LMFDB - Embedded newform 26.10.c.b.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,10,Mod(3,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.3"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3909317403$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 10384 x^{10} + 120855 x^{9} + 81803040 x^{8} + 688592615 x^{7} + \cdots + 27\!\cdots\!00 $ x^12 - 3x^11 + 10384x^10 + 120855x^9 + 81803040x^8 + 688592615x^7 + 235441918375x^6 + 326685836650x^5 + 490232889649600x^4 + 270381215117000x^3 + 434580563567230000x^2 - 1152225642325800000*x + 279661605363396000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{7}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.1
Root			$-37.9111 + 65.6639i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.10.c.b.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 - 13.8564i) q^{2} +(-121.233 - 209.982i) q^{3} +(-128.000 + 221.703i) q^{4} -2071.64 q^{5} +(-1939.73 + 3359.71i) q^{6} +(-161.624 + 279.942i) q^{7} +4096.00 q^{8} +(-19553.5 + 33867.6i) q^{9} +(16573.1 + 28705.5i) q^{10} +(-44160.4 - 76488.0i) q^{11} +62071.4 q^{12} +(37298.7 - 95986.0i) q^{13} +5171.98 q^{14} +(251152. + 435008. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(226022. - 391481. i) q^{17} +625712. q^{18} +(-324857. + 562669. i) q^{19} +(265170. - 459289. i) q^{20} +78377.0 q^{21} +(-706566. + 1.22381e6i) q^{22} +(791116. + 1.37025e6i) q^{23} +(-496571. - 860087. i) q^{24} +2.33858e6 q^{25} +(-1.62841e6 + 251062. i) q^{26} +4.70966e6 q^{27} +(-41375.9 - 71665.1i) q^{28} +(-1.46336e6 - 2.53461e6i) q^{29} +(4.01843e6 - 6.96013e6i) q^{30} +1.27453e6 q^{31} +(-524288. + 908093. i) q^{32} +(-1.07074e7 + 1.85458e7i) q^{33} -7.23270e6 q^{34} +(334828. - 579939. i) q^{35} +(-5.00569e6 - 8.67011e6i) q^{36} +(-4.00996e6 - 6.94546e6i) q^{37} +1.03954e7 q^{38} +(-2.46772e7 + 3.80464e6i) q^{39} -8.48545e6 q^{40} +(-2.41322e6 - 4.17982e6i) q^{41} +(-627016. - 1.08602e6i) q^{42} +(-1.41479e7 + 2.45049e7i) q^{43} +2.26101e7 q^{44} +(4.05079e7 - 7.01617e7i) q^{45} +(1.26579e7 - 2.19241e7i) q^{46} +1.19241e7 q^{47} +(-7.94514e6 + 1.37614e7i) q^{48} +(2.01246e7 + 3.48568e7i) q^{49} +(-1.87087e7 - 3.24043e7i) q^{50} -1.09605e8 q^{51} +(1.65061e7 + 2.05554e7i) q^{52} -3.78650e6 q^{53} +(-3.76773e7 - 6.52590e7i) q^{54} +(9.14845e7 + 1.58456e8i) q^{55} +(-662014. + 1.14664e6i) q^{56} +1.57534e8 q^{57} +(-2.34137e7 + 4.05538e7i) q^{58} +(-1.13286e7 + 1.96217e7i) q^{59} -1.28590e8 q^{60} +(-1.02955e7 + 1.78323e7i) q^{61} +(-1.01962e7 - 1.76604e7i) q^{62} +(-6.32064e6 - 1.09477e7i) q^{63} +1.67772e7 q^{64} +(-7.72695e7 + 1.98849e8i) q^{65} +3.42637e8 q^{66} +(-8.13920e7 - 1.40975e8i) q^{67} +(5.78616e7 + 1.00219e8i) q^{68} +(1.91819e8 - 3.32241e8i) q^{69} -1.07145e7 q^{70} +(1.91396e7 - 3.31507e7i) q^{71} +(-8.00911e7 + 1.38722e8i) q^{72} +3.92315e8 q^{73} +(-6.41594e7 + 1.11127e8i) q^{74} +(-2.83514e8 - 4.91060e8i) q^{75} +(-8.31634e7 - 1.44043e8i) q^{76} +2.85496e7 q^{77} +(2.50136e8 + 3.11500e8i) q^{78} -1.33317e8 q^{79} +(6.78836e7 + 1.17578e8i) q^{80} +(-1.86096e8 - 3.22328e8i) q^{81} +(-3.86115e7 + 6.68772e7i) q^{82} -5.40870e8 q^{83} +(-1.00323e7 + 1.73764e7i) q^{84} +(-4.68237e8 + 8.11010e8i) q^{85} +4.52732e8 q^{86} +(-3.54815e8 + 6.14558e8i) q^{87} +(-1.80881e8 - 3.13295e8i) q^{88} +(-4.29672e8 - 7.44214e8i) q^{89} -1.29625e9 q^{90} +(2.08421e7 + 2.59551e7i) q^{91} -4.05052e8 q^{92} +(-1.54515e8 - 2.67628e8i) q^{93} +(-9.53930e7 - 1.65226e8i) q^{94} +(6.72988e8 - 1.16565e9i) q^{95} +2.54244e8 q^{96} +(-3.66476e8 + 6.34755e8i) q^{97} +(3.21993e8 - 5.57708e8i) q^{98} +3.45396e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 96 q^{2} - 81 q^{3} - 1536 q^{4} + 3386 q^{5} - 1296 q^{6} - 473 q^{7} + 49152 q^{8} - 69813 q^{9} - 27088 q^{10} - 14011 q^{11} + 41472 q^{12} + 152853 q^{13} + 15136 q^{14} + 294780 q^{15} - 393216 q^{16}+ \cdots - 1763539020 q^{99}+O(q^{100}) $ 12 * q - 96 * q^2 - 81 * q^3 - 1536 * q^4 + 3386 * q^5 - 1296 * q^6 - 473 * q^7 + 49152 * q^8 - 69813 * q^9 - 27088 * q^10 - 14011 * q^11 + 41472 * q^12 + 152853 * q^13 + 15136 * q^14 + 294780 * q^15 - 393216 * q^16 + 173558 * q^17 + 2234016 * q^18 - 322367 * q^19 - 433408 * q^20 + 4513770 * q^21 - 224176 * q^22 + 1644771 * q^23 - 331776 * q^24 + 5375138 * q^25 - 4031808 * q^26 - 1845990 * q^27 - 121088 * q^28 - 10801236 * q^29 + 4716480 * q^30 + 20870244 * q^31 - 6291456 * q^32 - 26201763 * q^33 - 5553856 * q^34 - 2168950 * q^35 - 17872128 * q^36 + 15710464 * q^37 + 10315744 * q^38 - 22298325 * q^39 + 13869056 * q^40 + 1525478 * q^41 - 36110160 * q^42 - 50959661 * q^43 + 7173632 * q^44 - 18619731 * q^45 + 26316336 * q^46 + 136313996 * q^47 - 5308416 * q^48 - 162536361 * q^49 - 43001104 * q^50 - 169357962 * q^51 + 25378560 * q^52 + 144556418 * q^53 + 14767920 * q^54 + 353372330 * q^55 - 1937408 * q^56 + 35902050 * q^57 - 172819776 * q^58 + 5665291 * q^59 - 150927360 * q^60 + 353387956 * q^61 - 166961952 * q^62 + 224088894 * q^63 + 201326592 * q^64 - 205394773 * q^65 + 838456416 * q^66 - 371115369 * q^67 + 44430848 * q^68 - 280317279 * q^69 + 69406400 * q^70 - 156688763 * q^71 - 285954048 * q^72 + 932803326 * q^73 + 251367424 * q^74 - 1149481845 * q^75 - 82525952 * q^76 + 624920666 * q^77 - 420616752 * q^78 + 325086960 * q^79 - 110952448 * q^80 - 295496586 * q^81 + 24407648 * q^82 - 870229152 * q^83 - 577762560 * q^84 - 2307296767 * q^85 + 1630709152 * q^86 + 617376057 * q^87 - 57389056 * q^88 - 163315063 * q^89 + 595831392 * q^90 - 208860497 * q^91 - 842122752 * q^92 - 2056270836 * q^93 - 1090511968 * q^94 + 537110948 * q^95 + 169869312 * q^96 + 1500514705 * q^97 - 2600581776 * q^98 - 1763539020 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$3$	−121.233	−	209.982i	−0.864124	−	1.49671i	−0.867914	−	0.496714i	$-0.834540\pi$
$3$	−121.233	−	209.982i	−0.864124	−	1.49671i	0.00379061	−	0.999993i	$-0.498793\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−2071.64			−1.48235			−0.741174	−	0.671313i	$-0.765731\pi$
$5$	−2071.64			−1.48235			−0.741174	+	0.671313i	$0.765731\pi$
$6$	−1939.73	+	3359.71i	−0.611028	+	1.05833i
$7$	−161.624	+	279.942i	−0.0254429	+	0.0440683i	−0.878466	−	0.477804i	$-0.841433\pi$
$7$	−161.624	+	279.942i	−0.0254429	+	0.0440683i	0.853024	+	0.521872i	$0.174766\pi$
$8$	4096.00			0.353553
$9$	−19553.5	+	33867.6i	−0.993420	+	1.72065i
$10$	16573.1	+	28705.5i	0.524089	+	0.907749i
$11$	−44160.4	−	76488.0i	−0.909422	−	1.57517i	−0.814869	−	0.579645i	$-0.803191\pi$
$11$	−44160.4	−	76488.0i	−0.909422	−	1.57517i	−0.0945530	−	0.995520i	$-0.530142\pi$
$12$	62071.4			0.864124
$13$	37298.7	−	95986.0i	0.362200	−	0.932100i
$13$	37298.7	−	95986.0i	0.362200	−	0.932100i
$14$	5171.98			0.0359816
$15$	251152.	+	435008.i	1.28093	+	2.21864i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	226022.	−	391481.i	0.656342	−	1.13682i	−0.325213	−	0.945641i	$-0.605436\pi$
$17$	226022.	−	391481.i	0.656342	−	1.13682i	0.981556	−	0.191177i	$-0.0612306\pi$
$18$	625712.			1.40491
$19$	−324857.	+	562669.i	−0.571875	+	0.990517i	0.424498	+	0.905429i	$0.360451\pi$
$19$	−324857.	+	562669.i	−0.571875	+	0.990517i	−0.996373	+	0.0850882i	$0.972883\pi$
$20$	265170.	−	459289.i	0.370587	−	0.641875i
$21$	78377.0			0.0879431
$22$	−706566.	+	1.22381e6i	−0.643058	+	1.11381i
$23$	791116.	+	1.37025e6i	0.589475	+	1.02100i	0.994301	+	0.106607i	$0.0339985\pi$
$23$	791116.	+	1.37025e6i	0.589475	+	1.02100i	−0.404827	+	0.914393i	$0.632668\pi$
$24$	−496571.	−	860087.i	−0.305514	−	0.529166i
$25$	2.33858e6			1.19735
$26$	−1.62841e6	+	251062.i	−0.698850	+	0.107746i
$27$	4.70966e6			1.70550
$28$	−41375.9	−	71665.1i	−0.0127214	−	0.0220342i
$29$	−1.46336e6	−	2.53461e6i	−0.384202	−	0.665458i	0.607456	−	0.794353i	$-0.292190\pi$
$29$	−1.46336e6	−	2.53461e6i	−0.384202	−	0.665458i	−0.991658	+	0.128896i	$0.958857\pi$
$30$	4.01843e6	−	6.96013e6i	0.905756	−	1.56881i
$31$	1.27453e6			0.247869			0.123935	−	0.992290i	$-0.460449\pi$
$31$	1.27453e6			0.247869			0.123935	+	0.992290i	$0.460449\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$	−1.07074e7	+	1.85458e7i	−1.57171	+	2.72228i
$34$	−7.23270e6			−0.928208
$35$	334828.	−	579939.i	0.0377151	−	0.0653246i
$36$	−5.00569e6	−	8.67011e6i	−0.496710	−	0.860327i
$37$	−4.00996e6	−	6.94546e6i	−0.351749	−	0.609247i	0.634807	−	0.772671i	$-0.281080\pi$
$37$	−4.00996e6	−	6.94546e6i	−0.351749	−	0.609247i	−0.986556	+	0.163424i	$0.947746\pi$
$38$	1.03954e7			0.808754
$39$	−2.46772e7	+	3.80464e6i	−1.70807	+	0.263343i
$40$	−8.48545e6			−0.524089
$41$	−2.41322e6	−	4.17982e6i	−0.133374	−	0.231010i	0.791601	−	0.611038i	$-0.209248\pi$
$41$	−2.41322e6	−	4.17982e6i	−0.133374	−	0.231010i	−0.924975	+	0.380028i	$0.875914\pi$
$42$	−627016.	−	1.08602e6i	−0.0310926	−	0.0538539i
$43$	−1.41479e7	+	2.45049e7i	−0.631079	+	1.09306i	0.356253	+	0.934390i	$0.384054\pi$
$43$	−1.41479e7	+	2.45049e7i	−0.631079	+	1.09306i	−0.987332	+	0.158671i	$0.949279\pi$
$44$	2.26101e7			0.909422
$45$	4.05079e7	−	7.01617e7i	1.47259	−	2.55061i
$46$	1.26579e7	−	2.19241e7i	0.416822	−	0.721956i
$47$	1.19241e7			0.356440			0.178220	−	0.983991i	$-0.442966\pi$
$47$	1.19241e7			0.356440			0.178220	+	0.983991i	$0.442966\pi$
$48$	−7.94514e6	+	1.37614e7i	−0.216031	+	0.374177i
$49$	2.01246e7	+	3.48568e7i	0.498705	+	0.863783i
$50$	−1.87087e7	−	3.24043e7i	−0.423329	−	0.733227i
$51$	−1.09605e8			−2.26864
$52$	1.65061e7	+	2.05554e7i	0.313061	+	0.389862i
$53$	−3.78650e6			−0.0659168			−0.0329584	−	0.999457i	$-0.510493\pi$
$53$	−3.78650e6			−0.0659168			−0.0329584	+	0.999457i	$0.510493\pi$
$54$	−3.76773e7	−	6.52590e7i	−0.602987	−	1.04440i
$55$	9.14845e7	+	1.58456e8i	1.34808	+	2.33494i
$56$	−662014.	+	1.14664e6i	−0.00899541	+	0.0155805i
$57$	1.57534e8			1.97668
$58$	−2.34137e7	+	4.05538e7i	−0.271672	+	0.470550i
$59$	−1.13286e7	+	1.96217e7i	−0.121714	+	0.210816i	−0.920444	−	0.390875i	$-0.872173\pi$
$59$	−1.13286e7	+	1.96217e7i	−0.121714	+	0.210816i	0.798729	+	0.601690i	$0.205506\pi$
$60$	−1.28590e8			−1.28093
$61$	−1.02955e7	+	1.78323e7i	−0.0952056	+	0.164901i	−0.909694	−	0.415278i	$-0.863684\pi$
$61$	−1.02955e7	+	1.78323e7i	−0.0952056	+	0.164901i	0.814489	+	0.580179i	$0.197018\pi$
$62$	−1.01962e7	−	1.76604e7i	−0.0876350	−	0.151788i
$63$	−6.32064e6	−	1.09477e7i	−0.0505509	−	0.0875567i
$64$	1.67772e7			0.125000
$65$	−7.72695e7	+	1.98849e8i	−0.536906	+	1.38170i
$66$	3.42637e8			2.22273
$67$	−8.13920e7	−	1.40975e8i	−0.493452	−	0.854685i	0.506519	−	0.862229i	$-0.330932\pi$
$67$	−8.13920e7	−	1.40975e8i	−0.493452	−	0.854685i	−0.999972	+	0.00754416i	$0.997599\pi$
$68$	5.78616e7	+	1.00219e8i	0.328171	+	0.568409i
$69$	1.91819e8	−	3.32241e8i	1.01876	−	1.76454i
$70$	−1.07145e7			−0.0533373
$71$	1.91396e7	−	3.31507e7i	0.0893860	−	0.154821i	−0.817866	−	0.575409i	$-0.804843\pi$
$71$	1.91396e7	−	3.31507e7i	0.0893860	−	0.154821i	0.907252	+	0.420588i	$0.138176\pi$
$72$	−8.00911e7	+	1.38722e8i	−0.351227	+	0.608343i
$73$	3.92315e8			1.61690			0.808448	−	0.588567i	$-0.200308\pi$
$73$	3.92315e8			1.61690			0.808448	+	0.588567i	$0.200308\pi$
$74$	−6.41594e7	+	1.11127e8i	−0.248724	+	0.430803i
$75$	−2.83514e8	−	4.91060e8i	−1.03466	−	1.79209i
$76$	−8.31634e7	−	1.44043e8i	−0.285938	−	0.495259i
$77$	2.85496e7			0.0925532
$78$	2.50136e8	+	3.11500e8i	0.765157	+	0.952867i
$79$	−1.33317e8			−0.385092			−0.192546	−	0.981288i	$-0.561675\pi$
$79$	−1.33317e8			−0.385092			−0.192546	+	0.981288i	$0.561675\pi$
$80$	6.78836e7	+	1.17578e8i	0.185293	+	0.320938i
$81$	−1.86096e8	−	3.22328e8i	−0.480347	−	0.831985i
$82$	−3.86115e7	+	6.68772e7i	−0.0943094	+	0.163349i
$83$	−5.40870e8			−1.25096			−0.625478	−	0.780242i	$-0.715096\pi$
$83$	−5.40870e8			−1.25096			−0.625478	+	0.780242i	$0.715096\pi$
$84$	−1.00323e7	+	1.73764e7i	−0.0219858	+	0.0380805i
$85$	−4.68237e8	+	8.11010e8i	−0.972927	+	1.68516i
$86$	4.52732e8			0.892480
$87$	−3.54815e8	+	6.14558e8i	−0.663996	+	1.15008i
$88$	−1.80881e8	−	3.13295e8i	−0.321529	−	0.556905i
$89$	−4.29672e8	−	7.44214e8i	−0.725909	−	1.25731i	−0.958599	−	0.284761i	$-0.908086\pi$
$89$	−4.29672e8	−	7.44214e8i	−0.725909	−	1.25731i	0.232690	−	0.972551i	$-0.425247\pi$
$90$	−1.29625e9			−2.08256
$91$	2.08421e7	+	2.59551e7i	0.0318607	+	0.0396768i
$92$	−4.05052e8			−0.589475
$93$	−1.54515e8	−	2.67628e8i	−0.214190	−	0.370987i
$94$	−9.53930e7	−	1.65226e8i	−0.126021	−	0.218274i
$95$	6.72988e8	−	1.16565e9i	0.847718	−	1.46829i
$96$	2.54244e8			0.305514
$97$	−3.66476e8	+	6.34755e8i	−0.420313	+	0.728003i	−0.995970	−	0.0896878i	$-0.971413\pi$
$97$	−3.66476e8	+	6.34755e8i	−0.420313	+	0.728003i	0.575657	+	0.817691i	$0.304746\pi$
$98$	3.21993e8	−	5.57708e8i	0.352638	−	0.610787i
$99$	3.45396e9			3.61375
$100$	−2.99338e8	+	5.18469e8i	−0.299338	+	0.518469i
$101$	−9.85472e7	−	1.70689e8i	−0.0942319	−	0.163215i	0.815056	−	0.579382i	$-0.196706\pi$
$101$	−9.85472e7	−	1.70689e8i	−0.0942319	−	0.163215i	−0.909288	+	0.416168i	$0.863373\pi$
$102$	8.76844e8	+	1.51874e9i	0.802087	+	1.38925i
$103$	−5.00520e7			−0.0438181			−0.0219091	−	0.999760i	$-0.506974\pi$
$103$	−5.00520e7			−0.0438181			−0.0219091	+	0.999760i	$0.506974\pi$
$104$	1.52775e8	−	3.93159e8i	0.128057	−	0.329547i
$105$	−1.62369e8			−0.130362
$106$	3.02920e7	+	5.24672e7i	0.0233051	+	0.0403656i
$107$	1.81309e8	+	3.14036e8i	0.133719	+	0.231607i	0.925107	−	0.379706i	$-0.123975\pi$
$107$	1.81309e8	+	3.14036e8i	0.133719	+	0.231607i	−0.791389	+	0.611313i	$0.790641\pi$
$108$	−6.02837e8	+	1.04414e9i	−0.426376	+	0.738505i
$109$	3.93006e8			0.266673			0.133337	−	0.991071i	$-0.457431\pi$
$109$	3.93006e8			0.266673			0.133337	+	0.991071i	$0.457431\pi$
$110$	1.46375e9	−	2.53529e9i	0.953236	−	1.65105i
$111$	−9.72282e8	+	1.68404e9i	−0.607909	+	1.05293i
$112$	2.11844e7			0.0127214
$113$	−2.81487e7	+	4.87550e7i	−0.0162407	+	0.0281297i	−0.874032	−	0.485869i	$-0.838503\pi$
$113$	−2.81487e7	+	4.87550e7i	−0.0162407	+	0.0281297i	0.857791	+	0.513999i	$0.171836\pi$
$114$	−1.26027e9	−	2.18285e9i	−0.698863	−	1.21047i
$115$	−1.63891e9	−	2.83868e9i	−0.873806	−	1.51348i
$116$	7.49239e8			0.384202
$117$	2.52150e9	+	3.14008e9i	1.24401	+	1.54919i
$118$	3.62515e8			0.172130
$119$	7.30613e7	+	1.26546e8i	0.0333984	+	0.0578478i
$120$	1.02872e9	+	1.78179e9i	0.452878	+	0.784407i
$121$	−2.72130e9	+	4.71343e9i	−1.15410	+	1.99895i
$122$	3.29455e8			0.134641
$123$	−5.85125e8	+	1.01347e9i	−0.230503	+	0.399242i
$124$	−1.63140e8	+	2.82566e8i	−0.0619673	+	0.107330i
$125$	−7.98529e8			−0.292547
$126$	−1.01130e8	+	1.75163e8i	−0.0357449	+	0.0619119i
$127$	−1.31349e9	−	2.27503e9i	−0.448032	−	0.776015i	0.550226	−	0.835016i	$-0.314542\pi$
$127$	−1.31349e9	−	2.27503e9i	−0.448032	−	0.776015i	−0.998258	+	0.0590015i	$0.981208\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$	6.86078e9			2.18132
$130$	3.37349e9	−	5.20112e8i	1.03594	−	0.159717i
$131$	5.16288e9			1.53169			0.765846	−	0.643024i	$-0.222320\pi$
$131$	5.16288e9			1.53169			0.765846	+	0.643024i	$0.222320\pi$
$132$	−2.74110e9	−	4.74772e9i	−0.785853	−	1.36114i
$133$	−1.05010e8	−	1.81882e8i	−0.0291003	−	0.0504032i
$134$	−1.30227e9	+	2.25560e9i	−0.348923	+	0.604353i
$135$	−9.75674e9			−2.52815
$136$	9.25786e8	−	1.60351e9i	0.232052	−	0.401926i
$137$	1.81323e9	−	3.14061e9i	0.439755	−	0.761679i	−0.557915	−	0.829898i	$-0.688399\pi$
$137$	1.81323e9	−	3.14061e9i	0.439755	−	0.761679i	0.997670	+	0.0682196i	$0.0217318\pi$
$138$	−6.13821e9			−1.44074
$139$	−4.24322e8	+	7.34948e8i	−0.0964116	+	0.166990i	−0.910197	−	0.414176i	$-0.864070\pi$
$139$	−4.24322e8	+	7.34948e8i	−0.0964116	+	0.166990i	0.813785	+	0.581166i	$0.197403\pi$
$140$	8.57160e7	+	1.48464e8i	0.0188576	+	0.0326623i
$141$	−1.44560e9	−	2.50385e9i	−0.308008	−	0.533486i
$142$	−6.12466e8			−0.126411
$143$	−8.98890e9	+	1.38588e9i	−1.79760	+	0.277148i
$144$	2.56291e9			0.496710
$145$	3.03156e9	+	5.25081e9i	0.569521	+	0.986439i
$146$	−3.13852e9	−	5.43608e9i	−0.571659	−	0.990143i
$147$	4.87953e9	−	8.45159e9i	0.861886	−	1.49283i
$148$	2.05310e9			0.351749
$149$	3.43821e9	−	5.95515e9i	0.571470	−	0.989816i	−0.424945	−	0.905219i	$-0.639707\pi$
$149$	3.43821e9	−	5.95515e9i	0.571470	−	0.989816i	0.996415	−	0.0845965i	$-0.0269601\pi$
$150$	−4.53622e9	+	7.85697e9i	−0.731617	+	1.26720i
$151$	−7.47346e9			−1.16984			−0.584919	−	0.811092i	$-0.698874\pi$
$151$	−7.47346e9			−1.16984			−0.584919	+	0.811092i	$0.698874\pi$
$152$	−1.33062e9	+	2.30469e9i	−0.202188	+	0.350201i
$153$	8.83903e9	+	1.53097e10i	1.30405	+	2.25868i
$154$	−2.28397e8	−	3.95594e8i	−0.0327225	−	0.0566770i
$155$	−2.64037e9			−0.367428
$156$	2.31518e9	−	5.95799e9i	0.312986	−	0.805450i
$157$	−6.66627e9			−0.875657			−0.437829	−	0.899058i	$-0.644252\pi$
$157$	−6.66627e9			−0.875657			−0.437829	+	0.899058i	$0.644252\pi$
$158$	1.06654e9	+	1.84730e9i	0.136151	+	0.235820i
$159$	4.59049e8	+	7.95096e8i	0.0569603	+	0.0986581i
$160$	1.08614e9	−	1.88125e9i	0.131022	−	0.226937i
$161$	−5.11455e8			−0.0599917
$162$	−2.97754e9	+	5.15725e9i	−0.339657	+	0.588303i
$163$	−7.44144e9	+	1.28890e10i	−0.825682	+	1.43012i	0.0757147	+	0.997130i	$0.475876\pi$
$163$	−7.44144e9	+	1.28890e10i	−0.825682	+	1.43012i	−0.901397	+	0.432994i	$0.857457\pi$
$164$	1.23557e9			0.133374
$165$	2.21819e10	−	3.84202e10i	2.32982	−	4.03536i
$166$	4.32696e9	+	7.49452e9i	0.442279	+	0.766051i
$167$	4.93294e9	+	8.54410e9i	0.490774	+	0.850046i	0.999944	−	0.0106206i	$-0.00338071\pi$
$167$	4.93294e9	+	8.54410e9i	0.490774	+	0.850046i	−0.509170	+	0.860666i	$0.670047\pi$
$168$	3.21032e8			0.0310926
$169$	−7.82212e9	−	7.16030e9i	−0.737623	−	0.675213i
$170$	1.49836e10			1.37593
$171$	−1.27042e10	−	2.20043e10i	−1.13622	−	1.96800i
$172$	−3.62186e9	−	6.27324e9i	−0.315539	−	0.546530i
$173$	−1.01634e10	+	1.76036e10i	−0.862648	+	1.49415i	0.00671672	+	0.999977i	$0.497862\pi$
$173$	−1.01634e10	+	1.76036e10i	−0.862648	+	1.49415i	−0.869364	+	0.494172i	$0.835471\pi$
$174$	1.13541e10			0.939033
$175$	−3.77972e8	+	6.54667e8i	−0.0304641	+	0.0527654i
$176$	−2.89409e9	+	5.01272e9i	−0.227355	+	0.393791i
$177$	5.49361e9			0.420705
$178$	−6.87476e9	+	1.19074e10i	−0.513295	+	0.889054i
$179$	4.56669e9	+	7.90975e9i	0.332478	+	0.575869i	0.982997	−	0.183621i	$-0.0587818\pi$
$179$	4.56669e9	+	7.90975e9i	0.332478	+	0.575869i	−0.650519	+	0.759490i	$0.725449\pi$
$180$	1.03700e10	+	1.79614e10i	0.736297	+	1.27530i
$181$	2.57653e10			1.78436			0.892180	−	0.451681i	$-0.149175\pi$
$181$	2.57653e10			1.78436			0.892180	+	0.451681i	$0.149175\pi$
$182$	1.92908e8	−	4.96438e8i	0.0130325	−	0.0335385i
$183$	4.99262e9			0.329078
$184$	3.24041e9	+	5.61256e9i	0.208411	+	0.360978i
$185$	8.30721e9	+	1.43885e10i	0.521414	+	0.903115i
$186$	−2.47225e9	+	4.28206e9i	−0.151455	+	0.262328i
$187$	−3.99248e10			−2.38757
$188$	−1.52629e9	+	2.64361e9i	−0.0891100	+	0.154343i
$189$	−7.61197e8	+	1.31843e9i	−0.0433929	+	0.0751587i
$190$	−2.15356e10			−1.19885
$191$	7.44655e9	−	1.28978e10i	0.404860	−	0.701238i	−0.589445	−	0.807808i	$-0.700654\pi$
$191$	7.44655e9	−	1.28978e10i	0.404860	−	0.701238i	0.994305	+	0.106570i	$0.0339870\pi$
$192$	−2.03396e9	−	3.52292e9i	−0.108015	−	0.187088i
$193$	−1.77345e9	−	3.07171e9i	−0.0920051	−	0.159357i	0.816350	−	0.577558i	$-0.195994\pi$
$193$	−1.77345e9	−	3.07171e9i	−0.0920051	−	0.159357i	−0.908355	+	0.418201i	$0.862661\pi$
$194$	1.17272e10			0.594412
$195$	5.11223e10	−	7.88185e9i	2.53195	−	0.390366i
$196$	−1.03038e10			−0.498705
$197$	−8.68151e9	−	1.50368e10i	−0.410674	−	0.711308i	0.584290	−	0.811545i	$-0.301373\pi$
$197$	−8.68151e9	−	1.50368e10i	−0.410674	−	0.711308i	−0.994964	+	0.100237i	$0.968040\pi$
$198$	−2.76316e10	−	4.78594e10i	−1.27765	−	2.21296i
$199$	−1.88138e9	+	3.25865e9i	−0.0850429	+	0.147299i	−0.905410	−	0.424539i	$-0.860436\pi$
$199$	−1.88138e9	+	3.25865e9i	−0.0850429	+	0.147299i	0.820367	+	0.571838i	$0.193769\pi$
$200$	9.57883e9			0.423329
$201$	−1.97348e10	+	3.41817e10i	−0.852808	+	1.47711i
$202$	−1.57676e9	+	2.73102e9i	−0.0666320	+	0.115410i
$203$	9.46058e8			0.0391008
$204$	1.40295e10	−	2.42998e10i	0.567161	−	0.982352i
$205$	4.99934e9	+	8.65910e9i	0.197706	+	0.342437i
$206$	4.00416e8	+	6.93540e8i	0.0154920	+	0.0268330i
$207$	−6.18763e10			−2.34238
$208$	−6.66997e9	+	1.02835e9i	−0.247081	+	0.0380940i
$209$	5.73832e10			2.08030
$210$	1.29895e9	+	2.24985e9i	0.0460900	+	0.0798302i
$211$	2.16285e10	+	3.74617e10i	0.751201	+	1.30112i	0.947241	+	0.320522i	$0.103858\pi$
$211$	2.16285e10	+	3.74617e10i	0.751201	+	1.30112i	−0.196041	+	0.980596i	$0.562808\pi$
$212$	4.84671e8	−	8.39475e8i	0.0164792	−	0.0285428i
$213$	−9.28140e9			−0.308962
$214$	2.90094e9	−	5.02458e9i	0.0945534	−	0.163771i
$215$	2.93094e10	−	5.07653e10i	0.935478	−	1.62030i
$216$	1.92908e10			0.602987
$217$	−2.05995e8	+	3.56794e8i	−0.00630650	+	0.0109232i
$218$	−3.14405e9	−	5.44565e9i	−0.0942833	−	0.163303i
$219$	−4.75616e10	−	8.23792e10i	−1.39720	−	2.42002i
$220$	−4.68401e10			−1.34808
$221$	−2.91464e10	−	3.62967e10i	−0.821902	−	1.02353i
$222$	3.11130e10			0.859713
$223$	1.64345e10	+	2.84655e10i	0.445027	+	0.770809i	0.998054	−	0.0623544i	$-0.0198609\pi$
$223$	1.64345e10	+	2.84655e10i	0.445027	+	0.770809i	−0.553028	+	0.833163i	$0.686528\pi$
$224$	−1.69475e8	−	2.93540e8i	−0.00449770	−	0.00779025i
$225$	−4.57274e10	+	7.92022e10i	−1.18948	+	2.06023i
$226$	9.00758e8			0.0229678
$227$	−3.45806e10	+	5.98954e10i	−0.864404	+	1.49719i	0.00323433	+	0.999995i	$0.498970\pi$
$227$	−3.45806e10	+	5.98954e10i	−0.864404	+	1.49719i	−0.867638	+	0.497196i	$0.834363\pi$
$228$	−2.01643e10	+	3.49257e10i	−0.494171	+	0.855929i
$229$	−3.37155e10			−0.810158			−0.405079	−	0.914282i	$-0.632756\pi$
$229$	−3.37155e10			−0.810158			−0.405079	+	0.914282i	$0.632756\pi$
$230$	−2.62226e10	+	4.54188e10i	−0.617874	+	1.07019i
$231$	−3.46116e9	−	5.99490e9i	−0.0799774	−	0.138525i
$232$	−5.99392e9	−	1.03818e10i	−0.135836	−	0.235275i
$233$	−1.18954e10			−0.264410			−0.132205	−	0.991222i	$-0.542206\pi$
$233$	−1.18954e10			−0.264410			−0.132205	+	0.991222i	$0.542206\pi$
$234$	2.33382e10	−	6.00595e10i	0.508858	−	1.30952i
$235$	−2.47025e10			−0.528368
$236$	−2.90012e9	−	5.02316e9i	−0.0608572	−	0.105408i
$237$	1.61625e10	+	2.79943e10i	0.332768	+	0.576370i
$238$	1.16898e9	−	2.02473e9i	0.0236163	−	0.0409046i
$239$	1.57903e10			0.313040			0.156520	−	0.987675i	$-0.449972\pi$
$239$	1.57903e10			0.313040			0.156520	+	0.987675i	$0.449972\pi$
$240$	1.64595e10	−	2.85087e10i	0.320233	−	0.554660i
$241$	−1.10417e10	+	1.91248e10i	−0.210843	+	0.365191i	−0.951979	−	0.306164i	$-0.900954\pi$
$241$	−1.10417e10	+	1.91248e10i	−0.210843	+	0.365191i	0.741135	+	0.671356i	$0.234288\pi$
$242$	8.70816e10			1.63214
$243$	1.22804e9	−	2.12703e9i	0.0225936	−	0.0391332i
$244$	−2.63564e9	−	4.56507e9i	−0.0476028	−	0.0824505i
$245$	−4.16909e10	−	7.22108e10i	−0.739255	−	1.28043i
$246$	1.87240e10			0.325980
$247$	4.18916e10	+	5.21686e10i	0.716128	+	0.891810i
$248$	5.22047e9			0.0876350
$249$	6.55715e10	+	1.13573e11i	1.08098	+	1.87231i
$250$	6.38823e9	+	1.10647e10i	0.103431	+	0.179148i
$251$	3.14893e10	−	5.45411e10i	0.500762	−	0.867345i	−0.499238	−	0.866465i	$-0.666387\pi$
$251$	3.14893e10	−	5.45411e10i	0.500762	−	0.867345i	1.00000		0.000880102i	$-0.000280145\pi$
$252$	3.23617e9			0.0505509
$253$	6.98720e10	−	1.21022e11i	1.07216	−	1.85704i
$254$	−2.10158e10	+	3.64004e10i	−0.316807	+	0.548725i
$255$	2.27063e11			3.36292
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	1.77228e10	+	3.06968e10i	0.253416	+	0.438929i	0.964464	−	0.264214i	$-0.0851126\pi$
$257$	1.77228e10	+	3.06968e10i	0.253416	+	0.438929i	−0.711048	+	0.703143i	$0.751779\pi$
$258$	−5.48862e10	−	9.50657e10i	−0.771213	−	1.33578i
$259$	2.59243e9			0.0357980
$260$	−3.41948e10	−	4.25835e10i	−0.464066	−	0.577911i
$261$	1.14455e11			1.52670
$262$	−4.13031e10	−	7.15390e10i	−0.541535	−	0.937966i
$263$	−3.23660e10	−	5.60595e10i	−0.417146	−	0.722518i	0.578505	−	0.815679i	$-0.303636\pi$
$263$	−3.23660e10	−	5.60595e10i	−0.417146	−	0.722518i	−0.995651	+	0.0931609i	$0.970303\pi$
$264$	−4.38575e10	+	7.59635e10i	−0.555682	+	0.962470i
$265$	7.84427e9			0.0977116
$266$	−1.68016e9	+	2.91011e9i	−0.0205770	+	0.0356404i
$267$	−1.04181e11	+	1.80447e11i	−1.25455	+	2.17295i
$268$	4.16727e10			0.493452
$269$	−5.48593e10	+	9.50191e10i	−0.638800	+	1.10643i	0.346896	+	0.937904i	$0.387236\pi$
$269$	−5.48593e10	+	9.50191e10i	−0.638800	+	1.10643i	−0.985696	+	0.168531i	$0.946098\pi$
$270$	7.80539e10	+	1.35193e11i	0.893836	+	1.54817i
$271$	−4.32455e10	−	7.49034e10i	−0.487056	−	0.843606i	0.512833	−	0.858488i	$-0.328596\pi$
$271$	−4.32455e10	−	7.49034e10i	−0.487056	−	0.843606i	−0.999889	+	0.0148825i	$0.995263\pi$
$272$	−2.96251e10			−0.328171
$273$	2.92336e9	−	7.52309e9i	0.0318530	−	0.0819718i
$274$	−5.80235e10			−0.621908
$275$	−1.03273e11	−	1.78873e11i	−1.08890	−	1.88603i
$276$	4.91057e10	+	8.50536e10i	0.509379	+	0.882271i
$277$	3.88715e10	−	6.73275e10i	0.396710	−	0.687121i	−0.596608	−	0.802533i	$-0.703485\pi$
$277$	3.88715e10	−	6.73275e10i	0.396710	−	0.687121i	0.993318	+	0.115412i	$0.0368187\pi$
$278$	1.35783e10			0.136347
$279$	−2.49215e10	+	4.31653e10i	−0.246238	+	0.426497i
$280$	1.37146e9	−	2.37543e9i	0.0133343	−	0.0230957i
$281$	−9.42110e10			−0.901411			−0.450706	−	0.892673i	$-0.648828\pi$
$281$	−9.42110e10			−0.901411			−0.450706	+	0.892673i	$0.648828\pi$
$282$	−2.31296e10	+	4.00617e10i	−0.217795	+	0.377231i
$283$	8.89846e10	+	1.54126e11i	0.824661	+	1.42836i	0.902178	+	0.431364i	$0.141968\pi$
$283$	8.89846e10	+	1.54126e11i	0.824661	+	1.42836i	−0.0775164	+	0.996991i	$0.524699\pi$
$284$	4.89973e9	+	8.48658e9i	0.0446930	+	0.0774105i
$285$	−3.26354e11			−2.93013
$286$	9.11144e10	+	1.13467e11i	0.805267	+	1.00282i
$287$	1.56014e9			0.0135736
$288$	−2.05033e10	−	3.55128e10i	−0.175614	−	0.304172i
$289$	−4.28778e10	−	7.42666e10i	−0.361570	−	0.626258i
$290$	4.85049e10	−	8.40130e10i	0.402712	−	0.697518i
$291$	1.77716e11			1.45281
$292$	−5.02163e10	+	8.69773e10i	−0.404224	+	0.700137i
$293$	3.41027e10	−	5.90676e10i	0.270324	−	0.468215i	−0.698621	−	0.715492i	$-0.746203\pi$
$293$	3.41027e10	−	5.90676e10i	0.270324	−	0.468215i	0.968945	+	0.247277i	$0.0795359\pi$
$294$	−1.56145e11			−1.21889
$295$	2.34688e10	−	4.06492e10i	0.180423	−	0.312502i
$296$	−1.64248e10	−	2.84486e10i	−0.124362	−	0.215401i
$297$	−2.07980e11	−	3.60233e11i	−1.55102	−	2.68645i
$298$	−1.10023e11			−0.808181
$299$	1.61033e11	−	2.48274e10i	1.16518	−	0.179644i
$300$	1.45159e11			1.03466
$301$	−4.57329e9	−	7.92117e9i	−0.0321129	−	0.0556211i
$302$	5.97877e10	+	1.03555e11i	0.413600	+	0.716376i
$303$	−2.38944e10	+	4.13863e10i	−0.162856	+	0.282075i
$304$	4.25797e10			0.285938
$305$	2.13286e10	−	3.69422e10i	0.141128	−	0.244440i
$306$	1.41425e11	−	2.44954e11i	0.922101	−	1.59712i
$307$	−1.38459e11			−0.889605			−0.444803	−	0.895629i	$-0.646726\pi$
$307$	−1.38459e11			−0.889605			−0.444803	+	0.895629i	$0.646726\pi$
$308$	−3.65434e9	+	6.32951e9i	−0.0231383	+	0.0400767i
$309$	6.06796e9	+	1.05100e10i	0.0378643	+	0.0655829i
$310$	2.11230e10	+	3.65861e10i	0.129905	+	0.225003i
$311$	−2.41824e11			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$311$	−2.41824e11			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$312$	−1.01078e11	+	1.55838e10i	−0.603893	+	0.0931060i
$313$	2.23726e11			1.31755			0.658776	−	0.752339i	$-0.271075\pi$
$313$	2.23726e11			1.31755			0.658776	+	0.752339i	$0.271075\pi$
$314$	5.33301e10	+	9.23705e10i	0.309592	+	0.536229i
$315$	1.30941e10	+	2.26797e10i	0.0749340	+	0.129789i
$316$	1.70646e10	−	2.95568e10i	0.0962731	−	0.166750i
$317$	−6.73120e10			−0.374391			−0.187196	−	0.982323i	$-0.559940\pi$
$317$	−6.73120e10			−0.374391			−0.187196	+	0.982323i	$0.559940\pi$
$318$	7.34478e9	−	1.27215e10i	0.0402770	−	0.0697618i
$319$	−1.29245e11	+	2.23859e11i	−0.698804	+	1.21036i
$320$	−3.47564e10			−0.185293
$321$	4.39613e10	−	7.61432e10i	0.231099	−	0.400275i
$322$	4.09164e9	+	7.08693e9i	0.0212103	+	0.0367372i
$323$	1.46850e11	+	2.54351e11i	0.750692	+	1.30024i
$324$	9.52813e10			0.480347
$325$	8.72260e10	−	2.24471e11i	0.433681	−	1.11605i
$326$	2.38126e11			1.16769
$327$	−4.76454e10	−	8.25242e10i	−0.230439	−	0.399132i
$328$	−9.88456e9	−	1.71206e10i	−0.0471547	−	0.0816743i
$329$	−1.92723e9	+	3.33806e9i	−0.00906885	+	0.0157077i
$330$	−7.09822e11			−3.29486
$331$	−6.52886e9	+	1.13083e10i	−0.0298959	+	0.0517812i	−0.880586	−	0.473886i	$-0.842851\pi$
$331$	−6.52886e9	+	1.13083e10i	−0.0298959	+	0.0517812i	0.850690	+	0.525667i	$0.176184\pi$
$332$	6.92314e10	−	1.19912e11i	0.312739	−	0.541680i
$333$	3.13635e11			1.39774
$334$	7.89270e10	−	1.36706e11i	0.347030	−	0.601073i
$335$	1.68615e11	+	2.92050e11i	0.731468	+	1.26694i
$336$	−2.56826e9	−	4.44835e9i	−0.0109929	−	0.0190402i
$337$	9.86243e10			0.416533			0.208266	−	0.978072i	$-0.433218\pi$
$337$	9.86243e10			0.416533			0.208266	+	0.978072i	$0.433218\pi$
$338$	−3.66391e10	+	1.65669e11i	−0.152693	+	0.690424i
$339$	1.36502e10			0.0561360
$340$	−1.19869e11	−	2.07619e11i	−0.486464	−	0.842580i
$341$	−5.62837e10	−	9.74862e10i	−0.225418	−	0.390435i
$342$	−2.03267e11	+	3.52069e11i	−0.803432	+	1.39159i
$343$	−2.60547e10			−0.101640
$344$	−5.79497e10	+	1.00372e11i	−0.223120	+	0.386455i
$345$	−3.97381e11	+	6.88284e11i	−1.51015	+	2.61566i
$346$	3.25230e11			1.21997
$347$	1.35369e11	−	2.34466e11i	0.501229	−	0.868154i	−0.498770	−	0.866734i	$-0.666215\pi$
$347$	1.35369e11	−	2.34466e11i	0.501229	−	0.868154i	0.999999	−	0.00141969i	$-0.000451901\pi$
$348$	−9.08327e10	−	1.57327e11i	−0.331998	−	0.575038i
$349$	2.24645e11	+	3.89096e11i	0.810553	+	1.40392i	0.912477	+	0.409127i	$0.134167\pi$
$349$	2.24645e11	+	3.89096e11i	0.810553	+	1.40392i	−0.101924	+	0.994792i	$0.532500\pi$
$350$	1.20951e10			0.0430827
$351$	1.75664e11	−	4.52062e11i	0.617733	−	1.58970i
$352$	9.26110e10			0.321529
$353$	1.95560e11	+	3.38719e11i	0.670337	+	1.16106i	0.977809	+	0.209500i	$0.0671836\pi$
$353$	1.95560e11	+	3.38719e11i	0.670337	+	1.16106i	−0.307472	+	0.951557i	$0.599483\pi$
$354$	−4.39489e10	−	7.61217e10i	−0.148742	−	0.257628i
$355$	−3.96504e10	+	6.86764e10i	−0.132501	+	0.229499i
$356$	2.19992e11			0.725909
$357$	1.77149e10	−	3.06831e10i	0.0577208	−	0.0999753i
$358$	7.30671e10	−	1.26556e11i	0.235098	−	0.407201i
$359$	−4.82667e11			−1.53364			−0.766818	−	0.641865i	$-0.778161\pi$
$359$	−4.82667e11			−1.53364			−0.766818	+	0.641865i	$0.778161\pi$
$360$	1.65920e11	−	2.87382e11i	0.520641	−	0.901776i
$361$	−4.97206e10	−	8.61186e10i	−0.154083	−	0.266879i
$362$	−2.06123e11	−	3.57015e11i	−0.630866	−	1.09269i
$363$	1.31965e12			3.98913
$364$	−8.42211e9	+	1.29849e9i	−0.0251457	+	0.00387688i
$365$	−8.12737e11			−2.39680
$366$	−3.99409e10	−	6.91797e10i	−0.116347	−	0.201518i
$367$	−4.37748e9	−	7.58202e9i	−0.0125958	−	0.0218166i	0.859659	−	0.510869i	$-0.170676\pi$
$367$	−4.37748e9	−	7.58202e9i	−0.0125958	−	0.0218166i	−0.872255	+	0.489052i	$0.837343\pi$
$368$	5.18466e10	−	8.98010e10i	0.147369	−	0.255250i
$369$	1.88748e11			0.529984
$370$	1.32915e11	−	2.30216e11i	0.368695	−	0.638599i
$371$	6.11990e8	−	1.06000e9i	0.00167711	−	0.00290484i
$372$	7.91119e10			0.214190
$373$	1.22189e11	−	2.11638e11i	0.326846	−	0.566115i	−0.655038	−	0.755596i	$-0.727347\pi$
$373$	1.22189e11	−	2.11638e11i	0.326846	−	0.566115i	0.981884	+	0.189481i	$0.0606807\pi$
$374$	3.19399e11	+	5.53215e11i	0.844133	+	1.46208i
$375$	9.68083e10	+	1.67677e11i	0.252797	+	0.437857i
$376$	4.88412e10			0.126021
$377$	−2.97868e11	+	4.59243e10i	−0.759431	+	0.117086i
$378$	2.43583e10			0.0613668
$379$	−4.96265e10	−	8.59557e10i	−0.123549	−	0.213992i	0.797616	−	0.603165i	$-0.206094\pi$
$379$	−4.96265e10	−	8.59557e10i	−0.123549	−	0.213992i	−0.921165	+	0.389173i	$0.872761\pi$
$380$	1.72285e11	+	2.98406e11i	0.423859	+	0.734145i
$381$	−3.18477e11	+	5.51618e11i	−0.774311	+	1.34115i
$382$	−2.38289e11			−0.572558
$383$	−3.38657e11	+	5.86570e11i	−0.804202	+	1.39292i	0.112627	+	0.993637i	$0.464073\pi$
$383$	−3.38657e11	+	5.86570e11i	−0.804202	+	1.39292i	−0.916829	+	0.399281i	$0.869260\pi$
$384$	−3.25433e10	+	5.63666e10i	−0.0763785	+	0.132291i
$385$	−5.91445e10			−0.137196
$386$	−2.83753e10	+	4.91474e10i	−0.0650574	+	0.112683i
$387$	−5.53281e11	−	9.58311e11i	−1.25385	−	2.17174i
$388$	−9.38179e10	−	1.62497e11i	−0.210157	−	0.364002i
$389$	−8.14332e11			−1.80314			−0.901568	−	0.432637i	$-0.857583\pi$
$389$	−8.14332e11			−1.80314			−0.901568	+	0.432637i	$0.857583\pi$
$390$	−5.18193e11	−	6.45317e11i	−1.13423	−	1.41248i
$391$	7.15238e11			1.54759
$392$	8.24302e10	+	1.42773e11i	0.176319	+	0.305393i
$393$	−6.25913e11	−	1.08411e12i	−1.32357	−	2.29249i
$394$	−1.38904e11	+	2.40589e11i	−0.290390	+	0.502971i
$395$	2.76186e11			0.570841
$396$	−4.42106e11	+	7.65751e11i	−0.903438	+	1.56480i
$397$	2.54389e11	−	4.40615e11i	0.513975	−	0.890230i	−0.485894	−	0.874018i	$-0.661506\pi$
$397$	2.54389e11	−	4.40615e11i	0.513975	−	0.890230i	0.999869	−	0.0162123i	$-0.00516075\pi$
$398$	6.02042e10			0.120269
$399$	−2.54613e10	+	4.41003e10i	−0.0502925	+	0.0871091i
$400$	−7.66307e10	−	1.32728e11i	−0.149669	−	0.259235i
$401$	−2.58186e11	−	4.47191e11i	−0.498635	−	0.863662i	0.501363	−	0.865237i	$-0.332832\pi$
$401$	−2.58186e11	−	4.47191e11i	−0.498635	−	0.863662i	−0.999999	+	0.00157498i	$0.999499\pi$
$402$	6.31515e11			1.20605
$403$	4.75383e10	−	1.22337e11i	0.0897781	−	0.231039i
$404$	5.04562e10			0.0942319
$405$	3.85525e11	+	6.67749e11i	0.712041	+	1.23329i
$406$	−7.56846e9	−	1.31090e10i	−0.0138242	−	0.0239442i
$407$	−3.54163e11	+	6.13428e11i	−0.639776	+	1.10812i
$408$	−4.48944e11			−0.802087
$409$	1.31146e11	−	2.27151e11i	0.231739	−	0.401384i	−0.726581	−	0.687081i	$-0.758892\pi$
$409$	1.31146e11	−	2.27151e11i	0.231739	−	0.401384i	0.958320	+	0.285697i	$0.0922252\pi$
$410$	7.99894e10	−	1.38546e11i	0.139799	−	0.242139i
$411$	−8.79296e11			−1.52001
$412$	6.40665e9	−	1.10966e10i	0.0109545	−	0.0189738i
$413$	−3.66196e9	−	6.34269e9i	−0.00619352	−	0.0107275i
$414$	4.95011e11	+	8.57384e11i	0.828158	+	1.43441i
$415$	1.12049e12			1.85435
$416$	6.76090e10	+	8.41950e10i	0.110684	+	0.137837i
$417$	2.05768e11			0.333246
$418$	−4.59066e11	−	7.95125e11i	−0.735498	−	1.27392i
$419$	1.60166e10	+	2.77416e10i	0.0253868	+	0.0439712i	0.878440	−	0.477853i	$-0.158585\pi$
$419$	1.60166e10	+	2.77416e10i	0.0253868	+	0.0439712i	−0.853053	+	0.521824i	$0.825252\pi$
$420$	2.07833e10	−	3.59977e10i	0.0325906	−	0.0564485i
$421$	−2.73798e10			−0.0424777			−0.0212389	−	0.999774i	$-0.506761\pi$
$421$	−2.73798e10			−0.0424777			−0.0212389	+	0.999774i	$0.506761\pi$
$422$	3.46056e11	−	5.99387e11i	0.531179	−	0.920029i
$423$	−2.33158e11	+	4.03842e11i	−0.354095	+	0.613310i
$424$	−1.55095e10			−0.0233051
$425$	5.28571e11	−	9.15511e11i	0.785874	−	1.36117i
$426$	7.42512e10	+	1.28607e11i	0.109235	+	0.189200i
$427$	−3.32800e9	−	5.76427e9i	−0.00484460	−	0.00839110i
$428$	−9.28301e10			−0.133719
$429$	1.38076e12	+	1.71949e12i	1.96816	+	2.45100i
$430$	−9.37900e11			−1.32297
$431$	1.61751e11	+	2.80161e11i	0.225787	+	0.391075i	0.956555	−	0.291551i	$-0.0941713\pi$
$431$	1.61751e11	+	2.80161e11i	0.225787	+	0.391075i	−0.730768	+	0.682626i	$0.760838\pi$
$432$	−1.54326e11	−	2.67301e11i	−0.213188	−	0.369253i
$433$	4.29629e11	−	7.44139e11i	0.587351	−	1.01732i	−0.407227	−	0.913327i	$-0.633504\pi$
$433$	4.29629e11	−	7.44139e11i	0.587351	−	1.01732i	0.994578	−	0.103995i	$-0.0331626\pi$
$434$	6.59184e9			0.00891873
$435$	7.35051e11	−	1.27315e12i	0.984273	−	1.70481i
$436$	−5.03047e10	+	8.71304e10i	−0.0666683	+	0.115473i
$437$	−1.02800e12			−1.34842
$438$	−7.60986e11	+	1.31807e12i	−0.987969	+	1.71121i
$439$	−3.59294e11	−	6.22316e11i	−0.461700	−	0.799688i	0.537346	−	0.843362i	$-0.319427\pi$
$439$	−3.59294e11	−	6.22316e11i	−0.461700	−	0.799688i	−0.999046	+	0.0436743i	$0.986094\pi$
$440$	3.74721e11	+	6.49035e11i	0.476618	+	0.825527i
$441$	−1.57402e12			−1.98170
$442$	−2.69770e11	+	6.94238e11i	−0.336197	+	0.865183i
$443$	2.12241e11			0.261826			0.130913	−	0.991394i	$-0.458209\pi$
$443$	2.12241e11			0.261826			0.130913	+	0.991394i	$0.458209\pi$
$444$	−2.48904e11	−	4.31115e11i	−0.303955	−	0.526465i
$445$	8.90128e11	+	1.54175e12i	1.07605	+	1.86377i
$446$	2.62953e11	−	4.55448e11i	0.314681	−	0.545044i
$447$	−1.66730e12			−1.97528
$448$	−2.71161e9	+	4.69664e9i	−0.00318036	+	0.00550854i
$449$	4.48884e11	−	7.77491e11i	0.521226	−	0.902790i	−0.478469	−	0.878104i	$-0.658808\pi$
$449$	4.48884e11	−	7.77491e11i	0.521226	−	0.902790i	0.999695	−	0.0246855i	$-0.00785845\pi$
$450$	1.46328e12			1.68217
$451$	−2.13137e11	+	3.69165e11i	−0.242586	+	0.420171i
$452$	−7.20607e9	−	1.24813e10i	−0.00812036	−	0.0140649i
$453$	9.06032e11	+	1.56929e12i	1.01088	+	1.75090i
$454$	1.10658e12			1.22245
$455$	−4.31774e10	−	5.37698e10i	−0.0472286	−	0.0588148i
$456$	6.45259e11			0.698863
$457$	−5.70504e11	−	9.88142e11i	−0.611837	−	1.05973i	−0.990931	−	0.134375i	$-0.957097\pi$
$457$	−5.70504e11	−	9.88142e11i	−0.611837	−	1.05973i	0.379094	−	0.925358i	$-0.376236\pi$
$458$	2.69724e11	+	4.67176e11i	0.286434	+	0.496119i
$459$	1.06449e12	−	1.84375e12i	1.11939	−	1.93885i
$460$	8.39123e11			0.873806
$461$	3.94639e11	−	6.83535e11i	0.406955	−	0.704867i	−0.587592	−	0.809157i	$-0.699924\pi$
$461$	3.94639e11	−	6.83535e11i	0.406955	−	0.704867i	0.994547	+	0.104291i	$0.0332573\pi$
$462$	−5.53785e10	+	9.59184e10i	−0.0565526	+	0.0979519i
$463$	−7.23863e11			−0.732052			−0.366026	−	0.930605i	$-0.619282\pi$
$463$	−7.23863e11			−0.732052			−0.366026	+	0.930605i	$0.619282\pi$
$464$	−9.59027e10	+	1.66108e11i	−0.0960505	+	0.166364i
$465$	3.20101e11	+	5.54431e11i	0.317503	+	0.549932i
$466$	9.51633e10	+	1.64828e11i	0.0934830	+	0.161917i
$467$	−6.62553e11			−0.644607			−0.322303	−	0.946636i	$-0.604457\pi$
$467$	−6.62553e11			−0.644607			−0.322303	+	0.946636i	$0.604457\pi$
$468$	−1.01892e12	+	1.57093e11i	−0.981820	+	0.151373i
$469$	5.26198e10			0.0502193
$470$	1.97620e11	+	3.42288e11i	0.186806	+	0.323558i
$471$	8.08173e11	+	1.39980e12i	0.756677	+	1.31060i
$472$	−4.64019e10	+	8.03705e10i	−0.0430325	+	0.0745346i
$473$	2.49910e12			2.29567
$474$	2.58600e11	−	4.47908e11i	0.235302	−	0.407555i
$475$	−7.59705e11	+	1.31585e12i	−0.684737	+	1.18600i
$476$	−3.74074e10			−0.0333984
$477$	7.40392e10	−	1.28240e11i	0.0654831	−	0.113420i
$478$	−1.26322e11	−	2.18797e11i	−0.110676	−	0.191697i
$479$	−1.12538e12	−	1.94922e12i	−0.976763	−	1.69180i	−0.673989	−	0.738742i	$-0.735420\pi$
$479$	−1.12538e12	−	1.94922e12i	−0.976763	−	1.69180i	−0.302775	−	0.953062i	$-0.597913\pi$
$480$	−5.26704e11			−0.452878
$481$	−8.16233e11	+	1.25844e11i	−0.695283	+	0.107196i
$482$	3.53335e11			0.298178
$483$	6.20053e10	+	1.07396e11i	0.0518402	+	0.0897899i
$484$	−6.96653e11	−	1.20664e12i	−0.577048	−	0.999477i
$485$	7.59208e11	−	1.31499e12i	0.623050	−	1.07915i
$486$	−3.92973e10			−0.0319521
$487$	−2.39496e11	+	4.14819e11i	−0.192938	+	0.334178i	−0.946223	−	0.323516i	$-0.895135\pi$
$487$	−2.39496e11	+	4.14819e11i	−0.192938	+	0.334178i	0.753285	+	0.657695i	$0.228468\pi$
$488$	−4.21703e10	+	7.30411e10i	−0.0336603	+	0.0583013i
$489$	3.60860e12			2.85397
$490$	−6.67055e11	+	1.15537e12i	−0.522732	+	0.905398i
$491$	7.18045e9	+	1.24369e10i	0.00557551	+	0.00965707i	0.868800	−	0.495164i	$-0.164892\pi$
$491$	7.18045e9	+	1.24369e10i	0.00557551	+	0.00965707i	−0.863224	+	0.504821i	$0.831559\pi$
$492$	−1.49792e11	−	2.59447e11i	−0.115251	−	0.199621i
$493$	−1.32300e12			−1.00867
$494$	3.87736e11	−	9.97816e11i	0.292930	−	0.753840i
$495$	−7.15537e12			−5.35684
$496$	−4.17638e10	−	7.23370e10i	−0.0309836	−	0.0536652i
$497$	6.18684e9	+	1.07159e10i	0.00454847	+	0.00787818i
$498$	1.04914e12	−	1.81717e12i	0.764369	−	1.32393i
$499$	1.19092e11			0.0859862			0.0429931	−	0.999075i	$-0.486311\pi$
$499$	1.19092e11			0.0859862			0.0429931	+	0.999075i	$0.486311\pi$
$500$	1.02212e11	−	1.77036e11i	0.0731368	−	0.126677i
$501$	1.19607e12	−	2.07166e12i	0.848179	−	1.46909i
$502$	−1.00766e12			−0.708184
$503$	−9.64716e11	+	1.67094e12i	−0.671960	+	1.16387i	0.305387	+	0.952228i	$0.401214\pi$
$503$	−9.64716e11	+	1.67094e12i	−0.671960	+	1.16387i	−0.977347	+	0.211641i	$0.932119\pi$
$504$	−2.58894e10	−	4.48417e10i	−0.0178724	−	0.0309560i
$505$	2.04155e11	+	3.53606e11i	0.139684	+	0.241941i
$506$	−2.23590e12			−1.51627
$507$	−5.55234e11	+	2.51057e12i	−0.373199	+	1.68747i
$508$	6.72506e11			0.448032
$509$	1.29118e12	+	2.23639e12i	0.852624	+	1.47679i	0.878832	+	0.477131i	$0.158323\pi$
$509$	1.29118e12	+	2.23639e12i	0.852624	+	1.47679i	−0.0262082	+	0.999657i	$0.508343\pi$
$510$	−1.81651e12	−	3.14628e12i	−1.18897	−	2.05936i
$511$	−6.34077e10	+	1.09825e11i	−0.0411385	+	0.0712539i
$512$	6.87195e10			0.0441942
$513$	−1.52997e12	+	2.64998e12i	−0.975336	+	1.68933i
$514$	2.83565e11	−	4.91149e11i	0.179192	−	0.310370i
$515$	1.03690e11			0.0649537
$516$	−8.78179e11	+	1.52105e12i	−0.545330	+	0.944539i
$517$	−5.26574e11	−	9.12052e11i	−0.324154	−	0.561452i
$518$	−2.07395e10	−	3.59218e10i	−0.0126565	−	0.0219217i
$519$	4.92859e12			2.98174
$520$	−3.16496e11	+	8.14484e11i	−0.189825	+	0.488504i
$521$	−2.01270e12			−1.19676			−0.598382	−	0.801211i	$-0.704189\pi$
$521$	−2.01270e12			−1.19676			−0.598382	+	0.801211i	$0.704189\pi$
$522$	−9.15640e11	−	1.58594e12i	−0.539769	−	0.934907i
$523$	1.20639e12	+	2.08953e12i	0.705067	+	1.22121i	0.966667	+	0.256035i	$0.0824163\pi$
$523$	1.20639e12	+	2.08953e12i	0.705067	+	1.22121i	−0.261601	+	0.965176i	$0.584250\pi$
$524$	−6.60849e11	+	1.14462e12i	−0.382923	+	0.663242i
$525$	1.83291e11			0.105299
$526$	−5.17856e11	+	8.96952e11i	−0.294967	+	0.510897i
$527$	2.88072e11	−	4.98955e11i	0.162687	−	0.281782i
$528$	1.40344e12			0.785853
$529$	−3.51154e11	+	6.08217e11i	−0.194961	+	0.337682i
$530$	−6.27541e10	−	1.08693e11i	−0.0345463	−	0.0598359i
$531$	−4.43027e11	−	7.67346e11i	−0.241827	−	0.418857i
$532$	5.37650e10			0.0291003
$533$	−4.91214e11	+	7.57336e10i	−0.263632	+	0.0406459i
$534$	3.33380e12			1.77420
$535$	−3.75607e11	−	6.50571e11i	−0.198217	−	0.343323i
$536$	−3.33382e11	−	5.77434e11i	−0.174462	−	0.302177i
$537$	1.10727e12	−	1.91785e12i	0.574605	−	0.995245i
$538$	1.75550e12			0.903400
$539$	1.77742e12	−	3.07857e12i	0.907067	−	1.57109i
$540$	1.24886e12	−	2.16309e12i	0.632038	−	1.09472i
$541$	−1.72399e12			−0.865260			−0.432630	−	0.901572i	$-0.642414\pi$
$541$	−1.72399e12			−0.865260			−0.432630	+	0.901572i	$0.642414\pi$
$542$	−6.91928e11	+	1.19845e12i	−0.344401	+	0.596519i
$543$	−3.12362e12	−	5.41026e12i	−1.54191	−	2.67066i
$544$	2.37001e11	+	4.10498e11i	0.116026	+	0.200963i
$545$	−8.14168e11			−0.395303
$546$	−1.27630e11	+	1.96775e10i	−0.0614590	+	0.00947553i
$547$	1.89229e12			0.903741			0.451870	−	0.892084i	$-0.350757\pi$
$547$	1.89229e12			0.903741			0.451870	+	0.892084i	$0.350757\pi$
$548$	4.64188e11	+	8.03997e11i	0.219878	+	0.380839i
$549$	−4.02625e11	−	6.97367e11i	−0.189158	−	0.327632i
$550$	−1.65236e12	+	2.86197e12i	−0.769969	+	1.33362i
$551$	1.90153e12			0.878863
$552$	7.85691e11	−	1.36086e12i	0.360185	−	0.623859i
$553$	2.15474e10	−	3.73211e10i	0.00979785	−	0.0169704i
$554$	−1.24389e12			−0.561032
$555$	2.01422e12	−	3.48873e12i	0.901132	−	1.56081i
$556$	−1.08626e11	−	1.88147e11i	−0.0482058	−	0.0834949i
$557$	−1.04122e11	−	1.80345e11i	−0.0458347	−	0.0793880i	0.842198	−	0.539169i	$-0.181261\pi$
$557$	−1.04122e11	−	1.80345e11i	−0.0458347	−	0.0793880i	−0.888033	+	0.459780i	$0.847928\pi$
$558$	7.97488e11			0.348233
$559$	1.82443e12	+	2.27200e12i	0.790265	+	0.984135i
$560$	−4.38866e10			−0.0188576
$561$	4.84021e12	+	8.38350e12i	2.06315	+	3.57349i
$562$	7.53688e11	+	1.30543e12i	0.318697	+	0.552000i
$563$	−7.61175e11	+	1.31839e12i	−0.319299	+	0.553041i	−0.980342	−	0.197306i	$-0.936781\pi$
$563$	−7.61175e11	+	1.31839e12i	−0.319299	+	0.553041i	0.661043	+	0.750348i	$0.270114\pi$
$564$	7.40147e11			0.308008
$565$	5.83141e10	−	1.01003e11i	0.0240744	−	0.0416981i
$566$	1.42375e12	−	2.46601e12i	0.583124	−	1.01000i
$567$	1.20311e11			0.0488856
$568$	7.83956e10	−	1.35785e11i	0.0316027	−	0.0547375i
$569$	1.24926e12	+	2.16379e12i	0.499631	+	0.865386i	1.00000		0.000426417i	$-0.000135733\pi$
$569$	1.24926e12	+	2.16379e12i	0.499631	+	0.865386i	−0.500369	+	0.865812i	$0.666802\pi$
$570$	2.61083e12	+	4.52210e12i	1.03596	+	1.79433i
$571$	−1.73010e12			−0.681098			−0.340549	−	0.940227i	$-0.610613\pi$
$571$	−1.73010e12			−0.681098			−0.340549	+	0.940227i	$0.610613\pi$
$572$	8.43327e11	−	2.17025e12i	0.329392	−	0.847673i
$573$	−3.61108e12			−1.39940
$574$	−1.24811e10	−	2.16180e10i	−0.00479900	−	0.00831211i
$575$	1.85009e12	+	3.20445e12i	0.705810	+	1.22250i
$576$	−3.28053e11	+	5.68205e11i	−0.124178	+	0.215082i
$577$	−3.24966e12			−1.22052			−0.610262	−	0.792199i	$-0.708936\pi$
$577$	−3.24966e12			−1.22052			−0.610262	+	0.792199i	$0.708936\pi$
$578$	−6.86045e11	+	1.18827e12i	−0.255669	+	0.442831i
$579$	−4.30003e11	+	7.44787e11i	−0.159008	+	0.275409i
$580$	−1.55216e12			−0.569521
$581$	8.74179e10	−	1.51412e11i	0.0318279	−	0.0551275i
$582$	−1.42173e12	−	2.46251e12i	−0.513646	−	0.889661i
$583$	1.67213e11	+	2.89621e11i	0.0599462	+	0.103830i
$584$	1.60692e12			0.571659
$585$	−5.22365e12	−	6.50512e12i	−1.84405	−	2.29643i
$586$	−1.09129e12			−0.382296
$587$	−1.05512e12	−	1.82752e12i	−0.366802	−	0.635319i	0.622262	−	0.782809i	$-0.286214\pi$
$587$	−1.05512e12	−	1.82752e12i	−0.366802	−	0.635319i	−0.989064	+	0.147490i	$0.952881\pi$
$588$	1.24916e12	+	2.16361e12i	0.430943	+	0.746415i
$589$	−4.14040e11	+	7.17139e11i	−0.141750	+	0.245519i
$590$	−7.51002e11			−0.255157
$591$	−2.10497e12	+	3.64592e12i	−0.709746	+	1.22932i
$592$	−2.62797e11	+	4.55178e11i	−0.0879372	+	0.152312i
$593$	−2.79941e11			−0.0929651			−0.0464826	−	0.998919i	$-0.514801\pi$
$593$	−2.79941e11			−0.0929651			−0.0464826	+	0.998919i	$0.514801\pi$
$594$	−3.32769e12	+	5.76372e12i	−1.09674	+	1.89961i
$595$	−1.51357e11	−	2.62158e11i	−0.0495081	−	0.0857505i
$596$	8.80181e11	+	1.52452e12i	0.285735	+	0.494908i
$597$	9.12344e11			0.293951
$598$	−1.63228e12	−	2.03272e12i	−0.521963	−	0.650012i
$599$	−5.96835e11			−0.189423			−0.0947117	−	0.995505i	$-0.530193\pi$
$599$	−5.96835e11			−0.189423			−0.0947117	+	0.995505i	$0.530193\pi$
$600$	−1.16127e12	−	2.01138e12i	−0.365808	−	0.633599i
$601$	−1.09460e11	−	1.89591e11i	−0.0342232	−	0.0592764i	0.848406	−	0.529345i	$-0.177562\pi$
$601$	−1.09460e11	−	1.89591e11i	−0.0342232	−	0.0592764i	−0.882630	+	0.470069i	$0.844229\pi$
$602$	−7.31726e10	+	1.26739e11i	−0.0227072	+	0.0393301i
$603$	6.36599e12			1.96082
$604$	9.56603e11	−	1.65689e12i	0.292459	−	0.506555i
$605$	5.63756e12	−	9.76454e12i	1.71077	−	2.96314i
$606$	7.64621e11			0.230313
$607$	2.27198e12	−	3.93518e12i	0.679290	−	1.17656i	−0.295905	−	0.955217i	$-0.595621\pi$
$607$	2.27198e12	−	3.93518e12i	0.679290	−	1.17656i	0.975195	−	0.221347i	$-0.0710454\pi$
$608$	−3.40637e11	−	5.90001e11i	−0.101094	−	0.175100i
$609$	−1.14694e11	−	1.98655e11i	−0.0337879	−	0.0585224i
$610$	−6.82514e11			−0.199585
$611$	4.44754e11	−	1.14455e12i	0.129102	−	0.332238i
$612$	−4.52558e12			−1.30405
$613$	9.43843e11	+	1.63478e12i	0.269978	+	0.467615i	0.968856	−	0.247626i	$-0.0796504\pi$
$613$	9.43843e11	+	1.63478e12i	0.269978	+	0.467615i	−0.698878	+	0.715241i	$0.746317\pi$
$614$	1.10767e12	+	1.91854e12i	0.314523	+	0.544770i
$615$	1.21217e12	−	2.09954e12i	0.341685	−	0.591816i
$616$	1.16939e11			0.0327225
$617$	−2.18626e12	+	3.78672e12i	−0.607322	+	1.05191i	0.384358	+	0.923184i	$0.374423\pi$
$617$	−2.18626e12	+	3.78672e12i	−0.607322	+	1.05191i	−0.991680	+	0.128728i	$0.958911\pi$
$618$	9.70874e10	−	1.68160e11i	0.0267741	−	0.0463741i
$619$	−3.63885e11			−0.0996221			−0.0498111	−	0.998759i	$-0.515862\pi$
$619$	−3.63885e11			−0.0996221			−0.0498111	+	0.998759i	$0.515862\pi$
$620$	3.37968e11	−	5.85377e11i	0.0918570	−	0.159101i
$621$	3.72589e12	+	6.45343e12i	1.00535	+	1.74132i
$622$	1.93459e12	+	3.35081e12i	0.518242	+	0.897622i
$623$	2.77782e11			0.0738768
$624$	1.02456e12	+	1.27590e12i	0.270524	+	0.336889i
$625$	−2.91327e12			−0.763697
$626$	−1.78981e12	−	3.10004e12i	−0.465825	−	0.806832i
$627$	−6.95675e12	−	1.20495e13i	−1.79764	−	3.11360i
$628$	8.53282e11	−	1.47793e12i	0.218914	−	0.379171i
$629$	−3.62536e12			−0.923470
$630$	2.09506e11	−	3.62875e11i	0.0529863	−	0.0917750i
$631$	−2.57743e12	+	4.46425e12i	−0.647225	+	1.12103i	0.336557	+	0.941663i	$0.390737\pi$
$631$	−2.57743e12	+	4.46425e12i	−0.647225	+	1.12103i	−0.983783	+	0.179364i	$0.942596\pi$
$632$	−5.46068e11			−0.136151
$633$	5.24419e12	−	9.08321e12i	1.29826	−	2.24865i
$634$	5.38496e11	+	9.32702e11i	0.132367	+	0.229267i
$635$	2.72108e12	+	4.71305e12i	0.664139	+	1.15032i
$636$	−2.35033e11			−0.0569603
$637$	4.09638e12	−	6.31565e11i	0.985763	−	0.151981i
$638$	4.13583e12			0.988258
$639$	7.48490e11	+	1.29642e12i	0.177596	+	0.307605i
$640$	2.78051e11	+	4.81599e11i	0.0655111	+	0.113469i
$641$	2.10552e12	−	3.64686e12i	0.492603	−	0.853214i	−0.507360	−	0.861734i	$-0.669379\pi$
$641$	2.10552e12	−	3.64686e12i	0.492603	−	0.853214i	0.999964	+	0.00852011i	$0.00271207\pi$
$642$	−1.40676e12			−0.326823
$643$	−1.32304e12	+	2.29157e12i	−0.305227	+	0.528669i	−0.977312	−	0.211805i	$-0.932066\pi$
$643$	−1.32304e12	+	2.29157e12i	−0.305227	+	0.528669i	0.672085	+	0.740474i	$0.265399\pi$
$644$	6.54662e10	−	1.13391e11i	0.0149979	−	0.0259772i
$645$	−1.42131e13			−3.23347
$646$	2.34959e12	−	4.06962e12i	0.530819	−	0.919406i
$647$	8.22916e11	+	1.42533e12i	0.184623	+	0.319777i	0.943449	−	0.331516i	$-0.107560\pi$
$647$	8.22916e11	+	1.42533e12i	0.184623	+	0.319777i	−0.758826	+	0.651293i	$0.774227\pi$
$648$	−7.62250e11	−	1.32026e12i	−0.169828	−	0.294151i
$649$	2.00110e12			0.442759
$650$	−3.80817e12	+	5.87130e11i	−0.836770	+	0.129010i
$651$	9.98938e10			0.0217984
$652$	−1.90501e12	−	3.29957e12i	−0.412841	−	0.715062i
$653$	6.70759e11	+	1.16179e12i	0.144363	+	0.250045i	0.929135	−	0.369740i	$-0.120553\pi$
$653$	6.70759e11	+	1.16179e12i	0.144363	+	0.250045i	−0.784772	+	0.619785i	$0.787220\pi$
$654$	−7.62326e11	+	1.32039e12i	−0.162945	+	0.282229i
$655$	−1.06957e13			−2.27050
$656$	−1.58153e11	+	2.73929e11i	−0.0333434	+	0.0577525i
$657$	−7.67113e12	+	1.32868e13i	−1.60626	+	2.78212i
$658$	6.16714e10			0.0128253
$659$	−1.43708e12	+	2.48909e12i	−0.296822	+	0.514110i	−0.975407	−	0.220411i	$-0.929260\pi$
$659$	−1.43708e12	+	2.48909e12i	−0.296822	+	0.514110i	0.678585	+	0.734522i	$0.262593\pi$
$660$	5.67857e12	+	9.83558e12i	1.16491	+	2.01768i
$661$	−2.91709e12	−	5.05254e12i	−0.594351	−	1.02945i	−0.993638	−	0.112620i	$-0.964076\pi$
$661$	−2.91709e12	−	5.05254e12i	−0.594351	−	1.02945i	0.399287	−	0.916826i	$-0.369258\pi$
$662$	2.08923e11			0.0422792
$663$	−4.08814e12	+	1.05206e13i	−0.821702	+	2.11460i
$664$	−2.21541e12			−0.442279
$665$	2.17543e11	+	3.76795e11i	0.0431367	+	0.0747150i
$666$	−2.50908e12	−	4.34586e12i	−0.494175	−	0.855936i
$667$	2.31537e12	−	4.01034e12i	0.452955	−	0.784541i
$668$	−2.52566e12			−0.490774
$669$	3.98483e12	−	6.90192e12i	0.769116	−	1.33215i
$670$	2.69784e12	−	4.67280e12i	0.517226	−	0.895861i
$671$	1.81861e12			0.346328
$672$	−4.10921e10	+	7.11736e10i	−0.00777315	+	0.0134635i
$673$	−1.52726e12	−	2.64530e12i	−0.286976	−	0.497058i	0.686110	−	0.727498i	$-0.259317\pi$
$673$	−1.52726e12	−	2.64530e12i	−0.286976	−	0.497058i	−0.973087	+	0.230440i	$0.925983\pi$
$674$	−7.88994e11	−	1.36658e12i	−0.147267	−	0.255073i
$675$	1.10139e13			2.04209
$676$	2.58869e12	−	8.17665e11i	0.476782	−	0.150597i
$677$	3.54962e12			0.649431			0.324715	−	0.945812i	$-0.394731\pi$
$677$	3.54962e12			0.649431			0.324715	+	0.945812i	$0.394731\pi$
$678$	−1.09202e11	−	1.89143e11i	−0.0198471	−	0.0343761i
$679$	−1.18463e11	−	2.05184e11i	−0.0213879	−	0.0370450i
$680$	−1.91790e12	+	3.32190e12i	−0.343982	+	0.595794i
$681$	1.67693e13			2.98781
$682$	−9.00539e11	+	1.55978e12i	−0.159394	+	0.276079i
$683$	−1.05902e12	+	1.83428e12i	−0.186214	+	0.322531i	−0.943985	−	0.329989i	$-0.892955\pi$
$683$	−1.05902e12	+	1.83428e12i	−0.186214	+	0.322531i	0.757771	+	0.652520i	$0.226288\pi$
$684$	6.50454e12			1.13622
$685$	−3.75637e12	+	6.50623e12i	−0.651870	+	1.12907i
$686$	2.08438e11	+	3.61025e11i	0.0359350	+	0.0622413i
$687$	4.08744e12	+	7.07965e12i	0.700077	+	1.21257i
$688$	1.85439e12			0.315539
$689$	−1.41231e11	+	3.63450e11i	−0.0238750	+	0.0614411i
$690$	1.27162e13			2.13568
$691$	−2.26573e12	−	3.92436e12i	−0.378056	−	0.654813i	0.612723	−	0.790298i	$-0.290074\pi$
$691$	−2.26573e12	−	3.92436e12i	−0.378056	−	0.654813i	−0.990779	+	0.135485i	$0.956741\pi$
$692$	−2.60184e12	−	4.50652e12i	−0.431324	−	0.747075i
$693$	−5.58244e11	+	9.66906e11i	−0.0919442	+	0.159252i
$694$	−4.33180e12			−0.708845
$695$	8.79044e11	−	1.52255e12i	0.142915	−	0.247537i
$696$	−1.45332e12	+	2.51723e12i	−0.234758	+	0.406613i
$697$	−2.18176e12			−0.350155
$698$	3.59431e12	−	6.22553e12i	0.573148	−	0.992721i
$699$	1.44212e12	+	2.49782e12i	0.228483	+	0.395744i
$700$	−9.67608e10	−	1.67595e11i	−0.0152321	−	0.0263827i
$701$	−8.76423e12			−1.37083			−0.685413	−	0.728154i	$-0.740378\pi$
$701$	−8.76423e12			−1.37083			−0.685413	+	0.728154i	$0.740378\pi$
$702$	−7.66926e12	+	1.18242e12i	−1.19189	+	0.183761i
$703$	5.21066e12			0.804626
$704$	−7.40888e11	−	1.28326e12i	−0.113678	−	0.196896i
$705$	2.99477e12	+	5.18709e12i	0.456575	+	0.790811i
$706$	3.12895e12	−	5.41951e12i	0.474000	−	0.820991i
$707$	6.37105e10			0.00959012
$708$	−7.03182e11	+	1.21795e12i	−0.105176	+	0.182171i
$709$	6.14629e12	−	1.06457e13i	0.913493	−	1.58222i	0.104399	−	0.994535i	$-0.466708\pi$
$709$	6.14629e12	−	1.06457e13i	0.913493	−	1.58222i	0.809093	−	0.587680i	$-0.199959\pi$
$710$	1.26881e12			0.187385
$711$	2.60682e12	−	4.51515e12i	0.382559	−	0.662611i
$712$	−1.75994e12	−	3.04830e12i	−0.256648	−	0.444527i
$713$	1.00830e12	+	1.74643e12i	0.146113	+	0.253074i
$714$	−5.66877e11			−0.0816295
$715$	1.86218e13	−	2.87104e12i	2.66467	−	0.410830i
$716$	−2.33815e12			−0.332478
$717$	−1.91431e12	−	3.31568e12i	−0.270505	−	0.468529i
$718$	3.86133e12	+	6.68803e12i	0.542222	+	0.939156i
$719$	−6.84710e12	+	1.18595e13i	−0.955492	+	1.65496i	−0.222253	+	0.974989i	$0.571341\pi$
$719$	−6.84710e12	+	1.18595e13i	−0.955492	+	1.65496i	−0.733239	+	0.679971i	$0.761992\pi$
$720$	−5.30945e12			−0.736297
$721$	8.08962e9	−	1.40116e10i	0.00111486	−	0.00193099i
$722$	−7.95529e11	+	1.37790e12i	−0.108953	+	0.188712i
$723$	5.35449e12			0.728779
$724$	−3.29796e12	+	5.71224e12i	−0.446090	+	0.772650i
$725$	−3.42218e12	−	5.92740e12i	−0.460026	−	0.796788i
$726$	−1.05572e13	−	1.82856e13i	−1.41037	−	2.44283i
$727$	−6.80422e12			−0.903386			−0.451693	−	0.892173i	$-0.649180\pi$
$727$	−6.80422e12			−0.903386			−0.451693	+	0.892173i	$0.649180\pi$
$728$	8.53693e10	+	1.06312e11i	0.0112645	+	0.0140279i
$729$	−7.92138e12			−1.03879
$730$	6.50190e12	+	1.12616e13i	0.847398	+	1.46774i
$731$	6.39546e12	+	1.10773e13i	0.828407	+	1.43484i
$732$	−6.39055e11	+	1.10688e12i	−0.0822694	+	0.142495i
$733$	1.07488e13			1.37529			0.687644	−	0.726048i	$-0.258645\pi$
$733$	1.07488e13			1.37529			0.687644	+	0.726048i	$0.258645\pi$
$734$	−7.00397e10	+	1.21312e11i	−0.00890660	+	0.0154267i
$735$	−1.01086e13	+	1.75087e13i	−1.27762	+	2.21289i
$736$	−1.65909e12			−0.208411
$737$	−7.18860e12	+	1.24510e13i	−0.897513	+	1.55454i
$738$	−1.50998e12	−	2.61536e12i	−0.187378	−	0.324548i
$739$	1.33527e12	+	2.31276e12i	0.164691	+	0.285253i	0.936546	−	0.350546i	$-0.114004\pi$
$739$	1.33527e12	+	2.31276e12i	0.164691	+	0.285253i	−0.771854	+	0.635799i	$0.780671\pi$
$740$	−4.25329e12			−0.521414
$741$	5.87581e12	−	1.51211e13i	0.715955	−	1.84247i
$742$	−1.95837e10			−0.00237179
$743$	−8.50092e11	−	1.47240e12i	−0.102333	−	0.177246i	0.810312	−	0.585998i	$-0.199297\pi$
$743$	−8.50092e11	−	1.47240e12i	−0.102333	−	0.177246i	−0.912646	+	0.408752i	$0.865964\pi$
$744$	−6.32895e11	−	1.09621e12i	−0.0757275	−	0.131164i
$745$	−7.12274e12	+	1.23369e13i	−0.847118	+	1.46725i
$746$	−3.91006e12			−0.462231
$747$	1.05759e13	−	1.83180e13i	1.24272	−	2.15246i
$748$	5.11038e12	−	8.85143e12i	0.596892	−	1.03385i
$749$	−1.17216e11			−0.0136087
$750$	1.54893e12	−	2.68283e12i	0.178754	−	0.309612i
$751$	−3.77713e12	−	6.54219e12i	−0.433294	−	0.750487i	0.563861	−	0.825870i	$-0.309315\pi$
$751$	−3.77713e12	−	6.54219e12i	−0.433294	−	0.750487i	−0.997155	+	0.0753828i	$0.975982\pi$
$752$	−3.90730e11	−	6.76764e11i	−0.0445550	−	0.0771715i
$753$	−1.52702e13			−1.73088
$754$	3.01929e12	+	3.75999e12i	0.340200	+	0.423658i
$755$	1.54823e13			1.73411
$756$	−1.94866e11	−	3.37518e11i	−0.0216965	−	0.0375794i
$757$	2.73735e12	+	4.74123e12i	0.302970	+	0.524759i	0.976807	−	0.214121i	$-0.0686886\pi$
$757$	2.73735e12	+	4.74123e12i	0.302970	+	0.524759i	−0.673838	+	0.738879i	$0.735355\pi$
$758$	−7.94025e11	+	1.37529e12i	−0.0873620	+	0.151315i
$759$	−3.38832e13			−3.70592
$760$	2.75656e12	−	4.77450e12i	0.299714	−	0.519119i
$761$	−1.35245e12	+	2.34250e12i	−0.146180	+	0.253192i	−0.929813	−	0.368033i	$-0.880031\pi$
$761$	−1.35245e12	+	2.34250e12i	−0.146180	+	0.253192i	0.783632	+	0.621225i	$0.213365\pi$
$762$	1.01913e13			1.09504
$763$	−6.35193e10	+	1.10019e11i	−0.00678493	+	0.0117518i
$764$	1.90632e12	+	3.30184e12i	0.202430	+	0.350619i
$765$	−1.83113e13	−	3.17161e13i	−1.93305	−	3.34814i
$766$	1.08370e13			1.13731
$767$	1.46087e12	+	1.81925e12i	0.152416	+	0.189807i
$768$	1.04139e12			0.108015
$769$	−5.69875e12	−	9.87053e12i	−0.587640	−	1.01782i	−0.994541	−	0.104350i	$-0.966724\pi$
$769$	−5.69875e12	−	9.87053e12i	−0.587640	−	1.01782i	0.406901	−	0.913472i	$-0.366609\pi$
$770$	4.73156e11	+	8.19531e11i	0.0485061	+	0.0840150i
$771$	4.29719e12	−	7.44295e12i	0.437965	−	0.758578i
$772$	9.08008e11			0.0920051
$773$	2.28026e12	−	3.94953e12i	0.229709	−	0.397867i	−0.728013	−	0.685563i	$-0.759556\pi$
$773$	2.28026e12	−	3.94953e12i	0.229709	−	0.397867i	0.957722	+	0.287696i	$0.0928894\pi$
$774$	−8.85250e12	+	1.53330e13i	−0.886608	+	1.53565i
$775$	2.98059e12			0.296787
$776$	−1.50109e12	+	2.59996e12i	−0.148603	+	0.257388i
$777$	−3.14289e11	−	5.44364e11i	−0.0309339	−	0.0535791i
$778$	6.51466e12	+	1.12837e13i	0.637505	+	1.10419i
$779$	3.13581e12			0.305092
$780$	−4.79623e12	+	1.23428e13i	−0.463953	+	1.19396i
$781$	−3.38084e12			−0.325158
$782$	−5.72191e12	−	9.91063e12i	−0.547155	−	0.947700i
$783$	−6.89192e12	−	1.19372e13i	−0.655258	−	1.13494i
$784$	1.31888e12	−	2.28437e12i	0.124676	−	0.215946i
$785$	1.38101e13			1.29803
$786$	−1.00146e13	+	1.73458e13i	−0.935907	+	1.62104i
$787$	−5.65338e12	+	9.79195e12i	−0.525318	+	0.909877i	0.474247	+	0.880392i	$0.342720\pi$
$787$	−5.65338e12	+	9.79195e12i	−0.525318	+	0.909877i	−0.999565	+	0.0294855i	$0.990613\pi$
$788$	4.44493e12			0.410674
$789$	−7.84766e12	+	1.35926e13i	−0.720931	+	1.24869i
$790$	−2.20949e12	−	3.82695e12i	−0.201823	−	0.349567i
$791$	−9.09903e9	−	1.57600e10i	−0.000826420	−	0.00143140i
$792$	1.41474e13			1.27765
$793$	1.32764e12	+	1.65334e12i	0.119221	+	0.148468i
$794$	−8.14046e12			−0.726870
$795$	−9.50986e11	−	1.64716e12i	−0.0844349	−	0.146246i
$796$	−4.81634e11	−	8.34214e11i	−0.0425215	−	0.0736493i
$797$	−1.03896e13	+	1.79953e13i	−0.912088	+	1.57978i	−0.100978	+	0.994889i	$0.532197\pi$
$797$	−1.03896e13	+	1.79953e13i	−0.912088	+	1.57978i	−0.811110	+	0.584894i	$0.801136\pi$
$798$	8.14763e11			0.0711243
$799$	2.69511e12	−	4.66807e12i	0.233947	−	0.405207i
$800$	−1.22609e12	+	2.12365e12i	−0.105832	+	0.183307i
$801$	3.36064e13			2.88453
$802$	−4.13098e12	+	7.15506e12i	−0.352588	+	0.610701i
$803$	−1.73248e13	−	3.00074e13i	−1.47044	−	2.54688i
$804$	−5.05212e12	−	8.75052e12i	−0.426404	−	0.738553i
$805$	1.05955e12			0.0889285
$806$	−2.07546e12	+	3.19986e11i	−0.173223	+	0.0267069i
$807$	2.66031e13			2.20801
$808$	−4.03649e11	−	6.99141e11i	−0.0333160	−	0.0577050i
$809$	−8.12600e12	−	1.40747e13i	−0.666974	−	1.15523i	−0.978746	−	0.205075i	$-0.934256\pi$
$809$	−8.12600e12	−	1.40747e13i	−0.666974	−	1.15523i	0.311773	−	0.950157i	$-0.399077\pi$
$810$	6.16840e12	−	1.06840e13i	0.503489	−	0.872069i
$811$	1.58175e13			1.28394			0.641969	−	0.766730i	$-0.278118\pi$
$811$	1.58175e13			1.28394			0.641969	+	0.766730i	$0.278118\pi$
$812$	−1.21095e11	+	2.09743e11i	−0.00977520	+	0.0169311i
$813$	−1.04856e13	+	1.81616e13i	−0.841753	+	1.45796i
$814$	1.13332e13			0.904780
$815$	1.54160e13	−	2.67013e13i	1.22395	−	2.11994i
$816$	3.59155e12	+	6.22075e12i	0.283580	+	0.491176i
$817$	−9.19209e12	−	1.59212e13i	−0.721797	−	1.25019i
$818$	−4.19666e12			−0.327728
$819$	−1.28657e12	+	1.98359e11i	−0.0999212	+	0.0154055i
$820$	−2.55966e12			−0.197706
$821$	1.01169e13	+	1.75230e13i	0.777149	+	1.34606i	0.933579	+	0.358372i	$0.116668\pi$
$821$	1.01169e13	+	1.75230e13i	0.777149	+	1.34606i	−0.156430	+	0.987689i	$0.549999\pi$
$822$	7.03437e12	+	1.21839e13i	0.537405	+	0.930814i
$823$	−6.56463e12	+	1.13703e13i	−0.498782	+	0.863916i	−0.999999	−	0.00140551i	$-0.999553\pi$
$823$	−6.56463e12	+	1.13703e13i	−0.498782	+	0.863916i	0.501217	+	0.865322i	$0.332886\pi$
$824$	−2.05013e11			−0.0154920
$825$	−2.50401e13	+	4.33708e13i	−1.88189	+	3.25953i
$826$	−5.85913e10	+	1.01483e11i	−0.00437948	+	0.00758549i
$827$	−6.91456e12			−0.514032			−0.257016	−	0.966407i	$-0.582739\pi$
$827$	−6.91456e12			−0.514032			−0.257016	+	0.966407i	$0.582739\pi$
$828$	7.92017e12	−	1.37181e13i	0.585596	−	1.01428i
$829$	1.28157e13	+	2.21975e13i	0.942426	+	1.63233i	0.760824	+	0.648958i	$0.224795\pi$
$829$	1.28157e13	+	2.21975e13i	0.942426	+	1.63233i	0.181603	+	0.983372i	$0.441872\pi$
$830$	−8.96392e12	−	1.55260e13i	−0.655612	−	1.13555i
$831$	−1.88501e13			−1.37122
$832$	6.25768e11	−	1.61038e12i	0.0452750	−	0.116513i
$833$	1.81944e13			1.30929
$834$	−1.64614e12	−	2.85120e12i	−0.117820	−	0.204071i
$835$	−1.02193e13	−	1.77003e13i	−0.727498	−	1.26006i
$836$	−7.34505e12	+	1.27220e13i	−0.520076	+	0.900798i
$837$	6.00261e12			0.422742
$838$	2.56266e11	−	4.43865e11i	0.0179512	−	0.0310923i
$839$	4.95699e12	−	8.58576e12i	0.345374	−	0.598205i	−0.640048	−	0.768335i	$-0.721085\pi$
$839$	4.95699e12	−	8.58576e12i	0.345374	−	0.598205i	0.985422	+	0.170130i	$0.0544188\pi$
$840$	−6.65064e11			−0.0460900
$841$	2.97074e12	−	5.14547e12i	0.204778	−	0.354685i
$842$	2.19038e11	+	3.79386e11i	0.0150181	+	0.0260122i
$843$	1.14215e13	+	1.97826e13i	0.778931	+	1.34915i
$844$	−1.10738e13			−0.751201
$845$	1.62046e13	+	1.48336e13i	1.09341	+	1.00090i
$846$	7.46107e12			0.500765
$847$	−8.79657e11	−	1.52361e12i	−0.0587270	−	0.101718i
$848$	1.24076e11	+	2.14906e11i	0.00823960	+	0.0142714i
$849$	2.15758e13	−	3.73703e13i	1.42522	−	2.46855i
$850$	−1.69143e13			−1.11139
$851$	6.34470e12	−	1.09893e13i	0.414694	−	0.718271i
$852$	1.18802e12	−	2.05771e12i	0.0772406	−	0.133785i
$853$	1.42759e13			0.923280			0.461640	−	0.887067i	$-0.347261\pi$
$853$	1.42759e13			0.923280			0.461640	+	0.887067i	$0.347261\pi$
$854$	−5.32480e10	+	9.22283e10i	−0.00342565	+	0.00593340i
$855$	2.63185e13	+	4.55850e13i	1.68428	+	2.91726i
$856$	7.42641e11	+	1.28629e12i	0.0472767	+	0.0818856i
$857$	2.99825e12			0.189869			0.0949344	−	0.995484i	$-0.469736\pi$
$857$	2.99825e12			0.189869			0.0949344	+	0.995484i	$0.469736\pi$
$858$	1.27799e13	−	3.28883e13i	0.805072	−	2.07181i
$859$	7.23194e12			0.453196			0.226598	−	0.973988i	$-0.427240\pi$
$859$	7.23194e12			0.453196			0.226598	+	0.973988i	$0.427240\pi$
$860$	7.50320e12	+	1.29959e13i	0.467739	+	0.810148i
$861$	−1.89141e11	−	3.27602e11i	−0.0117293	−	0.0203157i
$862$	2.58802e12	−	4.48257e12i	0.159656	−	0.276532i
$863$	−2.46804e13			−1.51462			−0.757311	−	0.653054i	$-0.773487\pi$
$863$	−2.46804e13			−1.51462			−0.757311	+	0.653054i	$0.773487\pi$
$864$	−2.46922e12	+	4.27681e12i	−0.150747	+	0.261101i
$865$	2.10550e13	−	3.64684e13i	1.27874	−	2.21485i
$866$	−1.37481e13			−0.830640
$867$	−1.03964e13	+	1.80072e13i	−0.624883	+	1.08233i
$868$	−5.27348e10	−	9.13393e10i	−0.00315325	−	0.00546159i
$869$	5.88734e12	+	1.01972e13i	0.350212	+	0.606584i
$870$	−2.35216e13			−1.39197
$871$	−1.65674e13	+	2.55431e12i	−0.975380	+	0.150381i
$872$	1.60975e12			0.0942833
$873$	−1.43318e13	−	2.48234e13i	−0.835095	−	1.44643i
$874$	8.22400e12	+	1.42444e13i	0.476740	+	0.825738i
$875$	1.29062e11	−	2.23542e11i	0.00744323	−	0.0128921i
$876$	2.43516e13			1.39720
$877$	−4.11530e12	+	7.12791e12i	−0.234911	+	0.406878i	−0.959247	−	0.282570i	$-0.908813\pi$
$877$	−4.11530e12	+	7.12791e12i	−0.234911	+	0.406878i	0.724336	+	0.689447i	$0.242147\pi$
$878$	−5.74871e12	+	9.95705e12i	−0.326471	+	0.565464i
$879$	−1.65375e13			−0.934373
$880$	5.99553e12	−	1.03846e13i	0.337020	−	0.583735i
$881$	−5.86792e12	−	1.01635e13i	−0.328165	−	0.568399i	0.653983	−	0.756510i	$-0.273097\pi$
$881$	−5.86792e12	−	1.01635e13i	−0.328165	−	0.568399i	−0.982148	+	0.188111i	$0.939764\pi$
$882$	1.25922e13	+	2.18103e13i	0.700635	+	1.21354i
$883$	−1.84130e13			−1.01930			−0.509649	−	0.860382i	$-0.670225\pi$
$883$	−1.84130e13			−1.01930			−0.509649	+	0.860382i	$0.670225\pi$
$884$	1.17778e13	−	1.81586e12i	0.648678	−	0.100011i
$885$	−1.13808e13			−0.623632
$886$	−1.69793e12	−	2.94090e12i	−0.0925694	−	0.160335i
$887$	1.19885e13	+	2.07648e13i	0.650294	+	1.12634i	0.983051	+	0.183330i	$0.0586878\pi$
$887$	1.19885e13	+	2.07648e13i	0.650294	+	1.12634i	−0.332757	+	0.943013i	$0.607979\pi$
$888$	−3.98247e12	+	6.89783e12i	−0.214928	+	0.372267i
$889$	8.49167e11			0.0455969
$890$	1.42420e13	−	2.46679e13i	0.760882	−	1.31789i
$891$	−1.64362e13	+	2.84683e13i	−0.873676	+	1.51325i
$892$	−8.41449e12			−0.445027
$893$	−3.87364e12	+	6.70934e12i	−0.203839	+	0.353060i
$894$	1.33384e13	+	2.31028e13i	0.698369	+	1.20961i
$895$	−9.46056e12	−	1.63862e13i	−0.492848	−	0.853638i
$896$	8.67715e10			0.00449770
$897$	−2.47358e13	−	3.08041e13i	−1.27574	−	1.58870i
$898$	−1.43643e13			−0.737125
$899$	−1.86509e12	−	3.23044e12i	−0.0952318	−	0.164946i
$900$	−1.17062e13	−	2.02758e13i	−0.594738	−	1.03012i
$901$	−8.55831e11	+	1.48234e12i	−0.0432640	+	0.0749354i
$902$	6.82040e12			0.343068
$903$	−1.10887e12	+	1.92062e12i	−0.0554990	+	0.0961271i
$904$	−1.15297e11	+	1.99700e11i	−0.00574196	+	0.00994537i
$905$	−5.33766e13			−2.64504
$906$	1.44965e13	−	2.51087e13i	0.714803	−	1.23808i
$907$	2.60851e12	+	4.51808e12i	0.127985	+	0.221677i	0.922896	−	0.385050i	$-0.125816\pi$
$907$	2.60851e12	+	4.51808e12i	0.127985	+	0.221677i	−0.794911	+	0.606727i	$0.792482\pi$
$908$	−8.85264e12	−	1.53332e13i	−0.432202	−	0.748596i
$909$	7.70777e12			0.374448
$910$	−3.99637e11	+	1.02844e12i	−0.0193188	+	0.0497157i
$911$	−2.45077e13			−1.17888			−0.589441	−	0.807811i	$-0.700652\pi$
$911$	−2.45077e13			−1.17888			−0.589441	+	0.807811i	$0.700652\pi$
$912$	−5.16207e12	−	8.94097e12i	−0.247086	−	0.427965i
$913$	2.38850e13	+	4.13701e13i	1.13765	+	1.97046i
$914$	−9.12806e12	+	1.58103e13i	−0.432634	+	0.749344i
$915$	−1.03429e13			−0.487807
$916$	4.31558e12	−	7.47481e12i	0.202540	−	0.350809i
$917$	−8.34448e11	+	1.44531e12i	−0.0389706	+	0.0674991i
$918$	−3.40636e13			−1.58306
$919$	1.44130e13	−	2.49641e13i	0.666554	−	1.15451i	−0.312307	−	0.949981i	$-0.601102\pi$
$919$	1.44130e13	−	2.49641e13i	0.666554	−	1.15451i	0.978861	−	0.204525i	$-0.0655649\pi$
$920$	−6.71298e12	−	1.16272e13i	−0.308937	−	0.535095i
$921$	1.67858e13	+	2.90738e13i	0.768729	+	1.33148i
$922$	−1.26285e13			−0.575521
$923$	−2.46812e12	−	3.07361e12i	−0.111933	−	0.139393i
$924$	1.77211e12			0.0799774
$925$	−9.37763e12	−	1.62425e13i	−0.421168	−	0.729484i
$926$	5.79091e12	+	1.00301e13i	0.258820	+	0.448289i
$927$	9.78691e11	−	1.69514e12i	0.0435298	−	0.0753958i
$928$	3.06888e12			0.135836
$929$	6.24808e12	−	1.08220e13i	0.275218	−	0.476691i	−0.694972	−	0.719036i	$-0.744583\pi$
$929$	6.24808e12	−	1.08220e13i	0.275218	−	0.476691i	0.970190	+	0.242346i	$0.0779168\pi$
$930$	5.12161e12	−	8.87089e12i	0.224509	−	0.388861i
$931$	−2.61504e13			−1.14079
$932$	1.52261e12	−	2.63724e12i	0.0661025	−	0.114493i
$933$	2.93171e13	+	5.07787e13i	1.26664	+	2.19389i
$934$	5.30043e12	+	9.18061e12i	0.227903	+	0.394739i
$935$	8.27100e13			3.53921
$936$	1.03281e13	+	1.28618e13i	0.439823	+	0.547721i
$937$	4.48550e13			1.90100			0.950501	−	0.310722i	$-0.100571\pi$
$937$	4.48550e13			1.90100			0.950501	+	0.310722i	$0.100571\pi$
$938$	−4.20958e11	−	7.29121e11i	−0.0177552	−	0.0307529i
$939$	−2.71231e13	−	4.69785e13i	−1.13853	−	1.97199i
$940$	3.16193e12	−	5.47662e12i	0.132092	−	0.228790i
$941$	−2.65409e13			−1.10348			−0.551738	−	0.834017i	$-0.686035\pi$
$941$	−2.65409e13			−1.10348			−0.551738	+	0.834017i	$0.686035\pi$
$942$	1.29308e13	−	2.23967e13i	0.535051	−	0.926736i
$943$	3.81828e12	−	6.61345e12i	0.157241	−	0.272349i
$944$	1.48486e12			0.0608572
$945$	1.57693e12	−	2.73132e12i	0.0643234	−	0.111411i
$946$	−1.99928e13	−	3.46286e13i	−0.811641	−	1.40580i
$947$	−1.31021e13	−	2.26935e13i	−0.529377	−	0.916908i	−0.999413	−	0.0342608i	$-0.989092\pi$
$947$	−1.31021e13	−	2.26935e13i	−0.529377	−	0.916908i	0.470036	−	0.882647i	$-0.344241\pi$
$948$	−8.27520e12			−0.332768
$949$	1.46328e13	−	3.76568e13i	0.585640	−	1.50711i
$950$	2.43106e13			0.968364
$951$	8.16044e12	+	1.41343e13i	0.323520	+	0.560354i
$952$	2.99259e11	+	5.18332e11i	0.0118081	+	0.0204523i
$953$	−1.10378e13	+	1.91180e13i	−0.433475	+	0.750801i	−0.997170	−	0.0751825i	$-0.976046\pi$
$953$	−1.10378e13	+	1.91180e13i	−0.433475	+	0.750801i	0.563695	+	0.825983i	$0.309379\pi$
$954$	−2.36925e12			−0.0926070
$955$	−1.54266e13	+	2.67196e13i	−0.600143	+	1.03948i
$956$	−2.02116e12	+	3.50075e12i	−0.0782599	+	0.135550i
$957$	6.26751e13			2.41541
$958$	−1.80061e13	+	3.11874e13i	−0.690676	+	1.19629i
$959$	5.86126e11	+	1.01520e12i	0.0223773	+	0.0387585i
$960$	4.21363e12	+	7.29822e12i	0.160116	+	0.277330i
$961$	−2.48152e13			−0.938561
$962$	8.27361e12	+	1.03033e13i	0.311463	+	0.387872i
$963$	−1.41809e13			−0.531355
$964$	−2.82668e12	−	4.89595e12i	−0.105422	−	0.182596i
$965$	3.67396e12	+	6.36349e12i	0.136384	+	0.236223i
$966$	9.92085e11	−	1.71834e12i	0.0366566	−	0.0634911i
$967$	1.80518e13			0.663898			0.331949	−	0.943297i	$-0.392294\pi$
$967$	1.80518e13			0.663898			0.331949	+	0.943297i	$0.392294\pi$
$968$	−1.11464e13	+	1.93062e13i	−0.408035	+	0.706737i
$969$	3.56061e13	−	6.16716e13i	1.29738	−	2.24713i
$970$	−2.42946e13			−0.881126
$971$	8.05915e12	−	1.39589e13i	0.290940	−	0.503922i	−0.683093	−	0.730332i	$-0.739365\pi$
$971$	8.05915e12	−	1.39589e13i	0.290940	−	0.503922i	0.974032	+	0.226410i	$0.0726988\pi$
$972$	3.14379e11	+	5.44520e11i	0.0112968	+	0.0195666i
$973$	−1.37162e11	−	2.37571e11i	−0.00490597	−	0.00849739i
$974$	7.66387e12			0.272856
$975$	−5.77096e13	+	8.89746e12i	−2.04516	+	0.315315i
$976$	1.34945e12			0.0476028
$977$	1.54590e13	+	2.67757e13i	0.542818	+	0.940189i	0.998741	+	0.0501694i	$0.0159761\pi$
$977$	1.54590e13	+	2.67757e13i	0.542818	+	0.940189i	−0.455922	+	0.890020i	$0.650691\pi$
$978$	−2.88688e13	−	5.00022e13i	−1.00903	−	1.74769i
$979$	−3.79490e13	+	6.57295e13i	−1.32032	+	2.28685i
$980$	2.13457e13			0.739255
$981$	−7.68463e12	+	1.33102e13i	−0.264919	+	0.458853i
$982$	1.14887e11	−	1.98990e11i	0.00394248	−	0.00682858i
$983$	1.01227e13			0.345784			0.172892	−	0.984941i	$-0.444689\pi$
$983$	1.01227e13			0.345784			0.172892	+	0.984941i	$0.444689\pi$
$984$	−2.39667e12	+	4.15116e12i	−0.0814950	+	0.141153i
$985$	1.79850e13	+	3.11509e13i	0.608761	+	1.05441i
$986$	1.05840e13	+	1.83321e13i	0.356619	+	0.617683i
$987$	9.34577e11			0.0313464
$988$	−1.69280e13	+	2.60990e12i	−0.565197	+	0.0871401i
$989$	−4.47705e13			−1.48802
$990$	5.72429e13	+	9.91476e13i	1.89393	+	3.28038i
$991$	−3.89477e12	−	6.74595e12i	−0.128278	−	0.222183i	0.794732	−	0.606961i	$-0.207612\pi$
$991$	−3.89477e12	−	6.74595e12i	−0.128278	−	0.222183i	−0.923009	+	0.384777i	$0.874278\pi$
$992$	−6.68221e11	+	1.15739e12i	−0.0219087	+	0.0379470i
$993$	3.16606e12			0.103335
$994$	9.89895e10	−	1.71455e11i	0.00321625	−	0.00557071i
$995$	3.89755e12	−	6.75076e12i	0.126063	−	0.218348i
$996$	−3.35726e13			−1.08098
$997$	−2.23331e12	+	3.86821e12i	−0.0715849	+	0.123989i	−0.899596	−	0.436723i	$-0.856139\pi$
$997$	−2.23331e12	+	3.86821e12i	−0.0715849	+	0.123989i	0.828011	+	0.560712i	$0.189472\pi$
$998$	−9.52733e11	−	1.65018e12i	−0.0304007	−	0.0526556i
$999$	−1.88856e13	−	3.27108e13i	−0.599909	−	1.03907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.10.c.b.3.1	✓	12
13.3	even	3		338.10.a.l.1.6		6
13.9	even	3	inner	26.10.c.b.9.1	yes	12
13.10	even	6		338.10.a.k.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.c.b.3.1	✓	12	1.1	even	1	trivial
26.10.c.b.9.1	yes	12	13.9	even	3	inner
338.10.a.k.1.6		6	13.10	even	6
338.10.a.l.1.6		6	13.3	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-121.233 - 209.982i) q^{3} +(-128.000 + 221.703i) q^{4} -2071.64 q^{5} +(-1939.73 + 3359.71i) q^{6} +(-161.624 + 279.942i) q^{7} +4096.00 q^{8} +(-19553.5 + 33867.6i) q^{9} +(16573.1 + 28705.5i) q^{10} +(-44160.4 - 76488.0i) q^{11} +62071.4 q^{12} +(37298.7 - 95986.0i) q^{13} +5171.98 q^{14} +(251152. + 435008. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(226022. - 391481. i) q^{17} +625712. q^{18} +(-324857. + 562669. i) q^{19} +(265170. - 459289. i) q^{20} +78377.0 q^{21} +(-706566. + 1.22381e6i) q^{22} +(791116. + 1.37025e6i) q^{23} +(-496571. - 860087. i) q^{24} +2.33858e6 q^{25} +(-1.62841e6 + 251062. i) q^{26} +4.70966e6 q^{27} +(-41375.9 - 71665.1i) q^{28} +(-1.46336e6 - 2.53461e6i) q^{29} +(4.01843e6 - 6.96013e6i) q^{30} +1.27453e6 q^{31} +(-524288. + 908093. i) q^{32} +(-1.07074e7 + 1.85458e7i) q^{33} -7.23270e6 q^{34} +(334828. - 579939. i) q^{35} +(-5.00569e6 - 8.67011e6i) q^{36} +(-4.00996e6 - 6.94546e6i) q^{37} +1.03954e7 q^{38} +(-2.46772e7 + 3.80464e6i) q^{39} -8.48545e6 q^{40} +(-2.41322e6 - 4.17982e6i) q^{41} +(-627016. - 1.08602e6i) q^{42} +(-1.41479e7 + 2.45049e7i) q^{43} +2.26101e7 q^{44} +(4.05079e7 - 7.01617e7i) q^{45} +(1.26579e7 - 2.19241e7i) q^{46} +1.19241e7 q^{47} +(-7.94514e6 + 1.37614e7i) q^{48} +(2.01246e7 + 3.48568e7i) q^{49} +(-1.87087e7 - 3.24043e7i) q^{50} -1.09605e8 q^{51} +(1.65061e7 + 2.05554e7i) q^{52} -3.78650e6 q^{53} +(-3.76773e7 - 6.52590e7i) q^{54} +(9.14845e7 + 1.58456e8i) q^{55} +(-662014. + 1.14664e6i) q^{56} +1.57534e8 q^{57} +(-2.34137e7 + 4.05538e7i) q^{58} +(-1.13286e7 + 1.96217e7i) q^{59} -1.28590e8 q^{60} +(-1.02955e7 + 1.78323e7i) q^{61} +(-1.01962e7 - 1.76604e7i) q^{62} +(-6.32064e6 - 1.09477e7i) q^{63} +1.67772e7 q^{64} +(-7.72695e7 + 1.98849e8i) q^{65} +3.42637e8 q^{66} +(-8.13920e7 - 1.40975e8i) q^{67} +(5.78616e7 + 1.00219e8i) q^{68} +(1.91819e8 - 3.32241e8i) q^{69} -1.07145e7 q^{70} +(1.91396e7 - 3.31507e7i) q^{71} +(-8.00911e7 + 1.38722e8i) q^{72} +3.92315e8 q^{73} +(-6.41594e7 + 1.11127e8i) q^{74} +(-2.83514e8 - 4.91060e8i) q^{75} +(-8.31634e7 - 1.44043e8i) q^{76} +2.85496e7 q^{77} +(2.50136e8 + 3.11500e8i) q^{78} -1.33317e8 q^{79} +(6.78836e7 + 1.17578e8i) q^{80} +(-1.86096e8 - 3.22328e8i) q^{81} +(-3.86115e7 + 6.68772e7i) q^{82} -5.40870e8 q^{83} +(-1.00323e7 + 1.73764e7i) q^{84} +(-4.68237e8 + 8.11010e8i) q^{85} +4.52732e8 q^{86} +(-3.54815e8 + 6.14558e8i) q^{87} +(-1.80881e8 - 3.13295e8i) q^{88} +(-4.29672e8 - 7.44214e8i) q^{89} -1.29625e9 q^{90} +(2.08421e7 + 2.59551e7i) q^{91} -4.05052e8 q^{92} +(-1.54515e8 - 2.67628e8i) q^{93} +(-9.53930e7 - 1.65226e8i) q^{94} +(6.72988e8 - 1.16565e9i) q^{95} +2.54244e8 q^{96} +(-3.66476e8 + 6.34755e8i) q^{97} +(3.21993e8 - 5.57708e8i) q^{98} +3.45396e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 96 q^{2} - 81 q^{3} - 1536 q^{4} + 3386 q^{5} - 1296 q^{6} - 473 q^{7} + 49152 q^{8} - 69813 q^{9} - 27088 q^{10} - 14011 q^{11} + 41472 q^{12} + 152853 q^{13} + 15136 q^{14} + 294780 q^{15} - 393216 q^{16}+ \cdots - 1763539020 q^{99}+O(q^{100}) \) 12 * q - 96 * q^2 - 81 * q^3 - 1536 * q^4 + 3386 * q^5 - 1296 * q^6 - 473 * q^7 + 49152 * q^8 - 69813 * q^9 - 27088 * q^10 - 14011 * q^11 + 41472 * q^12 + 152853 * q^13 + 15136 * q^14 + 294780 * q^15 - 393216 * q^16 + 173558 * q^17 + 2234016 * q^18 - 322367 * q^19 - 433408 * q^20 + 4513770 * q^21 - 224176 * q^22 + 1644771 * q^23 - 331776 * q^24 + 5375138 * q^25 - 4031808 * q^26 - 1845990 * q^27 - 121088 * q^28 - 10801236 * q^29 + 4716480 * q^30 + 20870244 * q^31 - 6291456 * q^32 - 26201763 * q^33 - 5553856 * q^34 - 2168950 * q^35 - 17872128 * q^36 + 15710464 * q^37 + 10315744 * q^38 - 22298325 * q^39 + 13869056 * q^40 + 1525478 * q^41 - 36110160 * q^42 - 50959661 * q^43 + 7173632 * q^44 - 18619731 * q^45 + 26316336 * q^46 + 136313996 * q^47 - 5308416 * q^48 - 162536361 * q^49 - 43001104 * q^50 - 169357962 * q^51 + 25378560 * q^52 + 144556418 * q^53 + 14767920 * q^54 + 353372330 * q^55 - 1937408 * q^56 + 35902050 * q^57 - 172819776 * q^58 + 5665291 * q^59 - 150927360 * q^60 + 353387956 * q^61 - 166961952 * q^62 + 224088894 * q^63 + 201326592 * q^64 - 205394773 * q^65 + 838456416 * q^66 - 371115369 * q^67 + 44430848 * q^68 - 280317279 * q^69 + 69406400 * q^70 - 156688763 * q^71 - 285954048 * q^72 + 932803326 * q^73 + 251367424 * q^74 - 1149481845 * q^75 - 82525952 * q^76 + 624920666 * q^77 - 420616752 * q^78 + 325086960 * q^79 - 110952448 * q^80 - 295496586 * q^81 + 24407648 * q^82 - 870229152 * q^83 - 577762560 * q^84 - 2307296767 * q^85 + 1630709152 * q^86 + 617376057 * q^87 - 57389056 * q^88 - 163315063 * q^89 + 595831392 * q^90 - 208860497 * q^91 - 842122752 * q^92 - 2056270836 * q^93 - 1090511968 * q^94 + 537110948 * q^95 + 169869312 * q^96 + 1500514705 * q^97 - 2600581776 * q^98 - 1763539020 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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