LMFDB - Embedded newform 8.18.b.a.5.6

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			5.6
Root			$-108.197 - 150.760i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.18.b.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-200.394 + 301.520i) q^{2} -13481.8i q^{3} +(-50756.5 - 120846. i) q^{4} -1.59197e6i q^{5} +(4.06504e6 + 2.70168e6i) q^{6} -1.66055e7 q^{7} +(4.66086e7 + 8.91263e6i) q^{8} -5.26193e7 q^{9} +O(q^{10})$	\(q+(-200.394 + 301.520i) q^{2} -13481.8i q^{3} +(-50756.5 - 120846. i) q^{4} -1.59197e6i q^{5} +(4.06504e6 + 2.70168e6i) q^{6} -1.66055e7 q^{7} +(4.66086e7 + 8.91263e6i) q^{8} -5.26193e7 q^{9} +(4.80011e8 + 3.19021e8i) q^{10} +6.79322e8i q^{11} +(-1.62922e9 + 6.84290e8i) q^{12} -3.13276e9i q^{13} +(3.32765e9 - 5.00690e9i) q^{14} -2.14627e10 q^{15} +(-1.20274e10 + 1.22674e10i) q^{16} -1.26774e10 q^{17} +(1.05446e10 - 1.58658e10i) q^{18} +5.87947e9i q^{19} +(-1.92383e11 + 8.08028e10i) q^{20} +2.23873e11i q^{21} +(-2.04829e11 - 1.36132e11i) q^{22} +5.43400e11 q^{23} +(1.20158e11 - 6.28369e11i) q^{24} -1.77143e12 q^{25} +(9.44589e11 + 6.27786e11i) q^{26} -1.03164e12i q^{27} +(8.42839e11 + 2.00671e12i) q^{28} +2.82120e12i q^{29} +(4.30099e12 - 6.47142e12i) q^{30} +8.42117e11 q^{31} +(-1.28864e12 - 6.08482e12i) q^{32} +9.15850e12 q^{33} +(2.54047e12 - 3.82248e12i) q^{34} +2.64355e13i q^{35} +(2.67077e12 + 6.35881e12i) q^{36} +6.17985e12i q^{37} +(-1.77278e12 - 1.17821e12i) q^{38} -4.22353e13 q^{39} +(1.41886e13 - 7.41996e13i) q^{40} -6.38887e13 q^{41} +(-6.75021e13 - 4.48628e13i) q^{42} +5.41782e13i q^{43} +(8.20931e13 - 3.44800e13i) q^{44} +8.37684e13i q^{45} +(-1.08894e14 + 1.63846e14i) q^{46} -3.89159e13 q^{47} +(1.65387e14 + 1.62152e14i) q^{48} +4.31135e13 q^{49} +(3.54984e14 - 5.34121e14i) q^{50} +1.70914e14i q^{51} +(-3.78580e14 + 1.59008e14i) q^{52} -5.92171e14i q^{53} +(3.11060e14 + 2.06734e14i) q^{54} +1.08146e15 q^{55} +(-7.73962e14 - 1.47999e14i) q^{56} +7.92660e13 q^{57} +(-8.50647e14 - 5.65351e14i) q^{58} -7.11422e14i q^{59} +(1.08937e15 + 2.59367e15i) q^{60} -9.01392e14i q^{61} +(-1.68755e14 + 2.53915e14i) q^{62} +8.73773e14 q^{63} +(2.09293e15 + 8.30811e14i) q^{64} -4.98726e15 q^{65} +(-1.83531e15 + 2.76147e15i) q^{66} +8.96950e14i q^{67} +(6.43458e14 + 1.53200e15i) q^{68} -7.32602e15i q^{69} +(-7.97084e15 - 5.29752e15i) q^{70} +8.49830e13 q^{71} +(-2.45252e15 - 4.68977e14i) q^{72} +1.01538e16 q^{73} +(-1.86335e15 - 1.23840e15i) q^{74} +2.38821e16i q^{75} +(7.10508e14 - 2.98421e14i) q^{76} -1.12805e16i q^{77} +(8.46370e15 - 1.27348e16i) q^{78} +3.99449e15 q^{79} +(1.95293e16 + 1.91473e16i) q^{80} -2.07037e16 q^{81} +(1.28029e16 - 1.92637e16i) q^{82} -2.19564e15i q^{83} +(2.70540e16 - 1.13630e16i) q^{84} +2.01820e16i q^{85} +(-1.63358e16 - 1.08570e16i) q^{86} +3.80349e16 q^{87} +(-6.05455e15 + 3.16623e16i) q^{88} -6.74113e16 q^{89} +(-2.52578e16 - 1.67867e16i) q^{90} +5.20212e16i q^{91} +(-2.75811e16 - 6.56674e16i) q^{92} -1.13533e16i q^{93} +(7.79850e15 - 1.17339e16i) q^{94} +9.35994e15 q^{95} +(-8.20345e16 + 1.73732e16i) q^{96} -1.67025e15 q^{97} +(-8.63968e15 + 1.29996e16i) q^{98} -3.57455e16i 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 $

$2$	−200.394	+	301.520i	−0.553515	+	0.832839i
$2$	−200.394	+	301.520i	−0.553515	+	0.832839i
$3$		−	13481.8i		−	1.18636i	−0.805068	−	0.593182i	$-0.797871\pi$
$3$		−	13481.8i		−	1.18636i	0.805068	−	0.593182i	$-0.202129\pi$
$4$	−50756.5	−	120846.i	−0.387241	−	0.921978i
$5$		−	1.59197e6i		−	1.82259i	−0.411750	−	0.911297i	$-0.635082\pi$
$5$		−	1.59197e6i		−	1.82259i	0.411750	−	0.911297i	$-0.364918\pi$
$6$	4.06504e6	+	2.70168e6i	0.988050	+	0.656671i
$7$	−1.66055e7			−1.08873			−0.544364	−	0.838849i	$-0.683229\pi$
$7$	−1.66055e7			−1.08873			−0.544364	+	0.838849i	$0.683229\pi$
$8$	4.66086e7	+	8.91263e6i	0.982204	+	0.187820i
$9$	−5.26193e7			−0.407459
$10$	4.80011e8	+	3.19021e8i	1.51793	+	1.00883i
$11$			6.79322e8i			0.955516i	0.878492	+	0.477758i	$0.158550\pi$
$11$			6.79322e8i			0.955516i	−0.878492	+	0.477758i	$0.841450\pi$
$12$	−1.62922e9	+	6.84290e8i	−1.09380	+	0.459409i
$13$		−	3.13276e9i		−	1.06514i	−0.846385	−	0.532572i	$-0.821225\pi$
$13$		−	3.13276e9i		−	1.06514i	0.846385	−	0.532572i	$-0.178775\pi$
$14$	3.32765e9	−	5.00690e9i	0.602628	−	0.906736i
$15$	−2.14627e10			−2.16226
$16$	−1.20274e10	+	1.22674e10i	−0.700088	+	0.714056i
$17$	−1.26774e10			−0.440771			−0.220385	−	0.975413i	$-0.570732\pi$
$17$	−1.26774e10			−0.440771			−0.220385	+	0.975413i	$0.570732\pi$
$18$	1.05446e10	−	1.58658e10i	0.225535	−	0.339348i
$19$			5.87947e9i			0.0794205i	0.999211	+	0.0397103i	$0.0126435\pi$
$19$			5.87947e9i			0.0794205i	−0.999211	+	0.0397103i	$0.987357\pi$
$20$	−1.92383e11	+	8.08028e10i	−1.68039	+	0.705784i
$21$			2.23873e11i			1.29163i
$22$	−2.04829e11	−	1.36132e11i	−0.795791	−	0.528893i
$23$	5.43400e11			1.44688			0.723441	−	0.690387i	$-0.242560\pi$
$23$	5.43400e11			1.44688			0.723441	+	0.690387i	$0.242560\pi$
$24$	1.20158e11	−	6.28369e11i	0.222822	−	1.16525i
$25$	−1.77143e12			−2.32185
$26$	9.44589e11	+	6.27786e11i	0.887094	+	0.589574i
$27$		−	1.03164e12i		−	0.702969i
$28$	8.42839e11	+	2.00671e12i	0.421601	+	1.00378i
$29$			2.82120e12i			1.04725i	0.851949	+	0.523625i	$0.175421\pi$
$29$			2.82120e12i			1.04725i	−0.851949	+	0.523625i	$0.824579\pi$
$30$	4.30099e12	−	6.47142e12i	1.19684	−	1.80081i
$31$	8.42117e11			0.177336			0.0886682	−	0.996061i	$-0.471739\pi$
$31$	8.42117e11			0.177336			0.0886682	+	0.996061i	$0.471739\pi$
$32$	−1.28864e12	−	6.08482e12i	−0.207184	−	0.978302i
$33$	9.15850e12			1.13359
$34$	2.54047e12	−	3.82248e12i	0.243974	−	0.367091i
$35$			2.64355e13i			1.98431i
$36$	2.67077e12	+	6.35881e12i	0.157785	+	0.375669i
$37$			6.17985e12i			0.289243i	0.989487	+	0.144622i	$0.0461965\pi$
$37$			6.17985e12i			0.289243i	−0.989487	+	0.144622i	$0.953804\pi$
$38$	−1.77278e12	−	1.17821e12i	−0.0661445	−	0.0439605i
$39$	−4.22353e13			−1.26365
$40$	1.41886e13	−	7.41996e13i	0.342319	−	1.79016i
$41$	−6.38887e13			−1.24957			−0.624786	−	0.780796i	$-0.714814\pi$
$41$	−6.38887e13			−1.24957			−0.624786	+	0.780796i	$0.714814\pi$
$42$	−6.75021e13	−	4.48628e13i	−1.07572	−	0.714936i
$43$			5.41782e13i			0.706875i	0.935458	+	0.353438i	$0.114987\pi$
$43$			5.41782e13i			0.706875i	−0.935458	+	0.353438i	$0.885013\pi$
$44$	8.20931e13	−	3.44800e13i	0.880965	−	0.370015i
$45$			8.37684e13i			0.742633i
$46$	−1.08894e14	+	1.63846e14i	−0.800871	+	1.20502i
$47$	−3.89159e13			−0.238394			−0.119197	−	0.992871i	$-0.538032\pi$
$47$	−3.89159e13			−0.238394			−0.119197	+	0.992871i	$0.538032\pi$
$48$	1.65387e14	+	1.62152e14i	0.847131	+	0.830559i
$49$	4.31135e13			0.185330
$50$	3.54984e14	−	5.34121e14i	1.28518	−	1.93373i
$51$			1.70914e14i			0.522915i
$52$	−3.78580e14	+	1.59008e14i	−0.982040	+	0.412468i
$53$		−	5.92171e14i		−	1.30648i	−0.757152	−	0.653239i	$-0.773410\pi$
$53$		−	5.92171e14i		−	1.30648i	0.757152	−	0.653239i	$-0.226590\pi$
$54$	3.11060e14	+	2.06734e14i	0.585460	+	0.389104i
$55$	1.08146e15			1.74152
$56$	−7.73962e14	−	1.47999e14i	−1.06935	−	0.204485i
$57$	7.92660e13			0.0942216
$58$	−8.50647e14	−	5.65351e14i	−0.872191	−	0.579669i
$59$		−	7.11422e14i		−	0.630791i	−0.948960	−	0.315395i	$-0.897863\pi$
$59$		−	7.11422e14i		−	0.630791i	0.948960	−	0.315395i	$-0.102137\pi$
$60$	1.08937e15	+	2.59367e15i	0.837316	+	1.99356i
$61$		−	9.01392e14i		−	0.602019i	−0.953621	−	0.301009i	$-0.902676\pi$
$61$		−	9.01392e14i		−	0.602019i	0.953621	−	0.301009i	$-0.0973236\pi$
$62$	−1.68755e14	+	2.53915e14i	−0.0981585	+	0.147693i
$63$	8.73773e14			0.443612
$64$	2.09293e15	+	8.30811e14i	0.929448	+	0.368954i
$65$	−4.98726e15			−1.94133
$66$	−1.83531e15	+	2.76147e15i	−0.627459	+	0.944097i
$67$			8.96950e14i			0.269856i	0.990855	+	0.134928i	$0.0430804\pi$
$67$			8.96950e14i			0.269856i	−0.990855	+	0.134928i	$0.956920\pi$
$68$	6.43458e14	+	1.53200e15i	0.170685	+	0.406381i
$69$		−	7.32602e15i		−	1.71653i
$70$	−7.97084e15	−	5.29752e15i	−1.65261	−	1.09835i
$71$	8.49830e13			0.0156184			0.00780919	−	0.999970i	$-0.497514\pi$
$71$	8.49830e13			0.0156184			0.00780919	+	0.999970i	$0.497514\pi$
$72$	−2.45252e15	−	4.68977e14i	−0.400208	−	0.0765288i
$73$	1.01538e16			1.47361			0.736806	−	0.676104i	$-0.236333\pi$
$73$	1.01538e16			1.47361			0.736806	+	0.676104i	$0.236333\pi$
$74$	−1.86335e15	−	1.23840e15i	−0.240893	−	0.160101i
$75$			2.38821e16i			2.75456i
$76$	7.10508e14	−	2.98421e14i	0.0732240	−	0.0307549i
$77$		−	1.12805e16i		−	1.04030i
$78$	8.46370e15	−	1.27348e16i	0.699449	−	1.05242i
$79$	3.99449e15			0.296232			0.148116	−	0.988970i	$-0.452679\pi$
$79$	3.99449e15			0.296232			0.148116	+	0.988970i	$0.452679\pi$
$80$	1.95293e16	+	1.91473e16i	1.30143	+	1.27598i
$81$	−2.07037e16			−1.24144
$82$	1.28029e16	−	1.92637e16i	0.691658	−	1.04069i
$83$		−	2.19564e15i		−	0.107003i	−0.998568	−	0.0535016i	$-0.982962\pi$
$83$		−	2.19564e15i		−	0.107003i	0.998568	−	0.0535016i	$-0.0170382\pi$
$84$	2.70540e16	−	1.13630e16i	1.19085	−	0.500172i
$85$			2.01820e16i			0.803346i
$86$	−1.63358e16	−	1.08570e16i	−0.588713	−	0.391266i
$87$	3.80349e16			1.24242
$88$	−6.05455e15	+	3.16623e16i	−0.179465	+	0.938511i
$89$	−6.74113e16			−1.81517			−0.907586	−	0.419866i	$-0.862077\pi$
$89$	−6.74113e16			−1.81517			−0.907586	+	0.419866i	$0.862077\pi$
$90$	−2.52578e16	−	1.67867e16i	−0.618493	−	0.411059i
$91$			5.20212e16i			1.15965i
$92$	−2.75811e16	−	6.56674e16i	−0.560292	−	1.33399i
$93$		−	1.13533e16i		−	0.210386i
$94$	7.79850e15	−	1.17339e16i	0.131955	−	0.198544i
$95$	9.35994e15			0.144751
$96$	−8.20345e16	+	1.73732e16i	−1.16062	+	0.245796i
$97$	−1.67025e15			−0.0216383			−0.0108191	−	0.999941i	$-0.503444\pi$
$97$	−1.67025e15			−0.0216383			−0.0108191	+	0.999941i	$0.503444\pi$
$98$	−8.63968e15	+	1.29996e16i	−0.102583	+	0.154350i
$99$		−	3.57455e16i		−	0.389334i
$100$	8.99116e16	+	2.14069e17i	0.899116	+	2.14069i
$101$		−	9.20491e16i		−	0.845840i	−0.906167	−	0.422920i	$-0.861005\pi$
$101$		−	9.20491e16i		−	0.845840i	0.906167	−	0.422920i	$-0.138995\pi$
$102$	−5.15339e16	−	3.42501e16i	−0.435504	−	0.289441i
$103$	−1.51701e17			−1.17998			−0.589988	−	0.807412i	$-0.700868\pi$
$103$	−1.51701e17			−1.17998			−0.589988	+	0.807412i	$0.700868\pi$
$104$	2.79211e16	−	1.46014e17i	0.200055	−	1.04619i
$105$	3.56399e17			2.35411
$106$	1.78551e17	+	1.18667e17i	1.08809	+	0.723156i
$107$			4.02158e15i			0.0226274i	0.999936	+	0.0113137i	$0.00360134\pi$
$107$			4.02158e15i			0.0226274i	−0.999936	+	0.0113137i	$0.996399\pi$
$108$	−1.24669e17	+	5.23624e16i	−0.648122	+	0.272219i
$109$		−	6.68975e16i		−	0.321577i	−0.986989	−	0.160788i	$-0.948596\pi$
$109$		−	6.68975e16i		−	0.321577i	0.986989	−	0.160788i	$-0.0514037\pi$
$110$	−2.16718e17	+	3.26082e17i	−0.963957	+	1.45040i
$111$	8.33156e16			0.343148
$112$	1.99722e17	−	2.03707e17i	0.762206	−	0.777414i
$113$	−1.74001e17			−0.615721			−0.307860	−	0.951432i	$-0.599613\pi$
$113$	−1.74001e17			−0.615721			−0.307860	+	0.951432i	$0.599613\pi$
$114$	−1.58844e16	+	2.39003e16i	−0.0521531	+	0.0784714i
$115$		−	8.65076e17i		−	2.63708i
$116$	3.40929e17	−	1.43194e17i	0.965542	−	0.405539i
$117$			1.64844e17i			0.434003i
$118$	2.14508e17	+	1.42565e17i	0.525347	+	0.349153i
$119$	2.10514e17			0.479880
$120$	−1.00035e18	−	1.91289e17i	−2.12378	−	0.406115i
$121$	4.39685e16			0.0869893
$122$	2.71788e17	+	1.80634e17i	0.501385	+	0.333227i
$123$			8.61336e17i			1.48245i
$124$	−4.27429e16	−	1.01766e17i	−0.0686720	−	0.163500i
$125$			1.60549e18i			2.40919i
$126$	−1.75099e17	+	2.63460e17i	−0.245546	+	0.369458i
$127$	−9.21764e17			−1.20861			−0.604307	−	0.796751i	$-0.706550\pi$
$127$	−9.21764e17			−1.20861			−0.604307	+	0.796751i	$0.706550\pi$
$128$	−6.69917e17	+	4.64571e17i	−0.821743	+	0.569858i
$129$	7.30421e17			0.838611
$130$	9.99417e17	−	1.50376e18i	1.07455	−	1.61681i
$131$		−	1.81435e18i		−	1.82774i	−0.406003	−	0.913872i	$-0.633078\pi$
$131$		−	1.81435e18i		−	1.82774i	0.406003	−	0.913872i	$-0.366922\pi$
$132$	−4.64853e17	−	1.10676e18i	−0.438973	−	1.04515i
$133$		−	9.76318e16i		−	0.0864674i
$134$	−2.70448e17	−	1.79743e17i	−0.224747	−	0.149370i
$135$	−1.64234e18			−1.28123
$136$	−5.90874e17	−	1.12989e17i	−0.432927	−	0.0827854i
$137$	−2.37631e18			−1.63598			−0.817989	−	0.575234i	$-0.804911\pi$
$137$	−2.37631e18			−1.63598			−0.817989	+	0.575234i	$0.804911\pi$
$138$	2.20894e18	+	1.46809e18i	1.42959	+	0.950124i
$139$			2.37238e18i			1.44397i	0.691908	+	0.721986i	$0.256770\pi$
$139$			2.37238e18i			1.44397i	−0.691908	+	0.721986i	$0.743230\pi$
$140$	3.19462e18	−	1.34177e18i	1.82949	−	0.768407i
$141$			5.24657e17i			0.282822i
$142$	−1.70301e16	+	2.56241e16i	−0.00864501	+	0.0130076i
$143$	2.12815e18			1.01776
$144$	6.32875e17	−	6.45502e17i	0.285257	−	0.290949i
$145$	4.49126e18			1.90871
$146$	−2.03476e18	+	3.06157e18i	−0.815667	+	1.22728i
$147$		−	5.81248e17i		−	0.219869i
$148$	7.46807e17	−	3.13668e17i	0.266676	−	0.112007i
$149$		−	4.84759e17i		−	0.163472i	−0.996654	−	0.0817359i	$-0.973954\pi$
$149$		−	4.84759e17i		−	0.163472i	0.996654	−	0.0817359i	$-0.0260464\pi$
$150$	−7.20093e18	−	4.78583e18i	−2.29410	−	1.52469i
$151$	3.48930e18			1.05059			0.525296	−	0.850920i	$-0.323955\pi$
$151$	3.48930e18			1.05059			0.525296	+	0.850920i	$0.323955\pi$
$152$	−5.24015e16	+	2.74034e17i	−0.0149167	+	0.0780071i
$153$	6.67074e17			0.179596
$154$	3.40130e18	+	2.26055e18i	0.866400	+	0.575821i
$155$		−	1.34063e18i		−	0.323212i
$156$	2.14372e18	+	5.10395e18i	0.489337	+	1.16506i
$157$		−	5.04719e18i		−	1.09120i	−0.838047	−	0.545598i	$-0.816303\pi$
$157$		−	5.04719e18i		−	1.09120i	0.838047	−	0.545598i	$-0.183697\pi$
$158$	−8.00472e17	+	1.20442e18i	−0.163969	+	0.246713i
$159$	−7.98354e18			−1.54996
$160$	−9.68685e18	+	2.05148e18i	−1.78305	+	0.377613i
$161$	−9.02345e18			−1.57526
$162$	4.14889e18	−	6.24256e18i	0.687154	−	1.03392i
$163$			4.62747e18i			0.727359i	0.931524	+	0.363680i	$0.118480\pi$
$163$			4.62747e18i			0.727359i	−0.931524	+	0.363680i	$0.881520\pi$
$164$	3.24277e18	+	7.72067e18i	0.483886	+	1.15208i
$165$		−	1.45801e19i		−	2.06607i
$166$	6.62028e17	+	4.39993e17i	0.0891164	+	0.0592279i
$167$	6.00884e18			0.768600			0.384300	−	0.923208i	$-0.374443\pi$
$167$	6.00884e18			0.768600			0.384300	+	0.923208i	$0.374443\pi$
$168$	−1.99530e18	+	1.04344e19i	−0.242593	+	1.26864i
$169$	−1.16377e18			−0.134533
$170$	−6.08527e18	−	4.04435e18i	−0.669058	−	0.444665i
$171$		−	3.09374e17i		−	0.0323606i
$172$	6.54720e18	−	2.74990e18i	0.651724	−	0.273731i
$173$			1.31182e19i			1.24304i	0.783400	+	0.621518i	$0.213484\pi$
$173$			1.31182e19i			1.24304i	−0.783400	+	0.621518i	$0.786516\pi$
$174$	−7.62196e18	+	1.14683e19i	−0.687699	+	1.03474i
$175$	2.94155e19			2.52786
$176$	−8.33351e18	−	8.17050e18i	−0.682292	−	0.668946i
$177$	−9.59127e18			−0.748348
$178$	1.35088e19	−	2.03259e19i	1.00473	−	1.51175i
$179$			1.01351e19i			0.718749i	0.933193	+	0.359375i	$0.117010\pi$
$179$			1.01351e19i			0.718749i	−0.933193	+	0.359375i	$0.882990\pi$
$180$	1.01230e19	−	4.25179e18i	0.684691	−	0.287578i
$181$		−	5.37640e18i		−	0.346916i	−0.984841	−	0.173458i	$-0.944506\pi$
$181$		−	5.37640e18i		−	0.346916i	0.984841	−	0.173458i	$-0.0554940\pi$
$182$	−1.56854e19	−	1.04247e19i	−0.965805	−	0.641886i
$183$	−1.21524e19			−0.714213
$184$	2.53271e19	+	4.84312e18i	1.42113	+	0.271753i
$185$	9.83814e18			0.527173
$186$	3.42324e18	+	2.27513e18i	0.175217	+	0.116452i
$187$		−	8.61201e18i		−	0.421164i
$188$	1.97523e18	+	4.70281e18i	0.0923159	+	0.219794i
$189$			1.71309e19i			0.765343i
$190$	−1.87568e18	+	2.82221e18i	−0.0801221	+	0.120555i
$191$	−3.15290e19			−1.28803			−0.644016	−	0.765012i	$-0.722733\pi$
$191$	−3.15290e19			−1.28803			−0.644016	+	0.765012i	$0.722733\pi$
$192$	1.12008e19	−	2.82165e19i	0.437714	−	1.10266i
$193$	5.88587e18			0.220077			0.110038	−	0.993927i	$-0.464903\pi$
$193$	5.88587e18			0.220077			0.110038	+	0.993927i	$0.464903\pi$
$194$	3.34709e17	−	5.03615e17i	0.0119771	−	0.0180212i
$195$			6.72373e19i			2.30312i
$196$	−2.18829e18	−	5.21007e18i	−0.0717675	−	0.170870i
$197$		−	4.95627e19i		−	1.55665i	−0.627859	−	0.778327i	$-0.716069\pi$
$197$		−	4.95627e19i		−	1.55665i	0.627859	−	0.778327i	$-0.283931\pi$
$198$	1.07780e19	+	7.16318e18i	0.324252	+	0.215502i
$199$	−2.52157e19			−0.726810			−0.363405	−	0.931631i	$-0.618386\pi$
$199$	−2.52157e19			−0.726810			−0.363405	+	0.931631i	$0.618386\pi$
$200$	−8.25639e19	−	1.57881e19i	−2.28053	−	0.436089i
$201$	1.20925e19			0.320148
$202$	2.77546e19	+	1.84461e19i	0.704448	+	0.468185i
$203$		−	4.68475e19i		−	1.14017i
$204$	2.06542e19	−	8.67499e18i	0.482116	−	0.202494i
$205$			1.01709e20i			2.27746i
$206$	3.04001e19	−	4.57410e19i	0.653135	−	0.982731i
$207$	−2.85933e19			−0.589545
$208$	3.84308e19	+	3.76790e19i	0.760573	+	0.745695i
$209$	−3.99405e18			−0.0758876
$210$	−7.14202e19	+	1.07461e20i	−1.30304	+	1.96060i
$211$		−	9.05451e19i		−	1.58659i	−0.608839	−	0.793294i	$-0.708364\pi$
$211$		−	9.05451e19i		−	1.58659i	0.608839	−	0.793294i	$-0.291636\pi$
$212$	−7.15612e19	+	3.00565e19i	−1.20454	+	0.505922i
$213$		−	1.14573e18i		−	0.0185291i
$214$	−1.21259e18	−	8.05901e17i	−0.0188450	−	0.0125246i
$215$	8.62501e19			1.28835
$216$	9.19462e18	−	4.80833e19i	0.132031	−	0.690459i
$217$	−1.39838e19			−0.193071
$218$	2.01709e19	+	1.34059e19i	0.267822	+	0.177998i
$219$		−	1.36891e20i		−	1.74824i
$220$	−5.48912e19	−	1.30690e20i	−0.674388	−	1.60564i
$221$			3.97151e19i			0.469485i
$222$	−1.66959e19	+	2.51213e19i	−0.189938	+	0.285787i
$223$	1.01974e20			1.11660			0.558302	−	0.829637i	$-0.311453\pi$
$223$	1.01974e20			1.11660			0.558302	+	0.829637i	$0.311453\pi$
$224$	2.13986e19	+	1.01042e20i	0.225567	+	1.06511i
$225$	9.32115e19			0.946058
$226$	3.48687e19	−	5.24646e19i	0.340811	−	0.512796i
$227$			4.34756e18i			0.0409285i	0.999791	+	0.0204643i	$0.00651443\pi$
$227$			4.34756e18i			0.0409285i	−0.999791	+	0.0204643i	$0.993486\pi$
$228$	−4.02326e18	−	9.57894e18i	−0.0364865	−	0.0868703i
$229$		−	5.56510e19i		−	0.486263i	−0.969993	−	0.243132i	$-0.921825\pi$
$229$		−	5.56510e19i		−	0.486263i	0.969993	−	0.243132i	$-0.0781747\pi$
$230$	2.60838e20	+	1.73356e20i	2.19626	+	1.45966i
$231$	−1.52082e20			−1.23417
$232$	−2.51443e19	+	1.31492e20i	−0.196694	+	1.02861i
$233$	8.39273e19			0.632963			0.316481	−	0.948599i	$-0.397499\pi$
$233$	8.39273e19			0.632963			0.316481	+	0.948599i	$0.397499\pi$
$234$	−4.97037e19	−	3.30337e19i	−0.361455	−	0.240227i
$235$			6.19529e19i			0.434495i
$236$	−8.59722e19	+	3.61093e19i	−0.581576	+	0.244268i
$237$		−	5.38530e19i		−	0.351438i
$238$	−4.21858e19	+	6.34743e19i	−0.265621	+	0.399663i
$239$	−2.51863e20			−1.53032			−0.765158	−	0.643842i	$-0.777339\pi$
$239$	−2.51863e20			−1.53032			−0.765158	+	0.643842i	$0.777339\pi$
$240$	2.58141e20	−	2.63291e20i	1.51377	−	1.54397i
$241$	−5.48650e19			−0.310563			−0.155282	−	0.987870i	$-0.549629\pi$
$241$	−5.48650e19			−0.310563			−0.155282	+	0.987870i	$0.549629\pi$
$242$	−8.81102e18	+	1.32574e19i	−0.0481499	+	0.0724481i
$243$			1.45897e20i			0.769826i
$244$	−1.08929e20	+	4.57515e19i	−0.555048	+	0.233127i
$245$		−	6.86353e19i		−	0.337782i
$246$	−2.59710e20	−	1.72607e20i	−1.23464	−	0.820558i
$247$	1.84190e19			0.0845943
$248$	3.92499e19	+	7.50548e18i	0.174181	+	0.0333073i
$249$	−2.96012e19			−0.126945
$250$	−4.84086e20	−	3.21730e20i	−2.00647	−	1.33353i
$251$			2.36559e20i			0.947792i	0.880581	+	0.473896i	$0.157153\pi$
$251$			2.36559e20i			0.947792i	−0.880581	+	0.473896i	$0.842847\pi$
$252$	−4.43496e19	−	1.05592e20i	−0.171785	−	0.409001i
$253$			3.69143e20i			1.38252i
$254$	1.84716e20	−	2.77930e20i	0.668987	−	1.00658i
$255$	2.72090e20			0.953061
$256$	−5.83000e18	−	2.95090e20i	−0.0197528	−	0.999805i
$257$	−1.56566e20			−0.513177			−0.256588	−	0.966521i	$-0.582598\pi$
$257$	−1.56566e20			−0.513177			−0.256588	+	0.966521i	$0.582598\pi$
$258$	−1.46372e20	+	2.20237e20i	−0.464184	+	0.698428i
$259$		−	1.02620e20i		−	0.314907i
$260$	2.53136e20	+	6.02688e20i	0.751762	+	1.78986i
$261$		−	1.48450e20i		−	0.426712i
$262$	5.47063e20	+	3.63585e20i	1.52222	+	1.01168i
$263$	4.99732e20			1.34621			0.673106	−	0.739546i	$-0.264960\pi$
$263$	4.99732e20			1.34621			0.673106	+	0.739546i	$0.264960\pi$
$264$	4.26865e20	+	8.16263e19i	1.11342	+	0.212910i
$265$	−9.42718e20			−2.38118
$266$	2.94379e19	+	1.95648e19i	0.0720134	+	0.0478610i
$267$			9.08827e20i			2.15345i
$268$	1.08392e20	−	4.55261e19i	0.248802	−	0.104500i
$269$		−	4.92718e20i		−	1.09573i	−0.836566	−	0.547865i	$-0.815441\pi$
$269$		−	4.92718e20i		−	1.09573i	0.836566	−	0.547865i	$-0.184559\pi$
$270$	3.29115e20	−	4.95198e20i	0.709179	−	1.06706i
$271$	−1.88474e20			−0.393561			−0.196780	−	0.980448i	$-0.563049\pi$
$271$	−1.88474e20			−0.393561			−0.196780	+	0.980448i	$0.563049\pi$
$272$	1.52476e20	−	1.55518e20i	0.308579	−	0.314735i
$273$	7.01340e20			1.37577
$274$	4.76197e20	−	7.16504e20i	0.905539	−	1.36251i
$275$		−	1.20337e21i		−	2.21856i
$276$	−8.85317e20	+	3.71843e20i	−1.58260	+	0.664710i
$277$		−	4.10225e20i		−	0.711122i	−0.934653	−	0.355561i	$-0.884290\pi$
$277$		−	4.10225e20i		−	0.711122i	0.934653	−	0.355561i	$-0.115710\pi$
$278$	−7.15320e20	−	4.75411e20i	−1.20260	−	0.799260i
$279$	−4.43116e19			−0.0722574
$280$	−2.35610e20	+	1.23212e21i	−0.372692	+	1.94900i
$281$	5.23813e20			0.803845			0.401922	−	0.915674i	$-0.368342\pi$
$281$	5.23813e20			0.803845			0.401922	+	0.915674i	$0.368342\pi$
$282$	−1.58194e20	−	1.05138e20i	−0.235545	−	0.156546i
$283$			8.12727e20i			1.17425i	0.809497	+	0.587124i	$0.199740\pi$
$283$			8.12727e20i			1.17425i	−0.809497	+	0.587124i	$0.800260\pi$
$284$	−4.31344e18	−	1.02698e19i	−0.00604808	−	0.0143998i
$285$		−	1.26189e20i		−	0.171728i
$286$	−4.26469e20	+	6.41680e20i	−0.563347	+	0.847632i
$287$	1.06091e21			1.36045
$288$	6.78074e19	+	3.20179e20i	0.0844191	+	0.398618i
$289$	−6.66525e20			−0.805721
$290$	−9.00022e20	+	1.35421e21i	−1.05650	+	1.58965i
$291$			2.25181e19i			0.0256709i
$292$	−5.15370e20	−	1.22704e21i	−0.570644	−	1.35864i
$293$			1.33596e20i			0.143687i	0.997416	+	0.0718436i	$0.0228882\pi$
$293$			1.33596e20i			0.143687i	−0.997416	+	0.0718436i	$0.977112\pi$
$294$	1.75258e20	+	1.16479e20i	0.183115	+	0.121701i
$295$	−1.13256e21			−1.14968
$296$	−5.50787e19	+	2.88034e20i	−0.0543255	+	0.284096i
$297$	7.00816e20			0.671698
$298$	1.46165e20	+	9.71428e19i	0.136146	+	0.0904841i
$299$		−	1.70234e21i		−	1.54114i
$300$	2.88605e21	−	1.21217e21i	2.53964	−	1.06668i
$301$		−	8.99659e20i		−	0.769596i
$302$	−6.99234e20	+	1.05209e21i	−0.581519	+	0.874974i
$303$	−1.24099e21			−1.00347
$304$	−7.21258e19	−	7.07149e19i	−0.0567107	−	0.0556014i
$305$	−1.43499e21			−1.09724
$306$	−1.33678e20	+	2.01136e20i	−0.0994092	+	0.149575i
$307$			1.20452e21i			0.871243i	0.900130	+	0.435622i	$0.143471\pi$
$307$			1.20452e21i			0.871243i	−0.900130	+	0.435622i	$0.856529\pi$
$308$	−1.36320e21	+	5.72559e20i	−0.959132	+	0.402846i
$309$			2.04521e21i			1.39988i
$310$	4.04225e20	+	2.68653e20i	0.269184	+	0.178903i
$311$	1.25790e21			0.815050			0.407525	−	0.913194i	$-0.366392\pi$
$311$	1.25790e21			0.815050			0.407525	+	0.913194i	$0.366392\pi$
$312$	−1.96853e21	−	3.76428e20i	−1.24116	−	0.237338i
$313$	2.89626e21			1.77709			0.888546	−	0.458787i	$-0.151716\pi$
$313$	2.89626e21			1.77709			0.888546	+	0.458787i	$0.151716\pi$
$314$	1.52183e21	+	1.01143e21i	0.908790	+	0.603993i
$315$		−	1.39102e21i		−	0.808525i
$316$	−2.02746e20	−	4.82717e20i	−0.114713	−	0.273119i
$317$		−	5.55170e20i		−	0.305789i	−0.988242	−	0.152895i	$-0.951140\pi$
$317$		−	5.55170e20i		−	0.305789i	0.988242	−	0.152895i	$-0.0488595\pi$
$318$	1.59985e21	−	2.40720e21i	0.857926	−	1.29087i
$319$	−1.91650e21			−1.00066
$320$	1.32263e21	−	3.33188e21i	0.672454	−	1.69401i
$321$	5.42182e19			0.0268443
$322$	1.80824e21	−	2.72075e21i	0.871931	−	1.31194i
$323$		−	7.45362e19i		−	0.0350063i
$324$	1.05085e21	+	2.50194e21i	0.480735	+	1.14458i
$325$			5.54946e21i			2.47310i
$326$	−1.39527e21	−	9.27317e20i	−0.605773	−	0.402605i
$327$	−9.01900e20			−0.381507
$328$	−2.97777e21	−	5.69416e20i	−1.22733	−	0.234694i
$329$	6.46219e20			0.259546
$330$	4.39618e21	+	2.92176e21i	1.72071	+	1.14360i
$331$		−	8.74883e20i		−	0.333743i	−0.985979	−	0.166871i	$-0.946634\pi$
$331$		−	8.74883e20i		−	0.333743i	0.985979	−	0.166871i	$-0.0533665\pi$
$332$	−2.65333e20	+	1.11443e20i	−0.0986547	+	0.0414361i
$333$		−	3.25180e20i		−	0.117855i
$334$	−1.20414e21	+	1.81178e21i	−0.425432	+	0.640120i
$335$	1.42792e21			0.491839
$336$	−2.74634e21	−	2.69261e21i	−0.922295	−	0.904254i
$337$	1.38557e21			0.453706			0.226853	−	0.973929i	$-0.427156\pi$
$337$	1.38557e21			0.453706			0.226853	+	0.973929i	$0.427156\pi$
$338$	2.33212e20	−	3.50899e20i	0.0744661	−	0.112044i
$339$			2.34584e21i			0.730469i
$340$	2.43890e21	−	1.02437e21i	0.740668	−	0.311089i
$341$			5.72069e20i			0.169448i
$342$	9.32824e19	+	6.19967e19i	0.0269512	+	0.0179121i
$343$	3.14703e21			0.886954
$344$	−4.82870e20	+	2.52517e21i	−0.132765	+	0.694296i
$345$	−1.16628e22			−3.12853
$346$	−3.95541e21	−	2.62882e21i	−1.03525	−	0.688040i
$347$		−	3.85582e21i		−	0.984727i	−0.870390	−	0.492364i	$-0.836133\pi$
$347$		−	3.85582e21i		−	0.984727i	0.870390	−	0.492364i	$-0.163867\pi$
$348$	−1.93052e21	−	4.59635e21i	−0.481116	−	1.14548i
$349$			1.47067e20i			0.0357684i	0.999840	+	0.0178842i	$0.00569302\pi$
$349$			1.47067e20i			0.0357684i	−0.999840	+	0.0178842i	$0.994307\pi$
$350$	−5.89470e21	+	8.86937e21i	−1.39921	+	2.10530i
$351$	−3.23188e21			−0.748764
$352$	4.13355e21	−	8.75401e20i	0.934783	−	0.197968i
$353$	5.92536e21			1.30807			0.654033	−	0.756466i	$-0.273076\pi$
$353$	5.92536e21			1.30807			0.654033	+	0.756466i	$0.273076\pi$
$354$	1.92203e21	−	2.89196e21i	0.414222	−	0.623253i
$355$		−	1.35290e20i		−	0.0284660i
$356$	3.42156e21	+	8.14636e21i	0.702910	+	1.67355i
$357$		−	2.83812e21i		−	0.569312i
$358$	−3.05593e21	−	2.03101e21i	−0.598602	−	0.397839i
$359$	−7.67655e21			−1.46846			−0.734232	−	0.678899i	$-0.762457\pi$
$359$	−7.67655e21			−1.46846			−0.734232	+	0.678899i	$0.762457\pi$
$360$	−7.46597e20	+	3.90433e21i	−0.139481	+	0.729416i
$361$	5.44582e21			0.993692
$362$	1.62109e21	+	1.07740e21i	0.288925	+	0.192023i
$363$		−	5.92775e20i		−	0.103201i
$364$	6.28653e21	−	2.64041e21i	1.06918	−	0.449066i
$365$		−	1.61645e22i		−	2.68580i
$366$	2.43527e21	−	3.66419e21i	0.395328	−	0.594825i
$367$	1.69701e21			0.269168			0.134584	−	0.990902i	$-0.457030\pi$
$367$	1.69701e21			0.269168			0.134584	+	0.990902i	$0.457030\pi$
$368$	−6.53570e21	+	6.66610e21i	−1.01294	+	1.03315i
$369$	3.36178e21			0.509150
$370$	−1.97150e21	+	2.96639e21i	−0.291798	+	0.439050i
$371$			9.83331e21i			1.42240i
$372$	−1.37199e21	+	5.76252e20i	−0.193971	+	0.0814700i
$373$		−	2.45745e21i		−	0.339594i	−0.985479	−	0.169797i	$-0.945689\pi$
$373$		−	2.45745e21i		−	0.339594i	0.985479	−	0.169797i	$-0.0543113\pi$
$374$	2.59669e21	+	1.72580e21i	0.350762	+	0.233121i
$375$	2.16449e22			2.85818
$376$	−1.81382e21	−	3.46843e20i	−0.234151	−	0.0447750i
$377$	8.83814e21			1.11547
$378$	−5.16532e21	−	3.43294e21i	−0.637407	−	0.423629i
$379$			5.05987e21i			0.610529i	0.952268	+	0.305264i	$0.0987448\pi$
$379$			5.05987e21i			0.610529i	−0.952268	+	0.305264i	$0.901255\pi$
$380$	−4.75078e20	−	1.13111e21i	−0.0560537	−	0.133458i
$381$			1.24271e22i			1.43386i
$382$	6.31822e21	−	9.50662e21i	0.712945	−	1.07272i
$383$	2.16009e21			0.238387			0.119194	−	0.992871i	$-0.461969\pi$
$383$	2.16009e21			0.238387			0.119194	+	0.992871i	$0.461969\pi$
$384$	6.26326e21	+	9.03170e21i	0.676059	+	0.974886i
$385$	−1.79582e22			−1.89604
$386$	−1.17949e21	+	1.77471e21i	−0.121816	+	0.183288i
$387$		−	2.85082e21i		−	0.288023i
$388$	8.47762e19	+	2.01843e20i	0.00837923	+	0.0199500i
$389$		−	1.57073e22i		−	1.51891i	−0.650562	−	0.759453i	$-0.725467\pi$
$389$		−	1.57073e22i		−	1.51891i	0.650562	−	0.759453i	$-0.274533\pi$
$390$	−2.02734e22	−	1.34740e22i	−1.91813	−	1.27481i
$391$	−6.88887e21			−0.637743
$392$	2.00946e21	+	3.84254e20i	0.182032	+	0.0348086i
$393$	−2.44607e22			−2.16837
$394$	1.49441e22	+	9.93207e21i	1.29644	+	0.861632i
$395$		−	6.35911e21i		−	0.539910i
$396$	−4.31968e21	+	1.81432e21i	−0.358957	+	0.150766i
$397$			1.27818e21i			0.103961i	0.998648	+	0.0519807i	$0.0165534\pi$
$397$			1.27818e21i			0.103961i	−0.998648	+	0.0519807i	$0.983447\pi$
$398$	5.05308e21	−	7.60305e21i	0.402300	−	0.605315i
$399$	−1.31625e21			−0.102582
$400$	2.13057e22	−	2.17308e22i	1.62550	−	1.65793i
$401$	−1.13639e22			−0.848793			−0.424396	−	0.905477i	$-0.639514\pi$
$401$	−1.13639e22			−0.848793			−0.424396	+	0.905477i	$0.639514\pi$
$402$	−2.42327e21	+	3.64614e21i	−0.177207	+	0.266632i
$403$		−	2.63815e21i		−	0.188889i
$404$	−1.11237e22	+	4.67209e21i	−0.779846	+	0.327544i
$405$			3.29596e22i			2.26263i
$406$	1.41255e22	+	9.38796e21i	0.949579	+	0.631103i
$407$	−4.19811e21			−0.276377
$408$	−1.52329e21	+	7.96606e21i	−0.0982136	+	0.513609i
$409$	1.19704e22			0.755891			0.377945	−	0.925828i	$-0.376631\pi$
$409$	1.19704e22			0.755891			0.377945	+	0.925828i	$0.376631\pi$
$410$	−3.06673e22	−	2.03819e22i	−1.89676	−	1.26061i
$411$			3.20369e22i			1.94087i
$412$	7.69984e21	+	1.83324e22i	0.456936	+	1.08791i
$413$			1.18136e22i			0.686760i
$414$	5.72993e21	−	8.62146e21i	0.326322	−	0.490996i
$415$	−3.49539e21			−0.195023
$416$	−1.90623e22	+	4.03700e21i	−1.04203	+	0.220681i
$417$	3.19840e22			1.71308
$418$	8.00385e20	−	1.20429e21i	0.0420049	−	0.0632021i
$419$		−	4.18757e21i		−	0.215349i	−0.994186	−	0.107674i	$-0.965660\pi$
$419$		−	4.18757e21i		−	0.215349i	0.994186	−	0.107674i	$-0.0343404\pi$
$420$	−1.80896e22	−	4.30692e22i	−0.911610	−	2.17044i
$421$		−	2.74877e22i		−	1.35750i	−0.734368	−	0.678751i	$-0.762521\pi$
$421$		−	2.74877e22i		−	1.35750i	0.734368	−	0.678751i	$-0.237479\pi$
$422$	2.73011e22	+	1.81447e22i	1.32137	+	0.878201i
$423$	2.04773e21			0.0971357
$424$	5.27780e21	−	2.76003e22i	0.245382	−	1.28323i
$425$	2.24571e22			1.02340
$426$	3.45459e20	+	2.29596e20i	0.0154317	+	0.0102561i
$427$			1.49681e22i			0.655435i
$428$	4.85990e20	−	2.04121e20i	0.0208620	−	0.00876227i
$429$		−	2.86914e22i		−	1.20744i
$430$	−1.72840e22	+	2.60061e22i	−0.713120	+	1.07299i
$431$	−4.37127e22			−1.76828			−0.884139	−	0.467224i	$-0.845254\pi$
$431$	−4.37127e22			−1.76828			−0.884139	+	0.467224i	$0.845254\pi$
$432$	1.26555e22	+	1.24080e22i	0.501959	+	0.492140i
$433$	6.06049e21			0.235701			0.117850	−	0.993031i	$-0.462400\pi$
$433$	6.06049e21			0.235701			0.117850	+	0.993031i	$0.462400\pi$
$434$	2.80227e21	−	4.21640e21i	0.106868	−	0.160797i
$435$		−	6.05504e22i		−	2.26443i
$436$	−8.08426e21	+	3.39548e21i	−0.296487	+	0.124528i
$437$			3.19490e21i			0.114912i
$438$	4.12755e22	+	2.74322e22i	1.45600	+	0.967678i
$439$	1.64448e22			0.568959			0.284480	−	0.958682i	$-0.408179\pi$
$439$	1.64448e22			0.568959			0.284480	+	0.958682i	$0.408179\pi$
$440$	5.04054e22	+	9.63866e21i	1.71052	+	0.327091i
$441$	−2.26860e21			−0.0755145
$442$	−1.19749e22	−	7.95867e21i	−0.391005	−	0.259867i
$443$		−	3.31744e22i		−	1.06260i	−0.847182	−	0.531302i	$-0.821703\pi$
$443$		−	3.31744e22i		−	1.06260i	0.847182	−	0.531302i	$-0.178297\pi$
$444$	−4.22881e21	−	1.00683e22i	−0.132881	−	0.316375i
$445$			1.07317e23i			3.30832i
$446$	−2.04350e22	+	3.07473e22i	−0.618058	+	0.929952i
$447$	−6.53544e21			−0.193937
$448$	−3.47542e22	−	1.37961e22i	−1.01192	−	0.401691i
$449$	−2.57130e22			−0.734615			−0.367307	−	0.930100i	$-0.619720\pi$
$449$	−2.57130e22			−0.734615			−0.367307	+	0.930100i	$0.619720\pi$
$450$	−1.86790e22	+	2.81051e22i	−0.523658	+	0.787914i
$451$		−	4.34010e22i		−	1.19399i
$452$	8.83166e21	+	2.10272e22i	0.238433	+	0.567681i
$453$		−	4.70421e22i		−	1.24638i
$454$	−1.31088e21	−	8.71226e20i	−0.0340869	−	0.0226546i
$455$	8.28161e22			2.11358
$456$	3.69448e21	+	7.06468e20i	0.0925448	+	0.0176967i
$457$	2.71668e22			0.667960			0.333980	−	0.942580i	$-0.391608\pi$
$457$	2.71668e22			0.667960			0.333980	+	0.942580i	$0.391608\pi$
$458$	1.67799e22	+	1.11521e22i	0.404979	+	0.269154i
$459$			1.30785e22i			0.309848i
$460$	−1.04541e23	+	4.39082e22i	−2.43133	+	1.02119i
$461$		−	1.14852e22i		−	0.262230i	−0.991367	−	0.131115i	$-0.958144\pi$
$461$		−	1.14852e22i		−	0.262230i	0.991367	−	0.131115i	$-0.0418557\pi$
$462$	3.04763e22	−	4.58557e22i	0.683133	−	1.02787i
$463$	−4.81356e22			−1.05932			−0.529661	−	0.848209i	$-0.677681\pi$
$463$	−4.81356e22			−1.05932			−0.529661	+	0.848209i	$0.677681\pi$
$464$	−3.46088e22	−	3.39318e22i	−0.747796	−	0.733168i
$465$	−1.80741e22			−0.383447
$466$	−1.68185e22	+	2.53058e22i	−0.350355	+	0.527156i
$467$			1.45571e22i			0.297770i	0.988855	+	0.148885i	$0.0475684\pi$
$467$			1.45571e22i			0.297770i	−0.988855	+	0.148885i	$0.952432\pi$
$468$	1.99206e22	−	8.36689e21i	0.400141	−	0.168064i
$469$		−	1.48943e22i		−	0.293800i
$470$	−1.86800e22	−	1.24150e22i	−0.361864	−	0.240500i
$471$	−6.80453e22			−1.29455
$472$	6.34064e21	−	3.31584e22i	0.118475	−	0.619565i
$473$	−3.68045e22			−0.675431
$474$	1.62378e22	+	1.07918e22i	0.292692	+	0.194527i
$475$		−	1.04151e22i		−	0.184402i
$476$	−1.06850e22	−	2.54397e22i	−0.185829	−	0.442439i
$477$			3.11596e22i			0.532336i
$478$	5.04717e22	−	7.59416e22i	0.847054	−	1.27451i
$479$	4.36285e22			0.719314			0.359657	−	0.933085i	$-0.382894\pi$
$479$	4.36285e22			0.719314			0.359657	+	0.933085i	$0.382894\pi$
$480$	2.76576e22	+	1.30596e23i	0.447986	+	2.11534i
$481$	1.93600e22			0.308086
$482$	1.09946e22	−	1.65429e22i	0.171902	−	0.258649i
$483$			1.21652e23i			1.86883i
$484$	−2.23169e21	−	5.31340e21i	−0.0336859	−	0.0802022i
$485$			2.65899e21i			0.0394378i
$486$	−4.39908e22	−	2.92368e22i	−0.641141	−	0.426111i
$487$	1.77302e22			0.253932			0.126966	−	0.991907i	$-0.459476\pi$
$487$	1.77302e22			0.253932			0.126966	+	0.991907i	$0.459476\pi$
$488$	8.03377e21	−	4.20127e22i	0.113071	−	0.591305i
$489$	6.23867e22			0.862913
$490$	2.06949e22	+	1.37541e22i	0.281318	+	0.186967i
$491$			3.92177e20i			0.00523949i	0.999997	+	0.00261975i	$0.000833892\pi$
$491$			3.92177e20i			0.00523949i	−0.999997	+	0.00261975i	$0.999166\pi$
$492$	1.04089e23	−	4.37184e22i	1.36678	−	0.574065i
$493$		−	3.57653e22i		−	0.461598i
$494$	−3.69105e21	+	5.55369e21i	−0.0468243	+	0.0704534i
$495$	−5.69057e22			−0.709597
$496$	−1.01285e22	+	1.03306e22i	−0.124151	+	0.126628i
$497$	−1.41119e21			−0.0170042
$498$	5.93190e21	−	8.92535e21i	0.0702659	−	0.105725i
$499$			3.85769e22i			0.449234i	0.974447	+	0.224617i	$0.0721130\pi$
$499$			3.85769e22i			0.449234i	−0.974447	+	0.224617i	$0.927887\pi$
$500$	1.94016e23	−	8.14889e22i	2.22122	−	0.932939i
$501$		−	8.10101e22i		−	0.911840i
$502$	−7.13273e22	−	4.74050e22i	−0.789358	−	0.524618i
$503$	1.70508e23			1.85531			0.927656	−	0.373435i	$-0.121820\pi$
$503$	1.70508e23			1.85531			0.927656	+	0.373435i	$0.121820\pi$
$504$	4.07253e22	+	7.78761e21i	0.435718	+	0.0833191i
$505$	−1.46539e23			−1.54162
$506$	−1.11304e23	−	7.39741e22i	−1.15141	−	0.765245i
$507$			1.56897e22i			0.159605i
$508$	4.67855e22	+	1.11391e23i	0.468026	+	1.11432i
$509$			1.15058e23i			1.13192i	0.824434	+	0.565959i	$0.191494\pi$
$509$			1.15058e23i			1.13192i	−0.824434	+	0.565959i	$0.808506\pi$
$510$	−5.45252e22	+	8.20405e22i	−0.527534	+	0.793746i
$511$	−1.68609e23			−1.60436
$512$	9.01439e22	+	5.73765e22i	0.843610	+	0.536957i
$513$	6.06550e21			0.0558302
$514$	3.13750e22	−	4.72079e22i	0.284051	−	0.427394i
$515$			2.41504e23i			2.15062i
$516$	−3.70736e22	−	8.82681e22i	−0.324745	−	0.773182i
$517$		−	2.64364e22i		−	0.227789i
$518$	3.09419e22	+	2.05644e22i	0.262267	+	0.174306i
$519$	1.76858e23			1.47469
$520$	−2.32449e23	−	4.44496e22i	−1.90678	−	0.364619i
$521$	−1.62883e23			−1.31448			−0.657241	−	0.753680i	$-0.728277\pi$
$521$	−1.62883e23			−1.31448			−0.657241	+	0.753680i	$0.728277\pi$
$522$	4.47605e22	+	2.97484e22i	0.355382	+	0.236192i
$523$		−	2.36470e23i		−	1.84719i	−0.383366	−	0.923596i	$-0.625235\pi$
$523$		−	2.36470e23i		−	1.84719i	0.383366	−	0.923596i	$-0.374765\pi$
$524$	−2.19256e23	+	9.20901e22i	−1.68514	+	0.707778i
$525$		−	3.96575e23i		−	2.99897i
$526$	−1.00143e23	+	1.50679e23i	−0.745149	+	1.12118i
$527$	−1.06758e22			−0.0781648
$528$	−1.10153e23	+	1.12351e23i	−0.793613	+	0.809447i
$529$	1.54233e23			1.09346
$530$	1.88915e23	−	2.84248e23i	1.31802	−	1.98314i
$531$			3.74346e22i			0.257022i
$532$	−1.17984e22	+	4.95545e21i	−0.0797211	+	0.0334837i
$533$			2.00148e23i			1.33098i
$534$	−2.74030e23	−	1.82124e23i	−1.79348	−	1.19197i
$535$	6.40224e21			0.0412406
$536$	−7.99419e21	+	4.18056e22i	−0.0506843	+	0.265054i
$537$	1.36640e23			0.852698
$538$	1.48564e23	+	9.87377e22i	0.912567	+	0.606504i
$539$			2.92879e22i			0.177086i
$540$	8.33594e22	+	1.98470e23i	0.496144	+	1.18126i
$541$			1.05868e23i			0.620281i	0.950691	+	0.310141i	$0.100376\pi$
$541$			1.05868e23i			0.620281i	−0.950691	+	0.310141i	$0.899624\pi$
$542$	3.77690e22	−	5.68286e22i	0.217842	−	0.327773i
$543$	−7.24837e22			−0.411568
$544$	1.63365e22	+	7.71395e22i	0.0913208	+	0.431207i
$545$	−1.06499e23			−0.586104
$546$	−1.40544e23	+	2.11468e23i	−0.761510	+	1.14580i
$547$		−	2.89118e23i		−	1.54235i	−0.636625	−	0.771174i	$-0.719670\pi$
$547$		−	2.89118e23i		−	1.54235i	0.636625	−	0.771174i	$-0.280330\pi$
$548$	1.20613e23	+	2.87166e23i	0.633518	+	1.50834i
$549$			4.74307e22i			0.245298i
$550$	3.62840e23	+	2.41148e23i	1.84771	+	1.22801i
$551$	−1.65872e22			−0.0831732
$552$	6.52941e22	−	3.41456e23i	0.322397	−	1.68598i
$553$	−6.63307e22			−0.322516
$554$	1.23691e23	+	8.22066e22i	0.592250	+	0.393617i
$555$		−	1.32636e23i		−	0.625419i
$556$	2.86692e23	−	1.20414e23i	1.33131	−	0.559165i
$557$		−	3.41183e23i		−	1.56034i	−0.625570	−	0.780168i	$-0.715134\pi$
$557$		−	3.41183e23i		−	1.56034i	0.625570	−	0.780168i	$-0.284866\pi$
$558$	8.87979e21	−	1.33608e22i	0.0399956	−	0.0601787i
$559$	1.69727e23			0.752925
$560$	−3.24295e23	−	3.17951e23i	−1.41691	−	1.38919i
$561$	−1.16106e23			−0.499653
$562$	−1.04969e23	+	1.57940e23i	−0.444941	+	0.669473i
$563$		−	1.44889e23i		−	0.604941i	−0.953159	−	0.302471i	$-0.902189\pi$
$563$		−	1.44889e23i		−	0.604941i	0.953159	−	0.302471i	$-0.0978114\pi$
$564$	6.34024e22	−	2.66297e22i	0.260756	−	0.109520i
$565$			2.77004e23i			1.12221i
$566$	−2.45053e23	−	1.62866e23i	−0.977960	−	0.649965i
$567$	3.43795e23			1.35159
$568$	3.96094e21	+	7.57422e20i	0.0153404	+	0.00293344i
$569$	4.55076e23			1.73632			0.868160	−	0.496285i	$-0.165303\pi$
$569$	4.55076e23			1.73632			0.868160	+	0.496285i	$0.165303\pi$
$570$	3.80485e22	+	2.52875e22i	0.143022	+	0.0950540i
$571$			2.17154e23i			0.804193i	0.915597	+	0.402097i	$0.131718\pi$
$571$			2.17154e23i			0.804193i	−0.915597	+	0.402097i	$0.868282\pi$
$572$	−1.08018e23	−	2.57178e23i	−0.394120	−	0.938355i
$573$			4.25068e23i			1.52807i
$574$	−2.12599e23	+	3.19884e23i	−0.753027	+	1.13303i
$575$	−9.62594e23			−3.35944
$576$	−1.10129e23	−	4.37167e22i	−0.378712	−	0.150334i
$577$	2.28537e23			0.774394			0.387197	−	0.921997i	$-0.373443\pi$
$577$	2.28537e23			0.774394			0.387197	+	0.921997i	$0.373443\pi$
$578$	1.33568e23	−	2.00970e23i	0.445979	−	0.671036i
$579$		−	7.93523e22i		−	0.261091i
$580$	−2.27961e23	−	5.42749e23i	−0.739132	−	1.75979i
$581$			3.64597e22i			0.116497i
$582$	−6.78964e21	−	4.51248e21i	−0.0213797	−	0.0142092i
$583$	4.02275e23			1.24836
$584$	4.73254e23	+	9.04968e22i	1.44739	+	0.276773i
$585$	2.62426e23			0.791011
$586$	−4.02818e22	−	2.67718e22i	−0.119668	−	0.0795331i
$587$			5.49823e23i			1.60990i	0.593342	+	0.804951i	$0.297808\pi$
$587$			5.49823e23i			1.60990i	−0.593342	+	0.804951i	$0.702192\pi$
$588$	−7.02412e22	+	2.95021e22i	−0.202714	+	0.0851424i
$589$			4.95120e21i			0.0140842i
$590$	2.26959e23	−	3.41490e23i	0.636363	−	0.957495i
$591$	−6.68196e23			−1.84676
$592$	−7.58106e22	−	7.43277e22i	−0.206536	−	0.202496i
$593$	−4.92814e23			−1.32348			−0.661741	−	0.749732i	$-0.730182\pi$
$593$	−4.92814e23			−1.32348			−0.661741	+	0.749732i	$0.730182\pi$
$594$	−1.40439e23	+	2.11310e23i	−0.371795	+	0.559416i
$595$		−	3.35133e23i		−	0.874626i
$596$	−5.85810e22	+	2.46047e22i	−0.150717	+	0.0633030i
$597$			3.39954e23i			0.862261i
$598$	5.13290e23	+	3.41139e23i	1.28352	+	0.853043i
$599$	−4.19943e23			−1.03529			−0.517646	−	0.855595i	$-0.673191\pi$
$599$	−4.19943e23			−1.03529			−0.517646	+	0.855595i	$0.673191\pi$
$600$	−2.12852e23	+	1.11311e24i	−0.517360	+	2.70554i
$601$	2.16713e23			0.519341			0.259671	−	0.965697i	$-0.416386\pi$
$601$	2.16713e23			0.519341			0.259671	+	0.965697i	$0.416386\pi$
$602$	2.71265e23	+	1.80286e23i	0.640949	+	0.425983i
$603$		−	4.71969e22i		−	0.109955i
$604$	−1.77105e23	−	4.21666e23i	−0.406833	−	0.968623i
$605$		−	6.99965e22i		−	0.158546i
$606$	2.48687e23	−	3.74183e23i	0.555438	−	0.835732i
$607$	−4.33551e23			−0.954852			−0.477426	−	0.878672i	$-0.658430\pi$
$607$	−4.33551e23			−0.954852			−0.477426	+	0.878672i	$0.658430\pi$
$608$	3.57755e22	−	7.57652e21i	0.0776972	−	0.0164547i
$609$	−6.31590e23			−1.35266
$610$	2.87563e23	−	4.32678e23i	0.607337	−	0.913821i
$611$			1.21914e23i			0.253924i
$612$	−3.38584e22	−	8.06130e22i	−0.0695471	−	0.165584i
$613$			2.71131e23i			0.549244i	0.961552	+	0.274622i	$0.0885528\pi$
$613$			2.71131e23i			0.549244i	−0.961552	+	0.274622i	$0.911447\pi$
$614$	−3.63188e23	−	2.41380e23i	−0.725605	−	0.482247i
$615$	1.37122e24			2.70190
$616$	1.00539e23	−	5.25769e23i	0.195388	−	1.02178i
$617$	−5.91051e23			−1.13292			−0.566462	−	0.824088i	$-0.691688\pi$
$617$	−5.91051e23			−1.13292			−0.566462	+	0.824088i	$0.691688\pi$
$618$	−6.16672e23	−	4.09848e23i	−1.16588	−	0.774856i
$619$		−	9.44262e23i		−	1.76085i	−0.474187	−	0.880424i	$-0.657258\pi$
$619$		−	9.44262e23i		−	1.76085i	0.474187	−	0.880424i	$-0.342742\pi$
$620$	−1.62009e23	+	6.80454e22i	−0.297995	+	0.125161i
$621$		−	5.60593e23i		−	1.01711i
$622$	−2.52077e23	+	3.79283e23i	−0.451143	+	0.678806i
$623$	1.11940e24			1.97623
$624$	5.07982e23	−	5.18117e23i	0.884666	−	0.902317i
$625$	1.20439e24			2.06913
$626$	−5.80392e23	+	8.73279e23i	−0.983648	+	1.48003i
$627$			5.38471e22i			0.0900303i
$628$	−6.09930e23	+	2.56178e23i	−1.00606	+	0.422556i
$629$		−	7.83442e22i		−	0.127490i
$630$	4.19420e23	+	2.78752e23i	0.673371	+	0.447531i
$631$	3.35285e23			0.531086			0.265543	−	0.964099i	$-0.414449\pi$
$631$	3.35285e23			0.531086			0.265543	+	0.964099i	$0.414449\pi$
$632$	1.86178e23	+	3.56014e22i	0.290960	+	0.0556381i
$633$	−1.22071e24			−1.88227
$634$	1.67395e23	+	1.11253e23i	0.254673	+	0.169259i
$635$			1.46742e24i			2.20281i
$636$	4.05216e23	+	9.64775e23i	0.600208	+	1.42903i
$637$		−	1.35064e23i		−	0.197403i
$638$	3.84056e23	−	5.77864e23i	0.553883	−	0.833392i
$639$	−4.47175e21			−0.00636385
$640$	7.39582e23	+	1.06649e24i	1.03862	+	1.49770i
$641$	1.02554e24			1.42122			0.710609	−	0.703587i	$-0.248419\pi$
$641$	1.02554e24			1.42122			0.710609	+	0.703587i	$0.248419\pi$
$642$	−1.08650e22	+	1.63479e22i	−0.0148588	+	0.0223570i
$643$		−	1.00641e24i		−	1.35826i	−0.734017	−	0.679131i	$-0.762357\pi$
$643$		−	1.00641e24i		−	1.35826i	0.734017	−	0.679131i	$-0.237643\pi$
$644$	4.57999e23	+	1.09044e24i	0.610006	+	1.45236i
$645$		−	1.16281e24i		−	1.52845i
$646$	2.24741e22	+	1.49366e22i	0.0291546	+	0.0193765i
$647$	3.80957e23			0.487742			0.243871	−	0.969808i	$-0.421583\pi$
$647$	3.80957e23			0.487742			0.243871	+	0.969808i	$0.421583\pi$
$648$	−9.64969e23	−	1.84524e23i	−1.21934	−	0.233166i
$649$	4.83285e23			0.602731
$650$	−1.67327e24	−	1.11208e24i	−2.05970	−	1.36890i
$651$			1.88527e23i			0.229053i
$652$	5.59209e23	−	2.34874e23i	0.670610	−	0.281664i
$653$		−	4.03993e23i		−	0.478202i	−0.970995	−	0.239101i	$-0.923147\pi$
$653$		−	4.03993e23i		−	0.478202i	0.970995	−	0.239101i	$-0.0768527\pi$
$654$	1.80735e23	−	2.71941e23i	0.211170	−	0.317734i
$655$	−2.88839e24			−3.33123
$656$	7.68417e23	−	7.83748e23i	0.874811	−	0.892265i
$657$	−5.34285e23			−0.600437
$658$	−1.29498e23	+	1.94848e23i	−0.143663	+	0.216160i
$659$			3.09111e23i			0.338523i	0.985571	+	0.169262i	$0.0541383\pi$
$659$			3.09111e23i			0.338523i	−0.985571	+	0.169262i	$0.945862\pi$
$660$	−1.76194e24	+	7.40033e23i	−1.90487	+	0.800069i
$661$		−	4.95209e23i		−	0.528537i	−0.964449	−	0.264269i	$-0.914869\pi$
$661$		−	4.95209e23i		−	0.528537i	0.964449	−	0.264269i	$-0.0851306\pi$
$662$	2.63794e23	+	1.75321e23i	0.277954	+	0.184732i
$663$	5.35432e23			0.556980
$664$	1.95689e22	−	1.02336e23i	0.0200973	−	0.105099i
$665$	−1.55427e23			−0.157595
$666$	9.80481e22	+	6.51640e22i	0.0981541	+	0.0652345i
$667$			1.53304e24i			1.51525i
$668$	−3.04988e23	−	7.26142e23i	−0.297634	−	0.708633i
$669$		−	1.37480e24i		−	1.32470i
$670$	−2.86146e23	+	4.30546e23i	−0.272240	+	0.409622i
$671$	6.12336e23			0.575239
$672$	1.36223e24	−	2.88492e23i	1.26360	−	0.267605i
$673$	−7.41478e23			−0.679157			−0.339579	−	0.940578i	$-0.610284\pi$
$673$	−7.41478e23			−0.679157			−0.339579	+	0.940578i	$0.610284\pi$
$674$	−2.77660e23	+	4.17777e23i	−0.251133	+	0.377864i
$675$			1.82748e24i			1.63219i
$676$	5.90687e22	+	1.40636e23i	0.0520968	+	0.124037i
$677$		−	1.13904e22i		−	0.00992051i	−0.999988	−	0.00496025i	$-0.998421\pi$
$677$		−	1.13904e22i		−	0.00992051i	0.999988	−	0.00496025i	$-0.00157890\pi$
$678$	−7.07319e23	−	4.70093e23i	−0.608363	−	0.404326i
$679$	2.77355e22			0.0235582
$680$	−1.79874e23	+	9.40655e23i	−0.150884	+	0.789050i
$681$	5.86131e22			0.0485561
$682$	−1.72490e23	−	1.14639e23i	−0.141123	−	0.0937920i
$683$		−	2.41181e24i		−	1.94880i	−0.224828	−	0.974398i	$-0.572182\pi$
$683$		−	2.41181e24i		−	1.94880i	0.224828	−	0.974398i	$-0.427818\pi$
$684$	−3.73865e22	+	1.57027e22i	−0.0298358	+	0.0125314i
$685$			3.78301e24i			2.98172i
$686$	−6.30647e23	+	9.48893e23i	−0.490943	+	0.738690i
$687$	−7.50277e23			−0.576885
$688$	−6.64626e23	−	6.51625e23i	−0.504749	−	0.494875i
$689$	−1.85513e24			−1.39159
$690$	2.33716e24	−	3.51657e24i	1.73169	−	2.60556i
$691$			3.17702e23i			0.232518i	0.993219	+	0.116259i	$0.0370902\pi$
$691$			3.17702e23i			0.232518i	−0.993219	+	0.116259i	$0.962910\pi$
$692$	1.58528e24	−	6.65836e23i	1.14605	−	0.481355i
$693$			5.93573e23i			0.423879i
$694$	1.16261e24	+	7.72683e23i	0.820119	+	0.545062i
$695$	3.77676e24			2.63177
$696$	1.77275e24	+	3.38991e23i	1.22031	+	0.233351i
$697$	8.09940e23			0.550775
$698$	−4.43437e22	−	2.94714e22i	−0.0297893	−	0.0197984i
$699$		−	1.13149e24i		−	0.750924i
$700$	−1.49303e24	−	3.55474e24i	−0.978893	−	2.33063i
$701$			3.50256e23i			0.226873i	0.993545	+	0.113436i	$0.0361858\pi$
$701$			3.50256e23i			0.226873i	−0.993545	+	0.113436i	$0.963814\pi$
$702$	6.47649e23	−	9.74476e23i	0.414452	−	0.623600i
$703$	−3.63342e22			−0.0229718
$704$	−5.64388e23	+	1.42177e24i	−0.352542	+	0.888102i
$705$	8.35238e23			0.515469
$706$	−1.18741e24	+	1.78661e24i	−0.724035	+	1.08941i
$707$			1.52853e24i			0.920890i
$708$	4.86819e23	+	1.15906e24i	0.289791	+	0.689960i
$709$			3.69006e23i			0.217041i	0.994094	+	0.108520i	$0.0346112\pi$
$709$			3.69006e23i			0.217041i	−0.994094	+	0.108520i	$0.965389\pi$
$710$	4.07927e22	+	2.71114e22i	0.0237076	+	0.0157563i
$711$	−2.10188e23			−0.120702
$712$	−3.14195e24	−	6.00812e23i	−1.78287	−	0.340925i
$713$	4.57606e23			0.256585
$714$	8.55749e23	+	5.68742e23i	0.474145	+	0.315123i
$715$		−	3.38796e24i		−	1.85497i
$716$	1.22478e24	−	5.14422e23i	0.662671	−	0.278329i
$717$			3.39557e24i			1.81551i
$718$	1.53833e24	−	2.31463e24i	0.812817	−	1.22299i
$719$	−3.63965e24			−1.90048			−0.950242	−	0.311512i	$-0.899165\pi$
$719$	−3.63965e24			−1.90048			−0.950242	+	0.311512i	$0.899165\pi$
$720$	−1.02762e24	−	1.00752e24i	−0.530281	−	0.519908i
$721$	2.51909e24			1.28467
$722$	−1.09131e24	+	1.64202e24i	−0.550024	+	0.827586i
$723$			7.39680e23i			0.368441i
$724$	−6.49714e23	+	2.72887e23i	−0.319849	+	0.134340i
$725$		−	4.99755e24i		−	2.43156i
$726$	1.78734e23	+	1.18789e23i	0.0859498	+	0.0571233i
$727$	−2.92373e24			−1.38962			−0.694808	−	0.719196i	$-0.744510\pi$
$727$	−2.92373e24			−1.38962			−0.694808	+	0.719196i	$0.744510\pi$
$728$	−4.63645e23	+	2.42464e24i	−0.217806	+	1.13902i
$729$	−7.06719e23			−0.328143
$730$	4.87392e24	+	3.23927e24i	2.23684	+	1.48663i
$731$		−	6.86837e23i		−	0.311570i
$732$	6.16814e23	+	1.46856e24i	0.276573	+	0.658489i
$733$		−	8.20457e22i		−	0.0363640i	−0.999835	−	0.0181820i	$-0.994212\pi$
$733$		−	8.20457e22i		−	0.0363640i	0.999835	−	0.0181820i	$-0.00578783\pi$
$734$	−3.40071e23	+	5.11684e23i	−0.148989	+	0.224174i
$735$	−9.25329e23			−0.400732
$736$	−7.00246e23	−	3.30649e24i	−0.299771	−	1.41549i
$737$	−6.09318e23			−0.257852
$738$	−6.73681e23	+	1.01364e24i	−0.281822	+	0.424040i
$739$			3.42591e22i			0.0141677i	0.999975	+	0.00708383i	$0.00225487\pi$
$739$			3.42591e22i			0.0141677i	−0.999975	+	0.00708383i	$0.997745\pi$
$740$	−4.99349e23	−	1.18889e24i	−0.204143	−	0.486042i
$741$		−	2.48321e23i		−	0.100360i
$742$	−2.96494e24	−	1.97054e24i	−1.18463	−	0.787320i
$743$	1.12234e24			0.443324			0.221662	−	0.975124i	$-0.428852\pi$
$743$	1.12234e24			0.443324			0.221662	+	0.975124i	$0.428852\pi$
$744$	1.01187e23	−	5.29160e23i	0.0395145	−	0.206641i
$745$	−7.71722e23			−0.297943
$746$	7.40971e23	+	4.92459e23i	0.282827	+	0.187971i
$747$			1.15533e23i			0.0435994i
$748$	−1.04072e24	+	4.37116e23i	−0.388304	+	0.163092i
$749$		−	6.67805e22i		−	0.0246351i
$750$	−4.33750e24	+	6.52636e24i	−1.58205	+	2.38040i
$751$	5.53313e22			0.0199540			0.00997702	−	0.999950i	$-0.496824\pi$
$751$	5.53313e22			0.0199540			0.00997702	+	0.999950i	$0.496824\pi$
$752$	4.68058e23	−	4.77396e23i	0.166897	−	0.170227i
$753$	3.18925e24			1.12443
$754$	−1.77111e24	+	2.66487e24i	−0.617432	+	0.929010i
$755$		−	5.55486e24i		−	1.91480i
$756$	2.07020e24	−	8.69507e23i	0.705629	−	0.296372i
$757$			4.11071e24i			1.38548i	0.721185	+	0.692742i	$0.243598\pi$
$757$			4.11071e24i			1.38548i	−0.721185	+	0.692742i	$0.756402\pi$
$758$	−1.52565e24	−	1.01397e24i	−0.508472	−	0.337937i
$759$	4.97673e24			1.64017
$760$	4.36254e23	+	8.34217e22i	0.142175	+	0.0271871i
$761$	5.58495e24			1.79991			0.899954	−	0.435986i	$-0.143600\pi$
$761$	5.58495e24			1.79991			0.899954	+	0.435986i	$0.143600\pi$
$762$	−3.74700e24	−	2.49031e24i	−1.19417	−	0.793662i
$763$			1.11087e24i			0.350110i
$764$	1.60030e24	+	3.81014e24i	0.498779	+	1.18754i
$765$		−	1.06196e24i		−	0.327331i
$766$	−4.32870e23	+	6.51311e23i	−0.131951	+	0.198538i
$767$	−2.22872e24			−0.671884
$768$	−3.97835e24	+	7.85990e22i	−1.18613	+	0.0234340i
$769$	−3.49045e24			−1.02922			−0.514609	−	0.857425i	$-0.672063\pi$
$769$	−3.49045e24			−1.02922			−0.514609	+	0.857425i	$0.672063\pi$
$770$	3.59872e24	−	5.41477e24i	1.04949	−	1.57910i
$771$			2.11080e24i			0.608814i
$772$	−2.98746e23	−	7.11282e23i	−0.0852228	−	0.202906i
$773$		−	5.74685e23i		−	0.162145i	−0.996708	−	0.0810726i	$-0.974165\pi$
$773$		−	5.74685e23i		−	0.162145i	0.996708	−	0.0810726i	$-0.0258346\pi$
$774$	8.59580e23	+	5.71288e23i	0.239877	+	0.159425i
$775$	−1.49175e24			−0.411748
$776$	−7.78482e22	−	1.48863e22i	−0.0212532	−	0.00406409i
$777$	−1.38350e24			−0.373595
$778$	4.73607e24	+	3.14766e24i	1.26500	+	0.840738i
$779$		−	3.75632e23i		−	0.0992417i
$780$	8.12533e24	−	3.41273e24i	2.12343	−	0.891863i
$781$			5.77308e22i			0.0149236i
$782$	1.38049e24	−	2.07713e24i	0.353001	−	0.531137i
$783$	2.91046e24			0.736185
$784$	−5.18544e23	+	5.28890e23i	−0.129747	+	0.132336i
$785$	−8.03497e24			−1.98881
$786$	4.90179e24	−	7.37540e24i	1.20023	−	1.80590i
$787$		−	5.04324e24i		−	1.22159i	−0.791790	−	0.610794i	$-0.790850\pi$
$787$		−	5.04324e24i		−	1.22159i	0.791790	−	0.610794i	$-0.209150\pi$
$788$	−5.98943e24	+	2.51563e24i	−1.43520	+	0.602801i
$789$		−	6.73730e24i		−	1.59710i
$790$	1.91740e24	+	1.27433e24i	0.449658	+	0.298848i
$791$	2.88937e24			0.670353
$792$	3.18586e23	−	1.66605e24i	0.0731245	−	0.382405i
$793$	−2.82384e24			−0.641237
$794$	−3.85396e23	−	2.56139e23i	−0.0865831	−	0.0575442i
$795$			1.27096e25i			2.82494i
$796$	1.27986e24	+	3.04721e24i	0.281451	+	0.670103i
$797$		−	5.78429e24i		−	1.25850i	−0.777201	−	0.629252i	$-0.783361\pi$
$797$		−	5.78429e24i		−	1.25850i	0.777201	−	0.629252i	$-0.216639\pi$
$798$	2.63769e23	−	3.96877e23i	0.0567806	−	0.0854341i
$799$	4.93350e23			0.105077
$800$	2.28273e24	+	1.07788e25i	0.481050	+	2.27147i
$801$	3.54714e24			0.739608
$802$	2.27726e24	−	3.42645e24i	0.469820	−	0.706908i
$803$			6.89768e24i			1.40806i
$804$	−6.13774e23	−	1.46133e24i	−0.123974	−	0.295169i
$805$			1.43651e25i			2.87106i
$806$	7.95455e23	+	5.28669e23i	0.157314	+	0.104553i
$807$	−6.64273e24			−1.29994
$808$	8.20400e23	−	4.29028e24i	0.158865	−	0.830787i
$809$	5.81148e24			1.11359			0.556793	−	0.830651i	$-0.312031\pi$
$809$	5.81148e24			1.11359			0.556793	+	0.830651i	$0.312031\pi$
$810$	−9.93798e24	−	6.60491e24i	−1.88441	−	1.25240i
$811$		−	3.15834e23i		−	0.0592627i	−0.999561	−	0.0296314i	$-0.990567\pi$
$811$		−	3.15834e23i		−	0.0592627i	0.999561	−	0.0296314i	$-0.00943334\pi$
$812$	−5.66131e24	+	2.37782e24i	−1.05121	+	0.441522i
$813$			2.54097e24i			0.466906i
$814$	8.41276e23	−	1.26581e24i	0.152979	−	0.230177i
$815$	7.36679e24			1.32568
$816$	−2.09667e24	−	2.05565e24i	−0.373391	−	0.366086i
$817$	−3.18539e23			−0.0561404
$818$	−2.39879e24	+	3.60930e24i	−0.418397	+	0.629535i
$819$		−	2.73732e24i		−	0.472511i
$820$	1.22911e25	−	5.16239e24i	2.09977	−	0.881928i
$821$		−	3.64320e24i		−	0.615980i	−0.951390	−	0.307990i	$-0.900344\pi$
$821$		−	3.64320e24i		−	0.615980i	0.951390	−	0.307990i	$-0.0996563\pi$
$822$	−9.65977e24	−	6.42001e24i	−1.61643	−	1.07430i
$823$	2.26743e24			0.375522			0.187761	−	0.982215i	$-0.439877\pi$
$823$	2.26743e24			0.375522			0.187761	+	0.982215i	$0.439877\pi$
$824$	−7.07060e24	−	1.35206e24i	−1.15898	−	0.221623i
$825$	−1.62236e25			−2.63202
$826$	−3.56202e24	−	2.36737e24i	−0.571961	−	0.380132i
$827$			1.05054e25i			1.66962i	0.550539	+	0.834809i	$0.314422\pi$
$827$			1.05054e25i			1.66962i	−0.550539	+	0.834809i	$0.685578\pi$
$828$	1.45130e24	+	3.45538e24i	0.228296	+	0.543548i
$829$		−	8.95945e24i		−	1.39498i	−0.716595	−	0.697489i	$-0.754300\pi$
$829$		−	8.95945e24i		−	1.39498i	0.716595	−	0.697489i	$-0.245700\pi$
$830$	7.00455e23	−	1.05393e24i	0.107948	−	0.162423i
$831$	−5.53058e24			−0.843649
$832$	2.60273e24	−	6.55665e24i	0.392990	−	0.989996i
$833$	−5.46565e23			−0.0816882
$834$	−6.40940e24	+	9.64382e24i	−0.948214	+	1.42672i
$835$		−	9.56589e24i		−	1.40085i
$836$	2.02724e23	+	4.82664e23i	0.0293868	+	0.0699667i
$837$		−	8.68762e23i		−	0.124662i
$838$	1.26263e24	+	8.39163e23i	0.179351	+	0.119199i
$839$	−7.86032e22			−0.0110526			−0.00552629	−	0.999985i	$-0.501759\pi$
$839$	−7.86032e22			−0.0110526			−0.00552629	+	0.999985i	$0.501759\pi$
$840$	1.66113e25	+	3.17645e24i	2.31222	+	0.442149i
$841$	−7.02012e23			−0.0967339
$842$	8.28809e24	+	5.50837e24i	1.13058	+	0.751399i
$843$		−	7.06195e24i		−	0.953652i
$844$	−1.09420e25	+	4.59575e24i	−1.46280	+	0.614392i
$845$			1.85268e24i			0.245199i
$846$	−4.10352e23	+	6.17430e23i	−0.0537661	+	0.0808984i
$847$	−7.30120e23			−0.0947077
$848$	7.26439e24	+	7.12229e24i	0.932899	+	0.914650i
$849$	1.09570e25			1.39309
$850$	−4.50026e24	+	6.77125e24i	−0.566470	+	0.852330i
$851$			3.35813e24i			0.418501i
$852$	−1.38456e23	+	5.81530e22i	−0.0170834	+	0.00717523i
$853$		−	4.09750e24i		−	0.500555i	−0.968174	−	0.250277i	$-0.919478\pi$
$853$		−	4.09750e24i		−	0.500555i	0.968174	−	0.250277i	$-0.0805218\pi$
$854$	−4.51318e24	−	2.99952e24i	−0.545872	−	0.362794i
$855$	−4.92514e23			−0.0589803
$856$	−3.58429e22	+	1.87440e23i	−0.00424987	+	0.0222247i
$857$	2.30079e24			0.270110			0.135055	−	0.990838i	$-0.456879\pi$
$857$	2.30079e24			0.270110			0.135055	+	0.990838i	$0.456879\pi$
$858$	8.65102e24	+	5.74958e24i	1.00560	+	0.668335i
$859$			6.99290e24i			0.804851i	0.915453	+	0.402426i	$0.131833\pi$
$859$			6.99290e24i			0.804851i	−0.915453	+	0.402426i	$0.868167\pi$
$860$	−4.37775e24	−	1.04229e25i	−0.498901	−	1.18783i
$861$		−	1.43030e25i		−	1.61398i
$862$	8.75975e24	−	1.31802e25i	0.978769	−	1.47269i
$863$	3.06286e24			0.338871			0.169436	−	0.985541i	$-0.445806\pi$
$863$	3.06286e24			0.338871			0.169436	+	0.985541i	$0.445806\pi$
$864$	−6.27734e24	+	1.32941e24i	−0.687716	+	0.145644i
$865$	2.08839e25			2.26555
$866$	−1.21449e24	+	1.82736e24i	−0.130464	+	0.196301i
$867$			8.98597e24i			0.955878i
$868$	7.09769e23	+	1.68988e24i	0.0747652	+	0.178008i
$869$			2.71355e24i			0.283054i
$870$	1.82572e25	+	1.21339e25i	1.88590	+	1.25340i
$871$	2.80993e24			0.287436
$872$	5.96232e23	−	3.11800e24i	0.0603984	−	0.315854i
$873$	8.78876e22			0.00881671
$874$	−9.63327e23	−	6.40239e23i	−0.0957032	−	0.0636056i
$875$		−	2.66600e25i		−	2.62296i
$876$	−1.65427e25	+	6.94813e24i	−1.61184	+	0.676991i
$877$			1.21076e25i			1.16832i	0.811637	+	0.584162i	$0.198577\pi$
$877$			1.21076e25i			1.16832i	−0.811637	+	0.584162i	$0.801423\pi$
$878$	−3.29545e24	+	4.95845e24i	−0.314928	+	0.473852i
$879$	1.80112e24			0.170465
$880$	−1.30072e25	+	1.32667e25i	−1.21922	+	1.24354i
$881$	−1.51486e25			−1.40629			−0.703147	−	0.711045i	$-0.748222\pi$
$881$	−1.51486e25			−1.40629			−0.703147	+	0.711045i	$0.748222\pi$
$882$	4.54614e23	−	6.84028e23i	0.0417984	−	0.0628914i
$883$		−	1.55372e25i		−	1.41484i	−0.706795	−	0.707418i	$-0.749860\pi$
$883$		−	1.55372e25i		−	1.41484i	0.706795	−	0.707418i	$-0.250140\pi$
$884$	4.79940e24	−	2.01580e24i	0.432855	−	0.181804i
$885$			1.52690e25i			1.36393i
$886$	1.00027e25	+	6.64795e24i	0.884978	+	0.588168i
$887$	−1.56055e25			−1.36750			−0.683750	−	0.729716i	$-0.739652\pi$
$887$	−1.56055e25			−1.36750			−0.683750	+	0.729716i	$0.739652\pi$
$888$	3.88323e24	+	7.42561e23i	0.337041	+	0.0644499i
$889$	1.53064e25			1.31585
$890$	−3.23582e25	−	2.15056e25i	−2.75530	−	1.83121i
$891$		−	1.40645e25i		−	1.18621i
$892$	−5.17586e24	−	1.23231e25i	−0.432396	−	1.02949i
$893$		−	2.28805e23i		−	0.0189334i
$894$	1.30966e24	−	1.97056e24i	0.107347	−	0.161518i
$895$	1.61348e25			1.30999
$896$	1.11243e25	−	7.71444e24i	0.894655	−	0.620421i
$897$	−2.29507e25			−1.82835
$898$	5.15274e24	−	7.75299e24i	0.406621	−	0.611816i
$899$			2.37578e24i			0.185716i
$900$	−4.73109e24	−	1.12642e25i	−0.366353	−	0.872245i
$901$			7.50716e24i			0.575857i
$902$	1.30863e25	+	8.69730e24i	0.994398	+	0.660890i
$903$	−1.21290e25			−0.913020
$904$	−8.10993e24	−	1.55080e24i	−0.604763	−	0.115644i
$905$	−8.55907e24			−0.632286
$906$	1.41841e25	+	9.42695e24i	1.03804	+	0.689893i
$907$			1.36420e25i			0.989048i	0.869164	+	0.494524i	$0.164658\pi$
$907$			1.36420e25i			0.989048i	−0.869164	+	0.494524i	$0.835342\pi$
$908$	5.25384e23	−	2.20667e23i	0.0377352	−	0.0158492i
$909$			4.84356e24i			0.344645i
$910$	−1.65959e25	+	2.49707e25i	−1.16990	+	1.76027i
$911$	3.50650e24			0.244888			0.122444	−	0.992475i	$-0.460927\pi$
$911$	3.50650e24			0.244888			0.122444	+	0.992475i	$0.460927\pi$
$912$	−9.53366e23	+	9.72387e23i	−0.0659635	+	0.0672795i
$913$	1.49155e24			0.102243
$914$	−5.44406e24	+	8.19133e24i	−0.369726	+	0.556303i
$915$			1.93463e25i			1.30172i
$916$	−6.72518e24	+	2.82465e24i	−0.448324	+	0.188301i
$917$			3.01283e25i			1.98992i
$918$	−3.94342e24	−	2.62085e24i	−0.258054	−	0.171506i
$919$	−1.32969e25			−0.862123			−0.431061	−	0.902323i	$-0.641861\pi$
$919$	−1.32969e25			−0.862123			−0.431061	+	0.902323i	$0.641861\pi$
$920$	7.71010e24	−	4.03200e25i	0.495295	−	2.59015i
$921$	1.62392e25			1.03361
$922$	3.46303e24	+	2.30157e24i	0.218395	+	0.145148i
$923$		−	2.66231e23i		−	0.0166358i
$924$	7.71914e24	+	1.83784e25i	0.477922	+	1.13788i
$925$		−	1.09472e25i		−	0.671579i
$926$	9.64608e24	−	1.45138e25i	0.586351	−	0.882244i
$927$	7.98243e24			0.480792
$928$	1.71665e25	−	3.63551e24i	1.02453	−	0.216974i
$929$	−7.82134e24			−0.462538			−0.231269	−	0.972890i	$-0.574288\pi$
$929$	−7.82134e24			−0.462538			−0.231269	+	0.972890i	$0.574288\pi$
$930$	3.62193e24	−	5.44969e24i	0.212244	−	0.319350i
$931$			2.53484e23i			0.0147190i
$932$	−4.25986e24	−	1.01422e25i	−0.245109	−	0.583578i
$933$		−	1.69588e25i		−	0.966946i
$934$	−4.38925e24	−	2.91715e24i	−0.247995	−	0.164820i
$935$	−1.37101e25			−0.767610
$936$	−1.46919e24	+	7.68314e24i	−0.0815142	+	0.426279i
$937$	−2.58422e23			−0.0142083			−0.00710417	−	0.999975i	$-0.502261\pi$
$937$	−2.58422e23			−0.0142083			−0.00710417	+	0.999975i	$0.502261\pi$
$938$	4.49094e24	+	2.98474e24i	0.244688	+	0.162623i
$939$		−	3.90468e25i		−	2.10828i
$940$	7.48673e24	−	3.14451e24i	0.400595	−	0.168254i
$941$			2.37973e24i			0.126187i	0.998008	+	0.0630936i	$0.0200967\pi$
$941$			2.37973e24i			0.126187i	−0.998008	+	0.0630936i	$0.979903\pi$
$942$	1.36359e25	−	2.05170e25i	0.716556	−	1.07816i
$943$	−3.47171e25			−1.80798
$944$	8.72730e24	+	8.55658e24i	0.450420	+	0.441609i
$945$	2.72719e25			1.39491
$946$	7.37539e24	−	1.10973e25i	0.373861	−	0.562525i
$947$			3.48762e25i			1.75208i	0.482237	+	0.876041i	$0.339824\pi$
$947$			3.48762e25i			1.75208i	−0.482237	+	0.876041i	$0.660176\pi$
$948$	−6.50790e24	+	2.73339e24i	−0.324019	+	0.136092i
$949$		−	3.18093e25i		−	1.56961i
$950$	3.14035e24	+	2.08712e24i	0.153577	+	0.102070i
$951$	−7.48470e24			−0.362777
$952$	9.81179e24	+	1.87624e24i	0.471340	+	0.0901309i
$953$	2.89815e25			1.37985			0.689924	−	0.723882i	$-0.257644\pi$
$953$	2.89815e25			1.37985			0.689924	+	0.723882i	$0.257644\pi$
$954$	−9.39525e24	−	6.24420e24i	−0.443350	−	0.294656i
$955$			5.01932e25i			2.34756i
$956$	1.27837e25	+	3.04365e25i	0.592602	+	1.41092i
$957$			2.58379e25i			1.18715i
$958$	−8.74289e24	+	1.31549e25i	−0.398151	+	0.599072i
$959$	3.94598e25			1.78114
$960$	−4.49198e25	−	1.78314e25i	−2.00971	−	0.797775i
$961$	−2.18410e25			−0.968552
$962$	−3.87962e24	+	5.83742e24i	−0.170530	+	0.256586i
$963$		−	2.11613e23i		−	0.00921974i
$964$	2.78475e24	+	6.63019e24i	0.120263	+	0.286333i
$965$		−	9.37014e24i		−	0.401110i
$966$	−3.66806e25	−	2.43784e25i	−1.55644	−	1.03443i
$967$	2.14679e25			0.902953			0.451476	−	0.892283i	$-0.350897\pi$
$967$	2.14679e25			0.902953			0.451476	+	0.892283i	$0.350897\pi$
$968$	2.04931e24	+	3.91875e23i	0.0854412	+	0.0163383i
$969$	−1.00488e24			−0.0415302
$970$	−8.01739e23	−	5.32846e23i	−0.0328453	−	0.0218294i
$971$		−	2.38828e25i		−	0.969887i	−0.874546	−	0.484943i	$-0.838840\pi$
$971$		−	2.38828e25i		−	0.969887i	0.874546	−	0.484943i	$-0.161160\pi$
$972$	1.76310e25	−	7.40521e24i	0.709763	−	0.298108i
$973$		−	3.93947e25i		−	1.57209i
$974$	−3.55302e24	+	5.34601e24i	−0.140555	+	0.211484i
$975$	7.48169e25			2.93400
$976$	1.10577e25	+	1.08414e25i	0.429875	+	0.421466i
$977$	−6.22623e24			−0.239950			−0.119975	−	0.992777i	$-0.538282\pi$
$977$	−6.22623e24			−0.239950			−0.119975	+	0.992777i	$0.538282\pi$
$978$	−1.25019e25	+	1.88108e25i	−0.477636	+	0.718667i
$979$		−	4.57940e25i		−	1.73443i
$980$	−8.29427e24	+	3.48369e24i	−0.311427	+	0.130803i
$981$			3.52010e24i			0.131029i
$982$	−1.18249e23	−	7.85899e22i	−0.00436365	−	0.00290014i
$983$	−4.13991e25			−1.51456			−0.757278	−	0.653092i	$-0.773471\pi$
$983$	−4.13991e25			−1.51456			−0.757278	+	0.653092i	$0.773471\pi$
$984$	−7.67677e24	+	4.01457e25i	−0.278433	+	1.45607i
$985$	−7.89024e25			−2.83715
$986$	1.07840e25	+	7.16716e24i	0.384437	+	0.255501i
$987$		−	8.71221e24i		−	0.307916i
$988$	−9.34882e23	−	2.22585e24i	−0.0327584	−	0.0779941i
$989$			2.94404e25i			1.02276i
$990$	1.14036e25	−	1.71582e25i	0.392773	−	0.590980i
$991$	1.74916e25			0.597315			0.298657	−	0.954360i	$-0.403461\pi$
$991$	1.74916e25			0.597315			0.298657	+	0.954360i	$0.403461\pi$
$992$	−1.08519e24	−	5.12413e24i	−0.0367413	−	0.173489i
$993$	−1.17950e25			−0.395940
$994$	2.82794e23	−	4.25501e23i	0.00941207	−	0.0141617i
$995$			4.01427e25i			1.32468i
$996$	1.50245e24	+	3.57717e24i	0.0491583	+	0.117040i
$997$		−	4.25273e25i		−	1.37962i	−0.723991	−	0.689810i	$-0.757694\pi$
$997$		−	4.25273e25i		−	1.37962i	0.723991	−	0.689810i	$-0.242306\pi$
$998$	−1.16317e25	−	7.73057e24i	−0.374139	−	0.248658i
$999$	6.37538e24			0.203329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.18.b.a.5.6	yes	16
3.2	odd	2		72.18.d.b.37.11		16
4.3	odd	2		32.18.b.a.17.12		16
8.3	odd	2		32.18.b.a.17.5		16
8.5	even	2	inner	8.18.b.a.5.5	✓	16
24.5	odd	2		72.18.d.b.37.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.5	✓	16	8.5	even	2	inner
8.18.b.a.5.6	yes	16	1.1	even	1	trivial
32.18.b.a.17.5		16	8.3	odd	2
32.18.b.a.17.12		16	4.3	odd	2
72.18.d.b.37.11		16	3.2	odd	2
72.18.d.b.37.12		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)

\(f(q)\)	\(=\)	\(q+(-200.394 + 301.520i) q^{2} -13481.8i q^{3} +(-50756.5 - 120846. i) q^{4} -1.59197e6i q^{5} +(4.06504e6 + 2.70168e6i) q^{6} -1.66055e7 q^{7} +(4.66086e7 + 8.91263e6i) q^{8} -5.26193e7 q^{9} +O(q^{10})\)	\(q+(-200.394 + 301.520i) q^{2} -13481.8i q^{3} +(-50756.5 - 120846. i) q^{4} -1.59197e6i q^{5} +(4.06504e6 + 2.70168e6i) q^{6} -1.66055e7 q^{7} +(4.66086e7 + 8.91263e6i) q^{8} -5.26193e7 q^{9} +(4.80011e8 + 3.19021e8i) q^{10} +6.79322e8i q^{11} +(-1.62922e9 + 6.84290e8i) q^{12} -3.13276e9i q^{13} +(3.32765e9 - 5.00690e9i) q^{14} -2.14627e10 q^{15} +(-1.20274e10 + 1.22674e10i) q^{16} -1.26774e10 q^{17} +(1.05446e10 - 1.58658e10i) q^{18} +5.87947e9i q^{19} +(-1.92383e11 + 8.08028e10i) q^{20} +2.23873e11i q^{21} +(-2.04829e11 - 1.36132e11i) q^{22} +5.43400e11 q^{23} +(1.20158e11 - 6.28369e11i) q^{24} -1.77143e12 q^{25} +(9.44589e11 + 6.27786e11i) q^{26} -1.03164e12i q^{27} +(8.42839e11 + 2.00671e12i) q^{28} +2.82120e12i q^{29} +(4.30099e12 - 6.47142e12i) q^{30} +8.42117e11 q^{31} +(-1.28864e12 - 6.08482e12i) q^{32} +9.15850e12 q^{33} +(2.54047e12 - 3.82248e12i) q^{34} +2.64355e13i q^{35} +(2.67077e12 + 6.35881e12i) q^{36} +6.17985e12i q^{37} +(-1.77278e12 - 1.17821e12i) q^{38} -4.22353e13 q^{39} +(1.41886e13 - 7.41996e13i) q^{40} -6.38887e13 q^{41} +(-6.75021e13 - 4.48628e13i) q^{42} +5.41782e13i q^{43} +(8.20931e13 - 3.44800e13i) q^{44} +8.37684e13i q^{45} +(-1.08894e14 + 1.63846e14i) q^{46} -3.89159e13 q^{47} +(1.65387e14 + 1.62152e14i) q^{48} +4.31135e13 q^{49} +(3.54984e14 - 5.34121e14i) q^{50} +1.70914e14i q^{51} +(-3.78580e14 + 1.59008e14i) q^{52} -5.92171e14i q^{53} +(3.11060e14 + 2.06734e14i) q^{54} +1.08146e15 q^{55} +(-7.73962e14 - 1.47999e14i) q^{56} +7.92660e13 q^{57} +(-8.50647e14 - 5.65351e14i) q^{58} -7.11422e14i q^{59} +(1.08937e15 + 2.59367e15i) q^{60} -9.01392e14i q^{61} +(-1.68755e14 + 2.53915e14i) q^{62} +8.73773e14 q^{63} +(2.09293e15 + 8.30811e14i) q^{64} -4.98726e15 q^{65} +(-1.83531e15 + 2.76147e15i) q^{66} +8.96950e14i q^{67} +(6.43458e14 + 1.53200e15i) q^{68} -7.32602e15i q^{69} +(-7.97084e15 - 5.29752e15i) q^{70} +8.49830e13 q^{71} +(-2.45252e15 - 4.68977e14i) q^{72} +1.01538e16 q^{73} +(-1.86335e15 - 1.23840e15i) q^{74} +2.38821e16i q^{75} +(7.10508e14 - 2.98421e14i) q^{76} -1.12805e16i q^{77} +(8.46370e15 - 1.27348e16i) q^{78} +3.99449e15 q^{79} +(1.95293e16 + 1.91473e16i) q^{80} -2.07037e16 q^{81} +(1.28029e16 - 1.92637e16i) q^{82} -2.19564e15i q^{83} +(2.70540e16 - 1.13630e16i) q^{84} +2.01820e16i q^{85} +(-1.63358e16 - 1.08570e16i) q^{86} +3.80349e16 q^{87} +(-6.05455e15 + 3.16623e16i) q^{88} -6.74113e16 q^{89} +(-2.52578e16 - 1.67867e16i) q^{90} +5.20212e16i q^{91} +(-2.75811e16 - 6.56674e16i) q^{92} -1.13533e16i q^{93} +(7.79850e15 - 1.17339e16i) q^{94} +9.35994e15 q^{95} +(-8.20345e16 + 1.73732e16i) q^{96} -1.67025e15 q^{97} +(-8.63968e15 + 1.29996e16i) q^{98} -3.57455e16i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more