Properties

Label 108.4.i.a.25.1
Level 108
Weight 4
Character 108.25
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 25.1
Character \(\chi\) \(=\) 108.25
Dual form 108.4.i.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.52704 - 2.55067i) q^{3} +(-1.73722 + 1.45770i) q^{5} +(-5.32680 + 1.93880i) q^{7} +(13.9881 + 23.0940i) q^{9} +O(q^{10})\) \(q+(-4.52704 - 2.55067i) q^{3} +(-1.73722 + 1.45770i) q^{5} +(-5.32680 + 1.93880i) q^{7} +(13.9881 + 23.0940i) q^{9} +(19.5694 + 16.4207i) q^{11} +(6.38352 + 36.2027i) q^{13} +(11.5826 - 2.16798i) q^{15} +(49.6174 + 85.9398i) q^{17} +(-15.2603 + 26.4317i) q^{19} +(29.0598 + 4.80992i) q^{21} +(55.1467 + 20.0717i) q^{23} +(-20.8130 + 118.036i) q^{25} +(-4.41958 - 140.226i) q^{27} +(-3.73992 + 21.2102i) q^{29} +(-226.385 - 82.3974i) q^{31} +(-46.7076 - 124.252i) q^{33} +(6.42762 - 11.1330i) q^{35} +(-23.8246 - 41.2654i) q^{37} +(63.4429 - 180.173i) q^{39} +(16.7572 + 95.0347i) q^{41} +(-124.156 - 104.179i) q^{43} +(-57.9645 - 19.7288i) q^{45} +(323.003 - 117.563i) q^{47} +(-238.137 + 199.821i) q^{49} +(-5.41531 - 515.610i) q^{51} +343.554 q^{53} -57.9326 q^{55} +(136.503 - 80.7331i) q^{57} +(-212.363 + 178.194i) q^{59} +(-327.611 + 119.241i) q^{61} +(-119.286 - 95.8968i) q^{63} +(-63.8622 - 53.5868i) q^{65} +(-78.4747 - 445.052i) q^{67} +(-198.455 - 231.527i) q^{69} +(407.568 + 705.928i) q^{71} +(71.6513 - 124.104i) q^{73} +(395.293 - 481.268i) q^{75} +(-136.078 - 49.5285i) q^{77} +(-156.000 + 884.718i) q^{79} +(-337.664 + 646.083i) q^{81} +(81.0870 - 459.867i) q^{83} +(-211.470 - 76.9690i) q^{85} +(71.0310 - 86.4799i) q^{87} +(-218.426 + 378.326i) q^{89} +(-104.193 - 180.468i) q^{91} +(814.684 + 950.450i) q^{93} +(-12.0189 - 68.1626i) q^{95} +(1103.50 + 925.949i) q^{97} +(-105.479 + 681.629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

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
\(3\) −4.52704 2.55067i −0.871229 0.490877i
\(4\) 0 0
\(5\) −1.73722 + 1.45770i −0.155381 + 0.130381i −0.717164 0.696904i \(-0.754560\pi\)
0.561783 + 0.827285i \(0.310116\pi\)
\(6\) 0 0
\(7\) −5.32680 + 1.93880i −0.287620 + 0.104685i −0.481801 0.876281i \(-0.660017\pi\)
0.194181 + 0.980966i \(0.437795\pi\)
\(8\) 0 0
\(9\) 13.9881 + 23.0940i 0.518079 + 0.855333i
\(10\) 0 0
\(11\) 19.5694 + 16.4207i 0.536399 + 0.450092i 0.870304 0.492514i \(-0.163922\pi\)
−0.333905 + 0.942607i \(0.608367\pi\)
\(12\) 0 0
\(13\) 6.38352 + 36.2027i 0.136190 + 0.772372i 0.974024 + 0.226446i \(0.0727108\pi\)
−0.837834 + 0.545926i \(0.816178\pi\)
\(14\) 0 0
\(15\) 11.5826 2.16798i 0.199374 0.0373180i
\(16\) 0 0
\(17\) 49.6174 + 85.9398i 0.707881 + 1.22609i 0.965642 + 0.259877i \(0.0836821\pi\)
−0.257761 + 0.966209i \(0.582985\pi\)
\(18\) 0 0
\(19\) −15.2603 + 26.4317i −0.184261 + 0.319150i −0.943327 0.331864i \(-0.892323\pi\)
0.759066 + 0.651014i \(0.225656\pi\)
\(20\) 0 0
\(21\) 29.0598 + 4.80992i 0.301970 + 0.0499814i
\(22\) 0 0
\(23\) 55.1467 + 20.0717i 0.499951 + 0.181967i 0.579672 0.814850i \(-0.303181\pi\)
−0.0797209 + 0.996817i \(0.525403\pi\)
\(24\) 0 0
\(25\) −20.8130 + 118.036i −0.166504 + 0.944290i
\(26\) 0 0
\(27\) −4.41958 140.226i −0.0315018 0.999504i
\(28\) 0 0
\(29\) −3.73992 + 21.2102i −0.0239478 + 0.135815i −0.994438 0.105327i \(-0.966411\pi\)
0.970490 + 0.241142i \(0.0775220\pi\)
\(30\) 0 0
\(31\) −226.385 82.3974i −1.31161 0.477387i −0.410850 0.911703i \(-0.634768\pi\)
−0.900761 + 0.434316i \(0.856990\pi\)
\(32\) 0 0
\(33\) −46.7076 124.252i −0.246386 0.655440i
\(34\) 0 0
\(35\) 6.42762 11.1330i 0.0310419 0.0537662i
\(36\) 0 0
\(37\) −23.8246 41.2654i −0.105858 0.183351i 0.808230 0.588866i \(-0.200426\pi\)
−0.914088 + 0.405515i \(0.867092\pi\)
\(38\) 0 0
\(39\) 63.4429 180.173i 0.260487 0.739765i
\(40\) 0 0
\(41\) 16.7572 + 95.0347i 0.0638300 + 0.361998i 0.999947 + 0.0103090i \(0.00328150\pi\)
−0.936117 + 0.351689i \(0.885607\pi\)
\(42\) 0 0
\(43\) −124.156 104.179i −0.440315 0.369468i 0.395512 0.918461i \(-0.370567\pi\)
−0.835827 + 0.548993i \(0.815011\pi\)
\(44\) 0 0
\(45\) −57.9645 19.7288i −0.192019 0.0653555i
\(46\) 0 0
\(47\) 323.003 117.563i 1.00244 0.364859i 0.211916 0.977288i \(-0.432030\pi\)
0.790526 + 0.612429i \(0.209807\pi\)
\(48\) 0 0
\(49\) −238.137 + 199.821i −0.694278 + 0.582569i
\(50\) 0 0
\(51\) −5.41531 515.610i −0.0148685 1.41568i
\(52\) 0 0
\(53\) 343.554 0.890391 0.445196 0.895433i \(-0.353134\pi\)
0.445196 + 0.895433i \(0.353134\pi\)
\(54\) 0 0
\(55\) −57.9326 −0.142030
\(56\) 0 0
\(57\) 136.503 80.7331i 0.317197 0.187603i
\(58\) 0 0
\(59\) −212.363 + 178.194i −0.468598 + 0.393201i −0.846283 0.532734i \(-0.821165\pi\)
0.377685 + 0.925934i \(0.376720\pi\)
\(60\) 0 0
\(61\) −327.611 + 119.241i −0.687643 + 0.250282i −0.662126 0.749393i \(-0.730346\pi\)
−0.0255176 + 0.999674i \(0.508123\pi\)
\(62\) 0 0
\(63\) −119.286 95.8968i −0.238550 0.191776i
\(64\) 0 0
\(65\) −63.8622 53.5868i −0.121864 0.102256i
\(66\) 0 0
\(67\) −78.4747 445.052i −0.143093 0.811519i −0.968879 0.247536i \(-0.920379\pi\)
0.825786 0.563983i \(-0.190732\pi\)
\(68\) 0 0
\(69\) −198.455 231.527i −0.346248 0.403950i
\(70\) 0 0
\(71\) 407.568 + 705.928i 0.681259 + 1.17998i 0.974597 + 0.223967i \(0.0719007\pi\)
−0.293338 + 0.956009i \(0.594766\pi\)
\(72\) 0 0
\(73\) 71.6513 124.104i 0.114879 0.198976i −0.802852 0.596178i \(-0.796685\pi\)
0.917731 + 0.397202i \(0.130019\pi\)
\(74\) 0 0
\(75\) 395.293 481.268i 0.608594 0.740960i
\(76\) 0 0
\(77\) −136.078 49.5285i −0.201397 0.0733025i
\(78\) 0 0
\(79\) −156.000 + 884.718i −0.222169 + 1.25998i 0.645855 + 0.763460i \(0.276501\pi\)
−0.868024 + 0.496522i \(0.834610\pi\)
\(80\) 0 0
\(81\) −337.664 + 646.083i −0.463188 + 0.886260i
\(82\) 0 0
\(83\) 81.0870 459.867i 0.107234 0.608157i −0.883070 0.469241i \(-0.844527\pi\)
0.990304 0.138915i \(-0.0443615\pi\)
\(84\) 0 0
\(85\) −211.470 76.9690i −0.269849 0.0982171i
\(86\) 0 0
\(87\) 71.0310 86.4799i 0.0875324 0.106570i
\(88\) 0 0
\(89\) −218.426 + 378.326i −0.260148 + 0.450589i −0.966281 0.257490i \(-0.917105\pi\)
0.706133 + 0.708079i \(0.250438\pi\)
\(90\) 0 0
\(91\) −104.193 180.468i −0.120027 0.207892i
\(92\) 0 0
\(93\) 814.684 + 950.450i 0.908374 + 1.05975i
\(94\) 0 0
\(95\) −12.0189 68.1626i −0.0129801 0.0736140i
\(96\) 0 0
\(97\) 1103.50 + 925.949i 1.15509 + 0.969236i 0.999826 0.0186370i \(-0.00593269\pi\)
0.155264 + 0.987873i \(0.450377\pi\)
\(98\) 0 0
\(99\) −105.479 + 681.629i −0.107082 + 0.691983i
\(100\) 0 0
\(101\) 405.014 147.413i 0.399014 0.145229i −0.134716 0.990884i \(-0.543012\pi\)
0.533730 + 0.845655i \(0.320790\pi\)
\(102\) 0 0
\(103\) −422.424 + 354.456i −0.404104 + 0.339083i −0.822077 0.569376i \(-0.807185\pi\)
0.417973 + 0.908459i \(0.362741\pi\)
\(104\) 0 0
\(105\) −57.4947 + 34.0046i −0.0534372 + 0.0316049i
\(106\) 0 0
\(107\) 860.291 0.777266 0.388633 0.921393i \(-0.372947\pi\)
0.388633 + 0.921393i \(0.372947\pi\)
\(108\) 0 0
\(109\) 2113.40 1.85713 0.928563 0.371176i \(-0.121045\pi\)
0.928563 + 0.371176i \(0.121045\pi\)
\(110\) 0 0
\(111\) 2.60025 + 247.579i 0.00222347 + 0.211704i
\(112\) 0 0
\(113\) −1627.93 + 1366.00i −1.35525 + 1.13719i −0.377829 + 0.925875i \(0.623329\pi\)
−0.977419 + 0.211313i \(0.932226\pi\)
\(114\) 0 0
\(115\) −125.060 + 45.5182i −0.101408 + 0.0369095i
\(116\) 0 0
\(117\) −746.772 + 653.830i −0.590078 + 0.516637i
\(118\) 0 0
\(119\) −430.921 361.586i −0.331954 0.278542i
\(120\) 0 0
\(121\) −117.803 668.095i −0.0885072 0.501949i
\(122\) 0 0
\(123\) 166.542 472.968i 0.122086 0.346716i
\(124\) 0 0
\(125\) −277.641 480.888i −0.198663 0.344095i
\(126\) 0 0
\(127\) 1062.08 1839.58i 0.742083 1.28533i −0.209462 0.977817i \(-0.567171\pi\)
0.951545 0.307509i \(-0.0994954\pi\)
\(128\) 0 0
\(129\) 296.330 + 788.302i 0.202251 + 0.538032i
\(130\) 0 0
\(131\) −1522.41 554.114i −1.01537 0.369566i −0.219880 0.975527i \(-0.570566\pi\)
−0.795494 + 0.605961i \(0.792789\pi\)
\(132\) 0 0
\(133\) 30.0431 170.383i 0.0195870 0.111083i
\(134\) 0 0
\(135\) 212.086 + 237.161i 0.135211 + 0.151197i
\(136\) 0 0
\(137\) 498.807 2828.87i 0.311065 1.76414i −0.282418 0.959291i \(-0.591136\pi\)
0.593483 0.804847i \(-0.297752\pi\)
\(138\) 0 0
\(139\) −2332.30 848.889i −1.42319 0.517999i −0.488218 0.872722i \(-0.662353\pi\)
−0.934971 + 0.354723i \(0.884575\pi\)
\(140\) 0 0
\(141\) −1762.11 291.661i −1.05246 0.174200i
\(142\) 0 0
\(143\) −469.551 + 813.287i −0.274586 + 0.475598i
\(144\) 0 0
\(145\) −24.4210 42.2983i −0.0139866 0.0242254i
\(146\) 0 0
\(147\) 1587.74 297.186i 0.890845 0.166745i
\(148\) 0 0
\(149\) −553.705 3140.22i −0.304438 1.72655i −0.626138 0.779712i \(-0.715365\pi\)
0.321700 0.946842i \(-0.395746\pi\)
\(150\) 0 0
\(151\) 950.851 + 797.859i 0.512445 + 0.429992i 0.861989 0.506928i \(-0.169219\pi\)
−0.349544 + 0.936920i \(0.613663\pi\)
\(152\) 0 0
\(153\) −1290.64 + 2348.00i −0.681973 + 1.24068i
\(154\) 0 0
\(155\) 513.390 186.859i 0.266042 0.0968313i
\(156\) 0 0
\(157\) 1992.20 1671.65i 1.01271 0.849761i 0.0240121 0.999712i \(-0.492356\pi\)
0.988693 + 0.149951i \(0.0479115\pi\)
\(158\) 0 0
\(159\) −1555.28 876.293i −0.775734 0.437073i
\(160\) 0 0
\(161\) −332.670 −0.162845
\(162\) 0 0
\(163\) 1268.83 0.609708 0.304854 0.952399i \(-0.401392\pi\)
0.304854 + 0.952399i \(0.401392\pi\)
\(164\) 0 0
\(165\) 262.263 + 147.767i 0.123740 + 0.0697192i
\(166\) 0 0
\(167\) −1848.70 + 1551.25i −0.856628 + 0.718796i −0.961239 0.275717i \(-0.911085\pi\)
0.104611 + 0.994513i \(0.466640\pi\)
\(168\) 0 0
\(169\) 794.616 289.216i 0.361682 0.131642i
\(170\) 0 0
\(171\) −823.877 + 17.3078i −0.368441 + 0.00774012i
\(172\) 0 0
\(173\) −2855.25 2395.84i −1.25480 1.05290i −0.996216 0.0869166i \(-0.972299\pi\)
−0.258587 0.965988i \(-0.583257\pi\)
\(174\) 0 0
\(175\) −117.982 669.107i −0.0509633 0.289027i
\(176\) 0 0
\(177\) 1415.89 265.021i 0.601270 0.112543i
\(178\) 0 0
\(179\) 1808.10 + 3131.73i 0.754995 + 1.30769i 0.945377 + 0.325979i \(0.105694\pi\)
−0.190382 + 0.981710i \(0.560973\pi\)
\(180\) 0 0
\(181\) 1109.38 1921.50i 0.455577 0.789083i −0.543144 0.839640i \(-0.682766\pi\)
0.998721 + 0.0505564i \(0.0160995\pi\)
\(182\) 0 0
\(183\) 1787.25 + 295.822i 0.721952 + 0.119496i
\(184\) 0 0
\(185\) 101.541 + 36.9579i 0.0403538 + 0.0146876i
\(186\) 0 0
\(187\) −440.207 + 2496.54i −0.172145 + 0.976283i
\(188\) 0 0
\(189\) 295.413 + 738.389i 0.113694 + 0.284179i
\(190\) 0 0
\(191\) 113.936 646.162i 0.0431628 0.244789i −0.955591 0.294696i \(-0.904782\pi\)
0.998754 + 0.0499076i \(0.0158927\pi\)
\(192\) 0 0
\(193\) 377.376 + 137.354i 0.140747 + 0.0512276i 0.411433 0.911440i \(-0.365028\pi\)
−0.270686 + 0.962668i \(0.587251\pi\)
\(194\) 0 0
\(195\) 152.424 + 405.481i 0.0559761 + 0.148908i
\(196\) 0 0
\(197\) 1359.16 2354.14i 0.491555 0.851398i −0.508398 0.861122i \(-0.669762\pi\)
0.999953 + 0.00972432i \(0.00309540\pi\)
\(198\) 0 0
\(199\) 262.797 + 455.177i 0.0936138 + 0.162144i 0.909029 0.416732i \(-0.136825\pi\)
−0.815415 + 0.578876i \(0.803491\pi\)
\(200\) 0 0
\(201\) −779.925 + 2214.93i −0.273690 + 0.777260i
\(202\) 0 0
\(203\) −21.2004 120.233i −0.00732992 0.0415700i
\(204\) 0 0
\(205\) −167.643 140.669i −0.0571155 0.0479256i
\(206\) 0 0
\(207\) 307.862 + 1554.32i 0.103372 + 0.521898i
\(208\) 0 0
\(209\) −732.662 + 266.667i −0.242484 + 0.0882571i
\(210\) 0 0
\(211\) −3546.31 + 2975.70i −1.15705 + 0.970881i −0.999861 0.0166873i \(-0.994688\pi\)
−0.157190 + 0.987568i \(0.550244\pi\)
\(212\) 0 0
\(213\) −44.4825 4235.34i −0.0143094 1.36244i
\(214\) 0 0
\(215\) 367.546 0.116588
\(216\) 0 0
\(217\) 1365.66 0.427221
\(218\) 0 0
\(219\) −640.916 + 379.063i −0.197759 + 0.116962i
\(220\) 0 0
\(221\) −2794.52 + 2344.88i −0.850588 + 0.713728i
\(222\) 0 0
\(223\) −1359.00 + 494.635i −0.408096 + 0.148535i −0.537907 0.843004i \(-0.680785\pi\)
0.129812 + 0.991539i \(0.458563\pi\)
\(224\) 0 0
\(225\) −3017.06 + 1170.45i −0.893945 + 0.346801i
\(226\) 0 0
\(227\) 4668.86 + 3917.63i 1.36512 + 1.14547i 0.974363 + 0.224981i \(0.0722319\pi\)
0.390759 + 0.920493i \(0.372212\pi\)
\(228\) 0 0
\(229\) −184.191 1044.60i −0.0531514 0.301437i 0.946630 0.322321i \(-0.104463\pi\)
−0.999782 + 0.0208842i \(0.993352\pi\)
\(230\) 0 0
\(231\) 489.701 + 571.309i 0.139480 + 0.162725i
\(232\) 0 0
\(233\) 444.253 + 769.468i 0.124910 + 0.216350i 0.921698 0.387909i \(-0.126803\pi\)
−0.796788 + 0.604259i \(0.793469\pi\)
\(234\) 0 0
\(235\) −389.754 + 675.074i −0.108190 + 0.187391i
\(236\) 0 0
\(237\) 2962.84 3607.25i 0.812057 0.988675i
\(238\) 0 0
\(239\) 4785.72 + 1741.86i 1.29524 + 0.471429i 0.895444 0.445175i \(-0.146858\pi\)
0.399797 + 0.916604i \(0.369081\pi\)
\(240\) 0 0
\(241\) −401.648 + 2277.86i −0.107354 + 0.608837i 0.882899 + 0.469562i \(0.155588\pi\)
−0.990254 + 0.139275i \(0.955523\pi\)
\(242\) 0 0
\(243\) 3176.57 2063.57i 0.838588 0.544766i
\(244\) 0 0
\(245\) 122.418 694.265i 0.0319224 0.181041i
\(246\) 0 0
\(247\) −1054.31 383.739i −0.271597 0.0988532i
\(248\) 0 0
\(249\) −1540.06 + 1875.01i −0.391956 + 0.477204i
\(250\) 0 0
\(251\) −2065.57 + 3577.67i −0.519433 + 0.899684i 0.480312 + 0.877098i \(0.340524\pi\)
−0.999745 + 0.0225867i \(0.992810\pi\)
\(252\) 0 0
\(253\) 749.595 + 1298.34i 0.186271 + 0.322631i
\(254\) 0 0
\(255\) 761.012 + 887.833i 0.186888 + 0.218032i
\(256\) 0 0
\(257\) −88.6207 502.593i −0.0215098 0.121988i 0.972162 0.234309i \(-0.0752827\pi\)
−0.993672 + 0.112321i \(0.964172\pi\)
\(258\) 0 0
\(259\) 206.914 + 173.622i 0.0496410 + 0.0416537i
\(260\) 0 0
\(261\) −542.142 + 210.321i −0.128574 + 0.0498794i
\(262\) 0 0
\(263\) 2625.90 955.748i 0.615664 0.224083i −0.0153157 0.999883i \(-0.504875\pi\)
0.630980 + 0.775799i \(0.282653\pi\)
\(264\) 0 0
\(265\) −596.828 + 500.798i −0.138350 + 0.116090i
\(266\) 0 0
\(267\) 1953.81 1155.56i 0.447832 0.264866i
\(268\) 0 0
\(269\) 4160.31 0.942968 0.471484 0.881875i \(-0.343719\pi\)
0.471484 + 0.881875i \(0.343719\pi\)
\(270\) 0 0
\(271\) −5111.90 −1.14585 −0.572926 0.819607i \(-0.694192\pi\)
−0.572926 + 0.819607i \(0.694192\pi\)
\(272\) 0 0
\(273\) 11.3718 + 1082.75i 0.00252107 + 0.240040i
\(274\) 0 0
\(275\) −2345.53 + 1968.13i −0.514330 + 0.431574i
\(276\) 0 0
\(277\) 411.220 149.672i 0.0891980 0.0324654i −0.297036 0.954866i \(-0.595998\pi\)
0.386234 + 0.922401i \(0.373776\pi\)
\(278\) 0 0
\(279\) −1263.82 6380.71i −0.271193 1.36919i
\(280\) 0 0
\(281\) −533.382 447.561i −0.113235 0.0950151i 0.584412 0.811457i \(-0.301325\pi\)
−0.697647 + 0.716442i \(0.745770\pi\)
\(282\) 0 0
\(283\) −205.873 1167.56i −0.0432433 0.245245i 0.955522 0.294919i \(-0.0952928\pi\)
−0.998765 + 0.0496742i \(0.984182\pi\)
\(284\) 0 0
\(285\) −119.450 + 339.231i −0.0248268 + 0.0705063i
\(286\) 0 0
\(287\) −273.515 473.742i −0.0562546 0.0974358i
\(288\) 0 0
\(289\) −2467.27 + 4273.43i −0.502191 + 0.869821i
\(290\) 0 0
\(291\) −2633.81 7006.48i −0.530572 1.41143i
\(292\) 0 0
\(293\) 6216.76 + 2262.72i 1.23955 + 0.451158i 0.876857 0.480752i \(-0.159636\pi\)
0.362690 + 0.931910i \(0.381858\pi\)
\(294\) 0 0
\(295\) 109.168 619.122i 0.0215458 0.122192i
\(296\) 0 0
\(297\) 2216.12 2816.72i 0.432971 0.550312i
\(298\) 0 0
\(299\) −374.622 + 2124.59i −0.0724581 + 0.410930i
\(300\) 0 0
\(301\) 863.333 + 314.227i 0.165321 + 0.0601720i
\(302\) 0 0
\(303\) −2209.52 365.714i −0.418922 0.0693390i
\(304\) 0 0
\(305\) 395.314 684.704i 0.0742152 0.128544i
\(306\) 0 0
\(307\) −2737.00 4740.62i −0.508823 0.881308i −0.999948 0.0102185i \(-0.996747\pi\)
0.491124 0.871089i \(-0.336586\pi\)
\(308\) 0 0
\(309\) 2816.43 527.169i 0.518515 0.0970538i
\(310\) 0 0
\(311\) −1849.24 10487.6i −0.337173 1.91220i −0.404628 0.914482i \(-0.632599\pi\)
0.0674546 0.997722i \(-0.478512\pi\)
\(312\) 0 0
\(313\) −5515.11 4627.73i −0.995950 0.835701i −0.00953196 0.999955i \(-0.503034\pi\)
−0.986418 + 0.164253i \(0.947479\pi\)
\(314\) 0 0
\(315\) 347.015 7.29001i 0.0620701 0.00130395i
\(316\) 0 0
\(317\) 82.0633 29.8686i 0.0145398 0.00529207i −0.334740 0.942311i \(-0.608648\pi\)
0.349280 + 0.937018i \(0.386426\pi\)
\(318\) 0 0
\(319\) −421.473 + 353.658i −0.0739748 + 0.0620722i
\(320\) 0 0
\(321\) −3894.57 2194.32i −0.677176 0.381542i
\(322\) 0 0
\(323\) −3028.71 −0.521740
\(324\) 0 0
\(325\) −4406.10 −0.752019
\(326\) 0 0
\(327\) −9567.42 5390.58i −1.61798 0.911621i
\(328\) 0 0
\(329\) −1492.64 + 1252.47i −0.250127 + 0.209882i
\(330\) 0 0
\(331\) −3752.27 + 1365.71i −0.623091 + 0.226787i −0.634221 0.773151i \(-0.718679\pi\)
0.0111304 + 0.999938i \(0.496457\pi\)
\(332\) 0 0
\(333\) 619.722 1127.43i 0.101984 0.185534i
\(334\) 0 0
\(335\) 785.079 + 658.760i 0.128040 + 0.107438i
\(336\) 0 0
\(337\) 1144.62 + 6491.47i 0.185019 + 1.04930i 0.925931 + 0.377694i \(0.123283\pi\)
−0.740911 + 0.671603i \(0.765606\pi\)
\(338\) 0 0
\(339\) 10853.9 2031.60i 1.73895 0.325490i
\(340\) 0 0
\(341\) −3077.19 5329.85i −0.488678 0.846416i
\(342\) 0 0
\(343\) 1853.27 3209.96i 0.291741 0.505311i
\(344\) 0 0
\(345\) 682.255 + 112.925i 0.106468 + 0.0176223i
\(346\) 0 0
\(347\) 9057.25 + 3296.57i 1.40121 + 0.509997i 0.928536 0.371242i \(-0.121068\pi\)
0.472670 + 0.881240i \(0.343290\pi\)
\(348\) 0 0
\(349\) 1123.06 6369.21i 0.172253 0.976895i −0.769014 0.639232i \(-0.779253\pi\)
0.941267 0.337663i \(-0.109636\pi\)
\(350\) 0 0
\(351\) 5048.37 1055.14i 0.767698 0.160453i
\(352\) 0 0
\(353\) −1919.44 + 10885.7i −0.289410 + 1.64133i 0.399683 + 0.916653i \(0.369120\pi\)
−0.689093 + 0.724673i \(0.741991\pi\)
\(354\) 0 0
\(355\) −1737.06 632.240i −0.259701 0.0945234i
\(356\) 0 0
\(357\) 1028.51 + 2736.05i 0.152478 + 0.405622i
\(358\) 0 0
\(359\) 1362.21 2359.42i 0.200264 0.346868i −0.748349 0.663305i \(-0.769153\pi\)
0.948614 + 0.316437i \(0.102487\pi\)
\(360\) 0 0
\(361\) 2963.74 + 5133.35i 0.432096 + 0.748411i
\(362\) 0 0
\(363\) −1170.79 + 3324.97i −0.169286 + 0.480759i
\(364\) 0 0
\(365\) 56.4319 + 320.041i 0.00809255 + 0.0458951i
\(366\) 0 0
\(367\) 4765.13 + 3998.42i 0.677760 + 0.568708i 0.915351 0.402657i \(-0.131913\pi\)
−0.237591 + 0.971365i \(0.576358\pi\)
\(368\) 0 0
\(369\) −1960.33 + 1716.35i −0.276560 + 0.242140i
\(370\) 0 0
\(371\) −1830.04 + 666.080i −0.256094 + 0.0932107i
\(372\) 0 0
\(373\) 6859.41 5755.73i 0.952190 0.798982i −0.0274753 0.999622i \(-0.508747\pi\)
0.979665 + 0.200641i \(0.0643023\pi\)
\(374\) 0 0
\(375\) 30.3021 + 2885.17i 0.00417278 + 0.397305i
\(376\) 0 0
\(377\) −791.740 −0.108161
\(378\) 0 0
\(379\) 569.718 0.0772148 0.0386074 0.999254i \(-0.487708\pi\)
0.0386074 + 0.999254i \(0.487708\pi\)
\(380\) 0 0
\(381\) −9500.26 + 5618.82i −1.27746 + 0.755541i
\(382\) 0 0
\(383\) −1839.24 + 1543.30i −0.245380 + 0.205898i −0.757180 0.653206i \(-0.773423\pi\)
0.511800 + 0.859105i \(0.328979\pi\)
\(384\) 0 0
\(385\) 308.595 112.320i 0.0408506 0.0148684i
\(386\) 0 0
\(387\) 669.201 4324.51i 0.0879003 0.568029i
\(388\) 0 0
\(389\) −2278.94 1912.26i −0.297036 0.249243i 0.482073 0.876131i \(-0.339884\pi\)
−0.779109 + 0.626888i \(0.784328\pi\)
\(390\) 0 0
\(391\) 1011.27 + 5735.20i 0.130798 + 0.741794i
\(392\) 0 0
\(393\) 5478.66 + 6391.67i 0.703211 + 0.820400i
\(394\) 0 0
\(395\) −1018.65 1764.35i −0.129756 0.224744i
\(396\) 0 0
\(397\) −5487.38 + 9504.43i −0.693713 + 1.20155i 0.276900 + 0.960899i \(0.410693\pi\)
−0.970613 + 0.240647i \(0.922640\pi\)
\(398\) 0 0
\(399\) −570.598 + 694.700i −0.0715930 + 0.0871641i
\(400\) 0 0
\(401\) 12728.6 + 4632.81i 1.58512 + 0.576937i 0.976310 0.216378i \(-0.0694244\pi\)
0.608811 + 0.793315i \(0.291647\pi\)
\(402\) 0 0
\(403\) 1537.88 8721.74i 0.190092 1.07807i
\(404\) 0 0
\(405\) −355.198 1614.60i −0.0435801 0.198099i
\(406\) 0 0
\(407\) 211.373 1198.76i 0.0257429 0.145995i
\(408\) 0 0
\(409\) 11812.0 + 4299.21i 1.42803 + 0.519761i 0.936367 0.351023i \(-0.114166\pi\)
0.491665 + 0.870784i \(0.336388\pi\)
\(410\) 0 0
\(411\) −9473.65 + 11534.1i −1.13698 + 1.38427i
\(412\) 0 0
\(413\) 785.733 1360.93i 0.0936160 0.162148i
\(414\) 0 0
\(415\) 529.482 + 917.090i 0.0626295 + 0.108478i
\(416\) 0 0
\(417\) 8393.18 + 9791.89i 0.985650 + 1.14991i
\(418\) 0 0
\(419\) −2394.23 13578.3i −0.279154 1.58316i −0.725448 0.688277i \(-0.758368\pi\)
0.446294 0.894886i \(-0.352744\pi\)
\(420\) 0 0
\(421\) −3826.83 3211.09i −0.443013 0.371732i 0.393823 0.919186i \(-0.371152\pi\)
−0.836835 + 0.547455i \(0.815597\pi\)
\(422\) 0 0
\(423\) 7233.21 + 5814.93i 0.831420 + 0.668396i
\(424\) 0 0
\(425\) −11176.7 + 4067.99i −1.27565 + 0.464297i
\(426\) 0 0
\(427\) 1513.93 1270.34i 0.171579 0.143972i
\(428\) 0 0
\(429\) 4200.11 2484.11i 0.472688 0.279566i
\(430\) 0 0
\(431\) −13508.3 −1.50968 −0.754838 0.655912i \(-0.772284\pi\)
−0.754838 + 0.655912i \(0.772284\pi\)
\(432\) 0 0
\(433\) −6126.85 −0.679994 −0.339997 0.940427i \(-0.610426\pi\)
−0.339997 + 0.940427i \(0.610426\pi\)
\(434\) 0 0
\(435\) 2.66534 + 253.776i 0.000293777 + 0.0279716i
\(436\) 0 0
\(437\) −1372.09 + 1151.32i −0.150196 + 0.126030i
\(438\) 0 0
\(439\) 13612.4 4954.50i 1.47992 0.538646i 0.529144 0.848532i \(-0.322513\pi\)
0.950774 + 0.309886i \(0.100291\pi\)
\(440\) 0 0
\(441\) −7945.76 2704.42i −0.857981 0.292022i
\(442\) 0 0
\(443\) 3551.99 + 2980.47i 0.380948 + 0.319653i 0.813074 0.582160i \(-0.197792\pi\)
−0.432126 + 0.901813i \(0.642237\pi\)
\(444\) 0 0
\(445\) −172.031 975.633i −0.0183259 0.103931i
\(446\) 0 0
\(447\) −5503.02 + 15628.2i −0.582291 + 1.65367i
\(448\) 0 0
\(449\) −4160.46 7206.13i −0.437292 0.757412i 0.560187 0.828366i \(-0.310729\pi\)
−0.997480 + 0.0709535i \(0.977396\pi\)
\(450\) 0 0
\(451\) −1232.60 + 2134.93i −0.128694 + 0.222905i
\(452\) 0 0
\(453\) −2269.46 6037.25i −0.235383 0.626169i
\(454\) 0 0
\(455\) 444.075 + 161.630i 0.0457551 + 0.0166535i
\(456\) 0 0
\(457\) 1535.70 8709.37i 0.157192 0.891482i −0.799562 0.600584i \(-0.794935\pi\)
0.956754 0.290898i \(-0.0939541\pi\)
\(458\) 0 0
\(459\) 11831.7 7337.49i 1.20318 0.746154i
\(460\) 0 0
\(461\) −890.872 + 5052.38i −0.0900044 + 0.510440i 0.906160 + 0.422936i \(0.139000\pi\)
−0.996164 + 0.0875046i \(0.972111\pi\)
\(462\) 0 0
\(463\) 11339.2 + 4127.13i 1.13818 + 0.414264i 0.841256 0.540637i \(-0.181817\pi\)
0.296925 + 0.954901i \(0.404039\pi\)
\(464\) 0 0
\(465\) −2800.75 463.574i −0.279316 0.0462317i
\(466\) 0 0
\(467\) 92.2875 159.847i 0.00914466 0.0158390i −0.861417 0.507899i \(-0.830422\pi\)
0.870562 + 0.492060i \(0.163756\pi\)
\(468\) 0 0
\(469\) 1280.88 + 2218.56i 0.126110 + 0.218429i
\(470\) 0 0
\(471\) −13282.6 + 2486.19i −1.29943 + 0.243222i
\(472\) 0 0
\(473\) −718.961 4077.43i −0.0698898 0.396365i
\(474\) 0 0
\(475\) −2802.29 2351.40i −0.270690 0.227136i
\(476\) 0 0
\(477\) 4805.67 + 7934.03i 0.461293 + 0.761581i
\(478\) 0 0
\(479\) 85.0550 30.9575i 0.00811329 0.00295299i −0.337960 0.941160i \(-0.609737\pi\)
0.346074 + 0.938207i \(0.387515\pi\)
\(480\) 0 0
\(481\) 1341.84 1125.94i 0.127199 0.106732i
\(482\) 0 0
\(483\) 1506.01 + 848.533i 0.141875 + 0.0799370i
\(484\) 0 0
\(485\) −3266.78 −0.305849
\(486\) 0 0
\(487\) 12807.1 1.19167 0.595835 0.803107i \(-0.296821\pi\)
0.595835 + 0.803107i \(0.296821\pi\)
\(488\) 0 0
\(489\) −5744.04 3236.37i −0.531195 0.299292i
\(490\) 0 0
\(491\) −4314.38 + 3620.19i −0.396548 + 0.332743i −0.819158 0.573568i \(-0.805559\pi\)
0.422609 + 0.906312i \(0.361114\pi\)
\(492\) 0 0
\(493\) −2008.36 + 730.984i −0.183473 + 0.0667786i
\(494\) 0 0
\(495\) −810.369 1337.90i −0.0735826 0.121483i
\(496\) 0 0
\(497\) −3539.68 2970.15i −0.319470 0.268067i
\(498\) 0 0
\(499\) −401.541 2277.25i −0.0360229 0.204296i 0.961484 0.274860i \(-0.0886314\pi\)
−0.997507 + 0.0705635i \(0.977520\pi\)
\(500\) 0 0
\(501\) 12325.9 2307.11i 1.09916 0.205737i
\(502\) 0 0
\(503\) −7235.56 12532.4i −0.641387 1.11092i −0.985123 0.171849i \(-0.945026\pi\)
0.343736 0.939066i \(-0.388308\pi\)
\(504\) 0 0
\(505\) −488.714 + 846.477i −0.0430643 + 0.0745896i
\(506\) 0 0
\(507\) −4334.95 717.511i −0.379728 0.0628517i
\(508\) 0 0
\(509\) 12136.9 + 4417.47i 1.05689 + 0.384678i 0.811261 0.584685i \(-0.198782\pi\)
0.245633 + 0.969363i \(0.421004\pi\)
\(510\) 0 0
\(511\) −141.060 + 799.993i −0.0122116 + 0.0692556i
\(512\) 0 0
\(513\) 3773.87 + 2023.09i 0.324796 + 0.174116i
\(514\) 0 0
\(515\) 217.153 1231.53i 0.0185804 0.105375i
\(516\) 0 0
\(517\) 8251.43 + 3003.28i 0.701929 + 0.255481i
\(518\) 0 0
\(519\) 6814.83 + 18128.9i 0.576373 + 1.53327i
\(520\) 0 0
\(521\) 5815.68 10073.0i 0.489039 0.847041i −0.510881 0.859651i \(-0.670681\pi\)
0.999920 + 0.0126104i \(0.00401413\pi\)
\(522\) 0 0
\(523\) −7100.15 12297.8i −0.593629 1.02820i −0.993739 0.111728i \(-0.964361\pi\)
0.400110 0.916467i \(-0.368972\pi\)
\(524\) 0 0
\(525\) −1172.57 + 3330.01i −0.0974762 + 0.276826i
\(526\) 0 0
\(527\) −4151.41 23543.8i −0.343147 1.94608i
\(528\) 0 0
\(529\) −6682.18 5607.02i −0.549205 0.460838i
\(530\) 0 0
\(531\) −7085.76 2411.71i −0.579088 0.197099i
\(532\) 0 0
\(533\) −3333.55 + 1213.31i −0.270904 + 0.0986011i
\(534\) 0 0
\(535\) −1494.51 + 1254.04i −0.120773 + 0.101340i
\(536\) 0 0
\(537\) −197.339 18789.3i −0.0158581 1.50991i
\(538\) 0 0
\(539\) −7941.40 −0.634620
\(540\) 0 0
\(541\) −14803.9 −1.17647 −0.588235 0.808690i \(-0.700177\pi\)
−0.588235 + 0.808690i \(0.700177\pi\)
\(542\) 0 0
\(543\) −9923.32 + 5869.04i −0.784255 + 0.463839i
\(544\) 0 0
\(545\) −3671.43 + 3080.69i −0.288563 + 0.242133i
\(546\) 0 0
\(547\) 8475.32 3084.76i 0.662483 0.241124i 0.0111752 0.999938i \(-0.496443\pi\)
0.651308 + 0.758813i \(0.274221\pi\)
\(548\) 0 0
\(549\) −7336.40 5897.88i −0.570328 0.458498i
\(550\) 0 0
\(551\) −503.548 422.527i −0.0389326 0.0326683i
\(552\) 0 0
\(553\) −884.309 5015.17i −0.0680012 0.385654i
\(554\) 0 0
\(555\) −365.413 426.308i −0.0279476 0.0326050i
\(556\) 0 0
\(557\) 2010.86 + 3482.91i 0.152967 + 0.264947i 0.932317 0.361642i \(-0.117784\pi\)
−0.779350 + 0.626589i \(0.784450\pi\)
\(558\) 0 0
\(559\) 2979.01 5159.80i 0.225400 0.390405i
\(560\) 0 0
\(561\) 8360.69 10179.1i 0.629213 0.766064i
\(562\) 0 0
\(563\) 2100.11 + 764.377i 0.157210 + 0.0572196i 0.419426 0.907789i \(-0.362231\pi\)
−0.262217 + 0.965009i \(0.584454\pi\)
\(564\) 0 0
\(565\) 836.860 4746.07i 0.0623132 0.353396i
\(566\) 0 0
\(567\) 546.046 4096.22i 0.0404440 0.303395i
\(568\) 0 0
\(569\) −1240.71 + 7036.41i −0.0914117 + 0.518421i 0.904376 + 0.426736i \(0.140337\pi\)
−0.995788 + 0.0916855i \(0.970775\pi\)
\(570\) 0 0
\(571\) −5058.44 1841.12i −0.370734 0.134936i 0.149932 0.988696i \(-0.452094\pi\)
−0.520667 + 0.853760i \(0.674317\pi\)
\(572\) 0 0
\(573\) −2163.94 + 2634.59i −0.157766 + 0.192079i
\(574\) 0 0
\(575\) −3516.96 + 6091.56i −0.255074 + 0.441801i
\(576\) 0 0
\(577\) −869.206 1505.51i −0.0627132 0.108622i 0.832964 0.553327i \(-0.186642\pi\)
−0.895677 + 0.444705i \(0.853309\pi\)
\(578\) 0 0
\(579\) −1358.05 1584.37i −0.0974761 0.113720i
\(580\) 0 0
\(581\) 459.655 + 2606.83i 0.0328222 + 0.186144i
\(582\) 0 0
\(583\) 6723.13 + 5641.38i 0.477605 + 0.400758i
\(584\) 0 0
\(585\) 344.219 2224.41i 0.0243277 0.157211i
\(586\) 0 0
\(587\) −3342.33 + 1216.51i −0.235013 + 0.0855379i −0.456842 0.889548i \(-0.651020\pi\)
0.221829 + 0.975086i \(0.428797\pi\)
\(588\) 0 0
\(589\) 5632.61 4726.32i 0.394037 0.330636i
\(590\) 0 0
\(591\) −12157.6 + 7190.49i −0.846189 + 0.500469i
\(592\) 0 0
\(593\) 1926.38 0.133402 0.0667008 0.997773i \(-0.478753\pi\)
0.0667008 + 0.997773i \(0.478753\pi\)
\(594\) 0 0
\(595\) 1275.69 0.0878959
\(596\) 0 0
\(597\) −28.6820 2730.91i −0.00196629 0.187217i
\(598\) 0 0
\(599\) 2265.90 1901.31i 0.154561 0.129692i −0.562228 0.826982i \(-0.690056\pi\)
0.716789 + 0.697290i \(0.245611\pi\)
\(600\) 0 0
\(601\) −9704.79 + 3532.26i −0.658680 + 0.239740i −0.649666 0.760219i \(-0.725091\pi\)
−0.00901370 + 0.999959i \(0.502869\pi\)
\(602\) 0 0
\(603\) 9180.31 8037.74i 0.619986 0.542823i
\(604\) 0 0
\(605\) 1178.53 + 988.904i 0.0791968 + 0.0664540i
\(606\) 0 0
\(607\) 1586.82 + 8999.33i 0.106107 + 0.601765i 0.990772 + 0.135537i \(0.0432761\pi\)
−0.884665 + 0.466228i \(0.845613\pi\)
\(608\) 0 0
\(609\) −210.701 + 598.375i −0.0140197 + 0.0398151i
\(610\) 0 0
\(611\) 6318.01 + 10943.1i 0.418329 + 0.724568i
\(612\) 0 0
\(613\) −7350.25 + 12731.0i −0.484296 + 0.838826i −0.999837 0.0180389i \(-0.994258\pi\)
0.515541 + 0.856865i \(0.327591\pi\)
\(614\) 0 0
\(615\) 400.124 + 1064.42i 0.0262351 + 0.0697909i
\(616\) 0 0
\(617\) 27125.0 + 9872.69i 1.76987 + 0.644181i 0.999982 + 0.00600359i \(0.00191101\pi\)
0.769890 + 0.638177i \(0.220311\pi\)
\(618\) 0 0
\(619\) −4390.06 + 24897.3i −0.285059 + 1.61665i 0.420015 + 0.907517i \(0.362025\pi\)
−0.705074 + 0.709133i \(0.749086\pi\)
\(620\) 0 0
\(621\) 2570.87 7821.73i 0.166128 0.505435i
\(622\) 0 0
\(623\) 430.017 2438.75i 0.0276537 0.156832i
\(624\) 0 0
\(625\) −12895.3 4693.51i −0.825299 0.300384i
\(626\) 0 0
\(627\) 3996.97 + 661.569i 0.254583 + 0.0421380i
\(628\) 0 0
\(629\) 2364.23 4094.96i 0.149870 0.259582i
\(630\) 0 0
\(631\) 8143.24 + 14104.5i 0.513752 + 0.889844i 0.999873 + 0.0159525i \(0.00507807\pi\)
−0.486121 + 0.873891i \(0.661589\pi\)
\(632\) 0 0
\(633\) 23644.3 4425.65i 1.48464 0.277889i
\(634\) 0 0
\(635\) 836.486 + 4743.95i 0.0522755 + 0.296469i
\(636\) 0 0
\(637\) −8754.22 7345.67i −0.544513 0.456901i
\(638\) 0 0
\(639\) −10601.6 + 19287.0i −0.656326 + 1.19402i
\(640\) 0 0
\(641\) 13181.2 4797.57i 0.812211 0.295621i 0.0976741 0.995218i \(-0.468860\pi\)
0.714537 + 0.699598i \(0.246637\pi\)
\(642\) 0 0
\(643\) −6177.76 + 5183.75i −0.378891 + 0.317927i −0.812267 0.583286i \(-0.801767\pi\)
0.433376 + 0.901213i \(0.357322\pi\)
\(644\) 0 0
\(645\) −1663.90 937.491i −0.101575 0.0572305i
\(646\) 0 0
\(647\) 18799.9 1.14235 0.571175 0.820828i \(-0.306488\pi\)
0.571175 + 0.820828i \(0.306488\pi\)
\(648\) 0 0
\(649\) −7081.87 −0.428332
\(650\) 0 0
\(651\) −6182.38 3483.35i −0.372207 0.209713i
\(652\) 0 0
\(653\) −22715.5 + 19060.6i −1.36130 + 1.14226i −0.385718 + 0.922617i \(0.626046\pi\)
−0.975579 + 0.219648i \(0.929509\pi\)
\(654\) 0 0
\(655\) 3452.50 1256.61i 0.205954 0.0749613i
\(656\) 0 0
\(657\) 3868.32 81.2647i 0.229707 0.00482563i
\(658\) 0 0
\(659\) 24740.9 + 20760.1i 1.46247 + 1.22716i 0.922795 + 0.385291i \(0.125899\pi\)
0.539679 + 0.841871i \(0.318546\pi\)
\(660\) 0 0
\(661\) 2315.53 + 13132.0i 0.136254 + 0.772732i 0.973979 + 0.226640i \(0.0727741\pi\)
−0.837725 + 0.546092i \(0.816115\pi\)
\(662\) 0 0
\(663\) 18631.9 3487.46i 1.09141 0.204286i
\(664\) 0 0
\(665\) 196.176 + 339.786i 0.0114396 + 0.0198140i
\(666\) 0 0
\(667\) −631.969 + 1094.60i −0.0366866 + 0.0635430i
\(668\) 0 0
\(669\) 7413.89 + 1227.13i 0.428457 + 0.0709172i
\(670\) 0 0
\(671\) −8369.15 3046.12i −0.481501 0.175252i
\(672\) 0 0
\(673\) 2027.20 11496.8i 0.116111 0.658500i −0.870083 0.492906i \(-0.835935\pi\)
0.986194 0.165594i \(-0.0529542\pi\)
\(674\) 0 0
\(675\) 16643.8 + 2396.86i 0.949067 + 0.136674i
\(676\) 0 0
\(677\) 789.566 4477.85i 0.0448235 0.254206i −0.954159 0.299299i \(-0.903247\pi\)
0.998983 + 0.0450926i \(0.0143583\pi\)
\(678\) 0 0
\(679\) −7673.36 2792.88i −0.433692 0.157851i
\(680\) 0 0
\(681\) −11143.5 29644.0i −0.627047 1.66808i
\(682\) 0 0
\(683\) −16526.3 + 28624.4i −0.925859 + 1.60364i −0.135686 + 0.990752i \(0.543324\pi\)
−0.790173 + 0.612884i \(0.790009\pi\)
\(684\) 0 0
\(685\) 3257.11 + 5641.48i 0.181675 + 0.314671i
\(686\) 0 0
\(687\) −1830.59 + 5198.74i −0.101661 + 0.288711i
\(688\) 0 0
\(689\) 2193.08 + 12437.6i 0.121262 + 0.687713i
\(690\) 0 0
\(691\) 4182.26 + 3509.33i 0.230247 + 0.193200i 0.750611 0.660745i \(-0.229759\pi\)
−0.520364 + 0.853944i \(0.674204\pi\)
\(692\) 0 0
\(693\) −759.672 3835.40i −0.0416415 0.210238i
\(694\) 0 0
\(695\) 5289.14 1925.09i 0.288674 0.105069i
\(696\) 0 0
\(697\) −7335.81 + 6155.48i −0.398657 + 0.334513i
\(698\) 0 0
\(699\) −48.4863 4616.55i −0.00262364 0.249806i
\(700\) 0 0
\(701\) 27349.1 1.47355 0.736776 0.676136i \(-0.236347\pi\)
0.736776 + 0.676136i \(0.236347\pi\)
\(702\) 0 0
\(703\) 1454.29 0.0780220
\(704\) 0 0
\(705\) 3486.32 2061.95i 0.186245 0.110152i
\(706\) 0 0
\(707\) −1871.62 + 1570.48i −0.0995610 + 0.0835416i
\(708\) 0 0
\(709\) −24616.2 + 8959.56i −1.30392 + 0.474589i −0.898272 0.439440i \(-0.855177\pi\)
−0.405649 + 0.914029i \(0.632955\pi\)
\(710\) 0 0
\(711\) −22613.8 + 8772.90i −1.19281 + 0.462742i
\(712\) 0 0
\(713\) −10830.5 9087.88i −0.568872 0.477340i
\(714\) 0 0
\(715\) −369.814 2097.32i −0.0193430 0.109700i
\(716\) 0 0
\(717\) −17222.2 20092.3i −0.897037 1.04653i
\(718\) 0 0
\(719\) −356.549 617.561i −0.0184938 0.0320322i 0.856630 0.515931i \(-0.172554\pi\)
−0.875124 + 0.483898i \(0.839220\pi\)
\(720\) 0 0
\(721\) 1562.95 2707.11i 0.0807314 0.139831i
\(722\) 0 0
\(723\) 7628.35 9287.48i 0.392395 0.477738i
\(724\) 0 0
\(725\) −2425.73 882.893i −0.124261 0.0452274i
\(726\) 0 0
\(727\) −1496.29 + 8485.89i −0.0763334 + 0.432908i 0.922559 + 0.385856i \(0.126094\pi\)
−0.998892 + 0.0470521i \(0.985017\pi\)
\(728\) 0 0
\(729\) −19643.9 + 1239.48i −0.998015 + 0.0629723i
\(730\) 0 0
\(731\) 2792.84 15839.0i 0.141309 0.801403i
\(732\) 0 0
\(733\) −14280.8 5197.80i −0.719611 0.261917i −0.0438506 0.999038i \(-0.513963\pi\)
−0.675761 + 0.737121i \(0.736185\pi\)
\(734\) 0 0
\(735\) −2325.03 + 2830.72i −0.116680 + 0.142058i
\(736\) 0 0
\(737\) 5772.35 9998.00i 0.288504 0.499703i
\(738\) 0 0
\(739\) −8197.80 14199.0i −0.408066 0.706792i 0.586607 0.809872i \(-0.300463\pi\)
−0.994673 + 0.103080i \(0.967130\pi\)
\(740\) 0 0
\(741\) 3794.13 + 4426.41i 0.188098 + 0.219444i
\(742\) 0 0
\(743\) −2634.69 14942.1i −0.130091 0.737781i −0.978153 0.207885i \(-0.933342\pi\)
0.848063 0.529896i \(-0.177769\pi\)
\(744\) 0 0
\(745\) 5539.39 + 4648.10i 0.272413 + 0.228582i
\(746\) 0 0
\(747\) 11754.4 4560.06i 0.575732 0.223352i
\(748\) 0 0
\(749\) −4582.59 + 1667.93i −0.223557 + 0.0813682i
\(750\) 0 0
\(751\) −5652.00 + 4742.59i −0.274626 + 0.230439i −0.769690 0.638418i \(-0.779589\pi\)
0.495064 + 0.868857i \(0.335145\pi\)
\(752\) 0 0
\(753\) 18476.4 10927.7i 0.894180 0.528853i
\(754\) 0 0
\(755\) −2814.87 −0.135687
\(756\) 0 0
\(757\) 23826.1 1.14395 0.571977 0.820270i \(-0.306177\pi\)
0.571977 + 0.820270i \(0.306177\pi\)
\(758\) 0 0
\(759\) −81.8118 7789.59i −0.00391249 0.372522i
\(760\) 0 0
\(761\) 7406.28 6214.60i 0.352795 0.296030i −0.449116 0.893473i \(-0.648261\pi\)
0.801911 + 0.597443i \(0.203817\pi\)
\(762\) 0 0
\(763\) −11257.6 + 4097.44i −0.534146 + 0.194413i
\(764\) 0 0
\(765\) −1180.56 5960.35i −0.0557949 0.281695i
\(766\) 0 0
\(767\) −7806.72 6550.62i −0.367515 0.308382i
\(768\) 0 0
\(769\) −4584.14 25997.9i −0.214965 1.21913i −0.880967 0.473178i \(-0.843107\pi\)
0.666002 0.745950i \(-0.268004\pi\)
\(770\) 0 0
\(771\) −880.761 + 2501.30i −0.0411412 + 0.116838i
\(772\) 0 0
\(773\) 18402.1 + 31873.4i 0.856247 + 1.48306i 0.875484 + 0.483248i \(0.160543\pi\)
−0.0192370 + 0.999815i \(0.506124\pi\)
\(774\) 0 0
\(775\) 14437.6 25006.7i 0.669180 1.15905i
\(776\) 0 0
\(777\) −493.856 1313.76i −0.0228018 0.0606576i
\(778\) 0 0
\(779\) −2767.65 1007.34i −0.127293 0.0463309i
\(780\) 0 0
\(781\) −3615.96 + 20507.1i −0.165671 + 0.939567i
\(782\) 0