LMFDB - Embedded newform 5.19.c.a.3.7

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			3.7
Root			$482.444i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.19.c.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(514.444 - 514.444i) q^{2} +(11708.2 + 11708.2i) q^{3} -267162. i q^{4} +(-1.06274e6 - 1.63869e6i) q^{5} +1.20464e7 q^{6} +(4.54981e7 - 4.54981e7i) q^{7} +(-2.58155e6 - 2.58155e6i) q^{8} -1.13259e8i q^{9} +O(q^{10})$	\(q+(514.444 - 514.444i) q^{2} +(11708.2 + 11708.2i) q^{3} -267162. i q^{4} +(-1.06274e6 - 1.63869e6i) q^{5} +1.20464e7 q^{6} +(4.54981e7 - 4.54981e7i) q^{7} +(-2.58155e6 - 2.58155e6i) q^{8} -1.13259e8i q^{9} +(-1.38973e9 - 2.96294e8i) q^{10} +3.09896e8 q^{11} +(3.12798e9 - 3.12798e9i) q^{12} +(-8.68254e8 - 8.68254e8i) q^{13} -4.68125e10i q^{14} +(6.74331e9 - 3.16287e10i) q^{15} +6.73788e10 q^{16} +(-1.22332e11 + 1.22332e11i) q^{17} +(-5.82653e10 - 5.82653e10i) q^{18} +3.40010e11i q^{19} +(-4.37795e11 + 2.83923e11i) q^{20} +1.06540e12 q^{21} +(1.59424e11 - 1.59424e11i) q^{22} +(2.24314e10 + 2.24314e10i) q^{23} -6.04503e10i q^{24} +(-1.55588e12 + 3.48298e12i) q^{25} -8.93337e11 q^{26} +(5.86203e12 - 5.86203e12i) q^{27} +(-1.21554e13 - 1.21554e13i) q^{28} +1.17353e13i q^{29} +(-1.28021e13 - 1.97402e13i) q^{30} +3.42479e13 q^{31} +(3.53394e13 - 3.53394e13i) q^{32} +(3.62831e12 + 3.62831e12i) q^{33} +1.25866e14i q^{34} +(-1.22910e14 - 2.62046e13i) q^{35} -3.02584e13 q^{36} +(-7.33851e13 + 7.33851e13i) q^{37} +(1.74916e14 + 1.74916e14i) q^{38} -2.03313e13i q^{39} +(-1.48684e12 + 6.97384e12i) q^{40} +9.80356e13 q^{41} +(5.48088e14 - 5.48088e14i) q^{42} +(-6.23419e14 - 6.23419e14i) q^{43} -8.27924e13i q^{44} +(-1.85595e14 + 1.20364e14i) q^{45} +2.30794e13 q^{46} +(-6.89773e14 + 6.89773e14i) q^{47} +(7.88882e14 + 7.88882e14i) q^{48} -2.51174e15i q^{49} +(9.91384e14 + 2.59221e15i) q^{50} -2.86455e15 q^{51} +(-2.31965e14 + 2.31965e14i) q^{52} +(4.54980e15 + 4.54980e15i) q^{53} -6.03138e15i q^{54} +(-3.29337e14 - 5.07822e14i) q^{55} -2.34911e14 q^{56} +(-3.98089e15 + 3.98089e15i) q^{57} +(6.03714e15 + 6.03714e15i) q^{58} +2.86344e15i q^{59} +(-8.44998e15 - 1.80156e15i) q^{60} -1.35867e16 q^{61} +(1.76186e16 - 1.76186e16i) q^{62} +(-5.15306e15 - 5.15306e15i) q^{63} -1.86974e16i q^{64} +(-5.00071e14 + 2.34552e15i) q^{65} +3.73313e15 q^{66} +(2.72637e16 - 2.72637e16i) q^{67} +(3.26823e16 + 3.26823e16i) q^{68} +5.25260e14i q^{69} +(-7.67110e16 + 4.97493e16i) q^{70} -1.52953e16 q^{71} +(-2.92383e14 + 2.92383e14i) q^{72} +(8.25139e15 + 8.25139e15i) q^{73} +7.55051e16i q^{74} +(-5.89958e16 + 2.25627e16i) q^{75} +9.08378e16 q^{76} +(1.40997e16 - 1.40997e16i) q^{77} +(-1.04593e16 - 1.04593e16i) q^{78} -9.97051e16i q^{79} +(-7.16059e16 - 1.10413e17i) q^{80} +9.33884e16 q^{81} +(5.04339e16 - 5.04339e16i) q^{82} +(8.47982e16 + 8.47982e16i) q^{83} -2.84634e17i q^{84} +(3.30469e17 + 7.04568e16i) q^{85} -6.41429e17 q^{86} +(-1.37398e17 + 1.37398e17i) q^{87} +(-8.00010e14 - 8.00010e14i) q^{88} -7.13356e16i q^{89} +(-3.35579e16 + 1.57399e17i) q^{90} -7.90079e16 q^{91} +(5.99281e15 - 5.99281e15i) q^{92} +(4.00980e17 + 4.00980e17i) q^{93} +7.09700e17i q^{94} +(5.57170e17 - 3.61341e17i) q^{95} +8.27518e17 q^{96} +(-1.73783e17 + 1.73783e17i) q^{97} +(-1.29215e18 - 1.29215e18i) q^{98} -3.50984e16i 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 $

$2$	514.444	−	514.444i	1.00477	−	1.00477i	0.00478571	−	0.999989i	$-0.498477\pi$
$2$	514.444	−	514.444i	1.00477	−	1.00477i	0.999989	−	0.00478571i	$-0.00152335\pi$
$3$	11708.2	+	11708.2i	0.594836	+	0.594836i	0.938934	−	0.344098i	$-0.111815\pi$
$3$	11708.2	+	11708.2i	0.594836	+	0.594836i	−0.344098	+	0.938934i	$0.611815\pi$
$4$		−	267162.i		−	1.01914i
$5$	−1.06274e6	−	1.63869e6i	−0.544121	−	0.839007i
$5$	−1.06274e6	−	1.63869e6i	−0.544121	−	0.839007i
$6$	1.20464e7			1.19535
$7$	4.54981e7	−	4.54981e7i	1.12749	−	1.12749i	0.136901	−	0.990585i	$-0.456286\pi$
$7$	4.54981e7	−	4.54981e7i	1.12749	−	1.12749i	0.990585	−	0.136901i	$-0.0437143\pi$
$8$	−2.58155e6	−	2.58155e6i	−0.0192340	−	0.0192340i
$9$		−	1.13259e8i		−	0.292340i
$10$	−1.38973e9	−	2.96294e8i	−1.38973	−	0.296294i
$11$	3.09896e8			0.131426			0.0657130	−	0.997839i	$-0.479068\pi$
$11$	3.09896e8			0.131426			0.0657130	+	0.997839i	$0.479068\pi$
$12$	3.12798e9	−	3.12798e9i	0.606223	−	0.606223i
$13$	−8.68254e8	−	8.68254e8i	−0.0818760	−	0.0818760i	0.664983	−	0.746859i	$-0.268439\pi$
$13$	−8.68254e8	−	8.68254e8i	−0.0818760	−	0.0818760i	−0.746859	+	0.664983i	$0.768439\pi$
$14$		−	4.68125e10i		−	2.26574i
$15$	6.74331e9	−	3.16287e10i	0.175409	−	0.822734i
$16$	6.73788e10			0.980491
$17$	−1.22332e11	+	1.22332e11i	−1.03157	+	1.03157i	−0.0320833	+	0.999485i	$0.510214\pi$
$17$	−1.22332e11	+	1.22332e11i	−1.03157	+	1.03157i	−0.999485	+	0.0320833i	$0.989786\pi$
$18$	−5.82653e10	−	5.82653e10i	−0.293736	−	0.293736i
$19$			3.40010e11i			1.05368i	0.849964	+	0.526841i	$0.176624\pi$
$19$			3.40010e11i			1.05368i	−0.849964	+	0.526841i	$0.823376\pi$
$20$	−4.37795e11	+	2.83923e11i	−0.855068	+	0.554537i
$21$	1.06540e12			1.34134
$22$	1.59424e11	−	1.59424e11i	0.132054	−	0.132054i
$23$	2.24314e10	+	2.24314e10i	0.0124539	+	0.0124539i	0.713306	−	0.700852i	$-0.247197\pi$
$23$	2.24314e10	+	2.24314e10i	0.0124539	+	0.0124539i	−0.700852	+	0.713306i	$0.747197\pi$
$24$		−	6.04503e10i		−	0.0228822i
$25$	−1.55588e12	+	3.48298e12i	−0.407865	+	0.913042i
$26$	−8.93337e11			−0.164534
$27$	5.86203e12	−	5.86203e12i	0.768731	−	0.768731i
$28$	−1.21554e13	−	1.21554e13i	−1.14907	−	1.14907i
$29$			1.17353e13i			0.808930i	0.914553	+	0.404465i	$0.132542\pi$
$29$			1.17353e13i			0.808930i	−0.914553	+	0.404465i	$0.867458\pi$
$30$	−1.28021e13	−	1.97402e13i	−0.650415	−	1.00291i
$31$	3.42479e13			1.29532			0.647662	−	0.761927i	$-0.275747\pi$
$31$	3.42479e13			1.29532			0.647662	+	0.761927i	$0.275747\pi$
$32$	3.53394e13	−	3.53394e13i	1.00441	−	1.00441i
$33$	3.62831e12	+	3.62831e12i	0.0781769	+	0.0781769i
$34$			1.25866e14i			2.07299i
$35$	−1.22910e14	−	2.62046e13i	−1.55946	−	0.332480i
$36$	−3.02584e13			−0.297937
$37$	−7.33851e13	+	7.33851e13i	−0.564667	+	0.564667i	−0.930630	−	0.365963i	$-0.880740\pi$
$37$	−7.33851e13	+	7.33851e13i	−0.564667	+	0.564667i	0.365963	+	0.930630i	$0.380740\pi$
$38$	1.74916e14	+	1.74916e14i	1.05871	+	1.05871i
$39$		−	2.03313e13i		−	0.0974056i
$40$	−1.48684e12	+	6.97384e12i	−0.00567185	+	0.0266031i
$41$	9.80356e13			0.299453			0.149727	−	0.988727i	$-0.452161\pi$
$41$	9.80356e13			0.299453			0.149727	+	0.988727i	$0.452161\pi$
$42$	5.48088e14	−	5.48088e14i	1.34774	−	1.34774i
$43$	−6.23419e14	−	6.23419e14i	−1.24041	−	1.24041i	−0.959833	−	0.280573i	$-0.909476\pi$
$43$	−6.23419e14	−	6.23419e14i	−1.24041	−	1.24041i	−0.280573	−	0.959833i	$-0.590524\pi$
$44$		−	8.27924e13i		−	0.133942i
$45$	−1.85595e14	+	1.20364e14i	−0.245276	+	0.159068i
$46$	2.30794e13			0.0250267
$47$	−6.89773e14	+	6.89773e14i	−0.616347	+	0.616347i	−0.944593	−	0.328245i	$-0.893543\pi$
$47$	−6.89773e14	+	6.89773e14i	−0.616347	+	0.616347i	0.328245	+	0.944593i	$0.393543\pi$
$48$	7.88882e14	+	7.88882e14i	0.583231	+	0.583231i
$49$		−	2.51174e15i		−	1.54245i
$50$	9.91384e14	+	2.59221e15i	0.507588	+	1.32721i
$51$	−2.86455e15			−1.22723
$52$	−2.31965e14	+	2.31965e14i	−0.0834433	+	0.0834433i
$53$	4.54980e15	+	4.54980e15i	1.37883	+	1.37883i	0.846607	+	0.532219i	$0.178642\pi$
$53$	4.54980e15	+	4.54980e15i	1.37883	+	1.37883i	0.532219	+	0.846607i	$0.321358\pi$
$54$		−	6.03138e15i		−	1.54480i
$55$	−3.29337e14	−	5.07822e14i	−0.0715116	−	0.110267i
$56$	−2.34911e14			−0.0433722
$57$	−3.98089e15	+	3.98089e15i	−0.626768	+	0.626768i
$58$	6.03714e15	+	6.03714e15i	0.812792	+	0.812792i
$59$			2.86344e15i			0.330537i	0.986249	+	0.165268i	$0.0528490\pi$
$59$			2.86344e15i			0.330537i	−0.986249	+	0.165268i	$0.947151\pi$
$60$	−8.44998e15	−	1.80156e15i	−0.838483	−	0.178767i
$61$	−1.35867e16			−1.16184			−0.580921	−	0.813960i	$-0.697307\pi$
$61$	−1.35867e16			−1.16184			−0.580921	+	0.813960i	$0.697307\pi$
$62$	1.76186e16	−	1.76186e16i	1.30151	−	1.30151i
$63$	−5.15306e15	−	5.15306e15i	−0.329610	−	0.329610i
$64$		−	1.86974e16i		−	1.03791i
$65$	−5.00071e14	+	2.34552e15i	−0.0241441	+	0.113245i
$66$	3.73313e15			0.157100
$67$	2.72637e16	−	2.72637e16i	1.00210	−	1.00210i	0.00210466	−	0.999998i	$-0.499330\pi$
$67$	2.72637e16	−	2.72637e16i	1.00210	−	1.00210i	0.999998	−	0.00210466i	$-0.000669936\pi$
$68$	3.26823e16	+	3.26823e16i	1.05132	+	1.05132i
$69$			5.25260e14i			0.0148161i
$70$	−7.67110e16	+	4.97493e16i	−1.90097	+	1.23283i
$71$	−1.52953e16			−0.333605			−0.166802	−	0.985990i	$-0.553344\pi$
$71$	−1.52953e16			−0.333605			−0.166802	+	0.985990i	$0.553344\pi$
$72$	−2.92383e14	+	2.92383e14i	−0.00562288	+	0.00562288i
$73$	8.25139e15	+	8.25139e15i	0.140159	+	0.140159i	0.773705	−	0.633546i	$-0.218401\pi$
$73$	8.25139e15	+	8.25139e15i	0.140159	+	0.140159i	−0.633546	+	0.773705i	$0.718401\pi$
$74$			7.55051e16i			1.13473i
$75$	−5.89958e16	+	2.25627e16i	−0.785723	+	0.300497i
$76$	9.08378e16			1.07385
$77$	1.40997e16	−	1.40997e16i	0.148181	−	0.148181i
$78$	−1.04593e16	−	1.04593e16i	−0.0978706	−	0.0978706i
$79$		−	9.97051e16i		−	0.831904i	−0.909386	−	0.415952i	$-0.863448\pi$
$79$		−	9.97051e16i		−	0.831904i	0.909386	−	0.415952i	$-0.136552\pi$
$80$	−7.16059e16	−	1.10413e17i	−0.533505	−	0.822639i
$81$	9.33884e16			0.622197
$82$	5.04339e16	−	5.04339e16i	0.300883	−	0.300883i
$83$	8.47982e16	+	8.47982e16i	0.453611	+	0.453611i	0.896551	−	0.442940i	$-0.146064\pi$
$83$	8.47982e16	+	8.47982e16i	0.453611	+	0.453611i	−0.442940	+	0.896551i	$0.646064\pi$
$84$		−	2.84634e17i		−	1.36701i
$85$	3.30469e17	+	7.04568e16i	1.42679	+	0.304195i
$86$	−6.41429e17			−2.49266
$87$	−1.37398e17	+	1.37398e17i	−0.481181	+	0.481181i
$88$	−8.00010e14	−	8.00010e14i	−0.00252785	−	0.00252785i
$89$		−	7.13356e16i		−	0.203609i	−0.994804	−	0.101804i	$-0.967538\pi$
$89$		−	7.13356e16i		−	0.203609i	0.994804	−	0.101804i	$-0.0324616\pi$
$90$	−3.35579e16	+	1.57399e17i	−0.0866188	+	0.406275i
$91$	−7.90079e16			−0.184628
$92$	5.99281e15	−	5.99281e15i	0.0126923	−	0.0126923i
$93$	4.00980e17	+	4.00980e17i	0.770506	+	0.770506i
$94$			7.09700e17i			1.23858i
$95$	5.57170e17	−	3.61341e17i	0.884046	−	0.573330i
$96$	8.27518e17			1.19491
$97$	−1.73783e17	+	1.73783e17i	−0.228592	+	0.228592i	−0.812104	−	0.583512i	$-0.801678\pi$
$97$	−1.73783e17	+	1.73783e17i	−0.228592	+	0.228592i	0.583512	+	0.812104i	$0.301678\pi$
$98$	−1.29215e18	−	1.29215e18i	−1.54981	−	1.54981i
$99$		−	3.50984e16i		−	0.0384212i
$100$	9.30520e17	+	4.15673e17i	0.930520	+	0.415673i
$101$	−1.06901e18			−0.977440			−0.488720	−	0.872441i	$-0.662536\pi$
$101$	−1.06901e18			−0.977440			−0.488720	+	0.872441i	$0.662536\pi$
$102$	−1.47365e18	+	1.47365e18i	−1.23309	+	1.23309i
$103$	7.71840e16	+	7.71840e16i	0.0591551	+	0.0591551i	0.736065	−	0.676910i	$-0.236682\pi$
$103$	7.71840e16	+	7.71840e16i	0.0591551	+	0.0591551i	−0.676910	+	0.736065i	$0.736682\pi$
$104$			4.48288e15i			0.00314961i
$105$	−1.13224e18	−	1.74585e18i	−0.729850	−	1.12539i
$106$	4.68124e18			2.77082
$107$	2.95516e17	−	2.95516e17i	0.160741	−	0.160741i	−0.622154	−	0.782895i	$-0.713742\pi$
$107$	2.95516e17	−	2.95516e17i	0.160741	−	0.160741i	0.782895	+	0.622154i	$0.213742\pi$
$108$	−1.56611e18	−	1.56611e18i	−0.783446	−	0.783446i
$109$			5.03683e17i			0.231910i	0.993254	+	0.115955i	$0.0369928\pi$
$109$			5.03683e17i			0.231910i	−0.993254	+	0.115955i	$0.963007\pi$
$110$	−4.30672e17	−	9.18203e16i	−0.182647	−	0.0389408i
$111$	−1.71841e18			−0.671768
$112$	3.06561e18	−	3.06561e18i	1.10549	−	1.10549i
$113$	−2.40642e18	−	2.40642e18i	−0.801059	−	0.801059i	0.182202	−	0.983261i	$-0.441678\pi$
$113$	−2.40642e18	−	2.40642e18i	−0.801059	−	0.801059i	−0.983261	+	0.182202i	$0.941678\pi$
$114$			4.09589e18i			1.25952i
$115$	1.29194e16	−	6.05966e16i	0.00367249	−	0.0172253i
$116$	3.13522e18			0.824415
$117$	−9.83373e16	+	9.83373e16i	−0.0239357	+	0.0239357i
$118$	1.47308e18	+	1.47308e18i	0.332115	+	0.332115i
$119$			1.11317e19i			2.32616i
$120$	−9.90590e16	+	6.42427e16i	−0.0191983	+	0.0124507i
$121$	−5.46388e18			−0.982727
$122$	−6.98962e18	+	6.98962e18i	−1.16739	+	1.16739i
$123$	1.14782e18	+	1.14782e18i	0.178126	+	0.178126i
$124$		−	9.14974e18i		−	1.32012i
$125$	7.36100e18	−	1.15188e18i	0.987977	−	0.154603i
$126$	−5.30192e18			−0.662367
$127$	6.44985e18	−	6.44985e18i	0.750440	−	0.750440i	−0.224121	−	0.974561i	$-0.571951\pi$
$127$	6.44985e18	−	6.44985e18i	0.750440	−	0.750440i	0.974561	+	0.224121i	$0.0719510\pi$
$128$	−3.54740e17	−	3.54740e17i	−0.0384610	−	0.0384610i
$129$		−	1.45982e19i		−	1.47568i
$130$	9.49381e17	+	1.46390e18i	0.0895262	+	0.138045i
$131$	2.34023e18			0.205976			0.102988	−	0.994683i	$-0.467160\pi$
$131$	2.34023e18			0.205976			0.102988	+	0.994683i	$0.467160\pi$
$132$	9.69346e17	−	9.69346e17i	0.0796735	−	0.0796735i
$133$	1.54698e19	+	1.54698e19i	1.18801	+	1.18801i
$134$		−	2.80514e19i		−	2.01377i
$135$	−1.58358e19	−	3.37624e18i	−1.06325	−	0.226688i
$136$	6.31609e17			0.0396824
$137$	−6.37189e18	+	6.37189e18i	−0.374786	+	0.374786i	−0.869217	−	0.494431i	$-0.835376\pi$
$137$	−6.37189e18	+	6.37189e18i	−0.374786	+	0.374786i	0.494431	+	0.869217i	$0.335376\pi$
$138$	2.70217e17	+	2.70217e17i	0.0148868	+	0.0148868i
$139$			1.02362e19i			0.528451i	0.964461	+	0.264226i	$0.0851164\pi$
$139$			1.02362e19i			0.528451i	−0.964461	+	0.264226i	$0.914884\pi$
$140$	−7.00089e18	+	3.28368e19i	−0.338845	+	1.58931i
$141$	−1.61519e19			−0.733251
$142$	−7.86857e18	+	7.86857e18i	−0.335198	+	0.335198i
$143$	−2.69068e17	−	2.69068e17i	−0.0107606	−	0.0107606i
$144$		−	7.63124e18i		−	0.286637i
$145$	1.92304e19	−	1.24715e19i	0.678698	−	0.440156i
$146$	8.48976e18			0.281657
$147$	2.94079e19	−	2.94079e19i	0.917504	−	0.917504i
$148$	1.96057e19	+	1.96057e19i	0.575476	+	0.575476i
$149$			1.72802e19i			0.477390i	0.971095	+	0.238695i	$0.0767196\pi$
$149$			1.72802e19i			0.477390i	−0.971095	+	0.238695i	$0.923280\pi$
$150$	−1.87428e19	+	4.19573e19i	−0.487543	+	1.09141i
$151$	−1.21577e19			−0.297893			−0.148946	−	0.988845i	$-0.547588\pi$
$151$	−1.21577e19			−0.297893			−0.148946	+	0.988845i	$0.547588\pi$
$152$	8.77752e17	−	8.77752e17i	0.0202665	−	0.0202665i
$153$	1.38551e19	+	1.38551e19i	0.301569	+	0.301569i
$154$		−	1.45070e19i		−	0.297777i
$155$	−3.63965e19	−	5.61215e19i	−0.704813	−	1.08679i
$156$	−5.43175e18			−0.0992702
$157$	5.29319e19	−	5.29319e19i	0.913314	−	0.913314i	−0.0832172	−	0.996531i	$-0.526520\pi$
$157$	5.29319e19	−	5.29319e19i	0.913314	−	0.913314i	0.996531	+	0.0832172i	$0.0265195\pi$
$158$	−5.12927e19	−	5.12927e19i	−0.835876	−	0.835876i
$159$			1.06539e20i			1.64035i
$160$	−9.54666e19	−	2.03537e19i	−1.38922	−	0.296186i
$161$	2.04117e18			0.0280832
$162$	4.80431e19	−	4.80431e19i	0.625167	−	0.625167i
$163$	3.07411e19	+	3.07411e19i	0.378470	+	0.378470i	0.870550	−	0.492080i	$-0.163763\pi$
$163$	3.07411e19	+	3.07411e19i	0.378470	+	0.378470i	−0.492080	+	0.870550i	$0.663763\pi$
$164$		−	2.61914e19i		−	0.305186i
$165$	2.08972e18	−	9.80159e18i	0.0230533	−	0.108129i
$166$	8.72480e19			0.911554
$167$	−7.48607e19	+	7.48607e19i	−0.740979	+	0.740979i	−0.972766	−	0.231788i	$-0.925543\pi$
$167$	−7.48607e19	+	7.48607e19i	−0.740979	+	0.740979i	0.231788	+	0.972766i	$0.425543\pi$
$168$	−2.75037e18	−	2.75037e18i	−0.0257993	−	0.0257993i
$169$		−	1.10948e20i		−	0.986593i
$170$	2.06254e20	−	1.33762e20i	1.73925	−	1.12795i
$171$	3.85091e19			0.308034
$172$	−1.66554e20	+	1.66554e20i	−1.26415	+	1.26415i
$173$	−7.97405e19	−	7.97405e19i	−0.574465	−	0.574465i	0.358908	−	0.933373i	$-0.383149\pi$
$173$	−7.97405e19	−	7.97405e19i	−0.574465	−	0.574465i	−0.933373	+	0.358908i	$0.883149\pi$
$174$			1.41368e20i			0.966956i
$175$	8.76792e19	+	2.29259e20i	0.569579	+	1.48930i
$176$	2.08804e19			0.128862
$177$	−3.35256e19	+	3.35256e19i	−0.196615	+	0.196615i
$178$	−3.66982e19	−	3.66982e19i	−0.204581	−	0.204581i
$179$			7.45354e19i			0.395080i	0.980295	+	0.197540i	$0.0632953\pi$
$179$			7.45354e19i			0.395080i	−0.980295	+	0.197540i	$0.936705\pi$
$180$	3.21567e19	+	4.95841e19i	0.162113	+	0.249971i
$181$	−3.45032e20			−1.65483			−0.827413	−	0.561593i	$-0.810189\pi$
$181$	−3.45032e20			−1.65483			−0.827413	+	0.561593i	$0.810189\pi$
$182$	−4.06451e19	+	4.06451e19i	−0.185510	+	0.185510i
$183$	−1.59076e20	−	1.59076e20i	−0.691105	−	0.691105i
$184$		−	1.15815e17i		−	0.000479077i
$185$	1.98244e20	+	4.22661e19i	0.781006	+	0.166513i
$186$	4.12564e20			1.54837
$187$	−3.79100e19	+	3.79100e19i	−0.135575	+	0.135575i
$188$	1.84281e20	+	1.84281e20i	0.628146	+	0.628146i
$189$		−	5.33423e20i		−	1.73347i
$190$	1.00743e20	−	4.72523e20i	0.312200	−	1.46433i
$191$	3.52881e19			0.104311			0.0521553	−	0.998639i	$-0.483391\pi$
$191$	3.52881e19			0.104311			0.0521553	+	0.998639i	$0.483391\pi$
$192$	2.18912e20	−	2.18912e20i	0.617387	−	0.617387i
$193$	−3.04873e20	−	3.04873e20i	−0.820545	−	0.820545i	0.165641	−	0.986186i	$-0.447031\pi$
$193$	−3.04873e20	−	3.04873e20i	−0.820545	−	0.820545i	−0.986186	+	0.165641i	$0.947031\pi$
$194$			1.78803e20i			0.459367i
$195$	−3.33166e19	+	2.16068e19i	−0.0817240	+	0.0530004i
$196$	−6.71043e20			−1.57198
$197$	−3.42123e19	+	3.42123e19i	−0.0765572	+	0.0765572i	−0.744349	−	0.667791i	$-0.767240\pi$
$197$	−3.42123e19	+	3.42123e19i	−0.0765572	+	0.0765572i	0.667791	+	0.744349i	$0.267240\pi$
$198$	−1.80562e19	−	1.80562e19i	−0.0386046	−	0.0386046i
$199$			4.00893e20i			0.819127i	0.912282	+	0.409564i	$0.134319\pi$
$199$			4.00893e20i			0.819127i	−0.912282	+	0.409564i	$0.865681\pi$
$200$	1.30081e19	−	4.97489e18i	0.0254064	−	0.00971658i
$201$	6.38416e20			1.19217
$202$	−5.49947e20	+	5.49947e20i	−0.982106	+	0.982106i
$203$	5.33933e20	+	5.33933e20i	0.912057	+	0.912057i
$204$			7.65300e20i			1.25072i
$205$	−1.04186e20	−	1.60650e20i	−0.162939	−	0.251243i
$206$	7.94138e19			0.118875
$207$	2.54055e18	−	2.54055e18i	0.00364078	−	0.00364078i
$208$	−5.85019e19	−	5.85019e19i	−0.0802787	−	0.0802787i
$209$			1.05368e20i			0.138481i
$210$	−1.48062e21	−	3.15671e20i	−1.86410	−	0.397431i
$211$	2.76408e20			0.333433			0.166716	−	0.986005i	$-0.446684\pi$
$211$	2.76408e20			0.333433			0.166716	+	0.986005i	$0.446684\pi$
$212$	1.21553e21	−	1.21553e21i	1.40522	−	1.40522i
$213$	−1.79080e20	−	1.79080e20i	−0.198440	−	0.198440i
$214$		−	3.04053e20i		−	0.323017i
$215$	−3.59058e20	+	1.68412e21i	−0.365779	+	1.71564i
$216$	−3.02662e19			−0.0295716
$217$	1.55822e21	−	1.55822e21i	1.46046	−	1.46046i
$218$	2.59117e20	+	2.59117e20i	0.233017	+	0.233017i
$219$			1.93217e20i			0.166743i
$220$	−1.35671e20	+	8.79865e19i	−0.112378	+	0.0728806i
$221$	2.12430e20			0.168921
$222$	−8.84025e20	+	8.84025e20i	−0.674975	+	0.674975i
$223$	6.91582e19	+	6.91582e19i	0.0507108	+	0.0507108i	0.732007	−	0.681297i	$-0.238584\pi$
$223$	6.91582e19	+	6.91582e19i	0.0507108	+	0.0507108i	−0.681297	+	0.732007i	$0.738584\pi$
$224$		−	3.21575e21i		−	2.26491i
$225$	3.94478e20	+	1.76217e20i	0.266919	+	0.119236i
$226$	−2.47593e21			−1.60977
$227$	−1.23387e21	+	1.23387e21i	−0.770971	+	0.770971i	−0.978276	−	0.207305i	$-0.933531\pi$
$227$	−1.23387e21	+	1.23387e21i	−0.770971	+	0.770971i	0.207305	+	0.978276i	$0.433531\pi$
$228$	1.06354e21	+	1.06354e21i	0.638766	+	0.638766i
$229$		−	8.37298e20i		−	0.483460i	−0.970343	−	0.241730i	$-0.922285\pi$
$229$		−	8.37298e20i		−	0.483460i	0.970343	−	0.241730i	$-0.0777149\pi$
$230$	−2.45273e19	−	3.78199e19i	−0.0136176	−	0.0209976i
$231$	3.30162e20			0.176287
$232$	3.02951e19	−	3.02951e19i	0.0155590	−	0.0155590i
$233$	−1.99651e21	−	1.99651e21i	−0.986432	−	0.986432i	0.0134772	−	0.999909i	$-0.495710\pi$
$233$	−1.99651e21	−	1.99651e21i	−0.986432	−	0.986432i	−0.999909	+	0.0134772i	$0.995710\pi$
$234$			1.01178e20i			0.0480999i
$235$	1.86337e21	+	3.97275e20i	0.852487	+	0.181752i
$236$	7.65003e20			0.336864
$237$	1.16736e21	−	1.16736e21i	0.494847	−	0.494847i
$238$	5.72665e21	+	5.72665e21i	2.33726	+	2.33726i
$239$		−	1.68704e21i		−	0.663046i	−0.943447	−	0.331523i	$-0.892438\pi$
$239$		−	1.68704e21i		−	0.663046i	0.943447	−	0.331523i	$-0.107562\pi$
$240$	4.54356e20	−	2.13110e21i	0.171987	−	0.806683i
$241$	−1.62015e21			−0.590747			−0.295373	−	0.955382i	$-0.595444\pi$
$241$	−1.62015e21			−0.590747			−0.295373	+	0.955382i	$0.595444\pi$
$242$	−2.81086e21	+	2.81086e21i	−0.987419	+	0.987419i
$243$	−1.17766e21	−	1.17766e21i	−0.398626	−	0.398626i
$244$			3.62986e21i			1.18408i
$245$	−4.11596e21	+	2.66932e21i	−1.29413	+	0.839278i
$246$	1.18098e21			0.357952
$247$	2.95215e20	−	2.95215e20i	0.0862712	−	0.0862712i
$248$	−8.84126e19	−	8.84126e19i	−0.0249143	−	0.0249143i
$249$			1.98566e21i			0.539649i
$250$	3.19425e21	−	4.37940e21i	0.837352	−	1.14803i
$251$	−6.23779e21			−1.57749			−0.788746	−	0.614719i	$-0.789269\pi$
$251$	−6.23779e21			−1.57749			−0.788746	+	0.614719i	$0.789269\pi$
$252$	−1.37670e21	+	1.37670e21i	−0.335919	+	0.335919i
$253$	6.95139e18	+	6.95139e18i	0.00163677	+	0.00163677i
$254$		−	6.63618e21i		−	1.50805i
$255$	3.04426e21	+	4.69410e21i	0.667760	+	1.02965i
$256$	4.53641e21			0.960623
$257$	4.34881e21	−	4.34881e21i	0.889145	−	0.889145i	−0.105296	−	0.994441i	$-0.533579\pi$
$257$	4.34881e21	−	4.34881e21i	0.889145	−	0.889145i	0.994441	+	0.105296i	$0.0335790\pi$
$258$	−7.50995e21	−	7.50995e21i	−1.48272	−	1.48272i
$259$			6.67777e21i			1.27331i
$260$	6.26634e20	+	1.33600e20i	0.115413	+	0.0246063i
$261$	1.32912e21			0.236483
$262$	1.20392e21	−	1.20392e21i	0.206959	−	0.206959i
$263$	−2.90958e21	−	2.90958e21i	−0.483313	−	0.483313i	0.422875	−	0.906188i	$-0.361021\pi$
$263$	−2.90958e21	−	2.90958e21i	−0.483313	−	0.483313i	−0.906188	+	0.422875i	$0.861021\pi$
$264$		−	1.87333e19i		−	0.00300731i
$265$	2.62046e21	−	1.22909e22i	0.406597	−	1.90709i
$266$	1.59167e22			2.38737
$267$	8.35209e20	−	8.35209e20i	0.121114	−	0.121114i
$268$	−7.28384e21	−	7.28384e21i	−1.02129	−	1.02129i
$269$			1.40831e22i			1.90953i	0.297362	+	0.954765i	$0.403893\pi$
$269$			1.40831e22i			1.90953i	−0.297362	+	0.954765i	$0.596107\pi$
$270$	−9.88353e21	+	6.40976e21i	−1.29610	+	0.840558i
$271$	−1.00083e20			−0.0126951			−0.00634756	−	0.999980i	$-0.502021\pi$
$271$	−1.00083e20			−0.0126951			−0.00634756	+	0.999980i	$0.502021\pi$
$272$	−8.24255e21	+	8.24255e21i	−1.01144	+	1.01144i
$273$	−9.25036e20	−	9.25036e20i	−0.109823	−	0.109823i
$274$			6.55596e21i			0.753150i
$275$	−4.82162e20	+	1.07936e21i	−0.0536042	+	0.119998i
$276$	1.40330e20			0.0150997
$277$	1.67510e21	−	1.67510e21i	0.174471	−	0.174471i	−0.614470	−	0.788940i	$-0.710630\pi$
$277$	1.67510e21	−	1.67510e21i	0.174471	−	0.174471i	0.788940	+	0.614470i	$0.210630\pi$
$278$	5.26595e21	+	5.26595e21i	0.530974	+	0.530974i
$279$		−	3.87887e21i		−	0.378676i
$280$	2.49648e20	+	3.84945e20i	0.0235997	+	0.0363896i
$281$	−6.52949e21			−0.597753			−0.298877	−	0.954292i	$-0.596612\pi$
$281$	−6.52949e21			−0.597753			−0.298877	+	0.954292i	$0.596612\pi$
$282$	−8.30927e21	+	8.30927e21i	−0.736752	+	0.736752i
$283$	1.00354e22	+	1.00354e22i	0.861897	+	0.861897i	0.991558	−	0.129662i	$-0.0413891\pi$
$283$	1.00354e22	+	1.00354e22i	0.861897	+	0.861897i	−0.129662	+	0.991558i	$0.541389\pi$
$284$			4.08632e21i			0.339991i
$285$	1.07541e22	+	2.29279e21i	0.866900	+	0.184825i
$286$	−2.76841e20			−0.0216240
$287$	4.46044e21	−	4.46044e21i	0.337629	−	0.337629i
$288$	−4.00249e21	−	4.00249e21i	−0.293629	−	0.293629i
$289$		−	1.58669e22i		−	1.12827i
$290$	3.47709e21	−	1.63089e22i	0.239681	−	1.12420i
$291$	−4.06935e21			−0.271950
$292$	2.20446e21	−	2.20446e21i	0.142842	−	0.142842i
$293$	2.25541e21	+	2.25541e21i	0.141716	+	0.141716i	0.774405	−	0.632690i	$-0.218049\pi$
$293$	2.25541e21	+	2.25541e21i	0.141716	+	0.141716i	−0.632690	+	0.774405i	$0.718049\pi$
$294$		−	3.02575e22i		−	1.84377i
$295$	4.69228e21	−	3.04308e21i	0.277323	−	0.179852i
$296$	3.78894e20			0.0217216
$297$	1.81662e21	−	1.81662e21i	0.101031	−	0.101031i
$298$	8.88972e21	+	8.88972e21i	0.479669	+	0.479669i
$299$		−	3.89523e19i		−	0.00203935i
$300$	6.02791e21	+	1.57614e22i	0.306249	+	0.800764i
$301$	−5.67288e22			−2.79708
$302$	−6.25447e21	+	6.25447e21i	−0.299315	+	0.299315i
$303$	−1.25162e22	−	1.25162e22i	−0.581416	−	0.581416i
$304$			2.29095e22i			1.03313i
$305$	1.44391e22	+	2.22644e22i	0.632182	+	0.974793i
$306$	1.42554e22			0.606018
$307$	2.09987e22	−	2.09987e22i	0.866856	−	0.866856i	−0.125267	−	0.992123i	$-0.539979\pi$
$307$	2.09987e22	−	2.09987e22i	0.866856	−	0.866856i	0.992123	+	0.125267i	$0.0399787\pi$
$308$	−3.76690e21	−	3.76690e21i	−0.151018	−	0.151018i
$309$			1.80736e21i			0.0703752i
$310$	−4.75954e22	−	1.01475e22i	−1.80015	−	0.383797i
$311$	4.48809e22			1.64899			0.824495	−	0.565869i	$-0.191459\pi$
$311$	4.48809e22			1.64899			0.824495	+	0.565869i	$0.191459\pi$
$312$	−5.24862e19	+	5.24862e19i	−0.00187350	+	0.00187350i
$313$	2.93050e22	+	2.93050e22i	1.01635	+	1.01635i	0.999864	+	0.0164840i	$0.00524725\pi$
$313$	2.93050e22	+	2.93050e22i	1.01635	+	1.01635i	0.0164840	+	0.999864i	$0.494753\pi$
$314$		−	5.44610e22i		−	1.83535i
$315$	−2.96790e21	+	1.39206e22i	−0.0971974	+	0.455892i
$316$	−2.66374e22			−0.847829
$317$	−8.34466e21	+	8.34466e21i	−0.258152	+	0.258152i	−0.824302	−	0.566150i	$-0.808432\pi$
$317$	−8.34466e21	+	8.34466e21i	−0.258152	+	0.258152i	0.566150	+	0.824302i	$0.308432\pi$
$318$	5.48086e22	+	5.48086e22i	1.64818	+	1.64818i
$319$			3.63671e21i			0.106315i
$320$	−3.06391e22	+	1.98703e22i	−0.870815	+	0.564749i
$321$	6.91990e21			0.191229
$322$	1.05007e21	−	1.05007e21i	0.0282173	−	0.0282173i
$323$	−4.15939e22	−	4.15939e22i	−1.08694	−	1.08694i
$324$		−	2.49498e22i		−	0.634107i
$325$	4.37501e21	−	1.67321e21i	0.108151	−	0.0413618i
$326$	3.16292e22			0.760553
$327$	−5.89720e21	+	5.89720e21i	−0.137948	+	0.137948i
$328$	−2.53084e20	−	2.53084e20i	−0.00575969	−	0.00575969i
$329$			6.27668e22i			1.38985i
$330$	−3.96733e21	−	6.11742e21i	−0.0854815	−	0.131808i
$331$	−3.83337e22			−0.803765			−0.401882	−	0.915691i	$-0.631644\pi$
$331$	−3.83337e22			−0.803765			−0.401882	+	0.915691i	$0.631644\pi$
$332$	2.26549e22	−	2.26549e22i	0.462295	−	0.462295i
$333$	8.31150e21	+	8.31150e21i	0.165075	+	0.165075i
$334$			7.70234e22i			1.48903i
$335$	−7.36508e22	−	1.57025e22i	−1.38604	−	0.295506i
$336$	7.17853e22			1.31517
$337$	2.54143e22	−	2.54143e22i	0.453324	−	0.453324i	−0.443132	−	0.896456i	$-0.646133\pi$
$337$	2.54143e22	−	2.54143e22i	0.453324	−	0.453324i	0.896456	+	0.443132i	$0.146133\pi$
$338$	−5.70764e22	−	5.70764e22i	−0.991303	−	0.991303i
$339$		−	5.63494e22i		−	0.952998i
$340$	1.88234e22	−	8.82888e22i	0.310019	−	1.45410i
$341$	1.06133e22			0.170239
$342$	1.98108e22	−	1.98108e22i	0.309504	−	0.309504i
$343$	−4.01899e22	−	4.01899e22i	−0.611603	−	0.611603i
$344$			3.21877e21i			0.0477160i
$345$	8.60736e20	−	5.58213e20i	0.0124308	−	0.00806172i
$346$	−8.20441e22			−1.15442
$347$	3.62099e22	−	3.62099e22i	0.496435	−	0.496435i	−0.413891	−	0.910326i	$-0.635831\pi$
$347$	3.62099e22	−	3.62099e22i	0.496435	−	0.496435i	0.910326	+	0.413891i	$0.135831\pi$
$348$	3.67076e22	+	3.67076e22i	0.490392	+	0.490392i
$349$			4.97742e22i			0.648001i	0.946057	+	0.324000i	$0.105028\pi$
$349$			4.97742e22i			0.648001i	−0.946057	+	0.324000i	$0.894972\pi$
$350$	1.63047e23	+	7.28348e22i	2.06871	+	0.924116i
$351$	−1.01795e22			−0.125881
$352$	1.09515e22	−	1.09515e22i	0.132005	−	0.132005i
$353$	2.66903e22	+	2.66903e22i	0.313604	+	0.313604i	0.846304	−	0.532700i	$-0.178823\pi$
$353$	2.66903e22	+	2.66903e22i	0.313604	+	0.313604i	−0.532700	+	0.846304i	$0.678823\pi$
$354$			3.44941e22i			0.395108i
$355$	1.62548e22	+	2.50642e22i	0.181521	+	0.279897i
$356$	−1.90582e22			−0.207506
$357$	−1.30332e23	+	1.30332e23i	−1.38368	+	1.38368i
$358$	3.83443e22	+	3.83443e22i	0.396967	+	0.396967i
$359$		−	1.03152e23i		−	1.04142i	−0.853733	−	0.520711i	$-0.825667\pi$
$359$		−	1.03152e23i		−	1.04142i	0.853733	−	0.520711i	$-0.174333\pi$
$360$	7.89849e20	+	1.68398e20i	0.00777717	+	0.00165811i
$361$	−1.14795e22			−0.110245
$362$	−1.77500e23	+	1.77500e23i	−1.66273	+	1.66273i
$363$	−6.39720e22	−	6.39720e22i	−0.584561	−	0.584561i
$364$			2.11079e22i			0.188162i
$365$	4.75239e21	−	2.22905e22i	0.0413310	−	0.193858i
$366$	−1.63671e23			−1.38881
$367$	−4.77233e22	+	4.77233e22i	−0.395127	+	0.395127i	−0.876510	−	0.481384i	$-0.840134\pi$
$367$	−4.77233e22	+	4.77233e22i	−0.395127	+	0.395127i	0.481384	+	0.876510i	$0.340134\pi$
$368$	1.51140e21	+	1.51140e21i	0.0122109	+	0.0122109i
$369$		−	1.11034e22i		−	0.0875423i
$370$	1.23729e23	−	8.02419e22i	0.952042	−	0.617427i
$371$	4.14015e23			3.10921
$372$	1.07127e23	−	1.07127e23i	0.785255	−	0.785255i
$373$	−1.41044e22	−	1.41044e22i	−0.100920	−	0.100920i	0.654844	−	0.755764i	$-0.272734\pi$
$373$	−1.41044e22	−	1.41044e22i	−0.100920	−	0.100920i	−0.755764	+	0.654844i	$0.772734\pi$
$374$			3.90052e22i			0.272445i
$375$	9.96701e22	+	7.26973e22i	0.679647	+	0.495721i
$376$	3.56136e21			0.0237097
$377$	1.01892e22	−	1.01892e22i	0.0662320	−	0.0662320i
$378$	−2.74416e23	−	2.74416e23i	−1.74174	−	1.74174i
$379$		−	1.16384e23i		−	0.721341i	−0.932693	−	0.360671i	$-0.882548\pi$
$379$		−	1.16384e23i		−	0.721341i	0.932693	−	0.360671i	$-0.117452\pi$
$380$	−9.65366e22	−	1.48855e23i	−0.584305	−	0.900969i
$381$	1.51032e23			0.892778
$382$	1.81538e22	−	1.81538e22i	0.104809	−	0.104809i
$383$	8.23735e22	+	8.23735e22i	0.464514	+	0.464514i	0.900132	−	0.435618i	$-0.143470\pi$
$383$	8.23735e22	+	8.23735e22i	0.464514	+	0.464514i	−0.435618	+	0.900132i	$0.643470\pi$
$384$		−	8.30670e21i		−	0.0457560i
$385$	−3.80892e22	−	8.12071e21i	−0.204953	−	0.0436966i
$386$	−3.13680e23			−1.64893
$387$	−7.06076e22	+	7.06076e22i	−0.362621	+	0.362621i
$388$	4.64282e22	+	4.64282e22i	0.232968	+	0.232968i
$389$			1.22594e22i			0.0601066i	0.999548	+	0.0300533i	$0.00956771\pi$
$389$			1.22594e22i			0.0601066i	−0.999548	+	0.0300533i	$0.990432\pi$
$390$	−6.02405e21	+	2.82550e22i	−0.0288607	+	0.135368i
$391$	−5.48813e21			−0.0256941
$392$	−6.48419e21	+	6.48419e21i	−0.0296675	+	0.0296675i
$393$	2.73998e22	+	2.73998e22i	0.122522	+	0.122522i
$394$			3.52006e22i			0.153845i
$395$	−1.63385e23	+	1.05960e23i	−0.697974	+	0.452656i
$396$	−9.37696e21			−0.0391566
$397$	2.14140e23	−	2.14140e23i	0.874146	−	0.874146i	−0.118775	−	0.992921i	$-0.537897\pi$
$397$	2.14140e23	−	2.14140e23i	0.874146	−	0.874146i	0.992921	+	0.118775i	$0.0378967\pi$
$398$	2.06237e23	+	2.06237e23i	0.823038	+	0.823038i
$399$			3.62246e23i			1.41334i
$400$	−1.04834e23	+	2.34679e23i	−0.399908	+	0.895229i
$401$	−3.97111e23			−1.48120			−0.740598	−	0.671948i	$-0.765458\pi$
$401$	−3.97111e23			−1.48120			−0.740598	+	0.671948i	$0.765458\pi$
$402$	3.28430e23	−	3.28430e23i	1.19786	−	1.19786i
$403$	−2.97359e22	−	2.97359e22i	−0.106056	−	0.106056i
$404$			2.85599e23i			0.996151i
$405$	−9.92471e22	−	1.53034e23i	−0.338550	−	0.522027i
$406$	5.49357e23			1.83282
$407$	−2.27417e22	+	2.27417e22i	−0.0742119	+	0.0742119i
$408$	7.39498e21	+	7.39498e21i	0.0236045	+	0.0236045i
$409$		−	1.10759e23i		−	0.345836i	−0.984936	−	0.172918i	$-0.944680\pi$
$409$		−	1.10759e23i		−	0.345836i	0.984936	−	0.172918i	$-0.0553196\pi$
$410$	−1.36243e23	−	2.90474e22i	−0.416160	−	0.0887263i
$411$	−1.49206e23			−0.445872
$412$	2.06206e22	−	2.06206e22i	0.0602875	−	0.0602875i
$413$	1.30281e23	+	1.30281e23i	0.372676	+	0.372676i
$414$		−	2.61394e21i		−	0.00731632i
$415$	4.88395e22	−	2.29076e23i	0.133764	−	0.627403i
$416$	−6.13671e22			−0.164474
$417$	−1.19847e23	+	1.19847e23i	−0.314342	+	0.314342i
$418$	5.42058e22	+	5.42058e22i	0.139142	+	0.139142i
$419$		−	6.06052e23i		−	1.52259i	−0.648405	−	0.761296i	$-0.724564\pi$
$419$		−	6.06052e23i		−	1.52259i	0.648405	−	0.761296i	$-0.275436\pi$
$420$	−4.66426e23	+	3.02491e23i	−1.14694	+	0.743821i
$421$	3.29882e23			0.793999			0.397000	−	0.917819i	$-0.370051\pi$
$421$	3.29882e23			0.793999			0.397000	+	0.917819i	$0.370051\pi$
$422$	1.42196e23	−	1.42196e23i	0.335025	−	0.335025i
$423$	7.81228e22	+	7.81228e22i	0.180183	+	0.180183i
$424$		−	2.34910e22i		−	0.0530407i
$425$	−2.35745e23	−	6.16412e23i	−0.521124	−	1.36261i
$426$	−1.84253e23			−0.398775
$427$	−6.18171e23	+	6.18171e23i	−1.30996	+	1.30996i
$428$	−7.89508e22	−	7.89508e22i	−0.163818	−	0.163818i
$429$		−	6.30059e21i		−	0.0128016i
$430$	6.81669e23	+	1.05110e24i	1.35631	+	2.09136i
$431$	−5.90484e23			−1.15057			−0.575284	−	0.817954i	$-0.695109\pi$
$431$	−5.90484e23			−1.15057			−0.575284	+	0.817954i	$0.695109\pi$
$432$	3.94977e23	−	3.94977e23i	0.753733	−	0.753733i
$433$	1.62662e23	+	1.62662e23i	0.304016	+	0.304016i	0.842583	−	0.538567i	$-0.181034\pi$
$433$	1.62662e23	+	1.62662e23i	0.304016	+	0.304016i	−0.538567	+	0.842583i	$0.681034\pi$
$434$		−	1.60323e24i		−	2.93487i
$435$	3.71171e23	+	7.91346e22i	0.665534	+	0.141894i
$436$	1.34565e23			0.236349
$437$	−7.62689e21	+	7.62689e21i	−0.0131224	+	0.0131224i
$438$	9.93995e22	+	9.93995e22i	0.167539	+	0.167539i
$439$		−	7.48498e23i		−	1.23598i	−0.786188	−	0.617988i	$-0.787948\pi$
$439$		−	7.48498e23i		−	1.23598i	0.786188	−	0.617988i	$-0.212052\pi$
$440$	−4.60766e20	+	2.16117e21i	−0.000745429	+	0.00349634i
$441$	−2.84477e23			−0.450920
$442$	1.09283e23	−	1.09283e23i	0.169728	−	0.169728i
$443$	8.56187e23	+	8.56187e23i	1.30297	+	1.30297i	0.926379	+	0.376592i	$0.122904\pi$
$443$	8.56187e23	+	8.56187e23i	1.30297	+	1.30297i	0.376592	+	0.926379i	$0.377096\pi$
$444$			4.59093e23i			0.684628i
$445$	−1.16897e23	+	7.58109e22i	−0.170829	+	0.110788i
$446$	7.11561e22			0.101906
$447$	−2.02320e23	+	2.02320e23i	−0.283969	+	0.283969i
$448$	−8.50695e23	−	8.50695e23i	−1.17023	−	1.17023i
$449$			1.02420e24i			1.38091i	0.723375	+	0.690455i	$0.242590\pi$
$449$			1.02420e24i			1.38091i	−0.723375	+	0.690455i	$0.757410\pi$
$450$	2.93591e23	−	1.12283e23i	0.387998	−	0.148389i
$451$	3.03808e22			0.0393560
$452$	−6.42903e23	+	6.42903e23i	−0.816394	+	0.816394i
$453$	−1.42345e23	−	1.42345e23i	−0.177197	−	0.177197i
$454$			1.26952e24i			1.54930i
$455$	8.39645e22	+	1.29469e23i	0.100460	+	0.154904i
$456$	2.05537e22			0.0241105
$457$	2.93797e23	−	2.93797e23i	0.337911	−	0.337911i	−0.517670	−	0.855581i	$-0.673200\pi$
$457$	2.93797e23	−	2.93797e23i	0.337911	−	0.337911i	0.855581	+	0.517670i	$0.173200\pi$
$458$	−4.30744e23	−	4.30744e23i	−0.485769	−	0.485769i
$459$			1.43422e24i			1.58600i
$460$	−1.61891e22	−	3.45156e21i	−0.0175551	−	0.00374279i
$461$	7.81447e23			0.830982			0.415491	−	0.909597i	$-0.363610\pi$
$461$	7.81447e23			0.830982			0.415491	+	0.909597i	$0.363610\pi$
$462$	1.69850e23	−	1.69850e23i	0.177128	−	0.177128i
$463$	−2.86591e23	−	2.86591e23i	−0.293112	−	0.293112i	0.545196	−	0.838308i	$-0.316455\pi$
$463$	−2.86591e23	−	2.86591e23i	−0.293112	−	0.293112i	−0.838308	+	0.545196i	$0.816455\pi$
$464$			7.90709e23i			0.793149i
$465$	2.30944e23	−	1.08322e24i	0.227212	−	1.06571i
$466$	−2.05418e24			−1.98228
$467$	−1.08185e23	+	1.08185e23i	−0.102403	+	0.102403i	−0.756452	−	0.654049i	$-0.773069\pi$
$467$	−1.08185e23	+	1.08185e23i	−0.102403	+	0.102403i	0.654049	+	0.756452i	$0.273069\pi$
$468$	2.62720e22	+	2.62720e22i	0.0243939	+	0.0243939i
$469$		−	2.48090e24i		−	2.25971i
$470$	1.16297e24	−	7.54223e23i	1.03918	−	0.673937i
$471$	1.23947e24			1.08654
$472$	7.39210e21	−	7.39210e21i	0.00635755	−	0.00635755i
$473$	−1.93195e23	−	1.93195e23i	−0.163022	−	0.163022i
$474$		−	1.20109e24i		−	0.994418i
$475$	−1.18425e24	−	5.29016e23i	−0.962056	−	0.429760i
$476$	2.97397e24			2.37069
$477$	5.15304e23	−	5.15304e23i	0.403087	−	0.403087i
$478$	−8.67887e23	−	8.67887e23i	−0.666211	−	0.666211i
$479$			2.16217e24i			1.62881i	0.580299	+	0.814404i	$0.302936\pi$
$479$			2.16217e24i			1.62881i	−0.580299	+	0.814404i	$0.697064\pi$
$480$	−8.79433e23	−	1.35604e24i	−0.650177	−	1.00254i
$481$	1.27434e23			0.0924653
$482$	−8.33476e23	+	8.33476e23i	−0.593567	+	0.593567i
$483$	2.38983e22	+	2.38983e22i	0.0167049	+	0.0167049i
$484$			1.45974e24i			1.00154i
$485$	4.69461e23	+	1.00090e23i	0.316172	+	0.0674087i
$486$	−1.21169e24			−0.801058
$487$	8.70611e23	−	8.70611e23i	0.565020	−	0.565020i	−0.365709	−	0.930729i	$-0.619174\pi$
$487$	8.70611e23	−	8.70611e23i	0.565020	−	0.565020i	0.930729	+	0.365709i	$0.119174\pi$
$488$	3.50748e22	+	3.50748e22i	0.0223469	+	0.0223469i
$489$			7.19843e23i			0.450255i
$490$	−7.44215e23	+	3.49065e24i	−0.457019	+	2.14359i
$491$	−1.00188e23			−0.0604064			−0.0302032	−	0.999544i	$-0.509615\pi$
$491$	−1.00188e23			−0.0604064			−0.0302032	+	0.999544i	$0.509615\pi$
$492$	3.06653e23	−	3.06653e23i	0.181535	−	0.181535i
$493$	−1.43559e24	−	1.43559e24i	−0.834467	−	0.834467i
$494$		−	3.03744e23i		−	0.173366i
$495$	−5.75152e22	+	3.73003e22i	−0.0322356	+	0.0209057i
$496$	2.30758e24			1.27005
$497$	−6.95907e23	+	6.95907e23i	−0.376135	+	0.376135i
$498$	1.02151e24	+	1.02151e24i	0.542225	+	0.542225i
$499$			1.48372e24i			0.773477i	0.922189	+	0.386738i	$0.126398\pi$
$499$			1.48372e24i			0.773477i	−0.922189	+	0.386738i	$0.873602\pi$
$500$	−3.07739e23	−	1.96658e24i	−0.157563	−	1.00689i
$501$	−1.75296e24			−0.881522
$502$	−3.20900e24	+	3.20900e24i	−1.58502	+	1.58502i
$503$	1.41462e23	+	1.41462e23i	0.0686320	+	0.0686320i	0.740590	−	0.671958i	$-0.234546\pi$
$503$	1.41462e23	+	1.41462e23i	0.0686320	+	0.0686320i	−0.671958	+	0.740590i	$0.734546\pi$
$504$			2.66057e22i			0.0126794i
$505$	1.13608e24	+	1.75177e24i	0.531845	+	0.820079i
$506$	7.15221e21			0.00328916
$507$	1.29899e24	−	1.29899e24i	0.586861	−	0.586861i
$508$	−1.72316e24	−	1.72316e24i	−0.764806	−	0.764806i
$509$		−	2.04253e24i		−	0.890653i	−0.895368	−	0.445327i	$-0.853088\pi$
$509$		−	2.04253e24i		−	0.890653i	0.895368	−	0.445327i	$-0.146912\pi$
$510$	3.98096e24	+	8.48750e23i	1.70552	+	0.363621i
$511$	7.50845e23			0.316055
$512$	2.42672e24	−	2.42672e24i	1.00367	−	1.00367i
$513$	1.99315e24	+	1.99315e24i	0.809997	+	0.809997i
$514$		−	4.47444e24i		−	1.78678i
$515$	4.44541e22	−	2.08507e23i	0.0174440	−	0.0818191i
$516$	−3.90008e24			−1.50392
$517$	−2.13758e23	+	2.13758e23i	−0.0810041	+	0.0810041i
$518$	3.43534e24	+	3.43534e24i	1.27939	+	1.27939i
$519$		−	1.86723e24i		−	0.683425i
$520$	7.34603e21	−	4.76411e21i	0.00264254	−	0.00171377i
$521$	−2.17020e24			−0.767292			−0.383646	−	0.923480i	$-0.625332\pi$
$521$	−2.17020e24			−0.767292			−0.383646	+	0.923480i	$0.625332\pi$
$522$	6.83759e23	−	6.83759e23i	0.237612	−	0.237612i
$523$	−2.79500e22	−	2.79500e22i	−0.00954701	−	0.00954701i	0.702317	−	0.711864i	$-0.252149\pi$
$523$	−2.79500e22	−	2.79500e22i	−0.00954701	−	0.00954701i	−0.711864	+	0.702317i	$0.752149\pi$
$524$		−	6.25221e23i		−	0.209919i
$525$	−1.65764e24	+	3.71076e24i	−0.547085	+	1.22470i
$526$	−2.99363e24			−0.971241
$527$	−4.18960e24	+	4.18960e24i	−1.33622	+	1.33622i
$528$	2.44471e23	+	2.44471e23i	0.0766518	+	0.0766518i
$529$		−	3.24314e24i		−	0.999690i
$530$	−4.97492e24	−	7.67108e24i	−1.50766	−	2.32473i
$531$	3.24309e23			0.0966293
$532$	4.13295e24	−	4.13295e24i	1.21075	−	1.21075i
$533$	−8.51198e22	−	8.51198e22i	−0.0245180	−	0.0245180i
$534$		−	8.59337e23i		−	0.243384i
$535$	−7.98314e23	−	1.70203e23i	−0.222326	−	0.0474004i
$536$	−1.40765e23			−0.0385489
$537$	−8.72673e23	+	8.72673e23i	−0.235008	+	0.235008i
$538$	7.24495e24	+	7.24495e24i	1.91865	+	1.91865i
$539$		−	7.78379e23i		−	0.202718i
$540$	−9.02002e23	+	4.23073e24i	−0.231028	+	1.08361i
$541$	7.18172e24			1.80906			0.904530	−	0.426409i	$-0.140222\pi$
$541$	7.18172e24			1.80906			0.904530	+	0.426409i	$0.140222\pi$
$542$	−5.14871e22	+	5.14871e22i	−0.0127557	+	0.0127557i
$543$	−4.03969e24	−	4.03969e24i	−0.984350	−	0.984350i
$544$			8.64624e24i			2.07223i
$545$	8.25378e23	−	5.35282e23i	0.194574	−	0.126187i
$546$	−9.51759e23			−0.220695
$547$	6.03797e24	−	6.03797e24i	1.37723	−	1.37723i	0.527950	−	0.849275i	$-0.322961\pi$
$547$	6.03797e24	−	6.03797e24i	1.37723	−	1.37723i	0.849275	−	0.527950i	$-0.177039\pi$
$548$	1.70233e24	+	1.70233e24i	0.381960	+	0.381960i
$549$			1.53882e24i			0.339653i
$550$	3.07226e23	+	8.03316e23i	0.0667103	+	0.174430i
$551$	−3.99011e24			−0.852355
$552$	1.35598e21	−	1.35598e21i	0.000284972	−	0.000284972i
$553$	−4.53639e24	−	4.53639e24i	−0.937960	−	0.937960i
$554$		−	1.72349e24i		−	0.350607i
$555$	1.82621e24	+	2.81593e24i	0.365523	+	0.563618i
$556$	2.73472e24			0.538567
$557$	−4.27906e24	+	4.27906e24i	−0.829185	+	0.829185i	−0.987404	−	0.158219i	$-0.949425\pi$
$557$	−4.27906e24	+	4.27906e24i	−0.829185	+	0.829185i	0.158219	+	0.987404i	$0.449425\pi$
$558$	−1.99546e24	−	1.99546e24i	−0.380484	−	0.380484i
$559$			1.08257e24i			0.203119i
$560$	−8.28150e24	−	1.76564e24i	−1.52903	−	0.325994i
$561$	−8.87713e23			−0.161290
$562$	−3.35906e24	+	3.35906e24i	−0.600607	+	0.600607i
$563$	5.52381e23	+	5.52381e23i	0.0971993	+	0.0971993i	0.754034	−	0.656835i	$-0.228105\pi$
$563$	5.52381e23	+	5.52381e23i	0.0971993	+	0.0971993i	−0.656835	+	0.754034i	$0.728105\pi$
$564$			4.31519e24i			0.747287i
$565$	−1.38597e24	+	6.50074e24i	−0.236221	+	1.10797i
$566$	1.03253e25			1.73202
$567$	4.24899e24	−	4.24899e24i	0.701518	−	0.701518i
$568$	3.94855e22	+	3.94855e22i	0.00641656	+	0.00641656i
$569$			3.53272e24i			0.565066i	0.959258	+	0.282533i	$0.0911746\pi$
$569$			3.53272e24i			0.565066i	−0.959258	+	0.282533i	$0.908825\pi$
$570$	6.71188e24	−	4.35285e24i	1.05675	−	0.685331i
$571$	−7.27280e24			−1.12714			−0.563569	−	0.826069i	$-0.690572\pi$
$571$	−7.27280e24			−1.12714			−0.563569	+	0.826069i	$0.690572\pi$
$572$	−7.18849e22	+	7.18849e22i	−0.0109666	+	0.0109666i
$573$	4.13159e23	+	4.13159e23i	0.0620476	+	0.0620476i
$574$		−	4.58929e24i		−	0.678483i
$575$	−1.13029e23	+	4.32274e22i	−0.0164505	+	0.00629142i
$576$	−2.11764e24			−0.303424
$577$	6.81728e24	−	6.81728e24i	0.961676	−	0.961676i	−0.0376159	−	0.999292i	$-0.511976\pi$
$577$	6.81728e24	−	6.81728e24i	0.961676	−	0.961676i	0.999292	+	0.0376159i	$0.0119763\pi$
$578$	−8.16265e24	−	8.16265e24i	−1.13365	−	1.13365i
$579$		−	7.13899e24i		−	0.976180i
$580$	−3.33191e24	−	5.13764e24i	−0.448581	−	0.691690i
$581$	7.71632e24			1.02288
$582$	−2.09346e24	+	2.09346e24i	−0.273248	+	0.273248i
$583$	1.40996e24	+	1.40996e24i	0.181214	+	0.181214i
$584$		−	4.26027e22i		−	0.00539165i
$585$	2.65651e23	+	5.66374e22i	0.0331061	+	0.00705830i
$586$	2.32057e24			0.284784
$587$	2.55631e24	−	2.55631e24i	0.308938	−	0.308938i	−0.535560	−	0.844497i	$-0.679899\pi$
$587$	2.55631e24	−	2.55631e24i	0.308938	−	0.308938i	0.844497	+	0.535560i	$0.179899\pi$
$588$	−7.85667e24	−	7.85667e24i	−0.935067	−	0.935067i
$589$			1.16446e25i			1.36486i
$590$	8.48420e23	−	3.97941e24i	0.0979362	−	0.459357i
$591$	−8.01126e23			−0.0910780
$592$	−4.94460e24	+	4.94460e24i	−0.553651	+	0.553651i
$593$	1.05028e25	+	1.05028e25i	1.15828	+	1.15828i	0.984845	+	0.173438i	$0.0554876\pi$
$593$	1.05028e25	+	1.05028e25i	1.15828	+	1.15828i	0.173438	+	0.984845i	$0.444512\pi$
$594$		−	1.86910e24i		−	0.203027i
$595$	1.82414e25	−	1.18301e25i	1.95166	−	1.26571i
$596$	4.61662e24			0.486528
$597$	−4.69372e24	+	4.69372e24i	−0.487246	+	0.487246i
$598$	−2.00388e22	−	2.00388e22i	−0.00204909	−	0.00204909i
$599$		−	4.15761e24i		−	0.418796i	−0.977830	−	0.209398i	$-0.932850\pi$
$599$		−	4.15761e24i		−	0.418796i	0.977830	−	0.209398i	$-0.0671505\pi$
$600$	2.10547e23	+	9.40536e22i	0.0208924	+	0.00933285i
$601$	−1.22302e25			−1.19554			−0.597770	−	0.801668i	$-0.703946\pi$
$601$	−1.22302e25			−1.19554			−0.597770	+	0.801668i	$0.703946\pi$
$602$	−2.91838e25	+	2.91838e25i	−2.81043	+	2.81043i
$603$	−3.08786e24	−	3.08786e24i	−0.292955	−	0.292955i
$604$			3.24808e24i			0.303595i
$605$	5.80666e24	+	8.95358e24i	0.534722	+	0.824515i
$606$	−1.28777e25			−1.16838
$607$	−4.32512e24	+	4.32512e24i	−0.386633	+	0.386633i	−0.873485	−	0.486851i	$-0.838145\pi$
$607$	−4.32512e24	+	4.32512e24i	−0.386633	+	0.386633i	0.486851	+	0.873485i	$0.338145\pi$
$608$	1.20158e25	+	1.20158e25i	1.05832	+	1.05832i
$609$			1.25027e25i			1.08505i
$610$	1.88819e25	+	4.02567e24i	1.61465	+	0.344247i
$611$	1.19780e24			0.100928
$612$	3.70156e24	−	3.70156e24i	0.307342	−	0.307342i
$613$	−9.48466e24	−	9.48466e24i	−0.776028	−	0.776028i	0.203125	−	0.979153i	$-0.434890\pi$
$613$	−9.48466e24	−	9.48466e24i	−0.776028	−	0.776028i	−0.979153	+	0.203125i	$0.934890\pi$
$614$		−	2.16053e25i		−	1.74199i
$615$	6.61085e23	−	3.10074e24i	0.0525268	−	0.246370i
$616$	−7.27979e22			−0.00570023
$617$	1.21871e25	−	1.21871e25i	0.940444	−	0.940444i	−0.0578795	−	0.998324i	$-0.518434\pi$
$617$	1.21871e25	−	1.21871e25i	0.940444	−	0.940444i	0.998324	+	0.0578795i	$0.0184339\pi$
$618$	9.29789e23	+	9.29789e23i	0.0707112	+	0.0707112i
$619$			1.24532e25i			0.933392i	0.884418	+	0.466696i	$0.154556\pi$
$619$			1.24532e25i			0.933392i	−0.884418	+	0.466696i	$0.845444\pi$
$620$	−1.49935e25	+	9.72376e24i	−1.10759	+	0.718305i
$621$	2.62987e23			0.0191474
$622$	2.30887e25	−	2.30887e25i	1.65686	−	1.65686i
$623$	−3.24564e24	−	3.24564e24i	−0.229566	−	0.229566i
$624$		−	1.36990e24i		−	0.0955053i
$625$	−9.71037e24	−	1.08382e25i	−0.667292	−	0.744797i
$626$	3.01516e25			2.04240
$627$	−1.23366e24	+	1.23366e24i	−0.0823736	+	0.0823736i
$628$	−1.41414e25	−	1.41414e25i	−0.930797	−	0.930797i
$629$		−	1.79546e25i		−	1.16498i
$630$	5.63454e24	+	8.68819e24i	0.360407	+	0.555730i
$631$	−2.82220e25			−1.77960			−0.889802	−	0.456348i	$-0.849157\pi$
$631$	−2.82220e25			−1.77960			−0.889802	+	0.456348i	$0.849157\pi$
$632$	−2.57393e23	+	2.57393e23i	−0.0160009	+	0.0160009i
$633$	3.23623e24	+	3.23623e24i	0.198338	+	0.198338i
$634$			8.58573e24i			0.518769i
$635$	−1.74238e25	−	3.71479e24i	−1.03795	−	0.221295i
$636$	2.84633e25			1.67175
$637$	−2.18083e24	+	2.18083e24i	−0.126290	+	0.126290i
$638$	1.87089e24	+	1.87089e24i	0.106822	+	0.106822i
$639$			1.73232e24i			0.0975262i
$640$	−2.04313e23	+	9.58302e23i	−0.0113416	+	0.0531965i
$641$	3.08248e24			0.168724			0.0843622	−	0.996435i	$-0.473115\pi$
$641$	3.08248e24			0.168724			0.0843622	+	0.996435i	$0.473115\pi$
$642$	3.55990e24	−	3.55990e24i	0.192142	−	0.192142i
$643$	1.11895e25	+	1.11895e25i	0.595539	+	0.595539i	0.939122	−	0.343583i	$-0.111641\pi$
$643$	1.11895e25	+	1.11895e25i	0.595539	+	0.595539i	−0.343583	+	0.939122i	$0.611641\pi$
$644$		−	5.45324e23i		−	0.0286208i
$645$	−2.39218e25	+	1.55140e25i	−1.23810	+	0.802946i
$646$	−4.27955e25			−2.18427
$647$	−6.46529e23	+	6.46529e23i	−0.0325424	+	0.0325424i	−0.723191	−	0.690648i	$-0.757325\pi$
$647$	−6.46529e23	+	6.46529e23i	−0.0325424	+	0.0325424i	0.690648	+	0.723191i	$0.257325\pi$
$648$	−2.41086e23	−	2.41086e23i	−0.0119673	−	0.0119673i
$649$			8.87368e23i			0.0434412i
$650$	1.38993e24	−	3.11147e24i	0.0671077	−	0.150226i
$651$	3.64876e25			1.73747
$652$	8.21286e24	−	8.21286e24i	0.385715	−	0.385715i
$653$	−2.12074e25	−	2.12074e25i	−0.982357	−	0.982357i	0.0174899	−	0.999847i	$-0.494433\pi$
$653$	−2.12074e25	−	2.12074e25i	−0.982357	−	0.982357i	−0.999847	+	0.0174899i	$0.994433\pi$
$654$			6.06756e24i			0.277214i
$655$	−2.48705e24	−	3.83490e24i	−0.112076	−	0.172815i
$656$	6.60552e24			0.293611
$657$	9.34542e23	−	9.34542e23i	0.0409742	−	0.0409742i
$658$	3.22900e25	+	3.22900e25i	1.39648	+	1.39648i
$659$			8.76231e24i			0.373809i	0.982378	+	0.186905i	$0.0598455\pi$
$659$			8.76231e24i			0.373809i	−0.982378	+	0.186905i	$0.940155\pi$
$660$	−2.61861e24	−	5.58295e23i	−0.110199	−	0.0234946i
$661$	−7.04682e24			−0.292536			−0.146268	−	0.989245i	$-0.546726\pi$
$661$	−7.04682e24			−0.292536			−0.146268	+	0.989245i	$0.546726\pi$
$662$	−1.97206e25	+	1.97206e25i	−0.807602	+	0.807602i
$663$	2.48716e24	+	2.48716e24i	0.100481	+	0.100481i
$664$		−	4.37821e23i		−	0.0174495i
$665$	8.90984e24	−	4.17905e25i	0.350328	−	1.64317i
$666$	8.55161e24			0.331726
$667$	−2.63238e23	+	2.63238e23i	−0.0100743	+	0.0100743i
$668$	2.00000e25	+	2.00000e25i	0.755163	+	0.755163i
$669$			1.61943e24i			0.0603292i
$670$	−4.59673e25	+	2.98112e25i	−1.68957	+	1.09574i
$671$	−4.21047e24			−0.152696
$672$	3.76505e25	−	3.76505e25i	1.34725	−	1.34725i
$673$	3.91313e25	+	3.91313e25i	1.38162	+	1.38162i	0.841743	+	0.539878i	$0.181530\pi$
$673$	3.91313e25	+	3.91313e25i	1.38162	+	1.38162i	0.539878	+	0.841743i	$0.318470\pi$
$674$		−	2.61485e25i		−	0.910977i
$675$	1.12967e25	+	2.95380e25i	0.388345	+	1.01542i
$676$	−2.96410e25			−1.00548
$677$	2.07331e24	−	2.07331e24i	0.0694010	−	0.0694010i	−0.671554	−	0.740955i	$-0.734373\pi$
$677$	2.07331e24	−	2.07331e24i	0.0694010	−	0.0694010i	0.740955	+	0.671554i	$0.234373\pi$
$678$	−2.89886e25	−	2.89886e25i	−0.957547	−	0.957547i
$679$			1.58136e25i			0.515469i
$680$	−6.71233e23	−	1.03501e24i	−0.0215920	−	0.0332938i
$681$	−2.88928e25			−0.917203
$682$	5.45994e24	−	5.45994e24i	0.171052	−	0.171052i
$683$	1.44974e25	+	1.44974e25i	0.448234	+	0.448234i	0.894767	−	0.446533i	$-0.147342\pi$
$683$	1.44974e25	+	1.44974e25i	0.448234	+	0.448234i	−0.446533	+	0.894767i	$0.647342\pi$
$684$		−	1.02882e25i		−	0.313930i
$685$	1.72131e25	+	3.66989e24i	0.518376	+	0.110519i
$686$	−4.13509e25			−1.22905
$687$	9.80322e24	−	9.80322e24i	0.287580	−	0.287580i
$688$	−4.20052e25	−	4.20052e25i	−1.21621	−	1.21621i
$689$		−	7.90076e24i		−	0.225785i
$690$	1.55632e23	−	7.29970e23i	0.00438991	−	0.0205903i
$691$	1.75229e24			0.0487869			0.0243934	−	0.999702i	$-0.492235\pi$
$691$	1.75229e24			0.0487869			0.0243934	+	0.999702i	$0.492235\pi$
$692$	−2.13036e25	+	2.13036e25i	−0.585462	+	0.585462i
$693$	−1.59691e24	−	1.59691e24i	−0.0433193	−	0.0433193i
$694$		−	3.72560e25i		−	0.997610i
$695$	1.67739e25	−	1.08784e25i	0.443374	−	0.287541i
$696$	7.09401e23			0.0185101
$697$	−1.19928e25	+	1.19928e25i	−0.308907	+	0.308907i
$698$	2.56061e25	+	2.56061e25i	0.651095	+	0.651095i
$699$		−	4.67508e25i		−	1.17353i
$700$	6.12493e25	−	2.34246e25i	1.51781	−	0.580483i
$701$	4.99793e25			1.22272			0.611361	−	0.791352i	$-0.290622\pi$
$701$	4.99793e25			1.22272			0.611361	+	0.791352i	$0.290622\pi$
$702$	−5.23677e24	+	5.23677e24i	−0.126482	+	0.126482i
$703$	−2.49517e25	−	2.49517e25i	−0.594979	−	0.594979i
$704$		−	5.79423e24i		−	0.136409i
$705$	1.71652e25	+	2.64679e25i	0.398977	+	0.615203i
$706$	2.74614e25			0.630203
$707$	−4.86380e25	+	4.86380e25i	−1.10205	+	1.10205i
$708$	8.95677e24	+	8.95677e24i	0.200379	+	0.200379i
$709$		−	8.07324e25i		−	1.78333i	−0.452695	−	0.891665i	$-0.649537\pi$
$709$		−	8.07324e25i		−	1.78333i	0.452695	−	0.891665i	$-0.350463\pi$
$710$	2.12563e25	+	4.53190e24i	0.463621	+	0.0988452i
$711$	−1.12925e25			−0.243199
$712$	−1.84156e23	+	1.84156e23i	−0.00391622	+	0.00391622i
$713$	7.68228e23	+	7.68228e23i	0.0161318	+	0.0161318i
$714$			1.34097e26i			2.78058i
$715$	−1.54970e23	+	7.26867e23i	−0.00317317	+	0.0148833i
$716$	1.99130e25			0.402643
$717$	1.97521e25	−	1.97521e25i	0.394403	−	0.394403i
$718$	−5.30658e25	−	5.30658e25i	−1.04639	−	1.04639i
$719$			4.57638e25i			0.891173i	0.895239	+	0.445586i	$0.147005\pi$
$719$			4.57638e25i			0.891173i	−0.895239	+	0.445586i	$0.852995\pi$
$720$	−1.25052e25	+	8.10999e24i	−0.240491	+	0.155965i
$721$	7.02346e24			0.133393
$722$	−5.90556e24	+	5.90556e24i	−0.110771	+	0.110771i
$723$	−1.89689e25	−	1.89689e25i	−0.351397	−	0.351397i
$724$			9.21795e25i			1.68650i
$725$	−4.08737e25	−	1.82587e25i	−0.738587	−	0.329935i
$726$	−6.58201e25			−1.17470
$727$	−7.47038e25	+	7.47038e25i	−1.31684	+	1.31684i	−0.400578	+	0.916263i	$0.631191\pi$
$727$	−7.47038e25	+	7.47038e25i	−1.31684	+	1.31684i	−0.916263	+	0.400578i	$0.868809\pi$
$728$	2.03962e23	+	2.03962e23i	0.00355114	+	0.00355114i
$729$		−	6.37571e25i		−	1.09643i
$730$	−9.02237e24	−	1.39121e25i	−0.153255	−	0.236312i
$731$	1.52528e26			2.55913
$732$	−4.24990e25	+	4.24990e25i	−0.704334	+	0.704334i
$733$	5.83039e25	+	5.83039e25i	0.954470	+	0.954470i	0.999008	−	0.0445380i	$-0.0141816\pi$
$733$	5.83039e25	+	5.83039e25i	0.954470	+	0.954470i	−0.0445380	+	0.999008i	$0.514182\pi$
$734$			4.91020e25i			0.794026i
$735$	−7.94431e25	−	1.69375e25i	−1.26902	−	0.270559i
$736$	1.58542e24			0.0250175
$737$	8.44892e24	−	8.44892e24i	0.131702	−	0.131702i
$738$	−5.71208e24	−	5.71208e24i	−0.0879603	−	0.0879603i
$739$			7.38335e25i			1.12319i	0.827412	+	0.561596i	$0.189812\pi$
$739$			7.38335e25i			1.12319i	−0.827412	+	0.561596i	$0.810188\pi$
$740$	1.12919e25	−	5.29633e25i	0.169700	−	0.795957i
$741$	6.91285e24			0.102634
$742$	2.12987e26	−	2.12987e26i	3.12406	−	3.12406i
$743$	−6.71150e25	−	6.71150e25i	−0.972568	−	0.972568i	0.0270652	−	0.999634i	$-0.491384\pi$
$743$	−6.71150e25	−	6.71150e25i	−0.972568	−	0.972568i	−0.999634	+	0.0270652i	$0.991384\pi$
$744$		−	2.07030e24i		−	0.0296398i
$745$	2.83169e25	−	1.83643e25i	0.400533	−	0.259758i
$746$	−1.45119e25			−0.202803
$747$	9.60414e24	−	9.60414e24i	0.132609	−	0.132609i
$748$	1.01281e25	+	1.01281e25i	0.138170	+	0.138170i
$749$		−	2.68909e25i		−	0.362467i
$750$	8.86735e25	−	1.38760e25i	1.18098	−	0.184805i
$751$	5.68691e25			0.748371			0.374186	−	0.927354i	$-0.377922\pi$
$751$	5.68691e25			0.748371			0.374186	+	0.927354i	$0.377922\pi$
$752$	−4.64761e25	+	4.64761e25i	−0.604323	+	0.604323i
$753$	−7.30330e25	−	7.30330e25i	−0.938349	−	0.938349i
$754$		−	1.04835e25i		−	0.133096i
$755$	1.29204e25	+	1.99227e25i	0.162090	+	0.249934i
$756$	−1.42510e26			−1.76665
$757$	−4.37454e25	+	4.37454e25i	−0.535883	+	0.535883i	−0.922317	−	0.386434i	$-0.873707\pi$
$757$	−4.37454e25	+	4.37454e25i	−0.535883	+	0.535883i	0.386434	+	0.922317i	$0.373707\pi$
$758$	−5.98732e25	−	5.98732e25i	−0.724785	−	0.724785i
$759$			1.62776e23i			0.00194722i
$760$	−2.37118e24	−	5.05541e23i	−0.0280312	−	0.00597632i
$761$	−1.29060e26			−1.50775			−0.753874	−	0.657019i	$-0.771817\pi$
$761$	−1.29060e26			−1.50775			−0.753874	+	0.657019i	$0.771817\pi$
$762$	7.76974e25	−	7.76974e25i	0.897040	−	0.897040i
$763$	2.29166e25	+	2.29166e25i	0.261475	+	0.261475i
$764$		−	9.42765e24i		−	0.106307i
$765$	7.97985e24	−	3.74285e25i	0.0889287	−	0.417109i
$766$	8.47532e25			0.933463
$767$	2.48619e24	−	2.48619e24i	0.0270630	−	0.0270630i
$768$	5.31130e25	+	5.31130e25i	0.571413	+	0.571413i
$769$			4.12094e25i			0.438187i	0.975704	+	0.219094i	$0.0703100\pi$
$769$			4.12094e25i			0.438187i	−0.975704	+	0.219094i	$0.929690\pi$
$770$	−2.37724e25	+	1.54171e25i	−0.249837	+	0.162027i
$771$	1.01833e26			1.05779
$772$	−8.14504e25	+	8.14504e25i	−0.836253	+	0.836253i
$773$	6.57712e25	+	6.57712e25i	0.667453	+	0.667453i	0.957126	−	0.289673i	$-0.0935466\pi$
$773$	6.57712e25	+	6.57712e25i	0.667453	+	0.667453i	−0.289673	+	0.957126i	$0.593547\pi$
$774$			7.26474e25i			0.728704i
$775$	−5.32857e25	+	1.19285e26i	−0.528318	+	1.18269i
$776$	8.97257e23			0.00879349
$777$	−7.81843e25	+	7.81843e25i	−0.757409	+	0.757409i
$778$	6.30677e24	+	6.30677e24i	0.0603936	+	0.0603936i
$779$			3.33331e25i			0.315528i
$780$	5.77252e24	+	8.90094e24i	0.0540150	+	0.0832884i
$781$	−4.73994e24			−0.0438444
$782$	−2.82334e24	+	2.82334e24i	−0.0258168	+	0.0258168i
$783$	6.87925e25	+	6.87925e25i	0.621849	+	0.621849i
$784$		−	1.69238e26i		−	1.51236i
$785$	−1.42991e26	−	3.04861e25i	−1.26323	−	0.269324i
$786$	2.81913e25			0.246214
$787$	8.32552e25	−	8.32552e25i	0.718851	−	0.718851i	−0.249519	−	0.968370i	$-0.580272\pi$
$787$	8.32552e25	−	8.32552e25i	0.718851	−	0.718851i	0.968370	+	0.249519i	$0.0802724\pi$
$788$	9.14023e24	+	9.14023e24i	0.0780227	+	0.0780227i
$789$		−	6.81316e25i		−	0.574984i
$790$	−2.95420e25	+	1.38563e26i	−0.246488	+	1.15612i
$791$	−2.18975e26			−1.80637
$792$	−9.06081e22	+	9.06081e22i	−0.000738993	+	0.000738993i
$793$	1.17967e25	+	1.17967e25i	0.0951269	+	0.0951269i
$794$		−	2.20327e26i		−	1.75664i
$795$	1.74585e26	−	1.13223e26i	1.37627	−	0.892548i
$796$	1.07104e26			0.834807
$797$	1.00222e26	−	1.00222e26i	0.772395	−	0.772395i	−0.206130	−	0.978525i	$-0.566087\pi$
$797$	1.00222e26	−	1.00222e26i	0.772395	−	0.772395i	0.978525	+	0.206130i	$0.0660869\pi$
$798$	1.86355e26	+	1.86355e26i	1.42009	+	1.42009i
$799$		−	1.68762e26i		−	1.27161i
$800$	6.81024e25	+	1.78070e26i	0.507402	+	1.32673i
$801$	−8.07938e24			−0.0595231
$802$	−2.04292e26	+	2.04292e26i	−1.48827	+	1.48827i
$803$	2.55707e24	+	2.55707e24i	0.0184206	+	0.0184206i
$804$		−	1.70561e26i		−	1.21499i
$805$	−2.16923e24	−	3.34484e24i	−0.0152806	−	0.0235620i
$806$	−3.05949e25			−0.213125
$807$	−1.64887e26	+	1.64887e26i	−1.13586	+	1.13586i
$808$	2.75970e24	+	2.75970e24i	0.0188001	+	0.0188001i
$809$			1.13885e26i			0.767240i	0.923491	+	0.383620i	$0.125323\pi$
$809$			1.13885e26i			0.767240i	−0.923491	+	0.383620i	$0.874677\pi$
$810$	−1.29785e26	−	2.76704e25i	−0.864686	−	0.184353i
$811$	−1.82302e25			−0.120117			−0.0600583	−	0.998195i	$-0.519129\pi$
$811$	−1.82302e25			−0.120117			−0.0600583	+	0.998195i	$0.519129\pi$
$812$	1.42647e26	−	1.42647e26i	0.929517	−	0.929517i
$813$	−1.17179e24	−	1.17179e24i	−0.00755151	−	0.00755151i
$814$			2.33987e25i			0.149132i
$815$	1.77053e25	−	8.30447e25i	0.111606	−	0.523472i
$816$	−1.93010e26			−1.20329
$817$	2.11969e26	−	2.11969e26i	1.30699	−	1.30699i
$818$	−5.69795e25	−	5.69795e25i	−0.347488	−	0.347488i
$819$			8.94833e24i			0.0539743i
$820$	−4.29195e25	+	2.78345e25i	−0.256053	+	0.166058i
$821$	−7.75019e25			−0.457324			−0.228662	−	0.973506i	$-0.573435\pi$
$821$	−7.75019e25			−0.457324			−0.228662	+	0.973506i	$0.573435\pi$
$822$	−7.67582e25	+	7.67582e25i	−0.448001	+	0.448001i
$823$	−1.94271e26	−	1.94271e26i	−1.12152	−	1.12152i	−0.991512	−	0.130013i	$-0.958498\pi$
$823$	−1.94271e26	−	1.94271e26i	−1.12152	−	1.12152i	−0.130013	−	0.991512i	$-0.541502\pi$
$824$		−	3.98508e23i		−	0.00227558i
$825$	−1.82825e25	+	6.99210e24i	−0.103265	+	0.0394932i
$826$	1.34045e26			0.748910
$827$	1.62207e26	−	1.62207e26i	0.896438	−	0.896438i	−0.0986809	−	0.995119i	$-0.531462\pi$
$827$	1.62207e26	−	1.62207e26i	0.896438	−	0.896438i	0.995119	+	0.0986809i	$0.0314623\pi$
$828$	−6.78738e23	−	6.78738e23i	−0.00371047	−	0.00371047i
$829$			3.29834e26i			1.78363i	0.452398	+	0.891816i	$0.350569\pi$
$829$			3.29834e26i			1.78363i	−0.452398	+	0.891816i	$0.649431\pi$
$830$	−9.27215e25	−	1.42972e26i	−0.495995	−	0.764800i
$831$	3.92246e25			0.207563
$832$	−1.62341e25	+	1.62341e25i	−0.0849801	+	0.0849801i
$833$	3.07265e26	+	3.07265e26i	1.59114	+	1.59114i
$834$			1.23309e26i			0.631685i
$835$	2.02230e26	+	4.31160e25i	1.02487	+	0.218505i
$836$	2.81503e25			0.141132
$837$	2.00762e26	−	2.00762e26i	0.995756	−	0.995756i
$838$	−3.11780e26	−	3.11780e26i	−1.52986	−	1.52986i
$839$			3.41571e24i			0.0165815i	0.999966	+	0.00829075i	$0.00263906\pi$
$839$			3.41571e24i			0.0165815i	−0.999966	+	0.00829075i	$0.997361\pi$
$840$	−1.58408e24	+	7.42992e24i	−0.00760787	+	0.0356838i
$841$	7.27407e25			0.345632
$842$	1.69706e26	−	1.69706e26i	0.797790	−	0.797790i
$843$	−7.64482e25	−	7.64482e25i	−0.355565	−	0.355565i
$844$		−	7.38457e25i		−	0.339816i
$845$	−1.81808e26	+	1.17908e26i	−0.827758	+	0.536825i
$846$	8.03797e25			0.362087
$847$	−2.48596e26	+	2.48596e26i	−1.10801	+	1.10801i
$848$	3.06560e26	+	3.06560e26i	1.35193	+	1.35193i
$849$			2.34991e26i			1.02537i
$850$	−4.38387e26	−	1.95832e26i	−1.89272	−	0.845500i
$851$	−3.29226e24			−0.0140646
$852$	−4.78433e25	+	4.78433e25i	−0.202239	+	0.202239i
$853$	6.73088e25	+	6.73088e25i	0.281534	+	0.281534i	0.833720	−	0.552187i	$-0.186206\pi$
$853$	6.73088e25	+	6.73088e25i	0.281534	+	0.281534i	−0.552187	+	0.833720i	$0.686206\pi$
$854$			6.36029e26i			2.63243i
$855$	−4.09250e25	−	6.31043e25i	−0.167608	−	0.258442i
$856$	−1.52578e24			−0.00618340
$857$	−1.87254e26	+	1.87254e26i	−0.750935	+	0.750935i	−0.974654	−	0.223718i	$-0.928180\pi$
$857$	−1.87254e26	+	1.87254e26i	−0.750935	+	0.750935i	0.223718	+	0.974654i	$0.428180\pi$
$858$	−3.24130e24	−	3.24130e24i	−0.0128627	−	0.0128627i
$859$		−	2.23551e26i		−	0.877884i	−0.898515	−	0.438942i	$-0.855353\pi$
$859$		−	2.23551e26i		−	0.877884i	0.898515	−	0.438942i	$-0.144647\pi$
$860$	4.49932e26	+	9.59267e25i	1.74848	+	0.372781i
$861$	1.04447e26			0.401668
$862$	−3.03771e26	+	3.03771e26i	−1.15606	+	1.15606i
$863$	−1.57856e26	−	1.57856e26i	−0.594517	−	0.594517i	0.344331	−	0.938848i	$-0.388106\pi$
$863$	−1.57856e26	−	1.57856e26i	−0.594517	−	0.594517i	−0.938848	+	0.344331i	$0.888106\pi$
$864$		−	4.14321e26i		−	1.54424i
$865$	−4.59265e25	+	2.15413e26i	−0.169402	+	0.794559i
$866$	1.67362e26			0.610935
$867$	1.85772e26	−	1.85772e26i	0.671134	−	0.671134i
$868$	−4.16296e26	−	4.16296e26i	−1.48842	−	1.48842i
$869$		−	3.08982e25i		−	0.109334i
$870$	2.31657e26	−	1.50236e26i	0.811283	−	0.526141i
$871$	−4.73437e25			−0.164096
$872$	1.30028e24	−	1.30028e24i	0.00446056	−	0.00446056i
$873$	1.96824e25	+	1.96824e25i	0.0668268	+	0.0668268i
$874$			7.84723e24i			0.0263702i
$875$	2.82503e26	−	3.87320e26i	0.939617	−	1.28824i
$876$	5.16203e25			0.169935
$877$	−1.32860e26	+	1.32860e26i	−0.432909	+	0.432909i	−0.889617	−	0.456708i	$-0.849029\pi$
$877$	−1.32860e26	+	1.32860e26i	−0.432909	+	0.432909i	0.456708	+	0.889617i	$0.349029\pi$
$878$	−3.85060e26	−	3.85060e26i	−1.24188	−	1.24188i
$879$			5.28135e25i			0.168595i
$880$	−2.21904e25	−	3.42164e25i	−0.0701165	−	0.108116i
$881$	−1.97429e26			−0.617486			−0.308743	−	0.951145i	$-0.599908\pi$
$881$	−1.97429e26			−0.617486			−0.308743	+	0.951145i	$0.599908\pi$
$882$	−1.46348e26	+	1.46348e26i	−0.453073	+	0.453073i
$883$	2.23309e26	+	2.23309e26i	0.684320	+	0.684320i	0.960970	−	0.276651i	$-0.0892246\pi$
$883$	2.23309e26	+	2.23309e26i	0.684320	+	0.684320i	−0.276651	+	0.960970i	$0.589225\pi$
$884$		−	5.67532e25i		−	0.172155i
$885$	9.05667e25	+	1.93091e25i	0.271944	+	0.0579791i
$886$	8.80921e26			2.61838
$887$	1.76217e26	−	1.76217e26i	0.518483	−	0.518483i	−0.398629	−	0.917112i	$-0.630514\pi$
$887$	1.76217e26	−	1.76217e26i	0.518483	−	0.518483i	0.917112	+	0.398629i	$0.130514\pi$
$888$	4.43615e24	+	4.43615e24i	0.0129208	+	0.0129208i
$889$		−	5.86912e26i		−	1.69222i
$890$	−2.11363e25	+	9.91373e25i	−0.0603281	+	0.282961i
$891$	2.89407e25			0.0817728
$892$	1.84765e25	−	1.84765e25i	0.0516815	−	0.0516815i
$893$	−2.34530e26	−	2.34530e26i	−0.649434	−	0.649434i
$894$			2.08164e26i			0.570649i
$895$	1.22140e26	−	7.92115e25i	0.331475	−	0.214971i
$896$	−3.22800e25			−0.0867285
$897$	4.56059e23	−	4.56059e23i	0.00121308	−	0.00121308i
$898$	5.26891e26	+	5.26891e26i	1.38750	+	1.38750i
$899$			4.01908e26i			1.04783i
$900$	4.70786e25	−	1.05389e26i	0.121518	−	0.272029i
$901$	−1.11317e27			−2.84471
$902$	1.56292e25	−	1.56292e25i	0.0395439	−	0.0395439i
$903$	−6.64189e26	−	6.64189e26i	−1.66380	−	1.66380i
$904$			1.24245e25i			0.0308152i
$905$	3.66678e26	+	5.65399e26i	0.900425	+	1.38841i
$906$	−1.46457e26			−0.356086
$907$	−2.67834e26	+	2.67834e26i	−0.644763	+	0.644763i	−0.951723	−	0.306960i	$-0.900688\pi$
$907$	−2.67834e26	+	2.67834e26i	−0.644763	+	0.644763i	0.306960	+	0.951723i	$0.400688\pi$
$908$	3.29644e26	+	3.29644e26i	0.785730	+	0.785730i
$909$			1.21075e26i			0.285745i
$910$	1.09800e26	+	2.34096e25i	0.256583	+	0.0547042i
$911$	−5.76143e26			−1.33311			−0.666553	−	0.745457i	$-0.732231\pi$
$911$	−5.76143e26			−1.33311			−0.666553	+	0.745457i	$0.732231\pi$
$912$	−2.68228e26	+	2.68228e26i	−0.614540	+	0.614540i
$913$	2.62786e25	+	2.62786e25i	0.0596164	+	0.0596164i
$914$		−	3.02285e26i		−	0.679048i
$915$	−9.16196e25	+	4.29730e26i	−0.203797	+	0.955886i
$916$	−2.23694e26			−0.492715
$917$	1.06476e26	−	1.06476e26i	0.232235	−	0.232235i
$918$	7.37827e26	+	7.37827e26i	1.59357	+	1.59357i
$919$			2.42026e26i			0.517633i	0.965927	+	0.258817i	$0.0833325\pi$
$919$			2.42026e26i			0.517633i	−0.965927	+	0.258817i	$0.916667\pi$
$920$	−1.89785e23	+	1.23081e23i	−0.000401949	+	0.000260676i
$921$	4.91712e26			1.03127
$922$	4.02011e26	−	4.02011e26i	0.834949	−	0.834949i
$923$	1.32802e25	+	1.32802e25i	0.0273142	+	0.0273142i
$924$		−	8.82069e25i		−	0.179661i
$925$	−1.41420e26	−	3.69777e26i	−0.285256	−	0.745873i
$926$	−2.94871e26			−0.589023
$927$	8.74176e24	−	8.74176e24i	0.0172934	−	0.0172934i
$928$	4.14717e26	+	4.14717e26i	0.812494	+	0.812494i
$929$		−	8.98057e26i		−	1.74246i	−0.490877	−	0.871229i	$-0.663323\pi$
$929$		−	8.98057e26i		−	1.74246i	0.490877	−	0.871229i	$-0.336677\pi$
$930$	−4.38446e26	−	6.76062e26i	−0.842499	−	1.29909i
$931$	8.54018e26			1.62525
$932$	−5.33391e26	+	5.33391e26i	−1.00531	+	1.00531i
$933$	5.25473e26	+	5.25473e26i	0.980879	+	0.980879i
$934$			1.11310e26i			0.205784i
$935$	1.02411e26	+	2.18343e25i	0.187518	+	0.0399792i
$936$	5.07725e23			0.000920758
$937$	3.02375e26	−	3.02375e26i	0.543112	−	0.543112i	−0.381328	−	0.924440i	$-0.624533\pi$
$937$	3.02375e26	−	3.02375e26i	0.543112	−	0.543112i	0.924440	+	0.381328i	$0.124533\pi$
$938$	−1.27628e27	−	1.27628e27i	−2.27050	−	2.27050i
$939$			6.86215e26i			1.20912i
$940$	1.06137e26	−	4.97821e26i	0.185232	−	0.868806i
$941$	6.92218e26			1.19657			0.598283	−	0.801285i	$-0.295850\pi$
$941$	6.92218e26			1.19657			0.598283	+	0.801285i	$0.295850\pi$
$942$	6.37638e26	−	6.37638e26i	1.09173	−	1.09173i
$943$	2.19907e24	+	2.19907e24i	0.00372936	+	0.00372936i
$944$			1.92935e26i			0.324088i
$945$	−8.74112e26	+	5.66887e26i	−1.45439	+	0.943214i
$946$	−1.98776e26			−0.327600
$947$	4.30648e26	−	4.30648e26i	0.703028	−	0.703028i	−0.262032	−	0.965059i	$-0.584392\pi$
$947$	4.30648e26	−	4.30648e26i	0.703028	−	0.703028i	0.965059	+	0.262032i	$0.0843925\pi$
$948$	−3.11875e26	−	3.11875e26i	−0.504319	−	0.504319i
$949$		−	1.43286e25i		−	0.0229513i
$950$	−8.81379e26	+	3.37080e26i	−1.39846	+	0.534837i
$951$	−1.95401e26			−0.307116
$952$	2.87370e25	−	2.87370e25i	0.0447414	−	0.0447414i
$953$	−4.88115e26	−	4.88115e26i	−0.752810	−	0.752810i	0.222192	−	0.975003i	$-0.428679\pi$
$953$	−4.88115e26	−	4.88115e26i	−0.752810	−	0.752810i	−0.975003	+	0.222192i	$0.928679\pi$
$954$		−	5.30191e26i		−	0.810022i
$955$	−3.75019e25	−	5.78261e25i	−0.0567575	−	0.0875173i
$956$	−4.50712e26			−0.675738
$957$	−4.25792e25	+	4.25792e25i	−0.0632397	+	0.0632397i
$958$	1.11232e27	+	1.11232e27i	1.63658	+	1.63658i
$959$			5.79818e26i			0.845131i
$960$	−5.91372e26	−	1.26082e26i	−0.853925	−	0.182059i
$961$	4.73865e26			0.677866
$962$	6.55576e25	−	6.55576e25i	0.0929068	−	0.0929068i
$963$	−3.34698e25	−	3.34698e25i	−0.0469912	−	0.0469912i
$964$			4.32842e26i			0.602055i
$965$	−1.75591e26	+	8.23589e26i	−0.241968	+	1.13492i
$966$	2.45887e25			0.0335693
$967$	2.74723e26	−	2.74723e26i	0.371584	−	0.371584i	−0.496470	−	0.868054i	$-0.665371\pi$
$967$	2.74723e26	−	2.74723e26i	0.371584	−	0.371584i	0.868054	+	0.496470i	$0.165371\pi$
$968$	1.41053e25	+	1.41053e25i	0.0189018	+	0.0189018i
$969$		−	9.73977e26i		−	1.29311i
$970$	2.93002e26	−	1.90021e26i	0.385412	−	0.249951i
$971$	1.00811e27			1.31382			0.656912	−	0.753968i	$-0.271862\pi$
$971$	1.00811e27			1.31382			0.656912	+	0.753968i	$0.271862\pi$
$972$	−3.14627e26	+	3.14627e26i	−0.406256	+	0.406256i
$973$	4.65727e26	+	4.65727e26i	0.595821	+	0.595821i
$974$		−	8.95762e26i		−	1.13543i
$975$	7.08135e25	+	3.16331e25i	0.0889354	+	0.0397284i
$976$	−9.15459e26			−1.13917
$977$	2.87323e26	−	2.87323e26i	0.354258	−	0.354258i	−0.507433	−	0.861691i	$-0.669406\pi$
$977$	2.87323e26	−	2.87323e26i	0.354258	−	0.354258i	0.861691	+	0.507433i	$0.169406\pi$
$978$	3.70319e26	+	3.70319e26i	0.452404	+	0.452404i
$979$		−	2.21066e25i		−	0.0267595i
$980$	7.13141e26	+	1.09963e27i	0.855344	+	1.31890i
$981$	5.70465e25			0.0677966
$982$	−5.15413e25	+	5.15413e25i	−0.0606948	+	0.0606948i
$983$	−2.47845e26	−	2.47845e26i	−0.289200	−	0.289200i	0.547564	−	0.836764i	$-0.315555\pi$
$983$	−2.47845e26	−	2.47845e26i	−0.289200	−	0.289200i	−0.836764	+	0.547564i	$0.815555\pi$
$984$		−	5.92628e24i		−	0.00685214i
$985$	9.24218e25	+	1.97046e25i	0.105888	+	0.0225757i
$986$	−1.47707e27			−1.67690
$987$	−7.34883e26	+	7.34883e26i	−0.826730	+	0.826730i
$988$	−7.88703e25	−	7.88703e25i	−0.0879227	−	0.0879227i
$989$		−	2.79683e25i		−	0.0308958i
$990$	−1.03995e25	+	4.87773e25i	−0.0113840	+	0.0533951i
$991$	−3.81522e26			−0.413863			−0.206931	−	0.978355i	$-0.566348\pi$
$991$	−3.81522e26			−0.413863			−0.206931	+	0.978355i	$0.566348\pi$
$992$	1.21030e27	−	1.21030e27i	1.30103	−	1.30103i
$993$	−4.48817e26	−	4.48817e26i	−0.478108	−	0.478108i
$994$			7.16011e26i			0.755861i
$995$	6.56938e26	−	4.26044e26i	0.687253	−	0.445704i
$996$	5.30494e26			0.549979
$997$	−2.39641e25	+	2.39641e25i	−0.0246210	+	0.0246210i	−0.719310	−	0.694689i	$-0.755542\pi$
$997$	−2.39641e25	+	2.39641e25i	−0.0246210	+	0.0246210i	0.694689	+	0.719310i	$0.255542\pi$
$998$	7.63292e26	+	7.63292e26i	0.777170	+	0.777170i
$999$			8.60371e26i			0.868153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.19.c.a.3.7	yes	16
3.2	odd	2		45.19.g.a.28.2		16
5.2	odd	4	inner	5.19.c.a.2.7	✓	16
5.3	odd	4		25.19.c.b.7.2		16
5.4	even	2		25.19.c.b.18.2		16
15.2	even	4		45.19.g.a.37.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.19.c.a.2.7	✓	16	5.2	odd	4	inner
5.19.c.a.3.7	yes	16	1.1	even	1	trivial
25.19.c.b.7.2		16	5.3	odd	4
25.19.c.b.18.2		16	5.4	even	2
45.19.g.a.28.2		16	3.2	odd	2
45.19.g.a.37.2		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)

\(f(q)\)	\(=\)	\(q+(514.444 - 514.444i) q^{2} +(11708.2 + 11708.2i) q^{3} -267162. i q^{4} +(-1.06274e6 - 1.63869e6i) q^{5} +1.20464e7 q^{6} +(4.54981e7 - 4.54981e7i) q^{7} +(-2.58155e6 - 2.58155e6i) q^{8} -1.13259e8i q^{9} +O(q^{10})\)	\(q+(514.444 - 514.444i) q^{2} +(11708.2 + 11708.2i) q^{3} -267162. i q^{4} +(-1.06274e6 - 1.63869e6i) q^{5} +1.20464e7 q^{6} +(4.54981e7 - 4.54981e7i) q^{7} +(-2.58155e6 - 2.58155e6i) q^{8} -1.13259e8i q^{9} +(-1.38973e9 - 2.96294e8i) q^{10} +3.09896e8 q^{11} +(3.12798e9 - 3.12798e9i) q^{12} +(-8.68254e8 - 8.68254e8i) q^{13} -4.68125e10i q^{14} +(6.74331e9 - 3.16287e10i) q^{15} +6.73788e10 q^{16} +(-1.22332e11 + 1.22332e11i) q^{17} +(-5.82653e10 - 5.82653e10i) q^{18} +3.40010e11i q^{19} +(-4.37795e11 + 2.83923e11i) q^{20} +1.06540e12 q^{21} +(1.59424e11 - 1.59424e11i) q^{22} +(2.24314e10 + 2.24314e10i) q^{23} -6.04503e10i q^{24} +(-1.55588e12 + 3.48298e12i) q^{25} -8.93337e11 q^{26} +(5.86203e12 - 5.86203e12i) q^{27} +(-1.21554e13 - 1.21554e13i) q^{28} +1.17353e13i q^{29} +(-1.28021e13 - 1.97402e13i) q^{30} +3.42479e13 q^{31} +(3.53394e13 - 3.53394e13i) q^{32} +(3.62831e12 + 3.62831e12i) q^{33} +1.25866e14i q^{34} +(-1.22910e14 - 2.62046e13i) q^{35} -3.02584e13 q^{36} +(-7.33851e13 + 7.33851e13i) q^{37} +(1.74916e14 + 1.74916e14i) q^{38} -2.03313e13i q^{39} +(-1.48684e12 + 6.97384e12i) q^{40} +9.80356e13 q^{41} +(5.48088e14 - 5.48088e14i) q^{42} +(-6.23419e14 - 6.23419e14i) q^{43} -8.27924e13i q^{44} +(-1.85595e14 + 1.20364e14i) q^{45} +2.30794e13 q^{46} +(-6.89773e14 + 6.89773e14i) q^{47} +(7.88882e14 + 7.88882e14i) q^{48} -2.51174e15i q^{49} +(9.91384e14 + 2.59221e15i) q^{50} -2.86455e15 q^{51} +(-2.31965e14 + 2.31965e14i) q^{52} +(4.54980e15 + 4.54980e15i) q^{53} -6.03138e15i q^{54} +(-3.29337e14 - 5.07822e14i) q^{55} -2.34911e14 q^{56} +(-3.98089e15 + 3.98089e15i) q^{57} +(6.03714e15 + 6.03714e15i) q^{58} +2.86344e15i q^{59} +(-8.44998e15 - 1.80156e15i) q^{60} -1.35867e16 q^{61} +(1.76186e16 - 1.76186e16i) q^{62} +(-5.15306e15 - 5.15306e15i) q^{63} -1.86974e16i q^{64} +(-5.00071e14 + 2.34552e15i) q^{65} +3.73313e15 q^{66} +(2.72637e16 - 2.72637e16i) q^{67} +(3.26823e16 + 3.26823e16i) q^{68} +5.25260e14i q^{69} +(-7.67110e16 + 4.97493e16i) q^{70} -1.52953e16 q^{71} +(-2.92383e14 + 2.92383e14i) q^{72} +(8.25139e15 + 8.25139e15i) q^{73} +7.55051e16i q^{74} +(-5.89958e16 + 2.25627e16i) q^{75} +9.08378e16 q^{76} +(1.40997e16 - 1.40997e16i) q^{77} +(-1.04593e16 - 1.04593e16i) q^{78} -9.97051e16i q^{79} +(-7.16059e16 - 1.10413e17i) q^{80} +9.33884e16 q^{81} +(5.04339e16 - 5.04339e16i) q^{82} +(8.47982e16 + 8.47982e16i) q^{83} -2.84634e17i q^{84} +(3.30469e17 + 7.04568e16i) q^{85} -6.41429e17 q^{86} +(-1.37398e17 + 1.37398e17i) q^{87} +(-8.00010e14 - 8.00010e14i) q^{88} -7.13356e16i q^{89} +(-3.35579e16 + 1.57399e17i) q^{90} -7.90079e16 q^{91} +(5.99281e15 - 5.99281e15i) q^{92} +(4.00980e17 + 4.00980e17i) q^{93} +7.09700e17i q^{94} +(5.57170e17 - 3.61341e17i) q^{95} +8.27518e17 q^{96} +(-1.73783e17 + 1.73783e17i) q^{97} +(-1.29215e18 - 1.29215e18i) q^{98} -3.50984e16i 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

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