LMFDB - Embedded newform 12.17.d.a.7.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,17,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	12.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.4789452628$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + \cdots + 43\!\cdots\!49 $ x^16 - x^15 + 37115x^14 + 433616x^13 + 965822723x^12 + 11579264195x^11 + 12661863519850x^10 + 162120109773543x^9 + 120758933936870280x^8 + 1240343233445130327x^7 + 553297868296926315210x^6 + 3641854073469392130003x^5 + 1781463130185670341595803x^4 + 12984494303085096280528944x^3 + 125765846444242947670566147x^2 - 206760575884676576961270033x + 435779119237071236287541049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{106}\cdot 3^{51} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.16
Root			$-4.60413 - 7.97459i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(252.543 + 41.9299i) q^{2} -3788.00i q^{3} +(62019.8 + 21178.2i) q^{4} -380576. q^{5} +(158830. - 956631. i) q^{6} +8.07663e6i q^{7} +(1.47746e7 + 7.94889e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(252.543 + 41.9299i) q^{2} -3788.00i q^{3} +(62019.8 + 21178.2i) q^{4} -380576. q^{5} +(158830. - 956631. i) q^{6} +8.07663e6i q^{7} +(1.47746e7 + 7.94889e6i) q^{8} -1.43489e7 q^{9} +(-9.61118e7 - 1.59575e7i) q^{10} +2.42044e8i q^{11} +(8.02230e7 - 2.34931e8i) q^{12} +1.45985e9 q^{13} +(-3.38653e8 + 2.03969e9i) q^{14} +1.44162e9i q^{15} +(3.39793e9 + 2.62694e9i) q^{16} -2.24623e9 q^{17} +(-3.62371e9 - 6.01649e8i) q^{18} -1.14852e10i q^{19} +(-2.36033e10 - 8.05993e9i) q^{20} +3.05942e10 q^{21} +(-1.01489e10 + 6.11264e10i) q^{22} +1.29284e11i q^{23} +(3.01104e10 - 5.59663e10i) q^{24} -7.74955e9 q^{25} +(3.68676e11 + 6.12116e10i) q^{26} +5.43536e10i q^{27} +(-1.71049e11 + 5.00910e11i) q^{28} -1.75072e11 q^{29} +(-6.04471e10 + 3.64071e11i) q^{30} +7.71736e11i q^{31} +(7.47977e11 + 8.05889e11i) q^{32} +9.16860e11 q^{33} +(-5.67269e11 - 9.41843e10i) q^{34} -3.07377e12i q^{35} +(-8.89916e11 - 3.03884e11i) q^{36} -2.05634e12 q^{37} +(4.81575e11 - 2.90051e12i) q^{38} -5.52992e12i q^{39} +(-5.62288e12 - 3.02516e12i) q^{40} -1.95728e12 q^{41} +(7.72635e12 + 1.28281e12i) q^{42} -1.76749e13i q^{43} +(-5.12605e12 + 1.50115e13i) q^{44} +5.46085e12 q^{45} +(-5.42087e12 + 3.26497e13i) q^{46} -3.06304e13i q^{47} +(9.95082e12 - 1.28714e13i) q^{48} -3.19990e13 q^{49} +(-1.95709e12 - 3.24938e11i) q^{50} +8.50871e12i q^{51} +(9.05398e13 + 3.09171e13i) q^{52} +1.13022e12 q^{53} +(-2.27904e12 + 1.37266e13i) q^{54} -9.21160e13i q^{55} +(-6.42002e13 + 1.19329e14i) q^{56} -4.35059e13 q^{57} +(-4.42131e13 - 7.34074e12i) q^{58} -4.12684e12i q^{59} +(-3.05310e13 + 8.94090e13i) q^{60} +3.30172e14 q^{61} +(-3.23588e13 + 1.94896e14i) q^{62} -1.15891e14i q^{63} +(1.55105e14 + 2.34884e14i) q^{64} -5.55586e14 q^{65} +(2.31546e14 + 3.84439e13i) q^{66} +3.23169e13i q^{67} +(-1.39311e14 - 4.75712e13i) q^{68} +4.89727e14 q^{69} +(1.28883e14 - 7.76259e14i) q^{70} +2.47977e14i q^{71} +(-2.12000e14 - 1.14058e14i) q^{72} +3.30356e14 q^{73} +(-5.19314e14 - 8.62223e13i) q^{74} +2.93552e13i q^{75} +(2.43236e14 - 7.12310e14i) q^{76} -1.95490e15 q^{77} +(2.31869e14 - 1.39654e15i) q^{78} -1.08940e15i q^{79} +(-1.29317e15 - 9.99749e14i) q^{80} +2.05891e14 q^{81} +(-4.94297e14 - 8.20686e13i) q^{82} +2.59936e15i q^{83} +(1.89745e15 + 6.47931e14i) q^{84} +8.54862e14 q^{85} +(7.41109e14 - 4.46368e15i) q^{86} +6.63171e14i q^{87} +(-1.92398e15 + 3.57611e15i) q^{88} +4.71085e15 q^{89} +(1.37910e15 + 2.28973e14i) q^{90} +1.17907e16i q^{91} +(-2.73800e15 + 8.01816e15i) q^{92} +2.92333e15 q^{93} +(1.28433e15 - 7.73549e15i) q^{94} +4.37100e15i q^{95} +(3.05270e15 - 2.83333e15i) q^{96} +1.18395e15 q^{97} +(-8.08111e15 - 1.34172e15i) q^{98} -3.47306e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) $ 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9 - 49800172 * q^10 + 425284020 * q^12 - 906419296 * q^13 - 806064072 * q^14 - 2108540816 * q^16 + 12240765600 * q^17 + 2668896702 * q^18 + 1002788712 * q^20 + 39806479296 * q^21 + 216706355928 * q^22 - 111931394832 * q^24 + 206381182512 * q^25 + 1054507182588 * q^26 - 1526063922288 * q^28 + 327679573728 * q^29 + 1192344308100 * q^30 - 5158730488416 * q^32 + 679591529280 * q^33 + 9473293385948 * q^34 - 1959888509316 * q^36 - 8149494749152 * q^37 + 23318999782920 * q^38 - 28671795971776 * q^40 - 25536724613472 * q^41 + 5103781482168 * q^42 - 11442227373552 * q^44 - 5081579320608 * q^45 + 9929654732736 * q^46 + 29246734238832 * q^48 - 93287012964080 * q^49 - 133601044957998 * q^50 + 302261844234872 * q^52 - 86928436629792 * q^53 - 22406076560826 * q^54 + 530930989929024 * q^56 + 48687411524544 * q^57 - 189801665049916 * q^58 + 268455359263896 * q^60 + 476028596468000 * q^61 - 419080420491096 * q^62 + 305944925720704 * q^64 - 1276571708976192 * q^65 - 64815073701480 * q^66 - 1393626893610696 * q^68 + 384812600884992 * q^69 + 1815049064679696 * q^70 - 210694758737760 * q^72 - 368686901901280 * q^73 + 875633111941836 * q^74 - 4351002030861264 * q^76 - 81504772370688 * q^77 + 1907392409236620 * q^78 - 8190389938127328 * q^80 + 3294258113514384 * q^81 + 2390391408733340 * q^82 - 510964995024720 * q^84 + 10085047677398464 * q^85 - 894939801424296 * q^86 + 669091386916800 * q^88 - 5711067674201568 * q^89 + 714578036612004 * q^90 + 7708247605922304 * q^92 + 7132614781502016 * q^93 - 9487273535547696 * q^94 + 8786531038601952 * q^96 - 13564951560560608 * q^97 - 33011660914531290 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	252.543	+	41.9299i	0.986495	+	0.163789i
$2$	252.543	+	41.9299i	0.986495	+	0.163789i
$3$		−	3788.00i		−	0.577350i
$3$		−	3788.00i		−	0.577350i
$4$	62019.8	+	21178.2i	0.946346	+	0.323154i
$5$	−380576.			−0.974275			−0.487138	−	0.873325i	$-0.661959\pi$
$5$	−380576.			−0.974275			−0.487138	+	0.873325i	$0.661959\pi$
$6$	158830.	−	956631.i	0.0945635	−	0.569553i
$7$			8.07663e6i			1.40102i	0.713640	+	0.700512i	$0.247045\pi$
$7$			8.07663e6i			1.40102i	−0.713640	+	0.700512i	$0.752955\pi$
$8$	1.47746e7	+	7.94889e6i	0.880637	+	0.473791i
$9$	−1.43489e7			−0.333333
$10$	−9.61118e7	−	1.59575e7i	−0.961118	−	0.159575i
$11$			2.42044e8i			1.12915i	0.825381	+	0.564575i	$0.190960\pi$
$11$			2.42044e8i			1.12915i	−0.825381	+	0.564575i	$0.809040\pi$
$12$	8.02230e7	−	2.34931e8i	0.186573	−	0.546373i
$13$	1.45985e9			1.78963			0.894814	−	0.446439i	$-0.147308\pi$
$13$	1.45985e9			1.78963			0.894814	+	0.446439i	$0.147308\pi$
$14$	−3.38653e8	+	2.03969e9i	−0.229472	+	1.38210i
$15$			1.44162e9i			0.562498i
$16$	3.39793e9	+	2.62694e9i	0.791143	+	0.611631i
$17$	−2.24623e9			−0.322005			−0.161003	−	0.986954i	$-0.551473\pi$
$17$	−2.24623e9			−0.322005			−0.161003	+	0.986954i	$0.551473\pi$
$18$	−3.62371e9	−	6.01649e8i	−0.328832	−	0.0545963i
$19$		−	1.14852e10i		−	0.676255i	−0.941100	−	0.338127i	$-0.890207\pi$
$19$		−	1.14852e10i		−	0.676255i	0.941100	−	0.338127i	$-0.109793\pi$
$20$	−2.36033e10	−	8.05993e9i	−0.922002	−	0.314841i
$21$	3.05942e10			0.808882
$22$	−1.01489e10	+	6.11264e10i	−0.184942	+	1.11390i
$23$			1.29284e11i			1.65090i	0.564472	+	0.825452i	$0.309080\pi$
$23$			1.29284e11i			1.65090i	−0.564472	+	0.825452i	$0.690920\pi$
$24$	3.01104e10	−	5.59663e10i	0.273543	−	0.508436i
$25$	−7.74955e9			−0.0507874
$26$	3.68676e11	+	6.12116e10i	1.76546	+	0.293121i
$27$			5.43536e10i			0.192450i
$28$	−1.71049e11	+	5.00910e11i	−0.452746	+	1.32585i
$29$	−1.75072e11			−0.349971			−0.174985	−	0.984571i	$-0.555988\pi$
$29$	−1.75072e11			−0.349971			−0.174985	+	0.984571i	$0.555988\pi$
$30$	−6.04471e10	+	3.64071e11i	−0.0921309	+	0.554902i
$31$			7.71736e11i			0.904847i	0.891803	+	0.452423i	$0.149440\pi$
$31$			7.71736e11i			0.904847i	−0.891803	+	0.452423i	$0.850560\pi$
$32$	7.47977e11	+	8.05889e11i	0.680281	+	0.732952i
$33$	9.16860e11			0.651916
$34$	−5.67269e11	−	9.41843e10i	−0.317657	−	0.0527409i
$35$		−	3.07377e12i		−	1.36498i
$36$	−8.89916e11	−	3.03884e11i	−0.315449	−	0.107718i
$37$	−2.05634e12			−0.585439			−0.292719	−	0.956198i	$-0.594560\pi$
$37$	−2.05634e12			−0.585439			−0.292719	+	0.956198i	$0.594560\pi$
$38$	4.81575e11	−	2.90051e12i	0.110763	−	0.667122i
$39$		−	5.52992e12i		−	1.03324i
$40$	−5.62288e12	−	3.02516e12i	−0.857983	−	0.461603i
$41$	−1.95728e12			−0.245122			−0.122561	−	0.992461i	$-0.539111\pi$
$41$	−1.95728e12			−0.245122			−0.122561	+	0.992461i	$0.539111\pi$
$42$	7.72635e12	+	1.28281e12i	0.797958	+	0.132486i
$43$		−	1.76749e13i		−	1.51220i	−0.654454	−	0.756102i	$-0.727101\pi$
$43$		−	1.76749e13i		−	1.51220i	0.654454	−	0.756102i	$-0.272899\pi$
$44$	−5.12605e12	+	1.50115e13i	−0.364889	+	1.06857i
$45$	5.46085e12			0.324758
$46$	−5.42087e12	+	3.26497e13i	−0.270400	+	1.62861i
$47$		−	3.06304e13i		−	1.28638i	−0.765706	−	0.643191i	$-0.777610\pi$
$47$		−	3.06304e13i		−	1.28638i	0.765706	−	0.643191i	$-0.222390\pi$
$48$	9.95082e12	−	1.28714e13i	0.353125	−	0.456767i
$49$	−3.19990e13			−0.962870
$50$	−1.95709e12	−	3.24938e11i	−0.0501016	−	0.00831841i
$51$			8.50871e12i			0.185910i
$52$	9.05398e13	+	3.09171e13i	1.69361	+	0.578325i
$53$	1.13022e12			0.0181533			0.00907664	−	0.999959i	$-0.497111\pi$
$53$	1.13022e12			0.0181533			0.00907664	+	0.999959i	$0.497111\pi$
$54$	−2.27904e12	+	1.37266e13i	−0.0315212	+	0.189851i
$55$		−	9.21160e13i		−	1.10010i
$56$	−6.42002e13	+	1.19329e14i	−0.663792	+	1.23379i
$57$	−4.35059e13			−0.390436
$58$	−4.42131e13	−	7.34074e12i	−0.345245	−	0.0573213i
$59$		−	4.12684e12i		−	0.0281061i	−0.999901	−	0.0140531i	$-0.995527\pi$
$59$		−	4.12684e12i		−	0.0281061i	0.999901	−	0.0140531i	$-0.00447338\pi$
$60$	−3.05310e13	+	8.94090e13i	−0.181773	+	0.532318i
$61$	3.30172e14			1.72227			0.861135	−	0.508376i	$-0.169754\pi$
$61$	3.30172e14			1.72227			0.861135	+	0.508376i	$0.169754\pi$
$62$	−3.23588e13	+	1.94896e14i	−0.148204	+	0.892627i
$63$		−	1.15891e14i		−	0.467008i
$64$	1.55105e14	+	2.34884e14i	0.551045	+	0.834476i
$65$	−5.55586e14			−1.74359
$66$	2.31546e14	+	3.84439e13i	0.643112	+	0.106776i
$67$			3.23169e13i			0.0795851i	0.999208	+	0.0397926i	$0.0126697\pi$
$67$			3.23169e13i			0.0795851i	−0.999208	+	0.0397926i	$0.987330\pi$
$68$	−1.39311e14	−	4.75712e13i	−0.304729	−	0.104057i
$69$	4.89727e14			0.953150
$70$	1.28883e14	−	7.76259e14i	0.223569	−	1.34655i
$71$			2.47977e14i			0.384012i	0.981394	+	0.192006i	$0.0614994\pi$
$71$			2.47977e14i			0.384012i	−0.981394	+	0.192006i	$0.938501\pi$
$72$	−2.12000e14	−	1.14058e14i	−0.293546	−	0.157930i
$73$	3.30356e14			0.409637			0.204819	−	0.978800i	$-0.434340\pi$
$73$	3.30356e14			0.409637			0.204819	+	0.978800i	$0.434340\pi$
$74$	−5.19314e14	−	8.62223e13i	−0.577533	−	0.0958883i
$75$			2.93552e13i			0.0293221i
$76$	2.43236e14	−	7.12310e14i	0.218534	−	0.639971i
$77$	−1.95490e15			−1.58197
$78$	2.31869e14	−	1.39654e15i	0.169234	−	1.01929i
$79$		−	1.08940e15i		−	0.718077i	−0.933323	−	0.359039i	$-0.883105\pi$
$79$		−	1.08940e15i		−	0.718077i	0.933323	−	0.359039i	$-0.116895\pi$
$80$	−1.29317e15	−	9.99749e14i	−0.770791	−	0.595897i
$81$	2.05891e14			0.111111
$82$	−4.94297e14	−	8.20686e13i	−0.241812	−	0.0401482i
$83$			2.59936e15i			1.15410i	0.816711	+	0.577048i	$0.195795\pi$
$83$			2.59936e15i			1.15410i	−0.816711	+	0.577048i	$0.804205\pi$
$84$	1.89745e15	+	6.47931e14i	0.765482	+	0.261393i
$85$	8.54862e14			0.313722
$86$	7.41109e14	−	4.46368e15i	0.247682	−	1.49178i
$87$			6.63171e14i			0.202056i
$88$	−1.92398e15	+	3.57611e15i	−0.534981	+	0.994372i
$89$	4.71085e15			1.19668			0.598342	−	0.801241i	$-0.295826\pi$
$89$	4.71085e15			1.19668			0.598342	+	0.801241i	$0.295826\pi$
$90$	1.37910e15	+	2.28973e14i	0.320373	+	0.0531918i
$91$			1.17907e16i			2.50731i
$92$	−2.73800e15	+	8.01816e15i	−0.533496	+	1.56233i
$93$	2.92333e15			0.522413
$94$	1.28433e15	−	7.73549e15i	0.210695	−	1.26901i
$95$			4.37100e15i			0.658859i
$96$	3.05270e15	−	2.83333e15i	0.423170	−	0.392760i
$97$	1.18395e15			0.151064			0.0755319	−	0.997143i	$-0.475935\pi$
$97$	1.18395e15			0.151064			0.0755319	+	0.997143i	$0.475935\pi$
$98$	−8.08111e15	−	1.34172e15i	−0.949866	−	0.157707i
$99$		−	3.47306e15i		−	0.376384i
$100$	−4.80625e14	−	1.64122e14i	−0.0480625	−	0.0164122i
$101$	−1.63343e16			−1.50845			−0.754224	−	0.656618i	$-0.771987\pi$
$101$	−1.63343e16			−1.50845			−0.754224	+	0.656618i	$0.771987\pi$
$102$	−3.56770e14	+	2.14881e15i	−0.0304500	+	0.183399i
$103$		−	1.77929e16i		−	1.40459i	−0.711887	−	0.702294i	$-0.752159\pi$
$103$		−	1.77929e16i		−	1.40459i	0.711887	−	0.702294i	$-0.247841\pi$
$104$	2.15688e16	+	1.16042e16i	1.57601	+	0.847909i
$105$	−1.16434e16			−0.788074
$106$	2.85429e14	+	4.73900e13i	0.0179081	+	0.00297331i
$107$		−	1.63226e16i		−	0.949988i	−0.879989	−	0.474994i	$-0.842450\pi$
$107$		−	1.63226e16i		−	0.949988i	0.879989	−	0.474994i	$-0.157550\pi$
$108$	−1.15111e15	+	3.37100e15i	−0.0621910	+	0.182124i
$109$	2.93758e16			1.47427			0.737136	−	0.675745i	$-0.236178\pi$
$109$	2.93758e16			1.47427			0.737136	+	0.675745i	$0.236178\pi$
$110$	3.86242e15	−	2.32632e16i	0.180185	−	1.08525i
$111$			7.78941e15i			0.338003i
$112$	−2.12168e16	+	2.74438e16i	−0.856910	+	1.10841i
$113$	−8.38169e15			−0.315286			−0.157643	−	0.987496i	$-0.550389\pi$
$113$	−8.38169e15			−0.315286			−0.157643	+	0.987496i	$0.550389\pi$
$114$	−1.09871e16	−	1.82420e15i	−0.385163	−	0.0639491i
$115$		−	4.92024e16i		−	1.60843i
$116$	−1.08579e16	−	3.70770e15i	−0.331194	−	0.113094i
$117$	−2.09473e16			−0.596543
$118$	1.73038e14	−	1.04220e15i	0.00460347	−	0.0277266i
$119$		−	1.81420e16i		−	0.451137i
$120$	−1.14593e16	+	2.12994e16i	−0.266506	+	0.495357i
$121$	−1.26353e16			−0.274982
$122$	8.33825e16	+	1.38441e16i	1.69901	+	0.282089i
$123$			7.41416e15i			0.141521i
$124$	−1.63440e16	+	4.78629e16i	−0.292405	+	0.856298i
$125$	6.10206e16			1.02376
$126$	4.85929e15	−	2.92674e16i	0.0764907	−	0.460701i
$127$			1.80665e16i			0.266959i	0.991052	+	0.133479i	$0.0426150\pi$
$127$			1.80665e16i			0.266959i	−0.991052	+	0.133479i	$0.957385\pi$
$128$	2.93220e16	+	6.58218e16i	0.406925	+	0.913462i
$129$	−6.69526e16			−0.873071
$130$	−1.40309e17	−	2.32957e16i	−1.72004	−	0.285581i
$131$		−	7.70210e16i		−	0.888053i	−0.896014	−	0.444026i	$-0.853550\pi$
$131$		−	7.70210e16i		−	0.888053i	0.896014	−	0.444026i	$-0.146450\pi$
$132$	5.68634e16	+	1.94174e16i	0.616938	+	0.210669i
$133$	9.27618e16			0.947450
$134$	−1.35505e15	+	8.16141e15i	−0.0130352	+	0.0785104i
$135$		−	2.06857e16i		−	0.187499i
$136$	−3.31873e16	−	1.78550e16i	−0.283570	−	0.152563i
$137$	−4.59749e16			−0.370473			−0.185236	−	0.982694i	$-0.559305\pi$
$137$	−4.59749e16			−0.370473			−0.185236	+	0.982694i	$0.559305\pi$
$138$	1.23677e17	+	2.05342e16i	0.940278	+	0.156115i
$139$			2.32569e17i			1.66891i	0.551077	+	0.834455i	$0.314217\pi$
$139$			2.32569e17i			1.66891i	−0.551077	+	0.834455i	$0.685783\pi$
$140$	6.50970e16	−	1.90635e17i	0.441100	−	1.29175i
$141$	−1.16028e17			−0.742693
$142$	−1.03977e16	+	6.26249e16i	−0.0628969	+	0.378826i
$143$			3.53348e17i			2.02076i
$144$	−4.87566e16	−	3.76937e16i	−0.263714	−	0.203877i
$145$	6.66281e16			0.340968
$146$	8.34291e16	+	1.38518e16i	0.404105	+	0.0670940i
$147$			1.21212e17i			0.555913i
$148$	−1.27534e17	−	4.35496e16i	−0.554028	−	0.189187i
$149$	1.46577e17			0.603357			0.301679	−	0.953410i	$-0.402453\pi$
$149$	1.46577e17			0.603357			0.301679	+	0.953410i	$0.402453\pi$
$150$	−1.23086e15	+	7.41346e15i	−0.00480264	+	0.0289261i
$151$		−	2.31544e17i		−	0.856679i	−0.903618	−	0.428339i	$-0.859099\pi$
$151$		−	2.31544e17i		−	0.856679i	0.903618	−	0.428339i	$-0.140901\pi$
$152$	9.12947e16	−	1.69690e17i	0.320403	−	0.595535i
$153$	3.22310e16			0.107335
$154$	−4.93695e17	−	8.19686e16i	−1.56060	−	0.259109i
$155$		−	2.93704e17i		−	0.881570i
$156$	1.17114e17	−	3.42964e17i	0.333896	−	0.977805i
$157$	5.48760e17			1.48657			0.743284	−	0.668975i	$-0.233267\pi$
$157$	5.48760e17			1.48657			0.743284	+	0.668975i	$0.233267\pi$
$158$	4.56785e16	−	2.75121e17i	0.117613	−	0.708380i
$159$		−	4.28126e15i		−	0.0104808i
$160$	−2.84662e17	−	3.06702e17i	−0.662781	−	0.714097i
$161$	−1.04418e18			−2.31296
$162$	5.19963e16	+	8.63300e15i	0.109611	+	0.0181988i
$163$		−	2.11095e17i		−	0.423620i	−0.977311	−	0.211810i	$-0.932064\pi$
$163$		−	2.11095e17i		−	0.423620i	0.977311	−	0.211810i	$-0.0679359\pi$
$164$	−1.21390e17	−	4.14517e16i	−0.231970	−	0.0792121i
$165$	−3.48935e17			−0.635145
$166$	−1.08991e17	+	6.56450e17i	−0.189028	+	1.13851i
$167$			5.68106e17i			0.939068i	0.882914	+	0.469534i	$0.155578\pi$
$167$			5.68106e17i			0.939068i	−0.882914	+	0.469534i	$0.844422\pi$
$168$	4.52019e17	+	2.43190e17i	0.712332	+	0.383241i
$169$	1.46576e18			2.20277
$170$	2.15889e17	+	3.58443e16i	0.309485	+	0.0513841i
$171$			1.64800e17i			0.225418i
$172$	3.74324e17	−	1.09620e18i	0.488674	−	1.43107i
$173$	−1.28912e18			−1.60666			−0.803328	−	0.595537i	$-0.796939\pi$
$173$	−1.28912e18			−1.60666			−0.803328	+	0.595537i	$0.796939\pi$
$174$	−2.78067e16	+	1.67479e17i	−0.0330945	+	0.199327i
$175$		−	6.25902e16i		−	0.0711544i
$176$	−6.35833e17	+	8.22448e17i	−0.690624	+	0.893320i
$177$	−1.56324e16			−0.0162271
$178$	1.18969e18	+	1.97526e17i	1.18052	+	0.196004i
$179$			5.10893e17i			0.484736i	0.970184	+	0.242368i	$0.0779242\pi$
$179$			5.10893e17i			0.484736i	−0.970184	+	0.242368i	$0.922076\pi$
$180$	3.38681e17	+	1.15651e17i	0.307334	+	0.104947i
$181$	9.01274e17			0.782399			0.391199	−	0.920306i	$-0.372060\pi$
$181$	9.01274e17			0.782399			0.391199	+	0.920306i	$0.372060\pi$
$182$	−4.94383e17	+	2.97766e18i	−0.410670	+	2.47345i
$183$		−	1.25069e18i		−	0.994353i
$184$	−1.02766e18	+	1.91012e18i	−0.782183	+	1.45385i
$185$	7.82595e17			0.570379
$186$	7.38266e17	+	1.22575e17i	0.515358	+	0.0855655i
$187$		−	5.43686e17i		−	0.363593i
$188$	6.48697e17	−	1.89969e18i	0.415699	−	1.21736i
$189$	−4.38994e17			−0.269627
$190$	−1.83276e17	+	1.10387e18i	−0.107914	+	0.649961i
$191$		−	2.58811e18i		−	1.46122i	−0.682794	−	0.730611i	$-0.739235\pi$
$191$		−	2.58811e18i		−	1.46122i	0.682794	−	0.730611i	$-0.260765\pi$
$192$	8.89740e17	−	5.87538e17i	0.481785	−	0.318146i
$193$	−1.74038e18			−0.904036			−0.452018	−	0.892009i	$-0.649296\pi$
$193$	−1.74038e18			−0.904036			−0.452018	+	0.892009i	$0.649296\pi$
$194$	2.98999e17	+	4.96431e16i	0.149024	+	0.0247426i
$195$			2.10456e18i			1.00666i
$196$	−1.98457e18	−	6.77681e17i	−0.911208	−	0.311155i
$197$	−5.05318e17			−0.222759			−0.111379	−	0.993778i	$-0.535527\pi$
$197$	−5.05318e17			−0.222759			−0.111379	+	0.993778i	$0.535527\pi$
$198$	1.45625e17	−	8.77096e17i	0.0616474	−	0.371301i
$199$		−	2.34041e18i		−	0.951628i	−0.879546	−	0.475814i	$-0.842154\pi$
$199$		−	2.34041e18i		−	0.951628i	0.879546	−	0.475814i	$-0.157846\pi$
$200$	−1.14497e17	−	6.16003e16i	−0.0447253	−	0.0240626i
$201$	1.22416e17			0.0459485
$202$	−4.12512e18	−	6.84897e17i	−1.48808	−	0.247067i
$203$		−	1.41399e18i		−	0.490318i
$204$	−1.80199e17	+	5.27708e17i	−0.0600775	+	0.175935i
$205$	7.44894e17			0.238816
$206$	7.46055e17	−	4.49347e18i	0.230056	−	1.38562i
$207$		−	1.85508e18i		−	0.550301i
$208$	4.96049e18	+	3.83494e18i	1.41585	+	1.09459i
$209$	2.77992e18			0.763594
$210$	−2.94047e18	−	4.88209e17i	−0.777431	−	0.129078i
$211$			1.78865e18i			0.455267i	0.973747	+	0.227633i	$0.0730988\pi$
$211$			1.78865e18i			0.455267i	−0.973747	+	0.227633i	$0.926901\pi$
$212$	7.00959e16	+	2.39360e16i	0.0171793	+	0.00586631i
$213$	9.39337e17			0.221710
$214$	6.84404e17	−	4.12215e18i	0.155597	−	0.937159i
$215$			6.72666e18i			1.47330i
$216$	−4.32051e17	+	8.03055e17i	−0.0911811	+	0.169479i
$217$	−6.23302e18			−1.26771
$218$	7.41864e18	+	1.23172e18i	1.45436	+	0.241469i
$219$		−	1.25139e18i		−	0.236504i
$220$	1.95085e18	−	5.71301e18i	0.355503	−	1.04108i
$221$	−3.27917e18			−0.576270
$222$	−3.26610e17	+	1.96716e18i	−0.0553612	+	0.333439i
$223$			7.40800e18i			1.21133i	0.795720	+	0.605664i	$0.207093\pi$
$223$			7.40800e18i			1.21133i	−0.795720	+	0.605664i	$0.792907\pi$
$224$	−6.50886e18	+	6.04113e18i	−1.02688	+	0.953090i
$225$	1.11198e17			0.0169291
$226$	−2.11674e18	−	3.51444e17i	−0.311028	−	0.0516403i
$227$		−	3.69435e18i		−	0.523999i	−0.965068	−	0.262000i	$-0.915618\pi$
$227$		−	3.69435e18i		−	0.523999i	0.965068	−	0.262000i	$-0.0843819\pi$
$228$	−2.69823e18	−	9.21378e17i	−0.369488	−	0.126171i
$229$	5.94281e18			0.785793			0.392897	−	0.919583i	$-0.371473\pi$
$229$	5.94281e18			0.785793			0.392897	+	0.919583i	$0.371473\pi$
$230$	2.06305e18	−	1.24257e19i	0.263444	−	1.58671i
$231$			7.40513e18i			0.913350i
$232$	−2.58662e18	−	1.39163e18i	−0.308197	−	0.165813i
$233$	1.62547e19			1.87125			0.935625	−	0.352995i	$-0.114837\pi$
$233$	1.62547e19			1.87125			0.935625	+	0.352995i	$0.114837\pi$
$234$	−5.29010e18	−	8.78320e17i	−0.588487	−	0.0977070i
$235$			1.16572e19i			1.25329i
$236$	8.73990e16	−	2.55945e17i	0.00908261	−	0.0265981i
$237$	−4.12665e18			−0.414582
$238$	7.60692e17	−	4.58162e18i	0.0738912	−	0.445045i
$239$			4.21205e18i			0.395649i	0.980237	+	0.197825i	$0.0633876\pi$
$239$			4.21205e18i			0.395649i	−0.980237	+	0.197825i	$0.936612\pi$
$240$	−3.78705e18	+	4.89853e18i	−0.344041	+	0.445017i
$241$	−1.31232e19			−1.15319			−0.576596	−	0.817029i	$-0.695619\pi$
$241$	−1.31232e19			−1.15319			−0.576596	+	0.817029i	$0.695619\pi$
$242$	−3.19096e18	−	5.29799e17i	−0.271268	−	0.0450389i
$243$		−	7.79915e17i		−	0.0641500i
$244$	2.04772e19	+	6.99245e18i	1.62986	+	0.556558i
$245$	1.21781e19			0.938100
$246$	−3.10875e17	+	1.87239e18i	−0.0231796	+	0.139610i
$247$		−	1.67668e19i		−	1.21024i
$248$	−6.13444e18	+	1.14021e19i	−0.428708	+	0.796842i
$249$	9.84636e18			0.666317
$250$	1.54103e19	+	2.55859e18i	1.00993	+	0.167680i
$251$			5.24986e18i			0.333241i	0.986021	+	0.166620i	$0.0532855\pi$
$251$			5.24986e18i			0.333241i	−0.986021	+	0.166620i	$0.946715\pi$
$252$	2.45436e18	−	7.18752e18i	0.150915	−	0.441951i
$253$	−3.12923e19			−1.86412
$254$	−7.57528e17	+	4.56257e18i	−0.0437249	+	0.263354i
$255$		−	3.23821e18i		−	0.181127i
$256$	4.64517e18	+	1.78523e19i	0.251815	+	0.967775i
$257$	1.00197e18			0.0526490			0.0263245	−	0.999653i	$-0.491620\pi$
$257$	1.00197e18			0.0526490			0.0263245	+	0.999653i	$0.491620\pi$
$258$	−1.69084e19	−	2.80732e18i	−0.861281	−	0.142999i
$259$		−	1.66083e19i		−	0.820214i
$260$	−3.44573e19	−	1.17663e19i	−1.65004	−	0.563448i
$261$	2.51209e18			0.116657
$262$	3.22949e18	−	1.94511e19i	0.145453	−	0.876060i
$263$		−	4.00348e19i		−	1.74901i	−0.485018	−	0.874504i	$-0.661187\pi$
$263$		−	4.00348e19i		−	1.74901i	0.485018	−	0.874504i	$-0.338813\pi$
$264$	1.35463e19	+	7.28802e18i	0.574101	+	0.308872i
$265$	−4.30134e17			−0.0176863
$266$	2.34263e19	+	3.88950e18i	0.934655	+	0.155182i
$267$		−	1.78447e19i		−	0.690906i
$268$	−6.84415e17	+	2.00429e18i	−0.0257182	+	0.0753151i
$269$	−3.79909e19			−1.38568			−0.692838	−	0.721093i	$-0.743640\pi$
$269$	−3.79909e19			−1.38568			−0.692838	+	0.721093i	$0.743640\pi$
$270$	8.67350e17	−	5.22402e18i	0.0307103	−	0.184967i
$271$			3.16181e18i			0.108688i	0.998522	+	0.0543440i	$0.0173068\pi$
$271$			3.16181e18i			0.108688i	−0.998522	+	0.0543440i	$0.982693\pi$
$272$	−7.63254e18	−	5.90070e18i	−0.254752	−	0.196948i
$273$	4.46631e19			1.44760
$274$	−1.16106e19	−	1.92772e18i	−0.365469	−	0.0606793i
$275$		−	1.87573e18i		−	0.0573467i
$276$	3.03727e19	+	1.03715e19i	0.902010	+	0.308014i
$277$	−3.17714e18			−0.0916638			−0.0458319	−	0.998949i	$-0.514594\pi$
$277$	−3.17714e18			−0.0916638			−0.0458319	+	0.998949i	$0.514594\pi$
$278$	−9.75159e18	+	5.87335e19i	−0.273349	+	1.64637i
$279$		−	1.10736e19i		−	0.301616i
$280$	2.44331e19	−	4.54139e19i	0.646717	−	1.20206i
$281$	−1.44244e19			−0.371062			−0.185531	−	0.982638i	$-0.559400\pi$
$281$	−1.44244e19			−0.371062			−0.185531	+	0.982638i	$0.559400\pi$
$282$	−2.93020e19	−	4.86504e18i	−0.732663	−	0.121645i
$283$			2.59560e19i			0.630880i	0.948946	+	0.315440i	$0.102152\pi$
$283$			2.59560e19i			0.630880i	−0.948946	+	0.315440i	$0.897848\pi$
$284$	−5.25172e18	+	1.53795e19i	−0.124095	+	0.363409i
$285$	1.65573e19			0.380392
$286$	−1.48159e19	+	8.92356e19i	−0.330978	+	1.99347i
$287$		−	1.58082e19i		−	0.343422i
$288$	−1.07326e19	−	1.15636e19i	−0.226760	−	0.244317i
$289$	−4.36156e19			−0.896313
$290$	1.68265e19	+	2.79371e18i	0.336363	+	0.0558468i
$291$		−	4.48481e18i		−	0.0872168i
$292$	2.04886e19	+	6.99635e18i	0.387659	+	0.132376i
$293$	8.14913e19			1.50027			0.750136	−	0.661283i	$-0.229988\pi$
$293$	8.14913e19			1.50027			0.750136	+	0.661283i	$0.229988\pi$
$294$	−5.08241e18	+	3.06112e19i	−0.0910523	+	0.548406i
$295$			1.57058e18i			0.0273831i
$296$	−3.03817e19	−	1.63456e19i	−0.515559	−	0.277376i
$297$	−1.31559e19			−0.217305
$298$	3.70169e19	+	6.14595e18i	0.595209	+	0.0988232i
$299$			1.88736e20i			2.95450i
$300$	−6.21692e17	+	1.82060e18i	−0.00947556	+	0.0277489i
$301$	1.42754e20			2.11863
$302$	9.70863e18	−	5.84748e19i	0.140314	−	0.845110i
$303$			6.18743e19i			0.870903i
$304$	3.01709e19	−	3.90260e19i	0.413618	−	0.535014i
$305$	−1.25656e20			−1.67797
$306$	8.13970e18	+	1.35144e18i	0.105886	+	0.0175803i
$307$		−	8.26931e18i		−	0.104800i	−0.998626	−	0.0524001i	$-0.983313\pi$
$307$		−	8.26931e18i		−	0.104800i	0.998626	−	0.0524001i	$-0.0166871\pi$
$308$	−1.21242e20	−	4.14012e19i	−1.49709	−	0.511219i
$309$	−6.73994e19			−0.810939
$310$	1.23150e19	−	7.41729e19i	0.144391	−	0.869665i
$311$		−	1.25504e20i		−	1.43409i	−0.697029	−	0.717043i	$-0.745495\pi$
$311$		−	1.25504e20i		−	1.43409i	0.697029	−	0.717043i	$-0.254505\pi$
$312$	4.39568e19	−	8.17026e19i	0.489541	−	0.909912i
$313$	−3.22147e19			−0.349703			−0.174851	−	0.984595i	$-0.555944\pi$
$313$	−3.22147e19			−0.349703			−0.174851	+	0.984595i	$0.555944\pi$
$314$	1.38585e20	+	2.30095e19i	1.46649	+	0.243483i
$315$			4.41053e19i			0.454995i
$316$	2.30716e19	−	6.75644e19i	0.232050	−	0.679550i
$317$	−4.41229e18			−0.0432703			−0.0216351	−	0.999766i	$-0.506887\pi$
$317$	−4.41229e18			−0.0432703			−0.0216351	+	0.999766i	$0.506887\pi$
$318$	1.79513e17	−	1.08120e18i	0.00171664	−	0.0103393i
$319$		−	4.23750e19i		−	0.395170i
$320$	−5.90294e19	−	8.93913e19i	−0.536869	−	0.813009i
$321$	−6.18298e19			−0.548476
$322$	−2.63700e20	−	4.37823e19i	−2.28172	−	0.378836i
$323$			2.57984e19i			0.217758i
$324$	1.27693e19	+	4.36041e18i	0.105150	+	0.0359060i
$325$	−1.13132e19			−0.0908906
$326$	8.85119e18	−	5.33105e19i	0.0693843	−	0.417900i
$327$		−	1.11275e20i		−	0.851171i
$328$	−2.89181e19	−	1.55582e19i	−0.215863	−	0.116136i
$329$	2.47390e20			1.80225
$330$	−8.81210e19	−	1.46308e19i	−0.626568	−	0.104030i
$331$			1.39165e20i			0.965839i	0.875665	+	0.482919i	$0.160424\pi$
$331$			1.39165e20i			0.965839i	−0.875665	+	0.482919i	$0.839576\pi$
$332$	−5.50498e19	+	1.61212e20i	−0.372950	+	1.09217i
$333$	2.95063e19			0.195146
$334$	−2.38206e19	+	1.43471e20i	−0.153809	+	0.926387i
$335$		−	1.22991e19i		−	0.0775378i
$336$	1.03957e20	+	8.03690e19i	0.639941	+	0.494737i
$337$	1.15497e20			0.694273			0.347137	−	0.937815i	$-0.387154\pi$
$337$	1.15497e20			0.694273			0.347137	+	0.937815i	$0.387154\pi$
$338$	3.70167e20	+	6.14592e19i	2.17302	+	0.360789i
$339$			3.17498e19i			0.182030i
$340$	5.30184e19	+	1.81045e19i	0.296890	+	0.101380i
$341$	−1.86794e20			−1.02171
$342$	−6.91007e18	+	4.16191e19i	−0.0369210	+	0.222374i
$343$			9.96619e18i			0.0520207i
$344$	1.40496e20	−	2.61141e20i	0.716468	−	1.33170i
$345$	−1.86378e20			−0.928630
$346$	−3.25557e20	−	5.40525e19i	−1.58496	−	0.263152i
$347$		−	9.35734e19i		−	0.445160i	−0.974914	−	0.222580i	$-0.928552\pi$
$347$		−	9.35734e19i		−	0.445160i	0.974914	−	0.222580i	$-0.0714479\pi$
$348$	−1.40448e19	+	4.11297e19i	−0.0652951	+	0.191215i
$349$	1.21152e20			0.550464			0.275232	−	0.961378i	$-0.411245\pi$
$349$	1.21152e20			0.550464			0.275232	+	0.961378i	$0.411245\pi$
$350$	2.62440e18	−	1.58067e19i	0.0116543	−	0.0701935i
$351$			7.93484e19i			0.344414i
$352$	−1.95060e20	+	1.81043e20i	−0.827613	+	0.768140i
$353$	1.80187e19			0.0747354			0.0373677	−	0.999302i	$-0.488103\pi$
$353$	1.80187e19			0.0747354			0.0373677	+	0.999302i	$0.488103\pi$
$354$	−3.94786e18	−	6.55467e17i	−0.0160079	−	0.00265782i
$355$		−	9.43743e19i		−	0.374134i
$356$	2.92166e20	+	9.97675e19i	1.13248	+	0.386713i
$357$	−6.87217e19			−0.260464
$358$	−2.14217e19	+	1.29022e20i	−0.0793944	+	0.478190i
$359$		−	1.17833e20i		−	0.427082i	−0.976934	−	0.213541i	$-0.931500\pi$
$359$		−	1.17833e20i		−	0.427082i	0.976934	−	0.213541i	$-0.0684996\pi$
$360$	8.06822e19	+	4.34077e19i	0.285994	+	0.153868i
$361$	1.56531e20			0.542679
$362$	2.27610e20	+	3.77904e19i	0.771833	+	0.128148i
$363$			4.78626e19i			0.158761i
$364$	−2.49706e20	+	7.31257e20i	−0.810248	+	2.37279i
$365$	−1.25726e20			−0.399100
$366$	5.24413e19	−	3.15853e20i	0.162864	−	0.980925i
$367$		−	4.77325e20i		−	1.45039i	−0.688542	−	0.725196i	$-0.741749\pi$
$367$		−	4.77325e20i		−	1.45039i	0.688542	−	0.725196i	$-0.258251\pi$
$368$	−3.39620e20	+	4.39298e20i	−1.00974	+	1.30610i
$369$	2.80848e19			0.0817073
$370$	1.97639e20	+	3.28142e19i	0.562676	+	0.0934217i
$371$			9.12835e18i			0.0254332i
$372$	1.81304e20	+	6.19109e19i	0.494384	+	0.168820i
$373$	−3.46897e20			−0.925826			−0.462913	−	0.886404i	$-0.653196\pi$
$373$	−3.46897e20			−0.925826			−0.462913	+	0.886404i	$0.653196\pi$
$374$	2.27967e19	−	1.37304e20i	0.0595524	−	0.358682i
$375$		−	2.31146e20i		−	0.591066i
$376$	2.43478e20	−	4.52553e20i	0.609476	−	1.13284i
$377$	−2.55579e20			−0.626318
$378$	−1.10865e20	−	1.84070e19i	−0.265986	−	0.0441619i
$379$			1.05233e20i			0.247195i	0.992332	+	0.123598i	$0.0394432\pi$
$379$			1.05233e20i			0.247195i	−0.992332	+	0.123598i	$0.960557\pi$
$380$	−9.25700e19	+	2.71089e20i	−0.212913	+	0.623508i
$381$	6.84358e19			0.154129
$382$	1.08519e20	−	6.53609e20i	0.239332	−	1.44149i
$383$			1.51822e19i			0.0327902i	0.999866	+	0.0163951i	$0.00521895\pi$
$383$			1.51822e19i			0.0327902i	−0.999866	+	0.0163951i	$0.994781\pi$
$384$	2.49333e20	−	1.11072e20i	0.527387	−	0.234938i
$385$	7.43987e20			1.54127
$386$	−4.39521e20	−	7.29741e19i	−0.891828	−	0.148071i
$387$			2.53616e20i			0.504068i
$388$	7.34285e19	+	2.50740e19i	0.142959	+	0.0488169i
$389$	2.06160e20			0.393195			0.196597	−	0.980484i	$-0.437011\pi$
$389$	2.06160e20			0.393195			0.196597	+	0.980484i	$0.437011\pi$
$390$	−8.82440e19	+	5.31491e20i	−0.164880	+	0.993068i
$391$		−	2.90401e20i		−	0.531600i
$392$	−4.72773e20	−	2.54356e20i	−0.847939	−	0.456199i
$393$	−2.91755e20			−0.512717
$394$	−1.27614e20	−	2.11879e19i	−0.219751	−	0.0364854i
$395$			4.14600e20i			0.699605i
$396$	7.35532e19	−	2.15398e20i	0.121630	−	0.356189i
$397$	5.46369e20			0.885446			0.442723	−	0.896658i	$-0.354013\pi$
$397$	5.46369e20			0.885446			0.442723	+	0.896658i	$0.354013\pi$
$398$	9.81332e19	−	5.91054e20i	0.155866	−	0.938777i
$399$		−	3.51381e20i		−	0.547010i
$400$	−2.63324e19	−	2.03576e19i	−0.0401801	−	0.0310632i
$401$	−7.69150e20			−1.15042			−0.575210	−	0.818006i	$-0.695080\pi$
$401$	−7.69150e20			−1.15042			−0.575210	+	0.818006i	$0.695080\pi$
$402$	3.09154e19	+	5.13291e18i	0.0453280	+	0.00752585i
$403$			1.12662e21i			1.61934i
$404$	−1.01305e21	−	3.45932e20i	−1.42751	−	0.487461i
$405$	−7.83573e19			−0.108253
$406$	5.92885e19	−	3.57093e20i	0.0803086	−	0.483696i
$407$		−	4.97724e20i		−	0.661049i
$408$	−6.76348e19	+	1.25713e20i	−0.0880824	+	0.163719i
$409$	−1.19870e20			−0.153082			−0.0765409	−	0.997066i	$-0.524388\pi$
$409$	−1.19870e20			−0.153082			−0.0765409	+	0.997066i	$0.524388\pi$
$410$	1.88118e20	+	3.12334e19i	0.235591	+	0.0391154i
$411$			1.74153e20i			0.213892i
$412$	3.76822e20	−	1.10351e21i	0.453898	−	1.32923i
$413$	3.33309e19			0.0393774
$414$	7.77835e19	−	4.68488e20i	0.0901332	−	0.542870i
$415$		−	9.89255e20i		−	1.12441i
$416$	1.09194e21	+	1.17648e21i	1.21745	+	1.31171i
$417$	8.80969e20			0.963545
$418$	7.02049e20	+	1.16562e20i	0.753282	+	0.125068i
$419$			1.13590e21i			1.19571i	0.801603	+	0.597857i	$0.203981\pi$
$419$			1.13590e21i			1.19571i	−0.801603	+	0.597857i	$0.796019\pi$
$420$	−7.22123e20	−	2.46587e20i	−0.745791	−	0.254669i
$421$	−1.79904e21			−1.82299			−0.911494	−	0.411314i	$-0.865070\pi$
$421$	−1.79904e21			−1.82299			−0.911494	+	0.411314i	$0.865070\pi$
$422$	−7.49980e19	+	4.51711e20i	−0.0745676	+	0.449119i
$423$			4.39513e20i			0.428794i
$424$	1.66986e19	+	8.98398e18i	0.0159865	+	0.00860086i
$425$	1.74073e19			0.0163538
$426$	2.37223e20	+	3.93863e19i	0.218716	+	0.0363136i
$427$			2.66667e21i			2.41294i
$428$	3.45683e20	−	1.01232e21i	0.306992	−	0.899018i
$429$	1.33848e21			1.16669
$430$	−2.82049e20	+	1.69877e21i	−0.241311	+	1.45341i
$431$			1.65354e21i			1.38866i	0.719657	+	0.694330i	$0.244299\pi$
$431$			1.65354e21i			1.38866i	−0.719657	+	0.694330i	$0.755701\pi$
$432$	−1.42783e20	+	1.84690e20i	−0.117708	+	0.152256i
$433$	5.96108e20			0.482416			0.241208	−	0.970473i	$-0.422456\pi$
$433$	5.96108e20			0.482416			0.241208	+	0.970473i	$0.422456\pi$
$434$	−1.57410e21	−	2.61350e20i	−1.25059	−	0.207637i
$435$		−	2.52387e20i		−	0.196858i
$436$	1.82188e21	+	6.22127e20i	1.39517	+	0.476417i
$437$	1.48485e21			1.11643
$438$	5.24706e19	−	3.16029e20i	0.0387368	−	0.233310i
$439$		−	1.40215e21i		−	1.01643i	−0.861230	−	0.508215i	$-0.830306\pi$
$439$		−	1.40215e21i		−	1.01643i	0.861230	−	0.508215i	$-0.169694\pi$
$440$	7.32220e20	−	1.36098e21i	0.521219	−	0.968793i
$441$	4.59150e20			0.320957
$442$	−8.28131e20	−	1.37495e20i	−0.568487	−	0.0943866i
$443$		−	7.90031e20i		−	0.532616i	−0.963888	−	0.266308i	$-0.914196\pi$
$443$		−	7.90031e20i		−	0.532616i	0.963888	−	0.266308i	$-0.0858038\pi$
$444$	−1.64966e20	+	4.83098e20i	−0.109227	+	0.319868i
$445$	−1.79284e21			−1.16590
$446$	−3.10617e20	+	1.87084e21i	−0.198402	+	1.19497i
$447$		−	5.55231e20i		−	0.348348i
$448$	−1.89707e21	+	1.25273e21i	−1.16912	+	0.772027i
$449$	3.48960e20			0.211254			0.105627	−	0.994406i	$-0.466315\pi$
$449$	3.48960e20			0.211254			0.105627	+	0.994406i	$0.466315\pi$
$450$	2.80821e19	+	4.66251e18i	0.0167005	+	0.00277280i
$451$		−	4.73747e20i		−	0.276779i
$452$	−5.19831e20	−	1.77509e20i	−0.298369	−	0.101886i
$453$	−8.77087e20			−0.494604
$454$	1.54904e20	−	9.32981e20i	0.0858252	−	0.516923i
$455$		−	4.48726e21i		−	2.44281i
$456$	−6.42785e20	−	3.45824e20i	−0.343833	−	0.184985i
$457$	−2.70745e21			−1.42309			−0.711543	−	0.702642i	$-0.752003\pi$
$457$	−2.70745e21			−1.42309			−0.711543	+	0.702642i	$0.752003\pi$
$458$	1.50081e21	+	2.49182e20i	0.775181	+	0.128704i
$459$		−	1.22091e20i		−	0.0619699i
$460$	1.04202e21	−	3.05152e21i	0.519772	−	1.52214i
$461$	9.08827e20			0.445527			0.222763	−	0.974873i	$-0.428492\pi$
$461$	9.08827e20			0.445527			0.222763	+	0.974873i	$0.428492\pi$
$462$	−3.10497e20	+	1.87011e21i	−0.149596	+	0.901015i
$463$		−	1.70441e21i		−	0.807097i	−0.914958	−	0.403548i	$-0.867777\pi$
$463$		−	1.70441e21i		−	0.807097i	0.914958	−	0.403548i	$-0.132223\pi$
$464$	−5.94882e20	−	4.59902e20i	−0.276877	−	0.214053i
$465$	−1.11255e21			−0.508975
$466$	4.10501e21	+	6.81559e20i	1.84598	+	0.306490i
$467$		−	8.02401e20i		−	0.354696i	−0.984148	−	0.177348i	$-0.943248\pi$
$467$		−	8.02401e20i		−	0.354696i	0.984148	−	0.177348i	$-0.0567518\pi$
$468$	−1.29915e21	−	4.43627e20i	−0.564536	−	0.192775i
$469$	−2.61012e20			−0.111501
$470$	−4.88786e20	+	2.94394e21i	−0.205275	+	1.23636i
$471$		−	2.07870e21i		−	0.858271i
$472$	3.28038e19	−	6.09725e19i	0.0133164	−	0.0247513i
$473$	4.27810e21			1.70751
$474$	−1.04216e21	−	1.73030e20i	−0.408983	−	0.0679039i
$475$			8.90052e19i			0.0343452i
$476$	3.84214e20	−	1.12516e21i	0.145787	−	0.426932i
$477$	−1.62174e19			−0.00605110
$478$	−1.76611e20	+	1.06372e21i	−0.0648029	+	0.390306i
$479$		−	3.56009e21i		−	1.28463i	−0.766442	−	0.642313i	$-0.777975\pi$
$479$		−	3.56009e21i		−	1.28463i	0.766442	−	0.642313i	$-0.222025\pi$
$480$	−1.16179e21	+	1.07830e21i	−0.412284	+	0.382657i
$481$	−3.00196e21			−1.04772
$482$	−3.31416e21	−	5.50253e20i	−1.13762	−	0.188880i
$483$			3.95534e21i			1.33539i
$484$	−7.83640e20	−	2.67594e20i	−0.260228	−	0.0888613i
$485$	−4.50584e20			−0.147178
$486$	3.27018e19	−	1.96962e20i	0.0105071	−	0.0632837i
$487$			3.76780e21i			1.19085i	0.803412	+	0.595424i	$0.203016\pi$
$487$			3.76780e21i			1.19085i	−0.803412	+	0.595424i	$0.796984\pi$
$488$	4.87817e21	+	2.62450e21i	1.51670	+	0.815996i
$489$	−7.99626e20			−0.244577
$490$	3.07548e21	+	5.10625e20i	0.925431	+	0.153650i
$491$			6.57554e21i			1.94661i	0.229508	+	0.973307i	$0.426288\pi$
$491$			6.57554e21i			1.94661i	−0.229508	+	0.973307i	$0.573712\pi$
$492$	−1.57019e20	+	4.59825e20i	−0.0457331	+	0.133928i
$493$	3.93251e20			0.112692
$494$	7.03029e20	−	4.23432e21i	0.198225	−	1.19390i
$495$			1.32176e21i			0.366701i
$496$	−2.02730e21	+	2.62231e21i	−0.553432	+	0.715863i
$497$	−2.00282e21			−0.538011
$498$	2.48663e21	+	4.12857e20i	0.657319	+	0.109135i
$499$		−	5.37165e21i		−	1.39735i	−0.715442	−	0.698673i	$-0.753774\pi$
$499$		−	5.37165e21i		−	1.39735i	0.715442	−	0.698673i	$-0.246226\pi$
$500$	3.78449e21	+	1.29231e21i	0.968828	+	0.330831i
$501$	2.15198e21			0.542171
$502$	−2.20126e20	+	1.32582e21i	−0.0545811	+	0.328741i
$503$			1.31342e21i			0.320523i	0.987075	+	0.160261i	$0.0512337\pi$
$503$			1.31342e21i			0.320523i	−0.987075	+	0.160261i	$0.948766\pi$
$504$	9.21203e20	−	1.71224e21i	0.221264	−	0.411265i
$505$	6.21646e21			1.46964
$506$	−7.90265e21	−	1.31209e21i	−1.83895	−	0.305322i
$507$		−	5.55229e21i		−	1.27177i
$508$	−3.82616e20	+	1.12048e21i	−0.0862688	+	0.252636i
$509$	−3.34431e21			−0.742274			−0.371137	−	0.928578i	$-0.621032\pi$
$509$	−3.34431e21			−0.742274			−0.371137	+	0.928578i	$0.621032\pi$
$510$	1.35778e20	−	8.17788e20i	0.0296666	−	0.178681i
$511$			2.66816e21i			0.573912i
$512$	4.24557e20	+	4.70324e21i	0.0899035	+	0.995950i
$513$	6.24263e20			0.130145
$514$	2.53040e20	+	4.20126e19i	0.0519380	+	0.00862332i
$515$			6.77155e21i			1.36845i
$516$	−4.15238e21	−	1.41794e21i	−0.826228	−	0.282136i
$517$	7.41389e21			1.45252
$518$	6.96385e20	−	4.19431e21i	0.134342	−	0.809138i
$519$			4.88316e21i			0.927603i
$520$	−8.20859e21	−	4.41629e21i	−1.53547	−	0.826097i
$521$	6.59852e20			0.121547			0.0607735	−	0.998152i	$-0.480643\pi$
$521$	6.59852e20			0.121547			0.0607735	+	0.998152i	$0.480643\pi$
$522$	6.34410e20	+	1.05332e20i	0.115082	+	0.0191071i
$523$			1.90751e21i			0.340764i	0.985378	+	0.170382i	$0.0545002\pi$
$523$			1.90751e21i			0.340764i	−0.985378	+	0.170382i	$0.945500\pi$
$524$	1.63117e21	−	4.77682e21i	0.286978	−	0.840405i
$525$	−2.37091e20			−0.0410810
$526$	1.67866e21	−	1.01105e22i	0.286468	−	1.72539i
$527$		−	1.73350e21i		−	0.291365i
$528$	3.11543e21	+	2.40853e21i	0.515758	+	0.398732i
$529$	−1.05817e22			−1.72548
$530$	−1.08627e20	−	1.80355e19i	−0.0174475	−	0.00289682i
$531$			5.92156e19i			0.00936871i
$532$	5.75307e21	+	1.96453e21i	0.896616	+	0.306172i
$533$	−2.85734e21			−0.438677
$534$	7.48227e20	−	4.50655e21i	0.113163	−	0.681576i
$535$			6.21198e21i			0.925550i
$536$	−2.56884e20	+	4.77471e20i	−0.0377067	+	0.0700856i
$537$	1.93526e21			0.279863
$538$	−9.59434e21	−	1.59296e21i	−1.36696	−	0.226958i
$539$		−	7.74514e21i		−	1.08722i
$540$	4.38086e20	−	1.28292e21i	0.0605912	−	0.177439i
$541$	6.71055e21			0.914492			0.457246	−	0.889340i	$-0.348836\pi$
$541$	6.71055e21			0.914492			0.457246	+	0.889340i	$0.348836\pi$
$542$	−1.32575e20	+	7.98493e20i	−0.0178019	+	0.107220i
$543$		−	3.41402e21i		−	0.451718i
$544$	−1.68013e21	−	1.81021e21i	−0.219054	−	0.236014i
$545$	−1.11797e22			−1.43635
$546$	1.12794e22	+	1.87272e21i	1.42805	+	0.237100i
$547$			1.05057e22i			1.31077i	0.755296	+	0.655384i	$0.227493\pi$
$547$			1.05057e22i			1.31077i	−0.755296	+	0.655384i	$0.772507\pi$
$548$	−2.85135e21	−	9.73666e20i	−0.350595	−	0.119720i
$549$	−4.73760e21			−0.574090
$550$	7.86491e19	−	4.73701e20i	0.00939274	−	0.0565722i
$551$			2.01074e21i			0.236670i
$552$	7.23554e21	+	3.89278e21i	0.839379	+	0.451594i
$553$	8.79869e21			1.00604
$554$	−8.02364e20	−	1.33217e20i	−0.0904260	−	0.0150135i
$555$		−	2.96447e21i		−	0.329308i
$556$	−4.92539e21	+	1.44238e22i	−0.539314	+	1.57937i
$557$	8.95826e21			0.966901			0.483450	−	0.875372i	$-0.339383\pi$
$557$	8.95826e21			0.966901			0.483450	+	0.875372i	$0.339383\pi$
$558$	4.64314e20	−	2.79655e21i	0.0494013	−	0.297542i
$559$		−	2.58028e22i		−	2.70628i
$560$	8.07460e21	−	1.04445e22i	0.834866	−	1.07990i
$561$	−2.05948e21			−0.209920
$562$	−3.64277e21	−	6.04812e20i	−0.366050	−	0.0607757i
$563$			4.28877e21i			0.424880i	0.977174	+	0.212440i	$0.0681409\pi$
$563$			4.28877e21i			0.424880i	−0.977174	+	0.212440i	$0.931859\pi$
$564$	−7.19602e21	−	2.45726e21i	−0.702845	−	0.240004i
$565$	3.18987e21			0.307175
$566$	−1.08833e21	+	6.55501e21i	−0.103331	+	0.622360i
$567$			1.66291e21i			0.155669i
$568$	−1.97114e21	+	3.66378e21i	−0.181942	+	0.338176i
$569$	−6.08795e21			−0.554081			−0.277040	−	0.960858i	$-0.589354\pi$
$569$	−6.08795e21			−0.554081			−0.277040	+	0.960858i	$0.589354\pi$
$570$	4.18144e21	+	6.94248e20i	0.375255	+	0.0623040i
$571$		−	1.33521e22i		−	1.18157i	−0.806828	−	0.590786i	$-0.798818\pi$
$571$		−	1.33521e22i		−	1.18157i	0.806828	−	0.590786i	$-0.201182\pi$
$572$	−7.48329e21	+	2.19146e22i	−0.653017	+	1.91234i
$573$	−9.80376e21			−0.843637
$574$	6.62838e20	−	3.99225e21i	0.0562486	−	0.338784i
$575$		−	1.00189e21i		−	0.0838451i
$576$	−2.22559e21	−	3.37033e21i	−0.183682	−	0.278159i
$577$	1.16462e22			0.947934			0.473967	−	0.880542i	$-0.342822\pi$
$577$	1.16462e22			0.947934			0.473967	+	0.880542i	$0.342822\pi$
$578$	−1.10148e22	−	1.82880e21i	−0.884208	−	0.146806i
$579$			6.59255e21i			0.521946i
$580$	4.13226e21	+	1.41106e21i	0.322674	+	0.110185i
$581$	−2.09941e22			−1.61692
$582$	1.88048e20	−	1.13261e21i	0.0142851	−	0.0860389i
$583$			2.73562e20i			0.0204978i
$584$	4.88090e21	+	2.62597e21i	0.360742	+	0.194082i
$585$	7.97205e21			0.581197
$586$	2.05800e22	+	3.41693e21i	1.48001	+	0.245728i
$587$			5.35292e21i			0.379739i	0.981809	+	0.189870i	$0.0608065\pi$
$587$			5.35292e21i			0.379739i	−0.981809	+	0.189870i	$0.939193\pi$
$588$	−2.56705e21	+	7.51754e21i	−0.179645	+	0.526086i
$589$	8.86355e21			0.611907
$590$	−6.58542e19	+	3.96638e20i	−0.00448505	+	0.0270133i
$591$			1.91414e21i			0.128610i
$592$	−6.98731e21	−	5.40188e21i	−0.463166	−	0.358073i
$593$	1.48188e22			0.969117			0.484558	−	0.874759i	$-0.338980\pi$
$593$	1.48188e22			0.969117			0.484558	+	0.874759i	$0.338980\pi$
$594$	−3.32244e21	−	5.51628e20i	−0.214371	−	0.0355922i
$595$			6.90440e21i			0.439532i
$596$	9.09064e21	+	3.10423e21i	0.570985	+	0.194977i
$597$	−8.86546e21			−0.549423
$598$	−7.91368e21	+	4.76639e22i	−0.483915	+	2.91460i
$599$		−	4.64806e21i		−	0.280451i	−0.990120	−	0.140226i	$-0.955217\pi$
$599$		−	4.64806e21i		−	0.280451i	0.990120	−	0.140226i	$-0.0447828\pi$
$600$	−2.33342e20	+	4.33713e20i	−0.0138926	+	0.0258222i
$601$	7.32731e21			0.430476			0.215238	−	0.976562i	$-0.430947\pi$
$601$	7.32731e21			0.430476			0.215238	+	0.976562i	$0.430947\pi$
$602$	3.60515e22	+	5.98566e21i	2.09002	+	0.347009i
$603$		−	4.63713e20i		−	0.0265284i
$604$	4.90369e21	−	1.43603e22i	0.276839	−	0.810715i
$605$	4.80871e21			0.267908
$606$	−2.59439e21	+	1.56259e22i	−0.142644	+	0.859141i
$607$			1.58518e22i			0.860140i	0.902796	+	0.430070i	$0.141511\pi$
$607$			1.58518e22i			0.860140i	−0.902796	+	0.430070i	$0.858489\pi$
$608$	9.25581e21	−	8.59067e21i	0.495662	−	0.460043i
$609$	−5.35618e21			−0.283085
$610$	−3.17334e22	−	5.26873e21i	−1.65531	−	0.274832i
$611$		−	4.47159e22i		−	2.30214i
$612$	1.99896e21	+	6.82594e20i	0.101576	+	0.0346858i
$613$	−1.53250e22			−0.768627			−0.384314	−	0.923203i	$-0.625562\pi$
$613$	−1.53250e22			−0.768627			−0.384314	+	0.923203i	$0.625562\pi$
$614$	3.46732e20	−	2.08835e21i	0.0171651	−	0.103385i
$615$		−	2.82166e21i		−	0.137881i
$616$	−2.88829e22	−	1.55392e22i	−1.39314	−	0.749522i
$617$	3.75217e21			0.178649			0.0893247	−	0.996003i	$-0.471529\pi$
$617$	3.75217e21			0.178649			0.0893247	+	0.996003i	$0.471529\pi$
$618$	−1.70212e22	−	2.82605e21i	−0.799988	−	0.132823i
$619$		−	1.97077e22i		−	0.914344i	−0.889378	−	0.457172i	$-0.848862\pi$
$619$		−	1.97077e22i		−	0.914344i	0.889378	−	0.457172i	$-0.151138\pi$
$620$	6.22013e21	−	1.82155e22i	0.284883	−	0.834270i
$621$	−7.02704e21			−0.317717
$622$	5.26238e21	−	3.16952e22i	0.234887	−	1.41472i
$623$			3.80478e22i			1.67658i
$624$	1.45267e22	−	1.87903e22i	0.631963	−	0.817443i
$625$	−2.20405e22			−0.946633
$626$	−8.13559e21	−	1.35076e21i	−0.344980	−	0.0572774i
$627$		−	1.05303e22i		−	0.440861i
$628$	3.40340e22	+	1.16218e22i	1.40681	+	0.480391i
$629$	4.61902e21			0.188514
$630$	−1.84933e21	+	1.11385e22i	−0.0745230	+	0.448850i
$631$			2.01318e22i			0.801029i	0.916290	+	0.400515i	$0.131169\pi$
$631$			2.01318e22i			0.801029i	−0.916290	+	0.400515i	$0.868831\pi$
$632$	8.65953e21	−	1.60955e22i	0.340218	−	0.632366i
$633$	6.77540e21			0.262848
$634$	−1.11429e21	−	1.85007e20i	−0.0426859	−	0.00708719i
$635$		−	6.87569e21i		−	0.260092i
$636$	9.06695e19	−	2.65523e20i	0.00338691	−	0.00991847i
$637$	−4.67139e22			−1.72318
$638$	1.77678e21	−	1.07015e22i	0.0647244	−	0.389833i
$639$		−	3.55820e21i		−	0.128004i
$640$	−1.11593e22	−	2.50502e22i	−0.396457	−	0.889963i
$641$	3.74662e22			1.31455			0.657273	−	0.753652i	$-0.271710\pi$
$641$	3.74662e22			1.31455			0.657273	+	0.753652i	$0.271710\pi$
$642$	−1.56147e22	−	2.59252e21i	−0.541069	−	0.0898342i
$643$			1.66776e22i			0.570750i	0.958416	+	0.285375i	$0.0921181\pi$
$643$			1.66776e22i			0.570750i	−0.958416	+	0.285375i	$0.907882\pi$
$644$	−6.47597e22	−	2.21138e22i	−2.18886	−	0.747441i
$645$	2.54806e22			0.850612
$646$	−1.08173e21	+	6.51521e21i	−0.0356663	+	0.214817i
$647$			2.53541e22i			0.825684i	0.910803	+	0.412842i	$0.135464\pi$
$647$			2.53541e22i			0.825684i	−0.910803	+	0.412842i	$0.864536\pi$
$648$	3.04197e21	+	1.63661e21i	0.0978486	+	0.0526434i
$649$	9.98874e20			0.0317361
$650$	−2.85707e21	−	4.74362e20i	−0.0896632	−	0.0148869i
$651$			2.36106e22i			0.731914i
$652$	4.47061e21	−	1.30921e22i	0.136895	−	0.400892i
$653$	5.01852e22			1.51799			0.758997	−	0.651094i	$-0.225690\pi$
$653$	5.01852e22			1.51799			0.758997	+	0.651094i	$0.225690\pi$
$654$	4.66577e21	−	2.81018e22i	0.139412	−	0.839676i
$655$			2.93124e22i			0.865208i
$656$	−6.65071e21	−	5.14165e21i	−0.193926	−	0.149924i
$657$	−4.74025e21			−0.136546
$658$	6.24766e22	+	1.03731e22i	1.77791	+	0.295189i
$659$		−	4.69046e22i		−	1.31866i	−0.751854	−	0.659329i	$-0.770840\pi$
$659$		−	4.69046e22i		−	1.31866i	0.751854	−	0.659329i	$-0.229160\pi$
$660$	−2.16409e22	−	7.38982e21i	−0.601067	−	0.205250i
$661$	3.27127e22			0.897646			0.448823	−	0.893621i	$-0.351843\pi$
$661$	3.27127e22			0.897646			0.448823	+	0.893621i	$0.351843\pi$
$662$	−5.83516e21	+	3.51450e22i	−0.158194	+	0.952795i
$663$			1.24215e22i			0.332710i
$664$	−2.06620e22	+	3.84046e22i	−0.546800	+	1.01634i
$665$	−3.53030e22			−0.923077
$666$	7.45159e21	+	1.23720e21i	0.192511	+	0.0319628i
$667$		−	2.26339e22i		−	0.577768i
$668$	−1.20315e22	+	3.52338e22i	−0.303464	+	0.888684i
$669$	2.80615e22			0.699361
$670$	5.15699e20	−	3.10604e21i	0.0126998	−	0.0764907i
$671$			7.99159e22i			1.94470i
$672$	2.28838e22	+	2.46555e22i	0.550267	+	0.592871i
$673$	−6.24415e22			−1.48372			−0.741861	−	0.670553i	$-0.766057\pi$
$673$	−6.24415e22			−1.48372			−0.741861	+	0.670553i	$0.766057\pi$
$674$	2.91679e22	+	4.84277e21i	0.684898	+	0.113714i
$675$		−	4.21216e20i		−	0.00977404i
$676$	9.09061e22	+	3.10422e22i	2.08458	+	0.711834i
$677$	−2.80645e22			−0.635987			−0.317994	−	0.948093i	$-0.603009\pi$
$677$	−2.80645e22			−0.635987			−0.317994	+	0.948093i	$0.603009\pi$
$678$	−1.33127e21	+	8.01819e21i	−0.0298145	+	0.179572i
$679$			9.56235e21i			0.211644i
$680$	1.26303e22	+	6.79521e21i	0.276275	+	0.148639i
$681$	−1.39942e22			−0.302531
$682$	−4.71734e22	−	7.83224e21i	−1.00791	−	0.167344i
$683$			5.74146e22i			1.21243i	0.795301	+	0.606215i	$0.207313\pi$
$683$			5.74146e22i			1.21243i	−0.795301	+	0.606215i	$0.792687\pi$
$684$	−3.49018e21	+	1.02209e22i	−0.0728448	+	0.213324i
$685$	1.74969e22			0.360942
$686$	−4.17882e20	+	2.51689e21i	−0.00852041	+	0.0513182i
$687$		−	2.25113e22i		−	0.453678i
$688$	4.64309e22	−	6.00583e22i	0.924911	−	1.19637i
$689$	1.64995e21			0.0324876
$690$	−4.70685e22	−	7.81484e21i	−0.916090	−	0.152099i
$691$		−	1.56264e22i		−	0.300632i	−0.988638	−	0.150316i	$-0.951971\pi$
$691$		−	1.56264e22i		−	0.300632i	0.988638	−	0.150316i	$-0.0480291\pi$
$692$	−7.99506e22	−	2.73012e22i	−1.52045	−	0.519197i
$693$	2.80506e22			0.527323
$694$	3.92353e21	−	2.36313e22i	0.0729123	−	0.439149i
$695$		−	8.85101e22i		−	1.62598i
$696$	−5.27147e21	+	9.79811e21i	−0.0957322	+	0.177938i
$697$	4.39650e21			0.0789305
$698$	3.05962e22	+	5.07991e21i	0.543030	+	0.0901598i
$699$		−	6.15728e22i		−	1.08037i
$700$	1.32555e21	−	3.88183e21i	0.0229938	−	0.0673367i
$701$	−7.49528e21			−0.128542			−0.0642708	−	0.997932i	$-0.520472\pi$
$701$	−7.49528e21			−0.128542			−0.0642708	+	0.997932i	$0.520472\pi$
$702$	−3.32707e21	+	2.00389e22i	−0.0564112	+	0.339763i
$703$			2.36175e22i			0.395906i
$704$	−5.68522e22	+	3.75422e22i	−0.942249	+	0.622212i
$705$	4.41574e22			0.723587
$706$	4.55050e21	+	7.55524e20i	0.0737261	+	0.0122408i
$707$		−	1.31926e23i		−	2.11337i
$708$	−9.69520e20	−	3.31067e20i	−0.0153564	−	0.00524385i
$709$	−8.67150e22			−1.35808			−0.679038	−	0.734103i	$-0.737603\pi$
$709$	−8.67150e22			−1.35808			−0.679038	+	0.734103i	$0.737603\pi$
$710$	3.95711e21	−	2.38336e22i	0.0612789	−	0.369081i
$711$			1.56317e22i			0.239359i
$712$	6.96012e22	+	3.74461e22i	1.05385	+	0.566978i
$713$	−9.97730e22			−1.49381
$714$	−1.73552e22	−	2.88150e21i	−0.256947	−	0.0426611i
$715$		−	1.34476e23i		−	1.96878i
$716$	−1.08198e22	+	3.16854e22i	−0.156644	+	0.458728i
$717$	1.59552e22			0.228428
$718$	4.94072e21	−	2.97578e22i	0.0699512	−	0.421314i
$719$			3.06960e22i			0.429785i	0.976638	+	0.214892i	$0.0689401\pi$
$719$			3.06960e22i			0.429785i	−0.976638	+	0.214892i	$0.931060\pi$
$720$	1.85556e22	+	1.43453e22i	0.256930	+	0.198632i
$721$	1.43707e23			1.96786
$722$	3.95308e22	+	6.56334e21i	0.535351	+	0.0888848i
$723$			4.97104e22i			0.665796i
$724$	5.58968e22	+	1.90874e22i	0.740420	+	0.252835i
$725$	1.35673e21			0.0177741
$726$	−2.00687e21	+	1.20873e22i	−0.0260032	+	0.156617i
$727$			1.14967e22i			0.147333i	0.997283	+	0.0736664i	$0.0234700\pi$
$727$			1.14967e22i			0.147333i	−0.997283	+	0.0736664i	$0.976530\pi$
$728$	−9.37230e22	+	1.74203e23i	−1.18794	+	2.20803i
$729$	−2.95431e21			−0.0370370
$730$	−3.17511e22	−	5.27167e21i	−0.393710	−	0.0653681i
$731$			3.97020e22i			0.486938i
$732$	2.64874e22	−	7.75674e22i	0.321329	−	0.941003i
$733$	−2.43786e22			−0.292535			−0.146267	−	0.989245i	$-0.546726\pi$
$733$	−2.43786e22			−0.292535			−0.146267	+	0.989245i	$0.546726\pi$
$734$	2.00142e22	−	1.20545e23i	0.237558	−	1.43081i
$735$		−	4.61304e22i		−	0.541612i
$736$	−1.04188e23	+	9.67013e22i	−1.21003	+	1.12308i
$737$	−7.82211e21			−0.0898636
$738$	7.09262e21	+	1.17759e21i	0.0806038	+	0.0133827i
$739$		−	6.59982e22i		−	0.741953i	−0.928642	−	0.370977i	$-0.879023\pi$
$739$		−	6.59982e22i		−	0.741953i	0.928642	−	0.370977i	$-0.120977\pi$
$740$	4.85364e22	+	1.65740e22i	0.539776	+	0.184320i
$741$	−6.35124e22			−0.698735
$742$	−3.82751e20	+	2.30530e21i	−0.00416567	+	0.0250897i
$743$		−	2.66867e20i		−	0.00287333i	−0.999999	−	0.00143666i	$-0.999543\pi$
$743$		−	2.66867e20i		−	0.00287333i	0.999999	−	0.00143666i	$-0.000457304\pi$
$744$	4.31912e22	+	2.32372e22i	0.460057	+	0.247515i
$745$	−5.57836e22			−0.587836
$746$	−8.76062e22	−	1.45454e22i	−0.913323	−	0.151640i
$747$		−	3.72980e22i		−	0.384698i
$748$	1.15143e22	−	3.37192e22i	0.117496	−	0.344084i
$749$	1.31831e23			1.33096
$750$	9.69193e21	−	5.83742e22i	0.0968100	−	0.583084i
$751$			4.33769e22i			0.428685i	0.976759	+	0.214343i	$0.0687609\pi$
$751$			4.33769e22i			0.428685i	−0.976759	+	0.214343i	$0.931239\pi$
$752$	8.04641e22	−	1.04080e23i	0.786791	−	1.01771i
$753$	1.98865e22			0.192397
$754$	−6.45447e22	−	1.07164e22i	−0.617860	−	0.102584i
$755$			8.81202e22i			0.834641i
$756$	−2.72263e22	−	9.29710e21i	−0.255161	−	0.0871311i
$757$	−7.63333e22			−0.707859			−0.353930	−	0.935272i	$-0.615155\pi$
$757$	−7.63333e22			−0.707859			−0.353930	+	0.935272i	$0.615155\pi$
$758$	−4.41243e21	+	2.65759e22i	−0.0404878	+	0.243857i
$759$			1.18535e23i			1.07625i
$760$	−3.47446e22	+	6.45800e22i	−0.312161	+	0.580215i
$761$	1.13937e23			1.01295			0.506473	−	0.862256i	$-0.330949\pi$
$761$	1.13937e23			1.01295			0.506473	+	0.862256i	$0.330949\pi$
$762$	1.72830e22	+	2.86951e21i	0.152047	+	0.0252446i
$763$			2.37257e23i			2.06549i
$764$	5.48116e22	−	1.60514e23i	0.472199	−	1.38282i
$765$	−1.22663e22			−0.104574
$766$	−6.36588e20	+	3.83415e21i	−0.00537067	+	0.0323474i
$767$		−	6.02458e21i		−	0.0502995i
$768$	6.76244e22	−	1.75959e22i	0.558745	−	0.145385i
$769$	−4.36037e22			−0.356544			−0.178272	−	0.983981i	$-0.557051\pi$
$769$	−4.36037e22			−0.356544			−0.178272	+	0.983981i	$0.557051\pi$
$770$	1.87889e23	+	3.11953e22i	1.52046	+	0.252443i
$771$		−	3.79546e21i		−	0.0303969i
$772$	−1.07938e23	−	3.68582e22i	−0.855531	−	0.292143i
$773$	1.03362e23			0.810820			0.405410	−	0.914135i	$-0.367129\pi$
$773$	1.03362e23			0.810820			0.405410	+	0.914135i	$0.367129\pi$
$774$	−1.06341e22	+	6.40489e22i	−0.0825607	+	0.497261i
$775$		−	5.98060e21i		−	0.0459548i
$776$	1.74925e22	+	9.41111e21i	0.133032	+	0.0715727i
$777$	−6.29122e22			−0.473551
$778$	5.20642e22	+	8.64428e21i	0.387885	+	0.0644009i
$779$			2.24798e22i			0.165765i
$780$	−4.45708e22	+	1.30524e23i	−0.325307	+	0.952652i
$781$	−6.00213e22			−0.433608
$782$	1.21765e22	−	7.33388e22i	0.0870701	−	0.524421i
$783$		−	9.51577e21i		−	0.0673519i
$784$	−1.08730e23	−	8.40592e22i	−0.761768	−	0.588921i
$785$	−2.08845e23			−1.44833
$786$	−7.36807e22	−	1.22333e22i	−0.505793	−	0.0839774i
$787$			1.31941e23i			0.896567i	0.893891	+	0.448284i	$0.147965\pi$
$787$			1.31941e23i			0.896567i	−0.893891	+	0.448284i	$0.852035\pi$
$788$	−3.13397e22	−	1.07017e22i	−0.210807	−	0.0719854i
$789$	−1.51652e23			−1.00979
$790$	−1.73842e22	+	1.04704e23i	−0.114588	+	0.690157i
$791$		−	6.76958e22i		−	0.441723i
$792$	2.76070e22	−	5.13132e22i	0.178327	−	0.331457i
$793$	4.82003e23			3.08222
$794$	1.37982e23	+	2.29092e22i	0.873488	+	0.145026i
$795$			1.62935e21i			0.0102112i
$796$	4.95657e22	−	1.45152e23i	0.307522	−	0.900570i
$797$	5.73703e22			0.352387			0.176194	−	0.984356i	$-0.443621\pi$
$797$	5.73703e22			0.352387			0.176194	+	0.984356i	$0.443621\pi$
$798$	1.47334e22	−	8.87388e22i	0.0895942	−	0.539623i
$799$			6.88029e22i			0.414222i
$800$	−5.79648e21	−	6.24527e21i	−0.0345497	−	0.0372247i
$801$	−6.75956e22			−0.398895
$802$	−1.94243e23	−	3.22504e22i	−1.13488	−	0.188426i
$803$			7.99606e22i			0.462542i
$804$	7.59224e21	+	2.59256e21i	0.0434832	+	0.0148484i
$805$	3.97389e23			2.25346
$806$	−4.72392e22	+	2.84520e23i	−0.265230	+	1.59747i
$807$			1.43909e23i			0.800020i
$808$	−2.41334e23	−	1.29840e23i	−1.32840	−	0.714689i
$809$	−2.35339e23			−1.28264			−0.641321	−	0.767273i	$-0.721613\pi$
$809$	−2.35339e23			−1.28264			−0.641321	+	0.767273i	$0.721613\pi$
$810$	−1.97886e22	−	3.28552e21i	−0.106791	−	0.0177306i
$811$		−	3.09205e23i		−	1.65226i	−0.563477	−	0.826132i	$-0.690537\pi$
$811$		−	3.09205e23i		−	1.65226i	0.563477	−	0.826132i	$-0.309463\pi$
$812$	2.99458e22	−	8.76952e22i	0.158448	−	0.464010i
$813$	1.19769e22			0.0627510
$814$	2.08695e22	−	1.25697e23i	0.108272	−	0.652122i
$815$			8.03377e22i			0.412723i
$816$	−2.23518e22	+	2.89120e22i	−0.113708	+	0.147081i
$817$	−2.03001e23			−1.02264
$818$	−3.02723e22	−	5.02614e21i	−0.151015	−	0.0250731i
$819$		−	1.69184e23i		−	0.835771i
$820$	4.61982e22	+	1.57755e22i	0.226003	+	0.0771744i
$821$	−2.73719e22			−0.132605			−0.0663026	−	0.997800i	$-0.521120\pi$
$821$	−2.73719e22			−0.132605			−0.0663026	+	0.997800i	$0.521120\pi$
$822$	−7.30221e21	+	4.39810e22i	−0.0350332	+	0.211004i
$823$		−	2.03803e23i		−	0.968305i	−0.874984	−	0.484152i	$-0.839128\pi$
$823$		−	2.03803e23i		−	0.968305i	0.874984	−	0.484152i	$-0.160872\pi$
$824$	1.41434e23	−	2.62884e23i	0.665481	−	1.23693i
$825$	−7.10525e21			−0.0331091
$826$	8.41749e21	+	1.39756e21i	0.0388456	+	0.00644958i
$827$		−	4.11311e22i		−	0.187986i	−0.995573	−	0.0939931i	$-0.970037\pi$
$827$		−	4.11311e22i		−	0.187986i	0.995573	−	0.0939931i	$-0.0299632\pi$
$828$	3.92873e22	−	1.15052e23i	0.177832	−	0.520776i
$829$	−5.97239e22			−0.267739			−0.133870	−	0.990999i	$-0.542740\pi$
$829$	−5.97239e22			−0.267739			−0.133870	+	0.990999i	$0.542740\pi$
$830$	4.14794e22	−	2.49829e23i	0.184165	−	1.10922i
$831$			1.20350e22i			0.0529221i
$832$	2.26431e23	+	3.42897e23i	0.986165	+	1.49340i
$833$	7.18771e22			0.310049
$834$	2.22482e23	+	3.69390e22i	0.950533	+	0.157818i
$835$		−	2.16208e23i		−	0.914911i
$836$	1.72410e23	+	5.88738e22i	0.722624	+	0.246758i
$837$	−4.19466e22			−0.174138
$838$	−4.76282e22	+	2.86863e23i	−0.195845	+	1.17957i
$839$		−	1.47577e23i		−	0.601067i	−0.953771	−	0.300533i	$-0.902835\pi$
$839$		−	1.47577e23i		−	0.601067i	0.953771	−	0.300533i	$-0.0971647\pi$
$840$	−1.72028e23	−	9.25524e22i	−0.694007	−	0.373382i
$841$	−2.19596e23			−0.877520
$842$	−4.54334e23	−	7.54336e22i	−1.79837	−	0.298585i
$843$			5.46394e22i			0.214232i
$844$	−3.78804e22	+	1.10932e23i	−0.147121	+	0.430840i
$845$	−5.57833e23			−2.14610
$846$	−1.84287e22	+	1.10996e23i	−0.0702316	+	0.423003i
$847$		−	1.02051e23i		−	0.385256i
$848$	3.84041e21	+	2.96901e21i	0.0143619	+	0.0111031i
$849$	9.83213e22			0.364239
$850$	4.39608e21	+	7.29886e20i	0.0161330	+	0.00267857i
$851$		−	2.65852e23i		−	0.966503i
$852$	5.82575e22	+	1.98935e22i	0.209814	+	0.0716463i
$853$	9.72860e22			0.347103			0.173551	−	0.984825i	$-0.444476\pi$
$853$	9.72860e22			0.347103			0.173551	+	0.984825i	$0.444476\pi$
$854$	−1.11814e23	+	6.73450e23i	−0.395213	+	2.38036i
$855$		−	6.27191e22i		−	0.219620i
$856$	1.29746e23	−	2.41160e23i	0.450096	−	0.836595i
$857$	4.19404e23			1.44141			0.720703	−	0.693244i	$-0.243819\pi$
$857$	4.19404e23			1.44141			0.720703	+	0.693244i	$0.243819\pi$
$858$	3.38024e23	+	5.61225e22i	1.15093	+	0.191090i
$859$			2.23268e23i			0.753149i	0.926386	+	0.376574i	$0.122898\pi$
$859$			2.23268e23i			0.753149i	−0.926386	+	0.376574i	$0.877102\pi$
$860$	−1.42459e23	+	4.17186e23i	−0.476103	+	1.39425i
$861$	−5.98814e22			−0.198275
$862$	−6.93327e22	+	4.17589e23i	−0.227447	+	1.36991i
$863$		−	8.60773e21i		−	0.0279771i	−0.999902	−	0.0139885i	$-0.995547\pi$
$863$		−	8.60773e21i		−	0.0279771i	0.999902	−	0.0139885i	$-0.00445283\pi$
$864$	−4.38030e22	+	4.06552e22i	−0.141057	+	0.130920i
$865$	4.90607e23			1.56533
$866$	1.50543e23	+	2.49948e22i	0.475901	+	0.0790144i
$867$			1.65216e23i			0.517486i
$868$	−3.86570e23	−	1.32004e23i	−1.19969	−	0.409666i
$869$	2.63683e23			0.810818
$870$	1.05826e22	−	6.37385e22i	0.0322431	−	0.194199i
$871$			4.71781e22i			0.142428i
$872$	4.34017e23	+	2.33505e23i	1.29830	+	0.698496i
$873$	−1.69884e22			−0.0503546
$874$	3.74989e23	+	6.22598e22i	1.10135	+	0.182859i
$875$			4.92841e23i			1.43431i
$876$	2.65022e22	−	7.76108e22i	0.0764273	−	0.223815i
$877$	−3.51034e23			−1.00312			−0.501560	−	0.865123i	$-0.667240\pi$
$877$	−3.51034e23			−1.00312			−0.501560	+	0.865123i	$0.667240\pi$
$878$	5.87920e22	−	3.54102e23i	0.166480	−	1.00270i
$879$		−	3.08689e23i		−	0.866183i
$880$	2.41983e23	−	3.13004e23i	0.672858	−	0.870340i
$881$	−7.45054e22			−0.205296			−0.102648	−	0.994718i	$-0.532732\pi$
$881$	−7.45054e22			−0.205296			−0.102648	+	0.994718i	$0.532732\pi$
$882$	1.15955e23	+	1.92521e22i	0.316622	+	0.0525691i
$883$			6.69162e23i			1.81070i	0.424669	+	0.905349i	$0.360390\pi$
$883$			6.69162e23i			1.81070i	−0.424669	+	0.905349i	$0.639610\pi$
$884$	−2.03373e23	−	6.94470e22i	−0.545351	−	0.186224i
$885$	5.94934e21			0.0158097
$886$	3.31260e22	−	1.99517e23i	0.0872366	−	0.525423i
$887$		−	1.73318e23i		−	0.452330i	−0.974089	−	0.226165i	$-0.927381\pi$
$887$		−	1.73318e23i		−	0.452330i	0.974089	−	0.226165i	$-0.0726189\pi$
$888$	−6.19172e22	+	1.15086e23i	−0.160143	+	0.297658i
$889$	−1.45916e23			−0.374016
$890$	−4.52769e23	−	7.51737e22i	−1.15016	−	0.190961i
$891$			4.98346e22i			0.125461i
$892$	−1.56888e23	+	4.59442e23i	−0.391446	+	1.14634i
$893$	−3.51797e23			−0.869922
$894$	2.32808e22	−	1.40220e23i	0.0570556	−	0.343644i
$895$		−	1.94434e23i		−	0.472266i
$896$	−5.31618e23	+	2.36823e23i	−1.27978	+	0.570112i
$897$	7.14930e23			1.70578
$898$	8.81273e22	+	1.46319e22i	0.208401	+	0.0346010i
$899$		−	1.35109e23i		−	0.316670i
$900$	6.89644e21	+	2.35496e21i	0.0160208	+	0.00547072i
$901$	−2.53873e21			−0.00584546
$902$	1.98642e22	−	1.19641e23i	0.0453334	−	0.273042i
$903$		−	5.40751e23i		−	1.22319i
$904$	−1.23837e23	−	6.66251e22i	−0.277652	−	0.149379i
$905$	−3.43004e23			−0.762272
$906$	−2.21502e23	−	3.67762e22i	−0.487924	−	0.0810106i
$907$		−	4.46186e23i		−	0.974222i	−0.873340	−	0.487111i	$-0.838051\pi$
$907$		−	4.46186e23i		−	0.974222i	0.873340	−	0.487111i	$-0.161949\pi$
$908$	7.82396e22	−	2.29122e23i	0.169332	−	0.495885i
$909$	2.34380e23			0.502816
$910$	1.88151e23	−	1.13323e24i	0.400106	−	2.40982i
$911$		−	3.66007e21i		−	0.00771511i	−0.999993	−	0.00385755i	$-0.998772\pi$
$911$		−	3.66007e21i		−	0.00771511i	0.999993	−	0.00385755i	$-0.00122790\pi$
$912$	−1.47830e23	−	1.14287e23i	−0.308891	−	0.238803i
$913$	−6.29158e23			−1.30315
$914$	−6.83748e23	−	1.13523e23i	−1.40387	−	0.233086i
$915$			4.75983e23i			0.968774i
$916$	3.68572e23	+	1.25858e23i	0.743632	+	0.253932i
$917$	6.22070e23			1.24418
$918$	5.11926e21	−	3.08331e22i	0.0101500	−	0.0611331i
$919$		−	6.54183e22i		−	0.128581i	−0.997931	−	0.0642903i	$-0.979522\pi$
$919$		−	6.54183e22i		−	0.128581i	0.997931	−	0.0642903i	$-0.0204784\pi$
$920$	3.91104e23	−	7.26948e23i	0.762062	−	1.41645i
$921$	−3.13241e22			−0.0605064
$922$	2.29518e23	+	3.81071e22i	0.439510	+	0.0729723i
$923$			3.62011e23i			0.687239i
$924$	−1.56827e23	+	4.59265e23i	−0.295152	+	0.864345i
$925$	1.59357e22			0.0297329
$926$	7.14657e22	−	4.30436e23i	0.132193	−	0.796197i
$927$			2.55309e23i			0.468196i
$928$	−1.30950e23	−	1.41088e23i	−0.238078	−	0.256512i
$929$	−4.59645e23			−0.828509			−0.414254	−	0.910161i	$-0.635958\pi$
$929$	−4.59645e23			−0.828509			−0.414254	+	0.910161i	$0.635958\pi$
$930$	−2.80967e23	−	4.66492e22i	−0.502101	−	0.0833643i
$931$			3.67515e23i			0.651145i
$932$	1.00811e24	+	3.44246e23i	1.77085	+	0.604702i
$933$	−4.75409e23			−0.827970
$934$	3.36446e22	−	2.02640e23i	0.0580952	−	0.349906i
$935$			2.06914e23i			0.354239i
$936$	−3.09489e23	−	1.66508e23i	−0.525338	−	0.282636i
$937$	−4.26921e23			−0.718507			−0.359253	−	0.933240i	$-0.616969\pi$
$937$	−4.26921e23			−0.718507			−0.359253	+	0.933240i	$0.616969\pi$
$938$	−6.59167e22	−	1.09442e22i	−0.109995	−	0.0182626i
$939$			1.22029e23i			0.201901i
$940$	−2.46879e23	+	7.22977e23i	−0.405005	+	1.18605i
$941$	8.13726e23			1.32361			0.661807	−	0.749675i	$-0.269790\pi$
$941$	8.13726e23			1.32361			0.661807	+	0.749675i	$0.269790\pi$
$942$	8.71597e22	−	5.24961e23i	0.140575	−	0.846680i
$943$		−	2.53045e23i		−	0.404673i
$944$	1.08409e22	−	1.40227e22i	0.0171906	−	0.0222360i
$945$	1.67071e23			0.262691
$946$	1.08040e24	+	1.79381e23i	1.68445	+	0.279670i
$947$			6.60173e23i			1.02061i	0.859995	+	0.510303i	$0.170467\pi$
$947$			6.60173e23i			1.02061i	−0.859995	+	0.510303i	$0.829533\pi$
$948$	−2.55934e23	−	8.73950e22i	−0.392338	−	0.133974i
$949$	4.82272e23			0.733099
$950$	−3.73198e21	+	2.24776e22i	−0.00562537	+	0.0338814i
$951$			1.67137e22i			0.0249821i
$952$	1.44209e23	−	2.68041e23i	0.213745	−	0.397288i
$953$	1.80001e23			0.264565			0.132282	−	0.991212i	$-0.457769\pi$
$953$	1.80001e23			0.264565			0.132282	+	0.991212i	$0.457769\pi$
$954$	−4.09559e21	−	6.79994e20i	−0.00596938	−	0.000991102i
$955$			9.84974e23i			1.42363i
$956$	−8.92037e22	+	2.61230e23i	−0.127856	+	0.374421i
$957$	−1.60516e23			−0.228151
$958$	1.49274e23	−	8.99075e23i	0.210408	−	1.26728i
$959$		−	3.71322e23i		−	0.519041i
$960$	−3.38614e23	+	2.23603e23i	−0.469391	+	0.309962i
$961$	1.31847e23			0.181253
$962$	−7.58124e23	−	1.25872e23i	−1.03357	−	0.171605i
$963$			2.34211e23i			0.316663i
$964$	−8.13895e23	−	2.77925e23i	−1.09132	−	0.372659i
$965$	6.62348e23			0.880780
$966$	−1.65847e23	+	9.98893e23i	−0.218721	+	1.31735i
$967$		−	1.55234e23i		−	0.203037i	−0.994834	−	0.101519i	$-0.967630\pi$
$967$		−	1.55234e23i		−	0.203037i	0.994834	−	0.101519i	$-0.0323702\pi$
$968$	−1.86682e23	−	1.00437e23i	−0.242159	−	0.130284i
$969$	9.77244e22			0.125722
$970$	−1.13792e23	−	1.88930e22i	−0.145190	−	0.0241061i
$971$		−	1.12163e24i		−	1.41937i	−0.704521	−	0.709683i	$-0.748838\pi$
$971$		−	1.12163e24i		−	1.41937i	0.704521	−	0.709683i	$-0.251162\pi$
$972$	1.65172e22	−	4.83701e22i	0.0207303	−	0.0607082i
$973$	−1.87837e24			−2.33818
$974$	−1.57984e23	+	9.51532e23i	−0.195048	+	1.17477i
$975$			4.28544e22i			0.0524757i
$976$	1.12190e24	+	8.67340e23i	1.36256	+	1.05339i
$977$	6.16903e23			0.743123			0.371561	−	0.928408i	$-0.378823\pi$
$977$	6.16903e23			0.743123			0.371561	+	0.928408i	$0.378823\pi$
$978$	−2.01940e23	−	3.35283e22i	−0.241274	−	0.0400590i
$979$			1.14023e24i			1.35124i
$980$	7.55280e23	+	2.57909e23i	0.887768	+	0.303151i
$981$	−4.21510e23			−0.491424
$982$	−2.75712e23	+	1.66061e24i	−0.318834	+	1.92033i
$983$		−	8.30372e23i		−	0.952456i	−0.879322	−	0.476228i	$-0.842004\pi$
$983$		−	8.30372e23i		−	0.952456i	0.879322	−	0.476228i	$-0.157996\pi$
$984$	−5.89344e22	+	1.09542e23i	−0.0670514	+	0.124629i
$985$	1.92312e23			0.217028
$986$	9.93128e22	+	1.64890e22i	0.111171	+	0.0184578i
$987$		−	9.37113e23i		−	1.04053i
$988$	3.55090e23	−	1.03987e24i	0.391095	−	1.14531i
$989$	2.28509e24			2.49650
$990$	−5.54215e22	+	3.33802e23i	−0.0600616	+	0.361749i
$991$		−	1.82546e24i		−	1.96238i	−0.193055	−	0.981188i	$-0.561839\pi$
$991$		−	1.82546e24i		−	1.96238i	0.193055	−	0.981188i	$-0.438161\pi$
$992$	−6.21933e23	+	5.77240e23i	−0.663209	+	0.615550i
$993$	5.27155e23			0.557627
$994$	−5.05798e23	−	8.39782e22i	−0.530745	−	0.0881202i
$995$			8.90704e23i			0.927148i
$996$	6.10669e23	+	2.08528e23i	0.630567	+	0.215323i
$997$	−4.00530e23			−0.410273			−0.205137	−	0.978733i	$-0.565764\pi$
$997$	−4.00530e23			−0.410273			−0.205137	+	0.978733i	$0.565764\pi$
$998$	2.25233e23	−	1.35657e24i	0.228870	−	1.37847i
$999$		−	1.11770e23i		−	0.112668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.16	yes	16
3.2	odd	2		36.17.d.d.19.1		16
4.3	odd	2	inner	12.17.d.a.7.15	✓	16
12.11	even	2		36.17.d.d.19.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.15	✓	16	4.3	odd	2	inner
12.17.d.a.7.16	yes	16	1.1	even	1	trivial
36.17.d.d.19.1		16	3.2	odd	2
36.17.d.d.19.2		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(252.543 + 41.9299i) q^{2} -3788.00i q^{3} +(62019.8 + 21178.2i) q^{4} -380576. q^{5} +(158830. - 956631. i) q^{6} +8.07663e6i q^{7} +(1.47746e7 + 7.94889e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(252.543 + 41.9299i) q^{2} -3788.00i q^{3} +(62019.8 + 21178.2i) q^{4} -380576. q^{5} +(158830. - 956631. i) q^{6} +8.07663e6i q^{7} +(1.47746e7 + 7.94889e6i) q^{8} -1.43489e7 q^{9} +(-9.61118e7 - 1.59575e7i) q^{10} +2.42044e8i q^{11} +(8.02230e7 - 2.34931e8i) q^{12} +1.45985e9 q^{13} +(-3.38653e8 + 2.03969e9i) q^{14} +1.44162e9i q^{15} +(3.39793e9 + 2.62694e9i) q^{16} -2.24623e9 q^{17} +(-3.62371e9 - 6.01649e8i) q^{18} -1.14852e10i q^{19} +(-2.36033e10 - 8.05993e9i) q^{20} +3.05942e10 q^{21} +(-1.01489e10 + 6.11264e10i) q^{22} +1.29284e11i q^{23} +(3.01104e10 - 5.59663e10i) q^{24} -7.74955e9 q^{25} +(3.68676e11 + 6.12116e10i) q^{26} +5.43536e10i q^{27} +(-1.71049e11 + 5.00910e11i) q^{28} -1.75072e11 q^{29} +(-6.04471e10 + 3.64071e11i) q^{30} +7.71736e11i q^{31} +(7.47977e11 + 8.05889e11i) q^{32} +9.16860e11 q^{33} +(-5.67269e11 - 9.41843e10i) q^{34} -3.07377e12i q^{35} +(-8.89916e11 - 3.03884e11i) q^{36} -2.05634e12 q^{37} +(4.81575e11 - 2.90051e12i) q^{38} -5.52992e12i q^{39} +(-5.62288e12 - 3.02516e12i) q^{40} -1.95728e12 q^{41} +(7.72635e12 + 1.28281e12i) q^{42} -1.76749e13i q^{43} +(-5.12605e12 + 1.50115e13i) q^{44} +5.46085e12 q^{45} +(-5.42087e12 + 3.26497e13i) q^{46} -3.06304e13i q^{47} +(9.95082e12 - 1.28714e13i) q^{48} -3.19990e13 q^{49} +(-1.95709e12 - 3.24938e11i) q^{50} +8.50871e12i q^{51} +(9.05398e13 + 3.09171e13i) q^{52} +1.13022e12 q^{53} +(-2.27904e12 + 1.37266e13i) q^{54} -9.21160e13i q^{55} +(-6.42002e13 + 1.19329e14i) q^{56} -4.35059e13 q^{57} +(-4.42131e13 - 7.34074e12i) q^{58} -4.12684e12i q^{59} +(-3.05310e13 + 8.94090e13i) q^{60} +3.30172e14 q^{61} +(-3.23588e13 + 1.94896e14i) q^{62} -1.15891e14i q^{63} +(1.55105e14 + 2.34884e14i) q^{64} -5.55586e14 q^{65} +(2.31546e14 + 3.84439e13i) q^{66} +3.23169e13i q^{67} +(-1.39311e14 - 4.75712e13i) q^{68} +4.89727e14 q^{69} +(1.28883e14 - 7.76259e14i) q^{70} +2.47977e14i q^{71} +(-2.12000e14 - 1.14058e14i) q^{72} +3.30356e14 q^{73} +(-5.19314e14 - 8.62223e13i) q^{74} +2.93552e13i q^{75} +(2.43236e14 - 7.12310e14i) q^{76} -1.95490e15 q^{77} +(2.31869e14 - 1.39654e15i) q^{78} -1.08940e15i q^{79} +(-1.29317e15 - 9.99749e14i) q^{80} +2.05891e14 q^{81} +(-4.94297e14 - 8.20686e13i) q^{82} +2.59936e15i q^{83} +(1.89745e15 + 6.47931e14i) q^{84} +8.54862e14 q^{85} +(7.41109e14 - 4.46368e15i) q^{86} +6.63171e14i q^{87} +(-1.92398e15 + 3.57611e15i) q^{88} +4.71085e15 q^{89} +(1.37910e15 + 2.28973e14i) q^{90} +1.17907e16i q^{91} +(-2.73800e15 + 8.01816e15i) q^{92} +2.92333e15 q^{93} +(1.28433e15 - 7.73549e15i) q^{94} +4.37100e15i q^{95} +(3.05270e15 - 2.83333e15i) q^{96} +1.18395e15 q^{97} +(-8.08111e15 - 1.34172e15i) q^{98} -3.47306e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9 - 49800172 * q^10 + 425284020 * q^12 - 906419296 * q^13 - 806064072 * q^14 - 2108540816 * q^16 + 12240765600 * q^17 + 2668896702 * q^18 + 1002788712 * q^20 + 39806479296 * q^21 + 216706355928 * q^22 - 111931394832 * q^24 + 206381182512 * q^25 + 1054507182588 * q^26 - 1526063922288 * q^28 + 327679573728 * q^29 + 1192344308100 * q^30 - 5158730488416 * q^32 + 679591529280 * q^33 + 9473293385948 * q^34 - 1959888509316 * q^36 - 8149494749152 * q^37 + 23318999782920 * q^38 - 28671795971776 * q^40 - 25536724613472 * q^41 + 5103781482168 * q^42 - 11442227373552 * q^44 - 5081579320608 * q^45 + 9929654732736 * q^46 + 29246734238832 * q^48 - 93287012964080 * q^49 - 133601044957998 * q^50 + 302261844234872 * q^52 - 86928436629792 * q^53 - 22406076560826 * q^54 + 530930989929024 * q^56 + 48687411524544 * q^57 - 189801665049916 * q^58 + 268455359263896 * q^60 + 476028596468000 * q^61 - 419080420491096 * q^62 + 305944925720704 * q^64 - 1276571708976192 * q^65 - 64815073701480 * q^66 - 1393626893610696 * q^68 + 384812600884992 * q^69 + 1815049064679696 * q^70 - 210694758737760 * q^72 - 368686901901280 * q^73 + 875633111941836 * q^74 - 4351002030861264 * q^76 - 81504772370688 * q^77 + 1907392409236620 * q^78 - 8190389938127328 * q^80 + 3294258113514384 * q^81 + 2390391408733340 * q^82 - 510964995024720 * q^84 + 10085047677398464 * q^85 - 894939801424296 * q^86 + 669091386916800 * q^88 - 5711067674201568 * q^89 + 714578036612004 * q^90 + 7708247605922304 * q^92 + 7132614781502016 * q^93 - 9487273535547696 * q^94 + 8786531038601952 * q^96 - 13564951560560608 * q^97 - 33011660914531290 * q^98

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