Properties

Label 225.4.h.d.46.16
Level $225$
Weight $4$
Character 225.46
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 46.16
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.16

$q$-expansion

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

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 0.106571 0.994305i \(-0.466013\pi\)
0.498220 0.867050i \(-0.333987\pi\)
\(3\) 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 \(-0.806390\pi\)
0.999799 + 0.0200732i \(0.00638993\pi\)
\(12\) 0 0
\(13\) −1.85672 5.71440i −0.0396125 0.121915i 0.929295 0.369339i \(-0.120416\pi\)
−0.968907 + 0.247424i \(0.920416\pi\)
\(14\) −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 \(-0.749029\pi\)
0.456706 + 0.889618i \(0.349029\pi\)
\(18\) 0 0
\(19\) −85.2864 + 61.9642i −1.02979 + 0.748187i −0.968267 0.249918i \(-0.919596\pi\)
−0.0615244 + 0.998106i \(0.519596\pi\)
\(20\) −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 \(-0.908957\pi\)
0.941985 + 0.335654i \(0.108957\pi\)
\(24\) 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 \(-0.565524\pi\)
−0.994140 + 0.108097i \(0.965524\pi\)
\(30\) 0 0
\(31\) 142.099 103.241i 0.823280 0.598148i −0.0943701 0.995537i \(-0.530084\pi\)
0.917650 + 0.397389i \(0.130084\pi\)
\(32\) 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 −0.922889 0.385066i \(-0.874179\pi\)
0.520296 0.853986i \(-0.325821\pi\)
\(38\) 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 \(-0.135788\pi\)
−0.979722 + 0.200362i \(0.935788\pi\)
\(42\) 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 \(-0.218640\pi\)
−0.364149 + 0.931341i \(0.618640\pi\)
\(48\) 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 \(-0.411538\pi\)
−0.829787 + 0.558080i \(0.811538\pi\)
\(54\) 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 0.976623 + 0.214958i \(0.0689616\pi\)
−0.663755 + 0.747950i \(0.731038\pi\)
\(60\) 0 0
\(61\) 185.460 570.786i 0.389273 1.19806i −0.544059 0.839047i \(-0.683113\pi\)
0.933333 0.359013i \(-0.116887\pi\)
\(62\) −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 −0.805824 0.592155i \(-0.798277\pi\)
0.314160 + 0.949370i \(0.398277\pi\)
\(68\) 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 \(-0.564691\pi\)
−0.993854 + 0.110698i \(0.964691\pi\)
\(72\) 0 0
\(73\) 100.853 310.394i 0.161698 0.497656i −0.837080 0.547081i \(-0.815739\pi\)
0.998778 + 0.0494250i \(0.0157389\pi\)
\(74\) −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 0.541442 0.840738i \(-0.317879\pi\)
−0.632275 + 0.774744i \(0.717879\pi\)
\(80\) 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 −0.410862 + 0.911698i \(0.634772\pi\)
−0.994039 + 0.109023i \(0.965228\pi\)
\(84\) 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 −0.497161 0.867658i \(-0.665624\pi\)
0.912209 0.409726i \(-0.134376\pi\)
\(90\) 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 0.608544 0.793520i \(-0.291754\pi\)
−0.566632 + 0.823971i \(0.691754\pi\)
\(98\) 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 \(-0.627400\pi\)
−0.389640 + 0.920967i \(0.627400\pi\)
\(102\) 0 0
\(103\) 46.4033 + 33.7140i 0.0443908 + 0.0322518i 0.609759 0.792587i \(-0.291266\pi\)
−0.565369 + 0.824838i \(0.691266\pi\)
\(104\) 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 \(-0.568241\pi\)
−0.212748 + 0.977107i \(0.568241\pi\)
\(108\) 0 0
\(109\) −71.2432 219.264i −0.0626042 0.192676i 0.914863 0.403765i \(-0.132299\pi\)
−0.977467 + 0.211090i \(0.932299\pi\)
\(110\) −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 \(-0.123505\pi\)
−0.971263 + 0.238009i \(0.923505\pi\)
\(114\) 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 −0.999645 0.0266600i \(-0.991513\pi\)
0.824400 + 0.566008i \(0.191513\pi\)
\(128\) −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 \(-0.556946\pi\)
0.880888 + 0.473325i \(0.156946\pi\)
\(132\) 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 0.999204 + 0.0398976i \(0.0127032\pi\)
−0.784922 + 0.619595i \(0.787297\pi\)
\(138\) 0 0
\(139\) 7.34441 22.6038i 0.00448162 0.0137930i −0.948791 0.315905i \(-0.897692\pi\)
0.953272 + 0.302112i \(0.0976918\pi\)
\(140\) 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 \(-0.294278\pi\)
0.602232 + 0.798321i \(0.294278\pi\)
\(150\) 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 −0.968856 0.247626i \(-0.920350\pi\)
0.638270 0.769813i \(-0.279650\pi\)
\(164\) −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 \(-0.745913\pi\)
0.465394 + 0.885103i \(0.345913\pi\)
\(168\) 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 −0.623509 0.781816i \(-0.714293\pi\)
0.963969 0.266013i \(-0.0857066\pi\)
\(174\) 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 \(-0.418805\pi\)
−0.842311 + 0.538992i \(0.818805\pi\)
\(180\) 0 0
\(181\) 275.217 199.957i 0.113020 0.0821142i −0.529839 0.848098i \(-0.677748\pi\)
0.642860 + 0.765984i \(0.277748\pi\)
\(182\) 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 0.986157 + 0.165815i \(0.0530256\pi\)
−0.700354 + 0.713796i \(0.746974\pi\)
\(192\) 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 \(-0.144978\pi\)
−0.140833 + 0.990033i \(0.544978\pi\)
\(198\) 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 0.0805394 0.996751i \(-0.474336\pi\)
0.520718 0.853729i \(-0.325664\pi\)
\(212\) 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 −0.466297 0.884628i \(-0.654412\pi\)
0.897213 0.441597i \(-0.145588\pi\)
\(224\) −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 \(-0.836634\pi\)
0.993384 + 0.114836i \(0.0366343\pi\)
\(228\) 0 0
\(229\) 2577.13 + 1872.40i 0.743675 + 0.540312i 0.893860 0.448346i \(-0.147987\pi\)
−0.150185 + 0.988658i \(0.547987\pi\)
\(230\) 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 \(-0.796636\pi\)
0.319052 + 0.947737i \(0.396636\pi\)
\(234\) 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 −0.538754 0.842463i \(-0.681105\pi\)
0.931049 0.364895i \(-0.118895\pi\)
\(240\) 0 0
\(241\) −1069.17 3290.58i −0.285774 0.879522i −0.986166 0.165763i \(-0.946991\pi\)
0.700391 0.713759i \(-0.253009\pi\)
\(242\) 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 \(-0.255348\pi\)
0.695128 + 0.718886i \(0.255348\pi\)
\(252\) 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 \(-0.410350\pi\)
0.277934 + 0.960600i \(0.410350\pi\)
\(258\) 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 \(-0.0204720\pi\)
−0.845122 + 0.534574i \(0.820472\pi\)
\(264\) 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 −0.654787 + 0.755814i \(0.727242\pi\)
−0.921162 + 0.389180i \(0.872758\pi\)
\(270\) 0 0
\(271\) 3304.58 + 2400.92i 0.740734 + 0.538175i 0.892941 0.450174i \(-0.148638\pi\)
−0.152207 + 0.988349i \(0.548638\pi\)
\(272\) −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 0.743526 + 0.668707i \(0.233152\pi\)
−0.994581 + 0.103962i \(0.966848\pi\)
\(278\) −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 \(-0.832658\pi\)
0.209985 + 0.977705i \(0.432658\pi\)
\(282\) 0 0
\(283\) −2689.86 + 1954.30i −0.565003 + 0.410499i −0.833287 0.552841i \(-0.813544\pi\)
0.268284 + 0.963340i \(0.413544\pi\)
\(284\) 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 \(-0.716818\pi\)
−0.629691 + 0.776846i \(0.716818\pi\)
\(294\) 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 \(-0.913162\pi\)
0.937469 + 0.348069i \(0.113162\pi\)
\(312\) 0 0
\(313\) −1961.96 6038.28i −0.354302 1.09043i −0.956413 0.292016i \(-0.905674\pi\)
0.602112 0.798412i \(-0.294326\pi\)
\(314\) 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 \(-0.923462\pi\)
−0.0736400 + 0.997285i \(0.523462\pi\)
\(318\) 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 −0.841013 0.541015i \(-0.818040\pi\)
0.254648 + 0.967034i \(0.418040\pi\)
\(332\) 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 0.990235 0.139408i \(-0.0445201\pi\)
−0.883059 + 0.469262i \(0.844520\pi\)
\(338\) −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 \(-0.501440\pi\)
−0.952445 + 0.304710i \(0.901440\pi\)
\(348\) 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 \(-0.143144\pi\)
−0.135125 + 0.990829i \(0.543144\pi\)
\(354\) 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 −0.974916 0.222575i \(-0.928554\pi\)
0.657897 0.753108i \(-0.271446\pi\)
\(360\) 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 −0.719145 0.694860i \(-0.755466\pi\)
0.438623 + 0.898671i \(0.355466\pi\)
\(368\) −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 −0.890904 0.454191i \(-0.849928\pi\)
0.987724 + 0.156212i \(0.0499283\pi\)
\(374\) 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 0.966454 0.256838i \(-0.0826807\pi\)
0.0543834 + 0.998520i \(0.482681\pi\)
\(380\) 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 \(-0.843828\pi\)
0.175555 + 0.984470i \(0.443828\pi\)
\(384\) 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 0.768339 + 0.640043i \(0.221083\pi\)
−0.997807 + 0.0661869i \(0.978917\pi\)
\(390\) 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 0.944415 0.328757i \(-0.106630\pi\)
−0.0208261 + 0.999783i \(0.506630\pi\)
\(398\) 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 \(-0.525615\pi\)
−0.0803859 + 0.996764i \(0.525615\pi\)
\(402\) 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 0.841248 0.540649i \(-0.181821\pi\)
−0.998370 + 0.0570792i \(0.981821\pi\)
\(410\) −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 \(-0.595305\pi\)
0.817598 + 0.575790i \(0.195305\pi\)
\(420\) 0 0
\(421\) 5750.48 + 4177.97i 0.665704 + 0.483662i 0.868584 0.495541i \(-0.165030\pi\)
−0.202881 + 0.979203i \(0.565030\pi\)
\(422\) −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 \(-0.597162\pi\)
0.814226 + 0.580549i \(0.197162\pi\)
\(432\) 0 0
\(433\) 12267.7 8913.00i 1.36154 0.989218i 0.363196 0.931713i \(-0.381685\pi\)
0.998345 0.0575050i \(-0.0183145\pi\)
\(434\) 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 −0.914282 0.405077i \(-0.867245\pi\)
0.977769 + 0.209687i \(0.0672446\pi\)
\(440\) 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 \(-0.784037\pi\)
−0.778536 + 0.627600i \(0.784037\pi\)
\(444\) 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 \(-0.809691\pi\)
−0.826535 + 0.562885i \(0.809691\pi\)
\(450\) 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 \(-0.991732\pi\)
0.824010 + 0.566576i \(0.191732\pi\)
\(462\) 0 0
\(463\) −1365.98 4204.05i −0.137111 0.421985i 0.858801 0.512309i \(-0.171210\pi\)
−0.995912 + 0.0903241i \(0.971210\pi\)
\(464\) 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 \(-0.620682\pi\)
0.769145 + 0.639075i \(0.220682\pi\)
\(468\) 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 \(-0.411815\pi\)
−0.830272 + 0.557358i \(0.811815\pi\)
\(480\) 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 0.875835 + 0.482610i \(0.160311\pi\)
−0.424894 + 0.905243i \(0.639689\pi\)
\(488\) 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 0.937232 + 0.348707i \(0.113379\pi\)
−0.553271 + 0.833001i \(0.686621\pi\)
\(492\) 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 \(-0.534046\pi\)
−0.978611 + 0.205720i \(0.934046\pi\)
\(504\) 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 \(-0.00906222\pi\)
−0.825421 + 0.564518i \(0.809062\pi\)
\(510\) 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 \(-0.523223\pi\)
−0.971052 + 0.238869i \(0.923223\pi\)
\(522\) 0 0
\(523\) −1899.57 + 5846.27i −0.158819 + 0.488795i −0.998528 0.0542423i \(-0.982726\pi\)
0.839709 + 0.543037i \(0.182726\pi\)
\(524\) −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 −0.992648 0.121039i \(-0.961377\pi\)
0.731924 0.681386i \(-0.238623\pi\)
\(542\) 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 −0.999977 0.00683023i \(-0.997826\pi\)
−0.315506 0.948924i \(-0.602174\pi\)
\(548\) 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 \(-0.389576\pi\)
0.339990 + 0.940429i \(0.389576\pi\)
\(558\) 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 0.998211 + 0.0597931i \(0.0190441\pi\)
−0.772424 + 0.635107i \(0.780956\pi\)
\(564\) 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 \(-0.531668\pi\)
0.915661 + 0.401952i \(0.131668\pi\)
\(570\) 0 0
\(571\) 9324.33 + 6774.52i 0.683382 + 0.496506i 0.874478 0.485065i \(-0.161204\pi\)
−0.191096 + 0.981571i \(0.561204\pi\)
\(572\) 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 −0.601125 0.799155i \(-0.705280\pi\)
0.956052 0.293198i \(-0.0947195\pi\)
\(578\) 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 0.932235 + 0.361853i \(0.117856\pi\)
−0.541502 + 0.840700i \(0.682144\pi\)
\(588\) 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 \(-0.502542\pi\)
−0.00798607 + 0.999968i \(0.502542\pi\)
\(594\) 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 \(-0.624867\pi\)
−0.382298 + 0.924039i \(0.624867\pi\)
\(600\) 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 0.840010 0.542571i \(-0.182549\pi\)
−0.998498 + 0.0547965i \(0.982549\pi\)
\(614\) −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 \(-0.690427\pi\)
0.611848 + 0.790976i \(0.290427\pi\)
\(618\) 0 0
\(619\) 6014.72 4369.95i 0.390553 0.283753i −0.375129 0.926972i \(-0.622402\pi\)
0.765682 + 0.643219i \(0.222402\pi\)
\(620\) −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 −0.388812 0.921317i \(-0.627114\pi\)
0.756075 + 0.654485i \(0.227114\pi\)
\(632\) 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 \(-0.0851687\pi\)
−0.935631 + 0.352979i \(0.885169\pi\)
\(642\) 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 \(-0.318679\pi\)
−0.634221 + 0.773152i \(0.718679\pi\)
\(648\) 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 −0.992850 0.119368i \(-0.961913\pi\)
−0.420333 0.907370i \(-0.638087\pi\)
\(654\) 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 −0.979008 0.203820i \(-0.934664\pi\)
0.672232 0.740341i \(-0.265336\pi\)
\(660\) 0 0
\(661\) 7008.62 21570.3i 0.412411 1.26927i −0.502135 0.864789i \(-0.667452\pi\)
0.914546 0.404482i \(-0.132548\pi\)
\(662\) 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 −0.886709 0.462328i \(-0.847014\pi\)
0.989112 + 0.147163i \(0.0470142\pi\)
\(674\) 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 \(-0.988533\pi\)
0.829662 + 0.558267i \(0.188533\pi\)
\(678\) 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 0.326832 0.945082i \(-0.394019\pi\)
0.999823 0.0187892i \(-0.00598113\pi\)
\(684\) 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 −0.950197 0.311650i \(-0.899119\pi\)
0.585543 0.810642i \(-0.300881\pi\)
\(692\) −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 \(-0.351194\pi\)
0.450646 + 0.892703i \(0.351194\pi\)
\(702\) 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 −0.988506 0.151178i \(-0.951693\pi\)
0.710858 0.703335i \(-0.248307\pi\)
\(710\) −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 \(-0.765390\pi\)
0.410397 + 0.911907i \(0.365390\pi\)
\(720\) 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 −0.862348 0.506316i \(-0.831007\pi\)
0.995259 + 0.0972567i \(0.0310068\pi\)
\(728\) −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 −0.927731 0.373249i \(-0.878244\pi\)
0.0682959 + 0.997665i \(0.478244\pi\)
\(734\) 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 −0.984246 0.176803i \(-0.943424\pi\)
0.900194 + 0.435489i \(0.143424\pi\)
\(740\) −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 \(-0.400959\pi\)
0.306150 + 0.951983i \(0.400959\pi\)
\(744\) 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 0.422296 + 0.906458i \(0.361224\pi\)
−0.874447 + 0.485121i \(0.838776\pi\)
\(762\) 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 −0.629499 0.777001i \(-0.716740\pi\)
0.544446 + 0.838796i \(0.316740\pi\)
\(770\) 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 0.364810 + 0.931082i \(0.381134\pi\)
−0.842414 + 0.538831i \(0.818866\pi\)
\(774\) 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 0.933550 0.358447i \(-0.116693\pi\)
−0.965948 + 0.258738i \(0.916693\pi\)
\(788\) −18108.8