Properties

Label 177.5.c.a.58.15
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 58.15
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.26

$q$-expansion

\(f(q)\) \(=\) \(q-2.33963i q^{2} -5.19615 q^{3} +10.5261 q^{4} +30.0439 q^{5} +12.1571i q^{6} -41.7287 q^{7} -62.0613i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-2.33963i q^{2} -5.19615 q^{3} +10.5261 q^{4} +30.0439 q^{5} +12.1571i q^{6} -41.7287 q^{7} -62.0613i q^{8} +27.0000 q^{9} -70.2916i q^{10} -117.370i q^{11} -54.6954 q^{12} +118.348i q^{13} +97.6298i q^{14} -156.113 q^{15} +23.2175 q^{16} +263.868 q^{17} -63.1700i q^{18} +373.890 q^{19} +316.246 q^{20} +216.829 q^{21} -274.603 q^{22} -503.177i q^{23} +322.480i q^{24} +277.635 q^{25} +276.891 q^{26} -140.296 q^{27} -439.242 q^{28} -549.815 q^{29} +365.246i q^{30} -450.839i q^{31} -1047.30i q^{32} +609.873i q^{33} -617.355i q^{34} -1253.69 q^{35} +284.206 q^{36} -1430.88i q^{37} -874.765i q^{38} -614.954i q^{39} -1864.56i q^{40} +1441.61 q^{41} -507.299i q^{42} -3202.06i q^{43} -1235.45i q^{44} +811.185 q^{45} -1177.25 q^{46} +967.133i q^{47} -120.642 q^{48} -659.713 q^{49} -649.564i q^{50} -1371.10 q^{51} +1245.75i q^{52} +1662.12 q^{53} +328.241i q^{54} -3526.26i q^{55} +2589.74i q^{56} -1942.79 q^{57} +1286.36i q^{58} +(-34.3306 + 3480.83i) q^{59} -1643.26 q^{60} +1712.94i q^{61} -1054.80 q^{62} -1126.68 q^{63} -2078.82 q^{64} +3555.63i q^{65} +1426.88 q^{66} -5062.54i q^{67} +2777.51 q^{68} +2614.58i q^{69} +2933.18i q^{70} +6150.31 q^{71} -1675.66i q^{72} +4170.58i q^{73} -3347.74 q^{74} -1442.64 q^{75} +3935.62 q^{76} +4897.71i q^{77} -1438.77 q^{78} -5990.22 q^{79} +697.544 q^{80} +729.000 q^{81} -3372.84i q^{82} -2937.78i q^{83} +2282.37 q^{84} +7927.64 q^{85} -7491.63 q^{86} +2856.92 q^{87} -7284.15 q^{88} -3877.47i q^{89} -1897.87i q^{90} -4938.51i q^{91} -5296.50i q^{92} +2342.63i q^{93} +2262.73 q^{94} +11233.1 q^{95} +5441.94i q^{96} -2340.59i q^{97} +1543.48i q^{98} -3168.99i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.33963i 0.584908i −0.956280 0.292454i \(-0.905528\pi\)
0.956280 0.292454i \(-0.0944718\pi\)
\(3\) −5.19615 −0.577350
\(4\) 10.5261 0.657883
\(5\) 30.0439 1.20176 0.600878 0.799341i \(-0.294818\pi\)
0.600878 + 0.799341i \(0.294818\pi\)
\(6\) 12.1571i 0.337697i
\(7\) −41.7287 −0.851607 −0.425803 0.904816i \(-0.640008\pi\)
−0.425803 + 0.904816i \(0.640008\pi\)
\(8\) 62.0613i 0.969708i
\(9\) 27.0000 0.333333
\(10\) 70.2916i 0.702916i
\(11\) 117.370i 0.970001i −0.874514 0.485000i \(-0.838819\pi\)
0.874514 0.485000i \(-0.161181\pi\)
\(12\) −54.6954 −0.379829
\(13\) 118.348i 0.700284i 0.936697 + 0.350142i \(0.113867\pi\)
−0.936697 + 0.350142i \(0.886133\pi\)
\(14\) 97.6298i 0.498111i
\(15\) −156.113 −0.693834
\(16\) 23.2175 0.0906934
\(17\) 263.868 0.913040 0.456520 0.889713i \(-0.349096\pi\)
0.456520 + 0.889713i \(0.349096\pi\)
\(18\) 63.1700i 0.194969i
\(19\) 373.890 1.03571 0.517854 0.855469i \(-0.326731\pi\)
0.517854 + 0.855469i \(0.326731\pi\)
\(20\) 316.246 0.790615
\(21\) 216.829 0.491675
\(22\) −274.603 −0.567361
\(23\) 503.177i 0.951185i −0.879666 0.475592i \(-0.842234\pi\)
0.879666 0.475592i \(-0.157766\pi\)
\(24\) 322.480i 0.559861i
\(25\) 277.635 0.444217
\(26\) 276.891 0.409601
\(27\) −140.296 −0.192450
\(28\) −439.242 −0.560258
\(29\) −549.815 −0.653763 −0.326882 0.945065i \(-0.605998\pi\)
−0.326882 + 0.945065i \(0.605998\pi\)
\(30\) 365.246i 0.405829i
\(31\) 450.839i 0.469135i −0.972100 0.234568i \(-0.924633\pi\)
0.972100 0.234568i \(-0.0753674\pi\)
\(32\) 1047.30i 1.02276i
\(33\) 609.873i 0.560030i
\(34\) 617.355i 0.534044i
\(35\) −1253.69 −1.02342
\(36\) 284.206 0.219294
\(37\) 1430.88i 1.04520i −0.852577 0.522601i \(-0.824962\pi\)
0.852577 0.522601i \(-0.175038\pi\)
\(38\) 874.765i 0.605793i
\(39\) 614.954i 0.404309i
\(40\) 1864.56i 1.16535i
\(41\) 1441.61 0.857591 0.428796 0.903401i \(-0.358938\pi\)
0.428796 + 0.903401i \(0.358938\pi\)
\(42\) 507.299i 0.287585i
\(43\) 3202.06i 1.73178i −0.500236 0.865889i \(-0.666753\pi\)
0.500236 0.865889i \(-0.333247\pi\)
\(44\) 1235.45i 0.638147i
\(45\) 811.185 0.400585
\(46\) −1177.25 −0.556355
\(47\) 967.133i 0.437815i 0.975746 + 0.218907i \(0.0702493\pi\)
−0.975746 + 0.218907i \(0.929751\pi\)
\(48\) −120.642 −0.0523618
\(49\) −659.713 −0.274766
\(50\) 649.564i 0.259826i
\(51\) −1371.10 −0.527144
\(52\) 1245.75i 0.460705i
\(53\) 1662.12 0.591713 0.295856 0.955232i \(-0.404395\pi\)
0.295856 + 0.955232i \(0.404395\pi\)
\(54\) 328.241i 0.112566i
\(55\) 3526.26i 1.16570i
\(56\) 2589.74i 0.825810i
\(57\) −1942.79 −0.597966
\(58\) 1286.36i 0.382391i
\(59\) −34.3306 + 3480.83i −0.00986228 + 0.999951i
\(60\) −1643.26 −0.456462
\(61\) 1712.94i 0.460343i 0.973150 + 0.230172i \(0.0739288\pi\)
−0.973150 + 0.230172i \(0.926071\pi\)
\(62\) −1054.80 −0.274401
\(63\) −1126.68 −0.283869
\(64\) −2078.82 −0.507524
\(65\) 3555.63i 0.841570i
\(66\) 1426.88 0.327566
\(67\) 5062.54i 1.12777i −0.825854 0.563883i \(-0.809307\pi\)
0.825854 0.563883i \(-0.190693\pi\)
\(68\) 2777.51 0.600673
\(69\) 2614.58i 0.549167i
\(70\) 2933.18i 0.598608i
\(71\) 6150.31 1.22006 0.610028 0.792380i \(-0.291158\pi\)
0.610028 + 0.792380i \(0.291158\pi\)
\(72\) 1675.66i 0.323236i
\(73\) 4170.58i 0.782619i 0.920259 + 0.391309i \(0.127978\pi\)
−0.920259 + 0.391309i \(0.872022\pi\)
\(74\) −3347.74 −0.611347
\(75\) −1442.64 −0.256469
\(76\) 3935.62 0.681374
\(77\) 4897.71i 0.826059i
\(78\) −1438.77 −0.236483
\(79\) −5990.22 −0.959818 −0.479909 0.877318i \(-0.659330\pi\)
−0.479909 + 0.877318i \(0.659330\pi\)
\(80\) 697.544 0.108991
\(81\) 729.000 0.111111
\(82\) 3372.84i 0.501612i
\(83\) 2937.78i 0.426445i −0.977004 0.213222i \(-0.931604\pi\)
0.977004 0.213222i \(-0.0683959\pi\)
\(84\) 2282.37 0.323465
\(85\) 7927.64 1.09725
\(86\) −7491.63 −1.01293
\(87\) 2856.92 0.377450
\(88\) −7284.15 −0.940618
\(89\) 3877.47i 0.489518i −0.969584 0.244759i \(-0.921291\pi\)
0.969584 0.244759i \(-0.0787088\pi\)
\(90\) 1897.87i 0.234305i
\(91\) 4938.51i 0.596367i
\(92\) 5296.50i 0.625769i
\(93\) 2342.63i 0.270855i
\(94\) 2262.73 0.256081
\(95\) 11233.1 1.24467
\(96\) 5441.94i 0.590488i
\(97\) 2340.59i 0.248760i −0.992235 0.124380i \(-0.960306\pi\)
0.992235 0.124380i \(-0.0396942\pi\)
\(98\) 1543.48i 0.160713i
\(99\) 3168.99i 0.323334i
\(100\) 2922.43 0.292243
\(101\) 18031.3i 1.76761i 0.467860 + 0.883803i \(0.345025\pi\)
−0.467860 + 0.883803i \(0.654975\pi\)
\(102\) 3207.87i 0.308330i
\(103\) 12277.9i 1.15731i 0.815572 + 0.578656i \(0.196423\pi\)
−0.815572 + 0.578656i \(0.803577\pi\)
\(104\) 7344.83 0.679071
\(105\) 6514.38 0.590874
\(106\) 3888.75i 0.346097i
\(107\) 7815.43 0.682630 0.341315 0.939949i \(-0.389128\pi\)
0.341315 + 0.939949i \(0.389128\pi\)
\(108\) −1476.78 −0.126610
\(109\) 4707.99i 0.396262i 0.980176 + 0.198131i \(0.0634872\pi\)
−0.980176 + 0.198131i \(0.936513\pi\)
\(110\) −8250.13 −0.681829
\(111\) 7435.08i 0.603448i
\(112\) −968.837 −0.0772351
\(113\) 8859.89i 0.693860i 0.937891 + 0.346930i \(0.112776\pi\)
−0.937891 + 0.346930i \(0.887224\pi\)
\(114\) 4545.41i 0.349755i
\(115\) 15117.4i 1.14309i
\(116\) −5787.42 −0.430100
\(117\) 3195.40i 0.233428i
\(118\) 8143.86 + 80.3209i 0.584879 + 0.00576852i
\(119\) −11010.9 −0.777551
\(120\) 9688.56i 0.672817i
\(121\) 865.256 0.0590981
\(122\) 4007.64 0.269258
\(123\) −7490.83 −0.495131
\(124\) 4745.59i 0.308636i
\(125\) −10436.2 −0.667916
\(126\) 2636.00i 0.166037i
\(127\) −7759.81 −0.481109 −0.240554 0.970636i \(-0.577329\pi\)
−0.240554 + 0.970636i \(0.577329\pi\)
\(128\) 11893.2i 0.725901i
\(129\) 16638.4i 0.999843i
\(130\) 8318.87 0.492241
\(131\) 26570.9i 1.54833i 0.632984 + 0.774165i \(0.281830\pi\)
−0.632984 + 0.774165i \(0.718170\pi\)
\(132\) 6419.60i 0.368435i
\(133\) −15602.0 −0.882015
\(134\) −11844.5 −0.659639
\(135\) −4215.04 −0.231278
\(136\) 16376.0i 0.885382i
\(137\) −6370.46 −0.339414 −0.169707 0.985495i \(-0.554282\pi\)
−0.169707 + 0.985495i \(0.554282\pi\)
\(138\) 6117.16 0.321212
\(139\) 26487.6 1.37092 0.685461 0.728109i \(-0.259601\pi\)
0.685461 + 0.728109i \(0.259601\pi\)
\(140\) −13196.5 −0.673293
\(141\) 5025.37i 0.252773i
\(142\) 14389.4i 0.713620i
\(143\) 13890.5 0.679276
\(144\) 626.873 0.0302311
\(145\) −16518.6 −0.785664
\(146\) 9757.60 0.457760
\(147\) 3427.97 0.158636
\(148\) 15061.7i 0.687621i
\(149\) 37732.0i 1.69956i 0.527136 + 0.849781i \(0.323266\pi\)
−0.527136 + 0.849781i \(0.676734\pi\)
\(150\) 3375.24i 0.150010i
\(151\) 19425.6i 0.851961i −0.904732 0.425981i \(-0.859929\pi\)
0.904732 0.425981i \(-0.140071\pi\)
\(152\) 23204.1i 1.00433i
\(153\) 7124.45 0.304347
\(154\) 11458.8 0.483168
\(155\) 13545.0i 0.563786i
\(156\) 6473.09i 0.265988i
\(157\) 40542.8i 1.64480i 0.568907 + 0.822402i \(0.307366\pi\)
−0.568907 + 0.822402i \(0.692634\pi\)
\(158\) 14014.9i 0.561405i
\(159\) −8636.63 −0.341626
\(160\) 31465.0i 1.22910i
\(161\) 20996.9i 0.810036i
\(162\) 1705.59i 0.0649897i
\(163\) −6024.65 −0.226755 −0.113377 0.993552i \(-0.536167\pi\)
−0.113377 + 0.993552i \(0.536167\pi\)
\(164\) 15174.6 0.564195
\(165\) 18323.0i 0.673020i
\(166\) −6873.32 −0.249431
\(167\) −38348.4 −1.37504 −0.687519 0.726167i \(-0.741300\pi\)
−0.687519 + 0.726167i \(0.741300\pi\)
\(168\) 13456.7i 0.476782i
\(169\) 14554.8 0.509602
\(170\) 18547.7i 0.641790i
\(171\) 10095.0 0.345236
\(172\) 33705.3i 1.13931i
\(173\) 6642.40i 0.221938i −0.993824 0.110969i \(-0.964604\pi\)
0.993824 0.110969i \(-0.0353955\pi\)
\(174\) 6684.14i 0.220774i
\(175\) −11585.4 −0.378298
\(176\) 2725.04i 0.0879727i
\(177\) 178.387 18086.9i 0.00569399 0.577322i
\(178\) −9071.85 −0.286323
\(179\) 15505.0i 0.483910i 0.970287 + 0.241955i \(0.0777887\pi\)
−0.970287 + 0.241955i \(0.922211\pi\)
\(180\) 8538.64 0.263538
\(181\) −7207.84 −0.220013 −0.110006 0.993931i \(-0.535087\pi\)
−0.110006 + 0.993931i \(0.535087\pi\)
\(182\) −11554.3 −0.348819
\(183\) 8900.68i 0.265779i
\(184\) −31227.8 −0.922372
\(185\) 42989.3i 1.25608i
\(186\) 5480.88 0.158425
\(187\) 30970.3i 0.885649i
\(188\) 10180.2i 0.288031i
\(189\) 5854.38 0.163892
\(190\) 26281.3i 0.728015i
\(191\) 24422.5i 0.669459i 0.942314 + 0.334729i \(0.108645\pi\)
−0.942314 + 0.334729i \(0.891355\pi\)
\(192\) 10801.9 0.293019
\(193\) −42315.7 −1.13602 −0.568011 0.823021i \(-0.692287\pi\)
−0.568011 + 0.823021i \(0.692287\pi\)
\(194\) −5476.11 −0.145502
\(195\) 18475.6i 0.485881i
\(196\) −6944.23 −0.180764
\(197\) −3081.53 −0.0794024 −0.0397012 0.999212i \(-0.512641\pi\)
−0.0397012 + 0.999212i \(0.512641\pi\)
\(198\) −7414.27 −0.189120
\(199\) 71081.9 1.79495 0.897476 0.441064i \(-0.145399\pi\)
0.897476 + 0.441064i \(0.145399\pi\)
\(200\) 17230.4i 0.430761i
\(201\) 26305.8i 0.651116i
\(202\) 42186.7 1.03389
\(203\) 22943.1 0.556749
\(204\) −14432.4 −0.346799
\(205\) 43311.6 1.03062
\(206\) 28725.8 0.676920
\(207\) 13585.8i 0.317062i
\(208\) 2747.74i 0.0635111i
\(209\) 43883.5i 1.00464i
\(210\) 15241.2i 0.345606i
\(211\) 31417.1i 0.705670i 0.935686 + 0.352835i \(0.114782\pi\)
−0.935686 + 0.352835i \(0.885218\pi\)
\(212\) 17495.7 0.389278
\(213\) −31957.9 −0.704400
\(214\) 18285.2i 0.399275i
\(215\) 96202.3i 2.08117i
\(216\) 8706.96i 0.186620i
\(217\) 18812.9i 0.399519i
\(218\) 11015.0 0.231777
\(219\) 21670.9i 0.451845i
\(220\) 37117.8i 0.766897i
\(221\) 31228.3i 0.639387i
\(222\) 17395.3 0.352961
\(223\) −55061.3 −1.10723 −0.553613 0.832774i \(-0.686751\pi\)
−0.553613 + 0.832774i \(0.686751\pi\)
\(224\) 43702.6i 0.870986i
\(225\) 7496.16 0.148072
\(226\) 20728.9 0.405844
\(227\) 23259.5i 0.451386i −0.974198 0.225693i \(-0.927535\pi\)
0.974198 0.225693i \(-0.0724646\pi\)
\(228\) −20450.1 −0.393392
\(229\) 16859.6i 0.321496i 0.986995 + 0.160748i \(0.0513907\pi\)
−0.986995 + 0.160748i \(0.948609\pi\)
\(230\) −35369.1 −0.668603
\(231\) 25449.2i 0.476926i
\(232\) 34122.3i 0.633960i
\(233\) 56400.3i 1.03889i −0.854504 0.519445i \(-0.826139\pi\)
0.854504 0.519445i \(-0.173861\pi\)
\(234\) 7476.04 0.136534
\(235\) 29056.4i 0.526147i
\(236\) −361.368 + 36639.7i −0.00648823 + 0.657851i
\(237\) 31126.1 0.554151
\(238\) 25761.4i 0.454795i
\(239\) 17569.0 0.307575 0.153788 0.988104i \(-0.450853\pi\)
0.153788 + 0.988104i \(0.450853\pi\)
\(240\) −3624.55 −0.0629261
\(241\) 97271.4 1.67475 0.837377 0.546625i \(-0.184088\pi\)
0.837377 + 0.546625i \(0.184088\pi\)
\(242\) 2024.38i 0.0345670i
\(243\) −3788.00 −0.0641500
\(244\) 18030.6i 0.302852i
\(245\) −19820.3 −0.330202
\(246\) 17525.8i 0.289606i
\(247\) 44249.2i 0.725289i
\(248\) −27979.7 −0.454924
\(249\) 15265.1i 0.246208i
\(250\) 24416.8i 0.390669i
\(251\) −41339.8 −0.656177 −0.328089 0.944647i \(-0.606404\pi\)
−0.328089 + 0.944647i \(0.606404\pi\)
\(252\) −11859.5 −0.186753
\(253\) −59057.9 −0.922650
\(254\) 18155.1i 0.281404i
\(255\) −41193.2 −0.633498
\(256\) −61086.7 −0.932109
\(257\) −14776.8 −0.223725 −0.111863 0.993724i \(-0.535682\pi\)
−0.111863 + 0.993724i \(0.535682\pi\)
\(258\) 38927.7 0.584816
\(259\) 59708.9i 0.890102i
\(260\) 37427.1i 0.553655i
\(261\) −14845.0 −0.217921
\(262\) 62166.1 0.905630
\(263\) 46511.4 0.672431 0.336216 0.941785i \(-0.390853\pi\)
0.336216 + 0.941785i \(0.390853\pi\)
\(264\) 37849.5 0.543066
\(265\) 49936.6 0.711094
\(266\) 36502.8i 0.515897i
\(267\) 20147.9i 0.282623i
\(268\) 53289.0i 0.741939i
\(269\) 52167.3i 0.720931i −0.932773 0.360465i \(-0.882618\pi\)
0.932773 0.360465i \(-0.117382\pi\)
\(270\) 9861.64i 0.135276i
\(271\) −118272. −1.61044 −0.805220 0.592977i \(-0.797953\pi\)
−0.805220 + 0.592977i \(0.797953\pi\)
\(272\) 6126.37 0.0828066
\(273\) 25661.3i 0.344312i
\(274\) 14904.5i 0.198526i
\(275\) 32586.1i 0.430891i
\(276\) 27521.4i 0.361288i
\(277\) −116769. −1.52184 −0.760919 0.648847i \(-0.775252\pi\)
−0.760919 + 0.648847i \(0.775252\pi\)
\(278\) 61971.2i 0.801863i
\(279\) 12172.6i 0.156378i
\(280\) 77805.9i 0.992422i
\(281\) 148473. 1.88034 0.940169 0.340710i \(-0.110667\pi\)
0.940169 + 0.340710i \(0.110667\pi\)
\(282\) −11757.5 −0.147849
\(283\) 30655.6i 0.382769i 0.981515 + 0.191385i \(0.0612978\pi\)
−0.981515 + 0.191385i \(0.938702\pi\)
\(284\) 64738.9 0.802655
\(285\) −58369.0 −0.718609
\(286\) 32498.7i 0.397314i
\(287\) −60156.6 −0.730331
\(288\) 28277.1i 0.340919i
\(289\) −13894.4 −0.166359
\(290\) 38647.4i 0.459541i
\(291\) 12162.0i 0.143622i
\(292\) 43900.0i 0.514872i
\(293\) 77404.6 0.901636 0.450818 0.892616i \(-0.351132\pi\)
0.450818 + 0.892616i \(0.351132\pi\)
\(294\) 8020.18i 0.0927875i
\(295\) −1031.42 + 104578.i −0.0118520 + 1.20170i
\(296\) −88802.5 −1.01354
\(297\) 16466.6i 0.186677i
\(298\) 88278.8 0.994086
\(299\) 59550.0 0.666100
\(300\) −15185.4 −0.168726
\(301\) 133618.i 1.47479i
\(302\) −45448.7 −0.498319
\(303\) 93693.6i 1.02053i
\(304\) 8680.80 0.0939318
\(305\) 51463.3i 0.553220i
\(306\) 16668.6i 0.178015i
\(307\) −124048. −1.31617 −0.658085 0.752943i \(-0.728633\pi\)
−0.658085 + 0.752943i \(0.728633\pi\)
\(308\) 51553.9i 0.543451i
\(309\) 63798.0i 0.668174i
\(310\) −31690.2 −0.329762
\(311\) −3890.57 −0.0402247 −0.0201123 0.999798i \(-0.506402\pi\)
−0.0201123 + 0.999798i \(0.506402\pi\)
\(312\) −38164.9 −0.392062
\(313\) 18870.8i 0.192620i −0.995351 0.0963099i \(-0.969296\pi\)
0.995351 0.0963099i \(-0.0307040\pi\)
\(314\) 94855.1 0.962058
\(315\) −33849.7 −0.341141
\(316\) −63053.9 −0.631448
\(317\) −31502.4 −0.313491 −0.156745 0.987639i \(-0.550100\pi\)
−0.156745 + 0.987639i \(0.550100\pi\)
\(318\) 20206.5i 0.199819i
\(319\) 64531.9i 0.634151i
\(320\) −62455.8 −0.609920
\(321\) −40610.2 −0.394117
\(322\) 49125.1 0.473796
\(323\) 98657.8 0.945642
\(324\) 7673.55 0.0730981
\(325\) 32857.6i 0.311078i
\(326\) 14095.4i 0.132631i
\(327\) 24463.4i 0.228782i
\(328\) 89468.3i 0.831614i
\(329\) 40357.2i 0.372846i
\(330\) 42868.9 0.393654
\(331\) 4457.32 0.0406834 0.0203417 0.999793i \(-0.493525\pi\)
0.0203417 + 0.999793i \(0.493525\pi\)
\(332\) 30923.4i 0.280551i
\(333\) 38633.8i 0.348401i
\(334\) 89721.1i 0.804270i
\(335\) 152099.i 1.35530i
\(336\) 5034.22 0.0445917
\(337\) 46555.0i 0.409927i 0.978770 + 0.204964i \(0.0657076\pi\)
−0.978770 + 0.204964i \(0.934292\pi\)
\(338\) 34052.7i 0.298070i
\(339\) 46037.4i 0.400600i
\(340\) 83447.3 0.721863
\(341\) −52915.0 −0.455061
\(342\) 23618.7i 0.201931i
\(343\) 127720. 1.08560
\(344\) −198724. −1.67932
\(345\) 78552.3i 0.659964i
\(346\) −15540.8 −0.129814
\(347\) 173485.i 1.44080i 0.693560 + 0.720399i \(0.256041\pi\)
−0.693560 + 0.720399i \(0.743959\pi\)
\(348\) 30072.3 0.248318
\(349\) 160924.i 1.32120i −0.750737 0.660601i \(-0.770301\pi\)
0.750737 0.660601i \(-0.229699\pi\)
\(350\) 27105.5i 0.221269i
\(351\) 16603.8i 0.134770i
\(352\) −122922. −0.992074
\(353\) 109289.i 0.877055i 0.898718 + 0.438527i \(0.144500\pi\)
−0.898718 + 0.438527i \(0.855500\pi\)
\(354\) −42316.7 417.359i −0.337680 0.00333046i
\(355\) 184779. 1.46621
\(356\) 40814.8i 0.322045i
\(357\) 57214.3 0.448919
\(358\) 36275.9 0.283043
\(359\) 127764. 0.991336 0.495668 0.868512i \(-0.334923\pi\)
0.495668 + 0.868512i \(0.334923\pi\)
\(360\) 50343.2i 0.388451i
\(361\) 9472.92 0.0726891
\(362\) 16863.7i 0.128687i
\(363\) −4496.00 −0.0341203
\(364\) 51983.4i 0.392339i
\(365\) 125300.i 0.940516i
\(366\) −20824.3 −0.155456
\(367\) 131014.i 0.972718i 0.873759 + 0.486359i \(0.161675\pi\)
−0.873759 + 0.486359i \(0.838325\pi\)
\(368\) 11682.5i 0.0862662i
\(369\) 38923.5 0.285864
\(370\) −100579. −0.734690
\(371\) −69358.2 −0.503907
\(372\) 24658.8i 0.178191i
\(373\) 162049. 1.16474 0.582369 0.812924i \(-0.302126\pi\)
0.582369 + 0.812924i \(0.302126\pi\)
\(374\) −72459.0 −0.518023
\(375\) 54228.0 0.385621
\(376\) 60021.6 0.424553
\(377\) 65069.5i 0.457820i
\(378\) 13697.1i 0.0958615i
\(379\) −170314. −1.18569 −0.592847 0.805315i \(-0.701996\pi\)
−0.592847 + 0.805315i \(0.701996\pi\)
\(380\) 118241. 0.818845
\(381\) 40321.1 0.277768
\(382\) 57139.7 0.391572
\(383\) 197908. 1.34916 0.674582 0.738200i \(-0.264324\pi\)
0.674582 + 0.738200i \(0.264324\pi\)
\(384\) 61798.7i 0.419099i
\(385\) 147146.i 0.992722i
\(386\) 99003.0i 0.664468i
\(387\) 86455.6i 0.577259i
\(388\) 24637.3i 0.163655i
\(389\) −130696. −0.863699 −0.431849 0.901946i \(-0.642139\pi\)
−0.431849 + 0.901946i \(0.642139\pi\)
\(390\) −43226.1 −0.284195
\(391\) 132772.i 0.868470i
\(392\) 40942.7i 0.266443i
\(393\) 138066.i 0.893929i
\(394\) 7209.64i 0.0464431i
\(395\) −179970. −1.15347
\(396\) 33357.2i 0.212716i
\(397\) 35127.3i 0.222876i −0.993771 0.111438i \(-0.964454\pi\)
0.993771 0.111438i \(-0.0355457\pi\)
\(398\) 166305.i 1.04988i
\(399\) 81070.2 0.509232
\(400\) 6446.00 0.0402875
\(401\) 177132.i 1.10156i −0.834650 0.550780i \(-0.814330\pi\)
0.834650 0.550780i \(-0.185670\pi\)
\(402\) 61545.7 0.380843
\(403\) 53355.9 0.328528
\(404\) 189800.i 1.16288i
\(405\) 21902.0 0.133528
\(406\) 53678.3i 0.325647i
\(407\) −167943. −1.01385
\(408\) 85092.3i 0.511176i
\(409\) 194928.i 1.16527i 0.812733 + 0.582636i \(0.197979\pi\)
−0.812733 + 0.582636i \(0.802021\pi\)
\(410\) 101333.i 0.602815i
\(411\) 33101.9 0.195961
\(412\) 129239.i 0.761376i
\(413\) 1432.57 145251.i 0.00839878 0.851565i
\(414\) −31785.7 −0.185452
\(415\) 88262.3i 0.512483i
\(416\) 123946. 0.716219
\(417\) −137634. −0.791502
\(418\) −102671. −0.587620
\(419\) 86241.5i 0.491234i −0.969367 0.245617i \(-0.921009\pi\)
0.969367 0.245617i \(-0.0789906\pi\)
\(420\) 68571.2 0.388726
\(421\) 51752.7i 0.291990i 0.989285 + 0.145995i \(0.0466384\pi\)
−0.989285 + 0.145995i \(0.953362\pi\)
\(422\) 73504.5 0.412752
\(423\) 26112.6i 0.145938i
\(424\) 103153.i 0.573789i
\(425\) 73259.2 0.405587
\(426\) 74769.7i 0.412009i
\(427\) 71478.7i 0.392031i
\(428\) 82266.2 0.449091
\(429\) −72177.2 −0.392180
\(430\) −225078. −1.21729
\(431\) 184933.i 0.995545i −0.867308 0.497773i \(-0.834151\pi\)
0.867308 0.497773i \(-0.165849\pi\)
\(432\) −3257.33 −0.0174539
\(433\) −201660. −1.07558 −0.537790 0.843079i \(-0.680741\pi\)
−0.537790 + 0.843079i \(0.680741\pi\)
\(434\) 44015.3 0.233681
\(435\) 85833.1 0.453603
\(436\) 49556.9i 0.260694i
\(437\) 188133.i 0.985149i
\(438\) −50702.0 −0.264288
\(439\) 264954. 1.37480 0.687402 0.726277i \(-0.258751\pi\)
0.687402 + 0.726277i \(0.258751\pi\)
\(440\) −218844. −1.13039
\(441\) −17812.3 −0.0915887
\(442\) 73062.7 0.373982
\(443\) 377029.i 1.92117i −0.277978 0.960587i \(-0.589664\pi\)
0.277978 0.960587i \(-0.410336\pi\)
\(444\) 78262.7i 0.396998i
\(445\) 116494.i 0.588281i
\(446\) 128823.i 0.647625i
\(447\) 196061.i 0.981242i
\(448\) 86746.5 0.432211
\(449\) 108089. 0.536155 0.268078 0.963397i \(-0.413612\pi\)
0.268078 + 0.963397i \(0.413612\pi\)
\(450\) 17538.2i 0.0866086i
\(451\) 169202.i 0.831864i
\(452\) 93260.4i 0.456479i
\(453\) 100938.i 0.491880i
\(454\) −54418.5 −0.264019
\(455\) 148372.i 0.716687i
\(456\) 120572.i 0.579852i
\(457\) 265515.i 1.27132i −0.771968 0.635662i \(-0.780727\pi\)
0.771968 0.635662i \(-0.219273\pi\)
\(458\) 39445.2 0.188046
\(459\) −37019.7 −0.175715
\(460\) 159128.i 0.752021i
\(461\) 216820. 1.02023 0.510114 0.860107i \(-0.329603\pi\)
0.510114 + 0.860107i \(0.329603\pi\)
\(462\) −59541.8 −0.278957
\(463\) 245917.i 1.14716i −0.819148 0.573582i \(-0.805553\pi\)
0.819148 0.573582i \(-0.194447\pi\)
\(464\) −12765.3 −0.0592920
\(465\) 70381.6i 0.325502i
\(466\) −131956. −0.607654
\(467\) 198167.i 0.908651i 0.890836 + 0.454326i \(0.150120\pi\)
−0.890836 + 0.454326i \(0.849880\pi\)
\(468\) 33635.2i 0.153568i
\(469\) 211254.i 0.960414i
\(470\) 67981.3 0.307747
\(471\) 210666.i 0.949628i
\(472\) 216025. + 2130.60i 0.969661 + 0.00956353i
\(473\) −375826. −1.67983
\(474\) 72823.6i 0.324127i
\(475\) 103805. 0.460078
\(476\) −115902. −0.511538
\(477\) 44877.3 0.197238
\(478\) 41105.0i 0.179903i
\(479\) −419986. −1.83048 −0.915238 0.402915i \(-0.867997\pi\)
−0.915238 + 0.402915i \(0.867997\pi\)
\(480\) 163497.i 0.709623i
\(481\) 169342. 0.731939
\(482\) 227579.i 0.979577i
\(483\) 109103.i 0.467674i
\(484\) 9107.80 0.0388797
\(485\) 70320.3i 0.298949i
\(486\) 8862.51i 0.0375218i
\(487\) −336768. −1.41995 −0.709975 0.704227i \(-0.751294\pi\)
−0.709975 + 0.704227i \(0.751294\pi\)
\(488\) 106307. 0.446399
\(489\) 31305.0 0.130917
\(490\) 46372.3i 0.193137i
\(491\) 279399. 1.15894 0.579471 0.814993i \(-0.303259\pi\)
0.579471 + 0.814993i \(0.303259\pi\)
\(492\) −78849.5 −0.325738
\(493\) −145079. −0.596912
\(494\) 103527. 0.424227
\(495\) 95208.9i 0.388568i
\(496\) 10467.4i 0.0425474i
\(497\) −256644. −1.03901
\(498\) 35714.8 0.144009
\(499\) 23800.2 0.0955826 0.0477913 0.998857i \(-0.484782\pi\)
0.0477913 + 0.998857i \(0.484782\pi\)
\(500\) −109853. −0.439410
\(501\) 199264. 0.793878
\(502\) 96719.9i 0.383803i
\(503\) 25529.1i 0.100902i 0.998727 + 0.0504509i \(0.0160659\pi\)
−0.998727 + 0.0504509i \(0.983934\pi\)
\(504\) 69923.0i 0.275270i
\(505\) 541732.i 2.12423i
\(506\) 138174.i 0.539665i
\(507\) −75628.7 −0.294219
\(508\) −81680.7 −0.316513
\(509\) 6537.03i 0.0252316i 0.999920 + 0.0126158i \(0.00401584\pi\)
−0.999920 + 0.0126158i \(0.995984\pi\)
\(510\) 96376.9i 0.370538i
\(511\) 174033.i 0.666483i
\(512\) 47370.3i 0.180703i
\(513\) −52455.3 −0.199322
\(514\) 34572.3i 0.130859i
\(515\) 368877.i 1.39081i
\(516\) 175138.i 0.657780i
\(517\) 113513. 0.424681
\(518\) 139697. 0.520627
\(519\) 34514.9i 0.128136i
\(520\) 220667. 0.816078
\(521\) −307294. −1.13208 −0.566042 0.824376i \(-0.691526\pi\)
−0.566042 + 0.824376i \(0.691526\pi\)
\(522\) 34731.8i 0.127464i
\(523\) −92199.8 −0.337075 −0.168537 0.985695i \(-0.553904\pi\)
−0.168537 + 0.985695i \(0.553904\pi\)
\(524\) 279689.i 1.01862i
\(525\) 60199.4 0.218410
\(526\) 108819.i 0.393310i
\(527\) 118962.i 0.428339i
\(528\) 14159.7i 0.0507910i
\(529\) 26654.1 0.0952472
\(530\) 116833.i 0.415924i
\(531\) −926.926 + 93982.4i −0.00328743 + 0.333317i
\(532\) −164228. −0.580263
\(533\) 170612.i 0.600557i
\(534\) 47138.7 0.165308
\(535\) 234806. 0.820354
\(536\) −314188. −1.09360
\(537\) 80566.2i 0.279386i
\(538\) −122052. −0.421678
\(539\) 77430.6i 0.266523i
\(540\) −44368.1 −0.152154
\(541\) 234603.i 0.801564i 0.916173 + 0.400782i \(0.131262\pi\)
−0.916173 + 0.400782i \(0.868738\pi\)
\(542\) 276713.i 0.941958i
\(543\) 37453.0 0.127024
\(544\) 276350.i 0.933816i
\(545\) 141446.i 0.476210i
\(546\) 60037.9 0.201391
\(547\) −246372. −0.823411 −0.411706 0.911317i \(-0.635067\pi\)
−0.411706 + 0.911317i \(0.635067\pi\)
\(548\) −67056.3 −0.223295
\(549\) 46249.3i 0.153448i
\(550\) −76239.4 −0.252031
\(551\) −205570. −0.677107
\(552\) 162265. 0.532532
\(553\) 249964. 0.817387
\(554\) 273197.i 0.890134i
\(555\) 223379.i 0.725197i
\(556\) 278812. 0.901907
\(557\) 567300. 1.82853 0.914266 0.405115i \(-0.132769\pi\)
0.914266 + 0.405115i \(0.132769\pi\)
\(558\) −28479.5 −0.0914669
\(559\) 378957. 1.21274
\(560\) −29107.6 −0.0928177
\(561\) 160926.i 0.511330i
\(562\) 347373.i 1.09982i
\(563\) 327570.i 1.03344i 0.856153 + 0.516722i \(0.172848\pi\)
−0.856153 + 0.516722i \(0.827152\pi\)
\(564\) 52897.7i 0.166295i
\(565\) 266186.i 0.833850i
\(566\) 71722.8 0.223885
\(567\) −30420.2 −0.0946230
\(568\) 381696.i 1.18310i
\(569\) 379301.i 1.17154i 0.810476 + 0.585772i \(0.199209\pi\)
−0.810476 + 0.585772i \(0.800791\pi\)
\(570\) 136562.i 0.420320i
\(571\) 580504.i 1.78046i −0.455509 0.890231i \(-0.650543\pi\)
0.455509 0.890231i \(-0.349457\pi\)
\(572\) 146213. 0.446884
\(573\) 126903.i 0.386512i
\(574\) 140744.i 0.427176i
\(575\) 139700.i 0.422532i
\(576\) −56128.1 −0.169175
\(577\) −34030.7 −0.102216 −0.0511080 0.998693i \(-0.516275\pi\)
−0.0511080 + 0.998693i \(0.516275\pi\)
\(578\) 32507.8i 0.0973044i
\(579\) 219879. 0.655882
\(580\) −173877. −0.516875
\(581\) 122590.i 0.363163i
\(582\) 28454.7 0.0840055
\(583\) 195083.i 0.573962i
\(584\) 258831. 0.758912
\(585\) 96002.1i 0.280523i
\(586\) 181098.i 0.527374i
\(587\) 360445.i 1.04607i 0.852310 + 0.523037i \(0.175201\pi\)
−0.852310 + 0.523037i \(0.824799\pi\)
\(588\) 36083.3 0.104364
\(589\) 168564.i 0.485886i
\(590\) 244673. + 2413.15i 0.702882 + 0.00693235i
\(591\) 16012.1 0.0458430
\(592\) 33221.5i 0.0947930i
\(593\) 203460. 0.578589 0.289294 0.957240i \(-0.406579\pi\)
0.289294 + 0.957240i \(0.406579\pi\)
\(594\) 38525.7 0.109189
\(595\) −330810. −0.934426
\(596\) 397172.i 1.11811i
\(597\) −369352. −1.03632
\(598\) 139325.i 0.389607i
\(599\) 68798.6 0.191746 0.0958729 0.995394i \(-0.469436\pi\)
0.0958729 + 0.995394i \(0.469436\pi\)
\(600\) 89531.9i 0.248700i
\(601\) 549707.i 1.52189i −0.648818 0.760943i \(-0.724737\pi\)
0.648818 0.760943i \(-0.275263\pi\)
\(602\) 312616. 0.862618
\(603\) 136689.i 0.375922i
\(604\) 204476.i 0.560491i
\(605\) 25995.7 0.0710215
\(606\) −219208. −0.596914
\(607\) −350392. −0.950991 −0.475495 0.879718i \(-0.657731\pi\)
−0.475495 + 0.879718i \(0.657731\pi\)
\(608\) 391576.i 1.05928i
\(609\) −119216. −0.321439
\(610\) 120405. 0.323583
\(611\) −114458. −0.306595
\(612\) 74992.9 0.200224
\(613\) 450003.i 1.19755i 0.800917 + 0.598776i \(0.204346\pi\)
−0.800917 + 0.598776i \(0.795654\pi\)
\(614\) 290226.i 0.769838i
\(615\) −225054. −0.595026
\(616\) 303958. 0.801037
\(617\) 165810. 0.435552 0.217776 0.975999i \(-0.430120\pi\)
0.217776 + 0.975999i \(0.430120\pi\)
\(618\) −149264. −0.390820
\(619\) −286451. −0.747599 −0.373799 0.927510i \(-0.621945\pi\)
−0.373799 + 0.927510i \(0.621945\pi\)
\(620\) 142576.i 0.370905i
\(621\) 70593.8i 0.183056i
\(622\) 9102.49i 0.0235277i
\(623\) 161802.i 0.416877i
\(624\) 14277.7i 0.0366682i
\(625\) −487066. −1.24689
\(626\) −44150.6 −0.112665
\(627\) 228026.i 0.580027i
\(628\) 426758.i 1.08209i
\(629\) 377565.i 0.954312i
\(630\) 79195.8i 0.199536i
\(631\) 94171.7 0.236517 0.118258 0.992983i \(-0.462269\pi\)
0.118258 + 0.992983i \(0.462269\pi\)
\(632\) 371761.i 0.930743i
\(633\) 163248.i 0.407419i
\(634\) 73703.9i 0.183363i
\(635\) −233135. −0.578175
\(636\) −90910.3 −0.224750
\(637\) 78075.7i 0.192414i
\(638\) 150981. 0.370920
\(639\) 166058. 0.406686
\(640\) 357317.i 0.872356i
\(641\) 739487. 1.79976 0.899880 0.436137i \(-0.143654\pi\)
0.899880 + 0.436137i \(0.143654\pi\)
\(642\) 95012.8i 0.230522i
\(643\) 446727. 1.08049 0.540244 0.841508i \(-0.318332\pi\)
0.540244 + 0.841508i \(0.318332\pi\)
\(644\) 221016.i 0.532909i
\(645\) 499882.i 1.20157i
\(646\) 230823.i 0.553113i
\(647\) −370357. −0.884732 −0.442366 0.896835i \(-0.645861\pi\)
−0.442366 + 0.896835i \(0.645861\pi\)
\(648\) 45242.7i 0.107745i
\(649\) 408546. + 4029.38i 0.969954 + 0.00956642i
\(650\) 76874.6 0.181952
\(651\) 97754.8i 0.230662i
\(652\) −63416.2 −0.149178
\(653\) −339613. −0.796449 −0.398224 0.917288i \(-0.630373\pi\)
−0.398224 + 0.917288i \(0.630373\pi\)
\(654\) −57235.4 −0.133816
\(655\) 798293.i 1.86071i
\(656\) 33470.6 0.0777779
\(657\) 112606.i 0.260873i
\(658\) −94421.0 −0.218081
\(659\) 387109.i 0.891378i 0.895188 + 0.445689i \(0.147041\pi\)
−0.895188 + 0.445689i \(0.852959\pi\)
\(660\) 192870.i 0.442768i
\(661\) −367793. −0.841784 −0.420892 0.907111i \(-0.638283\pi\)
−0.420892 + 0.907111i \(0.638283\pi\)
\(662\) 10428.5i 0.0237961i
\(663\) 162267.i 0.369150i
\(664\) −182322. −0.413527
\(665\) −468744. −1.05997
\(666\) −90388.9 −0.203782
\(667\) 276654.i 0.621850i
\(668\) −403660. −0.904614
\(669\) 286107. 0.639257
\(670\) −355854. −0.792725
\(671\) 201048. 0.446533
\(672\) 227085.i 0.502864i
\(673\) 356274.i 0.786600i 0.919410 + 0.393300i \(0.128667\pi\)
−0.919410 + 0.393300i \(0.871333\pi\)
\(674\) 108922. 0.239770
\(675\) −38951.2 −0.0854896
\(676\) 153205. 0.335259
\(677\) 427232. 0.932152 0.466076 0.884745i \(-0.345667\pi\)
0.466076 + 0.884745i \(0.345667\pi\)
\(678\) −107710. −0.234314
\(679\) 97669.7i 0.211846i
\(680\) 492000.i 1.06401i
\(681\) 120860.i 0.260608i
\(682\) 123802.i 0.266169i
\(683\) 816072.i 1.74939i −0.484673 0.874695i \(-0.661061\pi\)
0.484673 0.874695i \(-0.338939\pi\)
\(684\) 106262. 0.227125
\(685\) −191393. −0.407893
\(686\) 298817.i 0.634975i
\(687\) 87605.0i 0.185616i
\(688\) 74343.8i 0.157061i
\(689\) 196709.i 0.414367i
\(690\) 183783. 0.386018
\(691\) 101566.i 0.212712i −0.994328 0.106356i \(-0.966082\pi\)
0.994328 0.106356i \(-0.0339183\pi\)
\(692\) 69918.7i 0.146010i
\(693\) 132238.i 0.275353i
\(694\) 405891. 0.842733
\(695\) 795790. 1.64751
\(696\) 177304.i 0.366017i
\(697\) 380396. 0.783015
\(698\) −376502. −0.772782
\(699\) 293064.i 0.599803i
\(700\) −121949. −0.248876
\(701\) 265473.i 0.540236i 0.962827 + 0.270118i \(0.0870628\pi\)
−0.962827 + 0.270118i \(0.912937\pi\)
\(702\) −38846.7 −0.0788278
\(703\) 534993.i 1.08252i
\(704\) 243991.i 0.492299i
\(705\) 150982.i 0.303771i
\(706\) 255696. 0.512996
\(707\) 752425.i 1.50530i
\(708\) 1877.72 190385.i 0.00374598 0.379811i
\(709\) −380605. −0.757150 −0.378575 0.925571i \(-0.623586\pi\)
−0.378575 + 0.925571i \(0.623586\pi\)
\(710\) 432315.i 0.857597i
\(711\) −161736. −0.319939
\(712\) −240641. −0.474689
\(713\) −226852. −0.446234
\(714\) 133860.i 0.262576i
\(715\) 417325. 0.816324
\(716\) 163207.i 0.318356i
\(717\) −91291.2 −0.177579
\(718\) 298921.i 0.579840i
\(719\) 356832.i 0.690249i −0.938557 0.345124i \(-0.887837\pi\)
0.938557 0.345124i \(-0.112163\pi\)
\(720\) 18833.7 0.0363304
\(721\) 512342.i 0.985575i
\(722\) 22163.1i 0.0425164i
\(723\) −505437. −0.966920
\(724\) −75870.6 −0.144743
\(725\) −152648. −0.290413
\(726\) 10519.0i 0.0199572i
\(727\) 84925.0 0.160682 0.0803409 0.996767i \(-0.474399\pi\)
0.0803409 + 0.996767i \(0.474399\pi\)
\(728\) −306491. −0.578302
\(729\) 19683.0 0.0370370
\(730\) 293156. 0.550115
\(731\) 844922.i 1.58118i
\(732\) 93689.8i 0.174852i
\(733\) −359849. −0.669750 −0.334875 0.942263i \(-0.608694\pi\)
−0.334875 + 0.942263i \(0.608694\pi\)
\(734\) 306525. 0.568950
\(735\) 102990. 0.190642
\(736\) −526978. −0.972830
\(737\) −594191. −1.09393
\(738\) 91066.6i 0.167204i
\(739\) 813633.i 1.48984i 0.667154 + 0.744920i \(0.267512\pi\)
−0.667154 + 0.744920i \(0.732488\pi\)
\(740\) 452511.i 0.826353i
\(741\) 229925.i 0.418746i
\(742\) 162273.i 0.294739i
\(743\) −407788. −0.738680 −0.369340 0.929294i \(-0.620416\pi\)
−0.369340 + 0.929294i \(0.620416\pi\)
\(744\) 145387. 0.262651
\(745\) 1.13361e6i 2.04246i
\(746\) 379135.i 0.681265i
\(747\) 79320.0i 0.142148i
\(748\) 325997.i 0.582654i
\(749\) −326128. −0.581332
\(750\) 126873.i 0.225553i
\(751\) 726139.i 1.28748i −0.765245 0.643739i \(-0.777382\pi\)
0.765245 0.643739i \(-0.222618\pi\)
\(752\) 22454.4i 0.0397069i
\(753\) 214808. 0.378844
\(754\) −152239. −0.267782
\(755\) 583620.i 1.02385i
\(756\) 61624.0 0.107822
\(757\) 226073. 0.394508 0.197254 0.980352i \(-0.436798\pi\)
0.197254 + 0.980352i \(0.436798\pi\)
\(758\) 398472.i 0.693521i
\(759\) 306874. 0.532692
\(760\) 697142.i 1.20696i
\(761\) −32895.1 −0.0568018 −0.0284009 0.999597i \(-0.509042\pi\)
−0.0284009 + 0.999597i \(0.509042\pi\)
\(762\) 94336.5i 0.162469i
\(763\) 196458.i 0.337459i
\(764\) 257075.i 0.440426i
\(765\) 214046. 0.365750
\(766\) 463031.i 0.789137i
\(767\) −411949. 4062.96i −0.700250 0.00690639i
\(768\) 317416. 0.538153
\(769\) 954320.i 1.61377i 0.590710 + 0.806884i \(0.298848\pi\)
−0.590710 + 0.806884i \(0.701152\pi\)
\(770\) 344268. 0.580650
\(771\) 76782.7 0.129168
\(772\) −445420. −0.747370
\(773\) 430986.i 0.721280i −0.932705 0.360640i \(-0.882558\pi\)
0.932705 0.360640i \(-0.117442\pi\)
\(774\) −202274. −0.337643
\(775\) 125169.i 0.208398i
\(776\) −145260. −0.241225
\(777\) 310257.i 0.513900i
\(778\) 305780.i 0.505184i
\(779\) 539004. 0.888213
\(780\) 194477.i 0.319653i
\(781\) 721862.i 1.18346i
\(782\) −310639. −0.507974
\(783\) 77136.9 0.125817
\(784\) −15316.9 −0.0249195
\(785\) 1.21806e6i 1.97665i
\(786\) −323024. −0.522866
\(787\) 449468. 0.725687 0.362844 0.931850i \(-0.381806\pi\)
0.362844 + 0.931850i \(0.381806\pi\)
\(788\) −32436.6 −0.0522375
\(789\) −241680. −0.388228