Properties

Label 225.4.k.d.124.12
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.12
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.d.49.12

$q$-expansion

\(f(q)\) \(=\) \(q+(3.69081 + 2.13089i) q^{2} +(-2.76977 - 4.39640i) q^{3} +(5.08138 + 8.80120i) q^{4} +(-0.854448 - 22.1284i) q^{6} +(-26.6423 - 15.3820i) q^{7} +9.21718i q^{8} +(-11.6567 + 24.3541i) q^{9} +O(q^{10})\) \(q+(3.69081 + 2.13089i) q^{2} +(-2.76977 - 4.39640i) q^{3} +(5.08138 + 8.80120i) q^{4} +(-0.854448 - 22.1284i) q^{6} +(-26.6423 - 15.3820i) q^{7} +9.21718i q^{8} +(-11.6567 + 24.3541i) q^{9} +(-20.3573 + 35.2599i) q^{11} +(24.6194 - 46.7171i) q^{12} +(-54.7482 + 31.6089i) q^{13} +(-65.5545 - 113.544i) q^{14} +(21.0102 - 36.3908i) q^{16} -6.58990i q^{17} +(-94.9186 + 65.0470i) q^{18} -75.3803 q^{19} +(6.16789 + 159.735i) q^{21} +(-150.270 + 86.7584i) q^{22} +(54.0077 - 31.1814i) q^{23} +(40.5225 - 25.5295i) q^{24} -269.420 q^{26} +(139.357 - 16.2075i) q^{27} -312.646i q^{28} +(24.8042 - 42.9621i) q^{29} +(-51.5021 - 89.2043i) q^{31} +(218.948 - 126.410i) q^{32} +(211.402 - 8.16291i) q^{33} +(14.0423 - 24.3221i) q^{34} +(-273.577 + 21.1590i) q^{36} -282.029i q^{37} +(-278.214 - 160.627i) q^{38} +(290.606 + 153.146i) q^{39} +(78.7700 + 136.434i) q^{41} +(-317.613 + 602.695i) q^{42} +(-292.555 - 168.907i) q^{43} -413.773 q^{44} +265.776 q^{46} +(-38.5518 - 22.2579i) q^{47} +(-218.182 + 8.42472i) q^{48} +(301.710 + 522.577i) q^{49} +(-28.9719 + 18.2525i) q^{51} +(-556.393 - 321.234i) q^{52} -26.2752i q^{53} +(548.876 + 237.135i) q^{54} +(141.778 - 245.567i) q^{56} +(208.786 + 331.402i) q^{57} +(183.095 - 105.710i) q^{58} +(-212.963 - 368.863i) q^{59} +(-425.297 + 736.637i) q^{61} -438.981i q^{62} +(685.176 - 469.546i) q^{63} +741.296 q^{64} +(797.638 + 420.346i) q^{66} +(83.4048 - 48.1538i) q^{67} +(57.9990 - 33.4858i) q^{68} +(-286.675 - 151.075i) q^{69} +952.164 q^{71} +(-224.476 - 107.442i) q^{72} +50.8558i q^{73} +(600.973 - 1040.92i) q^{74} +(-383.036 - 663.437i) q^{76} +(1084.73 - 626.271i) q^{77} +(746.233 + 1184.48i) q^{78} +(-98.6395 + 170.849i) q^{79} +(-457.241 - 567.778i) q^{81} +671.400i q^{82} +(-171.247 - 98.8693i) q^{83} +(-1374.52 + 865.959i) q^{84} +(-719.844 - 1246.81i) q^{86} +(-257.581 + 9.94603i) q^{87} +(-324.997 - 187.637i) q^{88} -1364.54 q^{89} +1944.83 q^{91} +(548.868 + 316.889i) q^{92} +(-249.529 + 473.499i) q^{93} +(-94.8583 - 164.299i) q^{94} +(-1162.18 - 612.458i) q^{96} +(1239.42 + 715.579i) q^{97} +2571.64i q^{98} +(-621.422 - 906.799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.69081 + 2.13089i 1.30490 + 0.753383i 0.981240 0.192791i \(-0.0617539\pi\)
0.323658 + 0.946174i \(0.395087\pi\)
\(3\) −2.76977 4.39640i −0.533043 0.846088i
\(4\) 5.08138 + 8.80120i 0.635172 + 1.10015i
\(5\) 0 0
\(6\) −0.854448 22.1284i −0.0581378 1.50564i
\(7\) −26.6423 15.3820i −1.43855 0.830548i −0.440802 0.897604i \(-0.645306\pi\)
−0.997749 + 0.0670561i \(0.978639\pi\)
\(8\) 9.21718i 0.407346i
\(9\) −11.6567 + 24.3541i −0.431731 + 0.902003i
\(10\) 0 0
\(11\) −20.3573 + 35.2599i −0.557996 + 0.966478i 0.439667 + 0.898161i \(0.355096\pi\)
−0.997664 + 0.0683175i \(0.978237\pi\)
\(12\) 24.6194 46.7171i 0.592250 1.12384i
\(13\) −54.7482 + 31.6089i −1.16803 + 0.674364i −0.953216 0.302290i \(-0.902249\pi\)
−0.214817 + 0.976654i \(0.568915\pi\)
\(14\) −65.5545 113.544i −1.25144 2.16756i
\(15\) 0 0
\(16\) 21.0102 36.3908i 0.328285 0.568606i
\(17\) 6.58990i 0.0940168i −0.998894 0.0470084i \(-0.985031\pi\)
0.998894 0.0470084i \(-0.0149687\pi\)
\(18\) −94.9186 + 65.0470i −1.24292 + 0.851763i
\(19\) −75.3803 −0.910180 −0.455090 0.890445i \(-0.650393\pi\)
−0.455090 + 0.890445i \(0.650393\pi\)
\(20\) 0 0
\(21\) 6.16789 + 159.735i 0.0640926 + 1.65986i
\(22\) −150.270 + 86.7584i −1.45626 + 0.840770i
\(23\) 54.0077 31.1814i 0.489626 0.282686i −0.234793 0.972045i \(-0.575441\pi\)
0.724419 + 0.689360i \(0.242108\pi\)
\(24\) 40.5225 25.5295i 0.344651 0.217133i
\(25\) 0 0
\(26\) −269.420 −2.03222
\(27\) 139.357 16.2075i 0.993305 0.115524i
\(28\) 312.646i 2.11016i
\(29\) 24.8042 42.9621i 0.158828 0.275099i −0.775618 0.631202i \(-0.782562\pi\)
0.934446 + 0.356104i \(0.115895\pi\)
\(30\) 0 0
\(31\) −51.5021 89.2043i −0.298389 0.516824i 0.677379 0.735634i \(-0.263116\pi\)
−0.975767 + 0.218810i \(0.929783\pi\)
\(32\) 218.948 126.410i 1.20953 0.698321i
\(33\) 211.402 8.16291i 1.11516 0.0430600i
\(34\) 14.0423 24.3221i 0.0708306 0.122682i
\(35\) 0 0
\(36\) −273.577 + 21.1590i −1.26656 + 0.0979582i
\(37\) 282.029i 1.25312i −0.779374 0.626559i \(-0.784463\pi\)
0.779374 0.626559i \(-0.215537\pi\)
\(38\) −278.214 160.627i −1.18769 0.685714i
\(39\) 290.606 + 153.146i 1.19318 + 0.628794i
\(40\) 0 0
\(41\) 78.7700 + 136.434i 0.300044 + 0.519692i 0.976146 0.217117i \(-0.0696653\pi\)
−0.676102 + 0.736808i \(0.736332\pi\)
\(42\) −317.613 + 602.695i −1.16688 + 2.21423i
\(43\) −292.555 168.907i −1.03754 0.599025i −0.118406 0.992965i \(-0.537778\pi\)
−0.919136 + 0.393940i \(0.871112\pi\)
\(44\) −413.773 −1.41770
\(45\) 0 0
\(46\) 265.776 0.851882
\(47\) −38.5518 22.2579i −0.119646 0.0690777i 0.438983 0.898496i \(-0.355339\pi\)
−0.558629 + 0.829418i \(0.688672\pi\)
\(48\) −218.182 + 8.42472i −0.656081 + 0.0253334i
\(49\) 301.710 + 522.577i 0.879620 + 1.52355i
\(50\) 0 0
\(51\) −28.9719 + 18.2525i −0.0795465 + 0.0501150i
\(52\) −556.393 321.234i −1.48380 0.856675i
\(53\) 26.2752i 0.0680978i −0.999420 0.0340489i \(-0.989160\pi\)
0.999420 0.0340489i \(-0.0108402\pi\)
\(54\) 548.876 + 237.135i 1.38319 + 0.597592i
\(55\) 0 0
\(56\) 141.778 245.567i 0.338320 0.585988i
\(57\) 208.786 + 331.402i 0.485165 + 0.770093i
\(58\) 183.095 105.710i 0.414509 0.239317i
\(59\) −212.963 368.863i −0.469923 0.813930i 0.529486 0.848319i \(-0.322385\pi\)
−0.999409 + 0.0343889i \(0.989052\pi\)
\(60\) 0 0
\(61\) −425.297 + 736.637i −0.892684 + 1.54617i −0.0560400 + 0.998429i \(0.517847\pi\)
−0.836644 + 0.547746i \(0.815486\pi\)
\(62\) 438.981i 0.899204i
\(63\) 685.176 469.546i 1.37022 0.939004i
\(64\) 741.296 1.44784
\(65\) 0 0
\(66\) 797.638 + 420.346i 1.48761 + 0.783955i
\(67\) 83.4048 48.1538i 0.152082 0.0878048i −0.422028 0.906583i \(-0.638681\pi\)
0.574110 + 0.818778i \(0.305348\pi\)
\(68\) 57.9990 33.4858i 0.103433 0.0597168i
\(69\) −286.675 151.075i −0.500169 0.263583i
\(70\) 0 0
\(71\) 952.164 1.59156 0.795782 0.605583i \(-0.207060\pi\)
0.795782 + 0.605583i \(0.207060\pi\)
\(72\) −224.476 107.442i −0.367427 0.175864i
\(73\) 50.8558i 0.0815373i 0.999169 + 0.0407686i \(0.0129807\pi\)
−0.999169 + 0.0407686i \(0.987019\pi\)
\(74\) 600.973 1040.92i 0.944077 1.63519i
\(75\) 0 0
\(76\) −383.036 663.437i −0.578121 1.00134i
\(77\) 1084.73 626.271i 1.60541 0.926886i
\(78\) 746.233 + 1184.48i 1.08326 + 1.71944i
\(79\) −98.6395 + 170.849i −0.140479 + 0.243316i −0.927677 0.373384i \(-0.878197\pi\)
0.787198 + 0.616700i \(0.211531\pi\)
\(80\) 0 0
\(81\) −457.241 567.778i −0.627217 0.778844i
\(82\) 671.400i 0.904192i
\(83\) −171.247 98.8693i −0.226467 0.130751i 0.382474 0.923966i \(-0.375072\pi\)
−0.608941 + 0.793215i \(0.708405\pi\)
\(84\) −1374.52 + 865.959i −1.78539 + 1.12481i
\(85\) 0 0
\(86\) −719.844 1246.81i −0.902590 1.56333i
\(87\) −257.581 + 9.94603i −0.317420 + 0.0122566i
\(88\) −324.997 187.637i −0.393691 0.227298i
\(89\) −1364.54 −1.62519 −0.812593 0.582832i \(-0.801944\pi\)
−0.812593 + 0.582832i \(0.801944\pi\)
\(90\) 0 0
\(91\) 1944.83 2.24037
\(92\) 548.868 + 316.889i 0.621993 + 0.359108i
\(93\) −249.529 + 473.499i −0.278225 + 0.527953i
\(94\) −94.8583 164.299i −0.104084 0.180279i
\(95\) 0 0
\(96\) −1162.18 612.458i −1.23557 0.651132i
\(97\) 1239.42 + 715.579i 1.29736 + 0.749031i 0.979947 0.199256i \(-0.0638527\pi\)
0.317413 + 0.948288i \(0.397186\pi\)
\(98\) 2571.64i 2.65076i
\(99\) −621.422 906.799i −0.630862 0.920573i
\(100\) 0 0
\(101\) −553.808 + 959.224i −0.545604 + 0.945013i 0.452965 + 0.891528i \(0.350366\pi\)
−0.998569 + 0.0534851i \(0.982967\pi\)
\(102\) −145.824 + 5.63073i −0.141556 + 0.00546593i
\(103\) −458.018 + 264.437i −0.438154 + 0.252969i −0.702814 0.711373i \(-0.748074\pi\)
0.264660 + 0.964342i \(0.414740\pi\)
\(104\) −291.345 504.624i −0.274699 0.475793i
\(105\) 0 0
\(106\) 55.9896 96.9769i 0.0513037 0.0888607i
\(107\) 490.910i 0.443533i 0.975100 + 0.221766i \(0.0711823\pi\)
−0.975100 + 0.221766i \(0.928818\pi\)
\(108\) 850.770 + 1144.15i 0.758013 + 1.01941i
\(109\) 351.634 0.308994 0.154497 0.987993i \(-0.450624\pi\)
0.154497 + 0.987993i \(0.450624\pi\)
\(110\) 0 0
\(111\) −1239.91 + 781.157i −1.06025 + 0.667965i
\(112\) −1119.52 + 646.357i −0.944509 + 0.545313i
\(113\) −1526.33 + 881.226i −1.27066 + 0.733618i −0.975113 0.221710i \(-0.928836\pi\)
−0.295550 + 0.955327i \(0.595503\pi\)
\(114\) 64.4085 + 1668.04i 0.0529159 + 1.37041i
\(115\) 0 0
\(116\) 504.158 0.403533
\(117\) −131.620 1701.80i −0.104002 1.34471i
\(118\) 1815.20i 1.41613i
\(119\) −101.366 + 175.570i −0.0780854 + 0.135248i
\(120\) 0 0
\(121\) −163.340 282.914i −0.122720 0.212557i
\(122\) −3139.38 + 1812.52i −2.32972 + 1.34507i
\(123\) 381.642 724.195i 0.279769 0.530882i
\(124\) 523.403 906.561i 0.379056 0.656545i
\(125\) 0 0
\(126\) 3529.40 272.971i 2.49543 0.193001i
\(127\) 1506.12i 1.05234i −0.850380 0.526169i \(-0.823628\pi\)
0.850380 0.526169i \(-0.176372\pi\)
\(128\) 984.399 + 568.343i 0.679761 + 0.392460i
\(129\) 67.7286 + 1754.03i 0.0462262 + 1.19716i
\(130\) 0 0
\(131\) −637.562 1104.29i −0.425222 0.736506i 0.571219 0.820798i \(-0.306471\pi\)
−0.996441 + 0.0842915i \(0.973137\pi\)
\(132\) 1146.06 + 1819.11i 0.755692 + 1.19950i
\(133\) 2008.31 + 1159.50i 1.30934 + 0.755948i
\(134\) 410.441 0.264603
\(135\) 0 0
\(136\) 60.7403 0.0382973
\(137\) −1246.58 719.712i −0.777389 0.448826i 0.0581150 0.998310i \(-0.481491\pi\)
−0.835504 + 0.549484i \(0.814824\pi\)
\(138\) −736.140 1168.46i −0.454090 0.720768i
\(139\) −1269.75 2199.27i −0.774811 1.34201i −0.934901 0.354909i \(-0.884512\pi\)
0.160090 0.987102i \(-0.448822\pi\)
\(140\) 0 0
\(141\) 8.92502 + 231.139i 0.00533065 + 0.138052i
\(142\) 3514.25 + 2028.96i 2.07683 + 1.19906i
\(143\) 2573.89i 1.50517i
\(144\) 641.353 + 935.882i 0.371153 + 0.541598i
\(145\) 0 0
\(146\) −108.368 + 187.699i −0.0614288 + 0.106398i
\(147\) 1461.79 2773.86i 0.820180 1.55635i
\(148\) 2482.20 1433.10i 1.37862 0.795945i
\(149\) 46.8796 + 81.1979i 0.0257754 + 0.0446442i 0.878625 0.477512i \(-0.158461\pi\)
−0.852850 + 0.522156i \(0.825128\pi\)
\(150\) 0 0
\(151\) 534.065 925.027i 0.287825 0.498527i −0.685465 0.728105i \(-0.740401\pi\)
0.973290 + 0.229578i \(0.0737345\pi\)
\(152\) 694.794i 0.370758i
\(153\) 160.491 + 76.8166i 0.0848034 + 0.0405899i
\(154\) 5338.06 2.79320
\(155\) 0 0
\(156\) 128.809 + 3335.87i 0.0661087 + 1.71207i
\(157\) 157.370 90.8574i 0.0799966 0.0461861i −0.459468 0.888194i \(-0.651960\pi\)
0.539465 + 0.842008i \(0.318627\pi\)
\(158\) −728.119 + 420.380i −0.366621 + 0.211668i
\(159\) −115.517 + 72.7764i −0.0576167 + 0.0362990i
\(160\) 0 0
\(161\) −1918.52 −0.939136
\(162\) −477.719 3069.89i −0.231686 1.48885i
\(163\) 1103.07i 0.530056i 0.964241 + 0.265028i \(0.0853813\pi\)
−0.964241 + 0.265028i \(0.914619\pi\)
\(164\) −800.520 + 1386.54i −0.381159 + 0.660187i
\(165\) 0 0
\(166\) −421.359 729.816i −0.197011 0.341233i
\(167\) −3500.22 + 2020.85i −1.62189 + 0.936396i −0.635470 + 0.772126i \(0.719194\pi\)
−0.986415 + 0.164270i \(0.947473\pi\)
\(168\) −1472.31 + 56.8506i −0.676137 + 0.0261078i
\(169\) 899.745 1558.40i 0.409534 0.709333i
\(170\) 0 0
\(171\) 878.687 1835.82i 0.392953 0.820985i
\(172\) 3433.12i 1.52194i
\(173\) −2379.63 1373.88i −1.04578 0.603780i −0.124314 0.992243i \(-0.539673\pi\)
−0.921465 + 0.388463i \(0.873006\pi\)
\(174\) −971.875 512.167i −0.423435 0.223145i
\(175\) 0 0
\(176\) 855.423 + 1481.64i 0.366363 + 0.634560i
\(177\) −1031.81 + 1957.94i −0.438168 + 0.831456i
\(178\) −5036.27 2907.69i −2.12070 1.22439i
\(179\) 2838.32 1.18517 0.592587 0.805506i \(-0.298107\pi\)
0.592587 + 0.805506i \(0.298107\pi\)
\(180\) 0 0
\(181\) 3442.25 1.41359 0.706796 0.707417i \(-0.250140\pi\)
0.706796 + 0.707417i \(0.250140\pi\)
\(182\) 7177.99 + 4144.21i 2.92345 + 1.68785i
\(183\) 4416.53 170.537i 1.78404 0.0688876i
\(184\) 287.405 + 497.799i 0.115151 + 0.199447i
\(185\) 0 0
\(186\) −1929.94 + 1215.88i −0.760806 + 0.479314i
\(187\) 232.359 + 134.153i 0.0908652 + 0.0524610i
\(188\) 452.403i 0.175505i
\(189\) −3962.10 1711.77i −1.52487 0.658801i
\(190\) 0 0
\(191\) 373.148 646.311i 0.141361 0.244845i −0.786648 0.617402i \(-0.788185\pi\)
0.928010 + 0.372557i \(0.121519\pi\)
\(192\) −2053.22 3259.04i −0.771763 1.22500i
\(193\) −93.4506 + 53.9538i −0.0348535 + 0.0201227i −0.517326 0.855789i \(-0.673072\pi\)
0.482472 + 0.875911i \(0.339739\pi\)
\(194\) 3049.64 + 5282.13i 1.12861 + 1.95482i
\(195\) 0 0
\(196\) −3066.20 + 5310.82i −1.11742 + 1.93543i
\(197\) 3361.02i 1.21555i −0.794110 0.607774i \(-0.792063\pi\)
0.794110 0.607774i \(-0.207937\pi\)
\(198\) −361.264 4671.00i −0.129666 1.67653i
\(199\) −1368.99 −0.487663 −0.243831 0.969818i \(-0.578404\pi\)
−0.243831 + 0.969818i \(0.578404\pi\)
\(200\) 0 0
\(201\) −442.716 233.306i −0.155357 0.0818714i
\(202\) −4088.00 + 2360.21i −1.42391 + 0.822097i
\(203\) −1321.68 + 763.074i −0.456965 + 0.263829i
\(204\) −307.861 162.239i −0.105660 0.0556815i
\(205\) 0 0
\(206\) −2253.94 −0.762329
\(207\) 129.840 + 1678.78i 0.0435966 + 0.563688i
\(208\) 2656.44i 0.885534i
\(209\) 1534.54 2657.90i 0.507877 0.879669i
\(210\) 0 0
\(211\) −1251.27 2167.27i −0.408252 0.707114i 0.586442 0.809991i \(-0.300528\pi\)
−0.994694 + 0.102878i \(0.967195\pi\)
\(212\) 231.254 133.514i 0.0749178 0.0432538i
\(213\) −2637.28 4186.10i −0.848372 1.34660i
\(214\) −1046.07 + 1811.85i −0.334150 + 0.578765i
\(215\) 0 0
\(216\) 149.388 + 1284.48i 0.0470581 + 0.404619i
\(217\) 3168.81i 0.991305i
\(218\) 1297.81 + 749.292i 0.403206 + 0.232791i
\(219\) 223.583 140.859i 0.0689877 0.0434629i
\(220\) 0 0
\(221\) 208.299 + 360.785i 0.0634015 + 0.109815i
\(222\) −6240.85 + 240.979i −1.88675 + 0.0728535i
\(223\) 1623.39 + 937.263i 0.487489 + 0.281452i 0.723532 0.690291i \(-0.242517\pi\)
−0.236043 + 0.971743i \(0.575851\pi\)
\(224\) −7777.72 −2.31996
\(225\) 0 0
\(226\) −7511.18 −2.21078
\(227\) −4398.32 2539.37i −1.28602 0.742484i −0.308078 0.951361i \(-0.599686\pi\)
−0.977942 + 0.208877i \(0.933019\pi\)
\(228\) −1855.82 + 3521.55i −0.539055 + 1.02290i
\(229\) 432.933 + 749.861i 0.124930 + 0.216385i 0.921706 0.387890i \(-0.126796\pi\)
−0.796776 + 0.604275i \(0.793463\pi\)
\(230\) 0 0
\(231\) −5757.80 3034.30i −1.63998 0.864252i
\(232\) 395.990 + 228.625i 0.112060 + 0.0646981i
\(233\) 1142.10i 0.321122i −0.987026 0.160561i \(-0.948670\pi\)
0.987026 0.160561i \(-0.0513304\pi\)
\(234\) 3140.56 6561.48i 0.877371 1.83307i
\(235\) 0 0
\(236\) 2164.29 3748.66i 0.596964 1.03397i
\(237\) 1024.33 39.5527i 0.280748 0.0108406i
\(238\) −748.242 + 431.998i −0.203787 + 0.117657i
\(239\) −1574.68 2727.43i −0.426183 0.738171i 0.570347 0.821404i \(-0.306809\pi\)
−0.996530 + 0.0832330i \(0.973475\pi\)
\(240\) 0 0
\(241\) −2252.18 + 3900.90i −0.601975 + 1.04265i 0.390547 + 0.920583i \(0.372286\pi\)
−0.992522 + 0.122068i \(0.961047\pi\)
\(242\) 1392.24i 0.369821i
\(243\) −1229.72 + 3582.83i −0.324637 + 0.945839i
\(244\) −8644.39 −2.26803
\(245\) 0 0
\(246\) 2951.75 1859.63i 0.765027 0.481973i
\(247\) 4126.94 2382.69i 1.06312 0.613793i
\(248\) 822.212 474.704i 0.210526 0.121547i
\(249\) 39.6448 + 1026.72i 0.0100899 + 0.261307i
\(250\) 0 0
\(251\) 886.861 0.223021 0.111510 0.993763i \(-0.464431\pi\)
0.111510 + 0.993763i \(0.464431\pi\)
\(252\) 7614.21 + 3644.43i 1.90337 + 0.911023i
\(253\) 2539.08i 0.630950i
\(254\) 3209.38 5558.81i 0.792813 1.37319i
\(255\) 0 0
\(256\) −543.033 940.561i −0.132576 0.229629i
\(257\) 1958.98 1131.02i 0.475478 0.274517i −0.243052 0.970013i \(-0.578149\pi\)
0.718530 + 0.695496i \(0.244815\pi\)
\(258\) −3487.66 + 6618.09i −0.841598 + 1.59699i
\(259\) −4338.17 + 7513.92i −1.04077 + 1.80267i
\(260\) 0 0
\(261\) 757.166 + 1104.88i 0.179569 + 0.262032i
\(262\) 5434.30i 1.28142i
\(263\) 6305.20 + 3640.31i 1.47831 + 0.853503i 0.999699 0.0245245i \(-0.00780717\pi\)
0.478611 + 0.878027i \(0.341141\pi\)
\(264\) 75.2391 + 1948.53i 0.0175403 + 0.454257i
\(265\) 0 0
\(266\) 4941.52 + 8558.96i 1.13904 + 1.97287i
\(267\) 3779.48 + 5999.09i 0.866293 + 1.37505i
\(268\) 847.622 + 489.375i 0.193197 + 0.111542i
\(269\) 106.781 0.0242028 0.0121014 0.999927i \(-0.496148\pi\)
0.0121014 + 0.999927i \(0.496148\pi\)
\(270\) 0 0
\(271\) 5908.85 1.32449 0.662246 0.749287i \(-0.269603\pi\)
0.662246 + 0.749287i \(0.269603\pi\)
\(272\) −239.811 138.455i −0.0534585 0.0308643i
\(273\) −5386.73 8550.25i −1.19421 1.89555i
\(274\) −3067.25 5312.64i −0.676276 1.17134i
\(275\) 0 0
\(276\) −127.067 3290.75i −0.0277120 0.717681i
\(277\) −2849.30 1645.04i −0.618042 0.356827i 0.158064 0.987429i \(-0.449475\pi\)
−0.776106 + 0.630602i \(0.782808\pi\)
\(278\) 10822.8i 2.33492i
\(279\) 2772.83 214.456i 0.595000 0.0460184i
\(280\) 0 0
\(281\) −169.861 + 294.209i −0.0360608 + 0.0624591i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(282\) −459.590 + 872.107i −0.0970504 + 0.184160i
\(283\) −2251.37 + 1299.83i −0.472898 + 0.273028i −0.717452 0.696608i \(-0.754692\pi\)
0.244554 + 0.969636i \(0.421358\pi\)
\(284\) 4838.30 + 8380.19i 1.01092 + 1.75096i
\(285\) 0 0
\(286\) 5484.67 9499.73i 1.13397 1.96409i
\(287\) 4846.55i 0.996804i
\(288\) 526.373 + 6805.80i 0.107697 + 1.39248i
\(289\) 4869.57 0.991161
\(290\) 0 0
\(291\) −286.934 7430.98i −0.0578020 1.49695i
\(292\) −447.592 + 258.418i −0.0897033 + 0.0517902i
\(293\) −154.227 + 89.0427i −0.0307509 + 0.0177540i −0.515297 0.857012i \(-0.672318\pi\)
0.484546 + 0.874766i \(0.338985\pi\)
\(294\) 11306.0 7122.86i 2.24278 1.41297i
\(295\) 0 0
\(296\) 2599.52 0.510452
\(297\) −2265.45 + 5243.65i −0.442609 + 1.02447i
\(298\) 399.581i 0.0776749i
\(299\) −1971.22 + 3414.25i −0.381266 + 0.660372i
\(300\) 0 0
\(301\) 5196.24 + 9000.16i 0.995038 + 1.72346i
\(302\) 3942.26 2276.07i 0.751164 0.433685i
\(303\) 5751.06 222.067i 1.09039 0.0421037i
\(304\) −1583.76 + 2743.15i −0.298798 + 0.517534i
\(305\) 0 0
\(306\) 428.653 + 625.504i 0.0800800 + 0.116855i
\(307\) 1537.60i 0.285848i 0.989734 + 0.142924i \(0.0456505\pi\)
−0.989734 + 0.142924i \(0.954349\pi\)
\(308\) 11023.9 + 6364.64i 2.03943 + 1.17746i
\(309\) 2431.18 + 1281.20i 0.447589 + 0.235874i
\(310\) 0 0
\(311\) −472.662 818.674i −0.0861807 0.149269i 0.819713 0.572774i \(-0.194133\pi\)
−0.905894 + 0.423505i \(0.860800\pi\)
\(312\) −1411.57 + 2678.57i −0.256137 + 0.486038i
\(313\) 1719.52 + 992.767i 0.310521 + 0.179280i 0.647160 0.762354i \(-0.275957\pi\)
−0.336638 + 0.941634i \(0.609290\pi\)
\(314\) 774.428 0.139183
\(315\) 0 0
\(316\) −2004.90 −0.356913
\(317\) 4488.81 + 2591.62i 0.795321 + 0.459179i 0.841833 0.539739i \(-0.181477\pi\)
−0.0465112 + 0.998918i \(0.514810\pi\)
\(318\) −581.428 + 22.4508i −0.102531 + 0.00395906i
\(319\) 1009.89 + 1749.19i 0.177251 + 0.307008i
\(320\) 0 0
\(321\) 2158.24 1359.71i 0.375268 0.236422i
\(322\) −7080.91 4088.16i −1.22548 0.707529i
\(323\) 496.748i 0.0855722i
\(324\) 2673.71 6909.37i 0.458455 1.18473i
\(325\) 0 0
\(326\) −2350.52 + 4071.22i −0.399336 + 0.691670i
\(327\) −973.945 1545.92i −0.164707 0.261437i
\(328\) −1257.53 + 726.037i −0.211694 + 0.122222i
\(329\) 684.741 + 1186.01i 0.114745 + 0.198744i
\(330\) 0 0
\(331\) 1086.68 1882.19i 0.180451 0.312551i −0.761583 0.648067i \(-0.775578\pi\)
0.942034 + 0.335517i \(0.108911\pi\)
\(332\) 2009.57i 0.332197i
\(333\) 6868.56 + 3287.54i 1.13032 + 0.541009i
\(334\) −17224.8 −2.82186
\(335\) 0 0
\(336\) 5942.47 + 3131.61i 0.964846 + 0.508463i
\(337\) −6798.57 + 3925.16i −1.09894 + 0.634472i −0.935942 0.352155i \(-0.885449\pi\)
−0.162995 + 0.986627i \(0.552116\pi\)
\(338\) 6641.58 3834.52i 1.06880 0.617071i
\(339\) 8101.81 + 4269.56i 1.29802 + 0.684043i
\(340\) 0 0
\(341\) 4193.78 0.665999
\(342\) 7154.99 4903.26i 1.13128 0.775257i
\(343\) 8011.53i 1.26117i
\(344\) 1556.85 2696.54i 0.244010 0.422638i
\(345\) 0 0
\(346\) −5855.16 10141.4i −0.909756 1.57574i
\(347\) −8116.60 + 4686.12i −1.25568 + 0.724969i −0.972232 0.234018i \(-0.924813\pi\)
−0.283451 + 0.958987i \(0.591479\pi\)
\(348\) −1396.40 2216.48i −0.215101 0.341425i
\(349\) −588.952 + 1020.10i −0.0903321 + 0.156460i −0.907651 0.419726i \(-0.862126\pi\)
0.817319 + 0.576186i \(0.195460\pi\)
\(350\) 0 0
\(351\) −7117.23 + 5292.25i −1.08231 + 0.804784i
\(352\) 10293.4i 1.55864i
\(353\) −6289.19 3631.06i −0.948271 0.547484i −0.0557274 0.998446i \(-0.517748\pi\)
−0.892543 + 0.450962i \(0.851081\pi\)
\(354\) −7980.37 + 5027.70i −1.19817 + 0.754856i
\(355\) 0 0
\(356\) −6933.77 12009.6i −1.03227 1.78795i
\(357\) 1052.64 40.6458i 0.156055 0.00602578i
\(358\) 10475.7 + 6048.15i 1.54653 + 0.892890i
\(359\) 1939.95 0.285199 0.142600 0.989780i \(-0.454454\pi\)
0.142600 + 0.989780i \(0.454454\pi\)
\(360\) 0 0
\(361\) −1176.81 −0.171572
\(362\) 12704.7 + 7335.05i 1.84459 + 1.06498i
\(363\) −791.388 + 1501.72i −0.114427 + 0.217134i
\(364\) 9882.41 + 17116.8i 1.42302 + 2.46474i
\(365\) 0 0
\(366\) 16664.0 + 8781.72i 2.37989 + 1.25417i
\(367\) −5630.85 3250.97i −0.800893 0.462396i 0.0428901 0.999080i \(-0.486343\pi\)
−0.843783 + 0.536684i \(0.819677\pi\)
\(368\) 2620.51i 0.371205i
\(369\) −4240.91 + 328.000i −0.598301 + 0.0462737i
\(370\) 0 0
\(371\) −404.165 + 700.034i −0.0565585 + 0.0979622i
\(372\) −5435.32 + 209.875i −0.757548 + 0.0292514i
\(373\) −11533.8 + 6659.02i −1.60106 + 0.924372i −0.609784 + 0.792568i \(0.708744\pi\)
−0.991276 + 0.131805i \(0.957923\pi\)
\(374\) 571.729 + 990.263i 0.0790465 + 0.136913i
\(375\) 0 0
\(376\) 205.155 355.339i 0.0281385 0.0487373i
\(377\) 3136.13i 0.428432i
\(378\) −10975.7 14760.6i −1.49347 2.00848i
\(379\) 3198.42 0.433488 0.216744 0.976228i \(-0.430456\pi\)
0.216744 + 0.976228i \(0.430456\pi\)
\(380\) 0 0
\(381\) −6621.53 + 4171.62i −0.890370 + 0.560941i
\(382\) 2754.43 1590.27i 0.368924 0.212999i
\(383\) 2026.93 1170.25i 0.270422 0.156128i −0.358658 0.933469i \(-0.616765\pi\)
0.629079 + 0.777341i \(0.283432\pi\)
\(384\) −227.895 5902.00i −0.0302858 0.784336i
\(385\) 0 0
\(386\) −459.878 −0.0606403
\(387\) 7523.81 5156.01i 0.988261 0.677248i
\(388\) 14544.5i 1.90305i
\(389\) 1995.97 3457.12i 0.260153 0.450599i −0.706129 0.708083i \(-0.749560\pi\)
0.966282 + 0.257484i \(0.0828936\pi\)
\(390\) 0 0
\(391\) −205.482 355.906i −0.0265772 0.0460330i
\(392\) −4816.69 + 2780.91i −0.620611 + 0.358310i
\(393\) −3089.00 + 5861.61i −0.396488 + 0.752365i
\(394\) 7161.96 12404.9i 0.915773 1.58616i
\(395\) 0 0
\(396\) 4823.24 10077.1i 0.612063 1.27876i
\(397\) 4960.90i 0.627155i −0.949563 0.313577i \(-0.898472\pi\)
0.949563 0.313577i \(-0.101528\pi\)
\(398\) −5052.66 2917.16i −0.636350 0.367397i
\(399\) −464.937 12040.9i −0.0583358 1.51077i
\(400\) 0 0
\(401\) −413.811 716.742i −0.0515330 0.0892578i 0.839108 0.543965i \(-0.183077\pi\)
−0.890641 + 0.454707i \(0.849744\pi\)
\(402\) −1136.83 1804.47i −0.141044 0.223877i
\(403\) 5639.30 + 3255.85i 0.697056 + 0.402445i
\(404\) −11256.4 −1.38621
\(405\) 0 0
\(406\) −6504.11 −0.795058
\(407\) 9944.33 + 5741.36i 1.21111 + 0.699235i
\(408\) −168.237 267.039i −0.0204141 0.0324029i
\(409\) −4183.82 7246.59i −0.505811 0.876090i −0.999977 0.00672263i \(-0.997860\pi\)
0.494167 0.869367i \(-0.335473\pi\)
\(410\) 0 0
\(411\) 288.592 + 7473.90i 0.0346354 + 0.896983i
\(412\) −4654.73 2687.41i −0.556607 0.321357i
\(413\) 13103.2i 1.56117i
\(414\) −3098.08 + 6472.74i −0.367784 + 0.768400i
\(415\) 0 0
\(416\) −7991.34 + 13841.4i −0.941845 + 1.63132i
\(417\) −6151.96 + 11673.8i −0.722453 + 1.37091i
\(418\) 11327.4 6539.87i 1.32546 0.765252i
\(419\) 2100.36 + 3637.93i 0.244891 + 0.424163i 0.962101 0.272694i \(-0.0879145\pi\)
−0.717210 + 0.696857i \(0.754581\pi\)
\(420\) 0 0
\(421\) −3469.38 + 6009.14i −0.401632 + 0.695648i −0.993923 0.110077i \(-0.964890\pi\)
0.592291 + 0.805724i \(0.298224\pi\)
\(422\) 10665.3i 1.23028i
\(423\) 991.459 679.440i 0.113963 0.0780981i
\(424\) 242.184 0.0277394
\(425\) 0 0
\(426\) −813.575 21069.8i −0.0925301 2.39633i
\(427\) 22661.8 13083.8i 2.56835 1.48283i
\(428\) −4320.60 + 2494.50i −0.487953 + 0.281720i
\(429\) −11315.9 + 7129.09i −1.27351 + 0.802321i
\(430\) 0 0
\(431\) 6827.09 0.762991 0.381496 0.924371i \(-0.375409\pi\)
0.381496 + 0.924371i \(0.375409\pi\)
\(432\) 2338.11 5411.83i 0.260399 0.602724i
\(433\) 2199.59i 0.244124i 0.992522 + 0.122062i \(0.0389507\pi\)
−0.992522 + 0.122062i \(0.961049\pi\)
\(434\) −6752.39 + 11695.5i −0.746832 + 1.29355i
\(435\) 0 0
\(436\) 1786.78 + 3094.80i 0.196265 + 0.339940i
\(437\) −4071.12 + 2350.46i −0.445648 + 0.257295i
\(438\) 1125.36 43.4536i 0.122766 0.00474040i
\(439\) 4162.16 7209.07i 0.452504 0.783759i −0.546037 0.837761i \(-0.683864\pi\)
0.998541 + 0.0540018i \(0.0171977\pi\)
\(440\) 0 0
\(441\) −16243.8 + 1256.33i −1.75400 + 0.135658i
\(442\) 1775.45i 0.191063i
\(443\) −9410.93 5433.41i −1.00932 0.582729i −0.0983247 0.995154i \(-0.531348\pi\)
−0.910991 + 0.412426i \(0.864682\pi\)
\(444\) −13175.6 6943.39i −1.40830 0.742159i
\(445\) 0 0
\(446\) 3994.41 + 6918.51i 0.424082 + 0.734532i
\(447\) 227.133 431.001i 0.0240336 0.0456055i
\(448\) −19749.9 11402.6i −2.08280 1.20250i
\(449\) 4947.73 0.520040 0.260020 0.965603i \(-0.416271\pi\)
0.260020 + 0.965603i \(0.416271\pi\)
\(450\) 0 0
\(451\) −6414.18 −0.669694
\(452\) −15511.7 8955.69i −1.61418 0.931947i
\(453\) −5546.03 + 214.150i −0.575221 + 0.0222112i
\(454\) −10822.2 18744.7i −1.11875 1.93773i
\(455\) 0 0
\(456\) −3054.59 + 1924.42i −0.313694 + 0.197630i
\(457\) 12295.6 + 7098.85i 1.25856 + 0.726630i 0.972795 0.231669i \(-0.0744186\pi\)
0.285766 + 0.958299i \(0.407752\pi\)
\(458\) 3690.13i 0.376481i
\(459\) −106.806 918.347i −0.0108612 0.0933873i
\(460\) 0 0
\(461\) 9114.02 15785.9i 0.920786 1.59485i 0.122584 0.992458i \(-0.460882\pi\)
0.798202 0.602390i \(-0.205785\pi\)
\(462\) −14785.2 23468.3i −1.48890 2.36329i
\(463\) −3759.58 + 2170.59i −0.377370 + 0.217875i −0.676674 0.736283i \(-0.736579\pi\)
0.299303 + 0.954158i \(0.403246\pi\)
\(464\) −1042.28 1805.29i −0.104282 0.180621i
\(465\) 0 0
\(466\) 2433.69 4215.28i 0.241928 0.419032i
\(467\) 4919.63i 0.487481i 0.969841 + 0.243740i \(0.0783744\pi\)
−0.969841 + 0.243740i \(0.921626\pi\)
\(468\) 14309.1 9805.90i 1.41333 0.968542i
\(469\) −2962.80 −0.291704
\(470\) 0 0
\(471\) −835.324 440.206i −0.0817191 0.0430650i
\(472\) 3399.88 1962.92i 0.331551 0.191421i
\(473\) 11911.3 6876.98i 1.15789 0.668508i
\(474\) 3864.88 + 2036.75i 0.374515 + 0.197365i
\(475\) 0 0
\(476\) −2060.31 −0.198391
\(477\) 639.909 + 306.283i 0.0614244 + 0.0293999i
\(478\) 13421.9i 1.28432i
\(479\) 2286.41 3960.19i 0.218098 0.377757i −0.736128 0.676842i \(-0.763348\pi\)
0.954226 + 0.299085i \(0.0966814\pi\)
\(480\) 0 0
\(481\) 8914.64 + 15440.6i 0.845057 + 1.46368i
\(482\) −16624.8 + 9598.31i −1.57103 + 0.907035i
\(483\) 5313.87 + 8434.61i 0.500600 + 0.794592i
\(484\) 1659.99 2875.19i 0.155897 0.270021i
\(485\) 0 0
\(486\) −12173.3 + 10603.1i −1.13620 + 0.989646i
\(487\) 15751.5i 1.46564i 0.680421 + 0.732822i \(0.261797\pi\)
−0.680421 + 0.732822i \(0.738203\pi\)
\(488\) −6789.72 3920.04i −0.629828 0.363631i
\(489\) 4849.55 3055.26i 0.448475 0.282543i
\(490\) 0 0
\(491\) −7654.18 13257.4i −0.703520 1.21853i −0.967223 0.253928i \(-0.918277\pi\)
0.263703 0.964604i \(-0.415056\pi\)
\(492\) 8313.05 320.994i 0.761751 0.0294137i
\(493\) −283.116 163.457i −0.0258639 0.0149325i
\(494\) 20309.0 1.84968
\(495\) 0 0
\(496\) −4328.28 −0.391826
\(497\) −25367.9 14646.2i −2.28955 1.32187i
\(498\) −2041.49 + 3873.89i −0.183698 + 0.348580i
\(499\) 8866.05 + 15356.5i 0.795389 + 1.37765i 0.922592 + 0.385777i \(0.126067\pi\)
−0.127203 + 0.991877i \(0.540600\pi\)
\(500\) 0 0
\(501\) 18579.3 + 9791.07i 1.65681 + 0.873119i
\(502\) 3273.23 + 1889.80i 0.291019 + 0.168020i
\(503\) 10511.5i 0.931775i 0.884844 + 0.465887i \(0.154265\pi\)
−0.884844 + 0.465887i \(0.845735\pi\)
\(504\) 4327.89 + 6315.39i 0.382499 + 0.558155i
\(505\) 0 0
\(506\) −5410.49 + 9371.25i −0.475347 + 0.823326i
\(507\) −9343.47 + 360.782i −0.818457 + 0.0316033i
\(508\) 13255.7 7653.18i 1.15773 0.668416i
\(509\) 9815.42 + 17000.8i 0.854737 + 1.48045i 0.876889 + 0.480693i \(0.159615\pi\)
−0.0221524 + 0.999755i \(0.507052\pi\)
\(510\) 0 0
\(511\) 782.262 1354.92i 0.0677206 0.117296i
\(512\) 13722.1i 1.18444i
\(513\) −10504.8 + 1221.73i −0.904086 + 0.105147i
\(514\) 9640.30 0.827267
\(515\) 0 0
\(516\) −15093.4 + 9508.96i −1.28769 + 0.811257i
\(517\) 1569.62 906.223i 0.133524 0.0770902i
\(518\) −32022.7 + 18488.3i −2.71621 + 1.56820i
\(519\) 550.900 + 14267.1i 0.0465931 + 1.20666i
\(520\) 0 0
\(521\) 88.4336 0.00743636 0.00371818 0.999993i \(-0.498816\pi\)
0.00371818 + 0.999993i \(0.498816\pi\)
\(522\) 440.179 + 5691.34i 0.0369082 + 0.477209i
\(523\) 21346.4i 1.78473i −0.451317 0.892363i \(-0.649046\pi\)
0.451317 0.892363i \(-0.350954\pi\)
\(524\) 6479.39 11222.6i 0.540178 0.935616i
\(525\) 0 0
\(526\) 15514.2 + 26871.4i 1.28603 + 2.22747i
\(527\) −587.847 + 339.394i −0.0485902 + 0.0280535i
\(528\) 4144.55 7864.58i 0.341606 0.648224i
\(529\) −4138.94 + 7168.86i −0.340178 + 0.589205i
\(530\) 0 0
\(531\) 11465.8 886.783i 0.937047 0.0724729i
\(532\) 23567.4i 1.92063i
\(533\) −8625.03 4979.67i −0.700923 0.404678i
\(534\) 1165.93 + 30195.1i 0.0944847 + 2.44695i
\(535\) 0 0
\(536\) 443.842 + 768.757i 0.0357669 + 0.0619501i
\(537\) −7861.51 12478.4i −0.631749 1.00276i
\(538\) 394.108 + 227.538i 0.0315821 + 0.0182340i
\(539\) −24568.0 −1.96330
\(540\) 0 0
\(541\) −14432.6 −1.14696 −0.573480 0.819220i \(-0.694407\pi\)
−0.573480 + 0.819220i \(0.694407\pi\)
\(542\) 21808.4 + 12591.1i 1.72833 + 0.997850i
\(543\) −9534.24 15133.5i −0.753505 1.19602i
\(544\) −833.027 1442.84i −0.0656539 0.113716i
\(545\) 0 0
\(546\) −1661.75 43035.9i −0.130250 3.37320i
\(547\) 14349.7 + 8284.80i 1.12166 + 0.647592i 0.941825 0.336105i \(-0.109110\pi\)
0.179837 + 0.983696i \(0.442443\pi\)
\(548\) 14628.5i 1.14033i
\(549\) −12982.5 18944.5i −1.00925 1.47273i
\(550\) 0 0
\(551\) −1869.75 + 3238.50i −0.144562 + 0.250389i
\(552\) 1392.48 2642.34i 0.107369 0.203742i
\(553\) 5255.98 3034.54i 0.404172 0.233349i
\(554\) −7010.80 12143.1i −0.537654 0.931245i
\(555\) 0 0
\(556\) 12904.1 22350.6i 0.984277 1.70482i
\(557\) 11597.0i 0.882191i 0.897460 + 0.441096i \(0.145410\pi\)
−0.897460 + 0.441096i \(0.854590\pi\)
\(558\) 10691.0 + 5117.08i 0.811084 + 0.388214i
\(559\) 21355.9 1.61584
\(560\) 0 0
\(561\) −53.7928 1393.12i −0.00404836 0.104844i
\(562\) −1253.85 + 723.912i −0.0941113 + 0.0543352i
\(563\) 19961.3 11524.6i 1.49426 0.862709i 0.494278 0.869304i \(-0.335432\pi\)
0.999978 + 0.00659429i \(0.00209904\pi\)
\(564\) −1988.95 + 1253.05i −0.148493 + 0.0935516i
\(565\) 0 0
\(566\) −11079.2 −0.822778
\(567\) 3448.45 + 22160.2i 0.255417 + 1.64134i
\(568\) 8776.27i 0.648317i
\(569\) 7366.96 12759.9i 0.542775 0.940114i −0.455968 0.889996i \(-0.650707\pi\)
0.998743 0.0501179i \(-0.0159597\pi\)
\(570\) 0 0
\(571\) −7555.94 13087.3i −0.553776 0.959169i −0.997998 0.0632515i \(-0.979853\pi\)
0.444221 0.895917i \(-0.353480\pi\)
\(572\) 22653.3 13078.9i 1.65591 0.956043i
\(573\) −3874.98 + 149.625i −0.282512 + 0.0109087i
\(574\) 10327.5 17887.7i 0.750975 1.30073i
\(575\) 0 0
\(576\) −8641.09 + 18053.6i −0.625079 + 1.30596i
\(577\) 26150.5i 1.88676i −0.331715 0.943380i \(-0.607627\pi\)
0.331715 0.943380i \(-0.392373\pi\)
\(578\) 17972.7 + 10376.5i 1.29336 + 0.746724i
\(579\) 496.039 + 261.407i 0.0356040 + 0.0187629i
\(580\) 0 0
\(581\) 3041.61 + 5268.22i 0.217190 + 0.376184i
\(582\) 14775.6 28037.7i 1.05235 1.99691i
\(583\) 926.463 + 534.894i 0.0658150 + 0.0379983i
\(584\) −468.747 −0.0332139
\(585\) 0 0
\(586\) −758.961 −0.0535023
\(587\) −1811.33 1045.77i −0.127362 0.0735326i 0.434965 0.900447i \(-0.356761\pi\)
−0.562327 + 0.826915i \(0.690094\pi\)
\(588\) 31841.2 1229.49i 2.23318 0.0862303i
\(589\) 3882.24 + 6724.24i 0.271587 + 0.470403i
\(590\) 0 0
\(591\) −14776.4 + 9309.26i −1.02846 + 0.647939i
\(592\) −10263.3 5925.50i −0.712530 0.411379i
\(593\) 3260.34i 0.225778i −0.993608 0.112889i \(-0.963990\pi\)
0.993608 0.112889i \(-0.0360104\pi\)
\(594\) −19535.0 + 14525.9i −1.34938 + 1.00337i
\(595\) 0 0
\(596\) −476.426 + 825.194i −0.0327436 + 0.0567135i
\(597\) 3791.78 + 6018.61i 0.259945 + 0.412606i
\(598\) −14550.8 + 8400.90i −0.995026 + 0.574479i
\(599\) −11499.6 19917.9i −0.784410 1.35864i −0.929351 0.369197i \(-0.879633\pi\)
0.144941 0.989440i \(-0.453701\pi\)
\(600\) 0 0
\(601\) 7146.93 12378.9i 0.485074 0.840173i −0.514779 0.857323i \(-0.672126\pi\)
0.999853 + 0.0171500i \(0.00545928\pi\)
\(602\) 44290.5i 2.99858i
\(603\) 200.513 + 2592.56i 0.0135415 + 0.175087i
\(604\) 10855.1 0.731274
\(605\) 0 0
\(606\) 21699.3 + 11435.3i 1.45457 + 0.766544i
\(607\) −14232.3 + 8217.04i −0.951685 + 0.549455i −0.893604 0.448856i \(-0.851831\pi\)
−0.0580809 + 0.998312i \(0.518498\pi\)
\(608\) −16504.4 + 9528.80i −1.10089 + 0.635598i
\(609\) 7015.54 + 3697.11i 0.466805 + 0.246001i
\(610\) 0 0
\(611\) 2814.19 0.186334
\(612\) 139.435 + 1802.85i 0.00920971 + 0.119078i
\(613\) 3674.45i 0.242104i −0.992646 0.121052i \(-0.961373\pi\)
0.992646 0.121052i \(-0.0386267\pi\)
\(614\) −3276.45 + 5674.99i −0.215353 + 0.373003i
\(615\) 0 0
\(616\) 5772.46 + 9998.19i 0.377563 + 0.653958i
\(617\) 7471.69 4313.78i 0.487519 0.281469i −0.236026 0.971747i \(-0.575845\pi\)
0.723544 + 0.690278i \(0.242512\pi\)
\(618\) 6242.91 + 9909.25i 0.406354 + 0.644998i
\(619\) −654.905 + 1134.33i −0.0425248 + 0.0736551i −0.886504 0.462720i \(-0.846873\pi\)
0.843980 + 0.536375i \(0.180207\pi\)
\(620\) 0 0
\(621\) 7020.97 5220.67i 0.453691 0.337356i
\(622\) 4028.76i 0.259708i
\(623\) 36354.7 + 20989.4i 2.33791 + 1.34979i
\(624\) 11678.8 7357.73i 0.749240 0.472027i
\(625\) 0 0
\(626\) 4230.95 + 7328.23i 0.270132 + 0.467883i
\(627\) −15935.5 + 615.323i −1.01500 + 0.0391924i
\(628\) 1599.31 + 923.362i 0.101623 + 0.0586722i
\(629\) −1858.54 −0.117814
\(630\) 0 0
\(631\) 14447.2 0.911463 0.455731 0.890117i \(-0.349378\pi\)
0.455731 + 0.890117i \(0.349378\pi\)
\(632\) −1574.74 909.179i −0.0991138 0.0572234i
\(633\) −6062.45 + 11503.9i −0.380665 + 0.722339i
\(634\) 11044.9 + 19130.3i 0.691875 + 1.19836i
\(635\) 0 0
\(636\) −1227.50 646.881i −0.0765310 0.0403309i
\(637\) −33036.2 19073.4i −2.05485 1.18637i
\(638\) 8607.88i 0.534152i
\(639\) −11099.1 + 23189.1i −0.687127 + 1.43560i
\(640\) 0 0
\(641\) 10036.6 17383.8i 0.618440 1.07117i −0.371330 0.928501i \(-0.621098\pi\)
0.989770 0.142669i \(-0.0455685\pi\)
\(642\) 10863.0 419.457i 0.667803 0.0257860i
\(643\) 15359.8 8867.96i 0.942037 0.543885i 0.0514386 0.998676i \(-0.483619\pi\)
0.890598 + 0.454791i \(0.150286\pi\)
\(644\) −9748.75 16885.3i −0.596513 1.03319i
\(645\) 0 0
\(646\) −1058.52 + 1833.40i −0.0644686 + 0.111663i
\(647\) 11456.8i 0.696158i −0.937465 0.348079i \(-0.886834\pi\)
0.937465 0.348079i \(-0.113166\pi\)
\(648\) 5233.31 4214.48i 0.317259 0.255494i
\(649\) 17341.4 1.04886
\(650\) 0 0
\(651\) 13931.4 8776.89i 0.838731 0.528408i
\(652\) −9708.36 + 5605.12i −0.583142 + 0.336677i
\(653\) −25177.0 + 14536.0i −1.50881 + 0.871113i −0.508864 + 0.860847i \(0.669935\pi\)
−0.999947 + 0.0102660i \(0.996732\pi\)
\(654\) −300.453 7781.08i −0.0179643 0.465236i
\(655\) 0 0
\(656\) 6619.90 0.393999
\(657\) −1238.55 592.812i −0.0735468 0.0352021i
\(658\) 5836.43i 0.345787i
\(659\) −2177.54 + 3771.62i −0.128718 + 0.222946i −0.923180 0.384368i \(-0.874419\pi\)
0.794462 + 0.607314i \(0.207753\pi\)
\(660\) 0 0
\(661\) −13647.7 23638.5i −0.803075 1.39097i −0.917583 0.397545i \(-0.869862\pi\)
0.114508 0.993422i \(-0.463471\pi\)
\(662\) 8021.46 4631.19i 0.470941 0.271898i
\(663\) 1009.22 1915.06i 0.0591172 0.112179i
\(664\) 911.297 1578.41i 0.0532608 0.0922504i
\(665\) 0 0
\(666\) 18345.2 + 26769.8i 1.06736 + 1.55752i
\(667\) 3093.72i 0.179594i
\(668\) −35571.8 20537.4i −2.06035 1.18955i
\(669\) −375.825 9733.06i −0.0217194 0.562484i
\(670\) 0 0
\(671\) −17315.8 29991.9i −0.996230 1.72552i
\(672\) 21542.5 + 34194.0i 1.23664 + 1.96289i
\(673\) −15380.6 8880.01i −0.880951 0.508617i −0.00997909 0.999950i \(-0.503176\pi\)
−0.870972 + 0.491333i \(0.836510\pi\)
\(674\) −33456.3 −1.91200
\(675\) 0 0
\(676\) 18287.8 1.04050
\(677\) −1677.78 968.667i −0.0952472 0.0549910i 0.451620 0.892210i \(-0.350846\pi\)
−0.546867 + 0.837219i \(0.684180\pi\)
\(678\) 20804.3 + 33022.2i 1.17844 + 1.87052i
\(679\) −22014.0 38129.4i −1.24421 2.15504i
\(680\) 0 0
\(681\) 1018.24 + 26370.3i 0.0572968 + 1.48386i
\(682\) 15478.4 + 8936.48i 0.869061 + 0.501753i
\(683\) 2125.71i 0.119090i 0.998226 + 0.0595448i \(0.0189649\pi\)
−0.998226 + 0.0595448i \(0.981035\pi\)
\(684\) 20622.3 1594.97i 1.15280 0.0891596i
\(685\) 0 0
\(686\) 17071.7 29569.0i 0.950146 1.64570i
\(687\) 2097.57 3980.29i 0.116488 0.221045i
\(688\) −12293.3 + 7097.55i −0.681218 + 0.393301i
\(689\) 830.532 + 1438.52i 0.0459227 + 0.0795405i
\(690\) 0 0
\(691\) −6913.13 + 11973.9i −0.380590 + 0.659201i −0.991147 0.132771i \(-0.957612\pi\)
0.610557 + 0.791973i \(0.290946\pi\)
\(692\) 27924.8i 1.53402i
\(693\) 2607.81 + 33717.9i 0.142947 + 1.84825i
\(694\) −39942.4 −2.18472
\(695\) 0 0
\(696\) −91.6744 2374.17i −0.00499268 0.129300i
\(697\) 899.084 519.086i 0.0488597 0.0282092i
\(698\) −4347.42 + 2509.98i −0.235748 + 0.136109i
\(699\) −5021.14 + 3163.36i −0.271698 + 0.171172i
\(700\) 0 0
\(701\) −24464.0 −1.31810 −0.659052 0.752097i \(-0.729042\pi\)
−0.659052 + 0.752097i \(0.729042\pi\)
\(702\) −37545.5 + 4366.64i −2.01861 + 0.234769i
\(703\) 21259.5i 1.14056i
\(704\) −15090.8 + 26138.0i −0.807892 + 1.39931i
\(705\) 0 0
\(706\) −15474.8 26803.1i −0.824931 1.42882i
\(707\) 29509.5 17037.3i 1.56976 0.906300i
\(708\) −22475.2 + 867.842i −1.19304 + 0.0460671i
\(709\) −14749.1 + 25546.2i −0.781263 + 1.35319i 0.149944 + 0.988695i \(0.452091\pi\)
−0.931206 + 0.364492i \(0.881243\pi\)
\(710\) 0 0
\(711\) −3011.05 4393.81i −0.158823 0.231759i
\(712\) 12577.3i 0.662012i
\(713\) −5563.02 3211.81i −0.292198 0.168700i
\(714\) 3971.70 + 2093.04i 0.208175 + 0.109706i
\(715\) 0 0
\(716\) 14422.6 + 24980.7i 0.752790 + 1.30387i
\(717\) −7629.38 + 14477.3i −0.397384 + 0.754065i
\(718\) 7159.98 + 4133.81i 0.372156 + 0.214864i
\(719\) 3857.66 0.200093 0.100046 0.994983i \(-0.468101\pi\)
0.100046 + 0.994983i \(0.468101\pi\)
\(720\) 0 0
\(721\) 16270.2 0.840410
\(722\) −4343.39 2507.66i −0.223884 0.129260i
\(723\) 23387.9 903.085i 1.20305 0.0464538i
\(724\) 17491.4 + 30295.9i 0.897874 + 1.55516i
\(725\) 0 0
\(726\) −6120.86 + 3856.19i −0.312901 + 0.197130i
\(727\) −7573.48 4372.55i −0.386361 0.223066i 0.294221 0.955737i \(-0.404940\pi\)
−0.680582 + 0.732672i \(0.738273\pi\)
\(728\) 17925.8i 0.912604i
\(729\) 19157.6 4517.26i 0.973309 0.229501i
\(730\) 0 0
\(731\) −1113.08 + 1927.91i −0.0563184 + 0.0975463i
\(732\) 23943.0 + 38004.2i 1.20896 + 1.91896i
\(733\) 8156.58 4709.20i 0.411010 0.237296i −0.280214 0.959938i \(-0.590405\pi\)
0.691223 + 0.722641i \(0.257072\pi\)
\(734\) −13854.9 23997.4i −0.696723 1.20676i
\(735\) 0 0
\(736\) 7883.26 13654.2i 0.394811 0.683832i
\(737\) 3921.13i 0.195979i
\(738\) −16351.3 7826.33i −0.815584 0.390368i
\(739\) −6219.42 −0.309587 −0.154794 0.987947i \(-0.549471\pi\)
−0.154794 + 0.987947i \(0.549471\pi\)
\(740\) 0 0
\(741\) −21905.9 11544.2i −1.08601 0.572316i
\(742\) −2983.39 + 1722.46i −0.147606 + 0.0852204i
\(743\) 25450.3 14693.7i 1.25663 0.725518i 0.284216 0.958760i \(-0.408267\pi\)
0.972419 + 0.233242i \(0.0749334\pi\)
\(744\) −4364.33 2299.95i −0.215059 0.113334i
\(745\) 0 0
\(746\) −56758.5 −2.78563
\(747\) 4404.05 3018.06i 0.215710 0.147825i
\(748\) 2726.72i 0.133287i
\(749\) 7551.15 13079.0i 0.368375 0.638045i
\(750\) 0 0
\(751\) 10823.6 + 18747.0i 0.525909 + 0.910901i 0.999544 + 0.0301801i \(0.00960808\pi\)
−0.473636 + 0.880721i \(0.657059\pi\)
\(752\) −1619.97 + 935.287i −0.0785559 + 0.0453543i
\(753\) −2456.40 3899.00i −0.118880 0.188695i
\(754\) −6682.75 + 11574.9i −0.322774 + 0.559061i
\(755\) 0 0
\(756\) −5067.23 43569.4i −0.243774 2.09604i
\(757\) 13907.2i 0.667722i −0.942622 0.333861i \(-0.891648\pi\)
0.942622 0.333861i \(-0.108352\pi\)
\(758\) 11804.8 + 6815.48i 0.565657 + 0.326582i
\(759\) 11162.8 7032.66i 0.533840 0.336324i
\(760\) 0 0
\(761\) 11953.0 + 20703.3i 0.569379 + 0.986193i 0.996628 + 0.0820585i \(0.0261494\pi\)
−0.427249 + 0.904134i \(0.640517\pi\)
\(762\) −33328.0 + 1286.90i −1.58445 + 0.0611806i
\(763\) −9368.35 5408.82i −0.444504 0.256635i
\(764\) 7584.42 0.359155
\(765\) 0 0
\(766\) 9974.70 0.470497
\(767\) 23318.7 + 13463.1i 1.09777 + 0.633798i
\(768\) −2631.01 + 4992.53i −0.123618 + 0.234573i
\(769\) −12555.8 21747.3i −0.588783 1.01980i −0.994392 0.105755i \(-0.966274\pi\)
0.405609 0.914047i \(-0.367059\pi\)
\(770\) 0 0
\(771\) −10398.3 5479.81i −0.485716 0.255967i
\(772\) −949.716 548.319i −0.0442759 0.0255627i
\(773\) 14909.4i 0.693729i −0.937915 0.346865i \(-0.887246\pi\)
0.937915 0.346865i \(-0.112754\pi\)
\(774\) 38755.8 2997.45i 1.79981 0.139200i
\(775\) 0 0
\(776\) −6595.62 + 11424.0i −0.305115 + 0.528474i
\(777\) 45050.0 1739.53i 2.08000 0.0803155i
\(778\) 14733.5 8506.37i 0.678947 0.391990i