LMFDB - Embedded newform 12.17.d.a.7.2

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			7.2
Root			$0.857908 + 1.48594i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-254.964 + 23.0089i) q^{2} -3788.00i q^{3} +(64477.2 - 11732.9i) q^{4} -363465. q^{5} +(87157.5 + 965802. i) q^{6} -2.07768e6i q^{7} +(-1.61694e7 + 4.47501e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(-254.964 + 23.0089i) q^{2} -3788.00i q^{3} +(64477.2 - 11732.9i) q^{4} -363465. q^{5} +(87157.5 + 965802. i) q^{6} -2.07768e6i q^{7} +(-1.61694e7 + 4.47501e6i) q^{8} -1.43489e7 q^{9} +(9.26704e7 - 8.36292e6i) q^{10} -4.00917e8i q^{11} +(-4.44441e7 - 2.44239e8i) q^{12} +2.75836e8 q^{13} +(4.78050e7 + 5.29733e8i) q^{14} +1.37680e9i q^{15} +(4.01965e9 - 1.51300e9i) q^{16} -7.49616e9 q^{17} +(3.65845e9 - 3.30152e8i) q^{18} +1.26547e10i q^{19} +(-2.34352e10 + 4.26449e9i) q^{20} -7.87023e9 q^{21} +(9.22466e9 + 1.02219e11i) q^{22} +1.11334e11i q^{23} +(1.69513e10 + 6.12496e10i) q^{24} -2.04812e10 q^{25} +(-7.03282e10 + 6.34667e9i) q^{26} +5.43536e10i q^{27} +(-2.43771e10 - 1.33963e11i) q^{28} +4.40939e11 q^{29} +(-3.16787e10 - 3.51035e11i) q^{30} +9.68295e11i q^{31} +(-9.90052e11 + 4.78249e11i) q^{32} -1.51867e12 q^{33} +(1.91125e12 - 1.72478e11i) q^{34} +7.55163e11i q^{35} +(-9.25177e11 + 1.68354e11i) q^{36} +2.64747e12 q^{37} +(-2.91170e11 - 3.22649e12i) q^{38} -1.04486e12i q^{39} +(5.87701e12 - 1.62651e12i) q^{40} -7.96145e12 q^{41} +(2.00663e12 - 1.81085e11i) q^{42} +6.27235e12i q^{43} +(-4.70391e12 - 2.58500e13i) q^{44} +5.21532e12 q^{45} +(-2.56167e12 - 2.83861e13i) q^{46} +1.17525e13i q^{47} +(-5.73125e12 - 1.52264e13i) q^{48} +2.89162e13 q^{49} +(5.22196e12 - 4.71249e11i) q^{50} +2.83954e13i q^{51} +(1.77851e13 - 3.23635e12i) q^{52} -5.56077e13 q^{53} +(-1.25062e12 - 1.38582e13i) q^{54} +1.45719e14i q^{55} +(9.29762e12 + 3.35948e13i) q^{56} +4.79359e13 q^{57} +(-1.12423e14 + 1.01455e13i) q^{58} +2.82548e14i q^{59} +(1.61539e13 + 8.87724e13i) q^{60} -1.86371e14 q^{61} +(-2.22794e13 - 2.46880e14i) q^{62} +2.98124e13i q^{63} +(2.41424e14 - 1.44716e14i) q^{64} -1.00257e14 q^{65} +(3.87207e14 - 3.49430e13i) q^{66} -8.81821e13i q^{67} +(-4.83331e14 + 8.79514e13i) q^{68} +4.21732e14 q^{69} +(-1.73755e13 - 1.92539e14i) q^{70} -1.09310e15i q^{71} +(2.32013e14 - 6.42114e13i) q^{72} +5.03458e14 q^{73} +(-6.75009e14 + 6.09153e13i) q^{74} +7.75826e13i q^{75} +(1.48476e14 + 8.15939e14i) q^{76} -8.32977e14 q^{77} +(2.40412e13 + 2.66403e14i) q^{78} -1.56854e15i q^{79} +(-1.46100e15 + 5.49924e14i) q^{80} +2.05891e14 q^{81} +(2.02988e15 - 1.83184e14i) q^{82} -8.07330e14i q^{83} +(-5.07450e14 + 9.23404e13i) q^{84} +2.72459e15 q^{85} +(-1.44320e14 - 1.59922e15i) q^{86} -1.67027e15i q^{87} +(1.79411e15 + 6.48259e15i) q^{88} -5.95350e15 q^{89} +(-1.32972e15 + 1.19999e14i) q^{90} -5.73098e14i q^{91} +(1.30626e15 + 7.17849e15i) q^{92} +3.66790e15 q^{93} +(-2.70411e14 - 2.99645e15i) q^{94} -4.59954e15i q^{95} +(1.81161e15 + 3.75031e15i) q^{96} -2.50681e15 q^{97} +(-7.37258e15 + 6.65329e14i) q^{98} +5.75272e15i 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 $

$2$	−254.964	+	23.0089i	−0.995953	+	0.0898784i
$2$	−254.964	+	23.0089i	−0.995953	+	0.0898784i
$3$		−	3788.00i		−	0.577350i
$3$		−	3788.00i		−	0.577350i
$4$	64477.2	−	11732.9i	0.983844	−	0.179029i
$5$	−363465.			−0.930470			−0.465235	−	0.885187i	$-0.654030\pi$
$5$	−363465.			−0.930470			−0.465235	+	0.885187i	$0.654030\pi$
$6$	87157.5	+	965802.i	0.0518913	+	0.575014i
$7$		−	2.07768e6i		−	0.360408i	−0.983629	−	0.180204i	$-0.942324\pi$
$7$		−	2.07768e6i		−	0.360408i	0.983629	−	0.180204i	$-0.0576757\pi$
$8$	−1.61694e7	+	4.47501e6i	−0.963771	+	0.266731i
$9$	−1.43489e7			−0.333333
$10$	9.26704e7	−	8.36292e6i	0.926704	−	0.0836292i
$11$		−	4.00917e8i		−	1.87031i	−0.354240	−	0.935154i	$-0.615261\pi$
$11$		−	4.00917e8i		−	1.87031i	0.354240	−	0.935154i	$-0.384739\pi$
$12$	−4.44441e7	−	2.44239e8i	−0.103363	−	0.568022i
$13$	2.75836e8			0.338146			0.169073	−	0.985604i	$-0.445923\pi$
$13$	2.75836e8			0.338146			0.169073	+	0.985604i	$0.445923\pi$
$14$	4.78050e7	+	5.29733e8i	0.0323929	+	0.358949i
$15$			1.37680e9i			0.537207i
$16$	4.01965e9	−	1.51300e9i	0.935897	−	0.352274i
$17$	−7.49616e9			−1.07460			−0.537301	−	0.843391i	$-0.680556\pi$
$17$	−7.49616e9			−1.07460			−0.537301	+	0.843391i	$0.680556\pi$
$18$	3.65845e9	−	3.30152e8i	0.331984	−	0.0299595i
$19$			1.26547e10i			0.745115i	0.928009	+	0.372557i	$0.121519\pi$
$19$			1.26547e10i			0.745115i	−0.928009	+	0.372557i	$0.878481\pi$
$20$	−2.34352e10	+	4.26449e9i	−0.915437	+	0.166581i
$21$	−7.87023e9			−0.208081
$22$	9.22466e9	+	1.02219e11i	0.168100	+	1.86274i
$23$			1.11334e11i			1.42169i	0.703350	+	0.710844i	$0.251687\pi$
$23$			1.11334e11i			1.42169i	−0.703350	+	0.710844i	$0.748313\pi$
$24$	1.69513e10	+	6.12496e10i	0.153997	+	0.556433i
$25$	−2.04812e10			−0.134225
$26$	−7.03282e10	+	6.34667e9i	−0.336777	+	0.0303920i
$27$			5.43536e10i			0.192450i
$28$	−2.43771e10	−	1.33963e11i	−0.0645235	−	0.354585i
$29$	4.40939e11			0.881443			0.440722	−	0.897644i	$-0.354723\pi$
$29$	4.40939e11			0.881443			0.440722	+	0.897644i	$0.354723\pi$
$30$	−3.16787e10	−	3.51035e11i	−0.0482833	−	0.535033i
$31$			9.68295e11i			1.13531i	0.823267	+	0.567654i	$0.192149\pi$
$31$			9.68295e11i			1.13531i	−0.823267	+	0.567654i	$0.807851\pi$
$32$	−9.90052e11	+	4.78249e11i	−0.900447	+	0.434965i
$33$	−1.51867e12			−1.07982
$34$	1.91125e12	−	1.72478e11i	1.07025	−	0.0965835i
$35$			7.55163e11i			0.335348i
$36$	−9.25177e11	+	1.68354e11i	−0.327948	+	0.0596765i
$37$	2.64747e12			0.753732			0.376866	−	0.926268i	$-0.377002\pi$
$37$	2.64747e12			0.753732			0.376866	+	0.926268i	$0.377002\pi$
$38$	−2.91170e11	−	3.22649e12i	−0.0669697	−	0.742099i
$39$		−	1.04486e12i		−	0.195229i
$40$	5.87701e12	−	1.62651e12i	0.896760	−	0.248185i
$41$	−7.96145e12			−0.997059			−0.498530	−	0.866873i	$-0.666127\pi$
$41$	−7.96145e12			−0.997059			−0.498530	+	0.866873i	$0.666127\pi$
$42$	2.00663e12	−	1.81085e11i	0.207239	−	0.0187020i
$43$			6.27235e12i			0.536639i	0.963330	+	0.268320i	$0.0864684\pi$
$43$			6.27235e12i			0.536639i	−0.963330	+	0.268320i	$0.913532\pi$
$44$	−4.70391e12	−	2.58500e13i	−0.334840	−	1.84009i
$45$	5.21532e12			0.310157
$46$	−2.56167e12	−	2.83861e13i	−0.127779	−	1.41593i
$47$			1.17525e13i			0.493567i	0.969071	+	0.246783i	$0.0793736\pi$
$47$			1.17525e13i			0.493567i	−0.969071	+	0.246783i	$0.920626\pi$
$48$	−5.73125e12	−	1.52264e13i	−0.203385	−	0.540340i
$49$	2.89162e13			0.870106
$50$	5.22196e12	−	4.71249e11i	0.133682	−	0.0120640i
$51$			2.83954e13i			0.620421i
$52$	1.77851e13	−	3.23635e12i	0.332683	−	0.0605380i
$53$	−5.56077e13			−0.893157			−0.446578	−	0.894745i	$-0.647358\pi$
$53$	−5.56077e13			−0.893157			−0.446578	+	0.894745i	$0.647358\pi$
$54$	−1.25062e12	−	1.38582e13i	−0.0172971	−	0.191671i
$55$			1.45719e14i			1.74027i
$56$	9.29762e12	+	3.35948e13i	0.0961319	+	0.347350i
$57$	4.79359e13			0.430192
$58$	−1.12423e14	+	1.01455e13i	−0.877876	+	0.0792227i
$59$			2.82548e14i			1.92431i	0.272498	+	0.962156i	$0.412150\pi$
$59$			2.82548e14i			1.92431i	−0.272498	+	0.962156i	$0.587850\pi$
$60$	1.61539e13	+	8.87724e13i	0.0961759	+	0.528528i
$61$	−1.86371e14			−0.972162			−0.486081	−	0.873914i	$-0.661574\pi$
$61$	−1.86371e14			−0.972162			−0.486081	+	0.873914i	$0.661574\pi$
$62$	−2.22794e13	−	2.46880e14i	−0.102040	−	1.13071i
$63$			2.98124e13i			0.120136i
$64$	2.41424e14	−	1.44716e14i	0.857709	−	0.514135i
$65$	−1.00257e14			−0.314634
$66$	3.87207e14	−	3.49430e13i	1.07545	−	0.0970528i
$67$		−	8.81821e13i		−	0.217161i	−0.994088	−	0.108581i	$-0.965369\pi$
$67$		−	8.81821e13i		−	0.217161i	0.994088	−	0.108581i	$-0.0346305\pi$
$68$	−4.83331e14	+	8.79514e13i	−1.05724	+	0.192385i
$69$	4.21732e14			0.820812
$70$	−1.73755e13	−	1.92539e14i	−0.0301406	−	0.333991i
$71$		−	1.09310e15i		−	1.69275i	−0.532586	−	0.846376i	$-0.678780\pi$
$71$		−	1.09310e15i		−	1.69275i	0.532586	−	0.846376i	$-0.321220\pi$
$72$	2.32013e14	−	6.42114e13i	0.321257	−	0.0889104i
$73$	5.03458e14			0.624282			0.312141	−	0.950036i	$-0.398954\pi$
$73$	5.03458e14			0.624282			0.312141	+	0.950036i	$0.398954\pi$
$74$	−6.75009e14	+	6.09153e13i	−0.750682	+	0.0677443i
$75$			7.75826e13i			0.0774951i
$76$	1.48476e14	+	8.15939e14i	0.133397	+	0.733076i
$77$	−8.32977e14			−0.674073
$78$	2.40412e13	+	2.66403e14i	0.0175468	+	0.194438i
$79$		−	1.56854e15i		−	1.03390i	−0.856015	−	0.516951i	$-0.827067\pi$
$79$		−	1.56854e15i		−	1.03390i	0.856015	−	0.516951i	$-0.172933\pi$
$80$	−1.46100e15	+	5.49924e14i	−0.870824	+	0.327780i
$81$	2.05891e14			0.111111
$82$	2.02988e15	−	1.83184e14i	0.993024	−	0.0896142i
$83$		−	8.07330e14i		−	0.358448i	−0.983808	−	0.179224i	$-0.942641\pi$
$83$		−	8.07330e14i		−	0.358448i	0.983808	−	0.179224i	$-0.0573587\pi$
$84$	−5.07450e14	+	9.23404e13i	−0.204720	+	0.0372527i
$85$	2.72459e15			0.999884
$86$	−1.44320e14	−	1.59922e15i	−0.0482323	−	0.534468i
$87$		−	1.67027e15i		−	0.508901i
$88$	1.79411e15	+	6.48259e15i	0.498870	+	1.80255i
$89$	−5.95350e15			−1.51235			−0.756176	−	0.654369i	$-0.772934\pi$
$89$	−5.95350e15			−1.51235			−0.756176	+	0.654369i	$0.772934\pi$
$90$	−1.32972e15	+	1.19999e14i	−0.308901	+	0.0278764i
$91$		−	5.73098e14i		−	0.121870i
$92$	1.30626e15	+	7.17849e15i	0.254524	+	1.39872i
$93$	3.66790e15			0.655471
$94$	−2.70411e14	−	2.99645e15i	−0.0443610	−	0.491569i
$95$		−	4.59954e15i		−	0.693307i
$96$	1.81161e15	+	3.75031e15i	0.251127	+	0.519874i
$97$	−2.50681e15			−0.319851			−0.159926	−	0.987129i	$-0.551125\pi$
$97$	−2.50681e15			−0.319851			−0.159926	+	0.987129i	$0.551125\pi$
$98$	−7.37258e15	+	6.65329e14i	−0.866585	+	0.0782038i
$99$			5.75272e15i			0.623436i
$100$	−1.32057e15	+	2.40303e14i	−0.132057	+	0.0240303i
$101$	3.45042e15			0.318641			0.159320	−	0.987227i	$-0.449070\pi$
$101$	3.45042e15			0.318641			0.159320	+	0.987227i	$0.449070\pi$
$102$	−6.53347e14	−	7.23980e15i	−0.0557625	−	0.617910i
$103$			1.20028e16i			0.947510i	0.880657	+	0.473755i	$0.157102\pi$
$103$			1.20028e16i			0.947510i	−0.880657	+	0.473755i	$0.842898\pi$
$104$	−4.46010e15	+	1.23437e15i	−0.325895	+	0.0901940i
$105$	2.86055e15			0.193614
$106$	1.41779e16	−	1.27947e15i	0.889542	−	0.0802755i
$107$			1.78228e16i			1.03730i	0.854985	+	0.518652i	$0.173566\pi$
$107$			1.78228e16i			1.03730i	−0.854985	+	0.518652i	$0.826434\pi$
$108$	6.37724e14	+	3.50457e15i	0.0344542	+	0.189341i
$109$	−2.01473e16			−1.01113			−0.505563	−	0.862790i	$-0.668715\pi$
$109$	−2.01473e16			−1.01113			−0.505563	+	0.862790i	$0.668715\pi$
$110$	−3.35284e15	−	3.71532e16i	−0.156412	−	1.73322i
$111$		−	1.00286e16i		−	0.435168i
$112$	−3.14354e15	−	8.35153e15i	−0.126962	−	0.337304i
$113$	4.97373e16			1.87092			0.935458	−	0.353438i	$-0.114988\pi$
$113$	4.97373e16			1.87092			0.935458	+	0.353438i	$0.114988\pi$
$114$	−1.22219e16	+	1.10295e15i	−0.428451	+	0.0386650i
$115$		−	4.04659e16i		−	1.32284i
$116$	2.84305e16	−	5.17348e15i	0.867202	−	0.157804i
$117$	−3.95794e15			−0.112715
$118$	−6.50111e15	−	7.20395e16i	−0.172954	−	1.91652i
$119$			1.55746e16i			0.387294i
$120$	−6.16120e15	−	2.22621e16i	−0.143290	−	0.517745i
$121$	−1.14785e17			−2.49805
$122$	4.75178e16	−	4.28818e15i	0.968227	−	0.0873764i
$123$			3.01579e16i			0.575653i
$124$	1.13609e16	+	6.24329e16i	0.203254	+	1.11697i
$125$	6.29045e16			1.05536
$126$	−6.85950e14	−	7.60109e15i	−0.0107976	−	0.119650i
$127$			1.28707e17i			1.90183i	0.309458	+	0.950913i	$0.399852\pi$
$127$			1.28707e17i			1.90183i	−0.309458	+	0.950913i	$0.600148\pi$
$128$	−5.82245e16	+	4.24523e16i	−0.808028	+	0.589144i
$129$	2.37596e16			0.309829
$130$	2.55618e16	−	2.30679e15i	0.313361	−	0.0282789i
$131$			5.58699e16i			0.644180i	0.946709	+	0.322090i	$0.104385\pi$
$131$			5.58699e16i			0.644180i	−0.946709	+	0.322090i	$0.895615\pi$
$132$	−9.79197e16	+	1.78184e16i	−1.06238	+	0.193320i
$133$	2.62924e16			0.268545
$134$	2.02897e15	+	2.24832e16i	0.0195181	+	0.216282i
$135$		−	1.97556e16i		−	0.179069i
$136$	1.21208e17	−	3.35454e16i	1.03567	−	0.286630i
$137$	−4.13685e16			−0.333354			−0.166677	−	0.986012i	$-0.553304\pi$
$137$	−4.13685e16			−0.333354			−0.166677	+	0.986012i	$0.553304\pi$
$138$	−1.07526e17	+	9.70358e15i	−0.817490	+	0.0737733i
$139$		−	1.23079e17i		−	0.883214i	−0.897209	−	0.441607i	$-0.854409\pi$
$139$		−	1.23079e17i		−	0.883214i	0.897209	−	0.441607i	$-0.145591\pi$
$140$	8.86023e15	+	4.86908e16i	0.0600372	+	0.329930i
$141$	4.45183e16			0.284961
$142$	2.51510e16	+	2.78701e17i	0.152142	+	1.68590i
$143$		−	1.10587e17i		−	0.632437i
$144$	−5.76775e16	+	2.17100e16i	−0.311966	+	0.117425i
$145$	−1.60266e17			−0.820156
$146$	−1.28364e17	+	1.15840e16i	−0.621755	+	0.0561095i
$147$		−	1.09534e17i		−	0.502356i
$148$	1.70701e17	−	3.10624e16i	0.741555	−	0.134940i
$149$	3.17368e17			1.30639			0.653196	−	0.757189i	$-0.273428\pi$
$149$	3.17368e17			1.30639			0.653196	+	0.757189i	$0.273428\pi$
$150$	−1.78509e15	−	1.97808e16i	−0.00696514	−	0.0771815i
$151$		−	3.69595e17i		−	1.36745i	−0.729741	−	0.683723i	$-0.760360\pi$
$151$		−	3.69595e17i		−	1.36745i	0.729741	−	0.683723i	$-0.239640\pi$
$152$	−5.66299e16	−	2.04619e17i	−0.198745	−	0.718120i
$153$	1.07562e17			0.358200
$154$	2.12379e17	−	1.91659e16i	0.671345	−	0.0605847i
$155$		−	3.51941e17i		−	1.05637i
$156$	−1.22593e16	−	6.73699e16i	−0.0349516	−	0.192074i
$157$	−6.48205e17			−1.75596			−0.877981	−	0.478696i	$-0.841110\pi$
$157$	−6.48205e17			−1.75596			−0.877981	+	0.478696i	$0.841110\pi$
$158$	3.60904e16	+	3.99921e17i	0.0929255	+	1.02972i
$159$			2.10642e17i			0.515664i
$160$	3.59849e17	−	1.73827e17i	0.837839	−	0.404722i
$161$	2.31316e17			0.512387
$162$	−5.24948e16	+	4.73732e15i	−0.110661	+	0.00998649i
$163$			3.08754e16i			0.0619601i	0.999520	+	0.0309801i	$0.00986284\pi$
$163$			3.08754e16i			0.0619601i	−0.999520	+	0.0309801i	$0.990137\pi$
$164$	−5.13332e17	+	9.34106e16i	−0.980951	+	0.178503i
$165$	5.51984e17			1.00474
$166$	1.85758e16	+	2.05840e17i	0.0322168	+	0.356997i
$167$			6.62760e16i			0.109553i	0.998499	+	0.0547765i	$0.0174446\pi$
$167$			6.62760e16i			0.109553i	−0.998499	+	0.0547765i	$0.982555\pi$
$168$	1.27257e17	−	3.52193e16i	0.200543	−	0.0555018i
$169$	−5.89331e17			−0.885657
$170$	−6.94672e17	+	6.26898e16i	−0.995838	+	0.0898681i
$171$		−	1.81581e17i		−	0.248372i
$172$	7.35927e16	+	4.04423e17i	0.0960742	+	0.527969i
$173$	−3.18033e17			−0.396372			−0.198186	−	0.980164i	$-0.563505\pi$
$173$	−3.18033e17			−0.396372			−0.198186	+	0.980164i	$0.563505\pi$
$174$	3.84311e16	+	4.25859e17i	0.0457393	+	0.506842i
$175$			4.25533e16i			0.0483759i
$176$	−6.06590e17	−	1.61155e18i	−0.658861	−	1.75042i
$177$	1.07029e18			1.11100
$178$	1.51793e18	−	1.36983e17i	1.50623	−	0.135928i
$179$			1.31547e18i			1.24812i	0.781378	+	0.624058i	$0.214517\pi$
$179$			1.31547e18i			1.24812i	−0.781378	+	0.624058i	$0.785483\pi$
$180$	3.36269e17	−	6.11907e16i	0.305146	−	0.0555272i
$181$	4.11057e17			0.356840			0.178420	−	0.983954i	$-0.442901\pi$
$181$	4.11057e17			0.356840			0.178420	+	0.983954i	$0.442901\pi$
$182$	1.31863e16	+	1.46119e17i	0.0109535	+	0.121377i
$183$			7.05971e17i			0.561278i
$184$	−4.98219e17	−	1.80020e18i	−0.379208	−	1.37018i
$185$	−9.62262e17			−0.701325
$186$	−9.35181e17	+	8.43942e16i	−0.652818	+	0.0589127i
$187$			3.00534e18i			2.00984i
$188$	1.37890e17	+	7.57765e17i	0.0883629	+	0.485593i
$189$	1.12929e17			0.0693605
$190$	1.05830e17	+	1.17272e18i	0.0623133	+	0.690501i
$191$			3.17928e17i			0.179499i	0.995964	+	0.0897496i	$0.0286067\pi$
$191$			3.17928e17i			0.179499i	−0.995964	+	0.0897496i	$0.971393\pi$
$192$	−5.48185e17	−	9.14511e17i	−0.296836	−	0.495199i
$193$	−2.01229e18			−1.04528			−0.522640	−	0.852554i	$-0.675053\pi$
$193$	−2.01229e18			−1.04528			−0.522640	+	0.852554i	$0.675053\pi$
$194$	6.39147e17	−	5.76790e16i	0.318557	−	0.0287477i
$195$			3.79772e17i			0.181654i
$196$	1.86443e18	−	3.39270e17i	0.856049	−	0.155775i
$197$	−6.87244e17			−0.302957			−0.151479	−	0.988461i	$-0.548403\pi$
$197$	−6.87244e17			−0.302957			−0.151479	+	0.988461i	$0.548403\pi$
$198$	−1.32364e17	−	1.46674e18i	−0.0560335	−	0.620913i
$199$		−	2.26181e18i		−	0.919670i	−0.888004	−	0.459835i	$-0.847909\pi$
$199$		−	2.26181e18i		−	0.919670i	0.888004	−	0.459835i	$-0.152091\pi$
$200$	3.31168e17	−	9.16534e16i	0.129363	−	0.0358021i
$201$	−3.34033e17			−0.125378
$202$	−8.79734e17	+	7.93904e16i	−0.317351	+	0.0286389i
$203$		−	9.16129e17i		−	0.317679i
$204$	3.33160e17	+	1.83086e18i	0.111074	+	0.610398i
$205$	2.89371e18			0.927734
$206$	−2.76170e17	−	3.06027e18i	−0.0851607	−	0.943675i
$207$		−	1.59752e18i		−	0.473896i
$208$	1.10876e18	−	4.17341e17i	0.316470	−	0.119120i
$209$	5.07349e18			1.39359
$210$	−7.29338e17	+	6.58181e16i	−0.192830	+	0.0174017i
$211$		−	3.18768e18i		−	0.811363i	−0.914015	−	0.405681i	$-0.867034\pi$
$211$		−	3.18768e18i		−	0.811363i	0.914015	−	0.405681i	$-0.132966\pi$
$212$	−3.58543e18	+	6.52437e17i	−0.878727	+	0.159901i
$213$	−4.14066e18			−0.977310
$214$	−4.10083e17	−	4.54418e18i	−0.0932313	−	1.03311i
$215$		−	2.27978e18i		−	0.499327i
$216$	−2.43233e17	−	8.78865e17i	−0.0513324	−	0.185478i
$217$	2.01180e18			0.409174
$218$	5.13684e18	−	4.63567e17i	1.00703	−	0.0908784i
$219$		−	1.90710e18i		−	0.360429i
$220$	1.70971e18	+	9.39557e18i	0.311559	+	1.71215i
$221$	−2.06771e18			−0.363372
$222$	2.30747e17	+	2.55693e18i	0.0391122	+	0.433406i
$223$			1.67258e18i			0.273494i	0.990606	+	0.136747i	$0.0436647\pi$
$223$			1.67258e18i			0.273494i	−0.990606	+	0.136747i	$0.956335\pi$
$224$	9.93648e17	+	2.05701e18i	0.156765	+	0.324528i
$225$	2.93883e17			0.0447418
$226$	−1.26812e19	+	1.14440e18i	−1.86334	+	0.168155i
$227$		−	1.18440e18i		−	0.167993i	−0.996466	−	0.0839966i	$-0.973232\pi$
$227$		−	1.18440e18i		−	0.167993i	0.996466	−	0.0839966i	$-0.0267685\pi$
$228$	3.09077e18	−	5.62426e17i	0.423242	−	0.0770170i
$229$	−5.49562e18			−0.726663			−0.363332	−	0.931660i	$-0.618361\pi$
$229$	−5.49562e18			−0.726663			−0.363332	+	0.931660i	$0.618361\pi$
$230$	9.31076e17	+	1.03173e19i	0.118895	+	1.31748i
$231$			3.15531e18i			0.389176i
$232$	−7.12971e18	+	1.97320e18i	−0.849509	+	0.235108i
$233$	1.00120e19			1.15259			0.576293	−	0.817243i	$-0.304499\pi$
$233$	1.00120e19			1.15259			0.576293	+	0.817243i	$0.304499\pi$
$234$	1.00913e18	−	9.10678e16i	0.112259	−	0.0101307i
$235$		−	4.27161e18i		−	0.459249i
$236$	3.31509e18	+	1.82179e19i	0.344508	+	1.89322i
$237$	−5.94163e18			−0.596923
$238$	−3.58354e17	−	3.97096e18i	−0.0348094	−	0.385727i
$239$		−	5.24204e17i		−	0.0492399i	−0.999697	−	0.0246200i	$-0.992162\pi$
$239$		−	5.24204e17i		−	0.0492399i	0.999697	−	0.0246200i	$-0.00783757\pi$
$240$	2.08311e18	+	5.53426e18i	0.189244	+	0.502771i
$241$	−2.53720e18			−0.222956			−0.111478	−	0.993767i	$-0.535558\pi$
$241$	−2.53720e18			−0.222956			−0.111478	+	0.993767i	$0.535558\pi$
$242$	2.92660e19	−	2.64107e18i	2.48794	−	0.224521i
$243$		−	7.79915e17i		−	0.0641500i
$244$	−1.20166e19	+	2.18666e18i	−0.956455	+	0.174046i
$245$	−1.05100e19			−0.809608
$246$	−6.93900e17	−	7.68918e18i	−0.0517388	−	0.573323i
$247$			3.49062e18i			0.251957i
$248$	−4.33312e18	−	1.56567e19i	−0.302822	−	1.09418i
$249$	−3.05816e18			−0.206950
$250$	−1.60384e19	+	1.44736e18i	−1.05109	+	0.0948544i
$251$			1.04227e19i			0.661593i	0.943702	+	0.330797i	$0.107317\pi$
$251$			1.04227e19i			0.661593i	−0.943702	+	0.330797i	$0.892683\pi$
$252$	3.49785e17	+	1.92222e18i	0.0215078	+	0.118195i
$253$	4.46356e19			2.65900
$254$	−2.96139e18	−	3.28155e19i	−0.170933	−	1.89413i
$255$		−	1.03207e19i		−	0.577283i
$256$	1.38684e19	−	1.21635e19i	0.751806	−	0.659384i
$257$	−2.66097e19			−1.39822			−0.699110	−	0.715014i	$-0.746420\pi$
$257$	−2.66097e19			−1.39822			−0.699110	+	0.715014i	$0.746420\pi$
$258$	−6.05785e18	+	5.46683e17i	−0.308575	+	0.0278469i
$259$		−	5.50059e18i		−	0.271651i
$260$	−6.46427e18	+	1.17630e18i	−0.309551	+	0.0563288i
$261$	−6.32699e18			−0.293814
$262$	−1.28550e18	−	1.42448e19i	−0.0578979	−	0.641573i
$263$		−	1.19002e19i		−	0.519884i	−0.965624	−	0.259942i	$-0.916297\pi$
$263$		−	1.19002e19i		−	0.519884i	0.965624	−	0.259942i	$-0.0837035\pi$
$264$	2.45560e19	−	6.79607e18i	1.04070	−	0.288022i
$265$	2.02114e19			0.831056
$266$	−6.70361e18	+	6.04958e17i	−0.267458	+	0.0241364i
$267$			2.25518e19i			0.873156i
$268$	−1.03463e18	−	5.68573e18i	−0.0388782	−	0.213653i
$269$	−8.57790e18			−0.312869			−0.156435	−	0.987688i	$-0.550000\pi$
$269$	−8.57790e18			−0.312869			−0.156435	+	0.987688i	$0.550000\pi$
$270$	4.54555e17	+	5.03697e18i	0.0160944	+	0.178344i
$271$			3.85518e19i			1.32523i	0.748961	+	0.662614i	$0.230553\pi$
$271$			3.85518e19i			1.32523i	−0.748961	+	0.662614i	$0.769447\pi$
$272$	−3.01319e19	+	1.13417e19i	−1.00572	+	0.378554i
$273$	−2.17089e18			−0.0703618
$274$	1.05475e19	−	9.51844e17i	0.332005	−	0.0299613i
$275$			8.21126e18i			0.251043i
$276$	2.71921e19	−	4.94812e18i	0.807551	−	0.146949i
$277$	9.47812e18			0.273454			0.136727	−	0.990609i	$-0.456342\pi$
$277$	9.47812e18			0.273454			0.136727	+	0.990609i	$0.456342\pi$
$278$	2.83191e18	+	3.13807e19i	0.0793819	+	0.879640i
$279$		−	1.38940e19i		−	0.378436i
$280$	−3.37936e18	−	1.22105e19i	−0.0894479	−	0.323199i
$281$	−2.91956e19			−0.751047			−0.375523	−	0.926813i	$-0.622537\pi$
$281$	−2.91956e19			−0.751047			−0.375523	+	0.926813i	$0.622537\pi$
$282$	−1.13505e19	+	1.02432e18i	−0.283808	+	0.0256118i
$283$			4.76515e19i			1.15820i	0.815255	+	0.579102i	$0.196597\pi$
$283$			4.76515e19i			1.15820i	−0.815255	+	0.579102i	$0.803403\pi$
$284$	−1.28252e19	−	7.04800e19i	−0.303052	−	1.66540i
$285$	−1.74230e19			−0.400281
$286$	2.54449e18	+	2.81958e19i	0.0568424	+	0.629877i
$287$			1.65413e19i			0.359348i
$288$	1.42062e19	−	6.86235e18i	0.300149	−	0.144988i
$289$	7.53119e18			0.154768
$290$	4.08620e19	−	3.68754e18i	0.816837	−	0.0737144i
$291$			9.49579e18i			0.184666i
$292$	3.24616e19	−	5.90701e18i	0.614196	−	0.111765i
$293$	−2.60757e19			−0.480059			−0.240029	−	0.970766i	$-0.577157\pi$
$293$	−2.60757e19			−0.480059			−0.240029	+	0.970766i	$0.577157\pi$
$294$	2.52026e18	+	2.79273e19i	0.0451510	+	0.500323i
$295$		−	1.02696e20i		−	1.79052i
$296$	−4.28080e19	+	1.18474e19i	−0.726425	+	0.201044i
$297$	2.17913e19			0.359941
$298$	−8.09174e19	+	7.30229e18i	−1.30110	+	0.117416i
$299$			3.07098e19i			0.480738i
$300$	9.10267e17	+	5.00231e18i	0.0138739	+	0.0762431i
$301$	1.30319e19			0.193409
$302$	8.50397e18	+	9.42334e19i	0.122904	+	1.36191i
$303$		−	1.30702e19i		−	0.183967i
$304$	1.91466e19	+	5.08674e19i	0.262484	+	0.697350i
$305$	6.77391e19			0.904567
$306$	−2.74243e19	+	2.47487e18i	−0.356751	+	0.0321945i
$307$			3.72489e19i			0.472069i	0.971745	+	0.236035i	$0.0758479\pi$
$307$			3.72489e19i			0.472069i	−0.971745	+	0.236035i	$0.924152\pi$
$308$	−5.37080e19	+	9.77321e18i	−0.663183	+	0.120679i
$309$	4.54665e19			0.547045
$310$	8.09777e18	+	8.97323e19i	0.0949450	+	1.05210i
$311$		−	1.25152e20i		−	1.43006i	−0.699093	−	0.715031i	$-0.746413\pi$
$311$		−	1.25152e20i		−	1.43006i	0.699093	−	0.715031i	$-0.253587\pi$
$312$	4.67578e18	+	1.68948e19i	0.0520735	+	0.188156i
$313$	−1.11292e20			−1.20812			−0.604059	−	0.796940i	$-0.706451\pi$
$313$	−1.11292e20			−1.20812			−0.604059	+	0.796940i	$0.706451\pi$
$314$	1.65269e20	−	1.49145e19i	1.74885	−	0.157823i
$315$		−	1.08358e19i		−	0.111783i
$316$	−1.84035e19	−	1.01135e20i	−0.185099	−	1.01720i
$317$	1.09756e18			0.0107635			0.00538177	−	0.999986i	$-0.498287\pi$
$317$	1.09756e18			0.0107635			0.00538177	+	0.999986i	$0.498287\pi$
$318$	−4.84663e18	−	5.37060e19i	−0.0463471	−	0.513577i
$319$		−	1.76780e20i		−	1.64857i
$320$	−8.77490e19	+	5.25993e19i	−0.798073	+	0.478388i
$321$	6.75128e19			0.598888
$322$	−5.89772e19	+	5.32232e18i	−0.510313	+	0.0460526i
$323$		−	9.48616e19i		−	0.800701i
$324$	1.32753e19	−	2.41569e18i	0.109316	−	0.0198922i
$325$	−5.64944e18			−0.0453878
$326$	−7.10409e17	−	7.87212e18i	−0.00556888	−	0.0617094i
$327$			7.63179e19i			0.583774i
$328$	1.28732e20	−	3.56275e19i	0.960937	−	0.265947i
$329$	2.44178e19			0.177885
$330$	−1.40736e20	+	1.27005e19i	−1.00068	+	0.0903048i
$331$			9.28071e19i			0.644106i	0.946722	+	0.322053i	$0.104373\pi$
$331$			9.28071e19i			0.644106i	−0.946722	+	0.322053i	$0.895627\pi$
$332$	−9.47230e18	−	5.20544e19i	−0.0641728	−	0.352657i
$333$	−3.79883e19			−0.251244
$334$	−1.52494e18	−	1.68980e19i	−0.00984646	−	0.109110i
$335$			3.20511e19i			0.202062i
$336$	−3.16356e19	+	1.19077e19i	−0.194743	+	0.0733016i
$337$	−2.54699e20			−1.53105			−0.765523	−	0.643409i	$-0.777519\pi$
$337$	−2.54699e20			−1.53105			−0.765523	+	0.643409i	$0.777519\pi$
$338$	1.50258e20	−	1.35599e19i	0.882073	−	0.0796015i
$339$		−	1.88404e20i		−	1.08017i
$340$	1.75674e20	−	3.19673e19i	0.983730	−	0.179009i
$341$	3.88206e20			2.12338
$342$	4.17798e18	+	4.62966e19i	0.0223232	+	0.247366i
$343$		−	1.29126e20i		−	0.674000i
$344$	−2.80688e19	−	1.01420e20i	−0.143138	−	0.517198i
$345$	−1.53285e20			−0.763741
$346$	8.10869e19	−	7.31758e18i	0.394768	−	0.0356253i
$347$			3.33158e20i			1.58495i	0.609906	+	0.792474i	$0.291207\pi$
$347$			3.33158e20i			1.58495i	−0.609906	+	0.792474i	$0.708793\pi$
$348$	−1.95971e19	−	1.07695e20i	−0.0911083	−	0.500679i
$349$	−1.77058e20			−0.804472			−0.402236	−	0.915536i	$-0.631767\pi$
$349$	−1.77058e20			−0.804472			−0.402236	+	0.915536i	$0.631767\pi$
$350$	−9.79104e17	−	1.08496e19i	−0.00434795	−	0.0481801i
$351$			1.49927e19i			0.0650762i
$352$	1.91738e20	+	3.96929e20i	0.813519	+	1.68411i
$353$	1.12220e20			0.465448			0.232724	−	0.972543i	$-0.425236\pi$
$353$	1.12220e20			0.465448			0.232724	+	0.972543i	$0.425236\pi$
$354$	−2.72885e20	+	2.46262e19i	−1.10651	+	0.0998552i
$355$			3.97304e20i			1.57505i
$356$	−3.83865e20	+	6.98517e19i	−1.48792	+	0.270755i
$357$	5.89965e19			0.223605
$358$	−3.02674e19	−	3.35396e20i	−0.112179	−	1.24306i
$359$			1.82387e20i			0.661055i	0.943796	+	0.330528i	$0.107227\pi$
$359$			1.82387e20i			0.661055i	−0.943796	+	0.330528i	$0.892773\pi$
$360$	−8.43286e19	+	2.33386e19i	−0.298920	+	0.0827284i
$361$	1.28300e20			0.444804
$362$	−1.04805e20	+	9.45797e18i	−0.355396	+	0.0320723i
$363$			4.34805e20i			1.44225i
$364$	−6.72408e18	−	3.69517e19i	−0.0218184	−	0.119901i
$365$	−1.82989e20			−0.580875
$366$	−1.62436e19	−	1.79997e20i	−0.0504468	−	0.559006i
$367$			3.87362e20i			1.17703i	0.808486	+	0.588516i	$0.200288\pi$
$367$			3.87362e20i			1.17703i	−0.808486	+	0.588516i	$0.799712\pi$
$368$	1.68449e20	+	4.47523e20i	0.500824	+	1.33055i
$369$	1.14238e20			0.332353
$370$	2.45342e20	−	2.21406e19i	0.698487	−	0.0630340i
$371$			1.15535e20i			0.321900i
$372$	2.36496e20	−	4.30349e19i	0.644881	−	0.117349i
$373$	−5.24390e20			−1.39954			−0.699768	−	0.714371i	$-0.746713\pi$
$373$	−5.24390e20			−1.39954			−0.699768	+	0.714371i	$0.746713\pi$
$374$	−6.91495e19	−	7.66253e20i	−0.180641	−	2.00170i
$375$		−	2.38282e20i		−	0.609314i
$376$	−5.25923e19	−	1.90030e20i	−0.131650	−	0.475685i
$377$	1.21627e20			0.298056
$378$	−2.87929e19	+	2.59838e18i	−0.0690797	+	0.00623401i
$379$		−	4.26070e20i		−	1.00085i	−0.865781	−	0.500423i	$-0.833178\pi$
$379$		−	4.26070e20i		−	1.00085i	0.865781	−	0.500423i	$-0.166822\pi$
$380$	−5.39658e19	−	2.96565e20i	−0.124122	−	0.682106i
$381$	4.87540e20			1.09802
$382$	−7.31518e18	−	8.10603e19i	−0.0161331	−	0.178773i
$383$		−	7.93640e20i		−	1.71409i	−0.515243	−	0.857044i	$-0.672298\pi$
$383$		−	7.93640e20i		−	1.71409i	0.515243	−	0.857044i	$-0.327702\pi$
$384$	1.60809e20	+	2.20554e20i	0.340143	+	0.466515i
$385$	3.02758e20			0.627205
$386$	5.13062e20	−	4.63006e19i	1.04105	−	0.0939481i
$387$		−	9.00014e19i		−	0.178880i
$388$	−1.61632e20	+	2.94121e19i	−0.314684	+	0.0572628i
$389$	−3.22822e20			−0.615695			−0.307848	−	0.951436i	$-0.599609\pi$
$389$	−3.22822e20			−0.615695			−0.307848	+	0.951436i	$0.599609\pi$
$390$	−8.73812e18	−	9.68281e19i	−0.0163268	−	0.180919i
$391$		−	8.34576e20i		−	1.52775i
$392$	−4.67557e20	+	1.29400e20i	−0.838583	+	0.232084i
$393$	2.11635e20			0.371918
$394$	1.75223e20	−	1.58127e19i	0.301731	−	0.0272293i
$395$			5.70110e20i			0.962015i
$396$	6.74960e19	+	3.70919e20i	0.111613	+	0.613364i
$397$	−3.57851e20			−0.579933			−0.289966	−	0.957037i	$-0.593644\pi$
$397$	−3.57851e20			−0.579933			−0.289966	+	0.957037i	$0.593644\pi$
$398$	5.20418e19	+	5.76681e20i	0.0826585	+	0.915948i
$399$		−	9.95954e19i		−	0.155044i
$400$	−8.23271e19	+	3.09881e19i	−0.125621	+	0.0472841i
$401$	−8.64609e20			−1.29320			−0.646599	−	0.762830i	$-0.723809\pi$
$401$	−8.64609e20			−1.29320			−0.646599	+	0.762830i	$0.723809\pi$
$402$	8.51664e19	−	7.68573e18i	0.124871	−	0.0112688i
$403$			2.67090e20i			0.383900i
$404$	2.22474e20	−	4.04834e19i	0.313493	−	0.0570461i
$405$	−7.48342e19			−0.103386
$406$	2.10791e19	+	2.33580e20i	0.0285525	+	0.316393i
$407$		−	1.06142e21i		−	1.40971i
$408$	−1.27070e20	−	4.59137e20i	−0.165486	−	0.597944i
$409$	1.07480e21			1.37259			0.686296	−	0.727322i	$-0.259236\pi$
$409$	1.07480e21			1.37259			0.686296	+	0.727322i	$0.259236\pi$
$410$	−7.37790e20	+	6.65809e19i	−0.923979	+	0.0833833i
$411$			1.56704e20i			0.192462i
$412$	1.40827e20	+	7.73905e20i	0.169632	+	0.932202i
$413$	5.87043e20			0.693537
$414$	3.67571e19	+	4.07310e20i	0.0425930	+	0.471978i
$415$			2.93436e20i			0.333525i
$416$	−2.73092e20	+	1.31918e20i	−0.304482	+	0.147082i
$417$	−4.66223e20			−0.509924
$418$	−1.29356e21	+	1.16735e20i	−1.38795	+	0.125254i
$419$			3.64964e20i			0.384183i	0.981377	+	0.192091i	$0.0615270\pi$
$419$			3.64964e20i			0.384183i	−0.981377	+	0.192091i	$0.938473\pi$
$420$	1.84440e20	−	3.35625e19i	0.190485	−	0.0346625i
$421$	3.34227e20			0.338676			0.169338	−	0.985558i	$-0.445837\pi$
$421$	3.34227e20			0.338676			0.169338	+	0.985558i	$0.445837\pi$
$422$	7.33449e19	+	8.12743e20i	0.0729240	+	0.808079i
$423$		−	1.68635e20i		−	0.164522i
$424$	8.99142e20	−	2.48845e20i	0.860799	−	0.238233i
$425$	1.53530e20			0.144239
$426$	1.05572e21	−	9.52719e19i	0.973355	−	0.0878391i
$427$			3.87218e20i			0.350374i
$428$	2.09113e20	+	1.14917e21i	0.185708	+	1.02055i
$429$	−4.18904e20			−0.365138
$430$	5.24552e19	+	5.81261e20i	0.0448787	+	0.497306i
$431$		−	1.07898e21i		−	0.906143i	−0.891474	−	0.453072i	$-0.850328\pi$
$431$		−	1.07898e21i		−	0.906143i	0.891474	−	0.453072i	$-0.149672\pi$
$432$	8.22372e19	+	2.18482e20i	0.0677951	+	0.180113i
$433$	5.72559e20			0.463358			0.231679	−	0.972792i	$-0.425578\pi$
$433$	5.72559e20			0.463358			0.231679	+	0.972792i	$0.425578\pi$
$434$	−5.12938e20	+	4.62894e19i	−0.407518	+	0.0367759i
$435$			6.07086e20i			0.473517i
$436$	−1.29904e21	+	2.36386e20i	−0.994789	+	0.181021i
$437$	−1.40890e21			−1.05932
$438$	4.38802e19	+	4.86241e20i	0.0323948	+	0.358970i
$439$		−	2.13684e21i		−	1.54902i	−0.632562	−	0.774510i	$-0.717997\pi$
$439$		−	2.13684e21i		−	1.54902i	0.632562	−	0.774510i	$-0.282003\pi$
$440$	−6.52095e20	−	2.35619e21i	−0.464183	−	1.67722i
$441$	−4.14916e20			−0.290035
$442$	5.27191e20	−	4.75757e19i	0.361901	−	0.0326593i
$443$			1.95631e21i			1.31889i	0.751754	+	0.659444i	$0.229208\pi$
$443$			1.95631e21i			1.31889i	−0.751754	+	0.659444i	$0.770792\pi$
$444$	−1.17664e20	−	6.46616e20i	−0.0779078	−	0.428137i
$445$	2.16389e21			1.40720
$446$	−3.84842e19	−	4.26447e20i	−0.0245812	−	0.272387i
$447$		−	1.20219e21i		−	0.754245i
$448$	−3.00674e20	−	5.01601e20i	−0.185298	−	0.309125i
$449$	−1.11036e21			−0.672193			−0.336097	−	0.941828i	$-0.609107\pi$
$449$	−1.11036e21			−0.672193			−0.336097	+	0.941828i	$0.609107\pi$
$450$	−7.49294e19	+	6.76191e18i	−0.0445607	+	0.00402133i
$451$			3.19188e21i			1.86481i
$452$	3.20692e21	−	5.83561e20i	1.84069	−	0.334949i
$453$	−1.40002e21			−0.789496
$454$	2.72517e19	+	3.01979e20i	0.0150990	+	0.167313i
$455$			2.08301e20i			0.113397i
$456$	−7.75095e20	+	2.14514e20i	−0.414607	+	0.114746i
$457$	4.76768e19			0.0250598			0.0125299	−	0.999921i	$-0.496012\pi$
$457$	4.76768e19			0.0250598			0.0125299	+	0.999921i	$0.496012\pi$
$458$	1.40119e21	−	1.26448e20i	0.723722	−	0.0653114i
$459$		−	4.07443e20i		−	0.206807i
$460$	−4.74781e20	−	2.60913e21i	−0.236827	−	1.30147i
$461$	8.26966e20			0.405397			0.202698	−	0.979241i	$-0.435029\pi$
$461$	8.26966e20			0.405397			0.202698	+	0.979241i	$0.435029\pi$
$462$	−7.26002e19	−	8.04491e20i	−0.0349786	−	0.387601i
$463$			8.20408e20i			0.388492i	0.980953	+	0.194246i	$0.0622260\pi$
$463$			8.20408e20i			0.388492i	−0.980953	+	0.194246i	$0.937774\pi$
$464$	1.77242e21	−	6.67142e20i	0.824940	−	0.310509i
$465$	−1.33315e21			−0.609896
$466$	−2.55270e21	+	2.30365e20i	−1.14792	+	0.103593i
$467$			4.07930e20i			0.180323i	0.995927	+	0.0901615i	$0.0287383\pi$
$467$			4.07930e20i			0.180323i	−0.995927	+	0.0901615i	$0.971262\pi$
$468$	−2.55197e20	+	4.64380e19i	−0.110894	+	0.0201793i
$469$	−1.83214e20			−0.0782665
$470$	9.82849e19	+	1.08911e21i	0.0412766	+	0.457390i
$471$			2.45540e21i			1.01380i
$472$	−1.26440e21	−	4.56862e21i	−0.513274	−	1.85460i
$473$	2.51469e21			1.00368
$474$	1.51490e21	−	1.36710e20i	0.594507	−	0.0536505i
$475$		−	2.59183e20i		−	0.100013i
$476$	1.82735e20	+	1.00421e21i	0.0693371	+	0.381037i
$477$	7.97909e20			0.297719
$478$	1.20614e19	+	1.33653e20i	0.00442561	+	0.0490406i
$479$		−	1.33160e21i		−	0.480497i	−0.970711	−	0.240248i	$-0.922771\pi$
$479$		−	1.33160e21i		−	0.480497i	0.970711	−	0.240248i	$-0.0772289\pi$
$480$	−6.58455e20	−	1.36311e21i	−0.233666	−	0.483727i
$481$	7.30267e20			0.254871
$482$	6.46895e20	−	5.83782e19i	0.222053	−	0.0200389i
$483$		−	8.76223e20i		−	0.295827i
$484$	−7.40101e21	+	1.34676e21i	−2.45770	+	0.447225i
$485$	9.11138e20			0.297612
$486$	1.79450e19	+	1.98850e20i	0.00576571	+	0.0638904i
$487$		−	2.89682e21i		−	0.915565i	−0.889064	−	0.457783i	$-0.848644\pi$
$487$		−	2.89682e21i		−	0.915565i	0.889064	−	0.457783i	$-0.151356\pi$
$488$	3.01350e21	−	8.34009e20i	0.936941	−	0.259306i
$489$	1.16956e20			0.0357727
$490$	2.67968e21	−	2.41824e20i	0.806331	−	0.0727663i
$491$			1.68428e21i			0.498612i	0.968425	+	0.249306i	$0.0802025\pi$
$491$			1.68428e21i			0.498612i	−0.968425	+	0.249306i	$0.919798\pi$
$492$	3.53839e20	+	1.94450e21i	0.103059	+	0.566352i
$493$	−3.30535e21			−0.947200
$494$	−8.03153e19	−	8.89982e20i	−0.0226455	−	0.250938i
$495$		−	2.09091e21i		−	0.580089i
$496$	1.46503e21	+	3.89220e21i	0.399940	+	1.06253i
$497$	−2.27111e21			−0.610080
$498$	7.79721e20	−	7.03649e19i	0.206113	−	0.0186004i
$499$			3.33834e21i			0.868412i	0.900814	+	0.434206i	$0.142971\pi$
$499$			3.33834e21i			0.868412i	−0.900814	+	0.434206i	$0.857029\pi$
$500$	4.05591e21	−	7.38051e20i	1.03831	−	0.188941i
$501$	2.51053e20			0.0632505
$502$	−2.39815e20	−	2.65742e21i	−0.0594630	−	0.658916i
$503$			4.84911e21i			1.18336i	0.806171	+	0.591682i	$0.201536\pi$
$503$			4.84911e21i			1.18336i	−0.806171	+	0.591682i	$0.798464\pi$
$504$	−1.33411e20	−	4.82049e20i	−0.0320440	−	0.115783i
$505$	−1.25411e21			−0.296486
$506$	−1.13805e22	+	1.02702e21i	−2.64823	+	0.238986i
$507$			2.23238e21i			0.511335i
$508$	1.51010e21	+	8.29864e21i	0.340483	+	1.87110i
$509$	2.89455e21			0.642450			0.321225	−	0.947003i	$-0.395905\pi$
$509$	2.89455e21			0.642450			0.321225	+	0.947003i	$0.395905\pi$
$510$	2.37469e20	+	2.63141e21i	0.0518853	+	0.574947i
$511$		−	1.04602e21i		−	0.224996i
$512$	−3.25607e21	+	3.42035e21i	−0.689499	+	0.724287i
$513$	−6.87828e20			−0.143397
$514$	6.78452e21	−	6.12260e20i	1.39256	−	0.125670i
$515$		−	4.36259e21i		−	0.881630i
$516$	1.53195e21	−	2.78769e20i	0.304823	−	0.0554685i
$517$	4.71176e21			0.923122
$518$	1.26562e20	+	1.40245e21i	0.0244156	+	0.270551i
$519$			1.20471e21i			0.228845i
$520$	1.62109e21	−	4.48649e20i	0.303236	−	0.0839228i
$521$	−4.09134e21			−0.753640			−0.376820	−	0.926286i	$-0.622983\pi$
$521$	−4.09134e21			−0.753640			−0.376820	+	0.926286i	$0.622983\pi$
$522$	1.61315e21	−	1.45577e20i	0.292625	−	0.0264076i
$523$		−	2.51392e21i		−	0.449095i	−0.974463	−	0.224547i	$-0.927910\pi$
$523$		−	2.51392e21i		−	0.449095i	0.974463	−	0.224547i	$-0.0720903\pi$
$524$	6.55514e20	+	3.60233e21i	0.115327	+	0.633773i
$525$	1.61192e20			0.0279298
$526$	2.73809e20	+	3.03411e21i	0.0467264	+	0.517780i
$527$		−	7.25849e21i		−	1.22000i
$528$	−6.10453e21	+	2.29776e21i	−1.01060	+	0.380393i
$529$	−6.26260e21			−1.02120
$530$	−5.15319e21	+	4.65042e20i	−0.827692	+	0.0746940i
$531$		−	4.05425e21i		−	0.641438i
$532$	1.69526e21	−	3.08485e20i	0.264206	−	0.0480774i
$533$	−2.19605e21			−0.337151
$534$	−5.18893e20	−	5.74991e21i	−0.0784779	−	0.869622i
$535$		−	6.47797e21i		−	0.965181i
$536$	3.94615e20	+	1.42585e21i	0.0579236	+	0.209294i
$537$	4.98298e21			0.720600
$538$	2.18705e21	−	1.97368e20i	0.311603	−	0.0281202i
$539$		−	1.15930e22i		−	1.62737i
$540$	−2.31790e20	−	1.27379e21i	−0.0320586	−	0.176176i
$541$	8.56679e21			1.16746			0.583728	−	0.811950i	$-0.301594\pi$
$541$	8.56679e21			1.16746			0.583728	+	0.811950i	$0.301594\pi$
$542$	−8.87034e20	−	9.82932e21i	−0.119109	−	1.31986i
$543$		−	1.55708e21i		−	0.206022i
$544$	7.42159e21	−	3.58503e21i	0.967622	−	0.467414i
$545$	7.32284e21			0.940822
$546$	5.53499e20	−	4.99498e19i	0.0700771	−	0.00632401i
$547$			1.51571e21i			0.189111i	0.995520	+	0.0945555i	$0.0301430\pi$
$547$			1.51571e21i			0.189111i	−0.995520	+	0.0945555i	$0.969857\pi$
$548$	−2.66733e21	+	4.85372e20i	−0.327968	+	0.0596801i
$549$	2.67421e21			0.324054
$550$	−1.88932e20	−	2.09357e21i	−0.0225634	−	0.250027i
$551$			5.57995e21i			0.656776i
$552$	−6.81915e21	+	1.88725e21i	−0.791075	+	0.218936i
$553$	−3.25892e21			−0.372626
$554$	−2.41658e21	+	2.18081e20i	−0.272347	+	0.0245776i
$555$			3.64504e21i			0.404910i
$556$	−1.44407e21	−	7.93580e21i	−0.158121	−	0.868945i
$557$	−1.03623e22			−1.11845			−0.559225	−	0.829016i	$-0.688901\pi$
$557$	−1.03623e22			−1.11845			−0.559225	+	0.829016i	$0.688901\pi$
$558$	3.19685e20	+	3.54246e21i	0.0340133	+	0.376905i
$559$			1.73014e21i			0.181462i
$560$	1.14256e21	+	3.03549e21i	0.118134	+	0.313852i
$561$	1.13842e22			1.16038
$562$	7.44383e21	−	6.71758e20i	0.748007	−	0.0675029i
$563$			1.91056e22i			1.89275i	0.323066	+	0.946376i	$0.395286\pi$
$563$			1.91056e22i			1.89275i	−0.323066	+	0.946376i	$0.604714\pi$
$564$	2.87041e21	−	5.22327e20i	0.280357	−	0.0510164i
$565$	−1.80777e22			−1.74083
$566$	−1.09641e21	−	1.21494e22i	−0.104098	−	1.15352i
$567$		−	4.27775e20i		−	0.0400453i
$568$	4.89163e21	+	1.76748e22i	0.451510	+	1.63142i
$569$	2.42125e21			0.220365			0.110182	−	0.993911i	$-0.464856\pi$
$569$	2.42125e21			0.220365			0.110182	+	0.993911i	$0.464856\pi$
$570$	4.44224e21	−	4.00884e20i	0.398661	−	0.0359766i
$571$			6.12261e20i			0.0541811i	0.999633	+	0.0270905i	$0.00862424\pi$
$571$			6.12261e20i			0.0541811i	−0.999633	+	0.0270905i	$0.991376\pi$
$572$	−1.29751e21	−	7.13036e21i	−0.113225	−	0.622219i
$573$	1.20431e21			0.103634
$574$	−3.80597e20	−	4.21744e21i	−0.0322976	−	0.357893i
$575$		−	2.28025e21i		−	0.190827i
$576$	−3.46417e21	+	2.07652e21i	−0.285903	+	0.171378i
$577$	−1.52521e21			−0.124143			−0.0620715	−	0.998072i	$-0.519771\pi$
$577$	−1.52521e21			−0.124143			−0.0620715	+	0.998072i	$0.519771\pi$
$578$	−1.92018e21	+	1.73284e20i	−0.154142	+	0.0139103i
$579$			7.62255e21i			0.603493i
$580$	−1.03335e22	+	1.88038e21i	−0.806906	+	0.146832i
$581$	−1.67737e21			−0.129187
$582$	−2.18488e20	−	2.42108e21i	−0.0165975	−	0.183919i
$583$			2.22941e22i			1.67048i
$584$	−8.14062e21	+	2.25298e21i	−0.601665	+	0.166515i
$585$	1.43857e21			0.104878
$586$	6.64835e21	−	5.99972e20i	0.478116	−	0.0431469i
$587$			1.08203e22i			0.767596i	0.923417	+	0.383798i	$0.125384\pi$
$587$			1.08203e22i			0.767596i	−0.923417	+	0.383798i	$0.874616\pi$
$588$	−1.28515e21	−	7.06247e21i	−0.0899365	−	0.494240i
$589$	−1.22535e22			−0.845935
$590$	2.36292e21	+	2.61838e22i	0.160929	+	1.78327i
$591$			2.60328e21i			0.174912i
$592$	1.06419e22	−	4.00563e21i	0.705416	−	0.265520i
$593$	6.66353e21			0.435779			0.217890	−	0.975973i	$-0.430083\pi$
$593$	6.66353e21			0.435779			0.217890	+	0.975973i	$0.430083\pi$
$594$	−5.55599e21	+	5.01393e20i	−0.358484	+	0.0323509i
$595$		−	5.66082e21i		−	0.360366i
$596$	2.04630e22	−	3.72364e21i	1.28528	−	0.233882i
$597$	−8.56773e21			−0.530972
$598$	−7.06599e20	−	7.82990e21i	−0.0432080	−	0.478792i
$599$		−	4.67643e21i		−	0.282163i	−0.989998	−	0.141081i	$-0.954942\pi$
$599$		−	4.67643e21i		−	0.282163i	0.989998	−	0.141081i	$-0.0450579\pi$
$600$	−3.47183e20	−	1.25446e21i	−0.0206704	−	0.0746875i
$601$	−1.96529e22			−1.15460			−0.577299	−	0.816533i	$-0.695893\pi$
$601$	−1.96529e22			−1.15460			−0.577299	+	0.816533i	$0.695893\pi$
$602$	−3.32267e21	+	2.99850e20i	−0.192626	+	0.0173833i
$603$			1.26532e21i			0.0723870i
$604$	−4.33641e21	−	2.38304e22i	−0.244813	−	1.34535i
$605$	4.17203e22			2.32437
$606$	3.00730e20	+	3.33243e21i	0.0165347	+	0.183223i
$607$			7.83703e21i			0.425248i	0.977134	+	0.212624i	$0.0682009\pi$
$607$			7.83703e21i			0.425248i	−0.977134	+	0.212624i	$0.931799\pi$
$608$	−6.05210e21	−	1.25288e22i	−0.324099	−	0.670936i
$609$	−3.47029e21			−0.183412
$610$	−1.72710e22	+	1.55860e21i	−0.900906	+	0.0813011i
$611$			3.24175e21i			0.166897i
$612$	6.93527e21	−	1.26201e21i	0.352413	−	0.0641284i
$613$	2.09738e22			1.05195			0.525973	−	0.850501i	$-0.323701\pi$
$613$	2.09738e22			1.05195			0.525973	+	0.850501i	$0.323701\pi$
$614$	−8.57055e20	−	9.49711e21i	−0.0424289	−	0.470159i
$615$		−	1.09613e22i		−	0.535627i
$616$	1.34687e22	−	3.72758e21i	0.649652	−	0.179796i
$617$	1.80800e22			0.860827			0.430414	−	0.902632i	$-0.358368\pi$
$617$	1.80800e22			0.860827			0.430414	+	0.902632i	$0.358368\pi$
$618$	−1.15923e22	+	1.04613e21i	−0.544831	+	0.0491676i
$619$		−	4.17757e22i		−	1.93820i	−0.246672	−	0.969099i	$-0.579337\pi$
$619$		−	4.17757e22i		−	1.93820i	0.246672	−	0.969099i	$-0.420663\pi$
$620$	−4.12928e21	−	2.26922e22i	−0.189121	−	1.03930i
$621$	−6.05139e21			−0.273604
$622$	2.87961e21	+	3.19093e22i	0.128532	+	1.42427i
$623$			1.23695e22i			0.545063i
$624$	−1.58089e21	−	4.19999e21i	−0.0687739	−	0.182714i
$625$	−1.97384e22			−0.847758
$626$	2.83754e22	−	2.56070e21i	1.20323	−	0.108584i
$627$		−	1.92183e22i		−	0.804592i
$628$	−4.17944e22	+	7.60530e21i	−1.72759	+	0.314369i
$629$	−1.98459e22			−0.809962
$630$	2.49319e20	+	2.76273e21i	0.0100469	+	0.111330i
$631$			1.75827e22i			0.699600i	0.936824	+	0.349800i	$0.113750\pi$
$631$			1.75827e22i			0.699600i	−0.936824	+	0.349800i	$0.886250\pi$
$632$	7.01923e21	+	2.53624e22i	0.275774	+	0.996444i
$633$	−1.20749e22			−0.468440
$634$	−2.79839e20	+	2.52537e19i	−0.0107200	+	0.000967409i
$635$		−	4.67803e22i		−	1.76959i
$636$	2.47143e21	+	1.35816e22i	0.0923191	+	0.507333i
$637$	7.97612e21			0.294223
$638$	4.06751e21	+	4.50725e22i	0.148171	+	1.64190i
$639$			1.56848e22i			0.564250i
$640$	2.11626e22	−	1.54299e22i	0.751846	−	0.548181i
$641$	−3.00851e22			−1.05557			−0.527786	−	0.849378i	$-0.676978\pi$
$641$	−3.00851e22			−1.05557			−0.527786	+	0.849378i	$0.676978\pi$
$642$	−1.72133e22	+	1.55339e21i	−0.596464	+	0.0538271i
$643$		−	2.10447e22i		−	0.720205i	−0.932913	−	0.360102i	$-0.882742\pi$
$643$		−	2.10447e22i		−	0.720205i	0.932913	−	0.360102i	$-0.117258\pi$
$644$	1.49146e22	−	2.71400e21i	0.504109	−	0.0917323i
$645$	−8.63579e21			−0.288287
$646$	2.18266e21	+	2.41863e22i	0.0719658	+	0.797460i
$647$		−	1.77979e21i		−	0.0579609i	−0.999580	−	0.0289804i	$-0.990774\pi$
$647$		−	1.77979e21i		−	0.0579609i	0.999580	−	0.0289804i	$-0.00922605\pi$
$648$	−3.32913e21	+	9.21364e20i	−0.107086	+	0.0296368i
$649$	1.13278e23			3.59906
$650$	1.44040e21	−	1.29987e20i	0.0452041	−	0.00407938i
$651$		−	7.62071e21i		−	0.236237i
$652$	3.62258e20	+	1.99076e21i	0.0110927	+	0.0609591i
$653$	−3.59385e22			−1.08706			−0.543531	−	0.839389i	$-0.682913\pi$
$653$	−3.59385e22			−1.08706			−0.543531	+	0.839389i	$0.682913\pi$
$654$	−1.75599e21	−	1.94583e22i	−0.0524687	−	0.581411i
$655$		−	2.03067e22i		−	0.599390i
$656$	−3.20022e22	+	1.20457e22i	−0.933145	+	0.351238i
$657$	−7.22408e21			−0.208094
$658$	−6.22566e21	+	5.61827e20i	−0.177165	+	0.0159880i
$659$		−	5.99046e22i		−	1.68413i	−0.539373	−	0.842067i	$-0.681339\pi$
$659$		−	5.99046e22i		−	1.68413i	0.539373	−	0.842067i	$-0.318661\pi$
$660$	3.55904e22	−	6.47636e21i	0.988510	−	0.179879i
$661$	−1.11504e22			−0.305970			−0.152985	−	0.988229i	$-0.548889\pi$
$661$	−1.11504e22			−0.305970			−0.152985	+	0.988229i	$0.548889\pi$
$662$	−2.13539e21	−	2.36625e22i	−0.0578913	−	0.641499i
$663$			7.83247e21i			0.209793i
$664$	3.61281e21	+	1.30540e22i	0.0956093	+	0.345462i
$665$	−9.55636e21			−0.249873
$666$	9.68564e21	−	8.74068e20i	0.250227	−	0.0225814i
$667$			4.90914e22i			1.25314i
$668$	7.77608e20	+	4.27329e21i	0.0196132	+	0.107783i
$669$	6.33572e21			0.157902
$670$	−7.37460e20	−	8.17187e21i	−0.0181610	−	0.201244i
$671$			7.47192e22i			1.81824i
$672$	7.79194e21	−	3.76393e21i	0.187366	−	0.0905081i
$673$	−3.02379e22			−0.718506			−0.359253	−	0.933240i	$-0.616969\pi$
$673$	−3.02379e22			−0.718506			−0.359253	+	0.933240i	$0.616969\pi$
$674$	6.49390e22	−	5.86034e21i	1.52485	−	0.137608i
$675$		−	1.11323e21i		−	0.0258317i
$676$	−3.79984e22	+	6.91455e21i	−0.871349	+	0.158559i
$677$	2.09689e21			0.0475190			0.0237595	−	0.999718i	$-0.492436\pi$
$677$	2.09689e21			0.0475190			0.0237595	+	0.999718i	$0.492436\pi$
$678$	4.33498e21	+	4.80363e22i	0.0970843	+	1.07580i
$679$			5.20835e21i			0.115277i
$680$	−4.40550e22	+	1.21926e22i	−0.963660	+	0.266700i
$681$	−4.48650e21			−0.0969909
$682$	−9.89785e22	+	8.93219e21i	−2.11478	+	0.190846i
$683$			1.19210e22i			0.251736i	0.992047	+	0.125868i	$0.0401716\pi$
$683$			1.19210e22i			0.251736i	−0.992047	+	0.125868i	$0.959828\pi$
$684$	−2.13047e21	−	1.17078e22i	−0.0444658	−	0.244359i
$685$	1.50360e22			0.310176
$686$	2.97104e21	+	3.29224e22i	0.0605781	+	0.671273i
$687$			2.08174e22i			0.419539i
$688$	9.49009e21	+	2.52126e22i	0.189044	+	0.502239i
$689$	−1.53386e22			−0.302017
$690$	3.90821e22	−	3.52691e21i	0.760650	−	0.0686439i
$691$		−	1.75286e22i		−	0.337228i	−0.985682	−	0.168614i	$-0.946071\pi$
$691$		−	1.75286e22i		−	0.337228i	0.985682	−	0.168614i	$-0.0539292\pi$
$692$	−2.05059e22	+	3.73144e21i	−0.389968	+	0.0709622i
$693$	1.19523e22			0.224691
$694$	−7.66560e21	−	8.49434e22i	−0.142453	−	1.57853i
$695$			4.47349e22i			0.821804i
$696$	7.47448e21	+	2.70073e22i	0.135740	+	0.490464i
$697$	5.96803e22			1.07144
$698$	4.51433e22	−	4.07390e21i	0.801216	−	0.0723047i
$699$		−	3.79254e22i		−	0.665446i
$700$	4.99272e20	+	2.74372e21i	0.00866070	+	0.0475943i
$701$	4.33851e22			0.744040			0.372020	−	0.928225i	$-0.378665\pi$
$701$	4.33851e22			0.744040			0.372020	+	0.928225i	$0.378665\pi$
$702$	−3.44965e20	−	3.82259e21i	−0.00584894	−	0.0648128i
$703$			3.35029e22i			0.561617i
$704$	−5.80193e22	−	9.67909e22i	−0.961592	−	1.60418i
$705$	−1.61808e22			−0.265148
$706$	−2.86119e22	+	2.58205e21i	−0.463564	+	0.0418337i
$707$		−	7.16887e21i		−	0.114841i
$708$	6.90092e22	−	1.25576e22i	1.09305	−	0.198902i
$709$	−2.79315e22			−0.437445			−0.218723	−	0.975787i	$-0.570189\pi$
$709$	−2.79315e22			−0.437445			−0.218723	+	0.975787i	$0.570189\pi$
$710$	−9.14151e21	−	1.01298e23i	−0.141563	−	1.56868i
$711$			2.25069e22i			0.344634i
$712$	9.62646e22	−	2.66420e22i	1.45756	−	0.403391i
$713$	−1.07804e23			−1.61406
$714$	−1.50420e22	+	1.35744e21i	−0.222700	+	0.0200972i
$715$			4.01946e22i			0.588464i
$716$	1.54342e22	+	8.48175e22i	0.223449	+	1.22795i
$717$	−1.98568e21			−0.0284287
$718$	−4.19652e21	−	4.65020e22i	−0.0594146	−	0.658380i
$719$		−	3.16812e22i		−	0.443578i	−0.975095	−	0.221789i	$-0.928810\pi$
$719$		−	3.16812e22i		−	0.443578i	0.975095	−	0.221789i	$-0.0711896\pi$
$720$	2.09638e22	−	7.89081e21i	0.290275	−	0.109260i
$721$	2.49379e22			0.341490
$722$	−3.27119e22	+	2.95204e21i	−0.443004	+	0.0399783i
$723$			9.61090e21i			0.128724i
$724$	2.65038e22	−	4.82288e21i	0.351075	−	0.0638849i
$725$	−9.03095e21			−0.118312
$726$	−1.00044e22	−	1.10860e23i	−0.129627	−	1.43642i
$727$			4.87349e22i			0.624547i	0.949992	+	0.312273i	$0.101091\pi$
$727$			4.87349e22i			0.624547i	−0.949992	+	0.312273i	$0.898909\pi$
$728$	2.56462e21	+	9.26665e21i	0.0325066	+	0.117455i
$729$	−2.95431e21			−0.0370370
$730$	4.66557e22	−	4.21038e21i	0.578524	−	0.0522082i
$731$		−	4.70185e22i		−	0.576673i
$732$	8.28306e21	+	4.55190e22i	0.100485	+	0.552210i
$733$	9.12805e22			1.09533			0.547666	−	0.836697i	$-0.315516\pi$
$733$	9.12805e22			1.09533			0.547666	+	0.836697i	$0.315516\pi$
$734$	−8.91276e21	−	9.87633e22i	−0.105790	−	1.17227i
$735$			3.98119e22i			0.467427i
$736$	−5.32453e22	−	1.10226e23i	−0.618385	−	1.28016i
$737$	−3.53537e22			−0.406158
$738$	−2.91266e22	+	2.62849e21i	−0.331008	+	0.0298714i
$739$		−	1.46123e23i		−	1.64272i	−0.570409	−	0.821361i	$-0.693215\pi$
$739$		−	1.46123e23i		−	1.64272i	0.570409	−	0.821361i	$-0.306785\pi$
$740$	−6.20440e22	+	1.12901e22i	−0.689995	+	0.125558i
$741$	1.32224e22			0.145468
$742$	−2.65833e21	−	2.94572e22i	−0.0289319	−	0.320598i
$743$		−	3.89731e22i		−	0.419618i	−0.977742	−	0.209809i	$-0.932716\pi$
$743$		−	3.89731e22i		−	0.419618i	0.977742	−	0.209809i	$-0.0672842\pi$
$744$	−5.93077e22	+	1.64139e22i	−0.631724	+	0.174834i
$745$	−1.15352e23			−1.21556
$746$	1.33701e23	−	1.20656e22i	1.39387	−	0.125788i
$747$			1.15843e22i			0.119483i
$748$	3.52613e22	+	1.93776e23i	0.359820	+	1.97736i
$749$	3.70301e22			0.373852
$750$	5.48260e21	+	6.07533e22i	0.0547642	+	0.606848i
$751$			5.23880e22i			0.517741i	0.965912	+	0.258871i	$0.0833503\pi$
$751$			5.23880e22i			0.517741i	−0.965912	+	0.258871i	$0.916650\pi$
$752$	1.77815e22	+	4.72407e22i	0.173871	+	0.461928i
$753$	3.94812e22			0.381971
$754$	−3.10104e22	+	2.79849e21i	−0.296850	+	0.0267888i
$755$			1.34335e23i			1.27237i
$756$	7.28136e21	−	1.32498e21i	0.0682399	−	0.0124176i
$757$	5.73502e22			0.531824			0.265912	−	0.963997i	$-0.414327\pi$
$757$	5.73502e22			0.531824			0.265912	+	0.963997i	$0.414327\pi$
$758$	9.80338e21	+	1.08632e23i	0.0899544	+	0.996794i
$759$		−	1.69080e23i		−	1.53517i
$760$	2.05830e22	+	7.43718e22i	0.184927	+	0.668189i
$761$	−2.70367e22			−0.240367			−0.120184	−	0.992752i	$-0.538348\pi$
$761$	−2.70367e22			−0.240367			−0.120184	+	0.992752i	$0.538348\pi$
$762$	−1.24305e23	+	1.12177e22i	−1.09358	+	0.0986883i
$763$			4.18596e22i			0.364417i
$764$	3.73021e21	+	2.04991e22i	0.0321356	+	0.176599i
$765$	−3.90949e22			−0.333295
$766$	1.82608e22	+	2.02349e23i	0.154060	+	1.70715i
$767$			7.79368e22i			0.650698i
$768$	−4.60752e22	−	5.25333e22i	−0.380696	−	0.434056i
$769$	8.86749e22			0.725087			0.362543	−	0.931967i	$-0.381908\pi$
$769$	8.86749e22			0.725087			0.362543	+	0.931967i	$0.381908\pi$
$770$	−7.71923e22	+	6.96612e21i	−0.624667	+	0.0563722i
$771$			1.00797e23i			0.807262i
$772$	−1.29747e23	+	2.36100e22i	−1.02839	+	0.187136i
$773$	1.84361e23			1.44622			0.723108	−	0.690735i	$-0.242713\pi$
$773$	1.84361e23			1.44622			0.723108	+	0.690735i	$0.242713\pi$
$774$	2.07083e21	+	2.29471e22i	0.0160774	+	0.178156i
$775$		−	1.98318e22i		−	0.152387i
$776$	4.05336e22	−	1.12180e22i	0.308263	−	0.0853143i
$777$	−2.08362e22			−0.156838
$778$	8.23079e22	−	7.42776e21i	0.613203	−	0.0553377i
$779$		−	1.00750e23i		−	0.742923i
$780$	4.45581e21	+	2.44866e22i	0.0325215	+	0.178719i
$781$	−4.38243e23			−3.16597
$782$	1.92027e22	+	2.12787e23i	0.137312	+	1.52156i
$783$			2.39666e22i			0.169634i
$784$	1.16233e23	−	4.37503e22i	0.814330	−	0.306516i
$785$	2.35600e23			1.63387
$786$	−5.39592e22	+	4.86948e21i	−0.370412	+	0.0334274i
$787$		−	1.34135e23i		−	0.911475i	−0.890114	−	0.455738i	$-0.849376\pi$
$787$		−	1.34135e23i		−	0.911475i	0.890114	−	0.455738i	$-0.150624\pi$
$788$	−4.43116e22	+	8.06335e21i	−0.298063	+	0.0542383i
$789$	−4.50777e22			−0.300155
$790$	−1.31176e22	−	1.45357e23i	−0.0864644	−	0.958121i
$791$		−	1.03338e23i		−	0.674292i
$792$	−2.57435e22	−	9.30181e22i	−0.166290	−	0.600850i
$793$	−5.14077e22			−0.328732
$794$	9.12390e22	−	8.23374e21i	0.577586	−	0.0521234i
$795$		−	7.65608e22i		−	0.479810i
$796$	−2.65376e22	−	1.45835e23i	−0.164648	−	0.904812i
$797$	−4.43256e22			−0.272263			−0.136131	−	0.990691i	$-0.543467\pi$
$797$	−4.43256e22			−0.272263			−0.136131	+	0.990691i	$0.543467\pi$
$798$	2.29158e21	+	2.53932e22i	0.0139352	+	0.154417i
$799$		−	8.80983e22i		−	0.530387i
$800$	2.02774e22	−	9.79511e21i	0.120863	−	0.0583834i
$801$	8.54263e22			0.504117
$802$	2.20444e23	−	1.98937e22i	1.28796	−	0.116231i
$803$		−	2.01845e23i		−	1.16760i
$804$	−2.15375e22	+	3.91917e21i	−0.123352	+	0.0224463i
$805$	−8.40752e22			−0.476761
$806$	−6.14545e21	−	6.80984e22i	−0.0345043	−	0.382346i
$807$			3.24930e22i			0.180635i
$808$	−5.57913e22	+	1.54407e22i	−0.307097	+	0.0849914i
$809$	1.26634e23			0.690182			0.345091	−	0.938569i	$-0.387848\pi$
$809$	1.26634e23			0.690182			0.345091	+	0.938569i	$0.387848\pi$
$810$	1.90800e22	−	1.72185e21i	0.102967	−	0.00929213i
$811$		−	8.77902e21i		−	0.0469115i	−0.999725	−	0.0234557i	$-0.992533\pi$
$811$		−	8.77902e21i		−	0.0469115i	0.999725	−	0.0234557i	$-0.00746688\pi$
$812$	−1.07488e22	−	5.90694e22i	−0.0568738	−	0.312546i
$813$	1.46034e23			0.765121
$814$	2.44220e22	+	2.70623e23i	0.126703	+	1.40401i
$815$		−	1.12221e22i		−	0.0576521i
$816$	4.29624e22	+	1.14140e23i	0.218558	+	0.580650i
$817$	−7.93747e22			−0.399858
$818$	−2.74035e23	+	2.47300e22i	−1.36704	+	0.123366i
$819$			8.22333e21i			0.0406234i
$820$	1.86578e23	−	3.39515e22i	0.912745	−	0.166092i
$821$	1.71008e23			0.828460			0.414230	−	0.910172i	$-0.364051\pi$
$821$	1.71008e23			0.828460			0.414230	+	0.910172i	$0.364051\pi$
$822$	−3.60558e21	−	3.99538e22i	−0.0172982	−	0.191683i
$823$		−	5.26971e22i		−	0.250373i	−0.992133	−	0.125187i	$-0.960047\pi$
$823$		−	5.26971e22i		−	0.250373i	0.992133	−	0.125187i	$-0.0399530\pi$
$824$	−5.37125e22	−	1.94078e23i	−0.252730	−	0.913183i
$825$	3.11042e22			0.144940
$826$	−1.49675e23	+	1.35072e22i	−0.690730	+	0.0623340i
$827$			1.93464e23i			0.884213i	0.896963	+	0.442107i	$0.145769\pi$
$827$			1.93464e23i			0.884213i	−0.896963	+	0.442107i	$0.854231\pi$
$828$	−1.87435e22	−	1.03003e23i	−0.0848413	−	0.466240i
$829$	−2.56991e23			−1.15208			−0.576040	−	0.817422i	$-0.695403\pi$
$829$	−2.56991e23			−1.15208			−0.576040	+	0.817422i	$0.695403\pi$
$830$	−6.75164e21	−	7.48156e22i	−0.0299767	−	0.332175i
$831$		−	3.59031e22i		−	0.157879i
$832$	6.65933e22	−	3.99179e22i	0.290031	−	0.173853i
$833$	−2.16760e23			−0.935017
$834$	1.18870e23	−	1.07273e22i	0.507860	−	0.0458312i
$835$		−	2.40890e22i		−	0.101936i
$836$	3.27124e23	−	5.95266e22i	1.37108	−	0.249494i
$837$	−5.26303e22			−0.218490
$838$	−8.39741e21	−	9.30526e22i	−0.0345297	−	0.382628i
$839$			3.64356e23i			1.48399i	0.670407	+	0.741994i	$0.266120\pi$
$839$			3.64356e23i			1.48399i	−0.670407	+	0.741994i	$0.733880\pi$
$840$	−4.62534e22	+	1.28010e22i	−0.186599	+	0.0516428i
$841$	−5.58195e22			−0.223058
$842$	−8.52159e22	+	7.69019e21i	−0.337306	+	0.0304397i
$843$			1.10593e23i			0.433617i
$844$	−3.74006e22	−	2.05533e23i	−0.145258	−	0.798254i
$845$	2.14201e23			0.824078
$846$	3.88010e21	+	4.29958e22i	0.0147870	+	0.163856i
$847$			2.38486e23i			0.900318i
$848$	−2.23523e23	+	8.41347e22i	−0.835903	+	0.314636i
$849$	1.80504e23			0.668689
$850$	−3.91447e22	+	3.53256e21i	−0.143655	+	0.0129640i
$851$			2.94753e23i			1.07157i
$852$	−2.66978e23	+	4.85818e22i	−0.961521	+	0.174967i
$853$	3.22578e23			1.15091			0.575457	−	0.817832i	$-0.304824\pi$
$853$	3.22578e23			1.15091			0.575457	+	0.817832i	$0.304824\pi$
$854$	−8.90945e21	−	9.87266e22i	−0.0314911	−	0.348956i
$855$			6.59984e22i			0.231102i
$856$	−7.97572e22	−	2.88184e23i	−0.276681	−	0.999724i
$857$	−2.36855e23			−0.814021			−0.407011	−	0.913423i	$-0.633429\pi$
$857$	−2.36855e23			−0.814021			−0.407011	+	0.913423i	$0.633429\pi$
$858$	1.06805e23	−	9.63852e21i	0.363660	−	0.0328180i
$859$			3.99298e23i			1.34695i	0.739210	+	0.673475i	$0.235199\pi$
$859$			3.99298e23i			1.34695i	−0.739210	+	0.673475i	$0.764801\pi$
$860$	−2.67483e22	−	1.46994e23i	−0.0893942	−	0.491260i
$861$	6.26584e22			0.207470
$862$	2.48262e22	+	2.75102e23i	0.0814427	+	0.902476i
$863$		−	3.41785e23i		−	1.11088i	−0.831557	−	0.555440i	$-0.812550\pi$
$863$		−	3.41785e23i		−	1.11088i	0.831557	−	0.555440i	$-0.187450\pi$
$864$	−2.59946e22	−	5.38129e22i	−0.0837091	−	0.173291i
$865$	1.15594e23			0.368812
$866$	−1.45982e23	+	1.31739e22i	−0.461483	+	0.0416459i
$867$		−	2.85281e22i		−	0.0893553i
$868$	1.29715e23	−	2.36042e22i	0.402563	−	0.0732541i
$869$	−6.28855e23			−1.93372
$870$	−1.39684e22	−	1.54785e23i	−0.0425590	−	0.471601i
$871$		−	2.43238e22i		−	0.0734321i
$872$	3.25770e23	−	9.01593e22i	0.974493	−	0.269699i
$873$	3.59700e22			0.106617
$874$	3.59218e23	−	3.24171e22i	1.05503	−	0.0952101i
$875$		−	1.30695e23i		−	0.380361i
$876$	−2.23757e22	−	1.22964e23i	−0.0645274	−	0.354606i
$877$	2.80711e23			0.802164			0.401082	−	0.916042i	$-0.368634\pi$
$877$	2.80711e23			0.802164			0.401082	+	0.916042i	$0.368634\pi$
$878$	4.91664e22	+	5.44818e23i	0.139223	+	1.54275i
$879$			9.87745e22i			0.277162i
$880$	2.20474e23	+	5.85740e23i	0.613050	+	1.62871i
$881$	−1.47052e23			−0.405195			−0.202597	−	0.979262i	$-0.564938\pi$
$881$	−1.47052e23			−0.405195			−0.202597	+	0.979262i	$0.564938\pi$
$882$	1.05789e23	−	9.54675e21i	0.288862	−	0.0260679i
$883$			4.38492e23i			1.18652i	0.805010	+	0.593261i	$0.202160\pi$
$883$			4.38492e23i			1.18652i	−0.805010	+	0.593261i	$0.797840\pi$
$884$	−1.33320e23	+	2.42602e22i	−0.357501	+	0.0650542i
$885$	−3.89013e23			−1.03375
$886$	−4.50125e22	−	4.98788e23i	−0.118540	−	1.31355i
$887$		−	2.97487e23i		−	0.776388i	−0.921578	−	0.388194i	$-0.873099\pi$
$887$		−	2.97487e23i		−	0.776388i	0.921578	−	0.388194i	$-0.126901\pi$
$888$	4.48781e22	+	1.62156e23i	0.116073	+	0.419402i
$889$	2.67411e23			0.685433
$890$	−5.51714e23	+	4.97887e22i	−1.40150	+	0.126477i
$891$		−	8.25453e22i		−	0.207812i
$892$	1.96242e22	+	1.07843e23i	0.0489635	+	0.269075i
$893$	−1.48724e23			−0.367764
$894$	2.76610e22	+	3.06515e23i	0.0677904	+	0.751193i
$895$		−	4.78125e23i		−	1.16133i
$896$	8.82022e22	+	1.20972e23i	0.212332	+	0.291219i
$897$	1.16329e23			0.277554
$898$	2.83102e23	−	2.55482e22i	0.669473	−	0.0604157i
$899$			4.26959e23i			1.00071i
$900$	1.89487e22	−	3.44809e21i	0.0440190	−	0.00801010i
$901$	4.16844e23			0.959787
$902$	−7.34416e22	−	8.13814e23i	−0.167606	−	1.85726i
$903$		−	4.93649e22i		−	0.111665i
$904$	−8.04221e23	+	2.22574e23i	−1.80313	+	0.499031i
$905$	−1.49405e23			−0.332029
$906$	3.56955e23	−	3.22130e22i	0.786300	−	0.0709586i
$907$		−	2.39210e23i		−	0.522301i	−0.965298	−	0.261150i	$-0.915898\pi$
$907$		−	2.39210e23i		−	0.522301i	0.965298	−	0.261150i	$-0.0841019\pi$
$908$	−1.38964e22	−	7.63668e22i	−0.0300757	−	0.165279i
$909$	−4.95098e22			−0.106214
$910$	−4.79277e21	−	5.31092e22i	−0.0101919	−	0.112938i
$911$		−	1.25620e22i		−	0.0264796i	−0.999912	−	0.0132398i	$-0.995786\pi$
$911$		−	1.25620e22i		−	0.0264796i	0.999912	−	0.0132398i	$-0.00421449\pi$
$912$	1.92686e23	−	7.25273e22i	0.402615	−	0.151545i
$913$	−3.23673e23			−0.670409
$914$	−1.21559e22	+	1.09699e21i	−0.0249584	+	0.00225234i
$915$		−	2.56596e23i		−	0.522252i
$916$	−3.54342e23	+	6.44794e22i	−0.714923	+	0.130094i
$917$	1.16080e23			0.232167
$918$	9.37481e21	+	1.03883e23i	0.0185875	+	0.205970i
$919$		−	6.42061e23i		−	1.26198i	−0.775791	−	0.630990i	$-0.782649\pi$
$919$		−	6.42061e23i		−	1.26198i	0.775791	−	0.630990i	$-0.217351\pi$
$920$	1.81085e23	+	6.54309e23i	0.352842	+	1.27491i
$921$	1.41098e23			0.272549
$922$	−2.10846e23	+	1.90276e22i	−0.403756	+	0.0364364i
$923$		−	3.01516e23i		−	0.572397i
$924$	3.70209e22	+	2.03446e23i	0.0696740	+	0.382889i
$925$	−5.42233e22			−0.101170
$926$	−1.88767e22	−	2.09174e23i	−0.0349170	−	0.386919i
$927$		−	1.72227e23i		−	0.315837i
$928$	−4.36552e23	+	2.10879e23i	−0.793693	+	0.383397i
$929$	4.46521e23			0.804852			0.402426	−	0.915452i	$-0.368167\pi$
$929$	4.46521e23			0.804852			0.402426	+	0.915452i	$0.368167\pi$
$930$	3.39905e23	−	3.06743e22i	0.607428	−	0.0548165i
$931$			3.65926e23i			0.648329i
$932$	6.45545e23	−	1.17469e23i	1.13396	−	0.206347i
$933$	−4.74075e23			−0.825647
$934$	−9.38602e21	−	1.04008e23i	−0.0162071	−	0.179593i
$935$		−	1.09234e24i		−	1.87009i
$936$	6.39975e22	−	1.77118e22i	0.108632	−	0.0300647i
$937$	5.19426e23			0.874191			0.437096	−	0.899415i	$-0.356007\pi$
$937$	5.19426e23			0.874191			0.437096	+	0.899415i	$0.356007\pi$
$938$	4.67129e22	−	4.21555e21i	0.0779497	−	0.00703447i
$939$			4.21573e23i			0.697507i
$940$	−5.01182e22	−	2.75421e23i	−0.0822191	−	0.451829i
$941$	1.04009e24			1.69182			0.845909	−	0.533327i	$-0.179059\pi$
$941$	1.04009e24			1.69182			0.845909	+	0.533327i	$0.179059\pi$
$942$	−5.64959e22	−	6.26037e23i	−0.0911192	−	1.00970i
$943$		−	8.86378e23i		−	1.41751i
$944$	4.27496e23	+	1.13574e24i	0.677885	+	1.80096i
$945$	−4.10458e22			−0.0645378
$946$	−6.41156e23	+	5.78603e22i	−0.999619	+	0.0902093i
$947$		−	1.98252e22i		−	0.0306491i	−0.999883	−	0.0153245i	$-0.995122\pi$
$947$		−	1.98252e22i		−	0.0306491i	0.999883	−	0.0153245i	$-0.00487814\pi$
$948$	−3.83099e23	+	6.97123e22i	−0.587279	+	0.106867i
$949$	1.38872e23			0.211098
$950$	5.96352e21	+	6.60824e22i	0.00898904	+	0.0996086i
$951$		−	4.15756e21i		−	0.00621433i
$952$	−6.96964e22	−	2.51832e23i	−0.103303	−	0.373263i
$953$	−9.30478e23			−1.36761			−0.683806	−	0.729664i	$-0.739676\pi$
$953$	−9.30478e23			−1.36761			−0.683806	+	0.729664i	$0.739676\pi$
$954$	−2.03438e23	+	1.83590e22i	−0.296514	+	0.0267585i
$955$		−	1.15556e23i		−	0.167019i
$956$	−6.15042e21	−	3.37992e22i	−0.00881539	−	0.0484444i
$957$	−6.69642e23			−0.951803
$958$	3.06387e22	+	3.39510e23i	0.0431863	+	0.478552i
$959$			8.59505e22i			0.120143i
$960$	1.99246e23	+	3.32393e23i	0.276197	+	0.460767i
$961$	−2.10172e23			−0.288926
$962$	−1.86192e23	+	1.68026e22i	−0.253840	+	0.0229074i
$963$		−	2.55738e23i		−	0.345768i
$964$	−1.63592e23	+	2.97686e22i	−0.219354	+	0.0399156i
$965$	7.31397e23			0.972601
$966$	2.01609e22	+	2.23405e23i	0.0265885	+	0.294630i
$967$			2.80402e23i			0.366749i	0.983043	+	0.183374i	$0.0587020\pi$
$967$			2.80402e23i			0.366749i	−0.983043	+	0.183374i	$0.941298\pi$
$968$	1.85600e24	−	5.13663e23i	2.40755	−	0.666309i
$969$	−3.59335e23			−0.462285
$970$	−2.32307e23	+	2.09643e22i	−0.296407	+	0.0267489i
$971$			1.51191e24i			1.91325i	0.291329	+	0.956623i	$0.405903\pi$
$971$			1.51191e24i			1.91325i	−0.291329	+	0.956623i	$0.594097\pi$
$972$	−9.15064e21	−	5.02867e22i	−0.0114847	−	0.0631136i
$973$	−2.55719e23			−0.318317
$974$	6.66525e22	+	7.38584e23i	0.0822896	+	0.911860i
$975$			2.14001e22i			0.0262046i
$976$	−7.49144e23	+	2.81979e23i	−0.909843	+	0.342467i
$977$	−9.63725e23			−1.16090			−0.580452	−	0.814294i	$-0.697124\pi$
$977$	−9.63725e23			−1.16090			−0.580452	+	0.814294i	$0.697124\pi$
$978$	−2.98196e22	+	2.69103e21i	−0.0356279	+	0.00321519i
$979$			2.38686e24i			2.82856i
$980$	−6.77656e23	+	1.23313e23i	−0.796528	+	0.144944i
$981$	2.89092e23			0.337042
$982$	−3.87534e22	−	4.29431e23i	−0.0448145	−	0.496594i
$983$			5.76517e23i			0.661278i	0.943757	+	0.330639i	$0.107264\pi$
$983$			5.76517e23i			0.661278i	−0.943757	+	0.330639i	$0.892736\pi$
$984$	−1.34957e23	−	4.87635e23i	−0.153544	−	0.554797i
$985$	2.49789e23			0.281893
$986$	8.42744e23	−	7.60523e22i	0.943366	−	0.0851328i
$987$		−	9.24946e22i		−	0.102702i
$988$	4.09550e22	+	2.25065e23i	0.0451078	+	0.247887i
$989$	−6.98325e23			−0.762934
$990$	4.81096e22	+	5.33107e23i	0.0521375	+	0.577741i
$991$			7.09157e23i			0.762348i	0.924503	+	0.381174i	$0.124480\pi$
$991$			7.09157e23i			0.762348i	−0.924503	+	0.381174i	$0.875520\pi$
$992$	−4.63086e23	−	9.58662e23i	−0.493820	−	1.02229i
$993$	3.51553e23			0.371875
$994$	5.79051e23	−	5.22557e22i	0.607611	−	0.0548331i
$995$			8.22089e23i			0.855725i
$996$	−1.97182e23	+	3.58810e22i	−0.203607	+	0.0370502i
$997$	6.99549e23			0.716567			0.358284	−	0.933613i	$-0.383362\pi$
$997$	6.99549e23			0.716567			0.358284	+	0.933613i	$0.383362\pi$
$998$	−7.68114e22	−	8.51155e23i	−0.0780515	−	0.864897i
$999$			1.43899e23i			0.145056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.2	yes	16
3.2	odd	2		36.17.d.d.19.15		16
4.3	odd	2	inner	12.17.d.a.7.1	✓	16
12.11	even	2		36.17.d.d.19.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.1	✓	16	4.3	odd	2	inner
12.17.d.a.7.2	yes	16	1.1	even	1	trivial
36.17.d.d.19.15		16	3.2	odd	2
36.17.d.d.19.16		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)

\(f(q)\)	\(=\)	\(q+(-254.964 + 23.0089i) q^{2} -3788.00i q^{3} +(64477.2 - 11732.9i) q^{4} -363465. q^{5} +(87157.5 + 965802. i) q^{6} -2.07768e6i q^{7} +(-1.61694e7 + 4.47501e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(-254.964 + 23.0089i) q^{2} -3788.00i q^{3} +(64477.2 - 11732.9i) q^{4} -363465. q^{5} +(87157.5 + 965802. i) q^{6} -2.07768e6i q^{7} +(-1.61694e7 + 4.47501e6i) q^{8} -1.43489e7 q^{9} +(9.26704e7 - 8.36292e6i) q^{10} -4.00917e8i q^{11} +(-4.44441e7 - 2.44239e8i) q^{12} +2.75836e8 q^{13} +(4.78050e7 + 5.29733e8i) q^{14} +1.37680e9i q^{15} +(4.01965e9 - 1.51300e9i) q^{16} -7.49616e9 q^{17} +(3.65845e9 - 3.30152e8i) q^{18} +1.26547e10i q^{19} +(-2.34352e10 + 4.26449e9i) q^{20} -7.87023e9 q^{21} +(9.22466e9 + 1.02219e11i) q^{22} +1.11334e11i q^{23} +(1.69513e10 + 6.12496e10i) q^{24} -2.04812e10 q^{25} +(-7.03282e10 + 6.34667e9i) q^{26} +5.43536e10i q^{27} +(-2.43771e10 - 1.33963e11i) q^{28} +4.40939e11 q^{29} +(-3.16787e10 - 3.51035e11i) q^{30} +9.68295e11i q^{31} +(-9.90052e11 + 4.78249e11i) q^{32} -1.51867e12 q^{33} +(1.91125e12 - 1.72478e11i) q^{34} +7.55163e11i q^{35} +(-9.25177e11 + 1.68354e11i) q^{36} +2.64747e12 q^{37} +(-2.91170e11 - 3.22649e12i) q^{38} -1.04486e12i q^{39} +(5.87701e12 - 1.62651e12i) q^{40} -7.96145e12 q^{41} +(2.00663e12 - 1.81085e11i) q^{42} +6.27235e12i q^{43} +(-4.70391e12 - 2.58500e13i) q^{44} +5.21532e12 q^{45} +(-2.56167e12 - 2.83861e13i) q^{46} +1.17525e13i q^{47} +(-5.73125e12 - 1.52264e13i) q^{48} +2.89162e13 q^{49} +(5.22196e12 - 4.71249e11i) q^{50} +2.83954e13i q^{51} +(1.77851e13 - 3.23635e12i) q^{52} -5.56077e13 q^{53} +(-1.25062e12 - 1.38582e13i) q^{54} +1.45719e14i q^{55} +(9.29762e12 + 3.35948e13i) q^{56} +4.79359e13 q^{57} +(-1.12423e14 + 1.01455e13i) q^{58} +2.82548e14i q^{59} +(1.61539e13 + 8.87724e13i) q^{60} -1.86371e14 q^{61} +(-2.22794e13 - 2.46880e14i) q^{62} +2.98124e13i q^{63} +(2.41424e14 - 1.44716e14i) q^{64} -1.00257e14 q^{65} +(3.87207e14 - 3.49430e13i) q^{66} -8.81821e13i q^{67} +(-4.83331e14 + 8.79514e13i) q^{68} +4.21732e14 q^{69} +(-1.73755e13 - 1.92539e14i) q^{70} -1.09310e15i q^{71} +(2.32013e14 - 6.42114e13i) q^{72} +5.03458e14 q^{73} +(-6.75009e14 + 6.09153e13i) q^{74} +7.75826e13i q^{75} +(1.48476e14 + 8.15939e14i) q^{76} -8.32977e14 q^{77} +(2.40412e13 + 2.66403e14i) q^{78} -1.56854e15i q^{79} +(-1.46100e15 + 5.49924e14i) q^{80} +2.05891e14 q^{81} +(2.02988e15 - 1.83184e14i) q^{82} -8.07330e14i q^{83} +(-5.07450e14 + 9.23404e13i) q^{84} +2.72459e15 q^{85} +(-1.44320e14 - 1.59922e15i) q^{86} -1.67027e15i q^{87} +(1.79411e15 + 6.48259e15i) q^{88} -5.95350e15 q^{89} +(-1.32972e15 + 1.19999e14i) q^{90} -5.73098e14i q^{91} +(1.30626e15 + 7.17849e15i) q^{92} +3.66790e15 q^{93} +(-2.70411e14 - 2.99645e15i) q^{94} -4.59954e15i q^{95} +(1.81161e15 + 3.75031e15i) q^{96} -2.50681e15 q^{97} +(-7.37258e15 + 6.65329e14i) q^{98} +5.75272e15i 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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