LMFDB - Embedded newform 27.7.f.a.2.9

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			2.9
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.698460 - 0.123157i) q^{2} +(20.3194 + 17.7798i) q^{3} +(-59.6676 - 21.7172i) q^{4} +(95.6034 + 113.936i) q^{5} +(-12.0026 - 14.9210i) q^{6} +(-285.640 + 103.964i) q^{7} +(78.3107 + 45.2127i) q^{8} +(96.7599 + 722.550i) q^{9} +O(q^{10})$	\(q+(-0.698460 - 0.123157i) q^{2} +(20.3194 + 17.7798i) q^{3} +(-59.6676 - 21.7172i) q^{4} +(95.6034 + 113.936i) q^{5} +(-12.0026 - 14.9210i) q^{6} +(-285.640 + 103.964i) q^{7} +(78.3107 + 45.2127i) q^{8} +(96.7599 + 722.550i) q^{9} +(-52.7432 - 91.3539i) q^{10} +(-448.154 + 534.089i) q^{11} +(-826.286 - 1502.16i) q^{12} +(509.487 + 2889.45i) q^{13} +(212.312 - 37.4364i) q^{14} +(-83.1416 + 4014.92i) q^{15} +(3063.93 + 2570.94i) q^{16} +(-3110.01 + 1795.56i) q^{17} +(21.4044 - 516.589i) q^{18} +(4614.82 - 7993.10i) q^{19} +(-3230.06 - 8874.52i) q^{20} +(-7652.51 - 2966.11i) q^{21} +(378.795 - 317.847i) q^{22} +(7854.47 - 21580.0i) q^{23} +(787.359 + 2311.04i) q^{24} +(-1128.08 + 6397.67i) q^{25} -2080.91i q^{26} +(-10880.7 + 16402.2i) q^{27} +19301.3 q^{28} +(19445.2 + 3428.72i) q^{29} +(552.538 - 2794.02i) q^{30} +(4807.00 + 1749.61i) q^{31} +(-5543.36 - 6606.32i) q^{32} +(-18602.2 + 2884.33i) q^{33} +(2393.35 - 871.109i) q^{34} +(-39153.4 - 22605.2i) q^{35} +(9918.36 - 45214.2i) q^{36} +(7330.00 + 12695.9i) q^{37} +(-4207.68 + 5014.52i) q^{38} +(-41021.2 + 67770.5i) q^{39} +(2335.43 + 13244.9i) q^{40} +(-19034.2 + 3356.25i) q^{41} +(4979.68 + 3014.17i) q^{42} +(110794. + 92967.0i) q^{43} +(38339.3 - 22135.2i) q^{44} +(-73073.7 + 80102.7i) q^{45} +(-8143.77 + 14105.4i) q^{46} +(-1395.99 - 3835.45i) q^{47} +(16546.6 + 106716. i) q^{48} +(-19342.8 + 16230.6i) q^{49} +(1575.84 - 4329.59i) q^{50} +(-95118.3 - 18810.3i) q^{51} +(32350.9 - 183471. i) q^{52} -180475. i q^{53} +(9619.76 - 10116.2i) q^{54} -103697. q^{55} +(-27069.2 - 4773.02i) q^{56} +(235886. - 80365.0i) q^{57} +(-13159.4 - 4789.65i) q^{58} +(173969. + 207328. i) q^{59} +(92153.8 - 237755. i) q^{60} +(-129113. + 46993.3i) q^{61} +(-3142.02 - 1814.05i) q^{62} +(-102758. - 196330. i) q^{63} +(-124931. - 216387. i) q^{64} +(-280502. + 334290. i) q^{65} +(13348.1 + 276.416i) q^{66} +(10208.1 + 57893.2i) q^{67} +(224561. - 39596.2i) q^{68} +(543285. - 298843. i) q^{69} +(24563.1 + 20610.9i) q^{70} +(-205914. + 118885. i) q^{71} +(-25091.1 + 60958.1i) q^{72} +(211223. - 365848. i) q^{73} +(-3556.12 - 9770.35i) q^{74} +(-136671. + 109940. i) q^{75} +(-448944. + 376708. i) q^{76} +(72484.4 - 199149. i) q^{77} +(36998.1 - 42283.0i) q^{78} +(-32884.7 + 186499. i) q^{79} +594882. i q^{80} +(-512716. + 139828. i) q^{81} +13708.0 q^{82} +(757527. + 133572. i) q^{83} +(392191. + 343172. i) q^{84} +(-501906. - 182679. i) q^{85} +(-65935.4 - 78578.8i) q^{86} +(334154. + 415401. i) q^{87} +(-59242.9 + 21562.6i) q^{88} +(-835996. - 482662. i) q^{89} +(60904.3 - 46949.0i) q^{90} +(-445930. - 772373. i) q^{91} +(-937315. + 1.11705e6i) q^{92} +(66568.0 + 121018. i) q^{93} +(502.679 + 2850.83i) q^{94} +(1.35189e6 - 238375. i) q^{95} +(4820.78 - 232796. i) q^{96} +(1.19506e6 + 1.00277e6i) q^{97} +(15509.1 - 8954.19i) q^{98} +(-429270. - 272135. i) 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 $

$2$	−0.698460	−	0.123157i	−0.0873076	−	0.0153947i	0.129824	−	0.991537i	$-0.458559\pi$
$2$	−0.698460	−	0.123157i	−0.0873076	−	0.0153947i	−0.217131	+	0.976142i	$0.569670\pi$
$3$	20.3194	+	17.7798i	0.752572	+	0.658510i
$3$	20.3194	+	17.7798i	0.752572	+	0.658510i
$4$	−59.6676	−	21.7172i	−0.932307	−	0.339332i
$5$	95.6034	+	113.936i	0.764827	+	0.911486i	0.998143	−	0.0609152i	$-0.0194019\pi$
$5$	95.6034	+	113.936i	0.764827	+	0.911486i	−0.233316	+	0.972401i	$0.574957\pi$
$6$	−12.0026	−	14.9210i	−0.0555677	−	0.0690785i
$7$	−285.640	+	103.964i	−0.832769	+	0.303103i	−0.722995	−	0.690853i	$-0.757235\pi$
$7$	−285.640	+	103.964i	−0.832769	+	0.303103i	−0.109774	+	0.993957i	$0.535013\pi$
$8$	78.3107	+	45.2127i	0.152951	+	0.0883060i
$9$	96.7599	+	722.550i	0.132730	+	0.991152i
$10$	−52.7432	−	91.3539i	−0.0527432	−	0.0913539i
$11$	−448.154	+	534.089i	−0.336705	+	0.401269i	−0.907656	−	0.419715i	$-0.862130\pi$
$11$	−448.154	+	534.089i	−0.336705	+	0.401269i	0.570951	+	0.820984i	$0.306575\pi$
$12$	−826.286	−	1502.16i	−0.478175	−	0.869305i
$13$	509.487	+	2889.45i	0.231901	+	1.31518i	0.849042	+	0.528325i	$0.177180\pi$
$13$	509.487	+	2889.45i	0.231901	+	1.31518i	−0.617141	+	0.786853i	$0.711709\pi$
$14$	212.312	−	37.4364i	0.0773732	−	0.0136430i
$15$	−83.1416	+	4014.92i	−0.0246345	+	1.18961i
$16$	3063.93	+	2570.94i	0.748029	+	0.627671i
$17$	−3110.01	+	1795.56i	−0.633016	+	0.365472i	−0.781919	−	0.623380i	$-0.785759\pi$
$17$	−3110.01	+	1795.56i	−0.633016	+	0.365472i	0.148903	+	0.988852i	$0.452426\pi$
$18$	21.4044	−	516.589i	0.00367017	−	0.0885784i
$19$	4614.82	−	7993.10i	0.672812	−	1.16534i	−0.304291	−	0.952579i	$-0.598420\pi$
$19$	4614.82	−	7993.10i	0.672812	−	1.16534i	0.977103	−	0.212766i	$-0.0682471\pi$
$20$	−3230.06	−	8874.52i	−0.403758	−	1.10932i
$21$	−7652.51	−	2966.11i	−0.826315	−	0.320280i
$22$	378.795	−	317.847i	0.0355743	−	0.0298504i
$23$	7854.47	−	21580.0i	0.645555	−	1.77365i	0.0120277	−	0.999928i	$-0.496171\pi$
$23$	7854.47	−	21580.0i	0.645555	−	1.77365i	0.633527	−	0.773720i	$-0.281606\pi$
$24$	787.359	+	2311.04i	0.0569559	+	0.167176i
$25$	−1128.08	+	6397.67i	−0.0721973	+	0.409451i
$26$		−	2080.91i		−	0.118395i
$27$	−10880.7	+	16402.2i	−0.552795	+	0.833317i
$28$	19301.3			0.879249
$29$	19445.2	+	3428.72i	0.797295	+	0.140585i	0.557432	−	0.830222i	$-0.311787\pi$
$29$	19445.2	+	3428.72i	0.797295	+	0.140585i	0.239862	+	0.970807i	$0.422898\pi$
$30$	552.538	−	2794.02i	0.0204644	−	0.103482i
$31$	4807.00	+	1749.61i	0.161358	+	0.0587293i	0.421436	−	0.906858i	$-0.361526\pi$
$31$	4807.00	+	1749.61i	0.161358	+	0.0587293i	−0.260078	+	0.965587i	$0.583748\pi$
$32$	−5543.36	−	6606.32i	−0.169170	−	0.201609i
$33$	−18602.2	+	2884.33i	−0.517634	+	0.0802606i
$34$	2393.35	−	871.109i	0.0608934	−	0.0221634i
$35$	−39153.4	−	22605.2i	−0.913199	−	0.527236i
$36$	9918.36	−	45214.2i	0.212585	−	0.969098i
$37$	7330.00	+	12695.9i	0.144710	+	0.250645i	0.929265	−	0.369414i	$-0.120442\pi$
$37$	7330.00	+	12695.9i	0.144710	+	0.250645i	−0.784555	+	0.620060i	$0.787108\pi$
$38$	−4207.68	+	5014.52i	−0.0766817	+	0.0913857i
$39$	−41021.2	+	67770.5i	−0.691535	+	1.14248i
$40$	2335.43	+	13244.9i	0.0364911	+	0.206951i
$41$	−19034.2	+	3356.25i	−0.276174	+	0.0486970i	−0.310020	−	0.950730i	$-0.600336\pi$
$41$	−19034.2	+	3356.25i	−0.276174	+	0.0486970i	0.0338455	+	0.999427i	$0.489225\pi$
$42$	4979.68	+	3014.17i	0.0672130	+	0.0406837i
$43$	110794.	+	92967.0i	1.39351	+	1.16929i	0.963896	+	0.266280i	$0.0857945\pi$
$43$	110794.	+	92967.0i	1.39351	+	1.16929i	0.429613	+	0.903013i	$0.358650\pi$
$44$	38339.3	−	22135.2i	0.450076	−	0.259851i
$45$	−73073.7	+	80102.7i	−0.801906	+	0.879042i
$46$	−8143.77	+	14105.4i	−0.0836666	+	0.144915i
$47$	−1395.99	−	3835.45i	−0.0134459	−	0.0369422i	0.932788	−	0.360425i	$-0.117368\pi$
$47$	−1395.99	−	3835.45i	−0.0134459	−	0.0369422i	−0.946234	+	0.323483i	$0.895146\pi$
$48$	16546.6	+	106716.i	0.149618	+	0.964952i
$49$	−19342.8	+	16230.6i	−0.164411	+	0.137957i
$50$	1575.84	−	4329.59i	0.0126067	−	0.0346367i
$51$	−95118.3	−	18810.3i	−0.717057	−	0.141803i
$52$	32350.9	−	183471.i	0.230079	−	1.30484i
$53$		−	180475.i		−	1.21225i	−0.795371	−	0.606123i	$-0.792724\pi$
$53$		−	180475.i		−	1.21225i	0.795371	−	0.606123i	$-0.207276\pi$
$54$	9619.76	−	10116.2i	0.0610918	−	0.0642448i
$55$	−103697.			−0.623272
$56$	−27069.2	−	4773.02i	−0.154138	−	0.0271787i
$57$	235886.	−	80365.0i	1.27373	−	0.433953i
$58$	−13159.4	−	4789.65i	−0.0674456	−	0.0245482i
$59$	173969.	+	207328.i	0.847063	+	1.00949i	0.999775	+	0.0212195i	$0.00675489\pi$
$59$	173969.	+	207328.i	0.847063	+	1.00949i	−0.152712	+	0.988271i	$0.548801\pi$
$60$	92153.8	−	237755.i	0.426638	−	1.10072i
$61$	−129113.	+	46993.3i	−0.568827	+	0.207036i	−0.610392	−	0.792100i	$-0.708988\pi$
$61$	−129113.	+	46993.3i	−0.568827	+	0.207036i	0.0415645	+	0.999136i	$0.486766\pi$
$62$	−3142.02	−	1814.05i	−0.0131836	−	0.00761156i
$63$	−102758.	−	196330.i	−0.410955	−	0.785170i
$64$	−124931.	−	216387.i	−0.476575	−	0.825453i
$65$	−280502.	+	334290.i	−1.02140	+	1.21726i
$66$	13348.1	+	276.416i	0.0464290	+	0.000961459i
$67$	10208.1	+	57893.2i	0.0339408	+	0.192488i	0.997064	−	0.0765731i	$-0.0243979\pi$
$67$	10208.1	+	57893.2i	0.0339408	+	0.192488i	−0.963123	+	0.269061i	$0.913287\pi$
$68$	224561.	−	39596.2i	0.714181	−	0.125929i
$69$	543285.	−	298843.i	1.65379	−	0.909694i
$70$	24563.1	+	20610.9i	0.0716126	+	0.0600901i
$71$	−205914.	+	118885.i	−0.575322	+	0.332162i	−0.759272	−	0.650773i	$-0.774445\pi$
$71$	−205914.	+	118885.i	−0.575322	+	0.332162i	0.183950	+	0.982936i	$0.441111\pi$
$72$	−25091.1	+	60958.1i	−0.0672236	+	0.163318i
$73$	211223.	−	365848.i	0.542965	−	0.940443i	−0.455767	−	0.890099i	$-0.650635\pi$
$73$	211223.	−	365848.i	0.542965	−	0.940443i	0.998732	−	0.0503437i	$-0.0160317\pi$
$74$	−3556.12	−	9770.35i	−0.00877568	−	0.0241110i
$75$	−136671.	+	109940.i	−0.323961	+	0.260599i
$76$	−448944.	+	376708.i	−1.02271	+	0.858153i
$77$	72484.4	−	199149.i	0.158772	−	0.436221i
$78$	36998.1	−	42283.0i	0.0779643	−	0.0891008i
$79$	−32884.7	+	186499.i	−0.0666981	+	0.378263i	0.933127	+	0.359548i	$0.117069\pi$
$79$	−32884.7	+	186499.i	−0.0666981	+	0.378263i	−0.999825	+	0.0187160i	$0.994042\pi$
$80$			594882.i			1.16188i
$81$	−512716.	+	139828.i	−0.964766	+	0.263111i
$82$	13708.0			0.0248618
$83$	757527.	+	133572.i	1.32484	+	0.233605i	0.790915	−	0.611926i	$-0.209605\pi$
$83$	757527.	+	133572.i	1.32484	+	0.233605i	0.533926	+	0.845531i	$0.320716\pi$
$84$	392191.	+	343172.i	0.661699	+	0.578994i
$85$	−501906.	−	182679.i	−0.817270	−	0.297462i
$86$	−65935.4	−	78578.8i	−0.103663	−	0.123541i
$87$	334154.	+	415401.i	0.507445	+	0.630826i
$88$	−59242.9	+	21562.6i	−0.0869337	+	0.0316413i
$89$	−835996.	−	482662.i	−1.18586	−	0.684657i	−0.228498	−	0.973544i	$-0.573382\pi$
$89$	−835996.	−	482662.i	−1.18586	−	0.684657i	−0.957363	+	0.288887i	$0.906715\pi$
$90$	60904.3	−	46949.0i	0.0835450	−	0.0644019i
$91$	−445930.	−	772373.i	−0.591755	−	1.02495i
$92$	−937315.	+	1.11705e6i	−1.20371	+	1.43453i
$93$	66568.0	+	121018.i	0.0827593	+	0.150454i
$94$	502.679	+	2850.83i	0.000605212	+	0.00343233i
$95$	1.35189e6	−	238375.i	1.57678	−	0.278029i
$96$	4820.78	−	232796.i	0.00544884	−	0.263125i
$97$	1.19506e6	+	1.00277e6i	1.30940	+	1.09872i	0.988438	+	0.151629i	$0.0484518\pi$
$97$	1.19506e6	+	1.00277e6i	1.30940	+	1.09872i	0.320965	+	0.947091i	$0.395993\pi$
$98$	15509.1	−	8954.19i	0.0164782	−	0.00951367i
$99$	−429270.	−	272135.i	−0.442410	−	0.280465i
$100$	206250.	−	357235.i	0.206250	−	0.357235i
$101$	209874.	+	576625.i	0.203702	+	0.559667i	0.998910	−	0.0466695i	$-0.0148608\pi$
$101$	209874.	+	576625.i	0.203702	+	0.559667i	−0.795208	+	0.606336i	$0.792639\pi$
$102$	64119.7	+	24852.8i	0.0604215	+	0.0234193i
$103$	−622064.	+	521974.i	−0.569277	+	0.477680i	−0.881406	−	0.472360i	$-0.843402\pi$
$103$	−622064.	+	521974.i	−0.569277	+	0.477680i	0.312129	+	0.950040i	$0.398958\pi$
$104$	−90741.3	+	249310.i	−0.0806687	+	0.221635i
$105$	−393660.	−	1.15546e6i	−0.340058	−	0.998134i
$106$	−22226.9	+	126055.i	−0.0186621	+	0.105838i
$107$		−	1.97346e6i		−	1.61093i	−0.592645	−	0.805464i	$-0.701916\pi$
$107$		−	1.97346e6i		−	1.61093i	0.592645	−	0.805464i	$-0.298084\pi$
$108$	1.00543e6	−	742382.i	0.798146	−	0.589327i
$109$	249082.			0.192337			0.0961685	−	0.995365i	$-0.469341\pi$
$109$	249082.			0.192337			0.0961685	+	0.995365i	$0.469341\pi$
$110$	72428.2	+	12771.0i	0.0544164	+	0.00959508i
$111$	−76789.1	+	388300.i	−0.0561475	+	0.283922i
$112$	−1.14247e6	−	415824.i	−0.813185	−	0.295975i
$113$	−589274.	−	702269.i	−0.408396	−	0.486708i	0.522165	−	0.852845i	$-0.325125\pi$
$113$	−589274.	−	702269.i	−0.408396	−	0.486708i	−0.930561	+	0.366137i	$0.880680\pi$
$114$	−174655.	+	27080.7i	−0.117887	+	0.0182787i
$115$	3.20964e6	−	1.16821e6i	2.11039	−	0.768120i
$116$	−1.08579e6	−	626880.i	−0.695618	−	0.401615i
$117$	−2.03847e6	+	647713.i	−1.27276	+	0.404413i
$118$	−95976.4	−	166236.i	−0.0584142	−	0.101176i
$119$	701667.	−	836214.i	0.416380	−	0.496223i
$120$	−188036.	+	310652.i	−0.108817	+	0.179775i
$121$	223219.	+	1.26594e6i	0.126001	+	0.714589i
$122$	95967.9	−	16921.7i	0.0528502	−	0.00931891i
$123$	−446438.	−	270227.i	−0.239909	−	0.145216i
$124$	−248826.	−	208790.i	−0.130506	−	0.109508i
$125$	1.17582e6	−	678862.i	0.602022	−	0.347578i
$126$	47593.0	+	149784.i	0.0237920	+	0.0748778i
$127$	347107.	−	601208.i	0.169454	−	0.293504i	−0.768774	−	0.639521i	$-0.779133\pi$
$127$	347107.	−	601208.i	0.169454	−	0.293504i	0.938228	+	0.346017i	$0.112466\pi$
$128$	249382.	+	685171.i	0.118914	+	0.326715i
$129$	598336.	+	3.85892e6i	0.278725	+	1.79762i
$130$	237090.	−	198942.i	0.107915	−	0.0905518i
$131$	791028.	−	2.17333e6i	0.351867	−	0.966746i	−0.629903	−	0.776673i	$-0.716906\pi$
$131$	791028.	−	2.17333e6i	0.351867	−	0.966746i	0.981770	−	0.190072i	$-0.0608722\pi$
$132$	1.17259e6	+	231888.i	0.509829	+	0.100822i
$133$	−487178.	+	2.76293e6i	−0.207078	+	1.17440i
$134$		−	41693.3i		−	0.0173281i
$135$	−2.90902e6	+	328409.i	−1.18235	+	0.133479i
$136$	−324729.			−0.129093
$137$	−4.03534e6	−	711540.i	−1.56935	−	0.276718i	−0.679743	−	0.733451i	$-0.737909\pi$
$137$	−4.03534e6	−	711540.i	−1.56935	−	0.276718i	−0.889604	+	0.456732i	$0.849020\pi$
$138$	−416268.	+	141820.i	−0.158393	+	0.0539636i
$139$	3.57904e6	+	1.30266e6i	1.33267	+	0.485052i	0.907496	−	0.420060i	$-0.137991\pi$
$139$	3.57904e6	+	1.30266e6i	1.33267	+	0.485052i	0.425173	+	0.905112i	$0.360213\pi$
$140$	1.84527e6	+	2.19911e6i	0.672474	+	0.801423i
$141$	39827.6	−	102755.i	0.0142078	−	0.0366559i
$142$	158464.	−	57676.3i	0.0553435	−	0.0201434i
$143$	−1.77155e6	−	1.02281e6i	−0.605823	−	0.349772i
$144$	−1.56117e6	+	2.46261e6i	−0.522832	+	0.824722i
$145$	1.46838e6	+	2.54330e6i	0.481652	+	0.834246i
$146$	−192588.	+	229517.i	−0.0618828	+	0.0737490i
$147$	−681611.	−	14114.9i	−0.214578	−	0.00444351i
$148$	−161643.	−	916724.i	−0.0498623	−	0.282783i
$149$	68252.5	−	12034.8i	0.0206329	−	0.00363813i	−0.163322	−	0.986573i	$-0.552221\pi$
$149$	68252.5	−	12034.8i	0.0206329	−	0.00363813i	0.183955	+	0.982935i	$0.441110\pi$
$150$	108999.	−	59956.8i	0.0322961	−	0.0177650i
$151$	−2.45359e6	−	2.05881e6i	−0.712641	−	0.597977i	0.212697	−	0.977118i	$-0.431775\pi$
$151$	−2.45359e6	−	2.05881e6i	−0.712641	−	0.597977i	−0.925339	+	0.379141i	$0.876220\pi$
$152$	722779.	−	417297.i	0.205814	−	0.118827i
$153$	−1.59831e6	−	2.07340e6i	−0.446258	−	0.578906i
$154$	−75154.2	+	130171.i	−0.0205774	+	0.0356412i
$155$	260223.	+	714958.i	0.0698797	+	0.191993i
$156$	3.91943e6	−	3.15284e6i	1.03240	−	0.830478i
$157$	−1.76719e6	+	1.48285e6i	−0.456651	+	0.383175i	−0.841897	−	0.539638i	$-0.818561\pi$
$157$	−1.76719e6	+	1.48285e6i	−0.456651	+	0.383175i	0.385246	+	0.922814i	$0.374116\pi$
$158$	45937.4	−	126212.i	0.0116465	−	0.0319985i
$159$	3.20881e6	−	3.66716e6i	0.798276	−	0.912302i
$160$	222731.	−	1.26317e6i	0.0543778	−	0.308392i
$161$			6.98069e6i			1.67271i
$162$	375333.	−	34519.4i	0.0882818	−	0.00811929i
$163$	155795.			0.0359741			0.0179871	−	0.999838i	$-0.494274\pi$
$163$	155795.			0.0359741			0.0179871	+	0.999838i	$0.494274\pi$
$164$	1.20862e6	+	213111.i	0.274004	+	0.0483143i
$165$	−2.10706e6	−	1.84371e6i	−0.469057	−	0.410431i
$166$	−512652.	−	186590.i	−0.112072	−	0.0407910i
$167$	337227.	+	401891.i	0.0724057	+	0.0862898i	0.801031	−	0.598622i	$-0.204285\pi$
$167$	337227.	+	401891.i	0.0724057	+	0.0862898i	−0.728626	+	0.684912i	$0.759841\pi$
$168$	−465167.	−	578268.i	−0.0981028	−	0.121956i
$169$	−3.55361e6	+	1.29341e6i	−0.736223	+	0.267963i
$170$	328063.	+	189407.i	0.0667745	+	0.0385523i
$171$	6.22194e6	+	2.56103e6i	1.24434	+	0.512183i
$172$	−4.59181e6	−	7.95325e6i	−0.902400	−	1.56300i
$173$	2.53118e6	−	3.01654e6i	0.488860	−	0.582600i	−0.464067	−	0.885800i	$-0.653610\pi$
$173$	2.53118e6	−	3.01654e6i	0.488860	−	0.582600i	0.952927	+	0.303200i	$0.0980549\pi$
$174$	−182234.	−	331295.i	−0.0345924	−	0.0628879i
$175$	−342905.	−	1.94471e6i	−0.0639823	−	0.362861i
$176$	−2.74622e6	+	484234.i	−0.503730	+	0.0888212i
$177$	−151292.	+	7.30592e6i	−0.0272833	+	1.31751i
$178$	524466.	+	440080.i	0.0929946	+	0.0780317i
$179$	3.38776e6	−	1.95593e6i	0.590683	−	0.341031i	−0.174685	−	0.984624i	$-0.555891\pi$
$179$	3.38776e6	−	1.95593e6i	0.590683	−	0.341031i	0.765367	+	0.643594i	$0.222557\pi$
$180$	6.09974e6	−	3.19258e6i	1.04591	−	0.547424i
$181$	486674.	−	842944.i	0.0820733	−	0.142155i	−0.822067	−	0.569391i	$-0.807179\pi$
$181$	486674.	−	842944.i	0.0820733	−	0.142155i	0.904140	+	0.427236i	$0.140512\pi$
$182$	216341.	+	594391.i	0.0358859	+	0.0985958i
$183$	−3.45903e6	−	1.34072e6i	−0.564419	−	0.218769i
$184$	1.59078e6	−	1.33482e6i	0.255362	−	0.214274i
$185$	−745747.	+	2.04892e6i	−0.117781	+	0.323601i
$186$	−31590.8	−	92724.9i	−0.00490933	−	0.0144098i
$187$	434771.	−	2.46571e6i	0.0664869	−	0.377066i
$188$			259169.i			0.0390041i
$189$	1.40271e6	−	5.81632e6i	0.207769	−	0.861515i
$190$	−973601.			−0.141945
$191$	2.22284e6	+	391947.i	0.319013	+	0.0562506i	0.330862	−	0.943679i	$-0.392661\pi$
$191$	2.22284e6	+	391947.i	0.319013	+	0.0562506i	−0.0118489	+	0.999930i	$0.503772\pi$
$192$	1.30878e6	−	6.61812e6i	0.184911	−	0.935042i
$193$	−7.72327e6	−	2.81104e6i	−1.07431	−	0.391017i	−0.256523	−	0.966538i	$-0.582577\pi$
$193$	−7.72327e6	−	2.81104e6i	−1.07431	−	0.391017i	−0.817786	+	0.575522i	$0.804799\pi$
$194$	−711201.	−	847576.i	−0.0974063	−	0.116084i
$195$	−1.16433e7	+	1.80532e6i	−1.57026	+	0.243472i
$196$	1.50662e6	−	548366.i	0.200095	−	0.0728287i
$197$	−2.43738e6	−	1.40722e6i	−0.318805	−	0.184062i	0.332055	−	0.943260i	$-0.392258\pi$
$197$	−2.43738e6	−	1.40722e6i	−0.318805	−	0.184062i	−0.650860	+	0.759198i	$0.725591\pi$
$198$	266312.	+	242944.i	0.0343080	+	0.0312975i
$199$	6.72192e6	+	1.16427e7i	0.852971	+	1.47739i	0.878515	+	0.477715i	$0.158535\pi$
$199$	6.72192e6	+	1.16427e7i	0.852971	+	1.47739i	−0.0255440	+	0.999674i	$0.508132\pi$
$200$	−377597.	+	450002.i	−0.0471996	+	0.0562503i
$201$	−821904.	+	1.35786e6i	−0.101212	+	0.167211i
$202$	−75573.3	−	428598.i	−0.00916884	−	0.0519991i
$203$	−5.91079e6	+	1.04223e6i	−0.706574	+	0.124588i
$204$	5.26698e6	+	3.18808e6i	0.620399	+	0.375524i
$205$	−2.20213e6	−	1.84781e6i	−0.255612	−	0.214484i
$206$	498772.	−	287966.i	0.0570559	−	0.0329412i
$207$	1.63526e7	+	3.58717e6i	1.84364	+	0.404428i
$208$	−5.86756e6	+	1.01629e7i	−0.652030	+	1.12935i
$209$	2.20088e6	+	6.04687e6i	0.241078	+	0.662356i
$210$	132652.	+	855528.i	0.0143237	+	0.0923797i
$211$	7.32784e6	−	6.14879e6i	0.780061	−	0.654549i	−0.163203	−	0.986593i	$-0.552183\pi$
$211$	7.32784e6	−	6.14879e6i	0.780061	−	0.654549i	0.943264	+	0.332044i	$0.107738\pi$
$212$	−3.91943e6	+	1.07685e7i	−0.411354	+	1.13018i
$213$	−6.29780e6	−	1.24544e6i	−0.651703	−	0.128879i
$214$	−243046.	+	1.37838e6i	−0.0247997	+	0.140646i
$215$			2.15113e7i			2.16447i
$216$	−1.59366e6	+	792522.i	−0.158137	+	0.0786412i
$217$	−1.55497e6			−0.152175
$218$	−173974.	−	30676.3i	−0.0167925	−	0.00296097i
$219$	1.07966e7	−	3.67835e6i	1.02791	−	0.350203i
$220$	6.18735e6	+	2.25201e6i	0.581081	+	0.211496i
$221$	−6.77269e6	−	8.07138e6i	−0.627458	−	0.747775i
$222$	101456.	−	261755.i	0.00927299	−	0.0239241i
$223$	−1.88794e7	+	6.87154e6i	−1.70245	+	0.619640i	−0.996100	−	0.0882267i	$-0.971880\pi$
$223$	−1.88794e7	+	6.87154e6i	−1.70245	+	0.619640i	−0.706346	+	0.707867i	$0.749658\pi$
$224$	2.27023e6	+	1.31072e6i	0.201988	+	0.116618i
$225$	−4.73179e6	−	196057.i	−0.415411	−	0.0172122i
$226$	325095.	+	563081.i	0.0281634	+	0.0487804i
$227$	1.17986e7	−	1.40611e7i	1.00868	−	1.20210i	0.0294066	−	0.999568i	$-0.490638\pi$
$227$	1.17986e7	−	1.40611e7i	1.00868	−	1.20210i	0.979275	−	0.202533i	$-0.0649173\pi$
$228$	−1.58201e7	−	327605.i	−1.33476	−	0.0276405i
$229$	−1.68693e6	−	9.56708e6i	−0.140473	−	0.796660i	−0.970891	−	0.239520i	$-0.923010\pi$
$229$	−1.68693e6	−	9.56708e6i	−0.140473	−	0.796660i	0.830419	−	0.557140i	$-0.188101\pi$
$230$	−2.38568e6	+	420660.i	−0.196078	+	0.0345739i
$231$	5.01367e6	−	2.75785e6i	0.406743	−	0.223735i
$232$	1.36775e6	+	1.14768e6i	0.109532	+	0.0919084i
$233$	1.57596e7	−	9.09880e6i	1.24588	−	0.719310i	0.275597	−	0.961273i	$-0.411125\pi$
$233$	1.57596e7	−	9.09880e6i	1.24588	−	0.719310i	0.970285	+	0.241963i	$0.0777913\pi$
$234$	1.50356e6	−	201349.i	0.117348	−	0.0157145i
$235$	303533.	−	525735.i	0.0233885	−	0.0405101i
$236$	−5.87772e6	−	1.61489e7i	−0.447170	−	1.22859i
$237$	−3.98410e6	+	3.20487e6i	−0.299285	+	0.240749i
$238$	−593073.	+	497647.i	−0.0439923	+	0.0369140i
$239$	1.77612e6	−	4.87985e6i	0.130100	−	0.357448i	−0.857490	−	0.514501i	$-0.827977\pi$
$239$	1.77612e6	−	4.87985e6i	0.130100	−	0.357448i	0.987590	+	0.157053i	$0.0501994\pi$
$240$	−1.05769e7	+	1.20877e7i	−0.765108	+	0.874397i
$241$	3.64620e6	−	2.06786e7i	0.260489	−	1.47731i	−0.521092	−	0.853501i	$-0.674475\pi$
$241$	3.64620e6	−	2.06786e7i	0.260489	−	1.47731i	0.781580	−	0.623805i	$-0.214414\pi$
$242$		−	911699.i		−	0.0643288i
$243$	−1.29042e7	−	6.27475e6i	−0.899317	−	0.437298i
$244$	8.72443e6			0.600576
$245$	−3.69848e6	−	652142.i	−0.251492	−	0.0443449i
$246$	278539.	+	243725.i	0.0187103	+	0.0163717i
$247$	2.54468e7	+	9.26189e6i	1.68866	+	0.614623i
$248$	297335.	+	354350.i	0.0194936	+	0.0232315i
$249$	1.30176e7	+	1.61828e7i	0.843207	+	1.04823i
$250$	−904874.	+	329347.i	−0.0579119	+	0.0210782i
$251$	−1.55032e7	−	8.95076e6i	−0.980391	−	0.566029i	−0.0780026	−	0.996953i	$-0.524854\pi$
$251$	−1.55032e7	−	8.95076e6i	−0.980391	−	0.566029i	−0.902388	+	0.430924i	$0.858188\pi$
$252$	1.86759e6	+	1.39461e7i	0.116702	+	0.871470i
$253$	8.00562e6	+	1.38661e7i	0.494349	+	0.856237i
$254$	−316484.	+	377171.i	−0.0193130	+	0.0230164i
$255$	−6.95047e6	−	1.26357e7i	−0.419173	−	0.762042i
$256$	2.68705e6	+	1.52390e7i	0.160160	+	0.908315i
$257$	−2.42188e6	+	427043.i	−0.142677	+	0.0251578i	−0.244530	−	0.969642i	$-0.578634\pi$
$257$	−2.42188e6	+	427043.i	−0.142677	+	0.0251578i	0.101854	+	0.994799i	$0.467523\pi$
$258$	57340.8	−	2.76899e6i	0.00333891	−	0.161236i
$259$	−3.41366e6	−	2.86441e6i	−0.196481	−	0.164868i
$260$	2.39968e7	−	1.38545e7i	1.36532	−	0.788265i
$261$	−595901.	+	1.43819e7i	−0.0335160	+	0.808900i
$262$	−820164.	+	1.42057e6i	−0.0456034	+	0.0789873i
$263$	−1.12215e7	−	3.08308e7i	−0.616856	−	1.69480i	−0.714552	−	0.699583i	$-0.753369\pi$
$263$	−1.12215e7	−	3.08308e7i	−0.616856	−	1.69480i	0.0976952	−	0.995216i	$-0.468853\pi$
$264$	−1.58716e6	−	615183.i	−0.0862600	−	0.0334343i
$265$	2.05626e7	−	1.72541e7i	1.10494	−	0.927159i
$266$	680550.	−	1.86979e6i	0.0361589	−	0.0993457i
$267$	−8.40535e6	−	2.46712e7i	−0.441593	−	1.29616i
$268$	648186.	−	3.67604e6i	0.0336740	−	0.190975i
$269$			2.68813e7i			1.38100i	0.723332	+	0.690500i	$0.242610\pi$
$269$			2.68813e7i			1.38100i	−0.723332	+	0.690500i	$0.757390\pi$
$270$	2.07228e6	+	128887.i	0.105283	+	0.00654814i
$271$	−299648.			−0.0150558			−0.00752788	−	0.999972i	$-0.502396\pi$
$271$	−299648.			−0.0150558			−0.00752788	+	0.999972i	$0.502396\pi$
$272$	−1.41451e7	−	2.49417e6i	−0.702910	−	0.123942i
$273$	4.67156e6	−	2.36227e7i	0.229601	−	1.16103i
$274$	2.73090e6	+	993965.i	0.132756	+	0.0483192i
$275$	−2.91137e6	−	3.46964e6i	−0.139991	−	0.166835i
$276$	−3.89066e7	+	6.03257e6i	−1.85053	+	0.286930i
$277$	−724787.	+	263801.i	−0.0341013	+	0.0124119i	−0.359014	−	0.933332i	$-0.616887\pi$
$277$	−724787.	+	263801.i	−0.0341013	+	0.0124119i	0.324913	+	0.945744i	$0.394665\pi$
$278$	−2.33939e6	−	1.35065e6i	−0.108885	−	0.0628647i
$279$	−799052.	+	3.64259e6i	−0.0367928	+	0.167725i
$280$	−2.04409e6	−	3.54046e6i	−0.0931162	−	0.161282i
$281$	−1.70367e7	+	2.03035e7i	−0.767830	+	0.915065i	−0.998316	−	0.0580110i	$-0.981524\pi$
$281$	−1.70367e7	+	2.03035e7i	−0.767830	+	0.915065i	0.230485	+	0.973076i	$0.425969\pi$
$282$	−40473.0	+	66864.9i	−0.00180475	+	0.00298161i
$283$	−709019.	−	4.02104e6i	−0.0312823	−	0.177411i	0.965163	−	0.261648i	$-0.0842658\pi$
$283$	−709019.	−	4.02104e6i	−0.0312823	−	0.177411i	−0.996446	+	0.0842370i	$0.973155\pi$
$284$	1.48683e7	−	2.62167e6i	0.649090	−	0.114452i
$285$	3.17080e7	+	1.91927e7i	1.36973	+	0.829089i
$286$	1.11139e6	+	932569.i	0.0475083	+	0.0398642i
$287$	5.08800e6	−	2.93756e6i	0.215229	−	0.124263i
$288$	4.23702e6	−	4.64458e6i	0.177371	−	0.194433i
$289$	−5.62069e6	+	9.73533e6i	−0.232861	+	0.403327i
$290$	−712376.	−	1.95724e6i	−0.0292089	−	0.0802508i
$291$	6.45385e6	+	4.16236e7i	0.261903	+	1.68912i
$292$	−2.05484e7	+	1.72421e7i	−0.825332	+	0.692536i
$293$	−6.91365e6	+	1.89951e7i	−0.274855	+	0.755159i	0.723070	+	0.690775i	$0.242731\pi$
$293$	−6.91365e6	+	1.89951e7i	−0.274855	+	0.755159i	−0.997925	+	0.0643841i	$0.979492\pi$
$294$	474340.	+	93804.1i	0.0186658	+	0.00369131i
$295$	−6.99005e6	+	3.96426e7i	−0.272279	+	1.54417i
$296$			1.32564e6i			0.0511151i
$297$	−3.88402e6	−	1.31620e7i	−0.148256	−	0.502402i
$298$	−49153.8			−0.00185741
$299$	6.63559e7	+	1.17003e7i	2.48237	+	0.437709i
$300$	1.05424e7	−	3.59175e6i	0.390461	−	0.133028i
$301$	−4.13124e7	−	1.50365e7i	−1.51489	−	0.551374i
$302$	1.46018e6	+	1.74017e6i	0.0530133	+	0.0631788i
$303$	−5.98773e6	+	1.54482e7i	−0.215246	+	0.555329i
$304$	3.46893e7	−	1.26259e7i	1.23474	−	0.449407i
$305$	−1.76979e7	−	1.02179e7i	−0.623765	−	0.360131i
$306$	861001.	+	1.64503e6i	0.0300496	+	0.0574129i
$307$	−6.39756e6	−	1.10809e7i	−0.221106	−	0.382966i	0.734038	−	0.679108i	$-0.237633\pi$
$307$	−6.39756e6	−	1.10809e7i	−0.221106	−	0.382966i	−0.955144	+	0.296142i	$0.904300\pi$
$308$	−8.64995e6	+	1.03086e7i	−0.296048	+	0.352816i
$309$	−2.19206e7	−	453935.i	−0.742979	−	0.0153857i
$310$	−93703.3	−	531418.i	−0.00314536	−	0.0178382i
$311$	−2.88960e7	+	5.09514e6i	−0.960631	+	0.169385i	−0.631910	−	0.775042i	$-0.717729\pi$
$311$	−2.88960e7	+	5.09514e6i	−0.960631	+	0.169385i	−0.328721	+	0.944427i	$0.606618\pi$
$312$	−6.27648e6	+	3.45248e6i	−0.206658	+	0.113676i
$313$	−1.48292e7	−	1.24432e7i	−0.483599	−	0.405788i	0.368127	−	0.929776i	$-0.379999\pi$
$313$	−1.48292e7	−	1.24432e7i	−0.483599	−	0.405788i	−0.851726	+	0.523988i	$0.824444\pi$
$314$	1.41694e6	−	818068.i	0.0457679	−	0.0264241i
$315$	1.25449e7	−	3.04776e7i	0.401362	−	0.975099i
$316$	6.01239e6	−	1.04138e7i	0.190540	−	0.330025i
$317$	1.42300e7	+	3.90966e7i	0.446711	+	1.22733i	0.935000	+	0.354647i	$0.115399\pi$
$317$	1.42300e7	+	3.90966e7i	0.446711	+	1.22733i	−0.488289	+	0.872682i	$0.662379\pi$
$318$	−2.69287e6	+	2.16618e6i	−0.0837401	+	0.0673617i
$319$	−1.05457e7	+	8.84889e6i	−0.324865	+	0.272594i
$320$	1.27104e7	−	3.49215e7i	0.387891	−	1.06572i
$321$	3.50876e7	−	4.00995e7i	1.06081	−	1.21234i
$322$	859723.	−	4.87573e6i	0.0257508	−	0.146040i
$323$			3.31448e7i			0.983575i
$324$	3.36292e7	+	2.79159e6i	0.988740	+	0.0820760i
$325$	−1.90605e7			−0.555244
$326$	−108817.	−	19187.3i	−0.00314081	−	0.000553810i
$327$	5.06121e6	+	4.42862e6i	0.144748	+	0.126656i
$328$	−1.64233e6	−	597758.i	−0.0465413	−	0.0169396i
$329$	797500.	+	950424.i	0.0223946	+	0.0266888i
$330$	1.24464e6	+	1.54726e6i	0.0346338	+	0.0430547i
$331$	3.76110e6	−	1.36893e6i	0.103712	−	0.0377482i	−0.289643	−	0.957135i	$-0.593536\pi$
$331$	3.76110e6	−	1.36893e6i	0.103712	−	0.0377482i	0.393355	+	0.919387i	$0.371314\pi$
$332$	−4.22990e7	−	2.44213e7i	−1.15589	−	0.667352i
$333$	−8.46419e6	+	6.52475e6i	−0.229220	+	0.176698i
$334$	−186044.	−	322237.i	−0.00499316	−	0.00864841i
$335$	−5.62017e6	+	6.69786e6i	−0.149491	+	0.178156i
$336$	−1.58210e7	−	2.87621e7i	−0.417078	−	0.758233i
$337$	−7.02138e6	−	3.98202e7i	−0.183456	−	1.04043i	−0.927923	−	0.372773i	$-0.878407\pi$
$337$	−7.02138e6	−	3.98202e7i	−0.183456	−	1.04043i	0.744466	−	0.667660i	$-0.232704\pi$
$338$	2.64135e6	−	465741.i	0.0684030	−	0.0120613i
$339$	512462.	−	2.47469e7i	0.0131542	−	0.635216i
$340$	2.59803e7	+	2.18000e7i	0.661008	+	0.554652i
$341$	−3.08872e6	+	1.78328e6i	−0.0778961	+	0.0449734i
$342$	−4.03037e6	−	2.55505e6i	−0.100755	−	0.0638736i
$343$	2.17187e7	−	3.76178e7i	0.538209	−	0.932205i
$344$	4.47304e6	+	1.22896e7i	0.109882	+	0.301899i
$345$	8.59888e7	+	3.33292e7i	2.09404	+	0.811649i
$346$	−2.13944e6	+	1.79520e6i	−0.0516501	+	0.0433396i
$347$	3.86856e6	−	1.06288e7i	0.0925894	−	0.254387i	−0.884750	−	0.466066i	$-0.845671\pi$
$347$	3.86856e6	−	1.06288e7i	0.0925894	−	0.254387i	0.977339	+	0.211679i	$0.0678931\pi$
$348$	−1.09168e7	−	3.20429e7i	−0.259035	−	0.760316i
$349$	−3.26874e6	+	1.85380e7i	−0.0768962	+	0.436100i	0.921917	+	0.387388i	$0.126623\pi$
$349$	−3.26874e6	+	1.85380e7i	−0.0768962	+	0.436100i	−0.998813	+	0.0487117i	$0.984488\pi$
$350$			1.40053e6i			0.0326655i
$351$	−5.29368e7	−	2.30824e7i	−1.22415	−	0.533776i
$352$	6.01264e6			0.137860
$353$	−2.78966e7	−	4.91893e6i	−0.634202	−	0.111827i	−0.152701	−	0.988272i	$-0.548797\pi$
$353$	−2.78966e7	−	4.91893e6i	−0.634202	−	0.111827i	−0.481501	+	0.876445i	$0.659908\pi$
$354$	1.00545e6	−	5.08426e6i	0.0226647	−	0.114609i
$355$	−3.32313e7	−	1.20952e7i	−0.742783	−	0.270351i
$356$	3.93998e7	+	4.69548e7i	0.873261	+	1.04071i
$357$	2.91252e7	−	4.51594e6i	0.640124	−	0.0992529i
$358$	−2.60711e6	+	948909.i	−0.0568211	+	0.0206812i
$359$	−5.02652e7	−	2.90206e7i	−1.08639	−	0.627226i	−0.153774	−	0.988106i	$-0.549143\pi$
$359$	−5.02652e7	−	2.90206e7i	−1.08639	−	0.627226i	−0.932612	+	0.360880i	$0.882476\pi$
$360$	−9.34411e6	+	2.96904e6i	−0.200277	+	0.0636368i
$361$	−1.90702e7	−	3.30305e7i	−0.405353	−	0.702091i
$362$	−443737.	+	528825.i	−0.00935406	+	0.0111477i
$363$	−1.79724e7	+	2.96919e7i	−0.375739	+	0.620753i
$364$	9.83376e6	+	5.57700e7i	0.203899	+	1.15637i
$365$	6.18768e7	−	1.09105e7i	1.27247	−	0.224372i
$366$	2.25088e6	+	1.36245e6i	0.0459102	+	0.0277892i
$367$	−2.11947e7	−	1.77845e7i	−0.428775	−	0.359785i	0.402714	−	0.915326i	$-0.368067\pi$
$367$	−2.11947e7	−	1.77845e7i	−0.428775	−	0.359785i	−0.831489	+	0.555541i	$0.812511\pi$
$368$	7.95464e7	−	4.59261e7i	1.59616	−	0.921544i
$369$	−4.26680e6	−	1.34284e7i	−0.0849227	−	0.267267i
$370$	773215.	−	1.33925e6i	0.0152649	−	0.0264396i
$371$	1.87630e7	+	5.15510e7i	0.367436	+	1.00952i
$372$	−1.34377e6	−	8.66656e6i	−0.0261034	−	0.168352i
$373$	−2.33543e7	+	1.95966e7i	−0.450030	+	0.377620i	−0.839447	−	0.543442i	$-0.817121\pi$
$373$	−2.33543e7	+	1.95966e7i	−0.450030	+	0.377620i	0.389417	+	0.921061i	$0.372676\pi$
$374$	−607341.	+	1.66866e6i	−0.0116096	+	0.0318972i
$375$	3.59621e7	+	7.11177e6i	0.681948	+	0.134860i
$376$	64090.1	−	363473.i	0.00120567	−	0.00683767i
$377$			5.79328e7i			1.08119i
$378$	−1.69606e6	+	3.88972e6i	−0.0314026	+	0.0720182i
$379$	−1.64433e7			−0.302045			−0.151023	−	0.988530i	$-0.548257\pi$
$379$	−1.64433e7			−0.302045			−0.151023	+	0.988530i	$0.548257\pi$
$380$	−8.58411e7	−	1.51361e7i	−1.56439	−	0.275844i
$381$	1.77424e7	−	6.04472e6i	0.320802	−	0.109295i
$382$	−1.50429e6	−	547519.i	−0.0269863	−	0.00982220i
$383$	1.45340e7	+	1.73210e7i	0.258696	+	0.308302i	0.879722	−	0.475488i	$-0.157728\pi$
$383$	1.45340e7	+	1.73210e7i	0.258696	+	0.308302i	−0.621026	+	0.783790i	$0.713284\pi$
$384$	−7.11487e6	+	1.83562e7i	−0.125653	+	0.324183i
$385$	2.96200e7	−	1.07808e7i	0.519042	−	0.188916i
$386$	5.04820e6	+	2.91458e6i	0.0877757	+	0.0506773i
$387$	−5.64529e7	+	8.90495e7i	−0.973987	+	1.53638i
$388$	−4.95288e7	−	8.57864e7i	−0.847935	−	1.46867i
$389$	−9.00112e6	+	1.07271e7i	−0.152914	+	0.182236i	−0.837063	−	0.547106i	$-0.815729\pi$
$389$	−9.00112e6	+	1.07271e7i	−0.152914	+	0.182236i	0.684149	+	0.729342i	$0.260174\pi$
$390$	8.35469e6	+	173010.i	0.140843	+	0.00291661i
$391$	1.43208e7	+	8.12170e7i	0.239572	+	1.35868i
$392$	−2.24858e6	+	396485.i	−0.0373293	+	0.00658215i
$393$	5.47146e7	−	3.00966e7i	0.901417	−	0.495838i
$394$	1.52910e6	+	1.28307e6i	0.0250005	+	0.0209779i
$395$	−2.43928e7	+	1.40832e7i	−0.395794	+	0.228512i
$396$	1.97035e7	+	2.55602e7i	0.317291	+	0.411604i
$397$	−2.06450e6	+	3.57582e6i	−0.0329946	+	0.0571483i	−0.882051	−	0.471154i	$-0.843838\pi$
$397$	−2.06450e6	+	3.57582e6i	−0.0329946	+	0.0571483i	0.849057	+	0.528302i	$0.177171\pi$
$398$	−3.26111e6	−	8.95983e6i	−0.0517269	−	0.142118i
$399$	−5.90234e7	+	4.74792e7i	−0.929191	+	0.747454i
$400$	−1.99044e7	+	1.67018e7i	−0.311006	+	0.260965i
$401$	1.43065e7	−	3.93068e7i	0.221871	−	0.609586i	−0.777953	−	0.628322i	$-0.783742\pi$
$401$	1.43065e7	−	3.93068e7i	0.221871	−	0.609586i	0.999824	+	0.0187362i	$0.00596426\pi$
$402$	741297.	−	847185.i	0.0114108	−	0.0130407i
$403$	−2.60628e6	+	1.47810e7i	−0.0398205	+	0.225833i
$404$		−	3.89638e7i		−	0.590904i
$405$	−6.49488e7	−	4.50487e7i	−0.977701	−	0.678136i
$406$	4.25681e6			0.0636072
$407$	−1.00657e7	−	1.77486e6i	−0.149301	−	0.0263258i
$408$	−6.59831e6	−	5.77360e6i	−0.0971521	−	0.0850093i
$409$	7.53331e7	+	2.74190e7i	1.10107	+	0.400757i	0.827711	−	0.561154i	$-0.189642\pi$
$409$	7.53331e7	+	2.74190e7i	1.10107	+	0.400757i	0.273361	+	0.961912i	$0.411865\pi$
$410$	1.31053e6	+	1.56183e6i	0.0190150	+	0.0226612i
$411$	−6.93450e7	−	8.62056e7i	−0.998825	−	1.24168i
$412$	4.84529e7	−	1.76354e7i	0.692833	−	0.252171i
$413$	−7.12472e7	−	4.11346e7i	−1.01139	−	0.583925i
$414$	−1.09799e7	−	4.51944e6i	−0.154738	−	0.0636918i
$415$	5.72035e7	+	9.90793e7i	0.800347	+	1.38624i
$416$	1.62643e7	−	1.93831e7i	0.225921	−	0.269242i
$417$	4.95631e7	+	9.01039e7i	0.683518	+	1.24261i
$418$	−792511.	−	4.49455e6i	−0.0108512	−	0.0615400i
$419$	8.65871e7	−	1.52676e7i	1.17709	−	0.207553i	0.449320	−	0.893371i	$-0.351666\pi$
$419$	8.65871e7	−	1.52676e7i	1.17709	−	0.207553i	0.727774	+	0.685817i	$0.240555\pi$
$420$	−1.60474e6	+	7.74931e7i	−0.0216599	+	1.04596i
$421$	6.94296e7	+	5.82583e7i	0.930461	+	0.780749i	0.975900	−	0.218218i	$-0.0700243\pi$
$421$	6.94296e7	+	5.82583e7i	0.930461	+	0.780749i	−0.0454393	+	0.998967i	$0.514469\pi$
$422$	−5.87547e6	+	3.39221e6i	−0.0781818	+	0.0451383i
$423$	2.63623e6	−	1.37979e6i	0.0348307	−	0.0182302i
$424$	8.15978e6	−	1.41332e7i	0.107049	−	0.185414i
$425$	−7.97908e6	−	2.19223e7i	−0.103941	−	0.285575i
$426$	4.24538e6	+	1.64551e6i	0.0549146	+	0.0212849i
$427$	3.19942e7	−	2.68463e7i	0.410949	−	0.344827i
$428$	−4.28580e7	+	1.17751e8i	−0.546639	+	1.50188i
$429$	−1.78117e7	−	5.22806e7i	−0.225597	−	0.662169i
$430$	2.64928e6	−	1.50248e7i	0.0333213	−	0.188975i
$431$		−	1.19228e8i		−	1.48918i	−0.667524	−	0.744589i	$-0.732646\pi$
$431$		−	1.19228e8i		−	1.48918i	0.667524	−	0.744589i	$-0.267354\pi$
$432$	−7.55066e7	+	2.22816e7i	−0.936556	+	0.276372i
$433$	1.44119e8			1.77524			0.887619	−	0.460578i	$-0.152358\pi$
$433$	1.44119e8			1.77524			0.887619	+	0.460578i	$0.152358\pi$
$434$	1.08608e6	+	191506.i	0.0132860	+	0.00234268i
$435$	−1.53827e7	+	7.77859e7i	−0.186881	+	0.945003i
$436$	−1.48621e7	−	5.40938e6i	−0.179317	−	0.0652661i
$437$	−1.36244e8	−	1.62369e8i	−1.63257	−	1.94563i
$438$	−7.99403e6	+	1.23950e6i	−0.0951357	+	0.0147510i
$439$	−7.23436e7	+	2.63309e7i	−0.855080	+	0.311223i	−0.732110	−	0.681187i	$-0.761464\pi$
$439$	−7.23436e7	+	2.63309e7i	−0.855080	+	0.311223i	−0.122970	+	0.992410i	$0.539242\pi$
$440$	−8.12058e6	−	4.68842e6i	−0.0953298	−	0.0550387i
$441$	−1.35990e7	−	1.24057e7i	−0.158559	−	0.144646i
$442$	3.73641e6	+	6.47165e6i	0.0432700	+	0.0749459i
$443$	1.89783e7	−	2.26174e7i	0.218296	−	0.260155i	−0.645772	−	0.763530i	$-0.723464\pi$
$443$	1.89783e7	−	2.26174e7i	0.218296	−	0.260155i	0.864068	+	0.503375i	$0.167909\pi$
$444$	1.30146e7	−	2.15013e7i	0.148690	−	0.245649i
$445$	−2.49316e7	−	1.41394e8i	−0.282924	−	1.60454i
$446$	1.40328e7	−	2.47436e6i	0.158176	−	0.0278906i
$447$	1.60083e6	+	968974.i	0.0179235	+	0.0108490i
$448$	5.81820e7	+	4.88205e7i	0.647075	+	0.542960i
$449$	5.67833e7	−	3.27839e7i	0.627309	−	0.362177i	−0.152400	−	0.988319i	$-0.548700\pi$
$449$	5.67833e7	−	3.27839e7i	0.627309	−	0.362177i	0.779709	+	0.626142i	$0.215367\pi$
$450$	3.28082e6	+	719694.i	0.0360035	+	0.00789787i
$451$	6.73773e6	−	1.16701e7i	0.0734487	−	0.127217i
$452$	1.99092e7	+	5.47002e7i	0.215595	+	0.592343i
$453$	−1.32505e7	−	8.54581e7i	−0.142540	−	0.919302i
$454$	−9.97261e6	+	8.36801e6i	−0.106572	+	0.0894241i
$455$	4.53684e7	−	1.24649e8i	0.481637	−	1.32329i
$456$	2.21059e7	+	4.37160e6i	0.233138	+	0.0461048i
$457$	1.29816e7	−	7.36223e7i	0.136013	−	0.771367i	−0.838136	−	0.545461i	$-0.816355\pi$
$457$	1.29816e7	−	7.36223e7i	0.136013	−	0.771367i	0.974149	−	0.225906i	$-0.0725342\pi$
$458$			6.88999e6i			0.0717170i
$459$	4.38776e6	−	7.05478e7i	0.0453738	−	0.729534i
$460$	−2.16882e8			−2.22818
$461$	1.11001e8	+	1.95725e7i	1.13299	+	0.199776i	0.708536	−	0.705675i	$-0.249356\pi$
$461$	1.11001e8	+	1.95725e7i	1.13299	+	0.199776i	0.424451	+	0.905451i	$0.360467\pi$
$462$	−3.84150e6	+	1.30878e6i	−0.0389561	+	0.0132721i
$463$	−6.01926e7	−	2.19083e7i	−0.606457	−	0.220732i	0.0204952	−	0.999790i	$-0.493476\pi$
$463$	−6.01926e7	−	2.19083e7i	−0.606457	−	0.220732i	−0.626952	+	0.779058i	$0.715698\pi$
$464$	5.07637e7	+	6.04978e7i	0.508159	+	0.605600i
$465$	−7.42418e6	+	1.91542e7i	−0.0738397	+	0.190505i
$466$	−1.21280e7	+	4.41424e6i	−0.119848	+	0.0436213i
$467$	1.81264e7	+	1.04653e7i	0.177975	+	0.102754i	0.586341	−	0.810064i	$-0.300568\pi$
$467$	1.81264e7	+	1.04653e7i	0.177975	+	0.102754i	−0.408366	+	0.912818i	$0.633901\pi$
$468$	1.35697e8	+	5.62250e6i	1.32383	+	0.0548519i
$469$	−8.93468e6	−	1.54753e7i	−0.0866085	−	0.150010i
$470$	−276754.	+	329823.i	−0.00266563	+	0.00317678i
$471$	−6.22730e7	−	1.28956e6i	−0.595987	−	0.0123418i
$472$	4.24976e6	+	2.41016e7i	0.0404146	+	0.229203i
$473$	−9.93053e7	+	1.75102e7i	−0.938403	+	0.165466i
$474$	3.17744e6	−	1.74780e6i	0.0298361	−	0.0164118i
$475$	4.59313e7	+	3.85410e7i	0.428576	+	0.359618i
$476$	−6.00271e7	+	3.46567e7i	−0.556579	+	0.321341i
$477$	1.30403e8	−	1.74628e7i	1.20152	−	0.160901i
$478$	−1.84154e6	+	3.18964e6i	−0.0168615	+	0.0292050i
$479$	3.86866e6	+	1.06291e7i	0.0352009	+	0.0967138i	0.956048	−	0.293210i	$-0.0947235\pi$
$479$	3.86866e6	+	1.06291e7i	0.0352009	+	0.0967138i	−0.920847	+	0.389924i	$0.872501\pi$
$480$	2.69847e7	−	2.17069e7i	0.244002	−	0.196279i
$481$	−3.29497e7	+	2.76481e7i	−0.296085	+	0.248445i
$482$	−5.09345e6	+	1.39941e7i	−0.0454853	+	0.124970i
$483$	−1.24115e8	+	1.41844e8i	−1.10150	+	1.25883i
$484$	1.41737e7	−	8.03833e7i	0.125011	−	0.708973i
$485$			2.32028e8i			2.03383i
$486$	8.24030e6	+	5.97191e6i	0.0717851	+	0.0520241i
$487$	1.15354e8			0.998722			0.499361	−	0.866394i	$-0.333568\pi$
$487$	1.15354e8			0.998722			0.499361	+	0.866394i	$0.333568\pi$
$488$	−1.22356e7	−	2.15747e6i	−0.105285	−	0.0185646i
$489$	3.16567e6	+	2.77000e6i	0.0270731	+	0.0236893i
$490$	2.50293e6	+	910990.i	0.0212745	+	0.00774329i
$491$	4.63127e7	+	5.51934e7i	0.391251	+	0.466275i	0.925332	−	0.379158i	$-0.123786\pi$
$491$	4.63127e7	+	5.51934e7i	0.391251	+	0.466275i	−0.534080	+	0.845434i	$0.679342\pi$
$492$	2.07693e7	+	2.58192e7i	0.174392	+	0.216794i
$493$	−6.66312e7	+	2.42518e7i	−0.556080	+	0.202396i
$494$	−1.66329e7	−	9.60303e6i	−0.137971	−	0.0796576i
$495$	−1.00337e7	−	7.49262e7i	−0.0827267	−	0.617758i
$496$	1.02302e7	+	1.77192e7i	0.0838374	+	0.145211i
$497$	4.64575e7	−	5.53659e7i	0.378431	−	0.450997i
$498$	−7.09928e6	−	1.29062e7i	−0.0574812	−	0.104499i
$499$	7.33769e6	+	4.16141e7i	0.0590551	+	0.334918i	0.999993	−	0.00366012i	$-0.00116506\pi$
$499$	7.33769e6	+	4.16141e7i	0.0590551	+	0.334918i	−0.940938	+	0.338578i	$0.890054\pi$
$500$	−8.49017e7	+	1.49705e7i	−0.679213	+	0.119764i
$501$	−293270.	+	1.41620e7i	−0.00233214	+	0.112619i
$502$	9.72599e6	+	8.16108e6i	0.0768817	+	0.0645114i
$503$	3.88395e6	−	2.24240e6i	0.0305189	−	0.0176201i	−0.484663	−	0.874701i	$-0.661058\pi$
$503$	3.88395e6	−	2.24240e6i	0.0305189	−	0.0176201i	0.515182	+	0.857081i	$0.327724\pi$
$504$	829538.	−	2.00207e7i	0.00647955	−	0.156382i
$505$	−4.56335e7	+	7.90395e7i	−0.354331	+	0.613720i
$506$	−3.88389e6	−	1.06709e7i	−0.0299789	−	0.0823663i
$507$	−9.52038e7	−	3.69010e7i	−0.730517	−	0.283148i
$508$	−3.37677e7	+	2.83344e7i	−0.257579	+	0.216134i
$509$	−3.06663e7	+	8.42550e7i	−0.232546	+	0.638914i	−0.999998	−	0.00219238i	$-0.999302\pi$
$509$	−3.06663e7	+	8.42550e7i	−0.232546	+	0.638914i	0.767452	+	0.641107i	$0.221524\pi$
$510$	3.29844e6	+	9.68154e6i	0.0248656	+	0.0729851i
$511$	−2.22984e7	+	1.26460e8i	−0.167113	+	0.947746i
$512$		−	5.76399e7i		−	0.429451i
$513$	8.08921e7	+	1.62663e8i	0.599175	+	1.20486i
$514$	1.74418e6			0.0128441
$515$	−1.18943e8	−	2.09728e7i	−0.870797	−	0.153545i
$516$	4.81039e7	−	2.43247e8i	0.350131	−	1.77051i
$517$	2.67409e6	+	973289.i	0.0193510	+	0.00704320i
$518$	2.03154e6	+	2.42109e6i	0.0146162	+	0.0174190i
$519$	1.05065e8	−	1.62907e7i	0.751550	−	0.116530i
$520$	−3.70805e7	+	1.34962e7i	−0.263715	+	0.0959845i
$521$	1.91104e8	+	1.10334e8i	1.35131	+	0.780180i	0.988433	−	0.151656i	$-0.0484607\pi$
$521$	1.91104e8	+	1.10334e8i	1.35131	+	0.780180i	0.362878	+	0.931837i	$0.381794\pi$
$522$	2.18745e6	−	9.97180e6i	0.0153790	−	0.0701071i
$523$	1.19091e7	+	2.06272e7i	0.0832480	+	0.144190i	0.904643	−	0.426170i	$-0.140137\pi$
$523$	1.19091e7	+	2.06272e7i	0.0832480	+	0.144190i	−0.821395	+	0.570359i	$0.806804\pi$
$524$	−9.43976e7	+	1.12499e8i	−0.656095	+	0.781904i
$525$	2.76089e7	−	4.56122e7i	0.190797	−	0.315212i
$526$	4.04073e6	+	2.29161e7i	0.0277653	+	0.157465i
$527$	−1.80913e7	+	3.18999e6i	−0.123606	+	0.0217950i
$528$	−6.44113e7	−	3.89879e7i	−0.437583	−	0.264867i
$529$	−2.90601e8	−	2.43843e8i	−1.96304	−	1.64719i
$530$	−1.64871e7	+	9.51885e6i	−0.110743	+	0.0639377i
$531$	−1.32972e8	+	1.45762e8i	−0.888128	+	0.973558i
$532$	8.90719e7	−	1.54277e8i	0.591570	−	1.02463i
$533$	−1.93954e7	−	5.32884e7i	−0.128090	−	0.351926i
$534$	2.83236e6	+	1.82671e7i	0.0186005	+	0.119962i
$535$	2.24847e8	−	1.88669e8i	1.46834	−	1.23208i
$536$	−1.81810e6	+	4.99519e6i	−0.0118066	+	0.0324383i
$537$	1.03613e8	+	2.04903e7i	0.669103	+	0.132320i
$538$	3.31064e6	−	1.87755e7i	0.0212601	−	0.120572i
$539$		−	1.76046e7i		−	0.112424i
$540$	1.80707e8	+	4.35806e7i	1.14761	+	0.276765i
$541$	−9.37600e7			−0.592142			−0.296071	−	0.955166i	$-0.595676\pi$
$541$	−9.37600e7			−0.592142			−0.296071	+	0.955166i	$0.595676\pi$
$542$	209292.	+	36903.8i	0.00131448	+	0.000231779i
$543$	2.48763e7	−	8.47520e6i	0.155377	−	0.0529359i
$544$	2.91019e7	+	1.05922e7i	0.180769	+	0.0657947i
$545$	2.38131e7	+	2.83793e7i	0.147105	+	0.175312i
$546$	−6.17221e6	+	1.59242e7i	−0.0379195	+	0.0978317i
$547$	−8.34800e7	+	3.03842e7i	−0.510059	+	0.185646i	−0.584213	−	0.811601i	$-0.698597\pi$
$547$	−8.34800e7	+	3.03842e7i	−0.510059	+	0.185646i	0.0741538	+	0.997247i	$0.476374\pi$
$548$	2.25327e8	+	1.30093e8i	1.36921	+	0.790516i
$549$	−4.64480e7	−	8.87435e7i	−0.280705	−	0.536315i
$550$	1.60617e6	+	2.78196e6i	0.00965390	+	0.0167210i
$551$	1.17142e8	−	1.39605e8i	0.700259	−	0.834536i
$552$	5.60565e7	+	1.16083e6i	0.333280	+	0.00690161i
$553$	−9.99603e6	−	5.66903e7i	−0.0591088	−	0.335223i
$554$	538724.	−	94991.6i	0.00316838	−	0.000558670i
$555$	−5.15825e7	+	2.83738e7i	−0.301734	+	0.165973i
$556$	−1.85263e8	−	1.55454e8i	−1.07786	−	0.904434i
$557$	−1.72953e8	+	9.98544e7i	−1.00083	+	0.577832i	−0.908495	−	0.417895i	$-0.862768\pi$
$557$	−1.72953e8	+	9.98544e7i	−1.00083	+	0.577832i	−0.0923396	+	0.995728i	$0.529435\pi$
$558$	1.00672e6	−	2.44580e6i	0.00579436	−	0.0140772i
$559$	−2.12175e8	+	3.67498e8i	−1.21467	+	2.10387i
$560$	−6.18465e7	−	1.69922e8i	−0.352169	−	0.967577i
$561$	5.26741e7	−	4.23717e7i	0.298338	−	0.239987i
$562$	1.44000e7	−	1.20830e7i	0.0811245	−	0.0680716i
$563$	−5.66304e6	+	1.55591e7i	−0.0317340	+	0.0871883i	−0.954548	−	0.298058i	$-0.903661\pi$
$563$	−5.66304e6	+	1.55591e7i	−0.0317340	+	0.0871883i	0.922814	+	0.385246i	$0.125883\pi$
$564$	−4.60797e6	+	5.26617e6i	−0.0256846	+	0.0293534i
$565$	2.36770e7	−	1.34279e8i	0.131275	−	0.744495i
$566$			2.89586e6i			0.0159709i
$567$	1.31915e8	−	9.32446e7i	0.723678	−	0.511534i
$568$	−2.15004e7			−0.117328
$569$	1.92631e8	+	3.39661e7i	1.04566	+	0.184378i	0.669985	−	0.742374i	$-0.266300\pi$
$569$	1.92631e8	+	3.39661e7i	1.04566	+	0.184378i	0.375673	+	0.926752i	$0.377412\pi$
$570$	−1.97830e7	−	1.73104e7i	−0.106824	−	0.0934722i
$571$	1.53073e8	+	5.57140e7i	0.822223	+	0.299265i	0.718663	−	0.695358i	$-0.244754\pi$
$571$	1.53073e8	+	5.57140e7i	0.822223	+	0.299265i	0.103560	+	0.994623i	$0.466977\pi$
$572$	8.34918e7	+	9.95017e7i	0.446124	+	0.531670i
$573$	3.81982e7	+	4.74857e7i	0.203039	+	0.252406i
$574$	−3.91555e6	+	1.42514e6i	−0.0207041	+	0.00753569i
$575$	1.29201e8	+	7.45943e7i	0.679615	+	0.392376i
$576$	1.44262e8	−	1.11207e8i	0.754894	−	0.581921i
$577$	1.92427e7	+	3.33294e7i	0.100170	+	0.173500i	0.911755	−	0.410735i	$-0.134728\pi$
$577$	1.92427e7	+	3.33294e7i	0.100170	+	0.173500i	−0.811584	+	0.584235i	$0.801395\pi$
$578$	5.12481e6	−	6.10751e6i	0.0265396	−	0.0316287i
$579$	−1.06953e8	−	1.94437e8i	−0.551007	−	1.00171i
$580$	−3.23810e7	−	1.83642e8i	−0.165961	−	0.941213i
$581$	−2.30267e8	+	4.06022e7i	−1.17409	+	0.207024i
$582$	618496.	−	2.98673e7i	0.00313739	−	0.151505i
$583$	9.63900e7	+	8.08808e7i	0.486437	+	0.408169i
$584$	3.30820e7	−	1.90999e7i	0.166094	−	0.0958941i
$585$	−2.68683e8	−	1.70331e8i	−1.34206	−	0.850798i
$586$	7.16830e6	−	1.24159e7i	0.0356224	−	0.0616998i
$587$	−8.64805e7	−	2.37603e8i	−0.427567	−	1.17473i	−0.947285	−	0.320392i	$-0.896185\pi$
$587$	−8.64805e7	−	2.37603e8i	−0.427567	−	1.17473i	0.519718	−	0.854338i	$-0.326037\pi$
$588$	4.03636e7	+	1.56449e7i	0.198544	+	0.0769558i
$589$	3.61682e7	−	3.03487e7i	0.177003	−	0.148523i
$590$	9.76455e6	−	2.68279e7i	0.0475441	−	0.130626i
$591$	−2.45061e7	−	7.19300e7i	−0.118717	−	0.348456i
$592$	−1.01819e7	+	5.77444e7i	−0.0490754	+	0.278320i
$593$		−	1.71186e8i		−	0.820927i	−0.911877	−	0.410464i	$-0.865367\pi$
$593$		−	1.71186e8i		−	0.820927i	0.911877	−	0.410464i	$-0.134633\pi$
$594$	1.09184e6	+	9.67145e6i	0.00520955	+	0.0461458i
$595$	1.62356e8			0.770759
$596$	−4.33383e6	−	764171.i	−0.0204707	−	0.00360954i
$597$	−7.04189e7	+	3.56088e8i	−0.330953	+	1.67353i
$598$	−4.49060e7	−	1.63445e7i	−0.209991	−	0.0764305i
$599$	−2.33951e8	−	2.78811e8i	−1.08854	−	1.29727i	−0.951819	−	0.306660i	$-0.900789\pi$
$599$	−2.33951e8	−	2.78811e8i	−1.08854	−	1.29727i	−0.136719	−	0.990610i	$-0.543656\pi$
$600$	−1.56735e7	+	2.43022e6i	−0.0725625	+	0.0112510i
$601$	7.44373e7	−	2.70930e7i	0.342900	−	0.124805i	−0.164829	−	0.986322i	$-0.552707\pi$
$601$	7.44373e7	−	2.70930e7i	0.342900	−	0.124805i	0.507729	+	0.861517i	$0.330485\pi$
$602$	2.70032e7	+	1.55903e7i	0.123773	+	0.0714603i
$603$	−4.08430e7	+	1.29776e7i	−0.186280	+	0.0591893i
$604$	1.01688e8	+	1.76129e8i	0.461488	+	0.799320i
$605$	−1.22895e8	+	1.46461e8i	−0.554969	+	0.661386i
$606$	6.08476e6	−	1.00525e7i	0.0273417	−	0.0451708i
$607$	1.03015e7	+	5.84229e7i	0.0460612	+	0.261226i	0.999138	−	0.0415011i	$-0.0132140\pi$
$607$	1.03015e7	+	5.84229e7i	0.0460612	+	0.261226i	−0.953077	+	0.302727i	$0.902103\pi$
$608$	−7.83865e7	+	1.38217e7i	−0.348763	+	0.0614964i
$609$	−1.38635e8	−	8.39149e7i	−0.613790	−	0.371524i
$610$	1.11028e7	+	9.31640e6i	0.0489153	+	0.0410448i
$611$	1.03711e7	−	5.98775e6i	0.0454674	−	0.0262506i
$612$	5.03388e7	+	1.58426e8i	0.219608	+	0.691148i
$613$	7.06033e6	−	1.22288e7i	0.0306509	−	0.0530889i	−0.850293	−	0.526310i	$-0.823575\pi$
$613$	7.06033e6	−	1.22288e7i	0.0306509	−	0.0530889i	0.880944	+	0.473221i	$0.156909\pi$
$614$	3.10375e6	+	8.52748e6i	0.0134085	+	0.0368397i
$615$	−1.18925e7	−	7.66999e7i	−0.0511268	−	0.329738i
$616$	1.46804e7	−	1.23183e7i	0.0628051	−	0.0526998i
$617$	−1.41606e8	+	3.89059e8i	−0.602873	+	1.65638i	0.142548	+	0.989788i	$0.454470\pi$
$617$	−1.41606e8	+	3.89059e8i	−0.602873	+	1.65638i	−0.745422	+	0.666593i	$0.767752\pi$
$618$	1.52547e7	+	3.01674e6i	0.0646308	+	0.0127812i
$619$	−4.00915e7	+	2.27370e8i	−0.169037	+	0.958654i	0.775768	+	0.631019i	$0.217363\pi$
$619$	−4.00915e7	+	2.27370e8i	−0.169037	+	0.958654i	−0.944804	+	0.327635i	$0.893748\pi$
$620$		−	4.83112e7i		−	0.202709i
$621$	2.68497e8	+	3.63635e8i	1.12115	+	1.51842i
$622$	2.08102e7			0.0864779
$623$	2.88973e8	+	5.09538e7i	1.19507	+	0.210723i
$624$	−2.99920e8	+	1.02181e8i	−1.23439	+	0.420549i
$625$	2.85144e8	+	1.03784e8i	1.16795	+	0.425099i
$626$	8.82515e6	+	1.05174e7i	0.0359749	+	0.0428732i
$627$	−6.27912e7	+	1.62000e8i	−0.254740	+	0.657223i
$628$	1.37647e8	−	5.00995e7i	0.555762	−	0.202281i
$629$	−4.55927e7	−	2.63229e7i	−0.183207	−	0.105775i
$630$	−1.25157e7	+	1.97424e7i	−0.0500533	+	0.0789547i
$631$	9.36939e7	+	1.62283e8i	0.372927	+	0.645928i	0.990014	−	0.140966i	$-0.0450210\pi$
$631$	9.36939e7	+	1.62283e8i	0.372927	+	0.645928i	−0.617088	+	0.786894i	$0.711688\pi$
$632$	−1.10073e7	+	1.31180e7i	−0.0436044	+	0.0519658i
$633$	2.58222e8	+	5.34730e6i	1.01808	+	0.0210825i
$634$	−5.12405e6	−	2.90600e7i	−0.0201069	−	0.114032i
$635$	1.01684e8	−	1.79296e7i	0.397128	−	0.0700243i
$636$	−2.71103e8	+	1.49124e8i	−1.05381	+	0.579665i
$637$	−5.67522e7	−	4.76208e7i	−0.219566	−	0.184238i
$638$	8.45556e6	−	4.88182e6i	0.0325597	−	0.0187983i
$639$	−1.05824e8	−	1.37280e8i	−0.405586	−	0.526144i
$640$	−5.42237e7	+	9.39181e7i	−0.206847	+	0.358269i
$641$	−2.97908e7	−	8.18497e7i	−0.113112	−	0.310773i	0.870200	−	0.492698i	$-0.163989\pi$
$641$	−2.97908e7	−	8.18497e7i	−0.113112	−	0.310773i	−0.983312	+	0.181925i	$0.941767\pi$
$642$	−2.94458e7	+	2.36866e7i	−0.111280	+	0.0895155i
$643$	−1.56252e8	+	1.31111e8i	−0.587748	+	0.493179i	−0.887481	−	0.460844i	$-0.847547\pi$
$643$	−1.56252e8	+	1.31111e8i	−0.587748	+	0.493179i	0.299733	+	0.954023i	$0.403102\pi$
$644$	1.51601e8	−	4.16521e8i	0.567604	−	1.55948i
$645$	−3.82466e8	+	4.37098e8i	−1.42533	+	1.62892i
$646$	4.08203e6	−	2.31503e7i	0.0151418	−	0.0858736i
$647$		−	4.80555e8i		−	1.77431i	−0.461469	−	0.887157i	$-0.652677\pi$
$647$		−	4.80555e8i		−	1.77431i	0.461469	−	0.887157i	$-0.347323\pi$
$648$	−4.64731e7	−	1.22313e7i	−0.170796	−	0.0449517i
$649$	−1.88697e8			−0.690288
$650$	1.33130e7	+	2.34744e6i	0.0484770	+	0.00854780i
$651$	−3.15961e7	−	2.76470e7i	−0.114522	−	0.100208i
$652$	−9.29591e6	−	3.38344e6i	−0.0335389	−	0.0122072i
$653$	3.45488e7	+	4.11737e7i	0.124078	+	0.147870i	0.824507	−	0.565852i	$-0.191453\pi$
$653$	3.45488e7	+	4.11737e7i	0.124078	+	0.147870i	−0.700429	+	0.713722i	$0.747008\pi$
$654$	−2.98964e6	−	3.71654e6i	−0.0106877	−	0.0132864i
$655$	3.23245e8	−	1.17652e8i	1.15029	−	0.418672i
$656$	−6.69482e7	−	3.86525e7i	−0.237152	−	0.136920i
$657$	2.84782e8	+	1.17219e8i	1.00419	+	0.413336i
$658$	−439971.	−	762051.i	−0.00154435	−	0.00267489i
$659$	1.46624e8	−	1.74739e8i	0.512328	−	0.610569i	−0.446421	−	0.894823i	$-0.647302\pi$
$659$	1.46624e8	−	1.74739e8i	0.512328	−	0.610569i	0.958749	+	0.284254i	$0.0917460\pi$
$660$	8.56834e7	+	1.55769e8i	0.298033	+	0.541814i
$661$	−1.39724e7	−	7.92417e7i	−0.0483802	−	0.274378i	0.951015	−	0.309144i	$-0.100043\pi$
$661$	−1.39724e7	−	7.92417e7i	−0.0483802	−	0.274378i	−0.999395	+	0.0347660i	$0.988931\pi$
$662$	−2.79557e6	+	492935.i	−0.00963600	+	0.00169909i
$663$	5.88987e6	−	2.84423e8i	0.0202100	−	0.975942i
$664$	5.32832e7	+	4.47100e7i	0.182006	+	0.152721i
$665$	−3.61372e8	+	2.08638e8i	−1.22882	+	0.709461i
$666$	6.71548e6	−	3.51485e6i	0.0227329	−	0.0118983i
$667$	2.26723e8	−	3.92697e8i	0.764045	−	1.32336i
$668$	−1.13936e7	−	3.13036e7i	−0.0382235	−	0.105018i
$669$	−5.05793e8	−	1.96045e8i	−1.68925	−	0.654754i
$670$	4.75036e6	−	3.98602e6i	0.0157944	−	0.0132530i
$671$	3.27639e7	−	9.00181e7i	0.108450	−	0.297963i
$672$	2.28255e7	+	6.69971e7i	0.0752165	+	0.220774i
$673$	−3.64773e7	+	2.06873e8i	−0.119668	+	0.678670i	0.864665	+	0.502349i	$0.167531\pi$
$673$	−3.64773e7	+	2.06873e8i	−0.119668	+	0.678670i	−0.984333	+	0.176321i	$0.943580\pi$
$674$			2.86776e7i			0.0936619i
$675$	−9.26615e7	−	8.81139e7i	−0.301292	−	0.286506i
$676$	2.40125e8			0.777314
$677$	−4.35784e8	−	7.68405e7i	−1.40445	−	0.247642i	−0.580478	−	0.814276i	$-0.697134\pi$
$677$	−4.35784e8	−	7.68405e7i	−1.40445	−	0.247642i	−0.823970	+	0.566634i	$0.808245\pi$
$678$	−3.40570e6	+	1.72216e7i	−0.0109274	+	0.0552566i
$679$	−4.45608e8	−	1.62188e8i	−1.42346	−	0.518096i
$680$	−3.10452e7	−	3.69982e7i	−0.0987342	−	0.117667i
$681$	4.89744e8	−	7.59362e7i	1.55070	−	0.240440i
$682$	2.37698e6	−	865148.i	0.00749327	−	0.00272733i
$683$	4.67606e8	+	2.69973e8i	1.46764	+	0.847340i	0.999343	−	0.0362338i	$-0.0115361\pi$
$683$	4.67606e8	+	2.69973e8i	1.46764	+	0.847340i	0.468292	+	0.883574i	$0.344869\pi$
$684$	−3.15630e8	−	2.87934e8i	−0.986303	−	0.899755i
$685$	−3.04723e8	−	5.27796e8i	−0.948055	−	1.64208i
$686$	−1.98025e7	+	2.35997e7i	−0.0613407	+	0.0731030i
$687$	1.35823e8	−	2.24391e8i	0.418893	−	0.692047i
$688$	1.00451e8	+	5.69688e8i	0.308454	+	1.74933i
$689$	5.21474e8	−	9.19500e7i	1.59432	−	0.281121i
$690$	−5.59550e7	−	3.38693e7i	−0.170330	−	0.103100i
$691$	2.10990e8	+	1.77041e8i	0.639480	+	0.536587i	0.903858	−	0.427832i	$-0.140722\pi$
$691$	2.10990e8	+	1.77041e8i	0.639480	+	0.536587i	−0.264378	+	0.964419i	$0.585167\pi$
$692$	−2.16540e8	+	1.25020e8i	−0.653462	+	0.377277i
$693$	1.50909e8	+	3.31039e7i	0.453435	+	0.0994672i
$694$	−4.01105e6	+	6.94735e6i	−0.0120000	+	0.0207845i
$695$	1.93749e8	+	5.32320e8i	0.577144	+	1.58569i
$696$	7.38645e6	+	4.76383e7i	0.0219083	+	0.141296i
$697$	5.31702e7	−	4.46151e7i	0.157025	−	0.131760i
$698$	4.56618e6	−	1.25455e7i	0.0134272	−	0.0368910i
$699$	4.82001e8	+	9.53191e7i	1.41129	+	0.279093i
$700$	−2.17734e7	+	1.23483e8i	−0.0634794	+	0.360010i
$701$		−	1.47665e8i		−	0.428670i	−0.976760	−	0.214335i	$-0.931242\pi$
$701$		−	1.47665e8i		−	0.428670i	0.976760	−	0.214335i	$-0.0687585\pi$
$702$	3.41315e7	+	2.26417e7i	0.0986607	+	0.0654482i
$703$	1.35306e8			0.389451
$704$	1.71559e8	+	3.02504e7i	0.491694	+	0.0866989i
$705$	1.55151e7	−	5.28589e6i	0.0442778	−	0.0150852i
$706$	1.88789e7	+	6.87136e6i	0.0536491	+	0.0195267i
$707$	−1.19897e8	−	1.42888e8i	−0.339274	−	0.404331i
$708$	1.67692e8	−	4.32641e8i	0.472511	−	1.21907i
$709$	−4.69863e8	+	1.71016e8i	−1.31836	+	0.479842i	−0.902931	−	0.429785i	$-0.858589\pi$
$709$	−4.69863e8	+	1.71016e8i	−1.31836	+	0.479842i	−0.415425	+	0.909628i	$0.636367\pi$
$710$	2.17211e7	+	1.25407e7i	0.0606886	+	0.0350386i
$711$	−1.37937e8	−	5.71527e6i	−0.383770	−	0.0159011i
$712$	−4.36449e7	−	7.55952e7i	−0.120919	−	0.209437i
$713$	7.55129e7	−	8.99927e7i	0.208330	−	0.248278i
$714$	−2.08990e7	−	432779.i	−0.0574156	−	0.00118897i
$715$	−5.28323e7	−	2.99627e8i	−0.144538	−	0.819714i
$716$	−2.44617e8	+	4.31326e7i	−0.666420	+	0.117508i
$717$	1.22852e8	−	6.75768e7i	0.333293	−	0.183333i
$718$	3.15342e7	+	2.64603e7i	0.0851938	+	0.0714861i
$719$	−4.69589e8	+	2.71117e8i	−1.26337	+	0.729408i	−0.973725	−	0.227726i	$-0.926871\pi$
$719$	−4.69589e8	+	2.71117e8i	−1.26337	+	0.729408i	−0.289646	+	0.957134i	$0.593537\pi$
$720$	−4.29832e8	+	5.75607e7i	−1.15160	+	0.154216i
$721$	1.23420e8	−	2.13769e8i	0.329290	−	0.570347i
$722$	9.25181e6	+	2.54191e7i	0.0245819	+	0.0675381i
$723$	4.41750e8	−	3.55349e8i	1.16886	−	0.940244i
$724$	−4.73451e7	+	3.97272e7i	−0.124755	+	0.104682i
$725$	−4.38716e7	+	1.20536e8i	−0.115125	+	0.316303i
$726$	1.62098e7	−	1.85252e7i	0.0423611	−	0.0484120i
$727$	1.13129e8	−	6.41588e8i	0.294423	−	1.66976i	−0.375114	−	0.926979i	$-0.622397\pi$
$727$	1.13129e8	−	6.41588e8i	0.294423	−	1.66976i	0.669537	−	0.742778i	$-0.266492\pi$
$728$		−	8.06467e7i		−	0.209022i
$729$	−1.50643e8	−	3.56933e8i	−0.388836	−	0.921307i
$730$	−4.45622e7			−0.114551
$731$	−5.11497e8	−	9.01907e7i	−1.30946	−	0.230892i
$732$	1.77276e8	+	1.55118e8i	0.451977	+	0.395485i
$733$	−4.99096e7	−	1.81656e7i	−0.126728	−	0.0461252i	0.277878	−	0.960616i	$-0.410369\pi$
$733$	−4.99096e7	−	1.81656e7i	−0.126728	−	0.0461252i	−0.404606	+	0.914491i	$0.632591\pi$
$734$	1.26134e7	+	1.50320e7i	0.0318965	+	0.0380128i
$735$	−6.35561e7	−	7.90093e7i	−0.160065	−	0.198983i
$736$	−1.86104e8	+	6.77364e7i	−0.466791	+	0.169898i
$737$	−3.54950e7	−	2.04930e7i	−0.0886674	−	0.0511922i
$738$	1.32638e6	+	9.90471e6i	0.00329990	+	0.0246418i
$739$	4.05786e7	+	7.02843e7i	0.100546	+	0.174151i	0.911910	−	0.410391i	$-0.134608\pi$
$739$	4.05786e7	+	7.02843e7i	0.100546	+	0.174151i	−0.811364	+	0.584541i	$0.801274\pi$
$740$	8.89939e7	−	1.06059e8i	0.219617	−	0.261729i
$741$	3.52391e8	+	6.40635e8i	0.866105	+	1.57455i
$742$	−6.75635e6	−	3.83171e7i	−0.0165387	−	0.0937954i
$743$	6.87876e8	−	1.21291e8i	1.67704	−	0.295708i	0.747455	−	0.664312i	$-0.231275\pi$
$743$	6.87876e8	−	1.21291e8i	1.67704	−	0.295708i	0.929586	+	0.368604i	$0.120164\pi$
$744$	−258578.	+	1.24867e7i	−0.000627873	+	0.0303201i
$745$	7.89636e6	+	6.62583e6i	0.0190967	+	0.0160240i
$746$	1.87255e7	−	1.08112e7i	0.0451043	−	0.0260410i
$747$	−2.32145e7	+	5.60275e8i	−0.0556926	+	1.34413i
$748$	−7.94902e7	+	1.37681e8i	−0.189937	+	0.328980i
$749$	2.05169e8	+	5.63698e8i	0.488278	+	1.34153i
$750$	−2.42422e7	−	9.39629e6i	−0.0574631	−	0.0222727i
$751$	−2.48860e8	+	2.08818e8i	−0.587537	+	0.493002i	−0.887413	−	0.460976i	$-0.847499\pi$
$751$	−2.48860e8	+	2.08818e8i	−0.587537	+	0.493002i	0.299875	+	0.953978i	$0.403055\pi$
$752$	5.58350e6	−	1.53405e7i	0.0131296	−	0.0360734i
$753$	−1.55873e8	−	4.57517e8i	−0.365079	−	1.07157i
$754$	7.13485e6	−	4.04638e7i	0.0166445	−	0.0943957i
$755$		−	4.76380e8i		−	1.10691i
$756$	−2.10011e8	+	3.16583e8i	−0.486044	+	0.732694i
$757$	−5.24421e8			−1.20891			−0.604453	−	0.796641i	$-0.706608\pi$
$757$	−5.24421e8			−1.20891			−0.604453	+	0.796641i	$0.706608\pi$
$758$	1.14850e7	+	2.02512e6i	0.0263708	+	0.00464989i
$759$	−8.38670e7	+	4.24091e8i

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)

\(f(q)\)	\(=\)	\(q+(-0.698460 - 0.123157i) q^{2} +(20.3194 + 17.7798i) q^{3} +(-59.6676 - 21.7172i) q^{4} +(95.6034 + 113.936i) q^{5} +(-12.0026 - 14.9210i) q^{6} +(-285.640 + 103.964i) q^{7} +(78.3107 + 45.2127i) q^{8} +(96.7599 + 722.550i) q^{9} +O(q^{10})\)	\(q+(-0.698460 - 0.123157i) q^{2} +(20.3194 + 17.7798i) q^{3} +(-59.6676 - 21.7172i) q^{4} +(95.6034 + 113.936i) q^{5} +(-12.0026 - 14.9210i) q^{6} +(-285.640 + 103.964i) q^{7} +(78.3107 + 45.2127i) q^{8} +(96.7599 + 722.550i) q^{9} +(-52.7432 - 91.3539i) q^{10} +(-448.154 + 534.089i) q^{11} +(-826.286 - 1502.16i) q^{12} +(509.487 + 2889.45i) q^{13} +(212.312 - 37.4364i) q^{14} +(-83.1416 + 4014.92i) q^{15} +(3063.93 + 2570.94i) q^{16} +(-3110.01 + 1795.56i) q^{17} +(21.4044 - 516.589i) q^{18} +(4614.82 - 7993.10i) q^{19} +(-3230.06 - 8874.52i) q^{20} +(-7652.51 - 2966.11i) q^{21} +(378.795 - 317.847i) q^{22} +(7854.47 - 21580.0i) q^{23} +(787.359 + 2311.04i) q^{24} +(-1128.08 + 6397.67i) q^{25} -2080.91i q^{26} +(-10880.7 + 16402.2i) q^{27} +19301.3 q^{28} +(19445.2 + 3428.72i) q^{29} +(552.538 - 2794.02i) q^{30} +(4807.00 + 1749.61i) q^{31} +(-5543.36 - 6606.32i) q^{32} +(-18602.2 + 2884.33i) q^{33} +(2393.35 - 871.109i) q^{34} +(-39153.4 - 22605.2i) q^{35} +(9918.36 - 45214.2i) q^{36} +(7330.00 + 12695.9i) q^{37} +(-4207.68 + 5014.52i) q^{38} +(-41021.2 + 67770.5i) q^{39} +(2335.43 + 13244.9i) q^{40} +(-19034.2 + 3356.25i) q^{41} +(4979.68 + 3014.17i) q^{42} +(110794. + 92967.0i) q^{43} +(38339.3 - 22135.2i) q^{44} +(-73073.7 + 80102.7i) q^{45} +(-8143.77 + 14105.4i) q^{46} +(-1395.99 - 3835.45i) q^{47} +(16546.6 + 106716. i) q^{48} +(-19342.8 + 16230.6i) q^{49} +(1575.84 - 4329.59i) q^{50} +(-95118.3 - 18810.3i) q^{51} +(32350.9 - 183471. i) q^{52} -180475. i q^{53} +(9619.76 - 10116.2i) q^{54} -103697. q^{55} +(-27069.2 - 4773.02i) q^{56} +(235886. - 80365.0i) q^{57} +(-13159.4 - 4789.65i) q^{58} +(173969. + 207328. i) q^{59} +(92153.8 - 237755. i) q^{60} +(-129113. + 46993.3i) q^{61} +(-3142.02 - 1814.05i) q^{62} +(-102758. - 196330. i) q^{63} +(-124931. - 216387. i) q^{64} +(-280502. + 334290. i) q^{65} +(13348.1 + 276.416i) q^{66} +(10208.1 + 57893.2i) q^{67} +(224561. - 39596.2i) q^{68} +(543285. - 298843. i) q^{69} +(24563.1 + 20610.9i) q^{70} +(-205914. + 118885. i) q^{71} +(-25091.1 + 60958.1i) q^{72} +(211223. - 365848. i) q^{73} +(-3556.12 - 9770.35i) q^{74} +(-136671. + 109940. i) q^{75} +(-448944. + 376708. i) q^{76} +(72484.4 - 199149. i) q^{77} +(36998.1 - 42283.0i) q^{78} +(-32884.7 + 186499. i) q^{79} +594882. i q^{80} +(-512716. + 139828. i) q^{81} +13708.0 q^{82} +(757527. + 133572. i) q^{83} +(392191. + 343172. i) q^{84} +(-501906. - 182679. i) q^{85} +(-65935.4 - 78578.8i) q^{86} +(334154. + 415401. i) q^{87} +(-59242.9 + 21562.6i) q^{88} +(-835996. - 482662. i) q^{89} +(60904.3 - 46949.0i) q^{90} +(-445930. - 772373. i) q^{91} +(-937315. + 1.11705e6i) q^{92} +(66568.0 + 121018. i) q^{93} +(502.679 + 2850.83i) q^{94} +(1.35189e6 - 238375. i) q^{95} +(4820.78 - 232796. i) q^{96} +(1.19506e6 + 1.00277e6i) q^{97} +(15509.1 - 8954.19i) q^{98} +(-429270. - 272135. i) 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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