LMFDB - Embedded newform 29.13.c.a.12.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,13,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$26.5058207010$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.13
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.2710 - 12.2710i) q^{2} +(762.089 + 762.089i) q^{3} -3794.84i q^{4} -6703.86i q^{5} -18703.2i q^{6} -134602. q^{7} +(-96828.8 + 96828.8i) q^{8} +630118. i q^{9} +O(q^{10})$	\(q+(-12.2710 - 12.2710i) q^{2} +(762.089 + 762.089i) q^{3} -3794.84i q^{4} -6703.86i q^{5} -18703.2i q^{6} -134602. q^{7} +(-96828.8 + 96828.8i) q^{8} +630118. i q^{9} +(-82263.3 + 82263.3i) q^{10} +(783954. + 783954. i) q^{11} +(2.89201e6 - 2.89201e6i) q^{12} +7.18629e6i q^{13} +(1.65171e6 + 1.65171e6i) q^{14} +(5.10894e6 - 5.10894e6i) q^{15} -1.31673e7 q^{16} +(9.84902e6 + 9.84902e6i) q^{17} +(7.73220e6 - 7.73220e6i) q^{18} +(3.12250e7 + 3.12250e7i) q^{19} -2.54401e7 q^{20} +(-1.02579e8 - 1.02579e8i) q^{21} -1.92398e7i q^{22} -1.53820e8 q^{23} -1.47584e8 q^{24} +1.99199e8 q^{25} +(8.81831e7 - 8.81831e7i) q^{26} +(-7.52006e7 + 7.52006e7i) q^{27} +5.10794e8i q^{28} +(-6.59140e7 + 5.91160e8i) q^{29} -1.25384e8 q^{30} +(9.12762e8 + 9.12762e8i) q^{31} +(5.58187e8 + 5.58187e8i) q^{32} +1.19489e9i q^{33} -2.41715e8i q^{34} +9.02354e8i q^{35} +2.39120e9 q^{36} +(-3.24793e8 + 3.24793e8i) q^{37} -7.66326e8i q^{38} +(-5.47659e9 + 5.47659e9i) q^{39} +(6.49127e8 + 6.49127e8i) q^{40} +(-2.02494e9 + 2.02494e9i) q^{41} +2.51749e9i q^{42} +(-6.46858e9 - 6.46858e9i) q^{43} +(2.97498e9 - 2.97498e9i) q^{44} +4.22422e9 q^{45} +(1.88753e9 + 1.88753e9i) q^{46} +(-9.97973e9 + 9.97973e9i) q^{47} +(-1.00347e10 - 1.00347e10i) q^{48} +4.27644e9 q^{49} +(-2.44438e9 - 2.44438e9i) q^{50} +1.50117e10i q^{51} +2.72708e10 q^{52} +1.63202e10 q^{53} +1.84558e9 q^{54} +(5.25552e9 - 5.25552e9i) q^{55} +(1.30334e10 - 1.30334e10i) q^{56} +4.75924e10i q^{57} +(8.06297e9 - 6.44531e9i) q^{58} -5.12067e10 q^{59} +(-1.93876e10 - 1.93876e10i) q^{60} +(-4.31317e9 - 4.31317e9i) q^{61} -2.24011e10i q^{62} -8.48152e10i q^{63} +4.02342e10i q^{64} +4.81759e10 q^{65} +(1.46625e10 - 1.46625e10i) q^{66} -1.19197e11i q^{67} +(3.73755e10 - 3.73755e10i) q^{68} +(-1.17224e11 - 1.17224e11i) q^{69} +(1.10728e10 - 1.10728e10i) q^{70} -2.08870e10i q^{71} +(-6.10135e10 - 6.10135e10i) q^{72} +(-1.23070e11 + 1.23070e11i) q^{73} +7.97108e9 q^{74} +(1.51807e11 + 1.51807e11i) q^{75} +(1.18494e11 - 1.18494e11i) q^{76} +(-1.05522e11 - 1.05522e11i) q^{77} +1.34407e11 q^{78} +(-5.47369e10 - 5.47369e10i) q^{79} +8.82718e10i q^{80} +2.20251e11 q^{81} +4.96961e10 q^{82} +4.76998e11 q^{83} +(-3.89270e11 + 3.89270e11i) q^{84} +(6.60265e10 - 6.60265e10i) q^{85} +1.58752e11i q^{86} +(-5.00749e11 + 4.00284e11i) q^{87} -1.51819e11 q^{88} +(-3.28855e11 - 3.28855e11i) q^{89} +(-5.18356e10 - 5.18356e10i) q^{90} -9.67289e11i q^{91} +5.83722e11i q^{92} +1.39121e12i q^{93} +2.44923e11 q^{94} +(2.09328e11 - 2.09328e11i) q^{95} +8.50776e11i q^{96} +(4.32702e11 - 4.32702e11i) q^{97} +(-5.24764e10 - 5.24764e10i) q^{98} +(-4.93983e11 + 4.93983e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) $ 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} - 1957890 q^{10} + 4120990 q^{11} + 2920062 q^{12} - 1824520 q^{14} - 8383600 q^{15} - 133743512 q^{16} + 33971578 q^{17} - 122384158 q^{18} + 65838718 q^{19} - 59408388 q^{20} + 200896236 q^{21} + 104539676 q^{23} + 163907064 q^{24} - 3086882294 q^{25} + 607848030 q^{26} - 1190867840 q^{27} + 817714294 q^{29} + 5793833612 q^{30} - 1059975938 q^{31} + 2323254598 q^{32} + 517001400 q^{36} - 864725342 q^{37} + 18048639408 q^{39} - 22547920086 q^{40} - 17292603926 q^{41} - 3344004962 q^{43} - 53750811886 q^{44} - 16067938640 q^{45} + 43310099300 q^{46} - 15159905282 q^{47} - 4602803862 q^{48} + 32036753022 q^{49} - 16057299278 q^{50} + 81167587800 q^{52} - 69552844564 q^{53} + 38996274808 q^{54} + 3944882736 q^{55} - 156397031424 q^{56} + 107434998568 q^{58} + 82613255468 q^{59} - 147410252946 q^{60} + 128229759922 q^{61} + 125938412928 q^{65} + 364716671994 q^{66} - 141670411468 q^{68} + 529640675916 q^{69} + 518962441956 q^{70} - 180699442320 q^{72} - 428225274062 q^{73} + 307721180948 q^{74} - 617987210610 q^{75} - 455232145048 q^{76} - 963484794004 q^{77} + 688403957040 q^{78} - 183006289538 q^{79} + 1001949265154 q^{81} - 1176460419184 q^{82} + 361042835756 q^{83} - 402324805420 q^{84} + 832273178976 q^{85} - 1065344596322 q^{87} - 1836857960940 q^{88} + 1922736257242 q^{89} - 1170237151648 q^{90} - 2759662014220 q^{94} + 5518358548560 q^{95} + 1356111950818 q^{97} - 2518255928616 q^{98} + 3259343912178 q^{99}+O(q^{100}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8 - 1957890 * q^10 + 4120990 * q^11 + 2920062 * q^12 - 1824520 * q^14 - 8383600 * q^15 - 133743512 * q^16 + 33971578 * q^17 - 122384158 * q^18 + 65838718 * q^19 - 59408388 * q^20 + 200896236 * q^21 + 104539676 * q^23 + 163907064 * q^24 - 3086882294 * q^25 + 607848030 * q^26 - 1190867840 * q^27 + 817714294 * q^29 + 5793833612 * q^30 - 1059975938 * q^31 + 2323254598 * q^32 + 517001400 * q^36 - 864725342 * q^37 + 18048639408 * q^39 - 22547920086 * q^40 - 17292603926 * q^41 - 3344004962 * q^43 - 53750811886 * q^44 - 16067938640 * q^45 + 43310099300 * q^46 - 15159905282 * q^47 - 4602803862 * q^48 + 32036753022 * q^49 - 16057299278 * q^50 + 81167587800 * q^52 - 69552844564 * q^53 + 38996274808 * q^54 + 3944882736 * q^55 - 156397031424 * q^56 + 107434998568 * q^58 + 82613255468 * q^59 - 147410252946 * q^60 + 128229759922 * q^61 + 125938412928 * q^65 + 364716671994 * q^66 - 141670411468 * q^68 + 529640675916 * q^69 + 518962441956 * q^70 - 180699442320 * q^72 - 428225274062 * q^73 + 307721180948 * q^74 - 617987210610 * q^75 - 455232145048 * q^76 - 963484794004 * q^77 + 688403957040 * q^78 - 183006289538 * q^79 + 1001949265154 * q^81 - 1176460419184 * q^82 + 361042835756 * q^83 - 402324805420 * q^84 + 832273178976 * q^85 - 1065344596322 * q^87 - 1836857960940 * q^88 + 1922736257242 * q^89 - 1170237151648 * q^90 - 2759662014220 * q^94 + 5518358548560 * q^95 + 1356111950818 * q^97 - 2518255928616 * q^98 + 3259343912178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−12.2710	−	12.2710i	−0.191735	−	0.191735i	0.604711	−	0.796445i	$-0.293289\pi$
$2$	−12.2710	−	12.2710i	−0.191735	−	0.191735i	−0.796445	+	0.604711i	$0.793289\pi$
$3$	762.089	+	762.089i	1.04539	+	1.04539i	0.998920	+	0.0464697i	$0.0147971\pi$
$3$	762.089	+	762.089i	1.04539	+	1.04539i	0.0464697	+	0.998920i	$0.485203\pi$
$4$		−	3794.84i		−	0.926476i
$5$		−	6703.86i		−	0.429047i	−0.976719	−	0.214524i	$-0.931180\pi$
$5$		−	6703.86i		−	0.429047i	0.976719	−	0.214524i	$-0.0688199\pi$
$6$		−	18703.2i		−	0.400875i
$7$	−134602.			−1.14410			−0.572050	−	0.820219i	$-0.693852\pi$
$7$	−134602.			−1.14410			−0.572050	+	0.820219i	$0.693852\pi$
$8$	−96828.8	+	96828.8i	−0.369372	+	0.369372i
$9$			630118.i			1.18568i
$10$	−82263.3	+	82263.3i	−0.0822633	+	0.0822633i
$11$	783954.	+	783954.i	0.442522	+	0.442522i	0.892859	−	0.450337i	$-0.148696\pi$
$11$	783954.	+	783954.i	0.442522	+	0.442522i	−0.450337	+	0.892859i	$0.648696\pi$
$12$	2.89201e6	−	2.89201e6i	0.968528	−	0.968528i
$13$			7.18629e6i			1.48883i	0.667719	+	0.744414i	$0.267271\pi$
$13$			7.18629e6i			1.48883i	−0.667719	+	0.744414i	$0.732729\pi$
$14$	1.65171e6	+	1.65171e6i	0.219364	+	0.219364i
$15$	5.10894e6	−	5.10894e6i	0.448521	−	0.448521i
$16$	−1.31673e7			−0.784832
$17$	9.84902e6	+	9.84902e6i	0.408037	+	0.408037i	0.881054	−	0.473017i	$-0.156835\pi$
$17$	9.84902e6	+	9.84902e6i	0.408037	+	0.408037i	−0.473017	+	0.881054i	$0.656835\pi$
$18$	7.73220e6	−	7.73220e6i	0.227336	−	0.227336i
$19$	3.12250e7	+	3.12250e7i	0.663714	+	0.663714i	0.956253	−	0.292540i	$-0.0945003\pi$
$19$	3.12250e7	+	3.12250e7i	0.663714	+	0.663714i	−0.292540	+	0.956253i	$0.594500\pi$
$20$	−2.54401e7			−0.397502
$21$	−1.02579e8	−	1.02579e8i	−1.19603	−	1.19603i
$22$		−	1.92398e7i		−	0.169694i
$23$	−1.53820e8			−1.03907			−0.519535	−	0.854449i	$-0.673895\pi$
$23$	−1.53820e8			−1.03907			−0.519535	+	0.854449i	$0.673895\pi$
$24$	−1.47584e8			−0.772276
$25$	1.99199e8			0.815919
$26$	8.81831e7	−	8.81831e7i	0.285460	−	0.285460i
$27$	−7.52006e7	+	7.52006e7i	−0.194106	+	0.194106i
$28$			5.10794e8i			1.05998i
$29$	−6.59140e7	+	5.91160e8i	−0.110813	+	0.993841i
$29$	−6.59140e7	+	5.91160e8i	−0.110813	+	0.993841i
$30$	−1.25384e8			−0.171994
$31$	9.12762e8	+	9.12762e8i	1.02846	+	1.02846i	0.999583	+	0.0288769i	$0.00919307\pi$
$31$	9.12762e8	+	9.12762e8i	1.02846	+	1.02846i	0.0288769	+	0.999583i	$0.490807\pi$
$32$	5.58187e8	+	5.58187e8i	0.519852	+	0.519852i
$33$			1.19489e9i			0.925215i
$34$		−	2.41715e8i		−	0.156470i
$35$			9.02354e8i			0.490872i
$36$	2.39120e9			1.09850
$37$	−3.24793e8	+	3.24793e8i	−0.126589	+	0.126589i	−0.767563	−	0.640974i	$-0.778531\pi$
$37$	−3.24793e8	+	3.24793e8i	−0.126589	+	0.126589i	0.640974	+	0.767563i	$0.278531\pi$
$38$		−	7.66326e8i		−	0.254514i
$39$	−5.47659e9	+	5.47659e9i	−1.55640	+	1.55640i
$40$	6.49127e8	+	6.49127e8i	0.158478	+	0.158478i
$41$	−2.02494e9	+	2.02494e9i	−0.426293	+	0.426293i	−0.887364	−	0.461070i	$-0.847466\pi$
$41$	−2.02494e9	+	2.02494e9i	−0.426293	+	0.426293i	0.461070	+	0.887364i	$0.347466\pi$
$42$			2.51749e9i			0.458641i
$43$	−6.46858e9	−	6.46858e9i	−1.02329	−	1.02329i	−0.999722	−	0.0235668i	$-0.992498\pi$
$43$	−6.46858e9	−	6.46858e9i	−1.02329	−	1.02329i	−0.0235668	−	0.999722i	$-0.507502\pi$
$44$	2.97498e9	−	2.97498e9i	0.409985	−	0.409985i
$45$	4.22422e9			0.508712
$46$	1.88753e9	+	1.88753e9i	0.199226	+	0.199226i
$47$	−9.97973e9	+	9.97973e9i	−0.925831	+	0.925831i	−0.997433	−	0.0716023i	$-0.977189\pi$
$47$	−9.97973e9	+	9.97973e9i	−0.925831	+	0.925831i	0.0716023	+	0.997433i	$0.477189\pi$
$48$	−1.00347e10	−	1.00347e10i	−0.820455	−	0.820455i
$49$	4.27644e9			0.308963
$50$	−2.44438e9	−	2.44438e9i	−0.156440	−	0.156440i
$51$			1.50117e10i			0.853115i
$52$	2.72708e10			1.37936
$53$	1.63202e10			0.736328			0.368164	−	0.929761i	$-0.379987\pi$
$53$	1.63202e10			0.736328			0.368164	+	0.929761i	$0.379987\pi$
$54$	1.84558e9			0.0744337
$55$	5.25552e9	−	5.25552e9i	0.189863	−	0.189863i
$56$	1.30334e10	−	1.30334e10i	0.422599	−	0.422599i
$57$			4.75924e10i			1.38768i
$58$	8.06297e9	−	6.44531e9i	0.211801	−	0.169307i
$59$	−5.12067e10			−1.21399			−0.606994	−	0.794706i	$-0.707625\pi$
$59$	−5.12067e10			−1.21399			−0.606994	+	0.794706i	$0.707625\pi$
$60$	−1.93876e10	−	1.93876e10i	−0.415544	−	0.415544i
$61$	−4.31317e9	−	4.31317e9i	−0.0837178	−	0.0837178i	0.664008	−	0.747726i	$-0.268854\pi$
$61$	−4.31317e9	−	4.31317e9i	−0.0837178	−	0.0837178i	−0.747726	+	0.664008i	$0.768854\pi$
$62$		−	2.24011e10i		−	0.394383i
$63$		−	8.48152e10i		−	1.35653i
$64$			4.02342e10i			0.585485i
$65$	4.81759e10			0.638777
$66$	1.46625e10	−	1.46625e10i	0.177396	−	0.177396i
$67$		−	1.19197e11i		−	1.31770i	−0.752274	−	0.658851i	$-0.771043\pi$
$67$		−	1.19197e11i		−	1.31770i	0.752274	−	0.658851i	$-0.228957\pi$
$68$	3.73755e10	−	3.73755e10i	0.378036	−	0.378036i
$69$	−1.17224e11	−	1.17224e11i	−1.08623	−	1.08623i
$70$	1.10728e10	−	1.10728e10i	0.0941174	−	0.0941174i
$71$		−	2.08870e10i		−	0.163052i	−0.996671	−	0.0815259i	$-0.974021\pi$
$71$		−	2.08870e10i		−	0.163052i	0.996671	−	0.0815259i	$-0.0259793\pi$
$72$	−6.10135e10	−	6.10135e10i	−0.437957	−	0.437957i
$73$	−1.23070e11	+	1.23070e11i	−0.813235	+	0.813235i	−0.985117	−	0.171883i	$-0.945015\pi$
$73$	−1.23070e11	+	1.23070e11i	−0.813235	+	0.813235i	0.171883	+	0.985117i	$0.445015\pi$
$74$	7.97108e9			0.0485430
$75$	1.51807e11	+	1.51807e11i	0.852953	+	0.852953i
$76$	1.18494e11	−	1.18494e11i	0.614915	−	0.614915i
$77$	−1.05522e11	−	1.05522e11i	−0.506289	−	0.506289i
$78$	1.34407e11			0.596834
$79$	−5.47369e10	−	5.47369e10i	−0.225174	−	0.225174i	0.585499	−	0.810673i	$-0.300898\pi$
$79$	−5.47369e10	−	5.47369e10i	−0.225174	−	0.225174i	−0.810673	+	0.585499i	$0.800898\pi$
$80$			8.82718e10i			0.336730i
$81$	2.20251e11			0.779846
$82$	4.96961e10			0.163470
$83$	4.76998e11			1.45898			0.729488	−	0.683994i	$-0.239759\pi$
$83$	4.76998e11			1.45898			0.729488	+	0.683994i	$0.239759\pi$
$84$	−3.89270e11	+	3.89270e11i	−1.10809	+	1.10809i
$85$	6.60265e10	−	6.60265e10i	0.175067	−	0.175067i
$86$			1.58752e11i			0.392400i
$87$	−5.00749e11	+	4.00284e11i	−1.15479	+	0.923109i
$88$	−1.51819e11			−0.326911
$89$	−3.28855e11	−	3.28855e11i	−0.661705	−	0.661705i	0.294077	−	0.955782i	$-0.404988\pi$
$89$	−3.28855e11	−	3.28855e11i	−0.661705	−	0.661705i	−0.955782	+	0.294077i	$0.904988\pi$
$90$	−5.18356e10	−	5.18356e10i	−0.0975378	−	0.0975378i
$91$		−	9.67289e11i		−	1.70337i
$92$			5.83722e11i			0.962674i
$93$			1.39121e12i			2.15028i
$94$	2.44923e11			0.355028
$95$	2.09328e11	−	2.09328e11i	0.284765	−	0.284765i
$96$			8.50776e11i			1.08690i
$97$	4.32702e11	−	4.32702e11i	0.519467	−	0.519467i	−0.397943	−	0.917410i	$-0.630276\pi$
$97$	4.32702e11	−	4.32702e11i	0.519467	−	0.519467i	0.917410	+	0.397943i	$0.130276\pi$
$98$	−5.24764e10	−	5.24764e10i	−0.0592390	−	0.0592390i
$99$	−4.93983e11	+	4.93983e11i	−0.524688	+	0.524688i
$100$		−	7.55929e11i		−	0.755929i
$101$	3.70010e11	+	3.70010e11i	0.348566	+	0.348566i	0.859575	−	0.511009i	$-0.170728\pi$
$101$	3.70010e11	+	3.70010e11i	0.348566	+	0.348566i	−0.511009	+	0.859575i	$0.670728\pi$
$102$	1.84208e11	−	1.84208e11i	0.163572	−	0.163572i
$103$	−1.04901e12			−0.878530			−0.439265	−	0.898358i	$-0.644761\pi$
$103$	−1.04901e12			−0.878530			−0.439265	+	0.898358i	$0.644761\pi$
$104$	−6.95839e11	−	6.95839e11i	−0.549932	−	0.549932i
$105$	−6.87674e11	+	6.87674e11i	−0.513153	+	0.513153i
$106$	−2.00266e11	−	2.00266e11i	−0.141180	−	0.141180i
$107$	2.76589e12			1.84303			0.921515	−	0.388342i	$-0.126952\pi$
$107$	2.76589e12			1.84303			0.921515	+	0.388342i	$0.126952\pi$
$108$	2.85374e11	+	2.85374e11i	0.179834	+	0.179834i
$109$			1.64280e12i			0.979549i	0.871849	+	0.489775i	$0.162921\pi$
$109$			1.64280e12i			0.979549i	−0.871849	+	0.489775i	$0.837079\pi$
$110$	−1.28981e11			−0.0728066
$111$	−4.95042e11			−0.264670
$112$	1.77235e12			0.897926
$113$	−7.93215e11	+	7.93215e11i	−0.380996	+	0.380996i	−0.871461	−	0.490465i	$-0.836827\pi$
$113$	−7.93215e11	+	7.93215e11i	−0.380996	+	0.380996i	0.490465	+	0.871461i	$0.336827\pi$
$114$	5.84008e11	−	5.84008e11i	0.266066	−	0.266066i
$115$			1.03119e12i			0.445810i
$116$	2.24336e12	+	2.50133e11i	0.920770	+	0.102665i
$117$	−4.52821e12			−1.76527
$118$	6.28359e11	+	6.28359e11i	0.232764	+	0.232764i
$119$	−1.32570e12	−	1.32570e12i	−0.466835	−	0.466835i
$120$			9.89385e11i			0.331343i
$121$		−	1.90926e12i		−	0.608349i
$122$			1.05854e11i			0.0321032i
$123$	−3.08636e12			−0.891285
$124$	3.46379e12	−	3.46379e12i	0.952843	−	0.952843i
$125$		−	2.97209e12i		−	0.779115i
$126$	−1.04077e12	+	1.04077e12i	−0.260095	+	0.260095i
$127$	1.98447e12	+	1.98447e12i	0.472958	+	0.472958i	0.902871	−	0.429912i	$-0.141456\pi$
$127$	1.98447e12	+	1.98447e12i	0.472958	+	0.472958i	−0.429912	+	0.902871i	$0.641456\pi$
$128$	2.78005e12	−	2.78005e12i	0.632110	−	0.632110i
$129$		−	9.85927e12i		−	2.13947i
$130$	−5.91167e11	−	5.91167e11i	−0.122476	−	0.122476i
$131$	5.05726e11	−	5.05726e11i	0.100066	−	0.100066i	−0.655301	−	0.755368i	$-0.727458\pi$
$131$	5.05726e11	−	5.05726e11i	0.100066	−	0.100066i	0.755368	+	0.655301i	$0.227458\pi$
$132$	4.53440e12			0.857189
$133$	−4.20295e12	−	4.20295e12i	−0.759354	−	0.759354i
$134$	−1.46267e12	+	1.46267e12i	−0.252649	+	0.252649i
$135$	5.04134e11	+	5.04134e11i	0.0832805	+	0.0832805i
$136$	−1.90734e12			−0.301435
$137$	−2.48880e12	−	2.48880e12i	−0.376415	−	0.376415i	0.493392	−	0.869807i	$-0.335757\pi$
$137$	−2.48880e12	−	2.48880e12i	−0.376415	−	0.376415i	−0.869807	+	0.493392i	$0.835757\pi$
$138$			2.87693e12i			0.416538i
$139$	7.72772e12			1.07143			0.535713	−	0.844400i	$-0.320043\pi$
$139$	7.72772e12			1.07143			0.535713	+	0.844400i	$0.320043\pi$
$140$	3.42429e12			0.454781
$141$	−1.52109e13			−1.93571
$142$	−2.56305e11	+	2.56305e11i	−0.0312627	+	0.0312627i
$143$	−5.63372e12	+	5.63372e12i	−0.658838	+	0.658838i
$144$		−	8.29695e12i		−	0.930558i
$145$	3.96305e12	+	4.41878e11i	0.426405	+	0.0475439i
$146$	3.02040e12			0.311851
$147$	3.25903e12	+	3.25903e12i	0.322987	+	0.322987i
$148$	1.23254e12	+	1.23254e12i	0.117282	+	0.117282i
$149$		−	4.25788e12i		−	0.389113i	−0.980891	−	0.194557i	$-0.937673\pi$
$149$		−	4.25788e12i		−	0.389113i	0.980891	−	0.194557i	$-0.0623268\pi$
$150$		−	3.72566e12i		−	0.327081i
$151$			1.05423e13i			0.889348i	0.895693	+	0.444674i	$0.146680\pi$
$151$			1.05423e13i			0.889348i	−0.895693	+	0.444674i	$0.853320\pi$
$152$	−6.04696e12			−0.490315
$153$	−6.20604e12	+	6.20604e12i	−0.483800	+	0.483800i
$154$			2.58972e12i			0.194146i
$155$	6.11903e12	−	6.11903e12i	0.441258	−	0.441258i
$156$	2.07828e13	+	2.07828e13i	1.44197	+	1.44197i
$157$	−9.74530e12	+	9.74530e12i	−0.650725	+	0.650725i	−0.953168	−	0.302443i	$-0.902198\pi$
$157$	−9.74530e12	+	9.74530e12i	−0.650725	+	0.650725i	0.302443	+	0.953168i	$0.402198\pi$
$158$			1.34336e12i			0.0863473i
$159$	1.24375e13	+	1.24375e13i	0.769749	+	0.769749i
$160$	3.74201e12	−	3.74201e12i	0.223041	−	0.223041i
$161$	2.07045e13			1.18880
$162$	−2.70271e12	−	2.70271e12i	−0.149524	−	0.149524i
$163$	−1.76318e13	+	1.76318e13i	−0.940093	+	0.940093i	−0.998304	−	0.0582113i	$-0.981460\pi$
$163$	−1.76318e13	+	1.76318e13i	−0.940093	+	0.940093i	0.0582113	+	0.998304i	$0.481460\pi$
$164$	7.68432e12	+	7.68432e12i	0.394950	+	0.394950i
$165$	8.01035e12			0.396961
$166$	−5.85325e12	−	5.85325e12i	−0.279736	−	0.279736i
$167$		−	2.57887e13i		−	1.18886i	−0.804148	−	0.594430i	$-0.797378\pi$
$167$		−	2.57887e13i		−	1.18886i	0.804148	−	0.594430i	$-0.202622\pi$
$168$	1.98652e13			0.883560
$169$	−2.83446e13			−1.21661
$170$	−1.62043e12			−0.0671329
$171$	−1.96754e13	+	1.96754e13i	−0.786951	+	0.786951i
$172$	−2.45473e13	+	2.45473e13i	−0.948052	+	0.948052i
$173$		−	1.34014e13i		−	0.499890i	−0.968260	−	0.249945i	$-0.919587\pi$
$173$		−	1.34014e13i		−	0.499890i	0.968260	−	0.249945i	$-0.0804125\pi$
$174$	1.10566e13	+	1.23280e12i	0.398406	+	0.0444221i
$175$	−2.68126e13			−0.933492
$176$	−1.03226e13	−	1.03226e13i	−0.347305	−	0.347305i
$177$	−3.90240e13	−	3.90240e13i	−1.26909	−	1.26909i
$178$			8.07078e12i			0.253744i
$179$			2.56198e12i			0.0778857i	0.999241	+	0.0389429i	$0.0123990\pi$
$179$			2.56198e12i			0.0778857i	−0.999241	+	0.0389429i	$0.987601\pi$
$180$		−	1.60303e13i		−	0.471309i
$181$	3.48898e13			0.992264			0.496132	−	0.868247i	$-0.334753\pi$
$181$	3.48898e13			0.992264			0.496132	+	0.868247i	$0.334753\pi$
$182$	−1.18696e13	+	1.18696e13i	−0.326595	+	0.326595i
$183$		−	6.57404e12i		−	0.175035i
$184$	1.48942e13	−	1.48942e13i	0.383804	−	0.383804i
$185$	2.17737e12	+	2.17737e12i	0.0543127	+	0.0543127i
$186$	1.70716e13	−	1.70716e13i	0.412284	−	0.412284i
$187$			1.54424e13i			0.361130i
$188$	3.78715e13	+	3.78715e13i	0.857760	+	0.857760i
$189$	1.01222e13	−	1.01222e13i	0.222076	−	0.222076i
$190$	−5.13734e12			−0.109199
$191$	4.80263e13	+	4.80263e13i	0.989189	+	0.989189i	0.999942	−	0.0107534i	$-0.00342296\pi$
$191$	4.80263e13	+	4.80263e13i	0.989189	+	0.989189i	−0.0107534	+	0.999942i	$0.503423\pi$
$192$	−3.06620e13	+	3.06620e13i	−0.612060	+	0.612060i
$193$	−1.72064e13	−	1.72064e13i	−0.332925	−	0.332925i	0.520771	−	0.853696i	$-0.325645\pi$
$193$	−1.72064e13	−	1.72064e13i	−0.332925	−	0.332925i	−0.853696	+	0.520771i	$0.825645\pi$
$194$	−1.06194e13			−0.199200
$195$	3.67143e13	+	3.67143e13i	0.667771	+	0.667771i
$196$		−	1.62284e13i		−	0.286247i
$197$	−8.17044e13			−1.39781			−0.698905	−	0.715215i	$-0.746329\pi$
$197$	−8.17044e13			−1.39781			−0.698905	+	0.715215i	$0.746329\pi$
$198$	1.21234e13			0.201202
$199$	4.07627e13			0.656363			0.328181	−	0.944615i	$-0.393564\pi$
$199$	4.07627e13			0.656363			0.328181	+	0.944615i	$0.393564\pi$
$200$	−1.92882e13	+	1.92882e13i	−0.301378	+	0.301378i
$201$	9.08388e13	−	9.08388e13i	1.37751	−	1.37751i
$202$		−	9.08081e12i		−	0.133665i
$203$	8.87217e12	−	7.95714e13i	0.126781	−	1.13705i
$204$	5.69669e13			0.790390
$205$	1.35749e13	+	1.35749e13i	0.182900	+	0.182900i
$206$	1.28724e13	+	1.28724e13i	0.168445	+	0.168445i
$207$		−	9.69246e13i		−	1.23200i
$208$		−	9.46240e13i		−	1.16848i
$209$			4.89579e13i			0.587415i
$210$	1.68769e13			0.196779
$211$	−7.70893e13	+	7.70893e13i	−0.873573	+	0.873573i	−0.992860	−	0.119287i	$-0.961939\pi$
$211$	−7.70893e13	+	7.70893e13i	−0.873573	+	0.873573i	0.119287	+	0.992860i	$0.461939\pi$
$212$		−	6.19328e13i		−	0.682190i
$213$	1.59177e13	−	1.59177e13i	0.170453	−	0.170453i
$214$	−3.39403e13	−	3.39403e13i	−0.353373	−	0.353373i
$215$	−4.33645e13	+	4.33645e13i	−0.439039	+	0.439039i
$216$		−	1.45632e13i		−	0.143395i
$217$	−1.22860e14	−	1.22860e14i	−1.17666	−	1.17666i
$218$	2.01589e13	−	2.01589e13i	0.187814	−	0.187814i
$219$	−1.87581e14			−1.70029
$220$	−1.99439e13	−	1.99439e13i	−0.175903	−	0.175903i
$221$	−7.07779e13	+	7.07779e13i	−0.607497	+	0.607497i
$222$	6.07467e12	+	6.07467e12i	0.0507464	+	0.0507464i
$223$	4.66534e13			0.379362			0.189681	−	0.981846i	$-0.439255\pi$
$223$	4.66534e13			0.379362			0.189681	+	0.981846i	$0.439255\pi$
$224$	−7.51332e13	−	7.51332e13i	−0.594762	−	0.594762i
$225$			1.25519e14i			0.967417i
$226$	1.94671e13			0.146100
$227$	2.20862e14			1.61423			0.807114	−	0.590395i	$-0.201028\pi$
$227$	2.20862e14			1.61423			0.807114	+	0.590395i	$0.201028\pi$
$228$	1.80606e14			1.28565
$229$	−9.21548e12	+	9.21548e12i	−0.0639006	+	0.0639006i	−0.738335	−	0.674434i	$-0.764388\pi$
$229$	−9.21548e12	+	9.21548e12i	−0.0639006	+	0.0639006i	0.674434	+	0.738335i	$0.264388\pi$
$230$	1.26537e13	−	1.26537e13i	0.0854774	−	0.0854774i
$231$		−	1.60834e14i		−	1.05854i
$232$	−5.08589e13	−	6.36237e13i	−0.326166	−	0.408029i
$233$	−1.98847e14			−1.24275			−0.621373	−	0.783515i	$-0.713425\pi$
$233$	−1.98847e14			−1.24275			−0.621373	+	0.783515i	$0.713425\pi$
$234$	5.55658e13	+	5.55658e13i	0.338464	+	0.338464i
$235$	6.69027e13	+	6.69027e13i	0.397225	+	0.397225i
$236$			1.94321e14i			1.12473i
$237$		−	8.34287e13i		−	0.470788i
$238$			3.25354e13i			0.179017i
$239$	2.74588e14			1.47331			0.736655	−	0.676269i	$-0.236404\pi$
$239$	2.74588e14			1.47331			0.736655	+	0.676269i	$0.236404\pi$
$240$	−6.72709e13	+	6.72709e13i	−0.352014	+	0.352014i
$241$			1.28113e14i			0.653867i	0.945047	+	0.326933i	$0.106015\pi$
$241$			1.28113e14i			0.653867i	−0.945047	+	0.326933i	$0.893985\pi$
$242$	−2.34286e13	+	2.34286e13i	−0.116642	+	0.116642i
$243$	2.07816e14	+	2.07816e14i	1.00935	+	1.00935i
$244$	−1.63678e13	+	1.63678e13i	−0.0775625	+	0.0775625i
$245$		−	2.86687e13i		−	0.132560i
$246$	3.78729e13	+	3.78729e13i	0.170890	+	0.170890i
$247$	−2.24392e14	+	2.24392e14i	−0.988155	+	0.988155i
$248$	−1.76763e14			−0.759769
$249$	3.63515e14	+	3.63515e14i	1.52520	+	1.52520i
$250$	−3.64706e13	+	3.64706e13i	−0.149383	+	0.149383i
$251$	5.43300e13	+	5.43300e13i	0.217269	+	0.217269i	0.807346	−	0.590078i	$-0.200903\pi$
$251$	5.43300e13	+	5.43300e13i	0.217269	+	0.217269i	−0.590078	+	0.807346i	$0.700903\pi$
$252$	−3.21860e14			−1.25679
$253$	−1.20588e14	−	1.20588e14i	−0.459811	−	0.459811i
$254$		−	4.87030e13i		−	0.181365i
$255$	1.00636e14			0.366027
$256$	9.65712e13			0.343090
$257$	4.88392e13			0.169500			0.0847500	−	0.996402i	$-0.472991\pi$
$257$	4.88392e13			0.169500			0.0847500	+	0.996402i	$0.472991\pi$
$258$	−1.20983e14	+	1.20983e14i	−0.410211	+	0.410211i
$259$	4.37178e13	−	4.37178e13i	0.144830	−	0.144830i
$260$		−	1.82820e14i		−	0.591811i
$261$	−3.72500e14	−	4.15336e13i	−1.17838	−	0.131388i
$262$	−1.24116e13			−0.0383724
$263$	4.23022e14	+	4.23022e14i	1.27829	+	1.27829i	0.941626	+	0.336661i	$0.109298\pi$
$263$	4.23022e14	+	4.23022e14i	1.27829	+	1.27829i	0.336661	+	0.941626i	$0.390702\pi$
$264$	−1.15699e14	−	1.15699e14i	−0.341749	−	0.341749i
$265$		−	1.09409e14i		−	0.315919i
$266$			1.03149e14i			0.291189i
$267$		−	5.01234e14i		−	1.38348i
$268$	−4.52335e14			−1.22082
$269$	1.39402e14	−	1.39402e14i	0.367921	−	0.367921i	−0.498798	−	0.866719i	$-0.666225\pi$
$269$	1.39402e14	−	1.39402e14i	0.367921	−	0.367921i	0.866719	+	0.498798i	$0.166225\pi$
$270$		−	1.23725e13i		−	0.0319356i
$271$	−3.84587e13	+	3.84587e13i	−0.0970910	+	0.0970910i	−0.753984	−	0.656893i	$-0.771870\pi$
$271$	−3.84587e13	+	3.84587e13i	−0.0970910	+	0.0970910i	0.656893	+	0.753984i	$0.271870\pi$
$272$	−1.29685e14	−	1.29685e14i	−0.320241	−	0.320241i
$273$	7.37160e14	−	7.37160e14i	1.78068	−	1.78068i
$274$			6.10804e13i			0.144344i
$275$	1.56163e14	+	1.56163e14i	0.361062	+	0.361062i
$276$	−4.44848e14	+	4.44848e14i	−1.00637	+	1.00637i
$277$	−7.24320e14			−1.60344			−0.801718	−	0.597702i	$-0.796080\pi$
$277$	−7.24320e14			−1.60344			−0.801718	+	0.597702i	$0.796080\pi$
$278$	−9.48271e13	−	9.48271e13i	−0.205430	−	0.205430i
$279$	−5.75148e14	+	5.75148e14i	−1.21942	+	1.21942i
$280$	−8.73738e13	−	8.73738e13i	−0.181315	−	0.181315i
$281$	8.93268e14			1.81445			0.907223	−	0.420650i	$-0.138198\pi$
$281$	8.93268e14			1.81445			0.907223	+	0.420650i	$0.138198\pi$
$282$	1.86653e14	+	1.86653e14i	0.371143	+	0.371143i
$283$		−	8.37107e14i		−	1.62953i	−0.579791	−	0.814765i	$-0.696866\pi$
$283$		−	8.37107e14i		−	1.62953i	0.579791	−	0.814765i	$-0.303134\pi$
$284$	−7.92628e13			−0.151063
$285$	3.19053e14			0.595380
$286$	1.38263e14			0.252645
$287$	2.72561e14	−	2.72561e14i	0.487722	−	0.487722i
$288$	−3.51724e14	+	3.51724e14i	−0.616377	+	0.616377i
$289$		−	3.88616e14i		−	0.667012i
$290$	−4.32085e13	−	5.40531e13i	−0.0726408	−	0.0908725i
$291$	6.59514e14			1.08609
$292$	4.67032e14	+	4.67032e14i	0.753442	+	0.753442i
$293$	−1.30037e14	−	1.30037e14i	−0.205524	−	0.205524i	0.596838	−	0.802362i	$-0.296424\pi$
$293$	−1.30037e14	−	1.30037e14i	−0.205524	−	0.205524i	−0.802362	+	0.596838i	$0.796424\pi$
$294$		−	7.99833e13i		−	0.123856i
$295$			3.43283e14i			0.520858i
$296$		−	6.28986e13i		−	0.0935170i
$297$	−1.17908e14			−0.171792
$298$	−5.22486e13	+	5.22486e13i	−0.0746065	+	0.0746065i
$299$		−	1.10539e15i		−	1.54700i
$300$	5.76085e14	−	5.76085e14i	0.790240	−	0.790240i
$301$	8.70685e14	+	8.70685e14i	1.17074	+	1.17074i
$302$	1.29364e14	−	1.29364e14i	0.170519	−	0.170519i
$303$			5.63961e14i			0.728775i
$304$	−4.11149e14	−	4.11149e14i	−0.520904	−	0.520904i
$305$	−2.89149e13	+	2.89149e13i	−0.0359189	+	0.0359189i
$306$	1.52309e14			0.185523
$307$	−1.10740e15	−	1.10740e15i	−1.32274	−	1.32274i	−0.911550	−	0.411188i	$-0.865114\pi$
$307$	−1.10740e15	−	1.10740e15i	−1.32274	−	1.32274i	−0.411188	−	0.911550i	$-0.634886\pi$
$308$	−4.00439e14	+	4.00439e14i	−0.469064	+	0.469064i
$309$	−7.99439e14	−	7.99439e14i	−0.918406	−	0.918406i
$310$	−1.50174e14			−0.169209
$311$	−4.45674e14	−	4.45674e14i	−0.492556	−	0.492556i	0.416555	−	0.909111i	$-0.363237\pi$
$311$	−4.45674e14	−	4.45674e14i	−0.492556	−	0.492556i	−0.909111	+	0.416555i	$0.863237\pi$
$312$		−	1.06058e15i		−	1.14979i
$313$	−1.72036e14			−0.182959			−0.0914795	−	0.995807i	$-0.529160\pi$
$313$	−1.72036e14			−0.182959			−0.0914795	+	0.995807i	$0.529160\pi$
$314$	2.39170e14			0.249533
$315$	−5.68589e14			−0.582017
$316$	−2.07718e14	+	2.07718e14i	−0.208618	+	0.208618i
$317$	−4.15410e14	+	4.15410e14i	−0.409375	+	0.409375i	−0.881521	−	0.472145i	$-0.843480\pi$
$317$	−4.15410e14	+	4.15410e14i	−0.409375	+	0.409375i	0.472145	+	0.881521i	$0.343480\pi$
$318$		−	3.05241e14i		−	0.295176i
$319$	−5.15116e14	+	4.11769e14i	−0.488833	+	0.390759i
$320$	2.69725e14			0.251201
$321$	2.10786e15	+	2.10786e15i	1.92668	+	1.92668i
$322$	−2.54065e14	−	2.54065e14i	−0.227934	−	0.227934i
$323$			6.15071e14i			0.541639i
$324$		−	8.35820e14i		−	0.722508i
$325$			1.43150e15i			1.21476i
$326$	4.32720e14			0.360497
$327$	−1.25196e15	+	1.25196e15i	−1.02401	+	1.02401i
$328$		−	3.92144e14i		−	0.314922i
$329$	1.34329e15	−	1.34329e15i	1.05924	−	1.05924i
$330$	−9.82952e13	−	9.82952e13i	−0.0761112	−	0.0761112i
$331$	1.56814e15	−	1.56814e15i	1.19239	−	1.19239i	0.215992	−	0.976395i	$-0.430701\pi$
$331$	1.56814e15	−	1.56814e15i	1.19239	−	1.19239i	0.976395	−	0.215992i	$-0.0692987\pi$
$332$		−	1.81013e15i		−	1.35170i
$333$	−2.04658e14	−	2.04658e14i	−0.150094	−	0.150094i
$334$	−3.16454e14	+	3.16454e14i	−0.227946	+	0.227946i
$335$	−7.99081e14			−0.565356
$336$	1.35069e15	+	1.35069e15i	0.938682	+	0.938682i
$337$	−1.65853e15	+	1.65853e15i	−1.13225	+	1.13225i	−0.142453	+	0.989802i	$0.545499\pi$
$337$	−1.65853e15	+	1.65853e15i	−1.13225	+	1.13225i	−0.989802	+	0.142453i	$0.954501\pi$
$338$	3.47818e14	+	3.47818e14i	0.233266	+	0.233266i
$339$	−1.20900e15			−0.796579
$340$	−2.50560e14	−	2.50560e14i	−0.162195	−	0.162195i
$341$			1.43113e15i			0.910231i
$342$	4.82876e14			0.301772
$343$	1.28745e15			0.790615
$344$	1.25269e15			0.755950
$345$	−7.85856e14	+	7.85856e14i	−0.466045	+	0.466045i
$346$	−1.64449e14	+	1.64449e14i	−0.0958463	+	0.0958463i
$347$			3.54148e14i			0.202865i	0.994842	+	0.101433i	$0.0323427\pi$
$347$			3.54148e14i			0.202865i	−0.994842	+	0.101433i	$0.967657\pi$
$348$	1.51902e15	+	1.90026e15i	0.855238	+	1.06989i
$349$	−1.18993e15			−0.658520			−0.329260	−	0.944239i	$-0.606799\pi$
$349$	−1.18993e15			−0.658520			−0.329260	+	0.944239i	$0.606799\pi$
$350$	3.29018e14	+	3.29018e14i	0.178983	+	0.178983i
$351$	−5.40413e14	−	5.40413e14i	−0.288990	−	0.288990i
$352$			8.75186e14i			0.460092i
$353$			2.02873e15i			1.04852i	0.851559	+	0.524258i	$0.175657\pi$
$353$			2.02873e15i			1.04852i	−0.851559	+	0.524258i	$0.824343\pi$
$354$			9.57730e14i			0.486658i
$355$	−1.40023e14			−0.0699569
$356$	−1.24795e15	+	1.24795e15i	−0.613054	+	0.613054i
$357$		−	2.02060e15i		−	0.976048i
$358$	3.14382e13	−	3.14382e13i	0.0149334	−	0.0149334i
$359$	3.00166e15	+	3.00166e15i	1.40215	+	1.40215i	0.793240	+	0.608909i	$0.208393\pi$
$359$	3.00166e15	+	3.00166e15i	1.40215	+	1.40215i	0.608909	+	0.793240i	$0.291607\pi$
$360$	−4.09026e14	+	4.09026e14i	−0.187904	+	0.187904i
$361$		−	2.63314e14i		−	0.118968i
$362$	−4.28134e14	−	4.28134e14i	−0.190252	−	0.190252i
$363$	1.45503e15	−	1.45503e15i	0.635962	−	0.635962i
$364$	−3.67071e15			−1.57813
$365$	8.25046e14	+	8.25046e14i	0.348916	+	0.348916i
$366$	−8.06703e13	+	8.06703e13i	−0.0335604	+	0.0335604i
$367$	−2.97023e15	−	2.97023e15i	−1.21561	−	1.21561i	−0.969154	−	0.246455i	$-0.920734\pi$
$367$	−2.97023e15	−	2.97023e15i	−1.21561	−	1.21561i	−0.246455	−	0.969154i	$-0.579266\pi$
$368$	2.02539e15			0.815496
$369$	−1.27595e15	−	1.27595e15i	−0.505446	−	0.505446i
$370$		−	5.34370e13i		−	0.0208273i
$371$	−2.19674e15			−0.842432
$372$	5.27943e15			1.99218
$373$	−2.34588e15			−0.871071			−0.435536	−	0.900172i	$-0.643441\pi$
$373$	−2.34588e15			−0.871071			−0.435536	+	0.900172i	$0.643441\pi$
$374$	1.89494e14	−	1.89494e14i	0.0692413	−	0.0692413i
$375$	2.26499e15	−	2.26499e15i	0.814478	−	0.814478i
$376$		−	1.93265e15i		−	0.683953i
$377$	−4.24824e15	−	4.73677e14i	−1.47966	−	0.164981i
$378$	−2.48418e14			−0.0851595
$379$	−2.55156e15	−	2.55156e15i	−0.860936	−	0.860936i	0.130511	−	0.991447i	$-0.458338\pi$
$379$	−2.55156e15	−	2.55156e15i	−0.860936	−	0.860936i	−0.991447	+	0.130511i	$0.958338\pi$
$380$	−7.94367e14	−	7.94367e14i	−0.263827	−	0.263827i
$381$			3.02469e15i			0.988851i
$382$		−	1.17867e15i		−	0.379324i
$383$			1.38736e15i			0.439538i	0.975552	+	0.219769i	$0.0705304\pi$
$383$			1.38736e15i			0.439538i	−0.975552	+	0.219769i	$0.929470\pi$
$384$	4.23729e15			1.32160
$385$	−7.07404e14	+	7.07404e14i	−0.217222	+	0.217222i
$386$			4.22281e14i			0.127667i
$387$	4.07597e15	−	4.07597e15i	1.21329	−	1.21329i
$388$	−1.64203e15	−	1.64203e15i	−0.481274	−	0.481274i
$389$	−7.41078e14	+	7.41078e14i	−0.213878	+	0.213878i	−0.805913	−	0.592035i	$-0.798325\pi$
$389$	−7.41078e14	+	7.41078e14i	−0.213878	+	0.213878i	0.592035	+	0.805913i	$0.298325\pi$
$390$		−	9.01044e14i		−	0.256070i
$391$	−1.51497e15	−	1.51497e15i	−0.423979	−	0.423979i
$392$	−4.14083e14	+	4.14083e14i	−0.114122	+	0.114122i
$393$	7.70816e14			0.209216
$394$	1.00260e15	+	1.00260e15i	0.268009	+	0.268009i
$395$	−3.66949e14	+	3.66949e14i	−0.0966101	+	0.0966101i
$396$	1.87459e15	+	1.87459e15i	0.486111	+	0.486111i
$397$	5.39987e15			1.37924			0.689620	−	0.724171i	$-0.257778\pi$
$397$	5.39987e15			1.37924			0.689620	+	0.724171i	$0.257778\pi$
$398$	−5.00200e14	−	5.00200e14i	−0.125848	−	0.125848i
$399$		−	6.40604e15i		−	1.58764i
$400$	−2.62291e15			−0.640359
$401$	7.46713e15			1.79592			0.897961	−	0.440075i	$-0.145048\pi$
$401$	7.46713e15			1.79592			0.897961	+	0.440075i	$0.145048\pi$
$402$	−2.22937e15			−0.528234
$403$	−6.55937e15	+	6.55937e15i	−1.53120	+	1.53120i
$404$	1.40413e15	−	1.40413e15i	0.322938	−	0.322938i
$405$		−	1.47654e15i		−	0.334591i
$406$	−1.08529e15	+	8.67552e14i	−0.242321	+	0.193704i
$407$	−5.09245e14			−0.112037
$408$	−1.45356e15	−	1.45356e15i	−0.315117	−	0.315117i
$409$	−2.66994e14	−	2.66994e14i	−0.0570377	−	0.0570377i	0.678013	−	0.735050i	$-0.262841\pi$
$409$	−2.66994e14	−	2.66994e14i	−0.0570377	−	0.0570377i	−0.735050	+	0.678013i	$0.762841\pi$
$410$		−	3.33156e14i		−	0.0701365i
$411$		−	3.79338e15i		−	0.787001i
$412$			3.98083e15i			0.813936i
$413$	6.89253e15			1.38892
$414$	−1.18936e15	+	1.18936e15i	−0.236218	+	0.236218i
$415$		−	3.19773e15i		−	0.625969i
$416$	−4.01129e15	+	4.01129e15i	−0.773970	+	0.773970i
$417$	5.88921e15	+	5.88921e15i	1.12006	+	1.12006i
$418$	6.00764e14	−	6.00764e14i	0.112628	−	0.112628i
$419$		−	8.52849e15i		−	1.57612i	−0.615601	−	0.788058i	$-0.711087\pi$
$419$		−	8.52849e15i		−	1.57612i	0.615601	−	0.788058i	$-0.288913\pi$
$420$	2.60962e15	+	2.60962e15i	0.475424	+	0.475424i
$421$	−4.15539e15	+	4.15539e15i	−0.746309	+	0.746309i	−0.973784	−	0.227475i	$-0.926953\pi$
$421$	−4.15539e15	+	4.15539e15i	−0.746309	+	0.746309i	0.227475	+	0.973784i	$0.426953\pi$
$422$	1.89193e15			0.334989
$423$	−6.28841e15	−	6.28841e15i	−1.09774	−	1.09774i
$424$	−1.58027e15	+	1.58027e15i	−0.271979	+	0.271979i
$425$	1.96191e15	+	1.96191e15i	0.332925	+	0.332925i
$426$	−3.90654e14			−0.0653634
$427$	5.80562e14	+	5.80562e14i	0.0957815	+	0.0957815i
$428$		−	1.04961e16i		−	1.70752i
$429$	−8.58679e15			−1.37749
$430$	1.06425e15			0.168358
$431$	3.60607e15			0.562562			0.281281	−	0.959626i	$-0.409241\pi$
$431$	3.60607e15			0.562562			0.281281	+	0.959626i	$0.409241\pi$
$432$	9.90188e14	−	9.90188e14i	0.152340	−	0.152340i
$433$	1.32359e15	−	1.32359e15i	0.200829	−	0.200829i	−0.599526	−	0.800355i	$-0.704644\pi$
$433$	1.32359e15	−	1.32359e15i	0.200829	−	0.200829i	0.800355	+	0.599526i	$0.204644\pi$
$434$			3.01523e15i			0.451213i
$435$	2.68345e15	+	3.35695e15i	0.396057	+	0.495461i
$436$	6.23418e15			0.907528
$437$	−4.80302e15	−	4.80302e15i	−0.689646	−	0.689646i
$438$	2.30181e15	+	2.30181e15i	0.326005	+	0.326005i
$439$			1.72904e15i			0.241556i	0.992680	+	0.120778i	$0.0385389\pi$
$439$			1.72904e15i			0.241556i	−0.992680	+	0.120778i	$0.961461\pi$
$440$			1.01777e15i			0.140260i
$441$			2.69466e15i			0.366330i
$442$	1.73703e15			0.232956
$443$	−9.65756e15	+	9.65756e15i	−1.27775	+	1.27775i	−0.335823	+	0.941925i	$0.609014\pi$
$443$	−9.65756e15	+	9.65756e15i	−1.27775	+	1.27775i	−0.941925	+	0.335823i	$0.890986\pi$
$444$			1.87861e15i			0.245210i
$445$	−2.20460e15	+	2.20460e15i	−0.283903	+	0.283903i
$446$	−5.72485e14	−	5.72485e14i	−0.0727369	−	0.0727369i
$447$	3.24488e15	−	3.24488e15i	0.406775	−	0.406775i
$448$		−	5.41561e15i		−	0.669853i
$449$	7.14066e14	+	7.14066e14i	0.0871486	+	0.0871486i	0.749337	−	0.662189i	$-0.230372\pi$
$449$	7.14066e14	+	7.14066e14i	0.0871486	+	0.0871486i	−0.662189	+	0.749337i	$0.730372\pi$
$450$	1.54024e15	−	1.54024e15i	0.185487	−	0.185487i
$451$	−3.17491e15			−0.377288
$452$	3.01013e15	+	3.01013e15i	0.352984	+	0.352984i
$453$	−8.03413e15	+	8.03413e15i	−0.929715	+	0.929715i
$454$	−2.71020e15	−	2.71020e15i	−0.309504	−	0.309504i
$455$	−6.48457e15			−0.730824
$456$	−4.60832e15	−	4.60832e15i	−0.512570	−	0.512570i
$457$		−	4.05214e15i		−	0.444823i	−0.974953	−	0.222411i	$-0.928607\pi$
$457$		−	4.05214e15i		−	0.444823i	0.974953	−	0.222411i	$-0.0713928\pi$
$458$	2.26167e14			0.0245040
$459$	−1.48130e15			−0.158405
$460$	3.91319e15			0.413032
$461$	6.38258e15	−	6.38258e15i	0.664953	−	0.664953i	−0.291590	−	0.956543i	$-0.594184\pi$
$461$	6.38258e15	−	6.38258e15i	0.664953	−	0.664953i	0.956543	+	0.291590i	$0.0941844\pi$
$462$	−1.97360e15	+	1.97360e15i	−0.202959	+	0.202959i
$463$			7.30457e15i			0.741496i	0.928734	+	0.370748i	$0.120899\pi$
$463$			7.30457e15i			0.741496i	−0.928734	+	0.370748i	$0.879101\pi$
$464$	8.67910e14	−	7.78398e15i	0.0869694	−	0.779999i
$465$	9.32649e15			0.922572
$466$	2.44005e15	+	2.44005e15i	0.238278	+	0.238278i
$467$	8.87217e15	+	8.87217e15i	0.855320	+	0.855320i	0.990782	−	0.135463i	$-0.0432521\pi$
$467$	8.87217e15	+	8.87217e15i	0.855320	+	0.855320i	−0.135463	+	0.990782i	$0.543252\pi$
$468$			1.71838e16i			1.63548i
$469$			1.60442e16i			1.50758i
$470$		−	1.64193e15i		−	0.152324i
$471$	−1.48536e16			−1.36052
$472$	4.95828e15	−	4.95828e15i	0.448414	−	0.448414i
$473$		−	1.01421e16i		−	0.905655i
$474$	−1.02376e15	+	1.02376e15i	−0.0902665	+	0.0902665i
$475$	6.21998e15	+	6.21998e15i	0.541536	+	0.541536i
$476$	−5.03082e15	+	5.03082e15i	−0.432511	+	0.432511i
$477$			1.02837e16i			0.873048i
$478$	−3.36948e15	−	3.36948e15i	−0.282485	−	0.282485i
$479$	−8.07670e15	+	8.07670e15i	−0.668684	+	0.668684i	−0.957411	−	0.288727i	$-0.906768\pi$
$479$	−8.07670e15	+	8.07670e15i	−0.668684	+	0.668684i	0.288727	+	0.957411i	$0.406768\pi$
$480$	5.70349e15			0.466330
$481$	−2.33405e15	−	2.33405e15i	−0.188469	−	0.188469i
$482$	1.57207e15	−	1.57207e15i	0.125369	−	0.125369i
$483$	1.57786e16	+	1.57786e16i	1.24276	+	1.24276i
$484$	−7.24534e15			−0.563621
$485$	−2.90077e15	−	2.90077e15i	−0.222876	−	0.222876i
$486$		−	5.10023e15i		−	0.387054i
$487$	2.41593e16			1.81097			0.905483	−	0.424384i	$-0.139509\pi$
$487$	2.41593e16			1.81097			0.905483	+	0.424384i	$0.139509\pi$
$488$	8.35279e14			0.0618461
$489$	−2.68740e16			−1.96553
$490$	−3.51794e14	+	3.51794e14i	−0.0254163	+	0.0254163i
$491$	1.42827e16	−	1.42827e16i	1.01935	−	1.01935i	0.0195375	−	0.999809i	$-0.493781\pi$
$491$	1.42827e16	−	1.42827e16i	1.01935	−	1.01935i	0.999809	−	0.0195375i	$-0.00621938\pi$
$492$			1.17123e16i			0.825753i
$493$	−6.47153e15	+	5.17316e15i	−0.450740	+	0.360308i
$494$	5.50704e15			0.378928
$495$	3.31160e15	+	3.31160e15i	0.225116	+	0.225116i
$496$	−1.20186e16	−	1.20186e16i	−0.807169	−	0.807169i
$497$			2.81143e15i			0.186547i
$498$		−	8.92140e15i		−	0.584867i
$499$			5.05060e15i			0.327145i	0.986531	+	0.163572i	$0.0523017\pi$
$499$			5.05060e15i			0.327145i	−0.986531	+	0.163572i	$0.947698\pi$
$500$	−1.12786e16			−0.721831
$501$	1.96533e16	−	1.96533e16i	1.24282	−	1.24282i
$502$		−	1.33337e15i		−	0.0833159i
$503$	2.04199e16	−	2.04199e16i	1.26080	−	1.26080i	0.310090	−	0.950707i	$-0.399641\pi$
$503$	2.04199e16	−	2.04199e16i	1.26080	−	1.26080i	0.950707	−	0.310090i	$-0.100359\pi$
$504$	8.21255e15	+	8.21255e15i	0.501066	+	0.501066i
$505$	2.48050e15	−	2.48050e15i	0.149551	−	0.149551i
$506$			2.95947e15i			0.176324i
$507$	−2.16011e16	−	2.16011e16i	−1.27183	−	1.27183i
$508$	7.53076e15	−	7.53076e15i	0.438184	−	0.438184i
$509$	6.69413e15			0.384935			0.192468	−	0.981303i	$-0.438351\pi$
$509$	6.69413e15			0.384935			0.192468	+	0.981303i	$0.438351\pi$
$510$	−1.23491e15	−	1.23491e15i	−0.0701800	−	0.0701800i
$511$	1.65655e16	−	1.65655e16i	0.930421	−	0.930421i
$512$	−1.25721e16	−	1.25721e16i	−0.697892	−	0.697892i
$513$	−4.69627e15			−0.257661
$514$	−5.99307e14	−	5.99307e14i	−0.0324990	−	0.0324990i
$515$			7.03242e15i			0.376931i
$516$	−3.74144e16			−1.98217
$517$	−1.56473e16			−0.819400
$518$	−1.07292e15			−0.0555381
$519$	1.02131e16	−	1.02131e16i	0.522579	−	0.522579i
$520$	−4.66481e15	+	4.66481e15i	−0.235947	+	0.235947i
$521$			5.35528e15i			0.267766i	0.990997	+	0.133883i	$0.0427447\pi$
$521$			5.35528e15i			0.267766i	−0.990997	+	0.133883i	$0.957255\pi$
$522$	4.06130e15	+	5.08062e15i	0.200744	+	0.251127i
$523$	1.03198e16			0.504266			0.252133	−	0.967693i	$-0.418868\pi$
$523$	1.03198e16			0.504266			0.252133	+	0.967693i	$0.418868\pi$
$524$	−1.91915e15	−	1.91915e15i	−0.0927089	−	0.0927089i
$525$	−2.04336e16	−	2.04336e16i	−0.975862	−	0.975862i
$526$		−	1.03818e16i		−	0.490184i
$527$			1.79796e16i			0.839299i
$528$		−	1.57334e16i		−	0.726139i
$529$	1.74589e15			0.0796679
$530$	−1.34256e15	+	1.34256e15i	−0.0605728	+	0.0605728i
$531$		−	3.22662e16i		−	1.43940i
$532$	−1.59495e16	+	1.59495e16i	−0.703523	+	0.703523i
$533$	−1.45518e16	−	1.45518e16i	−0.634677	−	0.634677i
$534$	−6.15065e15	+	6.15065e15i	−0.265261	+	0.265261i
$535$		−	1.85422e16i		−	0.790747i
$536$	1.15417e16	+	1.15417e16i	0.486723	+	0.486723i
$537$	−1.95246e15	+	1.95246e15i	−0.0814209	+	0.0814209i
$538$	−3.42121e15			−0.141087
$539$	3.35254e15	+	3.35254e15i	0.136723	+	0.136723i
$540$	1.91311e15	−	1.91311e15i	0.0771574	−	0.0771574i
$541$	1.54797e16	+	1.54797e16i	0.617417	+	0.617417i	0.944868	−	0.327451i	$-0.106190\pi$
$541$	1.54797e16	+	1.54797e16i	0.617417	+	0.617417i	−0.327451	+	0.944868i	$0.606190\pi$
$542$	9.43856e14			0.0372315
$543$	2.65891e16	+	2.65891e16i	1.03730	+	1.03730i
$544$			1.09952e16i			0.424238i
$545$	1.10131e16			0.420273
$546$	−1.80914e16			−0.682837
$547$	3.04293e16			1.13597			0.567986	−	0.823038i	$-0.307723\pi$
$547$	3.04293e16			1.13597			0.567986	+	0.823038i	$0.307723\pi$
$548$	−9.44462e15	+	9.44462e15i	−0.348740	+	0.348740i
$549$	2.71781e15	−	2.71781e15i	0.0992624	−	0.0992624i
$550$		−	3.83256e15i		−	0.138456i
$551$	−2.05171e16	+	1.64008e16i	−0.733174	+	0.586078i
$552$	2.27014e16			0.802449
$553$	7.36770e15	+	7.36770e15i	0.257621	+	0.257621i
$554$	8.88815e15	+	8.88815e15i	0.307435	+	0.307435i
$555$			3.31869e15i			0.113556i
$556$		−	2.93255e16i		−	0.992651i
$557$			3.13465e16i			1.04968i	0.851201	+	0.524841i	$0.175875\pi$
$557$			3.13465e16i			1.04968i	−0.851201	+	0.524841i	$0.824125\pi$
$558$	1.41153e16			0.467611
$559$	4.64851e16	−	4.64851e16i	1.52350	−	1.52350i
$560$		−	1.18816e16i		−	0.385253i
$561$	−1.17684e16	+	1.17684e16i	−0.377522	+	0.377522i
$562$	−1.09613e16	−	1.09613e16i	−0.347892	−	0.347892i
$563$	−7.90617e15	+	7.90617e15i	−0.248265	+	0.248265i	−0.820258	−	0.571993i	$-0.806170\pi$
$563$	−7.90617e15	+	7.90617e15i	−0.248265	+	0.248265i	0.571993	+	0.820258i	$0.306170\pi$
$564$			5.77229e16i			1.79339i
$565$	5.31761e15	+	5.31761e15i	0.163465	+	0.163465i
$566$	−1.02722e16	+	1.02722e16i	−0.312438	+	0.312438i
$567$	−2.96463e16			−0.892221
$568$	2.02246e15	+	2.02246e15i	0.0602268	+	0.0602268i
$569$	3.07590e16	−	3.07590e16i	0.906354	−	0.906354i	−0.0896216	−	0.995976i	$-0.528566\pi$
$569$	3.07590e16	−	3.07590e16i	0.906354	−	0.906354i	0.995976	+	0.0896216i	$0.0285658\pi$
$570$	−3.91511e15	−	3.91511e15i	−0.114155	−	0.114155i
$571$	4.98237e16			1.43754			0.718768	−	0.695250i	$-0.244706\pi$
$571$	4.98237e16			1.43754			0.718768	+	0.695250i	$0.244706\pi$
$572$	2.13791e16	+	2.13791e16i	0.610398	+	0.610398i
$573$			7.32007e16i			2.06818i
$574$	−6.68920e15			−0.187026
$575$	−3.06407e16			−0.847797
$576$	−2.53523e16			−0.694196
$577$	7.98266e15	−	7.98266e15i	0.216318	−	0.216318i	−0.590627	−	0.806945i	$-0.701119\pi$
$577$	7.98266e15	−	7.98266e15i	0.216318	−	0.216318i	0.806945	+	0.590627i	$0.201119\pi$
$578$	−4.76872e15	+	4.76872e15i	−0.127889	+	0.127889i
$579$		−	2.62257e16i		−	0.696073i
$580$	1.67686e15	−	1.50392e16i	0.0440483	−	0.395054i
$581$	−6.42049e16			−1.66921
$582$	−8.09292e15	−	8.09292e15i	−0.208241	−	0.208241i
$583$	1.27943e16	+	1.27943e16i	0.325841	+	0.325841i
$584$		−	2.38335e16i		−	0.600773i
$585$			3.03565e16i			0.757384i
$586$			3.19138e15i			0.0788122i
$587$	−6.98788e16			−1.70811			−0.854056	−	0.520180i	$-0.825865\pi$
$587$	−6.98788e16			−1.70811			−0.854056	+	0.520180i	$0.825865\pi$
$588$	1.23675e16	−	1.23675e16i	0.299239	−	0.299239i
$589$			5.70020e16i			1.36521i
$590$	4.21243e15	−	4.21243e15i	0.0998667	−	0.0998667i
$591$	−6.22660e16	−	6.22660e16i	−1.46126	−	1.46126i
$592$	4.27664e15	−	4.27664e15i	0.0993511	−	0.0993511i
$593$			4.89894e16i			1.12661i	0.826249	+	0.563306i	$0.190471\pi$
$593$			4.89894e16i			1.12661i	−0.826249	+	0.563306i	$0.809529\pi$
$594$	1.44685e15	+	1.44685e15i	0.0329385	+	0.0329385i
$595$	−8.88730e15	+	8.88730e15i	−0.200294	+	0.200294i
$596$	−1.61580e16			−0.360504
$597$	3.10648e16	+	3.10648e16i	0.686155	+	0.686155i
$598$	−1.35643e16	+	1.35643e16i	−0.296613	+	0.296613i
$599$	−2.92987e16	−	2.92987e16i	−0.634289	−	0.634289i	0.314852	−	0.949141i	$-0.398045\pi$
$599$	−2.92987e16	−	2.92987e16i	−0.634289	−	0.634289i	−0.949141	+	0.314852i	$0.898045\pi$
$600$	−2.93986e16			−0.630114
$601$	−8.56060e15	−	8.56060e15i	−0.181659	−	0.181659i	0.610419	−	0.792078i	$-0.291001\pi$
$601$	−8.56060e15	−	8.56060e15i	−0.181659	−	0.181659i	−0.792078	+	0.610419i	$0.791001\pi$
$602$		−	2.13684e16i		−	0.448945i
$603$	7.51083e16			1.56237
$604$	4.00062e16			0.823959
$605$	−1.27994e16			−0.261010
$606$	6.92039e15	−	6.92039e15i	0.139732	−	0.139732i
$607$	1.64006e16	−	1.64006e16i	0.327889	−	0.327889i	−0.523894	−	0.851783i	$-0.675521\pi$
$607$	1.64006e16	−	1.64006e16i	0.327889	−	0.327889i	0.851783	+	0.523894i	$0.175521\pi$
$608$			3.48588e16i			0.690066i
$609$	6.74018e16	−	5.38791e16i	1.32120	−	1.05613i
$610$	7.09632e14			0.0137738
$611$	−7.17172e16	−	7.17172e16i	−1.37840	−	1.37840i
$612$	2.35510e16	+	2.35510e16i	0.448229	+	0.448229i
$613$			6.15663e16i			1.16033i	0.814500	+	0.580163i	$0.197011\pi$
$613$			6.15663e16i			1.16033i	−0.814500	+	0.580163i	$0.802989\pi$
$614$			2.71779e16i			0.507230i
$615$			2.06906e16i			0.382403i
$616$	2.04351e16			0.374018
$617$	1.47013e16	−	1.47013e16i	0.266467	−	0.266467i	−0.561208	−	0.827675i	$-0.689663\pi$
$617$	1.47013e16	−	1.47013e16i	0.266467	−	0.266467i	0.827675	+	0.561208i	$0.189663\pi$
$618$			1.96199e16i			0.352181i
$619$	−2.34230e16	+	2.34230e16i	−0.416389	+	0.416389i	−0.883957	−	0.467568i	$-0.845130\pi$
$619$	−2.34230e16	+	2.34230e16i	−0.416389	+	0.416389i	0.467568	+	0.883957i	$0.345130\pi$
$620$	−2.32208e16	−	2.32208e16i	−0.408815	−	0.408815i
$621$	1.15673e16	−	1.15673e16i	0.201690	−	0.201690i
$622$			1.09378e16i			0.188880i
$623$	4.42646e16	+	4.42646e16i	0.757057	+	0.757057i
$624$	7.21119e16	−	7.21119e16i	1.22152	−	1.22152i
$625$	2.87081e16			0.481642
$626$	2.11106e15	+	2.11106e15i	0.0350796	+	0.0350796i
$627$	−3.73103e16	+	3.73103e16i	−0.614078	+	0.614078i
$628$	3.69819e16	+	3.69819e16i	0.602881	+	0.602881i
$629$	−6.39778e15			−0.103306
$630$	6.97718e15	+	6.97718e15i	0.111593	+	0.111593i
$631$			3.91892e16i			0.620854i	0.950597	+	0.310427i	$0.100472\pi$
$631$			3.91892e16i			0.620854i	−0.950597	+	0.310427i	$0.899528\pi$
$632$	1.06002e16			0.166346
$633$	−1.17498e17			−1.82645
$634$	1.01950e16			0.156983
$635$	1.33036e16	−	1.33036e16i	0.202921	−	0.202921i
$636$	4.71983e16	−	4.71983e16i	0.713154	−	0.713154i
$637$			3.07317e16i			0.459992i
$638$	1.13738e16	+	1.26818e15i	0.168649	+	0.0188042i
$639$	1.31613e16			0.193327
$640$	−1.86371e16	−	1.86371e16i	−0.271205	−	0.271205i
$641$	6.66875e16	+	6.66875e16i	0.961382	+	0.961382i	0.999282	−	0.0378992i	$-0.0120666\pi$
$641$	6.66875e16	+	6.66875e16i	0.961382	+	0.961382i	−0.0378992	+	0.999282i	$0.512067\pi$
$642$		−	5.17311e16i		−	0.738825i
$643$		−	1.01725e17i		−	1.43934i	−0.694316	−	0.719670i	$-0.744293\pi$
$643$		−	1.01725e17i		−	1.43934i	0.694316	−	0.719670i	$-0.255707\pi$
$644$		−	7.85702e16i		−	1.10139i
$645$	−6.60952e16			−0.917934
$646$	7.54756e15	−	7.54756e15i	0.103851	−	0.103851i
$647$			4.52448e16i			0.616799i	0.951257	+	0.308399i	$0.0997933\pi$
$647$			4.52448e16i			0.616799i	−0.951257	+	0.308399i	$0.900207\pi$
$648$	−2.13267e16	+	2.13267e16i	−0.288054	+	0.288054i
$649$	−4.01437e16	−	4.01437e16i	−0.537216	−	0.537216i
$650$	1.75660e16	−	1.75660e16i	0.232912	−	0.232912i
$651$		−	1.87260e17i		−	2.46014i
$652$	6.69099e16	+	6.69099e16i	0.870973	+	0.870973i
$653$	−2.49516e16	+	2.49516e16i	−0.321825	+	0.321825i	−0.849467	−	0.527642i	$-0.823076\pi$
$653$	−2.49516e16	+	2.49516e16i	−0.321825	+	0.321825i	0.527642	+	0.849467i	$0.323076\pi$
$654$	3.07257e16			0.392677
$655$	−3.39032e15	−	3.39032e15i	−0.0429331	−	0.0429331i
$656$	2.66630e16	−	2.66630e16i	0.334569	−	0.334569i
$657$	−7.75487e16	−	7.75487e16i	−0.964234	−	0.964234i
$658$	−3.29672e16			−0.406187
$659$	−4.93485e16	−	4.93485e16i	−0.602506	−	0.602506i	0.338471	−	0.940977i	$-0.390090\pi$
$659$	−4.93485e16	−	4.93485e16i	−0.602506	−	0.602506i	−0.940977	+	0.338471i	$0.890090\pi$
$660$		−	3.03980e16i		−	0.367774i
$661$	5.93214e15			0.0711218			0.0355609	−	0.999368i	$-0.488678\pi$
$661$	5.93214e15			0.0711218			0.0355609	+	0.999368i	$0.488678\pi$
$662$	−3.84854e16			−0.457244
$663$	−1.07878e17			−1.27014
$664$	−4.61871e16	+	4.61871e16i	−0.538905	+	0.538905i
$665$	−2.81760e16	+	2.81760e16i	−0.325799	+	0.325799i
$666$			5.02272e15i			0.0575564i
$667$	1.01389e16	−	9.09321e16i	0.115142	−	1.03267i
$668$	−9.78640e16			−1.10145
$669$	3.55540e16	+	3.55540e16i	0.396581	+	0.396581i
$670$	9.80555e15	+	9.80555e15i	0.108398	+	0.108398i
$671$		−	6.76266e15i		−	0.0740939i
$672$		−	1.14516e17i		−	1.24352i
$673$		−	1.80696e17i		−	1.94473i	−0.233471	−	0.972364i	$-0.575008\pi$
$673$		−	1.80696e17i		−	1.94473i	0.233471	−	0.972364i	$-0.424992\pi$
$674$	4.07037e16			0.434185
$675$	−1.49799e16	+	1.49799e16i	−0.158374	+	0.158374i
$676$			1.07563e17i			1.12716i
$677$	5.54991e16	−	5.54991e16i	0.576440	−	0.576440i	−0.357481	−	0.933921i	$-0.616364\pi$
$677$	5.54991e16	−	5.54991e16i	0.576440	−	0.576440i	0.933921	+	0.357481i	$0.116364\pi$
$678$	1.48357e16	+	1.48357e16i	0.152732	+	0.152732i
$679$	−5.82425e16	+	5.82425e16i	−0.594322	+	0.594322i
$680$			1.27865e16i			0.129330i
$681$	1.68316e17	+	1.68316e17i	1.68750	+	1.68750i
$682$	1.75614e16	−	1.75614e16i	0.174523	−	0.174523i
$683$	1.63469e17			1.61031			0.805156	−	0.593063i	$-0.202082\pi$
$683$	1.63469e17			1.61031			0.805156	+	0.593063i	$0.202082\pi$
$684$	7.46652e16	+	7.46652e16i	0.729091	+	0.729091i
$685$	−1.66846e16	+	1.66846e16i	−0.161500	+	0.161500i
$686$	−1.57983e16	−	1.57983e16i	−0.151588	−	0.151588i
$687$	−1.40460e16			−0.133602
$688$	8.51738e16	+	8.51738e16i	0.803110	+	0.803110i
$689$			1.17282e17i			1.09627i
$690$	1.92865e16			0.178714
$691$	4.39617e15			0.0403837			0.0201918	−	0.999796i	$-0.493572\pi$
$691$	4.39617e15			0.0403837			0.0201918	+	0.999796i	$0.493572\pi$
$692$	−5.08563e16			−0.463136
$693$	6.64912e16	−	6.64912e16i	0.600295	−	0.600295i
$694$	4.34576e15	−	4.34576e15i	0.0388964	−	0.0388964i
$695$		−	5.18056e16i		−	0.459693i
$696$	9.72787e15	−	8.72459e16i	0.0855780	−	0.767520i
$697$	−3.98873e16			−0.347887
$698$	1.46017e16	+	1.46017e16i	0.126261	+	0.126261i
$699$	−1.51539e17	−	1.51539e17i	−1.29915	−	1.29915i
$700$			1.01750e17i			0.864857i
$701$			1.66768e16i			0.140541i	0.997528	+	0.0702705i	$0.0223863\pi$
$701$			1.66768e16i			0.140541i	−0.997528	+	0.0702705i	$0.977614\pi$
$702$			1.32628e16i			0.110819i
$703$	−2.02833e16			−0.168038
$704$	−3.15418e16	+	3.15418e16i	−0.259090	+	0.259090i
$705$			1.01972e17i			0.830510i
$706$	2.48946e16	−	2.48946e16i	0.201037	−	0.201037i
$707$	−4.98042e16	−	4.98042e16i	−0.398794	−	0.398794i
$708$	−1.48090e17	+	1.48090e17i	−1.17578	+	1.17578i
$709$			2.19805e17i			1.73046i	0.501377	+	0.865229i	$0.332827\pi$
$709$			2.19805e17i			1.73046i	−0.501377	+	0.865229i	$0.667173\pi$
$710$	1.71823e15	+	1.71823e15i	0.0134132	+	0.0134132i
$711$	3.44907e16	−	3.44907e16i	0.266983	−	0.266983i
$712$	6.36853e16			0.488831
$713$	−1.40401e17	−	1.40401e17i	−1.06864	−	1.06864i
$714$	−2.47949e16	+	2.47949e16i	−0.187142	+	0.187142i
$715$	3.77677e16	+	3.77677e16i	0.282673	+	0.282673i
$716$	9.72232e15			0.0721592
$717$	2.09260e17	+	2.09260e17i	1.54018	+	1.54018i
$718$		−	7.36668e16i		−	0.537682i
$719$	1.02950e17			0.745167			0.372583	−	0.927999i	$-0.378472\pi$
$719$	1.02950e17			0.745167			0.372583	+	0.927999i	$0.378472\pi$
$720$	−5.56216e16			−0.399253
$721$	1.41199e17			1.00513
$722$	−3.23113e15	+	3.23113e15i	−0.0228103	+	0.0228103i
$723$	−9.76331e16	+	9.76331e16i	−0.683546	+	0.683546i
$724$		−	1.32401e17i		−	0.919308i
$725$	−1.31300e16	+	1.17758e17i	−0.0904142	+	0.810894i
$726$	−3.57093e16			−0.243872
$727$	−7.97668e16	−	7.97668e16i	−0.540276	−	0.540276i	0.383334	−	0.923610i	$-0.374776\pi$
$727$	−7.97668e16	−	7.97668e16i	−0.540276	−	0.540276i	−0.923610	+	0.383334i	$0.874776\pi$
$728$	9.36614e16	+	9.36614e16i	0.629177	+	0.629177i
$729$			1.99698e17i			1.33048i
$730$		−	2.02483e16i		−	0.133799i
$731$		−	1.27418e17i		−	0.835079i
$732$	−2.49475e16			−0.162166
$733$	7.75086e16	−	7.75086e16i	0.499719	−	0.499719i	−0.411631	−	0.911351i	$-0.635041\pi$
$733$	7.75086e16	−	7.75086e16i	0.499719	−	0.499719i	0.911351	+	0.411631i	$0.135041\pi$
$734$			7.28956e16i			0.466149i
$735$	2.18481e16	−	2.18481e16i	0.138576	−	0.138576i
$736$	−8.58602e16	−	8.58602e16i	−0.540163	−	0.540163i
$737$	9.34451e16	−	9.34451e16i	0.583111	−	0.583111i
$738$			3.13144e16i			0.193823i
$739$	6.26233e16	+	6.26233e16i	0.384476	+	0.384476i	0.872712	−	0.488236i	$-0.162359\pi$
$739$	6.26233e16	+	6.26233e16i	0.384476	+	0.384476i	−0.488236	+	0.872712i	$0.662359\pi$
$740$	8.26276e15	−	8.26276e15i	0.0503193	−	0.0503193i
$741$	−3.42013e17			−2.06601
$742$	2.69562e16	+	2.69562e16i	0.161524	+	0.161524i
$743$	−1.28493e17	+	1.28493e17i	−0.763739	+	0.763739i	−0.976996	−	0.213257i	$-0.931593\pi$
$743$	−1.28493e17	+	1.28493e17i	−0.763739	+	0.763739i	0.213257	+	0.976996i	$0.431593\pi$
$744$	−1.34709e17	−	1.34709e17i	−0.794255	−	0.794255i
$745$	−2.85442e16			−0.166948
$746$	2.87864e16	+	2.87864e16i	0.167015	+	0.167015i
$747$			3.00565e17i			1.72987i
$748$	5.86013e16			0.334578
$749$	−3.72295e17			−2.10861
$750$	−5.55876e16			−0.312328
$751$	3.77277e15	−	3.77277e15i	0.0210291	−	0.0210291i	−0.696514	−	0.717543i	$-0.745267\pi$
$751$	3.77277e15	−	3.77277e15i	0.0210291	−	0.0210291i	0.717543	+	0.696514i	$0.245267\pi$
$752$	1.31406e17	−	1.31406e17i	0.726622	−	0.726622i
$753$			8.28085e16i			0.454261i
$754$	4.63178e16	+	5.79428e16i	0.252069	+	0.315335i
$755$	7.06738e16			0.381572
$756$	−3.84120e16	−	3.84120e16i	−0.205748	−	0.205748i
$757$	−1.83849e17	−	1.83849e17i	−0.976982	−	0.976982i	0.0227592	−	0.999741i	$-0.492755\pi$
$757$	−1.83849e17	−	1.83849e17i	−0.976982	−	0.976982i	−0.999741	+	0.0227592i	$0.992755\pi$
$758$			6.26206e16i			0.330143i
$759$		−	1.83797e17i		−	0.961364i
$760$			4.05380e16i			0.210368i
$761$	2.63773e17			1.35807			0.679035	−	0.734106i	$-0.262399\pi$
$761$	2.63773e17			1.35807			0.679035	+	0.734106i	$0.262399\pi$
$762$	3.71160e16	−	3.71160e16i	0.189597	−	0.189597i
$763$		−	2.21125e17i		−	1.12070i
$764$	1.82252e17	−	1.82252e17i	0.916459	−	0.916459i
$765$	4.16045e16	+	4.16045e16i	0.207573	+	0.207573i
$766$	1.70243e16	−	1.70243e16i	0.0842748	−	0.0842748i
$767$		−	3.67986e17i		−	1.80742i
$768$	7.35958e16	+	7.35958e16i	0.358662	+	0.358662i
$769$	4.44830e15	−	4.44830e15i	0.0215098	−	0.0215098i	−0.696270	−	0.717780i	$-0.745158\pi$
$769$	4.44830e15	−	4.44830e15i	0.0215098	−	0.0215098i	0.717780	+	0.696270i	$0.245158\pi$
$770$	1.73612e16			0.0832979
$771$	3.72198e16	+	3.72198e16i	0.177193	+	0.177193i
$772$	−6.52957e16	+	6.52957e16i	−0.308447	+	0.308447i
$773$	1.72682e17	+	1.72682e17i	0.809415	+	0.809415i	0.984545	−	0.175131i	$-0.0560348\pi$
$773$	1.72682e17	+	1.72682e17i	0.809415	+	0.809415i	−0.175131	+	0.984545i	$0.556035\pi$
$774$	−1.00033e17			−0.465260
$775$	1.81821e17	+	1.81821e17i	0.839139	+	0.839139i
$776$			8.37959e16i			0.383754i
$777$	6.66337e16			0.302808
$778$	1.81876e16			0.0820157
$779$	−1.26457e17			−0.565873
$780$	1.39325e17	−	1.39325e17i	0.618673	−	0.618673i
$781$	1.63744e16	−	1.63744e16i	0.0721539	−	0.0721539i
$782$			3.71806e16i			0.162583i
$783$	−3.94988e16	−	4.94123e16i	−0.171401	−	0.214420i
$784$	−5.63092e16			−0.242484
$785$	6.53312e16	+	6.53312e16i	0.279192	+	0.279192i
$786$	−9.45871e15	−	9.45871e15i	−0.0401141	−	0.0401141i
$787$		−	1.29635e17i		−	0.545599i	−0.962071	−	0.272799i	$-0.912050\pi$
$787$		−	1.29635e17i		−	0.545599i	0.962071	−	0.272799i	$-0.0879496\pi$
$788$			3.10055e17i			1.29504i
$789$			6.44761e17i			2.67262i
$790$	9.00567e15			0.0370470
$791$	1.06768e17	−	1.06768e17i	0.435897	−	0.435897i
$792$		−	9.56636e16i		−	0.387611i
$793$	3.09957e16	−	3.09957e16i	0.124641	−	0.124641i
$794$	−6.62619e16	−	6.62619e16i	−0.264448	−	0.264448i
$795$	8.33791e16	−	8.33791e16i	0.330259	−	0.330259i
$796$		−	1.54688e17i		−	0.608104i
$797$	−9.67730e16	−	9.67730e16i	−0.377576	−	0.377576i	0.492651	−	0.870227i	$-0.336028\pi$
$797$	−9.67730e16	−	9.67730e16i	−0.377576	−	0.377576i	−0.870227	+	0.492651i	$0.836028\pi$
$798$	−7.86088e16	+	7.86088e16i	−0.304406	+	0.304406i
$799$	−1.96581e17			−0.755546
$800$	1.11190e17	+	1.11190e17i	0.424157	+	0.424157i
$801$	2.07218e17	−	2.07218e17i	0.784569	−	0.784569i
$802$	−9.16293e16	−	9.16293e16i	−0.344341	−	0.344341i
$803$	−1.92963e17			−0.719748
$804$	−3.44719e17	−	3.44719e17i	−1.27623	−	1.27623i
$805$		−	1.38800e17i		−	0.510051i
$806$	1.60980e17			0.587168
$807$	2.12473e17			0.769241
$808$	−7.16553e16			−0.257502
$809$	1.94717e17	−	1.94717e17i	0.694564	−	0.694564i	−0.268669	−	0.963233i	$-0.586584\pi$
$809$	1.94717e17	−	1.94717e17i	0.694564	−	0.694564i	0.963233	+	0.268669i	$0.0865836\pi$
$810$	−1.81186e16	+	1.81186e16i	−0.0641527	+	0.0641527i
$811$			2.15748e17i			0.758267i	0.925342	+	0.379133i	$0.123778\pi$
$811$			2.15748e17i			0.758267i	−0.925342	+	0.379133i	$0.876222\pi$
$812$	−3.01961e17	−	3.36685e16i	−1.05345	−	0.117459i
$813$	−5.86179e16			−0.202996
$814$	6.24896e15	+	6.24896e15i	0.0214813	+	0.0214813i
$815$	1.18201e17	+	1.18201e17i	0.403344	+	0.403344i
$816$		−	1.97663e17i		−	0.669552i
$817$		−	4.03963e17i		−	1.35834i
$818$			6.55259e15i			0.0218722i
$819$	6.09506e17			2.01964
$820$	5.15146e16	−	5.15146e16i	0.169452	−	0.169452i
$821$		−	1.83205e16i		−	0.0598243i	−0.999553	−	0.0299121i	$-0.990477\pi$
$821$		−	1.83205e16i		−	0.0598243i	0.999553	−	0.0299121i	$-0.00952275\pi$
$822$	−4.65487e16	+	4.65487e16i	−0.150896	+	0.150896i
$823$	1.09047e16	+	1.09047e16i	0.0350924	+	0.0350924i	0.724435	−	0.689343i	$-0.242101\pi$
$823$	1.09047e16	+	1.09047e16i	0.0350924	+	0.0350924i	−0.689343	+	0.724435i	$0.742101\pi$
$824$	1.01574e17	−	1.01574e17i	0.324505	−	0.324505i
$825$			2.38020e17i			0.754900i
$826$	−8.45784e16	−	8.45784e16i	−0.266305	−	0.266305i
$827$	−7.53612e16	+	7.53612e16i	−0.235567	+	0.235567i	−0.815012	−	0.579445i	$-0.803270\pi$
$827$	−7.53612e16	+	7.53612e16i	−0.235567	+	0.235567i	0.579445	+	0.815012i	$0.303270\pi$
$828$	−3.67814e17			−1.14142
$829$	−3.26992e17	−	3.26992e17i	−1.00742	−	1.00742i	−0.999972	−	0.00744725i	$-0.997629\pi$
$829$	−3.26992e17	−	3.26992e17i	−1.00742	−	1.00742i	−0.00744725	−	0.999972i	$-0.502371\pi$
$830$	−3.92394e16	+	3.92394e16i	−0.120020	+	0.120020i
$831$	−5.51996e17	−	5.51996e17i	−1.67622	−	1.67622i
$832$	−2.89135e17			−0.871686
$833$	4.21188e16	+	4.21188e16i	0.126068	+	0.126068i
$834$		−	1.44533e17i		−	0.429508i
$835$	−1.72884e17			−0.510077
$836$	1.85788e17			0.544226
$837$	−1.37280e17			−0.399260
$838$	−1.04653e17	+	1.04653e17i	−0.302196	+	0.302196i
$839$	3.60275e17	−	3.60275e17i	1.03291	−	1.03291i	0.0334690	−	0.999440i	$-0.489344\pi$
$839$	3.60275e17	−	3.60275e17i	1.03291	−	1.03291i	0.999440	−	0.0334690i	$-0.0106555\pi$
$840$		−	1.33173e17i		−	0.379089i
$841$	−3.45125e17	−	7.79315e16i	−0.975441	−	0.220261i
$842$	1.01982e17			0.286187
$843$	6.80750e17	+	6.80750e17i	1.89680	+	1.89680i
$844$	2.92542e17	+	2.92542e17i	0.809344	+	0.809344i
$845$			1.90018e17i			0.521982i
$846$			1.54330e17i			0.420949i
$847$			2.56991e17i			0.696012i
$848$	−2.14894e17			−0.577894
$849$	6.37950e17	−	6.37950e17i	1.70349	−	1.70349i
$850$		−	4.81494e16i		−	0.127667i
$851$	4.99595e16	−	4.99595e16i	0.131535	−	0.131535i
$852$	−6.04053e16	−	6.04053e16i	−0.157920	−	0.157920i
$853$	−3.29162e17	+	3.29162e17i	−0.854506	+	0.854506i	−0.990684	−	0.136179i	$-0.956518\pi$
$853$	−3.29162e17	+	3.29162e17i	−0.854506	+	0.854506i	0.136179	+	0.990684i	$0.456518\pi$
$854$		−	1.42482e16i		−	0.0367293i
$855$	1.31901e17	+	1.31901e17i	0.337639	+	0.337639i
$856$	−2.67818e17	+	2.67818e17i	−0.680765	+	0.680765i
$857$	−1.10966e17			−0.280094			−0.140047	−	0.990145i	$-0.544725\pi$
$857$	−1.10966e17			−0.280094			−0.140047	+	0.990145i	$0.544725\pi$
$858$	1.05369e17	+	1.05369e17i	0.264112	+	0.264112i
$859$	−4.90137e17	+	4.90137e17i	−1.22000	+	1.22000i	−0.252365	+	0.967632i	$0.581208\pi$
$859$	−4.90137e17	+	4.90137e17i	−1.22000	+	1.22000i	−0.967632	+	0.252365i	$0.918792\pi$
$860$	1.64561e17	+	1.64561e17i	0.406759	+	0.406759i
$861$	4.15431e17			1.01972
$862$	−4.42501e16	−	4.42501e16i	−0.107863	−	0.107863i
$863$		−	2.14105e17i		−	0.518277i	−0.965840	−	0.259139i	$-0.916561\pi$
$863$		−	2.14105e17i		−	0.518277i	0.965840	−	0.259139i	$-0.0834386\pi$
$864$	−8.39519e16			−0.201813
$865$	−8.98413e16			−0.214476
$866$	−3.24836e16			−0.0770118
$867$	2.96160e17	−	2.96160e17i	0.697287	−	0.697287i
$868$	−4.66233e17	+	4.66233e17i	−1.09015	+	1.09015i
$869$		−	8.58224e16i		−	0.199288i
$870$	8.26455e15	−	7.41219e16i	0.0190592	−	0.170935i
$871$	8.56585e17			1.96183
$872$	−1.59071e17	−	1.59071e17i	−0.361819	−	0.361819i
$873$	2.72653e17	+	2.72653e17i	0.615921	+	0.615921i
$874$			1.17876e17i			0.264458i
$875$			4.00049e17i			0.891384i
$876$			7.11840e17i			1.57528i
$877$	−4.33373e17			−0.952499			−0.476250	−	0.879310i	$-0.658004\pi$
$877$	−4.33373e17			−0.952499			−0.476250	+	0.879310i	$0.658004\pi$
$878$	2.12171e16	−	2.12171e16i	0.0463147	−	0.0463147i
$879$		−	1.98200e17i		−	0.429705i
$880$	−6.92010e16	+	6.92010e16i	−0.149010	+	0.149010i
$881$	3.04454e17	+	3.04454e17i	0.651128	+	0.651128i	0.953265	−	0.302136i	$-0.0976998\pi$
$881$	3.04454e17	+	3.04454e17i	0.651128	+	0.651128i	−0.302136	+	0.953265i	$0.597700\pi$
$882$	3.30663e16	−	3.30663e16i	0.0702383	−	0.0702383i
$883$		−	2.32060e17i		−	0.489595i	−0.969574	−	0.244797i	$-0.921279\pi$
$883$		−	2.32060e17i		−	0.489595i	0.969574	−	0.244797i	$-0.0787214\pi$
$884$	2.68591e17	+	2.68591e17i	0.562831	+	0.562831i
$885$	−2.61612e17	+	2.61612e17i	−0.544500	+	0.544500i
$886$	2.37016e17			0.489978
$887$	1.32524e17	+	1.32524e17i	0.272116	+	0.272116i	0.829952	−	0.557835i	$-0.188368\pi$
$887$	1.32524e17	+	1.32524e17i	0.272116	+	0.272116i	−0.557835	+	0.829952i	$0.688368\pi$
$888$	4.79343e16	−	4.79343e16i	0.0977617	−	0.0977617i
$889$	−2.67114e17	−	2.67114e17i	−0.541111	−	0.541111i
$890$	5.41054e16			0.108868
$891$	1.72667e17	+	1.72667e17i	0.345099	+	0.345099i
$892$		−	1.77042e17i		−	0.351470i
$893$	−6.23234e17			−1.22897
$894$	−7.96361e16			−0.155986
$895$	1.71752e16			0.0334167
$896$	−3.74201e17	+	3.74201e17i	−0.723197	+	0.723197i
$897$	8.42407e17	−	8.42407e17i	1.61721	−	1.61721i
$898$		−	1.75246e16i		−	0.0334188i
$899$	−5.99752e17	+	4.79425e17i	−1.13609	+	0.908159i
$900$	4.76324e17			0.896288
$901$	1.60738e17	+	1.60738e17i	0.300449	+	0.300449i
$902$	3.89595e16	+	3.89595e16i	0.0723392	+	0.0723392i
$903$			1.32708e18i			2.44777i
$904$		−	1.53612e17i		−	0.281459i
$905$		−	2.33897e17i		−	0.425728i
$906$	1.97174e17			0.356517
$907$	−5.25673e17	+	5.25673e17i	−0.944216	+	0.944216i	−0.998524	−	0.0543078i	$-0.982705\pi$
$907$	−5.25673e17	+	5.25673e17i	−0.944216	+	0.944216i	0.0543078	+	0.998524i	$0.482705\pi$
$908$		−	8.38135e17i		−	1.49554i
$909$	−2.33150e17	+	2.33150e17i	−0.413287	+	0.413287i
$910$	7.95724e16	+	7.95724e16i	0.140124	+	0.140124i
$911$	−4.47701e17	+	4.47701e17i	−0.783209	+	0.783209i	−0.980371	−	0.197162i	$-0.936827\pi$
$911$	−4.47701e17	+	4.47701e17i	−0.783209	+	0.783209i	0.197162	+	0.980371i	$0.436827\pi$
$912$		−	6.26664e17i		−	1.08910i
$913$	3.73944e17	+	3.73944e17i	0.645628	+	0.645628i
$914$	−4.97239e16	+	4.97239e16i	−0.0852880	+	0.0852880i
$915$	−4.40715e16			−0.0750985
$916$	3.49713e16	+	3.49713e16i	0.0592024	+	0.0592024i
$917$	−6.80718e16	+	6.80718e16i	−0.114486	+	0.114486i
$918$	1.81771e16	+	1.81771e16i	0.0303717	+	0.0303717i
$919$	−2.67327e17			−0.443761			−0.221880	−	0.975074i	$-0.571219\pi$
$919$	−2.67327e17			−0.443761			−0.221880	+	0.975074i	$0.571219\pi$
$920$	−9.98485e16	−	9.98485e16i	−0.164670	−	0.164670i
$921$		−	1.68787e18i		−	2.76555i
$922$	−1.56642e17			−0.254989
$923$	1.50100e17			0.242756
$924$	−6.10340e17			−0.980709
$925$	−6.46983e16	+	6.46983e16i	−0.103286	+	0.103286i
$926$	8.96346e16	−	8.96346e16i	0.142171	−	0.142171i
$927$		−	6.61000e17i		−	1.04165i
$928$	−3.66770e17	+	2.93185e17i	−0.574257	+	0.459044i
$929$	3.21756e17			0.500532			0.250266	−	0.968177i	$-0.419482\pi$
$929$	3.21756e17			0.500532			0.250266	+	0.968177i	$0.419482\pi$
$930$	−1.14446e17	−	1.14446e17i	−0.176889	−	0.176889i
$931$	1.33532e17	+	1.33532e17i	0.205063	+	0.205063i
$932$			7.54592e17i			1.15137i
$933$		−	6.79287e17i		−	1.02982i
$934$		−	2.17741e17i		−	0.327989i
$935$	1.03523e17			0.154942
$936$	4.38461e17	−	4.38461e17i	0.652042	−	0.652042i
$937$		−	3.14076e17i		−	0.464084i	−0.972706	−	0.232042i	$-0.925459\pi$
$937$		−	3.14076e17i		−	0.464084i	0.972706	−	0.232042i	$-0.0745407\pi$
$938$	1.96879e17	−	1.96879e17i	0.289056	−	0.289056i
$939$	−1.31107e17	−	1.31107e17i	−0.191263	−	0.191263i
$940$	2.53885e17	−	2.53885e17i	0.368019	−	0.368019i
$941$		−	9.74771e17i		−	1.40399i	−0.712181	−	0.701996i	$-0.752292\pi$
$941$		−	9.74771e17i		−	1.40399i	0.712181	−	0.701996i	$-0.247708\pi$
$942$	1.82269e17	+	1.82269e17i	0.260859	+	0.260859i
$943$	3.11475e17	−	3.11475e17i	0.442949	−	0.442949i
$944$	6.74254e17			0.952778
$945$	−6.78575e16	−	6.78575e16i	−0.0952812	−	0.0952812i
$946$	−1.24455e17	+	1.24455e17i	−0.173646	+	0.173646i
$947$	6.52968e17	+	6.52968e17i	0.905299	+	0.905299i	0.995888	−	0.0905891i	$-0.0288750\pi$
$947$	6.52968e17	+	6.52968e17i	0.905299	+	0.905299i	−0.0905891	+	0.995888i	$0.528875\pi$
$948$	−3.16599e17			−0.436174
$949$	−8.84418e17	−	8.84418e17i	−1.21077	−	1.21077i
$950$		−	1.52651e17i		−	0.207663i
$951$	−6.33159e17			−0.855913
$952$	2.56732e17			0.344872
$953$	−2.24558e17			−0.299758			−0.149879	−	0.988704i	$-0.547888\pi$
$953$	−2.24558e17			−0.299758			−0.149879	+	0.988704i	$0.547888\pi$
$954$	1.26191e17	−	1.26191e17i	0.167394	−	0.167394i
$955$	3.21962e17	−	3.21962e17i	0.424409	−	0.424409i
$956$		−	1.04202e18i		−	1.36499i
$957$	−7.06368e17	−	7.87597e16i	−0.919517	−	0.102526i
$958$	1.98219e17			0.256420
$959$	3.34998e17	+	3.34998e17i	0.430656	+	0.430656i
$960$	2.05554e17	+	2.05554e17i	0.262602	+	0.262602i
$961$			8.78606e17i			1.11546i
$962$			5.72825e16i			0.0722722i
$963$			1.74284e18i			2.18524i
$964$	4.86167e17			0.605792
$965$	−1.15350e17	+	1.15350e17i	−0.142841	+	0.142841i
$966$		−	3.87240e17i		−	0.476560i
$967$	4.88740e17	−	4.88740e17i	0.597749	−	0.597749i	−0.341964	−	0.939713i	$-0.611092\pi$
$967$	4.88740e17	−	4.88740e17i	0.597749	−	0.597749i	0.939713	+	0.341964i	$0.111092\pi$
$968$	1.84871e17	+	1.84871e17i	0.224707	+	0.224707i
$969$	−4.68739e17	+	4.68739e17i	−0.566224	+	0.566224i
$970$			7.11909e16i			0.0854661i
$971$	−8.90277e17	−	8.90277e17i	−1.06221	−	1.06221i	−0.997932	−	0.0642765i	$-0.979526\pi$
$971$	−8.90277e17	−	8.90277e17i	−1.06221	−	1.06221i	−0.0642765	−	0.997932i	$-0.520474\pi$
$972$	7.88629e17	−	7.88629e17i	0.935136	−	0.935136i
$973$	−1.04017e18			−1.22582
$974$	−2.96459e17	−	2.96459e17i	−0.347225	−	0.347225i
$975$	−1.09093e18	+	1.09093e18i	−1.26990	+	1.26990i
$976$	5.67929e16	+	5.67929e16i	0.0657045	+	0.0657045i
$977$	−6.18121e17			−0.710733			−0.355366	−	0.934727i	$-0.615644\pi$
$977$	−6.18121e17			−0.710733			−0.355366	+	0.934727i	$0.615644\pi$
$978$	3.29771e17	+	3.29771e17i	0.376860	+	0.376860i
$979$		−	5.15615e17i		−	0.585638i
$980$	−1.08793e17			−0.122813
$981$	−1.03516e18			−1.16143
$982$	−3.50527e17			−0.390889
$983$	−4.75875e17	+	4.75875e17i	−0.527439	+	0.527439i	−0.919808	−	0.392369i	$-0.871656\pi$
$983$	−4.75875e17	+	4.75875e17i	−0.527439	+	0.527439i	0.392369	+	0.919808i	$0.371656\pi$
$984$	2.98849e17	−	2.98849e17i	0.329216	−	0.329216i
$985$			5.47735e17i			0.599726i
$986$	1.42892e17	+	1.59324e16i	0.155506	+	0.0173388i
$987$	2.04742e18			2.21464
$988$	8.51532e17	+	8.51532e17i	0.915502	+	0.915502i
$989$	9.94996e17	+	9.94996e17i	1.06327	+	1.06327i
$990$		−	8.12734e16i		−	0.0863251i
$991$		−	1.82069e18i		−	1.92218i	−0.276227	−	0.961092i	$-0.589084\pi$
$991$		−	1.82069e18i		−	1.92218i	0.276227	−	0.961092i	$-0.410916\pi$
$992$			1.01898e18i			1.06929i
$993$	2.39013e18			2.49302
$994$	3.44992e16	−	3.44992e16i	0.0357676	−	0.0357676i
$995$		−	2.73267e17i		−	0.281611i
$996$	1.37948e18	−	1.37948e18i	1.41306	−	1.41306i
$997$	−3.09593e17	−	3.09593e17i	−0.315225	−	0.315225i	0.531705	−	0.846930i	$-0.321552\pi$
$997$	−3.09593e17	−	3.09593e17i	−0.315225	−	0.315225i	−0.846930	+	0.531705i	$0.821552\pi$
$998$	6.19761e16	−	6.19761e16i	0.0627250	−	0.0627250i
$999$		−	4.88492e16i		−	0.0491433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.13	✓	58
29.17	odd	4	inner	29.13.c.a.17.13	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.13	✓	58	1.1	even	1	trivial
29.13.c.a.17.13	yes	58	29.17	odd	4	inner

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.2710 - 12.2710i) q^{2} +(762.089 + 762.089i) q^{3} -3794.84i q^{4} -6703.86i q^{5} -18703.2i q^{6} -134602. q^{7} +(-96828.8 + 96828.8i) q^{8} +630118. i q^{9} +O(q^{10})\)	\(q+(-12.2710 - 12.2710i) q^{2} +(762.089 + 762.089i) q^{3} -3794.84i q^{4} -6703.86i q^{5} -18703.2i q^{6} -134602. q^{7} +(-96828.8 + 96828.8i) q^{8} +630118. i q^{9} +(-82263.3 + 82263.3i) q^{10} +(783954. + 783954. i) q^{11} +(2.89201e6 - 2.89201e6i) q^{12} +7.18629e6i q^{13} +(1.65171e6 + 1.65171e6i) q^{14} +(5.10894e6 - 5.10894e6i) q^{15} -1.31673e7 q^{16} +(9.84902e6 + 9.84902e6i) q^{17} +(7.73220e6 - 7.73220e6i) q^{18} +(3.12250e7 + 3.12250e7i) q^{19} -2.54401e7 q^{20} +(-1.02579e8 - 1.02579e8i) q^{21} -1.92398e7i q^{22} -1.53820e8 q^{23} -1.47584e8 q^{24} +1.99199e8 q^{25} +(8.81831e7 - 8.81831e7i) q^{26} +(-7.52006e7 + 7.52006e7i) q^{27} +5.10794e8i q^{28} +(-6.59140e7 + 5.91160e8i) q^{29} -1.25384e8 q^{30} +(9.12762e8 + 9.12762e8i) q^{31} +(5.58187e8 + 5.58187e8i) q^{32} +1.19489e9i q^{33} -2.41715e8i q^{34} +9.02354e8i q^{35} +2.39120e9 q^{36} +(-3.24793e8 + 3.24793e8i) q^{37} -7.66326e8i q^{38} +(-5.47659e9 + 5.47659e9i) q^{39} +(6.49127e8 + 6.49127e8i) q^{40} +(-2.02494e9 + 2.02494e9i) q^{41} +2.51749e9i q^{42} +(-6.46858e9 - 6.46858e9i) q^{43} +(2.97498e9 - 2.97498e9i) q^{44} +4.22422e9 q^{45} +(1.88753e9 + 1.88753e9i) q^{46} +(-9.97973e9 + 9.97973e9i) q^{47} +(-1.00347e10 - 1.00347e10i) q^{48} +4.27644e9 q^{49} +(-2.44438e9 - 2.44438e9i) q^{50} +1.50117e10i q^{51} +2.72708e10 q^{52} +1.63202e10 q^{53} +1.84558e9 q^{54} +(5.25552e9 - 5.25552e9i) q^{55} +(1.30334e10 - 1.30334e10i) q^{56} +4.75924e10i q^{57} +(8.06297e9 - 6.44531e9i) q^{58} -5.12067e10 q^{59} +(-1.93876e10 - 1.93876e10i) q^{60} +(-4.31317e9 - 4.31317e9i) q^{61} -2.24011e10i q^{62} -8.48152e10i q^{63} +4.02342e10i q^{64} +4.81759e10 q^{65} +(1.46625e10 - 1.46625e10i) q^{66} -1.19197e11i q^{67} +(3.73755e10 - 3.73755e10i) q^{68} +(-1.17224e11 - 1.17224e11i) q^{69} +(1.10728e10 - 1.10728e10i) q^{70} -2.08870e10i q^{71} +(-6.10135e10 - 6.10135e10i) q^{72} +(-1.23070e11 + 1.23070e11i) q^{73} +7.97108e9 q^{74} +(1.51807e11 + 1.51807e11i) q^{75} +(1.18494e11 - 1.18494e11i) q^{76} +(-1.05522e11 - 1.05522e11i) q^{77} +1.34407e11 q^{78} +(-5.47369e10 - 5.47369e10i) q^{79} +8.82718e10i q^{80} +2.20251e11 q^{81} +4.96961e10 q^{82} +4.76998e11 q^{83} +(-3.89270e11 + 3.89270e11i) q^{84} +(6.60265e10 - 6.60265e10i) q^{85} +1.58752e11i q^{86} +(-5.00749e11 + 4.00284e11i) q^{87} -1.51819e11 q^{88} +(-3.28855e11 - 3.28855e11i) q^{89} +(-5.18356e10 - 5.18356e10i) q^{90} -9.67289e11i q^{91} +5.83722e11i q^{92} +1.39121e12i q^{93} +2.44923e11 q^{94} +(2.09328e11 - 2.09328e11i) q^{95} +8.50776e11i q^{96} +(4.32702e11 - 4.32702e11i) q^{97} +(-5.24764e10 - 5.24764e10i) q^{98} +(-4.93983e11 + 4.93983e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} - 1957890 q^{10} + 4120990 q^{11} + 2920062 q^{12} - 1824520 q^{14} - 8383600 q^{15} - 133743512 q^{16} + 33971578 q^{17} - 122384158 q^{18} + 65838718 q^{19} - 59408388 q^{20} + 200896236 q^{21} + 104539676 q^{23} + 163907064 q^{24} - 3086882294 q^{25} + 607848030 q^{26} - 1190867840 q^{27} + 817714294 q^{29} + 5793833612 q^{30} - 1059975938 q^{31} + 2323254598 q^{32} + 517001400 q^{36} - 864725342 q^{37} + 18048639408 q^{39} - 22547920086 q^{40} - 17292603926 q^{41} - 3344004962 q^{43} - 53750811886 q^{44} - 16067938640 q^{45} + 43310099300 q^{46} - 15159905282 q^{47} - 4602803862 q^{48} + 32036753022 q^{49} - 16057299278 q^{50} + 81167587800 q^{52} - 69552844564 q^{53} + 38996274808 q^{54} + 3944882736 q^{55} - 156397031424 q^{56} + 107434998568 q^{58} + 82613255468 q^{59} - 147410252946 q^{60} + 128229759922 q^{61} + 125938412928 q^{65} + 364716671994 q^{66} - 141670411468 q^{68} + 529640675916 q^{69} + 518962441956 q^{70} - 180699442320 q^{72} - 428225274062 q^{73} + 307721180948 q^{74} - 617987210610 q^{75} - 455232145048 q^{76} - 963484794004 q^{77} + 688403957040 q^{78} - 183006289538 q^{79} + 1001949265154 q^{81} - 1176460419184 q^{82} + 361042835756 q^{83} - 402324805420 q^{84} + 832273178976 q^{85} - 1065344596322 q^{87} - 1836857960940 q^{88} + 1922736257242 q^{89} - 1170237151648 q^{90} - 2759662014220 q^{94} + 5518358548560 q^{95} + 1356111950818 q^{97} - 2518255928616 q^{98} + 3259343912178 q^{99}+O(q^{100}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8 - 1957890 * q^10 + 4120990 * q^11 + 2920062 * q^12 - 1824520 * q^14 - 8383600 * q^15 - 133743512 * q^16 + 33971578 * q^17 - 122384158 * q^18 + 65838718 * q^19 - 59408388 * q^20 + 200896236 * q^21 + 104539676 * q^23 + 163907064 * q^24 - 3086882294 * q^25 + 607848030 * q^26 - 1190867840 * q^27 + 817714294 * q^29 + 5793833612 * q^30 - 1059975938 * q^31 + 2323254598 * q^32 + 517001400 * q^36 - 864725342 * q^37 + 18048639408 * q^39 - 22547920086 * q^40 - 17292603926 * q^41 - 3344004962 * q^43 - 53750811886 * q^44 - 16067938640 * q^45 + 43310099300 * q^46 - 15159905282 * q^47 - 4602803862 * q^48 + 32036753022 * q^49 - 16057299278 * q^50 + 81167587800 * q^52 - 69552844564 * q^53 + 38996274808 * q^54 + 3944882736 * q^55 - 156397031424 * q^56 + 107434998568 * q^58 + 82613255468 * q^59 - 147410252946 * q^60 + 128229759922 * q^61 + 125938412928 * q^65 + 364716671994 * q^66 - 141670411468 * q^68 + 529640675916 * q^69 + 518962441956 * q^70 - 180699442320 * q^72 - 428225274062 * q^73 + 307721180948 * q^74 - 617987210610 * q^75 - 455232145048 * q^76 - 963484794004 * q^77 + 688403957040 * q^78 - 183006289538 * q^79 + 1001949265154 * q^81 - 1176460419184 * q^82 + 361042835756 * q^83 - 402324805420 * q^84 + 832273178976 * q^85 - 1065344596322 * q^87 - 1836857960940 * q^88 + 1922736257242 * q^89 - 1170237151648 * q^90 - 2759662014220 * q^94 + 5518358548560 * q^95 + 1356111950818 * q^97 - 2518255928616 * q^98 + 3259343912178 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more