LMFDB - Embedded newform 5.19.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,19,Mod(2,5)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 19, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, 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:	$10.2693068855$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1365649 x^{14} + 735328563216 x^{12} + \cdots + 22\!\cdots\!00 $ x^16 + 1365649x^14 + 735328563216x^12 + 196541937723225664x^10 + 26804517896227604816896x^8 + 1698608176414048875695308800x^6 + 38033703783600508125786931200000x^4 + 174469353400289826571825446912000000*x^2 + 223860255706571447791285331558400000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{12}\cdot 5^{25} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-601.773i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.19.c.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-569.773 + 569.773i) q^{2} +(-12889.4 - 12889.4i) q^{3} -387139. i q^{4} +(1.81741e6 + 715334. i) q^{5} +1.46881e7 q^{6} +(8.52951e6 - 8.52951e6i) q^{7} +(7.12189e7 + 7.12189e7i) q^{8} -5.51474e7i q^{9} +O(q^{10})$	\(q+(-569.773 + 569.773i) q^{2} +(-12889.4 - 12889.4i) q^{3} -387139. i q^{4} +(1.81741e6 + 715334. i) q^{5} +1.46881e7 q^{6} +(8.52951e6 - 8.52951e6i) q^{7} +(7.12189e7 + 7.12189e7i) q^{8} -5.51474e7i q^{9} +(-1.44309e9 + 6.27936e8i) q^{10} -2.42567e9 q^{11} +(-4.98999e9 + 4.98999e9i) q^{12} +(1.15852e10 + 1.15852e10i) q^{13} +9.71977e9i q^{14} +(-1.42051e10 - 3.26456e10i) q^{15} +2.03289e10 q^{16} +(-1.49387e11 + 1.49387e11i) q^{17} +(3.14215e10 + 3.14215e10i) q^{18} -1.13834e11i q^{19} +(2.76934e11 - 7.03592e11i) q^{20} -2.19880e11 q^{21} +(1.38208e12 - 1.38208e12i) q^{22} +(1.71509e12 + 1.71509e12i) q^{23} -1.83594e12i q^{24} +(2.79129e12 + 2.60012e12i) q^{25} -1.32019e13 q^{26} +(-5.70443e12 + 5.70443e12i) q^{27} +(-3.30211e12 - 3.30211e12i) q^{28} +1.04915e12i q^{29} +(2.66943e13 + 1.05069e13i) q^{30} +6.69104e12 q^{31} +(-3.02525e13 + 3.02525e13i) q^{32} +(3.12655e13 + 3.12655e13i) q^{33} -1.70234e14i q^{34} +(2.16031e13 - 9.40020e12i) q^{35} -2.13497e13 q^{36} +(-8.48624e13 + 8.48624e13i) q^{37} +(6.48595e13 + 6.48595e13i) q^{38} -2.98652e14i q^{39} +(7.84889e13 + 1.80380e14i) q^{40} +7.40493e13 q^{41} +(1.25282e14 - 1.25282e14i) q^{42} +(5.59392e13 + 5.59392e13i) q^{43} +9.39073e14i q^{44} +(3.94488e13 - 1.00226e14i) q^{45} -1.95442e15 q^{46} +(3.53716e14 - 3.53716e14i) q^{47} +(-2.62028e14 - 2.62028e14i) q^{48} +1.48291e15i q^{49} +(-3.07188e15 + 1.08926e14i) q^{50} +3.85102e15 q^{51} +(4.48508e15 - 4.48508e15i) q^{52} +(3.52414e15 + 3.52414e15i) q^{53} -6.50047e15i q^{54} +(-4.40845e15 - 1.73517e15i) q^{55} +1.21492e15 q^{56} +(-1.46725e15 + 1.46725e15i) q^{57} +(-5.97779e14 - 5.97779e14i) q^{58} +1.14079e16i q^{59} +(-1.26384e16 + 5.49937e15i) q^{60} +1.56132e15 q^{61} +(-3.81238e15 + 3.81238e15i) q^{62} +(-4.70380e14 - 4.70380e14i) q^{63} -2.91450e16i q^{64} +(1.27678e16 + 2.93424e16i) q^{65} -3.56284e16 q^{66} +(2.64545e16 - 2.64545e16i) q^{67} +(5.78336e16 + 5.78336e16i) q^{68} -4.42129e16i q^{69} +(-6.95288e15 + 1.76648e16i) q^{70} -4.96895e16 q^{71} +(3.92754e15 - 3.92754e15i) q^{72} +(-1.07108e16 - 1.07108e16i) q^{73} -9.67047e16i q^{74} +(-2.46412e15 - 6.94920e16i) q^{75} -4.40696e16 q^{76} +(-2.06898e16 + 2.06898e16i) q^{77} +(1.70164e17 + 1.70164e17i) q^{78} +2.32376e16i q^{79} +(3.69461e16 + 1.45420e16i) q^{80} +1.25688e17 q^{81} +(-4.21913e16 + 4.21913e16i) q^{82} +(-1.37697e17 - 1.37697e17i) q^{83} +8.51243e16i q^{84} +(-3.78360e17 + 1.64637e17i) q^{85} -6.37454e16 q^{86} +(1.35229e16 - 1.35229e16i) q^{87} +(-1.72754e17 - 1.72754e17i) q^{88} +2.43337e17i q^{89} +(3.46290e16 + 7.95828e16i) q^{90} +1.97632e17 q^{91} +(6.63977e17 - 6.63977e17i) q^{92} +(-8.62435e16 - 8.62435e16i) q^{93} +4.03075e17i q^{94} +(8.14293e16 - 2.06883e17i) q^{95} +7.79873e17 q^{96} +(1.08004e17 - 1.08004e17i) q^{97} +(-8.44922e17 - 8.44922e17i) q^{98} +1.33770e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8}+O(q^{10}) $ 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8	$ 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 11\!\cdots\!80 q^{42}+ \cdots - 43\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8 - 635093930 * q^10 + 4719921012 * q^11 - 22715951880 * q^12 + 8689116940 * q^13 - 59706310410 * q^15 + 10530345976 * q^16 - 221748184620 * q^17 + 654304109970 * q^18 - 878373508140 * q^20 + 1431507507492 * q^21 + 2209421844320 * q^22 - 3507966822690 * q^23 + 10464353188900 * q^25 - 23324455191468 * q^26 + 11679867134280 * q^27 + 8077754165240 * q^28 - 80865025845360 * q^30 + 53033402941772 * q^31 + 20394786468360 * q^32 - 4953707733660 * q^33 - 82375887392730 * q^35 + 263454471040956 * q^36 - 29247362581160 * q^37 + 391580910829560 * q^38 - 918259855204500 * q^40 - 717170436410748 * q^41 + 1119760897992480 * q^42 + 1295649718427950 * q^43 - 2413910465914410 * q^45 - 6165422784262408 * q^46 + 5324712362382270 * q^47 + 7675815427929360 * q^48 - 10266398091964350 * q^50 - 5996743906200468 * q^51 + 5457051468349900 * q^52 + 25019175284457720 * q^53 - 28447209909214060 * q^55 - 22879869030140400 * q^56 + 26327201869272960 * q^57 + 72036625362175440 * q^58 - 129993967558538280 * q^60 - 55112667981951388 * q^61 + 98952816959518920 * q^62 + 129200567352114030 * q^63 - 145786436727900960 * q^65 - 217789774433419296 * q^66 + 132604737823930030 * q^67 + 291394918710173220 * q^68 - 344767752141139080 * q^70 - 148288220084109108 * q^71 + 428373837658219140 * q^72 + 357896091854250160 * q^73 - 656924515001553450 * q^75 - 254554257141486000 * q^76 + 201286979542193700 * q^77 + 866949362074211400 * q^78 - 608571216720410880 * q^80 - 330578957555881164 * q^81 - 167911799138733280 * q^82 + 314012877447835830 * q^83 - 37755360901186580 * q^85 - 149686440788368488 * q^86 + 359090097519437040 * q^87 - 966828856938988320 * q^88 + 2368537241357586390 * q^90 + 498102030062089052 * q^91 - 1299658879961370120 * q^92 - 3025937916654554460 * q^93 + 2986575636848949000 * q^95 + 3531977749160666592 * q^96 - 1689002222572272080 * q^97 - 4330619740553781090 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−569.773	+	569.773i	−1.11284	+	1.11284i	−0.120073	+	0.992765i	$0.538313\pi$
$2$	−569.773	+	569.773i	−1.11284	+	1.11284i	−0.992765	+	0.120073i	$0.961687\pi$
$3$	−12889.4	−	12889.4i	−0.654849	−	0.654849i	0.299308	−	0.954157i	$-0.403244\pi$
$3$	−12889.4	−	12889.4i	−0.654849	−	0.654849i	−0.954157	+	0.299308i	$0.903244\pi$
$4$		−	387139.i		−	1.47682i
$5$	1.81741e6	+	715334.i	0.930516	+	0.366251i
$5$	1.81741e6	+	715334.i	0.930516	+	0.366251i
$6$	1.46881e7			1.45748
$7$	8.52951e6	−	8.52951e6i	0.211369	−	0.211369i	−0.593480	−	0.804849i	$-0.702246\pi$
$7$	8.52951e6	−	8.52951e6i	0.211369	−	0.211369i	0.804849	+	0.593480i	$0.202246\pi$
$8$	7.12189e7	+	7.12189e7i	0.530622	+	0.530622i
$9$		−	5.51474e7i		−	0.142345i
$10$	−1.44309e9	+	6.27936e8i	−1.44309	+	0.627936i
$11$	−2.42567e9			−1.02872			−0.514361	−	0.857574i	$-0.671971\pi$
$11$	−2.42567e9			−1.02872			−0.514361	+	0.857574i	$0.671971\pi$
$12$	−4.98999e9	+	4.98999e9i	−0.967094	+	0.967094i
$13$	1.15852e10	+	1.15852e10i	1.09248	+	1.09248i	0.995263	+	0.0972146i	$0.0309933\pi$
$13$	1.15852e10	+	1.15852e10i	1.09248	+	1.09248i	0.0972146	+	0.995263i	$0.469007\pi$
$14$			9.71977e9i			0.470439i
$15$	−1.42051e10	−	3.26456e10i	−0.369508	−	0.849187i
$16$	2.03289e10			0.295825
$17$	−1.49387e11	+	1.49387e11i	−1.25972	+	1.25972i	−0.308489	+	0.951228i	$0.599823\pi$
$17$	−1.49387e11	+	1.49387e11i	−1.25972	+	1.25972i	−0.951228	+	0.308489i	$0.900177\pi$
$18$	3.14215e10	+	3.14215e10i	0.158407	+	0.158407i
$19$		−	1.13834e11i		−	0.352768i	−0.984321	−	0.176384i	$-0.943560\pi$
$19$		−	1.13834e11i		−	0.352768i	0.984321	−	0.176384i	$-0.0564400\pi$
$20$	2.76934e11	−	7.03592e11i	0.540886	−	1.37420i
$21$	−2.19880e11			−0.276830
$22$	1.38208e12	−	1.38208e12i	1.14480	−	1.14480i
$23$	1.71509e12	+	1.71509e12i	0.952216	+	0.952216i	0.998909	−	0.0466931i	$-0.0148683\pi$
$23$	1.71509e12	+	1.71509e12i	0.952216	+	0.952216i	−0.0466931	+	0.998909i	$0.514868\pi$
$24$		−	1.83594e12i		−	0.694955i
$25$	2.79129e12	+	2.60012e12i	0.731720	+	0.681605i
$26$	−1.32019e13			−2.43150
$27$	−5.70443e12	+	5.70443e12i	−0.748064	+	0.748064i
$28$	−3.30211e12	−	3.30211e12i	−0.312154	−	0.312154i
$29$			1.04915e12i			0.0723197i	0.999346	+	0.0361598i	$0.0115125\pi$
$29$			1.04915e12i			0.0723197i	−0.999346	+	0.0361598i	$0.988487\pi$
$30$	2.66943e13	+	1.05069e13i	1.35621	+	0.533805i
$31$	6.69104e12			0.253069			0.126534	−	0.991962i	$-0.459615\pi$
$31$	6.69104e12			0.253069			0.126534	+	0.991962i	$0.459615\pi$
$32$	−3.02525e13	+	3.02525e13i	−0.859828	+	0.859828i
$33$	3.12655e13	+	3.12655e13i	0.673658	+	0.673658i
$34$		−	1.70234e14i		−	2.80372i
$35$	2.16031e13	−	9.40020e12i	0.274096	−	0.119268i
$36$	−2.13497e13			−0.210218
$37$	−8.48624e13	+	8.48624e13i	−0.652980	+	0.652980i	−0.953709	−	0.300730i	$-0.902770\pi$
$37$	−8.48624e13	+	8.48624e13i	−0.652980	+	0.652980i	0.300730	+	0.953709i	$0.402770\pi$
$38$	6.48595e13	+	6.48595e13i	0.392574	+	0.392574i
$39$		−	2.98652e14i		−	1.43082i
$40$	7.84889e13	+	1.80380e14i	0.299412	+	0.688094i
$41$	7.40493e13			0.226186			0.113093	−	0.993584i	$-0.463924\pi$
$41$	7.40493e13			0.226186			0.113093	+	0.993584i	$0.463924\pi$
$42$	1.25282e14	−	1.25282e14i	0.308067	−	0.308067i
$43$	5.59392e13	+	5.59392e13i	0.111301	+	0.111301i	0.760564	−	0.649263i	$-0.224922\pi$
$43$	5.59392e13	+	5.59392e13i	0.111301	+	0.111301i	−0.649263	+	0.760564i	$0.724922\pi$
$44$			9.39073e14i			1.51924i
$45$	3.94488e13	−	1.00226e14i	0.0521340	−	0.132454i
$46$	−1.95442e15			−2.11933
$47$	3.53716e14	−	3.53716e14i	0.316063	−	0.316063i	−0.531190	−	0.847253i	$-0.678255\pi$
$47$	3.53716e14	−	3.53716e14i	0.316063	−	0.316063i	0.847253	+	0.531190i	$0.178255\pi$
$48$	−2.62028e14	−	2.62028e14i	−0.193721	−	0.193721i
$49$			1.48291e15i			0.910646i
$50$	−3.07188e15	+	1.08926e14i	−1.57280	+	0.0557702i
$51$	3.85102e15			1.64985
$52$	4.48508e15	−	4.48508e15i	1.61339	−	1.61339i
$53$	3.52414e15	+	3.52414e15i	1.06800	+	1.06800i	0.997513	+	0.0704842i	$0.0224544\pi$
$53$	3.52414e15	+	3.52414e15i	1.06800	+	1.06800i	0.0704842	+	0.997513i	$0.477546\pi$
$54$		−	6.50047e15i		−	1.66495i
$55$	−4.40845e15	−	1.73517e15i	−0.957242	−	0.376771i
$56$	1.21492e15			0.224314
$57$	−1.46725e15	+	1.46725e15i	−0.231010	+	0.231010i
$58$	−5.97779e14	−	5.97779e14i	−0.0804801	−	0.0804801i
$59$			1.14079e16i			1.31685i	0.752646	+	0.658425i	$0.228777\pi$
$59$			1.14079e16i			1.31685i	−0.752646	+	0.658425i	$0.771223\pi$
$60$	−1.26384e16	+	5.49937e15i	−1.25410	+	0.545697i
$61$	1.56132e15			0.133513			0.0667563	−	0.997769i	$-0.478735\pi$
$61$	1.56132e15			0.133513			0.0667563	+	0.997769i	$0.478735\pi$
$62$	−3.81238e15	+	3.81238e15i	−0.281625	+	0.281625i
$63$	−4.70380e14	−	4.70380e14i	−0.0300873	−	0.0300873i
$64$		−	2.91450e16i		−	1.61787i
$65$	1.27678e16	+	2.93424e16i	0.616447	+	1.41669i
$66$	−3.56284e16			−1.49934
$67$	2.64545e16	−	2.64545e16i	0.972358	−	0.972358i	−0.0272698	−	0.999628i	$-0.508681\pi$
$67$	2.64545e16	−	2.64545e16i	0.972358	−	0.972358i	0.999628	+	0.0272698i	$0.00868131\pi$
$68$	5.78336e16	+	5.78336e16i	1.86037	+	1.86037i
$69$		−	4.42129e16i		−	1.24712i
$70$	−6.95288e15	+	1.76648e16i	−0.172299	+	0.437751i
$71$	−4.96895e16			−1.08378			−0.541888	−	0.840451i	$-0.682290\pi$
$71$	−4.96895e16			−1.08378			−0.541888	+	0.840451i	$0.682290\pi$
$72$	3.92754e15	−	3.92754e15i	0.0755314	−	0.0755314i
$73$	−1.07108e16	−	1.07108e16i	−0.181934	−	0.181934i	0.610264	−	0.792198i	$-0.291063\pi$
$73$	−1.07108e16	−	1.07108e16i	−0.181934	−	0.181934i	−0.792198	+	0.610264i	$0.791063\pi$
$74$		−	9.67047e16i		−	1.45332i
$75$	−2.46412e15	−	6.94920e16i	−0.0328179	−	0.925515i
$76$	−4.40696e16			−0.520974
$77$	−2.06898e16	+	2.06898e16i	−0.217440	+	0.217440i
$78$	1.70164e17	+	1.70164e17i	1.59227	+	1.59227i
$79$			2.32376e16i			0.193887i	0.995290	+	0.0969434i	$0.0309066\pi$
$79$			2.32376e16i			0.193887i	−0.995290	+	0.0969434i	$0.969093\pi$
$80$	3.69461e16	+	1.45420e16i	0.275270	+	0.108346i
$81$	1.25688e17			0.837393
$82$	−4.21913e16	+	4.21913e16i	−0.251709	+	0.251709i
$83$	−1.37697e17	−	1.37697e17i	−0.736584	−	0.736584i	0.235331	−	0.971915i	$-0.424383\pi$
$83$	−1.37697e17	−	1.37697e17i	−0.736584	−	0.736584i	−0.971915	+	0.235331i	$0.924383\pi$
$84$			8.51243e16i			0.408827i
$85$	−3.78360e17	+	1.64637e17i	−1.63356	+	0.710814i
$86$	−6.37454e16			−0.247721
$87$	1.35229e16	−	1.35229e16i	0.0473585	−	0.0473585i
$88$	−1.72754e17	−	1.72754e17i	−0.545863	−	0.545863i
$89$			2.43337e17i			0.694542i	0.937765	+	0.347271i	$0.112892\pi$
$89$			2.43337e17i			0.694542i	−0.937765	+	0.347271i	$0.887108\pi$
$90$	3.46290e16	+	7.95828e16i	0.0893835	+	0.205417i
$91$	1.97632e17			0.461832
$92$	6.63977e17	−	6.63977e17i	1.40625	−	1.40625i
$93$	−8.62435e16	−	8.62435e16i	−0.165722	−	0.165722i
$94$			4.03075e17i			0.703454i
$95$	8.14293e16	−	2.06883e17i	0.129202	−	0.328256i
$96$	7.79873e17			1.12612
$97$	1.08004e17	−	1.08004e17i	0.142067	−	0.142067i	−0.632496	−	0.774563i	$-0.717970\pi$
$97$	1.08004e17	−	1.08004e17i	0.142067	−	0.142067i	0.774563	+	0.632496i	$0.217970\pi$
$98$	−8.44922e17	−	8.44922e17i	−1.01340	−	1.01340i
$99$			1.33770e17i			0.146433i
$100$	1.00661e18	−	1.08062e18i	1.00661	−	1.08062i
$101$	8.72668e17			0.797915			0.398958	−	0.916969i	$-0.369372\pi$
$101$	8.72668e17			0.797915			0.398958	+	0.916969i	$0.369372\pi$
$102$	−2.19421e18	+	2.19421e18i	−1.83602	+	1.83602i
$103$	−3.11858e17	−	3.11858e17i	−0.239013	−	0.239013i	0.577428	−	0.816442i	$-0.304056\pi$
$103$	−3.11858e17	−	3.11858e17i	−0.239013	−	0.239013i	−0.816442	+	0.577428i	$0.804056\pi$
$104$			1.65017e18i			1.15939i
$105$	−3.99614e17	−	1.57288e17i	−0.257595	−	0.101389i
$106$	−4.01592e18			−2.37702
$107$	−1.02716e18	+	1.02716e18i	−0.558705	+	0.558705i	−0.928939	−	0.370234i	$-0.879278\pi$
$107$	−1.02716e18	+	1.02716e18i	−0.558705	+	0.558705i	0.370234	+	0.928939i	$0.379278\pi$
$108$	2.20841e18	+	2.20841e18i	1.10475	+	1.10475i
$109$		−	2.30651e18i		−	1.06198i	−0.847378	−	0.530990i	$-0.821820\pi$
$109$		−	2.30651e18i		−	1.06198i	0.847378	−	0.530990i	$-0.178180\pi$
$110$	3.50047e18	−	1.52317e18i	1.48454	−	0.645971i
$111$	2.18765e18			0.855207
$112$	1.73396e17	−	1.73396e17i	0.0625283	−	0.0625283i
$113$	−7.46932e17	−	7.46932e17i	−0.248642	−	0.248642i	0.571771	−	0.820413i	$-0.306257\pi$
$113$	−7.46932e17	−	7.46932e17i	−0.248642	−	0.248642i	−0.820413	+	0.571771i	$0.806257\pi$
$114$		−	1.67200e18i		−	0.514153i
$115$	1.89016e18	+	4.34388e18i	0.537302	+	1.23480i
$116$	4.06168e17			0.106803
$117$	6.38893e17	−	6.38893e17i	0.155509	−	0.155509i
$118$	−6.49990e18	−	6.49990e18i	−1.46544	−	1.46544i
$119$			2.54840e18i			0.532530i
$120$	1.31331e18	−	3.33666e18i	0.254528	−	0.646667i
$121$	3.23971e17			0.0582691
$122$	−8.89597e17	+	8.89597e17i	−0.148578	+	0.148578i
$123$	−9.54451e17	−	9.54451e17i	−0.148118	−	0.148118i
$124$		−	2.59036e18i		−	0.373737i
$125$	3.21298e18	+	6.72220e18i	0.431239	+	0.902238i
$126$	5.36020e17			0.0669647
$127$	−1.06703e17	+	1.06703e17i	−0.0124149	+	0.0124149i	−0.713287	−	0.700872i	$-0.752794\pi$
$127$	−1.06703e17	+	1.06703e17i	−0.0124149	+	0.0124149i	0.700872	+	0.713287i	$0.252794\pi$
$128$	8.67554e18	+	8.67554e18i	0.940604	+	0.940604i
$129$		−	1.44205e18i		−	0.145771i
$130$	−2.39932e19	−	9.44374e18i	−2.26255	−	0.890541i
$131$	1.50191e19			1.32191			0.660954	−	0.750426i	$-0.270152\pi$
$131$	1.50191e19			1.32191			0.660954	+	0.750426i	$0.270152\pi$
$132$	1.21041e19	−	1.21041e19i	0.994871	−	0.994871i
$133$	−9.70947e17	−	9.70947e17i	−0.0745643	−	0.0745643i
$134$			3.01461e19i			2.16416i
$135$	−1.44479e19	+	6.28674e18i	−0.970064	+	0.422106i
$136$	−2.12784e19			−1.33687
$137$	−1.31564e19	+	1.31564e19i	−0.773842	+	0.773842i	−0.978776	−	0.204933i	$-0.934302\pi$
$137$	−1.31564e19	+	1.31564e19i	−0.773842	+	0.773842i	0.204933	+	0.978776i	$0.434302\pi$
$138$	2.51913e19	+	2.51913e19i	1.38784	+	1.38784i
$139$		−	2.95832e19i		−	1.52726i	−0.645656	−	0.763628i	$-0.723416\pi$
$139$		−	2.95832e19i		−	1.52726i	0.645656	−	0.763628i	$-0.276584\pi$
$140$	−3.63918e18	−	8.36340e18i	−0.176137	−	0.404791i
$141$	−9.11836e18			−0.413947
$142$	2.83117e19	−	2.83117e19i	1.20607	−	1.20607i
$143$	−2.81019e19	−	2.81019e19i	−1.12386	−	1.12386i
$144$		−	1.12109e18i		−	0.0421092i
$145$	−7.50494e17	+	1.90674e18i	−0.0264872	+	0.0672946i
$146$	1.22054e19			0.404927
$147$	1.91138e19	−	1.91138e19i	0.596336	−	0.596336i
$148$	3.28536e19	+	3.28536e19i	0.964333	+	0.964333i
$149$		−	2.03499e19i		−	0.562194i	−0.959679	−	0.281097i	$-0.909302\pi$
$149$		−	2.03499e19i		−	0.562194i	0.959679	−	0.281097i	$-0.0906982\pi$
$150$	4.09987e19	+	3.81907e19i	1.06647	+	0.993428i
$151$	2.91613e18			0.0714521			0.0357260	−	0.999362i	$-0.488626\pi$
$151$	2.91613e18			0.0714521			0.0357260	+	0.999362i	$0.488626\pi$
$152$	8.10713e18	−	8.10713e18i	0.187187	−	0.187187i
$153$	8.23831e18	+	8.23831e18i	0.179314	+	0.179314i
$154$		−	2.35770e19i		−	0.483951i
$155$	1.21604e19	+	4.78633e18i	0.235484	+	0.0926867i
$156$	−1.15620e20			−2.11306
$157$	−6.91340e19	+	6.91340e19i	−1.19287	+	1.19287i	−0.216618	+	0.976256i	$0.569503\pi$
$157$	−6.91340e19	+	6.91340e19i	−1.19287	+	1.19287i	−0.976256	+	0.216618i	$0.930497\pi$
$158$	−1.32402e19	−	1.32402e19i	−0.215765	−	0.215765i
$159$		−	9.08480e19i		−	1.39875i
$160$	−7.66220e19	+	3.33407e19i	−1.11500	+	0.485171i
$161$	2.92577e19			0.402538
$162$	−7.16138e19	+	7.16138e19i	−0.931883	+	0.931883i
$163$	5.62914e19	+	5.62914e19i	0.693032	+	0.693032i	0.962898	−	0.269866i	$-0.0869794\pi$
$163$	5.62914e19	+	5.62914e19i	0.693032	+	0.693032i	−0.269866	+	0.962898i	$0.586979\pi$
$164$		−	2.86674e19i		−	0.334036i
$165$	3.44570e19	+	7.91875e19i	0.380122	+	0.873577i
$166$	1.56912e20			1.63940
$167$	8.12673e18	−	8.12673e18i	0.0804392	−	0.0804392i	−0.665742	−	0.746182i	$-0.731885\pi$
$167$	8.12673e18	−	8.12673e18i	0.0804392	−	0.0804392i	0.746182	+	0.665742i	$0.231885\pi$
$168$	−1.56596e19	−	1.56596e19i	−0.146892	−	0.146892i
$169$			1.55977e20i			1.38702i
$170$	1.21774e20	−	3.09385e20i	1.02687	−	2.60891i
$171$	−6.27764e18			−0.0502148
$172$	2.16563e19	−	2.16563e19i	0.164372	−	0.164372i
$173$	−1.20271e20	−	1.20271e20i	−0.866458	−	0.866458i	0.125620	−	0.992078i	$-0.459908\pi$
$173$	−1.20271e20	−	1.20271e20i	−0.866458	−	0.866458i	−0.992078	+	0.125620i	$0.959908\pi$
$174$			1.54100e19i			0.105405i
$175$	4.59860e19	−	1.63062e18i	0.298733	−	0.0105928i
$176$	−4.93114e19			−0.304322
$177$	1.47041e20	−	1.47041e20i	0.862338	−	0.862338i
$178$	−1.38647e20	−	1.38647e20i	−0.772912	−	0.772912i
$179$			2.84738e20i			1.50927i	0.656143	+	0.754637i	$0.272187\pi$
$179$			2.84738e20i			1.50927i	−0.656143	+	0.754637i	$0.727813\pi$
$180$	−3.88013e19	−	1.52722e19i	−0.195611	−	0.0769925i
$181$	3.53756e19			0.169667			0.0848334	−	0.996395i	$-0.472964\pi$
$181$	3.53756e19			0.169667			0.0848334	+	0.996395i	$0.472964\pi$
$182$	−1.12605e20	+	1.12605e20i	−0.513945	+	0.513945i
$183$	−2.01244e19	−	2.01244e19i	−0.0874307	−	0.0874307i
$184$			2.44293e20i			1.01053i
$185$	−2.14935e20	+	9.35252e19i	−0.846763	+	0.368454i
$186$	9.82784e19			0.368843
$187$	3.62364e20	−	3.62364e20i	1.29590	−	1.29590i
$188$	−1.36937e20	−	1.36937e20i	−0.466768	−	0.466768i
$189$			9.73120e19i			0.316235i
$190$	7.14804e19	+	1.64273e20i	0.221516	+	0.509077i
$191$	6.97968e18			0.0206317			0.0103159	−	0.999947i	$-0.496716\pi$
$191$	6.97968e18			0.0206317			0.0103159	+	0.999947i	$0.496716\pi$
$192$	−3.75662e20	+	3.75662e20i	−1.05946	+	1.05946i
$193$	5.20628e19	+	5.20628e19i	0.140124	+	0.140124i	0.773689	−	0.633565i	$-0.218409\pi$
$193$	5.20628e19	+	5.20628e19i	0.140124	+	0.140124i	−0.633565	+	0.773689i	$0.718409\pi$
$194$			1.23075e20i			0.316195i
$195$	2.13636e20	−	5.42774e20i	0.524038	−	1.33140i
$196$	5.74092e20			1.34486
$197$	−3.21003e20	+	3.21003e20i	−0.718313	+	0.718313i	−0.968260	−	0.249947i	$-0.919587\pi$
$197$	−3.21003e20	+	3.21003e20i	−0.718313	+	0.718313i	0.249947	+	0.968260i	$0.419587\pi$
$198$	−7.62183e19	−	7.62183e19i	−0.162957	−	0.162957i
$199$		−	2.13998e20i		−	0.437253i	−0.975809	−	0.218626i	$-0.929842\pi$
$199$		−	2.13998e20i		−	0.437253i	0.975809	−	0.218626i	$-0.0701576\pi$
$200$	1.36152e19	+	3.83970e20i	0.0265923	+	0.749942i
$201$	−6.81965e20			−1.27350
$202$	−4.97223e20	+	4.97223e20i	−0.887951	+	0.887951i
$203$	8.94875e18	+	8.94875e18i	0.0152861	+	0.0152861i
$204$		−	1.49088e21i		−	2.43653i
$205$	1.34578e20	+	5.29700e19i	0.210470	+	0.0828410i
$206$	3.55377e20			0.531967
$207$	9.45825e19	−	9.45825e19i	0.135543	−	0.135543i
$208$	2.35515e20	+	2.35515e20i	0.323182	+	0.323182i
$209$			2.76124e20i			0.362900i
$210$	3.17308e20	−	1.38071e20i	0.399491	−	0.173831i
$211$	1.83777e19			0.0221692			0.0110846	−	0.999939i	$-0.496472\pi$
$211$	1.83777e19			0.0221692			0.0110846	+	0.999939i	$0.496472\pi$
$212$	1.36433e21	−	1.36433e21i	1.57724	−	1.57724i
$213$	6.40467e20	+	6.40467e20i	0.709709	+	0.709709i
$214$		−	1.17049e21i		−	1.24350i
$215$	6.16495e19	+	1.41680e20i	0.0628034	+	0.144332i
$216$	−8.12527e20			−0.793879
$217$	5.70713e19	−	5.70713e19i	0.0534909	−	0.0534909i
$218$	1.31419e21	+	1.31419e21i	1.18181	+	1.18181i
$219$			2.76110e20i			0.238279i
$220$	−6.71751e20	+	1.70668e21i	−0.556422	+	1.41367i
$221$	−3.46135e21			−2.75243
$222$	−1.24646e21	+	1.24646e21i	−0.951707	+	0.951707i
$223$	−9.70979e20	−	9.70979e20i	−0.711977	−	0.711977i	0.254972	−	0.966949i	$-0.417934\pi$
$223$	−9.70979e20	−	9.70979e20i	−0.711977	−	0.711977i	−0.966949	+	0.254972i	$0.917934\pi$
$224$			5.16078e20i			0.363482i
$225$	1.43390e20	−	1.53932e20i	0.0970231	−	0.104157i
$226$	8.51164e20			0.553398
$227$	1.94064e21	−	1.94064e21i	1.21258	−	1.21258i	0.242411	−	0.970174i	$-0.422062\pi$
$227$	1.94064e21	−	1.94064e21i	1.21258	−	1.21258i	0.970174	−	0.242411i	$-0.0779382\pi$
$228$	5.68030e20	+	5.68030e20i	0.341160	+	0.341160i
$229$			1.92225e21i			1.10991i	0.831879	+	0.554957i	$0.187265\pi$
$229$			1.92225e21i			1.10991i	−0.831879	+	0.554957i	$0.812735\pi$
$230$	−3.55199e21	−	1.39806e21i	−1.97207	−	0.776205i
$231$	5.33358e20			0.284781
$232$	−7.47195e19	+	7.47195e19i	−0.0383744	+	0.0383744i
$233$	3.82439e20	+	3.82439e20i	0.188955	+	0.188955i	0.795244	−	0.606289i	$-0.207343\pi$
$233$	3.82439e20	+	3.82439e20i	0.188955	+	0.188955i	−0.606289	+	0.795244i	$0.707343\pi$
$234$			7.28048e20i			0.346112i
$235$	8.95873e20	−	3.89823e20i	0.409860	−	0.178343i
$236$	4.41643e21			1.94475
$237$	2.99519e20	−	2.99519e20i	0.126967	−	0.126967i
$238$	−1.45201e21	−	1.45201e21i	−0.592620	−	0.592620i
$239$		−	3.64203e21i		−	1.43140i	−0.698405	−	0.715702i	$-0.746107\pi$
$239$		−	3.64203e21i		−	1.43140i	0.698405	−	0.715702i	$-0.253893\pi$
$240$	−2.88776e20	−	6.63651e20i	−0.109310	−	0.251211i
$241$	3.54048e21			1.29095			0.645474	−	0.763782i	$-0.276660\pi$
$241$	3.54048e21			1.29095			0.645474	+	0.763782i	$0.276660\pi$
$242$	−1.84590e20	+	1.84590e20i	−0.0648441	+	0.0648441i
$243$	5.89969e20	+	5.89969e20i	0.199698	+	0.199698i
$244$		−	6.04447e20i		−	0.197174i
$245$	−1.06078e21	+	2.69506e21i	−0.333525	+	0.847371i
$246$	1.08764e21			0.329663
$247$	1.31879e21	−	1.31879e21i	0.385391	−	0.385391i
$248$	4.76529e20	+	4.76529e20i	0.134284	+	0.134284i
$249$			3.54967e21i			0.964703i
$250$	−5.66080e21	−	1.99946e21i	−1.48394	−	0.524146i
$251$	−7.42071e21			−1.87664			−0.938322	−	0.345764i	$-0.887620\pi$
$251$	−7.42071e21			−1.87664			−0.938322	+	0.345764i	$0.887620\pi$
$252$	−1.82102e20	+	1.82102e20i	−0.0444336	+	0.0444336i
$253$	−4.16024e21	−	4.16024e21i	−0.979566	−	0.979566i
$254$		−	1.21593e20i		−	0.0276315i
$255$	6.99890e21	+	2.75477e21i	1.53521	+	0.604259i
$256$	−2.24599e21			−0.475607
$257$	−1.21084e21	+	1.21084e21i	−0.247564	+	0.247564i	−0.819970	−	0.572406i	$-0.806010\pi$
$257$	−1.21084e21	+	1.21084e21i	−0.247564	+	0.247564i	0.572406	+	0.819970i	$0.306010\pi$
$258$	8.21639e20	+	8.21639e20i	0.162220	+	0.162220i
$259$			1.44767e21i			0.276040i
$260$	1.13596e22	−	4.94291e21i	2.09219	−	0.910381i
$261$	5.78580e19			0.0102943
$262$	−8.55747e21	+	8.55747e21i	−1.47107	+	1.47107i
$263$	3.62126e21	+	3.62126e21i	0.601531	+	0.601531i	0.940719	−	0.339188i	$-0.110152\pi$
$263$	3.62126e21	+	3.62126e21i	0.601531	+	0.601531i	−0.339188	+	0.940719i	$0.610152\pi$
$264$			4.45338e21i			0.714916i
$265$	3.88388e21	+	8.92575e21i	0.602633	+	1.38494i
$266$	1.10644e21			0.165956
$267$	3.13647e21	−	3.13647e21i	0.454820	−	0.454820i
$268$	−1.02416e22	−	1.02416e22i	−1.43600	−	1.43600i
$269$			1.22343e21i			0.165885i	0.996554	+	0.0829425i	$0.0264318\pi$
$269$			1.22343e21i			0.165885i	−0.996554	+	0.0829425i	$0.973568\pi$
$270$	4.65001e21	−	1.18140e22i	0.609789	−	1.54926i
$271$	4.70229e21			0.596466			0.298233	−	0.954493i	$-0.403603\pi$
$271$	4.70229e21			0.596466			0.298233	+	0.954493i	$0.403603\pi$
$272$	−3.03688e21	+	3.03688e21i	−0.372656	+	0.372656i
$273$	−2.54735e21	−	2.54735e21i	−0.302430	−	0.302430i
$274$		−	1.49923e22i		−	1.72232i
$275$	−6.77076e21	−	6.30703e21i	−0.752737	−	0.701182i
$276$	−1.71165e22			−1.84176
$277$	−4.10970e21	+	4.10970e21i	−0.428047	+	0.428047i	−0.887963	−	0.459915i	$-0.847880\pi$
$277$	−4.10970e21	+	4.10970e21i	−0.428047	+	0.428047i	0.459915	+	0.887963i	$0.347880\pi$
$278$	1.68557e22	+	1.68557e22i	1.69959	+	1.69959i
$279$		−	3.68993e20i		−	0.0360231i
$280$	2.20802e21	+	8.69077e20i	0.208728	+	0.0821554i
$281$	7.88789e21			0.722111			0.361056	−	0.932544i	$-0.382416\pi$
$281$	7.88789e21			0.722111			0.361056	+	0.932544i	$0.382416\pi$
$282$	5.19540e21	−	5.19540e21i	0.460656	−	0.460656i
$283$	−6.66881e21	−	6.66881e21i	−0.572757	−	0.572757i	0.360141	−	0.932898i	$-0.382729\pi$
$283$	−6.66881e21	−	6.66881e21i	−0.572757	−	0.572757i	−0.932898	+	0.360141i	$0.882729\pi$
$284$			1.92367e22i			1.60054i
$285$	−3.71618e21	+	1.61703e21i	−0.299566	+	0.130351i
$286$	3.20234e22			2.50134
$287$	6.31604e20	−	6.31604e20i	0.0478088	−	0.0478088i
$288$	1.66835e21	+	1.66835e21i	0.122392	+	0.122392i
$289$		−	3.05699e22i		−	2.17377i
$290$	−6.58800e20	−	1.51402e21i	−0.0454121	−	0.104364i
$291$	−2.78420e21			−0.186065
$292$	−4.14655e21	+	4.14655e21i	−0.268684	+	0.268684i
$293$	−2.19887e22	−	2.19887e22i	−1.38163	−	1.38163i	−0.841734	−	0.539892i	$-0.818465\pi$
$293$	−2.19887e22	−	2.19887e22i	−1.38163	−	1.38163i	−0.539892	−	0.841734i	$-0.681535\pi$
$294$			2.17811e22i			1.32725i
$295$	−8.16044e21	+	2.07328e22i	−0.482298	+	1.22535i
$296$	−1.20876e22			−0.692971
$297$	1.38371e22	−	1.38371e22i	0.769550	−	0.769550i
$298$	1.15948e22	+	1.15948e22i	0.625631	+	0.625631i
$299$			3.97392e22i			2.08055i
$300$	−2.69031e22	+	9.53959e20i	−1.36682	+	0.0484661i
$301$	9.54268e20			0.0470513
$302$	−1.66154e21	+	1.66154e21i	−0.0795146	+	0.0795146i
$303$	−1.12482e22	−	1.12482e22i	−0.522514	−	0.522514i
$304$		−	2.31412e21i		−	0.104358i
$305$	2.83756e21	+	1.11686e21i	0.124236	+	0.0488992i
$306$	−9.38794e21			−0.399096
$307$	9.35073e21	−	9.35073e21i	0.386012	−	0.386012i	−0.487251	−	0.873262i	$-0.662000\pi$
$307$	9.35073e21	−	9.35073e21i	0.386012	−	0.386012i	0.873262	+	0.487251i	$0.162000\pi$
$308$	8.00983e21	+	8.00983e21i	0.321120	+	0.321120i
$309$			8.03933e21i			0.313035i
$310$	−9.65579e21	+	4.20154e21i	−0.365201	+	0.158911i
$311$	−2.20771e22			−0.811144			−0.405572	−	0.914063i	$-0.632928\pi$
$311$	−2.20771e22			−0.811144			−0.405572	+	0.914063i	$0.632928\pi$
$312$	2.12697e22	−	2.12697e22i	0.759223	−	0.759223i
$313$	1.46014e22	+	1.46014e22i	0.506402	+	0.506402i	0.913420	−	0.407018i	$-0.133431\pi$
$313$	1.46014e22	+	1.46014e22i	0.506402	+	0.506402i	−0.407018	+	0.913420i	$0.633431\pi$
$314$		−	7.87814e22i		−	2.65495i
$315$	−5.18396e20	−	1.19135e21i	−0.0169772	−	0.0390163i
$316$	8.99620e21			0.286336
$317$	2.52720e22	−	2.52720e22i	0.781819	−	0.781819i	−0.198318	−	0.980138i	$-0.563548\pi$
$317$	2.52720e22	−	2.52720e22i	0.781819	−	0.781819i	0.980138	+	0.198318i	$0.0635480\pi$
$318$	5.17628e22	+	5.17628e22i	1.55659	+	1.55659i
$319$		−	2.54490e21i		−	0.0743968i
$320$	2.08484e22	−	5.29686e22i	0.592548	−	1.50546i
$321$	2.64788e22			0.731735
$322$	−1.66702e22	+	1.66702e22i	−0.447960	+	0.447960i
$323$	1.70053e22	+	1.70053e22i	0.444388	+	0.444388i
$324$		−	4.86588e22i		−	1.23668i
$325$	2.21479e21	+	6.24604e22i	0.0547498	+	1.54403i
$326$	−6.41466e22			−1.54247
$327$	−2.97295e22	+	2.97295e22i	−0.695437	+	0.695437i
$328$	5.27371e21	+	5.27371e21i	0.120019	+	0.120019i
$329$		−	6.03404e21i		−	0.133612i
$330$	−6.47516e22	−	2.54862e22i	−1.39516	−	0.549137i
$331$	−1.56997e22			−0.329184			−0.164592	−	0.986362i	$-0.552631\pi$
$331$	−1.56997e22			−0.329184			−0.164592	+	0.986362i	$0.552631\pi$
$332$	−5.33080e22	+	5.33080e22i	−1.08780	+	1.08780i
$333$	4.67994e21	+	4.67994e21i	0.0929484	+	0.0929484i
$334$			9.26079e21i			0.179032i
$335$	6.70026e22	−	2.91550e22i	1.26092	−	0.548668i
$336$	−4.46994e21			−0.0818932
$337$	−1.36859e22	+	1.36859e22i	−0.244120	+	0.244120i	−0.818552	−	0.574432i	$-0.805223\pi$
$337$	−1.36859e22	+	1.36859e22i	−0.244120	+	0.244120i	0.574432	+	0.818552i	$0.305223\pi$
$338$	−8.88718e22	−	8.88718e22i	−1.54353	−	1.54353i
$339$			1.92550e22i			0.325647i
$340$	6.37373e22	+	1.46478e23i	1.04974	+	2.41247i
$341$	−1.62303e22			−0.260337
$342$	3.57683e21	−	3.57683e21i	0.0558809	−	0.0558809i
$343$	2.65380e22	+	2.65380e22i	0.403852	+	0.403852i
$344$			7.96786e21i			0.118118i
$345$	3.16270e22	−	8.03531e22i	0.456758	−	1.16046i
$346$	1.37055e23			1.92846
$347$	1.65389e22	−	1.65389e22i	0.226746	−	0.226746i	−0.584586	−	0.811332i	$-0.698743\pi$
$347$	1.65389e22	−	1.65389e22i	0.226746	−	0.226746i	0.811332	+	0.584586i	$0.198743\pi$
$348$	−5.23526e21	−	5.23526e21i	−0.0699399	−	0.0699399i
$349$		−	4.56756e22i		−	0.594642i	−0.954778	−	0.297321i	$-0.903907\pi$
$349$		−	4.56756e22i		−	0.594642i	0.954778	−	0.297321i	$-0.0960932\pi$
$350$	−2.52725e22	+	2.71307e22i	−0.320654	+	0.344230i
$351$	−1.32174e23			−1.63449
$352$	7.33827e22	−	7.33827e22i	0.884524	−	0.884524i
$353$	2.22615e22	+	2.22615e22i	0.261567	+	0.261567i	0.825690	−	0.564124i	$-0.190786\pi$
$353$	2.22615e22	+	2.22615e22i	0.261567	+	0.261567i	−0.564124	+	0.825690i	$0.690786\pi$
$354$			1.67560e23i			1.91929i
$355$	−9.03064e22	−	3.55446e22i	−1.00847	−	0.396934i
$356$	9.42053e22			1.02571
$357$	3.28473e22	−	3.28473e22i	0.348727	−	0.348727i
$358$	−1.62236e23	−	1.62236e23i	−1.67958	−	1.67958i
$359$			1.42040e22i			0.143404i	0.997426	+	0.0717021i	$0.0228431\pi$
$359$			1.42040e22i			0.143404i	−0.997426	+	0.0717021i	$0.977157\pi$
$360$	9.94746e21	−	4.32846e21i	0.0979467	−	0.0426198i
$361$	9.11692e22			0.875555
$362$	−2.01561e22	+	2.01561e22i	−0.188812	+	0.188812i
$363$	−4.17580e21	−	4.17580e21i	−0.0381575	−	0.0381575i
$364$		−	7.65110e22i		−	0.682042i
$365$	−1.18041e22	−	2.71276e22i	−0.102659	−	0.235926i
$366$	2.29327e22			0.194592
$367$	−6.85003e22	+	6.85003e22i	−0.567150	+	0.567150i	−0.931329	−	0.364179i	$-0.881350\pi$
$367$	−6.85003e22	+	6.85003e22i	−0.567150	+	0.567150i	0.364179	+	0.931329i	$0.381350\pi$
$368$	3.48659e22	+	3.48659e22i	0.281689	+	0.281689i
$369$		−	4.08363e21i		−	0.0321965i
$370$	6.91761e22	−	1.75752e23i	0.532281	−	1.35234i
$371$	6.01183e22			0.451483
$372$	−3.33882e22	+	3.33882e22i	−0.244741	+	0.244741i
$373$	−6.20916e22	−	6.20916e22i	−0.444277	−	0.444277i	0.449170	−	0.893446i	$-0.351720\pi$
$373$	−6.20916e22	−	6.20916e22i	−0.444277	−	0.444277i	−0.893446	+	0.449170i	$0.851720\pi$
$374$			4.12931e23i			2.88425i
$375$	4.52317e22	−	1.28058e23i	0.308433	−	0.873226i
$376$	5.03825e22			0.335420
$377$	−1.21546e22	+	1.21546e22i	−0.0790077	+	0.0790077i
$378$	−5.54458e22	−	5.54458e22i	−0.351919	−	0.351919i
$379$			2.62950e23i			1.62975i	0.579639	+	0.814874i	$0.303194\pi$
$379$			2.62950e23i			1.62975i	−0.579639	+	0.814874i	$0.696806\pi$
$380$	−8.00926e22	−	3.15245e22i	−0.484775	−	0.190807i
$381$	2.75067e21			0.0162597
$382$	−3.97683e21	+	3.97683e21i	−0.0229598	+	0.0229598i
$383$	2.14582e23	+	2.14582e23i	1.21005	+	1.21005i	0.971008	+	0.239047i	$0.0768349\pi$
$383$	2.14582e23	+	2.14582e23i	1.21005	+	1.21005i	0.239047	+	0.971008i	$0.423165\pi$
$384$		−	2.23645e23i		−	1.23191i
$385$	−5.24020e22	+	2.28018e22i	−0.281969	+	0.122694i
$386$	−5.93280e22			−0.311870
$387$	3.08490e21	−	3.08490e21i	0.0158432	−	0.0158432i
$388$	−4.18124e22	−	4.18124e22i	−0.209807	−	0.209807i
$389$		−	2.84717e23i		−	1.39594i	−0.716127	−	0.697970i	$-0.754087\pi$
$389$		−	2.84717e23i		−	1.39594i	0.716127	−	0.697970i	$-0.245913\pi$
$390$	1.87534e23	+	4.30982e23i	0.898461	+	2.06480i
$391$	−5.12424e23			−2.39905
$392$	−1.05611e23	+	1.05611e23i	−0.483209	+	0.483209i
$393$	−1.93587e23	−	1.93587e23i	−0.865651	−	0.865651i
$394$		−	3.65798e23i		−	1.59873i
$395$	−1.66227e22	+	4.22324e22i	−0.0710112	+	0.180415i
$396$	5.17874e22			0.216256
$397$	−1.16346e23	+	1.16346e23i	−0.474938	+	0.474938i	−0.903508	−	0.428570i	$-0.859017\pi$
$397$	−1.16346e23	+	1.16346e23i	−0.474938	+	0.474938i	0.428570	+	0.903508i	$0.359017\pi$
$398$	1.21930e23	+	1.21930e23i	0.486592	+	0.486592i
$399$			2.50298e22i			0.0976567i
$400$	5.67440e22	+	5.28576e22i	0.216461	+	0.201636i
$401$	2.24269e23			0.836508			0.418254	−	0.908330i	$-0.362642\pi$
$401$	2.24269e23			0.836508			0.418254	+	0.908330i	$0.362642\pi$
$402$	3.88566e23	−	3.88566e23i	1.41720	−	1.41720i
$403$	7.75169e22	+	7.75169e22i	0.276472	+	0.276472i
$404$		−	3.37844e23i		−	1.17838i
$405$	2.28427e23	+	8.99090e22i	0.779207	+	0.306696i
$406$	−1.01975e22			−0.0340220
$407$	2.05848e23	−	2.05848e23i	0.671735	−	0.671735i
$408$	2.74265e23	+	2.74265e23i	0.875447	+	0.875447i
$409$		−	1.03130e23i		−	0.322014i	−0.986953	−	0.161007i	$-0.948526\pi$
$409$		−	1.03130e23i		−	0.322014i	0.986953	−	0.161007i	$-0.0514742\pi$
$410$	−1.06860e23	+	4.64982e22i	−0.326408	+	0.142030i
$411$	3.39157e23			1.01350
$412$	−1.20733e23	+	1.20733e23i	−0.352979	+	0.352979i
$413$	9.73035e22	+	9.73035e22i	0.278341	+	0.278341i
$414$			1.07781e23i			0.301675i
$415$	−1.51753e23	−	3.48752e23i	−0.415629	−	0.955178i
$416$	−7.00961e23			−1.87869
$417$	−3.81310e23	+	3.81310e23i	−1.00012	+	1.00012i
$418$	−1.57328e23	−	1.57328e23i	−0.403849	−	0.403849i
$419$		−	5.72941e23i		−	1.43941i	−0.694281	−	0.719704i	$-0.744278\pi$
$419$		−	5.72941e23i		−	1.43941i	0.694281	−	0.719704i	$-0.255722\pi$
$420$	−6.08923e22	+	1.54706e23i	−0.149733	+	0.380420i
$421$	3.63677e23			0.875341			0.437671	−	0.899135i	$-0.355804\pi$
$421$	3.63677e23			0.875341			0.437671	+	0.899135i	$0.355804\pi$
$422$	−1.04711e22	+	1.04711e22i	−0.0246707	+	0.0246707i
$423$	−1.95065e22	−	1.95065e22i	−0.0449900	−	0.0449900i
$424$			5.01971e23i			1.13341i
$425$	−8.05407e23	+	2.85590e22i	−1.78039	+	0.0631310i
$426$	−7.29842e23			−1.57958
$427$	1.33173e22	−	1.33173e22i	0.0282205	−	0.0282205i
$428$	3.97652e23	+	3.97652e23i	0.825106	+	0.825106i
$429$			7.24432e23i			1.47191i
$430$	−1.15852e23	−	4.55992e22i	−0.230508	−	0.0907280i
$431$	1.01672e24			1.98111			0.990553	−	0.137132i	$-0.0437884\pi$
$431$	1.01672e24			1.98111			0.990553	+	0.137132i	$0.0437884\pi$
$432$	−1.15965e23	+	1.15965e23i	−0.221296	+	0.221296i
$433$	3.90865e23	+	3.90865e23i	0.730526	+	0.730526i	0.970724	−	0.240198i	$-0.0772122\pi$
$433$	3.90865e23	+	3.90865e23i	0.730526	+	0.730526i	−0.240198	+	0.970724i	$0.577212\pi$
$434$			6.50354e22i			0.119053i
$435$	3.42502e22	−	1.49034e22i	0.0614129	−	0.0267227i
$436$	−8.92939e23			−1.56835
$437$	1.95235e23	−	1.95235e23i	0.335911	−	0.335911i
$438$	−1.57320e23	−	1.57320e23i	−0.265166	−	0.265166i
$439$			2.08678e23i			0.344584i	0.985046	+	0.172292i	$0.0551172\pi$
$439$			2.08678e23i			0.344584i	−0.985046	+	0.172292i	$0.944883\pi$
$440$	−1.90388e23	−	4.37542e23i	−0.308011	−	0.707857i
$441$	8.17785e22			0.129626
$442$	1.97219e24	−	1.97219e24i	3.06300	−	3.06300i
$443$	−3.58836e23	−	3.58836e23i	−0.546087	−	0.546087i	0.379219	−	0.925307i	$-0.376193\pi$
$443$	−3.58836e23	−	3.58836e23i	−0.546087	−	0.546087i	−0.925307	+	0.379219i	$0.876193\pi$
$444$		−	8.46925e23i		−	1.26299i
$445$	−1.74067e23	+	4.42244e23i	−0.254377	+	0.646282i
$446$	1.10648e24			1.58463
$447$	−2.62298e23	+	2.62298e23i	−0.368152	+	0.368152i
$448$	−2.48593e23	−	2.48593e23i	−0.341968	−	0.341968i
$449$			2.97361e23i			0.400929i	0.979701	+	0.200464i	$0.0642451\pi$
$449$			2.97361e23i			0.400929i	−0.979701	+	0.200464i	$0.935755\pi$
$450$	6.00699e21	+	1.69406e23i	0.00793861	+	0.223881i
$451$	−1.79619e23			−0.232683
$452$	−2.89167e23	+	2.89167e23i	−0.367200	+	0.367200i
$453$	−3.75872e22	−	3.75872e22i	−0.0467903	−	0.0467903i
$454$			2.21145e24i			2.69882i
$455$	3.59179e23	+	1.41373e23i	0.429742	+	0.169147i
$456$	−2.08992e23			−0.245158
$457$	−8.32620e23	+	8.32620e23i	−0.957638	+	0.957638i	−0.999138	−	0.0415007i	$-0.986786\pi$
$457$	−8.32620e23	+	8.32620e23i	−0.957638	+	0.957638i	0.0415007	+	0.999138i	$0.486786\pi$
$458$	−1.09524e24	−	1.09524e24i	−1.23516	−	1.23516i
$459$		−	1.70434e24i		−	1.88470i
$460$	1.68169e24	−	7.31756e23i	1.82358	−	0.793498i
$461$	1.62795e22			0.0173114			0.00865571	−	0.999963i	$-0.497245\pi$
$461$	1.62795e22			0.0173114			0.00865571	+	0.999963i	$0.497245\pi$
$462$	−3.03893e23	+	3.03893e23i	−0.316915	+	0.316915i
$463$	−1.68844e23	−	1.68844e23i	−0.172686	−	0.172686i	0.615473	−	0.788158i	$-0.288965\pi$
$463$	−1.68844e23	−	1.68844e23i	−0.172686	−	0.172686i	−0.788158	+	0.615473i	$0.788965\pi$
$464$			2.13282e22i			0.0213940i
$465$	−9.50472e22	−	2.18433e23i	−0.0935110	−	0.214903i
$466$	−4.35807e23			−0.420553
$467$	−8.65181e23	+	8.65181e23i	−0.818945	+	0.818945i	−0.985955	−	0.167010i	$-0.946589\pi$
$467$	−8.65181e23	+	8.65181e23i	−0.818945	+	0.818945i	0.167010	+	0.985955i	$0.446589\pi$
$468$	−2.47340e23	−	2.47340e23i	−0.229658	−	0.229658i
$469$		−	4.51288e23i		−	0.411053i
$470$	−2.88334e23	+	7.32555e23i	−0.257641	+	0.654575i
$471$	1.78219e24			1.56231
$472$	−8.12456e23	+	8.12456e23i	−0.698750	+	0.698750i
$473$	−1.35690e23	−	1.35690e23i	−0.114498	−	0.114498i
$474$			3.41316e23i			0.282587i
$475$	2.95981e23	−	3.17744e23i	0.240448	−	0.258128i
$476$	9.86584e23			0.786451
$477$	1.94347e23	−	1.94347e23i	0.152024	−	0.152024i
$478$	2.07513e24	+	2.07513e24i	1.59292	+	1.59292i
$479$		−	8.55245e23i		−	0.644275i	−0.946693	−	0.322137i	$-0.895599\pi$
$479$		−	8.55245e23i		−	0.644275i	0.946693	−	0.322137i	$-0.104401\pi$
$480$	1.41735e24	+	5.57870e23i	1.04787	+	0.412441i
$481$	−1.96629e24			−1.42673
$482$	−2.01727e24	+	2.01727e24i	−1.43662	+	1.43662i
$483$	−3.77114e23	−	3.77114e23i	−0.263602	−	0.263602i
$484$		−	1.25422e23i		−	0.0860529i
$485$	2.73546e23	−	1.19029e23i	0.184228	−	0.0801633i
$486$	−6.72298e23			−0.444463
$487$	1.12269e24	−	1.12269e24i	0.728619	−	0.728619i	−0.241725	−	0.970345i	$-0.577713\pi$
$487$	1.12269e24	−	1.12269e24i	0.728619	−	0.728619i	0.970345	+	0.241725i	$0.0777133\pi$
$488$	1.11195e23	+	1.11195e23i	0.0708448	+	0.0708448i
$489$		−	1.45112e24i		−	0.907663i
$490$	−9.31171e23	−	2.13997e24i	−0.571827	−	1.31415i
$491$	−2.01927e24			−1.21748			−0.608740	−	0.793370i	$-0.708325\pi$
$491$	−2.01927e24			−1.21748			−0.608740	+	0.793370i	$0.708325\pi$
$492$	−3.69505e23	+	3.69505e23i	−0.218743	+	0.218743i
$493$	−1.56730e23	−	1.56730e23i	−0.0911023	−	0.0911023i
$494$			1.50282e24i			0.857757i
$495$	−9.56899e22	+	2.43115e23i	−0.0536314	+	0.136259i
$496$	1.36022e23			0.0748641
$497$	−4.23827e23	+	4.23827e23i	−0.229077	+	0.229077i
$498$	−2.02251e24	−	2.02251e24i	−1.07356	−	1.07356i
$499$			2.71433e24i			1.41501i	0.706711	+	0.707503i	$0.250178\pi$
$499$			2.71433e24i			1.41501i	−0.706711	+	0.707503i	$0.749822\pi$
$500$	2.60243e24	−	1.24387e24i	1.33244	−	0.636862i
$501$	−2.09497e23			−0.105351
$502$	4.22812e24	−	4.22812e24i	2.08840	−	2.08840i
$503$	−1.96856e23	−	1.96856e23i	−0.0955073	−	0.0955073i	0.657739	−	0.753246i	$-0.271513\pi$
$503$	−1.96856e23	−	1.96856e23i	−0.0955073	−	0.0955073i	−0.753246	+	0.657739i	$0.771513\pi$
$504$		−	6.69999e22i		−	0.0319300i
$505$	1.58600e24	+	6.24249e23i	0.742473	+	0.292237i
$506$	4.74079e24			2.18020
$507$	2.01046e24	−	2.01046e24i	0.908287	−	0.908287i
$508$	4.13088e22	+	4.13088e22i	0.0183345	+	0.0183345i
$509$			9.11240e23i			0.397349i	0.980065	+	0.198675i	$0.0636637\pi$
$509$			9.11240e23i			0.397349i	−0.980065	+	0.198675i	$0.936336\pi$
$510$	−5.55738e24	+	2.41819e24i	−2.38088	+	1.03600i
$511$	−1.82715e23			−0.0769105
$512$	−9.94535e23	+	9.94535e23i	−0.411330	+	0.411330i
$513$	6.49358e23	+	6.49358e23i	0.263893	+	0.263893i
$514$		−	1.37980e24i		−	0.550997i
$515$	−3.43693e23	−	7.89858e23i	−0.134867	−	0.309945i
$516$	−5.58272e23			−0.215278
$517$	−8.57998e23	+	8.57998e23i	−0.325141	+	0.325141i
$518$	−8.24843e23	−	8.24843e23i	−0.307187	−	0.307187i
$519$			3.10045e24i			1.13480i
$520$	−1.18042e24	+	2.99904e24i	−0.424626	+	1.07883i
$521$	−1.22287e23			−0.0432357			−0.0216178	−	0.999766i	$-0.506882\pi$
$521$	−1.22287e23			−0.0432357			−0.0216178	+	0.999766i	$0.506882\pi$
$522$	−3.29659e22	+	3.29659e22i	−0.0114559	+	0.0114559i
$523$	3.11493e24	+	3.11493e24i	1.06398	+	1.06398i	0.997808	+	0.0661724i	$0.0210787\pi$
$523$	3.11493e24	+	3.11493e24i	1.06398	+	1.06398i	0.0661724	+	0.997808i	$0.478921\pi$
$524$		−	5.81447e24i		−	1.95222i
$525$	−6.13750e23	−	5.71715e23i	−0.202562	−	0.188689i
$526$	−4.12660e24			−1.33881
$527$	−9.99555e23	+	9.99555e23i	−0.318795	+	0.318795i
$528$	6.35594e23	+	6.35594e23i	0.199285	+	0.199285i
$529$			2.63889e24i			0.813431i
$530$	−7.29859e24	−	2.87272e24i	−2.21185	−	0.870585i
$531$	6.29114e23			0.187447
$532$	−3.75892e23	+	3.75892e23i	−0.110118	+	0.110118i
$533$	8.57875e23	+	8.57875e23i	0.247104	+	0.247104i
$534$			3.57415e24i			1.01228i
$535$	−2.60153e24	+	1.13201e24i	−0.724510	+	0.315258i
$536$	3.76812e24			1.03191
$537$	3.67010e24	−	3.67010e24i	0.988347	−	0.988347i
$538$	−6.97075e23	−	6.97075e23i	−0.184603	−	0.184603i
$539$		−	3.59705e24i		−	0.936802i
$540$	2.43384e24	+	5.59335e24i	0.623374	+	1.43261i
$541$	1.41207e24			0.355698			0.177849	−	0.984058i	$-0.443086\pi$
$541$	1.41207e24			0.355698			0.177849	+	0.984058i	$0.443086\pi$
$542$	−2.67924e24	+	2.67924e24i	−0.663771	+	0.663771i
$543$	−4.55971e23	−	4.55971e23i	−0.111106	−	0.111106i
$544$		−	9.03867e24i		−	2.16628i
$545$	1.64992e24	−	4.19188e24i	0.388951	−	0.988189i
$546$	2.90283e24			0.673112
$547$	−1.58515e24	+	1.58515e24i	−0.361564	+	0.361564i	−0.864388	−	0.502825i	$-0.832294\pi$
$547$	−1.58515e24	+	1.58515e24i	−0.361564	+	0.361564i	0.502825	+	0.864388i	$0.332294\pi$
$548$	5.09336e24	+	5.09336e24i	1.14283	+	1.14283i
$549$		−	8.61025e22i		−	0.0190049i
$550$	7.45138e24	−	2.64219e23i	1.61798	−	0.0573720i
$551$	1.19429e23			0.0255121
$552$	3.14879e24	−	3.14879e24i	0.661747	−	0.661747i
$553$	1.98206e23	+	1.98206e23i	0.0409817	+	0.0409817i
$554$		−	4.68319e24i		−	0.952695i
$555$	3.97587e24	+	1.56490e24i	0.795784	+	0.313220i
$556$	−1.14528e25			−2.25548
$557$	4.44848e24	−	4.44848e24i	0.862015	−	0.862015i	−0.129557	−	0.991572i	$-0.541356\pi$
$557$	4.44848e24	−	4.44848e24i	0.862015	−	0.862015i	0.991572	+	0.129557i	$0.0413556\pi$
$558$	2.10243e23	+	2.10243e23i	0.0400879	+	0.0400879i
$559$			1.29613e24i			0.243189i
$560$	4.39168e23	−	1.91096e23i	0.0810846	−	0.0352825i
$561$	−9.34131e24			−1.69724
$562$	−4.49431e24	+	4.49431e24i	−0.803593	+	0.803593i
$563$	−4.44995e24	−	4.44995e24i	−0.783032	−	0.783032i	0.197309	−	0.980341i	$-0.436780\pi$
$563$	−4.44995e24	−	4.44995e24i	−0.783032	−	0.783032i	−0.980341	+	0.197309i	$0.936780\pi$
$564$			3.53008e24i			0.611325i
$565$	−8.23179e23	−	1.89179e24i	−0.140300	−	0.322431i
$566$	7.59942e24			1.27477
$567$	1.07206e24	−	1.07206e24i	0.176999	−	0.176999i
$568$	−3.53883e24	−	3.53883e24i	−0.575075	−	0.575075i
$569$			4.87656e24i			0.780015i	0.920812	+	0.390007i	$0.127528\pi$
$569$			4.87656e24i			0.780015i	−0.920812	+	0.390007i	$0.872472\pi$
$570$	1.19604e24	−	3.03872e24i	0.188309	−	0.478428i
$571$	−9.08320e24			−1.40771			−0.703856	−	0.710342i	$-0.748540\pi$
$571$	−9.08320e24			−1.40771			−0.703856	+	0.710342i	$0.748540\pi$
$572$	−1.08793e25	+	1.08793e25i	−1.65973	+	1.65973i
$573$	−8.99639e22	−	8.99639e22i	−0.0135107	−	0.0135107i
$574$			7.19742e23i			0.106407i
$575$	3.27881e23	+	9.24673e24i	0.0477205	+	1.34579i
$576$	−1.60727e24			−0.230296
$577$	7.34011e24	−	7.34011e24i	1.03543	−	1.03543i	0.0360795	−	0.999349i	$-0.488513\pi$
$577$	7.34011e24	−	7.34011e24i	1.03543	−	1.03543i	0.999349	−	0.0360795i	$-0.0114869\pi$
$578$	1.74179e25	+	1.74179e25i	2.41906	+	2.41906i
$579$		−	1.34212e24i		−	0.183520i
$580$	7.38175e23	+	2.90546e23i	0.0993820	+	0.0391167i
$581$	−2.34898e24			−0.311382
$582$	1.58636e24	−	1.58636e24i	0.207060	−	0.207060i
$583$	−8.54841e24	−	8.54841e24i	−1.09867	−	1.09867i
$584$		−	1.52562e24i		−	0.193077i
$585$	1.61815e24	−	7.04111e23i	0.201659	−	0.0877482i
$586$	2.50571e25			3.07505
$587$	−6.08464e24	+	6.08464e24i	−0.735346	+	0.735346i	−0.971674	−	0.236327i	$-0.924056\pi$
$587$	−6.08464e24	+	6.08464e24i	−0.735346	+	0.735346i	0.236327	+	0.971674i	$0.424056\pi$
$588$	−7.39970e24	−	7.39970e24i	−0.880680	−	0.880680i
$589$		−	7.61667e23i		−	0.0892745i
$590$	−7.16341e24	−	1.64626e25i	−0.826897	−	1.90034i
$591$	8.27508e24			0.940773
$592$	−1.72516e24	+	1.72516e24i	−0.193168	+	0.193168i
$593$	2.75687e24	+	2.75687e24i	0.304036	+	0.304036i	0.842590	−	0.538555i	$-0.181030\pi$
$593$	2.75687e24	+	2.75687e24i	0.304036	+	0.304036i	−0.538555	+	0.842590i	$0.681030\pi$
$594$			1.57680e25i			1.71277i
$595$	−1.82296e24	+	4.63149e24i	−0.195040	+	0.495528i
$596$	−7.87825e24			−0.830258
$597$	−2.75831e24	+	2.75831e24i	−0.286335	+	0.286335i
$598$	−2.26423e25	−	2.26423e25i	−2.31532	−	2.31532i
$599$			4.64294e24i			0.467683i	0.972275	+	0.233841i	$0.0751296\pi$
$599$			4.64294e24i			0.467683i	−0.972275	+	0.233841i	$0.924870\pi$
$600$	4.77365e24	−	5.12464e24i	0.473685	−	0.508513i
$601$	1.10374e25			1.07894			0.539470	−	0.842005i	$-0.318624\pi$
$601$	1.10374e25			1.07894			0.539470	+	0.842005i	$0.318624\pi$
$602$	−5.43716e23	+	5.43716e23i	−0.0523605	+	0.0523605i
$603$	−1.45890e24	−	1.45890e24i	−0.138410	−	0.138410i
$604$		−	1.12895e24i		−	0.105522i
$605$	5.88790e23	+	2.31748e23i	0.0542203	+	0.0213411i
$606$	1.28178e25			1.16295
$607$	−1.54308e24	+	1.54308e24i	−0.137940	+	0.137940i	−0.772705	−	0.634765i	$-0.781097\pi$
$607$	−1.54308e24	+	1.54308e24i	−0.137940	+	0.137940i	0.634765	+	0.772705i	$0.281097\pi$
$608$	3.44376e24	+	3.44376e24i	0.303320	+	0.303320i
$609$		−	2.30688e23i		−	0.0200202i
$610$	−2.25312e24	+	9.80407e23i	−0.192671	+	0.0838374i
$611$	8.19572e24			0.690584
$612$	3.18937e24	−	3.18937e24i	0.264815	−	0.264815i
$613$	−3.91302e24	−	3.91302e24i	−0.320161	−	0.320161i	0.528668	−	0.848829i	$-0.322692\pi$
$613$	−3.91302e24	−	3.91302e24i	−0.320161	−	0.320161i	−0.848829	+	0.528668i	$0.822692\pi$
$614$			1.06556e25i			0.859137i
$615$	−1.05188e24	−	2.41738e24i	−0.0835778	−	0.192074i
$616$	−2.94701e24			−0.230757
$617$	1.03729e25	−	1.03729e25i	0.800453	−	0.800453i	−0.182713	−	0.983166i	$-0.558488\pi$
$617$	1.03729e25	−	1.03729e25i	0.800453	−	0.800453i	0.983166	+	0.182713i	$0.0584880\pi$
$618$	−4.58060e24	−	4.58060e24i	−0.348358	−	0.348358i
$619$			6.70656e24i			0.502671i	0.967900	+	0.251336i	$0.0808698\pi$
$619$			6.70656e24i			0.502671i	−0.967900	+	0.251336i	$0.919130\pi$
$620$	1.85298e24	−	4.70776e24i	0.136881	−	0.347768i
$621$	−1.95672e25			−1.42464
$622$	1.25789e25	−	1.25789e25i	0.902673	−	0.902673i
$623$	2.07554e24	+	2.07554e24i	0.146805	+	0.146805i
$624$		−	6.07128e24i		−	0.423271i
$625$	1.03070e24	+	1.45154e25i	0.0708291	+	0.997488i
$626$	−1.66390e25			−1.12709
$627$	3.55907e24	−	3.55907e24i	0.237645	−	0.237645i
$628$	2.67645e25	+	2.67645e25i	1.76166	+	1.76166i
$629$		−	2.53547e25i		−	1.64514i
$630$	9.74170e23	+	3.83433e23i	0.0623117	+	0.0245259i
$631$	4.78292e24			0.301598			0.150799	−	0.988564i	$-0.451815\pi$
$631$	4.78292e24			0.301598			0.150799	+	0.988564i	$0.451815\pi$
$632$	−1.65496e24	+	1.65496e24i	−0.102881	+	0.102881i
$633$	−2.36878e23	−	2.36878e23i	−0.0145175	−	0.0145175i
$634$			2.87986e25i			1.74008i
$635$	−2.70251e23	+	1.17595e23i	−0.0160992	+	0.00700527i
$636$	−3.51708e25			−2.06571
$637$	−1.71798e25	+	1.71798e25i	−0.994861	+	0.994861i
$638$	1.45002e24	+	1.45002e24i	0.0827917	+	0.0827917i
$639$			2.74024e24i			0.154270i
$640$	9.56114e24	+	2.19730e25i	0.530750	+	1.21974i
$641$	2.18242e25			1.19458			0.597291	−	0.802024i	$-0.296244\pi$
$641$	2.18242e25			1.19458			0.597291	+	0.802024i	$0.296244\pi$
$642$	−1.50869e25	+	1.50869e25i	−0.814303	+	0.814303i
$643$	−1.27768e25	−	1.27768e25i	−0.680025	−	0.680025i	0.279981	−	0.960006i	$-0.409672\pi$
$643$	−1.27768e25	−	1.27768e25i	−0.680025	−	0.680025i	−0.960006	+	0.279981i	$0.909672\pi$
$644$		−	1.13268e25i		−	0.594476i
$645$	1.03154e24	−	2.62079e24i	0.0533889	−	0.135642i
$646$	−1.93784e25			−0.989064
$647$	−1.68925e25	+	1.68925e25i	−0.850267	+	0.850267i	−0.990166	−	0.139899i	$-0.955322\pi$
$647$	−1.68925e25	+	1.68925e25i	−0.850267	+	0.850267i	0.139899	+	0.990166i	$0.455322\pi$
$648$	8.95138e24	+	8.95138e24i	0.444339	+	0.444339i
$649$		−	2.76718e25i		−	1.35467i
$650$	−3.68502e25	−	3.43264e25i	−1.77918	−	1.65732i
$651$	−1.47123e24			−0.0700569
$652$	2.17926e25	−	2.17926e25i	1.02348	−	1.02348i
$653$	1.20098e25	+	1.20098e25i	0.556308	+	0.556308i	0.928254	−	0.371946i	$-0.121309\pi$
$653$	1.20098e25	+	1.20098e25i	0.556308	+	0.556308i	−0.371946	+	0.928254i	$0.621309\pi$
$654$		−	3.38781e25i		−	1.54782i
$655$	2.72959e25	+	1.07437e25i	1.23006	+	0.484150i
$656$	1.50534e24			0.0669116
$657$	−5.90670e23	+	5.90670e23i	−0.0258974	+	0.0258974i
$658$	3.43803e24	+	3.43803e24i	0.148688	+	0.148688i
$659$		−	1.99651e25i		−	0.851730i	−0.904787	−	0.425865i	$-0.859970\pi$
$659$		−	1.99651e25i		−	0.851730i	0.904787	−	0.425865i	$-0.140030\pi$
$660$	3.06566e25	−	1.33397e25i	1.29012	−	0.561371i
$661$	2.35079e25			0.975890			0.487945	−	0.872874i	$-0.337747\pi$
$661$	2.35079e25			0.975890			0.487945	+	0.872874i	$0.337747\pi$
$662$	8.94526e24	−	8.94526e24i	0.366329	−	0.366329i
$663$	4.46148e25	+	4.46148e25i	1.80242	+	1.80242i
$664$		−	1.96133e25i		−	0.781696i
$665$	−1.07006e24	−	2.45916e24i	−0.0420740	−	0.0966925i
$666$	−5.33301e24			−0.206873
$667$	−1.79939e24	+	1.79939e24i	−0.0688640	+	0.0688640i
$668$	−3.14618e24	−	3.14618e24i	−0.118794	−	0.118794i
$669$			2.50307e25i			0.932475i
$670$	−2.15646e25	+	5.47880e25i	−0.792624	+	2.01378i
$671$	−3.78724e24			−0.137347
$672$	6.65193e24	−	6.65193e24i	0.238026	−	0.238026i
$673$	−1.52382e25	−	1.52382e25i	−0.538019	−	0.538019i	0.384928	−	0.922947i	$-0.374226\pi$
$673$	−1.52382e25	−	1.52382e25i	−0.538019	−	0.538019i	−0.922947	+	0.384928i	$0.874226\pi$
$674$		−	1.55957e25i		−	0.543333i
$675$	−3.07549e25	+	1.09054e24i	−1.05726	+	0.0374894i
$676$	6.03850e25			2.04837
$677$	1.23882e25	−	1.23882e25i	0.414678	−	0.414678i	−0.468686	−	0.883365i	$-0.655273\pi$
$677$	1.23882e25	−	1.23882e25i	0.414678	−	0.414678i	0.883365	+	0.468686i	$0.155273\pi$
$678$	−1.09710e25	−	1.09710e25i	−0.362392	−	0.362392i
$679$		−	1.84243e24i		−	0.0600571i
$680$	−3.86716e25	−	1.52212e25i	−1.24398	−	0.489629i
$681$	−5.00273e25			−1.58812
$682$	9.24758e24	−	9.24758e24i	0.289713	−	0.289713i
$683$	−3.43685e25	−	3.43685e25i	−1.06261	−	1.06261i	−0.997904	−	0.0647055i	$-0.979389\pi$
$683$	−3.43685e25	−	3.43685e25i	−1.06261	−	1.06261i	−0.0647055	−	0.997904i	$-0.520611\pi$
$684$			2.43032e24i			0.0741581i
$685$	−3.33219e25	+	1.44994e25i	−1.00349	+	0.436652i
$686$	−3.02413e25			−0.898843
$687$	2.47766e25	−	2.47766e25i	0.726827	−	0.726827i
$688$	1.13719e24	+	1.13719e24i	0.0329257	+	0.0329257i
$689$			8.16556e25i			2.33353i
$690$	2.77628e25	+	6.38032e25i	0.783109	+	1.79970i
$691$	5.33756e24			0.148607			0.0743037	−	0.997236i	$-0.476327\pi$
$691$	5.33756e24			0.148607			0.0743037	+	0.997236i	$0.476327\pi$
$692$	−4.65618e25	+	4.65618e25i	−1.27960	+	1.27960i
$693$	1.14099e24	+	1.14099e24i	0.0309515	+	0.0309515i
$694$			1.88468e25i			0.504664i
$695$	2.11619e25	−	5.37649e25i	0.559359	−	1.42114i
$696$	1.92618e24			0.0502589
$697$	−1.10620e25	+	1.10620e25i	−0.284931	+	0.284931i
$698$	2.60248e25	+	2.60248e25i	0.661741	+	0.661741i
$699$		−	9.85882e24i		−	0.247474i
$700$	−6.31278e23	−	1.78030e25i	−0.0156437	−	0.441175i
$701$	2.67330e25			0.654011			0.327005	−	0.945023i	$-0.393961\pi$
$701$	2.67330e25			0.654011			0.327005	+	0.945023i	$0.393961\pi$
$702$	7.53091e25	−	7.53091e25i	1.81892	−	1.81892i
$703$	9.66022e24	+	9.66022e24i	0.230350	+	0.230350i
$704$			7.06963e25i			1.66434i
$705$	−1.65718e25	−	6.52268e24i	−0.385184	−	0.151609i
$706$	−2.53680e25			−0.582163
$707$	7.44343e24	−	7.44343e24i	0.168655	−	0.168655i
$708$	−5.69252e25	−	5.69252e25i	−1.27352	−	1.27352i
$709$		−	1.61053e25i		−	0.355757i	−0.984052	−	0.177878i	$-0.943077\pi$
$709$		−	1.61053e25i		−	0.355757i	0.984052	−	0.177878i	$-0.0569233\pi$
$710$	7.17065e25	−	3.12018e25i	1.56399	−	0.680541i
$711$	1.28149e24			0.0275988
$712$	−1.73302e25	+	1.73302e25i	−0.368539	+	0.368539i
$713$	1.14757e25	+	1.14757e25i	0.240976	+	0.240976i
$714$			3.74310e25i			0.776154i
$715$	−3.09705e25	−	7.11749e25i	−0.634153	−	1.45738i
$716$	1.10233e26			2.22892
$717$	−4.69436e25	+	4.69436e25i	−0.937354	+	0.937354i
$718$	−8.09308e24	−	8.09308e24i	−0.159586	−	0.159586i
$719$		−	1.82683e25i		−	0.355745i	−0.984054	−	0.177872i	$-0.943079\pi$
$719$		−	1.82683e25i		−	0.355745i	0.984054	−	0.177872i	$-0.0569214\pi$
$720$	8.01953e23	−	2.03748e24i	0.0154226	−	0.0391833i
$721$	−5.31999e24			−0.101040
$722$	−5.19458e25	+	5.19458e25i	−0.974351	+	0.974351i
$723$	−4.56347e25	−	4.56347e25i	−0.845377	−	0.845377i
$724$		−	1.36953e25i		−	0.250567i
$725$	−2.72792e24	+	2.92849e24i	−0.0492935	+	0.0529178i
$726$	4.75851e24			0.0849262
$727$	4.95733e25	−	4.95733e25i	0.873852	−	0.873852i	−0.119037	−	0.992890i	$-0.537981\pi$
$727$	4.95733e25	−	4.95733e25i	0.873852	−	0.873852i	0.992890	+	0.119037i	$0.0379809\pi$
$728$	1.40751e25	+	1.40751e25i	0.245058	+	0.245058i
$729$		−	6.39029e25i		−	1.09894i
$730$	2.21823e25	+	8.73094e24i	0.376791	+	0.148305i
$731$	−1.67132e25			−0.280416
$732$	−7.79096e24	+	7.79096e24i	−0.129119	+	0.129119i
$733$	3.23091e25	+	3.23091e25i	0.528919	+	0.528919i	0.920250	−	0.391331i	$-0.127985\pi$
$733$	3.23091e25	+	3.23091e25i	0.528919	+	0.528919i	−0.391331	+	0.920250i	$0.627985\pi$
$734$		−	7.80592e25i		−	1.26229i
$735$	4.84104e25	−	2.10649e25i	0.773309	−	0.336491i
$736$	−1.03771e26			−1.63748
$737$	−6.41700e25	+	6.41700e25i	−1.00029	+	1.00029i
$738$	2.32674e24	+	2.32674e24i	0.0358295	+	0.0358295i
$739$			3.22294e25i			0.490289i	0.969486	+	0.245145i	$0.0788355\pi$
$739$			3.22294e25i			0.490289i	−0.969486	+	0.245145i	$0.921165\pi$
$740$	3.62073e25	+	8.32098e25i	0.544139	+	1.25052i
$741$	−3.39967e25			−0.504746
$742$	−3.42538e25	+	3.42538e25i	−0.502428	+	0.502428i
$743$	7.85608e25	+	7.85608e25i	1.13843	+	1.13843i	0.988732	+	0.149699i	$0.0478305\pi$
$743$	7.85608e25	+	7.85608e25i	1.13843	+	1.13843i	0.149699	+	0.988732i	$0.452169\pi$
$744$		−	1.22843e25i		−	0.175871i
$745$	1.45570e25	−	3.69842e25i	0.205904	−	0.523130i
$746$	7.07563e25			0.988817
$747$	−7.59364e24	+	7.59364e24i	−0.104849	+	0.104849i
$748$	−1.40285e26	−	1.40285e26i	−1.91381	−	1.91381i
$749$			1.75223e25i			0.236186i
$750$	4.71925e25	+	9.87361e25i	0.628523	+	1.31500i
$751$	7.19429e25			0.946736			0.473368	−	0.880865i	$-0.343038\pi$
$751$	7.19429e25			0.946736			0.473368	+	0.880865i	$0.343038\pi$
$752$	7.19067e24	−	7.19067e24i	0.0934993	−	0.0934993i
$753$	9.56484e25	+	9.56484e25i	1.22892	+	1.22892i
$754$		−	1.38508e25i		−	0.175846i
$755$	5.29982e24	+	2.08601e24i	0.0664873	+	0.0261694i
$756$	3.76733e25			0.467022
$757$	4.64384e25	−	4.64384e25i	0.568871	−	0.568871i	−0.362941	−	0.931812i	$-0.618227\pi$
$757$	4.64384e25	−	4.64384e25i	0.568871	−	0.568871i	0.931812	+	0.362941i	$0.118227\pi$
$758$	−1.49822e26	−	1.49822e26i	−1.81365	−	1.81365i
$759$			1.07246e26i			1.28294i
$760$	2.05333e25	−	8.93470e24i	0.242737	−	0.105623i
$761$	−4.53072e25			−0.529305			−0.264652	−	0.964344i	$-0.585257\pi$
$761$	−4.53072e25			−0.529305			−0.264652	+	0.964344i	$0.585257\pi$
$762$	−1.56726e24	+	1.56726e24i	−0.0180945	+	0.0180945i
$763$	−1.96734e25	−	1.96734e25i	−0.224470	−	0.224470i
$764$		−	2.70211e24i		−	0.0304693i
$765$	9.07928e24	+	2.08656e25i	0.101181	+	0.232529i
$766$	−2.44527e26			−2.69319
$767$	−1.32162e26	+	1.32162e26i	−1.43863	+	1.43863i
$768$	2.89495e25	+	2.89495e25i	0.311451	+	0.311451i
$769$		−	4.99098e25i		−	0.530699i	−0.964152	−	0.265350i	$-0.914513\pi$
$769$		−	4.99098e25i		−	0.530699i	0.964152	−	0.265350i	$-0.0854874\pi$
$770$	1.68654e25	−	4.28491e25i	0.177248	−	0.450324i
$771$	3.12139e25			0.324234
$772$	2.01556e25	−	2.01556e25i	0.206938	−	0.206938i
$773$	−4.82147e25	−	4.82147e25i	−0.489287	−	0.489287i	0.418794	−	0.908081i	$-0.362453\pi$
$773$	−4.82147e25	−	4.82147e25i	−0.489287	−	0.489287i	−0.908081	+	0.418794i	$0.862453\pi$
$774$			3.51539e24i			0.0352618i
$775$	1.86766e25	+	1.73975e25i	0.185175	+	0.172493i
$776$	1.53838e25			0.150768
$777$	1.86596e25	−	1.86596e25i	0.180764	−	0.180764i
$778$	1.62224e26	+	1.62224e26i	1.55346	+	1.55346i
$779$		−	8.42932e24i		−	0.0797913i
$780$	−2.10129e26	−	8.27069e25i	−1.96623	−	0.773909i
$781$	1.20530e26			1.11490
$782$	2.91965e26	−	2.91965e26i	2.66975	−	2.66975i
$783$	−5.98482e24	−	5.98482e24i	−0.0540997	−	0.0540997i
$784$			3.01460e25i			0.269392i
$785$	−1.75099e26	+	7.61912e25i	−1.54688	+	0.673097i
$786$	2.20601e26			1.92666
$787$	9.23789e24	−	9.23789e24i	0.0797627	−	0.0797627i	−0.666100	−	0.745863i	$-0.732038\pi$
$787$	9.23789e24	−	9.23789e24i	0.0797627	−	0.0797627i	0.745863	+	0.666100i	$0.232038\pi$
$788$	1.24273e26	+	1.24273e26i	1.06082	+	1.06082i
$789$		−	9.33518e25i		−	0.787824i
$790$	−1.45917e25	−	3.35340e25i	−0.121748	−	0.279796i
$791$	−1.27419e25			−0.105111
$792$	−9.52692e24	+	9.52692e24i	−0.0777009	+	0.0777009i
$793$	1.80881e25	+	1.80881e25i	0.145860	+	0.145860i
$794$		−	1.32582e26i		−	1.05706i
$795$	6.49867e25	−	1.65108e26i	0.512295	−	1.30156i
$796$	−8.28471e25			−0.645743
$797$	1.04860e26	−	1.04860e26i	0.808136	−	0.808136i	−0.176215	−	0.984352i	$-0.556386\pi$
$797$	1.04860e26	−	1.04860e26i	0.808136	−	0.808136i	0.984352	+	0.176215i	$0.0563855\pi$
$798$	−1.42613e25	−	1.42613e25i	−0.108676	−	0.108676i
$799$			1.05681e26i			0.796299i
$800$	−1.63104e26	+	5.78351e24i	−1.21522	+	0.0430905i
$801$	1.34194e25			0.0988645
$802$	−1.27782e26	+	1.27782e26i	−0.930898	+	0.930898i
$803$	2.59808e25	+	2.59808e25i	0.187160	+	0.187160i
$804$			2.64015e26i			1.88072i
$805$	5.31733e25	+	2.09290e25i	0.374568	+	0.147430i
$806$	−8.83341e25			−0.615337
$807$	1.57692e25	−	1.57692e25i	0.108630	−	0.108630i
$808$	6.21505e25	+	6.21505e25i	0.423392	+	0.423392i
$809$		−	1.93948e26i		−	1.30662i	−0.757091	−	0.653309i	$-0.773380\pi$
$809$		−	1.93948e26i		−	1.30662i	0.757091	−	0.653309i	$-0.226620\pi$
$810$	−1.81380e26	+	7.89241e25i	−1.20844	+	0.525829i
$811$	−2.67326e26			−1.76138			−0.880692	−	0.473690i	$-0.842922\pi$
$811$	−2.67326e26			−1.76138			−0.880692	+	0.473690i	$0.842922\pi$
$812$	3.46441e24	−	3.46441e24i	0.0225749	−	0.0225749i
$813$	−6.06097e25	−	6.06097e25i	−0.390596	−	0.390596i
$814$			2.34574e26i			1.49506i
$815$	6.20376e25	+	1.42572e26i	0.391054	+	0.898701i
$816$	7.82872e25			0.488067
$817$	6.36778e24	−	6.36778e24i	0.0392636	−	0.0392636i
$818$	5.87606e25	+	5.87606e25i	0.358349	+	0.358349i
$819$		−	1.08989e25i		−	0.0657395i
$820$	2.05068e25	−	5.21005e25i	0.122341	−	0.310826i
$821$	1.30779e25			0.0771699			0.0385850	−	0.999255i	$-0.487715\pi$
$821$	1.30779e25			0.0771699			0.0385850	+	0.999255i	$0.487715\pi$
$822$	−1.93242e26	+	1.93242e26i	−1.12786	+	1.12786i
$823$	−1.24725e26	−	1.24725e26i	−0.720039	−	0.720039i	0.248574	−	0.968613i	$-0.420038\pi$
$823$	−1.24725e26	−	1.24725e26i	−0.720039	−	0.720039i	−0.968613	+	0.248574i	$0.920038\pi$
$824$		−	4.44204e25i		−	0.253652i
$825$	5.97716e24	+	1.68565e26i	0.0337605	+	0.952098i
$826$	−1.10882e26			−0.619498
$827$	−3.47068e25	+	3.47068e25i	−0.191807	+	0.191807i	−0.796477	−	0.604669i	$-0.793305\pi$
$827$	−3.47068e25	+	3.47068e25i	−0.191807	+	0.191807i	0.604669	+	0.796477i	$0.293305\pi$
$828$	−3.66166e25	−	3.66166e25i	−0.200173	−	0.200173i
$829$		−	1.09345e26i		−	0.591301i	−0.955296	−	0.295651i	$-0.904464\pi$
$829$		−	1.09345e26i		−	0.591301i	0.955296	−	0.295651i	$-0.0955365\pi$
$830$	2.85175e26	+	1.12245e26i	1.52549	+	0.600431i
$831$	1.05943e26			0.560613
$832$	3.37650e26	−	3.37650e26i	1.76749	−	1.76749i
$833$	−2.21527e26	−	2.21527e26i	−1.14716	−	1.14716i
$834$		−	4.34520e26i		−	2.22595i
$835$	2.05830e25	−	8.95631e24i	0.104311	−	0.0453890i
$836$	1.06898e26			0.535938
$837$	−3.81686e25	+	3.81686e25i	−0.189311	+	0.189311i
$838$	3.26446e26	+	3.26446e26i	1.60183	+	1.60183i
$839$		−	9.50222e25i		−	0.461283i	−0.973039	−	0.230642i	$-0.925918\pi$
$839$		−	9.50222e25i		−	0.461283i	0.973039	−	0.230642i	$-0.0740825\pi$
$840$	−1.72582e25	−	3.96619e25i	−0.0828860	−	0.190485i
$841$	2.09357e26			0.994770
$842$	−2.07214e26	+	2.07214e26i	−0.974114	+	0.974114i
$843$	−1.01670e26	−	1.01670e26i	−0.472874	−	0.472874i
$844$		−	7.11474e24i		−	0.0327399i
$845$	−1.11576e26	+	2.83476e26i	−0.507996	+	1.29064i
$846$	2.22286e25			0.100133
$847$	2.76332e24	−	2.76332e24i	0.0123163	−	0.0123163i
$848$	7.16420e25	+	7.16420e25i	0.315940	+	0.315940i
$849$			1.71914e26i			0.750139i
$850$	4.42627e26	−	4.75172e26i	1.91103	−	2.05154i
$851$	−2.91093e26			−1.24356
$852$	2.47950e26	−	2.47950e26i	1.04811	−	1.04811i
$853$	2.95714e26	+	2.95714e26i	1.23689	+	1.23689i	0.961265	+	0.275625i	$0.0888848\pi$
$853$	2.95714e26	+	2.95714e26i	1.23689	+	1.23689i	0.275625	+	0.961265i	$0.411115\pi$
$854$			1.51756e25i			0.0628096i
$855$	−1.14091e25	−	4.49061e24i	−0.0467257	−	0.0183912i
$856$	−1.46306e26			−0.592922
$857$	−7.44674e24	+	7.44674e24i	−0.0298634	+	0.0298634i	−0.721881	−	0.692017i	$-0.756722\pi$
$857$	−7.44674e24	+	7.44674e24i	−0.0298634	+	0.0298634i	0.692017	+	0.721881i	$0.256722\pi$
$858$	−4.12762e26	−	4.12762e26i	−1.63800	−	1.63800i
$859$		−	7.19881e25i		−	0.282698i	−0.989960	−	0.141349i	$-0.954856\pi$
$859$		−	7.19881e25i		−	0.282698i	0.989960	−	0.141349i	$-0.0451439\pi$
$860$	5.48499e25	−	2.38669e25i	0.213152	−	0.0927493i
$861$	−1.62820e25			−0.0626151
$862$	−5.79302e26	+	5.79302e26i	−2.20465	+	2.20465i
$863$	1.29225e26	+	1.29225e26i	0.486688	+	0.486688i	0.907260	−	0.420571i	$-0.138170\pi$
$863$	1.29225e26	+	1.29225e26i	0.486688	+	0.486688i	−0.420571	+	0.907260i	$0.638170\pi$
$864$		−	3.45147e26i		−	1.28641i
$865$	−1.32549e26	−	3.04617e26i	−0.488912	−	1.12359i
$866$	−4.45409e26			−1.62592
$867$	−3.94028e26	+	3.94028e26i	−1.42349	+	1.42349i
$868$	−2.20945e25	−	2.20945e25i	−0.0789964	−	0.0789964i
$869$		−	5.63669e25i		−	0.199456i
$870$	−1.10233e25	+	2.80064e25i	−0.0386046	+	0.0980807i
$871$	6.12960e26			2.12456
$872$	1.64267e26	−	1.64267e26i	0.563510	−	0.563510i
$873$	−5.95612e24	−	5.95612e24i	−0.0202225	−	0.0202225i
$874$			2.22479e26i			0.747630i
$875$	8.47421e25	+	2.99319e25i	0.281856	+	0.0995546i
$876$	1.06893e26			0.351895
$877$	2.96815e26	−	2.96815e26i	0.967141	−	0.967141i	−0.0323365	−	0.999477i	$-0.510295\pi$
$877$	2.96815e26	−	2.96815e26i	0.967141	−	0.967141i	0.999477	+	0.0323365i	$0.0102948\pi$
$878$	−1.18899e26	−	1.18899e26i	−0.383466	−	0.383466i
$879$			5.66842e26i			1.80951i
$880$	−8.96192e25	−	3.52741e25i	−0.283176	−	0.111458i
$881$	3.08785e26			0.965770			0.482885	−	0.875684i	$-0.339589\pi$
$881$	3.08785e26			0.965770			0.482885	+	0.875684i	$0.339589\pi$
$882$	−4.65952e25	+	4.65952e25i	−0.144253	+	0.144253i
$883$	−3.96547e26	−	3.96547e26i	−1.21520	−	1.21520i	−0.969293	−	0.245910i	$-0.920913\pi$
$883$	−3.96547e26	−	3.96547e26i	−1.21520	−	1.21520i	−0.245910	−	0.969293i	$-0.579087\pi$
$884$			1.34003e27i			4.06483i
$885$	3.72417e26	−	1.62050e26i	1.11825	−	0.486587i
$886$	4.08910e26			1.21541
$887$	1.11601e26	−	1.11601e26i	0.328365	−	0.328365i	−0.523599	−	0.851965i	$-0.675411\pi$
$887$	1.11601e26	−	1.11601e26i	0.328365	−	0.328365i	0.851965	+	0.523599i	$0.175411\pi$
$888$	1.55802e26	+	1.55802e26i	0.453792	+	0.453792i
$889$			1.82024e24i			0.00524824i
$890$	−1.52800e26	−	3.51158e26i	−0.436127	−	1.00229i
$891$	−3.04878e26			−0.861444
$892$	−3.75904e26	+	3.75904e26i	−1.05146	+	1.05146i
$893$	−4.02648e25	−	4.02648e25i	−0.111497	−	0.111497i
$894$		−	2.98901e26i		−	0.819388i
$895$	−2.03683e26	+	5.17487e26i	−0.552773	+	1.40440i
$896$	1.47996e26			0.397629
$897$	5.12214e26	−	5.12214e26i	1.36245	−	1.36245i
$898$	−1.69428e26	−	1.69428e26i	−0.446169	−	0.446169i
$899$			7.01992e24i			0.0183018i
$900$	−5.95933e25	−	5.55118e25i	−0.153821	−	0.143286i
$901$	−1.05292e27			−2.69075
$902$	1.02342e26	−	1.02342e26i	0.258938	−	0.258938i
$903$	−1.22999e25	−	1.22999e25i	−0.0308115	−	0.0308115i
$904$		−	1.06391e26i		−	0.263870i
$905$	6.42922e25	+	2.53054e25i	0.157878	+	0.0621407i
$906$	4.28324e25			0.104140
$907$	3.17067e26	−	3.17067e26i	0.763282	−	0.763282i	−0.213632	−	0.976914i	$-0.568529\pi$
$907$	3.17067e26	−	3.17067e26i	0.763282	−	0.763282i	0.976914	+	0.213632i	$0.0685295\pi$
$908$	−7.51297e26	−	7.51297e26i	−1.79077	−	1.79077i
$909$		−	4.81254e25i		−	0.113579i
$910$	−2.85201e26	+	1.24100e26i	−0.666466	+	0.290001i
$911$	5.48540e26			1.26924			0.634619	−	0.772825i	$-0.281157\pi$
$911$	5.48540e26			1.26924			0.634619	+	0.772825i	$0.281157\pi$
$912$	−2.98277e25	+	2.98277e25i	−0.0683385	+	0.0683385i
$913$	3.34008e26	+	3.34008e26i	0.757740	+	0.757740i
$914$		−	9.48810e26i		−	2.13139i
$915$	−2.21787e25	−	5.09701e25i	−0.0493341	−	0.113377i
$916$	7.44177e26			1.63914
$917$	1.28105e26	−	1.28105e26i	0.279411	−	0.279411i
$918$	9.71086e26	+	9.71086e26i	2.09736	+	2.09736i
$919$			8.69537e26i			1.85972i	0.367908	+	0.929862i	$0.380074\pi$
$919$			8.69537e26i			1.85972i	−0.367908	+	0.929862i	$0.619926\pi$
$920$	−1.74751e26	+	4.43982e26i	−0.370109	+	0.940318i
$921$	−2.41051e26			−0.505559
$922$	−9.27563e24	+	9.27563e24i	−0.0192648	+	0.0192648i
$923$	−5.75662e26	−	5.75662e26i	−1.18400	−	1.18400i
$924$		−	2.06484e26i		−	0.420570i
$925$	−4.57528e26	+	1.62235e25i	−0.922873	+	0.0327242i
$926$	1.92405e26			0.384343
$927$	−1.71982e25	+	1.71982e25i	−0.0340224	+	0.0340224i
$928$	−3.17395e25	−	3.17395e25i	−0.0621825	−	0.0621825i
$929$		−	4.53737e25i		−	0.0880365i	−0.999031	−	0.0440182i	$-0.985984\pi$
$929$		−	4.53737e25i		−	0.0880365i	0.999031	−	0.0440182i	$-0.0140160\pi$
$930$	1.78613e26	+	7.03019e25i	0.343215	+	0.135089i
$931$	1.68805e26			0.321247
$932$	1.48057e26	−	1.48057e26i	0.279053	−	0.279053i
$933$	2.84560e26	+	2.84560e26i	0.531177	+	0.531177i
$934$		−	9.85914e26i		−	1.82271i
$935$	9.17778e26	−	3.99354e26i	1.68048	−	0.731230i
$936$	9.10025e25			0.165033
$937$	−1.68406e26	+	1.68406e26i	−0.302484	+	0.302484i	−0.841985	−	0.539501i	$-0.818613\pi$
$937$	−1.68406e26	+	1.68406e26i	−0.302484	+	0.302484i	0.539501	+	0.841985i	$0.318613\pi$
$938$	2.57132e26	+	2.57132e26i	0.457436	+	0.457436i
$939$		−	3.76406e26i		−	0.663234i
$940$	−1.50916e26	−	3.46827e26i	−0.263381	−	0.605289i
$941$	−5.97255e26			−1.03241			−0.516206	−	0.856465i	$-0.672656\pi$
$941$	−5.97255e26			−1.03241			−0.516206	+	0.856465i	$0.672656\pi$
$942$	−1.01544e27	+	1.01544e27i	−1.73859	+	1.73859i
$943$	1.27001e26	+	1.27001e26i	0.215378	+	0.215378i
$944$			2.31910e26i			0.389557i
$945$	−6.96106e25	+	1.76856e26i	−0.115821	+	0.294262i
$946$	1.54625e26			0.254836
$947$	−4.26927e26	+	4.26927e26i	−0.696953	+	0.696953i	−0.963752	−	0.266799i	$-0.914034\pi$
$947$	−4.26927e26	+	4.26927e26i	−0.696953	+	0.696953i	0.266799	+	0.963752i	$0.414034\pi$
$948$	−1.15956e26	−	1.15956e26i	−0.187507	−	0.187507i
$949$		−	2.48172e26i		−	0.397518i
$950$	1.23995e25	+	3.49684e26i	0.0196739	+	0.554835i
$951$	−6.51482e26			−1.02395
$952$	−1.81494e26	+	1.81494e26i	−0.282572	+	0.282572i
$953$	7.21365e26	+	7.21365e26i	1.11255	+	1.11255i	0.992805	+	0.119744i	$0.0382073\pi$
$953$	7.21365e26	+	7.21365e26i	1.11255	+	1.11255i	0.119744	+	0.992805i	$0.461793\pi$
$954$			2.21467e26i			0.338357i
$955$	1.26850e25	+	4.99280e24i	0.0191981	+	0.00755638i
$956$	−1.40997e27			−2.11393
$957$	−3.28022e25	+	3.28022e25i	−0.0487187	+	0.0487187i
$958$	4.87296e26	+	4.87296e26i	0.716974	+	0.716974i
$959$			2.24435e26i			0.327133i
$960$	−9.51457e26	+	4.14009e26i	−1.37388	+	0.597818i
$961$	−6.54284e26			−0.935956
$962$	1.12034e27	−	1.12034e27i	1.58772	−	1.58772i
$963$	5.66450e25	+	5.66450e25i	0.0795289	+	0.0795289i
$964$		−	1.37066e27i		−	1.90650i
$965$	5.73774e25	+	1.31862e26i	0.0790670	+	0.181708i
$966$	4.29739e26			0.586692
$967$	−1.40222e26	+	1.40222e26i	−0.189660	+	0.189660i	−0.795549	−	0.605889i	$-0.792818\pi$
$967$	−1.40222e26	+	1.40222e26i	−0.189660	+	0.189660i	0.605889	+	0.795549i	$0.292818\pi$
$968$	2.30729e25	+	2.30729e25i	0.0309189	+	0.0309189i
$969$		−	4.38377e26i		−	0.582014i
$970$	−8.80399e25	+	2.23679e26i	−0.115807	+	0.294224i
$971$	−2.91753e26			−0.380226			−0.190113	−	0.981762i	$-0.560885\pi$
$971$	−2.91753e26			−0.380226			−0.190113	+	0.981762i	$0.560885\pi$
$972$	2.28400e26	−	2.28400e26i	0.294917	−	0.294917i
$973$	−2.52330e26	−	2.52330e26i	−0.322815	−	0.322815i
$974$			1.27936e27i			1.62167i
$975$	7.76530e26	−	8.33625e26i	0.975252	−	1.04696i
$976$	3.17399e25			0.0394964
$977$	8.16600e26	−	8.16600e26i	1.00683	−	1.00683i	0.00685837	−	0.999976i	$-0.497817\pi$
$977$	8.16600e26	−	8.16600e26i	1.00683	−	1.00683i	0.999976	−	0.00685837i	$-0.00218310\pi$
$978$	8.26811e26	+	8.26811e26i	1.01008	+	1.01008i
$979$		−	5.90256e26i		−	0.714490i
$980$	1.04336e27	+	4.10668e26i	1.25141	+	0.492556i
$981$	−1.27198e26			−0.151168
$982$	1.15053e27	−	1.15053e27i	1.35486	−	1.35486i
$983$	4.57736e25	+	4.57736e25i	0.0534113	+	0.0534113i	0.733308	−	0.679897i	$-0.237975\pi$
$983$	4.57736e25	+	4.57736e25i	0.0534113	+	0.0534113i	−0.679897	+	0.733308i	$0.737975\pi$
$984$		−	1.35950e26i		−	0.157189i
$985$	−8.13021e26	+	3.53772e26i	−0.931485	+	0.405319i
$986$	1.78601e26			0.202764
$987$	−7.77751e25	+	7.77751e25i	−0.0874956	+	0.0874956i
$988$	−5.10554e26	−	5.10554e26i	−0.569153	−	0.569153i
$989$			1.91881e26i			0.211966i
$990$	−8.39987e25	−	1.93042e26i	−0.0919508	−	0.211317i
$991$	1.20409e27			1.30615			0.653077	−	0.757291i	$-0.273478\pi$
$991$	1.20409e27			1.30615			0.653077	+	0.757291i	$0.273478\pi$
$992$	−2.02421e26	+	2.02421e26i	−0.217595	+	0.217595i
$993$	2.02359e26	+	2.02359e26i	0.215566	+	0.215566i
$994$		−	4.82970e26i		−	0.509851i
$995$	1.53080e26	−	3.88923e26i	0.160144	−	0.406871i
$996$	1.37422e27			1.42469
$997$	−1.07297e27	+	1.07297e27i	−1.10238	+	1.10238i	−0.108256	+	0.994123i	$0.534526\pi$
$997$	−1.07297e27	+	1.07297e27i	−1.10238	+	1.10238i	−0.994123	+	0.108256i	$0.965474\pi$
$998$	−1.54655e27	−	1.54655e27i	−1.57467	−	1.57467i
$999$		−	9.68184e26i		−	0.976941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.19.c.a.3.1	yes	16
3.2	odd	2		45.19.g.a.28.8		16
5.2	odd	4	inner	5.19.c.a.2.1	✓	16
5.3	odd	4		25.19.c.b.7.8		16
5.4	even	2		25.19.c.b.18.8		16
15.2	even	4		45.19.g.a.37.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.19.c.a.2.1	✓	16	5.2	odd	4	inner
5.19.c.a.3.1	yes	16	1.1	even	1	trivial
25.19.c.b.7.8		16	5.3	odd	4
25.19.c.b.18.8		16	5.4	even	2
45.19.g.a.28.8		16	3.2	odd	2
45.19.g.a.37.8		16	15.2	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-569.773 + 569.773i) q^{2} +(-12889.4 - 12889.4i) q^{3} -387139. i q^{4} +(1.81741e6 + 715334. i) q^{5} +1.46881e7 q^{6} +(8.52951e6 - 8.52951e6i) q^{7} +(7.12189e7 + 7.12189e7i) q^{8} -5.51474e7i q^{9} +O(q^{10})\)	\(q+(-569.773 + 569.773i) q^{2} +(-12889.4 - 12889.4i) q^{3} -387139. i q^{4} +(1.81741e6 + 715334. i) q^{5} +1.46881e7 q^{6} +(8.52951e6 - 8.52951e6i) q^{7} +(7.12189e7 + 7.12189e7i) q^{8} -5.51474e7i q^{9} +(-1.44309e9 + 6.27936e8i) q^{10} -2.42567e9 q^{11} +(-4.98999e9 + 4.98999e9i) q^{12} +(1.15852e10 + 1.15852e10i) q^{13} +9.71977e9i q^{14} +(-1.42051e10 - 3.26456e10i) q^{15} +2.03289e10 q^{16} +(-1.49387e11 + 1.49387e11i) q^{17} +(3.14215e10 + 3.14215e10i) q^{18} -1.13834e11i q^{19} +(2.76934e11 - 7.03592e11i) q^{20} -2.19880e11 q^{21} +(1.38208e12 - 1.38208e12i) q^{22} +(1.71509e12 + 1.71509e12i) q^{23} -1.83594e12i q^{24} +(2.79129e12 + 2.60012e12i) q^{25} -1.32019e13 q^{26} +(-5.70443e12 + 5.70443e12i) q^{27} +(-3.30211e12 - 3.30211e12i) q^{28} +1.04915e12i q^{29} +(2.66943e13 + 1.05069e13i) q^{30} +6.69104e12 q^{31} +(-3.02525e13 + 3.02525e13i) q^{32} +(3.12655e13 + 3.12655e13i) q^{33} -1.70234e14i q^{34} +(2.16031e13 - 9.40020e12i) q^{35} -2.13497e13 q^{36} +(-8.48624e13 + 8.48624e13i) q^{37} +(6.48595e13 + 6.48595e13i) q^{38} -2.98652e14i q^{39} +(7.84889e13 + 1.80380e14i) q^{40} +7.40493e13 q^{41} +(1.25282e14 - 1.25282e14i) q^{42} +(5.59392e13 + 5.59392e13i) q^{43} +9.39073e14i q^{44} +(3.94488e13 - 1.00226e14i) q^{45} -1.95442e15 q^{46} +(3.53716e14 - 3.53716e14i) q^{47} +(-2.62028e14 - 2.62028e14i) q^{48} +1.48291e15i q^{49} +(-3.07188e15 + 1.08926e14i) q^{50} +3.85102e15 q^{51} +(4.48508e15 - 4.48508e15i) q^{52} +(3.52414e15 + 3.52414e15i) q^{53} -6.50047e15i q^{54} +(-4.40845e15 - 1.73517e15i) q^{55} +1.21492e15 q^{56} +(-1.46725e15 + 1.46725e15i) q^{57} +(-5.97779e14 - 5.97779e14i) q^{58} +1.14079e16i q^{59} +(-1.26384e16 + 5.49937e15i) q^{60} +1.56132e15 q^{61} +(-3.81238e15 + 3.81238e15i) q^{62} +(-4.70380e14 - 4.70380e14i) q^{63} -2.91450e16i q^{64} +(1.27678e16 + 2.93424e16i) q^{65} -3.56284e16 q^{66} +(2.64545e16 - 2.64545e16i) q^{67} +(5.78336e16 + 5.78336e16i) q^{68} -4.42129e16i q^{69} +(-6.95288e15 + 1.76648e16i) q^{70} -4.96895e16 q^{71} +(3.92754e15 - 3.92754e15i) q^{72} +(-1.07108e16 - 1.07108e16i) q^{73} -9.67047e16i q^{74} +(-2.46412e15 - 6.94920e16i) q^{75} -4.40696e16 q^{76} +(-2.06898e16 + 2.06898e16i) q^{77} +(1.70164e17 + 1.70164e17i) q^{78} +2.32376e16i q^{79} +(3.69461e16 + 1.45420e16i) q^{80} +1.25688e17 q^{81} +(-4.21913e16 + 4.21913e16i) q^{82} +(-1.37697e17 - 1.37697e17i) q^{83} +8.51243e16i q^{84} +(-3.78360e17 + 1.64637e17i) q^{85} -6.37454e16 q^{86} +(1.35229e16 - 1.35229e16i) q^{87} +(-1.72754e17 - 1.72754e17i) q^{88} +2.43337e17i q^{89} +(3.46290e16 + 7.95828e16i) q^{90} +1.97632e17 q^{91} +(6.63977e17 - 6.63977e17i) q^{92} +(-8.62435e16 - 8.62435e16i) q^{93} +4.03075e17i q^{94} +(8.14293e16 - 2.06883e17i) q^{95} +7.79873e17 q^{96} +(1.08004e17 - 1.08004e17i) q^{97} +(-8.44922e17 - 8.44922e17i) q^{98} +1.33770e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8}+O(q^{10}) \) 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8	\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 11\!\cdots\!80 q^{42}+ \cdots - 43\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8 - 635093930 * q^10 + 4719921012 * q^11 - 22715951880 * q^12 + 8689116940 * q^13 - 59706310410 * q^15 + 10530345976 * q^16 - 221748184620 * q^17 + 654304109970 * q^18 - 878373508140 * q^20 + 1431507507492 * q^21 + 2209421844320 * q^22 - 3507966822690 * q^23 + 10464353188900 * q^25 - 23324455191468 * q^26 + 11679867134280 * q^27 + 8077754165240 * q^28 - 80865025845360 * q^30 + 53033402941772 * q^31 + 20394786468360 * q^32 - 4953707733660 * q^33 - 82375887392730 * q^35 + 263454471040956 * q^36 - 29247362581160 * q^37 + 391580910829560 * q^38 - 918259855204500 * q^40 - 717170436410748 * q^41 + 1119760897992480 * q^42 + 1295649718427950 * q^43 - 2413910465914410 * q^45 - 6165422784262408 * q^46 + 5324712362382270 * q^47 + 7675815427929360 * q^48 - 10266398091964350 * q^50 - 5996743906200468 * q^51 + 5457051468349900 * q^52 + 25019175284457720 * q^53 - 28447209909214060 * q^55 - 22879869030140400 * q^56 + 26327201869272960 * q^57 + 72036625362175440 * q^58 - 129993967558538280 * q^60 - 55112667981951388 * q^61 + 98952816959518920 * q^62 + 129200567352114030 * q^63 - 145786436727900960 * q^65 - 217789774433419296 * q^66 + 132604737823930030 * q^67 + 291394918710173220 * q^68 - 344767752141139080 * q^70 - 148288220084109108 * q^71 + 428373837658219140 * q^72 + 357896091854250160 * q^73 - 656924515001553450 * q^75 - 254554257141486000 * q^76 + 201286979542193700 * q^77 + 866949362074211400 * q^78 - 608571216720410880 * q^80 - 330578957555881164 * q^81 - 167911799138733280 * q^82 + 314012877447835830 * q^83 - 37755360901186580 * q^85 - 149686440788368488 * q^86 + 359090097519437040 * q^87 - 966828856938988320 * q^88 + 2368537241357586390 * q^90 + 498102030062089052 * q^91 - 1299658879961370120 * q^92 - 3025937916654554460 * q^93 + 2986575636848949000 * q^95 + 3531977749160666592 * q^96 - 1689002222572272080 * q^97 - 4330619740553781090 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more