LMFDB - Embedded newform 5.26.b.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,26,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	5.b (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:	$19.7998389976$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 71168091 x^{10} + \cdots + 10\!\cdots\!36 $ x^12 + 71168091x^10 + 1813581965257740x^8 + 20299276558981985144320x^6 + 100647952747482434827869143040x^4 + 189155799423092547840968636818784256*x^2 + 108016131559589051821063489995287755227136
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{20}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.4
Root			$-2840.59i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.26.b.a.4.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5681.18i q^{2} -1.63997e6i q^{3} +1.27857e6 q^{4} +(4.20624e8 + 3.47992e8i) q^{5} -9.31697e9 q^{6} -6.01315e10i q^{7} -1.97893e11i q^{8} -1.84221e12 q^{9} +O(q^{10})$	\(q-5681.18i q^{2} -1.63997e6i q^{3} +1.27857e6 q^{4} +(4.20624e8 + 3.47992e8i) q^{5} -9.31697e9 q^{6} -6.01315e10i q^{7} -1.97893e11i q^{8} -1.84221e12 q^{9} +(1.97701e12 - 2.38965e12i) q^{10} +1.89490e11 q^{11} -2.09682e12i q^{12} +1.09278e13i q^{13} -3.41618e14 q^{14} +(5.70696e14 - 6.89812e14i) q^{15} -1.08136e15 q^{16} +1.44629e15i q^{17} +1.04660e16i q^{18} +1.43053e16 q^{19} +(5.37798e14 + 4.44932e14i) q^{20} -9.86138e16 q^{21} -1.07653e15i q^{22} -1.47077e16i q^{23} -3.24538e17 q^{24} +(5.58267e16 + 2.92748e17i) q^{25} +6.20831e16 q^{26} +1.63165e18i q^{27} -7.68823e16i q^{28} +1.47720e16 q^{29} +(-3.91895e18 - 3.24223e18i) q^{30} +3.62565e18 q^{31} -4.96752e17i q^{32} -3.10758e17i q^{33} +8.21663e18 q^{34} +(2.09253e19 - 2.52928e19i) q^{35} -2.35540e18 q^{36} +4.70927e19i q^{37} -8.12710e19i q^{38} +1.79213e19 q^{39} +(6.88650e19 - 8.32385e19i) q^{40} -5.52362e19 q^{41} +5.60243e20i q^{42} -5.36564e19i q^{43} +2.42276e17 q^{44} +(-7.74880e20 - 6.41075e20i) q^{45} -8.35569e19 q^{46} -3.09960e20i q^{47} +1.77340e21i q^{48} -2.27472e21 q^{49} +(1.66315e21 - 3.17162e20i) q^{50} +2.37187e21 q^{51} +1.39720e19i q^{52} +1.46016e21i q^{53} +9.26969e21 q^{54} +(7.97041e19 + 6.59409e19i) q^{55} -1.18996e22 q^{56} -2.34602e22i q^{57} -8.39227e19i q^{58} -1.97523e21 q^{59} +(7.29675e20 - 8.81972e20i) q^{60} +2.98959e22 q^{61} -2.05980e22i q^{62} +1.10775e23i q^{63} -3.91067e22 q^{64} +(-3.80280e21 + 4.59652e21i) q^{65} -1.76547e21 q^{66} -5.17058e22i q^{67} +1.84918e21i q^{68} -2.41201e22 q^{69} +(-1.43693e23 - 1.18880e23i) q^{70} -9.98491e22 q^{71} +3.64561e23i q^{72} -2.29804e23i q^{73} +2.67543e23 q^{74} +(4.80097e23 - 9.15541e22i) q^{75} +1.82903e22 q^{76} -1.13943e22i q^{77} -1.01814e23i q^{78} -2.98638e23 q^{79} +(-4.54848e23 - 3.76306e23i) q^{80} +1.11497e24 q^{81} +3.13807e23i q^{82} -5.05140e23i q^{83} -1.26085e23 q^{84} +(-5.03296e23 + 6.08344e23i) q^{85} -3.04832e23 q^{86} -2.42257e22i q^{87} -3.74987e22i q^{88} -9.04391e23 q^{89} +(-3.64207e24 + 4.40224e24i) q^{90} +6.57107e23 q^{91} -1.88048e22i q^{92} -5.94596e24i q^{93} -1.76094e24 q^{94} +(6.01715e24 + 4.97812e24i) q^{95} -8.14659e23 q^{96} -7.24563e24i q^{97} +1.29231e25i q^{98} -3.49081e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9}+O(q^{10}) $ 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9	$ 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9} + 4435846671960 q^{10} - 1090673824176 q^{11} - 890646861445848 q^{14} + 443085522435120 q^{15} + 22\!\cdots\!32 q^{16}+ \cdots - 10\!\cdots\!72 q^{99}+O(q^{100}) $ 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9 + 4435846671960 * q^10 - 1090673824176 * q^11 - 890646861445848 * q^14 + 443085522435120 * q^15 + 2206145875609632 * q^16 + 6329834351210160 * q^19 - 45407795215923720 * q^20 + 13538972741781744 * q^21 - 1238774108159908320 * q^24 + 883359578467451100 * q^25 + 487725686068642704 * q^26 - 5990455853511966360 * q^29 + 8784171220269562920 * q^30 - 35669623242168576 * q^31 - 45224081273675172288 * q^34 + 37959801679716705360 * q^35 + 95509342682184062232 * q^36 + 59576177650244745888 * q^39 - 135247056564421048800 * q^40 - 149504768291960577576 * q^41 + 1795327120321140441312 * q^44 - 1757089887558453396180 * q^45 - 2632260904857596314776 * q^46 - 1924948130789206201884 * q^49 + 4613478251192179347600 * q^50 + 6601362996360626974464 * q^51 - 4543556632841187026640 * q^54 - 4976317493836251356880 * q^55 + 6789286242764162655840 * q^56 - 31976684482970870043120 * q^59 + 38198563842186313414560 * q^60 + 33892026990475241838024 * q^61 - 45154694563657190239104 * q^64 - 23988754129834728629280 * q^65 - 84625057142490628840032 * q^66 + 454638912158488569862128 * q^69 - 514001938945682971911240 * q^70 - 118991523615678935618976 * q^71 - 276076790459758393833168 * q^74 - 256450000750992984232800 * q^75 + 1770023872374606472757280 * q^76 - 741918285485353377639360 * q^79 + 504838130357233934552160 * q^80 + 2020576746978155938317372 * q^81 - 6598941205046486172215328 * q^84 - 1447445120396229235779840 * q^85 + 6309456694176729359288664 * q^86 + 576066549612764658926520 * q^89 - 14281964558091964746137880 * q^90 + 12216814388553519240480864 * q^91 - 11673168428062976516959608 * q^94 - 23618191778193292124785200 * q^95 + 57292208364908004705120384 * q^96 - 10068680551503914801051472 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	5681.18i		−	0.980763i	−0.871508	−	0.490381i	$-0.836857\pi$
$2$		−	5681.18i		−	0.980763i	0.871508	−	0.490381i	$-0.163143\pi$
$3$		−	1.63997e6i		−	1.78164i	−0.454355	−	0.890821i	$-0.650130\pi$
$3$		−	1.63997e6i		−	1.78164i	0.454355	−	0.890821i	$-0.349870\pi$
$4$	1.27857e6			0.0381044
$5$	4.20624e8	+	3.47992e8i	0.770494	+	0.637447i
$5$	4.20624e8	+	3.47992e8i	0.770494	+	0.637447i
$6$	−9.31697e9			−1.74737
$7$		−	6.01315e10i		−	1.64201i	−0.570920	−	0.821006i	$-0.693413\pi$
$7$		−	6.01315e10i		−	1.64201i	0.570920	−	0.821006i	$-0.306587\pi$
$8$		−	1.97893e11i		−	1.01813i
$9$	−1.84221e12			−2.17425
$10$	1.97701e12	−	2.38965e12i	0.625184	−	0.755672i
$11$	1.89490e11			0.0182045			0.00910223	−	0.999959i	$-0.497103\pi$
$11$	1.89490e11			0.0182045			0.00910223	+	0.999959i	$0.497103\pi$
$12$		−	2.09682e12i		−	0.0678883i
$13$			1.09278e13i			0.130090i	0.997882	+	0.0650448i	$0.0207190\pi$
$13$			1.09278e13i			0.130090i	−0.997882	+	0.0650448i	$0.979281\pi$
$14$	−3.41618e14			−1.61042
$15$	5.70696e14	−	6.89812e14i	1.13570	−	1.37274i
$16$	−1.08136e15			−0.960444
$17$			1.44629e15i			0.602065i	0.953614	+	0.301032i	$0.0973312\pi$
$17$			1.44629e15i			0.602065i	−0.953614	+	0.301032i	$0.902669\pi$
$18$			1.04660e16i			2.13242i
$19$	1.43053e16			1.48278			0.741390	−	0.671075i	$-0.234167\pi$
$19$	1.43053e16			1.48278			0.741390	+	0.671075i	$0.234167\pi$
$20$	5.37798e14	+	4.44932e14i	0.0293592	+	0.0242895i
$21$	−9.86138e16			−2.92548
$22$		−	1.07653e15i		−	0.0178543i
$23$		−	1.47077e16i		−	0.139941i	−0.997549	−	0.0699706i	$-0.977709\pi$
$23$		−	1.47077e16i		−	0.139941i	0.997549	−	0.0699706i	$-0.0222905\pi$
$24$	−3.24538e17			−1.81395
$25$	5.58267e16	+	2.92748e17i	0.187323	+	0.982298i
$26$	6.20831e16			0.127587
$27$			1.63165e18i			2.09208i
$28$		−	7.68823e16i		−	0.0625678i
$29$	1.47720e16			0.00775292			0.00387646	−	0.999992i	$-0.498766\pi$
$29$	1.47720e16			0.00775292			0.00387646	+	0.999992i	$0.498766\pi$
$30$	−3.91895e18	−	3.24223e18i	−1.34634	−	1.11385i
$31$	3.62565e18			0.826733			0.413366	−	0.910565i	$-0.364353\pi$
$31$	3.62565e18			0.826733			0.413366	+	0.910565i	$0.364353\pi$
$32$		−	4.96752e17i		−	0.0761667i
$33$		−	3.10758e17i		−	0.0324338i
$34$	8.21663e18			0.590483
$35$	2.09253e19	−	2.52928e19i	1.04669	−	1.26516i
$36$	−2.35540e18			−0.0828482
$37$			4.70927e19i			1.17607i	0.808836	+	0.588034i	$0.200098\pi$
$37$			4.70927e19i			1.17607i	−0.808836	+	0.588034i	$0.799902\pi$
$38$		−	8.12710e19i		−	1.45425i
$39$	1.79213e19			0.231773
$40$	6.88650e19	−	8.32385e19i	0.649006	−	0.784467i
$41$	−5.52362e19			−0.382319			−0.191159	−	0.981559i	$-0.561225\pi$
$41$	−5.52362e19			−0.382319			−0.191159	+	0.981559i	$0.561225\pi$
$42$			5.60243e20i			2.86920i
$43$		−	5.36564e19i		−	0.204770i	−0.994745	−	0.102385i	$-0.967353\pi$
$43$		−	5.36564e19i		−	0.204770i	0.994745	−	0.102385i	$-0.0326474\pi$
$44$	2.42276e17			0.000693669
$45$	−7.74880e20	−	6.41075e20i	−1.67524	−	1.38597i
$46$	−8.35569e19			−0.137249
$47$		−	3.09960e20i		−	0.389119i	−0.980891	−	0.194560i	$-0.937672\pi$
$47$		−	3.09960e20i		−	0.389119i	0.980891	−	0.194560i	$-0.0623277\pi$
$48$			1.77340e21i			1.71117i
$49$	−2.27472e21			−1.69620
$50$	1.66315e21	−	3.17162e20i	0.963402	−	0.183720i
$51$	2.37187e21			1.07266
$52$			1.39720e19i			0.00495698i
$53$			1.46016e21i			0.408275i	0.978942	+	0.204138i	$0.0654390\pi$
$53$			1.46016e21i			0.408275i	−0.978942	+	0.204138i	$0.934561\pi$
$54$	9.26969e21			2.05184
$55$	7.97041e19	+	6.59409e19i	0.0140264	+	0.0116044i
$56$	−1.18996e22			−1.67179
$57$		−	2.34602e22i		−	2.64178i
$58$		−	8.39227e19i		−	0.00760378i
$59$	−1.97523e21			−0.144533			−0.0722667	−	0.997385i	$-0.523023\pi$
$59$	−1.97523e21			−0.144533			−0.0722667	+	0.997385i	$0.523023\pi$
$60$	7.29675e20	−	8.81972e20i	0.0432752	−	0.0523075i
$61$	2.98959e22			1.44208			0.721040	−	0.692894i	$-0.243665\pi$
$61$	2.98959e22			1.44208			0.721040	+	0.692894i	$0.243665\pi$
$62$		−	2.05980e22i		−	0.810829i
$63$			1.10775e23i			3.57014i
$64$	−3.91067e22			−1.03515
$65$	−3.80280e21	+	4.59652e21i	−0.0829252	+	0.100233i
$66$	−1.76547e21			−0.0318099
$67$		−	5.17058e22i		−	0.771977i	−0.922503	−	0.385989i	$-0.873860\pi$
$67$		−	5.17058e22i		−	0.771977i	0.922503	−	0.385989i	$-0.126140\pi$
$68$			1.84918e21i			0.0229413i
$69$	−2.41201e22			−0.249325
$70$	−1.43693e23	−	1.18880e23i	−1.24082	−	1.02656i
$71$	−9.98491e22			−0.722129			−0.361064	−	0.932541i	$-0.617587\pi$
$71$	−9.98491e22			−0.722129			−0.361064	+	0.932541i	$0.617587\pi$
$72$			3.64561e23i			2.21367i
$73$		−	2.29804e23i		−	1.17442i	−0.809435	−	0.587209i	$-0.800227\pi$
$73$		−	2.29804e23i		−	1.17442i	0.809435	−	0.587209i	$-0.199773\pi$
$74$	2.67543e23			1.15344
$75$	4.80097e23	−	9.15541e22i	1.75010	−	0.333743i
$76$	1.82903e22			0.0565003
$77$		−	1.13943e22i		−	0.0298919i
$78$		−	1.01814e23i		−	0.227314i
$79$	−2.98638e23			−0.568600			−0.284300	−	0.958735i	$-0.591761\pi$
$79$	−2.98638e23			−0.568600			−0.284300	+	0.958735i	$0.591761\pi$
$80$	−4.54848e23	−	3.76306e23i	−0.740017	−	0.612232i
$81$	1.11497e24			1.55310
$82$			3.13807e23i			0.374964i
$83$		−	5.05140e23i		−	0.518723i	−0.965780	−	0.259362i	$-0.916488\pi$
$83$		−	5.05140e23i		−	0.518723i	0.965780	−	0.259362i	$-0.0835121\pi$
$84$	−1.26085e23			−0.111473
$85$	−5.03296e23	+	6.08344e23i	−0.383784	+	0.463888i
$86$	−3.04832e23			−0.200831
$87$		−	2.42257e22i		−	0.0138129i
$88$		−	3.74987e22i		−	0.0185346i
$89$	−9.04391e23			−0.388133			−0.194067	−	0.980988i	$-0.562168\pi$
$89$	−9.04391e23			−0.388133			−0.194067	+	0.980988i	$0.562168\pi$
$90$	−3.64207e24	+	4.40224e24i	−1.35930	+	1.64302i
$91$	6.57107e23			0.213609
$92$		−	1.88048e22i		−	0.00533237i
$93$		−	5.94596e24i		−	1.47294i
$94$	−1.76094e24			−0.381633
$95$	6.01715e24	+	4.97812e24i	1.14247	+	0.945193i
$96$	−8.14659e23			−0.135702
$97$		−	7.24563e24i		−	1.06030i	−0.847903	−	0.530151i	$-0.822135\pi$
$97$		−	7.24563e24i		−	1.06030i	0.847903	−	0.530151i	$-0.177865\pi$
$98$			1.29231e25i			1.66357i
$99$	−3.49081e23			−0.0395810
$100$	7.13783e22	+	3.74298e23i	0.00713783	+	0.0374298i
$101$	2.22053e25			1.96083			0.980413	−	0.196951i	$-0.0631041\pi$
$101$	2.22053e25			1.96083			0.980413	+	0.196951i	$0.0631041\pi$
$102$		−	1.34750e25i		−	1.05203i
$103$		−	1.42724e25i		−	0.986349i	−0.869931	−	0.493174i	$-0.835836\pi$
$103$		−	1.42724e25i		−	0.986349i	0.869931	−	0.493174i	$-0.164164\pi$
$104$	2.16254e24			0.132449
$105$	−4.14794e25	−	3.43168e25i	−2.25406	−	1.86483i
$106$	8.29546e24			0.400421
$107$			3.47726e25i			1.49259i	0.665617	+	0.746294i	$0.268169\pi$
$107$			3.47726e25i			1.49259i	−0.665617	+	0.746294i	$0.731831\pi$
$108$			2.08617e24i			0.0797175i
$109$	3.39534e24			0.115625			0.0578126	−	0.998327i	$-0.481587\pi$
$109$	3.39534e24			0.115625			0.0578126	+	0.998327i	$0.481587\pi$
$110$	3.74623e23	−	4.52814e23i	0.0113811	−	0.0137566i
$111$	7.72307e25			2.09533
$112$			6.50240e25i			1.57706i
$113$			4.13463e25i			0.897338i	0.893698	+	0.448669i	$0.148102\pi$
$113$			4.13463e25i			0.897338i	−0.893698	+	0.448669i	$0.851898\pi$
$114$	−1.33282e26			−2.59096
$115$	5.11814e24	−	6.18640e24i	0.0892050	−	0.107824i
$116$	1.88871e22			0.000295420
$117$		−	2.01314e25i		−	0.282847i
$118$			1.12217e25i			0.141753i
$119$	8.69674e25			0.988597
$120$	−1.36509e26	−	1.12937e26i	−1.39764	−	1.15630i
$121$	−1.08311e26			−0.999669
$122$		−	1.69844e26i		−	1.41434i
$123$			9.05858e25i			0.681155i
$124$	4.63565e24			0.0315021
$125$	−7.83917e25	+	1.42564e26i	−0.481831	+	0.876264i
$126$	6.29333e26			3.50146
$127$		−	1.07886e26i		−	0.543773i	−0.962329	−	0.271886i	$-0.912353\pi$
$127$		−	1.07886e26i		−	0.543773i	0.962329	−	0.271886i	$-0.0876475\pi$
$128$			2.05504e26i			0.939065i
$129$	−8.79950e25			−0.364827
$130$	2.61137e25	+	2.16044e25i	0.0983051	+	0.0813299i
$131$	3.53651e26			1.20972			0.604858	−	0.796333i	$-0.293230\pi$
$131$	3.53651e26			1.20972			0.604858	+	0.796333i	$0.293230\pi$
$132$		−	3.97326e23i		−	0.00123587i
$133$		−	8.60198e26i		−	2.43474i
$134$	−2.93750e26			−0.757127
$135$	−5.67800e26	+	6.86311e26i	−1.33359	+	1.61194i
$136$	2.86210e26			0.612983
$137$		−	4.15666e26i		−	0.812340i	−0.913798	−	0.406170i	$-0.866864\pi$
$137$		−	4.15666e26i		−	0.812340i	0.913798	−	0.406170i	$-0.133136\pi$
$138$			1.37031e26i			0.244529i
$139$	−7.45099e26			−1.21487			−0.607434	−	0.794370i	$-0.707801\pi$
$139$	−7.45099e26			−1.21487			−0.607434	+	0.794370i	$0.707801\pi$
$140$	2.67544e25	−	3.23386e25i	0.0398836	−	0.0482081i
$141$	−5.08325e26			−0.693270
$142$			5.67261e26i			0.708237i
$143$			2.07072e24i			0.00236821i
$144$	1.99210e27			2.08824
$145$	6.21348e24	+	5.14055e24i	0.00597358	+	0.00494207i
$146$	−1.30556e27			−1.15183
$147$			3.73048e27i			3.02202i
$148$			6.02113e25i			0.0448133i
$149$	−2.11847e27			−1.44942			−0.724709	−	0.689055i	$-0.758026\pi$
$149$	−2.11847e27			−1.44942			−0.724709	+	0.689055i	$0.758026\pi$
$150$	−5.20136e26	−	2.72752e27i	−0.327323	−	1.71644i
$151$	3.13064e27			1.81310			0.906549	−	0.422102i	$-0.138707\pi$
$151$	3.13064e27			1.81310			0.906549	+	0.422102i	$0.138707\pi$
$152$		−	2.83091e27i		−	1.50967i
$153$		−	2.66437e27i		−	1.30904i
$154$	−6.47332e25			−0.0293169
$155$	1.52504e27	+	1.26170e27i	0.636993	+	0.526998i
$156$	2.29137e25			0.00883156
$157$			3.03643e27i			1.08048i	0.841510	+	0.540241i	$0.181667\pi$
$157$			3.03643e27i			1.08048i	−0.841510	+	0.540241i	$0.818333\pi$
$158$			1.69662e27i			0.557662i
$159$	2.39463e27			0.727400
$160$	1.72866e26	−	2.08946e26i	0.0485522	−	0.0586860i
$161$	−8.84393e26			−0.229785
$162$		−	6.33433e27i		−	1.52322i
$163$		−	2.73509e27i		−	0.609013i	−0.952510	−	0.304507i	$-0.901508\pi$
$163$		−	2.73509e27i		−	0.609013i	0.952510	−	0.304507i	$-0.0984915\pi$
$164$	−7.06234e25			−0.0145680
$165$	1.08141e26	−	1.30712e26i	0.0206748	−	0.0249901i
$166$	−2.86979e27			−0.508744
$167$		−	7.68173e27i		−	1.26329i	−0.775258	−	0.631645i	$-0.782380\pi$
$167$		−	7.68173e27i		−	1.26329i	0.775258	−	0.631645i	$-0.217620\pi$
$168$			1.95150e28i			2.97853i
$169$	6.93699e27			0.983077
$170$	3.45612e27	+	2.85932e27i	0.454964	+	0.376401i
$171$	−2.63534e28			−3.22393
$172$		−	6.86035e25i		−	0.00780263i
$173$			5.96323e27i			0.630820i	0.948956	+	0.315410i	$0.102142\pi$
$173$			5.96323e27i			0.630820i	−0.948956	+	0.315410i	$0.897858\pi$
$174$	−1.37631e26			−0.0135472
$175$	1.76033e28	−	3.35694e27i	1.61295	−	0.307587i
$176$	−2.04908e26			−0.0174844
$177$			3.23932e27i			0.257507i
$178$			5.13801e27i			0.380667i
$179$	−1.46270e28			−1.01040			−0.505199	−	0.863003i	$-0.668581\pi$
$179$	−1.46270e28			−1.01040			−0.505199	+	0.863003i	$0.668581\pi$
$180$	−9.90738e26	−	8.19659e26i	−0.0638341	−	0.0528113i
$181$	1.13212e28			0.680631			0.340316	−	0.940311i	$-0.389466\pi$
$181$	1.13212e28			0.680631			0.340316	+	0.940311i	$0.389466\pi$
$182$		−	3.73315e27i		−	0.209499i
$183$		−	4.90284e28i		−	2.56927i
$184$	−2.91054e27			−0.142479
$185$	−1.63879e28	+	1.98084e28i	−0.749681	+	0.906154i
$186$	−3.37801e28			−1.44461
$187$			2.74057e26i			0.0109603i
$188$		−	3.96306e26i		−	0.0148271i
$189$	9.81133e28			3.43523
$190$	2.82816e28	−	3.41846e28i	0.927010	−	1.12050i
$191$	2.28110e28			0.700209			0.350104	−	0.936711i	$-0.386146\pi$
$191$	2.28110e28			0.700209			0.350104	+	0.936711i	$0.386146\pi$
$192$			6.41338e28i			1.84426i
$193$		−	3.15645e28i		−	0.850615i	−0.905049	−	0.425308i	$-0.860166\pi$
$193$		−	3.15645e28i		−	0.850615i	0.905049	−	0.425308i	$-0.139834\pi$
$194$	−4.11638e28			−1.03990
$195$	7.53815e27	+	6.23648e27i	0.178580	+	0.147743i
$196$	−2.90839e27			−0.0646327
$197$			7.20861e28i			1.50322i	0.659605	+	0.751612i	$0.270724\pi$
$197$			7.20861e28i			1.50322i	−0.659605	+	0.751612i	$0.729276\pi$
$198$			1.98319e27i			0.0388195i
$199$	−7.72451e28			−1.41974			−0.709868	−	0.704335i	$-0.751245\pi$
$199$	−7.72451e28			−1.41974			−0.709868	+	0.704335i	$0.751245\pi$
$200$	5.79326e28	−	1.10477e28i	1.00011	−	0.190720i
$201$	−8.47960e28			−1.37539
$202$		−	1.26152e29i		−	1.92311i
$203$		−	8.88264e26i		−	0.0127304i
$204$	3.03260e27			0.0408731
$205$	−2.32337e28	−	1.92218e28i	−0.294575	−	0.243708i
$206$	−8.10839e28			−0.967374
$207$			2.70946e28i			0.304266i
$208$		−	1.18170e28i		−	0.124944i
$209$	2.71071e27			0.0269932
$210$	−1.94960e29	+	2.35652e29i	−1.82896	+	2.21070i
$211$	1.89884e29			1.67864			0.839322	−	0.543635i	$-0.182952\pi$
$211$	1.89884e29			1.67864			0.839322	+	0.543635i	$0.182952\pi$
$212$			1.86692e27i			0.0155571i
$213$			1.63749e29i			1.28657i
$214$	1.97550e29			1.46387
$215$	1.86720e28	−	2.25692e28i	0.130530	−	0.157774i
$216$	3.22891e29			2.13002
$217$		−	2.18016e29i		−	1.35750i
$218$		−	1.92896e28i		−	0.113401i
$219$	−3.76872e29			−2.09239
$220$	1.01907e26	+	8.43101e25i	0.000534468	+	0.000442177i
$221$	−1.58048e28			−0.0783224
$222$		−	4.38762e29i		−	2.05502i
$223$			1.08082e29i			0.478566i	0.970950	+	0.239283i	$0.0769124\pi$
$223$			1.08082e29i			0.478566i	−0.970950	+	0.239283i	$0.923088\pi$
$224$	−2.98704e28			−0.125067
$225$	−1.02845e29	−	5.39304e29i	−0.407287	−	2.13576i
$226$	2.34896e29			0.880075
$227$			5.33857e29i			1.89279i	0.323015	+	0.946394i	$0.395304\pi$
$227$			5.33857e29i			1.89279i	−0.323015	+	0.946394i	$0.604696\pi$
$228$		−	2.99956e28i		−	0.100663i
$229$	2.20943e29			0.701999			0.350999	−	0.936376i	$-0.385842\pi$
$229$	2.20943e29			0.701999			0.350999	+	0.936376i	$0.385842\pi$
$230$	−3.51461e28	−	2.90771e28i	−0.105750	−	0.0874890i
$231$	−1.86863e28			−0.0532567
$232$		−	2.92328e27i		−	0.00789351i
$233$			5.28355e29i			1.35200i	0.736902	+	0.676000i	$0.236288\pi$
$233$			5.28355e29i			1.35200i	−0.736902	+	0.676000i	$0.763712\pi$
$234$	−1.14370e29			−0.277405
$235$	1.07864e29	−	1.30377e29i	0.248043	−	0.299814i
$236$	−2.52547e27			−0.00550735
$237$			4.89758e29i			1.01304i
$238$		−	4.94078e29i		−	0.969580i
$239$	−2.76077e29			−0.514110			−0.257055	−	0.966397i	$-0.582752\pi$
$239$	−2.76077e29			−0.514110			−0.257055	+	0.966397i	$0.582752\pi$
$240$	−6.17130e29	+	7.45937e29i	−1.09078	+	1.31844i
$241$	1.66531e29			0.279435			0.139718	−	0.990191i	$-0.455381\pi$
$241$	1.66531e29			0.279435			0.139718	+	0.990191i	$0.455381\pi$
$242$			6.15336e29i			0.980438i
$243$		−	4.46034e29i		−	0.674979i
$244$	3.82240e28			0.0549495
$245$	−9.56805e29	−	7.91585e29i	−1.30691	−	1.08124i
$246$	5.14635e29			0.668052
$247$			1.56326e29i			0.192894i
$248$		−	7.17490e29i		−	0.841725i
$249$	−8.28415e29			−0.924179
$250$	8.09933e29	+	4.45358e29i	0.859407	+	0.472562i
$251$	6.82180e29			0.688616			0.344308	−	0.938857i	$-0.388114\pi$
$251$	6.82180e29			0.688616			0.344308	+	0.938857i	$0.388114\pi$
$252$			1.41634e29i			0.136038i
$253$		−	2.78695e27i		−	0.00254755i
$254$	−6.12919e29			−0.533312
$255$	9.97666e29	+	8.25391e29i	0.826481	+	0.683766i
$256$	−1.44696e29			−0.114145
$257$		−	2.27178e30i		−	1.70688i	−0.521194	−	0.853438i	$-0.674513\pi$
$257$		−	2.27178e30i		−	1.70688i	0.521194	−	0.853438i	$-0.325487\pi$
$258$			4.99916e29i			0.357808i
$259$	2.83175e30			1.93112
$260$	−4.86214e27	+	5.87697e27i	−0.00315981	+	0.00381932i
$261$	−2.72132e28			−0.0168568
$262$		−	2.00915e30i		−	1.18644i
$263$		−	3.01461e29i		−	0.169740i	−0.996392	−	0.0848701i	$-0.972952\pi$
$263$		−	3.01461e29i		−	0.169740i	0.996392	−	0.0848701i	$-0.0270475\pi$
$264$	−6.14967e28			−0.0330220
$265$	−5.08125e29	+	6.14181e29i	−0.260254	+	0.314574i
$266$	−4.88694e30			−2.38790
$267$			1.48317e30i			0.691515i
$268$		−	6.61095e28i		−	0.0294157i
$269$	3.73578e30			1.58664			0.793319	−	0.608807i	$-0.208352\pi$
$269$	3.73578e30			1.58664			0.793319	+	0.608807i	$0.208352\pi$
$270$	3.89906e30	+	3.22577e30i	1.58093	+	1.30794i
$271$	−1.36148e30			−0.527104			−0.263552	−	0.964645i	$-0.584894\pi$
$271$	−1.36148e30			−0.527104			−0.263552	+	0.964645i	$0.584894\pi$
$272$		−	1.56396e30i		−	0.578249i
$273$		−	1.07764e30i		−	0.380574i
$274$	−2.36148e30			−0.796713
$275$	1.05786e28	+	5.54728e28i	0.00341012	+	0.0178822i
$276$	−3.08392e28			−0.00950036
$277$			3.03746e30i			0.894362i	0.894444	+	0.447181i	$0.147572\pi$
$277$			3.03746e30i			0.894362i	−0.894444	+	0.447181i	$0.852428\pi$
$278$			4.23305e30i			1.19150i
$279$	−6.67923e30			−1.79752
$280$	−5.00525e30	−	4.14096e30i	−1.28810	−	1.06568i
$281$	−5.97099e29			−0.146966			−0.0734831	−	0.997296i	$-0.523411\pi$
$281$	−5.97099e29			−0.146966			−0.0734831	+	0.997296i	$0.523411\pi$
$282$			2.88789e30i			0.679934i
$283$		−	1.64461e30i		−	0.370453i	−0.982696	−	0.185227i	$-0.940698\pi$
$283$		−	1.64461e30i		−	0.370453i	0.982696	−	0.185227i	$-0.0593019\pi$
$284$	−1.27664e29			−0.0275162
$285$	8.16397e30	−	9.86795e30i	1.68399	−	2.03548i
$286$	1.17641e28			0.00232265
$287$			3.32144e30i			0.627772i
$288$			9.15123e29i			0.165605i
$289$	3.67888e30			0.637518
$290$	2.92044e28	−	3.52999e28i	0.00484700	−	0.00585867i
$291$	−1.18826e31			−1.88908
$292$		−	2.93821e29i		−	0.0447504i
$293$			6.71024e30i			0.979248i	0.871934	+	0.489624i	$0.162866\pi$
$293$			6.71024e30i			0.979248i	−0.871934	+	0.489624i	$0.837134\pi$
$294$	2.11935e31			2.96389
$295$	−8.30831e29	−	6.87365e29i	−0.111362	−	0.0921323i
$296$	9.31931e30			1.19739
$297$			3.09181e29i			0.0380852i
$298$			1.20354e31i			1.42153i
$299$	1.60723e29			0.0182049
$300$	6.13838e29	−	1.17058e29i	0.0666865	−	0.0127171i
$301$	−3.22644e30			−0.336235
$302$		−	1.77857e31i		−	1.77822i
$303$		−	3.64160e31i		−	3.49349i
$304$	−1.54692e31			−1.42413
$305$	1.25750e31	+	1.04035e31i	1.11111	+	0.919249i
$306$	−1.51368e31			−1.28385
$307$			7.56621e30i			0.616096i	0.951371	+	0.308048i	$0.0996758\pi$
$307$			7.56621e30i			0.616096i	−0.951371	+	0.308048i	$0.900324\pi$
$308$		−	1.45684e28i		−	0.00113901i
$309$	−2.34062e31			−1.75732
$310$	7.16794e30	−	8.66403e30i	0.516860	−	0.624739i
$311$	1.83094e31			1.26815			0.634073	−	0.773273i	$-0.281382\pi$
$311$	1.83094e31			1.26815			0.634073	+	0.773273i	$0.281382\pi$
$312$		−	3.54650e30i		−	0.235976i
$313$			2.67376e31i			1.70930i	0.519204	+	0.854650i	$0.326228\pi$
$313$			2.67376e31i			1.70930i	−0.519204	+	0.854650i	$0.673772\pi$
$314$	1.72505e31			1.05970
$315$	−3.85488e31	+	4.65947e31i	−2.27577	+	2.75077i
$316$	−3.81830e29			−0.0216661
$317$		−	5.22384e29i		−	0.0284937i	−0.999899	−	0.0142468i	$-0.995465\pi$
$317$		−	5.22384e29i		−	0.0284937i	0.999899	−	0.0142468i	$-0.00453506\pi$
$318$		−	1.36043e31i		−	0.713407i
$319$	2.79915e27			0.000141138
$320$	−1.64492e31	−	1.36088e31i	−0.797574	−	0.659850i
$321$	5.70260e31			2.65926
$322$			5.02440e30i			0.225365i
$323$			2.06896e31i			0.892729i
$324$	1.42556e30			0.0591798
$325$	−3.19910e30	+	6.10065e29i	−0.127787	+	0.0243688i
$326$	−1.55386e31			−0.597297
$327$		−	5.56826e30i		−	0.206003i
$328$			1.09308e31i			0.389252i
$329$	−1.86383e31			−0.638938
$330$	−7.42601e29	−	6.14370e29i	−0.0245093	−	0.0202771i
$331$	−5.26456e31			−1.67306			−0.836532	−	0.547919i	$-0.815420\pi$
$331$	−5.26456e31			−1.67306			−0.836532	+	0.547919i	$0.815420\pi$
$332$		−	6.45857e29i		−	0.0197656i
$333$		−	8.67549e31i		−	2.55706i
$334$	−4.36413e31			−1.23899
$335$	1.79932e31	−	2.17487e31i	0.492095	−	0.594804i
$336$	1.06637e32			2.80975
$337$		−	4.35758e31i		−	1.10630i	−0.833083	−	0.553148i	$-0.813426\pi$
$337$		−	4.35758e31i		−	1.10630i	0.833083	−	0.553148i	$-0.186574\pi$
$338$		−	3.94103e31i		−	0.964165i
$339$	6.78067e31			1.59873
$340$	−6.43499e29	+	7.77811e29i	−0.0146239	+	0.0176761i
$341$	6.87025e29			0.0150502
$342$			1.49718e32i			3.16191i
$343$			5.61420e31i			1.14317i
$344$	−1.06182e31			−0.208483
$345$	−1.01455e31	−	8.39360e30i	−0.192103	−	0.158931i
$346$	3.38782e31			0.618684
$347$			2.38371e31i			0.419889i	0.977713	+	0.209945i	$0.0673284\pi$
$347$			2.38371e31i			0.419889i	−0.977713	+	0.209945i	$0.932672\pi$
$348$		−	3.09742e28i		−	0.000526332i
$349$	−1.20425e31			−0.197424			−0.0987120	−	0.995116i	$-0.531472\pi$
$349$	−1.20425e31			−0.197424			−0.0987120	+	0.995116i	$0.531472\pi$
$350$	−1.90714e31	−	1.00008e32i	−0.301670	−	1.58192i
$351$	−1.78304e31			−0.272158
$352$		−	9.41295e28i		−	0.00138657i
$353$			3.19706e31i			0.454534i	0.973832	+	0.227267i	$0.0729790\pi$
$353$			3.19706e31i			0.454534i	−0.973832	+	0.227267i	$0.927021\pi$
$354$	1.84032e31			0.252553
$355$	−4.19990e31	−	3.47467e31i	−0.556396	−	0.460319i
$356$	−1.15633e30			−0.0147896
$357$		−	1.42624e32i		−	1.76133i
$358$			8.30988e31i			0.990961i
$359$	−1.22719e32			−1.41329			−0.706643	−	0.707570i	$-0.749791\pi$
$359$	−1.22719e32			−1.41329			−0.706643	+	0.707570i	$0.749791\pi$
$360$	−1.26864e32	+	1.53343e32i	−1.41110	+	1.70562i
$361$	1.11565e32			1.19863
$362$		−	6.43180e31i		−	0.667538i
$363$			1.77627e32i			1.78105i
$364$	8.40157e29			0.00813942
$365$	7.99700e31	−	9.66614e31i	0.748629	−	0.904882i
$366$	−2.78540e32			−2.51984
$367$		−	5.93939e31i		−	0.519297i	−0.965703	−	0.259649i	$-0.916393\pi$
$367$		−	5.93939e31i		−	0.519297i	0.965703	−	0.259649i	$-0.0836068\pi$
$368$			1.59043e31i			0.134406i
$369$	1.01757e32			0.831255
$370$	1.12535e32	+	9.31026e31i	0.888722	+	0.735259i
$371$	8.78018e31			0.670393
$372$		−	7.60233e30i		−	0.0561255i
$373$			1.63881e31i			0.116995i	0.998288	+	0.0584975i	$0.0186310\pi$
$373$			1.63881e31i			0.116995i	−0.998288	+	0.0584975i	$0.981369\pi$
$374$	1.55697e30			0.0107494
$375$	2.33801e32	+	1.28560e32i	1.56119	+	0.858450i
$376$	−6.13388e31			−0.396175
$377$			1.61426e29i			0.00100857i
$378$		−	5.57400e32i		−	3.36914i
$379$	−8.67906e31			−0.507554			−0.253777	−	0.967263i	$-0.581673\pi$
$379$	−8.67906e31			−0.507554			−0.253777	+	0.967263i	$0.581673\pi$
$380$	7.69335e30	+	6.36487e30i	0.0435332	+	0.0360160i
$381$	−1.76929e32			−0.968808
$382$		−	1.29594e32i		−	0.686739i
$383$			2.84898e32i			1.46118i	0.682814	+	0.730592i	$0.260756\pi$
$383$			2.84898e32i			1.46118i	−0.682814	+	0.730592i	$0.739244\pi$
$384$	3.37020e32			1.67308
$385$	3.96513e30	−	4.79273e30i	0.0190545	−	0.0230316i
$386$	−1.79324e32			−0.834252
$387$			9.88466e31i			0.445220i
$388$		−	9.26404e30i		−	0.0404021i
$389$	2.79107e32			1.17869			0.589346	−	0.807881i	$-0.299385\pi$
$389$	2.79107e32			1.17869			0.589346	+	0.807881i	$0.299385\pi$
$390$	3.54306e31	−	4.28256e31i	0.144901	−	0.175144i
$391$	2.12715e31			0.0842536
$392$			4.50151e32i			1.72696i
$393$		−	5.79977e32i		−	2.15528i
$394$	4.09535e32			1.47431
$395$	−1.25615e32	−	1.03924e32i	−0.438103	−	0.362452i
$396$	−4.46324e29			−0.00150821
$397$		−	1.95582e32i		−	0.640393i	−0.947351	−	0.320197i	$-0.896251\pi$
$397$		−	1.95582e32i		−	0.640393i	0.947351	−	0.320197i	$-0.103749\pi$
$398$			4.38844e32i			1.39242i
$399$	−1.41070e33			−4.33783
$400$	−6.03690e31	−	3.16567e32i	−0.179914	−	0.943442i
$401$	−6.72544e31			−0.194275			−0.0971373	−	0.995271i	$-0.530969\pi$
$401$	−6.72544e31			−0.194275			−0.0971373	+	0.995271i	$0.530969\pi$
$402$			4.81742e32i			1.34893i
$403$			3.96206e31i			0.107549i
$404$	2.83910e31			0.0747160
$405$	4.68982e32	+	3.87999e32i	1.19665	+	0.990017i
$406$	−5.04639e30			−0.0124855
$407$			8.92360e30i			0.0214097i
$408$		−	4.69376e32i		−	1.09212i
$409$	4.53332e32			1.02300			0.511500	−	0.859284i	$-0.329090\pi$
$409$	4.53332e32			1.02300			0.511500	+	0.859284i	$0.329090\pi$
$410$	−1.09202e32	+	1.31995e32i	−0.239020	+	0.288908i
$411$	−6.81680e32			−1.44730
$412$		−	1.82482e31i		−	0.0375842i
$413$			1.18774e32i			0.237326i
$414$	1.53930e32			0.298413
$415$	1.75785e32	−	2.12474e32i	0.330658	−	0.399673i
$416$	5.42843e30			0.00990849
$417$			1.22194e33i			2.16446i
$418$		−	1.54000e31i		−	0.0264739i
$419$	5.67932e32			0.947591			0.473796	−	0.880635i	$-0.342884\pi$
$419$	5.67932e32			0.947591			0.473796	+	0.880635i	$0.342884\pi$
$420$	−5.30343e31	−	4.38764e31i	−0.0858896	−	0.0710583i
$421$	5.93550e31			0.0933106			0.0466553	−	0.998911i	$-0.485144\pi$
$421$	5.93550e31			0.0933106			0.0466553	+	0.998911i	$0.485144\pi$
$422$		−	1.07877e33i		−	1.64635i
$423$			5.71012e32i			0.846040i
$424$	2.88956e32			0.415679
$425$	−4.23397e32	+	8.07415e31i	−0.591407	+	0.112781i
$426$	9.30291e32			1.26182
$427$		−	1.79769e33i		−	2.36791i
$428$			4.44592e31i			0.0568741i
$429$	3.39591e30			0.00421930
$430$	−1.28220e32	−	1.06079e32i	−0.154739	−	0.128019i
$431$	−3.19554e32			−0.374609			−0.187305	−	0.982302i	$-0.559975\pi$
$431$	−3.19554e32			−0.374609			−0.187305	+	0.982302i	$0.559975\pi$
$432$		−	1.76440e33i		−	2.00933i
$433$			8.78664e31i			0.0972130i	0.998818	+	0.0486065i	$0.0154780\pi$
$433$			8.78664e31i			0.0972130i	−0.998818	+	0.0486065i	$0.984522\pi$
$434$	−1.23859e33			−1.33139
$435$	8.43034e30	−	1.01899e31i	0.00880500	−	0.0106428i
$436$	4.34118e30			0.00440582
$437$		−	2.10397e32i		−	0.207502i
$438$			2.14108e33i			2.05214i
$439$	−1.17424e33			−1.09383			−0.546914	−	0.837189i	$-0.684197\pi$
$439$	−1.17424e33			−1.09383			−0.546914	+	0.837189i	$0.684197\pi$
$440$	1.30492e31	−	1.57729e31i	0.0118148	−	0.0142808i
$441$	4.19053e33			3.68796
$442$			8.97900e31i			0.0768156i
$443$		−	1.62585e31i		−	0.0135218i	−0.999977	−	0.00676089i	$-0.997848\pi$
$443$		−	1.62585e31i		−	0.0135218i	0.999977	−	0.00676089i	$-0.00215207\pi$
$444$	9.87448e31			0.0798412
$445$	−3.80409e32	−	3.14721e32i	−0.299055	−	0.247414i
$446$	6.14033e32			0.469360
$447$			3.47422e33i			2.58234i
$448$			2.35154e33i			1.69972i
$449$	−7.39518e32			−0.519840			−0.259920	−	0.965630i	$-0.583696\pi$
$449$	−7.39518e32			−0.519840			−0.259920	+	0.965630i	$0.583696\pi$
$450$	−3.06388e33	+	5.84280e32i	−2.09467	+	0.399452i
$451$	−1.04667e31			−0.00695991
$452$			5.28641e31i			0.0341925i
$453$		−	5.13415e33i		−	3.23029i
$454$	3.03294e33			1.85638
$455$	2.76395e32	+	2.28668e32i	0.164584	+	0.136164i
$456$	−4.64261e33			−2.68969
$457$			1.13814e33i			0.641568i	0.947152	+	0.320784i	$0.103946\pi$
$457$			1.13814e33i			0.641568i	−0.947152	+	0.320784i	$0.896054\pi$
$458$		−	1.25522e33i		−	0.688494i
$459$	−2.35983e33			−1.25957
$460$	6.54390e30	−	7.90974e30i	0.00339910	−	0.00410856i
$461$	−1.17544e33			−0.594209			−0.297105	−	0.954845i	$-0.596021\pi$
$461$	−1.17544e33			−0.594209			−0.297105	+	0.954845i	$0.596021\pi$
$462$			1.06160e32i			0.0522322i
$463$		−	1.51961e33i		−	0.727730i	−0.931452	−	0.363865i	$-0.881457\pi$
$463$		−	1.51961e33i		−	0.727730i	0.931452	−	0.363865i	$-0.118543\pi$
$464$	−1.59739e31			−0.00744624
$465$	2.06915e33	−	2.50102e33i	0.938921	−	1.13489i
$466$	3.00168e33			1.32599
$467$			2.96991e33i			1.27727i	0.769510	+	0.638634i	$0.220500\pi$
$467$			2.96991e33i			1.27727i	−0.769510	+	0.638634i	$0.779500\pi$
$468$		−	2.57394e31i		−	0.0107777i
$469$	−3.10915e33			−1.26760
$470$	−7.40695e32	−	6.12793e32i	−0.294046	−	0.243271i
$471$	4.97966e33			1.92503
$472$			3.90884e32i			0.147154i
$473$		−	1.01674e31i		−	0.00372773i
$474$	2.78241e33			0.993553
$475$	7.98617e32	+	4.18784e33i	0.277759	+	1.45653i
$476$	1.11194e32			0.0376699
$477$		−	2.68993e33i		−	0.887691i
$478$			1.56844e33i			0.504220i
$479$	3.94151e33			1.23444			0.617219	−	0.786792i	$-0.288259\pi$
$479$	3.94151e33			1.23444			0.617219	+	0.786792i	$0.288259\pi$
$480$	−3.42665e32	−	2.83494e32i	−0.104557	−	0.0865026i
$481$	−5.14622e32			−0.152994
$482$		−	9.46091e32i		−	0.274060i
$483$			1.45038e33i			0.409394i
$484$	−1.38483e32			−0.0380917
$485$	2.52142e33	−	3.04769e33i	0.675886	−	0.816957i
$486$	−2.53400e33			−0.661994
$487$		−	5.60271e33i		−	1.42655i	−0.700886	−	0.713273i	$-0.747212\pi$
$487$		−	5.60271e33i		−	1.42655i	0.700886	−	0.713273i	$-0.252788\pi$
$488$		−	5.91619e33i		−	1.46823i
$489$	−4.48547e33			−1.08504
$490$	−4.49714e33	+	5.43578e33i	−1.06044	+	1.28177i
$491$	2.14159e33			0.492287			0.246144	−	0.969233i	$-0.420837\pi$
$491$	2.14159e33			0.492287			0.246144	+	0.969233i	$0.420837\pi$
$492$			1.15820e32i			0.0259550i
$493$			2.13646e31i			0.00466776i
$494$	8.88116e32			0.189183
$495$	−1.46832e32	−	1.21477e32i	−0.0304969	−	0.0252307i
$496$	−3.92065e33			−0.794030
$497$			6.00407e33i			1.18574i
$498$			4.70638e33i			0.906400i
$499$	−5.31896e33			−0.999010			−0.499505	−	0.866311i	$-0.666485\pi$
$499$	−5.31896e33			−0.999010			−0.499505	+	0.866311i	$0.666485\pi$
$500$	−1.00229e32	+	1.82278e32i	−0.0183599	+	0.0333895i
$501$	−1.25978e34			−2.25073
$502$		−	3.87559e33i		−	0.675369i
$503$			4.25067e33i			0.722533i	0.932463	+	0.361267i	$0.117656\pi$
$503$			4.25067e33i			0.722533i	−0.932463	+	0.361267i	$0.882344\pi$
$504$	2.19216e34			3.63488
$505$	9.34009e33	+	7.72726e33i	1.51081	+	1.24992i
$506$	−1.58332e31			−0.00249854
$507$		−	1.13765e34i		−	1.75149i
$508$		−	1.37939e32i		−	0.0207201i
$509$	−9.24574e33			−1.35509			−0.677547	−	0.735480i	$-0.736957\pi$
$509$	−9.24574e33			−1.35509			−0.677547	+	0.735480i	$0.736957\pi$
$510$	4.68920e33	−	5.66793e33i	0.670612	−	0.810582i
$511$	−1.38185e34			−1.92841
$512$			7.71762e33i			1.05101i
$513$			2.33412e34i			3.10210i
$514$	−1.29064e34			−1.67404
$515$	4.96666e33	−	6.00330e33i	0.628745	−	0.759976i
$516$	−1.12508e32			−0.0139015
$517$		−	5.87343e31i		−	0.00708370i
$518$		−	1.60877e34i		−	1.89397i
$519$	9.77952e33			1.12389
$520$	9.09617e32	+	7.52546e32i	0.102051	+	0.0844289i
$521$	1.37566e34			1.50674			0.753370	−	0.657597i	$-0.228427\pi$
$521$	1.37566e34			1.50674			0.753370	+	0.657597i	$0.228427\pi$
$522$			1.54603e32i			0.0165325i
$523$		−	9.55800e32i		−	0.0997920i	−0.998754	−	0.0498960i	$-0.984111\pi$
$523$		−	9.55800e32i		−	0.0997920i	0.998754	−	0.0498960i	$-0.0158890\pi$
$524$	4.52167e32			0.0460954
$525$	−5.50528e33	−	2.88690e34i	−0.548010	−	2.87369i
$526$	−1.71266e33			−0.166475
$527$			5.24374e33i			0.497747i
$528$			3.36042e32i			0.0311508i
$529$	1.08295e34			0.980416
$530$	3.48927e33	+	2.88675e33i	0.308522	+	0.255247i
$531$	3.63880e33			0.314251
$532$		−	1.09982e33i		−	0.0927742i
$533$		−	6.03613e32i		−	0.0497357i
$534$	8.42619e33			0.678212
$535$	−1.21006e34	+	1.46262e34i	−0.951445	+	1.15003i
$536$	−1.02322e34			−0.785977
$537$			2.39879e34i			1.80017i
$538$		−	2.12236e34i		−	1.55611i
$539$	−4.31037e32			−0.0308784
$540$	−7.25971e32	+	8.77496e32i	−0.0508157	+	0.0614219i
$541$	1.50257e34			1.02770			0.513852	−	0.857879i	$-0.328218\pi$
$541$	1.50257e34			1.02770			0.513852	+	0.857879i	$0.328218\pi$
$542$			7.73485e33i			0.516964i
$543$		−	1.85665e34i		−	1.21264i
$544$	7.18447e32			0.0458573
$545$	1.42816e33	+	1.18155e33i	0.0890885	+	0.0737049i
$546$	−6.12225e33			−0.373253
$547$		−	2.15255e34i		−	1.28266i	−0.767265	−	0.641330i	$-0.778383\pi$
$547$		−	2.15255e34i		−	1.28266i	0.767265	−	0.641330i	$-0.221617\pi$
$548$		−	5.31458e32i		−	0.0309537i
$549$	−5.50747e34			−3.13543
$550$	3.15151e32	−	6.00990e31i	0.0175382	−	0.00334452i
$551$	2.11318e32			0.0114959
$552$			4.77319e33i			0.253846i
$553$			1.79576e34i			0.933648i
$554$	1.72564e34			0.877157
$555$	3.24851e34	+	2.68756e34i	1.61444	+	1.33566i
$556$	−9.52661e32			−0.0462917
$557$		−	2.23535e33i		−	0.106208i	−0.998589	−	0.0531039i	$-0.983089\pi$
$557$		−	2.23535e33i		−	0.106208i	0.998589	−	0.0531039i	$-0.0169115\pi$
$558$			3.79459e34i			1.76294i
$559$	5.86349e32			0.0266384
$560$	−2.26278e34	+	2.73507e34i	−1.00529	+	1.21512i
$561$	4.49445e32			0.0195273
$562$			3.39223e33i			0.144139i
$563$		−	2.12292e34i		−	0.882224i	−0.897452	−	0.441112i	$-0.854584\pi$
$563$		−	2.12292e34i		−	0.882224i	0.897452	−	0.441112i	$-0.145416\pi$
$564$	−6.49929e32			−0.0264166
$565$	−1.43882e34	+	1.73913e34i	−0.572005	+	0.691394i
$566$	−9.34335e33			−0.363327
$567$		−	6.70445e34i		−	2.55020i
$568$			1.97594e34i			0.735224i
$569$	2.43835e34			0.887550			0.443775	−	0.896138i	$-0.353639\pi$
$569$	2.43835e34			0.887550			0.443775	+	0.896138i	$0.353639\pi$
$570$	−5.60616e34	−	4.63810e34i	−1.99632	−	1.65160i
$571$	3.19085e34			1.11162			0.555809	−	0.831310i	$-0.312409\pi$
$571$	3.19085e34			1.11162			0.555809	+	0.831310i	$0.312409\pi$
$572$			2.64756e30i			9.02391e-5i
$573$		−	3.74094e34i		−	1.24752i
$574$	1.88697e34			0.615696
$575$	4.30563e33	−	8.21080e32i	0.137464	−	0.0262142i
$576$	7.20428e34			2.25066
$577$			3.31742e33i			0.101415i	0.998714	+	0.0507076i	$0.0161477\pi$
$577$			3.31742e33i			0.101415i	−0.998714	+	0.0507076i	$0.983852\pi$
$578$		−	2.09004e34i		−	0.625254i
$579$	−5.17649e34			−1.51549
$580$	7.94437e30	+	6.57255e30i	0.000227619	+	0.000188315i
$581$	−3.03748e34			−0.851750
$582$			6.75073e34i			1.85274i
$583$			2.76686e32i			0.00743243i
$584$	−4.54766e34			−1.19571
$585$	7.00557e33	−	8.46777e33i	0.180300	−	0.217932i
$586$	3.81221e34			0.960410
$587$		−	2.85285e34i		−	0.703561i	−0.936082	−	0.351781i	$-0.885576\pi$
$587$		−	2.85285e34i		−	0.703561i	0.936082	−	0.351781i	$-0.114424\pi$
$588$			4.76968e33i			0.115152i
$589$	5.18660e34			1.22586
$590$	−3.90505e33	+	4.72011e33i	−0.0903600	+	0.109220i
$591$	1.18219e35			2.67821
$592$		−	5.09244e34i		−	1.12955i
$593$			1.86951e34i			0.406018i	0.979177	+	0.203009i	$0.0650720\pi$
$593$			1.86951e34i			0.406018i	−0.979177	+	0.203009i	$0.934928\pi$
$594$	1.75651e33			0.0373526
$595$	3.65806e34	+	3.02639e34i	0.761709	+	0.630178i
$596$	−2.70861e33			−0.0552291
$597$			1.26680e35i			2.52946i
$598$		−	9.13096e32i		−	0.0178547i
$599$	−3.44101e34			−0.658947			−0.329474	−	0.944165i	$-0.606871\pi$
$599$	−3.44101e34			−0.658947			−0.329474	+	0.944165i	$0.606871\pi$
$600$	−1.81179e34	−	9.50078e34i	−0.339795	−	1.78184i
$601$	−8.24179e34			−1.51388			−0.756939	−	0.653486i	$-0.773306\pi$
$601$	−8.24179e34			−1.51388			−0.756939	+	0.653486i	$0.773306\pi$
$602$			1.83300e34i			0.329766i
$603$			9.52532e34i			1.67847i
$604$	4.00274e33			0.0690869
$605$	−4.55583e34	−	3.76914e34i	−0.770239	−	0.637235i
$606$	−2.06886e35			−3.42628
$607$		−	6.57346e34i		−	1.06644i	−0.845978	−	0.533219i	$-0.820982\pi$
$607$		−	6.57346e34i		−	1.06644i	0.845978	−	0.533219i	$-0.179018\pi$
$608$		−	7.10618e33i		−	0.112938i
$609$	−1.45673e33			−0.0226810
$610$	5.91044e34	−	7.14407e34i	0.901565	−	1.08974i
$611$	3.38719e33			0.0506203
$612$		−	3.40658e33i		−	0.0498800i
$613$		−	9.01994e34i		−	1.29404i	−0.762473	−	0.647020i	$-0.776015\pi$
$613$		−	9.01994e34i		−	1.29404i	0.762473	−	0.647020i	$-0.223985\pi$
$614$	4.29850e34			0.604245
$615$	−3.15231e34	+	3.81026e34i	−0.434200	+	0.524826i
$616$	−2.25485e33			−0.0304340
$617$			1.00902e35i			1.33455i	0.744809	+	0.667277i	$0.232540\pi$
$617$			1.00902e35i			1.33455i	−0.744809	+	0.667277i	$0.767460\pi$
$618$			1.32975e35i			1.72351i
$619$	3.28407e34			0.417138			0.208569	−	0.978008i	$-0.433119\pi$
$619$	3.28407e34			0.417138			0.208569	+	0.978008i	$0.433119\pi$
$620$	1.94987e33	+	1.61317e33i	0.0242722	+	0.0200809i
$621$	2.39977e34			0.292769
$622$		−	1.04019e35i		−	1.24375i
$623$			5.43823e34i			0.637320i
$624$	−1.93795e34			−0.222605
$625$	−8.25846e34	+	3.26863e34i	−0.929820	+	0.368015i
$626$	1.51901e35			1.67642
$627$		−	4.44548e33i		−	0.0480922i
$628$			3.88229e33i			0.0411711i
$629$	−6.81097e34			−0.708069
$630$	2.64713e35	+	2.19003e35i	2.69785	+	2.23199i
$631$	−3.59177e34			−0.358874			−0.179437	−	0.983769i	$-0.557428\pi$
$631$	−3.59177e34			−0.358874			−0.179437	+	0.983769i	$0.557428\pi$
$632$			5.90984e34i			0.578911i
$633$		−	3.11405e35i		−	2.99074i
$634$	−2.96776e33			−0.0279456
$635$	3.75433e34	−	4.53794e34i	0.346626	−	0.418974i
$636$	3.06170e33			0.0277171
$637$		−	2.48578e34i		−	0.220658i
$638$		−	1.59025e31i		−	0.000138423i
$639$	1.83943e35			1.57009
$640$	−7.15137e34	+	8.64400e34i	−0.598604	+	0.723544i
$641$	−2.23468e35			−1.83439			−0.917193	−	0.398444i	$-0.869550\pi$
$641$	−2.23468e35			−1.83439			−0.917193	+	0.398444i	$0.869550\pi$
$642$		−	3.23975e35i		−	2.60810i
$643$			9.82691e34i			0.775853i	0.921690	+	0.387927i	$0.126809\pi$
$643$			9.82691e34i			0.775853i	−0.921690	+	0.387927i	$0.873191\pi$
$644$	−1.13076e33			−0.00875581
$645$	−3.70128e34	−	3.06215e34i	−0.281097	−	0.232558i
$646$	1.17541e35			0.875556
$647$		−	1.62869e35i		−	1.18997i	−0.803738	−	0.594984i	$-0.797158\pi$
$647$		−	1.62869e35i		−	1.18997i	0.803738	−	0.594984i	$-0.202842\pi$
$648$		−	2.20644e35i		−	1.58126i
$649$	−3.74287e32			−0.00263115
$650$	3.46589e33	+	1.81747e34i	0.0239000	+	0.125328i
$651$	−3.57539e35			−2.41859
$652$		−	3.49700e33i		−	0.0232060i
$653$			1.22992e35i			0.800685i	0.916366	+	0.400342i	$0.131109\pi$
$653$			1.22992e35i			0.800685i	−0.916366	+	0.400342i	$0.868891\pi$
$654$	−3.16343e34			−0.202040
$655$	1.48754e35	+	1.23068e35i	0.932079	+	0.771129i
$656$	5.97304e34			0.367196
$657$			4.23349e35i			2.55347i
$658$			1.05888e35i			0.626647i
$659$	2.07463e35			1.20468			0.602341	−	0.798239i	$-0.294235\pi$
$659$	2.07463e35			1.20468			0.602341	+	0.798239i	$0.294235\pi$
$660$	1.38266e32	−	1.67125e32i	0.000787801	−	0.000952230i
$661$	7.05700e34			0.394550			0.197275	−	0.980348i	$-0.436791\pi$
$661$	7.05700e34			0.394550			0.197275	+	0.980348i	$0.436791\pi$
$662$			2.99089e35i			1.64088i
$663$			2.59194e34i			0.139542i
$664$	−9.99636e34			−0.528130
$665$	2.99342e35	−	3.61820e35i	1.55202	−	1.87595i
$666$	−4.92870e35			−2.50787
$667$		−	2.17262e32i		−	0.00108495i
$668$		−	9.82163e33i		−	0.0481369i
$669$	1.77251e35			0.852633
$670$	−1.23559e35	−	1.02223e35i	−0.583362	−	0.482628i
$671$	5.66498e33			0.0262523
$672$			4.89866e34i			0.222824i
$673$			9.50489e34i			0.424384i	0.977228	+	0.212192i	$0.0680602\pi$
$673$			9.50489e34i			0.424384i	−0.977228	+	0.212192i	$0.931940\pi$
$674$	−2.47562e35			−1.08501
$675$	−4.77661e35	+	9.10895e34i	−2.05505	+	0.391896i
$676$	8.86943e33			0.0374595
$677$			2.06773e35i			0.857303i	0.903470	+	0.428652i	$0.141011\pi$
$677$			2.06773e35i			0.857303i	−0.903470	+	0.428652i	$0.858989\pi$
$678$		−	3.85222e35i		−	1.56798i
$679$	−4.35690e35			−1.74103
$680$	1.20387e35	+	9.95987e34i	0.472300	+	0.390744i
$681$	8.75510e35			3.37227
$682$		−	3.90312e33i		−	0.0147607i
$683$			7.23555e34i			0.268666i	0.990936	+	0.134333i	$0.0428892\pi$
$683$			7.23555e34i			0.268666i	−0.990936	+	0.134333i	$0.957111\pi$
$684$	−3.36946e34			−0.122846
$685$	1.44648e35	−	1.74839e35i	0.517823	−	0.625903i
$686$	3.18953e35			1.12118
$687$		−	3.62340e35i		−	1.25071i
$688$			5.80221e34i			0.196670i
$689$	−1.59564e34			−0.0531124
$690$	−4.76856e34	+	5.76385e34i	−0.155874	+	0.188408i
$691$	−3.09872e35			−0.994733			−0.497367	−	0.867540i	$-0.665700\pi$
$691$	−3.09872e35			−0.994733			−0.497367	+	0.867540i	$0.665700\pi$
$692$			7.62440e33i			0.0240370i
$693$			2.09907e34i			0.0649924i
$694$	1.35423e35			0.411812
$695$	−3.13407e35	−	2.59288e35i	−0.936049	−	0.774413i
$696$	−4.79409e33			−0.0140634
$697$		−	7.98875e34i		−	0.230181i
$698$			6.84159e34i			0.193626i
$699$	8.66486e35			2.40878
$700$	2.25071e34	−	4.29208e33i	0.0614602	−	0.0117204i
$701$	5.69729e34			0.152825			0.0764123	−	0.997076i	$-0.475653\pi$
$701$	5.69729e34			0.152825			0.0764123	+	0.997076i	$0.475653\pi$
$702$			1.01298e35i			0.266923i
$703$			6.73675e35i			1.74385i
$704$	−7.41032e33			−0.0188443
$705$	−2.13814e35	−	1.76893e35i	−0.534161	−	0.441923i
$706$	1.81631e35			0.445790
$707$		−	1.33524e36i		−	3.21970i
$708$			4.14170e33i			0.00981212i
$709$	−1.74880e33			−0.00407064			−0.00203532	−	0.999998i	$-0.500648\pi$
$709$	−1.74880e33			−0.00407064			−0.00203532	+	0.999998i	$0.500648\pi$
$710$	−1.97402e35	+	2.38604e35i	−0.451463	+	0.545693i
$711$	5.50156e35			1.23628
$712$			1.78972e35i			0.395172i
$713$		−	5.33248e34i		−	0.115694i
$714$	−8.10273e35			−1.72744
$715$	−7.20592e32	+	8.70994e32i	−0.00150961	+	0.00182469i
$716$	−1.87017e34			−0.0385006
$717$			4.52758e35i			0.915960i
$718$			6.97187e35i			1.38610i
$719$	−8.15998e35			−1.59433			−0.797164	−	0.603762i	$-0.793668\pi$
$719$	−8.15998e35			−1.59433			−0.797164	+	0.603762i	$0.793668\pi$
$720$	8.37927e35	+	6.93235e35i	1.60898	+	1.33114i
$721$	−8.58218e35			−1.61960
$722$		−	6.33819e35i		−	1.17558i
$723$		−	2.73105e35i		−	0.497853i
$724$	1.44750e34			0.0259350
$725$	8.24674e32	+	4.32448e33i	0.00145230	+	0.00761568i
$726$	1.00913e36			1.74679
$727$			1.09494e36i			1.86300i	0.363746	+	0.931498i	$0.381498\pi$
$727$			1.09494e36i			1.86300i	−0.363746	+	0.931498i	$0.618502\pi$
$728$		−	1.30037e35i		−	0.217482i
$729$	2.13214e35			0.350528
$730$	−5.49151e35	−	4.54325e35i	−0.887475	−	0.734227i
$731$	7.76027e34			0.123285
$732$		−	6.26863e34i		−	0.0979003i
$733$		−	1.02201e36i		−	1.56912i	−0.620053	−	0.784560i	$-0.712889\pi$
$733$		−	1.02201e36i		−	1.56912i	0.620053	−	0.784560i	$-0.287111\pi$
$734$	−3.37428e35			−0.509307
$735$	−1.29818e36	+	1.56913e36i	−1.92638	+	2.32845i
$736$	−7.30606e33			−0.0106588
$737$		−	9.79774e33i		−	0.0140534i
$738$		−	5.78100e35i		−	0.815264i
$739$	6.07706e35			0.842632			0.421316	−	0.906914i	$-0.361568\pi$
$739$	6.07706e35			0.842632			0.421316	+	0.906914i	$0.361568\pi$
$740$	−2.09531e34	+	2.53264e34i	−0.0285661	+	0.0345284i
$741$	2.56370e35			0.343668
$742$		−	4.98818e35i		−	0.657497i
$743$		−	7.63663e34i		−	0.0989787i	−0.998775	−	0.0494893i	$-0.984241\pi$
$743$		−	7.63663e34i		−	0.0989787i	0.998775	−	0.0494893i	$-0.0157594\pi$
$744$	−1.17666e36			−1.49965
$745$	−8.91079e35	−	7.37209e35i	−1.11677	−	0.923926i
$746$	9.31036e34			0.114744
$747$			9.30576e35i			1.12783i
$748$			3.50401e32i			0.000417634i
$749$	2.09093e36			2.45085
$750$	7.30373e35	−	1.32827e36i	0.841936	−	1.53116i
$751$	−9.18660e34			−0.104149			−0.0520746	−	0.998643i	$-0.516583\pi$
$751$	−9.18660e34			−0.104149			−0.0520746	+	0.998643i	$0.516583\pi$
$752$			3.35179e35i			0.373727i
$753$		−	1.11875e36i		−	1.22687i
$754$	9.17093e32			0.000989172
$755$	1.31682e36	+	1.08944e36i	1.39698	+	1.15575i
$756$	1.25445e35			0.130897
$757$			1.25062e36i			1.28359i	0.766877	+	0.641794i	$0.221810\pi$
$757$			1.25062e36i			1.28359i	−0.766877	+	0.641794i	$0.778190\pi$
$758$			4.93073e35i			0.497790i
$759$	−4.57052e33			−0.00453882
$760$	9.85134e35	−	1.19075e36i	0.962333	−	1.16319i
$761$	−5.09758e35			−0.489842			−0.244921	−	0.969543i	$-0.578762\pi$
$761$	−5.09758e35			−0.489842			−0.244921	+	0.969543i	$0.578762\pi$
$762$			1.00517e36i			0.950171i
$763$		−	2.04167e35i		−	0.189858i
$764$	2.91655e34			0.0266810
$765$	9.27179e35	−	1.12070e36i	0.834441	−	1.00861i
$766$	1.61856e36			1.43307
$767$		−	2.15850e34i		−	0.0188023i
$768$			2.37297e35i			0.203365i
$769$	−6.50005e35			−0.548072			−0.274036	−	0.961719i	$-0.588359\pi$
$769$	−6.50005e35			−0.548072			−0.274036	+	0.961719i	$0.588359\pi$
$770$	−2.72284e34	−	2.25266e34i	−0.0225885	−	0.0186880i
$771$	−3.72565e36			−3.04104
$772$		−	4.03575e34i		−	0.0324121i
$773$			1.84525e36i			1.45818i	0.684417	+	0.729091i	$0.260057\pi$
$773$			1.84525e36i			1.45818i	−0.684417	+	0.729091i	$0.739943\pi$
$774$	5.61566e35			0.436655
$775$	2.02408e35	+	1.06140e36i	0.154866	+	0.812098i
$776$	−1.43386e36			−1.07953
$777$		−	4.64399e36i		−	3.44056i
$778$		−	1.58566e36i		−	1.15602i
$779$	−7.90170e35			−0.566895
$780$	9.63805e33	+	7.97377e33i	0.00680467	+	0.00562965i
$781$	−1.89204e34			−0.0131460
$782$		−	1.20847e35i		−	0.0826328i
$783$			2.41027e34i			0.0162198i
$784$	2.45980e36			1.62911
$785$	−1.05665e36	+	1.27720e36i	−0.688750	+	0.832506i
$786$	−3.29495e36			−2.11382
$787$			8.29802e35i			0.523951i	0.965075	+	0.261975i	$0.0843739\pi$
$787$			8.29802e35i			0.523951i	−0.965075	+	0.261975i	$0.915626\pi$
$788$			9.21672e34i			0.0572794i
$789$	−4.94387e35			−0.302416
$790$	−5.90410e35	+	7.13640e35i	−0.355480	+	0.429675i
$791$	2.48621e36			1.47344
$792$			6.90806e34i			0.0402987i
$793$			3.26698e35i			0.187599i
$794$	−1.11114e36			−0.628074
$795$	1.00724e36	+	8.33310e35i	0.560458	+	0.463679i
$796$	−9.87632e34			−0.0540981
$797$			1.34226e36i			0.723781i	0.932221	+	0.361891i	$0.117869\pi$
$797$			1.34226e36i			0.723781i	−0.932221	+	0.361891i	$0.882131\pi$
$798$			8.01444e36i			4.25439i
$799$	4.48291e35			0.234275
$800$	1.45423e35	−	2.77320e34i	0.0748184	−	0.0142678i
$801$	1.66608e36			0.843897
$802$			3.82084e35i			0.190537i
$803$		−	4.35456e34i		−	0.0213796i
$804$	−1.08418e35			−0.0524082
$805$	−3.71997e35	−	3.07761e35i	−0.177048	−	0.146476i
$806$	2.25092e35			0.105480
$807$		−	6.12656e36i		−	2.82682i
$808$		−	4.39426e36i		−	1.99638i
$809$	6.60545e35			0.295492			0.147746	−	0.989025i	$-0.452798\pi$
$809$	6.60545e35			0.295492			0.147746	+	0.989025i	$0.452798\pi$
$810$	2.20429e36	−	2.66437e36i	0.970972	−	1.17363i
$811$	−1.01354e36			−0.439622			−0.219811	−	0.975543i	$-0.570544\pi$
$811$	−1.01354e36			−0.439622			−0.219811	+	0.975543i	$0.570544\pi$
$812$		−	1.13571e33i		−	0.000485083i
$813$			2.23279e36i			0.939111i
$814$	5.06966e34			0.0209978
$815$	9.51789e35	−	1.15045e36i	0.388213	−	0.469241i
$816$	−2.56485e36			−1.03023
$817$		−	7.67571e35i		−	0.303629i
$818$		−	2.57546e36i		−	1.00332i
$819$	−1.21053e36			−0.464437
$820$	−2.97059e34	−	2.45764e34i	−0.0112246	−	0.00928633i
$821$	−1.25808e36			−0.468188			−0.234094	−	0.972214i	$-0.575212\pi$
$821$	−1.25808e36			−0.468188			−0.234094	+	0.972214i	$0.575212\pi$
$822$			3.87275e36i			1.41946i
$823$		−	1.64400e36i		−	0.593476i	−0.954959	−	0.296738i	$-0.904101\pi$
$823$		−	1.64400e36i		−	0.593476i	0.954959	−	0.296738i	$-0.0958988\pi$
$824$	−2.82440e36			−1.00424
$825$	9.09737e34	−	1.73486e34i	0.0318597	−	0.00607561i
$826$	6.74775e35			0.232760
$827$			1.24420e36i			0.422738i	0.977406	+	0.211369i	$0.0677922\pi$
$827$			1.24420e36i			0.422738i	−0.977406	+	0.211369i	$0.932208\pi$
$828$			3.46424e34i			0.0115939i
$829$	4.13721e36			1.36388			0.681939	−	0.731409i	$-0.261137\pi$
$829$	4.13721e36			1.36388			0.681939	+	0.731409i	$0.261137\pi$
$830$	−1.20711e36	−	9.98665e35i	−0.391985	−	0.324297i
$831$	4.98134e36			1.59343
$832$		−	4.27352e35i		−	0.134662i
$833$		−	3.28991e36i		−	1.02122i
$834$	6.94207e36			2.12282
$835$	2.67318e36	−	3.23112e36i	0.805280	−	0.973358i
$836$	3.46583e33			0.00102856
$837$			5.91579e36i			1.72959i
$838$		−	3.22653e36i		−	0.929362i
$839$	−2.84132e36			−0.806298			−0.403149	−	0.915134i	$-0.632084\pi$
$839$	−2.84132e36			−0.806298			−0.403149	+	0.915134i	$0.632084\pi$
$840$	−6.79104e36	+	8.20847e36i	−1.89865	+	2.29494i
$841$	−3.63014e36			−0.999940
$842$		−	3.37207e35i		−	0.0915155i
$843$			9.79225e35i			0.261841i
$844$	2.42780e35			0.0639636
$845$	2.91787e36	+	2.41402e36i	0.757455	+	0.626659i
$846$	3.24403e36			0.829765
$847$			6.51291e36i			1.64147i
$848$		−	1.57897e36i		−	0.392126i
$849$	−2.69712e36			−0.660014
$850$	4.58707e35	+	2.40540e36i	0.110611	+	0.580030i
$851$	6.92623e35			0.164580
$852$			2.09365e35i			0.0490241i
$853$			1.14175e35i			0.0263455i	0.999913	+	0.0131728i	$0.00419314\pi$
$853$			1.14175e35i			0.0263455i	−0.999913	+	0.0131728i	$0.995807\pi$
$854$	−1.02130e37			−2.32236
$855$	−1.10849e37	−	9.17076e36i	−2.48402	−	2.05508i
$856$	6.88124e36			1.51965
$857$		−	2.22307e36i		−	0.483831i	−0.970297	−	0.241916i	$-0.922224\pi$
$857$		−	2.22307e36i		−	0.483831i	0.970297	−	0.241916i	$-0.0777757\pi$
$858$		−	1.92928e34i		−	0.00413813i
$859$	−4.49719e36			−0.950663			−0.475331	−	0.879807i	$-0.657672\pi$
$859$	−4.49719e36			−0.950663			−0.475331	+	0.879807i	$0.657672\pi$
$860$	2.38735e34	−	2.88563e34i	0.00497376	−	0.00601188i
$861$	5.44705e36			1.11846
$862$			1.81545e36i			0.367403i
$863$		−	4.37496e36i		−	0.872649i	−0.899789	−	0.436324i	$-0.856280\pi$
$863$		−	4.37496e36i		−	0.872649i	0.899789	−	0.436324i	$-0.143720\pi$
$864$	8.10524e35			0.159347
$865$	−2.07515e36	+	2.50828e36i	−0.402114	+	0.486043i
$866$	4.99186e35			0.0953429
$867$		−	6.03325e36i		−	1.13583i
$868$		−	2.78748e35i		−	0.0517268i
$869$	−5.65890e34			−0.0103511
$870$	−5.78908e34	−	4.78943e34i	−0.0104380	−	0.00863562i
$871$	5.65033e35			0.100426
$872$		−	6.71913e35i		−	0.117722i
$873$			1.33480e37i			2.30536i
$874$	−1.19530e36			−0.203510
$875$	8.57259e36	+	4.71381e36i	1.43884	+	0.791173i
$876$	−4.81858e35			−0.0797292
$877$		−	4.17303e35i		−	0.0680701i	−0.999421	−	0.0340351i	$-0.989164\pi$
$877$		−	4.17303e35i		−	0.0680701i	0.999421	−	0.0340351i	$-0.0108358\pi$
$878$			6.67105e36i			1.07279i
$879$	1.10046e37			1.74467
$880$	−8.61891e34	−	7.13061e34i	−0.0134716	−	0.0111453i
$881$	−2.64254e36			−0.407215			−0.203607	−	0.979053i	$-0.565267\pi$
$881$	−2.64254e36			−0.407215			−0.203607	+	0.979053i	$0.565267\pi$
$882$		−	2.38072e37i		−	3.61701i
$883$			6.39816e36i			0.958399i	0.877706	+	0.479199i	$0.159073\pi$
$883$			6.39816e36i			0.958399i	−0.877706	+	0.479199i	$0.840927\pi$
$884$	−2.02075e34			−0.00298442
$885$	−1.12726e36	+	1.36254e36i	−0.164147	+	0.198407i
$886$	−9.23675e34			−0.0132617
$887$			3.90715e36i			0.553114i	0.960998	+	0.276557i	$0.0891934\pi$
$887$			3.90715e36i			0.553114i	−0.960998	+	0.276557i	$0.910807\pi$
$888$		−	1.52834e37i		−	2.13333i
$889$	−6.48732e36			−0.892881
$890$	−1.78799e36	+	2.16117e36i	−0.242655	+	0.293302i
$891$	2.11275e35			0.0282733
$892$			1.38190e35i			0.0182355i
$893$		−	4.43407e36i		−	0.576978i
$894$	1.97377e37			2.53266
$895$	−6.15248e36	−	5.09008e36i	−0.778507	−	0.644075i
$896$	1.23573e37			1.54196
$897$		−	2.63581e35i		−	0.0324346i
$898$			4.20134e36i			0.509839i
$899$	5.35583e34			0.00640959
$900$	−1.31494e35	−	6.89537e35i	−0.0155194	−	0.0813817i
$901$	−2.11182e36			−0.245808
$902$			5.94633e34i			0.00682602i
$903$			5.29127e36i			0.599050i
$904$	8.18213e36			0.913610
$905$	4.76199e36	+	3.93970e36i	0.524422	+	0.433866i
$906$	−2.91681e37			−3.16815
$907$			4.51261e36i			0.483433i	0.970347	+	0.241716i	$0.0777104\pi$
$907$			4.51261e36i			0.483433i	−0.970347	+	0.241716i	$0.922290\pi$
$908$			6.82574e35i			0.0721235i
$909$	−4.09069e37			−4.26332
$910$	1.29910e36	−	1.57025e36i	0.133545	−	0.161418i
$911$	1.89844e37			1.92494			0.962469	−	0.271391i	$-0.0874836\pi$
$911$	1.89844e37			1.92494			0.962469	+	0.271391i	$0.0874836\pi$
$912$			2.53690e37i			2.53728i
$913$		−	9.57190e34i		−	0.00944307i
$914$	6.46598e36			0.629226
$915$	1.70615e37	−	2.06226e37i	1.63777	−	1.97961i
$916$	2.82491e35			0.0267492
$917$		−	2.12655e37i		−	1.98637i
$918$			1.34066e37i			1.23534i
$919$	−4.52781e36			−0.411571			−0.205785	−	0.978597i	$-0.565975\pi$
$919$	−4.52781e36			−0.411571			−0.205785	+	0.978597i	$0.565975\pi$
$920$	−1.22424e36	−	1.01284e36i	−0.109779	−	0.0908227i
$921$	1.24084e37			1.09766
$922$			6.67790e36i			0.582778i
$923$		−	1.09113e36i		−	0.0939414i
$924$	−2.38918e34			−0.00202931
$925$	−1.37863e37	+	2.62903e36i	−1.15525	+	0.220305i
$926$	−8.63320e36			−0.713731
$927$			2.62927e37i			2.14456i
$928$		−	7.33804e33i		−	0.000590514i
$929$	−7.25771e36			−0.576240			−0.288120	−	0.957594i	$-0.593030\pi$
$929$	−7.25771e36			−0.576240			−0.288120	+	0.957594i	$0.593030\pi$
$930$	−1.42087e37	−	1.17552e37i	−1.11306	−	0.920859i
$931$	−3.25406e37			−2.51509
$932$			6.75539e35i			0.0515171i
$933$		−	3.00269e37i		−	2.25938i
$934$	1.68726e37			1.25270
$935$	−9.53696e34	+	1.15275e35i	−0.00698658	+	0.00844482i
$936$	−3.98386e36			−0.287976
$937$			1.00841e37i			0.719271i	0.933093	+	0.359636i	$0.117099\pi$
$937$			1.00841e37i			0.719271i	−0.933093	+	0.359636i	$0.882901\pi$
$938$			1.76636e37i			1.24321i
$939$	4.38489e37			3.04536
$940$	1.37911e35	−	1.66696e35i	0.00945150	−	0.0114242i
$941$	−1.57617e37			−1.06594			−0.532969	−	0.846135i	$-0.678924\pi$
$941$	−1.57617e37			−1.06594			−0.532969	+	0.846135i	$0.678924\pi$
$942$		−	2.82903e37i		−	1.88800i
$943$			8.12395e35i			0.0535021i
$944$	2.13594e36			0.138816
$945$	4.12689e37	+	3.41426e37i	2.64682	+	2.18977i
$946$	−5.77626e34			−0.00365601
$947$			1.34188e37i			0.838184i	0.907944	+	0.419092i	$0.137652\pi$
$947$			1.34188e37i			0.838184i	−0.907944	+	0.419092i	$0.862348\pi$
$948$			6.26190e35i			0.0386013i
$949$	2.51127e36			0.152779
$950$	2.37919e37	−	4.53709e36i	1.42851	−	0.272416i
$951$	−8.56693e35			−0.0507655
$952$		−	1.72102e37i		−	1.00652i
$953$		−	1.03643e37i		−	0.598245i	−0.954215	−	0.299123i	$-0.903306\pi$
$953$		−	1.03643e37i		−	0.598245i	0.954215	−	0.299123i	$-0.0966939\pi$
$954$	−1.52820e37			−0.870614
$955$	9.59487e36	+	7.93804e36i	0.539507	+	0.446346i
$956$	−3.52983e35			−0.0195898
$957$		−	4.59053e33i		−	0.000251457i
$958$		−	2.23925e37i		−	1.21069i
$959$	−2.49946e37			−1.33387
$960$	−2.23180e37	+	2.69762e37i	−1.17562	+	1.42099i
$961$	−6.08743e36			−0.316513
$962$			2.92366e36i			0.150051i
$963$		−	6.40585e37i		−	3.24525i
$964$	2.12921e35			0.0106477
$965$	1.09842e37	−	1.32768e37i	0.542222	−	0.655394i
$966$	8.23986e36			0.401519
$967$		−	2.17672e37i		−	1.04706i	−0.852007	−	0.523530i	$-0.824615\pi$
$967$		−	2.17672e37i		−	1.04706i	0.852007	−	0.523530i	$-0.175385\pi$
$968$			2.14340e37i			1.01780i
$969$	3.39303e37			1.59052
$970$	−1.73145e37	−	1.43247e37i	−0.801241	−	0.662884i
$971$	2.61957e37			1.19671			0.598355	−	0.801231i	$-0.295821\pi$
$971$	2.61957e37			1.19671			0.598355	+	0.801231i	$0.295821\pi$
$972$		−	5.70286e35i		−	0.0257196i
$973$			4.48039e37i			1.99483i
$974$	−3.18300e37			−1.39910
$975$	1.00049e36	+	5.24643e36i	0.0434165	+	0.227670i
$976$	−3.23284e37			−1.38504
$977$		−	1.84608e37i		−	0.780853i	−0.920634	−	0.390426i	$-0.872328\pi$
$977$		−	1.84608e37i		−	0.780853i	0.920634	−	0.390426i	$-0.127672\pi$
$978$			2.54828e37i			1.06417i
$979$	−1.71373e35			−0.00706576
$980$	−1.22334e36	−	1.01210e36i	−0.0497991	−	0.0411999i
$981$	−6.25494e36			−0.251397
$982$		−	1.21668e37i		−	0.482817i
$983$		−	1.57934e37i		−	0.618811i	−0.950930	−	0.309405i	$-0.899870\pi$
$983$		−	1.57934e37i		−	0.618811i	0.950930	−	0.309405i	$-0.100130\pi$
$984$	1.79263e37			0.693507
$985$	−2.50854e37	+	3.03212e37i	−0.958226	+	1.15823i
$986$	1.21376e35			0.00457797
$987$			3.05663e37i			1.13836i
$988$			1.99874e35i			0.00735010i
$989$	−7.89160e35			−0.0286557
$990$	−6.90135e35	+	8.34180e35i	−0.0247454	+	0.0299102i
$991$	5.32037e37			1.88374			0.941870	−	0.335978i	$-0.109067\pi$
$991$	5.32037e37			1.88374			0.941870	+	0.335978i	$0.109067\pi$
$992$		−	1.80105e36i		−	0.0629695i
$993$			8.63372e37i			2.98080i
$994$	3.41102e37			1.16293
$995$	−3.24912e37	−	2.68807e37i	−1.09390	−	0.905006i
$996$	−1.05919e36			−0.0352152
$997$		−	3.54532e37i		−	1.16403i	−0.813176	−	0.582017i	$-0.802264\pi$
$997$		−	3.54532e37i		−	1.16403i	0.813176	−	0.582017i	$-0.197736\pi$
$998$			3.02180e37i			0.979792i
$999$	−7.68387e37			−2.46043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.b.a.4.4	✓	12
3.2	odd	2		45.26.b.b.19.9		12
5.2	odd	4		25.26.a.f.1.9		12
5.3	odd	4		25.26.a.f.1.4		12
5.4	even	2	inner	5.26.b.a.4.9	yes	12
15.14	odd	2		45.26.b.b.19.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.b.a.4.4	✓	12	1.1	even	1	trivial
5.26.b.a.4.9	yes	12	5.4	even	2	inner
25.26.a.f.1.4		12	5.3	odd	4
25.26.a.f.1.9		12	5.2	odd	4
45.26.b.b.19.4		12	15.14	odd	2
45.26.b.b.19.9		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5681.18i q^{2} -1.63997e6i q^{3} +1.27857e6 q^{4} +(4.20624e8 + 3.47992e8i) q^{5} -9.31697e9 q^{6} -6.01315e10i q^{7} -1.97893e11i q^{8} -1.84221e12 q^{9} +O(q^{10})\)	\(q-5681.18i q^{2} -1.63997e6i q^{3} +1.27857e6 q^{4} +(4.20624e8 + 3.47992e8i) q^{5} -9.31697e9 q^{6} -6.01315e10i q^{7} -1.97893e11i q^{8} -1.84221e12 q^{9} +(1.97701e12 - 2.38965e12i) q^{10} +1.89490e11 q^{11} -2.09682e12i q^{12} +1.09278e13i q^{13} -3.41618e14 q^{14} +(5.70696e14 - 6.89812e14i) q^{15} -1.08136e15 q^{16} +1.44629e15i q^{17} +1.04660e16i q^{18} +1.43053e16 q^{19} +(5.37798e14 + 4.44932e14i) q^{20} -9.86138e16 q^{21} -1.07653e15i q^{22} -1.47077e16i q^{23} -3.24538e17 q^{24} +(5.58267e16 + 2.92748e17i) q^{25} +6.20831e16 q^{26} +1.63165e18i q^{27} -7.68823e16i q^{28} +1.47720e16 q^{29} +(-3.91895e18 - 3.24223e18i) q^{30} +3.62565e18 q^{31} -4.96752e17i q^{32} -3.10758e17i q^{33} +8.21663e18 q^{34} +(2.09253e19 - 2.52928e19i) q^{35} -2.35540e18 q^{36} +4.70927e19i q^{37} -8.12710e19i q^{38} +1.79213e19 q^{39} +(6.88650e19 - 8.32385e19i) q^{40} -5.52362e19 q^{41} +5.60243e20i q^{42} -5.36564e19i q^{43} +2.42276e17 q^{44} +(-7.74880e20 - 6.41075e20i) q^{45} -8.35569e19 q^{46} -3.09960e20i q^{47} +1.77340e21i q^{48} -2.27472e21 q^{49} +(1.66315e21 - 3.17162e20i) q^{50} +2.37187e21 q^{51} +1.39720e19i q^{52} +1.46016e21i q^{53} +9.26969e21 q^{54} +(7.97041e19 + 6.59409e19i) q^{55} -1.18996e22 q^{56} -2.34602e22i q^{57} -8.39227e19i q^{58} -1.97523e21 q^{59} +(7.29675e20 - 8.81972e20i) q^{60} +2.98959e22 q^{61} -2.05980e22i q^{62} +1.10775e23i q^{63} -3.91067e22 q^{64} +(-3.80280e21 + 4.59652e21i) q^{65} -1.76547e21 q^{66} -5.17058e22i q^{67} +1.84918e21i q^{68} -2.41201e22 q^{69} +(-1.43693e23 - 1.18880e23i) q^{70} -9.98491e22 q^{71} +3.64561e23i q^{72} -2.29804e23i q^{73} +2.67543e23 q^{74} +(4.80097e23 - 9.15541e22i) q^{75} +1.82903e22 q^{76} -1.13943e22i q^{77} -1.01814e23i q^{78} -2.98638e23 q^{79} +(-4.54848e23 - 3.76306e23i) q^{80} +1.11497e24 q^{81} +3.13807e23i q^{82} -5.05140e23i q^{83} -1.26085e23 q^{84} +(-5.03296e23 + 6.08344e23i) q^{85} -3.04832e23 q^{86} -2.42257e22i q^{87} -3.74987e22i q^{88} -9.04391e23 q^{89} +(-3.64207e24 + 4.40224e24i) q^{90} +6.57107e23 q^{91} -1.88048e22i q^{92} -5.94596e24i q^{93} -1.76094e24 q^{94} +(6.01715e24 + 4.97812e24i) q^{95} -8.14659e23 q^{96} -7.24563e24i q^{97} +1.29231e25i q^{98} -3.49081e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9}+O(q^{10}) \) 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9	\( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9} + 4435846671960 q^{10} - 1090673824176 q^{11} - 890646861445848 q^{14} + 443085522435120 q^{15} + 22\!\cdots\!32 q^{16}+ \cdots - 10\!\cdots\!72 q^{99}+O(q^{100}) \) 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9 + 4435846671960 * q^10 - 1090673824176 * q^11 - 890646861445848 * q^14 + 443085522435120 * q^15 + 2206145875609632 * q^16 + 6329834351210160 * q^19 - 45407795215923720 * q^20 + 13538972741781744 * q^21 - 1238774108159908320 * q^24 + 883359578467451100 * q^25 + 487725686068642704 * q^26 - 5990455853511966360 * q^29 + 8784171220269562920 * q^30 - 35669623242168576 * q^31 - 45224081273675172288 * q^34 + 37959801679716705360 * q^35 + 95509342682184062232 * q^36 + 59576177650244745888 * q^39 - 135247056564421048800 * q^40 - 149504768291960577576 * q^41 + 1795327120321140441312 * q^44 - 1757089887558453396180 * q^45 - 2632260904857596314776 * q^46 - 1924948130789206201884 * q^49 + 4613478251192179347600 * q^50 + 6601362996360626974464 * q^51 - 4543556632841187026640 * q^54 - 4976317493836251356880 * q^55 + 6789286242764162655840 * q^56 - 31976684482970870043120 * q^59 + 38198563842186313414560 * q^60 + 33892026990475241838024 * q^61 - 45154694563657190239104 * q^64 - 23988754129834728629280 * q^65 - 84625057142490628840032 * q^66 + 454638912158488569862128 * q^69 - 514001938945682971911240 * q^70 - 118991523615678935618976 * q^71 - 276076790459758393833168 * q^74 - 256450000750992984232800 * q^75 + 1770023872374606472757280 * q^76 - 741918285485353377639360 * q^79 + 504838130357233934552160 * q^80 + 2020576746978155938317372 * q^81 - 6598941205046486172215328 * q^84 - 1447445120396229235779840 * q^85 + 6309456694176729359288664 * q^86 + 576066549612764658926520 * q^89 - 14281964558091964746137880 * q^90 + 12216814388553519240480864 * q^91 - 11673168428062976516959608 * q^94 - 23618191778193292124785200 * q^95 + 57292208364908004705120384 * q^96 - 10068680551503914801051472 * q^99

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