Properties

Label 117.4.q.a.10.1
Level $117$
Weight $4$
Character 117.10
Analytic conductor $6.903$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.4.q.a.82.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{2} +(-2.50000 + 4.33013i) q^{4} -1.73205i q^{5} +(-12.0000 - 6.92820i) q^{7} -22.5167i q^{8} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{2} +(-2.50000 + 4.33013i) q^{4} -1.73205i q^{5} +(-12.0000 - 6.92820i) q^{7} -22.5167i q^{8} +(1.50000 + 2.59808i) q^{10} +(-12.0000 + 6.92820i) q^{11} +(45.5000 - 11.2583i) q^{13} +24.0000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(58.5000 - 101.325i) q^{17} +(-99.0000 - 57.1577i) q^{19} +(7.50000 + 4.33013i) q^{20} +(12.0000 - 20.7846i) q^{22} +(-39.0000 - 67.5500i) q^{23} +122.000 q^{25} +(-58.5000 + 56.2917i) q^{26} +(60.0000 - 34.6410i) q^{28} +(-70.5000 - 122.110i) q^{29} -155.885i q^{31} +(157.500 + 90.9327i) q^{32} +202.650i q^{34} +(-12.0000 + 20.7846i) q^{35} +(-124.500 + 71.8801i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(-235.500 + 135.966i) q^{41} +(-52.0000 + 90.0666i) q^{43} -69.2820i q^{44} +(117.000 + 67.5500i) q^{46} +301.377i q^{47} +(-75.5000 - 130.770i) q^{49} +(-183.000 + 105.655i) q^{50} +(-65.0000 + 225.167i) q^{52} -93.0000 q^{53} +(12.0000 + 20.7846i) q^{55} +(-156.000 + 270.200i) q^{56} +(211.500 + 122.110i) q^{58} +(246.000 + 142.028i) q^{59} +(-72.5000 + 125.574i) q^{61} +(135.000 + 233.827i) q^{62} -307.000 q^{64} +(-19.5000 - 78.8083i) q^{65} +(-681.000 + 393.176i) q^{67} +(292.500 + 506.625i) q^{68} -41.5692i q^{70} +(-915.000 - 528.275i) q^{71} -458.993i q^{73} +(124.500 - 215.640i) q^{74} +(495.000 - 285.788i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(-1.50000 + 0.866025i) q^{80} +(235.500 - 407.898i) q^{82} -789.815i q^{83} +(-175.500 - 101.325i) q^{85} -180.133i q^{86} +(156.000 + 270.200i) q^{88} +(846.000 - 488.438i) q^{89} +(-624.000 - 180.133i) q^{91} +390.000 q^{92} +(-261.000 - 452.065i) q^{94} +(-99.0000 + 171.473i) q^{95} +(174.000 + 100.459i) q^{97} +(226.500 + 130.770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - 5 q^{4} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - 5 q^{4} - 24 q^{7} + 3 q^{10} - 24 q^{11} + 91 q^{13} + 48 q^{14} - q^{16} + 117 q^{17} - 198 q^{19} + 15 q^{20} + 24 q^{22} - 78 q^{23} + 244 q^{25} - 117 q^{26} + 120 q^{28} - 141 q^{29} + 315 q^{32} - 24 q^{35} - 249 q^{37} + 396 q^{38} - 78 q^{40} - 471 q^{41} - 104 q^{43} + 234 q^{46} - 151 q^{49} - 366 q^{50} - 130 q^{52} - 186 q^{53} + 24 q^{55} - 312 q^{56} + 423 q^{58} + 492 q^{59} - 145 q^{61} + 270 q^{62} - 614 q^{64} - 39 q^{65} - 1362 q^{67} + 585 q^{68} - 1830 q^{71} + 249 q^{74} + 990 q^{76} + 384 q^{77} + 2552 q^{79} - 3 q^{80} + 471 q^{82} - 351 q^{85} + 312 q^{88} + 1692 q^{89} - 1248 q^{91} + 780 q^{92} - 522 q^{94} - 198 q^{95} + 348 q^{97} + 453 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 + 0.866025i −0.530330 + 0.306186i −0.741151 0.671339i \(-0.765720\pi\)
0.210821 + 0.977525i \(0.432386\pi\)
\(3\) 0 0
\(4\) −2.50000 + 4.33013i −0.312500 + 0.541266i
\(5\) 1.73205i 0.154919i −0.996995 0.0774597i \(-0.975319\pi\)
0.996995 0.0774597i \(-0.0246809\pi\)
\(6\) 0 0
\(7\) −12.0000 6.92820i −0.647939 0.374088i 0.139727 0.990190i \(-0.455377\pi\)
−0.787666 + 0.616102i \(0.788711\pi\)
\(8\) 22.5167i 0.995105i
\(9\) 0 0
\(10\) 1.50000 + 2.59808i 0.0474342 + 0.0821584i
\(11\) −12.0000 + 6.92820i −0.328921 + 0.189903i −0.655362 0.755315i \(-0.727484\pi\)
0.326441 + 0.945218i \(0.394151\pi\)
\(12\) 0 0
\(13\) 45.5000 11.2583i 0.970725 0.240192i
\(14\) 24.0000 0.458162
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.00781250 0.0135316i
\(17\) 58.5000 101.325i 0.834608 1.44558i −0.0597414 0.998214i \(-0.519028\pi\)
0.894349 0.447369i \(-0.147639\pi\)
\(18\) 0 0
\(19\) −99.0000 57.1577i −1.19538 0.690151i −0.235856 0.971788i \(-0.575789\pi\)
−0.959521 + 0.281637i \(0.909123\pi\)
\(20\) 7.50000 + 4.33013i 0.0838525 + 0.0484123i
\(21\) 0 0
\(22\) 12.0000 20.7846i 0.116291 0.201422i
\(23\) −39.0000 67.5500i −0.353568 0.612398i 0.633304 0.773903i \(-0.281698\pi\)
−0.986872 + 0.161506i \(0.948365\pi\)
\(24\) 0 0
\(25\) 122.000 0.976000
\(26\) −58.5000 + 56.2917i −0.441261 + 0.424604i
\(27\) 0 0
\(28\) 60.0000 34.6410i 0.404962 0.233805i
\(29\) −70.5000 122.110i −0.451432 0.781903i 0.547043 0.837104i \(-0.315753\pi\)
−0.998475 + 0.0552014i \(0.982420\pi\)
\(30\) 0 0
\(31\) 155.885i 0.903151i −0.892233 0.451576i \(-0.850862\pi\)
0.892233 0.451576i \(-0.149138\pi\)
\(32\) 157.500 + 90.9327i 0.870073 + 0.502337i
\(33\) 0 0
\(34\) 202.650i 1.02218i
\(35\) −12.0000 + 20.7846i −0.0579534 + 0.100378i
\(36\) 0 0
\(37\) −124.500 + 71.8801i −0.553180 + 0.319379i −0.750404 0.660980i \(-0.770141\pi\)
0.197223 + 0.980359i \(0.436808\pi\)
\(38\) 198.000 0.845259
\(39\) 0 0
\(40\) −39.0000 −0.154161
\(41\) −235.500 + 135.966i −0.897047 + 0.517910i −0.876241 0.481873i \(-0.839957\pi\)
−0.0208059 + 0.999784i \(0.506623\pi\)
\(42\) 0 0
\(43\) −52.0000 + 90.0666i −0.184417 + 0.319419i −0.943380 0.331714i \(-0.892373\pi\)
0.758963 + 0.651134i \(0.225706\pi\)
\(44\) 69.2820i 0.237379i
\(45\) 0 0
\(46\) 117.000 + 67.5500i 0.375015 + 0.216515i
\(47\) 301.377i 0.935326i 0.883907 + 0.467663i \(0.154904\pi\)
−0.883907 + 0.467663i \(0.845096\pi\)
\(48\) 0 0
\(49\) −75.5000 130.770i −0.220117 0.381253i
\(50\) −183.000 + 105.655i −0.517602 + 0.298838i
\(51\) 0 0
\(52\) −65.0000 + 225.167i −0.173344 + 0.600481i
\(53\) −93.0000 −0.241029 −0.120514 0.992712i \(-0.538454\pi\)
−0.120514 + 0.992712i \(0.538454\pi\)
\(54\) 0 0
\(55\) 12.0000 + 20.7846i 0.0294196 + 0.0509563i
\(56\) −156.000 + 270.200i −0.372257 + 0.644768i
\(57\) 0 0
\(58\) 211.500 + 122.110i 0.478816 + 0.276444i
\(59\) 246.000 + 142.028i 0.542822 + 0.313398i 0.746222 0.665698i \(-0.231866\pi\)
−0.203400 + 0.979096i \(0.565199\pi\)
\(60\) 0 0
\(61\) −72.5000 + 125.574i −0.152175 + 0.263575i −0.932027 0.362389i \(-0.881961\pi\)
0.779852 + 0.625964i \(0.215294\pi\)
\(62\) 135.000 + 233.827i 0.276533 + 0.478968i
\(63\) 0 0
\(64\) −307.000 −0.599609
\(65\) −19.5000 78.8083i −0.0372104 0.150384i
\(66\) 0 0
\(67\) −681.000 + 393.176i −1.24175 + 0.716926i −0.969451 0.245286i \(-0.921118\pi\)
−0.272301 + 0.962212i \(0.587785\pi\)
\(68\) 292.500 + 506.625i 0.521630 + 0.903490i
\(69\) 0 0
\(70\) 41.5692i 0.0709782i
\(71\) −915.000 528.275i −1.52944 0.883025i −0.999385 0.0350641i \(-0.988836\pi\)
−0.530059 0.847961i \(-0.677830\pi\)
\(72\) 0 0
\(73\) 458.993i 0.735906i −0.929844 0.367953i \(-0.880059\pi\)
0.929844 0.367953i \(-0.119941\pi\)
\(74\) 124.500 215.640i 0.195579 0.338752i
\(75\) 0 0
\(76\) 495.000 285.788i 0.747110 0.431344i
\(77\) 192.000 0.284161
\(78\) 0 0
\(79\) 1276.00 1.81723 0.908615 0.417634i \(-0.137141\pi\)
0.908615 + 0.417634i \(0.137141\pi\)
\(80\) −1.50000 + 0.866025i −0.00209631 + 0.00121031i
\(81\) 0 0
\(82\) 235.500 407.898i 0.317154 0.549327i
\(83\) 789.815i 1.04450i −0.852793 0.522250i \(-0.825093\pi\)
0.852793 0.522250i \(-0.174907\pi\)
\(84\) 0 0
\(85\) −175.500 101.325i −0.223949 0.129297i
\(86\) 180.133i 0.225864i
\(87\) 0 0
\(88\) 156.000 + 270.200i 0.188973 + 0.327311i
\(89\) 846.000 488.438i 1.00759 0.581734i 0.0971073 0.995274i \(-0.469041\pi\)
0.910486 + 0.413540i \(0.135708\pi\)
\(90\) 0 0
\(91\) −624.000 180.133i −0.718824 0.207507i
\(92\) 390.000 0.441960
\(93\) 0 0
\(94\) −261.000 452.065i −0.286384 0.496032i
\(95\) −99.0000 + 171.473i −0.106918 + 0.185187i
\(96\) 0 0
\(97\) 174.000 + 100.459i 0.182134 + 0.105155i 0.588295 0.808646i \(-0.299799\pi\)
−0.406161 + 0.913802i \(0.633133\pi\)
\(98\) 226.500 + 130.770i 0.233469 + 0.134793i
\(99\) 0 0
\(100\) −305.000 + 528.275i −0.305000 + 0.528275i
\(101\) 214.500 + 371.525i 0.211322 + 0.366021i 0.952129 0.305698i \(-0.0988897\pi\)
−0.740806 + 0.671719i \(0.765556\pi\)
\(102\) 0 0
\(103\) 182.000 0.174107 0.0870534 0.996204i \(-0.472255\pi\)
0.0870534 + 0.996204i \(0.472255\pi\)
\(104\) −253.500 1024.51i −0.239017 0.965974i
\(105\) 0 0
\(106\) 139.500 80.5404i 0.127825 0.0737997i
\(107\) −753.000 1304.23i −0.680330 1.17837i −0.974880 0.222729i \(-0.928503\pi\)
0.294551 0.955636i \(-0.404830\pi\)
\(108\) 0 0
\(109\) 1551.92i 1.36373i −0.731477 0.681866i \(-0.761169\pi\)
0.731477 0.681866i \(-0.238831\pi\)
\(110\) −36.0000 20.7846i −0.0312042 0.0180158i
\(111\) 0 0
\(112\) 13.8564i 0.0116902i
\(113\) −343.500 + 594.959i −0.285962 + 0.495302i −0.972842 0.231470i \(-0.925647\pi\)
0.686880 + 0.726771i \(0.258980\pi\)
\(114\) 0 0
\(115\) −117.000 + 67.5500i −0.0948722 + 0.0547745i
\(116\) 705.000 0.564290
\(117\) 0 0
\(118\) −492.000 −0.383833
\(119\) −1404.00 + 810.600i −1.08155 + 0.624433i
\(120\) 0 0
\(121\) −569.500 + 986.403i −0.427874 + 0.741099i
\(122\) 251.147i 0.186376i
\(123\) 0 0
\(124\) 675.000 + 389.711i 0.488845 + 0.282235i
\(125\) 427.817i 0.306121i
\(126\) 0 0
\(127\) −143.000 247.683i −0.0999149 0.173058i 0.811734 0.584027i \(-0.198524\pi\)
−0.911649 + 0.410969i \(0.865190\pi\)
\(128\) −799.500 + 461.592i −0.552082 + 0.318745i
\(129\) 0 0
\(130\) 97.5000 + 101.325i 0.0657794 + 0.0683599i
\(131\) 1974.00 1.31656 0.658279 0.752774i \(-0.271285\pi\)
0.658279 + 0.752774i \(0.271285\pi\)
\(132\) 0 0
\(133\) 792.000 + 1371.78i 0.516354 + 0.894352i
\(134\) 681.000 1179.53i 0.439026 0.760415i
\(135\) 0 0
\(136\) −2281.50 1317.22i −1.43851 0.830523i
\(137\) 733.500 + 423.486i 0.457424 + 0.264094i 0.710961 0.703232i \(-0.248260\pi\)
−0.253536 + 0.967326i \(0.581594\pi\)
\(138\) 0 0
\(139\) −118.000 + 204.382i −0.0720045 + 0.124716i −0.899780 0.436344i \(-0.856273\pi\)
0.827775 + 0.561060i \(0.189606\pi\)
\(140\) −60.0000 103.923i −0.0362209 0.0627364i
\(141\) 0 0
\(142\) 1830.00 1.08148
\(143\) −468.000 + 450.333i −0.273679 + 0.263348i
\(144\) 0 0
\(145\) −211.500 + 122.110i −0.121132 + 0.0699355i
\(146\) 397.500 + 688.490i 0.225324 + 0.390273i
\(147\) 0 0
\(148\) 718.801i 0.399224i
\(149\) 40.5000 + 23.3827i 0.0222677 + 0.0128563i 0.511093 0.859526i \(-0.329241\pi\)
−0.488825 + 0.872382i \(0.662574\pi\)
\(150\) 0 0
\(151\) 1770.16i 0.953995i 0.878905 + 0.476998i \(0.158275\pi\)
−0.878905 + 0.476998i \(0.841725\pi\)
\(152\) −1287.00 + 2229.15i −0.686773 + 1.18953i
\(153\) 0 0
\(154\) −288.000 + 166.277i −0.150699 + 0.0870063i
\(155\) −270.000 −0.139916
\(156\) 0 0
\(157\) 1211.00 0.615594 0.307797 0.951452i \(-0.400408\pi\)
0.307797 + 0.951452i \(0.400408\pi\)
\(158\) −1914.00 + 1105.05i −0.963732 + 0.556411i
\(159\) 0 0
\(160\) 157.500 272.798i 0.0778217 0.134791i
\(161\) 1080.80i 0.529062i
\(162\) 0 0
\(163\) −870.000 502.295i −0.418059 0.241367i 0.276187 0.961104i \(-0.410929\pi\)
−0.694247 + 0.719737i \(0.744262\pi\)
\(164\) 1359.66i 0.647388i
\(165\) 0 0
\(166\) 684.000 + 1184.72i 0.319811 + 0.553930i
\(167\) −792.000 + 457.261i −0.366987 + 0.211880i −0.672141 0.740423i \(-0.734625\pi\)
0.305154 + 0.952303i \(0.401292\pi\)
\(168\) 0 0
\(169\) 1943.50 1024.51i 0.884615 0.466321i
\(170\) 351.000 0.158356
\(171\) 0 0
\(172\) −260.000 450.333i −0.115261 0.199637i
\(173\) 1287.00 2229.15i 0.565600 0.979648i −0.431394 0.902164i \(-0.641978\pi\)
0.996994 0.0774841i \(-0.0246887\pi\)
\(174\) 0 0
\(175\) −1464.00 845.241i −0.632389 0.365110i
\(176\) 12.0000 + 6.92820i 0.00513940 + 0.00296723i
\(177\) 0 0
\(178\) −846.000 + 1465.31i −0.356238 + 0.617022i
\(179\) 1872.00 + 3242.40i 0.781675 + 1.35390i 0.930965 + 0.365108i \(0.118968\pi\)
−0.149290 + 0.988793i \(0.547699\pi\)
\(180\) 0 0
\(181\) −637.000 −0.261590 −0.130795 0.991409i \(-0.541753\pi\)
−0.130795 + 0.991409i \(0.541753\pi\)
\(182\) 1092.00 270.200i 0.444750 0.110047i
\(183\) 0 0
\(184\) −1521.00 + 878.150i −0.609400 + 0.351837i
\(185\) 124.500 + 215.640i 0.0494780 + 0.0856983i
\(186\) 0 0
\(187\) 1621.20i 0.633978i
\(188\) −1305.00 753.442i −0.506260 0.292289i
\(189\) 0 0
\(190\) 342.946i 0.130947i
\(191\) −1299.00 + 2249.93i −0.492106 + 0.852353i −0.999959 0.00909077i \(-0.997106\pi\)
0.507852 + 0.861444i \(0.330440\pi\)
\(192\) 0 0
\(193\) 967.500 558.586i 0.360840 0.208331i −0.308609 0.951189i \(-0.599863\pi\)
0.669449 + 0.742858i \(0.266530\pi\)
\(194\) −348.000 −0.128788
\(195\) 0 0
\(196\) 755.000 0.275146
\(197\) −1776.00 + 1025.37i −0.642308 + 0.370837i −0.785503 0.618858i \(-0.787596\pi\)
0.143195 + 0.989695i \(0.454262\pi\)
\(198\) 0 0
\(199\) 1261.00 2184.12i 0.449196 0.778030i −0.549138 0.835732i \(-0.685044\pi\)
0.998334 + 0.0577019i \(0.0183773\pi\)
\(200\) 2747.03i 0.971223i
\(201\) 0 0
\(202\) −643.500 371.525i −0.224141 0.129408i
\(203\) 1953.75i 0.675500i
\(204\) 0 0
\(205\) 235.500 + 407.898i 0.0802343 + 0.138970i
\(206\) −273.000 + 157.617i −0.0923340 + 0.0533091i
\(207\) 0 0
\(208\) −32.5000 33.7750i −0.0108340 0.0112590i
\(209\) 1584.00 0.524247
\(210\) 0 0
\(211\) −521.000 902.398i −0.169986 0.294425i 0.768428 0.639936i \(-0.221039\pi\)
−0.938415 + 0.345511i \(0.887706\pi\)
\(212\) 232.500 402.702i 0.0753215 0.130461i
\(213\) 0 0
\(214\) 2259.00 + 1304.23i 0.721598 + 0.416615i
\(215\) 156.000 + 90.0666i 0.0494842 + 0.0285697i
\(216\) 0 0
\(217\) −1080.00 + 1870.61i −0.337858 + 0.585187i
\(218\) 1344.00 + 2327.88i 0.417556 + 0.723228i
\(219\) 0 0
\(220\) −120.000 −0.0367745
\(221\) 1521.00 5268.90i 0.462957 1.60373i
\(222\) 0 0
\(223\) −2085.00 + 1203.78i −0.626107 + 0.361483i −0.779243 0.626722i \(-0.784396\pi\)
0.153136 + 0.988205i \(0.451063\pi\)
\(224\) −1260.00 2182.38i −0.375836 0.650967i
\(225\) 0 0
\(226\) 1189.92i 0.350231i
\(227\) −2085.00 1203.78i −0.609631 0.351971i 0.163190 0.986595i \(-0.447822\pi\)
−0.772821 + 0.634624i \(0.781155\pi\)
\(228\) 0 0
\(229\) 2508.01i 0.723729i −0.932231 0.361864i \(-0.882140\pi\)
0.932231 0.361864i \(-0.117860\pi\)
\(230\) 117.000 202.650i 0.0335424 0.0580971i
\(231\) 0 0
\(232\) −2749.50 + 1587.42i −0.778076 + 0.449222i
\(233\) 5850.00 1.64483 0.822417 0.568885i \(-0.192625\pi\)
0.822417 + 0.568885i \(0.192625\pi\)
\(234\) 0 0
\(235\) 522.000 0.144900
\(236\) −1230.00 + 710.141i −0.339263 + 0.195874i
\(237\) 0 0
\(238\) 1404.00 2431.80i 0.382386 0.662312i
\(239\) 5383.21i 1.45695i −0.685072 0.728475i \(-0.740229\pi\)
0.685072 0.728475i \(-0.259771\pi\)
\(240\) 0 0
\(241\) 4258.50 + 2458.65i 1.13823 + 0.657159i 0.945992 0.324189i \(-0.105091\pi\)
0.192240 + 0.981348i \(0.438425\pi\)
\(242\) 1972.81i 0.524036i
\(243\) 0 0
\(244\) −362.500 627.868i −0.0951094 0.164734i
\(245\) −226.500 + 130.770i −0.0590635 + 0.0341003i
\(246\) 0 0
\(247\) −5148.00 1486.10i −1.32615 0.382827i
\(248\) −3510.00 −0.898731
\(249\) 0 0
\(250\) 370.500 + 641.725i 0.0937299 + 0.162345i
\(251\) −1989.00 + 3445.05i −0.500178 + 0.866333i 0.499822 + 0.866128i \(0.333399\pi\)
−1.00000 0.000205037i \(0.999935\pi\)
\(252\) 0 0
\(253\) 936.000 + 540.400i 0.232592 + 0.134287i
\(254\) 429.000 + 247.683i 0.105976 + 0.0611852i
\(255\) 0 0
\(256\) 2027.50 3511.73i 0.494995 0.857357i
\(257\) 1033.50 + 1790.07i 0.250848 + 0.434482i 0.963760 0.266772i \(-0.0859572\pi\)
−0.712911 + 0.701254i \(0.752624\pi\)
\(258\) 0 0
\(259\) 1992.00 0.477903
\(260\) 390.000 + 112.583i 0.0930261 + 0.0268543i
\(261\) 0 0
\(262\) −2961.00 + 1709.53i −0.698211 + 0.403112i
\(263\) −1026.00 1777.08i −0.240555 0.416653i 0.720318 0.693644i \(-0.243996\pi\)
−0.960872 + 0.276991i \(0.910663\pi\)
\(264\) 0 0
\(265\) 161.081i 0.0373400i
\(266\) −2376.00 1371.78i −0.547676 0.316201i
\(267\) 0 0
\(268\) 3931.76i 0.896157i
\(269\) 1665.00 2883.86i 0.377386 0.653652i −0.613295 0.789854i \(-0.710156\pi\)
0.990681 + 0.136202i \(0.0434897\pi\)
\(270\) 0 0
\(271\) 2430.00 1402.96i 0.544694 0.314479i −0.202285 0.979327i \(-0.564837\pi\)
0.746979 + 0.664848i \(0.231504\pi\)
\(272\) −117.000 −0.0260815
\(273\) 0 0
\(274\) −1467.00 −0.323448
\(275\) −1464.00 + 845.241i −0.321027 + 0.185345i
\(276\) 0 0
\(277\) −188.500 + 326.492i −0.0408876 + 0.0708194i −0.885745 0.464172i \(-0.846352\pi\)
0.844857 + 0.534992i \(0.179685\pi\)
\(278\) 408.764i 0.0881872i
\(279\) 0 0
\(280\) 468.000 + 270.200i 0.0998870 + 0.0576698i
\(281\) 36.3731i 0.00772183i −0.999993 0.00386092i \(-0.998771\pi\)
0.999993 0.00386092i \(-0.00122897\pi\)
\(282\) 0 0
\(283\) 3562.00 + 6169.56i 0.748194 + 1.29591i 0.948688 + 0.316215i \(0.102412\pi\)
−0.200493 + 0.979695i \(0.564255\pi\)
\(284\) 4575.00 2641.38i 0.955902 0.551891i
\(285\) 0 0
\(286\) 312.000 1080.80i 0.0645068 0.223458i
\(287\) 3768.00 0.774976
\(288\) 0 0
\(289\) −4388.00 7600.24i −0.893141 1.54696i
\(290\) 211.500 366.329i 0.0428266 0.0741778i
\(291\) 0 0
\(292\) 1987.50 + 1147.48i 0.398321 + 0.229971i
\(293\) 7207.50 + 4161.25i 1.43709 + 0.829703i 0.997646 0.0685685i \(-0.0218432\pi\)
0.439441 + 0.898271i \(0.355177\pi\)
\(294\) 0 0
\(295\) 246.000 426.084i 0.0485514 0.0840936i
\(296\) 1618.50 + 2803.32i 0.317816 + 0.550473i
\(297\) 0 0
\(298\) −81.0000 −0.0157457
\(299\) −2535.00 2634.45i −0.490310 0.509546i
\(300\) 0 0
\(301\) 1248.00 720.533i 0.238982 0.137976i
\(302\) −1533.00 2655.23i −0.292100 0.505932i
\(303\) 0 0
\(304\) 114.315i 0.0215672i
\(305\) 217.500 + 125.574i 0.0408328 + 0.0235748i
\(306\) 0 0
\(307\) 2220.49i 0.412801i 0.978468 + 0.206401i \(0.0661750\pi\)
−0.978468 + 0.206401i \(0.933825\pi\)
\(308\) −480.000 + 831.384i −0.0888004 + 0.153807i
\(309\) 0 0
\(310\) 405.000 233.827i 0.0742015 0.0428402i
\(311\) −4914.00 −0.895972 −0.447986 0.894041i \(-0.647859\pi\)
−0.447986 + 0.894041i \(0.647859\pi\)
\(312\) 0 0
\(313\) −518.000 −0.0935434 −0.0467717 0.998906i \(-0.514893\pi\)
−0.0467717 + 0.998906i \(0.514893\pi\)
\(314\) −1816.50 + 1048.76i −0.326468 + 0.188487i
\(315\) 0 0
\(316\) −3190.00 + 5525.24i −0.567885 + 0.983605i
\(317\) 3916.17i 0.693861i 0.937891 + 0.346930i \(0.112776\pi\)
−0.937891 + 0.346930i \(0.887224\pi\)
\(318\) 0 0
\(319\) 1692.00 + 976.877i 0.296971 + 0.171456i
\(320\) 531.740i 0.0928911i
\(321\) 0 0
\(322\) −936.000 1621.20i −0.161991 0.280577i
\(323\) −11583.0 + 6687.45i −1.99534 + 1.15201i
\(324\) 0 0
\(325\) 5551.00 1373.52i 0.947428 0.234428i
\(326\) 1740.00 0.295613
\(327\) 0 0
\(328\) 3061.50 + 5302.67i 0.515375 + 0.892656i
\(329\) 2088.00 3616.52i 0.349894 0.606034i
\(330\) 0 0
\(331\) −6456.00 3727.37i −1.07207 0.618958i −0.143321 0.989676i \(-0.545778\pi\)
−0.928745 + 0.370719i \(0.879111\pi\)
\(332\) 3420.00 + 1974.54i 0.565352 + 0.326406i
\(333\) 0 0
\(334\) 792.000 1371.78i 0.129749 0.224733i
\(335\) 681.000 + 1179.53i 0.111066 + 0.192371i
\(336\) 0 0
\(337\) −3575.00 −0.577871 −0.288936 0.957349i \(-0.593301\pi\)
−0.288936 + 0.957349i \(0.593301\pi\)
\(338\) −2028.00 + 3219.88i −0.326357 + 0.518161i
\(339\) 0 0
\(340\) 877.500 506.625i 0.139968 0.0808106i
\(341\) 1080.00 + 1870.61i 0.171511 + 0.297066i
\(342\) 0 0
\(343\) 6845.06i 1.07755i
\(344\) 2028.00 + 1170.87i 0.317856 + 0.183514i
\(345\) 0 0
\(346\) 4458.30i 0.692716i
\(347\) −3483.00 + 6032.73i −0.538839 + 0.933297i 0.460128 + 0.887853i \(0.347804\pi\)
−0.998967 + 0.0454442i \(0.985530\pi\)
\(348\) 0 0
\(349\) −5760.00 + 3325.54i −0.883455 + 0.510063i −0.871796 0.489869i \(-0.837045\pi\)
−0.0116588 + 0.999932i \(0.503711\pi\)
\(350\) 2928.00 0.447166
\(351\) 0 0
\(352\) −2520.00 −0.381581
\(353\) −4876.50 + 2815.45i −0.735269 + 0.424508i −0.820347 0.571867i \(-0.806219\pi\)
0.0850777 + 0.996374i \(0.472886\pi\)
\(354\) 0 0
\(355\) −915.000 + 1584.83i −0.136798 + 0.236940i
\(356\) 4884.38i 0.727168i
\(357\) 0 0
\(358\) −5616.00 3242.40i −0.829092 0.478676i
\(359\) 7129.12i 1.04808i −0.851694 0.524040i \(-0.824424\pi\)
0.851694 0.524040i \(-0.175576\pi\)
\(360\) 0 0
\(361\) 3104.50 + 5377.15i 0.452617 + 0.783956i
\(362\) 955.500 551.658i 0.138729 0.0800953i
\(363\) 0 0
\(364\) 2340.00 2251.67i 0.336949 0.324229i
\(365\) −795.000 −0.114006
\(366\) 0 0
\(367\) −1.00000 1.73205i −0.000142233 0.000246355i 0.865954 0.500123i \(-0.166712\pi\)
−0.866097 + 0.499877i \(0.833379\pi\)
\(368\) −39.0000 + 67.5500i −0.00552450 + 0.00956871i
\(369\) 0 0
\(370\) −373.500 215.640i −0.0524793 0.0302989i
\(371\) 1116.00 + 644.323i 0.156172 + 0.0901660i
\(372\) 0 0
\(373\) −1749.50 + 3030.22i −0.242857 + 0.420641i −0.961527 0.274711i \(-0.911418\pi\)
0.718670 + 0.695351i \(0.244751\pi\)
\(374\) −1404.00 2431.80i −0.194115 0.336218i
\(375\) 0 0
\(376\) 6786.00 0.930748
\(377\) −4582.50 4762.27i −0.626023 0.650582i
\(378\) 0 0
\(379\) 4779.00 2759.16i 0.647706 0.373953i −0.139871 0.990170i \(-0.544669\pi\)
0.787577 + 0.616216i \(0.211335\pi\)
\(380\) −495.000 857.365i −0.0668236 0.115742i
\(381\) 0 0
\(382\) 4499.87i 0.602705i
\(383\) 6378.00 + 3682.34i 0.850915 + 0.491276i 0.860960 0.508673i \(-0.169864\pi\)
−0.0100443 + 0.999950i \(0.503197\pi\)
\(384\) 0 0
\(385\) 332.554i 0.0440221i
\(386\) −967.500 + 1675.76i −0.127576 + 0.220969i
\(387\) 0 0
\(388\) −870.000 + 502.295i −0.113834 + 0.0657220i
\(389\) 1209.00 0.157580 0.0787901 0.996891i \(-0.474894\pi\)
0.0787901 + 0.996891i \(0.474894\pi\)
\(390\) 0 0
\(391\) −9126.00 −1.18036
\(392\) −2944.50 + 1700.01i −0.379387 + 0.219039i
\(393\) 0 0
\(394\) 1776.00 3076.12i 0.227090 0.393332i
\(395\) 2210.10i 0.281524i
\(396\) 0 0
\(397\) 10128.0 + 5847.40i 1.28038 + 0.739226i 0.976917 0.213618i \(-0.0685248\pi\)
0.303460 + 0.952844i \(0.401858\pi\)
\(398\) 4368.23i 0.550150i
\(399\) 0 0
\(400\) −61.0000 105.655i −0.00762500 0.0132069i
\(401\) 2581.50 1490.43i 0.321481 0.185607i −0.330571 0.943781i \(-0.607241\pi\)
0.652053 + 0.758174i \(0.273908\pi\)
\(402\) 0 0
\(403\) −1755.00 7092.75i −0.216930 0.876712i
\(404\) −2145.00 −0.264153
\(405\) 0 0
\(406\) −1692.00 2930.63i −0.206829 0.358238i
\(407\) 996.000 1725.12i 0.121302 0.210101i
\(408\) 0 0
\(409\) 37.5000 + 21.6506i 0.00453363 + 0.00261749i 0.502265 0.864714i \(-0.332500\pi\)
−0.497731 + 0.867331i \(0.665833\pi\)
\(410\) −706.500 407.898i −0.0851013 0.0491333i
\(411\) 0 0
\(412\) −455.000 + 788.083i −0.0544084 + 0.0942380i
\(413\) −1968.00 3408.68i −0.234477 0.406126i
\(414\) 0 0
\(415\) −1368.00 −0.161813
\(416\) 8190.00 + 2364.25i 0.965259 + 0.278646i
\(417\) 0 0
\(418\) −2376.00 + 1371.78i −0.278024 + 0.160517i
\(419\) −4731.00 8194.33i −0.551610 0.955416i −0.998159 0.0606569i \(-0.980680\pi\)
0.446549 0.894759i \(-0.352653\pi\)
\(420\) 0 0
\(421\) 7068.50i 0.818284i −0.912471 0.409142i \(-0.865828\pi\)
0.912471 0.409142i \(-0.134172\pi\)
\(422\) 1563.00 + 902.398i 0.180298 + 0.104095i
\(423\) 0 0
\(424\) 2094.05i 0.239849i
\(425\) 7137.00 12361.6i 0.814577 1.41089i
\(426\) 0 0
\(427\) 1740.00 1004.59i 0.197200 0.113854i
\(428\) 7530.00 0.850412
\(429\) 0 0
\(430\) −312.000 −0.0349906
\(431\) 8598.00 4964.06i 0.960907 0.554780i 0.0644552 0.997921i \(-0.479469\pi\)
0.896452 + 0.443140i \(0.146136\pi\)
\(432\) 0 0
\(433\) 3308.50 5730.49i 0.367197 0.636004i −0.621929 0.783074i \(-0.713651\pi\)
0.989126 + 0.147070i \(0.0469841\pi\)
\(434\) 3741.23i 0.413790i
\(435\) 0 0
\(436\) 6720.00 + 3879.79i 0.738141 + 0.426166i
\(437\) 8916.60i 0.976061i
\(438\) 0 0
\(439\) −6994.00 12114.0i −0.760377 1.31701i −0.942656 0.333765i \(-0.891681\pi\)
0.182280 0.983247i \(-0.441652\pi\)
\(440\) 468.000 270.200i 0.0507069 0.0292756i
\(441\) 0 0
\(442\) 2281.50 + 9220.57i 0.245520 + 0.992258i
\(443\) −2004.00 −0.214928 −0.107464 0.994209i \(-0.534273\pi\)
−0.107464 + 0.994209i \(0.534273\pi\)
\(444\) 0 0
\(445\) −846.000 1465.31i −0.0901219 0.156096i
\(446\) 2085.00 3611.33i 0.221362 0.383411i
\(447\) 0 0
\(448\) 3684.00 + 2126.96i 0.388510 + 0.224307i
\(449\) −7866.00 4541.44i −0.826769 0.477336i 0.0259758 0.999663i \(-0.491731\pi\)
−0.852745 + 0.522327i \(0.825064\pi\)
\(450\) 0 0
\(451\) 1884.00 3263.18i 0.196705 0.340704i
\(452\) −1717.50 2974.80i −0.178727 0.309563i
\(453\) 0 0
\(454\) 4170.00 0.431074
\(455\) −312.000 + 1080.80i −0.0321468 + 0.111360i
\(456\) 0 0
\(457\) 2185.50 1261.80i 0.223705 0.129156i −0.383959 0.923350i \(-0.625440\pi\)
0.607665 + 0.794194i \(0.292106\pi\)
\(458\) 2172.00 + 3762.01i 0.221596 + 0.383815i
\(459\) 0 0
\(460\) 675.500i 0.0684681i
\(461\) −16963.5 9793.88i −1.71382 0.989472i −0.929270 0.369400i \(-0.879563\pi\)
−0.784545 0.620072i \(-0.787103\pi\)
\(462\) 0 0
\(463\) 8632.54i 0.866497i −0.901274 0.433249i \(-0.857367\pi\)
0.901274 0.433249i \(-0.142633\pi\)
\(464\) −70.5000 + 122.110i −0.00705362 + 0.0122172i
\(465\) 0 0
\(466\) −8775.00 + 5066.25i −0.872305 + 0.503625i
\(467\) −5460.00 −0.541025 −0.270512 0.962716i \(-0.587193\pi\)
−0.270512 + 0.962716i \(0.587193\pi\)
\(468\) 0 0
\(469\) 10896.0 1.07277
\(470\) −783.000 + 452.065i −0.0768449 + 0.0443664i
\(471\) 0 0
\(472\) 3198.00 5539.10i 0.311864 0.540165i
\(473\) 1441.07i 0.140085i
\(474\) 0 0
\(475\) −12078.0 6973.24i −1.16669 0.673587i
\(476\) 8106.00i 0.780542i
\(477\) 0 0
\(478\) 4662.00 + 8074.82i 0.446098 + 0.772665i
\(479\) 2211.00 1276.52i 0.210904 0.121766i −0.390827 0.920464i \(-0.627811\pi\)
0.601732 + 0.798698i \(0.294478\pi\)
\(480\) 0 0
\(481\) −4855.50 + 4672.21i −0.460274 + 0.442899i
\(482\) −8517.00 −0.804852
\(483\) 0 0
\(484\) −2847.50 4932.01i −0.267421 0.463187i
\(485\) 174.000 301.377i 0.0162906 0.0282161i
\(486\) 0 0
\(487\) 9378.00 + 5414.39i 0.872603 + 0.503798i 0.868212 0.496193i \(-0.165269\pi\)
0.00439074 + 0.999990i \(0.498602\pi\)
\(488\) 2827.50 + 1632.46i 0.262285 + 0.151430i
\(489\) 0 0
\(490\) 226.500 392.310i 0.0208821 0.0361689i
\(491\) 5694.00 + 9862.30i 0.523354 + 0.906475i 0.999631 + 0.0271797i \(0.00865264\pi\)
−0.476277 + 0.879295i \(0.658014\pi\)
\(492\) 0 0
\(493\) −16497.0 −1.50707
\(494\) 9009.00 2229.15i 0.820514 0.203025i
\(495\) 0 0
\(496\) −135.000 + 77.9423i −0.0122211 + 0.00705587i
\(497\) 7320.00 + 12678.6i 0.660658 + 1.14429i
\(498\) 0 0
\(499\) 17677.3i 1.58586i 0.609311 + 0.792931i \(0.291446\pi\)
−0.609311 + 0.792931i \(0.708554\pi\)
\(500\) 1852.50 + 1069.54i 0.165693 + 0.0956627i
\(501\) 0 0
\(502\) 6890.10i 0.612590i
\(503\) 1938.00 3356.71i 0.171792 0.297552i −0.767255 0.641343i \(-0.778378\pi\)
0.939046 + 0.343791i \(0.111711\pi\)
\(504\) 0 0
\(505\) 643.500 371.525i 0.0567037 0.0327379i
\(506\) −1872.00 −0.164467
\(507\) 0 0
\(508\) 1430.00 0.124894
\(509\) 14779.5 8532.95i 1.28701 0.743058i 0.308893 0.951097i \(-0.400042\pi\)
0.978120 + 0.208039i \(0.0667082\pi\)
\(510\) 0 0
\(511\) −3180.00 + 5507.92i −0.275293 + 0.476822i
\(512\) 361.999i 0.0312465i
\(513\) 0 0
\(514\) −3100.50 1790.07i −0.266065 0.153612i
\(515\) 315.233i 0.0269725i
\(516\) 0 0
\(517\) −2088.00 3616.52i −0.177621 0.307649i
\(518\) −2988.00 + 1725.12i −0.253446 + 0.146327i
\(519\) 0 0
\(520\) −1774.50 + 439.075i −0.149648 + 0.0370283i
\(521\) −2121.00 −0.178355 −0.0891773 0.996016i \(-0.528424\pi\)
−0.0891773 + 0.996016i \(0.528424\pi\)
\(522\) 0 0
\(523\) 5732.00 + 9928.12i 0.479241 + 0.830069i 0.999717 0.0238072i \(-0.00757878\pi\)
−0.520476 + 0.853876i \(0.674245\pi\)
\(524\) −4935.00 + 8547.67i −0.411425 + 0.712608i
\(525\) 0 0
\(526\) 3078.00 + 1777.08i 0.255147 + 0.147309i
\(527\) −15795.0 9119.25i −1.30558 0.753777i
\(528\) 0 0
\(529\) 3041.50 5268.03i 0.249979 0.432977i
\(530\) −139.500 241.621i −0.0114330 0.0198025i
\(531\) 0 0
\(532\) −7920.00 −0.645443
\(533\) −9184.50 + 8837.79i −0.746388 + 0.718212i
\(534\) 0 0
\(535\) −2259.00 + 1304.23i −0.182552 + 0.105396i
\(536\) 8853.00 + 15333.8i 0.713417 + 1.23567i
\(537\) 0 0
\(538\) 5767.73i 0.462202i
\(539\) 1812.00 + 1046.16i 0.144802 + 0.0836016i
\(540\) 0 0
\(541\) 4764.87i 0.378665i 0.981913 + 0.189333i \(0.0606324\pi\)
−0.981913 + 0.189333i \(0.939368\pi\)
\(542\) −2430.00 + 4208.88i −0.192578 + 0.333555i
\(543\) 0 0
\(544\) 18427.5 10639.1i 1.45234 0.838508i
\(545\) −2688.00 −0.211268
\(546\) 0 0
\(547\) 6554.00 0.512301 0.256151 0.966637i \(-0.417546\pi\)
0.256151 + 0.966637i \(0.417546\pi\)
\(548\) −3667.50 + 2117.43i −0.285890 + 0.165059i
\(549\) 0 0
\(550\) 1464.00 2535.72i 0.113500 0.196588i
\(551\) 16118.5i 1.24622i
\(552\) 0 0
\(553\) −15312.0 8840.39i −1.17745 0.679804i
\(554\) 652.983i 0.0500769i
\(555\) 0 0
\(556\) −590.000 1021.91i −0.0450028 0.0779472i
\(557\) 15685.5 9056.03i 1.19321 0.688898i 0.234174 0.972195i \(-0.424761\pi\)
0.959032 + 0.283297i \(0.0914281\pi\)
\(558\) 0 0
\(559\) −1352.00 + 4683.47i −0.102296 + 0.354364i
\(560\) 24.0000 0.00181104
\(561\) 0 0
\(562\) 31.5000 + 54.5596i 0.00236432 + 0.00409512i
\(563\) −6084.00 + 10537.8i −0.455435 + 0.788837i −0.998713 0.0507160i \(-0.983850\pi\)
0.543278 + 0.839553i \(0.317183\pi\)
\(564\) 0 0
\(565\) 1030.50 + 594.959i 0.0767318 + 0.0443011i
\(566\) −10686.0 6169.56i −0.793580 0.458173i
\(567\) 0 0
\(568\) −11895.0 + 20602.7i −0.878703 + 1.52196i
\(569\) −3861.00 6687.45i −0.284467 0.492711i 0.688013 0.725698i \(-0.258483\pi\)
−0.972480 + 0.232988i \(0.925150\pi\)
\(570\) 0 0
\(571\) 11440.0 0.838440 0.419220 0.907885i \(-0.362304\pi\)
0.419220 + 0.907885i \(0.362304\pi\)
\(572\) −780.000 3152.33i −0.0570165 0.230429i
\(573\) 0 0
\(574\) −5652.00 + 3263.18i −0.410993 + 0.237287i
\(575\) −4758.00 8241.10i −0.345082 0.597700i
\(576\) 0 0
\(577\) 15444.7i 1.11433i −0.830400 0.557167i \(-0.811888\pi\)
0.830400 0.557167i \(-0.188112\pi\)
\(578\) 13164.0 + 7600.24i 0.947319 + 0.546935i
\(579\) 0 0
\(580\) 1221.10i 0.0874194i
\(581\) −5472.00 + 9477.78i −0.390735 + 0.676772i
\(582\) 0 0
\(583\) 1116.00 644.323i 0.0792796 0.0457721i
\(584\) −10335.0 −0.732304
\(585\) 0 0
\(586\) −14415.0 −1.01617
\(587\) 12186.0 7035.59i 0.856848 0.494702i −0.00610719 0.999981i \(-0.501944\pi\)
0.862956 + 0.505280i \(0.168611\pi\)
\(588\) 0 0
\(589\) −8910.00 + 15432.6i −0.623311 + 1.07961i
\(590\) 852.169i 0.0594631i
\(591\) 0 0
\(592\) 124.500 + 71.8801i 0.00864344 + 0.00499029i
\(593\) 26938.6i 1.86549i 0.360538 + 0.932745i \(0.382593\pi\)
−0.360538 + 0.932745i \(0.617407\pi\)
\(594\) 0 0
\(595\) 1404.00 + 2431.80i 0.0967368 + 0.167553i
\(596\) −202.500 + 116.913i −0.0139173 + 0.00803517i
\(597\) 0 0
\(598\) 6084.00 + 1756.30i 0.416042 + 0.120101i
\(599\) 10554.0 0.719908 0.359954 0.932970i \(-0.382792\pi\)
0.359954 + 0.932970i \(0.382792\pi\)
\(600\) 0 0
\(601\) 7415.50 + 12844.0i 0.503302 + 0.871745i 0.999993 + 0.00381713i \(0.00121503\pi\)
−0.496691 + 0.867928i \(0.665452\pi\)
\(602\) −1248.00 + 2161.60i −0.0844928 + 0.146346i
\(603\) 0 0
\(604\) −7665.00 4425.39i −0.516365 0.298123i
\(605\) 1708.50 + 986.403i 0.114811 + 0.0662859i
\(606\) 0 0
\(607\) 3977.00 6888.37i 0.265933 0.460610i −0.701874 0.712301i \(-0.747653\pi\)
0.967808 + 0.251691i \(0.0809866\pi\)
\(608\) −10395.0 18004.7i −0.693377 1.20096i
\(609\) 0 0
\(610\) −435.000 −0.0288732
\(611\) 3393.00 + 13712.6i 0.224658 + 0.907945i
\(612\) 0 0
\(613\) 21841.5 12610.2i 1.43910 0.830866i 0.441315 0.897352i \(-0.354512\pi\)
0.997787 + 0.0664859i \(0.0211787\pi\)
\(614\) −1923.00 3330.73i −0.126394 0.218921i
\(615\) 0 0
\(616\) 4323.20i 0.282771i
\(617\) 15055.5 + 8692.30i 0.982353 + 0.567162i 0.902980 0.429683i \(-0.141375\pi\)
0.0793731 + 0.996845i \(0.474708\pi\)
\(618\) 0 0
\(619\) 8209.92i 0.533093i 0.963822 + 0.266547i \(0.0858826\pi\)
−0.963822 + 0.266547i \(0.914117\pi\)
\(620\) 675.000 1169.13i 0.0437236 0.0757316i
\(621\) 0 0
\(622\) 7371.00 4255.65i 0.475161 0.274334i
\(623\) −13536.0 −0.870479
\(624\) 0 0
\(625\) 14509.0 0.928576
\(626\) 777.000 448.601i 0.0496089 0.0286417i
\(627\) 0 0
\(628\) −3027.50 + 5243.78i −0.192373 + 0.333200i
\(629\) 16819.9i 1.06622i
\(630\) 0 0
\(631\) 11142.0 + 6432.84i 0.702941 + 0.405843i 0.808442 0.588576i \(-0.200311\pi\)
−0.105501 + 0.994419i \(0.533645\pi\)
\(632\) 28731.3i 1.80834i
\(633\) 0 0
\(634\) −3391.50 5874.25i −0.212451 0.367975i
\(635\) −429.000 + 247.683i −0.0268100 + 0.0154788i
\(636\) 0 0
\(637\) −4907.50 5100.02i −0.305247 0.317222i
\(638\) −3384.00 −0.209990
\(639\) 0 0
\(640\) 799.500 + 1384.77i 0.0493797 + 0.0855282i
\(641\) 3100.50 5370.22i 0.191049 0.330907i −0.754549 0.656244i \(-0.772144\pi\)
0.945598 + 0.325337i \(0.105478\pi\)
\(642\) 0 0
\(643\) −14568.0 8410.84i −0.893477 0.515849i −0.0183989 0.999831i \(-0.505857\pi\)
−0.875078 + 0.483981i \(0.839190\pi\)
\(644\) −4680.00 2702.00i −0.286363 0.165332i
\(645\) 0 0
\(646\) 11583.0 20062.3i 0.705460 1.22189i
\(647\) −6747.00 11686.1i −0.409972 0.710092i 0.584914 0.811095i \(-0.301128\pi\)
−0.994886 + 0.101003i \(0.967795\pi\)
\(648\) 0 0
\(649\) −3936.00 −0.238061
\(650\) −7137.00 + 6867.58i −0.430671 + 0.414413i
\(651\) 0 0
\(652\) 4350.00 2511.47i 0.261287 0.150854i
\(653\) −5667.00 9815.53i −0.339612 0.588226i 0.644747 0.764396i \(-0.276963\pi\)
−0.984360 + 0.176170i \(0.943629\pi\)
\(654\) 0 0
\(655\) 3419.07i 0.203960i
\(656\) 235.500 + 135.966i 0.0140164 + 0.00809235i
\(657\) 0 0
\(658\) 7233.04i 0.428531i
\(659\) 6618.00 11462.7i 0.391200 0.677578i −0.601408 0.798942i \(-0.705393\pi\)
0.992608 + 0.121364i \(0.0387268\pi\)
\(660\) 0 0
\(661\) −10264.5 + 5926.21i −0.603998 + 0.348718i −0.770613 0.637304i \(-0.780050\pi\)
0.166615 + 0.986022i \(0.446716\pi\)
\(662\) 12912.0 0.758065
\(663\) 0 0
\(664\) −17784.0 −1.03939
\(665\) 2376.00 1371.78i 0.138552 0.0799932i
\(666\) 0 0
\(667\) −5499.00 + 9524.55i −0.319224 + 0.552911i
\(668\) 4572.61i 0.264850i
\(669\) 0 0
\(670\) −2043.00 1179.53i −0.117803 0.0680136i
\(671\) 2009.18i 0.115594i
\(672\) 0 0
\(673\) −4010.50 6946.39i −0.229708 0.397866i 0.728014 0.685563i \(-0.240444\pi\)
−0.957722 + 0.287697i \(0.907110\pi\)
\(674\) 5362.50 3096.04i 0.306463 0.176936i
\(675\) 0 0
\(676\) −422.500 + 10976.9i −0.0240385 + 0.624538i
\(677\) 21630.0 1.22793 0.613965 0.789333i \(-0.289574\pi\)
0.613965 + 0.789333i \(0.289574\pi\)
\(678\) 0 0
\(679\) −1392.00 2411.01i −0.0786746 0.136268i
\(680\) −2281.50 + 3951.67i −0.128664 + 0.222853i
\(681\) 0 0
\(682\) −3240.00 1870.61i −0.181915 0.105029i
\(683\) 22983.0 + 13269.2i 1.28758 + 0.743387i 0.978223 0.207557i \(-0.0665514\pi\)
0.309361 + 0.950945i \(0.399885\pi\)
\(684\) 0 0
\(685\) 733.500 1270.46i 0.0409133 0.0708639i
\(686\) −5928.00 10267.6i −0.329930 0.571456i
\(687\) 0 0
\(688\) 104.000 0.00576303
\(689\) −4231.50 + 1047.02i −0.233973 + 0.0578933i
\(690\) 0 0
\(691\) −720.000 + 415.692i −0.0396383 + 0.0228852i −0.519688 0.854356i \(-0.673952\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(692\) 6435.00 + 11145.7i 0.353500 + 0.612280i
\(693\) 0 0
\(694\) 12065.5i 0.659941i
\(695\) 354.000 + 204.382i 0.0193208 + 0.0111549i
\(696\) 0 0
\(697\) 31816.0i 1.72901i
\(698\) 5760.00 9976.61i 0.312348 0.541003i
\(699\) 0 0
\(700\) 7320.00 4226.20i 0.395243 0.228194i
\(701\) −30186.0 −1.62640 −0.813202 0.581981i \(-0.802278\pi\)
−0.813202 + 0.581981i \(0.802278\pi\)
\(702\) 0 0
\(703\) 16434.0 0.881679
\(704\) 3684.00 2126.96i 0.197224 0.113868i
\(705\) 0 0
\(706\) 4876.50 8446.35i 0.259957 0.450258i
\(707\) 5944.40i 0.316212i
\(708\) 0 0
\(709\) −10288.5 5940.07i −0.544983 0.314646i 0.202113 0.979362i \(-0.435219\pi\)
−0.747096 + 0.664716i \(0.768552\pi\)
\(710\) 3169.65i 0.167542i
\(711\) 0 0
\(712\) −10998.0 19049.1i −0.578887 1.00266i
\(713\) −10530.0 + 6079.50i −0.553088 + 0.319325i
\(714\) 0 0
\(715\) 780.000 + 810.600i 0.0407977 + 0.0423982i
\(716\) −18720.0 −0.977094
\(717\) 0 0
\(718\) 6174.00 + 10693.7i 0.320908 + 0.555828i
\(719\) 9204.00 15941.8i 0.477401 0.826883i −0.522264 0.852784i \(-0.674912\pi\)
0.999665 + 0.0259014i \(0.00824561\pi\)
\(720\) 0 0
\(721\) −2184.00 1260.93i −0.112811 0.0651312i
\(722\) −9313.50 5377.15i −0.480073 0.277170i
\(723\) 0 0
\(724\) 1592.50 2758.29i 0.0817470 0.141590i
\(725\) −8601.00 14897.4i −0.440597 0.763137i
\(726\) 0 0
\(727\) 21112.0 1.07703 0.538515 0.842616i \(-0.318986\pi\)
0.538515 + 0.842616i \(0.318986\pi\)
\(728\) −4056.00 + 14050.4i −0.206491 + 0.715305i
\(729\) 0 0
\(730\) 1192.50 688.490i 0.0604608 0.0349071i
\(731\) 6084.00 + 10537.8i 0.307832 + 0.533180i
\(732\) 0 0
\(733\) 23959.5i 1.20732i 0.797243 + 0.603658i \(0.206291\pi\)
−0.797243 + 0.603658i \(0.793709\pi\)
\(734\) 3.00000 + 1.73205i 0.000150861 + 8.70997e-5i
\(735\) 0 0
\(736\) 14185.5i 0.710441i
\(737\) 5448.00 9436.21i 0.272293 0.471625i
\(738\) 0 0
\(739\) 2742.00 1583.09i 0.136490 0.0788025i −0.430200 0.902734i \(-0.641557\pi\)
0.566690 + 0.823931i \(0.308224\pi\)
\(740\) −1245.00 −0.0618474
\(741\) 0 0
\(742\) −2232.00 −0.110430
\(743\) 26070.0 15051.5i 1.28723 0.743185i 0.309075 0.951038i \(-0.399981\pi\)
0.978160 + 0.207852i \(0.0666474\pi\)
\(744\) 0 0
\(745\) 40.5000 70.1481i 0.00199168 0.00344970i
\(746\) 6060.45i 0.297438i
\(747\) 0 0
\(748\) −7020.00 4053.00i −0.343151 0.198118i
\(749\) 20867.7i 1.01801i
\(750\) 0 0
\(751\) −14248.0 24678.3i −0.692299 1.19910i −0.971083 0.238744i \(-0.923264\pi\)
0.278783 0.960354i \(-0.410069\pi\)
\(752\) 261.000 150.688i 0.0126565 0.00730724i
\(753\) 0 0
\(754\) 10998.0 + 3174.85i 0.531198 + 0.153344i
\(755\) 3066.00 0.147792
\(756\) 0 0
\(757\) −8711.00 15087.9i −0.418239 0.724411i 0.577524 0.816374i \(-0.304019\pi\)
−0.995762 + 0.0919633i \(0.970686\pi\)
\(758\) −4779.00 + 8277.47i −0.228999 + 0.396638i
\(759\) 0 0
\(760\) 3861.00 + 2229.15i 0.184281 + 0.106394i
\(761\) −35790.0 20663.4i −1.70484 0.984292i −0.940695 0.339252i \(-0.889826\pi\)
−0.764149 0.645040i \(-0.776841\pi\)
\(762\) 0 0
\(763\) −10752.0 + 18623.0i −0.510155 + 0.883615i
\(764\) −6495.00 11249.7i −0.307567 0.532721i
\(765\) 0 0
\(766\) −12756.0 −0.601688
\(767\) 12792.0 + 3692.73i 0.602206 + 0.173842i
\(768\) 0 0
\(769\) −12186.0 + 7035.59i −0.571441 + 0.329922i −0.757725 0.652574i \(-0.773689\pi\)
0.186283 + 0.982496i \(0.440356\pi\)
\(770\) 288.000 + 498.831i 0.0134790 + 0.0233462i
\(771\) 0 0
\(772\) 5585.86i 0.260414i
\(773\) −174.000 100.459i −0.00809618 0.00467433i 0.495946 0.868353i \(-0.334821\pi\)
−0.504043 + 0.863679i \(0.668155\pi\)
\(774\) 0 0
\(775\) 19017.9i 0.881476i
\(776\) 2262.00 3917.90i 0.104641 0.181243i
\(777\) 0 0
\(778\) −1813.50 + 1047.02i −0.0835696 + 0.0482489i
\(779\) 31086.0 1.42975
\(780\) 0 0
\(781\) 14640.0 0.670756
\(782\) 13689.0 7903.35i 0.625982 0.361411i
\(783\) 0 0