Properties

Label 76.5.j.a.29.4
Level $76$
Weight $5$
Character 76.29
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 29.4
Character \(\chi\) \(=\) 76.29
Dual form 76.5.j.a.21.4

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 0.861673 0.507464i \(-0.169417\pi\)
−0.649382 + 0.760462i \(0.724972\pi\)
\(4\) 0 0
\(5\) −16.1447 5.87619i −0.645788 0.235048i −0.00169937 0.999999i \(-0.500541\pi\)
−0.644088 + 0.764951i \(0.722763\pi\)
\(6\) 0 0
\(7\) 23.9804 41.5352i 0.489396 0.847658i −0.510530 0.859860i \(-0.670551\pi\)
0.999926 + 0.0122020i \(0.00388410\pi\)
\(8\) 0 0
\(9\) 12.5313 71.0685i 0.154707 0.877389i
\(10\) 0 0
\(11\) 41.5971 + 72.0483i 0.343778 + 0.595440i 0.985131 0.171805i \(-0.0549600\pi\)
−0.641353 + 0.767246i \(0.721627\pi\)
\(12\) 0 0
\(13\) 175.663 209.347i 1.03943 1.23874i 0.0689296 0.997622i \(-0.478042\pi\)
0.970496 0.241118i \(-0.0775139\pi\)
\(14\) 0 0
\(15\) −17.4664 47.9885i −0.0776283 0.213282i
\(16\) 0 0
\(17\) 17.7920 + 100.903i 0.0615640 + 0.349147i 0.999993 + 0.00367529i \(0.00116988\pi\)
−0.938429 + 0.345471i \(0.887719\pi\)
\(18\) 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 0.562626 0.826712i \(-0.309791\pi\)
0.962396 + 0.271649i \(0.0875691\pi\)
\(24\) 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 −0.293489 0.955962i \(-0.594816\pi\)
−0.602748 + 0.797932i \(0.705928\pi\)
\(30\) 0 0
\(31\) −222.015 128.180i −0.231025 0.133382i 0.380020 0.924978i \(-0.375917\pi\)
−0.611045 + 0.791596i \(0.709250\pi\)
\(32\) 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 \(0.401941\pi\)
−0.303213 + 0.952923i \(0.598059\pi\)
\(38\) 0 0
\(39\) 812.306 0.534060
\(40\) 0 0
\(41\) 531.864 + 633.851i 0.316397 + 0.377068i 0.900680 0.434482i \(-0.143069\pi\)
−0.584283 + 0.811550i \(0.698624\pi\)
\(42\) 0 0
\(43\) −2421.67 881.415i −1.30972 0.476698i −0.409568 0.912280i \(-0.634321\pi\)
−0.900149 + 0.435582i \(0.856543\pi\)
\(44\) 0 0
\(45\) −619.926 + 1073.74i −0.306136 + 0.530244i
\(46\) 0 0
\(47\) −100.427 + 569.549i −0.0454626 + 0.257831i −0.999065 0.0432384i \(-0.986232\pi\)
0.953602 + 0.301069i \(0.0973436\pi\)
\(48\) 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 0.977133 + 0.212628i \(0.0682022\pi\)
−0.611853 + 0.790971i \(0.709576\pi\)
\(54\) 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 0.0557273 0.998446i \(-0.482252\pi\)
0.393855 + 0.919172i \(0.371141\pi\)
\(60\) 0 0
\(61\) −2684.30 + 977.005i −0.721392 + 0.262565i −0.676517 0.736427i \(-0.736511\pi\)
−0.0448755 + 0.998993i \(0.514289\pi\)
\(62\) 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 0.509638 0.860389i \(-0.329779\pi\)
0.184632 + 0.982808i \(0.440891\pi\)
\(68\) 0 0
\(69\) 2209.96 + 1275.92i 0.464179 + 0.267994i
\(70\) 0 0
\(71\) 2711.28 7449.18i 0.537846 1.47772i −0.311688 0.950185i \(-0.600894\pi\)
0.849534 0.527535i \(-0.176884\pi\)
\(72\) 0 0
\(73\) 4107.82 3446.87i 0.770843 0.646814i −0.170082 0.985430i \(-0.554403\pi\)
0.940925 + 0.338616i \(0.109959\pi\)
\(74\) 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 0.960809 0.277212i \(-0.0894106\pi\)
−0.439844 + 0.898074i \(0.644966\pi\)
\(80\) 0 0
\(81\) −4221.21 1536.40i −0.643379 0.234171i
\(82\) 0 0
\(83\) 3648.20 6318.86i 0.529568 0.917239i −0.469837 0.882753i \(-0.655687\pi\)
0.999405 0.0344859i \(-0.0109794\pi\)
\(84\) 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 −0.917314 0.398165i \(-0.869647\pi\)
0.551406 + 0.834237i \(0.314091\pi\)
\(90\) 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 −0.228742 0.973487i \(-0.573461\pi\)
0.118005 + 0.993013i \(0.462350\pi\)
\(98\) 0 0
\(99\) 5641.63 2053.39i 0.575618 0.209508i
\(100\) 0 0
\(101\) 11167.0 + 9370.25i 1.09470 + 0.918562i 0.997057 0.0766599i \(-0.0244256\pi\)
0.0976419 + 0.995222i \(0.468870\pi\)
\(102\) 0 0
\(103\) 1597.71 922.439i 0.150600 0.0869487i −0.422807 0.906220i \(-0.638955\pi\)
0.573406 + 0.819271i \(0.305622\pi\)
\(104\) 0 0
\(105\) −2412.06 425.312i −0.218781 0.0385770i
\(106\) 0 0
\(107\) −2023.06 1168.01i −0.176702 0.102019i 0.409040 0.912516i \(-0.365864\pi\)
−0.585742 + 0.810497i \(0.699197\pi\)
\(108\) 0 0
\(109\) −640.112 + 1758.69i −0.0538770 + 0.148026i −0.963712 0.266945i \(-0.913986\pi\)
0.909835 + 0.414970i \(0.136208\pi\)
\(110\) 0 0
\(111\) −5940.90 + 4985.01i −0.482177 + 0.404594i
\(112\) 0 0
\(113\) 9207.05i 0.721047i 0.932750 + 0.360524i \(0.117402\pi\)
−0.932750 + 0.360524i \(0.882598\pi\)
\(114\) 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 −0.970481 0.241178i \(-0.922466\pi\)
0.406036 + 0.913857i \(0.366911\pi\)
\(128\) 0 0
\(129\) −2619.91 7198.16i −0.157437 0.432556i
\(130\) 0 0
\(131\) 5497.76 + 31179.4i 0.320364 + 1.81687i 0.540430 + 0.841389i \(0.318262\pi\)
−0.220066 + 0.975485i \(0.570627\pi\)
\(132\) 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 −0.253351 0.967375i \(-0.581533\pi\)
0.427739 + 0.903902i \(0.359310\pi\)
\(138\) 0 0
\(139\) 2046.85 + 1717.51i 0.105939 + 0.0888933i 0.694219 0.719764i \(-0.255750\pi\)
−0.588280 + 0.808658i \(0.700195\pi\)
\(140\) 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 −0.995617 0.0935262i \(-0.970186\pi\)
−0.0807817 + 0.996732i \(0.525742\pi\)
\(150\) 0 0
\(151\) 14183.7i 0.622064i −0.950399 0.311032i \(-0.899325\pi\)
0.950399 0.311032i \(-0.100675\pi\)
\(152\) 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 −0.141333 0.989962i \(-0.545139\pi\)
−0.744603 + 0.667508i \(0.767361\pi\)
\(158\) 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 0.812867 0.582449i \(-0.197905\pi\)
−0.910849 + 0.412740i \(0.864572\pi\)
\(164\) 0 0
\(165\) 2730.94 3254.60i 0.100310 0.119545i
\(166\) 0 0
\(167\) 604.919 + 1662.00i 0.0216902 + 0.0595935i 0.950065 0.312051i \(-0.101016\pi\)
−0.928375 + 0.371645i \(0.878794\pi\)
\(168\) 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 0.754945 0.655788i \(-0.227663\pi\)
0.933709 + 0.358032i \(0.116552\pi\)
\(174\) 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 0.246272 0.969201i \(-0.420794\pi\)
0.962488 + 0.271323i \(0.0874611\pi\)
\(180\) 0 0
\(181\) 51296.0 + 9044.86i 1.56576 + 0.276086i 0.888228 0.459404i \(-0.151937\pi\)
0.677536 + 0.735490i \(0.263048\pi\)
\(182\) 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 0.652152 0.758089i \(-0.273867\pi\)
−0.859816 + 0.510603i \(0.829422\pi\)
\(194\) 0 0
\(195\) −13114.4 4773.26i −0.344890 0.125530i
\(196\) 0 0
\(197\) −29311.6 + 50769.2i −0.755279 + 1.30818i 0.189956 + 0.981793i \(0.439166\pi\)
−0.945235 + 0.326390i \(0.894168\pi\)
\(198\) 0 0
\(199\) −5197.71 + 29477.7i −0.131252 + 0.744367i 0.846145 + 0.532953i \(0.178918\pi\)
−0.977397 + 0.211414i \(0.932193\pi\)
\(200\) 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 −0.103075 0.994674i \(-0.532868\pi\)
0.243340 + 0.969941i \(0.421757\pi\)
\(212\) 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 −0.394270 0.918995i \(-0.629002\pi\)
0.892747 0.450559i \(-0.148775\pi\)
\(224\) 0 0
\(225\) −18232.9 + 15299.2i −0.360156 + 0.302207i
\(226\) 0 0
\(227\) 75365.9i 1.46259i 0.682060 + 0.731296i \(0.261084\pi\)
−0.682060 + 0.731296i \(0.738916\pi\)
\(228\) 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 −0.602680 0.797983i \(-0.705900\pi\)
−0.974613 + 0.223896i \(0.928123\pi\)
\(234\) 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 0.862416 + 0.506200i \(0.168950\pi\)
0.00717402 + 0.999974i \(0.497716\pi\)
\(240\) 0 0
\(241\) −24084.6 + 28702.9i −0.414673 + 0.494188i −0.932436 0.361336i \(-0.882321\pi\)
0.517763 + 0.855524i \(0.326765\pi\)
\(242\) 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 −0.777472 0.628917i \(-0.783498\pi\)
−0.191318 + 0.981528i \(0.561276\pi\)
\(252\) 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 −0.368211 0.929742i \(-0.620029\pi\)
−0.663995 + 0.747737i \(0.731141\pi\)
\(258\) 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 −0.951486 0.307693i \(-0.900443\pi\)
0.137794 + 0.990461i \(0.455999\pi\)
\(264\) 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 0.963272 0.268526i \(-0.0865365\pi\)
−0.431717 + 0.902009i \(0.642092\pi\)
\(270\) 0 0
\(271\) −40217.6 14638.0i −0.547618 0.199317i 0.0533699 0.998575i \(-0.483004\pi\)
−0.600988 + 0.799258i \(0.705226\pi\)
\(272\) 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 0.947936 + 0.318459i \(0.103165\pi\)
−0.198174 + 0.980167i \(0.563501\pi\)
\(278\) 0 0
\(279\) −11891.7 + 14172.0i −0.152769 + 0.182063i
\(280\) 0 0
\(281\) −41424.5 113813.i −0.524619 1.44138i −0.865326 0.501210i \(-0.832888\pi\)
0.340706 0.940170i \(-0.389334\pi\)
\(282\) 0 0
\(283\) 1875.66 + 10637.4i 0.0234197 + 0.132820i 0.994276 0.106843i \(-0.0340743\pi\)
−0.970856 + 0.239663i \(0.922963\pi\)
\(284\) 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 −0.572622 0.819820i \(-0.694074\pi\)
0.423674 + 0.905815i \(0.360740\pi\)
\(294\) 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 0.308174 0.951330i \(-0.400282\pi\)
−0.990391 + 0.138295i \(0.955838\pi\)
\(308\) 0 0
\(309\) 5153.00 + 1875.54i 0.0539689 + 0.0196431i
\(310\) 0 0
\(311\) 76935.4 133256.i 0.795437 1.37774i −0.127125 0.991887i \(-0.540575\pi\)
0.922561 0.385850i \(-0.126092\pi\)
\(312\) 0 0
\(313\) −3330.62 + 18888.9i −0.0339967 + 0.192805i −0.997076 0.0764118i \(-0.975654\pi\)
0.963080 + 0.269217i \(0.0867648\pi\)
\(314\) 0 0
\(315\) 29732.1 + 51497.5i 0.299643 + 0.518998i
\(316\) 0 0
\(317\) −82830.1 + 98713.1i −0.824270 + 0.982327i −0.999998 0.00211182i \(-0.999328\pi\)
0.175728 + 0.984439i \(0.443772\pi\)
\(318\) 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 0.476638 0.879100i \(-0.341855\pi\)
0.999642 + 0.0267690i \(0.00852186\pi\)
\(332\) 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 0.00619703 0.999981i \(-0.498027\pi\)
0.638028 0.770013i \(-0.279750\pi\)
\(338\) 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 −0.421551 0.906805i \(-0.638514\pi\)
−0.905810 + 0.423685i \(0.860736\pi\)
\(348\) 0 0
\(349\) −24175.3 + 41872.8i −0.198482 + 0.343780i −0.948036 0.318162i \(-0.896934\pi\)
0.749555 + 0.661942i \(0.230268\pi\)
\(350\) 0 0
\(351\) 21604.7 122527.i 0.175362 0.994525i
\(352\) 0 0
\(353\) 26418.5 + 45758.2i 0.212011 + 0.367214i 0.952344 0.305027i \(-0.0986654\pi\)
−0.740333 + 0.672241i \(0.765332\pi\)
\(354\) 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 −0.909121 0.416531i \(-0.863246\pi\)
0.711832 0.702349i \(-0.247866\pi\)
\(360\) 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 0.694093 0.719886i \(-0.255806\pi\)
−0.588421 + 0.808555i \(0.700250\pi\)
\(368\) 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 0.785072 0.619404i \(-0.212626\pi\)
−0.143884 + 0.989595i \(0.545959\pi\)
\(374\) 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 \(-0.974718\pi\)
0.996848 0.0793408i \(-0.0252815\pi\)
\(380\) 0 0
\(381\) −42098.6 −0.290013
\(382\) 0 0
\(383\) 77114.8 + 91901.8i 0.525702 + 0.626508i 0.961919 0.273334i \(-0.0881264\pi\)
−0.436217 + 0.899842i \(0.643682\pi\)
\(384\) 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 −0.770986 0.636852i \(-0.780236\pi\)
0.942306 0.334752i \(-0.108653\pi\)
\(390\) 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 0.989805 + 0.142426i \(0.0454902\pi\)
−0.881400 + 0.472370i \(0.843399\pi\)
\(398\) 0 0
\(399\) −39162.1 33389.1i −0.245991 0.209729i
\(400\) 0 0
\(401\) −137641. + 24269.8i −0.855970 + 0.150931i −0.584378 0.811482i \(-0.698661\pi\)
−0.271592 + 0.962412i \(0.587550\pi\)
\(402\) 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 0.778434 0.627726i \(-0.216014\pi\)
0.516794 + 0.856110i \(0.327125\pi\)
\(410\) 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 0.766288 0.642498i \(-0.222102\pi\)
−0.765801 + 0.643078i \(0.777657\pi\)
\(422\) 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 −0.902271 0.431169i \(-0.858101\pi\)
0.581296 + 0.813692i \(0.302546\pi\)
\(432\) 0 0
\(433\) −44616.5 122583.i −0.237969 0.653813i −0.999980 0.00625025i \(-0.998010\pi\)
0.762012 0.647563i \(-0.224212\pi\)
\(434\) 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 0.902044 0.431644i \(-0.142066\pi\)
0.995275 + 0.0970952i \(0.0309551\pi\)
\(440\) 0 0
\(441\) 6833.15 2487.06i 0.0351353 0.0127882i
\(442\) 0 0
\(443\) −156372. 131211.i −0.796802 0.668596i 0.150617 0.988592i \(-0.451874\pi\)
−0.947419 + 0.319996i \(0.896318\pi\)
\(444\) 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 0.618610 0.785698i \(-0.287696\pi\)
−0.371129 + 0.928581i \(0.621029\pi\)
\(450\) 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 0.0567687 0.998387i \(-0.481920\pi\)
−0.598264 + 0.801299i \(0.704142\pi\)
\(462\) 0 0
\(463\) 42930.7 74358.2i 0.200266 0.346870i −0.748348 0.663306i \(-0.769153\pi\)
0.948614 + 0.316436i \(0.102486\pi\)
\(464\) 0 0
\(465\) −2273.38 + 12893.0i −0.0105140 + 0.0596277i
\(466\) 0 0
\(467\) 40903.8 + 70847.4i 0.187555 + 0.324856i 0.944435 0.328699i \(-0.106610\pi\)
−0.756879 + 0.653555i \(0.773277\pi\)
\(468\) 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 0.477839 0.878447i \(-0.341420\pi\)
0.930701 + 0.365780i \(0.119198\pi\)
\(480\) 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 0.523460 0.852050i \(-0.324641\pi\)
−0.476167 + 0.879355i \(0.657974\pi\)
\(488\) 0 0
\(489\) 5293.08 14542.6i 0.0221356 0.0608170i
\(490\) 0 0
\(491\) 19005.8 15947.7i 0.0788356 0.0661509i −0.602518 0.798105i \(-0.705836\pi\)
0.681354 + 0.731954i \(0.261391\pi\)
\(492\) 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 −0.0422999 0.999105i \(-0.513469\pi\)
−0.674616 + 0.738169i \(0.735691\pi\)
\(500\) 0 0
\(501\) −2628.59 + 4552.85i −0.0104724 + 0.0181388i
\(502\) 0 0
\(503\) −2082.98 + 11813.1i −0.00823281 + 0.0466906i −0.988647 0.150254i \(-0.951991\pi\)
0.980415 + 0.196945i \(0.0631019\pi\)
\(504\) 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 0.899180 0.437579i \(-0.144164\pi\)
−0.970082 + 0.242777i \(0.921942\pi\)
\(510\) 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 0.0432004 0.999066i \(-0.486245\pi\)
0.886817 + 0.462121i \(0.152911\pi\)
\(522\) 0 0
\(523\) −320281. 56474.2i −1.17092 0.206465i −0.445830 0.895117i \(-0.647092\pi\)
−0.725092 + 0.688652i \(0.758203\pi\)
\(524\) 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 −0.989972 0.141266i \(-0.954883\pi\)
0.978585 + 0.205843i \(0.0659938\pi\)
\(542\) 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 0.993239 0.116090i \(-0.0370361\pi\)
−0.835486 + 0.549511i \(0.814814\pi\)
\(548\) 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 −0.964175 0.265268i \(-0.914540\pi\)
−0.428665 0.903464i \(-0.641016\pi\)
\(558\) 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 0.895065 0.445935i \(-0.147129\pi\)
0.0613417 + 0.998117i \(0.480462\pi\)
\(564\) 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 \(-0.989577\pi\)
0.999464 0.0327393i \(-0.0104231\pi\)
\(570\) 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 0.405537 + 0.914079i \(0.367085\pi\)
−0.994384 + 0.105834i \(0.966249\pi\)
\(578\) 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 0.854942 + 0.518724i \(0.173593\pi\)
−0.625968 + 0.779849i \(0.715296\pi\)
\(588\) 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 −0.704144 0.710058i \(-0.748669\pi\)
−0.0829890 + 0.996550i \(0.526447\pi\)
\(594\) 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 0.749925 0.661523i \(-0.230090\pi\)
0.478445 + 0.878118i \(0.341201\pi\)
\(600\) 0 0
\(601\) −135466. 78211.5i −0.375044 0.216532i 0.300616 0.953745i \(-0.402808\pi\)
−0.675660 + 0.737214i \(0.736141\pi\)
\(602\) 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 \(-0.894780\pi\)
0.945861 0.324572i \(-0.105220\pi\)
\(608\) 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 0.675001 0.737817i \(-0.264143\pi\)
0.0428211 + 0.999083i \(0.486365\pi\)
\(614\) 0 0
\(615\) 21127.8 36594.4i 0.0558604 0.0967530i
\(616\) 0 0
\(617\) −92784.5 + 526207.i −0.243728 + 1.38225i 0.579701 + 0.814829i \(0.303169\pi\)
−0.823429 + 0.567419i \(0.807942\pi\)
\(618\) 0 0
\(619\) 54937.5 + 95154.5i 0.143380 + 0.248341i 0.928767 0.370664i \(-0.120870\pi\)
−0.785388 + 0.619004i \(0.787536\pi\)
\(620\) 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 −0.911423 0.411471i \(-0.865015\pi\)
−0.433702 + 0.901056i \(0.642793\pi\)
\(632\) 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 −0.256507 + 0.966542i \(0.582572\pi\)
−0.424785 + 0.905294i \(0.639650\pi\)
\(642\) 0 0
\(643\) 140685. 118049.i 0.340272 0.285522i −0.456597 0.889673i \(-0.650932\pi\)
0.796870 + 0.604151i \(0.206488\pi\)
\(644\) 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 −0.695139 0.718876i \(-0.744657\pi\)
0.970134 + 0.242570i \(0.0779903\pi\)
\(654\) 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 −0.873063 0.487608i \(-0.837870\pi\)
0.631805 + 0.775127i \(0.282314\pi\)
\(660\) 0 0
\(661\) −51551.4 141636.i −0.117988 0.324169i 0.866614 0.498979i \(-0.166291\pi\)
−0.984602 + 0.174809i \(0.944069\pi\)
\(662\) 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 −0.616482 0.787369i \(-0.711443\pi\)
0.373641 + 0.927574i \(0.378109\pi\)
\(674\) 0 0
\(675\) −147875. 26074.3i −0.324553 0.0572275i
\(676\) 0 0
\(677\) −23991.9 13851.8i −0.0523465 0.0302223i 0.473598 0.880741i \(-0.342955\pi\)
−0.525945 + 0.850519i \(0.676288\pi\)
\(678\) 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 \(0.221082\pi\)
−0.768342 + 0.640040i \(0.778918\pi\)
\(684\) 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 −0.0964250 0.995340i \(-0.530741\pi\)
0.910202 0.414164i \(-0.135926\pi\)
\(692\) 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 0.957156 0.289572i \(-0.0935131\pi\)
−0.998472 + 0.0552576i \(0.982402\pi\)
\(702\) 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 0.225326 0.974283i \(-0.427655\pi\)
−0.920354 + 0.391086i \(0.872100\pi\)
\(710\) 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 0.478543 0.878064i \(-0.341165\pi\)
0.947822 0.318799i \(-0.103279\pi\)
\(720\) 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 0.868504 0.495683i \(-0.165082\pi\)
0.346694 + 0.937978i \(0.387304\pi\)
\(728\) 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 0.875357 0.483477i \(-0.160626\pi\)
−0.856382 + 0.516343i \(0.827293\pi\)
\(734\) 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 0.986106 + 0.166115i \(0.0531222\pi\)
−0.869822 + 0.493365i \(0.835767\pi\)
\(740\) 0 0
\(741\) −186720. 226112.i −0.340060 0.411800i
\(742\) 0 0
\(743\) −610254. + 107604.i −1.10543 + 0.194918i −0.696437 0.717617i \(-0.745233\pi\)
−0.408998 + 0.912535i \(0.634122\pi\)
\(744\) 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 −0.472835 0.881151i \(-0.656769\pi\)
−0.745691 + 0.666292i \(0.767881\pi\)
\(752\) 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 −0.514893 0.857255i \(-0.672168\pi\)
0.754821 + 0.655931i \(0.227724\pi\)
\(758\) 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 0.808245 + 0.588846i \(0.200418\pi\)
−0.960899 + 0.276898i \(0.910694\pi\)
\(770\) 0 0
\(771\) −102886. 178205.i −0.173081 0.299785i
\(772\) 0 0
\(773\) 458750. 546717.i 0.767745 0.914963i −0.230566 0.973057i \(-0.574058\pi\)
0.998311 + 0.0580935i \(0.0185022\pi\)
\(774\) 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 −0.749001 0.662569i \(-0.769466\pi\)
0.199302 + 0.979938i \(0.436133\pi\)
\(788\) 0 0
\(789\) −215068. 37922.3i −0.345479 0.0609173i
\(790\) 0 0
\(791\) 382417. + 220789.i 0.611201 + 0.352877i
\(792\) 0