LMFDB - Embedded newform 20.9.d.c.19.10

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			19.10
Root			$-2.02968 + 7.73824i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.9.d.c.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.05935 + 15.4765i) q^{2} +75.2390 q^{3} +(-223.043 - 125.649i) q^{4} +(-200.884 - 591.837i) q^{5} +(-305.422 + 1164.44i) q^{6} -4411.35 q^{7} +(2850.02 - 2941.87i) q^{8} -900.091 q^{9} +O(q^{10})$	\(q+(-4.05935 + 15.4765i) q^{2} +75.2390 q^{3} +(-223.043 - 125.649i) q^{4} +(-200.884 - 591.837i) q^{5} +(-305.422 + 1164.44i) q^{6} -4411.35 q^{7} +(2850.02 - 2941.87i) q^{8} -900.091 q^{9} +(9975.01 - 706.503i) q^{10} +330.765i q^{11} +(-16781.6 - 9453.71i) q^{12} -26705.2i q^{13} +(17907.2 - 68272.1i) q^{14} +(-15114.3 - 44529.2i) q^{15} +(33960.6 + 56050.4i) q^{16} -68677.1i q^{17} +(3653.79 - 13930.2i) q^{18} +194166. i q^{19} +(-29557.9 + 157246. i) q^{20} -331905. q^{21} +(-5119.08 - 1342.69i) q^{22} +248604. q^{23} +(214433. - 221344. i) q^{24} +(-309916. + 237781. i) q^{25} +(413302. + 108406. i) q^{26} -561365. q^{27} +(983921. + 554281. i) q^{28} -496543. q^{29} +(750510. - 53156.6i) q^{30} -734331. i q^{31} +(-1.00532e6 + 298063. i) q^{32} +24886.4i q^{33} +(1.06288e6 + 278785. i) q^{34} +(886168. + 2.61080e6i) q^{35} +(200759. + 113096. i) q^{36} -1.92223e6i q^{37} +(-3.00500e6 - 788187. i) q^{38} -2.00927e6i q^{39} +(-2.31363e6 - 1.09577e6i) q^{40} -879710. q^{41} +(1.34732e6 - 5.13673e6i) q^{42} -1.87238e6 q^{43} +(41560.3 - 73774.9i) q^{44} +(180814. + 532707. i) q^{45} +(-1.00917e6 + 3.84752e6i) q^{46} +521085. q^{47} +(2.55516e6 + 4.21717e6i) q^{48} +1.36952e7 q^{49} +(-2.42195e6 - 5.76165e6i) q^{50} -5.16720e6i q^{51} +(-3.35548e6 + 5.95641e6i) q^{52} +882323. i q^{53} +(2.27878e6 - 8.68796e6i) q^{54} +(195759. - 66445.4i) q^{55} +(-1.25724e7 + 1.29776e7i) q^{56} +1.46088e7i q^{57} +(2.01564e6 - 7.68474e6i) q^{58} +3.24496e6i q^{59} +(-2.22391e6 + 1.18310e7i) q^{60} -976271. q^{61} +(1.13649e7 + 2.98091e6i) q^{62} +3.97061e6 q^{63} +(-532013. - 1.67688e7i) q^{64} +(-1.58051e7 + 5.36464e6i) q^{65} +(-385155. - 101023. i) q^{66} +1.58747e7 q^{67} +(-8.62922e6 + 1.53180e7i) q^{68} +1.87047e7 q^{69} +(-4.40032e7 + 3.11663e6i) q^{70} +1.19330e7i q^{71} +(-2.56527e6 + 2.64795e6i) q^{72} -4.92987e7i q^{73} +(2.97494e7 + 7.80302e6i) q^{74} +(-2.33178e7 + 1.78904e7i) q^{75} +(2.43967e7 - 4.33074e7i) q^{76} -1.45912e6i q^{77} +(3.10964e7 + 8.15634e6i) q^{78} -5.67639e7i q^{79} +(2.63505e7 - 3.13588e7i) q^{80} -3.63311e7 q^{81} +(3.57106e6 - 1.36148e7i) q^{82} -3.12722e7 q^{83} +(7.40292e7 + 4.17036e7i) q^{84} +(-4.06456e7 + 1.37961e7i) q^{85} +(7.60065e6 - 2.89779e7i) q^{86} -3.73594e7 q^{87} +(973069. + 942686. i) q^{88} -4.74735e7 q^{89} +(-8.97841e6 + 635917. i) q^{90} +1.17806e8i q^{91} +(-5.54495e7 - 3.12369e7i) q^{92} -5.52504e7i q^{93} +(-2.11527e6 + 8.06456e6i) q^{94} +(1.14914e8 - 3.90048e7i) q^{95} +(-7.56394e7 + 2.24260e7i) q^{96} +2.28701e7i q^{97} +(-5.55935e7 + 2.11953e8i) q^{98} -297718. i 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 $

$2$	−4.05935	+	15.4765i	−0.253710	+	0.967280i
$2$	−4.05935	+	15.4765i	−0.253710	+	0.967280i
$3$	75.2390			0.928877			0.464438	−	0.885605i	$-0.346256\pi$
$3$	75.2390			0.928877			0.464438	+	0.885605i	$0.346256\pi$
$4$	−223.043	−	125.649i	−0.871263	−	0.490817i
$5$	−200.884	−	591.837i	−0.321414	−	0.946939i
$5$	−200.884	−	591.837i	−0.321414	−	0.946939i
$6$	−305.422	+	1164.44i	−0.235665	+	0.898484i
$7$	−4411.35			−1.83730			−0.918648	−	0.395078i	$-0.870718\pi$
$7$	−4411.35			−1.83730			−0.918648	+	0.395078i	$0.870718\pi$
$8$	2850.02	−	2941.87i	0.695805	−	0.718231i
$9$	−900.091			−0.137188
$10$	9975.01	−	706.503i	0.997501	−	0.0706503i
$11$			330.765i			0.0225917i	0.999936	+	0.0112958i	$0.00359566\pi$
$11$			330.765i			0.0225917i	−0.999936	+	0.0112958i	$0.996404\pi$
$12$	−16781.6	−	9453.71i	−0.809296	−	0.455908i
$13$		−	26705.2i		−	0.935022i	−0.883987	−	0.467511i	$-0.845151\pi$
$13$		−	26705.2i		−	0.935022i	0.883987	−	0.467511i	$-0.154849\pi$
$14$	17907.2	−	68272.1i	0.466139	−	1.77718i
$15$	−15114.3	−	44529.2i	−0.298554	−	0.879589i
$16$	33960.6	+	56050.4i	0.518198	+	0.855261i
$17$		−	68677.1i		−	0.822274i	−0.911574	−	0.411137i	$-0.865132\pi$
$17$		−	68677.1i		−	0.822274i	0.911574	−	0.411137i	$-0.134868\pi$
$18$	3653.79	−	13930.2i	0.0348059	−	0.132699i
$19$			194166.i			1.48990i	0.667118	+	0.744952i	$0.267528\pi$
$19$			194166.i			1.48990i	−0.667118	+	0.744952i	$0.732472\pi$
$20$	−29557.9	+	157246.i	−0.184737	+	0.982788i
$21$	−331905.			−1.70662
$22$	−5119.08	−	1342.69i	−0.0218525	−	0.00573173i
$23$	248604.			0.888376			0.444188	−	0.895933i	$-0.353492\pi$
$23$	248604.			0.888376			0.444188	+	0.895933i	$0.353492\pi$
$24$	214433.	−	221344.i	0.646317	−	0.667148i
$25$	−309916.	+	237781.i	−0.793386	+	0.608719i
$26$	413302.	+	108406.i	0.904429	+	0.237224i
$27$	−561365.			−1.05631
$28$	983921.	+	554281.i	1.60077	+	0.901775i
$29$	−496543.			−0.702044			−0.351022	−	0.936367i	$-0.614166\pi$
$29$	−496543.			−0.702044			−0.351022	+	0.936367i	$0.614166\pi$
$30$	750510.	−	53156.6i	0.926556	−	0.0656254i
$31$		−	734331.i		−	0.795143i	−0.917571	−	0.397572i	$-0.869853\pi$
$31$		−	734331.i		−	0.795143i	0.917571	−	0.397572i	$-0.130147\pi$
$32$	−1.00532e6	+	298063.i	−0.958749	+	0.284255i
$33$			24886.4i			0.0209849i
$34$	1.06288e6	+	278785.i	0.795369	+	0.208619i
$35$	886168.	+	2.61080e6i	0.590533	+	1.73981i
$36$	200759.	+	113096.i	0.119527	+	0.0673342i
$37$		−	1.92223e6i		−	1.02565i	−0.858493	−	0.512825i	$-0.828599\pi$
$37$		−	1.92223e6i		−	1.02565i	0.858493	−	0.512825i	$-0.171401\pi$
$38$	−3.00500e6	−	788187.i	−1.44115	−	0.378003i
$39$		−	2.00927e6i		−	0.868520i
$40$	−2.31363e6	−	1.09577e6i	−0.903762	−	0.428035i
$41$	−879710.			−0.311318			−0.155659	−	0.987811i	$-0.549750\pi$
$41$	−879710.			−0.311318			−0.155659	+	0.987811i	$0.549750\pi$
$42$	1.34732e6	−	5.13673e6i	0.432986	−	1.65078i
$43$	−1.87238e6			−0.547672			−0.273836	−	0.961776i	$-0.588292\pi$
$43$	−1.87238e6			−0.547672			−0.273836	+	0.961776i	$0.588292\pi$
$44$	41560.3	−	73774.9i	0.0110884	−	0.0196833i
$45$	180814.	+	532707.i	0.0440942	+	0.129909i
$46$	−1.00917e6	+	3.84752e6i	−0.225390	+	0.859309i
$47$	521085.			0.106787			0.0533933	−	0.998574i	$-0.482996\pi$
$47$	521085.			0.106787			0.0533933	+	0.998574i	$0.482996\pi$
$48$	2.55516e6	+	4.21717e6i	0.481342	+	0.794432i
$49$	1.36952e7			2.37565
$50$	−2.42195e6	−	5.76165e6i	−0.387513	−	0.921864i
$51$		−	5.16720e6i		−	0.763791i
$52$	−3.35548e6	+	5.95641e6i	−0.458924	+	0.814650i
$53$			882323.i			0.111821i	0.998436	+	0.0559106i	$0.0178062\pi$
$53$			882323.i			0.111821i	−0.998436	+	0.0559106i	$0.982194\pi$
$54$	2.27878e6	−	8.68796e6i	0.267995	−	1.02175i
$55$	195759.	−	66445.4i	0.0213930	−	0.00726129i
$56$	−1.25724e7	+	1.29776e7i	−1.27840	+	1.31960i
$57$			1.46088e7i			1.38394i
$58$	2.01564e6	−	7.68474e6i	0.178115	−	0.679074i
$59$			3.24496e6i			0.267794i	0.990995	+	0.133897i	$0.0427492\pi$
$59$			3.24496e6i			0.267794i	−0.990995	+	0.133897i	$0.957251\pi$
$60$	−2.22391e6	+	1.18310e7i	−0.171598	+	0.912889i
$61$	−976271.			−0.0705101			−0.0352550	−	0.999378i	$-0.511224\pi$
$61$	−976271.			−0.0705101			−0.0352550	+	0.999378i	$0.511224\pi$
$62$	1.13649e7	+	2.98091e6i	0.769126	+	0.201735i
$63$	3.97061e6			0.252055
$64$	−532013.	−	1.67688e7i	−0.0317104	−	0.999497i
$65$	−1.58051e7	+	5.36464e6i	−0.885409	+	0.300529i
$66$	−385155.	−	101023.i	−0.0202983	−	0.00532407i
$67$	1.58747e7			0.787781			0.393890	−	0.919157i	$-0.371129\pi$
$67$	1.58747e7			0.787781			0.393890	+	0.919157i	$0.371129\pi$
$68$	−8.62922e6	+	1.53180e7i	−0.403586	+	0.716417i
$69$	1.87047e7			0.825192
$70$	−4.40032e7	+	3.11663e6i	−1.83270	+	0.129805i
$71$			1.19330e7i			0.469588i	0.972045	+	0.234794i	$0.0754416\pi$
$71$			1.19330e7i			0.469588i	−0.972045	+	0.234794i	$0.924558\pi$
$72$	−2.56527e6	+	2.64795e6i	−0.0954561	+	0.0985326i
$73$		−	4.92987e7i		−	1.73598i	−0.496585	−	0.867988i	$-0.665413\pi$
$73$		−	4.92987e7i		−	1.73598i	0.496585	−	0.867988i	$-0.334587\pi$
$74$	2.97494e7	+	7.80302e6i	0.992091	+	0.260217i
$75$	−2.33178e7	+	1.78904e7i	−0.736958	+	0.565425i
$76$	2.43967e7	−	4.33074e7i	0.731269	−	1.29810i
$77$		−	1.45912e6i		−	0.0415076i
$78$	3.10964e7	+	8.15634e6i	0.840103	+	0.220352i
$79$		−	5.67639e7i		−	1.45735i	−0.684860	−	0.728674i	$-0.740137\pi$
$79$		−	5.67639e7i		−	1.45735i	0.684860	−	0.728674i	$-0.259863\pi$
$80$	2.63505e7	−	3.13588e7i	0.643323	−	0.765595i
$81$	−3.63311e7			−0.843991
$82$	3.57106e6	−	1.36148e7i	0.0789844	−	0.301132i
$83$	−3.12722e7			−0.658941			−0.329470	−	0.944166i	$-0.606870\pi$
$83$	−3.12722e7			−0.658941			−0.329470	+	0.944166i	$0.606870\pi$
$84$	7.40292e7	+	4.17036e7i	1.48692	+	0.837638i
$85$	−4.06456e7	+	1.37961e7i	−0.778643	+	0.264291i
$86$	7.60065e6	−	2.89779e7i	0.138950	−	0.529752i
$87$	−3.73594e7			−0.652113
$88$	973069.	+	942686.i	0.0162260	+	0.0157194i
$89$	−4.74735e7			−0.756644			−0.378322	−	0.925674i	$-0.623499\pi$
$89$	−4.74735e7			−0.756644			−0.378322	+	0.925674i	$0.623499\pi$
$90$	−8.97841e6	+	635917.i	−0.136845	+	0.00969238i
$91$			1.17806e8i			1.71791i
$92$	−5.54495e7	−	3.12369e7i	−0.774009	−	0.436030i
$93$		−	5.52504e7i		−	0.738590i
$94$	−2.11527e6	+	8.06456e6i	−0.0270928	+	0.103293i
$95$	1.14914e8	−	3.90048e7i	1.41085	−	0.478876i
$96$	−7.56394e7	+	2.24260e7i	−0.890559	+	0.264038i
$97$			2.28701e7i			0.258333i	0.991623	+	0.129167i	$0.0412302\pi$
$97$			2.28701e7i			0.258333i	−0.991623	+	0.129167i	$0.958770\pi$
$98$	−5.55935e7	+	2.11953e8i	−0.602726	+	2.29792i
$99$		−	297718.i		−	0.00309931i
$100$	9.90017e7	−	1.40948e7i	0.990017	−	0.140948i
$101$	3.20930e7			0.308407			0.154204	−	0.988039i	$-0.450719\pi$
$101$	3.20930e7			0.308407			0.154204	+	0.988039i	$0.450719\pi$
$102$	7.99701e7	+	2.09755e7i	0.738800	+	0.193781i
$103$	−2.04446e7			−0.181648			−0.0908240	−	0.995867i	$-0.528950\pi$
$103$	−2.04446e7			−0.181648			−0.0908240	+	0.995867i	$0.528950\pi$
$104$	−7.85632e7	−	7.61102e7i	−0.671562	−	0.650593i
$105$	6.66744e7	+	1.96434e8i	0.548532	+	1.61607i
$106$	−1.36553e7	−	3.58166e6i	−0.108163	−	0.0283701i
$107$	9.07923e7			0.692650			0.346325	−	0.938115i	$-0.387429\pi$
$107$	9.07923e7			0.692650			0.346325	+	0.938115i	$0.387429\pi$
$108$	1.25209e8	+	7.05350e7i	0.920321	+	0.518453i
$109$	7.14225e7			0.505975			0.252988	−	0.967470i	$-0.418587\pi$
$109$	7.14225e7			0.505975			0.252988	+	0.967470i	$0.418587\pi$
$110$	233687.	+	3.29938e6i	0.00159611	+	0.0225352i
$111$		−	1.44627e8i		−	0.952702i
$112$	−1.49812e8	−	2.47258e8i	−0.952083	−	1.57137i
$113$		−	1.08885e8i		−	0.667811i	−0.942607	−	0.333906i	$-0.891633\pi$
$113$		−	1.08885e8i		−	0.667811i	0.942607	−	0.333906i	$-0.108367\pi$
$114$	−2.26093e8	−	5.93024e7i	−1.33865	−	0.351118i
$115$	−4.99406e7	−	1.47133e8i	−0.285537	−	0.841238i
$116$	1.10751e8	+	6.23901e7i	0.611665	+	0.344575i
$117$			2.40371e7i			0.128274i
$118$	−5.02206e7	−	1.31724e7i	−0.259032	−	0.0679420i
$119$			3.02959e8i			1.51076i
$120$	−1.74075e8	−	8.24447e7i	−0.839484	−	0.397592i
$121$	2.14249e8			0.999490
$122$	3.96303e6	−	1.51093e7i	0.0178891	−	0.0682030i
$123$	−6.61886e7			−0.289176
$124$	−9.22680e7	+	1.63788e8i	−0.390269	+	0.692779i
$125$	2.02985e8	+	1.35653e8i	0.831425	+	0.555637i
$126$	−1.61181e7	+	6.14511e7i	−0.0639487	+	0.243808i
$127$	−3.04697e8			−1.17126			−0.585631	−	0.810578i	$-0.699153\pi$
$127$	−3.04697e8			−1.17126			−0.585631	+	0.810578i	$0.699153\pi$
$128$	2.61681e8	+	5.98367e7i	0.974839	+	0.222909i
$129$	−1.40876e8			−0.508719
$130$	−1.88673e7	−	2.66384e8i	−0.0660596	−	0.932686i
$131$		−	4.38648e8i		−	1.48947i	−0.667362	−	0.744733i	$-0.732577\pi$
$131$		−	4.38648e8i		−	1.48947i	0.667362	−	0.744733i	$-0.267423\pi$
$132$	3.12696e6	−	5.55075e6i	0.0102997	−	0.0182834i
$133$		−	8.56532e8i		−	2.73739i
$134$	−6.44409e7	+	2.45684e8i	−0.199868	+	0.762005i
$135$	1.12769e8	+	3.32236e8i	0.339512	+	1.00026i
$136$	−2.02039e8	−	1.95731e8i	−0.590582	−	0.572142i
$137$			5.38563e8i			1.52881i	0.644735	+	0.764406i	$0.276968\pi$
$137$			5.38563e8i			1.52881i	−0.644735	+	0.764406i	$0.723032\pi$
$138$	−7.59291e7	+	2.89484e8i	−0.209359	+	0.798192i
$139$		−	1.52244e8i		−	0.407832i	−0.978988	−	0.203916i	$-0.934633\pi$
$139$		−	1.52244e8i		−	0.407832i	0.978988	−	0.203916i	$-0.0653669\pi$
$140$	1.30390e8	−	6.93667e8i	0.339416	−	1.80567i
$141$	3.92059e7			0.0991916
$142$	−1.84681e8	−	4.84404e7i	−0.454224	−	0.119139i
$143$	8.83314e6			0.0211237
$144$	−3.05676e7	−	5.04504e7i	−0.0710906	−	0.117332i
$145$	9.97475e7	+	2.93872e8i	0.225647	+	0.664793i
$146$	7.62970e8	+	2.00121e8i	1.67918	+	0.440434i
$147$	1.03041e9			2.20669
$148$	−2.41527e8	+	4.28741e8i	−0.503406	+	0.893611i
$149$	−8.29509e8			−1.68297			−0.841485	−	0.540281i	$-0.818318\pi$
$149$	−8.29509e8			−1.68297			−0.841485	+	0.540281i	$0.818318\pi$
$150$	−1.82225e8	−	4.33501e8i	−0.359951	−	0.856298i
$151$			4.66185e8i			0.896708i	0.893856	+	0.448354i	$0.147990\pi$
$151$			4.66185e8i			0.896708i	−0.893856	+	0.448354i	$0.852010\pi$
$152$	5.71211e8	+	5.53376e8i	1.07009	+	1.03668i
$153$			6.18156e7i			0.112806i
$154$	2.25820e7	+	5.92308e6i	0.0401495	+	0.0105309i
$155$	−4.34604e8	+	1.47515e8i	−0.752952	+	0.255570i
$156$	−2.52463e8	+	4.48154e8i	−0.426284	+	0.756710i
$157$		−	1.15560e7i		−	0.0190199i	−0.999955	−	0.00950995i	$-0.996973\pi$
$157$		−	1.15560e7i		−	0.0190199i	0.999955	−	0.00950995i	$-0.00302716\pi$
$158$	8.78505e8	+	2.30425e8i	1.40966	+	0.369743i
$159$			6.63852e7i			0.103868i
$160$	3.78357e8	+	5.35110e8i	0.577328	+	0.816513i
$161$	−1.09668e9			−1.63221
$162$	1.47481e8	−	5.62277e8i	0.214129	−	0.816376i
$163$	−7.56904e8			−1.07224			−0.536118	−	0.844143i	$-0.680110\pi$
$163$	−7.56904e8			−1.07224			−0.536118	+	0.844143i	$0.680110\pi$
$164$	1.96214e8	+	1.10535e8i	0.271240	+	0.152800i
$165$	1.47287e7	−	4.99928e6i	0.0198714	−	0.00674485i
$166$	1.26945e8	−	4.83984e8i	0.167180	−	0.637381i
$167$	−8.44002e8			−1.08512			−0.542560	−	0.840017i	$-0.682545\pi$
$167$	−8.44002e8			−1.08512			−0.542560	+	0.840017i	$0.682545\pi$
$168$	−9.45936e8	+	9.76423e8i	−1.18748	+	1.22575i
$169$	1.02565e8			0.125734
$170$	−4.85206e7	−	6.85055e8i	−0.0580939	−	0.820219i
$171$		−	1.74767e8i		−	0.204397i
$172$	4.17622e8	+	2.35263e8i	0.477166	+	0.268806i
$173$		−	1.32596e9i		−	1.48029i	−0.672446	−	0.740146i	$-0.734756\pi$
$173$		−	1.32596e9i		−	1.48029i	0.672446	−	0.740146i	$-0.265244\pi$
$174$	1.51655e8	−	5.78192e8i	0.165447	−	0.630776i
$175$	1.36715e9	−	1.04893e9i	1.45768	−	1.11840i
$176$	−1.85395e7	+	1.12330e7i	−0.0193218	+	0.0117070i
$177$			2.44148e8i			0.248748i
$178$	1.92712e8	−	7.34723e8i	0.191968	−	0.731887i
$179$			9.50768e8i			0.926110i	0.886330	+	0.463055i	$0.153247\pi$
$179$			9.50768e8i			0.926110i	−0.886330	+	0.463055i	$0.846753\pi$
$180$	2.66048e7	−	1.41536e8i	0.0253437	−	0.134827i
$181$	1.08081e9			1.00702			0.503508	−	0.863991i	$-0.332042\pi$
$181$	1.08081e9			1.00702			0.503508	+	0.863991i	$0.332042\pi$
$182$	−1.82322e9	−	4.78215e8i	−1.66170	−	0.435851i
$183$	−7.34537e7			−0.0654952
$184$	7.08526e8	−	7.31362e8i	0.618137	−	0.638059i
$185$	−1.13765e9	+	3.86146e8i	−0.971227	+	0.329658i
$186$	8.55082e8	+	2.24281e8i	0.714424	+	0.187387i
$187$	2.27160e7			0.0185766
$188$	−1.16224e8	−	6.54738e7i	−0.0930392	−	0.0524127i
$189$	2.47638e9			1.94075
$190$	1.37179e8	+	1.93681e9i	0.105262	+	1.48618i
$191$		−	1.06586e7i		−	0.00800877i	−0.999992	−	0.00400439i	$-0.998725\pi$
$191$		−	1.06586e7i		−	0.00800877i	0.999992	−	0.00400439i	$-0.00127464\pi$
$192$	−4.00281e7	−	1.26167e9i	−0.0294551	−	0.928410i
$193$			1.44556e9i			1.04186i	0.853601	+	0.520928i	$0.174414\pi$
$193$			1.44556e9i			1.04186i	−0.853601	+	0.520928i	$0.825586\pi$
$194$	−3.53948e8	−	9.28377e7i	−0.249881	−	0.0655417i
$195$	−1.18916e9	+	4.03630e8i	−0.822436	+	0.279155i
$196$	−3.05462e9	−	1.72078e9i	−2.06982	−	1.16601i
$197$		−	1.99680e9i		−	1.32578i	−0.748718	−	0.662889i	$-0.769330\pi$
$197$		−	1.99680e9i		−	1.32578i	0.748718	−	0.662889i	$-0.230670\pi$
$198$	4.60764e6	+	1.20854e6i	0.00299790	+	0.000786325i
$199$		−	2.18065e9i		−	1.39051i	−0.718762	−	0.695256i	$-0.755291\pi$
$199$		−	2.18065e9i		−	1.39051i	0.718762	−	0.695256i	$-0.244709\pi$
$200$	−1.83746e8	+	1.58941e9i	−0.114841	+	0.993384i
$201$	1.19439e9			0.731751
$202$	−1.30277e8	+	4.96687e8i	−0.0782459	+	0.298316i
$203$	2.19042e9			1.28986
$204$	−6.49254e8	+	1.15251e9i	−0.374881	+	0.665463i
$205$	1.76720e8	+	5.20645e8i	0.100062	+	0.294799i
$206$	8.29921e7	−	3.16411e8i	0.0460859	−	0.175705i
$207$	−2.23766e8			−0.121875
$208$	1.49683e9	−	9.06924e8i	0.799688	−	0.484527i
$209$	−6.42232e7			−0.0336594
$210$	−3.31076e9	+	2.34492e8i	−1.70236	+	0.120573i
$211$			2.87675e9i			1.45135i	0.688036	+	0.725676i	$0.258473\pi$
$211$			2.87675e9i			1.45135i	−0.688036	+	0.725676i	$0.741527\pi$
$212$	1.10863e8	−	1.96796e8i	0.0548837	−	0.0974257i
$213$			8.97829e8i			0.436190i
$214$	−3.68558e8	+	1.40515e9i	−0.175732	+	0.669987i
$215$	3.76131e8	+	1.10814e9i	0.176029	+	0.518611i
$216$	−1.59990e9	+	1.65146e9i	−0.734984	+	0.758672i
$217$			3.23939e9i			1.46091i
$218$	−2.89929e8	+	1.10537e9i	−0.128371	+	0.489420i
$219$		−	3.70918e9i		−	1.61251i
$220$	−5.20115e7	−	9.77672e6i	−0.0222028	−	0.00417352i
$221$	−1.83403e9			−0.768844
$222$	2.23832e9	+	5.87092e8i	0.921530	+	0.241710i
$223$	−6.50587e8			−0.263079			−0.131539	−	0.991311i	$-0.541992\pi$
$223$	−6.50587e8			−0.263079			−0.131539	+	0.991311i	$0.541992\pi$
$224$	4.43482e9	−	1.31486e9i	1.76150	−	0.522260i
$225$	2.78953e8	−	2.14024e8i	0.108843	−	0.0835090i
$226$	1.68515e9	+	4.42002e8i	0.645961	+	0.169430i
$227$	−1.93354e9			−0.728199			−0.364099	−	0.931360i	$-0.618623\pi$
$227$	−1.93354e9			−0.728199			−0.364099	+	0.931360i	$0.618623\pi$
$228$	1.83559e9	−	3.25840e9i	0.679259	−	1.20577i
$229$	2.20853e9			0.803085			0.401542	−	0.915840i	$-0.368474\pi$
$229$	2.20853e9			0.803085			0.401542	+	0.915840i	$0.368474\pi$
$230$	2.47983e9	−	1.75640e8i	0.886156	−	0.0627641i
$231$		−	1.09783e8i		−	0.0385555i
$232$	−1.41516e9	+	1.46077e9i	−0.488486	+	0.504230i
$233$			3.02340e9i			1.02582i	0.858441	+	0.512912i	$0.171433\pi$
$233$			3.02340e9i			1.02582i	−0.858441	+	0.512912i	$0.828567\pi$
$234$	−3.72009e8	−	9.75750e7i	−0.124077	−	0.0325443i
$235$	−1.04678e8	−	3.08397e8i	−0.0343227	−	0.101120i
$236$	4.07726e8	−	7.23767e8i	0.131438	−	0.233319i
$237$		−	4.27086e9i		−	1.35370i
$238$	−4.68873e9	−	1.22982e9i	−1.46133	−	0.383294i
$239$			2.34377e9i			0.718328i	0.933274	+	0.359164i	$0.116938\pi$
$239$			2.34377e9i			0.718328i	−0.933274	+	0.359164i	$0.883062\pi$
$240$	1.98259e9	−	2.35940e9i	0.597568	−	0.711143i
$241$	−2.44863e9			−0.725865			−0.362932	−	0.931815i	$-0.618224\pi$
$241$	−2.44863e9			−0.725865			−0.362932	+	0.931815i	$0.618224\pi$
$242$	−8.69714e8	+	3.31583e9i	−0.253580	+	0.966787i
$243$	9.49603e8			0.272343
$244$	2.17751e8	+	1.22668e8i	0.0614328	+	0.0346075i
$245$	−2.75114e9	−	8.10530e9i	−0.763569	−	2.24960i
$246$	2.68683e8	−	1.02437e9i	0.0733668	−	0.279714i
$247$	5.18523e9			1.39309
$248$	−2.16031e9	−	2.09286e9i	−0.571096	−	0.553265i
$249$	−2.35289e9			−0.612075
$250$	−2.92343e9	+	2.59082e9i	−0.748397	+	0.663251i
$251$		−	3.17410e9i		−	0.799698i	−0.916581	−	0.399849i	$-0.869063\pi$
$251$		−	3.17410e9i		−	0.799698i	0.916581	−	0.399849i	$-0.130937\pi$
$252$	−8.85618e8	−	4.98904e8i	−0.219606	−	0.123713i
$253$			8.22296e7i			0.0200699i
$254$	1.23687e9	−	4.71564e9i	0.297160	−	1.13294i
$255$	−3.05814e9	+	1.03801e9i	−0.723263	+	0.245493i
$256$	−1.98832e9	+	3.80701e9i	−0.462942	+	0.886389i
$257$		−	1.47238e9i		−	0.337511i	−0.985658	−	0.168755i	$-0.946025\pi$
$257$		−	1.47238e9i		−	0.337511i	0.985658	−	0.168755i	$-0.0539748\pi$
$258$	5.71866e8	−	2.18027e9i	0.129067	−	0.492074i
$259$			8.47963e9i			1.88442i
$260$	4.19928e9	+	7.89349e8i	0.918929	+	0.172733i
$261$	4.46933e8			0.0963121
$262$	6.78873e9	+	1.78063e9i	1.44073	+	0.377892i
$263$	−5.32533e9			−1.11307			−0.556536	−	0.830824i	$-0.687870\pi$
$263$	−5.32533e9			−1.11307			−0.556536	+	0.830824i	$0.687870\pi$
$264$	7.32127e7	+	7.09268e7i	0.0150720	+	0.0146014i
$265$	5.22191e8	−	1.77245e8i	0.105888	−	0.0359409i
$266$	1.32561e10	+	3.47697e9i	2.64783	+	0.694503i
$267$	−3.57186e9			−0.702829
$268$	−3.54074e9	−	1.99464e9i	−0.686364	−	0.386656i
$269$	−6.88679e9			−1.31525			−0.657624	−	0.753346i	$-0.728438\pi$
$269$	−6.88679e9			−1.31525			−0.657624	+	0.753346i	$0.728438\pi$
$270$	−5.59962e9	+	3.96606e8i	−1.05367	+	0.0746285i
$271$		−	8.15744e9i		−	1.51244i	−0.654320	−	0.756218i	$-0.727045\pi$
$271$		−	8.15744e9i		−	1.51244i	0.654320	−	0.756218i	$-0.272955\pi$
$272$	3.84938e9	−	2.33232e9i	0.703259	−	0.426101i
$273$			8.86359e9i			1.59573i
$274$	−8.33506e9	−	2.18622e9i	−1.47879	−	0.387874i
$275$	−7.86496e7	−	1.02509e8i	−0.0137520	−	0.0179239i
$276$	−4.17196e9	−	2.35023e9i	−0.718959	−	0.405018i
$277$			1.39904e9i			0.237636i	0.992916	+	0.118818i	$0.0379105\pi$
$277$			1.39904e9i			0.237636i	−0.992916	+	0.118818i	$0.962090\pi$
$278$	2.35620e9	+	6.18012e8i	0.394488	+	0.103471i
$279$			6.60965e8i			0.109084i
$280$	1.02062e10	+	4.83382e9i	1.66048	+	0.786427i
$281$	3.34175e7			0.00535980			0.00267990	−	0.999996i	$-0.499147\pi$
$281$	3.34175e7			0.00535980			0.00267990	+	0.999996i	$0.499147\pi$
$282$	−1.59151e8	+	6.06770e8i	−0.0251659	+	0.0959461i
$283$	8.63810e9			1.34671			0.673353	−	0.739321i	$-0.264854\pi$
$283$	8.63810e9			1.34671			0.673353	+	0.739321i	$0.264854\pi$
$284$	1.49937e9	−	2.66158e9i	0.230482	−	0.409135i
$285$	8.64605e9	−	2.93468e9i	1.31050	−	0.444817i
$286$	−3.58568e7	+	1.36706e8i	−0.00535930	+	0.0204326i
$287$	3.88071e9			0.571983
$288$	9.04880e8	−	2.68284e8i	0.131529	−	0.0389964i
$289$	2.25921e9			0.323866
$290$	−4.95302e9	+	3.50809e8i	−0.700290	+	0.0495997i
$291$			1.72072e9i			0.239960i
$292$	−6.19433e9	+	1.09957e10i	−0.852046	+	1.51249i
$293$			7.50194e9i			1.01790i	0.860797	+	0.508948i	$0.169965\pi$
$293$			7.50194e9i			1.01790i	−0.860797	+	0.508948i	$0.830035\pi$
$294$	−4.18280e9	+	1.59471e10i	−0.559858	+	2.13449i
$295$	1.92049e9	−	6.51861e8i	0.253585	−	0.0860729i
$296$	−5.65496e9	−	5.47840e9i	−0.736653	−	0.713652i
$297$		−	1.85680e8i		−	0.0238638i
$298$	3.36727e9	−	1.28379e10i	0.426985	−	1.62790i
$299$		−	6.63902e9i		−	0.830652i
$300$	7.44879e9	−	1.06048e9i	0.919604	−	0.130923i
$301$	8.25972e9			1.00623
$302$	−7.21491e9	−	1.89241e9i	−0.867368	−	0.227503i
$303$	2.41465e9			0.286472
$304$	−1.08831e10	+	6.59399e9i	−1.27426	+	0.772065i
$305$	1.96117e8	+	5.77793e8i	0.0226629	+	0.0667687i
$306$	−9.56689e8	−	2.50932e8i	−0.109115	−	0.0286200i
$307$	−1.31945e10			−1.48539			−0.742696	−	0.669629i	$-0.766453\pi$
$307$	−1.31945e10			−1.48539			−0.742696	+	0.669629i	$0.766453\pi$
$308$	−1.83337e8	+	3.25447e8i	−0.0203726	+	0.0361640i
$309$	−1.53824e9			−0.168729
$310$	−5.18807e8	−	7.32496e9i	−0.0561771	−	0.793156i
$311$			1.38692e10i			1.48255i	0.671200	+	0.741276i	$0.265779\pi$
$311$			1.38692e10i			1.48255i	−0.671200	+	0.741276i	$0.734221\pi$
$312$	−5.91102e9	−	5.72646e9i	−0.623798	−	0.604321i
$313$		−	2.48561e9i		−	0.258974i	−0.991581	−	0.129487i	$-0.958667\pi$
$313$		−	2.48561e9i		−	0.258974i	0.991581	−	0.129487i	$-0.0413330\pi$
$314$	1.78846e8	+	4.69098e7i	0.0183976	+	0.00482553i
$315$	−7.97632e8	−	2.34995e9i	−0.0810140	−	0.238681i
$316$	−7.13233e9	+	1.26608e10i	−0.715291	+	1.26973i
$317$		−	7.47216e9i		−	0.739962i	−0.929039	−	0.369981i	$-0.879364\pi$
$317$		−	7.47216e9i		−	0.739962i	0.929039	−	0.369981i	$-0.120636\pi$
$318$	−1.02741e9	−	2.69481e8i	−0.100470	−	0.0263524i
$319$		−	1.64239e8i		−	0.0158604i
$320$	−9.81751e9	+	3.68344e9i	−0.936270	+	0.351280i
$321$	6.83112e9			0.643386
$322$	4.45181e9	−	1.69727e10i	0.414107	−	1.57880i
$323$	1.33347e10			1.22511
$324$	8.10340e9	+	4.56496e9i	0.735338	+	0.414245i
$325$	6.34998e9	+	8.27637e9i	0.569166	+	0.741833i
$326$	3.07254e9	−	1.17142e10i	0.272037	−	1.03715i
$327$	5.37376e9			0.469989
$328$	−2.50719e9	+	2.58800e9i	−0.216617	+	0.223598i
$329$	−2.29868e9			−0.196199
$330$	1.75823e7	+	2.48242e8i	0.00148259	+	0.0209325i
$331$		−	8.74537e9i		−	0.728561i	−0.931289	−	0.364281i	$-0.881315\pi$
$331$		−	8.74537e9i		−	0.728561i	0.931289	−	0.364281i	$-0.118685\pi$
$332$	6.97506e9	+	3.92933e9i	0.574111	+	0.323419i
$333$			1.73018e9i			0.140707i
$334$	3.42610e9	−	1.30622e10i	0.275305	−	1.04961i
$335$	−3.18897e9	−	9.39521e9i	−0.253204	−	0.745980i
$336$	−1.12717e10	−	1.86034e10i	−0.884367	−	1.45961i
$337$		−	1.18687e10i		−	0.920206i	−0.887866	−	0.460103i	$-0.847813\pi$
$337$		−	1.18687e10i		−	0.920206i	0.887866	−	0.460103i	$-0.152187\pi$
$338$	−4.16346e8	+	1.58734e9i	−0.0318998	+	0.121620i
$339$		−	8.19239e9i		−	0.620314i
$340$	1.07992e10	+	2.02995e9i	0.808121	+	0.151904i
$341$	2.42891e8			0.0179636
$342$	2.70477e9	+	7.09440e8i	0.197709	+	0.0518575i
$343$	−3.49836e10			−2.52748
$344$	−5.33632e9	+	5.50830e9i	−0.381073	+	0.393355i
$345$	−3.75748e9	−	1.10701e10i	−0.265229	−	0.781406i
$346$	2.05213e10	+	5.38256e9i	1.43186	+	0.375564i
$347$	−6.58114e9			−0.453924			−0.226962	−	0.973904i	$-0.572879\pi$
$347$	−6.58114e9			−0.453924			−0.226962	+	0.973904i	$0.572879\pi$
$348$	8.33276e9	+	4.69417e9i	0.568162	+	0.320068i
$349$	−1.94728e9			−0.131258			−0.0656292	−	0.997844i	$-0.520905\pi$
$349$	−1.94728e9			−0.131258			−0.0656292	+	0.997844i	$0.520905\pi$
$350$	1.06841e10	+	2.54166e10i	0.711975	+	1.69374i
$351$			1.49913e10i			0.987671i
$352$	−9.85888e7	−	3.32525e8i	−0.00642180	−	0.0216598i
$353$		−	6.28067e9i		−	0.404489i	−0.979335	−	0.202245i	$-0.935176\pi$
$353$		−	6.28067e9i		−	0.404489i	0.979335	−	0.202245i	$-0.0648236\pi$
$354$	−3.77855e9	−	9.91082e8i	−0.240609	−	0.0631097i
$355$	7.06240e9	−	2.39715e9i	0.444671	−	0.150932i
$356$	1.05886e10	+	5.96500e9i	0.659235	+	0.371373i
$357$			2.27943e10i			1.40331i
$358$	−1.47146e10	−	3.85950e9i	−0.895808	−	0.234963i
$359$			2.04439e10i			1.23080i	0.788216	+	0.615399i	$0.211005\pi$
$359$			2.04439e10i			1.23080i	−0.788216	+	0.615399i	$0.788995\pi$
$360$	2.08248e9	+	9.86292e8i	0.123985	+	0.0587213i
$361$	−2.07168e10			−1.21981
$362$	−4.38740e9	+	1.67272e10i	−0.255490	+	0.974067i
$363$	1.61199e10			0.928403
$364$	1.48022e10	−	2.62758e10i	0.843180	−	1.49675i
$365$	−2.91768e10	+	9.90331e9i	−1.64386	+	0.557968i
$366$	2.98175e8	−	1.13681e9i	0.0166168	−	0.0633522i
$367$	2.25899e10			1.24523			0.622615	−	0.782528i	$-0.286070\pi$
$367$	2.25899e10			1.24523			0.622615	+	0.782528i	$0.286070\pi$
$368$	8.44275e9	+	1.39344e10i	0.460355	+	0.759793i
$369$	7.91819e8			0.0427091
$370$	−1.35806e9	−	1.91743e10i	−0.0724625	−	1.02309i
$371$		−	3.89223e9i		−	0.205449i
$372$	−6.94216e9	+	1.23232e10i	−0.362512	+	0.643506i
$373$		−	1.58788e10i		−	0.820318i	−0.912014	−	0.410159i	$-0.865473\pi$
$373$		−	1.58788e10i		−	0.820318i	0.912014	−	0.410159i	$-0.134527\pi$
$374$	−9.22123e7	+	3.51564e8i	−0.00471305	+	0.0179687i
$375$	1.52724e10	+	1.02064e10i	0.772292	+	0.516118i
$376$	1.48510e9	−	1.53296e9i	0.0743027	−	0.0766974i
$377$			1.32603e10i			0.656427i
$378$	−1.00525e10	+	3.83256e10i	−0.492387	+	1.87725i
$379$			1.48883e10i			0.721584i	0.932646	+	0.360792i	$0.117494\pi$
$379$			1.48883e10i			0.721584i	−0.932646	+	0.360792i	$0.882506\pi$
$380$	−3.05318e10	−	5.73913e9i	−1.46426	−	0.275240i
$381$	−2.29251e10			−1.08796
$382$	1.64957e8	+	4.32670e7i	0.00774673	+	0.00203190i
$383$	−3.83942e9			−0.178431			−0.0892156	−	0.996012i	$-0.528436\pi$
$383$	−3.83942e9			−0.178431			−0.0892156	+	0.996012i	$0.528436\pi$
$384$	1.96887e10	+	4.50206e9i	0.905505	+	0.207055i
$385$	−8.63560e8	+	2.93114e8i	−0.0393052	+	0.0133411i
$386$	−2.23722e10	−	5.86805e9i	−1.00777	−	0.264329i
$387$	1.68531e9			0.0751340
$388$	2.87360e9	−	5.10102e9i	0.126794	−	0.225076i
$389$	1.16368e10			0.508199			0.254100	−	0.967178i	$-0.418221\pi$
$389$	1.16368e10			0.508199			0.254100	+	0.967178i	$0.418221\pi$
$390$	−1.41956e9	−	2.00425e10i	−0.0613612	−	0.866350i
$391$		−	1.70734e10i		−	0.730489i
$392$	3.90315e10	−	4.02894e10i	1.65299	−	1.70627i
$393$		−	3.30034e10i		−	1.38353i
$394$	3.09035e10	+	8.10574e9i	1.28240	+	0.336362i
$395$	−3.35949e10	+	1.14029e10i	−1.38002	+	0.468413i
$396$	−3.74081e7	+	6.64041e7i	−0.00152119	+	0.00270031i
$397$			6.76965e9i			0.272524i	0.990673	+	0.136262i	$0.0435089\pi$
$397$			6.76965e9i			0.272524i	−0.990673	+	0.136262i	$0.956491\pi$
$398$	3.37489e10	+	8.85205e9i	1.34501	+	0.352786i
$399$		−	6.44446e10i		−	2.54270i
$400$	−2.38527e10	−	9.29573e9i	−0.931745	−	0.363115i
$401$	3.60559e10			1.39444			0.697219	−	0.716858i	$-0.254420\pi$
$401$	3.60559e10			1.39444			0.697219	+	0.716858i	$0.254420\pi$
$402$	−4.84847e9	+	1.84850e10i	−0.185652	+	0.707809i
$403$	−1.96104e10			−0.743476
$404$	−7.15813e9	−	4.03245e9i	−0.268704	−	0.151371i
$405$	7.29833e9	+	2.15021e10i	0.271271	+	0.799208i
$406$	−8.89170e9	+	3.39000e10i	−0.327251	+	1.24766i
$407$	6.35807e8			0.0231712
$408$	−1.52012e10	−	1.47266e10i	−0.548578	−	0.531450i
$409$	3.60276e10			1.28749			0.643743	−	0.765242i	$-0.277381\pi$
$409$	3.60276e10			1.28749			0.643743	+	0.765242i	$0.277381\pi$
$410$	−8.77512e9	+	6.21518e8i	−0.310540	+	0.0219947i
$411$			4.05209e10i			1.42008i
$412$	4.56004e9	+	2.56885e9i	0.158263	+	0.0891559i
$413$		−	1.43146e10i		−	0.492017i
$414$	9.08346e8	−	3.46312e9i	0.0309208	−	0.117887i
$415$	6.28209e9	+	1.85081e10i	0.211793	+	0.623977i
$416$	7.95982e9	+	2.68473e10i	0.265785	+	0.896451i
$417$		−	1.14547e10i		−	0.378825i
$418$	2.60705e8	−	9.93950e8i	0.00853972	−	0.0325581i
$419$		−	1.16017e10i		−	0.376415i	−0.982129	−	0.188207i	$-0.939732\pi$
$419$		−	1.16017e10i		−	0.376415i	0.982129	−	0.188207i	$-0.0602677\pi$
$420$	9.81043e9	−	5.21908e10i	0.315276	−	1.67725i
$421$	−1.99023e10			−0.633542			−0.316771	−	0.948502i	$-0.602599\pi$
$421$	−1.99023e10			−0.633542			−0.316771	+	0.948502i	$0.602599\pi$
$422$	−4.45220e10	−	1.16778e10i	−1.40386	−	0.368222i
$423$	−4.69023e8			−0.0146498
$424$	2.59568e9	+	2.51464e9i	0.0803134	+	0.0778058i
$425$	1.63301e10	+	2.12842e10i	0.500534	+	0.652380i
$426$	−1.38952e10	−	3.64461e9i	−0.421918	−	0.110666i
$427$	4.30667e9			0.129548
$428$	−2.02506e10	−	1.14080e10i	−0.603480	−	0.339964i
$429$	6.64596e8			0.0196213
$430$	−1.86770e10	+	1.32284e9i	−0.546303	+	0.0386932i
$431$		−	6.42420e10i		−	1.86170i	−0.365400	−	0.930851i	$-0.619068\pi$
$431$		−	6.42420e10i		−	1.86170i	0.365400	−	0.930851i	$-0.380932\pi$
$432$	−1.90643e10	−	3.14647e10i	−0.547376	−	0.903418i
$433$		−	5.36499e10i		−	1.52622i	−0.646269	−	0.763110i	$-0.723672\pi$
$433$		−	5.36499e10i		−	1.52622i	0.646269	−	0.763110i	$-0.276328\pi$
$434$	−5.01344e10	−	1.31498e10i	−1.41311	−	0.370648i
$435$	7.50490e9	+	2.21107e10i	0.209598	+	0.617511i
$436$	−1.59303e10	−	8.97418e9i	−0.440837	−	0.248341i
$437$			4.82704e10i			1.32360i
$438$	5.74051e10	+	1.50569e10i	1.55975	+	0.409109i
$439$			2.08363e10i			0.561000i	0.959854	+	0.280500i	$0.0905002\pi$
$439$			2.08363e10i			0.561000i	−0.959854	+	0.280500i	$0.909500\pi$
$440$	3.62442e8	−	7.65268e8i	0.00967004	−	0.0204175i
$441$	−1.23269e10			−0.325911
$442$	7.44499e9	−	2.83844e10i	0.195063	−	0.743688i
$443$	1.84162e10			0.478173			0.239086	−	0.970998i	$-0.423152\pi$
$443$	1.84162e10			0.478173			0.239086	+	0.970998i	$0.423152\pi$
$444$	−1.81722e10	+	3.22581e10i	−0.467602	+	0.830054i
$445$	9.53667e9	+	2.80966e10i	0.243196	+	0.716495i
$446$	2.64096e9	−	1.00688e10i	0.0667456	−	0.254471i
$447$	−6.24115e10			−1.56327
$448$	2.34689e9	+	7.39729e10i	0.0582614	+	1.83637i
$449$	4.16964e10			1.02592			0.512960	−	0.858412i	$-0.328549\pi$
$449$	4.16964e10			1.02592			0.512960	+	0.858412i	$0.328549\pi$
$450$	2.17998e9	+	5.18601e9i	0.0531621	+	0.126469i
$451$		−	2.90977e8i		−	0.00703320i
$452$	−1.36813e10	+	2.42860e10i	−0.327773	+	0.581839i
$453$			3.50753e10i			0.832931i
$454$	7.84893e9	−	2.99244e10i	0.184751	−	0.704372i
$455$	6.97217e10	−	2.36653e10i	1.62676	−	0.552161i
$456$	4.29773e10	+	4.16354e10i	0.993986	+	0.962950i
$457$		−	2.82023e10i		−	0.646576i	−0.946301	−	0.323288i	$-0.895212\pi$
$457$		−	2.82023e10i		−	0.646576i	0.946301	−	0.323288i	$-0.104788\pi$
$458$	−8.96520e9	+	3.41803e10i	−0.203750	+	0.776808i
$459$			3.85529e10i			0.868574i
$460$	−7.34822e9	+	3.90920e10i	−0.164116	+	0.873086i
$461$	8.16833e10			1.80855			0.904273	−	0.426955i	$-0.140414\pi$
$461$	8.16833e10			1.80855			0.904273	+	0.426955i	$0.140414\pi$
$462$	1.69905e9	+	4.45647e8i	0.0372939	+	0.00978189i
$463$	3.35086e10			0.729176			0.364588	−	0.931169i	$-0.381210\pi$
$463$	3.35086e10			0.729176			0.364588	+	0.931169i	$0.381210\pi$
$464$	−1.68629e10	−	2.78314e10i	−0.363798	−	0.600431i
$465$	−3.26992e10	+	1.10989e10i	−0.699399	+	0.237393i
$466$	−4.67917e10	−	1.22731e10i	−0.992259	−	0.260261i
$467$	7.19768e10			1.51330			0.756650	−	0.653820i	$-0.226835\pi$
$467$	7.19768e10			1.51330			0.756650	+	0.653820i	$0.226835\pi$
$468$	3.02024e9	−	5.36131e9i	0.0629589	−	0.111760i
$469$	−7.00286e10			−1.44739
$470$	5.19783e9	−	3.68148e8i	0.106520	−	0.00754451i
$471$		−	8.69460e8i		−	0.0176671i
$472$	9.54626e9	+	9.24820e9i	0.192338	+	0.186333i
$473$		−	6.19318e8i		−	0.0123728i
$474$	6.60979e10	+	1.73369e10i	1.30940	+	0.343446i
$475$	−4.61689e10	−	6.01751e10i	−0.906933	−	1.18207i
$476$	3.80665e10	−	6.75729e10i	0.741506	−	1.31627i
$477$		−	7.94171e8i		−	0.0153405i
$478$	−3.62733e10	−	9.51418e9i	−0.694825	−	0.182247i
$479$			9.34121e10i			1.77444i	0.461348	+	0.887219i	$0.347366\pi$
$479$			9.34121e10i			1.77444i	−0.461348	+	0.887219i	$0.652634\pi$
$480$	2.84672e10	+	4.02611e10i	0.536266	+	0.758440i
$481$	−5.13336e10			−0.959005
$482$	9.93987e9	−	3.78963e10i	0.184159	−	0.702115i
$483$	−8.25130e10			−1.51612
$484$	−4.77869e10	−	2.69202e10i	−0.870818	−	0.490566i
$485$	1.35353e10	−	4.59423e9i	0.244626	−	0.0830321i
$486$	−3.85477e9	+	1.46965e10i	−0.0690962	+	0.263433i
$487$	−2.54303e10			−0.452101			−0.226050	−	0.974116i	$-0.572581\pi$
$487$	−2.54303e10			−0.452101			−0.226050	+	0.974116i	$0.572581\pi$
$488$	−2.78239e9	+	2.87207e9i	−0.0490613	+	0.0506425i
$489$	−5.69487e10			−0.995976
$490$	1.36609e11	−	9.67568e9i	2.36972	−	0.167841i
$491$		−	4.99214e10i		−	0.858935i	−0.903082	−	0.429468i	$-0.858701\pi$
$491$		−	4.99214e10i		−	0.858935i	0.903082	−	0.429468i	$-0.141299\pi$
$492$	1.47629e10	+	8.31653e9i	0.251948	+	0.141932i
$493$			3.41011e10i			0.577273i
$494$	−2.10487e10	+	8.02491e10i	−0.353441	+	1.34751i
$495$	−1.76201e8	+	5.98069e7i	−0.00293486	+	0.000996163i
$496$	4.11595e10	−	2.49383e10i	0.680055	−	0.412042i
$497$		−	5.26407e10i		−	0.862772i
$498$	9.55122e9	−	3.64145e10i	0.155289	−	0.592048i
$499$		−	5.96587e10i		−	0.962214i	−0.876662	−	0.481107i	$-0.840235\pi$
$499$		−	5.96587e10i		−	0.962214i	0.876662	−	0.481107i	$-0.159765\pi$
$500$	−2.82296e10	−	5.57614e10i	−0.451674	−	0.892183i
$501$	−6.35019e10			−1.00794
$502$	4.91239e10	+	1.28848e10i	0.773532	+	0.202891i
$503$	−7.46669e10			−1.16642			−0.583211	−	0.812320i	$-0.698204\pi$
$503$	−7.46669e10			−1.16642			−0.583211	+	0.812320i	$0.698204\pi$
$504$	1.13163e10	−	1.16810e10i	0.175381	−	0.181034i
$505$	−6.44697e9	−	1.89938e10i	−0.0991265	−	0.292043i
$506$	−1.27262e9	−	3.33799e8i	−0.0194133	−	0.00509193i
$507$	7.71687e9			0.116791
$508$	6.79607e10	+	3.82849e10i	1.02048	+	0.574875i
$509$	−7.72840e10			−1.15138			−0.575690	−	0.817668i	$-0.695266\pi$
$509$	−7.72840e10			−1.15138			−0.575690	+	0.817668i	$0.695266\pi$
$510$	−3.65064e9	−	5.15429e10i	−0.0539621	−	0.761882i
$511$			2.17473e11i			3.18950i
$512$	−5.08479e10	−	4.62262e10i	−0.739934	−	0.672680i
$513$		−	1.08998e11i		−	1.57380i
$514$	2.27873e10	+	5.97691e9i	0.326467	+	0.0856297i
$515$	4.10700e9	+	1.20999e10i	0.0583843	+	0.172010i
$516$	3.14215e10	+	1.77009e10i	0.443228	+	0.249688i
$517$			1.72357e8i			0.00241249i
$518$	−1.31235e11	−	3.44218e10i	−1.82276	−	0.478096i
$519$		−	9.97643e10i		−	1.37501i
$520$	−2.92627e10	+	6.17859e10i	−0.400222	+	0.845038i
$521$	8.53032e10			1.15775			0.578875	−	0.815417i	$-0.303492\pi$
$521$	8.53032e10			1.15775			0.578875	+	0.815417i	$0.303492\pi$
$522$	−1.81426e9	+	6.91696e9i	−0.0244353	+	0.0931608i
$523$	1.40707e11			1.88065			0.940324	−	0.340280i	$-0.110522\pi$
$523$	1.40707e11			1.88065			0.940324	+	0.340280i	$0.110522\pi$
$524$	−5.51157e10	+	9.78375e10i	−0.731055	+	1.29772i
$525$	1.02863e11	−	7.89208e10i	1.35401	−	1.03885i
$526$	2.16174e10	−	8.24173e10i	0.282397	−	1.07665i
$527$	−5.04318e10			−0.653825
$528$	−1.39489e9	+	8.45159e8i	−0.0179476	+	0.0108743i
$529$	−1.65070e10			−0.210787
$530$	6.23364e8	+	8.80119e9i	0.00790021	+	0.111542i
$531$		−	2.92076e9i		−	0.0367382i
$532$	−1.07622e11	+	1.91044e11i	−1.34356	+	2.38499i
$533$			2.34928e10i			0.291089i
$534$	1.44994e10	−	5.52799e10i	0.178314	−	0.679832i
$535$	−1.82387e10	−	5.37342e10i	−0.222628	−	0.655897i
$536$	4.52431e10	−	4.67012e10i	0.548142	−	0.565808i
$537$			7.15349e10i			0.860242i
$538$	2.79559e10	−	1.06583e11i	0.333691	−	1.27221i
$539$			4.52988e9i			0.0536700i
$540$	1.65928e10	−	8.82725e10i	0.195139	−	1.03813i
$541$	5.74336e9			0.0670467			0.0335233	−	0.999438i	$-0.489327\pi$
$541$	5.74336e9			0.0670467			0.0335233	+	0.999438i	$0.489327\pi$
$542$	1.26249e11	+	3.31139e10i	1.46295	+	0.383719i
$543$	8.13193e10			0.935393
$544$	2.04701e10	+	6.90426e10i	0.233735	+	0.788354i
$545$	−1.43476e10	−	4.22705e10i	−0.162628	−	0.479128i
$546$	−1.37177e11	−	3.59804e10i	−1.54352	−	0.404852i
$547$	3.31595e10			0.370390			0.185195	−	0.982702i	$-0.440708\pi$
$547$	3.31595e10			0.370390			0.185195	+	0.982702i	$0.440708\pi$
$548$	6.76699e10	−	1.20123e11i	0.750366	−	1.33200i
$549$	8.78733e8			0.00967314
$550$	1.90575e9	−	8.01098e8i	0.0208265	−	0.00875457i
$551$		−	9.64116e10i		−	1.04598i
$552$	5.33088e10	−	5.50269e10i	0.574173	−	0.592678i
$553$			2.50405e11i			2.67758i
$554$	−2.16523e10	−	5.67921e9i	−0.229860	−	0.0602904i
$555$	−8.55955e10	+	2.90532e10i	−0.902151	+	0.306212i
$556$	−1.91293e10	+	3.39570e10i	−0.200171	+	0.355329i
$557$			1.05328e10i			0.109427i	0.998502	+	0.0547135i	$0.0174245\pi$
$557$			1.05328e10i			0.109427i	−0.998502	+	0.0547135i	$0.982575\pi$
$558$	−1.02294e10	−	2.68309e9i	−0.105515	−	0.0276757i
$559$			5.00022e10i			0.512085i
$560$	−1.16241e11	+	1.38334e11i	−1.18197	+	1.40662i
$561$	1.70913e9			0.0172553
$562$	−1.35653e8	+	5.17185e8i	−0.00135983	+	0.00518443i
$563$	−7.61345e10			−0.757788			−0.378894	−	0.925440i	$-0.623696\pi$
$563$	−7.61345e10			−0.757788			−0.378894	+	0.925440i	$0.623696\pi$
$564$	−8.74461e9	−	4.92618e9i	−0.0864220	−	0.0486849i
$565$	−6.44420e10	+	2.18732e10i	−0.632376	+	0.214644i
$566$	−3.50651e10	+	1.33688e11i	−0.341672	+	1.30264i
$567$	1.60269e11			1.55066
$568$	3.51055e10	+	3.40093e10i	0.337273	+	0.326742i
$569$	8.24989e10			0.787045			0.393522	−	0.919315i	$-0.371256\pi$
$569$	8.24989e10			0.787045			0.393522	+	0.919315i	$0.371256\pi$
$570$	1.03212e10	+	1.45723e11i	0.0977755	+	1.38048i
$571$		−	4.08590e10i		−	0.384365i	−0.981359	−	0.192182i	$-0.938443\pi$
$571$		−	4.08590e10i		−	0.384365i	0.981359	−	0.192182i	$-0.0615565\pi$
$572$	−1.97017e9	−	1.10988e9i	−0.0184043	−	0.0103679i
$573$		−	8.01941e8i		−	0.00743916i
$574$	−1.57532e10	+	6.00597e10i	−0.145118	+	0.553268i
$575$	−7.70465e10	+	5.91133e10i	−0.704825	+	0.540772i
$576$	4.78860e8	+	1.50934e10i	0.00435029	+	0.137119i
$577$		−	1.06396e9i		−	0.00959888i	−0.999988	−	0.00479944i	$-0.998472\pi$
$577$		−	1.06396e9i		−	0.00959888i	0.999988	−	0.00479944i	$-0.00152771\pi$
$578$	−9.17093e9	+	3.49646e10i	−0.0821678	+	0.313269i
$579$			1.08763e11i			0.967756i
$580$	1.46768e10	−	7.80794e10i	0.129694	−	0.689961i
$581$	1.37953e11			1.21067
$582$	−2.66307e10	−	6.98502e9i	−0.232109	−	0.0608801i
$583$	−2.91842e8			−0.00252623
$584$	−1.45030e11	−	1.40502e11i	−1.24683	−	1.20790i
$585$	1.42260e10	−	4.82866e9i	0.121467	−	0.0412290i
$586$	−1.16104e11	−	3.04530e10i	−0.984590	−	0.258250i
$587$	−9.73847e10			−0.820235			−0.410118	−	0.912033i	$-0.634512\pi$
$587$	−9.73847e10			−0.820235			−0.410118	+	0.912033i	$0.634512\pi$
$588$	−2.29826e11	−	1.29470e11i	−1.92261	−	1.08308i
$589$	1.42582e11			1.18469
$590$	2.29258e9	+	3.23685e10i	0.0189198	+	0.267125i
$591$		−	1.50238e11i		−	1.23148i
$592$	1.07742e11	−	6.52802e10i	0.877198	−	0.531490i
$593$			9.82363e10i			0.794426i	0.917727	+	0.397213i	$0.130023\pi$
$593$			9.82363e10i			0.794426i	−0.917727	+	0.397213i	$0.869977\pi$
$594$	2.87367e9	+	7.53741e8i	0.0230830	+	0.00605447i
$595$	1.79302e11	−	6.08595e10i	1.43060	−	0.485580i
$596$	1.85016e11	+	1.04227e11i	1.46631	+	0.826029i
$597$		−	1.64070e11i		−	1.29161i
$598$	1.02749e11	+	2.69501e10i	0.803473	+	0.210744i
$599$			3.84481e9i			0.0298654i	0.999889	+	0.0149327i	$0.00475340\pi$
$599$			3.84481e9i			0.0298654i	−0.999889	+	0.0149327i	$0.995247\pi$
$600$	−1.38248e10	+	1.19586e11i	−0.106673	+	0.922731i
$601$	−9.90199e10			−0.758970			−0.379485	−	0.925198i	$-0.623899\pi$
$601$	−9.90199e10			−0.758970			−0.379485	+	0.925198i	$0.623899\pi$
$602$	−3.35291e10	+	1.27831e11i	−0.255291	+	0.973311i
$603$	−1.42886e10			−0.108074
$604$	5.85758e10	−	1.03980e11i	0.440119	−	0.781268i
$605$	−4.30393e10	−	1.26801e11i	−0.321250	−	0.946455i
$606$	−9.80190e9	+	3.73702e10i	−0.0726808	+	0.277099i
$607$	−2.07848e11			−1.53106			−0.765529	−	0.643401i	$-0.777523\pi$
$607$	−2.07848e11			−1.53106			−0.765529	+	0.643401i	$0.777523\pi$
$608$	−5.78736e10	−	1.95199e11i	−0.423512	−	1.42844i
$609$	1.64805e11			1.19812
$610$	−9.73832e9	+	6.89739e8i	−0.0703339	+	0.00498156i
$611$		−	1.39157e10i		−	0.0998479i
$612$	7.76708e9	−	1.37876e10i	0.0553671	−	0.0982838i
$613$			9.57838e10i			0.678345i	0.940724	+	0.339172i	$0.110147\pi$
$613$			9.57838e10i			0.678345i	−0.940724	+	0.339172i	$0.889853\pi$
$614$	5.35613e10	−	2.04205e11i	0.376858	−	1.43679i
$615$	1.32962e10	+	3.91728e10i	0.0929453	+	0.273832i
$616$	−4.29254e9	−	4.15851e9i	−0.0298120	−	0.0288812i
$617$			4.01279e10i			0.276889i	0.990370	+	0.138445i	$0.0442103\pi$
$617$			4.01279e10i			0.276889i	−0.990370	+	0.138445i	$0.955790\pi$
$618$	6.24424e9	−	2.38065e10i	0.0428081	−	0.163208i
$619$		−	1.17122e11i		−	0.797768i	−0.917001	−	0.398884i	$-0.869398\pi$
$619$		−	1.17122e11i		−	0.797768i	0.917001	−	0.398884i	$-0.130602\pi$
$620$	1.15471e11	+	2.17053e10i	0.781457	+	0.146892i
$621$	−1.39558e11			−0.938399
$622$	−2.14647e11	−	5.63000e10i	−1.43404	−	0.376138i
$623$	2.09422e11			1.39018
$624$	1.12620e11	−	6.82361e10i	0.742811	−	0.450065i
$625$	3.95083e10	−	1.47384e11i	0.258922	−	0.965898i
$626$	3.84685e10	+	1.00900e10i	0.250500	+	0.0657042i
$627$	−4.83209e9			−0.0312655
$628$	−1.45200e9	+	2.57748e9i	−0.00933528	+	0.0165713i
$629$	−1.32013e11			−0.843365
$630$	3.96069e10	−	2.80525e9i	0.251425	−	0.0178078i
$631$			4.04189e10i			0.254957i	0.991841	+	0.127479i	$0.0406884\pi$
$631$			4.04189e10i			0.254957i	−0.991841	+	0.127479i	$0.959312\pi$
$632$	−1.66992e11	−	1.61778e11i	−1.04671	−	1.01403i
$633$			2.16444e11i			1.34813i
$634$	1.15643e11	+	3.03321e10i	0.715750	+	0.187735i
$635$	6.12088e10	+	1.80331e11i	0.376460	+	1.10911i
$636$	8.34123e9	−	1.48068e10i	0.0509802	−	0.0904965i
$637$		−	3.65732e11i		−	2.22129i
$638$	2.54184e9	+	6.66704e8i	0.0153414	+	0.00402393i
$639$		−	1.07408e10i		−	0.0644219i
$640$	−1.71540e10	−	1.66893e11i	−0.102246	−	0.994759i
$641$	−1.48066e11			−0.877047			−0.438523	−	0.898720i	$-0.644498\pi$
$641$	−1.48066e11			−0.877047			−0.438523	+	0.898720i	$0.644498\pi$
$642$	−2.77299e10	+	1.05722e11i	−0.163233	+	0.622335i
$643$	−1.41417e11			−0.827290			−0.413645	−	0.910438i	$-0.635744\pi$
$643$	−1.41417e11			−0.827290			−0.413645	+	0.910438i	$0.635744\pi$
$644$	2.44607e11	+	1.37797e11i	1.42208	+	0.801116i
$645$	2.82997e10	+	8.33756e10i	0.163510	+	0.481726i
$646$	−5.41304e10	+	2.06375e11i	−0.310822	+	1.18502i
$647$	1.34750e11			0.768972			0.384486	−	0.923131i	$-0.374379\pi$
$647$	1.34750e11			0.768972			0.384486	+	0.923131i	$0.374379\pi$
$648$	−1.03544e11	+	1.06881e11i	−0.587254	+	0.606180i
$649$	−1.07332e9			−0.00604993
$650$	−1.53866e11	+	6.46787e10i	−0.861964	+	0.362333i
$651$			2.43728e11i			1.35701i
$652$	1.68822e11	+	9.51043e10i	0.934200	+	0.526272i
$653$		−	2.46390e11i		−	1.35509i	−0.735479	−	0.677547i	$-0.763043\pi$
$653$		−	2.46390e11i		−	1.35509i	0.735479	−	0.677547i	$-0.236957\pi$
$654$	−2.18140e10	+	8.31669e10i	−0.119241	+	0.454611i
$655$	−2.59608e11	+	8.81173e10i	−1.41043	+	0.478736i
$656$	−2.98755e10	−	4.93081e10i	−0.161324	−	0.266258i
$657$			4.43733e10i			0.238155i
$658$	9.33117e9	−	3.55756e10i	0.0497775	−	0.189779i
$659$		−	1.86489e11i		−	0.988807i	−0.869232	−	0.494404i	$-0.835386\pi$
$659$		−	1.86489e11i		−	0.988807i	0.869232	−	0.494404i	$-0.164614\pi$
$660$	−3.91329e9	−	7.35591e8i	−0.0206237	−	0.00387669i
$661$	9.60365e9			0.0503073			0.0251536	−	0.999684i	$-0.491993\pi$
$661$	9.60365e9			0.0503073			0.0251536	+	0.999684i	$0.491993\pi$
$662$	1.35348e11	+	3.55005e10i	0.704723	+	0.184843i
$663$	−1.37991e11			−0.714162
$664$	−8.91264e10	+	9.19989e10i	−0.458494	+	0.473272i
$665$	−5.06927e11	+	1.72064e11i	−2.59214	+	0.879837i
$666$	−2.67772e10	−	7.02343e9i	−0.136103	−	0.0356987i
$667$	−1.23443e11			−0.623680
$668$	1.88249e11	+	1.06048e11i	0.945424	+	0.532595i
$669$	−4.89495e10			−0.244368
$670$	1.58350e11	−	1.12155e10i	0.785812	−	0.0556570i
$671$		−	3.22916e8i		−	0.00159294i
$672$	3.33671e11	−	9.89286e10i	1.63622	−	0.485115i
$673$			9.30331e10i			0.453500i	0.973953	+	0.226750i	$0.0728100\pi$
$673$			9.30331e10i			0.453500i	−0.973953	+	0.226750i	$0.927190\pi$
$674$	1.83686e11	+	4.81794e10i	0.890097	+	0.233465i
$675$	1.73976e11	−	1.33482e11i	0.838059	−	0.642995i
$676$	−2.28764e10	−	1.28872e10i	−0.109547	−	0.0617121i
$677$			3.02772e11i			1.44132i	0.693287	+	0.720662i	$0.256162\pi$
$677$			3.02772e11i			1.44132i	−0.693287	+	0.720662i	$0.743838\pi$
$678$	1.26789e11	+	3.32558e10i	0.600018	+	0.157380i
$679$		−	1.00888e11i		−	0.474635i
$680$	−7.52544e10	+	1.58894e11i	−0.351962	+	0.743140i
$681$	−1.45478e11			−0.676407
$682$	−9.85981e8	+	3.75910e9i	−0.00455755	+	0.0173759i
$683$	1.27530e11			0.586044			0.293022	−	0.956106i	$-0.405339\pi$
$683$	1.27530e11			0.586044			0.293022	+	0.956106i	$0.405339\pi$
$684$	−2.19593e10	+	3.89805e10i	−0.100321	+	0.178083i
$685$	3.18741e11	−	1.08189e11i	1.44769	−	0.491382i
$686$	1.42011e11	−	5.41423e11i	0.641246	−	2.44478i
$687$	1.66168e11			0.745967
$688$	−6.35872e10	−	1.04948e11i	−0.283802	−	0.468402i
$689$	2.35626e10			0.104555
$690$	1.86580e11	−	1.32150e10i	0.823130	−	0.0583001i
$691$		−	7.80441e10i		−	0.342316i	−0.985244	−	0.171158i	$-0.945249\pi$
$691$		−	7.80441e10i		−	0.342316i	0.985244	−	0.171158i	$-0.0547509\pi$
$692$	−1.66606e11	+	2.95748e11i	−0.726552	+	1.28972i
$693$			1.31334e9i			0.00569435i
$694$	2.67152e10	−	1.01853e11i	0.115165	−	0.439072i
$695$	−9.01036e10	+	3.05834e10i	−0.386192	+	0.131083i
$696$	−1.06475e11	+	1.09907e11i	−0.453743	+	0.468367i
$697$			6.04160e10i			0.255989i
$698$	7.90471e9	−	3.01371e10i	0.0333015	−	0.126964i
$699$			2.27478e11i			0.952863i
$700$	−4.36731e11	+	6.21768e10i	−1.81895	+	0.258962i
$701$	3.19804e11			1.32438			0.662188	−	0.749338i	$-0.269628\pi$
$701$	3.19804e11			1.32438			0.662188	+	0.749338i	$0.269628\pi$
$702$	−2.32013e11	−	6.08552e10i	−0.955355	−	0.250582i
$703$	3.73232e11			1.52812
$704$	5.54653e9	−	1.75971e8i	0.0225803	−	0.000716393i
$705$	−7.87583e9	−	2.32035e10i	−0.0318816	−	0.0939284i
$706$	9.72027e10	+	2.54955e10i	0.391255	+	0.102623i
$707$	−1.41573e11			−0.566635
$708$	3.06769e10	−	5.44555e10i	0.122090	−	0.216725i
$709$	−1.45293e11			−0.574990			−0.287495	−	0.957782i	$-0.592823\pi$
$709$	−1.45293e11			−0.574990			−0.287495	+	0.957782i	$0.592823\pi$
$710$	8.43072e9	+	1.19032e11i	0.0331766	+	0.468415i
$711$			5.10926e10i			0.199931i
$712$	−1.35300e11	+	1.39661e11i	−0.526477	+	0.543445i
$713$		−	1.82558e11i		−	0.706386i
$714$	−3.52776e11	−	9.25301e10i	−1.35739	−	0.356033i
$715$	−1.77444e9	−	5.22777e9i	−0.00678947	−	0.0200029i
$716$	1.19463e11	−	2.12062e11i	0.454550	−	0.806885i
$717$			1.76343e11i			0.667238i
$718$	−3.16400e11	−	8.29891e10i	−1.19053	−	0.312265i
$719$		−	2.03065e10i		−	0.0759835i	−0.999278	−	0.0379918i	$-0.987904\pi$
$719$		−	2.03065e10i		−	0.0759835i	0.999278	−	0.0379918i	$-0.0120961\pi$
$720$	−2.37179e10	+	2.82257e10i	−0.0882562	+	0.105030i
$721$	9.01884e10			0.333741
$722$	8.40966e10	−	3.20623e11i	0.309478	−	1.17990i
$723$	−1.84233e11			−0.674239
$724$	−2.41068e11	−	1.35803e11i	−0.877375	−	0.494260i
$725$	1.53887e11	−	1.18068e11i	0.556992	−	0.427348i
$726$	−6.54365e10	+	2.49480e11i	−0.235545	+	0.898026i
$727$	2.48916e11			0.891077			0.445538	−	0.895263i	$-0.353012\pi$
$727$	2.48916e11			0.891077			0.445538	+	0.895263i	$0.353012\pi$
$728$	3.46569e11	+	3.35748e11i	1.23386	+	1.19533i
$729$	3.09815e11			1.09696
$730$	−3.48297e10	−	4.91755e11i	−0.122647	−	1.73164i
$731$			1.28590e11i			0.450336i
$732$	1.63834e10	+	9.22939e9i	0.0570635	+	0.0321461i
$733$		−	4.74744e11i		−	1.64454i	−0.569101	−	0.822268i	$-0.692709\pi$
$733$		−	4.74744e11i		−	1.64454i	0.569101	−	0.822268i	$-0.307291\pi$
$734$	−9.17003e10	+	3.49612e11i	−0.315927	+	1.20449i
$735$	−2.06993e11	−	6.09835e11i	−0.709261	−	2.08960i
$736$	−2.49927e11	+	7.40997e10i	−0.851730	+	0.252525i
$737$			5.25078e9i			0.0177973i
$738$	−3.21427e9	+	1.22546e10i	−0.0108357	+	0.0413117i
$739$			3.21015e11i			1.07633i	0.842838	+	0.538167i	$0.180883\pi$
$739$			3.21015e11i			1.07633i	−0.842838	+	0.538167i	$0.819117\pi$
$740$	3.02264e11	+	5.68172e10i	1.00800	+	0.189475i
$741$	3.90131e11			1.29401
$742$	6.02381e10	+	1.58000e10i	0.198726	+	0.0521243i
$743$	−4.89920e11			−1.60757			−0.803785	−	0.594920i	$-0.797184\pi$
$743$	−4.89920e11			−1.60757			−0.803785	+	0.594920i	$0.797184\pi$
$744$	−1.62540e11	−	1.57465e11i	−0.530478	−	0.513915i
$745$	1.66635e11	+	4.90934e11i	0.540930	+	1.59367i
$746$	2.45748e11	+	6.44576e10i	0.793478	+	0.208123i
$747$	2.81478e10			0.0903988
$748$	−5.06665e9	−	2.85424e9i	−0.0161851	−	0.00911769i
$749$	−4.00516e11			−1.27260
$750$	−2.19956e11	+	1.94931e11i	−0.695169	+	0.616078i
$751$		−	1.97462e11i		−	0.620759i	−0.950613	−	0.310380i	$-0.899544\pi$
$751$		−	1.97462e11i		−	0.620759i	0.950613	−	0.310380i	$-0.100456\pi$
$752$	1.76964e10	+	2.92070e10i	0.0553366	+	0.0913304i
$753$		−	2.38816e11i		−	0.742821i
$754$	−2.05222e11	−	5.38281e10i	−0.634949	−	0.166542i
$755$	2.75906e11	−	9.36492e10i	0.849127	−	0.288215i
$756$	−5.52339e11	−	3.11154e11i	−1.69090	−	0.952552i
$757$		−	1.73135e11i		−	0.527231i	−0.964628	−	0.263615i	$-0.915085\pi$
$757$		−	1.73135e11i		−	0.527231i	0.964628	−	0.263615i	$-0.0849150\pi$
$758$	−2.30418e11	−	6.04367e10i	−0.697974	−	0.183073i
$759$			6.18687e9i			0.0186425i
$760$	2.12761e11	−	4.49228e11i	0.637731	−	1.34652i
$761$	−1.07600e11			−0.320829			−0.160415	−	0.987050i	$-0.551283\pi$
$761$	−1.07600e11			−0.320829			−0.160415	+	0.987050i	$0.551283\pi$
$762$	9.30612e10	−	3.54800e11i	0.276025	−	1.05236i
$763$	−3.15069e11			−0.929626
$764$	−1.33924e9	+	2.37733e9i	−0.00393084	+	0.00697775i
$765$	3.65848e10	−	1.24178e10i	0.106820	−	0.0362575i
$766$	1.55856e10	−	5.94208e10i	0.0452697	−	0.172593i
$767$	8.66572e10			0.250394
$768$	−1.49599e11	+	2.86436e11i	−0.430016	+	0.823346i
$769$	3.79310e11			1.08465			0.542325	−	0.840169i	$-0.317544\pi$
$769$	3.79310e11			1.08465			0.542325	+	0.840169i	$0.317544\pi$
$770$	−1.03087e9	−	1.45547e10i	−0.00293253	−	0.0414039i
$771$		−	1.10780e11i		−	0.313506i
$772$	1.81634e11	−	3.22423e11i	0.511360	−	0.907731i
$773$			3.22413e11i			0.903013i	0.892268	+	0.451507i	$0.149113\pi$
$773$			3.22413e11i			0.903013i	−0.892268	+	0.451507i	$0.850887\pi$
$774$	−6.84128e9	+	2.60827e10i	−0.0190622	+	0.0726756i
$775$	1.74610e11	+	2.27581e11i	0.484019	+	0.630855i
$776$	6.72808e10	+	6.51801e10i	0.185543	+	0.179750i
$777$			6.37999e11i			1.75040i
$778$	−4.72378e10	+	1.80096e11i	−0.128935	+	0.491571i
$779$		−	1.70810e11i		−	0.463834i
$780$	3.15950e11	+	5.93898e10i	0.853571	+	0.160448i
$781$	−3.94703e9			−0.0106088
$782$	2.64237e11	+	6.93071e10i	0.706587	+	0.185332i
$783$	2.78742e11			0.741575
$784$	4.65096e11	+	7.67619e11i	1.23106	+	2.03180i
$785$	−6.83925e9	+	2.32141e9i	−0.0180107	+	0.00611327i
$786$	5.10777e11	+	1.33973e11i	1.33826	+	0.351015i
$787$	7.47811e10			0.194936			0.0974682	−	0.995239i	$-0.468926\pi$
$787$	7.47811e10			0.194936			0.0974682	+	0.995239i	$0.468926\pi$
$788$	−2.50897e11	+	4.45374e11i	−0.650714	+	1.15510i
$789$	−4.00672e11			−1.03391
$790$	−4.01038e10	−	5.66220e11i	−0.102962	−	1.45371i
$791$			4.80329e11i			1.22697i
$792$	−8.75850e8	−	8.48503e8i	−0.00222602	−	0.00215652i
$793$			2.60715e10i			0.0659285i
$794$	−1.04770e11	−	2.74804e10i	−0.263607	−	0.0691419i
$795$	3.92892e10	−	1.33357e10i	0.0983568	−	0.0333847i
$796$	−2.73997e11	+	4.86380e11i	−0.682486	+	1.21150i
$797$		−	3.03877e11i		−	0.753120i	−0.926392	−	0.376560i	$-0.877107\pi$
$797$		−	3.03877e11i		−	0.753120i	0.926392	−	0.376560i	$-0.122893\pi$
$798$	9.97376e11	+	2.61604e11i	2.45950	+	0.645107i
$799$		−	3.57866e10i		−	0.0878078i
$800$	2.40692e11	−	3.31421e11i	0.587626	−	0.809133i
$801$	4.27305e10			0.103802
$802$	−1.46364e11	+	5.58019e11i	−0.353782	+	1.34881i
$803$	1.63063e10			0.0392187
$804$	−2.66402e11	−	1.50075e11i	−0.637548	−	0.359156i
$805$	2.20305e11	+	6.49055e11i	0.524615	+	1.54560i
$806$	7.96057e10	−	3.03501e11i	0.188627	−	0.719150i
$807$	−5.18155e11			−1.22170
$808$	9.14656e10	−	9.44135e10i	0.214591	−	0.221508i
$809$	−7.38329e11			−1.72368			−0.861839	−	0.507183i	$-0.830687\pi$
$809$	−7.38329e11			−1.72368			−0.861839	+	0.507183i	$0.830687\pi$
$810$	−3.62403e11	+	2.56680e10i	−0.841882	+	0.0596283i
$811$		−	4.96912e11i		−	1.14867i	−0.818620	−	0.574336i	$-0.805260\pi$
$811$		−	4.96912e11i		−	1.14867i	0.818620	−	0.574336i	$-0.194740\pi$
$812$	−4.88559e11	−	2.75224e11i	−1.12381	−	0.633086i
$813$		−	6.13758e11i		−	1.40487i
$814$	−2.58097e9	+	9.84007e9i	−0.00587875	+	0.0224130i
$815$	1.52050e11	+	4.47964e11i	0.344632	+	1.01534i
$816$	2.89623e11	−	1.75481e11i	0.653240	−	0.395795i
$817$		−	3.63552e11i		−	0.815978i
$818$	−1.46249e11	+	5.57581e11i	−0.326647	+	1.24536i
$819$		−	1.06036e11i		−	0.235677i
$820$	2.60024e10	−	1.38331e11i	0.0575120	−	0.305960i
$821$	−6.54758e11			−1.44115			−0.720573	−	0.693379i	$-0.756121\pi$
$821$	−6.54758e11			−1.44115			−0.720573	+	0.693379i	$0.756121\pi$
$822$	−6.27122e11	−	1.64489e11i	−1.37361	−	0.360287i
$823$	2.94557e11			0.642052			0.321026	−	0.947070i	$-0.395972\pi$
$823$	2.94557e11			0.642052			0.321026	+	0.947070i	$0.395972\pi$
$824$	−5.82676e10	+	6.01455e10i	−0.126392	+	0.130465i
$825$	−5.91752e9	−	7.71271e9i	−0.0127739	−	0.0166491i
$826$	2.21540e11	+	5.81082e10i	0.475919	+	0.124830i
$827$	5.32863e11			1.13918			0.569592	−	0.821928i	$-0.307101\pi$
$827$	5.32863e11			1.13918			0.569592	+	0.821928i	$0.307101\pi$
$828$	4.99096e10	+	2.81160e10i	0.106185	+	0.0598181i
$829$	−3.43104e11			−0.726453			−0.363226	−	0.931701i	$-0.618325\pi$
$829$	−3.43104e11			−0.726453			−0.363226	+	0.931701i	$0.618325\pi$
$830$	−3.11941e11	+	2.20939e10i	−0.657294	+	0.0465544i
$831$			1.05263e11i			0.220734i
$832$	−4.47813e11	+	1.42075e10i	−0.934552	+	0.0296500i
$833$		−	9.40545e11i		−	1.95344i
$834$	1.77278e11	+	4.64986e10i	0.366430	+	0.0961116i
$835$	1.69546e11	+	4.99511e11i	0.348773	+	1.02754i
$836$	1.43246e10	+	8.06959e9i	0.0293262	+	0.0165206i
$837$			4.12228e11i			0.839916i
$838$	1.79554e11	+	4.70955e10i	0.364099	+	0.0955000i
$839$			6.28226e11i			1.26785i	0.773394	+	0.633926i	$0.218558\pi$
$839$			6.28226e11i			1.26785i	−0.773394	+	0.633926i	$0.781442\pi$
$840$	7.67906e11	+	3.63692e11i	1.54238	+	0.730494i
$841$	−2.53692e11			−0.507134
$842$	8.07906e10	−	3.08018e11i	0.160736	−	0.612813i
$843$	2.51430e9			0.00497859
$844$	3.61461e11	−	6.41641e11i	0.712348	−	1.26451i
$845$	−2.06036e10	−	6.07015e10i	−0.0404126	−	0.119062i
$846$	1.90393e9	−	7.25883e9i	0.00371681	−	0.0141705i
$847$	−9.45128e11			−1.83636
$848$	−4.94546e10	+	2.99643e10i	−0.0956363	+	0.0579455i
$849$	6.49922e11			1.25092
$850$	−3.95694e11	+	1.66333e11i	−0.758025	+	0.318642i
$851$		−	4.77875e11i		−	0.911163i
$852$	1.12811e11	−	2.00255e11i	0.214089	−	0.380036i
$853$			3.45716e11i			0.653015i	0.945195	+	0.326508i	$0.105872\pi$
$853$			3.45716e11i			0.653015i	−0.945195	+	0.326508i	$0.894128\pi$
$854$	−1.74823e10	+	6.66521e10i	−0.0328675	+	0.125309i
$855$	−1.03433e11	+	3.51078e10i	−0.193551	+	0.0656961i
$856$	2.58760e11	−	2.67099e11i	0.481949	−	0.497482i
$857$		−	7.59517e10i		−	0.140804i	−0.997519	−	0.0704018i	$-0.977572\pi$
$857$		−	7.59517e10i		−	0.140804i	0.997519	−	0.0704018i	$-0.0224282\pi$
$858$	−2.69783e9	+	1.02856e10i	−0.00497812	+	0.0189793i
$859$		−	5.47486e11i		−	1.00554i	−0.864420	−	0.502771i	$-0.832314\pi$
$859$		−	5.47486e11i		−	1.00554i	0.864420	−	0.502771i	$-0.167686\pi$
$860$	5.53437e10	−	2.94424e11i	0.101175	−	0.538245i
$861$	2.91981e11			0.531302
$862$	9.94241e11	+	2.60781e11i	1.80079	+	0.472332i
$863$	−1.40426e11			−0.253166			−0.126583	−	0.991956i	$-0.540401\pi$
$863$	−1.40426e11			−0.253166			−0.126583	+	0.991956i	$0.540401\pi$
$864$	5.64352e11	−	1.67322e11i	1.01273	−	0.300261i
$865$	−7.84755e11	+	2.66365e11i	−1.40175	+	0.475787i
$866$	8.30311e11	+	2.17784e11i	1.47628	+	0.387217i
$867$	1.69981e11			0.300831
$868$	4.07026e11	−	7.22524e11i	0.717040	−	1.27284i
$869$	1.87755e10			0.0329240
$870$	−3.72660e11	+	2.63945e10i	−0.650483	+	0.0460720i
$871$		−	4.23936e11i		−	0.736593i
$872$	2.03556e11	−	2.10116e11i	0.352060	−	0.363407i
$873$		−	2.05851e10i		−	0.0354403i
$874$	−7.47056e11	−	1.95947e11i	−1.28029	−	0.335809i
$875$	−8.95436e11	−	5.98414e11i	−1.52757	−	1.02087i
$876$	−4.66056e11	+	8.27309e11i	−0.791446	+	1.40492i
$877$		−	3.72289e11i		−	0.629335i	−0.949202	−	0.314668i	$-0.898107\pi$
$877$		−	3.72289e11i		−	0.629335i	0.949202	−	0.314668i	$-0.101893\pi$
$878$	−3.22473e11	−	8.45819e10i	−0.542644	−	0.142331i
$879$			5.64439e11i			0.945499i
$880$	1.03724e10	+	8.71583e9i	0.0172961	+	0.0145338i
$881$	3.06330e11			0.508494			0.254247	−	0.967139i	$-0.418172\pi$
$881$	3.06330e11			0.508494			0.254247	+	0.967139i	$0.418172\pi$
$882$	5.00392e10	−	1.90777e11i	0.0826868	−	0.315247i
$883$	−7.05191e11			−1.16002			−0.580008	−	0.814611i	$-0.696950\pi$
$883$	−7.05191e11			−1.16002			−0.580008	+	0.814611i	$0.696950\pi$
$884$	4.09069e11	+	2.30445e11i	0.669865	+	0.377362i
$885$	1.44496e11	−	4.90453e10i	0.235549	−	0.0799511i
$886$	−7.47578e10	+	2.85018e11i	−0.121317	+	0.462527i
$887$	4.76446e10			0.0769695			0.0384848	−	0.999259i	$-0.487747\pi$
$887$	4.76446e10			0.0769695			0.0384848	+	0.999259i	$0.487747\pi$
$888$	−4.25474e11	−	4.12189e11i	−0.684260	−	0.662895i
$889$	1.34413e12			2.15195
$890$	−4.73549e11	+	3.35402e10i	−0.754753	+	0.0534571i
$891$		−	1.20170e10i		−	0.0190672i
$892$	1.45109e11	+	8.17456e10i	0.229211	+	0.129123i
$893$			1.01177e11i			0.159102i
$894$	2.53350e11	−	9.65910e11i	0.396617	−	1.51212i
$895$	5.62700e11	−	1.90994e11i	0.876969	−	0.297665i
$896$	−1.15437e12	−	2.63960e11i	−1.79107	−	0.409550i
$897$		−	4.99513e11i		−	0.771573i
$898$	−1.69261e11	+	6.45314e11i	−0.260286	+	0.992353i
$899$			3.64627e11i			0.558226i
$900$	−8.91105e10	+	1.26866e10i	−0.135818	+	0.0193363i
$901$	6.05955e10			0.0919477
$902$	4.50331e9	+	1.18118e9i	0.00680308	+	0.00178439i
$903$	6.21453e11			0.934668
$904$	−3.20325e11	−	3.10324e11i	−0.479642	−	0.464666i
$905$	−2.17118e11	−	6.39665e11i	−0.323669	−	0.953582i
$906$	−5.42843e11	−	1.42383e11i	−0.805678	−	0.211323i
$907$	1.23146e12			1.81967			0.909835	−	0.414970i	$-0.136208\pi$
$907$	1.23146e12			1.81967			0.909835	+	0.414970i	$0.136208\pi$
$908$	4.31263e11	+	2.42948e11i	0.634453	+	0.357412i
$909$	−2.88866e10			−0.0423098
$910$	8.32301e10	+	1.17511e12i	0.121371	+	1.71362i
$911$		−	9.01648e10i		−	0.130907i	−0.997856	−	0.0654536i	$-0.979151\pi$
$911$		−	9.01648e10i		−	0.130907i	0.997856	−	0.0654536i	$-0.0208494\pi$
$912$	−8.18831e11	+	4.96125e11i	−1.18363	+	0.717153i
$913$		−	1.03438e10i		−	0.0148866i
$914$	4.36472e11	+	1.14483e11i	0.625420	+	0.164043i
$915$	1.47557e10	+	4.34726e10i	0.0210511	+	0.0620199i
$916$	−4.92598e11	−	2.77500e11i	−0.699698	−	0.394167i
$917$			1.93503e12i			2.73659i
$918$	−5.96664e11	−	1.56500e11i	−0.840155	−	0.220366i
$919$		−	8.83703e11i		−	1.23892i	−0.785027	−	0.619462i	$-0.787351\pi$
$919$		−	8.83703e11i		−	1.23892i	0.785027	−	0.619462i	$-0.212649\pi$
$920$	−5.75178e11	−	2.72413e11i	−0.802881	−	0.380256i
$921$	−9.92745e11			−1.37975
$922$	−3.31581e11	+	1.26417e12i	−0.458845	+	1.74937i
$923$	3.18674e11			0.439076
$924$	−1.37941e10	+	2.44863e10i	−0.0189237	+	0.0335919i
$925$	4.57070e11	+	5.95731e11i	0.624333	+	0.813736i
$926$	−1.36023e11	+	5.18596e11i	−0.184999	+	0.705318i
$927$	1.84020e10			0.0249199
$928$	4.99185e11	−	1.48001e11i	0.673084	−	0.199560i
$929$	1.27216e12			1.70797			0.853984	−	0.520299i	$-0.174179\pi$
$929$	1.27216e12			1.70797			0.853984	+	0.520299i	$0.174179\pi$
$930$	−3.90346e10	−	5.51123e11i	−0.0521816	−	0.736744i
$931$			2.65913e12i			3.53949i
$932$	3.79888e11	−	6.74350e11i	0.503491	−	0.893762i
$933$			1.04351e12i			1.37711i
$934$	−2.92179e11	+	1.11395e12i	−0.383939	+	1.46379i
$935$	−4.56328e9	−	1.34442e10i	−0.00597077	−	0.0175909i
$936$	7.07140e10	+	6.85061e10i	0.0921302	+	0.0892536i
$937$			2.02100e10i			0.0262184i	0.999914	+	0.0131092i	$0.00417291\pi$
$937$			2.02100e10i			0.0262184i	−0.999914	+	0.0131092i	$0.995827\pi$
$938$	2.84271e11	−	1.08380e12i	0.367216	−	1.40003i
$939$		−	1.87015e11i		−	0.240555i
$940$	−1.54022e10	+	8.19385e10i	−0.0197274	+	0.104949i
$941$	9.48679e11			1.20993			0.604966	−	0.796252i	$-0.293187\pi$
$941$	9.48679e11			1.20993			0.604966	+	0.796252i	$0.293187\pi$
$942$	1.34562e10	+	3.52945e9i	0.0170891	+	0.00448232i
$943$	−2.18700e11			−0.276568
$944$	−1.81881e11	+	1.10201e11i	−0.229034	+	0.138771i
$945$	−4.97464e11	−	1.46561e12i	−0.623784	−	1.83777i
$946$	9.58487e9	+	2.51403e9i	0.0119680	+	0.00313911i
$947$	−6.70657e11			−0.833874			−0.416937	−	0.908935i	$-0.636896\pi$
$947$	−6.70657e11			−0.833874			−0.416937	+	0.908935i	$0.636896\pi$
$948$	−5.36629e11	+	9.52586e11i	−0.664417	+	1.17943i
$949$	−1.31653e12			−1.62318
$950$	1.11872e12	−	4.70260e11i	1.37349	−	0.577356i
$951$		−	5.62198e11i		−	0.687333i
$952$	8.91265e11	+	8.63437e11i	1.08507	+	1.05119i
$953$			9.98173e11i			1.21014i	0.796174	+	0.605068i	$0.206854\pi$
$953$			9.98173e11i			1.21014i	−0.796174	+	0.605068i	$0.793146\pi$
$954$	1.22910e10	+	3.22382e9i	0.0148386	+	0.00389204i
$955$	−6.30814e9	+	2.14114e9i	−0.00758382	+	0.00257413i
$956$	2.94492e11	−	5.22761e11i	0.352567	−	0.625852i
$957$		−	1.23572e10i		−	0.0147323i
$958$	−1.44569e12	−	3.79193e11i	−1.71638	−	0.450192i
$959$		−	2.37579e12i		−	2.80888i
$960$	−7.38659e11	+	2.77139e11i	−0.869680	+	0.326296i
$961$	3.13649e11			0.367748
$962$	2.08381e11	−	7.94463e11i	0.243309	−	0.927627i
$963$	−8.17213e10			−0.0950233
$964$	5.46152e11	+	3.07669e11i	0.632419	+	0.356267i
$965$	8.55537e11	−	2.90390e11i	0.986574	−	0.334867i
$966$	3.34950e11	−	1.27701e12i	0.384655	−	1.46651i
$967$	4.02861e11			0.460733			0.230367	−	0.973104i	$-0.426007\pi$
$967$	4.02861e11			0.460733			0.230367	+	0.973104i	$0.426007\pi$
$968$	6.10615e11	−	6.30295e11i	0.695450	−	0.717864i
$969$	1.00329e12			1.13797
$970$	1.61578e10	+	2.28129e11i	0.0182513	+	0.257688i
$971$		−	3.09841e11i		−	0.348548i	−0.984697	−	0.174274i	$-0.944242\pi$
$971$		−	3.09841e11i		−	0.348548i	0.984697	−	0.174274i	$-0.0557578\pi$
$972$	−2.11803e11	−	1.19317e11i	−0.237283	−	0.133671i
$973$			6.71601e11i			0.749307i
$974$	1.03231e11	−	3.93571e11i	0.114702	−	0.437308i
$975$	4.77766e11	+	6.22706e11i	0.528685	+	0.689072i
$976$	−3.31548e10	−	5.47204e10i	−0.0365382	−	0.0603045i
$977$		−	1.49710e12i		−	1.64313i	−0.570116	−	0.821564i	$-0.693102\pi$
$977$		−	1.49710e12i		−	1.64313i	0.570116	−	0.821564i	$-0.306898\pi$
$978$	2.31175e11	−	8.81366e11i	0.252689	−	0.963388i
$979$		−	1.57026e10i		−	0.0170939i
$980$	−4.04801e11	+	2.15351e12i	−0.438871	+	2.33476i
$981$	−6.42868e10			−0.0694137
$982$	7.72607e11	+	2.02648e11i	0.830831	+	0.217920i
$983$	−4.89964e11			−0.524747			−0.262374	−	0.964966i	$-0.584505\pi$
$983$	−4.89964e11			−0.524747			−0.262374	+	0.964966i	$0.584505\pi$
$984$	−1.88639e11	+	1.94718e11i	−0.201210	+	0.207695i
$985$	−1.18178e12	+	4.01126e11i	−1.25543	+	0.426124i
$986$	−5.27766e11	−	1.38429e11i	−0.558385	−	0.146460i
$987$	−1.72951e11			−0.182244
$988$	−1.15653e12	−	6.51519e11i	−1.21375	−	0.683753i
$989$	−4.65481e11			−0.486539
$990$	−2.10339e8	−	2.96975e9i	−0.000218967	−	0.00309157i
$991$			4.56280e11i			0.473082i	0.971621	+	0.236541i	$0.0760138\pi$
$991$			4.56280e11i			0.473082i	−0.971621	+	0.236541i	$0.923986\pi$
$992$	2.18877e11	+	7.38239e11i	0.226023	+	0.762342i
$993$		−	6.57993e11i		−	0.676743i
$994$	8.14693e11	+	2.13687e11i	0.834543	+	0.218894i
$995$	−1.29059e12	+	4.38059e11i	−1.31673	+	0.446930i
$996$	5.24797e11	+	2.95639e11i	0.533278	+	0.300417i
$997$		−	1.27383e12i		−	1.28923i	−0.764507	−	0.644615i	$-0.777018\pi$
$997$		−	1.27383e12i		−	1.28923i	0.764507	−	0.644615i	$-0.222982\pi$
$998$	9.23308e11	+	2.42176e11i	0.930731	+	0.244123i
$999$			1.07907e12i			1.08340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.d.c.19.10	yes	20
4.3	odd	2	inner	20.9.d.c.19.12	yes	20
5.2	odd	4		100.9.b.g.51.1		20
5.3	odd	4		100.9.b.g.51.20		20
5.4	even	2	inner	20.9.d.c.19.11	yes	20
8.3	odd	2		320.9.h.g.319.16		20
8.5	even	2		320.9.h.g.319.6		20
20.3	even	4		100.9.b.g.51.19		20
20.7	even	4		100.9.b.g.51.2		20
20.19	odd	2	inner	20.9.d.c.19.9	✓	20
40.19	odd	2		320.9.h.g.319.5		20
40.29	even	2		320.9.h.g.319.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.9	✓	20	20.19	odd	2	inner
20.9.d.c.19.10	yes	20	1.1	even	1	trivial
20.9.d.c.19.11	yes	20	5.4	even	2	inner
20.9.d.c.19.12	yes	20	4.3	odd	2	inner
100.9.b.g.51.1		20	5.2	odd	4
100.9.b.g.51.2		20	20.7	even	4
100.9.b.g.51.19		20	20.3	even	4
100.9.b.g.51.20		20	5.3	odd	4
320.9.h.g.319.5		20	40.19	odd	2
320.9.h.g.319.6		20	8.5	even	2
320.9.h.g.319.15		20	40.29	even	2
320.9.h.g.319.16		20	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-4.05935 + 15.4765i) q^{2} +75.2390 q^{3} +(-223.043 - 125.649i) q^{4} +(-200.884 - 591.837i) q^{5} +(-305.422 + 1164.44i) q^{6} -4411.35 q^{7} +(2850.02 - 2941.87i) q^{8} -900.091 q^{9} +O(q^{10})\)	\(q+(-4.05935 + 15.4765i) q^{2} +75.2390 q^{3} +(-223.043 - 125.649i) q^{4} +(-200.884 - 591.837i) q^{5} +(-305.422 + 1164.44i) q^{6} -4411.35 q^{7} +(2850.02 - 2941.87i) q^{8} -900.091 q^{9} +(9975.01 - 706.503i) q^{10} +330.765i q^{11} +(-16781.6 - 9453.71i) q^{12} -26705.2i q^{13} +(17907.2 - 68272.1i) q^{14} +(-15114.3 - 44529.2i) q^{15} +(33960.6 + 56050.4i) q^{16} -68677.1i q^{17} +(3653.79 - 13930.2i) q^{18} +194166. i q^{19} +(-29557.9 + 157246. i) q^{20} -331905. q^{21} +(-5119.08 - 1342.69i) q^{22} +248604. q^{23} +(214433. - 221344. i) q^{24} +(-309916. + 237781. i) q^{25} +(413302. + 108406. i) q^{26} -561365. q^{27} +(983921. + 554281. i) q^{28} -496543. q^{29} +(750510. - 53156.6i) q^{30} -734331. i q^{31} +(-1.00532e6 + 298063. i) q^{32} +24886.4i q^{33} +(1.06288e6 + 278785. i) q^{34} +(886168. + 2.61080e6i) q^{35} +(200759. + 113096. i) q^{36} -1.92223e6i q^{37} +(-3.00500e6 - 788187. i) q^{38} -2.00927e6i q^{39} +(-2.31363e6 - 1.09577e6i) q^{40} -879710. q^{41} +(1.34732e6 - 5.13673e6i) q^{42} -1.87238e6 q^{43} +(41560.3 - 73774.9i) q^{44} +(180814. + 532707. i) q^{45} +(-1.00917e6 + 3.84752e6i) q^{46} +521085. q^{47} +(2.55516e6 + 4.21717e6i) q^{48} +1.36952e7 q^{49} +(-2.42195e6 - 5.76165e6i) q^{50} -5.16720e6i q^{51} +(-3.35548e6 + 5.95641e6i) q^{52} +882323. i q^{53} +(2.27878e6 - 8.68796e6i) q^{54} +(195759. - 66445.4i) q^{55} +(-1.25724e7 + 1.29776e7i) q^{56} +1.46088e7i q^{57} +(2.01564e6 - 7.68474e6i) q^{58} +3.24496e6i q^{59} +(-2.22391e6 + 1.18310e7i) q^{60} -976271. q^{61} +(1.13649e7 + 2.98091e6i) q^{62} +3.97061e6 q^{63} +(-532013. - 1.67688e7i) q^{64} +(-1.58051e7 + 5.36464e6i) q^{65} +(-385155. - 101023. i) q^{66} +1.58747e7 q^{67} +(-8.62922e6 + 1.53180e7i) q^{68} +1.87047e7 q^{69} +(-4.40032e7 + 3.11663e6i) q^{70} +1.19330e7i q^{71} +(-2.56527e6 + 2.64795e6i) q^{72} -4.92987e7i q^{73} +(2.97494e7 + 7.80302e6i) q^{74} +(-2.33178e7 + 1.78904e7i) q^{75} +(2.43967e7 - 4.33074e7i) q^{76} -1.45912e6i q^{77} +(3.10964e7 + 8.15634e6i) q^{78} -5.67639e7i q^{79} +(2.63505e7 - 3.13588e7i) q^{80} -3.63311e7 q^{81} +(3.57106e6 - 1.36148e7i) q^{82} -3.12722e7 q^{83} +(7.40292e7 + 4.17036e7i) q^{84} +(-4.06456e7 + 1.37961e7i) q^{85} +(7.60065e6 - 2.89779e7i) q^{86} -3.73594e7 q^{87} +(973069. + 942686. i) q^{88} -4.74735e7 q^{89} +(-8.97841e6 + 635917. i) q^{90} +1.17806e8i q^{91} +(-5.54495e7 - 3.12369e7i) q^{92} -5.52504e7i q^{93} +(-2.11527e6 + 8.06456e6i) q^{94} +(1.14914e8 - 3.90048e7i) q^{95} +(-7.56394e7 + 2.24260e7i) q^{96} +2.28701e7i q^{97} +(-5.55935e7 + 2.11953e8i) q^{98} -297718. i 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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