Properties

Label 108.4.b.a.107.8
Level 108
Weight 4
Character 108.107
Analytic conductor 6.372
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.8
Root \(-2.48442 - 1.43438i\) of \(x^{12} - 12 x^{10} + 112 x^{8} - 368 x^{6} + 928 x^{4} - 256 x^{2} + 64\)
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.a.107.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.889241 + 2.68500i) q^{2} +(-6.41850 + 4.77523i) q^{4} -14.9230i q^{5} -30.0528i q^{7} +(-18.5291 - 12.9874i) q^{8} +O(q^{10})\) \(q+(0.889241 + 2.68500i) q^{2} +(-6.41850 + 4.77523i) q^{4} -14.9230i q^{5} -30.0528i q^{7} +(-18.5291 - 12.9874i) q^{8} +(40.0683 - 13.2701i) q^{10} -55.9380 q^{11} +57.4627 q^{13} +(80.6918 - 26.7241i) q^{14} +(18.3943 - 61.2997i) q^{16} +29.2840i q^{17} +0.709738i q^{19} +(71.2608 + 95.7833i) q^{20} +(-49.7423 - 150.194i) q^{22} -48.0368 q^{23} -97.6960 q^{25} +(51.0981 + 154.288i) q^{26} +(143.509 + 192.894i) q^{28} -172.964i q^{29} -45.2268i q^{31} +(180.947 - 5.12130i) q^{32} +(-78.6277 + 26.0405i) q^{34} -448.477 q^{35} +248.625 q^{37} +(-1.90565 + 0.631128i) q^{38} +(-193.811 + 276.510i) q^{40} +51.3323i q^{41} -19.9660i q^{43} +(359.038 - 267.117i) q^{44} +(-42.7163 - 128.979i) q^{46} +10.8215 q^{47} -560.168 q^{49} +(-86.8753 - 262.314i) q^{50} +(-368.824 + 274.398i) q^{52} -37.0817i q^{53} +834.763i q^{55} +(-390.306 + 556.851i) q^{56} +(464.410 - 153.807i) q^{58} -411.262 q^{59} -308.855 q^{61} +(121.434 - 40.2175i) q^{62} +(174.656 + 481.289i) q^{64} -857.516i q^{65} -113.616i q^{67} +(-139.838 - 187.959i) q^{68} +(-398.804 - 1204.16i) q^{70} +1134.56 q^{71} +728.560 q^{73} +(221.088 + 667.560i) q^{74} +(-3.38916 - 4.55545i) q^{76} +1681.09i q^{77} -487.025i q^{79} +(-914.775 - 274.499i) q^{80} +(-137.827 + 45.6468i) q^{82} +1165.71 q^{83} +437.005 q^{85} +(53.6088 - 17.7546i) q^{86} +(1036.48 + 726.488i) q^{88} +1198.68i q^{89} -1726.91i q^{91} +(308.324 - 229.387i) q^{92} +(9.62289 + 29.0557i) q^{94} +10.5914 q^{95} +624.472 q^{97} +(-498.124 - 1504.05i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{4} + O(q^{10}) \) \( 12q - 12q^{4} + 24q^{10} + 36q^{13} + 24q^{16} + 120q^{22} - 132q^{25} + 420q^{28} - 360q^{34} + 516q^{37} - 1152q^{40} - 696q^{46} - 720q^{49} + 204q^{52} + 2832q^{58} - 972q^{61} + 2496q^{64} - 1848q^{70} + 660q^{73} - 5004q^{76} - 3888q^{82} + 1056q^{85} + 3168q^{88} + 7608q^{94} + 2532q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.889241 + 2.68500i 0.314394 + 0.949293i
\(3\) 0 0
\(4\) −6.41850 + 4.77523i −0.802313 + 0.596904i
\(5\) 14.9230i 1.33475i −0.744720 0.667377i \(-0.767417\pi\)
0.744720 0.667377i \(-0.232583\pi\)
\(6\) 0 0
\(7\) 30.0528i 1.62270i −0.584563 0.811348i \(-0.698734\pi\)
0.584563 0.811348i \(-0.301266\pi\)
\(8\) −18.5291 12.9874i −0.818879 0.573966i
\(9\) 0 0
\(10\) 40.0683 13.2701i 1.26707 0.419639i
\(11\) −55.9380 −1.53327 −0.766634 0.642085i \(-0.778070\pi\)
−0.766634 + 0.642085i \(0.778070\pi\)
\(12\) 0 0
\(13\) 57.4627 1.22594 0.612972 0.790105i \(-0.289974\pi\)
0.612972 + 0.790105i \(0.289974\pi\)
\(14\) 80.6918 26.7241i 1.54041 0.510166i
\(15\) 0 0
\(16\) 18.3943 61.2997i 0.287411 0.957807i
\(17\) 29.2840i 0.417789i 0.977938 + 0.208895i \(0.0669865\pi\)
−0.977938 + 0.208895i \(0.933013\pi\)
\(18\) 0 0
\(19\) 0.709738i 0.00856974i 0.999991 + 0.00428487i \(0.00136392\pi\)
−0.999991 + 0.00428487i \(0.998636\pi\)
\(20\) 71.2608 + 95.7833i 0.796720 + 1.07089i
\(21\) 0 0
\(22\) −49.7423 150.194i −0.482050 1.45552i
\(23\) −48.0368 −0.435494 −0.217747 0.976005i \(-0.569871\pi\)
−0.217747 + 0.976005i \(0.569871\pi\)
\(24\) 0 0
\(25\) −97.6960 −0.781568
\(26\) 51.0981 + 154.288i 0.385430 + 1.16378i
\(27\) 0 0
\(28\) 143.509 + 192.894i 0.968594 + 1.30191i
\(29\) 172.964i 1.10754i −0.832670 0.553770i \(-0.813189\pi\)
0.832670 0.553770i \(-0.186811\pi\)
\(30\) 0 0
\(31\) 45.2268i 0.262031i −0.991380 0.131016i \(-0.958176\pi\)
0.991380 0.131016i \(-0.0418238\pi\)
\(32\) 180.947 5.12130i 0.999600 0.0282914i
\(33\) 0 0
\(34\) −78.6277 + 26.0405i −0.396604 + 0.131350i
\(35\) −448.477 −2.16590
\(36\) 0 0
\(37\) 248.625 1.10470 0.552348 0.833613i \(-0.313732\pi\)
0.552348 + 0.833613i \(0.313732\pi\)
\(38\) −1.90565 + 0.631128i −0.00813519 + 0.00269427i
\(39\) 0 0
\(40\) −193.811 + 276.510i −0.766104 + 1.09300i
\(41\) 51.3323i 0.195531i 0.995209 + 0.0977653i \(0.0311695\pi\)
−0.995209 + 0.0977653i \(0.968831\pi\)
\(42\) 0 0
\(43\) 19.9660i 0.0708090i −0.999373 0.0354045i \(-0.988728\pi\)
0.999373 0.0354045i \(-0.0112720\pi\)
\(44\) 359.038 267.117i 1.23016 0.915213i
\(45\) 0 0
\(46\) −42.7163 128.979i −0.136917 0.413411i
\(47\) 10.8215 0.0335845 0.0167923 0.999859i \(-0.494655\pi\)
0.0167923 + 0.999859i \(0.494655\pi\)
\(48\) 0 0
\(49\) −560.168 −1.63314
\(50\) −86.8753 262.314i −0.245720 0.741937i
\(51\) 0 0
\(52\) −368.824 + 274.398i −0.983591 + 0.731771i
\(53\) 37.0817i 0.0961051i −0.998845 0.0480525i \(-0.984699\pi\)
0.998845 0.0480525i \(-0.0153015\pi\)
\(54\) 0 0
\(55\) 834.763i 2.04653i
\(56\) −390.306 + 556.851i −0.931373 + 1.32879i
\(57\) 0 0
\(58\) 464.410 153.807i 1.05138 0.348204i
\(59\) −411.262 −0.907487 −0.453744 0.891132i \(-0.649912\pi\)
−0.453744 + 0.891132i \(0.649912\pi\)
\(60\) 0 0
\(61\) −308.855 −0.648275 −0.324138 0.946010i \(-0.605074\pi\)
−0.324138 + 0.946010i \(0.605074\pi\)
\(62\) 121.434 40.2175i 0.248744 0.0823811i
\(63\) 0 0
\(64\) 174.656 + 481.289i 0.341125 + 0.940018i
\(65\) 857.516i 1.63633i
\(66\) 0 0
\(67\) 113.616i 0.207170i −0.994621 0.103585i \(-0.966969\pi\)
0.994621 0.103585i \(-0.0330314\pi\)
\(68\) −139.838 187.959i −0.249380 0.335197i
\(69\) 0 0
\(70\) −398.804 1204.16i −0.680946 2.05607i
\(71\) 1134.56 1.89645 0.948224 0.317603i \(-0.102878\pi\)
0.948224 + 0.317603i \(0.102878\pi\)
\(72\) 0 0
\(73\) 728.560 1.16810 0.584051 0.811717i \(-0.301467\pi\)
0.584051 + 0.811717i \(0.301467\pi\)
\(74\) 221.088 + 667.560i 0.347310 + 1.04868i
\(75\) 0 0
\(76\) −3.38916 4.55545i −0.00511531 0.00687561i
\(77\) 1681.09i 2.48803i
\(78\) 0 0
\(79\) 487.025i 0.693602i −0.937939 0.346801i \(-0.887268\pi\)
0.937939 0.346801i \(-0.112732\pi\)
\(80\) −914.775 274.499i −1.27844 0.383623i
\(81\) 0 0
\(82\) −137.827 + 45.6468i −0.185616 + 0.0614737i
\(83\) 1165.71 1.54161 0.770803 0.637074i \(-0.219855\pi\)
0.770803 + 0.637074i \(0.219855\pi\)
\(84\) 0 0
\(85\) 437.005 0.557646
\(86\) 53.6088 17.7546i 0.0672184 0.0222619i
\(87\) 0 0
\(88\) 1036.48 + 726.488i 1.25556 + 0.880044i
\(89\) 1198.68i 1.42764i 0.700332 + 0.713818i \(0.253035\pi\)
−0.700332 + 0.713818i \(0.746965\pi\)
\(90\) 0 0
\(91\) 1726.91i 1.98934i
\(92\) 308.324 229.387i 0.349402 0.259948i
\(93\) 0 0
\(94\) 9.62289 + 29.0557i 0.0105588 + 0.0318815i
\(95\) 10.5914 0.0114385
\(96\) 0 0
\(97\) 624.472 0.653665 0.326833 0.945082i \(-0.394019\pi\)
0.326833 + 0.945082i \(0.394019\pi\)
\(98\) −498.124 1504.05i −0.513450 1.55033i
\(99\) 0 0
\(100\) 627.062 466.521i 0.627062 0.466521i
\(101\) 1757.10i 1.73107i −0.500849 0.865535i \(-0.666979\pi\)
0.500849 0.865535i \(-0.333021\pi\)
\(102\) 0 0
\(103\) 3.90175i 0.00373254i −0.999998 0.00186627i \(-0.999406\pi\)
0.999998 0.00186627i \(-0.000594052\pi\)
\(104\) −1064.73 746.289i −1.00390 0.703651i
\(105\) 0 0
\(106\) 99.5646 32.9746i 0.0912318 0.0302149i
\(107\) 77.3509 0.0698859 0.0349429 0.999389i \(-0.488875\pi\)
0.0349429 + 0.999389i \(0.488875\pi\)
\(108\) 0 0
\(109\) −1660.75 −1.45937 −0.729683 0.683785i \(-0.760333\pi\)
−0.729683 + 0.683785i \(0.760333\pi\)
\(110\) −2241.34 + 742.305i −1.94276 + 0.643418i
\(111\) 0 0
\(112\) −1842.22 552.800i −1.55423 0.466381i
\(113\) 253.390i 0.210946i −0.994422 0.105473i \(-0.966364\pi\)
0.994422 0.105473i \(-0.0336357\pi\)
\(114\) 0 0
\(115\) 716.853i 0.581277i
\(116\) 825.945 + 1110.17i 0.661095 + 0.888594i
\(117\) 0 0
\(118\) −365.711 1104.24i −0.285309 0.861471i
\(119\) 880.065 0.677945
\(120\) 0 0
\(121\) 1798.06 1.35091
\(122\) −274.646 829.276i −0.203814 0.615403i
\(123\) 0 0
\(124\) 215.968 + 290.288i 0.156408 + 0.210231i
\(125\) 407.457i 0.291553i
\(126\) 0 0
\(127\) 1429.82i 0.999022i 0.866307 + 0.499511i \(0.166487\pi\)
−0.866307 + 0.499511i \(0.833513\pi\)
\(128\) −1136.95 + 896.934i −0.785104 + 0.619364i
\(129\) 0 0
\(130\) 2302.43 762.538i 1.55336 0.514454i
\(131\) 2037.82 1.35912 0.679560 0.733620i \(-0.262171\pi\)
0.679560 + 0.733620i \(0.262171\pi\)
\(132\) 0 0
\(133\) 21.3296 0.0139061
\(134\) 305.059 101.032i 0.196665 0.0651330i
\(135\) 0 0
\(136\) 380.322 542.607i 0.239797 0.342119i
\(137\) 804.869i 0.501931i 0.967996 + 0.250966i \(0.0807481\pi\)
−0.967996 + 0.250966i \(0.919252\pi\)
\(138\) 0 0
\(139\) 413.813i 0.252512i 0.991998 + 0.126256i \(0.0402961\pi\)
−0.991998 + 0.126256i \(0.959704\pi\)
\(140\) 2878.55 2141.58i 1.73773 1.29283i
\(141\) 0 0
\(142\) 1008.90 + 3046.31i 0.596232 + 1.80028i
\(143\) −3214.35 −1.87970
\(144\) 0 0
\(145\) −2581.15 −1.47829
\(146\) 647.865 + 1956.19i 0.367245 + 1.10887i
\(147\) 0 0
\(148\) −1595.80 + 1187.24i −0.886312 + 0.659398i
\(149\) 1459.08i 0.802233i 0.916027 + 0.401116i \(0.131378\pi\)
−0.916027 + 0.401116i \(0.868622\pi\)
\(150\) 0 0
\(151\) 1668.38i 0.899144i 0.893244 + 0.449572i \(0.148424\pi\)
−0.893244 + 0.449572i \(0.851576\pi\)
\(152\) 9.21763 13.1508i 0.00491874 0.00701757i
\(153\) 0 0
\(154\) −4513.74 + 1494.89i −2.36187 + 0.782221i
\(155\) −674.920 −0.349747
\(156\) 0 0
\(157\) −1773.81 −0.901691 −0.450846 0.892602i \(-0.648877\pi\)
−0.450846 + 0.892602i \(0.648877\pi\)
\(158\) 1307.66 433.082i 0.658431 0.218064i
\(159\) 0 0
\(160\) −76.4251 2700.27i −0.0377621 1.33422i
\(161\) 1443.64i 0.706674i
\(162\) 0 0
\(163\) 3549.13i 1.70546i −0.522356 0.852728i \(-0.674947\pi\)
0.522356 0.852728i \(-0.325053\pi\)
\(164\) −245.124 329.476i −0.116713 0.156877i
\(165\) 0 0
\(166\) 1036.60 + 3129.94i 0.484672 + 1.46343i
\(167\) −1888.67 −0.875146 −0.437573 0.899183i \(-0.644162\pi\)
−0.437573 + 0.899183i \(0.644162\pi\)
\(168\) 0 0
\(169\) 1104.96 0.502939
\(170\) 388.603 + 1173.36i 0.175320 + 0.529369i
\(171\) 0 0
\(172\) 95.3422 + 128.152i 0.0422661 + 0.0568109i
\(173\) 2104.10i 0.924694i −0.886699 0.462347i \(-0.847008\pi\)
0.886699 0.462347i \(-0.152992\pi\)
\(174\) 0 0
\(175\) 2936.03i 1.26825i
\(176\) −1028.94 + 3428.98i −0.440678 + 1.46857i
\(177\) 0 0
\(178\) −3218.45 + 1065.91i −1.35524 + 0.448840i
\(179\) 1830.10 0.764178 0.382089 0.924126i \(-0.375205\pi\)
0.382089 + 0.924126i \(0.375205\pi\)
\(180\) 0 0
\(181\) 3333.54 1.36895 0.684475 0.729036i \(-0.260032\pi\)
0.684475 + 0.729036i \(0.260032\pi\)
\(182\) 4636.77 1535.64i 1.88846 0.625435i
\(183\) 0 0
\(184\) 890.079 + 623.872i 0.356617 + 0.249959i
\(185\) 3710.24i 1.47450i
\(186\) 0 0
\(187\) 1638.09i 0.640582i
\(188\) −69.4576 + 51.6750i −0.0269453 + 0.0200467i
\(189\) 0 0
\(190\) 9.41832 + 28.4380i 0.00359619 + 0.0108585i
\(191\) −3622.23 −1.37223 −0.686114 0.727494i \(-0.740685\pi\)
−0.686114 + 0.727494i \(0.740685\pi\)
\(192\) 0 0
\(193\) −2588.68 −0.965479 −0.482740 0.875764i \(-0.660358\pi\)
−0.482740 + 0.875764i \(0.660358\pi\)
\(194\) 555.306 + 1676.71i 0.205508 + 0.620520i
\(195\) 0 0
\(196\) 3595.44 2674.93i 1.31029 0.974829i
\(197\) 1752.24i 0.633717i −0.948473 0.316858i \(-0.897372\pi\)
0.948473 0.316858i \(-0.102628\pi\)
\(198\) 0 0
\(199\) 3316.58i 1.18144i 0.806877 + 0.590719i \(0.201156\pi\)
−0.806877 + 0.590719i \(0.798844\pi\)
\(200\) 1810.22 + 1268.82i 0.640010 + 0.448594i
\(201\) 0 0
\(202\) 4717.82 1562.49i 1.64329 0.544238i
\(203\) −5198.05 −1.79720
\(204\) 0 0
\(205\) 766.032 0.260985
\(206\) 10.4762 3.46960i 0.00354327 0.00117349i
\(207\) 0 0
\(208\) 1056.99 3522.44i 0.352350 1.17422i
\(209\) 39.7013i 0.0131397i
\(210\) 0 0
\(211\) 5960.10i 1.94460i −0.233738 0.972300i \(-0.575096\pi\)
0.233738 0.972300i \(-0.424904\pi\)
\(212\) 177.074 + 238.009i 0.0573655 + 0.0771063i
\(213\) 0 0
\(214\) 68.7836 + 207.687i 0.0219717 + 0.0663422i
\(215\) −297.953 −0.0945125
\(216\) 0 0
\(217\) −1359.19 −0.425197
\(218\) −1476.81 4459.12i −0.458816 1.38537i
\(219\) 0 0
\(220\) −3986.19 5357.93i −1.22158 1.64196i
\(221\) 1682.74i 0.512186i
\(222\) 0 0
\(223\) 1995.23i 0.599150i 0.954073 + 0.299575i \(0.0968449\pi\)
−0.954073 + 0.299575i \(0.903155\pi\)
\(224\) −153.909 5437.95i −0.0459084 1.62205i
\(225\) 0 0
\(226\) 680.354 225.325i 0.200250 0.0663203i
\(227\) −2280.12 −0.666682 −0.333341 0.942806i \(-0.608176\pi\)
−0.333341 + 0.942806i \(0.608176\pi\)
\(228\) 0 0
\(229\) 4647.94 1.34124 0.670621 0.741800i \(-0.266028\pi\)
0.670621 + 0.741800i \(0.266028\pi\)
\(230\) −1924.75 + 637.455i −0.551802 + 0.182750i
\(231\) 0 0
\(232\) −2246.35 + 3204.88i −0.635691 + 0.906941i
\(233\) 2824.81i 0.794247i −0.917765 0.397124i \(-0.870008\pi\)
0.917765 0.397124i \(-0.129992\pi\)
\(234\) 0 0
\(235\) 161.489i 0.0448271i
\(236\) 2639.69 1963.87i 0.728089 0.541683i
\(237\) 0 0
\(238\) 782.590 + 2362.98i 0.213142 + 0.643568i
\(239\) 2405.85 0.651136 0.325568 0.945519i \(-0.394445\pi\)
0.325568 + 0.945519i \(0.394445\pi\)
\(240\) 0 0
\(241\) −226.108 −0.0604352 −0.0302176 0.999543i \(-0.509620\pi\)
−0.0302176 + 0.999543i \(0.509620\pi\)
\(242\) 1598.91 + 4827.80i 0.424718 + 1.28241i
\(243\) 0 0
\(244\) 1982.38 1474.85i 0.520120 0.386958i
\(245\) 8359.39i 2.17984i
\(246\) 0 0
\(247\) 40.7834i 0.0105060i
\(248\) −587.377 + 838.012i −0.150397 + 0.214572i
\(249\) 0 0
\(250\) 1094.02 362.328i 0.276769 0.0916624i
\(251\) 1071.12 0.269357 0.134679 0.990889i \(-0.457000\pi\)
0.134679 + 0.990889i \(0.457000\pi\)
\(252\) 0 0
\(253\) 2687.08 0.667729
\(254\) −3839.07 + 1271.45i −0.948365 + 0.314087i
\(255\) 0 0
\(256\) −3419.30 2255.13i −0.834789 0.550569i
\(257\) 1844.28i 0.447638i −0.974631 0.223819i \(-0.928148\pi\)
0.974631 0.223819i \(-0.0718525\pi\)
\(258\) 0 0
\(259\) 7471.88i 1.79259i
\(260\) 4094.84 + 5503.96i 0.976734 + 1.31285i
\(261\) 0 0
\(262\) 1812.11 + 5471.54i 0.427299 + 1.29020i
\(263\) 7502.45 1.75901 0.879507 0.475886i \(-0.157872\pi\)
0.879507 + 0.475886i \(0.157872\pi\)
\(264\) 0 0
\(265\) −553.371 −0.128277
\(266\) 18.9671 + 57.2700i 0.00437199 + 0.0132009i
\(267\) 0 0
\(268\) 542.542 + 729.243i 0.123661 + 0.166215i
\(269\) 3465.21i 0.785418i −0.919663 0.392709i \(-0.871538\pi\)
0.919663 0.392709i \(-0.128462\pi\)
\(270\) 0 0
\(271\) 2922.27i 0.655038i −0.944845 0.327519i \(-0.893788\pi\)
0.944845 0.327519i \(-0.106212\pi\)
\(272\) 1795.10 + 538.660i 0.400161 + 0.120077i
\(273\) 0 0
\(274\) −2161.08 + 715.722i −0.476480 + 0.157804i
\(275\) 5464.92 1.19835
\(276\) 0 0
\(277\) −6644.62 −1.44129 −0.720643 0.693306i \(-0.756153\pi\)
−0.720643 + 0.693306i \(0.756153\pi\)
\(278\) −1111.09 + 367.980i −0.239708 + 0.0793883i
\(279\) 0 0
\(280\) 8309.89 + 5824.54i 1.77361 + 1.24315i
\(281\) 6612.13i 1.40373i 0.712312 + 0.701863i \(0.247648\pi\)
−0.712312 + 0.701863i \(0.752352\pi\)
\(282\) 0 0
\(283\) 2658.33i 0.558379i 0.960236 + 0.279190i \(0.0900658\pi\)
−0.960236 + 0.279190i \(0.909934\pi\)
\(284\) −7282.19 + 5417.80i −1.52154 + 1.13200i
\(285\) 0 0
\(286\) −2858.33 8630.53i −0.590967 1.78439i
\(287\) 1542.68 0.317287
\(288\) 0 0
\(289\) 4055.45 0.825452
\(290\) −2295.26 6930.39i −0.464767 1.40333i
\(291\) 0 0
\(292\) −4676.26 + 3479.04i −0.937184 + 0.697245i
\(293\) 5553.60i 1.10732i −0.832743 0.553660i \(-0.813231\pi\)
0.832743 0.553660i \(-0.186769\pi\)
\(294\) 0 0
\(295\) 6137.26i 1.21127i
\(296\) −4606.81 3228.99i −0.904613 0.634059i
\(297\) 0 0
\(298\) −3917.64 + 1297.48i −0.761554 + 0.252217i
\(299\) −2760.32 −0.533891
\(300\) 0 0
\(301\) −600.033 −0.114901
\(302\) −4479.61 + 1483.59i −0.853551 + 0.282686i
\(303\) 0 0
\(304\) 43.5067 + 13.0551i 0.00820815 + 0.00246304i
\(305\) 4609.04i 0.865288i
\(306\) 0 0
\(307\) 8694.95i 1.61644i 0.588880 + 0.808220i \(0.299569\pi\)
−0.588880 + 0.808220i \(0.700431\pi\)
\(308\) −8027.60 10790.1i −1.48511 1.99618i
\(309\) 0 0
\(310\) −600.166 1812.16i −0.109959 0.332013i
\(311\) 6717.09 1.22473 0.612365 0.790575i \(-0.290218\pi\)
0.612365 + 0.790575i \(0.290218\pi\)
\(312\) 0 0
\(313\) −1389.06 −0.250844 −0.125422 0.992103i \(-0.540028\pi\)
−0.125422 + 0.992103i \(0.540028\pi\)
\(314\) −1577.34 4762.69i −0.283486 0.855969i
\(315\) 0 0
\(316\) 2325.66 + 3125.97i 0.414014 + 0.556486i
\(317\) 1457.63i 0.258260i 0.991628 + 0.129130i \(0.0412185\pi\)
−0.991628 + 0.129130i \(0.958782\pi\)
\(318\) 0 0
\(319\) 9675.28i 1.69816i
\(320\) 7182.28 2606.39i 1.25469 0.455318i
\(321\) 0 0
\(322\) −3876.17 + 1283.74i −0.670841 + 0.222174i
\(323\) −20.7840 −0.00358034
\(324\) 0 0
\(325\) −5613.87 −0.958159
\(326\) 9529.43 3156.03i 1.61898 0.536185i
\(327\) 0 0
\(328\) 666.672 951.142i 0.112228 0.160116i
\(329\) 325.215i 0.0544975i
\(330\) 0 0
\(331\) 4966.82i 0.824776i −0.911008 0.412388i \(-0.864695\pi\)
0.911008 0.412388i \(-0.135305\pi\)
\(332\) −7482.11 + 5566.53i −1.23685 + 0.920190i
\(333\) 0 0
\(334\) −1679.48 5071.08i −0.275141 0.830769i
\(335\) −1695.49 −0.276521
\(336\) 0 0
\(337\) −4892.90 −0.790899 −0.395450 0.918488i \(-0.629411\pi\)
−0.395450 + 0.918488i \(0.629411\pi\)
\(338\) 982.574 + 2966.82i 0.158121 + 0.477437i
\(339\) 0 0
\(340\) −2804.92 + 2086.80i −0.447406 + 0.332861i
\(341\) 2529.90i 0.401764i
\(342\) 0 0
\(343\) 6526.50i 1.02740i
\(344\) −259.306 + 369.952i −0.0406420 + 0.0579840i
\(345\) 0 0
\(346\) 5649.53 1871.05i 0.877805 0.290718i
\(347\) −253.981 −0.0392923 −0.0196461 0.999807i \(-0.506254\pi\)
−0.0196461 + 0.999807i \(0.506254\pi\)
\(348\) 0 0
\(349\) −6464.21 −0.991465 −0.495732 0.868475i \(-0.665100\pi\)
−0.495732 + 0.868475i \(0.665100\pi\)
\(350\) −7883.27 + 2610.84i −1.20394 + 0.398730i
\(351\) 0 0
\(352\) −10121.8 + 286.475i −1.53265 + 0.0433783i
\(353\) 4033.67i 0.608188i 0.952642 + 0.304094i \(0.0983537\pi\)
−0.952642 + 0.304094i \(0.901646\pi\)
\(354\) 0 0
\(355\) 16931.1i 2.53129i
\(356\) −5723.96 7693.71i −0.852161 1.14541i
\(357\) 0 0
\(358\) 1627.40 + 4913.82i 0.240253 + 0.725428i
\(359\) 10670.4 1.56870 0.784350 0.620319i \(-0.212997\pi\)
0.784350 + 0.620319i \(0.212997\pi\)
\(360\) 0 0
\(361\) 6858.50 0.999927
\(362\) 2964.32 + 8950.56i 0.430390 + 1.29953i
\(363\) 0 0
\(364\) 8246.40 + 11084.2i 1.18744 + 1.59607i
\(365\) 10872.3i 1.55913i
\(366\) 0 0
\(367\) 2559.84i 0.364094i 0.983290 + 0.182047i \(0.0582724\pi\)
−0.983290 + 0.182047i \(0.941728\pi\)
\(368\) −883.604 + 2944.64i −0.125166 + 0.417119i
\(369\) 0 0
\(370\) 9962.01 3299.29i 1.39973 0.463573i
\(371\) −1114.41 −0.155949
\(372\) 0 0
\(373\) 1935.92 0.268735 0.134368 0.990932i \(-0.457100\pi\)
0.134368 + 0.990932i \(0.457100\pi\)
\(374\) 4398.28 1456.65i 0.608100 0.201395i
\(375\) 0 0
\(376\) −200.512 140.542i −0.0275017 0.0192764i
\(377\) 9938.99i 1.35778i
\(378\) 0 0
\(379\) 5944.90i 0.805722i −0.915261 0.402861i \(-0.868016\pi\)
0.915261 0.402861i \(-0.131984\pi\)
\(380\) −67.9810 + 50.5765i −0.00917724 + 0.00682768i
\(381\) 0 0
\(382\) −3221.03 9725.71i −0.431420 1.30264i
\(383\) 1696.80 0.226378 0.113189 0.993573i \(-0.463893\pi\)
0.113189 + 0.993573i \(0.463893\pi\)
\(384\) 0 0
\(385\) 25086.9 3.32090
\(386\) −2301.96 6950.63i −0.303541 0.916522i
\(387\) 0 0
\(388\) −4008.17 + 2982.00i −0.524444 + 0.390175i
\(389\) 3913.71i 0.510111i 0.966926 + 0.255055i \(0.0820937\pi\)
−0.966926 + 0.255055i \(0.917906\pi\)
\(390\) 0 0
\(391\) 1406.71i 0.181945i
\(392\) 10379.4 + 7275.11i 1.33735 + 0.937369i
\(393\) 0 0
\(394\) 4704.78 1558.17i 0.601583 0.199237i
\(395\) −7267.87 −0.925788
\(396\) 0 0
\(397\) 5079.98 0.642208 0.321104 0.947044i \(-0.395946\pi\)
0.321104 + 0.947044i \(0.395946\pi\)
\(398\) −8905.04 + 2949.24i −1.12153 + 0.371437i
\(399\) 0 0
\(400\) −1797.05 + 5988.73i −0.224632 + 0.748592i
\(401\) 9374.44i 1.16742i 0.811961 + 0.583712i \(0.198400\pi\)
−0.811961 + 0.583712i \(0.801600\pi\)
\(402\) 0 0
\(403\) 2598.85i 0.321236i
\(404\) 8390.56 + 11278.0i 1.03328 + 1.38886i
\(405\) 0 0
\(406\) −4622.32 13956.8i −0.565029 1.70607i
\(407\) −13907.6 −1.69379
\(408\) 0 0
\(409\) −12392.7 −1.49824 −0.749120 0.662434i \(-0.769523\pi\)
−0.749120 + 0.662434i \(0.769523\pi\)
\(410\) 681.187 + 2056.80i 0.0820522 + 0.247751i
\(411\) 0 0
\(412\) 18.6318 + 25.0434i 0.00222797 + 0.00299466i
\(413\) 12359.6i 1.47258i
\(414\) 0 0
\(415\) 17395.9i 2.05766i
\(416\) 10397.7 294.283i 1.22545 0.0346837i
\(417\) 0 0
\(418\) 106.598 35.3040i 0.0124734 0.00413104i
\(419\) 266.866 0.0311151 0.0155576 0.999879i \(-0.495048\pi\)
0.0155576 + 0.999879i \(0.495048\pi\)
\(420\) 0 0
\(421\) −9952.62 −1.15216 −0.576082 0.817392i \(-0.695419\pi\)
−0.576082 + 0.817392i \(0.695419\pi\)
\(422\) 16002.9 5299.97i 1.84599 0.611371i
\(423\) 0 0
\(424\) −481.595 + 687.092i −0.0551611 + 0.0786984i
\(425\) 2860.93i 0.326531i
\(426\) 0 0
\(427\) 9281.94i 1.05195i
\(428\) −496.477 + 369.368i −0.0560703 + 0.0417152i
\(429\) 0 0
\(430\) −264.952 800.004i −0.0297142 0.0897200i
\(431\) −6583.33 −0.735749 −0.367875 0.929875i \(-0.619914\pi\)
−0.367875 + 0.929875i \(0.619914\pi\)
\(432\) 0 0
\(433\) −13747.0 −1.52572 −0.762860 0.646564i \(-0.776205\pi\)
−0.762860 + 0.646564i \(0.776205\pi\)
\(434\) −1208.65 3649.43i −0.133679 0.403637i
\(435\) 0 0
\(436\) 10659.5 7930.46i 1.17087 0.871102i
\(437\) 34.0935i 0.00373207i
\(438\) 0 0
\(439\) 13380.0i 1.45466i 0.686290 + 0.727328i \(0.259238\pi\)
−0.686290 + 0.727328i \(0.740762\pi\)
\(440\) 10841.4 15467.4i 1.17464 1.67586i
\(441\) 0 0
\(442\) −4518.16 + 1496.36i −0.486214 + 0.161028i
\(443\) 16108.1 1.72758 0.863791 0.503851i \(-0.168084\pi\)
0.863791 + 0.503851i \(0.168084\pi\)
\(444\) 0 0
\(445\) 17887.9 1.90554
\(446\) −5357.20 + 1774.24i −0.568769 + 0.188369i
\(447\) 0 0
\(448\) 14464.1 5248.90i 1.52536 0.553542i
\(449\) 11283.5i 1.18597i −0.805214 0.592984i \(-0.797950\pi\)
0.805214 0.592984i \(-0.202050\pi\)
\(450\) 0 0
\(451\) 2871.42i 0.299801i
\(452\) 1210.00 + 1626.39i 0.125915 + 0.169245i
\(453\) 0 0
\(454\) −2027.57 6122.13i −0.209601 0.632876i
\(455\) −25770.7 −2.65527
\(456\) 0 0
\(457\) 1984.72 0.203154 0.101577 0.994828i \(-0.467611\pi\)
0.101577 + 0.994828i \(0.467611\pi\)
\(458\) 4133.14 + 12479.7i 0.421679 + 1.27323i
\(459\) 0 0
\(460\) −3423.14 4601.12i −0.346967 0.466366i
\(461\) 9634.41i 0.973360i −0.873580 0.486680i \(-0.838208\pi\)
0.873580 0.486680i \(-0.161792\pi\)
\(462\) 0 0
\(463\) 1392.38i 0.139762i 0.997555 + 0.0698808i \(0.0222619\pi\)
−0.997555 + 0.0698808i \(0.977738\pi\)
\(464\) −10602.7 3181.56i −1.06081 0.318320i
\(465\) 0 0
\(466\) 7584.64 2511.94i 0.753973 0.249707i
\(467\) −15161.4 −1.50232 −0.751161 0.660119i \(-0.770506\pi\)
−0.751161 + 0.660119i \(0.770506\pi\)
\(468\) 0 0
\(469\) −3414.47 −0.336174
\(470\) 433.598 143.602i 0.0425540 0.0140934i
\(471\) 0 0
\(472\) 7620.32 + 5341.22i 0.743122 + 0.520867i
\(473\) 1116.86i 0.108569i
\(474\) 0 0
\(475\) 69.3385i 0.00669783i
\(476\) −5648.70 + 4202.51i −0.543924 + 0.404668i
\(477\) 0 0
\(478\) 2139.38 + 6459.72i 0.204713 + 0.618118i
\(479\) 273.224 0.0260625 0.0130312 0.999915i \(-0.495852\pi\)
0.0130312 + 0.999915i \(0.495852\pi\)
\(480\) 0 0
\(481\) 14286.7 1.35430
\(482\) −201.064 607.100i −0.0190005 0.0573707i
\(483\) 0 0
\(484\) −11540.8 + 8586.15i −1.08385 + 0.806362i
\(485\) 9319.00i 0.872482i
\(486\) 0 0
\(487\) 8706.60i 0.810131i 0.914288 + 0.405065i \(0.132751\pi\)
−0.914288 + 0.405065i \(0.867249\pi\)
\(488\) 5722.80 + 4011.21i 0.530859 + 0.372088i
\(489\) 0 0
\(490\) −22445.0 + 7433.51i −2.06931 + 0.685330i
\(491\) −4442.47 −0.408321 −0.204161 0.978937i \(-0.565446\pi\)
−0.204161 + 0.978937i \(0.565446\pi\)
\(492\) 0 0
\(493\) 5065.09 0.462718
\(494\) −109.504 + 36.2663i −0.00997328 + 0.00330303i
\(495\) 0 0
\(496\) −2772.39 831.916i −0.250975 0.0753108i
\(497\) 34096.7i 3.07736i
\(498\) 0 0
\(499\) 4920.29i 0.441408i 0.975341 + 0.220704i \(0.0708355\pi\)
−0.975341 + 0.220704i \(0.929165\pi\)
\(500\) 1945.70 + 2615.27i 0.174029 + 0.233916i
\(501\) 0 0
\(502\) 952.486 + 2875.97i 0.0846843 + 0.255699i
\(503\) −5575.54 −0.494237 −0.247118 0.968985i \(-0.579484\pi\)
−0.247118 + 0.968985i \(0.579484\pi\)
\(504\) 0 0
\(505\) −26221.2 −2.31055
\(506\) 2389.46 + 7214.83i 0.209930 + 0.633870i
\(507\) 0 0
\(508\) −6827.71 9177.29i −0.596320 0.801528i
\(509\) 17508.5i 1.52466i 0.647190 + 0.762328i \(0.275944\pi\)
−0.647190 + 0.762328i \(0.724056\pi\)
\(510\) 0 0
\(511\) 21895.2i 1.89548i
\(512\) 3014.46 11186.2i 0.260199 0.965555i
\(513\) 0 0
\(514\) 4951.90 1640.01i 0.424940 0.140735i
\(515\) −58.2259 −0.00498202
\(516\) 0 0
\(517\) −605.331 −0.0514941
\(518\) 20062.0 6644.30i 1.70169 0.563579i
\(519\) 0 0
\(520\) −11136.9 + 15889.0i −0.939201 + 1.33996i
\(521\) 12662.1i 1.06475i 0.846507 + 0.532377i \(0.178701\pi\)
−0.846507 + 0.532377i \(0.821299\pi\)
\(522\) 0 0
\(523\) 2988.40i 0.249854i 0.992166 + 0.124927i \(0.0398697\pi\)
−0.992166 + 0.124927i \(0.960130\pi\)
\(524\) −13079.7 + 9731.04i −1.09044 + 0.811264i
\(525\) 0 0
\(526\) 6671.48 + 20144.1i 0.553024 + 1.66982i
\(527\) 1324.42 0.109474
\(528\) 0 0
\(529\) −9859.47 −0.810345
\(530\) −492.080 1485.80i −0.0403294 0.121772i
\(531\) 0 0
\(532\) −136.904 + 101.854i −0.0111570 + 0.00830059i
\(533\) 2949.69i 0.239710i
\(534\) 0 0
\(535\) 1154.31i 0.0932805i
\(536\) −1475.57 + 2105.20i −0.118909 + 0.169647i
\(537\) 0 0
\(538\) 9304.10 3081.40i 0.745591 0.246931i
\(539\) 31334.7 2.50404
\(540\) 0 0
\(541\) 9079.39 0.721541 0.360770 0.932655i \(-0.382514\pi\)
0.360770 + 0.932655i \(0.382514\pi\)
\(542\) 7846.31 2598.60i 0.621822 0.205940i
\(543\) 0 0
\(544\) 149.972 + 5298.85i 0.0118199 + 0.417622i
\(545\) 24783.4i 1.94790i
\(546\) 0 0
\(547\) 21690.2i 1.69544i 0.530444 + 0.847720i \(0.322025\pi\)
−0.530444 + 0.847720i \(0.677975\pi\)
\(548\) −3843.43 5166.05i −0.299605 0.402706i
\(549\) 0 0
\(550\) 4859.63 + 14673.3i 0.376755 + 1.13759i
\(551\) 122.759 0.00949133
\(552\) 0 0
\(553\) −14636.4 −1.12551
\(554\) −5908.66 17840.8i −0.453132 1.36820i
\(555\) 0 0
\(556\) −1976.05 2656.06i −0.150725 0.202594i
\(557\) 18129.0i 1.37908i 0.724247 + 0.689541i \(0.242188\pi\)
−0.724247 + 0.689541i \(0.757812\pi\)
\(558\) 0 0
\(559\) 1147.30i 0.0868078i
\(560\) −8249.44 + 27491.5i −0.622504 + 2.07451i
\(561\) 0 0
\(562\) −17753.6 + 5879.78i −1.33255 + 0.441323i
\(563\) 4922.54 0.368491 0.184245 0.982880i \(-0.441016\pi\)
0.184245 + 0.982880i \(0.441016\pi\)
\(564\) 0 0
\(565\) −3781.34 −0.281562
\(566\) −7137.63 + 2363.90i −0.530065 + 0.175551i
\(567\) 0 0
\(568\) −21022.4 14735.0i −1.55296 1.08850i
\(569\) 17731.7i 1.30641i 0.757179 + 0.653207i \(0.226577\pi\)
−0.757179 + 0.653207i \(0.773423\pi\)
\(570\) 0 0
\(571\) 17237.0i 1.26330i 0.775254 + 0.631650i \(0.217622\pi\)
−0.775254 + 0.631650i \(0.782378\pi\)
\(572\) 20631.3 15349.2i 1.50811 1.12200i
\(573\) 0 0
\(574\) 1371.81 + 4142.09i 0.0997531 + 0.301198i
\(575\) 4693.00 0.340368
\(576\) 0 0
\(577\) 6166.73 0.444929 0.222465 0.974941i \(-0.428590\pi\)
0.222465 + 0.974941i \(0.428590\pi\)
\(578\) 3606.27 + 10888.9i 0.259517 + 0.783596i
\(579\) 0 0
\(580\) 16567.1 12325.6i 1.18605 0.882399i
\(581\) 35032.8i 2.50156i
\(582\) 0 0
\(583\) 2074.28i 0.147355i
\(584\) −13499.6 9462.09i −0.956535 0.670452i
\(585\) 0 0
\(586\) 14911.5 4938.49i 1.05117 0.348135i
\(587\) −11268.2 −0.792311 −0.396155 0.918183i \(-0.629656\pi\)
−0.396155 + 0.918183i \(0.629656\pi\)
\(588\) 0 0
\(589\) 32.0992 0.00224554
\(590\) −16478.6 + 5457.51i −1.14985 + 0.380817i
\(591\) 0 0
\(592\) 4573.30 15240.7i 0.317502 1.05809i
\(593\) 4766.20i 0.330058i 0.986289 + 0.165029i \(0.0527718\pi\)
−0.986289 + 0.165029i \(0.947228\pi\)
\(594\) 0 0
\(595\) 13133.2i 0.904889i
\(596\) −6967.46 9365.12i −0.478856 0.643642i
\(597\) 0 0
\(598\) −2454.59 7411.48i −0.167852 0.506819i
\(599\) 11994.7 0.818177 0.409089 0.912495i \(-0.365847\pi\)
0.409089 + 0.912495i \(0.365847\pi\)
\(600\) 0 0
\(601\) 23975.3 1.62724 0.813622 0.581394i \(-0.197493\pi\)
0.813622 + 0.581394i \(0.197493\pi\)
\(602\) −533.574 1611.09i −0.0361243 0.109075i
\(603\) 0 0
\(604\) −7966.90 10708.5i −0.536703 0.721395i
\(605\) 26832.4i 1.80313i
\(606\) 0 0
\(607\) 18629.0i 1.24568i −0.782349 0.622840i \(-0.785979\pi\)
0.782349 0.622840i \(-0.214021\pi\)
\(608\) 3.63478 + 128.425i 0.000242450 + 0.00856630i
\(609\) 0 0
\(610\) −12375.3 + 4098.55i −0.821412 + 0.272041i
\(611\) 621.830 0.0411728
\(612\) 0 0
\(613\) 18552.5 1.22240 0.611198 0.791478i \(-0.290688\pi\)
0.611198 + 0.791478i \(0.290688\pi\)
\(614\) −23346.0 + 7731.91i −1.53447 + 0.508199i
\(615\) 0 0
\(616\) 21833.0 31149.1i 1.42804 2.03739i
\(617\) 7836.95i 0.511351i 0.966763 + 0.255676i \(0.0822979\pi\)
−0.966763 + 0.255676i \(0.917702\pi\)
\(618\) 0 0
\(619\) 16023.6i 1.04045i 0.854028 + 0.520227i \(0.174153\pi\)
−0.854028 + 0.520227i \(0.825847\pi\)
\(620\) 4331.97 3222.90i 0.280607 0.208766i
\(621\) 0 0
\(622\) 5973.11 + 18035.4i 0.385048 + 1.16263i
\(623\) 36023.6 2.31662
\(624\) 0 0
\(625\) −18292.5 −1.17072
\(626\) −1235.21 3729.62i −0.0788638 0.238124i
\(627\) 0 0
\(628\) 11385.2 8470.36i 0.723438 0.538223i
\(629\) 7280.75i 0.461530i
\(630\) 0 0
\(631\) 18451.1i 1.16407i 0.813164 + 0.582035i \(0.197743\pi\)
−0.813164 + 0.582035i \(0.802257\pi\)
\(632\) −6325.18 + 9024.14i −0.398104 + 0.567976i
\(633\) 0 0
\(634\) −3913.73 + 1296.18i −0.245164 + 0.0811955i
\(635\) 21337.2 1.33345
\(636\) 0 0
\(637\) −32188.7 −2.00214
\(638\) −25978.2 + 8603.65i −1.61205 + 0.533890i
\(639\) 0 0
\(640\) 13385.0 + 16966.7i 0.826698 + 1.04792i
\(641\) 20544.4i 1.26592i −0.774185 0.632960i \(-0.781840\pi\)
0.774185 0.632960i \(-0.218160\pi\)
\(642\) 0 0
\(643\) 27413.8i 1.68133i −0.541555 0.840665i \(-0.682164\pi\)
0.541555 0.840665i \(-0.317836\pi\)
\(644\) −6893.70 9265.99i −0.421817 0.566974i
\(645\) 0 0
\(646\) −18.4819 55.8050i −0.00112564 0.00339879i
\(647\) −23051.0 −1.40066 −0.700332 0.713817i \(-0.746965\pi\)
−0.700332 + 0.713817i \(0.746965\pi\)
\(648\) 0 0
\(649\) 23005.2 1.39142
\(650\) −4992.09 15073.3i −0.301240 0.909573i
\(651\) 0 0
\(652\) 16947.9 + 22780.1i 1.01799 + 1.36831i
\(653\) 27762.7i 1.66376i 0.554953 + 0.831882i \(0.312736\pi\)
−0.554953 + 0.831882i \(0.687264\pi\)
\(654\) 0 0
\(655\) 30410.3i 1.81409i
\(656\) 3146.65 + 944.223i 0.187281 + 0.0561977i
\(657\) 0 0
\(658\) 873.203 289.194i 0.0517341 0.0171337i
\(659\) 9857.22 0.582675 0.291338 0.956620i \(-0.405900\pi\)
0.291338 + 0.956620i \(0.405900\pi\)
\(660\) 0 0
\(661\) 3542.53 0.208454 0.104227 0.994554i \(-0.466763\pi\)
0.104227 + 0.994554i \(0.466763\pi\)
\(662\) 13335.9 4416.70i 0.782954 0.259305i
\(663\) 0 0
\(664\) −21599.6 15139.5i −1.26239 0.884830i
\(665\) 318.301i 0.0185612i
\(666\) 0 0
\(667\) 8308.65i 0.482327i
\(668\) 12122.4 9018.82i 0.702141 0.522378i
\(669\) 0 0
\(670\) −1507.70 4552.40i −0.0869365 0.262499i
\(671\) 17276.7 0.993979
\(672\) 0 0
\(673\) 19216.6 1.10066 0.550330 0.834947i \(-0.314502\pi\)
0.550330 + 0.834947i \(0.314502\pi\)
\(674\) −4350.96 13137.5i −0.248654 0.750795i
\(675\) 0 0
\(676\) −7092.17 + 5276.43i −0.403515 + 0.300206i
\(677\) 15731.9i 0.893093i 0.894760 + 0.446547i \(0.147346\pi\)
−0.894760 + 0.446547i \(0.852654\pi\)
\(678\) 0 0
\(679\) 18767.1i 1.06070i
\(680\) −8097.32 5675.55i −0.456644 0.320070i
\(681\) 0 0
\(682\) −6792.78 + 2249.69i −0.381392 + 0.126312i
\(683\) −16870.5 −0.945142 −0.472571 0.881293i \(-0.656674\pi\)
−0.472571 + 0.881293i \(0.656674\pi\)
\(684\) 0 0
\(685\) 12011.1 0.669955
\(686\) −17523.7 + 5803.63i −0.975302 + 0.323008i
\(687\) 0 0
\(688\) −1223.91 367.261i −0.0678213 0.0203513i
\(689\) 2130.82i 0.117819i
\(690\) 0 0
\(691\) 29234.5i 1.60945i −0.593645 0.804727i \(-0.702312\pi\)
0.593645 0.804727i \(-0.297688\pi\)
\(692\) 10047.6 + 13505.2i 0.551953 + 0.741894i
\(693\) 0 0
\(694\) −225.850 681.941i −0.0123533 0.0372999i
\(695\) 6175.33 0.337041
\(696\) 0 0
\(697\) −1503.21 −0.0816905
\(698\) −5748.24 17356.4i −0.311711 0.941190i
\(699\) 0 0
\(700\) −14020.2 18844.9i −0.757022 1.01753i
\(701\) 14904.4i 0.803041i −0.915850 0.401520i \(-0.868482\pi\)
0.915850 0.401520i \(-0.131518\pi\)
\(702\) 0 0
\(703\) 176.459i 0.00946696i
\(704\) −9769.91 26922.3i −0.523036 1.44130i
\(705\) 0 0
\(706\) −10830.4 + 3586.90i −0.577348 + 0.191211i
\(707\) −52805.7 −2.80900
\(708\) 0 0
\(709\) −17930.1 −0.949758 −0.474879 0.880051i \(-0.657508\pi\)
−0.474879 + 0.880051i \(0.657508\pi\)
\(710\) 45460.0 15055.8i 2.40294 0.795823i
\(711\) 0 0
\(712\) 15567.7 22210.4i 0.819415 1.16906i
\(713\) 2172.55i 0.114113i
\(714\) 0 0
\(715\) 47967.7i 2.50894i
\(716\) −11746.5 + 8739.13i −0.613109 + 0.456141i
\(717\) 0 0
\(718\) 9488.57 + 28650.1i 0.493190 + 1.48915i
\(719\) 19033.4 0.987238 0.493619 0.869678i \(-0.335674\pi\)
0.493619 + 0.869678i \(0.335674\pi\)
\(720\) 0 0
\(721\) −117.258 −0.00605677
\(722\) 6098.85 + 18415.1i 0.314371 + 0.949223i
\(723\) 0 0
\(724\) −21396.3 + 15918.4i −1.09833 + 0.817131i
\(725\) 16897.9i 0.865618i
\(726\) 0 0
\(727\) 19643.0i 1.00209i −0.865422 0.501043i \(-0.832950\pi\)
0.865422 0.501043i \(-0.167050\pi\)
\(728\) −22428.0 + 31998.1i −1.14181 + 1.62902i
\(729\) 0 0
\(730\) 29192.2 9668.10i 1.48007 0.490181i
\(731\) 584.684 0.0295832
\(732\) 0 0
\(733\) 8335.12 0.420006 0.210003 0.977701i \(-0.432653\pi\)
0.210003 + 0.977701i \(0.432653\pi\)
\(734\) −6873.19 + 2276.32i −0.345632 + 0.114469i
\(735\) 0 0
\(736\) −8692.10 + 246.011i −0.435320 + 0.0123208i
\(737\) 6355.44i 0.317647i
\(738\) 0 0
\(739\) 12308.0i 0.612661i 0.951925 + 0.306331i \(0.0991013\pi\)
−0.951925 + 0.306331i \(0.900899\pi\)
\(740\) 17717.2 + 23814.2i 0.880134 + 1.18301i
\(741\) 0 0
\(742\) −990.977 2992.19i −0.0490295 0.148042i
\(743\) 26227.7 1.29502 0.647511 0.762056i \(-0.275810\pi\)
0.647511 + 0.762056i \(0.275810\pi\)
\(744\) 0 0
\(745\) 21773.9 1.07078
\(746\) 1721.50 + 5197.96i 0.0844887 + 0.255108i
\(747\) 0 0
\(748\) 7822.25 + 10514.1i 0.382366 + 0.513947i
\(749\) 2324.61i 0.113404i
\(750\) 0 0
\(751\) 2741.63i 0.133214i −0.997779 0.0666068i \(-0.978783\pi\)
0.997779 0.0666068i \(-0.0212173\pi\)
\(752\) 199.054 663.352i 0.00965258 0.0321675i
\(753\) 0 0
\(754\) 26686.2 8838.16i 1.28893 0.426879i
\(755\) 24897.2 1.20014
\(756\) 0 0
\(757\) −17816.8 −0.855434 −0.427717 0.903913i \(-0.640682\pi\)
−0.427717 + 0.903913i \(0.640682\pi\)
\(758\) 15962.1 5286.44i 0.764866 0.253314i
\(759\) 0 0
\(760\) −196.250 137.555i −0.00936674 0.00656531i
\(761\) 32228.2i 1.53518i −0.640940 0.767591i \(-0.721455\pi\)
0.640940 0.767591i \(-0.278545\pi\)
\(762\) 0 0
\(763\) 49910.1i 2.36811i
\(764\) 23249.3 17297.0i 1.10096 0.819088i
\(765\) 0 0
\(766\) 1508.87 + 4555.93i 0.0711718 + 0.214899i
\(767\) −23632.2 −1.11253
\(768\) 0 0
\(769\) −4236.60 −0.198668 −0.0993340 0.995054i \(-0.531671\pi\)
−0.0993340 + 0.995054i \(0.531671\pi\)
\(770\) 22308.3 + 67358.5i 1.04407 + 3.15251i
\(771\) 0 0
\(772\) 16615.5 12361.6i 0.774616 0.576298i
\(773\) 1754.64i 0.0816431i 0.999166 + 0.0408215i \(0.0129975\pi\)
−0.999166 + 0.0408215i \(0.987002\pi\)
\(774\) 0 0
\(775\) 4418.48i 0.204795i
\(776\) −11570.9 8110.25i −0.535273 0.375182i
\(777\) 0 0
\(778\) −10508.3 + 3480.23i −0.484244 + 0.160376i
\(779\) −36.4324 −0.00167565
\(780\) 0 0
\(781\) −63465.1 −2.90776
\(782\) 3777.02 1250.90i 0.172719 0.0572023i
\(783\) 0 0
\(784\) −10303.9 + 34338.1i −0.469384 + 1.56424i
\(785\) 26470.6i 1.20354i
\(786\) 0 0
\(787\) 11896.9i 0.538857i 0.963020 + 0.269428i \(0.0868347\pi\)
−0.963020 + 0.269428i \(0.913165\pi\)
\(788\) 8367.37 + 11246.8i 0.378268 + 0.508439i
\(789\) 0 0
\(790\) −6462.89 19514.3i −0.291062