LMFDB - Embedded newform 13.11.d.a.8.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,11,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.25964428476$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
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} - 6 x^{19} + 18 x^{18} + 32284 x^{17} + 16288321 x^{16} - 1399914 x^{15} + 236338034 x^{14} + \cdots + 84\!\cdots\!04 $ x^20 - 6x^19 + 18x^18 + 32284x^17 + 16288321x^16 - 1399914x^15 + 236338034x^14 + 223248859576x^13 + 68334664655952x^12 + 197812095245952x^11 + 941899764571520x^10 + 335247771330255360x^9 + 58398135128630811648x^8 + 300750323152050266112x^7 + 1118531393884122341376x^6 + 105977196796457311174656x^5 + 10666527336316281117671424x^4 + 85502397039865581748617216x^3 + 318723107626870315852234752x^2 - 2323063126834144103834320896*x + 8466004130416338670089928704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{6}\cdot 13^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.5
Root			$-6.55552 + 6.55552i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.11.d.a.5.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.55552 - 8.55552i) q^{2} +347.925 q^{3} -877.606i q^{4} +(1886.34 + 1886.34i) q^{5} +(-2976.68 - 2976.68i) q^{6} +(1469.56 - 1469.56i) q^{7} +(-16269.2 + 16269.2i) q^{8} +62003.1 q^{9} -32277.3i q^{10} +(166265. - 166265. i) q^{11} -305342. i q^{12} +(182221. - 323502. i) q^{13} -25145.7 q^{14} +(656306. + 656306. i) q^{15} -620285. q^{16} +1.32216e6i q^{17} +(-530469. - 530469. i) q^{18} +(-853777. - 853777. i) q^{19} +(1.65546e6 - 1.65546e6i) q^{20} +(511297. - 511297. i) q^{21} -2.84496e6 q^{22} +8.82268e6i q^{23} +(-5.66048e6 + 5.66048e6i) q^{24} -2.64906e6i q^{25} +(-4.32673e6 + 1.20873e6i) q^{26} +1.02782e6 q^{27} +(-1.28969e6 - 1.28969e6i) q^{28} -1.21072e7 q^{29} -1.12301e7i q^{30} +(8.03380e6 + 8.03380e6i) q^{31} +(2.19666e7 + 2.19666e7i) q^{32} +(5.78477e7 - 5.78477e7i) q^{33} +(1.13118e7 - 1.13118e7i) q^{34} +5.54418e6 q^{35} -5.44143e7i q^{36} +(-8.13044e7 + 8.13044e7i) q^{37} +1.46090e7i q^{38} +(6.33995e7 - 1.12555e8i) q^{39} -6.13786e7 q^{40} +(3.01838e7 + 3.01838e7i) q^{41} -8.74883e6 q^{42} +1.89716e8i q^{43} +(-1.45915e8 - 1.45915e8i) q^{44} +(1.16959e8 + 1.16959e8i) q^{45} +(7.54826e7 - 7.54826e7i) q^{46} +(7.61863e7 - 7.61863e7i) q^{47} -2.15813e8 q^{48} +2.78156e8i q^{49} +(-2.26641e7 + 2.26641e7i) q^{50} +4.60013e8i q^{51} +(-2.83908e8 - 1.59919e8i) q^{52} -5.83118e8 q^{53} +(-8.79351e6 - 8.79351e6i) q^{54} +6.27263e8 q^{55} +4.78172e7i q^{56} +(-2.97051e8 - 2.97051e8i) q^{57} +(1.03584e8 + 1.03584e8i) q^{58} +(7.74150e8 - 7.74150e8i) q^{59} +(5.75978e8 - 5.75978e8i) q^{60} +3.47707e8 q^{61} -1.37467e8i q^{62} +(9.11173e7 - 9.11173e7i) q^{63} +2.59301e8i q^{64} +(9.53968e8 - 2.66504e8i) q^{65} -9.89834e8 q^{66} +(-1.48037e9 - 1.48037e9i) q^{67} +1.16034e9 q^{68} +3.06964e9i q^{69} +(-4.74334e7 - 4.74334e7i) q^{70} +(-4.39607e8 - 4.39607e8i) q^{71} +(-1.00874e9 + 1.00874e9i) q^{72} +(-7.85564e8 + 7.85564e8i) q^{73} +1.39120e9 q^{74} -9.21675e8i q^{75} +(-7.49280e8 + 7.49280e8i) q^{76} -4.88671e8i q^{77} +(-1.50538e9 + 4.20549e8i) q^{78} +3.93240e9 q^{79} +(-1.17007e9 - 1.17007e9i) q^{80} -3.30362e9 q^{81} -5.16477e8i q^{82} +(1.14577e9 + 1.14577e9i) q^{83} +(-4.48718e8 - 4.48718e8i) q^{84} +(-2.49405e9 + 2.49405e9i) q^{85} +(1.62312e9 - 1.62312e9i) q^{86} -4.21241e9 q^{87} +5.40999e9i q^{88} +(1.31299e9 - 1.31299e9i) q^{89} -2.00129e9i q^{90} +(-2.07621e8 - 7.43192e8i) q^{91} +7.74284e9 q^{92} +(2.79517e9 + 2.79517e9i) q^{93} -1.30363e9 q^{94} -3.22103e9i q^{95} +(7.64272e9 + 7.64272e9i) q^{96} +(-1.02242e10 - 1.02242e10i) q^{97} +(2.37977e9 - 2.37977e9i) q^{98} +(1.03089e10 - 1.03089e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) $ 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−8.55552	−	8.55552i	−0.267360	−	0.267360i	0.560676	−	0.828036i	$-0.310542\pi$
$2$	−8.55552	−	8.55552i	−0.267360	−	0.267360i	−0.828036	+	0.560676i	$0.810542\pi$
$3$	347.925			1.43179			0.715896	−	0.698207i	$-0.246018\pi$
$3$	347.925			1.43179			0.715896	+	0.698207i	$0.246018\pi$
$4$		−	877.606i		−	0.857037i
$5$	1886.34	+	1886.34i	0.603629	+	0.603629i	0.941274	−	0.337645i	$-0.109630\pi$
$5$	1886.34	+	1886.34i	0.603629	+	0.603629i	−0.337645	+	0.941274i	$0.609630\pi$
$6$	−2976.68	−	2976.68i	−0.382804	−	0.382804i
$7$	1469.56	−	1469.56i	0.0874374	−	0.0874374i	−0.662035	−	0.749473i	$-0.730307\pi$
$7$	1469.56	−	1469.56i	0.0874374	−	0.0874374i	0.749473	+	0.662035i	$0.230307\pi$
$8$	−16269.2	+	16269.2i	−0.496498	+	0.496498i
$9$	62003.1			1.05003
$10$		−	32277.3i		−	0.322773i
$11$	166265.	−	166265.i	1.03237	−	1.03237i	0.0329135	−	0.999458i	$-0.489521\pi$
$11$	166265.	−	166265.i	1.03237	−	1.03237i	0.999458	−	0.0329135i	$-0.0104786\pi$
$12$		−	305342.i		−	1.22710i
$13$	182221.	−	323502.i	0.490775	−	0.871286i
$13$	182221.	−	323502.i	0.490775	−	0.871286i
$14$	−25145.7			−0.0467545
$15$	656306.	+	656306.i	0.864271	+	0.864271i
$16$	−620285.			−0.591550
$17$			1.32216e6i			0.931193i	0.884997	+	0.465596i	$0.154160\pi$
$17$			1.32216e6i			0.931193i	−0.884997	+	0.465596i	$0.845840\pi$
$18$	−530469.	−	530469.i	−0.280736	−	0.280736i
$19$	−853777.	−	853777.i	−0.344807	−	0.344807i	0.513364	−	0.858171i	$-0.328399\pi$
$19$	−853777.	−	853777.i	−0.344807	−	0.344807i	−0.858171	+	0.513364i	$0.828399\pi$
$20$	1.65546e6	−	1.65546e6i	0.517333	−	0.517333i
$21$	511297.	−	511297.i	0.125192	−	0.125192i
$22$	−2.84496e6			−0.552030
$23$			8.82268e6i			1.37076i	0.728186	+	0.685380i	$0.240364\pi$
$23$			8.82268e6i			1.37076i	−0.728186	+	0.685380i	$0.759636\pi$
$24$	−5.66048e6	+	5.66048e6i	−0.710881	+	0.710881i
$25$		−	2.64906e6i		−	0.271264i
$26$	−4.32673e6	+	1.20873e6i	−0.364161	+	0.101733i
$27$	1.02782e6			0.0716303
$28$	−1.28969e6	−	1.28969e6i	−0.0749371	−	0.0749371i
$29$	−1.21072e7			−0.590276			−0.295138	−	0.955455i	$-0.595366\pi$
$29$	−1.21072e7			−0.590276			−0.295138	+	0.955455i	$0.595366\pi$
$30$		−	1.12301e7i		−	0.462143i
$31$	8.03380e6	+	8.03380e6i	0.280616	+	0.280616i	0.833355	−	0.552739i	$-0.186417\pi$
$31$	8.03380e6	+	8.03380e6i	0.280616	+	0.280616i	−0.552739	+	0.833355i	$0.686417\pi$
$32$	2.19666e7	+	2.19666e7i	0.654654	+	0.654654i
$33$	5.78477e7	−	5.78477e7i	1.47814	−	1.47814i
$34$	1.13118e7	−	1.13118e7i	0.248964	−	0.248964i
$35$	5.54418e6			0.105559
$36$		−	5.44143e7i		−	0.899913i
$37$	−8.13044e7	+	8.13044e7i	−1.17248	+	1.17248i	−0.190863	+	0.981617i	$0.561128\pi$
$37$	−8.13044e7	+	8.13044e7i	−1.17248	+	1.17248i	−0.981617	+	0.190863i	$0.938872\pi$
$38$			1.46090e7i			0.184375i
$39$	6.33995e7	−	1.12555e8i	0.702688	−	1.24750i
$40$	−6.13786e7			−0.599401
$41$	3.01838e7	+	3.01838e7i	0.260528	+	0.260528i	0.825269	−	0.564740i	$-0.191024\pi$
$41$	3.01838e7	+	3.01838e7i	0.260528	+	0.260528i	−0.564740	+	0.825269i	$0.691024\pi$
$42$	−8.74883e6			−0.0669428
$43$			1.89716e8i			1.29051i	0.763967	+	0.645255i	$0.223249\pi$
$43$			1.89716e8i			1.29051i	−0.763967	+	0.645255i	$0.776751\pi$
$44$	−1.45915e8	−	1.45915e8i	−0.884781	−	0.884781i
$45$	1.16959e8	+	1.16959e8i	0.633828	+	0.633828i
$46$	7.54826e7	−	7.54826e7i	0.366486	−	0.366486i
$47$	7.61863e7	−	7.61863e7i	0.332191	−	0.332191i	−0.521227	−	0.853418i	$-0.674526\pi$
$47$	7.61863e7	−	7.61863e7i	0.332191	−	0.332191i	0.853418	+	0.521227i	$0.174526\pi$
$48$	−2.15813e8			−0.846976
$49$			2.78156e8i			0.984709i
$50$	−2.26641e7	+	2.26641e7i	−0.0725251	+	0.0725251i
$51$			4.60013e8i			1.33327i
$52$	−2.83908e8	−	1.59919e8i	−0.746725	−	0.420613i
$53$	−5.83118e8			−1.39437			−0.697183	−	0.716893i	$-0.745564\pi$
$53$	−5.83118e8			−1.39437			−0.697183	+	0.716893i	$0.745564\pi$
$54$	−8.79351e6	−	8.79351e6i	−0.0191511	−	0.0191511i
$55$	6.27263e8			1.24634
$56$			4.78172e7i			0.0868249i
$57$	−2.97051e8	−	2.97051e8i	−0.493692	−	0.493692i
$58$	1.03584e8	+	1.03584e8i	0.157816	+	0.157816i
$59$	7.74150e8	−	7.74150e8i	1.08284	−	1.08284i	0.0865989	−	0.996243i	$-0.472400\pi$
$59$	7.74150e8	−	7.74150e8i	1.08284	−	1.08284i	0.996243	−	0.0865989i	$-0.0275999\pi$
$60$	5.75978e8	−	5.75978e8i	0.740713	−	0.740713i
$61$	3.47707e8			0.411684			0.205842	−	0.978585i	$-0.434007\pi$
$61$	3.47707e8			0.411684			0.205842	+	0.978585i	$0.434007\pi$
$62$		−	1.37467e8i		−	0.150051i
$63$	9.11173e7	−	9.11173e7i	0.0918117	−	0.0918117i
$64$			2.59301e8i			0.241493i
$65$	9.53968e8	−	2.66504e8i	0.822180	−	0.229687i
$66$	−9.89834e8			−0.790392
$67$	−1.48037e9	−	1.48037e9i	−1.09647	−	1.09647i	−0.994821	−	0.101647i	$-0.967589\pi$
$67$	−1.48037e9	−	1.48037e9i	−1.09647	−	1.09647i	−0.101647	−	0.994821i	$-0.532411\pi$
$68$	1.16034e9			0.798067
$69$			3.06964e9i			1.96264i
$70$	−4.74334e7	−	4.74334e7i	−0.0282224	−	0.0282224i
$71$	−4.39607e8	−	4.39607e8i	−0.243653	−	0.243653i	0.574706	−	0.818360i	$-0.305116\pi$
$71$	−4.39607e8	−	4.39607e8i	−0.243653	−	0.243653i	−0.818360	+	0.574706i	$0.805116\pi$
$72$	−1.00874e9	+	1.00874e9i	−0.521337	+	0.521337i
$73$	−7.85564e8	+	7.85564e8i	−0.378937	+	0.378937i	−0.870719	−	0.491782i	$-0.836346\pi$
$73$	−7.85564e8	+	7.85564e8i	−0.378937	+	0.378937i	0.491782	+	0.870719i	$0.336346\pi$
$74$	1.39120e9			0.626948
$75$		−	9.21675e8i		−	0.388393i
$76$	−7.49280e8	+	7.49280e8i	−0.295513	+	0.295513i
$77$		−	4.88671e8i		−	0.180536i
$78$	−1.50538e9	+	4.20549e8i	−0.521403	+	0.145661i
$79$	3.93240e9			1.27797			0.638987	−	0.769218i	$-0.279354\pi$
$79$	3.93240e9			1.27797			0.638987	+	0.769218i	$0.279354\pi$
$80$	−1.17007e9	−	1.17007e9i	−0.357077	−	0.357077i
$81$	−3.30362e9			−0.947469
$82$		−	5.16477e8i		−	0.139310i
$83$	1.14577e9	+	1.14577e9i	0.290876	+	0.290876i	0.837426	−	0.546550i	$-0.184059\pi$
$83$	1.14577e9	+	1.14577e9i	0.290876	+	0.290876i	−0.546550	+	0.837426i	$0.684059\pi$
$84$	−4.48718e8	−	4.48718e8i	−0.107294	−	0.107294i
$85$	−2.49405e9	+	2.49405e9i	−0.562095	+	0.562095i
$86$	1.62312e9	−	1.62312e9i	0.345031	−	0.345031i
$87$	−4.21241e9			−0.845152
$88$			5.40999e9i			1.02514i
$89$	1.31299e9	−	1.31299e9i	0.235133	−	0.235133i	−0.579698	−	0.814831i	$-0.696830\pi$
$89$	1.31299e9	−	1.31299e9i	0.235133	−	0.235133i	0.814831	+	0.579698i	$0.196830\pi$
$90$		−	2.00129e9i		−	0.338920i
$91$	−2.07621e8	−	7.43192e8i	−0.0332709	−	0.119095i
$92$	7.74284e9			1.17479
$93$	2.79517e9	+	2.79517e9i	0.401784	+	0.401784i
$94$	−1.30363e9			−0.177629
$95$		−	3.22103e9i		−	0.416272i
$96$	7.64272e9	+	7.64272e9i	0.937329	+	0.937329i
$97$	−1.02242e10	−	1.02242e10i	−1.19061	−	1.19061i	−0.976896	−	0.213715i	$-0.931443\pi$
$97$	−1.02242e10	−	1.02242e10i	−1.19061	−	1.19061i	−0.213715	−	0.976896i	$-0.568557\pi$
$98$	2.37977e9	−	2.37977e9i	0.263272	−	0.263272i
$99$	1.03089e10	−	1.03089e10i	1.08402	−	1.08402i
$100$	−2.32483e9			−0.232483
$101$		−	1.48865e10i		−	1.41639i	−0.706015	−	0.708197i	$-0.749509\pi$
$101$		−	1.48865e10i		−	1.41639i	0.706015	−	0.708197i	$-0.250491\pi$
$102$	3.93565e9	−	3.93565e9i	0.356464	−	0.356464i
$103$			5.72829e9i			0.494127i	0.968999	+	0.247064i	$0.0794656\pi$
$103$			5.72829e9i			0.494127i	−0.968999	+	0.247064i	$0.920534\pi$
$104$	2.29853e9	+	8.22774e9i	0.188923	+	0.676260i
$105$	1.92896e9			0.151139
$106$	4.98888e9	+	4.98888e9i	0.372798	+	0.372798i
$107$	−2.24746e10			−1.60241			−0.801205	−	0.598390i	$-0.795807\pi$
$107$	−2.24746e10			−1.60241			−0.801205	+	0.598390i	$0.795807\pi$
$108$		−	9.02019e8i		−	0.0613899i
$109$	6.29393e9	+	6.29393e9i	0.409062	+	0.409062i	0.881412	−	0.472349i	$-0.156594\pi$
$109$	6.29393e9	+	6.29393e9i	0.409062	+	0.409062i	−0.472349	+	0.881412i	$0.656594\pi$
$110$	−5.36656e9	−	5.36656e9i	−0.333221	−	0.333221i
$111$	−2.82879e10	+	2.82879e10i	−1.67875	+	1.67875i
$112$	−9.11546e8	+	9.11546e8i	−0.0517236	+	0.0517236i
$113$	2.58237e10			1.40161			0.700803	−	0.713355i	$-0.252825\pi$
$113$	2.58237e10			1.40161			0.700803	+	0.713355i	$0.252825\pi$
$114$			5.08285e9i			0.263987i
$115$	−1.66426e10	+	1.66426e10i	−0.827431	+	0.827431i
$116$			1.06254e10i			0.505888i
$117$	1.12983e10	−	2.00582e10i	0.515328	−	0.914875i
$118$	−1.32465e10			−0.579018
$119$	1.94299e9	+	1.94299e9i	0.0814210	+	0.0814210i
$120$	−2.13552e10			−0.858217
$121$		−	2.93503e10i		−	1.13158i
$122$	−2.97482e9	−	2.97482e9i	−0.110068	−	0.110068i
$123$	1.05017e10	+	1.05017e10i	0.373023	+	0.373023i
$124$	7.05052e9	−	7.05052e9i	0.240499	−	0.240499i
$125$	2.34183e10	−	2.34183e10i	0.767372	−	0.767372i
$126$	−1.55911e9			−0.0490936
$127$			4.21867e10i			1.27690i	0.769663	+	0.638451i	$0.220424\pi$
$127$			4.21867e10i			1.27690i	−0.769663	+	0.638451i	$0.779576\pi$
$128$	2.47122e10	−	2.47122e10i	0.719220	−	0.719220i
$129$			6.60070e10i			1.84774i
$130$	−1.04418e10	−	5.88161e9i	−0.281227	−	0.158409i
$131$	1.53975e10			0.399110			0.199555	−	0.979887i	$-0.436050\pi$
$131$	1.53975e10			0.399110			0.199555	+	0.979887i	$0.436050\pi$
$132$	−5.07675e10	−	5.07675e10i	−1.26682	−	1.26682i
$133$	−2.50935e9			−0.0602981
$134$			2.53306e10i			0.586303i
$135$	1.93881e9	+	1.93881e9i	0.0432382	+	0.0432382i
$136$	−2.15105e10	−	2.15105e10i	−0.462335	−	0.462335i
$137$	3.79474e10	−	3.79474e10i	0.786284	−	0.786284i	−0.194599	−	0.980883i	$-0.562341\pi$
$137$	3.79474e10	−	3.79474e10i	0.786284	−	0.786284i	0.980883	+	0.194599i	$0.0623405\pi$
$138$	2.62623e10	−	2.62623e10i	0.524732	−	0.524732i
$139$	4.22084e10			0.813438			0.406719	−	0.913553i	$-0.366673\pi$
$139$	4.22084e10			0.813438			0.406719	+	0.913553i	$0.366673\pi$
$140$		−	4.86561e9i		−	0.0904684i
$141$	2.65072e10	−	2.65072e10i	0.475628	−	0.475628i
$142$			7.52213e9i			0.130286i
$143$	−2.34900e10	−	8.40839e10i	−0.392829	−	1.40615i
$144$	−3.84596e10			−0.621144
$145$	−2.28384e10	−	2.28384e10i	−0.356307	−	0.356307i
$146$	1.34418e10			0.202625
$147$			9.67776e10i			1.40990i
$148$	7.13532e10	+	7.13532e10i	1.00486	+	1.00486i
$149$	2.25798e10	+	2.25798e10i	0.307460	+	0.307460i	0.843924	−	0.536463i	$-0.180240\pi$
$149$	2.25798e10	+	2.25798e10i	0.307460	+	0.307460i	−0.536463	+	0.843924i	$0.680240\pi$
$150$	−7.88541e9	+	7.88541e9i	−0.103841	+	0.103841i
$151$	2.02062e10	−	2.02062e10i	0.257395	−	0.257395i	−0.566599	−	0.823994i	$-0.691741\pi$
$151$	2.02062e10	−	2.02062e10i	0.257395	−	0.257395i	0.823994	+	0.566599i	$0.191741\pi$
$152$	2.77806e10			0.342392
$153$			8.19781e10i			0.977779i
$154$	−4.18084e9	+	4.18084e9i	−0.0482680	+	0.0482680i
$155$			3.03090e10i			0.338776i
$156$	−9.87787e10	−	5.56398e10i	−1.06915	−	0.602230i
$157$	−1.19373e11			−1.25144			−0.625719	−	0.780049i	$-0.715194\pi$
$157$	−1.19373e11			−1.25144			−0.625719	+	0.780049i	$0.715194\pi$
$158$	−3.36437e10	−	3.36437e10i	−0.341679	−	0.341679i
$159$	−2.02881e11			−1.99644
$160$			8.28728e10i			0.790337i
$161$	1.29655e10	+	1.29655e10i	0.119856	+	0.119856i
$162$	2.82642e10	+	2.82642e10i	0.253315	+	0.253315i
$163$	8.64801e9	−	8.64801e9i	0.0751585	−	0.0751585i	−0.668528	−	0.743687i	$-0.733075\pi$
$163$	8.64801e9	−	8.64801e9i	0.0751585	−	0.0751585i	0.743687	+	0.668528i	$0.233075\pi$
$164$	2.64895e10	−	2.64895e10i	0.223283	−	0.223283i
$165$	2.18241e11			1.78450
$166$		−	1.96054e10i		−	0.155537i
$167$	−1.01896e11	+	1.01896e11i	−0.784471	+	0.784471i	−0.980582	−	0.196111i	$-0.937169\pi$
$167$	−1.01896e11	+	1.01896e11i	−0.784471	+	0.784471i	0.196111	+	0.980582i	$0.437169\pi$
$168$			1.66368e10i			0.124315i
$169$	−7.14492e10	−	1.17898e11i	−0.518279	−	0.855211i
$170$	4.26757e10			0.300564
$171$	−5.29369e10	−	5.29369e10i	−0.362058	−	0.362058i
$172$	1.66496e11			1.10601
$173$		−	1.09144e10i		−	0.0704321i	−0.999380	−	0.0352161i	$-0.988788\pi$
$173$		−	1.09144e10i		−	0.0704321i	0.999380	−	0.0352161i	$-0.0112119\pi$
$174$	3.60394e10	+	3.60394e10i	0.225960	+	0.225960i
$175$	−3.89295e9	−	3.89295e9i	−0.0237186	−	0.0237186i
$176$	−1.03131e11	+	1.03131e11i	−0.610699	+	0.610699i
$177$	2.69347e11	−	2.69347e11i	1.55040	−	1.55040i
$178$	−2.24667e10			−0.125730
$179$		−	1.64576e10i		−	0.0895576i	−0.998997	−	0.0447788i	$-0.985742\pi$
$179$		−	1.64576e10i		−	0.0895576i	0.998997	−	0.0447788i	$-0.0142583\pi$
$180$	1.02644e11	−	1.02644e11i	0.543214	−	0.543214i
$181$			1.46045e11i			0.751785i	0.926663	+	0.375892i	$0.122664\pi$
$181$			1.46045e11i			0.751785i	−0.926663	+	0.375892i	$0.877336\pi$
$182$	−4.58209e9	+	8.13470e9i	−0.0229460	+	0.0407366i
$183$	1.20976e11			0.589446
$184$	−1.43538e11	−	1.43538e11i	−0.680579	−	0.680579i
$185$	−3.06735e11			−1.41549
$186$		−	4.78282e10i		−	0.214842i
$187$	2.19828e11	+	2.19828e11i	0.961337	+	0.961337i
$188$	−6.68616e10	−	6.68616e10i	−0.284700	−	0.284700i
$189$	1.51044e9	−	1.51044e9i	0.00626317	−	0.00626317i
$190$	−2.75576e10	+	2.75576e10i	−0.111294	+	0.111294i
$191$	−2.65821e11			−1.04574			−0.522868	−	0.852413i	$-0.675138\pi$
$191$	−2.65821e11			−1.04574			−0.522868	+	0.852413i	$0.675138\pi$
$192$			9.02175e10i			0.345768i
$193$	1.29740e11	−	1.29740e11i	0.484493	−	0.484493i	−0.422070	−	0.906563i	$-0.638696\pi$
$193$	1.29740e11	−	1.29740e11i	0.484493	−	0.484493i	0.906563	+	0.422070i	$0.138696\pi$
$194$			1.74946e11i			0.636644i
$195$	3.31910e11	−	9.27236e10i	1.17719	−	0.328865i
$196$	2.44111e11			0.843933
$197$	2.59470e11	+	2.59470e11i	0.874493	+	0.874493i	0.992958	−	0.118465i	$-0.0377974\pi$
$197$	2.59470e11	+	2.59470e11i	0.874493	+	0.874493i	−0.118465	+	0.992958i	$0.537797\pi$
$198$	−1.76396e11			−0.579647
$199$		−	5.80039e11i		−	1.85863i	−0.369293	−	0.929313i	$-0.620400\pi$
$199$		−	5.80039e11i		−	1.85863i	0.369293	−	0.929313i	$-0.379600\pi$
$200$	4.30982e10	+	4.30982e10i	0.134682	+	0.134682i
$201$	−5.15058e11	−	5.15058e11i	−1.56991	−	1.56991i
$202$	−1.27361e11	+	1.27361e11i	−0.378687	+	0.378687i
$203$	−1.77923e10	+	1.77923e10i	−0.0516121	+	0.0516121i
$204$	4.03711e11			1.14267
$205$			1.13874e11i			0.314525i
$206$	4.90085e10	−	4.90085e10i	0.132110	−	0.132110i
$207$			5.47034e11i			1.43934i
$208$	−1.13029e11	+	2.00664e11i	−0.290318	+	0.515409i
$209$	−2.83906e11			−0.711939
$210$	−1.65033e10	−	1.65033e10i	−0.0404086	−	0.0404086i
$211$	−6.94257e11			−1.66000			−0.830000	−	0.557763i	$-0.811660\pi$
$211$	−6.94257e11			−1.66000			−0.830000	+	0.557763i	$0.811660\pi$
$212$			5.11748e11i			1.19502i
$213$	−1.52950e11	−	1.52950e11i	−0.348861	−	0.348861i
$214$	1.92282e11	+	1.92282e11i	0.428421	+	0.428421i
$215$	−3.57869e11	+	3.57869e11i	−0.778989	+	0.778989i
$216$	−1.67218e10	+	1.67218e10i	−0.0355643	+	0.0355643i
$217$	2.36123e10			0.0490727
$218$		−	1.07696e11i		−	0.218734i
$219$	−2.73318e11	+	2.73318e11i	−0.542559	+	0.542559i
$220$		−	5.50490e11i		−	1.06816i
$221$	4.27722e11	+	2.40926e11i	0.811335	+	0.457006i
$222$	4.84035e11			0.897660
$223$	2.32333e11	+	2.32333e11i	0.421296	+	0.421296i	0.885650	−	0.464354i	$-0.153713\pi$
$223$	2.32333e11	+	2.32333e11i	0.421296	+	0.421296i	−0.464354	+	0.885650i	$0.653713\pi$
$224$	6.45623e10			0.114483
$225$		−	1.64250e11i		−	0.284835i
$226$	−2.20935e11	−	2.20935e11i	−0.374734	−	0.374734i
$227$	−1.59849e11	−	1.59849e11i	−0.265205	−	0.265205i	0.561960	−	0.827164i	$-0.310048\pi$
$227$	−1.59849e11	−	1.59849e11i	−0.265205	−	0.265205i	−0.827164	+	0.561960i	$0.810048\pi$
$228$	−2.60694e11	+	2.60694e11i	−0.423113	+	0.423113i
$229$	7.44142e11	−	7.44142e11i	1.18162	−	1.18162i	0.202298	−	0.979324i	$-0.435159\pi$
$229$	7.44142e11	−	7.44142e11i	1.18162	−	1.18162i	0.979324	−	0.202298i	$-0.0648408\pi$
$230$	2.84772e11			0.442444
$231$		−	1.70021e11i		−	0.258490i
$232$	1.96975e11	−	1.96975e11i	0.293070	−	0.293070i
$233$		−	4.72387e11i		−	0.687889i	−0.938990	−	0.343944i	$-0.888237\pi$
$233$		−	4.72387e11i		−	0.687889i	0.938990	−	0.343944i	$-0.111763\pi$
$234$	−2.68271e11	+	7.49452e10i	−0.382379	+	0.106823i
$235$	2.87427e11			0.401040
$236$	−6.79399e11	−	6.79399e11i	−0.928036	−	0.928036i
$237$	1.36818e12			1.82979
$238$		−	3.32467e10i		−	0.0435375i
$239$	7.08814e11	+	7.08814e11i	0.908956	+	0.908956i	0.996188	−	0.0872323i	$-0.0278022\pi$
$239$	7.08814e11	+	7.08814e11i	0.908956	+	0.908956i	−0.0872323	+	0.996188i	$0.527802\pi$
$240$	−4.07097e11	−	4.07097e11i	−0.511260	−	0.511260i
$241$	7.70003e11	−	7.70003e11i	0.947125	−	0.947125i	−0.0515461	−	0.998671i	$-0.516415\pi$
$241$	7.70003e11	−	7.70003e11i	0.947125	−	0.947125i	0.998671	+	0.0515461i	$0.0164149\pi$
$242$	−2.51108e11	+	2.51108e11i	−0.302540	+	0.302540i
$243$	−1.21010e12			−1.42821
$244$		−	3.05150e11i		−	0.352829i
$245$	−5.24697e11	+	5.24697e11i	−0.594399	+	0.594399i
$246$		−	1.79695e11i		−	0.199463i
$247$	−4.31776e11	+	1.20623e11i	−0.469649	+	0.131203i
$248$	−2.61408e11			−0.278651
$249$	3.98643e11	+	3.98643e11i	0.416474	+	0.416474i
$250$	−4.00712e11			−0.410329
$251$			3.75882e11i			0.377297i	0.982045	+	0.188648i	$0.0604106\pi$
$251$			3.75882e11i			0.377297i	−0.982045	+	0.188648i	$0.939589\pi$
$252$	−7.99651e10	−	7.99651e10i	−0.0786861	−	0.0786861i
$253$	1.46690e12	+	1.46690e12i	1.41513	+	1.41513i
$254$	3.60930e11	−	3.60930e11i	0.341393	−	0.341393i
$255$	−8.67742e11	+	8.67742e11i	−0.804803	+	0.804803i
$256$	−1.57327e11			−0.143088
$257$		−	1.41838e11i		−	0.126511i	−0.997997	−	0.0632555i	$-0.979852\pi$
$257$		−	1.41838e11i		−	0.126511i	0.997997	−	0.0632555i	$-0.0201483\pi$
$258$	5.64724e11	−	5.64724e11i	0.494012	−	0.494012i
$259$			2.38963e11i			0.205037i
$260$	−2.33886e11	−	8.37208e11i	−0.196851	−	0.704639i
$261$	−7.50686e11			−0.619806
$262$	−1.31733e11	−	1.31733e11i	−0.106706	−	0.106706i
$263$	1.14954e12			0.913575			0.456787	−	0.889576i	$-0.349000\pi$
$263$	1.14954e12			0.913575			0.456787	+	0.889576i	$0.349000\pi$
$264$			1.88227e12i			1.46779i
$265$	−1.09996e12	−	1.09996e12i	−0.841680	−	0.841680i
$266$	2.14688e10	+	2.14688e10i	0.0161213	+	0.0161213i
$267$	4.56824e11	−	4.56824e11i	0.336661	−	0.336661i
$268$	−1.29918e12	+	1.29918e12i	−0.939713	+	0.939713i
$269$	−7.08991e11			−0.503361			−0.251680	−	0.967810i	$-0.580983\pi$
$269$	−7.08991e11			−0.503361			−0.251680	+	0.967810i	$0.580983\pi$
$270$		−	3.31751e10i		−	0.0231203i
$271$	−5.80450e11	+	5.80450e11i	−0.397117	+	0.397117i	−0.877215	−	0.480098i	$-0.840601\pi$
$271$	−5.80450e11	+	5.80450e11i	−0.397117	+	0.397117i	0.480098	+	0.877215i	$0.340601\pi$
$272$		−	8.20116e11i		−	0.550847i
$273$	−7.22366e10	−	2.58575e11i	−0.0476370	−	0.170519i
$274$	−6.49320e11			−0.420442
$275$	−4.40445e11	−	4.40445e11i	−0.280045	−	0.280045i
$276$	2.69393e12			1.68206
$277$			2.27870e10i			0.0139730i	0.999976	+	0.00698648i	$0.00222388\pi$
$277$			2.27870e10i			0.0139730i	−0.999976	+	0.00698648i	$0.997776\pi$
$278$	−3.61115e11	−	3.61115e11i	−0.217481	−	0.217481i
$279$	4.98121e11	+	4.98121e11i	0.294655	+	0.294655i
$280$	−9.01996e10	+	9.01996e10i	−0.0524100	+	0.0524100i
$281$	−3.72608e11	+	3.72608e11i	−0.212677	+	0.212677i	−0.805404	−	0.592727i	$-0.798051\pi$
$281$	−3.72608e11	+	3.72608e11i	−0.212677	+	0.212677i	0.592727	+	0.805404i	$0.298051\pi$
$282$	−4.53565e11			−0.254328
$283$			1.45714e12i			0.802729i	0.915918	+	0.401365i	$0.131464\pi$
$283$			1.45714e12i			0.802729i	−0.915918	+	0.401365i	$0.868536\pi$
$284$	−3.85801e11	+	3.85801e11i	−0.208820	+	0.208820i
$285$		−	1.12068e12i		−	0.596014i
$286$	−5.18413e11	+	9.20351e11i	−0.270923	+	0.480976i
$287$	8.87139e10			0.0455598
$288$	1.36200e12	+	1.36200e12i	0.687406	+	0.687406i
$289$	2.67885e11			0.132880
$290$			3.90788e11i			0.190525i
$291$	−3.55725e12	−	3.55725e12i	−1.70471	−	1.70471i
$292$	6.89415e11	+	6.89415e11i	0.324763	+	0.324763i
$293$	2.07296e12	−	2.07296e12i	0.959960	−	0.959960i	−0.0392687	−	0.999229i	$-0.512503\pi$
$293$	2.07296e12	−	2.07296e12i	0.959960	−	0.959960i	0.999229	+	0.0392687i	$0.0125028\pi$
$294$	8.27983e11	−	8.27983e11i	0.376951	−	0.376951i
$295$	2.92062e12			1.30727
$296$		−	2.64552e12i		−	1.16427i
$297$	1.70889e11	−	1.70889e11i	0.0739491	−	0.0739491i
$298$		−	3.86364e11i		−	0.164405i
$299$	2.85416e12	+	1.60768e12i	1.19432	+	0.672735i
$300$	−8.08868e11			−0.332867
$301$	2.78799e11	+	2.78799e11i	0.112839	+	0.112839i
$302$	−3.45749e11			−0.137634
$303$		−	5.17938e12i		−	2.02798i
$304$	5.29585e11	+	5.29585e11i	0.203971	+	0.203971i
$305$	6.55894e11	+	6.55894e11i	0.248505	+	0.248505i
$306$	7.01365e11	−	7.01365e11i	0.261419	−	0.261419i
$307$	−2.74366e12	+	2.74366e12i	−1.00609	+	1.00609i	−0.00611257	+	0.999981i	$0.501946\pi$
$307$	−2.74366e12	+	2.74366e12i	−1.00609	+	1.00609i	−0.999981	+	0.00611257i	$0.998054\pi$
$308$	−4.28861e11			−0.154726
$309$			1.99302e12i			0.707487i
$310$	2.59309e11	−	2.59309e11i	0.0905753	−	0.0905753i
$311$		−	1.59962e12i		−	0.549813i	−0.961471	−	0.274906i	$-0.911353\pi$
$311$		−	1.59962e12i		−	0.549813i	0.961471	−	0.274906i	$-0.0886469\pi$
$312$	7.99718e11	+	2.86264e12i	0.270498	+	0.968264i
$313$	−3.40405e12			−1.13311			−0.566557	−	0.824022i	$-0.691725\pi$
$313$	−3.40405e12			−1.13311			−0.566557	+	0.824022i	$0.691725\pi$
$314$	1.02130e12	+	1.02130e12i	0.334585	+	0.334585i
$315$	3.43757e11			0.110840
$316$		−	3.45109e12i		−	1.09527i
$317$	2.36760e12	+	2.36760e12i	0.739627	+	0.739627i	0.972506	−	0.232879i	$-0.0748145\pi$
$317$	2.36760e12	+	2.36760e12i	0.739627	+	0.739627i	−0.232879	+	0.972506i	$0.574815\pi$
$318$	1.73576e12	+	1.73576e12i	0.533769	+	0.533769i
$319$	−2.01300e12	+	2.01300e12i	−0.609384	+	0.609384i
$320$	−4.89130e11	+	4.89130e11i	−0.145772	+	0.145772i
$321$	−7.81950e12			−2.29432
$322$		−	2.21853e11i		−	0.0640892i
$323$	1.12883e12	−	1.12883e12i	0.321082	−	0.321082i
$324$			2.89928e12i			0.812016i
$325$	−8.56977e11	−	4.82716e11i	−0.236348	−	0.133130i
$326$	−1.47976e11			−0.0401888
$327$	2.18982e12	+	2.18982e12i	0.585692	+	0.585692i
$328$	−9.82136e11			−0.258703
$329$		−	2.23921e11i		−	0.0580918i
$330$	−1.86716e12	−	1.86716e12i	−0.477104	−	0.477104i
$331$	−1.91101e12	−	1.91101e12i	−0.480977	−	0.480977i	0.424467	−	0.905443i	$-0.360462\pi$
$331$	−1.91101e12	−	1.91101e12i	−0.480977	−	0.480977i	−0.905443	+	0.424467i	$0.860462\pi$
$332$	1.00554e12	−	1.00554e12i	0.249292	−	0.249292i
$333$	−5.04112e12	+	5.04112e12i	−1.23114	+	1.23114i
$334$	1.74355e12			0.419472
$335$		−	5.58496e12i		−	1.32372i
$336$	−3.17150e11	+	3.17150e11i	−0.0740574	+	0.0740574i
$337$		−	5.86636e12i		−	1.34964i	−0.737981	−	0.674822i	$-0.764221\pi$
$337$		−	5.86636e12i		−	1.34964i	0.737981	−	0.674822i	$-0.235779\pi$
$338$	−3.97395e11	+	1.61997e12i	−0.0900822	+	0.367217i
$339$	8.98472e12			2.00681
$340$	2.18879e12	+	2.18879e12i	0.481736	+	0.481736i
$341$	2.67147e12			0.579401
$342$			9.05805e11i			0.193599i
$343$	8.23881e11	+	8.23881e11i	0.173538	+	0.173538i
$344$	−3.08653e12	−	3.08653e12i	−0.640735	−	0.640735i
$345$	−5.79038e12	+	5.79038e12i	−1.18471	+	1.18471i
$346$	−9.33787e10	+	9.33787e10i	−0.0188307	+	0.0188307i
$347$	1.20213e12			0.238948			0.119474	−	0.992837i	$-0.461879\pi$
$347$	1.20213e12			0.238948			0.119474	+	0.992837i	$0.461879\pi$
$348$			3.69684e12i			0.724327i
$349$	−2.84919e12	+	2.84919e12i	−0.550294	+	0.550294i	−0.926526	−	0.376232i	$-0.877220\pi$
$349$	−2.84919e12	+	2.84919e12i	−0.550294	+	0.550294i	0.376232	+	0.926526i	$0.377220\pi$
$350$			6.66125e10i			0.0126828i
$351$	1.87290e11	−	3.32501e11i	0.0351544	−	0.0624105i
$352$	7.30452e12			1.35169
$353$	2.53227e12	+	2.53227e12i	0.461994	+	0.461994i	0.899309	−	0.437315i	$-0.144070\pi$
$353$	2.53227e12	+	2.53227e12i	0.461994	+	0.461994i	−0.437315	+	0.899309i	$0.644070\pi$
$354$	−4.60880e12			−0.829033
$355$		−	1.65850e12i		−	0.294153i
$356$	−1.15229e12	−	1.15229e12i	−0.201517	−	0.201517i
$357$	6.76017e11	+	6.76017e11i	0.116578	+	0.116578i
$358$	−1.40804e11	+	1.40804e11i	−0.0239441	+	0.0239441i
$359$	2.20158e12	−	2.20158e12i	0.369201	−	0.369201i	−0.497985	−	0.867186i	$-0.665927\pi$
$359$	2.20158e12	−	2.20158e12i	0.369201	−	0.369201i	0.867186	+	0.497985i	$0.165927\pi$
$360$	−3.80567e12			−0.629388
$361$		−	4.67320e12i		−	0.762216i
$362$	1.24949e12	−	1.24949e12i	0.200997	−	0.200997i
$363$		−	1.02117e13i		−	1.62019i
$364$	−6.52229e11	+	1.82209e11i	−0.102069	+	0.0285144i
$365$	−2.96368e12			−0.457475
$366$	−1.03501e12	−	1.03501e12i	−0.157594	−	0.157594i
$367$	5.13957e12			0.771962			0.385981	−	0.922507i	$-0.373863\pi$
$367$	5.13957e12			0.771962			0.385981	+	0.922507i	$0.373863\pi$
$368$		−	5.47258e12i		−	0.810873i
$369$	1.87149e12	+	1.87149e12i	0.273562	+	0.273562i
$370$	2.62428e12	+	2.62428e12i	0.378444	+	0.378444i
$371$	−8.56926e11	+	8.56926e11i	−0.121920	+	0.121920i
$372$	2.45305e12	−	2.45305e12i	0.344344	−	0.344344i
$373$	7.03479e12			0.974332			0.487166	−	0.873310i	$-0.338031\pi$
$373$	7.03479e12			0.974332			0.487166	+	0.873310i	$0.338031\pi$
$374$		−	3.76149e12i		−	0.514046i
$375$	8.14783e12	−	8.14783e12i	1.09872	−	1.09872i
$376$			2.47899e12i			0.329864i
$377$	−2.20620e12	+	3.91672e12i	−0.289693	+	0.514299i
$378$	−2.58452e10			−0.00334904
$379$	−7.01305e12	−	7.01305e12i	−0.896832	−	0.896832i	0.0983225	−	0.995155i	$-0.468652\pi$
$379$	−7.01305e12	−	7.01305e12i	−0.896832	−	0.896832i	−0.995155	+	0.0983225i	$0.968652\pi$
$380$	−2.82680e12			−0.356760
$381$			1.46778e13i			1.82826i
$382$	2.27424e12	+	2.27424e12i	0.279588	+	0.279588i
$383$	1.18560e12	+	1.18560e12i	0.143861	+	0.143861i	0.775369	−	0.631508i	$-0.217564\pi$
$383$	1.18560e12	+	1.18560e12i	0.143861	+	0.143861i	−0.631508	+	0.775369i	$0.717564\pi$
$384$	8.59801e12	−	8.59801e12i	1.02977	−	1.02977i
$385$	9.21801e11	−	9.21801e11i	0.108977	−	0.108977i
$386$	−2.21999e12			−0.259068
$387$			1.17630e13i			1.35507i
$388$	−8.97281e12	+	8.97281e12i	−1.02040	+	1.02040i
$389$			6.01039e12i			0.674769i	0.941367	+	0.337384i	$0.109542\pi$
$389$			6.01039e12i			0.674769i	−0.941367	+	0.337384i	$0.890458\pi$
$390$	−3.63296e12	−	2.04636e12i	−0.402659	−	0.226809i
$391$	−1.16650e13			−1.27644
$392$	−4.52539e12	−	4.52539e12i	−0.488906	−	0.488906i
$393$	5.35717e12			0.571443
$394$		−	4.43981e12i		−	0.467609i
$395$	7.41784e12	+	7.41784e12i	0.771422	+	0.771422i
$396$	−9.04717e12	−	9.04717e12i	−0.929045	−	0.929045i
$397$	−4.24959e12	+	4.24959e12i	−0.430918	+	0.430918i	−0.888941	−	0.458023i	$-0.848558\pi$
$397$	−4.24959e12	+	4.24959e12i	−0.430918	+	0.430918i	0.458023	+	0.888941i	$0.348558\pi$
$398$	−4.96254e12	+	4.96254e12i	−0.496922	+	0.496922i
$399$	−8.73068e11			−0.0863343
$400$			1.64317e12i			0.160466i
$401$	−1.29881e12	+	1.29881e12i	−0.125263	+	0.125263i	−0.766959	−	0.641696i	$-0.778231\pi$
$401$	−1.29881e12	+	1.29881e12i	−0.125263	+	0.125263i	0.641696	+	0.766959i	$0.278231\pi$
$402$			8.81318e12i			0.839464i
$403$	4.06289e12	−	1.13502e12i	0.382217	−	0.106778i
$404$	−1.30644e13			−1.21390
$405$	−6.23175e12	−	6.23175e12i	−0.571920	−	0.571920i
$406$	3.04445e11			0.0275980
$407$			2.70361e13i			2.42087i
$408$	−7.48406e12	−	7.48406e12i	−0.661968	−	0.661968i
$409$	3.44092e12	+	3.44092e12i	0.300648	+	0.300648i	0.841267	−	0.540619i	$-0.181810\pi$
$409$	3.44092e12	+	3.44092e12i	0.300648	+	0.300648i	−0.540619	+	0.841267i	$0.681810\pi$
$410$	9.74252e11	−	9.74252e11i	0.0840915	−	0.0840915i
$411$	1.32029e13	−	1.32029e13i	1.12580	−	1.12580i
$412$	5.02718e12			0.423485
$413$		−	2.27532e12i		−	0.189362i
$414$	4.68016e12	−	4.68016e12i	0.384821	−	0.384821i
$415$			4.32263e12i			0.351162i
$416$	1.11090e13	−	3.10346e12i	0.891680	−	0.249103i
$417$	1.46854e13			1.16467
$418$	2.42896e12	+	2.42896e12i	0.190344	+	0.190344i
$419$	−1.03975e13			−0.805115			−0.402557	−	0.915395i	$-0.631879\pi$
$419$	−1.03975e13			−0.805115			−0.402557	+	0.915395i	$0.631879\pi$
$420$		−	1.69287e12i		−	0.129532i
$421$	−1.35823e13	−	1.35823e13i	−1.02698	−	1.02698i	−0.999626	−	0.0273550i	$-0.991292\pi$
$421$	−1.35823e13	−	1.35823e13i	−1.02698	−	1.02698i	−0.0273550	−	0.999626i	$-0.508708\pi$
$422$	5.93973e12	+	5.93973e12i	0.443818	+	0.443818i
$423$	4.72379e12	−	4.72379e12i	0.348810	−	0.348810i
$424$	9.48688e12	−	9.48688e12i	0.692299	−	0.692299i
$425$	3.50248e12			0.252599
$426$			2.61714e12i			0.186543i
$427$	5.10976e11	−	5.10976e11i	0.0359966	−	0.0359966i
$428$			1.97239e13i			1.37333i
$429$	−8.17278e12	−	2.92549e13i	−0.562449	−	2.01332i
$430$	6.12351e12			0.416541
$431$	−1.05573e13	−	1.05573e13i	−0.709852	−	0.709852i	0.256652	−	0.966504i	$-0.417381\pi$
$431$	−1.05573e13	−	1.05573e13i	−0.709852	−	0.709852i	−0.966504	+	0.256652i	$0.917381\pi$
$432$	−6.37540e11			−0.0423729
$433$		−	1.13143e13i		−	0.743340i	−0.928365	−	0.371670i	$-0.878785\pi$
$433$		−	1.13143e13i		−	0.743340i	0.928365	−	0.371670i	$-0.121215\pi$
$434$	−2.02016e11	−	2.02016e11i	−0.0131201	−	0.0131201i
$435$	−7.94605e12	−	7.94605e12i	−0.510158	−	0.510158i
$436$	5.52359e12	−	5.52359e12i	0.350582	−	0.350582i
$437$	7.53260e12	−	7.53260e12i	0.472648	−	0.472648i
$438$	4.67675e12			0.290117
$439$			1.96435e13i			1.20475i	0.798214	+	0.602374i	$0.205778\pi$
$439$			1.96435e13i			1.20475i	−0.798214	+	0.602374i	$0.794222\pi$
$440$	−1.02051e13	+	1.02051e13i	−0.618804	+	0.618804i
$441$			1.72465e13i			1.03397i
$442$	−1.59814e12	−	5.72063e12i	−0.0947334	−	0.339104i
$443$	−2.07381e13			−1.21549			−0.607744	−	0.794133i	$-0.707925\pi$
$443$	−2.07381e13			−1.21549			−0.607744	+	0.794133i	$0.707925\pi$
$444$	2.48256e13	+	2.48256e13i	1.43875	+	1.43875i
$445$	4.95351e12			0.283866
$446$		−	3.97546e12i		−	0.225275i
$447$	7.85610e12	+	7.85610e12i	0.440219	+	0.440219i
$448$	3.81059e11	+	3.81059e11i	0.0211155	+	0.0211155i
$449$	−8.53438e12	+	8.53438e12i	−0.467671	+	0.467671i	−0.901159	−	0.433488i	$-0.857283\pi$
$449$	−8.53438e12	+	8.53438e12i	−0.467671	+	0.467671i	0.433488	+	0.901159i	$0.357283\pi$
$450$	−1.40524e12	+	1.40524e12i	−0.0761534	+	0.0761534i
$451$	1.00370e13			0.537924
$452$		−	2.26630e13i		−	1.20123i
$453$	7.03025e12	−	7.03025e12i	0.368536	−	0.368536i
$454$			2.73519e12i			0.141810i
$455$	1.01027e12	−	1.79356e12i	0.0518060	−	0.0919725i
$456$	9.66558e12			0.490234
$457$	−2.13889e13	−	2.13889e13i	−1.07302	−	1.07302i	−0.997115	−	0.0759052i	$-0.975815\pi$
$457$	−2.13889e13	−	2.13889e13i	−1.07302	−	1.07302i	−0.0759052	−	0.997115i	$-0.524185\pi$
$458$	−1.27330e13			−0.631837
$459$			1.35894e12i			0.0667017i
$460$	1.46056e13	+	1.46056e13i	0.709139	+	0.709139i
$461$	6.25441e12	+	6.25441e12i	0.300388	+	0.300388i	0.841165	−	0.540778i	$-0.181870\pi$
$461$	6.25441e12	+	6.25441e12i	0.300388	+	0.300388i	−0.540778	+	0.841165i	$0.681870\pi$
$462$	−1.45462e12	+	1.45462e12i	−0.0691098	+	0.0691098i
$463$	1.96851e13	−	1.96851e13i	0.925194	−	0.925194i	−0.0721969	−	0.997390i	$-0.523001\pi$
$463$	1.96851e13	−	1.96851e13i	0.925194	−	0.925194i	0.997390	+	0.0721969i	$0.0230010\pi$
$464$	7.50993e12			0.349177
$465$			1.05453e13i			0.485057i
$466$	−4.04152e12	+	4.04152e12i	−0.183914	+	0.183914i
$467$		−	2.36488e13i		−	1.06469i	−0.846526	−	0.532347i	$-0.821310\pi$
$467$		−	2.36488e13i		−	1.06469i	0.846526	−	0.532347i	$-0.178690\pi$
$468$	−1.76032e13	−	9.91546e12i	−0.784082	−	0.441655i
$469$	−4.35098e12			−0.191744
$470$	−2.45909e12	−	2.45909e12i	−0.107222	−	0.107222i
$471$	−4.15330e13			−1.79180
$472$			2.51897e13i			1.07526i
$473$	3.15430e13	+	3.15430e13i	1.33229	+	1.33229i
$474$	−1.17055e13	−	1.17055e13i	−0.489213	−	0.489213i
$475$	−2.26171e12	+	2.26171e12i	−0.0935337	+	0.0935337i
$476$	1.70518e12	−	1.70518e12i	0.0697809	−	0.0697809i
$477$	−3.61551e13			−1.46412
$478$		−	1.21285e13i		−	0.486037i
$479$	−1.15403e13	+	1.15403e13i	−0.457658	+	0.457658i	−0.897886	−	0.440228i	$-0.854898\pi$
$479$	−1.15403e13	+	1.15403e13i	−0.457658	+	0.457658i	0.440228	+	0.897886i	$0.354898\pi$
$480$			2.88336e13i			1.13160i
$481$	1.14868e13	+	4.11176e13i	0.446141	+	1.59699i
$482$	−1.31756e13			−0.506447
$483$	4.51101e12	+	4.51101e12i	0.171608	+	0.171608i
$484$	−2.57580e13			−0.969809
$485$		−	3.85726e13i		−	1.43738i
$486$	1.03531e13	+	1.03531e13i	0.381846	+	0.381846i
$487$	−5.70701e12	−	5.70701e12i	−0.208336	−	0.208336i	0.595224	−	0.803560i	$-0.297063\pi$
$487$	−5.70701e12	−	5.70701e12i	−0.208336	−	0.208336i	−0.803560	+	0.595224i	$0.797063\pi$
$488$	−5.65693e12	+	5.65693e12i	−0.204400	+	0.204400i
$489$	3.00886e12	−	3.00886e12i	0.107611	−	0.107611i
$490$	8.97812e12			0.317837
$491$			2.24267e13i			0.785882i	0.919564	+	0.392941i	$0.128542\pi$
$491$			2.24267e13i			0.785882i	−0.919564	+	0.392941i	$0.871458\pi$
$492$	9.21638e12	−	9.21638e12i	0.319694	−	0.319694i
$493$		−	1.60077e13i		−	0.549660i
$494$	4.72605e12	+	2.66208e12i	0.160644	+	0.0904869i
$495$	3.88923e13			1.30869
$496$	−4.98325e12	−	4.98325e12i	−0.165999	−	0.165999i
$497$	−1.29206e12			−0.0426088
$498$		−	6.82120e12i		−	0.222697i
$499$	7.10056e12	+	7.10056e12i	0.229504	+	0.229504i	0.812485	−	0.582982i	$-0.198114\pi$
$499$	7.10056e12	+	7.10056e12i	0.229504	+	0.229504i	−0.582982	+	0.812485i	$0.698114\pi$
$500$	−2.05521e13	−	2.05521e13i	−0.657666	−	0.657666i
$501$	−3.54524e13	+	3.54524e13i	−1.12320	+	1.12320i
$502$	3.21587e12	−	3.21587e12i	0.100874	−	0.100874i
$503$	4.86990e13			1.51245			0.756223	−	0.654314i	$-0.227043\pi$
$503$	4.86990e13			1.51245			0.756223	+	0.654314i	$0.227043\pi$
$504$			2.96482e12i			0.0911686i
$505$	2.80809e13	−	2.80809e13i	0.854977	−	0.854977i
$506$		−	2.51002e13i		−	0.756701i
$507$	−2.48590e13	−	4.10198e13i	−0.742068	−	1.22448i
$508$	3.70233e13			1.09435
$509$	1.35877e13	+	1.35877e13i	0.397703	+	0.397703i	0.877422	−	0.479719i	$-0.159262\pi$
$509$	1.35877e13	+	1.35877e13i	0.397703	+	0.397703i	−0.479719	+	0.877422i	$0.659262\pi$
$510$	1.48480e13			0.430345
$511$			2.30887e12i			0.0662665i
$512$	−2.39593e13	−	2.39593e13i	−0.680964	−	0.680964i
$513$	−8.77527e11	−	8.77527e11i	−0.0246987	−	0.0246987i
$514$	−1.21350e12	+	1.21350e12i	−0.0338240	+	0.0338240i
$515$	−1.08055e13	+	1.08055e13i	−0.298270	+	0.298270i
$516$	5.79281e13			1.58358
$517$		−	2.53342e13i		−	0.685889i
$518$	2.04446e12	−	2.04446e12i	0.0548187	−	0.0548187i
$519$		−	3.79741e12i		−	0.100844i
$520$	−1.11845e13	+	1.98561e13i	−0.294171	+	0.522250i
$521$	1.79049e13			0.466427			0.233214	−	0.972426i	$-0.425076\pi$
$521$	1.79049e13			0.466427			0.233214	+	0.972426i	$0.425076\pi$
$522$	6.42251e12	+	6.42251e12i	0.165711	+	0.165711i
$523$	−3.42297e13			−0.874772			−0.437386	−	0.899274i	$-0.644096\pi$
$523$	−3.42297e13			−0.874772			−0.437386	+	0.899274i	$0.644096\pi$
$524$		−	1.35129e13i		−	0.342052i
$525$	−1.35446e12	−	1.35446e12i	−0.0339601	−	0.0339601i
$526$	−9.83489e12	−	9.83489e12i	−0.244253	−	0.244253i
$527$	−1.06220e13	+	1.06220e13i	−0.261308	+	0.261308i
$528$	−3.58820e13	+	3.58820e13i	−0.874395	+	0.874395i
$529$	−3.64132e13			−0.878983
$530$			1.88214e13i			0.450063i
$531$	4.79997e13	−	4.79997e13i	1.13702	−	1.13702i
$532$			2.20222e12i			0.0516777i
$533$	1.52647e13	−	4.26440e12i	0.354856	−	0.0991339i
$534$	−7.81674e12			−0.180019
$535$	−4.23948e13	−	4.23948e13i	−0.967262	−	0.967262i
$536$	4.81689e13			1.08879
$537$		−	5.72603e12i		−	0.128228i
$538$	6.06579e12	+	6.06579e12i	0.134579	+	0.134579i
$539$	4.62475e13	+	4.62475e13i	1.01659	+	1.01659i
$540$	1.70151e12	−	1.70151e12i	0.0370567	−	0.0370567i
$541$	−4.39266e12	+	4.39266e12i	−0.0947853	+	0.0947853i	−0.752909	−	0.658124i	$-0.771350\pi$
$541$	−4.39266e12	+	4.39266e12i	−0.0947853	+	0.0947853i	0.658124	+	0.752909i	$0.271350\pi$
$542$	9.93210e12			0.212346
$543$			5.08127e13i			1.07640i
$544$	−2.90433e13	+	2.90433e13i	−0.609609	+	0.609609i
$545$			2.37450e13i			0.493844i
$546$	−1.59422e12	+	2.83027e12i	−0.0328539	+	0.0583263i
$547$	−4.46770e13			−0.912320			−0.456160	−	0.889898i	$-0.650776\pi$
$547$	−4.46770e13			−0.912320			−0.456160	+	0.889898i	$0.650776\pi$
$548$	−3.33029e13	−	3.33029e13i	−0.673875	−	0.673875i
$549$	2.15589e13			0.432280
$550$			7.53647e12i			0.149746i
$551$	1.03369e13	+	1.03369e13i	0.203531	+	0.203531i
$552$	−4.99406e13	−	4.99406e13i	−0.974448	−	0.974448i
$553$	5.77889e12	−	5.77889e12i	0.111743	−	0.111743i
$554$	1.94955e11	−	1.94955e11i	0.00373581	−	0.00373581i
$555$	−1.06721e14			−2.02668
$556$		−	3.70423e13i		−	0.697147i
$557$	2.32684e12	−	2.32684e12i	0.0434000	−	0.0434000i	−0.685074	−	0.728474i	$-0.740230\pi$
$557$	2.32684e12	−	2.32684e12i	0.0434000	−	0.0434000i	0.728474	+	0.685074i	$0.240230\pi$
$558$		−	8.52337e12i		−	0.157558i
$559$	6.13735e13	+	3.45703e13i	1.12440	+	0.633350i
$560$	−3.43897e12			−0.0624437
$561$	7.64839e13	+	7.64839e13i	1.37643	+	1.37643i
$562$	6.37571e12			0.113723
$563$			5.62491e12i			0.0994428i	0.998763	+	0.0497214i	$0.0158333\pi$
$563$			5.62491e12i			0.0994428i	−0.998763	+	0.0497214i	$0.984167\pi$
$564$	−2.32628e13	−	2.32628e13i	−0.407631	−	0.407631i
$565$	4.87123e13	+	4.87123e13i	0.846050	+	0.846050i
$566$	1.24666e13	−	1.24666e13i	0.214618	−	0.214618i
$567$	−4.85487e12	+	4.85487e12i	−0.0828442	+	0.0828442i
$568$	1.43041e13			0.241947
$569$		−	9.52194e13i		−	1.59648i	−0.602338	−	0.798241i	$-0.705764\pi$
$569$		−	9.52194e13i		−	1.59648i	0.602338	−	0.798241i	$-0.294236\pi$
$570$	−9.58799e12	+	9.58799e12i	−0.159350	+	0.159350i
$571$			8.45068e13i			1.39223i	0.717930	+	0.696115i	$0.245090\pi$
$571$			8.45068e13i			1.39223i	−0.717930	+	0.696115i	$0.754910\pi$
$572$	−7.37926e13	+	2.06150e13i	−1.20513	+	0.336669i
$573$	−9.24859e13			−1.49728
$574$	−7.58994e11	−	7.58994e11i	−0.0121809	−	0.0121809i
$575$	2.33718e13			0.371837
$576$			1.60775e13i			0.253575i
$577$	−2.50814e13	−	2.50814e13i	−0.392169	−	0.392169i	0.483291	−	0.875460i	$-0.339441\pi$
$577$	−2.50814e13	−	2.50814e13i	−0.392169	−	0.392169i	−0.875460	+	0.483291i	$0.839441\pi$
$578$	−2.29190e12	−	2.29190e12i	−0.0355268	−	0.0355268i
$579$	4.51398e13	−	4.51398e13i	0.693693	−	0.693693i
$580$	−2.00431e13	+	2.00431e13i	−0.305369	+	0.305369i
$581$	3.36756e12			0.0508669
$582$			6.08683e13i			0.911542i
$583$	−9.69518e13	+	9.69518e13i	−1.43950	+	1.43950i
$584$		−	2.55610e13i		−	0.376283i
$585$	5.91490e13	−	1.65241e13i	0.863312	−	0.241178i
$586$	−3.54705e13			−0.513310
$587$	1.12334e11	+	1.12334e11i	0.00161184	+	0.00161184i	0.707912	−	0.706300i	$-0.249637\pi$
$587$	1.12334e11	+	1.12334e11i	0.00161184	+	0.00161184i	−0.706300	+	0.707912i	$0.749637\pi$
$588$	8.49326e13			1.20834
$589$		−	1.37182e13i		−	0.193517i
$590$	−2.49875e13	−	2.49875e13i	−0.349512	−	0.349512i
$591$	9.02763e13	+	9.02763e13i	1.25209	+	1.25209i
$592$	5.04319e13	−	5.04319e13i	0.693580	−	0.693580i
$593$	6.54689e13	−	6.54689e13i	0.892815	−	0.892815i	−0.101972	−	0.994787i	$-0.532515\pi$
$593$	6.54689e13	−	6.54689e13i	0.892815	−	0.892815i	0.994787	+	0.101972i	$0.0325152\pi$
$594$	−2.92410e12			−0.0395421
$595$			7.33030e12i			0.0982962i
$596$	1.98162e13	−	1.98162e13i	0.263505	−	0.263505i
$597$		−	2.01810e14i		−	2.66117i
$598$	−1.06643e13	−	3.81734e13i	−0.139452	−	0.499177i
$599$	−2.27603e13			−0.295151			−0.147575	−	0.989051i	$-0.547147\pi$
$599$	−2.27603e13			−0.295151			−0.147575	+	0.989051i	$0.547147\pi$
$600$	1.49950e13	+	1.49950e13i	0.192836	+	0.192836i
$601$	3.17960e13			0.405509			0.202754	−	0.979230i	$-0.435011\pi$
$601$	3.17960e13			0.405509			0.202754	+	0.979230i	$0.435011\pi$
$602$		−	4.77054e12i		−	0.0603372i
$603$	−9.17875e13	−	9.17875e13i	−1.15132	−	1.15132i
$604$	−1.77331e13	−	1.77331e13i	−0.220597	−	0.220597i
$605$	5.53648e13	−	5.53648e13i	0.683056	−	0.683056i
$606$	−4.43123e13	+	4.43123e13i	−0.542202	+	0.542202i
$607$	−6.56660e12			−0.0796888			−0.0398444	−	0.999206i	$-0.512686\pi$
$607$	−6.56660e12			−0.0796888			−0.0398444	+	0.999206i	$0.512686\pi$
$608$		−	3.75091e13i		−	0.451459i
$609$	−6.19039e12	+	6.19039e12i	−0.0738978	+	0.0738978i
$610$		−	1.12230e13i		−	0.132880i
$611$	−1.07637e13	−	3.85292e13i	−0.126402	−	0.452464i
$612$	7.19445e13			0.837993
$613$	6.69565e13	+	6.69565e13i	0.773554	+	0.773554i	0.978726	−	0.205172i	$-0.0657754\pi$
$613$	6.69565e13	+	6.69565e13i	0.773554	+	0.773554i	−0.205172	+	0.978726i	$0.565775\pi$
$614$	4.69469e13			0.537979
$615$			3.96197e13i			0.450335i
$616$	7.95031e12	+	7.95031e12i	0.0896356	+	0.0896356i
$617$	6.40551e13	+	6.40551e13i	0.716354	+	0.716354i	0.967857	−	0.251502i	$-0.0809247\pi$
$617$	6.40551e13	+	6.40551e13i	0.716354	+	0.716354i	−0.251502	+	0.967857i	$0.580925\pi$
$618$	1.70513e13	−	1.70513e13i	0.189154	−	0.189154i
$619$	−1.83276e13	+	1.83276e13i	−0.201675	+	0.201675i	−0.800717	−	0.599042i	$-0.795548\pi$
$619$	−1.83276e13	+	1.83276e13i	−0.201675	+	0.201675i	0.599042	+	0.800717i	$0.295548\pi$
$620$	2.65994e13			0.290344
$621$			9.06810e12i			0.0981880i
$622$	−1.36856e13	+	1.36856e13i	−0.146998	+	0.146998i
$623$		−	3.85905e12i		−	0.0411187i
$624$	−3.93257e13	+	6.98160e13i	−0.415675	+	0.737959i
$625$	6.24802e13			0.655152
$626$	2.91234e13	+	2.91234e13i	0.302950	+	0.302950i
$627$	−9.87780e13			−1.01935
$628$			1.04763e14i			1.07253i
$629$	−1.07497e14	−	1.07497e14i	−1.09180	−	1.09180i
$630$	−2.94102e12	−	2.94102e12i	−0.0296343	−	0.0296343i
$631$	2.44020e13	−	2.44020e13i	0.243938	−	0.243938i	−0.574539	−	0.818477i	$-0.694819\pi$
$631$	2.44020e13	−	2.44020e13i	0.243938	−	0.243938i	0.818477	+	0.574539i	$0.194819\pi$
$632$	−6.39771e13	+	6.39771e13i	−0.634511	+	0.634511i
$633$	−2.41550e14			−2.37678
$634$		−	4.05122e13i		−	0.395493i
$635$	−7.95786e13	+	7.95786e13i	−0.770775	+	0.770775i
$636$			1.78050e14i			1.71103i
$637$	8.99842e13	+	5.06860e13i	0.857964	+	0.483271i
$638$	3.44446e13			0.325850
$639$	−2.72570e13	−	2.72570e13i	−0.255843	−	0.255843i
$640$	9.32313e13			0.868284
$641$		−	1.55378e13i		−	0.143582i	−0.997420	−	0.0717911i	$-0.977128\pi$
$641$		−	1.55378e13i		−	0.143582i	0.997420	−	0.0717911i	$-0.0228715\pi$
$642$	6.68999e13	+	6.68999e13i	0.613409	+	0.613409i
$643$	−1.26308e14	−	1.26308e14i	−1.14914	−	1.14914i	−0.986721	−	0.162423i	$-0.948069\pi$
$643$	−1.26308e14	−	1.26308e14i	−1.14914	−	1.14914i	−0.162423	−	0.986721i	$-0.551931\pi$
$644$	1.13786e13	−	1.13786e13i	0.102721	−	0.102721i
$645$	−1.24512e14	+	1.24512e14i	−1.11535	+	1.11535i
$646$	−1.93155e13			−0.171689
$647$			9.33071e13i			0.822987i	0.911413	+	0.411494i	$0.134993\pi$
$647$			9.33071e13i			0.822987i	−0.911413	+	0.411494i	$0.865007\pi$
$648$	5.37473e13	−	5.37473e13i	0.470416	−	0.470416i
$649$		−	2.57427e14i		−	2.23579i
$650$	3.20201e12	+	1.14618e13i	0.0275966	+	0.0987836i
$651$	8.21533e12			0.0702619
$652$	−7.58954e12	−	7.58954e12i	−0.0644136	−	0.0644136i
$653$	4.61508e13			0.388699			0.194350	−	0.980932i	$-0.437740\pi$
$653$	4.61508e13			0.388699			0.194350	+	0.980932i	$0.437740\pi$
$654$		−	3.74701e13i		−	0.313181i
$655$	2.90449e13	+	2.90449e13i	0.240915	+	0.240915i
$656$	−1.87226e13	−	1.87226e13i	−0.154116	−	0.154116i
$657$	−4.87074e13	+	4.87074e13i	−0.397895	+	0.397895i
$658$	−1.91576e12	+	1.91576e12i	−0.0155314	+	0.0155314i
$659$	−6.11804e13			−0.492249			−0.246125	−	0.969238i	$-0.579157\pi$
$659$	−6.11804e13			−0.492249			−0.246125	+	0.969238i	$0.579157\pi$
$660$		−	1.91529e14i		−	1.52938i
$661$	2.81299e13	−	2.81299e13i	0.222926	−	0.222926i	−0.586803	−	0.809729i	$-0.699614\pi$
$661$	2.81299e13	−	2.81299e13i	0.222926	−	0.222926i	0.809729	+	0.586803i	$0.199614\pi$
$662$			3.26994e13i			0.257188i
$663$	1.48815e14	+	8.38243e13i	1.16166	+	0.654338i
$664$	−3.72817e13			−0.288838
$665$	−4.73350e12	−	4.73350e12i	−0.0363977	−	0.0363977i
$666$	8.62589e13			0.658314
$667$		−	1.06818e14i		−	0.809126i
$668$	8.94249e13	+	8.94249e13i	0.672321	+	0.672321i
$669$	8.08346e13	+	8.08346e13i	0.603208	+	0.603208i
$670$	−4.77822e13	+	4.77822e13i	−0.353910	+	0.353910i
$671$	5.78113e13	−	5.78113e13i	0.425011	−	0.425011i
$672$	2.24629e13			0.163915
$673$			1.06939e14i			0.774567i	0.921961	+	0.387283i	$0.126587\pi$
$673$			1.06939e14i			0.774567i	−0.921961	+	0.387283i	$0.873413\pi$
$674$	−5.01898e13	+	5.01898e13i	−0.360841	+	0.360841i
$675$		−	2.72275e12i		−	0.0194307i
$676$	−1.03468e14	+	6.27042e13i	−0.732948	+	0.444185i
$677$	−6.88255e12			−0.0483956			−0.0241978	−	0.999707i	$-0.507703\pi$
$677$	−6.88255e12			−0.0483956			−0.0241978	+	0.999707i	$0.507703\pi$
$678$	−7.68690e13	−	7.68690e13i	−0.536540	−	0.536540i
$679$	−3.00501e13			−0.208208
$680$		−	8.11524e13i		−	0.558158i
$681$	−5.56156e13	−	5.56156e13i	−0.379718	−	0.379718i
$682$	−2.28558e13	−	2.28558e13i	−0.154909	−	0.154909i
$683$	−1.70018e14	+	1.70018e14i	−1.14391	+	1.14391i	−0.156180	+	0.987729i	$0.549918\pi$
$683$	−1.70018e14	+	1.70018e14i	−1.14391	+	1.14391i	−0.987729	+	0.156180i	$0.950082\pi$
$684$	−4.64577e13	+	4.64577e13i	−0.310297	+	0.310297i
$685$	1.43164e14			0.949248
$686$		−	1.40975e13i		−	0.0927941i
$687$	2.58906e14	−	2.58906e14i	1.69184	−	1.69184i
$688$		−	1.17678e14i		−	0.763401i
$689$	−1.06257e14	+	1.88640e14i	−0.684321	+	1.21489i
$690$	9.90794e13			0.633488
$691$	−3.41672e13	−	3.41672e13i	−0.216880	−	0.216880i	0.590302	−	0.807182i	$-0.299009\pi$
$691$	−3.41672e13	−	3.41672e13i	−0.216880	−	0.216880i	−0.807182	+	0.590302i	$0.799009\pi$
$692$	−9.57857e12			−0.0603629
$693$		−	3.02991e13i		−	0.189568i
$694$	−1.02848e13	−	1.02848e13i	−0.0638851	−	0.0638851i
$695$	7.96194e13	+	7.96194e13i	0.491015	+	0.491015i
$696$	6.85327e13	−	6.85327e13i	0.419616	−	0.419616i
$697$	−3.99079e13	+	3.99079e13i	−0.242602	+	0.242602i
$698$	4.87527e13			0.294253
$699$		−	1.64355e14i		−	0.984914i
$700$	−3.41648e12	+	3.41648e12i	−0.0203277	+	0.0203277i
$701$		−	6.91414e13i		−	0.408459i	−0.978923	−	0.204229i	$-0.934531\pi$
$701$		−	6.91414e13i		−	0.408459i	0.978923	−	0.204229i	$-0.0654688\pi$
$702$	−4.44709e12	+	1.24236e12i	−0.0260850	+	0.00728720i
$703$	1.38832e14			0.808559
$704$	4.31126e13	+	4.31126e13i	0.249311	+	0.249311i
$705$	1.00003e14			0.574206
$706$		−	4.33298e13i		−	0.247037i
$707$	−2.18765e13	−	2.18765e13i	−0.123846	−	0.123846i
$708$	−2.36380e14	−	2.36380e14i	−1.32875	−	1.32875i
$709$	−1.46498e14	+	1.46498e14i	−0.817710	+	0.817710i	−0.985776	−	0.168066i	$-0.946248\pi$
$709$	−1.46498e14	+	1.46498e14i	−0.817710	+	0.817710i	0.168066	+	0.985776i	$0.446248\pi$
$710$	−1.41893e13	+	1.41893e13i	−0.0786446	+	0.0786446i
$711$	2.43821e14			1.34191
$712$			4.27228e13i			0.233486i
$713$	−7.08797e13	+	7.08797e13i	−0.384657	+	0.384657i
$714$		−	1.15674e13i		−	0.0623366i
$715$	1.14301e14	−	2.02921e14i	0.611673	−	1.08592i
$716$	−1.44433e13			−0.0767542
$717$	2.46614e14	+	2.46614e14i	1.30144	+	1.30144i
$718$	−3.76714e13			−0.197419
$719$			5.11951e13i			0.266430i	0.991087	+	0.133215i	$0.0425302\pi$
$719$			5.11951e13i			0.266430i	−0.991087	+	0.133215i	$0.957470\pi$
$720$	−7.25479e13	−	7.25479e13i	−0.374941	−	0.374941i
$721$	8.41806e12	+	8.41806e12i	0.0432052	+	0.0432052i
$722$	−3.99816e13	+	3.99816e13i	−0.203786	+	0.203786i
$723$	2.67904e14	−	2.67904e14i	1.35609	−	1.35609i
$724$	1.28170e14			0.644307
$725$			3.20728e13i			0.160120i
$726$	−8.73667e13	+	8.73667e13i	−0.433174	+	0.433174i
$727$			8.61028e13i			0.423980i	0.977272	+	0.211990i	$0.0679944\pi$
$727$			8.61028e13i			0.423980i	−0.977272	+	0.211990i	$0.932006\pi$
$728$	1.54690e13	+	8.71332e12i	0.0756493	+	0.0426115i
$729$	−2.25951e14			−1.09743
$730$	2.53558e13	+	2.53558e13i	0.122310	+	0.122310i
$731$	−2.50835e14			−1.20171
$732$		−	1.06169e14i		−	0.505177i
$733$	1.14861e14	+	1.14861e14i	0.542816	+	0.542816i	0.924353	−	0.381538i	$-0.124605\pi$
$733$	1.14861e14	+	1.14861e14i	0.542816	+	0.542816i	−0.381538	+	0.924353i	$0.624605\pi$
$734$	−4.39717e13	−	4.39717e13i	−0.206392	−	0.206392i
$735$	−1.82555e14	+	1.82555e14i	−0.851056	+	0.851056i
$736$	−1.93804e14	+	1.93804e14i	−0.897374	+	0.897374i
$737$	−4.92265e14			−2.26392
$738$		−	3.20232e13i		−	0.146279i
$739$	1.78697e14	−	1.78697e14i	0.810764	−	0.810764i	−0.173985	−	0.984748i	$-0.555664\pi$
$739$	1.78697e14	−	1.78697e14i	0.810764	−	0.810764i	0.984748	+	0.173985i	$0.0556643\pi$
$740$			2.69193e14i			1.21312i
$741$	−1.50226e14	+	4.19676e13i	−0.672440	+	0.187855i
$742$	1.46629e13			0.0651929
$743$	−1.11856e14	−	1.11856e14i	−0.493986	−	0.493986i	0.415574	−	0.909559i	$-0.363581\pi$
$743$	−1.11856e14	−	1.11856e14i	−0.493986	−	0.493986i	−0.909559	+	0.415574i	$0.863581\pi$
$744$	−9.09504e13			−0.398970
$745$			8.51865e13i			0.371184i
$746$	−6.01863e13	−	6.01863e13i	−0.260497	−	0.260497i
$747$	7.10415e13	+	7.10415e13i	0.305428	+	0.305428i
$748$	1.92923e14	−	1.92923e14i	0.823902	−	0.823902i
$749$	−3.30278e13	+	3.30278e13i	−0.140111	+	0.140111i
$750$	−1.39418e14			−0.587506
$751$			1.27679e14i			0.534466i	0.963632	+	0.267233i	$0.0861093\pi$
$751$			1.27679e14i			0.534466i	−0.963632	+	0.267233i	$0.913891\pi$
$752$	−4.72572e13	+	4.72572e13i	−0.196507	+	0.196507i
$753$			1.30779e14i			0.540210i
$754$	5.23847e13	−	1.46344e13i	0.214955	−	0.0600507i
$755$	7.62316e13			0.310742
$756$	−1.32557e12	−	1.32557e12i	−0.00536777	−	0.00536777i
$757$	−1.90185e14			−0.765062			−0.382531	−	0.923943i	$-0.624947\pi$
$757$	−1.90185e14			−0.765062			−0.382531	+	0.923943i	$0.624947\pi$
$758$			1.20001e14i			0.479554i
$759$	5.10371e14	+	5.10371e14i	2.02618	+	2.02618i
$760$	5.24037e13	+	5.24037e13i	0.206678	+	0.206678i
$761$	3.35142e14	−	3.35142e14i	1.31312	−	1.31312i	0.394022	−	0.919101i	$-0.371083\pi$
$761$	3.35142e14	−	3.35142e14i	1.31312	−	1.31312i	0.919101	−	0.394022i	$-0.128917\pi$
$762$	1.25577e14	−	1.25577e14i	0.488803	−	0.488803i
$763$	1.84986e13			0.0715347
$764$			2.33286e14i			0.896235i
$765$	−1.54639e14	+	1.54639e14i	−0.590216	+	0.590216i
$766$		−	2.02869e13i		−	0.0769256i
$767$	−1.09373e14	−	3.91506e14i	−0.412033	−	1.47490i
$768$	−5.47382e13			−0.204873
$769$	−2.17200e14	−	2.17200e14i	−0.807660	−	0.807660i	0.176619	−	0.984279i	$-0.443484\pi$
$769$	−2.17200e14	−	2.17200e14i	−0.807660	−	0.807660i	−0.984279	+	0.176619i	$0.943484\pi$
$770$	−1.57730e13			−0.0582720
$771$		−	4.93492e13i		−	0.181137i
$772$	−1.13861e14	−	1.13861e14i	−0.415228	−	0.415228i
$773$	2.24769e14	+	2.24769e14i	0.814402	+	0.814402i	0.985290	−	0.170889i	$-0.0546639\pi$
$773$	2.24769e14	+	2.24769e14i	0.814402	+	0.814402i	−0.170889	+	0.985290i	$0.554664\pi$
$774$	1.00638e14	−	1.00638e14i	0.362292	−	0.362292i
$775$	2.12820e13	−	2.12820e13i	0.0761210	−	0.0761210i
$776$	3.32679e14			1.18227
$777$			8.31414e13i			0.293570i
$778$	5.14221e13	−	5.14221e13i	0.180406	−	0.180406i
$779$		−	5.15405e13i		−	0.179664i
$780$	−8.13748e13	−	2.91286e14i	−0.281849	−	1.00890i
$781$	−1.46182e14			−0.503082
$782$	9.98002e13	+	9.98002e13i	0.341270	+	0.341270i
$783$	−1.24440e13			−0.0422816
$784$		−	1.72536e14i		−	0.582505i
$785$	−2.25179e14	−	2.25179e14i	−0.755404	−	0.755404i
$786$	−4.58334e13	−	4.58334e13i	−0.152781	−	0.152781i
$787$	1.40161e14	−	1.40161e14i	0.464253	−	0.464253i	−0.435794	−	0.900046i	$-0.643532\pi$
$787$	1.40161e14	−	1.40161e14i	0.464253	−	0.464253i	0.900046	+	0.435794i	$0.143532\pi$
$788$	2.27713e14	−	2.27713e14i	0.749473	−	0.749473i
$789$	3.99953e14			1.30805
$790$		−	1.26927e14i		−	0.412495i
$791$	3.79495e13	−	3.79495e13i	0.122553	−	0.122553i
$792$			3.35436e14i			1.07643i
$793$	6.33597e13	−	1.12484e14i	0.202044	−	0.358695i
$794$	7.27149e13			0.230420
$795$	−3.82704e14	−	3.82704e14i	−1.20511	−	1.20511i
$796$	−5.09046e14			−1.59291
$797$			1.72310e14i			0.535821i	0.963444	+	0.267910i	$0.0863331\pi$
$797$			1.72310e14i			0.535821i	−0.963444	+	0.267910i	$0.913667\pi$
$798$	7.46955e12	+	7.46955e12i	0.0230824	+	0.0230824i
$799$	1.00731e14	+	1.00731e14i	0.309334	+	0.309334i
$800$	5.81907e13	−	5.81907e13i	0.177584	−	0.177584i
$801$	8.14098e13	−	8.14098e13i	0.246896	−	0.246896i
$802$	2.22240e13			0.0669807
$803$			2.61223e14i			0.782408i
$804$	−4.52018e14	+	4.52018e14i	−1.34547	+	1.34547i
$805$			4.89146e13i			0.144697i
$806$	−4.44708e13	−	2.50494e13i	−0.130738	−	0.0736414i
$807$	−2.46676e14			−0.720708
$808$	2.42191e14	+	2.42191e14i	0.703237	+	0.703237i
$809$	5.71629e14			1.64957			0.824787	−	0.565443i	$-0.191295\pi$
$809$	5.71629e14			1.64957			0.824787	+	0.565443i	$0.191295\pi$
$810$			1.06632e14i			0.305817i
$811$	1.55856e14	+	1.55856e14i	0.444241	+	0.444241i	0.893434	−	0.449194i	$-0.148289\pi$
$811$	1.55856e14	+	1.55856e14i	0.444241	+	0.444241i	−0.449194	+	0.893434i	$0.648289\pi$
$812$	1.56146e13	+	1.56146e13i	0.0442335	+	0.0442335i
$813$	−2.01953e14	+	2.01953e14i	−0.568589	+	0.568589i
$814$	2.31308e14	−	2.31308e14i	0.647244	−	0.647244i
$815$	3.26262e13			0.0907357
$816$		−	2.85339e14i		−	0.788698i
$817$	1.61975e14	−	1.61975e14i	0.444977	−	0.444977i
$818$		−	5.88777e13i		−	0.160762i
$819$	−1.28731e13	−	4.60802e13i	−0.0349354	−	0.125053i
$820$	9.99365e13			0.269560
$821$	−2.27737e14	−	2.27737e14i	−0.610545	−	0.610545i	0.332543	−	0.943088i	$-0.392093\pi$
$821$	−2.27737e14	−	2.27737e14i	−0.610545	−	0.610545i	−0.943088	+	0.332543i	$0.892093\pi$
$822$	−2.25915e14			−0.601985
$823$			1.91631e14i			0.507535i	0.967265	+	0.253767i	$0.0816698\pi$
$823$			1.91631e14i			0.507535i	−0.967265	+	0.253767i	$0.918330\pi$
$824$	−9.31948e13	−	9.31948e13i	−0.245333	−	0.245333i
$825$	−1.53242e14	−	1.53242e14i	−0.400966	−	0.400966i
$826$	−1.94666e13	+	1.94666e13i	−0.0506278	+	0.0506278i
$827$	4.86930e14	−	4.86930e14i	1.25875	−	1.25875i	0.307057	−	0.951691i	$-0.400656\pi$
$827$	4.86930e14	−	4.86930e14i	1.25875	−	1.25875i	0.951691	−	0.307057i	$-0.0993444\pi$
$828$	4.80080e14			1.23357
$829$			3.00719e14i			0.768048i	0.923323	+	0.384024i	$0.125462\pi$
$829$			3.00719e14i			0.768048i	−0.923323	+	0.384024i	$0.874538\pi$
$830$	3.69824e13	−	3.69824e13i	0.0938868	−	0.0938868i
$831$			7.92818e12i			0.0200064i
$832$	8.38846e13	+	4.72502e13i	0.210410	+	0.118519i
$833$	−3.67767e14			−0.916954
$834$	−1.25641e14	−	1.25641e14i	−0.311387	−	0.311387i
$835$	−3.84423e14			−0.947059
$836$			2.49157e14i			0.610158i
$837$	8.25728e12	+	8.25728e12i	0.0201006	+	0.0201006i
$838$	8.89559e13	+	8.89559e13i	0.215256	+	0.215256i
$839$	−3.09051e14	+	3.09051e14i	−0.743396	+	0.743396i	−0.973230	−	0.229834i	$-0.926182\pi$
$839$	−3.09051e14	+	3.09051e14i	−0.743396	+	0.743396i	0.229834	+	0.973230i	$0.426182\pi$
$840$	−3.13827e13	+	3.13827e13i	−0.0750403	+	0.0750403i
$841$	−2.74122e14			−0.651575
$842$			2.32407e14i			0.549147i
$843$	−1.29640e14	+	1.29640e14i	−0.304509	+	0.304509i
$844$			6.09284e14i			1.42268i
$845$	8.76186e13	−	3.57174e14i	0.203382	−	0.829079i
$846$	−8.08290e13			−0.186516
$847$	−4.31321e13	−	4.31321e13i	−0.0989426	−	0.0989426i
$848$	3.61699e14			0.824837
$849$			5.06976e14i			1.14934i
$850$	−2.99656e13	−	2.99656e13i	−0.0675348	−	0.0675348i
$851$	−7.17322e14	−	7.17322e14i	−1.60719	−	1.60719i
$852$	−1.34230e14	+	1.34230e14i	−0.298987	+	0.298987i
$853$	−6.35116e14	+	6.35116e14i	−1.40640	+	1.40640i	−0.628953	+	0.777443i	$0.716516\pi$
$853$	−6.35116e14	+	6.35116e14i	−1.40640	+	1.40640i	−0.777443	+	0.628953i	$0.783484\pi$
$854$	−8.74334e12			−0.0192481
$855$		−	1.99714e14i		−	0.437097i
$856$	3.65645e14	−	3.65645e14i	0.795593	−	0.795593i
$857$			1.37507e14i			0.297455i	0.988878	+	0.148728i	$0.0475178\pi$
$857$			1.37507e14i			0.297455i	−0.988878	+	0.148728i	$0.952482\pi$
$858$	−1.80369e14	+	3.20214e14i	−0.387905	+	0.688658i
$859$	1.18596e14			0.253574			0.126787	−	0.991930i	$-0.459533\pi$
$859$	1.18596e14			0.253574			0.126787	+	0.991930i	$0.459533\pi$
$860$	3.14068e14	+	3.14068e14i	0.667623	+	0.667623i
$861$	3.08658e13			0.0652322
$862$			1.80647e14i			0.379572i
$863$	3.74638e14	+	3.74638e14i	0.782633	+	0.782633i	0.980274	−	0.197642i	$-0.0633283\pi$
$863$	3.74638e14	+	3.74638e14i	0.782633	+	0.782633i	−0.197642	+	0.980274i	$0.563328\pi$
$864$	2.25776e13	+	2.25776e13i	0.0468931	+	0.0468931i
$865$	2.05883e13	−	2.05883e13i	0.0425149	−	0.0425149i
$866$	−9.67996e13	+	9.67996e13i	−0.198740	+	0.198740i
$867$	9.32041e13			0.190257
$868$		−	2.07223e13i		−	0.0420571i
$869$	6.53818e14	−	6.53818e14i	1.31934	−	1.31934i
$870$			1.35965e14i			0.272792i
$871$	−7.48658e14	+	2.09148e14i	−1.49346	+	0.417218i
$872$	−2.04795e14			−0.406197
$873$	−6.33931e14	−	6.33931e14i	−1.25018	−	1.25018i
$874$	−1.28891e14			−0.252734
$875$		−	6.88293e13i		−	0.134194i
$876$	2.39865e14	+	2.39865e14i	0.464993	+	0.464993i
$877$	4.99646e13	+	4.99646e13i	0.0963084	+	0.0963084i	0.753619	−	0.657311i	$-0.228306\pi$
$877$	4.99646e13	+	4.99646e13i	0.0963084	+	0.0963084i	−0.657311	+	0.753619i	$0.728306\pi$
$878$	1.68060e14	−	1.68060e14i	0.322101	−	0.322101i
$879$	7.21236e14	−	7.21236e14i	1.37446	−	1.37446i
$880$	−3.89082e14			−0.737272
$881$		−	3.94168e14i		−	0.742681i	−0.928497	−	0.371340i	$-0.878898\pi$
$881$		−	3.94168e14i		−	0.742681i	0.928497	−	0.371340i	$-0.121102\pi$
$882$	1.47553e14	−	1.47553e14i	0.276443	−	0.276443i
$883$		−	5.39165e13i		−	0.100443i	−0.998738	−	0.0502214i	$-0.984007\pi$
$883$		−	5.39165e13i		−	0.100443i	0.998738	−	0.0502214i	$-0.0159927\pi$
$884$	2.11438e14	−	3.75372e14i	0.391672	−	0.695345i
$885$	1.01616e15			1.87174
$886$	1.77425e14	+	1.77425e14i	0.324973	+	0.324973i
$887$	8.99859e13			0.163892			0.0819458	−	0.996637i	$-0.473887\pi$
$887$	8.99859e13			0.163892			0.0819458	+	0.996637i	$0.473887\pi$
$888$		−	9.20443e14i		−	1.66699i
$889$	6.19960e13	+	6.19960e13i	0.111649	+	0.111649i
$890$	−4.23799e13	−	4.23799e13i	−0.0758944	−	0.0758944i
$891$	−5.49275e14	+	5.49275e14i	−0.978140	+	0.978140i
$892$	2.03897e14	−	2.03897e14i	0.361066	−	0.361066i
$893$	−1.30092e14			−0.229084
$894$		−	1.34426e14i		−	0.235394i
$895$	3.10447e13	−	3.10447e13i	0.0540596	−	0.0540596i
$896$		−	7.26321e13i		−	0.125773i
$897$	9.93035e14	+	5.59353e14i	1.71002	+	0.963217i
$898$	1.46032e14			0.250073
$899$	−9.72671e13	−	9.72671e13i	−0.165641	−	0.165641i
$900$	−1.44147e14			−0.244114
$901$		−	7.70975e14i		−	1.29842i
$902$	−8.58718e13	−	8.58718e13i	−0.143819	−	0.143819i
$903$	9.70012e13	+	9.70012e13i	0.161562	+	0.161562i
$904$	−4.20132e14	+	4.20132e14i	−0.695894	+	0.695894i
$905$	−2.75490e14	+	2.75490e14i	−0.453799	+	0.453799i
$906$	−1.20295e14			−0.197064
$907$			8.48384e14i			1.38215i	0.722782	+	0.691076i	$0.242863\pi$
$907$			8.48384e14i			1.38215i	−0.722782	+	0.691076i	$0.757137\pi$
$908$	−1.40285e14	+	1.40285e14i	−0.227290	+	0.227290i
$909$		−	9.23006e14i		−	1.48725i
$910$	−2.39882e13	+	6.70144e12i	−0.0384406	+	0.0107389i
$911$	6.46289e14			1.02999			0.514997	−	0.857192i	$-0.327793\pi$
$911$	6.46289e14			1.02999			0.514997	+	0.857192i	$0.327793\pi$
$912$	1.84256e14	+	1.84256e14i	0.292044	+	0.292044i
$913$	3.81003e14			0.600584
$914$			3.65987e14i			0.573766i
$915$	2.28202e14	+	2.28202e14i	0.355807	+	0.355807i
$916$	−6.53064e14	−	6.53064e14i	−1.01269	−	1.01269i
$917$	2.26275e13	−	2.26275e13i	0.0348972	−	0.0348972i
$918$	1.16264e13	−	1.16264e13i	0.0178334	−	0.0178334i
$919$	5.50622e14			0.839994			0.419997	−	0.907525i	$-0.362031\pi$
$919$	5.50622e14			0.839994			0.419997	+	0.907525i	$0.362031\pi$
$920$		−	5.41524e14i		−	0.821635i
$921$	−9.54589e14	+	9.54589e14i	−1.44052	+	1.44052i
$922$		−	1.07020e14i		−	0.160623i
$923$	−2.22320e14	+	6.21081e13i	−0.331871	+	0.0927128i
$924$	−1.49212e14			−0.221535
$925$	2.15380e14	+	2.15380e14i	0.318051	+	0.318051i
$926$	−3.36833e14			−0.494720
$927$			3.55172e14i			0.518848i
$928$	−2.65954e14	−	2.65954e14i	−0.386426	−	0.386426i
$929$	2.19831e14	+	2.19831e14i	0.317695	+	0.317695i	0.847881	−	0.530186i	$-0.177878\pi$
$929$	2.19831e14	+	2.19831e14i	0.317695	+	0.317695i	−0.530186	+	0.847881i	$0.677878\pi$
$930$	9.02203e13	−	9.02203e13i	0.129685	−	0.129685i
$931$	2.37483e14	−	2.37483e14i	0.339535	−	0.339535i
$932$	−4.14570e14			−0.589546
$933$		−	5.56548e14i		−	0.787217i
$934$	−2.02328e14	+	2.02328e14i	−0.284657	+	0.284657i
$935$			8.29343e14i			1.16058i
$936$	1.42516e14	+	5.10146e14i	0.198374	+	0.710093i
$937$	1.06311e15			1.47191			0.735956	−	0.677029i	$-0.236733\pi$
$937$	1.06311e15			1.47191			0.735956	+	0.677029i	$0.236733\pi$
$938$	3.72249e13	+	3.72249e13i	0.0512648	+	0.0512648i
$939$	−1.18435e15			−1.62238
$940$		−	2.52247e14i		−	0.343706i
$941$	−6.00417e14	−	6.00417e14i	−0.813775	−	0.813775i	0.171422	−	0.985198i	$-0.445164\pi$
$941$	−6.00417e14	−	6.00417e14i	−0.813775	−	0.813775i	−0.985198	+	0.171422i	$0.945164\pi$
$942$	3.55337e14	+	3.55337e14i	0.479055	+	0.479055i
$943$	−2.66302e14	+	2.66302e14i	−0.357122	+	0.357122i
$944$	−4.80194e14	+	4.80194e14i	−0.640555	+	0.640555i
$945$	5.69841e12			0.00756126
$946$		−	5.39734e14i		−	0.712400i
$947$	4.39254e13	−	4.39254e13i	0.0576721	−	0.0576721i	−0.677682	−	0.735355i	$-0.737016\pi$
$947$	4.39254e13	−	4.39254e13i	0.0576721	−	0.0576721i	0.735355	+	0.677682i	$0.237016\pi$
$948$		−	1.20072e15i		−	1.56820i
$949$	1.10985e14	+	3.97278e14i	0.144190	+	0.516135i
$950$	3.87002e13			0.0500144
$951$	8.23750e14	+	8.23750e14i	1.05899	+	1.05899i
$952$	−6.32220e13			−0.0808507
$953$			3.54465e14i			0.450929i	0.974251	+	0.225465i	$0.0723900\pi$
$953$			3.54465e14i			0.450929i	−0.974251	+	0.225465i	$0.927610\pi$
$954$	3.09326e14	+	3.09326e14i	0.391448	+	0.391448i
$955$	−5.01429e14	−	5.01429e14i	−0.631237	−	0.631237i
$956$	6.22059e14	−	6.22059e14i	0.779009	−	0.779009i
$957$	−7.00375e14	+	7.00375e14i	−0.872511	+	0.872511i
$958$	1.97467e14			0.244719
$959$		−	1.11532e14i		−	0.137501i
$960$	−1.70181e14	+	1.70181e14i	−0.208716	+	0.208716i
$961$		−	6.90544e14i		−	0.842509i
$962$	2.53507e14	−	4.50057e14i	0.307691	−	0.546251i
$963$	−1.39350e15			−1.68258
$964$	−6.75759e14	−	6.75759e14i	−0.811721	−	0.811721i
$965$	4.89468e14			0.584908
$966$		−	7.71881e13i		−	0.0917624i
$967$	1.43043e13	+	1.43043e13i	0.0169174	+	0.0169174i	0.715515	−	0.698597i	$-0.246192\pi$
$967$	1.43043e13	+	1.43043e13i	0.0169174	+	0.0169174i	−0.698597	+	0.715515i	$0.746192\pi$
$968$	4.77508e14	+	4.77508e14i	0.561828	+	0.561828i
$969$	3.92749e14	−	3.92749e14i	0.459723	−	0.459723i
$970$	−3.30009e14	+	3.30009e14i	−0.384297	+	0.384297i
$971$	−2.33615e14			−0.270648			−0.135324	−	0.990801i	$-0.543208\pi$
$971$	−2.33615e14			−0.270648			−0.135324	+	0.990801i	$0.543208\pi$
$972$			1.06200e15i			1.22403i
$973$	6.20277e13	−	6.20277e13i	0.0711249	−	0.0711249i
$974$			9.76528e13i			0.111401i
$975$	−2.98164e14	−	1.67949e14i	−0.338402	−	0.190614i
$976$	−2.15677e14			−0.243532
$977$	1.03005e15	+	1.03005e15i	1.15714	+	1.15714i	0.985089	+	0.172047i	$0.0550382\pi$
$977$	1.03005e15	+	1.03005e15i	1.15714	+	1.15714i	0.172047	+	0.985089i	$0.444962\pi$
$978$	−5.14848e13			−0.0575419
$979$		−	4.36609e14i		−	0.485488i
$980$	4.60477e14	+	4.60477e14i	0.509422	+	0.509422i
$981$	3.90243e14	+	3.90243e14i	0.429527	+	0.429527i
$982$	1.91872e14	−	1.91872e14i	0.210113	−	0.210113i
$983$	−3.27518e14	+	3.27518e14i	−0.356835	+	0.356835i	−0.862645	−	0.505810i	$-0.831194\pi$
$983$	−3.27518e14	+	3.27518e14i	−0.356835	+	0.356835i	0.505810	+	0.862645i	$0.331194\pi$
$984$	−3.41710e14			−0.370410
$985$			9.78899e14i			1.05574i
$986$	−1.36954e14	+	1.36954e14i	−0.146957	+	0.146957i
$987$		−	7.79077e13i		−	0.0831754i
$988$	1.05859e14	+	3.78929e14i	0.112446	+	0.402507i
$989$	−1.67380e15			−1.76898
$990$	−3.32744e14	−	3.32744e14i	−0.349892	−	0.349892i
$991$	1.58316e15			1.65637			0.828185	−	0.560455i	$-0.189374\pi$
$991$	1.58316e15			1.65637			0.828185	+	0.560455i	$0.189374\pi$
$992$			3.52950e14i			0.367413i
$993$	−6.64890e14	−	6.64890e14i	−0.688658	−	0.688658i
$994$	1.10542e13	+	1.10542e13i	0.0113919	+	0.0113919i
$995$	1.09415e15	−	1.09415e15i	1.12192	−	1.12192i
$996$	3.49852e14	−	3.49852e14i	0.356934	−	0.356934i
$997$	−1.62529e15			−1.64989			−0.824946	−	0.565211i	$-0.808795\pi$
$997$	−1.62529e15			−1.64989			−0.824946	+	0.565211i	$0.808795\pi$
$998$		−	1.21498e14i		−	0.122720i
$999$	−8.35660e13	+	8.35660e13i	−0.0839851	+	0.0839851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.11.d.a.8.5	yes	20
13.5	odd	4	inner	13.11.d.a.5.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.11.d.a.5.5	✓	20	13.5	odd	4	inner
13.11.d.a.8.5	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.55552 - 8.55552i) q^{2} +347.925 q^{3} -877.606i q^{4} +(1886.34 + 1886.34i) q^{5} +(-2976.68 - 2976.68i) q^{6} +(1469.56 - 1469.56i) q^{7} +(-16269.2 + 16269.2i) q^{8} +62003.1 q^{9} -32277.3i q^{10} +(166265. - 166265. i) q^{11} -305342. i q^{12} +(182221. - 323502. i) q^{13} -25145.7 q^{14} +(656306. + 656306. i) q^{15} -620285. q^{16} +1.32216e6i q^{17} +(-530469. - 530469. i) q^{18} +(-853777. - 853777. i) q^{19} +(1.65546e6 - 1.65546e6i) q^{20} +(511297. - 511297. i) q^{21} -2.84496e6 q^{22} +8.82268e6i q^{23} +(-5.66048e6 + 5.66048e6i) q^{24} -2.64906e6i q^{25} +(-4.32673e6 + 1.20873e6i) q^{26} +1.02782e6 q^{27} +(-1.28969e6 - 1.28969e6i) q^{28} -1.21072e7 q^{29} -1.12301e7i q^{30} +(8.03380e6 + 8.03380e6i) q^{31} +(2.19666e7 + 2.19666e7i) q^{32} +(5.78477e7 - 5.78477e7i) q^{33} +(1.13118e7 - 1.13118e7i) q^{34} +5.54418e6 q^{35} -5.44143e7i q^{36} +(-8.13044e7 + 8.13044e7i) q^{37} +1.46090e7i q^{38} +(6.33995e7 - 1.12555e8i) q^{39} -6.13786e7 q^{40} +(3.01838e7 + 3.01838e7i) q^{41} -8.74883e6 q^{42} +1.89716e8i q^{43} +(-1.45915e8 - 1.45915e8i) q^{44} +(1.16959e8 + 1.16959e8i) q^{45} +(7.54826e7 - 7.54826e7i) q^{46} +(7.61863e7 - 7.61863e7i) q^{47} -2.15813e8 q^{48} +2.78156e8i q^{49} +(-2.26641e7 + 2.26641e7i) q^{50} +4.60013e8i q^{51} +(-2.83908e8 - 1.59919e8i) q^{52} -5.83118e8 q^{53} +(-8.79351e6 - 8.79351e6i) q^{54} +6.27263e8 q^{55} +4.78172e7i q^{56} +(-2.97051e8 - 2.97051e8i) q^{57} +(1.03584e8 + 1.03584e8i) q^{58} +(7.74150e8 - 7.74150e8i) q^{59} +(5.75978e8 - 5.75978e8i) q^{60} +3.47707e8 q^{61} -1.37467e8i q^{62} +(9.11173e7 - 9.11173e7i) q^{63} +2.59301e8i q^{64} +(9.53968e8 - 2.66504e8i) q^{65} -9.89834e8 q^{66} +(-1.48037e9 - 1.48037e9i) q^{67} +1.16034e9 q^{68} +3.06964e9i q^{69} +(-4.74334e7 - 4.74334e7i) q^{70} +(-4.39607e8 - 4.39607e8i) q^{71} +(-1.00874e9 + 1.00874e9i) q^{72} +(-7.85564e8 + 7.85564e8i) q^{73} +1.39120e9 q^{74} -9.21675e8i q^{75} +(-7.49280e8 + 7.49280e8i) q^{76} -4.88671e8i q^{77} +(-1.50538e9 + 4.20549e8i) q^{78} +3.93240e9 q^{79} +(-1.17007e9 - 1.17007e9i) q^{80} -3.30362e9 q^{81} -5.16477e8i q^{82} +(1.14577e9 + 1.14577e9i) q^{83} +(-4.48718e8 - 4.48718e8i) q^{84} +(-2.49405e9 + 2.49405e9i) q^{85} +(1.62312e9 - 1.62312e9i) q^{86} -4.21241e9 q^{87} +5.40999e9i q^{88} +(1.31299e9 - 1.31299e9i) q^{89} -2.00129e9i q^{90} +(-2.07621e8 - 7.43192e8i) q^{91} +7.74284e9 q^{92} +(2.79517e9 + 2.79517e9i) q^{93} -1.30363e9 q^{94} -3.22103e9i q^{95} +(7.64272e9 + 7.64272e9i) q^{96} +(-1.02242e10 - 1.02242e10i) q^{97} +(2.37977e9 - 2.37977e9i) q^{98} +(1.03089e10 - 1.03089e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) \) 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

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