LMFDB - Embedded newform 27.7.f.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.34855 - 1.11942i) q^{2} +(2.13616 - 26.9154i) q^{3} +(-21.0893 - 7.67587i) q^{4} +(-34.3281 - 40.9106i) q^{5} +(-43.6912 + 168.482i) q^{6} +(90.1091 - 32.7970i) q^{7} +(482.595 + 278.626i) q^{8} +(-719.874 - 114.991i) q^{9} +O(q^{10})$	\(q+(-6.34855 - 1.11942i) q^{2} +(2.13616 - 26.9154i) q^{3} +(-21.0893 - 7.67587i) q^{4} +(-34.3281 - 40.9106i) q^{5} +(-43.6912 + 168.482i) q^{6} +(90.1091 - 32.7970i) q^{7} +(482.595 + 278.626i) q^{8} +(-719.874 - 114.991i) q^{9} +(172.137 + 298.151i) q^{10} +(-1591.86 + 1897.10i) q^{11} +(-251.649 + 551.229i) q^{12} +(127.968 + 725.743i) q^{13} +(-608.776 + 107.344i) q^{14} +(-1174.45 + 836.561i) q^{15} +(-1651.58 - 1385.84i) q^{16} +(-1847.61 + 1066.72i) q^{17} +(4441.43 + 1535.87i) q^{18} +(3686.89 - 6385.89i) q^{19} +(409.930 + 1126.27i) q^{20} +(-690.256 - 2495.38i) q^{21} +(12229.6 - 10261.9i) q^{22} +(-3015.51 + 8285.04i) q^{23} +(8530.23 - 12394.0i) q^{24} +(2217.99 - 12578.9i) q^{25} -4750.67i q^{26} +(-4632.79 + 19130.0i) q^{27} -2152.08 q^{28} +(-14295.7 - 2520.72i) q^{29} +(8392.55 - 3996.24i) q^{30} +(-38276.2 - 13931.4i) q^{31} +(-13990.7 - 16673.4i) q^{32} +(47660.7 + 46897.9i) q^{33} +(12923.7 - 4703.86i) q^{34} +(-4435.02 - 2560.56i) q^{35} +(14299.0 + 7950.74i) q^{36} +(27241.5 + 47183.7i) q^{37} +(-30554.9 + 36414.0i) q^{38} +(19807.0 - 1894.00i) q^{39} +(-5167.78 - 29307.9i) q^{40} +(-85176.1 + 15018.8i) q^{41} +(1588.75 + 16614.7i) q^{42} +(-69112.5 - 57992.3i) q^{43} +(48133.0 - 27789.6i) q^{44} +(20007.5 + 33397.9i) q^{45} +(28418.6 - 49222.4i) q^{46} +(894.621 + 2457.95i) q^{47} +(-40828.5 + 41492.5i) q^{48} +(-83080.4 + 69712.7i) q^{49} +(-28162.1 + 77374.7i) q^{50} +(24764.3 + 52007.7i) q^{51} +(2871.95 - 16287.7i) q^{52} -55555.2i q^{53} +(50826.1 - 116262. i) q^{54} +132257. q^{55} +(52624.3 + 9279.08i) q^{56} +(-164003. - 112875. i) q^{57} +(87935.5 + 32005.9i) q^{58} +(-30517.7 - 36369.5i) q^{59} +(31189.7 - 8627.52i) q^{60} +(46240.1 - 16830.0i) q^{61} +(227403. + 131291. i) q^{62} +(-68638.5 + 13248.0i) q^{63} +(139147. + 241010. i) q^{64} +(25297.7 - 30148.6i) q^{65} +(-250078. - 351086. i) q^{66} +(-77364.4 - 438755. i) q^{67} +(47152.7 - 8314.29i) q^{68} +(216553. + 98861.6i) q^{69} +(25289.6 + 21220.5i) q^{70} +(488793. - 282205. i) q^{71} +(-315368. - 256070. i) q^{72} +(-189832. + 328799. i) q^{73} +(-120126. - 330043. i) q^{74} +(-333827. - 86568.5i) q^{75} +(-126771. + 106374. i) q^{76} +(-81221.4 + 223154. i) q^{77} +(-127866. - 10148.2i) q^{78} +(-126342. + 716523. i) q^{79} +115140. i q^{80} +(504995. + 165558. i) q^{81} +557557. q^{82} +(-217936. - 38427.9i) q^{83} +(-4597.19 + 57924.1i) q^{84} +(107065. + 38968.4i) q^{85} +(373847. + 445533. i) q^{86} +(-98384.2 + 379390. i) q^{87} +(-1.29680e6 + 471998. i) q^{88} +(89261.8 + 51535.3i) q^{89} +(-89632.5 - 234425. i) q^{90} +(35333.3 + 61199.0i) q^{91} +(127190. - 151579. i) q^{92} +(-456732. + 1.00046e6i) q^{93} +(-2928.07 - 16605.9i) q^{94} +(-387814. + 68382.1i) q^{95} +(-478657. + 340947. i) q^{96} +(-472027. - 396077. i) q^{97} +(605478. - 349573. i) q^{98} +(1.36408e6 - 1.18262e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−6.34855	−	1.11942i	−0.793569	−	0.139928i	−0.237855	−	0.971301i	$-0.576444\pi$
$2$	−6.34855	−	1.11942i	−0.793569	−	0.139928i	−0.555715	+	0.831373i	$0.687555\pi$
$3$	2.13616	−	26.9154i	0.0791170	−	0.996865i
$3$	2.13616	−	26.9154i	0.0791170	−	0.996865i
$4$	−21.0893	−	7.67587i	−0.329520	−	0.119936i
$5$	−34.3281	−	40.9106i	−0.274625	−	0.327285i	0.611049	−	0.791592i	$-0.290748\pi$
$5$	−34.3281	−	40.9106i	−0.274625	−	0.327285i	−0.885674	+	0.464308i	$0.846303\pi$
$6$	−43.6912	+	168.482i	−0.202274	+	0.780011i
$7$	90.1091	−	32.7970i	0.262709	−	0.0956181i	−0.207308	−	0.978276i	$-0.566470\pi$
$7$	90.1091	−	32.7970i	0.262709	−	0.0956181i	0.470016	+	0.882658i	$0.344248\pi$
$8$	482.595	+	278.626i	0.942568	+	0.544192i
$9$	−719.874	−	114.991i	−0.987481	−	0.157738i
$10$	172.137	+	298.151i	0.172137	+	0.298151i
$11$	−1591.86	+	1897.10i	−1.19598	+	1.42532i	−0.317029	+	0.948416i	$0.602685\pi$
$11$	−1591.86	+	1897.10i	−1.19598	+	1.42532i	−0.878956	+	0.476903i	$0.841759\pi$
$12$	−251.649	+	551.229i	−0.145630	+	0.318998i
$13$	127.968	+	725.743i	0.0582467	+	0.330333i	0.999982	−	0.00602184i	$-0.00191682\pi$
$13$	127.968	+	725.743i	0.0582467	+	0.330333i	−0.941735	+	0.336355i	$0.890806\pi$
$14$	−608.776	+	107.344i	−0.221857	+	0.0391194i
$15$	−1174.45	+	836.561i	−0.347986	+	0.247870i
$16$	−1651.58	−	1385.84i	−0.403218	−	0.338340i
$17$	−1847.61	+	1066.72i	−0.376065	+	0.217121i	−0.676105	−	0.736805i	$-0.736333\pi$
$17$	−1847.61	+	1066.72i	−0.376065	+	0.217121i	0.300040	+	0.953927i	$0.403000\pi$
$18$	4441.43	+	1535.87i	0.761563	+	0.263352i
$19$	3686.89	−	6385.89i	0.537526	−	0.931023i	−0.461510	−	0.887135i	$-0.652692\pi$
$19$	3686.89	−	6385.89i	0.537526	−	0.931023i	0.999036	−	0.0438880i	$-0.0139745\pi$
$20$	409.930	+	1126.27i	0.0512413	+	0.140784i
$21$	−690.256	−	2495.38i	−0.0745337	−	0.269450i
$22$	12229.6	−	10261.9i	1.14854	−	0.963738i
$23$	−3015.51	+	8285.04i	−0.247843	+	0.680943i	0.751922	+	0.659252i	$0.229127\pi$
$23$	−3015.51	+	8285.04i	−0.247843	+	0.680943i	−0.999765	+	0.0216908i	$0.993095\pi$
$24$	8530.23	−	12394.0i	0.617059	−	0.896558i
$25$	2217.99	−	12578.9i	0.141951	−	0.805047i
$26$		−	4750.67i		−	0.270293i
$27$	−4632.79	+	19130.0i	−0.235370	+	0.971906i
$28$	−2152.08			−0.0980358
$29$	−14295.7	−	2520.72i	−0.586155	−	0.103355i	−0.127297	−	0.991865i	$-0.540630\pi$
$29$	−14295.7	−	2520.72i	−0.586155	−	0.103355i	−0.458858	+	0.888510i	$0.651741\pi$
$30$	8392.55	−	3996.24i	0.310835	−	0.148009i
$31$	−38276.2	−	13931.4i	−1.28482	−	0.467637i	−0.392799	−	0.919625i	$-0.628493\pi$
$31$	−38276.2	−	13931.4i	−1.28482	−	0.467637i	−0.892024	+	0.451987i	$0.850715\pi$
$32$	−13990.7	−	16673.4i	−0.426961	−	0.508832i
$33$	47660.7	+	46897.9i	1.32623	+	1.30500i
$34$	12923.7	−	4703.86i	0.328815	−	0.119679i
$35$	−4435.02	−	2560.56i	−0.103441	−	0.0597215i
$36$	14299.0	+	7950.74i	0.306476	+	0.170412i
$37$	27241.5	+	47183.7i	0.537807	+	0.931509i	0.999022	+	0.0442205i	$0.0140804\pi$
$37$	27241.5	+	47183.7i	0.537807	+	0.931509i	−0.461215	+	0.887288i	$0.652586\pi$
$38$	−30554.9	+	36414.0i	−0.556840	+	0.663616i
$39$	19807.0	−	1894.00i	0.333906	−	0.0319291i
$40$	−5167.78	−	29307.9i	−0.0807466	−	0.457937i
$41$	−85176.1	+	15018.8i	−1.23585	+	0.217914i	−0.753137	−	0.657864i	$-0.771460\pi$
$41$	−85176.1	+	15018.8i	−1.23585	+	0.217914i	−0.482714	+	0.875778i	$0.660349\pi$
$42$	1588.75	+	16614.7i	0.0214441	+	0.224257i
$43$	−69112.5	−	57992.3i	−0.869263	−	0.729398i	0.0946796	−	0.995508i	$-0.469817\pi$
$43$	−69112.5	−	57992.3i	−0.869263	−	0.729398i	−0.963943	+	0.266109i	$0.914262\pi$
$44$	48133.0	−	27789.6i	0.565047	−	0.326230i
$45$	20007.5	+	33397.9i	0.219561	+	0.366506i
$46$	28418.6	−	49222.4i	0.291963	−	0.505696i
$47$	894.621	+	2457.95i	0.00861679	+	0.0236744i	0.943926	−	0.330156i	$-0.107101\pi$
$47$	894.621	+	2457.95i	0.00861679	+	0.0236744i	−0.935310	+	0.353830i	$0.884879\pi$
$48$	−40828.5	+	41492.5i	−0.369181	+	0.375186i
$49$	−83080.4	+	69712.7i	−0.706171	+	0.592548i
$50$	−28162.1	+	77374.7i	−0.225297	+	0.618998i
$51$	24764.3	+	52007.7i	0.186687	+	0.392064i
$52$	2871.95	−	16287.7i	0.0204253	−	0.115837i
$53$		−	55555.2i		−	0.373162i	−0.982440	−	0.186581i	$-0.940259\pi$
$53$		−	55555.2i		−	0.373162i	0.982440	−	0.186581i	$-0.0597407\pi$
$54$	50826.1	−	116262.i	0.322779	−	0.738340i
$55$	132257.			0.794932
$56$	52624.3	+	9279.08i	0.299655	+	0.0528373i
$57$	−164003.	−	112875.i	−0.885577	−	0.609501i
$58$	87935.5	+	32005.9i	0.450693	+	0.164039i
$59$	−30517.7	−	36369.5i	−0.148592	−	0.177085i	0.686614	−	0.727022i	$-0.259096\pi$
$59$	−30517.7	−	36369.5i	−0.148592	−	0.177085i	−0.835206	+	0.549937i	$0.814652\pi$
$60$	31189.7	−	8627.52i	0.144397	−	0.0399422i
$61$	46240.1	−	16830.0i	0.203718	−	0.0741472i	−0.238146	−	0.971229i	$-0.576540\pi$
$61$	46240.1	−	16830.0i	0.203718	−	0.0741472i	0.441864	+	0.897082i	$0.354317\pi$
$62$	227403.	+	131291.i	0.954161	+	0.550885i
$63$	−68638.5	+	13248.0i	−0.274502	+	0.0529819i
$64$	139147.	+	241010.i	0.530805	+	0.919382i
$65$	25297.7	−	30148.6i	0.0921171	−	0.109781i
$66$	−250078.	−	351086.i	−0.869848	−	1.22119i
$67$	−77364.4	−	438755.i	−0.257227	−	1.45881i	−0.790291	−	0.612732i	$-0.790070\pi$
$67$	−77364.4	−	438755.i	−0.257227	−	1.45881i	0.533063	−	0.846075i	$-0.321041\pi$
$68$	47152.7	−	8314.29i	0.149962	−	0.0264423i
$69$	216553.	+	98861.6i	0.659200	+	0.300940i
$70$	25289.6	+	21220.5i	0.0737306	+	0.0618673i
$71$	488793.	−	282205.i	1.36568	−	0.788477i	0.375309	−	0.926900i	$-0.377536\pi$
$71$	488793.	−	282205.i	1.36568	−	0.788477i	0.990373	+	0.138422i	$0.0442032\pi$
$72$	−315368.	−	256070.i	−0.844928	−	0.686058i
$73$	−189832.	+	328799.i	−0.487979	+	0.845205i	−0.999904	−	0.0138252i	$-0.995599\pi$
$73$	−189832.	+	328799.i	−0.487979	+	0.845205i	0.511925	+	0.859030i	$0.328932\pi$
$74$	−120126.	−	330043.i	−0.296443	−	0.814471i
$75$	−333827.	−	86568.5i	−0.791293	−	0.205199i
$76$	−126771.	+	106374.i	−0.288788	+	0.242322i
$77$	−81221.4	+	223154.i	−0.177909	+	0.488801i
$78$	−127866.	−	10148.2i	−0.269446	−	0.0213848i
$79$	−126342.	+	716523.i	−0.256252	+	1.45328i	0.536586	+	0.843846i	$0.319714\pi$
$79$	−126342.	+	716523.i	−0.256252	+	1.45328i	−0.792838	+	0.609433i	$0.791397\pi$
$80$			115140.i			0.224884i
$81$	504995.	+	165558.i	0.950237	+	0.311527i
$82$	557557.			1.01123
$83$	−217936.	−	38427.9i	−0.381148	−	0.0672067i	−0.0202083	−	0.999796i	$-0.506433\pi$
$83$	−217936.	−	38427.9i	−0.381148	−	0.0672067i	−0.360940	+	0.932589i	$0.617544\pi$
$84$	−4597.19	+	57924.1i	−0.00775630	+	0.0977285i
$85$	107065.	+	38968.4i	0.174337	+	0.0634535i
$86$	373847.	+	445533.i	0.587758	+	0.700462i
$87$	−98384.2	+	379390.i	−0.149406	+	0.576141i
$88$	−1.29680e6	+	471998.i	−1.90294	+	0.692615i
$89$	89261.8	+	51535.3i	0.126618	+	0.0731029i	0.561971	−	0.827157i	$-0.310043\pi$
$89$	89261.8	+	51535.3i	0.126618	+	0.0731029i	−0.435353	+	0.900260i	$0.643377\pi$
$90$	−89632.5	−	234425.i	−0.122953	−	0.321571i
$91$	35333.3	+	61199.0i	0.0468878	+	0.0812120i
$92$	127190.	−	151579.i	0.163339	−	0.194659i
$93$	−456732.	+	1.00046e6i	−0.567823	+	1.24380i
$94$	−2928.07	−	16605.9i	−0.00352531	−	0.0199930i
$95$	−387814.	+	68382.1i	−0.452328	+	0.0797576i
$96$	−478657.	+	340947.i	−0.541017	+	0.385365i
$97$	−472027.	−	396077.i	−0.517192	−	0.433975i	0.346460	−	0.938065i	$-0.387384\pi$
$97$	−472027.	−	396077.i	−0.517192	−	0.433975i	−0.863651	+	0.504090i	$0.831828\pi$
$98$	605478.	−	349573.i	0.643310	−	0.371415i
$99$	1.36408e6	−	1.18262e6i	1.40584	−	1.21882i
$100$	−143330.	+	248254.i	−0.143330	+	0.248254i
$101$	−578152.	−	1.58846e6i	−0.561149	−	1.54174i	−0.817956	−	0.575281i	$-0.804893\pi$
$101$	−578152.	−	1.58846e6i	−0.561149	−	1.54174i	0.256807	−	0.966463i	$-0.417330\pi$
$102$	−98998.9	−	357895.i	−0.0932888	−	0.337253i
$103$	1.18024e6	−	990342.i	1.08009	−	0.906304i	0.0841622	−	0.996452i	$-0.473179\pi$
$103$	1.18024e6	−	990342.i	1.08009	−	0.906304i	0.995928	+	0.0901485i	$0.0287342\pi$
$104$	−140454.	+	385895.i	−0.124863	+	0.343059i
$105$	−78392.2	+	113900.i	−0.0677182	+	0.0983914i
$106$	−62189.7	+	352695.i	−0.0522157	+	0.296130i
$107$		−	211812.i		−	0.172902i	−0.996256	−	0.0864509i	$-0.972447\pi$
$107$		−	211812.i		−	0.172902i	0.996256	−	0.0864509i	$-0.0275526\pi$
$108$	244542.	−	367878.i	0.194125	−	0.292033i
$109$	567134.			0.437932			0.218966	−	0.975733i	$-0.429732\pi$
$109$	567134.			0.437932			0.218966	+	0.975733i	$0.429732\pi$
$110$	−839640.	−	148051.i	−0.630834	−	0.111233i
$111$	1.32816e6	−	632424.i	0.971139	−	0.462423i
$112$	−194274.	−	70709.9i	−0.138280	−	0.0503299i
$113$	684185.	+	815380.i	0.474175	+	0.565099i	0.949119	−	0.314916i	$-0.101976\pi$
$113$	684185.	+	815380.i	0.474175	+	0.565099i	−0.474945	+	0.880016i	$0.657532\pi$
$114$	914825.	+	900183.i	0.617481	+	0.607598i
$115$	442462.	−	161043.i	0.290926	−	0.105888i
$116$	282138.	+	162893.i	0.180754	+	0.104358i
$117$	−8666.92	−	537158.i	−0.00541137	−	0.335386i
$118$	153030.	+	265056.i	0.0931389	+	0.161321i
$119$	−131501.	+	156717.i	−0.0780348	+	0.0929982i
$120$	−799873.	+	76486.3i	−0.462890	+	0.0442629i
$121$	−757354.	−	4.29517e6i	−0.427507	−	2.42451i
$122$	−312398.	+	55084.1i	−0.172040	+	0.0303352i
$123$	222288.	+	2.32463e6i	0.119454	+	1.24922i
$124$	700281.	+	587606.i	0.367289	+	0.308192i
$125$	−1.31341e6	+	758295.i	−0.672464	+	0.388247i
$126$	450585.	−	7270.09i	0.225250	−	0.00363436i
$127$	1.16556e6	−	2.01881e6i	0.569016	−	0.985565i	−0.427647	−	0.903946i	$-0.640658\pi$
$127$	1.16556e6	−	2.01881e6i	0.569016	−	0.985565i	0.996664	−	0.0816192i	$-0.0260091\pi$
$128$	−137159.	−	376842.i	−0.0654027	−	0.179692i
$129$	−1.70852e6	+	1.73631e6i	−0.795886	+	0.808831i
$130$	−194353.	+	163081.i	−0.0884627	+	0.0742290i
$131$	−1.29487e6	+	3.55761e6i	−0.575985	+	1.58250i	0.218902	+	0.975747i	$0.429753\pi$
$131$	−1.29487e6	+	3.55761e6i	−0.575985	+	1.58250i	−0.794887	+	0.606758i	$0.792470\pi$
$132$	−645147.	−	1.35488e6i	−0.280503	−	0.589086i
$133$	122784.	−	696345.i	0.0521901	−	0.295985i
$134$			2.87207e6i			1.19366i
$135$	941655.	−	467167.i	0.382728	−	0.189876i
$136$	−1.18886e6			−0.472622
$137$	−2.45149e6	−	432264.i	−0.953385	−	0.168108i	−0.324743	−	0.945802i	$-0.605278\pi$
$137$	−2.45149e6	−	432264.i	−0.953385	−	0.168108i	−0.628642	+	0.777695i	$0.716389\pi$
$138$	−1.26413e6	−	870043.i	−0.481011	−	0.331057i
$139$	3.90181e6	+	1.42014e6i	1.45285	+	0.528795i	0.943386	−	0.331696i	$-0.107621\pi$
$139$	3.90181e6	+	1.42014e6i	1.45285	+	0.528795i	0.509465	+	0.860491i	$0.329843\pi$
$140$	73876.8	+	88043.0i	0.0269230	+	0.0320856i
$141$	68067.7	−	18828.5i	0.0242820	−	0.00671673i
$142$	−3.41903e6	+	1.24443e6i	−1.19409	+	0.434615i
$143$	−1.58051e6	−	912509.i	−0.540493	−	0.312054i
$144$	1.02957e6	+	1.18755e6i	0.344801	+	0.397707i
$145$	387621.	+	671379.i	0.127146	+	0.220224i
$146$	1.57322e6	−	1.87490e6i	0.505513	−	0.602447i
$147$	1.69887e6	+	2.38506e6i	0.534821	+	0.750838i
$148$	−212328.	−	1.20417e6i	−0.0654972	−	0.371453i
$149$	−1.59430e6	+	281118.i	−0.481959	+	0.0849824i	−0.409349	−	0.912378i	$-0.634244\pi$
$149$	−1.59430e6	+	281118.i	−0.481959	+	0.0849824i	−0.0726105	+	0.997360i	$0.523133\pi$
$150$	2.02241e6	+	923277.i	0.599232	+	0.273564i
$151$	−240683.	−	201957.i	−0.0699061	−	0.0586582i	0.607165	−	0.794576i	$-0.292307\pi$
$151$	−240683.	−	201957.i	−0.0699061	−	0.0586582i	−0.677071	+	0.735918i	$0.736751\pi$
$152$	3.55855e6	−	2.05453e6i	1.01331	−	0.585035i
$153$	1.45271e6	−	555443.i	0.405605	−	0.155083i
$154$	765442.	−	1.32578e6i	0.209580	−	0.363003i
$155$	744006.	+	2.04414e6i	0.199793	+	0.548928i
$156$	−432253.	−	112093.i	−0.113858	−	0.0295259i
$157$	−5.32562e6	+	4.46872e6i	−1.37617	+	1.15474i	−0.405560	+	0.914068i	$0.632923\pi$
$157$	−5.32562e6	+	4.46872e6i	−1.37617	+	1.15474i	−0.970606	+	0.240672i	$0.922632\pi$
$158$	1.60418e6	−	4.40745e6i	0.406708	−	1.11742i
$159$	−1.49529e6	−	118675.i	−0.371992	−	0.0295235i
$160$	−201847.	+	1.14473e6i	−0.0492791	+	0.279476i
$161$			845456.i			0.202588i
$162$	−3.02066e6	−	1.61636e6i	−0.710488	−	0.380182i
$163$	−213551.			−0.0493104			−0.0246552	−	0.999696i	$-0.507849\pi$
$163$	−213551.			−0.0493104			−0.0246552	+	0.999696i	$0.507849\pi$
$164$	1.91159e6	+	337064.i	0.433373	+	0.0764154i
$165$	282522.	−	3.55974e6i	0.0628926	−	0.792440i
$166$	1.34056e6	+	487924.i	0.293063	+	0.106666i
$167$	−3.43308e6	−	4.09138e6i	−0.737113	−	0.878457i	0.259060	−	0.965861i	$-0.416587\pi$
$167$	−3.43308e6	−	4.09138e6i	−0.737113	−	0.878457i	−0.996173	+	0.0874039i	$0.972143\pi$
$168$	362164.	−	1.39658e6i	0.0763795	−	0.294536i
$169$	4.02539e6	−	1.46512e6i	0.833965	−	0.303538i
$170$	−636085.	−	367244.i	−0.129470	−	0.0747494i
$171$	−3.38842e6	+	4.17307e6i	−0.677655	+	0.834579i
$172$	1.01239e6	+	1.75351e6i	0.198959	+	0.344607i
$173$	−3.23579e6	+	3.85626e6i	−0.624945	+	0.744780i	−0.981912	−	0.189337i	$-0.939366\pi$
$173$	−3.23579e6	+	3.85626e6i	−0.624945	+	0.744780i	0.356968	+	0.934117i	$0.383811\pi$
$174$	1.04930e6	−	2.29845e6i	0.199182	−	0.436302i
$175$	−212688.	−	1.20621e6i	−0.0396852	−	0.225066i
$176$	5.25816e6	−	927155.i	0.964485	−	0.170065i
$177$	−1.04409e6	+	743703.i	−0.188286	+	0.134116i
$178$	−508994.	−	427096.i	−0.0902510	−	0.0757296i
$179$	8.81346e6	−	5.08845e6i	1.53669	−	0.887210i	0.537664	−	0.843159i	$-0.319307\pi$
$179$	8.81346e6	−	5.08845e6i	1.53669	−	0.887210i	0.999029	−	0.0440515i	$-0.0140266\pi$
$180$	−165586.	−	857913.i	−0.0283927	−	0.147104i
$181$	−4.68042e6	+	8.10673e6i	−0.789313	+	1.36713i	0.137076	+	0.990561i	$0.456230\pi$
$181$	−4.68042e6	+	8.10673e6i	−0.789313	+	1.36713i	−0.926388	+	0.376569i	$0.877104\pi$
$182$	−155808.	−	428078.i	−0.0258449	−	0.0710082i
$183$	−354210.	−	1.28052e6i	−0.0577973	−	0.208946i
$184$	−3.76370e6	+	3.15812e6i	−0.604173	+	0.506961i
$185$	995165.	−	2.73419e6i	0.157174	−	0.431831i
$186$	4.01952e6	−	5.84018e6i	0.624648	−	0.907585i
$187$	917456.	−	5.20315e6i	0.140301	−	0.795686i
$188$		−	58703.4i		−	0.00883466i
$189$	209951.	+	1.87573e6i	0.0310981	+	0.277834i
$190$	2.53861e6			0.370114
$191$	7.92365e6	+	1.39715e6i	1.13717	+	0.200514i	0.710367	−	0.703831i	$-0.248529\pi$
$191$	7.92365e6	+	1.39715e6i	1.13717	+	0.200514i	0.426802	+	0.904345i	$0.359640\pi$
$192$	6.78413e6	−	3.23037e6i	0.958496	−	0.456403i
$193$	−761444.	−	277143.i	−0.105917	−	0.0385507i	0.288518	−	0.957474i	$-0.406837\pi$
$193$	−761444.	−	277143.i	−0.105917	−	0.0385507i	−0.394435	+	0.918924i	$0.629060\pi$
$194$	2.55331e6	+	3.04292e6i	0.349702	+	0.416759i
$195$	−757420.	−	745298.i	−0.102149	−	0.100514i
$196$	2.28721e6	−	832477.i	0.303765	−	0.110562i
$197$	−1.00995e7	−	5.83096e6i	−1.32100	−	0.762679i	−0.337111	−	0.941465i	$-0.609450\pi$
$197$	−1.00995e7	−	5.83096e6i	−1.32100	−	0.762679i	−0.983888	+	0.178786i	$0.942783\pi$
$198$	−9.98382e6	+	5.98096e6i	−1.28618	+	0.770505i
$199$	−1.56535e6	−	2.71126e6i	−0.198633	−	0.344042i	0.749452	−	0.662058i	$-0.230317\pi$
$199$	−1.56535e6	−	2.71126e6i	−0.198633	−	0.344042i	−0.948085	+	0.318016i	$0.896984\pi$
$200$	4.57519e6	−	5.45250e6i	0.571899	−	0.681562i
$201$	−1.19745e7	+	1.14504e6i	−1.47459	+	0.141004i
$202$	1.89227e6	+	1.07316e7i	0.229578	+	1.30200i
$203$	−1.37085e6	+	241717.i	−0.163871	+	0.0288948i
$204$	−123057.	−	1.28689e6i	−0.0144949	−	0.151583i
$205$	3.53836e6	+	2.96904e6i	0.410715	+	0.344631i
$206$	−8.60145e6	+	4.96605e6i	−0.983944	+	0.568080i
$207$	3.12349e6	−	5.61742e6i	0.352151	−	0.633324i
$208$	794415.	−	1.37597e6i	0.0882790	−	0.152904i
$209$	6.24566e6	+	1.71598e7i	0.684131	+	1.87964i
$210$	625180.	−	635348.i	0.0675067	−	0.0686047i
$211$	−817660.	+	686098.i	−0.0870413	+	0.0730364i	−0.685270	−	0.728289i	$-0.740316\pi$
$211$	−817660.	+	686098.i	−0.0870413	+	0.0730364i	0.598229	+	0.801325i	$0.295871\pi$
$212$	−426435.	+	1.17162e6i	−0.0447554	+	0.122964i
$213$	−6.55150e6	−	1.37589e7i	−0.677957	−	1.42378i
$214$	−237107.	+	1.34470e6i	−0.0241937	+	0.137210i
$215$			4.81820e6i			0.484807i
$216$	−7.56589e6	+	7.94123e6i	−0.750755	+	0.788001i
$217$	−3.90594e6			−0.382249
$218$	−3.60048e6	−	634862.i	−0.347529	−	0.0612788i
$219$	8.44423e6	+	5.81177e6i	0.803948	+	0.553320i
$220$	−2.78920e6	−	1.01519e6i	−0.261946	−	0.0953406i
$221$	−1.01060e6	−	1.20438e6i	−0.0936269	−	0.111580i
$222$	−9.13984e6	+	2.52821e6i	−0.835372	+	0.231075i
$223$	1.20786e7	−	4.39626e6i	1.08919	−	0.396432i	0.265868	−	0.964010i	$-0.414342\pi$
$223$	1.20786e7	−	4.39626e6i	1.08919	−	0.396432i	0.823320	+	0.567578i	$0.192119\pi$
$224$	−1.80752e6	−	1.04357e6i	−0.160820	−	0.0928494i
$225$	−3.04313e6	+	8.80014e6i	−0.267161	+	0.772577i
$226$	−3.43083e6	−	5.94238e6i	−0.297217	−	0.514796i
$227$	−3.79274e6	+	4.52001e6i	−0.324246	+	0.386422i	−0.903402	−	0.428796i	$-0.858938\pi$
$227$	−3.79274e6	+	4.52001e6i	−0.324246	+	0.386422i	0.579155	+	0.815217i	$0.303383\pi$
$228$	2.59228e6	+	3.63932e6i	0.218715	+	0.307055i
$229$	1.54236e6	+	8.74716e6i	0.128434	+	0.728384i	0.979209	+	0.202854i	$0.0650218\pi$
$229$	1.54236e6	+	8.74716e6i	0.128434	+	0.728384i	−0.850775	+	0.525530i	$0.823867\pi$
$230$	−2.98927e6	+	527089.i	−0.245687	+	0.0433212i
$231$	5.83277e6	+	2.66280e6i	0.473193	+	0.216024i
$232$	−6.19671e6	−	5.19966e6i	−0.496246	−	0.416400i
$233$	8.96192e6	−	5.17417e6i	0.708490	−	0.409047i	−0.102012	−	0.994783i	$-0.532528\pi$
$233$	8.96192e6	−	5.17417e6i	0.708490	−	0.409047i	0.810502	+	0.585737i	$0.199195\pi$
$234$	−546284.	+	3.41988e6i	−0.0426354	+	0.266909i
$235$	69845.7	−	120976.i	0.00538190	−	0.00932173i
$236$	364428.	+	1.00126e6i	0.0277252	+	0.0761745i
$237$	1.90156e7	+	4.93116e6i	1.42845	+	0.370428i
$238$	1.01027e6	−	847720.i	0.0749390	−	0.0628813i
$239$	6.68698e6	−	1.83723e7i	0.489820	−	1.34577i	−0.411024	−	0.911625i	$-0.634829\pi$
$239$	6.68698e6	−	1.83723e7i	0.489820	−	1.34577i	0.900843	−	0.434144i	$-0.142949\pi$
$240$	3.09905e6	+	245958.i	0.224179	+	0.0177921i
$241$	1.79431e6	−	1.01760e7i	0.128188	−	0.726989i	−0.851176	−	0.524881i	$-0.824110\pi$
$241$	1.79431e6	−	1.01760e7i	0.128188	−	0.726989i	0.979363	−	0.202108i	$-0.0647791\pi$
$242$			2.81159e7i			1.98384i
$243$	5.53480e6	−	1.32385e7i	0.385730	−	0.922612i
$244$	−1.10436e6			−0.0760220
$245$	5.70398e6	+	1.00577e6i	0.387864	+	0.0683909i
$246$	1.19103e6	−	1.50069e7i	0.0800052	−	1.00806i
$247$	5.10631e6	+	1.85855e6i	0.338857	+	0.123334i
$248$	−1.45902e7	−	1.73880e7i	−0.956548	−	1.13997i
$249$	−1.49985e6	+	5.78373e6i	−0.0971514	+	0.374636i
$250$	9.18708e6	−	3.34382e6i	0.587973	−	0.214005i
$251$	−2.66456e7	−	1.53839e7i	−1.68502	−	0.972846i	−0.958237	−	0.285977i	$-0.907682\pi$
$251$	−2.66456e7	−	1.53839e7i	−1.68502	−	0.972846i	−0.726782	−	0.686869i	$-0.758985\pi$
$252$	1.54923e6	+	247470.i	0.0968085	+	0.0154640i
$253$	−1.09173e7	−	1.89093e7i	−0.674145	−	1.16765i
$254$	−9.65954e6	+	1.15118e7i	−0.589462	+	0.702493i
$255$	1.27756e6	−	2.79845e6i	0.0770477	−	0.168770i
$256$	−2.64391e6	−	1.49943e7i	−0.157589	−	0.893733i
$257$	1.33457e7	−	2.35320e6i	0.786214	−	0.138631i	0.233893	−	0.972262i	$-0.424853\pi$
$257$	1.33457e7	−	2.35320e6i	0.786214	−	0.138631i	0.552321	+	0.833631i	$0.313742\pi$
$258$	1.27903e7	−	9.11049e6i	0.744768	−	0.530497i
$259$	4.00219e6	+	3.35824e6i	0.230356	+	0.193291i
$260$	−764927.	+	441631.i	−0.0435211	+	0.0251269i
$261$	1.00013e7	+	3.45849e6i	0.562514	+	0.194520i
$262$	1.22030e7	−	2.11362e7i	0.678520	−	1.17523i
$263$	−7.03835e6	−	1.93377e7i	−0.386904	−	1.06301i	−0.968387	−	0.249452i	$-0.919750\pi$
$263$	−7.03835e6	−	1.93377e7i	−0.386904	−	1.06301i	0.581483	−	0.813558i	$-0.302473\pi$
$264$	9.93381e6	+	3.59122e7i	0.539888	+	1.95178i
$265$	−2.27280e6	+	1.90710e6i	−0.122130	+	0.102479i
$266$	−1.55901e6	+	4.28334e6i	−0.0828330	+	0.227582i
$267$	1.57777e6	−	2.29243e6i	0.0828914	−	0.120437i
$268$	−1.73627e6	+	9.84688e6i	−0.0902013	+	0.511557i
$269$			3.69934e6i			0.190050i	0.995475	+	0.0950250i	$0.0302931\pi$
$269$			3.69934e6i			0.190050i	−0.995475	+	0.0950250i	$0.969707\pi$
$270$	−6.50111e6	+	1.91172e6i	−0.330290	+	0.0971256i
$271$	−3.36875e7			−1.69263			−0.846314	−	0.532684i	$-0.821183\pi$
$271$	−3.36875e7			−1.69263			−0.846314	+	0.532684i	$0.821183\pi$
$272$	4.52977e6	+	798721.i	0.225097	+	0.0396907i
$273$	1.72267e6	−	820277.i	0.0846670	−	0.0403155i
$274$	1.50795e7	+	5.48850e6i	0.733054	+	0.266810i
$275$	2.03326e7	+	2.42315e7i	0.977677	+	1.16515i
$276$	−3.80810e6	−	3.74716e6i	−0.181126	−	0.178227i
$277$	−1.11750e7	+	4.06737e6i	−0.525786	+	0.191370i	−0.591256	−	0.806484i	$-0.701368\pi$
$277$	−1.11750e7	+	4.06737e6i	−0.525786	+	0.191370i	0.0654700	+	0.997855i	$0.479145\pi$
$278$	−2.31811e7	−	1.33836e7i	−1.07895	−	0.622929i
$279$	2.59520e7	+	1.44302e7i	1.19497	+	0.664448i
$280$	−1.42688e6	−	2.47142e6i	−0.0649999	−	0.112583i
$281$	1.05969e7	−	1.26289e7i	0.477595	−	0.569175i	−0.472423	−	0.881372i	$-0.656620\pi$
$281$	1.05969e7	−	1.26289e7i	0.477595	−	0.569175i	0.950017	+	0.312197i	$0.101065\pi$
$282$	−453209.	+	43337.2i	−0.0202093	+	0.00193247i
$283$	2.57492e6	+	1.46031e7i	0.113607	+	0.644297i	0.987430	+	0.158054i	$0.0505220\pi$
$283$	2.57492e6	+	1.46031e7i	0.113607	+	0.644297i	−0.873823	+	0.486243i	$0.838367\pi$
$284$	−1.24745e7	+	2.19958e6i	−0.544586	+	0.0960253i
$285$	1.01210e6	+	1.05842e7i	0.0437207	+	0.457220i
$286$	9.01249e6	+	7.56237e6i	0.385253	+	0.323266i
$287$	−7.18256e6	+	4.14686e6i	−0.303832	+	0.175418i
$288$	8.15422e6	+	1.36116e7i	0.341354	+	0.569810i
$289$	−9.79302e6	+	1.69620e7i	−0.405717	+	0.702722i
$290$	−1.70928e6	−	4.69620e6i	−0.0700839	−	0.192554i
$291$	−1.16689e7	+	1.18587e7i	−0.473534	+	0.481235i
$292$	6.52725e6	−	5.47701e6i	0.262169	−	0.219986i
$293$	−5.64899e6	+	1.55205e7i	−0.224578	+	0.617024i	−0.999894	−	0.0145496i	$-0.995369\pi$
$293$	−5.64899e6	+	1.55205e7i	−0.224578	+	0.617024i	0.775316	+	0.631574i	$0.217591\pi$
$294$	−8.11549e6	−	1.70434e7i	−0.319354	−	0.670679i
$295$	−440287.	+	2.49699e6i	−0.0171502	+	0.0972638i
$296$			3.03608e7i			1.17068i
$297$	−2.89168e7	−	3.92411e7i	−1.10378	−	1.49786i
$298$	1.04362e7			0.394360
$299$	−6.39869e6	−	1.12826e6i	−0.239374	−	0.0422082i
$300$	6.37567e6	+	4.38808e6i	0.236136	+	0.162521i
$301$	−8.12964e6	−	2.95895e6i	−0.298107	−	0.108502i
$302$	1.30192e6	+	1.55156e6i	0.0472674	+	0.0563311i
$303$	−4.39890e7	+	1.21680e7i	−1.58131	+	0.437412i
$304$	−1.49390e7	+	5.43736e6i	−0.531743	+	0.193539i
$305$	−2.27586e6	−	1.31397e6i	−0.0802132	−	0.0463111i
$306$	−9.84436e6	+	1.90007e6i	−0.343576	+	0.0663140i
$307$	1.55678e7	+	2.69642e7i	0.538036	+	0.931905i	0.999010	+	0.0444917i	$0.0141668\pi$
$307$	1.55678e7	+	2.69642e7i	0.538036	+	0.931905i	−0.460974	+	0.887414i	$0.652500\pi$
$308$	3.42580e6	−	4.08271e6i	0.117249	−	0.139732i
$309$	−2.41342e7	−	3.38822e7i	−0.818009	−	1.14841i
$310$	−2.43511e6	−	1.38102e7i	−0.0817397	−	0.463569i
$311$	2.78387e7	−	4.90871e6i	0.925480	−	0.163187i	0.309455	−	0.950914i	$-0.399853\pi$
$311$	2.78387e7	−	4.90871e6i	0.925480	−	0.163187i	0.616025	+	0.787727i	$0.288742\pi$
$312$	1.00865e7	+	4.60471e6i	0.332105	+	0.151614i
$313$	563473.	+	472810.i	0.0183755	+	0.0154189i	0.651929	−	0.758280i	$-0.273960\pi$
$313$	563473.	+	472810.i	0.0183755	+	0.0154189i	−0.633554	+	0.773699i	$0.718404\pi$
$314$	3.88124e7	−	2.24083e7i	1.25366	−	0.723803i
$315$	2.89821e6	+	2.35326e6i	0.0927253	+	0.0752903i
$316$	8.16441e6	−	1.41412e7i	0.258740	−	0.448151i
$317$	7.13768e6	+	1.96106e7i	0.224068	+	0.615621i	0.999882	−	0.0153401i	$-0.00488311\pi$
$317$	7.13768e6	+	1.96106e7i	0.224068	+	0.615621i	−0.775815	+	0.630961i	$0.782661\pi$
$318$	9.36008e6	+	2.42727e6i	0.291070	+	0.0754809i
$319$	2.75388e7	−	2.31078e7i	0.848346	−	0.711847i
$320$	5.08322e6	−	1.39660e7i	0.155128	−	0.426209i
$321$	−5.70100e6	−	452464.i	−0.172360	−	0.0136795i
$322$	946422.	−	5.36743e6i	0.0283477	−	0.160768i
$323$			1.57315e7i			0.466834i
$324$	−9.37919e6	−	7.36778e6i	−0.275759	−	0.216621i
$325$	9.41284e6			0.274202
$326$	1.35574e6	+	239054.i	0.0391313	+	0.00689990i
$327$	1.21149e6	−	1.52646e7i	0.0346478	−	0.436559i
$328$	−4.52902e7	−	1.64843e7i	−1.28346	−	0.467141i
$329$	161227.	+	192143.i	0.00452741	+	0.00539556i
$330$	−5.77845e6	+	2.22829e7i	−0.160794	+	0.620056i
$331$	5.34517e6	−	1.94548e6i	0.147393	−	0.0536467i	−0.267270	−	0.963622i	$-0.586122\pi$
$331$	5.34517e6	−	1.94548e6i	0.147393	−	0.0536467i	0.414663	+	0.909975i	$0.363899\pi$
$332$	4.30114e6	+	2.48326e6i	0.117536	+	0.0678592i
$333$	−1.41848e7	−	3.70988e7i	−0.384140	−	1.00468i
$334$	1.72151e7	+	2.98174e7i	0.462030	+	0.800259i
$335$	−1.52940e7	+	1.82266e7i	−0.406805	+	0.484811i
$336$	−2.31818e6	+	5.07791e6i	−0.0611125	+	0.133865i
$337$	1.08872e7	+	6.17445e7i	0.284464	+	1.61328i	0.707194	+	0.707020i	$0.249961\pi$
$337$	1.08872e7	+	6.17445e7i	0.284464	+	1.61328i	−0.422730	+	0.906256i	$0.638928\pi$
$338$	−2.71955e7	+	4.79530e6i	−0.704283	+	0.124184i
$339$	2.34078e7	−	1.66733e7i	0.600843	−	0.427979i
$340$	−1.95880e6	−	1.64363e6i	−0.0498373	−	0.0418184i
$341$	8.73593e7	−	5.04369e7i	2.20316	−	1.27200i
$342$	2.61830e7	−	2.26999e7i	0.654547	−	0.567474i
$343$	−1.08407e7	+	1.87767e7i	−0.268643	+	0.465304i
$344$	−1.71952e7	−	4.72433e7i	−0.422407	−	1.16055i
$345$	−3.38936e6	−	1.22531e7i	−0.0825393	−	0.298392i
$346$	2.48594e7	−	2.08595e7i	0.600152	−	0.503588i
$347$	−1.02585e7	+	2.81850e7i	−0.245525	+	0.674573i	0.754312	+	0.656516i	$0.227970\pi$
$347$	−1.02585e7	+	2.81850e7i	−0.245525	+	0.674573i	−0.999837	+	0.0180574i	$0.994252\pi$
$348$	4.98701e6	−	7.24589e6i	0.118332	−	0.171931i
$349$	−5.67238e6	+	3.21697e7i	−0.133441	+	0.756781i	0.842492	+	0.538709i	$0.181088\pi$
$349$	−5.67238e6	+	3.21697e7i	−0.133441	+	0.756781i	−0.975933	+	0.218072i	$0.930023\pi$
$350$			7.89579e6i			0.184158i
$351$	−1.44763e7	−	914182.i	−0.334763	−	0.0211403i
$352$	5.39022e7			1.23589
$353$	−4.73483e6	−	834878.i	−0.107642	−	0.0189801i	0.119568	−	0.992826i	$-0.461849\pi$
$353$	−4.73483e6	−	834878.i	−0.107642	−	0.0189801i	−0.227209	+	0.973846i	$0.572960\pi$
$354$	7.46098e6	−	3.55266e6i	0.168184	−	0.0800837i
$355$	−2.83245e7	−	1.03093e7i	−0.633107	−	0.230432i
$356$	−1.48689e6	−	1.77201e6i	−0.0329555	−	0.0392749i
$357$	3.93718e6	+	3.87417e6i	0.0865328	+	0.0851479i
$358$	−6.16488e7	+	2.24383e7i	−1.34362	+	0.489037i
$359$	−1.25093e7	−	7.22225e6i	−0.270365	−	0.156095i	0.358689	−	0.933457i	$-0.383224\pi$
$359$	−1.25093e7	−	7.22225e6i	−0.270365	−	0.156095i	−0.629053	+	0.777362i	$0.716557\pi$
$360$	350000.	+	2.16923e7i	0.00750171	+	0.464941i
$361$	−3.66343e6	−	6.34524e6i	−0.0778692	−	0.134873i
$362$	3.87887e7	−	4.62266e7i	0.817674	−	0.974466i
$363$	−1.17224e8	+	1.12093e7i	−2.45073	+	0.234347i
$364$	−275398.	−	1.56186e6i	−0.00571026	−	0.0323845i
$365$	1.99679e7	−	3.52089e6i	0.410634	−	0.0724058i
$366$	815278.	+	8.52596e6i	0.0166289	+	0.173900i
$367$	−3.53212e7	−	2.96380e7i	−0.714558	−	0.599585i	0.211316	−	0.977418i	$-0.432225\pi$
$367$	−3.53212e7	−	2.96380e7i	−0.714558	−	0.599585i	−0.925874	+	0.377833i	$0.876669\pi$
$368$	1.64621e7	−	9.50440e6i	0.330325	−	0.190713i
$369$	6.30431e7	−	1.01718e6i	1.25475	−	0.0202451i
$370$	−9.37858e6	+	1.62442e7i	−0.185153	+	0.320695i
$371$	−1.82205e6	−	5.00603e6i	−0.0356810	−	0.0980329i
$372$	1.73115e7	−	1.75931e7i	0.336285	−	0.341754i
$373$	1.55746e7	−	1.30686e7i	0.300117	−	0.251828i	−0.480276	−	0.877117i	$-0.659464\pi$
$373$	1.55746e7	−	1.30686e7i	0.300117	−	0.251828i	0.780393	+	0.625290i	$0.215019\pi$
$374$	−1.16490e7	+	3.20055e7i	−0.222677	+	0.611800i
$375$	1.76041e7	+	3.69706e7i	0.333827	+	0.701073i
$376$	−253110.	+	1.43546e6i	−0.00476153	+	0.0270040i
$377$		−	1.06976e7i		−	0.199647i
$378$	766845.	−	1.21432e7i	0.0141982	−	0.224832i
$379$	2.43501e7			0.447284			0.223642	−	0.974671i	$-0.428205\pi$
$379$	2.43501e7			0.447284			0.223642	+	0.974671i	$0.428205\pi$
$380$	8.70362e6	+	1.53468e6i	0.158617	+	0.0279684i
$381$	−5.18473e7	−	3.56841e7i	−0.937457	−	0.645207i
$382$	−4.87397e7	−	1.77398e7i	−0.874365	−	0.318243i
$383$	−5.03989e6	−	6.00631e6i	−0.0897067	−	0.106908i	0.719324	−	0.694675i	$-0.244452\pi$
$383$	−5.03989e6	−	6.00631e6i	−0.0897067	−	0.106908i	−0.809031	+	0.587767i	$0.800007\pi$
$384$	−1.04358e7	+	2.88670e6i	−0.184304	+	0.0509809i
$385$	1.19175e7	−	4.33763e6i	0.208835	−	0.0760099i
$386$	4.52383e6	+	2.61183e6i	0.0786582	+	0.0454134i
$387$	4.30837e7	+	4.96944e7i	0.743327	+	0.857383i
$388$	6.91447e6	+	1.19762e7i	0.118376	+	0.205033i
$389$	−3.10410e7	+	3.69933e7i	−0.527336	+	0.628455i	−0.962299	−	0.271994i	$-0.912317\pi$
$389$	−3.10410e7	+	3.69933e7i	−0.527336	+	0.628455i	0.434963	+	0.900448i	$0.356761\pi$
$390$	3.97422e6	+	5.57944e6i	0.0669975	+	0.0940582i
$391$	−3.26631e6	−	1.85242e7i	−0.0546421	−	0.309891i
$392$	−5.95179e7	+	1.04946e7i	−0.988074	+	0.174224i
$393$	9.29885e7	+	4.24514e7i	1.53197	+	0.699382i
$394$	5.75901e7	+	4.83238e7i	0.941584	+	0.790083i
$395$	3.36505e7	−	1.94281e7i	0.546009	−	0.315238i
$396$	−3.78452e7	+	1.44701e7i	−0.609432	+	0.233017i
$397$	−2.51928e7	+	4.36352e7i	−0.402629	+	0.697373i	−0.994042	−	0.108995i	$-0.965237\pi$
$397$	−2.51928e7	+	4.36352e7i	−0.402629	+	0.697373i	0.591414	+	0.806368i	$0.298570\pi$
$398$	6.90265e6	+	1.89649e7i	0.109488	+	0.300816i
$399$	−1.84801e7	−	4.79229e6i	−0.290928	−	0.0754440i
$400$	−2.10955e7	+	1.77012e7i	−0.329617	+	0.276582i
$401$	−3.83400e6	+	1.05338e7i	−0.0594592	+	0.163363i	−0.965865	−	0.259044i	$-0.916592\pi$
$401$	−3.83400e6	+	1.05338e7i	−0.0594592	+	0.163363i	0.906406	+	0.422407i	$0.138815\pi$
$402$	7.73027e7	+	6.13519e6i	1.18992	+	0.0944387i
$403$	5.21247e6	−	2.95614e7i	0.0796395	−	0.451658i
$404$			3.79373e7i			0.575337i
$405$	−1.05624e7	−	2.63429e7i	−0.159001	−	0.396551i
$406$	8.97349e6			0.134086
$407$	−1.32877e8	−	2.34298e7i	−1.97091	−	0.347524i
$408$	−2.53960e6	+	3.19986e7i	−0.0373925	+	0.471141i
$409$	2.00014e7	+	7.27990e6i	0.292341	+	0.106403i	0.484028	−	0.875053i	$-0.339173\pi$
$409$	2.00014e7	+	7.27990e6i	0.292341	+	0.106403i	−0.191686	+	0.981456i	$0.561396\pi$
$410$	−1.91399e7	−	2.28100e7i	−0.277707	−	0.330959i
$411$	−1.68713e7	+	6.50594e7i	−0.243010	+	0.937096i
$412$	−3.24923e7	+	1.18262e7i	−0.464610	+	0.169104i
$413$	−3.94273e6	−	2.27634e6i	−0.0559689	−	0.0323137i
$414$	−2.61179e7	+	3.21660e7i	−0.368076	+	0.453311i
$415$	5.90920e6	+	1.02350e7i	0.0826769	+	0.143201i
$416$	1.03103e7	−	1.22873e7i	0.143215	−	0.170677i
$417$	4.65585e7	−	1.01985e8i	0.642082	−	1.40646i
$418$	−2.04419e7	−	1.15932e8i	−0.279893	−	1.58735i
$419$	−6.91014e7	+	1.21844e7i	−0.939387	+	0.165639i	−0.622319	−	0.782763i	$-0.713809\pi$
$419$	−6.91014e7	+	1.21844e7i	−0.939387	+	0.165639i	−0.317068	+	0.948403i	$0.602698\pi$
$420$	2.52752e6	−	1.80035e6i	0.0341151	−	0.0243001i
$421$	−9.06580e7	−	7.60711e7i	−1.21495	−	1.01947i	−0.999073	−	0.0430476i	$-0.986293\pi$
$421$	−9.06580e7	−	7.60711e7i	−1.21495	−	1.01947i	−0.215881	−	0.976420i	$-0.569262\pi$
$422$	5.95899e6	−	3.44043e6i	0.0792931	−	0.0457799i
$423$	−361372.	−	1.87229e6i	−0.00477456	−	0.0247373i
$424$	1.54791e7	−	2.68107e7i	0.203072	−	0.351731i
$425$	9.32010e6	+	2.56068e7i	0.121410	+	0.333571i
$426$	2.61906e7	+	9.46828e7i	0.338779	+	1.22474i
$427$	3.61468e6	−	3.03307e6i	0.0464286	−	0.0389582i
$428$	−1.62584e6	+	4.46697e6i	−0.0207371	+	0.0569746i
$429$	−2.79367e7	+	4.05908e7i	−0.353838	+	0.514110i
$430$	5.39359e6	−	3.05886e7i	0.0678380	−	0.384728i
$431$			4.12957e7i			0.515791i	0.966173	+	0.257895i	$0.0830290\pi$
$431$			4.12957e7i			0.515791i	−0.966173	+	0.257895i	$0.916971\pi$
$432$	3.41626e7	−	2.51745e7i	0.423740	−	0.312255i
$433$	6.44485e7			0.793869			0.396935	−	0.917847i	$-0.370074\pi$
$433$	6.44485e7			0.793869			0.396935	+	0.917847i	$0.370074\pi$
$434$	2.47971e7	+	4.37239e6i	0.303341	+	0.0534872i
$435$	1.88984e7	−	8.99878e6i	0.229593	−	0.109324i
$436$	−1.19605e7	−	4.35325e6i	−0.144307	−	0.0525236i
$437$	4.17895e7	+	4.98027e7i	0.500752	+	0.596773i
$438$	−4.71029e7	−	4.63490e7i	−0.560564	−	0.551592i
$439$	1.04711e8	−	3.81116e7i	1.23765	−	0.450468i	0.361439	−	0.932396i	$-0.382286\pi$
$439$	1.04711e8	−	3.81116e7i	1.23765	−	0.450468i	0.876211	+	0.481928i	$0.160063\pi$
$440$	6.38264e7	+	3.68502e7i	0.749277	+	0.432595i
$441$	6.78237e7	−	4.06308e7i	0.790798	−	0.473740i
$442$	5.06761e6	+	8.77737e6i	0.0586863	+	0.101648i
$443$	−1.63554e7	+	1.94916e7i	−0.188127	+	0.224201i	−0.851861	−	0.523768i	$-0.824526\pi$
$443$	−1.63554e7	+	1.94916e7i	−0.188127	+	0.224201i	0.663735	+	0.747968i	$0.268970\pi$
$444$	−3.28643e7	+	3.14259e6i	−0.375471	+	0.0359036i
$445$	−955844.	−	5.42086e6i	−0.0108469	−	0.0615160i
$446$	−8.16030e7	+	1.43888e7i	−0.919818	+	0.162189i
$447$	4.16071e6	+	4.35116e7i	0.0465849	+	0.487172i
$448$	2.04429e7	+	1.71536e7i	0.227357	+	0.190775i
$449$	−2.49349e7	+	1.43962e7i	−0.275466	+	0.159041i	−0.631369	−	0.775482i	$-0.717507\pi$
$449$	−2.49349e7	+	1.43962e7i	−0.275466	+	0.159041i	0.355903	+	0.934523i	$0.384173\pi$
$450$	2.91705e7	−	5.24616e7i	0.320116	−	0.575710i
$451$	1.07096e8	−	1.85495e8i	1.16746	−	2.02210i
$452$	−8.17022e6	−	2.24475e7i	−0.0884746	−	0.243082i
$453$	−5.94989e6	+	6.04666e6i	−0.0640050	+	0.0650461i
$454$	2.91382e7	−	2.44498e7i	0.311383	−	0.261281i
$455$	1.29077e6	−	3.54635e6i	0.0137029	−	0.0376485i
$456$	−4.76968e7	−	1.00169e8i	−0.503031	−	1.05642i
$457$	−3.91505e6	+	2.22033e7i	−0.0410193	+	0.232632i	−0.998424	−	0.0561166i	$-0.982128\pi$
$457$	−3.91505e6	+	2.22033e7i	−0.0410193	+	0.232632i	0.957405	+	0.288749i	$0.0932392\pi$
$458$		−	5.72584e7i		−	0.595995i
$459$	−1.18467e7	−	4.02866e7i	−0.122507	−	0.416604i
$460$	−1.05674e7			−0.108566
$461$	5.63734e7	+	9.94015e6i	0.575402	+	0.101459i	0.453774	−	0.891117i	$-0.350077\pi$
$461$	5.63734e7	+	9.94015e6i	0.575402	+	0.101459i	0.121628	+	0.992576i	$0.461189\pi$
$462$	−3.40489e7	−	2.34342e7i	−0.345284	−	0.237643i
$463$	1.43957e8	+	5.23962e7i	1.45041	+	0.527906i	0.942706	−	0.333625i	$-0.108272\pi$
$463$	1.43957e8	+	5.23962e7i	1.45041	+	0.527906i	0.507704	+	0.861531i	$0.330494\pi$
$464$	2.01173e7	+	2.39748e7i	0.201379	+	0.239995i
$465$	5.66080e7	−	1.56586e7i	0.563014	−	0.155738i
$466$	−6.26873e7	+	2.28163e7i	−0.619473	+	0.225470i
$467$	−1.51170e8	−	8.72781e7i	−1.48428	−	0.856949i	−0.484438	−	0.874825i	$-0.660976\pi$
$467$	−1.51170e8	−	8.72781e7i	−1.48428	−	0.856949i	−0.999840	+	0.0178768i	$0.994309\pi$
$468$	−3.94038e6	+	1.13948e7i	−0.0384415	+	0.111165i
$469$	−2.13611e7	−	3.69985e7i	−0.207064	−	0.358646i
$470$	−578842.	+	689837.i	−0.00557528	+	0.00664436i
$471$	1.08901e8	+	1.52887e8i	1.04224	+	1.46321i
$472$	−4.59416e6	−	2.60548e7i	−0.0436898	−	0.247777i
$473$	2.20034e8	−	3.87980e7i	2.07925	−	0.366628i
$474$	−1.15201e8	−	5.25922e7i	−1.08174	−	0.493840i
$475$	−7.21497e7	−	6.05408e7i	−0.673214	−	0.564894i
$476$	3.97620e6	−	2.29566e6i	0.0368678	−	0.0212856i
$477$	−6.38835e6	+	3.99928e7i	−0.0588618	+	0.368490i
$478$	−6.30190e7	+	1.09152e8i	−0.577016	+	0.999422i
$479$	−3.07268e7	−	8.44212e7i	−0.279583	−	0.768148i	−0.997410	−	0.0719263i	$-0.977085\pi$
$479$	−3.07268e7	−	8.44212e7i	−0.279583	−	0.768148i	0.717827	−	0.696221i	$-0.245137\pi$
$480$	3.03797e7	+	7.87812e6i	0.274701	+	0.0712359i
$481$	−3.07572e7	+	2.58083e7i	−0.276383	+	0.231913i
$482$	−2.27826e7	+	6.25946e7i	−0.203452	+	0.558979i
$483$	2.27558e7	+	1.80603e6i	0.201953	+	0.0160282i
$484$	−1.69971e7	+	9.63954e7i	−0.149913	+	0.850198i
$485$			3.29075e7i			0.288449i
$486$	−4.99574e7	+	7.78494e7i	−0.435202	+	0.678182i
$487$	−2.12349e8			−1.83850			−0.919249	−	0.393677i	$-0.871203\pi$
$487$	−2.12349e8			−1.83850			−0.919249	+	0.393677i	$0.871203\pi$
$488$	2.70045e7	+	4.76162e6i	0.232368	+	0.0409728i
$489$	−456179.	+	5.74780e6i	−0.00390130	+	0.0491559i
$490$	−3.50861e7	−	1.27703e7i	−0.298227	−	0.108546i
$491$	−1.12938e7	−	1.34594e7i	−0.0954103	−	0.113706i	0.716227	−	0.697868i	$-0.245868\pi$
$491$	−1.12938e7	−	1.34594e7i	−0.0954103	−	0.113706i	−0.811637	+	0.584162i	$0.801423\pi$
$492$	1.31557e7	−	5.07310e7i	0.110463	−	0.425969i
$493$	2.91018e7	−	1.05922e7i	0.242873	−	0.0883986i
$494$	−3.03372e7	−	1.75152e7i	−0.251649	−	0.145290i
$495$	−9.52082e7	−	1.52083e7i	−0.784980	−	0.125391i
$496$	4.39095e7	+	7.60535e7i	0.359843	+	0.623267i
$497$	3.47892e7	−	4.14601e7i	0.283384	−	0.337724i
$498$	1.59963e7	−	3.50394e7i	0.129518	−	0.283706i
$499$	1.76959e7	+	1.00358e8i	0.142420	+	0.807703i	0.969403	+	0.245476i	$0.0789442\pi$
$499$	1.76959e7	+	1.00358e8i	0.142420	+	0.807703i	−0.826983	+	0.562227i	$0.809945\pi$
$500$	3.35194e7	−	5.91037e6i	0.268155	−	0.0472829i
$501$	−1.17455e8	+	8.36627e7i	−0.934022	+	0.665302i
$502$	1.51940e8	+	1.27493e8i	1.20105	+	1.00780i
$503$	−1.17695e8	+	6.79512e7i	−0.924813	+	0.533941i	−0.885167	−	0.465273i	$-0.845956\pi$
$503$	−1.17695e8	+	6.79512e7i	−0.924813	+	0.533941i	−0.0396455	+	0.999214i	$0.512623\pi$
$504$	−3.68158e7	−	1.27311e7i	−0.287569	−	0.0994429i
$505$	−4.51380e7	+	7.81813e7i	−0.350484	+	0.607056i
$506$	4.81415e7	+	1.32268e8i	0.371594	+	1.02095i
$507$	−3.08354e7	−	1.11475e8i	−0.236606	−	0.855366i
$508$	−4.00771e7	+	3.36286e7i	−0.305706	+	0.256518i
$509$	4.09870e7	−	1.12611e8i	0.310809	−	0.853939i	−0.681685	−	0.731645i	$-0.738753\pi$
$509$	4.09870e7	−	1.12611e8i	0.310809	−	0.853939i	0.992494	−	0.122294i	$-0.0390251\pi$
$510$	−1.12433e7	+	1.63360e7i	−0.0847583	+	0.123150i
$511$	−6.32198e6	+	3.58537e7i	−0.0473795	+	0.268702i
$512$			1.23818e8i			0.922515i
$513$	1.05082e8	+	1.00115e8i	0.778349	+	0.741560i
$514$	−8.73599e7			−0.643314
$515$	−8.10310e7	−	1.42880e7i	−0.593239	−	0.104604i
$516$	4.93591e7	−	2.35031e7i	0.359268	−	0.171071i
$517$	−6.08709e6	−	2.21552e6i	−0.0440492	−	0.0160326i
$518$	−2.16489e7	−	2.58001e7i	−0.155756	−	0.185623i
$519$	9.68805e7	+	9.53300e7i	0.693002	+	0.681911i
$520$	2.06087e7	−	7.50096e6i	0.146569	−	0.0533466i
$521$	8.60755e7	+	4.96957e7i	0.608648	+	0.351403i	0.772436	−	0.635092i	$-0.219038\pi$
$521$	8.60755e7	+	4.96957e7i	0.608648	+	0.351403i	−0.163788	+	0.986496i	$0.552371\pi$
$522$	−5.96221e7	−	3.31520e7i	−0.419175	−	0.233076i
$523$	−4.51581e7	−	7.82161e7i	−0.315668	−	0.546753i	0.663911	−	0.747811i	$-0.268895\pi$
$523$	−4.51581e7	−	7.82161e7i	−0.315668	−	0.546753i	−0.979579	+	0.201058i	$0.935562\pi$
$524$	5.46156e7	−	6.50883e7i	0.379597	−	0.452386i
$525$	−3.29200e7	+	3.14791e6i	−0.227500	+	0.0217542i
$526$	2.30363e7	+	1.30645e8i	0.158291	+	0.897711i
$527$	8.55801e7	−	1.50901e7i	0.584711	−	0.103100i
$528$	−1.37225e7	−	1.43506e8i	−0.0932245	−	0.974917i
$529$	5.38535e7	+	4.51885e7i	0.363787	+	0.305253i
$530$	1.65638e7	−	9.56314e6i	0.111259	−	0.0642351i
$531$	1.77867e7	+	2.96907e7i	0.118799	+	0.198307i
$532$	−7.93450e6	+	1.37429e7i	−0.0526968	+	0.0912736i
$533$	−2.17996e7	−	5.98940e7i	−0.143968	−	0.395550i
$534$	−1.25827e7	+	1.27874e7i	−0.0826326	+	0.0839766i
$535$	−8.66536e6	+	7.27110e6i	−0.0565881	+	0.0474831i
$536$	8.49131e7	−	2.33297e8i	0.551417	−	1.51501i
$537$	−1.18131e8	−	2.48087e8i	−0.762851	−	1.60207i
$538$	4.14113e6	−	2.34855e7i	0.0265933	−	0.150818i
$539$		−	2.68584e8i		−	1.71520i
$540$	−2.34448e7	+	2.62418e6i	−0.148890	+	0.0166653i
$541$	−1.40524e8			−0.887482			−0.443741	−	0.896155i	$-0.646349\pi$
$541$	−1.40524e8			−0.887482			−0.443741	+	0.896155i	$0.646349\pi$
$542$	2.13867e8	+	3.77106e7i	1.34322	+	0.236846i
$543$	2.08197e8	+	1.43292e8i	1.30040	+	0.895002i
$544$	4.36351e7	+	1.58819e7i	0.271043	+	0.0986517i
$545$	−1.94686e7	−	2.32018e7i	−0.120267	−	0.143328i
$546$	−1.18547e7	+	3.27918e6i	−0.0728304	+	0.0201459i
$547$	1.53507e7	−	5.58719e6i	0.0937920	−	0.0341375i	−0.294698	−	0.955590i	$-0.595219\pi$
$547$	1.53507e7	−	5.58719e6i	0.0937920	−	0.0341375i	0.388490	+	0.921453i	$0.372997\pi$
$548$	4.83822e7	+	2.79335e7i	0.293998	+	0.169740i
$549$	−3.52223e7	+	6.79829e6i	−0.212863	+	0.0410849i
$550$	−1.01958e8	−	1.76596e8i	−0.612818	−	1.06143i
$551$	−6.88039e7	+	8.19973e7i	−0.411300	+	0.490168i
$552$	7.69620e7	+	1.08047e8i	0.457572	+	0.642388i
$553$	1.21152e7	+	6.87089e7i	0.0716401	+	0.406291i
$554$	7.54983e7	−	1.33124e7i	0.444025	−	0.0782936i
$555$	−7.14660e7	−	3.26259e7i	−0.418043	−	0.190846i
$556$	−7.13855e7	−	5.98995e7i	−0.415323	−	0.348497i
$557$	−2.26469e8	+	1.30752e8i	−1.31052	+	0.756628i	−0.982182	−	0.187933i	$-0.939821\pi$
$557$	−2.26469e8	+	1.30752e8i	−1.31052	+	0.756628i	−0.328336	+	0.944561i	$0.606488\pi$
$558$	−1.48604e8	−	1.20662e8i	−0.855320	−	0.694496i
$559$	3.32433e7	−	5.75790e7i	0.190313	−	0.329632i
$560$	3.77626e6	+	1.03752e7i	0.0215030	+	0.0590789i
$561$	−1.38085e8	−	3.58084e7i	−0.782092	−	0.202813i
$562$	−8.14120e7	+	6.83128e7i	−0.458648	+	0.384851i
$563$	−1.00570e7	+	2.76314e7i	−0.0563565	+	0.154838i	−0.964676	−	0.263438i	$-0.915143\pi$
$563$	−1.00570e7	+	2.76314e7i	−0.0563565	+	0.154838i	0.908320	+	0.418276i	$0.137366\pi$
$564$	−1.58002e6	−	125400.i	−0.00880697	−	0.000698972i
$565$	9.87093e6	−	5.59808e7i	0.0547284	−	0.310380i
$566$		−	9.55911e7i		−	0.527191i
$567$	5.09344e7	−	1.64406e6i	0.279423	−	0.00901920i
$568$	3.14518e8			1.71633
$569$	9.54714e7	+	1.68342e7i	0.518246	+	0.0913808i	0.426653	−	0.904416i	$-0.359693\pi$
$569$	9.54714e7	+	1.68342e7i	0.518246	+	0.0913808i	0.0915939	+	0.995796i	$0.470804\pi$
$570$	5.42287e6	−	6.83276e7i	0.0292823	−	0.368953i
$571$	2.82497e8	+	1.02820e8i	1.51742	+	0.552295i	0.960502	−	0.278274i	$-0.0897625\pi$
$571$	2.82497e8	+	1.02820e8i	1.51742	+	0.552295i	0.556916	+	0.830569i	$0.311985\pi$
$572$	2.63276e7	+	3.13760e7i	0.140677	+	0.167652i
$573$	5.45311e7	−	2.10283e8i	0.289854	−	1.11774i
$574$	5.02410e7	−	1.82862e7i	0.265658	−	0.0966915i
$575$	9.75279e7	+	5.63078e7i	0.513010	+	0.296186i
$576$	−7.24546e7	−	1.89498e8i	−0.379139	−	0.991601i
$577$	−6.91638e7	−	1.19795e8i	−0.360040	−	0.623608i	0.627927	−	0.778273i	$-0.283904\pi$
$577$	−6.91638e7	−	1.19795e8i	−0.360040	−	0.623608i	−0.987967	+	0.154664i	$0.950570\pi$
$578$	8.11591e7	−	9.67217e7i	0.420295	−	0.500888i
$579$	−9.08597e6	+	1.99025e7i	−0.0468097	+	0.102535i
$580$	−3.02123e6	−	1.71342e7i	−0.0154846	−	0.0878174i
$581$	−2.08983e7	+	3.68493e6i	−0.106557	+	0.0187889i
$582$	8.73555e7	−	6.22231e7i	0.443120	−	0.315633i
$583$	1.05394e8	+	8.84359e7i	0.531875	+	0.446296i
$584$	−1.83224e8	+	1.05784e8i	−0.919907	+	0.531109i
$585$	−2.16779e7	+	1.87942e7i	−0.108281	+	0.0938762i
$586$	5.32369e7	−	9.22090e7i	0.264557	−	0.458227i
$587$	1.20411e8	+	3.30827e8i	0.595324	+	1.63564i	0.760473	+	0.649370i	$0.224967\pi$
$587$	1.20411e8	+	3.30827e8i	0.595324	+	1.63564i	−0.165149	+	0.986269i	$0.552811\pi$
$588$	−1.75206e7	−	6.33394e7i	−0.0861819	−	0.311560i
$589$	−2.30084e8	+	1.93064e8i	−1.12601	+	0.944832i
$590$	5.59037e6	−	1.53594e7i	0.0272198	−	0.0747857i
$591$	−1.78517e8	+	2.59377e8i	−0.864802	+	1.25652i
$592$	2.03975e7	−	1.15680e8i	0.0983134	−	0.557563i
$593$			1.77875e7i			0.0853005i	0.999090	+	0.0426502i	$0.0135801\pi$
$593$			1.77875e7i			0.0853005i	−0.999090	+	0.0426502i	$0.986420\pi$
$594$	1.39653e8	+	2.81494e8i	0.666331	+	1.34311i
$595$	1.09256e7			0.0518672
$596$	3.57804e7	+	6.30905e6i	0.169008	+	0.0298006i
$597$	−7.63184e7	+	3.63402e7i	−0.358679	+	0.170791i
$598$	3.93594e7	+	1.43257e7i	0.184054	+	0.0669902i
$599$	−1.45837e8	−	1.73802e8i	−0.678560	−	0.808676i	0.311362	−	0.950291i	$-0.399215\pi$
$599$	−1.45837e8	−	1.73802e8i	−0.678560	−	0.808676i	−0.989922	+	0.141615i	$0.954770\pi$
$600$	−1.36983e8	−	1.34790e8i	−0.634179	−	0.624029i
$601$	1.04774e8	−	3.81347e7i	0.482648	−	0.175670i	−0.0892253	−	0.996011i	$-0.528439\pi$
$601$	1.04774e8	−	3.81347e7i	0.482648	−	0.175670i	0.571873	+	0.820342i	$0.306217\pi$
$602$	4.82991e7	+	2.78855e7i	0.221386	+	0.127817i
$603$	5.23968e6	+	3.24745e8i	0.0238975	+	1.48112i
$604$	3.52564e6	+	6.10659e6i	0.0160003	+	0.0277133i
$605$	−1.49719e8	+	1.78429e8i	−0.676102	+	0.805747i
$606$	2.92888e8	−	2.80068e7i	1.31608	−	0.125848i
$607$	−5.99781e7	−	3.40153e8i	−0.268180	−	1.52092i	−0.759824	−	0.650128i	$-0.774715\pi$
$607$	−5.99781e7	−	3.40153e8i	−0.268180	−	1.52092i	0.491644	−	0.870796i	$-0.336396\pi$
$608$	−1.58057e8	+	2.78697e7i	−0.703238	+	0.124000i
$609$	3.57756e6	+	3.74132e7i	0.0158393	+	0.165643i
$610$	1.29775e7	+	1.08894e7i	0.0571745	+	0.0479751i
$611$	−1.66936e6	+	963804.i	−0.00731856	+	0.00422537i
$612$	−3.49001e7	+	563104.i	−0.152255	+	0.00245660i
$613$	−1.25373e8	+	2.17152e8i	−0.544280	+	0.942721i	0.454372	+	0.890812i	$0.349864\pi$
$613$	−1.25373e8	+	2.17152e8i	−0.544280	+	0.942721i	−0.998652	+	0.0519086i	$0.983470\pi$
$614$	−6.86486e7	−	1.88610e8i	−0.296569	−	0.814818i
$615$	8.74712e7	−	8.88939e7i	0.376045	−	0.382161i
$616$	−1.01374e8	+	8.50625e7i	−0.433693	+	0.363912i
$617$	−3.97303e7	+	1.09158e8i	−0.169148	+	0.464730i	−0.995084	−	0.0990337i	$-0.968425\pi$
$617$	−3.97303e7	+	1.09158e8i	−0.169148	+	0.464730i	0.825936	+	0.563764i	$0.190647\pi$
$618$	1.15289e8	+	2.42120e8i	0.488453	+	1.02580i
$619$	6.45575e7	−	3.66124e8i	0.272191	−	1.54367i	−0.475553	−	0.879687i	$-0.657752\pi$
$619$	6.45575e7	−	3.66124e8i	0.272191	−	1.54367i	0.747744	−	0.663987i	$-0.231137\pi$
$620$		−	4.88203e7i		−	0.204845i
$621$	−1.44523e8	−	9.60695e7i	−0.603478	−	0.401154i
$622$	−1.82230e8			−0.757267
$623$	9.73350e6	+	1.71628e6i	0.0402536	+	0.00709780i
$624$	−3.53376e7	−	2.43212e7i	−0.145440	−	0.100100i
$625$	−1.11432e8	−	4.05578e7i	−0.456424	−	0.166125i
$626$	−3.04797e6	−	3.63242e6i	−0.0124247	−	0.0148072i
$627$	4.75204e8	−	1.31448e8i	1.92787	−	0.533276i
$628$	1.46615e8	−	5.33634e7i	0.591969	−	0.215459i
$629$	−1.00663e8	−	5.81180e7i	−0.404501	−	0.233539i
$630$	−1.57651e7	−	1.81841e7i	−0.0630487	−	0.0727229i
$631$	8.26931e7	+	1.43229e8i	0.329141	+	0.570088i	0.982342	−	0.187096i	$-0.0599077\pi$
$631$	8.26931e7	+	1.43229e8i	0.329141	+	0.570088i	−0.653201	+	0.757185i	$0.726574\pi$
$632$	−2.60614e8	+	3.10588e8i	−1.03240	+	1.23036i
$633$	1.67199e7	+	2.34732e7i	0.0659210	+	0.0925469i
$634$	−2.33614e7	−	1.32489e8i	−0.0916708	−	0.519891i
$635$	−1.22602e8	+	2.16181e7i	−0.478826	+	0.0844300i
$636$	3.06237e7	+	1.39804e7i	0.119038	+	0.0543437i
$637$	−6.12251e7	−	5.13740e7i	−0.236871	−	0.198758i
$638$	−2.00699e8	+	1.15874e8i	−0.772829	+	0.446193i
$639$	−3.84320e8	+	1.46945e8i	−1.47296	+	0.563186i
$640$	−1.07084e7	+	1.85475e7i	−0.0408494	+	0.0707532i
$641$	1.73358e7	+	4.76296e7i	0.0658217	+	0.180844i	0.968243	−	0.250011i	$-0.0804343\pi$
$641$	1.73358e7	+	4.76296e7i	0.0658217	+	0.180844i	−0.902421	+	0.430855i	$0.858212\pi$
$642$	3.56866e7	+	9.25432e6i	0.134865	+	0.0349735i
$643$	−7.82521e7	+	6.56613e7i	−0.294349	+	0.246989i	−0.777988	−	0.628279i	$-0.783759\pi$
$643$	−7.82521e7	+	6.56613e7i	−0.294349	+	0.246989i	0.483638	+	0.875268i	$0.339315\pi$
$644$	6.48962e6	−	1.78301e7i	0.0242975	−	0.0667568i
$645$	1.29684e8	+	1.02924e7i	0.483288	+	0.0383565i
$646$	1.76102e7	−	9.98722e7i	0.0653229	−	0.370465i
$647$		−	1.82504e8i		−	0.673843i	−0.941533	−	0.336922i	$-0.890614\pi$
$647$		−	1.82504e8i		−	0.673843i	0.941533	−	0.336922i	$-0.109386\pi$
$648$	1.97579e8	+	2.20602e8i	0.726133	+	0.810746i
$649$	1.17576e8			0.430116
$650$	−5.97579e7	−	1.05369e7i	−0.217598	−	0.0383685i
$651$	−8.34370e6	+	1.05130e8i	−0.0302424	+	0.381050i
$652$	4.50364e6	+	1.63919e6i	0.0162488	+	0.00591407i
$653$	2.20885e7	+	2.63241e7i	0.0793281	+	0.0945395i	0.804249	−	0.594293i	$-0.202568\pi$
$653$	2.20885e7	+	2.63241e7i	0.0793281	+	0.0945395i	−0.724921	+	0.688832i	$0.758124\pi$
$654$	−2.47788e7	+	9.55521e7i	−0.0885821	+	0.341592i
$655$	1.89994e8	−	6.91523e7i	0.676109	−	0.246084i
$656$	1.61489e8	+	9.32357e7i	0.572047	+	0.330271i
$657$	1.74464e8	−	2.14865e8i	0.615191	−	0.757651i
$658$	−808469.	−	1.40031e6i	−0.00283783	−	0.00491526i
$659$	1.06916e8	−	1.27418e8i	0.373582	−	0.445218i	−0.546195	−	0.837658i	$-0.683924\pi$
$659$	1.06916e8	−	1.27418e8i	0.373582	−	0.445218i	0.919778	+	0.392440i	$0.128369\pi$
$660$	−3.32823e7	+	7.29038e7i	−0.115766	+	0.253582i
$661$	−1.13586e7	−	6.44180e7i	−0.0393298	−	0.223050i	0.958808	−	0.284056i	$-0.0916803\pi$
$661$	−1.13586e7	−	6.44180e7i	−0.0393298	−	0.223050i	−0.998137	+	0.0610059i	$0.980569\pi$
$662$	−3.61119e7	+	6.36750e6i	−0.124473	+	0.0219480i
$663$	−3.45752e7	+	2.46278e7i	−0.118638	+	0.0845056i
$664$	−9.44676e7	−	7.92677e7i	−0.322685	−	0.270765i
$665$	−3.27029e7	+	1.88810e7i	−0.111204	+	0.0642037i
$666$	4.85235e7	+	2.51403e8i	0.164259	+	0.851035i
$667$	6.39932e7	−	1.10839e8i	0.215653	−	0.373523i
$668$	4.09962e7	+	1.12636e8i	0.137535	+	0.377875i
$669$	−9.25250e7	−	3.34491e8i	−0.309016	−	1.11714i
$670$	1.17498e8	−	9.85925e7i	0.390666	−	0.327808i
$671$	−4.16793e7	+	1.14513e8i	−0.137960	+	0.379042i
$672$	−3.19493e7	+	4.64209e7i	−0.105282	+	0.152970i
$673$	−4.74614e7	+	2.69167e8i	−0.155703	+	0.883033i	0.802438	+	0.596735i	$0.203536\pi$
$673$	−4.74614e7	+	2.69167e8i	−0.155703	+	0.883033i	−0.958141	+	0.286298i	$0.907575\pi$
$674$		−	4.04176e8i		−	1.32005i
$675$	2.30358e8	+	1.00705e8i	0.749019	+	0.327447i
$676$	−9.61387e7			−0.311213
$677$	8.17724e7	+	1.44187e7i	0.263537	+	0.0464686i	0.303855	−	0.952718i	$-0.401726\pi$
$677$	8.17724e7	+	1.44187e7i	0.263537	+	0.0464686i	−0.0403185	+	0.999187i	$0.512837\pi$
$678$	−1.67270e8	+	7.96482e7i	−0.536697	+	0.255557i
$679$	−5.55240e7	−	2.02091e7i	−0.177367	−	0.0645562i
$680$	4.08113e7	+	4.86370e7i	0.129794	+	0.154682i
$681$	1.13556e8	+	1.11738e8i	0.359557	+	0.353803i
$682$	−6.11066e8	+	2.22410e8i	−1.92635	+	0.701133i
$683$	1.78486e8	+	1.03049e8i	0.560199	+	0.323431i	0.753225	−	0.657763i	$-0.228497\pi$
$683$	1.78486e8	+	1.03049e8i	0.560199	+	0.323431i	−0.193026	+	0.981194i	$0.561830\pi$
$684$	1.03491e8	−	6.19981e7i	0.323397	−	0.193736i
$685$	6.64707e7	+	1.15131e8i	0.206804	+	0.358195i
$686$	8.98420e7	−	1.07069e8i	0.278296	−	0.331660i
$687$	2.38728e8	−	2.28279e7i	0.736262	−	0.0704036i
$688$	3.37768e7	+	1.91558e8i	0.103718	+	0.588213i
$689$	4.03188e7	−	7.10929e6i	0.123268	−	0.0217355i
$690$	7.80124e6	+	8.15833e7i	0.0237474	+	0.248344i
$691$	−1.49128e8	−	1.25133e8i	−0.451985	−	0.379261i	0.388187	−	0.921581i	$-0.373102\pi$
$691$	−1.49128e8	−	1.25133e8i	−0.451985	−	0.379261i	−0.840172	+	0.542320i	$0.817546\pi$
$692$	9.78406e7	−	5.64883e7i	0.295257	−	0.170467i
$693$	8.41298e7	−	1.51303e8i	0.252784	−	0.454619i
$694$	9.66774e7	−	1.67450e8i	0.289232	−	0.500965i
$695$	−7.58426e7	−	2.08376e8i	−0.225922	−	0.620716i
$696$	−1.53188e8	+	1.55679e8i	−0.454356	+	0.461746i
$697$	1.41351e8	−	1.18608e8i	0.417447	−	0.350279i
$698$	7.20229e7	−	1.97881e8i	0.211789	−	0.581886i
$699$	−1.20121e8	−	2.52266e8i	−0.351711	−	0.738631i
$700$	−4.77330e6	+	2.70707e7i	−0.0139163	+	0.0789234i
$701$		−	2.53816e8i		−	0.736827i	−0.929662	−	0.368414i	$-0.879901\pi$
$701$		−	2.53816e8i		−	0.736827i	0.929662	−	0.368414i	$-0.120099\pi$
$702$	9.08803e7	+	2.20088e7i	0.262699	+	0.0636188i
$703$	4.01747e8			1.15634
$704$	−6.78724e8	−	1.19677e8i	−1.94525	−	0.343000i
$705$	−3.10692e6	−	2.13835e6i	−0.00886671	−	0.00610254i
$706$	2.91247e7	+	1.06005e7i	0.0827652	+	0.0301241i
$707$	−1.04193e8	−	1.24173e8i	−0.294837	−	0.351373i
$708$	2.77277e7	−	7.66986e6i	0.0781293	−	0.0216116i
$709$	−1.72300e8	+	6.27121e7i	−0.483445	+	0.175959i	−0.572233	−	0.820091i	$-0.693923\pi$
$709$	−1.72300e8	+	6.27121e7i	−0.483445	+	0.175959i	0.0887884	+	0.996051i	$0.471701\pi$
$710$	1.68279e8	+	9.71560e7i	0.470170	+	0.271453i
$711$	1.73344e8	−	5.01278e8i	0.482281	−	1.39466i
$712$	2.87182e7	+	4.97413e7i	0.0795640	+	0.137809i
$713$	2.30844e8	−	2.75109e8i	0.636869	−	0.758991i
$714$	−2.06586e7	−	2.90027e7i	−0.0567553	−	0.0796791i
$715$	1.69246e7	+	9.59844e7i	0.0463022	+	0.262593i
$716$	−2.24928e8	+	3.96609e7i	−0.612780	+	0.108050i
$717$	−4.80213e8	−	2.19229e8i	−1.30280	−	0.594758i
$718$	7.13313e7	+	5.98540e7i	0.192711	+	0.161704i
$719$	6.60883e7	−	3.81561e7i	0.177803	−	0.102654i	−0.408457	−	0.912777i	$-0.633933\pi$
$719$	6.60883e7	−	3.81561e7i	0.177803	−	0.102654i	0.586260	+	0.810123i	$0.300600\pi$
$720$	1.32401e7	−	8.28866e7i	0.0354727	−	0.222068i
$721$	7.38704e7	−	1.27947e8i	0.197090	−	0.341370i
$722$	1.61545e7	+	4.43840e7i	0.0429221	+	0.117928i
$723$	−2.70059e8	−	7.00322e7i	−0.714568	−	0.185303i
$724$	1.60933e8	−	1.35039e8i	0.424062	−	0.355830i
$725$	−6.34157e7	+	1.74233e8i	−0.166411	+	0.457211i
$726$	7.56750e8	+	6.00601e7i	1.97762	+	0.156955i
$727$	−4.62614e7	+	2.62361e8i	−0.120397	+	0.682804i	0.863539	+	0.504282i	$0.168243\pi$
$727$	−4.62614e7	+	2.62361e8i	−0.120397	+	0.682804i	−0.983936	+	0.178522i	$0.942868\pi$
$728$			3.93791e7i			0.102064i
$729$	−3.44495e8	−	1.77251e8i	−0.889202	−	0.457515i
$730$	−1.30709e8			−0.335998
$731$	1.89554e8	+	3.34235e7i	0.485267	+	0.0855657i
$732$	−2.35908e6	+	2.97241e7i	−0.00601464	+	0.0757837i
$733$	−3.57075e8	−	1.29965e8i	−0.906668	−	0.330000i	−0.153746	−	0.988110i	$-0.549134\pi$
$733$	−3.57075e8	−	1.29965e8i	−0.906668	−	0.330000i	−0.752921	+	0.658110i	$0.771356\pi$
$734$	1.91061e8	+	2.27698e8i	0.483152	+	0.575799i
$735$	3.92551e7	−	1.51376e8i	0.0988632	−	0.381237i
$736$	1.80329e8	−	6.56343e7i	0.452305	−	0.164626i
$737$	9.55515e8	+	5.51667e8i	2.38691	+	1.37808i
$738$	−4.01371e8	−	6.41141e7i	−0.998566	−	0.159509i
$739$	2.37679e8	+	4.11672e8i	0.588921	+	1.02004i	0.994374	+	0.105926i	$0.0337805\pi$
$739$	2.37679e8	+	4.11672e8i	0.588921	+	1.02004i	−0.405453	+	0.914116i	$0.632886\pi$
$740$	−4.19746e7	+	5.00234e7i	−0.103584	+	0.123446i
$741$	6.09314e7	−	1.33468e8i	0.149757	−	0.328037i
$742$	5.96350e6	+	3.38207e7i	0.0145979	+	0.0827886i
$743$	3.47023e8	−	6.11895e7i	0.846042	−	0.149180i	0.266209	−	0.963915i	$-0.414229\pi$
$743$	3.47023e8	−	6.11895e7i	0.846042	−	0.149180i	0.579833	+	0.814735i	$0.303118\pi$
$744$	−4.99170e8	+	3.55558e8i	−1.21208	+	0.863359i
$745$	6.62298e7	+	5.55734e7i	0.160171	+	0.134400i
$746$	−1.13505e8	+	6.55324e7i	−0.273401	+	0.157848i
$747$	1.52467e8	+	5.27239e7i	0.365776	+	0.126487i
$748$	−5.92872e7	+	1.02689e8i	−0.141663	+	0.245368i
$749$	−6.94680e6	−	1.90862e7i	−0.0165325	−	0.0454228i
$750$	−7.03752e7	−	2.54417e8i	−0.166815	−	0.603061i
$751$	4.10668e8	−	3.44591e8i	0.969552	−	0.813550i	−0.0129287	−	0.999916i	$-0.504115\pi$
$751$	4.10668e8	−	3.44591e8i	0.969552	−	0.813550i	0.982480	+	0.186366i	$0.0596710\pi$
$752$	1.92879e6	−	5.29931e6i	0.00453557	−	0.0124614i
$753$	−4.70981e8	+	6.84314e8i	−1.10311	+	1.60277i
$754$	−1.19751e7	+	6.79143e7i	−0.0279361	+	0.158434i
$755$			1.67793e7i			0.0389882i
$756$	9.97014e6	−	4.11694e7i	0.0230747	−	0.0952815i
$757$	−2.54164e8			−0.585903			−0.292952	−	0.956127i	$-0.594637\pi$
$757$	−2.54164e8			−0.585903			−0.292952	+	0.956127i	$0.594637\pi$
$758$	−1.54588e8	−	2.72581e7i	−0.354951	−	0.0625874i
$759$	−5.32272e8	+	2.53450e8i	&mi

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.34855 - 1.11942i) q^{2} +(2.13616 - 26.9154i) q^{3} +(-21.0893 - 7.67587i) q^{4} +(-34.3281 - 40.9106i) q^{5} +(-43.6912 + 168.482i) q^{6} +(90.1091 - 32.7970i) q^{7} +(482.595 + 278.626i) q^{8} +(-719.874 - 114.991i) q^{9} +O(q^{10})\)	\(q+(-6.34855 - 1.11942i) q^{2} +(2.13616 - 26.9154i) q^{3} +(-21.0893 - 7.67587i) q^{4} +(-34.3281 - 40.9106i) q^{5} +(-43.6912 + 168.482i) q^{6} +(90.1091 - 32.7970i) q^{7} +(482.595 + 278.626i) q^{8} +(-719.874 - 114.991i) q^{9} +(172.137 + 298.151i) q^{10} +(-1591.86 + 1897.10i) q^{11} +(-251.649 + 551.229i) q^{12} +(127.968 + 725.743i) q^{13} +(-608.776 + 107.344i) q^{14} +(-1174.45 + 836.561i) q^{15} +(-1651.58 - 1385.84i) q^{16} +(-1847.61 + 1066.72i) q^{17} +(4441.43 + 1535.87i) q^{18} +(3686.89 - 6385.89i) q^{19} +(409.930 + 1126.27i) q^{20} +(-690.256 - 2495.38i) q^{21} +(12229.6 - 10261.9i) q^{22} +(-3015.51 + 8285.04i) q^{23} +(8530.23 - 12394.0i) q^{24} +(2217.99 - 12578.9i) q^{25} -4750.67i q^{26} +(-4632.79 + 19130.0i) q^{27} -2152.08 q^{28} +(-14295.7 - 2520.72i) q^{29} +(8392.55 - 3996.24i) q^{30} +(-38276.2 - 13931.4i) q^{31} +(-13990.7 - 16673.4i) q^{32} +(47660.7 + 46897.9i) q^{33} +(12923.7 - 4703.86i) q^{34} +(-4435.02 - 2560.56i) q^{35} +(14299.0 + 7950.74i) q^{36} +(27241.5 + 47183.7i) q^{37} +(-30554.9 + 36414.0i) q^{38} +(19807.0 - 1894.00i) q^{39} +(-5167.78 - 29307.9i) q^{40} +(-85176.1 + 15018.8i) q^{41} +(1588.75 + 16614.7i) q^{42} +(-69112.5 - 57992.3i) q^{43} +(48133.0 - 27789.6i) q^{44} +(20007.5 + 33397.9i) q^{45} +(28418.6 - 49222.4i) q^{46} +(894.621 + 2457.95i) q^{47} +(-40828.5 + 41492.5i) q^{48} +(-83080.4 + 69712.7i) q^{49} +(-28162.1 + 77374.7i) q^{50} +(24764.3 + 52007.7i) q^{51} +(2871.95 - 16287.7i) q^{52} -55555.2i q^{53} +(50826.1 - 116262. i) q^{54} +132257. q^{55} +(52624.3 + 9279.08i) q^{56} +(-164003. - 112875. i) q^{57} +(87935.5 + 32005.9i) q^{58} +(-30517.7 - 36369.5i) q^{59} +(31189.7 - 8627.52i) q^{60} +(46240.1 - 16830.0i) q^{61} +(227403. + 131291. i) q^{62} +(-68638.5 + 13248.0i) q^{63} +(139147. + 241010. i) q^{64} +(25297.7 - 30148.6i) q^{65} +(-250078. - 351086. i) q^{66} +(-77364.4 - 438755. i) q^{67} +(47152.7 - 8314.29i) q^{68} +(216553. + 98861.6i) q^{69} +(25289.6 + 21220.5i) q^{70} +(488793. - 282205. i) q^{71} +(-315368. - 256070. i) q^{72} +(-189832. + 328799. i) q^{73} +(-120126. - 330043. i) q^{74} +(-333827. - 86568.5i) q^{75} +(-126771. + 106374. i) q^{76} +(-81221.4 + 223154. i) q^{77} +(-127866. - 10148.2i) q^{78} +(-126342. + 716523. i) q^{79} +115140. i q^{80} +(504995. + 165558. i) q^{81} +557557. q^{82} +(-217936. - 38427.9i) q^{83} +(-4597.19 + 57924.1i) q^{84} +(107065. + 38968.4i) q^{85} +(373847. + 445533. i) q^{86} +(-98384.2 + 379390. i) q^{87} +(-1.29680e6 + 471998. i) q^{88} +(89261.8 + 51535.3i) q^{89} +(-89632.5 - 234425. i) q^{90} +(35333.3 + 61199.0i) q^{91} +(127190. - 151579. i) q^{92} +(-456732. + 1.00046e6i) q^{93} +(-2928.07 - 16605.9i) q^{94} +(-387814. + 68382.1i) q^{95} +(-478657. + 340947. i) q^{96} +(-472027. - 396077. i) q^{97} +(605478. - 349573. i) q^{98} +(1.36408e6 - 1.18262e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Introduction

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