Properties

Label 108.4.i.a.13.1
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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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 13.1
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.1

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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 0.561783 0.827285i \(-0.310116\pi\)
−0.717164 + 0.696904i \(0.754560\pi\)
\(6\) 0 0
\(7\) −5.32680 1.93880i −0.287620 0.104685i 0.194181 0.980966i \(-0.437795\pi\)
−0.481801 + 0.876281i \(0.660017\pi\)
\(8\) 0 0
\(9\) 13.9881 23.0940i 0.518079 0.855333i
\(10\) 0 0
\(11\) 19.5694 16.4207i 0.536399 0.450092i −0.333905 0.942607i \(-0.608367\pi\)
0.870304 + 0.492514i \(0.163922\pi\)
\(12\) 0 0
\(13\) 6.38352 36.2027i 0.136190 0.772372i −0.837834 0.545926i \(-0.816178\pi\)
0.974024 0.226446i \(-0.0727108\pi\)
\(14\) 0 0
\(15\) 11.5826 + 2.16798i 0.199374 + 0.0373180i
\(16\) 0 0
\(17\) 49.6174 85.9398i 0.707881 1.22609i −0.257761 0.966209i \(-0.582985\pi\)
0.965642 0.259877i \(-0.0836821\pi\)
\(18\) 0 0
\(19\) −15.2603 26.4317i −0.184261 0.319150i 0.759066 0.651014i \(-0.225656\pi\)
−0.943327 + 0.331864i \(0.892323\pi\)
\(20\) 0 0
\(21\) 29.0598 4.80992i 0.301970 0.0499814i
\(22\) 0 0
\(23\) 55.1467 20.0717i 0.499951 0.181967i −0.0797209 0.996817i \(-0.525403\pi\)
0.579672 + 0.814850i \(0.303181\pi\)
\(24\) 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 0.970490 0.241142i \(-0.0775220\pi\)
−0.994438 + 0.105327i \(0.966411\pi\)
\(30\) 0 0
\(31\) −226.385 + 82.3974i −1.31161 + 0.477387i −0.900761 0.434316i \(-0.856990\pi\)
−0.410850 + 0.911703i \(0.634768\pi\)
\(32\) 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 −0.914088 0.405515i \(-0.867092\pi\)
0.808230 + 0.588866i \(0.200426\pi\)
\(38\) 0 0
\(39\) 63.4429 + 180.173i 0.260487 + 0.739765i
\(40\) 0 0
\(41\) 16.7572 95.0347i 0.0638300 0.361998i −0.936117 0.351689i \(-0.885607\pi\)
0.999947 0.0103090i \(-0.00328150\pi\)
\(42\) 0 0
\(43\) −124.156 + 104.179i −0.440315 + 0.369468i −0.835827 0.548993i \(-0.815011\pi\)
0.395512 + 0.918461i \(0.370567\pi\)
\(44\) 0 0
\(45\) −57.9645 + 19.7288i −0.192019 + 0.0653555i
\(46\) 0 0
\(47\) 323.003 + 117.563i 1.00244 + 0.364859i 0.790526 0.612429i \(-0.209807\pi\)
0.211916 + 0.977288i \(0.432030\pi\)
\(48\) 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 0.377685 0.925934i \(-0.376720\pi\)
−0.846283 + 0.532734i \(0.821165\pi\)
\(60\) 0 0
\(61\) −327.611 119.241i −0.687643 0.250282i −0.0255176 0.999674i \(-0.508123\pi\)
−0.662126 + 0.749393i \(0.730346\pi\)
\(62\) 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 0.825786 + 0.563983i \(0.190732\pi\)
−0.968879 + 0.247536i \(0.920379\pi\)
\(68\) 0 0
\(69\) −198.455 + 231.527i −0.346248 + 0.403950i
\(70\) 0 0
\(71\) 407.568 705.928i 0.681259 1.17998i −0.293338 0.956009i \(-0.594766\pi\)
0.974597 0.223967i \(-0.0719007\pi\)
\(72\) 0 0
\(73\) 71.6513 + 124.104i 0.114879 + 0.198976i 0.917731 0.397202i \(-0.130019\pi\)
−0.802852 + 0.596178i \(0.796685\pi\)
\(74\) 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 −0.868024 0.496522i \(-0.834610\pi\)
0.645855 0.763460i \(-0.276501\pi\)
\(80\) 0 0
\(81\) −337.664 646.083i −0.463188 0.886260i
\(82\) 0 0
\(83\) 81.0870 + 459.867i 0.107234 + 0.608157i 0.990304 + 0.138915i \(0.0443615\pi\)
−0.883070 + 0.469241i \(0.844527\pi\)
\(84\) 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 0.706133 0.708079i \(-0.250438\pi\)
−0.966281 + 0.257490i \(0.917105\pi\)
\(90\) 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 0.155264 0.987873i \(-0.450377\pi\)
0.999826 + 0.0186370i \(0.00593269\pi\)
\(98\) 0 0
\(99\) −105.479 681.629i −0.107082 0.691983i
\(100\) 0 0
\(101\) 405.014 + 147.413i 0.399014 + 0.145229i 0.533730 0.845655i \(-0.320790\pi\)
−0.134716 + 0.990884i \(0.543012\pi\)
\(102\) 0 0
\(103\) −422.424 354.456i −0.404104 0.339083i 0.417973 0.908459i \(-0.362741\pi\)
−0.822077 + 0.569376i \(0.807185\pi\)
\(104\) 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 −0.977419 0.211313i \(-0.932226\pi\)
−0.377829 0.925875i \(-0.623329\pi\)
\(114\) 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 0.951545 + 0.307509i \(0.0994954\pi\)
−0.209462 + 0.977817i \(0.567171\pi\)
\(128\) 0 0
\(129\) 296.330 788.302i 0.202251 0.538032i
\(130\) 0 0
\(131\) −1522.41 + 554.114i −1.01537 + 0.369566i −0.795494 0.605961i \(-0.792789\pi\)
−0.219880 + 0.975527i \(0.570566\pi\)
\(132\) 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 0.593483 + 0.804847i \(0.297752\pi\)
−0.282418 + 0.959291i \(0.591136\pi\)
\(138\) 0 0
\(139\) −2332.30 + 848.889i −1.42319 + 0.517999i −0.934971 0.354723i \(-0.884575\pi\)
−0.488218 + 0.872722i \(0.662353\pi\)
\(140\) 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 0.321700 + 0.946842i \(0.395746\pi\)
−0.626138 + 0.779712i \(0.715365\pi\)
\(150\) 0 0
\(151\) 950.851 797.859i 0.512445 0.429992i −0.349544 0.936920i \(-0.613663\pi\)
0.861989 + 0.506928i \(0.169219\pi\)
\(152\) 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 0.988693 0.149951i \(-0.0479115\pi\)
0.0240121 + 0.999712i \(0.492356\pi\)
\(158\) 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 0.104611 0.994513i \(-0.466640\pi\)
−0.961239 + 0.275717i \(0.911085\pi\)
\(168\) 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 −0.258587 + 0.965988i \(0.583257\pi\)
−0.996216 + 0.0869166i \(0.972299\pi\)
\(174\) 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 −0.190382 0.981710i \(-0.560973\pi\)
0.945377 0.325979i \(-0.105694\pi\)
\(180\) 0 0
\(181\) 1109.38 + 1921.50i 0.455577 + 0.789083i 0.998721 0.0505564i \(-0.0160995\pi\)
−0.543144 + 0.839640i \(0.682766\pi\)
\(182\) 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 0.998754 0.0499076i \(-0.0158927\pi\)
−0.955591 + 0.294696i \(0.904782\pi\)
\(192\) 0 0
\(193\) 377.376 137.354i 0.140747 0.0512276i −0.270686 0.962668i \(-0.587251\pi\)
0.411433 + 0.911440i \(0.365028\pi\)
\(194\) 0 0
\(195\) 152.424 405.481i 0.0559761 0.148908i
\(196\) 0 0
\(197\) 1359.16 + 2354.14i 0.491555 + 0.851398i 0.999953 0.00972432i \(-0.00309540\pi\)
−0.508398 + 0.861122i \(0.669762\pi\)
\(198\) 0 0
\(199\) 262.797 455.177i 0.0936138 0.162144i −0.815415 0.578876i \(-0.803491\pi\)
0.909029 + 0.416732i \(0.136825\pi\)
\(200\) 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 −0.157190 0.987568i \(-0.550244\pi\)
−0.999861 + 0.0166873i \(0.994688\pi\)
\(212\) 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 0.129812 0.991539i \(-0.458563\pi\)
−0.537907 + 0.843004i \(0.680785\pi\)
\(224\) 0 0
\(225\) −3017.06 1170.45i −0.893945 0.346801i
\(226\) 0 0
\(227\) 4668.86 3917.63i 1.36512 1.14547i 0.390759 0.920493i \(-0.372212\pi\)
0.974363 0.224981i \(-0.0722319\pi\)
\(228\) 0 0
\(229\) −184.191 + 1044.60i −0.0531514 + 0.301437i −0.999782 0.0208842i \(-0.993352\pi\)
0.946630 + 0.322321i \(0.104463\pi\)
\(230\) 0 0
\(231\) 489.701 571.309i 0.139480 0.162725i
\(232\) 0 0
\(233\) 444.253 769.468i 0.124910 0.216350i −0.796788 0.604259i \(-0.793469\pi\)
0.921698 + 0.387909i \(0.126803\pi\)
\(234\) 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 0.399797 0.916604i \(-0.369081\pi\)
0.895444 + 0.445175i \(0.146858\pi\)
\(240\) 0 0
\(241\) −401.648 2277.86i −0.107354 0.608837i −0.990254 0.139275i \(-0.955523\pi\)
0.882899 0.469562i \(-0.155588\pi\)
\(242\) 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 −0.999745 0.0225867i \(-0.992810\pi\)
0.480312 0.877098i \(-0.340524\pi\)
\(252\) 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 −0.993672 0.112321i \(-0.964172\pi\)
0.972162 + 0.234309i \(0.0752827\pi\)
\(258\) 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 0.630980 0.775799i \(-0.282653\pi\)
−0.0153157 + 0.999883i \(0.504875\pi\)
\(264\) 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 0.386234 0.922401i \(-0.373776\pi\)
−0.297036 + 0.954866i \(0.595998\pi\)
\(278\) 0 0
\(279\) −1263.82 + 6380.71i −0.271193 + 1.36919i
\(280\) 0 0
\(281\) −533.382 + 447.561i −0.113235 + 0.0950151i −0.697647 0.716442i \(-0.745770\pi\)
0.584412 + 0.811457i \(0.301325\pi\)
\(282\) 0 0
\(283\) −205.873 + 1167.56i −0.0432433 + 0.245245i −0.998765 0.0496742i \(-0.984182\pi\)
0.955522 + 0.294919i \(0.0952928\pi\)
\(284\) 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 0.362690 0.931910i \(-0.381858\pi\)
0.876857 + 0.480752i \(0.159636\pi\)
\(294\) 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 0.491124 + 0.871089i \(0.336586\pi\)
−0.999948 + 0.0102185i \(0.996747\pi\)
\(308\) 0 0
\(309\) 2816.43 + 527.169i 0.518515 + 0.0970538i
\(310\) 0 0
\(311\) −1849.24 + 10487.6i −0.337173 + 1.91220i 0.0674546 + 0.997722i \(0.478512\pi\)
−0.404628 + 0.914482i \(0.632599\pi\)
\(312\) 0 0
\(313\) −5515.11 + 4627.73i −0.995950 + 0.835701i −0.986418 0.164253i \(-0.947479\pi\)
−0.00953196 + 0.999955i \(0.503034\pi\)
\(314\) 0 0
\(315\) 347.015 + 7.29001i 0.0620701 + 0.00130395i
\(316\) 0 0
\(317\) 82.0633 + 29.8686i 0.0145398 + 0.00529207i 0.349280 0.937018i \(-0.386426\pi\)
−0.334740 + 0.942311i \(0.608648\pi\)
\(318\) 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 0.0111304 0.999938i \(-0.496457\pi\)
−0.634221 + 0.773151i \(0.718679\pi\)
\(332\) 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 −0.740911 0.671603i \(-0.765606\pi\)
0.925931 0.377694i \(-0.123283\pi\)
\(338\) 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 0.472670 0.881240i \(-0.343290\pi\)
0.928536 + 0.371242i \(0.121068\pi\)
\(348\) 0 0
\(349\) 1123.06 + 6369.21i 0.172253 + 0.976895i 0.941267 + 0.337663i \(0.109636\pi\)
−0.769014 + 0.639232i \(0.779253\pi\)
\(350\) 0 0
\(351\) 5048.37 + 1055.14i 0.767698 + 0.160453i
\(352\) 0 0
\(353\) −1919.44 10885.7i −0.289410 1.64133i −0.689093 0.724673i \(-0.741991\pi\)
0.399683 0.916653i \(-0.369120\pi\)
\(354\) 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 0.948614 0.316437i \(-0.102487\pi\)
−0.748349 + 0.663305i \(0.769153\pi\)
\(360\) 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 −0.237591 0.971365i \(-0.576358\pi\)
0.915351 + 0.402657i \(0.131913\pi\)
\(368\) 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 0.979665 0.200641i \(-0.0643023\pi\)
−0.0274753 + 0.999622i \(0.508747\pi\)
\(374\) 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 0.511800 0.859105i \(-0.328979\pi\)
−0.757180 + 0.653206i \(0.773423\pi\)
\(384\) 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 −0.779109 0.626888i \(-0.784328\pi\)
0.482073 + 0.876131i \(0.339884\pi\)
\(390\) 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 −0.970613 0.240647i \(-0.922640\pi\)
0.276900 0.960899i \(-0.410693\pi\)
\(398\) 0 0
\(399\) −570.598 694.700i −0.0715930 0.0871641i
\(400\) 0 0
\(401\) 12728.6 4632.81i 1.58512 0.576937i 0.608811 0.793315i \(-0.291647\pi\)
0.976310 + 0.216378i \(0.0694244\pi\)
\(402\) 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 0.491665 0.870784i \(-0.336388\pi\)
0.936367 + 0.351023i \(0.114166\pi\)
\(410\) 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 0.446294 + 0.894886i \(0.352744\pi\)
−0.725448 + 0.688277i \(0.758368\pi\)
\(420\) 0 0
\(421\) −3826.83 + 3211.09i −0.443013 + 0.371732i −0.836835 0.547455i \(-0.815597\pi\)
0.393823 + 0.919186i \(0.371152\pi\)
\(422\) 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 0.950774 0.309886i \(-0.100291\pi\)
0.529144 + 0.848532i \(0.322513\pi\)
\(440\) 0 0
\(441\) −7945.76 + 2704.42i −0.857981 + 0.292022i
\(442\) 0 0
\(443\) 3551.99 2980.47i 0.380948 0.319653i −0.432126 0.901813i \(-0.642237\pi\)
0.813074 + 0.582160i \(0.197792\pi\)
\(444\) 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 −0.997480 0.0709535i \(-0.977396\pi\)
0.560187 + 0.828366i \(0.310729\pi\)
\(450\) 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 0.956754 + 0.290898i \(0.0939541\pi\)
−0.799562 + 0.600584i \(0.794935\pi\)
\(458\) 0 0
\(459\) 11831.7 + 7337.49i 1.20318 + 0.746154i
\(460\) 0 0
\(461\) −890.872 5052.38i −0.0900044 0.510440i −0.996164 0.0875046i \(-0.972111\pi\)
0.906160 0.422936i \(-0.139000\pi\)
\(462\) 0 0
\(463\) 11339.2 4127.13i 1.13818 0.414264i 0.296925 0.954901i \(-0.404039\pi\)
0.841256 + 0.540637i \(0.181817\pi\)
\(464\) 0 0
\(465\) −2800.75 + 463.574i −0.279316 + 0.0462317i
\(466\) 0 0
\(467\) 92.2875 + 159.847i 0.00914466 + 0.0158390i 0.870562 0.492060i \(-0.163756\pi\)
−0.861417 + 0.507899i \(0.830422\pi\)
\(468\) 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 0.346074 0.938207i \(-0.387515\pi\)
−0.337960 + 0.941160i \(0.609737\pi\)
\(480\) 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 0.422609 0.906312i \(-0.361114\pi\)
−0.819158 + 0.573568i \(0.805559\pi\)
\(492\) 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 −0.997507 0.0705635i \(-0.977520\pi\)
0.961484 + 0.274860i \(0.0886314\pi\)
\(500\) 0 0
\(501\) 12325.9 + 2307.11i 1.09916 + 0.205737i
\(502\) 0 0
\(503\) −7235.56 + 12532.4i −0.641387 + 1.11092i 0.343736 + 0.939066i \(0.388308\pi\)
−0.985123 + 0.171849i \(0.945026\pi\)
\(504\) 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 0.245633 0.969363i \(-0.421004\pi\)
0.811261 + 0.584685i \(0.198782\pi\)
\(510\) 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 0.999920 0.0126104i \(-0.00401413\pi\)
−0.510881 + 0.859651i \(0.670681\pi\)
\(522\) 0 0
\(523\) −7100.15 + 12297.8i −0.593629 + 1.02820i 0.400110 + 0.916467i \(0.368972\pi\)
−0.993739 + 0.111728i \(0.964361\pi\)
\(524\) 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 0.651308 0.758813i \(-0.274221\pi\)
0.0111752 + 0.999938i \(0.496443\pi\)
\(548\) 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 −0.779350 0.626589i \(-0.784450\pi\)
0.932317 + 0.361642i \(0.117784\pi\)
\(558\) 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 −0.262217 0.965009i \(-0.584454\pi\)
0.419426 + 0.907789i \(0.362231\pi\)
\(564\) 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 −0.995788 0.0916855i \(-0.970775\pi\)
0.904376 0.426736i \(-0.140337\pi\)
\(570\) 0 0
\(571\) −5058.44 + 1841.12i −0.370734 + 0.134936i −0.520667 0.853760i \(-0.674317\pi\)
0.149932 + 0.988696i \(0.452094\pi\)
\(572\) 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 −0.895677 0.444705i \(-0.853309\pi\)
0.832964 + 0.553327i \(0.186642\pi\)
\(578\) 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 0.221829 0.975086i \(-0.428797\pi\)
−0.456842 + 0.889548i \(0.651020\pi\)
\(588\) 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 0.716789 0.697290i \(-0.245611\pi\)
−0.562228 + 0.826982i \(0.690056\pi\)
\(600\) 0 0
\(601\) −9704.79 3532.26i −0.658680 0.239740i −0.00901370 0.999959i \(-0.502869\pi\)
−0.649666 + 0.760219i \(0.725091\pi\)
\(602\) 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 −0.884665 0.466228i \(-0.845613\pi\)
0.990772 0.135537i \(-0.0432761\pi\)
\(608\) 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 0.515541 0.856865i \(-0.327591\pi\)
−0.999837 + 0.0180389i \(0.994258\pi\)
\(614\) 0 0
\(615\) 400.124 1064.42i 0.0262351 0.0697909i
\(616\) 0 0
\(617\) 27125.0 9872.69i 1.76987 0.644181i 0.769890 0.638177i \(-0.220311\pi\)
0.999982 0.00600359i \(-0.00191101\pi\)
\(618\) 0 0
\(619\) −4390.06 24897.3i −0.285059 1.61665i −0.705074 0.709133i \(-0.749086\pi\)
0.420015 0.907517i \(-0.362025\pi\)
\(620\) 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 −0.486121 0.873891i \(-0.661589\pi\)
0.999873 0.0159525i \(-0.00507807\pi\)
\(632\) 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 0.714537 0.699598i \(-0.246637\pi\)
0.0976741 + 0.995218i \(0.468860\pi\)
\(642\) 0 0
\(643\) −6177.76 5183.75i −0.378891 0.317927i 0.433376 0.901213i \(-0.357322\pi\)
−0.812267 + 0.583286i \(0.801767\pi\)
\(644\) 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 −0.975579 0.219648i \(-0.929509\pi\)
−0.385718 0.922617i \(-0.626046\pi\)
\(654\) 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 0.539679 0.841871i \(-0.318546\pi\)
0.922795 0.385291i \(-0.125899\pi\)
\(660\) 0 0
\(661\) 2315.53 13132.0i 0.136254 0.772732i −0.837725 0.546092i \(-0.816115\pi\)
0.973979 0.226640i \(-0.0727741\pi\)
\(662\) 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 0.986194 + 0.165594i \(0.0529542\pi\)
−0.870083 + 0.492906i \(0.835935\pi\)
\(674\) 0 0
\(675\) 16643.8 2396.86i 0.949067 0.136674i
\(676\) 0 0
\(677\) 789.566 + 4477.85i 0.0448235 + 0.254206i 0.998983 0.0450926i \(-0.0143583\pi\)
−0.954159 + 0.299299i \(0.903247\pi\)
\(678\) 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 −0.790173 0.612884i \(-0.790009\pi\)
−0.135686 0.990752i \(-0.543324\pi\)
\(684\) 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 −0.520364 0.853944i \(-0.674204\pi\)
0.750611 + 0.660745i \(0.229759\pi\)
\(692\) 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 −0.405649 0.914029i \(-0.632955\pi\)
−0.898272 + 0.439440i \(0.855177\pi\)
\(710\) 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 −0.875124 0.483898i \(-0.839220\pi\)
0.856630 + 0.515931i \(0.172554\pi\)
\(720\) 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 −0.998892 0.0470521i \(-0.985017\pi\)
0.922559 0.385856i \(-0.126094\pi\)
\(728\) 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 −0.675761 0.737121i \(-0.736185\pi\)
−0.0438506 + 0.999038i \(0.513963\pi\)
\(734\) 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 −0.994673 0.103080i \(-0.967130\pi\)
0.586607 + 0.809872i \(0.300463\pi\)
\(740\) 0 0
\(741\) 3794.13 4426.41i 0.188098 0.219444i
\(742\) 0 0
\(743\) −2634.69 + 14942.1i −0.130091 + 0.737781i 0.848063 + 0.529896i \(0.177769\pi\)
−0.978153 + 0.207885i \(0.933342\pi\)
\(744\) 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 0.495064 0.868857i \(-0.335145\pi\)
−0.769690 + 0.638418i \(0.779589\pi\)
\(752\) 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 0.801911 0.597443i \(-0.203817\pi\)
−0.449116 + 0.893473i \(0.648261\pi\)
\(762\) 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 0.666002 + 0.745950i \(0.268004\pi\)
−0.880967 + 0.473178i \(0.843107\pi\)
\(770\) 0 0
\(771\) −880.761 2501.30i −0.0411412 0.116838i
\(772\) 0 0
\(773\) 18402.1 31873.4i 0.856247 1.48306i −0.0192370 0.999815i \(-0.506124\pi\)
0.875484 0.483248i \(-0.160543\pi\)
\(774\) 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