Properties

Label 108.3.k.a.5.2
Level 108
Weight 3
Character 108.5
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 108.5
Dual form 108.3.k.a.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.95183 + 2.27824i) q^{3} +(-3.25030 - 8.93012i) q^{5} +(0.410040 + 2.32545i) q^{7} +(-1.38071 - 8.89346i) q^{9} +O(q^{10})\) \(q+(-1.95183 + 2.27824i) q^{3} +(-3.25030 - 8.93012i) q^{5} +(0.410040 + 2.32545i) q^{7} +(-1.38071 - 8.89346i) q^{9} +(4.40911 - 12.1139i) q^{11} +(-12.2099 - 10.2453i) q^{13} +(26.6889 + 10.0251i) q^{15} +(12.2018 + 7.04474i) q^{17} +(-3.29274 - 5.70319i) q^{19} +(-6.09825 - 3.60472i) q^{21} +(-25.9779 - 4.58061i) q^{23} +(-50.0315 + 41.9814i) q^{25} +(22.9563 + 14.2129i) q^{27} +(0.977913 + 1.16543i) q^{29} +(-0.620995 + 3.52184i) q^{31} +(18.9925 + 33.6893i) q^{33} +(19.4338 - 11.2201i) q^{35} +(-11.0926 + 19.2129i) q^{37} +(47.1730 - 7.81990i) q^{39} +(31.4714 - 37.5062i) q^{41} +(78.8159 + 28.6866i) q^{43} +(-74.9319 + 41.2363i) q^{45} +(-34.9622 + 6.16478i) q^{47} +(40.8053 - 14.8519i) q^{49} +(-39.8655 + 14.0485i) q^{51} -65.8880i q^{53} -122.510 q^{55} +(19.4201 + 3.63003i) q^{57} +(-17.2513 - 47.3976i) q^{59} +(-11.5793 - 65.6697i) q^{61} +(20.1152 - 6.85745i) q^{63} +(-51.8062 + 142.336i) q^{65} +(72.5027 + 60.8370i) q^{67} +(61.1402 - 50.2432i) q^{69} +(71.8787 + 41.4992i) q^{71} +(-47.8713 - 82.9155i) q^{73} +(2.00947 - 195.924i) q^{75} +(29.9782 + 5.28597i) q^{77} +(-25.9904 + 21.8086i) q^{79} +(-77.1873 + 24.5587i) q^{81} +(7.14066 + 8.50991i) q^{83} +(23.2507 - 131.861i) q^{85} +(-4.56385 - 0.0468084i) q^{87} +(-8.83930 + 5.10337i) q^{89} +(18.8185 - 32.5945i) q^{91} +(-6.81149 - 8.28880i) q^{93} +(-40.2278 + 47.9416i) q^{95} +(66.7584 + 24.2981i) q^{97} +(-113.822 - 22.4863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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
\(3\) −1.95183 + 2.27824i −0.650610 + 0.759412i
\(4\) 0 0
\(5\) −3.25030 8.93012i −0.650060 1.78602i −0.617522 0.786553i \(-0.711863\pi\)
−0.0325374 0.999471i \(-0.510359\pi\)
\(6\) 0 0
\(7\) 0.410040 + 2.32545i 0.0585771 + 0.332207i 0.999987 0.00505674i \(-0.00160962\pi\)
−0.941410 + 0.337264i \(0.890499\pi\)
\(8\) 0 0
\(9\) −1.38071 8.89346i −0.153413 0.988162i
\(10\) 0 0
\(11\) 4.40911 12.1139i 0.400828 1.10127i −0.561049 0.827783i \(-0.689602\pi\)
0.961877 0.273483i \(-0.0881757\pi\)
\(12\) 0 0
\(13\) −12.2099 10.2453i −0.939224 0.788103i 0.0382260 0.999269i \(-0.487829\pi\)
−0.977450 + 0.211166i \(0.932274\pi\)
\(14\) 0 0
\(15\) 26.6889 + 10.0251i 1.77926 + 0.668343i
\(16\) 0 0
\(17\) 12.2018 + 7.04474i 0.717755 + 0.414396i 0.813926 0.580969i \(-0.197326\pi\)
−0.0961707 + 0.995365i \(0.530659\pi\)
\(18\) 0 0
\(19\) −3.29274 5.70319i −0.173302 0.300168i 0.766270 0.642518i \(-0.222110\pi\)
−0.939572 + 0.342350i \(0.888777\pi\)
\(20\) 0 0
\(21\) −6.09825 3.60472i −0.290393 0.171653i
\(22\) 0 0
\(23\) −25.9779 4.58061i −1.12947 0.199157i −0.422477 0.906374i \(-0.638839\pi\)
−0.706997 + 0.707217i \(0.749950\pi\)
\(24\) 0 0
\(25\) −50.0315 + 41.9814i −2.00126 + 1.67926i
\(26\) 0 0
\(27\) 22.9563 + 14.2129i 0.850234 + 0.526405i
\(28\) 0 0
\(29\) 0.977913 + 1.16543i 0.0337211 + 0.0401873i 0.782641 0.622473i \(-0.213872\pi\)
−0.748920 + 0.662660i \(0.769427\pi\)
\(30\) 0 0
\(31\) −0.620995 + 3.52184i −0.0200321 + 0.113608i −0.993184 0.116555i \(-0.962815\pi\)
0.973152 + 0.230163i \(0.0739259\pi\)
\(32\) 0 0
\(33\) 18.9925 + 33.6893i 0.575531 + 1.02089i
\(34\) 0 0
\(35\) 19.4338 11.2201i 0.555252 0.320575i
\(36\) 0 0
\(37\) −11.0926 + 19.2129i −0.299800 + 0.519269i −0.976090 0.217367i \(-0.930253\pi\)
0.676290 + 0.736635i \(0.263587\pi\)
\(38\) 0 0
\(39\) 47.1730 7.81990i 1.20956 0.200510i
\(40\) 0 0
\(41\) 31.4714 37.5062i 0.767595 0.914784i −0.230707 0.973023i \(-0.574104\pi\)
0.998303 + 0.0582388i \(0.0185485\pi\)
\(42\) 0 0
\(43\) 78.8159 + 28.6866i 1.83293 + 0.667131i 0.992040 + 0.125921i \(0.0401887\pi\)
0.840888 + 0.541210i \(0.182033\pi\)
\(44\) 0 0
\(45\) −74.9319 + 41.2363i −1.66515 + 0.916363i
\(46\) 0 0
\(47\) −34.9622 + 6.16478i −0.743877 + 0.131166i −0.532726 0.846288i \(-0.678832\pi\)
−0.211151 + 0.977453i \(0.567721\pi\)
\(48\) 0 0
\(49\) 40.8053 14.8519i 0.832762 0.303101i
\(50\) 0 0
\(51\) −39.8655 + 14.0485i −0.781676 + 0.275461i
\(52\) 0 0
\(53\) 65.8880i 1.24317i −0.783347 0.621585i \(-0.786489\pi\)
0.783347 0.621585i \(-0.213511\pi\)
\(54\) 0 0
\(55\) −122.510 −2.22745
\(56\) 0 0
\(57\) 19.4201 + 3.63003i 0.340703 + 0.0636847i
\(58\) 0 0
\(59\) −17.2513 47.3976i −0.292395 0.803349i −0.995715 0.0924754i \(-0.970522\pi\)
0.703320 0.710874i \(-0.251700\pi\)
\(60\) 0 0
\(61\) −11.5793 65.6697i −0.189825 1.07655i −0.919597 0.392862i \(-0.871485\pi\)
0.729772 0.683690i \(-0.239626\pi\)
\(62\) 0 0
\(63\) 20.1152 6.85745i 0.319288 0.108848i
\(64\) 0 0
\(65\) −51.8062 + 142.336i −0.797019 + 2.18979i
\(66\) 0 0
\(67\) 72.5027 + 60.8370i 1.08213 + 0.908015i 0.996096 0.0882774i \(-0.0281362\pi\)
0.0860340 + 0.996292i \(0.472581\pi\)
\(68\) 0 0
\(69\) 61.1402 50.2432i 0.886089 0.728163i
\(70\) 0 0
\(71\) 71.8787 + 41.4992i 1.01238 + 0.584496i 0.911887 0.410442i \(-0.134626\pi\)
0.100490 + 0.994938i \(0.467959\pi\)
\(72\) 0 0
\(73\) −47.8713 82.9155i −0.655771 1.13583i −0.981700 0.190434i \(-0.939010\pi\)
0.325929 0.945394i \(-0.394323\pi\)
\(74\) 0 0
\(75\) 2.00947 195.924i 0.0267929 2.61232i
\(76\) 0 0
\(77\) 29.9782 + 5.28597i 0.389328 + 0.0686490i
\(78\) 0 0
\(79\) −25.9904 + 21.8086i −0.328993 + 0.276058i −0.792289 0.610146i \(-0.791111\pi\)
0.463296 + 0.886203i \(0.346667\pi\)
\(80\) 0 0
\(81\) −77.1873 + 24.5587i −0.952929 + 0.303193i
\(82\) 0 0
\(83\) 7.14066 + 8.50991i 0.0860321 + 0.102529i 0.807343 0.590082i \(-0.200905\pi\)
−0.721311 + 0.692611i \(0.756460\pi\)
\(84\) 0 0
\(85\) 23.2507 131.861i 0.273538 1.55131i
\(86\) 0 0
\(87\) −4.56385 0.0468084i −0.0524580 0.000538028i
\(88\) 0 0
\(89\) −8.83930 + 5.10337i −0.0993180 + 0.0573412i −0.548836 0.835930i \(-0.684929\pi\)
0.449518 + 0.893271i \(0.351596\pi\)
\(90\) 0 0
\(91\) 18.8185 32.5945i 0.206796 0.358182i
\(92\) 0 0
\(93\) −6.81149 8.28880i −0.0732419 0.0891269i
\(94\) 0 0
\(95\) −40.2278 + 47.9416i −0.423450 + 0.504648i
\(96\) 0 0
\(97\) 66.7584 + 24.2981i 0.688231 + 0.250496i 0.662378 0.749170i \(-0.269547\pi\)
0.0258533 + 0.999666i \(0.491770\pi\)
\(98\) 0 0
\(99\) −113.822 22.4863i −1.14972 0.227135i
\(100\) 0 0
\(101\) −60.9870 + 10.7536i −0.603831 + 0.106472i −0.467202 0.884151i \(-0.654738\pi\)
−0.136629 + 0.990622i \(0.543627\pi\)
\(102\) 0 0
\(103\) 98.6549 35.9074i 0.957814 0.348616i 0.184638 0.982807i \(-0.440889\pi\)
0.773177 + 0.634191i \(0.218667\pi\)
\(104\) 0 0
\(105\) −12.3694 + 66.1745i −0.117804 + 0.630234i
\(106\) 0 0
\(107\) 20.2740i 0.189477i 0.995502 + 0.0947385i \(0.0302015\pi\)
−0.995502 + 0.0947385i \(0.969799\pi\)
\(108\) 0 0
\(109\) 145.914 1.33866 0.669328 0.742967i \(-0.266582\pi\)
0.669328 + 0.742967i \(0.266582\pi\)
\(110\) 0 0
\(111\) −22.1207 62.7719i −0.199286 0.565513i
\(112\) 0 0
\(113\) −22.6555 62.2454i −0.200491 0.550844i 0.798178 0.602422i \(-0.205797\pi\)
−0.998669 + 0.0515773i \(0.983575\pi\)
\(114\) 0 0
\(115\) 43.5306 + 246.874i 0.378527 + 2.14673i
\(116\) 0 0
\(117\) −74.2581 + 122.734i −0.634684 + 1.04901i
\(118\) 0 0
\(119\) −11.3789 + 31.2634i −0.0956214 + 0.262718i
\(120\) 0 0
\(121\) −34.6155 29.0458i −0.286078 0.240048i
\(122\) 0 0
\(123\) 24.0210 + 144.905i 0.195293 + 1.17809i
\(124\) 0 0
\(125\) 331.765 + 191.545i 2.65412 + 1.53236i
\(126\) 0 0
\(127\) 19.5642 + 33.8862i 0.154049 + 0.266820i 0.932712 0.360621i \(-0.117435\pi\)
−0.778663 + 0.627442i \(0.784102\pi\)
\(128\) 0 0
\(129\) −219.190 + 123.570i −1.69915 + 0.957905i
\(130\) 0 0
\(131\) −225.050 39.6824i −1.71794 0.302919i −0.774036 0.633142i \(-0.781765\pi\)
−0.943903 + 0.330223i \(0.892876\pi\)
\(132\) 0 0
\(133\) 11.9123 9.99563i 0.0895664 0.0751551i
\(134\) 0 0
\(135\) 52.3083 251.199i 0.387469 1.86073i
\(136\) 0 0
\(137\) 90.7406 + 108.140i 0.662340 + 0.789346i 0.987720 0.156237i \(-0.0499364\pi\)
−0.325379 + 0.945584i \(0.605492\pi\)
\(138\) 0 0
\(139\) 15.8432 89.8510i 0.113980 0.646410i −0.873271 0.487235i \(-0.838005\pi\)
0.987250 0.159175i \(-0.0508835\pi\)
\(140\) 0 0
\(141\) 54.1955 91.6847i 0.384365 0.650246i
\(142\) 0 0
\(143\) −177.946 + 102.737i −1.24438 + 0.718442i
\(144\) 0 0
\(145\) 7.22893 12.5209i 0.0498547 0.0863509i
\(146\) 0 0
\(147\) −45.8089 + 121.953i −0.311625 + 0.829610i
\(148\) 0 0
\(149\) 20.1684 24.0358i 0.135358 0.161314i −0.694107 0.719872i \(-0.744201\pi\)
0.829466 + 0.558558i \(0.188645\pi\)
\(150\) 0 0
\(151\) −91.3198 33.2377i −0.604767 0.220117i 0.0214449 0.999770i \(-0.493173\pi\)
−0.626212 + 0.779653i \(0.715396\pi\)
\(152\) 0 0
\(153\) 45.8048 118.243i 0.299378 0.772832i
\(154\) 0 0
\(155\) 33.4688 5.90146i 0.215928 0.0380739i
\(156\) 0 0
\(157\) 11.8874 4.32668i 0.0757162 0.0275584i −0.303884 0.952709i \(-0.598284\pi\)
0.379601 + 0.925150i \(0.376061\pi\)
\(158\) 0 0
\(159\) 150.108 + 128.602i 0.944078 + 0.808819i
\(160\) 0 0
\(161\) 62.2886i 0.386885i
\(162\) 0 0
\(163\) −167.367 −1.02679 −0.513397 0.858151i \(-0.671613\pi\)
−0.513397 + 0.858151i \(0.671613\pi\)
\(164\) 0 0
\(165\) 239.118 279.106i 1.44920 1.69155i
\(166\) 0 0
\(167\) 6.44485 + 17.7071i 0.0385919 + 0.106030i 0.957492 0.288460i \(-0.0931433\pi\)
−0.918900 + 0.394491i \(0.870921\pi\)
\(168\) 0 0
\(169\) 14.7686 + 83.7568i 0.0873881 + 0.495602i
\(170\) 0 0
\(171\) −46.1748 + 37.1583i −0.270028 + 0.217300i
\(172\) 0 0
\(173\) 70.3332 193.239i 0.406550 1.11699i −0.552441 0.833552i \(-0.686303\pi\)
0.958991 0.283436i \(-0.0914743\pi\)
\(174\) 0 0
\(175\) −118.141 99.1317i −0.675089 0.566467i
\(176\) 0 0
\(177\) 141.655 + 53.2095i 0.800308 + 0.300619i
\(178\) 0 0
\(179\) −125.847 72.6580i −0.703058 0.405911i 0.105427 0.994427i \(-0.466379\pi\)
−0.808485 + 0.588516i \(0.799712\pi\)
\(180\) 0 0
\(181\) −60.7901 105.292i −0.335857 0.581721i 0.647792 0.761817i \(-0.275693\pi\)
−0.983649 + 0.180096i \(0.942359\pi\)
\(182\) 0 0
\(183\) 172.212 + 101.796i 0.941049 + 0.556260i
\(184\) 0 0
\(185\) 207.628 + 36.6104i 1.12231 + 0.197894i
\(186\) 0 0
\(187\) 139.139 116.751i 0.744057 0.624338i
\(188\) 0 0
\(189\) −23.6385 + 59.2117i −0.125071 + 0.313289i
\(190\) 0 0
\(191\) −58.7864 70.0589i −0.307782 0.366801i 0.589875 0.807494i \(-0.299177\pi\)
−0.897658 + 0.440694i \(0.854732\pi\)
\(192\) 0 0
\(193\) −56.8849 + 322.610i −0.294740 + 1.67156i 0.373515 + 0.927624i \(0.378152\pi\)
−0.668256 + 0.743932i \(0.732959\pi\)
\(194\) 0 0
\(195\) −223.159 395.843i −1.14440 2.02997i
\(196\) 0 0
\(197\) −43.6830 + 25.2204i −0.221741 + 0.128022i −0.606756 0.794888i \(-0.707530\pi\)
0.385015 + 0.922910i \(0.374196\pi\)
\(198\) 0 0
\(199\) −3.02449 + 5.23856i −0.0151984 + 0.0263244i −0.873525 0.486780i \(-0.838171\pi\)
0.858326 + 0.513104i \(0.171505\pi\)
\(200\) 0 0
\(201\) −280.114 + 46.4347i −1.39360 + 0.231019i
\(202\) 0 0
\(203\) −2.30917 + 2.75196i −0.0113752 + 0.0135565i
\(204\) 0 0
\(205\) −437.226 159.137i −2.13281 0.776279i
\(206\) 0 0
\(207\) −4.86937 + 237.358i −0.0235235 + 1.14666i
\(208\) 0 0
\(209\) −83.6060 + 14.7420i −0.400029 + 0.0705359i
\(210\) 0 0
\(211\) 18.4132 6.70185i 0.0872663 0.0317623i −0.298018 0.954560i \(-0.596326\pi\)
0.385284 + 0.922798i \(0.374103\pi\)
\(212\) 0 0
\(213\) −234.840 + 82.7573i −1.10254 + 0.388532i
\(214\) 0 0
\(215\) 797.076i 3.70733i
\(216\) 0 0
\(217\) −8.44449 −0.0389147
\(218\) 0 0
\(219\) 282.338 + 52.7749i 1.28921 + 0.240981i
\(220\) 0 0
\(221\) −76.8077 211.028i −0.347546 0.954876i
\(222\) 0 0
\(223\) 17.4949 + 99.2183i 0.0784523 + 0.444925i 0.998578 + 0.0533028i \(0.0169748\pi\)
−0.920126 + 0.391622i \(0.871914\pi\)
\(224\) 0 0
\(225\) 442.439 + 386.989i 1.96640 + 1.71995i
\(226\) 0 0
\(227\) −12.2532 + 33.6653i −0.0539787 + 0.148305i −0.963752 0.266801i \(-0.914033\pi\)
0.909773 + 0.415106i \(0.136256\pi\)
\(228\) 0 0
\(229\) 131.729 + 110.534i 0.575235 + 0.482679i 0.883378 0.468661i \(-0.155263\pi\)
−0.308144 + 0.951340i \(0.599708\pi\)
\(230\) 0 0
\(231\) −70.5551 + 57.9802i −0.305433 + 0.250996i
\(232\) 0 0
\(233\) 110.221 + 63.6363i 0.473053 + 0.273117i 0.717517 0.696541i \(-0.245279\pi\)
−0.244464 + 0.969658i \(0.578612\pi\)
\(234\) 0 0
\(235\) 168.690 + 292.179i 0.717829 + 1.24332i
\(236\) 0 0
\(237\) 1.04388 101.779i 0.00440456 0.429447i
\(238\) 0 0
\(239\) 343.656 + 60.5957i 1.43789 + 0.253539i 0.837617 0.546257i \(-0.183948\pi\)
0.600272 + 0.799796i \(0.295059\pi\)
\(240\) 0 0
\(241\) 361.538 303.367i 1.50016 1.25878i 0.619532 0.784971i \(-0.287322\pi\)
0.880626 0.473811i \(-0.157122\pi\)
\(242\) 0 0
\(243\) 94.7061 223.785i 0.389737 0.920926i
\(244\) 0 0
\(245\) −265.259 316.123i −1.08269 1.29030i
\(246\) 0 0
\(247\) −18.2270 + 103.371i −0.0737937 + 0.418505i
\(248\) 0 0
\(249\) −33.3249 0.341792i −0.133835 0.00137266i
\(250\) 0 0
\(251\) −321.947 + 185.876i −1.28266 + 0.740542i −0.977333 0.211707i \(-0.932098\pi\)
−0.305323 + 0.952249i \(0.598764\pi\)
\(252\) 0 0
\(253\) −170.028 + 294.498i −0.672049 + 1.16402i
\(254\) 0 0
\(255\) 255.030 + 310.342i 1.00012 + 1.21703i
\(256\) 0 0
\(257\) 65.9115 78.5502i 0.256465 0.305643i −0.622414 0.782688i \(-0.713848\pi\)
0.878879 + 0.477045i \(0.158292\pi\)
\(258\) 0 0
\(259\) −49.2271 17.9172i −0.190066 0.0691784i
\(260\) 0 0
\(261\) 9.01450 10.3062i 0.0345383 0.0394872i
\(262\) 0 0
\(263\) 225.681 39.7937i 0.858103 0.151307i 0.272750 0.962085i \(-0.412067\pi\)
0.585353 + 0.810778i \(0.300956\pi\)
\(264\) 0 0
\(265\) −588.388 + 214.156i −2.22033 + 0.808134i
\(266\) 0 0
\(267\) 5.62613 30.0989i 0.0210717 0.112730i
\(268\) 0 0
\(269\) 111.782i 0.415546i 0.978177 + 0.207773i \(0.0666215\pi\)
−0.978177 + 0.207773i \(0.933378\pi\)
\(270\) 0 0
\(271\) −107.229 −0.395680 −0.197840 0.980234i \(-0.563393\pi\)
−0.197840 + 0.980234i \(0.563393\pi\)
\(272\) 0 0
\(273\) 37.5276 + 106.492i 0.137464 + 0.390080i
\(274\) 0 0
\(275\) 287.965 + 791.178i 1.04715 + 2.87701i
\(276\) 0 0
\(277\) −74.3484 421.651i −0.268406 1.52221i −0.759158 0.650906i \(-0.774389\pi\)
0.490752 0.871299i \(-0.336722\pi\)
\(278\) 0 0
\(279\) 32.1787 + 0.660142i 0.115336 + 0.00236610i
\(280\) 0 0
\(281\) −46.0248 + 126.452i −0.163789 + 0.450007i −0.994252 0.107067i \(-0.965854\pi\)
0.830463 + 0.557074i \(0.188076\pi\)
\(282\) 0 0
\(283\) −0.267348 0.224332i −0.000944693 0.000792692i 0.642315 0.766441i \(-0.277974\pi\)
−0.643260 + 0.765648i \(0.722418\pi\)
\(284\) 0 0
\(285\) −30.7045 185.222i −0.107735 0.649903i
\(286\) 0 0
\(287\) 100.123 + 57.8062i 0.348862 + 0.201415i
\(288\) 0 0
\(289\) −45.2434 78.3639i −0.156552 0.271155i
\(290\) 0 0
\(291\) −185.658 + 104.666i −0.637999 + 0.359676i
\(292\) 0 0
\(293\) −454.925 80.2156i −1.55265 0.273773i −0.669478 0.742832i \(-0.733482\pi\)
−0.883167 + 0.469059i \(0.844593\pi\)
\(294\) 0 0
\(295\) −367.194 + 308.113i −1.24473 + 1.04445i
\(296\) 0 0
\(297\) 273.391 215.425i 0.920509 0.725336i
\(298\) 0 0
\(299\) 270.258 + 322.081i 0.903873 + 1.07719i
\(300\) 0 0
\(301\) −34.3917 + 195.045i −0.114258 + 0.647991i
\(302\) 0 0
\(303\) 94.5369 159.932i 0.312003 0.527828i
\(304\) 0 0
\(305\) −548.802 + 316.851i −1.79935 + 1.03886i
\(306\) 0 0
\(307\) 164.184 284.376i 0.534803 0.926305i −0.464370 0.885641i \(-0.653719\pi\)
0.999173 0.0406640i \(-0.0129473\pi\)
\(308\) 0 0
\(309\) −110.752 + 294.844i −0.358421 + 0.954188i
\(310\) 0 0
\(311\) 104.035 123.985i 0.334519 0.398664i −0.572396 0.819977i \(-0.693986\pi\)
0.906915 + 0.421313i \(0.138431\pi\)
\(312\) 0 0
\(313\) 219.058 + 79.7305i 0.699865 + 0.254730i 0.667353 0.744741i \(-0.267427\pi\)
0.0325118 + 0.999471i \(0.489649\pi\)
\(314\) 0 0
\(315\) −126.618 157.342i −0.401962 0.499498i
\(316\) 0 0
\(317\) 391.166 68.9732i 1.23396 0.217581i 0.481636 0.876371i \(-0.340043\pi\)
0.752327 + 0.658790i \(0.228932\pi\)
\(318\) 0 0
\(319\) 18.4297 6.70785i 0.0577732 0.0210277i
\(320\) 0 0
\(321\) −46.1890 39.5715i −0.143891 0.123276i
\(322\) 0 0
\(323\) 92.7859i 0.287263i
\(324\) 0 0
\(325\) 1040.99 3.20306
\(326\) 0 0
\(327\) −284.799 + 332.425i −0.870944 + 1.01659i
\(328\) 0 0
\(329\) −28.6718 78.7751i −0.0871483 0.239438i
\(330\) 0 0
\(331\) −60.1296 341.012i −0.181660 1.03025i −0.930172 0.367125i \(-0.880342\pi\)
0.748511 0.663122i \(-0.230769\pi\)
\(332\) 0 0
\(333\) 186.185 + 72.1240i 0.559115 + 0.216588i
\(334\) 0 0
\(335\) 307.626 845.196i 0.918287 2.52297i
\(336\) 0 0
\(337\) −27.9604 23.4615i −0.0829685 0.0696188i 0.600360 0.799730i \(-0.295024\pi\)
−0.683329 + 0.730111i \(0.739468\pi\)
\(338\) 0 0
\(339\) 186.029 + 69.8780i 0.548759 + 0.206130i
\(340\) 0 0
\(341\) 39.9252 + 23.0508i 0.117083 + 0.0675977i
\(342\) 0 0
\(343\) 109.122 + 189.004i 0.318139 + 0.551033i
\(344\) 0 0
\(345\) −647.402 382.684i −1.87653 1.10923i
\(346\) 0 0
\(347\) 33.2515 + 5.86314i 0.0958257 + 0.0168967i 0.221355 0.975193i \(-0.428952\pi\)
−0.125530 + 0.992090i \(0.540063\pi\)
\(348\) 0 0
\(349\) −128.274 + 107.635i −0.367548 + 0.308410i −0.807791 0.589469i \(-0.799337\pi\)
0.440242 + 0.897879i \(0.354893\pi\)
\(350\) 0 0
\(351\) −134.678 408.734i −0.383699 1.16448i
\(352\) 0 0
\(353\) −249.417 297.244i −0.706564 0.842050i 0.286689 0.958024i \(-0.407445\pi\)
−0.993252 + 0.115974i \(0.963001\pi\)
\(354\) 0 0
\(355\) 136.966 776.771i 0.385819 2.18809i
\(356\) 0 0
\(357\) −49.0156 86.9448i −0.137299 0.243543i
\(358\) 0 0
\(359\) −309.401 + 178.633i −0.861841 + 0.497584i −0.864628 0.502412i \(-0.832446\pi\)
0.00278752 + 0.999996i \(0.499113\pi\)
\(360\) 0 0
\(361\) 158.816 275.077i 0.439933 0.761986i
\(362\) 0 0
\(363\) 133.737 22.1697i 0.368421 0.0610735i
\(364\) 0 0
\(365\) −584.849 + 696.996i −1.60233 + 1.90958i
\(366\) 0 0
\(367\) 530.990 + 193.265i 1.44684 + 0.526606i 0.941707 0.336435i \(-0.109221\pi\)
0.505133 + 0.863042i \(0.331444\pi\)
\(368\) 0 0
\(369\) −377.013 228.104i −1.02171 0.618169i
\(370\) 0 0
\(371\) 153.219 27.0167i 0.412990 0.0728213i
\(372\) 0 0
\(373\) −68.7050 + 25.0066i −0.184196 + 0.0670417i −0.432471 0.901648i \(-0.642358\pi\)
0.248276 + 0.968689i \(0.420136\pi\)
\(374\) 0 0
\(375\) −1083.93 + 381.976i −2.89049 + 1.01860i
\(376\) 0 0
\(377\) 24.2489i 0.0643206i
\(378\) 0 0
\(379\) 63.3568 0.167168 0.0835841 0.996501i \(-0.473363\pi\)
0.0835841 + 0.996501i \(0.473363\pi\)
\(380\) 0 0
\(381\) −115.387 21.5682i −0.302852 0.0566095i
\(382\) 0 0
\(383\) −21.5538 59.2185i −0.0562762 0.154618i 0.908369 0.418169i \(-0.137328\pi\)
−0.964645 + 0.263552i \(0.915106\pi\)
\(384\) 0 0
\(385\) −50.2338 284.890i −0.130477 0.739975i
\(386\) 0 0
\(387\) 146.301 740.554i 0.378039 1.91358i
\(388\) 0 0
\(389\) 10.7172 29.4454i 0.0275508 0.0756951i −0.925155 0.379590i \(-0.876065\pi\)
0.952706 + 0.303895i \(0.0982872\pi\)
\(390\) 0 0
\(391\) −284.709 238.899i −0.728156 0.610996i
\(392\) 0 0
\(393\) 529.665 435.264i 1.34775 1.10754i
\(394\) 0 0
\(395\) 279.230 + 161.213i 0.706911 + 0.408135i
\(396\) 0 0
\(397\) 247.263 + 428.273i 0.622830 + 1.07877i 0.988956 + 0.148208i \(0.0473505\pi\)
−0.366126 + 0.930565i \(0.619316\pi\)
\(398\) 0 0
\(399\) −0.478447 + 46.6489i −0.00119912 + 0.116914i
\(400\) 0 0
\(401\) 671.249 + 118.359i 1.67394 + 0.295160i 0.928477 0.371390i \(-0.121119\pi\)
0.745460 + 0.666550i \(0.232230\pi\)
\(402\) 0 0
\(403\) 43.6647 36.6390i 0.108349 0.0909157i
\(404\) 0 0
\(405\) 470.193 + 609.469i 1.16097 + 1.50486i
\(406\) 0 0
\(407\) 183.836 + 219.087i 0.451684 + 0.538297i
\(408\) 0 0
\(409\) −82.5079 + 467.926i −0.201731 + 1.14407i 0.700771 + 0.713386i \(0.252840\pi\)
−0.902502 + 0.430686i \(0.858272\pi\)
\(410\) 0 0
\(411\) −423.480 4.34336i −1.03036 0.0105678i
\(412\) 0 0
\(413\) 103.147 59.5520i 0.249751 0.144194i
\(414\) 0 0
\(415\) 52.7852 91.4267i 0.127193 0.220305i
\(416\) 0 0
\(417\) 173.779 + 211.468i 0.416735 + 0.507119i
\(418\) 0 0
\(419\) −150.860 + 179.788i −0.360048 + 0.429088i −0.915411 0.402519i \(-0.868135\pi\)
0.555364 + 0.831608i \(0.312579\pi\)
\(420\) 0 0
\(421\) −121.158 44.0979i −0.287786 0.104746i 0.194094 0.980983i \(-0.437823\pi\)
−0.481879 + 0.876238i \(0.660046\pi\)
\(422\) 0 0
\(423\) 103.099 + 302.423i 0.243733 + 0.714948i
\(424\) 0 0
\(425\) −906.224 + 159.792i −2.13229 + 0.375981i
\(426\) 0 0
\(427\) 147.964 53.8544i 0.346519 0.126123i
\(428\) 0 0
\(429\) 113.261 605.928i 0.264012 1.41242i
\(430\) 0 0
\(431\) 270.719i 0.628119i 0.949403 + 0.314059i \(0.101689\pi\)
−0.949403 + 0.314059i \(0.898311\pi\)
\(432\) 0 0
\(433\) −89.2999 −0.206235 −0.103118 0.994669i \(-0.532882\pi\)
−0.103118 + 0.994669i \(0.532882\pi\)
\(434\) 0 0
\(435\) 14.4159 + 40.9078i 0.0331399 + 0.0940410i
\(436\) 0 0
\(437\) 59.4144 + 163.240i 0.135960 + 0.373546i
\(438\) 0 0
\(439\) −108.018 612.599i −0.246054 1.39544i −0.818032 0.575172i \(-0.804935\pi\)
0.571978 0.820269i \(-0.306176\pi\)
\(440\) 0 0
\(441\) −188.426 342.394i −0.427269 0.776405i
\(442\) 0 0
\(443\) −213.946 + 587.813i −0.482949 + 1.32689i 0.424005 + 0.905660i \(0.360624\pi\)
−0.906953 + 0.421231i \(0.861598\pi\)
\(444\) 0 0
\(445\) 74.3041 + 62.3485i 0.166975 + 0.140109i
\(446\) 0 0
\(447\) 15.3938 + 92.8621i 0.0344381 + 0.207745i
\(448\) 0 0
\(449\) 86.6015 + 49.9994i 0.192876 + 0.111357i 0.593328 0.804960i \(-0.297814\pi\)
−0.400452 + 0.916318i \(0.631147\pi\)
\(450\) 0 0
\(451\) −315.586 546.611i −0.699747 1.21200i
\(452\) 0 0
\(453\) 253.964 143.174i 0.560627 0.316057i
\(454\) 0 0
\(455\) −352.239 62.1092i −0.774151 0.136504i
\(456\) 0 0
\(457\) −134.065 + 112.494i −0.293359 + 0.246158i −0.777574 0.628792i \(-0.783550\pi\)
0.484214 + 0.874949i \(0.339105\pi\)
\(458\) 0 0
\(459\) 179.983 + 335.145i 0.392120 + 0.730164i
\(460\) 0 0
\(461\) 494.766 + 589.639i 1.07325 + 1.27904i 0.958328 + 0.285669i \(0.0922159\pi\)
0.114917 + 0.993375i \(0.463340\pi\)
\(462\) 0 0
\(463\) −86.2655 + 489.236i −0.186319 + 1.05667i 0.737931 + 0.674876i \(0.235803\pi\)
−0.924249 + 0.381789i \(0.875308\pi\)
\(464\) 0 0
\(465\) −51.8806 + 87.7685i −0.111571 + 0.188750i
\(466\) 0 0
\(467\) −368.842 + 212.951i −0.789811 + 0.455997i −0.839896 0.542748i \(-0.817384\pi\)
0.0500853 + 0.998745i \(0.484051\pi\)
\(468\) 0 0
\(469\) −111.744 + 193.547i −0.238261 + 0.412680i
\(470\) 0 0
\(471\) −13.3451 + 35.5273i −0.0283335 + 0.0754296i
\(472\) 0 0
\(473\) 695.015 828.287i 1.46938 1.75114i
\(474\) 0 0
\(475\) 404.169 + 147.105i 0.850881 + 0.309695i
\(476\) 0 0
\(477\) −585.972 + 90.9725i −1.22845 + 0.190718i
\(478\) 0 0
\(479\) 696.066 122.735i 1.45316 0.256232i 0.609365 0.792890i \(-0.291424\pi\)
0.843800 + 0.536658i \(0.180313\pi\)
\(480\) 0 0
\(481\) 332.283 120.941i 0.690816 0.251437i
\(482\) 0 0
\(483\) 141.908 + 121.577i 0.293805 + 0.251712i
\(484\) 0 0
\(485\) 675.136i 1.39203i
\(486\) 0 0
\(487\) −835.437 −1.71548 −0.857738 0.514087i \(-0.828131\pi\)
−0.857738 + 0.514087i \(0.828131\pi\)
\(488\) 0 0
\(489\) 326.673 381.302i 0.668042 0.779759i
\(490\) 0 0
\(491\) 218.847 + 601.277i 0.445717 + 1.22460i 0.935679 + 0.352854i \(0.114789\pi\)
−0.489961 + 0.871744i \(0.662989\pi\)
\(492\) 0 0
\(493\) 3.72218 + 21.1095i 0.00755007 + 0.0428185i
\(494\) 0 0
\(495\) 169.151 + 1089.53i 0.341719 + 2.20108i
\(496\) 0 0
\(497\) −67.0312 + 184.167i −0.134872 + 0.370557i
\(498\) 0 0
\(499\) 517.161 + 433.949i 1.03639 + 0.869638i 0.991598 0.129358i \(-0.0412917\pi\)
0.0447962 + 0.998996i \(0.485736\pi\)
\(500\) 0 0
\(501\) −52.9201 19.8783i −0.105629 0.0396773i
\(502\) 0 0
\(503\) −530.717 306.409i −1.05510 0.609164i −0.131029 0.991378i \(-0.541828\pi\)
−0.924074 + 0.382215i \(0.875162\pi\)
\(504\) 0 0
\(505\) 294.257 + 509.668i 0.582687 + 1.00924i
\(506\) 0 0
\(507\) −219.643 129.833i −0.433222 0.256080i
\(508\) 0 0
\(509\) 473.492 + 83.4894i 0.930239 + 0.164026i 0.618180 0.786036i \(-0.287870\pi\)
0.312059 + 0.950063i \(0.398981\pi\)
\(510\) 0 0
\(511\) 173.187 145.321i 0.338917 0.284385i
\(512\) 0 0
\(513\) 5.46993 177.724i 0.0106626 0.346440i
\(514\) 0 0
\(515\) −641.315 764.290i −1.24527 1.48406i
\(516\) 0 0
\(517\) −79.4724 + 450.711i −0.153718 + 0.871781i
\(518\) 0 0
\(519\) 302.965 + 537.405i 0.583748 + 1.03546i
\(520\) 0 0
\(521\) 194.362 112.215i 0.373055 0.215383i −0.301737 0.953391i \(-0.597567\pi\)
0.674792 + 0.738008i \(0.264233\pi\)
\(522\) 0 0
\(523\) −317.364 + 549.691i −0.606815 + 1.05104i 0.384946 + 0.922939i \(0.374220\pi\)
−0.991762 + 0.128096i \(0.959113\pi\)
\(524\) 0 0
\(525\) 456.436 75.6638i 0.869402 0.144121i
\(526\) 0 0
\(527\) −32.3877 + 38.5981i −0.0614567 + 0.0732412i
\(528\) 0 0
\(529\) 156.772 + 57.0604i 0.296355 + 0.107865i
\(530\) 0 0
\(531\) −397.709 + 218.866i −0.748982 + 0.412178i
\(532\) 0 0
\(533\) −768.526 + 135.512i −1.44189 + 0.254244i
\(534\) 0 0
\(535\) 181.050 65.8967i 0.338410 0.123171i
\(536\) 0 0
\(537\) 411.165 144.894i 0.765670 0.269821i
\(538\) 0 0
\(539\) 559.797i 1.03858i
\(540\) 0 0
\(541\) −322.531 −0.596176 −0.298088 0.954538i \(-0.596349\pi\)
−0.298088 + 0.954538i \(0.596349\pi\)
\(542\) 0 0
\(543\) 358.531 + 67.0171i 0.660278 + 0.123420i
\(544\) 0 0
\(545\) −474.263 1303.03i −0.870207 2.39087i
\(546\) 0 0
\(547\) 63.9102 + 362.453i 0.116838 + 0.662619i 0.985824 + 0.167783i \(0.0536608\pi\)
−0.868986 + 0.494836i \(0.835228\pi\)
\(548\) 0 0
\(549\) −568.043 + 193.651i −1.03469 + 0.352735i
\(550\) 0 0
\(551\) 3.42666 9.41468i 0.00621899 0.0170865i
\(552\) 0 0
\(553\) −61.3719 51.4971i −0.110980 0.0931232i
\(554\) 0 0
\(555\) −488.662 + 401.568i −0.880472 + 0.723546i
\(556\) 0 0
\(557\) 218.606 + 126.212i 0.392470 + 0.226593i 0.683230 0.730203i \(-0.260575\pi\)
−0.290760 + 0.956796i \(0.593908\pi\)
\(558\) 0 0
\(559\) −668.431 1157.76i −1.19576 2.07112i
\(560\) 0 0
\(561\) −5.58837 + 544.869i −0.00996144 + 0.971246i
\(562\) 0 0
\(563\) −654.162 115.346i −1.16192 0.204878i −0.440747 0.897631i \(-0.645287\pi\)
−0.721175 + 0.692753i \(0.756398\pi\)
\(564\) 0 0
\(565\) −482.222 + 404.632i −0.853490 + 0.716163i
\(566\) 0 0
\(567\) −88.7598 169.425i −0.156543 0.298810i
\(568\) 0 0
\(569\) −173.933 207.286i −0.305682 0.364298i 0.591233 0.806501i \(-0.298641\pi\)
−0.896915 + 0.442203i \(0.854197\pi\)
\(570\) 0 0
\(571\) 64.4159 365.321i 0.112812 0.639791i −0.874998 0.484127i \(-0.839137\pi\)
0.987810 0.155664i \(-0.0497517\pi\)
\(572\) 0 0
\(573\) 274.352 + 2.81385i 0.478799 + 0.00491073i
\(574\) 0 0
\(575\) 1492.01 861.414i 2.59481 1.49811i
\(576\) 0 0
\(577\) 172.890 299.454i 0.299636 0.518985i −0.676417 0.736519i \(-0.736468\pi\)
0.976053 + 0.217535i \(0.0698015\pi\)
\(578\) 0 0
\(579\) −623.953 759.278i −1.07764 1.31136i
\(580\) 0 0
\(581\) −16.8614 + 20.0947i −0.0290214 + 0.0345863i
\(582\) 0 0
\(583\) −798.162 290.507i −1.36906 0.498297i
\(584\) 0 0
\(585\) 1337.39 + 264.211i 2.28614 + 0.451642i
\(586\) 0 0
\(587\) 390.919 68.9295i 0.665960 0.117427i 0.169559 0.985520i \(-0.445766\pi\)
0.496401 + 0.868093i \(0.334655\pi\)
\(588\) 0 0
\(589\) 22.1305 8.05483i 0.0375730 0.0136754i
\(590\) 0 0
\(591\) 27.8038 148.746i 0.0470454 0.251685i
\(592\) 0 0
\(593\) 453.585i 0.764899i 0.923976 + 0.382449i \(0.124919\pi\)
−0.923976 + 0.382449i \(0.875081\pi\)
\(594\) 0 0
\(595\) 316.171 0.531380
\(596\) 0 0
\(597\) −6.03140 17.1153i −0.0101028 0.0286688i
\(598\) 0 0
\(599\) −127.690 350.827i −0.213173 0.585687i 0.786310 0.617832i \(-0.211989\pi\)
−0.999483 + 0.0321442i \(0.989766\pi\)
\(600\) 0 0
\(601\) 162.521 + 921.701i 0.270417 + 1.53361i 0.753153 + 0.657846i \(0.228532\pi\)
−0.482736 + 0.875766i \(0.660357\pi\)
\(602\) 0 0
\(603\) 440.946 728.798i 0.731253 1.20862i
\(604\) 0 0
\(605\) −146.872 + 403.528i −0.242764 + 0.666989i
\(606\) 0 0
\(607\) −825.430 692.618i −1.35985 1.14105i −0.976028 0.217645i \(-0.930163\pi\)
−0.383824 0.923406i \(-0.625393\pi\)
\(608\) 0 0
\(609\) −1.76251 10.6322i −0.00289410 0.0174585i
\(610\) 0 0
\(611\) 490.046 + 282.928i 0.802039 + 0.463057i
\(612\) 0 0
\(613\) 51.2650 + 88.7935i 0.0836296 + 0.144851i 0.904806 0.425823i \(-0.140015\pi\)
−0.821177 + 0.570674i \(0.806682\pi\)
\(614\) 0 0
\(615\) 1215.94 685.495i 1.97714 1.11463i
\(616\) 0 0
\(617\) −104.533 18.4319i −0.169421 0.0298735i 0.0882941 0.996094i \(-0.471858\pi\)
−0.257715 + 0.966221i \(0.582970\pi\)
\(618\) 0 0
\(619\) 59.1978 49.6728i 0.0956345 0.0802469i −0.593717 0.804674i \(-0.702340\pi\)
0.689351 + 0.724427i \(0.257896\pi\)
\(620\) 0 0
\(621\) −531.253 474.376i −0.855480 0.763891i
\(622\) 0 0
\(623\) −15.4921 18.4628i −0.0248669 0.0296353i
\(624\) 0 0
\(625\) 348.651 1977.30i 0.557842 3.16368i
\(626\) 0 0
\(627\) 129.599 219.248i 0.206697 0.349678i
\(628\) 0 0
\(629\) −270.700 + 156.289i −0.430366 + 0.248472i
\(630\) 0 0
\(631\) −489.646 + 848.091i −0.775983 + 1.34404i 0.158257 + 0.987398i \(0.449413\pi\)
−0.934240 + 0.356645i \(0.883921\pi\)
\(632\) 0 0
\(633\) −20.6710 + 55.0304i −0.0326556 + 0.0869359i
\(634\) 0 0
\(635\) 239.018 284.851i 0.376407 0.448584i
\(636\) 0 0
\(637\) −650.393 236.724i −1.02102 0.371623i
\(638\) 0 0
\(639\) 269.828 696.549i 0.422265 1.09006i
\(640\) 0 0
\(641\) 489.106 86.2426i 0.763036 0.134544i 0.221430 0.975176i \(-0.428928\pi\)
0.541606 + 0.840633i \(0.317817\pi\)
\(642\) 0 0
\(643\) −789.739 + 287.442i −1.22821 + 0.447032i −0.872984 0.487748i \(-0.837818\pi\)
−0.355226 + 0.934780i \(0.615596\pi\)
\(644\) 0 0
\(645\) 1815.93 + 1555.76i 2.81539 + 2.41203i
\(646\) 0 0
\(647\) 1032.02i 1.59508i 0.603263 + 0.797542i \(0.293867\pi\)
−0.603263 + 0.797542i \(0.706133\pi\)
\(648\) 0 0
\(649\) −650.234 −1.00190
\(650\) 0 0
\(651\) 16.4822 19.2385i 0.0253183 0.0295523i
\(652\) 0 0
\(653\) −318.739 875.728i −0.488115 1.34108i −0.902385 0.430930i \(-0.858185\pi\)
0.414270 0.910154i \(-0.364037\pi\)
\(654\) 0 0
\(655\) 377.111 + 2138.70i 0.575742 + 3.26519i
\(656\) 0 0
\(657\) −671.309 + 540.224i −1.02178 + 0.822258i
\(658\) 0 0
\(659\) 137.332 377.318i 0.208395 0.572561i −0.790825 0.612042i \(-0.790348\pi\)
0.999220 + 0.0394813i \(0.0125705\pi\)
\(660\) 0 0
\(661\) −51.6587 43.3468i −0.0781523 0.0655776i 0.602875 0.797836i \(-0.294022\pi\)
−0.681027 + 0.732258i \(0.738466\pi\)
\(662\) 0 0
\(663\) 630.686 + 236.904i 0.951261 + 0.357321i
\(664\) 0 0
\(665\) −127.981 73.8898i −0.192452 0.111112i
\(666\) 0 0
\(667\) −20.0657 34.7549i −0.0300836 0.0521063i
\(668\) 0 0
\(669\) −260.190 153.800i −0.388923 0.229895i
\(670\) 0 0
\(671\) −846.572 149.273i −1.26166 0.222464i
\(672\) 0 0
\(673\) 14.3494 12.0405i 0.0213215 0.0178909i −0.632065 0.774916i \(-0.717792\pi\)
0.653386 + 0.757025i \(0.273348\pi\)
\(674\) 0 0
\(675\) −1745.22 + 252.644i −2.58551 + 0.374288i
\(676\) 0 0
\(677\) 165.239 + 196.924i 0.244075 + 0.290877i 0.874149 0.485658i \(-0.161420\pi\)
−0.630074 + 0.776535i \(0.716975\pi\)
\(678\) 0 0
\(679\) −29.1304 + 165.207i −0.0429019 + 0.243309i
\(680\) 0 0
\(681\) −52.7813 93.6245i −0.0775056 0.137481i
\(682\) 0 0
\(683\) 266.287 153.741i 0.389879 0.225097i −0.292229 0.956348i \(-0.594397\pi\)
0.682108 + 0.731252i \(0.261064\pi\)
\(684\) 0 0
\(685\) 670.773 1161.81i 0.979231 1.69608i
\(686\) 0 0
\(687\) −508.934 + 84.3664i −0.740806 + 0.122804i
\(688\) 0 0
\(689\) −675.044 + 804.487i −0.979745 + 1.16761i
\(690\) 0 0
\(691\) 280.337 + 102.034i 0.405697 + 0.147662i 0.536805 0.843707i \(-0.319631\pi\)
−0.131108 + 0.991368i \(0.541853\pi\)
\(692\) 0 0
\(693\) 5.61920 273.909i 0.00810851 0.395251i
\(694\) 0 0
\(695\) −853.876 + 150.561i −1.22860 + 0.216635i
\(696\) 0 0
\(697\) 648.230 235.936i 0.930029 0.338503i
\(698\) 0 0
\(699\) −360.112 + 126.903i −0.515181 + 0.181549i
\(700\) 0 0
\(701\) 274.104i 0.391019i 0.980702 + 0.195510i \(0.0626361\pi\)
−0.980702 + 0.195510i \(0.937364\pi\)
\(702\) 0 0
\(703\) 146.100 0.207824
\(704\) 0 0
\(705\) −994.907 185.969i −1.41122 0.263786i
\(706\) 0 0
\(707\) −50.0142 137.413i −0.0707414 0.194360i
\(708\) 0 0
\(709\) 68.7370 + 389.827i 0.0969492 + 0.549826i 0.994133 + 0.108168i \(0.0344985\pi\)
−0.897183 + 0.441658i \(0.854390\pi\)
\(710\) 0 0
\(711\) 229.839 + 201.034i 0.323262 + 0.282748i
\(712\) 0 0
\(713\) 32.2643 88.6454i 0.0452514 0.124327i
\(714\) 0 0
\(715\) 1495.83 + 1255.15i 2.09207 + 1.75546i
\(716\) 0 0
\(717\) −808.809 + 664.656i −1.12805 + 0.926995i
\(718\) 0 0
\(719\) 80.2851 + 46.3526i 0.111662 + 0.0644682i 0.554791 0.831990i \(-0.312798\pi\)
−0.443129 + 0.896458i \(0.646132\pi\)
\(720\) 0 0
\(721\) 123.953 + 214.694i 0.171919 + 0.297772i
\(722\) 0 0
\(723\) −14.5208 + 1415.79i −0.0200841 + 1.95821i
\(724\) 0 0
\(725\) −97.8529 17.2541i −0.134970 0.0237988i
\(726\) 0 0
\(727\) 458.479 384.709i 0.630645 0.529174i −0.270484 0.962724i \(-0.587184\pi\)
0.901129 + 0.433550i \(0.142739\pi\)
\(728\) 0 0
\(729\) 324.985 + 652.553i 0.445796 + 0.895135i
\(730\) 0 0
\(731\) 759.609 + 905.267i 1.03914 + 1.23840i
\(732\) 0 0
\(733\) −127.319 + 722.063i −0.173696 + 0.985079i 0.765942 + 0.642910i \(0.222273\pi\)
−0.939638 + 0.342170i \(0.888838\pi\)
\(734\) 0 0
\(735\) 1237.94 + 12.6968i 1.68428 + 0.0172746i
\(736\) 0 0
\(737\) 1056.65 610.055i 1.43371 0.827755i
\(738\) 0 0
\(739\) 208.119 360.472i 0.281622 0.487784i −0.690162 0.723655i \(-0.742461\pi\)
0.971784 + 0.235871i \(0.0757942\pi\)
\(740\) 0 0
\(741\) −199.927 243.287i −0.269806 0.328323i
\(742\) 0 0
\(743\) 852.915 1016.46i 1.14793 1.36805i 0.229104 0.973402i \(-0.426420\pi\)
0.918830 0.394653i \(-0.129135\pi\)
\(744\) 0 0
\(745\) −280.196 101.983i −0.376101 0.136890i
\(746\) 0 0
\(747\) 65.8233 75.2550i 0.0881169 0.100743i
\(748\) 0 0
\(749\) −47.1463 + 8.31316i −0.0629456 + 0.0110990i
\(750\) 0 0
\(751\) 1209.13 440.087i 1.61002 0.586001i 0.628579 0.777745i \(-0.283637\pi\)
0.981445 + 0.191744i \(0.0614145\pi\)
\(752\) 0 0
\(753\) 204.916 1096.27i 0.272133 1.45587i
\(754\) 0 0
\(755\) 923.530i 1.22322i
\(756\) 0 0
\(757\) −519.945 −0.686849 −0.343425 0.939180i \(-0.611587\pi\)
−0.343425 + 0.939180i \(0.611587\pi\)
\(758\) 0 0
\(759\) −339.069 962.175i −0.446731 1.26769i
\(760\) 0 0
\(761\) 129.215 + 355.015i 0.169796 + 0.466511i 0.995180 0.0980603i \(-0.0312638\pi\)
−0.825384 + 0.564571i \(0.809042\pi\)
\(762\) 0 0
\(763\) 59.8304 + 339.315i 0.0784146 + 0.444711i
\(764\) 0 0
\(765\) −1204.81 24.7164i −1.57491 0.0323091i
\(766\) 0 0
\(767\) −274.967 + 755.466i −0.358497 + 0.984962i
\(768\) 0 0
\(769\) −176.852 148.396i −0.229976 0.192973i 0.520517 0.853851i \(-0.325739\pi\)
−0.750493 + 0.660879i \(0.770184\pi\)
\(770\) 0 0
\(771\) 50.3079 + 303.479i 0.0652502 + 0.393617i
\(772\) 0 0
\(773\) −184.241 106.372i −0.238346 0.137609i 0.376070 0.926591i \(-0.377275\pi\)
−0.614416 + 0.788982i \(0.710608\pi\)
\(774\) 0 0
\(775\) −116.782 202.273i −0.150687 0.260997i
\(776\) 0 0
\(777\) 136.903 77.1797i 0.176194 0.0993303i
\(778\) 0 0
\(779\) −317.532 55.9894i −0.407615 0.0718735i
\(780\) 0 0
\(781\) 819.639 687.759i 1.04947 0.880613i
\(782\) 0 0
\(783\) 5.88508 + 40.6530i 0.00751607 + 0.0519196i
\(784\) 0