Properties

Label 261.3.s.a.19.4
Level $261$
Weight $3$
Character 261.19
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 19.4
Character \(\chi\) \(=\) 261.19
Dual form 261.3.s.a.55.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.63282 + 2.59861i) q^{2} +(-2.35117 + 4.88225i) q^{4} +(4.43970 + 1.01333i) q^{5} +(10.7635 - 5.18344i) q^{7} +(-4.32723 + 0.487562i) q^{8} +O(q^{10})\) \(q+(1.63282 + 2.59861i) q^{2} +(-2.35117 + 4.88225i) q^{4} +(4.43970 + 1.01333i) q^{5} +(10.7635 - 5.18344i) q^{7} +(-4.32723 + 0.487562i) q^{8} +(4.61596 + 13.1917i) q^{10} +(-2.90150 - 0.326920i) q^{11} +(2.24911 - 1.79360i) q^{13} +(31.0446 + 19.5066i) q^{14} +(5.18193 + 6.49794i) q^{16} +(-2.44971 + 2.44971i) q^{17} +(-31.9711 + 11.1872i) q^{19} +(-15.3858 + 19.2932i) q^{20} +(-3.88808 - 8.07367i) q^{22} +(-9.24886 - 40.5219i) q^{23} +(-3.84011 - 1.84930i) q^{25} +(8.33326 + 2.91593i) q^{26} +64.7374i q^{28} +(-18.6826 + 22.1802i) q^{29} +(7.40308 + 11.7819i) q^{31} +(-14.1774 + 40.5168i) q^{32} +(-10.3658 - 2.36592i) q^{34} +(53.0394 - 12.1059i) q^{35} +(-19.6990 + 2.21954i) q^{37} +(-81.2741 - 64.8140i) q^{38} +(-19.7057 - 2.22030i) q^{40} +(15.2314 + 15.2314i) q^{41} +(1.58568 + 0.996350i) q^{43} +(8.41802 - 13.3972i) q^{44} +(90.1991 - 90.1991i) q^{46} +(0.858173 - 7.61650i) q^{47} +(58.4343 - 73.2743i) q^{49} +(-1.46458 - 12.9985i) q^{50} +(3.46879 + 15.1978i) q^{52} +(7.13045 - 31.2406i) q^{53} +(-12.5505 - 4.39161i) q^{55} +(-44.0490 + 27.6778i) q^{56} +(-88.1430 - 12.3325i) q^{58} +9.47914 q^{59} +(-19.5711 + 55.9310i) q^{61} +(-18.5288 + 38.4755i) q^{62} +(-96.0255 + 21.9172i) q^{64} +(11.8029 - 5.68397i) q^{65} +(-45.3801 - 36.1895i) q^{67} +(-6.20042 - 17.7198i) q^{68} +(118.062 + 118.062i) q^{70} +(61.2373 - 48.8352i) q^{71} +(40.7753 - 64.8935i) q^{73} +(-37.9326 - 47.5659i) q^{74} +(20.5509 - 182.394i) q^{76} +(-32.9249 + 11.5209i) q^{77} +(10.0312 + 89.0291i) q^{79} +(16.4217 + 34.0999i) q^{80} +(-14.7104 + 64.4505i) q^{82} +(-42.5654 - 20.4984i) q^{83} +(-13.3584 + 8.39361i) q^{85} +5.74743i q^{86} +12.7148 q^{88} +(31.5692 + 50.2421i) q^{89} +(14.9113 - 30.9636i) q^{91} +(219.584 + 50.1186i) q^{92} +(21.1936 - 10.2063i) q^{94} +(-153.279 + 17.2703i) q^{95} +(-41.8847 - 119.700i) q^{97} +(285.824 + 32.2047i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{9}{28}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.63282 + 2.59861i 0.816409 + 1.29931i 0.951244 + 0.308439i \(0.0998067\pi\)
−0.134835 + 0.990868i \(0.543050\pi\)
\(3\) 0 0
\(4\) −2.35117 + 4.88225i −0.587792 + 1.22056i
\(5\) 4.43970 + 1.01333i 0.887940 + 0.202667i 0.642079 0.766638i \(-0.278072\pi\)
0.245861 + 0.969305i \(0.420929\pi\)
\(6\) 0 0
\(7\) 10.7635 5.18344i 1.53765 0.740491i 0.542607 0.839986i \(-0.317437\pi\)
0.995038 + 0.0994954i \(0.0317229\pi\)
\(8\) −4.32723 + 0.487562i −0.540904 + 0.0609452i
\(9\) 0 0
\(10\) 4.61596 + 13.1917i 0.461596 + 1.31917i
\(11\) −2.90150 0.326920i −0.263772 0.0297200i −0.0209122 0.999781i \(-0.506657\pi\)
−0.242860 + 0.970061i \(0.578086\pi\)
\(12\) 0 0
\(13\) 2.24911 1.79360i 0.173008 0.137969i −0.533158 0.846016i \(-0.678995\pi\)
0.706166 + 0.708046i \(0.250423\pi\)
\(14\) 31.0446 + 19.5066i 2.21747 + 1.39333i
\(15\) 0 0
\(16\) 5.18193 + 6.49794i 0.323871 + 0.406121i
\(17\) −2.44971 + 2.44971i −0.144101 + 0.144101i −0.775477 0.631376i \(-0.782490\pi\)
0.631376 + 0.775477i \(0.282490\pi\)
\(18\) 0 0
\(19\) −31.9711 + 11.1872i −1.68269 + 0.588799i −0.991056 0.133450i \(-0.957395\pi\)
−0.691634 + 0.722248i \(0.743109\pi\)
\(20\) −15.3858 + 19.2932i −0.769292 + 0.964662i
\(21\) 0 0
\(22\) −3.88808 8.07367i −0.176731 0.366985i
\(23\) −9.24886 40.5219i −0.402124 1.76182i −0.618771 0.785571i \(-0.712369\pi\)
0.216647 0.976250i \(-0.430488\pi\)
\(24\) 0 0
\(25\) −3.84011 1.84930i −0.153604 0.0739720i
\(26\) 8.33326 + 2.91593i 0.320510 + 0.112151i
\(27\) 0 0
\(28\) 64.7374i 2.31205i
\(29\) −18.6826 + 22.1802i −0.644226 + 0.764835i
\(30\) 0 0
\(31\) 7.40308 + 11.7819i 0.238809 + 0.380063i 0.944529 0.328429i \(-0.106519\pi\)
−0.705720 + 0.708491i \(0.749376\pi\)
\(32\) −14.1774 + 40.5168i −0.443045 + 1.26615i
\(33\) 0 0
\(34\) −10.3658 2.36592i −0.304876 0.0695860i
\(35\) 53.0394 12.1059i 1.51541 0.345883i
\(36\) 0 0
\(37\) −19.6990 + 2.21954i −0.532405 + 0.0599876i −0.374075 0.927399i \(-0.622040\pi\)
−0.158330 + 0.987386i \(0.550611\pi\)
\(38\) −81.2741 64.8140i −2.13879 1.70563i
\(39\) 0 0
\(40\) −19.7057 2.22030i −0.492642 0.0555074i
\(41\) 15.2314 + 15.2314i 0.371497 + 0.371497i 0.868022 0.496526i \(-0.165391\pi\)
−0.496526 + 0.868022i \(0.665391\pi\)
\(42\) 0 0
\(43\) 1.58568 + 0.996350i 0.0368763 + 0.0231709i 0.550344 0.834938i \(-0.314497\pi\)
−0.513468 + 0.858109i \(0.671639\pi\)
\(44\) 8.41802 13.3972i 0.191319 0.304482i
\(45\) 0 0
\(46\) 90.1991 90.1991i 1.96085 1.96085i
\(47\) 0.858173 7.61650i 0.0182590 0.162053i −0.981274 0.192618i \(-0.938302\pi\)
0.999533 + 0.0305651i \(0.00973068\pi\)
\(48\) 0 0
\(49\) 58.4343 73.2743i 1.19254 1.49539i
\(50\) −1.46458 12.9985i −0.0292917 0.259971i
\(51\) 0 0
\(52\) 3.46879 + 15.1978i 0.0667075 + 0.292265i
\(53\) 7.13045 31.2406i 0.134537 0.589445i −0.862045 0.506832i \(-0.830816\pi\)
0.996582 0.0826126i \(-0.0263264\pi\)
\(54\) 0 0
\(55\) −12.5505 4.39161i −0.228191 0.0798475i
\(56\) −44.0490 + 27.6778i −0.786589 + 0.494246i
\(57\) 0 0
\(58\) −88.1430 12.3325i −1.51971 0.212630i
\(59\) 9.47914 0.160663 0.0803317 0.996768i \(-0.474402\pi\)
0.0803317 + 0.996768i \(0.474402\pi\)
\(60\) 0 0
\(61\) −19.5711 + 55.9310i −0.320838 + 0.916902i 0.664650 + 0.747155i \(0.268581\pi\)
−0.985488 + 0.169747i \(0.945705\pi\)
\(62\) −18.5288 + 38.4755i −0.298852 + 0.620573i
\(63\) 0 0
\(64\) −96.0255 + 21.9172i −1.50040 + 0.342456i
\(65\) 11.8029 5.68397i 0.181583 0.0874457i
\(66\) 0 0
\(67\) −45.3801 36.1895i −0.677315 0.540141i 0.223304 0.974749i \(-0.428316\pi\)
−0.900620 + 0.434608i \(0.856887\pi\)
\(68\) −6.20042 17.7198i −0.0911827 0.260585i
\(69\) 0 0
\(70\) 118.062 + 118.062i 1.68660 + 1.68660i
\(71\) 61.2373 48.8352i 0.862498 0.687819i −0.0888143 0.996048i \(-0.528308\pi\)
0.951312 + 0.308229i \(0.0997363\pi\)
\(72\) 0 0
\(73\) 40.7753 64.8935i 0.558566 0.888952i −0.441399 0.897311i \(-0.645518\pi\)
0.999965 + 0.00835868i \(0.00266068\pi\)
\(74\) −37.9326 47.5659i −0.512602 0.642783i
\(75\) 0 0
\(76\) 20.5509 182.394i 0.270406 2.39992i
\(77\) −32.9249 + 11.5209i −0.427596 + 0.149622i
\(78\) 0 0
\(79\) 10.0312 + 89.0291i 0.126977 + 1.12695i 0.881999 + 0.471252i \(0.156198\pi\)
−0.755022 + 0.655700i \(0.772374\pi\)
\(80\) 16.4217 + 34.0999i 0.205271 + 0.426249i
\(81\) 0 0
\(82\) −14.7104 + 64.4505i −0.179395 + 0.785981i
\(83\) −42.5654 20.4984i −0.512836 0.246969i 0.159523 0.987194i \(-0.449004\pi\)
−0.672359 + 0.740225i \(0.734719\pi\)
\(84\) 0 0
\(85\) −13.3584 + 8.39361i −0.157157 + 0.0987484i
\(86\) 5.74743i 0.0668306i
\(87\) 0 0
\(88\) 12.7148 0.144487
\(89\) 31.5692 + 50.2421i 0.354710 + 0.564518i 0.975648 0.219342i \(-0.0703909\pi\)
−0.620938 + 0.783860i \(0.713248\pi\)
\(90\) 0 0
\(91\) 14.9113 30.9636i 0.163860 0.340259i
\(92\) 219.584 + 50.1186i 2.38678 + 0.544767i
\(93\) 0 0
\(94\) 21.1936 10.2063i 0.225464 0.108578i
\(95\) −153.279 + 17.2703i −1.61346 + 0.181793i
\(96\) 0 0
\(97\) −41.8847 119.700i −0.431802 1.23402i −0.930195 0.367067i \(-0.880362\pi\)
0.498393 0.866951i \(-0.333924\pi\)
\(98\) 285.824 + 32.2047i 2.91657 + 0.328619i
\(99\) 0 0
\(100\) 18.0575 14.4004i 0.180575 0.144004i
\(101\) 59.5271 + 37.4034i 0.589377 + 0.370330i 0.793459 0.608623i \(-0.208278\pi\)
−0.204082 + 0.978954i \(0.565421\pi\)
\(102\) 0 0
\(103\) −54.4757 68.3104i −0.528891 0.663208i 0.443580 0.896235i \(-0.353708\pi\)
−0.972470 + 0.233027i \(0.925137\pi\)
\(104\) −8.85791 + 8.85791i −0.0851722 + 0.0851722i
\(105\) 0 0
\(106\) 92.8249 32.4808i 0.875707 0.306423i
\(107\) −24.4898 + 30.7092i −0.228877 + 0.287002i −0.882987 0.469397i \(-0.844471\pi\)
0.654111 + 0.756399i \(0.273043\pi\)
\(108\) 0 0
\(109\) 48.7351 + 101.200i 0.447111 + 0.928436i 0.995726 + 0.0923607i \(0.0294413\pi\)
−0.548614 + 0.836076i \(0.684844\pi\)
\(110\) −9.08058 39.7846i −0.0825507 0.361678i
\(111\) 0 0
\(112\) 89.4575 + 43.0805i 0.798728 + 0.384647i
\(113\) 32.7521 + 11.4605i 0.289842 + 0.101420i 0.471284 0.881982i \(-0.343791\pi\)
−0.181442 + 0.983402i \(0.558076\pi\)
\(114\) 0 0
\(115\) 189.277i 1.64589i
\(116\) −64.3635 143.362i −0.554858 1.23588i
\(117\) 0 0
\(118\) 15.4777 + 24.6326i 0.131167 + 0.208751i
\(119\) −13.6696 + 39.0654i −0.114870 + 0.328281i
\(120\) 0 0
\(121\) −109.654 25.0279i −0.906235 0.206842i
\(122\) −177.299 + 40.4674i −1.45327 + 0.331700i
\(123\) 0 0
\(124\) −74.9283 + 8.44239i −0.604261 + 0.0680838i
\(125\) −104.184 83.0841i −0.833473 0.664672i
\(126\) 0 0
\(127\) 159.395 + 17.9595i 1.25508 + 0.141413i 0.714353 0.699786i \(-0.246721\pi\)
0.540725 + 0.841199i \(0.318150\pi\)
\(128\) −92.3344 92.3344i −0.721363 0.721363i
\(129\) 0 0
\(130\) 34.0424 + 21.3903i 0.261865 + 0.164540i
\(131\) 81.0335 128.964i 0.618577 0.984459i −0.379662 0.925125i \(-0.623960\pi\)
0.998238 0.0593336i \(-0.0188976\pi\)
\(132\) 0 0
\(133\) −286.134 + 286.134i −2.15138 + 2.15138i
\(134\) 19.9449 177.016i 0.148843 1.32102i
\(135\) 0 0
\(136\) 9.40608 11.7948i 0.0691623 0.0867268i
\(137\) −6.05776 53.7641i −0.0442172 0.392439i −0.996255 0.0864595i \(-0.972445\pi\)
0.952038 0.305979i \(-0.0989839\pi\)
\(138\) 0 0
\(139\) −10.2366 44.8495i −0.0736447 0.322658i 0.924665 0.380782i \(-0.124345\pi\)
−0.998309 + 0.0581239i \(0.981488\pi\)
\(140\) −65.6005 + 287.415i −0.468575 + 2.05296i
\(141\) 0 0
\(142\) 226.893 + 79.3934i 1.59784 + 0.559108i
\(143\) −7.11214 + 4.46885i −0.0497352 + 0.0312507i
\(144\) 0 0
\(145\) −105.421 + 79.5419i −0.727041 + 0.548565i
\(146\) 235.212 1.61104
\(147\) 0 0
\(148\) 35.4793 101.394i 0.239725 0.685094i
\(149\) −99.1793 + 205.948i −0.665633 + 1.38220i 0.245219 + 0.969468i \(0.421140\pi\)
−0.910852 + 0.412734i \(0.864574\pi\)
\(150\) 0 0
\(151\) 82.0279 18.7223i 0.543231 0.123989i 0.0579049 0.998322i \(-0.481558\pi\)
0.485326 + 0.874333i \(0.338701\pi\)
\(152\) 132.892 63.9973i 0.874289 0.421035i
\(153\) 0 0
\(154\) −83.6987 66.7475i −0.543498 0.433425i
\(155\) 20.9285 + 59.8101i 0.135022 + 0.385872i
\(156\) 0 0
\(157\) −137.989 137.989i −0.878912 0.878912i 0.114510 0.993422i \(-0.463470\pi\)
−0.993422 + 0.114510i \(0.963470\pi\)
\(158\) −214.973 + 171.436i −1.36059 + 1.08503i
\(159\) 0 0
\(160\) −104.001 + 165.516i −0.650004 + 1.03447i
\(161\) −309.593 388.217i −1.92294 2.41129i
\(162\) 0 0
\(163\) 4.35863 38.6839i 0.0267401 0.237325i −0.973232 0.229826i \(-0.926184\pi\)
0.999972 0.00749896i \(-0.00238702\pi\)
\(164\) −110.175 + 38.5519i −0.671798 + 0.235072i
\(165\) 0 0
\(166\) −16.2341 144.081i −0.0977955 0.867959i
\(167\) 8.15009 + 16.9238i 0.0488029 + 0.101340i 0.923944 0.382527i \(-0.124946\pi\)
−0.875141 + 0.483867i \(0.839232\pi\)
\(168\) 0 0
\(169\) −35.7646 + 156.695i −0.211625 + 0.927188i
\(170\) −43.6235 21.0080i −0.256609 0.123576i
\(171\) 0 0
\(172\) −8.59264 + 5.39911i −0.0499572 + 0.0313902i
\(173\) 216.808i 1.25322i 0.779332 + 0.626612i \(0.215559\pi\)
−0.779332 + 0.626612i \(0.784441\pi\)
\(174\) 0 0
\(175\) −50.9188 −0.290965
\(176\) −12.9111 20.5478i −0.0733583 0.116749i
\(177\) 0 0
\(178\) −79.0131 + 164.072i −0.443894 + 0.921755i
\(179\) 64.5460 + 14.7322i 0.360592 + 0.0823028i 0.398979 0.916960i \(-0.369365\pi\)
−0.0383867 + 0.999263i \(0.512222\pi\)
\(180\) 0 0
\(181\) −31.6029 + 15.2191i −0.174602 + 0.0840837i −0.519143 0.854687i \(-0.673749\pi\)
0.344541 + 0.938771i \(0.388034\pi\)
\(182\) 104.810 11.8092i 0.575878 0.0648859i
\(183\) 0 0
\(184\) 59.7788 + 170.838i 0.324885 + 0.928468i
\(185\) −89.7067 10.1075i −0.484901 0.0546353i
\(186\) 0 0
\(187\) 7.90869 6.30697i 0.0422924 0.0337271i
\(188\) 35.1680 + 22.0975i 0.187064 + 0.117540i
\(189\) 0 0
\(190\) −295.155 370.112i −1.55345 1.94796i
\(191\) −100.170 + 100.170i −0.524450 + 0.524450i −0.918912 0.394463i \(-0.870931\pi\)
0.394463 + 0.918912i \(0.370931\pi\)
\(192\) 0 0
\(193\) 27.8003 9.72774i 0.144043 0.0504028i −0.257295 0.966333i \(-0.582831\pi\)
0.401338 + 0.915930i \(0.368545\pi\)
\(194\) 242.663 304.290i 1.25084 1.56851i
\(195\) 0 0
\(196\) 220.355 + 457.571i 1.12426 + 2.33455i
\(197\) 28.3314 + 124.128i 0.143814 + 0.630092i 0.994529 + 0.104464i \(0.0333126\pi\)
−0.850714 + 0.525628i \(0.823830\pi\)
\(198\) 0 0
\(199\) 272.856 + 131.401i 1.37114 + 0.660304i 0.967090 0.254435i \(-0.0818894\pi\)
0.404046 + 0.914739i \(0.367604\pi\)
\(200\) 17.5187 + 6.13005i 0.0875934 + 0.0306503i
\(201\) 0 0
\(202\) 215.761i 1.06812i
\(203\) −86.1204 + 335.577i −0.424238 + 1.65309i
\(204\) 0 0
\(205\) 52.1883 + 83.0571i 0.254577 + 0.405157i
\(206\) 88.5635 253.100i 0.429920 1.22864i
\(207\) 0 0
\(208\) 23.3094 + 5.32023i 0.112065 + 0.0255780i
\(209\) 96.4213 22.0075i 0.461346 0.105299i
\(210\) 0 0
\(211\) 116.261 13.0995i 0.551002 0.0620830i 0.167925 0.985800i \(-0.446293\pi\)
0.383076 + 0.923717i \(0.374865\pi\)
\(212\) 135.759 + 108.265i 0.640375 + 0.510682i
\(213\) 0 0
\(214\) −119.789 13.4970i −0.559761 0.0630699i
\(215\) 6.03032 + 6.03032i 0.0280480 + 0.0280480i
\(216\) 0 0
\(217\) 140.754 + 88.4417i 0.648637 + 0.407565i
\(218\) −183.403 + 291.884i −0.841298 + 1.33892i
\(219\) 0 0
\(220\) 50.9493 50.9493i 0.231588 0.231588i
\(221\) −1.11585 + 9.90347i −0.00504911 + 0.0448121i
\(222\) 0 0
\(223\) 157.783 197.854i 0.707547 0.887236i −0.290015 0.957022i \(-0.593660\pi\)
0.997562 + 0.0697862i \(0.0222317\pi\)
\(224\) 57.4171 + 509.591i 0.256326 + 2.27496i
\(225\) 0 0
\(226\) 23.6969 + 103.823i 0.104854 + 0.459394i
\(227\) 21.4599 94.0221i 0.0945372 0.414194i −0.905409 0.424540i \(-0.860436\pi\)
0.999946 + 0.0103453i \(0.00329308\pi\)
\(228\) 0 0
\(229\) 56.9198 + 19.9171i 0.248558 + 0.0869742i 0.451683 0.892179i \(-0.350824\pi\)
−0.203125 + 0.979153i \(0.565110\pi\)
\(230\) 491.859 309.055i 2.13852 1.34372i
\(231\) 0 0
\(232\) 70.0295 105.088i 0.301851 0.452965i
\(233\) −94.7649 −0.406716 −0.203358 0.979104i \(-0.565186\pi\)
−0.203358 + 0.979104i \(0.565186\pi\)
\(234\) 0 0
\(235\) 11.5281 32.9454i 0.0490557 0.140193i
\(236\) −22.2871 + 46.2796i −0.0944367 + 0.196100i
\(237\) 0 0
\(238\) −123.836 + 28.2647i −0.520319 + 0.118759i
\(239\) 92.0947 44.3505i 0.385333 0.185567i −0.231180 0.972911i \(-0.574259\pi\)
0.616514 + 0.787344i \(0.288544\pi\)
\(240\) 0 0
\(241\) −288.328 229.934i −1.19638 0.954084i −0.196731 0.980457i \(-0.563033\pi\)
−0.999652 + 0.0263733i \(0.991604\pi\)
\(242\) −114.008 325.816i −0.471107 1.34635i
\(243\) 0 0
\(244\) −227.054 227.054i −0.930551 0.930551i
\(245\) 333.682 266.103i 1.36197 1.08613i
\(246\) 0 0
\(247\) −51.8411 + 82.5046i −0.209883 + 0.334027i
\(248\) −37.7793 47.3737i −0.152336 0.191023i
\(249\) 0 0
\(250\) 45.7898 406.395i 0.183159 1.62558i
\(251\) 346.223 121.149i 1.37937 0.482663i 0.464202 0.885729i \(-0.346341\pi\)
0.915171 + 0.403066i \(0.132055\pi\)
\(252\) 0 0
\(253\) 13.5881 + 120.598i 0.0537079 + 0.476671i
\(254\) 213.593 + 443.531i 0.840917 + 1.74618i
\(255\) 0 0
\(256\) 1.50755 6.60499i 0.00588885 0.0258007i
\(257\) 348.410 + 167.786i 1.35568 + 0.652862i 0.963670 0.267097i \(-0.0860645\pi\)
0.392013 + 0.919960i \(0.371779\pi\)
\(258\) 0 0
\(259\) −200.525 + 125.999i −0.774230 + 0.486481i
\(260\) 70.9886i 0.273033i
\(261\) 0 0
\(262\) 467.441 1.78413
\(263\) −181.203 288.383i −0.688986 1.09651i −0.989749 0.142816i \(-0.954384\pi\)
0.300763 0.953699i \(-0.402759\pi\)
\(264\) 0 0
\(265\) 63.3142 131.473i 0.238921 0.496126i
\(266\) −1210.75 276.347i −4.55171 1.03890i
\(267\) 0 0
\(268\) 283.382 136.470i 1.05740 0.509216i
\(269\) −71.8537 + 8.09596i −0.267114 + 0.0300965i −0.244506 0.969648i \(-0.578626\pi\)
−0.0226084 + 0.999744i \(0.507197\pi\)
\(270\) 0 0
\(271\) 110.702 + 316.368i 0.408495 + 1.16741i 0.946005 + 0.324153i \(0.105079\pi\)
−0.537510 + 0.843257i \(0.680635\pi\)
\(272\) −28.6123 3.22383i −0.105192 0.0118523i
\(273\) 0 0
\(274\) 129.821 103.529i 0.473799 0.377842i
\(275\) 10.5375 + 6.62114i 0.0383181 + 0.0240769i
\(276\) 0 0
\(277\) −187.171 234.705i −0.675707 0.847310i 0.319244 0.947673i \(-0.396571\pi\)
−0.994951 + 0.100362i \(0.968000\pi\)
\(278\) 99.8321 99.8321i 0.359108 0.359108i
\(279\) 0 0
\(280\) −223.611 + 78.2449i −0.798611 + 0.279446i
\(281\) −212.195 + 266.084i −0.755142 + 0.946918i −0.999742 0.0227058i \(-0.992772\pi\)
0.244600 + 0.969624i \(0.421343\pi\)
\(282\) 0 0
\(283\) 43.3073 + 89.9286i 0.153029 + 0.317769i 0.963363 0.268199i \(-0.0864286\pi\)
−0.810334 + 0.585968i \(0.800714\pi\)
\(284\) 94.4462 + 413.796i 0.332557 + 1.45703i
\(285\) 0 0
\(286\) −23.2257 11.1849i −0.0812086 0.0391080i
\(287\) 242.894 + 84.9922i 0.846320 + 0.296140i
\(288\) 0 0
\(289\) 276.998i 0.958470i
\(290\) −378.832 144.071i −1.30632 0.496797i
\(291\) 0 0
\(292\) 220.957 + 351.651i 0.756702 + 1.20428i
\(293\) 61.7117 176.362i 0.210620 0.601917i −0.789307 0.613999i \(-0.789560\pi\)
0.999927 + 0.0120814i \(0.00384572\pi\)
\(294\) 0 0
\(295\) 42.0846 + 9.60553i 0.142660 + 0.0325611i
\(296\) 84.1598 19.2089i 0.284324 0.0648950i
\(297\) 0 0
\(298\) −697.121 + 78.5467i −2.33933 + 0.263580i
\(299\) −93.4818 74.5493i −0.312648 0.249329i
\(300\) 0 0
\(301\) 22.2320 + 2.50495i 0.0738606 + 0.00832209i
\(302\) 182.589 + 182.589i 0.604599 + 0.604599i
\(303\) 0 0
\(304\) −238.366 149.775i −0.784098 0.492681i
\(305\) −143.567 + 228.485i −0.470710 + 0.749131i
\(306\) 0 0
\(307\) 153.936 153.936i 0.501419 0.501419i −0.410460 0.911879i \(-0.634632\pi\)
0.911879 + 0.410460i \(0.134632\pi\)
\(308\) 21.1639 187.835i 0.0687141 0.609855i
\(309\) 0 0
\(310\) −121.251 + 152.044i −0.391132 + 0.490465i
\(311\) −1.32892 11.7945i −0.00427306 0.0379245i 0.991395 0.130906i \(-0.0417887\pi\)
−0.995668 + 0.0929819i \(0.970360\pi\)
\(312\) 0 0
\(313\) −66.0161 289.235i −0.210914 0.924074i −0.963948 0.266092i \(-0.914267\pi\)
0.753034 0.657982i \(-0.228590\pi\)
\(314\) 133.270 583.892i 0.424425 1.85953i
\(315\) 0 0
\(316\) −458.248 160.348i −1.45015 0.507430i
\(317\) −214.084 + 134.518i −0.675345 + 0.424347i −0.825566 0.564305i \(-0.809144\pi\)
0.150221 + 0.988652i \(0.452001\pi\)
\(318\) 0 0
\(319\) 61.4585 58.2481i 0.192660 0.182596i
\(320\) −448.534 −1.40167
\(321\) 0 0
\(322\) 503.318 1438.40i 1.56310 4.46708i
\(323\) 50.9146 105.725i 0.157630 0.327323i
\(324\) 0 0
\(325\) −11.9537 + 2.72836i −0.0367807 + 0.00839495i
\(326\) 107.641 51.8374i 0.330188 0.159010i
\(327\) 0 0
\(328\) −73.3358 58.4834i −0.223585 0.178303i
\(329\) −30.2427 86.4286i −0.0919230 0.262701i
\(330\) 0 0
\(331\) −111.869 111.869i −0.337973 0.337973i 0.517631 0.855604i \(-0.326814\pi\)
−0.855604 + 0.517631i \(0.826814\pi\)
\(332\) 200.157 159.620i 0.602882 0.480782i
\(333\) 0 0
\(334\) −30.6709 + 48.8125i −0.0918291 + 0.146145i
\(335\) −164.802 206.656i −0.491947 0.616882i
\(336\) 0 0
\(337\) −69.1598 + 613.810i −0.205222 + 1.82140i 0.294998 + 0.955498i \(0.404681\pi\)
−0.500220 + 0.865898i \(0.666748\pi\)
\(338\) −465.586 + 162.916i −1.37747 + 0.481999i
\(339\) 0 0
\(340\) −9.57198 84.9537i −0.0281529 0.249864i
\(341\) −17.6283 36.6055i −0.0516958 0.107347i
\(342\) 0 0
\(343\) 118.886 520.873i 0.346606 1.51858i
\(344\) −7.34739 3.53832i −0.0213587 0.0102858i
\(345\) 0 0
\(346\) −563.399 + 354.007i −1.62832 + 1.02314i
\(347\) 195.864i 0.564450i −0.959348 0.282225i \(-0.908928\pi\)
0.959348 0.282225i \(-0.0910724\pi\)
\(348\) 0 0
\(349\) 350.810 1.00519 0.502593 0.864523i \(-0.332380\pi\)
0.502593 + 0.864523i \(0.332380\pi\)
\(350\) −83.1411 132.318i −0.237546 0.378052i
\(351\) 0 0
\(352\) 54.3815 112.924i 0.154493 0.320808i
\(353\) 326.927 + 74.6189i 0.926139 + 0.211385i 0.658887 0.752242i \(-0.271027\pi\)
0.267251 + 0.963627i \(0.413885\pi\)
\(354\) 0 0
\(355\) 321.362 154.760i 0.905245 0.435943i
\(356\) −319.519 + 36.0012i −0.897526 + 0.101127i
\(357\) 0 0
\(358\) 67.1085 + 191.785i 0.187454 + 0.535713i
\(359\) 329.831 + 37.1631i 0.918751 + 0.103518i 0.558658 0.829398i \(-0.311317\pi\)
0.360093 + 0.932917i \(0.382745\pi\)
\(360\) 0 0
\(361\) 614.757 490.253i 1.70293 1.35804i
\(362\) −91.1504 57.2736i −0.251797 0.158214i
\(363\) 0 0
\(364\) 116.113 + 145.601i 0.318992 + 0.400003i
\(365\) 246.789 246.789i 0.676134 0.676134i
\(366\) 0 0
\(367\) −308.985 + 108.119i −0.841921 + 0.294601i −0.716573 0.697512i \(-0.754290\pi\)
−0.125348 + 0.992113i \(0.540005\pi\)
\(368\) 215.382 270.080i 0.585277 0.733914i
\(369\) 0 0
\(370\) −120.209 249.617i −0.324890 0.674641i
\(371\) −85.1847 373.219i −0.229608 1.00598i
\(372\) 0 0
\(373\) 369.998 + 178.182i 0.991951 + 0.477698i 0.858199 0.513316i \(-0.171583\pi\)
0.133752 + 0.991015i \(0.457298\pi\)
\(374\) 29.3028 + 10.2535i 0.0783498 + 0.0274158i
\(375\) 0 0
\(376\) 33.3767i 0.0887679i
\(377\) −2.23659 + 83.3948i −0.00593259 + 0.221206i
\(378\) 0 0
\(379\) 197.597 + 314.473i 0.521363 + 0.829745i 0.998803 0.0489200i \(-0.0155779\pi\)
−0.477440 + 0.878665i \(0.658435\pi\)
\(380\) 276.066 788.950i 0.726488 2.07618i
\(381\) 0 0
\(382\) −423.862 96.7437i −1.10959 0.253256i
\(383\) 418.965 95.6261i 1.09390 0.249676i 0.362748 0.931887i \(-0.381838\pi\)
0.731156 + 0.682211i \(0.238981\pi\)
\(384\) 0 0
\(385\) −157.851 + 17.7856i −0.410003 + 0.0461962i
\(386\) 70.6714 + 56.3586i 0.183087 + 0.146007i
\(387\) 0 0
\(388\) 682.883 + 76.9424i 1.76001 + 0.198305i
\(389\) −261.614 261.614i −0.672531 0.672531i 0.285768 0.958299i \(-0.407751\pi\)
−0.958299 + 0.285768i \(0.907751\pi\)
\(390\) 0 0
\(391\) 121.924 + 76.6099i 0.311826 + 0.195933i
\(392\) −217.133 + 345.565i −0.553910 + 0.881543i
\(393\) 0 0
\(394\) −276.301 + 276.301i −0.701272 + 0.701272i
\(395\) −45.6807 + 405.428i −0.115647 + 1.02640i
\(396\) 0 0
\(397\) −93.5455 + 117.302i −0.235631 + 0.295472i −0.885562 0.464521i \(-0.846226\pi\)
0.649931 + 0.759993i \(0.274798\pi\)
\(398\) 104.065 + 923.601i 0.261469 + 2.32060i
\(399\) 0 0
\(400\) −7.88256 34.5357i −0.0197064 0.0863394i
\(401\) −52.5601 + 230.281i −0.131073 + 0.574266i 0.866150 + 0.499784i \(0.166587\pi\)
−0.997222 + 0.0744818i \(0.976270\pi\)
\(402\) 0 0
\(403\) 37.7824 + 13.2206i 0.0937530 + 0.0328056i
\(404\) −322.571 + 202.685i −0.798443 + 0.501695i
\(405\) 0 0
\(406\) −1012.65 + 324.142i −2.49422 + 0.798381i
\(407\) 57.8821 0.142217
\(408\) 0 0
\(409\) 13.0580 37.3176i 0.0319266 0.0912410i −0.926817 0.375514i \(-0.877466\pi\)
0.958744 + 0.284273i \(0.0917521\pi\)
\(410\) −130.620 + 271.234i −0.318584 + 0.661547i
\(411\) 0 0
\(412\) 461.590 105.355i 1.12037 0.255716i
\(413\) 102.029 49.1345i 0.247043 0.118970i
\(414\) 0 0
\(415\) −168.206 134.140i −0.405315 0.323228i
\(416\) 40.7844 + 116.555i 0.0980395 + 0.280181i
\(417\) 0 0
\(418\) 214.628 + 214.628i 0.513463 + 0.513463i
\(419\) −490.816 + 391.413i −1.17140 + 0.934160i −0.998708 0.0508160i \(-0.983818\pi\)
−0.172691 + 0.984976i \(0.555246\pi\)
\(420\) 0 0
\(421\) −188.794 + 300.464i −0.448442 + 0.713692i −0.992077 0.125630i \(-0.959905\pi\)
0.543635 + 0.839322i \(0.317048\pi\)
\(422\) 223.874 + 280.729i 0.530508 + 0.665235i
\(423\) 0 0
\(424\) −15.6234 + 138.662i −0.0368477 + 0.327032i
\(425\) 13.9374 4.87691i 0.0327939 0.0114751i
\(426\) 0 0
\(427\) 79.2609 + 703.460i 0.185623 + 1.64745i
\(428\) −92.3506 191.768i −0.215772 0.448056i
\(429\) 0 0
\(430\) −5.82406 + 25.5169i −0.0135443 + 0.0593416i
\(431\) 433.295 + 208.664i 1.00532 + 0.484139i 0.862742 0.505644i \(-0.168745\pi\)
0.142583 + 0.989783i \(0.454459\pi\)
\(432\) 0 0
\(433\) 255.849 160.760i 0.590875 0.371271i −0.203158 0.979146i \(-0.565121\pi\)
0.794033 + 0.607875i \(0.207978\pi\)
\(434\) 510.175i 1.17552i
\(435\) 0 0
\(436\) −608.666 −1.39602
\(437\) 749.022 + 1192.06i 1.71401 + 2.72783i
\(438\) 0 0
\(439\) 60.9039 126.468i 0.138733 0.288083i −0.820013 0.572344i \(-0.806034\pi\)
0.958747 + 0.284262i \(0.0917484\pi\)
\(440\) 56.4501 + 12.8844i 0.128296 + 0.0292826i
\(441\) 0 0
\(442\) −27.5573 + 13.2709i −0.0623468 + 0.0300246i
\(443\) 454.976 51.2635i 1.02703 0.115719i 0.417661 0.908603i \(-0.362850\pi\)
0.609372 + 0.792884i \(0.291421\pi\)
\(444\) 0 0
\(445\) 89.2459 + 255.050i 0.200553 + 0.573146i
\(446\) 771.776 + 86.9583i 1.73044 + 0.194974i
\(447\) 0 0
\(448\) −919.965 + 733.648i −2.05349 + 1.63761i
\(449\) −422.069 265.204i −0.940021 0.590654i −0.0274722 0.999623i \(-0.508746\pi\)
−0.912549 + 0.408968i \(0.865889\pi\)
\(450\) 0 0
\(451\) −39.2143 49.1732i −0.0869497 0.109031i
\(452\) −132.959 + 132.959i −0.294157 + 0.294157i
\(453\) 0 0
\(454\) 279.367 97.7549i 0.615347 0.215319i
\(455\) 97.5780 122.359i 0.214457 0.268921i
\(456\) 0 0
\(457\) −4.22710 8.77767i −0.00924968 0.0192071i 0.896293 0.443463i \(-0.146250\pi\)
−0.905543 + 0.424256i \(0.860536\pi\)
\(458\) 41.1828 + 180.434i 0.0899188 + 0.393960i
\(459\) 0 0
\(460\) 924.100 + 445.023i 2.00891 + 0.967441i
\(461\) −736.203 257.609i −1.59697 0.558804i −0.622364 0.782728i \(-0.713828\pi\)
−0.974607 + 0.223924i \(0.928113\pi\)
\(462\) 0 0
\(463\) 21.7764i 0.0470332i 0.999723 + 0.0235166i \(0.00748626\pi\)
−0.999723 + 0.0235166i \(0.992514\pi\)
\(464\) −240.938 6.46177i −0.519262 0.0139262i
\(465\) 0 0
\(466\) −154.734 246.258i −0.332047 0.528450i
\(467\) 94.2773 269.429i 0.201878 0.576936i −0.797783 0.602944i \(-0.793994\pi\)
0.999662 + 0.0260088i \(0.00827980\pi\)
\(468\) 0 0
\(469\) −676.036 154.301i −1.44144 0.328999i
\(470\) 104.436 23.8367i 0.222203 0.0507165i
\(471\) 0 0
\(472\) −41.0184 + 4.62167i −0.0869034 + 0.00979166i
\(473\) −4.27512 3.40930i −0.00903831 0.00720781i
\(474\) 0 0
\(475\) 143.461 + 16.1642i 0.302023 + 0.0340298i
\(476\) −158.588 158.588i −0.333168 0.333168i
\(477\) 0 0
\(478\) 265.624 + 166.902i 0.555698 + 0.349168i
\(479\) −390.644 + 621.706i −0.815540 + 1.29792i 0.136095 + 0.990696i \(0.456545\pi\)
−0.951636 + 0.307229i \(0.900598\pi\)
\(480\) 0 0
\(481\) −40.3241 + 40.3241i −0.0838339 + 0.0838339i
\(482\) 126.723 1124.70i 0.262910 2.33339i
\(483\) 0 0
\(484\) 380.009 476.516i 0.785142 0.984537i
\(485\) −64.6601 573.874i −0.133320 1.18325i
\(486\) 0 0
\(487\) −142.396 623.876i −0.292394 1.28106i −0.881184 0.472774i \(-0.843253\pi\)
0.588790 0.808286i \(-0.299604\pi\)
\(488\) 57.4189 251.568i 0.117662 0.515509i
\(489\) 0 0
\(490\) 1236.34 + 432.614i 2.52314 + 0.882886i
\(491\) −110.365 + 69.3472i −0.224777 + 0.141237i −0.639713 0.768614i \(-0.720947\pi\)
0.414936 + 0.909851i \(0.363804\pi\)
\(492\) 0 0
\(493\) −8.56823 100.102i −0.0173798 0.203047i
\(494\) −299.045 −0.605354
\(495\) 0 0
\(496\) −38.1960 + 109.158i −0.0770082 + 0.220077i
\(497\) 405.995 843.058i 0.816892 1.69629i
\(498\) 0 0
\(499\) 66.2987 15.1322i 0.132863 0.0303251i −0.155572 0.987825i \(-0.549722\pi\)
0.288435 + 0.957499i \(0.406865\pi\)
\(500\) 650.592 313.309i 1.30118 0.626617i
\(501\) 0 0
\(502\) 880.137 + 701.886i 1.75326 + 1.39818i
\(503\) 287.544 + 821.754i 0.571658 + 1.63371i 0.758764 + 0.651365i \(0.225803\pi\)
−0.187106 + 0.982340i \(0.559911\pi\)
\(504\) 0 0
\(505\) 226.381 + 226.381i 0.448278 + 0.448278i
\(506\) −291.200 + 232.224i −0.575494 + 0.458941i
\(507\) 0 0
\(508\) −462.447 + 735.980i −0.910329 + 1.44878i
\(509\) 154.547 + 193.796i 0.303629 + 0.380739i 0.910115 0.414355i \(-0.135993\pi\)
−0.606486 + 0.795094i \(0.707421\pi\)
\(510\) 0 0
\(511\) 102.514 909.838i 0.200615 1.78051i
\(512\) −473.386 + 165.645i −0.924582 + 0.323525i
\(513\) 0 0
\(514\) 132.881 + 1179.35i 0.258523 + 2.29445i
\(515\) −172.635 358.480i −0.335213 0.696078i
\(516\) 0 0
\(517\) −4.97997 + 21.8187i −0.00963244 + 0.0422025i
\(518\) −654.843 315.356i −1.26418 0.608795i
\(519\) 0 0
\(520\) −48.3025 + 30.3505i −0.0928894 + 0.0583663i
\(521\) 250.623i 0.481041i 0.970644 + 0.240521i \(0.0773182\pi\)
−0.970644 + 0.240521i \(0.922682\pi\)
\(522\) 0 0
\(523\) 190.538 0.364318 0.182159 0.983269i \(-0.441691\pi\)
0.182159 + 0.983269i \(0.441691\pi\)
\(524\) 439.112 + 698.843i 0.838000 + 1.33367i
\(525\) 0 0
\(526\) 453.525 941.755i 0.862215 1.79041i
\(527\) −46.9978 10.7269i −0.0891798 0.0203547i
\(528\) 0 0
\(529\) −1079.87 + 520.038i −2.04134 + 0.983058i
\(530\) 445.029 50.1427i 0.839677 0.0946089i
\(531\) 0 0
\(532\) −724.228 2069.72i −1.36133 3.89046i
\(533\) 61.5760 + 6.93794i 0.115527 + 0.0130168i
\(534\) 0 0
\(535\) −139.846 + 111.523i −0.261394 + 0.208455i
\(536\) 214.015 + 134.474i 0.399281 + 0.250885i
\(537\) 0 0
\(538\) −138.362 173.501i −0.257179 0.322492i
\(539\) −193.502 + 193.502i −0.359001 + 0.359001i
\(540\) 0 0
\(541\) −692.929 + 242.466i −1.28083 + 0.448182i −0.883041 0.469295i \(-0.844508\pi\)
−0.397789 + 0.917477i \(0.630222\pi\)
\(542\) −641.363 + 804.243i −1.18333 + 1.48384i
\(543\) 0 0
\(544\) −64.5238 133.985i −0.118610 0.246296i
\(545\) 113.821 + 498.681i 0.208845 + 0.915011i
\(546\) 0 0
\(547\) −646.089 311.140i −1.18115 0.568812i −0.262904 0.964822i \(-0.584680\pi\)
−0.918246 + 0.396010i \(0.870394\pi\)
\(548\) 276.733 + 96.8330i 0.504987 + 0.176703i
\(549\) 0 0
\(550\) 38.1940i 0.0694436i
\(551\) 349.168 918.131i 0.633699 1.66630i
\(552\) 0 0
\(553\) 569.448 + 906.271i 1.02974 + 1.63883i
\(554\) 304.292 869.616i 0.549263 1.56970i
\(555\) 0 0
\(556\) 243.035 + 55.4711i 0.437113 + 0.0997681i
\(557\) −292.506 + 66.7627i −0.525146 + 0.119861i −0.476872 0.878973i \(-0.658229\pi\)
−0.0482744 + 0.998834i \(0.515372\pi\)
\(558\) 0 0
\(559\) 5.35342 0.603186i 0.00957678 0.00107904i
\(560\) 353.510 + 281.915i 0.631268 + 0.503419i
\(561\) 0 0
\(562\) −1037.93 116.946i −1.84684 0.208089i
\(563\) −748.523 748.523i −1.32953 1.32953i −0.905782 0.423743i \(-0.860716\pi\)
−0.423743 0.905782i \(-0.639284\pi\)
\(564\) 0 0
\(565\) 133.796 + 84.0699i 0.236808 + 0.148796i
\(566\) −162.977 + 259.376i −0.287945 + 0.458262i
\(567\) 0 0
\(568\) −241.178 + 241.178i −0.424609 + 0.424609i
\(569\) 37.2315 330.438i 0.0654331 0.580735i −0.917626 0.397445i \(-0.869897\pi\)
0.983059 0.183290i \(-0.0586746\pi\)
\(570\) 0 0
\(571\) 632.274 792.847i 1.10731 1.38852i 0.194126 0.980977i \(-0.437813\pi\)
0.913184 0.407546i \(-0.133616\pi\)
\(572\) −5.09623 45.2303i −0.00890949 0.0790739i
\(573\) 0 0
\(574\) 175.739 + 769.964i 0.306166 + 1.34140i
\(575\) −39.4205 + 172.712i −0.0685573 + 0.300369i
\(576\) 0 0
\(577\) 598.835 + 209.541i 1.03784 + 0.363156i 0.794808 0.606861i \(-0.207572\pi\)
0.243034 + 0.970018i \(0.421857\pi\)
\(578\) −719.811 + 452.287i −1.24535 + 0.782503i
\(579\) 0 0
\(580\) −140.481 701.708i −0.242209 1.20984i
\(581\) −564.405 −0.971438
\(582\) 0 0
\(583\) −30.9022 + 88.3133i −0.0530054 + 0.151481i
\(584\) −144.804 + 300.689i −0.247953 + 0.514879i
\(585\) 0 0
\(586\) 559.060 127.602i 0.954028 0.217751i
\(587\) 114.477 55.1294i 0.195021 0.0939171i −0.333825 0.942635i \(-0.608339\pi\)
0.528846 + 0.848718i \(0.322625\pi\)
\(588\) 0 0
\(589\) −368.491 293.862i −0.625622 0.498917i
\(590\) 43.7554 + 125.046i 0.0741616 + 0.211942i
\(591\) 0 0
\(592\) −116.501 116.501i −0.196793 0.196793i
\(593\) 80.0236 63.8167i 0.134947 0.107617i −0.553690 0.832723i \(-0.686781\pi\)
0.688637 + 0.725106i \(0.258209\pi\)
\(594\) 0 0
\(595\) −100.275 + 159.587i −0.168530 + 0.268214i
\(596\) −772.303 968.437i −1.29581 1.62489i
\(597\) 0 0
\(598\) 41.0860 364.649i 0.0687057 0.609780i
\(599\) −552.540 + 193.342i −0.922438 + 0.322775i −0.749383 0.662137i \(-0.769650\pi\)
−0.173055 + 0.984912i \(0.555364\pi\)
\(600\) 0 0
\(601\) −97.2205 862.856i −0.161765 1.43570i −0.768018 0.640429i \(-0.778757\pi\)
0.606253 0.795272i \(-0.292672\pi\)
\(602\) 29.7915 + 61.8626i 0.0494875 + 0.102762i
\(603\) 0 0
\(604\) −101.454 + 444.500i −0.167971 + 0.735928i
\(605\) −461.472 222.233i −0.762763 0.367327i
\(606\) 0 0
\(607\) 12.0856 7.59388i 0.0199104 0.0125105i −0.522040 0.852921i \(-0.674829\pi\)
0.541950 + 0.840410i \(0.317686\pi\)
\(608\) 1453.97i 2.39140i
\(609\) 0 0
\(610\) −828.163 −1.35764
\(611\) −11.7308 18.6695i −0.0191994 0.0305557i
\(612\) 0 0
\(613\) −210.870 + 437.876i −0.343997 + 0.714317i −0.999152 0.0411775i \(-0.986889\pi\)
0.655155 + 0.755495i \(0.272603\pi\)
\(614\) 651.368 + 148.671i 1.06086 + 0.242134i
\(615\) 0 0
\(616\) 136.856 65.9065i 0.222169 0.106991i
\(617\) −90.2086 + 10.1641i −0.146205 + 0.0164734i −0.184764 0.982783i \(-0.559152\pi\)
0.0385585 + 0.999256i \(0.487723\pi\)
\(618\) 0 0
\(619\) 357.144 + 1020.66i 0.576969 + 1.64888i 0.748063 + 0.663628i \(0.230984\pi\)
−0.171094 + 0.985255i \(0.554730\pi\)
\(620\) −341.214 38.4456i −0.550346 0.0620091i
\(621\) 0 0
\(622\) 28.4795 22.7116i 0.0457870 0.0365139i
\(623\) 600.223 + 377.145i 0.963439 + 0.605369i
\(624\) 0 0
\(625\) −311.919 391.134i −0.499070 0.625814i
\(626\) 643.819 643.819i 1.02846 1.02846i
\(627\) 0 0
\(628\) 998.134 349.262i 1.58939 0.556150i
\(629\) 42.8196 53.6940i 0.0680756 0.0853641i
\(630\) 0 0
\(631\) −36.5938 75.9878i −0.0579933 0.120424i 0.869958 0.493126i \(-0.164146\pi\)
−0.927951 + 0.372702i \(0.878432\pi\)
\(632\) −86.8144 380.359i −0.137365 0.601833i
\(633\) 0 0
\(634\) −699.121 336.679i −1.10272 0.531040i
\(635\) 689.467 + 241.255i 1.08577 + 0.379929i
\(636\) 0 0
\(637\) 269.610i 0.423249i
\(638\) 251.715 + 64.5985i 0.394538 + 0.101252i
\(639\) 0 0
\(640\) −316.372 503.503i −0.494331 0.786723i
\(641\) −254.096 + 726.165i −0.396406 + 1.13286i 0.556827 + 0.830628i \(0.312018\pi\)
−0.953233 + 0.302235i \(0.902267\pi\)
\(642\) 0 0
\(643\) −511.993 116.859i −0.796256 0.181740i −0.195007 0.980802i \(-0.562473\pi\)
−0.601249 + 0.799062i \(0.705330\pi\)
\(644\) 2623.28 598.747i 4.07342 0.929731i
\(645\) 0 0
\(646\) 357.874 40.3227i 0.553984 0.0624190i
\(647\) −810.314 646.204i −1.25242 0.998769i −0.999511 0.0312788i \(-0.990042\pi\)
−0.252907 0.967491i \(-0.581387\pi\)
\(648\) 0 0
\(649\) −27.5037 3.09892i −0.0423786 0.00477492i
\(650\) −26.6082 26.6082i −0.0409357 0.0409357i
\(651\) 0 0
\(652\) 178.617 + 112.232i 0.273952 + 0.172135i
\(653\) −172.974 + 275.286i −0.264891 + 0.421571i −0.952513 0.304497i \(-0.901512\pi\)
0.687623 + 0.726068i \(0.258654\pi\)
\(654\) 0 0
\(655\) 490.448 490.448i 0.748776 0.748776i
\(656\) −20.0446 + 177.900i −0.0305557 + 0.271190i
\(657\) 0 0
\(658\) 175.214 219.711i 0.266282 0.333908i
\(659\) 74.6830 + 662.830i 0.113328 + 1.00581i 0.913723 + 0.406339i \(0.133195\pi\)
−0.800395 + 0.599473i \(0.795377\pi\)
\(660\) 0 0
\(661\) 156.741 + 686.726i 0.237127 + 1.03892i 0.943576 + 0.331156i \(0.107439\pi\)
−0.706450 + 0.707763i \(0.749704\pi\)
\(662\) 108.043 473.367i 0.163207 0.715056i
\(663\) 0 0
\(664\) 194.184 + 67.9481i 0.292446 + 0.102331i
\(665\) −1560.30 + 980.399i −2.34631 + 1.47428i
\(666\) 0 0
\(667\) 1071.58 + 551.911i 1.60656 + 0.827453i
\(668\) −101.789 −0.152378
\(669\) 0 0
\(670\) 267.926 765.689i 0.399890 1.14282i
\(671\) 75.0705 155.885i 0.111878 0.232318i
\(672\) 0 0
\(673\) −764.739 + 174.547i −1.13631 + 0.259356i −0.748986 0.662586i \(-0.769459\pi\)
−0.387328 + 0.921942i \(0.626602\pi\)
\(674\) −1707.98 + 822.521i −2.53410 + 1.22036i
\(675\) 0 0
\(676\) −680.935 543.028i −1.00730 0.803295i
\(677\) −145.674 416.312i −0.215176 0.614937i 0.784813 0.619733i \(-0.212759\pi\)
−0.999988 + 0.00479615i \(0.998473\pi\)
\(678\) 0 0
\(679\) −1071.28 1071.28i −1.57774 1.57774i
\(680\) 53.7123 42.8341i 0.0789887 0.0629913i
\(681\) 0 0
\(682\) 66.3398 105.579i 0.0972724 0.154808i
\(683\) −158.493 198.744i −0.232054 0.290986i 0.652148 0.758092i \(-0.273868\pi\)
−0.884202 + 0.467106i \(0.845297\pi\)
\(684\) 0 0
\(685\) 27.5863 244.835i 0.0402720 0.357424i
\(686\) 1547.67 541.552i 2.25607 0.789434i
\(687\) 0 0
\(688\) 1.74268 + 15.4667i 0.00253296 + 0.0224806i
\(689\) −39.9960 83.0525i −0.0580493 0.120541i
\(690\) 0 0
\(691\) −100.393 + 439.849i −0.145286 + 0.636539i 0.848871 + 0.528599i \(0.177283\pi\)
−0.994157 + 0.107940i \(0.965575\pi\)
\(692\) −1058.51 509.751i −1.52964 0.736635i
\(693\) 0 0
\(694\) 508.975 319.810i 0.733394 0.460822i
\(695\) 209.492i 0.301427i
\(696\) 0 0
\(697\) −74.6249 −0.107066
\(698\) 572.808 + 911.619i 0.820642 + 1.30604i
\(699\) 0 0
\(700\) 119.719 248.599i 0.171027 0.355141i
\(701\) −391.700 89.4029i −0.558773 0.127536i −0.0661981 0.997806i \(-0.521087\pi\)
−0.492574 + 0.870270i \(0.663944\pi\)
\(702\) 0 0
\(703\) 604.968 291.337i 0.860552 0.414420i
\(704\) 285.783 32.2000i 0.405941 0.0457386i
\(705\) 0 0
\(706\) 339.906 + 971.396i 0.481454 + 1.37592i
\(707\) 834.599 + 94.0367i 1.18048 + 0.133008i
\(708\) 0 0
\(709\) −587.061 + 468.165i −0.828012 + 0.660318i −0.942906 0.333060i \(-0.891919\pi\)
0.114893 + 0.993378i \(0.463347\pi\)
\(710\) 926.886 + 582.401i 1.30547 + 0.820283i
\(711\) 0 0
\(712\) −161.103 202.017i −0.226269 0.283732i
\(713\) 408.956 408.956i 0.573571 0.573571i
\(714\) 0 0
\(715\) −36.1042 + 12.6334i −0.0504954 + 0.0176691i
\(716\) −223.685 + 280.492i −0.312409 + 0.391748i
\(717\) 0 0
\(718\) 441.982 + 917.785i 0.615574 + 1.27825i
\(719\) −147.275 645.255i −0.204834 0.897434i −0.967944 0.251166i \(-0.919186\pi\)
0.763110 0.646268i \(-0.223671\pi\)
\(720\) 0 0
\(721\) −940.433 452.889i −1.30435 0.628140i
\(722\) 2277.76 + 797.024i 3.15480 + 1.10391i
\(723\) 0 0
\(724\) 190.076i 0.262536i
\(725\) 112.761 50.6248i 0.155532 0.0698273i
\(726\) 0 0
\(727\) −43.7196 69.5794i −0.0601370 0.0957075i 0.815302 0.579035i \(-0.196571\pi\)
−0.875439 + 0.483328i \(0.839428\pi\)
\(728\) −49.4278 + 141.257i −0.0678954 + 0.194034i
\(729\) 0 0
\(730\) 1044.27 + 238.348i 1.43051 + 0.326504i
\(731\) −6.32523 + 1.44369i −0.00865285 + 0.00197496i
\(732\) 0 0
\(733\) 531.014 59.8309i 0.724440 0.0816248i 0.257959 0.966156i \(-0.416950\pi\)
0.466481 + 0.884531i \(0.345522\pi\)
\(734\) −785.475 626.395i −1.07013 0.853400i
\(735\) 0 0
\(736\) 1772.94 + 199.763i 2.40889 + 0.271416i
\(737\) 119.839 + 119.839i 0.162604 + 0.162604i
\(738\) 0 0
\(739\) −592.189 372.097i −0.801338 0.503514i 0.0680274 0.997683i \(-0.478329\pi\)
−0.869366 + 0.494169i \(0.835472\pi\)
\(740\) 260.263 414.207i 0.351707 0.559739i
\(741\) 0 0
\(742\) 830.760 830.760i 1.11962 1.11962i
\(743\) −90.3001 + 801.435i −0.121534 + 1.07865i 0.773855 + 0.633363i \(0.218326\pi\)
−0.895389 + 0.445284i \(0.853103\pi\)
\(744\) 0 0
\(745\) −649.021 + 813.846i −0.871169 + 1.09241i
\(746\) 141.114 + 1252.42i 0.189161 + 1.67885i
\(747\) 0 0
\(748\) 12.1976 + 53.4410i 0.0163069 + 0.0714451i
\(749\) −104.417 + 457.481i −0.139408 + 0.610788i
\(750\) 0 0
\(751\) 45.2480 + 15.8329i 0.0602503 + 0.0210825i 0.360236 0.932861i \(-0.382696\pi\)
−0.299986 + 0.953944i \(0.596982\pi\)
\(752\) 53.9385 33.8918i 0.0717268 0.0450689i
\(753\) 0 0
\(754\) −220.363 + 130.356i −0.292258 + 0.172886i
\(755\) 383.151 0.507485
\(756\) 0 0
\(757\) 241.576 690.385i 0.319123 0.912002i −0.666864 0.745180i \(-0.732364\pi\)
0.985987 0.166822i \(-0.0533506\pi\)
\(758\) −494.555 + 1026.95i −0.652448 + 1.35482i
\(759\) 0 0
\(760\) 654.851 149.465i 0.861646 0.196665i
\(761\) 152.528 73.4534i 0.200431 0.0965222i −0.330976 0.943639i \(-0.607378\pi\)
0.531407 + 0.847117i \(0.321664\pi\)
\(762\) 0 0
\(763\) 1049.12 + 836.648i 1.37500 + 1.09652i
\(764\) −253.538 724.571i −0.331856 0.948391i
\(765\) 0 0
\(766\) 932.589 + 932.589i 1.21748 + 1.21748i
\(767\) 21.3196 17.0018i 0.0277961 0.0221666i
\(768\) 0 0
\(769\) −247.966 + 394.636i −0.322453 + 0.513180i −0.968136 0.250425i \(-0.919430\pi\)
0.645683 + 0.763605i \(0.276573\pi\)
\(770\) −303.960 381.154i −0.394753 0.495005i
\(771\) 0 0
\(772\) −17.8699 + 158.600i −0.0231475 + 0.205440i
\(773\) 1232.54 431.285i 1.59449 0.557937i 0.620439 0.784255i \(-0.286955\pi\)
0.974053 + 0.226318i \(0.0726689\pi\)
\(774\) 0 0
\(775\) −6.64032 58.9345i −0.00856815 0.0760445i
\(776\) 239.606 + 497.547i 0.308770 + 0.641169i
\(777\) 0 0
\(778\) 252.666 1107.00i 0.324764 1.42288i
\(779\) −657.359 316.568i −0.843850 0.406377i
\(780\) 0 0
\(781\) −193.645 + 121.675i −0.247945 + 0.155794i
\(782\) 441.923i 0.565119i
\(783\) 0 0
\(784\) 778.935 0.993539
\(785\) −472.802 752.460i −0.602295 0.958548i
\(786\) 0 0
\(787\) 148.519 308.402i 0.188715 0.391871i −0.785048 0.619435i \(-0.787362\pi\)