LMFDB - Embedded newform 8.19.d.b.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,19,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	8.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.4308910168$
Analytic rank:	$0$
Dimension:	$16$
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} - 5 x^{15} + 56971 x^{14} - 14457953 x^{13} + 5222713963 x^{12} - 1887111404561 x^{11} + \cdots + 32\!\cdots\!30 $ x^16 - 5x^15 + 56971x^14 - 14457953x^13 + 5222713963x^12 - 1887111404561x^11 + 551417417640415x^10 - 120118761233202509x^9 + 30966377422568512537x^8 - 9791029903061915769567x^7 + 2760409144896820517353041x^6 - 573126276959276881630152915x^5 + 113556201106829558152115445753x^4 - 24602953293990202118839424410059x^3 + 5109186069446462658360003036354309x^2 - 959560421721305781394985245626434751*x + 326887106263049715278881269448539579330
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{13}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$-13.0246 + 256.000i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.19.d.b.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0491315 + 512.000i) q^{2} -9978.36 q^{3} +(-262144. - 50.3107i) q^{4} +3.00573e6i q^{5} +(490.252 - 5.10892e6i) q^{6} +5.44315e7i q^{7} +(38638.6 - 1.34218e8i) q^{8} -2.87853e8 q^{9} +O(q^{10})$	\(q+(-0.0491315 + 512.000i) q^{2} -9978.36 q^{3} +(-262144. - 50.3107i) q^{4} +3.00573e6i q^{5} +(490.252 - 5.10892e6i) q^{6} +5.44315e7i q^{7} +(38638.6 - 1.34218e8i) q^{8} -2.87853e8 q^{9} +(-1.53893e9 - 147676. i) q^{10} +1.04114e8 q^{11} +(2.61577e9 + 502018. i) q^{12} -4.11491e9i q^{13} +(-2.78689e10 - 2.67430e6i) q^{14} -2.99923e10i q^{15} +(6.87195e10 + 2.63773e7i) q^{16} +2.03047e11 q^{17} +(1.41426e7 - 1.47381e11i) q^{18} -4.23955e11 q^{19} +(1.51220e8 - 7.87934e11i) q^{20} -5.43137e11i q^{21} +(-5.11526e6 + 5.33062e10i) q^{22} -2.35018e12i q^{23} +(-3.85550e8 + 1.33927e12i) q^{24} -5.21971e12 q^{25} +(2.10683e12 + 2.02172e8i) q^{26} +6.73812e12 q^{27} +(2.73848e9 - 1.42689e13i) q^{28} +1.21360e13i q^{29} +(1.53560e13 + 1.47356e9i) q^{30} +4.32684e12i q^{31} +(-1.68815e10 + 3.51844e13i) q^{32} -1.03888e12 q^{33} +(-9.97601e9 + 1.03960e14i) q^{34} -1.63606e14 q^{35} +(7.54589e13 + 1.44821e10i) q^{36} +6.48214e13i q^{37} +(2.08295e10 - 2.17065e14i) q^{38} +4.10600e13i q^{39} +(4.03422e14 + 1.16137e11i) q^{40} -4.74123e14 q^{41} +(2.78086e14 + 2.66851e10i) q^{42} -9.30521e13 q^{43} +(-2.72928e13 - 5.23803e9i) q^{44} -8.65207e14i q^{45} +(1.20329e15 + 1.15468e11i) q^{46} -5.66741e14i q^{47} +(-6.85708e14 - 2.63202e11i) q^{48} -1.33437e15 q^{49} +(2.56452e11 - 2.67249e15i) q^{50} -2.02608e15 q^{51} +(-2.07024e11 + 1.07870e15i) q^{52} +3.33132e15i q^{53} +(-3.31054e11 + 3.44992e15i) q^{54} +3.12938e14i q^{55} +(7.30567e15 + 2.10315e12i) q^{56} +4.23038e15 q^{57} +(-6.21365e15 - 5.96262e11i) q^{58} +2.92612e15 q^{59} +(-1.50893e12 + 7.86229e15i) q^{60} +1.14012e16i q^{61} +(-2.21534e15 - 2.12584e11i) q^{62} -1.56682e16i q^{63} +(-1.80144e16 - 1.03720e13i) q^{64} +1.23683e16 q^{65} +(5.10420e10 - 5.31909e14i) q^{66} +2.86221e16 q^{67} +(-5.32276e16 - 1.02154e13i) q^{68} +2.34510e16i q^{69} +(8.03822e12 - 8.37664e16i) q^{70} -5.39130e16i q^{71} +(-1.11222e13 + 3.86349e16i) q^{72} +9.57943e15 q^{73} +(-3.31886e16 - 3.18477e12i) q^{74} +5.20842e16 q^{75} +(1.11137e17 + 2.13295e13i) q^{76} +5.66706e15i q^{77} +(-2.10227e16 - 2.01734e12i) q^{78} -9.24662e16i q^{79} +(-7.92829e13 + 2.06552e17i) q^{80} +4.42846e16 q^{81} +(2.32944e13 - 2.42751e17i) q^{82} -3.30678e17 q^{83} +(-2.73256e13 + 1.42380e17i) q^{84} +6.10305e17i q^{85} +(4.57179e12 - 4.76427e16i) q^{86} -1.21098e17i q^{87} +(4.02281e12 - 1.39739e16i) q^{88} -2.93496e17 q^{89} +(4.42986e17 + 4.25089e13i) q^{90} +2.23980e17 q^{91} +(-1.18239e14 + 6.16086e17i) q^{92} -4.31748e16i q^{93} +(2.90171e17 + 2.78448e13i) q^{94} -1.27429e18i q^{95} +(1.68449e14 - 3.51082e17i) q^{96} -8.93663e17 q^{97} +(6.55596e13 - 6.83197e17i) q^{98} -2.99694e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) $ 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9	$ 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) $ 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9 - 1569837600 * q^10 - 2471571264 * q^11 + 4764364056 * q^12 + 26163923904 * q^14 - 192320075504 * q^16 - 176439301344 * q^17 - 1044291511122 * q^18 - 833365634368 * q^19 + 1256486405760 * q^20 + 59927319356 * q^22 - 1968891910512 * q^24 - 15320509140080 * q^25 + 4184514840864 * q^26 + 11565649473408 * q^27 - 12301604294400 * q^28 - 36336510039360 * q^30 + 141481742931936 * q^32 - 900457491648 * q^33 + 80653465357268 * q^34 + 20487495736320 * q^35 + 277183098847068 * q^36 + 493456694265564 * q^38 - 519930573603840 * q^40 - 594931562445024 * q^41 - 222362598288000 * q^42 - 2540155017577792 * q^43 + 73781630442072 * q^44 + 153882272211264 * q^46 + 897135071530464 * q^48 - 3186415704132848 * q^49 + 5668141028706330 * q^50 + 2916050119466880 * q^51 - 4594372123628160 * q^52 - 1377307163285640 * q^54 + 8184134137073664 * q^56 + 9540488340840768 * q^57 - 10505700099162720 * q^58 + 556807886314176 * q^59 + 29677718651516160 * q^60 + 6212402633091840 * q^62 - 56432885385732032 * q^64 - 21153177930524160 * q^65 - 23515570511959320 * q^66 + 162428574934613696 * q^67 - 70717864614203736 * q^68 + 4248100663257600 * q^70 - 36801123950767128 * q^72 - 7655712852492256 * q^73 + 9613779604149984 * q^74 - 384388788469704000 * q^75 - 151130166278324584 * q^76 - 93022771634070720 * q^78 + 26870186366192640 * q^80 + 99506910981790800 * q^81 + 329788507250077556 * q^82 + 866357336138514624 * q^83 + 451843591950574080 * q^84 + 1269201398006865468 * q^86 - 758460699051663856 * q^88 - 883646550464284128 * q^89 - 1227675520905095520 * q^90 - 379834560933460992 * q^91 + 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 483149691255826368 * q^96 - 2614894858526780128 * q^97 - 81635840192738166 * q^98 - 816916348833567168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0491315	+	512.000i	−9.59600e−5	+	1.00000i
$2$	−0.0491315	+	512.000i	−9.59600e−5	+	1.00000i
$3$	−9978.36			−0.506953			−0.253477	−	0.967341i	$-0.581574\pi$
$3$	−9978.36			−0.506953			−0.253477	+	0.967341i	$0.581574\pi$
$4$	−262144.	−	50.3107i	−1.00000	−	0.000191920i
$5$			3.00573e6i			1.53893i	0.638687	+	0.769467i	$0.279478\pi$
$5$			3.00573e6i			1.53893i	−0.638687	+	0.769467i	$0.720522\pi$
$6$	490.252	−	5.10892e6i	4.86472e−5	−	0.506953i
$7$			5.44315e7i			1.34886i	0.738338	+	0.674431i	$0.235611\pi$
$7$			5.44315e7i			1.34886i	−0.738338	+	0.674431i	$0.764389\pi$
$8$	38638.6	−	1.34218e8i	0.000287880	−	1.00000i
$9$	−2.87853e8			−0.742998
$10$	−1.53893e9	−	147676.i	−1.53893	−	0.000147676i
$11$	1.04114e8			0.0441544			0.0220772	−	0.999756i	$-0.492972\pi$
$11$	1.04114e8			0.0441544			0.0220772	+	0.999756i	$0.492972\pi$
$12$	2.61577e9	+	502018.i	0.506953	+	9.72945e-5i
$13$		−	4.11491e9i		−	0.388034i	−0.980998	−	0.194017i	$-0.937848\pi$
$13$		−	4.11491e9i		−	0.388034i	0.980998	−	0.194017i	$-0.0621517\pi$
$14$	−2.78689e10	−	2.67430e6i	−1.34886	−	0.000129437i
$15$		−	2.99923e10i		−	0.780167i
$16$	6.87195e10	+	2.63773e7i	1.00000	+	0.000383840i
$17$	2.03047e11			1.71221			0.856104	−	0.516803i	$-0.172878\pi$
$17$	2.03047e11			1.71221			0.856104	+	0.516803i	$0.172878\pi$
$18$	1.41426e7	−	1.47381e11i	7.12981e−5	−	0.742998i
$19$	−4.23955e11			−1.31382			−0.656912	−	0.753967i	$-0.728138\pi$
$19$	−4.23955e11			−1.31382			−0.656912	+	0.753967i	$0.728138\pi$
$20$	1.51220e8	−	7.87934e11i	0.000295352	−	1.53893i
$21$		−	5.43137e11i		−	0.683810i
$22$	−5.11526e6	+	5.33062e10i	−4.23705e−6	+	0.0441544i
$23$		−	2.35018e12i		−	1.30482i	−0.757866	−	0.652411i	$-0.773758\pi$
$23$		−	2.35018e12i		−	1.30482i	0.757866	−	0.652411i	$-0.226242\pi$
$24$	−3.85550e8	+	1.33927e12i	−0.000145942	+	0.506953i
$25$	−5.21971e12			−1.36832
$26$	2.10683e12	+	2.02172e8i	0.388034	+	3.72357e-5i
$27$	6.73812e12			0.883619
$28$	2.73848e9	−	1.42689e13i	0.000258874	−	1.34886i
$29$			1.21360e13i			0.836556i	0.908319	+	0.418278i	$0.137366\pi$
$29$			1.21360e13i			0.836556i	−0.908319	+	0.418278i	$0.862634\pi$
$30$	1.53560e13	+	1.47356e9i	0.780167	+	7.48648e-5i
$31$			4.32684e12i			0.163650i	0.996647	+	0.0818249i	$0.0260748\pi$
$31$			4.32684e12i			0.163650i	−0.996647	+	0.0818249i	$0.973925\pi$
$32$	−1.68815e10	+	3.51844e13i	−0.000479800	+	1.00000i
$33$	−1.03888e12			−0.0223842
$34$	−9.97601e9	+	1.03960e14i	−0.000164304	+	1.71221i
$35$	−1.63606e14			−2.07581
$36$	7.54589e13	+	1.44821e10i	0.742998	+	0.000142596i
$37$			6.48214e13i			0.498773i	0.968404	+	0.249387i	$0.0802290\pi$
$37$			6.48214e13i			0.498773i	−0.968404	+	0.249387i	$0.919771\pi$
$38$	2.08295e10	−	2.17065e14i	0.000126075	−	1.31382i
$39$			4.10600e13i			0.196715i
$40$	4.03422e14	+	1.16137e11i	1.53893	+	0.000443028i
$41$	−4.74123e14			−1.44823			−0.724113	−	0.689681i	$-0.757751\pi$
$41$	−4.74123e14			−1.44823			−0.724113	+	0.689681i	$0.757751\pi$
$42$	2.78086e14	+	2.66851e10i	0.683810	+	6.56184e-5i
$43$	−9.30521e13			−0.185144			−0.0925721	−	0.995706i	$-0.529509\pi$
$43$	−9.30521e13			−0.185144			−0.0925721	+	0.995706i	$0.529509\pi$
$44$	−2.72928e13	−	5.23803e9i	−0.0441544	−	8.47410e-6i
$45$		−	8.65207e14i		−	1.14342i
$46$	1.20329e15	+	1.15468e11i	1.30482	+	0.000125211i
$47$		−	5.66741e14i		−	0.506412i	−0.967412	−	0.253206i	$-0.918515\pi$
$47$		−	5.66741e14i		−	0.506412i	0.967412	−	0.253206i	$-0.0814850\pi$
$48$	−6.85708e14	−	2.63202e11i	−0.506953	−	0.000194589i
$49$	−1.33437e15			−0.819429
$50$	2.56452e11	−	2.67249e15i	0.000131304	−	1.36832i
$51$	−2.02608e15			−0.868010
$52$	−2.07024e11	+	1.07870e15i	−7.44715e−5	+	0.388034i
$53$			3.33132e15i			1.00956i	0.863247	+	0.504781i	$0.168427\pi$
$53$			3.33132e15i			1.00956i	−0.863247	+	0.504781i	$0.831573\pi$
$54$	−3.31054e11	+	3.44992e15i	−8.47920e−5	+	0.883619i
$55$			3.12938e14i			0.0679506i
$56$	7.30567e15	+	2.10315e12i	1.34886	+	0.000388310i
$57$	4.23038e15			0.666048
$58$	−6.21365e15	−	5.96262e11i	−0.836556	−	8.02759e-5i
$59$	2.92612e15			0.337772			0.168886	−	0.985636i	$-0.445983\pi$
$59$	2.92612e15			0.337772			0.168886	+	0.985636i	$0.445983\pi$
$60$	−1.50893e12	+	7.86229e15i	−0.000149730	+	0.780167i
$61$			1.14012e16i			0.974951i	0.873137	+	0.487476i	$0.162082\pi$
$61$			1.14012e16i			0.974951i	−0.873137	+	0.487476i	$0.837918\pi$
$62$	−2.21534e15	−	2.12584e11i	−0.163650	−	1.57038e-5i
$63$		−	1.56682e16i		−	1.00220i
$64$	−1.80144e16	−	1.03720e13i	−1.00000	−	0.000575760i
$65$	1.23683e16			0.597159
$66$	5.10420e10	−	5.31909e14i	2.14799e−6	−	0.0223842i
$67$	2.86221e16			1.05203			0.526014	−	0.850476i	$-0.323686\pi$
$67$	2.86221e16			1.05203			0.526014	+	0.850476i	$0.323686\pi$
$68$	−5.32276e16	−	1.02154e13i	−1.71221	−	0.000328607i
$69$			2.34510e16i			0.661484i
$70$	8.03822e12	−	8.37664e16i	0.000199195	−	2.07581i
$71$		−	5.39130e16i		−	1.17589i	−0.808900	−	0.587947i	$-0.799936\pi$
$71$		−	5.39130e16i		−	1.17589i	0.808900	−	0.587947i	$-0.200064\pi$
$72$	−1.11222e13	+	3.86349e16i	−0.000213894	+	0.742998i
$73$	9.57943e15			0.162717			0.0813587	−	0.996685i	$-0.474074\pi$
$73$	9.57943e15			0.162717			0.0813587	+	0.996685i	$0.474074\pi$
$74$	−3.31886e16	−	3.18477e12i	−0.498773	−	4.78623e-5i
$75$	5.20842e16			0.693672
$76$	1.11137e17	+	2.13295e13i	1.31382	+	0.000252149i
$77$			5.66706e15i			0.0595582i
$78$	−2.10227e16	−	2.01734e12i	−0.196715	−	1.88768e-5i
$79$		−	9.24662e16i		−	0.771505i	−0.922602	−	0.385753i	$-0.873942\pi$
$79$		−	9.24662e16i		−	0.771505i	0.922602	−	0.385753i	$-0.126058\pi$
$80$	−7.92829e13	+	2.06552e17i	−0.000590704	+	1.53893i
$81$	4.42846e16			0.295045
$82$	2.32944e13	−	2.42751e17i	0.000138972	−	1.44823i
$83$	−3.30678e17			−1.76890			−0.884448	−	0.466639i	$-0.845465\pi$
$83$	−3.30678e17			−1.76890			−0.884448	+	0.466639i	$0.845465\pi$
$84$	−2.73256e13	+	1.42380e17i	−0.000131237	+	0.683810i
$85$			6.10305e17i			2.63498i
$86$	4.57179e12	−	4.76427e16i	1.77664e−5	−	0.185144i
$87$		−	1.21098e17i		−	0.424095i
$88$	4.02281e12	−	1.39739e16i	1.27112e−5	−	0.0441544i
$89$	−2.93496e17			−0.837707			−0.418853	−	0.908054i	$-0.637568\pi$
$89$	−2.93496e17			−0.837707			−0.418853	+	0.908054i	$0.637568\pi$
$90$	4.42986e17	+	4.25089e13i	1.14342	+	0.000109723i
$91$	2.23980e17			0.523405
$92$	−1.18239e14	+	6.16086e17i	−0.000250421	+	1.30482i
$93$		−	4.31748e16i		−	0.0829629i
$94$	2.90171e17	+	2.78448e13i	0.506412	+	4.85952e-5i
$95$		−	1.27429e18i		−	2.02189i
$96$	1.68449e14	−	3.51082e17i	0.000243236	−	0.506953i
$97$	−8.93663e17			−1.17551			−0.587757	−	0.809037i	$-0.699989\pi$
$97$	−8.93663e17			−1.17551			−0.587757	+	0.809037i	$0.699989\pi$
$98$	6.55596e13	−	6.83197e17i	7.86324e−5	−	0.819429i
$99$	−2.99694e16			−0.0328066
$100$	1.36832e18	+	2.62607e14i	1.36832	+	0.000262607i
$101$			1.38016e18i			1.26194i	0.775808	+	0.630969i	$0.217342\pi$
$101$			1.38016e18i			1.26194i	−0.775808	+	0.630969i	$0.782658\pi$
$102$	9.95443e13	−	1.03735e18i	8.32942e−5	−	0.868010i
$103$		−	3.21235e16i		−	0.0246200i	−0.999924	−	0.0123100i	$-0.996082\pi$
$103$		−	3.21235e16i		−	0.0246200i	0.999924	−	0.0123100i	$-0.00391849\pi$
$104$	−5.52294e17	−	1.58994e14i	−0.388034	−	0.000111707i
$105$	1.63252e18			1.05234
$106$	−1.70563e18	−	1.63673e14i	−1.00956	−	9.68776e-5i
$107$	−2.24996e18			−1.22383			−0.611914	−	0.790924i	$-0.709600\pi$
$107$	−2.24996e18			−1.22383			−0.611914	+	0.790924i	$0.709600\pi$
$108$	−1.76636e18	−	3.38999e14i	−0.883619	−	0.000169584i
$109$		−	2.02763e18i		−	0.933575i	−0.884370	−	0.466787i	$-0.845411\pi$
$109$		−	2.02763e18i		−	0.933575i	0.884370	−	0.466787i	$-0.154589\pi$
$110$	−1.60224e17	−	1.53751e13i	−0.0679506	−	6.52054e-6i
$111$		−	6.46812e17i		−	0.252855i
$112$	−1.43575e15	+	3.74050e18i	−0.000517747	+	1.34886i
$113$	3.67646e18			1.22384			0.611918	−	0.790921i	$-0.290398\pi$
$113$	3.67646e18			1.22384			0.611918	+	0.790921i	$0.290398\pi$
$114$	−2.07845e14	+	2.16595e18i	−6.39139e−5	+	0.666048i
$115$	7.06401e18			2.00803
$116$	6.10572e14	−	3.18139e18i	0.000160552	−	0.836556i
$117$			1.18449e18i			0.288309i
$118$	−1.43764e14	+	1.49817e18i	−3.24126e−5	+	0.337772i
$119$			1.10522e19i			2.30953i
$120$	−4.02549e18	−	1.15886e15i	−0.780167	−	0.000224595i
$121$	−5.54908e18			−0.998050
$122$	−5.83742e18	−	5.60159e14i	−0.974951	−	9.35563e-5i
$123$	4.73097e18			0.734183
$124$	2.17686e14	−	1.13426e18i	3.14077e−5	−	0.163650i
$125$		−	4.22309e18i		−	0.566813i
$126$	8.02214e18	+	7.69804e14i	1.00220	+	9.61713e-5i
$127$		−	9.82179e18i		−	1.14277i	−0.820684	−	0.571383i	$-0.806407\pi$
$127$		−	9.82179e18i		−	1.14277i	0.820684	−	0.571383i	$-0.193593\pi$
$128$	6.19552e15	−	9.22337e18i	0.000671720	−	1.00000i
$129$	9.28508e17			0.0938595
$130$	−6.07673e14	+	6.33257e18i	−5.73033e−5	+	0.597159i
$131$	−1.82942e19			−1.61017			−0.805083	−	0.593162i	$-0.797879\pi$
$131$	−1.82942e19			−1.61017			−0.805083	+	0.593162i	$0.797879\pi$
$132$	2.72337e17	+	5.22670e13i	0.0223842	+	4.29598e-6i
$133$		−	2.30765e19i		−	1.77217i
$134$	−1.40624e15	+	1.46545e19i	−0.000100953	+	1.05203i
$135$			2.02530e19i			1.35983i
$136$	7.84546e15	−	2.72525e19i	0.000492911	−	1.71221i
$137$	1.32785e19			0.781026			0.390513	−	0.920597i	$-0.372298\pi$
$137$	1.32785e19			0.781026			0.390513	+	0.920597i	$0.372298\pi$
$138$	−1.20069e19	−	1.15218e15i	−0.661484	−	6.34760e-5i
$139$	−7.78276e18			−0.401791			−0.200896	−	0.979613i	$-0.564385\pi$
$139$	−7.78276e18			−0.401791			−0.200896	+	0.979613i	$0.564385\pi$
$140$	4.28884e19	+	8.23114e15i	2.07581	+	0.000398389i
$141$			5.65514e18i			0.256727i
$142$	2.76034e19	+	2.64882e15i	1.17589	+	0.000112839i
$143$		−	4.28418e17i		−	0.0171334i
$144$	−1.97811e19	−	7.59277e15i	−0.742998	−	0.000285192i
$145$	−3.64777e19			−1.28740
$146$	−4.70652e14	+	4.90467e18i	−1.56144e−5	+	0.162717i
$147$	1.33148e19			0.415412
$148$	3.26121e15	−	1.69925e19i	9.57245e−5	−	0.498773i
$149$		−	2.11482e19i		−	0.584248i	−0.956380	−	0.292124i	$-0.905638\pi$
$149$		−	2.11482e19i		−	0.584248i	0.956380	−	0.292124i	$-0.0943621\pi$
$150$	−2.55897e15	+	2.66671e19i	−6.65648e−5	+	0.693672i
$151$			6.14844e19i			1.50651i	0.657728	+	0.753255i	$0.271518\pi$
$151$			6.14844e19i			1.50651i	−0.657728	+	0.753255i	$0.728482\pi$
$152$	−1.63810e16	+	5.69023e19i	−0.000378224	+	1.31382i
$153$	−5.84477e19			−1.27217
$154$	−2.90154e18	−	2.78431e14i	−0.0595582	−	5.71520e-6i
$155$	−1.30053e19			−0.251846
$156$	2.06576e15	−	1.07636e19i	3.77536e−5	−	0.196715i
$157$			7.70849e18i			0.133006i	0.997786	+	0.0665032i	$0.0211842\pi$
$157$			7.70849e18i			0.133006i	−0.997786	+	0.0665032i	$0.978816\pi$
$158$	4.73427e19	+	4.54300e15i	0.771505	+	7.40336e-5i
$159$		−	3.32411e19i		−	0.511801i
$160$	−1.05755e20	−	5.07411e16i	−1.53893	−	0.000738380i
$161$	1.27924e20			1.76002
$162$	−2.17577e15	+	2.26737e19i	−2.83125e−5	+	0.295045i
$163$	1.06682e18			0.0131341			0.00656707	−	0.999978i	$-0.497910\pi$
$163$	1.06682e18			0.0131341			0.00656707	+	0.999978i	$0.497910\pi$
$164$	1.24289e20	+	2.38534e16i	1.44823	+	0.000277944i
$165$		−	3.12261e18i		−	0.0344478i
$166$	1.62467e16	−	1.69307e20i	0.000169743	−	1.76890i
$167$		−	4.23777e19i		−	0.419458i	−0.977760	−	0.209729i	$-0.932742\pi$
$167$		−	4.23777e19i		−	0.419458i	0.977760	−	0.209729i	$-0.0672582\pi$
$168$	−7.28986e19	−	2.09860e16i	−0.683810	−	0.000196855i
$169$	9.55229e19			0.849429
$170$	−3.12476e20	−	2.99852e16i	−2.63498	−	0.000252852i
$171$	1.22037e20			0.976169
$172$	2.43931e19	+	4.68151e15i	0.185144	+	3.55329e-5i
$173$			1.44542e20i			1.04131i	0.853767	+	0.520656i	$0.174312\pi$
$173$			1.44542e20i			1.04131i	−0.853767	+	0.520656i	$0.825688\pi$
$174$	6.20021e19	+	5.94972e15i	0.424095	+	4.06961e-5i
$175$		−	2.84116e20i		−	1.84567i
$176$	7.15464e18	+	2.74624e15i	0.0441544	+	1.69482e-5i
$177$	−2.91978e19			−0.171235
$178$	1.44199e16	−	1.50270e20i	8.03863e−5	−	0.837707i
$179$	−1.16002e19			−0.0614877			−0.0307438	−	0.999527i	$-0.509788\pi$
$179$	−1.16002e19			−0.0614877			−0.0307438	+	0.999527i	$0.509788\pi$
$180$	−4.35292e16	+	2.26809e20i	−0.000219446	+	1.14342i
$181$			8.90013e19i			0.426864i	0.976958	+	0.213432i	$0.0684641\pi$
$181$			8.90013e19i			0.426864i	−0.976958	+	0.213432i	$0.931536\pi$
$182$	−1.10045e16	+	1.14678e20i	−5.02259e−5	+	0.523405i
$183$		−	1.13766e20i		−	0.494255i
$184$	−3.15436e20	−	9.08077e16i	−1.30482	−	0.000375632i
$185$	−1.94836e20			−0.767579
$186$	2.21055e19	+	2.12124e15i	0.0829629	+	7.96111e-6i
$187$	2.11400e19			0.0756015
$188$	−2.85131e16	+	1.48568e20i	−9.71905e−5	+	0.506412i
$189$			3.66766e20i			1.19188i
$190$	6.52439e20	+	6.26080e16i	2.02189	+	0.000194020i
$191$			3.46116e20i			1.02311i	0.859252	+	0.511553i	$0.170930\pi$
$191$			3.46116e20i			1.02311i	−0.859252	+	0.511553i	$0.829070\pi$
$192$	1.79754e20	+	1.03495e17i	0.506953	+	0.000291883i
$193$	6.64311e19			0.178795			0.0893975	−	0.995996i	$-0.471506\pi$
$193$	6.64311e19			0.178795			0.0893975	+	0.995996i	$0.471506\pi$
$194$	4.39070e16	−	4.57555e20i	0.000112802	−	1.17551i
$195$	−1.23415e20			−0.302732
$196$	3.49797e20	+	6.71330e16i	0.819429	+	0.000157265i
$197$			4.18419e20i			0.936301i	0.883649	+	0.468150i	$0.155079\pi$
$197$			4.18419e20i			0.936301i	−0.883649	+	0.468150i	$0.844921\pi$
$198$	1.47244e15	−	1.53443e19i	3.14812e−6	−	0.0328066i
$199$		−	7.21809e20i		−	1.47484i	−0.675435	−	0.737419i	$-0.736044\pi$
$199$		−	7.21809e20i		−	1.47484i	0.675435	−	0.737419i	$-0.263956\pi$
$200$	−2.01682e17	+	7.00578e20i	−0.000393911	+	1.36832i
$201$	−2.85601e20			−0.533329
$202$	−7.06643e20	−	6.78094e16i	−1.26194	−	0.000121095i
$203$	−6.60582e20			−1.12840
$204$	5.31124e20	+	1.01933e17i	0.868010	+	0.000166588i
$205$		−	1.42509e21i		−	2.22872i
$206$	1.64472e19	+	1.57827e15i	0.0246200	+	2.36253e-6i
$207$			6.76507e20i			0.969480i
$208$	1.08540e17	−	2.82774e20i	0.000148943	−	0.388034i
$209$	−4.41395e19			−0.0580111
$210$	−8.02083e16	+	8.35851e20i	−0.000100982	+	1.05234i
$211$	9.45611e19			0.114070			0.0570349	−	0.998372i	$-0.481835\pi$
$211$	9.45611e19			0.114070			0.0570349	+	0.998372i	$0.481835\pi$
$212$	1.67601e17	−	8.73285e20i	0.000193755	−	1.00956i
$213$			5.37963e20i			0.596123i
$214$	1.10544e17	−	1.15198e21i	0.000117439	−	1.22383i
$215$		−	2.79689e20i		−	0.284925i
$216$	2.60351e17	−	9.04375e20i	0.000254376	−	0.883619i
$217$	−2.35516e20			−0.220741
$218$	1.03814e21	+	9.96203e16i	0.933575	+	8.95858e-5i
$219$	−9.55870e19			−0.0824901
$220$	1.57441e16	−	8.20347e19i	1.30411e−5	−	0.0679506i
$221$		−	8.35521e20i		−	0.664396i
$222$	3.31168e20	+	3.17788e16i	0.252855	+	2.42639e-5i
$223$			1.34265e21i			0.984509i	0.870451	+	0.492255i	$0.163827\pi$
$223$			1.34265e21i			0.984509i	−0.870451	+	0.492255i	$0.836173\pi$
$224$	−1.91514e21	−	9.18882e17i	−1.34886	−	0.000647184i
$225$	1.50251e21			1.01666
$226$	−1.80630e17	+	1.88235e21i	−0.000117439	+	1.22384i
$227$	2.01374e21			1.25826			0.629130	−	0.777300i	$-0.283411\pi$
$227$	2.01374e21			1.25826			0.629130	+	0.777300i	$0.283411\pi$
$228$	−1.10897e21	−	2.12833e17i	−0.666048	−	0.000127828i
$229$		−	8.48420e20i		−	0.489882i	−0.969538	−	0.244941i	$-0.921231\pi$
$229$		−	8.48420e20i		−	0.489882i	0.969538	−	0.244941i	$-0.0787686\pi$
$230$	−3.47066e17	+	3.61677e21i	−0.000192691	+	2.00803i
$231$		−	5.65480e19i		−	0.0301932i
$232$	1.62887e21	+	4.68919e17i	0.836556	+	0.000240828i
$233$	−1.57879e21			−0.780047			−0.390023	−	0.920805i	$-0.627533\pi$
$233$	−1.57879e21			−0.780047			−0.390023	+	0.920805i	$0.627533\pi$
$234$	−6.06458e20	−	5.81957e16i	−0.288309	−	2.76661e-5i
$235$	1.70347e21			0.779334
$236$	−7.67064e20	−	1.47215e17i	−0.337772	−	6.48251e-5i
$237$			9.22661e20i			0.391117i
$238$	−5.65870e21	−	5.43009e17i	−2.30953	−	0.000221623i
$239$			3.95344e21i			1.55380i	0.629627	+	0.776898i	$0.283208\pi$
$239$			3.95344e21i			1.55380i	−0.629627	+	0.776898i	$0.716792\pi$
$240$	7.91114e17	−	2.06105e21i	0.000299459	−	0.780167i
$241$	2.84237e21			1.03640			0.518200	−	0.855259i	$-0.326602\pi$
$241$	2.84237e21			1.03640			0.518200	+	0.855259i	$0.326602\pi$
$242$	2.72635e17	−	2.84113e21i	9.57729e−5	−	0.998050i
$243$	−3.05237e21			−1.03319
$244$	5.73603e17	−	2.98876e21i	0.000187113	−	0.974951i
$245$		−	4.01075e21i		−	1.26105i
$246$	−2.32440e17	+	2.42226e21i	−7.04522e−5	+	0.734183i
$247$			1.74454e21i			0.509809i
$248$	5.80739e20	+	1.67183e17i	0.163650	+	4.71115e-5i
$249$	3.29962e21			0.896748
$250$	2.16222e21	+	2.07487e17i	0.566813	+	5.43914e-5i
$251$	3.56725e20			0.0902133			0.0451066	−	0.998982i	$-0.485637\pi$
$251$	3.56725e20			0.0902133			0.0451066	+	0.998982i	$0.485637\pi$
$252$	−7.88280e17	+	4.10734e21i	−0.000192343	+	1.00220i
$253$		−	2.44686e20i		−	0.0576136i
$254$	5.02876e21	+	4.82559e17i	1.14277	+	0.000109660i
$255$		−	6.08984e21i		−	1.33581i
$256$	4.72237e21	+	3.62526e18i	1.00000	+	0.000767680i
$257$	−4.75083e21			−0.971341			−0.485671	−	0.874142i	$-0.661425\pi$
$257$	−4.75083e21			−0.971341			−0.485671	+	0.874142i	$0.661425\pi$
$258$	−4.56190e16	+	4.75396e20i	−9.00675e−6	+	0.0938595i
$259$	−3.52832e21			−0.672776
$260$	−3.24228e21	−	6.22257e17i	−0.597159	−	0.000114607i
$261$		−	3.49339e21i		−	0.621560i
$262$	8.98819e17	−	9.36661e21i	0.000154511	−	1.61017i
$263$			4.50890e19i			0.00748978i	0.999993	+	0.00374489i	$0.00119204\pi$
$263$			4.50890e19i			0.00748978i	−0.999993	+	0.00374489i	$0.998808\pi$
$264$	−4.01410e16	+	1.39437e20i	−6.44396e−6	+	0.0223842i
$265$	−1.00130e22			−1.55365
$266$	1.18152e22	+	1.13378e18i	1.77217	+	0.000170057i
$267$	2.92861e21			0.424678
$268$	−7.50310e21	−	1.43999e18i	−1.05203	−	0.000201905i
$269$			7.55590e21i			1.02451i	0.858834	+	0.512254i	$0.171189\pi$
$269$			7.55590e21i			1.02451i	−0.858834	+	0.512254i	$0.828811\pi$
$270$	−1.03695e22	−	9.95059e17i	−1.35983	−	0.000130489i
$271$		−	6.80738e20i		−	0.0863488i	−0.999068	−	0.0431744i	$-0.986253\pi$
$271$		−	6.80738e20i		−	0.0863488i	0.999068	−	0.0431744i	$-0.0137471\pi$
$272$	1.39533e22	+	5.35583e18i	1.71221	+	0.000657214i
$273$	−2.23496e21			−0.265342
$274$	−6.52395e17	+	6.79861e21i	−7.49472e−5	+	0.781026i
$275$	−5.43443e20			−0.0604171
$276$	1.17983e18	−	6.14753e21i	0.000126952	−	0.661484i
$277$			1.30853e22i			1.36290i	0.731863	+	0.681452i	$0.238651\pi$
$277$			1.30853e22i			1.36290i	−0.731863	+	0.681452i	$0.761349\pi$
$278$	3.82379e17	−	3.98478e21i	3.85559e−5	−	0.401791i
$279$		−	1.24549e21i		−	0.121592i
$280$	−6.32151e18	+	2.19589e22i	−0.000597584	+	2.07581i
$281$	2.78547e21			0.255001			0.127500	−	0.991839i	$-0.459305\pi$
$281$	2.78547e21			0.255001			0.127500	+	0.991839i	$0.459305\pi$
$282$	−2.89543e21	−	2.77846e17i	−0.256727	−	2.46355e-5i
$283$	−1.06851e22			−0.917702			−0.458851	−	0.888513i	$-0.651739\pi$
$283$	−1.06851e22			−0.917702			−0.458851	+	0.888513i	$0.651739\pi$
$284$	−2.71240e18	+	1.41330e22i	−0.000225677	+	1.17589i
$285$			1.27154e22i			1.02500i
$286$	2.19350e20	+	2.10488e16i	0.0171334	+	1.64412e-6i
$287$		−	2.58072e22i		−	1.95346i
$288$	4.85937e18	−	1.01279e22i	0.000356490	−	0.742998i
$289$	2.71651e22			1.93166
$290$	1.79220e18	−	1.86766e22i	0.000123539	−	1.28740i
$291$	8.91729e21			0.595931
$292$	−2.51119e21	−	4.81947e17i	−0.162717	−	3.12287e-5i
$293$		−	6.15120e20i		−	0.0386502i	−0.999813	−	0.0193251i	$-0.993848\pi$
$293$		−	6.15120e20i		−	0.0386502i	0.999813	−	0.0193251i	$-0.00615175\pi$
$294$	−6.54177e17	+	6.81719e21i	−3.98630e−5	+	0.415412i
$295$			8.79511e21i			0.519808i
$296$	8.70018e21	+	2.50461e18i	0.498773	+	0.000143587i
$297$	7.01531e20			0.0390156
$298$	1.08279e22	+	1.03904e18i	0.584248	+	5.60645e-5i
$299$	−9.67079e21			−0.506315
$300$	−1.36536e22	−	2.62039e18i	−0.693672	−	0.000133130i
$301$		−	5.06496e21i		−	0.249734i
$302$	−3.14800e22	−	3.02082e18i	−1.50651	−	0.000144565i
$303$		−	1.37718e22i		−	0.639743i
$304$	−2.91340e22	−	1.11828e19i	−1.31382	−	0.000504298i
$305$	−3.42690e22			−1.50038
$306$	2.87162e18	−	2.99252e22i	0.000122077	−	1.27217i
$307$	4.15632e22			1.71579			0.857894	−	0.513827i	$-0.171773\pi$
$307$	4.15632e22			1.71579			0.857894	+	0.513827i	$0.171773\pi$
$308$	2.85114e17	−	1.48559e21i	1.14304e−5	−	0.0595582i
$309$			3.20540e20i			0.0124812i
$310$	6.38970e17	−	6.65872e21i	2.41672e−5	−	0.251846i
$311$			1.37864e22i			0.506531i	0.967397	+	0.253266i	$0.0815047\pi$
$311$			1.37864e22i			0.506531i	−0.967397	+	0.253266i	$0.918495\pi$
$312$	5.51099e21	+	1.58650e18i	0.196715	+	5.66304e-5i
$313$	1.44388e22			0.500762			0.250381	−	0.968147i	$-0.419444\pi$
$313$	1.44388e22			0.500762			0.250381	+	0.968147i	$0.419444\pi$
$314$	−3.94675e21	−	3.78730e17i	−0.133006	−	1.27633e-5i
$315$	4.70945e22			1.54232
$316$	−4.65203e18	+	2.42394e22i	−0.000148067	+	0.771505i
$317$		−	3.82155e22i		−	1.18224i	−0.806583	−	0.591121i	$-0.798686\pi$
$317$		−	3.82155e22i		−	1.18224i	0.806583	−	0.591121i	$-0.201314\pi$
$318$	1.70194e22	+	1.63318e18i	0.511801	+	4.91124e-5i
$319$			1.26353e21i			0.0369376i
$320$	3.11753e19	−	5.41464e22i	0.000886056	−	1.53893i
$321$	2.24509e22			0.620424
$322$	−6.28509e18	+	6.54970e22i	−0.000168892	+	1.76002i
$323$	−8.60829e22			−2.24954
$324$	−1.16090e22	−	2.22799e18i	−0.295045	−	5.66250e-5i
$325$			2.14786e22i			0.530953i
$326$	−5.24143e16	+	5.46210e20i	−1.26035e−6	+	0.0131341i
$327$			2.02324e22i			0.473279i
$328$	−1.83194e19	+	6.36357e22i	−0.000416915	+	1.44823i
$329$	3.08485e22			0.683079
$330$	1.59877e21	+	1.53418e17i	0.0344478	+	3.30561e-6i
$331$	−2.10859e22			−0.442120			−0.221060	−	0.975260i	$-0.570952\pi$
$331$	−2.10859e22			−0.442120			−0.221060	+	0.975260i	$0.570952\pi$
$332$	8.66852e22	+	1.66366e19i	1.76890	+	0.000339486i
$333$		−	1.86590e22i		−	0.370588i
$334$	2.16974e22	+	2.08208e18i	0.419458	+	4.02512e-5i
$335$			8.60301e22i			1.61900i
$336$	1.43265e19	−	3.73241e22i	0.000262474	−	0.683810i
$337$	−5.94380e22			−1.06022			−0.530109	−	0.847929i	$-0.677849\pi$
$337$	−5.94380e22			−1.06022			−0.530109	+	0.847929i	$0.677849\pi$
$338$	−4.69319e18	+	4.89077e22i	−8.15112e−5	+	0.849429i
$339$	−3.66850e22			−0.620428
$340$	3.07048e19	−	1.59988e23i	0.000505704	−	2.63498i
$341$			4.50483e20i			0.00722586i
$342$	−5.99584e18	+	6.24828e22i	−9.36732e−5	+	0.976169i
$343$			1.60052e22i			0.243565i
$344$	−3.59540e18	+	1.24892e22i	−5.32993e−5	+	0.185144i
$345$	−7.04873e22			−1.01798
$346$	−7.40057e22	−	7.10159e18i	−1.04131	−	9.99242e-5i
$347$	−4.43282e22			−0.607736			−0.303868	−	0.952714i	$-0.598278\pi$
$347$	−4.43282e22			−0.607736			−0.303868	+	0.952714i	$0.598278\pi$
$348$	−6.09251e18	+	3.17451e22i	−8.13923e−5	+	0.424095i
$349$		−	6.31471e22i		−	0.822100i	−0.911613	−	0.411050i	$-0.865162\pi$
$349$		−	6.31471e22i		−	0.822100i	0.911613	−	0.411050i	$-0.134838\pi$
$350$	1.45468e23	+	1.39591e19i	1.84567	+	0.000177110i
$351$		−	2.77268e22i		−	0.342874i
$352$	−1.75759e18	+	3.66318e21i	−2.11853e−5	+	0.0441544i
$353$	−6.11648e22			−0.718670			−0.359335	−	0.933209i	$-0.616996\pi$
$353$	−6.11648e22			−0.718670			−0.359335	+	0.933209i	$0.616996\pi$
$354$	1.43453e18	−	1.49493e22i	1.64317e−5	−	0.171235i
$355$	1.62048e23			1.80962
$356$	7.69382e22	+	1.47660e19i	0.837707	+	0.000160773i
$357$		−	1.10282e23i		−	1.17083i
$358$	5.69935e17	−	5.93930e21i	5.90035e−6	−	0.0614877i
$359$		−	1.18667e23i		−	1.19806i	−0.800727	−	0.599029i	$-0.795553\pi$
$359$		−	1.18667e23i		−	1.19806i	0.800727	−	0.599029i	$-0.204447\pi$
$360$	−1.16126e23	−	3.34304e19i	−1.14342	−	0.000329169i
$361$	7.56105e22			0.726135
$362$	−4.55687e22	−	4.37277e18i	−0.426864	−	4.09618e-5i
$363$	5.53707e22			0.505965
$364$	−5.87151e22	−	1.12686e19i	−0.523405	−	0.000100452i
$365$			2.87932e22i			0.250411i
$366$	5.82479e22	+	5.58947e18i	0.494255	+	4.74287e-5i
$367$			2.01231e23i			1.66609i	0.553202	+	0.833047i	$0.313406\pi$
$367$			2.01231e23i			1.66609i	−0.553202	+	0.833047i	$0.686594\pi$
$368$	6.19914e19	−	1.61503e23i	0.000500843	−	1.30482i
$369$	1.36478e23			1.07603
$370$	9.57257e18	−	9.97558e22i	7.36568e−5	−	0.767579i
$371$	−1.81328e23			−1.36176
$372$	−2.17215e18	+	1.13180e22i	−1.59222e−5	+	0.0829628i
$373$			3.64651e22i			0.260914i	0.991454	+	0.130457i	$0.0416445\pi$
$373$			3.64651e22i			0.260914i	−0.991454	+	0.130457i	$0.958355\pi$
$374$	−1.03864e18	+	1.08237e22i	−7.25472e−6	+	0.0756015i
$375$			4.21395e22i			0.287348i
$376$	−7.60666e22	−	2.18981e19i	−0.506411	−	0.000145786i
$377$	4.99387e22			0.324612
$378$	−1.87784e23	−	1.80198e19i	−1.19188	−	0.000114373i
$379$	4.71495e22			0.292229			0.146115	−	0.989268i	$-0.453323\pi$
$379$	4.71495e22			0.292229			0.146115	+	0.989268i	$0.453323\pi$
$380$	−6.41106e19	+	3.34049e23i	−0.000388041	+	2.02189i
$381$			9.80054e22i			0.579329i
$382$	−1.77211e23	−	1.70052e19i	−1.02311	−	9.81773e-5i
$383$		−	4.48102e22i		−	0.252690i	−0.991986	−	0.126345i	$-0.959675\pi$
$383$		−	4.48102e22i		−	0.252690i	0.991986	−	0.126345i	$-0.0403246\pi$
$384$	−6.18212e19	+	9.20341e22i	−0.000340531	+	0.506953i
$385$	−1.70336e22			−0.0916561
$386$	−3.26386e18	+	3.40127e22i	−1.71572e−5	+	0.178795i
$387$	2.67853e22			0.137562
$388$	2.34268e23	+	4.49608e19i	1.17551	+	0.000225605i
$389$			2.62893e22i			0.128894i	0.997921	+	0.0644469i	$0.0205283\pi$
$389$			2.62893e22i			0.128894i	−0.997921	+	0.0644469i	$0.979472\pi$
$390$	6.06358e18	−	6.31887e22i	2.90501e−5	−	0.302732i
$391$		−	4.77198e23i		−	2.23413i
$392$	−5.15582e19	+	1.79096e23i	−0.000235897	+	0.819429i
$393$	1.82546e23			0.816279
$394$	−2.14231e23	−	2.05576e19i	−0.936301	−	8.98474e-5i
$395$	2.77928e23			1.18730
$396$	7.85630e21	+	1.50778e18i	0.0328066	+	6.29625e-6i
$397$			3.67755e23i			1.50122i	0.660746	+	0.750610i	$0.270240\pi$
$397$			3.67755e23i			1.50122i	−0.660746	+	0.750610i	$0.729760\pi$
$398$	3.69566e23	+	3.54635e19i	1.47484	+	0.000141525i
$399$			2.30266e23i			0.898407i
$400$	−3.58696e23	−	1.37682e20i	−1.36832	−	0.000525214i
$401$	−3.91281e23			−1.45945			−0.729725	−	0.683741i	$-0.760352\pi$
$401$	−3.91281e23			−1.45945			−0.729725	+	0.683741i	$0.760352\pi$
$402$	1.40320e19	−	1.46228e23i	5.11783e−5	−	0.533329i
$403$	1.78046e22			0.0635017
$404$	6.94369e19	−	3.61801e23i	0.000242191	−	1.26194i
$405$			1.33108e23i			0.454054i
$406$	3.24554e19	−	3.38218e23i	0.000108281	−	1.12840i
$407$			6.74880e21i			0.0220230i
$408$	−7.82848e19	+	2.71936e23i	−0.000249883	+	0.868010i
$409$	1.61226e23			0.503413			0.251706	−	0.967804i	$-0.419008\pi$
$409$	1.61226e23			0.503413			0.251706	+	0.967804i	$0.419008\pi$
$410$	7.29644e23	+	7.00166e19i	2.22872	+	0.000213868i
$411$	−1.32498e23			−0.395944
$412$	−1.61615e18	+	8.42097e21i	−4.72506e−6	+	0.0246200i
$413$			1.59273e23i			0.455608i
$414$	−3.46371e23	−	3.32378e19i	−0.969480	−	9.30313e-5i
$415$		−	9.93928e23i		−	2.72221i
$416$	1.44780e23	+	6.94656e19i	0.388034	+	0.000186179i
$417$	7.76593e22			0.203690
$418$	2.16864e18	−	2.25994e22i	5.56674e−6	−	0.0580111i
$419$	−3.50842e23			−0.881424			−0.440712	−	0.897649i	$-0.645274\pi$
$419$	−3.50842e23			−0.881424			−0.440712	+	0.897649i	$0.645274\pi$
$420$	−4.27956e23	−	8.21333e19i	−1.05234	−	0.000201965i
$421$		−	5.69181e23i		−	1.36997i	−0.728557	−	0.684985i	$-0.759809\pi$
$421$		−	5.69181e23i		−	1.36997i	0.728557	−	0.684985i	$-0.240191\pi$
$422$	−4.64593e18	+	4.84153e22i	−1.09461e−5	+	0.114070i
$423$			1.63138e23i			0.376263i
$424$	4.47122e23	+	1.28717e20i	1.00956	+	0.000290633i
$425$	−1.05985e24			−2.34284
$426$	−2.75437e23	−	2.64309e19i	−0.596123	−	5.72040e-5i
$427$	−6.20585e23			−1.31507
$428$	5.89813e23	+	1.13197e20i	1.22383	+	0.000234877i
$429$			4.27491e21i			0.00868584i
$430$	1.43201e23	+	1.37416e19i	0.284925	+	2.73414e-5i
$431$			1.98619e23i			0.387012i	0.981099	+	0.193506i	$0.0619859\pi$
$431$			1.98619e23i			0.387012i	−0.981099	+	0.193506i	$0.938014\pi$
$432$	4.63040e23	+	1.77733e20i	0.883619	+	0.000339168i
$433$	6.79331e23			1.26967			0.634834	−	0.772649i	$-0.281068\pi$
$433$	6.79331e23			1.26967			0.634834	+	0.772649i	$0.281068\pi$
$434$	1.15713e19	−	1.20584e23i	2.11823e−5	−	0.220741i
$435$	3.63987e23			0.652654
$436$	−1.02011e20	+	5.31530e23i	−0.000179172	+	0.933575i
$437$			9.96372e23i			1.71431i
$438$	4.69633e18	−	4.89405e22i	7.91575e−6	−	0.0824901i
$439$			9.51831e23i			1.57173i	0.618395	+	0.785867i	$0.287783\pi$
$439$			9.51831e23i			1.57173i	−0.618395	+	0.785867i	$0.712217\pi$
$440$	4.20018e22	+	1.20915e19i	0.0679506	+	1.95616e-5i
$441$	3.84102e23			0.608835
$442$	4.27787e23	+	4.10504e19i	0.664396	+	6.37554e-5i
$443$	1.37661e23			0.209497			0.104748	−	0.994499i	$-0.466596\pi$
$443$	1.37661e23			0.209497			0.104748	+	0.994499i	$0.466596\pi$
$444$	−3.25415e19	+	1.69558e23i	−4.85279e−5	+	0.252855i
$445$		−	8.82169e23i		−	1.28917i
$446$	−6.87438e23	−	6.59665e19i	−0.984509	−	9.44735e-5i
$447$			2.11025e23i			0.296187i
$448$	5.64561e20	−	9.80550e23i	0.000776621	−	1.34886i
$449$	−4.32256e23			−0.582806			−0.291403	−	0.956600i	$-0.594122\pi$
$449$	−4.32256e23			−0.582806			−0.291403	+	0.956600i	$0.594122\pi$
$450$	−7.38205e19	+	7.69284e23i	−9.75583e−5	+	1.01666i
$451$	−4.93627e22			−0.0639455
$452$	−9.63761e23	−	1.84965e20i	−1.22384	−	0.000234879i
$453$		−	6.13513e23i		−	0.763731i
$454$	−9.89379e19	+	1.03103e24i	−0.000120742	+	1.25826i
$455$			6.73225e23i			0.805485i
$456$	1.63456e20	−	5.67792e23i	0.000191742	−	0.666048i
$457$	5.11671e23			0.588498			0.294249	−	0.955729i	$-0.404930\pi$
$457$	5.11671e23			0.588498			0.294249	+	0.955729i	$0.404930\pi$
$458$	4.34391e23	+	4.16841e19i	0.489882	+	4.70090e-5i
$459$	1.36816e24			1.51294
$460$	−1.85179e24	−	3.55395e20i	−2.00803	−	0.000385382i
$461$		−	1.41522e24i		−	1.50493i	−0.658632	−	0.752466i	$-0.728864\pi$
$461$		−	1.41522e24i		−	1.50493i	0.658632	−	0.752466i	$-0.271136\pi$
$462$	2.89526e22	+	2.77829e18i	0.0301932	+	2.89734e-6i
$463$		−	8.26861e22i		−	0.0845675i	−0.999106	−	0.0422838i	$-0.986537\pi$
$463$		−	8.26861e22i		−	0.0845675i	0.999106	−	0.0422838i	$-0.0134634\pi$
$464$	−3.20116e20	+	8.33982e23i	−0.000321104	+	0.836556i
$465$	1.29772e23			0.127674
$466$	7.75682e19	−	8.08340e23i	7.48533e−5	−	0.780047i
$467$	−1.01664e24			−0.962311			−0.481155	−	0.876635i	$-0.659783\pi$
$467$	−1.01664e24			−0.962311			−0.481155	+	0.876635i	$0.659783\pi$
$468$	5.95924e19	−	3.10506e23i	5.53322e−5	−	0.288309i
$469$			1.55794e24i			1.41904i
$470$	−8.36940e19	+	8.72176e23i	−7.47848e−5	+	0.779334i
$471$		−	7.69181e22i		−	0.0674280i
$472$	1.13061e20	−	3.92737e23i	9.72377e−5	−	0.337772i
$473$	−9.68800e21			−0.00817493
$474$	−4.72402e23	−	4.53317e19i	−0.391117	−	3.75316e-5i
$475$	2.21292e24			1.79773
$476$	5.56041e20	−	2.89726e24i	0.000443246	−	2.30953i
$477$		−	9.58929e23i		−	0.750103i
$478$	−2.02416e24	−	1.94238e20i	−1.55380	−	0.000149102i
$479$		−	5.06136e23i		−	0.381283i	−0.981660	−	0.190641i	$-0.938943\pi$
$479$		−	5.06136e23i		−	0.381283i	0.981660	−	0.190641i	$-0.0610568\pi$
$480$	1.05526e24	+	5.06313e20i	0.780167	+	0.000374324i
$481$	2.66734e23			0.193541
$482$	−1.39650e20	+	1.45529e24i	−9.94529e−5	+	1.03640i
$483$	−1.27647e24			−0.892250
$484$	1.45466e24	+	2.79178e20i	0.998050	+	0.000191546i
$485$		−	2.68611e24i		−	1.80904i
$486$	1.49968e20	−	1.56282e24i	9.91451e−5	−	1.03319i
$487$			1.31045e24i			0.850470i	0.905083	+	0.425235i	$0.139809\pi$
$487$			1.31045e24i			0.850470i	−0.905083	+	0.425235i	$0.860191\pi$
$488$	1.53025e24	+	4.40527e20i	0.974951	+	0.000280669i
$489$	−1.06451e22			−0.00665839
$490$	2.05351e24	+	1.97054e20i	1.26105	+	0.000121010i
$491$	−7.51596e23			−0.453159			−0.226580	−	0.973993i	$-0.572754\pi$
$491$	−7.51596e23			−0.453159			−0.226580	+	0.973993i	$0.572754\pi$
$492$	−1.24020e24	−	2.38018e20i	−0.734183	−	0.000140904i
$493$			2.46419e24i			1.43236i
$494$	−8.93203e23	−	8.57117e19i	−0.509809	−	4.89212e-5i
$495$		−	9.00800e22i		−	0.0504872i
$496$	−1.14130e20	+	2.97338e23i	−6.28153e−5	+	0.163650i
$497$	2.93456e24			1.58612
$498$	−1.62115e20	+	1.68941e24i	−8.60519e−5	+	0.896748i
$499$	−1.22090e24			−0.636467			−0.318234	−	0.948012i	$-0.603090\pi$
$499$	−1.22090e24			−0.636467			−0.318234	+	0.948012i	$0.603090\pi$
$500$	−2.12466e20	+	1.10706e24i	−0.000108783	+	0.566813i
$501$			4.22860e23i			0.212646i
$502$	−1.75265e19	+	1.82643e23i	−8.65686e−6	+	0.0902133i
$503$		−	3.39608e23i		−	0.164766i	−0.996601	−	0.0823828i	$-0.973747\pi$
$503$		−	3.39608e23i		−	0.164766i	0.996601	−	0.0823828i	$-0.0262530\pi$
$504$	−2.10296e24	−	6.05399e20i	−1.00220	−	0.000288514i
$505$	−4.14839e24			−1.94204
$506$	1.25279e23	+	1.20218e19i	0.0576136	+	5.52860e-6i
$507$	−9.53163e23			−0.430621
$508$	−4.94141e20	+	2.57472e24i	−0.000219320	+	1.14277i
$509$			8.94309e23i			0.389967i	0.980807	+	0.194983i	$0.0624653\pi$
$509$			8.94309e23i			0.389967i	−0.980807	+	0.194983i	$0.937535\pi$
$510$	3.11800e24	+	2.99203e20i	1.33581	+	0.000128184i
$511$			5.21422e23i			0.219483i
$512$	−2.08815e21	+	2.41785e24i	−0.000863640	+	1.00000i
$513$	−2.85666e24			−1.16092
$514$	2.33416e20	−	2.43243e24i	9.32099e−5	−	0.971341i
$515$	9.65544e22			0.0378885
$516$	−2.43403e23	−	4.67138e19i	−0.0938595	−	1.80135e-5i
$517$		−	5.90055e22i		−	0.0223603i
$518$	1.73352e20	−	1.80650e24i	6.45596e−5	−	0.672776i
$519$		−	1.44230e24i		−	0.527896i
$520$	4.77894e20	−	1.66005e24i	0.000171910	−	0.597159i
$521$	1.16339e24			0.411327			0.205664	−	0.978623i	$-0.434065\pi$
$521$	1.16339e24			0.411327			0.205664	+	0.978623i	$0.434065\pi$
$522$	1.78862e24	+	1.71636e20i	0.621560	+	5.96448e-5i
$523$	2.67802e24			0.914741			0.457371	−	0.889276i	$-0.348791\pi$
$523$	2.67802e24			0.914741			0.457371	+	0.889276i	$0.348791\pi$
$524$	4.79570e24	+	9.20391e20i	1.61017	+	0.000309023i
$525$			2.83502e24i			0.935668i
$526$	−2.30856e22	−	2.21529e18i	−0.00748978	−	7.18719e-7i
$527$			8.78553e23i			0.280203i
$528$	−7.13916e22	−	2.74029e19i	−0.0223842	−	8.59195e-6i
$529$	−2.27921e24			−0.702559
$530$	4.91955e20	−	5.12667e24i	0.000149088	−	1.55365i
$531$	−8.42291e23			−0.250964
$532$	−1.16099e21	+	6.04936e24i	−0.000340114	+	1.77217i
$533$			1.95097e24i			0.561961i
$534$	−1.43887e20	+	1.49945e24i	−4.07521e−5	+	0.424678i
$535$		−	6.76276e24i		−	1.88339i
$536$	1.10592e21	−	3.84159e24i	0.000302858	−	1.05203i
$537$	1.15751e23			0.0311714
$538$	−3.86862e24	−	3.71233e20i	−1.02451	−	9.83118e-5i
$539$	−1.38926e23			−0.0361814
$540$	1.01894e21	−	5.30919e24i	0.000260979	−	1.35983i
$541$		−	1.36666e24i		−	0.344258i	−0.985074	−	0.172129i	$-0.944935\pi$
$541$		−	1.36666e24i		−	0.344258i	0.985074	−	0.172129i	$-0.0550646\pi$
$542$	3.48538e23	+	3.34457e19i	0.0863488	+	8.28602e-6i
$543$		−	8.88087e23i		−	0.216400i
$544$	−3.42773e21	+	7.14409e24i	−0.000821518	+	1.71221i
$545$	6.09449e24			1.43671
$546$	1.09807e20	−	1.14430e24i	2.54622e−5	−	0.265342i
$547$	−4.41424e24			−1.00686			−0.503431	−	0.864035i	$-0.667929\pi$
$547$	−4.41424e24			−1.00686			−0.503431	+	0.864035i	$0.667929\pi$
$548$	−3.48089e24	−	6.68052e20i	−0.781026	−	0.000149894i
$549$		−	3.28187e24i		−	0.724387i
$550$	2.67002e19	−	2.78243e23i	5.79763e−6	−	0.0604171i
$551$		−	5.14514e24i		−	1.09909i
$552$	3.14754e24	+	9.06113e20i	0.661484	+	0.000190428i
$553$	5.03307e24			1.04065
$554$	−6.69966e24	−	6.42899e20i	−1.36290	−	0.000130784i
$555$	1.94414e24			0.389127
$556$	2.04020e24	+	3.91556e20i	0.401791	+	7.71118e-5i
$557$			5.94489e24i			1.15198i	0.817455	+	0.575992i	$0.195384\pi$
$557$			5.94489e24i			1.15198i	−0.817455	+	0.575992i	$0.804616\pi$
$558$	6.37692e23	+	6.11929e19i	0.121592	+	1.16679e-5i
$559$			3.82901e23i			0.0718423i
$560$	−1.12429e25	−	4.31549e21i	−2.07581	−	0.000796778i
$561$	−2.10943e23			−0.0383264
$562$	−1.36854e20	+	1.42616e24i	−2.44699e−5	+	0.255001i
$563$	2.02889e24			0.357013			0.178506	−	0.983939i	$-0.442873\pi$
$563$	2.02889e24			0.357013			0.178506	+	0.983939i	$0.442873\pi$
$564$	2.84514e20	−	1.48246e24i	4.92710e−5	−	0.256727i
$565$			1.10504e25i			1.88340i
$566$	5.24976e20	−	5.47079e24i	8.80627e−5	−	0.917702i
$567$			2.41048e24i			0.397975i
$568$	−7.23607e24	−	2.08312e21i	−1.17589	−	0.000338516i
$569$	−1.47134e23			−0.0235343			−0.0117672	−	0.999931i	$-0.503746\pi$
$569$	−1.47134e23			−0.0235343			−0.0117672	+	0.999931i	$0.503746\pi$
$570$	−6.51027e24	−	6.24725e20i	−1.02500	−	9.83593e-5i
$571$	1.08036e25			1.67433			0.837167	−	0.546948i	$-0.184210\pi$
$571$	1.08036e25			1.67433			0.837167	+	0.546948i	$0.184210\pi$
$572$	−2.15540e19	+	1.12307e23i	−3.28824e−6	+	0.0171334i
$573$		−	3.45367e24i		−	0.518667i
$574$	1.32133e25	+	1.26795e21i	1.95346	+	0.000187454i
$575$			1.22673e25i			1.78541i
$576$	5.18549e24	+	2.98560e21i	0.742998	+	0.000427789i
$577$	−4.81962e24			−0.679878			−0.339939	−	0.940448i	$-0.610406\pi$
$577$	−4.81962e24			−0.679878			−0.339939	+	0.940448i	$0.610406\pi$
$578$	−1.33466e21	+	1.39085e25i	−0.000185362	+	1.93166i
$579$	−6.62874e23			−0.0906408
$580$	9.56240e24	+	1.83521e21i	1.28740	+	0.000247078i
$581$		−	1.79993e25i		−	2.38600i
$582$	−4.38120e20	+	4.56565e24i	−5.71855e−5	+	0.595931i
$583$			3.46836e23i			0.0445766i
$584$	3.70136e20	−	1.28573e24i	4.68431e−5	−	0.162717i
$585$	−3.56025e24			−0.443688
$586$	3.14942e23	+	3.02218e19i	0.0386502	+	3.70887e-6i
$587$	1.53828e25			1.85906			0.929530	−	0.368747i	$-0.120213\pi$
$587$	1.53828e25			1.85906			0.929530	+	0.368747i	$0.120213\pi$
$588$	−3.49040e24	−	6.69878e20i	−0.415412	−	7.97259e-5i
$589$		−	1.83439e24i		−	0.215007i
$590$	−4.50310e24	−	4.32117e20i	−0.519808	−	4.98808e-5i
$591$		−	4.17514e24i		−	0.474661i
$592$	−1.70981e21	+	4.45449e24i	−0.000191449	+	0.498773i
$593$	−6.25528e24			−0.689850			−0.344925	−	0.938630i	$-0.612096\pi$
$593$	−6.25528e24			−0.689850			−0.344925	+	0.938630i	$0.612096\pi$
$594$	−3.44673e19	+	3.59184e23i	−3.74394e−6	+	0.0390156i
$595$	−3.32198e25			−3.55422
$596$	−1.06398e21	+	5.54388e24i	−0.000112129	+	0.584248i
$597$			7.20247e24i			0.747674i
$598$	4.75140e20	−	4.95144e24i	4.85860e−5	−	0.506315i
$599$			9.99849e24i			1.00715i	0.863952	+	0.503574i	$0.167982\pi$
$599$			9.99849e24i			1.00715i	−0.863952	+	0.503574i	$0.832018\pi$
$600$	2.01246e21	−	6.99062e24i	0.000199694	−	0.693672i
$601$	9.00294e24			0.880063			0.440032	−	0.897982i	$-0.354967\pi$
$601$	9.00294e24			0.880063			0.440032	+	0.897982i	$0.354967\pi$
$602$	2.59326e24	+	2.48849e20i	0.249734	+	2.39645e-5i
$603$	−8.23894e24			−0.781655
$604$	3.09332e21	−	1.61178e25i	0.000289129	−	1.50651i
$605$		−	1.66790e25i		−	1.53593i
$606$	7.05114e24	+	6.76627e20i	0.639743	+	6.13897e-5i
$607$			2.71764e24i			0.242937i	0.992595	+	0.121469i	$0.0387604\pi$
$607$			2.71764e24i			0.242937i	−0.992595	+	0.121469i	$0.961240\pi$
$608$	7.15698e21	−	1.49166e25i	0.000630373	−	1.31382i
$609$	6.59153e24			0.572046
$610$	1.68369e21	−	1.75457e25i	0.000143977	−	1.50038i
$611$	−2.33209e24			−0.196505
$612$	1.53217e25	+	2.94054e21i	1.27217	+	0.000244154i
$613$		−	3.83034e24i		−	0.313396i	−0.987647	−	0.156698i	$-0.949915\pi$
$613$		−	3.83034e24i		−	0.313396i	0.987647	−	0.156698i	$-0.0500849\pi$
$614$	−2.04206e21	+	2.12804e25i	−0.000164647	+	1.71579i
$615$			1.42200e25i			1.12986i
$616$	7.60620e23	+	2.18967e20i	0.0595582	+	1.71456e-5i
$617$	−8.98236e24			−0.693145			−0.346572	−	0.938023i	$-0.612655\pi$
$617$	−8.98236e24			−0.693145			−0.346572	+	0.938023i	$0.612655\pi$
$618$	−1.64116e23	−	1.57486e19i	−0.0124812	−	1.19769e-6i
$619$	4.25464e24			0.318894			0.159447	−	0.987206i	$-0.449029\pi$
$619$	4.25464e24			0.318894			0.159447	+	0.987206i	$0.449029\pi$
$620$	3.40926e24	+	6.54306e20i	0.251846	+	4.83343e-5i
$621$		−	1.58358e25i		−	1.15296i
$622$	−7.05862e24	−	6.77345e20i	−0.506531	−	4.86067e-5i
$623$		−	1.59754e25i		−	1.12995i
$624$	−1.08305e21	+	2.82162e24i	−7.55071e−5	+	0.196715i
$625$	−7.21815e24			−0.496028
$626$	−7.09399e20	+	7.39265e24i	−4.80531e−5	+	0.500762i
$627$	4.40440e23			0.0294089
$628$	3.87819e20	−	2.02073e24i	2.55266e−5	−	0.133006i
$629$			1.31618e25i			0.854004i
$630$	−2.31382e21	+	2.41124e25i	−0.000148001	+	1.54232i
$631$		−	9.32149e24i		−	0.587788i	−0.955838	−	0.293894i	$-0.905049\pi$
$631$		−	9.32149e24i		−	0.587788i	0.955838	−	0.293894i	$-0.0949513\pi$
$632$	−1.24106e25	−	3.57276e21i	−0.771505	−	0.000222101i
$633$	−9.43565e23			−0.0578280
$634$	1.95663e25	+	1.87758e21i	1.18224	+	0.000113448i
$635$	2.95216e25			1.75864
$636$	−1.67238e21	+	8.71395e24i	−9.82248e−5	+	0.511801i
$637$			5.49081e24i			0.317967i
$638$	−6.46926e23	−	6.20790e19i	−0.0369376	−	3.54453e-6i
$639$			1.55190e25i			0.873687i
$640$	2.77230e25	+	1.86221e22i	1.53893	+	0.00103373i
$641$	−9.97882e24			−0.546206			−0.273103	−	0.961985i	$-0.588050\pi$
$641$	−9.97882e24			−0.546206			−0.273103	+	0.961985i	$0.588050\pi$
$642$	−1.10305e21	+	1.14949e25i	−5.95358e−5	+	0.620424i
$643$	−8.49556e24			−0.452161			−0.226081	−	0.974109i	$-0.572591\pi$
$643$	−8.49556e24			−0.452161			−0.226081	+	0.974109i	$0.572591\pi$
$644$	−3.35345e25	−	6.43593e21i	−1.76002	−	0.000337784i
$645$			2.79084e24i			0.144443i
$646$	4.22938e21	−	4.40744e25i	0.000215866	−	2.24954i
$647$			3.14503e25i			1.58302i	0.611156	+	0.791510i	$0.290705\pi$
$647$			3.14503e25i			1.58302i	−0.611156	+	0.791510i	$0.709295\pi$
$648$	1.71110e21	−	5.94378e24i	8.49374e−5	−	0.295045i
$649$	3.04649e23			0.0149141
$650$	−1.09971e25	−	1.05528e21i	−0.530953	−	5.09503e-5i
$651$	2.35007e24			0.111905
$652$	−2.79660e23	−	5.36722e19i	−0.0131341	−	2.52070e-6i
$653$			3.10447e25i			1.43803i	0.694994	+	0.719016i	$0.255407\pi$
$653$			3.10447e25i			1.43803i	−0.694994	+	0.719016i	$0.744593\pi$
$654$	−1.03590e25	−	9.94047e20i	−0.473279	−	4.54158e-5i
$655$		−	5.49873e25i		−	2.47794i
$656$	−3.25815e25	−	1.25061e22i	−1.44823	−	0.000555887i
$657$	−2.75746e24			−0.120899
$658$	−1.51563e21	+	1.57944e25i	−6.55483e−5	+	0.683079i
$659$	−1.70361e25			−0.726776			−0.363388	−	0.931638i	$-0.618380\pi$
$659$	−1.70361e25			−0.726776			−0.363388	+	0.931638i	$0.618380\pi$
$660$	−1.57100e20	+	8.18572e23i	−6.61122e−6	+	0.0344478i
$661$			1.21446e25i			0.504164i	0.967706	+	0.252082i	$0.0811152\pi$
$661$			1.21446e25i			0.504164i	−0.967706	+	0.252082i	$0.918885\pi$
$662$	1.03598e21	−	1.07960e25i	4.24259e−5	−	0.442120i
$663$			8.33713e24i			0.336818i
$664$	−1.27769e22	+	4.43828e25i	−0.000509230	+	1.76890i
$665$	6.93617e25			2.72725
$666$	9.55342e24	+	9.16746e20i	0.370588	+	3.55616e-5i
$667$	2.85219e25			1.09156
$668$	−2.13205e21	+	1.11090e25i	−8.05024e−5	+	0.419458i
$669$		−	1.33975e25i		−	0.499100i
$670$	−4.40474e25	−	4.22679e21i	−1.61900	−	0.000155359i
$671$			1.18702e24i			0.0430484i
$672$	1.91099e25	+	9.16894e21i	0.683810	+	0.000328092i
$673$	1.55915e25			0.550492			0.275246	−	0.961374i	$-0.411241\pi$
$673$	1.55915e25			0.550492			0.275246	+	0.961374i	$0.411241\pi$
$674$	2.92028e21	−	3.04323e25i	0.000101739	−	1.06022i
$675$	−3.51710e25			−1.20907
$676$	−2.50408e25	−	4.80582e21i	−0.849429	−	0.000163022i
$677$		−	3.95727e25i		−	1.32464i	−0.749222	−	0.662319i	$-0.769572\pi$
$677$		−	3.95727e25i		−	1.32464i	0.749222	−	0.662319i	$-0.230428\pi$
$678$	1.80239e21	−	1.87827e25i	5.95363e−5	−	0.620428i
$679$		−	4.86434e25i		−	1.58561i
$680$	8.19137e25	+	2.35813e22i	2.63498	+	0.000758556i
$681$	−2.00938e25			−0.637879
$682$	−2.30648e23	−	2.21329e19i	−0.00722586	−	6.93393e-7i
$683$	4.98479e25			1.54121			0.770603	−	0.637315i	$-0.219955\pi$
$683$	4.98479e25			1.54121			0.770603	+	0.637315i	$0.219955\pi$
$684$	−3.19912e25	−	6.13974e21i	−0.976169	−	0.000187346i
$685$			3.99117e25i			1.20195i
$686$	−8.19468e24	−	7.86361e20i	−0.243565	−	2.33725e-5i
$687$			8.46584e24i			0.248347i
$688$	−6.39449e24	−	2.45446e21i	−0.185144	−	7.10657e-5i
$689$	1.37081e25			0.391745
$690$	3.46315e21	−	3.60895e25i	9.76853e−5	−	1.01798i
$691$	−4.97684e24			−0.138564			−0.0692821	−	0.997597i	$-0.522071\pi$
$691$	−4.97684e24			−0.138564			−0.0692821	+	0.997597i	$0.522071\pi$
$692$	7.27203e21	−	3.78909e25i	0.000199848	−	1.04131i
$693$		−	1.63128e24i		−	0.0442516i
$694$	2.17791e21	−	2.26960e25i	5.83183e−5	−	0.607736i
$695$		−	2.33929e25i		−	0.618330i
$696$	−1.62535e25	−	4.67905e21i	−0.424095	−	0.000122088i
$697$	−9.62694e25			−2.47967
$698$	3.23313e25	+	3.10251e21i	0.822100	+	7.88887e-5i
$699$	1.57537e25			0.395447
$700$	−1.42941e22	+	7.44794e25i	−0.000354221	+	1.84567i
$701$			4.52831e25i			1.10783i	0.832573	+	0.553916i	$0.186867\pi$
$701$			4.52831e25i			1.10783i	−0.832573	+	0.553916i	$0.813133\pi$
$702$	1.41961e25	+	1.36226e21i	0.342874	+	3.29022e-5i
$703$		−	2.74814e25i		−	0.655300i
$704$	−1.87555e24	−	1.07986e21i	−0.0441544	−	2.54223e-5i
$705$	−1.69978e25			−0.395086
$706$	3.00512e21	−	3.13164e25i	6.89635e−5	−	0.718670i
$707$	−7.51242e25			−1.70218
$708$	7.65404e24	+	1.46896e21i	0.171235	+	3.28633e-5i
$709$			5.46051e25i			1.20619i	0.797668	+	0.603096i	$0.206067\pi$
$709$			5.46051e25i			1.20619i	−0.797668	+	0.603096i	$0.793933\pi$
$710$	−7.96165e21	+	8.29684e25i	−0.000173651	+	1.80962i
$711$			2.66166e25i			0.573227i
$712$	−1.13403e22	+	3.93924e25i	−0.000241159	+	0.837707i
$713$	1.01689e25			0.213534
$714$	5.64646e25	+	5.41834e21i	1.17083	+	0.000112352i
$715$	1.28771e24			0.0263672
$716$	3.04092e24	+	5.83613e20i	0.0614877	+	1.18007e-5i
$717$		−	3.94488e25i		−	0.787702i
$718$	6.07572e25	+	5.83026e21i	1.19806	+	0.000114966i
$719$			5.30786e25i			1.03362i	0.856101	+	0.516808i	$0.172880\pi$
$719$			5.30786e25i			1.03362i	−0.856101	+	0.516808i	$0.827120\pi$
$720$	2.28218e22	−	5.94566e25i	0.000438892	−	1.14342i
$721$	1.74853e24			0.0332089
$722$	−3.71486e21	+	3.87126e25i	−6.96799e−5	+	0.726135i
$723$	−2.83622e25			−0.525406
$724$	4.47771e21	−	2.33312e25i	8.19236e−5	−	0.426864i
$725$		−	6.33466e25i		−	1.14467i
$726$	−2.72045e21	+	2.83498e25i	−4.85524e−5	+	0.505965i
$727$		−	5.11337e25i		−	0.901359i	−0.892686	−	0.450680i	$-0.851182\pi$
$727$		−	5.11337e25i		−	0.901359i	0.892686	−	0.450680i	$-0.148818\pi$
$728$	8.65429e21	−	3.00621e25i	0.000150678	−	0.523405i
$729$	1.33009e25			0.228736
$730$	−1.47421e25	−	1.41465e21i	−0.250411	−	2.40294e-5i
$731$	−1.88940e25			−0.317006
$732$	−5.72362e21	+	2.98229e25i	−9.48573e−5	+	0.494255i
$733$			7.52245e25i			1.23147i	0.787954	+	0.615734i	$0.211141\pi$
$733$			7.52245e25i			1.23147i	−0.787954	+	0.615734i	$0.788859\pi$
$734$	−1.03030e26	−	9.88677e21i	−1.66609	−	0.000159878i
$735$			4.00208e25i			0.639292i
$736$	8.26897e25	+	3.96745e22i	1.30482	+	0.000626053i
$737$	2.97995e24			0.0464517
$738$	−6.70535e21	+	6.98766e25i	−0.000103256	+	1.07603i
$739$	3.89147e25			0.591989			0.295995	−	0.955190i	$-0.404349\pi$
$739$	3.89147e25			0.591989			0.295995	+	0.955190i	$0.404349\pi$
$740$	5.10750e25	+	9.80231e21i	0.767579	+	0.000147314i
$741$		−	1.74076e25i		−	0.258449i
$742$	8.90894e21	−	9.28401e25i	0.000130674	−	1.36176i
$743$		−	1.21957e25i		−	0.176729i	−0.996088	−	0.0883644i	$-0.971836\pi$
$743$		−	1.21957e25i		−	0.176729i	0.996088	−	0.0883644i	$-0.0281640\pi$
$744$	−5.79482e24	−	1.66821e21i	−0.0829628	−	2.38833e-5i
$745$	6.35658e25			0.899119
$746$	−1.86701e25	−	1.79159e21i	−0.260914	−	2.50373e-5i
$747$	9.51865e25			1.31429
$748$	−5.54172e24	−	1.06357e21i	−0.0756015	−	1.45094e-5i
$749$		−	1.22468e26i		−	1.65078i
$750$	−2.15754e25	−	2.07038e21i	−0.287348	−	2.75739e-5i
$751$			1.21844e26i			1.60341i	0.597719	+	0.801705i	$0.296074\pi$
$751$			1.21844e26i			1.60341i	−0.597719	+	0.801705i	$0.703926\pi$
$752$	1.49491e22	−	3.89461e25i	0.000194381	−	0.506411i
$753$	−3.55953e24			−0.0457339
$754$	−2.45356e21	+	2.55686e25i	−3.11498e−5	+	0.324612i
$755$	−1.84805e26			−2.31842
$756$	1.84522e22	−	9.61454e25i	0.000228746	−	1.19188i
$757$			2.41693e25i			0.296074i	0.988982	+	0.148037i	$0.0472955\pi$
$757$			2.41693e25i			0.296074i	−0.988982	+	0.148037i	$0.952704\pi$
$758$	−2.31652e21	+	2.41405e25i	−2.80423e−5	+	0.292229i
$759$			2.44157e24i			0.0292074i
$760$	−1.71033e26	−	4.92369e22i	−2.02189	−	0.000582061i
$761$	−1.03284e26			−1.20662			−0.603312	−	0.797505i	$-0.706153\pi$
$761$	−1.03284e26			−1.20662			−0.603312	+	0.797505i	$0.706153\pi$
$762$	−5.01788e25	−	4.81515e21i	−0.579329	−	5.55924e-5i
$763$	1.10367e26			1.25926
$764$	1.74133e22	−	9.07321e25i	0.000196355	−	1.02311i
$765$		−	1.75678e26i		−	1.95778i
$766$	2.29428e25	+	2.20159e21i	0.252690	+	2.42481e-5i
$767$		−	1.20407e25i		−	0.131067i
$768$	−4.71215e25	−	3.61742e22i	−0.506953	−	0.000389178i
$769$	1.02838e26			1.09350			0.546748	−	0.837297i	$-0.315866\pi$
$769$	1.02838e26			1.09350			0.546748	+	0.837297i	$0.315866\pi$
$770$	8.36889e20	−	8.72123e24i	8.79531e−6	−	0.0916561i
$771$	4.74055e25			0.492425
$772$	−1.74145e25	−	3.34219e21i	−0.178795	−	3.43143e-5i
$773$		−	3.84596e25i		−	0.390292i	−0.980774	−	0.195146i	$-0.937482\pi$
$773$		−	3.84596e25i		−	0.390292i	0.980774	−	0.195146i	$-0.0625181\pi$
$774$	−1.31600e21	+	1.37141e25i	−1.32004e−5	+	0.137562i
$775$		−	2.25849e25i		−	0.223925i
$776$	−3.45299e22	+	1.19945e26i	−0.000338407	+	1.17551i
$777$	3.52069e25			0.341066
$778$	−1.34601e25	−	1.29163e21i	−0.128894	−	1.23687e-5i
$779$	2.01007e26			1.90272
$780$	3.23526e25	+	6.20911e21i	0.302732	+	5.81002e-5i
$781$		−	5.61308e24i		−	0.0519208i
$782$	2.44325e26	+	2.34455e22i	2.23413	+	0.000214387i
$783$			8.17741e25i			0.739197i
$784$	−9.16972e25	−	3.51970e22i	−0.819429	−	0.000314530i
$785$	−2.31696e25			−0.204688
$786$	−8.96875e21	+	9.34634e25i	−7.83301e−5	+	0.816279i
$787$	−1.83183e26			−1.58165			−0.790827	−	0.612039i	$-0.790349\pi$
$787$	−1.83183e26			−1.58165			−0.790827	+	0.612039i	$0.790349\pi$
$788$	2.10509e22	−	1.09686e26i	0.000179695	−	0.936301i
$789$		−	4.49915e23i		−	0.00379697i
$790$	−1.36550e22	+	1.42299e26i	−0.000113933	+	1.18730i
$791$			2.00115e26i			1.65079i
$792$	−1.15798e21	+	4.02243e24i	−9.44437e−6	+	0.0328066i
$793$	4.69150e25			0.378314
$794$	−1.88291e26	−	1.80684e22i	−1.50122	−	0.000144057i
$795$	9.99137e25			0.787628
$796$	−3.63147e22	+	1.89218e26i	−0.000283051	+	1.47484i
$797$			3.87594e25i			0.298712i	0.988784	+	0.149356i	$0.0477200\pi$
$797$			3.87594e25i			0.298712i	−0.988784	+	0.149356i	$0.952280\pi$
$798$	−1.17896e26	−	1.13133e22i	−0.898407	−	8.62111e-5i
$799$		−	1.15075e26i		−	0.867082i
$800$	8.81163e22	−	1.83652e26i	0.000656518	−	1.36832i
$801$	8.44836e25			0.622415
$802$	1.92242e22	−	2.00336e26i	0.000140049	−	1.45945i
$803$	9.97350e23			0.00718468
$804$	7.48686e25	+	1.43688e22i	0.533329	+	0.000102357i
$805$			3.84505e26i			2.70856i
$806$	−8.74764e20	+	9.11593e24i	−6.09362e−6	+	0.0635017i
$807$		−	7.53955e25i		−	0.519378i
$808$	1.85242e26	+	5.33275e22i	1.26194	+	0.000363286i
$809$	−1.83367e26			−1.23533			−0.617666	−	0.786441i	$-0.711922\pi$
$809$	−1.83367e26			−1.23533			−0.617666	+	0.786441i	$0.711922\pi$
$810$	−6.81511e25	−	6.53978e21i	−0.454054	−	4.35710e-5i
$811$	−1.25795e26			−0.828848			−0.414424	−	0.910084i	$-0.636017\pi$
$811$	−1.25795e26			−0.828848			−0.414424	+	0.910084i	$0.636017\pi$
$812$	1.73168e26	+	3.32343e22i	1.12840	+	0.000216562i
$813$			6.79265e24i			0.0437748i
$814$	−3.45538e24	−	3.31579e20i	−0.0220230	−	2.11333e-6i
$815$			3.20656e24i			0.0202126i
$816$	−1.39231e26	−	5.34424e22i	−0.868010	−	0.000333177i
$817$	3.94499e25			0.243247
$818$	−7.92126e21	+	8.25475e25i	−4.83075e−5	+	0.503413i
$819$	−6.44734e25			−0.388889
$820$	−7.16970e22	+	3.73578e26i	−0.000427737	+	2.22872i
$821$		−	2.98734e26i		−	1.76277i	−0.472399	−	0.881385i	$-0.656612\pi$
$821$		−	2.98734e26i		−	1.76277i	0.472399	−	0.881385i	$-0.343388\pi$
$822$	6.50983e21	−	6.78390e25i	3.79947e−5	−	0.395944i
$823$		−	2.45336e26i		−	1.41632i	−0.706050	−	0.708162i	$-0.749525\pi$
$823$		−	2.45336e26i		−	1.41632i	0.706050	−	0.708162i	$-0.250475\pi$
$824$	−4.31154e24	−	1.24121e21i	−0.0246200	−	7.08759e-6i
$825$	5.42268e24			0.0306287
$826$	−8.15476e25	−	7.82531e21i	−0.455608	−	4.37201e-5i
$827$	−3.22789e26			−1.78389			−0.891947	−	0.452141i	$-0.850661\pi$
$827$	−3.22789e26			−1.78389			−0.891947	+	0.452141i	$0.850661\pi$
$828$	3.40355e22	−	1.77342e26i	0.000186063	−	0.969480i
$829$			9.60169e25i			0.519226i	0.965713	+	0.259613i	$0.0835951\pi$
$829$			9.60169e25i			0.519226i	−0.965713	+	0.259613i	$0.916405\pi$
$830$	5.08891e26	+	4.88332e22i	2.72221	+	0.000261223i
$831$		−	1.30570e26i		−	0.690928i
$832$	−4.26797e22	+	7.41276e25i	−0.000223414	+	0.388034i
$833$	−2.70940e26			−1.40303
$834$	−3.81552e21	+	3.97615e25i	−1.95460e−5	+	0.203690i
$835$	1.27376e26			0.645518
$836$	1.15709e25	+	2.22069e21i	0.0580111	+	1.11335e-5i
$837$			2.91548e25i			0.144604i
$838$	1.72374e22	−	1.79631e26i	8.45814e−5	−	0.881424i
$839$			3.43218e25i			0.166614i	0.996524	+	0.0833071i	$0.0265482\pi$
$839$			3.43218e25i			0.166614i	−0.996524	+	0.0833071i	$0.973452\pi$
$840$	6.30783e22	−	2.19113e26i	0.000302947	−	1.05234i
$841$	6.31738e25			0.300174
$842$	2.91421e26	+	2.79647e22i	1.36997	+	0.000131462i
$843$	−2.77944e25			−0.129274
$844$	−2.47886e25	−	4.75743e21i	−0.114070	−	2.18923e-5i
$845$			2.87116e26i			1.30722i
$846$	−8.35266e25	−	8.01521e21i	−0.376263	−	3.61062e-5i
$847$		−	3.02044e26i		−	1.34623i
$848$	−8.78710e22	+	2.28926e26i	−0.000387510	+	1.00956i
$849$	1.06620e26			0.465232
$850$	5.20719e22	−	5.42642e26i	0.000224819	−	2.34284i
$851$	1.52342e26			0.650810
$852$	2.70653e22	−	1.41024e26i	0.000114408	−	0.596123i
$853$		−	1.02650e26i		−	0.429355i	−0.976685	−	0.214678i	$-0.931130\pi$
$853$		−	1.02650e26i		−	0.429355i	0.976685	−	0.214678i	$-0.0688701\pi$
$854$	3.04903e22	−	3.17740e26i	0.000126195	−	1.31507i
$855$			3.66809e26i			1.50226i
$856$	−8.69352e22	+	3.01984e26i	−0.000352316	+	1.22383i
$857$	−7.48022e25			−0.299976			−0.149988	−	0.988688i	$-0.547924\pi$
$857$	−7.48022e25			−0.299976			−0.149988	+	0.988688i	$0.547924\pi$
$858$	−2.18876e24	−	2.10033e20i	−0.00868584	−	8.33493e-7i
$859$	3.54872e26			1.39358			0.696792	−	0.717273i	$-0.254610\pi$
$859$	3.54872e26			1.39358			0.696792	+	0.717273i	$0.254610\pi$
$860$	−1.40714e22	+	7.33189e25i	−5.46827e−5	+	0.284925i
$861$			2.57514e26i			0.990312i
$862$	−1.01693e26	−	9.75843e21i	−0.387012	−	3.71377e-5i
$863$		−	2.82061e26i		−	1.06230i	−0.847279	−	0.531149i	$-0.821761\pi$
$863$		−	2.82061e26i		−	1.06230i	0.847279	−	0.531149i	$-0.178239\pi$
$864$	−1.13749e23	+	2.37077e26i	−0.000423960	+	0.883619i
$865$	−4.34456e26			−1.60251
$866$	−3.33765e22	+	3.47817e26i	−0.000121837	+	1.26967i
$867$	−2.71063e26			−0.979261
$868$	6.17392e25	+	1.18490e22i	0.220741	+	4.23646e-5i
$869$		−	9.62700e24i		−	0.0340653i
$870$	−1.78832e22	+	1.86361e26i	−6.26286e−5	+	0.652654i
$871$		−	1.17777e26i		−	0.408223i
$872$	−2.72143e26	−	7.83446e22i	−0.933575	−	0.000268757i
$873$	2.57243e26			0.873406
$874$	−5.10142e26	−	4.89533e22i	−1.71431	−	0.000164505i
$875$	2.29869e26			0.764553
$876$	2.50576e25	+	4.80905e21i	0.0824901	+	1.58315e-5i
$877$		−	2.47921e26i		−	0.807825i	−0.914798	−	0.403912i	$-0.867650\pi$
$877$		−	2.47921e26i		−	0.807825i	0.914798	−	0.403912i	$-0.132350\pi$
$878$	−4.87338e26	−	4.67649e22i	−1.57173	−	0.000150824i
$879$			6.13789e24i			0.0195938i
$880$	−8.25444e21	+	2.15049e25i	−2.60822e−5	+	0.0679506i
$881$	4.55260e26			1.42389			0.711945	−	0.702235i	$-0.247815\pi$
$881$	4.55260e26			1.42389			0.711945	+	0.702235i	$0.247815\pi$
$882$	−1.88715e22	+	1.96660e26i	−5.84237e−5	+	0.608835i
$883$	−2.17949e26			−0.667897			−0.333948	−	0.942591i	$-0.608381\pi$
$883$	−2.17949e26			−0.667897			−0.333948	+	0.942591i	$0.608381\pi$
$884$	−4.20356e22	+	2.19027e26i	−0.000127511	+	0.664396i
$885$		−	8.77608e25i		−	0.263519i
$886$	−6.76349e21	+	7.04824e25i	−2.01033e−5	+	0.209497i
$887$			5.12050e26i			1.50661i	0.657674	+	0.753303i	$0.271541\pi$
$887$			5.12050e26i			1.50661i	−0.657674	+	0.753303i	$0.728459\pi$
$888$	−8.68136e25	−	2.49919e22i	−0.252855	−	7.27918e-5i
$889$	5.34614e26			1.54143
$890$	4.51671e26	+	4.33423e22i	1.28917	+	0.000123709i
$891$	4.61064e24			0.0130275
$892$	6.75497e22	−	3.51968e26i	0.000188947	−	0.984509i
$893$			2.40273e26i			0.665336i
$894$	−1.08045e26	−	1.03680e22i	−0.296187	−	2.84221e-5i
$895$		−	3.48670e25i		−	0.0946254i
$896$	5.02041e26	+	3.37231e23i	1.34886	+	0.000906057i
$897$	9.64986e25			0.256678
$898$	2.12374e22	−	2.21315e26i	5.59261e−5	−	0.582806i
$899$	−5.25107e25			−0.136902
$900$	−3.93873e26	−	7.55922e22i	−1.01666	−	0.000195117i
$901$			6.76415e26i			1.72858i
$902$	2.42526e21	−	2.52737e25i	6.13621e−6	−	0.0639455i
$903$			5.05400e25i			0.126604i
$904$	1.42053e23	−	4.93446e26i	0.000352318	−	1.22384i
$905$	−2.67514e26			−0.656915
$906$	3.14119e26	+	3.01428e22i	0.763731	+	7.32876e-5i
$907$	1.69927e26			0.409069			0.204534	−	0.978859i	$-0.434432\pi$
$907$	1.69927e26			0.409069			0.204534	+	0.978859i	$0.434432\pi$
$908$	−5.27889e26	−	1.01312e23i	−1.25826	−	0.000241485i
$909$		−	3.97283e26i		−	0.937617i
$910$	−3.44691e26	−	3.30765e22i	−0.805485	−	7.72943e-5i
$911$			3.60954e26i			0.835193i	0.908633	+	0.417596i	$0.137127\pi$
$911$			3.60954e26i			0.835193i	−0.908633	+	0.417596i	$0.862873\pi$
$912$	2.90709e26	+	1.11586e23i	0.666048	+	0.000255656i
$913$	−3.44281e25			−0.0781045
$914$	−2.51392e22	+	2.61976e26i	−5.64723e−5	+	0.588498i
$915$	3.41948e26			0.760625
$916$	−4.26845e22	+	2.22408e26i	−9.40181e−5	+	0.489882i
$917$		−	9.95777e26i		−	2.17189i
$918$	−6.72196e22	+	7.00496e26i	−0.000145182	+	1.51294i
$919$		−	7.17573e26i		−	1.53471i	−0.641223	−	0.767355i	$-0.721573\pi$
$919$		−	7.17573e26i		−	1.53471i	0.641223	−	0.767355i	$-0.278427\pi$
$920$	2.72943e23	−	9.48116e26i	0.000578072	−	2.00803i
$921$	−4.14733e26			−0.869824
$922$	7.24594e26	+	6.95320e22i	1.50493	+	0.000144413i
$923$	−2.21847e26			−0.456287
$924$	−2.84497e21	+	1.48237e25i	−5.79468e−6	+	0.0301932i
$925$		−	3.38349e26i		−	0.682479i
$926$	4.23353e25	+	4.06249e21i	0.0845675	+	8.11510e-6i
$927$			9.24683e24i			0.0182926i
$928$	−4.26999e26	−	2.04874e23i	−0.836556	−	0.000401379i
$929$	−4.84827e25			−0.0940688			−0.0470344	−	0.998893i	$-0.514977\pi$
$929$	−4.84827e25			−0.0940688			−0.0470344	+	0.998893i	$0.514977\pi$
$930$	−6.37588e21	+	6.64431e25i	−1.22516e−5	+	0.127674i
$931$	5.65713e26			1.07659
$932$	4.13870e26	+	7.94299e22i	0.780047	+	0.000149707i
$933$		−	1.37565e26i		−	0.256788i
$934$	4.99491e22	−	5.20520e26i	9.23433e−5	−	0.962311i
$935$			6.35411e25i			0.116346i
$936$	1.58979e26	+	4.57669e22i	0.288309	+	8.29983e-5i
$937$	−4.83088e26			−0.867701			−0.433851	−	0.900985i	$-0.642845\pi$
$937$	−4.83088e26			−0.867701			−0.433851	+	0.900985i	$0.642845\pi$
$938$	−7.97665e26	−	7.65439e22i	−1.41904	−	0.000136171i
$939$	−1.44075e26			−0.253863
$940$	−4.46554e26	−	8.57026e22i	−0.779334	−	0.000149570i
$941$		−	1.53202e26i		−	0.264824i	−0.991195	−	0.132412i	$-0.957728\pi$
$941$		−	1.53202e26i		−	0.264824i	0.991195	−	0.132412i	$-0.0422721\pi$
$942$	3.93821e25	+	3.77910e21i	0.0674280	+	6.47039e-6i
$943$			1.11428e27i			1.88968i
$944$	2.01081e26	+	7.71830e22i	0.337772	+	0.000129650i
$945$	−1.10240e27			−1.83422
$946$	4.75986e20	−	4.96026e24i	7.84466e−7	−	0.00817493i
$947$	−7.43649e26			−1.21400			−0.606999	−	0.794702i	$-0.707627\pi$
$947$	−7.43649e26			−1.21400			−0.606999	+	0.794702i	$0.707627\pi$
$948$	4.64197e22	−	2.41870e26i	7.50632e−5	−	0.391117i
$949$		−	3.94185e25i		−	0.0631399i
$950$	−1.08724e23	+	1.13302e27i	−0.000172510	+	1.79773i
$951$			3.81328e26i			0.599341i
$952$	1.48340e27	+	4.27040e23i	2.30953	+	0.000664868i
$953$	1.12886e27			1.74103			0.870514	−	0.492143i	$-0.163786\pi$
$953$	1.12886e27			1.74103			0.870514	+	0.492143i	$0.163786\pi$
$954$	4.90971e26	+	4.71136e22i	0.750103	+	7.19799e-5i
$955$	−1.04033e27			−1.57449
$956$	1.98900e23	−	1.03637e27i	0.000298204	−	1.55380i
$957$		−	1.26079e25i		−	0.0187256i
$958$	2.59141e26	+	2.48672e22i	0.381283	+	3.65879e-5i
$959$			7.22771e26i			1.05350i
$960$	−3.11079e23	+	5.40292e26i	−0.000449189	+	0.780167i
$961$	6.80332e26			0.973219
$962$	−1.31051e22	+	1.36568e26i	−1.85722e−5	+	0.193541i
$963$	6.47657e26			0.909302
$964$	−7.45110e26	−	1.43002e23i	−1.03640	−	0.000198906i
$965$			1.99674e26i			0.275154i
$966$	6.27149e22	−	6.53553e26i	8.56203e−5	−	0.892250i
$967$		−	4.00937e26i		−	0.542298i	−0.962537	−	0.271149i	$-0.912596\pi$
$967$		−	4.00937e26i		−	0.542298i	0.962537	−	0.271149i	$-0.0874035\pi$
$968$	−2.14409e23	+	7.44785e26i	−0.000287319	+	0.998050i
$969$	8.58966e26			1.14041
$970$	1.37529e27	+	1.31973e23i	1.80904	+	0.000173595i
$971$	−8.79412e26			−1.14609			−0.573046	−	0.819523i	$-0.694238\pi$
$971$	−8.79412e26			−1.14609			−0.573046	+	0.819523i	$0.694238\pi$
$972$	8.00162e26	+	1.53567e23i	1.03319	+	0.000198290i
$973$		−	4.23627e26i		−	0.541961i
$974$	−6.70949e26	−	6.43843e22i	−0.850470	−	8.16111e-5i
$975$		−	2.14322e26i		−	0.269169i
$976$	−3.00733e23	+	7.83486e26i	−0.000374225	+	0.974951i
$977$	−8.81534e26			−1.08690			−0.543448	−	0.839443i	$-0.682882\pi$
$977$	−8.81534e26			−1.08690			−0.543448	+	0.839443i	$0.682882\pi$
$978$	5.23009e20	−	5.45028e24i	6.38939e−7	−	0.00665839i
$979$	−3.05569e25			−0.0369884
$980$	−2.01784e23	+	1.05140e27i	−0.000242020	+	1.26105i
$981$			5.83657e26i			0.693645i
$982$	3.69270e22	−	3.84817e26i	4.34851e−5	−	0.453159i
$983$		−	7.23169e26i		−	0.843836i	−0.906634	−	0.421918i	$-0.861357\pi$
$983$		−	7.23169e26i		−	0.843836i	0.906634	−	0.421918i	$-0.138643\pi$
$984$	1.82798e23	−	6.34980e26i	0.000211357	−	0.734183i
$985$	−1.25765e27			−1.44090
$986$	−1.26166e27	−	1.21069e23i	−1.43236	−	0.000137449i
$987$	−3.07818e26			−0.346289
$988$	8.77688e22	−	4.57320e26i	9.78425e−5	−	0.509809i
$989$			2.18689e26i			0.241580i
$990$	4.61209e25	+	4.42576e21i	0.0504872	+	4.84475e-6i
$991$			2.27193e26i			0.246452i	0.992379	+	0.123226i	$0.0393240\pi$
$991$			2.27193e26i			0.246452i	−0.992379	+	0.123226i	$0.960676\pi$
$992$	−1.52237e26	−	7.30434e22i	−0.163650	−	7.85192e-5i
$993$	2.10403e26			0.224134
$994$	−1.44179e23	+	1.50249e27i	−0.000152204	+	1.58612i
$995$	2.16956e27			2.26968
$996$	−8.64977e26	−	1.66006e23i	−0.896748	−	0.000172104i
$997$			9.00985e26i			0.925680i	0.886442	+	0.462840i	$0.153170\pi$
$997$			9.00985e26i			0.925680i	−0.886442	+	0.462840i	$0.846830\pi$
$998$	5.99848e22	−	6.25102e26i	6.10754e−5	−	0.636467i
$999$			4.36775e26i			0.440725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.19.d.b.3.8	yes	16
3.2	odd	2		72.19.b.b.19.9		16
4.3	odd	2		32.19.d.b.15.10		16
8.3	odd	2	inner	8.19.d.b.3.7	✓	16
8.5	even	2		32.19.d.b.15.9		16
24.11	even	2		72.19.b.b.19.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.7	✓	16	8.3	odd	2	inner
8.19.d.b.3.8	yes	16	1.1	even	1	trivial
32.19.d.b.15.9		16	8.5	even	2
32.19.d.b.15.10		16	4.3	odd	2
72.19.b.b.19.9		16	3.2	odd	2
72.19.b.b.19.10		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0491315 + 512.000i) q^{2} -9978.36 q^{3} +(-262144. - 50.3107i) q^{4} +3.00573e6i q^{5} +(490.252 - 5.10892e6i) q^{6} +5.44315e7i q^{7} +(38638.6 - 1.34218e8i) q^{8} -2.87853e8 q^{9} +O(q^{10})\)	\(q+(-0.0491315 + 512.000i) q^{2} -9978.36 q^{3} +(-262144. - 50.3107i) q^{4} +3.00573e6i q^{5} +(490.252 - 5.10892e6i) q^{6} +5.44315e7i q^{7} +(38638.6 - 1.34218e8i) q^{8} -2.87853e8 q^{9} +(-1.53893e9 - 147676. i) q^{10} +1.04114e8 q^{11} +(2.61577e9 + 502018. i) q^{12} -4.11491e9i q^{13} +(-2.78689e10 - 2.67430e6i) q^{14} -2.99923e10i q^{15} +(6.87195e10 + 2.63773e7i) q^{16} +2.03047e11 q^{17} +(1.41426e7 - 1.47381e11i) q^{18} -4.23955e11 q^{19} +(1.51220e8 - 7.87934e11i) q^{20} -5.43137e11i q^{21} +(-5.11526e6 + 5.33062e10i) q^{22} -2.35018e12i q^{23} +(-3.85550e8 + 1.33927e12i) q^{24} -5.21971e12 q^{25} +(2.10683e12 + 2.02172e8i) q^{26} +6.73812e12 q^{27} +(2.73848e9 - 1.42689e13i) q^{28} +1.21360e13i q^{29} +(1.53560e13 + 1.47356e9i) q^{30} +4.32684e12i q^{31} +(-1.68815e10 + 3.51844e13i) q^{32} -1.03888e12 q^{33} +(-9.97601e9 + 1.03960e14i) q^{34} -1.63606e14 q^{35} +(7.54589e13 + 1.44821e10i) q^{36} +6.48214e13i q^{37} +(2.08295e10 - 2.17065e14i) q^{38} +4.10600e13i q^{39} +(4.03422e14 + 1.16137e11i) q^{40} -4.74123e14 q^{41} +(2.78086e14 + 2.66851e10i) q^{42} -9.30521e13 q^{43} +(-2.72928e13 - 5.23803e9i) q^{44} -8.65207e14i q^{45} +(1.20329e15 + 1.15468e11i) q^{46} -5.66741e14i q^{47} +(-6.85708e14 - 2.63202e11i) q^{48} -1.33437e15 q^{49} +(2.56452e11 - 2.67249e15i) q^{50} -2.02608e15 q^{51} +(-2.07024e11 + 1.07870e15i) q^{52} +3.33132e15i q^{53} +(-3.31054e11 + 3.44992e15i) q^{54} +3.12938e14i q^{55} +(7.30567e15 + 2.10315e12i) q^{56} +4.23038e15 q^{57} +(-6.21365e15 - 5.96262e11i) q^{58} +2.92612e15 q^{59} +(-1.50893e12 + 7.86229e15i) q^{60} +1.14012e16i q^{61} +(-2.21534e15 - 2.12584e11i) q^{62} -1.56682e16i q^{63} +(-1.80144e16 - 1.03720e13i) q^{64} +1.23683e16 q^{65} +(5.10420e10 - 5.31909e14i) q^{66} +2.86221e16 q^{67} +(-5.32276e16 - 1.02154e13i) q^{68} +2.34510e16i q^{69} +(8.03822e12 - 8.37664e16i) q^{70} -5.39130e16i q^{71} +(-1.11222e13 + 3.86349e16i) q^{72} +9.57943e15 q^{73} +(-3.31886e16 - 3.18477e12i) q^{74} +5.20842e16 q^{75} +(1.11137e17 + 2.13295e13i) q^{76} +5.66706e15i q^{77} +(-2.10227e16 - 2.01734e12i) q^{78} -9.24662e16i q^{79} +(-7.92829e13 + 2.06552e17i) q^{80} +4.42846e16 q^{81} +(2.32944e13 - 2.42751e17i) q^{82} -3.30678e17 q^{83} +(-2.73256e13 + 1.42380e17i) q^{84} +6.10305e17i q^{85} +(4.57179e12 - 4.76427e16i) q^{86} -1.21098e17i q^{87} +(4.02281e12 - 1.39739e16i) q^{88} -2.93496e17 q^{89} +(4.42986e17 + 4.25089e13i) q^{90} +2.23980e17 q^{91} +(-1.18239e14 + 6.16086e17i) q^{92} -4.31748e16i q^{93} +(2.90171e17 + 2.78448e13i) q^{94} -1.27429e18i q^{95} +(1.68449e14 - 3.51082e17i) q^{96} -8.93663e17 q^{97} +(6.55596e13 - 6.83197e17i) q^{98} -2.99694e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) \) 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9	\( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) \) 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9 - 1569837600 * q^10 - 2471571264 * q^11 + 4764364056 * q^12 + 26163923904 * q^14 - 192320075504 * q^16 - 176439301344 * q^17 - 1044291511122 * q^18 - 833365634368 * q^19 + 1256486405760 * q^20 + 59927319356 * q^22 - 1968891910512 * q^24 - 15320509140080 * q^25 + 4184514840864 * q^26 + 11565649473408 * q^27 - 12301604294400 * q^28 - 36336510039360 * q^30 + 141481742931936 * q^32 - 900457491648 * q^33 + 80653465357268 * q^34 + 20487495736320 * q^35 + 277183098847068 * q^36 + 493456694265564 * q^38 - 519930573603840 * q^40 - 594931562445024 * q^41 - 222362598288000 * q^42 - 2540155017577792 * q^43 + 73781630442072 * q^44 + 153882272211264 * q^46 + 897135071530464 * q^48 - 3186415704132848 * q^49 + 5668141028706330 * q^50 + 2916050119466880 * q^51 - 4594372123628160 * q^52 - 1377307163285640 * q^54 + 8184134137073664 * q^56 + 9540488340840768 * q^57 - 10505700099162720 * q^58 + 556807886314176 * q^59 + 29677718651516160 * q^60 + 6212402633091840 * q^62 - 56432885385732032 * q^64 - 21153177930524160 * q^65 - 23515570511959320 * q^66 + 162428574934613696 * q^67 - 70717864614203736 * q^68 + 4248100663257600 * q^70 - 36801123950767128 * q^72 - 7655712852492256 * q^73 + 9613779604149984 * q^74 - 384388788469704000 * q^75 - 151130166278324584 * q^76 - 93022771634070720 * q^78 + 26870186366192640 * q^80 + 99506910981790800 * q^81 + 329788507250077556 * q^82 + 866357336138514624 * q^83 + 451843591950574080 * q^84 + 1269201398006865468 * q^86 - 758460699051663856 * q^88 - 883646550464284128 * q^89 - 1227675520905095520 * q^90 - 379834560933460992 * q^91 + 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 483149691255826368 * q^96 - 2614894858526780128 * q^97 - 81635840192738166 * q^98 - 816916348833567168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more