LMFDB - Embedded newform 15.11.d.c.14.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(14,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("15.14");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.d (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:	$9.53035879011$
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} + 17880 x^{14} + 140656106 x^{12} + 568287997200 x^{10} + \cdots + 16\!\cdots\!76 $ x^16 + 17880x^14 + 140656106x^12 + 568287997200x^10 + 2185320263599761x^8 + 14044998488243281560x^6 + 65358313992126025248056x^4 + 158088257382003622736619360*x^2 + 166976847233168897062137442576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{32}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.4
Root			$6.53233 - 63.3725i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.11.d.c.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-36.7249 q^{2} +(151.342 + 190.117i) q^{3} +324.720 q^{4} +(2839.18 + 1305.64i) q^{5} +(-5558.02 - 6982.05i) q^{6} -17185.2i q^{7} +25681.0 q^{8} +(-13240.3 + 57545.5i) q^{9} +O(q^{10})$	\(q-36.7249 q^{2} +(151.342 + 190.117i) q^{3} +324.720 q^{4} +(2839.18 + 1305.64i) q^{5} +(-5558.02 - 6982.05i) q^{6} -17185.2i q^{7} +25681.0 q^{8} +(-13240.3 + 57545.5i) q^{9} +(-104269. - 47949.4i) q^{10} +57743.7i q^{11} +(49143.8 + 61735.0i) q^{12} +726186. i q^{13} +631124. i q^{14} +(181462. + 737375. i) q^{15} -1.27565e6 q^{16} +853907. q^{17} +(486248. - 2.11335e6i) q^{18} -3.02605e6 q^{19} +(921940. + 423967. i) q^{20} +(3.26720e6 - 2.60084e6i) q^{21} -2.12063e6i q^{22} -1.73585e6 q^{23} +(3.88661e6 + 4.88240e6i) q^{24} +(6.35625e6 + 7.41388e6i) q^{25} -2.66691e7i q^{26} +(-1.29442e7 + 6.19183e6i) q^{27} -5.58038e6i q^{28} +2.25917e7i q^{29} +(-6.66419e6 - 2.70800e7i) q^{30} +1.06363e7 q^{31} +2.05507e7 q^{32} +(-1.09781e7 + 8.73903e6i) q^{33} -3.13597e7 q^{34} +(2.24376e7 - 4.87918e7i) q^{35} +(-4.29939e6 + 1.86862e7i) q^{36} -1.97180e7i q^{37} +1.11131e8 q^{38} +(-1.38061e8 + 1.09902e8i) q^{39} +(7.29129e7 + 3.35301e7i) q^{40} +8.40244e7i q^{41} +(-1.19988e8 + 9.55155e7i) q^{42} -7.92041e7i q^{43} +1.87506e7i q^{44} +(-1.12725e8 + 1.46095e8i) q^{45} +6.37488e7 q^{46} +1.87387e8 q^{47} +(-1.93059e8 - 2.42523e8i) q^{48} -1.28549e7 q^{49} +(-2.33433e8 - 2.72274e8i) q^{50} +(1.29232e8 + 1.62343e8i) q^{51} +2.35808e8i q^{52} +5.59650e8 q^{53} +(4.75375e8 - 2.27395e8i) q^{54} +(-7.53923e7 + 1.63945e8i) q^{55} -4.41332e8i q^{56} +(-4.57968e8 - 5.75304e8i) q^{57} -8.29680e8i q^{58} -6.70180e8i q^{59} +(5.89245e7 + 2.39441e8i) q^{60} -7.73815e8 q^{61} -3.90616e8 q^{62} +(9.88929e8 + 2.27536e8i) q^{63} +5.51539e8 q^{64} +(-9.48136e8 + 2.06177e9i) q^{65} +(4.03169e8 - 3.20940e8i) q^{66} +1.72739e9i q^{67} +2.77281e8 q^{68} +(-2.62706e8 - 3.30015e8i) q^{69} +(-8.24019e8 + 1.79187e9i) q^{70} +9.90045e8i q^{71} +(-3.40023e8 + 1.47782e9i) q^{72} -3.12724e9i q^{73} +7.24143e8i q^{74} +(-4.47540e8 + 2.33046e9i) q^{75} -9.82620e8 q^{76} +9.92335e8 q^{77} +(5.07027e9 - 4.03616e9i) q^{78} +1.32376e9 q^{79} +(-3.62179e9 - 1.66553e9i) q^{80} +(-3.13617e9 - 1.52383e9i) q^{81} -3.08579e9i q^{82} -1.92072e9 q^{83} +(1.06093e9 - 8.44545e8i) q^{84} +(2.42440e9 + 1.11489e9i) q^{85} +2.90877e9i q^{86} +(-4.29508e9 + 3.41908e9i) q^{87} +1.48291e9i q^{88} -1.80622e9i q^{89} +(4.13982e9 - 5.36532e9i) q^{90} +1.24796e10 q^{91} -5.63665e8 q^{92} +(1.60971e9 + 2.02214e9i) q^{93} -6.88179e9 q^{94} +(-8.59149e9 - 3.95092e9i) q^{95} +(3.11018e9 + 3.90704e9i) q^{96} -7.72264e8i q^{97} +4.72095e8 q^{98} +(-3.32289e9 - 7.64542e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9}+O(q^{10}) $ 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9	$ 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9} - 221680 q^{10} + 731640 q^{15} - 4218352 q^{16} + 1487600 q^{19} + 2444616 q^{21} + 28021368 q^{24} - 9324800 q^{25} - 35678700 q^{30} - 77667568 q^{31} + 251882368 q^{34} - 22344768 q^{36} - 70953984 q^{39} - 179966240 q^{40} - 484245000 q^{45} - 72018968 q^{46} + 89098816 q^{49} + 686556816 q^{51} + 441096084 q^{54} + 1424671200 q^{55} + 610091280 q^{60} - 1671368368 q^{61} - 4172730848 q^{64} + 2368350000 q^{66} - 2906594616 q^{69} + 2838634200 q^{70} - 1285884000 q^{75} + 4079367264 q^{76} - 3904999600 q^{79} - 11376681984 q^{81} + 13119851016 q^{84} + 8097594320 q^{85} - 15222287520 q^{90} + 19275224832 q^{91} - 9366481832 q^{94} - 5999937552 q^{96} + 42957756000 q^{99}+O(q^{100}) $ 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9 - 221680 * q^10 + 731640 * q^15 - 4218352 * q^16 + 1487600 * q^19 + 2444616 * q^21 + 28021368 * q^24 - 9324800 * q^25 - 35678700 * q^30 - 77667568 * q^31 + 251882368 * q^34 - 22344768 * q^36 - 70953984 * q^39 - 179966240 * q^40 - 484245000 * q^45 - 72018968 * q^46 + 89098816 * q^49 + 686556816 * q^51 + 441096084 * q^54 + 1424671200 * q^55 + 610091280 * q^60 - 1671368368 * q^61 - 4172730848 * q^64 + 2368350000 * q^66 - 2906594616 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 4079367264 * q^76 - 3904999600 * q^79 - 11376681984 * q^81 + 13119851016 * q^84 + 8097594320 * q^85 - 15222287520 * q^90 + 19275224832 * q^91 - 9366481832 * q^94 - 5999937552 * q^96 + 42957756000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−36.7249			−1.14765			−0.573827	−	0.818977i	$-0.694542\pi$
$2$	−36.7249			−1.14765			−0.573827	+	0.818977i	$0.694542\pi$
$3$	151.342	+	190.117i	0.622806	+	0.782376i
$3$	151.342	+	190.117i	0.622806	+	0.782376i
$4$	324.720			0.317110
$5$	2839.18	+	1305.64i	0.908537	+	0.417804i
$5$	2839.18	+	1305.64i	0.908537	+	0.417804i
$6$	−5558.02	−	6982.05i	−0.714766	−	0.897897i
$7$		−	17185.2i		−	1.02250i	−0.859432	−	0.511250i	$-0.829182\pi$
$7$		−	17185.2i		−	1.02250i	0.859432	−	0.511250i	$-0.170818\pi$
$8$	25681.0			0.783722
$9$	−13240.3	+	57545.5i	−0.224225	+	0.974537i
$10$	−104269.	−	47949.4i	−1.04269	−	0.479494i
$11$			57743.7i			0.358543i	0.983800	+	0.179271i	$0.0573740\pi$
$11$			57743.7i			0.358543i	−0.983800	+	0.179271i	$0.942626\pi$
$12$	49143.8	+	61735.0i	0.197498	+	0.248099i
$13$			726186.i			1.95583i	0.209002	+	0.977915i	$0.432979\pi$
$13$			726186.i			1.95583i	−0.209002	+	0.977915i	$0.567021\pi$
$14$			631124.i			1.17348i
$15$	181462.	+	737375.i	0.238963	+	0.971029i
$16$	−1.27565e6			−1.21655
$17$	853907.			0.601404			0.300702	−	0.953718i	$-0.402779\pi$
$17$	853907.			0.601404			0.300702	+	0.953718i	$0.402779\pi$
$18$	486248.	−	2.11335e6i	0.257333	−	1.11843i
$19$	−3.02605e6			−1.22210			−0.611051	−	0.791591i	$-0.709253\pi$
$19$	−3.02605e6			−1.22210			−0.611051	+	0.791591i	$0.709253\pi$
$20$	921940.	+	423967.i	0.288106	+	0.132490i
$21$	3.26720e6	−	2.60084e6i	0.799980	−	0.636820i
$22$		−	2.12063e6i		−	0.411483i
$23$	−1.73585e6			−0.269694			−0.134847	−	0.990866i	$-0.543054\pi$
$23$	−1.73585e6			−0.269694			−0.134847	+	0.990866i	$0.543054\pi$
$24$	3.88661e6	+	4.88240e6i	0.488107	+	0.613165i
$25$	6.35625e6	+	7.41388e6i	0.650880	+	0.759181i
$26$		−	2.66691e7i		−	2.24462i
$27$	−1.29442e7	+	6.19183e6i	−0.902104	+	0.431519i
$28$		−	5.58038e6i		−	0.324245i
$29$			2.25917e7i			1.10144i	0.834691	+	0.550718i	$0.185646\pi$
$29$			2.25917e7i			1.10144i	−0.834691	+	0.550718i	$0.814354\pi$
$30$	−6.66419e6	−	2.70800e7i	−0.274246	−	1.11441i
$31$	1.06363e7			0.371519			0.185760	−	0.982595i	$-0.440525\pi$
$31$	1.06363e7			0.371519			0.185760	+	0.982595i	$0.440525\pi$
$32$	2.05507e7			0.612458
$33$	−1.09781e7	+	8.73903e6i	−0.280515	+	0.223303i
$34$	−3.13597e7			−0.690204
$35$	2.24376e7	−	4.87918e7i	0.427205	−	0.928980i
$36$	−4.29939e6	+	1.86862e7i	−0.0711040	+	0.309035i
$37$		−	1.97180e7i		−	0.284351i	−0.989841	−	0.142175i	$-0.954590\pi$
$37$		−	1.97180e7i		−	0.284351i	0.989841	−	0.142175i	$-0.0454097\pi$
$38$	1.11131e8			1.40255
$39$	−1.38061e8	+	1.09902e8i	−1.53020	+	1.21810i
$40$	7.29129e7	+	3.35301e7i	0.712040	+	0.327442i
$41$			8.40244e7i			0.725248i	0.931936	+	0.362624i	$0.118119\pi$
$41$			8.40244e7i			0.725248i	−0.931936	+	0.362624i	$0.881881\pi$
$42$	−1.19988e8	+	9.55155e7i	−0.918101	+	0.730849i
$43$		−	7.92041e7i		−	0.538773i	−0.963032	−	0.269386i	$-0.913179\pi$
$43$		−	7.92041e7i		−	0.538773i	0.963032	−	0.269386i	$-0.0868208\pi$
$44$			1.87506e7i			0.113697i
$45$	−1.12725e8	+	1.46095e8i	−0.610882	+	0.791721i
$46$	6.37488e7			0.309516
$47$	1.87387e8			0.817054			0.408527	−	0.912746i	$-0.366043\pi$
$47$	1.87387e8			0.817054			0.408527	+	0.912746i	$0.366043\pi$
$48$	−1.93059e8	−	2.42523e8i	−0.757676	−	0.951801i
$49$	−1.28549e7			−0.0455080
$50$	−2.33433e8	−	2.72274e8i	−0.746985	−	0.871277i
$51$	1.29232e8	+	1.62343e8i	0.374558	+	0.470524i
$52$			2.35808e8i			0.620213i
$53$	5.59650e8			1.33825			0.669125	−	0.743149i	$-0.266669\pi$
$53$	5.59650e8			1.33825			0.669125	+	0.743149i	$0.266669\pi$
$54$	4.75375e8	−	2.27395e8i	1.03530	−	0.495235i
$55$	−7.53923e7	+	1.63945e8i	−0.149801	+	0.325749i
$56$		−	4.41332e8i		−	0.801356i
$57$	−4.57968e8	−	5.75304e8i	−0.761133	−	0.956144i
$58$		−	8.29680e8i		−	1.26407i
$59$		−	6.70180e8i		−	0.937414i	−0.883354	−	0.468707i	$-0.844720\pi$
$59$		−	6.70180e8i		−	0.937414i	0.883354	−	0.468707i	$-0.155280\pi$
$60$	5.89245e7	+	2.39441e8i	0.0757774	+	0.307923i
$61$	−7.73815e8			−0.916195			−0.458097	−	0.888902i	$-0.651469\pi$
$61$	−7.73815e8			−0.916195			−0.458097	+	0.888902i	$0.651469\pi$
$62$	−3.90616e8			−0.426375
$63$	9.88929e8	+	2.27536e8i	0.996465	+	0.229270i
$64$	5.51539e8			0.513661
$65$	−9.48136e8	+	2.06177e9i	−0.817154	+	1.77694i
$66$	4.03169e8	−	3.20940e8i	0.321935	−	0.256274i
$67$			1.72739e9i			1.27943i	0.768612	+	0.639715i	$0.220948\pi$
$67$			1.72739e9i			1.27943i	−0.768612	+	0.639715i	$0.779052\pi$
$68$	2.77281e8			0.190711
$69$	−2.62706e8	−	3.30015e8i	−0.167967	−	0.211003i
$70$	−8.24019e8	+	1.79187e9i	−0.490283	+	1.06615i
$71$			9.90045e8i			0.548736i	0.961625	+	0.274368i	$0.0884686\pi$
$71$			9.90045e8i			0.548736i	−0.961625	+	0.274368i	$0.911531\pi$
$72$	−3.40023e8	+	1.47782e9i	−0.175730	+	0.763766i
$73$		−	3.12724e9i		−	1.50851i	−0.656584	−	0.754253i	$-0.727999\pi$
$73$		−	3.12724e9i		−	1.50851i	0.656584	−	0.754253i	$-0.272001\pi$
$74$			7.24143e8i			0.326337i
$75$	−4.47540e8	+	2.33046e9i	−0.188593	+	0.982055i
$76$	−9.82620e8			−0.387541
$77$	9.92335e8			0.366610
$78$	5.07027e9	−	4.03616e9i	1.75613	−	1.39796i
$79$	1.32376e9			0.430203			0.215102	−	0.976592i	$-0.430992\pi$
$79$	1.32376e9			0.430203			0.215102	+	0.976592i	$0.430992\pi$
$80$	−3.62179e9	−	1.66553e9i	−1.10528	−	0.508280i
$81$	−3.13617e9	−	1.52383e9i	−0.899446	−	0.437032i
$82$		−	3.08579e9i		−	0.832333i
$83$	−1.92072e9			−0.487612			−0.243806	−	0.969824i	$-0.578396\pi$
$83$	−1.92072e9			−0.487612			−0.243806	+	0.969824i	$0.578396\pi$
$84$	1.06093e9	−	8.44545e8i	0.253682	−	0.201942i
$85$	2.42440e9	+	1.11489e9i	0.546398	+	0.251269i
$86$			2.90877e9i			0.618325i
$87$	−4.29508e9	+	3.41908e9i	−0.861738	+	0.685982i
$88$			1.48291e9i			0.280998i
$89$		−	1.80622e9i		−	0.323460i	−0.986835	−	0.161730i	$-0.948293\pi$
$89$		−	1.80622e9i		−	0.323460i	0.986835	−	0.161730i	$-0.0517074\pi$
$90$	4.13982e9	−	5.36532e9i	0.701082	−	0.908622i
$91$	1.24796e10			1.99984
$92$	−5.63665e8			−0.0855228
$93$	1.60971e9	+	2.02214e9i	0.231384	+	0.290668i
$94$	−6.88179e9			−0.937696
$95$	−8.59149e9	−	3.95092e9i	−1.11033	−	0.510599i
$96$	3.11018e9	+	3.90704e9i	0.381443	+	0.479173i
$97$		−	7.72264e8i		−	0.0899305i	−0.998989	−	0.0449653i	$-0.985682\pi$
$97$		−	7.72264e8i		−	0.0899305i	0.998989	−	0.0449653i	$-0.0143177\pi$
$98$	4.72095e8			0.0522275
$99$	−3.32289e9	−	7.64542e8i	−0.349413	−	0.0803943i
$100$	2.06400e9	+	2.40744e9i	0.206400	+	0.240744i
$101$		−	8.59370e9i		−	0.817661i	−0.912610	−	0.408830i	$-0.865937\pi$
$101$		−	8.59370e9i		−	0.817661i	0.912610	−	0.408830i	$-0.134063\pi$
$102$	−4.74603e9	−	5.96202e9i	−0.429863	−	0.539999i
$103$		−	8.48204e9i		−	0.731668i	−0.930680	−	0.365834i	$-0.880784\pi$
$103$		−	8.48204e9i		−	0.731668i	0.930680	−	0.365834i	$-0.119216\pi$
$104$			1.86492e10i			1.53283i
$105$	1.26719e10	−	3.11846e9i	0.992878	−	0.244340i
$106$	−2.05531e10			−1.53585
$107$	2.59046e10			1.84696			0.923482	−	0.383642i	$-0.125330\pi$
$107$	2.59046e10			1.84696			0.923482	+	0.383642i	$0.125330\pi$
$108$	−4.20325e9	+	2.01061e9i	−0.286066	+	0.136839i
$109$	−1.71341e10			−1.11360			−0.556800	−	0.830647i	$-0.687971\pi$
$109$	−1.71341e10			−1.11360			−0.556800	+	0.830647i	$0.687971\pi$
$110$	2.76878e9	−	6.02085e9i	0.171919	−	0.373848i
$111$	3.74874e9	−	2.98416e9i	0.222469	−	0.177096i
$112$			2.19222e10i			1.24392i
$113$	2.06259e9			0.111949			0.0559745	−	0.998432i	$-0.482173\pi$
$113$	2.06259e9			0.111949			0.0559745	+	0.998432i	$0.482173\pi$
$114$	1.68188e10	+	2.11280e10i	0.873517	+	1.09732i
$115$	−4.92838e9	−	2.26639e9i	−0.245027	−	0.112679i
$116$			7.33600e9i			0.349277i
$117$	−4.17887e10	−	9.61490e9i	−1.90603	−	0.438546i
$118$			2.46123e10i			1.07583i
$119$		−	1.46745e10i		−	0.614936i
$120$	4.66013e9	+	1.89365e10i	0.187280	+	0.761016i
$121$	2.26031e10			0.871447
$122$	2.84183e10			1.05147
$123$	−1.59745e10	+	1.27164e10i	−0.567416	+	0.451689i
$124$	3.45382e9			0.117812
$125$	8.36669e9	+	2.93483e10i	0.274160	+	0.961684i
$126$	−3.63183e10	−	8.35625e9i	−1.14360	−	0.263123i
$127$		−	4.05289e10i		−	1.22672i	−0.789803	−	0.613361i	$-0.789817\pi$
$127$		−	4.05289e10i		−	1.22672i	0.789803	−	0.613361i	$-0.210183\pi$
$128$	−4.12991e10			−1.20196
$129$	1.50581e10	−	1.19869e10i	0.421523	−	0.335551i
$130$	3.48202e10	−	7.57184e10i	0.937810	−	2.03932i
$131$		−	5.25628e10i		−	1.36245i	−0.732072	−	0.681227i	$-0.761447\pi$
$131$		−	5.25628e10i		−	1.36245i	0.732072	−	0.681227i	$-0.238553\pi$
$132$	−3.56481e9	+	2.83774e9i	−0.0889542	+	0.0708115i
$133$			5.20031e10i			1.24960i
$134$		−	6.34383e10i		−	1.46834i
$135$	−4.48352e10	+	6.79287e8i	−0.999885	+	0.0151490i
$136$	2.19292e10			0.471333
$137$	5.48676e10			1.13688			0.568438	−	0.822726i	$-0.307548\pi$
$137$	5.48676e10			1.13688			0.568438	+	0.822726i	$0.307548\pi$
$138$	9.64787e9	+	1.21198e10i	0.192768	+	0.242158i
$139$	3.59765e10			0.693338			0.346669	−	0.937988i	$-0.387313\pi$
$139$	3.59765e10			0.693338			0.346669	+	0.937988i	$0.387313\pi$
$140$	7.28595e9	−	1.58437e10i	0.135471	−	0.294589i
$141$	2.83595e10	+	3.56256e10i	0.508866	+	0.639244i
$142$		−	3.63593e10i		−	0.629759i
$143$	−4.19327e10			−0.701249
$144$	1.68899e10	−	7.34077e10i	0.272781	−	1.18557i
$145$	−2.94966e10	+	6.41420e10i	−0.460185	+	1.00070i
$146$			1.14848e11i			1.73124i
$147$	−1.94548e9	−	2.44394e9i	−0.0283427	−	0.0356044i
$148$		−	6.40285e9i		−	0.0901705i
$149$			4.09955e10i			0.558219i	0.960259	+	0.279110i	$0.0900393\pi$
$149$			4.09955e10i			0.558219i	−0.960259	+	0.279110i	$0.909961\pi$
$150$	1.64359e10	−	8.55861e10i	0.216440	−	1.12706i
$151$	−6.68405e10			−0.851442			−0.425721	−	0.904855i	$-0.639979\pi$
$151$	−6.68405e10			−0.851442			−0.425721	+	0.904855i	$0.639979\pi$
$152$	−7.77119e10			−0.957788
$153$	−1.13060e10	+	4.91385e10i	−0.134850	+	0.586091i
$154$	−3.64434e10			−0.420742
$155$	3.01983e10	+	1.38871e10i	0.337539	+	0.155222i
$156$	−4.48311e10	+	3.56876e10i	−0.485240	+	0.386273i
$157$			4.61509e10i			0.483817i	0.970299	+	0.241909i	$0.0777735\pi$
$157$			4.61509e10i			0.483817i	−0.970299	+	0.241909i	$0.922227\pi$
$158$	−4.86150e10			−0.493724
$159$	8.46986e10	+	1.06399e11i	0.833471	+	1.04702i
$160$	5.83471e10	+	2.68317e10i	0.556441	+	0.255887i
$161$			2.98308e10i			0.275763i
$162$	1.15176e11	+	5.59627e10i	1.03225	+	0.501561i
$163$		−	6.09521e9i		−	0.0529725i	−0.999649	−	0.0264862i	$-0.991568\pi$
$163$		−	6.09521e9i		−	0.0529725i	0.999649	−	0.0264862i	$-0.00843182\pi$
$164$			2.72845e10i			0.229983i
$165$	−4.25787e10	+	1.04783e10i	−0.348155	+	0.0856783i
$166$	7.05384e10			0.559610
$167$	−2.17918e9			−0.0167768			−0.00838842	−	0.999965i	$-0.502670\pi$
$167$	−2.17918e9			−0.0167768			−0.00838842	+	0.999965i	$0.502670\pi$
$168$	8.39050e10	−	6.67921e10i	0.626962	−	0.499089i
$169$	−3.89488e11			−2.82527
$170$	−8.90358e10	−	4.09444e10i	−0.627076	−	0.288370i
$171$	4.00657e10	−	1.74135e11i	0.274026	−	1.19098i
$172$		−	2.57192e10i		−	0.170850i
$173$	1.35971e11			0.877433			0.438717	−	0.898625i	$-0.355433\pi$
$173$	1.35971e11			0.877433			0.438717	+	0.898625i	$0.355433\pi$
$174$	1.57737e11	−	1.25565e11i	0.988977	−	0.787270i
$175$	1.27409e11	−	1.09233e11i	0.776263	−	0.665525i
$176$		−	7.36605e10i		−	0.436186i
$177$	1.27413e11	−	1.01426e11i	0.733411	−	0.583827i
$178$			6.63334e10i			0.371220i
$179$			1.70509e11i			0.927858i	0.885872	+	0.463929i	$0.153561\pi$
$179$			1.70509e11i			0.927858i	−0.885872	+	0.463929i	$0.846439\pi$
$180$	−3.66041e10	+	4.74400e10i	−0.193717	+	0.251063i
$181$	1.47301e11			0.758250			0.379125	−	0.925346i	$-0.376225\pi$
$181$	1.47301e11			0.758250			0.379125	+	0.925346i	$0.376225\pi$
$182$	−4.58314e11			−2.29512
$183$	−1.17111e11	−	1.47116e11i	−0.570612	−	0.716809i
$184$	−4.45782e10			−0.211365
$185$	2.57446e10	−	5.59830e10i	0.118803	−	0.258343i
$186$	−5.91166e10	−	7.42630e10i	−0.265549	−	0.333586i
$187$			4.93077e10i			0.215629i
$188$	6.08485e10			0.259096
$189$	1.06408e11	+	2.22448e11i	0.441229	+	0.922402i
$190$	3.15522e11	+	1.45097e11i	1.27427	+	0.585991i
$191$		−	4.11947e11i		−	1.62059i	−0.586019	−	0.810297i	$-0.699306\pi$
$191$		−	4.11947e11i		−	1.62059i	0.586019	−	0.810297i	$-0.300694\pi$
$192$	8.34710e10	+	1.04857e11i	0.319911	+	0.401876i
$193$		−	2.80177e11i		−	1.04628i	−0.852248	−	0.523138i	$-0.824761\pi$
$193$		−	2.80177e11i		−	1.04628i	0.852248	−	0.523138i	$-0.175239\pi$
$194$			2.83613e10i			0.103209i
$195$	−5.35472e11	+	1.31775e11i	−1.89917	+	0.467370i
$196$	−4.17425e9			−0.0144310
$197$	5.11823e10			0.172500			0.0862499	−	0.996274i	$-0.472512\pi$
$197$	5.11823e10			0.172500			0.0862499	+	0.996274i	$0.472512\pi$
$198$	1.22033e11	+	2.80777e10i	0.401006	+	0.0922648i
$199$	1.20927e11			0.387487			0.193743	−	0.981052i	$-0.437937\pi$
$199$	1.20927e11			0.387487			0.193743	+	0.981052i	$0.437937\pi$
$200$	1.63235e11	+	1.90396e11i	0.510109	+	0.594986i
$201$	−3.28407e11	+	2.61427e11i	−1.00100	+	0.796837i
$202$			3.15603e11i			0.938392i
$203$	3.88243e11			1.12622
$204$	4.19643e10	+	5.27160e10i	0.118776	+	0.149208i
$205$	−1.09705e11	+	2.38560e11i	−0.303011	+	0.658914i
$206$			3.11502e11i			0.839702i
$207$	2.29831e10	−	9.98901e10i	0.0604723	−	0.262827i
$208$		−	9.26357e11i		−	2.37937i
$209$		−	1.74735e11i		−	0.438176i
$210$	−4.65375e11	+	1.14525e11i	−1.13948	+	0.280417i
$211$	4.63289e11			1.10775			0.553873	−	0.832601i	$-0.313149\pi$
$211$	4.63289e11			1.10775			0.553873	+	0.832601i	$0.313149\pi$
$212$	1.81730e11			0.424373
$213$	−1.88225e11	+	1.49835e11i	−0.429318	+	0.341756i
$214$	−9.51346e11			−2.11968
$215$	1.03412e11	−	2.24875e11i	0.225101	−	0.489495i
$216$	−3.32420e11	+	1.59012e11i	−0.706998	+	0.338191i
$217$		−	1.82786e11i		−	0.379879i
$218$	6.29249e11			1.27803
$219$	5.94543e11	−	4.73282e11i	1.18022	−	0.939506i
$220$	−2.44814e10	+	5.32362e10i	−0.0475032	+	0.103298i
$221$			6.20096e11i			1.17624i
$222$	−1.37672e11	+	1.09593e11i	−0.255318	+	0.203244i
$223$			7.27823e11i			1.31978i	0.751362	+	0.659890i	$0.229397\pi$
$223$			7.27823e11i			1.31978i	−0.751362	+	0.659890i	$0.770603\pi$
$224$		−	3.53167e11i		−	0.626239i
$225$	−5.10793e11	+	2.67611e11i	−0.885794	+	0.464079i
$226$	−7.57484e10			−0.128479
$227$	−4.05951e11			−0.673510			−0.336755	−	0.941592i	$-0.609329\pi$
$227$	−4.05951e11			−0.673510			−0.336755	+	0.941592i	$0.609329\pi$
$228$	−1.48711e11	−	1.86813e11i	−0.241363	−	0.303203i
$229$	8.19857e10			0.130185			0.0650924	−	0.997879i	$-0.479266\pi$
$229$	8.19857e10			0.130185			0.0650924	+	0.997879i	$0.479266\pi$
$230$	1.80994e11	+	8.32328e10i	0.281207	+	0.129317i
$231$	1.50182e11	+	1.88660e11i	0.228327	+	0.286827i
$232$			5.80178e11i			0.863220i
$233$	−3.36869e11			−0.490548			−0.245274	−	0.969454i	$-0.578878\pi$
$233$	−3.36869e11			−0.490548			−0.245274	+	0.969454i	$0.578878\pi$
$234$	1.53469e12	+	3.53107e11i	2.18746	+	0.503299i
$235$	5.32026e11	+	2.44660e11i	0.742324	+	0.341368i
$236$		−	2.17621e11i		−	0.297263i
$237$	2.00340e11	+	2.51670e11i	0.267933	+	0.336581i
$238$			5.38922e11i			0.705734i
$239$		−	1.30858e12i		−	1.67808i	−0.544072	−	0.839038i	$-0.683118\pi$
$239$		−	1.30858e12i		−	1.67808i	0.544072	−	0.839038i	$-0.316882\pi$
$240$	−2.31482e11	−	9.40630e11i	−0.290710	−	1.18131i
$241$	−5.45295e11			−0.670728			−0.335364	−	0.942089i	$-0.608859\pi$
$241$	−5.45295e11			−0.670728			−0.335364	+	0.942089i	$0.608859\pi$
$242$	−8.30097e11			−1.00012
$243$	−1.84927e11	−	8.26862e11i	−0.218258	−	0.975891i
$244$	−2.51273e11			−0.290534
$245$	−3.64973e10	−	1.67838e10i	−0.0413457	−	0.0190134i
$246$	5.86663e11	−	4.67009e11i	0.651198	−	0.518382i
$247$		−	2.19747e12i		−	2.39023i
$248$	2.73150e11			0.291168
$249$	−2.90686e11	−	3.65163e11i	−0.303688	−	0.381496i
$250$	−3.07266e11	−	1.07781e12i	−0.314641	−	1.10368i
$251$		−	3.22417e11i		−	0.323630i	−0.986821	−	0.161815i	$-0.948265\pi$
$251$		−	3.22417e11i		−	0.323630i	0.986821	−	0.161815i	$-0.0517348\pi$
$252$	3.21125e11	+	7.38857e10i	0.315989	+	0.0727039i
$253$		−	1.00234e11i		−	0.0966970i
$254$			1.48842e12i			1.40785i
$255$	1.54952e11	+	6.29650e11i	0.143713	+	0.583980i
$256$	9.51932e11			0.865777
$257$	2.01099e12			1.79368			0.896839	−	0.442358i	$-0.145858\pi$
$257$	2.01099e12			1.79368			0.896839	+	0.442358i	$0.145858\pi$
$258$	−5.53007e11	+	4.40218e11i	−0.483762	+	0.385096i
$259$	−3.38858e11			−0.290749
$260$	−3.07879e11	+	6.69500e11i	−0.259127	+	0.563487i
$261$	−1.30005e12	−	2.99121e11i	−1.07339	−	0.246970i
$262$			1.93036e12i			1.56363i
$263$	−2.08594e12			−1.65776			−0.828882	−	0.559424i	$-0.811022\pi$
$263$	−2.08594e12			−1.65776			−0.828882	+	0.559424i	$0.811022\pi$
$264$	−2.81928e11	+	2.24427e11i	−0.219846	+	0.175007i
$265$	1.58895e12	+	7.30701e11i	1.21585	+	0.559126i
$266$		−	1.90981e12i		−	1.43411i
$267$	3.43394e11	−	2.73357e11i	0.253068	−	0.201453i
$268$			5.60919e11i			0.405720i
$269$			2.14609e12i			1.52365i	0.647781	+	0.761826i	$0.275697\pi$
$269$			2.14609e12i			1.52365i	−0.647781	+	0.761826i	$0.724303\pi$
$270$	1.64657e12	−	2.49468e10i	1.14752	−	0.0173858i
$271$	−2.87177e11			−0.196473			−0.0982364	−	0.995163i	$-0.531320\pi$
$271$	−2.87177e11			−0.196473			−0.0982364	+	0.995163i	$0.531320\pi$
$272$	−1.08928e12			−0.731639
$273$	1.88869e12	+	2.37260e12i	1.24551	+	1.56463i
$274$	−2.01501e12			−1.30474
$275$	−4.28104e11	+	3.67033e11i	−0.272199	+	0.233368i
$276$	−8.53061e10	−	1.07162e11i	−0.0532641	−	0.0669110i
$277$		−	8.41910e11i		−	0.516258i	−0.966110	−	0.258129i	$-0.916894\pi$
$277$		−	8.41910e11i		−	0.516258i	0.966110	−	0.258129i	$-0.0831059\pi$
$278$	−1.32123e12			−0.795712
$279$	−1.40827e11	+	6.12069e11i	−0.0833039	+	0.362059i
$280$	5.76220e11	−	1.25302e12i	0.334810	−	0.728062i
$281$			3.00772e12i			1.71675i	0.513025	+	0.858374i	$0.328525\pi$
$281$			3.00772e12i			1.71675i	−0.513025	+	0.858374i	$0.671475\pi$
$282$	−1.04150e12	−	1.30835e12i	−0.584003	−	0.733631i
$283$			2.02042e12i			1.11304i	0.830835	+	0.556519i	$0.187863\pi$
$283$			2.02042e12i			1.11304i	−0.830835	+	0.556519i	$0.812137\pi$
$284$			3.21488e11i			0.174009i
$285$	−5.49113e11	−	2.23133e12i	−0.292037	−	1.18670i
$286$	1.53997e12			0.804791
$287$	1.44397e12			0.741566
$288$	−2.72097e11	+	1.18260e12i	−0.137329	+	0.596863i
$289$	−1.28684e12			−0.638313
$290$	1.08326e12	−	2.35561e12i	0.528133	−	1.14845i
$291$	1.46821e11	−	1.16876e11i	0.0703595	−	0.0560093i
$292$		−	1.01548e12i		−	0.478362i
$293$	−1.85878e12			−0.860774			−0.430387	−	0.902644i	$-0.641623\pi$
$293$	−1.85878e12			−0.860774			−0.430387	+	0.902644i	$0.641623\pi$
$294$	7.14477e10	+	8.97535e10i	0.0325276	+	0.0408615i
$295$	8.75012e11	−	1.90276e12i	0.391655	−	0.851676i
$296$		−	5.06378e11i		−	0.222852i
$297$	−3.57539e11	−	7.47446e11i	−0.154718	−	0.323443i
$298$		−	1.50556e12i		−	0.640643i
$299$		−	1.26055e12i		−	0.527477i
$300$	−1.45326e11	+	7.56749e11i	−0.0598047	+	0.311419i
$301$	−1.36114e12			−0.550895
$302$	2.45471e12			0.977160
$303$	1.63381e12	−	1.30059e12i	0.639718	−	0.509244i
$304$	3.86017e12			1.48675
$305$	−2.19700e12	−	1.01032e12i	−0.832397	−	0.382790i
$306$	4.15211e11	−	1.80461e12i	0.154761	−	0.672629i
$307$			2.24705e12i			0.823988i	0.911187	+	0.411994i	$0.135168\pi$
$307$			2.24705e12i			0.823988i	−0.911187	+	0.411994i	$0.864832\pi$
$308$	3.22231e11			0.116256
$309$	1.61258e12	−	1.28369e12i	0.572440	−	0.455688i
$310$	−1.10903e12	−	5.10003e11i	−0.387378	−	0.178141i
$311$		−	4.03605e11i		−	0.138725i	−0.997592	−	0.0693625i	$-0.977903\pi$
$311$		−	4.03605e11i		−	0.138725i	0.997592	−	0.0693625i	$-0.0220965\pi$
$312$	−3.54553e12	+	2.82240e12i	−1.19925	+	0.954654i
$313$			8.52934e11i			0.283918i	0.989873	+	0.141959i	$0.0453402\pi$
$313$			8.52934e11i			0.283918i	−0.989873	+	0.141959i	$0.954660\pi$
$314$		−	1.69489e12i		−	0.555255i
$315$	2.51067e12	+	1.93720e12i	0.809536	+	0.624628i
$316$	4.29852e11			0.136422
$317$	1.62693e12			0.508246			0.254123	−	0.967172i	$-0.418213\pi$
$317$	1.62693e12			0.508246			0.254123	+	0.967172i	$0.418213\pi$
$318$	−3.11055e12	−	3.90751e12i	−0.956536	−	1.20161i
$319$	−1.30453e12			−0.394912
$320$	1.56592e12	+	7.20110e11i	0.466680	+	0.214610i
$321$	3.92046e12	+	4.92492e12i	1.15030	+	1.44502i
$322$		−	1.09553e12i		−	0.316480i
$323$	−2.58396e12			−0.734977
$324$	−1.01838e12	−	4.94820e11i	−0.285223	−	0.138587i
$325$	−5.38385e12	+	4.61582e12i	−1.48483	+	1.27301i
$326$			2.23846e11i			0.0607941i
$327$	−2.59311e12	−	3.25749e12i	−0.693557	−	0.871254i
$328$			2.15783e12i			0.568392i
$329$		−	3.22028e12i		−	0.835439i
$330$	1.56370e12	−	3.84815e11i	0.399562	−	0.0983291i
$331$	−9.37645e11			−0.235993			−0.117996	−	0.993014i	$-0.537647\pi$
$331$	−9.37645e11			−0.235993			−0.117996	+	0.993014i	$0.537647\pi$
$332$	−6.23698e11			−0.154627
$333$	1.13468e12	+	2.61072e11i	0.277111	+	0.0637586i
$334$	8.00301e10			0.0192540
$335$	−2.25535e12	+	4.90437e12i	−0.534551	+	1.16241i
$336$	−4.16779e12	+	3.31775e12i	−0.973217	+	0.774724i
$337$		−	1.28553e12i		−	0.295755i	−0.989006	−	0.147877i	$-0.952756\pi$
$337$		−	1.28553e12i		−	0.295755i	0.989006	−	0.147877i	$-0.0472441\pi$
$338$	1.43039e13			3.24244
$339$	3.12156e11	+	3.92134e11i	0.0697225	+	0.0875862i
$340$	7.87251e11	+	3.62029e11i	0.173268	+	0.0796798i
$341$			6.14177e11i			0.133205i
$342$	−1.47141e12	+	6.39511e12i	−0.314487	+	1.36684i
$343$		−	4.63347e12i		−	0.975969i
$344$		−	2.03404e12i		−	0.422248i
$345$	−3.14991e11	−	1.27997e12i	−0.0644469	−	0.261881i
$346$	−4.99351e12			−1.00699
$347$	6.96146e12			1.38374			0.691868	−	0.722024i	$-0.256788\pi$
$347$	6.96146e12			1.38374			0.691868	+	0.722024i	$0.256788\pi$
$348$	−1.39470e12	+	1.11024e12i	−0.273266	+	0.217532i
$349$	7.62023e12			1.47177			0.735887	−	0.677105i	$-0.236766\pi$
$349$	7.62023e12			1.47177			0.735887	+	0.677105i	$0.236766\pi$
$350$	−4.67908e12	+	4.01158e12i	−0.890881	+	0.763793i
$351$	−4.49642e12	−	9.39990e12i	−0.843979	−	1.76436i
$352$			1.18667e12i			0.219592i
$353$	−3.03938e12			−0.554513			−0.277256	−	0.960796i	$-0.589425\pi$
$353$	−3.03938e12			−0.554513			−0.277256	+	0.960796i	$0.589425\pi$
$354$	−4.67923e12	+	3.72488e12i	−0.841702	+	0.670032i
$355$	−1.29264e12	+	2.81091e12i	−0.229264	+	0.498547i
$356$		−	5.86517e11i		−	0.102572i
$357$	2.78989e12	−	2.22087e12i	0.481111	−	0.382986i
$358$		−	6.26192e12i		−	1.06486i
$359$			6.57631e12i			1.10283i	0.834230	+	0.551417i	$0.185913\pi$
$359$			6.57631e12i			1.10283i	−0.834230	+	0.551417i	$0.814087\pi$
$360$	−2.89489e12	+	3.75186e12i	−0.478762	+	0.620489i
$361$	3.02590e12			0.493535
$362$	−5.40961e12			−0.870208
$363$	3.42079e12	+	4.29724e12i	0.542743	+	0.681800i
$364$	4.05239e12			0.634168
$365$	4.08304e12	−	8.87879e12i	0.630260	−	1.37053i
$366$	4.30088e12	+	5.40281e12i	0.654865	+	0.822649i
$367$		−	2.32215e12i		−	0.348786i	−0.984676	−	0.174393i	$-0.944204\pi$
$367$		−	2.32215e12i		−	0.348786i	0.984676	−	0.174393i	$-0.0557963\pi$
$368$	2.21433e12			0.328097
$369$	−4.83522e12	−	1.11251e12i	−0.706781	−	0.162619i
$370$	−9.45468e11	+	2.05597e12i	−0.136345	+	0.296489i
$371$		−	9.61769e12i		−	1.36836i
$372$	5.22707e11	+	6.56631e11i	0.0733743	+	0.0921736i
$373$		−	6.74020e12i		−	0.933531i	−0.884381	−	0.466766i	$-0.845419\pi$
$373$		−	6.74020e12i		−	0.933531i	0.884381	−	0.466766i	$-0.154581\pi$
$374$		−	1.81082e12i		−	0.247467i
$375$	−4.31339e12	+	6.03228e12i	−0.581650	+	0.813439i
$376$	4.81229e12			0.640343
$377$	−1.64058e13			−2.15422
$378$	−3.90782e12	−	8.16940e12i	−0.506378	−	1.05860i
$379$	4.47192e12			0.571871			0.285936	−	0.958249i	$-0.407696\pi$
$379$	4.47192e12			0.571871			0.285936	+	0.958249i	$0.407696\pi$
$380$	−2.78983e12	−	1.28294e12i	−0.352095	−	0.161916i
$381$	7.70525e12	−	6.13372e12i	0.959758	−	0.764010i
$382$			1.51287e13i			1.85988i
$383$	2.03208e12			0.246574			0.123287	−	0.992371i	$-0.460656\pi$
$383$	2.03208e12			0.246574			0.123287	+	0.992371i	$0.460656\pi$
$384$	−6.25029e12	−	7.85169e12i	−0.748590	−	0.940388i
$385$	2.81742e12	+	1.29563e12i	0.333079	+	0.153171i
$386$			1.02895e13i			1.20076i
$387$	4.55784e12	+	1.04868e12i	0.525054	+	0.120806i
$388$		−	2.50770e11i		−	0.0285179i
$389$			5.60385e12i			0.629128i	0.949236	+	0.314564i	$0.101858\pi$
$389$			5.60385e12i			0.629128i	−0.949236	+	0.314564i	$0.898142\pi$
$390$	1.96652e13	−	4.83944e12i	2.17959	−	0.536380i
$391$	−1.48225e12			−0.162195
$392$	−3.30126e11			−0.0356656
$393$	9.99310e12	−	7.95495e12i	1.06595	−	0.848545i
$394$	−1.87967e12			−0.197970
$395$	3.75839e12	+	1.72835e12i	0.390856	+	0.179741i
$396$	−1.07901e12	−	2.48262e11i	−0.110802	−	0.0254938i
$397$		−	8.63100e12i		−	0.875203i	−0.899169	−	0.437602i	$-0.855828\pi$
$397$		−	8.63100e12i		−	0.875203i	0.899169	−	0.437602i	$-0.144172\pi$
$398$	−4.44103e12			−0.444701
$399$	−9.88670e12	+	7.87025e12i	−0.977658	+	0.778259i
$400$	−8.10832e12	−	9.45748e12i	−0.791829	−	0.923582i
$401$		−	2.34497e12i		−	0.226160i	−0.993586	−	0.113080i	$-0.963928\pi$
$401$		−	2.34497e12i		−	0.226160i	0.993586	−	0.113080i	$-0.0360716\pi$
$402$	1.20607e13	−	9.60087e12i	1.14880	−	0.914493i
$403$			7.72392e12i			0.726628i
$404$		−	2.79055e12i		−	0.259288i
$405$	−6.91459e12	−	8.42115e12i	−0.634587	−	0.772852i
$406$	−1.42582e13			−1.29251
$407$	1.13859e12			0.101952
$408$	3.31880e12	+	4.16912e12i	0.293549	+	0.368760i
$409$	−7.52569e12			−0.657552			−0.328776	−	0.944408i	$-0.606636\pi$
$409$	−7.52569e12			−0.657552			−0.328776	+	0.944408i	$0.606636\pi$
$410$	4.02892e12	−	8.76111e12i	0.347752	−	0.756206i
$411$	8.30377e12	+	1.04313e13i	0.708054	+	0.889465i
$412$		−	2.75429e12i		−	0.232019i
$413$	−1.15172e13			−0.958507
$414$	−8.44052e11	+	3.66846e12i	−0.0694012	+	0.301635i
$415$	−5.45328e12	−	2.50777e12i	−0.443014	−	0.203726i
$416$			1.49236e13i			1.19786i
$417$	5.44475e12	+	6.83976e12i	0.431815	+	0.542451i
$418$			6.41713e12i			0.502875i
$419$			1.38946e13i			1.07591i	0.842974	+	0.537955i	$0.180803\pi$
$419$			1.38946e13i			1.07591i	−0.842974	+	0.537955i	$0.819197\pi$
$420$	4.11483e12	−	1.01263e12i	0.314851	−	0.0774825i
$421$	−9.62790e11			−0.0727983			−0.0363991	−	0.999337i	$-0.511589\pi$
$421$	−9.62790e11			−0.0727983			−0.0363991	+	0.999337i	$0.511589\pi$
$422$	−1.70143e13			−1.27131
$423$	−2.48106e12	+	1.07833e13i	−0.183204	+	0.796250i
$424$	1.43724e13			1.04882
$425$	5.42765e12	+	6.33076e12i	0.391442	+	0.456574i
$426$	6.91254e12	−	5.50269e12i	0.492708	−	0.392218i
$427$			1.32981e13i			0.936810i
$428$	8.41176e12			0.585691
$429$	−6.34617e12	−	7.97213e12i	−0.436742	−	0.548640i
$430$	−3.79779e12	+	8.25851e12i	−0.258338	+	0.561771i
$431$		−	9.24299e11i		−	0.0621479i	−0.999517	−	0.0310739i	$-0.990107\pi$
$431$		−	9.24299e11i		−	0.0621479i	0.999517	−	0.0310739i	$-0.00989273\pi$
$432$	1.65122e13	−	7.89859e12i	1.09746	−	0.524965i
$433$			1.60295e13i			1.05313i	0.850135	+	0.526564i	$0.176520\pi$
$433$			1.60295e13i			1.05313i	−0.850135	+	0.526564i	$0.823480\pi$
$434$			6.71281e12i			0.435969i
$435$	−1.66586e13	+	4.09955e12i	−1.06953	+	0.263202i
$436$	−5.56380e12			−0.353133
$437$	5.25275e12			0.329594
$438$	−2.18345e13	+	1.73813e13i	−1.35448	+	1.07823i
$439$	1.19822e13			0.734874			0.367437	−	0.930048i	$-0.380235\pi$
$439$	1.19822e13			0.734874			0.367437	+	0.930048i	$0.380235\pi$
$440$	−1.93615e12	+	4.21026e12i	−0.117402	+	0.255297i
$441$	1.70202e11	−	7.39741e11i	0.0102040	−	0.0443493i
$442$		−	2.27730e13i		−	1.34992i
$443$	−1.12721e12			−0.0660672			−0.0330336	−	0.999454i	$-0.510517\pi$
$443$	−1.12721e12			−0.0660672			−0.0330336	+	0.999454i	$0.510517\pi$
$444$	1.21729e12	−	9.69019e11i	0.0705473	−	0.0561587i
$445$	2.35827e12	−	5.12819e12i	0.135143	−	0.293876i
$446$		−	2.67293e13i		−	1.51465i
$447$	−7.79396e12	+	6.20434e12i	−0.436738	+	0.347663i
$448$		−	9.47830e12i		−	0.525219i
$449$		−	3.07134e13i		−	1.68305i	−0.540221	−	0.841523i	$-0.681659\pi$
$449$		−	3.07134e13i		−	1.68305i	0.540221	−	0.841523i	$-0.318341\pi$
$450$	1.87588e13	−	9.82801e12i	1.01658	−	0.532602i
$451$	−4.85188e12			−0.260032
$452$	6.69765e11			0.0355001
$453$	−1.01158e13	−	1.27075e13i	−0.530283	−	0.666148i
$454$	1.49085e13			0.772956
$455$	3.54319e13	+	1.62939e13i	1.81693	+	0.835540i
$456$	−1.17611e13	−	1.47744e13i	−0.596516	−	0.749351i
$457$		−	7.89556e12i		−	0.396097i	−0.980192	−	0.198049i	$-0.936540\pi$
$457$		−	7.89556e12i		−	0.396097i	0.980192	−	0.198049i	$-0.0634604\pi$
$458$	−3.01092e12			−0.149407
$459$	−1.10532e13	+	5.28725e12i	−0.542529	+	0.259517i
$460$	−1.60035e12	−	7.35942e11i	−0.0777006	−	0.0357317i
$461$			9.79629e12i			0.470497i	0.971935	+	0.235249i	$0.0755904\pi$
$461$			9.79629e12i			0.470497i	−0.971935	+	0.235249i	$0.924410\pi$
$462$	−5.51542e12	−	6.92853e12i	−0.262041	−	0.329178i
$463$		−	1.24871e13i		−	0.586891i	−0.955976	−	0.293445i	$-0.905198\pi$
$463$		−	1.24871e13i		−	0.586891i	0.955976	−	0.293445i	$-0.0948018\pi$
$464$		−	2.88191e13i		−	1.33995i
$465$	1.93008e12	+	7.84292e12i	0.0887792	+	0.360756i
$466$	1.23715e13			0.562980
$467$	7.82498e12			0.352289			0.176144	−	0.984364i	$-0.443637\pi$
$467$	7.82498e12			0.352289			0.176144	+	0.984364i	$0.443637\pi$
$468$	−1.35697e13	−	3.12216e12i	−0.604421	−	0.139067i
$469$	2.96855e13			1.30822
$470$	−1.95386e13	−	8.98512e12i	−0.851931	−	0.391773i
$471$	−8.77408e12	+	6.98456e12i	−0.378527	+	0.301324i
$472$		−	1.72109e13i		−	0.734672i
$473$	4.57354e12			0.193173
$474$	−7.35748e12	−	9.24255e12i	−0.307495	−	0.386278i
$475$	−1.92343e13	−	2.24347e13i	−0.795442	−	0.927797i
$476$		−	4.76513e12i		−	0.195002i
$477$	−7.40992e12	+	3.22053e13i	−0.300069	+	1.30418i
$478$			4.80576e13i			1.92585i
$479$		−	1.27765e13i		−	0.506679i	−0.967377	−	0.253339i	$-0.918471\pi$
$479$		−	1.27765e13i		−	0.506679i	0.967377	−	0.253339i	$-0.0815289\pi$
$480$	3.72917e12	+	1.51536e13i	0.146355	+	0.594715i
$481$	1.43190e13			0.556142
$482$	2.00259e13			0.769763
$483$	−5.67136e12	+	4.51465e12i	−0.215750	+	0.171747i
$484$	7.33969e12			0.276344
$485$	1.00830e12	−	2.19260e12i	0.0375733	−	0.0817052i
$486$	6.79144e12	+	3.03664e13i	0.250484	+	1.11999i
$487$			1.60149e13i			0.584627i	0.956323	+	0.292314i	$0.0944251\pi$
$487$			1.60149e13i			0.584627i	−0.956323	+	0.292314i	$0.905575\pi$
$488$	−1.98723e13			−0.718042
$489$	1.15881e12	−	9.22460e11i	0.0414444	−	0.0329916i
$490$	1.34036e12	+	6.16385e11i	0.0474506	+	0.0218208i
$491$		−	2.98492e12i		−	0.104598i	−0.998631	−	0.0522992i	$-0.983345\pi$
$491$		−	2.98492e12i		−	0.104598i	0.998631	−	0.0522992i	$-0.0166550\pi$
$492$	−5.18725e12	+	4.12928e12i	−0.179933	+	0.143235i
$493$			1.92913e13i			0.662408i
$494$			8.07021e13i			2.74315i
$495$	−8.43605e12	−	6.50915e12i	−0.283866	−	0.219027i
$496$	−1.35681e13			−0.451972
$497$	1.70141e13			0.561083
$498$	1.06754e13	+	1.34106e13i	0.348528	+	0.437825i
$499$	−3.21812e13			−1.04016			−0.520080	−	0.854118i	$-0.674098\pi$
$499$	−3.21812e13			−1.04016			−0.520080	+	0.854118i	$0.674098\pi$
$500$	2.71684e12	+	9.52999e12i	0.0869388	+	0.304960i
$501$	−3.29801e11	−	4.14299e11i	−0.0104487	−	0.0131258i
$502$			1.18407e13i			0.371415i
$503$	2.05869e13			0.639367			0.319683	−	0.947524i	$-0.396423\pi$
$503$	2.05869e13			0.639367			0.319683	+	0.947524i	$0.396423\pi$
$504$	2.53967e13	+	5.84336e12i	0.780951	+	0.179684i
$505$	1.12203e13	−	2.43990e13i	0.341622	−	0.742875i
$506$			3.68109e12i			0.110975i
$507$	−5.89458e13	−	7.40484e13i	−1.75960	−	2.21043i
$508$		−	1.31606e13i		−	0.389006i
$509$		−	2.17795e13i		−	0.637468i	−0.947844	−	0.318734i	$-0.896742\pi$
$509$		−	2.17795e13i		−	0.637468i	0.947844	−	0.318734i	$-0.103258\pi$
$510$	−5.69060e12	−	2.31239e13i	−0.164933	−	0.670208i
$511$	−5.37422e13			−1.54245
$512$	7.33069e12			0.208351
$513$	3.91698e13	−	1.87368e13i	1.10246	−	0.527361i
$514$	−7.38535e13			−2.05852
$515$	1.10745e13	−	2.40820e13i	0.305694	−	0.664748i
$516$	4.88967e12	−	3.89239e12i	0.133669	−	0.106406i
$517$			1.08204e13i			0.292949i
$518$	1.24445e13			0.333679
$519$	2.05780e13	+	2.58504e13i	0.546471	+	0.686483i
$520$	−2.43491e13	+	5.29484e13i	−0.640421	+	1.39263i
$521$			2.84879e13i			0.742115i	0.928610	+	0.371057i	$0.121005\pi$
$521$			2.84879e13i			0.742115i	−0.928610	+	0.371057i	$0.878995\pi$
$522$	4.77443e13	+	1.09852e13i	1.23188	+	0.283436i
$523$		−	4.35895e13i		−	1.11397i	−0.830522	−	0.556985i	$-0.811958\pi$
$523$		−	4.35895e13i		−	1.11397i	0.830522	−	0.556985i	$-0.188042\pi$
$524$		−	1.70682e13i		−	0.432048i
$525$	4.00494e13	+	7.69106e12i	1.00415	+	0.192837i
$526$	7.66059e13			1.90254
$527$	9.08239e12			0.223433
$528$	1.40041e13	−	1.11479e13i	0.341261	−	0.271659i
$529$	−3.84133e13			−0.927265
$530$	−5.83540e13	−	2.68349e13i	−1.39538	−	0.641684i
$531$	3.85658e13	+	8.87337e12i	0.913545	+	0.210192i
$532$			1.68865e13i			0.396261i
$533$	−6.10174e13			−1.41846
$534$	−1.26111e13	+	1.00390e13i	−0.290434	+	0.231198i
$535$	7.35479e13	+	3.38220e13i	1.67804	+	0.771669i
$536$			4.43611e13i			1.00272i
$537$	−3.24167e13	+	2.58051e13i	−0.725934	+	0.577875i
$538$		−	7.88149e13i		−	1.74863i
$539$		−	7.42288e11i		−	0.0163166i
$540$	−1.45589e13	+	2.20578e11i	−0.317073	+	0.00480390i
$541$	2.73506e13			0.590175			0.295087	−	0.955470i	$-0.404651\pi$
$541$	2.73506e13			0.590175			0.295087	+	0.955470i	$0.404651\pi$
$542$	1.05465e13			0.225483
$543$	2.22928e13	+	2.80045e13i	0.472243	+	0.593237i
$544$	1.75484e13			0.368335
$545$	−4.86468e13	−	2.23709e13i	−1.01175	−	0.465266i
$546$	−6.93621e13	−	8.71334e13i	−1.42942	−	1.79565i
$547$			6.95316e13i			1.41986i	0.704272	+	0.709930i	$0.251273\pi$
$547$			6.95316e13i			1.41986i	−0.704272	+	0.709930i	$0.748727\pi$
$548$	1.78166e13			0.360515
$549$	1.02455e13	−	4.45295e13i	0.205434	−	0.892866i
$550$	1.57221e13	−	1.34793e13i	0.312390	−	0.267826i
$551$		−	6.83637e13i		−	1.34607i
$552$	−6.74656e12	−	8.47510e12i	−0.131640	−	0.165367i
$553$		−	2.27490e13i		−	0.439883i
$554$			3.09191e13i			0.592485i
$555$	1.45396e13	−	3.57808e12i	0.276113	−	0.0679493i
$556$	1.16823e13			0.219864
$557$	−5.31234e13			−0.990854			−0.495427	−	0.868650i	$-0.664988\pi$
$557$	−5.31234e13			−0.990854			−0.495427	+	0.868650i	$0.664988\pi$
$558$	5.17187e12	−	2.24782e13i	0.0956041	−	0.415519i
$559$	5.75169e13			1.05375
$560$	−2.86224e13	+	6.22411e13i	−0.519717	+	1.13015i
$561$	−9.37426e12	+	7.46233e12i	−0.168703	+	0.134295i
$562$		−	1.10458e14i		−	1.97023i
$563$	−4.21423e12			−0.0745034			−0.0372517	−	0.999306i	$-0.511860\pi$
$563$	−4.21423e12			−0.0745034			−0.0372517	+	0.999306i	$0.511860\pi$
$564$	9.20893e12	+	1.15684e13i	0.161367	+	0.202711i
$565$	5.85606e12	+	2.69299e12i	0.101710	+	0.0467727i
$566$		−	7.41999e13i		−	1.27738i
$567$	−2.61874e13	+	5.38957e13i	−0.446865	+	0.919685i
$568$			2.54253e13i			0.430056i
$569$			1.06431e14i			1.78446i	0.451577	+	0.892232i	$0.350862\pi$
$569$			1.06431e14i			1.78446i	−0.451577	+	0.892232i	$0.649138\pi$
$570$	2.01662e13	+	8.19455e13i	0.335157	+	1.36192i
$571$	−3.51947e13			−0.579824			−0.289912	−	0.957053i	$-0.593626\pi$
$571$	−3.51947e13			−0.579824			−0.289912	+	0.957053i	$0.593626\pi$
$572$	−1.36164e13			−0.222373
$573$	7.83183e13	−	6.23448e13i	1.26791	−	1.00932i
$574$	−5.30299e13			−0.851062
$575$	−1.10335e13	−	1.28693e13i	−0.175539	−	0.204747i
$576$	−7.30253e12	+	3.17386e13i	−0.115176	+	0.500582i
$577$		−	1.84177e12i		−	0.0287976i	−0.999896	−	0.0143988i	$-0.995417\pi$
$577$		−	1.84177e12i		−	0.0287976i	0.999896	−	0.0143988i	$-0.00458343\pi$
$578$	4.72590e13			0.732563
$579$	5.32665e13	−	4.24025e13i	0.818581	−	0.651627i
$580$	−9.57816e12	+	2.08282e13i	−0.145929	+	0.317331i
$581$			3.30080e13i			0.498584i
$582$	−5.39199e12	+	4.29226e12i	−0.0807484	+	0.0642793i
$583$			3.23163e13i			0.479820i
$584$		−	8.03106e13i		−	1.18225i
$585$	−1.06092e14	−	8.18593e13i	−1.54847	−	1.19478i
$586$	6.82635e13			0.987871
$587$	4.23190e13			0.607218			0.303609	−	0.952797i	$-0.401808\pi$
$587$	4.23190e13			0.607218			0.303609	+	0.952797i	$0.401808\pi$
$588$	−6.31738e11	−	7.93597e11i	−0.00898774	−	0.0112905i
$589$	−3.21859e13			−0.454034
$590$	−3.21348e13	+	6.98788e13i	−0.449485	+	0.977429i
$591$	7.74603e12	+	9.73065e12i	0.107434	+	0.134960i
$592$			2.51532e13i			0.345928i
$593$	8.58099e13			1.17021			0.585105	−	0.810958i	$-0.301053\pi$
$593$	8.58099e13			1.17021			0.585105	+	0.810958i	$0.301053\pi$
$594$	1.31306e13	+	2.74499e13i	0.177563	+	0.371200i
$595$	1.91596e13	−	4.16637e13i	0.256923	−	0.558692i
$596$			1.33121e13i			0.177017i
$597$	1.83013e13	+	2.29903e13i	0.241329	+	0.303161i
$598$			4.62935e13i			0.605361i
$599$		−	6.43173e13i		−	0.834053i	−0.908894	−	0.417027i	$-0.863072\pi$
$599$		−	6.43173e13i		−	0.834053i	0.908894	−	0.417027i	$-0.136928\pi$
$600$	−1.14933e13	+	5.98486e13i	−0.147805	+	0.769658i
$601$	−1.46385e14			−1.86692			−0.933459	−	0.358684i	$-0.883225\pi$
$601$	−1.46385e14			−1.86692			−0.933459	+	0.358684i	$0.883225\pi$
$602$	4.99876e13			0.632237
$603$	−9.94035e13	−	2.28711e13i	−1.24685	−	0.286880i
$604$	−2.17045e13			−0.270001
$605$	6.41742e13	+	2.95114e13i	0.791742	+	0.364094i
$606$	−6.00016e13	+	4.77639e13i	−0.734175	+	0.584436i
$607$			5.84050e12i			0.0708772i	0.999372	+	0.0354386i	$0.0112828\pi$
$607$			5.84050e12i			0.0708772i	−0.999372	+	0.0354386i	$0.988717\pi$
$608$	−6.21874e13			−0.748487
$609$	5.87574e13	+	7.38117e13i	0.701417	+	0.881128i
$610$	8.06846e13	+	3.71040e13i	0.955304	+	0.439310i
$611$			1.36078e14i			1.59802i
$612$	−3.67128e12	+	1.59563e13i	−0.0427622	+	0.185855i
$613$		−	9.69115e13i		−	1.11963i	−0.828619	−	0.559813i	$-0.810873\pi$
$613$		−	9.69115e13i		−	1.11963i	0.828619	−	0.559813i	$-0.189127\pi$
$614$		−	8.25228e13i		−	0.945653i
$615$	−6.19575e13	+	1.52473e13i	−0.704236	+	0.173307i
$616$	2.54841e13			0.287320
$617$	−4.73194e13			−0.529193			−0.264596	−	0.964359i	$-0.585239\pi$
$617$	−4.73194e13			−0.529193			−0.264596	+	0.964359i	$0.585239\pi$
$618$	−5.92220e13	+	4.71434e13i	−0.656963	+	0.522972i
$619$	−6.28987e13			−0.692131			−0.346065	−	0.938210i	$-0.612482\pi$
$619$	−6.28987e13			−0.692131			−0.346065	+	0.938210i	$0.612482\pi$
$620$	9.80600e12	+	4.50943e12i	0.107037	+	0.0492225i
$621$	2.24691e13	−	1.07481e13i	0.243292	−	0.116378i
$622$			1.48224e13i			0.159208i
$623$	−3.10402e13			−0.330738
$624$	1.76117e14	−	1.40197e14i	1.86156	−	1.48188i
$625$	−1.45637e13	+	9.42489e13i	−0.152711	+	0.988271i
$626$		−	3.13239e13i		−	0.325840i
$627$	3.32202e13	−	2.64447e13i	0.342819	−	0.272899i
$628$			1.49861e13i			0.153423i
$629$		−	1.68374e13i		−	0.171010i
$630$	−9.22040e13	−	7.11435e13i	−0.929067	−	0.716857i
$631$	1.04836e14			1.04800			0.524001	−	0.851718i	$-0.324439\pi$
$631$	1.04836e14			1.04800			0.524001	+	0.851718i	$0.324439\pi$
$632$	3.39955e13			0.337160
$633$	7.01151e13	+	8.80794e13i	0.689911	+	0.866674i
$634$	−5.97490e13			−0.583290
$635$	5.29160e13	−	1.15069e14i	0.512529	−	1.11452i
$636$	2.75034e13	+	3.45500e13i	0.264302	+	0.332019i
$637$		−	9.33504e12i		−	0.0890060i
$638$	4.79088e13			0.453223
$639$	−5.69726e13	−	1.31085e13i	−0.534763	−	0.123040i
$640$	−1.17256e14	−	5.39217e13i	−1.09203	−	0.502185i
$641$		−	5.73253e12i		−	0.0529732i	−0.999649	−	0.0264866i	$-0.991568\pi$
$641$		−	5.73253e12i		−	0.0529732i	0.999649	−	0.0264866i	$-0.00843193\pi$
$642$	−1.43978e14	−	1.80867e14i	−1.32015	−	1.65838i
$643$			1.19706e13i			0.108909i	0.998516	+	0.0544544i	$0.0173419\pi$
$643$			1.19706e13i			0.108909i	−0.998516	+	0.0544544i	$0.982658\pi$
$644$			9.68668e12i			0.0874471i
$645$	5.84031e13	−	1.43726e13i	0.523164	−	0.128747i
$646$	9.48959e13			0.843500
$647$	7.29754e12			0.0643658			0.0321829	−	0.999482i	$-0.489754\pi$
$647$	7.29754e12			0.0643658			0.0321829	+	0.999482i	$0.489754\pi$
$648$	−8.05401e13	−	3.91336e13i	−0.704915	−	0.342511i
$649$	3.86987e13			0.336103
$650$	1.97722e14	−	1.69516e14i	1.70407	−	1.46098i
$651$	3.47508e13	−	2.76632e13i	0.297208	−	0.236591i
$652$		−	1.97924e12i		−	0.0167981i
$653$	−1.25949e14			−1.06079			−0.530395	−	0.847751i	$-0.677956\pi$
$653$	−1.25949e14			−1.06079			−0.530395	+	0.847751i	$0.677956\pi$
$654$	9.52317e13	+	1.19631e14i	0.795963	+	0.999898i
$655$	6.86279e13	−	1.49235e14i	0.569239	−	1.23784i
$656$		−	1.07185e14i		−	0.882301i
$657$	1.79958e14	+	4.14055e13i	1.47009	+	0.338245i
$658$			1.18265e14i			0.958795i
$659$		−	5.00896e13i		−	0.403014i	−0.979487	−	0.201507i	$-0.935416\pi$
$659$		−	5.00896e13i		−	0.403014i	0.979487	−	0.201507i	$-0.0645839\pi$
$660$	−1.38262e13	+	3.40252e12i	−0.110403	+	0.0271694i
$661$	−7.45774e13			−0.591017			−0.295509	−	0.955340i	$-0.595489\pi$
$661$	−7.45774e13			−0.591017			−0.295509	+	0.955340i	$0.595489\pi$
$662$	3.44349e13			0.270838
$663$	−1.17891e14	+	9.38465e13i	−0.920265	+	0.732572i
$664$	−4.93261e13			−0.382152
$665$	−6.78972e13	+	1.47646e14i	−0.522088	+	1.13531i
$666$	−4.16711e13	−	9.58785e12i	−0.318027	−	0.0731729i
$667$		−	3.92158e13i		−	0.297051i
$668$	−7.07623e11			−0.00532010
$669$	−1.38372e14	+	1.10150e14i	−1.03256	+	0.821967i
$670$	8.28274e13	−	1.80113e14i	0.613480	−	1.33404i
$671$		−	4.46829e13i		−	0.328495i
$672$	6.71432e13	−	5.34490e13i	0.489955	−	0.390026i
$673$			1.40113e14i			1.01486i	0.861694	+	0.507428i	$0.169404\pi$
$673$			1.40113e14i			1.01486i	−0.861694	+	0.507428i	$0.830596\pi$
$674$			4.72109e13i			0.339424i
$675$	−1.28182e14	−	5.66099e13i	−0.914762	−	0.403993i
$676$	−1.26475e14			−0.895922
$677$	−1.95148e14			−1.37221			−0.686105	−	0.727502i	$-0.740681\pi$
$677$	−1.95148e14			−1.37221			−0.686105	+	0.727502i	$0.740681\pi$
$678$	−1.14639e13	−	1.44011e13i	−0.0800173	−	0.100519i
$679$	−1.32715e13			−0.0919540
$680$	6.22609e13	+	2.86316e13i	0.428224	+	0.196925i
$681$	−6.14373e13	−	7.71783e13i	−0.419466	−	0.526938i
$682$		−	2.25556e13i		−	0.152874i
$683$	1.95137e14			1.31291			0.656456	−	0.754364i	$-0.272055\pi$
$683$	1.95137e14			1.31291			0.656456	+	0.754364i	$0.272055\pi$
$684$	1.30101e13	−	5.65453e13i	0.0868964	−	0.377673i
$685$	1.55779e14	+	7.16372e13i	1.03290	+	0.474992i
$686$			1.70164e14i			1.12007i
$687$	1.24079e13	+	1.55869e13i	0.0810799	+	0.101854i
$688$			1.01036e14i			0.655444i
$689$			4.06410e14i			2.61739i
$690$	1.15680e13	+	4.70068e13i	0.0739628	+	0.300549i
$691$	2.59159e14			1.64504			0.822520	−	0.568737i	$-0.192568\pi$
$691$	2.59159e14			1.64504			0.822520	+	0.568737i	$0.192568\pi$
$692$	4.41524e13			0.278243
$693$	−1.31388e13	+	5.71044e13i	−0.0822032	+	0.357275i
$694$	−2.55659e14			−1.58805
$695$	1.02144e14	+	4.69722e13i	0.629923	+	0.289679i
$696$	−1.10302e14	+	8.78053e13i	−0.675363	+	0.537619i
$697$			7.17491e13i			0.436167i
$698$	−2.79852e14			−1.68909
$699$	−5.09824e13	−	6.40447e13i	−0.305516	−	0.383793i
$700$	4.13722e13	−	3.54703e13i	0.246161	−	0.211045i
$701$		−	2.90918e14i		−	1.71862i	−0.511451	−	0.859312i	$-0.670892\pi$
$701$		−	2.90918e14i		−	1.71862i	0.511451	−	0.859312i	$-0.329108\pi$
$702$	1.65131e14	+	3.45211e14i	0.968596	+	2.02488i
$703$			5.96677e13i			0.347506i
$704$			3.18479e13i			0.184169i
$705$	3.40037e13	+	1.38175e14i	0.195245	+	0.793383i
$706$	1.11621e14			0.636389
$707$	−1.47684e14			−0.836059
$708$	4.13736e13	−	3.29352e13i	0.232572	−	0.185137i
$709$	8.43977e13			0.471085			0.235543	−	0.971864i	$-0.424313\pi$
$709$	8.43977e13			0.471085			0.235543	+	0.971864i	$0.424313\pi$
$710$	4.74721e13	−	1.03231e14i	0.263116	−	0.572159i
$711$	−1.75269e13	+	7.61763e13i	−0.0964624	+	0.419249i
$712$		−	4.63856e13i		−	0.253503i
$713$	−1.84629e13			−0.100197
$714$	−1.02458e14	+	8.15614e13i	−0.552149	+	0.439535i
$715$	−1.19054e14	−	5.47488e13i	−0.637111	−	0.292985i
$716$			5.53677e13i			0.294233i
$717$	2.48784e14	−	1.98043e14i	1.31289	−	1.04512i
$718$		−	2.41514e14i		−	1.26567i
$719$		−	1.24176e14i		−	0.646237i	−0.946358	−	0.323119i	$-0.895269\pi$
$719$		−	1.24176e14i		−	0.646237i	0.946358	−	0.323119i	$-0.104731\pi$
$720$	1.43797e14	−	1.86365e14i	0.743170	−	0.963170i
$721$	−1.45765e14			−0.748132
$722$	−1.11126e14			−0.566408
$723$	−8.25260e13	−	1.03670e14i	−0.417733	−	0.524761i
$724$	4.78316e13			0.240448
$725$	−1.67492e14	+	1.43599e14i	−0.836190	+	0.716903i
$726$	−1.25628e14	−	1.57816e14i	−0.622881	−	0.782470i
$727$		−	3.84408e14i		−	1.89287i	−0.322900	−	0.946433i	$-0.604658\pi$
$727$		−	3.84408e14i		−	1.89287i	0.322900	−	0.946433i	$-0.395342\pi$
$728$	3.20489e14			1.56732
$729$	1.29214e14	−	1.60297e14i	0.627582	−	0.778550i
$730$	−1.49949e14	+	3.26073e14i	−0.723320	+	1.57290i
$731$		−	6.76330e13i		−	0.324020i
$732$	−3.80282e13	−	4.77715e13i	−0.180947	−	0.227307i
$733$		−	1.65534e14i		−	0.782291i	−0.920329	−	0.391146i	$-0.872079\pi$
$733$		−	1.65534e14i		−	0.782291i	0.920329	−	0.391146i	$-0.127921\pi$
$734$			8.52806e13i			0.400286i
$735$	−2.33268e12	−	9.47887e12i	−0.0108747	−	0.0441896i
$736$	−3.56728e13			−0.165177
$737$	−9.97459e13			−0.458730
$738$	1.77573e14	+	4.08567e13i	0.811140	+	0.186630i
$739$	7.39498e13			0.335517			0.167759	−	0.985828i	$-0.446347\pi$
$739$	7.39498e13			0.335517			0.167759	+	0.985828i	$0.446347\pi$
$740$	8.35979e12	−	1.81788e13i	0.0376736	−	0.0819233i
$741$	4.17778e14	−	3.32570e14i	1.87006	−	1.48865i
$742$			3.53209e14i			1.57041i
$743$	−3.00169e14			−1.32563			−0.662813	−	0.748785i	$-0.730638\pi$
$743$	−3.00169e14			−1.32563			−0.662813	+	0.748785i	$0.730638\pi$
$744$	4.13390e13	+	5.19306e13i	0.181341	+	0.227803i
$745$	−5.35253e13	+	1.16394e14i	−0.233226	+	0.507163i
$746$			2.47534e14i			1.07137i
$747$	2.54309e13	−	1.10529e14i	0.109335	−	0.475196i
$748$			1.60112e13i			0.0683781i
$749$		−	4.45175e14i		−	1.88852i
$750$	1.58409e14	−	2.21535e14i	0.667534	−	0.933546i
$751$	−2.13746e14			−0.894742			−0.447371	−	0.894348i	$-0.647640\pi$
$751$	−2.13746e14			−0.894742			−0.447371	+	0.894348i	$0.647640\pi$
$752$	−2.39040e14			−0.993988
$753$	6.12970e13	−	4.87951e13i	0.253200	−	0.201559i
$754$	6.02502e14			2.47230
$755$	−1.89772e14	−	8.72694e13i	−0.773566	−	0.355736i
$756$	3.45528e13	+	7.22335e13i	0.139918	+	0.292503i
$757$			1.39360e14i			0.560608i	0.959911	+	0.280304i	$0.0904352\pi$
$757$			1.39360e14i			0.560608i	−0.959911	+	0.280304i	$0.909565\pi$
$758$	−1.64231e14			−0.656310
$759$	1.90563e13	−	1.51696e13i	0.0756534	−	0.0602235i
$760$	−2.20638e14	−	1.01464e14i	−0.870186	−	0.400168i
$761$			3.76303e14i			1.47440i	0.675676	+	0.737198i	$0.263852\pi$
$761$			3.76303e14i			1.47440i	−0.675676	+	0.737198i	$0.736148\pi$
$762$	−2.82975e14	+	2.25260e14i	−1.10147	+	0.876819i
$763$			2.94453e14i			1.13866i
$764$		−	1.33768e14i		−	0.513907i
$765$	−9.62567e13	+	1.24751e14i	−0.367387	+	0.476144i
$766$	−7.46280e13			−0.282981
$767$	4.86676e14			1.83342
$768$	1.44067e14	+	1.80979e14i	0.539211	+	0.677363i
$769$	−1.23191e14			−0.458085			−0.229043	−	0.973416i	$-0.573560\pi$
$769$	−1.23191e14			−0.458085			−0.229043	+	0.973416i	$0.573560\pi$
$770$	−1.03469e14	−	4.75819e13i	−0.382260	−	0.175788i
$771$	3.04347e14	+	3.82324e14i	1.11711	+	1.40333i
$772$		−	9.09792e13i		−	0.331784i
$773$	4.52781e14			1.64056			0.820278	−	0.571965i	$-0.193819\pi$
$773$	4.52781e14			1.64056			0.820278	+	0.571965i	$0.193819\pi$
$774$	−1.67386e14	−	3.85128e13i	−0.602580	−	0.138644i
$775$	6.76068e13	+	7.88560e13i	0.241814	+	0.282050i
$776$		−	1.98325e13i		−	0.0704805i
$777$	−5.12833e13	−	6.44227e13i	−0.181080	−	0.227475i
$778$		−	2.05801e14i		−	0.722021i
$779$		−	2.54262e14i		−	0.886327i
$780$	−1.73879e14	+	4.27902e13i	−0.602245	+	0.148208i
$781$	−5.71688e13			−0.196745
$782$	5.44356e13			0.186144
$783$	−1.39884e14	−	2.92432e14i	−0.475291	−	0.993610i
$784$	1.63983e13			0.0553628
$785$	−6.02563e13	+	1.31031e14i	−0.202141	+	0.439566i
$786$	−3.66996e14	+	2.92145e14i	−1.22334	+	0.973836i
$787$		−	3.31476e12i		−	0.0109794i	−0.999985	−	0.00548970i	$-0.998253\pi$
$787$		−	3.31476e12i		−	0.0109794i	0.999985	−	0.00548970i	$-0.00174743\pi$
$788$	1.66199e13			0.0547014
$789$	−3.15690e14	−	3.96573e14i	−1.03247	−	1.29699i
$790$	−1.38027e14	−	6.34735e13i	−0.448567	−	0.206280i
$791$		−	3.54459e13i		−	0.114468i
$792$	−8.53350e13	−	1.96342e13i	−0.273843	−	0.0630067i
$793$		−	5.61933e14i		−	1.79192i
$794$			3.16973e14i			1.00443i
$795$	1.01555e14	+	4.12672e14i	0.319792	+	1.29948i
$796$	3.92674e13			0.122876
$797$	3.09187e13			0.0961455			0.0480727	−	0.998844i	$-0.484692\pi$
$797$	3.09187e13			0.0961455			0.0480727	+	0.998844i	$0.484692\pi$
$798$	3.63089e14	−	2.89035e14i	1.12201	−	0.893172i
$799$	1.60011e14			0.491380
$800$	1.30625e14	+	1.52360e14i	0.398637	+	0.464967i
$801$	1.03940e14	+	2.39149e13i	0.315224	+	0.0725279i
$802$			8.61188e13i			0.259553i
$803$	1.80578e14			0.540864
$804$	−1.06641e14	+	8.48906e13i	−0.317426	+	0.252685i
$805$	−3.89482e13	+	8.46950e13i	−0.115215	+	0.250541i
$806$		−	2.83660e14i		−	0.833918i
$807$	−4.08009e14	+	3.24793e14i	−1.19207	+	0.948940i
$808$		−	2.20695e14i		−	0.640818i
$809$			2.79430e14i			0.806363i	0.915120	+	0.403181i	$0.132096\pi$
$809$			2.79430e14i			0.806363i	−0.915120	+	0.403181i	$0.867904\pi$
$810$	2.53938e14	+	3.09266e14i	0.728286	+	0.886966i
$811$	−4.13858e14			−1.17963			−0.589816	−	0.807537i	$-0.700800\pi$
$811$	−4.13858e14			−1.17963			−0.589816	+	0.807537i	$0.700800\pi$
$812$	1.26070e14			0.357136
$813$	−4.34618e13	−	5.45973e13i	−0.122364	−	0.153716i
$814$	−4.18147e13			−0.117006
$815$	7.95813e12	−	1.73054e13i	0.0221321	−	0.0481275i
$816$	−1.64854e14	−	2.07092e14i	−0.455669	−	0.572417i
$817$			2.39675e14i			0.658435i
$818$	2.76381e14			0.754642
$819$	−1.65234e14	+	7.18146e14i	−0.448414	+	1.94892i
$820$	−3.56236e13	+	7.74654e13i	−0.0960879	+	0.208948i
$821$		−	2.71361e14i		−	0.727497i	−0.931497	−	0.363749i	$-0.881497\pi$
$821$		−	2.71361e14i		−	0.727497i	0.931497	−	0.363749i	$-0.118503\pi$
$822$	−3.04955e14	−	3.83089e14i	−0.812601	−	1.02080i
$823$			6.14560e14i			1.62767i	0.581099	+	0.813833i	$0.302623\pi$
$823$			6.14560e14i			1.62767i	−0.581099	+	0.813833i	$0.697377\pi$
$824$		−	2.17827e14i		−	0.573424i
$825$	−1.34569e14	−	2.58426e13i	−0.352109	−	0.0676187i
$826$	4.22967e14			1.10003
$827$	4.23837e14			1.09565			0.547825	−	0.836593i	$-0.315456\pi$
$827$	4.23837e14			1.09565			0.547825	+	0.836593i	$0.315456\pi$
$828$	7.46307e12	−	3.24363e13i	0.0191764	−	0.0833451i
$829$	5.18512e14			1.32430			0.662149	−	0.749372i	$-0.269645\pi$
$829$	5.18512e14			1.32430			0.662149	+	0.749372i	$0.269645\pi$
$830$	2.00271e14	+	9.20976e13i	0.508426	+	0.233807i
$831$	1.60062e14	−	1.27416e14i	0.403908	−	0.321529i
$832$			4.00520e14i			1.00463i
$833$	−1.09769e13			−0.0273687
$834$	−1.99958e14	−	2.51190e14i	−0.495574	−	0.622546i
$835$	−6.18707e12	−	2.84521e12i	−0.0152424	−	0.00700943i
$836$		−	5.67401e13i		−	0.138950i
$837$	−1.37678e14	+	6.58580e13i	−0.335149	+	0.160318i
$838$		−	5.10278e14i		−	1.23477i
$839$			6.00279e14i			1.44392i	0.691934	+	0.721960i	$0.256759\pi$
$839$			6.00279e14i			1.44392i	−0.691934	+	0.721960i	$0.743241\pi$
$840$	3.25427e14	−	8.00852e13i	0.778140	−	0.191494i
$841$	−8.96794e13			−0.213163
$842$	3.53584e13			0.0835473
$843$	−5.71821e14	+	4.55195e14i	−1.34314	+	1.06920i
$844$	1.50440e14			0.351277
$845$	−1.10583e15	−	5.08530e14i	−2.56687	−	1.18041i
$846$	9.11167e13	−	3.96015e14i	0.210255	−	0.913819i
$847$		−	3.88438e14i		−	0.891055i
$848$	−7.13916e14			−1.62805
$849$	−3.84117e14	+	3.05774e14i	−0.870814	+	0.693207i
$850$	−1.99330e14	−	2.32497e14i	−0.449240	−	0.523989i
$851$			3.42275e13i			0.0766879i
$852$	−6.11204e13	+	4.86546e13i	−0.136141	+	0.108374i
$853$		−	1.51930e14i		−	0.336433i	−0.985750	−	0.168216i	$-0.946199\pi$
$853$		−	1.51930e14i		−	0.336433i	0.985750	−	0.168216i	$-0.0538007\pi$
$854$		−	4.88373e14i		−	1.07513i
$855$	3.41111e14	−	4.42090e14i	0.746561	−	0.967565i
$856$	6.65257e14			1.44751
$857$	4.95461e14			1.07178			0.535889	−	0.844288i	$-0.319976\pi$
$857$	4.95461e14			1.07178			0.535889	+	0.844288i	$0.319976\pi$
$858$	2.33063e14	+	2.92776e14i	0.501229	+	0.629649i
$859$	3.38503e14			0.723763			0.361882	−	0.932224i	$-0.382134\pi$
$859$	3.38503e14			0.723763			0.361882	+	0.932224i	$0.382134\pi$
$860$	3.35799e13	−	7.30214e13i	0.0713818	−	0.155224i
$861$	2.18534e14	+	2.74525e14i	0.461852	+	0.580184i
$862$			3.39448e13i			0.0713243i
$863$	8.08631e14			1.68926			0.844629	−	0.535351i	$-0.179821\pi$
$863$	8.08631e14			1.68926			0.844629	+	0.535351i	$0.179821\pi$
$864$	−2.66012e14	+	1.27246e14i	−0.552501	+	0.264288i
$865$	3.86045e14	+	1.77528e14i	0.797181	+	0.366595i
$866$		−	5.88683e14i		−	1.20863i
$867$	−1.94752e14	−	2.44650e14i	−0.397545	−	0.499401i
$868$		−	5.93544e13i		−	0.120463i
$869$			7.64387e13i			0.154246i
$870$	6.11785e14	−	1.50556e14i	1.22745	−	0.302065i
$871$	−1.25441e15			−2.50235
$872$	−4.40021e14			−0.872752
$873$	4.44403e13	+	1.02250e13i	0.0876407	+	0.0201647i
$874$	−1.92907e14			−0.378260
$875$	5.04355e14	−	1.43783e14i	0.983323	−	0.280329i
$876$	1.93060e14	−	1.53684e14i	0.374259	−	0.297927i
$877$		−	9.66772e14i		−	1.86349i	−0.363118	−	0.931743i	$-0.618288\pi$
$877$		−	9.66772e14i		−	1.86349i	0.363118	−	0.931743i	$-0.381712\pi$
$878$	−4.40045e14			−0.843381
$879$	−2.81311e14	−	3.53386e14i	−0.536096	−	0.673449i
$880$	9.61739e13	−	2.09135e14i	0.182240	−	0.396291i
$881$		−	7.33479e13i		−	0.138200i	−0.997610	−	0.0691000i	$-0.977987\pi$
$881$		−	7.33479e13i		−	0.138200i	0.997610	−	0.0691000i	$-0.0220128\pi$
$882$	−6.25066e12	+	2.71669e13i	−0.0117107	+	0.0508976i
$883$			6.11724e14i			1.13960i	0.821784	+	0.569800i	$0.192979\pi$
$883$			6.11724e14i			1.13960i	−0.821784	+	0.569800i	$0.807021\pi$
$884$			2.01358e14i			0.372999i
$885$	4.94174e14	−	1.21612e14i	0.910256	−	0.224007i
$886$	4.13967e13			0.0758223
$887$	3.47616e14			0.633113			0.316557	−	0.948574i	$-0.397473\pi$
$887$	3.47616e14			0.633113			0.316557	+	0.948574i	$0.397473\pi$
$888$	9.62713e13	−	7.66363e13i	0.174354	−	0.138794i
$889$	−6.96496e14			−1.25432
$890$	−8.66073e13	+	1.88332e14i	−0.155097	+	0.337268i
$891$	8.79918e13	−	1.81094e14i	0.156694	−	0.322490i
$892$			2.36339e14i			0.418515i
$893$	−5.67043e14			−0.998524
$894$	2.86233e14	−	2.27854e14i	0.501224	−	0.398996i
$895$	−2.22623e14	+	4.84105e14i	−0.387663	+	0.842993i
$896$			7.09733e14i			1.22901i
$897$	2.39652e14	−	1.90774e14i	0.412685	−	0.328516i
$898$			1.12795e15i			1.93155i
$899$			2.40292e14i			0.409205i
$900$	−1.65865e14	+	8.68989e13i	−0.280894	+	0.147164i
$901$	4.77890e14			0.804829
$902$	1.78185e14			0.298427
$903$	−2.05997e14	−	2.58776e14i	−0.343101	−	0.431007i
$904$	5.29693e13			0.0877369
$905$	4.18213e14	+	1.92321e14i	0.688898	+	0.316800i
$906$	3.71501e14	+	4.66684e14i	0.608581	+	0.764507i
$907$			3.37948e14i			0.550571i	0.961362	+	0.275286i	$0.0887724\pi$
$907$			3.37948e14i			0.550571i	−0.961362	+	0.275286i	$0.911228\pi$
$908$	−1.31820e14			−0.213577
$909$	4.94528e14	+	1.13783e14i	0.796841	+	0.183340i
$910$	−1.30123e15	−	5.98391e14i	−2.08520	−	0.958911i
$911$			9.70578e14i			1.54682i	0.633908	+	0.773408i	$0.281450\pi$
$911$			9.70578e14i			1.54682i	−0.633908	+	0.773408i	$0.718550\pi$
$912$	5.84205e14	+	7.33885e14i	0.925957	+	1.16320i
$913$		−	1.10910e14i		−	0.174830i
$914$			2.89964e14i			0.454583i
$915$	−1.40418e14	−	5.70592e14i	−0.218936	−	0.889651i
$916$	2.66224e13			0.0412829
$917$	−9.03301e14			−1.39311
$918$	4.05926e14	−	1.94174e14i	0.622635	−	0.297836i
$919$	−4.30146e13			−0.0656204			−0.0328102	−	0.999462i	$-0.510446\pi$
$919$	−4.30146e13			−0.0656204			−0.0328102	+	0.999462i	$0.510446\pi$
$920$	−1.26566e14	−	5.82030e13i	−0.192033	−	0.0883093i
$921$	−4.27203e14	+	3.40073e14i	−0.644669	+	0.513185i
$922$		−	3.59768e14i		−	0.539968i
$923$	−7.18957e14			−1.07323
$924$	4.87671e13	+	6.12618e13i	0.0724048	+	0.0909557i
$925$	1.46187e14	−	1.25333e14i	0.215874	−	0.185078i
$926$			4.58588e14i			0.673547i
$927$	4.88103e14	+	1.12305e14i	0.713038	+	0.164058i
$928$			4.64276e14i			0.674584i
$929$		−	1.14012e15i		−	1.64768i	−0.566825	−	0.823838i	$-0.691828\pi$
$929$		−	1.14012e15i		−	1.64768i	0.566825	−	0.823838i	$-0.308172\pi$
$930$	−7.08821e13	−	2.88031e14i	−0.101888	−	0.414023i
$931$	3.88995e13			0.0556155
$932$	−1.09388e14			−0.155558
$933$	7.67324e13	−	6.10824e13i	0.108535	−	0.0863988i
$934$	−2.87372e14			−0.404306
$935$	−6.43780e13	+	1.39994e14i	−0.0900906	+	0.195907i
$936$	−1.07318e15	−	2.46920e14i	−1.49380	−	0.343698i
$937$			4.74829e14i			0.657414i	0.944432	+	0.328707i	$0.106613\pi$
$937$			4.74829e14i			0.657414i	−0.944432	+	0.328707i	$0.893387\pi$
$938$	−1.09020e15			−1.50138
$939$	−1.62158e14	+	1.29085e14i	−0.222131	+	0.176826i
$940$	1.72760e14	+	7.94461e13i	0.235398	+	0.108251i
$941$		−	5.41591e14i		−	0.734046i	−0.930212	−	0.367023i	$-0.880377\pi$
$941$		−	5.41591e14i		−	0.734046i	0.930212	−	0.367023i	$-0.119623\pi$
$942$	3.22228e14	−	2.56507e14i	0.434418	−	0.345816i
$943$		−	1.45853e14i		−	0.195595i
$944$			8.54913e14i			1.14041i
$945$	1.16737e13	+	7.70500e14i	0.0154899	+	1.02238i
$946$	−1.67963e14			−0.221696
$947$	4.19418e14			0.550678			0.275339	−	0.961347i	$-0.411210\pi$
$947$	4.19418e14			0.550678			0.275339	+	0.961347i	$0.411210\pi$
$948$	6.50546e13	+	8.17223e13i	0.0849642	+	0.106733i
$949$	2.27096e15			2.95038
$950$	7.06379e14	+	8.23914e14i	0.912892	+	1.06479i
$951$	2.46223e14	+	3.09308e14i	0.316538	+	0.397639i
$952$		−	3.76857e14i		−	0.481939i
$953$	8.57043e14			1.09028			0.545140	−	0.838345i	$-0.316477\pi$
$953$	8.57043e14			1.09028			0.545140	+	0.838345i	$0.316477\pi$
$954$	2.72129e14	−	1.18274e15i	0.344376	−	1.49674i
$955$	5.37853e14	−	1.16959e15i	0.677091	−	1.47237i
$956$		−	4.24924e14i		−	0.532135i
$957$	−1.97430e14	−	2.48014e14i	−0.245954	−	0.308970i
$958$			4.69214e14i			0.581492i
$959$		−	9.42910e14i		−	1.16246i
$960$	1.00084e14	+	4.06691e14i	0.122746	+	0.498780i
$961$	−7.06498e14			−0.861974
$962$	−5.25863e14			−0.638259
$963$	−3.42984e14	+	1.49069e15i	−0.414136	+	1.79994i
$964$	−1.77068e14			−0.212694
$965$	3.65810e14	−	7.95473e14i	0.437138	−	0.950580i
$966$	2.08280e14	−	1.65800e14i	0.247607	−	0.197106i
$967$		−	1.14967e15i		−	1.35969i	−0.733356	−	0.679845i	$-0.762047\pi$
$967$		−	1.14967e15i		−	1.35969i	0.733356	−	0.679845i	$-0.237953\pi$
$968$	5.80470e14			0.682972
$969$	−3.91062e14	−	4.91257e14i	−0.457748	−	0.575029i
$970$	−3.70296e13	+	8.05229e13i	−0.0431212	+	0.0937693i
$971$			9.55627e13i			0.110711i	0.998467	+	0.0553557i	$0.0176293\pi$
$971$			9.55627e13i			0.110711i	−0.998467	+	0.0553557i	$0.982371\pi$
$972$	−6.00496e13	−	2.68499e14i	−0.0692116	−	0.309465i
$973$		−	6.18262e14i		−	0.708938i
$974$		−	5.88146e14i		−	0.670950i
$975$	−1.69235e15	−	3.24998e14i	−1.92073	−	0.368856i
$976$	9.87114e14			1.11460
$977$	−5.87672e14			−0.660179			−0.330090	−	0.943950i	$-0.607079\pi$
$977$	−5.87672e14			−0.660179			−0.330090	+	0.943950i	$0.607079\pi$
$978$	−4.25570e13	+	3.38773e13i	−0.0475639	+	0.0378629i
$979$	1.04298e14			0.115974
$980$	−1.18514e13	−	5.45005e12i	−0.0131111	−	0.00602935i
$981$	2.26860e14	−	9.85990e14i	0.249697	−	1.08524i
$982$			1.09621e14i			0.120043i
$983$	−1.10930e15			−1.20860			−0.604300	−	0.796757i	$-0.706547\pi$
$983$	−1.10930e15			−1.20860			−0.604300	+	0.796757i	$0.706547\pi$
$984$	−4.10241e14	+	3.26570e14i	−0.444697	+	0.353998i
$985$	1.45316e14	+	6.68255e13i	0.156723	+	0.0720711i
$986$		−	7.08470e14i		−	0.760216i
$987$	6.12232e14	−	4.87364e14i	0.653627	−	0.520316i
$988$		−	7.13565e14i		−	0.757964i
$989$			1.37486e14i			0.145304i
$990$	3.09813e14	+	2.39048e14i	0.325780	+	0.251368i
$991$	1.00801e15			1.05462			0.527312	−	0.849671i	$-0.323200\pi$
$991$	1.00801e15			1.05462			0.527312	+	0.849671i	$0.323200\pi$
$992$	2.18583e14			0.227540
$993$	−1.41905e14	−	1.78263e14i	−0.146978	−	0.184635i
$994$	−6.24841e14			−0.643929
$995$	3.43333e14	+	1.57886e14i	0.352046	+	0.161894i
$996$	−9.43917e13	−	1.18576e14i	−0.0963024	−	0.120976i
$997$			1.85313e15i			1.88118i	0.339542	+	0.940591i	$0.389728\pi$
$997$			1.85313e15i			1.88118i	−0.339542	+	0.940591i	$0.610272\pi$
$998$	1.18185e15			1.19374
$999$	1.22091e14	+	2.55234e14i	0.122703	+	0.256514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.d.c.14.4	yes	16
3.2	odd	2	inner	15.11.d.c.14.14	yes	16
5.2	odd	4		75.11.c.h.26.4		16
5.3	odd	4		75.11.c.h.26.13		16
5.4	even	2	inner	15.11.d.c.14.13	yes	16
15.2	even	4		75.11.c.h.26.14		16
15.8	even	4		75.11.c.h.26.3		16
15.14	odd	2	inner	15.11.d.c.14.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.d.c.14.3	✓	16	15.14	odd	2	inner
15.11.d.c.14.4	yes	16	1.1	even	1	trivial
15.11.d.c.14.13	yes	16	5.4	even	2	inner
15.11.d.c.14.14	yes	16	3.2	odd	2	inner
75.11.c.h.26.3		16	15.8	even	4
75.11.c.h.26.4		16	5.2	odd	4
75.11.c.h.26.13		16	5.3	odd	4
75.11.c.h.26.14		16	15.2	even	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-36.7249 q^{2} +(151.342 + 190.117i) q^{3} +324.720 q^{4} +(2839.18 + 1305.64i) q^{5} +(-5558.02 - 6982.05i) q^{6} -17185.2i q^{7} +25681.0 q^{8} +(-13240.3 + 57545.5i) q^{9} +O(q^{10})\)	\(q-36.7249 q^{2} +(151.342 + 190.117i) q^{3} +324.720 q^{4} +(2839.18 + 1305.64i) q^{5} +(-5558.02 - 6982.05i) q^{6} -17185.2i q^{7} +25681.0 q^{8} +(-13240.3 + 57545.5i) q^{9} +(-104269. - 47949.4i) q^{10} +57743.7i q^{11} +(49143.8 + 61735.0i) q^{12} +726186. i q^{13} +631124. i q^{14} +(181462. + 737375. i) q^{15} -1.27565e6 q^{16} +853907. q^{17} +(486248. - 2.11335e6i) q^{18} -3.02605e6 q^{19} +(921940. + 423967. i) q^{20} +(3.26720e6 - 2.60084e6i) q^{21} -2.12063e6i q^{22} -1.73585e6 q^{23} +(3.88661e6 + 4.88240e6i) q^{24} +(6.35625e6 + 7.41388e6i) q^{25} -2.66691e7i q^{26} +(-1.29442e7 + 6.19183e6i) q^{27} -5.58038e6i q^{28} +2.25917e7i q^{29} +(-6.66419e6 - 2.70800e7i) q^{30} +1.06363e7 q^{31} +2.05507e7 q^{32} +(-1.09781e7 + 8.73903e6i) q^{33} -3.13597e7 q^{34} +(2.24376e7 - 4.87918e7i) q^{35} +(-4.29939e6 + 1.86862e7i) q^{36} -1.97180e7i q^{37} +1.11131e8 q^{38} +(-1.38061e8 + 1.09902e8i) q^{39} +(7.29129e7 + 3.35301e7i) q^{40} +8.40244e7i q^{41} +(-1.19988e8 + 9.55155e7i) q^{42} -7.92041e7i q^{43} +1.87506e7i q^{44} +(-1.12725e8 + 1.46095e8i) q^{45} +6.37488e7 q^{46} +1.87387e8 q^{47} +(-1.93059e8 - 2.42523e8i) q^{48} -1.28549e7 q^{49} +(-2.33433e8 - 2.72274e8i) q^{50} +(1.29232e8 + 1.62343e8i) q^{51} +2.35808e8i q^{52} +5.59650e8 q^{53} +(4.75375e8 - 2.27395e8i) q^{54} +(-7.53923e7 + 1.63945e8i) q^{55} -4.41332e8i q^{56} +(-4.57968e8 - 5.75304e8i) q^{57} -8.29680e8i q^{58} -6.70180e8i q^{59} +(5.89245e7 + 2.39441e8i) q^{60} -7.73815e8 q^{61} -3.90616e8 q^{62} +(9.88929e8 + 2.27536e8i) q^{63} +5.51539e8 q^{64} +(-9.48136e8 + 2.06177e9i) q^{65} +(4.03169e8 - 3.20940e8i) q^{66} +1.72739e9i q^{67} +2.77281e8 q^{68} +(-2.62706e8 - 3.30015e8i) q^{69} +(-8.24019e8 + 1.79187e9i) q^{70} +9.90045e8i q^{71} +(-3.40023e8 + 1.47782e9i) q^{72} -3.12724e9i q^{73} +7.24143e8i q^{74} +(-4.47540e8 + 2.33046e9i) q^{75} -9.82620e8 q^{76} +9.92335e8 q^{77} +(5.07027e9 - 4.03616e9i) q^{78} +1.32376e9 q^{79} +(-3.62179e9 - 1.66553e9i) q^{80} +(-3.13617e9 - 1.52383e9i) q^{81} -3.08579e9i q^{82} -1.92072e9 q^{83} +(1.06093e9 - 8.44545e8i) q^{84} +(2.42440e9 + 1.11489e9i) q^{85} +2.90877e9i q^{86} +(-4.29508e9 + 3.41908e9i) q^{87} +1.48291e9i q^{88} -1.80622e9i q^{89} +(4.13982e9 - 5.36532e9i) q^{90} +1.24796e10 q^{91} -5.63665e8 q^{92} +(1.60971e9 + 2.02214e9i) q^{93} -6.88179e9 q^{94} +(-8.59149e9 - 3.95092e9i) q^{95} +(3.11018e9 + 3.90704e9i) q^{96} -7.72264e8i q^{97} +4.72095e8 q^{98} +(-3.32289e9 - 7.64542e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9}+O(q^{10}) \) 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9	\( 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9} - 221680 q^{10} + 731640 q^{15} - 4218352 q^{16} + 1487600 q^{19} + 2444616 q^{21} + 28021368 q^{24} - 9324800 q^{25} - 35678700 q^{30} - 77667568 q^{31} + 251882368 q^{34} - 22344768 q^{36} - 70953984 q^{39} - 179966240 q^{40} - 484245000 q^{45} - 72018968 q^{46} + 89098816 q^{49} + 686556816 q^{51} + 441096084 q^{54} + 1424671200 q^{55} + 610091280 q^{60} - 1671368368 q^{61} - 4172730848 q^{64} + 2368350000 q^{66} - 2906594616 q^{69} + 2838634200 q^{70} - 1285884000 q^{75} + 4079367264 q^{76} - 3904999600 q^{79} - 11376681984 q^{81} + 13119851016 q^{84} + 8097594320 q^{85} - 15222287520 q^{90} + 19275224832 q^{91} - 9366481832 q^{94} - 5999937552 q^{96} + 42957756000 q^{99}+O(q^{100}) \) 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9 - 221680 * q^10 + 731640 * q^15 - 4218352 * q^16 + 1487600 * q^19 + 2444616 * q^21 + 28021368 * q^24 - 9324800 * q^25 - 35678700 * q^30 - 77667568 * q^31 + 251882368 * q^34 - 22344768 * q^36 - 70953984 * q^39 - 179966240 * q^40 - 484245000 * q^45 - 72018968 * q^46 + 89098816 * q^49 + 686556816 * q^51 + 441096084 * q^54 + 1424671200 * q^55 + 610091280 * q^60 - 1671368368 * q^61 - 4172730848 * q^64 + 2368350000 * q^66 - 2906594616 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 4079367264 * q^76 - 3904999600 * q^79 - 11376681984 * q^81 + 13119851016 * q^84 + 8097594320 * q^85 - 15222287520 * q^90 + 19275224832 * q^91 - 9366481832 * q^94 - 5999937552 * q^96 + 42957756000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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