Properties

Label 12.20.b.a.11.13
Level 12
Weight 20
Character 12.11
Analytic conductor 27.458
Analytic rank 0
Dimension 36
CM No

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(27.4580035868\)
Analytic rank: \(0\)
Dimension: \(36\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.13
Character \(\chi\) = 12.11
Dual form 12.20.b.a.11.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-246.303 - 680.898i) q^{2} +(12845.9 - 31579.2i) q^{3} +(-402957. + 335415. i) q^{4} +225554. i q^{5} +(-2.46662e7 - 968699. i) q^{6} +9.84546e7i q^{7} +(3.27633e8 + 1.91759e8i) q^{8} +(-8.32227e8 - 8.11326e8i) q^{9} +O(q^{10})\) \(q+(-246.303 - 680.898i) q^{2} +(12845.9 - 31579.2i) q^{3} +(-402957. + 335415. i) q^{4} +225554. i q^{5} +(-2.46662e7 - 968699. i) q^{6} +9.84546e7i q^{7} +(3.27633e8 + 1.91759e8i) q^{8} +(-8.32227e8 - 8.11326e8i) q^{9} +(1.53579e8 - 5.55547e7i) q^{10} +6.04702e9 q^{11} +(5.41578e9 + 1.70338e10i) q^{12} +4.74938e10 q^{13} +(6.70376e10 - 2.42497e10i) q^{14} +(7.12281e9 + 2.89744e9i) q^{15} +(4.98716e10 - 2.70316e11i) q^{16} +8.55357e11i q^{17} +(-3.47450e11 + 7.66494e11i) q^{18} -3.94199e11i q^{19} +(-7.56542e10 - 9.08887e10i) q^{20} +(3.10912e12 + 1.26474e12i) q^{21} +(-1.48940e12 - 4.11741e12i) q^{22} -5.41125e10 q^{23} +(1.02643e13 - 7.88307e12i) q^{24} +1.90226e13 q^{25} +(-1.16979e13 - 3.23384e13i) q^{26} +(-3.63117e13 + 1.58589e13i) q^{27} +(-3.30231e13 - 3.96730e13i) q^{28} -3.42747e12i q^{29} +(2.18494e11 - 5.56356e12i) q^{30} -2.38228e14i q^{31} +(-1.96341e14 + 3.26222e13i) q^{32} +(7.76794e13 - 1.90960e14i) q^{33} +(5.82411e14 - 2.10677e14i) q^{34} -2.22068e13 q^{35} +(6.07483e14 + 4.77882e13i) q^{36} +4.65196e14 q^{37} +(-2.68410e14 + 9.70925e13i) q^{38} +(6.10100e14 - 1.49981e15i) q^{39} +(-4.32521e13 + 7.38990e13i) q^{40} -2.62403e14i q^{41} +(9.53729e13 - 2.42850e15i) q^{42} +2.87474e13i q^{43} +(-2.43669e15 + 2.02826e15i) q^{44} +(1.82998e14 - 1.87712e14i) q^{45} +(1.33281e13 + 3.68451e13i) q^{46} -5.76501e15 q^{47} +(-7.89571e15 - 5.04735e15i) q^{48} +1.70559e15 q^{49} +(-4.68533e15 - 1.29525e16i) q^{50} +(2.70115e16 + 1.09878e16i) q^{51} +(-1.91380e16 + 1.59301e16i) q^{52} +3.52779e16i q^{53} +(1.97420e16 + 2.08185e16i) q^{54} +1.36393e15i q^{55} +(-1.88796e16 + 3.22570e16i) q^{56} +(-1.24485e16 - 5.06384e15i) q^{57} +(-2.33376e15 + 8.44196e14i) q^{58} +1.05866e17 q^{59} +(-3.84204e15 + 1.22155e15i) q^{60} -5.09395e16 q^{61} +(-1.62209e17 + 5.86764e16i) q^{62} +(7.98787e16 - 8.19366e16i) q^{63} +(7.05719e16 + 1.25653e17i) q^{64} +1.07124e16i q^{65} +(-1.49157e17 - 5.85774e15i) q^{66} -1.29179e17i q^{67} +(-2.86899e17 - 3.44672e17i) q^{68} +(-6.95124e14 + 1.70883e15i) q^{69} +(5.46961e15 + 1.51206e16i) q^{70} +4.53111e17 q^{71} +(-1.17086e17 - 4.25405e17i) q^{72} +8.94130e17 q^{73} +(-1.14579e17 - 3.16751e17i) q^{74} +(2.44362e17 - 6.00718e17i) q^{75} +(1.32220e17 + 1.58846e17i) q^{76} +5.95357e17i q^{77} +(-1.17149e18 - 4.60072e16i) q^{78} -6.91414e17i q^{79} +(6.09709e16 + 1.12487e16i) q^{80} +(3.43532e16 + 1.35041e18i) q^{81} +(-1.78670e17 + 6.46307e16i) q^{82} +2.08387e18 q^{83} +(-1.67705e18 + 5.33208e17i) q^{84} -1.92929e17 q^{85} +(1.95741e16 - 7.08058e15i) q^{86} +(-1.08237e17 - 4.40289e16i) q^{87} +(1.98120e18 + 1.15957e18i) q^{88} -2.97330e18i q^{89} +(-1.72886e17 - 7.83688e16i) q^{90} +4.67598e18i q^{91} +(2.18050e16 - 1.81501e16i) q^{92} +(-7.52305e18 - 3.06026e18i) q^{93} +(1.41994e18 + 3.92538e18i) q^{94} +8.89132e16 q^{95} +(-1.49200e18 + 6.61936e18i) q^{96} +9.21289e17 q^{97} +(-4.20091e17 - 1.16133e18i) q^{98} +(-5.03250e18 - 4.90610e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} + O(q^{10}) \) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} - 4162950000q^{10} - 2268767880q^{12} - 25913431656q^{13} + 791689296672q^{16} + 2852271258192q^{18} - 1650825908424q^{21} + 7247870602416q^{22} + 23719435803936q^{24} - 118879690462380q^{25} - 7629081673968q^{28} + 37456727138640q^{30} + 529254701828640q^{33} - 248241675948480q^{34} - 1177548745309416q^{36} + 1847838600168120q^{37} - 40433256181440q^{40} - 2709671988768336q^{42} - 4365410114088000q^{45} + 17206125364795104q^{46} + 1561106052682272q^{48} - 49399737041580084q^{49} + 16558671470242896q^{52} + 40087412948587896q^{54} + 44803667812766472q^{57} - 34645536255764880q^{58} + 50260381053157440q^{60} + 174742350239997144q^{61} - 139766490424918656q^{64} - 87772097712685968q^{66} - 957190369821780672q^{69} + 244663962371376480q^{70} + 54134736422921280q^{72} - 1445122541399481432q^{73} + 2744130151937256048q^{76} + 1125465917961999024q^{78} + 1033298241353042436q^{81} + 1064985418859680800q^{82} + 1920709484261873424q^{84} - 1802899595088057600q^{85} - 9209792381828477760q^{88} - 5194944179528261040q^{90} + 6719944190337314136q^{93} - 3835186345170303552q^{94} - 11947184361208227456q^{96} + 12765226159947004488q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −246.303 680.898i −0.340161 0.940367i
\(3\) 12845.9 31579.2i 0.376801 0.926294i
\(4\) −402957. + 335415.i −0.768580 + 0.639753i
\(5\) 225554.i 0.0516459i 0.999667 + 0.0258229i \(0.00822061\pi\)
−0.999667 + 0.0258229i \(0.991779\pi\)
\(6\) −2.46662e7 968699.i −0.999230 0.0392421i
\(7\) 9.84546e7i 0.922157i 0.887359 + 0.461078i \(0.152537\pi\)
−0.887359 + 0.461078i \(0.847463\pi\)
\(8\) 3.27633e8 + 1.91759e8i 0.863044 + 0.505128i
\(9\) −8.32227e8 8.11326e8i −0.716041 0.698058i
\(10\) 1.53579e8 5.55547e7i 0.0485661 0.0175679i
\(11\) 6.04702e9 0.773234 0.386617 0.922240i \(-0.373644\pi\)
0.386617 + 0.922240i \(0.373644\pi\)
\(12\) 5.41578e9 + 1.70338e10i 0.302997 + 0.952991i
\(13\) 4.74938e10 1.24215 0.621076 0.783750i \(-0.286696\pi\)
0.621076 + 0.783750i \(0.286696\pi\)
\(14\) 6.70376e10 2.42497e10i 0.867166 0.313682i
\(15\) 7.12281e9 + 2.89744e9i 0.0478393 + 0.0194602i
\(16\) 4.98716e10 2.70316e11i 0.181432 0.983404i
\(17\) 8.55357e11i 1.74937i 0.484689 + 0.874687i \(0.338933\pi\)
−0.484689 + 0.874687i \(0.661067\pi\)
\(18\) −3.47450e11 + 7.66494e11i −0.412861 + 0.910794i
\(19\) 3.94199e11i 0.280257i −0.990133 0.140129i \(-0.955248\pi\)
0.990133 0.140129i \(-0.0447516\pi\)
\(20\) −7.56542e10 9.08887e10i −0.0330406 0.0396940i
\(21\) 3.10912e12 + 1.26474e12i 0.854188 + 0.347470i
\(22\) −1.48940e12 4.11741e12i −0.263024 0.727124i
\(23\) −5.41125e10 −0.00626446 −0.00313223 0.999995i \(-0.500997\pi\)
−0.00313223 + 0.999995i \(0.500997\pi\)
\(24\) 1.02643e13 7.88307e12i 0.793094 0.609100i
\(25\) 1.90226e13 0.997333
\(26\) −1.16979e13 3.23384e13i −0.422532 1.16808i
\(27\) −3.63117e13 + 1.58589e13i −0.916412 + 0.400236i
\(28\) −3.30231e13 3.96730e13i −0.589953 0.708751i
\(29\) 3.42747e12i 0.0438725i −0.999759 0.0219362i \(-0.993017\pi\)
0.999759 0.0219362i \(-0.00698308\pi\)
\(30\) 2.18494e11 5.56356e12i 0.00202669 0.0516061i
\(31\) 2.38228e14i 1.61829i −0.587607 0.809146i \(-0.699930\pi\)
0.587607 0.809146i \(-0.300070\pi\)
\(32\) −1.96341e14 + 3.26222e13i −0.986476 + 0.163904i
\(33\) 7.76794e13 1.90960e14i 0.291356 0.716242i
\(34\) 5.82411e14 2.10677e14i 1.64505 0.595069i
\(35\) −2.22068e13 −0.0476256
\(36\) 6.07483e14 + 4.77882e13i 0.996920 + 0.0784237i
\(37\) 4.65196e14 0.588464 0.294232 0.955734i \(-0.404936\pi\)
0.294232 + 0.955734i \(0.404936\pi\)
\(38\) −2.68410e14 + 9.70925e13i −0.263544 + 0.0953326i
\(39\) 6.10100e14 1.49981e15i 0.468045 1.15060i
\(40\) −4.32521e13 + 7.38990e13i −0.0260878 + 0.0445727i
\(41\) 2.62403e14i 0.125176i −0.998039 0.0625881i \(-0.980065\pi\)
0.998039 0.0625881i \(-0.0199354\pi\)
\(42\) 9.53729e13 2.42850e15i 0.0361873 0.921446i
\(43\) 2.87474e13i 0.00872265i 0.999990 + 0.00436132i \(0.00138826\pi\)
−0.999990 + 0.00436132i \(0.998612\pi\)
\(44\) −2.43669e15 + 2.02826e15i −0.594293 + 0.494679i
\(45\) 1.82998e14 1.87712e14i 0.0360518 0.0369806i
\(46\) 1.33281e13 + 3.68451e13i 0.00213093 + 0.00589089i
\(47\) −5.76501e15 −0.751398 −0.375699 0.926742i \(-0.622597\pi\)
−0.375699 + 0.926742i \(0.622597\pi\)
\(48\) −7.89571e15 5.04735e15i −0.842557 0.538607i
\(49\) 1.70559e15 0.149627
\(50\) −4.68533e15 1.29525e16i −0.339254 0.937859i
\(51\) 2.70115e16 + 1.09878e16i 1.62043 + 0.659166i
\(52\) −1.91380e16 + 1.59301e16i −0.954694 + 0.794671i
\(53\) 3.52779e16i 1.46853i 0.678865 + 0.734263i \(0.262472\pi\)
−0.678865 + 0.734263i \(0.737528\pi\)
\(54\) 1.97420e16 + 2.08185e16i 0.688097 + 0.725619i
\(55\) 1.36393e15i 0.0399343i
\(56\) −1.88796e16 + 3.22570e16i −0.465807 + 0.795862i
\(57\) −1.24485e16 5.06384e15i −0.259600 0.105601i
\(58\) −2.33376e15 + 8.44196e14i −0.0412562 + 0.0149237i
\(59\) 1.05866e17 1.59097 0.795483 0.605976i \(-0.207217\pi\)
0.795483 + 0.605976i \(0.207217\pi\)
\(60\) −3.84204e15 + 1.22155e15i −0.0492181 + 0.0156486i
\(61\) −5.09395e16 −0.557727 −0.278863 0.960331i \(-0.589958\pi\)
−0.278863 + 0.960331i \(0.589958\pi\)
\(62\) −1.62209e17 + 5.86764e16i −1.52179 + 0.550481i
\(63\) 7.98787e16 8.19366e16i 0.643718 0.660302i
\(64\) 7.05719e16 + 1.25653e17i 0.489691 + 0.871896i
\(65\) 1.07124e16i 0.0641520i
\(66\) −1.49157e17 5.85774e15i −0.772638 0.0303433i
\(67\) 1.29179e17i 0.580070i −0.957016 0.290035i \(-0.906333\pi\)
0.957016 0.290035i \(-0.0936670\pi\)
\(68\) −2.86899e17 3.44672e17i −1.11917 1.34453i
\(69\) −6.95124e14 + 1.70883e15i −0.00236046 + 0.00580273i
\(70\) 5.46961e15 + 1.51206e16i 0.0162004 + 0.0447855i
\(71\) 4.53111e17 1.17287 0.586435 0.809996i \(-0.300531\pi\)
0.586435 + 0.809996i \(0.300531\pi\)
\(72\) −1.17086e17 4.25405e17i −0.265367 0.964148i
\(73\) 8.94130e17 1.77760 0.888799 0.458297i \(-0.151541\pi\)
0.888799 + 0.458297i \(0.151541\pi\)
\(74\) −1.14579e17 3.16751e17i −0.200173 0.553372i
\(75\) 2.44362e17 6.00718e17i 0.375796 0.923823i
\(76\) 1.32220e17 + 1.58846e17i 0.179295 + 0.215400i
\(77\) 5.95357e17i 0.713043i
\(78\) −1.17149e18 4.60072e16i −1.24120 0.0487446i
\(79\) 6.91414e17i 0.649054i −0.945876 0.324527i \(-0.894795\pi\)
0.945876 0.324527i \(-0.105205\pi\)
\(80\) 6.09709e16 + 1.12487e16i 0.0507887 + 0.00937020i
\(81\) 3.43532e16 + 1.35041e18i 0.0254308 + 0.999677i
\(82\) −1.78670e17 + 6.46307e16i −0.117712 + 0.0425801i
\(83\) 2.08387e18 1.22357 0.611785 0.791024i \(-0.290452\pi\)
0.611785 + 0.791024i \(0.290452\pi\)
\(84\) −1.67705e18 + 5.33208e17i −0.878807 + 0.279411i
\(85\) −1.92929e17 −0.0903479
\(86\) 1.95741e16 7.08058e15i 0.00820249 0.00296711i
\(87\) −1.08237e17 4.40289e16i −0.0406388 0.0165312i
\(88\) 1.98120e18 + 1.15957e18i 0.667335 + 0.390582i
\(89\) 2.97330e18i 0.899569i −0.893137 0.449784i \(-0.851501\pi\)
0.893137 0.449784i \(-0.148499\pi\)
\(90\) −1.72886e17 7.83688e16i −0.0470388 0.0213226i
\(91\) 4.67598e18i 1.14546i
\(92\) 2.18050e16 1.81501e16i 0.00481474 0.00400771i
\(93\) −7.52305e18 3.06026e18i −1.49902 0.609775i
\(94\) 1.41994e18 + 3.92538e18i 0.255597 + 0.706590i
\(95\) 8.89132e16 0.0144741
\(96\) −1.49200e18 + 6.61936e18i −0.219883 + 0.975526i
\(97\) 9.21289e17 0.123045 0.0615226 0.998106i \(-0.480404\pi\)
0.0615226 + 0.998106i \(0.480404\pi\)
\(98\) −4.20091e17 1.16133e18i −0.0508975 0.140705i
\(99\) −5.03250e18 4.90610e18i −0.553668 0.539762i
\(100\) −7.66530e18 + 6.38047e18i −0.766530 + 0.638047i
\(101\) 1.05473e19i 0.959598i 0.877378 + 0.479799i \(0.159290\pi\)
−0.877378 + 0.479799i \(0.840710\pi\)
\(102\) 8.28583e17 2.10984e19i 0.0686491 1.74803i
\(103\) 1.64189e19i 1.23991i 0.784637 + 0.619956i \(0.212849\pi\)
−0.784637 + 0.619956i \(0.787151\pi\)
\(104\) 1.55605e19 + 9.10738e18i 1.07203 + 0.627446i
\(105\) −2.85267e17 + 7.01274e17i −0.0179454 + 0.0441153i
\(106\) 2.40207e19 8.68905e18i 1.38095 0.499536i
\(107\) −3.57670e19 −1.88077 −0.940386 0.340108i \(-0.889536\pi\)
−0.940386 + 0.340108i \(0.889536\pi\)
\(108\) 9.31278e18 1.85699e19i 0.448284 0.893891i
\(109\) 3.59127e19 1.58379 0.791893 0.610659i \(-0.209095\pi\)
0.791893 + 0.610659i \(0.209095\pi\)
\(110\) 9.28698e17 3.35940e17i 0.0375529 0.0135841i
\(111\) 5.97586e18 1.46905e19i 0.221734 0.545091i
\(112\) 2.66138e19 + 4.91009e18i 0.906852 + 0.167308i
\(113\) 2.88218e19i 0.902559i −0.892383 0.451279i \(-0.850968\pi\)
0.892383 0.451279i \(-0.149032\pi\)
\(114\) −3.81860e17 + 9.72340e18i −0.0109979 + 0.280041i
\(115\) 1.22053e16i 0.000323533i
\(116\) 1.14962e18 + 1.38112e18i 0.0280676 + 0.0337195i
\(117\) −3.95256e19 3.85329e19i −0.889433 0.867094i
\(118\) −2.60750e19 7.20837e19i −0.541185 1.49609i
\(119\) −8.42138e19 −1.61320
\(120\) 1.77806e18 + 2.31516e18i 0.0314575 + 0.0409600i
\(121\) −2.45926e19 −0.402109
\(122\) 1.25466e19 + 3.46847e19i 0.189717 + 0.524468i
\(123\) −8.28647e18 3.37080e18i −0.115950 0.0471666i
\(124\) 7.99053e19 + 9.59959e19i 1.03531 + 1.24379i
\(125\) 8.59273e18i 0.103154i
\(126\) −7.54649e19 3.42081e19i −0.839895 0.380722i
\(127\) 2.77983e19i 0.287000i 0.989650 + 0.143500i \(0.0458358\pi\)
−0.989650 + 0.143500i \(0.954164\pi\)
\(128\) 6.81752e19 7.90011e19i 0.653329 0.757074i
\(129\) 9.07819e17 + 3.69286e17i 0.00807974 + 0.00328670i
\(130\) 7.29407e18 2.63850e18i 0.0603265 0.0218220i
\(131\) 2.22475e20 1.71082 0.855410 0.517951i \(-0.173305\pi\)
0.855410 + 0.517951i \(0.173305\pi\)
\(132\) 3.27493e19 + 1.03004e20i 0.234288 + 0.736885i
\(133\) 3.88107e19 0.258441
\(134\) −8.79576e19 + 3.18171e19i −0.545479 + 0.197317i
\(135\) −3.57703e18 8.19025e18i −0.0206705 0.0473289i
\(136\) −1.64023e20 + 2.80243e20i −0.883658 + 1.50979i
\(137\) 1.89296e20i 0.951251i 0.879648 + 0.475626i \(0.157778\pi\)
−0.879648 + 0.475626i \(0.842222\pi\)
\(138\) 1.33475e18 + 5.24188e16i 0.00625963 + 0.000245830i
\(139\) 1.47801e20i 0.647197i 0.946195 + 0.323598i \(0.104893\pi\)
−0.946195 + 0.323598i \(0.895107\pi\)
\(140\) 8.94841e18 7.44850e18i 0.0366041 0.0304686i
\(141\) −7.40567e19 + 1.82054e20i −0.283128 + 0.696016i
\(142\) −1.11603e20 3.08522e20i −0.398965 1.10293i
\(143\) 2.87196e20 0.960474
\(144\) −2.60819e20 + 1.84502e20i −0.816385 + 0.577508i
\(145\) 7.73079e17 0.00226583
\(146\) −2.20227e20 6.08812e20i −0.604670 1.67159i
\(147\) 2.19098e19 5.38610e19i 0.0563798 0.138599i
\(148\) −1.87454e20 + 1.56034e20i −0.452282 + 0.376472i
\(149\) 1.86831e20i 0.422844i 0.977395 + 0.211422i \(0.0678094\pi\)
−0.977395 + 0.211422i \(0.932191\pi\)
\(150\) −4.69216e20 1.84272e19i −0.996564 0.0391374i
\(151\) 7.06872e20i 1.40948i −0.709464 0.704742i \(-0.751063\pi\)
0.709464 0.704742i \(-0.248937\pi\)
\(152\) 7.55914e19 1.29153e20i 0.141566 0.241874i
\(153\) 6.93973e20 7.11851e20i 1.22116 1.25262i
\(154\) 4.05378e20 1.46638e20i 0.670522 0.242550i
\(155\) 5.37333e19 0.0835782
\(156\) 2.57216e20 + 8.08998e20i 0.376369 + 1.18376i
\(157\) −6.00889e20 −0.827461 −0.413731 0.910399i \(-0.635774\pi\)
−0.413731 + 0.910399i \(0.635774\pi\)
\(158\) −4.70783e20 + 1.70297e20i −0.610349 + 0.220783i
\(159\) 1.11405e21 + 4.53176e20i 1.36029 + 0.553343i
\(160\) −7.35807e18 4.42856e19i −0.00846494 0.0509474i
\(161\) 5.32763e18i 0.00577681i
\(162\) 9.11034e20 3.56003e20i 0.931412 0.363966i
\(163\) 1.43894e21i 1.38759i −0.720173 0.693795i \(-0.755937\pi\)
0.720173 0.693795i \(-0.244063\pi\)
\(164\) 8.80138e19 + 1.05737e20i 0.0800819 + 0.0962080i
\(165\) 4.30718e19 + 1.75209e19i 0.0369910 + 0.0150473i
\(166\) −5.13264e20 1.41890e21i −0.416211 1.15060i
\(167\) −1.21411e21 −0.929932 −0.464966 0.885329i \(-0.653933\pi\)
−0.464966 + 0.885329i \(0.653933\pi\)
\(168\) 7.76124e20 + 1.01057e21i 0.561685 + 0.731356i
\(169\) 7.93738e20 0.542942
\(170\) 4.75191e19 + 1.31365e20i 0.0307329 + 0.0849602i
\(171\) −3.19824e20 + 3.28063e20i −0.195636 + 0.200676i
\(172\) −9.64231e18 1.15840e19i −0.00558034 0.00670405i
\(173\) 3.05075e21i 1.67097i 0.549513 + 0.835485i \(0.314813\pi\)
−0.549513 + 0.835485i \(0.685187\pi\)
\(174\) −3.32018e18 + 8.45425e19i −0.00172165 + 0.0438387i
\(175\) 1.87286e21i 0.919697i
\(176\) 3.01574e20 1.63461e21i 0.140289 0.760401i
\(177\) 1.35994e21 3.34315e21i 0.599478 1.47370i
\(178\) −2.02452e21 + 7.32334e20i −0.845925 + 0.305999i
\(179\) −2.43304e21 −0.963931 −0.481965 0.876190i \(-0.660077\pi\)
−0.481965 + 0.876190i \(0.660077\pi\)
\(180\) −1.07788e19 + 1.37020e20i −0.00405026 + 0.0514868i
\(181\) −4.51227e21 −1.60860 −0.804300 0.594223i \(-0.797460\pi\)
−0.804300 + 0.594223i \(0.797460\pi\)
\(182\) 3.18387e21 1.15171e21i 1.07715 0.389641i
\(183\) −6.54364e20 + 1.60863e21i −0.210152 + 0.516619i
\(184\) −1.77291e19 1.03766e19i −0.00540650 0.00316435i
\(185\) 1.04927e20i 0.0303917i
\(186\) −2.30771e20 + 5.87619e21i −0.0635052 + 1.61705i
\(187\) 5.17236e21i 1.35268i
\(188\) 2.32305e21 1.93367e21i 0.577510 0.480709i
\(189\) −1.56138e21 3.57505e21i −0.369080 0.845075i
\(190\) −2.18996e19 6.05409e19i −0.00492354 0.0136110i
\(191\) −3.89391e21 −0.832855 −0.416427 0.909169i \(-0.636718\pi\)
−0.416427 + 0.909169i \(0.636718\pi\)
\(192\) 4.87459e21 6.14470e20i 0.992148 0.125066i
\(193\) 2.82327e21 0.546962 0.273481 0.961877i \(-0.411825\pi\)
0.273481 + 0.961877i \(0.411825\pi\)
\(194\) −2.26916e20 6.27304e20i −0.0418552 0.115708i
\(195\) 3.38289e20 + 1.37611e20i 0.0594237 + 0.0241726i
\(196\) −6.87279e20 + 5.72079e20i −0.115001 + 0.0957246i
\(197\) 4.84210e21i 0.771978i 0.922503 + 0.385989i \(0.126140\pi\)
−0.922503 + 0.385989i \(0.873860\pi\)
\(198\) −2.10104e21 + 4.63501e21i −0.319238 + 0.704257i
\(199\) 9.87146e21i 1.42981i −0.699224 0.714903i \(-0.746471\pi\)
0.699224 0.714903i \(-0.253529\pi\)
\(200\) 6.23244e21 + 3.64776e21i 0.860742 + 0.503781i
\(201\) −4.07936e21 1.65942e21i −0.537315 0.218571i
\(202\) 7.18166e21 2.59784e21i 0.902375 0.326418i
\(203\) 3.37450e20 0.0404573
\(204\) −1.45700e22 + 4.63242e21i −1.66714 + 0.530056i
\(205\) 5.91860e19 0.00646484
\(206\) 1.11796e22 4.04403e21i 1.16597 0.421770i
\(207\) 4.50339e19 + 4.39029e19i 0.00448561 + 0.00437295i
\(208\) 2.36859e21 1.28383e22i 0.225366 1.22154i
\(209\) 2.38373e21i 0.216704i
\(210\) 5.47758e20 + 2.15117e19i 0.0475889 + 0.00186893i
\(211\) 5.33404e21i 0.442968i 0.975164 + 0.221484i \(0.0710901\pi\)
−0.975164 + 0.221484i \(0.928910\pi\)
\(212\) −1.18327e22 1.42155e22i −0.939494 1.12868i
\(213\) 5.82061e21 1.43089e22i 0.441939 1.08642i
\(214\) 8.80952e21 + 2.43537e22i 0.639766 + 1.76862i
\(215\) −6.48409e18 −0.000450489
\(216\) −1.49380e22 1.76722e21i −0.993075 0.117485i
\(217\) 2.34547e22 1.49232
\(218\) −8.84542e21 2.44529e22i −0.538743 1.48934i
\(219\) 1.14859e22 2.82359e22i 0.669801 1.64658i
\(220\) −4.57483e20 5.49606e20i −0.0255481 0.0306928i
\(221\) 4.06241e22i 2.17299i
\(222\) −1.14746e22 4.50635e20i −0.588011 0.0230925i
\(223\) 1.17380e22i 0.576365i 0.957575 + 0.288183i \(0.0930511\pi\)
−0.957575 + 0.288183i \(0.906949\pi\)
\(224\) −3.21180e21 1.93307e22i −0.151145 0.909686i
\(225\) −1.58311e22 1.54335e22i −0.714132 0.696196i
\(226\) −1.96247e22 + 7.09889e21i −0.848736 + 0.307016i
\(227\) 7.18026e21 0.297779 0.148890 0.988854i \(-0.452430\pi\)
0.148890 + 0.988854i \(0.452430\pi\)
\(228\) 6.71470e21 2.13490e21i 0.267083 0.0849172i
\(229\) 1.25548e21 0.0479043 0.0239521 0.999713i \(-0.492375\pi\)
0.0239521 + 0.999713i \(0.492375\pi\)
\(230\) −8.31057e18 + 3.00620e18i −0.000304240 + 0.000110054i
\(231\) 1.88009e22 + 7.64789e21i 0.660487 + 0.268676i
\(232\) 6.57249e20 1.12295e21i 0.0221612 0.0378639i
\(233\) 3.40275e22i 1.10141i 0.834700 + 0.550705i \(0.185641\pi\)
−0.834700 + 0.550705i \(0.814359\pi\)
\(234\) −1.65017e22 + 3.64037e22i −0.512836 + 1.13134i
\(235\) 1.30032e21i 0.0388066i
\(236\) −4.26593e22 + 3.55089e22i −1.22278 + 1.01783i
\(237\) −2.18343e22 8.88183e21i −0.601215 0.244564i
\(238\) 2.07421e22 + 5.73411e22i 0.548747 + 1.51700i
\(239\) 4.70387e22 1.19585 0.597923 0.801554i \(-0.295993\pi\)
0.597923 + 0.801554i \(0.295993\pi\)
\(240\) 1.13845e21 1.78091e21i 0.0278168 0.0435146i
\(241\) −2.43119e22 −0.571027 −0.285513 0.958375i \(-0.592164\pi\)
−0.285513 + 0.958375i \(0.592164\pi\)
\(242\) 6.05724e21 + 1.67451e22i 0.136782 + 0.378130i
\(243\) 4.30863e22 + 1.62624e22i 0.935577 + 0.353123i
\(244\) 2.05265e22 1.70859e22i 0.428658 0.356807i
\(245\) 3.84702e20i 0.00772764i
\(246\) −2.54189e20 + 6.47248e21i −0.00491218 + 0.125080i
\(247\) 1.87220e22i 0.348122i
\(248\) 4.56825e22 7.80515e22i 0.817446 1.39666i
\(249\) 2.67692e22 6.58069e22i 0.461043 1.13339i
\(250\) 5.85078e21 2.11642e21i 0.0970026 0.0350890i
\(251\) −1.02020e23 −1.62849 −0.814243 0.580524i \(-0.802848\pi\)
−0.814243 + 0.580524i \(0.802848\pi\)
\(252\) −4.70497e21 + 5.98095e22i −0.0723189 + 0.919316i
\(253\) −3.27220e20 −0.00484389
\(254\) 1.89278e22 6.84680e21i 0.269886 0.0976264i
\(255\) −2.47835e21 + 6.09255e21i −0.0340432 + 0.0836888i
\(256\) −7.05835e22 2.69622e22i −0.934165 0.356841i
\(257\) 4.39093e22i 0.560005i 0.959999 + 0.280002i \(0.0903352\pi\)
−0.959999 + 0.280002i \(0.909665\pi\)
\(258\) 2.78476e19 7.09089e20i 0.000342295 0.00871593i
\(259\) 4.58007e22i 0.542656i
\(260\) −3.59310e21 4.31665e21i −0.0410415 0.0493060i
\(261\) −2.78079e21 + 2.85243e21i −0.0306255 + 0.0314145i
\(262\) −5.47964e22 1.51483e23i −0.581955 1.60880i
\(263\) −1.28065e23 −1.31175 −0.655877 0.754868i \(-0.727701\pi\)
−0.655877 + 0.754868i \(0.727701\pi\)
\(264\) 6.20687e22 4.76691e22i 0.613247 0.470977i
\(265\) −7.95707e21 −0.0758433
\(266\) −9.55920e21 2.64262e22i −0.0879116 0.243029i
\(267\) −9.38945e22 3.81948e22i −0.833265 0.338959i
\(268\) 4.33285e22 + 5.20535e22i 0.371102 + 0.445831i
\(269\) 1.26487e23i 1.04568i −0.852431 0.522841i \(-0.824872\pi\)
0.852431 0.522841i \(-0.175128\pi\)
\(270\) −4.69570e21 + 4.45288e21i −0.0374752 + 0.0355374i
\(271\) 1.05900e23i 0.815997i −0.912983 0.407998i \(-0.866227\pi\)
0.912983 0.407998i \(-0.133773\pi\)
\(272\) 2.31217e23 + 4.26580e22i 1.72034 + 0.317392i
\(273\) 1.47664e23 + 6.00672e22i 1.06103 + 0.431610i
\(274\) 1.28891e23 4.66241e22i 0.894525 0.323579i
\(275\) 1.15030e23 0.771172
\(276\) −2.93061e20 9.21740e20i −0.00189811 0.00596997i
\(277\) 8.95743e22 0.560564 0.280282 0.959918i \(-0.409572\pi\)
0.280282 + 0.959918i \(0.409572\pi\)
\(278\) 1.00637e23 3.64038e22i 0.608602 0.220151i
\(279\) −1.93281e23 + 1.98260e23i −1.12966 + 1.15876i
\(280\) −7.27570e21 4.25837e21i −0.0411030 0.0240570i
\(281\) 3.08712e22i 0.168594i 0.996441 + 0.0842972i \(0.0268645\pi\)
−0.996441 + 0.0842972i \(0.973135\pi\)
\(282\) 1.42201e23 + 5.58456e21i 0.750820 + 0.0294864i
\(283\) 2.18878e22i 0.111746i 0.998438 + 0.0558728i \(0.0177941\pi\)
−0.998438 + 0.0558728i \(0.982206\pi\)
\(284\) −1.82584e23 + 1.51980e23i −0.901445 + 0.750348i
\(285\) 1.14217e21 2.80781e21i 0.00545387 0.0134073i
\(286\) −7.07372e22 1.95551e23i −0.326716 0.903198i
\(287\) 2.58348e22 0.115432
\(288\) 1.89868e23 + 1.32148e23i 0.820772 + 0.571256i
\(289\) −4.92563e23 −2.06031
\(290\) −1.90412e20 5.26388e20i −0.000770749 0.00213071i
\(291\) 1.18348e22 2.90935e22i 0.0463636 0.113976i
\(292\) −3.60296e23 + 2.99905e23i −1.36623 + 1.13722i
\(293\) 2.67169e23i 0.980717i −0.871521 0.490358i \(-0.836866\pi\)
0.871521 0.490358i \(-0.163134\pi\)
\(294\) −4.20703e22 1.65220e21i −0.149512 0.00587169i
\(295\) 2.38784e22i 0.0821668i
\(296\) 1.52414e23 + 8.92057e22i 0.507870 + 0.297250i
\(297\) −2.19578e23 + 9.58988e22i −0.708601 + 0.309476i
\(298\) 1.27213e23 4.60171e22i 0.397628 0.143835i
\(299\) −2.57001e21 −0.00778141
\(300\) 1.03022e23 + 3.24027e23i 0.302189 + 0.950449i
\(301\) −2.83031e21 −0.00804364
\(302\) −4.81308e23 + 1.74105e23i −1.32543 + 0.479452i
\(303\) 3.33076e23 + 1.35490e23i 0.888870 + 0.361578i
\(304\) −1.06558e23 1.96593e22i −0.275606 0.0508475i
\(305\) 1.14896e22i 0.0288043i
\(306\) −6.55626e23 2.97194e23i −1.59332 0.722248i
\(307\) 6.29394e22i 0.148289i −0.997248 0.0741443i \(-0.976377\pi\)
0.997248 0.0741443i \(-0.0236226\pi\)
\(308\) −1.99692e23 2.39904e23i −0.456171 0.548031i
\(309\) 5.18496e23 + 2.10916e23i 1.14852 + 0.467200i
\(310\) −1.32347e22 3.65870e22i −0.0284301 0.0785941i
\(311\) 4.02991e23 0.839599 0.419800 0.907617i \(-0.362100\pi\)
0.419800 + 0.907617i \(0.362100\pi\)
\(312\) 4.87492e23 3.74397e23i 0.985143 0.756595i
\(313\) 3.51917e23 0.689873 0.344936 0.938626i \(-0.387900\pi\)
0.344936 + 0.938626i \(0.387900\pi\)
\(314\) 1.48001e23 + 4.09144e23i 0.281470 + 0.778117i
\(315\) 1.84811e22 + 1.80170e22i 0.0341019 + 0.0332454i
\(316\) 2.31910e23 + 2.78610e23i 0.415234 + 0.498850i
\(317\) 2.36002e23i 0.410065i 0.978755 + 0.205033i \(0.0657300\pi\)
−0.978755 + 0.205033i \(0.934270\pi\)
\(318\) 3.41736e22 8.70171e23i 0.0576280 1.46739i
\(319\) 2.07260e22i 0.0339237i
\(320\) −2.83417e22 + 1.59178e22i −0.0450298 + 0.0252905i
\(321\) −4.59459e23 + 1.12949e24i −0.708678 + 1.74215i
\(322\) −3.62757e21 + 1.31221e21i −0.00543232 + 0.00196505i
\(323\) 3.37181e23 0.490274
\(324\) −4.66792e23 5.32637e23i −0.659092 0.752062i
\(325\) 9.03456e23 1.23884
\(326\) −9.79774e23 + 3.54416e23i −1.30484 + 0.472005i
\(327\) 4.61331e23 1.13409e24i 0.596773 1.46705i
\(328\) 5.03182e22 8.59719e22i 0.0632301 0.108033i
\(329\) 5.67591e23i 0.692907i
\(330\) 1.32124e21 3.36430e22i 0.00156711 0.0399036i
\(331\) 6.46210e23i 0.744745i −0.928083 0.372373i \(-0.878544\pi\)
0.928083 0.372373i \(-0.121456\pi\)
\(332\) −8.39711e23 + 6.98961e23i −0.940412 + 0.782783i
\(333\) −3.87149e23 3.77426e23i −0.421364 0.410782i
\(334\) 2.99039e23 + 8.26685e23i 0.316327 + 0.874477i
\(335\) 2.91368e22 0.0299582
\(336\) 4.96935e23 7.77369e23i 0.496680 0.776970i
\(337\) 2.67782e23 0.260194 0.130097 0.991501i \(-0.458471\pi\)
0.130097 + 0.991501i \(0.458471\pi\)
\(338\) −1.95500e23 5.40455e23i −0.184688 0.510565i
\(339\) −9.10168e23 3.70241e23i −0.836035 0.340085i
\(340\) 7.77423e22 6.47113e22i 0.0694396 0.0578004i
\(341\) 1.44057e24i 1.25132i
\(342\) 3.02151e23 + 1.36965e23i 0.255256 + 0.115707i
\(343\) 1.29020e24i 1.06014i
\(344\) −5.51258e21 + 9.41860e21i −0.00440606 + 0.00752803i
\(345\) −3.85433e20 1.56788e20i −0.000299687 0.000121908i
\(346\) 2.07725e24 7.51410e23i 1.57133 0.568400i
\(347\) 1.02664e24 0.755590 0.377795 0.925889i \(-0.376682\pi\)
0.377795 + 0.925889i \(0.376682\pi\)
\(348\) 5.83827e22 1.85624e22i 0.0418101 0.0132932i
\(349\) −1.46442e24 −1.02053 −0.510264 0.860018i \(-0.670452\pi\)
−0.510264 + 0.860018i \(0.670452\pi\)
\(350\) 1.27523e24 4.61292e23i 0.864853 0.312845i
\(351\) −1.72458e24 + 7.53197e23i −1.13832 + 0.497154i
\(352\) −1.18728e24 + 1.97267e23i −0.762777 + 0.126736i
\(353\) 1.26315e24i 0.789940i −0.918694 0.394970i \(-0.870755\pi\)
0.918694 0.394970i \(-0.129245\pi\)
\(354\) −2.61130e24 1.02552e23i −1.58974 0.0624328i
\(355\) 1.02201e23i 0.0605739i
\(356\) 9.97291e23 + 1.19812e24i 0.575502 + 0.691391i
\(357\) −1.08180e24 + 2.65940e24i −0.607855 + 1.49429i
\(358\) 5.99266e23 + 1.65665e24i 0.327892 + 0.906449i
\(359\) 1.07718e23 0.0573972 0.0286986 0.999588i \(-0.490864\pi\)
0.0286986 + 0.999588i \(0.490864\pi\)
\(360\) 9.59517e22 2.64092e22i 0.0497942 0.0137051i
\(361\) 1.82303e24 0.921456
\(362\) 1.11139e24 + 3.07240e24i 0.547184 + 1.51268i
\(363\) −3.15914e23 + 7.76615e23i −0.151515 + 0.372471i
\(364\) −1.56839e24 1.88422e24i −0.732811 0.880377i
\(365\) 2.01675e23i 0.0918056i
\(366\) 1.25648e24 + 4.93451e22i 0.557297 + 0.0218864i
\(367\) 2.04349e24i 0.883169i 0.897220 + 0.441585i \(0.145584\pi\)
−0.897220 + 0.441585i \(0.854416\pi\)
\(368\) −2.69868e21 + 1.46275e22i −0.00113657 + 0.00616049i
\(369\) −2.12894e23 + 2.18379e23i −0.0873803 + 0.0896314i
\(370\) 7.14446e22 2.58438e22i 0.0285794 0.0103381i
\(371\) −3.47327e24 −1.35421
\(372\) 4.05793e24 1.29019e24i 1.54222 0.490339i
\(373\) −1.32926e24 −0.492466 −0.246233 0.969211i \(-0.579193\pi\)
−0.246233 + 0.969211i \(0.579193\pi\)
\(374\) 3.52185e24 1.27397e24i 1.27201 0.460128i
\(375\) 2.71351e23 + 1.10381e23i 0.0955509 + 0.0388686i
\(376\) −1.88881e24 1.10549e24i −0.648490 0.379553i
\(377\) 1.62783e23i 0.0544963i
\(378\) −2.04968e24 + 1.94369e24i −0.669134 + 0.634533i
\(379\) 3.00906e23i 0.0957985i 0.998852 + 0.0478992i \(0.0152526\pi\)
−0.998852 + 0.0478992i \(0.984747\pi\)
\(380\) −3.58283e22 + 2.98228e22i −0.0111245 + 0.00925986i
\(381\) 8.77846e23 + 3.57094e23i 0.265847 + 0.108142i
\(382\) 9.59083e23 + 2.65136e24i 0.283305 + 0.783189i
\(383\) −1.52499e24 −0.439418 −0.219709 0.975565i \(-0.570511\pi\)
−0.219709 + 0.975565i \(0.570511\pi\)
\(384\) −1.61902e24 3.16776e24i −0.455098 0.890441i
\(385\) −1.34285e23 −0.0368257
\(386\) −6.95379e23 1.92236e24i −0.186055 0.514345i
\(387\) 2.33235e22 2.39244e22i 0.00608891 0.00624578i
\(388\) −3.71240e23 + 3.09014e23i −0.0945701 + 0.0787185i
\(389\) 2.16535e22i 0.00538278i −0.999996 0.00269139i \(-0.999143\pi\)
0.999996 0.00269139i \(-0.000856697\pi\)
\(390\) 1.03771e22 2.64235e23i 0.00251746 0.0641026i
\(391\) 4.62855e22i 0.0109589i
\(392\) 5.58807e23 + 3.27062e23i 0.129135 + 0.0755810i
\(393\) 2.85789e24 7.02558e24i 0.644639 1.58472i
\(394\) 3.29698e24 1.19263e24i 0.725943 0.262597i
\(395\) 1.55951e23 0.0335209
\(396\) 3.67346e24 + 2.88977e23i 0.770853 + 0.0606399i
\(397\) −2.70653e24 −0.554501 −0.277250 0.960798i \(-0.589423\pi\)
−0.277250 + 0.960798i \(0.589423\pi\)
\(398\) −6.72146e24 + 2.43137e24i −1.34454 + 0.486365i
\(399\) 4.98558e23 1.22561e24i 0.0973809 0.239392i
\(400\) 9.48688e23 5.14211e24i 0.180948 0.980781i
\(401\) 1.94970e24i 0.363159i −0.983376 0.181579i \(-0.941879\pi\)
0.983376 0.181579i \(-0.0581209\pi\)
\(402\) −1.25135e23 + 3.18635e24i −0.0227632 + 0.579623i
\(403\) 1.13144e25i 2.01017i
\(404\) −3.53773e24 4.25013e24i −0.613906 0.737529i
\(405\) −3.04592e23 + 7.74851e21i −0.0516292 + 0.00131340i
\(406\) −8.31149e22 2.29769e23i −0.0137620 0.0380447i
\(407\) 2.81305e24 0.455020
\(408\) 6.74283e24 + 8.77968e24i 1.06554 + 1.38742i
\(409\) −5.63041e22 −0.00869297 −0.00434649 0.999991i \(-0.501384\pi\)
−0.00434649 + 0.999991i \(0.501384\pi\)
\(410\) −1.45777e22 4.02997e22i −0.00219909 0.00607932i
\(411\) 5.97780e24 + 2.43167e24i 0.881138 + 0.358433i
\(412\) −5.50715e24 6.61612e24i −0.793237 0.952972i
\(413\) 1.04230e25i 1.46712i
\(414\) 1.88014e22 4.14770e22i 0.00258635 0.00570563i
\(415\) 4.70025e23i 0.0631923i
\(416\) −9.32499e24 + 1.54935e24i −1.22535 + 0.203593i
\(417\) 4.66743e24 + 1.89863e24i 0.599494 + 0.243865i
\(418\) −1.62308e24 + 5.87120e23i −0.203782 + 0.0737144i
\(419\) 1.18666e24 0.145645 0.0728223 0.997345i \(-0.476799\pi\)
0.0728223 + 0.997345i \(0.476799\pi\)
\(420\) −1.20267e23 3.78266e23i −0.0144304 0.0453868i
\(421\) 4.08430e24 0.479113 0.239556 0.970882i \(-0.422998\pi\)
0.239556 + 0.970882i \(0.422998\pi\)
\(422\) 3.63194e24 1.31379e24i 0.416553 0.150681i
\(423\) 4.79780e24 + 4.67730e24i 0.538032 + 0.524519i
\(424\) −6.76486e24 + 1.15582e25i −0.741794 + 1.26740i
\(425\) 1.62711e25i 1.74471i
\(426\) −1.11765e25 4.38928e23i −1.17197 0.0460259i
\(427\) 5.01523e24i 0.514311i
\(428\) 1.44126e25 1.19968e25i 1.44553 1.20323i
\(429\) 3.68929e24 9.06941e24i 0.361908 0.889682i
\(430\) 1.59705e21 + 4.41501e21i 0.000153239 + 0.000423625i
\(431\) 1.42789e25 1.34018 0.670088 0.742281i \(-0.266256\pi\)
0.670088 + 0.742281i \(0.266256\pi\)
\(432\) 2.47598e24 + 1.06065e25i 0.227327 + 0.973818i
\(433\) −1.04818e25 −0.941456 −0.470728 0.882278i \(-0.656009\pi\)
−0.470728 + 0.882278i \(0.656009\pi\)
\(434\) −5.77696e24 1.59702e25i −0.507629 1.40333i
\(435\) 9.93089e21 2.44132e22i 0.000853769 0.00209883i
\(436\) −1.44713e25 + 1.20457e25i −1.21727 + 1.01323i
\(437\) 2.13311e22i 0.00175566i
\(438\) −2.20548e25 8.66143e23i −1.77623 0.0697566i
\(439\) 1.60045e25i 1.26133i 0.776055 + 0.630666i \(0.217218\pi\)
−0.776055 + 0.630666i \(0.782782\pi\)
\(440\) −2.61546e23 + 4.46869e23i −0.0201720 + 0.0344651i
\(441\) −1.41944e24 1.38379e24i −0.107139 0.104449i
\(442\) 2.76609e25 1.00059e25i 2.04341 0.739167i
\(443\) −1.62198e25 −1.17277 −0.586383 0.810034i \(-0.699449\pi\)
−0.586383 + 0.810034i \(0.699449\pi\)
\(444\) 2.51940e24 + 7.92405e24i 0.178303 + 0.560801i
\(445\) 6.70641e23 0.0464590
\(446\) 7.99239e24 2.89111e24i 0.541995 0.196057i
\(447\) 5.89997e24 + 2.40001e24i 0.391677 + 0.159328i
\(448\) −1.23712e25 + 6.94812e24i −0.804025 + 0.451571i
\(449\) 1.16119e25i 0.738864i −0.929258 0.369432i \(-0.879552\pi\)
0.929258 0.369432i \(-0.120448\pi\)
\(450\) −6.60941e24 + 1.45807e25i −0.411760 + 0.908365i
\(451\) 1.58676e24i 0.0967905i
\(452\) 9.66725e24 + 1.16139e25i 0.577415 + 0.693689i
\(453\) −2.23225e25 9.08041e24i −1.30560 0.531095i
\(454\) −1.76852e24 4.88903e24i −0.101293 0.280022i
\(455\) −1.05469e24 −0.0591582
\(456\) −3.10750e24 4.04620e24i −0.170704 0.222270i
\(457\) 4.45759e24 0.239826 0.119913 0.992784i \(-0.461738\pi\)
0.119913 + 0.992784i \(0.461738\pi\)
\(458\) −3.09230e23 8.54857e23i −0.0162952 0.0450476i
\(459\) −1.35650e25 3.10595e25i −0.700162 1.60315i
\(460\) 4.09384e21 + 4.91822e21i 0.000206981 + 0.000248661i
\(461\) 1.47546e25i 0.730750i 0.930860 + 0.365375i \(0.119059\pi\)
−0.930860 + 0.365375i \(0.880941\pi\)
\(462\) 5.76722e23 1.46852e25i 0.0279813 0.712494i
\(463\) 9.05908e24i 0.430591i 0.976549 + 0.215295i \(0.0690714\pi\)
−0.976549 + 0.215295i \(0.930929\pi\)
\(464\) −9.26498e23 1.70933e23i −0.0431443 0.00795986i
\(465\) 6.90253e23 1.69685e24i 0.0314924 0.0774180i
\(466\) 2.31693e25 8.38108e24i 1.03573 0.374657i
\(467\) 2.69416e24 0.118008 0.0590042 0.998258i \(-0.481207\pi\)
0.0590042 + 0.998258i \(0.481207\pi\)
\(468\) 2.88517e25 + 2.26964e24i 1.23833 + 0.0974142i
\(469\) 1.27182e25 0.534915
\(470\) −8.85387e23 + 3.20273e23i −0.0364925 + 0.0132005i
\(471\) −7.71896e24 + 1.89756e25i −0.311788 + 0.766472i
\(472\) 3.46851e25 + 2.03007e25i 1.37307 + 0.803642i
\(473\) 1.73836e23i 0.00674465i
\(474\) −6.69772e23 + 1.70545e25i −0.0254702 + 0.648554i
\(475\) 7.49870e24i 0.279510i
\(476\) 3.39346e25 2.82466e25i 1.23987 1.03205i
\(477\) 2.86218e25 2.93592e25i 1.02512 1.05153i
\(478\) −1.15858e25 3.20286e25i −0.406780 1.12453i
\(479\) −5.00164e25 −1.72157 −0.860785 0.508968i \(-0.830027\pi\)
−0.860785 + 0.508968i \(0.830027\pi\)
\(480\) −1.49302e24 3.36526e23i −0.0503819 0.0113560i
\(481\) 2.20939e25 0.730962
\(482\) 5.98809e24 + 1.65539e25i 0.194241 + 0.536975i
\(483\) −1.68242e23 6.84381e22i −0.00535102 0.00217671i
\(484\) 9.90978e24 8.24873e24i 0.309053 0.257251i
\(485\) 2.07800e23i 0.00635477i
\(486\) 4.60782e23 3.33429e25i 0.0138182 0.999905i
\(487\) 4.81418e24i 0.141578i 0.997491 + 0.0707892i \(0.0225518\pi\)
−0.997491 + 0.0707892i \(0.977448\pi\)
\(488\) −1.66895e25 9.76813e24i −0.481343 0.281724i
\(489\) −4.54406e25 1.84845e25i −1.28532 0.522846i
\(490\) 2.61943e23 9.47533e22i 0.00726681 0.00262864i
\(491\) −2.08283e25 −0.566735 −0.283368 0.959011i \(-0.591452\pi\)
−0.283368 + 0.959011i \(0.591452\pi\)
\(492\) 4.46971e24 1.42112e24i 0.119292 0.0379281i
\(493\) 2.93171e24 0.0767493
\(494\) −1.27478e25 + 4.61129e24i −0.327362 + 0.118418i
\(495\) 1.10659e24 1.13510e24i 0.0278765 0.0285946i
\(496\) −6.43969e25 1.18808e25i −1.59144 0.293610i
\(497\) 4.46108e25i 1.08157i
\(498\) −5.14012e25 2.01864e24i −1.22263 0.0480154i
\(499\) 1.09199e25i 0.254838i 0.991849 + 0.127419i \(0.0406693\pi\)
−0.991849 + 0.127419i \(0.959331\pi\)
\(500\) −2.88213e24 3.46250e24i −0.0659931 0.0792821i
\(501\) −1.55963e25 + 3.83405e25i −0.350399 + 0.861390i
\(502\) 2.51278e25 + 6.94651e25i 0.553948 + 1.53138i
\(503\) 1.66691e24 0.0360593 0.0180296 0.999837i \(-0.494261\pi\)
0.0180296 + 0.999837i \(0.494261\pi\)
\(504\) 4.18830e25 1.15277e25i 0.889095 0.244710i
\(505\) −2.37899e24 −0.0495593
\(506\) 8.05952e22 + 2.22803e23i 0.00164770 + 0.00455504i
\(507\) 1.01963e25 2.50656e25i 0.204581 0.502924i
\(508\) −9.32395e24 1.12015e25i −0.183609 0.220583i
\(509\) 7.55504e25i 1.46022i −0.683331 0.730109i \(-0.739469\pi\)
0.683331 0.730109i \(-0.260531\pi\)
\(510\) 4.75883e24 + 1.86890e23i 0.0902783 + 0.00354544i
\(511\) 8.80312e25i 1.63922i
\(512\) −9.73551e23 + 5.47011e25i −0.0177948 + 0.999842i
\(513\) 6.25155e24 + 1.43140e25i 0.112169 + 0.256831i
\(514\) 2.98978e25 1.08150e25i 0.526610 0.190492i
\(515\) −3.70335e24 −0.0640363
\(516\) −4.89677e23 + 1.55690e23i −0.00831261 + 0.00264294i
\(517\) −3.48611e25 −0.581007
\(518\) 3.11856e25 1.12809e25i 0.510296 0.184591i
\(519\) 9.63402e25 + 3.91896e25i 1.54781 + 0.629624i
\(520\) −2.05421e24 + 3.50974e24i −0.0324050 + 0.0553660i
\(521\) 6.38771e24i 0.0989435i 0.998776 + 0.0494717i \(0.0157538\pi\)
−0.998776 + 0.0494717i \(0.984246\pi\)
\(522\) 2.62713e24 + 1.19087e24i 0.0399588 + 0.0181132i
\(523\) 9.59352e25i 1.43289i −0.697645 0.716444i \(-0.745769\pi\)
0.697645 0.716444i \(-0.254231\pi\)
\(524\) −8.96481e25 + 7.46215e25i −1.31490 + 1.09450i
\(525\) 5.91435e25 + 2.40586e25i 0.851910 + 0.346543i
\(526\) 3.15429e25 + 8.71996e25i 0.446208 + 1.23353i
\(527\) 2.03770e26 2.83100
\(528\) −4.77455e25 3.05215e25i −0.651494 0.416469i
\(529\) −7.46125e25 −0.999961
\(530\) 1.95985e24 + 5.41796e24i 0.0257990 + 0.0713205i
\(531\) −8.81043e25 8.58915e25i −1.13920 1.11059i
\(532\) −1.56391e25 + 1.30177e25i −0.198633 + 0.165338i
\(533\) 1.24625e25i 0.155488i
\(534\) −2.88024e24 + 7.33401e25i −0.0353009 + 0.898876i
\(535\) 8.06739e24i 0.0971341i
\(536\) 2.47712e25 4.23233e25i 0.293010 0.500626i
\(537\) −3.12546e25 + 7.68335e25i −0.363210 + 0.892883i
\(538\) −8.61248e25 + 3.11542e25i −0.983324 + 0.355700i
\(539\) 1.03137e25 0.115697
\(540\) 4.18852e24 + 2.10053e24i 0.0461658 + 0.0231520i
\(541\) 5.95743e25 0.645186 0.322593 0.946538i \(-0.395446\pi\)
0.322593 + 0.946538i \(0.395446\pi\)
\(542\) −7.21073e25 + 2.60836e25i −0.767337 + 0.277571i
\(543\) −5.79641e25 + 1.42494e26i −0.606123 + 1.49004i
\(544\) −2.79036e25 1.67942e26i −0.286728 1.72572i
\(545\) 8.10026e24i 0.0817961i
\(546\) 4.52962e24 1.15339e26i 0.0449502 1.14458i
\(547\) 1.84206e26i 1.79648i −0.439501 0.898242i \(-0.644845\pi\)
0.439501 0.898242i \(-0.355155\pi\)
\(548\) −6.34926e25 7.62781e25i −0.608566 0.731113i
\(549\) 4.23933e25 + 4.13285e25i 0.399356 + 0.389326i
\(550\) −2.83323e25 7.83238e25i −0.262323 0.725184i
\(551\) −1.35110e24 −0.0122956
\(552\) −5.55430e23 + 4.26573e23i −0.00496830 + 0.00381568i
\(553\) 6.80729e25 0.598529
\(554\) −2.20624e25 6.09910e25i −0.190682 0.527136i
\(555\) 3.31350e24 + 1.34788e24i 0.0281517 + 0.0114516i
\(556\) −4.95746e25 5.95574e25i −0.414046 0.497423i
\(557\) 1.29717e26i 1.06506i −0.846411 0.532530i \(-0.821241\pi\)
0.846411 0.532530i \(-0.178759\pi\)
\(558\) 1.82601e26 + 8.27724e25i 1.47393 + 0.668130i
\(559\) 1.36532e24i 0.0108349i
\(560\) −1.10749e24 + 6.00286e24i −0.00864079 + 0.0468352i
\(561\) 1.63339e26 + 6.64436e25i 1.25298 + 0.509690i
\(562\) 2.10201e25 7.60367e24i 0.158541 0.0573493i
\(563\) 7.05450e25 0.523162 0.261581 0.965182i \(-0.415756\pi\)
0.261581 + 0.965182i \(0.415756\pi\)
\(564\) −3.12220e25 9.81998e25i −0.227672 0.716076i
\(565\) 6.50087e24 0.0466134
\(566\) 1.49033e25 5.39102e24i 0.105082 0.0380115i
\(567\) −1.32955e26 + 3.38223e24i −0.921858 + 0.0234512i
\(568\) 1.48454e26 + 8.68883e25i 1.01224 + 0.592450i
\(569\) 2.42100e26i 1.62341i −0.584067 0.811705i \(-0.698540\pi\)
0.584067 0.811705i \(-0.301460\pi\)
\(570\) −2.19315e24 8.61302e22i −0.0144630 0.000567995i
\(571\) 3.14163e24i 0.0203757i 0.999948 + 0.0101878i \(0.00324295\pi\)
−0.999948 + 0.0101878i \(0.996757\pi\)
\(572\) −1.15728e26 + 9.63298e25i −0.738202 + 0.614467i
\(573\) −5.00208e25 + 1.22967e26i −0.313821 + 0.771468i
\(574\) −6.36319e24 1.75909e25i −0.0392655 0.108549i
\(575\) −1.02936e24 −0.00624775
\(576\) 4.32141e25 1.61829e26i 0.257995 0.966146i
\(577\) −2.18079e26 −1.28069 −0.640346 0.768087i \(-0.721209\pi\)
−0.640346 + 0.768087i \(0.721209\pi\)
\(578\) 1.21320e26 + 3.35385e26i 0.700837 + 1.93745i
\(579\) 3.62674e25 8.91564e25i 0.206096 0.506648i
\(580\) −3.11518e23 + 2.59302e23i −0.00174147 + 0.00144957i
\(581\) 2.05167e26i 1.12832i
\(582\) −2.27247e25 8.92452e23i −0.122950 0.00482855i
\(583\) 2.13326e26i 1.13551i
\(584\) 2.92947e26 + 1.71458e26i 1.53415 + 0.897915i
\(585\) 8.69126e24 8.91516e24i 0.0447818 0.0459355i
\(586\) −1.81915e26 + 6.58046e25i −0.922234 + 0.333602i
\(587\) −2.91098e26 −1.45204 −0.726018 0.687676i \(-0.758631\pi\)
−0.726018 + 0.687676i \(0.758631\pi\)
\(588\) 9.23708e24 + 2.90526e25i 0.0453367 + 0.142594i
\(589\) −9.39094e25 −0.453538
\(590\) 1.62588e25 5.88133e24i 0.0772670 0.0279500i
\(591\) 1.52910e26 + 6.22012e25i 0.715079 + 0.290882i
\(592\) 2.32001e25 1.25750e26i 0.106766 0.578697i
\(593\) 1.47200e26i 0.666636i −0.942814 0.333318i \(-0.891832\pi\)
0.942814 0.333318i \(-0.108168\pi\)
\(594\) 1.19380e26 + 1.25890e26i 0.532060 + 0.561073i
\(595\) 1.89948e25i 0.0833149i
\(596\) −6.26659e25 7.52850e25i −0.270515 0.324989i
\(597\) −3.11733e26 1.26808e26i −1.32442 0.538753i
\(598\) 6.33001e23 + 1.74991e24i 0.00264693 + 0.00731738i
\(599\) −1.04065e26 −0.428300 −0.214150 0.976801i \(-0.568698\pi\)
−0.214150 + 0.976801i \(0.568698\pi\)
\(600\) 1.95255e26 1.49957e26i 0.790978 0.607475i
\(601\) 2.08805e26 0.832594 0.416297 0.909229i \(-0.363328\pi\)
0.416297 + 0.909229i \(0.363328\pi\)
\(602\) 6.97115e23 + 1.92716e24i 0.00273614 + 0.00756398i
\(603\) −1.04806e26 + 1.07506e26i −0.404922 + 0.415354i
\(604\) 2.37096e26 + 2.84840e26i 0.901722 + 1.08330i
\(605\) 5.54697e24i 0.0207673i
\(606\) 1.02172e25 2.60163e26i 0.0376566 0.958859i
\(607\) 4.56910e26i 1.65782i 0.559381 + 0.828911i \(0.311039\pi\)
−0.559381 + 0.828911i \(0.688961\pi\)
\(608\) 1.28596e25 + 7.73975e25i 0.0459351 + 0.276467i
\(609\) 4.33484e24 1.06564e25i 0.0152444 0.0374753i
\(610\) −7.82326e24 + 2.82993e24i −0.0270866 + 0.00979811i
\(611\) −2.73802e26 −0.933351
\(612\) −4.08760e25 + 5.19615e26i −0.137192 + 1.74399i
\(613\) −1.56175e26 −0.516104 −0.258052 0.966131i \(-0.583081\pi\)
−0.258052 + 0.966131i \(0.583081\pi\)
\(614\) −4.28553e25 + 1.55022e25i −0.139446 + 0.0504421i
\(615\) 7.60298e23 1.86905e24i 0.00243596 0.00598834i
\(616\) −1.14165e26 + 1.95059e26i −0.360178 + 0.615387i
\(617\) 3.15182e26i 0.979156i −0.871960 0.489578i \(-0.837151\pi\)
0.871960 0.489578i \(-0.162849\pi\)
\(618\) 1.59050e25 4.04992e26i 0.0486567 1.23896i
\(619\) 5.17028e26i 1.55759i −0.627279 0.778795i \(-0.715831\pi\)
0.627279 0.778795i \(-0.284169\pi\)
\(620\) −2.16523e25 + 1.80230e25i −0.0642365 + 0.0534694i
\(621\) 1.96492e24 8.58163e23i 0.00574082 0.00250726i
\(622\) −9.92581e25 2.74396e26i −0.285599 0.789532i
\(623\) 2.92735e26 0.829543
\(624\) −3.74997e26 2.39718e26i −1.04658 0.669032i
\(625\) 3.60889e26 0.992005
\(626\) −8.66783e25 2.39620e26i −0.234668 0.648734i
\(627\) −7.52763e25 3.06212e25i −0.200732 0.0816545i
\(628\) 2.42133e26 2.01547e26i 0.635970 0.529371i
\(629\) 3.97909e26i 1.02944i
\(630\) 7.71577e24 1.70214e25i 0.0196627 0.0433771i
\(631\) 5.35304e26i 1.34376i 0.740660 + 0.671880i \(0.234513\pi\)
−0.740660 + 0.671880i \(0.765487\pi\)
\(632\) 1.32585e26 2.26530e26i 0.327855 0.560162i
\(633\) 1.68445e26 + 6.85205e25i 0.410319 + 0.166911i
\(634\) 1.60693e26 5.81280e25i 0.385612 0.139488i
\(635\) −6.27001e24 −0.0148224
\(636\) −6.00915e26 + 1.91057e26i −1.39949 + 0.444960i
\(637\) 8.10047e25 0.185860
\(638\) −1.41123e25 + 5.10487e24i −0.0319007 + 0.0115395i
\(639\) −3.77091e26 3.67620e26i −0.839824 0.818731i
\(640\) 1.78190e25 + 1.53772e25i 0.0390998 + 0.0337417i
\(641\) 7.05666e26i 1.52563i 0.646620 + 0.762813i \(0.276182\pi\)
−0.646620 + 0.762813i \(0.723818\pi\)
\(642\) 8.82235e26 + 3.46474e25i 1.87932 + 0.0738054i
\(643\) 6.31189e26i 1.32482i −0.749144 0.662408i \(-0.769535\pi\)
0.749144 0.662408i \(-0.230465\pi\)
\(644\) 1.78697e24 + 2.14681e24i 0.00369573 + 0.00443994i
\(645\) −8.32940e22 + 2.04762e23i −0.000169745 + 0.000417285i
\(646\) −8.30487e25 2.29586e26i −0.166772 0.461038i
\(647\) 5.30086e26 1.04895 0.524476 0.851425i \(-0.324261\pi\)
0.524476 + 0.851425i \(0.324261\pi\)
\(648\) −2.47699e26 + 4.49028e26i −0.483017 + 0.875611i
\(649\) 6.40172e26 1.23019
\(650\) −2.22524e26 6.15162e26i −0.421405 1.16496i
\(651\) 3.01296e26 7.40679e26i 0.562308 1.38233i
\(652\) 4.82643e26 + 5.79833e26i 0.887715 + 1.06647i
\(653\) 3.23879e26i 0.587093i −0.955945 0.293547i \(-0.905164\pi\)
0.955945 0.293547i \(-0.0948356\pi\)
\(654\) −8.85831e26 3.47886e25i −1.58257 0.0621511i
\(655\) 5.01802e25i 0.0883568i
\(656\) −7.09317e25 1.30864e25i −0.123099 0.0227109i
\(657\) −7.44120e26 7.25431e26i −1.27283 1.24087i
\(658\) −3.86472e26 + 1.39800e26i −0.651587 + 0.235700i
\(659\) 4.40061e26 0.731310 0.365655 0.930750i \(-0.380845\pi\)
0.365655 + 0.930750i \(0.380845\pi\)
\(660\) −2.32329e25 + 7.38674e24i −0.0380571 + 0.0121000i
\(661\) 8.58416e25 0.138607 0.0693033 0.997596i \(-0.477922\pi\)
0.0693033 + 0.997596i \(0.477922\pi\)
\(662\) −4.40003e26 + 1.59164e26i −0.700334 + 0.253334i
\(663\) 1.28288e27 + 5.21853e26i 2.01283 + 0.818785i
\(664\) 6.82745e26 + 3.99602e26i 1.05599 + 0.618060i
\(665\) 8.75392e24i 0.0133474i
\(666\) −1.61632e26 + 3.56570e26i −0.242954 + 0.535969i
\(667\) 1.85469e23i 0.000274837i
\(668\) 4.89234e26 4.07230e26i 0.714727 0.594927i
\(669\) 3.70676e26 + 1.50785e26i 0.533884 + 0.217175i
\(670\) −7.17648e24 1.98392e25i −0.0101906 0.0281717i
\(671\) −3.08032e26 −0.431253
\(672\) −6.51706e26 1.46894e26i −0.899588 0.202766i
\(673\) −1.23415e27 −1.67968 −0.839839 0.542836i \(-0.817350\pi\)
−0.839839 + 0.542836i \(0.817350\pi\)
\(674\) −6.59554e25 1.82332e26i −0.0885078 0.244677i
\(675\) −6.90743e26 + 3.01677e26i −0.913968 + 0.399168i
\(676\) −3.19843e26 + 2.66232e26i −0.417295 + 0.347349i
\(677\) 1.43762e24i 0.00184949i 1.00000 0.000924747i \(0.000294356\pi\)
−1.00000 0.000924747i \(0.999706\pi\)
\(678\) −2.79196e25 + 7.10924e26i −0.0354183 + 0.901863i
\(679\) 9.07051e25i 0.113467i
\(680\) −6.32100e25 3.69960e25i −0.0779743 0.0456373i
\(681\) 9.22369e25 2.26747e26i 0.112204 0.275831i
\(682\) −9.80883e26 + 3.54817e26i −1.17670 + 0.425651i
\(683\) −2.64872e23 −0.000313357 −0.000156678 1.00000i \(-0.500050\pi\)
−0.000156678 1.00000i \(0.500050\pi\)
\(684\) 1.88381e25 2.39469e26i 0.0219788 0.279394i
\(685\) −4.26964e25 −0.0491282
\(686\) 8.78493e26 3.17780e26i 0.996917 0.360617i
\(687\) 1.61278e25 3.96472e25i 0.0180504 0.0443734i
\(688\) 7.77088e24 + 1.43368e24i 0.00857788 + 0.00158256i
\(689\) 1.67548e27i 1.82413i
\(690\) −1.18233e22 + 3.01058e23i −1.26961e−5 + 0.000323284i
\(691\) 2.09947e26i 0.222366i 0.993800 + 0.111183i \(0.0354640\pi\)
−0.993800 + 0.111183i \(0.964536\pi\)
\(692\) −1.02327e27 1.22932e27i −1.06901 1.28428i
\(693\) 4.83028e26 4.95472e26i 0.497745 0.510568i
\(694\) −2.52864e26 6.99034e26i −0.257023 0.710532i
\(695\) −3.33371e25 −0.0334250
\(696\) −2.70189e25 3.51807e25i −0.0267227 0.0347950i
\(697\) 2.24448e26 0.218980
\(698\) 3.60692e26 + 9.97122e26i 0.347144 + 0.959670i
\(699\) 1.07456e27 + 4.37114e26i 1.02023 + 0.415013i
\(700\) −6.28186e26 7.54684e26i −0.588379 0.706861i
\(701\) 8.01939e26i 0.741004i 0.928832 + 0.370502i \(0.120814\pi\)
−0.928832 + 0.370502i \(0.879186\pi\)
\(702\) 9.37620e26 + 9.88749e26i 0.854721 + 0.901329i
\(703\) 1.83380e26i 0.164921i
\(704\) 4.26750e26 + 7.59829e26i 0.378645 + 0.674180i
\(705\) −4.10631e25 1.67038e25i −0.0359463 0.0146224i
\(706\) −8.60075e26 + 3.11117e26i −0.742833 + 0.268707i
\(707\) −1.03843e27 −0.884900
\(708\) 5.73345e26 + 1.80329e27i 0.482058 + 1.51618i
\(709\) 2.30006e25 0.0190809 0.00954047 0.999954i \(-0.496963\pi\)
0.00954047 + 0.999954i \(0.496963\pi\)
\(710\) 6.95885e25 2.51724e25i 0.0569617 0.0206049i
\(711\) −5.60962e26 + 5.75413e26i −0.453077 + 0.464749i
\(712\) 5.70159e26 9.74153e26i 0.454398 0.776367i
\(713\) 1.28911e25i 0.0101377i
\(714\) 2.07723e27 + 8.15778e25i 1.61195 + 0.0633052i
\(715\) 6.47782e25i 0.0496045i
\(716\) 9.80412e26 8.16078e26i 0.740858 0.616678i
\(717\) 6.04254e26 1.48544e27i 0.450596 1.10770i
\(718\) −2.65313e25 7.33450e25i −0.0195243 0.0539745i
\(719\) −1.54969e27 −1.12544 −0.562718 0.826649i \(-0.690244\pi\)
−0.562718 + 0.826649i \(0.690244\pi\)
\(720\) −4.16152e25 5.88287e25i −0.0298259 0.0421629i
\(721\) −1.61652e27 −1.14339
\(722\) −4.49017e26 1.24130e27i −0.313444 0.866507i
\(723\) −3.12308e26 + 7.67749e26i −0.215164 + 0.528939i
\(724\) 1.81825e27 1.51348e27i 1.23634 1.02911i
\(725\) 6.51993e25i 0.0437555i
\(726\) 6.06607e26 + 2.38229e25i 0.401799 + 0.0157796i
\(727\) 7.09055e26i 0.463557i −0.972769 0.231778i \(-0.925546\pi\)
0.972769 0.231778i \(-0.0744544\pi\)
\(728\) −8.96663e26 + 1.53201e27i −0.578604 + 0.988582i
\(729\) 1.06704e27 1.15172e27i 0.679622 0.733562i
\(730\) 1.37320e26 4.96731e25i 0.0863310 0.0312287i
\(731\) −2.45893e25 −0.0152592
\(732\) −2.75877e26 8.67692e26i −0.168990 0.531509i
\(733\) 9.83813e26 0.594874 0.297437 0.954741i \(-0.403868\pi\)
0.297437 + 0.954741i \(0.403868\pi\)
\(734\) 1.39141e27 5.03317e26i 0.830503 0.300420i
\(735\) 1.21486e25 + 4.94184e24i 0.00715806 + 0.00291178i
\(736\) 1.06245e25 1.76527e24i 0.00617974 0.00102677i
\(737\) 7.81147e26i 0.448530i
\(738\) 2.01130e26 + 9.11719e25i 0.114010 + 0.0516804i
\(739\) 2.53086e27i 1.41627i −0.706076 0.708136i \(-0.749536\pi\)
0.706076 0.708136i \(-0.250464\pi\)
\(740\) −3.51940e25 4.22811e25i −0.0194432 0.0233585i
\(741\) −5.91226e26 2.40501e26i −0.322463 0.131173i
\(742\) 8.55477e26 + 2.36494e27i 0.460650 + 1.27346i
\(743\) −2.31813e27 −1.23238 −0.616189 0.787599i \(-0.711324\pi\)
−0.616189 + 0.787599i \(0.711324\pi\)
\(744\) −1.87797e27 2.44526e27i −0.985702 1.28346i
\(745\) −4.21405e25 −0.0218381
\(746\) 3.27401e26 + 9.05092e26i 0.167518 + 0.463099i
\(747\) −1.73425e27 1.69070e27i −0.876127 0.854122i
\(748\) −1.73489e27 2.08424e27i −0.865378 1.03964i
\(749\) 3.52142e27i 1.73437i
\(750\) 8.32377e24 2.11950e26i 0.00404798 0.103075i
\(751\) 2.61972e27i 1.25798i 0.777412 + 0.628992i \(0.216532\pi\)
−0.777412 + 0.628992i \(0.783468\pi\)
\(752\) −2.87510e26 + 1.55837e27i −0.136328 + 0.738928i
\(753\) −1.31054e27 + 3.22170e27i −0.613616 + 1.50846i
\(754\) −1.10839e26 + 4.00940e25i −0.0512465 + 0.0185375i
\(755\) 1.59438e26 0.0727940
\(756\) 1.82830e27 + 9.16886e26i 0.824307 + 0.413388i
\(757\) −2.21599e27 −0.986634 −0.493317 0.869850i \(-0.664216\pi\)
−0.493317 + 0.869850i \(0.664216\pi\)
\(758\) 2.04887e26 7.41141e25i 0.0900857 0.0325869i
\(759\) −4.20343e24 + 1.03333e25i −0.00182518 + 0.00448687i
\(760\) 2.91309e25 + 1.70499e25i 0.0124918 + 0.00731129i
\(761\) 4.16008e26i 0.176176i −0.996113 0.0880882i \(-0.971924\pi\)
0.996113 0.0880882i \(-0.0280757\pi\)
\(762\) 2.69282e25 6.85677e26i 0.0112625 0.286779i