LMFDB - Embedded newform 8.18.b.a.5.2

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			5.2
Root			$-189.013 - 1.56793i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.18.b.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-362.025 + 3.13586i) q^{2} -13867.2i q^{3} +(131052. - 2270.52i) q^{4} +665059. i q^{5} +(43485.7 + 5.02028e6i) q^{6} -7.57536e6 q^{7} +(-4.74371e7 + 1.23295e6i) q^{8} -6.31593e7 q^{9} +O(q^{10})$	\(q+(-362.025 + 3.13586i) q^{2} -13867.2i q^{3} +(131052. - 2270.52i) q^{4} +665059. i q^{5} +(43485.7 + 5.02028e6i) q^{6} -7.57536e6 q^{7} +(-4.74371e7 + 1.23295e6i) q^{8} -6.31593e7 q^{9} +(-2.08553e6 - 2.40768e8i) q^{10} +1.97863e8i q^{11} +(-3.14858e7 - 1.81733e9i) q^{12} +4.74981e9i q^{13} +(2.74247e9 - 2.37553e7i) q^{14} +9.22251e9 q^{15} +(1.71696e10 - 5.95115e8i) q^{16} +3.37447e10 q^{17} +(2.28652e10 - 1.98059e8i) q^{18} -1.00829e11i q^{19} +(1.51003e9 + 8.71575e10i) q^{20} +1.05049e11i q^{21} +(-6.20471e8 - 7.16313e10i) q^{22} +3.16250e11 q^{23} +(1.70976e10 + 6.57820e11i) q^{24} +3.20636e11 q^{25} +(-1.48948e10 - 1.71955e12i) q^{26} -9.14971e11i q^{27} +(-9.92769e11 + 1.72000e10i) q^{28} +3.54291e12i q^{29} +(-3.33878e12 + 2.89205e10i) q^{30} +2.76965e11 q^{31} +(-6.21394e12 + 2.69288e11i) q^{32} +2.74380e12 q^{33} +(-1.22164e13 + 1.05819e11i) q^{34} -5.03806e12i q^{35} +(-8.27717e12 + 1.43405e11i) q^{36} -2.12889e13i q^{37} +(3.16187e11 + 3.65027e13i) q^{38} +6.58666e13 q^{39} +(-8.19983e11 - 3.15485e13i) q^{40} +8.47798e13 q^{41} +(-3.29420e11 - 3.80304e13i) q^{42} +1.38239e14i q^{43} +(4.49252e11 + 2.59304e13i) q^{44} -4.20047e13i q^{45} +(-1.14490e14 + 9.91717e11i) q^{46} +8.21469e13 q^{47} +(-8.25258e12 - 2.38094e14i) q^{48} -1.75244e14 q^{49} +(-1.16078e14 + 1.00547e12i) q^{50} -4.67945e14i q^{51} +(1.07846e13 + 6.22474e14i) q^{52} +3.16386e14i q^{53} +(2.86922e12 + 3.31242e14i) q^{54} -1.31590e14 q^{55} +(3.59353e14 - 9.34003e12i) q^{56} -1.39822e15 q^{57} +(-1.11101e13 - 1.28262e15i) q^{58} -3.29635e14i q^{59} +(1.20863e15 - 2.09399e13i) q^{60} +6.60732e14i q^{61} +(-1.00268e14 + 8.68526e11i) q^{62} +4.78454e14 q^{63} +(2.24876e15 - 1.16975e14i) q^{64} -3.15891e15 q^{65} +(-9.93326e14 + 8.60420e12i) q^{66} +3.64311e15i q^{67} +(4.42232e15 - 7.66181e13i) q^{68} -4.38551e15i q^{69} +(1.57987e13 + 1.82390e15i) q^{70} +9.19058e15 q^{71} +(2.99609e15 - 7.78722e13i) q^{72} -5.44264e15 q^{73} +(6.67591e13 + 7.70712e15i) q^{74} -4.44633e15i q^{75} +(-2.28935e14 - 1.32139e16i) q^{76} -1.49888e15i q^{77} +(-2.38454e16 + 2.06549e14i) q^{78} +1.06400e16 q^{79} +(3.95786e14 + 1.14188e16i) q^{80} -2.08445e16 q^{81} +(-3.06924e16 + 2.65858e14i) q^{82} +9.38898e15i q^{83} +(2.38516e14 + 1.37669e16i) q^{84} +2.24422e16i q^{85} +(-4.33498e14 - 5.00459e16i) q^{86} +4.91303e16 q^{87} +(-2.43955e14 - 9.38604e15i) q^{88} +2.24169e16 q^{89} +(1.31721e14 + 1.52067e16i) q^{90} -3.59815e16i q^{91} +(4.14453e16 - 7.18053e14i) q^{92} -3.84074e15i q^{93} +(-2.97392e16 + 2.57601e14i) q^{94} +6.70573e16 q^{95} +(3.73427e15 + 8.61701e16i) q^{96} -4.00962e16 q^{97} +(6.34429e16 - 5.49543e14i) q^{98} -1.24969e16i 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 $

$2$	−362.025	+	3.13586i	−0.999962	+	0.00866168i
$2$	−362.025	+	3.13586i	−0.999962	+	0.00866168i
$3$		−	13867.2i		−	1.22028i	−0.792295	−	0.610138i	$-0.791114\pi$
$3$		−	13867.2i		−	1.22028i	0.792295	−	0.610138i	$-0.208886\pi$
$4$	131052.	−	2270.52i	0.999850	−	0.0173227i
$5$			665059.i			0.761404i	0.924698	+	0.380702i	$0.124318\pi$
$5$			665059.i			0.761404i	−0.924698	+	0.380702i	$0.875682\pi$
$6$	43485.7	+	5.02028e6i	0.0105697	+	1.22023i
$7$	−7.57536e6			−0.496672			−0.248336	−	0.968674i	$-0.579884\pi$
$7$	−7.57536e6			−0.496672			−0.248336	+	0.968674i	$0.579884\pi$
$8$	−4.74371e7	+	1.23295e6i	−0.999662	+	0.0259824i
$9$	−6.31593e7			−0.489075
$10$	−2.08553e6	−	2.40768e8i	−0.00659504	−	0.761375i
$11$			1.97863e8i			0.278308i	0.990271	+	0.139154i	$0.0444384\pi$
$11$			1.97863e8i			0.278308i	−0.990271	+	0.139154i	$0.955562\pi$
$12$	−3.14858e7	−	1.81733e9i	−0.0211385	−	1.22009i
$13$			4.74981e9i			1.61495i	0.589905	+	0.807473i	$0.299165\pi$
$13$			4.74981e9i			1.61495i	−0.589905	+	0.807473i	$0.700835\pi$
$14$	2.74247e9	−	2.37553e7i	0.496654	−	0.00430202i
$15$	9.22251e9			0.929124
$16$	1.71696e10	−	5.95115e8i	0.999400	−	0.0346402i
$17$	3.37447e10			1.17325			0.586624	−	0.809859i	$-0.300457\pi$
$17$	3.37447e10			1.17325			0.586624	+	0.809859i	$0.300457\pi$
$18$	2.28652e10	−	1.98059e8i	0.489057	−	0.00423622i
$19$		−	1.00829e11i		−	1.36201i	−0.732278	−	0.681005i	$-0.761543\pi$
$19$		−	1.00829e11i		−	1.36201i	0.732278	−	0.681005i	$-0.238457\pi$
$20$	1.51003e9	+	8.71575e10i	0.0131896	+	0.761290i
$21$			1.05049e11i			0.606078i
$22$	−6.20471e8	−	7.16313e10i	−0.00241062	−	0.278298i
$23$	3.16250e11			0.842062			0.421031	−	0.907046i	$-0.361668\pi$
$23$	3.16250e11			0.842062			0.421031	+	0.907046i	$0.361668\pi$
$24$	1.70976e10	+	6.57820e11i	0.0317058	+	1.21986i
$25$	3.20636e11			0.420264
$26$	−1.48948e10	−	1.71955e12i	−0.0139881	−	1.61489i
$27$		−	9.14971e11i		−	0.623469i
$28$	−9.92769e11	+	1.72000e10i	−0.496598	+	0.00860371i
$29$			3.54291e12i			1.31516i	0.753386	+	0.657578i	$0.228419\pi$
$29$			3.54291e12i			1.31516i	−0.753386	+	0.657578i	$0.771581\pi$
$30$	−3.33878e12	+	2.89205e10i	−0.929089	+	0.00804777i
$31$	2.76965e11			0.0583245			0.0291623	−	0.999575i	$-0.490716\pi$
$31$	2.76965e11			0.0583245			0.0291623	+	0.999575i	$0.490716\pi$
$32$	−6.21394e12	+	2.69288e11i	−0.999062	+	0.0432954i
$33$	2.74380e12			0.339613
$34$	−1.22164e13	+	1.05819e11i	−1.17320	+	0.0101623i
$35$		−	5.03806e12i		−	0.378168i
$36$	−8.27717e12	+	1.43405e11i	−0.489002	+	0.00847212i
$37$		−	2.12889e13i		−	0.996412i	−0.867059	−	0.498206i	$-0.833992\pi$
$37$		−	2.12889e13i		−	0.996412i	0.867059	−	0.498206i	$-0.166008\pi$
$38$	3.16187e11	+	3.65027e13i	0.0117973	+	1.36196i
$39$	6.58666e13			1.97068
$40$	−8.19983e11	−	3.15485e13i	−0.0197831	−	0.761147i
$41$	8.47798e13			1.65817			0.829086	−	0.559121i	$-0.188861\pi$
$41$	8.47798e13			1.65817			0.829086	+	0.559121i	$0.188861\pi$
$42$	−3.29420e11	−	3.80304e13i	−0.00524965	−	0.606055i
$43$			1.38239e14i			1.80363i	0.432122	+	0.901815i	$0.357765\pi$
$43$			1.38239e14i			1.80363i	−0.432122	+	0.901815i	$0.642235\pi$
$44$	4.49252e11	+	2.59304e13i	0.00482106	+	0.278267i
$45$		−	4.20047e13i		−	0.372384i
$46$	−1.14490e14	+	9.91717e11i	−0.842030	+	0.00729367i
$47$	8.21469e13			0.503221			0.251611	−	0.967829i	$-0.419040\pi$
$47$	8.21469e13			0.503221			0.251611	+	0.967829i	$0.419040\pi$
$48$	−8.25258e12	−	2.38094e14i	−0.0422707	−	1.21954i
$49$	−1.75244e14			−0.753317
$50$	−1.16078e14	+	1.00547e12i	−0.420248	+	0.00364019i
$51$		−	4.67945e14i		−	1.43169i
$52$	1.07846e13	+	6.22474e14i	0.0279752	+	1.61470i
$53$			3.16386e14i			0.698028i	0.937118	+	0.349014i	$0.113483\pi$
$53$			3.16386e14i			0.698028i	−0.937118	+	0.349014i	$0.886517\pi$
$54$	2.86922e12	+	3.31242e14i	0.00540029	+	0.623446i
$55$	−1.31590e14			−0.211905
$56$	3.59353e14	−	9.34003e12i	0.496505	−	0.0129048i
$57$	−1.39822e15			−1.66203
$58$	−1.11101e13	−	1.28262e15i	−0.0113915	−	1.31511i
$59$		−	3.29635e14i		−	0.292275i	−0.989264	−	0.146138i	$-0.953316\pi$
$59$		−	3.29635e14i		−	0.292275i	0.989264	−	0.146138i	$-0.0466842\pi$
$60$	1.20863e15	−	2.09399e13i	0.928984	−	0.0160949i
$61$			6.60732e14i			0.441288i	0.975354	+	0.220644i	$0.0708159\pi$
$61$			6.60732e14i			0.441288i	−0.975354	+	0.220644i	$0.929184\pi$
$62$	−1.00268e14	+	8.68526e11i	−0.0583223	+	0.000505189i
$63$	4.78454e14			0.242910
$64$	2.24876e15	−	1.16975e14i	0.998650	−	0.0519474i
$65$	−3.15891e15			−1.22963
$66$	−9.93326e14	+	8.60420e12i	−0.339600	+	0.00294162i
$67$			3.64311e15i			1.09607i	0.836457	+	0.548033i	$0.184623\pi$
$67$			3.64311e15i			1.09607i	−0.836457	+	0.548033i	$0.815377\pi$
$68$	4.42232e15	−	7.66181e13i	1.17307	−	0.0203238i
$69$		−	4.38551e15i		−	1.02755i
$70$	1.57987e13	+	1.82390e15i	0.00327557	+	0.378154i
$71$	9.19058e15			1.68907			0.844534	−	0.535502i	$-0.179878\pi$
$71$	9.19058e15			1.68907			0.844534	+	0.535502i	$0.179878\pi$
$72$	2.99609e15	−	7.78722e13i	0.488910	−	0.0127074i
$73$	−5.44264e15			−0.789888			−0.394944	−	0.918705i	$-0.629236\pi$
$73$	−5.44264e15			−0.789888			−0.394944	+	0.918705i	$0.629236\pi$
$74$	6.67591e13	+	7.70712e15i	0.00863060	+	0.996374i
$75$		−	4.44633e15i		−	0.512838i
$76$	−2.28935e14	−	1.32139e16i	−0.0235937	−	1.36181i
$77$		−	1.49888e15i		−	0.138228i
$78$	−2.38454e16	+	2.06549e14i	−1.97061	+	0.0170694i
$79$	1.06400e16			0.789059			0.394529	−	0.918883i	$-0.370908\pi$
$79$	1.06400e16			0.789059			0.394529	+	0.918883i	$0.370908\pi$
$80$	3.95786e14	+	1.14188e16i	0.0263752	+	0.760947i
$81$	−2.08445e16			−1.24988
$82$	−3.06924e16	+	2.65858e14i	−1.65811	+	0.0143626i
$83$			9.38898e15i			0.457567i	0.973477	+	0.228783i	$0.0734748\pi$
$83$			9.38898e15i			0.457567i	−0.973477	+	0.228783i	$0.926525\pi$
$84$	2.38516e14	+	1.37669e16i	0.0104989	+	0.605987i
$85$			2.24422e16i			0.893316i
$86$	−4.33498e14	−	5.00459e16i	−0.0156225	−	1.80356i
$87$	4.91303e16			1.60485
$88$	−2.43955e14	−	9.38604e15i	−0.00723113	−	0.278214i
$89$	2.24169e16			0.603616			0.301808	−	0.953369i	$-0.402410\pi$
$89$	2.24169e16			0.603616			0.301808	+	0.953369i	$0.402410\pi$
$90$	1.31721e14	+	1.52067e16i	0.00322547	+	0.372370i
$91$		−	3.59815e16i		−	0.802099i
$92$	4.14453e16	−	7.18053e14i	0.841936	−	0.0145868i
$93$		−	3.84074e15i		−	0.0711721i
$94$	−2.97392e16	+	2.57601e14i	−0.503203	+	0.00435874i
$95$	6.70573e16			1.03704
$96$	3.73427e15	+	8.61701e16i	0.0528324	+	1.21913i
$97$	−4.00962e16			−0.519450			−0.259725	−	0.965683i	$-0.583632\pi$
$97$	−4.00962e16			−0.519450			−0.259725	+	0.965683i	$0.583632\pi$
$98$	6.34429e16	−	5.49543e14i	0.753288	−	0.00652499i
$99$		−	1.24969e16i		−	0.136114i
$100$	4.20201e16	−	7.28011e14i	0.420201	−	0.00728011i
$101$		−	3.80297e16i		−	0.349455i	−0.984617	−	0.174728i	$-0.944096\pi$
$101$		−	3.80297e16i		−	0.349455i	0.984617	−	0.174728i	$-0.0559045\pi$
$102$	1.46741e15	+	1.69408e17i	0.0124008	+	1.43163i
$103$	−2.07629e17			−1.61500			−0.807498	−	0.589870i	$-0.799179\pi$
$103$	−2.07629e17			−1.61500			−0.807498	+	0.589870i	$0.799179\pi$
$104$	−5.85627e15	−	2.25317e17i	−0.0419602	−	1.61440i
$105$	−6.98638e16			−0.461470
$106$	−9.92144e14	−	1.14540e17i	−0.00604609	−	0.698001i
$107$			1.68191e17i			0.946325i	0.880975	+	0.473162i	$0.156888\pi$
$107$			1.68191e17i			0.946325i	−0.880975	+	0.473162i	$0.843112\pi$
$108$	−2.07746e15	−	1.19909e17i	−0.0108002	−	0.623376i
$109$			4.08973e15i			0.0196593i	0.999952	+	0.00982967i	$0.00312893\pi$
$109$			4.08973e15i			0.0196593i	−0.999952	+	0.00982967i	$0.996871\pi$
$110$	4.76390e16	−	4.12650e14i	0.211897	−	0.00183545i
$111$	−2.95218e17			−1.21590
$112$	−1.30066e17	+	4.50821e15i	−0.496374	+	0.0172048i
$113$	2.83148e16			0.100195			0.0500976	−	0.998744i	$-0.484047\pi$
$113$	2.83148e16			0.100195			0.0500976	+	0.998744i	$0.484047\pi$
$114$	5.06190e17	−	4.38462e15i	1.66197	−	0.0143960i
$115$			2.10325e17i			0.641149i
$116$	8.04426e15	+	4.64307e17i	0.0227821	+	1.31496i
$117$		−	2.99995e17i		−	0.789830i
$118$	1.03369e15	+	1.19336e17i	0.00253159	+	0.292264i
$119$	−2.55628e17			−0.582720
$120$	−4.37489e17	+	1.13709e16i	−0.928810	+	0.0241409i
$121$	4.66297e17			0.922544
$122$	−2.07197e15	−	2.39202e17i	−0.00382229	−	0.441271i
$123$		−	1.17566e18i		−	2.02343i
$124$	3.62970e16	−	6.28856e14i	0.0583158	−	0.00101034i
$125$			7.20642e17i			1.08139i
$126$	−1.73212e17	+	1.50037e15i	−0.242901	+	0.00210401i
$127$	−1.04849e17			−0.137478			−0.0687388	−	0.997635i	$-0.521898\pi$
$127$	−1.04849e17			−0.137478			−0.0687388	+	0.997635i	$0.521898\pi$
$128$	−8.13741e17	+	4.93997e16i	−0.998162	+	0.0605954i
$129$	1.91698e18			2.20093
$130$	1.14360e18	−	9.90590e15i	1.22958	−	0.0106506i
$131$			7.82237e17i			0.788011i	0.919108	+	0.394005i	$0.128911\pi$
$131$			7.82237e17i			0.788011i	−0.919108	+	0.394005i	$0.871089\pi$
$132$	3.59582e17	−	6.22987e15i	0.339562	−	0.00588302i
$133$			7.63817e17i			0.676473i
$134$	−1.14243e16	−	1.31890e18i	−0.00949377	−	1.09602i
$135$	6.08509e17			0.474712
$136$	−1.60075e18	+	4.16055e16i	−1.17285	+	0.0304839i
$137$	6.27442e17			0.431965			0.215983	−	0.976397i	$-0.430705\pi$
$137$	6.27442e17			0.431965			0.215983	+	0.976397i	$0.430705\pi$
$138$	1.37524e16	+	1.58766e18i	0.00890030	+	1.02751i
$139$		−	2.57262e17i		−	0.156585i	−0.996930	−	0.0782924i	$-0.975053\pi$
$139$		−	2.57262e17i		−	0.156585i	0.996930	−	0.0782924i	$-0.0249468\pi$
$140$	−1.14390e16	−	6.60250e17i	−0.00655090	−	0.378112i
$141$		−	1.13915e18i		−	0.614069i
$142$	−3.32722e18	+	2.88204e16i	−1.68900	+	0.0146302i
$143$	−9.39811e17			−0.449453
$144$	−1.08442e18	+	3.75870e16i	−0.488782	+	0.0169417i
$145$	−2.35625e18			−1.00137
$146$	1.97037e18	−	1.70674e16i	0.789859	−	0.00684176i
$147$			2.43015e18i			0.919255i
$148$	−4.83370e16	−	2.78996e18i	−0.0172606	−	0.996262i
$149$		−	5.12586e18i		−	1.72855i	−0.503016	−	0.864277i	$-0.667776\pi$
$149$		−	5.12586e18i		−	1.72855i	0.503016	−	0.864277i	$-0.332224\pi$
$150$	1.39431e16	+	1.60968e18i	0.00444204	+	0.512819i
$151$	−1.51399e18			−0.455848			−0.227924	−	0.973679i	$-0.573194\pi$
$151$	−1.51399e18			−0.455848			−0.227924	+	0.973679i	$0.573194\pi$
$152$	1.24317e17	+	4.78304e18i	0.0353884	+	1.36155i
$153$	−2.13129e18			−0.573807
$154$	4.70029e15	+	5.42633e17i	0.00119729	+	0.138223i
$155$			1.84198e17i			0.0444085i
$156$	8.63198e18	−	1.49552e17i	1.97039	−	0.0341375i
$157$			6.31795e18i			1.36593i	0.730450	+	0.682966i	$0.239310\pi$
$157$			6.31795e18i			1.36593i	−0.730450	+	0.682966i	$0.760690\pi$
$158$	−3.85193e18	+	3.33654e16i	−0.789029	+	0.00683458i
$159$	4.38739e18			0.851787
$160$	−1.79092e17	−	4.13264e18i	−0.0329653	−	0.760690i
$161$	−2.39571e18			−0.418229
$162$	7.54623e18	−	6.53655e16i	1.24983	−	0.0108261i
$163$		−	7.62696e18i		−	1.19883i	−0.800439	−	0.599414i	$-0.795400\pi$
$163$		−	7.62696e18i		−	1.19883i	0.800439	−	0.599414i	$-0.204600\pi$
$164$	1.11106e19	−	1.92494e17i	1.65792	−	0.0287240i
$165$			1.82479e18i			0.258583i
$166$	−2.94426e16	−	3.39905e18i	−0.00396330	−	0.457550i
$167$	7.60518e18			0.972791			0.486396	−	0.873739i	$-0.338311\pi$
$167$	7.60518e18			0.972791			0.486396	+	0.873739i	$0.338311\pi$
$168$	−1.29520e17	−	4.98323e18i	−0.0157474	−	0.605873i
$169$	−1.39103e19			−1.60805
$170$	−7.03757e16	−	8.12465e18i	−0.00773762	−	0.893282i
$171$			6.36830e18i			0.666126i
$172$	3.13874e17	+	1.81165e19i	0.0312438	+	1.80336i
$173$			9.85927e18i			0.934228i	0.884197	+	0.467114i	$0.154706\pi$
$173$			9.85927e18i			0.934228i	−0.884197	+	0.467114i	$0.845294\pi$
$174$	−1.77864e19	+	1.54066e17i	−1.60479	+	0.0139007i
$175$	−2.42893e18			−0.208734
$176$	1.17751e17	+	3.39722e18i	0.00964067	+	0.278141i
$177$	−4.57112e18			−0.356657
$178$	−8.11549e18	+	7.02964e16i	−0.603593	+	0.00522833i
$179$		−	1.05371e19i		−	0.747257i	−0.927578	−	0.373628i	$-0.878114\pi$
$179$		−	1.05371e19i		−	0.747257i	0.927578	−	0.373628i	$-0.121886\pi$
$180$	−9.53725e16	−	5.50481e18i	−0.00645070	−	0.372328i
$181$		−	2.64819e19i		−	1.70876i	−0.519649	−	0.854380i	$-0.673937\pi$
$181$		−	2.64819e19i		−	1.70876i	0.519649	−	0.854380i	$-0.326063\pi$
$182$	1.12833e17	+	1.30262e19i	0.00694753	+	0.802069i
$183$	9.16251e18			0.538493
$184$	−1.50020e19	+	3.89920e17i	−0.841778	+	0.0218788i
$185$	1.41584e19			0.758672
$186$	1.20440e16	+	1.39044e18i	0.000616470	+	0.0711694i
$187$			6.67682e18i			0.326525i
$188$	1.07655e19	−	1.86516e17i	0.503146	−	0.00871716i
$189$			6.93123e18i			0.309660i
$190$	−2.42764e19	+	2.10283e17i	−1.03700	+	0.00898251i
$191$	2.32908e19			0.951484			0.475742	−	0.879585i	$-0.342180\pi$
$191$	2.32908e19			0.951484			0.475742	+	0.879585i	$0.342180\pi$
$192$	−1.62212e18	−	3.11840e19i	−0.0633901	−	1.21863i
$193$	−2.61228e17			−0.00976748			−0.00488374	−	0.999988i	$-0.501555\pi$
$193$	−2.61228e17			−0.00976748			−0.00488374	+	0.999988i	$0.501555\pi$
$194$	1.45158e19	−	1.25736e17i	0.519431	−	0.00449931i
$195$			4.38052e19i			1.50048i
$196$	−2.29662e19	+	3.97896e17i	−0.753204	+	0.0130495i
$197$		−	6.46253e18i		−	0.202974i	−0.994837	−	0.101487i	$-0.967640\pi$
$197$		−	6.46253e18i		−	0.202974i	0.994837	−	0.101487i	$-0.0323600\pi$
$198$	3.91885e16	+	4.52418e18i	0.00117897	+	0.136109i
$199$	−1.82250e19			−0.525311			−0.262655	−	0.964890i	$-0.584598\pi$
$199$	−1.82250e19			−0.525311			−0.262655	+	0.964890i	$0.584598\pi$
$200$	−1.52100e19	+	3.95328e17i	−0.420122	+	0.0109195i
$201$	5.05198e19			1.33750
$202$	1.19256e17	+	1.37677e19i	0.00302687	+	0.349442i
$203$		−	2.68388e19i		−	0.653202i
$204$	−1.06248e18	−	6.13253e19i	−0.0248007	−	1.43147i
$205$			5.63836e19i			1.26254i
$206$	7.51669e19	−	6.51096e17i	1.61494	−	0.0139886i
$207$	−1.99741e19			−0.411832
$208$	2.82668e18	+	8.15522e19i	0.0559421	+	1.61398i
$209$	1.99503e19			0.379059
$210$	2.52925e19	−	2.19084e17i	0.461453	−	0.00399711i
$211$		−	7.73859e19i		−	1.35600i	−0.735060	−	0.678002i	$-0.762846\pi$
$211$		−	7.73859e19i		−	1.35600i	0.735060	−	0.678002i	$-0.237154\pi$
$212$	7.18362e17	+	4.14631e19i	0.0120917	+	0.697923i
$213$		−	1.27448e20i		−	2.06113i
$214$	−5.27424e17	−	6.08893e19i	−0.00819677	−	0.946289i
$215$	−9.19369e19			−1.37329
$216$	1.12811e18	+	4.34036e19i	0.0161993	+	0.623259i
$217$	−2.09811e18			−0.0289682
$218$	−1.28248e16	−	1.48058e18i	−0.000170283	−	0.0196586i
$219$			7.54743e19i			0.963882i
$220$	−1.72452e19	+	2.98779e17i	−0.211873	+	0.00367077i
$221$			1.60281e20i			1.89473i
$222$	1.06876e20	−	9.25763e17i	1.21585	−	0.0105317i
$223$	−1.34556e20			−1.47337			−0.736685	−	0.676236i	$-0.763610\pi$
$223$	−1.34556e20			−1.47337			−0.736685	+	0.676236i	$0.763610\pi$
$224$	4.70729e19	−	2.03995e18i	0.496207	−	0.0215036i
$225$	−2.02511e19			−0.205541
$226$	−1.02507e19	+	8.87915e16i	−0.100192	+	0.000867860i
$227$		−	7.95558e19i		−	0.748949i	−0.927237	−	0.374474i	$-0.877823\pi$
$227$		−	7.95558e19i		−	0.748949i	0.927237	−	0.374474i	$-0.122177\pi$
$228$	−1.83240e20	+	3.17469e18i	−1.66178	+	0.0287909i
$229$			3.46397e19i			0.302673i	0.988482	+	0.151336i	$0.0483576\pi$
$229$			3.46397e19i			0.302673i	−0.988482	+	0.151336i	$0.951642\pi$
$230$	−6.59550e17	−	7.61429e19i	−0.00555343	−	0.641125i
$231$	−2.07853e19			−0.168676
$232$	−4.36823e18	−	1.68066e20i	−0.0341710	−	1.31471i
$233$	−1.21528e20			−0.916538			−0.458269	−	0.888814i	$-0.651530\pi$
$233$	−1.21528e20			−0.916538			−0.458269	+	0.888814i	$0.651530\pi$
$234$	9.40743e17	+	1.08606e20i	0.00684126	+	0.789801i
$235$			5.46325e19i			0.383155i
$236$	−7.48445e17	−	4.31995e19i	−0.00506300	−	0.292231i
$237$		−	1.47546e20i		−	0.962870i
$238$	9.25438e19	−	8.01616e17i	0.582698	−	0.00504733i
$239$	−2.25849e19			−0.137226			−0.0686129	−	0.997643i	$-0.521857\pi$
$239$	−2.25849e19			−0.137226			−0.0686129	+	0.997643i	$0.521857\pi$
$240$	1.58346e20	−	5.48845e18i	0.928566	−	0.0321851i
$241$	2.85622e20			1.61677			0.808383	−	0.588657i	$-0.200343\pi$
$241$	2.85622e20			1.61677			0.808383	+	0.588657i	$0.200343\pi$
$242$	−1.68811e20	+	1.46225e18i	−0.922510	+	0.00799079i
$243$			1.70895e20i			0.901731i
$244$	1.50021e18	+	8.65905e19i	0.00764430	+	0.441222i
$245$		−	1.16548e20i		−	0.573578i
$246$	3.68671e18	+	4.25618e20i	0.0175263	+	2.02335i
$247$	4.78920e20			2.19957
$248$	−1.31384e19	+	3.41484e17i	−0.0583048	+	0.00151541i
$249$	1.30199e20			0.558358
$250$	−2.25983e18	−	2.60890e20i	−0.00936670	−	1.08135i
$251$		−	1.47186e20i		−	0.589713i	−0.955541	−	0.294857i	$-0.904728\pi$
$251$		−	1.47186e20i		−	0.589713i	0.955541	−	0.294857i	$-0.0952719\pi$
$252$	6.27026e19	−	1.08634e18i	0.242874	−	0.00420787i
$253$			6.25741e19i			0.234353i
$254$	3.79579e19	−	3.28792e17i	0.137472	−	0.00119079i
$255$	3.11211e20			1.09009
$256$	2.94440e20	−	2.04357e19i	0.997600	−	0.0692389i
$257$	−3.49632e20			−1.14599			−0.572993	−	0.819560i	$-0.694218\pi$
$257$	−3.49632e20			−1.14599			−0.572993	+	0.819560i	$0.694218\pi$
$258$	−6.93996e20	+	6.01140e18i	−2.20085	+	0.0190637i
$259$			1.61271e20i			0.494890i
$260$	−4.13982e20	+	7.17237e18i	−1.22944	+	0.0213005i
$261$		−	2.23768e20i		−	0.643211i
$262$	−2.45299e18	−	2.83189e20i	−0.00682550	−	0.787981i
$263$	−2.56287e20			−0.690402			−0.345201	−	0.938529i	$-0.612189\pi$
$263$	−2.56287e20			−0.690402			−0.345201	+	0.938529i	$0.612189\pi$
$264$	−1.30158e20	+	3.38297e18i	−0.339499	+	0.00882398i
$265$	−2.10415e20			−0.531481
$266$	−2.39523e18	−	2.76521e20i	−0.00585939	−	0.676448i
$267$		−	3.10860e20i		−	0.736579i
$268$	8.27177e18	+	4.77438e20i	0.0189868	+	1.09590i
$269$			6.85596e20i			1.52466i	0.647187	+	0.762331i	$0.275945\pi$
$269$			6.85596e20i			1.52466i	−0.647187	+	0.762331i	$0.724055\pi$
$270$	−2.20296e20	+	1.90820e18i	−0.474694	+	0.00411180i
$271$	5.06814e20			1.05830			0.529151	−	0.848528i	$-0.322511\pi$
$271$	5.06814e20			1.05830			0.529151	+	0.848528i	$0.322511\pi$
$272$	5.79382e20	−	2.00820e19i	1.17254	−	0.0406416i
$273$	−4.98964e20			−0.978783
$274$	−2.27150e20	+	1.96757e18i	−0.431949	+	0.00374154i
$275$			6.34419e19i			0.116963i
$276$	−9.95739e18	−	5.74731e20i	−0.0177999	−	1.02739i
$277$			5.87639e20i			1.01867i	0.860569	+	0.509334i	$0.170108\pi$
$277$			5.87639e20i			1.01867i	−0.860569	+	0.509334i	$0.829892\pi$
$278$	8.06738e17	+	9.31352e19i	0.00135629	+	0.156579i
$279$	−1.74929e19			−0.0285251
$280$	6.21167e18	+	2.38991e20i	0.00982574	+	0.378041i
$281$	−5.24336e20			−0.804647			−0.402324	−	0.915498i	$-0.631797\pi$
$281$	−5.24336e20			−0.804647			−0.402324	+	0.915498i	$0.631797\pi$
$282$	3.57221e18	+	4.12400e20i	0.00531887	+	0.614046i
$283$		−	7.51546e20i		−	1.08585i	−0.839780	−	0.542927i	$-0.817316\pi$
$283$		−	7.51546e20i		−	1.08585i	0.839780	−	0.542927i	$-0.182684\pi$
$284$	1.20445e21	−	2.08674e19i	1.68881	−	0.0292592i
$285$		−	9.29898e20i		−	1.26548i
$286$	3.40235e20	−	2.94712e18i	0.449436	−	0.00389302i
$287$	−6.42237e20			−0.823568
$288$	3.92468e20	−	1.70080e19i	0.488617	−	0.0211747i
$289$	3.11465e20			0.376511
$290$	8.53020e20	−	7.38887e18i	1.00133	−	0.00867351i
$291$			5.56023e20i			0.633873i
$292$	−7.13271e20	+	1.23576e19i	−0.789770	+	0.0136830i
$293$		−	7.51033e20i		−	0.807764i	−0.914811	−	0.403882i	$-0.867661\pi$
$293$		−	7.51033e20i		−	0.807764i	0.914811	−	0.403882i	$-0.132339\pi$
$294$	−7.62062e18	−	8.79776e20i	−0.00796229	−	0.919220i
$295$	2.19227e20			0.222539
$296$	2.62481e19	+	1.00988e21i	0.0258892	+	0.996075i
$297$	1.81039e20			0.173517
$298$	1.60740e19	+	1.85569e21i	0.0149722	+	1.72849i
$299$			1.50213e21i			1.35988i
$300$	−1.00955e19	−	5.82701e20i	−0.00888375	−	0.512762i
$301$		−	1.04721e21i		−	0.895813i
$302$	5.48104e20	−	4.74768e18i	0.455831	−	0.00394841i
$303$	−5.27366e20			−0.426432
$304$	−6.00049e19	−	1.73119e21i	−0.0471804	−	1.36119i
$305$	−4.39426e20			−0.335998
$306$	7.71581e20	−	6.68344e18i	0.573785	−	0.00497013i
$307$		−	5.89249e19i		−	0.0426209i	−0.999773	−	0.0213105i	$-0.993216\pi$
$307$		−	5.89249e19i		−	0.0426209i	0.999773	−	0.0213105i	$-0.00678384\pi$
$308$	−3.40325e18	−	1.96432e20i	−0.00239449	−	0.138207i
$309$			2.87923e21i			1.97074i
$310$	−5.77621e17	−	6.66844e19i	−0.000384653	−	0.0444069i
$311$	−9.05717e20			−0.586853			−0.293427	−	0.955982i	$-0.594796\pi$
$311$	−9.05717e20			−0.586853			−0.293427	+	0.955982i	$0.594796\pi$
$312$	−3.12452e21	+	8.12102e19i	−1.97002	+	0.0512031i
$313$	2.51738e21			1.54462			0.772311	−	0.635245i	$-0.219101\pi$
$313$	2.51738e21			1.54462			0.772311	+	0.635245i	$0.219101\pi$
$314$	−1.98122e19	−	2.28726e21i	−0.0118313	−	1.36588i
$315$			3.18200e20i			0.184953i
$316$	1.39439e21	−	2.41583e19i	0.788940	−	0.0136686i
$317$		−	1.88675e21i		−	1.03923i	−0.854401	−	0.519614i	$-0.826076\pi$
$317$		−	1.88675e21i		−	1.03923i	0.854401	−	0.519614i	$-0.173924\pi$
$318$	−1.58835e21	+	1.37583e19i	−0.851755	+	0.00737791i
$319$	−7.01010e20			−0.366019
$320$	7.77953e19	+	1.49556e21i	0.0395529	+	0.760376i
$321$	2.33234e21			1.15478
$322$	8.67307e20	−	7.51262e18i	0.418213	−	0.00362257i
$323$		−	3.40245e21i		−	1.59798i
$324$	−2.73172e21	+	4.73279e19i	−1.24969	+	0.0216513i
$325$			1.52296e21i			0.678704i
$326$	2.39171e19	+	2.76115e21i	0.0103839	+	1.19878i
$327$	5.67131e19			0.0239898
$328$	−4.02171e21	+	1.04529e20i	−1.65761	+	0.0430834i
$329$	−6.22292e20			−0.249936
$330$	−5.72230e18	−	6.60620e20i	−0.00223976	−	0.258573i
$331$		−	1.03084e21i		−	0.393236i	−0.980480	−	0.196618i	$-0.937004\pi$
$331$		−	1.03084e21i		−	0.393236i	0.980480	−	0.196618i	$-0.0629959\pi$
$332$	2.13179e19	+	1.23045e21i	0.00792630	+	0.457498i
$333$			1.34459e21i			0.487321i
$334$	−2.75327e21	+	2.38488e19i	−0.972755	+	0.00842601i
$335$	−2.42288e21			−0.834549
$336$	6.25163e19	+	1.80365e21i	0.0209947	+	0.605714i
$337$	2.14822e21			0.703435			0.351717	−	0.936106i	$-0.385598\pi$
$337$	2.14822e21			0.703435			0.351717	+	0.936106i	$0.385598\pi$
$338$	5.03588e21	−	4.36208e19i	1.60799	−	0.0139284i
$339$		−	3.92648e20i		−	0.122266i
$340$	5.09556e19	+	2.94110e21i	0.0154747	+	0.893181i
$341$			5.48012e19i			0.0162322i
$342$	−1.99701e19	−	2.30548e21i	−0.00576977	−	0.666101i
$343$	3.08980e21			0.870824
$344$	−1.70441e20	−	6.55764e21i	−0.0468627	−	1.80302i
$345$	2.91662e21			0.782380
$346$	−3.09173e19	−	3.56930e21i	−0.00809199	−	0.934193i
$347$			4.67482e21i			1.19389i	0.802282	+	0.596945i	$0.203619\pi$
$347$			4.67482e21i			1.19389i	−0.802282	+	0.596945i	$0.796381\pi$
$348$	6.43864e21	−	1.11551e20i	1.60461	−	0.0278004i
$349$		−	4.72313e21i		−	1.14872i	−0.818603	−	0.574360i	$-0.805251\pi$
$349$		−	4.72313e21i		−	1.14872i	0.818603	−	0.574360i	$-0.194749\pi$
$350$	8.79335e20	−	7.61680e18i	0.208726	−	0.00180798i
$351$	4.34594e21			1.00687
$352$	−5.32820e19	−	1.22951e21i	−0.0120495	−	0.278047i
$353$	−4.29922e21			−0.949084			−0.474542	−	0.880233i	$-0.657386\pi$
$353$	−4.29922e21			−0.949084			−0.474542	+	0.880233i	$0.657386\pi$
$354$	1.65486e21	−	1.43344e19i	0.356643	−	0.00308925i
$355$			6.11228e21i			1.28606i
$356$	2.93779e21	−	5.08981e19i	0.603525	−	0.0104563i
$357$			3.54485e21i			0.711079i
$358$	3.30429e19	+	3.81469e21i	0.00647250	+	0.747229i
$359$	−5.26993e21			−1.00810			−0.504048	−	0.863675i	$-0.668157\pi$
$359$	−5.26993e21			−1.00810			−0.504048	+	0.863675i	$0.668157\pi$
$360$	5.17896e19	+	1.99258e21i	0.00967545	+	0.372258i
$361$	−4.68613e21			−0.855073
$362$	8.30436e19	+	9.58710e21i	0.0148007	+	1.70870i
$363$		−	6.46624e21i		−	1.12576i
$364$	−8.16969e19	−	4.71546e21i	−0.0138945	−	0.801979i
$365$		−	3.61968e21i		−	0.601424i
$366$	−3.31706e21	+	2.87324e19i	−0.538473	+	0.00466426i
$367$	−7.39416e21			−1.17281			−0.586405	−	0.810018i	$-0.699457\pi$
$367$	−7.39416e21			−1.17281			−0.586405	+	0.810018i	$0.699457\pi$
$368$	5.42987e21	−	1.88205e20i	0.841557	−	0.0291692i
$369$	−5.35463e21			−0.810971
$370$	−5.12569e21	+	4.43988e19i	−0.758643	+	0.00657137i
$371$		−	2.39674e21i		−	0.346691i
$372$	−8.72048e18	−	5.03338e20i	−0.00123289	−	0.0711614i
$373$		−	3.45714e21i		−	0.477740i	−0.971052	−	0.238870i	$-0.923223\pi$
$373$		−	3.45714e21i		−	0.477740i	0.971052	−	0.238870i	$-0.0767769\pi$
$374$	−2.09376e19	−	2.41718e21i	−0.00282825	−	0.326512i
$375$	9.99329e21			1.31960
$376$	−3.89681e21	+	1.01283e20i	−0.503052	+	0.0130749i
$377$	−1.68282e22			−2.12391
$378$	−2.17354e19	−	2.50928e21i	−0.00268218	−	0.309648i
$379$			3.17249e21i			0.382795i	0.981513	+	0.191398i	$0.0613020\pi$
$379$			3.17249e21i			0.382795i	−0.981513	+	0.191398i	$0.938698\pi$
$380$	8.78802e21	−	1.52255e20i	1.03688	−	0.0179644i
$381$			1.45396e21i			0.167761i
$382$	−8.43187e21	+	7.30369e19i	−0.951448	+	0.00824145i
$383$	3.27971e21			0.361947			0.180974	−	0.983488i	$-0.442075\pi$
$383$	3.27971e21			0.361947			0.180974	+	0.983488i	$0.442075\pi$
$384$	6.85036e20	+	1.12843e22i	0.0739432	+	1.21803i
$385$	9.96845e20			0.105247
$386$	9.45711e19	−	8.19175e17i	0.00976711	−	8.46028e-5i
$387$		−	8.73105e21i		−	0.882112i
$388$	−5.25471e21	+	9.10394e19i	−0.519372	+	0.00899829i
$389$			1.09936e22i			1.06308i	0.847032	+	0.531542i	$0.178387\pi$
$389$			1.09936e22i			1.06308i	−0.847032	+	0.531542i	$0.821613\pi$
$390$	−1.37367e20	−	1.58586e22i	−0.0129967	−	1.50043i
$391$	1.06718e22			0.987947
$392$	8.31309e21	−	2.16067e20i	0.753062	−	0.0195730i
$393$	1.08474e22			0.961591
$394$	2.02656e19	+	2.33960e21i	0.00175809	+	0.202966i
$395$			7.07620e21i			0.600792i
$396$	−2.83744e19	−	1.63774e21i	−0.00235786	−	0.136093i
$397$			9.01100e21i			0.732915i	0.930435	+	0.366458i	$0.119430\pi$
$397$			9.01100e21i			0.732915i	−0.930435	+	0.366458i	$0.880570\pi$
$398$	6.59791e21	−	5.71511e19i	0.525291	−	0.00455008i
$399$	1.05920e22			0.825484
$400$	5.50518e21	−	1.90815e20i	0.420012	−	0.0145580i
$401$	1.05004e22			0.784296			0.392148	−	0.919902i	$-0.371732\pi$
$401$	1.05004e22			0.784296			0.392148	+	0.919902i	$0.371732\pi$
$402$	−1.82894e22	+	1.58423e20i	−1.33745	+	0.0115850i
$403$			1.31553e21i			0.0941910i
$404$	−8.63473e19	−	4.98388e21i	−0.00605351	−	0.349403i
$405$		−	1.38628e22i		−	0.951664i
$406$	8.41629e19	+	9.71633e21i	0.00565783	+	0.653177i
$407$	4.21228e21			0.277310
$408$	5.76952e20	+	2.21979e22i	0.0371987	+	1.43120i
$409$	5.86541e21			0.370382			0.185191	−	0.982703i	$-0.440710\pi$
$409$	5.86541e21			0.370382			0.185191	+	0.982703i	$0.440710\pi$
$410$	−1.76811e20	−	2.04123e22i	−0.0109357	−	1.26249i
$411$		−	8.70087e21i		−	0.527117i
$412$	−2.72103e22	+	4.71426e20i	−1.61475	+	0.0279761i
$413$			2.49711e21i			0.145165i
$414$	7.23114e21	−	6.26362e19i	0.411816	−	0.00356716i
$415$	−6.24423e21			−0.348393
$416$	−1.27907e21	−	2.95151e22i	−0.0699198	−	1.61343i
$417$	−3.56750e21			−0.191077
$418$	−7.22252e21	+	6.25615e19i	−0.379045	+	0.00328329i
$419$			5.02281e21i			0.258302i	0.991625	+	0.129151i	$0.0412252\pi$
$419$			5.02281e21i			0.258302i	−0.991625	+	0.129151i	$0.958775\pi$
$420$	−9.15582e21	+	1.58627e20i	−0.461401	+	0.00799391i
$421$		−	1.55885e22i		−	0.769848i	−0.922948	−	0.384924i	$-0.874228\pi$
$421$		−	1.55885e22i		−	0.769848i	0.922948	−	0.384924i	$-0.125772\pi$
$422$	2.42672e20	+	2.80156e22i	0.0117453	+	1.35595i
$423$	−5.18834e21			−0.246113
$424$	−3.90088e20	−	1.50084e22i	−0.0181365	−	0.697792i
$425$	1.08198e22			0.493074
$426$	3.99659e20	+	4.61393e22i	0.0178529	+	2.06105i
$427$		−	5.00528e21i		−	0.219175i
$428$	3.81881e20	+	2.20418e22i	0.0163929	+	0.946183i
$429$			1.30326e22i			0.548457i
$430$	3.32834e22	−	2.88301e20i	1.37324	−	0.0118950i
$431$	−2.78561e22			−1.12684			−0.563421	−	0.826170i	$-0.690515\pi$
$431$	−2.78561e22			−1.12684			−0.563421	+	0.826170i	$0.690515\pi$
$432$	−5.44512e20	−	1.57096e22i	−0.0215971	−	0.623095i
$433$	−1.24470e21			−0.0484079			−0.0242040	−	0.999707i	$-0.507705\pi$
$433$	−1.24470e21			−0.0484079			−0.0242040	+	0.999707i	$0.507705\pi$
$434$	7.59570e20	−	6.57940e18i	0.0289671	−	0.000250913i
$435$			3.26745e22i			1.22194i
$436$	9.28581e18	+	5.35968e20i	0.000340553	+	0.0196564i
$437$		−	3.18872e22i		−	1.14690i
$438$	−2.36677e20	−	2.73236e22i	−0.00834884	−	0.963846i
$439$	−2.09614e22			−0.725224			−0.362612	−	0.931940i	$-0.618115\pi$
$439$	−2.09614e22			−0.725224			−0.362612	+	0.931940i	$0.618115\pi$
$440$	6.24227e21	−	1.62244e20i	0.211834	−	0.00550581i
$441$	1.10683e22			0.368429
$442$	−5.02619e20	−	5.80257e22i	−0.0164116	−	1.89466i
$443$		−	1.11978e22i		−	0.358674i	−0.983788	−	0.179337i	$-0.942605\pi$
$443$		−	1.11978e22i		−	0.358674i	0.983788	−	0.179337i	$-0.0573952\pi$
$444$	−3.86890e22	+	6.70299e20i	−1.21572	+	0.0210627i
$445$			1.49086e22i			0.459596i
$446$	4.87127e22	−	4.21950e20i	1.47332	−	0.0127619i
$447$	−7.10813e22			−2.10931
$448$	−1.70352e22	+	8.86128e20i	−0.496002	+	0.0258008i
$449$	−1.44200e22			−0.411975			−0.205987	−	0.978555i	$-0.566041\pi$
$449$	−1.44200e22			−0.411975			−0.205987	+	0.978555i	$0.566041\pi$
$450$	7.33142e21	−	6.35048e19i	0.205533	−	0.00178033i
$451$			1.67748e22i			0.461483i
$452$	3.71072e21	−	6.42895e19i	0.100180	−	0.00173565i
$453$			2.09949e22i			0.556261i
$454$	2.49476e20	+	2.88012e22i	0.00648716	+	0.748921i
$455$	2.39298e22			0.610721
$456$	6.63275e22	−	1.72393e21i	1.66147	−	0.0431836i
$457$	2.99851e22			0.737254			0.368627	−	0.929577i	$-0.379828\pi$
$457$	2.99851e22			0.737254			0.368627	+	0.929577i	$0.379828\pi$
$458$	−1.08626e20	−	1.25405e22i	−0.00262165	−	0.302661i
$459$		−	3.08754e22i		−	0.731484i
$460$	4.77548e20	+	2.75636e22i	0.0111064	+	0.641053i
$461$			4.32706e22i			0.987950i	0.869476	+	0.493975i	$0.164456\pi$
$461$			4.32706e22i			0.987950i	−0.869476	+	0.493975i	$0.835544\pi$
$462$	7.52480e21	−	6.51799e19i	0.168670	−	0.00146102i
$463$	−1.79925e22			−0.395962			−0.197981	−	0.980206i	$-0.563438\pi$
$463$	−1.79925e22			−0.395962			−0.197981	+	0.980206i	$0.563438\pi$
$464$	2.10844e21	+	6.08302e22i	0.0455573	+	1.31437i
$465$	2.55432e21			0.0541907
$466$	4.39961e22	−	3.81095e20i	0.916504	−	0.00793876i
$467$		−	5.53566e22i		−	1.13234i	−0.824289	−	0.566169i	$-0.808425\pi$
$467$		−	5.53566e22i		−	1.13234i	0.824289	−	0.566169i	$-0.191575\pi$
$468$	−6.81145e20	−	3.93150e22i	−0.0136820	−	0.789712i
$469$		−	2.75979e22i		−	0.544386i
$470$	−1.71320e20	−	1.97783e22i	−0.00331877	−	0.383140i
$471$	8.76123e22			1.66682
$472$	4.06424e20	+	1.56370e22i	0.00759402	+	0.292176i
$473$	−2.73523e22			−0.501965
$474$	4.62686e20	+	5.34155e22i	0.00834008	+	0.962834i
$475$		−	3.23295e22i		−	0.572404i
$476$	−3.35007e22	+	5.80410e20i	−0.582632	+	0.0100943i
$477$		−	1.99827e22i		−	0.341388i
$478$	8.17630e21	−	7.08232e19i	0.137221	−	0.00118861i
$479$	−1.18108e22			−0.194727			−0.0973637	−	0.995249i	$-0.531041\pi$
$479$	−1.18108e22			−0.194727			−0.0973637	+	0.995249i	$0.531041\pi$
$480$	−5.73082e22	+	2.48351e21i	−0.928252	+	0.0402268i
$481$	1.01118e23			1.60915
$482$	−1.03402e23	+	8.95672e20i	−1.61670	+	0.0140039i
$483$			3.32218e22i			0.510355i
$484$	6.11094e22	−	1.05874e21i	0.922406	−	0.0159810i
$485$		−	2.66664e22i		−	0.395511i
$486$	−5.35905e20	−	6.18684e22i	−0.00781051	−	0.901697i
$487$	2.16692e22			0.310347			0.155173	−	0.987887i	$-0.450406\pi$
$487$	2.16692e22			0.310347			0.155173	+	0.987887i	$0.450406\pi$
$488$	−8.14649e20	−	3.13432e22i	−0.0114657	−	0.441139i
$489$	−1.05765e23			−1.46290
$490$	3.65478e20	+	4.21933e22i	0.00496815	+	0.573557i
$491$			1.30265e23i			1.74034i	0.492749	+	0.870172i	$0.335992\pi$
$491$			1.30265e23i			1.74034i	−0.492749	+	0.870172i	$0.664008\pi$
$492$	−2.66936e21	−	1.54073e23i	−0.0350513	−	2.02312i
$493$			1.19555e23i			1.54300i
$494$	−1.73381e23	+	1.50183e21i	−2.19949	+	0.0190520i
$495$	8.31116e21			0.103638
$496$	4.75537e21	−	1.64826e20i	0.0582895	−	0.00202038i
$497$	−6.96220e22			−0.838913
$498$	−4.71353e22	+	4.08286e20i	−0.558337	+	0.00483632i
$499$		−	5.17276e22i		−	0.602376i	−0.953565	−	0.301188i	$-0.902617\pi$
$499$		−	5.17276e22i		−	0.602376i	0.953565	−	0.301188i	$-0.0973832\pi$
$500$	1.63623e21	+	9.44418e22i	0.0187327	+	1.08123i
$501$		−	1.05463e23i		−	1.18707i
$502$	4.61556e20	+	5.32852e22i	0.00510791	+	0.589691i
$503$	1.07219e23			1.16665			0.583327	−	0.812237i	$-0.301751\pi$
$503$	1.07219e23			1.16665			0.583327	+	0.812237i	$0.301751\pi$
$504$	−2.26965e22	+	5.89910e20i	−0.242828	+	0.00631140i
$505$	2.52920e22			0.266076
$506$	−1.96224e20	−	2.26534e22i	−0.00202989	−	0.234344i
$507$			1.92897e23i			1.96227i
$508$	−1.37407e22	+	2.38062e20i	−0.137457	+	0.00238148i
$509$		−	1.48328e23i		−	1.45922i	−0.683861	−	0.729612i	$-0.739701\pi$
$509$		−	1.48328e23i		−	1.45922i	0.683861	−	0.729612i	$-0.260299\pi$
$510$	−1.12666e23	+	9.75915e20i	−1.09005	+	0.00944203i
$511$	4.12300e22			0.392316
$512$	−1.06530e23	+	8.32156e21i	−0.996963	+	0.0778772i
$513$	−9.22557e22			−0.849172
$514$	1.26576e23	−	1.09640e21i	1.14594	−	0.00992617i
$515$		−	1.38086e23i		−	1.22966i
$516$	2.51225e23	−	4.35256e21i	2.20060	−	0.0381261i
$517$			1.62538e22i			0.140051i
$518$	−5.05725e20	−	5.83842e22i	−0.00428658	−	0.494872i
$519$	1.36721e23			1.14002
$520$	1.49849e23	−	3.89477e21i	1.22921	−	0.0319487i
$521$	7.01242e22			0.565910			0.282955	−	0.959133i	$-0.408685\pi$
$521$	7.01242e22			0.565910			0.282955	+	0.959133i	$0.408685\pi$
$522$	7.01705e20	+	8.10096e22i	0.00557129	+	0.643187i
$523$		−	2.14598e23i		−	1.67634i	−0.545410	−	0.838169i	$-0.683626\pi$
$523$		−	2.14598e23i		−	1.67634i	0.545410	−	0.838169i	$-0.316374\pi$
$524$	1.77609e21	+	1.02514e23i	0.0136505	+	0.787893i
$525$			3.36825e22i			0.254713i
$526$	9.27822e22	−	8.03680e20i	0.690376	−	0.00598005i
$527$	9.34612e21			0.0684291
$528$	4.71099e22	−	1.63288e21i	0.339409	−	0.0117643i
$529$	−4.10359e22			−0.290932
$530$	7.61757e22	−	6.59834e20i	0.531461	−	0.00460352i
$531$			2.08195e22i			0.142945i
$532$	1.73426e21	+	1.00100e23i	0.0117183	+	0.676371i
$533$			4.02688e23i			2.67786i
$534$	9.74815e20	+	1.12539e23i	0.00638001	+	0.736551i
$535$	−1.11857e23			−0.720536
$536$	−4.49177e21	−	1.72819e23i	−0.0284785	−	1.09570i
$537$	−1.46120e23			−0.911860
$538$	−2.14993e21	−	2.48203e23i	−0.0132061	−	1.52460i
$539$		−	3.46743e22i		−	0.209654i
$540$	7.97466e22	−	1.38163e21i	0.474641	−	0.00822330i
$541$		−	1.34761e23i		−	0.789565i	−0.918775	−	0.394783i	$-0.870820\pi$
$541$		−	1.34761e23i		−	0.789565i	0.918775	−	0.394783i	$-0.129180\pi$
$542$	−1.83479e23	+	1.58930e21i	−1.05826	+	0.00916667i
$543$	−3.67230e23			−2.08516
$544$	−2.09688e23	+	9.08704e21i	−1.17215	+	0.0507963i
$545$	−2.71991e21			−0.0149687
$546$	1.80637e23	−	1.56468e21i	0.978746	−	0.00847791i
$547$			2.17960e23i			1.16274i	0.813638	+	0.581372i	$0.197484\pi$
$547$			2.17960e23i			1.16274i	−0.813638	+	0.581372i	$0.802516\pi$
$548$	8.22277e22	−	1.42462e21i	0.431900	−	0.00748281i
$549$		−	4.17314e22i		−	0.215823i
$550$	−1.98945e20	−	2.29676e22i	−0.00101310	−	0.116959i
$551$	3.57229e23			1.79126
$552$	5.40710e21	+	2.08036e23i	0.0266982	+	1.02720i
$553$	−8.06015e22			−0.391904
$554$	−1.84276e21	−	2.12740e23i	−0.00882337	−	1.01863i
$555$		−	1.96337e23i		−	0.925790i
$556$	−5.84119e20	−	3.37148e22i	−0.00271247	−	0.156561i
$557$		−	7.39588e22i		−	0.338237i	−0.985596	−	0.169118i	$-0.945908\pi$
$557$		−	7.39588e22i		−	0.338237i	0.985596	−	0.169118i	$-0.0540920\pi$
$558$	6.33288e21	−	5.48555e19i	0.0285240	−	0.000247075i
$559$	−6.56608e23			−2.91277
$560$	−2.99822e21	−	8.65013e22i	−0.0130998	−	0.377941i
$561$	9.25888e22			0.398450
$562$	1.89823e23	−	1.64424e21i	0.804617	−	0.00696960i
$563$		−	6.46778e21i		−	0.0270044i	−0.999909	−	0.0135022i	$-0.995702\pi$
$563$		−	6.46778e21i		−	0.0270044i	0.999909	−	0.0135022i	$-0.00429801\pi$
$564$	−2.58646e21	−	1.49288e23i	−0.0106374	−	0.613977i
$565$			1.88310e22i			0.0762891i
$566$	2.35675e21	+	2.72079e23i	0.00940532	+	1.08581i
$567$	1.57904e23			0.620781
$568$	−4.35975e23	+	1.13315e22i	−1.68850	+	0.0438861i
$569$	3.40211e23			1.29806			0.649029	−	0.760764i	$-0.275176\pi$
$569$	3.40211e23			1.29806			0.649029	+	0.760764i	$0.275176\pi$
$570$	2.91603e21	+	3.36646e23i	0.0109612	+	1.26543i
$571$			4.01054e23i			1.48524i	0.669715	+	0.742619i	$0.266416\pi$
$571$			4.01054e23i			1.48524i	−0.669715	+	0.742619i	$0.733584\pi$
$572$	−1.23164e23	+	2.13386e21i	−0.449385	+	0.00778575i
$573$		−	3.22979e23i		−	1.16107i
$574$	2.32506e23	−	2.01397e21i	0.823537	−	0.00713348i
$575$	1.01401e23			0.353888
$576$	−1.42030e23	+	7.38806e21i	−0.488415	+	0.0254062i
$577$	1.92304e23			0.651619			0.325810	−	0.945435i	$-0.394363\pi$
$577$	1.92304e23			0.651619			0.325810	+	0.945435i	$0.394363\pi$
$578$	−1.12758e23	+	9.76711e20i	−0.376496	+	0.00326121i
$579$			3.62250e21i			0.0119190i
$580$	−3.08791e23	+	5.34991e21i	−1.00122	+	0.0173464i
$581$		−	7.11249e22i		−	0.227261i
$582$	−1.74361e21	−	2.01294e23i	−0.00549041	−	0.633849i
$583$	−6.26010e22			−0.194267
$584$	2.58183e23	−	6.71050e21i	0.789622	−	0.0205232i
$585$	1.99514e23			0.601380
$586$	2.35514e21	+	2.71893e23i	0.00699659	+	0.807733i
$587$		−	1.13316e23i		−	0.331793i	−0.986143	−	0.165896i	$-0.946948\pi$
$587$		−	1.13316e23i		−	0.331793i	0.986143	−	0.165896i	$-0.0530517\pi$
$588$	5.51771e21	+	3.18477e23i	0.0159240	+	0.919117i
$589$		−	2.79262e22i		−	0.0794386i
$590$	−7.93657e22	+	6.87466e20i	−0.222531	+	0.00192757i
$591$	−8.96173e22			−0.247684
$592$	−1.26693e22	−	3.65521e23i	−0.0345159	−	0.995814i
$593$	4.06278e23			1.09108			0.545542	−	0.838084i	$-0.316324\pi$
$593$	4.06278e23			1.09108			0.545542	+	0.838084i	$0.316324\pi$
$594$	−6.55405e22	+	5.67712e20i	−0.173510	+	0.00150295i
$595$		−	1.70008e23i		−	0.443685i
$596$	−1.16384e22	−	6.71755e23i	−0.0299433	−	1.72830i
$597$			2.52730e23i			0.641025i
$598$	−4.71047e21	−	5.43808e23i	−0.0117789	−	1.35983i
$599$	5.15444e23			1.27073			0.635365	−	0.772212i	$-0.280850\pi$
$599$	5.15444e23			1.27073			0.635365	+	0.772212i	$0.280850\pi$
$600$	5.48209e21	+	2.10921e23i	0.0133248	+	0.512665i
$601$	3.97639e23			0.952918			0.476459	−	0.879197i	$-0.341920\pi$
$601$	3.97639e23			0.952918			0.476459	+	0.879197i	$0.341920\pi$
$602$	3.28390e21	+	3.79115e23i	0.00775925	+	0.895780i
$603$		−	2.30096e23i		−	0.536059i
$604$	−1.98413e23	+	3.43756e21i	−0.455780	+	0.00789653i
$605$			3.10115e23i			0.702429i
$606$	1.90920e23	−	1.65375e21i	0.426416	−	0.00369362i
$607$	−6.76629e23			−1.49021			−0.745104	−	0.666948i	$-0.767600\pi$
$607$	−6.76629e23			−1.49021			−0.745104	+	0.666948i	$0.767600\pi$
$608$	2.71521e22	+	6.26547e23i	0.0589688	+	1.36073i
$609$	−3.72180e23			−0.797087
$610$	1.59083e23	−	1.37798e21i	0.335986	−	0.00291031i
$611$			3.90182e23i			0.812675i
$612$	−2.79311e23	+	4.83915e21i	−0.573721	+	0.00993989i
$613$			6.69956e23i			1.35716i	0.734525	+	0.678582i	$0.237405\pi$
$613$			6.69956e23i			1.35716i	−0.734525	+	0.678582i	$0.762595\pi$
$614$	1.84781e20	+	2.13323e22i	0.000369169	+	0.0426193i
$615$	7.81882e23			1.54065
$616$	1.84804e21	+	7.11026e22i	0.00359150	+	0.138181i
$617$	−2.38236e23			−0.456649			−0.228325	−	0.973585i	$-0.573325\pi$
$617$	−2.38236e23			−0.456649			−0.228325	+	0.973585i	$0.573325\pi$
$618$	−9.02889e21	−	1.04236e24i	−0.0170699	−	1.97067i
$619$		−	1.75944e23i		−	0.328099i	−0.986452	−	0.164049i	$-0.947544\pi$
$619$		−	1.75944e23i		−	0.328099i	0.986452	−	0.164049i	$-0.0524556\pi$
$620$	4.18227e20	+	2.41396e22i	0.000769276	+	0.0444019i
$621$		−	2.89360e23i		−	0.525000i
$622$	3.27892e23	−	2.84021e21i	0.586831	−	0.00508314i
$623$	−1.69816e23			−0.299799
$624$	1.13090e24	−	3.91982e22i	1.96950	−	0.0682648i
$625$	−2.34643e23			−0.403114
$626$	−9.11355e23	+	7.89416e21i	−1.54456	+	0.0133790i
$627$		−	2.76655e23i		−	0.462557i
$628$	1.43451e22	+	8.27982e23i	0.0236617	+	1.36573i
$629$		−	7.18388e23i		−	1.16904i
$630$	−9.97833e20	−	1.15197e23i	−0.00160200	−	0.184946i
$631$	−5.34532e23			−0.846689			−0.423344	−	0.905969i	$-0.639144\pi$
$631$	−5.34532e23			−0.846689			−0.423344	+	0.905969i	$0.639144\pi$
$632$	−5.04729e23	+	1.31185e22i	−0.788792	+	0.0205017i
$633$	−1.07313e24			−1.65470
$634$	5.91659e21	+	6.83051e23i	0.00900146	+	1.03919i
$635$		−	6.97306e22i		−	0.104676i
$636$	5.74978e23	−	9.96168e21i	0.851659	−	0.0147553i
$637$		−	8.32378e23i		−	1.21657i
$638$	2.53783e23	−	2.19827e21i	0.366005	−	0.00317034i
$639$	−5.80471e23			−0.826082
$640$	−3.28537e22	−	5.41185e23i	−0.0461376	−	0.760005i
$641$	−1.21663e24			−1.68603			−0.843017	−	0.537887i	$-0.819223\pi$
$641$	−1.21663e24			−1.68603			−0.843017	+	0.537887i	$0.819223\pi$
$642$	−8.44365e23	+	7.31389e21i	−1.15474	+	0.0100023i
$643$		−	2.18465e23i		−	0.294842i	−0.989074	−	0.147421i	$-0.952903\pi$
$643$		−	2.18465e23i		−	0.294842i	0.989074	−	0.147421i	$-0.0470972\pi$
$644$	−3.13963e23	+	5.43951e21i	−0.418166	+	0.00724486i
$645$			1.27491e24i			1.67580i
$646$	1.06696e22	+	1.23177e24i	0.0138412	+	1.59792i
$647$	1.14703e24			1.46855			0.734275	−	0.678852i	$-0.237522\pi$
$647$	1.14703e24			1.46855			0.734275	+	0.678852i	$0.237522\pi$
$648$	9.88802e23	−	2.57002e22i	1.24946	−	0.0324750i
$649$	6.52226e22			0.0813426
$650$	−4.77580e21	−	5.51350e23i	−0.00587872	−	0.678678i
$651$			2.90950e22i			0.0353492i
$652$	−1.73172e22	−	9.99531e23i	−0.0207670	−	1.19865i
$653$			1.50867e23i			0.178580i	0.996006	+	0.0892898i	$0.0284597\pi$
$653$			1.50867e23i			0.178580i	−0.996006	+	0.0892898i	$0.971540\pi$
$654$	−2.05316e22	+	1.77844e20i	−0.0239889	+	0.000207792i
$655$	−5.20234e23			−0.599995
$656$	1.45563e24	−	5.04537e22i	1.65718	−	0.0574395i
$657$	3.43754e23			0.386315
$658$	2.25285e23	−	1.95142e21i	0.249927	−	0.00216487i
$659$			1.33218e24i			1.45894i	0.684013	+	0.729470i	$0.260233\pi$
$659$			1.33218e24i			1.45894i	−0.684013	+	0.729470i	$0.739767\pi$
$660$	4.14323e21	+	2.39143e23i	0.00447936	+	0.258544i
$661$		−	1.50165e24i		−	1.60272i	−0.598183	−	0.801359i	$-0.704111\pi$
$661$		−	1.50165e24i		−	1.60272i	0.598183	−	0.801359i	$-0.295889\pi$
$662$	3.23257e21	+	3.73190e23i	0.00340609	+	0.393221i
$663$	2.22265e24			2.31210
$664$	−1.15761e22	−	4.45386e23i	−0.0118887	−	0.457413i
$665$	−5.07983e23			−0.515069
$666$	−4.21646e21	−	4.86776e23i	−0.00422102	−	0.487302i
$667$			1.12045e24i			1.10744i
$668$	9.96677e23	−	1.72677e22i	0.972645	−	0.0168514i
$669$			1.86592e24i			1.79792i
$670$	8.77145e23	−	7.59783e21i	0.834517	−	0.00722860i
$671$	−1.30734e23			−0.122814
$672$	−2.82884e22	−	6.52769e23i	−0.0262404	−	0.605509i
$673$	1.95354e24			1.78935			0.894673	−	0.446722i	$-0.147409\pi$
$673$	1.95354e24			1.78935			0.894673	+	0.446722i	$0.147409\pi$
$674$	−7.77708e23	+	6.73651e21i	−0.703408	+	0.00609293i
$675$		−	2.93373e23i		−	0.262022i
$676$	−1.82298e24	+	3.15837e22i	−1.60781	+	0.0278558i
$677$		−	1.79219e24i		−	1.56092i	−0.625208	−	0.780458i	$-0.714986\pi$
$677$		−	1.79219e24i		−	1.56092i	0.625208	−	0.780458i	$-0.285014\pi$
$678$	1.23129e21	+	1.42148e23i	0.00105903	+	0.122261i
$679$	3.03743e23			0.257997
$680$	−2.76701e22	−	1.06459e24i	−0.0232105	−	0.893014i
$681$	−1.10322e24			−0.913925
$682$	−1.71849e20	−	1.98394e22i	−0.000140598	−	0.0162316i
$683$		−	2.23745e24i		−	1.80791i	−0.427628	−	0.903955i	$-0.640651\pi$
$683$		−	2.23745e24i		−	1.80791i	0.427628	−	0.903955i	$-0.359349\pi$
$684$	1.44594e22	+	8.34580e23i	0.0115391	+	0.666026i
$685$			4.17286e23i			0.328900i
$686$	−1.11858e24	+	9.68919e21i	−0.870791	+	0.00754280i
$687$	4.80356e23			0.369344
$688$	8.22678e22	+	2.37350e24i	0.0624782	+	1.80255i
$689$	−1.50278e24			−1.12728
$690$	−1.05589e24	+	9.14612e21i	−0.782350	+	0.00677672i
$691$		−	1.07548e24i		−	0.787114i	−0.919300	−	0.393557i	$-0.871244\pi$
$691$		−	1.07548e24i		−	0.787114i	0.919300	−	0.393557i	$-0.128756\pi$
$692$	2.23857e22	+	1.29208e24i	0.0161834	+	0.934088i
$693$			9.46683e22i			0.0676040i
$694$	−1.46596e22	−	1.69240e24i	−0.0103411	−	1.19384i
$695$	1.71094e23			0.119224
$696$	−2.33060e24	+	6.05751e22i	−1.60431	+	0.0416981i
$697$	2.86087e24			1.94545
$698$	1.48111e22	+	1.70989e24i	0.00994985	+	1.14868i
$699$			1.68525e24i			1.11843i
$700$	−3.18317e23	+	5.51495e21i	−0.208702	+	0.00361583i
$701$			4.83049e23i			0.312887i	0.987687	+	0.156444i	$0.0500030\pi$
$701$			4.83049e23i			0.312887i	−0.987687	+	0.156444i	$0.949997\pi$
$702$	−1.57334e24	+	1.36283e22i	−1.00683	+	0.00872118i
$703$	−2.14654e24			−1.35712
$704$	2.31450e22	+	4.44946e23i	0.0144574	+	0.277933i
$705$	7.57600e23			0.467555
$706$	1.55642e24	−	1.34818e22i	0.949048	−	0.00822066i
$707$			2.88089e23i			0.173565i
$708$	−5.99056e23	+	1.03788e22i	−0.356603	+	0.00617826i
$709$			6.46817e23i			0.380442i	0.981741	+	0.190221i	$0.0609204\pi$
$709$			6.46817e23i			0.380442i	−0.981741	+	0.190221i	$0.939080\pi$
$710$	−1.91673e22	−	2.21280e24i	−0.0111395	−	1.28601i
$711$	−6.72012e23			−0.385909
$712$	−1.06339e24	+	2.76389e22i	−0.603412	+	0.0156834i
$713$	8.75904e22			0.0491129
$714$	−1.11162e22	−	1.28332e24i	−0.00615914	−	0.711053i
$715$		−	6.25030e23i		−	0.342215i
$716$	−2.39247e22	−	1.38091e24i	−0.0129445	−	0.747145i
$717$			3.13189e23i			0.167454i
$718$	1.90785e24	−	1.65258e22i	1.00806	−	0.00873181i
$719$	−2.08660e24			−1.08954			−0.544770	−	0.838586i	$-0.683383\pi$
$719$	−2.08660e24			−1.08954			−0.544770	+	0.838586i	$0.683383\pi$
$720$	−2.49976e22	−	7.21201e23i	−0.0128995	−	0.372161i
$721$	1.57286e24			0.802124
$722$	1.69650e24	−	1.46951e22i	0.855041	−	0.00740637i
$723$		−	3.96078e24i		−	1.97290i
$724$	−6.01277e22	−	3.47051e24i	−0.0296003	−	1.70850i
$725$			1.13599e24i			0.552713i
$726$	2.02773e22	+	2.34094e24i	0.00975097	+	1.12572i
$727$	2.50710e24			1.19160			0.595799	−	0.803134i	$-0.296836\pi$
$727$	2.50710e24			1.19160			0.595799	+	0.803134i	$0.296836\pi$
$728$	4.43634e22	+	1.70686e24i	0.0208405	+	0.801828i
$729$	−3.22019e23			−0.149519
$730$	1.13508e22	+	1.31041e24i	0.00520934	+	0.601401i
$731$			4.66482e24i			2.11611i
$732$	1.20077e24	−	2.08037e22i	0.538412	−	0.00932816i
$733$			2.50202e24i			1.10894i	0.832205	+	0.554469i	$0.187079\pi$
$733$			2.50202e24i			1.10894i	−0.832205	+	0.554469i	$0.812921\pi$
$734$	2.67687e24	−	2.31871e22i	1.17277	−	0.0101585i
$735$	−1.61619e24			−0.699924
$736$	−1.96516e24	+	8.51623e22i	−0.841272	+	0.0364574i
$737$	−7.20836e23			−0.305044
$738$	1.93851e24	−	1.67914e22i	0.810941	−	0.00702437i
$739$			1.98150e24i			0.819440i	0.912211	+	0.409720i	$0.134374\pi$
$739$			1.98150e24i			0.819440i	−0.912211	+	0.409720i	$0.865626\pi$
$740$	1.85549e24	−	3.21469e22i	0.758558	−	0.0131423i
$741$		−	6.64128e24i		−	2.68409i
$742$	7.51585e21	+	8.67680e23i	0.00300293	+	0.346678i
$743$	−1.48113e24			−0.585043			−0.292521	−	0.956259i	$-0.594494\pi$
$743$	−1.48113e24			−0.585043			−0.292521	+	0.956259i	$0.594494\pi$
$744$	4.73543e21	+	1.82194e23i	0.00184922	+	0.0711480i
$745$	3.40900e24			1.31613
$746$	1.08411e22	+	1.25157e24i	0.00413803	+	0.477722i
$747$		−	5.93001e23i		−	0.223785i
$748$	1.51599e22	+	8.75013e23i	0.00565629	+	0.326476i
$749$		−	1.27411e24i		−	0.470013i
$750$	−3.61782e24	+	3.13376e22i	−1.31955	+	0.0114300i
$751$	−5.06055e24			−1.82498			−0.912490	−	0.409100i	$-0.865843\pi$
$751$	−5.06055e24			−1.82498			−0.912490	+	0.409100i	$0.865843\pi$
$752$	1.41043e24	−	4.88868e22i	0.502919	−	0.0174317i
$753$	−2.04106e24			−0.719614
$754$	6.09222e24	−	5.27709e22i	2.12383	−	0.0183966i
$755$		−	1.00690e24i		−	0.347085i
$756$	1.57375e22	+	9.08354e23i	0.00536415	+	0.309613i
$757$		−	1.15475e23i		−	0.0389200i	−0.999811	−	0.0194600i	$-0.993805\pi$
$757$		−	1.15475e23i		−	0.0389200i	0.999811	−	0.0194600i	$-0.00619470\pi$
$758$	−9.94849e21	−	1.14852e24i	−0.00331565	−	0.382781i
$759$	8.67728e23			0.285975
$760$	−3.18101e24	+	8.26782e22i	−1.03669	+	0.0269448i
$761$	−3.07347e24			−0.990510			−0.495255	−	0.868748i	$-0.664925\pi$
$761$	−3.07347e24			−0.990510			−0.495255	+	0.868748i	$0.664925\pi$
$762$	−4.55942e21	−	5.26370e23i	−0.00145309	−	0.167754i
$763$		−	3.09811e22i		−	0.00976425i
$764$	3.05232e24	−	5.28824e22i	0.951341	−	0.0164823i
$765$		−	1.41743e24i		−	0.436899i
$766$	−1.18734e24	+	1.02847e22i	−0.361934	+	0.00313507i
$767$	1.56571e24			0.472008
$768$	−2.83386e23	−	4.08305e24i	−0.0844906	−	1.21735i
$769$	1.56828e24			0.462434			0.231217	−	0.972902i	$-0.425729\pi$
$769$	1.56828e24			0.462434			0.231217	+	0.972902i	$0.425729\pi$
$770$	−3.60883e23	+	3.12597e21i	−0.105243	+	0.000911619i
$771$			4.84842e24i			1.39842i
$772$	−3.42345e22	+	5.93124e20i	−0.00976601	+	0.000169199i
$773$			3.06812e24i			0.865659i	0.901476	+	0.432830i	$0.142485\pi$
$773$			3.06812e24i			0.865659i	−0.901476	+	0.432830i	$0.857515\pi$
$774$	2.73794e22	+	3.16086e24i	0.00764057	+	0.882078i
$775$	8.88051e22			0.0245117
$776$	1.90205e24	−	4.94366e22i	0.519275	−	0.0134966i
$777$	2.23638e24			0.603903
$778$	−3.44744e22	−	3.97995e24i	−0.00920810	−	1.06304i
$779$		−	8.54827e24i		−	2.25845i
$780$	9.94607e22	+	5.74077e24i	0.0259925	+	1.50026i
$781$			1.81847e24i			0.470082i
$782$	−3.86345e24	+	3.34652e22i	−0.987910	+	0.00855729i
$783$	3.24166e24			0.819960
$784$	−3.00887e24	+	1.04291e23i	−0.752865	+	0.0260951i
$785$	−4.20181e24			−1.04003
$786$	−3.92704e24	+	3.40161e22i	−0.961555	+	0.00832900i
$787$			7.03196e23i			0.170330i	0.996367	+	0.0851650i	$0.0271417\pi$
$787$			7.03196e23i			0.170330i	−0.996367	+	0.0851650i	$0.972858\pi$
$788$	−1.46733e22	−	8.46930e23i	−0.00351606	−	0.202943i
$789$			3.55398e24i			0.842482i
$790$	−2.21900e22	−	2.56176e24i	−0.00520387	−	0.600770i
$791$	−2.14495e23			−0.0497642
$792$	1.54080e22	+	5.92815e23i	0.00353657	+	0.136068i
$793$	−3.13835e24			−0.712656
$794$	−2.82573e22	−	3.26221e24i	−0.00634828	−	0.732888i
$795$			2.91788e24i			0.648554i
$796$	−2.38843e24	+	4.13803e22i	−0.525232	+	0.00909981i
$797$			4.69599e24i			1.02172i	0.859664	+	0.510859i	$0.170673\pi$
$797$			4.69599e24i			1.02172i	−0.859664	+	0.510859i	$0.829327\pi$
$798$	−3.83457e24	+	3.32151e22i	−0.825453	+	0.00715008i
$799$	2.77202e24			0.590403
$800$	−1.99241e24	+	8.63434e22i	−0.419870	+	0.0181955i
$801$	−1.41584e24			−0.295214
$802$	−3.80142e24	+	3.29279e22i	−0.784267	+	0.00679333i
$803$		−	1.07690e24i		−	0.219832i
$804$	6.62074e24	−	1.14706e23i	1.33730	−	0.0231692i
$805$		−	1.59329e24i		−	0.318441i
$806$	−4.12534e21	−	4.76256e23i	−0.000815852	−	0.0941874i
$807$	9.50730e24			1.86051
$808$	4.68887e22	+	1.80402e24i	0.00907970	+	0.349337i
$809$	−4.37783e24			−0.838873			−0.419436	−	0.907785i	$-0.637772\pi$
$809$	−4.37783e24			−0.838873			−0.419436	+	0.907785i	$0.637772\pi$
$810$	4.34719e22	+	5.01869e24i	0.00824301	+	0.951628i
$811$		−	8.61180e24i		−	1.61591i	−0.589245	−	0.807954i	$-0.700575\pi$
$811$		−	8.61180e24i		−	1.61591i	0.589245	−	0.807954i	$-0.299425\pi$
$812$	−6.09382e22	−	3.51729e24i	−0.0113152	−	0.653104i
$813$		−	7.02809e24i		−	1.29142i
$814$	−1.52495e24	+	1.32091e22i	−0.277299	+	0.00240197i
$815$	5.07238e24			0.912793
$816$	−2.78481e23	−	8.03441e24i	−0.0495940	−	1.43083i
$817$	1.39385e25			2.45656
$818$	−2.12343e24	+	1.83931e22i	−0.370369	+	0.00320814i
$819$			2.27257e24i			0.392287i
$820$	1.28020e23	+	7.38920e24i	0.0218706	+	1.26235i
$821$			4.09648e24i			0.692619i	0.938120	+	0.346309i	$0.112565\pi$
$821$			4.09648e24i			0.692619i	−0.938120	+	0.346309i	$0.887435\pi$
$822$	2.72847e22	+	3.14993e24i	0.00456572	+	0.527097i
$823$	−4.02308e24			−0.666284			−0.333142	−	0.942877i	$-0.608109\pi$
$823$	−4.02308e24			−0.666284			−0.333142	+	0.942877i	$0.608109\pi$
$824$	9.84932e24	−	2.55996e23i	1.61445	−	0.0419616i
$825$	8.79762e23			0.142727
$826$	−7.83059e21	−	9.04015e23i	−0.00125737	−	0.145160i
$827$			6.80277e24i			1.08116i	0.841294	+	0.540579i	$0.181795\pi$
$827$			6.80277e24i			1.08116i	−0.841294	+	0.540579i	$0.818205\pi$
$828$	−2.61766e24	+	4.53517e22i	−0.411770	+	0.00713405i
$829$		−	9.06827e24i		−	1.41192i	−0.708251	−	0.705961i	$-0.750515\pi$
$829$		−	9.06827e24i		−	1.41192i	0.708251	−	0.705961i	$-0.249485\pi$
$830$	2.26057e24	−	1.95810e22i	0.348380	−	0.00301767i
$831$	8.14891e24			1.24306
$832$	5.55610e23	+	1.06812e25i	0.0838922	+	1.61277i
$833$	−5.91357e24			−0.883827
$834$	1.29153e24	−	1.11872e22i	0.191070	−	0.00165505i
$835$			5.05790e24i			0.740687i
$836$	2.61454e24	−	4.52977e22i	0.379002	−	0.00656633i
$837$		−	2.53415e23i		−	0.0363636i
$838$	−1.57509e22	−	1.81838e24i	−0.00223733	−	0.258292i
$839$	−2.26281e24			−0.318179			−0.159090	−	0.987264i	$-0.550856\pi$
$839$	−2.26281e24			−0.318179			−0.159090	+	0.987264i	$0.550856\pi$
$840$	3.31414e24	−	8.61385e22i	0.461314	−	0.0119901i
$841$	−5.29508e24			−0.729637
$842$	4.88833e22	+	5.64341e24i	0.00666818	+	0.769819i
$843$			7.27107e24i			0.981892i
$844$	−1.75707e23	−	1.01416e25i	−0.0234897	−	1.35580i
$845$		−	9.25117e24i		−	1.22438i
$846$	1.87831e24	−	1.62699e22i	0.246104	−	0.00213176i
$847$	−3.53237e24			−0.458202
$848$	1.88286e23	+	5.43221e24i	0.0241798	+	0.697609i
$849$	−1.04219e25			−1.32504
$850$	−3.91703e24	+	3.39293e22i	−0.493055	+	0.00427085i
$851$		−	6.73262e24i		−	0.839040i
$852$	−2.89373e23	−	1.67023e25i	−0.0357044	−	2.06082i
$853$			9.22743e24i			1.12723i	0.826036	+	0.563617i	$0.190591\pi$
$853$			9.22743e24i			1.12723i	−0.826036	+	0.563617i	$0.809409\pi$
$854$	1.56959e22	+	1.81204e24i	0.00189843	+	0.219167i
$855$	−4.23529e24			−0.507191
$856$	−2.07371e23	−	7.97849e24i	−0.0245878	−	0.946005i
$857$	4.23968e24			0.497733			0.248867	−	0.968538i	$-0.419942\pi$
$857$	4.23968e24			0.497733			0.248867	+	0.968538i	$0.419942\pi$
$858$	−4.08683e22	−	4.71811e24i	−0.00475056	−	0.548436i
$859$			2.28165e24i			0.262608i	0.991342	+	0.131304i	$0.0419164\pi$
$859$			2.28165e24i			0.262608i	−0.991342	+	0.131304i	$0.958084\pi$
$860$	−1.20485e25	+	2.08745e23i	−1.37309	+	0.0237891i
$861$			8.90604e24i			1.00498i
$862$	1.00846e25	−	8.73528e22i	1.12680	−	0.00976034i
$863$	−1.03258e25			−1.14244			−0.571220	−	0.820797i	$-0.693530\pi$
$863$	−1.03258e25			−1.14244			−0.571220	+	0.820797i	$0.693530\pi$
$864$	2.46390e23	+	5.68558e24i	0.0269934	+	0.622885i
$865$	−6.55700e24			−0.711325
$866$	4.50612e23	−	3.90320e21i	0.0484061	−	0.000419294i
$867$		−	4.31915e24i		−	0.459447i
$868$	−2.74963e23	+	4.76381e21i	−0.0289638	+	0.000501807i
$869$			2.10525e24i			0.219602i
$870$	−1.02463e23	−	1.18290e25i	−0.0105841	−	1.22190i
$871$	−1.73041e25			−1.77009
$872$	−5.04242e21	−	1.94005e23i	−0.000510798	−	0.0196527i
$873$	2.53245e24			0.254050
$874$	9.99940e22	+	1.15440e25i	0.00993406	+	1.14685i
$875$		−	5.45912e24i		−	0.537099i
$876$	1.71366e23	+	9.89108e24i	0.0166971	+	0.963738i
$877$			1.49582e24i			0.144338i	0.997392	+	0.0721692i	$0.0229921\pi$
$877$			1.49582e24i			0.144338i	−0.997392	+	0.0721692i	$0.977008\pi$
$878$	7.58855e24	−	6.57321e22i	0.725196	−	0.00628166i
$879$	−1.04147e25			−0.985695
$880$	−2.25935e24	+	7.83114e22i	−0.211778	+	0.00734044i
$881$	9.02128e24			0.837477			0.418739	−	0.908107i	$-0.362472\pi$
$881$	9.02128e24			0.837477			0.418739	+	0.908107i	$0.362472\pi$
$882$	−4.00701e24	+	3.47087e22i	−0.368415	+	0.00319121i
$883$		−	5.61859e24i		−	0.511636i	−0.966725	−	0.255818i	$-0.917655\pi$
$883$		−	5.61859e24i		−	0.511636i	0.966725	−	0.255818i	$-0.0823448\pi$
$884$	3.63922e23	+	2.10052e25i	0.0328219	+	1.89445i
$885$		−	3.04007e24i		−	0.271560i
$886$	3.51146e22	+	4.05387e24i	0.00310672	+	0.358660i
$887$	1.48729e25			1.30330			0.651649	−	0.758521i	$-0.274078\pi$
$887$	1.48729e25			1.30330			0.651649	+	0.758521i	$0.274078\pi$
$888$	1.40043e25	−	3.63988e23i	1.21549	−	0.0315920i
$889$	7.94267e23			0.0682813
$890$	−4.67512e22	−	5.39728e24i	−0.00398087	−	0.459578i
$891$		−	4.12435e24i		−	0.347852i
$892$	−1.76339e25	+	3.05513e23i	−1.47315	+	0.0255228i
$893$		−	8.28280e24i		−	0.685393i
$894$	2.57332e25	−	2.22901e23i	2.10924	−	0.0182702i
$895$	7.00778e24			0.568964
$896$	6.16438e24	−	3.74221e23i	0.495760	−	0.0300961i
$897$	2.08303e25			1.65944
$898$	5.22039e24	−	4.52191e22i	0.411959	−	0.00356839i
$899$			9.81264e23i			0.0767059i
$900$	−2.65396e24	+	4.59807e22i	−0.205510	+	0.00356053i
$901$			1.06764e25i			0.818959i
$902$	−5.26034e22	−	6.07288e24i	−0.00399722	−	0.461466i
$903$	−1.45218e25			−1.09314
$904$	−1.34317e24	+	3.49107e22i	−0.100161	+	0.00260332i
$905$	1.76120e25			1.30106
$906$	−6.58371e22	−	7.60067e24i	−0.00481816	−	0.556240i
$907$		−	1.26650e25i		−	0.918215i	−0.888381	−	0.459107i	$-0.848169\pi$
$907$		−	1.26650e25i		−	0.918215i	0.888381	−	0.459107i	$-0.151831\pi$
$908$	−1.80633e23	−	1.04260e25i	−0.0129738	−	0.748836i
$909$			2.40193e24i			0.170910i
$910$	−8.66321e24	+	7.50407e22i	−0.610698	+	0.00528987i
$911$	2.22052e25			1.55077			0.775387	−	0.631487i	$-0.217555\pi$
$911$	2.22052e25			1.55077			0.775387	+	0.631487i	$0.217555\pi$
$912$	−2.40068e25	+	8.32100e23i	−1.66103	+	0.0575731i
$913$	−1.85773e24			−0.127345
$914$	−1.08553e25	+	9.40291e22i	−0.737227	+	0.00638586i
$915$			6.09361e24i			0.410011i
$916$	7.86503e22	+	4.53962e24i	0.00524311	+	0.302627i
$917$		−	5.92572e24i		−	0.391383i
$918$	9.68211e22	+	1.11777e25i	0.00633588	+	0.731457i
$919$	−2.34055e25			−1.51753			−0.758763	−	0.651367i	$-0.774196\pi$
$919$	−2.34055e25			−1.51753			−0.758763	+	0.651367i	$0.774196\pi$
$920$	−2.59320e23	−	9.97721e24i	−0.0166586	−	0.640933i
$921$	−8.17124e23			−0.0520093
$922$	−1.35691e23	−	1.56650e25i	−0.00855731	−	0.987912i
$923$			4.36536e25i			2.72775i
$924$	−2.72396e24	+	4.71935e22i	−0.168651	+	0.00292193i
$925$		−	6.82599e24i		−	0.418756i
$926$	6.51374e24	−	5.64221e22i	0.395947	−	0.00342970i
$927$	1.31137e25			0.789855
$928$	−9.54063e23	−	2.20155e25i	−0.0569402	−	1.31392i
$929$	6.30561e24			0.372901			0.186450	−	0.982464i	$-0.440302\pi$
$929$	6.30561e24			0.372901			0.186450	+	0.982464i	$0.440302\pi$
$930$	−9.24727e23	+	8.00999e21i	−0.0541887	+	0.000469383i
$931$			1.76697e25i			1.02603i
$932$	−1.59265e25	+	2.75932e23i	−0.916401	+	0.0158769i
$933$			1.25598e25i			0.716123i
$934$	1.73591e23	+	2.00405e25i	0.00980795	+	1.13229i
$935$	−4.44048e24			−0.248617
$936$	3.69878e23	+	1.42309e25i	0.0205217	+	0.789564i
$937$	−8.24230e23			−0.0453171			−0.0226586	−	0.999743i	$-0.507213\pi$
$937$	−8.24230e23			−0.0453171			−0.0226586	+	0.999743i	$0.507213\pi$
$938$	8.65432e22	+	9.99113e24i	0.00471529	+	0.544365i
$939$		−	3.49090e25i		−	1.88487i
$940$	1.24044e23	+	7.15972e24i	0.00663728	+	0.383097i
$941$		−	6.73452e24i		−	0.357104i	−0.983930	−	0.178552i	$-0.942859\pi$
$941$		−	6.73452e24i		−	0.357104i	0.983930	−	0.178552i	$-0.0571413\pi$
$942$	−3.17179e25	+	2.74740e23i	−1.66675	+	0.0144374i
$943$	2.68116e25			1.39628
$944$	−1.96171e23	−	5.65970e24i	−0.0101245	−	0.292100i
$945$	−4.60968e24			−0.235776
$946$	9.90221e24	−	8.57730e22i	0.501947	−	0.00434787i
$947$		−	2.19407e25i		−	1.10224i	−0.834426	−	0.551119i	$-0.814201\pi$
$947$		−	2.19407e25i		−	1.10224i	0.834426	−	0.551119i	$-0.185799\pi$
$948$	−3.35008e23	−	1.93363e25i	−0.0166795	−	0.962726i
$949$		−	2.58515e25i		−	1.27563i
$950$	1.01381e23	+	1.17041e25i	0.00495798	+	0.572383i
$951$	−2.61639e25			−1.26814
$952$	1.21263e25	−	3.15177e23i	0.582523	−	0.0151405i
$953$	1.04120e25			0.495727			0.247864	−	0.968795i	$-0.420272\pi$
$953$	1.04120e25			0.495727			0.247864	+	0.968795i	$0.420272\pi$
$954$	6.26631e22	+	7.23425e24i	0.00295700	+	0.341375i
$955$			1.54898e25i			0.724464i
$956$	−2.95980e24	+	5.12795e22i	−0.137205	+	0.00237712i
$957$			9.72106e24i			0.446645i
$958$	4.27580e24	−	3.70370e22i	0.194720	−	0.00168667i
$959$	−4.75310e24			−0.214545
$960$	2.07392e25	−	1.07880e24i	0.927869	−	0.0482655i
$961$	−2.24734e25			−0.996598
$962$	−3.66074e25	+	3.17093e23i	−1.60909	+	0.0139380i
$963$		−	1.06228e25i		−	0.462824i
$964$	3.74315e25	−	6.48512e23i	1.61652	−	0.0280068i
$965$		−	1.73732e23i		−	0.00743700i
$966$	−1.04179e23	−	1.20271e25i	−0.00442053	−	0.510336i
$967$	2.11036e25			0.887630			0.443815	−	0.896118i	$-0.353625\pi$
$967$	2.11036e25			0.887630			0.443815	+	0.896118i	$0.353625\pi$
$968$	−2.21198e25	+	5.74921e23i	−0.922233	+	0.0239700i
$969$	−4.71825e25			−1.94997
$970$	8.36221e22	+	9.65389e24i	0.00342579	+	0.395497i
$971$			6.24704e24i			0.253694i	0.991922	+	0.126847i	$0.0404858\pi$
$971$			6.24704e24i			0.253694i	−0.991922	+	0.126847i	$0.959514\pi$
$972$	3.88022e23	+	2.23962e25i	0.0156204	+	0.901596i
$973$			1.94885e24i			0.0777713i
$974$	−7.84480e24	+	6.79517e22i	−0.310335	+	0.00268812i
$975$	2.11192e25			0.828206
$976$	3.93211e23	+	1.13445e25i	0.0152863	+	0.441023i
$977$	−1.86564e25			−0.718992			−0.359496	−	0.933147i	$-0.617051\pi$
$977$	−1.86564e25			−0.718992			−0.359496	+	0.933147i	$0.617051\pi$
$978$	3.82895e25	−	3.31664e23i	1.46285	−	0.0126712i
$979$			4.43547e24i			0.167991i
$980$	−2.64625e23	−	1.52739e25i	−0.00993593	−	0.573492i
$981$		−	2.58304e23i		−	0.00961490i
$982$	−4.08493e23	−	4.71592e25i	−0.0150743	−	1.74028i
$983$	−2.39881e25			−0.877589			−0.438794	−	0.898588i	$-0.644594\pi$
$983$	−2.39881e25			−0.877589			−0.438794	+	0.898588i	$0.644594\pi$
$984$	1.44953e24	+	5.57699e25i	0.0525736	+	2.02275i
$985$	4.29797e24			0.154545
$986$	−3.74907e23	−	4.32817e25i	−0.0133650	−	1.54295i
$987$			8.62945e24i			0.304991i
$988$	6.27635e25	−	1.08740e24i	2.19924	−	0.0381026i
$989$			4.37180e25i			1.51877i
$990$	−3.00885e24	+	2.60627e22i	−0.103634	+	0.000897676i
$991$	2.85777e25			0.975889			0.487945	−	0.872875i	$-0.337747\pi$
$991$	2.85777e25			0.975889			0.487945	+	0.872875i	$0.337747\pi$
$992$	−1.72105e24	+	7.45834e22i	−0.0582698	+	0.00252518i
$993$	−1.42949e25			−0.479857
$994$	2.52049e25	−	2.18325e23i	0.838882	−	0.00726640i
$995$		−	1.21207e25i		−	0.399974i
$996$	1.70629e25	−	2.95620e23i	0.558275	−	0.00967228i
$997$		−	1.00050e25i		−	0.324571i	−0.986744	−	0.162285i	$-0.948113\pi$
$997$		−	1.00050e25i		−	0.324571i	0.986744	−	0.162285i	$-0.0518865\pi$
$998$	1.62211e23	+	1.87267e25i	0.00521759	+	0.602353i
$999$	−1.94787e25			−0.621232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.18.b.a.5.2	yes	16
3.2	odd	2		72.18.d.b.37.15		16
4.3	odd	2		32.18.b.a.17.14		16
8.3	odd	2		32.18.b.a.17.3		16
8.5	even	2	inner	8.18.b.a.5.1	✓	16
24.5	odd	2		72.18.d.b.37.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.1	✓	16	8.5	even	2	inner
8.18.b.a.5.2	yes	16	1.1	even	1	trivial
32.18.b.a.17.3		16	8.3	odd	2
32.18.b.a.17.14		16	4.3	odd	2
72.18.d.b.37.15		16	3.2	odd	2
72.18.d.b.37.16		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)

\(f(q)\)	\(=\)	\(q+(-362.025 + 3.13586i) q^{2} -13867.2i q^{3} +(131052. - 2270.52i) q^{4} +665059. i q^{5} +(43485.7 + 5.02028e6i) q^{6} -7.57536e6 q^{7} +(-4.74371e7 + 1.23295e6i) q^{8} -6.31593e7 q^{9} +O(q^{10})\)	\(q+(-362.025 + 3.13586i) q^{2} -13867.2i q^{3} +(131052. - 2270.52i) q^{4} +665059. i q^{5} +(43485.7 + 5.02028e6i) q^{6} -7.57536e6 q^{7} +(-4.74371e7 + 1.23295e6i) q^{8} -6.31593e7 q^{9} +(-2.08553e6 - 2.40768e8i) q^{10} +1.97863e8i q^{11} +(-3.14858e7 - 1.81733e9i) q^{12} +4.74981e9i q^{13} +(2.74247e9 - 2.37553e7i) q^{14} +9.22251e9 q^{15} +(1.71696e10 - 5.95115e8i) q^{16} +3.37447e10 q^{17} +(2.28652e10 - 1.98059e8i) q^{18} -1.00829e11i q^{19} +(1.51003e9 + 8.71575e10i) q^{20} +1.05049e11i q^{21} +(-6.20471e8 - 7.16313e10i) q^{22} +3.16250e11 q^{23} +(1.70976e10 + 6.57820e11i) q^{24} +3.20636e11 q^{25} +(-1.48948e10 - 1.71955e12i) q^{26} -9.14971e11i q^{27} +(-9.92769e11 + 1.72000e10i) q^{28} +3.54291e12i q^{29} +(-3.33878e12 + 2.89205e10i) q^{30} +2.76965e11 q^{31} +(-6.21394e12 + 2.69288e11i) q^{32} +2.74380e12 q^{33} +(-1.22164e13 + 1.05819e11i) q^{34} -5.03806e12i q^{35} +(-8.27717e12 + 1.43405e11i) q^{36} -2.12889e13i q^{37} +(3.16187e11 + 3.65027e13i) q^{38} +6.58666e13 q^{39} +(-8.19983e11 - 3.15485e13i) q^{40} +8.47798e13 q^{41} +(-3.29420e11 - 3.80304e13i) q^{42} +1.38239e14i q^{43} +(4.49252e11 + 2.59304e13i) q^{44} -4.20047e13i q^{45} +(-1.14490e14 + 9.91717e11i) q^{46} +8.21469e13 q^{47} +(-8.25258e12 - 2.38094e14i) q^{48} -1.75244e14 q^{49} +(-1.16078e14 + 1.00547e12i) q^{50} -4.67945e14i q^{51} +(1.07846e13 + 6.22474e14i) q^{52} +3.16386e14i q^{53} +(2.86922e12 + 3.31242e14i) q^{54} -1.31590e14 q^{55} +(3.59353e14 - 9.34003e12i) q^{56} -1.39822e15 q^{57} +(-1.11101e13 - 1.28262e15i) q^{58} -3.29635e14i q^{59} +(1.20863e15 - 2.09399e13i) q^{60} +6.60732e14i q^{61} +(-1.00268e14 + 8.68526e11i) q^{62} +4.78454e14 q^{63} +(2.24876e15 - 1.16975e14i) q^{64} -3.15891e15 q^{65} +(-9.93326e14 + 8.60420e12i) q^{66} +3.64311e15i q^{67} +(4.42232e15 - 7.66181e13i) q^{68} -4.38551e15i q^{69} +(1.57987e13 + 1.82390e15i) q^{70} +9.19058e15 q^{71} +(2.99609e15 - 7.78722e13i) q^{72} -5.44264e15 q^{73} +(6.67591e13 + 7.70712e15i) q^{74} -4.44633e15i q^{75} +(-2.28935e14 - 1.32139e16i) q^{76} -1.49888e15i q^{77} +(-2.38454e16 + 2.06549e14i) q^{78} +1.06400e16 q^{79} +(3.95786e14 + 1.14188e16i) q^{80} -2.08445e16 q^{81} +(-3.06924e16 + 2.65858e14i) q^{82} +9.38898e15i q^{83} +(2.38516e14 + 1.37669e16i) q^{84} +2.24422e16i q^{85} +(-4.33498e14 - 5.00459e16i) q^{86} +4.91303e16 q^{87} +(-2.43955e14 - 9.38604e15i) q^{88} +2.24169e16 q^{89} +(1.31721e14 + 1.52067e16i) q^{90} -3.59815e16i q^{91} +(4.14453e16 - 7.18053e14i) q^{92} -3.84074e15i q^{93} +(-2.97392e16 + 2.57601e14i) q^{94} +6.70573e16 q^{95} +(3.73427e15 + 8.61701e16i) q^{96} -4.00962e16 q^{97} +(6.34429e16 - 5.49543e14i) q^{98} -1.24969e16i 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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