Properties

Label 108.4.i.a.13.5
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 13.5
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.173032 + 5.19327i) q^{3} +(6.54095 + 5.48851i) q^{5} +(11.9650 + 4.35489i) q^{7} +(-26.9401 - 1.79720i) q^{9} +O(q^{10})\) \(q+(-0.173032 + 5.19327i) q^{3} +(6.54095 + 5.48851i) q^{5} +(11.9650 + 4.35489i) q^{7} +(-26.9401 - 1.79720i) q^{9} +(-7.56521 + 6.34796i) q^{11} +(-6.10231 + 34.6079i) q^{13} +(-29.6351 + 33.0192i) q^{15} +(-44.7027 + 77.4273i) q^{17} +(-1.00444 - 1.73974i) q^{19} +(-24.6865 + 61.3838i) q^{21} +(33.9901 - 12.3714i) q^{23} +(-9.04572 - 51.3009i) q^{25} +(13.9949 - 139.596i) q^{27} +(40.5831 + 230.158i) q^{29} +(113.063 - 41.1517i) q^{31} +(-31.6577 - 40.3866i) q^{33} +(54.3604 + 94.1550i) q^{35} +(98.7263 - 170.999i) q^{37} +(-178.672 - 37.6792i) q^{39} +(-4.40922 + 25.0059i) q^{41} +(410.543 - 344.487i) q^{43} +(-166.350 - 159.617i) q^{45} +(-17.7125 - 6.44681i) q^{47} +(-138.558 - 116.264i) q^{49} +(-394.366 - 245.551i) q^{51} +366.433 q^{53} -84.3245 q^{55} +(9.20873 - 4.91529i) q^{57} +(-122.347 - 102.661i) q^{59} +(385.626 + 140.356i) q^{61} +(-314.511 - 138.825i) q^{63} +(-229.861 + 192.876i) q^{65} +(152.450 - 864.586i) q^{67} +(58.3667 + 178.661i) q^{69} +(69.1038 - 119.691i) q^{71} +(554.236 + 959.964i) q^{73} +(267.984 - 38.1002i) q^{75} +(-118.162 + 43.0075i) q^{77} +(-48.8286 - 276.921i) q^{79} +(722.540 + 96.8338i) q^{81} +(168.981 + 958.337i) q^{83} +(-717.359 + 261.097i) q^{85} +(-1202.29 + 170.934i) q^{87} +(530.757 + 919.298i) q^{89} +(-223.728 + 387.508i) q^{91} +(194.148 + 594.289i) q^{93} +(2.97859 - 16.8924i) q^{95} +(-158.761 + 133.216i) q^{97} +(215.216 - 157.419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

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
\(3\) −0.173032 + 5.19327i −0.0333000 + 0.999445i
\(4\) 0 0
\(5\) 6.54095 + 5.48851i 0.585040 + 0.490907i 0.886598 0.462541i \(-0.153062\pi\)
−0.301558 + 0.953448i \(0.597507\pi\)
\(6\) 0 0
\(7\) 11.9650 + 4.35489i 0.646048 + 0.235142i 0.644201 0.764856i \(-0.277190\pi\)
0.00184654 + 0.999998i \(0.499412\pi\)
\(8\) 0 0
\(9\) −26.9401 1.79720i −0.997782 0.0665631i
\(10\) 0 0
\(11\) −7.56521 + 6.34796i −0.207363 + 0.173998i −0.740555 0.671996i \(-0.765437\pi\)
0.533191 + 0.845995i \(0.320993\pi\)
\(12\) 0 0
\(13\) −6.10231 + 34.6079i −0.130191 + 0.738347i 0.847898 + 0.530159i \(0.177868\pi\)
−0.978089 + 0.208188i \(0.933243\pi\)
\(14\) 0 0
\(15\) −29.6351 + 33.0192i −0.510117 + 0.568369i
\(16\) 0 0
\(17\) −44.7027 + 77.4273i −0.637764 + 1.10464i 0.348158 + 0.937436i \(0.386807\pi\)
−0.985922 + 0.167204i \(0.946526\pi\)
\(18\) 0 0
\(19\) −1.00444 1.73974i −0.0121281 0.0210065i 0.859898 0.510466i \(-0.170527\pi\)
−0.872026 + 0.489460i \(0.837194\pi\)
\(20\) 0 0
\(21\) −24.6865 + 61.3838i −0.256525 + 0.637859i
\(22\) 0 0
\(23\) 33.9901 12.3714i 0.308149 0.112157i −0.183317 0.983054i \(-0.558683\pi\)
0.491466 + 0.870897i \(0.336461\pi\)
\(24\) 0 0
\(25\) −9.04572 51.3009i −0.0723658 0.410407i
\(26\) 0 0
\(27\) 13.9949 139.596i 0.0997524 0.995012i
\(28\) 0 0
\(29\) 40.5831 + 230.158i 0.259865 + 1.47377i 0.783269 + 0.621683i \(0.213551\pi\)
−0.523404 + 0.852085i \(0.675338\pi\)
\(30\) 0 0
\(31\) 113.063 41.1517i 0.655057 0.238421i 0.00695640 0.999976i \(-0.497786\pi\)
0.648101 + 0.761554i \(0.275563\pi\)
\(32\) 0 0
\(33\) −31.6577 40.3866i −0.166997 0.213042i
\(34\) 0 0
\(35\) 54.3604 + 94.1550i 0.262531 + 0.454717i
\(36\) 0 0
\(37\) 98.7263 170.999i 0.438662 0.759785i −0.558924 0.829219i \(-0.688786\pi\)
0.997587 + 0.0694333i \(0.0221191\pi\)
\(38\) 0 0
\(39\) −178.672 37.6792i −0.733602 0.154705i
\(40\) 0 0
\(41\) −4.40922 + 25.0059i −0.0167952 + 0.0952504i −0.992053 0.125820i \(-0.959844\pi\)
0.975258 + 0.221070i \(0.0709550\pi\)
\(42\) 0 0
\(43\) 410.543 344.487i 1.45598 1.22171i 0.527918 0.849296i \(-0.322973\pi\)
0.928065 0.372419i \(-0.121471\pi\)
\(44\) 0 0
\(45\) −166.350 159.617i −0.551067 0.528761i
\(46\) 0 0
\(47\) −17.7125 6.44681i −0.0549708 0.0200077i 0.314388 0.949294i \(-0.398201\pi\)
−0.369359 + 0.929287i \(0.620423\pi\)
\(48\) 0 0
\(49\) −138.558 116.264i −0.403959 0.338962i
\(50\) 0 0
\(51\) −394.366 245.551i −1.08279 0.674195i
\(52\) 0 0
\(53\) 366.433 0.949687 0.474844 0.880070i \(-0.342505\pi\)
0.474844 + 0.880070i \(0.342505\pi\)
\(54\) 0 0
\(55\) −84.3245 −0.206733
\(56\) 0 0
\(57\) 9.20873 4.91529i 0.0213987 0.0114219i
\(58\) 0 0
\(59\) −122.347 102.661i −0.269969 0.226531i 0.497745 0.867323i \(-0.334161\pi\)
−0.767714 + 0.640793i \(0.778606\pi\)
\(60\) 0 0
\(61\) 385.626 + 140.356i 0.809415 + 0.294603i 0.713382 0.700775i \(-0.247162\pi\)
0.0960331 + 0.995378i \(0.469385\pi\)
\(62\) 0 0
\(63\) −314.511 138.825i −0.628963 0.277624i
\(64\) 0 0
\(65\) −229.861 + 192.876i −0.438627 + 0.368051i
\(66\) 0 0
\(67\) 152.450 864.586i 0.277981 1.57651i −0.451351 0.892346i \(-0.649058\pi\)
0.729332 0.684160i \(-0.239831\pi\)
\(68\) 0 0
\(69\) 58.3667 + 178.661i 0.101834 + 0.311713i
\(70\) 0 0
\(71\) 69.1038 119.691i 0.115509 0.200067i −0.802474 0.596687i \(-0.796484\pi\)
0.917983 + 0.396620i \(0.129817\pi\)
\(72\) 0 0
\(73\) 554.236 + 959.964i 0.888608 + 1.53911i 0.841522 + 0.540223i \(0.181660\pi\)
0.0470856 + 0.998891i \(0.485007\pi\)
\(74\) 0 0
\(75\) 267.984 38.1002i 0.412589 0.0586591i
\(76\) 0 0
\(77\) −118.162 + 43.0075i −0.174881 + 0.0636515i
\(78\) 0 0
\(79\) −48.8286 276.921i −0.0695399 0.394380i −0.999634 0.0270585i \(-0.991386\pi\)
0.930094 0.367322i \(-0.119725\pi\)
\(80\) 0 0
\(81\) 722.540 + 96.8338i 0.991139 + 0.132831i
\(82\) 0 0
\(83\) 168.981 + 958.337i 0.223470 + 1.26736i 0.865588 + 0.500757i \(0.166945\pi\)
−0.642118 + 0.766606i \(0.721944\pi\)
\(84\) 0 0
\(85\) −717.359 + 261.097i −0.915394 + 0.333176i
\(86\) 0 0
\(87\) −1202.29 + 170.934i −1.48160 + 0.210644i
\(88\) 0 0
\(89\) 530.757 + 919.298i 0.632136 + 1.09489i 0.987114 + 0.160017i \(0.0511549\pi\)
−0.354978 + 0.934875i \(0.615512\pi\)
\(90\) 0 0
\(91\) −223.728 + 387.508i −0.257726 + 0.446394i
\(92\) 0 0
\(93\) 194.148 + 594.289i 0.216476 + 0.662634i
\(94\) 0 0
\(95\) 2.97859 16.8924i 0.00321681 0.0182434i
\(96\) 0 0
\(97\) −158.761 + 133.216i −0.166183 + 0.139444i −0.722087 0.691803i \(-0.756817\pi\)
0.555904 + 0.831247i \(0.312372\pi\)
\(98\) 0 0
\(99\) 215.216 157.419i 0.218485 0.159810i
\(100\) 0 0
\(101\) −1263.16 459.753i −1.24445 0.452942i −0.365927 0.930644i \(-0.619248\pi\)
−0.878522 + 0.477701i \(0.841470\pi\)
\(102\) 0 0
\(103\) −725.221 608.533i −0.693768 0.582141i 0.226225 0.974075i \(-0.427362\pi\)
−0.919993 + 0.391934i \(0.871806\pi\)
\(104\) 0 0
\(105\) −498.378 + 266.016i −0.463207 + 0.247243i
\(106\) 0 0
\(107\) 1007.69 0.910439 0.455219 0.890379i \(-0.349561\pi\)
0.455219 + 0.890379i \(0.349561\pi\)
\(108\) 0 0
\(109\) −542.749 −0.476935 −0.238467 0.971151i \(-0.576645\pi\)
−0.238467 + 0.971151i \(0.576645\pi\)
\(110\) 0 0
\(111\) 870.961 + 542.301i 0.744757 + 0.463720i
\(112\) 0 0
\(113\) −1544.12 1295.67i −1.28548 1.07864i −0.992464 0.122535i \(-0.960898\pi\)
−0.293013 0.956109i \(-0.594658\pi\)
\(114\) 0 0
\(115\) 290.228 + 105.634i 0.235339 + 0.0856562i
\(116\) 0 0
\(117\) 226.595 921.375i 0.179048 0.728044i
\(118\) 0 0
\(119\) −872.054 + 731.740i −0.671774 + 0.563685i
\(120\) 0 0
\(121\) −214.190 + 1214.73i −0.160924 + 0.912646i
\(122\) 0 0
\(123\) −129.100 27.2251i −0.0946383 0.0199577i
\(124\) 0 0
\(125\) 756.060 1309.53i 0.540993 0.937027i
\(126\) 0 0
\(127\) 731.061 + 1266.24i 0.510797 + 0.884726i 0.999922 + 0.0125122i \(0.00398286\pi\)
−0.489125 + 0.872214i \(0.662684\pi\)
\(128\) 0 0
\(129\) 1717.98 + 2191.67i 1.17255 + 1.49586i
\(130\) 0 0
\(131\) 1594.59 580.385i 1.06351 0.387087i 0.249766 0.968306i \(-0.419646\pi\)
0.813747 + 0.581219i \(0.197424\pi\)
\(132\) 0 0
\(133\) −4.44170 25.1901i −0.00289582 0.0164230i
\(134\) 0 0
\(135\) 857.716 836.282i 0.546818 0.533153i
\(136\) 0 0
\(137\) −323.495 1834.63i −0.201737 1.14411i −0.902492 0.430707i \(-0.858264\pi\)
0.700755 0.713402i \(-0.252847\pi\)
\(138\) 0 0
\(139\) −999.280 + 363.708i −0.609768 + 0.221938i −0.628402 0.777889i \(-0.716291\pi\)
0.0186335 + 0.999826i \(0.494068\pi\)
\(140\) 0 0
\(141\) 36.5448 90.8701i 0.0218272 0.0542741i
\(142\) 0 0
\(143\) −173.525 300.554i −0.101475 0.175759i
\(144\) 0 0
\(145\) −997.772 + 1728.19i −0.571452 + 0.989783i
\(146\) 0 0
\(147\) 627.765 699.451i 0.352225 0.392447i
\(148\) 0 0
\(149\) 578.529 3281.00i 0.318087 1.80396i −0.236278 0.971685i \(-0.575928\pi\)
0.554365 0.832274i \(-0.312961\pi\)
\(150\) 0 0
\(151\) 1959.73 1644.41i 1.05616 0.886224i 0.0624329 0.998049i \(-0.480114\pi\)
0.993728 + 0.111825i \(0.0356696\pi\)
\(152\) 0 0
\(153\) 1343.45 2005.56i 0.709878 1.05974i
\(154\) 0 0
\(155\) 965.403 + 351.378i 0.500278 + 0.182086i
\(156\) 0 0
\(157\) −2145.49 1800.28i −1.09063 0.915144i −0.0938671 0.995585i \(-0.529923\pi\)
−0.996759 + 0.0804405i \(0.974367\pi\)
\(158\) 0 0
\(159\) −63.4046 + 1902.98i −0.0316246 + 0.949160i
\(160\) 0 0
\(161\) 460.567 0.225452
\(162\) 0 0
\(163\) −1529.32 −0.734879 −0.367440 0.930047i \(-0.619766\pi\)
−0.367440 + 0.930047i \(0.619766\pi\)
\(164\) 0 0
\(165\) 14.5908 437.920i 0.00688422 0.206618i
\(166\) 0 0
\(167\) −2951.09 2476.26i −1.36744 1.14742i −0.973607 0.228233i \(-0.926705\pi\)
−0.393831 0.919183i \(-0.628850\pi\)
\(168\) 0 0
\(169\) 904.034 + 329.041i 0.411486 + 0.149769i
\(170\) 0 0
\(171\) 23.9330 + 48.6739i 0.0107029 + 0.0217672i
\(172\) 0 0
\(173\) −1403.86 + 1177.98i −0.616956 + 0.517688i −0.896845 0.442345i \(-0.854147\pi\)
0.279889 + 0.960032i \(0.409702\pi\)
\(174\) 0 0
\(175\) 115.178 653.206i 0.0497522 0.282159i
\(176\) 0 0
\(177\) 554.316 617.615i 0.235395 0.262276i
\(178\) 0 0
\(179\) −191.456 + 331.612i −0.0799448 + 0.138469i −0.903226 0.429165i \(-0.858808\pi\)
0.823281 + 0.567634i \(0.192141\pi\)
\(180\) 0 0
\(181\) 150.411 + 260.519i 0.0617677 + 0.106985i 0.895256 0.445553i \(-0.146993\pi\)
−0.833488 + 0.552538i \(0.813660\pi\)
\(182\) 0 0
\(183\) −795.634 + 1978.37i −0.321393 + 0.799156i
\(184\) 0 0
\(185\) 1584.29 576.636i 0.629619 0.229163i
\(186\) 0 0
\(187\) −153.321 869.525i −0.0599568 0.340032i
\(188\) 0 0
\(189\) 775.375 1609.32i 0.298414 0.619369i
\(190\) 0 0
\(191\) 566.341 + 3211.88i 0.214550 + 1.21677i 0.881686 + 0.471836i \(0.156409\pi\)
−0.667136 + 0.744936i \(0.732480\pi\)
\(192\) 0 0
\(193\) −1782.33 + 648.714i −0.664739 + 0.241945i −0.652281 0.757977i \(-0.726188\pi\)
−0.0124579 + 0.999922i \(0.503966\pi\)
\(194\) 0 0
\(195\) −961.885 1227.10i −0.353241 0.450639i
\(196\) 0 0
\(197\) −486.365 842.409i −0.175899 0.304666i 0.764573 0.644537i \(-0.222950\pi\)
−0.940472 + 0.339871i \(0.889616\pi\)
\(198\) 0 0
\(199\) −1402.61 + 2429.40i −0.499641 + 0.865403i −1.00000 0.000414695i \(-0.999868\pi\)
0.500359 + 0.865818i \(0.333201\pi\)
\(200\) 0 0
\(201\) 4463.65 + 941.314i 1.56638 + 0.330324i
\(202\) 0 0
\(203\) −516.738 + 2930.57i −0.178660 + 1.01323i
\(204\) 0 0
\(205\) −166.086 + 139.362i −0.0565850 + 0.0474804i
\(206\) 0 0
\(207\) −937.933 + 272.200i −0.314931 + 0.0913971i
\(208\) 0 0
\(209\) 18.6426 + 6.78534i 0.00617002 + 0.00224570i
\(210\) 0 0
\(211\) −6.10520 5.12287i −0.00199194 0.00167144i 0.641791 0.766880i \(-0.278192\pi\)
−0.643783 + 0.765208i \(0.722636\pi\)
\(212\) 0 0
\(213\) 609.632 + 379.585i 0.196109 + 0.122107i
\(214\) 0 0
\(215\) 4576.06 1.45156
\(216\) 0 0
\(217\) 1532.01 0.479261
\(218\) 0 0
\(219\) −5081.25 + 2712.19i −1.56785 + 0.836862i
\(220\) 0 0
\(221\) −2406.81 2019.55i −0.732577 0.614705i
\(222\) 0 0
\(223\) 3121.71 + 1136.21i 0.937422 + 0.341194i 0.765147 0.643855i \(-0.222666\pi\)
0.172275 + 0.985049i \(0.444888\pi\)
\(224\) 0 0
\(225\) 151.495 + 1398.31i 0.0448873 + 0.414314i
\(226\) 0 0
\(227\) −2498.72 + 2096.68i −0.730599 + 0.613046i −0.930295 0.366812i \(-0.880449\pi\)
0.199696 + 0.979858i \(0.436005\pi\)
\(228\) 0 0
\(229\) 0.498021 2.82442i 0.000143712 0.000815033i −0.984736 0.174056i \(-0.944313\pi\)
0.984880 + 0.173241i \(0.0554238\pi\)
\(230\) 0 0
\(231\) −202.904 621.090i −0.0577926 0.176904i
\(232\) 0 0
\(233\) −419.561 + 726.702i −0.117967 + 0.204325i −0.918962 0.394346i \(-0.870971\pi\)
0.800995 + 0.598671i \(0.204304\pi\)
\(234\) 0 0
\(235\) −80.4729 139.383i −0.0223382 0.0386909i
\(236\) 0 0
\(237\) 1446.57 205.664i 0.396477 0.0563684i
\(238\) 0 0
\(239\) 928.725 338.028i 0.251356 0.0914863i −0.213269 0.976993i \(-0.568411\pi\)
0.464626 + 0.885507i \(0.346189\pi\)
\(240\) 0 0
\(241\) 157.896 + 895.472i 0.0422032 + 0.239346i 0.998611 0.0526883i \(-0.0167790\pi\)
−0.956408 + 0.292034i \(0.905668\pi\)
\(242\) 0 0
\(243\) −627.907 + 3735.59i −0.165762 + 0.986166i
\(244\) 0 0
\(245\) −268.185 1520.95i −0.0699335 0.396612i
\(246\) 0 0
\(247\) 66.3381 24.1451i 0.0170890 0.00621990i
\(248\) 0 0
\(249\) −5006.14 + 711.739i −1.27410 + 0.181143i
\(250\) 0 0
\(251\) 2208.59 + 3825.39i 0.555398 + 0.961977i 0.997872 + 0.0651964i \(0.0207674\pi\)
−0.442475 + 0.896781i \(0.645899\pi\)
\(252\) 0 0
\(253\) −178.609 + 309.360i −0.0443837 + 0.0768748i
\(254\) 0 0
\(255\) −1231.82 3770.62i −0.302509 0.925981i
\(256\) 0 0
\(257\) −1181.55 + 6700.91i −0.286782 + 1.62642i 0.412066 + 0.911154i \(0.364807\pi\)
−0.698848 + 0.715270i \(0.746304\pi\)
\(258\) 0 0
\(259\) 1925.94 1616.06i 0.462054 0.387710i
\(260\) 0 0
\(261\) −679.672 6273.42i −0.161190 1.48780i
\(262\) 0 0
\(263\) 817.417 + 297.515i 0.191650 + 0.0697551i 0.436062 0.899916i \(-0.356373\pi\)
−0.244412 + 0.969671i \(0.578595\pi\)
\(264\) 0 0
\(265\) 2396.82 + 2011.17i 0.555605 + 0.466208i
\(266\) 0 0
\(267\) −4866.00 + 2597.30i −1.11533 + 0.595325i
\(268\) 0 0
\(269\) −4222.12 −0.956977 −0.478489 0.878094i \(-0.658815\pi\)
−0.478489 + 0.878094i \(0.658815\pi\)
\(270\) 0 0
\(271\) 7100.72 1.59165 0.795826 0.605525i \(-0.207037\pi\)
0.795826 + 0.605525i \(0.207037\pi\)
\(272\) 0 0
\(273\) −1973.72 1228.93i −0.437564 0.272448i
\(274\) 0 0
\(275\) 394.089 + 330.680i 0.0864162 + 0.0725118i
\(276\) 0 0
\(277\) −6209.30 2260.00i −1.34686 0.490218i −0.434895 0.900481i \(-0.643215\pi\)
−0.911967 + 0.410263i \(0.865437\pi\)
\(278\) 0 0
\(279\) −3119.90 + 905.434i −0.669475 + 0.194290i
\(280\) 0 0
\(281\) 1603.24 1345.28i 0.340360 0.285596i −0.456546 0.889700i \(-0.650913\pi\)
0.796905 + 0.604104i \(0.206469\pi\)
\(282\) 0 0
\(283\) 1511.14 8570.09i 0.317413 1.80014i −0.240946 0.970538i \(-0.577458\pi\)
0.558359 0.829599i \(-0.311431\pi\)
\(284\) 0 0
\(285\) 87.2114 + 18.3915i 0.0181262 + 0.00382253i
\(286\) 0 0
\(287\) −161.654 + 279.993i −0.0332479 + 0.0575870i
\(288\) 0 0
\(289\) −1540.16 2667.64i −0.313487 0.542975i
\(290\) 0 0
\(291\) −664.358 847.540i −0.133833 0.170734i
\(292\) 0 0
\(293\) 7336.53 2670.28i 1.46282 0.532421i 0.516676 0.856181i \(-0.327169\pi\)
0.946139 + 0.323760i \(0.104947\pi\)
\(294\) 0 0
\(295\) −236.807 1343.00i −0.0467371 0.265059i
\(296\) 0 0
\(297\) 780.279 + 1144.91i 0.152446 + 0.223686i
\(298\) 0 0
\(299\) 220.730 + 1251.82i 0.0426928 + 0.242123i
\(300\) 0 0
\(301\) 6412.34 2333.90i 1.22791 0.446923i
\(302\) 0 0
\(303\) 2606.19 6480.39i 0.494131 1.22868i
\(304\) 0 0
\(305\) 1752.01 + 3034.58i 0.328918 + 0.569703i
\(306\) 0 0
\(307\) 2400.44 4157.68i 0.446255 0.772936i −0.551884 0.833921i \(-0.686091\pi\)
0.998139 + 0.0609852i \(0.0194242\pi\)
\(308\) 0 0
\(309\) 3285.76 3660.97i 0.604920 0.673998i
\(310\) 0 0
\(311\) −1262.48 + 7159.88i −0.230189 + 1.30546i 0.622325 + 0.782759i \(0.286188\pi\)
−0.852513 + 0.522705i \(0.824923\pi\)
\(312\) 0 0
\(313\) 22.5342 18.9084i 0.00406935 0.00341459i −0.640751 0.767749i \(-0.721377\pi\)
0.644820 + 0.764334i \(0.276932\pi\)
\(314\) 0 0
\(315\) −1295.26 2634.24i −0.231681 0.471183i
\(316\) 0 0
\(317\) −3605.13 1312.16i −0.638752 0.232487i 0.00228399 0.999997i \(-0.499273\pi\)
−0.641036 + 0.767511i \(0.721495\pi\)
\(318\) 0 0
\(319\) −1768.05 1483.57i −0.310320 0.260389i
\(320\) 0 0
\(321\) −174.362 + 5233.20i −0.0303176 + 0.909934i
\(322\) 0 0
\(323\) 179.604 0.0309395
\(324\) 0 0
\(325\) 1830.62 0.312444
\(326\) 0 0
\(327\) 93.9129 2818.64i 0.0158819 0.476670i
\(328\) 0 0
\(329\) −183.854 154.272i −0.0308091 0.0258519i
\(330\) 0 0
\(331\) 2593.45 + 943.938i 0.430661 + 0.156748i 0.548250 0.836315i \(-0.315294\pi\)
−0.117589 + 0.993062i \(0.537516\pi\)
\(332\) 0 0
\(333\) −2967.02 + 4429.30i −0.488263 + 0.728902i
\(334\) 0 0
\(335\) 5742.45 4818.49i 0.936548 0.785857i
\(336\) 0 0
\(337\) −1738.35 + 9858.65i −0.280990 + 1.59358i 0.438275 + 0.898841i \(0.355590\pi\)
−0.719266 + 0.694735i \(0.755522\pi\)
\(338\) 0 0
\(339\) 6995.96 7794.86i 1.12085 1.24885i
\(340\) 0 0
\(341\) −594.118 + 1029.04i −0.0943499 + 0.163419i
\(342\) 0 0
\(343\) −3335.21 5776.75i −0.525027 0.909374i
\(344\) 0 0
\(345\) −598.807 + 1488.96i −0.0934455 + 0.232356i
\(346\) 0 0
\(347\) 376.101 136.890i 0.0581849 0.0211776i −0.312764 0.949831i \(-0.601255\pi\)
0.370949 + 0.928653i \(0.379033\pi\)
\(348\) 0 0
\(349\) −124.917 708.438i −0.0191594 0.108659i 0.973728 0.227713i \(-0.0731248\pi\)
−0.992888 + 0.119054i \(0.962014\pi\)
\(350\) 0 0
\(351\) 4745.74 + 1336.19i 0.721678 + 0.203193i
\(352\) 0 0
\(353\) −27.6907 157.042i −0.00417515 0.0236784i 0.982649 0.185475i \(-0.0593823\pi\)
−0.986824 + 0.161796i \(0.948271\pi\)
\(354\) 0 0
\(355\) 1108.93 403.618i 0.165791 0.0603431i
\(356\) 0 0
\(357\) −3649.23 4655.43i −0.541002 0.690172i
\(358\) 0 0
\(359\) −4825.04 8357.21i −0.709348 1.22863i −0.965099 0.261884i \(-0.915656\pi\)
0.255752 0.966743i \(-0.417677\pi\)
\(360\) 0 0
\(361\) 3427.48 5936.57i 0.499706 0.865516i
\(362\) 0 0
\(363\) −6271.37 1322.53i −0.906781 0.191226i
\(364\) 0 0
\(365\) −1643.54 + 9321.00i −0.235691 + 1.33667i
\(366\) 0 0
\(367\) −6305.46 + 5290.91i −0.896845 + 0.752543i −0.969571 0.244809i \(-0.921275\pi\)
0.0727258 + 0.997352i \(0.476830\pi\)
\(368\) 0 0
\(369\) 163.726 665.738i 0.0230981 0.0939212i
\(370\) 0 0
\(371\) 4384.36 + 1595.78i 0.613543 + 0.223311i
\(372\) 0 0
\(373\) 5136.29 + 4309.86i 0.712995 + 0.598274i 0.925438 0.378899i \(-0.123697\pi\)
−0.212443 + 0.977174i \(0.568142\pi\)
\(374\) 0 0
\(375\) 6669.95 + 4153.02i 0.918492 + 0.571896i
\(376\) 0 0
\(377\) −8212.94 −1.12198
\(378\) 0 0
\(379\) −7620.82 −1.03286 −0.516432 0.856328i \(-0.672740\pi\)
−0.516432 + 0.856328i \(0.672740\pi\)
\(380\) 0 0
\(381\) −6702.40 + 3577.50i −0.901245 + 0.481052i
\(382\) 0 0
\(383\) −8850.82 7426.72i −1.18082 0.990829i −0.999973 0.00731893i \(-0.997670\pi\)
−0.180851 0.983510i \(-0.557885\pi\)
\(384\) 0 0
\(385\) −1008.94 367.224i −0.133559 0.0486116i
\(386\) 0 0
\(387\) −11679.2 + 8542.68i −1.53407 + 1.12209i
\(388\) 0 0
\(389\) 596.696 500.687i 0.0777729 0.0652592i −0.603072 0.797686i \(-0.706057\pi\)
0.680845 + 0.732427i \(0.261613\pi\)
\(390\) 0 0
\(391\) −561.566 + 3184.80i −0.0726333 + 0.411924i
\(392\) 0 0
\(393\) 2738.18 + 8381.58i 0.351458 + 1.07581i
\(394\) 0 0
\(395\) 1200.50 2079.32i 0.152920 0.264866i
\(396\) 0 0
\(397\) 420.795 + 728.838i 0.0531967 + 0.0921394i 0.891398 0.453222i \(-0.149726\pi\)
−0.838201 + 0.545362i \(0.816392\pi\)
\(398\) 0 0
\(399\) 131.588 18.7082i 0.0165103 0.00234733i
\(400\) 0 0
\(401\) 14884.6 5417.54i 1.85362 0.674661i 0.870364 0.492409i \(-0.163883\pi\)
0.983252 0.182252i \(-0.0583388\pi\)
\(402\) 0 0
\(403\) 734.227 + 4164.01i 0.0907555 + 0.514700i
\(404\) 0 0
\(405\) 4194.63 + 4599.05i 0.514648 + 0.564269i
\(406\) 0 0
\(407\) 338.610 + 1920.35i 0.0412390 + 0.233878i
\(408\) 0 0
\(409\) 4496.30 1636.52i 0.543588 0.197850i −0.0556071 0.998453i \(-0.517709\pi\)
0.599196 + 0.800603i \(0.295487\pi\)
\(410\) 0 0
\(411\) 9583.70 1362.55i 1.15019 0.163527i
\(412\) 0 0
\(413\) −1016.79 1761.14i −0.121146 0.209831i
\(414\) 0 0
\(415\) −4154.55 + 7195.88i −0.491418 + 0.851161i
\(416\) 0 0
\(417\) −1715.93 5252.46i −0.201509 0.616821i
\(418\) 0 0
\(419\) −1644.96 + 9329.01i −0.191793 + 1.08771i 0.725119 + 0.688624i \(0.241785\pi\)
−0.916912 + 0.399090i \(0.869326\pi\)
\(420\) 0 0
\(421\) −7997.87 + 6711.01i −0.925873 + 0.776900i −0.975072 0.221889i \(-0.928778\pi\)
0.0491989 + 0.998789i \(0.484333\pi\)
\(422\) 0 0
\(423\) 465.590 + 205.511i 0.0535171 + 0.0236224i
\(424\) 0 0
\(425\) 4376.46 + 1592.90i 0.499504 + 0.181805i
\(426\) 0 0
\(427\) 4002.77 + 3358.72i 0.453647 + 0.380655i
\(428\) 0 0
\(429\) 1590.88 849.155i 0.179041 0.0955655i
\(430\) 0 0
\(431\) −8608.62 −0.962094 −0.481047 0.876695i \(-0.659743\pi\)
−0.481047 + 0.876695i \(0.659743\pi\)
\(432\) 0 0
\(433\) −4458.02 −0.494778 −0.247389 0.968916i \(-0.579573\pi\)
−0.247389 + 0.968916i \(0.579573\pi\)
\(434\) 0 0
\(435\) −8802.32 5480.73i −0.970205 0.604095i
\(436\) 0 0
\(437\) −55.6640 46.7076i −0.00609330 0.00511288i
\(438\) 0 0
\(439\) −621.671 226.270i −0.0675871 0.0245997i 0.308005 0.951385i \(-0.400339\pi\)
−0.375592 + 0.926785i \(0.622561\pi\)
\(440\) 0 0
\(441\) 3523.82 + 3381.18i 0.380501 + 0.365099i
\(442\) 0 0
\(443\) 12445.6 10443.1i 1.33478 1.12001i 0.351847 0.936057i \(-0.385554\pi\)
0.982934 0.183957i \(-0.0588908\pi\)
\(444\) 0 0
\(445\) −1573.92 + 8926.14i −0.167665 + 0.950876i
\(446\) 0 0
\(447\) 16939.0 + 3572.17i 1.79237 + 0.377982i
\(448\) 0 0
\(449\) −6286.72 + 10888.9i −0.660777 + 1.14450i 0.319635 + 0.947541i \(0.396440\pi\)
−0.980412 + 0.196959i \(0.936894\pi\)
\(450\) 0 0
\(451\) −125.380 217.164i −0.0130907 0.0226738i
\(452\) 0 0
\(453\) 8200.75 + 10461.9i 0.850562 + 1.08509i
\(454\) 0 0
\(455\) −3590.23 + 1306.74i −0.369918 + 0.134639i
\(456\) 0 0
\(457\) 344.908 + 1956.07i 0.0353044 + 0.200221i 0.997358 0.0726379i \(-0.0231418\pi\)
−0.962054 + 0.272859i \(0.912031\pi\)
\(458\) 0 0
\(459\) 10183.0 + 7323.92i 1.03551 + 0.744774i
\(460\) 0 0
\(461\) −2257.12 12800.8i −0.228036 1.29326i −0.856795 0.515657i \(-0.827548\pi\)
0.628759 0.777600i \(-0.283563\pi\)
\(462\) 0 0
\(463\) −11058.6 + 4024.98i −1.11001 + 0.404010i −0.830997 0.556277i \(-0.812229\pi\)
−0.279013 + 0.960287i \(0.590007\pi\)
\(464\) 0 0
\(465\) −1991.85 + 4952.80i −0.198644 + 0.493937i
\(466\) 0 0
\(467\) −8253.92 14296.2i −0.817871 1.41659i −0.907248 0.420597i \(-0.861821\pi\)
0.0893763 0.995998i \(-0.471513\pi\)
\(468\) 0 0
\(469\) 5589.23 9680.84i 0.550292 0.953133i
\(470\) 0 0
\(471\) 9720.56 10830.6i 0.950955 1.05955i
\(472\) 0 0
\(473\) −919.056 + 5212.23i −0.0893409 + 0.506677i
\(474\) 0 0
\(475\) −80.1642 + 67.2657i −0.00774355 + 0.00649761i
\(476\) 0 0
\(477\) −9871.74 658.555i −0.947581 0.0632141i
\(478\) 0 0
\(479\) −8477.76 3085.65i −0.808682 0.294336i −0.0956026 0.995420i \(-0.530478\pi\)
−0.713079 + 0.701083i \(0.752700\pi\)
\(480\) 0 0
\(481\) 5315.46 + 4460.20i 0.503876 + 0.422802i
\(482\) 0 0
\(483\) −79.6929 + 2391.85i −0.00750756 + 0.225327i
\(484\) 0 0
\(485\) −1769.61 −0.165678
\(486\) 0 0
\(487\) −14156.8 −1.31726 −0.658632 0.752465i \(-0.728865\pi\)
−0.658632 + 0.752465i \(0.728865\pi\)
\(488\) 0 0
\(489\) 264.621 7942.16i 0.0244715 0.734472i
\(490\) 0 0
\(491\) −3325.98 2790.83i −0.305702 0.256514i 0.477011 0.878897i \(-0.341720\pi\)
−0.782713 + 0.622383i \(0.786165\pi\)
\(492\) 0 0
\(493\) −19634.7 7146.44i −1.79372 0.652859i
\(494\) 0 0
\(495\) 2271.71 + 151.548i 0.206275 + 0.0137608i
\(496\) 0 0
\(497\) 1348.07 1131.16i 0.121668 0.102092i
\(498\) 0 0
\(499\) 1245.95 7066.16i 0.111777 0.633917i −0.876519 0.481367i \(-0.840140\pi\)
0.988296 0.152550i \(-0.0487485\pi\)
\(500\) 0 0
\(501\) 13370.5 14897.3i 1.19232 1.32847i
\(502\) 0 0
\(503\) 8090.46 14013.1i 0.717168 1.24217i −0.244949 0.969536i \(-0.578771\pi\)
0.962117 0.272636i \(-0.0878954\pi\)
\(504\) 0 0
\(505\) −5738.92 9940.10i −0.505700 0.875898i
\(506\) 0 0
\(507\) −1865.23 + 4637.96i −0.163388 + 0.406270i
\(508\) 0 0
\(509\) 16489.7 6001.77i 1.43594 0.522640i 0.497313 0.867571i \(-0.334320\pi\)
0.938628 + 0.344931i \(0.112098\pi\)
\(510\) 0 0
\(511\) 2450.87 + 13899.6i 0.212172 + 1.20329i
\(512\) 0 0
\(513\) −256.918 + 115.868i −0.0221115 + 0.00997216i
\(514\) 0 0
\(515\) −1403.70 7960.76i −0.120105 0.681152i
\(516\) 0 0
\(517\) 174.923 63.6666i 0.0148802 0.00541597i
\(518\) 0 0
\(519\) −5874.64 7494.45i −0.496856 0.633853i
\(520\) 0 0
\(521\) 525.762 + 910.646i 0.0442112 + 0.0765761i 0.887284 0.461223i \(-0.152589\pi\)
−0.843073 + 0.537799i \(0.819256\pi\)
\(522\) 0 0
\(523\) 5220.14 9041.55i 0.436445 0.755946i −0.560967 0.827838i \(-0.689571\pi\)
0.997412 + 0.0718925i \(0.0229039\pi\)
\(524\) 0 0
\(525\) 3372.35 + 711.176i 0.280345 + 0.0591205i
\(526\) 0 0
\(527\) −1867.97 + 10593.8i −0.154402 + 0.875659i
\(528\) 0 0
\(529\) −8318.18 + 6979.79i −0.683668 + 0.573665i
\(530\) 0 0
\(531\) 3111.53 + 2985.58i 0.254291 + 0.243998i
\(532\) 0 0
\(533\) −838.496 305.188i −0.0681413 0.0248014i
\(534\) 0 0
\(535\) 6591.24 + 5530.71i 0.532643 + 0.446941i
\(536\) 0 0
\(537\) −1689.02 1051.66i −0.135730 0.0845115i
\(538\) 0 0
\(539\) 1786.26 0.142745
\(540\) 0 0
\(541\) 19911.0 1.58233 0.791165 0.611603i \(-0.209475\pi\)
0.791165 + 0.611603i \(0.209475\pi\)
\(542\) 0 0
\(543\) −1378.97 + 736.047i −0.108982 + 0.0581709i
\(544\) 0 0
\(545\) −3550.09 2978.88i −0.279026 0.234131i
\(546\) 0 0
\(547\) 181.433 + 66.0364i 0.0141820 + 0.00516181i 0.349101 0.937085i \(-0.386487\pi\)
−0.334919 + 0.942247i \(0.608709\pi\)
\(548\) 0 0
\(549\) −10136.6 4474.27i −0.788011 0.347827i
\(550\) 0 0
\(551\) 359.651 301.783i 0.0278070 0.0233329i
\(552\) 0 0
\(553\) 621.728 3525.99i 0.0478093 0.271140i
\(554\) 0 0
\(555\) 2720.49 + 8327.44i 0.208069 + 0.636901i
\(556\) 0 0
\(557\) −5088.83 + 8814.12i −0.387111 + 0.670496i −0.992060 0.125769i \(-0.959860\pi\)
0.604949 + 0.796264i \(0.293194\pi\)
\(558\) 0 0
\(559\) 9416.71 + 16310.2i 0.712494 + 1.23408i
\(560\) 0 0
\(561\) 4542.21 645.780i 0.341840 0.0486005i
\(562\) 0 0
\(563\) 10169.9 3701.53i 0.761295 0.277089i 0.0679443 0.997689i \(-0.478356\pi\)
0.693351 + 0.720600i \(0.256134\pi\)
\(564\) 0 0
\(565\) −2988.72 16949.9i −0.222542 1.26210i
\(566\) 0 0
\(567\) 8223.47 + 4305.20i 0.609089 + 0.318874i
\(568\) 0 0
\(569\) −2827.77 16037.1i −0.208341 1.18156i −0.892095 0.451849i \(-0.850765\pi\)
0.683753 0.729713i \(-0.260346\pi\)
\(570\) 0 0
\(571\) 13023.1 4740.01i 0.954464 0.347396i 0.182602 0.983187i \(-0.441548\pi\)
0.771862 + 0.635791i \(0.219326\pi\)
\(572\) 0 0
\(573\) −16778.2 + 2385.40i −1.22324 + 0.173912i
\(574\) 0 0
\(575\) −942.129 1631.82i −0.0683296 0.118350i
\(576\) 0 0
\(577\) 8766.90 15184.7i 0.632532 1.09558i −0.354501 0.935056i \(-0.615349\pi\)
0.987032 0.160521i \(-0.0513175\pi\)
\(578\) 0 0
\(579\) −3060.55 9368.35i −0.219675 0.672427i
\(580\) 0 0
\(581\) −2151.61 + 12202.4i −0.153638 + 0.871324i
\(582\) 0 0
\(583\) −2772.14 + 2326.10i −0.196930 + 0.165244i
\(584\) 0 0
\(585\) 6539.12 4783.00i 0.462152 0.338039i
\(586\) 0 0
\(587\) 17793.1 + 6476.17i 1.25111 + 0.455367i 0.880777 0.473532i \(-0.157021\pi\)
0.370333 + 0.928899i \(0.379243\pi\)
\(588\) 0 0
\(589\) −185.158 155.366i −0.0129530 0.0108689i
\(590\) 0 0
\(591\) 4459.01 2380.06i 0.310354 0.165656i
\(592\) 0 0
\(593\) 8252.04 0.571451 0.285726 0.958311i \(-0.407765\pi\)
0.285726 + 0.958311i \(0.407765\pi\)
\(594\) 0 0
\(595\) −9720.22 −0.669732
\(596\) 0 0
\(597\) −12373.8 7704.51i −0.848285 0.528182i
\(598\) 0 0
\(599\) −12055.4 10115.7i −0.822320 0.690008i 0.131194 0.991357i \(-0.458119\pi\)
−0.953514 + 0.301348i \(0.902563\pi\)
\(600\) 0 0
\(601\) 3323.58 + 1209.69i 0.225577 + 0.0821033i 0.452336 0.891848i \(-0.350591\pi\)
−0.226759 + 0.973951i \(0.572813\pi\)
\(602\) 0 0
\(603\) −5660.85 + 23018.1i −0.382301 + 1.55451i
\(604\) 0 0
\(605\) −8068.07 + 6769.92i −0.542171 + 0.454936i
\(606\) 0 0
\(607\) −202.364 + 1147.67i −0.0135317 + 0.0767419i −0.990826 0.135145i \(-0.956850\pi\)
0.977294 + 0.211887i \(0.0679610\pi\)
\(608\) 0 0
\(609\) −15129.8 3190.64i −1.00672 0.212301i
\(610\) 0 0
\(611\) 331.198 573.651i 0.0219293 0.0379827i
\(612\) 0 0
\(613\) −1701.46 2947.01i −0.112107 0.194174i 0.804513 0.593935i \(-0.202426\pi\)
−0.916619 + 0.399761i \(0.869093\pi\)
\(614\) 0 0
\(615\) −695.008 886.642i −0.0455698 0.0581347i
\(616\) 0 0
\(617\) −6455.20 + 2349.50i −0.421194 + 0.153302i −0.543917 0.839139i \(-0.683059\pi\)
0.122723 + 0.992441i \(0.460837\pi\)
\(618\) 0 0
\(619\) 1533.49 + 8696.87i 0.0995739 + 0.564712i 0.993249 + 0.115998i \(0.0370066\pi\)
−0.893676 + 0.448714i \(0.851882\pi\)
\(620\) 0 0
\(621\) −1251.31 4918.04i −0.0808591 0.317800i
\(622\) 0 0
\(623\) 2347.05 + 13310.8i 0.150935 + 0.855994i
\(624\) 0 0
\(625\) 6013.91 2188.88i 0.384890 0.140089i
\(626\) 0 0
\(627\) −38.4639 + 95.6419i −0.00244992 + 0.00609182i
\(628\) 0 0
\(629\) 8826.66 + 15288.2i 0.559526 + 0.969128i
\(630\) 0 0
\(631\) −14372.3 + 24893.6i −0.906739 + 1.57052i −0.0881735 + 0.996105i \(0.528103\pi\)
−0.818566 + 0.574413i \(0.805230\pi\)
\(632\) 0 0
\(633\) 27.6608 30.8195i 0.00173684 0.00193518i
\(634\) 0 0
\(635\) −2167.91 + 12294.8i −0.135482 + 0.768354i
\(636\) 0 0
\(637\) 4869.17 4085.72i 0.302863 0.254132i
\(638\) 0 0
\(639\) −2076.77 + 3100.30i −0.128569 + 0.191934i
\(640\) 0 0
\(641\) 383.429 + 139.557i 0.0236264 + 0.00859932i 0.353806 0.935319i \(-0.384887\pi\)
−0.330180 + 0.943918i \(0.607109\pi\)
\(642\) 0 0
\(643\) −19820.7 16631.6i −1.21563 1.02004i −0.999041 0.0437759i \(-0.986061\pi\)
−0.216593 0.976262i \(-0.569494\pi\)
\(644\) 0 0
\(645\) −791.805 + 23764.7i −0.0483369 + 1.45075i
\(646\) 0 0
\(647\) −17713.1 −1.07631 −0.538156 0.842845i \(-0.680879\pi\)
−0.538156 + 0.842845i \(0.680879\pi\)
\(648\) 0 0
\(649\) 1577.26 0.0953976
\(650\) 0 0
\(651\) −265.087 + 7956.15i −0.0159594 + 0.478995i
\(652\) 0 0
\(653\) 15919.4 + 13357.9i 0.954017 + 0.800516i 0.979970 0.199147i \(-0.0638173\pi\)
−0.0259520 + 0.999663i \(0.508262\pi\)
\(654\) 0 0
\(655\) 13615.6 + 4955.67i 0.812222 + 0.295625i
\(656\) 0 0
\(657\) −13205.9 26857.6i −0.784189 1.59485i
\(658\) 0 0
\(659\) −17125.5 + 14370.0i −1.01232 + 0.849434i −0.988643 0.150286i \(-0.951981\pi\)
−0.0236732 + 0.999720i \(0.507536\pi\)
\(660\) 0 0
\(661\) −651.001 + 3692.01i −0.0383071 + 0.217251i −0.997952 0.0639633i \(-0.979626\pi\)
0.959645 + 0.281214i \(0.0907370\pi\)
\(662\) 0 0
\(663\) 10904.5 12149.8i 0.638759 0.711701i
\(664\) 0 0
\(665\) 109.203 189.146i 0.00636800 0.0110297i
\(666\) 0 0
\(667\) 4226.80 + 7321.03i 0.245371 + 0.424995i
\(668\) 0 0
\(669\) −6440.80 + 16015.3i −0.372221 + 0.925540i
\(670\) 0 0
\(671\) −3808.32 + 1386.11i −0.219104 + 0.0797472i
\(672\) 0 0
\(673\) −1678.26 9517.90i −0.0961252 0.545153i −0.994397 0.105712i \(-0.966288\pi\)
0.898271 0.439441i \(-0.144823\pi\)
\(674\) 0 0
\(675\) −7288.01 + 544.801i −0.415578 + 0.0310658i
\(676\) 0 0
\(677\) 2125.75 + 12055.7i 0.120678 + 0.684400i 0.983781 + 0.179372i \(0.0574067\pi\)
−0.863103 + 0.505028i \(0.831482\pi\)
\(678\) 0 0
\(679\) −2479.72 + 902.543i −0.140151 + 0.0510109i
\(680\) 0 0
\(681\) −10456.3 13339.3i −0.588377 0.750608i
\(682\) 0 0
\(683\) 9922.08 + 17185.5i 0.555868 + 0.962791i 0.997835 + 0.0657604i \(0.0209473\pi\)
−0.441968 + 0.897031i \(0.645719\pi\)
\(684\) 0 0
\(685\) 7953.41 13775.7i 0.443627 0.768384i
\(686\) 0 0
\(687\) 14.5818 + 3.07507i 0.000809796 + 0.000170773i
\(688\) 0 0
\(689\) −2236.09 + 12681.5i −0.123640 + 0.701199i
\(690\) 0 0
\(691\) 22107.7 18550.5i 1.21710 1.02127i 0.218129 0.975920i \(-0.430005\pi\)
0.998971 0.0453479i \(-0.0144396\pi\)
\(692\) 0 0
\(693\) 3260.60 946.266i 0.178730 0.0518697i
\(694\) 0 0
\(695\) −8532.45 3105.56i −0.465690 0.169497i
\(696\) 0 0
\(697\) −1739.04 1459.22i −0.0945060 0.0793000i
\(698\) 0 0
\(699\) −3701.36 2304.64i −0.200284 0.124706i
\(700\) 0 0
\(701\) 12315.2 0.663538 0.331769 0.943361i \(-0.392355\pi\)
0.331769 + 0.943361i \(0.392355\pi\)
\(702\) 0 0
\(703\) −396.658 −0.0212806
\(704\) 0 0
\(705\) 737.779 393.800i 0.0394133 0.0210374i
\(706\) 0 0
\(707\) −13111.5 11001.9i −0.697467 0.585245i
\(708\) 0 0
\(709\) 18496.8 + 6732.27i 0.979776 + 0.356609i 0.781753 0.623588i \(-0.214326\pi\)
0.198023 + 0.980197i \(0.436548\pi\)
\(710\) 0 0
\(711\) 817.765 + 7548.04i 0.0431345 + 0.398134i
\(712\) 0 0
\(713\) 3333.94 2797.50i 0.175115 0.146939i
\(714\) 0 0
\(715\) 514.574 2918.30i 0.0269147 0.152641i
\(716\) 0 0
\(717\) 1594.77 + 4881.61i 0.0830654 + 0.254264i
\(718\) 0 0
\(719\) 3523.96 6103.67i 0.182784 0.316590i −0.760044 0.649872i \(-0.774823\pi\)
0.942827 + 0.333281i \(0.108156\pi\)
\(720\) 0 0
\(721\) −6027.15 10439.3i −0.311322 0.539225i
\(722\) 0 0
\(723\) −4677.75 + 665.050i −0.240619 + 0.0342095i
\(724\) 0 0
\(725\) 11440.2 4163.89i 0.586039 0.213301i
\(726\) 0 0
\(727\) −598.760 3395.73i −0.0305458 0.173234i 0.965718 0.259592i \(-0.0835881\pi\)
−0.996264 + 0.0863584i \(0.972477\pi\)
\(728\) 0 0
\(729\) −19291.3 3907.27i −0.980099 0.198510i
\(730\) 0 0
\(731\) 8320.29 + 47186.7i 0.420981 + 2.38750i
\(732\) 0 0
\(733\) 708.598 257.909i 0.0357062 0.0129960i −0.324105 0.946021i \(-0.605063\pi\)
0.359812 + 0.933025i \(0.382841\pi\)
\(734\) 0 0
\(735\) 7945.12 1129.58i 0.398721 0.0566875i
\(736\) 0 0
\(737\) 4335.04 + 7508.52i 0.216667 + 0.375278i
\(738\) 0 0
\(739\) −9360.22 + 16212.4i −0.465929 + 0.807012i −0.999243 0.0389052i \(-0.987613\pi\)
0.533314 + 0.845917i \(0.320946\pi\)
\(740\) 0 0
\(741\) 113.913 + 348.690i 0.00564739 + 0.0172867i
\(742\) 0 0
\(743\) 4145.09 23508.0i 0.204668 1.16073i −0.693292 0.720656i \(-0.743841\pi\)
0.897961 0.440076i \(-0.145048\pi\)
\(744\) 0 0
\(745\) 21791.9 18285.6i 1.07167 0.899238i
\(746\) 0 0
\(747\) −2830.03 26121.4i −0.138615 1.27943i
\(748\) 0 0
\(749\) 12057.0 + 4388.38i 0.588187 + 0.214082i
\(750\) 0 0
\(751\) 2631.87 + 2208.40i 0.127880 + 0.107304i 0.704485 0.709719i \(-0.251178\pi\)
−0.576604 + 0.817024i \(0.695623\pi\)
\(752\) 0 0
\(753\) −20248.4 + 10807.9i −0.979939 + 0.523056i
\(754\) 0 0
\(755\) 21843.8 1.05295
\(756\) 0 0
\(757\) 16653.4 0.799573 0.399786 0.916608i \(-0.369084\pi\)
0.399786 + 0.916608i \(0.369084\pi\)
\(758\) 0 0
\(759\) −1575.69 981.096i −0.0753542 0.0469190i
\(760\) 0 0
\(761\) −15257.9 12802.9i −0.726806 0.609862i 0.202453 0.979292i \(-0.435109\pi\)
−0.929259 + 0.369430i \(0.879553\pi\)
\(762\) 0 0
\(763\) −6493.97 2363.61i −0.308123 0.112147i
\(764\) 0 0
\(765\) 19795.0 5744.75i 0.935541 0.271506i
\(766\) 0 0
\(767\) 4299.48 3607.69i 0.202406 0.169839i
\(768\) 0 0
\(769\) 3628.05 20575.7i 0.170131 0.964861i −0.773484 0.633816i \(-0.781488\pi\)
0.943615 0.331045i \(-0.107401\pi\)
\(770\) 0 0
\(771\) −34595.2 7295.58i −1.61597 0.340783i
\(772\) 0 0
\(773\) −8425.94 + 14594.1i −0.392057 + 0.679062i −0.992721 0.120439i \(-0.961570\pi\)
0.600664 + 0.799502i \(0.294903\pi\)
\(774\) 0 0
\(775\) −3133.86 5428.00i −0.145254 0.251586i
\(776\) 0 0
\(777\) 8059.36 + 10281.6i 0.372108 + 0.474709i
\(778\) 0 0
\(779\) 47.9325 17.4460i 0.00220457 0.000802398i
\(780\) 0 0
\(781\) 237.011 + 1344.16i 0.0108591 + 0.0615848i
\(782\) 0