LMFDB - Embedded newform 20.9.d.c.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.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:	$8.14757220122$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 94 x^{18} + 5343 x^{16} + 172772 x^{14} + 36131456 x^{12} + 3044563968 x^{10} + \cdots + 11\!\cdots\!76 $ x^20 + 94x^18 + 5343x^16 + 172772x^14 + 36131456x^12 + 3044563968x^10 + 147994443776x^8 + 2898633162752x^6 + 367168164200448x^4 + 26458647810801664*x^2 + 1152921504606846976
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{74}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.5
Root			$-3.61621 - 7.13604i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.9.d.c.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.23243 - 14.2721i) q^{2} +44.3270 q^{3} +(-151.384 + 206.443i) q^{4} +(530.961 - 329.705i) q^{5} +(-320.592 - 632.638i) q^{6} +2826.75 q^{7} +(4041.25 + 667.476i) q^{8} -4596.11 q^{9} +O(q^{10})$	\(q+(-7.23243 - 14.2721i) q^{2} +44.3270 q^{3} +(-151.384 + 206.443i) q^{4} +(530.961 - 329.705i) q^{5} +(-320.592 - 632.638i) q^{6} +2826.75 q^{7} +(4041.25 + 667.476i) q^{8} -4596.11 q^{9} +(-8545.71 - 5193.35i) q^{10} -18327.2i q^{11} +(-6710.40 + 9151.02i) q^{12} -13946.9i q^{13} +(-20444.3 - 40343.6i) q^{14} +(23535.9 - 14614.8i) q^{15} +(-19701.8 - 62504.5i) q^{16} -96189.1i q^{17} +(33241.1 + 65596.1i) q^{18} +153485. i q^{19} +(-12313.7 + 159525. i) q^{20} +125301. q^{21} +(-261567. + 132550. i) q^{22} +339368. q^{23} +(179137. + 29587.2i) q^{24} +(173215. - 350121. i) q^{25} +(-199051. + 100870. i) q^{26} -494562. q^{27} +(-427925. + 583564. i) q^{28} +758065. q^{29} +(-378806. - 230206. i) q^{30} +1.01418e6i q^{31} +(-749577. + 733244. i) q^{32} -812389. i q^{33} +(-1.37282e6 + 695681. i) q^{34} +(1.50090e6 - 931993. i) q^{35} +(695778. - 948838. i) q^{36} -135354. i q^{37} +(2.19055e6 - 1.11007e6i) q^{38} -618224. i q^{39} +(2.36582e6 - 978014. i) q^{40} -2.56309e6 q^{41} +(-906233. - 1.78831e6i) q^{42} -852539. q^{43} +(3.78352e6 + 2.77444e6i) q^{44} +(-2.44036e6 + 1.51536e6i) q^{45} +(-2.45445e6 - 4.84348e6i) q^{46} -1.25626e6 q^{47} +(-873321. - 2.77064e6i) q^{48} +2.22572e6 q^{49} +(-6.24971e6 + 60088.9i) q^{50} -4.26378e6i q^{51} +(2.87925e6 + 2.11134e6i) q^{52} +1.00203e7i q^{53} +(3.57688e6 + 7.05842e6i) q^{54} +(-6.04255e6 - 9.73101e6i) q^{55} +(1.14236e7 + 1.88679e6i) q^{56} +6.80354e6i q^{57} +(-5.48265e6 - 1.08192e7i) q^{58} +2.35908e7i q^{59} +(-545830. + 7.07129e6i) q^{60} -5.69128e6 q^{61} +(1.44744e7 - 7.33498e6i) q^{62} -1.29921e7 q^{63} +(1.58862e7 + 5.39488e6i) q^{64} +(-4.59836e6 - 7.40526e6i) q^{65} +(-1.15945e7 + 5.87554e6i) q^{66} +1.76526e7 q^{67} +(1.98576e7 + 1.45615e7i) q^{68} +1.50432e7 q^{69} +(-2.41566e7 - 1.46803e7i) q^{70} -3.89940e6i q^{71} +(-1.85740e7 - 3.06780e6i) q^{72} +9.62921e6i q^{73} +(-1.93178e6 + 978938. i) q^{74} +(7.67810e6 - 1.55198e7i) q^{75} +(-3.16860e7 - 2.32352e7i) q^{76} -5.18063e7i q^{77} +(-8.82334e6 + 4.47126e6i) q^{78} -2.34959e6i q^{79} +(-3.10689e7 - 2.66917e7i) q^{80} +8.23266e6 q^{81} +(1.85374e7 + 3.65806e7i) q^{82} +1.26930e7 q^{83} +(-1.89686e7 + 2.58677e7i) q^{84} +(-3.17140e7 - 5.10727e7i) q^{85} +(6.16593e6 + 1.21675e7i) q^{86} +3.36028e7 q^{87} +(1.22330e7 - 7.40646e7i) q^{88} +6.42709e7 q^{89} +(3.92770e7 + 2.38692e7i) q^{90} -3.94244e7i q^{91} +(-5.13749e7 + 7.00603e7i) q^{92} +4.49555e7i q^{93} +(9.08579e6 + 1.79294e7i) q^{94} +(5.06048e7 + 8.14947e7i) q^{95} +(-3.32265e7 + 3.25025e7i) q^{96} -6.62485e6i q^{97} +(-1.60973e7 - 3.17656e7i) q^{98} +8.42338e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9}+O(q^{10}) $ 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9	$ 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30} + 4342528 q^{34} - 7191312 q^{36} - 945280 q^{40} + 7068520 q^{41} + 2666880 q^{44} - 18729060 q^{45} + 561168 q^{46} + 11719036 q^{49} + 3914880 q^{50} + 37110816 q^{54} - 35044352 q^{56} - 22734720 q^{60} - 17660440 q^{61} + 20201728 q^{64} - 44202240 q^{65} + 31902720 q^{66} + 111747216 q^{69} - 47166000 q^{70} + 19114368 q^{74} - 54998400 q^{76} + 7968320 q^{80} - 154212444 q^{81} + 101289216 q^{84} + 68800000 q^{85} + 94429648 q^{86} + 105006376 q^{89} - 230808000 q^{90} - 192757872 q^{94} + 28850688 q^{96}+O(q^{100}) $ 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9 - 4160 * q^10 + 8848 * q^14 - 59200 * q^16 - 4240 * q^20 + 410256 * q^21 - 156672 * q^24 - 657260 * q^25 - 440448 * q^26 + 660136 * q^29 + 667920 * q^30 + 4342528 * q^34 - 7191312 * q^36 - 945280 * q^40 + 7068520 * q^41 + 2666880 * q^44 - 18729060 * q^45 + 561168 * q^46 + 11719036 * q^49 + 3914880 * q^50 + 37110816 * q^54 - 35044352 * q^56 - 22734720 * q^60 - 17660440 * q^61 + 20201728 * q^64 - 44202240 * q^65 + 31902720 * q^66 + 111747216 * q^69 - 47166000 * q^70 + 19114368 * q^74 - 54998400 * q^76 + 7968320 * q^80 - 154212444 * q^81 + 101289216 * q^84 + 68800000 * q^85 + 94429648 * q^86 + 105006376 * q^89 - 230808000 * q^90 - 192757872 * q^94 + 28850688 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−7.23243	−	14.2721i	−0.452027	−	0.892004i
$2$	−7.23243	−	14.2721i	−0.452027	−	0.892004i
$3$	44.3270			0.547247			0.273624	−	0.961837i	$-0.411778\pi$
$3$	44.3270			0.547247			0.273624	+	0.961837i	$0.411778\pi$
$4$	−151.384	+	206.443i	−0.591344	+	0.806420i
$5$	530.961	−	329.705i	0.849538	−	0.527527i
$5$	530.961	−	329.705i	0.849538	−	0.527527i
$6$	−320.592	−	632.638i	−0.247370	−	0.488147i
$7$	2826.75			1.17732			0.588661	−	0.808380i	$-0.299655\pi$
$7$	2826.75			1.17732			0.588661	+	0.808380i	$0.299655\pi$
$8$	4041.25	+	667.476i	0.986633	+	0.162958i
$9$	−4596.11			−0.700520
$10$	−8545.71	−	5193.35i	−0.854571	−	0.519335i
$11$		−	18327.2i		−	1.25177i	−0.779915	−	0.625885i	$-0.784738\pi$
$11$		−	18327.2i		−	1.25177i	0.779915	−	0.625885i	$-0.215262\pi$
$12$	−6710.40	+	9151.02i	−0.323611	+	0.441311i
$13$		−	13946.9i		−	0.488320i	−0.969735	−	0.244160i	$-0.921488\pi$
$13$		−	13946.9i		−	0.488320i	0.969735	−	0.244160i	$-0.0785122\pi$
$14$	−20444.3	−	40343.6i	−0.532181	−	1.05018i
$15$	23535.9	−	14614.8i	0.464907	−	0.288688i
$16$	−19701.8	−	62504.5i	−0.300625	−	0.953742i
$17$		−	96189.1i		−	1.15168i	−0.817564	−	0.575838i	$-0.804676\pi$
$17$		−	96189.1i		−	1.15168i	0.817564	−	0.575838i	$-0.195324\pi$
$18$	33241.1	+	65596.1i	0.316654	+	0.624867i
$19$			153485.i			1.17775i	0.808225	+	0.588873i	$0.200428\pi$
$19$			153485.i			1.17775i	−0.808225	+	0.588873i	$0.799572\pi$
$20$	−12313.7	+	159525.i	−0.0769607	+	0.997034i
$21$	125301.			0.644286
$22$	−261567.	+	132550.i	−1.11658	+	0.565833i
$23$	339368.			1.21272			0.606358	−	0.795191i	$-0.292630\pi$
$23$	339368.			1.21272			0.606358	+	0.795191i	$0.292630\pi$
$24$	179137.	+	29587.2i	0.539932	+	0.0891784i
$25$	173215.	−	350121.i	0.443430	−	0.896309i
$26$	−199051.	+	100870.i	−0.435583	+	0.220734i
$27$	−494562.			−0.930605
$28$	−427925.	+	583564.i	−0.696202	+	0.949416i
$29$	758065.			1.07180			0.535901	−	0.844281i	$-0.319972\pi$
$29$	758065.			1.07180			0.535901	+	0.844281i	$0.319972\pi$
$30$	−378806.	−	230206.i	−0.467661	−	0.284205i
$31$			1.01418e6i			1.09817i	0.835768	+	0.549083i	$0.185023\pi$
$31$			1.01418e6i			1.09817i	−0.835768	+	0.549083i	$0.814977\pi$
$32$	−749577.	+	733244.i	−0.714852	+	0.699276i
$33$		−	812389.i		−	0.685028i
$34$	−1.37282e6	+	695681.i	−1.02730	+	0.520588i
$35$	1.50090e6	−	931993.i	1.00018	−	0.621070i
$36$	695778.	−	948838.i	0.414248	−	0.564913i
$37$		−	135354.i		−	0.0722211i	−0.999348	−	0.0361106i	$-0.988503\pi$
$37$		−	135354.i		−	0.0722211i	0.999348	−	0.0361106i	$-0.0114968\pi$
$38$	2.19055e6	−	1.11007e6i	1.05056	−	0.532373i
$39$		−	618224.i		−	0.267232i
$40$	2.36582e6	−	978014.i	0.924147	−	0.382037i
$41$	−2.56309e6			−0.907045			−0.453523	−	0.891245i	$-0.649833\pi$
$41$	−2.56309e6			−0.907045			−0.453523	+	0.891245i	$0.649833\pi$
$42$	−906233.	−	1.78831e6i	−0.291235	−	0.574706i
$43$	−852539.			−0.249368			−0.124684	−	0.992197i	$-0.539792\pi$
$43$	−852539.			−0.249368			−0.124684	+	0.992197i	$0.539792\pi$
$44$	3.78352e6	+	2.77444e6i	1.00945	+	0.740226i
$45$	−2.44036e6	+	1.51536e6i	−0.595119	+	0.369544i
$46$	−2.45445e6	−	4.84348e6i	−0.548180	−	1.08175i
$47$	−1.25626e6			−0.257447			−0.128723	−	0.991681i	$-0.541088\pi$
$47$	−1.25626e6			−0.257447			−0.128723	+	0.991681i	$0.541088\pi$
$48$	−873321.	−	2.77064e6i	−0.164516	−	0.521933i
$49$	2.22572e6			0.386087
$50$	−6.24971e6	+	60088.9i	−0.999954	+	0.00961422i
$51$		−	4.26378e6i		−	0.630251i
$52$	2.87925e6	+	2.11134e6i	0.393791	+	0.288765i
$53$			1.00203e7i			1.26993i	0.772542	+	0.634963i	$0.218985\pi$
$53$			1.00203e7i			1.26993i	−0.772542	+	0.634963i	$0.781015\pi$
$54$	3.57688e6	+	7.05842e6i	0.420658	+	0.830104i
$55$	−6.04255e6	−	9.73101e6i	−0.660343	−	1.06343i
$56$	1.14236e7	+	1.88679e6i	1.16158	+	0.191854i
$57$			6.80354e6i			0.644519i
$58$	−5.48265e6	−	1.08192e7i	−0.484483	−	0.956052i
$59$			2.35908e7i			1.94686i	0.228979	+	0.973431i	$0.426461\pi$
$59$			2.35908e7i			1.94686i	−0.228979	+	0.973431i	$0.573539\pi$
$60$	−545830.	+	7.07129e6i	−0.0421165	+	0.545624i
$61$	−5.69128e6			−0.411046			−0.205523	−	0.978652i	$-0.565890\pi$
$61$	−5.69128e6			−0.411046			−0.205523	+	0.978652i	$0.565890\pi$
$62$	1.44744e7	−	7.33498e6i	0.979569	−	0.496400i
$63$	−1.29921e7			−0.824738
$64$	1.58862e7	+	5.39488e6i	0.946889	+	0.321560i
$65$	−4.59836e6	−	7.40526e6i	−0.257602	−	0.414846i
$66$	−1.15945e7	+	5.87554e6i	−0.611048	+	0.309651i
$67$	1.76526e7			0.876010			0.438005	−	0.898973i	$-0.355685\pi$
$67$	1.76526e7			0.876010			0.438005	+	0.898973i	$0.355685\pi$
$68$	1.98576e7	+	1.45615e7i	0.928734	+	0.681036i
$69$	1.50432e7			0.663656
$70$	−2.41566e7	−	1.46803e7i	−1.00610	−	0.611425i
$71$		−	3.89940e6i		−	0.153449i	−0.997052	−	0.0767246i	$-0.975554\pi$
$71$		−	3.89940e6i		−	0.153449i	0.997052	−	0.0767246i	$-0.0244462\pi$
$72$	−1.85740e7	−	3.06780e6i	−0.691157	−	0.114156i
$73$			9.62921e6i			0.339078i	0.985523	+	0.169539i	$0.0542278\pi$
$73$			9.62921e6i			0.339078i	−0.985523	+	0.169539i	$0.945772\pi$
$74$	−1.93178e6	+	978938.i	−0.0644216	+	0.0326459i
$75$	7.67810e6	−	1.55198e7i	0.242666	−	0.490503i
$76$	−3.16860e7	−	2.32352e7i	−0.949758	−	0.696453i
$77$		−	5.18063e7i		−	1.47374i
$78$	−8.82334e6	+	4.47126e6i	−0.238372	+	0.120796i
$79$		−	2.34959e6i		−	0.0603232i	−0.999545	−	0.0301616i	$-0.990398\pi$
$79$		−	2.34959e6i		−	0.0603232i	0.999545	−	0.0301616i	$-0.00960220\pi$
$80$	−3.10689e7	−	2.66917e7i	−0.758518	−	0.651653i
$81$	8.23266e6			0.191249
$82$	1.85374e7	+	3.65806e7i	0.410009	+	0.809088i
$83$	1.26930e7			0.267456			0.133728	−	0.991018i	$-0.457305\pi$
$83$	1.26930e7			0.267456			0.133728	+	0.991018i	$0.457305\pi$
$84$	−1.89686e7	+	2.58677e7i	−0.380995	+	0.519565i
$85$	−3.17140e7	−	5.10727e7i	−0.607540	−	0.978392i
$86$	6.16593e6	+	1.21675e7i	0.112721	+	0.222437i
$87$	3.36028e7			0.586541
$88$	1.22330e7	−	7.40646e7i	0.203986	−	1.23504i
$89$	6.42709e7			1.02436			0.512182	−	0.858877i	$-0.328837\pi$
$89$	6.42709e7			1.02436			0.512182	+	0.858877i	$0.328837\pi$
$90$	3.92770e7	+	2.38692e7i	0.598644	+	0.363805i
$91$		−	3.94244e7i		−	0.574910i
$92$	−5.13749e7	+	7.00603e7i	−0.717133	+	0.977959i
$93$			4.49555e7i			0.600968i
$94$	9.08579e6	+	1.79294e7i	0.116373	+	0.229643i
$95$	5.06048e7	+	8.14947e7i	0.621294	+	1.00054i
$96$	−3.32265e7	+	3.25025e7i	−0.391201	+	0.382677i
$97$		−	6.62485e6i		−	0.0748323i	−0.999300	−	0.0374161i	$-0.988087\pi$
$97$		−	6.62485e6i		−	0.0748323i	0.999300	−	0.0374161i	$-0.0119127\pi$
$98$	−1.60973e7	−	3.17656e7i	−0.174522	−	0.344392i
$99$			8.42338e7i			0.876891i
$100$	4.60582e7	+	8.87617e7i	0.460582	+	0.887617i
$101$	5.22160e7			0.501786			0.250893	−	0.968015i	$-0.419276\pi$
$101$	5.22160e7			0.501786			0.250893	+	0.968015i	$0.419276\pi$
$102$	−6.08529e7	+	3.08374e7i	−0.562187	+	0.284890i
$103$	−1.19619e8			−1.06280			−0.531401	−	0.847120i	$-0.678334\pi$
$103$	−1.19619e8			−1.06280			−0.531401	+	0.847120i	$0.678334\pi$
$104$	9.30923e6	−	5.63629e7i	0.0795757	−	0.481792i
$105$	6.65302e7	−	4.13125e7i	0.547346	−	0.339879i
$106$	1.43011e8	−	7.24713e7i	1.13278	−	0.574041i
$107$	−1.97409e8			−1.50602			−0.753011	−	0.658008i	$-0.771399\pi$
$107$	−1.97409e8			−1.50602			−0.753011	+	0.658008i	$0.771399\pi$
$108$	7.48687e7	−	1.02099e8i	0.550308	−	0.750458i
$109$	−2.24099e8			−1.58758			−0.793788	−	0.608195i	$-0.791894\pi$
$109$	−2.24099e8			−1.58758			−0.793788	+	0.608195i	$0.791894\pi$
$110$	−9.51794e7	+	1.56619e8i	−0.650088	+	1.06973i
$111$		−	5.99984e6i		−	0.0395228i
$112$	−5.56920e7	−	1.76685e8i	−0.353933	−	1.12286i
$113$			3.24514e8i			1.99031i	0.0983370	+	0.995153i	$0.468648\pi$
$113$			3.24514e8i			1.99031i	−0.0983370	+	0.995153i	$0.531352\pi$
$114$	9.71006e7	−	4.92061e7i	0.574913	−	0.291340i
$115$	1.80191e8	−	1.11891e8i	1.03025	−	0.639741i
$116$	−1.14759e8	+	1.56498e8i	−0.633804	+	0.864322i
$117$			6.41015e7i			0.342078i
$118$	3.36690e8	−	1.70619e8i	1.73661	−	0.880034i
$119$		−	2.71903e8i		−	1.35589i
$120$	1.04870e8	−	4.33525e7i	0.505737	−	0.209069i
$121$	−1.21526e8			−0.566928
$122$	4.11618e7	+	8.12264e7i	0.185804	+	0.366655i
$123$	−1.13614e8			−0.496378
$124$	−2.09371e8	−	1.53530e8i	−0.885582	−	0.649393i
$125$	−2.34661e7	−	2.43010e8i	−0.0961170	−	0.995370i
$126$	9.39642e7	+	1.85424e8i	0.372804	+	0.735670i
$127$	3.41089e8			1.31115			0.655576	−	0.755129i	$-0.272426\pi$
$127$	3.41089e8			1.31115			0.655576	+	0.755129i	$0.272426\pi$
$128$	−3.78995e7	−	2.65747e8i	−0.141187	−	0.989983i
$129$	−3.77905e7			−0.136466
$130$	−7.24312e7	+	1.19186e8i	−0.253602	+	0.417304i
$131$			2.72281e8i			0.924553i	0.886736	+	0.462277i	$0.152967\pi$
$131$			2.72281e8i			0.924553i	−0.886736	+	0.462277i	$0.847033\pi$
$132$	1.67712e8	+	1.22983e8i	0.552420	+	0.405087i
$133$			4.33864e8i			1.38659i
$134$	−1.27671e8	−	2.51939e8i	−0.395980	−	0.781404i
$135$	−2.62593e8	+	1.63059e8i	−0.790584	+	0.490920i
$136$	6.42040e7	−	3.88724e8i	0.187675	−	1.13628i
$137$		−	3.75590e8i		−	1.06618i	−0.846057	−	0.533092i	$-0.821030\pi$
$137$		−	3.75590e8i		−	1.06618i	0.846057	−	0.533092i	$-0.178970\pi$
$138$	−1.08799e8	−	2.14697e8i	−0.299990	−	0.591984i
$139$		−	5.07197e8i		−	1.35868i	−0.733823	−	0.679340i	$-0.762266\pi$
$139$		−	5.07197e8i		−	1.35868i	0.733823	−	0.679340i	$-0.237734\pi$
$140$	−3.48078e7	+	4.50939e8i	−0.0906075	+	1.17383i
$141$	−5.56861e7			−0.140887
$142$	−5.56526e7	+	2.82022e7i	−0.136877	+	0.0693632i
$143$	−2.55607e8			−0.611264
$144$	9.05516e7	+	2.87278e8i	0.210594	+	0.668116i
$145$	4.02503e8	−	2.49938e8i	0.910537	−	0.565405i
$146$	1.37429e8	−	6.96426e7i	0.302459	−	0.153272i
$147$	9.86594e7			0.211285
$148$	2.79429e7	+	2.04904e7i	0.0582405	+	0.0427075i
$149$	−7.01900e7			−0.142407			−0.0712033	−	0.997462i	$-0.522684\pi$
$149$	−7.01900e7			−0.142407			−0.0712033	+	0.997462i	$0.522684\pi$
$150$	−2.77031e8	+	2.66356e6i	−0.547222	+	0.00526136i
$151$			3.99910e8i			0.769228i	0.923078	+	0.384614i	$0.125665\pi$
$151$			3.99910e8i			0.769228i	−0.923078	+	0.384614i	$0.874335\pi$
$152$	−1.02448e8	+	6.20272e8i	−0.191923	+	1.16200i
$153$			4.42096e8i			0.806772i
$154$	−7.39383e8	+	3.74685e8i	−1.31458	+	0.666168i
$155$	3.34379e8	+	5.38490e8i	0.579312	+	0.932934i
$156$	1.27628e8	+	9.35893e7i	0.215501	+	0.158026i
$157$		−	6.98489e8i		−	1.14964i	−0.818281	−	0.574819i	$-0.805073\pi$
$157$		−	6.98489e8i		−	1.14964i	0.818281	−	0.574819i	$-0.194927\pi$
$158$	−3.35336e7	+	1.69933e7i	−0.0538086	+	0.0272677i
$159$			4.44171e8i			0.694964i
$160$	−1.56242e8	+	6.36463e8i	−0.238407	+	0.971165i
$161$	9.59308e8			1.42776
$162$	−5.95421e7	−	1.17497e8i	−0.0864498	−	0.170595i
$163$	−3.45753e8			−0.489796			−0.244898	−	0.969549i	$-0.578755\pi$
$163$	−3.45753e8			−0.489796			−0.244898	+	0.969549i	$0.578755\pi$
$164$	3.88011e8	−	5.29134e8i	0.536375	−	0.731459i
$165$	−2.67848e8	−	4.31347e8i	−0.361371	−	0.581957i
$166$	−9.18013e7	−	1.81156e8i	−0.120897	−	0.238572i
$167$	9.80032e8			1.26001			0.630006	−	0.776591i	$-0.283053\pi$
$167$	9.80032e8			1.26001			0.630006	+	0.776591i	$0.283053\pi$
$168$	5.06374e8	+	8.36358e7i	0.635674	+	0.104992i
$169$	6.21215e8			0.761544
$170$	−4.99544e8	+	8.22004e8i	−0.598106	+	0.984188i
$171$		−	7.05435e8i		−	0.825036i
$172$	1.29061e8	−	1.76001e8i	0.147462	−	0.201095i
$173$		−	9.30284e8i		−	1.03856i	−0.854604	−	0.519280i	$-0.826200\pi$
$173$		−	9.30284e8i		−	1.03856i	0.854604	−	0.519280i	$-0.173800\pi$
$174$	−2.43030e8	−	4.79581e8i	−0.265132	−	0.523197i
$175$	4.89635e8	−	9.89704e8i	0.522060	−	1.05524i
$176$	−1.14553e9	+	3.61077e8i	−1.19387	+	0.376313i
$177$			1.04571e9i			1.06542i
$178$	−4.64835e8	−	9.17279e8i	−0.463040	−	0.913737i
$179$			3.62399e8i			0.353000i	0.984301	+	0.176500i	$0.0564776\pi$
$179$			3.62399e8i			0.353000i	−0.984301	+	0.176500i	$0.943522\pi$
$180$	5.65952e7	−	7.33197e8i	0.0539125	−	0.698443i
$181$	−1.52080e9			−1.41696			−0.708479	−	0.705732i	$-0.750618\pi$
$181$	−1.52080e9			−1.41696			−0.708479	+	0.705732i	$0.750618\pi$
$182$	−5.62668e8	+	2.85134e8i	−0.512822	+	0.259874i
$183$	−2.52278e8			−0.224944
$184$	1.37147e9	+	2.26520e8i	1.19651	+	0.197622i
$185$	−4.46268e7	−	7.18677e7i	−0.0380986	−	0.0613546i
$186$	6.41609e8	−	3.25138e8i	0.536066	−	0.271654i
$187$	−1.76287e9			−1.44163
$188$	1.90177e8	−	2.59346e8i	0.152239	−	0.207610i
$189$	−1.39800e9			−1.09562
$190$	7.97103e8	−	1.31164e9i	0.611645	−	1.00647i
$191$		−	8.08221e8i		−	0.607290i	−0.952785	−	0.303645i	$-0.901796\pi$
$191$		−	8.08221e8i		−	0.607290i	0.952785	−	0.303645i	$-0.0982037\pi$
$192$	7.04186e8	+	2.39139e8i	0.518183	+	0.175973i
$193$			2.18420e9i			1.57421i	0.616817	+	0.787107i	$0.288422\pi$
$193$			2.18420e9i			1.57421i	−0.616817	+	0.787107i	$0.711578\pi$
$194$	−9.45503e7	+	4.79137e7i	−0.0667507	+	0.0338262i
$195$	−2.03831e8	−	3.28253e8i	−0.140972	−	0.227023i
$196$	−3.36938e8	+	4.59485e8i	−0.228310	+	0.311348i
$197$		−	1.02380e9i		−	0.679751i	−0.940470	−	0.339875i	$-0.889615\pi$
$197$		−	1.02380e9i		−	0.679751i	0.940470	−	0.339875i	$-0.110385\pi$
$198$	1.20219e9	−	6.09214e8i	0.782190	−	0.396378i
$199$			1.22571e9i			0.781585i	0.920479	+	0.390792i	$0.127799\pi$
$199$			1.22571e9i			0.781585i	−0.920479	+	0.390792i	$0.872201\pi$
$200$	9.33701e8	−	1.29931e9i	0.583563	−	0.812068i
$201$	7.82486e8			0.479394
$202$	−3.77649e8	−	7.45231e8i	−0.226820	−	0.447595i
$203$	2.14286e9			1.26186
$204$	8.80229e8	+	6.45468e8i	0.508247	+	0.372695i
$205$	−1.36090e9	+	8.45063e8i	−0.770569	+	0.478491i
$206$	8.65138e8	+	1.70722e9i	0.480415	+	0.948025i
$207$	−1.55977e9			−0.849533
$208$	−8.71743e8	+	2.74778e8i	−0.465731	+	0.146801i
$209$	2.81295e9			1.47427
$210$	−1.07079e9	−	6.50735e8i	−0.550588	−	0.334601i
$211$			2.22607e8i			0.112307i	0.998422	+	0.0561537i	$0.0178837\pi$
$211$			2.22607e8i			0.112307i	−0.998422	+	0.0561537i	$0.982116\pi$
$212$	−2.06863e9	−	1.51692e9i	−1.02409	−	0.750963i
$213$		−	1.72849e8i		−	0.0839747i
$214$	1.42774e9	+	2.81743e9i	0.680762	+	1.34338i
$215$	−4.52665e8	+	2.81086e8i	−0.211848	+	0.131548i
$216$	−1.99865e9	−	3.30108e8i	−0.918166	−	0.151650i
$217$			2.86683e9i			1.29289i
$218$	1.62078e9	+	3.19836e9i	0.717626	+	1.41612i
$219$			4.26834e8i			0.185559i
$220$	2.92365e9	+	2.25675e8i	1.24806	+	0.0963371i
$221$	−1.34154e9			−0.562386
$222$	−8.56302e7	+	4.33934e7i	−0.0352545	+	0.0178654i
$223$	−2.66616e9			−1.07812			−0.539059	−	0.842268i	$-0.681220\pi$
$223$	−2.66616e9			−1.07812			−0.539059	+	0.842268i	$0.681220\pi$
$224$	−2.11887e9	+	2.07270e9i	−0.841611	+	0.823273i
$225$	−7.96115e8	+	1.60920e9i	−0.310632	+	0.627883i
$226$	4.63149e9	−	2.34703e9i	1.77536	−	0.899672i
$227$	1.45410e9			0.547636			0.273818	−	0.961782i	$-0.411713\pi$
$227$	1.45410e9			0.547636			0.273818	+	0.961782i	$0.411713\pi$
$228$	−1.40455e9	−	1.02995e9i	−0.519752	−	0.381132i
$229$	1.32962e7			0.00483488			0.00241744	−	0.999997i	$-0.499231\pi$
$229$	1.32962e7			0.00483488			0.00241744	+	0.999997i	$0.499231\pi$
$230$	−2.90014e9	−	1.76246e9i	−1.03635	−	0.629807i
$231$		−	2.29642e9i		−	0.806498i
$232$	3.06353e9	+	5.05991e8i	1.05748	+	0.174659i
$233$		−	5.53873e9i		−	1.87926i	−0.342196	−	0.939628i	$-0.611171\pi$
$233$		−	5.53873e9i		−	1.87926i	0.342196	−	0.939628i	$-0.388829\pi$
$234$	9.14862e8	−	4.63610e8i	0.305135	−	0.154628i
$235$	−6.67024e8	+	4.14194e8i	−0.218711	+	0.135810i
$236$	−4.87017e9	−	3.57128e9i	−1.56999	−	1.15127i
$237$		−	1.04151e8i		−	0.0330117i
$238$	−3.88061e9	+	1.96652e9i	−1.20946	+	0.612900i
$239$			7.06175e8i			0.216432i	0.994127	+	0.108216i	$0.0345137\pi$
$239$			7.06175e8i			0.216432i	−0.994127	+	0.108216i	$0.965486\pi$
$240$	−1.37719e9	−	1.18316e9i	−0.415097	−	0.356615i
$241$	2.23345e9			0.662075			0.331038	−	0.943618i	$-0.392601\pi$
$241$	2.23345e9			0.662075			0.331038	+	0.943618i	$0.392601\pi$
$242$	8.78928e8	+	1.73443e9i	0.256267	+	0.505702i
$243$	3.60975e9			1.03527
$244$	8.61569e8	−	1.17493e9i	0.243070	−	0.331476i
$245$	1.18177e9	−	7.33829e8i	0.327996	−	0.203672i
$246$	8.21707e8	+	1.62151e9i	0.224376	+	0.442771i
$247$	2.14064e9			0.575117
$248$	−6.76941e8	+	4.09855e9i	−0.178955	+	1.08349i
$249$	5.62643e8			0.146365
$250$	−3.29854e9	+	2.09246e9i	−0.844427	+	0.535671i
$251$			3.22973e9i			0.813713i	0.913492	+	0.406857i	$0.133375\pi$
$251$			3.22973e9i			0.813713i	−0.913492	+	0.406857i	$0.866625\pi$
$252$	1.96679e9	−	2.68213e9i	0.487704	−	0.665085i
$253$		−	6.21965e9i		−	1.51804i
$254$	−2.46690e9	−	4.86805e9i	−0.592676	−	1.16955i
$255$	−1.40579e9	−	2.26390e9i	−0.332475	−	0.535422i
$256$	−3.51865e9	+	2.46290e9i	−0.819249	+	0.573438i
$257$		−	3.73492e9i		−	0.856148i	−0.903744	−	0.428074i	$-0.859192\pi$
$257$		−	3.73492e9i		−	0.856148i	0.903744	−	0.428074i	$-0.140808\pi$
$258$	2.73317e8	+	5.39349e8i	0.0616862	+	0.121728i
$259$		−	3.82612e8i		−	0.0850275i
$260$	2.22489e9	+	1.71738e8i	0.486871	+	0.0375814i
$261$	−3.48416e9			−0.750819
$262$	3.88601e9	−	1.96925e9i	0.824706	−	0.417923i
$263$	5.87828e9			1.22865			0.614324	−	0.789054i	$-0.289429\pi$
$263$	5.87828e9			1.22865			0.614324	+	0.789054i	$0.289429\pi$
$264$	5.42250e8	−	3.28306e9i	0.111631	−	0.675871i
$265$	3.30375e9	+	5.32041e9i	0.669921	+	1.07885i
$266$	6.19214e9	−	3.13789e9i	1.23684	−	0.626774i
$267$	2.84894e9			0.560580
$268$	−2.67232e9	+	3.64426e9i	−0.518023	+	0.706431i
$269$	−2.61826e9			−0.500039			−0.250019	−	0.968241i	$-0.580437\pi$
$269$	−2.61826e9			−0.500039			−0.250019	+	0.968241i	$0.580437\pi$
$270$	4.22638e9	+	2.56843e9i	0.795268	+	0.483296i
$271$			4.66174e9i			0.864312i	0.901799	+	0.432156i	$0.142247\pi$
$271$			4.66174e9i			0.864312i	−0.901799	+	0.432156i	$0.857753\pi$
$272$	−6.01225e9	+	1.89509e9i	−1.09840	+	0.346223i
$273$		−	1.74757e9i		−	0.314618i
$274$	−5.36045e9	+	2.71643e9i	−0.951041	+	0.481944i
$275$	−6.41672e9	−	3.17454e9i	−1.12197	−	0.555072i
$276$	−2.27730e9	+	3.10556e9i	−0.392449	+	0.535185i
$277$			3.79455e9i			0.644526i	0.946650	+	0.322263i	$0.104444\pi$
$277$			3.79455e9i			0.644526i	−0.946650	+	0.322263i	$0.895556\pi$
$278$	−7.23875e9	+	3.66826e9i	−1.21195	+	0.614160i
$279$		−	4.66128e9i		−	0.769288i
$280$	6.68757e9	−	2.76460e9i	1.08802	−	0.449780i
$281$	5.95287e9			0.954776			0.477388	−	0.878693i	$-0.341584\pi$
$281$	5.95287e9			0.954776			0.477388	+	0.878693i	$0.341584\pi$
$282$	4.02746e8	+	7.94756e8i	0.0636846	+	0.125672i
$283$	−6.09829e9			−0.950742			−0.475371	−	0.879785i	$-0.657686\pi$
$283$	−6.09829e9			−0.950742			−0.475371	+	0.879785i	$0.657686\pi$
$284$	8.05006e8	+	5.90307e8i	0.123744	+	0.0907413i
$285$	2.24316e9	+	3.61242e9i	0.340001	+	0.547543i
$286$	1.84866e9	+	3.64804e9i	0.276308	+	0.545250i
$287$	−7.24522e9			−1.06788
$288$	3.44514e9	−	3.37007e9i	0.500768	−	0.489857i
$289$	−2.27658e9			−0.326357
$290$	−6.47820e9	−	3.93690e9i	−0.915931	−	0.556625i
$291$		−	2.93660e8i		−	0.0409517i
$292$	−1.98789e9	−	1.45771e9i	−0.273439	−	0.200512i
$293$		−	3.58577e9i		−	0.486533i	−0.969960	−	0.243266i	$-0.921781\pi$
$293$		−	3.58577e9i		−	0.486533i	0.969960	−	0.243266i	$-0.0782189\pi$
$294$	−7.13547e8	−	1.40807e9i	−0.0955066	−	0.188467i
$295$	7.77801e9	+	1.25258e10i	1.02702	+	1.65393i
$296$	9.03456e7	−	5.46999e8i	0.0117690	−	0.0712557i
$297$			9.06391e9i			1.16490i
$298$	5.07644e8	+	1.00176e9i	0.0643716	+	0.127027i
$299$		−	4.73313e9i		−	0.592194i
$300$	2.04162e9	+	3.93454e9i	0.252052	+	0.485746i
$301$	−2.40992e9			−0.293586
$302$	5.70755e9	−	2.89232e9i	0.686155	−	0.347711i
$303$	2.31458e9			0.274601
$304$	9.59351e9	−	3.02393e9i	1.12327	−	0.354060i
$305$	−3.02185e9	+	1.87644e9i	−0.349199	+	0.216838i
$306$	6.30963e9	−	3.19743e9i	0.719644	−	0.364683i
$307$	−5.11579e9			−0.575917			−0.287958	−	0.957643i	$-0.592976\pi$
$307$	−5.11579e9			−0.575917			−0.287958	+	0.957643i	$0.592976\pi$
$308$	1.06951e10	+	7.84265e9i	1.18845	+	0.871485i
$309$	−5.30237e9			−0.581616
$310$	5.26699e9	−	8.66688e9i	0.570316	−	0.938460i
$311$			2.80934e9i			0.300305i	0.988663	+	0.150152i	$0.0479764\pi$
$311$			2.80934e9i			0.300305i	−0.988663	+	0.150152i	$0.952024\pi$
$312$	4.12650e8	−	2.49840e9i	0.0435476	−	0.263659i
$313$			4.69101e9i			0.488753i	0.969680	+	0.244376i	$0.0785833\pi$
$313$			4.69101e9i			0.488753i	−0.969680	+	0.244376i	$0.921417\pi$
$314$	−9.96888e9	+	5.05177e9i	−1.02548	+	0.519667i
$315$	−6.89829e9	+	4.28354e9i	−0.700647	+	0.435072i
$316$	4.85058e8	+	3.55691e8i	0.0486458	+	0.0356718i
$317$			2.44480e9i			0.242107i	0.992646	+	0.121053i	$0.0386272\pi$
$317$			2.44480e9i			0.242107i	−0.992646	+	0.121053i	$0.961373\pi$
$318$	6.33925e9	−	3.21244e9i	0.619911	−	0.314142i
$319$		−	1.38932e10i		−	1.34165i
$320$	1.02137e10	−	2.37327e9i	0.974050	−	0.226333i
$321$	−8.75054e9			−0.824166
$322$	−6.93813e9	−	1.36913e10i	−0.645385	−	1.27357i
$323$	1.47636e10			1.35638
$324$	−1.24629e9	+	1.69958e9i	−0.113094	+	0.154227i
$325$	−4.88310e9	−	2.41581e9i	−0.437685	−	0.216536i
$326$	2.50063e9	+	4.93461e9i	0.221401	+	0.436900i
$327$	−9.93365e9			−0.868796
$328$	−1.03581e10	−	1.71080e9i	−0.894921	−	0.147810i
$329$	−3.55112e9			−0.303097
$330$	−4.21902e9	+	6.94243e9i	−0.355759	+	0.585404i
$331$		−	2.14898e10i		−	1.79028i	−0.445786	−	0.895139i	$-0.647076\pi$
$331$		−	2.14898e10i		−	1.79028i	0.445786	−	0.895139i	$-0.352924\pi$
$332$	−1.92152e9	+	2.62039e9i	−0.158158	+	0.215682i
$333$			6.22103e8i			0.0505924i
$334$	−7.08801e9	−	1.39871e10i	−0.569559	−	1.12394i
$335$	9.37283e9	−	5.82014e9i	0.744204	−	0.462119i
$336$	−2.46866e9	−	7.83190e9i	−0.193689	−	0.614483i
$337$		−	4.77773e9i		−	0.370426i	−0.982698	−	0.185213i	$-0.940702\pi$
$337$		−	4.77773e9i		−	0.370426i	0.982698	−	0.185213i	$-0.0592975\pi$
$338$	−4.49289e9	−	8.86602e9i	−0.344238	−	0.679301i
$339$			1.43847e10i			1.08919i
$340$	1.53446e10	+	1.18444e9i	1.14826	+	0.0886338i
$341$	1.85870e10			1.37465
$342$	−1.00680e10	+	5.10201e9i	−0.735936	+	0.372938i
$343$	−1.00041e10			−0.722773
$344$	−3.44532e9	−	5.69050e8i	−0.246035	−	0.0406365i
$345$	7.98734e9	−	4.95980e9i	0.563801	−	0.350097i
$346$	−1.32771e10	+	6.72821e9i	−0.926399	+	0.469456i
$347$	7.28826e9			0.502696			0.251348	−	0.967897i	$-0.419126\pi$
$347$	7.28826e9			0.502696			0.251348	+	0.967897i	$0.419126\pi$
$348$	−5.08692e9	+	6.93707e9i	−0.346847	+	0.472998i
$349$	2.60410e9			0.175532			0.0877660	−	0.996141i	$-0.472027\pi$
$349$	2.60410e9			0.175532			0.0877660	+	0.996141i	$0.472027\pi$
$350$	−1.76664e10	+	1.69856e8i	−1.17727	+	0.0113190i
$351$			6.89760e9i			0.454433i
$352$	1.34383e10	+	1.37376e10i	0.875333	+	0.894830i
$353$		−	7.30914e9i		−	0.470725i	−0.971908	−	0.235363i	$-0.924372\pi$
$353$		−	7.30914e9i		−	0.470725i	0.971908	−	0.235363i	$-0.0756278\pi$
$354$	1.49245e10	−	7.56303e9i	0.950355	−	0.481596i
$355$	−1.28565e9	−	2.07043e9i	−0.0809487	−	0.130361i
$356$	−9.72959e9	+	1.32683e10i	−0.605751	+	0.826067i
$357$		−	1.20526e10i		−	0.742009i
$358$	5.17218e9	−	2.62102e9i	0.314878	−	0.159565i
$359$			1.69103e10i			1.01806i	0.860749	+	0.509029i	$0.169996\pi$
$359$			1.69103e10i			1.01806i	−0.860749	+	0.509029i	$0.830004\pi$
$360$	−1.08736e10	+	4.49506e9i	−0.647384	+	0.267625i
$361$	−6.57413e9			−0.387088
$362$	1.09991e10	+	2.17049e10i	0.640503	+	1.26393i
$363$	−5.38689e9			−0.310250
$364$	8.13891e9	+	5.96822e9i	0.463618	+	0.339969i
$365$	3.17480e9	+	5.11274e9i	0.178873	+	0.288060i
$366$	1.82458e9	+	3.60052e9i	0.101681	+	0.200651i
$367$	3.03452e10			1.67273			0.836364	−	0.548174i	$-0.184677\pi$
$367$	3.03452e10			1.67273			0.836364	+	0.548174i	$0.184677\pi$
$368$	−6.68615e9	−	2.12120e10i	−0.364573	−	1.15662i
$369$	1.17803e10			0.635404
$370$	−7.02941e8	+	1.15670e9i	−0.0375070	+	0.0617181i
$371$			2.83250e10i			1.49511i
$372$	−9.28077e9	−	6.80555e9i	−0.484632	−	0.355379i
$373$			9.46195e9i			0.488816i	0.969673	+	0.244408i	$0.0785936\pi$
$373$			9.46195e9i			0.488816i	−0.969673	+	0.244408i	$0.921406\pi$
$374$	1.27499e10	+	2.51599e10i	0.651657	+	1.28594i
$375$	−1.04018e9	−	1.07719e10i	−0.0525998	−	0.544713i
$376$	−5.07685e9	−	8.38522e8i	−0.254005	−	0.0419530i
$377$		−	1.05727e10i		−	0.523382i
$378$	1.01110e10	+	1.99524e10i	0.495250	+	0.977300i
$379$			1.10814e10i			0.537078i	0.963269	+	0.268539i	$0.0865409\pi$
$379$			1.10814e10i			0.537078i	−0.963269	+	0.268539i	$0.913459\pi$
$380$	−2.44848e10	−	1.88997e9i	−1.17425	−	0.0906402i
$381$	1.51195e10			0.717525
$382$	−1.15350e10	+	5.84540e9i	−0.541706	+	0.274511i
$383$	−3.17801e10			−1.47693			−0.738465	−	0.674292i	$-0.764449\pi$
$383$	−3.17801e10			−1.47693			−0.738465	+	0.674292i	$0.764449\pi$
$384$	−1.67997e9	−	1.17798e10i	−0.0772639	−	0.541765i
$385$	−1.70808e10	−	2.75072e10i	−0.777436	−	1.25200i
$386$	3.11731e10	−	1.57971e10i	1.40421	−	0.711586i
$387$	3.91837e9			0.174687
$388$	1.36766e9	+	1.00290e9i	0.0603462	+	0.0442516i
$389$	2.63166e10			1.14929			0.574647	−	0.818402i	$-0.305140\pi$
$389$	2.63166e10			1.14929			0.574647	+	0.818402i	$0.305140\pi$
$390$	−3.21066e9	+	5.28316e9i	−0.138783	+	0.228368i
$391$		−	3.26435e10i		−	1.39666i
$392$	8.99468e9	+	1.48561e9i	0.380927	+	0.0629161i
$393$			1.20694e10i			0.505959i
$394$	−1.46117e10	+	7.40455e9i	−0.606341	+	0.307266i
$395$	−7.74672e8	−	1.24754e9i	−0.0318221	−	0.0512469i
$396$	−1.73895e10	−	1.27516e10i	−0.707142	−	0.518544i
$397$		−	1.18226e9i		−	0.0475937i	−0.999717	−	0.0237969i	$-0.992425\pi$
$397$		−	1.18226e9i		−	0.0475937i	0.999717	−	0.0237969i	$-0.00757549\pi$
$398$	1.74934e10	−	8.86487e9i	0.697177	−	0.353297i
$399$			1.92319e10i			0.758806i
$400$	−2.52967e10	−	3.92870e9i	−0.988154	−	0.153465i
$401$	−4.04552e10			−1.56458			−0.782289	−	0.622916i	$-0.785948\pi$
$401$	−4.04552e10			−1.56458			−0.782289	+	0.622916i	$0.785948\pi$
$402$	−5.65927e9	−	1.11677e10i	−0.216699	−	0.427621i
$403$	1.41447e10			0.536256
$404$	−7.90467e9	+	1.07797e10i	−0.296728	+	0.404650i
$405$	4.37122e9	−	2.71435e9i	0.162474	−	0.100889i
$406$	−1.54981e10	−	3.05831e10i	−0.570393	−	1.12558i
$407$	−2.48066e9			−0.0904042
$408$	2.84597e9	−	1.72310e10i	0.102705	−	0.621827i
$409$	−2.26640e9			−0.0809921			−0.0404960	−	0.999180i	$-0.512894\pi$
$409$	−2.26640e9			−0.0809921			−0.0404960	+	0.999180i	$0.512894\pi$
$410$	2.19034e10	+	1.33110e10i	0.775134	+	0.471060i
$411$		−	1.66488e10i		−	0.583466i
$412$	1.81085e10	−	2.46946e10i	0.628482	−	0.857065i
$413$			6.66854e10i			2.29208i
$414$	1.12810e10	+	2.22612e10i	0.384012	+	0.757787i
$415$	6.73950e9	−	4.18494e9i	0.227214	−	0.141090i
$416$	1.02265e10	+	1.04543e10i	0.341470	+	0.349076i
$417$		−	2.24825e10i		−	0.743534i
$418$	−2.03444e10	−	4.01466e10i	−0.666408	−	1.31505i
$419$		−	5.97866e10i		−	1.93976i	−0.243587	−	0.969879i	$-0.578324\pi$
$419$		−	5.97866e10i		−	1.93976i	0.243587	−	0.969879i	$-0.421676\pi$
$420$	−1.54293e9	+	1.99888e10i	−0.0495847	+	0.642375i
$421$	1.37859e8			0.00438841			0.00219421	−	0.999998i	$-0.499302\pi$
$421$	1.37859e8			0.00438841			0.00219421	+	0.999998i	$0.499302\pi$
$422$	3.17706e9	−	1.60999e9i	0.100179	−	0.0507659i
$423$	5.77390e9			0.180347
$424$	−6.68834e9	+	4.04947e10i	−0.206945	+	1.25295i
$425$	−3.36778e10	−	1.66614e10i	−1.03226	−	0.510687i
$426$	−2.46691e9	+	1.25012e9i	−0.0749058	+	0.0379588i
$427$	−1.60878e10			−0.483934
$428$	2.98845e10	−	4.07537e10i	0.890577	−	1.21449i
$429$	−1.13303e10			−0.334512
$430$	7.28555e9	+	4.42754e9i	0.213102	+	0.129506i
$431$			1.87046e10i			0.542051i	0.962572	+	0.271026i	$0.0873628\pi$
$431$			1.87046e10i			0.542051i	−0.962572	+	0.271026i	$0.912637\pi$
$432$	9.74374e9	+	3.09123e10i	0.279763	+	0.887558i
$433$			1.46857e10i			0.417776i	0.977940	+	0.208888i	$0.0669844\pi$
$433$			1.46857e10i			0.417776i	−0.977940	+	0.208888i	$0.933016\pi$
$434$	4.09156e10	−	2.07341e10i	1.15327	−	0.584423i
$435$	1.78418e10	−	1.10790e10i	0.498289	−	0.309416i
$436$	3.39250e10	−	4.62638e10i	0.938803	−	1.28025i
$437$			5.20879e10i			1.42827i
$438$	6.09181e9	−	3.08705e9i	0.165520	−	0.0838778i
$439$			2.58143e10i			0.695029i	0.937675	+	0.347514i	$0.112974\pi$
$439$			2.58143e10i			0.695029i	−0.937675	+	0.347514i	$0.887026\pi$
$440$	−1.79242e10	−	4.33587e10i	−0.478222	−	1.15682i
$441$	−1.02297e10			−0.270462
$442$	9.70259e9	+	1.91465e10i	0.254213	+	0.501651i
$443$	−3.46551e10			−0.899813			−0.449906	−	0.893076i	$-0.648543\pi$
$443$	−3.46551e10			−0.899813			−0.449906	+	0.893076i	$0.648543\pi$
$444$	1.23863e9	+	9.08280e8i	0.0318720	+	0.0233716i
$445$	3.41254e10	−	2.11904e10i	0.870236	−	0.540380i
$446$	1.92828e10	+	3.80516e10i	0.487338	+	0.961686i
$447$	−3.11131e9			−0.0779316
$448$	4.49062e10	+	1.52500e10i	1.11479	+	0.378579i
$449$	−3.50756e10			−0.863018			−0.431509	−	0.902109i	$-0.642019\pi$
$449$	−3.50756e10			−0.863018			−0.431509	+	0.902109i	$0.642019\pi$
$450$	2.87244e10	−	2.76175e8i	0.700488	−	0.00673496i
$451$			4.69742e10i			1.13541i
$452$	−6.69938e10	−	4.91263e10i	−1.60502	−	1.17696i
$453$			1.77268e10i			0.420958i
$454$	−1.05167e10	−	2.07531e10i	−0.247546	−	0.488494i
$455$	−1.29984e10	−	2.09328e10i	−0.303281	−	0.488408i
$456$	−4.54120e9	+	2.74948e10i	−0.105030	+	0.635903i
$457$		−	1.80923e10i		−	0.414791i	−0.978257	−	0.207395i	$-0.933501\pi$
$457$		−	1.80923e10i		−	0.414791i	0.978257	−	0.207395i	$-0.0664987\pi$
$458$	−9.61638e7	−	1.89764e8i	−0.00218550	−	0.00431274i
$459$			4.75714e10i			1.07176i
$460$	−4.17888e9	+	5.41378e10i	−0.0933315	+	1.20912i
$461$	2.22531e10			0.492704			0.246352	−	0.969180i	$-0.420768\pi$
$461$	2.22531e10			0.492704			0.246352	+	0.969180i	$0.420768\pi$
$462$	−3.27747e10	+	1.66087e10i	−0.719400	+	0.364559i
$463$	−4.13307e10			−0.899391			−0.449695	−	0.893182i	$-0.648467\pi$
$463$	−4.13307e10			−0.899391			−0.449695	+	0.893182i	$0.648467\pi$
$464$	−1.49352e10	−	4.73825e10i	−0.322211	−	1.02222i
$465$	1.48220e10	+	2.38697e10i	0.317027	+	0.510545i
$466$	−7.90491e10	+	4.00584e10i	−1.67631	+	0.849474i
$467$	−3.60193e10			−0.757300			−0.378650	−	0.925540i	$-0.623612\pi$
$467$	−3.60193e10			−0.757300			−0.378650	+	0.925540i	$0.623612\pi$
$468$	−1.32333e10	−	9.70395e9i	−0.275858	−	0.202286i
$469$	4.98994e10			1.03135
$470$	1.07356e10	+	6.52419e9i	0.220006	+	0.133701i
$471$		−	3.09619e10i		−	0.629136i
$472$	−1.57463e10	+	9.53365e10i	−0.317257	+	1.92084i
$473$			1.56246e10i			0.312151i
$474$	−1.48644e9	+	7.53261e8i	−0.0294466	+	0.0149222i
$475$	5.37383e10	+	2.65859e10i	1.05563	+	0.522248i
$476$	5.61325e10	+	4.11617e10i	1.09342	+	0.801799i
$477$		−	4.60546e10i		−	0.889610i
$478$	1.00786e10	−	5.10736e9i	0.193058	−	0.0978328i
$479$		−	5.31999e10i		−	1.01058i	−0.862951	−	0.505288i	$-0.831386\pi$
$479$		−	5.31999e10i		−	1.01058i	0.862951	−	0.505288i	$-0.168614\pi$
$480$	−6.92575e9	+	2.82125e10i	−0.130467	+	0.531468i
$481$	−1.88777e9			−0.0352670
$482$	−1.61532e10	−	3.18759e10i	−0.299276	−	0.590574i
$483$	4.25233e10			0.781337
$484$	1.83971e10	−	2.50883e10i	0.335249	−	0.457182i
$485$	−2.18424e9	−	3.51754e9i	−0.0394761	−	0.0635729i
$486$	−2.61072e10	−	5.15186e10i	−0.467968	−	0.923462i
$487$	2.16155e10			0.384281			0.192140	−	0.981367i	$-0.438457\pi$
$487$	2.16155e10			0.384281			0.192140	+	0.981367i	$0.438457\pi$
$488$	−2.29999e10	−	3.79880e9i	−0.405552	−	0.0669833i
$489$	−1.53262e10			−0.268040
$490$	−1.90203e10	−	1.15589e10i	−0.329939	−	0.200509i
$491$		−	6.94657e9i		−	0.119521i	−0.998213	−	0.0597606i	$-0.980966\pi$
$491$		−	6.94657e9i		−	0.119521i	0.998213	−	0.0597606i	$-0.0190337\pi$
$492$	1.71994e10	−	2.34549e10i	0.293530	−	0.400289i
$493$		−	7.29176e10i		−	1.23437i
$494$	−1.54820e10	−	3.05514e10i	−0.259968	−	0.513007i
$495$	2.77723e10	+	4.47249e10i	0.462584	+	0.744952i
$496$	6.33907e10	−	1.99811e10i	1.04737	−	0.330136i
$497$		−	1.10226e10i		−	0.180659i
$498$	−4.06928e9	−	8.03009e9i	−0.0661607	−	0.130558i
$499$		−	3.04616e10i		−	0.491304i	−0.969358	−	0.245652i	$-0.920998\pi$
$499$		−	3.04616e10i		−	0.491304i	0.969358	−	0.245652i	$-0.0790021\pi$
$500$	5.37203e10	+	3.19435e10i	0.859524	+	0.511095i
$501$	4.34419e10			0.689538
$502$	4.60949e10	−	2.33588e10i	0.725836	−	0.367820i
$503$	2.80844e10			0.438725			0.219363	−	0.975643i	$-0.429602\pi$
$503$	2.80844e10			0.438725			0.219363	+	0.975643i	$0.429602\pi$
$504$	−5.25042e10	−	8.67190e9i	−0.813714	−	0.134398i
$505$	2.77247e10	−	1.72159e10i	0.426286	−	0.264706i
$506$	−8.87673e10	+	4.49832e10i	−1.35410	+	0.686196i
$507$	2.75366e10			0.416753
$508$	−5.16355e10	+	7.04157e10i	−0.775342	+	1.05734i
$509$	−1.09246e11			−1.62755			−0.813773	−	0.581183i	$-0.802590\pi$
$509$	−1.09246e11			−1.62755			−0.813773	+	0.581183i	$0.802590\pi$
$510$	−2.21433e10	+	3.64370e10i	−0.327312	+	0.538594i
$511$			2.72194e10i			0.399204i
$512$	6.05990e10	+	3.24057e10i	0.881831	+	0.471565i
$513$		−	7.59079e10i		−	1.09602i
$514$	−5.33051e10	+	2.70126e10i	−0.763688	+	0.387002i
$515$	−6.35132e10	+	3.94391e10i	−0.902891	+	0.560657i
$516$	5.72088e9	−	7.80160e9i	0.0806982	−	0.110049i
$517$			2.30236e10i			0.322264i
$518$	−5.46067e9	+	2.76721e9i	−0.0758449	+	0.0384347i
$519$		−	4.12367e10i		−	0.568349i
$520$	−1.36403e10	−	3.29958e10i	−0.186556	−	0.451279i
$521$	7.86075e10			1.06687			0.533437	−	0.845840i	$-0.320900\pi$
$521$	7.86075e10			1.06687			0.533437	+	0.845840i	$0.320900\pi$
$522$	2.51989e10	+	4.97261e10i	0.339390	+	0.669734i
$523$	7.29827e10			0.975468			0.487734	−	0.872992i	$-0.337824\pi$
$523$	7.29827e10			0.975468			0.487734	+	0.872992i	$0.337824\pi$
$524$	−5.62106e10	−	4.12190e10i	−0.745578	−	0.546729i
$525$	2.17041e10	−	4.38706e10i	0.285696	−	0.577480i
$526$	−4.25143e10	−	8.38953e10i	−0.555382	−	1.09596i
$527$	9.75530e10			1.26473
$528$	−5.07779e10	+	1.60055e10i	−0.653340	+	0.205936i
$529$	3.68596e10			0.470682
$530$	5.20391e10	−	8.56308e10i	0.659518	−	1.08524i
$531$		−	1.08426e11i		−	1.36382i
$532$	−8.95684e10	−	6.56801e10i	−1.11817	−	0.819950i
$533$			3.57472e10i			0.442928i
$534$	−2.06047e10	−	4.06602e10i	−0.253397	−	0.500040i
$535$	−1.04816e11	+	6.50866e10i	−1.27942	+	0.794468i
$536$	7.13385e10	+	1.17827e10i	0.864300	+	0.142753i
$537$			1.60641e10i			0.193178i
$538$	1.89364e10	+	3.73680e10i	0.226031	+	0.446037i
$539$		−	4.07911e10i		−	0.483293i
$540$	6.08989e9	−	7.88952e10i	0.0716200	−	0.927845i
$541$	−6.69135e10			−0.781133			−0.390566	−	0.920575i	$-0.627721\pi$
$541$	−6.69135e10			−0.781133			−0.390566	+	0.920575i	$0.627721\pi$
$542$	6.65327e10	−	3.37157e10i	0.770970	−	0.390692i
$543$	−6.74124e10			−0.775426
$544$	7.05301e10	+	7.21011e10i	0.805339	+	0.823277i
$545$	−1.18988e11	+	7.38865e10i	−1.34871	+	0.837489i
$546$	−2.49414e10	+	1.26391e10i	−0.280640	+	0.142216i
$547$	−1.11865e11			−1.24953			−0.624765	−	0.780813i	$-0.714805\pi$
$547$	−1.11865e11			−1.24953			−0.624765	+	0.780813i	$0.714805\pi$
$548$	7.75382e10	+	5.68584e10i	0.859792	+	0.630481i
$549$	2.61578e10			0.287946
$550$	1.10126e9	+	1.14539e11i	0.0120348	+	1.25171i
$551$			1.16352e11i			1.26231i
$552$	6.07932e10	+	1.00410e10i	0.654785	+	0.108148i
$553$		−	6.64172e9i		−	0.0710199i
$554$	5.41560e10	−	2.74438e10i	0.574920	−	0.291343i
$555$	−1.97818e9	−	3.18568e9i	−0.0208494	−	0.0335761i
$556$	1.04707e11	+	7.67815e10i	1.09567	+	0.803447i
$557$			2.01090e8i			0.00208915i	0.999999	+	0.00104458i	$0.000332499\pi$
$557$			2.01090e8i			0.00208915i	−0.999999	+	0.00104458i	$0.999668\pi$
$558$	−6.65262e10	+	3.37124e10i	−0.686208	+	0.347738i
$559$			1.18903e10i			0.121771i
$560$	−8.78240e10	−	7.54507e10i	−0.893020	−	0.767205i
$561$	−7.81429e10			−0.788930
$562$	−4.30537e10	−	8.49598e10i	−0.431584	−	0.851664i
$563$	−7.36627e10			−0.733185			−0.366593	−	0.930382i	$-0.619476\pi$
$563$	−7.36627e10			−0.733185			−0.366593	+	0.930382i	$0.619476\pi$
$564$	8.42999e9	−	1.14960e10i	0.0833126	−	0.113614i
$565$	1.06994e11	+	1.72304e11i	1.04994	+	1.69084i
$566$	4.41055e10	+	8.70353e10i	0.429761	+	0.848066i
$567$	2.32717e10			0.225162
$568$	2.60276e9	−	1.57585e10i	0.0250058	−	0.151398i
$569$	5.53549e10			0.528089			0.264045	−	0.964510i	$-0.414943\pi$
$569$	5.53549e10			0.528089			0.264045	+	0.964510i	$0.414943\pi$
$570$	3.53332e10	−	5.81410e10i	0.334721	−	0.550787i
$571$			2.98777e10i			0.281063i	0.990076	+	0.140531i	$0.0448811\pi$
$571$			2.98777e10i			0.281063i	−0.990076	+	0.140531i	$0.955119\pi$
$572$	3.86948e10	−	5.27684e10i	0.361467	−	0.492935i
$573$		−	3.58260e10i		−	0.332338i
$574$	5.24005e10	+	1.03404e11i	0.482712	+	0.952557i
$575$	5.87835e10	−	1.18820e11i	0.537755	−	1.08697i
$576$	−7.30146e10	−	2.47955e10i	−0.663315	−	0.225259i
$577$			1.20418e11i			1.08640i	0.839603	+	0.543200i	$0.182788\pi$
$577$			1.20418e11i			1.08640i	−0.839603	+	0.543200i	$0.817212\pi$
$578$	1.64652e10	+	3.24916e10i	0.147522	+	0.291112i
$579$			9.68192e10i			0.861484i
$580$	−9.33460e9	+	1.20931e11i	−0.0824867	+	1.06862i
$581$	3.58800e10			0.314882
$582$	−4.19113e9	+	2.12387e9i	−0.0365291	+	0.0185113i
$583$	1.83644e11			1.58966
$584$	−6.42727e9	+	3.89141e10i	−0.0552555	+	0.334545i
$585$	2.11346e10	+	3.40354e10i	0.180455	+	0.290608i
$586$	−5.11764e10	+	2.59338e10i	−0.433989	+	0.219926i
$587$	1.26290e10			0.106369			0.0531845	−	0.998585i	$-0.483063\pi$
$587$	1.26290e10			0.106369			0.0531845	+	0.998585i	$0.483063\pi$
$588$	−1.49355e10	+	2.03676e10i	−0.124942	+	0.170385i
$589$	−1.55661e11			−1.29336
$590$	1.22516e11	−	2.01600e11i	1.01107	−	1.66373i
$591$		−	4.53820e10i		−	0.371992i
$592$	−8.46023e9	+	2.66671e9i	−0.0688804	+	0.0217115i
$593$		−	9.56312e10i		−	0.773359i	−0.922214	−	0.386679i	$-0.873622\pi$
$593$		−	9.56312e10i		−	0.773359i	0.922214	−	0.386679i	$-0.126378\pi$
$594$	1.29361e11	−	6.55541e10i	1.03910	−	0.526567i
$595$	−8.96475e10	−	1.44370e11i	−0.715271	−	1.15188i
$596$	1.06256e10	−	1.44903e10i	0.0842113	−	0.114839i
$597$			5.43322e10i			0.427720i
$598$	−6.75516e10	+	3.42320e10i	−0.528239	+	0.267687i
$599$			5.13440e9i			0.0398825i	0.999801	+	0.0199413i	$0.00634792\pi$
$599$			5.13440e9i			0.0398825i	−0.999801	+	0.0199413i	$0.993652\pi$
$600$	4.13882e10	−	5.75945e10i	0.319353	−	0.444402i
$601$	−9.84800e8			−0.00754832			−0.00377416	−	0.999993i	$-0.501201\pi$
$601$	−9.84800e8			−0.00754832			−0.00377416	+	0.999993i	$0.501201\pi$
$602$	1.74295e10	+	3.43945e10i	0.132709	+	0.261880i
$603$	−8.11333e10			−0.613663
$604$	−8.25589e10	−	6.05400e10i	−0.620320	−	0.454878i
$605$	−6.45256e10	+	4.00677e10i	−0.481627	+	0.299070i
$606$	−1.67400e10	−	3.30339e10i	−0.124127	−	0.244945i
$607$	−2.29100e11			−1.68760			−0.843802	−	0.536654i	$-0.819688\pi$
$607$	−2.29100e11			−1.68760			−0.843802	+	0.536654i	$0.819688\pi$
$608$	−1.12542e11	−	1.15049e11i	−0.823570	−	0.841915i
$609$	9.49867e10			0.690547
$610$	4.86360e10	+	2.95568e10i	0.351268	+	0.213471i
$611$			1.75209e10i			0.125716i
$612$	−9.12678e10	−	6.69263e10i	−0.650597	−	0.477080i
$613$		−	1.82859e11i		−	1.29502i	−0.762058	−	0.647508i	$-0.775811\pi$
$613$		−	1.82859e11i		−	1.29502i	0.762058	−	0.647508i	$-0.224189\pi$
$614$	3.69996e10	+	7.30130e10i	0.260330	+	0.513720i
$615$	−6.03248e10	+	3.74591e10i	−0.421692	+	0.261853i
$616$	3.45795e10	−	2.09362e11i	0.240157	−	1.45404i
$617$			4.78934e10i			0.330472i	0.986254	+	0.165236i	$0.0528386\pi$
$617$			4.78934e10i			0.330472i	−0.986254	+	0.165236i	$0.947161\pi$
$618$	3.83490e10	+	7.56758e10i	0.262906	+	0.518804i
$619$			8.75787e10i			0.596535i	0.954482	+	0.298267i	$0.0964087\pi$
$619$			8.75787e10i			0.596535i	−0.954482	+	0.298267i	$0.903591\pi$
$620$	−1.61787e11	−	1.24883e10i	−1.09491	−	0.0845156i
$621$	−1.67838e11			−1.12856
$622$	4.00951e10	−	2.03183e10i	0.267873	−	0.135746i
$623$	1.81678e11			1.20601
$624$	−3.86418e10	+	1.21801e10i	−0.254870	+	0.0803365i
$625$	−9.25812e10	−	1.21292e11i	−0.606740	−	0.794900i
$626$	6.69505e10	−	3.39274e10i	0.435970	−	0.220929i
$627$	1.24690e11			0.806789
$628$	1.44198e11	+	1.05740e11i	0.927090	+	0.679831i
$629$	−1.30196e10			−0.0831753
$630$	1.11026e11	+	6.74724e10i	0.704797	+	0.428316i
$631$		−	1.79020e11i		−	1.12923i	−0.825354	−	0.564616i	$-0.809024\pi$
$631$		−	1.79020e11i		−	1.12923i	0.825354	−	0.564616i	$-0.190976\pi$
$632$	1.56830e9	−	9.49530e9i	0.00983016	−	0.0595169i
$633$			9.86749e9i			0.0614599i
$634$	3.48924e10	−	1.76819e10i	0.215960	−	0.109439i
$635$	1.81105e11	−	1.12459e11i	1.11387	−	0.691669i
$636$	−9.16963e10	−	6.72405e10i	−0.560432	−	0.410963i
$637$		−	3.10418e10i		−	0.188534i
$638$	−1.98285e11	+	1.00481e11i	−1.19676	+	0.606462i
$639$			1.79221e10i			0.107494i
$640$	−1.07741e11	−	1.28605e11i	−0.642186	−	0.766549i
$641$	9.29527e10			0.550592			0.275296	−	0.961360i	$-0.411224\pi$
$641$	9.29527e10			0.550592			0.275296	+	0.961360i	$0.411224\pi$
$642$	6.32877e10	+	1.24888e11i	0.372545	+	0.735160i
$643$	1.76187e11			1.03069			0.515347	−	0.856982i	$-0.327663\pi$
$643$	1.76187e11			1.03069			0.515347	+	0.856982i	$0.327663\pi$
$644$	−1.45224e11	+	1.98043e11i	−0.844296	+	1.15137i
$645$	−2.00653e10	+	1.24597e10i	−0.115933	+	0.0719895i
$646$	−1.06777e11	−	2.10707e11i	−0.613121	−	1.20990i
$647$	−2.37613e11			−1.35598			−0.677990	−	0.735071i	$-0.737149\pi$
$647$	−2.37613e11			−1.35598			−0.677990	+	0.735071i	$0.737149\pi$
$648$	3.32702e10	+	5.49511e9i	0.188693	+	0.0311657i
$649$	4.32353e11			2.43702
$650$	8.38054e8	+	8.71641e10i	0.00469481	+	0.488297i
$651$			1.27078e11i			0.707533i
$652$	5.23415e10	−	7.13784e10i	0.289638	−	0.394981i
$653$		−	2.96902e11i		−	1.63290i	−0.577415	−	0.816451i	$-0.695938\pi$
$653$		−	2.96902e11i		−	1.63290i	0.577415	−	0.816451i	$-0.304062\pi$
$654$	7.18444e10	+	1.41774e11i	0.392719	+	0.774970i
$655$	8.97723e10	+	1.44571e11i	0.487727	+	0.785443i
$656$	5.04974e10	+	1.60205e11i	0.272680	+	0.865087i
$657$		−	4.42570e10i		−	0.237531i
$658$	2.56832e10	+	5.06819e10i	0.137008	+	0.270364i
$659$			1.31179e11i			0.695541i	0.937580	+	0.347771i	$0.113061\pi$
$659$			1.31179e11i			0.695541i	−0.937580	+	0.347771i	$0.886939\pi$
$660$	1.29597e11	+	1.00035e10i	0.682996	+	0.0527202i
$661$	5.54817e10			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$661$	5.54817e10			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$662$	−3.06704e11	+	1.55423e11i	−1.59694	+	0.809254i
$663$	−5.94665e10			−0.307764
$664$	5.12956e10	+	8.47229e9i	0.263881	+	0.0435841i
$665$	1.43047e11	+	2.30365e11i	0.731463	+	1.17796i
$666$	8.87869e9	−	4.49931e9i	0.0451286	−	0.0228691i
$667$	2.57263e11			1.29979
$668$	−1.48361e11	+	2.02321e11i	−0.745100	+	1.01610i
$669$	−1.18183e11			−0.589997
$670$	−1.50854e11	−	9.16761e10i	−0.748612	−	0.454943i
$671$			1.04305e11i			0.514535i
$672$	−9.39230e10	+	9.18765e10i	−0.460569	+	0.450534i
$673$			5.91921e10i			0.288538i	0.989538	+	0.144269i	$0.0460831\pi$
$673$			5.91921e10i			0.288538i	−0.989538	+	0.144269i	$0.953917\pi$
$674$	−6.81881e10	+	3.45546e10i	−0.330422	+	0.167443i
$675$	−8.56654e10	+	1.73156e11i	−0.412658	+	0.834110i
$676$	−9.40420e10	+	1.28246e11i	−0.450334	+	0.614124i
$677$		−	2.84457e11i		−	1.35413i	−0.735922	−	0.677066i	$-0.763251\pi$
$677$		−	2.84457e11i		−	1.35413i	0.735922	−	0.677066i	$-0.236749\pi$
$678$	2.05300e11	−	1.04037e11i	0.971562	−	0.492343i
$679$		−	1.87268e10i		−	0.0881017i
$680$	−9.40743e10	−	2.27566e11i	−0.439982	−	1.06432i
$681$	6.44561e10			0.299692
$682$	−1.34429e11	−	2.65275e11i	−0.621379	−	1.22619i
$683$	−3.01776e11			−1.38676			−0.693381	−	0.720571i	$-0.743880\pi$
$683$	−3.01776e11			−1.38676			−0.693381	+	0.720571i	$0.743880\pi$
$684$	1.45632e11	+	1.06792e11i	0.665325	+	0.487880i
$685$	−1.23834e11	−	1.99424e11i	−0.562441	−	0.905764i
$686$	7.23540e10	+	1.42779e11i	0.326713	+	0.644717i
$687$	5.89381e8			0.00264588
$688$	1.67965e10	+	5.32875e10i	0.0749662	+	0.237833i
$689$	1.39753e11			0.620130
$690$	−1.28555e11	−	7.81245e10i	−0.567141	−	0.344660i
$691$		−	1.07258e11i		−	0.470455i	−0.971940	−	0.235227i	$-0.924417\pi$
$691$		−	1.07258e11i		−	0.470455i	0.971940	−	0.235227i	$-0.0755835\pi$
$692$	1.92051e11	+	1.40830e11i	0.837514	+	0.614145i
$693$			2.38108e11i			1.03238i
$694$	−5.27118e10	−	1.04019e11i	−0.227232	−	0.448407i
$695$	−1.67225e11	−	2.69302e11i	−0.716741	−	1.15425i
$696$	1.35797e11	+	2.24291e10i	0.578701	+	0.0955816i
$697$			2.46542e11i			1.04462i
$698$	−1.88340e10	−	3.71659e10i	−0.0793452	−	0.156575i
$699$		−	2.45515e11i		−	1.02842i
$700$	1.30195e11	+	2.50907e11i	0.542253	+	1.04501i
$701$	1.01471e11			0.420213			0.210107	−	0.977678i	$-0.432619\pi$
$701$	1.01471e11			0.420213			0.210107	+	0.977678i	$0.432619\pi$
$702$	9.84431e10	−	4.98864e10i	0.405356	−	0.205416i
$703$	2.07748e10			0.0850582
$704$	9.88728e10	−	2.91148e11i	0.402519	−	1.18529i
$705$	−2.95672e10	+	1.83600e10i	−0.119689	+	0.0743217i
$706$	−1.04317e11	+	5.28628e10i	−0.419889	+	0.212780i
$707$	1.47602e11			0.590763
$708$	−2.15880e11	−	1.58304e11i	−0.859172	−	0.630027i
$709$	−4.73489e11			−1.87381			−0.936904	−	0.349587i	$-0.886322\pi$
$709$	−4.73489e11			−1.87381			−0.936904	+	0.349587i	$0.886322\pi$
$710$	−2.02510e10	+	3.33232e10i	−0.0796916	+	0.131133i
$711$			1.07990e10i			0.0422577i
$712$	2.59735e11	+	4.28993e10i	1.01067	+	0.166928i
$713$			3.44180e11i			1.33176i
$714$	−1.72016e11	+	8.71698e10i	−0.661875	+	0.335408i
$715$	−1.35717e11	+	8.42748e10i	−0.519292	+	0.322458i
$716$	−7.48149e10	−	5.48614e10i	−0.284666	−	0.208744i
$717$			3.13026e10i			0.118442i
$718$	2.41345e11	−	1.22302e11i	0.908113	−	0.460190i
$719$			3.14505e11i			1.17683i	0.808561	+	0.588413i	$0.200247\pi$
$719$			3.14505e11i			1.17683i	−0.808561	+	0.588413i	$0.799753\pi$
$720$	1.42796e11	+	1.22678e11i	0.531357	+	0.456496i
$721$	−3.38134e11			−1.25126
$722$	4.75469e10	+	9.38264e10i	0.174974	+	0.345284i
$723$	9.90021e10			0.362319
$724$	2.30224e11	−	3.13959e11i	0.837909	−	1.14266i
$725$	1.31308e11	−	2.65414e11i	0.475269	−	0.960666i
$726$	3.89603e10	+	7.68821e10i	0.140241	+	0.276744i
$727$	3.23780e10			0.115908			0.0579538	−	0.998319i	$-0.481542\pi$
$727$	3.23780e10			0.115908			0.0579538	+	0.998319i	$0.481542\pi$
$728$	2.63149e10	−	1.59324e11i	0.0936862	−	0.567225i
$729$	1.05995e11			0.375297
$730$	5.00079e10	−	8.22884e10i	0.176095	−	0.289766i
$731$			8.20050e10i			0.287191i
$732$	3.81908e10	−	5.20810e10i	0.133019	−	0.181399i
$733$			9.11504e10i			0.315749i	0.987459	+	0.157875i	$0.0504642\pi$
$733$			9.11504e10i			0.315749i	−0.987459	+	0.157875i	$0.949536\pi$
$734$	−2.19469e11	−	4.33088e11i	−0.756118	−	1.49208i
$735$	5.23843e10	−	3.25285e10i	0.179495	−	0.111459i
$736$	−2.54382e11	+	2.48839e11i	−0.866913	+	0.848024i
$737$		−	3.23522e11i		−	1.09656i
$738$	−8.51999e10	−	1.68129e11i	−0.287219	−	0.566783i
$739$		−	2.00083e11i		−	0.670860i	−0.942065	−	0.335430i	$-0.891118\pi$
$739$		−	2.00083e11i		−	0.670860i	0.942065	−	0.335430i	$-0.108882\pi$
$740$	2.15924e10	+	1.66671e9i	0.0720069	+	0.00555819i
$741$	9.48883e10			0.314731
$742$	4.04256e11	−	2.04858e11i	1.33365	−	0.675831i
$743$	5.50175e10			0.180528			0.0902642	−	0.995918i	$-0.471229\pi$
$743$	5.50175e10			0.180528			0.0902642	+	0.995918i	$0.471229\pi$
$744$	−3.00068e10	+	1.81677e11i	−0.0979326	+	0.592935i
$745$	−3.72682e10	+	2.31420e10i	−0.120980	+	0.0751234i
$746$	1.35042e11	−	6.84329e10i	0.436026	−	0.220958i
$747$	−5.83385e10			−0.187358
$748$	2.66871e11	−	3.63934e11i	0.852501	−	1.16256i
$749$	−5.58025e11			−1.77307
$750$	−1.46215e11	+	9.27527e10i	−0.462110	+	0.293144i
$751$		−	5.26277e11i		−	1.65445i	−0.561869	−	0.827226i	$-0.689917\pi$
$751$		−	5.26277e11i		−	1.65445i	0.561869	−	0.827226i	$-0.310083\pi$
$752$	2.47505e10	+	7.85217e10i	0.0773949	+	0.245538i
$753$			1.43164e11i			0.445302i
$754$	−1.50894e11	+	7.64660e10i	−0.466859	+	0.236583i
$755$	1.31852e11	+	2.12337e11i	0.405789	+	0.653488i
$756$	2.11635e11	−	2.88608e11i	0.647889	−	0.883531i
$757$			4.33728e11i			1.32079i	0.750919	+	0.660395i	$0.229611\pi$
$757$			4.33728e11i			1.32079i	−0.750919	+	0.660395i	$0.770389\pi$
$758$	1.58154e11	−	8.01454e10i	0.479076	−	0.242774i
$759$		−	2.75699e11i		−	0.830745i
$760$	1.50111e11	+	3.63118e11i	0.449943	+	1.08841i
$761$	3.18871e11			0.950771			0.475385	−	0.879778i	$-0.342309\pi$
$761$	3.18871e11			0.950771			0.475385	+	0.879778i	$0.342309\pi$
$762$	−1.09351e11	−	2.15786e11i	−0.324340	−	0.640035i
$763$	−6.33472e11			−1.86909
$764$	1.66852e11	+	1.22352e11i	0.489731	+	0.359117i
$765$	1.45761e11	+	2.34736e11i	0.425594	+	0.685384i
$766$	2.29847e11	+	4.53567e11i	0.667611	+	1.31743i
$767$	3.29019e11			0.950691
$768$	−1.55971e11	+	1.09173e11i	−0.448332	+	0.313812i
$769$	−1.36365e11			−0.389941			−0.194970	−	0.980809i	$-0.562461\pi$
$769$	−1.36365e11			−0.389941			−0.194970	+	0.980809i	$0.562461\pi$
$770$	−2.69049e11	+	4.42722e11i	−0.765363	+	1.25941i
$771$		−	1.65558e11i		−	0.468525i
$772$	−4.50914e11	−	3.30653e11i	−1.26948	−	0.930901i
$773$			2.93754e11i			0.822746i	0.911467	+	0.411373i	$0.134951\pi$
$773$			2.93754e11i			0.822746i	−0.911467	+	0.411373i	$0.865049\pi$
$774$	−2.83393e10	−	5.59232e10i	−0.0789633	−	0.155822i
$775$	3.55085e11	+	1.75671e11i	0.984296	+	0.486959i
$776$	4.42193e9	−	2.67727e10i	0.0121945	−	0.0738320i
$777$		−	1.69601e10i		−	0.0465311i
$778$	−1.90333e11	−	3.75592e11i	−0.519511	−	1.02517i
$779$		−	3.93397e11i		−	1.06827i
$780$	9.86225e10	+	7.61264e9i	0.266439	+	0.0205663i
$781$	−7.14650e10			−0.192083
$782$	−4.65890e11	+	2.36092e11i	−1.24582	+	0.631326i
$783$	−3.74910e11			−0.997425
$784$	−4.38505e10	−	1.39117e11i	−0.116068	−	0.368228i
$785$	−2.30295e11	−	3.70871e11i	−0.606465	−	0.976661i
$786$	1.72255e11	−	8.72911e10i	0.451318	−	0.228707i
$787$	−4.49406e11			−1.17149			−0.585747	−	0.810494i	$-0.699199\pi$
$787$	−4.49406e11			−1.17149			−0.585747	+	0.810494i	$0.699199\pi$
$788$	2.11357e11	+	1.54987e11i	0.548164	+	0.401966i
$789$	2.60567e11			0.672374
$790$	−1.22023e10	+	2.00789e10i	−0.0313280	+	0.0515505i
$791$			9.17321e11i			2.34323i
$792$	−5.62240e10	+	3.40410e11i	−0.142896	+	0.865169i
$793$			7.93757e10i			0.200722i
$794$	−1.68732e10	+	8.55058e9i	−0.0424538	+	0.0215136i
$795$	1.46445e11	+	2.35838e11i	0.366612	+	0.590398i
$796$	−2.53040e11	−	1.85553e11i	−0.630285	−	0.462185i
$797$		−	4.56927e11i		−	1.13244i	−0.824256	−	0.566218i	$-0.808406\pi$
$797$		−	4.56927e11i		−	1.13244i	0.824256	−	0.566218i	$-0.191594\pi$
$798$	2.74479e11	−	1.39093e11i	0.676858	−	0.343001i
$799$			1.20838e11i			0.296495i
$800$	1.26886e11	+	3.89451e11i	0.309781	+	0.950808i
$801$	−2.95396e11			−0.717588
$802$	2.92589e11	+	5.77380e11i	0.707231	+	1.39561i
$803$	1.76476e11			0.424447
$804$	−1.18456e11	+	1.61539e11i	−0.283487	+	0.386593i
$805$	5.09356e11	−	3.16288e11i	1.21294	−	0.753182i
$806$	−1.02300e11	−	2.01873e11i	−0.242402	−	0.478343i
$807$	−1.16060e11			−0.273645
$808$	2.11018e11	+	3.48530e10i	0.495078	+	0.0817700i
$809$	7.90117e11			1.84458			0.922289	−	0.386500i	$-0.126316\pi$
$809$	7.90117e11			1.84458			0.922289	+	0.386500i	$0.126316\pi$
$810$	−7.03539e10	−	4.27551e10i	−0.163436	−	0.0993226i
$811$			1.98385e11i			0.458590i	0.973357	+	0.229295i	$0.0736420\pi$
$811$			1.98385e11i			0.458590i	−0.973357	+	0.229295i	$0.926358\pi$
$812$	−3.24395e11	+	4.42380e11i	−0.746191	+	1.01759i
$813$			2.06641e11i			0.472993i
$814$	1.79412e10	+	3.54041e10i	0.0408651	+	0.0806410i
$815$	−1.83581e11	+	1.13996e11i	−0.416100	+	0.258381i
$816$	−2.66505e11	+	8.40039e10i	−0.601097	+	0.189469i
$817$		−	1.30852e11i		−	0.293692i
$818$	1.63915e10	+	3.23462e10i	0.0366106	+	0.0722453i
$819$			1.81199e11i			0.402736i
$820$	3.15612e10	−	4.08879e11i	0.0698068	−	0.904355i
$821$	4.89572e11			1.07757			0.538783	−	0.842445i	$-0.318884\pi$
$821$	4.89572e11			1.07757			0.538783	+	0.842445i	$0.318884\pi$
$822$	−2.37613e11	+	1.20411e11i	−0.520455	+	0.263742i
$823$	4.10873e11			0.895587			0.447793	−	0.894137i	$-0.352210\pi$
$823$	4.10873e11			0.895587			0.447793	+	0.894137i	$0.352210\pi$
$824$	−4.83412e11	−	7.98431e10i	−1.04860	−	0.173192i
$825$	−2.84434e11	−	1.40718e11i	−0.613996	−	0.303762i
$826$	9.51739e11	−	4.82297e11i	2.04455	−	1.03608i
$827$	4.15118e11			0.887461			0.443731	−	0.896160i	$-0.353655\pi$
$827$	4.15118e11			0.887461			0.443731	+	0.896160i	$0.353655\pi$
$828$	2.36125e11	−	3.22005e11i	0.502366	−	0.685080i
$829$	−4.32301e11			−0.915310			−0.457655	−	0.889130i	$-0.651310\pi$
$829$	−4.32301e11			−0.915310			−0.457655	+	0.889130i	$0.651310\pi$
$830$	−1.08471e11	−	6.59193e10i	−0.228560	−	0.138899i
$831$			1.68201e11i			0.352715i
$832$	7.52418e10	−	2.21563e11i	0.157024	−	0.462385i
$833$		−	2.14090e11i		−	0.444647i
$834$	−3.20872e11	+	1.62603e11i	−0.663236	+	0.336097i
$835$	5.20359e11	−	3.23121e11i	1.07043	−	0.664690i
$836$	−4.25835e11	+	5.80714e11i	−0.871799	+	1.18888i
$837$		−	5.01574e11i		−	1.02196i
$838$	−8.53278e11	+	4.32402e11i	−1.73027	+	0.876822i
$839$		−	4.22053e11i		−	0.851764i	−0.904779	−	0.425882i	$-0.859964\pi$
$839$		−	4.22053e11i		−	0.851764i	0.904779	−	0.425882i	$-0.140036\pi$
$840$	2.96440e11	−	1.22547e11i	0.595415	−	0.246141i
$841$	7.44167e10			0.148760
$842$	−9.97057e8	−	1.96754e9i	−0.00198368	−	0.00391448i
$843$	2.63873e11			0.522498
$844$	−4.59557e10	−	3.36991e10i	−0.0905668	−	0.0664122i
$845$	3.29841e11	−	2.04817e11i	0.646961	−	0.401735i
$846$	−4.17593e10	−	8.24055e10i	−0.0815215	−	0.160870i
$847$	−3.43524e11			−0.667457
$848$	6.26315e11	−	1.97418e11i	1.21118	−	0.381772i
$849$	−2.70319e11			−0.520291
$850$	5.77990e9	+	6.01154e11i	0.0110725	+	1.15162i
$851$		−	4.59348e10i		−	0.0875838i
$852$	3.56835e10	+	2.61666e10i	0.0677188	+	0.0496579i
$853$			4.91131e11i			0.927687i	0.885917	+	0.463843i	$0.153530\pi$
$853$			4.91131e11i			0.927687i	−0.885917	+	0.463843i	$0.846470\pi$
$854$	1.16354e11	+	2.29607e11i	0.218751	+	0.431671i
$855$	−2.32585e11	−	3.74559e11i	−0.435229	−	0.700899i
$856$	−7.97778e11	−	1.31766e11i	−1.48589	−	0.245419i
$857$		−	2.87979e10i		−	0.0533873i	−0.999644	−	0.0266936i	$-0.991502\pi$
$857$		−	2.87979e10i		−	0.0533873i	0.999644	−	0.0266936i	$-0.00849786\pi$
$858$	8.19456e10	+	1.61707e11i	0.151209	+	0.298387i
$859$			3.71560e11i			0.682428i	0.939986	+	0.341214i	$0.110838\pi$
$859$			3.71560e11i			0.682428i	−0.939986	+	0.341214i	$0.889162\pi$
$860$	1.04979e10	−	1.36002e11i	0.0191915	−	0.248628i
$861$	−3.21159e11			−0.584397
$862$	2.66954e11	−	1.35280e11i	0.483512	−	0.245022i
$863$	8.63937e10			0.155754			0.0778769	−	0.996963i	$-0.475186\pi$
$863$	8.63937e10			0.155754			0.0778769	+	0.996963i	$0.475186\pi$
$864$	3.70712e11	−	3.62634e11i	0.665245	−	0.650750i
$865$	−3.06719e11	−	4.93945e11i	−0.547868	−	0.882295i
$866$	2.09596e11	−	1.06213e11i	0.372658	−	0.188846i
$867$	−1.00914e11			−0.178598
$868$	−5.91838e11	−	4.33992e11i	−1.04262	−	0.764545i
$869$	−4.30614e10			−0.0755108
$870$	−2.87159e11	−	1.74511e11i	−0.501241	−	0.304611i
$871$		−	2.46199e11i		−	0.427773i
$872$	−9.05641e11	−	1.49581e11i	−1.56635	−	0.258708i
$873$			3.04486e10i			0.0524215i
$874$	7.43403e11	−	3.76722e11i	1.27403	−	0.645618i
$875$	−6.63327e10	−	6.86929e11i	−0.113161	−	1.17187i
$876$	−8.81172e10	−	6.46159e10i	−0.149639	−	0.109729i
$877$			3.79999e11i			0.642369i	0.947017	+	0.321184i	$0.104081\pi$
$877$			3.79999e11i			0.642369i	−0.947017	+	0.321184i	$0.895919\pi$
$878$	3.68424e11	−	1.86700e11i	0.619969	−	0.314172i
$879$		−	1.58946e11i		−	0.266254i
$880$	−4.89183e11	+	5.69404e11i	−0.815719	+	0.949490i
$881$	−9.51956e11			−1.58020			−0.790102	−	0.612975i	$-0.789973\pi$
$881$	−9.51956e11			−1.58020			−0.790102	+	0.612975i	$0.789973\pi$
$882$	7.39852e10	+	1.45998e11i	0.122256	+	0.241253i
$883$	−5.76893e11			−0.948971			−0.474485	−	0.880263i	$-0.657366\pi$
$883$	−5.76893e11			−0.948971			−0.474485	+	0.880263i	$0.657366\pi$
$884$	2.03088e11	−	2.76952e11i	0.332563	−	0.453519i
$885$	3.44776e11	+	5.55232e11i	0.562036	+	0.905111i
$886$	2.50640e11	+	4.94600e11i	0.406739	+	0.802637i
$887$	6.27370e11			1.01351			0.506756	−	0.862089i	$-0.330844\pi$
$887$	6.27370e11			1.01351			0.506756	+	0.862089i	$0.330844\pi$
$888$	4.00475e9	−	2.42469e10i	0.00644056	−	0.0389945i
$889$	9.64175e11			1.54365
$890$	−5.49240e11	−	3.33781e11i	−0.875391	−	0.531988i
$891$		−	1.50881e11i		−	0.239400i
$892$	4.03613e11	−	5.50410e11i	0.637538	−	0.869415i
$893$		−	1.92817e11i		−	0.303207i
$894$	2.25023e10	+	4.44049e10i	0.0352272	+	0.0695153i
$895$	1.19485e11	+	1.92420e11i	0.186217	+	0.299887i
$896$	−1.07132e11	−	7.51199e11i	−0.166222	−	1.16553i
$897$		−	2.09806e11i		−	0.324076i
$898$	2.53682e11	+	5.00602e11i	0.390107	+	0.769816i
$899$			7.68814e11i			1.17702i
$900$	−2.11689e11	−	4.07959e11i	−0.322647	−	0.621794i
$901$	9.63847e11			1.46254
$902$	6.70419e11	−	3.39738e11i	1.01279	−	0.513236i
$903$	−1.06824e11			−0.160664
$904$	−2.16606e11	+	1.31144e12i	−0.324337	+	1.96370i
$905$	−8.07484e11	+	5.01414e11i	−1.20376	+	0.747484i
$906$	2.52999e11	−	1.28208e11i	0.375496	−	0.190284i
$907$	−3.89597e11			−0.575688			−0.287844	−	0.957677i	$-0.592938\pi$
$907$	−3.89597e11			−0.575688			−0.287844	+	0.957677i	$0.592938\pi$
$908$	−2.20128e11	+	3.00190e11i	−0.323841	+	0.441624i
$909$	−2.39991e11			−0.351511
$910$	−2.04745e11	+	3.36909e11i	−0.298571	+	0.491301i
$911$		−	1.13330e12i		−	1.64540i	−0.568475	−	0.822700i	$-0.692467\pi$
$911$		−	1.13330e12i		−	1.64540i	0.568475	−	0.822700i	$-0.307533\pi$
$912$	4.25252e11	−	1.34042e11i	0.614705	−	0.193758i
$913$		−	2.32627e11i		−	0.334793i
$914$	−2.58215e11	+	1.30851e11i	−0.369995	+	0.187497i
$915$	−1.33950e11	+	8.31771e10i	−0.191098	+	0.118664i
$916$	−2.01283e9	+	2.74491e9i	−0.00285908	+	0.00389894i
$917$			7.69670e11i			1.08850i
$918$	6.78943e11	−	3.44057e11i	0.956010	−	0.484462i
$919$			1.35023e12i			1.89298i	0.322739	+	0.946488i	$0.395396\pi$
$919$			1.35023e12i			1.89298i	−0.322739	+	0.946488i	$0.604604\pi$
$920$	8.02882e11	−	3.31907e11i	1.12073	−	0.463302i
$921$	−2.26768e11			−0.315169
$922$	−1.60944e11	−	3.17597e11i	−0.222715	−	0.439494i
$923$	−5.43846e10			−0.0749323
$924$	4.74081e11	+	3.47641e11i	0.650376	+	0.476918i
$925$	−4.73903e10	−	2.34453e10i	−0.0647325	−	0.0320250i
$926$	2.98921e11	+	5.89874e11i	0.406549	+	0.802260i
$927$	5.49784e11			0.744515
$928$	−5.68228e11	+	5.55847e11i	−0.766180	+	0.749485i
$929$	−3.18334e11			−0.427387			−0.213693	−	0.976901i	$-0.568549\pi$
$929$	−3.18334e11			−0.427387			−0.213693	+	0.976901i	$0.568549\pi$
$930$	2.33470e11	−	3.84177e11i	0.312104	−	0.513570i
$931$			3.41614e11i			0.454713i
$932$	1.14343e12	+	8.38474e11i	1.51547	+	1.11129i
$933$			1.24530e11i			0.164341i
$934$	2.60507e11	+	5.14070e11i	0.342320	+	0.675515i
$935$	−9.36018e11	+	5.81227e11i	−1.22472	+	0.760501i
$936$	−4.27863e10	+	2.59050e11i	−0.0557444	+	0.337505i
$937$			1.14781e12i			1.48906i	0.667587	+	0.744532i	$0.267327\pi$
$937$			1.14781e12i			1.48906i	−0.667587	+	0.744532i	$0.732673\pi$
$938$	−3.60894e11	−	7.12168e11i	−0.466196	−	0.919965i
$939$			2.07939e11i			0.267469i
$940$	1.54692e10	−	2.00405e11i	0.0198133	−	0.256683i
$941$	−2.67245e11			−0.340840			−0.170420	−	0.985372i	$-0.554512\pi$
$941$	−2.67245e11			−0.340840			−0.170420	+	0.985372i	$0.554512\pi$
$942$	−4.41891e11	+	2.23930e11i	−0.561192	+	0.284386i
$943$	−8.69831e11			−1.09999
$944$	1.47453e12	−	4.64781e11i	1.85681	−	0.585276i
$945$	−7.42285e11	+	4.60928e11i	−0.930773	+	0.577971i
$946$	2.22996e11	−	1.13004e11i	0.278440	−	0.141101i
$947$	−5.74285e11			−0.714049			−0.357024	−	0.934095i	$-0.616209\pi$
$947$	−5.74285e11			−0.714049			−0.357024	+	0.934095i	$0.616209\pi$
$948$	2.15012e10	+	1.57667e10i	0.0266213	+	0.0195213i
$949$	1.34298e11			0.165578
$950$	−9.22275e9	−	9.59238e11i	−0.0113231	−	1.17769i
$951$			1.08371e11i			0.132492i
$952$	1.81489e11	−	1.09883e12i	0.220954	−	1.33777i
$953$			1.67118e11i			0.202605i	0.994856	+	0.101303i	$0.0323010\pi$
$953$			1.67118e11i			0.202605i	−0.994856	+	0.101303i	$0.967699\pi$
$954$	−6.57294e11	+	3.33086e11i	−0.793536	+	0.402127i
$955$	−2.66474e11	−	4.29134e11i	−0.320362	−	0.515916i
$956$	−1.45785e11	−	1.06904e11i	−0.174535	−	0.127985i
$957$		−	6.15844e11i		−	0.734214i
$958$	−7.59273e11	+	3.84764e11i	−0.901438	+	0.456807i
$959$		−	1.06170e12i		−	1.25524i
$960$	4.52741e11	−	1.05200e11i	0.533046	−	0.123860i
$961$	−1.75668e11			−0.205968
$962$	1.36531e10	+	2.69424e10i	0.0159416	+	0.0314583i
$963$	9.07313e11			1.05500
$964$	−3.38108e11	+	4.61080e11i	−0.391514	+	0.533911i
$965$	7.20141e11	+	1.15973e12i	0.830440	+	1.33735i
$966$	−3.07547e11	−	6.06895e11i	−0.353185	−	0.696956i
$967$	8.24444e11			0.942877			0.471439	−	0.881899i	$-0.343735\pi$
$967$	8.24444e11			0.942877			0.471439	+	0.881899i	$0.343735\pi$
$968$	−4.91117e11	−	8.11158e10i	−0.559350	−	0.0923855i
$969$	6.54426e11			0.742276
$970$	−3.44052e10	+	5.66140e10i	−0.0388630	+	0.0639495i
$971$		−	8.36736e11i		−	0.941264i	−0.882330	−	0.470632i	$-0.844026\pi$
$971$		−	8.36736e11i		−	0.941264i	0.882330	−	0.470632i	$-0.155974\pi$
$972$	−5.46458e11	+	7.45209e11i	−0.612198	+	0.834859i
$973$		−	1.43372e12i		−	1.59960i
$974$	−1.56332e11	−	3.08498e11i	−0.173705	−	0.342780i
$975$	−2.16453e11	−	1.07086e11i	−0.239522	−	0.118498i
$976$	1.12128e11	+	3.55730e11i	0.123571	+	0.392032i
$977$		−	1.09033e12i		−	1.19669i	−0.801239	−	0.598344i	$-0.795826\pi$
$977$		−	1.09033e12i		−	1.19669i	0.801239	−	0.598344i	$-0.204174\pi$
$978$	1.10846e11	+	2.18737e11i	0.121161	+	0.239093i
$979$		−	1.17790e12i		−	1.28227i
$980$	−2.74068e10	+	3.55059e11i	−0.0297136	+	0.384942i
$981$	1.02999e12			1.11213
$982$	−9.91420e10	+	5.02406e10i	−0.106613	+	0.0540267i
$983$	1.28853e11			0.138000			0.0690001	−	0.997617i	$-0.478019\pi$
$983$	1.28853e11			0.138000			0.0690001	+	0.997617i	$0.478019\pi$
$984$	−4.59143e11	−	7.58348e10i	−0.489743	−	0.0808888i
$985$	−3.37551e11	−	5.43598e11i	−0.358587	−	0.577474i
$986$	−1.04069e12	+	5.27371e11i	−1.10106	+	0.557967i
$987$	−1.57411e11			−0.165869
$988$	−3.24059e11	+	4.41921e11i	−0.340092	+	0.463786i
$989$	−2.89324e11			−0.302413
$990$	4.37456e11	−	7.19837e11i	0.455400	−	0.749365i
$991$			1.29472e12i			1.34240i	0.741276	+	0.671201i	$0.234221\pi$
$991$			1.29472e12i			1.34240i	−0.741276	+	0.671201i	$0.765779\pi$
$992$	−7.43641e11	−	7.60205e11i	−0.767921	−	0.785026i
$993$		−	9.52579e11i		−	0.979725i
$994$	−1.57316e11	+	7.97204e10i	−0.161149	+	0.0816628i
$995$	4.04123e11	+	6.50805e11i	0.412307	+	0.663986i
$996$	−8.51752e10	+	1.16154e11i	−0.0865518	+	0.118031i
$997$			1.46628e12i			1.48401i	0.670393	+	0.742006i	$0.266125\pi$
$997$			1.46628e12i			1.48401i	−0.670393	+	0.742006i	$0.733875\pi$
$998$	−4.34750e11	+	2.20311e11i	−0.438246	+	0.222083i
$999$			6.69409e10i			0.0672094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.d.c.19.5	✓	20
4.3	odd	2	inner	20.9.d.c.19.15	yes	20
5.2	odd	4		100.9.b.g.51.15		20
5.3	odd	4		100.9.b.g.51.6		20
5.4	even	2	inner	20.9.d.c.19.16	yes	20
8.3	odd	2		320.9.h.g.319.14		20
8.5	even	2		320.9.h.g.319.8		20
20.3	even	4		100.9.b.g.51.5		20
20.7	even	4		100.9.b.g.51.16		20
20.19	odd	2	inner	20.9.d.c.19.6	yes	20
40.19	odd	2		320.9.h.g.319.7		20
40.29	even	2		320.9.h.g.319.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.5	✓	20	1.1	even	1	trivial
20.9.d.c.19.6	yes	20	20.19	odd	2	inner
20.9.d.c.19.15	yes	20	4.3	odd	2	inner
20.9.d.c.19.16	yes	20	5.4	even	2	inner
100.9.b.g.51.5		20	20.3	even	4
100.9.b.g.51.6		20	5.3	odd	4
100.9.b.g.51.15		20	5.2	odd	4
100.9.b.g.51.16		20	20.7	even	4
320.9.h.g.319.7		20	40.19	odd	2
320.9.h.g.319.8		20	8.5	even	2
320.9.h.g.319.13		20	40.29	even	2
320.9.h.g.319.14		20	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.23243 - 14.2721i) q^{2} +44.3270 q^{3} +(-151.384 + 206.443i) q^{4} +(530.961 - 329.705i) q^{5} +(-320.592 - 632.638i) q^{6} +2826.75 q^{7} +(4041.25 + 667.476i) q^{8} -4596.11 q^{9} +O(q^{10})\)	\(q+(-7.23243 - 14.2721i) q^{2} +44.3270 q^{3} +(-151.384 + 206.443i) q^{4} +(530.961 - 329.705i) q^{5} +(-320.592 - 632.638i) q^{6} +2826.75 q^{7} +(4041.25 + 667.476i) q^{8} -4596.11 q^{9} +(-8545.71 - 5193.35i) q^{10} -18327.2i q^{11} +(-6710.40 + 9151.02i) q^{12} -13946.9i q^{13} +(-20444.3 - 40343.6i) q^{14} +(23535.9 - 14614.8i) q^{15} +(-19701.8 - 62504.5i) q^{16} -96189.1i q^{17} +(33241.1 + 65596.1i) q^{18} +153485. i q^{19} +(-12313.7 + 159525. i) q^{20} +125301. q^{21} +(-261567. + 132550. i) q^{22} +339368. q^{23} +(179137. + 29587.2i) q^{24} +(173215. - 350121. i) q^{25} +(-199051. + 100870. i) q^{26} -494562. q^{27} +(-427925. + 583564. i) q^{28} +758065. q^{29} +(-378806. - 230206. i) q^{30} +1.01418e6i q^{31} +(-749577. + 733244. i) q^{32} -812389. i q^{33} +(-1.37282e6 + 695681. i) q^{34} +(1.50090e6 - 931993. i) q^{35} +(695778. - 948838. i) q^{36} -135354. i q^{37} +(2.19055e6 - 1.11007e6i) q^{38} -618224. i q^{39} +(2.36582e6 - 978014. i) q^{40} -2.56309e6 q^{41} +(-906233. - 1.78831e6i) q^{42} -852539. q^{43} +(3.78352e6 + 2.77444e6i) q^{44} +(-2.44036e6 + 1.51536e6i) q^{45} +(-2.45445e6 - 4.84348e6i) q^{46} -1.25626e6 q^{47} +(-873321. - 2.77064e6i) q^{48} +2.22572e6 q^{49} +(-6.24971e6 + 60088.9i) q^{50} -4.26378e6i q^{51} +(2.87925e6 + 2.11134e6i) q^{52} +1.00203e7i q^{53} +(3.57688e6 + 7.05842e6i) q^{54} +(-6.04255e6 - 9.73101e6i) q^{55} +(1.14236e7 + 1.88679e6i) q^{56} +6.80354e6i q^{57} +(-5.48265e6 - 1.08192e7i) q^{58} +2.35908e7i q^{59} +(-545830. + 7.07129e6i) q^{60} -5.69128e6 q^{61} +(1.44744e7 - 7.33498e6i) q^{62} -1.29921e7 q^{63} +(1.58862e7 + 5.39488e6i) q^{64} +(-4.59836e6 - 7.40526e6i) q^{65} +(-1.15945e7 + 5.87554e6i) q^{66} +1.76526e7 q^{67} +(1.98576e7 + 1.45615e7i) q^{68} +1.50432e7 q^{69} +(-2.41566e7 - 1.46803e7i) q^{70} -3.89940e6i q^{71} +(-1.85740e7 - 3.06780e6i) q^{72} +9.62921e6i q^{73} +(-1.93178e6 + 978938. i) q^{74} +(7.67810e6 - 1.55198e7i) q^{75} +(-3.16860e7 - 2.32352e7i) q^{76} -5.18063e7i q^{77} +(-8.82334e6 + 4.47126e6i) q^{78} -2.34959e6i q^{79} +(-3.10689e7 - 2.66917e7i) q^{80} +8.23266e6 q^{81} +(1.85374e7 + 3.65806e7i) q^{82} +1.26930e7 q^{83} +(-1.89686e7 + 2.58677e7i) q^{84} +(-3.17140e7 - 5.10727e7i) q^{85} +(6.16593e6 + 1.21675e7i) q^{86} +3.36028e7 q^{87} +(1.22330e7 - 7.40646e7i) q^{88} +6.42709e7 q^{89} +(3.92770e7 + 2.38692e7i) q^{90} -3.94244e7i q^{91} +(-5.13749e7 + 7.00603e7i) q^{92} +4.49555e7i q^{93} +(9.08579e6 + 1.79294e7i) q^{94} +(5.06048e7 + 8.14947e7i) q^{95} +(-3.32265e7 + 3.25025e7i) q^{96} -6.62485e6i q^{97} +(-1.60973e7 - 3.17656e7i) q^{98} +8.42338e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9}+O(q^{10}) \) 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9	\( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30} + 4342528 q^{34} - 7191312 q^{36} - 945280 q^{40} + 7068520 q^{41} + 2666880 q^{44} - 18729060 q^{45} + 561168 q^{46} + 11719036 q^{49} + 3914880 q^{50} + 37110816 q^{54} - 35044352 q^{56} - 22734720 q^{60} - 17660440 q^{61} + 20201728 q^{64} - 44202240 q^{65} + 31902720 q^{66} + 111747216 q^{69} - 47166000 q^{70} + 19114368 q^{74} - 54998400 q^{76} + 7968320 q^{80} - 154212444 q^{81} + 101289216 q^{84} + 68800000 q^{85} + 94429648 q^{86} + 105006376 q^{89} - 230808000 q^{90} - 192757872 q^{94} + 28850688 q^{96}+O(q^{100}) \) 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9 - 4160 * q^10 + 8848 * q^14 - 59200 * q^16 - 4240 * q^20 + 410256 * q^21 - 156672 * q^24 - 657260 * q^25 - 440448 * q^26 + 660136 * q^29 + 667920 * q^30 + 4342528 * q^34 - 7191312 * q^36 - 945280 * q^40 + 7068520 * q^41 + 2666880 * q^44 - 18729060 * q^45 + 561168 * q^46 + 11719036 * q^49 + 3914880 * q^50 + 37110816 * q^54 - 35044352 * q^56 - 22734720 * q^60 - 17660440 * q^61 + 20201728 * q^64 - 44202240 * q^65 + 31902720 * q^66 + 111747216 * q^69 - 47166000 * q^70 + 19114368 * q^74 - 54998400 * q^76 + 7968320 * q^80 - 154212444 * q^81 + 101289216 * q^84 + 68800000 * q^85 + 94429648 * q^86 + 105006376 * q^89 - 230808000 * q^90 - 192757872 * q^94 + 28850688 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more