Properties

Label 108.5.k.a.5.6
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.6
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23486 - 8.91488i) q^{3} +(5.87553 + 16.1429i) q^{5} +(8.12577 + 46.0835i) q^{7} +(-77.9503 + 22.0172i) q^{9} +O(q^{10})\) \(q+(-1.23486 - 8.91488i) q^{3} +(5.87553 + 16.1429i) q^{5} +(8.12577 + 46.0835i) q^{7} +(-77.9503 + 22.0172i) q^{9} +(-21.9431 + 60.2882i) q^{11} +(26.5065 + 22.2416i) q^{13} +(136.657 - 72.3139i) q^{15} +(211.894 + 122.337i) q^{17} +(215.694 + 373.592i) q^{19} +(400.795 - 129.347i) q^{21} +(364.888 + 64.3396i) q^{23} +(252.707 - 212.046i) q^{25} +(292.538 + 667.729i) q^{27} +(-478.762 - 570.567i) q^{29} +(-232.834 + 1320.47i) q^{31} +(564.559 + 121.173i) q^{33} +(-696.178 + 401.939i) q^{35} +(27.6012 - 47.8066i) q^{37} +(165.550 - 263.768i) q^{39} +(-603.231 + 718.902i) q^{41} +(1586.08 + 577.286i) q^{43} +(-813.421 - 1128.98i) q^{45} +(-3718.42 + 655.657i) q^{47} +(198.539 - 72.2624i) q^{49} +(828.960 - 2040.07i) q^{51} -1222.43i q^{53} -1102.15 q^{55} +(3064.18 - 2384.22i) q^{57} +(-1312.00 - 3604.69i) q^{59} +(308.780 + 1751.18i) q^{61} +(-1648.04 - 3413.32i) q^{63} +(-203.304 + 558.573i) q^{65} +(3270.92 + 2744.63i) q^{67} +(122.995 - 3332.39i) q^{69} +(-4353.90 - 2513.72i) q^{71} +(-496.098 - 859.268i) q^{73} +(-2202.42 - 1991.00i) q^{75} +(-2956.60 - 521.328i) q^{77} +(-8677.93 + 7281.65i) q^{79} +(5591.48 - 3432.50i) q^{81} +(-2884.98 - 3438.18i) q^{83} +(-729.883 + 4139.37i) q^{85} +(-4495.33 + 4972.68i) q^{87} +(1220.28 - 704.528i) q^{89} +(-809.586 + 1402.24i) q^{91} +(12059.3 + 445.098i) q^{93} +(-4763.55 + 5676.97i) q^{95} +(5073.22 + 1846.50i) q^{97} +(383.092 - 5182.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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
\(3\) −1.23486 8.91488i −0.137206 0.990542i
\(4\) 0 0
\(5\) 5.87553 + 16.1429i 0.235021 + 0.645716i 0.999999 + 0.00165851i \(0.000527920\pi\)
−0.764977 + 0.644057i \(0.777250\pi\)
\(6\) 0 0
\(7\) 8.12577 + 46.0835i 0.165832 + 0.940480i 0.948202 + 0.317667i \(0.102899\pi\)
−0.782370 + 0.622813i \(0.785990\pi\)
\(8\) 0 0
\(9\) −77.9503 + 22.0172i −0.962349 + 0.271818i
\(10\) 0 0
\(11\) −21.9431 + 60.2882i −0.181348 + 0.498250i −0.996742 0.0806569i \(-0.974298\pi\)
0.815394 + 0.578907i \(0.196520\pi\)
\(12\) 0 0
\(13\) 26.5065 + 22.2416i 0.156843 + 0.131607i 0.717832 0.696216i \(-0.245135\pi\)
−0.560989 + 0.827823i \(0.689579\pi\)
\(14\) 0 0
\(15\) 136.657 72.3139i 0.607362 0.321395i
\(16\) 0 0
\(17\) 211.894 + 122.337i 0.733196 + 0.423311i 0.819590 0.572950i \(-0.194201\pi\)
−0.0863944 + 0.996261i \(0.527535\pi\)
\(18\) 0 0
\(19\) 215.694 + 373.592i 0.597489 + 1.03488i 0.993190 + 0.116502i \(0.0371682\pi\)
−0.395701 + 0.918379i \(0.629498\pi\)
\(20\) 0 0
\(21\) 400.795 129.347i 0.908832 0.293304i
\(22\) 0 0
\(23\) 364.888 + 64.3396i 0.689770 + 0.121625i 0.507536 0.861630i \(-0.330556\pi\)
0.182233 + 0.983255i \(0.441667\pi\)
\(24\) 0 0
\(25\) 252.707 212.046i 0.404331 0.339274i
\(26\) 0 0
\(27\) 292.538 + 667.729i 0.401287 + 0.915952i
\(28\) 0 0
\(29\) −478.762 570.567i −0.569277 0.678438i 0.402205 0.915550i \(-0.368244\pi\)
−0.971483 + 0.237111i \(0.923799\pi\)
\(30\) 0 0
\(31\) −232.834 + 1320.47i −0.242283 + 1.37405i 0.584436 + 0.811440i \(0.301316\pi\)
−0.826719 + 0.562615i \(0.809795\pi\)
\(32\) 0 0
\(33\) 564.559 + 121.173i 0.518420 + 0.111270i
\(34\) 0 0
\(35\) −696.178 + 401.939i −0.568309 + 0.328113i
\(36\) 0 0
\(37\) 27.6012 47.8066i 0.0201615 0.0349208i −0.855769 0.517359i \(-0.826915\pi\)
0.875930 + 0.482438i \(0.160249\pi\)
\(38\) 0 0
\(39\) 165.550 263.768i 0.108843 0.173417i
\(40\) 0 0
\(41\) −603.231 + 718.902i −0.358852 + 0.427664i −0.915021 0.403406i \(-0.867826\pi\)
0.556169 + 0.831069i \(0.312271\pi\)
\(42\) 0 0
\(43\) 1586.08 + 577.286i 0.857805 + 0.312215i 0.733218 0.679993i \(-0.238017\pi\)
0.124586 + 0.992209i \(0.460240\pi\)
\(44\) 0 0
\(45\) −813.421 1128.98i −0.401689 0.557521i
\(46\) 0 0
\(47\) −3718.42 + 655.657i −1.68330 + 0.296812i −0.931814 0.362935i \(-0.881775\pi\)
−0.751488 + 0.659747i \(0.770664\pi\)
\(48\) 0 0
\(49\) 198.539 72.2624i 0.0826903 0.0300968i
\(50\) 0 0
\(51\) 828.960 2040.07i 0.318708 0.784343i
\(52\) 0 0
\(53\) 1222.43i 0.435185i −0.976040 0.217592i \(-0.930180\pi\)
0.976040 0.217592i \(-0.0698203\pi\)
\(54\) 0 0
\(55\) −1102.15 −0.364348
\(56\) 0 0
\(57\) 3064.18 2384.22i 0.943115 0.733831i
\(58\) 0 0
\(59\) −1312.00 3604.69i −0.376904 1.03553i −0.972633 0.232349i \(-0.925359\pi\)
0.595729 0.803185i \(-0.296863\pi\)
\(60\) 0 0
\(61\) 308.780 + 1751.18i 0.0829831 + 0.470620i 0.997774 + 0.0666918i \(0.0212444\pi\)
−0.914791 + 0.403928i \(0.867644\pi\)
\(62\) 0 0
\(63\) −1648.04 3413.32i −0.415227 0.859994i
\(64\) 0 0
\(65\) −203.304 + 558.573i −0.0481193 + 0.132207i
\(66\) 0 0
\(67\) 3270.92 + 2744.63i 0.728652 + 0.611411i 0.929764 0.368157i \(-0.120011\pi\)
−0.201112 + 0.979568i \(0.564455\pi\)
\(68\) 0 0
\(69\) 122.995 3332.39i 0.0258339 0.699934i
\(70\) 0 0
\(71\) −4353.90 2513.72i −0.863697 0.498656i 0.00155135 0.999999i \(-0.499506\pi\)
−0.865249 + 0.501343i \(0.832840\pi\)
\(72\) 0 0
\(73\) −496.098 859.268i −0.0930941 0.161244i 0.815717 0.578451i \(-0.196342\pi\)
−0.908812 + 0.417207i \(0.863009\pi\)
\(74\) 0 0
\(75\) −2202.42 1991.00i −0.391542 0.353956i
\(76\) 0 0
\(77\) −2956.60 521.328i −0.498667 0.0879285i
\(78\) 0 0
\(79\) −8677.93 + 7281.65i −1.39047 + 1.16674i −0.425323 + 0.905042i \(0.639840\pi\)
−0.965149 + 0.261703i \(0.915716\pi\)
\(80\) 0 0
\(81\) 5591.48 3432.50i 0.852230 0.523167i
\(82\) 0 0
\(83\) −2884.98 3438.18i −0.418780 0.499083i 0.514870 0.857268i \(-0.327840\pi\)
−0.933651 + 0.358185i \(0.883396\pi\)
\(84\) 0 0
\(85\) −729.883 + 4139.37i −0.101022 + 0.572923i
\(86\) 0 0
\(87\) −4495.33 + 4972.68i −0.593914 + 0.656980i
\(88\) 0 0
\(89\) 1220.28 704.528i 0.154056 0.0889443i −0.420990 0.907065i \(-0.638317\pi\)
0.575046 + 0.818121i \(0.304984\pi\)
\(90\) 0 0
\(91\) −809.586 + 1402.24i −0.0977643 + 0.169333i
\(92\) 0 0
\(93\) 12059.3 + 445.098i 1.39430 + 0.0514623i
\(94\) 0 0
\(95\) −4763.55 + 5676.97i −0.527817 + 0.629027i
\(96\) 0 0
\(97\) 5073.22 + 1846.50i 0.539188 + 0.196248i 0.597236 0.802065i \(-0.296265\pi\)
−0.0580481 + 0.998314i \(0.518488\pi\)
\(98\) 0 0
\(99\) 383.092 5182.61i 0.0390870 0.528784i
\(100\) 0 0
\(101\) −2412.93 + 425.465i −0.236539 + 0.0417082i −0.290661 0.956826i \(-0.593875\pi\)
0.0541220 + 0.998534i \(0.482764\pi\)
\(102\) 0 0
\(103\) 15177.4 5524.12i 1.43061 0.520701i 0.493507 0.869742i \(-0.335715\pi\)
0.937107 + 0.349041i \(0.113493\pi\)
\(104\) 0 0
\(105\) 4442.92 + 5710.01i 0.402986 + 0.517915i
\(106\) 0 0
\(107\) 16847.5i 1.47153i 0.677238 + 0.735764i \(0.263177\pi\)
−0.677238 + 0.735764i \(0.736823\pi\)
\(108\) 0 0
\(109\) 7711.13 0.649031 0.324515 0.945880i \(-0.394799\pi\)
0.324515 + 0.945880i \(0.394799\pi\)
\(110\) 0 0
\(111\) −460.274 187.027i −0.0373568 0.0151795i
\(112\) 0 0
\(113\) −7240.01 19891.8i −0.566999 1.55782i −0.809165 0.587582i \(-0.800080\pi\)
0.242166 0.970235i \(-0.422142\pi\)
\(114\) 0 0
\(115\) 1105.28 + 6268.38i 0.0835754 + 0.473980i
\(116\) 0 0
\(117\) −2555.89 1150.14i −0.186711 0.0840192i
\(118\) 0 0
\(119\) −3915.91 + 10758.9i −0.276528 + 0.759754i
\(120\) 0 0
\(121\) 8062.49 + 6765.23i 0.550679 + 0.462074i
\(122\) 0 0
\(123\) 7153.83 + 4489.99i 0.472856 + 0.296780i
\(124\) 0 0
\(125\) 14206.2 + 8201.94i 0.909196 + 0.524924i
\(126\) 0 0
\(127\) −2846.78 4930.77i −0.176501 0.305709i 0.764179 0.645005i \(-0.223145\pi\)
−0.940680 + 0.339296i \(0.889811\pi\)
\(128\) 0 0
\(129\) 3187.85 14852.6i 0.191566 0.892530i
\(130\) 0 0
\(131\) 21524.9 + 3795.42i 1.25429 + 0.221165i 0.761030 0.648716i \(-0.224694\pi\)
0.493260 + 0.869882i \(0.335805\pi\)
\(132\) 0 0
\(133\) −15463.8 + 12975.6i −0.874203 + 0.733543i
\(134\) 0 0
\(135\) −9060.26 + 8645.68i −0.497134 + 0.474386i
\(136\) 0 0
\(137\) −1116.26 1330.31i −0.0594739 0.0708782i 0.735487 0.677538i \(-0.236953\pi\)
−0.794961 + 0.606660i \(0.792509\pi\)
\(138\) 0 0
\(139\) 2361.73 13394.0i 0.122236 0.693236i −0.860675 0.509155i \(-0.829958\pi\)
0.982911 0.184081i \(-0.0589310\pi\)
\(140\) 0 0
\(141\) 10436.8 + 32339.6i 0.524965 + 1.62666i
\(142\) 0 0
\(143\) −1922.54 + 1109.98i −0.0940165 + 0.0542804i
\(144\) 0 0
\(145\) 6397.61 11081.0i 0.304286 0.527039i
\(146\) 0 0
\(147\) −889.379 1680.72i −0.0411578 0.0777788i
\(148\) 0 0
\(149\) 27688.4 32997.8i 1.24717 1.48632i 0.437744 0.899100i \(-0.355778\pi\)
0.809427 0.587221i \(-0.199778\pi\)
\(150\) 0 0
\(151\) −10633.6 3870.31i −0.466365 0.169743i 0.0981399 0.995173i \(-0.468711\pi\)
−0.564505 + 0.825430i \(0.690933\pi\)
\(152\) 0 0
\(153\) −19210.7 4870.88i −0.820653 0.208077i
\(154\) 0 0
\(155\) −22684.2 + 3999.83i −0.944190 + 0.166486i
\(156\) 0 0
\(157\) −18511.2 + 6737.53i −0.750992 + 0.273339i −0.689023 0.724739i \(-0.741960\pi\)
−0.0619689 + 0.998078i \(0.519738\pi\)
\(158\) 0 0
\(159\) −10897.9 + 1509.53i −0.431069 + 0.0597101i
\(160\) 0 0
\(161\) 17338.1i 0.668884i
\(162\) 0 0
\(163\) −22213.1 −0.836055 −0.418027 0.908434i \(-0.637278\pi\)
−0.418027 + 0.908434i \(0.637278\pi\)
\(164\) 0 0
\(165\) 1361.00 + 9825.57i 0.0499909 + 0.360902i
\(166\) 0 0
\(167\) 45.4798 + 124.955i 0.00163074 + 0.00448043i 0.940505 0.339779i \(-0.110352\pi\)
−0.938875 + 0.344259i \(0.888130\pi\)
\(168\) 0 0
\(169\) −4751.66 26948.0i −0.166369 0.943524i
\(170\) 0 0
\(171\) −25038.8 24372.6i −0.856292 0.833509i
\(172\) 0 0
\(173\) 4304.21 11825.7i 0.143814 0.395126i −0.846783 0.531939i \(-0.821464\pi\)
0.990597 + 0.136813i \(0.0436859\pi\)
\(174\) 0 0
\(175\) 11825.3 + 9922.58i 0.386131 + 0.324002i
\(176\) 0 0
\(177\) −30515.3 + 16147.6i −0.974027 + 0.515421i
\(178\) 0 0
\(179\) 38910.8 + 22465.2i 1.21441 + 0.701138i 0.963716 0.266929i \(-0.0860088\pi\)
0.250691 + 0.968067i \(0.419342\pi\)
\(180\) 0 0
\(181\) −30521.8 52865.4i −0.931652 1.61367i −0.780498 0.625158i \(-0.785035\pi\)
−0.151154 0.988510i \(-0.548299\pi\)
\(182\) 0 0
\(183\) 15230.2 4915.19i 0.454784 0.146770i
\(184\) 0 0
\(185\) 933.908 + 164.673i 0.0272873 + 0.00481149i
\(186\) 0 0
\(187\) −12025.1 + 10090.2i −0.343878 + 0.288548i
\(188\) 0 0
\(189\) −28394.2 + 18907.0i −0.794888 + 0.529297i
\(190\) 0 0
\(191\) −13921.7 16591.2i −0.381614 0.454790i 0.540709 0.841210i \(-0.318156\pi\)
−0.922323 + 0.386420i \(0.873712\pi\)
\(192\) 0 0
\(193\) 2671.39 15150.2i 0.0717171 0.406728i −0.927723 0.373269i \(-0.878237\pi\)
0.999440 0.0334585i \(-0.0106521\pi\)
\(194\) 0 0
\(195\) 5230.67 + 1122.67i 0.137559 + 0.0295246i
\(196\) 0 0
\(197\) 42526.8 24552.9i 1.09580 0.632659i 0.160684 0.987006i \(-0.448630\pi\)
0.935114 + 0.354347i \(0.115297\pi\)
\(198\) 0 0
\(199\) 38457.1 66609.6i 0.971114 1.68202i 0.278910 0.960317i \(-0.410027\pi\)
0.692204 0.721702i \(-0.256640\pi\)
\(200\) 0 0
\(201\) 20428.9 32549.1i 0.505653 0.805650i
\(202\) 0 0
\(203\) 22403.4 26699.3i 0.543653 0.647901i
\(204\) 0 0
\(205\) −15149.5 5513.95i −0.360487 0.131207i
\(206\) 0 0
\(207\) −29859.7 + 3018.54i −0.696859 + 0.0704459i
\(208\) 0 0
\(209\) −27256.2 + 4806.00i −0.623983 + 0.110025i
\(210\) 0 0
\(211\) 80895.2 29443.4i 1.81701 0.661338i 0.821123 0.570751i \(-0.193348\pi\)
0.995889 0.0905869i \(-0.0288743\pi\)
\(212\) 0 0
\(213\) −17033.1 + 41918.6i −0.375435 + 0.923948i
\(214\) 0 0
\(215\) 28995.8i 0.627275i
\(216\) 0 0
\(217\) −62743.7 −1.33245
\(218\) 0 0
\(219\) −7047.66 + 5483.73i −0.146946 + 0.114337i
\(220\) 0 0
\(221\) 2895.59 + 7955.58i 0.0592861 + 0.162887i
\(222\) 0 0
\(223\) 4374.88 + 24811.2i 0.0879743 + 0.498927i 0.996675 + 0.0814790i \(0.0259644\pi\)
−0.908701 + 0.417448i \(0.862925\pi\)
\(224\) 0 0
\(225\) −15029.9 + 22092.9i −0.296887 + 0.436404i
\(226\) 0 0
\(227\) −25727.7 + 70686.3i −0.499286 + 1.37178i 0.392680 + 0.919675i \(0.371548\pi\)
−0.891966 + 0.452103i \(0.850674\pi\)
\(228\) 0 0
\(229\) 13639.0 + 11444.5i 0.260083 + 0.218236i 0.763500 0.645808i \(-0.223479\pi\)
−0.503416 + 0.864044i \(0.667924\pi\)
\(230\) 0 0
\(231\) −996.599 + 27001.5i −0.0186765 + 0.506015i
\(232\) 0 0
\(233\) 5151.21 + 2974.05i 0.0948850 + 0.0547819i 0.546692 0.837334i \(-0.315887\pi\)
−0.451807 + 0.892116i \(0.649220\pi\)
\(234\) 0 0
\(235\) −32431.9 56173.6i −0.587268 1.01718i
\(236\) 0 0
\(237\) 75631.1 + 68370.9i 1.34649 + 1.21724i
\(238\) 0 0
\(239\) −6503.03 1146.66i −0.113847 0.0200742i 0.116435 0.993198i \(-0.462853\pi\)
−0.230281 + 0.973124i \(0.573965\pi\)
\(240\) 0 0
\(241\) −66257.5 + 55596.7i −1.14078 + 0.957226i −0.999464 0.0327387i \(-0.989577\pi\)
−0.141314 + 0.989965i \(0.545133\pi\)
\(242\) 0 0
\(243\) −37505.0 45608.8i −0.635150 0.772389i
\(244\) 0 0
\(245\) 2333.05 + 2780.42i 0.0388680 + 0.0463210i
\(246\) 0 0
\(247\) −2592.01 + 14700.0i −0.0424857 + 0.240948i
\(248\) 0 0
\(249\) −27088.5 + 29964.9i −0.436904 + 0.483297i
\(250\) 0 0
\(251\) 77901.6 44976.5i 1.23651 0.713901i 0.268133 0.963382i \(-0.413593\pi\)
0.968380 + 0.249481i \(0.0802599\pi\)
\(252\) 0 0
\(253\) −11885.7 + 20586.6i −0.185688 + 0.321621i
\(254\) 0 0
\(255\) 37803.3 + 1395.28i 0.581366 + 0.0214576i
\(256\) 0 0
\(257\) 54004.6 64360.2i 0.817645 0.974432i −0.182316 0.983240i \(-0.558359\pi\)
0.999961 + 0.00880836i \(0.00280382\pi\)
\(258\) 0 0
\(259\) 2427.38 + 883.493i 0.0361858 + 0.0131705i
\(260\) 0 0
\(261\) 49881.9 + 33934.8i 0.732255 + 0.498155i
\(262\) 0 0
\(263\) −1424.17 + 251.119i −0.0205897 + 0.00363052i −0.183934 0.982939i \(-0.558883\pi\)
0.163344 + 0.986569i \(0.447772\pi\)
\(264\) 0 0
\(265\) 19733.6 7182.45i 0.281006 0.102278i
\(266\) 0 0
\(267\) −7787.65 10008.6i −0.109241 0.140395i
\(268\) 0 0
\(269\) 124679.i 1.72301i 0.507748 + 0.861506i \(0.330478\pi\)
−0.507748 + 0.861506i \(0.669522\pi\)
\(270\) 0 0
\(271\) 75336.2 1.02581 0.512903 0.858447i \(-0.328570\pi\)
0.512903 + 0.858447i \(0.328570\pi\)
\(272\) 0 0
\(273\) 13500.6 + 5485.79i 0.181145 + 0.0736061i
\(274\) 0 0
\(275\) 7238.71 + 19888.2i 0.0957184 + 0.262984i
\(276\) 0 0
\(277\) 18002.8 + 102099.i 0.234629 + 1.33064i 0.843395 + 0.537295i \(0.180554\pi\)
−0.608766 + 0.793350i \(0.708335\pi\)
\(278\) 0 0
\(279\) −10923.5 108057.i −0.140332 1.38818i
\(280\) 0 0
\(281\) 18849.0 51787.1i 0.238712 0.655857i −0.761260 0.648447i \(-0.775419\pi\)
0.999973 0.00741027i \(-0.00235878\pi\)
\(282\) 0 0
\(283\) 74274.8 + 62323.9i 0.927403 + 0.778183i 0.975349 0.220667i \(-0.0708232\pi\)
−0.0479465 + 0.998850i \(0.515268\pi\)
\(284\) 0 0
\(285\) 56491.8 + 35456.2i 0.695498 + 0.436518i
\(286\) 0 0
\(287\) −38031.3 21957.4i −0.461718 0.266573i
\(288\) 0 0
\(289\) −11827.9 20486.5i −0.141616 0.245286i
\(290\) 0 0
\(291\) 10196.6 47507.3i 0.120412 0.561015i
\(292\) 0 0
\(293\) −3384.94 596.856i −0.0394290 0.00695240i 0.153899 0.988087i \(-0.450817\pi\)
−0.193328 + 0.981134i \(0.561928\pi\)
\(294\) 0 0
\(295\) 50481.5 42359.0i 0.580080 0.486745i
\(296\) 0 0
\(297\) −46675.4 + 2984.56i −0.529146 + 0.0338351i
\(298\) 0 0
\(299\) 8240.90 + 9821.12i 0.0921790 + 0.109855i
\(300\) 0 0
\(301\) −13715.3 + 77783.1i −0.151381 + 0.858523i
\(302\) 0 0
\(303\) 6772.60 + 20985.6i 0.0737683 + 0.228579i
\(304\) 0 0
\(305\) −26454.8 + 15273.7i −0.284384 + 0.164189i
\(306\) 0 0
\(307\) −2091.41 + 3622.43i −0.0221903 + 0.0384347i −0.876907 0.480660i \(-0.840397\pi\)
0.854717 + 0.519094i \(0.173731\pi\)
\(308\) 0 0
\(309\) −67988.8 128483.i −0.712066 1.34564i
\(310\) 0 0
\(311\) 7930.44 9451.12i 0.0819929 0.0977153i −0.723488 0.690337i \(-0.757462\pi\)
0.805481 + 0.592621i \(0.201907\pi\)
\(312\) 0 0
\(313\) −91607.2 33342.3i −0.935064 0.340335i −0.170849 0.985297i \(-0.554651\pi\)
−0.764215 + 0.644962i \(0.776873\pi\)
\(314\) 0 0
\(315\) 45417.7 46659.1i 0.457724 0.470236i
\(316\) 0 0
\(317\) −169962. + 29968.9i −1.69135 + 0.298230i −0.934659 0.355545i \(-0.884295\pi\)
−0.756689 + 0.653775i \(0.773184\pi\)
\(318\) 0 0
\(319\) 44904.0 16343.7i 0.441269 0.160609i
\(320\) 0 0
\(321\) 150194. 20804.3i 1.45761 0.201903i
\(322\) 0 0
\(323\) 105549.i 1.01169i
\(324\) 0 0
\(325\) 11414.6 0.108067
\(326\) 0 0
\(327\) −9522.15 68743.8i −0.0890512 0.642892i
\(328\) 0 0
\(329\) −60430.0 166030.i −0.558291 1.53389i
\(330\) 0 0
\(331\) 15558.1 + 88234.6i 0.142004 + 0.805347i 0.969724 + 0.244204i \(0.0785268\pi\)
−0.827719 + 0.561142i \(0.810362\pi\)
\(332\) 0 0
\(333\) −1098.95 + 4334.24i −0.00991034 + 0.0390863i
\(334\) 0 0
\(335\) −25087.8 + 68928.2i −0.223549 + 0.614197i
\(336\) 0 0
\(337\) −64856.8 54421.3i −0.571078 0.479191i 0.310925 0.950434i \(-0.399361\pi\)
−0.882003 + 0.471243i \(0.843806\pi\)
\(338\) 0 0
\(339\) −168392. + 89107.3i −1.46529 + 0.775379i
\(340\) 0 0
\(341\) −74499.4 43012.3i −0.640685 0.369899i
\(342\) 0 0
\(343\) 61120.1 + 105863.i 0.519512 + 0.899822i
\(344\) 0 0
\(345\) 54517.0 17594.0i 0.458030 0.147818i
\(346\) 0 0
\(347\) −169395. 29868.8i −1.40683 0.248062i −0.581881 0.813274i \(-0.697683\pi\)
−0.824946 + 0.565212i \(0.808794\pi\)
\(348\) 0 0
\(349\) −12779.7 + 10723.4i −0.104923 + 0.0880405i −0.693740 0.720226i \(-0.744038\pi\)
0.588817 + 0.808266i \(0.299594\pi\)
\(350\) 0 0
\(351\) −7097.20 + 24205.7i −0.0576066 + 0.196473i
\(352\) 0 0
\(353\) −122460. 145943.i −0.982757 1.17120i −0.985235 0.171207i \(-0.945233\pi\)
0.00247824 0.999997i \(-0.499211\pi\)
\(354\) 0 0
\(355\) 14997.3 85054.0i 0.119003 0.674898i
\(356\) 0 0
\(357\) 100750. + 21624.2i 0.790510 + 0.169670i
\(358\) 0 0
\(359\) −53628.4 + 30962.4i −0.416108 + 0.240240i −0.693411 0.720542i \(-0.743893\pi\)
0.277303 + 0.960783i \(0.410560\pi\)
\(360\) 0 0
\(361\) −27887.0 + 48301.6i −0.213987 + 0.370636i
\(362\) 0 0
\(363\) 50355.2 80230.2i 0.382148 0.608870i
\(364\) 0 0
\(365\) 10956.2 13057.1i 0.0822385 0.0980080i
\(366\) 0 0
\(367\) −22340.3 8131.21i −0.165866 0.0603703i 0.257753 0.966211i \(-0.417018\pi\)
−0.423618 + 0.905841i \(0.639240\pi\)
\(368\) 0 0
\(369\) 31193.7 69320.1i 0.229095 0.509104i
\(370\) 0 0
\(371\) 56334.0 9933.21i 0.409282 0.0721675i
\(372\) 0 0
\(373\) −61939.6 + 22544.2i −0.445195 + 0.162038i −0.554883 0.831928i \(-0.687237\pi\)
0.109688 + 0.993966i \(0.465015\pi\)
\(374\) 0 0
\(375\) 55576.7 136775.i 0.395212 0.972620i
\(376\) 0 0
\(377\) 25772.2i 0.181330i
\(378\) 0 0
\(379\) −25944.4 −0.180620 −0.0903099 0.995914i \(-0.528786\pi\)
−0.0903099 + 0.995914i \(0.528786\pi\)
\(380\) 0 0
\(381\) −40441.9 + 31467.5i −0.278600 + 0.216777i
\(382\) 0 0
\(383\) −7650.34 21019.1i −0.0521535 0.143290i 0.910881 0.412670i \(-0.135404\pi\)
−0.963034 + 0.269379i \(0.913181\pi\)
\(384\) 0 0
\(385\) −8955.84 50791.1i −0.0604206 0.342662i
\(386\) 0 0
\(387\) −136346. 10078.5i −0.910373 0.0672937i
\(388\) 0 0
\(389\) 31551.4 86686.7i 0.208506 0.572866i −0.790721 0.612177i \(-0.790294\pi\)
0.999227 + 0.0393109i \(0.0125163\pi\)
\(390\) 0 0
\(391\) 69446.4 + 58272.4i 0.454251 + 0.381162i
\(392\) 0 0
\(393\) 7255.53 196579.i 0.0469768 1.27277i
\(394\) 0 0
\(395\) −168534. 97303.4i −1.08018 0.623640i
\(396\) 0 0
\(397\) 60496.9 + 104784.i 0.383842 + 0.664834i 0.991608 0.129283i \(-0.0412674\pi\)
−0.607766 + 0.794116i \(0.707934\pi\)
\(398\) 0 0
\(399\) 134772. + 121835.i 0.846552 + 0.765288i
\(400\) 0 0
\(401\) 177505. + 31298.9i 1.10388 + 0.194644i 0.695753 0.718281i \(-0.255071\pi\)
0.408127 + 0.912925i \(0.366182\pi\)
\(402\) 0 0
\(403\) −35540.9 + 29822.4i −0.218836 + 0.183625i
\(404\) 0 0
\(405\) 88263.4 + 70095.0i 0.538109 + 0.427343i
\(406\) 0 0
\(407\) 2276.52 + 2713.05i 0.0137430 + 0.0163783i
\(408\) 0 0
\(409\) −10648.4 + 60390.1i −0.0636558 + 0.361010i 0.936296 + 0.351211i \(0.114230\pi\)
−0.999952 + 0.00979857i \(0.996881\pi\)
\(410\) 0 0
\(411\) −10481.2 + 11594.1i −0.0620476 + 0.0686363i
\(412\) 0 0
\(413\) 155456. 89752.5i 0.911396 0.526195i
\(414\) 0 0
\(415\) 38551.4 66773.1i 0.223843 0.387708i
\(416\) 0 0
\(417\) −122323. 4514.81i −0.703452 0.0259637i
\(418\) 0 0
\(419\) −190265. + 226748.i −1.08375 + 1.29157i −0.129821 + 0.991537i \(0.541440\pi\)
−0.953930 + 0.300028i \(0.903004\pi\)
\(420\) 0 0
\(421\) 103730. + 37754.5i 0.585246 + 0.213012i 0.617637 0.786463i \(-0.288090\pi\)
−0.0323910 + 0.999475i \(0.510312\pi\)
\(422\) 0 0
\(423\) 275416. 132978.i 1.53925 0.743188i
\(424\) 0 0
\(425\) 79488.0 14015.9i 0.440072 0.0775965i
\(426\) 0 0
\(427\) −78191.4 + 28459.3i −0.428848 + 0.156088i
\(428\) 0 0
\(429\) 12269.4 + 15768.6i 0.0666667 + 0.0856797i
\(430\) 0 0
\(431\) 114346.i 0.615556i 0.951458 + 0.307778i \(0.0995854\pi\)
−0.951458 + 0.307778i \(0.900415\pi\)
\(432\) 0 0
\(433\) 68905.4 0.367517 0.183759 0.982971i \(-0.441174\pi\)
0.183759 + 0.982971i \(0.441174\pi\)
\(434\) 0 0
\(435\) −106686. 43350.5i −0.563804 0.229095i
\(436\) 0 0
\(437\) 54667.3 + 150197.i 0.286262 + 0.786500i
\(438\) 0 0
\(439\) 19037.3 + 107966.i 0.0987818 + 0.560220i 0.993523 + 0.113634i \(0.0362491\pi\)
−0.894741 + 0.446586i \(0.852640\pi\)
\(440\) 0 0
\(441\) −13885.2 + 10004.2i −0.0713961 + 0.0514403i
\(442\) 0 0
\(443\) −58654.2 + 161151.i −0.298876 + 0.821156i 0.695812 + 0.718224i \(0.255045\pi\)
−0.994688 + 0.102932i \(0.967178\pi\)
\(444\) 0 0
\(445\) 18542.9 + 15559.3i 0.0936392 + 0.0785726i
\(446\) 0 0
\(447\) −328363. 206092.i −1.64338 1.03144i
\(448\) 0 0
\(449\) −134746. 77795.9i −0.668381 0.385890i 0.127082 0.991892i \(-0.459439\pi\)
−0.795463 + 0.606002i \(0.792772\pi\)
\(450\) 0 0
\(451\) −30104.6 52142.7i −0.148006 0.256354i
\(452\) 0 0
\(453\) −21372.4 + 99576.5i −0.104149 + 0.485244i
\(454\) 0 0
\(455\) −27393.0 4830.13i −0.132317 0.0233311i
\(456\) 0 0
\(457\) 242462. 203450.i 1.16094 0.974147i 0.161026 0.986950i \(-0.448520\pi\)
0.999918 + 0.0128029i \(0.00407542\pi\)
\(458\) 0 0
\(459\) −19700.8 + 177276.i −0.0935103 + 0.841442i
\(460\) 0 0
\(461\) 180926. + 215619.i 0.851332 + 1.01458i 0.999671 + 0.0256412i \(0.00816273\pi\)
−0.148339 + 0.988936i \(0.547393\pi\)
\(462\) 0 0
\(463\) −18880.2 + 107075.i −0.0880732 + 0.499488i 0.908578 + 0.417716i \(0.137169\pi\)
−0.996651 + 0.0817723i \(0.973942\pi\)
\(464\) 0 0
\(465\) 63669.7 + 197287.i 0.294461 + 0.912417i
\(466\) 0 0
\(467\) 323907. 187008.i 1.48520 0.857483i 0.485346 0.874322i \(-0.338693\pi\)
0.999858 + 0.0168386i \(0.00536014\pi\)
\(468\) 0 0
\(469\) −99903.3 + 173038.i −0.454186 + 0.786674i
\(470\) 0 0
\(471\) 82923.0 + 156705.i 0.373795 + 0.706386i
\(472\) 0 0
\(473\) −69607.1 + 82954.5i −0.311122 + 0.370781i
\(474\) 0 0
\(475\) 133726. + 48672.3i 0.592691 + 0.215722i
\(476\) 0 0
\(477\) 26914.6 + 95289.0i 0.118291 + 0.418799i
\(478\) 0 0
\(479\) 257523. 45408.3i 1.12239 0.197909i 0.418503 0.908215i \(-0.362555\pi\)
0.703892 + 0.710307i \(0.251444\pi\)
\(480\) 0 0
\(481\) 1794.91 653.293i 0.00775803 0.00282369i
\(482\) 0 0
\(483\) 154567. 21410.1i 0.662558 0.0917752i
\(484\) 0 0
\(485\) 92745.7i 0.394285i
\(486\) 0 0
\(487\) −325076. −1.37065 −0.685325 0.728237i \(-0.740340\pi\)
−0.685325 + 0.728237i \(0.740340\pi\)
\(488\) 0 0
\(489\) 27430.1 + 198028.i 0.114712 + 0.828148i
\(490\) 0 0
\(491\) 16561.1 + 45501.1i 0.0686950 + 0.188738i 0.969290 0.245922i \(-0.0790908\pi\)
−0.900595 + 0.434660i \(0.856869\pi\)
\(492\) 0 0
\(493\) −31645.3 179470.i −0.130202 0.738409i
\(494\) 0 0
\(495\) 85913.1 24266.4i 0.350630 0.0990363i
\(496\) 0 0
\(497\) 80462.5 221069.i 0.325747 0.894983i
\(498\) 0 0
\(499\) −111893. 93889.6i −0.449369 0.377065i 0.389833 0.920886i \(-0.372533\pi\)
−0.839202 + 0.543820i \(0.816977\pi\)
\(500\) 0 0
\(501\) 1057.80 559.748i 0.00421431 0.00223006i
\(502\) 0 0
\(503\) −404971. 233810.i −1.60062 0.924117i −0.991364 0.131141i \(-0.958136\pi\)
−0.609253 0.792976i \(-0.708531\pi\)
\(504\) 0 0
\(505\) −21045.5 36451.9i −0.0825233 0.142934i
\(506\) 0 0
\(507\) −234371. + 75637.4i −0.911774 + 0.294253i
\(508\) 0 0
\(509\) 292320. + 51543.9i 1.12830 + 0.198949i 0.706480 0.707733i \(-0.250282\pi\)
0.421815 + 0.906682i \(0.361393\pi\)
\(510\) 0 0
\(511\) 35566.9 29844.2i 0.136208 0.114292i
\(512\) 0 0
\(513\) −186360. + 253315.i −0.708137 + 0.962556i
\(514\) 0 0
\(515\) 178350. + 212550.i 0.672450 + 0.801394i
\(516\) 0 0
\(517\) 42065.2 238564.i 0.157377 0.892531i
\(518\) 0 0
\(519\) −110740. 23768.4i −0.411121 0.0882401i
\(520\) 0 0
\(521\) 343568. 198359.i 1.26572 0.730763i 0.291544 0.956558i \(-0.405831\pi\)
0.974175 + 0.225795i \(0.0724978\pi\)
\(522\) 0 0
\(523\) 101598. 175973.i 0.371433 0.643342i −0.618353 0.785901i \(-0.712200\pi\)
0.989786 + 0.142559i \(0.0455331\pi\)
\(524\) 0 0
\(525\) 73856.1 117674.i 0.267959 0.426934i
\(526\) 0 0
\(527\) −210878. + 251314.i −0.759293 + 0.904890i
\(528\) 0 0
\(529\) −133961. 48757.7i −0.478703 0.174234i
\(530\) 0 0
\(531\) 181636. + 252100.i 0.644189 + 0.894096i
\(532\) 0 0
\(533\) −31979.1 + 5638.78i −0.112567 + 0.0198486i
\(534\) 0 0
\(535\) −271968. + 98988.2i −0.950189 + 0.345841i
\(536\) 0 0
\(537\) 152225. 374627.i 0.527883 1.29912i
\(538\) 0 0
\(539\) 13555.2i 0.0466584i
\(540\) 0 0
\(541\) 545062. 1.86231 0.931153 0.364628i \(-0.118804\pi\)
0.931153 + 0.364628i \(0.118804\pi\)
\(542\) 0 0
\(543\) −433599. + 337380.i −1.47058 + 1.14425i
\(544\) 0 0
\(545\) 45307.0 + 124480.i 0.152536 + 0.419089i
\(546\) 0 0
\(547\) −77497.0 439507.i −0.259006 1.46890i −0.785576 0.618765i \(-0.787633\pi\)
0.526570 0.850132i \(-0.323478\pi\)
\(548\) 0 0
\(549\) −62625.6 129706.i −0.207782 0.430345i
\(550\) 0 0
\(551\) 109893. 301929.i 0.361966 0.994494i
\(552\) 0 0
\(553\) −406079. 340741.i −1.32788 1.11423i
\(554\) 0 0
\(555\) 314.798 8529.03i 0.00102199 0.0276894i
\(556\) 0 0
\(557\) −336771. 194435.i −1.08549 0.626705i −0.153115 0.988208i \(-0.548930\pi\)
−0.932371 + 0.361503i \(0.882264\pi\)
\(558\) 0 0
\(559\) 29201.7 + 50578.8i 0.0934511 + 0.161862i
\(560\) 0 0
\(561\) 104802. + 94742.1i 0.333001 + 0.301035i
\(562\) 0 0
\(563\) 178666. + 31503.7i 0.563671 + 0.0993904i 0.448221 0.893923i \(-0.352058\pi\)
0.115450 + 0.993313i \(0.463169\pi\)
\(564\) 0 0
\(565\) 278572. 233749.i 0.872650 0.732240i
\(566\) 0 0
\(567\) 203617. + 229784.i 0.633355 + 0.714748i
\(568\) 0 0
\(569\) −104051. 124003.i −0.321382 0.383009i 0.581030 0.813882i \(-0.302650\pi\)
−0.902412 + 0.430874i \(0.858205\pi\)
\(570\) 0 0
\(571\) 44974.8 255065.i 0.137942 0.782308i −0.834824 0.550518i \(-0.814430\pi\)
0.972766 0.231791i \(-0.0744585\pi\)
\(572\) 0 0
\(573\) −130717. + 144598.i −0.398129 + 0.440405i
\(574\) 0 0
\(575\) 105853. 61114.0i 0.320159 0.184844i
\(576\) 0 0
\(577\) −173118. + 299850.i −0.519986 + 0.900642i 0.479744 + 0.877409i \(0.340730\pi\)
−0.999730 + 0.0232338i \(0.992604\pi\)
\(578\) 0 0
\(579\) −138361. 5106.77i −0.412721 0.0152331i
\(580\) 0 0
\(581\) 135001. 160888.i 0.399930 0.476619i
\(582\) 0 0
\(583\) 73698.3 + 26824.0i 0.216831 + 0.0789199i
\(584\) 0 0
\(585\) 3549.37 48017.1i 0.0103714 0.140309i
\(586\) 0 0
\(587\) 496369. 87523.2i 1.44055 0.254008i 0.601853 0.798607i \(-0.294429\pi\)
0.838697 + 0.544599i \(0.183318\pi\)
\(588\) 0 0
\(589\) −543537. + 197831.i −1.56674 + 0.570249i
\(590\) 0 0
\(591\) −271400. 348802.i −0.777026 0.998629i
\(592\) 0 0
\(593\) 637062.i 1.81164i 0.423661 + 0.905821i \(0.360745\pi\)
−0.423661 + 0.905821i \(0.639255\pi\)
\(594\) 0 0
\(595\) −196688. −0.555575
\(596\) 0 0
\(597\) −641306. 260587.i −1.79935 0.731146i
\(598\) 0 0
\(599\) 63233.8 + 173734.i 0.176236 + 0.484206i 0.996088 0.0883710i \(-0.0281661\pi\)
−0.819851 + 0.572577i \(0.805944\pi\)
\(600\) 0 0
\(601\) −121142. 687032.i −0.335388 1.90208i −0.423373 0.905956i \(-0.639154\pi\)
0.0879853 0.996122i \(-0.471957\pi\)
\(602\) 0 0
\(603\) −315398. 141928.i −0.867410 0.390331i
\(604\) 0 0
\(605\) −61839.0 + 169901.i −0.168947 + 0.464179i
\(606\) 0 0
\(607\) −224939. 188746.i −0.610502 0.512272i 0.284300 0.958735i \(-0.408239\pi\)
−0.894802 + 0.446463i \(0.852683\pi\)
\(608\) 0 0
\(609\) −265687. 166754.i −0.716366 0.449616i
\(610\) 0 0
\(611\) −113145. 65324.4i −0.303077 0.174982i
\(612\) 0 0
\(613\) 281442. + 487472.i 0.748976 + 1.29726i 0.948314 + 0.317333i \(0.102787\pi\)
−0.199338 + 0.979931i \(0.563879\pi\)
\(614\) 0 0
\(615\) −30448.8 + 141865.i −0.0805045 + 0.375080i
\(616\) 0 0
\(617\) −572112. 100879.i −1.50283 0.264990i −0.639172 0.769064i \(-0.720723\pi\)
−0.863660 + 0.504074i \(0.831834\pi\)
\(618\) 0 0
\(619\) −168647. + 141511.i −0.440146 + 0.369326i −0.835764 0.549089i \(-0.814975\pi\)
0.395618 + 0.918415i \(0.370530\pi\)
\(620\) 0 0
\(621\) 63782.4 + 262468.i 0.165393 + 0.680603i
\(622\) 0 0
\(623\) 42382.8 + 50509.9i 0.109198 + 0.130137i
\(624\) 0 0
\(625\) −13131.7 + 74473.7i −0.0336172 + 0.190653i
\(626\) 0 0
\(627\) 76502.5 + 237051.i 0.194599 + 0.602985i
\(628\) 0 0
\(629\) 11697.0 6753.27i 0.0295647 0.0170692i
\(630\) 0 0
\(631\) −143576. + 248680.i −0.360597 + 0.624572i −0.988059 0.154075i \(-0.950760\pi\)
0.627462 + 0.778647i \(0.284094\pi\)
\(632\) 0 0
\(633\) −362379. 684812.i −0.904389 1.70909i
\(634\) 0 0
\(635\) 62870.6 74926.2i 0.155919 0.185817i
\(636\) 0 0
\(637\) 6869.82 + 2500.41i 0.0169304 + 0.00616215i
\(638\) 0 0
\(639\) 394733. + 100085.i 0.966722 + 0.245113i
\(640\) 0 0
\(641\) 348199. 61396.9i 0.847446 0.149428i 0.266970 0.963705i \(-0.413978\pi\)
0.580476 + 0.814277i \(0.302867\pi\)
\(642\) 0 0
\(643\) 604456. 220004.i 1.46198 0.532119i 0.516073 0.856545i \(-0.327393\pi\)
0.945911 + 0.324426i \(0.105171\pi\)
\(644\) 0 0
\(645\) 258494. 35805.7i 0.621343 0.0860662i
\(646\) 0 0
\(647\) 343334.i 0.820179i −0.912045 0.410089i \(-0.865497\pi\)
0.912045 0.410089i \(-0.134503\pi\)
\(648\) 0 0
\(649\) 246110. 0.584305
\(650\) 0 0
\(651\) 77479.5 + 559353.i 0.182821 + 1.31985i
\(652\) 0 0
\(653\) 141240. + 388054.i 0.331231 + 0.910050i 0.987792 + 0.155777i \(0.0497883\pi\)
−0.656561 + 0.754273i \(0.727990\pi\)
\(654\) 0 0
\(655\) 65201.1 + 369774.i 0.151975 + 0.861894i
\(656\) 0 0
\(657\) 57589.7 + 56057.4i 0.133418 + 0.129868i
\(658\) 0 0
\(659\) 140053. 384794.i 0.322495 0.886048i −0.667458 0.744648i \(-0.732617\pi\)
0.989953 0.141400i \(-0.0451603\pi\)
\(660\) 0 0
\(661\) −223989. 187949.i −0.512654 0.430168i 0.349408 0.936971i \(-0.386383\pi\)
−0.862062 + 0.506803i \(0.830827\pi\)
\(662\) 0 0
\(663\) 67347.4 35637.9i 0.153212 0.0810746i
\(664\) 0 0
\(665\) −300322. 173391.i −0.679117 0.392088i
\(666\) 0 0
\(667\) −137985. 238996.i −0.310155 0.537205i
\(668\) 0 0
\(669\) 215786. 69639.7i 0.482138 0.155598i
\(670\) 0 0
\(671\) −112351. 19810.5i −0.249535 0.0439998i
\(672\) 0 0
\(673\) 193341. 162232.i 0.426868 0.358185i −0.403900 0.914803i \(-0.632346\pi\)
0.830769 + 0.556618i \(0.187901\pi\)
\(674\) 0 0
\(675\) 215516. + 106708.i 0.473011 + 0.234201i
\(676\) 0 0
\(677\) 123728. + 147453.i 0.269954 + 0.321719i 0.883942 0.467597i \(-0.154880\pi\)
−0.613988 + 0.789316i \(0.710436\pi\)
\(678\) 0 0
\(679\) −43869.5 + 248796.i −0.0951531 + 0.539640i
\(680\) 0 0
\(681\) 661930. + 142072.i 1.42731 + 0.306348i
\(682\) 0 0
\(683\) 382344. 220747.i 0.819622 0.473209i −0.0306644 0.999530i \(-0.509762\pi\)
0.850286 + 0.526321i \(0.176429\pi\)
\(684\) 0 0
\(685\) 14916.4 25836.0i 0.0317895 0.0550611i
\(686\) 0 0
\(687\) 85184.2 135723.i 0.180487 0.287567i
\(688\) 0 0
\(689\) 27188.9 32402.5i 0.0572734 0.0682558i
\(690\) 0 0
\(691\) 450725. + 164051.i 0.943964 + 0.343575i 0.767730 0.640773i \(-0.221386\pi\)
0.176234 + 0.984348i \(0.443608\pi\)
\(692\) 0 0
\(693\) 241946. 24458.4i 0.503792 0.0509287i
\(694\) 0 0
\(695\) 230095. 40571.9i 0.476362 0.0839954i
\(696\) 0 0
\(697\) −215769. + 78533.5i −0.444144 + 0.161655i
\(698\) 0 0
\(699\) 20152.3 49595.0i 0.0412450 0.101504i
\(700\) 0 0
\(701\) 486026.i 0.989063i 0.869160 + 0.494531i \(0.164660\pi\)
−0.869160 + 0.494531i \(0.835340\pi\)
\(702\) 0 0
\(703\) 23813.6 0.0481852
\(704\) 0 0
\(705\) −460733. + 358493.i −0.926981 + 0.721277i
\(706\) 0 0
\(707\) −39213.8 107739.i −0.0784514 0.215543i
\(708\) 0 0
\(709\) −38195.6 216618.i −0.0759838 0.430926i −0.998940 0.0460216i \(-0.985346\pi\)
0.922957 0.384904i \(-0.125765\pi\)
\(710\) 0 0
\(711\) 516125. 758671.i 1.02098 1.50077i
\(712\) 0 0
\(713\) −169917. + 466842.i −0.334239 + 0.918313i
\(714\) 0 0
\(715\) −29214.3 24513.7i −0.0571456 0.0479508i
\(716\) 0 0
\(717\) −2192.02 + 59389.7i −0.00426389 + 0.115524i
\(718\) 0 0
\(719\) −757816. 437526.i −1.46591 0.846341i −0.466633 0.884451i \(-0.654533\pi\)
−0.999274 + 0.0381097i \(0.987866\pi\)
\(720\) 0 0
\(721\) 377899. + 654540.i 0.726950 + 1.25911i
\(722\) 0 0
\(723\) 577456. + 522024.i 1.10470 + 0.998651i
\(724\) 0 0
\(725\) −241973. 42666.3i −0.460353 0.0811726i
\(726\) 0 0
\(727\) −523516. + 439282.i −0.990515 + 0.831141i −0.985642 0.168847i \(-0.945995\pi\)
−0.00487274 + 0.999988i \(0.501551\pi\)
\(728\) 0 0
\(729\) −360283. + 390673.i −0.677937 + 0.735120i
\(730\) 0 0
\(731\) 265457. + 316359.i 0.496775 + 0.592033i
\(732\) 0 0
\(733\) −89439.8 + 507239.i −0.166465 + 0.944070i 0.781076 + 0.624436i \(0.214671\pi\)
−0.947541 + 0.319634i \(0.896440\pi\)
\(734\) 0 0
\(735\) 21906.1 24232.3i 0.0405500 0.0448559i
\(736\) 0 0
\(737\) −237243. + 136972.i −0.436775 + 0.252172i
\(738\) 0 0
\(739\) 134409. 232804.i 0.246116 0.426286i −0.716329 0.697763i \(-0.754179\pi\)
0.962445 + 0.271477i \(0.0875122\pi\)
\(740\) 0 0
\(741\) 134250. + 4955.02i 0.244499 + 0.00902421i
\(742\) 0 0
\(743\) −367472. + 437936.i −0.665651 + 0.793292i −0.988185 0.153266i \(-0.951021\pi\)
0.322534 + 0.946558i \(0.395465\pi\)
\(744\) 0 0
\(745\) 695364. + 253092.i 1.25285 + 0.456001i
\(746\) 0 0
\(747\) 300584. + 204488.i 0.538672 + 0.366460i
\(748\) 0 0
\(749\) −776394. + 136899.i −1.38394 + 0.244027i
\(750\) 0 0
\(751\) 161443. 58760.5i 0.286246 0.104185i −0.194907 0.980822i \(-0.562440\pi\)
0.481153 + 0.876637i \(0.340218\pi\)
\(752\) 0 0
\(753\) −497157. 638944.i −0.876807 1.12687i
\(754\) 0 0
\(755\) 194397.i 0.341033i
\(756\) 0 0
\(757\) 87387.1 0.152495 0.0762475 0.997089i \(-0.475706\pi\)
0.0762475 + 0.997089i \(0.475706\pi\)
\(758\) 0 0
\(759\) 198205. + 80538.1i 0.344057 + 0.139803i
\(760\) 0 0
\(761\) 182574. + 501618.i 0.315260 + 0.866171i 0.991572 + 0.129555i \(0.0413550\pi\)
−0.676312 + 0.736616i \(0.736423\pi\)
\(762\) 0 0
\(763\) 62658.9 + 355356.i 0.107630 + 0.610400i
\(764\) 0 0
\(765\) −34242.9 338735.i −0.0585124 0.578811i
\(766\) 0 0
\(767\) 45397.6 124729.i 0.0771689 0.212020i
\(768\) 0 0
\(769\) 770270. + 646334.i 1.30254 + 1.09296i 0.989701 + 0.143153i \(0.0457241\pi\)
0.312838 + 0.949807i \(0.398720\pi\)
\(770\) 0 0
\(771\) −640452. 401969.i −1.07740 0.676214i
\(772\) 0 0
\(773\) −540306. 311946.i −0.904234 0.522060i −0.0256627 0.999671i \(-0.508170\pi\)
−0.878572 + 0.477611i \(0.841503\pi\)
\(774\) 0 0
\(775\) 221161. + 383062.i 0.368218 + 0.637772i
\(776\) 0 0
\(777\) 4878.77 22730.8i 0.00808106 0.0376506i
\(778\) 0 0
\(779\) −398689. 70299.7i −0.656991 0.115845i
\(780\) 0 0
\(781\) 247086.