Properties

Label 324.5.d.f.163.15
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.15
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.43802 - 3.17113i) q^{2} +(-4.11208 - 15.4626i) q^{4} -22.1491 q^{5} -95.5959i q^{7} +(-59.0591 - 24.6582i) q^{8} +O(q^{10})\) \(q+(2.43802 - 3.17113i) q^{2} +(-4.11208 - 15.4626i) q^{4} -22.1491 q^{5} -95.5959i q^{7} +(-59.0591 - 24.6582i) q^{8} +(-54.0000 + 70.2376i) q^{10} +21.8693i q^{11} +126.225 q^{13} +(-303.147 - 233.065i) q^{14} +(-222.182 + 127.167i) q^{16} -283.865 q^{17} -323.729i q^{19} +(91.0790 + 342.482i) q^{20} +(69.3502 + 53.3178i) q^{22} +229.131i q^{23} -134.417 q^{25} +(307.739 - 400.274i) q^{26} +(-1478.16 + 393.098i) q^{28} +1209.64 q^{29} +829.727i q^{31} +(-138.422 + 1014.60i) q^{32} +(-692.070 + 900.172i) q^{34} +2117.36i q^{35} -318.650 q^{37} +(-1026.59 - 789.259i) q^{38} +(1308.11 + 546.156i) q^{40} +328.837 q^{41} +207.079i q^{43} +(338.155 - 89.9283i) q^{44} +(726.602 + 558.626i) q^{46} +1226.78i q^{47} -6737.58 q^{49} +(-327.712 + 426.253i) q^{50} +(-519.046 - 1951.76i) q^{52} -2834.27 q^{53} -484.385i q^{55} +(-2357.22 + 5645.81i) q^{56} +(2949.14 - 3835.93i) q^{58} +1475.86i q^{59} -1872.36 q^{61} +(2631.17 + 2022.89i) q^{62} +(2879.95 + 2912.58i) q^{64} -2795.76 q^{65} +247.871i q^{67} +(1167.28 + 4389.28i) q^{68} +(6714.43 + 5162.18i) q^{70} +4308.28i q^{71} +3010.75 q^{73} +(-776.875 + 1010.48i) q^{74} +(-5005.68 + 1331.20i) q^{76} +2090.61 q^{77} -7191.93i q^{79} +(4921.12 - 2816.63i) q^{80} +(801.712 - 1042.78i) q^{82} -3322.48i q^{83} +6287.36 q^{85} +(656.674 + 504.863i) q^{86} +(539.256 - 1291.58i) q^{88} -1549.85 q^{89} -12066.6i q^{91} +(3542.95 - 942.204i) q^{92} +(3890.28 + 2990.92i) q^{94} +7170.31i q^{95} +5837.37 q^{97} +(-16426.4 + 21365.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + O(q^{10}) \) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + 14q^{10} + 2q^{13} - 252q^{14} + q^{16} - 28q^{17} + 140q^{20} + 33q^{22} + 1752q^{25} + 548q^{26} - 258q^{28} - 526q^{29} + 121q^{32} - 385q^{34} - 4q^{37} - 1395q^{38} + 2276q^{40} + 2762q^{41} + 3357q^{44} + 1788q^{46} - 3428q^{49} - 6375q^{50} - 1438q^{52} - 5044q^{53} + 7506q^{56} + 4064q^{58} + 2q^{61} - 9162q^{62} + 4513q^{64} + 2014q^{65} + 11405q^{68} - 3666q^{70} - 1708q^{73} - 14620q^{74} - 1581q^{76} + 3942q^{77} + 22760q^{80} - 4243q^{82} + 1252q^{85} - 22113q^{86} - 1995q^{88} + 6524q^{89} + 30294q^{92} - 7524q^{94} - 5638q^{97} - 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.43802 3.17113i 0.609506 0.792782i
\(3\) 0 0
\(4\) −4.11208 15.4626i −0.257005 0.966410i
\(5\) −22.1491 −0.885964 −0.442982 0.896530i \(-0.646080\pi\)
−0.442982 + 0.896530i \(0.646080\pi\)
\(6\) 0 0
\(7\) 95.5959i 1.95094i −0.220138 0.975469i \(-0.570651\pi\)
0.220138 0.975469i \(-0.429349\pi\)
\(8\) −59.0591 24.6582i −0.922798 0.385284i
\(9\) 0 0
\(10\) −54.0000 + 70.2376i −0.540000 + 0.702376i
\(11\) 21.8693i 0.180738i 0.995908 + 0.0903689i \(0.0288046\pi\)
−0.995908 + 0.0903689i \(0.971195\pi\)
\(12\) 0 0
\(13\) 126.225 0.746892 0.373446 0.927652i \(-0.378176\pi\)
0.373446 + 0.927652i \(0.378176\pi\)
\(14\) −303.147 233.065i −1.54667 1.18911i
\(15\) 0 0
\(16\) −222.182 + 127.167i −0.867897 + 0.496745i
\(17\) −283.865 −0.982232 −0.491116 0.871094i \(-0.663411\pi\)
−0.491116 + 0.871094i \(0.663411\pi\)
\(18\) 0 0
\(19\) 323.729i 0.896756i −0.893844 0.448378i \(-0.852002\pi\)
0.893844 0.448378i \(-0.147998\pi\)
\(20\) 91.0790 + 342.482i 0.227697 + 0.856205i
\(21\) 0 0
\(22\) 69.3502 + 53.3178i 0.143286 + 0.110161i
\(23\) 229.131i 0.433139i 0.976267 + 0.216570i \(0.0694868\pi\)
−0.976267 + 0.216570i \(0.930513\pi\)
\(24\) 0 0
\(25\) −134.417 −0.215067
\(26\) 307.739 400.274i 0.455235 0.592122i
\(27\) 0 0
\(28\) −1478.16 + 393.098i −1.88541 + 0.501401i
\(29\) 1209.64 1.43834 0.719170 0.694835i \(-0.244522\pi\)
0.719170 + 0.694835i \(0.244522\pi\)
\(30\) 0 0
\(31\) 829.727i 0.863399i 0.902017 + 0.431700i \(0.142086\pi\)
−0.902017 + 0.431700i \(0.857914\pi\)
\(32\) −138.422 + 1014.60i −0.135178 + 0.990821i
\(33\) 0 0
\(34\) −692.070 + 900.172i −0.598676 + 0.778695i
\(35\) 2117.36i 1.72846i
\(36\) 0 0
\(37\) −318.650 −0.232761 −0.116380 0.993205i \(-0.537129\pi\)
−0.116380 + 0.993205i \(0.537129\pi\)
\(38\) −1026.59 789.259i −0.710932 0.546578i
\(39\) 0 0
\(40\) 1308.11 + 546.156i 0.817566 + 0.341348i
\(41\) 328.837 0.195620 0.0978099 0.995205i \(-0.468816\pi\)
0.0978099 + 0.995205i \(0.468816\pi\)
\(42\) 0 0
\(43\) 207.079i 0.111995i 0.998431 + 0.0559976i \(0.0178339\pi\)
−0.998431 + 0.0559976i \(0.982166\pi\)
\(44\) 338.155 89.9283i 0.174667 0.0464506i
\(45\) 0 0
\(46\) 726.602 + 558.626i 0.343385 + 0.264001i
\(47\) 1226.78i 0.555356i 0.960674 + 0.277678i \(0.0895648\pi\)
−0.960674 + 0.277678i \(0.910435\pi\)
\(48\) 0 0
\(49\) −6737.58 −2.80616
\(50\) −327.712 + 426.253i −0.131085 + 0.170501i
\(51\) 0 0
\(52\) −519.046 1951.76i −0.191955 0.721804i
\(53\) −2834.27 −1.00900 −0.504499 0.863412i \(-0.668323\pi\)
−0.504499 + 0.863412i \(0.668323\pi\)
\(54\) 0 0
\(55\) 484.385i 0.160127i
\(56\) −2357.22 + 5645.81i −0.751664 + 1.80032i
\(57\) 0 0
\(58\) 2949.14 3835.93i 0.876676 1.14029i
\(59\) 1475.86i 0.423975i 0.977272 + 0.211988i \(0.0679937\pi\)
−0.977272 + 0.211988i \(0.932006\pi\)
\(60\) 0 0
\(61\) −1872.36 −0.503187 −0.251594 0.967833i \(-0.580955\pi\)
−0.251594 + 0.967833i \(0.580955\pi\)
\(62\) 2631.17 + 2022.89i 0.684487 + 0.526247i
\(63\) 0 0
\(64\) 2879.95 + 2912.58i 0.703113 + 0.711078i
\(65\) −2795.76 −0.661719
\(66\) 0 0
\(67\) 247.871i 0.0552174i 0.999619 + 0.0276087i \(0.00878924\pi\)
−0.999619 + 0.0276087i \(0.991211\pi\)
\(68\) 1167.28 + 4389.28i 0.252439 + 0.949239i
\(69\) 0 0
\(70\) 6714.43 + 5162.18i 1.37029 + 1.05351i
\(71\) 4308.28i 0.854648i 0.904099 + 0.427324i \(0.140544\pi\)
−0.904099 + 0.427324i \(0.859456\pi\)
\(72\) 0 0
\(73\) 3010.75 0.564974 0.282487 0.959271i \(-0.408841\pi\)
0.282487 + 0.959271i \(0.408841\pi\)
\(74\) −776.875 + 1010.48i −0.141869 + 0.184528i
\(75\) 0 0
\(76\) −5005.68 + 1331.20i −0.866634 + 0.230471i
\(77\) 2090.61 0.352608
\(78\) 0 0
\(79\) 7191.93i 1.15237i −0.817320 0.576184i \(-0.804541\pi\)
0.817320 0.576184i \(-0.195459\pi\)
\(80\) 4921.12 2816.63i 0.768926 0.440098i
\(81\) 0 0
\(82\) 801.712 1042.78i 0.119231 0.155084i
\(83\) 3322.48i 0.482287i −0.970489 0.241144i \(-0.922477\pi\)
0.970489 0.241144i \(-0.0775225\pi\)
\(84\) 0 0
\(85\) 6287.36 0.870222
\(86\) 656.674 + 504.863i 0.0887877 + 0.0682617i
\(87\) 0 0
\(88\) 539.256 1291.58i 0.0696353 0.166785i
\(89\) −1549.85 −0.195664 −0.0978318 0.995203i \(-0.531191\pi\)
−0.0978318 + 0.995203i \(0.531191\pi\)
\(90\) 0 0
\(91\) 12066.6i 1.45714i
\(92\) 3542.95 942.204i 0.418590 0.111319i
\(93\) 0 0
\(94\) 3890.28 + 2990.92i 0.440276 + 0.338493i
\(95\) 7170.31i 0.794494i
\(96\) 0 0
\(97\) 5837.37 0.620403 0.310201 0.950671i \(-0.399604\pi\)
0.310201 + 0.950671i \(0.399604\pi\)
\(98\) −16426.4 + 21365.7i −1.71037 + 2.22467i
\(99\) 0 0
\(100\) 552.734 + 2078.43i 0.0552734 + 0.207843i
\(101\) −5499.00 −0.539065 −0.269532 0.962991i \(-0.586869\pi\)
−0.269532 + 0.962991i \(0.586869\pi\)
\(102\) 0 0
\(103\) 17933.3i 1.69038i −0.534464 0.845191i \(-0.679487\pi\)
0.534464 0.845191i \(-0.320513\pi\)
\(104\) −7454.72 3112.47i −0.689230 0.287765i
\(105\) 0 0
\(106\) −6910.03 + 8987.84i −0.614990 + 0.799915i
\(107\) 8715.17i 0.761217i −0.924736 0.380608i \(-0.875715\pi\)
0.924736 0.380608i \(-0.124285\pi\)
\(108\) 0 0
\(109\) −12162.1 −1.02366 −0.511830 0.859087i \(-0.671032\pi\)
−0.511830 + 0.859087i \(0.671032\pi\)
\(110\) −1536.05 1180.94i −0.126946 0.0975985i
\(111\) 0 0
\(112\) 12156.6 + 21239.7i 0.969118 + 1.69321i
\(113\) −20473.4 −1.60337 −0.801684 0.597748i \(-0.796062\pi\)
−0.801684 + 0.597748i \(0.796062\pi\)
\(114\) 0 0
\(115\) 5075.04i 0.383746i
\(116\) −4974.15 18704.2i −0.369661 1.39003i
\(117\) 0 0
\(118\) 4680.13 + 3598.18i 0.336120 + 0.258415i
\(119\) 27136.3i 1.91627i
\(120\) 0 0
\(121\) 14162.7 0.967334
\(122\) −4564.86 + 5937.49i −0.306696 + 0.398918i
\(123\) 0 0
\(124\) 12829.7 3411.90i 0.834398 0.221898i
\(125\) 16820.4 1.07651
\(126\) 0 0
\(127\) 8130.42i 0.504087i 0.967716 + 0.252044i \(0.0811026\pi\)
−0.967716 + 0.252044i \(0.918897\pi\)
\(128\) 16257.5 2031.76i 0.992281 0.124009i
\(129\) 0 0
\(130\) −6816.14 + 8865.72i −0.403322 + 0.524599i
\(131\) 16275.6i 0.948406i −0.880416 0.474203i \(-0.842736\pi\)
0.880416 0.474203i \(-0.157264\pi\)
\(132\) 0 0
\(133\) −30947.2 −1.74952
\(134\) 786.030 + 604.315i 0.0437754 + 0.0336554i
\(135\) 0 0
\(136\) 16764.8 + 6999.59i 0.906402 + 0.378438i
\(137\) 24662.9 1.31402 0.657011 0.753881i \(-0.271821\pi\)
0.657011 + 0.753881i \(0.271821\pi\)
\(138\) 0 0
\(139\) 19720.1i 1.02066i −0.859980 0.510328i \(-0.829524\pi\)
0.859980 0.510328i \(-0.170476\pi\)
\(140\) 32739.9 8706.78i 1.67040 0.444223i
\(141\) 0 0
\(142\) 13662.1 + 10503.7i 0.677549 + 0.520913i
\(143\) 2760.44i 0.134992i
\(144\) 0 0
\(145\) −26792.5 −1.27432
\(146\) 7340.28 9547.46i 0.344355 0.447901i
\(147\) 0 0
\(148\) 1310.31 + 4927.14i 0.0598207 + 0.224942i
\(149\) 29885.5 1.34613 0.673066 0.739583i \(-0.264977\pi\)
0.673066 + 0.739583i \(0.264977\pi\)
\(150\) 0 0
\(151\) 5963.00i 0.261524i −0.991414 0.130762i \(-0.958258\pi\)
0.991414 0.130762i \(-0.0417423\pi\)
\(152\) −7982.56 + 19119.1i −0.345506 + 0.827525i
\(153\) 0 0
\(154\) 5096.97 6629.60i 0.214917 0.279541i
\(155\) 18377.7i 0.764941i
\(156\) 0 0
\(157\) −34987.0 −1.41941 −0.709704 0.704500i \(-0.751172\pi\)
−0.709704 + 0.704500i \(0.751172\pi\)
\(158\) −22806.5 17534.1i −0.913576 0.702375i
\(159\) 0 0
\(160\) 3065.93 22472.5i 0.119763 0.877832i
\(161\) 21903.9 0.845027
\(162\) 0 0
\(163\) 14509.8i 0.546118i −0.961997 0.273059i \(-0.911965\pi\)
0.961997 0.273059i \(-0.0880354\pi\)
\(164\) −1352.20 5084.66i −0.0502753 0.189049i
\(165\) 0 0
\(166\) −10536.0 8100.28i −0.382349 0.293957i
\(167\) 44617.8i 1.59983i 0.600111 + 0.799917i \(0.295123\pi\)
−0.600111 + 0.799917i \(0.704877\pi\)
\(168\) 0 0
\(169\) −12628.3 −0.442153
\(170\) 15328.7 19938.0i 0.530406 0.689896i
\(171\) 0 0
\(172\) 3201.97 851.526i 0.108233 0.0287833i
\(173\) −52886.6 −1.76707 −0.883534 0.468367i \(-0.844842\pi\)
−0.883534 + 0.468367i \(0.844842\pi\)
\(174\) 0 0
\(175\) 12849.7i 0.419583i
\(176\) −2781.04 4858.95i −0.0897806 0.156862i
\(177\) 0 0
\(178\) −3778.57 + 4914.77i −0.119258 + 0.155119i
\(179\) 32840.8i 1.02496i −0.858698 0.512482i \(-0.828726\pi\)
0.858698 0.512482i \(-0.171274\pi\)
\(180\) 0 0
\(181\) −22758.6 −0.694685 −0.347343 0.937738i \(-0.612916\pi\)
−0.347343 + 0.937738i \(0.612916\pi\)
\(182\) −38264.6 29418.6i −1.15519 0.888135i
\(183\) 0 0
\(184\) 5649.94 13532.2i 0.166881 0.399700i
\(185\) 7057.80 0.206218
\(186\) 0 0
\(187\) 6207.92i 0.177526i
\(188\) 18969.2 5044.62i 0.536701 0.142729i
\(189\) 0 0
\(190\) 22738.0 + 17481.4i 0.629860 + 0.484249i
\(191\) 57503.3i 1.57625i −0.615513 0.788127i \(-0.711051\pi\)
0.615513 0.788127i \(-0.288949\pi\)
\(192\) 0 0
\(193\) −44941.6 −1.20652 −0.603259 0.797545i \(-0.706131\pi\)
−0.603259 + 0.797545i \(0.706131\pi\)
\(194\) 14231.6 18511.0i 0.378139 0.491844i
\(195\) 0 0
\(196\) 27705.5 + 104180.i 0.721197 + 2.71190i
\(197\) −44514.7 −1.14702 −0.573510 0.819198i \(-0.694419\pi\)
−0.573510 + 0.819198i \(0.694419\pi\)
\(198\) 0 0
\(199\) 19066.9i 0.481474i −0.970590 0.240737i \(-0.922611\pi\)
0.970590 0.240737i \(-0.0773892\pi\)
\(200\) 7938.54 + 3314.48i 0.198464 + 0.0828619i
\(201\) 0 0
\(202\) −13406.7 + 17438.0i −0.328563 + 0.427361i
\(203\) 115637.i 2.80611i
\(204\) 0 0
\(205\) −7283.44 −0.173312
\(206\) −56868.6 43721.7i −1.34010 1.03030i
\(207\) 0 0
\(208\) −28044.8 + 16051.6i −0.648225 + 0.371014i
\(209\) 7079.72 0.162078
\(210\) 0 0
\(211\) 952.918i 0.0214038i −0.999943 0.0107019i \(-0.996593\pi\)
0.999943 0.0107019i \(-0.00340658\pi\)
\(212\) 11654.8 + 43825.1i 0.259318 + 0.975106i
\(213\) 0 0
\(214\) −27636.9 21247.8i −0.603478 0.463966i
\(215\) 4586.61i 0.0992237i
\(216\) 0 0
\(217\) 79318.5 1.68444
\(218\) −29651.5 + 38567.6i −0.623927 + 0.811539i
\(219\) 0 0
\(220\) −7489.83 + 1991.83i −0.154749 + 0.0411535i
\(221\) −35830.8 −0.733621
\(222\) 0 0
\(223\) 43342.2i 0.871568i −0.900051 0.435784i \(-0.856471\pi\)
0.900051 0.435784i \(-0.143529\pi\)
\(224\) 96991.7 + 13232.6i 1.93303 + 0.263724i
\(225\) 0 0
\(226\) −49914.6 + 64923.7i −0.977262 + 1.27112i
\(227\) 6007.51i 0.116585i −0.998300 0.0582925i \(-0.981434\pi\)
0.998300 0.0582925i \(-0.0185656\pi\)
\(228\) 0 0
\(229\) −4076.35 −0.0777321 −0.0388660 0.999244i \(-0.512375\pi\)
−0.0388660 + 0.999244i \(0.512375\pi\)
\(230\) −16093.6 12373.1i −0.304227 0.233895i
\(231\) 0 0
\(232\) −71440.4 29827.6i −1.32730 0.554169i
\(233\) −37427.6 −0.689414 −0.344707 0.938710i \(-0.612022\pi\)
−0.344707 + 0.938710i \(0.612022\pi\)
\(234\) 0 0
\(235\) 27172.1i 0.492025i
\(236\) 22820.5 6068.85i 0.409734 0.108964i
\(237\) 0 0
\(238\) 86052.8 + 66159.0i 1.51919 + 1.16798i
\(239\) 25648.6i 0.449022i 0.974472 + 0.224511i \(0.0720785\pi\)
−0.974472 + 0.224511i \(0.927922\pi\)
\(240\) 0 0
\(241\) 76601.6 1.31888 0.659438 0.751759i \(-0.270794\pi\)
0.659438 + 0.751759i \(0.270794\pi\)
\(242\) 34529.1 44911.8i 0.589596 0.766884i
\(243\) 0 0
\(244\) 7699.30 + 28951.5i 0.129322 + 0.486285i
\(245\) 149231. 2.48615
\(246\) 0 0
\(247\) 40862.6i 0.669780i
\(248\) 20459.5 49002.9i 0.332654 0.796743i
\(249\) 0 0
\(250\) 41008.6 53339.6i 0.656137 0.853434i
\(251\) 66642.6i 1.05780i 0.848683 + 0.528902i \(0.177396\pi\)
−0.848683 + 0.528902i \(0.822604\pi\)
\(252\) 0 0
\(253\) −5010.92 −0.0782846
\(254\) 25782.6 + 19822.2i 0.399631 + 0.307244i
\(255\) 0 0
\(256\) 33193.3 56508.2i 0.506489 0.862246i
\(257\) 59426.4 0.899732 0.449866 0.893096i \(-0.351472\pi\)
0.449866 + 0.893096i \(0.351472\pi\)
\(258\) 0 0
\(259\) 30461.6i 0.454102i
\(260\) 11496.4 + 43229.7i 0.170065 + 0.639492i
\(261\) 0 0
\(262\) −51611.9 39680.3i −0.751878 0.578059i
\(263\) 25140.3i 0.363462i 0.983348 + 0.181731i \(0.0581700\pi\)
−0.983348 + 0.181731i \(0.941830\pi\)
\(264\) 0 0
\(265\) 62776.7 0.893936
\(266\) −75450.0 + 98137.4i −1.06634 + 1.38698i
\(267\) 0 0
\(268\) 3832.72 1019.27i 0.0533627 0.0141912i
\(269\) 2553.46 0.0352877 0.0176439 0.999844i \(-0.494383\pi\)
0.0176439 + 0.999844i \(0.494383\pi\)
\(270\) 0 0
\(271\) 4623.11i 0.0629499i 0.999505 + 0.0314750i \(0.0100204\pi\)
−0.999505 + 0.0314750i \(0.989980\pi\)
\(272\) 63069.6 36098.2i 0.852476 0.487918i
\(273\) 0 0
\(274\) 60128.6 78209.0i 0.800904 1.04173i
\(275\) 2939.60i 0.0388708i
\(276\) 0 0
\(277\) −9854.37 −0.128431 −0.0642154 0.997936i \(-0.520454\pi\)
−0.0642154 + 0.997936i \(0.520454\pi\)
\(278\) −62534.9 48078.0i −0.809157 0.622095i
\(279\) 0 0
\(280\) 52210.3 125050.i 0.665948 1.59502i
\(281\) −48417.2 −0.613178 −0.306589 0.951842i \(-0.599188\pi\)
−0.306589 + 0.951842i \(0.599188\pi\)
\(282\) 0 0
\(283\) 132230.i 1.65104i 0.564373 + 0.825520i \(0.309118\pi\)
−0.564373 + 0.825520i \(0.690882\pi\)
\(284\) 66617.0 17716.0i 0.825940 0.219649i
\(285\) 0 0
\(286\) 8753.71 + 6730.03i 0.107019 + 0.0822782i
\(287\) 31435.5i 0.381642i
\(288\) 0 0
\(289\) −2941.65 −0.0352205
\(290\) −65320.8 + 84962.5i −0.776704 + 1.01026i
\(291\) 0 0
\(292\) −12380.4 46553.9i −0.145201 0.545997i
\(293\) −89519.1 −1.04275 −0.521375 0.853327i \(-0.674581\pi\)
−0.521375 + 0.853327i \(0.674581\pi\)
\(294\) 0 0
\(295\) 32688.9i 0.375627i
\(296\) 18819.1 + 7857.31i 0.214791 + 0.0896789i
\(297\) 0 0
\(298\) 72861.5 94770.6i 0.820475 1.06719i
\(299\) 28921.9i 0.323508i
\(300\) 0 0
\(301\) 19795.9 0.218495
\(302\) −18909.4 14537.9i −0.207331 0.159400i
\(303\) 0 0
\(304\) 41167.5 + 71926.6i 0.445459 + 0.778292i
\(305\) 41471.1 0.445806
\(306\) 0 0
\(307\) 62726.9i 0.665545i −0.943007 0.332772i \(-0.892016\pi\)
0.943007 0.332772i \(-0.107984\pi\)
\(308\) −8596.78 32326.2i −0.0906221 0.340764i
\(309\) 0 0
\(310\) −58278.0 44805.3i −0.606431 0.466236i
\(311\) 122783.i 1.26945i 0.772737 + 0.634726i \(0.218887\pi\)
−0.772737 + 0.634726i \(0.781113\pi\)
\(312\) 0 0
\(313\) −48589.1 −0.495964 −0.247982 0.968765i \(-0.579767\pi\)
−0.247982 + 0.968765i \(0.579767\pi\)
\(314\) −85299.2 + 110948.i −0.865138 + 1.12528i
\(315\) 0 0
\(316\) −111206. + 29573.8i −1.11366 + 0.296164i
\(317\) −110133. −1.09598 −0.547988 0.836486i \(-0.684606\pi\)
−0.547988 + 0.836486i \(0.684606\pi\)
\(318\) 0 0
\(319\) 26454.0i 0.259962i
\(320\) −63788.3 64511.0i −0.622933 0.629990i
\(321\) 0 0
\(322\) 53402.3 69460.2i 0.515049 0.669922i
\(323\) 91895.4i 0.880823i
\(324\) 0 0
\(325\) −16966.7 −0.160632
\(326\) −46012.4 35375.3i −0.432952 0.332862i
\(327\) 0 0
\(328\) −19420.8 8108.51i −0.180518 0.0753691i
\(329\) 117275. 1.08346
\(330\) 0 0
\(331\) 184521.i 1.68418i 0.539335 + 0.842091i \(0.318676\pi\)
−0.539335 + 0.842091i \(0.681324\pi\)
\(332\) −51374.0 + 13662.3i −0.466087 + 0.123950i
\(333\) 0 0
\(334\) 141489. + 108779.i 1.26832 + 0.975108i
\(335\) 5490.12i 0.0489207i
\(336\) 0 0
\(337\) 65626.1 0.577852 0.288926 0.957351i \(-0.406702\pi\)
0.288926 + 0.957351i \(0.406702\pi\)
\(338\) −30788.2 + 40046.0i −0.269495 + 0.350531i
\(339\) 0 0
\(340\) −25854.1 97218.6i −0.223652 0.840992i
\(341\) −18145.5 −0.156049
\(342\) 0 0
\(343\) 414560.i 3.52370i
\(344\) 5106.19 12229.9i 0.0431499 0.103349i
\(345\) 0 0
\(346\) −128939. + 167710.i −1.07704 + 1.40090i
\(347\) 104869.i 0.870941i 0.900203 + 0.435470i \(0.143418\pi\)
−0.900203 + 0.435470i \(0.856582\pi\)
\(348\) 0 0
\(349\) 87343.9 0.717104 0.358552 0.933510i \(-0.383271\pi\)
0.358552 + 0.933510i \(0.383271\pi\)
\(350\) 40748.1 + 31327.9i 0.332637 + 0.255738i
\(351\) 0 0
\(352\) −22188.6 3027.20i −0.179079 0.0244318i
\(353\) −48708.6 −0.390892 −0.195446 0.980715i \(-0.562615\pi\)
−0.195446 + 0.980715i \(0.562615\pi\)
\(354\) 0 0
\(355\) 95424.6i 0.757187i
\(356\) 6373.12 + 23964.7i 0.0502866 + 0.189091i
\(357\) 0 0
\(358\) −104142. 80066.8i −0.812572 0.624721i
\(359\) 109409.i 0.848911i −0.905449 0.424456i \(-0.860465\pi\)
0.905449 0.424456i \(-0.139535\pi\)
\(360\) 0 0
\(361\) 25520.5 0.195828
\(362\) −55486.0 + 72170.4i −0.423415 + 0.550734i
\(363\) 0 0
\(364\) −186580. + 49618.7i −1.40819 + 0.374492i
\(365\) −66685.4 −0.500547
\(366\) 0 0
\(367\) 1284.97i 0.00954031i −0.999989 0.00477015i \(-0.998482\pi\)
0.999989 0.00477015i \(-0.00151839\pi\)
\(368\) −29137.8 50908.6i −0.215160 0.375920i
\(369\) 0 0
\(370\) 17207.1 22381.2i 0.125691 0.163486i
\(371\) 270945.i 1.96849i
\(372\) 0 0
\(373\) −73554.3 −0.528677 −0.264339 0.964430i \(-0.585154\pi\)
−0.264339 + 0.964430i \(0.585154\pi\)
\(374\) −19686.1 15135.1i −0.140740 0.108203i
\(375\) 0 0
\(376\) 30250.2 72452.5i 0.213970 0.512481i
\(377\) 152687. 1.07428
\(378\) 0 0
\(379\) 139070.i 0.968176i −0.875019 0.484088i \(-0.839152\pi\)
0.875019 0.484088i \(-0.160848\pi\)
\(380\) 110871. 29484.9i 0.767807 0.204189i
\(381\) 0 0
\(382\) −182350. 140194.i −1.24963 0.960736i
\(383\) 103923.i 0.708461i −0.935158 0.354230i \(-0.884743\pi\)
0.935158 0.354230i \(-0.115257\pi\)
\(384\) 0 0
\(385\) −46305.2 −0.312398
\(386\) −109569. + 142515.i −0.735380 + 0.956505i
\(387\) 0 0
\(388\) −24003.7 90260.7i −0.159447 0.599563i
\(389\) −100082. −0.661388 −0.330694 0.943738i \(-0.607283\pi\)
−0.330694 + 0.943738i \(0.607283\pi\)
\(390\) 0 0
\(391\) 65042.1i 0.425443i
\(392\) 397915. + 166136.i 2.58952 + 1.08117i
\(393\) 0 0
\(394\) −108528. + 141162.i −0.699116 + 0.909337i
\(395\) 159295.i 1.02096i
\(396\) 0 0
\(397\) 164388. 1.04301 0.521507 0.853247i \(-0.325370\pi\)
0.521507 + 0.853247i \(0.325370\pi\)
\(398\) −60463.4 46485.5i −0.381704 0.293461i
\(399\) 0 0
\(400\) 29865.0 17093.4i 0.186656 0.106833i
\(401\) −156453. −0.972961 −0.486481 0.873691i \(-0.661720\pi\)
−0.486481 + 0.873691i \(0.661720\pi\)
\(402\) 0 0
\(403\) 104732.i 0.644866i
\(404\) 22612.3 + 85028.6i 0.138542 + 0.520958i
\(405\) 0 0
\(406\) −366699. 281926.i −2.22463 1.71034i
\(407\) 6968.64i 0.0420687i
\(408\) 0 0
\(409\) 270702. 1.61825 0.809125 0.587637i \(-0.199942\pi\)
0.809125 + 0.587637i \(0.199942\pi\)
\(410\) −17757.2 + 23096.7i −0.105635 + 0.137399i
\(411\) 0 0
\(412\) −277294. + 73743.1i −1.63360 + 0.434437i
\(413\) 141086. 0.827149
\(414\) 0 0
\(415\) 73589.9i 0.427290i
\(416\) −17472.3 + 128068.i −0.100963 + 0.740036i
\(417\) 0 0
\(418\) 17260.5 22450.7i 0.0987874 0.128492i
\(419\) 57003.2i 0.324692i −0.986734 0.162346i \(-0.948094\pi\)
0.986734 0.162346i \(-0.0519060\pi\)
\(420\) 0 0
\(421\) 233625. 1.31812 0.659059 0.752091i \(-0.270955\pi\)
0.659059 + 0.752091i \(0.270955\pi\)
\(422\) −3021.82 2323.24i −0.0169685 0.0130457i
\(423\) 0 0
\(424\) 167390. + 69888.0i 0.931101 + 0.388750i
\(425\) 38156.3 0.211246
\(426\) 0 0
\(427\) 178990.i 0.981687i
\(428\) −134759. + 35837.5i −0.735647 + 0.195637i
\(429\) 0 0
\(430\) −14544.7 11182.3i −0.0786627 0.0604774i
\(431\) 333180.i 1.79360i −0.442439 0.896798i \(-0.645887\pi\)
0.442439 0.896798i \(-0.354113\pi\)
\(432\) 0 0
\(433\) −215343. −1.14856 −0.574282 0.818657i \(-0.694719\pi\)
−0.574282 + 0.818657i \(0.694719\pi\)
\(434\) 193380. 251529.i 1.02667 1.33539i
\(435\) 0 0
\(436\) 50011.6 + 188057.i 0.263086 + 0.989275i
\(437\) 74176.2 0.388420
\(438\) 0 0
\(439\) 31238.4i 0.162091i 0.996710 + 0.0810455i \(0.0258259\pi\)
−0.996710 + 0.0810455i \(0.974174\pi\)
\(440\) −11944.0 + 28607.3i −0.0616944 + 0.147765i
\(441\) 0 0
\(442\) −87356.3 + 113624.i −0.447146 + 0.581601i
\(443\) 213422.i 1.08751i −0.839245 0.543754i \(-0.817003\pi\)
0.839245 0.543754i \(-0.182997\pi\)
\(444\) 0 0
\(445\) 34327.8 0.173351
\(446\) −137444. 105669.i −0.690963 0.531226i
\(447\) 0 0
\(448\) 278430. 275312.i 1.38727 1.37173i
\(449\) −393053. −1.94966 −0.974828 0.222956i \(-0.928429\pi\)
−0.974828 + 0.222956i \(0.928429\pi\)
\(450\) 0 0
\(451\) 7191.43i 0.0353559i
\(452\) 84188.3 + 316571.i 0.412074 + 1.54951i
\(453\) 0 0
\(454\) −19050.6 14646.5i −0.0924265 0.0710593i
\(455\) 267264.i 1.29097i
\(456\) 0 0
\(457\) −72357.5 −0.346458 −0.173229 0.984882i \(-0.555420\pi\)
−0.173229 + 0.984882i \(0.555420\pi\)
\(458\) −9938.23 + 12926.6i −0.0473782 + 0.0616246i
\(459\) 0 0
\(460\) −78473.1 + 20869.0i −0.370856 + 0.0986246i
\(461\) 58191.8 0.273817 0.136908 0.990584i \(-0.456283\pi\)
0.136908 + 0.990584i \(0.456283\pi\)
\(462\) 0 0
\(463\) 74734.1i 0.348623i 0.984691 + 0.174312i \(0.0557700\pi\)
−0.984691 + 0.174312i \(0.944230\pi\)
\(464\) −268760. + 153826.i −1.24833 + 0.714487i
\(465\) 0 0
\(466\) −91249.4 + 118688.i −0.420202 + 0.546555i
\(467\) 264366.i 1.21219i 0.795392 + 0.606096i \(0.207265\pi\)
−0.795392 + 0.606096i \(0.792735\pi\)
\(468\) 0 0
\(469\) 23695.5 0.107726
\(470\) −86166.2 66246.2i −0.390069 0.299892i
\(471\) 0 0
\(472\) 36391.9 87162.8i 0.163351 0.391244i
\(473\) −4528.67 −0.0202418
\(474\) 0 0
\(475\) 43514.7i 0.192863i
\(476\) 419597. 111587.i 1.85191 0.492492i
\(477\) 0 0
\(478\) 81334.9 + 62531.9i 0.355976 + 0.273682i
\(479\) 279681.i 1.21897i −0.792799 0.609483i \(-0.791377\pi\)
0.792799 0.609483i \(-0.208623\pi\)
\(480\) 0 0
\(481\) −40221.4 −0.173847
\(482\) 186757. 242913.i 0.803863 1.04558i
\(483\) 0 0
\(484\) −58238.3 218992.i −0.248610 0.934841i
\(485\) −129293. −0.549655
\(486\) 0 0
\(487\) 62506.3i 0.263552i −0.991280 0.131776i \(-0.957932\pi\)
0.991280 0.131776i \(-0.0420679\pi\)
\(488\) 110580. + 46168.9i 0.464340 + 0.193870i
\(489\) 0 0
\(490\) 363830. 473232.i 1.51533 1.97098i
\(491\) 336874.i 1.39735i −0.715440 0.698674i \(-0.753774\pi\)
0.715440 0.698674i \(-0.246226\pi\)
\(492\) 0 0
\(493\) −343375. −1.41278
\(494\) −129580. 99624.0i −0.530989 0.408235i
\(495\) 0 0
\(496\) −105514. 184350.i −0.428889 0.749342i
\(497\) 411854. 1.66736
\(498\) 0 0
\(499\) 319430.i 1.28285i 0.767187 + 0.641424i \(0.221656\pi\)
−0.767187 + 0.641424i \(0.778344\pi\)
\(500\) −69166.9 260087.i −0.276668 1.04035i
\(501\) 0 0
\(502\) 211332. + 162476.i 0.838607 + 0.644737i
\(503\) 28287.7i 0.111805i 0.998436 + 0.0559025i \(0.0178036\pi\)
−0.998436 + 0.0559025i \(0.982196\pi\)
\(504\) 0 0
\(505\) 121798. 0.477592
\(506\) −12216.7 + 15890.3i −0.0477149 + 0.0620626i
\(507\) 0 0
\(508\) 125717. 33433.0i 0.487155 0.129553i
\(509\) 94557.1 0.364971 0.182486 0.983209i \(-0.441586\pi\)
0.182486 + 0.983209i \(0.441586\pi\)
\(510\) 0 0
\(511\) 287815.i 1.10223i
\(512\) −98268.5 243028.i −0.374865 0.927080i
\(513\) 0 0
\(514\) 144883. 188449.i 0.548392 0.713291i
\(515\) 397206.i 1.49762i
\(516\) 0 0
\(517\) −26828.8 −0.100374
\(518\) 96597.6 + 74266.1i 0.360003 + 0.276778i
\(519\) 0 0
\(520\) 165115. + 68938.4i 0.610633 + 0.254950i
\(521\) 369932. 1.36285 0.681423 0.731890i \(-0.261362\pi\)
0.681423 + 0.731890i \(0.261362\pi\)
\(522\) 0 0
\(523\) 65267.4i 0.238612i 0.992858 + 0.119306i \(0.0380670\pi\)
−0.992858 + 0.119306i \(0.961933\pi\)
\(524\) −251662. + 66926.6i −0.916549 + 0.243745i
\(525\) 0 0
\(526\) 79723.1 + 61292.6i 0.288146 + 0.221532i
\(527\) 235530.i 0.848058i
\(528\) 0 0
\(529\) 227340. 0.812391
\(530\) 153051. 199073.i 0.544859 0.708696i
\(531\) 0 0
\(532\) 127257. + 478523.i 0.449634 + 1.69075i
\(533\) 41507.3 0.146107
\(534\) 0 0
\(535\) 193033.i 0.674411i
\(536\) 6112.04 14639.0i 0.0212744 0.0509545i
\(537\) 0 0
\(538\) 6225.39 8097.33i 0.0215081 0.0279755i
\(539\) 147346.i 0.507179i
\(540\) 0 0
\(541\) 176002. 0.601343 0.300671 0.953728i \(-0.402789\pi\)
0.300671 + 0.953728i \(0.402789\pi\)
\(542\) 14660.5 + 11271.2i 0.0499055 + 0.0383684i
\(543\) 0 0
\(544\) 39293.3 288010.i 0.132776 0.973216i
\(545\) 269380. 0.906926
\(546\) 0 0
\(547\) 273097.i 0.912730i 0.889793 + 0.456365i \(0.150849\pi\)
−0.889793 + 0.456365i \(0.849151\pi\)
\(548\) −101416. 381351.i −0.337710 1.26988i
\(549\) 0 0
\(550\) −9321.85 7166.82i −0.0308160 0.0236920i
\(551\) 391597.i 1.28984i
\(552\) 0 0
\(553\) −687519. −2.24820
\(554\) −24025.2 + 31249.5i −0.0782794 + 0.101818i
\(555\) 0 0
\(556\) −304923. + 81090.6i −0.986372 + 0.262314i
\(557\) −454335. −1.46442 −0.732211 0.681078i \(-0.761511\pi\)
−0.732211 + 0.681078i \(0.761511\pi\)
\(558\) 0 0
\(559\) 26138.5i 0.0836482i
\(560\) −269258. 470439.i −0.858604 1.50013i
\(561\) 0 0
\(562\) −118042. + 153537.i −0.373736 + 0.486117i
\(563\) 32046.7i 0.101104i −0.998721 0.0505518i \(-0.983902\pi\)
0.998721 0.0505518i \(-0.0160980\pi\)
\(564\) 0 0
\(565\) 453468. 1.42053
\(566\) 419318. + 322380.i 1.30891 + 1.00632i
\(567\) 0 0
\(568\) 106234. 254443.i 0.329282 0.788667i
\(569\) −277128. −0.855964 −0.427982 0.903787i \(-0.640775\pi\)
−0.427982 + 0.903787i \(0.640775\pi\)
\(570\) 0 0
\(571\) 642532.i 1.97071i −0.170515 0.985355i \(-0.554543\pi\)
0.170515 0.985355i \(-0.445457\pi\)
\(572\) 42683.5 11351.2i 0.130457 0.0346935i
\(573\) 0 0
\(574\) −99685.8 76640.4i −0.302559 0.232613i
\(575\) 30799.0i 0.0931540i
\(576\) 0 0
\(577\) 451002. 1.35465 0.677324 0.735685i \(-0.263140\pi\)
0.677324 + 0.735685i \(0.263140\pi\)
\(578\) −7171.81 + 9328.34i −0.0214671 + 0.0279221i
\(579\) 0 0
\(580\) 110173. + 414281.i 0.327506 + 1.23151i
\(581\) −317615. −0.940913
\(582\) 0 0
\(583\) 61983.5i 0.182364i
\(584\) −177812. 74239.5i −0.521357 0.217675i
\(585\) 0 0
\(586\) −218250. + 283876.i −0.635563 + 0.826674i
\(587\) 378466.i 1.09838i −0.835699 0.549188i \(-0.814937\pi\)
0.835699 0.549188i \(-0.185063\pi\)
\(588\) 0 0
\(589\) 268607. 0.774259
\(590\) −103661. 79696.4i −0.297790 0.228947i
\(591\) 0 0
\(592\) 70798.0 40521.6i 0.202012 0.115623i
\(593\) 137966. 0.392339 0.196170 0.980570i \(-0.437150\pi\)
0.196170 + 0.980570i \(0.437150\pi\)
\(594\) 0 0
\(595\) 601046.i 1.69775i
\(596\) −122891. 462106.i −0.345963 1.30091i
\(597\) 0 0
\(598\) 91715.1 + 70512.4i 0.256471 + 0.197180i
\(599\) 208851.i 0.582080i 0.956711 + 0.291040i \(0.0940013\pi\)
−0.956711 + 0.291040i \(0.905999\pi\)
\(600\) 0 0
\(601\) 360007. 0.996695 0.498348 0.866977i \(-0.333940\pi\)
0.498348 + 0.866977i \(0.333940\pi\)
\(602\) 48262.9 62775.3i 0.133174 0.173219i
\(603\) 0 0
\(604\) −92203.3 + 24520.4i −0.252739 + 0.0672130i
\(605\) −313692. −0.857023
\(606\) 0 0
\(607\) 322980.i 0.876593i −0.898830 0.438297i \(-0.855582\pi\)
0.898830 0.438297i \(-0.144418\pi\)
\(608\) 328456. + 44811.4i 0.888525 + 0.121222i
\(609\) 0 0
\(610\) 101108. 131510.i 0.271721 0.353427i
\(611\) 154850.i 0.414791i
\(612\) 0 0
\(613\) −392554. −1.04467 −0.522334 0.852741i \(-0.674939\pi\)
−0.522334 + 0.852741i \(0.674939\pi\)
\(614\) −198915. 152930.i −0.527632 0.405654i
\(615\) 0 0
\(616\) −123470. 51550.7i −0.325386 0.135854i
\(617\) 384203. 1.00923 0.504616 0.863344i \(-0.331634\pi\)
0.504616 + 0.863344i \(0.331634\pi\)
\(618\) 0 0
\(619\) 695791.i 1.81592i −0.419052 0.907962i \(-0.637638\pi\)
0.419052 0.907962i \(-0.362362\pi\)
\(620\) −284166. + 75570.6i −0.739247 + 0.196594i
\(621\) 0 0
\(622\) 389360. + 299347.i 1.00640 + 0.773739i
\(623\) 148159.i 0.381727i
\(624\) 0 0
\(625\) −288546. −0.738679
\(626\) −118461. + 154082.i −0.302293 + 0.393191i
\(627\) 0 0
\(628\) 143869. + 540989.i 0.364795 + 1.37173i
\(629\) 90453.5 0.228625
\(630\) 0 0
\(631\) 230753.i 0.579546i −0.957095 0.289773i \(-0.906420\pi\)
0.957095 0.289773i \(-0.0935798\pi\)
\(632\) −177340. + 424749.i −0.443989 + 1.06340i
\(633\) 0 0
\(634\) −268508. + 349247.i −0.668004 + 0.868869i
\(635\) 180082.i 0.446603i
\(636\) 0 0
\(637\) −850449. −2.09590
\(638\) 83889.0 + 64495.5i 0.206093 + 0.158449i
\(639\) 0 0
\(640\) −360090. + 45001.6i −0.879126 + 0.109867i
\(641\) 518941. 1.26300 0.631498 0.775377i \(-0.282440\pi\)
0.631498 + 0.775377i \(0.282440\pi\)
\(642\) 0 0
\(643\) 225212.i 0.544716i 0.962196 + 0.272358i \(0.0878035\pi\)
−0.962196 + 0.272358i \(0.912197\pi\)
\(644\) −90070.8 338691.i −0.217176 0.816643i
\(645\) 0 0
\(646\) 291412. + 224043.i 0.698300 + 0.536867i
\(647\) 153505.i 0.366703i 0.983047 + 0.183352i \(0.0586947\pi\)
−0.983047 + 0.183352i \(0.941305\pi\)
\(648\) 0 0
\(649\) −32276.0 −0.0766284
\(650\) −41365.3 + 53803.7i −0.0979061 + 0.127346i
\(651\) 0 0
\(652\) −224359. + 59665.5i −0.527774 + 0.140355i
\(653\) 72240.7 0.169416 0.0847082 0.996406i \(-0.473004\pi\)
0.0847082 + 0.996406i \(0.473004\pi\)
\(654\) 0 0
\(655\) 360490.i 0.840254i
\(656\) −73061.5 + 41817.1i −0.169778 + 0.0971731i
\(657\) 0 0
\(658\) 285920. 371895.i 0.660378 0.858950i
\(659\) 234586.i 0.540171i 0.962836 + 0.270086i \(0.0870520\pi\)
−0.962836 + 0.270086i \(0.912948\pi\)
\(660\) 0 0
\(661\) 597947. 1.36855 0.684274 0.729225i \(-0.260119\pi\)
0.684274 + 0.729225i \(0.260119\pi\)
\(662\) 585138. + 449866.i 1.33519 + 1.02652i
\(663\) 0 0
\(664\) −81926.2 + 196223.i −0.185817 + 0.445054i
\(665\) 685452. 1.55001
\(666\) 0 0
\(667\) 277166.i 0.623001i
\(668\) 689905. 183472.i 1.54610 0.411166i
\(669\) 0 0
\(670\) −17409.9 13385.0i −0.0387834 0.0298174i
\(671\) 40947.2i 0.0909450i
\(672\) 0 0
\(673\) −751705. −1.65965 −0.829826 0.558022i \(-0.811561\pi\)
−0.829826 + 0.558022i \(0.811561\pi\)
\(674\) 159998. 208109.i 0.352204 0.458111i
\(675\) 0 0
\(676\) 51928.7 + 195266.i 0.113636 + 0.427301i
\(677\) −84647.6 −0.184687 −0.0923437 0.995727i \(-0.529436\pi\)
−0.0923437 + 0.995727i \(0.529436\pi\)
\(678\) 0 0
\(679\) 558029.i 1.21037i
\(680\) −371326. 155035.i −0.803040 0.335283i
\(681\) 0 0
\(682\) −44239.2 + 57541.8i −0.0951128 + 0.123713i
\(683\) 635506.i 1.36232i −0.732136 0.681159i \(-0.761476\pi\)
0.732136 0.681159i \(-0.238524\pi\)
\(684\) 0 0
\(685\) −546260. −1.16418
\(686\) 1.31462e6 + 1.01071e6i 2.79352 + 2.14771i
\(687\) 0 0
\(688\) −26333.5 46009.1i −0.0556330 0.0972002i
\(689\) −357755. −0.753612
\(690\) 0 0
\(691\) 444378.i 0.930672i −0.885134 0.465336i \(-0.845933\pi\)
0.885134 0.465336i \(-0.154067\pi\)
\(692\) 217474. + 817762.i 0.454145 + 1.70771i
\(693\) 0 0
\(694\) 332553. + 255673.i 0.690466 + 0.530844i
\(695\) 436782.i 0.904264i
\(696\) 0 0
\(697\) −93345.3 −0.192144
\(698\) 212947. 276979.i 0.437079 0.568506i
\(699\) 0 0
\(700\) 198690. 52839.1i 0.405489 0.107835i
\(701\) −374624. −0.762359 −0.381179 0.924501i \(-0.624482\pi\)
−0.381179 + 0.924501i \(0.624482\pi\)
\(702\) 0 0
\(703\) 103156.i 0.208730i
\(704\) −63695.9 + 62982.4i −0.128519 + 0.127079i
\(705\) 0 0
\(706\) −118753. + 154461.i −0.238251 + 0.309892i
\(707\) 525682.i 1.05168i
\(708\) 0 0
\(709\) 185631. 0.369282 0.184641 0.982806i \(-0.440888\pi\)
0.184641 + 0.982806i \(0.440888\pi\)
\(710\) −302603. 232647.i −0.600284 0.461510i
\(711\) 0 0
\(712\) 91532.8 + 38216.5i 0.180558 + 0.0753860i
\(713\) −190116. −0.373972
\(714\) 0 0
\(715\) 61141.4i 0.119598i
\(716\) −507804. + 135044.i −0.990535 + 0.263421i
\(717\) 0 0
\(718\) −346948. 266741.i −0.673001 0.517416i
\(719\) 651163.i 1.25960i −0.776759 0.629799i \(-0.783137\pi\)
0.776759 0.629799i \(-0.216863\pi\)
\(720\) 0 0
\(721\) −1.71435e6 −3.29783
\(722\) 62219.6 80928.7i 0.119358 0.155249i
\(723\) 0 0
\(724\) 93585.2 + 351906.i 0.178538 + 0.671351i
\(725\) −162597. −0.309340
\(726\) 0 0
\(727\) 240082.i 0.454246i −0.973866 0.227123i \(-0.927068\pi\)
0.973866 0.227123i \(-0.0729320\pi\)
\(728\) −297539. + 712640.i −0.561412 + 1.34465i
\(729\) 0 0
\(730\) −162581. + 211468.i −0.305086 + 0.396825i
\(731\) 58782.5i 0.110005i
\(732\) 0 0
\(733\) −55680.1 −0.103632 −0.0518158 0.998657i \(-0.516501\pi\)
−0.0518158 + 0.998657i \(0.516501\pi\)
\(734\) −4074.82 3132.80i −0.00756338 0.00581487i
\(735\) 0 0
\(736\) −232476. 31716.8i −0.429163 0.0585509i
\(737\) −5420.76 −0.00997988
\(738\) 0 0
\(739\) 327859.i 0.600341i 0.953886 + 0.300170i \(0.0970435\pi\)
−0.953886 + 0.300170i \(0.902957\pi\)
\(740\) −29022.3 109132.i −0.0529990 0.199291i
\(741\) 0 0
\(742\) 859201. + 660571.i 1.56058 + 1.19981i
\(743\) 12875.8i 0.0233237i −0.999932 0.0116618i \(-0.996288\pi\)
0.999932 0.0116618i \(-0.00371217\pi\)
\(744\) 0 0
\(745\) −661936. −1.19262
\(746\) −179327. + 233250.i −0.322232 + 0.419126i
\(747\) 0 0
\(748\) −95990.4 + 25527.5i −0.171563 + 0.0456252i
\(749\) −833135. −1.48509
\(750\) 0 0
\(751\) 531658.i 0.942655i 0.881958 + 0.471328i \(0.156225\pi\)
−0.881958 + 0.471328i \(0.843775\pi\)
\(752\) −156006. 272568.i −0.275870 0.481991i
\(753\) 0 0
\(754\) 372254. 484189.i 0.654782 0.851672i
\(755\) 132075.i 0.231701i
\(756\) 0 0
\(757\) 614542. 1.07241 0.536204 0.844089i \(-0.319858\pi\)
0.536204 + 0.844089i \(0.319858\pi\)
\(758\) −441008. 339055.i −0.767552 0.590109i
\(759\) 0 0
\(760\) 176807. 423472.i 0.306106 0.733158i
\(761\) −820697. −1.41714 −0.708571 0.705639i \(-0.750660\pi\)
−0.708571 + 0.705639i \(0.750660\pi\)
\(762\) 0 0
\(763\) 1.16265e6i 1.99710i
\(764\) −889149. + 236458.i −1.52331 + 0.405105i
\(765\) 0 0
\(766\) −329554. 253368.i −0.561654 0.431811i
\(767\) 186290.i 0.316664i
\(768\) 0 0
\(769\) −131443. −0.222273 −0.111136 0.993805i \(-0.535449\pi\)
−0.111136 + 0.993805i \(0.535449\pi\)
\(770\) −112893. + 146840.i −0.190409 + 0.247664i
\(771\) 0 0
\(772\) 184803. + 694912.i 0.310081 + 1.16599i
\(773\) −629.598 −0.00105367 −0.000526834 1.00000i \(-0.500168\pi\)
−0.000526834 1.00000i \(0.500168\pi\)
\(774\) 0 0
\(775\) 111529.i 0.185689i
\(776\) −344750. 143939.i −0.572507 0.239031i
\(777\) 0 0
\(778\) −244002. + 317372.i −0.403120 + 0.524336i
\(779\) 106454.i 0.175423i
\(780\) 0 0
\(781\) −94219.0 −0.154467
\(782\) −206257. 158574.i −0.337283 0.259310i
\(783\) 0 0
\(784\) 1.49697e6 856796.i 2.43545 1.39394i
\(785\) 774931. 1.25755
\(786\) 0 0