Properties

Label 33.5.c.a.10.4
Level $33$
Weight $5$
Character 33.10
Analytic conductor $3.411$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 33.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.41120878177\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 102 x^{6} + 2913 x^{4} + 23292 x^{2} + 41364\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 10.4
Root \(-1.57474i\) of defining polynomial
Character \(\chi\) \(=\) 33.10
Dual form 33.5.c.a.10.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.57474i q^{2} -5.19615 q^{3} +13.5202 q^{4} +15.5526 q^{5} +8.18260i q^{6} -93.8006i q^{7} -46.4867i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-1.57474i q^{2} -5.19615 q^{3} +13.5202 q^{4} +15.5526 q^{5} +8.18260i q^{6} -93.8006i q^{7} -46.4867i q^{8} +27.0000 q^{9} -24.4913i q^{10} +(60.9369 + 104.536i) q^{11} -70.2530 q^{12} +29.4527i q^{13} -147.712 q^{14} -80.8135 q^{15} +143.119 q^{16} +251.915i q^{17} -42.5180i q^{18} -80.2497i q^{19} +210.274 q^{20} +487.402i q^{21} +(164.617 - 95.9599i) q^{22} -702.557 q^{23} +241.552i q^{24} -383.118 q^{25} +46.3804 q^{26} -140.296 q^{27} -1268.20i q^{28} +1449.00i q^{29} +127.260i q^{30} +1279.46 q^{31} -969.161i q^{32} +(-316.638 - 543.183i) q^{33} +396.701 q^{34} -1458.84i q^{35} +365.045 q^{36} +115.552 q^{37} -126.373 q^{38} -153.041i q^{39} -722.987i q^{40} -1076.75i q^{41} +767.532 q^{42} +1887.47i q^{43} +(823.879 + 1413.34i) q^{44} +419.919 q^{45} +1106.35i q^{46} +1591.75 q^{47} -743.666 q^{48} -6397.55 q^{49} +603.311i q^{50} -1308.99i q^{51} +398.206i q^{52} +1190.69 q^{53} +220.930i q^{54} +(947.726 + 1625.80i) q^{55} -4360.48 q^{56} +416.990i q^{57} +2281.80 q^{58} +1895.56 q^{59} -1092.61 q^{60} +3776.15i q^{61} -2014.82i q^{62} -2532.62i q^{63} +763.719 q^{64} +458.065i q^{65} +(-855.373 + 498.622i) q^{66} -1253.00 q^{67} +3405.94i q^{68} +3650.59 q^{69} -2297.30 q^{70} -3591.39 q^{71} -1255.14i q^{72} +1750.75i q^{73} -181.965i q^{74} +1990.74 q^{75} -1084.99i q^{76} +(9805.50 - 5715.92i) q^{77} -241.000 q^{78} -6749.08i q^{79} +2225.86 q^{80} +729.000 q^{81} -1695.60 q^{82} -8616.78i q^{83} +6589.77i q^{84} +3917.92i q^{85} +2972.27 q^{86} -7529.24i q^{87} +(4859.51 - 2832.75i) q^{88} -9334.05 q^{89} -661.265i q^{90} +2762.68 q^{91} -9498.71 q^{92} -6648.27 q^{93} -2506.59i q^{94} -1248.09i q^{95} +5035.91i q^{96} +11068.8 q^{97} +10074.5i q^{98} +(1645.30 + 2822.46i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10}) \) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57474i 0.393685i −0.980435 0.196843i \(-0.936931\pi\)
0.980435 0.196843i \(-0.0630688\pi\)
\(3\) −5.19615 −0.577350
\(4\) 13.5202 0.845012
\(5\) 15.5526 0.622103 0.311051 0.950393i \(-0.399319\pi\)
0.311051 + 0.950393i \(0.399319\pi\)
\(6\) 8.18260i 0.227294i
\(7\) 93.8006i 1.91430i −0.289596 0.957149i \(-0.593521\pi\)
0.289596 0.957149i \(-0.406479\pi\)
\(8\) 46.4867i 0.726354i
\(9\) 27.0000 0.333333
\(10\) 24.4913i 0.244913i
\(11\) 60.9369 + 104.536i 0.503611 + 0.863931i
\(12\) −70.2530 −0.487868
\(13\) 29.4527i 0.174276i 0.996196 + 0.0871382i \(0.0277722\pi\)
−0.996196 + 0.0871382i \(0.972228\pi\)
\(14\) −147.712 −0.753631
\(15\) −80.8135 −0.359171
\(16\) 143.119 0.559057
\(17\) 251.915i 0.871677i 0.900025 + 0.435839i \(0.143548\pi\)
−0.900025 + 0.435839i \(0.856452\pi\)
\(18\) 42.5180i 0.131228i
\(19\) 80.2497i 0.222298i −0.993804 0.111149i \(-0.964547\pi\)
0.993804 0.111149i \(-0.0354531\pi\)
\(20\) 210.274 0.525684
\(21\) 487.402i 1.10522i
\(22\) 164.617 95.9599i 0.340117 0.198264i
\(23\) −702.557 −1.32809 −0.664043 0.747695i \(-0.731161\pi\)
−0.664043 + 0.747695i \(0.731161\pi\)
\(24\) 241.552i 0.419361i
\(25\) −383.118 −0.612988
\(26\) 46.3804 0.0686100
\(27\) −140.296 −0.192450
\(28\) 1268.20i 1.61760i
\(29\) 1449.00i 1.72295i 0.507798 + 0.861476i \(0.330460\pi\)
−0.507798 + 0.861476i \(0.669540\pi\)
\(30\) 127.260i 0.141400i
\(31\) 1279.46 1.33138 0.665692 0.746227i \(-0.268137\pi\)
0.665692 + 0.746227i \(0.268137\pi\)
\(32\) 969.161i 0.946447i
\(33\) −316.638 543.183i −0.290760 0.498791i
\(34\) 396.701 0.343167
\(35\) 1458.84i 1.19089i
\(36\) 365.045 0.281671
\(37\) 115.552 0.0844063 0.0422031 0.999109i \(-0.486562\pi\)
0.0422031 + 0.999109i \(0.486562\pi\)
\(38\) −126.373 −0.0875156
\(39\) 153.041i 0.100618i
\(40\) 722.987i 0.451867i
\(41\) 1076.75i 0.640541i −0.947326 0.320270i \(-0.896226\pi\)
0.947326 0.320270i \(-0.103774\pi\)
\(42\) 767.532 0.435109
\(43\) 1887.47i 1.02080i 0.859936 + 0.510402i \(0.170503\pi\)
−0.859936 + 0.510402i \(0.829497\pi\)
\(44\) 823.879 + 1413.34i 0.425557 + 0.730032i
\(45\) 419.919 0.207368
\(46\) 1106.35i 0.522848i
\(47\) 1591.75 0.720575 0.360287 0.932841i \(-0.382679\pi\)
0.360287 + 0.932841i \(0.382679\pi\)
\(48\) −743.666 −0.322772
\(49\) −6397.55 −2.66454
\(50\) 603.311i 0.241324i
\(51\) 1308.99i 0.503263i
\(52\) 398.206i 0.147266i
\(53\) 1190.69 0.423886 0.211943 0.977282i \(-0.432021\pi\)
0.211943 + 0.977282i \(0.432021\pi\)
\(54\) 220.930i 0.0757648i
\(55\) 947.726 + 1625.80i 0.313298 + 0.537454i
\(56\) −4360.48 −1.39046
\(57\) 416.990i 0.128344i
\(58\) 2281.80 0.678301
\(59\) 1895.56 0.544544 0.272272 0.962220i \(-0.412225\pi\)
0.272272 + 0.962220i \(0.412225\pi\)
\(60\) −1092.61 −0.303504
\(61\) 3776.15i 1.01482i 0.861704 + 0.507411i \(0.169397\pi\)
−0.861704 + 0.507411i \(0.830603\pi\)
\(62\) 2014.82i 0.524146i
\(63\) 2532.62i 0.638099i
\(64\) 763.719 0.186455
\(65\) 458.065i 0.108418i
\(66\) −855.373 + 498.622i −0.196367 + 0.114468i
\(67\) −1253.00 −0.279127 −0.139564 0.990213i \(-0.544570\pi\)
−0.139564 + 0.990213i \(0.544570\pi\)
\(68\) 3405.94i 0.736578i
\(69\) 3650.59 0.766770
\(70\) −2297.30 −0.468836
\(71\) −3591.39 −0.712437 −0.356218 0.934403i \(-0.615934\pi\)
−0.356218 + 0.934403i \(0.615934\pi\)
\(72\) 1255.14i 0.242118i
\(73\) 1750.75i 0.328533i 0.986416 + 0.164267i \(0.0525257\pi\)
−0.986416 + 0.164267i \(0.947474\pi\)
\(74\) 181.965i 0.0332295i
\(75\) 1990.74 0.353909
\(76\) 1084.99i 0.187845i
\(77\) 9805.50 5715.92i 1.65382 0.964061i
\(78\) −241.000 −0.0396120
\(79\) 6749.08i 1.08141i −0.841212 0.540705i \(-0.818157\pi\)
0.841212 0.540705i \(-0.181843\pi\)
\(80\) 2225.86 0.347791
\(81\) 729.000 0.111111
\(82\) −1695.60 −0.252171
\(83\) 8616.78i 1.25080i −0.780303 0.625401i \(-0.784935\pi\)
0.780303 0.625401i \(-0.215065\pi\)
\(84\) 6589.77i 0.933924i
\(85\) 3917.92i 0.542273i
\(86\) 2972.27 0.401876
\(87\) 7529.24i 0.994747i
\(88\) 4859.51 2832.75i 0.627520 0.365800i
\(89\) −9334.05 −1.17839 −0.589196 0.807990i \(-0.700556\pi\)
−0.589196 + 0.807990i \(0.700556\pi\)
\(90\) 661.265i 0.0816376i
\(91\) 2762.68 0.333617
\(92\) −9498.71 −1.12225
\(93\) −6648.27 −0.768675
\(94\) 2506.59i 0.283680i
\(95\) 1248.09i 0.138292i
\(96\) 5035.91i 0.546431i
\(97\) 11068.8 1.17640 0.588202 0.808714i \(-0.299836\pi\)
0.588202 + 0.808714i \(0.299836\pi\)
\(98\) 10074.5i 1.04899i
\(99\) 1645.30 + 2822.46i 0.167870 + 0.287977i
\(100\) −5179.82 −0.517982
\(101\) 9732.30i 0.954053i 0.878889 + 0.477027i \(0.158285\pi\)
−0.878889 + 0.477027i \(0.841715\pi\)
\(102\) −2061.32 −0.198127
\(103\) 2229.35 0.210138 0.105069 0.994465i \(-0.466494\pi\)
0.105069 + 0.994465i \(0.466494\pi\)
\(104\) 1369.16 0.126586
\(105\) 7580.36i 0.687561i
\(106\) 1875.04i 0.166878i
\(107\) 8911.94i 0.778404i 0.921152 + 0.389202i \(0.127249\pi\)
−0.921152 + 0.389202i \(0.872751\pi\)
\(108\) −1896.83 −0.162623
\(109\) 8075.42i 0.679692i −0.940481 0.339846i \(-0.889625\pi\)
0.940481 0.339846i \(-0.110375\pi\)
\(110\) 2560.21 1492.42i 0.211588 0.123341i
\(111\) −600.427 −0.0487320
\(112\) 13424.6i 1.07020i
\(113\) −16548.3 −1.29597 −0.647987 0.761652i \(-0.724389\pi\)
−0.647987 + 0.761652i \(0.724389\pi\)
\(114\) 656.651 0.0505272
\(115\) −10926.6 −0.826206
\(116\) 19590.8i 1.45592i
\(117\) 795.223i 0.0580921i
\(118\) 2985.01i 0.214379i
\(119\) 23629.8 1.66865
\(120\) 3756.75i 0.260886i
\(121\) −7214.38 + 12740.2i −0.492752 + 0.870170i
\(122\) 5946.46 0.399520
\(123\) 5594.95i 0.369816i
\(124\) 17298.5 1.12503
\(125\) −15678.8 −1.00344
\(126\) −3988.22 −0.251210
\(127\) 2165.25i 0.134246i 0.997745 + 0.0671228i \(0.0213819\pi\)
−0.997745 + 0.0671228i \(0.978618\pi\)
\(128\) 16709.2i 1.01985i
\(129\) 9807.56i 0.589361i
\(130\) 721.334 0.0426825
\(131\) 15267.4i 0.889658i −0.895616 0.444829i \(-0.853264\pi\)
0.895616 0.444829i \(-0.146736\pi\)
\(132\) −4281.00 7343.94i −0.245696 0.421484i
\(133\) −7527.47 −0.425545
\(134\) 1973.16i 0.109888i
\(135\) −2181.97 −0.119724
\(136\) 11710.7 0.633146
\(137\) 10391.2 0.553636 0.276818 0.960922i \(-0.410720\pi\)
0.276818 + 0.960922i \(0.410720\pi\)
\(138\) 5748.74i 0.301866i
\(139\) 21983.9i 1.13782i −0.822399 0.568911i \(-0.807365\pi\)
0.822399 0.568911i \(-0.192635\pi\)
\(140\) 19723.8i 1.00632i
\(141\) −8270.98 −0.416024
\(142\) 5655.52i 0.280476i
\(143\) −3078.86 + 1794.76i −0.150563 + 0.0877675i
\(144\) 3864.20 0.186352
\(145\) 22535.7i 1.07185i
\(146\) 2756.98 0.129339
\(147\) 33242.7 1.53837
\(148\) 1562.29 0.0713243
\(149\) 10316.9i 0.464705i −0.972632 0.232353i \(-0.925358\pi\)
0.972632 0.232353i \(-0.0746423\pi\)
\(150\) 3134.90i 0.139329i
\(151\) 20057.9i 0.879694i 0.898073 + 0.439847i \(0.144967\pi\)
−0.898073 + 0.439847i \(0.855033\pi\)
\(152\) −3730.54 −0.161467
\(153\) 6801.70i 0.290559i
\(154\) −9001.10 15441.1i −0.379537 0.651085i
\(155\) 19898.9 0.828258
\(156\) 2069.14i 0.0850238i
\(157\) −5742.18 −0.232958 −0.116479 0.993193i \(-0.537161\pi\)
−0.116479 + 0.993193i \(0.537161\pi\)
\(158\) −10628.1 −0.425735
\(159\) −6187.03 −0.244730
\(160\) 15073.0i 0.588787i
\(161\) 65900.3i 2.54235i
\(162\) 1147.99i 0.0437428i
\(163\) −24660.6 −0.928174 −0.464087 0.885790i \(-0.653617\pi\)
−0.464087 + 0.885790i \(0.653617\pi\)
\(164\) 14557.8i 0.541265i
\(165\) −4924.53 8447.89i −0.180883 0.310299i
\(166\) −13569.2 −0.492423
\(167\) 47391.6i 1.69930i −0.527351 0.849648i \(-0.676815\pi\)
0.527351 0.849648i \(-0.323185\pi\)
\(168\) 22657.7 0.802781
\(169\) 27693.5 0.969628
\(170\) 6169.71 0.213485
\(171\) 2166.74i 0.0740995i
\(172\) 25518.9i 0.862591i
\(173\) 1326.29i 0.0443147i −0.999754 0.0221573i \(-0.992947\pi\)
0.999754 0.0221573i \(-0.00705347\pi\)
\(174\) −11856.6 −0.391617
\(175\) 35936.7i 1.17344i
\(176\) 8721.21 + 14961.0i 0.281547 + 0.482986i
\(177\) −9849.60 −0.314392
\(178\) 14698.7i 0.463916i
\(179\) −53822.7 −1.67981 −0.839903 0.542736i \(-0.817388\pi\)
−0.839903 + 0.542736i \(0.817388\pi\)
\(180\) 5677.39 0.175228
\(181\) 9961.35 0.304061 0.152031 0.988376i \(-0.451419\pi\)
0.152031 + 0.988376i \(0.451419\pi\)
\(182\) 4350.51i 0.131340i
\(183\) 19621.5i 0.585907i
\(184\) 32659.5i 0.964660i
\(185\) 1797.13 0.0525094
\(186\) 10469.3i 0.302616i
\(187\) −26334.1 + 15350.9i −0.753069 + 0.438986i
\(188\) 21520.8 0.608894
\(189\) 13159.9i 0.368407i
\(190\) −1965.42 −0.0544437
\(191\) −54964.8 −1.50667 −0.753335 0.657637i \(-0.771556\pi\)
−0.753335 + 0.657637i \(0.771556\pi\)
\(192\) −3968.40 −0.107650
\(193\) 1722.76i 0.0462498i −0.999733 0.0231249i \(-0.992638\pi\)
0.999733 0.0231249i \(-0.00736154\pi\)
\(194\) 17430.5i 0.463133i
\(195\) 2380.18i 0.0625950i
\(196\) −86496.1 −2.25156
\(197\) 10387.5i 0.267656i −0.991005 0.133828i \(-0.957273\pi\)
0.991005 0.133828i \(-0.0427270\pi\)
\(198\) 4444.65 2590.92i 0.113372 0.0660881i
\(199\) 50964.3 1.28695 0.643473 0.765469i \(-0.277493\pi\)
0.643473 + 0.765469i \(0.277493\pi\)
\(200\) 17809.9i 0.445246i
\(201\) 6510.79 0.161154
\(202\) 15325.9 0.375597
\(203\) 135917. 3.29824
\(204\) 17697.8i 0.425263i
\(205\) 16746.2i 0.398482i
\(206\) 3510.66i 0.0827283i
\(207\) −18969.0 −0.442695
\(208\) 4215.23i 0.0974304i
\(209\) 8388.95 4890.17i 0.192050 0.111952i
\(210\) 11937.1 0.270683
\(211\) 68681.5i 1.54268i −0.636426 0.771338i \(-0.719588\pi\)
0.636426 0.771338i \(-0.280412\pi\)
\(212\) 16098.4 0.358188
\(213\) 18661.4 0.411326
\(214\) 14034.0 0.306446
\(215\) 29355.0i 0.635045i
\(216\) 6521.90i 0.139787i
\(217\) 120014.i 2.54866i
\(218\) −12716.7 −0.267585
\(219\) 9097.18i 0.189679i
\(220\) 12813.4 + 21981.1i 0.264740 + 0.454155i
\(221\) −7419.57 −0.151913
\(222\) 945.517i 0.0191851i
\(223\) −1628.89 −0.0327553 −0.0163777 0.999866i \(-0.505213\pi\)
−0.0163777 + 0.999866i \(0.505213\pi\)
\(224\) −90907.9 −1.81178
\(225\) −10344.2 −0.204329
\(226\) 26059.3i 0.510206i
\(227\) 42599.1i 0.826701i −0.910572 0.413351i \(-0.864358\pi\)
0.910572 0.413351i \(-0.135642\pi\)
\(228\) 5637.78i 0.108452i
\(229\) 32387.8 0.617605 0.308802 0.951126i \(-0.400072\pi\)
0.308802 + 0.951126i \(0.400072\pi\)
\(230\) 17206.5i 0.325265i
\(231\) −50950.9 + 29700.8i −0.954834 + 0.556601i
\(232\) 67359.3 1.25147
\(233\) 57867.1i 1.06591i 0.846144 + 0.532954i \(0.178918\pi\)
−0.846144 + 0.532954i \(0.821082\pi\)
\(234\) 1252.27 0.0228700
\(235\) 24755.8 0.448272
\(236\) 25628.3 0.460146
\(237\) 35069.3i 0.624352i
\(238\) 37210.8i 0.656923i
\(239\) 3758.46i 0.0657982i 0.999459 + 0.0328991i \(0.0104740\pi\)
−0.999459 + 0.0328991i \(0.989526\pi\)
\(240\) −11565.9 −0.200797
\(241\) 53393.2i 0.919288i −0.888103 0.459644i \(-0.847977\pi\)
0.888103 0.459644i \(-0.152023\pi\)
\(242\) 20062.5 + 11360.8i 0.342573 + 0.193989i
\(243\) −3788.00 −0.0641500
\(244\) 51054.3i 0.857536i
\(245\) −99498.4 −1.65762
\(246\) 8810.60 0.145591
\(247\) 2363.57 0.0387414
\(248\) 59477.8i 0.967056i
\(249\) 44774.1i 0.722151i
\(250\) 24690.1i 0.395041i
\(251\) 1857.31 0.0294807 0.0147403 0.999891i \(-0.495308\pi\)
0.0147403 + 0.999891i \(0.495308\pi\)
\(252\) 34241.5i 0.539201i
\(253\) −42811.7 73442.2i −0.668838 1.14737i
\(254\) 3409.70 0.0528505
\(255\) 20358.1i 0.313081i
\(256\) −14093.2 −0.215046
\(257\) −1262.77 −0.0191187 −0.00955933 0.999954i \(-0.503043\pi\)
−0.00955933 + 0.999954i \(0.503043\pi\)
\(258\) −15444.4 −0.232023
\(259\) 10838.9i 0.161579i
\(260\) 6193.13i 0.0916143i
\(261\) 39123.1i 0.574317i
\(262\) −24042.2 −0.350245
\(263\) 118343.i 1.71092i 0.517870 + 0.855459i \(0.326725\pi\)
−0.517870 + 0.855459i \(0.673275\pi\)
\(264\) −25250.8 + 14719.4i −0.362299 + 0.211195i
\(265\) 18518.4 0.263700
\(266\) 11853.8i 0.167531i
\(267\) 48501.1 0.680345
\(268\) −16940.8 −0.235866
\(269\) 100514. 1.38906 0.694528 0.719465i \(-0.255613\pi\)
0.694528 + 0.719465i \(0.255613\pi\)
\(270\) 3436.03i 0.0471335i
\(271\) 138354.i 1.88389i 0.335773 + 0.941943i \(0.391003\pi\)
−0.335773 + 0.941943i \(0.608997\pi\)
\(272\) 36053.7i 0.487317i
\(273\) −14355.3 −0.192614
\(274\) 16363.5i 0.217958i
\(275\) −23346.0 40049.4i −0.308707 0.529579i
\(276\) 49356.7 0.647930
\(277\) 40696.2i 0.530388i −0.964195 0.265194i \(-0.914564\pi\)
0.964195 0.265194i \(-0.0854360\pi\)
\(278\) −34618.9 −0.447944
\(279\) 34545.4 0.443795
\(280\) −67816.6 −0.865008
\(281\) 17381.6i 0.220129i −0.993924 0.110065i \(-0.964894\pi\)
0.993924 0.110065i \(-0.0351058\pi\)
\(282\) 13024.6i 0.163783i
\(283\) 102799.i 1.28355i 0.766891 + 0.641777i \(0.221802\pi\)
−0.766891 + 0.641777i \(0.778198\pi\)
\(284\) −48556.3 −0.602018
\(285\) 6485.26i 0.0798432i
\(286\) 2826.28 + 4848.40i 0.0345528 + 0.0592743i
\(287\) −101000. −1.22619
\(288\) 26167.4i 0.315482i
\(289\) 20059.9 0.240178
\(290\) 35487.9 0.421973
\(291\) −57515.1 −0.679197
\(292\) 23670.5i 0.277614i
\(293\) 106779.i 1.24380i −0.783098 0.621898i \(-0.786362\pi\)
0.783098 0.621898i \(-0.213638\pi\)
\(294\) 52348.6i 0.605634i
\(295\) 29480.8 0.338762
\(296\) 5371.64i 0.0613088i
\(297\) −8549.21 14665.9i −0.0969200 0.166264i
\(298\) −16246.5 −0.182948
\(299\) 20692.2i 0.231454i
\(300\) 26915.1 0.299057
\(301\) 177045. 1.95412
\(302\) 31586.0 0.346322
\(303\) 50570.5i 0.550823i
\(304\) 11485.2i 0.124277i
\(305\) 58728.8i 0.631323i
\(306\) 10710.9 0.114389
\(307\) 78416.1i 0.832010i −0.909362 0.416005i \(-0.863430\pi\)
0.909362 0.416005i \(-0.136570\pi\)
\(308\) 132572. 77280.3i 1.39750 0.814643i
\(309\) −11584.1 −0.121323
\(310\) 31335.6i 0.326073i
\(311\) −60684.2 −0.627415 −0.313707 0.949520i \(-0.601571\pi\)
−0.313707 + 0.949520i \(0.601571\pi\)
\(312\) −7114.35 −0.0730846
\(313\) −85739.0 −0.875165 −0.437582 0.899178i \(-0.644165\pi\)
−0.437582 + 0.899178i \(0.644165\pi\)
\(314\) 9042.45i 0.0917121i
\(315\) 39388.7i 0.396963i
\(316\) 91248.9i 0.913804i
\(317\) 117644. 1.17071 0.585357 0.810776i \(-0.300955\pi\)
0.585357 + 0.810776i \(0.300955\pi\)
\(318\) 9742.97i 0.0963468i
\(319\) −151472. + 88297.8i −1.48851 + 0.867698i
\(320\) 11877.8 0.115994
\(321\) 46307.8i 0.449412i
\(322\) 103776. 1.00089
\(323\) 20216.1 0.193773
\(324\) 9856.22 0.0938902
\(325\) 11283.8i 0.106829i
\(326\) 38834.1i 0.365408i
\(327\) 41961.1i 0.392420i
\(328\) −50054.5 −0.465259
\(329\) 149307.i 1.37940i
\(330\) −13303.2 + 7754.86i −0.122160 + 0.0712108i
\(331\) −109718. −1.00143 −0.500717 0.865611i \(-0.666930\pi\)
−0.500717 + 0.865611i \(0.666930\pi\)
\(332\) 116501.i 1.05694i
\(333\) 3119.91 0.0281354
\(334\) −74629.6 −0.668988
\(335\) −19487.4 −0.173646
\(336\) 69756.3i 0.617881i
\(337\) 73221.5i 0.644731i −0.946615 0.322365i \(-0.895522\pi\)
0.946615 0.322365i \(-0.104478\pi\)
\(338\) 43610.2i 0.381728i
\(339\) 85987.4 0.748230
\(340\) 52971.1i 0.458227i
\(341\) 77966.3 + 133749.i 0.670499 + 1.15022i
\(342\) −3412.06 −0.0291719
\(343\) 374879.i 3.18642i
\(344\) 87742.0 0.741465
\(345\) 56776.1 0.477010
\(346\) −2088.57 −0.0174460
\(347\) 160256.i 1.33093i 0.746428 + 0.665466i \(0.231767\pi\)
−0.746428 + 0.665466i \(0.768233\pi\)
\(348\) 101797.i 0.840573i
\(349\) 24791.6i 0.203542i −0.994808 0.101771i \(-0.967549\pi\)
0.994808 0.101771i \(-0.0324509\pi\)
\(350\) 56590.9 0.461967
\(351\) 4132.10i 0.0335395i
\(352\) 101312. 59057.7i 0.817664 0.476641i
\(353\) −140695. −1.12909 −0.564547 0.825401i \(-0.690949\pi\)
−0.564547 + 0.825401i \(0.690949\pi\)
\(354\) 15510.6i 0.123772i
\(355\) −55855.4 −0.443209
\(356\) −126198. −0.995756
\(357\) −122784. −0.963396
\(358\) 84756.8i 0.661315i
\(359\) 14603.5i 0.113310i 0.998394 + 0.0566552i \(0.0180436\pi\)
−0.998394 + 0.0566552i \(0.981956\pi\)
\(360\) 19520.7i 0.150622i
\(361\) 123881. 0.950583
\(362\) 15686.5i 0.119704i
\(363\) 37487.0 66199.8i 0.284491 0.502393i
\(364\) 37352.0 0.281910
\(365\) 27228.7i 0.204381i
\(366\) −30898.7 −0.230663
\(367\) −168034. −1.24757 −0.623785 0.781596i \(-0.714406\pi\)
−0.623785 + 0.781596i \(0.714406\pi\)
\(368\) −100549. −0.742475
\(369\) 29072.2i 0.213514i
\(370\) 2830.02i 0.0206722i
\(371\) 111688.i 0.811443i
\(372\) −89885.8 −0.649539
\(373\) 179739.i 1.29189i 0.763385 + 0.645944i \(0.223536\pi\)
−0.763385 + 0.645944i \(0.776464\pi\)
\(374\) 24173.7 + 41469.3i 0.172822 + 0.296472i
\(375\) 81469.5 0.579339
\(376\) 73995.2i 0.523393i
\(377\) −42677.0 −0.300270
\(378\) 20723.4 0.145036
\(379\) −88424.0 −0.615590 −0.307795 0.951453i \(-0.599591\pi\)
−0.307795 + 0.951453i \(0.599591\pi\)
\(380\) 16874.4i 0.116859i
\(381\) 11251.0i 0.0775067i
\(382\) 86555.4i 0.593154i
\(383\) 95956.7 0.654151 0.327075 0.944998i \(-0.393937\pi\)
0.327075 + 0.944998i \(0.393937\pi\)
\(384\) 86823.8i 0.588811i
\(385\) 152501. 88897.3i 1.02885 0.599745i
\(386\) −2712.90 −0.0182079
\(387\) 50961.6i 0.340268i
\(388\) 149652. 0.994075
\(389\) −118749. −0.784747 −0.392373 0.919806i \(-0.628346\pi\)
−0.392373 + 0.919806i \(0.628346\pi\)
\(390\) −3748.16 −0.0246428
\(391\) 176985.i 1.15766i
\(392\) 297401.i 1.93540i
\(393\) 79331.8i 0.513644i
\(394\) −16357.6 −0.105372
\(395\) 104966.i 0.672748i
\(396\) 22244.7 + 38160.2i 0.141852 + 0.243344i
\(397\) −159427. −1.01154 −0.505768 0.862670i \(-0.668791\pi\)
−0.505768 + 0.862670i \(0.668791\pi\)
\(398\) 80255.6i 0.506652i
\(399\) 39113.9 0.245689
\(400\) −54831.2 −0.342695
\(401\) −41646.5 −0.258994 −0.129497 0.991580i \(-0.541336\pi\)
−0.129497 + 0.991580i \(0.541336\pi\)
\(402\) 10252.8i 0.0634441i
\(403\) 37683.5i 0.232029i
\(404\) 131583.i 0.806186i
\(405\) 11337.8 0.0691225
\(406\) 214035.i 1.29847i
\(407\) 7041.40 + 12079.3i 0.0425079 + 0.0729212i
\(408\) −60850.5 −0.365547
\(409\) 265054.i 1.58449i −0.610206 0.792243i \(-0.708913\pi\)
0.610206 0.792243i \(-0.291087\pi\)
\(410\) −26371.0 −0.156877
\(411\) −53994.3 −0.319642
\(412\) 30141.3 0.177569
\(413\) 177804.i 1.04242i
\(414\) 29871.3i 0.174283i
\(415\) 134013.i 0.778128i
\(416\) 28544.4 0.164943
\(417\) 114232.i 0.656922i
\(418\) −7700.76 13210.4i −0.0440738 0.0756074i
\(419\) 255711. 1.45654 0.728270 0.685291i \(-0.240325\pi\)
0.728270 + 0.685291i \(0.240325\pi\)
\(420\) 102488.i 0.580997i
\(421\) 189209. 1.06753 0.533763 0.845634i \(-0.320778\pi\)
0.533763 + 0.845634i \(0.320778\pi\)
\(422\) −108156. −0.607329
\(423\) 42977.3 0.240192
\(424\) 55351.4i 0.307891i
\(425\) 96513.0i 0.534328i
\(426\) 29386.9i 0.161933i
\(427\) 354205. 1.94267
\(428\) 120491.i 0.657760i
\(429\) 15998.2 9325.83i 0.0869274 0.0506726i
\(430\) 46226.5 0.250008
\(431\) 110749.i 0.596190i −0.954536 0.298095i \(-0.903649\pi\)
0.954536 0.298095i \(-0.0963512\pi\)
\(432\) −20079.0 −0.107591
\(433\) 172877. 0.922062 0.461031 0.887384i \(-0.347480\pi\)
0.461031 + 0.887384i \(0.347480\pi\)
\(434\) −188991. −1.00337
\(435\) 117099.i 0.618835i
\(436\) 109181.i 0.574348i
\(437\) 56380.0i 0.295231i
\(438\) −14325.7 −0.0746737
\(439\) 155214.i 0.805383i 0.915336 + 0.402691i \(0.131925\pi\)
−0.915336 + 0.402691i \(0.868075\pi\)
\(440\) 75577.9 44056.6i 0.390382 0.227565i
\(441\) −172734. −0.888179
\(442\) 11683.9i 0.0598058i
\(443\) 104175. 0.530828 0.265414 0.964134i \(-0.414491\pi\)
0.265414 + 0.964134i \(0.414491\pi\)
\(444\) −8117.88 −0.0411791
\(445\) −145168. −0.733082
\(446\) 2565.08i 0.0128953i
\(447\) 53608.3i 0.268298i
\(448\) 71637.3i 0.356930i
\(449\) 88086.4 0.436934 0.218467 0.975844i \(-0.429894\pi\)
0.218467 + 0.975844i \(0.429894\pi\)
\(450\) 16289.4i 0.0804415i
\(451\) 112559. 65613.8i 0.553383 0.322583i
\(452\) −223736. −1.09511
\(453\) 104224.i 0.507891i
\(454\) −67082.5 −0.325460
\(455\) 42966.8 0.207544
\(456\) 19384.5 0.0932232
\(457\) 77946.3i 0.373219i 0.982434 + 0.186609i \(0.0597499\pi\)
−0.982434 + 0.186609i \(0.940250\pi\)
\(458\) 51002.4i 0.243142i
\(459\) 35342.7i 0.167754i
\(460\) −147729. −0.698154
\(461\) 115963.i 0.545653i 0.962063 + 0.272827i \(0.0879586\pi\)
−0.962063 + 0.272827i \(0.912041\pi\)
\(462\) 46771.1 + 80234.5i 0.219126 + 0.375904i
\(463\) −313839. −1.46401 −0.732007 0.681297i \(-0.761416\pi\)
−0.732007 + 0.681297i \(0.761416\pi\)
\(464\) 207379.i 0.963228i
\(465\) −103398. −0.478195
\(466\) 91125.7 0.419632
\(467\) −96033.3 −0.440340 −0.220170 0.975462i \(-0.570661\pi\)
−0.220170 + 0.975462i \(0.570661\pi\)
\(468\) 10751.6i 0.0490885i
\(469\) 117532.i 0.534333i
\(470\) 38984.0i 0.176478i
\(471\) 29837.2 0.134498
\(472\) 88118.1i 0.395532i
\(473\) −197307. + 115016.i −0.881904 + 0.514088i
\(474\) 55225.0 0.245798
\(475\) 30745.1i 0.136266i
\(476\) 319479. 1.41003
\(477\) 32148.7 0.141295
\(478\) 5918.60 0.0259038
\(479\) 215693.i 0.940082i 0.882645 + 0.470041i \(0.155761\pi\)
−0.882645 + 0.470041i \(0.844239\pi\)
\(480\) 78321.4i 0.339936i
\(481\) 3403.32i 0.0147100i
\(482\) −84080.5 −0.361910
\(483\) 342428.i 1.46783i
\(484\) −97539.8 + 172249.i −0.416381 + 0.735304i
\(485\) 172148. 0.731844
\(486\) 5965.11i 0.0252549i
\(487\) −281250. −1.18587 −0.592933 0.805252i \(-0.702030\pi\)
−0.592933 + 0.805252i \(0.702030\pi\)
\(488\) 175541. 0.737120
\(489\) 128140. 0.535881
\(490\) 156684.i 0.652579i
\(491\) 229094.i 0.950279i −0.879910 0.475139i \(-0.842398\pi\)
0.879910 0.475139i \(-0.157602\pi\)
\(492\) 75644.8i 0.312499i
\(493\) −365025. −1.50186
\(494\) 3722.01i 0.0152519i
\(495\) 25588.6 + 43896.5i 0.104433 + 0.179151i
\(496\) 183114. 0.744319
\(497\) 336875.i 1.36382i
\(498\) 70507.6 0.284300
\(499\) 37652.6 0.151215 0.0756073 0.997138i \(-0.475910\pi\)
0.0756073 + 0.997138i \(0.475910\pi\)
\(500\) −211981. −0.847922
\(501\) 246254.i 0.981088i
\(502\) 2924.79i 0.0116061i
\(503\) 353544.i 1.39736i −0.715435 0.698679i \(-0.753772\pi\)
0.715435 0.698679i \(-0.246228\pi\)
\(504\) −117733. −0.463486
\(505\) 151362.i 0.593519i
\(506\) −115653. + 67417.3i −0.451704 + 0.263312i
\(507\) −143900. −0.559815
\(508\) 29274.6i 0.113439i
\(509\) −240356. −0.927727 −0.463864 0.885907i \(-0.653537\pi\)
−0.463864 + 0.885907i \(0.653537\pi\)
\(510\) −32058.8 −0.123256
\(511\) 164222. 0.628910
\(512\) 245155.i 0.935191i
\(513\) 11258.7i 0.0427814i
\(514\) 1988.53i 0.00752673i
\(515\) 34672.2 0.130727
\(516\) 132600.i 0.498017i
\(517\) 96996.4 + 166395.i 0.362889 + 0.622527i
\(518\) −17068.4 −0.0636112
\(519\) 6891.62i 0.0255851i
\(520\) 21293.9 0.0787497
\(521\) 484627. 1.78539 0.892693 0.450666i \(-0.148813\pi\)
0.892693 + 0.450666i \(0.148813\pi\)
\(522\) 61608.7 0.226100
\(523\) 188211.i 0.688084i 0.938954 + 0.344042i \(0.111796\pi\)
−0.938954 + 0.344042i \(0.888204\pi\)
\(524\) 206418.i 0.751771i
\(525\) 186732.i 0.677487i
\(526\) 186359. 0.673564
\(527\) 322315.i 1.16054i
\(528\) −45316.7 77739.6i −0.162551 0.278852i
\(529\) 213746. 0.763811
\(530\) 29161.6i 0.103815i
\(531\) 51180.0 0.181515
\(532\) −101773. −0.359591
\(533\) 31713.2 0.111631
\(534\) 76376.8i 0.267842i
\(535\) 138604.i 0.484247i
\(536\) 58247.9i 0.202745i
\(537\) 279671. 0.969837
\(538\) 158283.i 0.546851i
\(539\) −389847. 668772.i −1.34189 2.30197i
\(540\) −29500.6 −0.101168
\(541\) 329143.i 1.12458i −0.826940 0.562290i \(-0.809920\pi\)
0.826940 0.562290i \(-0.190080\pi\)
\(542\) 217873. 0.741658
\(543\) −51760.7 −0.175550
\(544\) 244146. 0.824996
\(545\) 125594.i 0.422838i
\(546\) 22605.9i 0.0758292i
\(547\) 201214.i 0.672486i 0.941775 + 0.336243i \(0.109156\pi\)
−0.941775 + 0.336243i \(0.890844\pi\)
\(548\) 140491. 0.467829
\(549\) 101956.i 0.338274i
\(550\) −63067.5 + 36763.9i −0.208488 + 0.121534i
\(551\) 116282. 0.383010
\(552\) 169704.i 0.556947i
\(553\) −633068. −2.07014
\(554\) −64085.9 −0.208806
\(555\) −9338.18 −0.0303163
\(556\) 297226.i 0.961474i
\(557\) 52859.7i 0.170378i 0.996365 + 0.0851892i \(0.0271495\pi\)
−0.996365 + 0.0851892i \(0.972851\pi\)
\(558\) 54400.1i 0.174715i
\(559\) −55591.0 −0.177902
\(560\) 208787.i 0.665775i
\(561\) 136836. 79765.7i 0.434784 0.253449i
\(562\) −27371.5 −0.0866616
\(563\) 143681.i 0.453295i −0.973977 0.226648i \(-0.927223\pi\)
0.973977 0.226648i \(-0.0727766\pi\)
\(564\) −111825. −0.351545
\(565\) −257368. −0.806229
\(566\) 161881. 0.505316
\(567\) 68380.6i 0.212700i
\(568\) 166952.i 0.517481i
\(569\) 568025.i 1.75446i 0.480071 + 0.877230i \(0.340611\pi\)
−0.480071 + 0.877230i \(0.659389\pi\)
\(570\) 10212.6 0.0314331
\(571\) 165896.i 0.508818i −0.967097 0.254409i \(-0.918119\pi\)
0.967097 0.254409i \(-0.0818810\pi\)
\(572\) −41626.7 + 24265.5i −0.127227 + 0.0741645i
\(573\) 285606. 0.869876
\(574\) 159048.i 0.482731i
\(575\) 269162. 0.814100
\(576\) 20620.4 0.0621516
\(577\) 157238. 0.472286 0.236143 0.971718i \(-0.424117\pi\)
0.236143 + 0.971718i \(0.424117\pi\)
\(578\) 31589.2i 0.0945547i
\(579\) 8951.72i 0.0267023i
\(580\) 304687.i 0.905729i
\(581\) −808259. −2.39441
\(582\) 90571.4i 0.267390i
\(583\) 72557.3 + 124470.i 0.213473 + 0.366208i
\(584\) 81386.6 0.238631
\(585\) 12367.8i 0.0361393i
\(586\) −168149. −0.489664
\(587\) 9552.74 0.0277237 0.0138619 0.999904i \(-0.495587\pi\)
0.0138619 + 0.999904i \(0.495587\pi\)
\(588\) 449447. 1.29994
\(589\) 102676.i 0.295964i
\(590\) 46424.6i 0.133366i
\(591\) 53974.9i 0.154531i
\(592\) 16537.7 0.0471879
\(593\) 164511.i 0.467827i −0.972257 0.233913i \(-0.924847\pi\)
0.972257 0.233913i \(-0.0751532\pi\)
\(594\) −23095.1 + 13462.8i −0.0654555 + 0.0381560i
\(595\) 367503. 1.03807
\(596\) 139487.i 0.392681i
\(597\) −264818. −0.743018
\(598\) −32584.9 −0.0911200
\(599\) 318614. 0.887996 0.443998 0.896028i \(-0.353560\pi\)
0.443998 + 0.896028i \(0.353560\pi\)
\(600\) 92542.7i 0.257063i
\(601\) 385872.i 1.06830i −0.845389 0.534151i \(-0.820631\pi\)
0.845389 0.534151i \(-0.179369\pi\)
\(602\) 278801.i 0.769310i
\(603\) −33831.1 −0.0930425
\(604\) 271187.i 0.743351i
\(605\) −112202. + 198142.i −0.306542 + 0.541335i
\(606\) −79635.5 −0.216851
\(607\) 218753.i 0.593712i 0.954922 + 0.296856i \(0.0959381\pi\)
−0.954922 + 0.296856i \(0.904062\pi\)
\(608\) −77774.9 −0.210394
\(609\) −706247. −1.90424
\(610\) 92482.7 0.248543
\(611\) 46881.3i 0.125579i
\(612\) 91960.3i 0.245526i
\(613\) 348766.i 0.928140i 0.885799 + 0.464070i \(0.153611\pi\)
−0.885799 + 0.464070i \(0.846389\pi\)
\(614\) −123485. −0.327550
\(615\) 87015.9i 0.230064i
\(616\) −265714. 455825.i −0.700250 1.20126i
\(617\) 222234. 0.583767 0.291884 0.956454i \(-0.405718\pi\)
0.291884 + 0.956454i \(0.405718\pi\)
\(618\) 18241.9i 0.0477632i
\(619\) 478523. 1.24888 0.624441 0.781072i \(-0.285327\pi\)
0.624441 + 0.781072i \(0.285327\pi\)
\(620\) 269037. 0.699888
\(621\) 98566.0 0.255590
\(622\) 95561.9i 0.247004i
\(623\) 875539.i 2.25579i
\(624\) 21903.0i 0.0562515i
\(625\) −4397.54 −0.0112577
\(626\) 135017.i 0.344539i
\(627\) −43590.3 + 25410.1i −0.110880 + 0.0646355i
\(628\) −77635.4 −0.196852
\(629\) 29109.3i 0.0735750i
\(630\) −62027.0 −0.156279
\(631\) −332157. −0.834229 −0.417115 0.908854i \(-0.636959\pi\)
−0.417115 + 0.908854i \(0.636959\pi\)
\(632\) −313742. −0.785487
\(633\) 356879.i 0.890664i
\(634\) 185259.i 0.460893i
\(635\) 33675.2i 0.0835146i
\(636\) −83649.8 −0.206800
\(637\) 188425.i 0.464366i
\(638\) 139046. + 238530.i 0.341600 + 0.586005i
\(639\) −96967.6 −0.237479
\(640\) 259872.i 0.634452i
\(641\) −194677. −0.473803 −0.236902 0.971534i \(-0.576132\pi\)
−0.236902 + 0.971534i \(0.576132\pi\)
\(642\) −72922.8 −0.176927
\(643\) 598433. 1.44742 0.723709 0.690106i \(-0.242436\pi\)
0.723709 + 0.690106i \(0.242436\pi\)
\(644\) 890984.i 2.14832i
\(645\) 152533.i 0.366643i
\(646\) 31835.1i 0.0762854i
\(647\) −789504. −1.88602 −0.943008 0.332769i \(-0.892017\pi\)
−0.943008 + 0.332769i \(0.892017\pi\)
\(648\) 33888.8i 0.0807060i
\(649\) 115509. + 198153.i 0.274238 + 0.470448i
\(650\) −17769.1 −0.0420571
\(651\) 623611.i 1.47147i
\(652\) −333417. −0.784318
\(653\) 704147. 1.65134 0.825671 0.564151i \(-0.190797\pi\)
0.825671 + 0.564151i \(0.190797\pi\)
\(654\) 66077.9 0.154490
\(655\) 237448.i 0.553459i
\(656\) 154103.i 0.358099i
\(657\) 47270.3i 0.109511i
\(658\) −235120. −0.543048
\(659\) 603395.i 1.38941i −0.719294 0.694706i \(-0.755535\pi\)
0.719294 0.694706i \(-0.244465\pi\)
\(660\) −66580.6 114217.i −0.152848 0.262206i
\(661\) 257502. 0.589356 0.294678 0.955597i \(-0.404788\pi\)
0.294678 + 0.955597i \(0.404788\pi\)
\(662\) 172778.i 0.394250i
\(663\) 38553.2 0.0877069
\(664\) −400565. −0.908526
\(665\) −117072. −0.264733
\(666\) 4913.05i 0.0110765i
\(667\) 1.01801e6i 2.28823i
\(668\) 640744.i 1.43592i
\(669\) 8463.96 0.0189113
\(670\) 30687.6i 0.0683619i
\(671\) −394742. + 230107.i −0.876735 + 0.511075i
\(672\) 472371. 1.04603
\(673\) 10491.1i 0.0231629i −0.999933 0.0115814i \(-0.996313\pi\)
0.999933 0.0115814i \(-0.00368656\pi\)
\(674\) −115305. −0.253821
\(675\) 53749.9 0.117970
\(676\) 374422. 0.819347
\(677\) 243377.i 0.531008i −0.964110 0.265504i \(-0.914462\pi\)
0.964110 0.265504i \(-0.0855384\pi\)
\(678\) 135408.i 0.294567i
\(679\) 1.03826e6i 2.25199i
\(680\) 182131. 0.393882
\(681\) 221351.i 0.477296i
\(682\) 210620. 122777.i 0.452826 0.263966i
\(683\) 94210.5 0.201957 0.100978 0.994889i \(-0.467803\pi\)
0.100978 + 0.994889i \(0.467803\pi\)
\(684\) 29294.8i 0.0626149i
\(685\) 161610. 0.344419
\(686\) 590337. 1.25445
\(687\) −168292. −0.356574
\(688\) 270131.i 0.570687i
\(689\) 35069.2i 0.0738732i
\(690\) 89407.7i 0.187792i
\(691\) −49743.2 −0.104178 −0.0520892 0.998642i \(-0.516588\pi\)
−0.0520892 + 0.998642i \(0.516588\pi\)
\(692\) 17931.7i 0.0374464i
\(693\) 264749. 154330.i 0.551273 0.321354i
\(694\) 252362. 0.523968
\(695\) 341906.i 0.707843i
\(696\) −350009. −0.722539
\(697\) 271249. 0.558345
\(698\) −39040.3 −0.0801314
\(699\) 300686.i 0.615402i
\(700\) 485870.i 0.991572i
\(701\) 337972.i 0.687772i 0.939011 + 0.343886i \(0.111743\pi\)
−0.939011 + 0.343886i \(0.888257\pi\)
\(702\) −6506.99 −0.0132040
\(703\) 9273.03i 0.0187634i
\(704\) 46538.7 + 79835.8i 0.0939006 + 0.161084i
\(705\) −128635. −0.258810
\(706\) 221558.i 0.444507i
\(707\) 912895. 1.82634
\(708\) −133168. −0.265665
\(709\) 209306. 0.416379 0.208189 0.978089i \(-0.433243\pi\)
0.208189 + 0.978089i \(0.433243\pi\)
\(710\) 87957.8i 0.174485i
\(711\) 182225.i 0.360470i
\(712\) 433909.i 0.855930i
\(713\) −898894. −1.76819
\(714\) 193353.i 0.379275i
\(715\) −47884.1 + 27913.1i −0.0936655 + 0.0546004i
\(716\) −727693. −1.41946
\(717\) 19529.5i 0.0379886i
\(718\) 22996.8 0.0446086
\(719\) 382242. 0.739403 0.369701 0.929151i \(-0.379460\pi\)
0.369701 + 0.929151i \(0.379460\pi\)
\(720\) 60098.3 0.115930
\(721\) 209115.i 0.402267i
\(722\) 195081.i 0.374231i
\(723\) 277439.i 0.530751i
\(724\) 134679. 0.256935
\(725\) 555138.i 1.05615i
\(726\) −104248. 59032.4i −0.197785 0.112000i
\(727\) −573664. −1.08540 −0.542698 0.839928i \(-0.682597\pi\)
−0.542698 + 0.839928i \(0.682597\pi\)
\(728\) 128428.i 0.242324i
\(729\) 19683.0 0.0370370
\(730\) 42878.2 0.0804619
\(731\) −475481. −0.889812
\(732\) 265286.i 0.495099i
\(733\) 898874.i 1.67298i 0.547982 + 0.836490i \(0.315396\pi\)
−0.547982 + 0.836490i \(0.684604\pi\)
\(734\) 264610.i 0.491150i
\(735\) 517009. 0.957025
\(736\) 680891.i 1.25696i
\(737\) −76354.1 130983.i −0.140572 0.241147i
\(738\) −45781.2 −0.0840572
\(739\) 716712.i 1.31237i −0.754601 0.656184i \(-0.772170\pi\)
0.754601 0.656184i \(-0.227830\pi\)
\(740\) 24297.6 0.0443711
\(741\) −12281.5 −0.0223673
\(742\) −175879. −0.319453
\(743\) 327330.i 0.592937i −0.955043 0.296468i \(-0.904191\pi\)
0.955043 0.296468i \(-0.0958089\pi\)
\(744\) 309056.i 0.558330i
\(745\) 160455.i 0.289094i
\(746\) 283043. 0.508597
\(747\) 232653.i 0.416934i
\(748\) −356042. + 207547.i −0.636352 + 0.370949i
\(749\) 835946. 1.49010
\(750\) 128293.i 0.228077i
\(751\) 473695. 0.839883 0.419941 0.907551i \(-0.362051\pi\)
0.419941 + 0.907551i \(0.362051\pi\)
\(752\) 227809. 0.402842
\(753\) −9650.88 −0.0170207
\(754\) 67205.3i 0.118212i
\(755\) 311952.i 0.547260i
\(756\) 177924.i 0.311308i
\(757\) 168385. 0.293841 0.146920 0.989148i \(-0.453064\pi\)
0.146920 + 0.989148i \(0.453064\pi\)
\(758\) 139245.i 0.242349i
\(759\) 222456. + 381617.i 0.386154 + 0.662436i
\(760\) −58019.5 −0.100449
\(761\) 216244.i 0.373400i 0.982417 + 0.186700i \(0.0597792\pi\)
−0.982417 + 0.186700i \(0.940221\pi\)
\(762\) −17717.3 −0.0305133
\(763\) −757479. −1.30113
\(764\) −743135. −1.27315
\(765\) 105784.i 0.180758i
\(766\) 151107.i 0.257530i
\(767\) 55829.3i 0.0949011i
\(768\) 73230.6 0.124157
\(769\) 356784.i 0.603328i 0.953414 + 0.301664i \(0.0975420\pi\)
−0.953414 + 0.301664i \(0.902458\pi\)
\(770\) −139990. 240149.i −0.236111 0.405042i
\(771\) 6561.53 0.0110382
\(772\) 23292.0i 0.0390816i
\(773\) −91587.2 −0.153277 −0.0766383 0.997059i \(-0.524419\pi\)
−0.0766383 + 0.997059i \(0.524419\pi\)
\(774\) 80251.3 0.133959
\(775\) −490183. −0.816122
\(776\) 514551.i 0.854486i
\(777\) 56320.4i 0.0932875i
\(778\) 186998.i 0.308943i
\(779\) −86408.8 −0.142391
\(780\) 32180.4i 0.0528936i
\(781\) −218849. 375429.i −0.358791 0.615496i
\(782\) −278705. −0.455755
\(783\) 203289.i 0.331582i
\(784\) −915608. −1.48963
\(785\) −89305.7 −0.144924
\(786\) 124927.