Properties

Label 147.4.c.a.146.5
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} - 29 x^{9} + 6 x^{8} - 49 x^{7} + 1564 x^{6} - 441 x^{5} + 486 x^{4} - 21141 x^{3} - 59049 x + 531441\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.5
Root \(-2.23014 + 2.00661i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.a.146.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.90883i q^{2} +(-5.08298 - 1.07856i) q^{3} +4.35636 q^{4} +1.24741 q^{5} +(-2.05878 + 9.70256i) q^{6} -23.5862i q^{8} +(24.6734 + 10.9646i) q^{9} +O(q^{10})\) \(q-1.90883i q^{2} +(-5.08298 - 1.07856i) q^{3} +4.35636 q^{4} +1.24741 q^{5} +(-2.05878 + 9.70256i) q^{6} -23.5862i q^{8} +(24.6734 + 10.9646i) q^{9} -2.38110i q^{10} -40.6907i q^{11} +(-22.1433 - 4.69858i) q^{12} -19.5973i q^{13} +(-6.34057 - 1.34540i) q^{15} -10.1712 q^{16} -104.718 q^{17} +(20.9295 - 47.0974i) q^{18} -40.4544i q^{19} +5.43418 q^{20} -77.6716 q^{22} +80.4045i q^{23} +(-25.4391 + 119.888i) q^{24} -123.444 q^{25} -37.4079 q^{26} +(-113.589 - 82.3444i) q^{27} -211.712i q^{29} +(-2.56815 + 12.1031i) q^{30} -100.025i q^{31} -169.275i q^{32} +(-43.8872 + 206.830i) q^{33} +199.890i q^{34} +(107.486 + 47.7656i) q^{36} -189.975 q^{37} -77.2206 q^{38} +(-21.1368 + 99.6127i) q^{39} -29.4217i q^{40} +186.753 q^{41} +158.618 q^{43} -177.263i q^{44} +(30.7779 + 13.6773i) q^{45} +153.479 q^{46} +358.069 q^{47} +(51.6999 + 10.9702i) q^{48} +235.634i q^{50} +(532.282 + 112.945i) q^{51} -85.3729i q^{52} +423.152i q^{53} +(-157.182 + 216.822i) q^{54} -50.7580i q^{55} +(-43.6323 + 205.629i) q^{57} -404.123 q^{58} +625.562 q^{59} +(-27.6218 - 5.86106i) q^{60} -807.799i q^{61} -190.931 q^{62} -404.486 q^{64} -24.4459i q^{65} +(394.804 + 83.7732i) q^{66} +298.544 q^{67} -456.192 q^{68} +(86.7208 - 408.695i) q^{69} +455.386i q^{71} +(258.613 - 581.953i) q^{72} -501.679i q^{73} +362.630i q^{74} +(627.464 + 133.141i) q^{75} -176.234i q^{76} +(190.144 + 40.3465i) q^{78} -61.9122 q^{79} -12.6876 q^{80} +(488.557 + 541.067i) q^{81} -356.479i q^{82} +73.1180 q^{83} -130.627 q^{85} -302.775i q^{86} +(-228.343 + 1076.13i) q^{87} -959.739 q^{88} +114.745 q^{89} +(26.1077 - 58.7498i) q^{90} +350.271i q^{92} +(-107.883 + 508.425i) q^{93} -683.493i q^{94} -50.4633i q^{95} +(-182.572 + 860.420i) q^{96} +1416.51i q^{97} +(446.156 - 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 28q^{4} + 6q^{9} + O(q^{10}) \) \( 12q - 28q^{4} + 6q^{9} + 6q^{15} - 268q^{16} - 132q^{18} - 268q^{22} + 84q^{25} + 1644q^{30} + 852q^{36} - 1528q^{37} + 852q^{39} - 1012q^{43} - 1216q^{46} + 2682q^{51} + 270q^{57} - 5740q^{58} + 1836q^{60} - 548q^{64} - 1584q^{67} + 5424q^{72} + 4296q^{78} - 3348q^{79} - 1674q^{81} + 348q^{85} + 1108q^{88} + 2958q^{93} - 3354q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90883i 0.674874i −0.941348 0.337437i \(-0.890440\pi\)
0.941348 0.337437i \(-0.109560\pi\)
\(3\) −5.08298 1.07856i −0.978221 0.207568i
\(4\) 4.35636 0.544546
\(5\) 1.24741 0.111572 0.0557859 0.998443i \(-0.482234\pi\)
0.0557859 + 0.998443i \(0.482234\pi\)
\(6\) −2.05878 + 9.70256i −0.140082 + 0.660175i
\(7\) 0 0
\(8\) 23.5862i 1.04237i
\(9\) 24.6734 + 10.9646i 0.913831 + 0.406095i
\(10\) 2.38110i 0.0752969i
\(11\) 40.6907i 1.11534i −0.830064 0.557668i \(-0.811696\pi\)
0.830064 0.557668i \(-0.188304\pi\)
\(12\) −22.1433 4.69858i −0.532686 0.113030i
\(13\) 19.5973i 0.418101i −0.977905 0.209050i \(-0.932963\pi\)
0.977905 0.209050i \(-0.0670373\pi\)
\(14\) 0 0
\(15\) −6.34057 1.34540i −0.109142 0.0231588i
\(16\) −10.1712 −0.158925
\(17\) −104.718 −1.49400 −0.746999 0.664825i \(-0.768506\pi\)
−0.746999 + 0.664825i \(0.768506\pi\)
\(18\) 20.9295 47.0974i 0.274063 0.616720i
\(19\) 40.4544i 0.488467i −0.969716 0.244234i \(-0.921464\pi\)
0.969716 0.244234i \(-0.0785364\pi\)
\(20\) 5.43418 0.0607559
\(21\) 0 0
\(22\) −77.6716 −0.752711
\(23\) 80.4045i 0.728935i 0.931216 + 0.364467i \(0.118749\pi\)
−0.931216 + 0.364467i \(0.881251\pi\)
\(24\) −25.4391 + 119.888i −0.216364 + 1.01967i
\(25\) −123.444 −0.987552
\(26\) −37.4079 −0.282165
\(27\) −113.589 82.3444i −0.809636 0.586933i
\(28\) 0 0
\(29\) 211.712i 1.35565i −0.735222 0.677827i \(-0.762922\pi\)
0.735222 0.677827i \(-0.237078\pi\)
\(30\) −2.56815 + 12.1031i −0.0156292 + 0.0736570i
\(31\) 100.025i 0.579517i −0.957100 0.289758i \(-0.906425\pi\)
0.957100 0.289758i \(-0.0935749\pi\)
\(32\) 169.275i 0.935119i
\(33\) −43.8872 + 206.830i −0.231508 + 1.09105i
\(34\) 199.890i 1.00826i
\(35\) 0 0
\(36\) 107.486 + 47.7656i 0.497622 + 0.221137i
\(37\) −189.975 −0.844100 −0.422050 0.906572i \(-0.638689\pi\)
−0.422050 + 0.906572i \(0.638689\pi\)
\(38\) −77.2206 −0.329654
\(39\) −21.1368 + 99.6127i −0.0867844 + 0.408995i
\(40\) 29.4217i 0.116299i
\(41\) 186.753 0.711362 0.355681 0.934607i \(-0.384249\pi\)
0.355681 + 0.934607i \(0.384249\pi\)
\(42\) 0 0
\(43\) 158.618 0.562536 0.281268 0.959629i \(-0.409245\pi\)
0.281268 + 0.959629i \(0.409245\pi\)
\(44\) 177.263i 0.607352i
\(45\) 30.7779 + 13.6773i 0.101958 + 0.0453088i
\(46\) 153.479 0.491939
\(47\) 358.069 1.11127 0.555635 0.831426i \(-0.312475\pi\)
0.555635 + 0.831426i \(0.312475\pi\)
\(48\) 51.6999 + 10.9702i 0.155463 + 0.0329877i
\(49\) 0 0
\(50\) 235.634i 0.666473i
\(51\) 532.282 + 112.945i 1.46146 + 0.310106i
\(52\) 85.3729i 0.227675i
\(53\) 423.152i 1.09669i 0.836254 + 0.548343i \(0.184741\pi\)
−0.836254 + 0.548343i \(0.815259\pi\)
\(54\) −157.182 + 216.822i −0.396105 + 0.546402i
\(55\) 50.7580i 0.124440i
\(56\) 0 0
\(57\) −43.6323 + 205.629i −0.101390 + 0.477829i
\(58\) −404.123 −0.914895
\(59\) 625.562 1.38036 0.690180 0.723638i \(-0.257531\pi\)
0.690180 + 0.723638i \(0.257531\pi\)
\(60\) −27.6218 5.86106i −0.0594327 0.0126110i
\(61\) 807.799i 1.69554i −0.530362 0.847772i \(-0.677944\pi\)
0.530362 0.847772i \(-0.322056\pi\)
\(62\) −190.931 −0.391101
\(63\) 0 0
\(64\) −404.486 −0.790012
\(65\) 24.4459i 0.0466483i
\(66\) 394.804 + 83.7732i 0.736318 + 0.156239i
\(67\) 298.544 0.544373 0.272187 0.962245i \(-0.412253\pi\)
0.272187 + 0.962245i \(0.412253\pi\)
\(68\) −456.192 −0.813550
\(69\) 86.7208 408.695i 0.151304 0.713059i
\(70\) 0 0
\(71\) 455.386i 0.761189i 0.924742 + 0.380594i \(0.124281\pi\)
−0.924742 + 0.380594i \(0.875719\pi\)
\(72\) 258.613 581.953i 0.423302 0.952553i
\(73\) 501.679i 0.804344i −0.915564 0.402172i \(-0.868255\pi\)
0.915564 0.402172i \(-0.131745\pi\)
\(74\) 362.630i 0.569661i
\(75\) 627.464 + 133.141i 0.966043 + 0.204984i
\(76\) 176.234i 0.265993i
\(77\) 0 0
\(78\) 190.144 + 40.3465i 0.276020 + 0.0585685i
\(79\) −61.9122 −0.0881731 −0.0440865 0.999028i \(-0.514038\pi\)
−0.0440865 + 0.999028i \(0.514038\pi\)
\(80\) −12.6876 −0.0177315
\(81\) 488.557 + 541.067i 0.670174 + 0.742204i
\(82\) 356.479i 0.480080i
\(83\) 73.1180 0.0966957 0.0483478 0.998831i \(-0.484604\pi\)
0.0483478 + 0.998831i \(0.484604\pi\)
\(84\) 0 0
\(85\) −130.627 −0.166688
\(86\) 302.775i 0.379641i
\(87\) −228.343 + 1076.13i −0.281391 + 1.32613i
\(88\) −959.739 −1.16260
\(89\) 114.745 0.136662 0.0683309 0.997663i \(-0.478233\pi\)
0.0683309 + 0.997663i \(0.478233\pi\)
\(90\) 26.1077 58.7498i 0.0305777 0.0688086i
\(91\) 0 0
\(92\) 350.271i 0.396938i
\(93\) −107.883 + 508.425i −0.120289 + 0.566895i
\(94\) 683.493i 0.749967i
\(95\) 50.4633i 0.0544992i
\(96\) −182.572 + 860.420i −0.194101 + 0.914753i
\(97\) 1416.51i 1.48273i 0.671101 + 0.741366i \(0.265822\pi\)
−0.671101 + 0.741366i \(0.734178\pi\)
\(98\) 0 0
\(99\) 446.156 1003.98i 0.452933 1.01923i
\(100\) −537.767 −0.537767
\(101\) 240.811 0.237244 0.118622 0.992940i \(-0.462152\pi\)
0.118622 + 0.992940i \(0.462152\pi\)
\(102\) 215.592 1016.04i 0.209283 0.986300i
\(103\) 1109.04i 1.06094i 0.847705 + 0.530469i \(0.177984\pi\)
−0.847705 + 0.530469i \(0.822016\pi\)
\(104\) −462.226 −0.435817
\(105\) 0 0
\(106\) 807.725 0.740124
\(107\) 1067.69i 0.964646i 0.875993 + 0.482323i \(0.160207\pi\)
−0.875993 + 0.482323i \(0.839793\pi\)
\(108\) −494.834 358.722i −0.440883 0.319612i
\(109\) 10.0875 0.00886430 0.00443215 0.999990i \(-0.498589\pi\)
0.00443215 + 0.999990i \(0.498589\pi\)
\(110\) −96.8885 −0.0839814
\(111\) 965.640 + 204.899i 0.825716 + 0.175208i
\(112\) 0 0
\(113\) 884.294i 0.736171i −0.929792 0.368086i \(-0.880013\pi\)
0.929792 0.368086i \(-0.119987\pi\)
\(114\) 392.511 + 83.2868i 0.322474 + 0.0684256i
\(115\) 100.297i 0.0813286i
\(116\) 922.295i 0.738215i
\(117\) 214.876 483.532i 0.169789 0.382073i
\(118\) 1194.09i 0.931569i
\(119\) 0 0
\(120\) −31.7330 + 149.550i −0.0241401 + 0.113767i
\(121\) −324.732 −0.243976
\(122\) −1541.95 −1.14428
\(123\) −949.260 201.423i −0.695869 0.147656i
\(124\) 435.745i 0.315573i
\(125\) −309.912 −0.221755
\(126\) 0 0
\(127\) −840.132 −0.587005 −0.293503 0.955958i \(-0.594821\pi\)
−0.293503 + 0.955958i \(0.594821\pi\)
\(128\) 582.101i 0.401961i
\(129\) −806.254 171.079i −0.550284 0.116765i
\(130\) −46.6631 −0.0314817
\(131\) −517.902 −0.345415 −0.172707 0.984973i \(-0.555252\pi\)
−0.172707 + 0.984973i \(0.555252\pi\)
\(132\) −191.189 + 901.027i −0.126067 + 0.594124i
\(133\) 0 0
\(134\) 569.871i 0.367383i
\(135\) −141.692 102.717i −0.0903325 0.0654852i
\(136\) 2469.91i 1.55730i
\(137\) 1098.07i 0.684777i −0.939558 0.342389i \(-0.888764\pi\)
0.939558 0.342389i \(-0.111236\pi\)
\(138\) −780.129 165.535i −0.481225 0.102111i
\(139\) 828.268i 0.505416i −0.967543 0.252708i \(-0.918679\pi\)
0.967543 0.252708i \(-0.0813212\pi\)
\(140\) 0 0
\(141\) −1820.06 386.197i −1.08707 0.230664i
\(142\) 869.255 0.513706
\(143\) −797.427 −0.466323
\(144\) −250.958 111.523i −0.145230 0.0645385i
\(145\) 264.092i 0.151253i
\(146\) −957.621 −0.542830
\(147\) 0 0
\(148\) −827.601 −0.459651
\(149\) 892.592i 0.490765i 0.969426 + 0.245382i \(0.0789135\pi\)
−0.969426 + 0.245382i \(0.921086\pi\)
\(150\) 254.144 1197.72i 0.138339 0.651957i
\(151\) 1425.04 0.767999 0.383999 0.923333i \(-0.374546\pi\)
0.383999 + 0.923333i \(0.374546\pi\)
\(152\) −954.166 −0.509165
\(153\) −2583.76 1148.19i −1.36526 0.606705i
\(154\) 0 0
\(155\) 124.772i 0.0646577i
\(156\) −92.0795 + 433.949i −0.0472581 + 0.222716i
\(157\) 282.754i 0.143734i −0.997414 0.0718670i \(-0.977104\pi\)
0.997414 0.0718670i \(-0.0228957\pi\)
\(158\) 118.180i 0.0595057i
\(159\) 456.393 2150.87i 0.227637 1.07280i
\(160\) 211.155i 0.104333i
\(161\) 0 0
\(162\) 1032.81 932.572i 0.500894 0.452283i
\(163\) 2316.13 1.11297 0.556484 0.830859i \(-0.312150\pi\)
0.556484 + 0.830859i \(0.312150\pi\)
\(164\) 813.562 0.387369
\(165\) −54.7454 + 258.002i −0.0258298 + 0.121730i
\(166\) 139.570i 0.0652574i
\(167\) 2344.70 1.08646 0.543229 0.839585i \(-0.317202\pi\)
0.543229 + 0.839585i \(0.317202\pi\)
\(168\) 0 0
\(169\) 1812.95 0.825192
\(170\) 249.345i 0.112493i
\(171\) 443.565 998.149i 0.198364 0.446376i
\(172\) 690.999 0.306327
\(173\) 1033.80 0.454326 0.227163 0.973857i \(-0.427055\pi\)
0.227163 + 0.973857i \(0.427055\pi\)
\(174\) 2054.15 + 435.869i 0.894969 + 0.189903i
\(175\) 0 0
\(176\) 413.872i 0.177255i
\(177\) −3179.72 674.704i −1.35030 0.286519i
\(178\) 219.028i 0.0922294i
\(179\) 144.882i 0.0604973i 0.999542 + 0.0302486i \(0.00962991\pi\)
−0.999542 + 0.0302486i \(0.990370\pi\)
\(180\) 134.080 + 59.5834i 0.0555207 + 0.0246727i
\(181\) 2057.17i 0.844797i 0.906410 + 0.422398i \(0.138812\pi\)
−0.906410 + 0.422398i \(0.861188\pi\)
\(182\) 0 0
\(183\) −871.257 + 4106.03i −0.351941 + 1.65862i
\(184\) 1896.44 0.759822
\(185\) −236.977 −0.0941778
\(186\) 970.498 + 205.930i 0.382583 + 0.0811800i
\(187\) 4261.07i 1.66631i
\(188\) 1559.88 0.605137
\(189\) 0 0
\(190\) −96.3259 −0.0367801
\(191\) 2948.72i 1.11708i −0.829479 0.558538i \(-0.811362\pi\)
0.829479 0.558538i \(-0.188638\pi\)
\(192\) 2056.00 + 436.261i 0.772806 + 0.163981i
\(193\) −2270.80 −0.846920 −0.423460 0.905915i \(-0.639185\pi\)
−0.423460 + 0.905915i \(0.639185\pi\)
\(194\) 2703.88 1.00066
\(195\) −26.3662 + 124.258i −0.00968270 + 0.0456323i
\(196\) 0 0
\(197\) 495.849i 0.179329i −0.995972 0.0896645i \(-0.971421\pi\)
0.995972 0.0896645i \(-0.0285795\pi\)
\(198\) −1916.43 851.636i −0.687851 0.305672i
\(199\) 839.706i 0.299121i 0.988753 + 0.149561i \(0.0477859\pi\)
−0.988753 + 0.149561i \(0.952214\pi\)
\(200\) 2911.58i 1.02940i
\(201\) −1517.50 321.997i −0.532517 0.112995i
\(202\) 459.668i 0.160109i
\(203\) 0 0
\(204\) 2318.81 + 492.028i 0.795831 + 0.168867i
\(205\) 232.957 0.0793680
\(206\) 2116.96 0.715999
\(207\) −881.601 + 1983.86i −0.296017 + 0.666123i
\(208\) 199.328i 0.0664465i
\(209\) −1646.12 −0.544805
\(210\) 0 0
\(211\) 4001.71 1.30564 0.652818 0.757514i \(-0.273586\pi\)
0.652818 + 0.757514i \(0.273586\pi\)
\(212\) 1843.40i 0.597195i
\(213\) 491.160 2314.72i 0.157999 0.744611i
\(214\) 2038.03 0.651014
\(215\) 197.862 0.0627632
\(216\) −1942.19 + 2679.13i −0.611803 + 0.843943i
\(217\) 0 0
\(218\) 19.2554i 0.00598228i
\(219\) −541.089 + 2550.03i −0.166956 + 0.786826i
\(220\) 221.120i 0.0677633i
\(221\) 2052.20i 0.624642i
\(222\) 391.117 1843.24i 0.118244 0.557254i
\(223\) 3040.54i 0.913047i −0.889711 0.456523i \(-0.849095\pi\)
0.889711 0.456523i \(-0.150905\pi\)
\(224\) 0 0
\(225\) −3045.79 1353.51i −0.902455 0.401040i
\(226\) −1687.97 −0.496823
\(227\) 4396.47 1.28548 0.642741 0.766084i \(-0.277797\pi\)
0.642741 + 0.766084i \(0.277797\pi\)
\(228\) −190.078 + 895.795i −0.0552116 + 0.260199i
\(229\) 1983.56i 0.572389i 0.958172 + 0.286194i \(0.0923903\pi\)
−0.958172 + 0.286194i \(0.907610\pi\)
\(230\) 191.451 0.0548865
\(231\) 0 0
\(232\) −4993.49 −1.41310
\(233\) 4373.75i 1.22976i −0.788621 0.614879i \(-0.789205\pi\)
0.788621 0.614879i \(-0.210795\pi\)
\(234\) −922.982 410.162i −0.257851 0.114586i
\(235\) 446.659 0.123986
\(236\) 2725.18 0.751669
\(237\) 314.699 + 66.7758i 0.0862527 + 0.0183019i
\(238\) 0 0
\(239\) 3826.41i 1.03561i 0.855500 + 0.517803i \(0.173250\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(240\) 64.4911 + 13.6843i 0.0173453 + 0.00368050i
\(241\) 3439.89i 0.919430i 0.888066 + 0.459715i \(0.152048\pi\)
−0.888066 + 0.459715i \(0.847952\pi\)
\(242\) 619.858i 0.164653i
\(243\) −1899.75 3277.17i −0.501520 0.865146i
\(244\) 3519.07i 0.923300i
\(245\) 0 0
\(246\) −384.483 + 1811.98i −0.0996493 + 0.469624i
\(247\) −792.797 −0.204229
\(248\) −2359.21 −0.604073
\(249\) −371.657 78.8618i −0.0945897 0.0200709i
\(250\) 591.569i 0.149656i
\(251\) 2046.61 0.514664 0.257332 0.966323i \(-0.417157\pi\)
0.257332 + 0.966323i \(0.417157\pi\)
\(252\) 0 0
\(253\) 3271.72 0.813008
\(254\) 1603.67i 0.396154i
\(255\) 663.975 + 140.889i 0.163058 + 0.0345991i
\(256\) −4347.02 −1.06128
\(257\) −6051.14 −1.46871 −0.734357 0.678763i \(-0.762516\pi\)
−0.734357 + 0.678763i \(0.762516\pi\)
\(258\) −326.560 + 1539.00i −0.0788014 + 0.371372i
\(259\) 0 0
\(260\) 106.495i 0.0254021i
\(261\) 2321.33 5223.66i 0.550524 1.23884i
\(262\) 988.588i 0.233111i
\(263\) 6274.28i 1.47106i −0.677492 0.735530i \(-0.736933\pi\)
0.677492 0.735530i \(-0.263067\pi\)
\(264\) 4878.34 + 1035.13i 1.13728 + 0.241318i
\(265\) 527.844i 0.122359i
\(266\) 0 0
\(267\) −583.245 123.758i −0.133685 0.0283666i
\(268\) 1300.57 0.296436
\(269\) −3336.35 −0.756212 −0.378106 0.925762i \(-0.623425\pi\)
−0.378106 + 0.925762i \(0.623425\pi\)
\(270\) −196.070 + 270.466i −0.0441942 + 0.0609631i
\(271\) 2843.17i 0.637308i −0.947871 0.318654i \(-0.896769\pi\)
0.947871 0.318654i \(-0.103231\pi\)
\(272\) 1065.11 0.237433
\(273\) 0 0
\(274\) −2096.03 −0.462138
\(275\) 5023.02i 1.10145i
\(276\) 377.787 1780.42i 0.0823918 0.388293i
\(277\) 6348.34 1.37702 0.688510 0.725226i \(-0.258265\pi\)
0.688510 + 0.725226i \(0.258265\pi\)
\(278\) −1581.02 −0.341092
\(279\) 1096.73 2467.96i 0.235339 0.529580i
\(280\) 0 0
\(281\) 3735.88i 0.793110i −0.918011 0.396555i \(-0.870206\pi\)
0.918011 0.396555i \(-0.129794\pi\)
\(282\) −737.185 + 3474.18i −0.155669 + 0.733633i
\(283\) 5517.12i 1.15886i −0.815021 0.579432i \(-0.803274\pi\)
0.815021 0.579432i \(-0.196726\pi\)
\(284\) 1983.83i 0.414502i
\(285\) −54.4275 + 256.504i −0.0113123 + 0.0533122i
\(286\) 1522.15i 0.314709i
\(287\) 0 0
\(288\) 1856.02 4176.59i 0.379747 0.854541i
\(289\) 6052.96 1.23203
\(290\) −504.107 −0.102077
\(291\) 1527.79 7200.11i 0.307768 1.45044i
\(292\) 2185.50i 0.438002i
\(293\) −7574.50 −1.51026 −0.755131 0.655574i \(-0.772427\pi\)
−0.755131 + 0.655574i \(0.772427\pi\)
\(294\) 0 0
\(295\) 780.333 0.154009
\(296\) 4480.79i 0.879868i
\(297\) −3350.65 + 4622.00i −0.654628 + 0.903016i
\(298\) 1703.81 0.331204
\(299\) 1575.71 0.304768
\(300\) 2733.46 + 580.012i 0.526055 + 0.111623i
\(301\) 0 0
\(302\) 2720.15i 0.518302i
\(303\) −1224.04 259.728i −0.232077 0.0492442i
\(304\) 411.469i 0.0776295i
\(305\) 1007.66i 0.189175i
\(306\) −2191.71 + 4931.97i −0.409449 + 0.921379i
\(307\) 10635.6i 1.97723i 0.150480 + 0.988613i \(0.451918\pi\)
−0.150480 + 0.988613i \(0.548082\pi\)
\(308\) 0 0
\(309\) 1196.16 5637.21i 0.220217 1.03783i
\(310\) −238.169 −0.0436358
\(311\) −5771.19 −1.05226 −0.526132 0.850403i \(-0.676358\pi\)
−0.526132 + 0.850403i \(0.676358\pi\)
\(312\) 2349.49 + 498.536i 0.426325 + 0.0904618i
\(313\) 2344.52i 0.423387i 0.977336 + 0.211694i \(0.0678979\pi\)
−0.977336 + 0.211694i \(0.932102\pi\)
\(314\) −539.730 −0.0970023
\(315\) 0 0
\(316\) −269.712 −0.0480142
\(317\) 7912.13i 1.40186i −0.713231 0.700929i \(-0.752769\pi\)
0.713231 0.700929i \(-0.247231\pi\)
\(318\) −4105.65 871.177i −0.724005 0.153626i
\(319\) −8614.71 −1.51201
\(320\) −504.560 −0.0881431
\(321\) 1151.56 5427.03i 0.200230 0.943637i
\(322\) 0 0
\(323\) 4236.32i 0.729769i
\(324\) 2128.33 + 2357.08i 0.364940 + 0.404164i
\(325\) 2419.17i 0.412896i
\(326\) 4421.11i 0.751112i
\(327\) −51.2747 10.8800i −0.00867124 0.00183995i
\(328\) 4404.78i 0.741505i
\(329\) 0 0
\(330\) 492.482 + 104.500i 0.0821523 + 0.0174319i
\(331\) −4880.03 −0.810365 −0.405182 0.914236i \(-0.632792\pi\)
−0.405182 + 0.914236i \(0.632792\pi\)
\(332\) 318.528 0.0526552
\(333\) −4687.34 2082.99i −0.771365 0.342785i
\(334\) 4475.64i 0.733222i
\(335\) 372.407 0.0607367
\(336\) 0 0
\(337\) −4136.39 −0.668616 −0.334308 0.942464i \(-0.608503\pi\)
−0.334308 + 0.942464i \(0.608503\pi\)
\(338\) 3460.61i 0.556900i
\(339\) −953.760 + 4494.85i −0.152806 + 0.720138i
\(340\) −569.059 −0.0907692
\(341\) −4070.09 −0.646356
\(342\) −1905.30 846.691i −0.301248 0.133871i
\(343\) 0 0
\(344\) 3741.20i 0.586373i
\(345\) 108.176 509.810i 0.0168812 0.0795573i
\(346\) 1973.35i 0.306613i
\(347\) 2320.76i 0.359034i −0.983755 0.179517i \(-0.942547\pi\)
0.983755 0.179517i \(-0.0574535\pi\)
\(348\) −994.747 + 4688.01i −0.153230 + 0.722137i
\(349\) 226.795i 0.0347853i 0.999849 + 0.0173926i \(0.00553653\pi\)
−0.999849 + 0.0173926i \(0.994463\pi\)
\(350\) 0 0
\(351\) −1613.73 + 2226.03i −0.245397 + 0.338509i
\(352\) −6887.90 −1.04297
\(353\) 1485.71 0.224012 0.112006 0.993708i \(-0.464272\pi\)
0.112006 + 0.993708i \(0.464272\pi\)
\(354\) −1287.90 + 6069.55i −0.193364 + 0.911280i
\(355\) 568.054i 0.0849272i
\(356\) 499.869 0.0744185
\(357\) 0 0
\(358\) 276.556 0.0408280
\(359\) 10877.2i 1.59910i 0.600599 + 0.799550i \(0.294929\pi\)
−0.600599 + 0.799550i \(0.705071\pi\)
\(360\) 322.596 725.934i 0.0472286 0.106278i
\(361\) 5222.44 0.761400
\(362\) 3926.79 0.570131
\(363\) 1650.61 + 350.241i 0.238662 + 0.0506416i
\(364\) 0 0
\(365\) 625.800i 0.0897421i
\(366\) 7837.72 + 1663.08i 1.11936 + 0.237516i
\(367\) 3810.15i 0.541930i −0.962589 0.270965i \(-0.912657\pi\)
0.962589 0.270965i \(-0.0873428\pi\)
\(368\) 817.809i 0.115846i
\(369\) 4607.83 + 2047.66i 0.650065 + 0.288881i
\(370\) 452.349i 0.0635581i
\(371\) 0 0
\(372\) −469.976 + 2214.89i −0.0655030 + 0.308700i
\(373\) −9739.09 −1.35193 −0.675967 0.736932i \(-0.736274\pi\)
−0.675967 + 0.736932i \(0.736274\pi\)
\(374\) 8133.66 1.12455
\(375\) 1575.28 + 334.257i 0.216925 + 0.0460292i
\(376\) 8445.48i 1.15836i
\(377\) −4148.98 −0.566800
\(378\) 0 0
\(379\) 320.171 0.0433933 0.0216967 0.999765i \(-0.493093\pi\)
0.0216967 + 0.999765i \(0.493093\pi\)
\(380\) 219.836i 0.0296773i
\(381\) 4270.38 + 906.129i 0.574220 + 0.121844i
\(382\) −5628.60 −0.753886
\(383\) −4370.26 −0.583054 −0.291527 0.956563i \(-0.594163\pi\)
−0.291527 + 0.956563i \(0.594163\pi\)
\(384\) −627.829 + 2958.81i −0.0834343 + 0.393206i
\(385\) 0 0
\(386\) 4334.57i 0.571564i
\(387\) 3913.66 + 1739.18i 0.514063 + 0.228443i
\(388\) 6170.84i 0.807415i
\(389\) 13714.8i 1.78758i 0.448483 + 0.893791i \(0.351964\pi\)
−0.448483 + 0.893791i \(0.648036\pi\)
\(390\) 237.187 + 50.3287i 0.0307960 + 0.00653460i
\(391\) 8419.84i 1.08903i
\(392\) 0 0
\(393\) 2632.49 + 558.587i 0.337892 + 0.0716971i
\(394\) −946.493 −0.121024
\(395\) −77.2300 −0.00983763
\(396\) 1943.62 4373.70i 0.246642 0.555017i
\(397\) 2519.10i 0.318464i 0.987241 + 0.159232i \(0.0509018\pi\)
−0.987241 + 0.159232i \(0.949098\pi\)
\(398\) 1602.86 0.201869
\(399\) 0 0
\(400\) 1255.57 0.156946
\(401\) 2619.97i 0.326272i −0.986604 0.163136i \(-0.947839\pi\)
0.986604 0.163136i \(-0.0521609\pi\)
\(402\) −614.637 + 2896.64i −0.0762570 + 0.359382i
\(403\) −1960.22 −0.242296
\(404\) 1049.06 0.129190
\(405\) 609.431 + 674.933i 0.0747725 + 0.0828091i
\(406\) 0 0
\(407\) 7730.22i 0.941456i
\(408\) 2663.94 12554.5i 0.323247 1.52339i
\(409\) 13924.2i 1.68339i −0.539954 0.841694i \(-0.681558\pi\)
0.539954 0.841694i \(-0.318442\pi\)
\(410\) 444.676i 0.0535634i
\(411\) −1184.33 + 5581.47i −0.142138 + 0.669863i
\(412\) 4831.36i 0.577729i
\(413\) 0 0
\(414\) 3786.85 + 1682.83i 0.449549 + 0.199774i
\(415\) 91.2082 0.0107885
\(416\) −3317.32 −0.390974
\(417\) −893.334 + 4210.07i −0.104908 + 0.494408i
\(418\) 3142.16i 0.367675i
\(419\) 15171.1 1.76887 0.884433 0.466666i \(-0.154545\pi\)
0.884433 + 0.466666i \(0.154545\pi\)
\(420\) 0 0
\(421\) −1052.53 −0.121846 −0.0609228 0.998142i \(-0.519404\pi\)
−0.0609228 + 0.998142i \(0.519404\pi\)
\(422\) 7638.60i 0.881140i
\(423\) 8834.78 + 3926.07i 1.01551 + 0.451281i
\(424\) 9980.54 1.14316
\(425\) 12926.9 1.47540
\(426\) −4418.41 937.541i −0.502518 0.106629i
\(427\) 0 0
\(428\) 4651.23i 0.525294i
\(429\) 4053.31 + 860.070i 0.456167 + 0.0967939i
\(430\) 377.685i 0.0423572i
\(431\) 7994.67i 0.893479i 0.894664 + 0.446740i \(0.147415\pi\)
−0.894664 + 0.446740i \(0.852585\pi\)
\(432\) 1155.33 + 837.540i 0.128671 + 0.0932781i
\(433\) 12889.4i 1.43055i 0.698845 + 0.715273i \(0.253697\pi\)
−0.698845 + 0.715273i \(0.746303\pi\)
\(434\) 0 0
\(435\) −284.838 + 1342.38i −0.0313953 + 0.147959i
\(436\) 43.9449 0.00482701
\(437\) 3252.72 0.356061
\(438\) 4867.57 + 1032.85i 0.531008 + 0.112674i
\(439\) 14383.8i 1.56378i −0.623415 0.781891i \(-0.714255\pi\)
0.623415 0.781891i \(-0.285745\pi\)
\(440\) −1197.19 −0.129713
\(441\) 0 0
\(442\) 3917.30 0.421554
\(443\) 3963.12i 0.425042i −0.977157 0.212521i \(-0.931833\pi\)
0.977157 0.212521i \(-0.0681674\pi\)
\(444\) 4206.68 + 892.614i 0.449640 + 0.0954089i
\(445\) 143.134 0.0152476
\(446\) −5803.87 −0.616191
\(447\) 962.710 4537.03i 0.101867 0.480076i
\(448\) 0 0
\(449\) 13479.1i 1.41675i −0.705838 0.708373i \(-0.749430\pi\)
0.705838 0.708373i \(-0.250570\pi\)
\(450\) −2583.62 + 5813.89i −0.270651 + 0.609043i
\(451\) 7599.09i 0.793408i
\(452\) 3852.31i 0.400879i
\(453\) −7243.44 1536.98i −0.751272 0.159412i
\(454\) 8392.13i 0.867538i
\(455\) 0 0
\(456\) 4850.01 + 1029.12i 0.498076 + 0.105686i
\(457\) 3979.58 0.407346 0.203673 0.979039i \(-0.434712\pi\)
0.203673 + 0.979039i \(0.434712\pi\)
\(458\) 3786.27 0.386290
\(459\) 11894.8 + 8622.98i 1.20959 + 0.876876i
\(460\) 436.932i 0.0442871i
\(461\) −9053.72 −0.914694 −0.457347 0.889288i \(-0.651200\pi\)
−0.457347 + 0.889288i \(0.651200\pi\)
\(462\) 0 0
\(463\) −5736.10 −0.575764 −0.287882 0.957666i \(-0.592951\pi\)
−0.287882 + 0.957666i \(0.592951\pi\)
\(464\) 2153.36i 0.215447i
\(465\) −134.574 + 634.215i −0.0134209 + 0.0632495i
\(466\) −8348.75 −0.829932
\(467\) 12392.6 1.22797 0.613984 0.789318i \(-0.289566\pi\)
0.613984 + 0.789318i \(0.289566\pi\)
\(468\) 936.077 2106.44i 0.0924576 0.208056i
\(469\) 0 0
\(470\) 852.596i 0.0836752i
\(471\) −304.966 + 1437.23i −0.0298346 + 0.140604i
\(472\) 14754.6i 1.43885i
\(473\) 6454.28i 0.627417i
\(474\) 127.464 600.707i 0.0123515 0.0582097i
\(475\) 4993.85i 0.482387i
\(476\) 0 0
\(477\) −4639.67 + 10440.6i −0.445359 + 1.00219i
\(478\) 7303.97 0.698903
\(479\) 8267.73 0.788648 0.394324 0.918972i \(-0.370979\pi\)
0.394324 + 0.918972i \(0.370979\pi\)
\(480\) −227.743 + 1073.30i −0.0216562 + 0.102061i
\(481\) 3723.00i 0.352919i
\(482\) 6566.17 0.620499
\(483\) 0 0
\(484\) −1414.65 −0.132856
\(485\) 1766.97i 0.165431i
\(486\) −6255.56 + 3626.31i −0.583864 + 0.338462i
\(487\) 940.150 0.0874790 0.0437395 0.999043i \(-0.486073\pi\)
0.0437395 + 0.999043i \(0.486073\pi\)
\(488\) −19052.9 −1.76739
\(489\) −11772.9 2498.08i −1.08873 0.231017i
\(490\) 0 0
\(491\) 1057.30i 0.0971801i 0.998819 + 0.0485900i \(0.0154728\pi\)
−0.998819 + 0.0485900i \(0.984527\pi\)
\(492\) −4135.32 877.472i −0.378932 0.0804055i
\(493\) 22170.2i 2.02534i
\(494\) 1513.32i 0.137828i
\(495\) 556.539 1252.37i 0.0505345 0.113717i
\(496\) 1017.37i 0.0920995i
\(497\) 0 0
\(498\) −150.534 + 709.431i −0.0135454 + 0.0638361i
\(499\) −6173.30 −0.553817 −0.276909 0.960896i \(-0.589310\pi\)
−0.276909 + 0.960896i \(0.589310\pi\)
\(500\) −1350.09 −0.120756
\(501\) −11918.1 2528.89i −1.06280 0.225514i
\(502\) 3906.63i 0.347333i
\(503\) 4284.28 0.379775 0.189887 0.981806i \(-0.439188\pi\)
0.189887 + 0.981806i \(0.439188\pi\)
\(504\) 0 0
\(505\) 300.390 0.0264697
\(506\) 6245.15i 0.548678i
\(507\) −9215.17 1955.36i −0.807219 0.171284i
\(508\) −3659.92 −0.319651
\(509\) 15101.0 1.31501 0.657507 0.753449i \(-0.271611\pi\)
0.657507 + 0.753449i \(0.271611\pi\)
\(510\) 268.932 1267.42i 0.0233500 0.110043i
\(511\) 0 0
\(512\) 3640.92i 0.314272i
\(513\) −3331.19 + 4595.17i −0.286697 + 0.395481i
\(514\) 11550.6i 0.991197i
\(515\) 1383.42i 0.118371i
\(516\) −3512.34 745.281i −0.299655 0.0635837i
\(517\) 14570.1i 1.23944i
\(518\) 0 0
\(519\) −5254.79 1115.01i −0.444431 0.0943037i
\(520\) −576.586 −0.0486249
\(521\) −13788.0 −1.15943 −0.579715 0.814819i \(-0.696836\pi\)
−0.579715 + 0.814819i \(0.696836\pi\)
\(522\) −9971.09 4431.03i −0.836059 0.371534i
\(523\) 961.304i 0.0803726i 0.999192 + 0.0401863i \(0.0127951\pi\)
−0.999192 + 0.0401863i \(0.987205\pi\)
\(524\) −2256.17 −0.188094
\(525\) 0 0
\(526\) −11976.5 −0.992780
\(527\) 10474.5i 0.865797i
\(528\) 446.384 2103.71i 0.0367924 0.173394i
\(529\) 5702.11 0.468654
\(530\) 1007.57 0.0825770
\(531\) 15434.8 + 6859.02i 1.26142 + 0.560557i
\(532\) 0 0
\(533\) 3659.84i 0.297421i
\(534\) −236.234 + 1113.32i −0.0191439 + 0.0902207i
\(535\) 1331.84i 0.107627i
\(536\) 7041.53i 0.567440i
\(537\) 156.264 736.434i 0.0125573 0.0591797i
\(538\) 6368.54i 0.510348i
\(539\) 0 0
\(540\) −617.261 447.474i −0.0491902 0.0356596i
\(541\) −1195.69 −0.0950218 −0.0475109 0.998871i \(-0.515129\pi\)
−0.0475109 + 0.998871i \(0.515129\pi\)
\(542\) −5427.14 −0.430102
\(543\) 2218.77 10456.6i 0.175353 0.826397i
\(544\) 17726.2i 1.39707i
\(545\) 12.5833 0.000989006
\(546\) 0 0
\(547\) 18601.8 1.45403 0.727014 0.686622i \(-0.240907\pi\)
0.727014 + 0.686622i \(0.240907\pi\)
\(548\) 4783.59i 0.372892i
\(549\) 8857.17 19931.2i 0.688552 1.54944i
\(550\) 9588.10 0.743341
\(551\) −8564.69 −0.662192
\(552\) −9639.56 2045.41i −0.743274 0.157715i
\(553\) 0 0
\(554\) 12117.9i 0.929315i
\(555\) 1204.55 + 255.593i 0.0921267 + 0.0195483i
\(556\) 3608.24i 0.275222i
\(557\) 6822.07i 0.518959i −0.965749 0.259480i \(-0.916449\pi\)
0.965749 0.259480i \(-0.0835511\pi\)
\(558\) −4710.92 2093.47i −0.357400 0.158824i
\(559\) 3108.49i 0.235197i
\(560\) 0 0
\(561\) 4595.80 21658.9i 0.345873 1.63002i
\(562\) −7131.16 −0.535249
\(563\) −11359.6 −0.850356 −0.425178 0.905110i \(-0.639789\pi\)
−0.425178 + 0.905110i \(0.639789\pi\)
\(564\) −7928.83 1682.42i −0.591957 0.125607i
\(565\) 1103.08i 0.0821360i
\(566\) −10531.2 −0.782087
\(567\) 0 0
\(568\) 10740.8 0.793443
\(569\) 21324.1i 1.57110i 0.618800 + 0.785549i \(0.287619\pi\)
−0.618800 + 0.785549i \(0.712381\pi\)
\(570\) 489.623 + 103.893i 0.0359790 + 0.00763437i
\(571\) −14768.0 −1.08235 −0.541175 0.840910i \(-0.682020\pi\)
−0.541175 + 0.840910i \(0.682020\pi\)
\(572\) −3473.88 −0.253934
\(573\) −3180.36 + 14988.3i −0.231870 + 1.09275i
\(574\) 0 0
\(575\) 9925.45i 0.719861i
\(576\) −9980.06 4435.01i −0.721937 0.320820i
\(577\) 19304.9i 1.39285i 0.717631 + 0.696424i \(0.245227\pi\)
−0.717631 + 0.696424i \(0.754773\pi\)
\(578\) 11554.1i 0.831464i
\(579\) 11542.4 + 2449.18i 0.828475 + 0.175794i
\(580\) 1150.48i 0.0823640i
\(581\) 0 0
\(582\) −13743.8 2916.29i −0.978863 0.207705i
\(583\) 17218.3 1.22317
\(584\) −11832.7 −0.838426
\(585\) 268.038 603.164i 0.0189436 0.0426286i
\(586\) 14458.4i 1.01924i
\(587\) −4397.46 −0.309204 −0.154602 0.987977i \(-0.549410\pi\)
−0.154602 + 0.987977i \(0.549410\pi\)
\(588\) 0 0
\(589\) −4046.45 −0.283075
\(590\) 1489.52i 0.103937i
\(591\) −534.801 + 2520.39i −0.0372230 + 0.175423i
\(592\) 1932.27 0.134148
\(593\) −21940.2 −1.51935 −0.759677 0.650301i \(-0.774643\pi\)
−0.759677 + 0.650301i \(0.774643\pi\)
\(594\) 8822.62 + 6395.82i 0.609422 + 0.441791i
\(595\) 0 0
\(596\) 3888.46i 0.267244i
\(597\) 905.670 4268.21i 0.0620881 0.292607i
\(598\) 3007.77i 0.205680i
\(599\) 5502.23i 0.375317i 0.982234 + 0.187659i \(0.0600899\pi\)
−0.982234 + 0.187659i \(0.939910\pi\)
\(600\) 3140.30 14799.5i 0.213670 1.00698i
\(601\) 5814.58i 0.394645i 0.980339 + 0.197322i \(0.0632246\pi\)
−0.980339 + 0.197322i \(0.936775\pi\)
\(602\) 0 0
\(603\) 7366.11 + 3273.41i 0.497465 + 0.221067i
\(604\) 6207.98 0.418210
\(605\) −405.074 −0.0272208
\(606\) −495.777 + 2336.48i −0.0332336 + 0.156622i
\(607\) 13291.4i 0.888765i 0.895837 + 0.444382i \(0.146577\pi\)
−0.895837 + 0.444382i \(0.853423\pi\)
\(608\) −6847.90 −0.456775
\(609\) 0 0
\(610\) −1923.45 −0.127669
\(611\) 7017.18i 0.464623i
\(612\) −11255.8 5001.94i −0.743447 0.330378i
\(613\) 19594.3 1.29104 0.645520 0.763743i \(-0.276641\pi\)
0.645520 + 0.763743i \(0.276641\pi\)
\(614\) 20301.7 1.33438
\(615\) −1184.12 251.257i −0.0776394 0.0164743i
\(616\) 0 0
\(617\) 348.388i 0.0227319i 0.999935 + 0.0113660i \(0.00361797\pi\)
−0.999935 + 0.0113660i \(0.996382\pi\)
\(618\) −10760.5 2283.26i −0.700405 0.148619i
\(619\) 6775.41i 0.439946i 0.975506 + 0.219973i \(0.0705970\pi\)
−0.975506 + 0.219973i \(0.929403\pi\)
\(620\) 543.553i 0.0352091i
\(621\) 6620.86 9133.05i 0.427836 0.590172i
\(622\) 11016.2i 0.710145i
\(623\) 0 0
\(624\) 214.986 1013.18i 0.0137922 0.0649994i
\(625\) 15043.9 0.962810
\(626\) 4475.29 0.285733
\(627\) 8367.19 + 1775.43i 0.532940 + 0.113084i
\(628\) 1231.78i 0.0782697i
\(629\) 19893.9 1.26108
\(630\) 0 0
\(631\) −7326.82 −0.462244 −0.231122 0.972925i \(-0.574240\pi\)
−0.231122 + 0.972925i \(0.574240\pi\)
\(632\) 1460.28i 0.0919092i
\(633\) −20340.6 4316.07i −1.27720 0.271009i
\(634\) −15102.9 −0.946078
\(635\) −1047.99 −0.0654932
\(636\) 1988.21 9369.98i 0.123959 0.584189i
\(637\) 0 0
\(638\) 16444.0i 1.02042i
\(639\) −4993.11 + 11235.9i −0.309115 + 0.695598i
\(640\) 726.120i 0.0448475i
\(641\) 2809.82i 0.173138i 0.996246 + 0.0865689i \(0.0275903\pi\)
−0.996246 + 0.0865689i \(0.972410\pi\)
\(642\) −10359.3 2198.13i −0.636836 0.135130i
\(643\) 27485.5i 1.68573i −0.538128 0.842863i \(-0.680868\pi\)
0.538128 0.842863i \(-0.319132\pi\)
\(644\) 0 0
\(645\) −1005.73 213.405i −0.0613962 0.0130276i
\(646\) 8086.43 0.492502
\(647\) 29319.8 1.78158 0.890790 0.454416i \(-0.150152\pi\)
0.890790 + 0.454416i \(0.150152\pi\)
\(648\) 12761.7 11523.2i 0.773654 0.698571i
\(649\) 25454.5i 1.53957i
\(650\) 4617.78 0.278653
\(651\) 0 0
\(652\) 10089.9 0.606061
\(653\) 16743.8i 1.00343i −0.865034 0.501713i \(-0.832704\pi\)
0.865034 0.501713i \(-0.167296\pi\)
\(654\) −20.7680 + 97.8747i −0.00124173 + 0.00585199i
\(655\) −646.037 −0.0385386
\(656\) −1899.49 −0.113053
\(657\) 5500.69 12378.1i 0.326640 0.735034i
\(658\) 0 0
\(659\) 9520.47i 0.562769i 0.959595 + 0.281385i \(0.0907937\pi\)
−0.959595 + 0.281385i \(0.909206\pi\)
\(660\) −238.491 + 1123.95i −0.0140655 + 0.0662875i
\(661\) 23345.1i 1.37371i −0.726797 0.686853i \(-0.758992\pi\)
0.726797 0.686853i \(-0.241008\pi\)
\(662\) 9315.16i 0.546894i
\(663\) 2213.41 10431.3i 0.129656 0.611037i
\(664\) 1724.58i 0.100793i
\(665\) 0 0
\(666\) −3976.08 + 8947.34i −0.231337 + 0.520574i
\(667\) 17022.6 0.988183
\(668\) 10214.4 0.591626
\(669\) −3279.39 + 15455.0i −0.189519 + 0.893161i
\(670\) 710.863i 0.0409896i
\(671\) −32869.9 −1.89110
\(672\) 0 0
\(673\) −12283.5 −0.703559 −0.351780 0.936083i \(-0.614423\pi\)
−0.351780 + 0.936083i \(0.614423\pi\)
\(674\) 7895.67i 0.451231i
\(675\) 14021.8 + 10164.9i 0.799557 + 0.579626i
\(676\) 7897.85 0.449354
\(677\) −12991.8 −0.737538 −0.368769 0.929521i \(-0.620221\pi\)
−0.368769 + 0.929521i \(0.620221\pi\)
\(678\) 8579.91 + 1820.57i 0.486002 + 0.103125i
\(679\) 0 0
\(680\) 3081.00i 0.173751i
\(681\) −22347.2 4741.84i −1.25748 0.266825i
\(682\) 7769.11i 0.436209i
\(683\) 8506.24i 0.476548i −0.971198 0.238274i \(-0.923418\pi\)
0.971198 0.238274i \(-0.0765816\pi\)
\(684\) 1932.33 4348.30i 0.108018 0.243072i
\(685\) 1369.74i 0.0764018i
\(686\) 0 0
\(687\) 2139.38 10082.4i 0.118810 0.559923i
\(688\) −1613.33 −0.0894009
\(689\) 8292.63 0.458525
\(690\) −973.142 206.491i −0.0536911 0.0113927i
\(691\) 25832.9i 1.42219i 0.703097 + 0.711093i \(0.251800\pi\)
−0.703097 + 0.711093i \(0.748200\pi\)
\(692\) 4503.61 0.247401
\(693\) 0 0
\(694\) −4429.93 −0.242303
\(695\) 1033.19i 0.0563902i
\(696\) 25381.8 + 5385.76i 1.38232 + 0.293314i
\(697\) −19556.4 −1.06277
\(698\) 432.913 0.0234757
\(699\) −4717.33 + 22231.7i −0.255259 + 1.20298i
\(700\) 0 0
\(701\) 22607.8i 1.21810i 0.793134 + 0.609048i \(0.208448\pi\)
−0.793134 + 0.609048i \(0.791552\pi\)
\(702\) 4249.12 + 3080.33i 0.228451 + 0.165612i
\(703\) 7685.33i 0.412315i
\(704\) 16458.8i 0.881129i
\(705\) −2270.36 481.747i −0.121286 0.0257356i
\(706\) 2835.96i 0.151180i
\(707\) 0 0
\(708\) −13852.0 2939.26i −0.735298 0.156023i
\(709\) −10944.8 −0.579748 −0.289874 0.957065i \(-0.593613\pi\)
−0.289874 + 0.957065i \(0.593613\pi\)
\(710\) 1084.32 0.0573152
\(711\) −1527.59 678.841i −0.0805753 0.0358066i
\(712\) 2706.39i 0.142453i
\(713\) 8042.46 0.422430
\(714\) 0 0
\(715\) −994.720 −0.0520285
\(716\) 631.160i 0.0329435i
\(717\) 4127.00 19449.6i 0.214959 1.01305i
\(718\) 20762.8 1.07919
\(719\) 25770.5 1.33669 0.668344 0.743852i \(-0.267003\pi\)
0.668344 + 0.743852i \(0.267003\pi\)
\(720\) −313.048 139.114i −0.0162036 0.00720068i
\(721\) 0 0
\(722\) 9968.76i 0.513849i
\(723\) 3710.11 17484.9i 0.190844 0.899405i
\(724\) 8961.78i 0.460030i
\(725\) 26134.6i 1.33878i
\(726\) 668.552 3150.73i 0.0341767 0.161067i
\(727\) 15593.1i 0.795485i −0.917497 0.397742i \(-0.869794\pi\)
0.917497 0.397742i \(-0.130206\pi\)
\(728\) 0 0
\(729\) 6121.81 + 18706.8i 0.311020 + 0.950403i
\(730\) −1194.55 −0.0605646
\(731\) −16610.3 −0.840428
\(732\) −3795.51 + 17887.4i −0.191648 + 0.903191i
\(733\) 800.044i 0.0403142i −0.999797 0.0201571i \(-0.993583\pi\)
0.999797 0.0201571i \(-0.00641664\pi\)
\(734\) −7272.94 −0.365734
\(735\) 0 0
\(736\) 13610.4 0.681641
\(737\) 12148.0i 0.607159i
\(738\) 3908.64 8795.56i 0.194958 0.438712i
\(739\) −908.890 −0.0452423 −0.0226211 0.999744i \(-0.507201\pi\)
−0.0226211 + 0.999744i \(0.507201\pi\)
\(740\) −1032.36 −0.0512841
\(741\) 4029.77 + 855.076i 0.199781 + 0.0423914i
\(742\) 0 0
\(743\) 8109.00i 0.400391i 0.979756 + 0.200195i \(0.0641577\pi\)
−0.979756 + 0.200195i \(0.935842\pi\)
\(744\) 11991.8 + 2544.54i 0.590916 + 0.125386i
\(745\) 1113.43i 0.0547555i
\(746\) 18590.3i 0.912384i
\(747\) 1804.07 + 801.707i 0.0883635 + 0.0392676i
\(748\) 18562.8i 0.907382i
\(749\) 0 0
\(750\) 638.041 3006.94i 0.0310639 0.146397i
\(751\) −20764.4 −1.00893 −0.504463 0.863433i \(-0.668310\pi\)
−0.504463 + 0.863433i \(0.668310\pi\)
\(752\) −3641.98 −0.176608
\(753\) −10402.9 2207.38i −0.503455 0.106828i
\(754\) 7919.71i 0.382518i
\(755\) 1777.61 0.0856870
\(756\) 0 0
\(757\) 23295.6 1.11848 0.559242 0.829005i \(-0.311092\pi\)
0.559242 + 0.829005i \(0.311092\pi\)
\(758\) 611.152i 0.0292850i
\(759\) −16630.1 3528.73i −0.795301 0.168755i
\(760\) −1190.24 −0.0568085
\(761\) 10028.8 0.477717 0.238858 0.971054i \(-0.423227\pi\)
0.238858 + 0.971054i \(0.423227\pi\)
\(762\) 1729.65 8151.43i 0.0822290 0.387526i
\(763\) 0 0
\(764\) 12845.7i 0.608299i
\(765\) −3223.02 1432.27i −0.152325 0.0676912i
\(766\) 8342.08i 0.393488i
\(767\) 12259.3i 0.577130i
\(768\) 22095.8 + 4688.51i 1.03817 + 0.220289i
\(769\) 13500.3i 0.633074i 0.948580 + 0.316537i \(0.102520\pi\)
−0.948580 + 0.316537i \(0.897480\pi\)
\(770\) 0 0
\(771\) 30757.8 + 6526.49i 1.43673 + 0.304858i
\(772\) −9892.42 −0.461187
\(773\) 23289.7 1.08367 0.541833 0.840486i \(-0.317731\pi\)
0.541833 + 0.840486i \(0.317731\pi\)
\(774\) 3319.80 7470.51i 0.154170 0.346928i
\(775\) 12347.5i 0.572303i
\(776\) 33410.2 1.54556
\(777\) 0 0
\(778\) 26179.3 1.20639
\(779\) 7554.96i 0.347477i
\(780\) −114.861 + 541.313i −0.00527267 + 0.0248489i
\(781\) 18530.0 0.848982
\(782\) −16072.0 −0.734956
\(783\) −17433.3 + 24048.1i −0.795677 + 1.09759i
\(784\) 0 0
\(785\) 352.711i 0.0160367i
\(786\) 1066.25 5024.98i 0.0483865 0.228034i
\(787\)