Properties

Label 76.5.j.a.21.4
Level $76$
Weight $5$
Character 76.21
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 21.4
Character \(\chi\) \(=\) 76.21
Dual form 76.5.j.a.29.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.91062 - 2.27699i) q^{3} +(-16.1447 + 5.87619i) q^{5} +(23.9804 + 41.5352i) q^{7} +(12.5313 + 71.0685i) q^{9} +O(q^{10})\) \(q+(1.91062 - 2.27699i) q^{3} +(-16.1447 + 5.87619i) q^{5} +(23.9804 + 41.5352i) q^{7} +(12.5313 + 71.0685i) q^{9} +(41.5971 - 72.0483i) q^{11} +(175.663 + 209.347i) q^{13} +(-17.4664 + 47.9885i) q^{15} +(17.7920 - 100.903i) q^{17} +(-229.865 + 278.358i) q^{19} +(140.393 + 24.7550i) q^{21} +(806.737 + 293.628i) q^{23} +(-252.656 + 212.004i) q^{25} +(394.273 + 227.633i) q^{27} +(-753.735 + 132.904i) q^{29} +(-222.015 + 128.180i) q^{31} +(-84.5769 - 232.373i) q^{33} +(-631.225 - 529.661i) q^{35} -2609.10i q^{37} +812.306 q^{39} +(531.864 - 633.851i) q^{41} +(-2421.67 + 881.415i) q^{43} +(-619.926 - 1073.74i) q^{45} +(-100.427 - 569.549i) q^{47} +(50.3825 - 87.2650i) q^{49} +(-195.762 - 233.300i) q^{51} +(1026.07 - 2819.11i) q^{53} +(-248.203 + 1407.63i) q^{55} +(194.634 + 1055.24i) q^{57} +(1565.00 + 275.951i) q^{59} +(-2684.30 - 977.005i) q^{61} +(-2651.34 + 2224.74i) q^{63} +(-4066.19 - 2347.61i) q^{65} +(3116.58 - 549.537i) q^{67} +(2209.96 - 1275.92i) q^{69} +(2711.28 + 7449.18i) q^{71} +(4107.82 + 3446.87i) q^{73} +980.354i q^{75} +3990.06 q^{77} +(3251.34 - 3874.80i) q^{79} +(-4221.21 + 1536.40i) q^{81} +(3648.20 + 6318.86i) q^{83} +(305.681 + 1733.60i) q^{85} +(-1137.48 + 1970.18i) q^{87} +(-2898.35 - 3454.12i) q^{89} +(-4482.81 + 12316.4i) q^{91} +(-132.321 + 750.430i) q^{93} +(2075.41 - 5844.73i) q^{95} +(-1041.93 - 183.720i) q^{97} +(5641.63 + 2053.39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.91062 2.27699i 0.212291 0.252999i −0.649382 0.760462i \(-0.724972\pi\)
0.861673 + 0.507464i \(0.169417\pi\)
\(4\) 0 0
\(5\) −16.1447 + 5.87619i −0.645788 + 0.235048i −0.644088 0.764951i \(-0.722763\pi\)
−0.00169937 + 0.999999i \(0.500541\pi\)
\(6\) 0 0
\(7\) 23.9804 + 41.5352i 0.489396 + 0.847658i 0.999926 0.0122020i \(-0.00388410\pi\)
−0.510530 + 0.859860i \(0.670551\pi\)
\(8\) 0 0
\(9\) 12.5313 + 71.0685i 0.154707 + 0.877389i
\(10\) 0 0
\(11\) 41.5971 72.0483i 0.343778 0.595440i −0.641353 0.767246i \(-0.721627\pi\)
0.985131 + 0.171805i \(0.0549600\pi\)
\(12\) 0 0
\(13\) 175.663 + 209.347i 1.03943 + 1.23874i 0.970496 + 0.241118i \(0.0775139\pi\)
0.0689296 + 0.997622i \(0.478042\pi\)
\(14\) 0 0
\(15\) −17.4664 + 47.9885i −0.0776283 + 0.213282i
\(16\) 0 0
\(17\) 17.7920 100.903i 0.0615640 0.349147i −0.938429 0.345471i \(-0.887719\pi\)
0.999993 0.00367529i \(-0.00116988\pi\)
\(18\) 0 0
\(19\) −229.865 + 278.358i −0.636745 + 0.771075i
\(20\) 0 0
\(21\) 140.393 + 24.7550i 0.318351 + 0.0561338i
\(22\) 0 0
\(23\) 806.737 + 293.628i 1.52502 + 0.555063i 0.962396 0.271649i \(-0.0875691\pi\)
0.562626 + 0.826712i \(0.309791\pi\)
\(24\) 0 0
\(25\) −252.656 + 212.004i −0.404250 + 0.339206i
\(26\) 0 0
\(27\) 394.273 + 227.633i 0.540840 + 0.312254i
\(28\) 0 0
\(29\) −753.735 + 132.904i −0.896237 + 0.158031i −0.602748 0.797932i \(-0.705928\pi\)
−0.293489 + 0.955962i \(0.594816\pi\)
\(30\) 0 0
\(31\) −222.015 + 128.180i −0.231025 + 0.133382i −0.611045 0.791596i \(-0.709250\pi\)
0.380020 + 0.924978i \(0.375917\pi\)
\(32\) 0 0
\(33\) −84.5769 232.373i −0.0776647 0.213382i
\(34\) 0 0
\(35\) −631.225 529.661i −0.515286 0.432376i
\(36\) 0 0
\(37\) 2609.10i 1.90585i −0.303213 0.952923i \(-0.598059\pi\)
0.303213 0.952923i \(-0.401941\pi\)
\(38\) 0 0
\(39\) 812.306 0.534060
\(40\) 0 0
\(41\) 531.864 633.851i 0.316397 0.377068i −0.584283 0.811550i \(-0.698624\pi\)
0.900680 + 0.434482i \(0.143069\pi\)
\(42\) 0 0
\(43\) −2421.67 + 881.415i −1.30972 + 0.476698i −0.900149 0.435582i \(-0.856543\pi\)
−0.409568 + 0.912280i \(0.634321\pi\)
\(44\) 0 0
\(45\) −619.926 1073.74i −0.306136 0.530244i
\(46\) 0 0
\(47\) −100.427 569.549i −0.0454626 0.257831i 0.953602 0.301069i \(-0.0973436\pi\)
−0.999065 + 0.0432384i \(0.986232\pi\)
\(48\) 0 0
\(49\) 50.3825 87.2650i 0.0209840 0.0363453i
\(50\) 0 0
\(51\) −195.762 233.300i −0.0752642 0.0896964i
\(52\) 0 0
\(53\) 1026.07 2819.11i 0.365280 1.00360i −0.611853 0.790971i \(-0.709576\pi\)
0.977133 0.212628i \(-0.0682022\pi\)
\(54\) 0 0
\(55\) −248.203 + 1407.63i −0.0820506 + 0.465332i
\(56\) 0 0
\(57\) 194.634 + 1055.24i 0.0599057 + 0.324788i
\(58\) 0 0
\(59\) 1565.00 + 275.951i 0.449583 + 0.0792735i 0.393855 0.919172i \(-0.371141\pi\)
0.0557273 + 0.998446i \(0.482252\pi\)
\(60\) 0 0
\(61\) −2684.30 977.005i −0.721392 0.262565i −0.0448755 0.998993i \(-0.514289\pi\)
−0.676517 + 0.736427i \(0.736511\pi\)
\(62\) 0 0
\(63\) −2651.34 + 2224.74i −0.668013 + 0.560529i
\(64\) 0 0
\(65\) −4066.19 2347.61i −0.962411 0.555648i
\(66\) 0 0
\(67\) 3116.58 549.537i 0.694270 0.122419i 0.184632 0.982808i \(-0.440891\pi\)
0.509638 + 0.860389i \(0.329779\pi\)
\(68\) 0 0
\(69\) 2209.96 1275.92i 0.464179 0.267994i
\(70\) 0 0
\(71\) 2711.28 + 7449.18i 0.537846 + 1.47772i 0.849534 + 0.527535i \(0.176884\pi\)
−0.311688 + 0.950185i \(0.600894\pi\)
\(72\) 0 0
\(73\) 4107.82 + 3446.87i 0.770843 + 0.646814i 0.940925 0.338616i \(-0.109959\pi\)
−0.170082 + 0.985430i \(0.554403\pi\)
\(74\) 0 0
\(75\) 980.354i 0.174285i
\(76\) 0 0
\(77\) 3990.06 0.672973
\(78\) 0 0
\(79\) 3251.34 3874.80i 0.520965 0.620862i −0.439844 0.898074i \(-0.644966\pi\)
0.960809 + 0.277212i \(0.0894106\pi\)
\(80\) 0 0
\(81\) −4221.21 + 1536.40i −0.643379 + 0.234171i
\(82\) 0 0
\(83\) 3648.20 + 6318.86i 0.529568 + 0.917239i 0.999405 + 0.0344859i \(0.0109794\pi\)
−0.469837 + 0.882753i \(0.655687\pi\)
\(84\) 0 0
\(85\) 305.681 + 1733.60i 0.0423088 + 0.239945i
\(86\) 0 0
\(87\) −1137.48 + 1970.18i −0.150282 + 0.260295i
\(88\) 0 0
\(89\) −2898.35 3454.12i −0.365908 0.436072i 0.551406 0.834237i \(-0.314091\pi\)
−0.917314 + 0.398165i \(0.869647\pi\)
\(90\) 0 0
\(91\) −4482.81 + 12316.4i −0.541337 + 1.48731i
\(92\) 0 0
\(93\) −132.321 + 750.430i −0.0152990 + 0.0867649i
\(94\) 0 0
\(95\) 2075.41 5844.73i 0.229963 0.647616i
\(96\) 0 0
\(97\) −1041.93 183.720i −0.110737 0.0195260i 0.118005 0.993013i \(-0.462350\pi\)
−0.228742 + 0.973487i \(0.573461\pi\)
\(98\) 0 0
\(99\) 5641.63 + 2053.39i 0.575618 + 0.209508i
\(100\) 0 0
\(101\) 11167.0 9370.25i 1.09470 0.918562i 0.0976419 0.995222i \(-0.468870\pi\)
0.997057 + 0.0766599i \(0.0244256\pi\)
\(102\) 0 0
\(103\) 1597.71 + 922.439i 0.150600 + 0.0869487i 0.573406 0.819271i \(-0.305622\pi\)
−0.422807 + 0.906220i \(0.638955\pi\)
\(104\) 0 0
\(105\) −2412.06 + 425.312i −0.218781 + 0.0385770i
\(106\) 0 0
\(107\) −2023.06 + 1168.01i −0.176702 + 0.102019i −0.585742 0.810497i \(-0.699197\pi\)
0.409040 + 0.912516i \(0.365864\pi\)
\(108\) 0 0
\(109\) −640.112 1758.69i −0.0538770 0.148026i 0.909835 0.414970i \(-0.136208\pi\)
−0.963712 + 0.266945i \(0.913986\pi\)
\(110\) 0 0
\(111\) −5940.90 4985.01i −0.482177 0.404594i
\(112\) 0 0
\(113\) 9207.05i 0.721047i −0.932750 0.360524i \(-0.882598\pi\)
0.932750 0.360524i \(-0.117402\pi\)
\(114\) 0 0
\(115\) −14749.9 −1.11531
\(116\) 0 0
\(117\) −12676.7 + 15107.5i −0.926049 + 1.10362i
\(118\) 0 0
\(119\) 4617.71 1680.71i 0.326086 0.118686i
\(120\) 0 0
\(121\) 3859.86 + 6685.48i 0.263634 + 0.456627i
\(122\) 0 0
\(123\) −427.081 2422.10i −0.0282293 0.160096i
\(124\) 0 0
\(125\) 8202.29 14206.8i 0.524947 0.909234i
\(126\) 0 0
\(127\) −9103.92 10849.6i −0.564444 0.672679i 0.406036 0.913857i \(-0.366911\pi\)
−0.970481 + 0.241178i \(0.922466\pi\)
\(128\) 0 0
\(129\) −2619.91 + 7198.16i −0.157437 + 0.432556i
\(130\) 0 0
\(131\) 5497.76 31179.4i 0.320364 1.81687i −0.220066 0.975485i \(-0.570627\pi\)
0.540430 0.841389i \(-0.318262\pi\)
\(132\) 0 0
\(133\) −17073.9 2872.36i −0.965228 0.162381i
\(134\) 0 0
\(135\) −7703.03 1358.25i −0.422663 0.0745268i
\(136\) 0 0
\(137\) 3273.09 + 1191.31i 0.174388 + 0.0634721i 0.427739 0.903902i \(-0.359310\pi\)
−0.253351 + 0.967375i \(0.581533\pi\)
\(138\) 0 0
\(139\) 2046.85 1717.51i 0.105939 0.0888933i −0.588280 0.808658i \(-0.700195\pi\)
0.694219 + 0.719764i \(0.255750\pi\)
\(140\) 0 0
\(141\) −1488.73 859.521i −0.0748822 0.0432333i
\(142\) 0 0
\(143\) 22390.2 3947.99i 1.09493 0.193065i
\(144\) 0 0
\(145\) 11387.9 6574.78i 0.541634 0.312713i
\(146\) 0 0
\(147\) −102.440 281.451i −0.00474060 0.0130247i
\(148\) 0 0
\(149\) −23897.1 20052.1i −1.07640 0.903206i −0.0807817 0.996732i \(-0.525742\pi\)
−0.995617 + 0.0935262i \(0.970186\pi\)
\(150\) 0 0
\(151\) 14183.7i 0.622064i 0.950399 + 0.311032i \(0.100675\pi\)
−0.950399 + 0.311032i \(0.899325\pi\)
\(152\) 0 0
\(153\) 7394.01 0.315862
\(154\) 0 0
\(155\) 2831.15 3374.03i 0.117842 0.140439i
\(156\) 0 0
\(157\) −21837.4 + 7948.17i −0.885935 + 0.322454i −0.744603 0.667508i \(-0.767361\pi\)
−0.141333 + 0.989962i \(0.545139\pi\)
\(158\) 0 0
\(159\) −4458.65 7722.60i −0.176364 0.305471i
\(160\) 0 0
\(161\) 7149.94 + 40549.3i 0.275836 + 1.56434i
\(162\) 0 0
\(163\) −2603.27 + 4509.00i −0.0979816 + 0.169709i −0.910849 0.412740i \(-0.864572\pi\)
0.812867 + 0.582449i \(0.197905\pi\)
\(164\) 0 0
\(165\) 2730.94 + 3254.60i 0.100310 + 0.119545i
\(166\) 0 0
\(167\) 604.919 1662.00i 0.0216902 0.0595935i −0.928375 0.371645i \(-0.878794\pi\)
0.950065 + 0.312051i \(0.101016\pi\)
\(168\) 0 0
\(169\) −8009.10 + 45421.9i −0.280421 + 1.59035i
\(170\) 0 0
\(171\) −22663.0 12848.0i −0.775042 0.439382i
\(172\) 0 0
\(173\) 50539.7 + 8911.52i 1.68865 + 0.297755i 0.933709 0.358032i \(-0.116552\pi\)
0.754945 + 0.655788i \(0.227663\pi\)
\(174\) 0 0
\(175\) −14864.4 5410.20i −0.485369 0.176660i
\(176\) 0 0
\(177\) 3618.45 3036.24i 0.115498 0.0969147i
\(178\) 0 0
\(179\) 38729.9 + 22360.7i 1.20876 + 0.697878i 0.962488 0.271323i \(-0.0874611\pi\)
0.246272 + 0.969201i \(0.420794\pi\)
\(180\) 0 0
\(181\) 51296.0 9044.86i 1.56576 0.276086i 0.677536 0.735490i \(-0.263048\pi\)
0.888228 + 0.459404i \(0.151937\pi\)
\(182\) 0 0
\(183\) −7353.31 + 4245.43i −0.219574 + 0.126771i
\(184\) 0 0
\(185\) 15331.6 + 42123.2i 0.447964 + 1.23077i
\(186\) 0 0
\(187\) −6529.82 5479.17i −0.186732 0.156687i
\(188\) 0 0
\(189\) 21834.9i 0.611264i
\(190\) 0 0
\(191\) 6618.27 0.181417 0.0907085 0.995877i \(-0.471087\pi\)
0.0907085 + 0.995877i \(0.471087\pi\)
\(192\) 0 0
\(193\) −7735.31 + 9218.58i −0.207665 + 0.247485i −0.859816 0.510603i \(-0.829422\pi\)
0.652152 + 0.758089i \(0.273867\pi\)
\(194\) 0 0
\(195\) −13114.4 + 4773.26i −0.344890 + 0.125530i
\(196\) 0 0
\(197\) −29311.6 50769.2i −0.755279 1.30818i −0.945235 0.326390i \(-0.894168\pi\)
0.189956 0.981793i \(-0.439166\pi\)
\(198\) 0 0
\(199\) −5197.71 29477.7i −0.131252 0.744367i −0.977397 0.211414i \(-0.932193\pi\)
0.846145 0.532953i \(-0.178918\pi\)
\(200\) 0 0
\(201\) 4703.31 8146.37i 0.116416 0.201638i
\(202\) 0 0
\(203\) −23595.1 28119.5i −0.572570 0.682363i
\(204\) 0 0
\(205\) −4862.16 + 13358.7i −0.115697 + 0.317874i
\(206\) 0 0
\(207\) −10758.3 + 61013.1i −0.251074 + 1.42391i
\(208\) 0 0
\(209\) 10493.5 + 28140.3i 0.240231 + 0.644222i
\(210\) 0 0
\(211\) 6244.72 + 1101.11i 0.140265 + 0.0247324i 0.243340 0.969941i \(-0.421757\pi\)
−0.103075 + 0.994674i \(0.532868\pi\)
\(212\) 0 0
\(213\) 22141.9 + 8059.00i 0.488041 + 0.177632i
\(214\) 0 0
\(215\) 33917.7 28460.3i 0.733753 0.615692i
\(216\) 0 0
\(217\) −10648.0 6147.63i −0.226125 0.130553i
\(218\) 0 0
\(219\) 15697.0 2767.80i 0.327286 0.0577094i
\(220\) 0 0
\(221\) 24249.2 14000.3i 0.496493 0.286650i
\(222\) 0 0
\(223\) 24788.8 + 68106.5i 0.498477 + 1.36955i 0.892747 + 0.450559i \(0.148775\pi\)
−0.394270 + 0.918995i \(0.629002\pi\)
\(224\) 0 0
\(225\) −18232.9 15299.2i −0.360156 0.302207i
\(226\) 0 0
\(227\) 75365.9i 1.46259i −0.682060 0.731296i \(-0.738916\pi\)
0.682060 0.731296i \(-0.261084\pi\)
\(228\) 0 0
\(229\) −38436.8 −0.732954 −0.366477 0.930427i \(-0.619436\pi\)
−0.366477 + 0.930427i \(0.619436\pi\)
\(230\) 0 0
\(231\) 7623.48 9085.32i 0.142866 0.170261i
\(232\) 0 0
\(233\) −85629.6 + 31166.6i −1.57729 + 0.574088i −0.974613 0.223896i \(-0.928123\pi\)
−0.602680 + 0.797983i \(0.705900\pi\)
\(234\) 0 0
\(235\) 4968.14 + 8605.06i 0.0899617 + 0.155818i
\(236\) 0 0
\(237\) −2610.79 14806.5i −0.0464810 0.263607i
\(238\) 0 0
\(239\) 49671.9 86034.2i 0.869590 1.50617i 0.00717402 0.999974i \(-0.497716\pi\)
0.862416 0.506200i \(-0.168950\pi\)
\(240\) 0 0
\(241\) −24084.6 28702.9i −0.414673 0.494188i 0.517763 0.855524i \(-0.326765\pi\)
−0.932436 + 0.361336i \(0.882321\pi\)
\(242\) 0 0
\(243\) −17179.3 + 47199.8i −0.290933 + 0.799333i
\(244\) 0 0
\(245\) −300.624 + 1704.92i −0.00500832 + 0.0284036i
\(246\) 0 0
\(247\) −98652.1 + 775.704i −1.61701 + 0.0127146i
\(248\) 0 0
\(249\) 21358.3 + 3766.04i 0.344483 + 0.0607416i
\(250\) 0 0
\(251\) −61034.8 22214.8i −0.968791 0.352611i −0.191318 0.981528i \(-0.561276\pi\)
−0.777472 + 0.628917i \(0.783498\pi\)
\(252\) 0 0
\(253\) 54713.3 45909.9i 0.854775 0.717242i
\(254\) 0 0
\(255\) 4531.44 + 2616.23i 0.0696876 + 0.0402342i
\(256\) 0 0
\(257\) −68176.2 + 12021.3i −1.03221 + 0.182006i −0.663995 0.747737i \(-0.731141\pi\)
−0.368211 + 0.929742i \(0.620029\pi\)
\(258\) 0 0
\(259\) 108370. 62567.3i 1.61551 0.932713i
\(260\) 0 0
\(261\) −18890.6 51901.4i −0.277309 0.761900i
\(262\) 0 0
\(263\) −56282.2 47226.4i −0.813691 0.682768i 0.137794 0.990461i \(-0.455999\pi\)
−0.951486 + 0.307693i \(0.900443\pi\)
\(264\) 0 0
\(265\) 51543.1i 0.733970i
\(266\) 0 0
\(267\) −13402.7 −0.188004
\(268\) 0 0
\(269\) 38463.9 45839.5i 0.531555 0.633483i −0.431717 0.902009i \(-0.642092\pi\)
0.963272 + 0.268526i \(0.0865365\pi\)
\(270\) 0 0
\(271\) −40217.6 + 14638.0i −0.547618 + 0.199317i −0.600988 0.799258i \(-0.705226\pi\)
0.0533699 + 0.998575i \(0.483004\pi\)
\(272\) 0 0
\(273\) 19479.4 + 33739.3i 0.261367 + 0.452700i
\(274\) 0 0
\(275\) 4764.74 + 27022.2i 0.0630048 + 0.357318i
\(276\) 0 0
\(277\) 57528.5 99642.3i 0.749762 1.29863i −0.198174 0.980167i \(-0.563501\pi\)
0.947936 0.318459i \(-0.103165\pi\)
\(278\) 0 0
\(279\) −11891.7 14172.0i −0.152769 0.182063i
\(280\) 0 0
\(281\) −41424.5 + 113813.i −0.524619 + 1.44138i 0.340706 + 0.940170i \(0.389334\pi\)
−0.865326 + 0.501210i \(0.832888\pi\)
\(282\) 0 0
\(283\) 1875.66 10637.4i 0.0234197 0.132820i −0.970856 0.239663i \(-0.922963\pi\)
0.994276 + 0.106843i \(0.0340743\pi\)
\(284\) 0 0
\(285\) −9343.07 15892.8i −0.115027 0.195663i
\(286\) 0 0
\(287\) 39081.4 + 6891.11i 0.474468 + 0.0836615i
\(288\) 0 0
\(289\) 68619.1 + 24975.3i 0.821579 + 0.299030i
\(290\) 0 0
\(291\) −2409.06 + 2021.44i −0.0284486 + 0.0238712i
\(292\) 0 0
\(293\) −12787.0 7382.59i −0.148948 0.0859950i 0.423674 0.905815i \(-0.360740\pi\)
−0.572622 + 0.819820i \(0.694074\pi\)
\(294\) 0 0
\(295\) −26887.9 + 4741.07i −0.308968 + 0.0544794i
\(296\) 0 0
\(297\) 32801.2 18937.8i 0.371858 0.214692i
\(298\) 0 0
\(299\) 80243.6 + 220467.i 0.897569 + 2.46605i
\(300\) 0 0
\(301\) −94682.3 79447.9i −1.04505 0.876898i
\(302\) 0 0
\(303\) 43330.2i 0.471960i
\(304\) 0 0
\(305\) 49078.3 0.527582
\(306\) 0 0
\(307\) −64298.3 + 76627.7i −0.682217 + 0.813035i −0.990391 0.138295i \(-0.955838\pi\)
0.308174 + 0.951330i \(0.400282\pi\)
\(308\) 0 0
\(309\) 5153.00 1875.54i 0.0539689 0.0196431i
\(310\) 0 0
\(311\) 76935.4 + 133256.i 0.795437 + 1.37774i 0.922561 + 0.385850i \(0.126092\pi\)
−0.127125 + 0.991887i \(0.540575\pi\)
\(312\) 0 0
\(313\) −3330.62 18888.9i −0.0339967 0.192805i 0.963080 0.269217i \(-0.0867648\pi\)
−0.997076 + 0.0764118i \(0.975654\pi\)
\(314\) 0 0
\(315\) 29732.1 51497.5i 0.299643 0.518998i
\(316\) 0 0
\(317\) −82830.1 98713.1i −0.824270 0.982327i 0.175728 0.984439i \(-0.443772\pi\)
−0.999998 + 0.00211182i \(0.999328\pi\)
\(318\) 0 0
\(319\) −21777.7 + 59833.8i −0.214008 + 0.587983i
\(320\) 0 0
\(321\) −1205.74 + 6838.11i −0.0117016 + 0.0663630i
\(322\) 0 0
\(323\) 23997.5 + 28146.7i 0.230018 + 0.269788i
\(324\) 0 0
\(325\) −88764.6 15651.6i −0.840375 0.148181i
\(326\) 0 0
\(327\) −5227.54 1902.67i −0.0488879 0.0177938i
\(328\) 0 0
\(329\) 21248.1 17829.2i 0.196303 0.164718i
\(330\) 0 0
\(331\) 161743. + 93382.2i 1.47628 + 0.852331i 0.999642 0.0267690i \(-0.00852186\pi\)
0.476638 + 0.879100i \(0.341855\pi\)
\(332\) 0 0
\(333\) 185425. 32695.4i 1.67217 0.294848i
\(334\) 0 0
\(335\) −47087.0 + 27185.7i −0.419577 + 0.242243i
\(336\) 0 0
\(337\) 73164.0 + 201016.i 0.644225 + 1.76999i 0.638028 + 0.770013i \(0.279750\pi\)
0.00619703 + 0.999981i \(0.498027\pi\)
\(338\) 0 0
\(339\) −20964.4 17591.2i −0.182424 0.153072i
\(340\) 0 0
\(341\) 21327.7i 0.183415i
\(342\) 0 0
\(343\) 119987. 1.01987
\(344\) 0 0
\(345\) −28181.5 + 33585.4i −0.236770 + 0.282171i
\(346\) 0 0
\(347\) −159826. + 58172.0i −1.32736 + 0.483120i −0.905810 0.423685i \(-0.860736\pi\)
−0.421551 + 0.906805i \(0.638514\pi\)
\(348\) 0 0
\(349\) −24175.3 41872.8i −0.198482 0.343780i 0.749555 0.661942i \(-0.230268\pi\)
−0.948036 + 0.318162i \(0.896934\pi\)
\(350\) 0 0
\(351\) 21604.7 + 122527.i 0.175362 + 0.994525i
\(352\) 0 0
\(353\) 26418.5 45758.2i 0.212011 0.367214i −0.740333 0.672241i \(-0.765332\pi\)
0.952344 + 0.305027i \(0.0986654\pi\)
\(354\) 0 0
\(355\) −87545.6 104333.i −0.694669 0.827874i
\(356\) 0 0
\(357\) 4995.73 13725.7i 0.0391979 0.107695i
\(358\) 0 0
\(359\) −25426.8 + 144202.i −0.197289 + 1.11888i 0.711832 + 0.702349i \(0.247866\pi\)
−0.909121 + 0.416531i \(0.863246\pi\)
\(360\) 0 0
\(361\) −24645.4 127969.i −0.189113 0.981955i
\(362\) 0 0
\(363\) 22597.5 + 3984.55i 0.171493 + 0.0302389i
\(364\) 0 0
\(365\) −86574.0 31510.4i −0.649833 0.236520i
\(366\) 0 0
\(367\) 14232.8 11942.7i 0.105672 0.0886689i −0.588421 0.808555i \(-0.700250\pi\)
0.694093 + 0.719886i \(0.255806\pi\)
\(368\) 0 0
\(369\) 51711.8 + 29855.8i 0.379784 + 0.219268i
\(370\) 0 0
\(371\) 141698. 24985.2i 1.02948 0.181524i
\(372\) 0 0
\(373\) 89208.0 51504.2i 0.641189 0.370191i −0.143884 0.989595i \(-0.545959\pi\)
0.785072 + 0.619404i \(0.212626\pi\)
\(374\) 0 0
\(375\) −16677.2 45820.3i −0.118594 0.325833i
\(376\) 0 0
\(377\) −160226. 134446.i −1.12733 0.945943i
\(378\) 0 0
\(379\) 22793.2i 0.158682i 0.996848 + 0.0793408i \(0.0252815\pi\)
−0.996848 + 0.0793408i \(0.974718\pi\)
\(380\) 0 0
\(381\) −42098.6 −0.290013
\(382\) 0 0
\(383\) 77114.8 91901.8i 0.525702 0.626508i −0.436217 0.899842i \(-0.643682\pi\)
0.961919 + 0.273334i \(0.0881264\pi\)
\(384\) 0 0
\(385\) −64418.3 + 23446.3i −0.434598 + 0.158181i
\(386\) 0 0
\(387\) −92987.4 161059.i −0.620872 1.07538i
\(388\) 0 0
\(389\) 25924.3 + 147024.i 0.171320 + 0.971604i 0.942306 + 0.334752i \(0.108653\pi\)
−0.770986 + 0.636852i \(0.780236\pi\)
\(390\) 0 0
\(391\) 43981.5 76178.2i 0.287685 0.498285i
\(392\) 0 0
\(393\) −60490.9 72090.3i −0.391656 0.466758i
\(394\) 0 0
\(395\) −29722.9 + 81663.0i −0.190501 + 0.523397i
\(396\) 0 0
\(397\) 17085.6 96897.4i 0.108405 0.614796i −0.881400 0.472370i \(-0.843399\pi\)
0.989805 0.142426i \(-0.0454902\pi\)
\(398\) 0 0
\(399\) −39162.1 + 33389.1i −0.245991 + 0.209729i
\(400\) 0 0
\(401\) −137641. 24269.8i −0.855970 0.150931i −0.271592 0.962412i \(-0.587550\pi\)
−0.584378 + 0.811482i \(0.698661\pi\)
\(402\) 0 0
\(403\) −65834.0 23961.6i −0.405359 0.147539i
\(404\) 0 0
\(405\) 59122.0 49609.3i 0.360445 0.302449i
\(406\) 0 0
\(407\) −187981. 108531.i −1.13482 0.655187i
\(408\) 0 0
\(409\) 216667. 38204.3i 1.29523 0.228384i 0.516794 0.856110i \(-0.327125\pi\)
0.778434 + 0.627726i \(0.216014\pi\)
\(410\) 0 0
\(411\) 8966.22 5176.65i 0.0530794 0.0306454i
\(412\) 0 0
\(413\) 26067.5 + 71619.9i 0.152827 + 0.419888i
\(414\) 0 0
\(415\) −96029.8 80578.6i −0.557584 0.467868i
\(416\) 0 0
\(417\) 7942.15i 0.0456737i
\(418\) 0 0
\(419\) −1845.34 −0.0105111 −0.00525554 0.999986i \(-0.501673\pi\)
−0.00525554 + 0.999986i \(0.501673\pi\)
\(420\) 0 0
\(421\) 86.2612 102.802i 0.000486689 0.000580013i −0.765801 0.643078i \(-0.777657\pi\)
0.766288 + 0.642498i \(0.222102\pi\)
\(422\) 0 0
\(423\) 39218.5 14274.4i 0.219185 0.0797767i
\(424\) 0 0
\(425\) 16896.6 + 29265.8i 0.0935454 + 0.162025i
\(426\) 0 0
\(427\) −23790.4 134922.i −0.130481 0.739992i
\(428\) 0 0
\(429\) 33789.6 58525.2i 0.183598 0.318001i
\(430\) 0 0
\(431\) −59624.7 71057.9i −0.320975 0.382523i 0.581296 0.813692i \(-0.302546\pi\)
−0.902271 + 0.431169i \(0.858101\pi\)
\(432\) 0 0
\(433\) −44616.5 + 122583.i −0.237969 + 0.653813i 0.762012 + 0.647563i \(0.224212\pi\)
−0.999980 + 0.00625025i \(0.998010\pi\)
\(434\) 0 0
\(435\) 6787.17 38491.9i 0.0358682 0.203419i
\(436\) 0 0
\(437\) −267174. + 157067.i −1.39904 + 0.822473i
\(438\) 0 0
\(439\) 365653. + 64474.5i 1.89732 + 0.334549i 0.995275 0.0970952i \(-0.0309551\pi\)
0.902044 + 0.431644i \(0.142066\pi\)
\(440\) 0 0
\(441\) 6833.15 + 2487.06i 0.0351353 + 0.0127882i
\(442\) 0 0
\(443\) −156372. + 131211.i −0.796802 + 0.668596i −0.947419 0.319996i \(-0.896318\pi\)
0.150617 + 0.988592i \(0.451874\pi\)
\(444\) 0 0
\(445\) 67090.1 + 38734.5i 0.338796 + 0.195604i
\(446\) 0 0
\(447\) −91316.7 + 16101.6i −0.457020 + 0.0805849i
\(448\) 0 0
\(449\) 49892.5 28805.4i 0.247481 0.142883i −0.371129 0.928581i \(-0.621029\pi\)
0.618610 + 0.785698i \(0.287696\pi\)
\(450\) 0 0
\(451\) −23543.9 64686.2i −0.115751 0.318023i
\(452\) 0 0
\(453\) 32296.1 + 27099.6i 0.157381 + 0.132059i
\(454\) 0 0
\(455\) 225187.i 1.08773i
\(456\) 0 0
\(457\) −306928. −1.46962 −0.734808 0.678275i \(-0.762728\pi\)
−0.734808 + 0.678275i \(0.762728\pi\)
\(458\) 0 0
\(459\) 29983.9 35733.4i 0.142319 0.169609i
\(460\) 0 0
\(461\) −115079. + 41885.4i −0.541495 + 0.197088i −0.598264 0.801299i \(-0.704142\pi\)
0.0567687 + 0.998387i \(0.481920\pi\)
\(462\) 0 0
\(463\) 42930.7 + 74358.2i 0.200266 + 0.346870i 0.948614 0.316436i \(-0.102486\pi\)
−0.748348 + 0.663306i \(0.769153\pi\)
\(464\) 0 0
\(465\) −2273.38 12893.0i −0.0105140 0.0596277i
\(466\) 0 0
\(467\) 40903.8 70847.4i 0.187555 0.324856i −0.756879 0.653555i \(-0.773277\pi\)
0.944435 + 0.328699i \(0.106610\pi\)
\(468\) 0 0
\(469\) 97561.9 + 116270.i 0.443542 + 0.528592i
\(470\) 0 0
\(471\) −23625.1 + 64909.5i −0.106496 + 0.292595i
\(472\) 0 0
\(473\) −37229.9 + 211141.i −0.166406 + 0.943737i
\(474\) 0 0
\(475\) −936.180 119061.i −0.00414927 0.527694i
\(476\) 0 0
\(477\) 213208. + 37594.3i 0.937058 + 0.165229i
\(478\) 0 0
\(479\) 323177. + 117627.i 1.40854 + 0.512667i 0.930701 0.365780i \(-0.119198\pi\)
0.477839 + 0.878447i \(0.341420\pi\)
\(480\) 0 0
\(481\) 546208. 458323.i 2.36085 1.98098i
\(482\) 0 0
\(483\) 105991. + 61194.0i 0.454334 + 0.262310i
\(484\) 0 0
\(485\) 17901.2 3156.46i 0.0761024 0.0134189i
\(486\) 0 0
\(487\) 11216.3 6475.72i 0.0472923 0.0273042i −0.476167 0.879355i \(-0.657974\pi\)
0.523460 + 0.852050i \(0.324641\pi\)
\(488\) 0 0
\(489\) 5293.08 + 14542.6i 0.0221356 + 0.0608170i
\(490\) 0 0
\(491\) 19005.8 + 15947.7i 0.0788356 + 0.0661509i 0.681354 0.731954i \(-0.261391\pi\)
−0.602518 + 0.798105i \(0.705836\pi\)
\(492\) 0 0
\(493\) 78419.1i 0.322647i
\(494\) 0 0
\(495\) −103148. −0.420971
\(496\) 0 0
\(497\) −244386. + 291248.i −0.989381 + 1.17910i
\(498\) 0 0
\(499\) −178513. + 64973.3i −0.716916 + 0.260936i −0.674616 0.738169i \(-0.735691\pi\)
−0.0422999 + 0.999105i \(0.513469\pi\)
\(500\) 0 0
\(501\) −2628.59 4552.85i −0.0104724 0.0181388i
\(502\) 0 0
\(503\) −2082.98 11813.1i −0.00823281 0.0466906i 0.980415 0.196945i \(-0.0631019\pi\)
−0.988647 + 0.150254i \(0.951991\pi\)
\(504\) 0 0
\(505\) −125227. + 216899.i −0.491038 + 0.850502i
\(506\) 0 0
\(507\) 88122.7 + 105021.i 0.342825 + 0.408563i
\(508\) 0 0
\(509\) −18369.4 + 50469.5i −0.0709021 + 0.194802i −0.970082 0.242777i \(-0.921942\pi\)
0.899180 + 0.437579i \(0.144164\pi\)
\(510\) 0 0
\(511\) −44659.5 + 253277.i −0.171030 + 0.969959i
\(512\) 0 0
\(513\) −153993. + 57424.1i −0.585149 + 0.218202i
\(514\) 0 0
\(515\) −31215.0 5504.04i −0.117692 0.0207524i
\(516\) 0 0
\(517\) −45212.5 16456.0i −0.169152 0.0615663i
\(518\) 0 0
\(519\) 116854. 98051.9i 0.433818 0.364017i
\(520\) 0 0
\(521\) 252445. + 145749.i 0.930018 + 0.536946i 0.886817 0.462121i \(-0.152911\pi\)
0.0432004 + 0.999066i \(0.486245\pi\)
\(522\) 0 0
\(523\) −320281. + 56474.2i −1.17092 + 0.206465i −0.725092 0.688652i \(-0.758203\pi\)
−0.445830 + 0.895117i \(0.647092\pi\)
\(524\) 0 0
\(525\) −40719.2 + 23509.3i −0.147734 + 0.0852944i
\(526\) 0 0
\(527\) 8983.75 + 24682.7i 0.0323472 + 0.0888731i
\(528\) 0 0
\(529\) 350236. + 293883.i 1.25155 + 1.05018i
\(530\) 0 0
\(531\) 114680.i 0.406723i
\(532\) 0 0
\(533\) 226123. 0.795960
\(534\) 0 0
\(535\) 25798.2 30745.1i 0.0901326 0.107416i
\(536\) 0 0
\(537\) 124913. 45464.7i 0.433171 0.157661i
\(538\) 0 0
\(539\) −4191.53 7259.95i −0.0144276 0.0249894i
\(540\) 0 0
\(541\) −3332.67 18900.5i −0.0113867 0.0645772i 0.978585 0.205843i \(-0.0659938\pi\)
−0.989972 + 0.141266i \(0.954883\pi\)
\(542\) 0 0
\(543\) 77412.1 134082.i 0.262548 0.454747i
\(544\) 0 0
\(545\) 20668.8 + 24632.2i 0.0695862 + 0.0829296i
\(546\) 0 0
\(547\) 47200.9 129684.i 0.157752 0.433421i −0.835486 0.549511i \(-0.814814\pi\)
0.993239 + 0.116090i \(0.0370361\pi\)
\(548\) 0 0
\(549\) 35796.6 203012.i 0.118767 0.673562i
\(550\) 0 0
\(551\) 136262. 240358.i 0.448820 0.791691i
\(552\) 0 0
\(553\) 238909. + 42126.1i 0.781237 + 0.137753i
\(554\) 0 0
\(555\) 125207. + 45571.6i 0.406483 + 0.147948i
\(556\) 0 0
\(557\) −432127. + 362598.i −1.39284 + 1.16873i −0.428665 + 0.903464i \(0.641016\pi\)
−0.964175 + 0.265268i \(0.914540\pi\)
\(558\) 0 0
\(559\) −609919. 352137.i −1.95186 1.12691i
\(560\) 0 0
\(561\) −24952.0 + 4399.72i −0.0792830 + 0.0139797i
\(562\) 0 0
\(563\) 303151. 175025.i 0.956407 0.552182i 0.0613417 0.998117i \(-0.480462\pi\)
0.895065 + 0.445935i \(0.147129\pi\)
\(564\) 0 0
\(565\) 54102.4 + 148645.i 0.169480 + 0.465644i
\(566\) 0 0
\(567\) −165041. 138486.i −0.513364 0.430763i
\(568\) 0 0
\(569\) 21199.4i 0.0654786i 0.999464 + 0.0327393i \(0.0104231\pi\)
−0.999464 + 0.0327393i \(0.989577\pi\)
\(570\) 0 0
\(571\) 10357.8 0.0317682 0.0158841 0.999874i \(-0.494944\pi\)
0.0158841 + 0.999874i \(0.494944\pi\)
\(572\) 0 0
\(573\) 12645.0 15069.7i 0.0385132 0.0458983i
\(574\) 0 0
\(575\) −266077. + 96844.2i −0.804770 + 0.292912i
\(576\) 0 0
\(577\) −196044. 339559.i −0.588847 1.01991i −0.994384 0.105834i \(-0.966249\pi\)
0.405537 0.914079i \(-0.367085\pi\)
\(578\) 0 0
\(579\) 6211.37 + 35226.4i 0.0185281 + 0.105078i
\(580\) 0 0
\(581\) −174970. + 303057.i −0.518337 + 0.897786i
\(582\) 0 0
\(583\) −160430. 191194.i −0.472008 0.562518i
\(584\) 0 0
\(585\) 115887. 318396.i 0.338628 0.930372i
\(586\) 0 0
\(587\) 78897.2 447448.i 0.228973 1.29857i −0.625968 0.779849i \(-0.715296\pi\)
0.854942 0.518724i \(-0.173593\pi\)
\(588\) 0 0
\(589\) 15353.4 91263.8i 0.0442561 0.263068i
\(590\) 0 0
\(591\) −171604. 30258.5i −0.491308 0.0866308i
\(592\) 0 0
\(593\) −276794. 100745.i −0.787132 0.286493i −0.0829890 0.996550i \(-0.526447\pi\)
−0.704144 + 0.710058i \(0.748669\pi\)
\(594\) 0 0
\(595\) −64675.3 + 54269.0i −0.182686 + 0.153292i
\(596\) 0 0
\(597\) −77051.2 44485.5i −0.216188 0.124816i
\(598\) 0 0
\(599\) 440740. 77714.4i 1.22837 0.216595i 0.478445 0.878118i \(-0.341201\pi\)
0.749925 + 0.661523i \(0.230090\pi\)
\(600\) 0 0
\(601\) −135466. + 78211.5i −0.375044 + 0.216532i −0.675660 0.737214i \(-0.736141\pi\)
0.300616 + 0.953745i \(0.402808\pi\)
\(602\) 0 0
\(603\) 78109.5 + 214604.i 0.214817 + 0.590206i
\(604\) 0 0
\(605\) −101601. 85253.7i −0.277581 0.232918i
\(606\) 0 0
\(607\) 239177.i 0.649144i 0.945861 + 0.324572i \(0.105220\pi\)
−0.945861 + 0.324572i \(0.894780\pi\)
\(608\) 0 0
\(609\) −109109. −0.294189
\(610\) 0 0
\(611\) 101592. 121073.i 0.272130 0.324312i
\(612\) 0 0
\(613\) 269735. 98175.6i 0.717822 0.261266i 0.0428211 0.999083i \(-0.486365\pi\)
0.675001 + 0.737817i \(0.264143\pi\)
\(614\) 0 0
\(615\) 21127.8 + 36594.4i 0.0558604 + 0.0967530i
\(616\) 0 0
\(617\) −92784.5 526207.i −0.243728 1.38225i −0.823429 0.567419i \(-0.807942\pi\)
0.579701 0.814829i \(-0.303169\pi\)
\(618\) 0 0
\(619\) 54937.5 95154.5i 0.143380 0.248341i −0.785388 0.619004i \(-0.787536\pi\)
0.928767 + 0.370664i \(0.120870\pi\)
\(620\) 0 0
\(621\) 251235. + 299410.i 0.651473 + 0.776395i
\(622\) 0 0
\(623\) 73964.2 203215.i 0.190566 0.523576i
\(624\) 0 0
\(625\) −13146.4 + 74557.1i −0.0336549 + 0.190866i
\(626\) 0 0
\(627\) 84124.1 + 29871.7i 0.213986 + 0.0759845i
\(628\) 0 0
\(629\) −263267. 46421.1i −0.665420 0.117331i
\(630\) 0 0
\(631\) −535576. 194934.i −1.34512 0.489585i −0.433702 0.901056i \(-0.642793\pi\)
−0.911423 + 0.411471i \(0.865015\pi\)
\(632\) 0 0
\(633\) 14438.5 12115.4i 0.0360342 0.0302363i
\(634\) 0 0
\(635\) 210735. + 121668.i 0.522623 + 0.301736i
\(636\) 0 0
\(637\) 27119.0 4781.81i 0.0668336 0.0117846i
\(638\) 0 0
\(639\) −495426. + 286035.i −1.21333 + 0.700514i
\(640\) 0 0
\(641\) −279930. 769102.i −0.681293 1.87184i −0.424785 0.905294i \(-0.639650\pi\)
−0.256507 0.966542i \(-0.582572\pi\)
\(642\) 0 0
\(643\) 140685. + 118049.i 0.340272 + 0.285522i 0.796870 0.604151i \(-0.206488\pi\)
−0.456597 + 0.889673i \(0.650932\pi\)
\(644\) 0 0
\(645\) 131607.i 0.316344i
\(646\) 0 0
\(647\) 554623. 1.32492 0.662459 0.749098i \(-0.269513\pi\)
0.662459 + 0.749098i \(0.269513\pi\)
\(648\) 0 0
\(649\) 84981.1 101277.i 0.201759 0.240447i
\(650\) 0 0
\(651\) −34342.4 + 12499.6i −0.0810342 + 0.0294940i
\(652\) 0 0
\(653\) 117261. + 203101.i 0.274995 + 0.476306i 0.970134 0.242570i \(-0.0779903\pi\)
−0.695139 + 0.718876i \(0.744657\pi\)
\(654\) 0 0
\(655\) 94456.1 + 535687.i 0.220165 + 1.24862i
\(656\) 0 0
\(657\) −193488. + 335131.i −0.448252 + 0.776396i
\(658\) 0 0
\(659\) −104774. 124864.i −0.241257 0.287519i 0.631805 0.775127i \(-0.282314\pi\)
−0.873063 + 0.487608i \(0.837870\pi\)
\(660\) 0 0
\(661\) −51551.4 + 141636.i −0.117988 + 0.324169i −0.984602 0.174809i \(-0.944069\pi\)
0.866614 + 0.498979i \(0.166291\pi\)
\(662\) 0 0
\(663\) 14452.5 81964.4i 0.0328789 0.186465i
\(664\) 0 0
\(665\) 292532. 53956.2i 0.661500 0.122011i
\(666\) 0 0
\(667\) −647090. 114099.i −1.45450 0.256467i
\(668\) 0 0
\(669\) 202440. + 73682.0i 0.452318 + 0.164630i
\(670\) 0 0
\(671\) −182051. + 152759.i −0.404341 + 0.339282i
\(672\) 0 0
\(673\) −109990. 63502.7i −0.242841 0.140205i 0.373641 0.927574i \(-0.378109\pi\)
−0.616482 + 0.787369i \(0.711443\pi\)
\(674\) 0 0
\(675\) −147875. + 26074.3i −0.324553 + 0.0572275i
\(676\) 0 0
\(677\) −23991.9 + 13851.8i −0.0523465 + 0.0302223i −0.525945 0.850519i \(-0.676288\pi\)
0.473598 + 0.880741i \(0.342955\pi\)
\(678\) 0 0
\(679\) −17355.0 47682.4i −0.0376431 0.103423i
\(680\) 0 0
\(681\) −171607. 143996.i −0.370034 0.310495i
\(682\) 0 0
\(683\) 597143.i 1.28008i −0.768342 0.640040i \(-0.778918\pi\)
0.768342 0.640040i \(-0.221082\pi\)
\(684\) 0 0
\(685\) −59843.4 −0.127537
\(686\) 0 0
\(687\) −73438.2 + 87520.2i −0.155600 + 0.185436i
\(688\) 0 0
\(689\) 770415. 280408.i 1.62288 0.590680i
\(690\) 0 0
\(691\) 388563. + 673011.i 0.813777 + 1.40950i 0.910202 + 0.414164i \(0.135926\pi\)
−0.0964250 + 0.995340i \(0.530741\pi\)
\(692\) 0 0
\(693\) 50000.6 + 283567.i 0.104114 + 0.590459i
\(694\) 0 0
\(695\) −22953.3 + 39756.3i −0.0475199 + 0.0823069i
\(696\) 0 0
\(697\) −54494.8 64944.4i −0.112173 0.133683i
\(698\) 0 0
\(699\) −92639.6 + 254525.i −0.189602 + 0.520927i
\(700\) 0 0
\(701\) −20302.7 + 115143.i −0.0413160 + 0.234315i −0.998472 0.0552576i \(-0.982402\pi\)
0.957156 + 0.289572i \(0.0935131\pi\)
\(702\) 0 0
\(703\) 726265. + 599741.i 1.46955 + 1.21354i
\(704\) 0 0
\(705\) 29085.9 + 5128.62i 0.0585199 + 0.0103186i
\(706\) 0 0
\(707\) 656985. + 239123.i 1.31437 + 0.478390i
\(708\) 0 0
\(709\) −349377. + 293162.i −0.695028 + 0.583198i −0.920354 0.391086i \(-0.872100\pi\)
0.225326 + 0.974283i \(0.427655\pi\)
\(710\) 0 0
\(711\) 316120. + 182512.i 0.625335 + 0.361037i
\(712\) 0 0
\(713\) −216745. + 38218.0i −0.426354 + 0.0751776i
\(714\) 0 0
\(715\) −338283. + 195308.i −0.661711 + 0.382039i
\(716\) 0 0
\(717\) −100995. 277481.i −0.196454 0.539753i
\(718\) 0 0
\(719\) 737375. + 618731.i 1.42637 + 1.19686i 0.947822 + 0.318799i \(0.103279\pi\)
0.478543 + 0.878064i \(0.341165\pi\)
\(720\) 0 0
\(721\) 88481.7i 0.170209i
\(722\) 0 0
\(723\) −111373. −0.213060
\(724\) 0 0
\(725\) 162260. 193374.i 0.308699 0.367893i
\(726\) 0 0
\(727\) 642267. 233766.i 1.21520 0.442296i 0.346694 0.937978i \(-0.387304\pi\)
0.868504 + 0.495683i \(0.165082\pi\)
\(728\) 0 0
\(729\) −107281. 185815.i −0.201867 0.349644i
\(730\) 0 0
\(731\) 45851.5 + 260037.i 0.0858062 + 0.486631i
\(732\) 0 0
\(733\) 10194.9 17658.1i 0.0189747 0.0328651i −0.856382 0.516343i \(-0.827293\pi\)
0.875357 + 0.483477i \(0.160626\pi\)
\(734\) 0 0
\(735\) 3307.72 + 3941.98i 0.00612285 + 0.00729693i
\(736\) 0 0
\(737\) 90047.4 247403.i 0.165782 0.455481i
\(738\) 0 0
\(739\) 63505.2 360156.i 0.116284 0.659480i −0.869822 0.493365i \(-0.835767\pi\)
0.986106 0.166115i \(-0.0531222\pi\)
\(740\) 0 0
\(741\) −186720. + 226112.i −0.340060 + 0.411800i
\(742\) 0 0
\(743\) −610254. 107604.i −1.10543 0.194918i −0.408998 0.912535i \(-0.634122\pi\)
−0.696437 + 0.717617i \(0.745233\pi\)
\(744\) 0 0
\(745\) 503642. + 183311.i 0.907421 + 0.330274i
\(746\) 0 0
\(747\) −403355. + 338455.i −0.722847 + 0.606541i
\(748\) 0 0
\(749\) −97027.5 56018.8i −0.172954 0.0998552i
\(750\) 0 0
\(751\) −687250. + 121181.i −1.21853 + 0.214859i −0.745691 0.666292i \(-0.767881\pi\)
−0.472835 + 0.881151i \(0.656769\pi\)
\(752\) 0 0
\(753\) −167197. + 96531.4i −0.294876 + 0.170247i
\(754\) 0 0
\(755\) −83346.0 228991.i −0.146215 0.401721i
\(756\) 0 0
\(757\) 137490. + 115368.i 0.239928 + 0.201323i 0.754821 0.655931i \(-0.227724\pi\)
−0.514893 + 0.857255i \(0.672168\pi\)
\(758\) 0 0
\(759\) 212298.i 0.368521i
\(760\) 0 0
\(761\) −202495. −0.349659 −0.174830 0.984599i \(-0.555937\pi\)
−0.174830 + 0.984599i \(0.555937\pi\)
\(762\) 0 0
\(763\) 57697.6 68761.4i 0.0991081 0.118112i
\(764\) 0 0
\(765\) −119374. + 43448.6i −0.203980 + 0.0742426i
\(766\) 0 0
\(767\) 217142. + 376102.i 0.369108 + 0.639314i
\(768\) 0 0
\(769\) −90273.7 511967.i −0.152654 0.865744i −0.960899 0.276898i \(-0.910694\pi\)
0.808245 0.588846i \(-0.200418\pi\)
\(770\) 0 0
\(771\) −102886. + 178205.i −0.173081 + 0.299785i
\(772\) 0 0
\(773\) 458750. + 546717.i 0.767745 + 0.914963i 0.998311 0.0580935i \(-0.0185022\pi\)
−0.230566 + 0.973057i \(0.574058\pi\)
\(774\) 0 0
\(775\) 28918.7 79453.6i 0.0481477 0.132285i
\(776\) 0 0
\(777\) 64588.4 366299.i 0.106982 0.606727i
\(778\) 0 0
\(779\) 54180.7 + 293749.i 0.0892831 + 0.484062i
\(780\) 0 0
\(781\) 649482. + 114521.i 1.06479 + 0.187752i
\(782\) 0 0
\(783\) −327431. 119175.i −0.534067 0.194384i
\(784\) 0 0
\(785\) 305853. 256642.i 0.496334 0.416474i
\(786\) 0 0
\(787\) −340466. 196568.i −0.549699 0.317369i 0.199302 0.979938i \(-0.436133\pi\)
−0.749001 + 0.662569i \(0.769466\pi\)
\(788\) 0 0
\(789\) −215068. + 37922.3i −0.345479 + 0.0609173i
\(790\) 0 0
\(791\) 382417. 220789.i 0.611201 0.352877i
\(792\) 0