Properties

Label 177.5.b.a.119.5
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.5
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.74

$q$-expansion

\(f(q)\) \(=\) \(q-7.37175i q^{2} +(8.47141 - 3.03895i) q^{3} -38.3427 q^{4} -40.5786i q^{5} +(-22.4024 - 62.4491i) q^{6} +39.1148 q^{7} +164.705i q^{8} +(62.5296 - 51.4883i) q^{9} +O(q^{10})\) \(q-7.37175i q^{2} +(8.47141 - 3.03895i) q^{3} -38.3427 q^{4} -40.5786i q^{5} +(-22.4024 - 62.4491i) q^{6} +39.1148 q^{7} +164.705i q^{8} +(62.5296 - 51.4883i) q^{9} -299.136 q^{10} -101.974i q^{11} +(-324.817 + 116.522i) q^{12} -227.096 q^{13} -288.344i q^{14} +(-123.316 - 343.758i) q^{15} +600.682 q^{16} +150.341i q^{17} +(-379.559 - 460.953i) q^{18} +458.086 q^{19} +1555.90i q^{20} +(331.357 - 118.868i) q^{21} -751.730 q^{22} -193.289i q^{23} +(500.530 + 1395.28i) q^{24} -1021.62 q^{25} +1674.10i q^{26} +(373.243 - 626.203i) q^{27} -1499.77 q^{28} +1038.06i q^{29} +(-2534.10 + 909.057i) q^{30} +1462.33 q^{31} -1792.79i q^{32} +(-309.895 - 863.867i) q^{33} +1108.28 q^{34} -1587.22i q^{35} +(-2397.56 + 1974.20i) q^{36} -693.059 q^{37} -3376.90i q^{38} +(-1923.82 + 690.133i) q^{39} +6683.51 q^{40} -119.484i q^{41} +(-876.263 - 2442.68i) q^{42} +1666.91 q^{43} +3909.98i q^{44} +(-2089.33 - 2537.36i) q^{45} -1424.88 q^{46} +2047.53i q^{47} +(5088.62 - 1825.44i) q^{48} -871.036 q^{49} +7531.16i q^{50} +(456.880 + 1273.60i) q^{51} +8707.48 q^{52} +0.219985i q^{53} +(-4616.21 - 2751.46i) q^{54} -4137.98 q^{55} +6442.40i q^{56} +(3880.63 - 1392.10i) q^{57} +7652.31 q^{58} -453.188i q^{59} +(4728.28 + 13180.6i) q^{60} +7367.02 q^{61} -10779.9i q^{62} +(2445.83 - 2013.95i) q^{63} -3605.13 q^{64} +9215.24i q^{65} +(-6368.21 + 2284.47i) q^{66} -2787.93 q^{67} -5764.50i q^{68} +(-587.394 - 1637.43i) q^{69} -11700.6 q^{70} -8947.65i q^{71} +(8480.39 + 10298.9i) q^{72} -8302.29 q^{73} +5109.06i q^{74} +(-8654.60 + 3104.66i) q^{75} -17564.3 q^{76} -3988.70i q^{77} +(5087.49 + 14181.9i) q^{78} -1825.77 q^{79} -24374.8i q^{80} +(1258.90 - 6439.09i) q^{81} -880.804 q^{82} -10928.3i q^{83} +(-12705.1 + 4557.71i) q^{84} +6100.64 q^{85} -12288.1i q^{86} +(3154.60 + 8793.81i) q^{87} +16795.7 q^{88} +7604.36i q^{89} +(-18704.8 + 15402.0i) q^{90} -8882.80 q^{91} +7411.21i q^{92} +(12388.0 - 4443.95i) q^{93} +15093.9 q^{94} -18588.5i q^{95} +(-5448.21 - 15187.5i) q^{96} -10747.3 q^{97} +6421.06i q^{98} +(-5250.49 - 6376.42i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.37175i 1.84294i −0.388452 0.921469i \(-0.626990\pi\)
0.388452 0.921469i \(-0.373010\pi\)
\(3\) 8.47141 3.03895i 0.941268 0.337661i
\(4\) −38.3427 −2.39642
\(5\) 40.5786i 1.62314i −0.584252 0.811572i \(-0.698612\pi\)
0.584252 0.811572i \(-0.301388\pi\)
\(6\) −22.4024 62.4491i −0.622288 1.73470i
\(7\) 39.1148 0.798260 0.399130 0.916894i \(-0.369312\pi\)
0.399130 + 0.916894i \(0.369312\pi\)
\(8\) 164.705i 2.57352i
\(9\) 62.5296 51.4883i 0.771970 0.635659i
\(10\) −299.136 −2.99136
\(11\) 101.974i 0.842764i −0.906883 0.421382i \(-0.861545\pi\)
0.906883 0.421382i \(-0.138455\pi\)
\(12\) −324.817 + 116.522i −2.25567 + 0.809178i
\(13\) −227.096 −1.34376 −0.671882 0.740659i \(-0.734514\pi\)
−0.671882 + 0.740659i \(0.734514\pi\)
\(14\) 288.344i 1.47114i
\(15\) −123.316 343.758i −0.548072 1.52781i
\(16\) 600.682 2.34641
\(17\) 150.341i 0.520212i 0.965580 + 0.260106i \(0.0837576\pi\)
−0.965580 + 0.260106i \(0.916242\pi\)
\(18\) −379.559 460.953i −1.17148 1.42269i
\(19\) 458.086 1.26894 0.634468 0.772949i \(-0.281219\pi\)
0.634468 + 0.772949i \(0.281219\pi\)
\(20\) 1555.90i 3.88974i
\(21\) 331.357 118.868i 0.751377 0.269541i
\(22\) −751.730 −1.55316
\(23\) 193.289i 0.365385i −0.983170 0.182692i \(-0.941519\pi\)
0.983170 0.182692i \(-0.0584812\pi\)
\(24\) 500.530 + 1395.28i 0.868976 + 2.42237i
\(25\) −1021.62 −1.63460
\(26\) 1674.10i 2.47647i
\(27\) 373.243 626.203i 0.511994 0.858989i
\(28\) −1499.77 −1.91297
\(29\) 1038.06i 1.23431i 0.786840 + 0.617157i \(0.211716\pi\)
−0.786840 + 0.617157i \(0.788284\pi\)
\(30\) −2534.10 + 909.057i −2.81567 + 1.01006i
\(31\) 1462.33 1.52168 0.760838 0.648942i \(-0.224788\pi\)
0.760838 + 0.648942i \(0.224788\pi\)
\(32\) 1792.79i 1.75078i
\(33\) −309.895 863.867i −0.284568 0.793266i
\(34\) 1108.28 0.958719
\(35\) 1587.22i 1.29569i
\(36\) −2397.56 + 1974.20i −1.84997 + 1.52331i
\(37\) −693.059 −0.506252 −0.253126 0.967433i \(-0.581459\pi\)
−0.253126 + 0.967433i \(0.581459\pi\)
\(38\) 3376.90i 2.33857i
\(39\) −1923.82 + 690.133i −1.26484 + 0.453736i
\(40\) 6683.51 4.17719
\(41\) 119.484i 0.0710789i −0.999368 0.0355395i \(-0.988685\pi\)
0.999368 0.0355395i \(-0.0113149\pi\)
\(42\) −876.263 2442.68i −0.496748 1.38474i
\(43\) 1666.91 0.901520 0.450760 0.892645i \(-0.351153\pi\)
0.450760 + 0.892645i \(0.351153\pi\)
\(44\) 3909.98i 2.01962i
\(45\) −2089.33 2537.36i −1.03177 1.25302i
\(46\) −1424.88 −0.673382
\(47\) 2047.53i 0.926905i 0.886122 + 0.463452i \(0.153389\pi\)
−0.886122 + 0.463452i \(0.846611\pi\)
\(48\) 5088.62 1825.44i 2.20860 0.792292i
\(49\) −871.036 −0.362780
\(50\) 7531.16i 3.01246i
\(51\) 456.880 + 1273.60i 0.175655 + 0.489659i
\(52\) 8707.48 3.22022
\(53\) 0.219985i 7.83144e-5i 1.00000 3.91572e-5i \(1.24641e-5\pi\)
−1.00000 3.91572e-5i \(0.999988\pi\)
\(54\) −4616.21 2751.46i −1.58306 0.943573i
\(55\) −4137.98 −1.36793
\(56\) 6442.40i 2.05434i
\(57\) 3880.63 1392.10i 1.19441 0.428470i
\(58\) 7652.31 2.27476
\(59\) 453.188i 0.130189i
\(60\) 4728.28 + 13180.6i 1.31341 + 3.66129i
\(61\) 7367.02 1.97985 0.989925 0.141594i \(-0.0452229\pi\)
0.989925 + 0.141594i \(0.0452229\pi\)
\(62\) 10779.9i 2.80435i
\(63\) 2445.83 2013.95i 0.616233 0.507421i
\(64\) −3605.13 −0.880158
\(65\) 9215.24i 2.18112i
\(66\) −6368.21 + 2284.47i −1.46194 + 0.524442i
\(67\) −2787.93 −0.621059 −0.310530 0.950564i \(-0.600506\pi\)
−0.310530 + 0.950564i \(0.600506\pi\)
\(68\) 5764.50i 1.24665i
\(69\) −587.394 1637.43i −0.123376 0.343925i
\(70\) −11700.6 −2.38788
\(71\) 8947.65i 1.77498i −0.460831 0.887488i \(-0.652449\pi\)
0.460831 0.887488i \(-0.347551\pi\)
\(72\) 8480.39 + 10298.9i 1.63588 + 1.98668i
\(73\) −8302.29 −1.55794 −0.778972 0.627058i \(-0.784259\pi\)
−0.778972 + 0.627058i \(0.784259\pi\)
\(74\) 5109.06i 0.932991i
\(75\) −8654.60 + 3104.66i −1.53860 + 0.551940i
\(76\) −17564.3 −3.04090
\(77\) 3988.70i 0.672745i
\(78\) 5087.49 + 14181.9i 0.836208 + 2.33102i
\(79\) −1825.77 −0.292544 −0.146272 0.989244i \(-0.546728\pi\)
−0.146272 + 0.989244i \(0.546728\pi\)
\(80\) 24374.8i 3.80857i
\(81\) 1258.90 6439.09i 0.191876 0.981419i
\(82\) −880.804 −0.130994
\(83\) 10928.3i 1.58634i −0.608998 0.793172i \(-0.708428\pi\)
0.608998 0.793172i \(-0.291572\pi\)
\(84\) −12705.1 + 4557.71i −1.80061 + 0.645934i
\(85\) 6100.64 0.844380
\(86\) 12288.1i 1.66145i
\(87\) 3154.60 + 8793.81i 0.416779 + 1.16182i
\(88\) 16795.7 2.16887
\(89\) 7604.36i 0.960025i 0.877262 + 0.480013i \(0.159368\pi\)
−0.877262 + 0.480013i \(0.840632\pi\)
\(90\) −18704.8 + 15402.0i −2.30924 + 1.90148i
\(91\) −8882.80 −1.07267
\(92\) 7411.21i 0.875616i
\(93\) 12388.0 4443.95i 1.43230 0.513810i
\(94\) 15093.9 1.70823
\(95\) 18588.5i 2.05967i
\(96\) −5448.21 15187.5i −0.591168 1.64795i
\(97\) −10747.3 −1.14224 −0.571119 0.820867i \(-0.693490\pi\)
−0.571119 + 0.820867i \(0.693490\pi\)
\(98\) 6421.06i 0.668582i
\(99\) −5250.49 6376.42i −0.535710 0.650589i
\(100\) 39171.9 3.91719
\(101\) 9016.80i 0.883913i −0.897037 0.441956i \(-0.854285\pi\)
0.897037 0.441956i \(-0.145715\pi\)
\(102\) 9388.69 3368.00i 0.902412 0.323722i
\(103\) 11441.8 1.07850 0.539250 0.842146i \(-0.318708\pi\)
0.539250 + 0.842146i \(0.318708\pi\)
\(104\) 37403.9i 3.45820i
\(105\) −4823.49 13446.0i −0.437504 1.21959i
\(106\) 1.62168 0.000144329
\(107\) 5080.56i 0.443755i −0.975074 0.221878i \(-0.928781\pi\)
0.975074 0.221878i \(-0.0712186\pi\)
\(108\) −14311.2 + 24010.3i −1.22695 + 2.05850i
\(109\) −18603.1 −1.56579 −0.782893 0.622157i \(-0.786257\pi\)
−0.782893 + 0.622157i \(0.786257\pi\)
\(110\) 30504.2i 2.52101i
\(111\) −5871.19 + 2106.17i −0.476519 + 0.170942i
\(112\) 23495.5 1.87305
\(113\) 20964.8i 1.64185i 0.571038 + 0.820924i \(0.306541\pi\)
−0.571038 + 0.820924i \(0.693459\pi\)
\(114\) −10262.2 28607.1i −0.789644 2.20122i
\(115\) −7843.38 −0.593072
\(116\) 39802.0i 2.95794i
\(117\) −14200.2 + 11692.8i −1.03735 + 0.854175i
\(118\) −3340.79 −0.239930
\(119\) 5880.57i 0.415265i
\(120\) 56618.7 20310.8i 3.93186 1.41047i
\(121\) 4242.22 0.289749
\(122\) 54307.8i 3.64874i
\(123\) −363.105 1012.20i −0.0240006 0.0669043i
\(124\) −56069.8 −3.64658
\(125\) 16094.5i 1.03005i
\(126\) −14846.4 18030.1i −0.935146 1.13568i
\(127\) −29996.7 −1.85980 −0.929900 0.367812i \(-0.880107\pi\)
−0.929900 + 0.367812i \(0.880107\pi\)
\(128\) 2108.59i 0.128698i
\(129\) 14121.1 5065.66i 0.848572 0.304408i
\(130\) 67932.5 4.01967
\(131\) 10098.3i 0.588445i 0.955737 + 0.294223i \(0.0950607\pi\)
−0.955737 + 0.294223i \(0.904939\pi\)
\(132\) 11882.2 + 33123.0i 0.681945 + 1.90100i
\(133\) 17917.9 1.01294
\(134\) 20552.0i 1.14457i
\(135\) −25410.5 15145.7i −1.39426 0.831040i
\(136\) −24762.0 −1.33878
\(137\) 4692.61i 0.250019i −0.992156 0.125010i \(-0.960104\pi\)
0.992156 0.125010i \(-0.0398961\pi\)
\(138\) −12070.7 + 4330.12i −0.633832 + 0.227375i
\(139\) 11174.9 0.578382 0.289191 0.957271i \(-0.406614\pi\)
0.289191 + 0.957271i \(0.406614\pi\)
\(140\) 60858.5i 3.10502i
\(141\) 6222.35 + 17345.5i 0.312979 + 0.872466i
\(142\) −65959.9 −3.27117
\(143\) 23158.0i 1.13247i
\(144\) 37560.4 30928.1i 1.81136 1.49152i
\(145\) 42123.0 2.00347
\(146\) 61202.4i 2.87120i
\(147\) −7378.90 + 2647.03i −0.341474 + 0.122497i
\(148\) 26573.8 1.21319
\(149\) 13264.6i 0.597476i −0.954335 0.298738i \(-0.903434\pi\)
0.954335 0.298738i \(-0.0965657\pi\)
\(150\) 22886.8 + 63799.5i 1.01719 + 2.83554i
\(151\) 24846.5 1.08971 0.544856 0.838529i \(-0.316584\pi\)
0.544856 + 0.838529i \(0.316584\pi\)
\(152\) 75449.1i 3.26563i
\(153\) 7740.83 + 9400.78i 0.330677 + 0.401588i
\(154\) −29403.7 −1.23983
\(155\) 59339.4i 2.46990i
\(156\) 73764.6 26461.6i 3.03109 1.08734i
\(157\) 16104.2 0.653342 0.326671 0.945138i \(-0.394073\pi\)
0.326671 + 0.945138i \(0.394073\pi\)
\(158\) 13459.1i 0.539141i
\(159\) 0.668524 + 1.86359i 2.64437e−5 + 7.37149e-5i
\(160\) −72749.1 −2.84176
\(161\) 7560.44i 0.291672i
\(162\) −47467.4 9280.30i −1.80869 0.353616i
\(163\) 16936.7 0.637462 0.318731 0.947845i \(-0.396743\pi\)
0.318731 + 0.947845i \(0.396743\pi\)
\(164\) 4581.33i 0.170335i
\(165\) −35054.5 + 12575.1i −1.28759 + 0.461896i
\(166\) −80560.9 −2.92353
\(167\) 38560.4i 1.38264i −0.722549 0.691320i \(-0.757030\pi\)
0.722549 0.691320i \(-0.242970\pi\)
\(168\) 19578.1 + 54576.2i 0.693669 + 1.93368i
\(169\) 23011.6 0.805700
\(170\) 44972.4i 1.55614i
\(171\) 28643.9 23586.1i 0.979581 0.806610i
\(172\) −63913.9 −2.16042
\(173\) 10278.6i 0.343431i −0.985147 0.171716i \(-0.945069\pi\)
0.985147 0.171716i \(-0.0549310\pi\)
\(174\) 64825.8 23255.0i 2.14116 0.768099i
\(175\) −39960.6 −1.30484
\(176\) 61254.1i 1.97747i
\(177\) −1377.21 3839.14i −0.0439597 0.122543i
\(178\) 56057.5 1.76927
\(179\) 26311.2i 0.821173i 0.911822 + 0.410587i \(0.134676\pi\)
−0.911822 + 0.410587i \(0.865324\pi\)
\(180\) 80110.5 + 97289.5i 2.47255 + 3.00276i
\(181\) 7323.15 0.223533 0.111766 0.993735i \(-0.464349\pi\)
0.111766 + 0.993735i \(0.464349\pi\)
\(182\) 65481.8i 1.97687i
\(183\) 62409.1 22388.0i 1.86357 0.668518i
\(184\) 31835.6 0.940324
\(185\) 28123.4i 0.821720i
\(186\) −32759.7 91321.3i −0.946921 2.63965i
\(187\) 15331.0 0.438416
\(188\) 78508.0i 2.22125i
\(189\) 14599.3 24493.8i 0.408704 0.685697i
\(190\) −137030. −3.79584
\(191\) 22139.5i 0.606878i 0.952851 + 0.303439i \(0.0981349\pi\)
−0.952851 + 0.303439i \(0.901865\pi\)
\(192\) −30540.5 + 10955.8i −0.828465 + 0.297195i
\(193\) 20014.2 0.537307 0.268654 0.963237i \(-0.413421\pi\)
0.268654 + 0.963237i \(0.413421\pi\)
\(194\) 79226.5i 2.10507i
\(195\) 28004.6 + 78066.1i 0.736480 + 2.05302i
\(196\) 33397.9 0.869375
\(197\) 5398.39i 0.139102i −0.997578 0.0695508i \(-0.977843\pi\)
0.997578 0.0695508i \(-0.0221566\pi\)
\(198\) −47005.4 + 38705.3i −1.19899 + 0.987280i
\(199\) 31903.3 0.805619 0.402810 0.915284i \(-0.368034\pi\)
0.402810 + 0.915284i \(0.368034\pi\)
\(200\) 168267.i 4.20667i
\(201\) −23617.7 + 8472.39i −0.584583 + 0.209707i
\(202\) −66469.6 −1.62900
\(203\) 40603.4i 0.985304i
\(204\) −17518.0 48833.4i −0.420944 1.17343i
\(205\) −4848.48 −0.115371
\(206\) 84346.1i 1.98761i
\(207\) −9952.11 12086.3i −0.232260 0.282066i
\(208\) −136412. −3.15302
\(209\) 46713.0i 1.06941i
\(210\) −99120.7 + 35557.6i −2.24763 + 0.806294i
\(211\) 58686.4 1.31817 0.659087 0.752067i \(-0.270943\pi\)
0.659087 + 0.752067i \(0.270943\pi\)
\(212\) 8.43484i 0.000187674i
\(213\) −27191.5 75799.2i −0.599340 1.67073i
\(214\) −37452.6 −0.817814
\(215\) 67641.0i 1.46330i
\(216\) 103139. + 61475.1i 2.21062 + 1.31762i
\(217\) 57198.7 1.21469
\(218\) 137137.i 2.88564i
\(219\) −70332.1 + 25230.2i −1.46644 + 0.526057i
\(220\) 158661. 3.27813
\(221\) 34141.9i 0.699042i
\(222\) 15526.2 + 43280.9i 0.315035 + 0.878195i
\(223\) 59945.6 1.20545 0.602723 0.797950i \(-0.294082\pi\)
0.602723 + 0.797950i \(0.294082\pi\)
\(224\) 70124.7i 1.39757i
\(225\) −63881.7 + 52601.7i −1.26186 + 1.03905i
\(226\) 154547. 3.02582
\(227\) 57698.6i 1.11973i 0.828584 + 0.559865i \(0.189147\pi\)
−0.828584 + 0.559865i \(0.810853\pi\)
\(228\) −148794. + 53376.9i −2.86231 + 1.02679i
\(229\) −38112.5 −0.726770 −0.363385 0.931639i \(-0.618379\pi\)
−0.363385 + 0.931639i \(0.618379\pi\)
\(230\) 57819.5i 1.09300i
\(231\) −12121.5 33789.9i −0.227160 0.633233i
\(232\) −170973. −3.17653
\(233\) 101881.i 1.87665i 0.345755 + 0.938325i \(0.387623\pi\)
−0.345755 + 0.938325i \(0.612377\pi\)
\(234\) 86196.4 + 104680.i 1.57419 + 1.91176i
\(235\) 83086.0 1.50450
\(236\) 17376.5i 0.311987i
\(237\) −15466.8 + 5548.42i −0.275363 + 0.0987808i
\(238\) 43350.1 0.765307
\(239\) 31516.2i 0.551745i −0.961194 0.275873i \(-0.911033\pi\)
0.961194 0.275873i \(-0.0889668\pi\)
\(240\) −74073.8 206489.i −1.28600 3.58488i
\(241\) −3021.93 −0.0520295 −0.0260148 0.999662i \(-0.508282\pi\)
−0.0260148 + 0.999662i \(0.508282\pi\)
\(242\) 31272.6i 0.533990i
\(243\) −8903.41 58373.9i −0.150780 0.988567i
\(244\) −282472. −4.74455
\(245\) 35345.4i 0.588845i
\(246\) −7461.65 + 2676.72i −0.123301 + 0.0442316i
\(247\) −104029. −1.70515
\(248\) 240853.i 3.91606i
\(249\) −33210.6 92578.3i −0.535646 1.49317i
\(250\) 118644. 1.89831
\(251\) 3350.92i 0.0531883i 0.999646 + 0.0265941i \(0.00846618\pi\)
−0.999646 + 0.0265941i \(0.991534\pi\)
\(252\) −93779.8 + 77220.5i −1.47675 + 1.21599i
\(253\) −19710.5 −0.307933
\(254\) 221128.i 3.42750i
\(255\) 51681.1 18539.5i 0.794788 0.285114i
\(256\) −73226.1 −1.11734
\(257\) 96436.2i 1.46007i 0.683409 + 0.730035i \(0.260496\pi\)
−0.683409 + 0.730035i \(0.739504\pi\)
\(258\) −37342.8 104097.i −0.561005 1.56387i
\(259\) −27108.8 −0.404121
\(260\) 353338.i 5.22689i
\(261\) 53447.9 + 64909.3i 0.784602 + 0.952854i
\(262\) 74442.2 1.08447
\(263\) 113800.i 1.64524i −0.568591 0.822620i \(-0.692511\pi\)
0.568591 0.822620i \(-0.307489\pi\)
\(264\) 142283. 51041.3i 2.04148 0.732342i
\(265\) 8.92670 0.000127116
\(266\) 132086.i 1.86679i
\(267\) 23109.3 + 64419.7i 0.324163 + 0.903641i
\(268\) 106897. 1.48832
\(269\) 35924.4i 0.496460i 0.968701 + 0.248230i \(0.0798489\pi\)
−0.968701 + 0.248230i \(0.920151\pi\)
\(270\) −111650. + 187320.i −1.53156 + 2.56954i
\(271\) 57390.3 0.781448 0.390724 0.920508i \(-0.372225\pi\)
0.390724 + 0.920508i \(0.372225\pi\)
\(272\) 90307.3i 1.22063i
\(273\) −75249.9 + 26994.4i −1.00967 + 0.362200i
\(274\) −34592.7 −0.460770
\(275\) 104180.i 1.37758i
\(276\) 22522.3 + 62783.4i 0.295661 + 0.824189i
\(277\) 9503.14 0.123853 0.0619266 0.998081i \(-0.480276\pi\)
0.0619266 + 0.998081i \(0.480276\pi\)
\(278\) 82378.7i 1.06592i
\(279\) 91438.9 75293.0i 1.17469 0.967267i
\(280\) 261424. 3.33449
\(281\) 123020.i 1.55798i −0.627037 0.778989i \(-0.715733\pi\)
0.627037 0.778989i \(-0.284267\pi\)
\(282\) 127867. 45869.6i 1.60790 0.576802i
\(283\) 76953.7 0.960852 0.480426 0.877035i \(-0.340482\pi\)
0.480426 + 0.877035i \(0.340482\pi\)
\(284\) 343078.i 4.25359i
\(285\) −56489.4 157471.i −0.695469 1.93870i
\(286\) 170715. 2.08708
\(287\) 4673.58i 0.0567395i
\(288\) −92308.0 112103.i −1.11290 1.35155i
\(289\) 60918.5 0.729379
\(290\) 310520.i 3.69227i
\(291\) −91044.9 + 32660.5i −1.07515 + 0.385689i
\(292\) 318332. 3.73349
\(293\) 14637.7i 0.170505i 0.996359 + 0.0852525i \(0.0271697\pi\)
−0.996359 + 0.0852525i \(0.972830\pi\)
\(294\) 19513.3 + 54395.4i 0.225754 + 0.629315i
\(295\) −18389.7 −0.211315
\(296\) 114150.i 1.30285i
\(297\) −63856.7 38061.3i −0.723925 0.431490i
\(298\) −97783.1 −1.10111
\(299\) 43895.1i 0.490991i
\(300\) 331841. 119041.i 3.68712 1.32268i
\(301\) 65200.8 0.719648
\(302\) 183163.i 2.00827i
\(303\) −27401.6 76385.0i −0.298463 0.831999i
\(304\) 275164. 2.97745
\(305\) 298943.i 3.21358i
\(306\) 69300.3 57063.5i 0.740103 0.609418i
\(307\) 59016.0 0.626171 0.313086 0.949725i \(-0.398637\pi\)
0.313086 + 0.949725i \(0.398637\pi\)
\(308\) 152938.i 1.61218i
\(309\) 96928.2 34771.0i 1.01516 0.364167i
\(310\) −437435. −4.55187
\(311\) 105910.i 1.09501i 0.836803 + 0.547505i \(0.184422\pi\)
−0.836803 + 0.547505i \(0.815578\pi\)
\(312\) −113668. 316864.i −1.16770 3.25509i
\(313\) −150512. −1.53632 −0.768161 0.640257i \(-0.778828\pi\)
−0.768161 + 0.640257i \(0.778828\pi\)
\(314\) 118716.i 1.20407i
\(315\) −81723.5 99248.4i −0.823618 1.00024i
\(316\) 70005.0 0.701059
\(317\) 140514.i 1.39830i 0.714974 + 0.699151i \(0.246439\pi\)
−0.714974 + 0.699151i \(0.753561\pi\)
\(318\) 13.7379 4.92819i 0.000135852 4.87341e-5i
\(319\) 105855. 1.04023
\(320\) 146291.i 1.42862i
\(321\) −15439.5 43039.5i −0.149839 0.417693i
\(322\) −55733.7 −0.537534
\(323\) 68869.3i 0.660116i
\(324\) −48269.7 + 246892.i −0.459816 + 2.35189i
\(325\) 232007. 2.19651
\(326\) 124853.i 1.17480i
\(327\) −157594. + 56533.8i −1.47382 + 0.528704i
\(328\) 19679.6 0.182923
\(329\) 80088.7i 0.739911i
\(330\) 92700.6 + 258413.i 0.851245 + 2.37294i
\(331\) 39780.2 0.363087 0.181544 0.983383i \(-0.441891\pi\)
0.181544 + 0.983383i \(0.441891\pi\)
\(332\) 419022.i 3.80155i
\(333\) −43336.7 + 35684.5i −0.390812 + 0.321803i
\(334\) −284258. −2.54812
\(335\) 113131.i 1.00807i
\(336\) 199040. 71401.6i 1.76304 0.632455i
\(337\) 56088.1 0.493868 0.246934 0.969032i \(-0.420577\pi\)
0.246934 + 0.969032i \(0.420577\pi\)
\(338\) 169636.i 1.48485i
\(339\) 63710.8 + 177601.i 0.554388 + 1.54542i
\(340\) −233915. −2.02349
\(341\) 149120.i 1.28241i
\(342\) −173871. 211156.i −1.48653 1.80531i
\(343\) −127985. −1.08785
\(344\) 274549.i 2.32008i
\(345\) −66444.5 + 23835.6i −0.558240 + 0.200257i
\(346\) −75771.0 −0.632923
\(347\) 163511.i 1.35797i 0.734154 + 0.678983i \(0.237579\pi\)
−0.734154 + 0.678983i \(0.762421\pi\)
\(348\) −120956. 337179.i −0.998779 2.78421i
\(349\) −42912.4 −0.352316 −0.176158 0.984362i \(-0.556367\pi\)
−0.176158 + 0.984362i \(0.556367\pi\)
\(350\) 294579.i 2.40473i
\(351\) −84762.1 + 142208.i −0.687998 + 1.15428i
\(352\) −182819. −1.47549
\(353\) 14104.9i 0.113193i 0.998397 + 0.0565967i \(0.0180249\pi\)
−0.998397 + 0.0565967i \(0.981975\pi\)
\(354\) −28301.2 + 10152.5i −0.225838 + 0.0810150i
\(355\) −363083. −2.88104
\(356\) 291572.i 2.30062i
\(357\) 17870.7 + 49816.7i 0.140219 + 0.390875i
\(358\) 193960. 1.51337
\(359\) 133490.i 1.03576i −0.855452 0.517882i \(-0.826721\pi\)
0.855452 0.517882i \(-0.173279\pi\)
\(360\) 417917. 344123.i 3.22467 2.65527i
\(361\) 79521.6 0.610198
\(362\) 53984.5i 0.411957i
\(363\) 35937.6 12891.9i 0.272732 0.0978370i
\(364\) 340591. 2.57058
\(365\) 336895.i 2.52877i
\(366\) −165039. 460064.i −1.23204 3.43444i
\(367\) 106223. 0.788652 0.394326 0.918971i \(-0.370978\pi\)
0.394326 + 0.918971i \(0.370978\pi\)
\(368\) 116105.i 0.857343i
\(369\) −6152.02 7471.27i −0.0451819 0.0548708i
\(370\) 207319. 1.51438
\(371\) 8.60467i 6.25153e-5i
\(372\) −474990. + 170393.i −3.43241 + 1.23131i
\(373\) 37218.8 0.267513 0.133756 0.991014i \(-0.457296\pi\)
0.133756 + 0.991014i \(0.457296\pi\)
\(374\) 113016.i 0.807974i
\(375\) 48910.2 + 136343.i 0.347806 + 0.969548i
\(376\) −337239. −2.38541
\(377\) 235739.i 1.65863i
\(378\) −180562. 107623.i −1.26370 0.753217i
\(379\) 7019.81 0.0488705 0.0244353 0.999701i \(-0.492221\pi\)
0.0244353 + 0.999701i \(0.492221\pi\)
\(380\) 712733.i 4.93583i
\(381\) −254114. + 91158.5i −1.75057 + 0.627982i
\(382\) 163207. 1.11844
\(383\) 27986.2i 0.190786i 0.995440 + 0.0953928i \(0.0304107\pi\)
−0.995440 + 0.0953928i \(0.969589\pi\)
\(384\) −6407.90 17862.7i −0.0434563 0.121139i
\(385\) −161856. −1.09196
\(386\) 147539.i 0.990224i
\(387\) 104231. 85826.5i 0.695947 0.573059i
\(388\) 412081. 2.73728
\(389\) 71584.3i 0.473062i −0.971624 0.236531i \(-0.923989\pi\)
0.971624 0.236531i \(-0.0760105\pi\)
\(390\) 575484. 206443.i 3.78359 1.35729i
\(391\) 29059.3 0.190078
\(392\) 143464.i 0.933622i
\(393\) 30688.2 + 85546.9i 0.198695 + 0.553885i
\(394\) −39795.6 −0.256356
\(395\) 74087.2i 0.474842i
\(396\) 201318. + 244489.i 1.28379 + 1.55908i
\(397\) −84214.2 −0.534324 −0.267162 0.963652i \(-0.586086\pi\)
−0.267162 + 0.963652i \(0.586086\pi\)
\(398\) 235183.i 1.48471i
\(399\) 151790. 54451.6i 0.953449 0.342031i
\(400\) −613671. −3.83544
\(401\) 72922.3i 0.453494i −0.973954 0.226747i \(-0.927191\pi\)
0.973954 0.226747i \(-0.0728091\pi\)
\(402\) 62456.3 + 174104.i 0.386478 + 1.07735i
\(403\) −332089. −2.04477
\(404\) 345729.i 2.11823i
\(405\) −261289. 51084.4i −1.59299 0.311443i
\(406\) 299318. 1.81585
\(407\) 70674.3i 0.426651i
\(408\) −209769. + 75250.4i −1.26015 + 0.452052i
\(409\) −172315. −1.03009 −0.515046 0.857163i \(-0.672225\pi\)
−0.515046 + 0.857163i \(0.672225\pi\)
\(410\) 35741.8i 0.212622i
\(411\) −14260.6 39753.0i −0.0844217 0.235335i
\(412\) −438710. −2.58454
\(413\) 17726.3i 0.103925i
\(414\) −89096.9 + 73364.5i −0.519831 + 0.428041i
\(415\) −443456. −2.57487
\(416\) 407136.i 2.35263i
\(417\) 94667.2 33960.0i 0.544412 0.195297i
\(418\) −344357. −1.97086
\(419\) 19352.7i 0.110233i 0.998480 + 0.0551166i \(0.0175531\pi\)
−0.998480 + 0.0551166i \(0.982447\pi\)
\(420\) 184946. + 515557.i 1.04844 + 2.92266i
\(421\) −34510.7 −0.194710 −0.0973552 0.995250i \(-0.531038\pi\)
−0.0973552 + 0.995250i \(0.531038\pi\)
\(422\) 432622.i 2.42931i
\(423\) 105424. + 128031.i 0.589195 + 0.715543i
\(424\) −36.2327 −0.000201544
\(425\) 153592.i 0.850338i
\(426\) −558773. + 200449.i −3.07905 + 1.10455i
\(427\) 288159. 1.58044
\(428\) 194802.i 1.06342i
\(429\) 70375.9 + 196181.i 0.382392 + 1.06596i
\(430\) −498632. −2.69677
\(431\) 27612.2i 0.148644i 0.997234 + 0.0743219i \(0.0236792\pi\)
−0.997234 + 0.0743219i \(0.976321\pi\)
\(432\) 224200. 376149.i 1.20135 2.01554i
\(433\) 245311. 1.30840 0.654200 0.756322i \(-0.273005\pi\)
0.654200 + 0.756322i \(0.273005\pi\)
\(434\) 421655.i 2.23861i
\(435\) 356841. 128009.i 1.88580 0.676493i
\(436\) 713293. 3.75228
\(437\) 88542.8i 0.463650i
\(438\) 185991. + 518471.i 0.969491 + 2.70256i
\(439\) 69211.8 0.359130 0.179565 0.983746i \(-0.442531\pi\)
0.179565 + 0.983746i \(0.442531\pi\)
\(440\) 681546.i 3.52038i
\(441\) −54465.5 + 44848.2i −0.280056 + 0.230605i
\(442\) −251686. −1.28829
\(443\) 76359.2i 0.389094i 0.980893 + 0.194547i \(0.0623236\pi\)
−0.980893 + 0.194547i \(0.937676\pi\)
\(444\) 225117. 80756.3i 1.14194 0.409648i
\(445\) 308574. 1.55826
\(446\) 441904.i 2.22156i
\(447\) −40310.3 112370.i −0.201744 0.562385i
\(448\) −141014. −0.702595
\(449\) 327103.i 1.62253i 0.584681 + 0.811263i \(0.301220\pi\)
−0.584681 + 0.811263i \(0.698780\pi\)
\(450\) 387767. + 470920.i 1.91490 + 2.32553i
\(451\) −12184.3 −0.0599027
\(452\) 803846.i 3.93456i
\(453\) 210485. 75507.3i 1.02571 0.367953i
\(454\) 425340. 2.06359
\(455\) 360452.i 1.74110i
\(456\) 229286. + 639160.i 1.10267 + 3.07383i
\(457\) −304096. −1.45606 −0.728029 0.685546i \(-0.759564\pi\)
−0.728029 + 0.685546i \(0.759564\pi\)
\(458\) 280956.i 1.33939i
\(459\) 94144.2 + 56113.9i 0.446857 + 0.266345i
\(460\) 300737. 1.42125
\(461\) 130871.i 0.615802i −0.951418 0.307901i \(-0.900373\pi\)
0.951418 0.307901i \(-0.0996265\pi\)
\(462\) −249091. + 89356.4i −1.16701 + 0.418641i
\(463\) −362078. −1.68904 −0.844520 0.535524i \(-0.820114\pi\)
−0.844520 + 0.535524i \(0.820114\pi\)
\(464\) 623542.i 2.89621i
\(465\) −180329. 502688.i −0.833989 2.32484i
\(466\) 751045. 3.45855
\(467\) 935.101i 0.00428771i 0.999998 + 0.00214385i \(0.000682410\pi\)
−0.999998 + 0.00214385i \(0.999318\pi\)
\(468\) 544475. 448334.i 2.48592 2.04696i
\(469\) −109049. −0.495767
\(470\) 612490.i 2.77270i
\(471\) 136426. 48939.9i 0.614970 0.220608i
\(472\) 74642.3 0.335043
\(473\) 169982.i 0.759769i
\(474\) 40901.6 + 114018.i 0.182047 + 0.507476i
\(475\) −467991. −2.07420
\(476\) 225477.i 0.995149i
\(477\) 11.3267 + 13.7556i 4.97813e−5 + 6.04564e-5i
\(478\) −232330. −1.01683
\(479\) 3931.82i 0.0171365i 0.999963 + 0.00856825i \(0.00272739\pi\)
−0.999963 + 0.00856825i \(0.997273\pi\)
\(480\) −616287. + 221081.i −2.67486 + 0.959552i
\(481\) 157391. 0.680283
\(482\) 22276.9i 0.0958872i
\(483\) −22975.8 64047.6i −0.0984863 0.274542i
\(484\) −162658. −0.694361
\(485\) 436111.i 1.85402i
\(486\) −430318. + 65633.7i −1.82187 + 0.277878i
\(487\) −74782.1 −0.315312 −0.157656 0.987494i \(-0.550394\pi\)
−0.157656 + 0.987494i \(0.550394\pi\)
\(488\) 1.21339e6i 5.09518i
\(489\) 143478. 51469.8i 0.600023 0.215246i
\(490\) 260558. 1.08521
\(491\) 274270.i 1.13767i 0.822453 + 0.568833i \(0.192605\pi\)
−0.822453 + 0.568833i \(0.807395\pi\)
\(492\) 13922.4 + 38810.3i 0.0575155 + 0.160331i
\(493\) −156063. −0.642105
\(494\) 766879.i 3.14248i
\(495\) −258746. + 213058.i −1.05600 + 0.869535i
\(496\) 878395. 3.57048
\(497\) 349985.i 1.41689i
\(498\) −682464. + 244820.i −2.75183 + 0.987163i
\(499\) −15103.7 −0.0606573 −0.0303287 0.999540i \(-0.509655\pi\)
−0.0303287 + 0.999540i \(0.509655\pi\)
\(500\) 617105.i 2.46842i
\(501\) −117183. 326661.i −0.466863 1.30143i
\(502\) 24702.1 0.0980227
\(503\) 100739.i 0.398164i 0.979983 + 0.199082i \(0.0637961\pi\)
−0.979983 + 0.199082i \(0.936204\pi\)
\(504\) 331709. + 402841.i 1.30586 + 1.58589i
\(505\) −365889. −1.43472
\(506\) 145301.i 0.567502i
\(507\) 194941. 69931.0i 0.758379 0.272053i
\(508\) 1.15016e6 4.45686
\(509\) 239942.i 0.926125i −0.886326 0.463063i \(-0.846750\pi\)
0.886326 0.463063i \(-0.153250\pi\)
\(510\) −136669. 380980.i −0.525448 1.46474i
\(511\) −324742. −1.24365
\(512\) 506067.i 1.93049i
\(513\) 170978. 286855.i 0.649687 1.09000i
\(514\) 710904. 2.69082
\(515\) 464293.i 1.75056i
\(516\) −541441. + 194231.i −2.03354 + 0.729490i
\(517\) 208796. 0.781162
\(518\) 199840.i 0.744770i
\(519\) −31236.0 87073.9i −0.115963 0.323261i
\(520\) −1.51780e6 −5.61316
\(521\) 194196.i 0.715425i 0.933832 + 0.357712i \(0.116443\pi\)
−0.933832 + 0.357712i \(0.883557\pi\)
\(522\) 478496. 394005.i 1.75605 1.44597i
\(523\) 407345. 1.48922 0.744610 0.667499i \(-0.232635\pi\)
0.744610 + 0.667499i \(0.232635\pi\)
\(524\) 387197.i 1.41016i
\(525\) −338522. + 121438.i −1.22820 + 0.440592i
\(526\) −838903. −3.03208
\(527\) 219849.i 0.791595i
\(528\) −186148. 518909.i −0.667715 1.86133i
\(529\) 242481. 0.866494
\(530\) 65.8054i 0.000234266i
\(531\) −23333.9 28337.6i −0.0827557 0.100502i
\(532\) −687022. −2.42743
\(533\) 27134.3i 0.0955133i
\(534\) 474886. 170356.i 1.66535 0.597412i
\(535\) −206162. −0.720279
\(536\) 459187.i 1.59831i
\(537\) 79958.4 + 222893.i 0.277278 + 0.772944i
\(538\) 264826. 0.914946
\(539\) 88823.4i 0.305738i
\(540\) 974306. + 580728.i 3.34124 + 1.99152i
\(541\) −197440. −0.674591 −0.337296 0.941399i \(-0.609512\pi\)
−0.337296 + 0.941399i \(0.609512\pi\)
\(542\) 423067.i 1.44016i
\(543\) 62037.4 22254.7i 0.210404 0.0754782i
\(544\) 269531. 0.910775
\(545\) 754888.i 2.54150i
\(546\) 198996. + 554723.i 0.667512 + 1.86076i
\(547\) 162871. 0.544337 0.272169 0.962250i \(-0.412259\pi\)
0.272169 + 0.962250i \(0.412259\pi\)
\(548\) 179927.i 0.599151i
\(549\) 460657. 379316.i 1.52838 1.25851i
\(550\) 767986. 2.53880
\(551\) 475520.i 1.56626i
\(552\) 269693. 96746.8i 0.885097 0.317511i
\(553\) −71414.5 −0.233527
\(554\) 70054.8i 0.228254i
\(555\) 85465.5 + 238245.i 0.277463 + 0.773459i
\(556\) −428477. −1.38605
\(557\) 162633.i 0.524201i −0.965041 0.262100i \(-0.915585\pi\)
0.965041 0.262100i \(-0.0844151\pi\)
\(558\) −555041. 674065.i −1.78261 2.16488i
\(559\) −378549. −1.21143
\(560\) 953415.i 3.04023i
\(561\) 129875. 46590.0i 0.412667 0.148036i
\(562\) −906870. −2.87126
\(563\) 361668.i 1.14102i −0.821291 0.570510i \(-0.806745\pi\)
0.821291 0.570510i \(-0.193255\pi\)
\(564\) −238582. 665074.i −0.750031 2.09079i
\(565\) 850721. 2.66496
\(566\) 567283.i 1.77079i
\(567\) 49241.6 251863.i 0.153167 0.783428i
\(568\) 1.47372e6 4.56793
\(569\) 136555.i 0.421776i 0.977510 + 0.210888i \(0.0676356\pi\)
−0.977510 + 0.210888i \(0.932364\pi\)
\(570\) −1.16084e6 + 416426.i −3.57290 + 1.28171i
\(571\) 17778.1 0.0545272 0.0272636 0.999628i \(-0.491321\pi\)
0.0272636 + 0.999628i \(0.491321\pi\)
\(572\) 887940.i 2.71389i
\(573\) 67280.8 + 187553.i 0.204919 + 0.571235i
\(574\) −34452.4 −0.104567
\(575\) 197468.i 0.597258i
\(576\) −225427. + 185622.i −0.679456 + 0.559480i
\(577\) −108734. −0.326597 −0.163298 0.986577i \(-0.552213\pi\)
−0.163298 + 0.986577i \(0.552213\pi\)
\(578\) 449076.i 1.34420i
\(579\) 169548. 60822.0i 0.505750 0.181428i
\(580\) −1.61511e6 −4.80116
\(581\) 427459.i 1.26632i
\(582\) 240765. + 671161.i 0.710801 + 1.98144i
\(583\) 22.4329 6.60006e−5
\(584\) 1.36743e6i 4.00940i
\(585\) 474478. + 576225.i 1.38645 + 1.68376i
\(586\) 107905. 0.314230
\(587\) 586908.i 1.70331i 0.524102 + 0.851655i \(0.324401\pi\)
−0.524102 + 0.851655i \(0.675599\pi\)
\(588\) 282927. 101494.i 0.818314 0.293554i
\(589\) 669873. 1.93091
\(590\) 135565.i 0.389441i
\(591\) −16405.4 45732.0i −0.0469691 0.130932i
\(592\) −416308. −1.18788
\(593\) 137926.i 0.392227i 0.980581 + 0.196113i \(0.0628321\pi\)
−0.980581 + 0.196113i \(0.937168\pi\)
\(594\) −280578. + 470736.i −0.795209 + 1.33415i
\(595\) 238625. 0.674035
\(596\) 508600.i 1.43180i
\(597\) 270266. 96952.6i 0.758304 0.272026i
\(598\) 323584. 0.904865
\(599\) 37284.7i 0.103915i 0.998649 + 0.0519574i \(0.0165460\pi\)
−0.998649 + 0.0519574i \(0.983454\pi\)
\(600\) −511354. 1.42546e6i −1.42043 3.95960i
\(601\) 152155. 0.421248 0.210624 0.977567i \(-0.432450\pi\)
0.210624 + 0.977567i \(0.432450\pi\)
\(602\) 480644.i 1.32627i
\(603\) −174328. + 143546.i −0.479439 + 0.394782i
\(604\) −952684. −2.61141
\(605\) 172143.i 0.470305i
\(606\) −563091. + 201998.i −1.53332 + 0.550048i
\(607\) 97390.8 0.264326 0.132163 0.991228i \(-0.457808\pi\)
0.132163 + 0.991228i \(0.457808\pi\)
\(608\) 821253.i 2.22162i
\(609\) 123392. + 343968.i 0.332699 + 0.927435i
\(610\) −2.20374e6 −5.92243
\(611\) 464986.i 1.24554i
\(612\) −296805. 360452.i −0.792442 0.962375i
\(613\) 177806. 0.473180 0.236590 0.971610i \(-0.423970\pi\)
0.236590 + 0.971610i \(0.423970\pi\)
\(614\) 435051.i 1.15399i
\(615\) −41073.5 + 14734.3i −0.108595 + 0.0389564i
\(616\) 656960. 1.73132
\(617\) 16269.5i 0.0427370i −0.999772 0.0213685i \(-0.993198\pi\)
0.999772 0.0213685i \(-0.00680232\pi\)
\(618\) −256324. 714531.i −0.671138 1.87087i
\(619\) −34352.4 −0.0896552 −0.0448276 0.998995i \(-0.514274\pi\)
−0.0448276 + 0.998995i \(0.514274\pi\)
\(620\) 2.27523e6i 5.91892i
\(621\) −121038. 72143.7i −0.313862 0.187075i
\(622\) 780745. 2.01803
\(623\) 297443.i 0.766350i
\(624\) −1.15561e6 + 414550.i −2.96784 + 1.06465i
\(625\) 14575.7 0.0373138
\(626\) 1.10954e6i 2.83135i
\(627\) −141958. 395725.i −0.361099 1.00660i
\(628\) −617480. −1.56568
\(629\) 104195.i 0.263359i
\(630\) −731635. + 602445.i −1.84337 + 1.51788i
\(631\) −726363. −1.82429 −0.912147 0.409864i \(-0.865576\pi\)
−0.912147 + 0.409864i \(0.865576\pi\)
\(632\) 300714.i 0.752868i
\(633\) 497157. 178345.i 1.24075 0.445096i
\(634\) 1.03583e6 2.57698
\(635\) 1.21723e6i 3.01872i
\(636\) −25.6330 71.4550i −6.33703e−5 0.000176652i
\(637\) 197809. 0.487491
\(638\) 780339.i 1.91709i
\(639\) −460700. 559493.i −1.12828 1.37023i
\(640\) −85563.7 −0.208896
\(641\) 368854.i 0.897714i −0.893604 0.448857i \(-0.851831\pi\)
0.893604 0.448857i \(-0.148169\pi\)
\(642\) −317276. + 113817.i −0.769782 + 0.276144i
\(643\) 248032. 0.599910 0.299955 0.953953i \(-0.403028\pi\)
0.299955 + 0.953953i \(0.403028\pi\)
\(644\) 289888.i 0.698969i
\(645\) −205557. 573014.i −0.494098 1.37736i
\(646\) 507687. 1.21655
\(647\) 491048.i 1.17305i 0.809932 + 0.586524i \(0.199504\pi\)
−0.809932 + 0.586524i \(0.800496\pi\)
\(648\) 1.06055e6 + 207347.i 2.52570 + 0.493797i
\(649\) −46213.5 −0.109718
\(650\) 1.71030e6i 4.04804i
\(651\) 484554. 173824.i 1.14335 0.410155i
\(652\) −649401. −1.52763
\(653\) 699337.i 1.64006i −0.572319 0.820031i \(-0.693956\pi\)
0.572319 0.820031i \(-0.306044\pi\)
\(654\) 416753. + 1.16175e6i 0.974369 + 2.71616i
\(655\) 409775. 0.955132
\(656\) 71771.7i 0.166780i
\(657\) −519139. + 427471.i −1.20269 + 0.990321i
\(658\) 590394. 1.36361
\(659\) 321977.i 0.741403i 0.928752 + 0.370702i \(0.120883\pi\)
−0.928752 + 0.370702i \(0.879117\pi\)
\(660\) 1.34409e6 482164.i 3.08560 1.10690i
\(661\) 197653. 0.452376 0.226188 0.974084i \(-0.427374\pi\)
0.226188 + 0.974084i \(0.427374\pi\)
\(662\) 293250.i 0.669147i
\(663\) −103756. 289230.i −0.236039 0.657986i
\(664\) 1.79995e6 4.08248
\(665\) 727084.i 1.64415i
\(666\) 263057. + 319467.i 0.593064 + 0.720241i
\(667\) 200645. 0.451000
\(668\) 1.47851e6i 3.31339i
\(669\) 507824. 182172.i 1.13465 0.407032i
\(670\) 833970. 1.85781
\(671\) 751248.i 1.66855i
\(672\) −213105. 594055.i −0.471906 1.31549i
\(673\) 430587. 0.950673 0.475337 0.879804i \(-0.342326\pi\)
0.475337 + 0.879804i \(0.342326\pi\)
\(674\) 413468.i 0.910168i
\(675\) −381314. + 639744.i −0.836904 + 1.40410i
\(676\) −882327. −1.93080
\(677\) 74792.4i 0.163185i −0.996666 0.0815925i \(-0.973999\pi\)
0.996666 0.0815925i \(-0.0260006\pi\)
\(678\) 1.30923e6 469660.i 2.84811 1.02170i
\(679\) −420379. −0.911803
\(680\) 1.00481e6i 2.17303i
\(681\) 175343. + 488789.i 0.378089 + 1.05397i
\(682\) −1.09928e6 −2.36341
\(683\) 424167.i 0.909275i 0.890677 + 0.454637i \(0.150231\pi\)
−0.890677 + 0.454637i \(0.849769\pi\)
\(684\) −1.09829e6 + 904355.i −2.34749 + 1.93298i
\(685\) −190420. −0.405817
\(686\) 943473.i 2.00485i
\(687\) −322867. + 115822.i −0.684085 + 0.245402i
\(688\) 1.00128e6 2.11534
\(689\) 49.9578i 0.000105236i
\(690\) 175710. + 489813.i 0.369062 + 1.02880i
\(691\) 450906. 0.944344 0.472172 0.881506i \(-0.343470\pi\)
0.472172 + 0.881506i \(0.343470\pi\)
\(692\) 394108.i 0.823006i
\(693\) −205372. 249412.i −0.427636 0.519339i
\(694\) 1.20537e6 2.50265
\(695\) 453462.i 0.938797i
\(696\) −1.44839e6 + 519579.i −2.98996 + 1.07259i
\(697\) 17963.3 0.0369761
\(698\) 316340.i 0.649296i
\(699\) 309612. + 863079.i 0.633671 + 1.76643i
\(700\) 1.53220e6 3.12693
\(701\) 183180.i 0.372770i 0.982477 + 0.186385i \(0.0596772\pi\)
−0.982477 + 0.186385i \(0.940323\pi\)
\(702\) 1.04832e6 + 624845.i 2.12726 + 1.26794i
\(703\) −317481. −0.642401
\(704\) 367631.i 0.741765i
\(705\) 703856. 252494.i 1.41614 0.508011i
\(706\) 103978. 0.208609
\(707\) 352690.i 0.705593i
\(708\) 52806.1 + 147203.i 0.105346 + 0.293664i
\(709\) −419548. −0.834622 −0.417311 0.908764i \(-0.637027\pi\)
−0.417311 + 0.908764i \(0.637027\pi\)
\(710\) 2.67656e6i 5.30958i
\(711\) −114165. + 94005.9i −0.225836 + 0.185958i
\(712\) −1.25248e6 −2.47064
\(713\) 282652.i 0.555997i
\(714\) 367236. 131739.i 0.720359 0.258414i
\(715\) 939719. 1.83817
\(716\) 1.00884e6i 1.96788i
\(717\) −95776.2 266987.i −0.186303 0.519340i
\(718\) −984057. −1.90885
\(719\) 388924.i 0.752327i 0.926553 + 0.376164i \(0.122757\pi\)
−0.926553 + 0.376164i \(0.877243\pi\)
\(720\) −1.25502e6 1.52415e6i −2.42095 2.94010i
\(721\) 447543. 0.860924
\(722\) 586214.i 1.12456i
\(723\) −25600.0 + 9183.47i −0.0489737 + 0.0175683i
\(724\) −280790. −0.535678
\(725\) 1.06050e6i 2.01761i
\(726\) −95035.8 264923.i −0.180308 0.502628i
\(727\) 142364. 0.269358 0.134679 0.990889i \(-0.457000\pi\)
0.134679 + 0.990889i \(0.457000\pi\)
\(728\) 1.46304e6i 2.76054i
\(729\) −252820. 467452.i −0.475725 0.879594i
\(730\) 2.48351e6 4.66037
\(731\) 250606.i 0.468982i
\(732\) −2.39293e6 + 858417.i −4.46589 + 1.60205i
\(733\) 576062. 1.07216 0.536082 0.844166i \(-0.319904\pi\)
0.536082 + 0.844166i \(0.319904\pi\)
\(734\) 783048.i 1.45344i
\(735\) 107413. + 299426.i 0.198830 + 0.554261i
\(736\) −346527. −0.639707
\(737\) 284298.i 0.523406i
\(738\) −55076.3 + 45351.2i −0.101124 + 0.0832675i
\(739\) −341810. −0.625887 −0.312944 0.949772i \(-0.601315\pi\)
−0.312944 + 0.949772i \(0.601315\pi\)
\(740\) 1.07833e6i 1.96919i
\(741\) −881276. + 316140.i −1.60500 + 0.575762i
\(742\) 63.4315 0.000115212
\(743\) 197408.i 0.357591i −0.983886 0.178795i \(-0.942780\pi\)
0.983886 0.178795i \(-0.0572200\pi\)
\(744\) 731941. + 2.04037e6i 1.32230 + 3.68606i
\(745\) −538258. −0.969790
\(746\) 274368.i 0.493009i
\(747\) −562681. 683344.i −1.00837 1.22461i
\(748\) −587831. −1.05063
\(749\) 198725.i 0.354232i
\(750\) 1.00508e6 360554.i 1.78682 0.640985i
\(751\) −297608. −0.527673 −0.263836 0.964567i \(-0.584988\pi\)
−0.263836 + 0.964567i \(0.584988\pi\)
\(752\) 1.22992e6i 2.17490i
\(753\) 10183.3 + 28387.0i 0.0179596 + 0.0500644i
\(754\) −1.73781e6 −3.05674
\(755\) 1.00824e6i 1.76876i
\(756\) −559778. + 939159.i −0.979427 + 1.64322i
\(757\) 507520. 0.885649 0.442824 0.896608i \(-0.353977\pi\)
0.442824 + 0.896608i \(0.353977\pi\)
\(758\) 51748.3i 0.0900654i
\(759\) −166976. + 59899.1i −0.289847 + 0.103977i
\(760\) 3.06162e6 5.30059
\(761\) 291086.i 0.502635i −0.967905 0.251317i \(-0.919136\pi\)
0.967905 0.251317i \(-0.0808637\pi\)
\(762\) 671998. + 1.87327e6i 1.15733 + 3.22619i
\(763\) −727655. −1.24990
\(764\) 848890.i 1.45433i
\(765\) 381471. 314112.i 0.651836 0.536737i
\(766\) 206307. 0.351606
\(767\) 102917.i 0.174943i
\(768\) −620328. + 222530.i −1.05172 + 0.377282i
\(769\) 173980. 0.294203 0.147102 0.989121i \(-0.453006\pi\)
0.147102 + 0.989121i \(0.453006\pi\)
\(770\) 1.19316e6i 2.01242i
\(771\) 293065. + 816951.i 0.493009 + 1.37432i
\(772\) −767398. −1.28761
\(773\) 98287.5i 0.164490i 0.996612 + 0.0822450i \(0.0262090\pi\)
−0.996612 + 0.0822450i \(0.973791\pi\)
\(774\) −632692. 768367.i −1.05611 1.28259i
\(775\) −1.49395e6 −2.48733
\(776\) 1.77014e6i 2.93957i
\(777\) −229650. + 82382.3i −0.380386 + 0.136456i
\(778\) −527702. −0.871825
\(779\) 54733.8i 0.0901946i
\(780\) −1.07377e6 2.99327e6i −1.76492 4.91990i
\(781\) −912432. −1.49589
\(782\) 214218.i 0.350301i