LMFDB - Embedded newform 8.18.b.a.5.14

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			5.14
Root			$156.321 - 75.9390i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.18.b.a.5.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(328.641 + 151.878i) q^{2} -4248.51i q^{3} +(84938.1 + 99826.8i) q^{4} +663971. i q^{5} +(645256. - 1.39624e6i) q^{6} -1.66742e7 q^{7} +(1.27527e7 + 4.57074e7i) q^{8} +1.11090e8 q^{9} +O(q^{10})$	\(q+(328.641 + 151.878i) q^{2} -4248.51i q^{3} +(84938.1 + 99826.8i) q^{4} +663971. i q^{5} +(645256. - 1.39624e6i) q^{6} -1.66742e7 q^{7} +(1.27527e7 + 4.57074e7i) q^{8} +1.11090e8 q^{9} +(-1.00843e8 + 2.18208e8i) q^{10} +1.05479e9i q^{11} +(4.24116e8 - 3.60861e8i) q^{12} -9.19407e7i q^{13} +(-5.47982e9 - 2.53244e9i) q^{14} +2.82089e9 q^{15} +(-2.75091e9 + 1.69582e10i) q^{16} -1.98326e10 q^{17} +(3.65088e10 + 1.68722e10i) q^{18} +8.44846e10i q^{19} +(-6.62821e10 + 5.63964e10i) q^{20} +7.08405e10i q^{21} +(-1.60199e11 + 3.46647e11i) q^{22} -2.72263e10 q^{23} +(1.94189e11 - 5.41799e10i) q^{24} +3.22082e11 q^{25} +(1.39638e10 - 3.02155e10i) q^{26} -1.02062e12i q^{27} +(-1.41627e12 - 1.66453e12i) q^{28} -3.75013e12i q^{29} +(9.27061e11 + 4.28431e11i) q^{30} +5.36921e12 q^{31} +(-3.47964e12 + 5.15536e12i) q^{32} +4.48129e12 q^{33} +(-6.51781e12 - 3.01214e12i) q^{34} -1.10712e13i q^{35} +(9.43580e12 + 1.10898e13i) q^{36} -1.92294e13i q^{37} +(-1.28314e13 + 2.77651e13i) q^{38} -3.90612e11 q^{39} +(-3.03484e13 + 8.46739e12i) q^{40} +5.42400e13 q^{41} +(-1.07591e13 + 2.32811e13i) q^{42} -3.96416e13i q^{43} +(-1.05296e14 + 8.95918e13i) q^{44} +7.37607e13i q^{45} +(-8.94769e12 - 4.13508e12i) q^{46} +4.48999e13 q^{47} +(7.20471e13 + 1.16873e13i) q^{48} +4.53979e13 q^{49} +(1.05850e14 + 4.89172e13i) q^{50} +8.42591e13i q^{51} +(9.17815e12 - 7.80927e12i) q^{52} -7.81803e14i q^{53} +(1.55010e14 - 3.35419e14i) q^{54} -7.00349e14 q^{55} +(-2.12640e14 - 7.62134e14i) q^{56} +3.58934e14 q^{57} +(5.69562e14 - 1.23245e15i) q^{58} +1.07092e15i q^{59} +(2.39601e14 + 2.81600e14i) q^{60} +1.92548e15i q^{61} +(1.76454e15 + 8.15466e14i) q^{62} -1.85234e15 q^{63} +(-1.92654e15 + 1.16578e15i) q^{64} +6.10460e13 q^{65} +(1.47274e15 + 6.80609e14i) q^{66} +3.68678e15i q^{67} +(-1.68454e15 - 1.97982e15i) q^{68} +1.15671e14i q^{69} +(1.68147e15 - 3.63844e15i) q^{70} -1.02421e16 q^{71} +(1.41670e15 + 5.07765e15i) q^{72} +1.25847e16 q^{73} +(2.92052e15 - 6.31956e15i) q^{74} -1.36837e15i q^{75} +(-8.43383e15 + 7.17596e15i) q^{76} -1.75877e16i q^{77} +(-1.28371e14 - 5.93253e13i) q^{78} +3.24102e15 q^{79} +(-1.12597e16 - 1.82652e15i) q^{80} +1.00101e16 q^{81} +(1.78255e16 + 8.23787e15i) q^{82} -4.28316e15i q^{83} +(-7.07178e15 + 6.01706e15i) q^{84} -1.31683e16i q^{85} +(6.02070e15 - 1.30279e16i) q^{86} -1.59325e16 q^{87} +(-4.82117e16 + 1.34514e16i) q^{88} +6.95255e16 q^{89} +(-1.12026e16 + 2.42408e16i) q^{90} +1.53304e15i q^{91} +(-2.31255e15 - 2.71792e15i) q^{92} -2.28112e16i q^{93} +(1.47560e16 + 6.81931e15i) q^{94} -5.60953e16 q^{95} +(2.19026e16 + 1.47833e16i) q^{96} -7.74223e16 q^{97} +(1.49196e16 + 6.89495e15i) q^{98} +1.17177e17i 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 $

$2$	328.641	+	151.878i	0.907752	+	0.419508i
$2$	328.641	+	151.878i	0.907752	+	0.419508i
$3$		−	4248.51i		−	0.373858i	−0.982373	−	0.186929i	$-0.940147\pi$
$3$		−	4248.51i		−	0.373858i	0.982373	−	0.186929i	$-0.0598534\pi$
$4$	84938.1	+	99826.8i	0.648026	+	0.761618i
$5$			663971.i			0.760158i	0.924954	+	0.380079i	$0.124103\pi$
$5$			663971.i			0.760158i	−0.924954	+	0.380079i	$0.875897\pi$
$6$	645256.	−	1.39624e6i	0.156836	−	0.339370i
$7$	−1.66742e7			−1.09323			−0.546615	−	0.837384i	$-0.684084\pi$
$7$	−1.66742e7			−1.09323			−0.546615	+	0.837384i	$0.684084\pi$
$8$	1.27527e7	+	4.57074e7i	0.268742	+	0.963212i
$9$	1.11090e8			0.860230
$10$	−1.00843e8	+	2.18208e8i	−0.318892	+	0.690035i
$11$			1.05479e9i			1.48364i	0.670600	+	0.741819i	$0.266037\pi$
$11$			1.05479e9i			1.48364i	−0.670600	+	0.741819i	$0.733963\pi$
$12$	4.24116e8	−	3.60861e8i	0.284737	−	0.242270i
$13$		−	9.19407e7i		−	0.0312600i	−0.999878	−	0.0156300i	$-0.995025\pi$
$13$		−	9.19407e7i		−	0.0312600i	0.999878	−	0.0156300i	$-0.00497539\pi$
$14$	−5.47982e9	−	2.53244e9i	−0.992381	−	0.458618i
$15$	2.82089e9			0.284191
$16$	−2.75091e9	+	1.69582e10i	−0.160124	+	0.987097i
$17$	−1.98326e10			−0.689547			−0.344773	−	0.938686i	$-0.612044\pi$
$17$	−1.98326e10			−0.689547			−0.344773	+	0.938686i	$0.612044\pi$
$18$	3.65088e10	+	1.68722e10i	0.780876	+	0.360873i
$19$			8.44846e10i			1.14123i	0.821219	+	0.570613i	$0.193294\pi$
$19$			8.44846e10i			1.14123i	−0.821219	+	0.570613i	$0.806706\pi$
$20$	−6.62821e10	+	5.63964e10i	−0.578950	+	0.492602i
$21$			7.08405e10i			0.408712i
$22$	−1.60199e11	+	3.46647e11i	−0.622398	+	1.34677i
$23$	−2.72263e10			−0.0724941			−0.0362470	−	0.999343i	$-0.511540\pi$
$23$	−2.72263e10			−0.0724941			−0.0362470	+	0.999343i	$0.511540\pi$
$24$	1.94189e11	−	5.41799e10i	0.360104	−	0.100471i
$25$	3.22082e11			0.422160
$26$	1.39638e10	−	3.02155e10i	0.0131138	−	0.0283764i
$27$		−	1.02062e12i		−	0.695462i
$28$	−1.41627e12	−	1.66453e12i	−0.708441	−	0.832623i
$29$		−	3.75013e12i		−	1.39208i	−0.718005	−	0.696038i	$-0.754944\pi$
$29$		−	3.75013e12i		−	1.39208i	0.718005	−	0.696038i	$-0.245056\pi$
$30$	9.27061e11	+	4.28431e11i	0.257975	+	0.119220i
$31$	5.36921e12			1.13067			0.565336	−	0.824861i	$-0.308747\pi$
$31$	5.36921e12			1.13067			0.565336	+	0.824861i	$0.308747\pi$
$32$	−3.47964e12	+	5.15536e12i	−0.559448	+	0.828866i
$33$	4.48129e12			0.554669
$34$	−6.51781e12	−	3.01214e12i	−0.625937	−	0.289270i
$35$		−	1.10712e13i		−	0.831027i
$36$	9.43580e12	+	1.10898e13i	0.557452	+	0.655167i
$37$		−	1.92294e13i		−	0.900015i	−0.893025	−	0.450008i	$-0.851421\pi$
$37$		−	1.92294e13i		−	0.900015i	0.893025	−	0.450008i	$-0.148579\pi$
$38$	−1.28314e13	+	2.77651e13i	−0.478754	+	1.03595i
$39$	−3.90612e11			−0.0116868
$40$	−3.03484e13	+	8.46739e12i	−0.732194	+	0.204287i
$41$	5.42400e13			1.06086			0.530429	−	0.847730i	$-0.322031\pi$
$41$	5.42400e13			1.06086			0.530429	+	0.847730i	$0.322031\pi$
$42$	−1.07591e13	+	2.32811e13i	−0.171458	+	0.371009i
$43$		−	3.96416e13i		−	0.517213i	−0.965983	−	0.258607i	$-0.916737\pi$
$43$		−	3.96416e13i		−	0.517213i	0.965983	−	0.258607i	$-0.0832634\pi$
$44$	−1.05296e14	+	8.95918e13i	−1.12996	+	0.961436i
$45$			7.37607e13i			0.653911i
$46$	−8.94769e12	−	4.13508e12i	−0.0658066	−	0.0304118i
$47$	4.48999e13			0.275051			0.137526	−	0.990498i	$-0.456085\pi$
$47$	4.48999e13			0.275051			0.137526	+	0.990498i	$0.456085\pi$
$48$	7.20471e13	+	1.16873e13i	0.369034	+	0.0598636i
$49$	4.53979e13			0.195150
$50$	1.05850e14	+	4.89172e13i	0.383216	+	0.177099i
$51$			8.42591e13i			0.257792i
$52$	9.17815e12	−	7.80927e12i	0.0238082	−	0.0202573i
$53$		−	7.81803e14i		−	1.72485i	−0.506181	−	0.862427i	$-0.668943\pi$
$53$		−	7.81803e14i		−	1.72485i	0.506181	−	0.862427i	$-0.331057\pi$
$54$	1.55010e14	−	3.35419e14i	0.291752	−	0.631306i
$55$	−7.00349e14			−1.12780
$56$	−2.12640e14	−	7.62134e14i	−0.293797	−	1.05301i
$57$	3.58934e14			0.426656
$58$	5.69562e14	−	1.23245e15i	0.583987	−	1.26366i
$59$			1.07092e15i			0.949541i	0.880110	+	0.474770i	$0.157469\pi$
$59$			1.07092e15i			0.949541i	−0.880110	+	0.474770i	$0.842531\pi$
$60$	2.39601e14	+	2.81600e14i	0.184163	+	0.216445i
$61$			1.92548e15i			1.28599i	0.765872	+	0.642993i	$0.222308\pi$
$61$			1.92548e15i			1.28599i	−0.765872	+	0.642993i	$0.777692\pi$
$62$	1.76454e15	+	8.15466e14i	1.02637	+	0.474325i
$63$	−1.85234e15			−0.940429
$64$	−1.92654e15	+	1.16578e15i	−0.855555	+	0.517711i
$65$	6.10460e13			0.0237626
$66$	1.47274e15	+	6.80609e14i	0.503502	+	0.232688i
$67$			3.68678e15i			1.10920i	0.832116	+	0.554602i	$0.187129\pi$
$67$			3.68678e15i			1.10920i	−0.832116	+	0.554602i	$0.812871\pi$
$68$	−1.68454e15	−	1.97982e15i	−0.446845	−	0.525171i
$69$			1.15671e14i			0.0271025i
$70$	1.68147e15	−	3.63844e15i	0.348622	−	0.754366i
$71$	−1.02421e16			−1.88232			−0.941162	−	0.337957i	$-0.890264\pi$
$71$	−1.02421e16			−1.88232			−0.941162	+	0.337957i	$0.890264\pi$
$72$	1.41670e15	+	5.07765e15i	0.231180	+	0.828584i
$73$	1.25847e16			1.82641			0.913204	−	0.407502i	$-0.133600\pi$
$73$	1.25847e16			1.82641			0.913204	+	0.407502i	$0.133600\pi$
$74$	2.92052e15	−	6.31956e15i	0.377564	−	0.816991i
$75$		−	1.36837e15i		−	0.157828i
$76$	−8.43383e15	+	7.17596e15i	−0.869179	+	0.739545i
$77$		−	1.75877e16i		−	1.62196i
$78$	−1.28371e14	−	5.93253e13i	−0.0106087	−	0.00490271i
$79$	3.24102e15			0.240354			0.120177	−	0.992752i	$-0.461654\pi$
$79$	3.24102e15			0.240354			0.120177	+	0.992752i	$0.461654\pi$
$80$	−1.12597e16	−	1.82652e15i	−0.750350	−	0.121720i
$81$	1.00101e16			0.600227
$82$	1.78255e16	+	8.23787e15i	0.962995	+	0.445038i
$83$		−	4.28316e15i		−	0.208737i	−0.994539	−	0.104369i	$-0.966718\pi$
$83$		−	4.28316e15i		−	0.208737i	0.994539	−	0.104369i	$-0.0332822\pi$
$84$	−7.07178e15	+	6.01706e15i	−0.311283	+	0.264856i
$85$		−	1.31683e16i		−	0.524165i
$86$	6.02070e15	−	1.30279e16i	0.216975	−	0.469501i
$87$	−1.59325e16			−0.520439
$88$	−4.82117e16	+	1.34514e16i	−1.42906	+	0.398716i
$89$	6.95255e16			1.87210			0.936050	−	0.351868i	$-0.114453\pi$
$89$	6.95255e16			1.87210			0.936050	+	0.351868i	$0.114453\pi$
$90$	−1.12026e16	+	2.42408e16i	−0.274321	+	0.593589i
$91$			1.53304e15i			0.0341744i
$92$	−2.31255e15	−	2.71792e15i	−0.0469781	−	0.0552128i
$93$		−	2.28112e16i		−	0.422710i
$94$	1.47560e16	+	6.81931e15i	0.249678	+	0.115386i
$95$	−5.60953e16			−0.867513
$96$	2.19026e16	+	1.47833e16i	0.309878	+	0.209154i
$97$	−7.74223e16			−1.00301			−0.501507	−	0.865154i	$-0.667221\pi$
$97$	−7.74223e16			−1.00301			−0.501507	+	0.865154i	$0.667221\pi$
$98$	1.49196e16	+	6.89495e15i	0.177148	+	0.0818671i
$99$			1.17177e17i			1.27627i
$100$	2.73571e16	+	3.21524e16i	0.273571	+	0.321524i
$101$			8.38662e16i			0.770646i	0.922782	+	0.385323i	$0.125910\pi$
$101$			8.38662e16i			0.770646i	−0.922782	+	0.385323i	$0.874090\pi$
$102$	−1.27971e16	+	2.76910e16i	−0.108146	+	0.234012i
$103$	8.10218e16			0.630210			0.315105	−	0.949057i	$-0.397960\pi$
$103$	8.10218e16			0.630210			0.315105	+	0.949057i	$0.397960\pi$
$104$	4.20238e15	−	1.17249e15i	0.0301101	−	0.00840089i
$105$	−4.70360e16			−0.310686
$106$	1.18739e17	−	2.56933e17i	0.723590	−	1.56574i
$107$		−	1.60731e17i		−	0.904351i	−0.891929	−	0.452175i	$-0.850648\pi$
$107$		−	1.60731e17i		−	0.904351i	0.891929	−	0.452175i	$-0.149352\pi$
$108$	1.01885e17	−	8.66897e16i	0.529676	−	0.450677i
$109$			1.05482e17i			0.507053i	0.967328	+	0.253526i	$0.0815905\pi$
$109$			1.05482e17i			0.507053i	−0.967328	+	0.253526i	$0.918410\pi$
$110$	−2.30164e17	−	1.06368e17i	−1.02376	−	0.473121i
$111$	−8.16962e16			−0.336478
$112$	4.58692e16	−	2.82764e17i	0.175052	−	1.07912i
$113$	−1.30124e17			−0.460458			−0.230229	−	0.973136i	$-0.573948\pi$
$113$	−1.30124e17			−0.460458			−0.230229	+	0.973136i	$0.573948\pi$
$114$	1.17961e17	+	5.45142e16i	0.387298	+	0.178986i
$115$		−	1.80775e16i		−	0.0551069i
$116$	3.74363e17	−	3.18529e17i	1.06023	−	0.902102i
$117$		−	1.02137e16i		−	0.0268908i
$118$	−1.62649e17	+	3.51947e17i	−0.398340	+	0.861947i
$119$	3.30692e17			0.753833
$120$	3.59738e16	+	1.28936e17i	0.0763741	+	0.273736i
$121$	−6.07133e17			−1.20118
$122$	−2.92439e17	+	6.32794e17i	−0.539481	+	1.16736i
$123$		−	2.30439e17i		−	0.396610i
$124$	4.56051e17	+	5.35991e17i	0.732705	+	0.861139i
$125$			7.20423e17i			1.08107i
$126$	−6.08755e17	−	2.81330e17i	−0.853676	−	0.394517i
$127$	1.12618e18			1.47664			0.738322	−	0.674448i	$-0.235619\pi$
$127$	1.12618e18			1.47664			0.738322	+	0.674448i	$0.235619\pi$
$128$	−8.10197e17	+	9.05251e16i	−0.993816	+	0.111041i
$129$	−1.68418e17			−0.193364
$130$	2.00622e16	+	9.27154e15i	0.0215705	+	0.00996859i
$131$			3.73512e17i			0.376269i	0.982143	+	0.188134i	$0.0602440\pi$
$131$			3.73512e17i			0.376269i	−0.982143	+	0.188134i	$0.939756\pi$
$132$	3.80632e17	+	4.47352e17i	0.359440	+	0.422446i
$133$		−	1.40871e18i		−	1.24762i
$134$	−5.59941e17	+	1.21163e18i	−0.465320	+	1.00688i
$135$	6.77664e17			0.528661
$136$	−2.52918e17	−	9.06497e17i	−0.185310	−	0.664180i
$137$	−3.64355e17			−0.250842			−0.125421	−	0.992104i	$-0.540028\pi$
$137$	−3.64355e17			−0.250842			−0.125421	+	0.992104i	$0.540028\pi$
$138$	−1.75680e16	+	3.80144e16i	−0.0113697	+	0.0246023i
$139$		−	2.51151e18i		−	1.52866i	−0.644828	−	0.764328i	$-0.723071\pi$
$139$		−	2.51151e18i		−	1.52866i	0.644828	−	0.764328i	$-0.276929\pi$
$140$	1.10520e18	−	9.40364e17i	0.632925	−	0.538527i
$141$		−	1.90758e17i		−	0.102830i
$142$	−3.36598e18	−	1.55555e18i	−1.70868	−	0.789649i
$143$	9.69781e16			0.0463786
$144$	−3.05599e17	+	1.88389e18i	−0.137743	+	0.849131i
$145$	2.48998e18			1.05820
$146$	4.13585e18	+	1.91134e18i	1.65793	+	0.766193i
$147$		−	1.92874e17i		−	0.0729585i
$148$	1.91960e18	−	1.63330e18i	0.685468	−	0.583234i
$149$			2.83942e18i			0.957517i	0.877947	+	0.478758i	$0.158913\pi$
$149$			2.83942e18i			0.957517i	−0.877947	+	0.478758i	$0.841087\pi$
$150$	2.07826e17	−	4.49703e17i	0.0662100	−	0.143268i
$151$	−2.74195e18			−0.825574			−0.412787	−	0.910828i	$-0.635445\pi$
$151$	−2.74195e18			−0.825574			−0.412787	+	0.910828i	$0.635445\pi$
$152$	−3.86157e18	+	1.07740e18i	−1.09924	+	0.306696i
$153$	−2.20321e18			−0.593169
$154$	2.67119e18	−	5.78006e18i	0.680423	−	1.47233i
$155$			3.56500e18i			0.859489i
$156$	−3.31778e16	−	3.89935e16i	−0.00757336	−	0.00890088i
$157$		−	3.26134e18i		−	0.705096i	−0.935794	−	0.352548i	$-0.885315\pi$
$157$		−	3.26134e18i		−	0.705096i	0.935794	−	0.352548i	$-0.114685\pi$
$158$	1.06513e18	+	4.92239e17i	0.218182	+	0.100830i
$159$	−3.32150e18			−0.644850
$160$	−3.42301e18	−	2.31038e18i	−0.630069	−	0.425269i
$161$	4.53977e17			0.0792526
$162$	3.28973e18	+	1.52031e18i	0.544857	+	0.251800i
$163$			7.80461e18i			1.22675i	0.789791	+	0.613376i	$0.210189\pi$
$163$			7.80461e18i			1.22675i	−0.789791	+	0.613376i	$0.789811\pi$
$164$	4.60704e18	+	5.41461e18i	0.687463	+	0.807968i
$165$			2.97544e18i			0.421636i
$166$	6.50518e17	−	1.40762e18i	0.0875670	−	0.189482i
$167$	−8.54007e18			−1.09237			−0.546187	−	0.837663i	$-0.683921\pi$
$167$	−8.54007e18			−1.09237			−0.546187	+	0.837663i	$0.683921\pi$
$168$	−3.23794e18	+	9.03405e17i	−0.393677	+	0.109838i
$169$	8.64196e18			0.999023
$170$	1.99997e18	−	4.32764e18i	0.219891	−	0.475811i
$171$			9.38542e18i			0.981718i
$172$	3.95730e18	−	3.36709e18i	0.393919	−	0.335168i
$173$			2.07391e18i			0.196516i	0.995161	+	0.0982581i	$0.0313271\pi$
$173$			2.07391e18i			0.196516i	−0.995161	+	0.0982581i	$0.968673\pi$
$174$	−5.23607e18	−	2.41979e18i	−0.472429	−	0.218328i
$175$	−5.37046e18			−0.461517
$176$	−1.78873e19	−	2.90163e18i	−1.46449	−	0.237566i
$177$	4.54981e18			0.354993
$178$	2.28489e19	+	1.05594e19i	1.69940	+	0.785360i
$179$		−	1.67289e19i		−	1.18636i	−0.805071	−	0.593179i	$-0.797873\pi$
$179$		−	1.67289e19i		−	1.18636i	0.805071	−	0.593179i	$-0.202127\pi$
$180$	−7.36329e18	+	6.26509e18i	−0.498030	+	0.423752i
$181$		−	3.02297e19i		−	1.95059i	−0.220907	−	0.975295i	$-0.570902\pi$
$181$		−	3.02297e19i		−	1.95059i	0.220907	−	0.975295i	$-0.429098\pi$
$182$	−2.32835e17	+	5.03819e17i	−0.0143364	+	0.0310219i
$183$	8.18045e18			0.480776
$184$	−3.47208e17	−	1.24445e18i	−0.0194822	−	0.0698272i
$185$	1.27677e19			0.684154
$186$	3.46452e18	−	7.49669e18i	0.177330	−	0.383716i
$187$		−	2.09192e19i		−	1.02304i
$188$	3.81371e18	+	4.48221e18i	0.178240	+	0.209484i
$189$			1.70180e19i			0.760299i
$190$	−1.84352e19	−	8.51965e18i	−0.787486	−	0.363928i
$191$	1.22397e18			0.0500019			0.0250009	−	0.999687i	$-0.492041\pi$
$191$	1.22397e18			0.0500019			0.0250009	+	0.999687i	$0.492041\pi$
$192$	4.95284e18	+	8.18493e18i	0.193550	+	0.319856i
$193$	−6.70836e18			−0.250830			−0.125415	−	0.992104i	$-0.540026\pi$
$193$	−6.70836e18			−0.250830			−0.125415	+	0.992104i	$0.540026\pi$
$194$	−2.54442e19	−	1.17588e19i	−0.910487	−	0.420772i
$195$		−	2.59355e17i		−	0.00888382i
$196$	3.85601e18	+	4.53193e18i	0.126463	+	0.148630i
$197$		−	1.35900e19i		−	0.426832i	−0.976961	−	0.213416i	$-0.931541\pi$
$197$		−	1.35900e19i		−	0.426832i	0.976961	−	0.213416i	$-0.0684590\pi$
$198$	−1.77966e19	+	3.85091e19i	−0.535405	+	1.15854i
$199$	2.94272e19			0.848198			0.424099	−	0.905616i	$-0.360591\pi$
$199$	2.94272e19			0.848198			0.424099	+	0.905616i	$0.360591\pi$
$200$	4.10741e18	+	1.47216e19i	0.113452	+	0.406629i
$201$	1.56633e19			0.414685
$202$	−1.27374e19	+	2.75619e19i	−0.323292	+	0.699556i
$203$			6.25303e19i			1.52186i
$204$	−8.41131e18	+	7.15681e18i	−0.196339	+	0.167056i
$205$			3.60138e19i			0.806419i
$206$	2.66271e19	+	1.23054e19i	0.572074	+	0.264378i
$207$	−3.02458e18			−0.0623616
$208$	1.55915e18	+	2.52921e17i	0.0308567	+	0.00500548i
$209$	−8.91134e19			−1.69317
$210$	−1.54580e19	−	7.14374e18i	−0.282026	−	0.130335i
$211$		−	7.34029e19i		−	1.28621i	−0.765777	−	0.643106i	$-0.777645\pi$
$211$		−	7.34029e19i		−	1.28621i	0.765777	−	0.643106i	$-0.222355\pi$
$212$	7.80449e19	−	6.64049e19i	1.31368	−	1.11775i
$213$			4.35138e19i			0.703721i
$214$	2.44115e19	−	5.28228e19i	0.379382	−	0.820926i
$215$	2.63209e19			0.393164
$216$	4.66500e19	−	1.30157e19i	0.669877	−	0.186900i
$217$	−8.95273e19			−1.23608
$218$	−1.60204e19	+	3.46657e19i	−0.212713	+	0.460278i
$219$		−	5.34662e19i		−	0.682817i
$220$	−5.94863e19	−	6.99136e19i	−0.730843	−	0.858952i
$221$			1.82342e18i			0.0215553i
$222$	−2.68487e19	−	1.24079e19i	−0.305438	−	0.141155i
$223$	7.73683e19			0.847172			0.423586	−	0.905856i	$-0.360771\pi$
$223$	7.73683e19			0.847172			0.423586	+	0.905856i	$0.360771\pi$
$224$	5.80202e19	−	8.59614e19i	0.611605	−	0.906140i
$225$	3.57802e19			0.363155
$226$	−4.27641e19	−	1.97630e19i	−0.417982	−	0.193166i
$227$			1.21923e20i			1.14780i	0.818924	+	0.573902i	$0.194571\pi$
$227$			1.21923e20i			1.14780i	−0.818924	+	0.573902i	$0.805429\pi$
$228$	3.04872e19	+	3.58312e19i	0.276485	+	0.324949i
$229$			1.42038e19i			0.124109i	0.998073	+	0.0620543i	$0.0197652\pi$
$229$			1.42038e19i			0.124109i	−0.998073	+	0.0620543i	$0.980235\pi$
$230$	2.74557e18	−	5.94101e18i	0.0231178	−	0.0500234i
$231$	−7.47218e19			−0.606381
$232$	1.71409e20	−	4.78241e19i	1.34087	−	0.374110i
$233$	−7.02873e19			−0.530092			−0.265046	−	0.964236i	$-0.585387\pi$
$233$	−7.02873e19			−0.530092			−0.265046	+	0.964236i	$0.585387\pi$
$234$	1.55124e18	−	3.35665e18i	0.0112809	−	0.0244102i
$235$			2.98122e19i			0.209082i
$236$	−1.06906e20	+	9.09616e19i	−0.723187	+	0.615327i
$237$		−	1.37695e19i		−	0.0898581i
$238$	1.08679e20	+	5.02249e19i	0.684293	+	0.316239i
$239$	4.12244e19			0.250480			0.125240	−	0.992126i	$-0.460030\pi$
$239$	4.12244e19			0.250480			0.125240	+	0.992126i	$0.460030\pi$
$240$	−7.76001e18	+	4.78372e19i	−0.0455058	+	0.280524i
$241$	9.34265e19			0.528841			0.264420	−	0.964408i	$-0.414819\pi$
$241$	9.34265e19			0.528841			0.264420	+	0.964408i	$0.414819\pi$
$242$	−1.99529e20	−	9.22102e19i	−1.09037	−	0.503904i
$243$		−	1.74331e20i		−	0.919861i
$244$	−1.92215e20	+	1.63547e20i	−0.979430	+	0.833353i
$245$			3.01429e19i			0.148345i
$246$	3.49987e19	−	7.57319e19i	0.166381	−	0.360023i
$247$	7.76758e18			0.0356748
$248$	6.84717e19	+	2.45413e20i	0.303859	+	1.08908i
$249$	−1.81971e19			−0.0780381
$250$	−1.09416e20	+	2.36761e20i	−0.453516	+	0.981340i
$251$		−	8.23914e19i		−	0.330107i	−0.986285	−	0.165054i	$-0.947220\pi$
$251$		−	8.23914e19i		−	0.330107i	0.986285	−	0.165054i	$-0.0527797\pi$
$252$	−1.57334e20	−	1.84913e20i	−0.609423	−	0.716248i
$253$		−	2.87180e19i		−	0.107555i
$254$	3.70109e20	+	1.71042e20i	1.34043	+	0.619464i
$255$	−5.59456e19			−0.195963
$256$	−2.80013e20	−	9.33009e19i	−0.948721	−	0.316116i
$257$	3.96731e20			1.30036			0.650182	−	0.759779i	$-0.274693\pi$
$257$	3.96731e20			1.30036			0.650182	+	0.759779i	$0.274693\pi$
$258$	−5.53491e19	−	2.55790e19i	−0.175527	−	0.0811178i
$259$			3.20634e20i			0.983923i
$260$	5.18513e18	+	6.09402e18i	0.0153988	+	0.0180980i
$261$		−	4.16603e20i		−	1.19751i
$262$	−5.67282e19	+	1.22751e20i	−0.157848	+	0.341559i
$263$	−3.01079e20			−0.811066			−0.405533	−	0.914080i	$-0.632914\pi$
$263$	−3.01079e20			−0.811066			−0.405533	+	0.914080i	$0.632914\pi$
$264$	5.71483e19	+	2.04828e20i	0.149063	+	0.534264i
$265$	5.19094e20			1.31116
$266$	2.13952e20	−	4.62961e20i	0.523387	−	1.13253i
$267$		−	2.95380e20i		−	0.699899i
$268$	−3.68039e20	+	3.13148e20i	−0.844790	+	0.718793i
$269$		−	7.99834e19i		−	0.177871i	−0.996037	−	0.0889356i	$-0.971653\pi$
$269$		−	7.99834e19i		−	0.177871i	0.996037	−	0.0889356i	$-0.0283465\pi$
$270$	2.22708e20	+	1.02922e20i	0.479893	+	0.221777i
$271$	−3.82151e20			−0.797986			−0.398993	−	0.916954i	$-0.630640\pi$
$271$	−3.82151e20			−0.797986			−0.398993	+	0.916954i	$0.630640\pi$
$272$	5.45577e19	−	3.36325e20i	0.110413	−	0.680650i
$273$	6.51313e18			0.0127764
$274$	−1.19742e20	−	5.53375e19i	−0.227702	−	0.105230i
$275$			3.39729e20i			0.626332i
$276$	−1.15471e19	+	9.82491e18i	−0.0206417	+	0.0175631i
$277$		−	3.87625e20i		−	0.671945i	−0.941872	−	0.335972i	$-0.890935\pi$
$277$		−	3.87625e20i		−	0.671945i	0.941872	−	0.335972i	$-0.109065\pi$
$278$	3.81444e20	−	8.25387e20i	0.641283	−	1.38764i
$279$	5.96467e20			0.972638
$280$	5.06035e20	−	1.41187e20i	0.800455	−	0.223332i
$281$	−5.68349e20			−0.872190			−0.436095	−	0.899901i	$-0.643639\pi$
$281$	−5.68349e20			−0.872190			−0.436095	+	0.899901i	$0.643639\pi$
$282$	2.89719e19	−	6.26909e19i	0.0431380	−	0.0933441i
$283$			4.50897e20i			0.651467i	0.945462	+	0.325734i	$0.105611\pi$
$283$			4.50897e20i			0.651467i	−0.945462	+	0.325734i	$0.894389\pi$
$284$	−8.69947e20	−	1.02244e21i	−1.21979	−	1.43361i
$285$			2.38322e20i			0.324326i
$286$	3.18710e19	+	1.47288e19i	0.0421002	+	0.0194562i
$287$	−9.04408e20			−1.15976
$288$	−3.86554e20	+	5.72710e20i	−0.481254	+	0.713015i
$289$	−4.33908e20			−0.524525
$290$	8.18309e20	+	3.78173e20i	0.960581	+	0.443923i
$291$			3.28930e20i			0.374984i
$292$	1.06892e21	+	1.25629e21i	1.18356	+	1.39103i
$293$			1.51002e21i			1.62408i	0.583602	+	0.812040i	$0.301643\pi$
$293$			1.51002e21i			1.62408i	−0.583602	+	0.812040i	$0.698357\pi$
$294$	2.92933e19	−	6.33863e19i	0.0306067	−	0.0662282i
$295$	−7.11057e20			−0.721801
$296$	8.78924e20	−	2.45225e20i	0.866906	−	0.241872i
$297$	1.07654e21			1.03181
$298$	−4.31246e20	+	9.33150e20i	−0.401686	+	0.869187i
$299$			2.50321e18i			0.00226617i
$300$	1.36600e20	−	1.16227e20i	0.120204	−	0.102276i
$301$			6.60992e20i			0.565433i
$302$	−9.01119e20	−	4.16443e20i	−0.749416	−	0.346335i
$303$	3.56307e20			0.288112
$304$	−1.43271e21	−	2.32409e20i	−1.12650	−	0.182738i
$305$	−1.27847e21			−0.977553
$306$	−7.24065e20	−	3.34619e20i	−0.538450	−	0.248839i
$307$		−	7.15201e20i		−	0.517311i	−0.965970	−	0.258655i	$-0.916721\pi$
$307$		−	7.15201e20i		−	0.517311i	0.965970	−	0.258655i	$-0.0832794\pi$
$308$	1.75573e21	−	1.49387e21i	1.23531	−	1.05107i
$309$		−	3.44222e20i		−	0.235609i
$310$	−5.41445e20	+	1.17161e21i	−0.360562	+	0.780202i
$311$	1.55199e21			1.00560			0.502801	−	0.864402i	$-0.332303\pi$
$311$	1.55199e21			1.00560			0.502801	+	0.864402i	$0.332303\pi$
$312$	−4.98134e18	−	1.78539e19i	−0.00314074	−	0.0112569i
$313$	−7.03438e20			−0.431617			−0.215809	−	0.976436i	$-0.569239\pi$
$313$	−7.03438e20			−0.431617			−0.215809	+	0.976436i	$0.569239\pi$
$314$	4.95325e20	−	1.07181e21i	0.295793	−	0.640052i
$315$		−	1.22990e21i		−	0.714875i
$316$	2.75286e20	+	3.23540e20i	0.155756	+	0.183058i
$317$		−	2.05646e21i		−	1.13270i	−0.824163	−	0.566352i	$-0.808354\pi$
$317$		−	2.05646e21i		−	1.13270i	0.824163	−	0.566352i	$-0.191646\pi$
$318$	−1.09158e21	−	5.04463e20i	−0.585364	−	0.270520i
$319$	3.95559e21			2.06534
$320$	−7.74046e20	−	1.27917e21i	−0.393543	−	0.650357i
$321$	−6.82867e20			−0.338099
$322$	1.49195e20	+	6.89491e19i	0.0719417	+	0.0332471i
$323$		−	1.67555e21i		−	0.786929i
$324$	8.50238e20	+	9.99275e20i	0.388963	+	0.457143i
$325$		−	2.96125e19i		−	0.0131967i
$326$	−1.18535e21	+	2.56492e21i	−0.514632	+	1.11359i
$327$	4.48142e20			0.189566
$328$	6.91704e20	+	2.47917e21i	0.285097	+	1.02183i
$329$	−7.48669e20			−0.300694
$330$	−4.51905e20	+	9.77853e20i	−0.176880	+	0.382741i
$331$		−	7.03264e20i		−	0.268275i	−0.990963	−	0.134138i	$-0.957174\pi$
$331$		−	7.03264e20i		−	0.268275i	0.990963	−	0.134138i	$-0.0428264\pi$
$332$	4.27574e20	−	3.63803e20i	0.158978	−	0.135267i
$333$		−	2.13619e21i		−	0.774221i
$334$	−2.80662e21	−	1.29705e21i	−0.991605	−	0.458260i
$335$	−2.44791e21			−0.843170
$336$	−1.20133e21	−	1.94876e20i	−0.403439	−	0.0654446i
$337$	8.84366e20			0.289586			0.144793	−	0.989462i	$-0.453748\pi$
$337$	8.84366e20			0.289586			0.144793	+	0.989462i	$0.453748\pi$
$338$	2.84011e21	+	1.31252e21i	0.906865	+	0.419098i
$339$			5.52833e20i			0.172146i
$340$	1.31455e21	−	1.11849e21i	0.399213	−	0.339672i
$341$			5.66339e21i			1.67751i
$342$	−1.42544e21	+	3.08444e21i	−0.411838	+	0.891156i
$343$	3.12195e21			0.879885
$344$	1.81192e21	−	5.05536e20i	0.498186	−	0.138997i
$345$	−7.68024e19			−0.0206022
$346$	−3.14982e20	+	6.81573e20i	−0.0824401	+	0.178388i
$347$			5.48605e21i			1.40107i	0.713620	+	0.700533i	$0.247055\pi$
$347$			5.48605e21i			1.40107i	−0.713620	+	0.700533i	$0.752945\pi$
$348$	−1.35327e21	−	1.59049e21i	−0.337258	−	0.396375i
$349$		−	2.09596e19i		−	0.00509762i	−0.999997	−	0.00254881i	$-0.999189\pi$
$349$		−	2.09596e19i		−	0.00509762i	0.999997	−	0.00254881i	$-0.000811312\pi$
$350$	−1.76495e21	−	8.15655e20i	−0.418943	−	0.193610i
$351$	−9.38368e19			−0.0217402
$352$	−5.43782e21	−	3.67029e21i	−1.22974	−	0.830018i
$353$	−8.34131e20			−0.184141			−0.0920703	−	0.995753i	$-0.529348\pi$
$353$	−8.34131e20			−0.184141			−0.0920703	+	0.995753i	$0.529348\pi$
$354$	1.49525e21	+	6.91016e20i	0.322246	+	0.148922i
$355$		−	6.80047e21i		−	1.43086i
$356$	5.90536e21	+	6.94051e21i	1.21317	+	1.42582i
$357$		−	1.40495e21i		−	0.281826i
$358$	2.54075e21	−	5.49780e21i	0.497687	−	1.07692i
$359$	−7.98650e21			−1.52775			−0.763877	−	0.645361i	$-0.776707\pi$
$359$	−7.98650e21			−1.52775			−0.763877	+	0.645361i	$0.776707\pi$
$360$	−3.37141e21	+	9.40645e20i	−0.629855	+	0.175733i
$361$	−1.65726e21			−0.302398
$362$	4.59123e21	−	9.93473e21i	0.818288	−	1.77065i
$363$			2.57941e21i			0.449071i
$364$	−1.53038e20	+	1.30213e20i	−0.0260278	+	0.0221459i
$365$			8.35586e21i			1.38836i
$366$	2.68843e21	+	1.24243e21i	0.436425	+	0.201689i
$367$	−4.95976e21			−0.786682			−0.393341	−	0.919393i	$-0.628681\pi$
$367$	−4.95976e21			−0.786682			−0.393341	+	0.919393i	$0.628681\pi$
$368$	7.48971e19	−	4.61709e20i	0.0116080	−	0.0715587i
$369$	6.02554e21			0.912581
$370$	4.19600e21	+	1.93914e21i	0.621042	+	0.287008i
$371$			1.30359e22i			1.88566i
$372$	2.27717e21	−	1.93754e21i	0.321944	−	0.273927i
$373$		−	1.32602e22i		−	1.83243i	−0.400692	−	0.916213i	$-0.631230\pi$
$373$		−	1.32602e22i		−	1.83243i	0.400692	−	0.916213i	$-0.368770\pi$
$374$	3.17717e21	−	6.87491e21i	0.429172	−	0.928664i
$375$	3.06073e21			0.404165
$376$	5.72593e20	+	2.05226e21i	0.0739178	+	0.264933i
$377$	−3.44790e20			−0.0435164
$378$	−2.58467e21	+	5.59283e21i	−0.318951	+	0.690163i
$379$		−	4.66066e21i		−	0.562360i	−0.959655	−	0.281180i	$-0.909274\pi$
$379$		−	4.66066e21i		−	0.562360i	0.959655	−	0.281180i	$-0.0907258\pi$
$380$	−4.76463e21	−	5.59981e21i	−0.562171	−	0.660713i
$381$		−	4.78459e21i		−	0.552055i
$382$	4.02246e20	+	1.85894e20i	0.0453893	+	0.0209762i
$383$	−9.41823e21			−1.03939			−0.519696	−	0.854351i	$-0.673955\pi$
$383$	−9.41823e21			−1.03939			−0.519696	+	0.854351i	$0.673955\pi$
$384$	3.84597e20	+	3.44213e21i	0.0415136	+	0.371546i
$385$	1.16778e22			1.23294
$386$	−2.20464e21	−	1.01885e21i	−0.227691	−	0.105225i
$387$		−	4.40380e21i		−	0.444923i
$388$	−6.57611e21	−	7.72882e21i	−0.649979	−	0.763913i
$389$			2.84056e21i			0.274683i	0.990524	+	0.137342i	$0.0438558\pi$
$389$			2.84056e21i			0.274683i	−0.990524	+	0.137342i	$0.956144\pi$
$390$	3.93903e19	−	8.52346e19i	0.00372683	−	0.00806431i
$391$	5.39969e20			0.0499881
$392$	5.78944e20	+	2.07502e21i	0.0524451	+	0.187971i
$393$	1.58687e21			0.140671
$394$	2.06403e21	−	4.46624e21i	0.179059	−	0.387458i
$395$			2.15194e21i			0.182707i
$396$	−1.16974e22	+	9.95278e21i	−0.972030	+	0.827056i
$397$		−	6.92645e20i		−	0.0563367i	−0.999603	−	0.0281683i	$-0.991033\pi$
$397$		−	6.92645e20i		−	0.0563367i	0.999603	−	0.0281683i	$-0.00896745\pi$
$398$	9.67098e21	+	4.46934e21i	0.769953	+	0.355826i
$399$	−5.98493e21			−0.466433
$400$	−8.86019e20	+	5.46193e21i	−0.0675979	+	0.416713i
$401$	−4.47868e21			−0.334521			−0.167260	−	0.985913i	$-0.553492\pi$
$401$	−4.47868e21			−0.334521			−0.167260	+	0.985913i	$0.553492\pi$
$402$	5.14762e21	+	2.37892e21i	0.376431	+	0.173963i
$403$		−	4.93650e20i		−	0.0353448i
$404$	−8.37209e21	+	7.12343e21i	−0.586938	+	0.499399i
$405$			6.64641e21i			0.456267i
$406$	−9.49699e21	+	2.05500e22i	−0.638432	+	1.38147i
$407$	2.02829e22			1.33530
$408$	−3.85127e21	+	1.07453e21i	−0.248309	+	0.0692797i
$409$	1.38245e22			0.872972			0.436486	−	0.899711i	$-0.356223\pi$
$409$	1.38245e22			0.872972			0.436486	+	0.899711i	$0.356223\pi$
$410$	−5.46970e21	+	1.18356e22i	−0.338299	+	0.732028i
$411$			1.54797e21i			0.0937791i
$412$	6.88184e21	+	8.08815e21i	0.408393	+	0.479979i
$413$		−	1.78567e22i		−	1.03807i
$414$	−9.94002e20	−	4.59367e20i	−0.0566088	−	0.0261612i
$415$	2.84389e21			0.158673
$416$	4.73988e20	+	3.19921e20i	0.0259104	+	0.0174884i
$417$	−1.06702e22			−0.571500
$418$	−2.92863e22	−	1.35344e22i	−1.53697	−	0.710297i
$419$			4.06502e21i			0.209047i	0.994522	+	0.104523i	$0.0333317\pi$
$419$			4.06502e21i			0.209047i	−0.994522	+	0.104523i	$0.966668\pi$
$420$	−3.99515e21	−	4.69546e21i	−0.201333	−	0.236624i
$421$			8.16114e21i			0.403045i	0.979484	+	0.201522i	$0.0645888\pi$
$421$			8.16114e21i			0.403045i	−0.979484	+	0.201522i	$0.935411\pi$
$422$	1.11483e22	−	2.41232e22i	0.539576	−	1.16756i
$423$	4.98794e21			0.236607
$424$	3.57342e22	−	9.97007e21i	1.66140	−	0.463541i
$425$	−6.38773e21			−0.291099
$426$	−6.60880e21	+	1.43004e22i	−0.295217	+	0.638804i
$427$		−	3.21059e22i		−	1.40588i
$428$	1.60452e22	−	1.36522e22i	0.688770	−	0.586043i
$429$		−	4.12013e20i		−	0.0173390i
$430$	8.65013e21	+	3.99757e21i	0.356895	+	0.164935i
$431$	−9.79174e21			−0.396098			−0.198049	−	0.980192i	$-0.563461\pi$
$431$	−9.79174e21			−0.396098			−0.198049	+	0.980192i	$0.563461\pi$
$432$	1.73079e22	+	2.80764e21i	0.686488	+	0.111360i
$433$	−2.60425e22			−1.01283			−0.506414	−	0.862290i	$-0.669029\pi$
$433$	−2.60425e22			−1.01283			−0.506414	+	0.862290i	$0.669029\pi$
$434$	−2.94223e22	−	1.35972e22i	−1.12206	−	0.518546i
$435$		−	1.05787e22i		−	0.395616i
$436$	−1.05299e22	+	8.95944e21i	−0.386181	+	0.328584i
$437$		−	2.30020e21i		−	0.0827321i
$438$	8.12034e21	−	1.75712e22i	0.286447	−	0.619828i
$439$	2.68066e22			0.927455			0.463727	−	0.885978i	$-0.346512\pi$
$439$	2.68066e22			0.927455			0.463727	+	0.885978i	$0.346512\pi$
$440$	−8.93131e21	−	3.20112e22i	−0.303087	−	1.08631i
$441$	5.04327e21			0.167874
$442$	−2.76938e20	+	5.99252e20i	−0.00904260	+	0.0195668i
$443$		−	6.73832e21i		−	0.215834i	−0.994160	−	0.107917i	$-0.965582\pi$
$443$		−	6.73832e21i		−	0.215834i	0.994160	−	0.107917i	$-0.0344181\pi$
$444$	−6.93912e21	−	8.15547e21i	−0.218046	−	0.256268i
$445$			4.61629e22i			1.42309i
$446$	2.54264e22	+	1.17506e22i	0.769022	+	0.355396i
$447$	1.20633e22			0.357975
$448$	3.21235e22	−	1.94385e22i	0.935318	−	0.565977i
$449$	−3.12876e22			−0.893878			−0.446939	−	0.894564i	$-0.647486\pi$
$449$	−3.12876e22			−0.893878			−0.446939	+	0.894564i	$0.647486\pi$
$450$	1.17589e22	+	5.43423e21i	0.329654	+	0.152346i
$451$			5.72118e22i			1.57393i
$452$	−1.10525e22	−	1.29899e22i	−0.298389	−	0.350693i
$453$			1.16492e22i			0.308647i
$454$	−1.85175e22	+	4.00691e22i	−0.481512	+	1.04192i
$455$	−1.01789e21			−0.0259779
$456$	4.57736e21	+	1.64060e22i	0.114661	+	0.410961i
$457$	−5.48338e22			−1.34822			−0.674110	−	0.738631i	$-0.735473\pi$
$457$	−5.48338e22			−1.34822			−0.674110	+	0.738631i	$0.735473\pi$
$458$	−2.15724e21	+	4.66794e21i	−0.0520645	+	0.112660i
$459$			2.02416e22i			0.479553i
$460$	1.80462e21	−	1.53547e21i	0.0419704	−	0.0357107i
$461$			6.78571e22i			1.54931i	0.632386	+	0.774653i	$0.282076\pi$
$461$			6.78571e22i			1.54931i	−0.632386	+	0.774653i	$0.717924\pi$
$462$	−2.45567e22	−	1.13486e22i	−0.550443	−	0.254382i
$463$	−1.64300e21			−0.0361576			−0.0180788	−	0.999837i	$-0.505755\pi$
$463$	−1.64300e21			−0.0361576			−0.0180788	+	0.999837i	$0.505755\pi$
$464$	6.35954e22	+	1.03163e22i	1.37411	+	0.222905i
$465$	1.51460e22			0.321327
$466$	−2.30993e22	−	1.06751e22i	−0.481192	−	0.222378i
$467$		−	4.77673e22i		−	0.977096i	−0.872537	−	0.488548i	$-0.837527\pi$
$467$		−	4.77673e22i		−	0.977096i	0.872537	−	0.488548i	$-0.162473\pi$
$468$	1.01960e21	−	8.67534e20i	0.0204805	−	0.0174260i
$469$		−	6.14740e22i		−	1.21261i
$470$	−4.52782e21	+	9.79752e21i	−0.0877117	+	0.189795i
$471$	−1.38558e22			−0.263606
$472$	−4.89489e22	+	1.36570e22i	−0.914609	+	0.255182i
$473$	4.18136e22			0.767357
$474$	2.09129e21	−	4.52523e21i	0.0376962	−	0.0815689i
$475$			2.72110e22i			0.481780i
$476$	2.80884e22	+	3.30120e22i	0.488504	+	0.574133i
$477$		−	8.68507e22i		−	1.48377i
$478$	1.35480e22	+	6.26109e21i	0.227373	+	0.105078i
$479$	−5.48658e22			−0.904585			−0.452293	−	0.891870i	$-0.649394\pi$
$479$	−5.48658e22			−0.904585			−0.452293	+	0.891870i	$0.649394\pi$
$480$	−9.81568e21	+	1.45427e22i	−0.158990	+	0.235556i
$481$	−1.76796e21			−0.0281345
$482$	3.07038e22	+	1.41894e22i	0.480056	+	0.221853i
$483$		−	1.92873e21i		−	0.0296292i
$484$	−5.15687e22	−	6.06081e22i	−0.778396	−	0.914840i
$485$		−	5.14062e22i		−	0.762448i
$486$	2.64771e22	−	5.72925e22i	0.385889	−	0.835005i
$487$	1.26074e23			1.80564			0.902818	−	0.430022i	$-0.141494\pi$
$487$	1.26074e23			1.80564			0.902818	+	0.430022i	$0.141494\pi$
$488$	−8.80089e22	+	2.45550e22i	−1.23868	+	0.345599i
$489$	3.31580e22			0.458630
$490$	−4.57805e21	+	9.90620e21i	−0.0622320	+	0.134661i
$491$		−	1.93871e22i		−	0.259013i	−0.991579	−	0.129506i	$-0.958661\pi$
$491$		−	1.93871e22i		−	0.259013i	0.991579	−	0.129506i	$-0.0413393\pi$
$492$	2.30040e22	−	1.95731e22i	0.302065	−	0.257013i
$493$			7.43748e22i			0.959902i
$494$	2.55275e21	+	1.17972e21i	0.0323839	+	0.0149659i
$495$	−7.78020e22			−0.970167
$496$	−1.47702e22	+	9.10522e22i	−0.181048	+	1.11608i
$497$	1.70779e23			2.05781
$498$	−5.98030e21	−	2.76373e21i	−0.0708392	−	0.0327376i
$499$		−	8.94608e22i		−	1.04178i	−0.853622	−	0.520892i	$-0.825599\pi$
$499$		−	8.94608e22i		−	1.04178i	0.853622	−	0.520892i	$-0.174401\pi$
$500$	−7.19175e22	+	6.11913e22i	−0.823359	+	0.700559i
$501$			3.62826e22i			0.408393i
$502$	1.25134e22	−	2.70772e22i	0.138483	−	0.299655i
$503$	3.84163e22			0.418011			0.209005	−	0.977914i	$-0.432977\pi$
$503$	3.84163e22			0.418011			0.209005	+	0.977914i	$0.432977\pi$
$504$	−2.36223e22	−	8.46657e22i	−0.252733	−	0.905833i
$505$	−5.56847e22			−0.585813
$506$	4.36164e21	−	9.43793e21i	0.0451201	−	0.0976331i
$507$		−	3.67155e22i		−	0.373492i
$508$	9.56555e22	+	1.12423e23i	0.956904	+	1.12464i
$509$		−	1.79276e23i		−	1.76369i	−0.471541	−	0.881844i	$-0.656302\pi$
$509$		−	1.79276e23i		−	1.76369i	0.471541	−	0.881844i	$-0.343698\pi$
$510$	−1.83860e22	−	8.49691e21i	−0.177886	−	0.0822080i
$511$	−2.09839e23			−1.99668
$512$	−7.78534e22	−	7.31903e22i	−0.728590	−	0.684950i
$513$	8.62269e22			0.793679
$514$	1.30382e23	+	6.02547e22i	1.18041	+	0.545513i
$515$			5.37961e22i			0.479059i
$516$	−1.43051e22	−	1.68126e22i	−0.125305	−	0.147270i
$517$			4.73599e22i			0.408076i
$518$	−4.86972e22	+	1.05373e23i	−0.412764	+	0.893158i
$519$	8.81104e21			0.0734691
$520$	7.78498e20	+	2.79025e21i	0.00638601	+	0.0228884i
$521$	6.78107e22			0.547240			0.273620	−	0.961838i	$-0.411779\pi$
$521$	6.78107e22			0.547240			0.273620	+	0.961838i	$0.411779\pi$
$522$	6.32728e22	−	1.36913e23i	0.502363	−	1.08704i
$523$			2.09501e23i			1.63652i	0.574845	+	0.818262i	$0.305062\pi$
$523$			2.09501e23i			1.63652i	−0.574845	+	0.818262i	$0.694938\pi$
$524$	−3.72865e22	+	3.17254e22i	−0.286573	+	0.243832i
$525$			2.28165e22i			0.172542i
$526$	−9.89468e22	−	4.57272e22i	−0.736246	−	0.340248i
$527$	−1.06485e23			−0.779651
$528$	−1.23276e22	+	7.59945e22i	−0.0888158	+	0.547512i
$529$	−1.40309e23			−0.994745
$530$	1.70596e23	+	7.88390e22i	1.19021	+	0.550043i
$531$			1.18968e23i			0.816824i
$532$	1.40627e23	−	1.19653e23i	0.950212	−	0.808492i
$533$		−	4.98687e21i		−	0.0331624i
$534$	4.48617e22	−	9.70740e22i	0.293613	−	0.635334i
$535$	1.06721e23			0.687450
$536$	−1.68513e23	+	4.70162e22i	−1.06840	+	0.298090i
$537$	−7.10728e22			−0.443529
$538$	1.21477e22	−	2.62858e22i	0.0746184	−	0.161463i
$539$			4.78852e22i			0.289532i
$540$	5.75595e22	+	6.76490e22i	0.342586	+	0.402638i
$541$			1.24185e23i			0.727600i	0.931477	+	0.363800i	$0.118521\pi$
$541$			1.24185e23i			0.727600i	−0.931477	+	0.363800i	$0.881479\pi$
$542$	−1.25590e23	−	5.80403e22i	−0.724374	−	0.334762i
$543$	−1.28431e23			−0.729243
$544$	6.90103e22	−	1.02244e23i	0.385765	−	0.571542i
$545$	−7.00370e22			−0.385440
$546$	2.14048e21	+	9.89202e20i	0.0115978	+	0.00535979i
$547$		−	1.22112e23i		−	0.651429i	−0.945468	−	0.325714i	$-0.894395\pi$
$547$		−	1.22112e23i		−	0.651429i	0.945468	−	0.325714i	$-0.105605\pi$
$548$	−3.09476e22	−	3.63724e22i	−0.162552	−	0.191046i
$549$			2.13903e23i			1.10624i
$550$	−5.15974e22	+	1.11649e23i	−0.262751	+	0.568554i
$551$	3.16828e23			1.58867
$552$	−5.28704e21	+	1.47512e21i	−0.0261054	+	0.00728358i
$553$	−5.40413e22			−0.262762
$554$	5.88717e22	−	1.27389e23i	0.281886	−	0.609959i
$555$		−	5.42439e22i		−	0.255776i
$556$	2.50716e23	−	2.13323e23i	1.16425	−	0.990609i
$557$		−	2.07273e23i		−	0.947924i	−0.880545	−	0.473962i	$-0.842823\pi$
$557$		−	2.07273e23i		−	0.947924i	0.880545	−	0.473962i	$-0.157177\pi$
$558$	1.96024e23	+	9.05903e22i	0.882913	+	0.408029i
$559$	−3.64468e21			−0.0161681
$560$	1.87747e23	+	3.04558e22i	0.820304	+	0.133067i
$561$	−8.88756e22			−0.382471
$562$	−1.86783e23	−	8.63197e22i	−0.791732	−	0.365891i
$563$		−	1.43541e23i		−	0.599314i	−0.954047	−	0.299657i	$-0.903128\pi$
$563$		−	1.43541e23i		−	0.599314i	0.954047	−	0.299657i	$-0.0968722\pi$
$564$	1.90427e22	−	1.62026e22i	0.0783172	−	0.0666365i
$565$		−	8.63985e22i		−	0.350021i
$566$	−6.84813e22	+	1.48183e23i	−0.273296	+	0.591370i
$567$	−1.66910e23			−0.656185
$568$	−1.30614e23	−	4.68141e23i	−0.505860	−	1.81308i
$569$	1.29010e23			0.492231			0.246116	−	0.969240i	$-0.420846\pi$
$569$	1.29010e23			0.492231			0.246116	+	0.969240i	$0.420846\pi$
$570$	−3.61958e22	+	7.83223e22i	−0.136057	+	0.294408i
$571$		−	2.64243e23i		−	0.978579i	−0.872121	−	0.489290i	$-0.837256\pi$
$571$		−	2.64243e23i		−	0.978579i	0.872121	−	0.489290i	$-0.162744\pi$
$572$	8.23713e21	+	9.68101e21i	0.0300545	+	0.0353228i
$573$		−	5.20005e21i		−	0.0186936i
$574$	−2.97226e23	−	1.37360e23i	−1.05277	−	0.486529i
$575$	−8.76912e21			−0.0306041
$576$	−2.14020e23	+	1.29507e23i	−0.735975	+	0.445351i
$577$	−9.70397e22			−0.328818			−0.164409	−	0.986392i	$-0.552572\pi$
$577$	−9.70397e22			−0.328818			−0.164409	+	0.986392i	$0.552572\pi$
$578$	−1.42600e23	−	6.59011e22i	−0.476138	−	0.220042i
$579$			2.85005e22i			0.0937746i
$580$	2.11494e23	+	2.48566e23i	0.685740	+	0.805943i
$581$			7.14182e22i			0.228198i
$582$	−4.99573e22	+	1.08100e23i	−0.157309	+	0.340393i
$583$	8.24637e23			2.55906
$584$	1.60488e23	+	5.75214e23i	0.490833	+	1.75922i
$585$	6.78161e21			0.0204413
$586$	−2.29339e23	+	4.96254e23i	−0.681314	+	1.47426i
$587$		−	3.02349e23i		−	0.885288i	−0.896697	−	0.442644i	$-0.854041\pi$
$587$		−	3.02349e23i		−	0.885288i	0.896697	−	0.442644i	$-0.145959\pi$
$588$	1.92540e22	−	1.63823e22i	0.0555665	−	0.0472790i
$589$			4.53616e23i			1.29035i
$590$	−2.33683e23	−	1.07994e23i	−0.655216	−	0.302801i
$591$	−5.77374e22			−0.159574
$592$	3.26095e23	+	5.28982e22i	0.888402	+	0.144114i
$593$	−3.18008e23			−0.854030			−0.427015	−	0.904245i	$-0.640435\pi$
$593$	−3.18008e23			−0.854030			−0.427015	+	0.904245i	$0.640435\pi$
$594$	3.53796e23	+	1.63503e23i	0.936630	+	0.432854i
$595$			2.19570e23i			0.573032i
$596$	−2.83450e23	+	2.41175e23i	−0.729262	+	0.620496i
$597$		−	1.25022e23i		−	0.317105i
$598$	−3.80183e20	+	8.22657e20i	−0.000950675	+	0.00205712i
$599$	3.24737e23			0.800578			0.400289	−	0.916389i	$-0.368910\pi$
$599$	3.24737e23			0.800578			0.400289	+	0.916389i	$0.368910\pi$
$600$	6.25447e22	−	1.74504e22i	0.152022	−	0.0424150i
$601$	−3.78448e23			−0.906929			−0.453464	−	0.891274i	$-0.649812\pi$
$601$	−3.78448e23			−0.906929			−0.453464	+	0.891274i	$0.649812\pi$
$602$	−1.00390e23	+	2.17229e23i	−0.237204	+	0.513273i
$603$			4.09565e23i			0.954171i
$604$	−2.32896e23	−	2.73721e23i	−0.534994	−	0.628772i
$605$		−	4.03118e23i		−	0.913087i
$606$	1.17097e23	+	5.41152e22i	0.261534	+	0.120865i
$607$	−2.72859e23			−0.600945			−0.300472	−	0.953791i	$-0.597144\pi$
$607$	−2.72859e23			−0.600945			−0.300472	+	0.953791i	$0.597144\pi$
$608$	−4.35548e23	−	2.93976e23i	−0.945924	−	0.638457i
$609$	2.65661e23			0.568959
$610$	−4.20156e23	−	1.94171e23i	−0.887375	−	0.410091i
$611$		−	4.12813e21i		−	0.00859811i
$612$	−1.87136e23	−	2.19939e23i	−0.384389	−	0.451768i
$613$		−	2.23929e23i		−	0.453625i	−0.973938	−	0.226813i	$-0.927169\pi$
$613$		−	2.23929e23i		−	0.453625i	0.973938	−	0.226813i	$-0.0728305\pi$
$614$	1.08623e23	−	2.35044e23i	0.217016	−	0.469590i
$615$	1.53005e23			0.301486
$616$	8.03891e23	−	2.24291e23i	1.56229	−	0.435888i
$617$	9.37688e23			1.79736			0.898679	−	0.438608i	$-0.144528\pi$
$617$	9.37688e23			1.79736			0.898679	+	0.438608i	$0.144528\pi$
$618$	5.22798e22	−	1.13126e23i	0.0988398	−	0.213874i
$619$		−	8.46873e23i		−	1.57924i	−0.613597	−	0.789619i	$-0.710278\pi$
$619$		−	8.46873e23i		−	1.57924i	0.613597	−	0.789619i	$-0.289722\pi$
$620$	−3.55883e23	+	3.02804e23i	−0.654602	+	0.556971i
$621$			2.77878e22i			0.0504168i
$622$	5.10048e23	+	2.35714e23i	0.912837	+	0.421858i
$623$	−1.15928e24			−2.04663
$624$	1.07454e21	−	6.62407e21i	0.00187134	−	0.0115360i
$625$	−2.32610e23			−0.399622
$626$	−2.31179e23	−	1.06837e23i	−0.391801	−	0.181067i
$627$			3.78600e23i			0.633003i
$628$	3.25569e23	−	2.77012e23i	0.537014	−	0.456921i
$629$			3.81368e23i			0.620603i
$630$	1.86795e23	−	4.04196e23i	0.299896	−	0.648929i
$631$	5.75474e23			0.911541			0.455771	−	0.890097i	$-0.349364\pi$
$631$	5.75474e23			0.911541			0.455771	+	0.890097i	$0.349364\pi$
$632$	4.13316e22	+	1.48139e23i	0.0645932	+	0.231512i
$633$	−3.11853e23			−0.480860
$634$	3.12331e23	−	6.75837e23i	0.475178	−	1.02821i
$635$			7.47750e23i			1.12248i
$636$	−2.82122e23	−	3.31575e23i	−0.417880	−	0.491130i
$637$		−	4.17392e21i		−	0.00610041i
$638$	1.29997e24	+	6.00768e23i	1.87481	+	0.866425i
$639$	−1.13780e24			−1.61923
$640$	−6.01060e22	−	5.37947e23i	−0.0844089	−	0.755457i
$641$	4.70111e23			0.651489			0.325745	−	0.945458i	$-0.394385\pi$
$641$	4.70111e23			0.651489			0.325745	+	0.945458i	$0.394385\pi$
$642$	−2.24418e23	−	1.03713e23i	−0.306910	−	0.141835i
$643$		−	1.44971e23i		−	0.195653i	−0.995203	−	0.0978266i	$-0.968811\pi$
$643$		−	1.44971e23i		−	0.195653i	0.995203	−	0.0978266i	$-0.0311891\pi$
$644$	3.85599e22	+	4.53190e22i	0.0513578	+	0.0603602i
$645$		−	1.11825e23i		−	0.146987i
$646$	2.54479e23	−	5.50655e23i	0.330123	−	0.714336i
$647$	1.43169e23			0.183300			0.0916502	−	0.995791i	$-0.470786\pi$
$647$	1.43169e23			0.183300			0.0916502	+	0.995791i	$0.470786\pi$
$648$	1.27655e23	+	4.57535e23i	0.161306	+	0.578146i
$649$	−1.12959e24			−1.40877
$650$	4.49749e21	−	9.73188e21i	0.00553613	−	0.0119794i
$651$			3.80358e23i			0.462119i
$652$	−7.79109e23	+	6.62909e23i	−0.934316	+	0.794967i
$653$		−	3.23785e23i		−	0.383260i	−0.981467	−	0.191630i	$-0.938623\pi$
$653$		−	3.23785e23i		−	0.383260i	0.981467	−	0.191630i	$-0.0613774\pi$
$654$	1.47278e23	+	6.80629e22i	0.172079	+	0.0795243i
$655$	−2.48001e23			−0.286024
$656$	−1.49209e23	+	9.19813e23i	−0.169869	+	1.04717i
$657$	1.39804e24			1.57113
$658$	−2.46043e23	−	1.13706e23i	−0.272955	−	0.126143i
$659$			8.58094e23i			0.939742i	0.882735	+	0.469871i	$0.155700\pi$
$659$			8.58094e23i			0.939742i	−0.882735	+	0.469871i	$0.844300\pi$
$660$	−2.97029e23	+	2.52728e23i	−0.321126	+	0.273231i
$661$			7.30451e23i			0.779612i	0.920897	+	0.389806i	$0.127458\pi$
$661$			7.30451e23i			0.779612i	−0.920897	+	0.389806i	$0.872542\pi$
$662$	1.06810e23	−	2.31121e23i	0.112543	−	0.243527i
$663$	7.74684e21			0.00805860
$664$	1.95772e23	−	5.46216e22i	0.201058	−	0.0560965i
$665$	9.35343e23			0.948390
$666$	3.24441e23	−	7.02041e23i	0.324792	−	0.702800i
$667$			1.02102e23i			0.100917i
$668$	−7.25378e23	−	8.52528e23i	−0.707887	−	0.831972i
$669$		−	3.28700e23i		−	0.316722i
$670$	−8.04485e23	−	3.71784e23i	−0.765389	−	0.353717i
$671$	−2.03098e24			−1.90794
$672$	−3.65208e23	−	2.46499e23i	−0.338768	−	0.228653i
$673$	−1.25481e23			−0.114934			−0.0574671	−	0.998347i	$-0.518302\pi$
$673$	−1.25481e23			−0.114934			−0.0574671	+	0.998347i	$0.518302\pi$
$674$	2.90639e23	+	1.34316e23i	0.262872	+	0.121484i
$675$		−	3.28724e23i		−	0.293596i
$676$	7.34032e23	+	8.62699e23i	0.647393	+	0.760874i
$677$		−	3.68442e22i		−	0.0320897i	−0.999871	−	0.0160448i	$-0.994893\pi$
$677$		−	3.68442e22i		−	0.0320897i	0.999871	−	0.0160448i	$-0.00510745\pi$
$678$	−8.39633e22	+	1.81684e23i	−0.0722166	+	0.156266i
$679$	1.29095e24			1.09652
$680$	6.01888e23	−	1.67930e23i	0.504882	−	0.140865i
$681$	5.17993e23			0.429115
$682$	−8.60144e23	+	1.86122e24i	−0.703727	+	1.52276i
$683$		−	3.46565e23i		−	0.280033i	−0.990149	−	0.140016i	$-0.955285\pi$
$683$		−	3.46565e23i		−	0.280033i	0.990149	−	0.140016i	$-0.0447155\pi$
$684$	−9.36916e23	+	7.97180e23i	−0.747694	+	0.636179i
$685$		−	2.41921e23i		−	0.190679i
$686$	1.02600e24	+	4.74156e23i	0.798717	+	0.369119i
$687$	6.03449e22			0.0463990
$688$	6.72251e23	+	1.09051e23i	0.510540	+	0.0828183i
$689$	−7.18795e22			−0.0539190
$690$	−2.52404e22	−	1.16646e22i	−0.0187016	−	0.00864277i
$691$		−	1.64173e24i		−	1.20154i	−0.799421	−	0.600771i	$-0.794860\pi$
$691$		−	1.64173e24i		−	1.20154i	0.799421	−	0.600771i	$-0.205140\pi$
$692$	−2.07032e23	+	1.76154e23i	−0.149670	+	0.127348i
$693$		−	1.95383e24i		−	1.39526i
$694$	−8.33210e23	+	1.80294e24i	−0.587759	+	1.27182i
$695$	1.66757e24			1.16202
$696$	−2.03181e23	−	7.28233e23i	−0.139864	−	0.501293i
$697$	−1.07572e24			−0.731511
$698$	3.18331e21	−	6.88820e21i	0.00213849	−	0.00462737i
$699$			2.98617e23i			0.198179i
$700$	−4.56157e23	−	5.36116e23i	−0.299075	−	0.351500i
$701$			1.08179e24i			0.700709i	0.936617	+	0.350355i	$0.113939\pi$
$701$			1.08179e24i			0.700709i	−0.936617	+	0.350355i	$0.886061\pi$
$702$	−3.08386e22	−	1.42518e22i	−0.0197347	−	0.00912017i
$703$	1.62458e24			1.02712
$704$	−1.22965e24	−	2.03209e24i	−0.768096	−	1.26933i
$705$	1.26658e23			0.0781670
$706$	−2.74130e23	−	1.26686e23i	−0.167154	−	0.0772484i
$707$		−	1.39840e24i		−	0.842493i
$708$	3.86452e23	+	4.54192e23i	0.230045	+	0.270369i
$709$		−	1.54173e23i		−	0.0906808i	−0.998972	−	0.0453404i	$-0.985563\pi$
$709$		−	1.54173e23i		−	0.0906808i	0.998972	−	0.0453404i	$-0.0144372\pi$
$710$	1.03284e24	−	2.23492e24i	0.600258	−	1.29887i
$711$	3.60045e23			0.206760
$712$	8.86635e23	+	3.17783e24i	0.503112	+	1.80323i
$713$	−1.46184e23			−0.0819669
$714$	2.13381e23	−	4.61725e23i	0.118228	−	0.255828i
$715$			6.43906e22i			0.0352550i
$716$	1.66999e24	−	1.42092e24i	0.903552	−	0.768791i
$717$		−	1.75143e23i		−	0.0936438i
$718$	−2.62469e24	−	1.21297e24i	−1.38682	−	0.640905i
$719$	−1.87407e24			−0.978565			−0.489283	−	0.872125i	$-0.662741\pi$
$719$	−1.87407e24			−0.978565			−0.489283	+	0.872125i	$0.662741\pi$
$720$	−1.25085e24	−	2.02909e23i	−0.645474	−	0.104707i
$721$	−1.35097e24			−0.688964
$722$	−5.44644e23	−	2.51701e23i	−0.274502	−	0.126858i
$723$		−	3.96924e23i		−	0.197711i
$724$	3.01773e24	−	2.56765e24i	1.48560	−	1.26403i
$725$		−	1.20785e24i		−	0.587679i
$726$	−3.91756e23	+	8.47701e23i	−0.188389	+	0.407645i
$727$	3.49121e24			1.65933			0.829667	−	0.558259i	$-0.188531\pi$
$727$	3.49121e24			1.65933			0.829667	+	0.558259i	$0.188531\pi$
$728$	−7.00712e22	+	1.95503e22i	−0.0329172	+	0.00918410i
$729$	5.52055e23			0.256329
$730$	−1.26907e24	+	2.74608e24i	−0.582428	+	1.26029i
$731$			7.86197e23i			0.356643i
$732$	6.94832e23	+	8.16628e23i	0.311556	+	0.366168i
$733$			4.17586e24i			1.85081i	0.378979	+	0.925405i	$0.376275\pi$
$733$			4.17586e24i			1.85081i	−0.378979	+	0.925405i	$0.623725\pi$
$734$	−1.62998e24	−	7.53279e23i	−0.714112	−	0.330019i
$735$	1.28063e23			0.0554600
$736$	9.47378e22	−	1.40361e23i	0.0405566	−	0.0600878i
$737$	−3.88877e24			−1.64566
$738$	1.98024e24	+	9.15147e23i	0.828397	+	0.382835i
$739$			3.77789e24i			1.56233i	0.624327	+	0.781163i	$0.285373\pi$
$739$			3.77789e24i			1.56233i	−0.624327	+	0.781163i	$0.714627\pi$
$740$	1.08447e24	+	1.27456e24i	0.443350	+	0.521064i
$741$		−	3.30007e22i		−	0.0133373i
$742$	−1.97987e24	+	4.28414e24i	−0.791050	+	1.71171i
$743$	−2.48774e24			−0.982651			−0.491326	−	0.870976i	$-0.663487\pi$
$743$	−2.48774e24			−0.982651			−0.491326	+	0.870976i	$0.663487\pi$
$744$	1.04264e24	−	2.90903e23i	0.407160	−	0.113600i
$745$	−1.88529e24			−0.727864
$746$	2.01394e24	−	4.35786e24i	0.768717	−	1.66339i
$747$		−	4.75817e23i		−	0.179562i
$748$	2.08830e24	−	1.77684e24i	0.779164	−	0.662955i
$749$			2.68005e24i			0.988663i
$750$	1.00588e24	+	4.64857e23i	0.366881	+	0.169550i
$751$	1.46920e22			0.00529836			0.00264918	−	0.999996i	$-0.499157\pi$
$751$	1.46920e22			0.00529836			0.00264918	+	0.999996i	$0.499157\pi$
$752$	−1.23515e23	+	7.61421e23i	−0.0440423	+	0.271502i
$753$	−3.50041e23			−0.123413
$754$	−1.13312e23	−	5.23660e22i	−0.0395021	−	0.0182555i
$755$		−	1.82058e24i		−	0.627567i
$756$	−1.69886e24	+	1.44548e24i	−0.579057	+	0.492694i
$757$			4.58159e24i			1.54419i	0.635506	+	0.772096i	$0.280792\pi$
$757$			4.58159e24i			1.54419i	−0.635506	+	0.772096i	$0.719208\pi$
$758$	7.07853e23	−	1.53169e24i	0.235914	−	0.510483i
$759$	−1.22009e23			−0.0402102
$760$	−7.15364e23	−	2.56397e24i	−0.233137	−	0.835599i
$761$	2.36360e24			0.761736			0.380868	−	0.924629i	$-0.375625\pi$
$761$	2.36360e24			0.761736			0.380868	+	0.924629i	$0.375625\pi$
$762$	7.26674e23	−	1.57241e24i	0.231591	−	0.501129i
$763$		−	1.75883e24i		−	0.554325i
$764$	1.03962e23	+	1.22185e23i	0.0324025	+	0.0380823i
$765$		−	1.46287e24i		−	0.450902i
$766$	−3.09522e24	−	1.43042e24i	−0.943510	−	0.436033i
$767$	9.84609e22			0.0296827
$768$	−3.96390e23	+	1.18964e24i	−0.118182	+	0.354687i
$769$	−9.13423e23			−0.269338			−0.134669	−	0.990891i	$-0.542997\pi$
$769$	−9.13423e23			−0.269338			−0.134669	+	0.990891i	$0.542997\pi$
$770$	3.83779e24	+	1.77359e24i	1.11921	+	0.517229i
$771$		−	1.68552e24i		−	0.486151i
$772$	−5.69795e23	−	6.69674e23i	−0.162544	−	0.191036i
$773$		−	1.76234e24i		−	0.497238i	−0.968601	−	0.248619i	$-0.920023\pi$
$773$		−	1.76234e24i		−	0.497238i	0.968601	−	0.248619i	$-0.0799766\pi$
$774$	6.68841e23	−	1.44727e24i	0.186649	−	0.403879i
$775$	1.72933e24			0.477324
$776$	−9.87341e23	−	3.53878e24i	−0.269552	−	0.966114i
$777$	1.36222e24			0.367847
$778$	−4.31418e23	+	9.33524e23i	−0.115232	+	0.249344i
$779$			4.58244e24i			1.21068i
$780$	2.58905e22	−	2.20291e22i	0.00676608	−	0.00575695i
$781$		−	1.08033e25i		−	2.79268i
$782$	1.77456e23	+	8.20094e22i	0.0453767	+	0.0209704i
$783$	−3.82747e24			−0.968136
$784$	−1.24886e23	+	7.69867e23i	−0.0312482	+	0.192632i
$785$	2.16543e24			0.535985
$786$	5.21511e23	+	2.41011e23i	0.127694	+	0.0590126i
$787$		−	3.12907e24i		−	0.757933i	−0.925410	−	0.378966i	$-0.876280\pi$
$787$		−	3.12907e24i		−	0.757933i	0.925410	−	0.378966i	$-0.123720\pi$
$788$	1.35665e24	−	1.15431e24i	0.325083	−	0.276598i
$789$			1.27914e24i			0.303223i
$790$	−3.26832e23	+	7.07216e23i	−0.0766470	+	0.165852i
$791$	2.16971e24			0.503387
$792$	−5.35585e24	+	1.49432e24i	−1.22932	+	0.342988i
$793$	1.77030e23			0.0402000
$794$	1.05198e23	−	2.27632e23i	0.0236337	−	0.0511397i
$795$		−	2.20538e24i		−	0.490188i
$796$	2.49949e24	+	2.93762e24i	0.549655	+	0.646003i
$797$		−	1.77982e24i		−	0.387241i	−0.981077	−	0.193620i	$-0.937977\pi$
$797$		−	1.77982e24i		−	0.387241i	0.981077	−	0.193620i	$-0.0620230\pi$
$798$	−1.96690e24	−	9.08980e23i	−0.423406	−	0.195672i
$799$	−8.90481e23			−0.189661
$800$	−1.12073e24	+	1.66045e24i	−0.236176	+	0.349914i
$801$	7.72360e24			1.61044
$802$	−1.47188e24	−	6.80214e23i	−0.303662	−	0.140334i
$803$			1.32742e25i			2.70973i
$804$	1.33041e24	+	1.56362e24i	0.268726	+	0.315831i
$805$			3.01427e23i			0.0602445i
$806$	7.49745e22	−	1.62234e23i	0.0148274	−	0.0320843i
$807$	−3.39811e23			−0.0664985
$808$	−3.83331e24	+	1.06952e24i	−0.742296	+	0.207105i
$809$	2.82672e23			0.0541653			0.0270826	−	0.999633i	$-0.491378\pi$
$809$	2.82672e23			0.0541653			0.0270826	+	0.999633i	$0.491378\pi$
$810$	−1.00944e24	+	2.18428e24i	−0.191408	+	0.414177i
$811$		−	9.40519e24i		−	1.76478i	−0.470519	−	0.882390i	$-0.655933\pi$
$811$		−	9.40519e24i		−	1.76478i	0.470519	−	0.882390i	$-0.344067\pi$
$812$	−6.24220e24	+	5.31121e24i	−1.15908	+	0.986205i
$813$			1.62357e24i			0.298333i
$814$	6.66580e24	+	3.08053e24i	1.21212	+	0.560167i
$815$	−5.18203e24			−0.932525
$816$	−1.42888e24	−	2.31789e23i	−0.254466	−	0.0412787i
$817$	3.34911e24			0.590258
$818$	4.54329e24	+	2.09963e24i	0.792442	+	0.366219i
$819$			1.70306e23i			0.0293979i
$820$	−3.59514e24	+	3.05894e24i	−0.614183	+	0.522581i
$821$		−	2.44785e24i		−	0.413875i	−0.978354	−	0.206937i	$-0.933650\pi$
$821$		−	2.44785e24i		−	0.413875i	0.978354	−	0.206937i	$-0.0663496\pi$
$822$	−2.35102e23	+	5.08726e23i	−0.0393411	+	0.0851282i
$823$	2.44893e24			0.405581			0.202791	−	0.979222i	$-0.434999\pi$
$823$	2.44893e24			0.405581			0.202791	+	0.979222i	$0.434999\pi$
$824$	1.03324e24	+	3.70330e24i	0.169364	+	0.607026i
$825$	1.44334e24			0.234159
$826$	2.71204e24	−	5.86844e24i	0.435477	−	0.942306i
$827$			3.39629e24i			0.539769i	0.962893	+	0.269885i	$0.0869855\pi$
$827$			3.39629e24i			0.539769i	−0.962893	+	0.269885i	$0.913014\pi$
$828$	−2.56902e23	−	3.01934e23i	−0.0404119	−	0.0474957i
$829$			3.76176e24i			0.585703i	0.956158	+	0.292851i	$0.0946041\pi$
$829$			3.76176e24i			0.585703i	−0.956158	+	0.292851i	$0.905396\pi$
$830$	9.34620e23	+	4.31925e23i	0.144036	+	0.0665647i
$831$	−1.64683e24			−0.251212
$832$	1.07183e23	+	1.77127e23i	0.0161837	+	0.0267447i
$833$	−9.00359e23			−0.134565
$834$	−3.50667e24	−	1.62057e24i	−0.518780	−	0.239749i
$835$		−	5.67036e24i		−	0.830377i
$836$	−7.56912e24	−	8.89591e24i	−1.09722	−	1.28955i
$837$		−	5.47994e24i		−	0.786338i
$838$	−6.17387e23	+	1.33593e24i	−0.0876967	+	0.189762i
$839$	−1.26128e25			−1.77352			−0.886758	−	0.462234i	$-0.847048\pi$
$839$	−1.26128e25			−1.77352			−0.886758	+	0.462234i	$0.847048\pi$
$840$	−5.99834e23	−	2.14990e24i	−0.0834944	−	0.299256i
$841$	−6.80632e24			−0.937877
$842$	−1.23950e24	+	2.68209e24i	−0.169080	+	0.365864i
$843$			2.41464e24i			0.326075i
$844$	7.32758e24	−	6.23471e24i	0.979602	−	0.833499i
$845$			5.73801e24i			0.759415i
$846$	1.63924e24	+	7.57559e23i	0.214781	+	0.0992586i
$847$	1.01234e25			1.31317
$848$	1.32580e25	+	2.15067e24i	1.70260	+	0.276190i
$849$	1.91564e24			0.243556
$850$	−2.09927e24	−	9.70156e23i	−0.264246	−	0.122118i
$851$			5.23545e23i			0.0652458i
$852$	−4.34385e24	+	3.69598e24i	−0.535967	+	0.456030i
$853$			3.35040e24i			0.409289i	0.978836	+	0.204644i	$0.0656038\pi$
$853$			3.35040e24i			0.409289i	−0.978836	+	0.204644i	$0.934396\pi$
$854$	4.87618e24	−	1.05513e25i	0.589777	−	1.27619i
$855$	−6.23164e24			−0.746261
$856$	7.34659e24	−	2.04974e24i	0.871082	−	0.243037i
$857$	7.08522e24			0.831795			0.415897	−	0.909412i	$-0.363468\pi$
$857$	7.08522e24			0.831795			0.415897	+	0.909412i	$0.363468\pi$
$858$	6.25757e22	−	1.35404e23i	0.00727384	−	0.0157395i
$859$			8.34929e24i			0.960966i	0.877004	+	0.480483i	$0.159539\pi$
$859$			8.34929e24i			0.960966i	−0.877004	+	0.480483i	$0.840461\pi$
$860$	2.23565e24	+	2.62753e24i	0.254781	+	0.299441i
$861$			3.84239e24i			0.433585i
$862$	−3.21797e24	−	1.48715e24i	−0.359559	−	0.166166i
$863$	6.81718e24			0.754246			0.377123	−	0.926163i	$-0.376913\pi$
$863$	6.81718e24			0.754246			0.377123	+	0.926163i	$0.376913\pi$
$864$	5.26168e24	+	3.55140e24i	0.576444	+	0.389074i
$865$	−1.37702e24			−0.149383
$866$	−8.55865e24	−	3.95529e24i	−0.919397	−	0.424890i
$867$			1.84347e24i			0.196098i
$868$	−7.60428e24	−	8.93722e24i	−0.801014	−	0.941423i
$869$			3.41859e24i			0.356598i
$870$	1.60667e24	−	3.47660e24i	0.165964	−	0.359121i
$871$	3.38965e23			0.0346738
$872$	−4.82131e24	+	1.34518e24i	−0.488400	+	0.136267i
$873$	−8.60087e24			−0.862822
$874$	3.49351e23	−	7.55942e23i	0.0347068	−	0.0751002i
$875$		−	1.20125e25i		−	1.18185i
$876$	5.33736e24	−	4.54132e24i	0.520046	−	0.442483i
$877$		−	1.56397e25i		−	1.50914i	−0.656217	−	0.754572i	$-0.727844\pi$
$877$		−	1.56397e25i		−	1.50914i	0.656217	−	0.754572i	$-0.272156\pi$
$878$	8.80974e24	+	4.07133e24i	0.841899	+	0.389075i
$879$	6.41533e24			0.607175
$880$	1.92660e24	−	1.18767e25i	0.180588	−	1.11325i
$881$	−1.62905e25			−1.51230			−0.756152	−	0.654396i	$-0.772923\pi$
$881$	−1.62905e25			−1.51230			−0.756152	+	0.654396i	$0.772923\pi$
$882$	1.65743e24	+	7.65962e23i	0.152388	+	0.0704246i
$883$			4.63346e24i			0.421929i	0.977494	+	0.210964i	$0.0676604\pi$
$883$			4.63346e24i			0.421929i	−0.977494	+	0.210964i	$0.932340\pi$
$884$	−1.82027e23	+	1.54878e23i	−0.0164169	+	0.0139684i
$885$			3.02094e24i			0.269851i
$886$	1.02340e24	−	2.21449e24i	0.0905441	−	0.195924i
$887$	−1.40637e24			−0.123239			−0.0616197	−	0.998100i	$-0.519627\pi$
$887$	−1.40637e24			−0.123239			−0.0616197	+	0.998100i	$0.519627\pi$
$888$	−1.04184e24	−	3.73412e24i	−0.0904258	−	0.324099i
$889$	−1.87781e25			−1.61431
$890$	−7.01113e24	+	1.51710e25i	−0.596998	+	1.29181i
$891$			1.05585e25i			0.890519i
$892$	6.57152e24	+	7.72343e24i	0.548990	+	0.645222i
$893$			3.79335e24i			0.313896i
$894$	3.96450e24	+	1.83215e24i	0.324952	+	0.150173i
$895$	1.11075e25			0.901820
$896$	1.35094e25	−	1.50943e24i	1.08647	−	0.121394i
$897$	1.06349e22			0.000847224
$898$	−1.02824e25	−	4.75190e24i	−0.811419	−	0.374989i
$899$		−	2.01352e25i		−	1.57398i
$900$	3.03910e24	+	3.57182e24i	0.235334	+	0.276585i
$901$			1.55052e25i			1.18937i
$902$	−8.68921e24	+	1.88021e25i	−0.660275	+	1.42874i
$903$	2.80823e24			0.211392
$904$	−1.65943e24	−	5.94763e24i	−0.123745	−	0.443519i
$905$	2.00716e25			1.48276
$906$	−1.76926e24	+	3.82842e24i	−0.129480	+	0.280175i
$907$		−	8.93640e24i		−	0.647889i	−0.946076	−	0.323945i	$-0.894991\pi$
$907$		−	8.93640e24i		−	0.647889i	0.946076	−	0.323945i	$-0.105009\pi$
$908$	−1.21712e25	+	1.03559e25i	−0.874188	+	0.743807i
$909$			9.31672e24i			0.662933i
$910$	−3.34521e23	−	1.54595e23i	−0.0235815	−	0.0108980i
$911$	1.71271e25			1.19613			0.598064	−	0.801448i	$-0.295937\pi$
$911$	1.71271e25			1.19613			0.598064	+	0.801448i	$0.295937\pi$
$912$	−9.87395e23	+	6.08687e24i	−0.0683179	+	0.421151i
$913$	4.51783e24			0.309691
$914$	−1.80207e25	−	8.32805e24i	−1.22385	−	0.565589i
$915$			5.43158e24i			0.365466i
$916$	−1.41792e24	+	1.20644e24i	−0.0945233	+	0.0804256i
$917$		−	6.22800e24i		−	0.411348i
$918$	−3.07426e24	+	6.65222e24i	−0.201176	+	0.435315i
$919$	−1.92318e25			−1.24692			−0.623459	−	0.781856i	$-0.714273\pi$
$919$	−1.92318e25			−1.24692			−0.623459	+	0.781856i	$0.714273\pi$
$920$	8.26275e23	−	2.30536e23i	0.0530797	−	0.0148096i
$921$	−3.03854e24			−0.193401
$922$	−1.03060e25	+	2.23006e25i	−0.649946	+	1.40639i
$923$			9.41669e23i			0.0588415i
$924$	−6.34673e24	−	7.45924e24i	−0.392951	−	0.461831i
$925$		−	6.19343e24i		−	0.379950i
$926$	−5.39958e23	−	2.49536e23i	−0.0328221	−	0.0151684i
$927$	9.00073e24			0.542126
$928$	1.93333e25	+	1.30491e25i	1.15384	+	0.778794i
$929$	−1.01792e25			−0.601979			−0.300989	−	0.953627i	$-0.597317\pi$
$929$	−1.01792e25			−0.601979			−0.300989	+	0.953627i	$0.597317\pi$
$930$	4.97759e24	+	2.30034e24i	0.291685	+	0.134799i
$931$			3.83543e24i			0.222711i
$932$	−5.97007e24	−	7.01656e24i	−0.343514	−	0.403728i
$933$		−	6.59366e24i		−	0.375952i
$934$	7.25480e24	−	1.56983e25i	0.409899	−	0.886960i
$935$	1.38897e25			0.777670
$936$	4.66843e23	−	1.30252e23i	0.0259016	−	0.00722670i
$937$	2.57324e25			1.41480			0.707399	−	0.706815i	$-0.249869\pi$
$937$	2.57324e25			1.41480			0.707399	+	0.706815i	$0.249869\pi$
$938$	9.33656e24	−	2.02029e25i	0.508701	−	1.10075i
$939$			2.98857e24i			0.161364i
$940$	−2.97606e24	+	2.53219e24i	−0.159241	+	0.135491i
$941$		−	1.64698e25i		−	0.873327i	−0.899625	−	0.436663i	$-0.856160\pi$
$941$		−	1.64698e25i		−	0.873327i	0.899625	−	0.436663i	$-0.143840\pi$
$942$	−4.55360e24	−	2.10440e24i	−0.239289	−	0.110585i
$943$	−1.47676e24			−0.0769058
$944$	−1.81608e25	−	2.94599e24i	−0.937289	−	0.152044i
$945$	−1.12995e25			−0.577947
$946$	1.37417e25	+	6.35057e24i	0.696570	+	0.321912i
$947$		−	3.53295e25i		−	1.77485i	−0.460949	−	0.887427i	$-0.652491\pi$
$947$		−	3.53295e25i		−	1.77485i	0.460949	−	0.887427i	$-0.347509\pi$
$948$	1.37457e24	−	1.16956e24i	0.0684376	−	0.0582304i
$949$		−	1.15705e24i		−	0.0570936i
$950$	−4.13275e24	+	8.94265e24i	−0.202110	+	0.437336i
$951$	−8.73690e24			−0.423470
$952$	4.21721e24	+	1.51151e25i	0.202587	+	0.726101i
$953$	−4.30929e24			−0.205171			−0.102585	−	0.994724i	$-0.532712\pi$
$953$	−4.30929e24			−0.205171			−0.102585	+	0.994724i	$0.532712\pi$
$954$	1.31907e25	−	2.85427e25i	0.622454	−	1.34690i
$955$			8.12679e23i			0.0380093i
$956$	3.50152e24	+	4.11530e24i	0.162317	+	0.190770i
$957$		−	1.68054e25i		−	0.772142i
$958$	−1.80311e25	−	8.33291e24i	−0.821139	−	0.379481i
$959$	6.07532e24			0.274228
$960$	−5.43455e24	+	3.28854e24i	−0.243141	+	0.147129i
$961$	6.27834e24			0.278417
$962$	−5.81025e23	−	2.68515e23i	−0.0255392	−	0.0118027i
$963$		−	1.78556e25i		−	0.777950i
$964$	7.93547e24	+	9.32646e24i	0.342703	+	0.402775i
$965$		−	4.45415e24i		−	0.190670i
$966$	2.92931e23	−	6.33859e23i	0.0124297	−	0.0268960i
$967$	−2.86774e25			−1.20619			−0.603094	−	0.797670i	$-0.706066\pi$
$967$	−2.86774e25			−1.20619			−0.603094	+	0.797670i	$0.706066\pi$
$968$	−7.74256e24	−	2.77505e25i	−0.322808	−	1.15699i
$969$	−7.11859e24			−0.294200
$970$	7.80747e24	−	1.68942e25i	0.319853	−	0.692114i
$971$			3.16457e25i			1.28514i	0.766225	+	0.642572i	$0.222133\pi$
$971$			3.16457e25i			1.28514i	−0.766225	+	0.642572i	$0.777867\pi$
$972$	1.74029e25	−	1.48074e25i	0.700583	−	0.596094i
$973$			4.18775e25i			1.67117i
$974$	4.14332e25	+	1.91479e25i	1.63907	+	0.757479i
$975$	−1.25809e23			−0.00493370
$976$	−3.26527e25	−	5.29683e24i	−1.26939	−	0.205917i
$977$	3.66143e25			1.41107			0.705533	−	0.708677i	$-0.250708\pi$
$977$	3.66143e25			1.41107			0.705533	+	0.708677i	$0.250708\pi$
$978$	1.08971e25	+	5.03597e24i	0.416323	+	0.192399i
$979$			7.33347e25i			2.77752i
$980$	−3.00907e24	+	2.56028e24i	−0.112982	+	0.0961315i
$981$			1.17180e25i			0.436182i
$982$	2.94448e24	−	6.37142e24i	0.108658	−	0.235119i
$983$	−4.80762e25			−1.75884			−0.879418	−	0.476051i	$-0.842068\pi$
$983$	−4.80762e25			−1.75884			−0.879418	+	0.476051i	$0.842068\pi$
$984$	1.05328e25	−	2.93872e24i	0.382019	−	0.106586i
$985$	9.02337e24			0.324460
$986$	−1.12959e25	+	2.44426e25i	−0.402687	+	0.871353i
$987$			3.18073e24i			0.112417i
$988$	6.59763e23	+	7.75412e23i	0.0231182	+	0.0271706i
$989$			1.07930e24i			0.0374949i
$990$	−2.55689e25	−	1.18164e25i	−0.880671	−	0.406993i
$991$	−2.82526e25			−0.964789			−0.482395	−	0.875954i	$-0.660233\pi$
$991$	−2.82526e25			−0.964789			−0.482395	+	0.875954i	$0.660233\pi$
$992$	−1.86829e25	+	2.76802e25i	−0.632551	+	0.937174i
$993$	−2.98783e24			−0.100297
$994$	5.61251e25	+	2.59376e25i	1.86798	+	0.863268i
$995$			1.95388e25i			0.644765i
$996$	−1.54562e24	−	1.81655e24i	−0.0505707	−	0.0594352i
$997$		−	2.70363e25i		−	0.877078i	−0.898712	−	0.438539i	$-0.855496\pi$
$997$		−	2.70363e25i		−	0.877078i	0.898712	−	0.438539i	$-0.144504\pi$
$998$	1.35871e25	−	2.94005e25i	0.437037	−	0.945682i
$999$	−1.96259e25			−0.625926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.18.b.a.5.14	yes	16
3.2	odd	2		72.18.d.b.37.3		16
4.3	odd	2		32.18.b.a.17.10		16
8.3	odd	2		32.18.b.a.17.7		16
8.5	even	2	inner	8.18.b.a.5.13	✓	16
24.5	odd	2		72.18.d.b.37.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.13	✓	16	8.5	even	2	inner
8.18.b.a.5.14	yes	16	1.1	even	1	trivial
32.18.b.a.17.7		16	8.3	odd	2
32.18.b.a.17.10		16	4.3	odd	2
72.18.d.b.37.3		16	3.2	odd	2
72.18.d.b.37.4		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)

\(f(q)\)	\(=\)	\(q+(328.641 + 151.878i) q^{2} -4248.51i q^{3} +(84938.1 + 99826.8i) q^{4} +663971. i q^{5} +(645256. - 1.39624e6i) q^{6} -1.66742e7 q^{7} +(1.27527e7 + 4.57074e7i) q^{8} +1.11090e8 q^{9} +O(q^{10})\)	\(q+(328.641 + 151.878i) q^{2} -4248.51i q^{3} +(84938.1 + 99826.8i) q^{4} +663971. i q^{5} +(645256. - 1.39624e6i) q^{6} -1.66742e7 q^{7} +(1.27527e7 + 4.57074e7i) q^{8} +1.11090e8 q^{9} +(-1.00843e8 + 2.18208e8i) q^{10} +1.05479e9i q^{11} +(4.24116e8 - 3.60861e8i) q^{12} -9.19407e7i q^{13} +(-5.47982e9 - 2.53244e9i) q^{14} +2.82089e9 q^{15} +(-2.75091e9 + 1.69582e10i) q^{16} -1.98326e10 q^{17} +(3.65088e10 + 1.68722e10i) q^{18} +8.44846e10i q^{19} +(-6.62821e10 + 5.63964e10i) q^{20} +7.08405e10i q^{21} +(-1.60199e11 + 3.46647e11i) q^{22} -2.72263e10 q^{23} +(1.94189e11 - 5.41799e10i) q^{24} +3.22082e11 q^{25} +(1.39638e10 - 3.02155e10i) q^{26} -1.02062e12i q^{27} +(-1.41627e12 - 1.66453e12i) q^{28} -3.75013e12i q^{29} +(9.27061e11 + 4.28431e11i) q^{30} +5.36921e12 q^{31} +(-3.47964e12 + 5.15536e12i) q^{32} +4.48129e12 q^{33} +(-6.51781e12 - 3.01214e12i) q^{34} -1.10712e13i q^{35} +(9.43580e12 + 1.10898e13i) q^{36} -1.92294e13i q^{37} +(-1.28314e13 + 2.77651e13i) q^{38} -3.90612e11 q^{39} +(-3.03484e13 + 8.46739e12i) q^{40} +5.42400e13 q^{41} +(-1.07591e13 + 2.32811e13i) q^{42} -3.96416e13i q^{43} +(-1.05296e14 + 8.95918e13i) q^{44} +7.37607e13i q^{45} +(-8.94769e12 - 4.13508e12i) q^{46} +4.48999e13 q^{47} +(7.20471e13 + 1.16873e13i) q^{48} +4.53979e13 q^{49} +(1.05850e14 + 4.89172e13i) q^{50} +8.42591e13i q^{51} +(9.17815e12 - 7.80927e12i) q^{52} -7.81803e14i q^{53} +(1.55010e14 - 3.35419e14i) q^{54} -7.00349e14 q^{55} +(-2.12640e14 - 7.62134e14i) q^{56} +3.58934e14 q^{57} +(5.69562e14 - 1.23245e15i) q^{58} +1.07092e15i q^{59} +(2.39601e14 + 2.81600e14i) q^{60} +1.92548e15i q^{61} +(1.76454e15 + 8.15466e14i) q^{62} -1.85234e15 q^{63} +(-1.92654e15 + 1.16578e15i) q^{64} +6.10460e13 q^{65} +(1.47274e15 + 6.80609e14i) q^{66} +3.68678e15i q^{67} +(-1.68454e15 - 1.97982e15i) q^{68} +1.15671e14i q^{69} +(1.68147e15 - 3.63844e15i) q^{70} -1.02421e16 q^{71} +(1.41670e15 + 5.07765e15i) q^{72} +1.25847e16 q^{73} +(2.92052e15 - 6.31956e15i) q^{74} -1.36837e15i q^{75} +(-8.43383e15 + 7.17596e15i) q^{76} -1.75877e16i q^{77} +(-1.28371e14 - 5.93253e13i) q^{78} +3.24102e15 q^{79} +(-1.12597e16 - 1.82652e15i) q^{80} +1.00101e16 q^{81} +(1.78255e16 + 8.23787e15i) q^{82} -4.28316e15i q^{83} +(-7.07178e15 + 6.01706e15i) q^{84} -1.31683e16i q^{85} +(6.02070e15 - 1.30279e16i) q^{86} -1.59325e16 q^{87} +(-4.82117e16 + 1.34514e16i) q^{88} +6.95255e16 q^{89} +(-1.12026e16 + 2.42408e16i) q^{90} +1.53304e15i q^{91} +(-2.31255e15 - 2.71792e15i) q^{92} -2.28112e16i q^{93} +(1.47560e16 + 6.81931e15i) q^{94} -5.60953e16 q^{95} +(2.19026e16 + 1.47833e16i) q^{96} -7.74223e16 q^{97} +(1.49196e16 + 6.89495e15i) q^{98} +1.17177e17i 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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