LMFDB - Embedded newform 20.9.d.c.19.6

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.23243 + 14.2721i) q^{2} +44.3270 q^{3} +(-151.384 - 206.443i) q^{4} +(530.961 + 329.705i) q^{5} +(-320.592 + 632.638i) q^{6} +2826.75 q^{7} +(4041.25 - 667.476i) q^{8} -4596.11 q^{9} +O(q^{10})$	\(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	$0.215262\pi$
$11$			18327.2i			1.25177i	−0.779915	+	0.625885i	$0.784738\pi$
$12$	−6710.40	−	9151.02i	−0.323611	−	0.441311i
$13$			13946.9i			0.488320i	0.969735	+	0.244160i	$0.0785122\pi$
$13$			13946.9i			0.488320i	−0.969735	+	0.244160i	$0.921488\pi$
$14$	−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	$0.195324\pi$
$17$			96189.1i			1.15168i	−0.817564	+	0.575838i	$0.804676\pi$
$18$	33241.1	−	65596.1i	0.316654	−	0.624867i
$19$		−	153485.i		−	1.17775i	−0.808225	−	0.588873i	$-0.799572\pi$
$19$		−	153485.i		−	1.17775i	0.808225	−	0.588873i	$-0.200428\pi$
$20$	−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	$-0.814977\pi$
$31$		−	1.01418e6i		−	1.09817i	0.835768	−	0.549083i	$-0.185023\pi$
$32$	−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	$0.0114968\pi$
$37$			135354.i			0.0722211i	−0.999348	+	0.0361106i	$0.988503\pi$
$38$	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	$-0.781015\pi$
$53$		−	1.00203e7i		−	1.26993i	0.772542	−	0.634963i	$-0.218985\pi$
$54$	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	$-0.573539\pi$
$59$		−	2.35908e7i		−	1.94686i	0.228979	−	0.973431i	$-0.426461\pi$
$60$	−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	$0.0244462\pi$
$71$			3.89940e6i			0.153449i	−0.997052	+	0.0767246i	$0.975554\pi$
$72$	−1.85740e7	+	3.06780e6i	−0.691157	+	0.114156i
$73$		−	9.62921e6i		−	0.339078i	−0.985523	−	0.169539i	$-0.945772\pi$
$73$		−	9.62921e6i		−	0.339078i	0.985523	−	0.169539i	$-0.0542278\pi$
$74$	−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	$0.00960220\pi$
$79$			2.34959e6i			0.0603232i	−0.999545	+	0.0301616i	$0.990398\pi$
$80$	−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	$0.0119127\pi$
$97$			6.62485e6i			0.0748323i	−0.999300	+	0.0374161i	$0.988087\pi$
$98$	−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	$-0.531352\pi$
$113$		−	3.24514e8i		−	1.99031i	0.0983370	−	0.995153i	$-0.468648\pi$
$114$	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	$-0.847033\pi$
$131$		−	2.72281e8i		−	0.924553i	0.886736	−	0.462277i	$-0.152967\pi$
$132$	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	$0.178970\pi$
$137$			3.75590e8i			1.06618i	−0.846057	+	0.533092i	$0.821030\pi$
$138$	−1.08799e8	+	2.14697e8i	−0.299990	+	0.591984i
$139$			5.07197e8i			1.35868i	0.733823	+	0.679340i	$0.237734\pi$
$139$			5.07197e8i			1.35868i	−0.733823	+	0.679340i	$0.762266\pi$
$140$	−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	$-0.874335\pi$
$151$		−	3.99910e8i		−	0.769228i	0.923078	−	0.384614i	$-0.125665\pi$
$152$	−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	$0.194927\pi$
$157$			6.98489e8i			1.14964i	−0.818281	+	0.574819i	$0.805073\pi$
$158$	−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	$0.173800\pi$
$173$			9.30284e8i			1.03856i	−0.854604	+	0.519280i	$0.826200\pi$
$174$	−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	$-0.943522\pi$
$179$		−	3.62399e8i		−	0.353000i	0.984301	−	0.176500i	$-0.0564776\pi$
$180$	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	$0.0982037\pi$
$191$			8.08221e8i			0.607290i	−0.952785	+	0.303645i	$0.901796\pi$
$192$	7.04186e8	−	2.39139e8i	0.518183	−	0.175973i
$193$		−	2.18420e9i		−	1.57421i	−0.616817	−	0.787107i	$-0.711578\pi$
$193$		−	2.18420e9i		−	1.57421i	0.616817	−	0.787107i	$-0.288422\pi$
$194$	−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	$0.110385\pi$
$197$			1.02380e9i			0.679751i	−0.940470	+	0.339875i	$0.889615\pi$
$198$	1.20219e9	+	6.09214e8i	0.782190	+	0.396378i
$199$		−	1.22571e9i		−	0.781585i	−0.920479	−	0.390792i	$-0.872201\pi$
$199$		−	1.22571e9i		−	0.781585i	0.920479	−	0.390792i	$-0.127799\pi$
$200$	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	$-0.982116\pi$
$211$		−	2.22607e8i		−	0.112307i	0.998422	−	0.0561537i	$-0.0178837\pi$
$212$	−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	$0.388829\pi$
$233$			5.53873e9i			1.87926i	−0.342196	+	0.939628i	$0.611171\pi$
$234$	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	$-0.965486\pi$
$239$		−	7.06175e8i		−	0.216432i	0.994127	−	0.108216i	$-0.0345137\pi$
$240$	−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	$-0.866625\pi$
$251$		−	3.22973e9i		−	0.813713i	0.913492	−	0.406857i	$-0.133375\pi$
$252$	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	$0.140808\pi$
$257$			3.73492e9i			0.856148i	−0.903744	+	0.428074i	$0.859192\pi$
$258$	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	$-0.857753\pi$
$271$		−	4.66174e9i		−	0.864312i	0.901799	−	0.432156i	$-0.142247\pi$
$272$	−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	$-0.895556\pi$
$277$		−	3.79455e9i		−	0.644526i	0.946650	−	0.322263i	$-0.104444\pi$
$278$	−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	$0.0782189\pi$
$293$			3.58577e9i			0.486533i	−0.969960	+	0.243266i	$0.921781\pi$
$294$	−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	$-0.952024\pi$
$311$		−	2.80934e9i		−	0.300305i	0.988663	−	0.150152i	$-0.0479764\pi$
$312$	4.12650e8	+	2.49840e9i	0.0435476	+	0.263659i
$313$		−	4.69101e9i		−	0.488753i	−0.969680	−	0.244376i	$-0.921417\pi$
$313$		−	4.69101e9i		−	0.488753i	0.969680	−	0.244376i	$-0.0785833\pi$
$314$	−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	$-0.961373\pi$
$317$		−	2.44480e9i		−	0.242107i	0.992646	−	0.121053i	$-0.0386272\pi$
$318$	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	$0.352924\pi$
$331$			2.14898e10i			1.79028i	−0.445786	+	0.895139i	$0.647076\pi$
$332$	−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	$0.0592975\pi$
$337$			4.77773e9i			0.370426i	−0.982698	+	0.185213i	$0.940702\pi$
$338$	−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	$0.0756278\pi$
$353$			7.30914e9i			0.470725i	−0.971908	+	0.235363i	$0.924372\pi$
$354$	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	$-0.830004\pi$
$359$		−	1.69103e10i		−	1.01806i	0.860749	−	0.509029i	$-0.169996\pi$
$360$	−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	$-0.921406\pi$
$373$		−	9.46195e9i		−	0.488816i	0.969673	−	0.244408i	$-0.0785936\pi$
$374$	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	$-0.913459\pi$
$379$		−	1.10814e10i		−	0.537078i	0.963269	−	0.268539i	$-0.0865409\pi$
$380$	−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	$0.00757549\pi$
$397$			1.18226e9i			0.0475937i	−0.999717	+	0.0237969i	$0.992425\pi$
$398$	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	$0.421676\pi$
$419$			5.97866e10i			1.93976i	−0.243587	+	0.969879i	$0.578324\pi$
$420$	−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	$-0.912637\pi$
$431$		−	1.87046e10i		−	0.542051i	0.962572	−	0.271026i	$-0.0873628\pi$
$432$	9.74374e9	−	3.09123e10i	0.279763	−	0.887558i
$433$		−	1.46857e10i		−	0.417776i	−0.977940	−	0.208888i	$-0.933016\pi$
$433$		−	1.46857e10i		−	0.417776i	0.977940	−	0.208888i	$-0.0669844\pi$
$434$	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	$-0.887026\pi$
$439$		−	2.58143e10i		−	0.695029i	0.937675	−	0.347514i	$-0.112974\pi$
$440$	−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	$0.0664987\pi$
$457$			1.80923e10i			0.414791i	−0.978257	+	0.207395i	$0.933501\pi$
$458$	−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	$0.168614\pi$
$479$			5.31999e10i			1.01058i	−0.862951	+	0.505288i	$0.831386\pi$
$480$	−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	$0.0190337\pi$
$491$			6.94657e9i			0.119521i	−0.998213	+	0.0597606i	$0.980966\pi$
$492$	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	$0.0790021\pi$
$499$			3.04616e10i			0.491304i	−0.969358	+	0.245652i	$0.920998\pi$
$500$	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	$-0.999668\pi$
$557$		−	2.01090e8i		−	0.00208915i	0.999999	−	0.00104458i	$-0.000332499\pi$
$558$	−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	$-0.955119\pi$
$571$		−	2.98777e10i		−	0.281063i	0.990076	−	0.140531i	$-0.0448811\pi$
$572$	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	$-0.817212\pi$
$577$		−	1.20418e11i		−	1.08640i	0.839603	−	0.543200i	$-0.182788\pi$
$578$	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	$0.126378\pi$
$593$			9.56312e10i			0.773359i	−0.922214	+	0.386679i	$0.873622\pi$
$594$	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	$-0.993652\pi$
$599$		−	5.13440e9i		−	0.0398825i	0.999801	−	0.0199413i	$-0.00634792\pi$
$600$	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	$0.224189\pi$
$613$			1.82859e11i			1.29502i	−0.762058	+	0.647508i	$0.775811\pi$
$614$	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	$-0.947161\pi$
$617$		−	4.78934e10i		−	0.330472i	0.986254	−	0.165236i	$-0.0528386\pi$
$618$	3.83490e10	−	7.56758e10i	0.262906	−	0.518804i
$619$		−	8.75787e10i		−	0.596535i	−0.954482	−	0.298267i	$-0.903591\pi$
$619$		−	8.75787e10i		−	0.596535i	0.954482	−	0.298267i	$-0.0964087\pi$
$620$	−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	$0.190976\pi$
$631$			1.79020e11i			1.12923i	−0.825354	+	0.564616i	$0.809024\pi$
$632$	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	$0.304062\pi$
$653$			2.96902e11i			1.63290i	−0.577415	+	0.816451i	$0.695938\pi$
$654$	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	$-0.886939\pi$
$659$		−	1.31179e11i		−	0.695541i	0.937580	−	0.347771i	$-0.113061\pi$
$660$	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	$-0.953917\pi$
$673$		−	5.91921e10i		−	0.288538i	0.989538	−	0.144269i	$-0.0460831\pi$
$674$	−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	$0.236749\pi$
$677$			2.84457e11i			1.35413i	−0.735922	+	0.677066i	$0.763251\pi$
$678$	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	$0.0755835\pi$
$691$			1.07258e11i			0.470455i	−0.971940	+	0.235227i	$0.924417\pi$
$692$	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	$-0.799753\pi$
$719$		−	3.14505e11i		−	1.17683i	0.808561	−	0.588413i	$-0.200247\pi$
$720$	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	$-0.949536\pi$
$733$		−	9.11504e10i		−	0.315749i	0.987459	−	0.157875i	$-0.0504642\pi$
$734$	−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	$0.108882\pi$
$739$			2.00083e11i			0.670860i	−0.942065	+	0.335430i	$0.891118\pi$
$740$	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	$0.310083\pi$
$751$			5.26277e11i			1.65445i	−0.561869	+	0.827226i	$0.689917\pi$
$752$	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	$-0.770389\pi$
$757$		−	4.33728e11i		−	1.32079i	0.750919	−	0.660395i	$-0.229611\pi$
$758$	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	$-0.865049\pi$
$773$		−	2.93754e11i		−	0.822746i	0.911467	−	0.411373i	$-0.134951\pi$
$774$	−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	$0.191594\pi$
$797$			4.56927e11i			1.13244i	−0.824256	+	0.566218i	$0.808406\pi$
$798$	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	$-0.926358\pi$
$811$		−	1.98385e11i		−	0.458590i	0.973357	−	0.229295i	$-0.0736420\pi$
$812$	−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	$0.140036\pi$
$839$			4.22053e11i			0.851764i	−0.904779	+	0.425882i	$0.859964\pi$
$840$	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	$-0.846470\pi$
$853$		−	4.91131e11i		−	0.927687i	0.885917	−	0.463843i	$-0.153530\pi$
$854$	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	$0.00849786\pi$
$857$			2.87979e10i			0.0533873i	−0.999644	+	0.0266936i	$0.991502\pi$
$858$	8.19456e10	−	1.61707e11i	0.151209	−	0.298387i
$859$		−	3.71560e11i		−	0.682428i	−0.939986	−	0.341214i	$-0.889162\pi$
$859$		−	3.71560e11i		−	0.682428i	0.939986	−	0.341214i	$-0.110838\pi$
$860$	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	$-0.895919\pi$
$877$		−	3.79999e11i		−	0.642369i	0.947017	−	0.321184i	$-0.104081\pi$
$878$	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	$0.307533\pi$
$911$			1.13330e12i			1.64540i	−0.568475	+	0.822700i	$0.692467\pi$
$912$	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	$-0.604604\pi$
$919$		−	1.35023e12i		−	1.89298i	0.322739	−	0.946488i	$-0.395396\pi$
$920$	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	$-0.732673\pi$
$937$		−	1.14781e12i		−	1.48906i	0.667587	−	0.744532i	$-0.267327\pi$
$938$	−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	$-0.967699\pi$
$953$		−	1.67118e11i		−	0.202605i	0.994856	−	0.101303i	$-0.0323010\pi$
$954$	−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	$0.155974\pi$
$971$			8.36736e11i			0.941264i	−0.882330	+	0.470632i	$0.844026\pi$
$972$	−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	$0.204174\pi$
$977$			1.09033e12i			1.19669i	−0.801239	+	0.598344i	$0.795826\pi$
$978$	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	$-0.765779\pi$
$991$		−	1.29472e12i		−	1.34240i	0.741276	−	0.671201i	$-0.234221\pi$
$992$	−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	$-0.733875\pi$
$997$		−	1.46628e12i		−	1.48401i	0.670393	−	0.742006i	$-0.266125\pi$
$998$	−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.19.6	yes	20
4.3	odd	2	inner	20.9.d.c.19.16	yes	20
5.2	odd	4		100.9.b.g.51.5		20
5.3	odd	4		100.9.b.g.51.16		20
5.4	even	2	inner	20.9.d.c.19.15	yes	20
8.3	odd	2		320.9.h.g.319.13		20
8.5	even	2		320.9.h.g.319.7		20
20.3	even	4		100.9.b.g.51.15		20
20.7	even	4		100.9.b.g.51.6		20
20.19	odd	2	inner	20.9.d.c.19.5	✓	20
40.19	odd	2		320.9.h.g.319.8		20
40.29	even	2		320.9.h.g.319.14		20

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

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