LMFDB - Embedded newform 29.13.c.a.12.18

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			12.18
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(26.4284 + 26.4284i) q^{2} +(-670.941 - 670.941i) q^{3} -2699.08i q^{4} +5810.81i q^{5} -35463.8i q^{6} -231201. q^{7} +(179583. - 179583. i) q^{8} +368882. i q^{9} +O(q^{10})$	\(q+(26.4284 + 26.4284i) q^{2} +(-670.941 - 670.941i) q^{3} -2699.08i q^{4} +5810.81i q^{5} -35463.8i q^{6} -231201. q^{7} +(179583. - 179583. i) q^{8} +368882. i q^{9} +(-153570. + 153570. i) q^{10} +(-790605. - 790605. i) q^{11} +(-1.81092e6 + 1.81092e6i) q^{12} -3.64967e6i q^{13} +(-6.11026e6 - 6.11026e6i) q^{14} +(3.89871e6 - 3.89871e6i) q^{15} -1.56326e6 q^{16} +(2.47419e7 + 2.47419e7i) q^{17} +(-9.74895e6 + 9.74895e6i) q^{18} +(2.06204e7 + 2.06204e7i) q^{19} +1.56838e7 q^{20} +(1.55122e8 + 1.55122e8i) q^{21} -4.17888e7i q^{22} -4.83747e7 q^{23} -2.40979e8 q^{24} +2.10375e8 q^{25} +(9.64549e7 - 9.64549e7i) q^{26} +(-1.09068e8 + 1.09068e8i) q^{27} +6.24029e8i q^{28} +(-1.75902e8 + 5.68219e8i) q^{29} +2.06073e8 q^{30} +(-5.08915e8 - 5.08915e8i) q^{31} +(-7.76886e8 - 7.76886e8i) q^{32} +1.06090e9i q^{33} +1.30778e9i q^{34} -1.34346e9i q^{35} +9.95642e8 q^{36} +(1.58184e9 - 1.58184e9i) q^{37} +1.08993e9i q^{38} +(-2.44871e9 + 2.44871e9i) q^{39} +(1.04352e9 + 1.04352e9i) q^{40} +(-3.72552e9 + 3.72552e9i) q^{41} +8.19924e9i q^{42} +(7.90746e9 + 7.90746e9i) q^{43} +(-2.13391e9 + 2.13391e9i) q^{44} -2.14350e9 q^{45} +(-1.27846e9 - 1.27846e9i) q^{46} +(-2.13073e9 + 2.13073e9i) q^{47} +(1.04886e9 + 1.04886e9i) q^{48} +3.96125e10 q^{49} +(5.55987e9 + 5.55987e9i) q^{50} -3.32007e10i q^{51} -9.85076e9 q^{52} -1.61600e10 q^{53} -5.76496e9 q^{54} +(4.59406e9 - 4.59406e9i) q^{55} +(-4.15197e10 + 4.15197e10i) q^{56} -2.76702e10i q^{57} +(-1.96659e10 + 1.03683e10i) q^{58} +1.21696e10 q^{59} +(-1.05229e10 - 1.05229e10i) q^{60} +(-2.09083e10 - 2.09083e10i) q^{61} -2.68996e10i q^{62} -8.52857e10i q^{63} -3.46606e10i q^{64} +2.12075e10 q^{65} +(-2.80378e10 + 2.80378e10i) q^{66} -9.32866e10i q^{67} +(6.67805e10 - 6.67805e10i) q^{68} +(3.24565e10 + 3.24565e10i) q^{69} +(3.55056e10 - 3.55056e10i) q^{70} +6.26401e10i q^{71} +(6.62449e10 + 6.62449e10i) q^{72} +(-9.95880e10 + 9.95880e10i) q^{73} +8.36109e10 q^{74} +(-1.41149e11 - 1.41149e11i) q^{75} +(5.56562e10 - 5.56562e10i) q^{76} +(1.82788e11 + 1.82788e11i) q^{77} -1.29431e11 q^{78} +(-2.55215e11 - 2.55215e11i) q^{79} -9.08381e9i q^{80} +3.42395e11 q^{81} -1.96919e11 q^{82} -5.07541e11 q^{83} +(4.18687e11 - 4.18687e11i) q^{84} +(-1.43771e11 + 1.43771e11i) q^{85} +4.17963e11i q^{86} +(4.99261e11 - 2.63222e11i) q^{87} -2.83959e11 q^{88} +(5.30413e10 + 5.30413e10i) q^{89} +(-5.66493e10 - 5.66493e10i) q^{90} +8.43806e11i q^{91} +1.30567e11i q^{92} +6.82904e11i q^{93} -1.12623e11 q^{94} +(-1.19821e11 + 1.19821e11i) q^{95} +1.04249e12i q^{96} +(8.40519e10 - 8.40519e10i) q^{97} +(1.04689e12 + 1.04689e12i) q^{98} +(2.91640e11 - 2.91640e11i) 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 $

$2$	26.4284	+	26.4284i	0.412943	+	0.412943i	0.882763	−	0.469819i	$-0.155681\pi$
$2$	26.4284	+	26.4284i	0.412943	+	0.412943i	−0.469819	+	0.882763i	$0.655681\pi$
$3$	−670.941	−	670.941i	−0.920358	−	0.920358i	0.0766968	−	0.997054i	$-0.475563\pi$
$3$	−670.941	−	670.941i	−0.920358	−	0.920358i	−0.997054	+	0.0766968i	$0.975563\pi$
$4$		−	2699.08i		−	0.658955i
$5$			5810.81i			0.371892i	0.982560	+	0.185946i	$0.0595349\pi$
$5$			5810.81i			0.371892i	−0.982560	+	0.185946i	$0.940465\pi$
$6$		−	35463.8i		−	0.760111i
$7$	−231201.			−1.96517			−0.982587	−	0.185805i	$-0.940511\pi$
$7$	−231201.			−1.96517			−0.982587	+	0.185805i	$0.940511\pi$
$8$	179583.	−	179583.i	0.685055	−	0.685055i
$9$			368882.i			0.694116i
$10$	−153570.	+	153570.i	−0.153570	+	0.153570i
$11$	−790605.	−	790605.i	−0.446276	−	0.446276i	0.447838	−	0.894115i	$-0.352194\pi$
$11$	−790605.	−	790605.i	−0.446276	−	0.446276i	−0.894115	+	0.447838i	$0.852194\pi$
$12$	−1.81092e6	+	1.81092e6i	−0.606475	+	0.606475i
$13$		−	3.64967e6i		−	0.756125i	−0.925780	−	0.378062i	$-0.876590\pi$
$13$		−	3.64967e6i		−	0.756125i	0.925780	−	0.378062i	$-0.123410\pi$
$14$	−6.11026e6	−	6.11026e6i	−0.811505	−	0.811505i
$15$	3.89871e6	−	3.89871e6i	0.342273	−	0.342273i
$16$	−1.56326e6			−0.0931776
$17$	2.47419e7	+	2.47419e7i	1.02504	+	1.02504i	0.999678	+	0.0253600i	$0.00807320\pi$
$17$	2.47419e7	+	2.47419e7i	1.02504	+	1.02504i	0.0253600	+	0.999678i	$0.491927\pi$
$18$	−9.74895e6	+	9.74895e6i	−0.286631	+	0.286631i
$19$	2.06204e7	+	2.06204e7i	0.438305	+	0.438305i	0.891441	−	0.453136i	$-0.149695\pi$
$19$	2.06204e7	+	2.06204e7i	0.438305	+	0.438305i	−0.453136	+	0.891441i	$0.649695\pi$
$20$	1.56838e7			0.245060
$21$	1.55122e8	+	1.55122e8i	1.80866	+	1.80866i
$22$		−	4.17888e7i		−	0.368574i
$23$	−4.83747e7			−0.326777			−0.163388	−	0.986562i	$-0.552242\pi$
$23$	−4.83747e7			−0.326777			−0.163388	+	0.986562i	$0.552242\pi$
$24$	−2.40979e8			−1.26099
$25$	2.10375e8			0.861696
$26$	9.64549e7	−	9.64549e7i	0.312237	−	0.312237i
$27$	−1.09068e8	+	1.09068e8i	−0.281522	+	0.281522i
$28$			6.24029e8i			1.29496i
$29$	−1.75902e8	+	5.68219e8i	−0.295721	+	0.955274i
$29$	−1.75902e8	+	5.68219e8i	−0.295721	+	0.955274i
$30$	2.06073e8			0.282679
$31$	−5.08915e8	−	5.08915e8i	−0.573423	−	0.573423i	0.359660	−	0.933083i	$-0.382893\pi$
$31$	−5.08915e8	−	5.08915e8i	−0.573423	−	0.573423i	−0.933083	+	0.359660i	$0.882893\pi$
$32$	−7.76886e8	−	7.76886e8i	−0.723532	−	0.723532i
$33$			1.06090e9i			0.821467i
$34$			1.30778e9i			0.846566i
$35$		−	1.34346e9i		−	0.730832i
$36$	9.95642e8			0.457392
$37$	1.58184e9	−	1.58184e9i	0.616527	−	0.616527i	−0.328112	−	0.944639i	$-0.606412\pi$
$37$	1.58184e9	−	1.58184e9i	0.616527	−	0.616527i	0.944639	+	0.328112i	$0.106412\pi$
$38$			1.08993e9i			0.361990i
$39$	−2.44871e9	+	2.44871e9i	−0.695905	+	0.695905i
$40$	1.04352e9	+	1.04352e9i	0.254766	+	0.254766i
$41$	−3.72552e9	+	3.72552e9i	−0.784303	+	0.784303i	−0.980554	−	0.196250i	$-0.937123\pi$
$41$	−3.72552e9	+	3.72552e9i	−0.784303	+	0.784303i	0.196250	+	0.980554i	$0.437123\pi$
$42$			8.19924e9i			1.49375i
$43$	7.90746e9	+	7.90746e9i	1.25091	+	1.25091i	0.955313	+	0.295598i	$0.0955187\pi$
$43$	7.90746e9	+	7.90746e9i	1.25091	+	1.25091i	0.295598	+	0.955313i	$0.404481\pi$
$44$	−2.13391e9	+	2.13391e9i	−0.294076	+	0.294076i
$45$	−2.14350e9			−0.258136
$46$	−1.27846e9	−	1.27846e9i	−0.134940	−	0.134940i
$47$	−2.13073e9	+	2.13073e9i	−0.197670	+	0.197670i	−0.799000	−	0.601331i	$-0.794638\pi$
$47$	−2.13073e9	+	2.13073e9i	−0.197670	+	0.197670i	0.601331	+	0.799000i	$0.294638\pi$
$48$	1.04886e9	+	1.04886e9i	0.0857567	+	0.0857567i
$49$	3.96125e10			2.86191
$50$	5.55987e9	+	5.55987e9i	0.355832	+	0.355832i
$51$		−	3.32007e10i		−	1.88680i
$52$	−9.85076e9			−0.498253
$53$	−1.61600e10			−0.729099			−0.364549	−	0.931184i	$-0.618777\pi$
$53$	−1.61600e10			−0.729099			−0.364549	+	0.931184i	$0.618777\pi$
$54$	−5.76496e9			−0.232506
$55$	4.59406e9	−	4.59406e9i	0.165966	−	0.165966i
$56$	−4.15197e10	+	4.15197e10i	−1.34625	+	1.34625i
$57$		−	2.76702e10i		−	0.806794i
$58$	−1.96659e10	+	1.03683e10i	−0.516590	+	0.272358i
$59$	1.21696e10			0.288513			0.144256	−	0.989540i	$-0.453921\pi$
$59$	1.21696e10			0.288513			0.144256	+	0.989540i	$0.453921\pi$
$60$	−1.05229e10	−	1.05229e10i	−0.225543	−	0.225543i
$61$	−2.09083e10	−	2.09083e10i	−0.405825	−	0.405825i	0.474455	−	0.880280i	$-0.342645\pi$
$61$	−2.09083e10	−	2.09083e10i	−0.405825	−	0.405825i	−0.880280	+	0.474455i	$0.842645\pi$
$62$		−	2.68996e10i		−	0.473583i
$63$		−	8.52857e10i		−	1.36406i
$64$		−	3.46606e10i		−	0.504378i
$65$	2.12075e10			0.281197
$66$	−2.80378e10	+	2.80378e10i	−0.339220	+	0.339220i
$67$		−	9.32866e10i		−	1.03127i	−0.856810	−	0.515633i	$-0.827557\pi$
$67$		−	9.32866e10i		−	1.03127i	0.856810	−	0.515633i	$-0.172443\pi$
$68$	6.67805e10	−	6.67805e10i	0.675455	−	0.675455i
$69$	3.24565e10	+	3.24565e10i	0.300751	+	0.300751i
$70$	3.55056e10	−	3.55056e10i	0.301792	−	0.301792i
$71$			6.26401e10i			0.488993i	0.969650	+	0.244496i	$0.0786226\pi$
$71$			6.26401e10i			0.488993i	−0.969650	+	0.244496i	$0.921377\pi$
$72$	6.62449e10	+	6.62449e10i	0.475508	+	0.475508i
$73$	−9.95880e10	+	9.95880e10i	−0.658067	+	0.658067i	−0.954922	−	0.296856i	$-0.904062\pi$
$73$	−9.95880e10	+	9.95880e10i	−0.658067	+	0.658067i	0.296856	+	0.954922i	$0.404062\pi$
$74$	8.36109e10			0.509182
$75$	−1.41149e11	−	1.41149e11i	−0.793069	−	0.793069i
$76$	5.56562e10	−	5.56562e10i	0.288823	−	0.288823i
$77$	1.82788e11	+	1.82788e11i	0.877010	+	0.877010i
$78$	−1.29431e11			−0.574739
$79$	−2.55215e11	−	2.55215e11i	−1.04989	−	1.04989i	−0.998688	−	0.0512023i	$-0.983695\pi$
$79$	−2.55215e11	−	2.55215e11i	−1.04989	−	1.04989i	−0.0512023	−	0.998688i	$-0.516305\pi$
$80$		−	9.08381e9i		−	0.0346520i
$81$	3.42395e11			1.21232
$82$	−1.96919e11			−0.647746
$83$	−5.07541e11			−1.55240			−0.776199	−	0.630488i	$-0.782855\pi$
$83$	−5.07541e11			−1.55240			−0.776199	+	0.630488i	$0.782855\pi$
$84$	4.18687e11	−	4.18687e11i	1.19183	−	1.19183i
$85$	−1.43771e11	+	1.43771e11i	−0.381203	+	0.381203i
$86$			4.17963e11i			1.03311i
$87$	4.99261e11	−	2.63222e11i	1.15136	−	0.607025i
$88$	−2.83959e11			−0.611447
$89$	5.30413e10	+	5.30413e10i	0.106727	+	0.106727i	0.758454	−	0.651727i	$-0.225955\pi$
$89$	5.30413e10	+	5.30413e10i	0.106727	+	0.106727i	−0.651727	+	0.758454i	$0.725955\pi$
$90$	−5.66493e10	−	5.66493e10i	−0.106596	−	0.106596i
$91$			8.43806e11i			1.48592i
$92$			1.30567e11i			0.215331i
$93$			6.82904e11i			1.05551i
$94$	−1.12623e11			−0.163253
$95$	−1.19821e11	+	1.19821e11i	−0.163002	+	0.163002i
$96$			1.04249e12i			1.33182i
$97$	8.40519e10	−	8.40519e10i	0.100906	−	0.100906i	−0.654852	−	0.755758i	$-0.727269\pi$
$97$	8.40519e10	−	8.40519e10i	0.100906	−	0.100906i	0.755758	+	0.654852i	$0.227269\pi$
$98$	1.04689e12	+	1.04689e12i	1.18181	+	1.18181i
$99$	2.91640e11	−	2.91640e11i	0.309768	−	0.309768i
$100$		−	5.67820e11i		−	0.567820i
$101$	−3.32945e11	−	3.32945e11i	−0.313649	−	0.313649i	0.532672	−	0.846322i	$-0.321188\pi$
$101$	−3.32945e11	−	3.32945e11i	−0.313649	−	0.313649i	−0.846322	+	0.532672i	$0.821188\pi$
$102$	8.77442e11	−	8.77442e11i	0.779143	−	0.779143i
$103$	6.10492e11			0.511277			0.255639	−	0.966772i	$-0.417714\pi$
$103$	6.10492e11			0.511277			0.255639	+	0.966772i	$0.417714\pi$
$104$	−6.55419e11	−	6.55419e11i	−0.517987	−	0.517987i
$105$	−9.01384e11	+	9.01384e11i	−0.672627	+	0.672627i
$106$	−4.27083e11	−	4.27083e11i	−0.301077	−	0.301077i
$107$	−2.60490e11			−0.173576			−0.0867879	−	0.996227i	$-0.527660\pi$
$107$	−2.60490e11			−0.173576			−0.0867879	+	0.996227i	$0.527660\pi$
$108$	2.94382e11	+	2.94382e11i	0.185511	+	0.185511i
$109$			1.06109e12i			0.632694i	0.948644	+	0.316347i	$0.102456\pi$
$109$			1.06109e12i			0.632694i	−0.948644	+	0.316347i	$0.897544\pi$
$110$	2.42827e11			0.137069
$111$	−2.12264e12			−1.13485
$112$	3.61427e11			0.183110
$113$	−1.79466e12	+	1.79466e12i	−0.862007	+	0.862007i	−0.991571	−	0.129564i	$-0.958642\pi$
$113$	−1.79466e12	+	1.79466e12i	−0.862007	+	0.862007i	0.129564	+	0.991571i	$0.458642\pi$
$114$	7.31278e11	−	7.31278e11i	0.333160	−	0.333160i
$115$		−	2.81096e11i		−	0.121526i
$116$	1.53367e12	+	4.74773e11i	0.629483	+	0.194867i
$117$	1.34630e12			0.524839
$118$	3.21623e11	+	3.21623e11i	0.119139	+	0.119139i
$119$	−5.72035e12	−	5.72035e12i	−2.01438	−	2.01438i
$120$		−	1.40028e12i		−	0.468952i
$121$		−	1.88831e12i		−	0.601675i
$122$		−	1.10514e12i		−	0.335166i
$123$	4.99921e12			1.44368
$124$	−1.37360e12	+	1.37360e12i	−0.377860	+	0.377860i
$125$			2.64110e12i			0.692350i
$126$	2.25396e12	−	2.25396e12i	0.563279	−	0.563279i
$127$	3.05157e12	+	3.05157e12i	0.727279	+	0.727279i	0.970077	−	0.242798i	$-0.0780651\pi$
$127$	3.05157e12	+	3.05157e12i	0.727279	+	0.727279i	−0.242798	+	0.970077i	$0.578065\pi$
$128$	−2.26610e12	+	2.26610e12i	−0.515252	+	0.515252i
$129$		−	1.06109e13i		−	2.30257i
$130$	5.60481e11	+	5.60481e11i	0.116118	+	0.116118i
$131$	−4.72978e12	+	4.72978e12i	−0.935864	+	0.935864i	−0.998064	−	0.0621997i	$-0.980188\pi$
$131$	−4.72978e12	+	4.72978e12i	−0.935864	+	0.935864i	0.0621997	+	0.998064i	$0.480188\pi$
$132$	2.86345e12			0.541310
$133$	−4.76746e12	−	4.76746e12i	−0.861345	−	0.861345i
$134$	2.46542e12	−	2.46542e12i	0.425855	−	0.425855i
$135$	−6.33771e11	−	6.33771e11i	−0.104696	−	0.104696i
$136$	8.88646e12			1.40441
$137$	8.04267e12	+	8.04267e12i	1.21640	+	1.21640i	0.968883	+	0.247519i	$0.0796152\pi$
$137$	8.04267e12	+	8.04267e12i	1.21640	+	1.21640i	0.247519	+	0.968883i	$0.420385\pi$
$138$			1.71555e12i			0.248387i
$139$	3.64322e12			0.505122			0.252561	−	0.967581i	$-0.418727\pi$
$139$	3.64322e12			0.505122			0.252561	+	0.967581i	$0.418727\pi$
$140$	−3.62612e12			−0.481586
$141$	2.85918e12			0.363854
$142$	−1.65548e12	+	1.65548e12i	−0.201926	+	0.201926i
$143$	−2.88545e12	+	2.88545e12i	−0.337440	+	0.337440i
$144$		−	5.76659e11i		−	0.0646761i
$145$	−3.30181e12	−	1.02213e12i	−0.355259	−	0.109976i
$146$	−5.26390e12			−0.543489
$147$	−2.65776e13	−	2.65776e13i	−2.63398	−	2.63398i
$148$	−4.26951e12	−	4.26951e12i	−0.406264	−	0.406264i
$149$		−	7.73334e12i		−	0.706724i	−0.935487	−	0.353362i	$-0.885038\pi$
$149$		−	7.73334e12i		−	0.706724i	0.935487	−	0.353362i	$-0.114962\pi$
$150$		−	7.46069e12i		−	0.654985i
$151$			1.22343e13i			1.03209i	0.856561	+	0.516046i	$0.172597\pi$
$151$			1.22343e13i			1.03209i	−0.856561	+	0.516046i	$0.827403\pi$
$152$	7.40616e12			0.600526
$153$	−9.12685e12	+	9.12685e12i	−0.711496	+	0.711496i
$154$			9.66161e12i			0.724311i
$155$	2.95721e12	−	2.95721e12i	0.213251	−	0.213251i
$156$	6.60927e12	+	6.60927e12i	0.458571	+	0.458571i
$157$	−5.89776e12	+	5.89776e12i	−0.393812	+	0.393812i	−0.876044	−	0.482232i	$-0.839826\pi$
$157$	−5.89776e12	+	5.89776e12i	−0.393812	+	0.393812i	0.482232	+	0.876044i	$0.339826\pi$
$158$		−	1.34899e13i		−	0.867091i
$159$	1.08424e13	+	1.08424e13i	0.671031	+	0.671031i
$160$	4.51434e12	−	4.51434e12i	0.269076	−	0.269076i
$161$	1.11843e13			0.642173
$162$	9.04894e12	+	9.04894e12i	0.500619	+	0.500619i
$163$	−2.35446e13	+	2.35446e13i	−1.25535	+	1.25535i	−0.302064	+	0.953288i	$0.597676\pi$
$163$	−2.35446e13	+	2.35446e13i	−1.25535	+	1.25535i	−0.953288	+	0.302064i	$0.902324\pi$
$164$	1.00555e13	+	1.00555e13i	0.516821	+	0.516821i
$165$	−6.16468e12			−0.305497
$166$	−1.34135e13	−	1.34135e13i	−0.641052	−	0.641052i
$167$			3.50293e13i			1.61485i	0.589969	+	0.807426i	$0.299140\pi$
$167$			3.50293e13i			1.61485i	−0.589969	+	0.807426i	$0.700860\pi$
$168$	5.57145e13			2.47807
$169$	9.97799e12			0.428275
$170$	−7.59925e12			−0.314831
$171$	−7.60651e12	+	7.60651e12i	−0.304235	+	0.304235i
$172$	2.13429e13	−	2.13429e13i	0.824294	−	0.824294i
$173$			4.02186e13i			1.50020i	0.661322	+	0.750102i	$0.269996\pi$
$173$			4.02186e13i			1.50020i	−0.661322	+	0.750102i	$0.730004\pi$
$174$	2.01512e13	+	6.23814e12i	0.726115	+	0.224781i
$175$	−4.86389e13			−1.69338
$176$	1.23592e12	+	1.23592e12i	0.0415829	+	0.0415829i
$177$	−8.16509e12	−	8.16509e12i	−0.265535	−	0.265535i
$178$			2.80359e12i			0.0881444i
$179$		−	3.32587e13i		−	1.01108i	−0.862802	−	0.505542i	$-0.831293\pi$
$179$		−	3.32587e13i		−	1.01108i	0.862802	−	0.505542i	$-0.168707\pi$
$180$			5.78549e12i			0.170100i
$181$	5.16526e13			1.46900			0.734498	−	0.678611i	$-0.237418\pi$
$181$	5.16526e13			1.46900			0.734498	+	0.678611i	$0.237418\pi$
$182$	−2.23004e13	+	2.23004e13i	−0.613599	+	0.613599i
$183$			2.80564e13i			0.747009i
$184$	−8.68727e12	+	8.68727e12i	−0.223860	+	0.223860i
$185$	9.19177e12	+	9.19177e12i	0.229281	+	0.229281i
$186$	−1.80480e13	+	1.80480e13i	−0.435865	+	0.435865i
$187$		−	3.91222e13i		−	0.914900i
$188$	5.75100e12	+	5.75100e12i	0.130256	+	0.130256i
$189$	2.52165e13	−	2.52165e13i	0.553240	−	0.553240i
$190$	−6.33337e12			−0.134621
$191$	−5.24970e13	−	5.24970e13i	−1.08127	−	1.08127i	−0.996391	−	0.0848791i	$-0.972950\pi$
$191$	−5.24970e13	−	5.24970e13i	−1.08127	−	1.08127i	−0.0848791	−	0.996391i	$-0.527050\pi$
$192$	−2.32552e13	+	2.32552e13i	−0.464208	+	0.464208i
$193$	−2.53361e12	−	2.53361e12i	−0.0490226	−	0.0490226i	0.682171	−	0.731193i	$-0.261036\pi$
$193$	−2.53361e12	−	2.53361e12i	−0.0490226	−	0.0490226i	−0.731193	+	0.682171i	$0.761036\pi$
$194$	4.44271e12			0.0833369
$195$	−1.42290e13	−	1.42290e13i	−0.258801	−	0.258801i
$196$		−	1.06917e14i		−	1.88587i
$197$	−5.53799e13			−0.947446			−0.473723	−	0.880674i	$-0.657090\pi$
$197$	−5.53799e13			−0.947446			−0.473723	+	0.880674i	$0.657090\pi$
$198$	1.54151e13			0.255833
$199$	4.66551e13			0.751244			0.375622	−	0.926773i	$-0.377429\pi$
$199$	4.66551e13			0.751244			0.375622	+	0.926773i	$0.377429\pi$
$200$	3.77798e13	−	3.77798e13i	0.590309	−	0.590309i
$201$	−6.25898e13	+	6.25898e13i	−0.949133	+	0.949133i
$202$		−	1.75984e13i		−	0.259039i
$203$	4.06686e13	−	1.31373e14i	0.581143	−	1.87728i
$204$	−8.96115e13			−1.24332
$205$	−2.16483e13	−	2.16483e13i	−0.291676	−	0.291676i
$206$	1.61343e13	+	1.61343e13i	0.211129	+	0.211129i
$207$		−	1.78445e13i		−	0.226821i
$208$			5.70539e12i			0.0704539i
$209$		−	3.26053e13i		−	0.391210i
$210$	−4.76442e13			−0.555514
$211$	6.46978e13	−	6.46978e13i	0.733153	−	0.733153i	−0.238090	−	0.971243i	$-0.576521\pi$
$211$	6.46978e13	−	6.46978e13i	0.733153	−	0.733153i	0.971243	+	0.238090i	$0.0765214\pi$
$212$			4.36172e13i			0.480443i
$213$	4.20278e13	−	4.20278e13i	0.450048	−	0.450048i
$214$	−6.88434e12	−	6.88434e12i	−0.0716770	−	0.0716770i
$215$	−4.59487e13	+	4.59487e13i	−0.465203	+	0.465203i
$216$			3.91734e13i			0.385717i
$217$	1.17662e14	+	1.17662e14i	1.12688	+	1.12688i
$218$	−2.80429e13	+	2.80429e13i	−0.261267	+	0.261267i
$219$	1.33635e14			1.21131
$220$	−1.23997e13	−	1.23997e13i	−0.109364	−	0.109364i
$221$	9.02999e13	−	9.02999e13i	0.775057	−	0.775057i
$222$	−5.60980e13	−	5.60980e13i	−0.468629	−	0.468629i
$223$	−1.12608e14			−0.915671			−0.457835	−	0.889037i	$-0.651375\pi$
$223$	−1.12608e14			−0.915671			−0.457835	+	0.889037i	$0.651375\pi$
$224$	1.79617e14	+	1.79617e14i	1.42187	+	1.42187i
$225$			7.76036e13i			0.598118i
$226$	−9.48597e13			−0.711920
$227$	−1.57157e12			−0.0114862			−0.00574312	−	0.999984i	$-0.501828\pi$
$227$	−1.57157e12			−0.0114862			−0.00574312	+	0.999984i	$0.501828\pi$
$228$	−7.46841e13			−0.531642
$229$	−6.05781e13	+	6.05781e13i	−0.420052	+	0.420052i	−0.885221	−	0.465170i	$-0.845993\pi$
$229$	−6.05781e13	+	6.05781e13i	−0.420052	+	0.420052i	0.465170	+	0.885221i	$0.345993\pi$
$230$	7.42891e12	−	7.42891e12i	0.0501832	−	0.0501832i
$231$		−	2.45280e14i		−	1.61433i
$232$	7.04536e13	+	1.33632e14i	0.451830	+	0.857000i
$233$	5.22864e12			0.0326778			0.0163389	−	0.999867i	$-0.494799\pi$
$233$	5.22864e12			0.0326778			0.0163389	+	0.999867i	$0.494799\pi$
$234$	3.55805e13	+	3.55805e13i	0.216729	+	0.216729i
$235$	−1.23812e13	−	1.23812e13i	−0.0735118	−	0.0735118i
$236$		−	3.28468e13i		−	0.190117i
$237$			3.42469e14i			1.93255i
$238$		−	3.02359e14i		−	1.66365i
$239$	−7.33962e13			−0.393809			−0.196905	−	0.980423i	$-0.563089\pi$
$239$	−7.33962e13			−0.393809			−0.196905	+	0.980423i	$0.563089\pi$
$240$	−6.09470e12	+	6.09470e12i	−0.0318922	+	0.0318922i
$241$		−	1.09602e14i		−	0.559394i	−0.960088	−	0.279697i	$-0.909766\pi$
$241$		−	1.09602e14i		−	0.559394i	0.960088	−	0.279697i	$-0.0902341\pi$
$242$	4.99051e13	−	4.99051e13i	0.248458	−	0.248458i
$243$	−1.71764e14	−	1.71764e14i	−0.834245	−	0.834245i
$244$	−5.64332e13	+	5.64332e13i	−0.267421	+	0.267421i
$245$			2.30180e14i			1.06432i
$246$	1.32121e14	+	1.32121e14i	0.596158	+	0.596158i
$247$	7.52578e13	−	7.52578e13i	0.331413	−	0.331413i
$248$	−1.82785e14			−0.785653
$249$	3.40530e14	+	3.40530e14i	1.42876	+	1.42876i
$250$	−6.98001e13	+	6.98001e13i	−0.285901	+	0.285901i
$251$	8.45735e11	+	8.45735e11i	0.00338214	+	0.00338214i	0.708796	−	0.705414i	$-0.249239\pi$
$251$	8.45735e11	+	8.45735e11i	0.00338214	+	0.00338214i	−0.705414	+	0.708796i	$0.749239\pi$
$252$	−2.30193e14			−0.898854
$253$	3.82453e13	+	3.82453e13i	0.145833	+	0.145833i
$254$			1.61296e14i			0.600650i
$255$	1.92923e14			0.701687
$256$	−2.61749e14			−0.929918
$257$	2.38514e14			0.827779			0.413889	−	0.910327i	$-0.364170\pi$
$257$	2.38514e14			0.827779			0.413889	+	0.910327i	$0.364170\pi$
$258$	2.80428e14	−	2.80428e14i	0.950831	−	0.950831i
$259$	−3.65722e14	+	3.65722e14i	−1.21158	+	1.21158i
$260$		−	5.72409e13i		−	0.185296i
$261$	−2.09606e14	−	6.48870e13i	−0.663071	−	0.205265i
$262$	−2.50001e14			−0.772918
$263$	3.16897e14	+	3.16897e14i	0.957600	+	0.957600i	0.999137	−	0.0415367i	$-0.0132254\pi$
$263$	3.16897e14	+	3.16897e14i	0.957600	+	0.957600i	−0.0415367	+	0.999137i	$0.513225\pi$
$264$	1.90519e14	+	1.90519e14i	0.562750	+	0.562750i
$265$		−	9.39027e13i		−	0.271146i
$266$		−	2.51992e14i		−	0.711374i
$267$		−	7.11751e13i		−	0.196454i
$268$	−2.51788e14			−0.679558
$269$	2.50605e14	−	2.50605e14i	0.661418	−	0.661418i	−0.294296	−	0.955714i	$-0.595085\pi$
$269$	2.50605e14	−	2.50605e14i	0.661418	−	0.661418i	0.955714	+	0.294296i	$0.0950851\pi$
$270$		−	3.34991e13i		−	0.0864669i
$271$	−3.86715e14	+	3.86715e14i	−0.976281	+	0.976281i	−0.999725	−	0.0234439i	$-0.992537\pi$
$271$	−3.86715e14	+	3.86715e14i	−0.976281	+	0.976281i	0.0234439	+	0.999725i	$0.492537\pi$
$272$	−3.86781e13	−	3.86781e13i	−0.0955106	−	0.0955106i
$273$	5.66144e14	−	5.66144e14i	1.36757	−	1.36757i
$274$			4.25110e14i			1.00461i
$275$	−1.66324e14	−	1.66324e14i	−0.384555	−	0.384555i
$276$	8.76028e13	−	8.76028e13i	0.198182	−	0.198182i
$277$	−2.76641e14			−0.612403			−0.306202	−	0.951967i	$-0.599058\pi$
$277$	−2.76641e14			−0.612403			−0.306202	+	0.951967i	$0.599058\pi$
$278$	9.62843e13	+	9.62843e13i	0.208587	+	0.208587i
$279$	1.87730e14	−	1.87730e14i	0.398022	−	0.398022i
$280$	−2.41263e14	−	2.41263e14i	−0.500660	−	0.500660i
$281$	−4.29757e14			−0.872941			−0.436471	−	0.899719i	$-0.643772\pi$
$281$	−4.29757e14			−0.872941			−0.436471	+	0.899719i	$0.643772\pi$
$282$	7.55635e13	+	7.55635e13i	0.150251	+	0.150251i
$283$			8.22035e14i			1.60019i	0.599872	+	0.800096i	$0.295218\pi$
$283$			8.22035e14i			1.60019i	−0.599872	+	0.800096i	$0.704782\pi$
$284$	1.69071e14			0.322224
$285$	1.60786e14			0.300040
$286$	−1.52515e14			−0.278688
$287$	8.61343e14	−	8.61343e14i	1.54129	−	1.54129i
$288$	2.86579e14	−	2.86579e14i	0.502215	−	0.502215i
$289$			6.41704e14i			1.10141i
$290$	−6.02483e13	−	1.14275e14i	−0.101288	−	0.192116i
$291$	−1.12788e14			−0.185739
$292$	2.68796e14	+	2.68796e14i	0.433637	+	0.433637i
$293$	−4.88922e13	−	4.88922e13i	−0.0772741	−	0.0772741i	0.667413	−	0.744687i	$-0.267401\pi$
$293$	−4.88922e13	−	4.88922e13i	−0.0772741	−	0.0772741i	−0.744687	+	0.667413i	$0.767401\pi$
$294$		−	1.40481e15i		−	2.17537i
$295$			7.07153e13i			0.107295i
$296$		−	5.68143e14i		−	0.844710i
$297$	1.72459e14			0.251273
$298$	2.04380e14	−	2.04380e14i	0.291837	−	0.291837i
$299$			1.76552e14i			0.247084i
$300$	−3.80973e14	+	3.80973e14i	−0.522597	+	0.522597i
$301$	−1.82821e15	−	1.82821e15i	−2.45826	−	2.45826i
$302$	−3.23334e14	+	3.23334e14i	−0.426196	+	0.426196i
$303$			4.46773e14i			0.577339i
$304$	−3.22351e13	−	3.22351e13i	−0.0408402	−	0.0408402i
$305$	1.21494e14	−	1.21494e14i	0.150923	−	0.150923i
$306$	−4.82416e14			−0.587615
$307$	−2.52042e14	−	2.52042e14i	−0.301052	−	0.301052i	0.540373	−	0.841425i	$-0.318283\pi$
$307$	−2.52042e14	−	2.52042e14i	−0.301052	−	0.301052i	−0.841425	+	0.540373i	$0.818283\pi$
$308$	4.93361e14	−	4.93361e14i	0.577910	−	0.577910i
$309$	−4.09604e14	−	4.09604e14i	−0.470558	−	0.470558i
$310$	1.56309e14			0.176122
$311$	4.17343e14	+	4.17343e14i	0.461244	+	0.461244i	0.899063	−	0.437819i	$-0.144249\pi$
$311$	4.17343e14	+	4.17343e14i	0.461244	+	0.461244i	−0.437819	+	0.899063i	$0.644249\pi$
$312$			8.79494e14i			0.953466i
$313$	1.21593e15			1.29313			0.646565	−	0.762859i	$-0.276205\pi$
$313$	1.21593e15			1.29313			0.646565	+	0.762859i	$0.276205\pi$
$314$	−3.11736e14			−0.325244
$315$	4.95579e14			0.507282
$316$	−6.88847e14	+	6.88847e14i	−0.691831	+	0.691831i
$317$	−2.48060e14	+	2.48060e14i	−0.244457	+	0.244457i	−0.818691	−	0.574234i	$-0.805300\pi$
$317$	−2.48060e14	+	2.48060e14i	−0.244457	+	0.244457i	0.574234	+	0.818691i	$0.305300\pi$
$318$			5.73094e14i			0.554196i
$319$	5.88306e14	−	3.10168e14i	0.558289	−	0.294343i
$320$	2.01406e14			0.187574
$321$	1.74774e14	+	1.74774e14i	0.159752	+	0.159752i
$322$	2.95582e14	+	2.95582e14i	0.265181	+	0.265181i
$323$			1.02038e15i			0.898559i
$324$		−	9.24151e14i		−	0.798864i
$325$		−	7.67800e14i		−	0.651550i
$326$	−1.24449e15			−1.03678
$327$	7.11929e14	−	7.11929e14i	0.582305	−	0.582305i
$328$			1.33808e15i			1.07458i
$329$	4.92625e14	−	4.92625e14i	0.388456	−	0.388456i
$330$	−1.62923e14	−	1.62923e14i	−0.126153	−	0.126153i
$331$	3.84672e13	−	3.84672e13i	0.0292498	−	0.0292498i	−0.692331	−	0.721580i	$-0.743416\pi$
$331$	3.84672e13	−	3.84672e13i	0.0292498	−	0.0292498i	0.721580	+	0.692331i	$0.243416\pi$
$332$			1.36990e15i			1.02296i
$333$	5.83512e14	+	5.83512e14i	0.427942	+	0.427942i
$334$	−9.25768e14	+	9.25768e14i	−0.666842	+	0.666842i
$335$	5.42071e14			0.383519
$336$	−2.42496e14	−	2.42496e14i	−0.168527	−	0.168527i
$337$	1.38252e15	−	1.38252e15i	0.943823	−	0.943823i	−0.0546808	−	0.998504i	$-0.517414\pi$
$337$	1.38252e15	−	1.38252e15i	0.943823	−	0.943823i	0.998504	+	0.0546808i	$0.0174141\pi$
$338$	2.63702e14	+	2.63702e14i	0.176853	+	0.176853i
$339$	2.40822e15			1.58671
$340$	3.88049e14	+	3.88049e14i	0.251196	+	0.251196i
$341$			8.04702e14i			0.511810i
$342$	−4.02055e14			−0.251263
$343$	−5.95831e15			−3.65897
$344$	2.84009e15			1.71388
$345$	−1.88599e14	+	1.88599e14i	−0.111847	+	0.111847i
$346$	−1.06291e15	+	1.06291e15i	−0.619500	+	0.619500i
$347$		−	2.94321e15i		−	1.68595i	−0.537953	−	0.842975i	$-0.680802\pi$
$347$		−	2.94321e15i		−	1.68595i	0.537953	−	0.842975i	$-0.319198\pi$
$348$	−7.10457e14	−	1.34755e15i	−0.400002	−	0.758697i
$349$	−1.60272e15			−0.886961			−0.443480	−	0.896284i	$-0.646256\pi$
$349$	−1.60272e15			−0.886961			−0.443480	+	0.896284i	$0.646256\pi$
$350$	−1.28545e15	−	1.28545e15i	−0.699271	−	0.699271i
$351$	3.98061e14	+	3.98061e14i	0.212866	+	0.212866i
$352$			1.22842e15i			0.645790i
$353$			9.01934e14i			0.466151i	0.972459	+	0.233075i	$0.0748789\pi$
$353$			9.01934e14i			0.466151i	−0.972459	+	0.233075i	$0.925121\pi$
$354$		−	4.31580e14i		−	0.219302i
$355$	−3.63990e14			−0.181852
$356$	1.43163e14	−	1.43163e14i	0.0703283	−	0.0703283i
$357$			7.67603e15i			3.70790i
$358$	8.78974e14	−	8.78974e14i	0.417521	−	0.417521i
$359$	4.62799e14	+	4.62799e14i	0.216185	+	0.216185i	0.806889	−	0.590703i	$-0.201150\pi$
$359$	4.62799e14	+	4.62799e14i	0.216185	+	0.216185i	−0.590703	+	0.806889i	$0.701150\pi$
$360$	−3.84937e14	+	3.84937e14i	−0.176837	+	0.176837i
$361$		−	1.36291e15i		−	0.615778i
$362$	1.36509e15	+	1.36509e15i	0.606612	+	0.606612i
$363$	−1.26695e15	+	1.26695e15i	−0.553756	+	0.553756i
$364$	2.27750e15			0.979153
$365$	−5.78687e14	−	5.78687e14i	−0.244730	−	0.244730i
$366$	−7.41486e14	+	7.41486e14i	−0.308473	+	0.308473i
$367$	9.42303e14	+	9.42303e14i	0.385651	+	0.385651i	0.873133	−	0.487482i	$-0.162085\pi$
$367$	9.42303e14	+	9.42303e14i	0.385651	+	0.385651i	−0.487482	+	0.873133i	$0.662085\pi$
$368$	7.56222e13			0.0304483
$369$	−1.37428e15	−	1.37428e15i	−0.544398	−	0.544398i
$370$			4.85847e14i			0.189360i
$371$	3.73620e15			1.43281
$372$	1.84321e15			0.695533
$373$	−4.53431e15			−1.68367			−0.841837	−	0.539732i	$-0.818525\pi$
$373$	−4.53431e15			−1.68367			−0.841837	+	0.539732i	$0.818525\pi$
$374$	1.03394e15	−	1.03394e15i	0.377802	−	0.377802i
$375$	1.77202e15	−	1.77202e15i	0.637209	−	0.637209i
$376$			7.65284e14i			0.270829i
$377$	2.07381e15	+	6.41984e14i	0.722307	+	0.223602i
$378$	1.33286e15			0.456914
$379$	−3.32357e14	−	3.32357e14i	−0.112142	−	0.112142i	0.648809	−	0.760951i	$-0.275267\pi$
$379$	−3.32357e14	−	3.32357e14i	−0.112142	−	0.112142i	−0.760951	+	0.648809i	$0.775267\pi$
$380$	3.23408e14	+	3.23408e14i	0.107411	+	0.107411i
$381$		−	4.09485e15i		−	1.33871i
$382$		−	2.77482e15i		−	0.893007i
$383$		−	2.75356e15i		−	0.872372i	−0.899857	−	0.436186i	$-0.856329\pi$
$383$		−	2.75356e15i		−	0.872372i	0.899857	−	0.436186i	$-0.143671\pi$
$384$	3.04084e15			0.948433
$385$	−1.06215e15	+	1.06215e15i	−0.326153	+	0.326153i
$386$		−	1.33919e14i		−	0.0404871i
$387$	−2.91692e15	+	2.91692e15i	−0.868277	+	0.868277i
$388$	−2.26863e14	−	2.26863e14i	−0.0664925	−	0.0664925i
$389$	−4.56731e15	+	4.56731e15i	−1.31814	+	1.31814i	−0.402898	+	0.915245i	$0.631997\pi$
$389$	−4.56731e15	+	4.56731e15i	−1.31814	+	1.31814i	−0.915245	+	0.402898i	$0.868003\pi$
$390$		−	7.52099e14i		−	0.213741i
$391$	−1.19688e15	−	1.19688e15i	−0.334959	−	0.334959i
$392$	7.11373e15	−	7.11373e15i	1.96056	−	1.96056i
$393$	6.34680e15			1.72266
$394$	−1.46360e15	−	1.46360e15i	−0.391242	−	0.391242i
$395$	1.48301e15	−	1.48301e15i	0.390446	−	0.390446i
$396$	−7.87160e14	−	7.87160e14i	−0.204123	−	0.204123i
$397$	−5.57069e15			−1.42287			−0.711437	−	0.702750i	$-0.751955\pi$
$397$	−5.57069e15			−1.42287			−0.711437	+	0.702750i	$0.751955\pi$
$398$	1.23302e15	+	1.23302e15i	0.310221	+	0.310221i
$399$			6.39737e15i			1.58549i
$400$	−3.28871e14			−0.0802908
$401$	−7.21028e15			−1.73415			−0.867073	−	0.498181i	$-0.834002\pi$
$401$	−7.21028e15			−1.73415			−0.867073	+	0.498181i	$0.834002\pi$
$402$	−3.30829e15			−0.783877
$403$	−1.85737e15	+	1.85737e15i	−0.433580	+	0.433580i
$404$	−8.98646e14	+	8.98646e14i	−0.206681	+	0.206681i
$405$			1.98959e15i			0.450851i
$406$	4.54677e15	−	2.39716e15i	1.01519	−	0.535231i
$407$	−2.50122e15			−0.550283
$408$	−5.96229e15	−	5.96229e15i	−1.29256	−	1.29256i
$409$	−1.94870e15	−	1.94870e15i	−0.416299	−	0.416299i	0.467627	−	0.883926i	$-0.345109\pi$
$409$	−1.94870e15	−	1.94870e15i	−0.416299	−	0.416299i	−0.883926	+	0.467627i	$0.845109\pi$
$410$		−	1.14426e15i		−	0.240891i
$411$		−	1.07923e16i		−	2.23905i
$412$		−	1.64777e15i		−	0.336909i
$413$	−2.81362e15			−0.566977
$414$	4.71602e14	−	4.71602e14i	0.0936642	−	0.0936642i
$415$		−	2.94923e15i		−	0.577324i
$416$	−2.83538e15	+	2.83538e15i	−0.547080	+	0.547080i
$417$	−2.44438e15	−	2.44438e15i	−0.464893	−	0.464893i
$418$	8.61704e14	−	8.61704e14i	0.161548	−	0.161548i
$419$		−	5.31503e15i		−	0.982249i	−0.871089	−	0.491124i	$-0.836586\pi$
$419$		−	5.31503e15i		−	0.982249i	0.871089	−	0.491124i	$-0.163414\pi$
$420$	2.43291e15	+	2.43291e15i	0.443231	+	0.443231i
$421$	6.72549e15	−	6.72549e15i	1.20790	−	1.20790i	0.236196	−	0.971705i	$-0.424099\pi$
$421$	6.72549e15	−	6.72549e15i	1.20790	−	1.20790i	0.971705	−	0.236196i	$-0.0759008\pi$
$422$	3.41971e15			0.605501
$423$	−7.85986e14	−	7.85986e14i	−0.137206	−	0.137206i
$424$	−2.90206e15	+	2.90206e15i	−0.499472	+	0.499472i
$425$	5.20509e15	+	5.20509e15i	0.883272	+	0.883272i
$426$	2.22145e15			0.371689
$427$	4.83401e15	+	4.83401e15i	0.797517	+	0.797517i
$428$			7.03085e14i			0.114379i
$429$	3.87193e15			0.621132
$430$	−2.42870e15			−0.384205
$431$	−6.93628e14			−0.108209			−0.0541045	−	0.998535i	$-0.517230\pi$
$431$	−6.93628e14			−0.108209			−0.0541045	+	0.998535i	$0.517230\pi$
$432$	1.70501e14	−	1.70501e14i	0.0262316	−	0.0262316i
$433$	−4.51940e15	+	4.51940e15i	−0.685731	+	0.685731i	−0.961285	−	0.275554i	$-0.911139\pi$
$433$	−4.51940e15	+	4.51940e15i	−0.685731	+	0.685731i	0.275554	+	0.961285i	$0.411139\pi$
$434$			6.21921e15i			0.930672i
$435$	1.52953e15	+	2.90111e15i	0.225748	+	0.428183i
$436$	2.86397e15			0.416917
$437$	−9.97507e14	−	9.97507e14i	−0.143228	−	0.143228i
$438$	3.53176e15	+	3.53176e15i	0.500204	+	0.500204i
$439$		−	4.38529e15i		−	0.612648i	−0.951927	−	0.306324i	$-0.900901\pi$
$439$		−	4.38529e15i		−	0.612648i	0.951927	−	0.306324i	$-0.0990991\pi$
$440$		−	1.65003e15i		−	0.227392i
$441$			1.46123e16i			1.98650i
$442$	4.77296e15			0.640109
$443$	−1.57223e15	+	1.57223e15i	−0.208015	+	0.208015i	−0.803423	−	0.595408i	$-0.796990\pi$
$443$	−1.57223e15	+	1.57223e15i	−0.208015	+	0.208015i	0.595408	+	0.803423i	$0.296990\pi$
$444$			5.72918e15i			0.747816i
$445$	−3.08213e14	+	3.08213e14i	−0.0396909	+	0.0396909i
$446$	−2.97604e15	−	2.97604e15i	−0.378120	−	0.378120i
$447$	−5.18862e15	+	5.18862e15i	−0.650439	+	0.650439i
$448$			8.01355e15i			0.991190i
$449$	8.59133e15	+	8.59133e15i	1.04853	+	1.04853i	0.998761	+	0.0497729i	$0.0158498\pi$
$449$	8.59133e15	+	8.59133e15i	1.04853	+	1.04853i	0.0497729	+	0.998761i	$0.484150\pi$
$450$	−2.05094e15	+	2.05094e15i	−0.246989	+	0.246989i
$451$	5.89084e15			0.700032
$452$	4.84392e15	+	4.84392e15i	0.568024	+	0.568024i
$453$	8.20852e15	−	8.20852e15i	0.949895	−	0.949895i
$454$	−4.15340e13	−	4.15340e13i	−0.00474316	−	0.00474316i
$455$	−4.90320e15			−0.552600
$456$	−4.96909e15	−	4.96909e15i	−0.552698	−	0.552698i
$457$			3.74468e14i			0.0411072i	0.999789	+	0.0205536i	$0.00654287\pi$
$457$			3.74468e14i			0.0411072i	−0.999789	+	0.0205536i	$0.993457\pi$
$458$	−3.20196e15			−0.346915
$459$	−5.39708e15			−0.577142
$460$	−7.58701e14			−0.0800799
$461$	5.02051e14	−	5.02051e14i	0.0523049	−	0.0523049i	−0.680471	−	0.732775i	$-0.738225\pi$
$461$	5.02051e14	−	5.02051e14i	0.0523049	−	0.0523049i	0.732775	+	0.680471i	$0.238225\pi$
$462$	6.48237e15	−	6.48237e15i	0.666625	−	0.666625i
$463$		−	1.34283e16i		−	1.36312i	−0.731761	−	0.681562i	$-0.761301\pi$
$463$		−	1.34283e16i		−	1.36312i	0.731761	−	0.681562i	$-0.238699\pi$
$464$	2.74980e14	−	8.88275e14i	0.0275546	−	0.0890102i
$465$	−3.96822e15			−0.392535
$466$	1.38184e14	+	1.38184e14i	0.0134941	+	0.0134941i
$467$	9.17081e13	+	9.17081e13i	0.00884110	+	0.00884110i	0.711514	−	0.702672i	$-0.248010\pi$
$467$	9.17081e13	+	9.17081e13i	0.00884110	+	0.00884110i	−0.702672	+	0.711514i	$0.748010\pi$
$468$		−	3.63377e15i		−	0.345845i
$469$			2.15679e16i			2.02662i
$470$		−	6.54432e14i		−	0.0607124i
$471$	7.91409e15			0.724896
$472$	2.18546e15	−	2.18546e15i	0.197647	−	0.197647i
$473$		−	1.25034e16i		−	1.11650i
$474$	−9.05089e15	+	9.05089e15i	−0.798034	+	0.798034i
$475$	4.33803e15	+	4.33803e15i	0.377686	+	0.377686i
$476$	−1.54397e16	+	1.54397e16i	−1.32739	+	1.32739i
$477$		−	5.96113e15i		−	0.506079i
$478$	−1.93974e15	−	1.93974e15i	−0.162621	−	0.162621i
$479$	−4.69779e15	+	4.69779e15i	−0.388938	+	0.388938i	−0.874309	−	0.485370i	$-0.838685\pi$
$479$	−4.69779e15	+	4.69779e15i	−0.388938	+	0.388938i	0.485370	+	0.874309i	$0.338685\pi$
$480$	−6.05771e15			−0.495291
$481$	−5.77319e15	−	5.77319e15i	−0.466171	−	0.466171i
$482$	2.89662e15	−	2.89662e15i	0.230998	−	0.230998i
$483$	−7.50397e15	−	7.50397e15i	−0.591028	−	0.591028i
$484$	−5.09672e15			−0.396477
$485$	4.88409e14	+	4.88409e14i	0.0375261	+	0.0375261i
$486$		−	9.07887e15i		−	0.688992i
$487$	−2.16384e15			−0.162200			−0.0811001	−	0.996706i	$-0.525843\pi$
$487$	−2.16384e15			−0.162200			−0.0811001	+	0.996706i	$0.525843\pi$
$488$	−7.50954e15			−0.556025
$489$	3.15940e16			2.31075
$490$	−6.08330e15	+	6.08330e15i	−0.439504	+	0.439504i
$491$	−1.23045e16	+	1.23045e16i	−0.878164	+	0.878164i	−0.993345	−	0.115180i	$-0.963255\pi$
$491$	−1.23045e16	+	1.23045e16i	−0.878164	+	0.878164i	0.115180	+	0.993345i	$0.463255\pi$
$492$		−	1.34933e16i		−	0.951320i
$493$	−1.84110e16	+	9.70670e15i	−1.28232	+	0.676067i
$494$	3.97788e15			0.273710
$495$	1.69466e15	+	1.69466e15i	0.115200	+	0.115200i
$496$	7.95567e14	+	7.95567e14i	0.0534302	+	0.0534302i
$497$		−	1.44824e16i		−	0.960955i
$498$			1.79993e16i			1.17999i
$499$			1.28086e16i			0.829656i	0.909900	+	0.414828i	$0.136158\pi$
$499$			1.28086e16i			0.829656i	−0.909900	+	0.414828i	$0.863842\pi$
$500$	7.12856e15			0.456228
$501$	2.35026e16	−	2.35026e16i	1.48624	−	1.48624i
$502$			4.47028e13i			0.00279327i
$503$	1.71353e16	−	1.71353e16i	1.05800	−	1.05800i	0.0597857	−	0.998211i	$-0.480958\pi$
$503$	1.71353e16	−	1.71353e16i	1.05800	−	1.05800i	0.998211	−	0.0597857i	$-0.0190417\pi$
$504$	−1.53159e16	−	1.53159e16i	−0.934455	−	0.934455i
$505$	1.93468e15	−	1.93468e15i	0.116644	−	0.116644i
$506$			2.02152e15i			0.120441i
$507$	−6.69464e15	−	6.69464e15i	−0.394166	−	0.394166i
$508$	8.23644e15	−	8.23644e15i	0.479245	−	0.479245i
$509$	8.67834e15			0.499034			0.249517	−	0.968370i	$-0.419728\pi$
$509$	8.67834e15			0.499034			0.249517	+	0.968370i	$0.419728\pi$
$510$	5.09865e15	+	5.09865e15i	0.289757	+	0.289757i
$511$	2.30248e16	−	2.30248e16i	1.29322	−	1.29322i
$512$	2.36437e15	+	2.36437e15i	0.131249	+	0.131249i
$513$	−4.49804e15			−0.246785
$514$	6.30353e15	+	6.30353e15i	0.341826	+	0.341826i
$515$			3.54745e15i			0.190140i
$516$	−2.86396e16			−1.51729
$517$	3.36913e15			0.176431
$518$	−1.93309e16			−1.00063
$519$	2.69843e16	−	2.69843e16i	1.38072	−	1.38072i
$520$	3.80851e15	−	3.80851e15i	0.192635	−	0.192635i
$521$			3.39074e16i			1.69538i	0.530490	+	0.847691i	$0.322008\pi$
$521$			3.39074e16i			1.69538i	−0.530490	+	0.847691i	$0.677992\pi$
$522$	−3.82468e15	−	7.25440e15i	−0.189048	−	0.358574i
$523$	−1.58826e16			−0.776091			−0.388045	−	0.921640i	$-0.626850\pi$
$523$	−1.58826e16			−0.776091			−0.388045	+	0.921640i	$0.626850\pi$
$524$	1.27660e16	+	1.27660e16i	0.616693	+	0.616693i
$525$	3.26338e16	+	3.26338e16i	1.55852	+	1.55852i
$526$			1.67502e16i			0.790870i
$527$		−	2.51831e16i		−	1.17556i
$528$		−	1.65846e15i		−	0.0765424i
$529$	−1.95745e16			−0.893217
$530$	2.48170e15	−	2.48170e15i	0.111968	−	0.111968i
$531$			4.48915e15i			0.200261i
$532$	−1.28678e16	+	1.28678e16i	−0.567588	+	0.567588i
$533$	1.35969e16	+	1.35969e16i	0.593031	+	0.593031i
$534$	1.88104e15	−	1.88104e15i	0.0811243	−	0.0811243i
$535$		−	1.51366e15i		−	0.0645514i
$536$	−1.67527e16	−	1.67527e16i	−0.706474	−	0.706474i
$537$	−2.23146e16	+	2.23146e16i	−0.930559	+	0.930559i
$538$	1.32462e16			0.546257
$539$	−3.13178e16	−	3.13178e16i	−1.27720	−	1.27720i
$540$	−1.71060e15	+	1.71060e15i	−0.0689899	+	0.0689899i
$541$	−1.82629e15	−	1.82629e15i	−0.0728429	−	0.0728429i	0.669747	−	0.742590i	$-0.266403\pi$
$541$	−1.82629e15	−	1.82629e15i	−0.0728429	−	0.0728429i	−0.742590	+	0.669747i	$0.766403\pi$
$542$	−2.04405e16			−0.806298
$543$	−3.46558e16	−	3.46558e16i	−1.35200	−	1.35200i
$544$		−	3.84433e16i		−	1.48330i
$545$	−6.16580e15			−0.235294
$546$	2.99245e16			1.12946
$547$	−7.96260e15			−0.297256			−0.148628	−	0.988893i	$-0.547486\pi$
$547$	−7.96260e15			−0.297256			−0.148628	+	0.988893i	$0.547486\pi$
$548$	2.17078e16	−	2.17078e16i	0.801555	−	0.801555i
$549$	7.71269e15	−	7.71269e15i	0.281690	−	0.281690i
$550$		−	8.79133e15i		−	0.317599i
$551$	−1.53441e16	+	8.08976e15i	−0.548317	+	0.289085i
$552$	1.16573e16			0.412062
$553$	5.90059e16	+	5.90059e16i	2.06322	+	2.06322i
$554$	−7.31117e15	−	7.31117e15i	−0.252888	−	0.252888i
$555$		−	1.23343e16i		−	0.422042i
$556$		−	9.83334e15i		−	0.332853i
$557$		−	3.21511e15i		−	0.107662i	−0.998550	−	0.0538312i	$-0.982857\pi$
$557$		−	3.21511e15i		−	0.107662i	0.998550	−	0.0538312i	$-0.0171433\pi$
$558$	9.92278e15			0.328721
$559$	2.88596e16	−	2.88596e16i	0.945844	−	0.945844i
$560$			2.10018e15i			0.0680972i
$561$	−2.62487e16	+	2.62487e16i	−0.842035	+	0.842035i
$562$	−1.13578e16	−	1.13578e16i	−0.360475	−	0.360475i
$563$	1.69904e16	−	1.69904e16i	0.533522	−	0.533522i	−0.388097	−	0.921619i	$-0.626867\pi$
$563$	1.69904e16	−	1.69904e16i	0.533522	−	0.533522i	0.921619	+	0.388097i	$0.126867\pi$
$564$		−	7.71716e15i		−	0.239763i
$565$	−1.04284e16	−	1.04284e16i	−0.320573	−	0.320573i
$566$	−2.17251e16	+	2.17251e16i	−0.660789	+	0.660789i
$567$	−7.91619e16			−2.38242
$568$	1.12491e16	+	1.12491e16i	0.334987	+	0.334987i
$569$	−3.53051e16	+	3.53051e16i	−1.04031	+	1.04031i	−0.0411591	+	0.999153i	$0.513105\pi$
$569$	−3.53051e16	+	3.53051e16i	−1.04031	+	1.04031i	−0.999153	+	0.0411591i	$0.986895\pi$
$570$	4.24932e15	+	4.24932e15i	0.123900	+	0.123900i
$571$	−8.97901e15			−0.259067			−0.129533	−	0.991575i	$-0.541348\pi$
$571$	−8.97901e15			−0.259067			−0.129533	+	0.991575i	$0.541348\pi$
$572$	7.78806e15	+	7.78806e15i	0.222358	+	0.222358i
$573$			7.04448e16i			1.99031i
$574$	4.55278e16			1.27293
$575$	−1.01768e16			−0.281582
$576$	1.27857e16			0.350097
$577$	−7.98683e14	+	7.98683e14i	−0.0216431	+	0.0216431i	−0.717846	−	0.696202i	$-0.754872\pi$
$577$	−7.98683e14	+	7.98683e14i	−0.0216431	+	0.0216431i	0.696202	+	0.717846i	$0.254872\pi$
$578$	−1.69592e16	+	1.69592e16i	−0.454819	+	0.454819i
$579$			3.39981e15i			0.0902366i
$580$	−2.75882e15	+	8.91187e15i	−0.0724695	+	0.234100i
$581$	1.17344e17			3.05073
$582$	−2.98079e15	−	2.98079e15i	−0.0766998	−	0.0766998i
$583$	1.27762e16	+	1.27762e16i	0.325379	+	0.325379i
$584$			3.57686e16i			0.901623i
$585$			7.82308e15i			0.195183i
$586$		−	2.58428e15i		−	0.0638197i
$587$	4.22685e16			1.03321			0.516604	−	0.856224i	$-0.327196\pi$
$587$	4.22685e16			1.03321			0.516604	+	0.856224i	$0.327196\pi$
$588$	−7.17351e16	+	7.17351e16i	−1.73567	+	1.73567i
$589$		−	2.09881e16i		−	0.502668i
$590$	−1.86889e15	+	1.86889e15i	−0.0443070	+	0.0443070i
$591$	3.71566e16	+	3.71566e16i	0.871990	+	0.871990i
$592$	−2.47283e15	+	2.47283e15i	−0.0574465	+	0.0574465i
$593$		−	7.44715e15i		−	0.171262i	−0.996327	−	0.0856312i	$-0.972709\pi$
$593$		−	7.44715e15i		−	0.171262i	0.996327	−	0.0856312i	$-0.0272907\pi$
$594$	4.55781e15	+	4.55781e15i	0.103762	+	0.103762i
$595$	3.32399e16	−	3.32399e16i	0.749131	−	0.749131i
$596$	−2.08729e16			−0.465699
$597$	−3.13028e16	−	3.13028e16i	−0.691413	−	0.691413i
$598$	−4.66597e15	+	4.66597e15i	−0.102032	+	0.102032i
$599$	−2.35158e16	−	2.35158e16i	−0.509096	−	0.509096i	0.405153	−	0.914249i	$-0.367218\pi$
$599$	−2.35158e16	−	2.35158e16i	−0.509096	−	0.509096i	−0.914249	+	0.405153i	$0.867218\pi$
$600$	−5.06960e16			−1.08659
$601$	2.21552e16	+	2.21552e16i	0.470143	+	0.470143i	0.901961	−	0.431818i	$-0.142128\pi$
$601$	2.21552e16	+	2.21552e16i	0.470143	+	0.470143i	−0.431818	+	0.901961i	$0.642128\pi$
$602$		−	9.66332e16i		−	2.03024i
$603$	3.44118e16			0.715818
$604$	3.30215e16			0.680103
$605$	1.09726e16			0.223758
$606$	−1.18075e16	+	1.18075e16i	−0.238408	+	0.238408i
$607$	−2.22248e16	+	2.22248e16i	−0.444330	+	0.444330i	−0.893464	−	0.449135i	$-0.851732\pi$
$607$	−2.22248e16	+	2.22248e16i	−0.444330	+	0.444330i	0.449135	+	0.893464i	$0.351732\pi$
$608$		−	3.20395e16i		−	0.634255i
$609$	−1.15430e17	+	6.08571e16i	−2.26263	+	1.19291i
$610$	6.42178e15			0.124645
$611$	7.77645e15	+	7.77645e15i	0.149463	+	0.149463i
$612$	2.46341e16	+	2.46341e16i	0.468844	+	0.468844i
$613$			3.85119e14i			0.00725825i	0.999993	+	0.00362913i	$0.00115519\pi$
$613$			3.85119e14i			0.00725825i	−0.999993	+	0.00362913i	$0.998845\pi$
$614$		−	1.33221e16i		−	0.248635i
$615$			2.90495e16i			0.536892i
$616$	6.56514e16			1.20160
$617$	−5.77143e16	+	5.77143e16i	−1.04610	+	1.04610i	−0.0472133	+	0.998885i	$0.515034\pi$
$617$	−5.77143e16	+	5.77143e16i	−1.04610	+	1.04610i	−0.998885	+	0.0472133i	$0.984966\pi$
$618$		−	2.16503e16i		−	0.388628i
$619$	7.27986e16	−	7.27986e16i	1.29413	−	1.29413i	0.361928	−	0.932206i	$-0.382119\pi$
$619$	7.27986e16	−	7.27986e16i	1.29413	−	1.29413i	0.932206	−	0.361928i	$-0.117881\pi$
$620$	−7.98175e15	−	7.98175e15i	−0.140523	−	0.140523i
$621$	5.27611e15	−	5.27611e15i	0.0919949	−	0.0919949i
$622$			2.20594e16i			0.380935i
$623$	−1.22632e16	−	1.22632e16i	−0.209737	−	0.209737i
$624$	3.82798e15	−	3.82798e15i	0.0648428	−	0.0648428i
$625$	3.60142e16			0.604217
$626$	3.21351e16	+	3.21351e16i	0.533990	+	0.533990i
$627$	−2.18762e16	+	2.18762e16i	−0.360053	+	0.360053i
$628$	1.59185e16	+	1.59185e16i	0.259505	+	0.259505i
$629$	7.82756e16			1.26393
$630$	1.30974e16	+	1.30974e16i	0.209479	+	0.209479i
$631$		−	5.33570e16i		−	0.845309i	−0.906291	−	0.422654i	$-0.861098\pi$
$631$		−	5.33570e16i		−	0.845309i	0.906291	−	0.422654i	$-0.138902\pi$
$632$	−9.16646e16			−1.43847
$633$	−8.68167e16			−1.34953
$634$	−1.31117e16			−0.201894
$635$	−1.77321e16	+	1.77321e16i	−0.270469	+	0.270469i
$636$	2.92645e16	−	2.92645e16i	0.442180	−	0.442180i
$637$		−	1.44572e17i		−	2.16396i
$638$	2.37452e16	+	7.35073e15i	0.352089	+	0.108995i
$639$	−2.31068e16			−0.339418
$640$	−1.31679e16	−	1.31679e16i	−0.191618	−	0.191618i
$641$	−8.50607e16	−	8.50607e16i	−1.22626	−	1.22626i	−0.965370	−	0.260885i	$-0.915986\pi$
$641$	−8.50607e16	−	8.50607e16i	−1.22626	−	1.22626i	−0.260885	−	0.965370i	$-0.584014\pi$
$642$			9.23797e15i			0.131937i
$643$			3.51484e16i			0.497325i	0.968590	+	0.248662i	$0.0799910\pi$
$643$			3.51484e16i			0.497325i	−0.968590	+	0.248662i	$0.920009\pi$
$644$		−	3.01872e16i		−	0.423163i
$645$	6.16577e16			0.856307
$646$	−2.69670e16	+	2.69670e16i	−0.371054	+	0.371054i
$647$			1.02353e17i			1.39532i	0.716427	+	0.697662i	$0.245776\pi$
$647$			1.02353e17i			1.39532i	−0.716427	+	0.697662i	$0.754224\pi$
$648$	6.14883e16	−	6.14883e16i	0.830505	−	0.830505i
$649$	−9.62136e15	−	9.62136e15i	−0.128756	−	0.128756i
$650$	2.02917e16	−	2.02917e16i	0.269053	−	0.269053i
$651$		−	1.57888e17i		−	2.07426i
$652$	6.35488e16	+	6.35488e16i	0.827221	+	0.827221i
$653$	4.46574e15	−	4.46574e15i	0.0575989	−	0.0575989i	−0.677721	−	0.735320i	$-0.737032\pi$
$653$	4.46574e15	−	4.46574e15i	0.0575989	−	0.0575989i	0.735320	+	0.677721i	$0.237032\pi$
$654$	3.76303e16			0.480918
$655$	−2.74838e16	−	2.74838e16i	−0.348040	−	0.348040i
$656$	5.82396e15	−	5.82396e15i	0.0730795	−	0.0730795i
$657$	−3.67362e16	−	3.67362e16i	−0.456775	−	0.456775i
$658$	2.60386e16			0.320820
$659$	−1.03029e17	−	1.03029e17i	−1.25790	−	1.25790i	−0.952092	−	0.305812i	$-0.901072\pi$
$659$	−1.03029e17	−	1.03029e17i	−1.25790	−	1.25790i	−0.305812	−	0.952092i	$-0.598928\pi$
$660$			1.66390e16i			0.201309i
$661$	−2.21901e16			−0.266042			−0.133021	−	0.991113i	$-0.542468\pi$
$661$	−2.21901e16			−0.266042			−0.133021	+	0.991113i	$0.542468\pi$
$662$	2.03325e15			0.0241570
$663$	−1.21172e17			−1.42666
$664$	−9.11458e16	+	9.11458e16i	−1.06348	+	1.06348i
$665$	2.77028e16	−	2.77028e16i	0.320327	−	0.320327i
$666$			3.08426e16i			0.353431i
$667$	8.50919e15	−	2.74874e16i	0.0966347	−	0.312161i
$668$	9.45469e16			1.06412
$669$	7.55531e16	+	7.55531e16i	0.842744	+	0.842744i
$670$	1.43261e16	+	1.43261e16i	0.158372	+	0.158372i
$671$			3.30604e16i			0.362220i
$672$		−	2.41024e17i		−	2.61725i
$673$			1.47790e17i			1.59057i	0.606234	+	0.795286i	$0.292679\pi$
$673$			1.47790e17i			1.59057i	−0.606234	+	0.795286i	$0.707321\pi$
$674$	7.30753e16			0.779491
$675$	−2.29451e16	+	2.29451e16i	−0.242587	+	0.242587i
$676$		−	2.69314e16i		−	0.282214i
$677$	4.28733e15	−	4.28733e15i	0.0445302	−	0.0445302i	−0.684491	−	0.729021i	$-0.739976\pi$
$677$	4.28733e15	−	4.28733e15i	0.0445302	−	0.0445302i	0.729021	+	0.684491i	$0.239976\pi$
$678$	6.36452e16	+	6.36452e16i	0.655221	+	0.655221i
$679$	−1.94328e16	+	1.94328e16i	−0.198298	+	0.198298i
$680$			5.16375e16i			0.522290i
$681$	1.05443e15	+	1.05443e15i	0.0105714	+	0.0105714i
$682$	−2.12670e16	+	2.12670e16i	−0.211349	+	0.211349i
$683$	−7.23924e16			−0.713130			−0.356565	−	0.934270i	$-0.616052\pi$
$683$	−7.23924e16			−0.713130			−0.356565	+	0.934270i	$0.616052\pi$
$684$	2.05306e16	+	2.05306e16i	0.200477	+	0.200477i
$685$	−4.67344e16	+	4.67344e16i	−0.452370	+	0.452370i
$686$	−1.57469e17	−	1.57469e17i	−1.51095	−	1.51095i
$687$	8.12886e16			0.773196
$688$	−1.23614e16	−	1.23614e16i	−0.116557	−	0.116557i
$689$			5.89787e16i			0.551290i
$690$	−9.96872e15			−0.0923729
$691$	1.63319e17			1.50027			0.750134	−	0.661286i	$-0.229989\pi$
$691$	1.63319e17			1.50027			0.750134	+	0.661286i	$0.229989\pi$
$692$	1.08553e17			0.988568
$693$	−6.74274e16	+	6.74274e16i	−0.608747	+	0.608747i
$694$	7.77843e16	−	7.77843e16i	0.696202	−	0.696202i
$695$			2.11700e16i			0.187851i
$696$	4.23887e16	−	1.36929e17i	0.372902	−	1.20459i
$697$	−1.84353e17			−1.60788
$698$	−4.23572e16	−	4.23572e16i	−0.366265	−	0.366265i
$699$	−3.50810e15	−	3.50810e15i	−0.0300753	−	0.0300753i
$700$			1.31280e17i			1.11586i
$701$		−	9.40822e16i		−	0.792865i	−0.918064	−	0.396433i	$-0.870248\pi$
$701$		−	9.40822e16i		−	0.792865i	0.918064	−	0.396433i	$-0.129752\pi$
$702$			2.10402e16i			0.175803i
$703$	6.52365e16			0.540454
$704$	−2.74028e16	+	2.74028e16i	−0.225092	+	0.225092i
$705$			1.66142e16i			0.135314i
$706$	−2.38366e16	+	2.38366e16i	−0.192494	+	0.192494i
$707$	7.69771e16	+	7.69771e16i	0.616375	+	0.616375i
$708$	−2.20382e16	+	2.20382e16i	−0.174976	+	0.174976i
$709$		−	1.87661e17i		−	1.47740i	−0.674036	−	0.738699i	$-0.735441\pi$
$709$		−	1.87661e17i		−	1.47740i	0.674036	−	0.738699i	$-0.264559\pi$
$710$	−9.61965e15	−	9.61965e15i	−0.0750947	−	0.0750947i
$711$	9.41443e16	−	9.41443e16i	0.728746	−	0.728746i
$712$	1.90506e16			0.146228
$713$	2.46186e16	+	2.46186e16i	0.187381	+	0.187381i
$714$	−2.02865e17	+	2.02865e17i	−1.53115	+	1.53115i
$715$	−1.67668e16	−	1.67668e16i	−0.125491	−	0.125491i
$716$	−8.97680e16			−0.666259
$717$	4.92445e16	+	4.92445e16i	0.362445	+	0.362445i
$718$			2.44621e16i			0.178545i
$719$	2.26036e16			0.163608			0.0818041	−	0.996648i	$-0.473932\pi$
$719$	2.26036e16			0.163608			0.0818041	+	0.996648i	$0.473932\pi$
$720$	3.35085e15			0.0240525
$721$	−1.41146e17			−1.00475
$722$	3.60195e16	−	3.60195e16i	0.254281	−	0.254281i
$723$	−7.35368e16	+	7.35368e16i	−0.514843	+	0.514843i
$724$		−	1.39414e17i		−	0.968002i
$725$	−3.70054e16	+	1.19539e17i	−0.254822	+	0.823157i
$726$	−6.69667e16			−0.457340
$727$	1.77792e17	+	1.77792e17i	1.20422	+	1.20422i	0.972871	+	0.231349i	$0.0743138\pi$
$727$	1.77792e17	+	1.77792e17i	1.20422	+	1.20422i	0.231349	+	0.972871i	$0.425686\pi$
$728$	1.51533e17	+	1.51533e17i	1.01793	+	1.01793i
$729$			4.85238e16i			0.323288i
$730$		−	3.05875e16i		−	0.202119i
$731$			3.91292e17i			2.56446i
$732$	7.57266e16			0.492246
$733$	1.77779e16	−	1.77779e16i	0.114619	−	0.114619i	−0.647471	−	0.762090i	$-0.724173\pi$
$733$	1.77779e16	−	1.77779e16i	0.114619	−	0.114619i	0.762090	+	0.647471i	$0.224173\pi$
$734$			4.98071e16i			0.318504i
$735$	1.54437e17	−	1.54437e17i	0.979555	−	0.979555i
$736$	3.75816e16	+	3.75816e16i	0.236433	+	0.236433i
$737$	−7.37529e16	+	7.37529e16i	−0.460229	+	0.460229i
$738$		−	7.26399e16i		−	0.449611i
$739$	1.08475e17	+	1.08475e17i	0.665984	+	0.665984i	0.956784	−	0.290800i	$-0.0939214\pi$
$739$	1.08475e17	+	1.08475e17i	0.665984	+	0.665984i	−0.290800	+	0.956784i	$0.593921\pi$
$740$	2.48093e16	−	2.48093e16i	0.151086	−	0.151086i
$741$	−1.00987e17			−0.610037
$742$	9.87418e16	+	9.87418e16i	0.591668	+	0.591668i
$743$	−8.28246e16	+	8.28246e16i	−0.492296	+	0.492296i	−0.909029	−	0.416733i	$-0.863175\pi$
$743$	−8.28246e16	+	8.28246e16i	−0.492296	+	0.492296i	0.416733	+	0.909029i	$0.363175\pi$
$744$	1.22638e17	+	1.22638e17i	0.723081	+	0.723081i
$745$	4.49370e16			0.262825
$746$	−1.19834e17	−	1.19834e17i	−0.695262	−	0.695262i
$747$		−	1.87223e17i		−	1.07754i
$748$	−1.05594e17			−0.602878
$749$	6.02256e16			0.341107
$750$	9.36635e16			0.526263
$751$	6.19546e16	−	6.19546e16i	0.345330	−	0.345330i	−0.513037	−	0.858367i	$-0.671480\pi$
$751$	6.19546e16	−	6.19546e16i	0.345330	−	0.345330i	0.858367	+	0.513037i	$0.171480\pi$
$752$	3.33088e15	−	3.33088e15i	0.0184184	−	0.0184184i
$753$		−	1.13488e15i		−	0.00622556i
$754$	3.78409e16	+	7.17741e16i	0.205937	+	0.390607i
$755$	−7.10914e16			−0.383827
$756$	−6.80614e16	−	6.80614e16i	−0.364561	−	0.364561i
$757$	−6.21700e16	−	6.21700e16i	−0.330374	−	0.330374i	0.522355	−	0.852728i	$-0.325054\pi$
$757$	−6.21700e16	−	6.21700e16i	−0.330374	−	0.330374i	−0.852728	+	0.522355i	$0.825054\pi$
$758$		−	1.75673e16i		−	0.0926168i
$759$		−	5.13206e16i		−	0.268436i
$760$			4.30358e16i			0.223331i
$761$	−1.50366e17			−0.774179			−0.387090	−	0.922042i	$-0.626520\pi$
$761$	−1.50366e17			−0.774179			−0.387090	+	0.922042i	$0.626520\pi$
$762$	1.08220e17	−	1.08220e17i	0.552813	−	0.552813i
$763$		−	2.45325e17i		−	1.24335i
$764$	−1.41694e17	+	1.41694e17i	−0.712509	+	0.712509i
$765$	−5.30344e16	−	5.30344e16i	−0.264599	−	0.264599i
$766$	7.27721e16	−	7.27721e16i	0.360240	−	0.360240i
$767$		−	4.44151e16i		−	0.218152i
$768$	1.75618e17	+	1.75618e17i	0.855857	+	0.855857i
$769$	−8.75414e16	+	8.75414e16i	−0.423307	+	0.423307i	−0.886341	−	0.463034i	$-0.846761\pi$
$769$	−8.75414e16	+	8.75414e16i	−0.423307	+	0.423307i	0.463034	+	0.886341i	$0.346761\pi$
$770$	−5.61418e16			−0.269365
$771$	−1.60028e17	−	1.60028e17i	−0.761853	−	0.761853i
$772$	−6.83842e15	+	6.83842e15i	−0.0323037	+	0.0323037i
$773$	6.43373e16	+	6.43373e16i	0.301569	+	0.301569i	0.841627	−	0.540059i	$-0.181598\pi$
$773$	6.43373e16	+	6.43373e16i	0.301569	+	0.301569i	−0.540059	+	0.841627i	$0.681598\pi$
$774$	−1.54179e17			−0.717099
$775$	−1.07063e17	−	1.07063e17i	−0.494117	−	0.494117i
$776$		−	3.01886e16i		−	0.138252i
$777$	4.90756e17			2.23018
$778$	−2.41413e17			−1.08864
$779$	−1.53644e17			−0.687528
$780$	−3.84052e16	+	3.84052e16i	−0.170539	+	0.170539i
$781$	4.95236e16	−	4.95236e16i	0.218226	−	0.218226i
$782$		−	6.32633e16i		−	0.276638i
$783$	−4.27891e16	−	8.11595e16i	−0.185679	−	0.352183i
$784$	−6.19246e16			−0.266666
$785$	−3.42707e16	−	3.42707e16i	−0.146455	−	0.146455i
$786$	1.67736e17	+	1.67736e17i	0.711361	+	0.711361i
$787$		−	1.34100e17i		−	0.564393i	−0.959357	−	0.282197i	$-0.908937\pi$
$787$		−	1.34100e17i		−	0.564393i	0.959357	−	0.282197i	$-0.0910630\pi$
$788$			1.49475e17i			0.624325i
$789$		−	4.25239e17i		−	1.76267i
$790$	7.83870e16			0.322464
$791$	4.14926e17	−	4.14926e17i	1.69399	−	1.69399i
$792$		−	1.04747e17i		−	0.424415i
$793$	−7.63083e16	+	7.63083e16i	−0.306855	+	0.306855i
$794$	−1.47224e17	−	1.47224e17i	−0.587566	−	0.587566i
$795$	−6.30031e16	+	6.30031e16i	−0.249551	+	0.249551i
$796$		−	1.25926e17i		−	0.495036i
$797$	2.68524e17	+	2.68524e17i	1.04769	+	1.04769i	0.998804	+	0.0488885i	$0.0155679\pi$
$797$	2.68524e17	+	2.68524e17i	1.04769	+	1.04769i	0.0488885	+	0.998804i	$0.484432\pi$
$798$	−1.69072e17	+	1.69072e17i	−0.654718	+	0.654718i
$799$	−1.05437e17			−0.405238
$800$	−1.63438e17	−	1.63438e17i	−0.623465	−	0.623465i
$801$	−1.95660e16	+	1.95660e16i	−0.0740809	+	0.0740809i
$802$	−1.90556e17	−	1.90556e17i	−0.716105	−	0.716105i
$803$	1.57470e17			0.587359
$804$	1.68935e17	+	1.68935e17i	0.625437	+	0.625437i
$805$			6.49896e16i			0.238819i
$806$	−9.81747e16			−0.358088
$807$	−3.36282e17			−1.21748
$808$	−1.19583e17			−0.429734
$809$	−1.88382e15	+	1.88382e15i	−0.00671967	+	0.00671967i	−0.710459	−	0.703739i	$-0.751512\pi$
$809$	−1.88382e15	+	1.88382e15i	−0.00671967	+	0.00671967i	0.703739	+	0.710459i	$0.251512\pi$
$810$	−5.25816e16	+	5.25816e16i	−0.186176	+	0.186176i
$811$		−	1.75429e17i		−	0.616560i	−0.951296	−	0.308280i	$-0.900247\pi$
$811$		−	1.75429e17i		−	0.616560i	0.951296	−	0.308280i	$-0.0997533\pi$
$812$	−3.54586e17	−	1.09768e17i	−1.23704	−	0.382948i
$813$	5.18925e17			1.79706
$814$	−6.61033e16	−	6.61033e16i	−0.227236	−	0.227236i
$815$	−1.36813e17	−	1.36813e17i	−0.466855	−	0.466855i
$816$			5.19014e16i			0.175808i
$817$			3.26110e17i			1.09656i
$818$		−	1.03002e17i		−	0.343816i
$819$	−3.11265e17			−1.03140
$820$	−5.84305e16	+	5.84305e16i	−0.192201	+	0.192201i
$821$		−	4.66173e17i		−	1.52226i	−0.648601	−	0.761129i	$-0.724646\pi$
$821$		−	4.66173e17i		−	1.52226i	0.648601	−	0.761129i	$-0.275354\pi$
$822$	2.85223e17	−	2.85223e17i	0.924601	−	0.924601i
$823$	−1.64492e17	−	1.64492e17i	−0.529354	−	0.529354i	0.391025	−	0.920380i	$-0.372120\pi$
$823$	−1.64492e17	−	1.64492e17i	−0.529354	−	0.529354i	−0.920380	+	0.391025i	$0.872120\pi$
$824$	1.09634e17	−	1.09634e17i	0.350253	−	0.350253i
$825$			2.23187e17i			0.707855i
$826$	−7.43595e16	−	7.43595e16i	−0.234130	−	0.234130i
$827$	−5.23796e16	+	5.23796e16i	−0.163730	+	0.163730i	−0.784217	−	0.620487i	$-0.786935\pi$
$827$	−5.23796e16	+	5.23796e16i	−0.163730	+	0.163730i	0.620487	+	0.784217i	$0.286935\pi$
$828$	−4.81639e16			−0.149465
$829$	3.89039e17	+	3.89039e17i	1.19858	+	1.19858i	0.974593	+	0.223982i	$0.0719058\pi$
$829$	3.89039e17	+	3.89039e17i	1.19858	+	1.19858i	0.223982	+	0.974593i	$0.428094\pi$
$830$	7.79433e16	−	7.79433e16i	0.238402	−	0.238402i
$831$	1.85610e17	+	1.85610e17i	0.563630	+	0.563630i
$832$	−1.26500e17			−0.381373
$833$	9.80089e17	+	9.80089e17i	2.93356	+	2.93356i
$834$		−	1.29202e17i		−	0.383949i
$835$	−2.03549e17			−0.600550
$836$	−8.80042e16			−0.257790
$837$	1.11012e17			0.322863
$838$	1.40468e17	−	1.40468e17i	0.405613	−	0.405613i
$839$	2.70471e17	−	2.70471e17i	0.775442	−	0.775442i	−0.203610	−	0.979052i	$-0.565268\pi$
$839$	2.70471e17	−	2.70471e17i	0.775442	−	0.775442i	0.979052	+	0.203610i	$0.0652676\pi$
$840$			3.23747e17i			0.921572i
$841$	−2.91932e17	−	1.99902e17i	−0.825098	−	0.564990i
$842$	3.55488e17			0.997590
$843$	2.88341e17	+	2.88341e17i	0.803418	+	0.803418i
$844$	−1.74624e17	−	1.74624e17i	−0.483115	−	0.483115i
$845$			5.79802e16i			0.159272i
$846$		−	4.15447e16i		−	0.113317i
$847$			4.36580e17i			1.18240i
$848$	2.52623e16			0.0679357
$849$	5.51537e17	−	5.51537e17i	1.47275	−	1.47275i
$850$			2.75124e17i			0.729483i
$851$	−7.65210e16	+	7.65210e16i	−0.201467	+	0.201467i
$852$	−1.13436e17	−	1.13436e17i	−0.296562	−	0.296562i
$853$	−1.43436e17	+	1.43436e17i	−0.372361	+	0.372361i	−0.868336	−	0.495976i	$-0.834810\pi$
$853$	−1.43436e17	+	1.43436e17i	−0.372361	+	0.372361i	0.495976	+	0.868336i	$0.334810\pi$
$854$			2.55510e17i			0.658659i
$855$	−4.42000e16	−	4.42000e16i	−0.113142	−	0.113142i
$856$	−4.67797e16	+	4.67797e16i	−0.118909	+	0.118909i
$857$	4.35036e16			0.109810			0.0549048	−	0.998492i	$-0.482514\pi$
$857$	4.35036e16			0.109810			0.0549048	+	0.998492i	$0.482514\pi$
$858$	1.02329e17	+	1.02329e17i	0.256492	+	0.256492i
$859$	−6.19688e16	+	6.19688e16i	−0.154246	+	0.154246i	−0.780011	−	0.625765i	$-0.784787\pi$
$859$	−6.19688e16	+	6.19688e16i	−0.154246	+	0.154246i	0.625765	+	0.780011i	$0.284787\pi$
$860$	1.24019e17	+	1.24019e17i	0.306548	+	0.306548i
$861$	−1.15582e18			−2.83708
$862$	−1.83315e16	−	1.83315e16i	−0.0446842	−	0.0446842i
$863$			4.04624e17i			0.979460i	0.871874	+	0.489730i	$0.162905\pi$
$863$			4.04624e17i			0.979460i	−0.871874	+	0.489730i	$0.837095\pi$
$864$	1.69466e17			0.407381
$865$	−2.33703e17			−0.557914
$866$	−2.38881e17			−0.566336
$867$	4.30546e17	−	4.30546e17i	1.01369	−	1.01369i
$868$	3.17578e17	−	3.17578e17i	0.742561	−	0.742561i
$869$			4.03549e17i			0.937082i
$870$	−3.62486e16	+	1.17095e17i	−0.0835942	+	0.270036i
$871$	−3.40465e17			−0.779766
$872$	1.90554e17	+	1.90554e17i	0.433430	+	0.433430i
$873$	3.10052e16	+	3.10052e16i	0.0700405	+	0.0700405i
$874$		−	5.27250e16i		−	0.118290i
$875$		−	6.10625e17i		−	1.36059i
$876$		−	3.60693e17i		−	0.798201i
$877$	−3.62736e17			−0.797247			−0.398624	−	0.917115i	$-0.630512\pi$
$877$	−3.62736e17			−0.797247			−0.398624	+	0.917115i	$0.630512\pi$
$878$	1.15896e17	−	1.15896e17i	0.252989	−	0.252989i
$879$			6.56076e16i			0.142240i
$880$	−7.18171e15	+	7.18171e15i	−0.0154644	+	0.0154644i
$881$	−1.93287e17	−	1.93287e17i	−0.413378	−	0.413378i	0.469536	−	0.882913i	$-0.344421\pi$
$881$	−1.93287e17	−	1.93287e17i	−0.413378	−	0.413378i	−0.882913	+	0.469536i	$0.844421\pi$
$882$	−3.86180e17	+	3.86180e17i	−0.820310	+	0.820310i
$883$			5.61493e17i			1.18462i	0.805709	+	0.592311i	$0.201784\pi$
$883$			5.61493e17i			1.18462i	−0.805709	+	0.592311i	$0.798216\pi$
$884$	−2.43727e17	−	2.43727e17i	−0.510728	−	0.510728i
$885$	4.74458e16	−	4.74458e16i	0.0987502	−	0.0987502i
$886$	−8.31033e16			−0.171797
$887$	−1.93345e17	−	1.93345e17i	−0.397001	−	0.397001i	0.480173	−	0.877174i	$-0.340574\pi$
$887$	−1.93345e17	−	1.93345e17i	−0.397001	−	0.397001i	−0.877174	+	0.480173i	$0.840574\pi$
$888$	−3.81190e17	+	3.81190e17i	−0.777435	+	0.777435i
$889$	−7.05525e17	−	7.05525e17i	−1.42923	−	1.42923i
$890$	−1.62911e16			−0.0327802
$891$	−2.70699e17	−	2.70699e17i	−0.541029	−	0.541029i
$892$			3.03938e17i			0.603386i
$893$	−8.78730e16			−0.173279
$894$	−2.74253e17			−0.537189
$895$	1.93260e17			0.376014
$896$	5.23925e17	−	5.23925e17i	1.01256	−	1.01256i
$897$	1.18456e17	−	1.18456e17i	0.227406	−	0.227406i
$898$			4.54110e17i			0.865970i
$899$	3.78695e17	−	1.99656e17i	0.717350	−	0.378203i
$900$	2.09458e17			0.394133
$901$	−3.99830e17	−	3.99830e17i	−0.747354	−	0.747354i
$902$	1.55685e17	+	1.55685e17i	0.289074	+	0.289074i
$903$			2.45324e18i			4.52495i
$904$			6.44579e17i			1.18104i
$905$			3.00143e17i			0.546307i
$906$	4.33876e17			0.784506
$907$	5.20546e17	−	5.20546e17i	0.935008	−	0.935008i	−0.0630053	−	0.998013i	$-0.520068\pi$
$907$	5.20546e17	−	5.20546e17i	0.935008	−	0.935008i	0.998013	+	0.0630053i	$0.0200685\pi$
$908$			4.24178e15i			0.00756891i
$909$	1.22817e17	−	1.22817e17i	0.217709	−	0.217709i
$910$	−1.29584e17	−	1.29584e17i	−0.228193	−	0.228193i
$911$	−2.47077e17	+	2.47077e17i	−0.432238	+	0.432238i	−0.889389	−	0.457151i	$-0.848870\pi$
$911$	−2.47077e17	+	2.47077e17i	−0.432238	+	0.432238i	0.457151	+	0.889389i	$0.348870\pi$
$912$			4.32557e16i			0.0751752i
$913$	4.01265e17	+	4.01265e17i	0.692798	+	0.692798i
$914$	−9.89658e15	+	9.89658e15i	−0.0169749	+	0.0169749i
$915$	−1.63031e17			−0.277807
$916$	1.63505e17	+	1.63505e17i	0.276795	+	0.276795i
$917$	1.09353e18	−	1.09353e18i	1.83914	−	1.83914i
$918$	−1.42636e17	−	1.42636e17i	−0.238327	−	0.238327i
$919$	−5.62541e17			−0.933815			−0.466908	−	0.884306i	$-0.654632\pi$
$919$	−5.62541e17			−0.933815			−0.466908	+	0.884306i	$0.654632\pi$
$920$	−5.04800e16	−	5.04800e16i	−0.0832516	−	0.0832516i
$921$			3.38210e17i			0.554152i
$922$	2.65368e16			0.0431979
$923$	2.28616e17			0.369739
$924$	−6.62032e17			−1.06377
$925$	3.32780e17	−	3.32780e17i	0.531259	−	0.531259i
$926$	3.54888e17	−	3.54888e17i	0.562893	−	0.562893i
$927$			2.25199e17i			0.354886i
$928$	5.78098e17	−	3.04786e17i	0.905135	−	0.477208i
$929$	7.41437e17			1.15340			0.576700	−	0.816956i	$-0.304340\pi$
$929$	7.41437e17			1.15340			0.576700	+	0.816956i	$0.304340\pi$
$930$	−1.04874e17	−	1.04874e17i	−0.162095	−	0.162095i
$931$	8.16826e17	+	8.16826e17i	1.25439	+	1.25439i
$932$		−	1.41125e16i		−	0.0215332i
$933$		−	5.60024e17i		−	0.849018i
$934$			4.84739e15i			0.00730175i
$935$	2.27332e17			0.340244
$936$	2.41772e17	−	2.41772e17i	0.359543	−	0.359543i
$937$			8.97585e17i			1.32629i	0.748491	+	0.663145i	$0.230779\pi$
$937$			8.97585e17i			1.32629i	−0.748491	+	0.663145i	$0.769221\pi$
$938$	−5.70006e17	+	5.70006e17i	−0.836878	+	0.836878i
$939$	−8.15817e17	−	8.15817e17i	−1.19014	−	1.19014i
$940$	−3.34180e16	+	3.34180e16i	−0.0484410	+	0.0484410i
$941$		−	8.07590e17i		−	1.16320i	−0.813476	−	0.581599i	$-0.802427\pi$
$941$		−	8.07590e17i		−	1.16320i	0.813476	−	0.581599i	$-0.197573\pi$
$942$	2.09157e17	+	2.09157e17i	0.299341	+	0.299341i
$943$	1.80221e17	−	1.80221e17i	0.256292	−	0.256292i
$944$	−1.90243e16			−0.0268829
$945$	1.46528e17	+	1.46528e17i	0.205746	+	0.205746i
$946$	3.30443e17	−	3.30443e17i	0.461052	−	0.461052i
$947$	3.38834e17	+	3.38834e17i	0.469772	+	0.469772i	0.901841	−	0.432068i	$-0.142216\pi$
$947$	3.38834e17	+	3.38834e17i	0.469772	+	0.469772i	−0.432068	+	0.901841i	$0.642216\pi$
$948$	9.24351e17			1.27346
$949$	3.63463e17	+	3.63463e17i	0.497581	+	0.497581i
$950$			2.29294e17i			0.311926i
$951$	3.32868e17			0.449975
$952$	−2.05456e18			−2.75992
$953$	−1.17925e18			−1.57415			−0.787076	−	0.616856i	$-0.788406\pi$
$953$	−1.17925e18			−1.57415			−0.787076	+	0.616856i	$0.788406\pi$
$954$	1.57543e17	−	1.57543e17i	0.208982	−	0.208982i
$955$	3.05050e17	−	3.05050e17i	0.402116	−	0.402116i
$956$			1.98102e17i			0.259503i
$957$	−6.02823e17	−	1.86614e17i	−0.784727	−	0.242925i
$958$	−2.48310e17			−0.321219
$959$	−1.85947e18	−	1.85947e18i	−2.39044	−	2.39044i
$960$	−1.35132e17	−	1.35132e17i	−0.172635	−	0.172635i
$961$		−	2.69673e17i		−	0.342372i
$962$		−	3.05152e17i		−	0.385005i
$963$		−	9.60902e16i		−	0.120482i
$964$	−2.95826e17			−0.368616
$965$	1.47223e16	−	1.47223e16i	0.0182311	−	0.0182311i
$966$		−	3.96636e17i		−	0.488123i
$967$	6.70845e17	−	6.70845e17i	0.820471	−	0.820471i	−0.165704	−	0.986176i	$-0.552990\pi$
$967$	6.70845e17	−	6.70845e17i	0.820471	−	0.820471i	0.986176	+	0.165704i	$0.0529897\pi$
$968$	−3.39109e17	−	3.39109e17i	−0.412181	−	0.412181i
$969$	6.84614e17	−	6.84614e17i	0.826995	−	0.826995i
$970$			2.58157e16i			0.0309923i
$971$	7.60313e17	+	7.60313e17i	0.907146	+	0.907146i	0.996041	−	0.0888952i	$-0.0283336\pi$
$971$	7.60313e17	+	7.60313e17i	0.907146	+	0.907146i	−0.0888952	+	0.996041i	$0.528334\pi$
$972$	−4.63604e17	+	4.63604e17i	−0.549730	+	0.549730i
$973$	−8.42314e17			−0.992652
$974$	−5.71868e16	−	5.71868e16i	−0.0669795	−	0.0669795i
$975$	−5.15148e17	+	5.15148e17i	−0.599659	+	0.599659i
$976$	3.26851e16	+	3.26851e16i	0.0378138	+	0.0378138i
$977$	6.52126e17			0.749832			0.374916	−	0.927059i	$-0.377672\pi$
$977$	6.52126e17			0.749832			0.374916	+	0.927059i	$0.377672\pi$
$978$	8.34979e17	+	8.34979e17i	0.954207	+	0.954207i
$979$		−	8.38694e16i		−	0.0952593i
$980$	6.21276e17			0.701339
$981$	−3.91417e17			−0.439163
$982$	−6.50377e17			−0.725264
$983$	−5.02288e17	+	5.02288e17i	−0.556713	+	0.556713i	−0.928370	−	0.371657i	$-0.878790\pi$
$983$	−5.02288e17	+	5.02288e17i	−0.556713	+	0.556713i	0.371657	+	0.928370i	$0.378790\pi$
$984$	8.97773e17	−	8.97773e17i	0.988999	−	0.988999i
$985$		−	3.21802e17i		−	0.352348i
$986$	−7.43105e17	−	2.30041e17i	−0.808703	−	0.250347i
$987$	−6.61045e17			−0.715036
$988$	−2.03127e17	−	2.03127e17i	−0.218387	−	0.218387i
$989$	−3.82521e17	−	3.82521e17i	−0.408768	−	0.408768i
$990$			8.95745e16i			0.0951422i
$991$		−	6.71112e17i		−	0.708522i	−0.935147	−	0.354261i	$-0.884732\pi$
$991$		−	6.71112e17i		−	0.708522i	0.935147	−	0.354261i	$-0.115268\pi$
$992$			7.90739e17i			0.829780i
$993$	−5.16184e16			−0.0538405
$994$	3.82747e17	−	3.82747e17i	0.396820	−	0.396820i
$995$			2.71104e17i			0.279382i
$996$	9.19119e17	−	9.19119e17i	0.941490	−	0.941490i
$997$	−1.02152e18	−	1.02152e18i	−1.04010	−	1.04010i	−0.999162	−	0.0409412i	$-0.986964\pi$
$997$	−1.02152e18	−	1.02152e18i	−1.04010	−	1.04010i	−0.0409412	−	0.999162i	$-0.513036\pi$
$998$	−3.38510e17	+	3.38510e17i	−0.342601	+	0.342601i
$999$			3.45055e17i			0.347132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.18	✓	58
29.17	odd	4	inner	29.13.c.a.17.18	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.18	✓	58	1.1	even	1	trivial
29.13.c.a.17.18	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)

\(f(q)\)	\(=\)	\(q+(26.4284 + 26.4284i) q^{2} +(-670.941 - 670.941i) q^{3} -2699.08i q^{4} +5810.81i q^{5} -35463.8i q^{6} -231201. q^{7} +(179583. - 179583. i) q^{8} +368882. i q^{9} +O(q^{10})\)	\(q+(26.4284 + 26.4284i) q^{2} +(-670.941 - 670.941i) q^{3} -2699.08i q^{4} +5810.81i q^{5} -35463.8i q^{6} -231201. q^{7} +(179583. - 179583. i) q^{8} +368882. i q^{9} +(-153570. + 153570. i) q^{10} +(-790605. - 790605. i) q^{11} +(-1.81092e6 + 1.81092e6i) q^{12} -3.64967e6i q^{13} +(-6.11026e6 - 6.11026e6i) q^{14} +(3.89871e6 - 3.89871e6i) q^{15} -1.56326e6 q^{16} +(2.47419e7 + 2.47419e7i) q^{17} +(-9.74895e6 + 9.74895e6i) q^{18} +(2.06204e7 + 2.06204e7i) q^{19} +1.56838e7 q^{20} +(1.55122e8 + 1.55122e8i) q^{21} -4.17888e7i q^{22} -4.83747e7 q^{23} -2.40979e8 q^{24} +2.10375e8 q^{25} +(9.64549e7 - 9.64549e7i) q^{26} +(-1.09068e8 + 1.09068e8i) q^{27} +6.24029e8i q^{28} +(-1.75902e8 + 5.68219e8i) q^{29} +2.06073e8 q^{30} +(-5.08915e8 - 5.08915e8i) q^{31} +(-7.76886e8 - 7.76886e8i) q^{32} +1.06090e9i q^{33} +1.30778e9i q^{34} -1.34346e9i q^{35} +9.95642e8 q^{36} +(1.58184e9 - 1.58184e9i) q^{37} +1.08993e9i q^{38} +(-2.44871e9 + 2.44871e9i) q^{39} +(1.04352e9 + 1.04352e9i) q^{40} +(-3.72552e9 + 3.72552e9i) q^{41} +8.19924e9i q^{42} +(7.90746e9 + 7.90746e9i) q^{43} +(-2.13391e9 + 2.13391e9i) q^{44} -2.14350e9 q^{45} +(-1.27846e9 - 1.27846e9i) q^{46} +(-2.13073e9 + 2.13073e9i) q^{47} +(1.04886e9 + 1.04886e9i) q^{48} +3.96125e10 q^{49} +(5.55987e9 + 5.55987e9i) q^{50} -3.32007e10i q^{51} -9.85076e9 q^{52} -1.61600e10 q^{53} -5.76496e9 q^{54} +(4.59406e9 - 4.59406e9i) q^{55} +(-4.15197e10 + 4.15197e10i) q^{56} -2.76702e10i q^{57} +(-1.96659e10 + 1.03683e10i) q^{58} +1.21696e10 q^{59} +(-1.05229e10 - 1.05229e10i) q^{60} +(-2.09083e10 - 2.09083e10i) q^{61} -2.68996e10i q^{62} -8.52857e10i q^{63} -3.46606e10i q^{64} +2.12075e10 q^{65} +(-2.80378e10 + 2.80378e10i) q^{66} -9.32866e10i q^{67} +(6.67805e10 - 6.67805e10i) q^{68} +(3.24565e10 + 3.24565e10i) q^{69} +(3.55056e10 - 3.55056e10i) q^{70} +6.26401e10i q^{71} +(6.62449e10 + 6.62449e10i) q^{72} +(-9.95880e10 + 9.95880e10i) q^{73} +8.36109e10 q^{74} +(-1.41149e11 - 1.41149e11i) q^{75} +(5.56562e10 - 5.56562e10i) q^{76} +(1.82788e11 + 1.82788e11i) q^{77} -1.29431e11 q^{78} +(-2.55215e11 - 2.55215e11i) q^{79} -9.08381e9i q^{80} +3.42395e11 q^{81} -1.96919e11 q^{82} -5.07541e11 q^{83} +(4.18687e11 - 4.18687e11i) q^{84} +(-1.43771e11 + 1.43771e11i) q^{85} +4.17963e11i q^{86} +(4.99261e11 - 2.63222e11i) q^{87} -2.83959e11 q^{88} +(5.30413e10 + 5.30413e10i) q^{89} +(-5.66493e10 - 5.66493e10i) q^{90} +8.43806e11i q^{91} +1.30567e11i q^{92} +6.82904e11i q^{93} -1.12623e11 q^{94} +(-1.19821e11 + 1.19821e11i) q^{95} +1.04249e12i q^{96} +(8.40519e10 - 8.40519e10i) q^{97} +(1.04689e12 + 1.04689e12i) q^{98} +(2.91640e11 - 2.91640e11i) 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

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