LMFDB - Embedded newform 15.11.d.c.14.11

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			14.11
Root			$29.3450 + 80.7929i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.11.d.c.14.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+26.2772 q^{2} +(17.3641 - 242.379i) q^{3} -333.511 q^{4} +(3042.13 + 714.880i) q^{5} +(456.279 - 6369.03i) q^{6} -22118.4i q^{7} -35671.5 q^{8} +(-58446.0 - 8417.38i) q^{9} +O(q^{10})$	\(q+26.2772 q^{2} +(17.3641 - 242.379i) q^{3} -333.511 q^{4} +(3042.13 + 714.880i) q^{5} +(456.279 - 6369.03i) q^{6} -22118.4i q^{7} -35671.5 q^{8} +(-58446.0 - 8417.38i) q^{9} +(79938.6 + 18785.0i) q^{10} -212733. i q^{11} +(-5791.12 + 80836.0i) q^{12} +146700. i q^{13} -581208. i q^{14} +(226096. - 724935. i) q^{15} -595831. q^{16} -194730. q^{17} +(-1.53579e6 - 221185. i) q^{18} +2.72613e6 q^{19} +(-1.01458e6 - 238420. i) q^{20} +(-5.36103e6 - 384066. i) q^{21} -5.59001e6i q^{22} +8.45856e6 q^{23} +(-619404. + 8.64602e6i) q^{24} +(8.74352e6 + 4.34952e6i) q^{25} +3.85485e6i q^{26} +(-3.05506e6 + 1.40199e7i) q^{27} +7.37672e6i q^{28} +2.69549e7i q^{29} +(5.94115e6 - 1.90492e7i) q^{30} -1.28206e7 q^{31} +2.08709e7 q^{32} +(-5.15619e7 - 3.69391e6i) q^{33} -5.11696e6 q^{34} +(1.58120e7 - 6.72871e7i) q^{35} +(1.94924e7 + 2.80729e6i) q^{36} -3.69810e7i q^{37} +7.16349e7 q^{38} +(3.55569e7 + 2.54731e6i) q^{39} +(-1.08518e8 - 2.55009e7i) q^{40} -1.87370e8i q^{41} +(-1.40873e8 - 1.00922e7i) q^{42} +1.57014e8i q^{43} +7.09486e7i q^{44} +(-1.71783e8 - 6.73887e7i) q^{45} +2.22267e8 q^{46} +1.71718e8 q^{47} +(-1.03461e7 + 1.44417e8i) q^{48} -2.06748e8 q^{49} +(2.29755e8 + 1.14293e8i) q^{50} +(-3.38132e6 + 4.71985e7i) q^{51} -4.89259e7i q^{52} +9.61149e7 q^{53} +(-8.02782e7 + 3.68403e8i) q^{54} +(1.52078e8 - 6.47161e8i) q^{55} +7.88997e8i q^{56} +(4.73368e7 - 6.60756e8i) q^{57} +7.08297e8i q^{58} -6.71639e8i q^{59} +(-7.54054e7 + 2.41774e8i) q^{60} -2.00164e8 q^{61} -3.36888e8 q^{62} +(-1.86179e8 + 1.29273e9i) q^{63} +1.15856e9 q^{64} +(-1.04873e8 + 4.46280e8i) q^{65} +(-1.35490e9 - 9.70655e7i) q^{66} -1.13079e8i q^{67} +6.49447e7 q^{68} +(1.46875e8 - 2.05018e9i) q^{69} +(4.15494e8 - 1.76811e9i) q^{70} -1.53489e9i q^{71} +(2.08486e9 + 3.00261e8i) q^{72} +3.09050e9i q^{73} -9.71755e8i q^{74} +(1.20606e9 - 2.04372e9i) q^{75} -9.09194e8 q^{76} -4.70530e9 q^{77} +(9.34334e8 + 6.69360e7i) q^{78} -4.13527e9 q^{79} +(-1.81260e9 - 4.25948e8i) q^{80} +(3.34508e9 + 9.83925e8i) q^{81} -4.92355e9i q^{82} +7.78970e8 q^{83} +(1.78796e9 + 1.28090e8i) q^{84} +(-5.92396e8 - 1.39209e8i) q^{85} +4.12589e9i q^{86} +(6.53329e9 + 4.68047e8i) q^{87} +7.58850e9i q^{88} +7.12474e9i q^{89} +(-4.51397e9 - 1.77078e9i) q^{90} +3.24476e9 q^{91} -2.82102e9 q^{92} +(-2.22617e8 + 3.10743e9i) q^{93} +4.51226e9 q^{94} +(8.29325e9 + 1.94886e9i) q^{95} +(3.62404e8 - 5.05866e9i) q^{96} -7.15495e8i q^{97} -5.43275e9 q^{98} +(-1.79065e9 + 1.24334e10i) 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 $

$2$	26.2772			0.821161			0.410581	−	0.911824i	$-0.365326\pi$
$2$	26.2772			0.821161			0.410581	+	0.911824i	$0.365326\pi$
$3$	17.3641	−	242.379i	0.0714572	−	0.997444i
$3$	17.3641	−	242.379i	0.0714572	−	0.997444i
$4$	−333.511			−0.325694
$5$	3042.13	+	714.880i	0.973482	+	0.228762i
$5$	3042.13	+	714.880i	0.973482	+	0.228762i
$6$	456.279	−	6369.03i	0.0586779	−	0.819062i
$7$		−	22118.4i		−	1.31602i	−0.753008	−	0.658011i	$-0.771398\pi$
$7$		−	22118.4i		−	1.31602i	0.753008	−	0.658011i	$-0.228602\pi$
$8$	−35671.5			−1.08861
$9$	−58446.0	−	8417.38i	−0.989788	−	0.142549i
$10$	79938.6	+	18785.0i	0.799386	+	0.187850i
$11$		−	212733.i		−	1.32090i	−0.750869	−	0.660451i	$-0.770365\pi$
$11$		−	212733.i		−	1.32090i	0.750869	−	0.660451i	$-0.229635\pi$
$12$	−5791.12	+	80836.0i	−0.0232732	+	0.324862i
$13$			146700.i			0.395105i	0.980292	+	0.197552i	$0.0632993\pi$
$13$			146700.i			0.395105i	−0.980292	+	0.197552i	$0.936701\pi$
$14$		−	581208.i		−	1.08067i
$15$	226096.	−	724935.i	0.297739	−	0.954647i
$16$	−595831.			−0.568229
$17$	−194730.			−0.137148			−0.0685740	−	0.997646i	$-0.521845\pi$
$17$	−194730.			−0.137148			−0.0685740	+	0.997646i	$0.521845\pi$
$18$	−1.53579e6	−	221185.i	−0.812775	−	0.117056i
$19$	2.72613e6			1.10098			0.550489	−	0.834843i	$-0.314441\pi$
$19$	2.72613e6			1.10098			0.550489	+	0.834843i	$0.314441\pi$
$20$	−1.01458e6	−	238420.i	−0.317058	−	0.0745064i
$21$	−5.36103e6	−	384066.i	−1.31266	−	0.0940393i
$22$		−	5.59001e6i		−	1.08467i
$23$	8.45856e6			1.31419			0.657094	−	0.753809i	$-0.271786\pi$
$23$	8.45856e6			1.31419			0.657094	+	0.753809i	$0.271786\pi$
$24$	−619404.	+	8.64602e6i	−0.0777890	+	1.08583i
$25$	8.74352e6	+	4.34952e6i	0.895336	+	0.445391i
$26$			3.85485e6i			0.324445i
$27$	−3.05506e6	+	1.40199e7i	−0.212912	+	0.977071i
$28$			7.37672e6i			0.428621i
$29$			2.69549e7i			1.31416i	0.753822	+	0.657078i	$0.228208\pi$
$29$			2.69549e7i			1.31416i	−0.753822	+	0.657078i	$0.771792\pi$
$30$	5.94115e6	−	1.90492e7i	0.244492	−	0.783919i
$31$	−1.28206e7			−0.447815			−0.223907	−	0.974610i	$-0.571881\pi$
$31$	−1.28206e7			−0.447815			−0.223907	+	0.974610i	$0.571881\pi$
$32$	2.08709e7			0.622001
$33$	−5.15619e7	−	3.69391e6i	−1.31753	−	0.0943880i
$34$	−5.11696e6			−0.112621
$35$	1.58120e7	−	6.72871e7i	0.301056	−	1.28112i
$36$	1.94924e7	+	2.80729e6i	0.322368	+	0.0464274i
$37$		−	3.69810e7i		−	0.533298i	−0.963794	−	0.266649i	$-0.914084\pi$
$37$		−	3.69810e7i		−	0.533298i	0.963794	−	0.266649i	$-0.0859164\pi$
$38$	7.16349e7			0.904080
$39$	3.55569e7	+	2.54731e6i	0.394095	+	0.0282331i
$40$	−1.08518e8	−	2.55009e7i	−1.05974	−	0.249032i
$41$		−	1.87370e8i		−	1.61726i	−0.588316	−	0.808631i	$-0.700209\pi$
$41$		−	1.87370e8i		−	1.61726i	0.588316	−	0.808631i	$-0.299791\pi$
$42$	−1.40873e8	−	1.00922e7i	−1.07790	−	0.0772215i
$43$			1.57014e8i			1.06806i	0.845465	+	0.534031i	$0.179323\pi$
$43$			1.57014e8i			1.06806i	−0.845465	+	0.534031i	$0.820677\pi$
$44$			7.09486e7i			0.430210i
$45$	−1.71783e8	−	6.73887e7i	−0.930931	−	0.365195i
$46$	2.22267e8			1.07916
$47$	1.71718e8			0.748732			0.374366	−	0.927281i	$-0.377860\pi$
$47$	1.71718e8			0.748732			0.374366	+	0.927281i	$0.377860\pi$
$48$	−1.03461e7	+	1.44417e8i	−0.0406041	+	0.566776i
$49$	−2.06748e8			−0.731915
$50$	2.29755e8	+	1.14293e8i	0.735215	+	0.365738i
$51$	−3.38132e6	+	4.71985e7i	−0.00980021	+	0.136797i
$52$		−	4.89259e7i		−	0.128683i
$53$	9.61149e7			0.229833			0.114916	−	0.993375i	$-0.463340\pi$
$53$	9.61149e7			0.229833			0.114916	+	0.993375i	$0.463340\pi$
$54$	−8.02782e7	+	3.68403e8i	−0.174835	+	0.802333i
$55$	1.52078e8	−	6.47161e8i	0.302172	−	1.28587i
$56$			7.88997e8i			1.43263i
$57$	4.73368e7	−	6.60756e8i	0.0786728	−	1.09816i
$58$			7.08297e8i			1.07913i
$59$		−	6.71639e8i		−	0.939454i	−0.882812	−	0.469727i	$-0.844352\pi$
$59$		−	6.71639e8i		−	0.939454i	0.882812	−	0.469727i	$-0.155648\pi$
$60$	−7.54054e7	+	2.41774e8i	−0.0969720	+	0.310923i
$61$	−2.00164e8			−0.236994			−0.118497	−	0.992954i	$-0.537808\pi$
$61$	−2.00164e8			−0.236994			−0.118497	+	0.992954i	$0.537808\pi$
$62$	−3.36888e8			−0.367728
$63$	−1.86179e8	+	1.29273e9i	−0.187598	+	1.30258i
$64$	1.15856e9			1.07899
$65$	−1.04873e8	+	4.46280e8i	−0.0903849	+	0.384628i
$66$	−1.35490e9	−	9.70655e7i	−1.08190	−	0.0775078i
$67$		−	1.13079e8i		−	0.0837542i	−0.999123	−	0.0418771i	$-0.986666\pi$
$67$		−	1.13079e8i		−	0.0837542i	0.999123	−	0.0418771i	$-0.0133338\pi$
$68$	6.49447e7			0.0446683
$69$	1.46875e8	−	2.05018e9i	0.0939082	−	1.31083i
$70$	4.15494e8	−	1.76811e9i	0.247215	−	1.05201i
$71$		−	1.53489e9i		−	0.850717i	−0.905025	−	0.425359i	$-0.860148\pi$
$71$		−	1.53489e9i		−	0.850717i	0.905025	−	0.425359i	$-0.139852\pi$
$72$	2.08486e9	+	3.00261e8i	1.07749	+	0.155180i
$73$			3.09050e9i			1.49079i	0.666626	+	0.745393i	$0.267738\pi$
$73$			3.09050e9i			1.49079i	−0.666626	+	0.745393i	$0.732262\pi$
$74$		−	9.71755e8i		−	0.437924i
$75$	1.20606e9	−	2.04372e9i	0.508231	−	0.861221i
$76$	−9.09194e8			−0.358582
$77$	−4.70530e9			−1.73834
$78$	9.34334e8	+	6.69360e7i	0.323615	+	0.0231839i
$79$	−4.13527e9			−1.34391			−0.671953	−	0.740594i	$-0.734544\pi$
$79$	−4.13527e9			−1.34391			−0.671953	+	0.740594i	$0.734544\pi$
$80$	−1.81260e9	−	4.25948e8i	−0.553161	−	0.129989i
$81$	3.34508e9	+	9.83925e8i	0.959359	+	0.282187i
$82$		−	4.92355e9i		−	1.32803i
$83$	7.78970e8			0.197756			0.0988782	−	0.995100i	$-0.468475\pi$
$83$	7.78970e8			0.197756			0.0988782	+	0.995100i	$0.468475\pi$
$84$	1.78796e9	+	1.28090e8i	0.427525	+	0.0306281i
$85$	−5.92396e8	−	1.39209e8i	−0.133511	−	0.0313742i
$86$			4.12589e9i			0.877051i
$87$	6.53329e9	+	4.68047e8i	1.31080	+	0.0939060i
$88$			7.58850e9i			1.43795i
$89$			7.12474e9i			1.27591i	0.770075	+	0.637954i	$0.220219\pi$
$89$			7.12474e9i			1.27591i	−0.770075	+	0.637954i	$0.779781\pi$
$90$	−4.51397e9	−	1.77078e9i	−0.764445	−	0.299884i
$91$	3.24476e9			0.519967
$92$	−2.82102e9			−0.428023
$93$	−2.22617e8	+	3.10743e9i	−0.0319996	+	0.446670i
$94$	4.51226e9			0.614830
$95$	8.29325e9	+	1.94886e9i	1.07178	+	0.251861i
$96$	3.62404e8	−	5.05866e9i	0.0444465	−	0.620411i
$97$		−	7.15495e8i		−	0.0833197i	−0.999132	−	0.0416599i	$-0.986735\pi$
$97$		−	7.15495e8i		−	0.0833197i	0.999132	−	0.0416599i	$-0.0132646\pi$
$98$	−5.43275e9			−0.601020
$99$	−1.79065e9	+	1.24334e10i	−0.188293	+	1.30741i
$100$	−2.91606e9	−	1.45061e9i	−0.291606	−	0.145061i
$101$		−	6.11596e9i		−	0.581912i	−0.956736	−	0.290956i	$-0.906027\pi$
$101$		−	6.11596e9i		−	0.581912i	0.956736	−	0.290956i	$-0.0939734\pi$
$102$	−8.88515e7	+	1.24024e9i	−0.00804756	+	0.112333i
$103$		−	1.04188e10i		−	0.898735i	−0.893347	−	0.449368i	$-0.851649\pi$
$103$		−	1.04188e10i		−	0.898735i	0.893347	−	0.449368i	$-0.148351\pi$
$104$		−	5.23300e9i		−	0.430115i
$105$	−1.60344e10	−	5.00087e9i	−1.25634	−	0.391832i
$106$	2.52563e9			0.188730
$107$	−3.48003e9			−0.248121			−0.124061	−	0.992275i	$-0.539592\pi$
$107$	−3.48003e9			−0.248121			−0.124061	+	0.992275i	$0.539592\pi$
$108$	1.01890e9	−	4.67579e9i	0.0693443	−	0.318226i
$109$	−7.75665e9			−0.504129			−0.252065	−	0.967710i	$-0.581110\pi$
$109$	−7.75665e9			−0.504129			−0.252065	+	0.967710i	$0.581110\pi$
$110$	3.99619e9	−	1.70055e10i	0.248132	−	1.05591i
$111$	−8.96341e9	−	6.42142e8i	−0.531935	−	0.0381080i
$112$			1.31788e10i			0.747802i
$113$	2.18370e10			1.18522			0.592612	−	0.805488i	$-0.298097\pi$
$113$	2.18370e10			1.18522			0.592612	+	0.805488i	$0.298097\pi$
$114$	1.24388e9	−	1.73628e10i	0.0646031	−	0.901769i
$115$	2.57321e10	+	6.04686e9i	1.27934	+	0.300636i
$116$		−	8.98974e9i		−	0.428013i
$117$	1.23483e9	−	8.57400e9i	0.0563219	−	0.391070i
$118$		−	1.76488e10i		−	0.771444i
$119$			4.30712e9i			0.180490i
$120$	−8.06518e9	+	2.58595e10i	−0.324122	+	1.03924i
$121$	−1.93177e10			−0.744782
$122$	−5.25974e9			−0.194610
$123$	−4.54145e10	−	3.25351e9i	−1.61313	−	0.115565i
$124$	4.27579e9			0.145851
$125$	2.34896e10	+	1.94824e10i	0.769706	+	0.638399i
$126$	−4.89225e9	+	3.39693e10i	−0.154048	+	1.06963i
$127$			3.48635e10i			1.05524i	0.849479	+	0.527622i	$0.176916\pi$
$127$			3.48635e10i			1.05524i	−0.849479	+	0.527622i	$0.823084\pi$
$128$	9.07185e9			0.264026
$129$	3.80569e10	+	2.72641e9i	1.06533	+	0.0763208i
$130$	−2.75576e9	+	1.17270e10i	−0.0742205	+	0.315841i
$131$			1.06052e10i			0.274892i	0.990509	+	0.137446i	$0.0438894\pi$
$131$			1.06052e10i			0.274892i	−0.990509	+	0.137446i	$0.956111\pi$
$132$	1.71964e10	+	1.23196e9i	0.429110	+	0.0307416i
$133$		−	6.02976e10i		−	1.44891i
$134$		−	2.97139e9i		−	0.0687757i
$135$	−1.93164e10	+	4.04664e10i	−0.430783	+	0.902456i
$136$	6.94633e9			0.149300
$137$	1.95745e10			0.405590			0.202795	−	0.979221i	$-0.434997\pi$
$137$	1.95745e10			0.405590			0.202795	+	0.979221i	$0.434997\pi$
$138$	3.85947e9	−	5.38728e10i	0.0771138	−	1.07640i
$139$	−5.65883e10			−1.09057			−0.545284	−	0.838251i	$-0.683578\pi$
$139$	−5.65883e10			−1.09057			−0.545284	+	0.838251i	$0.683578\pi$
$140$	−5.27347e9	+	2.24410e10i	−0.0980520	+	0.417255i
$141$	2.98173e9	−	4.16208e10i	0.0535023	−	0.746818i
$142$		−	4.03325e10i		−	0.698576i
$143$	3.12078e10			0.521895
$144$	3.48239e10	+	5.01534e9i	0.562426	+	0.0810006i
$145$	−1.92695e10	+	8.20002e10i	−0.300629	+	1.27931i
$146$			8.12097e10i			1.22418i
$147$	−3.58999e9	+	5.01113e10i	−0.0523006	+	0.730044i
$148$			1.23336e10i			0.173692i
$149$		−	1.01759e11i		−	1.38561i	−0.721127	−	0.692803i	$-0.756375\pi$
$149$		−	1.01759e11i		−	1.38561i	0.721127	−	0.692803i	$-0.243625\pi$
$150$	3.16917e10	−	5.37031e10i	0.417339	−	0.707201i
$151$	1.26124e11			1.60662			0.803310	−	0.595561i	$-0.203070\pi$
$151$	1.26124e11			1.60662			0.803310	+	0.595561i	$0.203070\pi$
$152$	−9.72452e10			−1.19853
$153$	1.13812e10	+	1.63912e9i	0.135747	+	0.0195503i
$154$	−1.23642e11			−1.42745
$155$	−3.90018e10	−	9.16516e9i	−0.435940	−	0.102443i
$156$	−1.18586e10	−	8.49555e8i	−0.128354	−	0.00919536i
$157$			2.19359e10i			0.229962i	0.993368	+	0.114981i	$0.0366807\pi$
$157$			2.19359e10i			0.229962i	−0.993368	+	0.114981i	$0.963319\pi$
$158$	−1.08663e11			−1.10356
$159$	1.66895e9	−	2.32962e10i	0.0164232	−	0.229245i
$160$	6.34920e10	+	1.49202e10i	0.605507	+	0.142290i
$161$		−	1.87090e11i		−	1.72950i
$162$	8.78992e10	+	2.58547e10i	0.787789	+	0.231721i
$163$		−	8.25768e10i		−	0.717662i	−0.933402	−	0.358831i	$-0.883175\pi$
$163$		−	8.25768e10i		−	0.717662i	0.933402	−	0.358831i	$-0.116825\pi$
$164$			6.24899e10i			0.526733i
$165$	−1.54217e11	−	4.80979e10i	−1.26100	−	0.393284i
$166$	2.04691e10			0.162390
$167$	5.22667e10			0.402386			0.201193	−	0.979552i	$-0.435518\pi$
$167$	5.22667e10			0.402386			0.201193	+	0.979552i	$0.435518\pi$
$168$	1.91236e11	+	1.37002e10i	1.42897	+	0.102372i
$169$	1.16338e11			0.843892
$170$	−1.55665e10	−	3.65802e9i	−0.109634	−	0.0257633i
$171$	−1.59331e11	−	2.29469e10i	−1.08973	−	0.156943i
$172$		−	5.23659e10i		−	0.347862i
$173$	−1.31416e11			−0.848040			−0.424020	−	0.905653i	$-0.639381\pi$
$173$	−1.31416e11			−0.848040			−0.424020	+	0.905653i	$0.639381\pi$
$174$	1.71676e11	+	1.22989e10i	1.07638	+	0.0771120i
$175$	9.62044e10	−	1.93393e11i	0.586145	−	1.17828i
$176$			1.26753e11i			0.750575i
$177$	−1.62791e11	−	1.16624e10i	−0.937053	−	0.0671308i
$178$			1.87218e11i			1.04773i
$179$			3.38914e11i			1.84427i	0.386867	+	0.922136i	$0.373557\pi$
$179$			3.38914e11i			1.84427i	−0.386867	+	0.922136i	$0.626443\pi$
$180$	5.72915e10	+	2.24749e10i	0.303199	+	0.118942i
$181$	−1.16482e11			−0.599605			−0.299803	−	0.954001i	$-0.596921\pi$
$181$	−1.16482e11			−0.599605			−0.299803	+	0.954001i	$0.596921\pi$
$182$	8.52631e10			0.426977
$183$	−3.47567e9	+	4.85155e10i	−0.0169349	+	0.236388i
$184$	−3.01730e11			−1.43064
$185$	2.64370e10	−	1.12501e11i	0.121998	−	0.519156i
$186$	−5.84975e9	+	8.16544e10i	−0.0262768	+	0.366788i
$187$			4.14255e10i			0.181159i
$188$	−5.72698e10			−0.243858
$189$	3.10098e11	+	6.75730e10i	1.28585	+	0.280197i
$190$	2.17923e11	+	5.12104e10i	0.880106	+	0.206819i
$191$			1.01308e11i			0.398545i	0.979944	+	0.199272i	$0.0638579\pi$
$191$			1.01308e11i			0.398545i	−0.979944	+	0.199272i	$0.936142\pi$
$192$	2.01173e10	−	2.80810e11i	0.0771018	−	1.07623i
$193$			3.56603e11i			1.33168i	0.746097	+	0.665838i	$0.231926\pi$
$193$			3.56603e11i			1.33168i	−0.746097	+	0.665838i	$0.768074\pi$
$194$		−	1.88012e10i		−	0.0684189i
$195$	1.06348e11	+	3.31682e10i	0.377186	+	0.117638i
$196$	6.89527e10			0.238380
$197$	2.04826e11			0.690326			0.345163	−	0.938543i	$-0.387824\pi$
$197$	2.04826e11			0.690326			0.345163	+	0.938543i	$0.387824\pi$
$198$	−4.70533e10	+	3.26713e11i	−0.154619	+	1.07360i
$199$	−3.29450e11			−1.05566			−0.527830	−	0.849350i	$-0.676994\pi$
$199$	−3.29450e11			−1.05566			−0.527830	+	0.849350i	$0.676994\pi$
$200$	−3.11895e11	−	1.55154e11i	−0.974671	−	0.484857i
$201$	−2.74079e10	−	1.96351e9i	−0.0835401	−	0.00598484i
$202$		−	1.60710e11i		−	0.477844i
$203$	5.96198e11			1.72946
$204$	1.12771e9	−	1.57412e10i	0.00319187	−	0.0445541i
$205$	1.33947e11	−	5.70004e11i	0.369968	−	1.57438i
$206$		−	2.73777e11i		−	0.738007i
$207$	−4.94369e11	−	7.11990e10i	−1.30077	−	0.187336i
$208$		−	8.74083e10i		−	0.224510i
$209$		−	5.79937e11i		−	1.45428i
$210$	−4.21338e11	−	1.31409e11i	−1.03166	−	0.321757i
$211$	−4.60048e9			−0.0110000			−0.00549998	−	0.999985i	$-0.501751\pi$
$211$	−4.60048e9			−0.0110000			−0.00549998	+	0.999985i	$0.501751\pi$
$212$	−3.20554e10			−0.0748551
$213$	−3.72025e11	−	2.66520e10i	−0.848542	−	0.0607899i
$214$	−9.14453e10			−0.203748
$215$	−1.12246e11	+	4.77658e11i	−0.244332	+	1.03974i
$216$	1.08979e11	−	5.00111e11i	0.231778	−	1.06365i
$217$			2.83570e11i			0.589334i
$218$	−2.03823e11			−0.413971
$219$	7.49073e11	+	5.36639e10i	1.48697	+	0.106527i
$220$	−5.07198e10	+	2.15835e11i	−0.0984156	+	0.418802i
$221$		−	2.85669e10i		−	0.0541878i
$222$	−2.35533e11	−	1.68737e10i	−0.436804	−	0.0312928i
$223$			5.82049e11i			1.05544i	0.849417	+	0.527722i	$0.176954\pi$
$223$			5.82049e11i			1.05544i	−0.849417	+	0.527722i	$0.823046\pi$
$224$		−	4.61630e11i		−	0.818567i
$225$	−4.74412e11	−	3.27810e11i	−0.822703	−	0.568472i
$226$	5.73814e11			0.973259
$227$	1.04544e12			1.73449			0.867244	−	0.497884i	$-0.165889\pi$
$227$	1.04544e12			1.73449			0.867244	+	0.497884i	$0.165889\pi$
$228$	−1.57873e10	+	2.20369e11i	−0.0256233	+	0.357665i
$229$	−9.32974e11			−1.48147			−0.740734	−	0.671799i	$-0.765522\pi$
$229$	−9.32974e11			−1.48147			−0.740734	+	0.671799i	$0.765522\pi$
$230$	6.76166e11	+	1.58894e11i	1.05054	+	0.246870i
$231$	−8.17034e10	+	1.14047e12i	−0.124217	+	1.73389i
$232$		−	9.61521e11i		−	1.43060i
$233$	−2.24385e11			−0.326749			−0.163374	−	0.986564i	$-0.552238\pi$
$233$	−2.24385e11			−0.326749			−0.163374	+	0.986564i	$0.552238\pi$
$234$	3.24478e10	−	2.25300e11i	0.0462493	−	0.321131i
$235$	5.22389e11	+	1.22758e11i	0.728878	+	0.171281i
$236$			2.23999e11i			0.305975i
$237$	−7.18053e10	+	1.00230e12i	−0.0960318	+	1.34047i
$238$			1.13179e11i			0.148211i
$239$			5.30289e11i			0.680022i	0.940421	+	0.340011i	$0.110431\pi$
$239$			5.30289e11i			0.680022i	−0.940421	+	0.340011i	$0.889569\pi$
$240$	−1.34715e11	+	4.31939e11i	−0.169184	+	0.542458i
$241$	9.71107e11			1.19449			0.597244	−	0.802060i	$-0.296262\pi$
$241$	9.71107e11			1.19449			0.597244	+	0.802060i	$0.296262\pi$
$242$	−5.07615e11			−0.611586
$243$	2.96567e11	−	7.93691e11i	0.350019	−	0.936743i
$244$	6.67568e10			0.0771874
$245$	−6.28954e11	−	1.47800e11i	−0.712506	−	0.167434i
$246$	−1.19336e12	−	8.54930e10i	−1.32464	−	0.0948976i
$247$			3.99922e11i			0.435002i
$248$	4.57329e11			0.487495
$249$	1.35261e10	−	1.88806e11i	0.0141311	−	0.197251i
$250$	6.17239e11	+	5.11942e11i	0.632052	+	0.524228i
$251$			9.55239e11i			0.958834i	0.877587	+	0.479417i	$0.159152\pi$
$251$			9.55239e11i			0.958834i	−0.877587	+	0.479417i	$0.840848\pi$
$252$	6.20927e10	−	4.31140e11i	0.0610995	−	0.424244i
$253$		−	1.79941e12i		−	1.73591i
$254$			9.16114e11i			0.866525i
$255$	−4.40277e10	+	1.41167e11i	−0.0408343	+	0.130928i
$256$	−9.47982e11			−0.862185
$257$	−8.34896e11			−0.744675			−0.372337	−	0.928097i	$-0.621444\pi$
$257$	−8.34896e11			−0.744675			−0.372337	+	0.928097i	$0.621444\pi$
$258$	1.00003e12	+	7.16423e10i	0.874809	+	0.0626717i
$259$	−8.17960e11			−0.701832
$260$	3.49762e10	−	1.48839e11i	0.0294378	−	0.125271i
$261$	2.26889e11	−	1.57540e12i	0.187332	−	1.30074i
$262$			2.78675e11i			0.225731i
$263$	−1.30500e12			−1.03713			−0.518563	−	0.855039i	$-0.673533\pi$
$263$	−1.30500e12			−1.03713			−0.518563	+	0.855039i	$0.673533\pi$
$264$	1.83929e12	+	1.31768e11i	1.43427	+	0.102752i
$265$	2.92394e11	+	6.87107e10i	0.223738	+	0.0525769i
$266$		−	1.58445e12i		−	1.18979i
$267$	1.72689e12	+	1.23715e11i	1.27265	+	0.0911728i
$268$			3.77130e10i			0.0272783i
$269$		−	7.62531e11i		−	0.541373i	−0.962668	−	0.270686i	$-0.912749\pi$
$269$		−	7.62531e11i		−	0.541373i	0.962668	−	0.270686i	$-0.0872506\pi$
$270$	−5.07581e11	+	1.06334e12i	−0.353742	+	0.741062i
$271$	−1.28476e12			−0.878972			−0.439486	−	0.898249i	$-0.644839\pi$
$271$	−1.28476e12			−0.878972			−0.439486	+	0.898249i	$0.644839\pi$
$272$	1.16027e11			0.0779315
$273$	5.63424e10	−	7.86461e11i	0.0371554	−	0.518638i
$274$	5.14362e11			0.333055
$275$	9.25285e11	−	1.86003e12i	0.588318	−	1.18265i
$276$	−4.89845e10	+	6.83756e11i	−0.0305854	+	0.426929i
$277$			2.02239e12i			1.24013i	0.784551	+	0.620064i	$0.212893\pi$
$277$			2.02239e12i			1.24013i	−0.784551	+	0.620064i	$0.787107\pi$
$278$	−1.48698e12			−0.895532
$279$	7.49310e11	+	1.07916e11i	0.443241	+	0.0638356i
$280$	−5.64038e11	+	2.40023e12i	−0.327732	+	1.39464i
$281$		−	3.74419e11i		−	0.213711i	−0.994275	−	0.106855i	$-0.965922\pi$
$281$		−	3.74419e11i		−	0.213711i	0.994275	−	0.106855i	$-0.0340782\pi$
$282$	7.83514e10	−	1.09368e12i	0.0439340	−	0.613258i
$283$		−	1.73567e12i		−	0.956170i	−0.878314	−	0.478085i	$-0.841331\pi$
$283$		−	1.73567e12i		−	0.956170i	0.878314	−	0.478085i	$-0.158669\pi$
$284$			5.11902e11i			0.277074i
$285$	6.16366e11	−	1.97627e12i	0.327804	−	1.05105i
$286$	8.20052e11			0.428560
$287$	−4.14432e12			−2.12835
$288$	−1.21982e12	−	1.75678e11i	−0.615649	−	0.0886657i
$289$	−1.97807e12			−0.981190
$290$	−5.06348e11	+	2.15473e12i	−0.246865	+	1.05052i
$291$	−1.73421e11	−	1.24239e10i	−0.0831067	−	0.00595380i
$292$		−	1.03072e12i		−	0.485540i
$293$	2.91837e12			1.35146			0.675728	−	0.737151i	$-0.263829\pi$
$293$	2.91837e12			1.35146			0.675728	+	0.737151i	$0.263829\pi$
$294$	−9.43348e10	+	1.31678e12i	−0.0429472	+	0.599484i
$295$	4.80141e11	−	2.04321e12i	0.214911	−	0.914542i
$296$			1.31917e12i			0.580553i
$297$	2.98249e12	+	6.49910e11i	1.29062	+	0.281236i
$298$		−	2.67393e12i		−	1.13781i
$299$			1.24087e12i			0.519242i
$300$	−4.02233e11	+	6.81602e11i	−0.165528	+	0.280495i
$301$	3.47290e12			1.40559
$302$	3.31418e12			1.31929
$303$	−1.48238e12	−	1.06198e11i	−0.580425	−	0.0415818i
$304$	−1.62431e12			−0.625607
$305$	−6.08925e11	−	1.43093e11i	−0.230709	−	0.0542151i
$306$	2.99066e11	+	4.30715e10i	0.111470	+	0.0160540i
$307$			4.09182e12i			1.50046i	0.661177	+	0.750230i	$0.270057\pi$
$307$			4.09182e12i			1.50046i	−0.661177	+	0.750230i	$0.729943\pi$
$308$	1.56927e12			0.566166
$309$	−2.52530e12	−	1.80913e11i	−0.896438	−	0.0642212i
$310$	−1.02486e12	−	2.40834e11i	−0.357977	−	0.0841221i
$311$			6.15311e11i			0.211492i	0.994393	+	0.105746i	$0.0337230\pi$
$311$			6.15311e11i			0.211492i	−0.994393	+	0.105746i	$0.966277\pi$
$312$	−1.26837e12	−	9.08664e10i	−0.429015	−	0.0307348i
$313$			7.66675e11i			0.255205i	0.991825	+	0.127603i	$0.0407282\pi$
$313$			7.66675e11i			0.255205i	−0.991825	+	0.127603i	$0.959272\pi$
$314$			5.76412e11i			0.188836i
$315$	−1.49053e12	+	3.79956e12i	−0.480604	+	1.22513i
$316$	1.37916e12			0.437702
$317$	−2.58124e12			−0.806367			−0.403184	−	0.915119i	$-0.632096\pi$
$317$	−2.58124e12			−0.806367			−0.403184	+	0.915119i	$0.632096\pi$
$318$	4.38553e10	−	6.12159e11i	0.0134861	−	0.188247i
$319$	5.73418e12			1.73587
$320$	3.52449e12	+	8.28231e11i	1.05038	+	0.246832i
$321$	−6.04276e10	+	8.43485e11i	−0.0177301	+	0.247487i
$322$		−	4.91619e12i		−	1.42020i
$323$	−5.30860e11			−0.150997
$324$	−1.11562e12	−	3.28150e11i	−0.312458	−	0.0919066i
$325$	−6.38073e11	+	1.28267e12i	−0.175976	+	0.353752i
$326$		−	2.16988e12i		−	0.589317i
$327$	−1.34687e11	+	1.88005e12i	−0.0360237	+	0.502841i
$328$			6.68377e12i			1.76057i
$329$		−	3.79812e12i		−	0.985348i
$330$	−4.05239e12	−	1.26388e12i	−1.03548	−	0.322950i
$331$	−6.08698e12			−1.53201			−0.766006	−	0.642833i	$-0.777759\pi$
$331$	−6.08698e12			−1.53201			−0.766006	+	0.642833i	$0.777759\pi$
$332$	−2.59795e11			−0.0644081
$333$	−3.11283e11	+	2.16139e12i	−0.0760212	+	0.527852i
$334$	1.37342e12			0.330423
$335$	8.08377e10	−	3.44000e11i	0.0191598	−	0.0815332i
$336$	3.19427e12	+	2.28839e11i	0.745891	+	0.0534359i
$337$		−	3.32556e12i		−	0.765095i	−0.923936	−	0.382547i	$-0.875047\pi$
$337$		−	3.32556e12i		−	0.765095i	0.923936	−	0.382547i	$-0.124953\pi$
$338$	3.05702e12			0.692972
$339$	3.79180e11	−	5.29282e12i	0.0846928	−	1.18219i
$340$	1.97570e11	+	4.64277e10i	0.0434838	+	0.0102184i
$341$			2.72735e12i			0.591519i
$342$	−4.18677e12	−	6.02979e11i	−0.894847	−	0.128876i
$343$		−	1.67497e12i		−	0.352806i
$344$		−	5.60094e12i		−	1.16270i
$345$	1.91244e12	−	6.13191e12i	0.391285	−	1.25459i
$346$	−3.45323e12			−0.696378
$347$	7.20562e12			1.43227			0.716134	−	0.697963i	$-0.245910\pi$
$347$	7.20562e12			1.43227			0.716134	+	0.697963i	$0.245910\pi$
$348$	−2.17892e12	−	1.56099e11i	−0.426919	−	0.0305846i
$349$	2.24266e11			0.0433149			0.0216574	−	0.999765i	$-0.493106\pi$
$349$	2.24266e11			0.0433149			0.0216574	+	0.999765i	$0.493106\pi$
$350$	2.52798e12	−	5.08181e12i	0.481319	−	0.967560i
$351$	−2.05672e12	−	4.48176e11i	−0.386046	−	0.0841227i
$352$		−	4.43992e12i		−	0.821602i
$353$	−2.86956e12			−0.523531			−0.261765	−	0.965132i	$-0.584305\pi$
$353$	−2.86956e12			−0.523531			−0.261765	+	0.965132i	$0.584305\pi$
$354$	−4.27769e12	−	3.06455e11i	−0.769472	−	0.0551252i
$355$	1.09726e12	−	4.66934e12i	0.194612	−	0.828158i
$356$		−	2.37618e12i		−	0.415556i
$357$	1.04396e12	+	7.47894e10i	0.180028	+	0.0128973i
$358$			8.90571e12i			1.51444i
$359$			3.12468e12i			0.524003i	0.965068	+	0.262001i	$0.0843825\pi$
$359$			3.12468e12i			0.524003i	−0.965068	+	0.262001i	$0.915618\pi$
$360$	6.12776e12	+	2.40386e12i	1.01342	+	0.397554i
$361$	1.30071e12			0.212151
$362$	−3.06081e12			−0.492372
$363$	−3.35435e11	+	4.68221e12i	−0.0532201	+	0.742878i
$364$	−1.08216e12			−0.169350
$365$	−2.20934e12	+	9.40172e12i	−0.341035	+	1.45125i
$366$	−9.13307e10	+	1.27485e12i	−0.0139063	+	0.194112i
$367$			5.31391e12i			0.798149i	0.916919	+	0.399074i	$0.130668\pi$
$367$			5.31391e12i			0.798149i	−0.916919	+	0.399074i	$0.869332\pi$
$368$	−5.03988e12			−0.746760
$369$	−1.57716e12	+	1.09510e13i	−0.230539	+	1.60075i
$370$	6.94689e11	−	2.95621e12i	0.100180	−	0.426311i
$371$		−	2.12591e12i		−	0.302465i
$372$	7.42453e10	−	1.03636e12i	0.0104221	−	0.145478i
$373$			2.73808e12i			0.379229i	0.981859	+	0.189614i	$0.0607238\pi$
$373$			2.73808e12i			0.379229i	−0.981859	+	0.189614i	$0.939276\pi$
$374$			1.08854e12i			0.148761i
$375$	5.12999e12	−	5.35508e12i	0.691768	−	0.722120i
$376$	−6.12544e12			−0.815076
$377$	−3.95427e12			−0.519229
$378$	8.14849e12	+	1.77563e12i	1.05589	+	0.230087i
$379$	1.04807e13			1.34028			0.670140	−	0.742235i	$-0.266234\pi$
$379$	1.04807e13			1.34028			0.670140	+	0.742235i	$0.266234\pi$
$380$	−2.76589e12	−	6.49965e11i	−0.349073	−	0.0820298i
$381$	8.45018e12	+	6.05374e11i	1.05255	+	0.0754048i
$382$			2.66209e12i			0.327270i
$383$	1.20420e13			1.46118			0.730591	−	0.682816i	$-0.239245\pi$
$383$	1.20420e13			1.46118			0.730591	+	0.682816i	$0.239245\pi$
$384$	1.57525e11	−	2.19882e12i	0.0188665	−	0.263351i
$385$	−1.43142e13	−	3.36373e12i	−1.69224	−	0.397665i
$386$			9.37051e12i			1.09352i
$387$	1.32165e12	−	9.17685e12i	0.152251	−	1.05715i
$388$			2.38625e11i			0.0271368i
$389$			1.30287e13i			1.46269i	0.682005	+	0.731347i	$0.261108\pi$
$389$			1.30287e13i			1.46269i	−0.682005	+	0.731347i	$0.738892\pi$
$390$	2.79452e12	+	8.71565e11i	0.309730	+	0.0966000i
$391$	−1.64714e12			−0.180238
$392$	7.37501e12			0.796769
$393$	2.57048e12	+	1.84150e11i	0.274190	+	0.0196431i
$394$	5.38225e12			0.566869
$395$	−1.25801e13	−	2.95623e12i	−1.30827	−	0.307434i
$396$	5.97202e11	−	4.14666e12i	0.0613261	−	0.425817i
$397$		−	3.17475e12i		−	0.321926i	−0.986960	−	0.160963i	$-0.948540\pi$
$397$		−	3.17475e12i		−	0.321926i	0.986960	−	0.160963i	$-0.0514600\pi$
$398$	−8.65700e12			−0.866867
$399$	−1.46149e13	−	1.04701e12i	−1.44521	−	0.103535i
$400$	−5.20966e12	−	2.59158e12i	−0.508756	−	0.253084i
$401$		−	6.88667e12i		−	0.664183i	−0.943247	−	0.332091i	$-0.892246\pi$
$401$		−	6.88667e12i		−	0.664183i	0.943247	−	0.332091i	$-0.107754\pi$
$402$	−7.20201e11	−	5.15955e10i	−0.0685999	−	0.00491452i
$403$		−	1.88077e12i		−	0.176934i
$404$			2.03974e12i			0.189525i
$405$	9.47279e12	+	5.38456e12i	0.869366	+	0.494169i
$406$	1.56664e13			1.42016
$407$	−7.86706e12			−0.704434
$408$	1.20617e11	−	1.68364e12i	0.0106686	−	0.148919i
$409$	1.02209e13			0.893047			0.446524	−	0.894772i	$-0.352662\pi$
$409$	1.02209e13			0.893047			0.446524	+	0.894772i	$0.352662\pi$
$410$	3.51975e12	−	1.49781e13i	0.303803	−	1.29282i
$411$	3.39893e11	−	4.74444e12i	0.0289824	−	0.404553i
$412$			3.47479e12i			0.292713i
$413$	−1.48556e13			−1.23634
$414$	−1.29906e13	−	1.87091e12i	−1.06814	−	0.153833i
$415$	2.36973e12	+	5.56870e11i	0.192512	+	0.0452391i
$416$			3.06175e12i			0.245756i
$417$	−9.82605e11	+	1.37158e13i	−0.0779290	+	1.08778i
$418$		−	1.52391e13i		−	1.19420i
$419$		−	1.22104e13i		−	0.945493i	−0.881199	−	0.472746i	$-0.843263\pi$
$419$		−	1.22104e13i		−	0.945493i	0.881199	−	0.472746i	$-0.156737\pi$
$420$	5.34765e12	+	1.66785e12i	0.409182	+	0.127617i
$421$	−5.46268e11			−0.0413043			−0.0206521	−	0.999787i	$-0.506574\pi$
$421$	−5.46268e11			−0.0413043			−0.0206521	+	0.999787i	$0.506574\pi$
$422$	−1.20888e11			−0.00903273
$423$	−1.00362e13	−	1.44542e12i	−0.741086	−	0.106731i
$424$	−3.42857e12			−0.250198
$425$	−1.70263e12	−	8.46984e11i	−0.122794	−	0.0610845i
$426$	−9.77575e12	−	7.00338e11i	−0.696790	−	0.0499183i
$427$			4.42730e12i			0.311889i
$428$	1.16063e12			0.0808117
$429$	5.41896e11	−	7.56411e12i	0.0372932	−	0.520561i
$430$	−2.94951e12	+	1.25515e13i	−0.200636	+	0.853794i
$431$		−	2.29837e13i		−	1.54537i	−0.634788	−	0.772686i	$-0.718913\pi$
$431$		−	2.29837e13i		−	1.54537i	0.634788	−	0.772686i	$-0.281087\pi$
$432$	1.82030e12	−	8.35350e12i	0.120983	−	0.555200i
$433$			9.44429e12i			0.620483i	0.950658	+	0.310241i	$0.100410\pi$
$433$			9.44429e12i			0.620483i	−0.950658	+	0.310241i	$0.899590\pi$
$434$			7.45141e12i			0.483938i
$435$	1.95405e13	+	6.09438e12i	1.25456	+	0.391276i
$436$	2.58693e12			0.164192
$437$	2.30591e13			1.44689
$438$	1.96835e13	+	1.41013e12i	1.22105	+	0.0874762i
$439$	−3.41243e12			−0.209287			−0.104643	−	0.994510i	$-0.533370\pi$
$439$	−3.41243e12			−0.209287			−0.104643	+	0.994510i	$0.533370\pi$
$440$	−5.42487e12	+	2.30852e13i	−0.328947	+	1.39981i
$441$	1.20836e13	+	1.74028e12i	0.724440	+	0.104334i
$442$		−	7.50657e11i		−	0.0444969i
$443$	1.14462e13			0.670874			0.335437	−	0.942063i	$-0.391116\pi$
$443$	1.14462e13			0.670874			0.335437	+	0.942063i	$0.391116\pi$
$444$	2.98939e12	+	2.14161e11i	0.173248	+	0.0124116i
$445$	−5.09334e12	+	2.16744e13i	−0.291879	+	1.24207i
$446$			1.52946e13i			0.866690i
$447$	−2.46641e13	−	1.76695e12i	−1.38206	−	0.0990116i
$448$		−	2.56255e13i		−	1.41998i
$449$		−	2.33764e12i		−	0.128099i	−0.997947	−	0.0640496i	$-0.979598\pi$
$449$		−	2.33764e12i		−	0.128099i	0.997947	−	0.0640496i	$-0.0204016\pi$
$450$	−1.24662e13	−	8.61390e12i	−0.675572	−	0.466807i
$451$	−3.98597e13			−2.13625
$452$	−7.28287e12			−0.386020
$453$	2.19003e12	−	3.05698e13i	0.114805	−	1.60251i
$454$	2.74713e13			1.42429
$455$	9.87099e12	+	2.31962e12i	0.506179	+	0.118948i
$456$	−1.68858e12	+	2.35702e13i	−0.0856439	+	1.19547i
$457$		−	1.41956e13i		−	0.712150i	−0.934457	−	0.356075i	$-0.884115\pi$
$457$		−	1.41956e13i		−	0.712150i	0.934457	−	0.356075i	$-0.115885\pi$
$458$	−2.45159e13			−1.21652
$459$	5.94913e11	−	2.73010e12i	0.0292005	−	0.134003i
$460$	−8.58192e12	−	2.01669e12i	−0.416673	−	0.0979153i
$461$			2.94588e13i			1.41485i	0.706788	+	0.707426i	$0.250144\pi$
$461$			2.94588e13i			1.41485i	−0.706788	+	0.707426i	$0.749856\pi$
$462$	−2.14693e12	+	2.99682e13i	−0.102002	+	1.42381i
$463$		−	1.98376e13i		−	0.932359i	−0.884690	−	0.466180i	$-0.845630\pi$
$463$		−	1.98376e13i		−	0.932359i	0.884690	−	0.466180i	$-0.154370\pi$
$464$		−	1.60605e13i		−	0.746742i
$465$	−2.89867e12	+	9.29407e12i	−0.133332	+	0.427505i
$466$	−5.89620e12			−0.268313
$467$	1.49516e13			0.673136			0.336568	−	0.941659i	$-0.390734\pi$
$467$	1.49516e13			0.673136			0.336568	+	0.941659i	$0.390734\pi$
$468$	−4.11828e11	+	2.85952e12i	−0.0183437	+	0.127369i
$469$	−2.50112e12			−0.110222
$470$	1.37269e13	+	3.22573e12i	0.598526	+	0.140650i
$471$	5.31679e12	+	3.80897e11i	0.229374	+	0.0164325i
$472$			2.39584e13i			1.02270i
$473$	3.34020e13			1.41081
$474$	−1.88684e12	+	2.63377e13i	−0.0788576	+	1.10074i
$475$	2.38360e13	+	1.18574e13i	0.985745	+	0.490365i
$476$		−	1.43647e12i		−	0.0587845i
$477$	−5.61753e12	−	8.09036e11i	−0.227485	−	0.0327624i
$478$			1.39345e13i			0.558408i
$479$		−	3.05321e13i		−	1.21082i	−0.795914	−	0.605410i	$-0.793009\pi$
$479$		−	3.05321e13i		−	1.21082i	0.795914	−	0.605410i	$-0.206991\pi$
$480$	4.71882e12	−	1.51300e13i	0.185194	−	0.593792i
$481$	5.42510e12			0.210709
$482$	2.55179e13			0.980867
$483$	−4.53466e13	−	3.24865e12i	−1.72508	−	0.123585i
$484$	6.44267e12			0.242571
$485$	5.11493e11	−	2.17663e12i	0.0190604	−	0.0811103i
$486$	7.79293e12	−	2.08560e13i	0.287422	−	0.769217i
$487$		−	6.02381e12i		−	0.219901i	−0.993937	−	0.109950i	$-0.964931\pi$
$487$		−	6.02381e12i		−	0.219901i	0.993937	−	0.109950i	$-0.0350692\pi$
$488$	7.14015e12			0.257993
$489$	−2.00149e13	−	1.43387e12i	−0.715828	−	0.0512822i
$490$	−1.65271e13	−	3.88376e12i	−0.585083	−	0.137490i
$491$		−	1.24291e13i		−	0.435544i	−0.976000	−	0.217772i	$-0.930121\pi$
$491$		−	1.24291e13i		−	0.435544i	0.976000	−	0.217772i	$-0.0698789\pi$
$492$	1.51462e13	+	1.08508e12i	0.525387	+	0.0376389i
$493$		−	5.24893e12i		−	0.180234i
$494$			1.05088e13i			0.357206i
$495$	−1.43358e13	+	3.65438e13i	−0.482386	+	1.22967i
$496$	7.63889e12			0.254461
$497$	−3.39493e13			−1.11956
$498$	3.55428e11	−	4.96128e12i	0.0116039	−	0.161975i
$499$	−2.64815e13			−0.855932			−0.427966	−	0.903795i	$-0.640770\pi$
$499$	−2.64815e13			−0.855932			−0.427966	+	0.903795i	$0.640770\pi$
$500$	−7.83402e12	−	6.49759e12i	−0.250689	−	0.207923i
$501$	9.07564e11	−	1.26683e13i	0.0287534	−	0.401357i
$502$			2.51010e13i			0.787357i
$503$	7.56997e12			0.235101			0.117550	−	0.993067i	$-0.462496\pi$
$503$	7.56997e12			0.235101			0.117550	+	0.993067i	$0.462496\pi$
$504$	6.64129e12	−	4.61137e13i	0.204221	−	1.41800i
$505$	4.37218e12	−	1.86055e13i	0.133119	−	0.566481i
$506$		−	4.72834e13i		−	1.42546i
$507$	2.02010e12	−	2.81978e13i	0.0603022	−	0.841735i
$508$		−	1.16274e13i		−	0.343687i
$509$			3.97683e13i			1.16399i	0.813193	+	0.581993i	$0.197727\pi$
$509$			3.97683e13i			1.16399i	−0.813193	+	0.581993i	$0.802273\pi$
$510$	−1.15692e12	+	3.70947e12i	−0.0335316	+	0.107513i
$511$	6.83570e13			1.96191
$512$	−3.41998e13			−0.972018
$513$	−8.32848e12	+	3.82201e13i	−0.234412	+	1.07573i
$514$	−2.19387e13			−0.611498
$515$	7.44820e12	−	3.16954e13i	0.205596	−	0.874903i
$516$	−1.26924e13	−	9.09288e11i	−0.346972	−	0.0248572i
$517$		−	3.65300e13i		−	0.989002i
$518$	−2.14937e13			−0.576317
$519$	−2.28192e12	+	3.18524e13i	−0.0605986	+	0.845873i
$520$	3.74097e12	−	1.59195e13i	0.0983937	−	0.418709i
$521$			7.92875e12i			0.206546i	0.994653	+	0.103273i	$0.0329315\pi$
$521$			7.92875e12i			0.206546i	−0.994653	+	0.103273i	$0.967069\pi$
$522$	5.96201e12	−	4.13971e13i	0.153830	−	1.06811i
$523$			4.26427e13i			1.08977i	0.838510	+	0.544887i	$0.183427\pi$
$523$			4.26427e13i			1.08977i	−0.838510	+	0.544887i	$0.816573\pi$
$524$		−	3.53695e12i		−	0.0895309i
$525$	−4.52037e13	−	2.66760e13i	−1.13339	−	0.668843i
$526$	−3.42917e13			−0.851648
$527$	2.49655e12			0.0614168
$528$	3.07222e13	+	2.20095e12i	0.748656	+	0.0536340i
$529$	3.01207e13			0.727089
$530$	7.68329e12	+	1.80552e12i	0.183725	+	0.0431741i
$531$	−5.65344e12	+	3.92546e13i	−0.133918	+	0.929860i
$532$			2.01099e13i			0.471902i
$533$	2.74871e13			0.638988
$534$	4.53777e13	+	3.25087e12i	1.04505	+	0.0748676i
$535$	−1.05867e13	−	2.48780e12i	−0.241542	−	0.0567606i
$536$			4.03369e12i			0.0911755i
$537$	8.21457e13	+	5.88495e12i	1.83956	+	0.131787i
$538$		−	2.00372e13i		−	0.444554i
$539$			4.39820e13i			0.966788i
$540$	6.44224e12	−	1.34960e13i	0.140303	−	0.293925i
$541$	−8.57918e12			−0.185123			−0.0925613	−	0.995707i	$-0.529505\pi$
$541$	−8.57918e12			−0.185123			−0.0925613	+	0.995707i	$0.529505\pi$
$542$	−3.37598e13			−0.721778
$543$	−2.02260e12	+	2.82327e13i	−0.0428461	+	0.598072i
$544$	−4.06420e12			−0.0853062
$545$	−2.35968e13	−	5.54508e12i	−0.490761	−	0.115325i
$546$	1.48052e12	−	2.06660e13i	0.0305106	−	0.425885i
$547$		−	1.05712e13i		−	0.215867i	−0.994158	−	0.107933i	$-0.965577\pi$
$547$		−	1.05712e13i		−	0.215867i	0.994158	−	0.107933i	$-0.0344233\pi$
$548$	−6.52830e12			−0.132098
$549$	1.16988e13	+	1.68486e12i	0.234573	+	0.0337832i
$550$	2.43139e13	−	4.88763e13i	0.483104	−	0.971147i
$551$			7.34824e13i			1.44686i
$552$	−5.23927e12	+	7.31329e13i	−0.102229	+	1.42698i
$553$			9.14656e13i			1.76861i
$554$			5.31427e13i			1.01834i
$555$	−2.68088e13	−	8.36124e12i	−0.509111	−	0.158784i
$556$	1.88728e13			0.355192
$557$	−4.86308e13			−0.907058			−0.453529	−	0.891241i	$-0.649835\pi$
$557$	−4.86308e13			−0.907058			−0.453529	+	0.891241i	$0.649835\pi$
$558$	1.96897e13	+	2.83571e12i	0.363973	+	0.0524193i
$559$	−2.30339e13			−0.421997
$560$	−9.42129e12	+	4.00917e13i	−0.171069	+	0.727972i
$561$	1.00407e13	+	7.19317e11i	0.180696	+	0.0129451i
$562$		−	9.83866e12i		−	0.175491i
$563$	8.69377e11			0.0153697			0.00768487	−	0.999970i	$-0.497554\pi$
$563$	8.69377e11			0.0153697			0.00768487	+	0.999970i	$0.497554\pi$
$564$	−9.94439e11	+	1.38810e13i	−0.0174254	+	0.243234i
$565$	6.64310e13	+	1.56108e13i	1.15379	+	0.271134i
$566$		−	4.56085e13i		−	0.785170i
$567$	2.17628e13	−	7.39878e13i	0.371364	−	1.26254i
$568$			5.47518e13i			0.926098i
$569$		−	4.20491e13i		−	0.705011i	−0.935810	−	0.352505i	$-0.885330\pi$
$569$		−	4.20491e13i		−	0.705011i	0.935810	−	0.352505i	$-0.114670\pi$
$570$	1.61964e13	−	5.19307e13i	0.269180	−	0.863078i
$571$	−7.75987e13			−1.27842			−0.639210	−	0.769032i	$-0.720739\pi$
$571$	−7.75987e13			−1.27842			−0.639210	+	0.769032i	$0.720739\pi$
$572$	−1.04081e13			−0.169978
$573$	2.45549e13	+	1.75912e12i	0.397526	+	0.0284789i
$574$	−1.08901e14			−1.74772
$575$	7.39576e13	+	3.67907e13i	1.17664	+	0.585327i
$576$	−6.77131e13	−	9.75204e12i	−1.06797	−	0.153809i
$577$		−	8.80927e13i		−	1.37740i	−0.725045	−	0.688701i	$-0.758181\pi$
$577$		−	8.80927e13i		−	1.37740i	0.725045	−	0.688701i	$-0.241819\pi$
$578$	−5.19782e13			−0.805716
$579$	8.64330e13	+	6.19209e12i	1.32827	+	0.0951579i
$580$	6.42659e12	−	2.73480e13i	0.0979130	−	0.416663i
$581$		−	1.72296e13i		−	0.260252i
$582$	−4.55701e12	−	3.26466e11i	−0.0682440	−	0.00488903i
$583$		−	2.04468e13i		−	0.303586i
$584$		−	1.10243e14i		−	1.62288i
$585$	9.88590e12	−	2.52005e13i	0.144290	−	0.367815i
$586$	7.66865e13			1.10976
$587$	1.82237e13			0.261485			0.130742	−	0.991416i	$-0.458264\pi$
$587$	1.82237e13			0.261485			0.130742	+	0.991416i	$0.458264\pi$
$588$	1.19730e12	−	1.67127e13i	0.0170340	−	0.237771i
$589$	−3.49505e13			−0.493034
$590$	1.26168e13	−	5.36899e13i	0.176477	−	0.750987i
$591$	3.55662e12	−	4.96455e13i	0.0493288	−	0.688561i
$592$			2.20344e13i			0.303035i
$593$	−8.41730e13			−1.14789			−0.573944	−	0.818895i	$-0.694587\pi$
$593$	−8.41730e13			−1.14789			−0.573944	+	0.818895i	$0.694587\pi$
$594$	7.83714e13	+	1.70778e13i	1.05980	+	0.230940i
$595$	−3.07908e12	+	1.31028e13i	−0.0412891	+	0.175704i
$596$			3.39376e13i			0.451284i
$597$	−5.72060e12	+	7.98516e13i	−0.0754345	+	1.05296i
$598$			3.26065e13i			0.426381i
$599$		−	1.11318e14i		−	1.44355i	−0.692126	−	0.721776i	$-0.743326\pi$
$599$		−	1.11318e14i		−	1.44355i	0.692126	−	0.721776i	$-0.256674\pi$
$600$	−4.30218e13	+	7.29025e13i	−0.553264	+	0.937533i
$601$	−5.32717e13			−0.679398			−0.339699	−	0.940534i	$-0.610325\pi$
$601$	−5.32717e13			−0.679398			−0.339699	+	0.940534i	$0.610325\pi$
$602$	9.12580e13			1.15422
$603$	−9.51826e11	+	6.60899e12i	−0.0119391	+	0.0828989i
$604$	−4.20637e13			−0.523267
$605$	−5.87671e13	−	1.38099e13i	−0.725032	−	0.170378i
$606$	−3.89527e13	−	2.79059e12i	−0.476622	−	0.0341454i
$607$			1.94515e13i			0.236053i	0.993010	+	0.118026i	$0.0376568\pi$
$607$			1.94515e13i			0.236053i	−0.993010	+	0.118026i	$0.962343\pi$
$608$	5.68967e13			0.684809
$609$	1.03524e13	−	1.44506e14i	0.123582	−	1.72504i
$610$	−1.60008e13	−	3.76008e12i	−0.189449	−	0.0445193i
$611$			2.51910e13i			0.295828i
$612$	−3.79576e12	−	5.46665e11i	−0.0442121	−	0.00636743i
$613$		−	2.93882e13i		−	0.339524i	−0.985485	−	0.169762i	$-0.945700\pi$
$613$		−	2.93882e13i		−	0.339524i	0.985485	−	0.169762i	$-0.0542999\pi$
$614$			1.07521e14i			1.23212i
$615$	−1.35831e14	−	4.23635e13i	−1.54392	−	0.481523i
$616$	1.67845e14			1.89237
$617$	−1.52231e14			−1.70246			−0.851230	−	0.524793i	$-0.824143\pi$
$617$	−1.52231e14			−1.70246			−0.851230	+	0.524793i	$0.824143\pi$
$618$	−6.63577e13	−	4.75389e12i	−0.736120	−	0.0527359i
$619$	8.77890e13			0.966022			0.483011	−	0.875614i	$-0.339543\pi$
$619$	8.77890e13			0.966022			0.483011	+	0.875614i	$0.339543\pi$
$620$	1.30075e13	+	3.05668e12i	0.141983	+	0.0333650i
$621$	−2.58414e13	+	1.18588e14i	−0.279807	+	1.28405i
$622$			1.61686e13i			0.173669i
$623$	1.57588e14			1.67912
$624$	−2.11859e13	−	1.51777e12i	−0.223936	−	0.0160429i
$625$	5.75308e13	+	7.60602e13i	0.603254	+	0.797549i
$626$			2.01460e13i			0.209565i
$627$	−1.40564e14	−	1.00701e13i	−1.45057	−	0.103919i
$628$		−	7.31585e12i		−	0.0748973i
$629$			7.20132e12i			0.0731407i
$630$	−3.91669e13	+	9.98417e13i	−0.394654	+	1.00603i
$631$	7.07071e13			0.706832			0.353416	−	0.935466i	$-0.385020\pi$
$631$	7.07071e13			0.706832			0.353416	+	0.935466i	$0.385020\pi$
$632$	1.47512e14			1.46299
$633$	−7.98832e10	+	1.11506e12i	−0.000786026	+	0.0109718i
$634$	−6.78278e13			−0.662157
$635$	−2.49232e13	+	1.06059e14i	−0.241399	+	1.02726i
$636$	−5.56613e11	+	7.76954e12i	−0.00534894	+	0.0746638i
$637$		−	3.03298e13i		−	0.289183i
$638$	1.50678e14			1.42543
$639$	−1.29198e13	+	8.97081e13i	−0.121269	+	0.842029i
$640$	2.75978e13	+	6.48529e12i	0.257024	+	0.0603989i
$641$		−	1.92565e14i		−	1.77946i	−0.456488	−	0.889729i	$-0.650893\pi$
$641$		−	1.92565e14i		−	1.77946i	0.456488	−	0.889729i	$-0.349107\pi$
$642$	−1.58787e12	+	2.21644e13i	−0.0145592	+	0.203227i
$643$		−	2.00414e14i		−	1.82337i	−0.410893	−	0.911684i	$-0.634783\pi$
$643$		−	2.00414e14i		−	1.82337i	0.410893	−	0.911684i	$-0.365217\pi$
$644$			6.23965e13i			0.563288i
$645$	1.13825e14	+	3.55002e13i	1.01962	+	0.318004i
$646$	−1.39495e13			−0.123993
$647$	2.12105e14			1.87081			0.935404	−	0.353581i	$-0.115036\pi$
$647$	2.12105e14			1.87081			0.935404	+	0.353581i	$0.115036\pi$
$648$	−1.19324e14	−	3.50981e13i	−1.04437	−	0.307191i
$649$	−1.42879e14			−1.24093
$650$	−1.67668e13	+	3.37050e13i	−0.144505	+	0.290487i
$651$	6.87313e13	+	4.92394e12i	0.587827	+	0.0421122i
$652$			2.75403e13i			0.233739i
$653$	−1.91603e14			−1.61375			−0.806876	−	0.590721i	$-0.798843\pi$
$653$	−1.91603e14			−1.61375			−0.806876	+	0.590721i	$0.798843\pi$
$654$	−3.53920e12	+	4.94023e13i	−0.0295813	+	0.412913i
$655$	−7.58146e12	+	3.22625e13i	−0.0628849	+	0.267603i
$656$			1.11641e14i			0.918976i
$657$	2.60140e13	−	1.80628e14i	0.212510	−	1.47556i
$658$		−	9.98039e13i		−	0.809130i
$659$			9.85772e13i			0.793139i	0.918005	+	0.396569i	$0.129799\pi$
$659$			9.85772e13i			0.793139i	−0.918005	+	0.396569i	$0.870201\pi$
$660$	5.14332e13	+	1.60412e13i	0.410699	+	0.128090i
$661$	−1.93372e13			−0.153245			−0.0766225	−	0.997060i	$-0.524414\pi$
$661$	−1.93372e13			−0.153245			−0.0766225	+	0.997060i	$0.524414\pi$
$662$	−1.59949e14			−1.25803
$663$	−6.92401e12	−	4.96039e11i	−0.0540493	−	0.00387211i
$664$	−2.77871e13			−0.215279
$665$	4.31056e13	−	1.83433e14i	0.331455	−	1.41049i
$666$	−8.17964e12	+	5.67952e13i	−0.0624256	+	0.433451i
$667$			2.27999e14i			1.72705i
$668$	−1.74315e13			−0.131055
$669$	1.41076e14	+	1.01068e13i	1.05275	+	0.0754192i
$670$	2.12419e12	−	9.03935e12i	0.0157332	−	0.0669519i
$671$			4.25814e13i			0.313045i
$672$	−1.11889e14	−	8.01580e12i	−0.816475	−	0.0584926i
$673$			3.67001e13i			0.265822i	0.991128	+	0.132911i	$0.0424325\pi$
$673$			3.67001e13i			0.265822i	−0.991128	+	0.132911i	$0.957568\pi$
$674$		−	8.73863e13i		−	0.628266i
$675$	−8.76918e13	+	1.09295e14i	−0.625807	+	0.779978i
$676$	−3.87999e13			−0.274851
$677$	1.31238e14			0.922818			0.461409	−	0.887187i	$-0.347344\pi$
$677$	1.31238e14			0.922818			0.461409	+	0.887187i	$0.347344\pi$
$678$	9.96376e12	−	1.39080e14i	0.0695464	−	0.970771i
$679$	−1.58256e13			−0.109651
$680$	2.11317e13	+	4.96580e12i	0.145341	+	0.0341542i
$681$	1.81532e13	−	2.53393e14i	0.123942	−	1.73005i
$682$			7.16670e13i			0.485733i
$683$	−1.02733e14			−0.691206			−0.345603	−	0.938381i	$-0.612326\pi$
$683$	−1.02733e14			−0.691206			−0.345603	+	0.938381i	$0.612326\pi$
$684$	5.31387e13	+	7.65303e12i	0.354920	+	0.0511156i
$685$	5.95482e13	+	1.39934e13i	0.394835	+	0.0927835i
$686$		−	4.40134e13i		−	0.289711i
$687$	−1.62003e13	+	2.26133e14i	−0.105862	+	1.47768i
$688$		−	9.35540e13i		−	0.606904i
$689$			1.41000e13i			0.0908079i
$690$	5.02536e13	−	1.61129e14i	0.321308	−	1.03022i
$691$	−1.22650e14			−0.778535			−0.389268	−	0.921125i	$-0.627272\pi$
$691$	−1.22650e14			−0.778535			−0.389268	+	0.921125i	$0.627272\pi$
$692$	4.38285e13			0.276202
$693$	2.75006e14	+	3.96063e13i	1.72058	+	0.247798i
$694$	1.89343e14			1.17612
$695$	−1.72149e14	−	4.04539e13i	−1.06165	−	0.249480i
$696$	−2.33052e14	−	1.66960e13i	−1.42694	−	0.102227i
$697$			3.64866e13i			0.221804i
$698$	5.89308e12			0.0355685
$699$	−3.89624e12	+	5.43861e13i	−0.0233486	+	0.325913i
$700$	−3.20852e13	+	6.44985e13i	−0.190904	+	0.383760i
$701$			4.30376e13i			0.254248i	0.991887	+	0.127124i	$0.0405747\pi$
$701$			4.30376e13i			0.254248i	−0.991887	+	0.127124i	$0.959425\pi$
$702$	−5.40446e13	−	1.17768e13i	−0.317006	−	0.0690783i
$703$		−	1.00815e14i		−	0.587149i
$704$		−	2.46463e14i		−	1.42524i
$705$	3.88247e13	−	1.24484e14i	0.222927	−	0.714775i
$706$	−7.54040e13			−0.429903
$707$	−1.35275e14			−0.765809
$708$	5.42926e13	+	3.88954e12i	0.305193	+	0.0218641i
$709$	−4.14116e13			−0.231149			−0.115574	−	0.993299i	$-0.536871\pi$
$709$	−4.14116e13			−0.231149			−0.115574	+	0.993299i	$0.536871\pi$
$710$	2.88329e13	−	1.22697e14i	0.159807	−	0.680051i
$711$	2.41690e14	+	3.48082e13i	1.33018	+	0.191573i
$712$		−	2.54150e14i		−	1.38896i
$713$	−1.08443e14			−0.588512
$714$	2.74322e13	+	1.96525e12i	0.147832	+	0.0105908i
$715$	9.49383e13	+	2.23098e13i	0.508055	+	0.119390i
$716$		−	1.13032e14i		−	0.600668i
$717$	1.28531e14	+	9.20800e12i	0.678284	+	0.0485925i
$718$			8.21078e13i			0.430291i
$719$			2.74351e14i			1.42778i	0.700257	+	0.713891i	$0.253069\pi$
$719$			2.74351e14i			1.42778i	−0.700257	+	0.713891i	$0.746931\pi$
$720$	1.02354e14	+	4.01523e13i	0.528982	+	0.207514i
$721$	−2.30447e14			−1.18276
$722$	3.41791e13			0.174211
$723$	1.68624e13	−	2.35376e14i	0.0853548	−	1.19143i
$724$	3.88480e13			0.195288
$725$	−1.17241e14	+	2.35680e14i	−0.585313	+	1.17661i
$726$	−8.81429e12	+	1.23035e14i	−0.0437023	+	0.610023i
$727$		−	1.47816e14i		−	0.727865i	−0.931425	−	0.363932i	$-0.881434\pi$
$727$		−	1.47816e14i		−	0.727865i	0.931425	−	0.363932i	$-0.118566\pi$
$728$	−1.15746e14			−0.566040
$729$	−1.87224e14	−	8.56633e13i	−0.909337	−	0.416061i
$730$	−5.80552e13	+	2.47051e14i	−0.280044	+	1.19171i
$731$		−	3.05754e13i		−	0.146483i
$732$	1.15917e12	−	1.61804e13i	0.00551560	−	0.0769901i
$733$			1.72506e14i			0.815236i	0.913153	+	0.407618i	$0.133640\pi$
$733$			1.72506e14i			0.815236i	−0.913153	+	0.407618i	$0.866360\pi$
$734$			1.39634e14i			0.655409i
$735$	−4.67448e13	+	1.49879e14i	−0.217920	+	0.698721i
$736$	1.76538e14			0.817426
$737$	−2.40555e13			−0.110631
$738$	−4.14434e13	+	2.87762e14i	−0.189310	+	1.31447i
$739$	−1.68467e13			−0.0764351			−0.0382176	−	0.999269i	$-0.512168\pi$
$739$	−1.68467e13			−0.0764351			−0.0382176	+	0.999269i	$0.512168\pi$
$740$	−8.81702e12	+	3.75203e13i	−0.0397341	+	0.169086i
$741$	9.69327e13	+	6.94429e12i	0.433890	+	0.0310840i
$742$		−	5.58628e13i		−	0.248372i
$743$	−9.12029e13			−0.402777			−0.201388	−	0.979511i	$-0.564545\pi$
$743$	−9.12029e13			−0.402777			−0.201388	+	0.979511i	$0.564545\pi$
$744$	7.94111e12	−	1.10847e14i	0.0348350	−	0.486249i
$745$	7.27452e13	−	3.09563e14i	0.316974	−	1.34886i
$746$			7.19489e13i			0.311408i
$747$	−4.55277e13	−	6.55689e12i	−0.195737	−	0.0281900i
$748$		−	1.38159e13i		−	0.0590024i
$749$			7.69726e13i			0.326533i
$750$	1.34802e14	−	1.40716e14i	0.568053	−	0.592977i
$751$	2.75068e14			1.15144			0.575719	−	0.817648i	$-0.304722\pi$
$751$	2.75068e14			1.15144			0.575719	+	0.817648i	$0.304722\pi$
$752$	−1.02315e14			−0.425451
$753$	2.31530e14	+	1.65869e13i	0.956383	+	0.0685156i
$754$	−1.03907e14			−0.426371
$755$	3.83686e14	+	9.01636e13i	1.56402	+	0.367533i
$756$	−1.03421e14	−	2.25363e13i	−0.418793	−	0.0912586i
$757$			1.85980e14i			0.748148i	0.927399	+	0.374074i	$0.122039\pi$
$757$			1.85980e14i			0.748148i	−0.927399	+	0.374074i	$0.877961\pi$
$758$	2.75404e14			1.10059
$759$	−4.36139e14	−	3.12452e13i	−1.73148	−	0.124044i
$760$	−2.95833e14	−	6.95187e13i	−1.16675	−	0.274179i
$761$			3.49741e14i			1.37032i	0.728391	+	0.685161i	$0.240268\pi$
$761$			3.49741e14i			1.37032i	−0.728391	+	0.685161i	$0.759732\pi$
$762$	2.22047e14	+	1.59075e13i	0.864310	+	0.0619195i
$763$			1.71565e14i			0.663445i
$764$		−	3.37873e13i		−	0.129804i
$765$	3.34514e13	+	1.31226e13i	0.127675	+	0.0500857i
$766$	3.16429e14			1.19987
$767$	9.85292e13			0.371183
$768$	−1.64609e13	+	2.29771e14i	−0.0616093	+	0.859981i
$769$	4.92965e14			1.83309			0.916545	−	0.399931i	$-0.130966\pi$
$769$	4.92965e14			1.83309			0.916545	+	0.399931i	$0.130966\pi$
$770$	−3.76135e14	−	8.83892e13i	−1.38960	−	0.326547i
$771$	−1.44972e13	+	2.02361e14i	−0.0532124	+	0.742771i
$772$		−	1.18931e14i		−	0.433719i
$773$	−1.09067e14			−0.395182			−0.197591	−	0.980285i	$-0.563312\pi$
$773$	−1.09067e14			−0.395182			−0.197591	+	0.980285i	$0.563312\pi$
$774$	3.47292e13	−	2.41141e14i	0.125023	−	0.868095i
$775$	−1.12097e14	−	5.57633e13i	−0.400945	−	0.199453i
$776$			2.55228e13i			0.0907026i
$777$	−1.42031e13	+	1.98256e14i	−0.0501510	+	0.700038i
$778$			3.42358e14i			1.20111i
$779$		−	5.10795e14i		−	1.78057i
$780$	−3.54681e13	−	1.10619e13i	−0.122847	−	0.0383141i
$781$	−3.26521e14			−1.12371
$782$	−4.32822e13			−0.148005
$783$	−3.77905e14	−	8.23486e13i	−1.28402	−	0.279800i
$784$	1.23187e14			0.415895
$785$	−1.56815e13	+	6.67318e13i	−0.0526065	+	0.223864i
$786$	6.75449e13	+	4.83894e12i	0.225154	+	0.0161301i
$787$		−	1.77907e14i		−	0.589278i	−0.955609	−	0.294639i	$-0.904801\pi$
$787$		−	1.77907e14i		−	0.589278i	0.955609	−	0.294639i	$-0.0951994\pi$
$788$	−6.83118e13			−0.224835
$789$	−2.26602e13	+	3.16304e14i	−0.0741102	+	1.03448i
$790$	−3.30568e14	−	7.76812e13i	−1.07430	−	0.252453i
$791$		−	4.82999e14i		−	1.55978i
$792$	6.38753e13	−	4.43517e14i	0.204978	−	1.42326i
$793$		−	2.93640e13i		−	0.0936373i
$794$		−	8.34233e13i		−	0.264353i
$795$	2.17312e13	−	6.96771e13i	0.0684302	−	0.219409i
$796$	1.09875e14			0.343822
$797$	−2.28314e14			−0.709971			−0.354986	−	0.934872i	$-0.615514\pi$
$797$	−2.28314e14			−0.709971			−0.354986	+	0.934872i	$0.615514\pi$
$798$	−3.84037e14	−	2.75126e13i	−1.18675	−	0.0850191i
$799$	−3.34387e13			−0.102687
$800$	1.82485e14	+	9.07784e13i	0.556900	+	0.277034i
$801$	5.99717e13	−	4.16412e14i	0.181879	−	1.26288i
$802$		−	1.80962e14i		−	0.545401i
$803$	6.57451e14			1.96918
$804$	9.14082e12	+	6.54852e11i	0.0272085	+	0.00194923i
$805$	1.33747e14	−	5.69152e14i	0.395643	−	1.68364i
$806$		−	4.94213e13i		−	0.145291i
$807$	−1.84821e14	−	1.32407e13i	−0.539989	−	0.0386850i
$808$			2.18165e14i			0.633475i
$809$		−	3.82660e14i		−	1.10426i	−0.833759	−	0.552129i	$-0.813816\pi$
$809$		−	3.82660e14i		−	1.10426i	0.833759	−	0.552129i	$-0.186184\pi$
$810$	2.48918e14	+	1.41491e14i	0.713890	+	0.405792i
$811$	−3.19351e14			−0.910258			−0.455129	−	0.890426i	$-0.650407\pi$
$811$	−3.19351e14			−0.910258			−0.455129	+	0.890426i	$0.650407\pi$
$812$	−1.98838e14			−0.563275
$813$	−2.23087e13	+	3.11398e14i	−0.0628089	+	0.876725i
$814$	−2.06724e14			−0.578454
$815$	5.90326e13	−	2.51210e14i	0.164174	−	0.698632i
$816$	2.01470e12	−	2.81224e13i	0.00556877	−	0.0777322i
$817$			4.28041e14i			1.17591i
$818$	2.68577e14			0.733336
$819$	−1.89643e14	−	2.73124e13i	−0.514657	−	0.0741208i
$820$	−4.46728e13	+	1.90103e14i	−0.120496	+	0.512765i
$821$			1.82884e14i			0.490297i	0.969486	+	0.245149i	$0.0788367\pi$
$821$			1.82884e14i			0.490297i	−0.969486	+	0.245149i	$0.921163\pi$
$822$	8.93143e12	−	1.24670e14i	0.0237992	−	0.332203i
$823$			1.19032e14i			0.315256i	0.987499	+	0.157628i	$0.0503847\pi$
$823$			1.19032e14i			0.315256i	−0.987499	+	0.157628i	$0.949615\pi$
$824$			3.71655e14i			0.978371i
$825$	−4.34765e14	−	2.56567e14i	−1.13759	−	0.671323i
$826$	−3.90362e14			−1.01524
$827$	4.50584e14			1.16479			0.582395	−	0.812906i	$-0.302116\pi$
$827$	4.50584e14			1.16479			0.582395	+	0.812906i	$0.302116\pi$
$828$	1.64877e14	+	2.37456e13i	0.423652	+	0.0610143i
$829$	4.52610e14			1.15598			0.577992	−	0.816042i	$-0.303836\pi$
$829$	4.52610e14			1.15598			0.577992	+	0.816042i	$0.303836\pi$
$830$	6.22698e13	+	1.46330e13i	0.158084	+	0.0371486i
$831$	4.90185e14	+	3.51170e13i	1.23696	+	0.0886161i
$832$			1.69960e14i			0.426315i
$833$	4.02601e13			0.100381
$834$	−2.58201e13	+	3.60412e14i	−0.0639922	+	0.893243i
$835$	1.59002e14	+	3.73644e13i	0.391715	+	0.0920504i
$836$			1.93415e14i			0.473652i
$837$	3.91675e13	−	1.79743e14i	0.0953452	−	0.437547i
$838$		−	3.20853e14i		−	0.776402i
$839$			3.11136e14i			0.748412i	0.927346	+	0.374206i	$0.122085\pi$
$839$			3.11136e14i			0.748412i	−0.927346	+	0.374206i	$0.877915\pi$
$840$	5.71972e14	+	1.78389e14i	1.36766	+	0.426551i
$841$	−3.05857e14			−0.727007
$842$	−1.43544e13			−0.0339175
$843$	−9.07512e13	−	6.50145e12i	−0.213164	−	0.0152712i
$844$	1.53431e12			0.00358262
$845$	3.53915e14	+	8.31675e13i	0.821514	+	0.193050i
$846$	−2.63723e14	−	3.79814e13i	−0.608551	−	0.0876435i
$847$			4.27277e14i			0.980150i
$848$	−5.72683e13			−0.130598
$849$	−4.20690e14	−	3.01384e13i	−0.953725	−	0.0683253i
$850$	−4.47403e13	−	2.22563e13i	−0.100833	−	0.0501602i
$851$		−	3.12806e14i		−	0.700853i
$852$	1.24074e14	+	8.88872e12i	0.276365	+	0.0197989i
$853$			3.14625e14i			0.696705i	0.937364	+	0.348352i	$0.113259\pi$
$853$			3.14625e14i			0.696705i	−0.937364	+	0.348352i	$0.886741\pi$
$854$			1.16337e14i			0.256111i
$855$	−4.68303e14	−	1.83710e14i	−1.02493	−	0.402071i
$856$	1.24138e14			0.270107
$857$	−2.87288e14			−0.621460			−0.310730	−	0.950498i	$-0.600574\pi$
$857$	−2.87288e14			−0.621460			−0.310730	+	0.950498i	$0.600574\pi$
$858$	1.42395e13	−	1.98763e14i	0.0306237	−	0.427464i
$859$	2.86257e14			0.612055			0.306028	−	0.952023i	$-0.401000\pi$
$859$	2.86257e14			0.612055			0.306028	+	0.952023i	$0.401000\pi$
$860$	3.74354e13	−	1.59304e14i	0.0795774	−	0.338637i
$861$	−7.19624e13	+	1.00450e15i	−0.152086	+	2.12291i
$862$		−	6.03946e14i		−	1.26900i
$863$	−7.57077e14			−1.58156			−0.790780	−	0.612100i	$-0.790325\pi$
$863$	−7.57077e14			−1.58156			−0.790780	+	0.612100i	$0.790325\pi$
$864$	−6.37618e13	+	2.92608e14i	−0.132432	+	0.607739i
$865$	−3.99784e14	−	9.39465e13i	−0.825552	−	0.193999i
$866$			2.48169e14i			0.509516i
$867$	−3.43475e13	+	4.79443e14i	−0.0701132	+	0.978682i
$868$		−	9.45737e13i		−	0.191943i
$869$			8.79707e14i			1.77517i
$870$	5.13469e14	+	1.60143e14i	1.03019	+	0.321301i
$871$	1.65886e13			0.0330917
$872$	2.76692e14			0.548800
$873$	−6.02260e12	+	4.18178e13i	−0.0118772	+	0.0824688i
$874$	6.05928e14			1.18813
$875$	4.30919e14	−	5.19551e14i	0.840147	−	1.01295i
$876$	−2.49824e14	−	1.78975e13i	−0.484299	−	0.0346954i
$877$		−	5.01306e14i		−	0.966284i	−0.875542	−	0.483142i	$-0.839495\pi$
$877$		−	5.01306e14i		−	0.966284i	0.875542	−	0.483142i	$-0.160505\pi$
$878$	−8.96690e13			−0.171858
$879$	5.06749e13	−	7.07351e14i	0.0965714	−	1.34800i
$880$	−9.06131e13	+	3.85599e14i	−0.171703	+	0.730672i
$881$		−	2.75288e14i		−	0.518691i	−0.965785	−	0.259345i	$-0.916493\pi$
$881$		−	2.75288e14i		−	0.518691i	0.965785	−	0.259345i	$-0.0835068\pi$
$882$	3.17522e14	+	4.57295e13i	0.594882	+	0.0856749i
$883$		−	9.33195e14i		−	1.73848i	−0.494394	−	0.869238i	$-0.664610\pi$
$883$		−	9.33195e14i		−	1.73848i	0.494394	−	0.869238i	$-0.335390\pi$
$884$			9.52737e12i			0.0176487i
$885$	−4.86895e14	−	1.51855e14i	−0.896848	−	0.279712i
$886$	3.00772e14			0.550896
$887$	−1.11980e14			−0.203949			−0.101975	−	0.994787i	$-0.532516\pi$
$887$	−1.11980e14			−0.203949			−0.101975	+	0.994787i	$0.532516\pi$
$888$	3.19738e14	+	2.29062e13i	0.579069	+	0.0414847i
$889$	7.71125e14			1.38872
$890$	−1.33838e14	+	5.69542e14i	−0.239679	+	1.01994i
$891$	2.09313e14	−	7.11607e14i	0.372741	−	1.26722i
$892$		−	1.94120e14i		−	0.343752i
$893$	4.68125e14			0.824337
$894$	−6.48103e14	−	4.64304e13i	−1.13490	−	0.0813045i
$895$	−2.42283e14	+	1.03102e15i	−0.421899	+	1.79537i
$896$		−	2.00655e14i		−	0.347464i
$897$	3.00760e14	+	2.15466e13i	0.517914	+	0.0371036i
$898$		−	6.14266e13i		−	0.105190i
$899$		−	3.45576e14i		−	0.588498i
$900$	1.58221e14	+	1.09328e14i	0.267949	+	0.185148i
$901$	−1.87165e13			−0.0315211
$902$	−1.04740e15			−1.75420
$903$	6.03038e13	−	8.41757e14i	0.100440	−	1.40200i
$904$	−7.78958e14			−1.29024
$905$	−3.54353e14	−	8.32706e13i	−0.583705	−	0.137167i
$906$	5.75478e13	−	8.03287e14i	0.0942731	−	1.31592i
$907$			3.30958e14i			0.539184i	0.962975	+	0.269592i	$0.0868889\pi$
$907$			3.30958e14i			0.539184i	−0.962975	+	0.269592i	$0.913111\pi$
$908$	−3.48667e14			−0.564913
$909$	−5.14804e13	+	3.57453e14i	−0.0829511	+	0.575970i
$910$	2.59382e14	+	6.09529e13i	0.415654	+	0.0976759i
$911$			2.42666e14i			0.386739i	0.981126	+	0.193369i	$0.0619415\pi$
$911$			2.42666e14i			0.386739i	−0.981126	+	0.193369i	$0.938058\pi$
$912$	−2.82048e13	+	3.93699e14i	−0.0447042	+	0.624008i
$913$		−	1.65712e14i		−	0.261217i
$914$		−	3.73019e14i		−	0.584790i
$915$	−4.52562e13	+	1.45106e14i	−0.0705623	+	0.226245i
$916$	3.11157e14			0.482505
$917$	2.34570e14			0.361765
$918$	1.56326e13	−	7.17393e13i	0.0239783	−	0.110038i
$919$	−6.74016e14			−1.02824			−0.514118	−	0.857719i	$-0.671881\pi$
$919$	−6.74016e14			−1.02824			−0.514118	+	0.857719i	$0.671881\pi$
$920$	−9.17902e14	−	2.15701e14i	−1.39270	−	0.327275i
$921$	9.91770e14	+	7.10508e13i	1.49662	+	0.107219i
$922$			7.74094e14i			1.16182i
$923$	2.25168e14			0.336122
$924$	2.72490e13	−	3.80358e14i	0.0404567	−	0.564719i
$925$	1.60850e14	−	3.23344e14i	0.237526	−	0.477481i
$926$		−	5.21275e14i		−	0.765617i
$927$	−8.76991e13	+	6.08937e14i	−0.128114	+	0.889557i
$928$			5.62572e14i			0.817407i
$929$		−	1.11678e15i		−	1.61395i	−0.590587	−	0.806974i	$-0.701104\pi$
$929$		−	1.11678e15i		−	1.61395i	0.590587	−	0.806974i	$-0.298896\pi$
$930$	−7.61689e13	+	2.44222e14i	−0.109487	+	0.351050i
$931$	−5.63621e14			−0.805822
$932$	7.48348e13			0.106420
$933$	1.49138e14	+	1.06843e13i	0.210951	+	0.0151126i
$934$	3.92885e14			0.552753
$935$	−2.96143e13	+	1.26022e14i	−0.0414422	+	0.176355i
$936$	−4.40482e13	+	3.05848e14i	−0.0613125	+	0.425722i
$937$			3.47654e14i			0.481337i	0.970607	+	0.240669i	$0.0773667\pi$
$937$			3.47654e14i			0.481337i	−0.970607	+	0.240669i	$0.922633\pi$
$938$	−6.57223e13			−0.0905104
$939$	1.85826e14	+	1.33126e13i	0.254553	+	0.0182363i
$940$	−1.74222e14	−	4.09411e13i	−0.237391	−	0.0557853i
$941$			9.96429e14i			1.35051i	0.737584	+	0.675256i	$0.235967\pi$
$941$			9.96429e14i			1.35051i	−0.737584	+	0.675256i	$0.764033\pi$
$942$	1.39710e14	+	1.00089e13i	0.188353	+	0.0134937i
$943$		−	1.58488e15i		−	2.12539i
$944$			4.00183e14i			0.533825i
$945$	8.95052e14	+	4.27249e14i	1.18765	+	0.566920i
$946$	8.77711e14			1.15850
$947$	−4.83589e12			−0.00634930			−0.00317465	−	0.999995i	$-0.501011\pi$
$947$	−4.83589e12			−0.00634930			−0.00317465	+	0.999995i	$0.501011\pi$
$948$	2.39479e13	−	3.34279e14i	0.0312770	−	0.436583i
$949$	−4.53376e14			−0.589016
$950$	6.26341e14	+	3.11578e14i	0.809456	+	0.402669i
$951$	−4.48210e13	+	6.25639e14i	−0.0576208	+	0.804306i
$952$		−	1.53642e14i		−	0.196483i
$953$	−1.27218e15			−1.61839			−0.809197	−	0.587537i	$-0.800098\pi$
$953$	−1.27218e15			−1.61839			−0.809197	+	0.587537i	$0.800098\pi$
$954$	−1.47613e14	−	2.12592e13i	−0.186802	−	0.0269032i
$955$	−7.24231e13	+	3.08193e14i	−0.0911718	+	0.387976i
$956$		−	1.76857e14i		−	0.221479i
$957$	9.95689e13	−	1.38984e15i	0.124041	−	1.73143i
$958$		−	8.02298e14i		−	0.994278i
$959$		−	4.32956e14i		−	0.533766i
$960$	2.61945e14	−	8.39880e14i	0.321258	−	1.03006i
$961$	−6.55262e14			−0.799462
$962$	1.42556e14			0.173026
$963$	2.03394e14	+	2.92927e13i	0.245587	+	0.0353695i
$964$	−3.23875e14			−0.389038
$965$	−2.54928e14	+	1.08483e15i	−0.304636	+	1.29636i
$966$	−1.19158e15	−	8.53652e13i	−1.41657	−	0.101483i
$967$			8.82927e12i			0.0104422i	0.999986	+	0.00522110i	$0.00166194\pi$
$967$			8.82927e12i			0.0104422i	−0.999986	+	0.00522110i	$0.998338\pi$
$968$	6.89093e14			0.810776
$969$	−9.21792e12	+	1.28669e14i	−0.0107898	+	0.150611i
$970$	1.34406e13	−	5.71957e13i	0.0156516	−	0.0666046i
$971$			1.15983e15i			1.34369i	0.740692	+	0.671844i	$0.234498\pi$
$971$			1.15983e15i			1.34369i	−0.740692	+	0.671844i	$0.765502\pi$
$972$	−9.89082e13	+	2.64705e14i	−0.113999	+	0.305092i
$973$			1.25164e15i			1.43521i
$974$		−	1.58289e14i		−	0.180574i
$975$	2.99813e14	+	1.76928e14i	0.340273	+	0.200804i
$976$	1.19264e14			0.134667
$977$	1.05657e15			1.18693			0.593466	−	0.804859i	$-0.297759\pi$
$977$	1.05657e15			1.18693			0.593466	+	0.804859i	$0.297759\pi$
$978$	−5.25934e14	−	3.76781e13i	−0.587810	−	0.0421109i
$979$	1.51566e15			1.68535
$980$	2.09763e14	+	4.92929e13i	0.232059	+	0.0545323i
$981$	4.53345e14	+	6.52907e13i	0.498981	+	0.0718632i
$982$		−	3.26601e14i		−	0.357652i
$983$	4.99718e14			0.544450			0.272225	−	0.962234i	$-0.412241\pi$
$983$	4.99718e14			0.544450			0.272225	+	0.962234i	$0.412241\pi$
$984$	1.62000e15	+	1.16058e14i	1.75607	+	0.125805i
$985$	6.23108e14	+	1.46426e14i	0.672020	+	0.157920i
$986$		−	1.37927e14i		−	0.148001i
$987$	−9.20585e14	−	6.59511e13i	−0.982829	−	0.0704103i
$988$		−	1.33378e14i		−	0.141677i
$989$			1.32811e15i			1.40363i
$990$	−3.76703e14	+	9.60268e14i	−0.396117	+	1.00976i
$991$	−1.53898e15			−1.61014			−0.805071	−	0.593178i	$-0.797873\pi$
$991$	−1.53898e15			−1.61014			−0.805071	+	0.593178i	$0.797873\pi$
$992$	−2.67576e14			−0.278541
$993$	−1.05695e14	+	1.47536e15i	−0.109473	+	1.52810i
$994$	−8.92090e14			−0.919342
$995$	−1.00223e15	−	2.35517e14i	−1.02767	−	0.241494i
$996$	−4.51111e12	+	6.29688e13i	−0.00460242	+	0.0642434i
$997$			4.46303e14i			0.453059i	0.974004	+	0.226529i	$0.0727379\pi$
$997$			4.46303e14i			0.453059i	−0.974004	+	0.226529i	$0.927262\pi$
$998$	−6.95857e14			−0.702858
$999$	5.18470e14	+	1.12979e14i	0.521070	+	0.113546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.d.c.14.11	yes	16
3.2	odd	2	inner	15.11.d.c.14.5	✓	16
5.2	odd	4		75.11.c.h.26.11		16
5.3	odd	4		75.11.c.h.26.6		16
5.4	even	2	inner	15.11.d.c.14.6	yes	16
15.2	even	4		75.11.c.h.26.5		16
15.8	even	4		75.11.c.h.26.12		16
15.14	odd	2	inner	15.11.d.c.14.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.d.c.14.5	✓	16	3.2	odd	2	inner
15.11.d.c.14.6	yes	16	5.4	even	2	inner
15.11.d.c.14.11	yes	16	1.1	even	1	trivial
15.11.d.c.14.12	yes	16	15.14	odd	2	inner
75.11.c.h.26.5		16	15.2	even	4
75.11.c.h.26.6		16	5.3	odd	4
75.11.c.h.26.11		16	5.2	odd	4
75.11.c.h.26.12		16	15.8	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)

\(f(q)\)	\(=\)	\(q+26.2772 q^{2} +(17.3641 - 242.379i) q^{3} -333.511 q^{4} +(3042.13 + 714.880i) q^{5} +(456.279 - 6369.03i) q^{6} -22118.4i q^{7} -35671.5 q^{8} +(-58446.0 - 8417.38i) q^{9} +O(q^{10})\)	\(q+26.2772 q^{2} +(17.3641 - 242.379i) q^{3} -333.511 q^{4} +(3042.13 + 714.880i) q^{5} +(456.279 - 6369.03i) q^{6} -22118.4i q^{7} -35671.5 q^{8} +(-58446.0 - 8417.38i) q^{9} +(79938.6 + 18785.0i) q^{10} -212733. i q^{11} +(-5791.12 + 80836.0i) q^{12} +146700. i q^{13} -581208. i q^{14} +(226096. - 724935. i) q^{15} -595831. q^{16} -194730. q^{17} +(-1.53579e6 - 221185. i) q^{18} +2.72613e6 q^{19} +(-1.01458e6 - 238420. i) q^{20} +(-5.36103e6 - 384066. i) q^{21} -5.59001e6i q^{22} +8.45856e6 q^{23} +(-619404. + 8.64602e6i) q^{24} +(8.74352e6 + 4.34952e6i) q^{25} +3.85485e6i q^{26} +(-3.05506e6 + 1.40199e7i) q^{27} +7.37672e6i q^{28} +2.69549e7i q^{29} +(5.94115e6 - 1.90492e7i) q^{30} -1.28206e7 q^{31} +2.08709e7 q^{32} +(-5.15619e7 - 3.69391e6i) q^{33} -5.11696e6 q^{34} +(1.58120e7 - 6.72871e7i) q^{35} +(1.94924e7 + 2.80729e6i) q^{36} -3.69810e7i q^{37} +7.16349e7 q^{38} +(3.55569e7 + 2.54731e6i) q^{39} +(-1.08518e8 - 2.55009e7i) q^{40} -1.87370e8i q^{41} +(-1.40873e8 - 1.00922e7i) q^{42} +1.57014e8i q^{43} +7.09486e7i q^{44} +(-1.71783e8 - 6.73887e7i) q^{45} +2.22267e8 q^{46} +1.71718e8 q^{47} +(-1.03461e7 + 1.44417e8i) q^{48} -2.06748e8 q^{49} +(2.29755e8 + 1.14293e8i) q^{50} +(-3.38132e6 + 4.71985e7i) q^{51} -4.89259e7i q^{52} +9.61149e7 q^{53} +(-8.02782e7 + 3.68403e8i) q^{54} +(1.52078e8 - 6.47161e8i) q^{55} +7.88997e8i q^{56} +(4.73368e7 - 6.60756e8i) q^{57} +7.08297e8i q^{58} -6.71639e8i q^{59} +(-7.54054e7 + 2.41774e8i) q^{60} -2.00164e8 q^{61} -3.36888e8 q^{62} +(-1.86179e8 + 1.29273e9i) q^{63} +1.15856e9 q^{64} +(-1.04873e8 + 4.46280e8i) q^{65} +(-1.35490e9 - 9.70655e7i) q^{66} -1.13079e8i q^{67} +6.49447e7 q^{68} +(1.46875e8 - 2.05018e9i) q^{69} +(4.15494e8 - 1.76811e9i) q^{70} -1.53489e9i q^{71} +(2.08486e9 + 3.00261e8i) q^{72} +3.09050e9i q^{73} -9.71755e8i q^{74} +(1.20606e9 - 2.04372e9i) q^{75} -9.09194e8 q^{76} -4.70530e9 q^{77} +(9.34334e8 + 6.69360e7i) q^{78} -4.13527e9 q^{79} +(-1.81260e9 - 4.25948e8i) q^{80} +(3.34508e9 + 9.83925e8i) q^{81} -4.92355e9i q^{82} +7.78970e8 q^{83} +(1.78796e9 + 1.28090e8i) q^{84} +(-5.92396e8 - 1.39209e8i) q^{85} +4.12589e9i q^{86} +(6.53329e9 + 4.68047e8i) q^{87} +7.58850e9i q^{88} +7.12474e9i q^{89} +(-4.51397e9 - 1.77078e9i) q^{90} +3.24476e9 q^{91} -2.82102e9 q^{92} +(-2.22617e8 + 3.10743e9i) q^{93} +4.51226e9 q^{94} +(8.29325e9 + 1.94886e9i) q^{95} +(3.62404e8 - 5.05866e9i) q^{96} -7.15495e8i q^{97} -5.43275e9 q^{98} +(-1.79065e9 + 1.24334e10i) 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

Properties

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