Properties

Label 177.5.c.a.58.9
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.9
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.32

$q$-expansion

\(f(q)\) \(=\) \(q-4.85825i q^{2} -5.19615 q^{3} -7.60257 q^{4} -12.5087 q^{5} +25.2442i q^{6} +50.4755 q^{7} -40.7968i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-4.85825i q^{2} -5.19615 q^{3} -7.60257 q^{4} -12.5087 q^{5} +25.2442i q^{6} +50.4755 q^{7} -40.7968i q^{8} +27.0000 q^{9} +60.7705i q^{10} -191.226i q^{11} +39.5041 q^{12} +0.640162i q^{13} -245.222i q^{14} +64.9972 q^{15} -319.842 q^{16} -549.428 q^{17} -131.173i q^{18} +524.497 q^{19} +95.0984 q^{20} -262.278 q^{21} -929.025 q^{22} +543.113i q^{23} +211.986i q^{24} -468.532 q^{25} +3.11006 q^{26} -140.296 q^{27} -383.743 q^{28} -296.169 q^{29} -315.773i q^{30} -1078.43i q^{31} +901.123i q^{32} +993.642i q^{33} +2669.26i q^{34} -631.384 q^{35} -205.269 q^{36} +1168.43i q^{37} -2548.14i q^{38} -3.32638i q^{39} +510.316i q^{40} -1128.78 q^{41} +1274.21i q^{42} -1522.74i q^{43} +1453.81i q^{44} -337.735 q^{45} +2638.58 q^{46} -103.190i q^{47} +1661.95 q^{48} +146.777 q^{49} +2276.24i q^{50} +2854.91 q^{51} -4.86687i q^{52} -2811.88 q^{53} +681.593i q^{54} +2392.00i q^{55} -2059.24i q^{56} -2725.37 q^{57} +1438.86i q^{58} +(-2562.55 - 2355.99i) q^{59} -494.146 q^{60} +4909.65i q^{61} -5239.30 q^{62} +1362.84 q^{63} -739.596 q^{64} -8.00760i q^{65} +4827.36 q^{66} +5854.39i q^{67} +4177.06 q^{68} -2822.10i q^{69} +3067.42i q^{70} +5828.87 q^{71} -1101.51i q^{72} -6751.02i q^{73} +5676.53 q^{74} +2434.56 q^{75} -3987.52 q^{76} -9652.25i q^{77} -16.1604 q^{78} -9333.98 q^{79} +4000.81 q^{80} +729.000 q^{81} +5483.90i q^{82} -1839.42i q^{83} +1993.99 q^{84} +6872.64 q^{85} -7397.84 q^{86} +1538.94 q^{87} -7801.43 q^{88} -5734.95i q^{89} +1640.80i q^{90} +32.3125i q^{91} -4129.05i q^{92} +5603.71i q^{93} -501.323 q^{94} -6560.79 q^{95} -4682.37i q^{96} -15272.6i q^{97} -713.079i q^{98} -5163.11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.85825i 1.21456i −0.794487 0.607281i \(-0.792260\pi\)
0.794487 0.607281i \(-0.207740\pi\)
\(3\) −5.19615 −0.577350
\(4\) −7.60257 −0.475160
\(5\) −12.5087 −0.500349 −0.250174 0.968201i \(-0.580488\pi\)
−0.250174 + 0.968201i \(0.580488\pi\)
\(6\) 25.2442i 0.701228i
\(7\) 50.4755 1.03011 0.515056 0.857156i \(-0.327771\pi\)
0.515056 + 0.857156i \(0.327771\pi\)
\(8\) 40.7968i 0.637450i
\(9\) 27.0000 0.333333
\(10\) 60.7705i 0.607705i
\(11\) 191.226i 1.58038i −0.612860 0.790192i \(-0.709981\pi\)
0.612860 0.790192i \(-0.290019\pi\)
\(12\) 39.5041 0.274334
\(13\) 0.640162i 0.00378794i 0.999998 + 0.00189397i \(0.000602869\pi\)
−0.999998 + 0.00189397i \(0.999397\pi\)
\(14\) 245.222i 1.25114i
\(15\) 64.9972 0.288877
\(16\) −319.842 −1.24938
\(17\) −549.428 −1.90113 −0.950567 0.310520i \(-0.899497\pi\)
−0.950567 + 0.310520i \(0.899497\pi\)
\(18\) 131.173i 0.404854i
\(19\) 524.497 1.45290 0.726450 0.687219i \(-0.241169\pi\)
0.726450 + 0.687219i \(0.241169\pi\)
\(20\) 95.0984 0.237746
\(21\) −262.278 −0.594736
\(22\) −929.025 −1.91947
\(23\) 543.113i 1.02668i 0.858186 + 0.513339i \(0.171592\pi\)
−0.858186 + 0.513339i \(0.828408\pi\)
\(24\) 211.986i 0.368032i
\(25\) −468.532 −0.749651
\(26\) 3.11006 0.00460068
\(27\) −140.296 −0.192450
\(28\) −383.743 −0.489469
\(29\) −296.169 −0.352163 −0.176081 0.984376i \(-0.556342\pi\)
−0.176081 + 0.984376i \(0.556342\pi\)
\(30\) 315.773i 0.350858i
\(31\) 1078.43i 1.12220i −0.827748 0.561100i \(-0.810378\pi\)
0.827748 0.561100i \(-0.189622\pi\)
\(32\) 901.123i 0.880003i
\(33\) 993.642i 0.912435i
\(34\) 2669.26i 2.30904i
\(35\) −631.384 −0.515416
\(36\) −205.269 −0.158387
\(37\) 1168.43i 0.853493i 0.904371 + 0.426747i \(0.140340\pi\)
−0.904371 + 0.426747i \(0.859660\pi\)
\(38\) 2548.14i 1.76464i
\(39\) 3.32638i 0.00218697i
\(40\) 510.316i 0.318947i
\(41\) −1128.78 −0.671494 −0.335747 0.941952i \(-0.608989\pi\)
−0.335747 + 0.941952i \(0.608989\pi\)
\(42\) 1274.21i 0.722343i
\(43\) 1522.74i 0.823547i −0.911286 0.411773i \(-0.864910\pi\)
0.911286 0.411773i \(-0.135090\pi\)
\(44\) 1453.81i 0.750936i
\(45\) −337.735 −0.166783
\(46\) 2638.58 1.24696
\(47\) 103.190i 0.0467135i −0.999727 0.0233567i \(-0.992565\pi\)
0.999727 0.0233567i \(-0.00743536\pi\)
\(48\) 1661.95 0.721332
\(49\) 146.777 0.0611316
\(50\) 2276.24i 0.910498i
\(51\) 2854.91 1.09762
\(52\) 4.86687i 0.00179988i
\(53\) −2811.88 −1.00103 −0.500513 0.865729i \(-0.666855\pi\)
−0.500513 + 0.865729i \(0.666855\pi\)
\(54\) 681.593i 0.233743i
\(55\) 2392.00i 0.790743i
\(56\) 2059.24i 0.656645i
\(57\) −2725.37 −0.838832
\(58\) 1438.86i 0.427723i
\(59\) −2562.55 2355.99i −0.736155 0.676813i
\(60\) −494.146 −0.137263
\(61\) 4909.65i 1.31944i 0.751510 + 0.659722i \(0.229326\pi\)
−0.751510 + 0.659722i \(0.770674\pi\)
\(62\) −5239.30 −1.36298
\(63\) 1362.84 0.343371
\(64\) −739.596 −0.180565
\(65\) 8.00760i 0.00189529i
\(66\) 4827.36 1.10821
\(67\) 5854.39i 1.30416i 0.758149 + 0.652082i \(0.226104\pi\)
−0.758149 + 0.652082i \(0.773896\pi\)
\(68\) 4177.06 0.903343
\(69\) 2822.10i 0.592753i
\(70\) 3067.42i 0.626004i
\(71\) 5828.87 1.15629 0.578146 0.815933i \(-0.303776\pi\)
0.578146 + 0.815933i \(0.303776\pi\)
\(72\) 1101.51i 0.212483i
\(73\) 6751.02i 1.26684i −0.773806 0.633422i \(-0.781650\pi\)
0.773806 0.633422i \(-0.218350\pi\)
\(74\) 5676.53 1.03662
\(75\) 2434.56 0.432811
\(76\) −3987.52 −0.690361
\(77\) 9652.25i 1.62797i
\(78\) −16.1604 −0.00265621
\(79\) −9333.98 −1.49559 −0.747795 0.663929i \(-0.768888\pi\)
−0.747795 + 0.663929i \(0.768888\pi\)
\(80\) 4000.81 0.625127
\(81\) 729.000 0.111111
\(82\) 5483.90i 0.815571i
\(83\) 1839.42i 0.267008i −0.991048 0.133504i \(-0.957377\pi\)
0.991048 0.133504i \(-0.0426229\pi\)
\(84\) 1993.99 0.282595
\(85\) 6872.64 0.951230
\(86\) −7397.84 −1.00025
\(87\) 1538.94 0.203321
\(88\) −7801.43 −1.00742
\(89\) 5734.95i 0.724018i −0.932175 0.362009i \(-0.882091\pi\)
0.932175 0.362009i \(-0.117909\pi\)
\(90\) 1640.80i 0.202568i
\(91\) 32.3125i 0.00390200i
\(92\) 4129.05i 0.487837i
\(93\) 5603.71i 0.647902i
\(94\) −501.323 −0.0567364
\(95\) −6560.79 −0.726957
\(96\) 4682.37i 0.508070i
\(97\) 15272.6i 1.62319i −0.584223 0.811593i \(-0.698601\pi\)
0.584223 0.811593i \(-0.301399\pi\)
\(98\) 713.079i 0.0742481i
\(99\) 5163.11i 0.526795i
\(100\) 3562.04 0.356204
\(101\) 13635.2i 1.33665i −0.743868 0.668327i \(-0.767011\pi\)
0.743868 0.668327i \(-0.232989\pi\)
\(102\) 13869.9i 1.33313i
\(103\) 4773.40i 0.449939i −0.974366 0.224969i \(-0.927772\pi\)
0.974366 0.224969i \(-0.0722282\pi\)
\(104\) 26.1166 0.00241462
\(105\) 3280.77 0.297575
\(106\) 13660.8i 1.21581i
\(107\) 10911.5 0.953051 0.476525 0.879161i \(-0.341896\pi\)
0.476525 + 0.879161i \(0.341896\pi\)
\(108\) 1066.61 0.0914446
\(109\) 1327.72i 0.111752i −0.998438 0.0558758i \(-0.982205\pi\)
0.998438 0.0558758i \(-0.0177951\pi\)
\(110\) 11620.9 0.960406
\(111\) 6071.35i 0.492764i
\(112\) −16144.2 −1.28700
\(113\) 7206.57i 0.564380i 0.959359 + 0.282190i \(0.0910608\pi\)
−0.959359 + 0.282190i \(0.908939\pi\)
\(114\) 13240.5i 1.01881i
\(115\) 6793.65i 0.513697i
\(116\) 2251.64 0.167334
\(117\) 17.2844i 0.00126265i
\(118\) −11446.0 + 12449.5i −0.822031 + 0.894105i
\(119\) −27732.6 −1.95838
\(120\) 2651.68i 0.184144i
\(121\) −21926.5 −1.49761
\(122\) 23852.3 1.60255
\(123\) 5865.32 0.387687
\(124\) 8198.86i 0.533225i
\(125\) 13678.7 0.875436
\(126\) 6621.01i 0.417045i
\(127\) 30152.5 1.86946 0.934729 0.355361i \(-0.115642\pi\)
0.934729 + 0.355361i \(0.115642\pi\)
\(128\) 18011.1i 1.09931i
\(129\) 7912.38i 0.475475i
\(130\) −38.9029 −0.00230195
\(131\) 30591.4i 1.78261i −0.453404 0.891305i \(-0.649790\pi\)
0.453404 0.891305i \(-0.350210\pi\)
\(132\) 7554.23i 0.433553i
\(133\) 26474.3 1.49665
\(134\) 28442.1 1.58399
\(135\) 1754.92 0.0962922
\(136\) 22414.9i 1.21188i
\(137\) 28251.4 1.50521 0.752607 0.658470i \(-0.228796\pi\)
0.752607 + 0.658470i \(0.228796\pi\)
\(138\) −13710.4 −0.719935
\(139\) 6125.81 0.317054 0.158527 0.987355i \(-0.449325\pi\)
0.158527 + 0.987355i \(0.449325\pi\)
\(140\) 4800.14 0.244905
\(141\) 536.191i 0.0269700i
\(142\) 28318.1i 1.40439i
\(143\) 122.416 0.00598640
\(144\) −8635.74 −0.416461
\(145\) 3704.69 0.176204
\(146\) −32798.1 −1.53866
\(147\) −762.676 −0.0352944
\(148\) 8883.08i 0.405546i
\(149\) 35941.9i 1.61893i 0.587166 + 0.809467i \(0.300244\pi\)
−0.587166 + 0.809467i \(0.699756\pi\)
\(150\) 11827.7i 0.525676i
\(151\) 3815.72i 0.167349i −0.996493 0.0836745i \(-0.973334\pi\)
0.996493 0.0836745i \(-0.0266656\pi\)
\(152\) 21397.8i 0.926152i
\(153\) −14834.5 −0.633711
\(154\) −46893.0 −1.97727
\(155\) 13489.8i 0.561491i
\(156\) 25.2890i 0.00103916i
\(157\) 14168.1i 0.574795i 0.957811 + 0.287398i \(0.0927901\pi\)
−0.957811 + 0.287398i \(0.907210\pi\)
\(158\) 45346.8i 1.81649i
\(159\) 14611.0 0.577943
\(160\) 11271.9i 0.440308i
\(161\) 27413.9i 1.05759i
\(162\) 3541.66i 0.134951i
\(163\) −5436.37 −0.204613 −0.102307 0.994753i \(-0.532622\pi\)
−0.102307 + 0.994753i \(0.532622\pi\)
\(164\) 8581.64 0.319068
\(165\) 12429.2i 0.456536i
\(166\) −8936.35 −0.324298
\(167\) 10745.5 0.385296 0.192648 0.981268i \(-0.438293\pi\)
0.192648 + 0.981268i \(0.438293\pi\)
\(168\) 10700.1i 0.379114i
\(169\) 28560.6 0.999986
\(170\) 33389.0i 1.15533i
\(171\) 14161.4 0.484300
\(172\) 11576.7i 0.391317i
\(173\) 27249.2i 0.910463i 0.890373 + 0.455231i \(0.150443\pi\)
−0.890373 + 0.455231i \(0.849557\pi\)
\(174\) 7476.54i 0.246946i
\(175\) −23649.4 −0.772225
\(176\) 61162.3i 1.97450i
\(177\) 13315.4 + 12242.1i 0.425019 + 0.390758i
\(178\) −27861.8 −0.879365
\(179\) 60313.1i 1.88237i −0.337890 0.941186i \(-0.609713\pi\)
0.337890 0.941186i \(-0.390287\pi\)
\(180\) 2567.66 0.0792486
\(181\) −27872.8 −0.850793 −0.425396 0.905007i \(-0.639865\pi\)
−0.425396 + 0.905007i \(0.639865\pi\)
\(182\) 156.982 0.00473922
\(183\) 25511.3i 0.761781i
\(184\) 22157.3 0.654456
\(185\) 14615.6i 0.427044i
\(186\) 27224.2 0.786917
\(187\) 105065.i 3.00452i
\(188\) 784.509i 0.0221964i
\(189\) −7081.52 −0.198245
\(190\) 31873.9i 0.882934i
\(191\) 32832.5i 0.899989i 0.893031 + 0.449995i \(0.148574\pi\)
−0.893031 + 0.449995i \(0.851426\pi\)
\(192\) 3843.05 0.104250
\(193\) −51056.4 −1.37068 −0.685339 0.728224i \(-0.740346\pi\)
−0.685339 + 0.728224i \(0.740346\pi\)
\(194\) −74197.9 −1.97146
\(195\) 41.6087i 0.00109425i
\(196\) −1115.88 −0.0290473
\(197\) 52427.0 1.35090 0.675449 0.737407i \(-0.263950\pi\)
0.675449 + 0.737407i \(0.263950\pi\)
\(198\) −25083.7 −0.639825
\(199\) −21283.2 −0.537440 −0.268720 0.963218i \(-0.586601\pi\)
−0.268720 + 0.963218i \(0.586601\pi\)
\(200\) 19114.6i 0.477865i
\(201\) 30420.3i 0.752959i
\(202\) −66243.2 −1.62345
\(203\) −14949.3 −0.362767
\(204\) −21704.6 −0.521546
\(205\) 14119.6 0.335981
\(206\) −23190.3 −0.546478
\(207\) 14664.0i 0.342226i
\(208\) 204.751i 0.00473259i
\(209\) 100298.i 2.29614i
\(210\) 15938.8i 0.361424i
\(211\) 67797.8i 1.52283i −0.648267 0.761413i \(-0.724506\pi\)
0.648267 0.761413i \(-0.275494\pi\)
\(212\) 21377.5 0.475648
\(213\) −30287.7 −0.667585
\(214\) 53010.7i 1.15754i
\(215\) 19047.5i 0.412061i
\(216\) 5723.63i 0.122677i
\(217\) 54434.5i 1.15599i
\(218\) −6450.40 −0.135729
\(219\) 35079.3i 0.731413i
\(220\) 18185.3i 0.375730i
\(221\) 351.722i 0.00720138i
\(222\) −29496.1 −0.598493
\(223\) 45072.8 0.906368 0.453184 0.891417i \(-0.350288\pi\)
0.453184 + 0.891417i \(0.350288\pi\)
\(224\) 45484.6i 0.906502i
\(225\) −12650.4 −0.249884
\(226\) 35011.3 0.685474
\(227\) 13186.6i 0.255906i −0.991780 0.127953i \(-0.959159\pi\)
0.991780 0.127953i \(-0.0408407\pi\)
\(228\) 20719.8 0.398580
\(229\) 5098.55i 0.0972244i −0.998818 0.0486122i \(-0.984520\pi\)
0.998818 0.0486122i \(-0.0154799\pi\)
\(230\) −33005.2 −0.623917
\(231\) 50154.6i 0.939911i
\(232\) 12082.7i 0.224486i
\(233\) 45461.0i 0.837390i −0.908127 0.418695i \(-0.862488\pi\)
0.908127 0.418695i \(-0.137512\pi\)
\(234\) 83.9717 0.00153356
\(235\) 1290.78i 0.0233730i
\(236\) 19482.0 + 17911.5i 0.349792 + 0.321595i
\(237\) 48500.8 0.863480
\(238\) 134732.i 2.37858i
\(239\) −80213.6 −1.40427 −0.702137 0.712041i \(-0.747771\pi\)
−0.702137 + 0.712041i \(0.747771\pi\)
\(240\) −20788.8 −0.360917
\(241\) 27279.2 0.469676 0.234838 0.972035i \(-0.424544\pi\)
0.234838 + 0.972035i \(0.424544\pi\)
\(242\) 106525.i 1.81894i
\(243\) −3788.00 −0.0641500
\(244\) 37325.9i 0.626947i
\(245\) −1835.99 −0.0305871
\(246\) 28495.2i 0.470870i
\(247\) 335.763i 0.00550350i
\(248\) −43996.7 −0.715346
\(249\) 9557.90i 0.154157i
\(250\) 66454.4i 1.06327i
\(251\) −87290.9 −1.38555 −0.692774 0.721155i \(-0.743612\pi\)
−0.692774 + 0.721155i \(0.743612\pi\)
\(252\) −10361.1 −0.163156
\(253\) 103858. 1.62255
\(254\) 146488.i 2.27057i
\(255\) −35711.3 −0.549193
\(256\) 75668.9 1.15462
\(257\) −1669.20 −0.0252721 −0.0126361 0.999920i \(-0.504022\pi\)
−0.0126361 + 0.999920i \(0.504022\pi\)
\(258\) 38440.3 0.577494
\(259\) 58977.2i 0.879194i
\(260\) 60.8783i 0.000900567i
\(261\) −7996.55 −0.117388
\(262\) −148620. −2.16509
\(263\) 99916.5 1.44453 0.722264 0.691618i \(-0.243102\pi\)
0.722264 + 0.691618i \(0.243102\pi\)
\(264\) 40537.4 0.581632
\(265\) 35173.1 0.500862
\(266\) 128618.i 1.81777i
\(267\) 29799.7i 0.418012i
\(268\) 44508.4i 0.619687i
\(269\) 24594.1i 0.339881i 0.985454 + 0.169940i \(0.0543575\pi\)
−0.985454 + 0.169940i \(0.945642\pi\)
\(270\) 8525.86i 0.116953i
\(271\) 12306.3 0.167567 0.0837836 0.996484i \(-0.473300\pi\)
0.0837836 + 0.996484i \(0.473300\pi\)
\(272\) 175730. 2.37524
\(273\) 167.901i 0.00225282i
\(274\) 137252.i 1.82818i
\(275\) 89595.7i 1.18474i
\(276\) 21455.2i 0.281653i
\(277\) 30853.9 0.402115 0.201058 0.979579i \(-0.435562\pi\)
0.201058 + 0.979579i \(0.435562\pi\)
\(278\) 29760.7i 0.385082i
\(279\) 29117.7i 0.374066i
\(280\) 25758.5i 0.328552i
\(281\) 6311.40 0.0799306 0.0399653 0.999201i \(-0.487275\pi\)
0.0399653 + 0.999201i \(0.487275\pi\)
\(282\) 2604.95 0.0327568
\(283\) 37474.9i 0.467916i 0.972247 + 0.233958i \(0.0751678\pi\)
−0.972247 + 0.233958i \(0.924832\pi\)
\(284\) −44314.3 −0.549424
\(285\) 34090.8 0.419709
\(286\) 594.726i 0.00727085i
\(287\) −56975.9 −0.691715
\(288\) 24330.3i 0.293334i
\(289\) 218350. 2.61431
\(290\) 17998.3i 0.214011i
\(291\) 79358.6i 0.937147i
\(292\) 51325.0i 0.601954i
\(293\) 13284.3 0.154740 0.0773700 0.997002i \(-0.475348\pi\)
0.0773700 + 0.997002i \(0.475348\pi\)
\(294\) 3705.27i 0.0428672i
\(295\) 32054.3 + 29470.4i 0.368334 + 0.338643i
\(296\) 47668.3 0.544059
\(297\) 26828.3i 0.304145i
\(298\) 174615. 1.96629
\(299\) −347.680 −0.00388899
\(300\) −18508.9 −0.205655
\(301\) 76861.0i 0.848346i
\(302\) −18537.7 −0.203256
\(303\) 70850.6i 0.771717i
\(304\) −167756. −1.81523
\(305\) 61413.4i 0.660182i
\(306\) 72069.9i 0.769682i
\(307\) 27275.0 0.289393 0.144697 0.989476i \(-0.453779\pi\)
0.144697 + 0.989476i \(0.453779\pi\)
\(308\) 73381.9i 0.773548i
\(309\) 24803.3i 0.259772i
\(310\) 65536.9 0.681966
\(311\) 74737.1 0.772708 0.386354 0.922351i \(-0.373734\pi\)
0.386354 + 0.922351i \(0.373734\pi\)
\(312\) −135.706 −0.00139408
\(313\) 147610.i 1.50670i −0.657618 0.753352i \(-0.728436\pi\)
0.657618 0.753352i \(-0.271564\pi\)
\(314\) 68832.3 0.698124
\(315\) −17047.4 −0.171805
\(316\) 70962.2 0.710645
\(317\) −75632.0 −0.752640 −0.376320 0.926490i \(-0.622811\pi\)
−0.376320 + 0.926490i \(0.622811\pi\)
\(318\) 70983.7i 0.701947i
\(319\) 56635.3i 0.556552i
\(320\) 9251.40 0.0903457
\(321\) −56697.7 −0.550244
\(322\) 133183. 1.28451
\(323\) −288173. −2.76216
\(324\) −5542.27 −0.0527956
\(325\) 299.936i 0.00283963i
\(326\) 26411.2i 0.248515i
\(327\) 6899.04i 0.0645198i
\(328\) 46050.7i 0.428044i
\(329\) 5208.57i 0.0481201i
\(330\) −60384.1 −0.554491
\(331\) 43603.6 0.397985 0.198992 0.980001i \(-0.436233\pi\)
0.198992 + 0.980001i \(0.436233\pi\)
\(332\) 13984.3i 0.126872i
\(333\) 31547.7i 0.284498i
\(334\) 52204.3i 0.467965i
\(335\) 73230.9i 0.652537i
\(336\) 83887.7 0.743053
\(337\) 111943.i 0.985682i −0.870119 0.492841i \(-0.835958\pi\)
0.870119 0.492841i \(-0.164042\pi\)
\(338\) 138754.i 1.21454i
\(339\) 37446.4i 0.325845i
\(340\) −52249.7 −0.451987
\(341\) −206225. −1.77351
\(342\) 68799.7i 0.588212i
\(343\) −113783. −0.967140
\(344\) −62122.9 −0.524970
\(345\) 35300.8i 0.296583i
\(346\) 132384. 1.10581
\(347\) 43440.9i 0.360778i 0.983595 + 0.180389i \(0.0577357\pi\)
−0.983595 + 0.180389i \(0.942264\pi\)
\(348\) −11699.9 −0.0966101
\(349\) 63411.1i 0.520612i 0.965526 + 0.260306i \(0.0838235\pi\)
−0.965526 + 0.260306i \(0.916177\pi\)
\(350\) 114895.i 0.937915i
\(351\) 89.8122i 0.000728989i
\(352\) 172318. 1.39074
\(353\) 152287.i 1.22212i −0.791585 0.611059i \(-0.790744\pi\)
0.791585 0.611059i \(-0.209256\pi\)
\(354\) 59475.0 64689.6i 0.474600 0.516212i
\(355\) −72911.7 −0.578549
\(356\) 43600.3i 0.344025i
\(357\) 144103. 1.13067
\(358\) −293016. −2.28626
\(359\) 38536.4 0.299008 0.149504 0.988761i \(-0.452232\pi\)
0.149504 + 0.988761i \(0.452232\pi\)
\(360\) 13778.5i 0.106316i
\(361\) 144776. 1.11092
\(362\) 135413.i 1.03334i
\(363\) 113934. 0.864647
\(364\) 245.658i 0.00185408i
\(365\) 84446.6i 0.633864i
\(366\) −123940. −0.925230
\(367\) 127968.i 0.950102i −0.879958 0.475051i \(-0.842430\pi\)
0.879958 0.475051i \(-0.157570\pi\)
\(368\) 173710.i 1.28271i
\(369\) −30477.1 −0.223831
\(370\) −71006.1 −0.518672
\(371\) −141931. −1.03117
\(372\) 42602.5i 0.307857i
\(373\) −181481. −1.30441 −0.652203 0.758044i \(-0.726155\pi\)
−0.652203 + 0.758044i \(0.726155\pi\)
\(374\) 510432. 3.64918
\(375\) −71076.5 −0.505433
\(376\) −4209.83 −0.0297775
\(377\) 189.596i 0.00133397i
\(378\) 34403.8i 0.240781i
\(379\) −52087.4 −0.362622 −0.181311 0.983426i \(-0.558034\pi\)
−0.181311 + 0.983426i \(0.558034\pi\)
\(380\) 49878.8 0.345421
\(381\) −156677. −1.07933
\(382\) 159508. 1.09309
\(383\) −129457. −0.882527 −0.441263 0.897378i \(-0.645470\pi\)
−0.441263 + 0.897378i \(0.645470\pi\)
\(384\) 93588.4i 0.634687i
\(385\) 120737.i 0.814554i
\(386\) 248045.i 1.66477i
\(387\) 41113.9i 0.274516i
\(388\) 116111.i 0.771274i
\(389\) −239714. −1.58414 −0.792070 0.610430i \(-0.790997\pi\)
−0.792070 + 0.610430i \(0.790997\pi\)
\(390\) 202.145 0.00132903
\(391\) 298401.i 1.95185i
\(392\) 5988.03i 0.0389684i
\(393\) 158957.i 1.02919i
\(394\) 254703.i 1.64075i
\(395\) 116756. 0.748317
\(396\) 39252.9i 0.250312i
\(397\) 63125.7i 0.400521i 0.979743 + 0.200260i \(0.0641788\pi\)
−0.979743 + 0.200260i \(0.935821\pi\)
\(398\) 103399.i 0.652755i
\(399\) −137564. −0.864092
\(400\) 149856. 0.936601
\(401\) 5633.87i 0.0350363i −0.999847 0.0175181i \(-0.994424\pi\)
0.999847 0.0175181i \(-0.00557648\pi\)
\(402\) −147789. −0.914515
\(403\) 690.372 0.00425082
\(404\) 103663.i 0.635125i
\(405\) −9118.86 −0.0555943
\(406\) 72627.2i 0.440603i
\(407\) 223435. 1.34885
\(408\) 116471.i 0.699678i
\(409\) 208211.i 1.24468i −0.782747 0.622340i \(-0.786182\pi\)
0.782747 0.622340i \(-0.213818\pi\)
\(410\) 68596.6i 0.408070i
\(411\) −146798. −0.869036
\(412\) 36290.1i 0.213793i
\(413\) −129346. 118920.i −0.758322 0.697194i
\(414\) 71241.6 0.415655
\(415\) 23008.8i 0.133597i
\(416\) −576.864 −0.00333340
\(417\) −31830.6 −0.183051
\(418\) −487271. −2.78880
\(419\) 29129.4i 0.165922i −0.996553 0.0829610i \(-0.973562\pi\)
0.996553 0.0829610i \(-0.0264377\pi\)
\(420\) −24942.2 −0.141396
\(421\) 297451.i 1.67823i −0.543956 0.839113i \(-0.683074\pi\)
0.543956 0.839113i \(-0.316926\pi\)
\(422\) −329378. −1.84957
\(423\) 2786.13i 0.0155712i
\(424\) 114716.i 0.638105i
\(425\) 257424. 1.42519
\(426\) 147145.i 0.810824i
\(427\) 247817.i 1.35917i
\(428\) −82955.2 −0.452852
\(429\) −636.091 −0.00345625
\(430\) 92537.5 0.500473
\(431\) 340194.i 1.83135i 0.401917 + 0.915676i \(0.368344\pi\)
−0.401917 + 0.915676i \(0.631656\pi\)
\(432\) 44872.6 0.240444
\(433\) −19705.6 −0.105103 −0.0525514 0.998618i \(-0.516735\pi\)
−0.0525514 + 0.998618i \(0.516735\pi\)
\(434\) −264456. −1.40402
\(435\) −19250.1 −0.101731
\(436\) 10094.1i 0.0530999i
\(437\) 284861.i 1.49166i
\(438\) 170424. 0.888347
\(439\) 29208.1 0.151557 0.0757783 0.997125i \(-0.475856\pi\)
0.0757783 + 0.997125i \(0.475856\pi\)
\(440\) 97585.9 0.504059
\(441\) 3962.98 0.0203772
\(442\) −1708.75 −0.00874652
\(443\) 136923.i 0.697698i 0.937179 + 0.348849i \(0.113427\pi\)
−0.937179 + 0.348849i \(0.886573\pi\)
\(444\) 46157.8i 0.234142i
\(445\) 71736.9i 0.362262i
\(446\) 218975.i 1.10084i
\(447\) 186760.i 0.934692i
\(448\) −37331.5 −0.186003
\(449\) 324943. 1.61181 0.805906 0.592043i \(-0.201678\pi\)
0.805906 + 0.592043i \(0.201678\pi\)
\(450\) 61458.6i 0.303499i
\(451\) 215853.i 1.06122i
\(452\) 54788.4i 0.268171i
\(453\) 19827.1i 0.0966190i
\(454\) −64063.8 −0.310814
\(455\) 404.188i 0.00195236i
\(456\) 111186.i 0.534714i
\(457\) 142683.i 0.683189i 0.939847 + 0.341595i \(0.110967\pi\)
−0.939847 + 0.341595i \(0.889033\pi\)
\(458\) −24770.0 −0.118085
\(459\) 77082.6 0.365873
\(460\) 51649.1i 0.244089i
\(461\) 107011. 0.503533 0.251767 0.967788i \(-0.418988\pi\)
0.251767 + 0.967788i \(0.418988\pi\)
\(462\) 243663. 1.14158
\(463\) 344520.i 1.60714i −0.595213 0.803568i \(-0.702932\pi\)
0.595213 0.803568i \(-0.297068\pi\)
\(464\) 94727.2 0.439986
\(465\) 70095.2i 0.324177i
\(466\) −220861. −1.01706
\(467\) 12985.4i 0.0595419i −0.999557 0.0297709i \(-0.990522\pi\)
0.999557 0.0297709i \(-0.00947778\pi\)
\(468\) 131.405i 0.000599959i
\(469\) 295503.i 1.34343i
\(470\) 6270.91 0.0283880
\(471\) 73619.7i 0.331858i
\(472\) −96116.8 + 104544.i −0.431435 + 0.469262i
\(473\) −291188. −1.30152
\(474\) 235629.i 1.04875i
\(475\) −245744. −1.08917
\(476\) 210839. 0.930545
\(477\) −75920.9 −0.333676
\(478\) 389697.i 1.70558i
\(479\) 148631. 0.647798 0.323899 0.946092i \(-0.395006\pi\)
0.323899 + 0.946092i \(0.395006\pi\)
\(480\) 58570.5i 0.254212i
\(481\) −747.985 −0.00323298
\(482\) 132529.i 0.570450i
\(483\) 142447.i 0.610602i
\(484\) 166698. 0.711606
\(485\) 191040.i 0.812159i
\(486\) 18403.0i 0.0779142i
\(487\) 174834. 0.737169 0.368584 0.929594i \(-0.379843\pi\)
0.368584 + 0.929594i \(0.379843\pi\)
\(488\) 200298. 0.841079
\(489\) 28248.2 0.118133
\(490\) 8919.71i 0.0371500i
\(491\) −289993. −1.20288 −0.601442 0.798916i \(-0.705407\pi\)
−0.601442 + 0.798916i \(0.705407\pi\)
\(492\) −44591.5 −0.184214
\(493\) 162723. 0.669508
\(494\) 1631.22 0.00668434
\(495\) 64583.9i 0.263581i
\(496\) 344928.i 1.40206i
\(497\) 294215. 1.19111
\(498\) 46434.6 0.187233
\(499\) −337039. −1.35356 −0.676782 0.736183i \(-0.736626\pi\)
−0.676782 + 0.736183i \(0.736626\pi\)
\(500\) −103993. −0.415972
\(501\) −55835.3 −0.222451
\(502\) 424081.i 1.68283i
\(503\) 424514.i 1.67786i 0.544238 + 0.838931i \(0.316819\pi\)
−0.544238 + 0.838931i \(0.683181\pi\)
\(504\) 55599.5i 0.218882i
\(505\) 170559.i 0.668793i
\(506\) 504566.i 1.97068i
\(507\) −148405. −0.577342
\(508\) −229236. −0.888292
\(509\) 166873.i 0.644095i −0.946724 0.322047i \(-0.895629\pi\)
0.946724 0.322047i \(-0.104371\pi\)
\(510\) 173494.i 0.667029i
\(511\) 340761.i 1.30499i
\(512\) 79440.3i 0.303041i
\(513\) −73584.9 −0.279611
\(514\) 8109.37i 0.0306945i
\(515\) 59709.1i 0.225126i
\(516\) 60154.4i 0.225927i
\(517\) −19732.7 −0.0738252
\(518\) 286526. 1.06784
\(519\) 141591.i 0.525656i
\(520\) −326.685 −0.00120815
\(521\) 234510. 0.863943 0.431972 0.901887i \(-0.357818\pi\)
0.431972 + 0.901887i \(0.357818\pi\)
\(522\) 38849.2i 0.142574i
\(523\) 133011. 0.486277 0.243138 0.969992i \(-0.421823\pi\)
0.243138 + 0.969992i \(0.421823\pi\)
\(524\) 232573.i 0.847026i
\(525\) 122886. 0.445844
\(526\) 485419.i 1.75447i
\(527\) 592521.i 2.13345i
\(528\) 317808.i 1.13998i
\(529\) −15130.5 −0.0540683
\(530\) 170879.i 0.608328i
\(531\) −69189.0 63611.6i −0.245385 0.225604i
\(532\) −201272. −0.711149
\(533\) 722.603i 0.00254358i
\(534\) 144774. 0.507702
\(535\) −136489. −0.476858
\(536\) 238840. 0.831339
\(537\) 313396.i 1.08679i
\(538\) 119484. 0.412806
\(539\) 28067.6i 0.0966114i
\(540\) −13341.9 −0.0457542
\(541\) 37399.8i 0.127784i −0.997957 0.0638918i \(-0.979649\pi\)
0.997957 0.0638918i \(-0.0203512\pi\)
\(542\) 59787.0i 0.203521i
\(543\) 144831. 0.491205
\(544\) 495102.i 1.67300i
\(545\) 16608.1i 0.0559148i
\(546\) −815.702 −0.00273619
\(547\) −3623.89 −0.0121116 −0.00605579 0.999982i \(-0.501928\pi\)
−0.00605579 + 0.999982i \(0.501928\pi\)
\(548\) −214783. −0.715218
\(549\) 132561.i 0.439814i
\(550\) 435278. 1.43894
\(551\) −155340. −0.511657
\(552\) −115133. −0.377851
\(553\) −471138. −1.54063
\(554\) 149896.i 0.488394i
\(555\) 75944.8i 0.246554i
\(556\) −46571.8 −0.150652
\(557\) 223715. 0.721082 0.360541 0.932743i \(-0.382592\pi\)
0.360541 + 0.932743i \(0.382592\pi\)
\(558\) −141461. −0.454327
\(559\) 974.798 0.00311954
\(560\) 201943. 0.643951
\(561\) 545934.i 1.73466i
\(562\) 30662.3i 0.0970807i
\(563\) 74625.8i 0.235436i 0.993047 + 0.117718i \(0.0375578\pi\)
−0.993047 + 0.117718i \(0.962442\pi\)
\(564\) 4076.43i 0.0128151i
\(565\) 90144.9i 0.282387i
\(566\) 182062. 0.568313
\(567\) 36796.6 0.114457
\(568\) 237799.i 0.737079i
\(569\) 319733.i 0.987558i −0.869588 0.493779i \(-0.835615\pi\)
0.869588 0.493779i \(-0.164385\pi\)
\(570\) 165622.i 0.509762i
\(571\) 25255.1i 0.0774598i 0.999250 + 0.0387299i \(0.0123312\pi\)
−0.999250 + 0.0387299i \(0.987669\pi\)
\(572\) −930.674 −0.00284450
\(573\) 170603.i 0.519609i
\(574\) 276803.i 0.840130i
\(575\) 254466.i 0.769650i
\(576\) −19969.1 −0.0601885
\(577\) 442259. 1.32839 0.664194 0.747560i \(-0.268775\pi\)
0.664194 + 0.747560i \(0.268775\pi\)
\(578\) 1.06080e6i 3.17524i
\(579\) 265297. 0.791362
\(580\) −28165.2 −0.0837252
\(581\) 92845.6i 0.275048i
\(582\) 385543. 1.13822
\(583\) 537706.i 1.58201i
\(584\) −275420. −0.807551
\(585\) 216.205i 0.000631763i
\(586\) 64538.3i 0.187941i
\(587\) 122543.i 0.355641i 0.984063 + 0.177821i \(0.0569047\pi\)
−0.984063 + 0.177821i \(0.943095\pi\)
\(588\) 5798.29 0.0167705
\(589\) 565635.i 1.63044i
\(590\) 143174. 155728.i 0.411302 0.447365i
\(591\) −272418. −0.779941
\(592\) 373714.i 1.06634i
\(593\) −531802. −1.51231 −0.756154 0.654393i \(-0.772924\pi\)
−0.756154 + 0.654393i \(0.772924\pi\)
\(594\) 130339. 0.369403
\(595\) 346900. 0.979874
\(596\) 273251.i 0.769253i
\(597\) 110591. 0.310291
\(598\) 1689.11i 0.00472342i
\(599\) 55605.2 0.154975 0.0774875 0.996993i \(-0.475310\pi\)
0.0774875 + 0.996993i \(0.475310\pi\)
\(600\) 99322.4i 0.275896i
\(601\) 351895.i 0.974236i −0.873336 0.487118i \(-0.838048\pi\)
0.873336 0.487118i \(-0.161952\pi\)
\(602\) −373410. −1.03037
\(603\) 158069.i 0.434721i
\(604\) 29009.3i 0.0795176i
\(605\) 274273. 0.749329
\(606\) 344210. 0.937298
\(607\) 130700. 0.354731 0.177365 0.984145i \(-0.443243\pi\)
0.177365 + 0.984145i \(0.443243\pi\)
\(608\) 472636.i 1.27856i
\(609\) 77678.7 0.209444
\(610\) −298362. −0.801832
\(611\) 66.0583 0.000176948
\(612\) 112781. 0.301114
\(613\) 509749.i 1.35655i 0.734808 + 0.678275i \(0.237272\pi\)
−0.734808 + 0.678275i \(0.762728\pi\)
\(614\) 132509.i 0.351486i
\(615\) −73367.7 −0.193979
\(616\) −393781. −1.03775
\(617\) −77698.9 −0.204101 −0.102050 0.994779i \(-0.532540\pi\)
−0.102050 + 0.994779i \(0.532540\pi\)
\(618\) 120501. 0.315509
\(619\) 221586. 0.578309 0.289155 0.957282i \(-0.406626\pi\)
0.289155 + 0.957282i \(0.406626\pi\)
\(620\) 102557.i 0.266798i
\(621\) 76196.6i 0.197584i
\(622\) 363091.i 0.938502i
\(623\) 289475.i 0.745820i
\(624\) 1063.92i 0.00273236i
\(625\) 121730. 0.311628
\(626\) −717127. −1.82998
\(627\) 521162.i 1.32568i
\(628\) 107714.i 0.273120i
\(629\) 641969.i 1.62260i
\(630\) 82820.3i 0.208668i
\(631\) 2526.90 0.00634642 0.00317321 0.999995i \(-0.498990\pi\)
0.00317321 + 0.999995i \(0.498990\pi\)
\(632\) 380797.i 0.953365i
\(633\) 352288.i 0.879204i
\(634\) 367439.i 0.914127i
\(635\) −377169. −0.935381
\(636\) −111081. −0.274616
\(637\) 93.9610i 0.000231563i
\(638\) 275148. 0.675967
\(639\) 157379. 0.385431
\(640\) 225296.i 0.550039i
\(641\) 359210. 0.874244 0.437122 0.899402i \(-0.355998\pi\)
0.437122 + 0.899402i \(0.355998\pi\)
\(642\) 275451.i 0.668305i
\(643\) 512961. 1.24069 0.620344 0.784330i \(-0.286993\pi\)
0.620344 + 0.784330i \(0.286993\pi\)
\(644\) 208416.i 0.502527i
\(645\) 98973.7i 0.237903i
\(646\) 1.40002e6i 3.35481i
\(647\) −621636. −1.48500 −0.742502 0.669844i \(-0.766361\pi\)
−0.742502 + 0.669844i \(0.766361\pi\)
\(648\) 29740.9i 0.0708278i
\(649\) −450527. + 490028.i −1.06962 + 1.16341i
\(650\) −1457.16 −0.00344891
\(651\) 282850.i 0.667412i
\(652\) 41330.3 0.0972241
\(653\) 194566. 0.456291 0.228145 0.973627i \(-0.426734\pi\)
0.228145 + 0.973627i \(0.426734\pi\)
\(654\) 33517.2 0.0783633
\(655\) 382659.i 0.891927i
\(656\) 361032. 0.838954
\(657\) 182277.i 0.422282i
\(658\) −25304.5 −0.0584449
\(659\) 481512.i 1.10876i −0.832265 0.554378i \(-0.812956\pi\)
0.832265 0.554378i \(-0.187044\pi\)
\(660\) 94493.7i 0.216928i
\(661\) 340031. 0.778244 0.389122 0.921186i \(-0.372778\pi\)
0.389122 + 0.921186i \(0.372778\pi\)
\(662\) 211837.i 0.483377i
\(663\) 1827.60i 0.00415772i
\(664\) −75042.4 −0.170204
\(665\) −331159. −0.748847
\(666\) 153266. 0.345540
\(667\) 160853.i 0.361558i
\(668\) −81693.4 −0.183077
\(669\) −234205. −0.523292
\(670\) −355774. −0.792546
\(671\) 938855. 2.08523
\(672\) 236345.i 0.523369i
\(673\) 413955.i 0.913951i 0.889479 + 0.456976i \(0.151067\pi\)
−0.889479 + 0.456976i \(0.848933\pi\)
\(674\) −543846. −1.19717
\(675\) 65733.2 0.144270
\(676\) −217134. −0.475153
\(677\) −374555. −0.817219 −0.408609 0.912709i \(-0.633986\pi\)
−0.408609 + 0.912709i \(0.633986\pi\)
\(678\) −181924. −0.395759
\(679\) 770890.i 1.67206i
\(680\) 280382.i 0.606362i
\(681\) 68519.6i 0.147748i
\(682\) 1.00189e6i 2.15403i
\(683\) 648839.i 1.39090i 0.718576 + 0.695449i \(0.244794\pi\)
−0.718576 + 0.695449i \(0.755206\pi\)
\(684\) −107663. −0.230120
\(685\) −353388. −0.753132
\(686\) 552786.i 1.17465i
\(687\) 26492.8i 0.0561326i
\(688\) 487036.i 1.02893i
\(689\) 1800.06i 0.00379183i
\(690\) 171500. 0.360219
\(691\) 622050.i 1.30277i −0.758746 0.651387i \(-0.774187\pi\)
0.758746 0.651387i \(-0.225813\pi\)
\(692\) 207164.i 0.432616i
\(693\) 260611.i 0.542658i
\(694\) 211047. 0.438187
\(695\) −76626.0 −0.158638
\(696\) 62783.8i 0.129607i
\(697\) 620184. 1.27660
\(698\) 308067. 0.632316
\(699\) 236223.i 0.483467i
\(700\) 179796. 0.366931
\(701\) 98359.5i 0.200161i 0.994979 + 0.100081i \(0.0319101\pi\)
−0.994979 + 0.100081i \(0.968090\pi\)
\(702\) −436.330 −0.000885402
\(703\) 612839.i 1.24004i
\(704\) 141430.i 0.285363i
\(705\) 6707.07i 0.0134944i
\(706\) −739847. −1.48434
\(707\) 688244.i 1.37690i
\(708\) −101231. 93071.1i −0.201952 0.185673i
\(709\) −772872. −1.53750 −0.768750 0.639549i \(-0.779121\pi\)
−0.768750 + 0.639549i \(0.779121\pi\)
\(710\) 354223.i 0.702684i
\(711\) −252018. −0.498530
\(712\) −233968. −0.461526
\(713\) 585711. 1.15214
\(714\) 700088.i 1.37327i
\(715\) −1531.27 −0.00299529
\(716\) 458534.i 0.894428i
\(717\) 416802. 0.810758
\(718\) 187220.i 0.363164i
\(719\) 273060.i 0.528202i 0.964495 + 0.264101i \(0.0850752\pi\)
−0.964495 + 0.264101i \(0.914925\pi\)
\(720\) 108022. 0.208376
\(721\) 240940.i 0.463487i
\(722\) 703358.i 1.34928i
\(723\) −141747. −0.271167
\(724\) 211905. 0.404263
\(725\) 138764. 0.263999
\(726\) 553518.i 1.05017i
\(727\) 31372.5 0.0593581 0.0296791 0.999559i \(-0.490551\pi\)
0.0296791 + 0.999559i \(0.490551\pi\)
\(728\) 1318.25 0.00248733
\(729\) 19683.0 0.0370370
\(730\) 410262. 0.769867
\(731\) 836634.i 1.56567i
\(732\) 193951.i 0.361968i
\(733\) 67831.8 0.126248 0.0631241 0.998006i \(-0.479894\pi\)
0.0631241 + 0.998006i \(0.479894\pi\)
\(734\) −621701. −1.15396
\(735\) 9540.10 0.0176595
\(736\) −489411. −0.903480
\(737\) 1.11951e6 2.06108
\(738\) 148065.i 0.271857i
\(739\) 788958.i 1.44466i −0.691549 0.722329i \(-0.743071\pi\)
0.691549 0.722329i \(-0.256929\pi\)
\(740\) 111116.i 0.202914i
\(741\) 1744.67i 0.00317745i
\(742\) 689537.i 1.25242i
\(743\) 50905.9 0.0922127 0.0461064 0.998937i \(-0.485319\pi\)
0.0461064 + 0.998937i \(0.485319\pi\)
\(744\) 228613. 0.413005
\(745\) 449588.i 0.810031i
\(746\) 881678.i 1.58428i
\(747\) 49664.3i 0.0890027i
\(748\) 798764.i 1.42763i
\(749\) 550762. 0.981749
\(750\) 345307.i 0.613880i
\(751\) 473502.i 0.839541i 0.907630 + 0.419770i \(0.137889\pi\)
−0.907630 + 0.419770i \(0.862111\pi\)
\(752\) 33004.5i 0.0583630i
\(753\) 453577. 0.799947
\(754\) −921.103 −0.00162019
\(755\) 47729.8i 0.0837329i
\(756\) 53837.7 0.0941983
\(757\) −5901.48 −0.0102984 −0.00514919 0.999987i \(-0.501639\pi\)
−0.00514919 + 0.999987i \(0.501639\pi\)
\(758\) 253053.i 0.440427i
\(759\) −539660. −0.936777
\(760\) 267659.i 0.463399i
\(761\) 559827. 0.966684 0.483342 0.875431i \(-0.339423\pi\)
0.483342 + 0.875431i \(0.339423\pi\)
\(762\) 761175.i 1.31092i
\(763\) 67017.4i 0.115117i
\(764\) 249611.i 0.427639i
\(765\) 185561. 0.317077
\(766\) 628934.i 1.07188i
\(767\) 1508.21 1640.45i 0.00256373 0.00278851i
\(768\) −393187. −0.666617
\(769\) 752520.i 1.27252i 0.771473 + 0.636262i \(0.219520\pi\)
−0.771473 + 0.636262i \(0.780480\pi\)
\(770\) 586572. 0.989327
\(771\) 8673.40 0.0145909
\(772\) 388160. 0.651292
\(773\) 293795.i 0.491684i 0.969310 + 0.245842i \(0.0790644\pi\)
−0.969310 + 0.245842i \(0.920936\pi\)
\(774\) −199742. −0.333416
\(775\) 505281.i 0.841258i
\(776\) −623072. −1.03470
\(777\) 306454.i 0.507603i
\(778\) 1.16459e6i 1.92404i
\(779\) −592043. −0.975614
\(780\) 316.333i 0.000519942i
\(781\) 1.11463e6i 1.82738i
\(782\) −1.44971e6 −2.37065
\(783\) 41551.3 0.0677737
\(784\) −46945.5 −0.0763768
\(785\) 177225.i 0.287598i
\(786\) 772255. 1.25002
\(787\) 642350. 1.03710 0.518552 0.855046i \(-0.326471\pi\)
0.518552 + 0.855046i \(0.326471\pi\)
\(788\) −398579. −0.641893
\(789\) −519181. −0.833998