LMFDB - Embedded newform 20.9.d.c.19.1

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			19.1
Root			$-7.46306 - 2.88145i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.9.d.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.9261 - 5.76290i) q^{2} -76.0331 q^{3} +(189.578 + 172.035i) q^{4} +(291.455 + 552.882i) q^{5} +(1134.88 + 438.171i) q^{6} -269.408 q^{7} +(-1838.24 - 3660.34i) q^{8} -779.974 q^{9} +O(q^{10})$	\(q+(-14.9261 - 5.76290i) q^{2} -76.0331 q^{3} +(189.578 + 172.035i) q^{4} +(291.455 + 552.882i) q^{5} +(1134.88 + 438.171i) q^{6} -269.408 q^{7} +(-1838.24 - 3660.34i) q^{8} -779.974 q^{9} +(-1164.08 - 9932.01i) q^{10} -4921.65i q^{11} +(-14414.2 - 13080.4i) q^{12} -24429.8i q^{13} +(4021.21 + 1552.57i) q^{14} +(-22160.2 - 42037.3i) q^{15} +(6343.62 + 65228.3i) q^{16} -62207.7i q^{17} +(11642.0 + 4494.91i) q^{18} -140205. i q^{19} +(-39861.9 + 154955. i) q^{20} +20483.9 q^{21} +(-28363.0 + 73461.1i) q^{22} +290300. q^{23} +(139767. + 278307. i) q^{24} +(-220733. + 322281. i) q^{25} +(-140786. + 364642. i) q^{26} +558157. q^{27} +(-51073.8 - 46347.7i) q^{28} -815278. q^{29} +(88508.9 + 755161. i) q^{30} -1.57652e6i q^{31} +(281218. - 1.01016e6i) q^{32} +374208. i q^{33} +(-358496. + 928519. i) q^{34} +(-78520.2 - 148951. i) q^{35} +(-147866. - 134183. i) q^{36} -2.27731e6i q^{37} +(-807988. + 2.09272e6i) q^{38} +1.85747e6i q^{39} +(1.48797e6 - 2.08315e6i) q^{40} +4.85062e6 q^{41} +(-305745. - 118047. i) q^{42} -3.94126e6 q^{43} +(846698. - 933036. i) q^{44} +(-227327. - 431234. i) q^{45} +(-4.33305e6 - 1.67297e6i) q^{46} -295625. q^{47} +(-482325. - 4.95950e6i) q^{48} -5.69222e6 q^{49} +(5.15196e6 - 3.53834e6i) q^{50} +4.72984e6i q^{51} +(4.20279e6 - 4.63135e6i) q^{52} +4.51616e6i q^{53} +(-8.33111e6 - 3.21660e6i) q^{54} +(2.72109e6 - 1.43444e6i) q^{55} +(495236. + 986124. i) q^{56} +1.06602e7i q^{57} +(1.21689e7 + 4.69837e6i) q^{58} +2.25388e7i q^{59} +(3.03082e6 - 1.17817e7i) q^{60} +9.61812e6 q^{61} +(-9.08530e6 + 2.35312e7i) q^{62} +210131. q^{63} +(-1.00190e7 + 1.34572e7i) q^{64} +(1.35068e7 - 7.12018e6i) q^{65} +(2.15652e6 - 5.58547e6i) q^{66} -8.33340e6 q^{67} +(1.07019e7 - 1.17932e7i) q^{68} -2.20724e7 q^{69} +(313613. + 2.67576e6i) q^{70} -2.78724e7i q^{71} +(1.43378e6 + 2.85497e6i) q^{72} -2.56987e7i q^{73} +(-1.31239e7 + 3.39915e7i) q^{74} +(1.67830e7 - 2.45040e7i) q^{75} +(2.41202e7 - 2.65798e7i) q^{76} +1.32593e6i q^{77} +(1.07044e7 - 2.77248e7i) q^{78} -2.31078e7i q^{79} +(-3.42147e7 + 2.25184e7i) q^{80} -3.73209e7 q^{81} +(-7.24010e7 - 2.79536e7i) q^{82} -3.83862e7 q^{83} +(3.88329e6 + 3.52395e6i) q^{84} +(3.43935e7 - 1.81307e7i) q^{85} +(5.88278e7 + 2.27131e7i) q^{86} +6.19881e7 q^{87} +(-1.80149e7 + 9.04717e6i) q^{88} -4.36166e6 q^{89} +(907956. + 7.74672e6i) q^{90} +6.58157e6i q^{91} +(5.50345e7 + 4.99419e7i) q^{92} +1.19867e8i q^{93} +(4.41254e6 + 1.70366e6i) q^{94} +(7.75169e7 - 4.08635e7i) q^{95} +(-2.13819e7 + 7.68057e7i) q^{96} -1.02959e8i q^{97} +(8.49628e7 + 3.28037e7i) q^{98} +3.83876e6i 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 $

$2$	−14.9261	−	5.76290i	−0.932882	−	0.360181i
$2$	−14.9261	−	5.76290i	−0.932882	−	0.360181i
$3$	−76.0331			−0.938680			−0.469340	−	0.883018i	$-0.655508\pi$
$3$	−76.0331			−0.938680			−0.469340	+	0.883018i	$0.655508\pi$
$4$	189.578	+	172.035i	0.740539	+	0.672013i
$5$	291.455	+	552.882i	0.466328	+	0.884612i
$5$	291.455	+	552.882i	0.466328	+	0.884612i
$6$	1134.88	+	438.171i	0.875678	+	0.338095i
$7$	−269.408			−0.112206			−0.0561032	−	0.998425i	$-0.517868\pi$
$7$	−269.408			−0.112206			−0.0561032	+	0.998425i	$0.517868\pi$
$8$	−1838.24	−	3660.34i	−0.448789	−	0.893638i
$9$	−779.974			−0.118880
$10$	−1164.08	−	9932.01i	−0.116408	−	0.993201i
$11$		−	4921.65i		−	0.336155i	−0.985774	−	0.168078i	$-0.946244\pi$
$11$		−	4921.65i		−	0.336155i	0.985774	−	0.168078i	$-0.0537559\pi$
$12$	−14414.2	−	13080.4i	−0.695129	−	0.630805i
$13$		−	24429.8i		−	0.855354i	−0.903932	−	0.427677i	$-0.859332\pi$
$13$		−	24429.8i		−	0.855354i	0.903932	−	0.427677i	$-0.140668\pi$
$14$	4021.21	+	1552.57i	0.104675	+	0.0404146i
$15$	−22160.2	−	42037.3i	−0.437733	−	0.830367i
$16$	6343.62	+	65228.3i	0.0967960	+	0.995304i
$17$		−	62207.7i		−	0.744815i	−0.928069	−	0.372407i	$-0.878532\pi$
$17$		−	62207.7i		−	0.744815i	0.928069	−	0.372407i	$-0.121468\pi$
$18$	11642.0	+	4494.91i	0.110901	+	0.0428185i
$19$		−	140205.i		−	1.07584i	−0.842995	−	0.537922i	$-0.819209\pi$
$19$		−	140205.i		−	1.07584i	0.842995	−	0.537922i	$-0.180791\pi$
$20$	−39861.9	+	154955.i	−0.249137	+	0.968468i
$21$	20483.9			0.105326
$22$	−28363.0	+	73461.1i	−0.121077	+	0.313593i
$23$	290300.			1.03737			0.518687	−	0.854964i	$-0.326421\pi$
$23$	290300.			1.03737			0.518687	+	0.854964i	$0.326421\pi$
$24$	139767.	+	278307.i	0.421269	+	0.838840i
$25$	−220733.	+	322281.i	−0.565077	+	0.825038i
$26$	−140786.	+	364642.i	−0.308082	+	0.797945i
$27$	558157.			1.05027
$28$	−51073.8	−	46347.7i	−0.0830932	−	0.0754042i
$29$	−815278.			−1.15269			−0.576347	−	0.817205i	$-0.695522\pi$
$29$	−815278.			−1.15269			−0.576347	+	0.817205i	$0.695522\pi$
$30$	88508.9	+	755161.i	0.109270	+	0.932298i
$31$		−	1.57652e6i		−	1.70707i	−0.521035	−	0.853535i	$-0.674454\pi$
$31$		−	1.57652e6i		−	1.70707i	0.521035	−	0.853535i	$-0.325546\pi$
$32$	281218.	−	1.01016e6i	0.268191	−	0.963366i
$33$			374208.i			0.315542i
$34$	−358496.	+	928519.i	−0.268268	+	0.694824i
$35$	−78520.2	−	148951.i	−0.0523250	−	0.0992591i
$36$	−147866.	−	134183.i	−0.0880356	−	0.0798892i
$37$		−	2.27731e6i		−	1.21511i	−0.794277	−	0.607556i	$-0.792150\pi$
$37$		−	2.27731e6i		−	1.21511i	0.794277	−	0.607556i	$-0.207850\pi$
$38$	−807988.	+	2.09272e6i	−0.387499	+	1.00364i
$39$			1.85747e6i			0.802903i
$40$	1.48797e6	−	2.08315e6i	0.581240	−	0.813732i
$41$	4.85062e6			1.71657			0.858286	−	0.513172i	$-0.171530\pi$
$41$	4.85062e6			1.71657			0.858286	+	0.513172i	$0.171530\pi$
$42$	−305745.	−	118047.i	−0.0982567	−	0.0379364i
$43$	−3.94126e6			−1.15282			−0.576410	−	0.817161i	$-0.695547\pi$
$43$	−3.94126e6			−1.15282			−0.576410	+	0.817161i	$0.695547\pi$
$44$	846698.	−	933036.i	0.225901	−	0.248936i
$45$	−227327.	−	431234.i	−0.0554373	−	0.105163i
$46$	−4.33305e6	−	1.67297e6i	−0.967749	−	0.373643i
$47$	−295625.			−0.0605829			−0.0302915	−	0.999541i	$-0.509644\pi$
$47$	−295625.			−0.0605829			−0.0302915	+	0.999541i	$0.509644\pi$
$48$	−482325.	−	4.95950e6i	−0.0908604	−	0.934272i
$49$	−5.69222e6			−0.987410
$50$	5.15196e6	−	3.53834e6i	0.824313	−	0.566134i
$51$			4.72984e6i			0.699142i
$52$	4.20279e6	−	4.63135e6i	0.574809	−	0.633423i
$53$			4.51616e6i			0.572356i	0.958177	+	0.286178i	$0.0923848\pi$
$53$			4.51616e6i			0.572356i	−0.958177	+	0.286178i	$0.907615\pi$
$54$	−8.33111e6	−	3.21660e6i	−0.979779	−	0.378288i
$55$	2.72109e6	−	1.43444e6i	0.297367	−	0.156759i
$56$	495236.	+	986124.i	0.0503570	+	0.100272i
$57$			1.06602e7i			1.00987i
$58$	1.21689e7	+	4.69837e6i	1.07533	+	0.415179i
$59$			2.25388e7i			1.86004i	0.367508	+	0.930021i	$0.380211\pi$
$59$			2.25388e7i			1.86004i	−0.367508	+	0.930021i	$0.619789\pi$
$60$	3.03082e6	−	1.17817e7i	0.233860	−	0.909081i
$61$	9.61812e6			0.694657			0.347329	−	0.937743i	$-0.387089\pi$
$61$	9.61812e6			0.694657			0.347329	+	0.937743i	$0.387089\pi$
$62$	−9.08530e6	+	2.35312e7i	−0.614855	+	1.59250i
$63$	210131.			0.0133391
$64$	−1.00190e7	+	1.34572e7i	−0.597177	+	0.802110i
$65$	1.35068e7	−	7.12018e6i	0.756656	−	0.398875i
$66$	2.15652e6	−	5.58547e6i	0.113652	−	0.294364i
$67$	−8.33340e6			−0.413545			−0.206773	−	0.978389i	$-0.566296\pi$
$67$	−8.33340e6			−0.413545			−0.206773	+	0.978389i	$0.566296\pi$
$68$	1.07019e7	−	1.17932e7i	0.500525	−	0.551564i
$69$	−2.20724e7			−0.973763
$70$	313613.	+	2.67576e6i	0.0130618	+	0.111444i
$71$		−	2.78724e7i		−	1.09683i	−0.836205	−	0.548417i	$-0.815230\pi$
$71$		−	2.78724e7i		−	1.09683i	0.836205	−	0.548417i	$-0.184770\pi$
$72$	1.43378e6	+	2.85497e6i	0.0533522	+	0.106236i
$73$		−	2.56987e7i		−	0.904940i	−0.891780	−	0.452470i	$-0.850543\pi$
$73$		−	2.56987e7i		−	0.904940i	0.891780	−	0.452470i	$-0.149457\pi$
$74$	−1.31239e7	+	3.39915e7i	−0.437660	+	1.13356i
$75$	1.67830e7	−	2.45040e7i	0.530426	−	0.774447i
$76$	2.41202e7	−	2.65798e7i	0.722982	−	0.796704i
$77$			1.32593e6i			0.0377188i
$78$	1.07044e7	−	2.77248e7i	0.289191	−	0.749014i
$79$		−	2.31078e7i		−	0.593266i	−0.954991	−	0.296633i	$-0.904136\pi$
$79$		−	2.31078e7i		−	0.593266i	0.954991	−	0.296633i	$-0.0958639\pi$
$80$	−3.42147e7	+	2.25184e7i	−0.835319	+	0.549765i
$81$	−3.73209e7			−0.866987
$82$	−7.24010e7	−	2.79536e7i	−1.60136	−	0.618277i
$83$	−3.83862e7			−0.808839			−0.404420	−	0.914574i	$-0.632526\pi$
$83$	−3.83862e7			−0.808839			−0.404420	+	0.914574i	$0.632526\pi$
$84$	3.88329e6	+	3.52395e6i	0.0779979	+	0.0707804i
$85$	3.43935e7	−	1.81307e7i	0.658872	−	0.347328i
$86$	5.88278e7	+	2.27131e7i	1.07545	+	0.415224i
$87$	6.19881e7			1.08201
$88$	−1.80149e7	+	9.04717e6i	−0.300401	+	0.150863i
$89$	−4.36166e6			−0.0695172			−0.0347586	−	0.999396i	$-0.511066\pi$
$89$	−4.36166e6			−0.0695172			−0.0347586	+	0.999396i	$0.511066\pi$
$90$	907956.	+	7.74672e6i	0.0138387	+	0.118072i
$91$			6.58157e6i			0.0959762i
$92$	5.50345e7	+	4.99419e7i	0.768217	+	0.697130i
$93$			1.19867e8i			1.60239i
$94$	4.41254e6	+	1.70366e6i	0.0565168	+	0.0218208i
$95$	7.75169e7	−	4.08635e7i	0.951704	−	0.501696i
$96$	−2.13819e7	+	7.68057e7i	−0.251745	+	0.904292i
$97$		−	1.02959e8i		−	1.16299i	−0.813550	−	0.581495i	$-0.802468\pi$
$97$		−	1.02959e8i		−	1.16299i	0.813550	−	0.581495i	$-0.197532\pi$
$98$	8.49628e7	+	3.28037e7i	0.921137	+	0.355646i
$99$			3.83876e6i			0.0399623i
$100$	−9.72898e7	+	2.31234e7i	−0.972898	+	0.231234i
$101$	−7.02605e7			−0.675190			−0.337595	−	0.941291i	$-0.609613\pi$
$101$	−7.02605e7			−0.675190			−0.337595	+	0.941291i	$0.609613\pi$
$102$	2.72576e7	−	7.05981e7i	0.251818	−	0.652217i
$103$	−2.00465e8			−1.78110			−0.890552	−	0.454881i	$-0.849682\pi$
$103$	−2.00465e8			−1.78110			−0.890552	+	0.454881i	$0.849682\pi$
$104$	−8.94212e7	+	4.49078e7i	−0.764377	+	0.383874i
$105$	5.97013e6	+	1.13252e7i	0.0491164	+	0.0931725i
$106$	2.60262e7	−	6.74088e7i	0.206152	−	0.533940i
$107$	1.08253e8			0.825861			0.412930	−	0.910763i	$-0.364505\pi$
$107$	1.08253e8			0.825861			0.412930	+	0.910763i	$0.364505\pi$
$108$	1.05814e8	+	9.60227e7i	0.777766	+	0.705796i
$109$	8.10227e7			0.573985			0.286993	−	0.957933i	$-0.407344\pi$
$109$	8.10227e7			0.573985			0.286993	+	0.957933i	$0.407344\pi$
$110$	−4.88819e7	+	5.72922e6i	−0.333870	+	0.0391313i
$111$			1.73151e8i			1.14060i
$112$	−1.70902e6	−	1.75730e7i	−0.0108611	−	0.111680i
$113$			6.16205e7i			0.377930i	0.981984	+	0.188965i	$0.0605133\pi$
$113$			6.16205e7i			0.377930i	−0.981984	+	0.188965i	$0.939487\pi$
$114$	6.14338e7	−	1.59116e8i	0.363737	−	0.942093i
$115$	8.46094e7	+	1.60502e8i	0.483757	+	0.917674i
$116$	−1.54559e8	−	1.40257e8i	−0.853615	−	0.774626i
$117$			1.90546e7i			0.101685i
$118$	1.29889e8	−	3.36417e8i	0.669952	−	1.73520i
$119$			1.67592e7i			0.0835730i
$120$	−1.13135e8	+	1.58389e8i	−0.545598	+	0.763834i
$121$	1.90136e8			0.887000
$122$	−1.43561e8	−	5.54282e7i	−0.648034	−	0.250203i
$123$	−3.68808e8			−1.61131
$124$	2.71216e8	−	2.98873e8i	1.14717	−	1.26415i
$125$	−2.42517e8	−	2.81091e7i	−0.993350	−	0.115135i
$126$	−3.13644e6	−	1.21096e6i	−0.0124439	−	0.00480451i
$127$	−1.32074e8			−0.507693			−0.253847	−	0.967244i	$-0.581696\pi$
$127$	−1.32074e8			−0.507693			−0.253847	+	0.967244i	$0.581696\pi$
$128$	2.27097e8	−	1.43125e8i	0.846000	−	0.533182i
$129$	2.99666e8			1.08213
$130$	−2.42637e8	+	2.84383e7i	−0.849539	+	0.0995704i
$131$		−	1.86805e8i		−	0.634312i	−0.948373	−	0.317156i	$-0.897272\pi$
$131$		−	1.86805e8i		−	0.634312i	0.948373	−	0.317156i	$-0.102728\pi$
$132$	−6.43770e7	+	7.09416e7i	−0.212049	+	0.233671i
$133$			3.77723e7i			0.120717i
$134$	1.24385e8	+	4.80246e7i	0.385789	+	0.148951i
$135$	1.62678e8	+	3.08595e8i	0.489770	+	0.929082i
$136$	−2.27701e8	+	1.14353e8i	−0.665594	+	0.334265i
$137$		−	6.43086e7i		−	0.182552i	−0.995826	−	0.0912760i	$-0.970905\pi$
$137$		−	6.43086e7i		−	0.182552i	0.995826	−	0.0912760i	$-0.0290945\pi$
$138$	3.29455e8	+	1.27201e8i	0.908406	+	0.350731i
$139$		−	3.09364e8i		−	0.828725i	−0.910112	−	0.414363i	$-0.864004\pi$
$139$		−	3.09364e8i		−	0.828725i	0.910112	−	0.414363i	$-0.135996\pi$
$140$	1.07391e7	−	4.17460e7i	0.0279548	−	0.108668i
$141$	2.24773e7			0.0568680
$142$	−1.60626e8	+	4.16027e8i	−0.395059	+	1.02322i
$143$	−1.20235e8			−0.287532
$144$	−4.94786e6	−	5.08764e7i	−0.0115071	−	0.118322i
$145$	−2.37617e8	−	4.50753e8i	−0.537533	−	1.01969i
$146$	−1.48099e8	+	3.83582e8i	−0.325942	+	0.844202i
$147$	4.32797e8			0.926861
$148$	3.91779e8	−	4.31729e8i	0.816571	−	0.899837i
$149$	−3.41456e8			−0.692771			−0.346385	−	0.938092i	$-0.612591\pi$
$149$	−3.41456e8			−0.692771			−0.346385	+	0.938092i	$0.612591\pi$
$150$	−3.91719e8	+	2.69031e8i	−0.773766	+	0.531418i
$151$		−	4.63956e7i		−	0.0892419i	−0.999004	−	0.0446210i	$-0.985792\pi$
$151$		−	4.63956e7i		−	0.0892419i	0.999004	−	0.0446210i	$-0.0142080\pi$
$152$	−5.13198e8	+	2.57731e8i	−0.961415	+	0.482827i
$153$			4.85204e7i			0.0885439i
$154$	7.64120e6	−	1.97910e7i	0.0135856	−	0.0351872i
$155$	8.71628e8	−	4.59483e8i	1.51009	−	0.796054i
$156$	−3.19551e8	+	3.52135e8i	−0.539562	+	0.594581i
$157$			7.30948e8i			1.20306i	0.798850	+	0.601530i	$0.205442\pi$
$157$			7.30948e8i			1.20306i	−0.798850	+	0.601530i	$0.794558\pi$
$158$	−1.33168e8	+	3.44909e8i	−0.213683	+	0.553448i
$159$		−	3.43378e8i		−	0.537259i
$160$	6.40463e8	−	1.38936e8i	0.977270	−	0.212000i
$161$	−7.82090e7			−0.116400
$162$	5.57057e8	+	2.15077e8i	0.808797	+	0.312272i
$163$	−6.51678e8			−0.923172			−0.461586	−	0.887095i	$-0.652720\pi$
$163$	−6.51678e8			−0.923172			−0.461586	+	0.887095i	$0.652720\pi$
$164$	9.19571e8	+	8.34479e8i	1.27119	+	1.15356i
$165$	−2.06893e8	+	1.09065e8i	−0.279132	+	0.147146i
$166$	5.72956e8	+	2.21216e8i	0.754552	+	0.291329i
$167$	3.56907e8			0.458869			0.229435	−	0.973324i	$-0.426312\pi$
$167$	3.56907e8			0.458869			0.229435	+	0.973324i	$0.426312\pi$
$168$	−3.76543e7	−	7.49780e7i	−0.0472691	−	0.0941232i
$169$	2.18917e8			0.268370
$170$	−6.17847e8	+	7.24150e7i	−0.739751	+	0.0867027i
$171$			1.09356e8i			0.127897i
$172$	−7.47177e8	−	6.78037e8i	−0.853708	−	0.774711i
$173$			9.32893e8i			1.04147i	0.853718	+	0.520736i	$0.174342\pi$
$173$			9.32893e8i			1.04147i	−0.853718	+	0.520736i	$0.825658\pi$
$174$	−9.25242e8	−	3.57231e8i	−1.00939	−	0.389720i
$175$	5.94672e7	−	8.68249e7i	0.0634052	−	0.0925746i
$176$	3.21031e8	−	3.12211e7i	0.334577	−	0.0325385i
$177$		−	1.71369e9i		−	1.74598i
$178$	6.51027e7	+	2.51358e7i	0.0648513	+	0.0250388i
$179$		−	5.60470e7i		−	0.0545934i	−0.999627	−	0.0272967i	$-0.991310\pi$
$179$		−	5.60470e7i		−	0.0545934i	0.999627	−	0.0272967i	$-0.00868989\pi$
$180$	3.10913e7	−	1.20861e8i	0.0296175	−	0.115132i
$181$	−5.45998e8			−0.508718			−0.254359	−	0.967110i	$-0.581864\pi$
$181$	−5.45998e8			−0.508718			−0.254359	+	0.967110i	$0.581864\pi$
$182$	3.79289e7	−	9.82372e7i	0.0345688	−	0.0895345i
$183$	−7.31295e8			−0.652061
$184$	−5.33641e8	−	1.06260e9i	−0.465563	−	0.927037i
$185$	1.25909e9	−	6.63735e8i	1.07490	−	0.566640i
$186$	6.90783e8	−	1.78915e9i	0.577152	−	1.49484i
$187$	−3.06164e8			−0.250373
$188$	−5.60441e7	−	5.08580e7i	−0.0448640	−	0.0407125i
$189$	−1.50372e8			−0.117847
$190$	−1.39252e9	+	1.63211e8i	−1.06853	+	0.125237i
$191$		−	6.78515e8i		−	0.509831i	−0.966963	−	0.254915i	$-0.917952\pi$
$191$		−	6.78515e8i		−	0.509831i	0.966963	−	0.254915i	$-0.0820476\pi$
$192$	7.61772e8	−	1.02319e9i	0.560558	−	0.752924i
$193$		−	1.34018e9i		−	0.965903i	−0.875647	−	0.482952i	$-0.839565\pi$
$193$		−	1.34018e9i		−	0.965903i	0.875647	−	0.482952i	$-0.160435\pi$
$194$	−5.93340e8	+	1.53677e9i	−0.418887	+	1.08493i
$195$	−1.02696e9	+	5.41369e8i	−0.710258	+	0.374416i
$196$	−1.07912e9	−	9.79264e8i	−0.731215	−	0.663553i
$197$			4.55148e8i			0.302196i	0.988519	+	0.151098i	$0.0482808\pi$
$197$			4.55148e8i			0.302196i	−0.988519	+	0.151098i	$0.951719\pi$
$198$	2.21224e7	−	5.72978e7i	0.0143937	−	0.0372801i
$199$			2.71338e9i			1.73021i	0.501592	+	0.865105i	$0.332748\pi$
$199$			2.71338e9i			1.73021i	−0.501592	+	0.865105i	$0.667252\pi$
$200$	1.58542e9	+	2.15529e8i	0.990886	+	0.134705i
$201$	6.33614e8			0.388187
$202$	1.04872e9	+	4.04904e8i	0.629873	+	0.243191i
$203$	2.19642e8			0.129340
$204$	−8.13700e8	+	8.96673e8i	−0.469833	+	0.517742i
$205$	1.41374e9	+	2.68182e9i	0.800485	+	1.51850i
$206$	2.99216e9	+	1.15526e9i	1.66156	+	0.641521i
$207$	−2.26427e8			−0.123324
$208$	1.59351e9	−	1.54973e8i	0.851337	−	0.0827948i
$209$	−6.90040e8			−0.361651
$210$	−2.38450e7	−	2.03446e8i	−0.0122608	−	0.104610i
$211$			2.29774e9i			1.15923i	0.814890	+	0.579616i	$0.196797\pi$
$211$			2.29774e9i			1.15923i	−0.814890	+	0.579616i	$0.803203\pi$
$212$	−7.76940e8	+	8.56165e8i	−0.384631	+	0.423852i
$213$			2.11923e9i			1.02958i
$214$	−1.61580e9	−	6.23854e8i	−0.770431	−	0.297459i
$215$	−1.14870e9	−	2.17906e9i	−0.537592	−	1.01980i
$216$	−1.02603e9	−	2.04304e9i	−0.471350	−	0.938561i
$217$			4.24725e8i			0.191544i
$218$	−1.20935e9	−	4.66926e8i	−0.535461	−	0.206739i
$219$			1.95395e9i			0.849449i
$220$	7.62634e8	+	1.96186e8i	0.325556	+	0.0837487i
$221$	−1.51972e9			−0.637080
$222$	9.97853e8	−	2.58447e9i	0.410823	−	1.06405i
$223$	4.71324e9			1.90590			0.952950	−	0.303127i	$-0.0980307\pi$
$223$	4.71324e9			1.90590			0.952950	+	0.303127i	$0.0980307\pi$
$224$	−7.57624e7	+	2.72145e8i	−0.0300927	+	0.108096i
$225$	1.72166e8	−	2.51371e8i	0.0671765	−	0.0980809i
$226$	3.55113e8	−	9.19755e8i	0.136123	−	0.352564i
$227$	−1.92423e8			−0.0724692			−0.0362346	−	0.999343i	$-0.511536\pi$
$227$	−1.92423e8			−0.0724692			−0.0362346	+	0.999343i	$0.511536\pi$
$228$	−1.83394e9	+	2.02094e9i	−0.678648	+	0.747850i
$229$	−2.77871e9			−1.01042			−0.505210	−	0.862996i	$-0.668585\pi$
$229$	−2.77871e9			−1.01042			−0.505210	+	0.862996i	$0.668585\pi$
$230$	−3.37934e8	−	2.88326e9i	−0.120759	−	1.03032i
$231$		−	1.00814e8i		−	0.0354059i
$232$	1.49868e9	+	2.98420e9i	0.517316	+	1.03009i
$233$		−	4.21986e9i		−	1.43177i	−0.698217	−	0.715886i	$-0.746023\pi$
$233$		−	4.21986e9i		−	1.43177i	0.698217	−	0.715886i	$-0.253977\pi$
$234$	1.09810e8	−	2.84411e8i	0.0366250	−	0.0948600i
$235$	−8.61615e7	−	1.63446e8i	−0.0282515	−	0.0535924i
$236$	−3.87747e9	+	4.27286e9i	−1.24997	+	1.37743i
$237$			1.75695e9i			0.556887i
$238$	9.65817e7	−	2.50150e8i	0.0301014	−	0.0779638i
$239$		−	5.37346e9i		−	1.64688i	−0.567401	−	0.823441i	$-0.692051\pi$
$239$		−	5.37346e9i		−	1.64688i	0.567401	−	0.823441i	$-0.307949\pi$
$240$	2.60145e9	−	1.71214e9i	0.784097	−	0.516053i
$241$	3.26342e9			0.967396			0.483698	−	0.875235i	$-0.339293\pi$
$241$	3.26342e9			0.967396			0.483698	+	0.875235i	$0.339293\pi$
$242$	−2.83800e9	−	1.09574e9i	−0.827466	−	0.319481i
$243$	−8.24440e8			−0.236447
$244$	1.82338e9	+	1.65466e9i	0.514421	+	0.466819i
$245$	−1.65903e9	−	3.14713e9i	−0.460457	−	0.873474i
$246$	5.50487e9	+	2.12540e9i	1.50316	+	0.580364i
$247$	−3.42518e9			−0.920227
$248$	−5.77058e9	+	2.89801e9i	−1.52550	+	0.766115i
$249$	2.91862e9			0.759241
$250$	3.45785e9	+	1.81716e9i	0.885209	+	0.465193i
$251$		−	6.76390e9i		−	1.70413i	−0.523437	−	0.852065i	$-0.675350\pi$
$251$		−	6.76390e9i		−	1.70413i	0.523437	−	0.852065i	$-0.324650\pi$
$252$	3.98362e7	+	3.61500e7i	0.00987816	+	0.00896409i
$253$		−	1.42875e9i		−	0.348719i
$254$	1.97135e9	+	7.61127e8i	0.473618	+	0.182862i
$255$	−2.61504e9	+	1.37853e9i	−0.618470	+	0.326030i
$256$	−4.21448e9	+	8.27567e8i	−0.981261	+	0.192683i
$257$		−	1.59340e9i		−	0.365252i	−0.983182	−	0.182626i	$-0.941540\pi$
$257$		−	1.59340e9i		−	0.365252i	0.983182	−	0.182626i	$-0.0584598\pi$
$258$	−4.47285e9	−	1.72695e9i	−1.00950	−	0.389763i
$259$			6.13526e8i			0.136343i
$260$	3.78551e9	+	9.73818e8i	0.828383	+	0.213100i
$261$	6.35896e8			0.137033
$262$	−1.07654e9	+	2.78827e9i	−0.228467	+	0.591738i
$263$	8.22403e9			1.71894			0.859472	−	0.511182i	$-0.170792\pi$
$263$	8.22403e9			1.71894			0.859472	+	0.511182i	$0.170792\pi$
$264$	1.36973e9	−	6.87884e8i	0.281980	−	0.141612i
$265$	−2.49691e9	+	1.31626e9i	−0.506313	+	0.266905i
$266$	2.17678e8	−	5.63794e8i	0.0434799	−	0.112614i
$267$	3.31631e8			0.0652543
$268$	−1.57983e9	−	1.43364e9i	−0.306247	−	0.277908i
$269$	−2.60732e9			−0.497950			−0.248975	−	0.968510i	$-0.580094\pi$
$269$	−2.60732e9			−0.497950			−0.248975	+	0.968510i	$0.580094\pi$
$270$	−6.49742e8	−	5.54362e9i	−0.122260	−	1.04313i
$271$		−	8.05765e8i		−	0.149393i	−0.997206	−	0.0746966i	$-0.976201\pi$
$271$		−	8.05765e8i		−	0.149393i	0.997206	−	0.0746966i	$-0.0237988\pi$
$272$	4.05770e9	−	3.94622e8i	0.741317	−	0.0720950i
$273$		−	5.00417e8i		−	0.0900909i
$274$	−3.70604e8	+	9.59877e8i	−0.0657518	+	0.170300i
$275$	1.58615e9	+	1.08637e9i	0.277341	+	0.189953i
$276$	−4.18444e9	−	3.79723e9i	−0.721109	−	0.654382i
$277$			6.77281e9i			1.15040i	0.818012	+	0.575201i	$0.195076\pi$
$277$			6.77281e9i			1.15040i	−0.818012	+	0.575201i	$0.804924\pi$
$278$	−1.78283e9	+	4.61760e9i	−0.298491	+	0.773103i
$279$			1.22964e9i			0.202937i
$280$	−4.00871e8	+	5.61218e8i	−0.0652188	+	0.0913060i
$281$	−5.90712e8			−0.0947437			−0.0473719	−	0.998877i	$-0.515085\pi$
$281$	−5.90712e8			−0.0947437			−0.0473719	+	0.998877i	$0.515085\pi$
$282$	−3.35499e8	−	1.29534e8i	−0.0530511	−	0.0204828i
$283$	4.02477e9			0.627473			0.313736	−	0.949510i	$-0.398419\pi$
$283$	4.02477e9			0.627473			0.313736	+	0.949510i	$0.398419\pi$
$284$	4.79504e9	−	5.28400e9i	0.737088	−	0.812249i
$285$	−5.89385e9	+	3.10697e9i	−0.893346	+	0.470932i
$286$	1.79464e9	+	6.92901e8i	0.268233	+	0.103564i
$287$	−1.30679e9			−0.192610
$288$	−2.19343e8	+	7.87901e8i	−0.0318826	+	0.114525i
$289$	3.10597e9			0.445251
$290$	9.49053e8	+	8.09736e9i	0.134183	+	1.14486i
$291$			7.82826e9i			1.09167i
$292$	4.42109e9	−	4.87191e9i	0.608132	−	0.670143i
$293$			1.60835e9i			0.218228i	0.994029	+	0.109114i	$0.0348014\pi$
$293$			1.60835e9i			0.218228i	−0.994029	+	0.109114i	$0.965199\pi$
$294$	−6.45998e9	−	2.49417e9i	−0.864653	−	0.333838i
$295$	−1.24613e10	+	6.56904e9i	−1.64541	+	0.867389i
$296$	−8.33574e9	+	4.18625e9i	−1.08587	+	0.545329i
$297$		−	2.74705e9i		−	0.353054i
$298$	5.09661e9	+	1.96778e9i	0.646274	+	0.249523i
$299$		−	7.09196e9i		−	0.887323i
$300$	7.39724e9	−	1.75814e9i	0.913240	−	0.217055i
$301$	1.06181e9			0.129354
$302$	−2.67373e8	+	6.92506e8i	−0.0321433	+	0.0832522i
$303$	5.34212e9			0.633787
$304$	9.14533e9	−	8.89408e8i	1.07079	−	0.104137i
$305$	2.80325e9	+	5.31769e9i	0.323938	+	0.614502i
$306$	2.79618e8	−	7.24221e8i	0.0318918	−	0.0826010i
$307$	−3.34245e9			−0.376281			−0.188140	−	0.982142i	$-0.560246\pi$
$307$	−3.34245e9			−0.376281			−0.188140	+	0.982142i	$0.560246\pi$
$308$	−2.28107e8	+	2.51367e8i	−0.0253475	+	0.0279322i
$309$	1.52420e10			1.67189
$310$	−1.56580e10	+	1.83520e9i	−1.69546	+	0.198717i
$311$			1.24714e10i			1.33313i	0.745447	+	0.666565i	$0.232236\pi$
$311$			1.24714e10i			1.33313i	−0.745447	+	0.666565i	$0.767764\pi$
$312$	6.79897e9	−	3.41448e9i	0.717505	−	0.360334i
$313$		−	8.98981e9i		−	0.936641i	−0.883559	−	0.468320i	$-0.844859\pi$
$313$		−	8.98981e9i		−	0.936641i	0.883559	−	0.468320i	$-0.155141\pi$
$314$	4.21238e9	−	1.09102e10i	0.433320	−	1.12231i
$315$	6.12437e7	+	1.16178e8i	0.00622042	+	0.0118000i
$316$	3.97536e9	−	4.38073e9i	0.398683	−	0.439337i
$317$		−	8.64005e9i		−	0.855617i	−0.903869	−	0.427808i	$-0.859286\pi$
$317$		−	8.64005e9i		−	0.855617i	0.903869	−	0.427808i	$-0.140714\pi$
$318$	−1.97885e9	+	5.12529e9i	−0.193510	+	0.501199i
$319$			4.01251e9i			0.387484i
$320$	−1.03603e10	−	1.61715e9i	−0.988036	−	0.154223i
$321$	−8.23084e9			−0.775219
$322$	1.16736e9	+	4.50711e8i	0.108588	+	0.0419251i
$323$	−8.72183e9			−0.801304
$324$	−7.07523e9	−	6.42053e9i	−0.642038	−	0.582627i
$325$	7.87324e9	+	5.39246e9i	0.705700	+	0.483340i
$326$	9.72703e9	+	3.75556e9i	0.861211	+	0.332509i
$327$	−6.16040e9			−0.538788
$328$	−8.91661e9	−	1.77549e10i	−0.770379	−	1.53399i
$329$	7.96437e7			0.00679780
$330$	3.71664e9	−	4.35610e8i	0.313397	−	0.0367318i
$331$		−	3.86145e9i		−	0.321690i	−0.986980	−	0.160845i	$-0.948578\pi$
$331$		−	3.86145e9i		−	0.321690i	0.986980	−	0.160845i	$-0.0514220\pi$
$332$	−7.27717e9	−	6.60378e9i	−0.598977	−	0.543551i
$333$			1.77625e9i			0.144453i
$334$	−5.32723e9	−	2.05682e9i	−0.428071	−	0.165276i
$335$	−2.42881e9	−	4.60739e9i	−0.192848	−	0.365827i
$336$	1.29942e8	+	1.33613e9i	0.0101951	+	0.104831i
$337$			4.45880e8i			0.0345699i	0.999851	+	0.0172850i	$0.00550225\pi$
$337$			4.45880e8i			0.0345699i	−0.999851	+	0.0172850i	$0.994498\pi$
$338$	−3.26759e9	−	1.26160e9i	−0.250357	−	0.0966617i
$339$		−	4.68520e9i		−	0.354755i
$340$	9.63938e9	+	2.47972e9i	0.721329	+	0.185561i
$341$	−7.75905e9			−0.573841
$342$	6.30210e8	−	1.63227e9i	0.0460660	−	0.119313i
$343$	3.08661e9			0.223000
$344$	7.24499e9	+	1.44264e10i	0.517373	+	1.03020i
$345$	−6.43311e9	−	1.22034e10i	−0.454093	−	0.861402i
$346$	5.37617e9	−	1.39245e10i	0.375118	−	0.971570i
$347$	1.67673e10			1.15650			0.578250	−	0.815860i	$-0.303736\pi$
$347$	1.67673e10			1.15650			0.578250	+	0.815860i	$0.303736\pi$
$348$	1.17516e10	+	1.06642e10i	0.801271	+	0.727125i
$349$	−1.17880e10			−0.794581			−0.397290	−	0.917693i	$-0.630049\pi$
$349$	−1.17880e10			−0.794581			−0.397290	+	0.917693i	$0.630049\pi$
$350$	−1.38798e9	+	9.53255e8i	−0.0924933	+	0.0635239i
$351$		−	1.36356e10i		−	0.898353i
$352$	−4.97166e9	−	1.38406e9i	−0.323840	−	0.0901537i
$353$			2.63254e10i			1.69542i	0.530462	+	0.847709i	$0.322018\pi$
$353$			2.63254e10i			1.69542i	−0.530462	+	0.847709i	$0.677982\pi$
$354$	−9.87584e9	+	2.55788e10i	−0.628870	+	1.62880i
$355$	1.54102e10	−	8.12355e9i	0.970273	−	0.511485i
$356$	−8.26875e8	−	7.50360e8i	−0.0514802	−	0.0467165i
$357$		−	1.27425e9i		−	0.0784483i
$358$	−3.22993e8	+	8.36564e8i	−0.0196635	+	0.0509292i
$359$		−	4.45286e7i		−	0.00268078i	−0.999999	−	0.00134039i	$-0.999573\pi$
$359$		−	4.45286e7i		−	0.00268078i	0.999999	−	0.00134039i	$-0.000426660\pi$
$360$	−1.16058e9	+	1.62481e9i	−0.0690980	+	0.0967368i
$361$	−2.67390e9			−0.157440
$362$	8.14964e9	+	3.14653e9i	0.474574	+	0.183231i
$363$	−1.44566e10			−0.832609
$364$	−1.13226e9	+	1.24772e9i	−0.0644973	+	0.0710741i
$365$	1.42084e10	−	7.49001e9i	0.800521	−	0.421999i
$366$	1.09154e10	+	4.21438e9i	0.608296	+	0.234860i
$367$	6.18488e9			0.340931			0.170466	−	0.985364i	$-0.445473\pi$
$367$	6.18488e9			0.340931			0.170466	+	0.985364i	$0.445473\pi$
$368$	1.84155e9	+	1.89358e10i	0.100414	+	1.03250i
$369$	−3.78336e9			−0.204067
$370$	−2.26183e10	+	2.65099e9i	−1.20685	+	0.141449i
$371$		−	1.21669e9i		−	0.0642220i
$372$	−2.06214e10	+	2.27242e10i	−1.07683	+	1.18663i
$373$		−	2.46497e10i		−	1.27344i	−0.771097	−	0.636718i	$-0.780292\pi$
$373$		−	2.46497e10i		−	1.27344i	0.771097	−	0.636718i	$-0.219708\pi$
$374$	4.56984e9	+	1.76439e9i	0.233569	+	0.0901798i
$375$	1.84393e10	+	2.13722e9i	0.932437	+	0.108075i
$376$	5.43431e8	+	1.08209e9i	0.0271890	+	0.0541392i
$377$			1.99171e10i			0.985961i
$378$	2.24447e9	+	8.66577e8i	0.109937	+	0.0424463i
$379$			7.22927e9i			0.350378i	0.984535	+	0.175189i	$0.0560537\pi$
$379$			7.22927e9i			0.350378i	−0.984535	+	0.175189i	$0.943946\pi$
$380$	2.17255e10	+	5.58885e9i	1.04192	+	0.268033i
$381$	1.00420e10			0.476561
$382$	−3.91021e9	+	1.01276e10i	−0.183631	+	0.475612i
$383$	−1.40958e9			−0.0655080			−0.0327540	−	0.999463i	$-0.510428\pi$
$383$	−1.40958e9			−0.0655080			−0.0327540	+	0.999463i	$0.510428\pi$
$384$	−1.72668e10	+	1.08822e10i	−0.794123	+	0.500487i
$385$	−7.33083e8	+	3.86449e8i	−0.0333665	+	0.0175893i
$386$	−7.72332e9	+	2.00037e10i	−0.347900	+	0.901074i
$387$	3.07408e9			0.137048
$388$	1.77125e10	−	1.95187e10i	0.781545	−	0.861239i
$389$	−1.52530e10			−0.666126			−0.333063	−	0.942904i	$-0.608082\pi$
$389$	−1.52530e10			−0.666126			−0.333063	+	0.942904i	$0.608082\pi$
$390$	1.84484e10	−	2.16225e9i	0.797445	−	0.0934648i
$391$		−	1.80589e10i		−	0.772652i
$392$	1.04637e10	+	2.08355e10i	0.443139	+	0.882387i
$393$			1.42033e10i			0.595416i
$394$	2.62297e9	−	6.79360e9i	0.108845	−	0.281913i
$395$	1.27759e10	−	6.73487e9i	0.524811	−	0.276657i
$396$	−6.60403e8	+	7.27744e8i	−0.0268552	+	0.0295936i
$397$		−	1.60867e10i		−	0.647597i	−0.946126	−	0.323799i	$-0.895040\pi$
$397$		−	1.60867e10i		−	0.647597i	0.946126	−	0.323799i	$-0.104960\pi$
$398$	1.56369e10	−	4.05003e10i	0.623189	−	1.61408i
$399$		−	2.87194e9i		−	0.113314i
$400$	−2.24221e10	−	1.23536e10i	−0.875861	−	0.482563i
$401$	2.11434e9			0.0817706			0.0408853	−	0.999164i	$-0.486982\pi$
$401$	2.11434e9			0.0817706			0.0408853	+	0.999164i	$0.486982\pi$
$402$	−9.45740e9	−	3.65146e9i	−0.362133	−	0.139818i
$403$	−3.85139e10			−1.46015
$404$	−1.33199e10	−	1.20873e10i	−0.500005	−	0.453737i
$405$	−1.08774e10	−	2.06341e10i	−0.404300	−	0.766947i
$406$	−3.27841e9	−	1.26578e9i	−0.120659	−	0.0465857i
$407$	−1.12081e10			−0.408466
$408$	1.73128e10	−	8.69458e9i	0.624780	−	0.313767i
$409$	−2.44741e10			−0.874606			−0.437303	−	0.899314i	$-0.644066\pi$
$409$	−2.44741e10			−0.874606			−0.437303	+	0.899314i	$0.644066\pi$
$410$	−5.64653e9	−	4.81764e10i	−0.199824	−	1.70490i
$411$			4.88958e9i			0.171358i
$412$	−3.80037e10	−	3.44871e10i	−1.31898	−	1.19693i
$413$		−	6.07212e9i		−	0.208709i
$414$	3.37967e9	+	1.30487e9i	0.115046	+	0.0444188i
$415$	−1.11878e10	−	2.12230e10i	−0.377184	−	0.715509i
$416$	−2.46780e10	−	6.87010e9i	−0.824019	−	0.229398i
$417$			2.35219e10i			0.777908i
$418$	1.02996e10	+	3.97663e9i	0.337377	+	0.130260i
$419$			5.33721e10i			1.73164i	0.500355	+	0.865821i	$0.333203\pi$
$419$			5.33721e10i			1.73164i	−0.500355	+	0.865821i	$0.666797\pi$
$420$	−8.16527e8	+	3.17408e9i	−0.0262406	+	0.102005i
$421$	5.93005e10			1.88769			0.943843	−	0.330393i	$-0.107181\pi$
$421$	5.93005e10			1.88769			0.943843	+	0.330393i	$0.107181\pi$
$422$	1.32416e10	−	3.42963e10i	0.417534	−	1.08143i
$423$	2.30580e8			0.00720213
$424$	1.65307e10	−	8.30179e9i	0.511479	−	0.256867i
$425$	2.00483e10	+	1.37313e10i	0.614501	+	0.420877i
$426$	1.22129e10	−	3.16318e10i	0.370834	−	0.960474i
$427$	−2.59119e9			−0.0779450
$428$	2.05225e10	+	1.86234e10i	0.611582	+	0.554989i
$429$	9.14181e9			0.269900
$430$	4.58796e9	+	3.91447e10i	0.134198	+	1.14498i
$431$			4.56118e10i			1.32181i	0.750471	+	0.660904i	$0.229827\pi$
$431$			4.56118e10i			1.32181i	−0.750471	+	0.660904i	$0.770173\pi$
$432$	3.54073e9	+	3.64076e10i	0.101662	+	1.04534i
$433$			3.14117e10i			0.893592i	0.894636	+	0.446796i	$0.147435\pi$
$433$			3.14117e10i			0.893592i	−0.894636	+	0.446796i	$0.852565\pi$
$434$	2.44765e9	−	6.33950e9i	0.0689906	−	0.178688i
$435$	1.80667e10	+	3.42721e10i	0.504572	+	0.957159i
$436$	1.53601e10	+	1.39388e10i	0.425059	+	0.385726i
$437$		−	4.07015e10i		−	1.11605i
$438$	1.12604e10	−	2.91649e10i	0.305955	−	0.792436i
$439$			7.72222e9i			0.207914i	0.994582	+	0.103957i	$0.0331505\pi$
$439$			7.72222e9i			0.207914i	−0.994582	+	0.103957i	$0.966850\pi$
$440$	−1.02526e10	−	7.32328e9i	−0.273540	−	0.195387i
$441$	4.43979e9			0.117384
$442$	2.26835e10	+	8.75798e9i	0.594321	+	0.229464i
$443$	−6.84724e10			−1.77787			−0.888936	−	0.458031i	$-0.848555\pi$
$443$	−6.84724e10			−1.77787			−0.888936	+	0.458031i	$0.848555\pi$
$444$	−2.97881e10	+	3.28256e10i	−0.766499	+	0.844659i
$445$	−1.27123e9	−	2.41149e9i	−0.0324178	−	0.0614957i
$446$	−7.03504e10	−	2.71619e10i	−1.77798	−	0.686469i
$447$	2.59619e10			0.650290
$448$	2.69918e9	−	3.62546e9i	0.0670071	−	0.0900019i
$449$	8.66689e9			0.213244			0.106622	−	0.994300i	$-0.465996\pi$
$449$	8.66689e9			0.213244			0.106622	+	0.994300i	$0.465996\pi$
$450$	−4.01840e9	+	2.75981e9i	−0.0979947	+	0.0673022i
$451$		−	2.38731e10i		−	0.577035i
$452$	−1.06009e10	+	1.16819e10i	−0.253974	+	0.279872i
$453$			3.52760e9i			0.0837696i
$454$	2.87213e9	+	1.10891e9i	0.0676052	+	0.0261020i
$455$	−3.63883e9	+	1.91823e9i	−0.0849017	+	0.0447564i
$456$	3.90200e10	−	1.95960e10i	0.902461	−	0.453220i
$457$		−	1.83897e10i		−	0.421610i	−0.977528	−	0.210805i	$-0.932392\pi$
$457$		−	1.83897e10i		−	0.421610i	0.977528	−	0.210805i	$-0.0676085\pi$
$458$	4.14754e10	+	1.60135e10i	0.942603	+	0.363934i
$459$		−	3.47216e10i		−	0.782257i
$460$	−1.15719e10	+	4.49834e10i	−0.258449	+	1.00466i
$461$	−2.87493e10			−0.636536			−0.318268	−	0.948001i	$-0.603101\pi$
$461$	−2.87493e10			−0.636536			−0.318268	+	0.948001i	$0.603101\pi$
$462$	−5.80984e8	+	1.50477e9i	−0.0127525	+	0.0330295i
$463$	2.07879e9			0.0452362			0.0226181	−	0.999744i	$-0.492800\pi$
$463$	2.07879e9			0.0452362			0.0226181	+	0.999744i	$0.492800\pi$
$464$	−5.17182e9	−	5.31792e10i	−0.111576	−	1.14728i
$465$	−6.62725e10	+	3.49359e10i	−1.41750	+	0.747240i
$466$	−2.43186e10	+	6.29861e10i	−0.515698	+	1.33568i
$467$	4.03126e10			0.847565			0.423782	−	0.905764i	$-0.360702\pi$
$467$	4.03126e10			0.847565			0.423782	+	0.905764i	$0.360702\pi$
$468$	−3.27806e9	+	3.61233e9i	−0.0683336	+	0.0753016i
$469$	2.24508e9			0.0464025
$470$	3.44133e8	+	2.93616e9i	0.00705237	+	0.0601711i
$471$		−	5.55762e10i		−	1.12929i
$472$	8.24996e10	−	4.14317e10i	1.66220	−	0.834766i
$473$			1.93975e10i			0.387527i
$474$	1.01252e10	−	2.62245e10i	0.200580	−	0.519510i
$475$	4.51854e10	+	3.09479e10i	0.887613	+	0.607934i
$476$	−2.88318e9	+	3.17718e9i	−0.0561622	+	0.0618890i
$477$		−	3.52249e9i		−	0.0680419i
$478$	−3.09667e10	+	8.02049e10i	−0.593176	+	1.53635i
$479$			2.13503e9i			0.0405566i	0.999794	+	0.0202783i	$0.00645523\pi$
$479$			2.13503e9i			0.0405566i	−0.999794	+	0.0202783i	$0.993545\pi$
$480$	−4.86964e10	+	1.05637e10i	−0.917343	+	0.199000i
$481$	−5.56343e10			−1.03935
$482$	−4.87101e10	−	1.88067e10i	−0.902466	−	0.348438i
$483$	5.94647e9			0.109262
$484$	3.60456e10	+	3.27102e10i	0.656858	+	0.596076i
$485$	5.69240e10	−	3.00078e10i	1.02879	−	0.542335i
$486$	1.23057e10	+	4.75117e9i	0.220577	+	0.0851638i
$487$	1.67761e10			0.298246			0.149123	−	0.988819i	$-0.452355\pi$
$487$	1.67761e10			0.298246			0.149123	+	0.988819i	$0.452355\pi$
$488$	−1.76804e10	−	3.52056e10i	−0.311755	−	0.620772i
$489$	4.95491e10			0.866563
$490$	6.62623e9	+	5.65352e10i	0.114943	+	0.980697i
$491$			6.25998e10i			1.07708i	0.842601	+	0.538539i	$0.181024\pi$
$491$			6.25998e10i			1.07708i	−0.842601	+	0.538539i	$0.818976\pi$
$492$	−6.99178e10	−	6.34480e10i	−1.19324	−	1.08282i
$493$			5.07166e10i			0.858543i
$494$	5.11246e10	+	1.97390e10i	0.858464	+	0.331449i
$495$	−2.12238e9	+	1.11883e9i	−0.0353511	+	0.0186355i
$496$	1.02833e11	−	1.00008e10i	1.69905	−	0.165237i
$497$			7.50904e9i			0.123072i
$498$	−4.35636e10	−	1.68197e10i	−0.708283	−	0.273464i
$499$		−	1.09018e11i		−	1.75830i	−0.476541	−	0.879152i	$-0.658110\pi$
$499$		−	1.09018e11i		−	1.75830i	0.476541	−	0.879152i	$-0.341890\pi$
$500$	−4.11401e10	−	4.70504e10i	−0.658242	−	0.752806i
$501$	−2.71367e10			−0.430731
$502$	−3.89797e10	+	1.00959e11i	−0.613795	+	1.58975i
$503$	−1.07703e10			−0.168251			−0.0841253	−	0.996455i	$-0.526810\pi$
$503$	−1.07703e10			−0.168251			−0.0841253	+	0.996455i	$0.526810\pi$
$504$	−3.86271e8	−	7.69151e8i	−0.00598646	−	0.0119204i
$505$	−2.04778e10	−	3.88458e10i	−0.314860	−	0.597281i
$506$	−8.23377e9	+	2.13258e10i	−0.125602	+	0.325314i
$507$	−1.66450e10			−0.251913
$508$	−2.50383e10	−	2.27213e10i	−0.375967	−	0.341177i
$509$	4.21312e10			0.627671			0.313836	−	0.949477i	$-0.398386\pi$
$509$	4.21312e10			0.627671			0.313836	+	0.949477i	$0.398386\pi$
$510$	4.69768e10	−	5.50593e9i	0.694389	−	0.0813861i
$511$			6.92343e9i			0.101540i
$512$	6.76751e10	+	1.19353e10i	0.984802	+	0.173681i
$513$		−	7.82564e10i		−	1.12993i
$514$	−9.18262e9	+	2.37833e10i	−0.131557	+	0.340737i
$515$	−5.84265e10	−	1.10834e11i	−0.830579	−	1.57559i
$516$	5.68101e10	+	5.15532e10i	0.801359	+	0.727205i
$517$			1.45496e9i			0.0203653i
$518$	3.53569e9	−	9.15756e9i	0.0491083	−	0.127192i
$519$		−	7.09307e10i		−	0.977608i
$520$	−5.08910e10	−	3.63508e10i	−0.696029	−	0.497166i
$521$	−4.63258e10			−0.628741			−0.314371	−	0.949300i	$-0.601793\pi$
$521$	−4.63258e10			−0.628741			−0.314371	+	0.949300i	$0.601793\pi$
$522$	−9.49146e9	−	3.66461e9i	−0.127835	−	0.0493566i
$523$	1.01874e11			1.36163			0.680813	−	0.732457i	$-0.261626\pi$
$523$	1.01874e11			1.36163			0.680813	+	0.732457i	$0.261626\pi$
$524$	3.21370e10	−	3.54141e10i	0.426266	−	0.469733i
$525$	−4.52147e9	+	6.60156e9i	−0.0595172	+	0.0868979i
$526$	−1.22753e11	−	4.73943e10i	−1.60357	−	0.619132i
$527$	−9.80713e10			−1.27145
$528$	−2.44089e10	+	2.37383e9i	−0.314060	+	0.0305432i
$529$	5.96313e9			0.0761467
$530$	4.48546e10	−	5.25719e9i	0.568464	−	0.0666270i
$531$		−	1.75797e10i		−	0.221122i
$532$	−6.49818e9	+	7.16080e9i	−0.0811232	+	0.0893954i
$533$		−	1.18500e11i		−	1.46828i
$534$	−4.94996e9	−	1.91115e9i	−0.0608746	−	0.0235034i
$535$	3.15510e10	+	5.98514e10i	0.385122	+	0.730566i
$536$	1.53188e10	+	3.05031e10i	0.185595	+	0.369560i
$537$			4.26142e9i			0.0512457i
$538$	3.89172e10	+	1.50257e10i	0.464529	+	0.179352i
$539$			2.80151e10i			0.331923i
$540$	−2.22492e10	+	8.64891e10i	−0.261661	+	1.01715i
$541$	−7.60274e7			−0.000887526			−0.000443763	−	1.00000i	$-0.500141\pi$
$541$	−7.60274e7			−0.000887526			−0.000443763		1.00000i	$0.500141\pi$
$542$	−4.64354e9	+	1.20269e10i	−0.0538086	+	0.139366i
$543$	4.15139e10			0.477523
$544$	−6.28398e10	−	1.74939e10i	−0.717529	−	0.199752i
$545$	2.36145e10	+	4.47960e10i	0.267665	+	0.507754i
$546$	−2.88385e9	+	7.46928e9i	−0.0324491	+	0.0840442i
$547$	−1.66947e10			−0.186479			−0.0932395	−	0.995644i	$-0.529722\pi$
$547$	−1.66947e10			−0.186479			−0.0932395	+	0.995644i	$0.529722\pi$
$548$	1.10634e10	−	1.21915e10i	0.122677	−	0.135187i
$549$	−7.50188e9			−0.0825812
$550$	−1.74145e10	−	2.53561e10i	−0.190309	−	0.277097i
$551$			1.14306e11i			1.24012i
$552$	4.05744e10	+	8.07925e10i	0.437014	+	0.870191i
$553$			6.22541e9i			0.0665683i
$554$	3.90310e10	−	1.01092e11i	0.414353	−	1.07319i
$555$	−9.57322e10	+	5.04658e10i	−1.00899	+	0.531894i
$556$	5.32216e10	−	5.86486e10i	0.556915	−	0.613703i
$557$			1.53337e11i			1.59304i	0.604611	+	0.796521i	$0.293329\pi$
$557$			1.53337e11i			1.59304i	−0.604611	+	0.796521i	$0.706671\pi$
$558$	7.08630e9	−	1.83538e10i	0.0730942	−	0.189317i
$559$			9.62841e10i			0.986069i
$560$	9.21770e9	−	6.06662e9i	0.0937282	−	0.0616872i
$561$	2.32786e10			0.235020
$562$	8.81704e9	+	3.40421e9i	0.0883848	+	0.0341249i
$563$	1.35193e11			1.34562			0.672809	−	0.739816i	$-0.265088\pi$
$563$	1.35193e11			1.34562			0.672809	+	0.739816i	$0.265088\pi$
$564$	4.26120e9	+	3.86689e9i	0.0421130	+	0.0382160i
$565$	−3.40689e10	+	1.79596e10i	−0.334321	+	0.176239i
$566$	−6.00741e10	−	2.31943e10i	−0.585358	−	0.226004i
$567$	1.00545e10			0.0972815
$568$	−1.02023e11	+	5.12362e10i	−0.980173	+	0.492248i
$569$	1.12811e11			1.07623			0.538114	−	0.842872i	$-0.319137\pi$
$569$	1.12811e11			1.07623			0.538114	+	0.842872i	$0.319137\pi$
$570$	1.05877e11	−	1.24094e10i	1.00301	−	0.117558i
$571$		−	6.98949e10i		−	0.657508i	−0.944416	−	0.328754i	$-0.893371\pi$
$571$		−	6.98949e10i		−	0.657508i	0.944416	−	0.328754i	$-0.106629\pi$
$572$	−2.27939e10	−	2.06846e10i	−0.212928	−	0.193225i
$573$			5.15896e10i			0.478568i
$574$	1.95054e10	+	7.53093e9i	0.179683	+	0.0693746i
$575$	−6.40788e10	+	9.35581e10i	−0.586196	+	0.855874i
$576$	7.81453e9	−	1.04962e10i	0.0709926	−	0.0953551i
$577$			1.18742e11i			1.07128i	0.844447	+	0.535639i	$0.179929\pi$
$577$			1.18742e11i			1.07128i	−0.844447	+	0.535639i	$0.820071\pi$
$578$	−4.63600e10	−	1.78994e10i	−0.415367	−	0.160371i
$579$			1.01898e11i			0.906674i
$580$	3.24986e10	−	1.26331e11i	0.287179	−	1.11635i
$581$	1.03415e10			0.0907570
$582$	4.51135e10	−	1.16846e11i	0.393201	−	1.01840i
$583$	2.22270e10			0.192400
$584$	−9.40660e10	+	4.72404e10i	−0.808688	+	0.406127i
$585$	−1.05349e10	+	5.55355e9i	−0.0899516	+	0.0474185i
$586$	9.26877e9	−	2.40065e10i	0.0786017	−	0.203581i
$587$	−8.30860e10			−0.699802			−0.349901	−	0.936787i	$-0.613785\pi$
$587$	−8.30860e10			−0.699802			−0.349901	+	0.936787i	$0.613785\pi$
$588$	8.20488e10	+	7.44564e10i	0.686377	+	0.622863i
$589$	−2.21035e11			−1.83654
$590$	2.23856e11	−	2.62371e10i	1.84740	−	0.216525i
$591$		−	3.46063e10i		−	0.283665i
$592$	1.48545e11	−	1.44464e10i	1.20941	−	0.117618i
$593$			7.58629e9i			0.0613494i	0.999529	+	0.0306747i	$0.00976560\pi$
$593$			7.58629e9i			0.0613494i	−0.999529	+	0.0306747i	$0.990234\pi$
$594$	−1.58310e10	+	4.10028e10i	−0.127163	+	0.329358i
$595$	−9.26588e9	+	4.88456e9i	−0.0739297	+	0.0389724i
$596$	−6.47325e10	−	5.87425e10i	−0.513024	−	0.465551i
$597$		−	2.06307e11i		−	1.62411i
$598$	−4.08703e10	+	1.05855e11i	−0.319597	+	0.827768i
$599$		−	1.75895e10i		−	0.136630i	−0.997664	−	0.0683149i	$-0.978238\pi$
$599$		−	1.75895e10i		−	0.136630i	0.997664	−	0.0683149i	$-0.0217622\pi$
$600$	−1.20544e11	−	1.63873e10i	−0.930124	−	0.126445i
$601$	2.00060e11			1.53342			0.766712	−	0.641991i	$-0.221891\pi$
$601$	2.00060e11			1.53342			0.766712	+	0.641991i	$0.221891\pi$
$602$	−1.58486e10	−	6.11908e9i	−0.120672	−	0.0465908i
$603$	6.49984e9			0.0491625
$604$	7.98169e9	−	8.79558e9i	0.0599718	−	0.0660871i
$605$	5.54162e10	+	1.05123e11i	0.413633	+	0.784650i
$606$	−7.97372e10	−	3.07861e10i	−0.591249	−	0.228278i
$607$	−5.59570e10			−0.412192			−0.206096	−	0.978532i	$-0.566076\pi$
$607$	−5.59570e10			−0.412192			−0.206096	+	0.978532i	$0.566076\pi$
$608$	−1.41630e11	−	3.94282e10i	−1.03643	−	0.288531i
$609$	−1.67001e10			−0.121408
$610$	−1.11963e10	−	9.55273e10i	−0.0808640	−	0.689935i
$611$			7.22206e9i			0.0518199i
$612$	−8.34722e9	+	9.19840e9i	−0.0595027	+	0.0655702i
$613$		−	2.08451e10i		−	0.147626i	−0.997272	−	0.0738128i	$-0.976483\pi$
$613$		−	2.08451e10i		−	0.147626i	0.997272	−	0.0738128i	$-0.0235167\pi$
$614$	4.98899e10	+	1.92622e10i	0.351026	+	0.135529i
$615$	−1.07491e11	−	2.03907e11i	−0.751399	−	1.42539i
$616$	4.85335e9	−	2.43738e9i	0.0337069	−	0.0169278i
$617$		−	2.50664e11i		−	1.72962i	−0.502099	−	0.864810i	$-0.667439\pi$
$617$		−	2.50664e11i		−	1.72962i	0.502099	−	0.864810i	$-0.332561\pi$
$618$	−2.27503e11	−	8.78379e10i	−1.55967	−	0.602182i
$619$			1.12271e11i			0.764728i	0.924012	+	0.382364i	$0.124890\pi$
$619$			1.12271e11i			0.764728i	−0.924012	+	0.382364i	$0.875110\pi$
$620$	2.44289e11	+	6.28429e10i	1.65324	+	0.425294i
$621$	1.62033e11			1.08952
$622$	7.18713e10	−	1.86149e11i	0.480169	−	1.24365i
$623$	1.17507e9			0.00780027
$624$	−1.21160e11	+	1.17831e10i	−0.799133	+	0.0777178i
$625$	−5.51417e10	−	1.42276e11i	−0.361377	−	0.932420i
$626$	−5.18074e10	+	1.34183e11i	−0.337360	+	0.873776i
$627$	5.24659e10			0.339474
$628$	−1.25749e11	+	1.38572e11i	−0.808473	+	0.890914i
$629$	−1.41666e11			−0.905033
$630$	−2.44610e8	−	2.08702e9i	−0.00155279	−	0.0132485i
$631$		−	1.23902e11i		−	0.781557i	−0.920485	−	0.390778i	$-0.872206\pi$
$631$		−	1.23902e11i		−	0.781557i	0.920485	−	0.390778i	$-0.127794\pi$
$632$	−8.45823e10	+	4.24776e10i	−0.530165	+	0.266252i
$633$		−	1.74704e11i		−	1.08815i
$634$	−4.97917e10	+	1.28962e11i	−0.308177	+	0.798190i
$635$	−3.84935e10	−	7.30212e10i	−0.236751	−	0.449111i
$636$	5.90731e10	−	6.50968e10i	0.361045	−	0.397861i
$637$			1.39060e11i			0.844585i
$638$	2.31237e10	−	5.98913e10i	0.139564	−	0.361477i
$639$			2.17398e10i			0.130392i
$640$	1.45320e11	+	8.38432e10i	0.866173	+	0.499744i
$641$	−1.74761e11			−1.03517			−0.517587	−	0.855631i	$-0.673170\pi$
$641$	−1.74761e11			−1.03517			−0.517587	+	0.855631i	$0.673170\pi$
$642$	1.22855e11	+	4.74335e10i	0.723188	+	0.279219i
$643$	8.28548e10			0.484701			0.242350	−	0.970189i	$-0.422082\pi$
$643$	8.28548e10			0.484701			0.242350	+	0.970189i	$0.422082\pi$
$644$	−1.48267e10	−	1.34547e10i	−0.0861988	−	0.0782224i
$645$	8.73392e10	+	1.65680e11i	0.504627	+	0.957264i
$646$	1.30183e11	+	5.02630e10i	0.747523	+	0.288615i
$647$	2.02420e11			1.15515			0.577573	−	0.816339i	$-0.304000\pi$
$647$	2.02420e11			1.15515			0.577573	+	0.816339i	$0.304000\pi$
$648$	6.86049e10	+	1.36607e11i	0.389094	+	0.774772i
$649$	1.10928e11			0.625263
$650$	−8.64407e10	−	1.25861e11i	−0.484245	−	0.705080i
$651$		−	3.22932e10i		−	0.179799i
$652$	−1.23544e11	−	1.12112e11i	−0.683645	−	0.620384i
$653$			1.44813e11i			0.796445i	0.917289	+	0.398222i	$0.130373\pi$
$653$			1.44813e11i			0.796445i	−0.917289	+	0.398222i	$0.869627\pi$
$654$	9.19509e10	+	3.55018e10i	0.502626	+	0.194061i
$655$	1.03281e11	−	5.44452e10i	0.561120	−	0.295797i
$656$	3.07705e10	+	3.16398e11i	0.166157	+	1.70851i
$657$			2.00443e10i			0.107580i
$658$	−1.18877e9	−	4.58979e8i	−0.00634154	−	0.00244844i
$659$		−	2.54526e11i		−	1.34955i	−0.738021	−	0.674777i	$-0.764240\pi$
$659$		−	2.54526e11i		−	1.34955i	0.738021	−	0.674777i	$-0.235760\pi$
$660$	−5.79854e10	−	1.49167e10i	−0.305593	−	0.0786132i
$661$	−1.76697e10			−0.0925598			−0.0462799	−	0.998929i	$-0.514737\pi$
$661$	−1.76697e10			−0.0925598			−0.0462799	+	0.998929i	$0.514737\pi$
$662$	−2.22531e10	+	5.76364e10i	−0.115867	+	0.300099i
$663$	1.15549e11			0.598014
$664$	7.05630e10	+	1.40506e11i	0.362998	+	0.722809i
$665$	−2.08837e10	+	1.10089e10i	−0.106787	+	0.0562935i
$666$	1.02363e10	−	2.65125e10i	0.0520292	−	0.134758i
$667$	−2.36675e11			−1.19578
$668$	6.76617e10	+	6.14006e10i	0.339810	+	0.308366i
$669$	−3.58362e11			−1.78903
$670$	9.70079e9	+	8.27675e10i	0.0481402	+	0.410734i
$671$		−	4.73370e10i		−	0.233513i
$672$	5.76044e9	−	2.06920e10i	0.0282474	−	0.101467i
$673$			6.26058e10i			0.305179i	0.988290	+	0.152589i	$0.0487612\pi$
$673$			6.26058e10i			0.305179i	−0.988290	+	0.152589i	$0.951239\pi$
$674$	2.56956e9	−	6.65526e9i	0.0124514	−	0.0322497i
$675$	−1.23204e11	+	1.79883e11i	−0.593483	+	0.866513i
$676$	4.15019e10	+	3.76615e10i	0.198738	+	0.180348i
$677$			2.21751e11i			1.05563i	0.849361	+	0.527813i	$0.176988\pi$
$677$			2.21751e11i			1.05563i	−0.849361	+	0.527813i	$0.823012\pi$
$678$	−2.70003e10	+	6.99318e10i	−0.127776	+	0.330945i
$679$			2.77378e10i			0.130495i
$680$	−1.29588e11	−	9.25633e10i	−0.606080	−	0.432916i
$681$	1.46305e10			0.0680253
$682$	1.15813e11	+	4.47146e10i	0.535326	+	0.206687i
$683$	3.01557e11			1.38575			0.692877	−	0.721056i	$-0.256343\pi$
$683$	3.01557e11			1.38575			0.692877	+	0.721056i	$0.256343\pi$
$684$	−1.88132e10	+	2.07316e10i	−0.0859484	+	0.0947126i
$685$	3.55551e10	−	1.87431e10i	0.161488	−	0.0851291i
$686$	−4.60711e10	−	1.77878e10i	−0.208033	−	0.0803205i
$687$	2.11274e11			0.948461
$688$	−2.50019e10	−	2.57082e11i	−0.111588	−	1.14741i
$689$	1.10329e11			0.489567
$690$	2.56941e10	+	2.19223e11i	0.113354	+	0.967143i
$691$			2.55417e10i			0.112031i	0.998430	+	0.0560154i	$0.0178396\pi$
$691$			2.55417e10i			0.112031i	−0.998430	+	0.0560154i	$0.982160\pi$
$692$	−1.60491e11	+	1.76856e11i	−0.699883	+	0.771250i
$693$		−	1.03419e9i		−	0.00448402i
$694$	−2.50271e11	−	9.66283e10i	−1.07888	−	0.416550i
$695$	1.71042e11	−	9.01657e10i	0.733100	−	0.386458i
$696$	−1.13949e11	−	2.26898e11i	−0.485594	−	0.966925i
$697$		−	3.01746e11i		−	1.27853i
$698$	1.75949e11	+	6.79330e10i	0.741250	+	0.286193i
$699$			3.20849e11i			1.34398i
$700$	2.62106e10	−	6.22962e9i	0.109165	−	0.0259460i
$701$	−3.37969e11			−1.39960			−0.699801	−	0.714338i	$-0.746728\pi$
$701$	−3.37969e11			−1.39960			−0.699801	+	0.714338i	$0.746728\pi$
$702$	−7.85808e10	+	2.03527e11i	−0.323570	+	0.838058i
$703$	−3.19291e11			−1.30727
$704$	6.62315e10	+	4.93098e10i	0.269633	+	0.200744i
$705$	6.55112e9	+	1.24273e10i	0.0265191	+	0.0503061i
$706$	1.51711e11	−	3.92936e11i	0.610657	−	1.58162i
$707$	1.89287e10			0.0757607
$708$	2.94816e11	−	3.24878e11i	1.17332	−	1.29297i
$709$	2.92561e11			1.15780			0.578898	−	0.815400i	$-0.303483\pi$
$709$	2.92561e11			1.15780			0.578898	+	0.815400i	$0.303483\pi$
$710$	−2.76829e11	+	3.24459e10i	−1.08938	+	0.127681i
$711$			1.80235e10i			0.0705278i
$712$	8.01778e9	+	1.59652e10i	0.0311985	+	0.0621232i
$713$		−	4.57662e11i		−	1.77087i
$714$	−7.34340e9	+	1.90197e10i	−0.0282556	+	0.0731830i
$715$	−3.50430e10	−	6.64757e10i	−0.134084	−	0.254354i
$716$	9.64207e9	−	1.06253e10i	0.0366875	−	0.0404285i
$717$			4.08561e11i			1.54590i
$718$	−2.56614e8	+	6.64639e8i	−0.000965567	+	0.00250085i
$719$		−	2.61373e11i		−	0.978013i	−0.872280	−	0.489006i	$-0.837359\pi$
$719$		−	2.61373e11i		−	0.978013i	0.872280	−	0.489006i	$-0.162641\pi$
$720$	2.66866e10	−	1.75638e10i	0.0993031	−	0.0653563i
$721$	5.40068e10			0.199851
$722$	3.99109e10	+	1.54094e10i	0.146873	+	0.0567071i
$723$	−2.48127e11			−0.908075
$724$	−1.03509e11	−	9.39311e10i	−0.376726	−	0.341865i
$725$	1.79959e11	−	2.62748e11i	0.651360	−	0.951017i
$726$	2.15782e11	+	8.33122e10i	0.776726	+	0.299890i
$727$	−5.04144e11			−1.80475			−0.902375	−	0.430951i	$-0.858178\pi$
$727$	−5.04144e11			−1.80475			−0.902375	+	0.430951i	$0.858178\pi$
$728$	2.40908e10	−	1.20985e10i	0.0857680	−	0.0430731i
$729$	3.07547e11			1.08894
$730$	−2.55240e11	+	2.99155e10i	−0.898788	+	0.105343i
$731$			2.45177e11i			0.858637i
$732$	−1.38637e11	−	1.25809e11i	−0.482876	−	0.438194i
$733$			1.57768e11i			0.546517i	0.961941	+	0.273258i	$0.0881014\pi$
$733$			1.57768e11i			0.546517i	−0.961941	+	0.273258i	$0.911899\pi$
$734$	−9.23162e10	−	3.56428e10i	−0.318049	−	0.122797i
$735$	1.26141e11	+	2.39286e11i	0.432221	+	0.819913i
$736$	8.16377e10	−	2.93250e11i	0.278214	−	0.999372i
$737$			4.10141e10i			0.139015i
$738$	5.64709e10	+	2.18031e10i	0.190370	+	0.0735010i
$739$			4.21510e10i			0.141329i	0.997500	+	0.0706643i	$0.0225119\pi$
$739$			4.21510e10i			0.141329i	−0.997500	+	0.0706643i	$0.977488\pi$
$740$	3.52881e11	+	9.07782e10i	1.17680	+	0.302729i
$741$	2.60427e11			0.863799
$742$	−7.01165e9	+	1.81604e10i	−0.0231315	+	0.0599115i
$743$	−4.74544e11			−1.55712			−0.778558	−	0.627573i	$-0.784049\pi$
$743$	−4.74544e11			−1.55712			−0.778558	+	0.627573i	$0.784049\pi$
$744$	4.38755e11	−	2.20345e11i	1.43196	−	0.719136i
$745$	−9.95190e10	−	1.88785e11i	−0.323058	−	0.612833i
$746$	−1.42054e11	+	3.67925e11i	−0.458668	+	1.18797i
$747$	2.99402e10			0.0961552
$748$	−5.80420e10	−	5.26711e10i	−0.185411	−	0.168254i
$749$	−2.91643e10			−0.0926669
$750$	−2.62911e11	−	1.38164e11i	−0.830928	−	0.436668i
$751$			2.85992e11i			0.899070i	0.893263	+	0.449535i	$0.148410\pi$
$751$			2.85992e11i			0.899070i	−0.893263	+	0.449535i	$0.851590\pi$
$752$	−1.87534e9	−	1.92831e10i	−0.00586418	−	0.0602985i
$753$			5.14280e11i			1.59963i
$754$	1.14780e11	−	2.97284e11i	0.355125	−	0.919786i
$755$	2.56513e10	−	1.35222e10i	0.0789445	−	0.0416160i
$756$	−2.85072e10	−	2.58693e10i	−0.0872704	−	0.0791948i
$757$		−	2.51823e11i		−	0.766852i	−0.923572	−	0.383426i	$-0.874744\pi$
$757$		−	2.51823e11i		−	0.766852i	0.923572	−	0.383426i	$-0.125256\pi$
$758$	4.16615e10	−	1.07905e11i	0.126200	−	0.326862i
$759$			1.08633e11i			0.327335i
$760$	−2.92069e11	−	2.08621e11i	−0.875449	−	0.625323i
$761$	−4.27075e11			−1.27340			−0.636700	−	0.771111i	$-0.719701\pi$
$761$	−4.27075e11			−1.27340			−0.636700	+	0.771111i	$0.719701\pi$
$762$	−1.49888e11	−	5.78708e10i	−0.444576	−	0.171648i
$763$	−2.18281e10			−0.0644048
$764$	1.16729e11	−	1.28632e11i	0.342613	−	0.377550i
$765$	−2.68261e10	+	1.41415e10i	−0.0783270	+	0.0412905i
$766$	2.10395e10	+	8.12326e9i	0.0611113	+	0.0235947i
$767$	5.50617e11			1.59099
$768$	3.20440e11	−	6.29224e10i	0.921090	−	0.180867i
$769$	5.01477e11			1.43399			0.716995	−	0.697078i	$-0.245517\pi$
$769$	5.01477e11			1.43399			0.716995	+	0.697078i	$0.245517\pi$
$770$	1.31692e10	−	1.54349e9i	0.0374623	−	0.00439079i
$771$			1.21151e11i			0.342855i
$772$	2.30558e11	−	2.54068e11i	0.649100	−	0.715289i
$773$			3.56317e11i			0.997973i	0.866610	+	0.498987i	$0.166294\pi$
$773$			3.56317e11i			0.997973i	−0.866610	+	0.498987i	$0.833706\pi$
$774$	−4.58841e10	−	1.77156e10i	−0.127849	−	0.0493620i
$775$	5.08080e11	+	3.47989e11i	1.40840	+	0.964625i
$776$	−3.76864e11	+	1.89263e11i	−1.03929	+	0.521937i
$777$		−	4.66482e10i		−	0.127983i
$778$	2.27668e11	+	8.79015e10i	0.621418	+	0.239926i
$779$		−	6.80082e11i		−	1.84676i
$780$	−2.87824e11	−	7.40423e10i	−0.777586	−	0.200033i
$781$	−1.37178e11			−0.368707
$782$	−1.04072e11	+	2.69549e11i	−0.278295	+	0.720793i
$783$	−4.55053e11			−1.21064
$784$	−3.61093e10	−	3.71294e11i	−0.0955773	−	0.982773i
$785$	−4.04128e11	+	2.13038e11i	−1.06424	+	0.561021i
$786$	8.18524e10	−	2.12001e11i	0.214458	−	0.555453i
$787$	1.33698e11			0.348518			0.174259	−	0.984700i	$-0.444247\pi$
$787$	1.33698e11			0.348518			0.174259	+	0.984700i	$0.444247\pi$
$788$	−7.83017e10	+	8.62861e10i	−0.203080	+	0.223788i
$789$	−6.25298e11			−1.61354
$790$	−2.29507e11	+	2.68994e10i	−0.589233	+	0.0690612i
$791$		−	1.66010e10i		−	0.0424062i
$792$	1.40512e10	−	7.05656e9i	0.0357118	−	0.0179346i
$793$		−	2.34968e11i		−	0.594178i
$794$	−9.27061e10	+	2.40112e11i	−0.233252	+	0.604132i
$795$	1.89847e11	−	1.00079e11i	0.475265	−	0.250539i
$796$	−4.66798e11	+	5.14397e11i	−1.16272	+	1.28129i
$797$		−	3.86963e11i		−	0.959040i	−0.877531	−	0.479520i	$-0.840811\pi$
$797$		−	3.86963e11i		−	0.959040i	0.877531	−	0.479520i	$-0.159189\pi$
$798$	−1.65507e10	+	4.28670e10i	−0.0408137	+	0.105709i
$799$			1.83902e10i			0.0451231i
$800$	2.63482e11	+	3.13607e11i	0.643266	+	0.765643i
$801$	3.40198e9			0.00826423
$802$	−3.15589e10	−	1.21847e10i	−0.0762823	−	0.0294522i
$803$	−1.26480e11			−0.304200
$804$	1.20119e11	+	1.09004e11i	0.287467	+	0.260867i
$805$	−2.27944e10	−	4.32404e10i	−0.0542806	−	0.102969i
$806$	5.74863e11	+	2.21952e11i	1.36215	+	0.525918i
$807$	1.98243e11			0.467415
$808$	1.29156e11	+	2.57177e11i	0.303018	+	0.603375i
$809$	5.87391e11			1.37130			0.685651	−	0.727930i	$-0.259518\pi$
$809$	5.87391e11			1.37130			0.685651	+	0.727930i	$0.259518\pi$
$810$	4.34447e10	+	3.70672e11i	0.100925	+	0.861093i
$811$		−	2.39959e11i		−	0.554695i	−0.960770	−	0.277348i	$-0.910545\pi$
$811$		−	2.39959e11i		−	0.554695i	0.960770	−	0.277348i	$-0.0894554\pi$
$812$	4.16393e10	+	3.77862e10i	0.0957810	+	0.0869180i
$813$			6.12647e10i			0.140232i
$814$	1.67294e11	+	6.45914e10i	0.381051	+	0.147122i
$815$	−1.89935e11	−	3.60301e11i	−0.430501	−	0.816649i
$816$	−3.08519e11	+	3.00043e10i	−0.695859	+	0.0676741i
$817$			5.52585e11i			1.24025i
$818$	3.65303e11	+	1.41042e11i	0.815905	+	0.315017i
$819$		−	5.13345e9i		−	0.0114097i
$820$	−1.93355e11	+	7.51628e11i	−0.427662	+	1.66245i
$821$	6.76311e11			1.48859			0.744293	−	0.667853i	$-0.232787\pi$
$821$	6.76311e11			1.48859			0.744293	+	0.667853i	$0.232787\pi$
$822$	2.81781e10	−	7.29824e10i	0.0617199	−	0.159857i
$823$	−5.16299e10			−0.112539			−0.0562694	−	0.998416i	$-0.517921\pi$
$823$	−5.16299e10			−0.112539			−0.0562694	+	0.998416i	$0.517921\pi$
$824$	3.68503e11	+	7.33770e11i	0.799341	+	1.59166i
$825$	−1.20600e11	−	8.26001e10i	−0.260334	−	0.178305i
$826$	−3.49930e10	+	9.06332e10i	−0.0751729	+	0.194701i
$827$	4.03317e11			0.862232			0.431116	−	0.902297i	$-0.358120\pi$
$827$	4.03317e11			0.862232			0.431116	+	0.902297i	$0.358120\pi$
$828$	−4.29255e10	−	3.89534e10i	−0.0913259	−	0.0828751i
$829$	−5.84365e11			−1.23727			−0.618637	−	0.785677i	$-0.712315\pi$
$829$	−5.84365e11			−1.23727			−0.618637	+	0.785677i	$0.712315\pi$
$830$	4.46847e10	+	3.81252e11i	0.0941557	+	0.803340i
$831$		−	5.14957e11i		−	1.07986i
$832$	3.28755e11	+	2.44761e11i	0.686088	+	0.510797i
$833$			3.54100e11i			0.735437i
$834$	1.35554e11	−	3.51091e11i	0.280188	−	0.725696i
$835$	1.04022e11	+	1.97327e11i	0.213983	+	0.405921i
$836$	−1.30816e11	−	1.18711e11i	−0.267816	−	0.243034i
$837$		−	8.79942e11i		−	1.79289i
$838$	3.07578e11	−	7.96638e11i	0.623705	−	1.61542i
$839$			3.84114e11i			0.775197i	0.921828	+	0.387598i	$0.126695\pi$
$839$			3.84114e11i			0.775197i	−0.921828	+	0.387598i	$0.873305\pi$
$840$	3.04795e10	−	4.26711e10i	0.0612196	−	0.0857071i
$841$	1.64432e11			0.328703
$842$	−8.85126e11	−	3.41743e11i	−1.76099	−	0.679909i
$843$	4.49136e10			0.0889340
$844$	−3.95292e11	+	4.35600e11i	−0.779019	+	0.858456i
$845$	6.38045e10	+	1.21036e11i	0.125148	+	0.237403i
$846$	−3.44167e9	−	1.32881e9i	−0.00671874	−	0.00259407i
$847$	−5.12242e10			−0.0995271
$848$	−2.94581e11	+	2.86488e10i	−0.569668	+	0.0554017i
$849$	−3.06015e11			−0.588996
$850$	−2.20112e11	−	3.20491e11i	−0.421665	−	0.613961i
$851$		−	6.61104e11i		−	1.26053i
$852$	−3.64582e11	+	4.01758e11i	−0.691889	+	0.762442i
$853$		−	5.42605e11i		−	1.02492i	−0.858712	−	0.512458i	$-0.828735\pi$
$853$		−	5.42605e11i		−	1.02492i	0.858712	−	0.512458i	$-0.171265\pi$
$854$	3.86765e10	+	1.49328e10i	0.0727135	+	0.0280743i
$855$	−6.04612e10	+	3.18725e10i	−0.113139	+	0.0596418i
$856$	−1.98996e11	−	3.96244e11i	−0.370637	−	0.738020i
$857$		−	4.89663e11i		−	0.907765i	−0.891061	−	0.453883i	$-0.850039\pi$
$857$		−	4.89663e11i		−	0.907765i	0.891061	−	0.453883i	$-0.149961\pi$
$858$	−1.36452e11	−	5.26834e10i	−0.251785	−	0.0972130i
$859$		−	4.05124e11i		−	0.744073i	−0.928218	−	0.372037i	$-0.878660\pi$
$859$		−	4.05124e11i		−	0.744073i	0.928218	−	0.372037i	$-0.121340\pi$
$860$	1.57106e11	−	6.10718e11i	0.287210	−	1.11647i
$861$	9.93596e10			0.180799
$862$	2.62856e11	−	6.80807e11i	0.476090	−	1.23309i
$863$	−8.73437e10			−0.157467			−0.0787333	−	0.996896i	$-0.525088\pi$
$863$	−8.73437e10			−0.157467			−0.0787333	+	0.996896i	$0.525088\pi$
$864$	1.56964e11	−	5.63829e11i	0.281673	−	1.01179i
$865$	−5.15780e11	+	2.71896e11i	−0.921298	+	0.485667i
$866$	1.81022e11	−	4.68854e11i	0.321855	−	0.833616i
$867$	−2.36156e11			−0.417948
$868$	−7.30678e10	+	8.05185e10i	−0.128720	+	0.141846i
$869$	−1.13728e11			−0.199430
$870$	−7.21594e10	−	6.15667e11i	−0.125955	−	1.07465i
$871$			2.03583e11i			0.353728i
$872$	−1.48939e11	−	2.96571e11i	−0.257598	−	0.512935i
$873$			8.03051e10i			0.138257i
$874$	−2.34559e11	+	6.07516e11i	−0.401982	+	1.04115i
$875$	6.53359e10	+	7.57282e9i	0.111460	+	0.0129189i
$876$	−3.36149e11	+	3.70426e11i	−0.570841	+	0.629050i
$877$			8.28251e11i			1.40011i	0.714087	+	0.700057i	$0.246842\pi$
$877$			8.28251e11i			1.40011i	−0.714087	+	0.700057i	$0.753158\pi$
$878$	4.45024e10	−	1.15263e11i	0.0748868	−	0.193959i
$879$		−	1.22288e11i		−	0.204846i
$880$	1.10828e11	+	1.68393e11i	0.184806	+	0.280797i
$881$	−4.17980e11			−0.693828			−0.346914	−	0.937897i	$-0.612770\pi$
$881$	−4.17980e11			−0.693828			−0.346914	+	0.937897i	$0.612770\pi$
$882$	−6.62688e10	−	2.55860e10i	−0.109505	−	0.0422794i
$883$	2.61660e11			0.430423			0.215211	−	0.976567i	$-0.430956\pi$
$883$	2.61660e11			0.430423			0.215211	+	0.976567i	$0.430956\pi$
$884$	−2.88105e11	−	2.61445e11i	−0.471783	−	0.428126i
$885$	9.47471e11	−	4.99464e11i	1.54452	−	0.814201i
$886$	1.02203e12	+	3.94600e11i	1.65855	+	0.640356i
$887$	−2.39448e11			−0.386827			−0.193413	−	0.981117i	$-0.561956\pi$
$887$	−2.39448e11			−0.386827			−0.193413	+	0.981117i	$0.561956\pi$
$888$	6.33792e11	−	3.18293e11i	1.01928	−	0.511889i
$889$	3.55816e10			0.0569664
$890$	5.07734e9	+	4.33201e10i	0.00809239	+	0.0690445i
$891$			1.83681e11i			0.291442i
$892$	8.93527e11	+	8.10844e11i	1.41139	+	1.28079i
$893$			4.14482e10i			0.0651778i
$894$	−3.87511e11	−	1.49616e11i	−0.606644	−	0.234222i
$895$	3.09874e10	−	1.63352e10i	0.0482940	−	0.0254584i
$896$	−6.11815e10	+	3.85590e10i	−0.0949267	+	0.0598265i
$897$			5.39224e11i			0.832912i
$898$	−1.29363e11	−	4.99464e10i	−0.198932	−	0.0768066i
$899$			1.28530e12i			1.96773i
$900$	7.58836e10	−	1.80357e10i	0.115659	−	0.0274892i
$901$	2.80940e11			0.426299
$902$	−1.37578e11	+	3.56332e11i	−0.207837	+	0.538305i
$903$	−8.07324e10			−0.121422
$904$	2.25552e11	−	1.13273e11i	0.337733	−	0.169611i
$905$	−1.59134e11	−	3.01873e11i	−0.237229	−	0.450018i
$906$	2.03292e10	−	5.26534e10i	0.0301722	−	0.0781472i
$907$	−5.42209e11			−0.801194			−0.400597	−	0.916254i	$-0.631197\pi$
$907$	−5.42209e11			−0.801194			−0.400597	+	0.916254i	$0.631197\pi$
$908$	−3.64791e10	−	3.31035e10i	−0.0536662	−	0.0487002i
$909$	5.48014e10			0.0802669
$910$	6.53682e10	−	7.66150e9i	0.0953237	−	0.0111724i
$911$			5.30218e11i			0.769806i	0.922957	+	0.384903i	$0.125765\pi$
$911$			5.30218e11i			0.769806i	−0.922957	+	0.384903i	$0.874235\pi$
$912$	−6.95348e11	+	6.76244e10i	−1.00513	+	0.0977516i
$913$			1.88923e11i			0.271896i
$914$	−1.05978e11	+	2.74487e11i	−0.151856	+	0.393312i
$915$	−2.13139e11	−	4.04320e11i	−0.304074	−	0.576821i
$916$	−5.26783e11	−	4.78037e11i	−0.748255	−	0.679016i
$917$			5.03266e10i			0.0711739i
$918$	−2.00097e11	+	5.18259e11i	−0.281754	+	0.729753i
$919$			4.26029e10i			0.0597279i	0.999554	+	0.0298639i	$0.00950740\pi$
$919$			4.26029e10i			0.0597279i	−0.999554	+	0.0298639i	$0.990493\pi$
$920$	4.31959e11	−	6.04740e11i	0.602963	−	0.844146i
$921$	2.54137e11			0.353207
$922$	4.29115e11	+	1.65679e11i	0.593813	+	0.229268i
$923$	−6.80917e11			−0.938182
$924$	1.73437e10	−	1.91122e10i	0.0237932	−	0.0262194i
$925$	7.33934e11	+	5.02679e11i	1.00251	+	0.686631i
$926$	−3.10282e10	−	1.19798e10i	−0.0422001	−	0.0162932i
$927$	1.56358e11			0.211738
$928$	−2.29271e11	+	8.23563e11i	−0.309142	+	1.11047i
$929$	−1.17340e11			−0.157537			−0.0787686	−	0.996893i	$-0.525099\pi$
$929$	−1.17340e11			−0.157537			−0.0787686	+	0.996893i	$0.525099\pi$
$930$	1.19052e12	−	1.39536e11i	1.59150	−	0.186532i
$931$			7.98078e11i			1.06230i
$932$	7.25965e11	−	7.99992e11i	0.962170	−	1.06028i
$933$		−	9.48236e11i		−	1.25138i
$934$	−6.01710e11	−	2.32317e11i	−0.790678	−	0.305277i
$935$	−8.92331e10	−	1.69273e11i	−0.116756	−	0.221483i
$936$	6.97463e10	−	3.50269e10i	0.0908694	−	0.0456351i
$937$			6.54206e11i			0.848704i	0.905497	+	0.424352i	$0.139498\pi$
$937$			6.54206e11i			0.848704i	−0.905497	+	0.424352i	$0.860502\pi$
$938$	−3.35104e10	−	1.29382e10i	−0.0432880	−	0.0167133i
$939$			6.83522e11i			0.879206i
$940$	1.17842e10	−	4.58086e10i	0.0150935	−	0.0586727i
$941$	3.32045e11			0.423486			0.211743	−	0.977325i	$-0.432086\pi$
$941$	3.32045e11			0.423486			0.211743	+	0.977325i	$0.432086\pi$
$942$	−3.20280e11	+	8.29537e11i	−0.406749	+	1.05349i
$943$	1.40814e12			1.78073
$944$	−1.47017e12	+	1.42978e11i	−1.85131	+	0.180044i
$945$	−4.38266e10	−	8.31379e10i	−0.0549554	−	0.104249i
$946$	1.11786e11	−	2.89530e11i	0.139580	−	0.361517i
$947$	5.01738e11			0.623846			0.311923	−	0.950107i	$-0.399027\pi$
$947$	5.01738e11			0.623846			0.311923	+	0.950107i	$0.399027\pi$
$948$	−3.02258e11	+	3.33080e11i	−0.374236	+	0.412397i
$949$	−6.27813e11			−0.774044
$950$	−4.96093e11	−	7.22331e11i	−0.609072	−	0.886833i
$951$			6.56929e11i			0.803150i
$952$	6.13444e10	−	3.08075e10i	0.0746840	−	0.0375066i
$953$			7.89235e11i			0.956830i	0.878134	+	0.478415i	$0.158789\pi$
$953$			7.89235e11i			0.956830i	−0.878134	+	0.478415i	$0.841211\pi$
$954$	−2.02998e10	+	5.25771e10i	−0.0245074	+	0.0634751i
$955$	3.75139e11	−	1.97757e11i	0.451002	−	0.237748i
$956$	9.24426e11	−	1.01869e12i	1.10673	−	1.21958i
$957$		−	3.05084e11i		−	0.363723i
$958$	1.23040e10	−	3.18677e10i	0.0146077	−	0.0378346i
$959$			1.73252e10i			0.0204835i
$960$	7.87726e11	+	1.22957e11i	0.927449	+	0.144766i
$961$	−1.63251e12			−1.91409
$962$	8.30403e11	+	3.20615e11i	0.969592	+	0.374354i
$963$	−8.44349e10			−0.0981786
$964$	6.18672e11	+	5.61423e11i	0.716394	+	0.650103i
$965$	7.40961e11	−	3.90602e11i	0.854449	−	0.450428i
$966$	−8.87578e10	−	3.42689e10i	−0.101929	−	0.0393543i
$967$	−1.40429e12			−1.60602			−0.803010	−	0.595966i	$-0.796769\pi$
$967$	−1.40429e12			−1.60602			−0.803010	+	0.595966i	$0.796769\pi$
$968$	−3.49516e11	−	6.95963e11i	−0.398076	−	0.792656i
$969$	6.63147e11			0.752168
$970$	−1.02259e12	+	1.19853e11i	−1.15508	+	0.135382i
$971$		−	7.36856e11i		−	0.828907i	−0.910071	−	0.414453i	$-0.863973\pi$
$971$		−	7.36856e11i		−	0.828907i	0.910071	−	0.414453i	$-0.136027\pi$
$972$	−1.56296e11	−	1.41833e11i	−0.175098	−	0.158896i
$973$			8.33450e10i			0.0929883i
$974$	−2.50402e11	−	9.66789e10i	−0.278228	−	0.107423i
$975$	−5.98627e11	−	4.10005e11i	−0.662426	−	0.453702i
$976$	6.10137e10	+	6.27373e11i	0.0672400	+	0.691395i
$977$			2.76836e10i			0.0303840i	0.999885	+	0.0151920i	$0.00483595\pi$
$977$			2.76836e10i			0.0303840i	−0.999885	+	0.0151920i	$0.995164\pi$
$978$	−7.39576e11	−	2.85546e11i	−0.808402	−	0.312120i
$979$			2.14666e10i			0.0233686i
$980$	2.26903e11	−	8.82038e11i	0.246000	−	0.956275i
$981$	−6.31956e10			−0.0682356
$982$	3.60756e11	−	9.34372e11i	0.387943	−	1.00479i
$983$	6.25460e11			0.669862			0.334931	−	0.942243i	$-0.391287\pi$
$983$	6.25460e11			0.669862			0.334931	+	0.942243i	$0.391287\pi$
$984$	6.77957e11	+	1.34996e12i	0.723139	+	1.43993i
$985$	−2.51644e11	+	1.32655e11i	−0.267326	+	0.140922i
$986$	2.92274e11	−	7.57001e11i	0.309231	−	0.800920i
$987$	−6.05556e9			−0.00638095
$988$	−6.49338e11	−	5.89252e11i	−0.681464	−	0.618405i
$989$	−1.14415e12			−1.19591
$990$	3.81266e10	−	4.46864e9i	0.0396906	−	0.00465195i
$991$		−	1.63053e12i		−	1.69058i	−0.534309	−	0.845289i	$-0.679428\pi$
$991$		−	1.63053e12i		−	1.69058i	0.534309	−	0.845289i	$-0.320572\pi$
$992$	−1.59254e12	−	4.43345e11i	−1.64453	−	0.457820i
$993$			2.93598e11i			0.301964i
$994$	4.32739e10	−	1.12081e11i	0.0443282	−	0.114812i
$995$	−1.50018e12	+	7.90829e11i	−1.53056	+	0.806845i
$996$	5.53305e11	+	5.02105e11i	0.562248	+	0.510220i
$997$		−	5.49356e11i		−	0.555998i	−0.960581	−	0.277999i	$-0.910329\pi$
$997$		−	5.49356e11i		−	0.555998i	0.960581	−	0.277999i	$-0.0896712\pi$
$998$	−6.28257e11	+	1.62721e12i	−0.633308	+	1.64029i
$999$		−	1.27110e12i		−	1.27620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.d.c.19.1	✓	20
4.3	odd	2	inner	20.9.d.c.19.19	yes	20
5.2	odd	4		100.9.b.g.51.11		20
5.3	odd	4		100.9.b.g.51.10		20
5.4	even	2	inner	20.9.d.c.19.20	yes	20
8.3	odd	2		320.9.h.g.319.3		20
8.5	even	2		320.9.h.g.319.17		20
20.3	even	4		100.9.b.g.51.9		20
20.7	even	4		100.9.b.g.51.12		20
20.19	odd	2	inner	20.9.d.c.19.2	yes	20
40.19	odd	2		320.9.h.g.319.18		20
40.29	even	2		320.9.h.g.319.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.1	✓	20	1.1	even	1	trivial
20.9.d.c.19.2	yes	20	20.19	odd	2	inner
20.9.d.c.19.19	yes	20	4.3	odd	2	inner
20.9.d.c.19.20	yes	20	5.4	even	2	inner
100.9.b.g.51.9		20	20.3	even	4
100.9.b.g.51.10		20	5.3	odd	4
100.9.b.g.51.11		20	5.2	odd	4
100.9.b.g.51.12		20	20.7	even	4
320.9.h.g.319.3		20	8.3	odd	2
320.9.h.g.319.4		20	40.29	even	2
320.9.h.g.319.17		20	8.5	even	2
320.9.h.g.319.18		20	40.19	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)

\(f(q)\)	\(=\)	\(q+(-14.9261 - 5.76290i) q^{2} -76.0331 q^{3} +(189.578 + 172.035i) q^{4} +(291.455 + 552.882i) q^{5} +(1134.88 + 438.171i) q^{6} -269.408 q^{7} +(-1838.24 - 3660.34i) q^{8} -779.974 q^{9} +O(q^{10})\)	\(q+(-14.9261 - 5.76290i) q^{2} -76.0331 q^{3} +(189.578 + 172.035i) q^{4} +(291.455 + 552.882i) q^{5} +(1134.88 + 438.171i) q^{6} -269.408 q^{7} +(-1838.24 - 3660.34i) q^{8} -779.974 q^{9} +(-1164.08 - 9932.01i) q^{10} -4921.65i q^{11} +(-14414.2 - 13080.4i) q^{12} -24429.8i q^{13} +(4021.21 + 1552.57i) q^{14} +(-22160.2 - 42037.3i) q^{15} +(6343.62 + 65228.3i) q^{16} -62207.7i q^{17} +(11642.0 + 4494.91i) q^{18} -140205. i q^{19} +(-39861.9 + 154955. i) q^{20} +20483.9 q^{21} +(-28363.0 + 73461.1i) q^{22} +290300. q^{23} +(139767. + 278307. i) q^{24} +(-220733. + 322281. i) q^{25} +(-140786. + 364642. i) q^{26} +558157. q^{27} +(-51073.8 - 46347.7i) q^{28} -815278. q^{29} +(88508.9 + 755161. i) q^{30} -1.57652e6i q^{31} +(281218. - 1.01016e6i) q^{32} +374208. i q^{33} +(-358496. + 928519. i) q^{34} +(-78520.2 - 148951. i) q^{35} +(-147866. - 134183. i) q^{36} -2.27731e6i q^{37} +(-807988. + 2.09272e6i) q^{38} +1.85747e6i q^{39} +(1.48797e6 - 2.08315e6i) q^{40} +4.85062e6 q^{41} +(-305745. - 118047. i) q^{42} -3.94126e6 q^{43} +(846698. - 933036. i) q^{44} +(-227327. - 431234. i) q^{45} +(-4.33305e6 - 1.67297e6i) q^{46} -295625. q^{47} +(-482325. - 4.95950e6i) q^{48} -5.69222e6 q^{49} +(5.15196e6 - 3.53834e6i) q^{50} +4.72984e6i q^{51} +(4.20279e6 - 4.63135e6i) q^{52} +4.51616e6i q^{53} +(-8.33111e6 - 3.21660e6i) q^{54} +(2.72109e6 - 1.43444e6i) q^{55} +(495236. + 986124. i) q^{56} +1.06602e7i q^{57} +(1.21689e7 + 4.69837e6i) q^{58} +2.25388e7i q^{59} +(3.03082e6 - 1.17817e7i) q^{60} +9.61812e6 q^{61} +(-9.08530e6 + 2.35312e7i) q^{62} +210131. q^{63} +(-1.00190e7 + 1.34572e7i) q^{64} +(1.35068e7 - 7.12018e6i) q^{65} +(2.15652e6 - 5.58547e6i) q^{66} -8.33340e6 q^{67} +(1.07019e7 - 1.17932e7i) q^{68} -2.20724e7 q^{69} +(313613. + 2.67576e6i) q^{70} -2.78724e7i q^{71} +(1.43378e6 + 2.85497e6i) q^{72} -2.56987e7i q^{73} +(-1.31239e7 + 3.39915e7i) q^{74} +(1.67830e7 - 2.45040e7i) q^{75} +(2.41202e7 - 2.65798e7i) q^{76} +1.32593e6i q^{77} +(1.07044e7 - 2.77248e7i) q^{78} -2.31078e7i q^{79} +(-3.42147e7 + 2.25184e7i) q^{80} -3.73209e7 q^{81} +(-7.24010e7 - 2.79536e7i) q^{82} -3.83862e7 q^{83} +(3.88329e6 + 3.52395e6i) q^{84} +(3.43935e7 - 1.81307e7i) q^{85} +(5.88278e7 + 2.27131e7i) q^{86} +6.19881e7 q^{87} +(-1.80149e7 + 9.04717e6i) q^{88} -4.36166e6 q^{89} +(907956. + 7.74672e6i) q^{90} +6.58157e6i q^{91} +(5.50345e7 + 4.99419e7i) q^{92} +1.19867e8i q^{93} +(4.41254e6 + 1.70366e6i) q^{94} +(7.75169e7 - 4.08635e7i) q^{95} +(-2.13819e7 + 7.68057e7i) q^{96} -1.02959e8i q^{97} +(8.49628e7 + 3.28037e7i) q^{98} +3.83876e6i 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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