Properties

Label 76.5.j.a.21.5
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 21.5
Character \(\chi\) \(=\) 76.21
Dual form 76.5.j.a.29.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.92113 - 3.48127i) q^{3} +(20.0929 - 7.31321i) q^{5} +(-36.0108 - 62.3725i) q^{7} +(10.4793 + 59.4309i) q^{9} +O(q^{10})\) \(q+(2.92113 - 3.48127i) q^{3} +(20.0929 - 7.31321i) q^{5} +(-36.0108 - 62.3725i) q^{7} +(10.4793 + 59.4309i) q^{9} +(55.1380 - 95.5017i) q^{11} +(-18.3793 - 21.9036i) q^{13} +(33.2347 - 91.3116i) q^{15} +(66.2932 - 375.967i) q^{17} +(-20.3946 - 360.423i) q^{19} +(-322.328 - 56.8351i) q^{21} +(225.549 + 82.0931i) q^{23} +(-128.537 + 107.855i) q^{25} +(556.293 + 321.176i) q^{27} +(1172.95 - 206.823i) q^{29} +(-806.771 + 465.789i) q^{31} +(-171.402 - 470.923i) q^{33} +(-1179.70 - 989.888i) q^{35} +1391.16i q^{37} -129.941 q^{39} +(-1665.47 + 1984.83i) q^{41} +(2036.86 - 741.355i) q^{43} +(645.190 + 1117.50i) q^{45} +(593.018 + 3363.17i) q^{47} +(-1393.05 + 2412.84i) q^{49} +(-1115.19 - 1329.03i) q^{51} +(-799.720 + 2197.21i) q^{53} +(409.456 - 2322.14i) q^{55} +(-1314.31 - 981.846i) q^{57} +(-186.660 - 32.9132i) q^{59} +(-1412.65 - 514.161i) q^{61} +(3329.49 - 2793.77i) q^{63} +(-529.478 - 305.695i) q^{65} +(7401.57 - 1305.10i) q^{67} +(944.647 - 545.392i) q^{69} +(-1338.30 - 3676.95i) q^{71} +(2645.33 + 2219.70i) q^{73} +762.533i q^{75} -7942.24 q^{77} +(685.145 - 816.524i) q^{79} +(-1850.27 + 673.444i) q^{81} +(-2624.90 - 4546.46i) q^{83} +(-1417.51 - 8039.08i) q^{85} +(2706.35 - 4687.53i) q^{87} +(-333.507 - 397.458i) q^{89} +(-704.329 + 1935.13i) q^{91} +(-735.146 + 4169.22i) q^{93} +(-3045.64 - 7092.79i) q^{95} +(13798.9 + 2433.11i) q^{97} +(6253.56 + 2276.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

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
\(3\) 2.92113 3.48127i 0.324570 0.386808i −0.578943 0.815368i \(-0.696535\pi\)
0.903513 + 0.428560i \(0.140979\pi\)
\(4\) 0 0
\(5\) 20.0929 7.31321i 0.803715 0.292528i 0.0926900 0.995695i \(-0.470453\pi\)
0.711025 + 0.703167i \(0.248231\pi\)
\(6\) 0 0
\(7\) −36.0108 62.3725i −0.734914 1.27291i −0.954761 0.297374i \(-0.903889\pi\)
0.219847 0.975534i \(-0.429444\pi\)
\(8\) 0 0
\(9\) 10.4793 + 59.4309i 0.129374 + 0.733715i
\(10\) 0 0
\(11\) 55.1380 95.5017i 0.455686 0.789271i −0.543042 0.839706i \(-0.682727\pi\)
0.998727 + 0.0504351i \(0.0160608\pi\)
\(12\) 0 0
\(13\) −18.3793 21.9036i −0.108753 0.129607i 0.708922 0.705287i \(-0.249182\pi\)
−0.817675 + 0.575680i \(0.804737\pi\)
\(14\) 0 0
\(15\) 33.2347 91.3116i 0.147710 0.405829i
\(16\) 0 0
\(17\) 66.2932 375.967i 0.229388 1.30092i −0.624728 0.780842i \(-0.714790\pi\)
0.854116 0.520082i \(-0.174099\pi\)
\(18\) 0 0
\(19\) −20.3946 360.423i −0.0564948 0.998403i
\(20\) 0 0
\(21\) −322.328 56.8351i −0.730902 0.128878i
\(22\) 0 0
\(23\) 225.549 + 82.0931i 0.426369 + 0.155185i 0.546287 0.837598i \(-0.316041\pi\)
−0.119918 + 0.992784i \(0.538263\pi\)
\(24\) 0 0
\(25\) −128.537 + 107.855i −0.205659 + 0.172569i
\(26\) 0 0
\(27\) 556.293 + 321.176i 0.763090 + 0.440570i
\(28\) 0 0
\(29\) 1172.95 206.823i 1.39471 0.245926i 0.574744 0.818333i \(-0.305102\pi\)
0.819969 + 0.572407i \(0.193990\pi\)
\(30\) 0 0
\(31\) −806.771 + 465.789i −0.839512 + 0.484692i −0.857098 0.515153i \(-0.827735\pi\)
0.0175864 + 0.999845i \(0.494402\pi\)
\(32\) 0 0
\(33\) −171.402 470.923i −0.157394 0.432436i
\(34\) 0 0
\(35\) −1179.70 989.888i −0.963023 0.808072i
\(36\) 0 0
\(37\) 1391.16i 1.01619i 0.861302 + 0.508094i \(0.169650\pi\)
−0.861302 + 0.508094i \(0.830350\pi\)
\(38\) 0 0
\(39\) −129.941 −0.0854311
\(40\) 0 0
\(41\) −1665.47 + 1984.83i −0.990760 + 1.18074i −0.00723414 + 0.999974i \(0.502303\pi\)
−0.983526 + 0.180768i \(0.942142\pi\)
\(42\) 0 0
\(43\) 2036.86 741.355i 1.10160 0.400949i 0.273693 0.961817i \(-0.411755\pi\)
0.827905 + 0.560868i \(0.189532\pi\)
\(44\) 0 0
\(45\) 645.190 + 1117.50i 0.318612 + 0.551852i
\(46\) 0 0
\(47\) 593.018 + 3363.17i 0.268456 + 1.52249i 0.759012 + 0.651077i \(0.225683\pi\)
−0.490556 + 0.871410i \(0.663206\pi\)
\(48\) 0 0
\(49\) −1393.05 + 2412.84i −0.580196 + 1.00493i
\(50\) 0 0
\(51\) −1115.19 1329.03i −0.428755 0.510971i
\(52\) 0 0
\(53\) −799.720 + 2197.21i −0.284699 + 0.782205i 0.712086 + 0.702092i \(0.247750\pi\)
−0.996786 + 0.0801131i \(0.974472\pi\)
\(54\) 0 0
\(55\) 409.456 2322.14i 0.135357 0.767650i
\(56\) 0 0
\(57\) −1314.31 981.846i −0.404527 0.302199i
\(58\) 0 0
\(59\) −186.660 32.9132i −0.0536225 0.00945509i 0.146773 0.989170i \(-0.453111\pi\)
−0.200395 + 0.979715i \(0.564223\pi\)
\(60\) 0 0
\(61\) −1412.65 514.161i −0.379641 0.138178i 0.145149 0.989410i \(-0.453634\pi\)
−0.524790 + 0.851232i \(0.675856\pi\)
\(62\) 0 0
\(63\) 3329.49 2793.77i 0.838873 0.703898i
\(64\) 0 0
\(65\) −529.478 305.695i −0.125320 0.0723537i
\(66\) 0 0
\(67\) 7401.57 1305.10i 1.64882 0.290732i 0.729425 0.684061i \(-0.239788\pi\)
0.919398 + 0.393329i \(0.128677\pi\)
\(68\) 0 0
\(69\) 944.647 545.392i 0.198414 0.114554i
\(70\) 0 0
\(71\) −1338.30 3676.95i −0.265483 0.729409i −0.998774 0.0494941i \(-0.984239\pi\)
0.733291 0.679915i \(-0.237983\pi\)
\(72\) 0 0
\(73\) 2645.33 + 2219.70i 0.496403 + 0.416532i 0.856314 0.516455i \(-0.172749\pi\)
−0.359911 + 0.932987i \(0.617193\pi\)
\(74\) 0 0
\(75\) 762.533i 0.135561i
\(76\) 0 0
\(77\) −7942.24 −1.33956
\(78\) 0 0
\(79\) 685.145 816.524i 0.109781 0.130832i −0.708356 0.705856i \(-0.750563\pi\)
0.818137 + 0.575024i \(0.195007\pi\)
\(80\) 0 0
\(81\) −1850.27 + 673.444i −0.282011 + 0.102643i
\(82\) 0 0
\(83\) −2624.90 4546.46i −0.381028 0.659960i 0.610182 0.792262i \(-0.291096\pi\)
−0.991209 + 0.132302i \(0.957763\pi\)
\(84\) 0 0
\(85\) −1417.51 8039.08i −0.196195 1.11268i
\(86\) 0 0
\(87\) 2706.35 4687.53i 0.357557 0.619306i
\(88\) 0 0
\(89\) −333.507 397.458i −0.0421042 0.0501778i 0.744581 0.667532i \(-0.232649\pi\)
−0.786686 + 0.617354i \(0.788205\pi\)
\(90\) 0 0
\(91\) −704.329 + 1935.13i −0.0850536 + 0.233683i
\(92\) 0 0
\(93\) −735.146 + 4169.22i −0.0849978 + 0.482047i
\(94\) 0 0
\(95\) −3045.64 7092.79i −0.337467 0.785905i
\(96\) 0 0
\(97\) 13798.9 + 2433.11i 1.46656 + 0.258594i 0.849193 0.528082i \(-0.177089\pi\)
0.617366 + 0.786676i \(0.288200\pi\)
\(98\) 0 0
\(99\) 6253.56 + 2276.11i 0.638053 + 0.232232i
\(100\) 0 0
\(101\) 5816.06 4880.25i 0.570146 0.478409i −0.311548 0.950230i \(-0.600848\pi\)
0.881694 + 0.471821i \(0.156403\pi\)
\(102\) 0 0
\(103\) −8868.49 5120.23i −0.835941 0.482631i 0.0199417 0.999801i \(-0.493652\pi\)
−0.855882 + 0.517171i \(0.826985\pi\)
\(104\) 0 0
\(105\) −6892.14 + 1215.27i −0.625137 + 0.110229i
\(106\) 0 0
\(107\) −849.798 + 490.631i −0.0742247 + 0.0428536i −0.536653 0.843803i \(-0.680312\pi\)
0.462428 + 0.886657i \(0.346978\pi\)
\(108\) 0 0
\(109\) 6094.78 + 16745.3i 0.512985 + 1.40942i 0.878111 + 0.478457i \(0.158804\pi\)
−0.365126 + 0.930958i \(0.618974\pi\)
\(110\) 0 0
\(111\) 4843.01 + 4063.77i 0.393069 + 0.329824i
\(112\) 0 0
\(113\) 10436.4i 0.817324i −0.912686 0.408662i \(-0.865996\pi\)
0.912686 0.408662i \(-0.134004\pi\)
\(114\) 0 0
\(115\) 5132.29 0.388075
\(116\) 0 0
\(117\) 1109.15 1321.83i 0.0810248 0.0965616i
\(118\) 0 0
\(119\) −25837.3 + 9404.00i −1.82454 + 0.664077i
\(120\) 0 0
\(121\) 1240.11 + 2147.94i 0.0847013 + 0.146707i
\(122\) 0 0
\(123\) 2044.67 + 11595.9i 0.135149 + 0.766467i
\(124\) 0 0
\(125\) −8475.91 + 14680.7i −0.542458 + 0.939565i
\(126\) 0 0
\(127\) 2218.85 + 2644.32i 0.137569 + 0.163948i 0.830430 0.557123i \(-0.188095\pi\)
−0.692861 + 0.721071i \(0.743650\pi\)
\(128\) 0 0
\(129\) 3369.07 9256.44i 0.202456 0.556243i
\(130\) 0 0
\(131\) −2311.17 + 13107.3i −0.134676 + 0.763784i 0.840409 + 0.541952i \(0.182315\pi\)
−0.975085 + 0.221832i \(0.928796\pi\)
\(132\) 0 0
\(133\) −21746.1 + 14251.2i −1.22936 + 0.805653i
\(134\) 0 0
\(135\) 13526.3 + 2385.06i 0.742186 + 0.130867i
\(136\) 0 0
\(137\) 504.996 + 183.804i 0.0269059 + 0.00979293i 0.355438 0.934700i \(-0.384332\pi\)
−0.328532 + 0.944493i \(0.606554\pi\)
\(138\) 0 0
\(139\) −7577.41 + 6358.20i −0.392185 + 0.329083i −0.817464 0.575980i \(-0.804621\pi\)
0.425278 + 0.905063i \(0.360176\pi\)
\(140\) 0 0
\(141\) 13440.4 + 7759.82i 0.676042 + 0.390313i
\(142\) 0 0
\(143\) −3105.23 + 547.535i −0.151852 + 0.0267757i
\(144\) 0 0
\(145\) 22055.5 12733.7i 1.04901 0.605647i
\(146\) 0 0
\(147\) 4330.45 + 11897.8i 0.200400 + 0.550595i
\(148\) 0 0
\(149\) −21693.6 18203.1i −0.977146 0.819923i 0.00651023 0.999979i \(-0.497928\pi\)
−0.983656 + 0.180056i \(0.942372\pi\)
\(150\) 0 0
\(151\) 17781.4i 0.779850i −0.920847 0.389925i \(-0.872501\pi\)
0.920847 0.389925i \(-0.127499\pi\)
\(152\) 0 0
\(153\) 23038.8 0.984185
\(154\) 0 0
\(155\) −12803.9 + 15259.1i −0.532942 + 0.635136i
\(156\) 0 0
\(157\) −30266.2 + 11016.0i −1.22789 + 0.446915i −0.872874 0.487946i \(-0.837746\pi\)
−0.355015 + 0.934861i \(0.615524\pi\)
\(158\) 0 0
\(159\) 5313.01 + 9202.39i 0.210158 + 0.364004i
\(160\) 0 0
\(161\) −3001.84 17024.3i −0.115807 0.656776i
\(162\) 0 0
\(163\) 20771.9 35978.0i 0.781810 1.35414i −0.149076 0.988826i \(-0.547630\pi\)
0.930886 0.365309i \(-0.119037\pi\)
\(164\) 0 0
\(165\) −6887.92 8208.71i −0.253000 0.301513i
\(166\) 0 0
\(167\) −8320.45 + 22860.3i −0.298342 + 0.819687i 0.696436 + 0.717619i \(0.254768\pi\)
−0.994777 + 0.102068i \(0.967454\pi\)
\(168\) 0 0
\(169\) 4817.60 27321.9i 0.168677 0.956617i
\(170\) 0 0
\(171\) 21206.6 4989.05i 0.725234 0.170618i
\(172\) 0 0
\(173\) −7993.40 1409.45i −0.267079 0.0470932i 0.0385050 0.999258i \(-0.487740\pi\)
−0.305584 + 0.952165i \(0.598852\pi\)
\(174\) 0 0
\(175\) 11355.9 + 4133.22i 0.370806 + 0.134962i
\(176\) 0 0
\(177\) −659.838 + 553.670i −0.0210616 + 0.0176728i
\(178\) 0 0
\(179\) −17021.7 9827.49i −0.531248 0.306716i 0.210277 0.977642i \(-0.432564\pi\)
−0.741525 + 0.670926i \(0.765897\pi\)
\(180\) 0 0
\(181\) 52617.3 9277.85i 1.60610 0.283198i 0.702533 0.711651i \(-0.252052\pi\)
0.903564 + 0.428453i \(0.140941\pi\)
\(182\) 0 0
\(183\) −5916.46 + 3415.87i −0.176669 + 0.102000i
\(184\) 0 0
\(185\) 10173.9 + 27952.4i 0.297264 + 0.816726i
\(186\) 0 0
\(187\) −32250.2 27061.2i −0.922253 0.773862i
\(188\) 0 0
\(189\) 46263.1i 1.29512i
\(190\) 0 0
\(191\) −3031.85 −0.0831075 −0.0415538 0.999136i \(-0.513231\pi\)
−0.0415538 + 0.999136i \(0.513231\pi\)
\(192\) 0 0
\(193\) 43770.8 52164.1i 1.17509 1.40041i 0.276845 0.960915i \(-0.410711\pi\)
0.898242 0.439500i \(-0.144844\pi\)
\(194\) 0 0
\(195\) −2610.88 + 950.283i −0.0686623 + 0.0249910i
\(196\) 0 0
\(197\) −3966.59 6870.34i −0.102208 0.177030i 0.810386 0.585896i \(-0.199257\pi\)
−0.912594 + 0.408867i \(0.865924\pi\)
\(198\) 0 0
\(199\) 10936.9 + 62026.3i 0.276178 + 1.56628i 0.735195 + 0.677855i \(0.237090\pi\)
−0.459018 + 0.888427i \(0.651799\pi\)
\(200\) 0 0
\(201\) 17077.6 29579.2i 0.422702 0.732141i
\(202\) 0 0
\(203\) −55139.1 65712.2i −1.33803 1.59461i
\(204\) 0 0
\(205\) −18948.6 + 52060.8i −0.450888 + 1.23881i
\(206\) 0 0
\(207\) −2515.28 + 14264.9i −0.0587010 + 0.332910i
\(208\) 0 0
\(209\) −35545.6 17925.3i −0.813754 0.410368i
\(210\) 0 0
\(211\) −40436.8 7130.10i −0.908264 0.160151i −0.300049 0.953924i \(-0.597003\pi\)
−0.608215 + 0.793773i \(0.708114\pi\)
\(212\) 0 0
\(213\) −16709.8 6081.87i −0.368309 0.134053i
\(214\) 0 0
\(215\) 35504.6 29791.9i 0.768082 0.644498i
\(216\) 0 0
\(217\) 58104.9 + 33546.9i 1.23394 + 0.712414i
\(218\) 0 0
\(219\) 15454.7 2725.09i 0.322236 0.0568188i
\(220\) 0 0
\(221\) −9453.45 + 5457.95i −0.193556 + 0.111749i
\(222\) 0 0
\(223\) 20272.3 + 55697.7i 0.407656 + 1.12003i 0.958419 + 0.285364i \(0.0921144\pi\)
−0.550763 + 0.834661i \(0.685663\pi\)
\(224\) 0 0
\(225\) −7756.93 6508.83i −0.153223 0.128570i
\(226\) 0 0
\(227\) 87779.7i 1.70350i 0.523947 + 0.851751i \(0.324459\pi\)
−0.523947 + 0.851751i \(0.675541\pi\)
\(228\) 0 0
\(229\) −30764.0 −0.586640 −0.293320 0.956014i \(-0.594760\pi\)
−0.293320 + 0.956014i \(0.594760\pi\)
\(230\) 0 0
\(231\) −23200.3 + 27649.1i −0.434781 + 0.518152i
\(232\) 0 0
\(233\) 26105.0 9501.45i 0.480853 0.175016i −0.0902096 0.995923i \(-0.528754\pi\)
0.571062 + 0.820907i \(0.306531\pi\)
\(234\) 0 0
\(235\) 36511.0 + 63239.0i 0.661132 + 1.14511i
\(236\) 0 0
\(237\) −841.141 4770.35i −0.0149752 0.0849285i
\(238\) 0 0
\(239\) 42411.9 73459.6i 0.742492 1.28603i −0.208865 0.977945i \(-0.566977\pi\)
0.951357 0.308090i \(-0.0996898\pi\)
\(240\) 0 0
\(241\) −28331.8 33764.5i −0.487797 0.581334i 0.464859 0.885385i \(-0.346105\pi\)
−0.952656 + 0.304051i \(0.901661\pi\)
\(242\) 0 0
\(243\) −20855.9 + 57301.1i −0.353197 + 0.970400i
\(244\) 0 0
\(245\) −10344.8 + 58668.5i −0.172342 + 0.977401i
\(246\) 0 0
\(247\) −7519.73 + 7071.04i −0.123256 + 0.115902i
\(248\) 0 0
\(249\) −23495.1 4142.83i −0.378948 0.0668187i
\(250\) 0 0
\(251\) −34909.5 12706.0i −0.554111 0.201680i 0.0497613 0.998761i \(-0.484154\pi\)
−0.603872 + 0.797081i \(0.706376\pi\)
\(252\) 0 0
\(253\) 20276.3 17013.9i 0.316773 0.265804i
\(254\) 0 0
\(255\) −32126.9 18548.5i −0.494070 0.285252i
\(256\) 0 0
\(257\) 64595.5 11389.9i 0.977993 0.172447i 0.338267 0.941050i \(-0.390159\pi\)
0.639725 + 0.768603i \(0.279048\pi\)
\(258\) 0 0
\(259\) 86770.2 50096.8i 1.29351 0.746811i
\(260\) 0 0
\(261\) 24583.4 + 67542.4i 0.360879 + 0.991506i
\(262\) 0 0
\(263\) −59033.7 49535.1i −0.853470 0.716146i 0.107081 0.994250i \(-0.465850\pi\)
−0.960551 + 0.278104i \(0.910294\pi\)
\(264\) 0 0
\(265\) 49996.9i 0.711952i
\(266\) 0 0
\(267\) −2357.88 −0.0330749
\(268\) 0 0
\(269\) −69947.8 + 83360.5i −0.966650 + 1.15201i 0.0216924 + 0.999765i \(0.493095\pi\)
−0.988343 + 0.152245i \(0.951350\pi\)
\(270\) 0 0
\(271\) −82365.7 + 29978.7i −1.12152 + 0.408201i −0.835208 0.549935i \(-0.814653\pi\)
−0.286315 + 0.958136i \(0.592430\pi\)
\(272\) 0 0
\(273\) 4679.26 + 8104.72i 0.0627845 + 0.108746i
\(274\) 0 0
\(275\) 3213.11 + 18222.4i 0.0424874 + 0.240958i
\(276\) 0 0
\(277\) 3982.46 6897.82i 0.0519029 0.0898985i −0.838907 0.544275i \(-0.816805\pi\)
0.890810 + 0.454377i \(0.150138\pi\)
\(278\) 0 0
\(279\) −36136.7 43066.0i −0.464237 0.553256i
\(280\) 0 0
\(281\) −34569.7 + 94979.4i −0.437807 + 1.20286i 0.503109 + 0.864223i \(0.332190\pi\)
−0.940916 + 0.338641i \(0.890033\pi\)
\(282\) 0 0
\(283\) −6296.57 + 35709.6i −0.0786196 + 0.445874i 0.919932 + 0.392077i \(0.128243\pi\)
−0.998552 + 0.0537968i \(0.982868\pi\)
\(284\) 0 0
\(285\) −33588.6 10116.3i −0.413526 0.124547i
\(286\) 0 0
\(287\) 183773. + 32404.2i 2.23110 + 0.393403i
\(288\) 0 0
\(289\) −58472.5 21282.2i −0.700093 0.254813i
\(290\) 0 0
\(291\) 48778.6 40930.1i 0.576028 0.483345i
\(292\) 0 0
\(293\) 86673.3 + 50040.9i 1.00960 + 0.582894i 0.911075 0.412241i \(-0.135254\pi\)
0.0985267 + 0.995134i \(0.468587\pi\)
\(294\) 0 0
\(295\) −3991.24 + 703.763i −0.0458631 + 0.00808690i
\(296\) 0 0
\(297\) 61345.7 35417.9i 0.695458 0.401523i
\(298\) 0 0
\(299\) −2347.30 6449.15i −0.0262558 0.0721373i
\(300\) 0 0
\(301\) −119589. 100347.i −1.31995 1.10757i
\(302\) 0 0
\(303\) 34503.1i 0.375814i
\(304\) 0 0
\(305\) −32144.3 −0.345544
\(306\) 0 0
\(307\) 19427.7 23153.0i 0.206132 0.245658i −0.653067 0.757300i \(-0.726518\pi\)
0.859199 + 0.511642i \(0.170963\pi\)
\(308\) 0 0
\(309\) −43730.9 + 15916.8i −0.458007 + 0.166701i
\(310\) 0 0
\(311\) −89682.7 155335.i −0.927231 1.60601i −0.787934 0.615760i \(-0.788849\pi\)
−0.139297 0.990251i \(-0.544484\pi\)
\(312\) 0 0
\(313\) −13398.2 75984.8i −0.136759 0.775600i −0.973618 0.228182i \(-0.926722\pi\)
0.836859 0.547418i \(-0.184389\pi\)
\(314\) 0 0
\(315\) 46467.5 80484.2i 0.468305 0.811128i
\(316\) 0 0
\(317\) 33428.4 + 39838.4i 0.332657 + 0.396445i 0.906283 0.422672i \(-0.138908\pi\)
−0.573625 + 0.819118i \(0.694463\pi\)
\(318\) 0 0
\(319\) 44922.3 123423.i 0.441449 1.21287i
\(320\) 0 0
\(321\) −774.353 + 4391.58i −0.00751500 + 0.0426197i
\(322\) 0 0
\(323\) −136859. 16225.9i −1.31181 0.155526i
\(324\) 0 0
\(325\) 4724.84 + 833.118i 0.0447323 + 0.00788750i
\(326\) 0 0
\(327\) 76098.4 + 27697.6i 0.711672 + 0.259028i
\(328\) 0 0
\(329\) 188414. 158098.i 1.74069 1.46062i
\(330\) 0 0
\(331\) 134064. + 77401.8i 1.22365 + 0.706473i 0.965693 0.259685i \(-0.0836187\pi\)
0.257953 + 0.966157i \(0.416952\pi\)
\(332\) 0 0
\(333\) −82678.0 + 14578.4i −0.745593 + 0.131468i
\(334\) 0 0
\(335\) 139174. 80352.3i 1.24014 0.715993i
\(336\) 0 0
\(337\) 56873.9 + 156260.i 0.500788 + 1.37590i 0.890507 + 0.454969i \(0.150350\pi\)
−0.389720 + 0.920934i \(0.627428\pi\)
\(338\) 0 0
\(339\) −36331.9 30486.1i −0.316147 0.265279i
\(340\) 0 0
\(341\) 102731.i 0.883469i
\(342\) 0 0
\(343\) 27735.7 0.235750
\(344\) 0 0
\(345\) 14992.1 17866.9i 0.125958 0.150110i
\(346\) 0 0
\(347\) −97436.4 + 35463.9i −0.809212 + 0.294529i −0.713298 0.700861i \(-0.752799\pi\)
−0.0959134 + 0.995390i \(0.530577\pi\)
\(348\) 0 0
\(349\) −91112.1 157811.i −0.748041 1.29564i −0.948761 0.315996i \(-0.897661\pi\)
0.200720 0.979649i \(-0.435672\pi\)
\(350\) 0 0
\(351\) −3189.37 18087.8i −0.0258875 0.146815i
\(352\) 0 0
\(353\) 79186.0 137154.i 0.635476 1.10068i −0.350938 0.936399i \(-0.614137\pi\)
0.986414 0.164278i \(-0.0525295\pi\)
\(354\) 0 0
\(355\) −53780.6 64093.2i −0.426745 0.508575i
\(356\) 0 0
\(357\) −42736.2 + 117417.i −0.335320 + 0.921285i
\(358\) 0 0
\(359\) −31561.2 + 178993.i −0.244886 + 1.38882i 0.575870 + 0.817542i \(0.304664\pi\)
−0.820756 + 0.571279i \(0.806448\pi\)
\(360\) 0 0
\(361\) −129489. + 14701.4i −0.993617 + 0.112809i
\(362\) 0 0
\(363\) 11100.1 + 1957.24i 0.0842390 + 0.0148536i
\(364\) 0 0
\(365\) 69385.5 + 25254.2i 0.520814 + 0.189561i
\(366\) 0 0
\(367\) −88559.0 + 74309.9i −0.657508 + 0.551714i −0.909339 0.416057i \(-0.863412\pi\)
0.251831 + 0.967771i \(0.418967\pi\)
\(368\) 0 0
\(369\) −135413. 78180.7i −0.994506 0.574179i
\(370\) 0 0
\(371\) 165844. 29242.8i 1.20490 0.212457i
\(372\) 0 0
\(373\) −158975. + 91784.3i −1.14265 + 0.659706i −0.947084 0.320985i \(-0.895986\pi\)
−0.195561 + 0.980692i \(0.562653\pi\)
\(374\) 0 0
\(375\) 26348.2 + 72391.2i 0.187365 + 0.514782i
\(376\) 0 0
\(377\) −26088.2 21890.6i −0.183553 0.154020i
\(378\) 0 0
\(379\) 227813.i 1.58599i −0.609228 0.792995i \(-0.708521\pi\)
0.609228 0.792995i \(-0.291479\pi\)
\(380\) 0 0
\(381\) 15687.1 0.108067
\(382\) 0 0
\(383\) 11702.7 13946.7i 0.0797789 0.0950768i −0.724679 0.689087i \(-0.758012\pi\)
0.804457 + 0.594010i \(0.202456\pi\)
\(384\) 0 0
\(385\) −159582. + 58083.3i −1.07662 + 0.391859i
\(386\) 0 0
\(387\) 65404.2 + 113283.i 0.436700 + 0.756387i
\(388\) 0 0
\(389\) 19572.2 + 111000.i 0.129342 + 0.733537i 0.978634 + 0.205612i \(0.0659186\pi\)
−0.849291 + 0.527925i \(0.822970\pi\)
\(390\) 0 0
\(391\) 45816.7 79356.8i 0.299688 0.519076i
\(392\) 0 0
\(393\) 38878.8 + 46334.0i 0.251726 + 0.299995i
\(394\) 0 0
\(395\) 7795.12 21416.9i 0.0499607 0.137266i
\(396\) 0 0
\(397\) −32755.9 + 185768.i −0.207830 + 1.17866i 0.685094 + 0.728455i \(0.259761\pi\)
−0.892924 + 0.450207i \(0.851350\pi\)
\(398\) 0 0
\(399\) −13910.9 + 117334.i −0.0873798 + 0.737015i
\(400\) 0 0
\(401\) 252009. + 44436.0i 1.56721 + 0.276341i 0.888784 0.458327i \(-0.151551\pi\)
0.678427 + 0.734668i \(0.262662\pi\)
\(402\) 0 0
\(403\) 25030.3 + 9110.30i 0.154119 + 0.0560948i
\(404\) 0 0
\(405\) −32252.2 + 27062.8i −0.196630 + 0.164992i
\(406\) 0 0
\(407\) 132858. + 76705.8i 0.802047 + 0.463062i
\(408\) 0 0
\(409\) 198698. 35035.8i 1.18781 0.209443i 0.455386 0.890294i \(-0.349501\pi\)
0.732422 + 0.680851i \(0.238390\pi\)
\(410\) 0 0
\(411\) 2115.03 1221.11i 0.0125208 0.00722890i
\(412\) 0 0
\(413\) 4668.89 + 12827.7i 0.0273724 + 0.0752052i
\(414\) 0 0
\(415\) −85991.0 72155.0i −0.499295 0.418958i
\(416\) 0 0
\(417\) 44952.2i 0.258511i
\(418\) 0 0
\(419\) −248905. −1.41777 −0.708884 0.705325i \(-0.750801\pi\)
−0.708884 + 0.705325i \(0.750801\pi\)
\(420\) 0 0
\(421\) −33536.2 + 39966.9i −0.189212 + 0.225494i −0.852308 0.523040i \(-0.824798\pi\)
0.663096 + 0.748535i \(0.269242\pi\)
\(422\) 0 0
\(423\) −193662. + 70487.2i −1.08234 + 0.393940i
\(424\) 0 0
\(425\) 32029.0 + 55475.8i 0.177323 + 0.307133i
\(426\) 0 0
\(427\) 18801.0 + 106626.i 0.103116 + 0.584797i
\(428\) 0 0
\(429\) −7164.66 + 12409.6i −0.0389297 + 0.0674282i
\(430\) 0 0
\(431\) −75081.8 89479.0i −0.404185 0.481689i 0.525106 0.851037i \(-0.324026\pi\)
−0.929291 + 0.369348i \(0.879581\pi\)
\(432\) 0 0
\(433\) −95539.5 + 262493.i −0.509574 + 1.40004i 0.372104 + 0.928191i \(0.378636\pi\)
−0.881678 + 0.471851i \(0.843586\pi\)
\(434\) 0 0
\(435\) 20097.4 113978.i 0.106209 0.602341i
\(436\) 0 0
\(437\) 24988.3 82967.4i 0.130850 0.434455i
\(438\) 0 0
\(439\) −104136. 18362.1i −0.540348 0.0952780i −0.103188 0.994662i \(-0.532904\pi\)
−0.437160 + 0.899384i \(0.644016\pi\)
\(440\) 0 0
\(441\) −157995. 57505.6i −0.812394 0.295687i
\(442\) 0 0
\(443\) 45631.2 38289.2i 0.232517 0.195105i −0.519083 0.854724i \(-0.673727\pi\)
0.751600 + 0.659619i \(0.229282\pi\)
\(444\) 0 0
\(445\) −9607.82 5547.08i −0.0485182 0.0280120i
\(446\) 0 0
\(447\) −126740. + 22347.7i −0.634305 + 0.111845i
\(448\) 0 0
\(449\) 278912. 161030.i 1.38349 0.798756i 0.390916 0.920426i \(-0.372158\pi\)
0.992571 + 0.121670i \(0.0388250\pi\)
\(450\) 0 0
\(451\) 97723.9 + 268494.i 0.480450 + 1.32002i
\(452\) 0 0
\(453\) −61901.7 51941.7i −0.301652 0.253116i
\(454\) 0 0
\(455\) 44033.2i 0.212695i
\(456\) 0 0
\(457\) 259740. 1.24367 0.621837 0.783146i \(-0.286386\pi\)
0.621837 + 0.783146i \(0.286386\pi\)
\(458\) 0 0
\(459\) 157630. 187856.i 0.748192 0.891661i
\(460\) 0 0
\(461\) 197505. 71885.8i 0.929342 0.338253i 0.167393 0.985890i \(-0.446465\pi\)
0.761949 + 0.647638i \(0.224243\pi\)
\(462\) 0 0
\(463\) 121468. + 210389.i 0.566631 + 0.981433i 0.996896 + 0.0787306i \(0.0250867\pi\)
−0.430265 + 0.902703i \(0.641580\pi\)
\(464\) 0 0
\(465\) 15719.2 + 89147.9i 0.0726983 + 0.412292i
\(466\) 0 0
\(467\) −79005.0 + 136841.i −0.362261 + 0.627454i −0.988333 0.152312i \(-0.951328\pi\)
0.626072 + 0.779765i \(0.284662\pi\)
\(468\) 0 0
\(469\) −347938. 414657.i −1.58182 1.88514i
\(470\) 0 0
\(471\) −50062.0 + 137544.i −0.225666 + 0.620012i
\(472\) 0 0
\(473\) 41507.4 235400.i 0.185525 1.05217i
\(474\) 0 0
\(475\) 41495.1 + 44128.1i 0.183912 + 0.195582i
\(476\) 0 0
\(477\) −138963. 24502.9i −0.610748 0.107691i
\(478\) 0 0
\(479\) −190477. 69328.0i −0.830179 0.302161i −0.108247 0.994124i \(-0.534524\pi\)
−0.721932 + 0.691964i \(0.756746\pi\)
\(480\) 0 0
\(481\) 30471.4 25568.6i 0.131705 0.110514i
\(482\) 0 0
\(483\) −68034.9 39280.0i −0.291634 0.168375i
\(484\) 0 0
\(485\) 295053. 52025.7i 1.25434 0.221174i
\(486\) 0 0
\(487\) −99429.3 + 57405.5i −0.419234 + 0.242045i −0.694750 0.719252i \(-0.744485\pi\)
0.275516 + 0.961297i \(0.411151\pi\)
\(488\) 0 0
\(489\) −64571.7 177409.i −0.270038 0.741922i
\(490\) 0 0
\(491\) 125947. + 105682.i 0.522428 + 0.438369i 0.865477 0.500949i \(-0.167015\pi\)
−0.343050 + 0.939317i \(0.611460\pi\)
\(492\) 0 0
\(493\) 454703.i 1.87083i
\(494\) 0 0
\(495\) 142298. 0.580748
\(496\) 0 0
\(497\) −181147. + 215883.i −0.733363 + 0.873988i
\(498\) 0 0
\(499\) −63335.8 + 23052.3i −0.254359 + 0.0925793i −0.466053 0.884757i \(-0.654324\pi\)
0.211693 + 0.977336i \(0.432102\pi\)
\(500\) 0 0
\(501\) 55277.6 + 95743.6i 0.220229 + 0.381447i
\(502\) 0 0
\(503\) −25707.1 145792.i −0.101606 0.576233i −0.992522 0.122066i \(-0.961048\pi\)
0.890916 0.454167i \(-0.150063\pi\)
\(504\) 0 0
\(505\) 81171.1 140592.i 0.318287 0.551289i
\(506\) 0 0
\(507\) −81042.2 96582.4i −0.315279 0.375735i
\(508\) 0 0
\(509\) 18261.1 50171.8i 0.0704839 0.193653i −0.899449 0.437026i \(-0.856032\pi\)
0.969933 + 0.243373i \(0.0782539\pi\)
\(510\) 0 0
\(511\) 43187.6 244929.i 0.165393 0.937991i
\(512\) 0 0
\(513\) 104414. 207051.i 0.396756 0.786761i
\(514\) 0 0
\(515\) −215639. 38022.9i −0.813041 0.143361i
\(516\) 0 0
\(517\) 353887. + 128804.i 1.32399 + 0.481891i
\(518\) 0 0
\(519\) −28256.5 + 23710.0i −0.104902 + 0.0880231i
\(520\) 0 0
\(521\) −309057. 178434.i −1.13858 0.657360i −0.192502 0.981297i \(-0.561660\pi\)
−0.946079 + 0.323937i \(0.894994\pi\)
\(522\) 0 0
\(523\) 112140. 19773.3i 0.409974 0.0722896i 0.0351424 0.999382i \(-0.488812\pi\)
0.374832 + 0.927093i \(0.377700\pi\)
\(524\) 0 0
\(525\) 47561.1 27459.4i 0.172557 0.0996259i
\(526\) 0 0
\(527\) 121638. + 334198.i 0.437974 + 1.20332i
\(528\) 0 0
\(529\) −170238. 142846.i −0.608337 0.510455i
\(530\) 0 0
\(531\) 11438.3i 0.0405669i
\(532\) 0 0
\(533\) 74085.0 0.260781
\(534\) 0 0
\(535\) −13486.8 + 16072.9i −0.0471196 + 0.0561549i
\(536\) 0 0
\(537\) −83934.8 + 30549.8i −0.291068 + 0.105940i
\(538\) 0 0
\(539\) 153620. + 266078.i 0.528774 + 0.915864i
\(540\) 0 0
\(541\) 36704.4 + 208161.i 0.125407 + 0.711221i 0.981065 + 0.193678i \(0.0620419\pi\)
−0.855658 + 0.517542i \(0.826847\pi\)
\(542\) 0 0
\(543\) 121403. 210277.i 0.411748 0.713168i
\(544\) 0 0
\(545\) 244923. + 291888.i 0.824588 + 0.982705i
\(546\) 0 0
\(547\) −2504.61 + 6881.36i −0.00837077 + 0.0229985i −0.943808 0.330495i \(-0.892784\pi\)
0.935437 + 0.353494i \(0.115006\pi\)
\(548\) 0 0
\(549\) 15753.6 89342.8i 0.0522678 0.296425i
\(550\) 0 0
\(551\) −98466.0 418542.i −0.324327 1.37859i
\(552\) 0 0
\(553\) −75601.2 13330.5i −0.247217 0.0435910i
\(554\) 0 0
\(555\) 127029. + 46234.8i 0.412399 + 0.150101i
\(556\) 0 0
\(557\) 330651. 277449.i 1.06576 0.894280i 0.0710994 0.997469i \(-0.477349\pi\)
0.994662 + 0.103189i \(0.0329048\pi\)
\(558\) 0 0
\(559\) −53674.3 30988.9i −0.171768 0.0991704i
\(560\) 0 0
\(561\) −188415. + 33222.6i −0.598672 + 0.105562i
\(562\) 0 0
\(563\) −227258. + 131207.i −0.716971 + 0.413943i −0.813637 0.581373i \(-0.802516\pi\)
0.0966658 + 0.995317i \(0.469182\pi\)
\(564\) 0 0
\(565\) −76323.6 209697.i −0.239090 0.656895i
\(566\) 0 0
\(567\) 108634. + 91154.8i 0.337909 + 0.283539i
\(568\) 0 0
\(569\) 592913.i 1.83133i 0.401943 + 0.915665i \(0.368335\pi\)
−0.401943 + 0.915665i \(0.631665\pi\)
\(570\) 0 0
\(571\) −37331.0 −0.114498 −0.0572489 0.998360i \(-0.518233\pi\)
−0.0572489 + 0.998360i \(0.518233\pi\)
\(572\) 0 0
\(573\) −8856.42 + 10554.7i −0.0269742 + 0.0321466i
\(574\) 0 0
\(575\) −37845.6 + 13774.7i −0.114467 + 0.0416625i
\(576\) 0 0
\(577\) −121380. 210236.i −0.364581 0.631473i 0.624128 0.781322i \(-0.285454\pi\)
−0.988709 + 0.149849i \(0.952121\pi\)
\(578\) 0 0
\(579\) −53736.7 304756.i −0.160293 0.909066i
\(580\) 0 0
\(581\) −189049. + 327443.i −0.560045 + 0.970027i
\(582\) 0 0
\(583\) 165743. + 197525.i 0.487638 + 0.581144i
\(584\) 0 0
\(585\) 12619.2 34670.9i 0.0368739 0.101310i
\(586\) 0 0
\(587\) 18243.6 103464.i 0.0529460 0.300272i −0.946823 0.321754i \(-0.895727\pi\)
0.999769 + 0.0214825i \(0.00683861\pi\)
\(588\) 0 0
\(589\) 184335. + 281280.i 0.531346 + 0.810789i
\(590\) 0 0
\(591\) −35504.5 6260.40i −0.101650 0.0179237i
\(592\) 0 0
\(593\) −177281. 64525.0i −0.504142 0.183493i 0.0774143 0.996999i \(-0.475334\pi\)
−0.581556 + 0.813506i \(0.697556\pi\)
\(594\) 0 0
\(595\) −450372. + 377907.i −1.27215 + 1.06746i
\(596\) 0 0
\(597\) 247879. + 143113.i 0.695489 + 0.401541i
\(598\) 0 0
\(599\) −345357. + 60895.7i −0.962530 + 0.169720i −0.632766 0.774343i \(-0.718080\pi\)
−0.329764 + 0.944063i \(0.606969\pi\)
\(600\) 0 0
\(601\) −184895. + 106749.i −0.511889 + 0.295539i −0.733610 0.679571i \(-0.762166\pi\)
0.221721 + 0.975110i \(0.428833\pi\)
\(602\) 0 0
\(603\) 155126. + 426205.i 0.426629 + 1.17215i
\(604\) 0 0
\(605\) 40625.7 + 34089.0i 0.110992 + 0.0931331i
\(606\) 0 0
\(607\) 94696.2i 0.257013i −0.991709 0.128507i \(-0.958982\pi\)
0.991709 0.128507i \(-0.0410183\pi\)
\(608\) 0 0
\(609\) −389830. −1.05109
\(610\) 0 0
\(611\) 62766.3 74802.0i 0.168130 0.200369i
\(612\) 0 0
\(613\) −81985.0 + 29840.1i −0.218179 + 0.0794108i −0.448797 0.893634i \(-0.648147\pi\)
0.230618 + 0.973044i \(0.425925\pi\)
\(614\) 0 0
\(615\) 125886. + 218042.i 0.332835 + 0.576486i
\(616\) 0 0
\(617\) 28590.9 + 162147.i 0.0751031 + 0.425931i 0.999057 + 0.0434262i \(0.0138274\pi\)
−0.923953 + 0.382505i \(0.875062\pi\)
\(618\) 0 0
\(619\) −161150. + 279120.i −0.420580 + 0.728466i −0.995996 0.0893948i \(-0.971507\pi\)
0.575416 + 0.817861i \(0.304840\pi\)
\(620\) 0 0
\(621\) 99104.9 + 118109.i 0.256988 + 0.306266i
\(622\) 0 0
\(623\) −12780.6 + 35114.5i −0.0329288 + 0.0904711i
\(624\) 0 0
\(625\) −44731.7 + 253686.i −0.114513 + 0.649436i
\(626\) 0 0
\(627\) −166236. + 71381.6i −0.422854 + 0.181573i
\(628\) 0 0
\(629\) 523031. + 92224.5i 1.32198 + 0.233101i
\(630\) 0 0
\(631\) 146067. + 53164.2i 0.366855 + 0.133524i 0.518868 0.854854i \(-0.326353\pi\)
−0.152013 + 0.988378i \(0.548576\pi\)
\(632\) 0 0
\(633\) −142943. + 119943.i −0.356743 + 0.299343i
\(634\) 0 0
\(635\) 63921.5 + 36905.1i 0.158526 + 0.0915248i
\(636\) 0 0
\(637\) 78453.1 13833.4i 0.193344 0.0340918i
\(638\) 0 0
\(639\) 204500. 118068.i 0.500832 0.289155i
\(640\) 0 0
\(641\) −221071. 607387.i −0.538041 1.47826i −0.849290 0.527927i \(-0.822969\pi\)
0.311248 0.950329i \(-0.399253\pi\)
\(642\) 0 0
\(643\) 375051. + 314705.i 0.907127 + 0.761170i 0.971570 0.236752i \(-0.0760828\pi\)
−0.0644434 + 0.997921i \(0.520527\pi\)
\(644\) 0 0
\(645\) 210627.i 0.506285i
\(646\) 0 0
\(647\) 230175. 0.549858 0.274929 0.961465i \(-0.411346\pi\)
0.274929 + 0.961465i \(0.411346\pi\)
\(648\) 0 0
\(649\) −13435.3 + 16011.6i −0.0318976 + 0.0380141i
\(650\) 0 0
\(651\) 286518. 104284.i 0.676067 0.246068i
\(652\) 0 0
\(653\) −361571. 626259.i −0.847944 1.46868i −0.883040 0.469298i \(-0.844507\pi\)
0.0350959 0.999384i \(-0.488826\pi\)
\(654\) 0 0
\(655\) 49418.4 + 280265.i 0.115188 + 0.653261i
\(656\) 0 0
\(657\) −104198. + 180475.i −0.241394 + 0.418107i
\(658\) 0 0
\(659\) −200214. 238606.i −0.461025 0.549428i 0.484580 0.874747i \(-0.338973\pi\)
−0.945604 + 0.325320i \(0.894528\pi\)
\(660\) 0 0
\(661\) 255188. 701123.i 0.584060 1.60469i −0.197117 0.980380i \(-0.563158\pi\)
0.781176 0.624311i \(-0.214620\pi\)
\(662\) 0 0
\(663\) −8614.18 + 48853.4i −0.0195969 + 0.111139i
\(664\) 0 0
\(665\) −332719. + 445381.i −0.752376 + 1.00714i
\(666\) 0 0
\(667\) 281537. + 49642.6i 0.632826 + 0.111584i
\(668\) 0 0
\(669\) 253117. + 92127.0i 0.565547 + 0.205842i
\(670\) 0 0
\(671\) −126994. + 106560.i −0.282057 + 0.236674i
\(672\) 0 0
\(673\) −166906. 96363.3i −0.368504 0.212756i 0.304301 0.952576i \(-0.401577\pi\)
−0.672805 + 0.739820i \(0.734911\pi\)
\(674\) 0 0
\(675\) −106145. + 18716.2i −0.232965 + 0.0410781i
\(676\) 0 0
\(677\) −48977.6 + 28277.2i −0.106861 + 0.0616963i −0.552478 0.833527i \(-0.686318\pi\)
0.445617 + 0.895224i \(0.352984\pi\)
\(678\) 0 0
\(679\) −345148. 948287.i −0.748628 2.05684i
\(680\) 0 0
\(681\) 305585. + 256416.i 0.658928 + 0.552906i
\(682\) 0 0
\(683\) 603564.i 1.29384i −0.762556 0.646922i \(-0.776056\pi\)
0.762556 0.646922i \(-0.223944\pi\)
\(684\) 0 0
\(685\) 11491.0 0.0244894
\(686\) 0 0
\(687\) −89865.7 + 107098.i −0.190406 + 0.226917i
\(688\) 0 0
\(689\) 62825.2 22866.5i 0.132341 0.0481683i
\(690\) 0 0
\(691\) −345267. 598020.i −0.723100 1.25245i −0.959751 0.280852i \(-0.909383\pi\)
0.236651 0.971595i \(-0.423950\pi\)
\(692\) 0 0
\(693\) −83228.9 472015.i −0.173304 0.982854i
\(694\) 0 0
\(695\) −105753. + 183170.i −0.218939 + 0.379214i
\(696\) 0 0
\(697\) 635821. + 757742.i 1.30879 + 1.55975i
\(698\) 0 0
\(699\) 43179.1 118634.i 0.0883729 0.242803i
\(700\) 0 0
\(701\) −105203. + 596633.i −0.214087 + 1.21415i 0.668397 + 0.743805i \(0.266981\pi\)
−0.882484 + 0.470343i \(0.844130\pi\)
\(702\) 0 0
\(703\) 501407. 28372.2i 1.01457 0.0574093i
\(704\) 0 0
\(705\) 326805. + 57624.6i 0.657523 + 0.115939i
\(706\) 0 0
\(707\) −513834. 187020.i −1.02798 0.374154i
\(708\) 0 0
\(709\) 304300. 255338.i 0.605353 0.507952i −0.287808 0.957688i \(-0.592927\pi\)
0.893161 + 0.449736i \(0.148482\pi\)
\(710\) 0 0
\(711\) 55706.6 + 32162.2i 0.110196 + 0.0636219i
\(712\) 0 0
\(713\) −220205. + 38828.0i −0.433159 + 0.0763776i
\(714\) 0 0
\(715\) −58388.7 + 33710.7i −0.114213 + 0.0659411i
\(716\) 0 0
\(717\) −131842. 362232.i −0.256457 0.704610i
\(718\) 0 0
\(719\) −186996. 156909.i −0.361722 0.303521i 0.443754 0.896148i \(-0.353646\pi\)
−0.805477 + 0.592627i \(0.798091\pi\)
\(720\) 0 0
\(721\) 737533.i 1.41877i
\(722\) 0 0
\(723\) −200304. −0.383189
\(724\) 0 0
\(725\) −128461. + 153094.i −0.244397 + 0.291261i
\(726\) 0 0
\(727\) 633293. 230500.i 1.19822 0.436116i 0.335616 0.941999i \(-0.391056\pi\)
0.862602 + 0.505883i \(0.168833\pi\)
\(728\) 0 0
\(729\) 58812.7 + 101867.i 0.110666 + 0.191680i
\(730\) 0 0
\(731\) −143695. 814938.i −0.268911 1.52507i
\(732\) 0 0
\(733\) −63729.5 + 110383.i −0.118613 + 0.205444i −0.919218 0.393748i \(-0.871178\pi\)
0.800605 + 0.599192i \(0.204511\pi\)
\(734\) 0 0
\(735\) 174022. + 207392.i 0.322129 + 0.383899i
\(736\) 0 0
\(737\) 283468. 778823.i 0.521879 1.43385i
\(738\) 0 0
\(739\) −43423.8 + 246269.i −0.0795132 + 0.450942i 0.918893 + 0.394507i \(0.129085\pi\)
−0.998406 + 0.0564352i \(0.982027\pi\)
\(740\) 0 0
\(741\) 2650.09 + 46833.7i 0.00482641 + 0.0852946i
\(742\) 0 0
\(743\) −592950. 104553.i −1.07409 0.189391i −0.391489 0.920183i \(-0.628040\pi\)
−0.682600 + 0.730792i \(0.739151\pi\)
\(744\) 0 0
\(745\) −569010. 207103.i −1.02520 0.373141i
\(746\) 0 0
\(747\) 242693. 203644.i 0.434927 0.364947i
\(748\) 0 0
\(749\) 61203.8 + 35336.0i 0.109097 + 0.0629874i
\(750\) 0 0
\(751\) 184265. 32491.0i 0.326711 0.0576080i −0.00788703 0.999969i \(-0.502511\pi\)
0.334598 + 0.942361i \(0.391399\pi\)
\(752\) 0 0
\(753\) −146208. + 84413.5i −0.257859 + 0.148875i
\(754\) 0 0
\(755\) −130039. 357278.i −0.228128 0.626777i
\(756\) 0 0
\(757\) 156846. + 131610.i 0.273705 + 0.229666i 0.769300 0.638888i \(-0.220605\pi\)
−0.495595 + 0.868554i \(0.665050\pi\)
\(758\) 0 0
\(759\) 120287.i 0.208803i
\(760\) 0 0
\(761\) −976866. −1.68681 −0.843404 0.537280i \(-0.819452\pi\)
−0.843404 + 0.537280i \(0.819452\pi\)
\(762\) 0 0
\(763\) 824966. 983156.i 1.41706 1.68878i
\(764\) 0 0
\(765\) 462915. 168487.i 0.791004 0.287902i
\(766\) 0 0
\(767\) 2709.76 + 4693.44i 0.00460617 + 0.00797813i
\(768\) 0 0
\(769\) 40758.6 + 231154.i 0.0689235 + 0.390884i 0.999681 + 0.0252479i \(0.00803752\pi\)
−0.930758 + 0.365636i \(0.880851\pi\)
\(770\) 0 0
\(771\) 149040. 258146.i 0.250724 0.434266i
\(772\) 0 0
\(773\) −91616.0 109184.i −0.153325 0.182725i 0.683914 0.729562i \(-0.260276\pi\)
−0.837239 + 0.546837i \(0.815832\pi\)
\(774\) 0 0
\(775\) 53462.1 146886.i 0.0890108 0.244555i
\(776\) 0 0
\(777\) 79066.8 448410.i 0.130964 0.742734i
\(778\) 0 0
\(779\) 749345. + 559794.i 1.23483 + 0.922472i
\(780\) 0 0
\(781\) −424946. 74929.5i −0.696677 0.122843i
\(782\) 0 0
\(783\) 718932. + 261670.i 1.17264 + 0.426806i
\(784\) 0 0
\(785\) −527573. + 442686.i −0.856137 + 0.718384i
\(786\) 0 0
\(787\) −230126. 132863.i −0.371549 0.214514i 0.302586 0.953122i \(-0.402150\pi\)
−0.674135 + 0.738608i \(0.735483\pi\)
\(788\) 0 0
\(789\) −344890. + 60813.5i −0.554022 + 0.0976890i
\(790\) 0 0
\(791\) −650945. + 375823.i −1.04038 + 0.600662i
\(792\) 0 0