1.23801e25			0.477112			0.238556	−	0.971129i	$-0.423326\pi$
$977$	1.23801e25			0.477112			0.238556	+	0.971129i	$0.423326\pi$
$978$	5.20231e25	+	1.26324e25i	1.98754	+	0.482620i
$979$			6.65740e24i			0.252146i
$980$	−7.62637e24	+	1.47776e25i	−0.286349	+	0.554860i
$981$			1.25456e26i			4.66987i
$982$	−3.32525e24	+	1.36941e25i	−0.122709	+	0.505344i
$983$	1.37346e25			0.502471			0.251235	−	0.967926i	$-0.419163\pi$
$983$	1.37346e25			0.502471			0.251235	+	0.967926i	$0.419163\pi$
$984$	3.90770e24	−	4.50391e24i	0.141730	−	0.163354i
$985$	−2.51300e25			−0.903617
$986$	1.97258e23	−	8.12354e23i	0.00703204	−	0.0289595i
$987$		−	7.64450e25i		−	2.70180i
$988$	−1.41841e24	−	7.32006e23i	−0.0497013	−	0.0256496i
$989$		−	5.21078e24i		−	0.181023i
$990$	−3.38322e25	−	8.21524e24i	−1.16528	−	0.282957i
$991$	−3.74894e25			−1.28021			−0.640106	−	0.768286i	$-0.721110\pi$
$991$	−3.74894e25			−1.28021			−0.640106	+	0.768286i	$0.721110\pi$
$992$	8.84815e24	+	2.21700e25i	0.299574	+	0.750614i
$993$	−3.51341e25			−1.17940
$994$	4.35067e25	+	1.05644e25i	1.44801	+	0.351610i
$995$		−	1.53624e24i		−	0.0506946i
$996$	8.50084e25	+	4.38707e25i	2.78136	+	1.43539i
$997$			1.39329e25i			0.451993i	0.974128	+	0.225997i	$0.0725638\pi$
$997$			1.39329e25i			0.451993i	−0.974128	+	0.225997i	$0.927436\pi$
$998$	−5.73091e24	+	2.36012e25i	−0.184338	+	0.759144i
$999$	−1.10098e26			−3.51134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.18.b.a.5.16	yes	16
3.2	odd	2		72.18.d.b.37.1		16
4.3	odd	2		32.18.b.a.17.1		16
8.3	odd	2		32.18.b.a.17.16		16
8.5	even	2	inner	8.18.b.a.5.15	✓	16
24.5	odd	2		72.18.d.b.37.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.15	✓	16	8.5	even	2	inner
8.18.b.a.5.16	yes	16	1.1	even	1	trivial
32.18.b.a.17.1		16	4.3	odd	2
32.18.b.a.17.16		16	8.3	odd	2
72.18.d.b.37.1		16	3.2	odd	2
72.18.d.b.37.2		16	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(351.815 + 85.4288i) q^{2} +21682.7i q^{3} +(116476. + 60110.3i) q^{4} +465248. i q^{5} +(-1.85232e6 + 7.62829e6i) q^{6} +2.24795e7 q^{7} +(3.58428e7 + 3.10981e7i) q^{8} -3.40998e8 q^{9} +O(q^{10})\)	\(q+(351.815 + 85.4288i) q^{2} +21682.7i q^{3} +(116476. + 60110.3i) q^{4} +465248. i q^{5} +(-1.85232e6 + 7.62829e6i) q^{6} +2.24795e7 q^{7} +(3.58428e7 + 3.10981e7i) q^{8} -3.40998e8 q^{9} +(-3.97456e7 + 1.63681e8i) q^{10} -6.06148e8i q^{11} +(-1.30335e9 + 2.52551e9i) q^{12} -2.12768e9i q^{13} +(7.90864e9 + 1.92040e9i) q^{14} -1.00878e10 q^{15} +(9.95338e9 + 1.40028e10i) q^{16} -5.45139e9 q^{17} +(-1.19968e11 - 2.91311e10i) q^{18} -5.72346e9i q^{19} +(-2.79662e10 + 5.41902e10i) q^{20} +4.87417e11i q^{21} +(5.17825e10 - 2.13252e11i) q^{22} -1.30247e11 q^{23} +(-6.74290e11 + 7.77168e11i) q^{24} +5.46483e11 q^{25} +(1.81765e11 - 7.48551e11i) q^{26} -4.59365e12i q^{27} +(2.61832e12 + 1.35125e12i) q^{28} +4.23568e11i q^{29} +(-3.54905e12 - 8.61791e11i) q^{30} +3.83783e12 q^{31} +(2.30551e12 + 5.77670e12i) q^{32} +1.31429e13 q^{33} +(-1.91788e12 - 4.65706e11i) q^{34} +1.04586e13i q^{35} +(-3.97181e13 - 2.04975e13i) q^{36} -2.39674e13i q^{37} +(4.88948e11 - 2.01360e12i) q^{38} +4.61339e13 q^{39} +(-1.44683e13 + 1.66758e13i) q^{40} -5.79528e12 q^{41} +(-4.16394e13 + 1.71481e14i) q^{42} +4.00069e13i q^{43} +(3.64357e13 - 7.06016e13i) q^{44} -1.58649e14i q^{45} +(-4.58229e13 - 1.11268e13i) q^{46} -1.56837e14 q^{47} +(-3.03618e14 + 2.15816e14i) q^{48} +2.72699e14 q^{49} +(1.92261e14 + 4.66854e13i) q^{50} -1.18201e14i q^{51} +(1.27896e14 - 2.47824e14i) q^{52} +6.45318e14i q^{53} +(3.92430e14 - 1.61612e15i) q^{54} +2.82010e14 q^{55} +(8.05730e14 + 6.99071e14i) q^{56} +1.24100e14 q^{57} +(-3.61849e13 + 1.49018e14i) q^{58} -8.37680e14i q^{59} +(-1.17499e15 - 6.06382e14i) q^{60} +3.98624e14i q^{61} +(1.35021e15 + 3.27862e14i) q^{62} -7.66548e15 q^{63} +(3.17616e14 + 2.22929e15i) q^{64} +9.89901e14 q^{65} +(4.62388e15 + 1.12278e15i) q^{66} +5.22273e15i q^{67} +(-6.34956e14 - 3.27685e14i) q^{68} -2.82410e15i q^{69} +(-8.93463e14 + 3.67948e15i) q^{70} +5.50116e15 q^{71} +(-1.22223e16 - 1.06044e16i) q^{72} +1.47400e15 q^{73} +(2.04751e15 - 8.43211e15i) q^{74} +1.18492e16i q^{75} +(3.44039e14 - 6.66645e14i) q^{76} -1.36259e16i q^{77} +(1.62306e16 + 3.94116e15i) q^{78} -1.94988e16 q^{79} +(-6.51478e15 + 4.63079e15i) q^{80} +5.55660e16 q^{81} +(-2.03887e15 - 4.95084e14i) q^{82} -3.36599e16i q^{83} +(-2.92987e16 + 5.67723e16i) q^{84} -2.53625e15i q^{85} +(-3.41774e15 + 1.40750e16i) q^{86} -9.18409e15 q^{87} +(1.88501e16 - 2.17261e16i) q^{88} -1.09831e16 q^{89} +(1.35532e16 - 5.58151e16i) q^{90} -4.78293e16i q^{91} +(-1.51706e16 - 7.82918e15i) q^{92} +8.32145e16i q^{93} +(-5.51777e16 - 1.33984e16i) q^{94} +2.66283e15 q^{95} +(-1.25254e17 + 4.99896e16i) q^{96} +6.57395e16 q^{97} +(9.59397e16 + 2.32964e16i) q^{98} +2.06695e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9}+O(q^{10}) \) 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9	\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + 131002712 q^{10} - 2795125400 q^{12} + 16363788528 q^{14} - 9993282176 q^{15} + 26500434192 q^{16} - 7489125600 q^{17} - 113450563870 q^{18} - 209445719856 q^{20} + 223126527100 q^{22} + 746845345920 q^{23} - 1099415493232 q^{24} - 1809682431664 q^{25} + 2467726531080 q^{26} + 3220542267040 q^{28} - 1188624268048 q^{30} - 318979758592 q^{31} + 1455647316000 q^{32} + 5633526177600 q^{33} - 4461251980292 q^{34} - 33088278002484 q^{36} + 24076283913900 q^{38} - 18457706051456 q^{39} + 60626292962592 q^{40} + 7482251536032 q^{41} - 51630378688160 q^{42} + 193654716236040 q^{44} - 195097141003568 q^{46} - 376698804821760 q^{47} - 329350060416480 q^{48} + 127691292101520 q^{49} + 474997408872102 q^{50} - 272251877663120 q^{52} + 735354219382520 q^{54} + 22\!\cdots\!52 q^{55}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9 + 131002712 * q^10 - 2795125400 * q^12 + 16363788528 * q^14 - 9993282176 * q^15 + 26500434192 * q^16 - 7489125600 * q^17 - 113450563870 * q^18 - 209445719856 * q^20 + 223126527100 * q^22 + 746845345920 * q^23 - 1099415493232 * q^24 - 1809682431664 * q^25 + 2467726531080 * q^26 + 3220542267040 * q^28 - 1188624268048 * q^30 - 318979758592 * q^31 + 1455647316000 * q^32 + 5633526177600 * q^33 - 4461251980292 * q^34 - 33088278002484 * q^36 + 24076283913900 * q^38 - 18457706051456 * q^39 + 60626292962592 * q^40 + 7482251536032 * q^41 - 51630378688160 * q^42 + 193654716236040 * q^44 - 195097141003568 * q^46 - 376698804821760 * q^47 - 329350060416480 * q^48 + 127691292101520 * q^49 + 474997408872102 * q^50 - 272251877663120 * q^52 + 735354219382520 * q^54 + 2209036687713152 * q^55 - 162767516076480 * q^56 - 190521298294720 * q^57 - 623262610679960 * q^58 - 1973616194963808 * q^60 + 695695648144320 * q^62 - 8131096607338880 * q^63 + 1111931745501248 * q^64 + 2385987975356160 * q^65 + 3598826202828312 * q^66 + 5981109959771880 * q^68 - 10044559836180288 * q^70 + 9025926285576576 * q^71 - 19918679666289160 * q^72 + 11332002046118560 * q^73 + 11098735408189464 * q^74 + 5959440926938280 * q^76 + 4184252259031760 * q^78 - 45299671392008448 * q^79 + 1337342539452480 * q^80 + 20101901999290832 * q^81 + 15639739637081420 * q^82 + 19796542864700224 * q^84 - 14252032276026564 * q^86 + 25965768920837760 * q^87 - 66964872768837680 * q^88 - 69879174608766048 * q^89 + 136151511125051240 * q^90 + 57336249810701280 * q^92 - 192318922166254176 * q^94 + 93790444358203776 * q^95 - 342799224184788928 * q^96 + 95593398602180640 * q^97 + 339641261743253790 * q^98

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