LMFDB - Embedded newform 54.9.f.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	54.11
Dual form			54.9.f.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.27231 + 8.66680i) q^{2} +(-14.8240 + 79.6320i) q^{3} +(-22.2270 - 126.055i) q^{4} +(332.225 - 912.782i) q^{5} +(-582.350 - 707.585i) q^{6} +(238.226 - 1351.05i) q^{7} +(1254.14 + 724.077i) q^{8} +(-6121.50 - 2360.92i) q^{9} +O(q^{10})$	\(q+(-7.27231 + 8.66680i) q^{2} +(-14.8240 + 79.6320i) q^{3} +(-22.2270 - 126.055i) q^{4} +(332.225 - 912.782i) q^{5} +(-582.350 - 707.585i) q^{6} +(238.226 - 1351.05i) q^{7} +(1254.14 + 724.077i) q^{8} +(-6121.50 - 2360.92i) q^{9} +(5494.85 + 9517.37i) q^{10} +(6463.89 + 17759.4i) q^{11} +(10367.5 + 98.6629i) q^{12} +(-20710.9 + 17378.5i) q^{13} +(9976.80 + 11889.9i) q^{14} +(67761.7 + 39986.8i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-76297.8 + 44050.6i) q^{17} +(64979.1 - 35884.5i) q^{18} +(8505.08 - 14731.2i) q^{19} +(-122445. - 21590.4i) q^{20} +(104055. + 38998.3i) q^{21} +(-200924. - 73130.5i) q^{22} +(46659.4 - 8227.30i) q^{23} +(-76251.0 + 89135.8i) q^{24} +(-423561. - 355410. i) q^{25} -305879. i q^{26} +(278750. - 452469. i) q^{27} -175602. q^{28} +(-484972. + 577967. i) q^{29} +(-839342. + 296481. i) q^{30} +(168597. + 956159. i) q^{31} +(63398.2 - 174185. i) q^{32} +(-1.51003e6 + 251468. i) q^{33} +(173084. - 981608. i) q^{34} +(-1.15407e6 - 666301. i) q^{35} +(-161545. + 824124. i) q^{36} +(1.55033e6 + 2.68525e6i) q^{37} +(65821.1 + 180842. i) q^{38} +(-1.07687e6 - 1.90687e6i) q^{39} +(1.07758e6 - 904198. i) q^{40} +(-2.28290e6 - 2.72065e6i) q^{41} +(-1.09471e6 + 618217. i) q^{42} +(-4.60117e6 + 1.67469e6i) q^{43} +(2.09499e6 - 1.20954e6i) q^{44} +(-4.18873e6 + 4.80324e6i) q^{45} +(-268017. + 464219. i) q^{46} +(-6.32013e6 - 1.11441e6i) q^{47} +(-218002. - 1.30908e6i) q^{48} +(3.64856e6 + 1.32797e6i) q^{49} +(6.16054e6 - 1.08627e6i) q^{50} +(-2.37680e6 - 6.72875e6i) q^{51} +(2.65099e6 + 2.22445e6i) q^{52} -4.04236e6i q^{53} +(1.89430e6 + 5.70636e6i) q^{54} +1.83579e7 q^{55} +(1.27703e6 - 1.52191e6i) q^{56} +(1.04700e6 + 895651. i) q^{57} +(-1.48226e6 - 8.40631e6i) q^{58} +(-2.68083e6 + 7.36551e6i) q^{59} +(3.53442e6 - 9.43052e6i) q^{60} +(-3.36027e6 + 1.90570e7i) q^{61} +(-9.51293e6 - 5.49229e6i) q^{62} +(-4.64802e6 + 7.70800e6i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(8.98209e6 + 2.46781e7i) q^{65} +(8.80202e6 - 1.49159e7i) q^{66} +(2.50926e7 - 2.10552e7i) q^{67} +(7.24868e6 + 8.63864e6i) q^{68} +(-36520.1 + 3.83754e6i) q^{69} +(1.41674e7 - 5.15652e6i) q^{70} +(-1.06532e7 + 6.15062e6i) q^{71} +(-5.96772e6 - 7.39336e6i) q^{72} +(-8.45017e6 + 1.46361e7i) q^{73} +(-3.45470e7 - 6.09158e6i) q^{74} +(3.45808e7 - 2.84604e7i) q^{75} +(-2.04599e6 - 744680. i) q^{76} +(2.55336e7 - 4.50227e6i) q^{77} +(2.43577e7 + 4.53433e6i) q^{78} +(-2.64361e7 - 2.21825e7i) q^{79} +1.59148e7i q^{80} +(3.18988e7 + 2.89048e7i) q^{81} +4.01813e7 q^{82} +(-7.33665e6 + 8.74347e6i) q^{83} +(2.60311e6 - 1.39835e7i) q^{84} +(1.48605e7 + 8.42780e7i) q^{85} +(1.89469e7 - 5.20563e7i) q^{86} +(-3.88354e7 - 4.71870e7i) q^{87} +(-4.75256e6 + 2.69531e7i) q^{88} +(-7.56650e7 - 4.36852e7i) q^{89} +(-1.11670e7 - 7.12335e7i) q^{90} +(1.85453e7 + 3.21214e7i) q^{91} +(-2.07419e6 - 5.69880e6i) q^{92} +(-7.86401e7 - 748381. i) q^{93} +(5.56203e7 - 4.66710e7i) q^{94} +(-1.06208e7 - 1.26574e7i) q^{95} +(1.29309e7 + 7.63063e6i) q^{96} +(-2.79578e7 + 1.01758e7i) q^{97} +(-3.80427e7 + 2.19640e7i) q^{98} +(2.35983e6 - 1.23975e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−7.27231	+	8.66680i	−0.454519	+	0.541675i
$2$	−7.27231	+	8.66680i	−0.454519	+	0.541675i
$3$	−14.8240	+	79.6320i	−0.183012	+	0.983111i
$3$	−14.8240	+	79.6320i	−0.183012	+	0.983111i
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	332.225	−	912.782i	0.531561	−	1.46045i	−0.325653	−	0.945490i	$-0.605584\pi$
$5$	332.225	−	912.782i	0.531561	−	1.46045i	0.857213	−	0.514962i	$-0.172194\pi$
$6$	−582.350	−	707.585i	−0.449344	−	0.545976i
$7$	238.226	−	1351.05i	0.0992195	−	0.562702i	−0.894153	−	0.447762i	$-0.852221\pi$
$7$	238.226	−	1351.05i	0.0992195	−	0.562702i	0.993372	−	0.114940i	$-0.0366676\pi$
$8$	1254.14	+	724.077i	0.306186	+	0.176777i
$9$	−6121.50	−	2360.92i	−0.933013	−	0.359842i
$10$	5494.85	+	9517.37i	0.549485	+	0.951737i
$11$	6463.89	+	17759.4i	0.441492	+	1.21299i	0.938511	+	0.345250i	$0.112206\pi$
$11$	6463.89	+	17759.4i	0.441492	+	1.21299i	−0.497019	+	0.867740i	$0.665572\pi$
$12$	10367.5	+	98.6629i	0.499977	+	0.00475805i
$13$	−20710.9	+	17378.5i	−0.725145	+	0.608469i	−0.928803	−	0.370573i	$-0.879161\pi$
$13$	−20710.9	+	17378.5i	−0.725145	+	0.608469i	0.203658	+	0.979042i	$0.434717\pi$
$14$	9976.80	+	11889.9i	0.259704	+	0.309504i
$15$	67761.7	+	39986.8i	1.33850	+	0.789863i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	−76297.8	+	44050.6i	−0.913517	+	0.527419i	−0.881561	−	0.472070i	$-0.843507\pi$
$17$	−76297.8	+	44050.6i	−0.913517	+	0.527419i	−0.0319559	+	0.999489i	$0.510174\pi$
$18$	64979.1	−	35884.5i	0.618990	−	0.341835i
$19$	8505.08	−	14731.2i	0.0652625	−	0.113038i	−0.831548	−	0.555453i	$-0.812545\pi$
$19$	8505.08	−	14731.2i	0.0652625	−	0.113038i	0.896810	+	0.442415i	$0.145878\pi$
$20$	−122445.	−	21590.4i	−0.765284	−	0.134940i
$21$	104055.	+	38998.3i	0.535040	+	0.200525i
$22$	−200924.	−	73130.5i	−0.857713	−	0.312182i
$23$	46659.4	−	8227.30i	0.166735	−	0.0293999i	−0.0896572	−	0.995973i	$-0.528577\pi$
$23$	46659.4	−	8227.30i	0.166735	−	0.0293999i	0.256392	+	0.966573i	$0.417466\pi$
$24$	−76251.0	+	89135.8i	−0.229827	+	0.268663i
$25$	−423561.	−	355410.i	−1.08432	−	0.909849i
$26$		−	305879.i		−	0.669354i
$27$	278750.	−	452469.i	0.524517	−	0.851400i
$28$	−175602.			−0.285691
$29$	−484972.	+	577967.i	−0.685685	+	0.817167i	−0.990827	−	0.135140i	$-0.956852\pi$
$29$	−484972.	+	577967.i	−0.685685	+	0.817167i	0.305142	+	0.952307i	$0.401296\pi$
$30$	−839342.	+	296481.i	−1.03622	+	0.366026i
$31$	168597.	+	956159.i	0.182559	+	1.03534i	0.929052	+	0.369949i	$0.120625\pi$
$31$	168597.	+	956159.i	0.182559	+	1.03534i	−0.746494	+	0.665393i	$0.768264\pi$
$32$	63398.2	−	174185.i	0.0604612	−	0.166116i
$33$	−1.51003e6	+	251468.i	−1.27330	+	0.212044i
$34$	173084.	−	981608.i	0.129521	−	0.734552i
$35$	−1.15407e6	−	666301.i	−0.769057	−	0.444015i
$36$	−161545.	+	824124.i	−0.0961795	+	0.490662i
$37$	1.55033e6	+	2.68525e6i	0.827214	+	1.43278i	0.900216	+	0.435444i	$0.143409\pi$
$37$	1.55033e6	+	2.68525e6i	0.827214	+	1.43278i	−0.0730022	+	0.997332i	$0.523258\pi$
$38$	65821.1	+	180842.i	0.0315668	+	0.0867291i
$39$	−1.07687e6	−	1.90687e6i	−0.465482	−	0.824255i
$40$	1.07758e6	−	904198.i	0.420930	−	0.353202i
$41$	−2.28290e6	−	2.72065e6i	−0.807887	−	0.962803i	0.191940	−	0.981407i	$-0.438522\pi$
$41$	−2.28290e6	−	2.72065e6i	−0.807887	−	0.962803i	−0.999827	+	0.0186042i	$0.994078\pi$
$42$	−1.09471e6	+	618217.i	−0.351805	+	0.198675i
$43$	−4.60117e6	+	1.67469e6i	−1.34584	+	0.489847i	−0.911648	−	0.410972i	$-0.865189\pi$
$43$	−4.60117e6	+	1.67469e6i	−1.34584	+	0.489847i	−0.434195	+	0.900819i	$0.642967\pi$
$44$	2.09499e6	−	1.20954e6i	0.558949	−	0.322709i
$45$	−4.18873e6	+	4.80324e6i	−1.02148	+	1.17134i
$46$	−268017.	+	464219.i	−0.0598592	+	0.103679i
$47$	−6.32013e6	−	1.11441e6i	−1.29519	−	0.228377i	−0.516774	−	0.856122i	$-0.672867\pi$
$47$	−6.32013e6	−	1.11441e6i	−1.29519	−	0.228377i	−0.778419	+	0.627745i	$0.783978\pi$
$48$	−218002.	−	1.30908e6i	−0.0410672	−	0.246604i
$49$	3.64856e6	+	1.32797e6i	0.632904	+	0.230358i
$50$	6.16054e6	−	1.08627e6i	0.985686	−	0.173803i
$51$	−2.37680e6	−	6.72875e6i	−0.351327	−	0.994612i
$52$	2.65099e6	+	2.22445e6i	0.362573	+	0.304234i
$53$		−	4.04236e6i		−	0.512309i	−0.966636	−	0.256154i	$-0.917544\pi$
$53$		−	4.04236e6i		−	0.512309i	0.966636	−	0.256154i	$-0.0824555\pi$
$54$	1.89430e6	+	5.70636e6i	0.222779	+	0.671096i
$55$	1.83579e7			2.00619
$56$	1.27703e6	−	1.52191e6i	0.129852	−	0.154752i
$57$	1.04700e6	+	895651.i	0.0991851	+	0.0848476i
$58$	−1.48226e6	−	8.40631e6i	−0.130982	−	0.742837i
$59$	−2.68083e6	+	7.36551e6i	−0.221238	+	0.607847i	−0.999806	−	0.0197137i	$-0.993725\pi$
$59$	−2.68083e6	+	7.36551e6i	−0.221238	+	0.607847i	0.778567	+	0.627561i	$0.215947\pi$
$60$	3.53442e6	−	9.43052e6i	0.272717	−	0.727663i
$61$	−3.36027e6	+	1.90570e7i	−0.242692	+	1.37637i	0.583101	+	0.812400i	$0.301839\pi$
$61$	−3.36027e6	+	1.90570e7i	−0.242692	+	1.37637i	−0.825793	+	0.563974i	$0.809272\pi$
$62$	−9.51293e6	−	5.49229e6i	−0.643795	−	0.371695i
$63$	−4.64802e6	+	7.70800e6i	−0.295057	+	0.489305i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	8.98209e6	+	2.46781e7i	0.503181	+	1.38248i
$66$	8.80202e6	−	1.49159e7i	0.463881	−	0.786094i
$67$	2.50926e7	−	2.10552e7i	1.24522	−	1.04486i	0.248122	−	0.968729i	$-0.420187\pi$
$67$	2.50926e7	−	2.10552e7i	1.24522	−	1.04486i	0.997098	−	0.0761342i	$-0.0242577\pi$
$68$	7.24868e6	+	8.63864e6i	0.339019	+	0.404027i
$69$	−36520.1	+	3.83754e6i	−0.00161115	+	0.169300i
$70$	1.41674e7	−	5.15652e6i	0.590064	−	0.214766i
$71$	−1.06532e7	+	6.15062e6i	−0.419224	+	0.242039i	−0.694745	−	0.719256i	$-0.744483\pi$
$71$	−1.06532e7	+	6.15062e6i	−0.419224	+	0.242039i	0.275521	+	0.961295i	$0.411150\pi$
$72$	−5.96772e6	−	7.39336e6i	−0.222064	−	0.275114i
$73$	−8.45017e6	+	1.46361e7i	−0.297560	+	0.515389i	−0.975577	−	0.219657i	$-0.929506\pi$
$73$	−8.45017e6	+	1.46361e7i	−0.297560	+	0.515389i	0.678017	+	0.735046i	$0.262839\pi$
$74$	−3.45470e7	−	6.09158e6i	−1.15208	−	0.203143i
$75$	3.45808e7	−	2.84604e7i	1.09293	−	0.899490i
$76$	−2.04599e6	−	744680.i	−0.0613267	−	0.0223211i
$77$	2.55336e7	−	4.50227e6i	0.726356	−	0.128076i
$78$	2.43577e7	+	4.53433e6i	0.658049	+	0.122500i
$79$	−2.64361e7	−	2.21825e7i	−0.678717	−	0.569512i	0.236914	−	0.971531i	$-0.423864\pi$
$79$	−2.64361e7	−	2.21825e7i	−0.678717	−	0.569512i	−0.915631	+	0.402019i	$0.868309\pi$
$80$			1.59148e7i			0.388545i
$81$	3.18988e7	+	2.89048e7i	0.741028	+	0.671474i
$82$	4.01813e7			0.888727
$83$	−7.33665e6	+	8.74347e6i	−0.154591	+	0.184235i	−0.837781	−	0.546006i	$-0.816148\pi$
$83$	−7.33665e6	+	8.74347e6i	−0.154591	+	0.184235i	0.683190	+	0.730241i	$0.260592\pi$
$84$	2.60311e6	−	1.39835e7i	0.0522849	−	0.280866i
$85$	1.48605e7	+	8.42780e7i	0.284680	+	1.61450i
$86$	1.89469e7	−	5.20563e7i	0.346374	−	0.951655i
$87$	−3.88354e7	−	4.71870e7i	−0.677877	−	0.823655i
$88$	−4.75256e6	+	2.69531e7i	−0.0792495	+	0.449446i
$89$	−7.56650e7	−	4.36852e7i	−1.20597	−	0.696265i	−0.244090	−	0.969753i	$-0.578489\pi$
$89$	−7.56650e7	−	4.36852e7i	−1.20597	−	0.696265i	−0.961875	+	0.273488i	$0.911823\pi$
$90$	−1.11670e7	−	7.12335e7i	−0.170203	−	1.08571i
$91$	1.85453e7	+	3.21214e7i	0.270438	+	0.468412i
$92$	−2.07419e6	−	5.69880e6i	−0.0289533	−	0.0795485i
$93$	−7.86401e7	−	748381.i	−1.05127	−	0.0100044i
$94$	5.56203e7	−	4.66710e7i	0.712397	−	0.597772i
$95$	−1.06208e7	−	1.26574e7i	−0.130396	−	0.155399i
$96$	1.29309e7	+	7.63063e6i	0.152245	+	0.0898412i
$97$	−2.79578e7	+	1.01758e7i	−0.315802	+	0.114943i	−0.495058	−	0.868860i	$-0.664853\pi$
$97$	−2.79578e7	+	1.01758e7i	−0.315802	+	0.114943i	0.179256	+	0.983802i	$0.442631\pi$
$98$	−3.80427e7	+	2.19640e7i	−0.412446	+	0.238126i
$99$	2.35983e6	−	1.23975e8i	0.0245664	−	1.29060i
$100$	−3.53869e7	+	6.12918e7i	−0.353869	+	0.612918i
$101$	−6.75822e7	−	1.19166e7i	−0.649452	−	0.114516i	−0.160789	−	0.986989i	$-0.551404\pi$
$101$	−6.75822e7	−	1.19166e7i	−0.649452	−	0.114516i	−0.488662	+	0.872473i	$0.662515\pi$
$102$	7.56016e7	+	2.83343e7i	0.698442	+	0.261765i
$103$	8.95125e7	+	3.25799e7i	0.795307	+	0.289468i	0.707540	−	0.706673i	$-0.249805\pi$
$103$	8.95125e7	+	3.25799e7i	0.795307	+	0.289468i	0.0877665	+	0.996141i	$0.472027\pi$
$104$	−3.85577e7	+	6.79876e6i	−0.329593	+	0.0581161i
$105$	7.01667e7	−	8.20234e7i	0.577263	−	0.674808i
$106$	3.50344e7	+	2.93973e7i	0.277505	+	0.232854i
$107$			2.41895e8i			1.84540i	0.385516	+	0.922701i	$0.374023\pi$
$107$			2.41895e8i			1.84540i	−0.385516	+	0.922701i	$0.625977\pi$
$108$	−6.32319e7	−	2.50809e7i	−0.464773	−	0.184352i
$109$	−3.64851e6			−0.0258470			−0.0129235	−	0.999916i	$-0.504114\pi$
$109$	−3.64851e6			−0.0258470			−0.0129235	+	0.999916i	$0.504114\pi$
$110$	−1.33504e8	+	1.59104e8i	−0.911853	+	1.08670i
$111$	−2.36814e8	+	8.36499e7i	−1.55997	+	0.551028i
$112$	3.90310e6	+	2.21356e7i	0.0248049	+	0.140675i
$113$	−4.02792e7	+	1.10666e8i	−0.247040	+	0.678736i	0.752751	+	0.658305i	$0.228726\pi$
$113$	−4.02792e7	+	1.10666e8i	−0.247040	+	0.678736i	−0.999791	+	0.0204315i	$0.993496\pi$
$114$	−1.53765e7	+	2.56067e6i	−0.0910414	+	0.0151612i
$115$	7.99169e6	−	4.53231e7i	0.0456928	−	0.259137i
$116$	8.36353e7	+	4.82869e7i	0.461910	+	0.266684i
$117$	1.67811e8	−	5.74856e7i	0.895523	−	0.306772i
$118$	−4.43396e7	−	7.67985e7i	−0.228699	−	0.396118i
$119$	4.13383e7	+	1.13576e8i	0.206141	+	0.566368i
$120$	5.60291e7	+	9.92137e7i	0.270202	+	0.478461i
$121$	−1.09405e8	+	9.18020e7i	−0.510384	+	0.428263i
$122$	−1.40727e8	−	1.67712e8i	−0.635239	−	0.757048i
$123$	2.50492e8	−	1.41461e8i	1.09439	−	0.618038i
$124$	1.16782e8	−	4.25050e7i	0.493956	−	0.179785i
$125$	−1.36526e8	+	7.88235e7i	−0.559211	+	0.322861i
$126$	−3.30019e7	−	9.63384e7i	−0.130935	−	0.382224i
$127$	4.21668e7	−	7.30351e7i	0.162090	−	0.280748i	−0.773528	−	0.633762i	$-0.781510\pi$
$127$	4.21668e7	−	7.30351e7i	0.162090	−	0.280748i	0.935618	+	0.353014i	$0.114843\pi$
$128$	−2.33661e7	−	4.12008e6i	−0.0870455	−	0.0153485i
$129$	−6.51512e7	−	3.91226e8i	−0.235268	−	1.41276i
$130$	−2.79201e8	−	1.01621e8i	−0.977559	−	0.355802i
$131$	−4.06300e8	+	7.16416e7i	−1.37963	+	0.243265i	−0.813745	−	0.581222i	$-0.802575\pi$
$131$	−4.06300e8	+	7.16416e7i	−1.37963	+	0.243265i	−0.565880	+	0.824487i	$0.691464\pi$
$132$	6.52623e7	+	1.84759e8i	0.214965	+	0.608568i
$133$	−1.78764e7	−	1.50001e7i	−0.0571314	−	0.0479389i
$134$			3.70592e8i			1.14942i
$135$	−3.20398e8	−	4.04759e8i	−0.964616	−	1.21860i
$136$	−1.27584e8			−0.372942
$137$	4.35416e8	−	5.18909e8i	1.23601	−	1.47302i	0.407346	−	0.913274i	$-0.366454\pi$
$137$	4.35416e8	−	5.18909e8i	1.23601	−	1.47302i	0.828664	−	0.559746i	$-0.189101\pi$
$138$	−3.29936e7	−	2.82243e7i	−0.0909732	−	0.0778228i
$139$	2.46669e7	+	1.39893e8i	0.0660777	+	0.374745i	0.999857	+	0.0168966i	$0.00537860\pi$
$139$	2.46669e7	+	1.39893e8i	0.0660777	+	0.374745i	−0.933780	+	0.357849i	$0.883510\pi$
$140$	−5.83394e7	+	1.60286e8i	−0.151862	+	0.417238i
$141$	1.82432e8	−	4.86764e8i	0.461556	−	1.23152i
$142$	2.41671e7	−	1.37058e8i	0.0594389	−	0.337095i
$143$	−4.42504e8	−	2.55480e8i	−1.05821	−	0.610959i
$144$	1.07476e8	+	2.04578e6i	0.249955	+	0.00475784i
$145$	3.66438e8	+	6.34689e8i	0.828950	+	1.43578i
$146$	−6.53962e7	−	1.79674e8i	−0.143927	−	0.395435i
$147$	−1.59835e8	+	2.70857e8i	−0.342296	+	0.580056i
$148$	3.04031e8	−	2.55113e8i	0.633682	−	0.531723i
$149$	−3.79666e7	−	4.52468e7i	−0.0770294	−	0.0918001i	0.726153	−	0.687533i	$-0.241306\pi$
$149$	−3.79666e7	−	4.52468e7i	−0.0770294	−	0.0918001i	−0.803183	+	0.595733i	$0.796862\pi$
$150$	−4.82182e6	+	5.06678e8i	−0.00952459	+	1.00085i
$151$	3.92179e8	−	1.42741e8i	0.754355	−	0.274563i	0.0639181	−	0.997955i	$-0.479640\pi$
$151$	3.92179e8	−	1.42741e8i	0.754355	−	0.274563i	0.690437	+	0.723392i	$0.257418\pi$
$152$	2.13331e7	−	1.23167e7i	0.0399650	−	0.0230738i
$153$	5.71057e8	−	8.95224e7i	1.04211	−	0.163368i
$154$	−1.46668e8	+	2.54037e8i	−0.260767	+	0.451662i
$155$	9.28777e8	+	1.63768e8i	1.60911	+	0.283729i
$156$	−2.16435e8	+	1.78129e8i	−0.365451	+	0.300770i
$157$	6.33366e8	+	2.30527e8i	1.04245	+	0.379422i	0.805810	−	0.592175i	$-0.201730\pi$
$157$	6.33366e8	+	2.30527e8i	1.04245	+	0.379422i	0.236643	+	0.971597i	$0.423953\pi$
$158$	3.84503e8	−	6.77983e7i	0.616981	−	0.108790i
$159$	3.21901e8	+	5.99238e7i	0.503656	+	0.0937586i
$160$	−1.37930e8	−	1.15737e8i	−0.210465	−	0.176601i
$161$		−	6.49989e7i		−	0.0967393i
$162$	−4.82490e8	+	6.62562e7i	−0.700533	+	0.0961982i
$163$	5.98366e8			0.847650			0.423825	−	0.905744i	$-0.360687\pi$
$163$	5.98366e8			0.847650			0.423825	+	0.905744i	$0.360687\pi$
$164$	−2.92211e8	+	3.48243e8i	−0.403944	+	0.481401i
$165$	−2.72137e8	+	1.46188e9i	−0.367157	+	1.97231i
$166$	−2.24236e7	−	1.27171e8i	−0.0295306	−	0.167477i
$167$	4.36130e8	−	1.19826e9i	0.560725	−	1.54058i	−0.257854	−	0.966184i	$-0.583015\pi$
$167$	4.36130e8	−	1.19826e9i	0.560725	−	1.54058i	0.818579	−	0.574394i	$-0.194762\pi$
$168$	1.02262e8	+	1.24253e8i	0.128374	+	0.155981i
$169$	−1.47217e7	+	8.34910e7i	−0.0180473	+	0.102351i
$170$	−8.38491e8	−	4.84103e8i	−1.00393	−	0.579618i
$171$	−8.68431e7	+	7.00974e7i	−0.101567	+	0.0819818i
$172$	3.13374e8	+	5.42779e8i	0.358054	+	0.620168i
$173$	4.07499e7	+	1.11959e8i	0.0454927	+	0.124990i	0.960359	−	0.278768i	$-0.0899260\pi$
$173$	4.07499e7	+	1.11959e8i	0.0454927	+	0.124990i	−0.914866	+	0.403758i	$0.867704\pi$
$174$	6.91384e8	+	6.57958e6i	0.754262	+	0.00717796i
$175$	−5.81079e8	+	4.87583e8i	−0.619559	+	0.519872i
$176$	−1.99035e8	−	2.37201e8i	−0.207433	−	0.247210i
$177$	−5.46789e8	−	3.22665e8i	−0.557092	−	0.328745i
$178$	9.28870e8	−	3.38081e8i	0.925284	−	0.336776i
$179$	1.64197e9	−	9.47995e8i	1.59939	−	0.923408i	0.607786	−	0.794101i	$-0.292058\pi$
$179$	1.64197e9	−	9.47995e8i	1.59939	−	0.923408i	0.991605	−	0.129307i	$-0.0412753\pi$
$180$	6.98577e8	+	4.21250e8i	0.665463	+	0.401282i
$181$	−6.87564e8	+	1.19090e9i	−0.640618	+	1.10958i	0.344677	+	0.938721i	$0.387988\pi$
$181$	−6.87564e8	+	1.19090e9i	−0.640618	+	1.10958i	−0.985295	+	0.170861i	$0.945345\pi$
$182$	−4.13257e8	−	7.28683e7i	−0.376647	−	0.0664130i
$183$	−1.46774e9	−	5.50086e8i	−1.30871	−	0.490485i
$184$	6.44745e7	+	2.34668e7i	0.0562493	+	0.0204731i
$185$	2.96611e9	−	5.23005e8i	2.53221	−	0.446498i
$186$	5.78382e8	−	6.76116e8i	0.483240	−	0.564897i
$187$	−1.27549e9	−	1.07026e9i	−1.04306	−	0.875235i
$188$			8.21456e8i			0.657587i
$189$	−5.44901e8	−	4.84394e8i	−0.427042	−	0.379622i
$190$	1.86937e8			0.143443
$191$	−1.39014e9	+	1.65670e9i	−1.04454	+	1.24483i	−0.0756999	+	0.997131i	$0.524119\pi$
$191$	−1.39014e9	+	1.65670e9i	−1.04454	+	1.24483i	−0.968837	+	0.247700i	$0.920325\pi$
$192$	−1.60171e8	+	5.65771e7i	−0.117863	+	0.0416328i
$193$	−4.03492e8	−	2.28832e9i	−0.290808	−	1.64925i	−0.683769	−	0.729698i	$-0.739660\pi$
$193$	−4.03492e8	−	2.28832e9i	−0.290808	−	1.64925i	0.392961	−	0.919555i	$-0.371451\pi$
$194$	1.15126e8	−	3.16306e8i	0.0812767	−	0.223306i
$195$	−2.09831e9	+	3.49434e8i	−1.45122	+	0.241672i
$196$	8.63011e7	−	4.89438e8i	0.0584780	−	0.331645i
$197$	−1.28035e9	−	7.39212e8i	−0.850089	−	0.490799i	0.0105916	−	0.999944i	$-0.496629\pi$
$197$	−1.28035e9	−	7.39212e8i	−0.850089	−	0.490799i	−0.860681	+	0.509145i	$0.829962\pi$
$198$	1.05730e9	+	9.22036e8i	0.687922	+	0.599911i
$199$	−2.19821e8	−	3.80741e8i	−0.140170	−	0.242782i	0.787390	−	0.616455i	$-0.211432\pi$
$199$	−2.19821e8	−	3.80741e8i	−0.140170	−	0.242782i	−0.927561	+	0.373672i	$0.878098\pi$
$200$	−2.73860e8	−	7.52424e8i	−0.171163	−	0.470265i
$201$	1.30469e9	+	2.31029e9i	0.799326	+	1.41541i
$202$	5.94757e8	−	4.99061e8i	0.357219	−	0.299742i
$203$	6.65327e8	+	7.92906e8i	0.391788	+	0.466915i
$204$	−7.95366e8	+	4.49168e8i	−0.459247	+	0.259351i
$205$	−3.24180e9	+	1.17992e9i	−1.83557	+	0.668092i
$206$	−9.33326e8	+	5.38856e8i	−0.518280	+	0.299229i
$207$	−3.05049e8	−	5.97957e7i	−0.166146	−	0.0325678i
$208$	2.21480e8	−	3.83614e8i	0.118326	−	0.204947i
$209$	3.16593e8	+	5.58240e7i	0.165927	+	0.0292574i
$210$	2.00607e8	+	1.20462e9i	0.103150	+	0.619403i
$211$	−2.21733e9	−	8.07041e8i	−1.11866	−	0.407161i	−0.284500	−	0.958676i	$-0.591827\pi$
$211$	−2.21733e9	−	8.07041e8i	−1.11866	−	0.407161i	−0.834165	+	0.551516i	$0.814050\pi$
$212$	−5.09562e8	+	8.98495e7i	−0.252263	+	0.0444807i
$213$	−3.31863e8	−	9.39510e8i	−0.161228	−	0.456439i
$214$	−2.09645e9	−	1.75913e9i	−0.999609	−	0.838771i
$215$			4.75624e9i			2.22592i
$216$	6.77213e8	−	3.65622e8i	0.311108	−	0.167965i
$217$	1.33198e9			0.600702
$218$	2.65331e7	−	3.16209e7i	0.0117480	−	0.0140007i
$219$	−1.04024e9	−	8.89869e8i	−0.452227	−	0.386856i
$220$	−4.08041e8	−	2.31411e9i	−0.174186	−	0.987857i
$221$	8.14662e8	−	2.23827e9i	0.341514	−	0.938302i
$222$	9.97208e8	−	2.66075e9i	0.410558	−	1.09545i
$223$	3.63437e8	−	2.06115e9i	0.146963	−	0.833471i	−0.818806	−	0.574070i	$-0.805364\pi$
$223$	3.63437e8	−	2.06115e9i	0.146963	−	0.833471i	0.965770	−	0.259401i	$-0.0835251\pi$
$224$	−2.20229e8	−	1.27149e8i	−0.0874747	−	0.0505035i
$225$	1.75373e9	+	3.17564e9i	0.684280	+	1.23908i
$226$	−6.66199e8	−	1.15389e9i	−0.255370	−	0.442314i
$227$	−1.03079e9	−	2.83207e9i	−0.388209	−	1.06660i	−0.967807	−	0.251693i	$-0.919013\pi$
$227$	−1.03079e9	−	2.83207e9i	−0.388209	−	1.06660i	0.579598	−	0.814903i	$-0.303210\pi$
$228$	8.96301e7	−	1.51887e8i	0.0331676	−	0.0562059i
$229$	−2.76704e9	+	2.32182e9i	−1.00617	+	0.844280i	−0.987828	−	0.155552i	$-0.950284\pi$
$229$	−2.76704e9	+	2.32182e9i	−1.00617	+	0.844280i	−0.0183460	+	0.999832i	$0.505840\pi$
$230$	3.34689e8	+	3.98866e8i	0.119600	+	0.142533i
$231$	−1.99850e7	+	2.10003e9i	−0.00701871	+	0.737528i
$232$	−1.02671e9	+	3.73694e8i	−0.354403	+	0.128992i
$233$	1.28628e9	−	7.42633e8i	0.436427	−	0.251971i	−0.265654	−	0.964068i	$-0.585588\pi$
$233$	1.28628e9	−	7.42633e8i	0.436427	−	0.251971i	0.702081	+	0.712097i	$0.252255\pi$
$234$	−7.22156e8	+	1.87244e9i	−0.240862	+	0.624516i
$235$	−3.11692e9	+	5.39866e9i	−1.02201	+	1.77017i
$236$	9.88049e8	+	1.74220e8i	0.318515	+	0.0561628i
$237$	2.15833e9	−	1.77633e9i	0.684106	−	0.563027i
$238$	−1.28497e9	−	4.67689e8i	−0.400483	−	0.145764i
$239$	3.01330e9	−	5.31327e8i	0.923531	−	0.162843i	0.308389	−	0.951260i	$-0.400210\pi$
$239$	3.01330e9	−	5.31327e8i	0.923531	−	0.162843i	0.615141	+	0.788417i	$0.289099\pi$
$240$	−1.26733e9	−	2.35920e8i	−0.381983	−	0.0711083i
$241$	3.70873e9	+	3.11200e9i	1.09940	+	0.922510i	0.997385	−	0.0722728i	$-0.0230252\pi$
$241$	3.70873e9	+	3.11200e9i	1.09940	+	0.922510i	0.102019	+	0.994782i	$0.467470\pi$
$242$		−	1.61581e9i		−	0.471116i
$243$	−2.77461e9	+	2.11168e9i	−0.795751	+	0.605625i
$244$	2.47693e9			0.698803
$245$	2.42429e9	−	2.88916e9i	0.672854	−	0.801876i
$246$	−5.95646e8	+	3.19971e9i	−0.162648	+	0.873717i
$247$	7.98588e7	+	4.52902e8i	0.0214553	+	0.121679i
$248$	−4.80890e8	+	1.32123e9i	−0.127127	+	0.349279i
$249$	−5.87502e8	−	7.13845e8i	−0.152831	−	0.185698i
$250$	3.09714e8	−	1.75647e9i	0.0792868	−	0.449658i
$251$	2.54004e9	+	1.46649e9i	0.639950	+	0.369475i	0.784595	−	0.620008i	$-0.212871\pi$
$251$	2.54004e9	+	1.46649e9i	0.639950	+	0.369475i	−0.144645	+	0.989484i	$0.546204\pi$
$252$	1.07495e9	+	4.14582e8i	0.266554	+	0.102804i
$253$	4.47713e8	+	7.75461e8i	0.109274	+	0.189268i
$254$	3.26331e8	+	8.96586e8i	0.0784012	+	0.215406i
$255$	−6.93152e9	−	6.59640e7i	−1.63933	−	0.0156008i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	3.06702e9	+	3.65513e9i	0.703046	+	0.837857i	0.992867	−	0.119224i	$-0.0380405\pi$
$257$	3.06702e9	+	3.65513e9i	0.703046	+	0.837857i	−0.289822	+	0.957081i	$0.593596\pi$
$258$	3.86448e9	+	2.28046e9i	0.872191	+	0.514688i
$259$	3.99723e9	−	1.45487e9i	0.888301	−	0.323315i
$260$	2.91116e9	−	1.68076e9i	0.637049	−	0.367800i
$261$	4.33329e9	−	2.39304e9i	0.933804	−	0.515690i
$262$	2.33383e9	−	4.04232e9i	0.495296	−	0.857878i
$263$	−6.49180e9	−	1.14468e9i	−1.35688	−	0.239255i	−0.552572	−	0.833465i	$-0.686354\pi$
$263$	−6.49180e9	−	1.14468e9i	−1.35688	−	0.239255i	−0.804310	+	0.594210i	$0.797465\pi$
$264$	−2.07588e9	−	7.78007e8i	−0.427352	−	0.160165i
$265$	−3.68980e9	−	1.34298e9i	−0.748202	−	0.272323i
$266$	2.60006e8	−	4.58461e7i	0.0519346	−	0.00915748i
$267$	4.60039e9	−	5.37776e9i	0.905211	−	1.05817i
$268$	−3.21185e9	−	2.69506e9i	−0.622610	−	0.522432i
$269$			8.30944e9i			1.58695i	0.608604	+	0.793474i	$0.291730\pi$
$269$			8.30944e9i			1.58695i	−0.608604	+	0.793474i	$0.708270\pi$
$270$	5.83800e9	+	1.66713e8i	1.09852	+	0.0313700i
$271$	−9.13449e8			−0.169359			−0.0846793	−	0.996408i	$-0.526987\pi$
$271$	−9.13449e8			−0.169359			−0.0846793	+	0.996408i	$0.526987\pi$
$272$	9.27831e8	−	1.10575e9i	0.169509	−	0.202013i
$273$	−2.83280e9	+	1.00063e9i	−0.509995	+	0.180145i
$274$	1.33080e9	+	7.54733e9i	0.236108	+	1.33903i
$275$	3.57401e9	−	9.81951e9i	0.624921	−	1.71696i
$276$	4.84554e8	−	8.06933e7i	0.0835037	−	0.0139060i
$277$	1.39547e9	−	7.91411e9i	0.237029	−	1.34426i	−0.601269	−	0.799047i	$-0.705338\pi$
$277$	1.39547e9	−	7.91411e9i	0.237029	−	1.34426i	0.838298	−	0.545213i	$-0.183551\pi$
$278$	−1.39181e9	−	8.03562e8i	−0.233024	−	0.134536i
$279$	1.22535e9	−	6.25117e9i	0.202229	−	1.03168i
$280$	−9.64906e8	−	1.67127e9i	−0.156983	−	0.271903i
$281$	−1.26984e9	−	3.48884e9i	−0.203668	−	0.559572i	0.795240	−	0.606294i	$-0.207345\pi$
$281$	−1.26984e9	−	3.48884e9i	−0.203668	−	0.559572i	−0.998908	+	0.0467221i	$0.985122\pi$
$282$	2.89199e9	+	5.12100e9i	0.457299	+	0.809764i
$283$	−3.72971e9	+	3.12960e9i	−0.581473	+	0.487914i	−0.885431	−	0.464772i	$-0.846136\pi$
$283$	−3.72971e9	+	3.12960e9i	−0.581473	+	0.487914i	0.303957	+	0.952686i	$0.401692\pi$
$284$	1.01211e9	+	1.20618e9i	0.155580	+	0.185413i
$285$	1.16537e9	−	6.58122e8i	0.176639	−	0.0997533i
$286$	5.43222e9	−	1.97717e9i	0.811920	−	0.295515i
$287$	−4.21957e9	+	2.43617e9i	−0.621929	+	0.359071i
$288$	−7.99329e8	+	9.16595e8i	−0.116186	+	0.133232i
$289$	3.93029e8	−	6.80745e8i	0.0563421	−	0.0975873i
$290$	−8.16557e9	−	1.43981e9i	−1.15450	−	0.203570i
$291$	−3.95874e8	−	2.37718e9i	−0.0552058	−	0.331505i
$292$	2.03278e9	+	7.39873e8i	0.279615	+	0.101771i
$293$	−3.77999e9	+	6.66514e8i	−0.512885	+	0.0904355i	−0.424100	−	0.905615i	$-0.639410\pi$
$293$	−3.77999e9	+	6.66514e8i	−0.512885	+	0.0904355i	−0.0887851	+	0.996051i	$0.528298\pi$
$294$	−1.18509e9	−	3.35501e9i	−0.158622	−	0.449060i
$295$	5.83246e9	+	4.89402e9i	0.770130	+	0.646216i
$296$			4.49024e9i			0.584928i
$297$	9.83737e9	+	2.02572e9i	1.26431	+	0.260347i
$298$	6.68251e8			0.0847372
$299$	−8.23378e8	+	9.81264e8i	−0.103018	+	0.122772i
$300$	−4.35622e9	−	3.72651e9i	−0.537804	−	0.460063i
$301$	1.16646e9	+	6.61535e9i	0.142104	+	0.805911i
$302$	−1.61493e9	+	4.43699e9i	−0.194145	+	0.533410i
$303$	1.95077e9	−	5.20505e9i	0.231439	−	0.617525i
$304$	−4.83948e7	+	2.74460e8i	−0.00566636	+	0.0321355i
$305$	1.62786e10	+	9.39843e9i	1.88112	+	1.08607i
$306$	−3.37703e9	+	5.60028e9i	−0.385168	+	0.638739i
$307$	2.17697e9	+	3.77062e9i	0.245075	+	0.424482i	0.962153	−	0.272511i	$-0.0878542\pi$
$307$	2.17697e9	+	3.77062e9i	0.245075	+	0.424482i	−0.717078	+	0.696993i	$0.754521\pi$
$308$	−1.13507e9	−	3.11858e9i	−0.126130	−	0.346540i
$309$	−3.92133e9	+	6.64509e9i	−0.430130	+	0.728898i
$310$	−8.17371e9	+	6.85855e9i	−0.885059	+	0.742653i
$311$	−7.24374e9	−	8.63276e9i	−0.774322	−	0.922801i	0.224340	−	0.974511i	$-0.427977\pi$
$311$	−7.24374e9	−	8.63276e9i	−0.774322	−	0.922801i	−0.998662	+	0.0517099i	$0.983533\pi$
$312$	3.01789e7	−	3.17121e9i	0.00318482	−	0.334662i
$313$	1.28418e10	−	4.67402e9i	1.33797	−	0.486982i	0.428799	−	0.903400i	$-0.358937\pi$
$313$	1.28418e10	−	4.67402e9i	1.33797	−	0.486982i	0.909174	+	0.416417i	$0.136714\pi$
$314$	−6.60397e9	+	3.81280e9i	−0.679339	+	0.392216i
$315$	5.49153e9	+	6.80342e9i	0.557765	+	0.691011i
$316$	−2.20863e9	+	3.82546e9i	−0.221501	+	0.383650i
$317$	4.53231e8	+	7.99169e7i	0.0448831	+	0.00791410i	0.196045	−	0.980595i	$-0.437190\pi$
$317$	4.53231e8	+	7.99169e7i	0.0448831	+	0.00791410i	−0.151162	+	0.988509i	$0.548301\pi$
$318$	−2.86031e9	+	2.35407e9i	−0.279708	+	0.230203i
$319$	−1.33991e10	−	4.87689e9i	−1.29394	−	0.470956i
$320$	2.00615e9	−	3.53738e8i	0.191321	−	0.0337351i
$321$	−1.92625e10	−	3.58584e9i	−1.81423	−	0.337730i
$322$	5.63333e8	+	4.72693e8i	0.0524013	+	0.0439699i
$323$			1.49861e9i			0.137683i
$324$	2.93459e9	−	4.66348e9i	0.266298	−	0.423185i
$325$	1.49488e10			1.33990
$326$	−4.35151e9	+	5.18592e9i	−0.385274	+	0.459151i
$327$	5.40854e7	−	2.90538e8i	0.00473030	−	0.0254104i
$328$	−8.93108e8	−	5.06507e9i	−0.0771629	−	0.437613i
$329$	−3.01124e9	+	8.27331e9i	−0.257017	+	0.706148i
$330$	−1.06907e10	−	1.29898e10i	−0.901471	−	1.09533i
$331$	2.01941e9	−	1.14527e10i	0.168234	−	0.954102i	−0.777433	−	0.628965i	$-0.783479\pi$
$331$	2.01941e9	−	1.14527e10i	0.168234	−	0.954102i	0.945667	−	0.325136i	$-0.105410\pi$
$332$	1.26523e9	+	7.30483e8i	0.104140	+	0.0601254i
$333$	−3.15068e9	−	2.00980e10i	−0.256229	−	1.63446i
$334$	7.21338e9	+	1.24939e10i	0.579633	+	1.00395i
$335$	−1.08824e10	−	2.98991e10i	−0.864062	−	2.37399i
$336$	−1.82056e9	−	1.73254e7i	−0.142839	−	0.00135933i
$337$	−4.81053e9	+	4.03651e9i	−0.372970	+	0.312959i	−0.809935	−	0.586520i	$-0.800498\pi$
$337$	−4.81053e9	+	4.03651e9i	−0.372970	+	0.312959i	0.436965	+	0.899478i	$0.356053\pi$
$338$	−6.16539e8	−	7.34763e8i	−0.0472383	−	0.0562964i
$339$	−8.21547e9	−	4.84802e9i	−0.622062	−	0.367084i
$340$	1.02934e10	−	3.74649e9i	0.770270	−	0.280355i
$341$	−1.58910e10	+	9.17468e9i	−1.17526	+	0.678537i
$342$	2.40299e7	−	1.26242e9i	0.00175650	−	0.0922784i
$343$	6.61767e9	−	1.14621e10i	0.478111	−	0.828112i
$344$	−6.98311e9	−	1.23131e9i	−0.498672	−	0.0879294i
$345$	3.49070e9	+	1.30826e9i	0.246398	+	0.0923461i
$346$	−1.26667e9	−	4.61032e8i	−0.0883814	−	0.0321682i
$347$	1.23212e10	−	2.17257e9i	0.849839	−	0.149849i	0.268267	−	0.963345i	$-0.413549\pi$
$347$	1.23212e10	−	2.17257e9i	0.849839	−	0.149849i	0.581572	+	0.813495i	$0.302438\pi$
$348$	−5.08498e9	+	5.94424e9i	−0.346715	+	0.405303i
$349$	1.93829e10	+	1.62642e10i	1.30652	+	1.09630i	0.988979	+	0.148058i	$0.0473023\pi$
$349$	1.93829e10	+	1.62642e10i	1.30652	+	1.09630i	0.317543	+	0.948244i	$0.397142\pi$
$350$		−	8.58195e9i		−	0.571892i
$351$	2.09007e9	+	1.42153e10i	0.137700	+	0.936541i
$352$	3.50322e9			0.228190
$353$	−1.10523e10	+	1.31716e10i	−0.711791	+	0.848279i	−0.993806	−	0.111131i	$-0.964553\pi$
$353$	−1.10523e10	+	1.31716e10i	−0.711791	+	0.848279i	0.282015	+	0.959410i	$0.408997\pi$
$354$	6.77290e9	−	2.39239e9i	0.431282	−	0.152342i
$355$	2.07491e9	+	1.17674e10i	0.130643	+	0.740914i
$356$	−3.82495e9	+	1.05090e10i	−0.238137	+	0.654275i
$357$	−9.65707e9	+	1.60820e9i	−0.594529	+	0.0990074i
$358$	−3.72487e9	+	2.11248e10i	−0.226767	+	1.28606i
$359$	−1.30954e10	−	7.56064e9i	−0.788390	−	0.455177i	0.0510054	−	0.998698i	$-0.483757\pi$
$359$	−1.30954e10	−	7.56064e9i	−0.788390	−	0.455177i	−0.839395	+	0.543521i	$0.817091\pi$
$360$	−8.73116e9	+	2.99096e9i	−0.519831	+	0.178074i
$361$	8.34711e9	+	1.44576e10i	0.491482	+	0.851271i
$362$	−5.32108e9	−	1.46195e10i	−0.309860	−	0.851333i
$363$	−5.68855e9	−	1.00730e10i	−0.327624	−	0.580141i
$364$	3.63687e9	−	3.05169e9i	0.207168	−	0.173834i
$365$	1.05522e10	+	1.25757e10i	0.594529	+	0.708532i
$366$	1.54413e10	−	8.72020e9i	0.860519	−	0.485962i
$367$	−2.08186e10	+	7.57734e9i	−1.14759	+	0.417689i	−0.844649	−	0.535321i	$-0.820191\pi$
$367$	−2.08186e10	+	7.57734e9i	−1.14759	+	0.417689i	−0.302941	+	0.953009i	$0.597969\pi$
$368$	−6.72261e8	+	3.88130e8i	−0.0366561	+	0.0211634i
$369$	7.55151e9	+	2.20442e10i	0.407313	+	1.18902i
$370$	−1.70377e10	+	2.95101e10i	−0.909084	+	1.57458i
$371$	−5.46142e9	−	9.62996e8i	−0.288277	−	0.0508310i
$372$	1.65359e9	+	9.92965e9i	0.0863490	+	0.518516i
$373$	−1.24122e10	−	4.51769e9i	−0.641232	−	0.233389i	0.000880763	−	1.00000i	$-0.499720\pi$
$373$	−1.24122e10	−	4.51769e9i	−0.641232	−	0.233389i	−0.642113	+	0.766610i	$0.721942\pi$
$374$	1.85515e10	−	3.27114e9i	0.948186	−	0.167191i
$375$	−4.25301e9	−	1.20403e10i	−0.215066	−	0.608854i
$376$	−7.11940e9	−	5.97389e9i	−0.356198	−	0.298886i
$377$		−	2.03983e10i		−	1.00978i
$378$	8.16084e9	−	1.19989e9i	0.399731	−	0.0587725i
$379$	5.23994e9			0.253962			0.126981	−	0.991905i	$-0.459471\pi$
$379$	5.23994e9			0.253962			0.126981	+	0.991905i	$0.459471\pi$
$380$	−1.35946e9	+	1.62014e9i	−0.0651978	+	0.0776997i
$381$	5.19085e9	+	4.44050e9i	0.246342	+	0.210733i
$382$	−4.24879e9	−	2.40961e10i	−0.199531	−	1.13160i
$383$	7.04274e7	−	1.93498e8i	0.00327300	−	0.00899251i	−0.938045	−	0.346512i	$-0.887366\pi$
$383$	7.04274e7	−	1.93498e8i	0.00327300	−	0.00899251i	0.941318	+	0.337520i	$0.109588\pi$
$384$	6.74468e8	−	1.79961e9i	0.0310196	−	0.0827664i
$385$	4.37333e9	−	2.48024e10i	0.199053	−	1.12889i
$386$	2.27667e10	+	1.31444e10i	1.02554	+	0.592094i
$387$	3.21199e10	+	6.11395e8i	1.43196	+	0.0272570i
$388$	1.90413e9	+	3.29805e9i	0.0840175	+	0.145523i
$389$	3.54413e8	+	9.73743e8i	0.0154779	+	0.0425252i	0.947191	−	0.320670i	$-0.103908\pi$
$389$	3.54413e8	+	9.73743e8i	0.0154779	+	0.0425252i	−0.931713	+	0.363195i	$0.881686\pi$
$390$	1.22311e10	−	2.07269e10i	0.528698	−	0.895933i
$391$	−3.19759e9	+	2.68310e9i	−0.136809	+	0.114797i
$392$	3.61425e9	+	4.30730e9i	0.153064	+	0.182415i
$393$	3.18009e8	−	3.34164e10i	0.0133312	−	1.40084i
$394$	1.57177e10	−	5.72078e9i	0.652236	−	0.237394i
$395$	−2.90305e10	+	1.67608e10i	−1.19252	+	0.688504i
$396$	−1.56801e10	+	2.45811e9i	−0.637631	+	0.0999588i
$397$	−2.72766e8	+	4.72444e8i	−0.0109806	+	0.0190190i	−0.871464	−	0.490460i	$-0.836829\pi$
$397$	−2.72766e8	+	4.72444e8i	−0.0109806	+	0.0190190i	0.860483	+	0.509479i	$0.170162\pi$
$398$	4.89841e9	+	8.63722e8i	0.195219	+	0.0344225i
$399$	1.45949e9	−	1.20118e9i	0.0575850	−	0.0473931i
$400$	8.51271e9	+	3.09837e9i	0.332528	+	0.121030i
$401$	−1.75900e10	+	3.10160e9i	−0.680282	+	0.119952i	−0.503103	−	0.864226i	$-0.667808\pi$
$401$	−1.75900e10	+	3.10160e9i	−0.680282	+	0.119952i	−0.177179	+	0.984179i	$0.556697\pi$
$402$	−2.95110e10	−	5.49364e9i	−1.13000	−	0.210357i
$403$	−2.01084e10	−	1.68729e10i	−0.762354	−	0.639691i
$404$			8.78397e9i			0.329735i
$405$	3.69814e10	−	1.95138e10i	1.37456	−	0.725305i
$406$	−1.17104e10			−0.430992
$407$	−3.76673e10	+	4.48901e10i	−1.37273	+	1.63596i
$408$	1.89130e9	−	1.01598e10i	0.0682528	−	0.366643i
$409$	−8.74260e9	−	4.95817e10i	−0.312426	−	1.77186i	−0.586303	−	0.810092i	$-0.699417\pi$
$409$	−8.74260e9	−	4.95817e10i	−0.312426	−	1.77186i	0.273877	−	0.961765i	$-0.411694\pi$
$410$	1.33492e10	−	3.66767e10i	0.472412	−	1.29794i
$411$	3.48671e10	+	4.23653e10i	1.22194	+	1.48472i
$412$	2.11728e9	−	1.20077e10i	0.0734834	−	0.416745i
$413$	9.31250e9	+	5.37658e9i	0.320086	+	0.184802i
$414$	2.73665e9	−	2.20895e9i	0.0931576	−	0.0751942i
$415$	5.54347e9	+	9.60156e9i	0.186891	+	0.323705i
$416$	1.71404e9	+	4.70929e9i	0.0572331	+	0.157247i
$417$	−1.15056e10	−	1.09493e8i	−0.380509	−	0.00362113i
$418$	−2.78618e9	+	2.33788e9i	−0.0912650	+	0.0765804i
$419$	1.01251e10	+	1.20666e10i	0.328505	+	0.391497i	0.904865	−	0.425699i	$-0.139972\pi$
$419$	1.01251e10	+	1.20666e10i	0.328505	+	0.391497i	−0.576360	+	0.817196i	$0.695527\pi$
$420$	−1.18991e10	−	7.02176e9i	−0.382399	−	0.225657i
$421$	1.65846e10	−	6.03631e9i	0.527931	−	0.192151i	−0.0642831	−	0.997932i	$-0.520476\pi$
$421$	1.65846e10	−	6.03631e9i	0.527931	−	0.192151i	0.592214	+	0.805780i	$0.298254\pi$
$422$	2.31196e10	−	1.33481e10i	0.729003	−	0.420890i
$423$	3.60576e10	+	2.17432e10i	1.12625	+	0.679144i
$424$	2.92698e9	−	5.06968e9i	0.0905642	−	0.156862i
$425$	4.79728e10	+	8.45890e9i	1.47041	+	0.259274i
$426$	1.05560e10	+	3.95622e9i	0.320523	+	0.120127i
$427$	2.49465e10	+	9.07977e9i	0.750408	+	0.273126i
$428$	3.04921e10	−	5.37658e9i	0.908683	−	0.160225i
$429$	2.69040e10	−	3.14502e10i	0.794306	−	0.928527i
$430$	−4.12214e10	−	3.45889e10i	−1.20573	−	1.01172i
$431$			1.96466e10i			0.569348i	0.958624	+	0.284674i	$0.0918853\pi$
$431$			1.96466e10i			0.569348i	−0.958624	+	0.284674i	$0.908115\pi$
$432$	−1.75613e9	+	8.52820e9i	−0.0504222	+	0.244862i
$433$	7.85047e9			0.223329			0.111664	−	0.993746i	$-0.464382\pi$
$433$	7.85047e9			0.223329			0.111664	+	0.993746i	$0.464382\pi$
$434$	−9.68658e9	+	1.15440e10i	−0.273031	+	0.325385i
$435$	−5.59736e10	+	1.97716e10i	−1.56324	+	0.552184i
$436$	8.10954e7	+	4.59915e8i	0.00224414	+	0.0127272i
$437$	2.75643e8	−	7.57324e8i	0.00755826	−	0.0207661i
$438$	1.52773e10	−	2.54414e9i	0.415097	−	0.0691264i
$439$	−2.49850e9	+	1.41697e10i	−0.0672701	+	0.381508i	0.932522	+	0.361113i	$0.117603\pi$
$439$	−2.49850e9	+	1.41697e10i	−0.0672701	+	0.381508i	−0.999792	+	0.0203943i	$0.993508\pi$
$440$	2.30234e10	+	1.32925e10i	0.614268	+	0.354648i
$441$	−1.91995e10	−	1.67431e10i	−0.507615	−	0.442673i
$442$	1.34741e10	+	2.33379e10i	0.353030	+	0.611466i
$443$	−3.80157e9	−	1.04447e10i	−0.0987071	−	0.271196i	0.880504	−	0.474038i	$-0.157204\pi$
$443$	−3.80157e9	−	1.04447e10i	−0.0987071	−	0.271196i	−0.979211	+	0.202843i	$0.934982\pi$
$444$	1.58082e10	+	2.79924e10i	0.406771	+	0.720291i
$445$	−6.50129e10	+	5.45523e10i	−1.65790	+	1.39115i
$446$	1.52206e10	+	1.81392e10i	0.384673	+	0.458435i
$447$	4.16591e9	−	2.35262e9i	0.104347	−	0.0589280i
$448$	2.70355e9	−	9.84012e8i	0.0671155	−	0.0244280i
$449$	−2.91247e10	+	1.68152e10i	−0.716600	+	0.413729i	−0.813500	−	0.581565i	$-0.802441\pi$
$449$	−2.91247e10	+	1.68152e10i	−0.716600	+	0.413729i	0.0969000	+	0.995294i	$0.469107\pi$
$450$	−4.02763e10	−	7.89495e9i	−0.982199	−	0.192530i
$451$	3.35607e10	−	5.81288e10i	0.811194	−	1.40503i
$452$	1.48454e10	+	2.61764e9i	0.355661	+	0.0627127i
$453$	5.55313e9	+	3.33459e10i	0.131870	+	0.791863i
$454$	3.20412e10	+	1.16620e10i	0.754197	+	0.274505i
$455$	3.54810e10	−	6.25626e9i	0.827848	−	0.145972i
$456$	6.64560e8	+	1.88138e9i	0.0153700	+	0.0435128i
$457$	9.88638e7	+	8.29566e7i	0.00226659	+	0.00190189i	0.643920	−	0.765093i	$-0.277307\pi$
$457$	9.88638e7	+	8.29566e7i	0.00226659	+	0.00190189i	−0.641654	+	0.766995i	$0.721751\pi$
$458$		−	4.08664e10i		−	0.928761i
$459$	−1.33649e9	+	4.68015e10i	−0.0301102	+	1.05441i
$460$	−5.89086e9			−0.131567
$461$	4.87961e10	−	5.81529e10i	1.08039	−	1.28756i	0.125021	−	0.992154i	$-0.460100\pi$
$461$	4.87961e10	−	5.81529e10i	1.08039	−	1.28756i	0.955372	−	0.295407i	$-0.0954552\pi$
$462$	−1.80552e10	−	1.54453e10i	−0.396310	−	0.339023i
$463$	3.57441e9	+	2.02715e10i	0.0777821	+	0.441124i	0.998682	+	0.0513252i	$0.0163445\pi$
$463$	3.57441e9	+	2.02715e10i	0.0777821	+	0.441124i	−0.920900	+	0.389799i	$0.872544\pi$
$464$	4.22786e9	−	1.16159e10i	0.0912113	−	0.250601i
$465$	−2.68094e10	+	7.15327e10i	−0.573422	+	1.53000i
$466$	−2.91796e9	+	1.65486e10i	−0.0618780	+	0.350927i
$467$	1.96332e10	+	1.13352e10i	0.412784	+	0.238321i	0.691985	−	0.721911i	$-0.256736\pi$
$467$	1.96332e10	+	1.13352e10i	0.412784	+	0.238321i	−0.279201	+	0.960233i	$0.590070\pi$
$468$	−1.09763e10	−	1.98757e10i	−0.228809	−	0.414324i
$469$	−2.24688e10	−	3.89171e10i	−0.464396	−	0.804358i
$470$	−2.41219e10	−	6.62745e10i	−0.494335	−	1.35817i
$471$	−2.77463e10	+	4.70189e10i	−0.563795	+	0.955408i
$472$	−8.69532e9	+	7.29624e9i	−0.175193	+	0.147005i
$473$	−5.94829e10	−	7.08889e10i	−1.18836	−	1.41623i
$474$	−3.00949e8	+	3.16238e10i	−0.00596182	+	0.626470i
$475$	−8.83804e9	+	3.21678e9i	−0.173613	+	0.0631899i
$476$	1.33980e10	−	7.73536e9i	0.260984	−	0.150679i
$477$	−9.54370e9	+	2.47453e10i	−0.184350	+	0.477991i
$478$	−1.73088e10	+	2.99797e10i	−0.331554	+	0.574269i
$479$	1.47001e10	+	2.59202e9i	0.279240	+	0.0492376i	0.311514	−	0.950241i	$-0.399164\pi$
$479$	1.47001e10	+	2.59202e9i	0.279240	+	0.0492376i	−0.0322739	+	0.999479i	$0.510275\pi$
$480$	1.12611e10	−	9.26799e9i	0.212136	−	0.174590i
$481$	−7.87743e10	−	2.86715e10i	−1.47165	−	0.535637i
$482$	−5.39421e10	+	9.51145e9i	−0.999401	+	0.176221i
$483$	5.17599e9	+	9.63542e8i	0.0951054	+	0.0177044i
$484$	1.40039e10	+	1.17507e10i	0.255192	+	0.214132i
$485$			2.89000e10i			0.522313i
$486$	1.87630e9	−	3.94038e10i	0.0336323	−	0.706306i
$487$	−6.12226e9			−0.108842			−0.0544210	−	0.998518i	$-0.517331\pi$
$487$	−6.12226e9			−0.108842			−0.0544210	+	0.998518i	$0.517331\pi$
$488$	−1.80130e10	+	2.14671e10i	−0.317620	+	0.378524i
$489$	−8.87016e9	+	4.76491e10i	−0.155130	+	0.833334i
$490$	7.40956e9	+	4.20217e10i	0.128531	+	0.728936i
$491$	2.52725e10	−	6.94358e10i	0.434834	−	1.19470i	−0.507978	−	0.861370i	$-0.669607\pi$
$491$	2.52725e10	−	6.94358e10i	0.434834	−	1.19470i	0.942812	−	0.333326i	$-0.108171\pi$
$492$	−2.33996e10	−	2.84317e10i	−0.399344	−	0.485223i
$493$	1.15425e10	−	6.54609e10i	0.195395	−	1.10814i
$494$	−4.50597e9	−	2.60152e9i	−0.0756625	−	0.0436837i
$495$	−1.12378e11	−	4.33416e10i	−1.87180	−	0.721912i
$496$	−7.95369e9	−	1.37762e10i	−0.131414	−	0.227616i
$497$	5.77191e9	+	1.58582e10i	0.0946006	+	0.259913i
$498$	1.04592e10	+	9.95358e7i	0.170053	+	0.00161831i
$499$	3.82057e10	−	3.20584e10i	0.616206	−	0.517058i	−0.280403	−	0.959882i	$-0.590468\pi$
$499$	3.82057e10	−	3.20584e10i	0.616206	−	0.517058i	0.896608	+	0.442825i	$0.146024\pi$
$500$	1.29707e10	+	1.54579e10i	0.207531	+	0.247326i
$501$	8.89543e10	+	5.24928e10i	1.41194	+	0.833198i
$502$	−3.11818e10	+	1.13493e10i	−0.491006	+	0.178711i
$503$	−2.01717e10	+	1.16461e10i	−0.315115	+	0.181932i	−0.649213	−	0.760606i	$-0.724902\pi$
$503$	−2.01717e10	+	1.16461e10i	−0.315115	+	0.181932i	0.334098	+	0.942538i	$0.391568\pi$
$504$	−1.14104e10	+	6.30138e9i	−0.176840	+	0.0976593i
$505$	−3.33297e10	+	5.77288e10i	−0.512468	+	0.887620i
$506$	−9.97667e9	−	1.75916e9i	−0.152189	−	0.0268351i
$507$	−6.43032e9	−	2.40999e9i	−0.0973197	−	0.0364740i
$508$	−1.01437e10	−	3.69201e9i	−0.152315	−	0.0554380i
$509$	−3.81836e10	+	6.73280e9i	−0.568861	+	0.100306i	−0.450678	−	0.892686i	$-0.648818\pi$
$509$	−3.81836e10	+	6.73280e9i	−0.568861	+	0.100306i	−0.118182	+	0.992992i	$0.537707\pi$
$510$	5.09798e10	−	5.95944e10i	0.753560	−	0.880896i
$511$	1.77610e10	+	1.49033e10i	0.260486	+	0.218574i
$512$			3.03700e9i			0.0441942i
$513$	−4.29463e9	−	7.95461e9i	−0.0620093	−	0.114855i
$514$	−5.39826e10			−0.773394
$515$	5.94766e10	−	7.08815e10i	0.845508	−	1.00764i
$516$	−4.78680e10	+	1.69084e10i	−0.675222	+	0.238509i
$517$	−2.10614e10	−	1.19445e11i	−0.294798	−	1.67188i
$518$	−1.64600e10	+	4.52235e10i	−0.228618	+	0.628124i
$519$	−9.51961e9	+	1.58531e9i	−0.131205	+	0.0218497i
$520$	−6.60406e9	+	3.74535e10i	−0.0903228	+	0.512246i
$521$	−4.49069e10	−	2.59270e10i	−0.609484	−	0.351886i	0.163279	−	0.986580i	$-0.447793\pi$
$521$	−4.49069e10	−	2.59270e10i	−0.609484	−	0.351886i	−0.772764	+	0.634694i	$0.781126\pi$
$522$	−1.07730e10	+	5.49587e10i	−0.145096	+	0.740210i
$523$	−7.25562e10	−	1.25671e11i	−0.969767	−	1.67969i	−0.696221	−	0.717828i	$-0.745137\pi$
$523$	−7.25562e10	−	1.25671e11i	−0.969767	−	1.67969i	−0.273547	−	0.961859i	$-0.588197\pi$
$524$	1.80616e10	+	4.96239e10i	0.239569	+	0.658212i
$525$	−3.02133e10	−	5.35004e10i	−0.397705	−	0.704238i
$526$	5.71311e10	−	4.79387e10i	0.746328	−	0.626243i
$527$	−5.49829e10	−	6.55261e10i	−0.712829	−	0.849517i
$528$	2.18392e10	−	1.23333e10i	0.280997	−	0.158688i
$529$	−7.14788e10	+	2.60162e10i	−0.912756	+	0.332216i
$530$	3.84726e10	−	2.22122e10i	0.487583	−	0.281506i
$531$	3.38001e10	−	3.87587e10i	0.425147	−	0.487519i
$532$	−1.49351e9	+	2.58683e9i	−0.0186449	+	0.0322940i
$533$	9.45615e10	+	1.66737e10i	1.17167	+	0.206597i
$534$	1.31525e10	+	7.89795e10i	0.161750	+	0.971291i
$535$	2.20797e11	+	8.03635e10i	2.69512	+	0.980943i
$536$	4.67151e10	−	8.23714e9i	0.565976	−	0.0997969i
$537$	5.11501e10	+	1.44807e11i	0.615105	+	1.74137i
$538$	−7.20163e10	−	6.04289e10i	−0.859611	−	0.721299i
$539$			7.33801e10i			0.869407i
$540$	−4.39006e10	+	4.93844e10i	−0.516292	+	0.580785i
$541$	−1.24636e11			−1.45497			−0.727485	−	0.686123i	$-0.759311\pi$
$541$	−1.24636e11			−1.45497			−0.727485	+	0.686123i	$0.759311\pi$
$542$	6.64289e9	−	7.91669e9i	0.0769768	−	0.0917374i
$543$	−8.46410e10	−	7.24059e10i	−0.973602	−	0.832865i
$544$	2.83581e9	+	1.60827e10i	0.0323803	+	0.183638i
$545$	−1.21213e9	+	3.33030e9i	−0.0137392	+	0.0377482i
$546$	1.19287e10	−	3.18282e10i	0.134222	−	0.358131i
$547$	−1.48206e10	+	8.40517e10i	−0.165545	+	0.938852i	0.782956	+	0.622077i	$0.213711\pi$
$547$	−1.48206e10	+	8.40517e10i	−0.165545	+	0.938852i	−0.948501	+	0.316775i	$0.897400\pi$
$548$	−7.50892e10	−	4.33528e10i	−0.832636	−	0.480723i
$549$	6.55621e10	−	1.08724e11i	0.721711	−	1.19684i
$550$	5.91125e10	+	1.02386e11i	0.645994	+	1.11889i
$551$	4.38944e9	+	1.20599e10i	0.0476214	+	0.130839i
$552$	−2.82448e9	+	4.78636e9i	−0.0304216	+	0.0515524i
$553$	−3.62674e10	+	3.04320e10i	−0.387807	+	0.325409i
$554$	5.84417e10	+	6.96482e10i	0.620418	+	0.739385i
$555$	−2.32156e9	+	2.43950e11i	−0.0244685	+	2.57116i
$556$	1.70860e10	−	6.21879e9i	0.178789	−	0.0650739i
$557$	5.89985e10	−	3.40628e10i	0.612943	−	0.353883i	−0.161173	−	0.986926i	$-0.551528\pi$
$557$	5.89985e10	−	3.40628e10i	0.612943	−	0.353883i	0.774116	+	0.633043i	$0.218195\pi$
$558$	4.52665e10	+	5.60804e10i	0.466918	+	0.578461i
$559$	6.61907e10	−	1.14646e11i	0.677875	−	1.17411i
$560$	2.15016e10	+	3.79132e9i	0.218635	+	0.0385512i
$561$	1.04135e11	−	8.57044e10i	1.05135	−	0.865270i
$562$	3.94718e10	+	1.43665e10i	0.395677	+	0.144015i
$563$	6.11949e10	−	1.07903e10i	0.609090	−	0.107399i	0.139408	−	0.990235i	$-0.455480\pi$
$563$	6.11949e10	−	1.07903e10i	0.609090	−	0.107399i	0.469681	+	0.882836i	$0.344369\pi$
$564$	−6.54142e10	−	1.21772e10i	−0.646481	−	0.120346i
$565$	8.76323e10	+	7.35322e10i	0.859945	+	0.721579i
$566$		−	5.50841e10i		−	0.536736i
$567$	4.66508e10	−	3.62109e10i	0.451364	−	0.350354i
$568$	−1.78141e10			−0.171147
$569$	−1.29634e11	+	1.54491e11i	−1.23671	+	1.47386i	−0.409163	+	0.912461i	$0.634179\pi$
$569$	−1.29634e11	+	1.54491e11i	−1.23671	+	1.47386i	−0.827548	+	0.561394i	$0.810265\pi$
$570$	−2.77114e9	+	1.48861e10i	−0.0262518	+	0.141021i
$571$	−2.41217e9	−	1.36801e10i	−0.0226915	−	0.128690i	0.971358	−	0.237622i	$-0.0763679\pi$
$571$	−2.41217e9	−	1.36801e10i	−0.0226915	−	0.128690i	−0.994049	+	0.108932i	$0.965257\pi$
$572$	−2.23691e10	+	6.14585e10i	−0.208960	+	0.574114i
$573$	−1.11319e11	−	1.35258e11i	−1.03264	−	1.25471i
$574$	9.57222e9	−	5.42868e10i	0.0881790	−	0.500088i
$575$	−2.26872e10	−	1.30984e10i	−0.207543	−	0.119825i
$576$	−2.13098e9	−	1.35934e10i	−0.0193593	−	0.123492i
$577$	9.58908e10	+	1.66088e11i	0.865115	+	1.49842i	0.866933	+	0.498425i	$0.166088\pi$
$577$	9.58908e10	+	1.66088e11i	0.865115	+	1.49842i	−0.00181803	+	0.999998i	$0.500579\pi$
$578$	3.04166e9	+	8.35689e9i	0.0272521	+	0.0748744i
$579$	1.88205e11	+	1.79106e9i	1.67462	+	0.0159366i
$580$	7.18611e10	−	6.02987e10i	0.635012	−	0.532839i
$581$	1.00651e10	+	1.19951e10i	0.0883308	+	0.105269i
$582$	2.34814e10	+	1.38566e10i	0.204660	+	0.120772i
$583$	7.17899e10	−	2.61294e10i	0.621425	−	0.226180i
$584$	−2.11954e10	+	1.22372e10i	−0.182217	+	0.105203i
$585$	3.27918e9	−	1.72273e11i	0.0279989	−	1.47094i
$586$	2.17127e10	−	3.76075e10i	0.184130	−	0.318922i
$587$	1.22292e11	+	2.15633e10i	1.03002	+	0.181620i	0.663019	−	0.748602i	$-0.269275\pi$
$587$	1.22292e11	+	2.15633e10i	1.03002	+	0.181620i	0.366997	+	0.930222i	$0.380386\pi$
$588$	3.76956e10	+	1.41277e10i	0.315342	+	0.118185i
$589$	1.55193e10	+	5.64857e9i	0.128947	+	0.0469329i
$590$	−8.48310e10	+	1.49580e10i	−0.700078	+	0.123443i
$591$	7.78448e10	−	9.09989e10i	0.638087	−	0.745910i
$592$	−3.89160e10	−	3.26544e10i	−0.316841	−	0.265861i
$593$		−	9.56319e10i		−	0.773364i	−0.922213	−	0.386682i	$-0.873621\pi$
$593$		−	9.56319e10i		−	0.773364i	0.922213	−	0.386682i	$-0.126379\pi$
$594$	−8.90969e10	+	7.05270e10i	−0.715677	+	0.566512i
$595$	1.17404e11			0.936729
$596$	−4.85973e9	+	5.79160e9i	−0.0385147	+	0.0459001i
$597$	3.35778e10	−	1.18607e10i	0.264335	−	0.0933710i
$598$	−2.51656e9	−	1.42721e10i	−0.0196790	−	0.111605i
$599$	2.23794e10	−	6.14868e10i	0.173836	−	0.477612i	−0.821924	−	0.569597i	$-0.807099\pi$
$599$	2.23794e10	−	6.14868e10i	0.173836	−	0.477612i	0.995760	+	0.0919857i	$0.0293214\pi$
$600$	6.39767e10	−	1.06541e10i	0.493647	−	0.0822076i
$601$	−1.54093e10	+	8.73906e10i	−0.118110	+	0.669833i	0.867054	+	0.498215i	$0.166011\pi$
$601$	−1.54093e10	+	8.73906e10i	−0.118110	+	0.669833i	−0.985163	+	0.171619i	$0.945100\pi$
$602$	−6.58168e10	−	3.79994e10i	−0.501131	−	0.289328i
$603$	−2.03314e11	+	6.96476e10i	−1.53779	+	0.526789i
$604$	−2.67103e10	−	4.62635e10i	−0.200692	−	0.347609i
$605$	4.74480e10	+	1.30362e11i	0.354157	+	0.973039i
$606$	3.09245e10	+	5.47597e10i	0.229304	+	0.406042i
$607$	2.92355e10	−	2.45315e10i	0.215355	−	0.180705i	−0.528728	−	0.848791i	$-0.677331\pi$
$607$	2.92355e10	−	2.45315e10i	0.215355	−	0.180705i	0.744084	+	0.668087i	$0.232886\pi$
$608$	−2.02675e9	−	2.41539e9i	−0.0148315	−	0.0176755i
$609$	−7.30035e10	+	4.12273e10i	−0.530731	+	0.299720i
$610$	−1.99837e11	+	7.27348e10i	−1.44330	+	0.525318i
$611$	1.50262e11	−	8.67539e10i	1.07816	−	0.622478i
$612$	−2.39777e10	−	6.99950e10i	−0.170923	−	0.498955i
$613$	1.28645e10	−	2.22820e10i	0.0911070	−	0.157802i	−0.816870	−	0.576822i	$-0.804293\pi$
$613$	1.28645e10	−	2.22820e10i	0.0911070	−	0.157802i	0.907977	+	0.419020i	$0.137626\pi$
$614$	−4.85108e10	−	8.55376e9i	−0.341323	−	0.0601844i
$615$	−4.59029e10	−	2.75642e11i	−0.320878	−	1.92683i
$616$	3.52827e10	+	1.28419e10i	0.245041	+	0.0891877i
$617$	−1.90741e11	+	3.36328e10i	−1.31615	+	0.232072i	−0.787260	−	0.616621i	$-0.788501\pi$
$617$	−1.90741e11	+	3.36328e10i	−1.31615	+	0.232072i	−0.528885	+	0.848693i	$0.677390\pi$
$618$	−2.90746e10	−	8.23106e10i	−0.199324	−	0.564289i
$619$	8.92504e10	+	7.48900e10i	0.607922	+	0.510107i	0.893981	−	0.448105i	$-0.147901\pi$
$619$	8.92504e10	+	7.48900e10i	0.607922	+	0.510107i	−0.286059	+	0.958212i	$0.592345\pi$
$620$		−	1.20717e11i		−	0.816965i
$621$	9.28369e9	−	2.34053e10i	0.0624244	−	0.157379i
$622$	1.27497e11			0.851803
$623$	−7.70461e10	+	9.18200e10i	−0.511445	+	0.609516i
$624$	2.72648e10	+	2.33236e10i	0.179830	+	0.153835i
$625$	−1.09141e10	−	6.18971e10i	−0.0715269	−	0.405649i
$626$	−5.28805e10	+	1.45288e11i	−0.344349	+	0.946090i
$627$	−9.13854e9	+	2.43834e10i	−0.0591298	+	0.157770i
$628$	1.49813e10	−	8.49632e10i	0.0963188	−	0.546251i
$629$	−2.36574e11	−	1.36586e11i	−1.51135	−	0.872577i
$630$	−9.89001e10	−	1.88254e9i	−0.627819	−	0.0119504i
$631$	4.03214e10	+	6.98387e10i	0.254342	+	0.440533i	0.964717	−	0.263291i	$-0.0848078\pi$
$631$	4.03214e10	+	6.98387e10i	0.254342	+	0.440533i	−0.710375	+	0.703824i	$0.751475\pi$
$632$	−1.70927e10	−	4.69617e10i	−0.107138	−	0.294358i
$633$	9.71358e10	−	1.64607e11i	0.605013	−	1.02526i
$634$	−3.98866e9	+	3.34689e9i	−0.0246871	+	0.0207149i
$635$	−5.26562e10	−	6.27532e10i	−0.323858	−	0.385959i
$636$	3.98831e8	−	4.19093e10i	0.00243759	−	0.256143i
$637$	−9.86430e10	+	3.59031e10i	−0.599113	+	0.218059i
$638$	1.39710e11	−	8.06614e10i	0.843226	−	0.486837i
$639$	7.97346e10	−	1.24997e10i	0.478237	−	0.0749713i
$640$	−1.15235e10	+	1.99594e10i	−0.0686857	+	0.118967i
$641$	2.36416e11	+	4.16865e10i	1.40037	+	0.246924i	0.822297	−	0.569058i	$-0.192692\pi$
$641$	2.36416e11	+	4.16865e10i	1.40037	+	0.246924i	0.578077	+	0.815982i	$0.303803\pi$
$642$	1.71161e11	−	1.40867e11i	1.00755	−	0.829221i
$643$	−1.05213e11	−	3.82942e10i	−0.615494	−	0.224021i	0.0154116	−	0.999881i	$-0.495094\pi$
$643$	−1.05213e11	−	3.82942e10i	−0.615494	−	0.224021i	−0.630905	+	0.775860i	$0.717316\pi$
$644$	−8.19347e9	+	1.44473e9i	−0.0476348	+	0.00839930i
$645$	−3.78749e11	−	7.05063e10i	−2.18833	−	0.407370i
$646$	−1.29882e10	−	1.08984e10i	−0.0745794	−	0.0625795i
$647$			3.23031e11i			1.84343i	0.387864	+	0.921716i	$0.373213\pi$
$647$			3.23031e11i			1.84343i	−0.387864	+	0.921716i	$0.626787\pi$
$648$	1.90762e10	+	5.93478e10i	0.108191	+	0.336593i
$649$	−1.48135e11			−0.834988
$650$	−1.08712e11	+	1.29558e11i	−0.609011	+	0.725792i
$651$	−1.97452e10	+	1.06068e11i	−0.109936	+	0.590556i
$652$	−1.32999e10	−	7.54273e10i	−0.0735965	−	0.417386i
$653$	−6.63656e10	+	1.82338e11i	−0.364998	+	1.00282i	0.612239	+	0.790673i	$0.290269\pi$
$653$	−6.63656e10	+	1.82338e11i	−0.364998	+	1.00282i	−0.977237	+	0.212151i	$0.931953\pi$
$654$	2.12471e9	+	2.58163e9i	0.0116142	+	0.0141118i
$655$	−6.95899e10	+	3.94664e11i	−0.378078	+	2.14419i
$656$	5.03929e10	+	2.90943e10i	0.272116	+	0.157106i
$657$	8.62825e10	−	6.96449e10i	0.463086	−	0.373790i
$658$	−4.98045e10	−	8.62639e10i	−0.265684	−	0.460178i
$659$	−3.10653e10	−	8.53512e10i	−0.164715	−	0.452551i	0.829685	−	0.558232i	$-0.188520\pi$
$659$	−3.10653e10	−	8.53512e10i	−0.164715	−	0.452551i	−0.994400	+	0.105681i	$0.966298\pi$
$660$	1.90326e11	+	1.81125e9i	1.00305	+	0.00954556i
$661$	−1.58113e11	+	1.32673e11i	−0.828251	+	0.694985i	−0.954889	−	0.296964i	$-0.904026\pi$
$661$	−1.58113e11	+	1.32673e11i	−0.828251	+	0.694985i	0.126638	+	0.991949i	$0.459581\pi$
$662$	8.45722e10	+	1.00789e11i	0.440348	+	0.524786i
$663$	1.66161e11	+	9.80531e10i	0.859954	+	0.507467i
$664$	−1.55321e10	+	5.65323e9i	−0.0799022	+	0.0290820i
$665$	−1.96309e10	+	1.13339e10i	−0.100381	+	0.0579551i
$666$	1.97098e11	+	1.18852e11i	1.00181	+	0.604103i
$667$	−1.78734e10	+	3.09576e10i	−0.0903032	+	0.156410i
$668$	−1.60740e11	−	2.83429e10i	−0.807271	−	0.142344i
$669$	1.58746e11	+	5.94956e10i	0.792498	+	0.297016i
$670$	3.38270e11	+	1.23120e11i	1.67866	+	0.610984i
$671$	−3.60162e11	+	6.35062e10i	−1.77667	+	0.313275i
$672$	1.33898e10	−	1.56524e10i	0.0656595	−	0.0767546i
$673$	5.46214e10	+	4.58328e10i	0.266258	+	0.223417i	0.766135	−	0.642679i	$-0.222177\pi$
$673$	5.46214e10	+	4.58328e10i	0.266258	+	0.223417i	−0.499878	+	0.866096i	$0.666622\pi$
$674$		−	7.10467e10i		−	0.344274i
$675$	−2.78879e11	+	9.25778e10i	−1.34339	+	0.445956i
$676$	1.08517e10			0.0519651
$677$	−1.17688e10	+	1.40256e10i	−0.0560247	+	0.0667676i	−0.793329	−	0.608793i	$-0.791654\pi$
$677$	−1.17688e10	+	1.40256e10i	−0.0560247	+	0.0667676i	0.737304	+	0.675561i	$0.236098\pi$
$678$	1.01762e11	−	3.59455e10i	0.481580	−	0.170108i
$679$	7.08771e9	+	4.01964e10i	0.0333447	+	0.189107i
$680$	−4.23867e10	+	1.16456e11i	−0.198241	+	0.544663i
$681$	2.40803e11	−	4.01012e10i	1.11963	−	0.186453i
$682$	3.60492e10	−	2.04445e11i	0.166632	−	0.945017i
$683$	−2.24895e11	−	1.29843e11i	−1.03347	−	0.596674i	−0.115492	−	0.993308i	$-0.536845\pi$
$683$	−2.24895e11	−	1.29843e11i	−1.03347	−	0.596674i	−0.917976	+	0.396635i	$0.870178\pi$
$684$	1.07664e10	+	9.38899e9i	0.0491866	+	0.0428938i
$685$	−3.28994e11	−	5.69834e11i	−1.49426	−	2.58813i
$686$	5.12143e10	+	1.40710e11i	0.231257	+	0.635374i
$687$	−1.43873e11	−	2.54763e11i	−0.645879	−	1.14369i
$688$	6.14549e10	−	5.15668e10i	0.274285	−	0.230153i
$689$	7.02501e10	+	8.37208e10i	0.311724	+	0.371498i
$690$	−3.67239e10	+	2.07391e10i	−0.162014	+	0.0914944i
$691$	1.19951e11	−	4.36587e10i	0.526130	−	0.191495i	−0.0652798	−	0.997867i	$-0.520794\pi$
$691$	1.19951e11	−	4.36587e10i	0.526130	−	0.191495i	0.591409	+	0.806372i	$0.298572\pi$
$692$	1.32073e10	−	7.62525e9i	0.0575958	−	0.0332529i
$693$	−1.66934e11	−	3.27223e10i	−0.723787	−	0.141877i
$694$	−7.07747e10	+	1.22585e11i	−0.305098	+	0.528446i
$695$	1.35887e11	+	2.39605e10i	0.582422	+	0.102697i
$696$	−1.45380e10	−	8.72989e10i	−0.0619537	−	0.372025i
$697$	2.94026e11	+	1.07017e11i	1.24582	+	0.453441i
$698$	−2.81917e11	+	4.97095e10i	−1.18768	+	0.209420i
$699$	4.00696e10	+	1.13438e11i	0.167844	+	0.475169i
$700$	7.43781e10	+	6.24106e10i	0.309780	+	0.259936i
$701$		−	1.79046e11i		−	0.741470i	−0.928739	−	0.370735i	$-0.879106\pi$
$701$		−	1.79046e11i		−	0.741470i	0.928739	−	0.370735i	$-0.120894\pi$
$702$	−1.38401e11	−	8.52636e10i	−0.569888	−	0.351087i
$703$	5.27428e10			0.215944
$704$	−2.54765e10	+	3.03617e10i	−0.103717	+	0.123605i
$705$	−3.83701e11	−	3.28236e11i	−1.55323	−	1.32871i
$706$	−3.37799e10	−	1.91576e11i	−0.135969	−	0.771119i
$707$	−3.21997e10	+	8.84679e10i	−0.128877	+	0.354085i
$708$	−2.85202e10	+	7.60976e10i	−0.113506	+	0.302857i
$709$	−5.03568e10	+	2.85587e11i	−0.199284	+	1.13020i	0.706900	+	0.707313i	$0.250093\pi$
$709$	−5.03568e10	+	2.85587e11i	−0.199284	+	1.13020i	−0.906184	+	0.422883i	$0.861018\pi$
$710$	−1.17075e11	−	6.75935e10i	−0.460715	−	0.265994i
$711$	1.09457e11	+	1.98204e11i	0.428318	+	0.775593i
$712$	−6.32629e10	−	1.09575e11i	−0.246167	−	0.426373i
$713$	1.57332e10	+	4.32267e10i	0.0608779	+	0.167261i
$714$	5.62913e10	−	9.53913e10i	0.216595	−	0.367042i
$715$	−3.80208e11	+	3.19033e11i	−1.45478	+	1.22071i
$716$	−1.55996e11	−	1.85909e11i	−0.593555	−	0.707372i
$717$	−2.35850e9	+	2.47832e11i	−0.00892399	+	0.937735i
$718$	1.60760e11	−	5.85120e10i	0.604897	−	0.220164i
$719$	1.09735e11	−	6.33556e10i	0.410610	−	0.237066i	−0.280442	−	0.959871i	$-0.590481\pi$
$719$	1.09735e11	−	6.33556e10i	0.410610	−	0.237066i	0.691052	+	0.722805i	$0.257148\pi$
$720$	3.75736e10	−	9.74225e10i	0.139815	−	0.362518i
$721$	6.53411e10	−	1.13174e11i	0.241794	−	0.418800i
$722$	−1.86004e11	−	3.27975e10i	−0.684500	−	0.120696i
$723$	−3.02792e11	+	2.49202e11i	−1.10813	+	0.912006i
$724$	1.65401e11	+	6.02012e10i	0.601984	+	0.219104i
$725$	4.10830e11	−	7.24405e10i	1.48700	−	0.262198i
$726$	1.28670e11	+	2.39527e10i	0.463160	+	0.0862199i
$727$	2.74808e11	+	2.30591e11i	0.983766	+	0.825478i	0.984653	−	0.174522i	$-0.0558379\pi$
$727$	2.74808e11	+	2.30591e11i	0.983766	+	0.825478i	−0.000886983		1.00000i	$0.500282\pi$
$728$			5.37129e10i			0.191229i
$729$	−1.27027e11	−	2.52251e11i	−0.449764	−	0.893147i
$730$	−1.85730e11			−0.654019
$731$	2.77288e11	−	3.30459e11i	0.971096	−	1.15731i
$732$	−3.67179e10	+	1.97243e11i	−0.127889	+	0.687001i
$733$	−1.76662e10	−	1.00190e11i	−0.0611966	−	0.347063i	−0.999997	−	0.00260052i	$-0.999172\pi$
$733$	−1.76662e10	−	1.00190e11i	−0.0611966	−	0.347063i	0.938800	−	0.344463i	$-0.111939\pi$
$734$	8.57279e10	−	2.35535e11i	0.295350	−	0.811469i
$735$	1.94132e11	+	2.35880e11i	0.665192	+	0.808242i
$736$	1.52504e9	−	8.64896e9i	0.00519722	−	0.0294749i
$737$	5.36122e11	+	3.09530e11i	1.81716	+	1.04914i
$738$	−2.45970e11	−	9.48649e10i	−0.829194	−	0.319801i
$739$	−7.45975e10	−	1.29207e11i	−0.250119	−	0.433219i	0.713440	−	0.700717i	$-0.247136\pi$
$739$	−7.45975e10	−	1.29207e11i	−0.250119	−	0.433219i	−0.963558	+	0.267498i	$0.913803\pi$
$740$	−1.31855e11	−	3.62269e11i	−0.439714	−	1.20810i
$741$	−3.72493e10	−	3.54484e8i	−0.123551	−	0.00117577i
$742$	4.80633e10	−	4.03299e10i	0.158561	−	0.133049i
$743$	−2.63575e11	−	3.14116e11i	−0.864865	−	1.03071i	−0.999209	−	0.0397713i	$-0.987337\pi$
$743$	−2.63575e11	−	3.14116e11i	−0.864865	−	1.03071i	0.134344	−	0.990935i	$-0.457107\pi$
$744$	−9.80837e10	−	5.78801e10i	−0.320114	−	0.188902i
$745$	−5.39140e10	+	1.96231e10i	−0.175015	+	0.0637004i
$746$	1.29420e11	−	7.47205e10i	0.417874	−	0.241259i
$747$	6.55539e10	−	3.62019e10i	0.210531	−	0.116265i
$748$	−1.06562e11	+	1.84571e11i	−0.340406	+	0.589601i
$749$	3.26811e11	+	5.76256e10i	1.03841	+	0.183100i
$750$	1.35280e11	+	5.07010e10i	0.427553	+	0.160240i
$751$	5.83956e11	+	2.12543e11i	1.83578	+	0.668169i	0.991138	+	0.132835i	$0.0424080\pi$
$751$	5.83956e11	+	2.12543e11i	1.83578	+	0.668169i	0.844640	+	0.535334i	$0.179814\pi$
$752$	1.03549e11	−	1.82585e10i	0.323798	−	0.0570944i
$753$	−1.54433e11	+	1.80529e11i	−0.480354	+	0.561524i
$754$	1.76788e11	+	1.48343e11i	0.546974	+	0.458966i
$755$		−	4.05396e11i		−	1.24765i

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.27231 + 8.66680i) q^{2} +(-14.8240 + 79.6320i) q^{3} +(-22.2270 - 126.055i) q^{4} +(332.225 - 912.782i) q^{5} +(-582.350 - 707.585i) q^{6} +(238.226 - 1351.05i) q^{7} +(1254.14 + 724.077i) q^{8} +(-6121.50 - 2360.92i) q^{9} +O(q^{10})\)	\(q+(-7.27231 + 8.66680i) q^{2} +(-14.8240 + 79.6320i) q^{3} +(-22.2270 - 126.055i) q^{4} +(332.225 - 912.782i) q^{5} +(-582.350 - 707.585i) q^{6} +(238.226 - 1351.05i) q^{7} +(1254.14 + 724.077i) q^{8} +(-6121.50 - 2360.92i) q^{9} +(5494.85 + 9517.37i) q^{10} +(6463.89 + 17759.4i) q^{11} +(10367.5 + 98.6629i) q^{12} +(-20710.9 + 17378.5i) q^{13} +(9976.80 + 11889.9i) q^{14} +(67761.7 + 39986.8i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-76297.8 + 44050.6i) q^{17} +(64979.1 - 35884.5i) q^{18} +(8505.08 - 14731.2i) q^{19} +(-122445. - 21590.4i) q^{20} +(104055. + 38998.3i) q^{21} +(-200924. - 73130.5i) q^{22} +(46659.4 - 8227.30i) q^{23} +(-76251.0 + 89135.8i) q^{24} +(-423561. - 355410. i) q^{25} -305879. i q^{26} +(278750. - 452469. i) q^{27} -175602. q^{28} +(-484972. + 577967. i) q^{29} +(-839342. + 296481. i) q^{30} +(168597. + 956159. i) q^{31} +(63398.2 - 174185. i) q^{32} +(-1.51003e6 + 251468. i) q^{33} +(173084. - 981608. i) q^{34} +(-1.15407e6 - 666301. i) q^{35} +(-161545. + 824124. i) q^{36} +(1.55033e6 + 2.68525e6i) q^{37} +(65821.1 + 180842. i) q^{38} +(-1.07687e6 - 1.90687e6i) q^{39} +(1.07758e6 - 904198. i) q^{40} +(-2.28290e6 - 2.72065e6i) q^{41} +(-1.09471e6 + 618217. i) q^{42} +(-4.60117e6 + 1.67469e6i) q^{43} +(2.09499e6 - 1.20954e6i) q^{44} +(-4.18873e6 + 4.80324e6i) q^{45} +(-268017. + 464219. i) q^{46} +(-6.32013e6 - 1.11441e6i) q^{47} +(-218002. - 1.30908e6i) q^{48} +(3.64856e6 + 1.32797e6i) q^{49} +(6.16054e6 - 1.08627e6i) q^{50} +(-2.37680e6 - 6.72875e6i) q^{51} +(2.65099e6 + 2.22445e6i) q^{52} -4.04236e6i q^{53} +(1.89430e6 + 5.70636e6i) q^{54} +1.83579e7 q^{55} +(1.27703e6 - 1.52191e6i) q^{56} +(1.04700e6 + 895651. i) q^{57} +(-1.48226e6 - 8.40631e6i) q^{58} +(-2.68083e6 + 7.36551e6i) q^{59} +(3.53442e6 - 9.43052e6i) q^{60} +(-3.36027e6 + 1.90570e7i) q^{61} +(-9.51293e6 - 5.49229e6i) q^{62} +(-4.64802e6 + 7.70800e6i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(8.98209e6 + 2.46781e7i) q^{65} +(8.80202e6 - 1.49159e7i) q^{66} +(2.50926e7 - 2.10552e7i) q^{67} +(7.24868e6 + 8.63864e6i) q^{68} +(-36520.1 + 3.83754e6i) q^{69} +(1.41674e7 - 5.15652e6i) q^{70} +(-1.06532e7 + 6.15062e6i) q^{71} +(-5.96772e6 - 7.39336e6i) q^{72} +(-8.45017e6 + 1.46361e7i) q^{73} +(-3.45470e7 - 6.09158e6i) q^{74} +(3.45808e7 - 2.84604e7i) q^{75} +(-2.04599e6 - 744680. i) q^{76} +(2.55336e7 - 4.50227e6i) q^{77} +(2.43577e7 + 4.53433e6i) q^{78} +(-2.64361e7 - 2.21825e7i) q^{79} +1.59148e7i q^{80} +(3.18988e7 + 2.89048e7i) q^{81} +4.01813e7 q^{82} +(-7.33665e6 + 8.74347e6i) q^{83} +(2.60311e6 - 1.39835e7i) q^{84} +(1.48605e7 + 8.42780e7i) q^{85} +(1.89469e7 - 5.20563e7i) q^{86} +(-3.88354e7 - 4.71870e7i) q^{87} +(-4.75256e6 + 2.69531e7i) q^{88} +(-7.56650e7 - 4.36852e7i) q^{89} +(-1.11670e7 - 7.12335e7i) q^{90} +(1.85453e7 + 3.21214e7i) q^{91} +(-2.07419e6 - 5.69880e6i) q^{92} +(-7.86401e7 - 748381. i) q^{93} +(5.56203e7 - 4.66710e7i) q^{94} +(-1.06208e7 - 1.26574e7i) q^{95} +(1.29309e7 + 7.63063e6i) q^{96} +(-2.79578e7 + 1.01758e7i) q^{97} +(-3.80427e7 + 2.19640e7i) q^{98} +(2.35983e6 - 1.23975e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

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