LMFDB - Embedded newform 4.25.b.b.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,25,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 25, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	4.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:	$14.5986860903$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} + 1157886 x^{8} - 1182314620 x^{7} + 1715110302918 x^{6} + \cdots + 10\!\cdots\!86 $ x^10 - 3x^9 + 1157886x^8 - 1182314620x^7 + 1715110302918x^6 - 2255628699630474x^5 + 1518357032488149568x^4 - 1731829168106243136300x^3 + 1460524813513291203716721x^2 - 1269695210566625624700394443*x + 1028204700608421275722350402186
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.6
Root			$112.122 + 988.545i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.25.b.b.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1068.49 + 3954.18i) q^{2} +193889. i q^{3} +(-1.44939e7 - 8.44998e6i) q^{4} +3.74285e8 q^{5} +(-7.66672e8 - 2.07168e8i) q^{6} +2.47654e10i q^{7} +(4.88993e10 - 4.82828e10i) q^{8} +2.44837e11 q^{9} +O(q^{10})$	\(q+(-1068.49 + 3954.18i) q^{2} +193889. i q^{3} +(-1.44939e7 - 8.44998e6i) q^{4} +3.74285e8 q^{5} +(-7.66672e8 - 2.07168e8i) q^{6} +2.47654e10i q^{7} +(4.88993e10 - 4.82828e10i) q^{8} +2.44837e11 q^{9} +(-3.99918e11 + 1.47999e12i) q^{10} -7.20071e11i q^{11} +(1.63836e12 - 2.81020e12i) q^{12} -1.13495e13 q^{13} +(-9.79267e13 - 2.64614e13i) q^{14} +7.25697e13i q^{15} +(1.38671e14 + 2.44946e14i) q^{16} -7.24578e14 q^{17} +(-2.61605e14 + 9.68129e14i) q^{18} +1.99560e15i q^{19} +(-5.42484e15 - 3.16270e15i) q^{20} -4.80173e15 q^{21} +(2.84729e15 + 7.69386e14i) q^{22} -4.43802e15i q^{23} +(9.36149e15 + 9.48102e15i) q^{24} +8.04846e16 q^{25} +(1.21268e16 - 4.48781e16i) q^{26} +1.02231e17i q^{27} +(2.09267e17 - 3.58946e17i) q^{28} +2.02893e16 q^{29} +(-2.86954e17 - 7.75397e16i) q^{30} +4.90083e17i q^{31} +(-1.11673e18 + 2.86608e17i) q^{32} +1.39614e17 q^{33} +(7.74202e17 - 2.86511e18i) q^{34} +9.26930e18i q^{35} +(-3.54864e18 - 2.06886e18i) q^{36} +1.00235e17 q^{37} +(-7.89096e18 - 2.13227e18i) q^{38} -2.20054e18i q^{39} +(1.83023e19 - 1.80715e19i) q^{40} +9.03467e18 q^{41} +(5.13058e18 - 1.89869e19i) q^{42} +4.53303e19i q^{43} +(-6.08458e18 + 1.04366e19i) q^{44} +9.16387e19 q^{45} +(1.75487e19 + 4.74197e18i) q^{46} -1.32515e20i q^{47} +(-4.74923e19 + 2.68867e19i) q^{48} -4.21742e20 q^{49} +(-8.59966e19 + 3.18251e20i) q^{50} -1.40488e20i q^{51} +(1.64499e20 + 9.59032e19i) q^{52} +2.48218e20 q^{53} +(-4.04240e20 - 1.09232e20i) q^{54} -2.69512e20i q^{55} +(1.19574e21 + 1.21101e21i) q^{56} -3.86924e20 q^{57} +(-2.16789e19 + 8.02277e19i) q^{58} -3.17904e21i q^{59} +(6.13212e20 - 1.05182e21i) q^{60} +2.83808e21 q^{61} +(-1.93788e21 - 5.23647e20i) q^{62} +6.06347e21i q^{63} +(5.99104e19 - 4.72199e21i) q^{64} -4.24795e21 q^{65} +(-1.49175e20 + 5.52058e20i) q^{66} +8.09517e21i q^{67} +(1.05020e22 + 6.12267e21i) q^{68} +8.60483e20 q^{69} +(-3.66525e22 - 9.90412e21i) q^{70} +7.22794e21i q^{71} +(1.19723e22 - 1.18214e22i) q^{72} +2.43394e21 q^{73} +(-1.07099e20 + 3.96346e20i) q^{74} +1.56051e22i q^{75} +(1.68628e22 - 2.89240e22i) q^{76} +1.78328e22 q^{77} +(8.70135e21 + 2.35125e21i) q^{78} -8.02491e22i q^{79} +(5.19024e22 + 9.16796e22i) q^{80} +4.93277e22 q^{81} +(-9.65342e21 + 3.57247e22i) q^{82} -5.98824e22i q^{83} +(6.95957e22 + 4.05745e22i) q^{84} -2.71199e23 q^{85} +(-1.79244e23 - 4.84348e22i) q^{86} +3.93387e21i q^{87} +(-3.47670e22 - 3.52109e22i) q^{88} +1.56264e23 q^{89} +(-9.79147e22 + 3.62356e23i) q^{90} -2.81075e23i q^{91} +(-3.75012e22 + 6.43242e22i) q^{92} -9.50217e22 q^{93} +(5.23987e23 + 1.41590e23i) q^{94} +7.46923e23i q^{95} +(-5.55700e22 - 2.16521e23i) q^{96} +2.43631e23 q^{97} +(4.50625e23 - 1.66764e24i) q^{98} -1.76300e23i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9}+O(q^{10}) $ 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9	$ 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9} - 279847745800 q^{10} + 12433669328640 q^{12} - 24798065342764 q^{13} - 3829480368768 q^{14} - 588864378801920 q^{16} - 16\!\cdots\!64 q^{17}+ \cdots + 25\!\cdots\!08 q^{98}+O(q^{100}) $ 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9 - 279847745800 * q^10 + 12433669328640 * q^12 - 24798065342764 * q^13 - 3829480368768 * q^14 - 588864378801920 * q^16 - 1625038130621164 * q^17 - 3063761223370692 * q^18 - 3121315867314400 * q^20 - 2850064322141184 * q^21 + 13916632990560960 * q^22 + 10666682388698112 * q^24 + 71169859613334750 * q^25 - 74430147208248328 * q^26 + 57921192425034240 * q^28 + 1565608550658446804 * q^29 + 168458533397673600 * q^30 - 2011315973261284352 * q^32 - 3113879011632238080 * q^33 - 7482312029820836488 * q^34 - 4814867106633363312 * q^36 + 18108949413006125396 * q^37 - 3611284956625913280 * q^38 - 3297305262340163200 * q^40 + 75081428813585343380 * q^41 - 36295172789431572480 * q^42 + 120819410323173239040 * q^44 - 81006988268625062700 * q^45 - 106055608197057981312 * q^46 + 168479244993419243520 * q^48 - 275007343618256059766 * q^49 - 299814709349559655500 * q^50 + 1421183854718604927776 * q^52 - 1107525951871034057644 * q^53 - 3208227550047955403136 * q^54 + 4524093845691909838848 * q^56 - 1196103002381444528640 * q^57 - 1979853653083682157064 * q^58 + 14021053781344411123200 * q^60 + 7517404483697744564180 * q^61 - 21697281489429749629440 * q^62 + 27630501101980402880512 * q^64 - 2258152381762360458200 * q^65 - 60089835931903418403840 * q^66 + 44229260314628142476576 * q^68 - 3522613303126336828416 * q^69 - 111574643945445039187200 * q^70 + 150836748983093603875008 * q^72 + 51509134469807151432596 * q^73 - 140974046625084701216008 * q^74 + 274189896308379651183360 * q^76 - 19744531096531028198400 * q^77 - 388532048156284380666240 * q^78 + 337741777000410839974400 * q^80 - 21177053453795724717174 * q^81 - 127986376736882271652744 * q^82 + 466232221405535207153664 * q^84 - 156954763950404735571800 * q^85 - 425659539471164537308992 * q^86 + 273874512491499757685760 * q^88 - 817895256767034869026156 * q^89 - 170393126837835789371400 * q^90 - 461144040688182763215360 * q^92 + 251375897269064448430080 * q^93 + 1709617022527703840285952 * q^94 - 3254103234068698697613312 * q^96 + 2233072706882417490518036 * q^97 + 2593191981481623434770108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−1068.49	+	3954.18i	−0.260861	+	0.965376i
$2$	−1068.49	+	3954.18i	−0.260861	+	0.965376i
$3$			193889.i			0.364836i	0.983221	+	0.182418i	$0.0583924\pi$
$3$			193889.i			0.364836i	−0.983221	+	0.182418i	$0.941608\pi$
$4$	−1.44939e7	−	8.44998e6i	−0.863903	−	0.503658i
$5$	3.74285e8			1.53307			0.766536	−	0.642202i	$-0.221979\pi$
$5$	3.74285e8			1.53307			0.766536	+	0.642202i	$0.221979\pi$
$6$	−7.66672e8	−	2.07168e8i	−0.352204	−	0.0951714i
$7$			2.47654e10i			1.78924i	0.446830	+	0.894619i	$0.352553\pi$
$7$			2.47654e10i			1.78924i	−0.446830	+	0.894619i	$0.647447\pi$
$8$	4.88993e10	−	4.82828e10i	0.711578	−	0.702607i
$9$	2.44837e11			0.866895
$10$	−3.99918e11	+	1.47999e12i	−0.399918	+	1.47999i
$11$		−	7.20071e11i		−	0.229437i	−0.993398	−	0.114718i	$-0.963403\pi$
$11$		−	7.20071e11i		−	0.229437i	0.993398	−	0.114718i	$-0.0365966\pi$
$12$	1.63836e12	−	2.81020e12i	0.183753	−	0.315183i
$13$	−1.13495e13			−0.487144			−0.243572	−	0.969883i	$-0.578319\pi$
$13$	−1.13495e13			−0.487144			−0.243572	+	0.969883i	$0.578319\pi$
$14$	−9.79267e13	−	2.64614e13i	−1.72729	−	0.466742i
$15$			7.25697e13i			0.559319i
$16$	1.38671e14	+	2.44946e14i	0.492657	+	0.870223i
$17$	−7.24578e14			−1.24365			−0.621825	−	0.783156i	$-0.713608\pi$
$17$	−7.24578e14			−1.24365			−0.621825	+	0.783156i	$0.713608\pi$
$18$	−2.61605e14	+	9.68129e14i	−0.226139	+	0.836880i
$19$			1.99560e15i			0.901634i	0.892617	+	0.450817i	$0.148867\pi$
$19$			1.99560e15i			0.901634i	−0.892617	+	0.450817i	$0.851133\pi$
$20$	−5.42484e15	−	3.16270e15i	−1.32442	−	0.772143i
$21$	−4.80173e15			−0.652778
$22$	2.84729e15	+	7.69386e14i	0.221493	+	0.0598511i
$23$		−	4.43802e15i		−	0.202514i	−0.994860	−	0.101257i	$-0.967714\pi$
$23$		−	4.43802e15i		−	0.202514i	0.994860	−	0.101257i	$-0.0322865\pi$
$24$	9.36149e15	+	9.48102e15i	0.256336	+	0.259609i
$25$	8.04846e16			1.35031
$26$	1.21268e16	−	4.48781e16i	0.127077	−	0.470277i
$27$			1.02231e17i			0.681110i
$28$	2.09267e17	−	3.58946e17i	0.901164	−	1.54573i
$29$	2.02893e16			0.0573445			0.0286722	−	0.999589i	$-0.490872\pi$
$29$	2.02893e16			0.0573445			0.0286722	+	0.999589i	$0.490872\pi$
$30$	−2.86954e17	−	7.75397e16i	−0.539954	−	0.145905i
$31$			4.90083e17i			0.622199i	0.950377	+	0.311100i	$0.100697\pi$
$31$			4.90083e17i			0.622199i	−0.950377	+	0.311100i	$0.899303\pi$
$32$	−1.11673e18	+	2.86608e17i	−0.968608	+	0.248593i
$33$	1.39614e17			0.0837068
$34$	7.74202e17	−	2.86511e18i	0.324420	−	1.20059i
$35$			9.26930e18i			2.74303i
$36$	−3.54864e18	−	2.06886e18i	−0.748913	−	0.436618i
$37$	1.00235e17			0.0152264			0.00761319	−	0.999971i	$-0.497577\pi$
$37$	1.00235e17			0.0152264			0.00761319	+	0.999971i	$0.497577\pi$
$38$	−7.89096e18	−	2.13227e18i	−0.870416	−	0.235201i
$39$		−	2.20054e18i		−	0.177728i
$40$	1.83023e19	−	1.80715e19i	1.09090	−	1.07715i
$41$	9.03467e18			0.400411			0.200206	−	0.979754i	$-0.435839\pi$
$41$	9.03467e18			0.400411			0.200206	+	0.979754i	$0.435839\pi$
$42$	5.13058e18	−	1.89869e19i	0.170284	−	0.630177i
$43$			4.53303e19i			1.13440i	0.823580	+	0.567201i	$0.191974\pi$
$43$			4.53303e19i			1.13440i	−0.823580	+	0.567201i	$0.808026\pi$
$44$	−6.08458e18	+	1.04366e19i	−0.115558	+	0.198211i
$45$	9.16387e19			1.32901
$46$	1.75487e19	+	4.74197e18i	0.195502	+	0.0528280i
$47$		−	1.32515e20i		−	1.14048i	−0.821477	−	0.570242i	$-0.806849\pi$
$47$		−	1.32515e20i		−	1.14048i	0.821477	−	0.570242i	$-0.193151\pi$
$48$	−4.74923e19	+	2.68867e19i	−0.317489	+	0.179739i
$49$	−4.21742e20			−2.20137
$50$	−8.59966e19	+	3.18251e20i	−0.352242	+	1.30355i
$51$		−	1.40488e20i		−	0.453728i
$52$	1.64499e20	+	9.59032e19i	0.420845	+	0.245354i
$53$	2.48218e20			0.505269			0.252635	−	0.967562i	$-0.418703\pi$
$53$	2.48218e20			0.505269			0.252635	+	0.967562i	$0.418703\pi$
$54$	−4.04240e20	−	1.09232e20i	−0.657528	−	0.177675i
$55$		−	2.69512e20i		−	0.351743i
$56$	1.19574e21	+	1.21101e21i	1.25713	+	1.27318i
$57$	−3.86924e20			−0.328948
$58$	−2.16789e19	+	8.02277e19i	−0.0149589	+	0.0553590i
$59$		−	3.17904e21i		−	1.78679i	−0.449276	−	0.893393i	$-0.648318\pi$
$59$		−	3.17904e21i		−	1.78679i	0.449276	−	0.893393i	$-0.351682\pi$
$60$	6.13212e20	−	1.05182e21i	0.281706	−	0.483198i
$61$	2.83808e21			1.06922			0.534610	−	0.845099i	$-0.320458\pi$
$61$	2.83808e21			1.06922			0.534610	+	0.845099i	$0.320458\pi$
$62$	−1.93788e21	−	5.23647e20i	−0.600657	−	0.162307i
$63$			6.06347e21i			1.55108i
$64$	5.99104e19	−	4.72199e21i	0.0126865	−	0.999920i
$65$	−4.24795e21			−0.746826
$66$	−1.49175e20	+	5.52058e20i	−0.0218358	+	0.0808086i
$67$			8.09517e21i			0.989301i	0.869092	+	0.494651i	$0.164704\pi$
$67$			8.09517e21i			0.989301i	−0.869092	+	0.494651i	$0.835296\pi$
$68$	1.05020e22	+	6.12267e21i	1.07439	+	0.626374i
$69$	8.60483e20			0.0738845
$70$	−3.66525e22	−	9.90412e21i	−2.64806	−	0.715549i
$71$			7.22794e21i			0.440468i	0.975447	+	0.220234i	$0.0706821\pi$
$71$			7.22794e21i			0.440468i	−0.975447	+	0.220234i	$0.929318\pi$
$72$	1.19723e22	−	1.18214e22i	0.616863	−	0.609086i
$73$	2.43394e21			0.106276			0.0531380	−	0.998587i	$-0.483078\pi$
$73$	2.43394e21			0.106276			0.0531380	+	0.998587i	$0.483078\pi$
$74$	−1.07099e20	+	3.96346e20i	−0.00397197	+	0.0146992i
$75$			1.56051e22i			0.492640i
$76$	1.68628e22	−	2.89240e22i	0.454115	−	0.778924i
$77$	1.78328e22			0.410517
$78$	8.70135e21	+	2.35125e21i	0.171574	+	0.0463622i
$79$		−	8.02491e22i		−	1.35805i	−0.734116	−	0.679024i	$-0.762403\pi$
$79$		−	8.02491e22i		−	1.35805i	0.734116	−	0.679024i	$-0.237597\pi$
$80$	5.19024e22	+	9.16796e22i	0.755279	+	1.33411i
$81$	4.93277e22			0.618401
$82$	−9.65342e21	+	3.57247e22i	−0.104452	+	0.386547i
$83$		−	5.98824e22i		−	0.560224i	−0.959967	−	0.280112i	$-0.909628\pi$
$83$		−	5.98824e22i		−	0.560224i	0.959967	−	0.280112i	$-0.0903716\pi$
$84$	6.95957e22	+	4.05745e22i	0.563937	+	0.328777i
$85$	−2.71199e23			−1.90660
$86$	−1.79244e23	−	4.84348e22i	−1.09512	−	0.295921i
$87$			3.93387e21i			0.0209213i
$88$	−3.47670e22	−	3.52109e22i	−0.161204	−	0.163262i
$89$	1.56264e23			0.632671			0.316336	−	0.948647i	$-0.397547\pi$
$89$	1.56264e23			0.632671			0.316336	+	0.948647i	$0.397547\pi$
$90$	−9.79147e22	+	3.62356e23i	−0.346687	+	1.28300i
$91$		−	2.81075e23i		−	0.871616i
$92$	−3.75012e22	+	6.43242e22i	−0.101998	+	0.174953i
$93$	−9.50217e22			−0.227001
$94$	5.23987e23	+	1.41590e23i	1.10100	+	0.297508i
$95$			7.46923e23i			1.38227i
$96$	−5.55700e22	−	2.16521e23i	−0.0906955	−	0.353383i
$97$	2.43631e23			0.351133			0.175566	−	0.984468i	$-0.443824\pi$
$97$	2.43631e23			0.351133			0.175566	+	0.984468i	$0.443824\pi$
$98$	4.50625e23	−	1.66764e24i	0.574252	−	2.12515i
$99$		−	1.76300e23i		−	0.198898i
$100$	−1.16653e24	−	6.80093e23i	−1.16653	−	0.680093i
$101$	1.26417e24			1.12189			0.560943	−	0.827855i	$-0.310439\pi$
$101$	1.26417e24			1.12189			0.560943	+	0.827855i	$0.310439\pi$
$102$	5.55513e23	+	1.50109e23i	0.438019	+	0.118360i
$103$			1.05068e24i			0.736926i	0.929642	+	0.368463i	$0.120116\pi$
$103$			1.05068e24i			0.736926i	−0.929642	+	0.368463i	$0.879884\pi$
$104$	−5.54983e23	+	5.47986e23i	−0.346641	+	0.342271i
$105$	−1.79721e24			−1.00076
$106$	−2.65217e23	+	9.81499e23i	−0.131805	+	0.487775i
$107$			1.04580e24i			0.464350i	0.972674	+	0.232175i	$0.0745842\pi$
$107$			1.04580e24i			0.464350i	−0.972674	+	0.232175i	$0.925416\pi$
$108$	8.63850e23	−	1.48173e24i	0.343047	−	0.588413i
$109$	1.69869e24			0.603945			0.301972	−	0.953317i	$-0.402355\pi$
$109$	1.69869e24			0.603945			0.301972	+	0.953317i	$0.402355\pi$
$110$	1.06570e24	+	2.87970e23i	0.339564	+	0.0917560i
$111$			1.94344e22i			0.00555513i
$112$	−6.06618e24	+	3.43423e24i	−1.55704	+	0.881481i
$113$	−4.13350e24			−0.953622			−0.476811	−	0.879006i	$-0.658207\pi$
$113$	−4.13350e24			−0.953622			−0.476811	+	0.879006i	$0.658207\pi$
$114$	4.13423e23	−	1.52997e24i	0.0858098	−	0.317559i
$115$		−	1.66108e24i		−	0.310469i
$116$	−2.94071e23	−	1.71444e23i	−0.0495401	−	0.0288820i
$117$	−2.77878e24			−0.422302
$118$	1.25705e25	+	3.39677e24i	1.72492	+	0.466102i
$119$		−	1.79444e25i		−	2.22519i
$120$	3.50387e24	+	3.54860e24i	0.392982	+	0.397999i
$121$	9.33123e24			0.947359
$122$	−3.03245e24	+	1.12223e25i	−0.278918	+	1.03220i
$123$			1.75172e24i			0.146084i
$124$	4.14119e24	−	7.10321e24i	0.313376	−	0.537520i
$125$	7.81503e24			0.537045
$126$	−2.39761e25	−	6.47873e24i	−1.49738	−	0.404616i
$127$			1.80124e25i			1.02312i	0.859248	+	0.511560i	$0.170932\pi$
$127$			1.80124e25i			1.02312i	−0.859248	+	0.511560i	$0.829068\pi$
$128$	1.86076e25	+	5.28227e24i	0.961989	+	0.273087i
$129$	−8.78903e24			−0.413870
$130$	4.53888e24	−	1.67972e25i	0.194818	−	0.720968i
$131$		−	1.16233e25i		−	0.455065i	−0.973771	−	0.227532i	$-0.926934\pi$
$131$		−	1.16233e25i		−	0.455065i	0.973771	−	0.227532i	$-0.0730658\pi$
$132$	−2.02355e24	−	1.17973e24i	−0.0723146	−	0.0421596i
$133$	−4.94217e25			−1.61324
$134$	−3.20098e25	−	8.64958e24i	−0.955048	−	0.258070i
$135$			3.82635e25i			1.04419i
$136$	−3.54313e25	+	3.49847e25i	−0.884954	+	0.873797i
$137$	5.72851e25			1.31037			0.655186	−	0.755467i	$-0.272590\pi$
$137$	5.72851e25			1.31037			0.655186	+	0.755467i	$0.272590\pi$
$138$	−9.19414e23	+	3.40251e24i	−0.0192736	+	0.0713263i
$139$			5.65058e25i			1.08621i	0.839663	+	0.543107i	$0.182752\pi$
$139$			5.65058e25i			1.08621i	−0.839663	+	0.543107i	$0.817248\pi$
$140$	7.83254e25	−	1.34348e26i	1.38155	−	2.36971i
$141$	2.56931e25			0.416090
$142$	−2.85806e25	−	7.72296e24i	−0.425217	−	0.114901i
$143$			8.17246e24i			0.111769i
$144$	3.39517e25	+	5.99718e25i	0.427082	+	0.754392i
$145$	7.59399e24			0.0879131
$146$	−2.60063e24	+	9.62423e24i	−0.0277233	+	0.102596i
$147$		−	8.17710e25i		−	0.803140i
$148$	−1.45279e24	−	8.46980e23i	−0.0131541	−	0.00766889i
$149$	5.90844e25			0.493443			0.246722	−	0.969086i	$-0.420647\pi$
$149$	5.90844e25			0.493443			0.246722	+	0.969086i	$0.420647\pi$
$150$	−6.17052e25	−	1.66738e25i	−0.475583	−	0.128511i
$151$		−	2.49594e26i		−	1.77628i	−0.459575	−	0.888139i	$-0.651998\pi$
$151$		−	2.49594e26i		−	1.77628i	0.459575	−	0.888139i	$-0.348002\pi$
$152$	9.63531e25	+	9.75833e25i	0.633494	+	0.641583i
$153$	−1.77403e26			−1.07811
$154$	−1.90541e25	+	7.05142e25i	−0.107088	+	0.396304i
$155$			1.83431e26i			0.953876i
$156$	−1.85945e25	+	3.18944e25i	−0.0895139	+	0.153539i
$157$	−1.35514e26			−0.604212			−0.302106	−	0.953274i	$-0.597690\pi$
$157$	−1.35514e26			−0.604212			−0.302106	+	0.953274i	$0.597690\pi$
$158$	3.17319e26	+	8.57450e25i	1.31103	+	0.354261i
$159$			4.81267e25i			0.184340i
$160$	−4.17975e26	+	1.07273e26i	−1.48495	+	0.381110i
$161$	1.09909e26			0.362346
$162$	−5.27059e25	+	1.95051e26i	−0.161317	+	0.596990i
$163$		−	2.30376e26i		−	0.654917i	−0.944866	−	0.327458i	$-0.893808\pi$
$163$		−	2.30376e26i		−	0.654917i	0.944866	−	0.327458i	$-0.106192\pi$
$164$	−1.30948e26	−	7.63428e25i	−0.345916	−	0.201670i
$165$	5.22553e25			0.128328
$166$	2.36786e26	+	6.39835e25i	0.540827	+	0.146141i
$167$		−	4.45920e26i		−	0.947674i	−0.880613	−	0.473837i	$-0.842869\pi$
$167$		−	4.45920e26i		−	0.947674i	0.880613	−	0.473837i	$-0.157131\pi$
$168$	−2.34801e26	+	2.31841e26i	−0.464503	+	0.458647i
$169$	−4.13989e26			−0.762691
$170$	2.89772e26	−	1.07237e27i	0.497358	−	1.84059i
$171$			4.88596e26i			0.781621i
$172$	3.83040e26	−	6.57012e26i	0.571350	−	0.980013i
$173$	1.19303e27			1.65997			0.829984	−	0.557787i	$-0.188349\pi$
$173$	1.19303e27			1.65997			0.829984	+	0.557787i	$0.188349\pi$
$174$	−1.55552e25	−	4.20329e24i	−0.0201970	−	0.00545756i
$175$			1.99323e27i			2.41602i
$176$	1.76379e26	−	9.98528e25i	0.199661	−	0.113034i
$177$	6.16381e26			0.651884
$178$	−1.66966e26	+	6.17895e26i	−0.165039	+	0.610766i
$179$		−	1.36574e27i		−	1.26221i	−0.775697	−	0.631105i	$-0.782602\pi$
$179$		−	1.36574e27i		−	1.26221i	0.775697	−	0.631105i	$-0.217398\pi$
$180$	−1.32820e27	−	7.74345e26i	−1.14814	−	0.669367i
$181$	−1.53542e27			−1.24190			−0.620948	−	0.783852i	$-0.713252\pi$
$181$	−1.53542e27			−1.24190			−0.620948	+	0.783852i	$0.713252\pi$
$182$	1.11142e27	+	3.00325e26i	0.841438	+	0.227371i
$183$			5.50273e26i			0.390090i
$184$	−2.14280e26	−	2.17016e26i	−0.142288	−	0.144105i
$185$	3.75163e25			0.0233431
$186$	1.01529e26	−	3.75733e26i	0.0592156	−	0.219141i
$187$			5.21748e26i			0.285339i
$188$	−1.11975e27	+	1.92065e27i	−0.574414	+	0.985268i
$189$	−2.53179e27			−1.21867
$190$	−2.95347e27	−	7.98076e26i	−1.33441	−	0.360580i
$191$		−	8.58551e26i		−	0.364222i	−0.983278	−	0.182111i	$-0.941707\pi$
$191$		−	8.58551e26i		−	0.364222i	0.983278	−	0.182111i	$-0.0582930\pi$
$192$	9.15540e26	+	1.16160e25i	0.364807	+	0.00462850i
$193$	4.66261e27			1.74559			0.872793	−	0.488090i	$-0.162306\pi$
$193$	4.66261e27			1.74559			0.872793	+	0.488090i	$0.162306\pi$
$194$	−2.60316e26	+	9.63360e26i	−0.0915968	+	0.338975i
$195$		−	8.23631e26i		−	0.272469i
$196$	6.11268e27	+	3.56371e27i	1.90177	+	1.10874i
$197$	−2.52221e27			−0.738222			−0.369111	−	0.929385i	$-0.620338\pi$
$197$	−2.52221e27			−0.738222			−0.369111	+	0.929385i	$0.620338\pi$
$198$	6.97121e26	+	1.88374e26i	0.192011	+	0.0518846i
$199$		−	6.79518e27i		−	1.76183i	−0.473273	−	0.880916i	$-0.656928\pi$
$199$		−	6.79518e27i		−	1.76183i	0.473273	−	0.880916i	$-0.343072\pi$
$200$	3.93564e27	−	3.88602e27i	0.960849	−	0.948735i
$201$	−1.56956e27			−0.360933
$202$	−1.35075e27	+	4.99875e27i	−0.292656	+	1.08304i
$203$			5.02472e26i			0.102603i
$204$	−1.18712e27	+	2.03621e27i	−0.228524	+	0.391977i
$205$	3.38154e27			0.613859
$206$	−4.15458e27	−	1.12264e27i	−0.711411	−	0.192235i
$207$		−	1.08659e27i		−	0.175558i
$208$	−1.57385e27	−	2.78002e27i	−0.239995	−	0.423924i
$209$	1.43697e27			0.206868
$210$	1.92030e27	−	7.10651e27i	0.261058	−	0.966106i
$211$			4.14619e27i			0.532426i	0.963914	+	0.266213i	$0.0857725\pi$
$211$			4.14619e27i			0.532426i	−0.963914	+	0.266213i	$0.914228\pi$
$212$	−3.59764e27	−	2.09744e27i	−0.436504	−	0.254483i
$213$	−1.40142e27			−0.160699
$214$	−4.13530e27	−	1.11743e27i	−0.448272	−	0.121131i
$215$			1.69664e28i			1.73912i
$216$	4.93600e27	+	4.99902e27i	0.478553	+	0.484663i
$217$	−1.21371e28			−1.11326
$218$	−1.81503e27	+	6.71694e27i	−0.157546	+	0.583034i
$219$			4.71913e26i			0.0387733i
$220$	−2.27737e27	+	3.90627e27i	−0.177158	+	0.303872i
$221$	8.22361e27			0.605836
$222$	−7.68470e25	−	2.07653e25i	−0.00536280	−	0.00144912i
$223$		−	3.05138e27i		−	0.201761i	−0.994899	−	0.100881i	$-0.967834\pi$
$223$		−	3.05138e27i		−	0.201761i	0.994899	−	0.100881i	$-0.0321660\pi$
$224$	−7.09794e27	−	2.76562e28i	−0.444791	−	1.73307i
$225$	1.97056e28			1.17057
$226$	4.41659e27	−	1.63446e28i	0.248763	−	0.920604i
$227$			1.18793e28i			0.634571i	0.948330	+	0.317285i	$0.102771\pi$
$227$			1.18793e28i			0.634571i	−0.948330	+	0.317285i	$0.897229\pi$
$228$	5.60804e27	+	3.26950e27i	0.284180	+	0.165677i
$229$	−2.06279e28			−0.991814			−0.495907	−	0.868376i	$-0.665164\pi$
$229$	−2.06279e28			−0.991814			−0.495907	+	0.868376i	$0.665164\pi$
$230$	6.56823e27	+	1.77485e27i	0.299719	+	0.0809891i
$231$			3.45758e27i			0.149771i
$232$	9.92133e26	−	9.79625e26i	0.0408051	−	0.0402906i
$233$	5.02642e27			0.196331			0.0981653	−	0.995170i	$-0.468703\pi$
$233$	5.02642e27			0.196331			0.0981653	+	0.995170i	$0.468703\pi$
$234$	2.96909e27	−	1.09878e28i	0.110162	−	0.407681i
$235$		−	4.95982e28i		−	1.74844i
$236$	−2.68629e28	+	4.60767e28i	−0.899929	+	1.54361i
$237$	1.55594e28			0.495464
$238$	7.09556e28	+	1.91734e28i	2.14814	+	0.580464i
$239$		−	2.91320e28i		−	0.838678i	−0.907830	−	0.419339i	$-0.862262\pi$
$239$		−	2.91320e28i		−	0.838678i	0.907830	−	0.419339i	$-0.137738\pi$
$240$	−1.77757e28	+	1.00633e28i	−0.486733	+	0.275553i
$241$	5.47767e28			1.42689			0.713447	−	0.700709i	$-0.247133\pi$
$241$	5.47767e28			1.42689			0.713447	+	0.700709i	$0.247133\pi$
$242$	−9.97029e27	+	3.68974e28i	−0.247129	+	0.914558i
$243$			3.84371e28i			0.906725i
$244$	−4.11349e28	−	2.39817e28i	−0.923703	−	0.538521i
$245$	−1.57852e29			−3.37486
$246$	−6.92663e27	−	1.87169e27i	−0.141026	−	0.0381077i
$247$		−	2.26491e28i		−	0.439225i
$248$	2.36626e28	+	2.39647e28i	0.437162	+	0.442743i
$249$	1.16105e28			0.204390
$250$	−8.35026e27	+	3.09021e28i	−0.140094	+	0.518451i
$251$			1.94301e28i			0.310735i	0.987857	+	0.155368i	$0.0496562\pi$
$251$			1.94301e28i			0.310735i	−0.987857	+	0.155368i	$0.950344\pi$
$252$	5.12362e28	−	8.78832e28i	0.781214	−	1.33998i
$253$	−3.19569e27			−0.0464642
$254$	−7.12243e28	−	1.92460e28i	−0.987696	−	0.266892i
$255$		−	5.25824e28i		−	0.695598i
$256$	−4.07690e28	+	6.79337e28i	−0.514577	+	0.857444i
$257$	1.05899e29			1.27555			0.637773	−	0.770224i	$-0.279856\pi$
$257$	1.05899e29			1.27555			0.637773	+	0.770224i	$0.279856\pi$
$258$	9.39096e27	−	3.47534e28i	0.107963	−	0.399541i
$259$			2.48235e27i			0.0272436i
$260$	6.15694e28	+	3.58951e28i	0.645185	+	0.376145i
$261$	4.96757e27			0.0497116
$262$	4.59606e28	+	1.24193e28i	0.439309	+	0.118709i
$263$			1.64096e29i			1.49840i	0.662343	+	0.749201i	$0.269562\pi$
$263$			1.64096e29i			1.49840i	−0.662343	+	0.749201i	$0.730438\pi$
$264$	6.82701e27	−	6.74094e27i	0.0595639	−	0.0588130i
$265$	9.29042e28			0.774613
$266$	5.28064e28	−	1.95422e29i	0.420830	−	1.55738i
$267$			3.02978e28i			0.230821i
$268$	6.84040e28	−	1.17331e29i	0.498269	−	0.854660i
$269$	−9.71636e27			−0.0676825			−0.0338412	−	0.999427i	$-0.510774\pi$
$269$	−9.71636e27			−0.0676825			−0.0338412	+	0.999427i	$0.510774\pi$
$270$	−1.51301e29	−	4.08840e28i	−1.00804	−	0.272388i
$271$			4.33237e28i			0.276118i	0.990424	+	0.138059i	$0.0440863\pi$
$271$			4.33237e28i			0.276118i	−0.990424	+	0.138059i	$0.955914\pi$
$272$	−1.00478e29	−	1.77483e29i	−0.612693	−	1.08225i
$273$	5.44973e28			0.317997
$274$	−6.12083e28	+	2.26516e29i	−0.341825	+	1.26500i
$275$		−	5.79546e28i		−	0.309810i
$276$	−1.24717e28	−	7.27106e27i	−0.0638290	−	0.0372125i
$277$	−3.24171e29			−1.58861			−0.794305	−	0.607520i	$-0.792165\pi$
$277$	−3.24171e29			−1.58861			−0.794305	+	0.607520i	$0.792165\pi$
$278$	−2.23434e29	−	6.03757e28i	−1.04861	−	0.283351i
$279$			1.19990e29i			0.539381i
$280$	4.47548e29	+	4.53262e29i	1.92727	+	1.95188i
$281$	3.64011e28			0.150189			0.0750946	−	0.997176i	$-0.476074\pi$
$281$	3.64011e28			0.150189			0.0750946	+	0.997176i	$0.476074\pi$
$282$	−2.74527e28	+	1.01595e29i	−0.108542	+	0.401683i
$283$		−	3.18947e29i		−	1.20860i	−0.796758	−	0.604299i	$-0.793453\pi$
$283$		−	3.18947e29i		−	1.20860i	0.796758	−	0.604299i	$-0.206547\pi$
$284$	6.10759e28	−	1.04761e29i	0.221845	−	0.380522i
$285$	−1.44820e29			−0.504301
$286$	−3.23154e28	−	8.73216e27i	−0.107899	−	0.0291561i
$287$			2.23747e29i			0.716431i
$288$	−2.73416e29	+	7.01721e28i	−0.839681	+	0.215504i
$289$	1.85565e29			0.546665
$290$	−8.11407e27	+	3.00280e28i	−0.0229331	+	0.0848693i
$291$			4.72373e28i			0.128106i
$292$	−3.52772e28	−	2.05667e28i	−0.0918122	−	0.0535267i
$293$	3.12973e29			0.781799			0.390899	−	0.920433i	$-0.372164\pi$
$293$	3.12973e29			0.781799			0.390899	+	0.920433i	$0.372164\pi$
$294$	3.23337e29	+	8.73712e28i	0.775332	+	0.209508i
$295$		−	1.18987e30i		−	2.73927i
$296$	4.90140e27	−	4.83961e27i	0.0108348	−	0.0106982i
$297$	7.36136e28			0.156272
$298$	−6.31308e28	+	2.33630e29i	−0.128720	+	0.476359i
$299$			5.03694e28i			0.0986535i
$300$	1.31862e29	−	2.26178e29i	0.248122	−	0.425594i
$301$	−1.12262e30			−2.02971
$302$	9.86940e29	+	2.66688e29i	1.71478	+	0.463361i
$303$			2.45108e29i			0.409304i
$304$	−4.88814e29	+	2.76731e29i	−0.784623	+	0.444196i
$305$	1.06225e30			1.63919
$306$	1.89553e29	−	7.01485e29i	0.281238	−	1.04079i
$307$			2.32663e29i			0.331945i	0.986130	+	0.165972i	$0.0530763\pi$
$307$			2.32663e29i			0.331945i	−0.986130	+	0.165972i	$0.946924\pi$
$308$	−2.58467e29	−	1.50687e29i	−0.354647	−	0.206760i
$309$	−2.03715e29			−0.268857
$310$	−7.25319e29	−	1.95993e29i	−0.920849	−	0.248829i
$311$			3.34060e29i			0.408037i	0.978967	+	0.204019i	$0.0654003\pi$
$311$			3.34060e29i			0.408037i	−0.978967	+	0.204019i	$0.934600\pi$
$312$	−1.06248e29	−	1.07605e29i	−0.124873	−	0.126467i
$313$	9.52149e29			1.07689			0.538447	−	0.842659i	$-0.319011\pi$
$313$	9.52149e29			1.07689			0.538447	+	0.842659i	$0.319011\pi$
$314$	1.44795e29	−	5.35848e29i	0.157615	−	0.583292i
$315$			2.26946e30i			2.37792i
$316$	−6.78103e29	+	1.16312e30i	−0.683991	+	1.17322i
$317$	−1.44546e30			−1.40376			−0.701881	−	0.712294i	$-0.747656\pi$
$317$	−1.44546e30			−1.40376			−0.701881	+	0.712294i	$0.747656\pi$
$318$	−1.90302e29	−	5.14227e28i	−0.177958	−	0.0480872i
$319$		−	1.46098e28i		−	0.0131569i
$320$	2.24236e28	−	1.76737e30i	0.0194493	−	1.53295i
$321$	−2.02770e29			−0.169411
$322$	−1.17436e29	+	4.34601e29i	−0.0945219	+	0.349800i
$323$		−	1.44597e30i		−	1.12132i
$324$	−7.14950e29	−	4.16818e29i	−0.534239	−	0.311463i
$325$	−9.13461e29			−0.657794
$326$	9.10949e29	+	2.46154e29i	0.632241	+	0.170842i
$327$			3.29358e29i			0.220341i
$328$	4.41789e29	−	4.36219e29i	0.284924	−	0.281332i
$329$	3.28177e30			2.04060
$330$	−5.58341e28	+	2.06627e29i	−0.0334759	+	0.123885i
$331$		−	1.57998e30i		−	0.913514i	−0.889591	−	0.456757i	$-0.849011\pi$
$331$		−	1.57998e30i		−	0.913514i	0.889591	−	0.456757i	$-0.150989\pi$
$332$	−5.06005e29	+	8.67928e29i	−0.282161	+	0.483979i
$333$	2.45411e28			0.0131997
$334$	1.76325e30	+	4.76459e29i	0.914862	+	0.247211i
$335$			3.02990e30i			1.51667i
$336$	−6.65859e29	−	1.17616e30i	−0.321596	−	0.568063i
$337$	−1.45755e30			−0.679303			−0.339651	−	0.940551i	$-0.610309\pi$
$337$	−1.45755e30			−0.679303			−0.339651	+	0.940551i	$0.610309\pi$
$338$	4.42342e29	−	1.63699e30i	0.198956	−	0.736284i
$339$		−	8.01439e29i		−	0.347916i
$340$	3.93072e30	+	2.29162e30i	1.64712	+	0.960276i
$341$	3.52895e29			0.142755
$342$	−1.93200e30	−	5.22058e29i	−0.754559	−	0.203894i
$343$		−	5.70001e30i		−	2.14954i
$344$	2.18867e30	+	2.21662e30i	0.797038	+	0.807215i
$345$	3.22066e29			0.113270
$346$	−1.27474e30	+	4.71748e30i	−0.433021	+	1.60249i
$347$		−	1.66816e30i		−	0.547372i	−0.961819	−	0.273686i	$-0.911757\pi$
$347$		−	1.66816e30i		−	0.547372i	0.961819	−	0.273686i	$-0.0882430\pi$
$348$	3.32411e28	−	5.70171e28i	0.0105372	−	0.0180740i
$349$	−1.34472e30			−0.411839			−0.205919	−	0.978569i	$-0.566018\pi$
$349$	−1.34472e30			−0.411839			−0.205919	+	0.978569i	$0.566018\pi$
$350$	−7.88159e30	−	2.12974e30i	−2.33237	−	0.630245i
$351$		−	1.16027e30i		−	0.331799i
$352$	2.06378e29	+	8.04124e29i	0.0570363	+	0.222234i
$353$	−5.79218e30			−1.54720			−0.773599	−	0.633676i	$-0.781545\pi$
$353$	−5.79218e30			−1.54720			−0.773599	+	0.633676i	$0.781545\pi$
$354$	−6.58595e29	+	2.43728e30i	−0.170051	+	0.629313i
$355$			2.70531e30i			0.675269i
$356$	−2.26487e30	−	1.32042e30i	−0.546567	−	0.318650i
$357$	3.47922e30			0.811828
$358$	5.40038e30	+	1.45927e30i	1.21851	+	0.329261i
$359$			7.40160e30i			1.61507i	0.589818	+	0.807536i	$0.299200\pi$
$359$			7.40160e30i			1.61507i	−0.589818	+	0.807536i	$0.700800\pi$
$360$	4.48106e30	−	4.42457e30i	0.945695	−	0.933773i
$361$	9.16348e29			0.187057
$362$	1.64058e30	−	6.07135e30i	0.323962	−	1.19890i
$363$			1.80922e30i			0.345631i
$364$	−2.37508e30	+	4.07387e30i	−0.438996	+	0.752992i
$365$	9.10986e29			0.162929
$366$	−2.17588e30	−	5.87959e29i	−0.376584	−	0.101759i
$367$		−	6.64670e30i		−	1.11330i	−0.830746	−	0.556651i	$-0.812086\pi$
$367$		−	6.64670e30i		−	1.11330i	0.830746	−	0.556651i	$-0.187914\pi$
$368$	1.08708e30	−	6.15424e29i	0.176233	−	0.0997701i
$369$	2.21202e30			0.347114
$370$	−4.00856e28	+	1.48346e29i	−0.00608931	+	0.0225349i
$371$			6.14721e30i			0.904047i
$372$	1.37723e30	+	8.02931e29i	0.196107	+	0.114331i
$373$	5.19114e30			0.715742			0.357871	−	0.933771i	$-0.383503\pi$
$373$	5.19114e30			0.715742			0.357871	+	0.933771i	$0.383503\pi$
$374$	−2.06309e30	−	5.57480e29i	−0.275460	−	0.0744338i
$375$			1.51525e30i			0.195933i
$376$	−6.39817e30	−	6.47987e30i	−0.801312	−	0.811544i
$377$	−2.30274e29			−0.0279350
$378$	2.70518e30	−	1.00111e31i	0.317903	−	1.17647i
$379$		−	8.29858e30i		−	0.944786i	−0.881388	−	0.472393i	$-0.843390\pi$
$379$		−	8.29858e30i		−	0.944786i	0.881388	−	0.472393i	$-0.156610\pi$
$380$	6.31148e30	−	1.08258e31i	0.696190	−	1.19415i
$381$	−3.49240e30			−0.373271
$382$	3.39487e30	+	9.17350e29i	0.351611	+	0.0950112i
$383$			1.01279e31i			1.01656i	0.861191	+	0.508281i	$0.169719\pi$
$383$			1.01279e31i			1.01656i	−0.861191	+	0.508281i	$0.830281\pi$
$384$	−1.02417e30	+	3.60780e30i	−0.0996320	+	0.350968i
$385$	6.67455e30			0.629352
$386$	−4.98193e30	+	1.84368e31i	−0.455355	+	1.68515i
$387$			1.10985e31i			0.983406i
$388$	−3.53116e30	−	2.05867e30i	−0.303345	−	0.176851i
$389$	−8.77832e30			−0.731166			−0.365583	−	0.930779i	$-0.619130\pi$
$389$	−8.77832e30			−0.731166			−0.365583	+	0.930779i	$0.619130\pi$
$390$	3.25678e30	+	8.80038e29i	0.263035	+	0.0710765i
$391$			3.21569e30i			0.251857i
$392$	−2.06229e31	+	2.03629e31i	−1.56645	+	1.54670i
$393$	2.25362e30			0.166024
$394$	2.69495e30	−	9.97329e30i	0.192573	−	0.712662i
$395$		−	3.00360e31i		−	2.08198i
$396$	−1.48973e30	+	2.55527e30i	−0.100176	+	0.171828i
$397$	−1.02352e31			−0.667743			−0.333871	−	0.942619i	$-0.608355\pi$
$397$	−1.02352e31			−0.667743			−0.333871	+	0.942619i	$0.608355\pi$
$398$	2.68694e31	+	7.26056e30i	1.70083	+	0.459593i
$399$		−	9.58232e30i		−	0.588567i
$400$	1.11609e31	+	1.97144e31i	0.665239	+	1.17507i
$401$	−2.49862e31			−1.44533			−0.722665	−	0.691198i	$-0.757083\pi$
$401$	−2.49862e31			−1.44533			−0.722665	+	0.691198i	$0.757083\pi$
$402$	1.67706e30	−	6.20634e30i	0.0941532	−	0.348436i
$403$		−	5.56221e30i		−	0.303101i
$404$	−1.83227e31	−	1.06822e31i	−0.969200	−	0.565047i
$405$	1.84626e31			0.948053
$406$	−1.98687e30	−	5.36885e29i	−0.0990504	−	0.0267651i
$407$		−	7.21760e28i		−	0.00349349i
$408$	−6.78313e30	−	6.86974e30i	−0.318793	−	0.322863i
$409$	−2.13620e31			−0.974906			−0.487453	−	0.873149i	$-0.662074\pi$
$409$	−2.13620e31			−0.974906			−0.487453	+	0.873149i	$0.662074\pi$
$410$	−3.61313e30	+	1.33712e31i	−0.160132	+	0.592605i
$411$			1.11069e31i			0.478071i
$412$	8.87823e30	−	1.52284e31i	0.371159	−	0.636633i
$413$	7.87302e31			3.19698
$414$	4.29658e30	+	1.16101e30i	0.169480	+	0.0457963i
$415$		−	2.24131e31i		−	0.858863i
$416$	1.26743e31	−	3.25286e30i	0.471851	−	0.121100i
$417$	−1.09559e31			−0.396290
$418$	−1.53539e30	+	5.68205e30i	−0.0539638	+	0.199705i
$419$			1.58008e31i			0.539648i	0.962910	+	0.269824i	$0.0869656\pi$
$419$			1.58008e31i			0.539648i	−0.962910	+	0.269824i	$0.913034\pi$
$420$	2.60486e31	+	1.51864e31i	0.864556	+	0.504038i
$421$	1.16728e30			0.0376523			0.0188261	−	0.999823i	$-0.494007\pi$
$421$	1.16728e30			0.0376523			0.0188261	+	0.999823i	$0.494007\pi$
$422$	−1.63948e31	−	4.43014e30i	−0.513991	−	0.138889i
$423$		−	3.24444e31i		−	0.988680i
$424$	1.21377e31	−	1.19847e31i	0.359538	−	0.355006i
$425$	−5.83173e31			−1.67931
$426$	1.49739e30	−	5.54146e30i	0.0419200	−	0.155135i
$427$			7.02862e31i			1.91309i
$428$	8.83702e30	−	1.51578e31i	0.233873	−	0.401153i
$429$	−1.58455e30			−0.0407773
$430$	−6.70883e31	−	1.81284e31i	−1.67890	−	0.453668i
$431$			5.13923e31i			1.25075i	0.780324	+	0.625375i	$0.215054\pi$
$431$			5.13923e31i			1.25075i	−0.780324	+	0.625375i	$0.784946\pi$
$432$	−2.50411e31	+	1.41765e31i	−0.592718	+	0.335554i
$433$	4.38354e31			1.00918			0.504592	−	0.863358i	$-0.331643\pi$
$433$	4.38354e31			1.00918			0.504592	+	0.863358i	$0.331643\pi$
$434$	1.29683e31	−	4.79922e31i	0.290407	−	1.07472i
$435$			1.47239e30i			0.0320739i
$436$	−2.46207e31	−	1.43539e31i	−0.521750	−	0.304181i
$437$	8.85651e30			0.182594
$438$	−1.86603e30	−	5.04233e29i	−0.0374308	−	0.0101144i
$439$			3.05818e31i			0.596882i	0.954428	+	0.298441i	$0.0964665\pi$
$439$			3.05818e31i			0.596882i	−0.954428	+	0.298441i	$0.903533\pi$
$440$	−1.30128e31	−	1.31789e31i	−0.247137	−	0.250293i
$441$	−1.03258e32			−1.90836
$442$	−8.78682e30	+	3.25177e31i	−0.158039	+	0.584860i
$443$		−	5.66961e31i		−	0.992449i	−0.868194	−	0.496225i	$-0.834719\pi$
$443$		−	5.66961e31i		−	0.992449i	0.868194	−	0.496225i	$-0.165281\pi$
$444$	1.64220e29	−	2.81680e29i	0.00279789	−	0.00479910i
$445$	5.84871e31			0.969930
$446$	1.20657e31	+	3.26035e30i	0.194775	+	0.0526316i
$447$			1.14558e31i			0.180026i
$448$	1.16942e32	+	1.48370e30i	1.78909	+	0.0226992i
$449$	3.41900e31			0.509264			0.254632	−	0.967038i	$-0.418046\pi$
$449$	3.41900e31			0.509264			0.254632	+	0.967038i	$0.418046\pi$
$450$	−2.10551e31	+	7.79194e31i	−0.305357	+	1.13004i
$451$		−	6.50561e30i		−	0.0918691i
$452$	5.99105e31	+	3.49280e31i	0.823837	+	0.480299i
$453$	4.83935e31			0.648050
$454$	−4.69728e31	−	1.26928e31i	−0.612599	−	0.165535i
$455$		−	1.05202e32i		−	1.33625i
$456$	−1.89203e31	+	1.86818e31i	−0.234072	+	0.231121i
$457$	3.67398e30			0.0442734			0.0221367	−	0.999755i	$-0.492953\pi$
$457$	3.67398e30			0.0442734			0.0221367	+	0.999755i	$0.492953\pi$
$458$	2.20407e31	−	8.15666e31i	0.258725	−	0.957474i
$459$		−	7.40743e31i		−	0.847063i
$460$	−1.40361e31	+	2.40756e31i	−0.156370	+	0.268215i
$461$	4.41661e30			0.0479378			0.0239689	−	0.999713i	$-0.492370\pi$
$461$	4.41661e30			0.0479378			0.0239689	+	0.999713i	$0.492370\pi$
$462$	−1.36719e31	−	3.69438e30i	−0.144586	−	0.0390695i
$463$			1.06447e32i			1.09688i	0.836189	+	0.548442i	$0.184779\pi$
$463$			1.06447e32i			1.09688i	−0.836189	+	0.548442i	$0.815221\pi$
$464$	2.81353e30	+	4.96979e30i	0.0282512	+	0.0499025i
$465$	−3.55652e31			−0.348008
$466$	−5.37066e30	+	1.98754e31i	−0.0512150	+	0.189533i
$467$		−	1.75777e32i		−	1.63365i	−0.576883	−	0.816827i	$-0.695731\pi$
$467$		−	1.75777e32i		−	1.63365i	0.576883	−	0.816827i	$-0.304269\pi$
$468$	4.02753e31	+	2.34806e31i	0.364828	+	0.212696i
$469$	−2.00480e32			−1.77010
$470$	1.96120e32	+	5.29950e31i	1.68791	+	0.456101i
$471$		−	2.62747e31i		−	0.220438i
$472$	−1.53493e32	−	1.55453e32i	−1.25541	−	1.27144i
$473$	3.26410e31			0.260273
$474$	−1.66250e31	+	6.15247e31i	−0.129247	+	0.478310i
$475$			1.60615e32i			1.21748i
$476$	−1.51630e32	+	2.60085e32i	−1.12073	+	1.92234i
$477$	6.07729e31			0.438015
$478$	1.15193e32	+	3.11271e31i	0.809640	+	0.218778i
$479$		−	2.62105e31i		−	0.179659i	−0.995957	−	0.0898296i	$-0.971368\pi$
$479$		−	2.62105e31i		−	0.179659i	0.995957	−	0.0898296i	$-0.0286322\pi$
$480$	−2.07990e31	−	8.10406e31i	−0.139043	−	0.541761i
$481$	−1.13761e30			−0.00741744
$482$	−5.85282e31	+	2.16597e32i	−0.372221	+	1.37749i
$483$			2.13102e31i			0.132197i
$484$	−1.35246e32	−	7.88487e31i	−0.818426	−	0.477145i
$485$	9.11873e31			0.538311
$486$	−1.51987e32	−	4.10696e31i	−0.875331	−	0.236529i
$487$			1.67958e32i			0.943744i	0.881667	+	0.471872i	$0.156422\pi$
$487$			1.67958e32i			0.943744i	−0.881667	+	0.471872i	$0.843578\pi$
$488$	1.38780e32	−	1.37031e32i	0.760834	−	0.751242i
$489$	4.46673e31			0.238937
$490$	1.68662e32	−	6.24174e32i	0.880369	−	3.25801i
$491$			2.06726e32i			1.05298i	0.850183	+	0.526488i	$0.176491\pi$
$491$			2.06726e32i			1.05298i	−0.850183	+	0.526488i	$0.823509\pi$
$492$	1.48020e31	−	2.53893e31i	0.0735766	−	0.126203i
$493$	−1.47012e31			−0.0713164
$494$	8.95586e31	+	2.42002e31i	0.424018	+	0.114577i
$495$		−	6.59864e31i		−	0.304924i
$496$	−1.20044e32	+	6.79602e31i	−0.541452	+	0.306531i
$497$	−1.79003e32			−0.788102
$498$	−1.24057e31	+	4.59101e31i	−0.0533173	+	0.197313i
$499$			7.08999e31i			0.297467i	0.988877	+	0.148734i	$0.0475197\pi$
$499$			7.08999e31i			0.297467i	−0.988877	+	0.148734i	$0.952480\pi$
$500$	−1.13270e32	−	6.60369e31i	−0.463955	−	0.270487i
$501$	8.64588e31			0.345746
$502$	−7.68302e31	−	2.07608e31i	−0.299977	−	0.0810587i
$503$		−	2.66560e32i		−	1.01620i	−0.861298	−	0.508099i	$-0.830348\pi$
$503$		−	2.66560e32i		−	1.01620i	0.861298	−	0.508099i	$-0.169652\pi$
$504$	2.92761e32	+	2.96499e32i	1.08980	+	1.10372i
$505$	4.73159e32			1.71993
$506$	3.41455e30	−	1.26363e31i	0.0121207	−	0.0448555i
$507$		−	8.02679e31i		−	0.278257i
$508$	1.52204e32	−	2.61070e32i	0.515303	−	0.883877i
$509$	−2.56748e30			−0.00848973			−0.00424487	−	0.999991i	$-0.501351\pi$
$509$	−2.56748e30			−0.00848973			−0.00424487	+	0.999991i	$0.501351\pi$
$510$	2.07920e32	+	5.61835e31i	0.671513	+	0.181454i
$511$			6.02773e31i			0.190153i
$512$	−2.25061e32	−	2.33794e32i	−0.693523	−	0.720434i
$513$	−2.04012e32			−0.614112
$514$	−1.13152e32	+	4.18746e32i	−0.332740	+	1.23138i
$515$			3.93254e32i			1.12976i
$516$	1.27387e32	+	7.42671e31i	0.357544	+	0.208449i
$517$	−9.54199e31			−0.261669
$518$	−9.81564e30	−	2.65235e30i	−0.0263004	−	0.00710680i
$519$			2.31316e32i			0.605616i
$520$	−2.07722e32	+	2.05103e32i	−0.531425	+	0.524725i
$521$	−4.01252e32			−1.00315			−0.501574	−	0.865115i	$-0.667246\pi$
$521$	−4.01252e32			−1.00315			−0.501574	+	0.865115i	$0.667246\pi$
$522$	−5.30778e30	+	1.96427e31i	−0.0129678	+	0.0479904i
$523$		−	7.13294e32i		−	1.70313i	−0.524248	−	0.851566i	$-0.675653\pi$
$523$		−	7.13294e32i		−	1.70313i	0.524248	−	0.851566i	$-0.324347\pi$
$524$	−9.82165e31	+	1.68467e32i	−0.229197	+	0.393132i
$525$	−3.86465e32			−0.881451
$526$	−6.48864e32	−	1.75334e32i	−1.44652	−	0.390874i
$527$		−	3.55104e32i		−	0.773798i
$528$	1.93603e31	+	3.41978e31i	0.0412388	+	0.0728436i
$529$	4.60555e32			0.958988
$530$	−9.92669e31	+	3.67360e32i	−0.202066	+	0.747794i
$531$		−	7.78347e32i		−	1.54895i
$532$	7.16313e32	+	4.17612e32i	1.39368	+	0.812520i
$533$	−1.02539e32			−0.195058
$534$	−1.19803e32	−	3.23728e31i	−0.222829	−	0.0602122i
$535$			3.91429e32i			0.711881i
$536$	3.90858e32	+	3.95848e32i	0.695090	+	0.703965i
$537$	2.64802e32			0.460500
$538$	1.03818e31	−	3.84203e31i	0.0176557	−	0.0653391i
$539$			3.03684e32i			0.505076i
$540$	3.23326e32	−	5.54587e32i	0.525915	−	0.902080i
$541$	−9.97054e32			−1.58618			−0.793088	−	0.609107i	$-0.791528\pi$
$541$	−9.97054e32			−1.58618			−0.793088	+	0.609107i	$0.791528\pi$
$542$	−1.71310e32	−	4.62908e31i	−0.266557	−	0.0720283i
$543$		−	2.97702e32i		−	0.453089i
$544$	8.09157e32	−	2.07670e32i	1.20461	−	0.309162i
$545$	6.35795e32			0.925890
$546$	−5.82296e31	+	2.15492e32i	−0.0829530	+	0.306987i
$547$			8.77146e32i			1.22243i	0.791464	+	0.611215i	$0.209319\pi$
$547$			8.77146e32i			1.22243i	−0.791464	+	0.611215i	$0.790681\pi$
$548$	−8.30284e32	−	4.84058e32i	−1.13204	−	0.659979i
$549$	6.94867e32			0.926901
$550$	2.29163e32	+	6.19237e31i	0.299083	+	0.0808173i
$551$			4.04893e31i			0.0517037i
$552$	4.20770e31	−	4.15465e31i	0.0525746	−	0.0519118i
$553$	1.98740e33			2.42987
$554$	3.46372e32	−	1.28183e33i	0.414406	−	1.53361i
$555$			7.27399e30i			0.00851641i
$556$	4.77473e32	−	8.18990e32i	0.547081	−	0.938385i
$557$	−1.54101e33			−1.72799			−0.863997	−	0.503497i	$-0.832047\pi$
$557$	−1.54101e33			−1.72799			−0.863997	+	0.503497i	$0.832047\pi$
$558$	−4.74464e32	−	1.28208e32i	−0.520706	−	0.140703i
$559$		−	5.14477e32i		−	0.552617i
$560$	−2.27048e33	+	1.28538e33i	−2.38705	+	1.35137i
$561$	−1.01161e32			−0.104102
$562$	−3.88941e31	+	1.43937e32i	−0.0391785	+	0.144989i
$563$			7.04341e32i			0.694516i	0.937770	+	0.347258i	$0.112887\pi$
$563$			7.04341e32i			0.694516i	−0.937770	+	0.347258i	$0.887113\pi$
$564$	−3.72393e32	−	2.17106e32i	−0.359461	−	0.209567i
$565$	−1.54711e33			−1.46197
$566$	1.26118e33	+	3.40791e32i	1.16675	+	0.315276i
$567$			1.22162e33i			1.10647i
$568$	3.48985e32	+	3.53441e32i	0.309476	+	0.313427i
$569$	1.12962e32			0.0980813			0.0490406	−	0.998797i	$-0.484384\pi$
$569$	1.12962e32			0.0980813			0.0490406	+	0.998797i	$0.484384\pi$
$570$	1.54738e32	−	5.72644e32i	0.131552	−	0.486840i
$571$			4.43464e32i			0.369169i	0.982817	+	0.184584i	$0.0590939\pi$
$571$			4.43464e32i			0.369169i	−0.982817	+	0.184584i	$0.940906\pi$
$572$	6.90571e31	−	1.18451e32i	0.0562932	−	0.0965574i
$573$	1.66463e32			0.132881
$574$	−8.84736e32	−	2.39070e32i	−0.691625	−	0.186889i
$575$		−	3.57192e32i		−	0.273456i
$576$	1.46683e31	−	1.15612e33i	0.0109979	−	0.866825i
$577$	4.76894e32			0.350197			0.175098	−	0.984551i	$-0.443976\pi$
$577$	4.76894e32			0.350197			0.175098	+	0.984551i	$0.443976\pi$
$578$	−1.98273e32	+	7.33757e32i	−0.142604	+	0.527737i
$579$			9.04028e32i			0.636853i
$580$	−1.10066e32	−	6.41690e31i	−0.0759484	−	0.0442781i
$581$	1.48301e33			1.00237
$582$	−1.86785e32	−	5.04724e31i	−0.123670	−	0.0334178i
$583$		−	1.78735e32i		−	0.115927i
$584$	1.19018e32	−	1.17517e32i	0.0756237	−	0.0746703i
$585$	−1.04005e33			−0.647420
$586$	−3.34407e32	+	1.23755e33i	−0.203941	+	0.754730i
$587$		−	1.12430e33i		−	0.671778i	−0.941902	−	0.335889i	$-0.890963\pi$
$587$		−	1.12430e33i		−	0.671778i	0.941902	−	0.335889i	$-0.109037\pi$
$588$	−6.90963e32	+	1.18518e33i	−0.404508	+	0.693835i
$589$	−9.78010e32			−0.560996
$590$	4.70496e33	+	1.27136e33i	2.64443	+	0.714568i
$591$		−	4.89029e32i		−	0.269330i
$592$	1.38996e31	+	2.45521e31i	0.00750139	+	0.0132504i
$593$	−9.54143e32			−0.504612			−0.252306	−	0.967648i	$-0.581189\pi$
$593$	−9.54143e32			−0.504612			−0.252306	+	0.967648i	$0.581189\pi$
$594$	−7.86551e31	+	2.91082e32i	−0.0407652	+	0.150861i
$595$		−	6.71633e33i		−	3.41137i
$596$	−8.56362e32	−	4.99262e32i	−0.426287	−	0.248527i
$597$	1.31751e33			0.642779
$598$	−1.99170e32	−	5.38190e31i	−0.0952378	−	0.0257349i
$599$		−	4.00768e32i		−	0.187833i	−0.995580	−	0.0939163i	$-0.970061\pi$
$599$		−	4.00768e32i		−	0.187833i	0.995580	−	0.0939163i	$-0.0299386\pi$
$600$	7.53456e32	+	7.63076e32i	0.346133	+	0.350552i
$601$	6.35675e31			0.0286247			0.0143124	−	0.999898i	$-0.495444\pi$
$601$	6.35675e31			0.0286247			0.0143124	+	0.999898i	$0.495444\pi$
$602$	1.19950e33	−	4.43904e33i	0.529473	−	1.95944i
$603$			1.98200e33i			0.857620i
$604$	−2.10906e33	+	3.61759e33i	−0.894636	+	1.53453i
$605$	3.49254e33			1.45237
$606$	−9.69202e32	−	2.61895e32i	−0.395133	−	0.106771i
$607$			1.65365e33i			0.660966i	0.943812	+	0.330483i	$0.107212\pi$
$607$			1.65365e33i			0.660966i	−0.943812	+	0.330483i	$0.892788\pi$
$608$	−5.71954e32	−	2.22854e33i	−0.224139	−	0.873330i
$609$	−9.74237e31			−0.0374332
$610$	−1.13500e33	+	4.20034e33i	−0.427601	+	1.58244i
$611$			1.50398e33i			0.555580i
$612$	2.57126e33	+	1.49905e33i	0.931386	+	0.543000i
$613$	−5.09843e33			−1.81097			−0.905483	−	0.424382i	$-0.860491\pi$
$613$	−5.09843e33			−1.81097			−0.905483	+	0.424382i	$0.860491\pi$
$614$	−9.19990e32	−	2.48597e32i	−0.320452	−	0.0865915i
$615$			6.55643e32i			0.223958i
$616$	8.72012e32	−	8.61018e32i	0.292115	−	0.288432i
$617$	−1.67729e31			−0.00551044			−0.00275522	−	0.999996i	$-0.500877\pi$
$617$	−1.67729e31			−0.00551044			−0.00275522	+	0.999996i	$0.500877\pi$
$618$	2.17667e32	−	8.05527e32i	0.0701343	−	0.259548i
$619$			1.29014e32i			0.0407709i	0.999792	+	0.0203855i	$0.00648934\pi$
$619$			1.29014e32i			0.0407709i	−0.999792	+	0.0203855i	$0.993511\pi$
$620$	1.54999e33	−	2.65863e33i	0.480427	−	0.824056i
$621$	4.53704e32			0.137935
$622$	−1.32093e33	−	3.56939e32i	−0.393910	−	0.106441i
$623$			3.86993e33i			1.13200i
$624$	5.39015e32	−	3.05151e32i	0.154663	−	0.0875588i
$625$	−1.87220e33			−0.526978
$626$	−1.01736e33	+	3.76497e33i	−0.280920	+	1.03961i
$627$			2.78613e32i			0.0754729i
$628$	1.96413e33	+	1.14509e33i	0.521981	+	0.304316i
$629$	−7.26278e31			−0.0189363
$630$	−8.97387e33	−	2.42489e33i	−2.29559	−	0.620306i
$631$		−	6.78727e33i		−	1.70350i	−0.523947	−	0.851751i	$-0.675541\pi$
$631$		−	6.78727e33i		−	1.70350i	0.523947	−	0.851751i	$-0.324459\pi$
$632$	−3.87465e33	−	3.92412e33i	−0.954174	−	0.966356i
$633$	−8.03899e32			−0.194248
$634$	1.54445e33	−	5.71559e33i	0.366187	−	1.35516i
$635$			6.74176e33i			1.56852i
$636$	4.06669e32	−	6.97543e32i	0.0928445	−	0.159252i
$637$	4.78656e33			1.07238
$638$	5.77696e31	+	1.56103e31i	0.0127014	+	0.00343213i
$639$			1.76967e33i			0.381839i
$640$	6.96454e33	+	1.97708e33i	1.47480	+	0.418662i
$641$	8.81260e33			1.83150			0.915751	−	0.401745i	$-0.131596\pi$
$641$	8.81260e33			1.83150			0.915751	+	0.401745i	$0.131596\pi$
$642$	2.16657e32	−	8.01789e32i	0.0441928	−	0.163546i
$643$			5.83164e33i			1.16751i	0.811931	+	0.583753i	$0.198416\pi$
$643$			5.83164e33i			1.16751i	−0.811931	+	0.583753i	$0.801584\pi$
$644$	−1.59301e33	−	9.28730e32i	−0.313032	−	0.182498i
$645$	−3.28960e33			−0.634493
$646$	5.71762e33	+	1.54500e33i	1.08249	+	0.292508i
$647$		−	2.33961e33i		−	0.434803i	−0.976082	−	0.217401i	$-0.930242\pi$
$647$		−	2.33961e33i		−	0.434803i	0.976082	−	0.217401i	$-0.0697580\pi$
$648$	2.41209e33	−	2.38168e33i	0.440041	−	0.434493i
$649$	−2.28914e33			−0.409954
$650$	9.76020e32	−	3.61199e33i	0.171593	−	0.635018i
$651$		−	2.35325e33i		−	0.406158i
$652$	−1.94667e33	+	3.33905e33i	−0.329854	+	0.565785i
$653$	1.66590e32			0.0277135			0.0138567	−	0.999904i	$-0.495589\pi$
$653$	1.66590e32			0.0277135			0.0138567	+	0.999904i	$0.495589\pi$
$654$	−1.30234e33	−	3.51914e32i	−0.212712	−	0.0574783i
$655$		−	4.35042e33i		−	0.697647i
$656$	1.25284e33	+	2.21301e33i	0.197266	+	0.348447i
$657$	5.95917e32			0.0921301
$658$	−3.50653e33	+	1.29767e34i	−0.532312	+	1.96994i
$659$		−	1.15981e34i		−	1.72887i	−0.502743	−	0.864436i	$-0.667676\pi$
$659$		−	1.15981e34i		−	1.72887i	0.502743	−	0.864436i	$-0.332324\pi$
$660$	−7.57383e32	−	4.41556e32i	−0.110863	−	0.0646337i
$661$	5.94550e33			0.854616			0.427308	−	0.904106i	$-0.359462\pi$
$661$	5.94550e33			0.854616			0.427308	+	0.904106i	$0.359462\pi$
$662$	6.24752e33	+	1.68819e33i	0.881885	+	0.238300i
$663$			1.59447e33i			0.221031i
$664$	−2.89129e33	−	2.92820e33i	−0.393617	−	0.398643i
$665$	−1.84978e34			−2.47321
$666$	−2.62218e31	+	9.70400e31i	−0.00344328	+	0.0127427i
$667$		−	9.00445e31i		−	0.0116131i
$668$	−3.76801e33	+	6.46311e33i	−0.477304	+	0.818699i
$669$	5.91628e32			0.0736097
$670$	−1.19808e34	−	3.23741e33i	−1.46416	−	0.395640i
$671$		−	2.04362e33i		−	0.245319i
$672$	5.36223e33	−	1.37621e33i	0.632286	−	0.162276i
$673$	−9.95537e33			−1.15313			−0.576563	−	0.817053i	$-0.695606\pi$
$673$	−9.95537e33			−1.15313			−0.576563	+	0.817053i	$0.695606\pi$
$674$	1.55737e33	−	5.76340e33i	0.177203	−	0.655783i
$675$			8.22802e33i			0.919708i
$676$	6.00031e33	+	3.49820e33i	0.658891	+	0.384135i
$677$	5.92405e33			0.639080			0.319540	−	0.947573i	$-0.396472\pi$
$677$	5.92405e33			0.639080			0.319540	+	0.947573i	$0.396472\pi$
$678$	3.16904e33	+	8.56326e32i	0.335870	+	0.0907576i
$679$			6.03360e33i			0.628260i
$680$	−1.32614e34	+	1.30942e34i	−1.35670	+	1.33959i
$681$	−2.30326e33			−0.231514
$682$	−3.77063e32	+	1.39541e33i	−0.0372393	+	0.137813i
$683$		−	1.31966e34i		−	1.28060i	−0.768125	−	0.640300i	$-0.778810\pi$
$683$		−	1.31966e34i		−	1.28060i	0.768125	−	0.640300i	$-0.221190\pi$
$684$	4.12862e33	−	7.08165e33i	0.393670	−	0.675245i
$685$	2.14409e34			2.00889
$686$	2.25389e34	+	6.09038e33i	2.07512	+	0.560731i
$687$		−	3.99953e33i		−	0.361849i
$688$	−1.11035e34	+	6.28598e33i	−0.987182	+	0.558871i
$689$	−2.81715e33			−0.246139
$690$	−3.44123e32	+	1.27351e33i	−0.0295477	+	0.109348i
$691$		−	1.13536e34i		−	0.958069i	−0.877796	−	0.479035i	$-0.840987\pi$
$691$		−	1.13536e34i		−	0.958069i	0.877796	−	0.479035i	$-0.159013\pi$
$692$	−1.72917e34	−	1.00811e34i	−1.43405	−	0.836056i
$693$	4.36613e33			0.355875
$694$	6.59619e33	+	1.78240e33i	0.528420	+	0.142788i
$695$			2.11493e34i			1.66524i
$696$	1.89938e32	+	1.92363e32i	0.0146995	+	0.0148872i
$697$	−6.54633e33			−0.497971
$698$	1.43682e33	−	5.31727e33i	0.107433	−	0.397579i
$699$			9.74567e32i			0.0716284i
$700$	1.68427e34	−	2.88896e34i	1.21685	−	2.08721i
$701$	−1.04847e34			−0.744632			−0.372316	−	0.928106i	$-0.621436\pi$
$701$	−1.04847e34			−0.744632			−0.372316	+	0.928106i	$0.621436\pi$
$702$	4.58793e33	+	1.23974e33i	0.320311	+	0.0865533i
$703$			2.00028e32i			0.0137286i
$704$	−3.40017e33	−	4.31397e31i	−0.229418	−	0.00291075i
$705$	9.61654e33			0.637895
$706$	6.18887e33	−	2.29033e34i	0.403603	−	1.49363i
$707$			3.13076e34i			2.00732i
$708$	−8.93376e33	−	5.20841e33i	−0.563164	−	0.328326i
$709$	1.25348e34			0.776893			0.388446	−	0.921471i	$-0.373012\pi$
$709$	1.25348e34			0.776893			0.388446	+	0.921471i	$0.373012\pi$
$710$	−1.06973e34	−	2.89059e33i	−0.651889	−	0.176151i
$711$		−	1.96479e34i		−	1.17728i
$712$	7.64118e33	−	7.54485e33i	0.450195	−	0.444519i
$713$	2.17500e33			0.126004
$714$	−3.71750e33	+	1.37575e34i	−0.211774	+	0.783719i
$715$			3.05883e33i			0.171349i
$716$	−1.15405e34	+	1.97949e34i	−0.635722	+	1.09043i
$717$	5.64836e33			0.305980
$718$	−2.92673e34	−	7.90850e33i	−1.55915	−	0.421309i
$719$			1.61198e34i			0.844527i	0.906473	+	0.422263i	$0.138764\pi$
$719$			1.61198e34i			0.844527i	−0.906473	+	0.422263i	$0.861236\pi$
$720$	1.27076e34	+	2.24465e34i	0.654747	+	1.15654i
$721$	−2.60205e34			−1.31854
$722$	−9.79105e32	+	3.62341e33i	−0.0487959	+	0.180580i
$723$			1.06206e34i			0.520582i
$724$	2.22543e34	+	1.29743e34i	1.07288	+	0.625491i
$725$	1.63298e33			0.0774326
$726$	−7.15399e33	−	1.93313e33i	−0.333664	−	0.0901615i
$727$			2.04682e33i			0.0939004i	0.998897	+	0.0469502i	$0.0149502\pi$
$727$			2.04682e33i			0.0939004i	−0.998897	+	0.0469502i	$0.985050\pi$
$728$	−1.35711e34	−	1.37444e34i	−0.612404	−	0.620223i
$729$	6.47906e33			0.287595
$730$	−9.73376e32	+	3.60221e33i	−0.0425017	+	0.157287i
$731$		−	3.28453e34i		−	1.41080i
$732$	4.64979e33	−	7.97559e33i	0.196472	−	0.337000i
$733$	−2.79486e34			−1.16175			−0.580875	−	0.813993i	$-0.697290\pi$
$733$	−2.79486e34			−1.16175			−0.580875	+	0.813993i	$0.697290\pi$
$734$	2.62823e34	+	7.10191e33i	1.07476	+	0.290417i
$735$		−	3.06056e34i		−	1.23127i
$736$	1.27197e33	+	4.95607e33i	0.0503435	+	0.196157i
$737$	5.82910e33			0.226982
$738$	−2.36351e33	+	8.74673e33i	−0.0905485	+	0.335096i
$739$			2.97126e34i			1.11997i	0.828502	+	0.559986i	$0.189193\pi$
$739$			2.97126e34i			1.11997i	−0.828502	+	0.559986i	$0.810807\pi$
$740$	−5.43757e32	−	3.17012e32i	−0.0201662	−	0.0117570i
$741$	4.39140e33			0.160245
$742$	−2.43072e34	−	6.56821e33i	−0.872745	−	0.235830i
$743$		−	6.03085e33i		−	0.213065i	−0.994309	−	0.106533i	$-0.966025\pi$
$743$		−	6.03085e33i		−	0.213065i	0.994309	−	0.106533i	$-0.0339749\pi$
$744$	−4.64649e33	+	4.58791e33i	−0.161529	+	0.159492i
$745$	2.21144e34			0.756484
$746$	−5.54666e33	+	2.05267e34i	−0.186709	+	0.690961i
$747$		−	1.46614e34i		−	0.485655i
$748$	4.40876e33	−	7.56215e33i	0.143713	−	0.246505i
$749$	−2.58997e34			−0.830832
$750$	−5.99156e33	−	1.61902e33i	−0.189149	−	0.0511114i
$751$		−	2.60544e33i		−	0.0809471i	−0.999181	−	0.0404735i	$-0.987113\pi$
$751$		−	2.60544e33i		−	0.0809471i	0.999181	−	0.0404735i	$-0.0128866\pi$
$752$	3.24589e34	−	1.83759e34i	0.992476	−	0.561868i
$753$	−3.76728e33			−0.113367
$754$	2.46045e32	−	9.10545e32i	0.00728715	−	0.0269678i
$755$		−	9.34193e34i		−	2.72316i
$756$	3.66954e34	+	2.13935e34i	1.05281	+	0.613792i
$757$	3.47764e34			0.982052			0.491026	−	0.871145i	$-0.336622\pi$
$757$	3.47764e34			0.982052			0.491026	+	0.871145i	$0.336622\pi$
$758$	3.28141e34	+	8.86692e33i	0.912074	+	0.246458i
$759$		−	6.19609e32i		−	0.0169518i
$760$	3.60635e34	+	3.65240e34i	0.971191	+	0.983592i
$761$	2.59400e34			0.687629			0.343814	−	0.939038i	$-0.388281\pi$
$761$	2.59400e34			0.687629			0.343814	+	0.939038i	$0.388281\pi$
$762$	3.73158e33	−	1.38096e34i	0.0973718	−	0.360347i
$763$			4.20688e34i			1.08060i
$764$	−7.25474e33	+	1.24437e34i	−0.183443	+	0.314652i
$765$	−6.63994e34			−1.65282
$766$	−4.00475e34	−	1.08215e34i	−0.981364	−	0.265181i
$767$			3.60806e34i			0.870422i
$768$	−1.31716e34	−	7.90465e33i	−0.312826	−	0.187736i
$769$	4.77229e34			1.11586			0.557932	−	0.829887i	$-0.311595\pi$
$769$	4.77229e34			1.11586			0.557932	+	0.829887i	$0.311595\pi$
$770$	−7.13167e33	+	2.63924e34i	−0.164173	+	0.607561i
$771$			2.05327e34i			0.465365i
$772$	−6.75794e34	−	3.93989e34i	−1.50802	−	0.879178i
$773$	−4.82828e33			−0.106081			−0.0530406	−	0.998592i	$-0.516891\pi$
$773$	−4.82828e33			−0.106081			−0.0530406	+	0.998592i	$0.516891\pi$
$774$	−4.38855e34	−	1.18586e34i	−0.949357	−	0.256532i
$775$			3.94441e34i			0.840160i
$776$	1.19134e34	−	1.17632e34i	0.249858	−	0.246708i
$777$	−4.81299e32			−0.00993946
$778$	9.37951e33	−	3.47111e34i	0.190733	−	0.705851i
$779$			1.80296e34i			0.361024i
$780$	−6.95966e33	+	1.19376e34i	−0.137231	+	0.235387i
$781$	5.20463e33			0.101060
$782$	−1.27154e34	−	3.43592e33i	−0.243137	−	0.0656996i
$783$			2.07420e33i			0.0390579i
$784$	−5.84832e34	−	1.03304e35i	−1.08452	−	1.91569i
$785$	−5.07210e34			−0.926300
$786$	−2.40797e33	+	8.91124e33i	−0.0433092	+	0.160276i
$787$			6.83022e34i			1.20987i	0.796276	+	0.604934i	$0.206800\pi$
$787$			6.83022e34i			1.20987i	−0.796276	+	0.604934i	$0.793200\pi$
$788$	3.65567e34	+	2.13126e34i	0.637753	+	0.371811i
$789$	−3.18163e34			−0.546671
$790$	1.18768e35	+	3.20931e34i	2.00990	+	0.543108i
$791$		−	1.02368e35i		−	1.70626i
$792$	−8.51225e33	−	8.62093e33i	−0.139747	−	0.141531i
$793$	−3.22109e34			−0.520864
$794$	1.09361e34	−	4.04717e34i	0.174188	−	0.644623i
$795$			1.80131e34i			0.282607i
$796$	−5.74192e34	+	9.84887e34i	−0.887360	+	1.52205i
$797$	5.98073e34			0.910447			0.455223	−	0.890377i	$-0.349559\pi$
$797$	5.98073e34			0.910447			0.455223	+	0.890377i	$0.349559\pi$
$798$	3.78902e34	+	1.02386e34i	0.568189	+	0.153534i
$799$			9.60171e34i			1.41836i
$800$	−8.98794e34	+	2.30675e34i	−1.30792	+	0.335676i
$801$	3.82591e34			0.548459
$802$	2.66974e34	−	9.87999e34i	0.377030	−	1.39529i
$803$		−	1.75261e33i		−	0.0243836i
$804$	2.27491e34	+	1.32628e34i	0.311811	+	0.181787i
$805$	4.11374e34			0.555502
$806$	2.19940e34	+	5.94314e33i	0.292606	+	0.0790671i
$807$		−	1.88389e33i		−	0.0246930i
$808$	6.18169e34	−	6.10376e34i	0.798309	−	0.788245i
$809$	1.45996e35			1.85763			0.928817	−	0.370539i	$-0.120827\pi$
$809$	1.45996e35			1.85763			0.928817	+	0.370539i	$0.120827\pi$
$810$	−1.97270e34	+	7.30045e34i	−0.247310	+	0.915228i
$811$		−	5.68147e34i		−	0.701796i	−0.936414	−	0.350898i	$-0.885876\pi$
$811$		−	5.68147e34i		−	0.701796i	0.936414	−	0.350898i	$-0.114124\pi$
$812$	4.24588e33	−	7.28278e33i	0.0516768	−	0.0886390i
$813$	−8.39998e33			−0.100738
$814$	2.85397e32	+	7.71191e31i	0.00337254	+	0.000911316i
$815$		−	8.62263e34i		−	1.00403i
$816$	3.44119e34	−	1.94815e34i	0.394845	−	0.223533i
$817$	−9.04610e34			−1.02281
$818$	2.28250e34	−	8.44693e34i	0.254315	−	0.941151i
$819$		−	6.88174e34i		−	0.755599i
$820$	−4.90117e34	−	2.85740e34i	−0.530315	−	0.309175i
$821$	−1.67574e35			−1.78685			−0.893425	−	0.449211i	$-0.851705\pi$
$821$	−1.67574e35			−1.78685			−0.893425	+	0.449211i	$0.851705\pi$
$822$	−4.39188e34	−	1.18676e34i	−0.461519	−	0.124710i
$823$		−	1.19678e35i		−	1.23942i	−0.784833	−	0.619708i	$-0.787251\pi$
$823$		−	1.19678e35i		−	1.23942i	0.784833	−	0.619708i	$-0.212749\pi$
$824$	5.07298e34	+	5.13775e34i	0.517770	+	0.524381i
$825$	1.12367e34			0.113030
$826$	−8.41221e34	+	3.11313e35i	−0.833968	+	3.08629i
$827$			1.56867e35i			1.53273i	0.642406	+	0.766365i	$0.277936\pi$
$827$			1.56867e35i			1.53273i	−0.642406	+	0.766365i	$0.722064\pi$
$828$	−9.18167e33	+	1.57489e34i	−0.0884214	+	0.151666i
$829$	−1.52219e35			−1.44482			−0.722412	−	0.691463i	$-0.756967\pi$
$829$	−1.52219e35			−1.44482			−0.722412	+	0.691463i	$0.756967\pi$
$830$	8.86253e34	+	2.39480e34i	0.829126	+	0.224044i
$831$		−	6.28532e34i		−	0.579582i
$832$	−6.79954e32	+	5.35923e34i	−0.00618016	+	0.487105i
$833$	3.05585e35			2.73774
$834$	1.17062e34	−	4.33214e34i	0.103377	−	0.382569i
$835$		−	1.66901e35i		−	1.45285i
$836$	−2.08273e34	−	1.21424e34i	−0.178714	−	0.104191i
$837$	−5.01017e34			−0.423786
$838$	−6.24792e34	−	1.68829e34i	−0.520964	−	0.140773i
$839$			9.92113e34i			0.815488i	0.913096	+	0.407744i	$0.133684\pi$
$839$			9.92113e34i			0.815488i	−0.913096	+	0.407744i	$0.866316\pi$
$840$	−8.78824e34	+	8.67745e34i	−0.712116	+	0.703138i
$841$	−1.24773e35			−0.996712
$842$	−1.24723e33	+	4.61565e33i	−0.00982200	+	0.0363486i
$843$			7.05777e33i			0.0547945i
$844$	3.50352e34	−	6.00944e34i	0.268161	−	0.459965i
$845$	−1.54950e35			−1.16926
$846$	1.28291e35	+	3.46664e34i	0.954448	+	0.257908i
$847$			2.31091e35i			1.69505i
$848$	3.44206e34	+	6.08000e34i	0.248925	+	0.439697i
$849$	6.18403e34			0.440940
$850$	6.23113e34	−	2.30597e35i	0.438066	−	1.62117i
$851$		−	4.44843e32i		−	0.00308356i
$852$	2.03120e34	+	1.18419e34i	0.138828	+	0.0809371i
$853$	1.95119e35			1.31496			0.657478	−	0.753474i	$-0.271623\pi$
$853$	1.95119e35			1.31496			0.657478	+	0.753474i	$0.271623\pi$
$854$	−2.77924e35	−	7.50998e34i	−1.84685	−	0.499050i
$855$			1.82874e35i			1.19828i
$856$	5.04944e34	+	5.11391e34i	0.326255	+	0.330421i
$857$	−1.51242e35			−0.963612			−0.481806	−	0.876278i	$-0.660019\pi$
$857$	−1.51242e35			−0.963612			−0.481806	+	0.876278i	$0.660019\pi$
$858$	1.69307e33	−	6.26559e33i	0.0106372	−	0.0393654i
$859$		−	2.46051e35i		−	1.52443i	−0.647325	−	0.762214i	$-0.724112\pi$
$859$		−	2.46051e35i		−	1.52443i	0.647325	−	0.762214i	$-0.275888\pi$
$860$	1.43366e35	−	2.45910e35i	0.875920	−	1.50243i
$861$	−4.33820e34			−0.261380
$862$	−2.03214e35	−	5.49119e34i	−1.20744	−	0.326272i
$863$		−	7.16485e34i		−	0.419834i	−0.977719	−	0.209917i	$-0.932681\pi$
$863$		−	7.16485e34i		−	0.419834i	0.977719	−	0.209917i	$-0.0673193\pi$
$864$	−2.93002e34	−	1.14164e35i	−0.169319	−	0.659729i
$865$	4.46535e35			2.54485
$866$	−4.68375e34	+	1.73333e35i	−0.263257	+	0.974243i
$867$			3.59789e34i			0.199443i
$868$	1.75914e35	+	1.02558e35i	0.961751	+	0.560704i
$869$	−5.77850e34			−0.311586
$870$	−5.82209e33	−	1.57323e33i	−0.0309634	−	0.00836682i
$871$		−	9.18763e34i		−	0.481932i
$872$	8.30649e34	−	8.20177e34i	0.429754	−	0.424336i
$873$	5.96497e34			0.304395
$874$	−9.46306e33	+	3.50203e34i	−0.0476315	+	0.176272i
$875$			1.93542e35i			0.960901i
$876$	3.98766e33	−	6.83986e33i	0.0195285	−	0.0334964i
$877$	3.63061e34			0.175382			0.0876909	−	0.996148i	$-0.472051\pi$
$877$	3.63061e34			0.175382			0.0876909	+	0.996148i	$0.472051\pi$
$878$	−1.20926e35	−	3.26762e34i	−0.576215	−	0.155703i
$879$			6.06819e34i			0.285228i
$880$	6.60158e34	−	3.73734e34i	0.306095	−	0.173289i
$881$	−2.46130e35			−1.12578			−0.562890	−	0.826532i	$-0.690311\pi$
$881$	−2.46130e35			−1.12578			−0.562890	+	0.826532i	$0.690311\pi$
$882$	1.10330e35	−	4.08300e35i	0.497816	−	1.84228i
$883$			3.13688e35i			1.39627i	0.715966	+	0.698135i	$0.245986\pi$
$883$			3.13688e35i			1.39627i	−0.715966	+	0.698135i	$0.754014\pi$
$884$	−1.19192e35	−	6.94893e34i	−0.523384	−	0.305134i
$885$	2.30702e35			0.999384
$886$	2.24187e35	+	6.05790e34i	0.958087	+	0.258891i
$887$			2.52387e35i			1.06410i	0.846712	+	0.532052i	$0.178579\pi$
$887$			2.52387e35i			1.06410i	−0.846712	+	0.532052i	$0.821421\pi$
$888$	9.38345e32	+	9.50326e32i	0.00390308	+	0.00395291i
$889$	−4.46083e35			−1.83061
$890$	−6.24927e34	+	2.31269e35i	−0.253017	+	0.936347i
$891$		−	3.55194e34i		−	0.141884i
$892$	−2.57841e34	+	4.42263e34i	−0.101619	+	0.174302i
$893$	2.64446e35			1.02830
$894$	−4.52983e34	−	1.22404e34i	−0.173793	−	0.0469617i
$895$		−	5.11176e35i		−	1.93506i
$896$	−1.30817e35	+	4.60823e35i	−0.488618	+	1.72123i
$897$	−9.76607e33			−0.0359924
$898$	−3.65316e34	+	1.35194e35i	−0.132847	+	0.491632i
$899$			9.94346e33i			0.0356797i
$900$	−2.85610e35	−	1.66512e35i	−1.01126	−	0.589569i
$901$	−1.79853e35			−0.628378
$902$	2.57244e34	+	6.95115e33i	0.0886882	+	0.0239650i
$903$		−	2.17663e35i		−	0.740513i
$904$	−2.02125e35	+	1.99577e35i	−0.678577	+	0.670022i
$905$	−5.74686e35			−1.90392
$906$	−5.17078e34	+	1.91357e35i	−0.169051	+	0.625612i
$907$		−	1.65415e35i		−	0.533688i	−0.963740	−	0.266844i	$-0.914019\pi$
$907$		−	1.65415e35i		−	0.533688i	0.963740	−	0.266844i	$-0.0859809\pi$
$908$	1.00380e35	−	1.72177e35i	0.319606	−	0.548208i
$909$	3.09515e35			0.972557
$910$	4.15988e35	+	1.12407e35i	1.28998	+	0.348575i
$911$		−	5.66140e35i		−	1.73262i	−0.499508	−	0.866309i	$-0.666486\pi$
$911$		−	5.66140e35i		−	1.73262i	0.499508	−	0.866309i	$-0.333514\pi$
$912$	−5.36551e34	−	9.47756e34i	−0.162059	−	0.286259i
$913$	−4.31196e34			−0.128536
$914$	−3.92560e33	+	1.45276e34i	−0.0115492	+	0.0427405i
$915$			2.05959e35i			0.598036i
$916$	2.98979e35	+	1.74306e35i	0.856831	+	0.499535i
$917$	2.87855e35			0.814219
$918$	2.92903e35	+	7.91474e34i	0.817734	+	0.220966i
$919$			3.94277e35i			1.08646i	0.839583	+	0.543231i	$0.182799\pi$
$919$			3.94277e35i			1.08646i	−0.839583	+	0.543231i	$0.817201\pi$
$920$	−8.02018e34	−	8.12258e34i	−0.218137	−	0.220923i
$921$	−4.51107e34			−0.121105
$922$	−4.71909e33	+	1.74641e34i	−0.0125051	+	0.0462780i
$923$		−	8.20336e34i		−	0.214571i
$924$	2.92165e34	−	5.01138e34i	0.0754336	−	0.129388i
$925$	8.06733e33			0.0205603
$926$	−4.20910e35	−	1.13737e35i	−1.05891	−	0.286134i
$927$			2.57245e35i			0.638837i
$928$	−2.26577e34	+	5.81508e33i	−0.0555443	+	0.0142554i
$929$	5.30490e35			1.28377			0.641887	−	0.766800i	$-0.278152\pi$
$929$	5.30490e35			1.28377			0.641887	+	0.766800i	$0.278152\pi$
$930$	3.80009e34	−	1.40631e35i	0.0907817	−	0.335959i
$931$		−	8.41627e35i		−	1.98483i
$932$	−7.28524e34	−	4.24731e34i	−0.169611	−	0.0988834i
$933$	−6.47705e34			−0.148867
$934$	6.95055e35	+	1.87815e35i	1.57709	+	0.426156i
$935$			1.95282e35i			0.437445i
$936$	−1.35880e35	+	1.34167e35i	−0.300501	+	0.296713i
$937$	5.17858e35			1.13067			0.565334	−	0.824862i	$-0.308747\pi$
$937$	5.17858e35			1.13067			0.565334	+	0.824862i	$0.308747\pi$
$938$	2.14210e35	−	7.92734e35i	0.461749	−	1.70881i
$939$			1.84611e35i			0.392890i
$940$	−4.19104e35	+	7.18871e35i	−0.880617	+	1.51049i
$941$	−1.91164e35			−0.396579			−0.198290	−	0.980143i	$-0.563539\pi$
$941$	−1.91164e35			−0.396579			−0.198290	+	0.980143i	$0.563539\pi$
$942$	1.03895e35	+	2.80742e34i	0.212806	+	0.0575037i
$943$		−	4.00961e34i		−	0.0810889i
$944$	7.78694e35	−	4.40840e35i	1.55490	−	0.880273i
$945$	−9.47610e35			−1.86831
$946$	−3.48765e34	+	1.29068e35i	−0.0678952	+	0.251262i
$947$			8.39380e35i			1.61346i	0.590918	+	0.806732i	$0.298766\pi$
$947$			8.39380e35i			1.61346i	−0.590918	+	0.806732i	$0.701234\pi$
$948$	−2.25516e35	−	1.31477e35i	−0.428033	−	0.249545i
$949$	−2.76240e34			−0.0517717
$950$	−6.35100e35	−	1.71615e35i	−1.17533	−	0.317593i
$951$		−	2.80258e35i		−	0.512143i
$952$	−8.66407e35	−	8.77470e35i	−1.56343	−	1.58339i
$953$	−5.98415e35			−1.06632			−0.533161	−	0.846014i	$-0.678996\pi$
$953$	−5.98415e35			−1.06632			−0.533161	+	0.846014i	$0.678996\pi$
$954$	−6.49350e34	+	2.40307e35i	−0.114261	+	0.422849i
$955$		−	3.21343e35i		−	0.558378i
$956$	−2.46165e35	+	4.22236e35i	−0.422407	+	0.724536i
$957$	2.83267e33			0.00480012
$958$	1.03641e35	+	2.80056e34i	0.173439	+	0.0468661i
$959$			1.41869e36i			2.34457i
$960$	3.42673e35	+	4.34768e33i	0.559274	+	0.00709582i
$961$	3.80231e35			0.612868
$962$	1.21552e33	−	4.49833e33i	0.00193492	−	0.00716062i
$963$			2.56051e35i			0.402542i
$964$	−7.93928e35	−	4.62862e35i	−1.23270	−	0.718666i
$965$	1.74514e36			2.67611
$966$	−8.42643e34	−	2.27696e34i	−0.127620	−	0.0344850i
$967$			2.56168e35i			0.383183i	0.981475	+	0.191592i	$0.0613649\pi$
$967$			2.56168e35i			0.383183i	−0.981475	+	0.191592i	$0.938635\pi$
$968$	4.56290e35	−	4.50538e35i	0.674120	−	0.665621i
$969$	2.80357e35			0.409097
$970$	−9.74324e34	+	3.60571e35i	−0.140424	+	0.519673i
$971$		−	4.97178e33i		−	0.00707752i	−0.999994	−	0.00353876i	$-0.998874\pi$
$971$		−	4.97178e33i		−	0.00707752i	0.999994	−	0.00353876i	$-0.00112643\pi$
$972$	3.24793e35	−	5.57104e35i	0.456679	−	0.783323i
$973$	−1.39939e36			−1.94350
$974$	−6.64138e35	−	1.79461e35i	−0.911069	−	0.246186i
$975$		−	1.77110e35i		−	0.239987i
$976$	3.93559e35	+	6.95178e35i	0.526759	+	0.930460i
$977$	−3.29818e35			−0.436054			−0.218027	−	0.975943i	$-0.569962\pi$
$977$	−3.29818e35			−0.436054			−0.218027	+	0.975943i	$0.569962\pi$
$978$	−4.77264e34	+	1.76623e35i	−0.0623294	+	0.230664i
$979$		−	1.12521e35i		−	0.145158i
$980$	2.28788e36	+	1.33384e36i	2.91555	+	1.69978i
$981$	4.15902e35			0.523556
$982$	−8.17434e35	−	2.20884e35i	−1.01652	−	0.274680i
$983$		−	1.26798e36i		−	1.55765i	−0.627243	−	0.778824i	$-0.715817\pi$
$983$		−	1.26798e36i		−	1.55765i	0.627243	−	0.778824i	$-0.284183\pi$
$984$	8.45780e34	+	8.56579e34i	0.102640	+	0.103950i
$985$	−9.44027e35			−1.13175
$986$	1.57080e34	−	5.81312e34i	0.0186037	−	0.0688472i
$987$			6.36299e35i			0.744483i
$988$	−1.91384e35	+	3.28273e35i	−0.221219	+	0.379448i
$989$	2.01177e35			0.229732
$990$	2.60922e35	+	7.05055e34i	0.294367	+	0.0795428i
$991$		−	1.23594e36i		−	1.37757i	−0.724967	−	0.688783i	$-0.758145\pi$
$991$		−	1.23594e36i		−	1.37757i	0.724967	−	0.688783i	$-0.241855\pi$
$992$	−1.40462e35	−	5.47290e35i	−0.154674	−	0.602667i
$993$	3.06340e35			0.333283
$994$	1.91262e35	−	7.07809e35i	0.205585	−	0.760815i
$995$		−	2.54333e36i		−	2.70101i
$996$	−1.68282e35	−	9.81086e34i	−0.176573	−	0.102943i
$997$	1.52773e36			1.58381			0.791906	−	0.610643i	$-0.209089\pi$
$997$	1.52773e36			1.58381			0.791906	+	0.610643i	$0.209089\pi$
$998$	−2.80351e35	−	7.57556e34i	−0.287168	−	0.0775976i
$999$			1.02471e34i			0.0103709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.25.b.b.3.6	yes	10
3.2	odd	2		36.25.d.b.19.5		10
4.3	odd	2	inner	4.25.b.b.3.5	✓	10
8.3	odd	2		64.25.c.d.63.6		10
8.5	even	2		64.25.c.d.63.5		10
12.11	even	2		36.25.d.b.19.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.25.b.b.3.5	✓	10	4.3	odd	2	inner
4.25.b.b.3.6	yes	10	1.1	even	1	trivial
36.25.d.b.19.5		10	3.2	odd	2
36.25.d.b.19.6		10	12.11	even	2
64.25.c.d.63.5		10	8.5	even	2
64.25.c.d.63.6		10	8.3	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1068.49 + 3954.18i) q^{2} +193889. i q^{3} +(-1.44939e7 - 8.44998e6i) q^{4} +3.74285e8 q^{5} +(-7.66672e8 - 2.07168e8i) q^{6} +2.47654e10i q^{7} +(4.88993e10 - 4.82828e10i) q^{8} +2.44837e11 q^{9} +O(q^{10})\)	\(q+(-1068.49 + 3954.18i) q^{2} +193889. i q^{3} +(-1.44939e7 - 8.44998e6i) q^{4} +3.74285e8 q^{5} +(-7.66672e8 - 2.07168e8i) q^{6} +2.47654e10i q^{7} +(4.88993e10 - 4.82828e10i) q^{8} +2.44837e11 q^{9} +(-3.99918e11 + 1.47999e12i) q^{10} -7.20071e11i q^{11} +(1.63836e12 - 2.81020e12i) q^{12} -1.13495e13 q^{13} +(-9.79267e13 - 2.64614e13i) q^{14} +7.25697e13i q^{15} +(1.38671e14 + 2.44946e14i) q^{16} -7.24578e14 q^{17} +(-2.61605e14 + 9.68129e14i) q^{18} +1.99560e15i q^{19} +(-5.42484e15 - 3.16270e15i) q^{20} -4.80173e15 q^{21} +(2.84729e15 + 7.69386e14i) q^{22} -4.43802e15i q^{23} +(9.36149e15 + 9.48102e15i) q^{24} +8.04846e16 q^{25} +(1.21268e16 - 4.48781e16i) q^{26} +1.02231e17i q^{27} +(2.09267e17 - 3.58946e17i) q^{28} +2.02893e16 q^{29} +(-2.86954e17 - 7.75397e16i) q^{30} +4.90083e17i q^{31} +(-1.11673e18 + 2.86608e17i) q^{32} +1.39614e17 q^{33} +(7.74202e17 - 2.86511e18i) q^{34} +9.26930e18i q^{35} +(-3.54864e18 - 2.06886e18i) q^{36} +1.00235e17 q^{37} +(-7.89096e18 - 2.13227e18i) q^{38} -2.20054e18i q^{39} +(1.83023e19 - 1.80715e19i) q^{40} +9.03467e18 q^{41} +(5.13058e18 - 1.89869e19i) q^{42} +4.53303e19i q^{43} +(-6.08458e18 + 1.04366e19i) q^{44} +9.16387e19 q^{45} +(1.75487e19 + 4.74197e18i) q^{46} -1.32515e20i q^{47} +(-4.74923e19 + 2.68867e19i) q^{48} -4.21742e20 q^{49} +(-8.59966e19 + 3.18251e20i) q^{50} -1.40488e20i q^{51} +(1.64499e20 + 9.59032e19i) q^{52} +2.48218e20 q^{53} +(-4.04240e20 - 1.09232e20i) q^{54} -2.69512e20i q^{55} +(1.19574e21 + 1.21101e21i) q^{56} -3.86924e20 q^{57} +(-2.16789e19 + 8.02277e19i) q^{58} -3.17904e21i q^{59} +(6.13212e20 - 1.05182e21i) q^{60} +2.83808e21 q^{61} +(-1.93788e21 - 5.23647e20i) q^{62} +6.06347e21i q^{63} +(5.99104e19 - 4.72199e21i) q^{64} -4.24795e21 q^{65} +(-1.49175e20 + 5.52058e20i) q^{66} +8.09517e21i q^{67} +(1.05020e22 + 6.12267e21i) q^{68} +8.60483e20 q^{69} +(-3.66525e22 - 9.90412e21i) q^{70} +7.22794e21i q^{71} +(1.19723e22 - 1.18214e22i) q^{72} +2.43394e21 q^{73} +(-1.07099e20 + 3.96346e20i) q^{74} +1.56051e22i q^{75} +(1.68628e22 - 2.89240e22i) q^{76} +1.78328e22 q^{77} +(8.70135e21 + 2.35125e21i) q^{78} -8.02491e22i q^{79} +(5.19024e22 + 9.16796e22i) q^{80} +4.93277e22 q^{81} +(-9.65342e21 + 3.57247e22i) q^{82} -5.98824e22i q^{83} +(6.95957e22 + 4.05745e22i) q^{84} -2.71199e23 q^{85} +(-1.79244e23 - 4.84348e22i) q^{86} +3.93387e21i q^{87} +(-3.47670e22 - 3.52109e22i) q^{88} +1.56264e23 q^{89} +(-9.79147e22 + 3.62356e23i) q^{90} -2.81075e23i q^{91} +(-3.75012e22 + 6.43242e22i) q^{92} -9.50217e22 q^{93} +(5.23987e23 + 1.41590e23i) q^{94} +7.46923e23i q^{95} +(-5.55700e22 - 2.16521e23i) q^{96} +2.43631e23 q^{97} +(4.50625e23 - 1.66764e24i) q^{98} -1.76300e23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9}+O(q^{10}) \) 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9	\( 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9} - 279847745800 q^{10} + 12433669328640 q^{12} - 24798065342764 q^{13} - 3829480368768 q^{14} - 588864378801920 q^{16} - 16\!\cdots\!64 q^{17}+ \cdots + 25\!\cdots\!08 q^{98}+O(q^{100}) \) 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9 - 279847745800 * q^10 + 12433669328640 * q^12 - 24798065342764 * q^13 - 3829480368768 * q^14 - 588864378801920 * q^16 - 1625038130621164 * q^17 - 3063761223370692 * q^18 - 3121315867314400 * q^20 - 2850064322141184 * q^21 + 13916632990560960 * q^22 + 10666682388698112 * q^24 + 71169859613334750 * q^25 - 74430147208248328 * q^26 + 57921192425034240 * q^28 + 1565608550658446804 * q^29 + 168458533397673600 * q^30 - 2011315973261284352 * q^32 - 3113879011632238080 * q^33 - 7482312029820836488 * q^34 - 4814867106633363312 * q^36 + 18108949413006125396 * q^37 - 3611284956625913280 * q^38 - 3297305262340163200 * q^40 + 75081428813585343380 * q^41 - 36295172789431572480 * q^42 + 120819410323173239040 * q^44 - 81006988268625062700 * q^45 - 106055608197057981312 * q^46 + 168479244993419243520 * q^48 - 275007343618256059766 * q^49 - 299814709349559655500 * q^50 + 1421183854718604927776 * q^52 - 1107525951871034057644 * q^53 - 3208227550047955403136 * q^54 + 4524093845691909838848 * q^56 - 1196103002381444528640 * q^57 - 1979853653083682157064 * q^58 + 14021053781344411123200 * q^60 + 7517404483697744564180 * q^61 - 21697281489429749629440 * q^62 + 27630501101980402880512 * q^64 - 2258152381762360458200 * q^65 - 60089835931903418403840 * q^66 + 44229260314628142476576 * q^68 - 3522613303126336828416 * q^69 - 111574643945445039187200 * q^70 + 150836748983093603875008 * q^72 + 51509134469807151432596 * q^73 - 140974046625084701216008 * q^74 + 274189896308379651183360 * q^76 - 19744531096531028198400 * q^77 - 388532048156284380666240 * q^78 + 337741777000410839974400 * q^80 - 21177053453795724717174 * q^81 - 127986376736882271652744 * q^82 + 466232221405535207153664 * q^84 - 156954763950404735571800 * q^85 - 425659539471164537308992 * q^86 + 273874512491499757685760 * q^88 - 817895256767034869026156 * q^89 - 170393126837835789371400 * q^90 - 461144040688182763215360 * q^92 + 251375897269064448430080 * q^93 + 1709617022527703840285952 * q^94 - 3254103234068698697613312 * q^96 + 2233072706882417490518036 * q^97 + 2593191981481623434770108 * q^98

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