LMFDB - Embedded newform 20.9.d.c.19.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [20,9,Mod(19,20)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			19.19
Root			$7.46306 - 2.88145i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.9.d.c.19.20

$q$-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} +(7536.50 + 6572.76i) 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} +(150369. + 54673.8i) 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} +(573023. + 499747. 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} +(2.55950e6 - 50493.3i) 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} +(-1.43742e6 + 6.08246e6i) 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} +(1.14330e7 + 4.15701e6i) 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} +(2.03039e6 + 1.77075e6i) 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} +(3.79124e7 - 1.55038e7i) 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} +(-5.87827e6 - 5.12659e6i) 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} - 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}+ \cdots + 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

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	$-0.344492\pi$
$3$	76.0331			0.938680			0.469340	+	0.883018i	$0.344492\pi$
$4$	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	$-0.482132\pi$
$7$	269.408			0.112206			0.0561032	+	0.998425i	$0.482132\pi$
$8$	1838.24	−	3660.34i	0.448789	−	0.893638i
$9$	−779.974			−0.118880
$10$	7536.50	+	6572.76i	0.753650	+	0.657276i
$11$			4921.65i			0.336155i	0.985774	+	0.168078i	$0.0537559\pi$
$11$			4921.65i			0.336155i	−0.985774	+	0.168078i	$0.946244\pi$
$12$	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	$0.180791\pi$
$19$			140205.i			1.07584i	−0.842995	+	0.537922i	$0.819209\pi$
$20$	150369.	+	54673.8i	0.939805	+	0.341711i
$21$	20483.9			0.105326
$22$	28363.0	+	73461.1i	0.121077	+	0.313593i
$23$	−290300.			−1.03737			−0.518687	−	0.854964i	$-0.673579\pi$
$23$	−290300.			−1.03737			−0.518687	+	0.854964i	$0.673579\pi$
$24$	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	$0.695522\pi$
$30$	573023.	+	499747.i	0.707436	+	0.616972i
$31$			1.57652e6i			1.70707i	0.521035	+	0.853535i	$0.325546\pi$
$31$			1.57652e6i			1.70707i	−0.521035	+	0.853535i	$0.674454\pi$
$32$	−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
$40$	2.55950e6	−	50493.3i	0.999805	−	0.0197240i
$41$	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	$-0.304453\pi$
$43$	3.94126e6			1.15282			0.576410	+	0.817161i	$0.304453\pi$
$44$	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	$-0.490356\pi$
$47$	295625.			0.0605829			0.0302915	+	0.999541i	$0.490356\pi$
$48$	482325.	−	4.95950e6i	0.0908604	−	0.934272i
$49$	−5.69222e6			−0.987410
$50$	−1.43742e6	+	6.08246e6i	−0.229987	+	0.973194i
$51$		−	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	$-0.619789\pi$
$59$		−	2.25388e7i		−	1.86004i	0.367508	−	0.930021i	$-0.380211\pi$
$60$	1.14330e7	+	4.15701e6i	0.882176	+	0.320757i
$61$	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	$-0.433704\pi$
$67$	8.33340e6			0.413545			0.206773	+	0.978389i	$0.433704\pi$
$68$	−1.07019e7	−	1.17932e7i	−0.500525	−	0.551564i
$69$	−2.20724e7			−0.973763
$70$	2.03039e6	+	1.77075e6i	0.0845643	+	0.0737506i
$71$			2.78724e7i			1.09683i	0.836205	+	0.548417i	$0.184770\pi$
$71$			2.78724e7i			1.09683i	−0.836205	+	0.548417i	$0.815230\pi$
$72$	−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	$0.0958639\pi$
$79$			2.31078e7i			0.593266i	−0.954991	+	0.296633i	$0.904136\pi$
$80$	3.79124e7	−	1.55038e7i	0.925597	−	0.378511i
$81$	−3.73209e7			−0.866987
$82$	7.24010e7	−	2.79536e7i	1.60136	−	0.618277i
$83$	3.83862e7			0.808839			0.404420	−	0.914574i	$-0.367474\pi$
$83$	3.83862e7			0.808839			0.404420	+	0.914574i	$0.367474\pi$
$84$	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	$0.511066\pi$
$90$	−5.87827e6	−	5.12659e6i	−0.0895942	−	0.0781373i
$91$		−	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
$100$	1.35976e7	+	9.90712e7i	0.135976	+	0.990712i
$101$	−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	$-0.150318\pi$
$103$	2.00465e8			1.78110			0.890552	+	0.454881i	$0.150318\pi$
$104$	−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	$-0.635495\pi$
$107$	−1.08253e8			−0.825861			−0.412930	+	0.910763i	$0.635495\pi$
$108$	−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	$0.407344\pi$
$110$	−3.23488e7	+	3.70920e7i	−0.220947	+	0.253343i
$111$		−	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
$120$	1.94607e8	−	3.83916e6i	0.938497	−	0.0185145i
$121$	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	$-0.418304\pi$
$127$	1.32074e8			0.507693			0.253847	+	0.967244i	$0.418304\pi$
$128$	−2.27097e8	−	1.43125e8i	−0.846000	−	0.533182i
$129$	2.99666e8			1.08213
$130$	1.60571e8	−	1.84115e8i	0.562204	−	0.644637i
$131$			1.86805e8i			0.634312i	0.948373	+	0.317156i	$0.102728\pi$
$131$			1.86805e8i			0.634312i	−0.948373	+	0.317156i	$0.897272\pi$
$132$	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	$0.135996\pi$
$139$			3.09364e8i			0.828725i	−0.910112	+	0.414363i	$0.864004\pi$
$140$	4.05105e7	+	1.47295e7i	0.105452	+	0.0383422i
$141$	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	$0.612591\pi$
$150$	−1.09291e8	+	4.62468e8i	−0.215884	+	0.913517i
$151$			4.63956e7i			0.0892419i	0.999004	+	0.0446210i	$0.0142080\pi$
$151$			4.63956e7i			0.0892419i	−0.999004	+	0.0446210i	$0.985792\pi$
$152$	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
$160$	4.76539e8	−	4.49897e8i	0.727140	−	0.686489i
$161$	−7.82090e7			−0.116400
$162$	−5.57057e8	+	2.15077e8i	−0.808797	+	0.312272i
$163$	6.51678e8			0.923172			0.461586	−	0.887095i	$-0.347280\pi$
$163$	6.51678e8			0.923172			0.461586	+	0.887095i	$0.347280\pi$
$164$	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	$-0.573688\pi$
$167$	−3.56907e8			−0.458869			−0.229435	+	0.973324i	$0.573688\pi$
$168$	3.76543e7	−	7.49780e7i	0.0472691	−	0.0941232i
$169$	2.18917e8			0.268370
$170$	4.08876e8	−	4.68828e8i	0.489549	−	0.561329i
$171$		−	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	$0.00868989\pi$
$179$			5.60470e7i			0.0545934i	−0.999627	+	0.0272967i	$0.991310\pi$
$180$	−1.17284e8	−	4.26441e7i	−0.111724	−	0.0406227i
$181$	−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
$190$	−9.21535e8	+	1.05666e9i	−0.707127	+	0.810810i
$191$			6.78515e8i			0.509831i	0.966963	+	0.254915i	$0.0820476\pi$
$191$			6.78515e8i			0.509831i	−0.966963	+	0.254915i	$0.917952\pi$
$192$	−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	$-0.667252\pi$
$199$		−	2.71338e9i		−	1.73021i	0.501592	−	0.865105i	$-0.332748\pi$
$200$	7.73896e8	+	1.40039e9i	0.483685	+	0.875242i
$201$	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
$210$	1.54377e8	+	1.34636e8i	0.0793788	+	0.0692282i
$211$		−	2.29774e9i		−	1.15923i	−0.814890	−	0.579616i	$-0.803203\pi$
$211$		−	2.29774e9i		−	1.15923i	0.814890	−	0.579616i	$-0.196797\pi$
$212$	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
$220$	−2.69085e8	+	7.40063e8i	−0.114868	+	0.315920i
$221$	−1.51972e9			−0.637080
$222$	−9.97853e8	−	2.58447e9i	−0.410823	−	1.06405i
$223$	−4.71324e9			−1.90590			−0.952950	−	0.303127i	$-0.901969\pi$
$223$	−4.71324e9			−1.90590			−0.952950	+	0.303127i	$0.901969\pi$
$224$	−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	$-0.488464\pi$
$227$	1.92423e8			0.0724692			0.0362346	+	0.999343i	$0.488464\pi$
$228$	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	$0.668585\pi$
$230$	−2.18785e9	−	1.90807e9i	−0.781817	−	0.681842i
$231$			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	$0.307949\pi$
$239$			5.37346e9i			1.64688i	−0.567401	+	0.823441i	$0.692051\pi$
$240$	2.88260e9	−	1.17880e9i	0.868839	−	0.355301i
$241$	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
$250$	−3.78183e9	+	9.78041e8i	−0.968148	+	0.250379i
$251$			6.76390e9i			1.70413i	0.523437	+	0.852065i	$0.324650\pi$
$251$			6.76390e9i			1.70413i	−0.523437	+	0.852065i	$0.675350\pi$
$252$	−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
$260$	1.33567e9	−	3.67347e9i	0.292284	−	0.803866i
$261$	6.35896e8			0.137033
$262$	1.07654e9	+	2.78827e9i	0.228467	+	0.591738i
$263$	−8.22403e9			−1.71894			−0.859472	−	0.511182i	$-0.829208\pi$
$263$	−8.22403e9			−1.71894			−0.859472	+	0.511182i	$0.829208\pi$
$264$	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	$0.580094\pi$
$270$	−4.20655e9	−	3.66863e9i	−0.791536	−	0.690318i
$271$			8.05765e8i			0.149393i	0.997206	+	0.0746966i	$0.0237988\pi$
$271$			8.05765e8i			0.149393i	−0.997206	+	0.0746966i	$0.976201\pi$
$272$	−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
$280$	6.89549e8	−	1.36033e7i	0.112185	−	0.00221316i
$281$	−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	$-0.601581\pi$
$283$	−4.02477e9			−0.627473			−0.313736	+	0.949510i	$0.601581\pi$
$284$	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
$290$	−6.14434e9	−	5.35863e9i	−0.868727	−	0.757638i
$291$		−	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
$300$	1.03386e9	+	7.53269e9i	0.127638	+	0.929961i
$301$	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	$-0.439754\pi$
$307$	3.34245e9			0.376281			0.188140	+	0.982142i	$0.439754\pi$
$308$	2.28107e8	+	2.51367e8i	0.0253475	+	0.0279322i
$309$	1.52420e10			1.67189
$310$	−1.03621e10	+	1.18814e10i	−1.12202	+	1.28653i
$311$		−	1.24714e10i		−	1.33313i	−0.745447	−	0.666565i	$-0.767764\pi$
$311$		−	1.24714e10i		−	1.33313i	0.745447	−	0.666565i	$-0.232236\pi$
$312$	−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
$320$	4.52016e9	−	9.46147e9i	0.431076	−	0.902316i
$321$	−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
$330$	−2.45958e9	+	2.82022e9i	−0.207398	+	0.237808i
$331$			3.86145e9i			0.321690i	0.986980	+	0.160845i	$0.0514220\pi$
$331$			3.86145e9i			0.321690i	−0.986980	+	0.160845i	$0.948578\pi$
$332$	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
$340$	3.40113e9	−	9.35409e9i	0.254511	−	0.699980i
$341$	−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	$-0.696264\pi$
$347$	−1.67673e10			−1.15650			−0.578250	+	0.815860i	$0.696264\pi$
$348$	−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	$0.630049\pi$
$350$	−3.87251e8	+	1.63866e9i	−0.0258060	+	0.109199i
$351$			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	$0.000426660\pi$
$359$			4.45286e7i			0.00268078i	−0.999999	+	0.00134039i	$0.999573\pi$
$360$	−1.99635e9	+	3.93835e7i	−0.118857	+	0.00234479i
$361$	−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	$-0.554527\pi$
$367$	−6.18488e9			−0.340931			−0.170466	+	0.985364i	$0.554527\pi$
$368$	−1.84155e9	+	1.89358e10i	−0.100414	+	1.03250i
$369$	−3.78336e9			−0.204067
$370$	1.49682e10	−	1.71630e10i	0.798664	−	0.915768i
$371$			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	$-0.943946\pi$
$379$		−	7.22927e9i		−	0.350378i	0.984535	−	0.175189i	$-0.0560537\pi$
$380$	−7.66554e9	+	2.10825e10i	−0.367628	+	1.01108i
$381$	1.00420e10			0.476561
$382$	3.91021e9	+	1.01276e10i	0.183631	+	0.475612i
$383$	1.40958e9			0.0655080			0.0327540	−	0.999463i	$-0.489572\pi$
$383$	1.40958e9			0.0655080			0.0327540	+	0.999463i	$0.489572\pi$
$384$	−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	$0.608082\pi$
$390$	1.22087e10	−	1.39988e10i	0.527729	−	0.605108i
$391$			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
$400$	1.96216e10	+	1.64425e10i	0.766467	+	0.642283i
$401$	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	$0.644066\pi$
$410$	3.65567e10	+	3.18820e10i	1.29369	+	1.12826i
$411$		−	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	$-0.666797\pi$
$419$		−	5.33721e10i		−	1.73164i	0.500355	−	0.865821i	$-0.333203\pi$
$420$	3.08014e9	+	1.11993e9i	0.0989858	+	0.0359910i
$421$	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
$430$	2.97033e10	+	2.59050e10i	0.868823	+	0.757721i
$431$		−	4.56118e10i		−	1.32181i	−0.750471	−	0.660904i	$-0.770173\pi$
$431$		−	4.56118e10i		−	1.32181i	0.750471	−	0.660904i	$-0.229827\pi$
$432$	−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	$-0.966850\pi$
$439$		−	7.72222e9i		−	0.207914i	0.994582	−	0.103957i	$-0.0331505\pi$
$440$	2.48511e8	+	1.25970e10i	0.00663031	+	0.336090i
$441$	4.43979e9			0.117384
$442$	−2.26835e10	+	8.75798e9i	−0.594321	+	0.229464i
$443$	6.84724e10			1.77787			0.888936	−	0.458031i	$-0.151445\pi$
$443$	6.84724e10			1.77787			0.888936	+	0.458031i	$0.151445\pi$
$444$	−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	$0.465996\pi$
$450$	1.12115e9	−	4.74416e9i	0.0273409	−	0.115694i
$451$			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
$460$	−4.36521e10	−	1.58718e10i	−0.974930	−	0.354482i
$461$	−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	$-0.507200\pi$
$463$	−2.07879e9			−0.0452362			−0.0226181	+	0.999744i	$0.507200\pi$
$464$	−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	$-0.639298\pi$
$467$	−4.03126e10			−0.847565			−0.423782	+	0.905764i	$0.639298\pi$
$468$	3.27806e9	+	3.61233e9i	0.0683336	+	0.0753016i
$469$	2.24508e9			0.0464025
$470$	2.22798e9	+	1.94308e9i	0.0456583	+	0.0398197i
$471$			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	$-0.993545\pi$
$479$		−	2.13503e9i		−	0.0405566i	0.999794	−	0.0202783i	$-0.00645523\pi$
$480$	3.62327e10	−	3.42071e10i	0.682552	−	0.644393i
$481$	−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	$-0.547645\pi$
$487$	−1.67761e10			−0.298246			−0.149123	+	0.988819i	$0.547645\pi$
$488$	1.76804e10	−	3.52056e10i	0.311755	−	0.620772i
$489$	4.95491e10			0.866563
$490$	−4.28994e10	−	3.74136e10i	−0.744161	−	0.649001i
$491$		−	6.25998e10i		−	1.07708i	−0.842601	−	0.538539i	$-0.818976\pi$
$491$		−	6.25998e10i		−	1.07708i	0.842601	−	0.538539i	$-0.181024\pi$
$492$	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	$0.341890\pi$
$499$			1.09018e11i			1.75830i	−0.476541	+	0.879152i	$0.658110\pi$
$500$	−5.08117e10	+	3.63927e10i	−0.812987	+	0.582282i
$501$	−2.71367e10			−0.430731
$502$	3.89797e10	+	1.00959e11i	0.613795	+	1.58975i
$503$	1.07703e10			0.168251			0.0841253	−	0.996455i	$-0.473190\pi$
$503$	1.07703e10			0.168251			0.0841253	+	0.996455i	$0.473190\pi$
$504$	−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	$0.398386\pi$
$510$	3.10881e10	−	3.56464e10i	0.459530	−	0.526908i
$511$		−	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
$520$	−1.23354e9	−	6.25280e10i	−0.0168710	−	0.855188i
$521$	−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	$-0.738374\pi$
$523$	−1.01874e11			−1.36163			−0.680813	+	0.732457i	$0.738374\pi$
$524$	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
$530$	−2.96837e10	+	3.40360e10i	−0.376196	+	0.431356i
$531$			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
$540$	−8.39294e10	−	3.05165e10i	−0.987049	−	0.358889i
$541$	−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	$-0.470278\pi$
$547$	1.66947e10			0.186479			0.0932395	+	0.995644i	$0.470278\pi$
$548$	−1.10634e10	−	1.21915e10i	−0.122677	−	0.135187i
$549$	−7.50188e9			−0.0825812
$550$	−2.99357e10	−	7.07446e9i	−0.327144	−	0.0773112i
$551$		−	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
$560$	1.02139e10	−	4.17685e9i	0.103858	−	0.0424714i
$561$	2.32786e10			0.235020
$562$	−8.81704e9	+	3.40421e9i	−0.0883848	+	0.0341249i
$563$	−1.35193e11			−1.34562			−0.672809	−	0.739816i	$-0.734912\pi$
$563$	−1.35193e11			−1.34562			−0.672809	+	0.739816i	$0.734912\pi$
$564$	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	$0.319137\pi$
$570$	−7.00671e10	+	8.03407e10i	−0.663766	+	0.761090i
$571$			6.98949e10i			0.657508i	0.944416	+	0.328754i	$0.106629\pi$
$571$			6.98949e10i			0.657508i	−0.944416	+	0.328754i	$0.893371\pi$
$572$	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
$580$	−1.22592e11	−	4.45743e10i	−1.08331	−	0.393888i
$581$	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	$-0.386215\pi$
$587$	8.30860e10			0.699802			0.349901	+	0.936787i	$0.386215\pi$
$588$	−8.20488e10	+	7.44564e10i	−0.686377	+	0.622863i
$589$	−2.21035e11			−1.83654
$590$	1.48142e11	−	1.69864e11i	1.22256	−	1.40182i
$591$			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	$0.0217622\pi$
$599$			1.75895e10i			0.136630i	−0.997664	+	0.0683149i	$0.978238\pi$
$600$	5.88417e10	+	1.06476e11i	0.454026	+	0.821572i
$601$	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	$-0.433924\pi$
$607$	5.59570e10			0.412192			0.206096	+	0.978532i	$0.433924\pi$
$608$	1.41630e11	−	3.94282e10i	1.03643	−	0.288531i
$609$	−1.67001e10			−0.121408
$610$	7.24869e10	+	6.32176e10i	0.523528	+	0.456582i
$611$		−	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	$-0.875110\pi$
$619$		−	1.12271e11i		−	0.764728i	0.924012	−	0.382364i	$-0.124890\pi$
$620$	−8.61940e10	+	2.37059e11i	−0.583325	+	1.60431i
$621$	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
$630$	−1.58365e9	−	1.38114e9i	−0.0100530	−	0.00876751i
$631$			1.23902e11i			0.781557i	0.920485	+	0.390778i	$0.127794\pi$
$631$			1.23902e11i			0.781557i	−0.920485	+	0.390778i	$0.872206\pi$
$632$	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
$640$	1.29429e10	−	1.67272e11i	0.0771458	−	0.997020i
$641$	−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	$-0.577918\pi$
$643$	−8.28548e10			−0.484701			−0.242350	+	0.970189i	$0.577918\pi$
$644$	−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	$-0.696000\pi$
$647$	−2.02420e11			−1.15515			−0.577573	+	0.816339i	$0.696000\pi$
$648$	−6.86049e10	+	1.36607e11i	−0.389094	+	0.774772i
$649$	1.10928e11			0.625263
$650$	1.48593e11	+	3.51157e10i	0.832425	+	0.196720i
$651$			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	$0.235760\pi$
$659$			2.54526e11i			1.34955i	−0.738021	+	0.674777i	$0.764240\pi$
$660$	−2.04594e10	+	5.62692e10i	−0.107824	+	0.296548i
$661$	−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
$670$	6.28047e10	+	5.47735e10i	0.311668	+	0.271814i
$671$			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
$680$	−3.14107e9	−	1.59221e11i	−0.0146907	−	0.744670i
$681$	1.46305e10			0.0680253
$682$	−1.15813e11	+	4.47146e10i	−0.535326	+	0.206687i
$683$	−3.01557e11			−1.38575			−0.692877	−	0.721056i	$-0.743657\pi$
$683$	−3.01557e11			−1.38575			−0.692877	+	0.721056i	$0.743657\pi$
$684$	−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
$690$	−1.66349e11	−	1.45077e11i	−0.733876	−	0.640031i
$691$		−	2.55417e10i		−	0.112031i	−0.998430	−	0.0560154i	$-0.982160\pi$
$691$		−	2.55417e10i		−	0.112031i	0.998430	−	0.0560154i	$-0.0178396\pi$
$692$	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
$700$	3.66329e9	+	2.66905e10i	0.0152573	+	0.111164i
$701$	−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	$0.303483\pi$
$710$	−1.83199e11	+	2.10060e11i	−0.720924	+	0.826629i
$711$		−	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	$0.162641\pi$
$719$			2.61373e11i			0.978013i	−0.872280	+	0.489006i	$0.837359\pi$
$720$	−2.95707e10	+	1.20926e10i	−0.110035	+	0.0449976i
$721$	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	$-0.141822\pi$
$727$	5.04144e11			1.80475			0.902375	+	0.430951i	$0.141822\pi$
$728$	−2.40908e10	−	1.20985e10i	−0.0857680	−	0.0430731i
$729$	3.07547e11			1.08894
$730$	1.68911e11	−	1.93678e11i	0.594796	−	0.682008i
$731$		−	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	$-0.977488\pi$
$739$		−	4.21510e10i		−	0.141329i	0.997500	−	0.0706643i	$-0.0225119\pi$
$740$	1.24509e11	−	3.42437e11i	0.415217	−	1.14197i
$741$	2.60427e11			0.863799
$742$	7.01165e9	+	1.81604e10i	0.0231315	+	0.0599115i
$743$	4.74544e11			1.55712			0.778558	−	0.627573i	$-0.215951\pi$
$743$	4.74544e11			1.55712			0.778558	+	0.627573i	$0.215951\pi$
$744$	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
$750$	−2.87544e11	+	7.43635e10i	−0.908781	+	0.235025i
$751$		−	2.85992e11i		−	0.899070i	−0.893263	−	0.449535i	$-0.851590\pi$
$751$		−	2.85992e11i		−	0.899070i	0.893263	−	0.449535i	$-0.148410\pi$
$752$	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
$760$	7.07942e9	+	3.58855e11i	0.0212199	+	1.07563i
$761$	−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	$0.245517\pi$
$770$	−8.71502e9	+	9.99287e9i	−0.0247917	+	0.0284267i
$771$		−	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
$780$	1.01555e11	−	2.79306e11i	0.274361	−	0.754573i
$781$	−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	$-0.555753\pi$
$787$	−1.33698e11			−0.348518			−0.174259	+	0.984700i	$0.555753\pi$
$788$	7.83017e10	+	8.62861e10i	0.203080	+	0.223788i
$789$	−6.25298e11			−1.61354
$790$	−1.51882e11	+	1.74152e11i	−0.389940	+	0.447115i
$791$			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
$800$	3.87630e11	+	1.32345e11i	0.946362	+	0.323108i
$801$	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	$0.259518\pi$
$810$	−2.81269e11	−	2.45302e11i	−0.653405	−	0.569850i
$811$			2.39959e11i			0.554695i	0.960770	+	0.277348i	$0.0894554\pi$
$811$			2.39959e11i			0.554695i	−0.960770	+	0.277348i	$0.910545\pi$
$812$	−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
$820$	7.29382e11	+	2.65202e11i	1.61324	+	0.586572i
$821$	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	$-0.482079\pi$
$823$	5.16299e10			0.112539			0.0562694	+	0.998416i	$0.482079\pi$
$824$	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	$-0.641880\pi$
$827$	−4.03317e11			−0.862232			−0.431116	+	0.902297i	$0.641880\pi$
$828$	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	$0.712315\pi$
$830$	2.89297e11	+	2.52303e11i	0.609581	+	0.531631i
$831$			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	$-0.873305\pi$
$839$		−	3.84114e11i		−	0.775197i	0.921828	−	0.387598i	$-0.126695\pi$
$840$	5.24285e10	−	1.03430e9i	0.105305	−	0.00207744i
$841$	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
$850$	3.78376e11	+	8.94183e10i	0.724849	+	0.171297i
$851$			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	$0.121340\pi$
$859$			4.05124e11i			0.744073i	−0.928218	+	0.372037i	$0.878660\pi$
$860$	5.92643e11	+	2.15484e11i	1.08343	+	0.393931i
$861$	9.93596e10			0.180799
$862$	−2.62856e11	−	6.80807e11i	−0.476090	−	1.23309i
$863$	8.73437e10			0.157467			0.0787333	−	0.996896i	$-0.474912\pi$
$863$	8.73437e10			0.157467			0.0787333	+	0.996896i	$0.474912\pi$
$864$	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
$870$	−4.67173e11	−	4.07433e11i	−0.815457	−	0.711180i
$871$		−	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
$880$	7.63044e10	+	1.86592e11i	0.127239	+	0.311144i
$881$	−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	$-0.569044\pi$
$883$	−2.61660e11			−0.430423			−0.215211	+	0.976567i	$0.569044\pi$
$884$	−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	$-0.438044\pi$
$887$	2.39448e11			0.386827			0.193413	+	0.981117i	$0.438044\pi$
$888$	−6.33792e11	−	3.18293e11i	−1.01928	−	0.511889i
$889$	3.55816e10			0.0569664
$890$	−3.28717e10	−	2.86682e10i	−0.0523916	−	0.0456920i
$891$		−	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
$900$	−1.06058e10	−	7.72730e10i	−0.0161648	−	0.117776i
$901$	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	$-0.368803\pi$
$907$	5.42209e11			0.801194			0.400597	+	0.916254i	$0.368803\pi$
$908$	3.64791e10	−	3.31035e10i	0.0536662	−	0.0487002i
$909$	5.48014e10			0.0802669
$910$	4.32591e10	−	4.96019e10i	0.0630829	−	0.0723324i
$911$		−	5.30218e11i		−	0.769806i	−0.922957	−	0.384903i	$-0.874235\pi$
$911$		−	5.30218e11i		−	0.769806i	0.922957	−	0.384903i	$-0.125765\pi$
$912$	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	$-0.990493\pi$
$919$		−	4.26029e10i		−	0.0597279i	0.999554	−	0.0298639i	$-0.00950740\pi$
$920$	−7.43024e11	+	1.46582e10i	−1.03717	+	0.0204611i
$921$	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	$0.525099\pi$
$930$	−7.87859e11	+	9.03379e11i	−1.05321	+	1.20764i
$931$		−	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
$940$	4.44528e10	+	1.61630e10i	0.0569362	+	0.0207019i
$941$	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	$-0.600973\pi$
$947$	−5.01738e11			−0.623846			−0.311923	+	0.950107i	$0.600973\pi$
$948$	3.02258e11	+	3.33080e11i	0.374236	+	0.412397i
$949$	−6.27813e11			−0.774044
$950$	−8.52792e11	−	2.01533e11i	−1.04700	−	0.247430i
$951$		−	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
$960$	3.43681e11	−	7.19384e11i	0.404642	−	0.846985i
$961$	−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	$-0.203231\pi$
$967$	1.40429e12			1.60602			0.803010	+	0.595966i	$0.203231\pi$
$968$	3.49516e11	−	6.95963e11i	0.398076	−	0.792656i
$969$	6.63147e11			0.752168
$970$	6.76723e11	−	7.75948e11i	0.764406	−	0.876487i
$971$			7.36856e11i			0.828907i	0.910071	+	0.414453i	$0.136027\pi$
$971$			7.36856e11i			0.828907i	−0.910071	+	0.414453i	$0.863973\pi$
$972$	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
$980$	−8.55932e11	−	3.11215e11i	−0.927973	−	0.337409i
$981$	−6.31956e10			−0.0682356
$982$	−3.60756e11	−	9.34372e11i	−0.387943	−	1.00479i
$983$	−6.25460e11			−0.669862			−0.334931	−	0.942243i	$-0.608713\pi$
$983$	−6.25460e11			−0.669862			−0.334931	+	0.942243i	$0.608713\pi$
$984$	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
$990$	2.52313e10	−	2.89308e10i	0.0262663	−	0.0301176i
$991$			1.63053e12i			1.69058i	0.534309	+	0.845289i	$0.320572\pi$
$991$			1.63053e12i			1.69058i	−0.534309	+	0.845289i	$0.679428\pi$
$992$	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.19.19	yes	20
4.3	odd	2	inner	20.9.d.c.19.1	✓	20
5.2	odd	4		100.9.b.g.51.12		20
5.3	odd	4		100.9.b.g.51.9		20
5.4	even	2	inner	20.9.d.c.19.2	yes	20
8.3	odd	2		320.9.h.g.319.17		20
8.5	even	2		320.9.h.g.319.3		20
20.3	even	4		100.9.b.g.51.10		20
20.7	even	4		100.9.b.g.51.11		20
20.19	odd	2	inner	20.9.d.c.19.20	yes	20
40.19	odd	2		320.9.h.g.319.4		20
40.29	even	2		320.9.h.g.319.18		20

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

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} +(7536.50 + 6572.76i) 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} +(150369. + 54673.8i) 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} +(573023. + 499747. 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} +(2.55950e6 - 50493.3i) 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} +(-1.43742e6 + 6.08246e6i) 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} +(1.14330e7 + 4.15701e6i) 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} +(2.03039e6 + 1.77075e6i) 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} +(3.79124e7 - 1.55038e7i) 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} +(-5.87827e6 - 5.12659e6i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30}+ \cdots + 28850688 q^{96}+O(q^{100}) \) 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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