Properties

Label 225.4.h.d.46.1
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 46.1
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.1

$q$-expansion

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

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 \(0.533987\pi\)
−0.498220 + 0.867050i \(0.666013\pi\)
\(3\) 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 −0.999799 0.0200732i \(-0.993610\pi\)
0.820653 + 0.571427i \(0.193610\pi\)
\(12\) 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 −0.456706 0.889618i \(-0.650971\pi\)
0.704947 + 0.709260i \(0.250971\pi\)
\(18\) 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 −0.941985 0.335654i \(-0.891043\pi\)
0.959374 + 0.282136i \(0.0910429\pi\)
\(24\) 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 0.994140 0.108097i \(-0.0344757\pi\)
0.204400 + 0.978887i \(0.434476\pi\)
\(30\) 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 0.979722 0.200362i \(-0.0642117\pi\)
−0.910381 + 0.413770i \(0.864212\pi\)
\(42\) 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 0.364149 0.931341i \(-0.381360\pi\)
−0.773229 + 0.634127i \(0.781360\pi\)
\(48\) 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 0.829787 0.558080i \(-0.188462\pi\)
−0.274347 + 0.961631i \(0.588462\pi\)
\(54\) 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 \(-0.931038\pi\)
0.663755 0.747950i \(-0.268962\pi\)
\(60\) 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 0.993854 0.110698i \(-0.0353087\pi\)
0.201838 + 0.979419i \(0.435309\pi\)
\(72\) 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 \(-0.365228\pi\)
0.994039 0.109023i \(-0.0347722\pi\)
\(84\) 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 \(0.334376\pi\)
−0.912209 + 0.409726i \(0.865624\pi\)
\(90\) 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 \(-0.372600\pi\)
0.389640 + 0.920967i \(0.372600\pi\)
\(102\) 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 \(-0.431759\pi\)
0.212748 + 0.977107i \(0.431759\pi\)
\(108\) 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 0.971263 0.238009i \(-0.0764949\pi\)
−0.925667 + 0.378340i \(0.876495\pi\)
\(114\) 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 −0.880888 0.473325i \(-0.843054\pi\)
0.177950 + 0.984040i \(0.443054\pi\)
\(132\) 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 \(-0.987297\pi\)
0.784922 0.619595i \(-0.212703\pi\)
\(138\) 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 \(-0.705722\pi\)
−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 −0.968856 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 −0.465394 0.885103i \(-0.654087\pi\)
0.697969 + 0.716128i \(0.254087\pi\)
\(168\) 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 \(0.285707\pi\)
−0.963969 + 0.266013i \(0.914293\pi\)
\(174\) 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 0.842311 0.538992i \(-0.181195\pi\)
−0.252324 + 0.967643i \(0.581195\pi\)
\(180\) 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 \(-0.946974\pi\)
0.700354 0.713796i \(-0.253026\pi\)
\(192\) 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 0.140833 0.990033i \(-0.455022\pi\)
−0.898058 + 0.439877i \(0.855022\pi\)
\(198\) 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 −0.993384 0.114836i \(-0.963366\pi\)
0.871164 + 0.490992i \(0.163366\pi\)
\(228\) 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 −0.319052 0.947737i \(-0.603364\pi\)
0.802759 + 0.596303i \(0.203364\pi\)
\(234\) 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 \(0.318895\pi\)
−0.931049 + 0.364895i \(0.881105\pi\)
\(240\) 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 \(-0.744652\pi\)
−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 0.845122 0.534574i \(-0.179528\pi\)
−0.997933 + 0.0642705i \(0.979528\pi\)
\(264\) 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 \(-0.272758\pi\)
0.921162 0.389180i \(-0.127242\pi\)
\(270\) 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 −0.209985 0.977705i \(-0.567342\pi\)
0.864963 + 0.501835i \(0.167342\pi\)
\(282\) 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 \(-0.283182\pi\)
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 −0.937469 0.348069i \(-0.886838\pi\)
0.963018 + 0.269437i \(0.0868376\pi\)
\(312\) 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 0.0736400 0.997285i \(-0.476538\pi\)
0.971230 + 0.238142i \(0.0765384\pi\)
\(318\) 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 0.952445 0.304710i \(-0.0985597\pi\)
0.00452493 + 0.999990i \(0.498560\pi\)
\(348\) 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 0.135125 0.990829i \(-0.456856\pi\)
−0.900578 + 0.434694i \(0.856856\pi\)
\(354\) 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 \(0.0714462\pi\)
−0.657897 + 0.753108i \(0.728554\pi\)
\(360\) 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 −0.175555 0.984470i \(-0.556172\pi\)
0.882037 + 0.471181i \(0.156172\pi\)
\(384\) 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 \(-0.778917\pi\)
0.997807 0.0661869i \(-0.0210833\pi\)
\(390\) 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 \(-0.474385\pi\)
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 0.841248 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 −0.817598 0.575790i \(-0.804695\pi\)
0.294957 + 0.955510i \(0.404695\pi\)
\(420\) 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 −0.814226 0.580549i \(-0.802838\pi\)
0.300525 + 0.953774i \(0.402838\pi\)
\(432\) 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 \(-0.215963\pi\)
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 −0.824010 0.566576i \(-0.808268\pi\)
0.999663 + 0.0259714i \(0.00826790\pi\)
\(462\) 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 −0.769145 0.639075i \(-0.779318\pi\)
0.370117 + 0.928985i \(0.379318\pi\)
\(468\) 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 0.830272 0.557358i \(-0.188185\pi\)
−0.273511 + 0.961869i \(0.588185\pi\)
\(480\) 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 \(-0.886621\pi\)
0.553271 0.833001i \(-0.313379\pi\)
\(492\) 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 0.978611 0.205720i \(-0.0659537\pi\)
0.106756 + 0.994285i \(0.465954\pi\)
\(504\) 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 0.825421 0.564518i \(-0.190938\pi\)
−0.999595 + 0.0284660i \(0.990938\pi\)
\(510\) 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 0.971052 0.238869i \(-0.0767766\pi\)
0.0728937 + 0.997340i \(0.476777\pi\)
\(522\) 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 \(-0.610424\pi\)
−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 −0.998211 0.0597931i \(-0.980956\pi\)
0.772424 0.635107i \(-0.219044\pi\)
\(564\) 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 −0.915661 0.401952i \(-0.868332\pi\)
0.0993244 + 0.995055i \(0.468332\pi\)
\(570\) 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 \(-0.882144\pi\)
0.541502 0.840700i \(-0.317856\pi\)
\(588\) 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 0.840010 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 −0.611848 0.790976i \(-0.709573\pi\)
0.563191 + 0.826327i \(0.309573\pi\)
\(618\) 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 0.935631 0.352979i \(-0.114831\pi\)
−0.964417 + 0.264384i \(0.914831\pi\)
\(642\) 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 0.634221 0.773152i \(-0.281321\pi\)
−0.539326 + 0.842097i \(0.681321\pi\)
\(648\) 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 \(0.0380868\pi\)
0.420333 + 0.907370i \(0.361913\pi\)
\(654\) 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 \(0.0653358\pi\)
−0.672232 + 0.740341i \(0.734664\pi\)
\(660\) 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 −0.829662 0.558267i \(-0.811467\pi\)
0.999351 + 0.0360158i \(0.0114667\pi\)
\(678\) 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 \(0.605981\pi\)
−0.999823 + 0.0187892i \(0.994019\pi\)
\(684\) 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 \(-0.648806\pi\)
−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 −0.988506 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 −0.410397 0.911907i \(-0.634610\pi\)
0.740455 + 0.672106i \(0.234610\pi\)
\(720\) 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 \(-0.599041\pi\)
−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 −0.422296 0.906458i \(-0.638776\pi\)
0.874447 0.485121i \(-0.161224\pi\)
\(762\) 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 \(-0.618866\pi\)
0.842414 0.538831i \(-0.181134\pi\)
\(774\) 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 </