Properties

Label 225.4.h.d.181.1
Level $225$
Weight $4$
Character 225.181
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
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.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.1
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.71061 - 5.26471i) q^{2} +(-18.3188 + 13.3094i) q^{4} +(-11.1283 + 1.07706i) q^{5} -30.2200 q^{7} +(65.5791 + 47.6460i) q^{8} +O(q^{10})\) \(q+(-1.71061 - 5.26471i) q^{2} +(-18.3188 + 13.3094i) q^{4} +(-11.1283 + 1.07706i) q^{5} -30.2200 q^{7} +(65.5791 + 47.6460i) q^{8} +(24.7066 + 56.7450i) q^{10} +(-6.53575 - 20.1150i) q^{11} +(-1.85672 + 5.71440i) q^{13} +(51.6946 + 159.100i) q^{14} +(82.6849 - 254.478i) q^{16} +(17.3999 + 12.6418i) q^{17} +(-85.2864 - 61.9642i) q^{19} +(189.523 - 167.842i) q^{20} +(-94.7194 + 68.8177i) q^{22} +(1.91808 + 5.90324i) q^{23} +(122.680 - 23.9717i) q^{25} +33.2608 q^{26} +(553.596 - 402.211i) q^{28} +(187.176 - 135.991i) q^{29} +(142.099 + 103.241i) q^{31} -832.711 q^{32} +(36.7909 - 113.231i) q^{34} +(336.299 - 32.5487i) q^{35} +(-90.6084 + 278.864i) q^{37} +(-180.332 + 555.004i) q^{38} +(-781.104 - 459.589i) q^{40} +(18.2039 - 56.0257i) q^{41} -379.656 q^{43} +(387.446 + 281.496i) q^{44} +(27.7978 - 20.1962i) q^{46} +(-131.812 + 95.7671i) q^{47} +570.251 q^{49} +(-336.061 - 604.868i) q^{50} +(-42.0424 - 129.393i) q^{52} +(214.314 - 155.708i) q^{53} +(94.3971 + 216.807i) q^{55} +(-1981.80 - 1439.87i) q^{56} +(-1036.14 - 752.798i) q^{58} +(-141.788 + 436.378i) q^{59} +(185.460 + 570.786i) q^{61} +(300.457 - 924.713i) q^{62} +(762.963 + 2348.16i) q^{64} +(14.5075 - 65.5916i) q^{65} +(-269.638 - 195.903i) q^{67} -487.002 q^{68} +(-746.635 - 1714.84i) q^{70} +(715.330 - 519.718i) q^{71} +(100.853 + 310.394i) q^{73} +1623.13 q^{74} +2387.05 q^{76} +(197.511 + 607.876i) q^{77} +(-63.7800 + 46.3389i) q^{79} +(-646.058 + 2920.97i) q^{80} -326.099 q^{82} +(1062.34 + 771.834i) q^{83} +(-207.248 - 121.941i) q^{85} +(649.442 + 1998.78i) q^{86} +(529.790 - 1630.53i) q^{88} +(-348.484 - 1072.52i) q^{89} +(56.1102 - 172.690i) q^{91} +(-113.706 - 82.6120i) q^{92} +(729.664 + 530.132i) q^{94} +(1015.83 + 597.700i) q^{95} +(40.0395 - 29.0904i) q^{97} +(-975.476 - 3002.21i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.71061 5.26471i −0.604791 1.86136i −0.498220 0.867050i \(-0.666013\pi\)
−0.106571 0.994305i \(-0.533987\pi\)
\(3\) 0 0
\(4\) −18.3188 + 13.3094i −2.28986 + 1.66368i
\(5\) −11.1283 + 1.07706i −0.995349 + 0.0963350i
\(6\) 0 0
\(7\) −30.2200 −1.63173 −0.815865 0.578243i \(-0.803739\pi\)
−0.815865 + 0.578243i \(0.803739\pi\)
\(8\) 65.5791 + 47.6460i 2.89822 + 2.10568i
\(9\) 0 0
\(10\) 24.7066 + 56.7450i 0.781292 + 1.79444i
\(11\) −6.53575 20.1150i −0.179146 0.551354i 0.820653 0.571427i \(-0.193610\pi\)
−0.999799 + 0.0200732i \(0.993610\pi\)
\(12\) 0 0
\(13\) −1.85672 + 5.71440i −0.0396125 + 0.121915i −0.968907 0.247424i \(-0.920416\pi\)
0.929295 + 0.369339i \(0.120416\pi\)
\(14\) 51.6946 + 159.100i 0.986855 + 3.03723i
\(15\) 0 0
\(16\) 82.6849 254.478i 1.29195 3.97622i
\(17\) 17.3999 + 12.6418i 0.248241 + 0.180358i 0.704947 0.709260i \(-0.250971\pi\)
−0.456706 + 0.889618i \(0.650971\pi\)
\(18\) 0 0
\(19\) −85.2864 61.9642i −1.02979 0.748187i −0.0615244 0.998106i \(-0.519596\pi\)
−0.968267 + 0.249918i \(0.919596\pi\)
\(20\) 189.523 167.842i 2.11893 1.87653i
\(21\) 0 0
\(22\) −94.7194 + 68.8177i −0.917920 + 0.666908i
\(23\) 1.91808 + 5.90324i 0.0173890 + 0.0535178i 0.959374 0.282136i \(-0.0910429\pi\)
−0.941985 + 0.335654i \(0.891043\pi\)
\(24\) 0 0
\(25\) 122.680 23.9717i 0.981439 0.191774i
\(26\) 33.2608 0.250884
\(27\) 0 0
\(28\) 553.596 402.211i 3.73642 2.71467i
\(29\) 187.176 135.991i 1.19854 0.870791i 0.204400 0.978887i \(-0.434476\pi\)
0.994140 + 0.108097i \(0.0344757\pi\)
\(30\) 0 0
\(31\) 142.099 + 103.241i 0.823280 + 0.598148i 0.917650 0.397389i \(-0.130084\pi\)
−0.0943701 + 0.995537i \(0.530084\pi\)
\(32\) −832.711 −4.60012
\(33\) 0 0
\(34\) 36.7909 113.231i 0.185576 0.571144i
\(35\) 336.299 32.5487i 1.62414 0.157193i
\(36\) 0 0
\(37\) −90.6084 + 278.864i −0.402592 + 1.23905i 0.520296 + 0.853986i \(0.325821\pi\)
−0.922889 + 0.385066i \(0.874179\pi\)
\(38\) −180.332 + 555.004i −0.769834 + 2.36930i
\(39\) 0 0
\(40\) −781.104 459.589i −3.08759 1.81668i
\(41\) 18.2039 56.0257i 0.0693406 0.213408i −0.910381 0.413770i \(-0.864212\pi\)
0.979722 + 0.200362i \(0.0642117\pi\)
\(42\) 0 0
\(43\) −379.656 −1.34644 −0.673220 0.739442i \(-0.735089\pi\)
−0.673220 + 0.739442i \(0.735089\pi\)
\(44\) 387.446 + 281.496i 1.32749 + 0.964480i
\(45\) 0 0
\(46\) 27.7978 20.1962i 0.0890990 0.0647342i
\(47\) −131.812 + 95.7671i −0.409080 + 0.297214i −0.773229 0.634127i \(-0.781360\pi\)
0.364149 + 0.931341i \(0.381360\pi\)
\(48\) 0 0
\(49\) 570.251 1.66254
\(50\) −336.061 604.868i −0.950525 1.71082i
\(51\) 0 0
\(52\) −42.0424 129.393i −0.112120 0.345069i
\(53\) 214.314 155.708i 0.555440 0.403551i −0.274347 0.961631i \(-0.588462\pi\)
0.829787 + 0.558080i \(0.188462\pi\)
\(54\) 0 0
\(55\) 94.3971 + 216.807i 0.231427 + 0.531532i
\(56\) −1981.80 1439.87i −4.72910 3.43589i
\(57\) 0 0
\(58\) −1036.14 752.798i −2.34572 1.70426i
\(59\) −141.788 + 436.378i −0.312868 + 0.962908i 0.663755 + 0.747950i \(0.268962\pi\)
−0.976623 + 0.214958i \(0.931038\pi\)
\(60\) 0 0
\(61\) 185.460 + 570.786i 0.389273 + 1.19806i 0.933333 + 0.359013i \(0.116887\pi\)
−0.544059 + 0.839047i \(0.683113\pi\)
\(62\) 300.457 924.713i 0.615454 1.89417i
\(63\) 0 0
\(64\) 762.963 + 2348.16i 1.49016 + 4.58625i
\(65\) 14.5075 65.5916i 0.0276836 0.125164i
\(66\) 0 0
\(67\) −269.638 195.903i −0.491665 0.357215i 0.314160 0.949370i \(-0.398277\pi\)
−0.805824 + 0.592155i \(0.798277\pi\)
\(68\) −487.002 −0.868494
\(69\) 0 0
\(70\) −746.635 1714.84i −1.27486 2.92803i
\(71\) 715.330 519.718i 1.19569 0.868721i 0.201838 0.979419i \(-0.435309\pi\)
0.993854 + 0.110698i \(0.0353087\pi\)
\(72\) 0 0
\(73\) 100.853 + 310.394i 0.161698 + 0.497656i 0.998778 0.0494250i \(-0.0157389\pi\)
−0.837080 + 0.547081i \(0.815739\pi\)
\(74\) 1623.13 2.54980
\(75\) 0 0
\(76\) 2387.05 3.60281
\(77\) 197.511 + 607.876i 0.292317 + 0.899661i
\(78\) 0 0
\(79\) −63.7800 + 46.3389i −0.0908330 + 0.0659940i −0.632275 0.774744i \(-0.717879\pi\)
0.541442 + 0.840738i \(0.317879\pi\)
\(80\) −646.058 + 2920.97i −0.902894 + 4.08218i
\(81\) 0 0
\(82\) −326.099 −0.439165
\(83\) 1062.34 + 771.834i 1.40490 + 1.02072i 0.994039 + 0.109023i \(0.0347722\pi\)
0.410862 + 0.911698i \(0.365228\pi\)
\(84\) 0 0
\(85\) −207.248 121.941i −0.264462 0.155605i
\(86\) 649.442 + 1998.78i 0.814315 + 2.50620i
\(87\) 0 0
\(88\) 529.790 1630.53i 0.641770 1.97517i
\(89\) −348.484 1072.52i −0.415047 1.27738i −0.912209 0.409726i \(-0.865624\pi\)
0.497161 0.867658i \(-0.334376\pi\)
\(90\) 0 0
\(91\) 56.1102 172.690i 0.0646368 0.198932i
\(92\) −113.706 82.6120i −0.128855 0.0936184i
\(93\) 0 0
\(94\) 729.664 + 530.132i 0.800629 + 0.581691i
\(95\) 1015.83 + 597.700i 1.09708 + 0.645502i
\(96\) 0 0
\(97\) 40.0395 29.0904i 0.0419113 0.0304503i −0.566632 0.823971i \(-0.691754\pi\)
0.608544 + 0.793520i \(0.291754\pi\)
\(98\) −975.476 3002.21i −1.00549 3.09458i
\(99\) 0 0
\(100\) −1928.30 + 2071.93i −1.92830 + 2.07193i
\(101\) 790.998 0.779279 0.389640 0.920967i \(-0.372600\pi\)
0.389640 + 0.920967i \(0.372600\pi\)
\(102\) 0 0
\(103\) 46.4033 33.7140i 0.0443908 0.0322518i −0.565369 0.824838i \(-0.691266\pi\)
0.609759 + 0.792587i \(0.291266\pi\)
\(104\) −394.031 + 286.280i −0.371518 + 0.269924i
\(105\) 0 0
\(106\) −1186.37 861.946i −1.08708 0.789808i
\(107\) 470.946 0.425496 0.212748 0.977107i \(-0.431759\pi\)
0.212748 + 0.977107i \(0.431759\pi\)
\(108\) 0 0
\(109\) −71.2432 + 219.264i −0.0626042 + 0.192676i −0.977467 0.211090i \(-0.932299\pi\)
0.914863 + 0.403765i \(0.132299\pi\)
\(110\) 979.949 867.845i 0.849404 0.752234i
\(111\) 0 0
\(112\) −2498.74 + 7690.33i −2.10811 + 6.48811i
\(113\) 54.7705 168.566i 0.0455962 0.140331i −0.925667 0.378340i \(-0.876495\pi\)
0.971263 + 0.238009i \(0.0764949\pi\)
\(114\) 0 0
\(115\) −27.7032 63.6274i −0.0224638 0.0515938i
\(116\) −1618.88 + 4982.40i −1.29577 + 3.98797i
\(117\) 0 0
\(118\) 2539.95 1.98153
\(119\) −525.827 382.036i −0.405063 0.294295i
\(120\) 0 0
\(121\) 714.905 519.409i 0.537119 0.390240i
\(122\) 2687.77 1952.78i 1.99459 1.44915i
\(123\) 0 0
\(124\) −3977.16 −2.88032
\(125\) −1339.40 + 398.899i −0.958400 + 0.285429i
\(126\) 0 0
\(127\) −250.813 771.924i −0.175245 0.539348i 0.824400 0.566008i \(-0.191513\pi\)
−0.999645 + 0.0266600i \(0.991513\pi\)
\(128\) 5667.82 4117.91i 3.91382 2.84356i
\(129\) 0 0
\(130\) −370.137 + 35.8238i −0.249717 + 0.0241689i
\(131\) −1053.96 765.747i −0.702938 0.510714i 0.177950 0.984040i \(-0.443054\pi\)
−0.880888 + 0.473325i \(0.843054\pi\)
\(132\) 0 0
\(133\) 2577.36 + 1872.56i 1.68034 + 1.22084i
\(134\) −570.130 + 1754.68i −0.367550 + 1.13120i
\(135\) 0 0
\(136\) 538.741 + 1658.08i 0.339682 + 1.04543i
\(137\) −343.611 + 1057.53i −0.214282 + 0.659493i 0.784922 + 0.619595i \(0.212703\pi\)
−0.999204 + 0.0398976i \(0.987297\pi\)
\(138\) 0 0
\(139\) 7.34441 + 22.6038i 0.00448162 + 0.0137930i 0.953272 0.302112i \(-0.0976918\pi\)
−0.948791 + 0.315905i \(0.897692\pi\)
\(140\) −5727.40 + 5072.20i −3.45753 + 3.06199i
\(141\) 0 0
\(142\) −3959.81 2876.97i −2.34014 1.70021i
\(143\) 127.080 0.0743146
\(144\) 0 0
\(145\) −1936.49 + 1714.96i −1.10908 + 0.982202i
\(146\) 1461.62 1061.93i 0.828521 0.601956i
\(147\) 0 0
\(148\) −2051.68 6314.41i −1.13950 3.50703i
\(149\) −2190.65 −1.20446 −0.602232 0.798321i \(-0.705722\pi\)
−0.602232 + 0.798321i \(0.705722\pi\)
\(150\) 0 0
\(151\) 891.600 0.480513 0.240256 0.970709i \(-0.422769\pi\)
0.240256 + 0.970709i \(0.422769\pi\)
\(152\) −2640.66 8127.11i −1.40912 4.33681i
\(153\) 0 0
\(154\) 2862.42 2079.67i 1.49780 1.08821i
\(155\) −1692.52 995.850i −0.877074 0.516055i
\(156\) 0 0
\(157\) 2339.90 1.18946 0.594728 0.803927i \(-0.297260\pi\)
0.594728 + 0.803927i \(0.297260\pi\)
\(158\) 353.063 + 256.515i 0.177773 + 0.129160i
\(159\) 0 0
\(160\) 9266.69 896.878i 4.57873 0.443153i
\(161\) −57.9644 178.396i −0.0283741 0.0873266i
\(162\) 0 0
\(163\) −687.964 + 2117.34i −0.330586 + 1.01744i 0.638270 + 0.769813i \(0.279650\pi\)
−0.968856 + 0.247626i \(0.920350\pi\)
\(164\) 412.196 + 1268.61i 0.196263 + 0.604035i
\(165\) 0 0
\(166\) 2246.24 6913.21i 1.05025 3.23234i
\(167\) 501.922 + 364.668i 0.232574 + 0.168975i 0.697969 0.716128i \(-0.254087\pi\)
−0.465394 + 0.885103i \(0.654087\pi\)
\(168\) 0 0
\(169\) 1748.20 + 1270.14i 0.795723 + 0.578127i
\(170\) −287.466 + 1299.70i −0.129692 + 0.586366i
\(171\) 0 0
\(172\) 6954.85 5052.99i 3.08315 2.24004i
\(173\) −774.704 2384.29i −0.340461 1.04783i −0.963969 0.266013i \(-0.914293\pi\)
0.623509 0.781816i \(-0.285707\pi\)
\(174\) 0 0
\(175\) −3707.39 + 724.427i −1.60144 + 0.312923i
\(176\) −5659.23 −2.42375
\(177\) 0 0
\(178\) −5050.40 + 3669.33i −2.12665 + 1.54510i
\(179\) 1412.93 1026.56i 0.589987 0.428651i −0.252324 0.967643i \(-0.581195\pi\)
0.842311 + 0.538992i \(0.181195\pi\)
\(180\) 0 0
\(181\) 275.217 + 199.957i 0.113020 + 0.0821142i 0.642860 0.765984i \(-0.277748\pi\)
−0.529839 + 0.848098i \(0.677748\pi\)
\(182\) −1005.14 −0.409374
\(183\) 0 0
\(184\) −155.480 + 478.518i −0.0622942 + 0.191722i
\(185\) 707.968 3200.88i 0.281356 1.27207i
\(186\) 0 0
\(187\) 140.568 432.623i 0.0549697 0.169179i
\(188\) 1140.04 3508.68i 0.442266 1.36115i
\(189\) 0 0
\(190\) 1409.02 6370.50i 0.538006 2.43245i
\(191\) −754.426 + 2321.89i −0.285803 + 0.879611i 0.700354 + 0.713796i \(0.253026\pi\)
−0.986157 + 0.165815i \(0.946974\pi\)
\(192\) 0 0
\(193\) −2643.56 −0.985946 −0.492973 0.870045i \(-0.664090\pi\)
−0.492973 + 0.870045i \(0.664090\pi\)
\(194\) −221.644 161.034i −0.0820264 0.0595957i
\(195\) 0 0
\(196\) −10446.3 + 7589.71i −3.80698 + 2.76593i
\(197\) −2093.75 + 1521.20i −0.757225 + 0.550156i −0.898058 0.439877i \(-0.855022\pi\)
0.140833 + 0.990033i \(0.455022\pi\)
\(198\) 0 0
\(199\) 772.004 0.275005 0.137502 0.990501i \(-0.456093\pi\)
0.137502 + 0.990501i \(0.456093\pi\)
\(200\) 9187.40 + 4273.16i 3.24824 + 1.51079i
\(201\) 0 0
\(202\) −1353.09 4164.37i −0.471301 1.45052i
\(203\) −5656.46 + 4109.66i −1.95569 + 1.42089i
\(204\) 0 0
\(205\) −142.236 + 643.080i −0.0484594 + 0.219096i
\(206\) −256.872 186.628i −0.0868792 0.0631215i
\(207\) 0 0
\(208\) 1300.67 + 944.990i 0.433582 + 0.315016i
\(209\) −688.997 + 2120.52i −0.228033 + 0.701814i
\(210\) 0 0
\(211\) 1842.83 + 5671.63i 0.601257 + 1.85048i 0.520718 + 0.853729i \(0.325664\pi\)
0.0805394 + 0.996751i \(0.474336\pi\)
\(212\) −1853.60 + 5704.80i −0.600499 + 1.84815i
\(213\) 0 0
\(214\) −805.603 2479.39i −0.257336 0.791998i
\(215\) 4224.94 408.911i 1.34018 0.129709i
\(216\) 0 0
\(217\) −4294.23 3119.94i −1.34337 0.976016i
\(218\) 1276.23 0.396501
\(219\) 0 0
\(220\) −4614.82 2715.28i −1.41423 0.832110i
\(221\) −104.547 + 75.9580i −0.0318217 + 0.0231198i
\(222\) 0 0
\(223\) 1435.00 + 4416.46i 0.430917 + 1.32623i 0.897213 + 0.441597i \(0.145588\pi\)
−0.466297 + 0.884628i \(0.654412\pi\)
\(224\) 25164.6 7.50615
\(225\) 0 0
\(226\) −981.143 −0.288782
\(227\) −418.007 1286.49i −0.122221 0.376156i 0.871164 0.490992i \(-0.163366\pi\)
−0.993384 + 0.114836i \(0.963366\pi\)
\(228\) 0 0
\(229\) 2577.13 1872.40i 0.743675 0.540312i −0.150185 0.988658i \(-0.547987\pi\)
0.893860 + 0.448346i \(0.147987\pi\)
\(230\) −287.590 + 254.690i −0.0824484 + 0.0730165i
\(231\) 0 0
\(232\) 18754.3 5.30723
\(233\) 1720.35 + 1249.91i 0.483708 + 0.351434i 0.802759 0.596303i \(-0.203364\pi\)
−0.319052 + 0.947737i \(0.603364\pi\)
\(234\) 0 0
\(235\) 1363.70 1207.70i 0.378545 0.335240i
\(236\) −3210.55 9881.05i −0.885546 2.72543i
\(237\) 0 0
\(238\) −1111.82 + 3421.84i −0.302810 + 0.931953i
\(239\) −1449.47 4461.01i −0.392295 1.20736i −0.931049 0.364895i \(-0.881105\pi\)
0.538754 0.842463i \(-0.318895\pi\)
\(240\) 0 0
\(241\) −1069.17 + 3290.58i −0.285774 + 0.879522i 0.700391 + 0.713759i \(0.253009\pi\)
−0.986166 + 0.165763i \(0.946991\pi\)
\(242\) −3957.46 2875.26i −1.05122 0.763756i
\(243\) 0 0
\(244\) −10994.2 7987.78i −2.88456 2.09576i
\(245\) −6345.95 + 614.194i −1.65481 + 0.160161i
\(246\) 0 0
\(247\) 512.442 372.311i 0.132008 0.0959091i
\(248\) 4399.70 + 13540.9i 1.12654 + 3.46712i
\(249\) 0 0
\(250\) 4391.28 + 6369.22i 1.11092 + 1.61130i
\(251\) −5528.48 −1.39026 −0.695128 0.718886i \(-0.744652\pi\)
−0.695128 + 0.718886i \(0.744652\pi\)
\(252\) 0 0
\(253\) 106.207 77.1642i 0.0263921 0.0191750i
\(254\) −3634.91 + 2640.92i −0.897932 + 0.652386i
\(255\) 0 0
\(256\) −15395.3 11185.4i −3.75862 2.73080i
\(257\) −2290.19 −0.555869 −0.277934 0.960600i \(-0.589650\pi\)
−0.277934 + 0.960600i \(0.589650\pi\)
\(258\) 0 0
\(259\) 2738.19 8427.28i 0.656922 2.02180i
\(260\) 607.226 + 1394.65i 0.144841 + 0.332663i
\(261\) 0 0
\(262\) −2228.52 + 6858.68i −0.525491 + 1.61729i
\(263\) −651.760 + 2005.91i −0.152811 + 0.470304i −0.997933 0.0642705i \(-0.979528\pi\)
0.845122 + 0.534574i \(0.179528\pi\)
\(264\) 0 0
\(265\) −2217.26 + 1963.61i −0.513981 + 0.455182i
\(266\) 5449.64 16772.3i 1.25616 3.86606i
\(267\) 0 0
\(268\) 7546.82 1.72013
\(269\) 6952.97 + 5051.63i 1.57595 + 1.14499i 0.921162 + 0.389180i \(0.127242\pi\)
0.654787 + 0.755814i \(0.272758\pi\)
\(270\) 0 0
\(271\) 3304.58 2400.92i 0.740734 0.538175i −0.152207 0.988349i \(-0.548638\pi\)
0.892941 + 0.450174i \(0.148638\pi\)
\(272\) 4655.77 3382.61i 1.03786 0.754048i
\(273\) 0 0
\(274\) 6155.35 1.35715
\(275\) −1284.00 2311.03i −0.281556 0.506765i
\(276\) 0 0
\(277\) −1157.41 3562.16i −0.251055 0.772669i −0.994581 0.103962i \(-0.966848\pi\)
0.743526 0.668707i \(-0.233152\pi\)
\(278\) 106.439 77.3324i 0.0229632 0.0166838i
\(279\) 0 0
\(280\) 23605.0 + 13888.8i 5.03810 + 2.96434i
\(281\) 3085.22 + 2241.55i 0.654978 + 0.475870i 0.864963 0.501835i \(-0.167342\pi\)
−0.209985 + 0.977705i \(0.567342\pi\)
\(282\) 0 0
\(283\) −2689.86 1954.30i −0.565003 0.410499i 0.268284 0.963340i \(-0.413544\pi\)
−0.833287 + 0.552841i \(0.813544\pi\)
\(284\) −6186.88 + 19041.3i −1.29269 + 3.97849i
\(285\) 0 0
\(286\) −217.384 669.040i −0.0449448 0.138326i
\(287\) −550.121 + 1693.10i −0.113145 + 0.348225i
\(288\) 0 0
\(289\) −1375.26 4232.61i −0.279922 0.861512i
\(290\) 12341.3 + 7261.42i 2.49899 + 1.47036i
\(291\) 0 0
\(292\) −5978.68 4343.77i −1.19820 0.870547i
\(293\) 6316.24 1.25938 0.629691 0.776846i \(-0.283182\pi\)
0.629691 + 0.776846i \(0.283182\pi\)
\(294\) 0 0
\(295\) 1107.86 5008.88i 0.218651 0.988570i
\(296\) −19228.8 + 13970.5i −3.77584 + 2.74331i
\(297\) 0 0
\(298\) 3747.34 + 11533.1i 0.728449 + 2.24193i
\(299\) −37.2948 −0.00721343
\(300\) 0 0
\(301\) 11473.2 2.19703
\(302\) −1525.18 4694.02i −0.290610 0.894405i
\(303\) 0 0
\(304\) −22820.4 + 16580.0i −4.30539 + 3.12805i
\(305\) −2678.63 6152.15i −0.502878 1.15499i
\(306\) 0 0
\(307\) −8592.04 −1.59731 −0.798655 0.601790i \(-0.794455\pi\)
−0.798655 + 0.601790i \(0.794455\pi\)
\(308\) −11708.6 8506.82i −2.16611 1.57377i
\(309\) 0 0
\(310\) −2347.62 + 10614.1i −0.430116 + 1.94465i
\(311\) 140.125 + 431.260i 0.0255490 + 0.0786319i 0.963018 0.269437i \(-0.0868376\pi\)
−0.937469 + 0.348069i \(0.886838\pi\)
\(312\) 0 0
\(313\) −1961.96 + 6038.28i −0.354302 + 1.09043i 0.602112 + 0.798412i \(0.294326\pi\)
−0.956413 + 0.292016i \(0.905674\pi\)
\(314\) −4002.65 12318.9i −0.719372 2.21400i
\(315\) 0 0
\(316\) 551.632 1697.75i 0.0982017 0.302234i
\(317\) 5897.27 + 4284.62i 1.04487 + 0.759143i 0.971230 0.238142i \(-0.0765384\pi\)
0.0736400 + 0.997285i \(0.476538\pi\)
\(318\) 0 0
\(319\) −3958.79 2876.23i −0.694827 0.504822i
\(320\) −11019.6 25309.4i −1.92505 4.42136i
\(321\) 0 0
\(322\) −840.049 + 610.332i −0.145385 + 0.105629i
\(323\) −700.639 2156.35i −0.120695 0.371462i
\(324\) 0 0
\(325\) −90.7984 + 745.551i −0.0154972 + 0.127248i
\(326\) 12324.0 2.09375
\(327\) 0 0
\(328\) 3863.19 2806.77i 0.650333 0.472494i
\(329\) 3983.37 2894.09i 0.667508 0.484973i
\(330\) 0 0
\(331\) −3531.10 2565.49i −0.586365 0.426019i 0.254648 0.967034i \(-0.418040\pi\)
−0.841013 + 0.541015i \(0.818040\pi\)
\(332\) −29733.5 −4.91517
\(333\) 0 0
\(334\) 1061.28 3266.28i 0.173864 0.535098i
\(335\) 3211.62 + 1889.66i 0.523790 + 0.308189i
\(336\) 0 0
\(337\) 663.043 2040.64i 0.107176 0.329853i −0.883059 0.469262i \(-0.844520\pi\)
0.990235 + 0.139408i \(0.0445201\pi\)
\(338\) 3696.45 11376.5i 0.594853 1.83077i
\(339\) 0 0
\(340\) 5419.52 524.529i 0.864455 0.0836664i
\(341\) 1147.96 3533.07i 0.182304 0.561075i
\(342\) 0 0
\(343\) −6867.55 −1.08109
\(344\) −24897.5 18089.1i −3.90227 2.83517i
\(345\) 0 0
\(346\) −11227.4 + 8157.18i −1.74448 + 1.26744i
\(347\) 6185.75 4494.21i 0.956970 0.695279i 0.00452493 0.999990i \(-0.498560\pi\)
0.952445 + 0.304710i \(0.0985597\pi\)
\(348\) 0 0
\(349\) 7655.39 1.17416 0.587082 0.809527i \(-0.300276\pi\)
0.587082 + 0.809527i \(0.300276\pi\)
\(350\) 10155.8 + 18279.1i 1.55100 + 2.79160i
\(351\) 0 0
\(352\) 5442.39 + 16750.0i 0.824093 + 2.53630i
\(353\) −5076.69 + 3688.43i −0.765453 + 0.556134i −0.900578 0.434694i \(-0.856856\pi\)
0.135125 + 0.990829i \(0.456856\pi\)
\(354\) 0 0
\(355\) −7400.67 + 6554.05i −1.10644 + 0.979867i
\(356\) 20658.5 + 15009.3i 3.07555 + 2.23452i
\(357\) 0 0
\(358\) −7821.50 5682.65i −1.15469 0.838931i
\(359\) 2156.39 6636.67i 0.317019 0.975683i −0.657897 0.753108i \(-0.728554\pi\)
0.974916 0.222575i \(-0.0714462\pi\)
\(360\) 0 0
\(361\) 1314.66 + 4046.10i 0.191669 + 0.589897i
\(362\) 581.926 1790.98i 0.0844899 0.260033i
\(363\) 0 0
\(364\) 1270.52 + 3910.27i 0.182949 + 0.563060i
\(365\) −1456.64 3345.55i −0.208888 0.479764i
\(366\) 0 0
\(367\) −1972.27 1432.94i −0.280522 0.203811i 0.438623 0.898671i \(-0.355466\pi\)
−0.719145 + 0.694860i \(0.755466\pi\)
\(368\) 1660.84 0.235264
\(369\) 0 0
\(370\) −18062.8 + 1748.21i −2.53794 + 0.245635i
\(371\) −6476.59 + 4705.52i −0.906328 + 0.658486i
\(372\) 0 0
\(373\) 697.469 + 2146.59i 0.0968193 + 0.297979i 0.987724 0.156212i \(-0.0499283\pi\)
−0.890904 + 0.454191i \(0.849928\pi\)
\(374\) −2518.09 −0.348148
\(375\) 0 0
\(376\) −13207.0 −1.81144
\(377\) 429.575 + 1322.10i 0.0586850 + 0.180614i
\(378\) 0 0
\(379\) 7532.09 5472.38i 1.02084 0.741682i 0.0543834 0.998520i \(-0.482681\pi\)
0.966454 + 0.256838i \(0.0826807\pi\)
\(380\) −26564.0 + 2571.00i −3.58606 + 0.347077i
\(381\) 0 0
\(382\) 13514.6 1.81012
\(383\) 5295.40 + 3847.33i 0.706481 + 0.513289i 0.882037 0.471181i \(-0.156172\pi\)
−0.175555 + 0.984470i \(0.556172\pi\)
\(384\) 0 0
\(385\) −2852.68 6551.92i −0.377627 0.867316i
\(386\) 4522.09 + 13917.6i 0.596291 + 1.83520i
\(387\) 0 0
\(388\) −346.301 + 1065.80i −0.0453112 + 0.139454i
\(389\) 1760.54 + 5418.39i 0.229468 + 0.706230i 0.997807 + 0.0661869i \(0.0210833\pi\)
−0.768339 + 0.640043i \(0.778917\pi\)
\(390\) 0 0
\(391\) −41.2531 + 126.964i −0.00533570 + 0.0164216i
\(392\) 37396.6 + 27170.2i 4.81840 + 3.50077i
\(393\) 0 0
\(394\) 11590.2 + 8420.80i 1.48200 + 1.07674i
\(395\) 659.856 584.369i 0.0840530 0.0744375i
\(396\) 0 0
\(397\) 7305.74 5307.93i 0.923589 0.671026i −0.0208261 0.999783i \(-0.506630\pi\)
0.944415 + 0.328757i \(0.106630\pi\)
\(398\) −1320.60 4064.38i −0.166320 0.511881i
\(399\) 0 0
\(400\) 4043.50 33201.4i 0.505437 4.15018i
\(401\) 1291.00 0.160772 0.0803859 0.996764i \(-0.474385\pi\)
0.0803859 + 0.996764i \(0.474385\pi\)
\(402\) 0 0
\(403\) −853.797 + 620.320i −0.105535 + 0.0766758i
\(404\) −14490.2 + 10527.7i −1.78444 + 1.29647i
\(405\) 0 0
\(406\) 31312.1 + 22749.6i 3.82758 + 2.78090i
\(407\) 6201.53 0.755279
\(408\) 0 0
\(409\) −1299.63 + 3999.85i −0.157121 + 0.483570i −0.998370 0.0570792i \(-0.981821\pi\)
0.841248 + 0.540649i \(0.181821\pi\)
\(410\) 3628.94 351.227i 0.437123 0.0423070i
\(411\) 0 0
\(412\) −401.341 + 1235.20i −0.0479919 + 0.147704i
\(413\) 4284.83 13187.4i 0.510515 1.57121i
\(414\) 0 0
\(415\) −12653.4 7445.03i −1.49670 0.880632i
\(416\) 1546.11 4758.45i 0.182222 0.560822i
\(417\) 0 0
\(418\) 12342.5 1.44424
\(419\) −4482.54 3256.76i −0.522641 0.379721i 0.294957 0.955510i \(-0.404695\pi\)
−0.817598 + 0.575790i \(0.804695\pi\)
\(420\) 0 0
\(421\) 5750.48 4177.97i 0.665704 0.483662i −0.202881 0.979203i \(-0.565030\pi\)
0.868584 + 0.495541i \(0.165030\pi\)
\(422\) 26707.1 19403.9i 3.08077 2.23831i
\(423\) 0 0
\(424\) 21473.4 2.45953
\(425\) 2437.67 + 1133.79i 0.278222 + 0.129404i
\(426\) 0 0
\(427\) −5604.60 17249.2i −0.635188 1.95491i
\(428\) −8627.18 + 6268.01i −0.974323 + 0.707887i
\(429\) 0 0
\(430\) −9380.00 21543.6i −1.05196 2.41610i
\(431\) −4596.49 3339.54i −0.513701 0.373225i 0.300525 0.953774i \(-0.402838\pi\)
−0.814226 + 0.580549i \(0.802838\pi\)
\(432\) 0 0
\(433\) 12267.7 + 8913.00i 1.36154 + 0.989218i 0.998345 + 0.0575050i \(0.0183145\pi\)
0.363196 + 0.931713i \(0.381685\pi\)
\(434\) −9079.84 + 27944.9i −1.00425 + 3.09078i
\(435\) 0 0
\(436\) −1613.18 4964.87i −0.177196 0.545353i
\(437\) 202.203 622.318i 0.0221343 0.0681224i
\(438\) 0 0
\(439\) 583.950 + 1797.21i 0.0634861 + 0.195390i 0.977769 0.209687i \(-0.0672446\pi\)
−0.914282 + 0.405077i \(0.867245\pi\)
\(440\) −4139.51 + 18715.7i −0.448508 + 2.02780i
\(441\) 0 0
\(442\) 578.736 + 420.476i 0.0622798 + 0.0452489i
\(443\) 14518.3 1.55707 0.778536 0.627600i \(-0.215963\pi\)
0.778536 + 0.627600i \(0.215963\pi\)
\(444\) 0 0
\(445\) 5033.22 + 11560.1i 0.536174 + 1.23146i
\(446\) 20796.7 15109.7i 2.20796 1.60418i
\(447\) 0 0
\(448\) −23056.8 70961.5i −2.43154 7.48351i
\(449\) 15727.5 1.65307 0.826535 0.562885i \(-0.190309\pi\)
0.826535 + 0.562885i \(0.190309\pi\)
\(450\) 0 0
\(451\) −1245.93 −0.130086
\(452\) 1240.19 + 3816.90i 0.129056 + 0.397194i
\(453\) 0 0
\(454\) −6057.96 + 4401.37i −0.626243 + 0.454992i
\(455\) −438.417 + 1982.18i −0.0451721 + 0.204233i
\(456\) 0 0
\(457\) −3024.30 −0.309564 −0.154782 0.987949i \(-0.549468\pi\)
−0.154782 + 0.987949i \(0.549468\pi\)
\(458\) −14266.1 10364.9i −1.45548 1.05747i
\(459\) 0 0
\(460\) 1354.33 + 796.867i 0.137274 + 0.0807698i
\(461\) 1738.63 + 5350.95i 0.175653 + 0.540604i 0.999663 0.0259714i \(-0.00826790\pi\)
−0.824010 + 0.566576i \(0.808268\pi\)
\(462\) 0 0
\(463\) −1365.98 + 4204.05i −0.137111 + 0.421985i −0.995912 0.0903241i \(-0.971210\pi\)
0.858801 + 0.512309i \(0.171210\pi\)
\(464\) −19130.1 58876.5i −1.91400 5.89068i
\(465\) 0 0
\(466\) 3637.55 11195.2i 0.361602 1.11290i
\(467\) −4026.97 2925.76i −0.399028 0.289911i 0.370117 0.928985i \(-0.379318\pi\)
−0.769145 + 0.639075i \(0.779318\pi\)
\(468\) 0 0
\(469\) 8148.47 + 5920.21i 0.802263 + 0.582878i
\(470\) −8690.94 5113.60i −0.852942 0.501857i
\(471\) 0 0
\(472\) −30090.0 + 21861.7i −2.93433 + 2.13192i
\(473\) 2481.34 + 7636.76i 0.241209 + 0.742365i
\(474\) 0 0
\(475\) −11948.3 5557.30i −1.15416 0.536813i
\(476\) 14717.2 1.41715
\(477\) 0 0
\(478\) −21006.4 + 15262.1i −2.01007 + 1.46040i
\(479\) 5836.76 4240.66i 0.556761 0.404511i −0.273511 0.961869i \(-0.588185\pi\)
0.830272 + 0.557358i \(0.188185\pi\)
\(480\) 0 0
\(481\) −1425.31 1035.55i −0.135111 0.0981639i
\(482\) 19152.9 1.80994
\(483\) 0 0
\(484\) −6183.20 + 19029.9i −0.580692 + 1.78718i
\(485\) −414.241 + 366.852i −0.0387829 + 0.0343462i
\(486\) 0 0
\(487\) 4846.33 14915.5i 0.450941 1.38785i −0.424894 0.905243i \(-0.639689\pi\)
0.875835 0.482610i \(-0.160311\pi\)
\(488\) −15033.4 + 46268.0i −1.39453 + 4.29192i
\(489\) 0 0
\(490\) 14089.0 + 32358.9i 1.29893 + 2.98332i
\(491\) −4177.42 + 12856.8i −0.383960 + 1.18171i 0.553271 + 0.833001i \(0.313379\pi\)
−0.937232 + 0.348707i \(0.886621\pi\)
\(492\) 0 0
\(493\) 4976.02 0.454581
\(494\) −2836.69 2060.98i −0.258358 0.187708i
\(495\) 0 0
\(496\) 38021.9 27624.5i 3.44200 2.50076i
\(497\) −21617.3 + 15705.9i −1.95104 + 1.41752i
\(498\) 0 0
\(499\) −19053.5 −1.70932 −0.854660 0.519188i \(-0.826234\pi\)
−0.854660 + 0.519188i \(0.826234\pi\)
\(500\) 19227.2 25134.1i 1.71974 2.24806i
\(501\) 0 0
\(502\) 9457.05 + 29105.8i 0.840815 + 2.58776i
\(503\) 12244.1 8895.89i 1.08537 0.788565i 0.106756 0.994285i \(-0.465954\pi\)
0.978611 + 0.205720i \(0.0659537\pi\)
\(504\) 0 0
\(505\) −8802.49 + 851.950i −0.775655 + 0.0750719i
\(506\) −587.926 427.153i −0.0516532 0.0375282i
\(507\) 0 0
\(508\) 14868.5 + 10802.6i 1.29859 + 0.943478i
\(509\) −2000.14 + 6155.78i −0.174174 + 0.536052i −0.999595 0.0284660i \(-0.990938\pi\)
0.825421 + 0.564518i \(0.190938\pi\)
\(510\) 0 0
\(511\) −3047.79 9380.13i −0.263848 0.812040i
\(512\) −15233.0 + 46882.2i −1.31486 + 4.04672i
\(513\) 0 0
\(514\) 3917.62 + 12057.2i 0.336185 + 1.03467i
\(515\) −480.080 + 425.160i −0.0410774 + 0.0363782i
\(516\) 0 0
\(517\) 2787.84 + 2025.49i 0.237155 + 0.172303i
\(518\) −49051.1 −4.16059
\(519\) 0 0
\(520\) 4076.57 3610.22i 0.343787 0.304459i
\(521\) 12414.6 9019.77i 1.04395 0.758471i 0.0728937 0.997340i \(-0.476777\pi\)
0.971052 + 0.238869i \(0.0767766\pi\)
\(522\) 0 0
\(523\) −1899.57 5846.27i −0.158819 0.488795i 0.839709 0.543037i \(-0.182726\pi\)
−0.998528 + 0.0542423i \(0.982726\pi\)
\(524\) 29499.0 2.45929
\(525\) 0 0
\(526\) 11675.5 0.967821
\(527\) 1167.36 + 3592.77i 0.0964915 + 0.296970i
\(528\) 0 0
\(529\) 9812.14 7128.94i 0.806455 0.585924i
\(530\) 14130.7 + 8314.24i 1.15811 + 0.681411i
\(531\) 0 0
\(532\) −72136.9 −5.87882
\(533\) 286.354 + 208.048i 0.0232709 + 0.0169073i
\(534\) 0 0
\(535\) −5240.84 + 507.236i −0.423517 + 0.0409901i
\(536\) −8348.60 25694.4i −0.672770 2.07057i
\(537\) 0 0
\(538\) 14701.6 45246.7i 1.17812 3.62588i
\(539\) −3727.02 11470.6i −0.297837 0.916648i
\(540\) 0 0
\(541\) −3280.78 + 10097.2i −0.260724 + 0.802425i 0.731924 + 0.681386i \(0.238623\pi\)
−0.992648 + 0.121039i \(0.961377\pi\)
\(542\) −18293.0 13290.6i −1.44972 1.05329i
\(543\) 0 0
\(544\) −14489.1 10527.0i −1.14194 0.829669i
\(545\) 556.658 2516.78i 0.0437516 0.197811i
\(546\) 0 0
\(547\) −16829.3 + 12227.2i −1.31548 + 0.955754i −0.315506 + 0.948924i \(0.602174\pi\)
−0.999977 + 0.00683023i \(0.997826\pi\)
\(548\) −7780.50 23945.9i −0.606508 1.86664i
\(549\) 0 0
\(550\) −9970.49 + 10713.1i −0.772987 + 0.830563i
\(551\) −24390.1 −1.88576
\(552\) 0 0
\(553\) 1927.43 1400.36i 0.148215 0.107684i
\(554\) −16773.8 + 12186.9i −1.28637 + 0.934606i
\(555\) 0 0
\(556\) −435.384 316.325i −0.0332094 0.0241280i
\(557\) −8938.79 −0.679980 −0.339990 0.940429i \(-0.610424\pi\)
−0.339990 + 0.940429i \(0.610424\pi\)
\(558\) 0 0
\(559\) 704.915 2169.51i 0.0533358 0.164151i
\(560\) 19523.9 88271.9i 1.47328 6.66102i
\(561\) 0 0
\(562\) 6523.48 20077.2i 0.489638 1.50695i
\(563\) −3016.21 + 9282.93i −0.225787 + 0.694900i 0.772424 + 0.635107i \(0.219044\pi\)
−0.998211 + 0.0597931i \(0.980956\pi\)
\(564\) 0 0
\(565\) −427.949 + 1934.85i −0.0318654 + 0.144071i
\(566\) −5687.52 + 17504.4i −0.422375 + 1.29994i
\(567\) 0 0
\(568\) 71673.2 5.29462
\(569\) −11079.9 8050.05i −0.816336 0.593103i 0.0993244 0.995055i \(-0.468332\pi\)
−0.915661 + 0.401952i \(0.868332\pi\)
\(570\) 0 0
\(571\) 9324.33 6774.52i 0.683382 0.496506i −0.191096 0.981571i \(-0.561204\pi\)
0.874478 + 0.485065i \(0.161204\pi\)
\(572\) −2327.96 + 1691.36i −0.170170 + 0.123635i
\(573\) 0 0
\(574\) 9854.71 0.716599
\(575\) 376.820 + 678.229i 0.0273296 + 0.0491897i
\(576\) 0 0
\(577\) 4919.30 + 15140.0i 0.354927 + 1.09235i 0.956052 + 0.293198i \(0.0947195\pi\)
−0.601125 + 0.799155i \(0.705280\pi\)
\(578\) −19930.9 + 14480.7i −1.43429 + 1.04207i
\(579\) 0 0
\(580\) 12649.1 57189.5i 0.905562 4.09425i
\(581\) −32103.9 23324.9i −2.29242 1.66554i
\(582\) 0 0
\(583\) −4532.78 3293.26i −0.322004 0.233950i
\(584\) −8175.19 + 25160.6i −0.579267 + 1.78280i
\(585\) 0 0
\(586\) −10804.6 33253.2i −0.761663 2.34416i
\(587\) −5556.96 + 17102.6i −0.390733 + 1.20255i 0.541502 + 0.840700i \(0.317856\pi\)
−0.932235 + 0.361853i \(0.882144\pi\)
\(588\) 0 0
\(589\) −5721.86 17610.1i −0.400280 1.23194i
\(590\) −28265.4 + 2735.67i −1.97232 + 0.190891i
\(591\) 0 0
\(592\) 63472.7 + 46115.6i 4.40661 + 3.20159i
\(593\) 230.646 0.0159721 0.00798607 0.999968i \(-0.497458\pi\)
0.00798607 + 0.999968i \(0.497458\pi\)
\(594\) 0 0
\(595\) 6263.05 + 3685.08i 0.431530 + 0.253905i
\(596\) 40130.2 29156.3i 2.75805 2.00384i
\(597\) 0 0
\(598\) 63.7968 + 196.346i 0.00436262 + 0.0134268i
\(599\) 11209.1 0.764597 0.382298 0.924039i \(-0.375133\pi\)
0.382298 + 0.924039i \(0.375133\pi\)
\(600\) 0 0
\(601\) 8219.09 0.557843 0.278922 0.960314i \(-0.410023\pi\)
0.278922 + 0.960314i \(0.410023\pi\)
\(602\) −19626.2 60403.1i −1.32874 4.08945i
\(603\) 0 0
\(604\) −16333.1 + 11866.7i −1.10030 + 0.799418i
\(605\) −7396.28 + 6550.16i −0.497027 + 0.440168i
\(606\) 0 0
\(607\) 9305.08 0.622210 0.311105 0.950376i \(-0.399301\pi\)
0.311105 + 0.950376i \(0.399301\pi\)
\(608\) 71018.9 + 51598.3i 4.73717 + 3.44175i
\(609\) 0 0
\(610\) −27807.2 + 24626.1i −1.84570 + 1.63456i
\(611\) −302.513 931.040i −0.0200301 0.0616463i
\(612\) 0 0
\(613\) −2405.39 + 7403.03i −0.158487 + 0.487774i −0.998498 0.0547965i \(-0.982549\pi\)
0.840010 + 0.542571i \(0.182549\pi\)
\(614\) 14697.6 + 45234.6i 0.966038 + 2.97316i
\(615\) 0 0
\(616\) −16010.3 + 49274.6i −1.04720 + 3.22294i
\(617\) −745.708 541.789i −0.0486565 0.0353510i 0.563191 0.826327i \(-0.309573\pi\)
−0.611848 + 0.790976i \(0.709573\pi\)
\(618\) 0 0
\(619\) 6014.72 + 4369.95i 0.390553 + 0.283753i 0.765682 0.643219i \(-0.222402\pi\)
−0.375129 + 0.926972i \(0.622402\pi\)
\(620\) 44259.2 4283.63i 2.86692 0.277475i
\(621\) 0 0
\(622\) 2030.76 1475.43i 0.130910 0.0951117i
\(623\) 10531.2 + 32411.7i 0.677245 + 2.08435i
\(624\) 0 0
\(625\) 14475.7 5881.70i 0.926446 0.376429i
\(626\) 35145.9 2.24395
\(627\) 0 0
\(628\) −42864.3 + 31142.7i −2.72368 + 1.97887i
\(629\) −5101.92 + 3706.76i −0.323413 + 0.234973i
\(630\) 0 0
\(631\) 5821.33 + 4229.44i 0.367264 + 0.266833i 0.756075 0.654485i \(-0.227114\pi\)
−0.388812 + 0.921317i \(0.627114\pi\)
\(632\) −6390.50 −0.402216
\(633\) 0 0
\(634\) 12469.4 38376.7i 0.781106 2.40400i
\(635\) 3622.54 + 8320.09i 0.226388 + 0.519957i
\(636\) 0 0
\(637\) −1058.80 + 3258.65i −0.0658573 + 0.202688i
\(638\) −8370.58 + 25762.0i −0.519427 + 1.59863i
\(639\) 0 0
\(640\) −58638.2 + 51930.1i −3.62169 + 3.20737i
\(641\) −467.168 + 1437.79i −0.0287863 + 0.0885951i −0.964417 0.264384i \(-0.914831\pi\)
0.935631 + 0.352979i \(0.114831\pi\)
\(642\) 0 0
\(643\) −22396.8 −1.37363 −0.686813 0.726834i \(-0.740991\pi\)
−0.686813 + 0.726834i \(0.740991\pi\)
\(644\) 3436.19 + 2496.54i 0.210256 + 0.152760i
\(645\) 0 0
\(646\) −10154.0 + 7377.32i −0.618428 + 0.449314i
\(647\) 1561.70 1134.64i 0.0948944 0.0689448i −0.539326 0.842097i \(-0.681321\pi\)
0.634221 + 0.773152i \(0.281321\pi\)
\(648\) 0 0
\(649\) 9704.42 0.586952
\(650\) 4080.43 797.319i 0.246227 0.0481130i
\(651\) 0 0
\(652\) −15577.8 47943.5i −0.935696 2.87978i
\(653\) 23581.3 17132.8i 1.41318 1.02674i 0.420333 0.907370i \(-0.361913\pi\)
0.992850 0.119368i \(-0.0380868\pi\)
\(654\) 0 0
\(655\) 12553.6 + 7386.31i 0.748868 + 0.440622i
\(656\) −12752.1 9264.95i −0.758973 0.551426i
\(657\) 0 0
\(658\) −22050.5 16020.6i −1.30641 0.949162i
\(659\) 5189.79 15972.5i 0.306776 0.944161i −0.672232 0.740341i \(-0.734664\pi\)
0.979008 0.203820i \(-0.0653358\pi\)
\(660\) 0 0
\(661\) 7008.62 + 21570.3i 0.412411 + 1.26927i 0.914546 + 0.404482i \(0.132548\pi\)
−0.502135 + 0.864789i \(0.667452\pi\)
\(662\) −7466.26 + 22978.8i −0.438345 + 1.34909i
\(663\) 0 0
\(664\) 32892.4 + 101232.i 1.92240 + 5.91654i
\(665\) −30698.6 18062.5i −1.79013 1.05329i
\(666\) 0 0
\(667\) 1161.81 + 844.102i 0.0674442 + 0.0490011i
\(668\) −14048.2 −0.813682
\(669\) 0 0
\(670\) 4454.71 20140.7i 0.256866 1.16135i
\(671\) 10269.2 7461.03i 0.590818 0.429255i
\(672\) 0 0
\(673\) 1787.87 + 5502.51i 0.102403 + 0.315165i 0.989112 0.147163i \(-0.0470142\pi\)
−0.886709 + 0.462328i \(0.847014\pi\)
\(674\) −11877.6 −0.678793
\(675\) 0 0
\(676\) −48929.9 −2.78391
\(677\) 2989.08 + 9199.45i 0.169690 + 0.522251i 0.999351 0.0360158i \(-0.0114667\pi\)
−0.829662 + 0.558267i \(0.811467\pi\)
\(678\) 0 0
\(679\) −1209.99 + 879.113i −0.0683878 + 0.0496867i
\(680\) −7781.14 17871.4i −0.438813 1.00785i
\(681\) 0 0
\(682\) −20564.3 −1.15462
\(683\) −23680.4 17204.8i −1.32666 0.963872i −0.999823 0.0187892i \(-0.994019\pi\)
−0.326832 0.945082i \(-0.605981\pi\)
\(684\) 0 0
\(685\) 2684.80 12138.6i 0.149753 0.677068i
\(686\) 11747.7 + 36155.6i 0.653831 + 2.01229i
\(687\) 0 0
\(688\) −31391.8 + 96613.9i −1.73954 + 5.35374i
\(689\) 491.859 + 1513.79i 0.0271964 + 0.0837020i
\(690\) 0 0
\(691\) −6623.67 + 20385.6i −0.364654 + 1.12229i 0.585543 + 0.810642i \(0.300881\pi\)
−0.950197 + 0.311650i \(0.899119\pi\)
\(692\) 45925.3 + 33366.7i 2.52286 + 1.83296i
\(693\) 0 0
\(694\) −34242.1 24878.4i −1.87293 1.36076i
\(695\) −106.077 243.632i −0.00578952 0.0132971i
\(696\) 0 0
\(697\) 1025.01 744.714i 0.0557031 0.0404707i
\(698\) −13095.4 40303.4i −0.710124 2.18554i
\(699\) 0 0
\(700\) 58273.4 62613.9i 3.14647 3.38083i
\(701\) −16727.9 −0.901292 −0.450646 0.892703i \(-0.648806\pi\)
−0.450646 + 0.892703i \(0.648806\pi\)
\(702\) 0 0
\(703\) 25007.2 18168.8i 1.34163 0.974751i
\(704\) 42246.6 30694.0i 2.26169 1.64321i
\(705\) 0 0
\(706\) 28102.7 + 20417.8i 1.49810 + 1.08844i
\(707\) −23904.0 −1.27157
\(708\) 0 0
\(709\) −5241.61 + 16132.0i −0.277648 + 0.854514i 0.710858 + 0.703335i \(0.248307\pi\)
−0.988506 + 0.151178i \(0.951693\pi\)
\(710\) 47164.8 + 27751.0i 2.49305 + 1.46687i
\(711\) 0 0
\(712\) 28248.2 86939.0i 1.48686 4.57609i
\(713\) −336.898 + 1036.87i −0.0176956 + 0.0544614i
\(714\) 0 0
\(715\) −1414.19 + 136.873i −0.0739689 + 0.00715909i
\(716\) −12220.4 + 37610.7i −0.637848 + 1.96310i
\(717\) 0 0
\(718\) −38628.9 −2.00782
\(719\) 6363.32 + 4623.22i 0.330058 + 0.239801i 0.740455 0.672106i \(-0.234610\pi\)
−0.410397 + 0.911907i \(0.634610\pi\)
\(720\) 0 0
\(721\) −1402.31 + 1018.84i −0.0724338 + 0.0526262i
\(722\) 19052.7 13842.6i 0.982088 0.713529i
\(723\) 0 0
\(724\) −7702.96 −0.395412
\(725\) 19702.8 21170.3i 1.00930 1.08448i
\(726\) 0 0
\(727\) 2605.34 + 8018.41i 0.132912 + 0.409060i 0.995259 0.0972567i \(-0.0310068\pi\)
−0.862348 + 0.506316i \(0.831007\pi\)
\(728\) 11907.6 8651.40i 0.606217 0.440443i
\(729\) 0 0
\(730\) −15121.6 + 13391.7i −0.766679 + 0.678972i
\(731\) −6605.98 4799.53i −0.334242 0.242841i
\(732\) 0 0
\(733\) −17055.7 12391.7i −0.859435 0.624416i 0.0682959 0.997665i \(-0.478244\pi\)
−0.927731 + 0.373249i \(0.878244\pi\)
\(734\) −4170.22 + 12834.6i −0.209708 + 0.645414i
\(735\) 0 0
\(736\) −1597.21 4915.69i −0.0799915 0.246189i
\(737\) −2178.31 + 6704.14i −0.108872 + 0.335075i
\(738\) 0 0
\(739\) −1688.56 5196.84i −0.0840522 0.258686i 0.900194 0.435489i \(-0.143424\pi\)
−0.984246 + 0.176803i \(0.943424\pi\)
\(740\) 29632.7 + 68059.1i 1.47205 + 3.38095i
\(741\) 0 0
\(742\) 35852.1 + 26048.1i 1.77382 + 1.28875i
\(743\) −12400.7 −0.612300 −0.306150 0.951983i \(-0.599041\pi\)
−0.306150 + 0.951983i \(0.599041\pi\)
\(744\) 0 0
\(745\) 24378.3 2359.46i 1.19886 0.116032i
\(746\) 10108.1 7343.95i 0.496090 0.360430i
\(747\) 0 0
\(748\) 3182.92 + 9796.03i 0.155587 + 0.478848i
\(749\) −14232.0 −0.694293
\(750\) 0 0
\(751\) −29073.8 −1.41267 −0.706336 0.707876i \(-0.749653\pi\)
−0.706336 + 0.707876i \(0.749653\pi\)
\(752\) 13471.7 + 41461.7i 0.653276 + 2.01058i
\(753\) 0 0
\(754\) 6225.62 4523.18i 0.300694 0.218467i
\(755\) −9922.03 + 960.305i −0.478278 + 0.0462902i
\(756\) 0 0
\(757\) −17652.4 −0.847539 −0.423770 0.905770i \(-0.639293\pi\)
−0.423770 + 0.905770i \(0.639293\pi\)
\(758\) −41695.0 30293.2i −1.99793 1.45158i
\(759\) 0 0
\(760\) 38139.5 + 87597.1i 1.82035 + 4.18090i
\(761\) 9492.07 + 29213.6i 0.452151 + 1.39158i 0.874447 + 0.485121i \(0.161224\pi\)
−0.422296 + 0.906458i \(0.638776\pi\)
\(762\) 0 0
\(763\) 2152.97 6626.17i 0.102153 0.314395i
\(764\) −17082.7 52575.2i −0.808942 2.48967i
\(765\) 0 0
\(766\) 11196.7 34460.0i 0.528139 1.62545i
\(767\) −2230.38 1620.47i −0.104999 0.0762863i
\(768\) 0 0
\(769\) −1813.75 1317.77i −0.0850527 0.0617944i 0.544446 0.838796i \(-0.316740\pi\)
−0.629499 + 0.777001i \(0.716740\pi\)
\(770\) −29614.1 + 26226.3i −1.38600 + 1.22744i
\(771\) 0 0
\(772\) 48426.9 35184.2i 2.25767 1.64030i
\(773\) 10264.5 + 31590.8i 0.477604 + 1.46991i 0.842414 + 0.538831i \(0.181134\pi\)
−0.364810 + 0.931082i \(0.618866\pi\)
\(774\) 0 0
\(775\) 19907.5 + 9259.21i 0.922708 + 0.429162i
\(776\) 4011.79 0.185586
\(777\) 0 0
\(778\) 25514.6 18537.5i 1.17576 0.854243i
\(779\) −5024.13 + 3650.24i −0.231076 + 0.167886i
\(780\) 0 0
\(781\) −15129.3 10992.1i −0.693176 0.503622i
\(782\) 738.996 0.0337934
\(783\) 0 0
\(784\) 47151.2 145116.i 2.14792 6.61062i
\(785\) −26039.2 + 2520.21i −1.18392 + 0.114586i
\(786\) 0 0
\(787\) −715.273 + 2201.38i −0.0323973 + 0.0997088i −0.965948 0.258738i