Properties

Label 74.5.d.a.31.2
Level $74$
Weight $5$
Character 74.31
Analytic conductor $7.649$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.64937726820\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.2
Root \(-9.51876i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.5.d.a.43.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 2.00000i) q^{2} -10.5188i q^{3} +8.00000i q^{4} +(30.2483 - 30.2483i) q^{5} +(-21.0375 + 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 - 16.0000i) q^{8} -29.6443 q^{9} +O(q^{10})\) \(q+(-2.00000 - 2.00000i) q^{2} -10.5188i q^{3} +8.00000i q^{4} +(30.2483 - 30.2483i) q^{5} +(-21.0375 + 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 - 16.0000i) q^{8} -29.6443 q^{9} -120.993 q^{10} +10.9953i q^{11} +84.1501 q^{12} +(80.0125 - 80.0125i) q^{13} +(-138.096 - 138.096i) q^{14} +(-318.174 - 318.174i) q^{15} -64.0000 q^{16} +(-345.037 + 345.037i) q^{17} +(59.2886 + 59.2886i) q^{18} +(121.486 - 121.486i) q^{19} +(241.986 + 241.986i) q^{20} -726.297i q^{21} +(21.9906 - 21.9906i) q^{22} +(-590.441 + 590.441i) q^{23} +(-168.300 - 168.300i) q^{24} -1204.92i q^{25} -320.050 q^{26} -540.198i q^{27} +552.382i q^{28} +(49.9544 + 49.9544i) q^{29} +1272.70i q^{30} +(947.769 + 947.769i) q^{31} +(128.000 + 128.000i) q^{32} +115.657 q^{33} +1380.15 q^{34} +(2088.58 - 2088.58i) q^{35} -237.155i q^{36} +(-917.114 + 1016.40i) q^{37} -485.944 q^{38} +(-841.632 - 841.632i) q^{39} -967.945i q^{40} +3127.67i q^{41} +(-1452.59 + 1452.59i) q^{42} +(522.294 - 522.294i) q^{43} -87.9624 q^{44} +(-896.689 + 896.689i) q^{45} +2361.76 q^{46} +315.367 q^{47} +673.201i q^{48} +2366.59 q^{49} +(-2409.83 + 2409.83i) q^{50} +(3629.36 + 3629.36i) q^{51} +(640.100 + 640.100i) q^{52} -3942.78 q^{53} +(-1080.40 + 1080.40i) q^{54} +(332.589 + 332.589i) q^{55} +(1104.76 - 1104.76i) q^{56} +(-1277.88 - 1277.88i) q^{57} -199.818i q^{58} +(3550.97 - 3550.97i) q^{59} +(2545.39 - 2545.39i) q^{60} +(-519.449 - 519.449i) q^{61} -3791.08i q^{62} -2046.87 q^{63} -512.000i q^{64} -4840.48i q^{65} +(-231.314 - 231.314i) q^{66} -3736.40i q^{67} +(-2760.30 - 2760.30i) q^{68} +(6210.71 + 6210.71i) q^{69} -8354.30 q^{70} -1195.01 q^{71} +(-474.309 + 474.309i) q^{72} -1212.04i q^{73} +(3867.02 - 198.567i) q^{74} -12674.2 q^{75} +(971.887 + 971.887i) q^{76} +759.201i q^{77} +3366.53i q^{78} +(-1838.99 + 1838.99i) q^{79} +(-1935.89 + 1935.89i) q^{80} -8083.40 q^{81} +(6255.34 - 6255.34i) q^{82} -1530.34 q^{83} +5810.37 q^{84} +20873.6i q^{85} -2089.17 q^{86} +(525.459 - 525.459i) q^{87} +(175.925 + 175.925i) q^{88} +(-5115.00 - 5115.00i) q^{89} +3586.76 q^{90} +(5524.68 - 5524.68i) q^{91} +(-4723.53 - 4723.53i) q^{92} +(9969.36 - 9969.36i) q^{93} +(-630.735 - 630.735i) q^{94} -7349.48i q^{95} +(1346.40 - 1346.40i) q^{96} +(-4016.43 + 4016.43i) q^{97} +(-4733.19 - 4733.19i) q^{98} -325.948i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + O(q^{10}) \) \( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 2.00000i −0.500000 0.500000i
\(3\) 10.5188i 1.16875i −0.811483 0.584376i \(-0.801340\pi\)
0.811483 0.584376i \(-0.198660\pi\)
\(4\) 8.00000i 0.500000i
\(5\) 30.2483 30.2483i 1.20993 1.20993i 0.238882 0.971049i \(-0.423219\pi\)
0.971049 0.238882i \(-0.0767810\pi\)
\(6\) −21.0375 + 21.0375i −0.584376 + 0.584376i
\(7\) 69.0478 1.40914 0.704569 0.709636i \(-0.251140\pi\)
0.704569 + 0.709636i \(0.251140\pi\)
\(8\) 16.0000 16.0000i 0.250000 0.250000i
\(9\) −29.6443 −0.365979
\(10\) −120.993 −1.20993
\(11\) 10.9953i 0.0908702i 0.998967 + 0.0454351i \(0.0144674\pi\)
−0.998967 + 0.0454351i \(0.985533\pi\)
\(12\) 84.1501 0.584376
\(13\) 80.0125 80.0125i 0.473447 0.473447i −0.429582 0.903028i \(-0.641339\pi\)
0.903028 + 0.429582i \(0.141339\pi\)
\(14\) −138.096 138.096i −0.704569 0.704569i
\(15\) −318.174 318.174i −1.41411 1.41411i
\(16\) −64.0000 −0.250000
\(17\) −345.037 + 345.037i −1.19390 + 1.19390i −0.217938 + 0.975963i \(0.569933\pi\)
−0.975963 + 0.217938i \(0.930067\pi\)
\(18\) 59.2886 + 59.2886i 0.182990 + 0.182990i
\(19\) 121.486 121.486i 0.336526 0.336526i −0.518532 0.855058i \(-0.673521\pi\)
0.855058 + 0.518532i \(0.173521\pi\)
\(20\) 241.986 + 241.986i 0.604965 + 0.604965i
\(21\) 726.297i 1.64693i
\(22\) 21.9906 21.9906i 0.0454351 0.0454351i
\(23\) −590.441 + 590.441i −1.11615 + 1.11615i −0.123844 + 0.992302i \(0.539522\pi\)
−0.992302 + 0.123844i \(0.960478\pi\)
\(24\) −168.300 168.300i −0.292188 0.292188i
\(25\) 1204.92i 1.92786i
\(26\) −320.050 −0.473447
\(27\) 540.198i 0.741012i
\(28\) 552.382i 0.704569i
\(29\) 49.9544 + 49.9544i 0.0593989 + 0.0593989i 0.736182 0.676783i \(-0.236627\pi\)
−0.676783 + 0.736182i \(0.736627\pi\)
\(30\) 1272.70i 1.41411i
\(31\) 947.769 + 947.769i 0.986232 + 0.986232i 0.999907 0.0136744i \(-0.00435284\pi\)
−0.0136744 + 0.999907i \(0.504353\pi\)
\(32\) 128.000 + 128.000i 0.125000 + 0.125000i
\(33\) 115.657 0.106205
\(34\) 1380.15 1.19390
\(35\) 2088.58 2088.58i 1.70496 1.70496i
\(36\) 237.155i 0.182990i
\(37\) −917.114 + 1016.40i −0.669915 + 0.742438i
\(38\) −485.944 −0.336526
\(39\) −841.632 841.632i −0.553341 0.553341i
\(40\) 967.945i 0.604965i
\(41\) 3127.67i 1.86060i 0.366799 + 0.930300i \(0.380454\pi\)
−0.366799 + 0.930300i \(0.619546\pi\)
\(42\) −1452.59 + 1452.59i −0.823466 + 0.823466i
\(43\) 522.294 522.294i 0.282474 0.282474i −0.551621 0.834095i \(-0.685991\pi\)
0.834095 + 0.551621i \(0.185991\pi\)
\(44\) −87.9624 −0.0454351
\(45\) −896.689 + 896.689i −0.442810 + 0.442810i
\(46\) 2361.76 1.11615
\(47\) 315.367 0.142765 0.0713824 0.997449i \(-0.477259\pi\)
0.0713824 + 0.997449i \(0.477259\pi\)
\(48\) 673.201i 0.292188i
\(49\) 2366.59 0.985670
\(50\) −2409.83 + 2409.83i −0.963932 + 0.963932i
\(51\) 3629.36 + 3629.36i 1.39537 + 1.39537i
\(52\) 640.100 + 640.100i 0.236723 + 0.236723i
\(53\) −3942.78 −1.40362 −0.701811 0.712363i \(-0.747625\pi\)
−0.701811 + 0.712363i \(0.747625\pi\)
\(54\) −1080.40 + 1080.40i −0.370506 + 0.370506i
\(55\) 332.589 + 332.589i 0.109947 + 0.109947i
\(56\) 1104.76 1104.76i 0.352284 0.352284i
\(57\) −1277.88 1277.88i −0.393315 0.393315i
\(58\) 199.818i 0.0593989i
\(59\) 3550.97 3550.97i 1.02010 1.02010i 0.0203075 0.999794i \(-0.493535\pi\)
0.999794 0.0203075i \(-0.00646453\pi\)
\(60\) 2545.39 2545.39i 0.707054 0.707054i
\(61\) −519.449 519.449i −0.139599 0.139599i 0.633854 0.773453i \(-0.281472\pi\)
−0.773453 + 0.633854i \(0.781472\pi\)
\(62\) 3791.08i 0.986232i
\(63\) −2046.87 −0.515715
\(64\) 512.000i 0.125000i
\(65\) 4840.48i 1.14568i
\(66\) −231.314 231.314i −0.0531023 0.0531023i
\(67\) 3736.40i 0.832345i −0.909286 0.416173i \(-0.863371\pi\)
0.909286 0.416173i \(-0.136629\pi\)
\(68\) −2760.30 2760.30i −0.596950 0.596950i
\(69\) 6210.71 + 6210.71i 1.30450 + 1.30450i
\(70\) −8354.30 −1.70496
\(71\) −1195.01 −0.237058 −0.118529 0.992951i \(-0.537818\pi\)
−0.118529 + 0.992951i \(0.537818\pi\)
\(72\) −474.309 + 474.309i −0.0914948 + 0.0914948i
\(73\) 1212.04i 0.227442i −0.993513 0.113721i \(-0.963723\pi\)
0.993513 0.113721i \(-0.0362770\pi\)
\(74\) 3867.02 198.567i 0.706176 0.0362614i
\(75\) −12674.2 −2.25319
\(76\) 971.887 + 971.887i 0.168263 + 0.168263i
\(77\) 759.201i 0.128049i
\(78\) 3366.53i 0.553341i
\(79\) −1838.99 + 1838.99i −0.294663 + 0.294663i −0.838919 0.544256i \(-0.816812\pi\)
0.544256 + 0.838919i \(0.316812\pi\)
\(80\) −1935.89 + 1935.89i −0.302483 + 0.302483i
\(81\) −8083.40 −1.23204
\(82\) 6255.34 6255.34i 0.930300 0.930300i
\(83\) −1530.34 −0.222143 −0.111071 0.993812i \(-0.535428\pi\)
−0.111071 + 0.993812i \(0.535428\pi\)
\(84\) 5810.37 0.823466
\(85\) 20873.6i 2.88907i
\(86\) −2089.17 −0.282474
\(87\) 525.459 525.459i 0.0694225 0.0694225i
\(88\) 175.925 + 175.925i 0.0227176 + 0.0227176i
\(89\) −5115.00 5115.00i −0.645752 0.645752i 0.306212 0.951963i \(-0.400938\pi\)
−0.951963 + 0.306212i \(0.900938\pi\)
\(90\) 3586.76 0.442810
\(91\) 5524.68 5524.68i 0.667151 0.667151i
\(92\) −4723.53 4723.53i −0.558073 0.558073i
\(93\) 9969.36 9969.36i 1.15266 1.15266i
\(94\) −630.735 630.735i −0.0713824 0.0713824i
\(95\) 7349.48i 0.814346i
\(96\) 1346.40 1346.40i 0.146094 0.146094i
\(97\) −4016.43 + 4016.43i −0.426871 + 0.426871i −0.887561 0.460690i \(-0.847602\pi\)
0.460690 + 0.887561i \(0.347602\pi\)
\(98\) −4733.19 4733.19i −0.492835 0.492835i
\(99\) 325.948i 0.0332566i
\(100\) 9639.32 0.963932
\(101\) 1115.89i 0.109390i −0.998503 0.0546952i \(-0.982581\pi\)
0.998503 0.0546952i \(-0.0174187\pi\)
\(102\) 14517.5i 1.39537i
\(103\) 12833.7 + 12833.7i 1.20970 + 1.20970i 0.971123 + 0.238578i \(0.0766813\pi\)
0.238578 + 0.971123i \(0.423319\pi\)
\(104\) 2560.40i 0.236723i
\(105\) −21969.2 21969.2i −1.99267 1.99267i
\(106\) 7885.55 + 7885.55i 0.701811 + 0.701811i
\(107\) 11472.8 1.00208 0.501038 0.865425i \(-0.332952\pi\)
0.501038 + 0.865425i \(0.332952\pi\)
\(108\) 4321.58 0.370506
\(109\) 528.108 528.108i 0.0444498 0.0444498i −0.684533 0.728982i \(-0.739994\pi\)
0.728982 + 0.684533i \(0.239994\pi\)
\(110\) 1330.35i 0.109947i
\(111\) 10691.2 + 9646.90i 0.867725 + 0.782964i
\(112\) −4419.06 −0.352284
\(113\) 3930.94 + 3930.94i 0.307850 + 0.307850i 0.844075 0.536225i \(-0.180150\pi\)
−0.536225 + 0.844075i \(0.680150\pi\)
\(114\) 5111.52i 0.393315i
\(115\) 35719.6i 2.70092i
\(116\) −399.636 + 399.636i −0.0296994 + 0.0296994i
\(117\) −2371.92 + 2371.92i −0.173272 + 0.173272i
\(118\) −14203.9 −1.02010
\(119\) −23824.0 + 23824.0i −1.68237 + 1.68237i
\(120\) −10181.6 −0.707054
\(121\) 14520.1 0.991743
\(122\) 2077.80i 0.139599i
\(123\) 32899.2 2.17458
\(124\) −7582.15 + 7582.15i −0.493116 + 0.493116i
\(125\) −17541.4 17541.4i −1.12265 1.12265i
\(126\) 4093.75 + 4093.75i 0.257858 + 0.257858i
\(127\) 15432.9 0.956842 0.478421 0.878131i \(-0.341209\pi\)
0.478421 + 0.878131i \(0.341209\pi\)
\(128\) −1024.00 + 1024.00i −0.0625000 + 0.0625000i
\(129\) −5493.88 5493.88i −0.330141 0.330141i
\(130\) −9680.95 + 9680.95i −0.572838 + 0.572838i
\(131\) 13940.0 + 13940.0i 0.812306 + 0.812306i 0.984979 0.172673i \(-0.0552404\pi\)
−0.172673 + 0.984979i \(0.555240\pi\)
\(132\) 925.255i 0.0531023i
\(133\) 8388.33 8388.33i 0.474212 0.474212i
\(134\) −7472.79 + 7472.79i −0.416173 + 0.416173i
\(135\) −16340.1 16340.1i −0.896574 0.896574i
\(136\) 11041.2i 0.596950i
\(137\) −33823.3 −1.80208 −0.901042 0.433731i \(-0.857197\pi\)
−0.901042 + 0.433731i \(0.857197\pi\)
\(138\) 24842.8i 1.30450i
\(139\) 16424.1i 0.850066i −0.905178 0.425033i \(-0.860263\pi\)
0.905178 0.425033i \(-0.139737\pi\)
\(140\) 16708.6 + 16708.6i 0.852480 + 0.852480i
\(141\) 3317.27i 0.166856i
\(142\) 2390.02 + 2390.02i 0.118529 + 0.118529i
\(143\) 879.761 + 879.761i 0.0430222 + 0.0430222i
\(144\) 1897.24 0.0914948
\(145\) 3022.07 0.143737
\(146\) −2424.08 + 2424.08i −0.113721 + 0.113721i
\(147\) 24893.6i 1.15200i
\(148\) −8131.18 7336.91i −0.371219 0.334958i
\(149\) 21406.1 0.964197 0.482099 0.876117i \(-0.339875\pi\)
0.482099 + 0.876117i \(0.339875\pi\)
\(150\) 25348.4 + 25348.4i 1.12660 + 1.12660i
\(151\) 11689.7i 0.512685i −0.966586 0.256342i \(-0.917483\pi\)
0.966586 0.256342i \(-0.0825175\pi\)
\(152\) 3887.55i 0.168263i
\(153\) 10228.4 10228.4i 0.436943 0.436943i
\(154\) 1518.40 1518.40i 0.0640243 0.0640243i
\(155\) 57336.7 2.38655
\(156\) 6733.06 6733.06i 0.276671 0.276671i
\(157\) −24556.9 −0.996265 −0.498132 0.867101i \(-0.665981\pi\)
−0.498132 + 0.867101i \(0.665981\pi\)
\(158\) 7355.96 0.294663
\(159\) 41473.1i 1.64049i
\(160\) 7743.56 0.302483
\(161\) −40768.6 + 40768.6i −1.57280 + 1.57280i
\(162\) 16166.8 + 16166.8i 0.616019 + 0.616019i
\(163\) −9561.68 9561.68i −0.359881 0.359881i 0.503888 0.863769i \(-0.331902\pi\)
−0.863769 + 0.503888i \(0.831902\pi\)
\(164\) −25021.4 −0.930300
\(165\) 3498.42 3498.42i 0.128500 0.128500i
\(166\) 3060.68 + 3060.68i 0.111071 + 0.111071i
\(167\) −14826.8 + 14826.8i −0.531635 + 0.531635i −0.921059 0.389423i \(-0.872674\pi\)
0.389423 + 0.921059i \(0.372674\pi\)
\(168\) −11620.7 11620.7i −0.411733 0.411733i
\(169\) 15757.0i 0.551697i
\(170\) 41747.1 41747.1i 1.44454 1.44454i
\(171\) −3601.37 + 3601.37i −0.123162 + 0.123162i
\(172\) 4178.35 + 4178.35i 0.141237 + 0.141237i
\(173\) 52583.7i 1.75695i −0.477791 0.878473i \(-0.658562\pi\)
0.477791 0.878473i \(-0.341438\pi\)
\(174\) −2101.84 −0.0694225
\(175\) 83196.7i 2.71663i
\(176\) 703.699i 0.0227176i
\(177\) −37351.8 37351.8i −1.19224 1.19224i
\(178\) 20460.0i 0.645752i
\(179\) −6643.45 6643.45i −0.207342 0.207342i 0.595795 0.803137i \(-0.296837\pi\)
−0.803137 + 0.595795i \(0.796837\pi\)
\(180\) −7173.51 7173.51i −0.221405 0.221405i
\(181\) −5056.88 −0.154357 −0.0771783 0.997017i \(-0.524591\pi\)
−0.0771783 + 0.997017i \(0.524591\pi\)
\(182\) −22098.7 −0.667151
\(183\) −5463.96 + 5463.96i −0.163157 + 0.163157i
\(184\) 18894.1i 0.558073i
\(185\) 3003.16 + 58485.4i 0.0877475 + 1.70885i
\(186\) −39877.4 −1.15266
\(187\) −3793.79 3793.79i −0.108490 0.108490i
\(188\) 2522.94i 0.0713824i
\(189\) 37299.5i 1.04419i
\(190\) −14699.0 + 14699.0i −0.407173 + 0.407173i
\(191\) 38695.9 38695.9i 1.06071 1.06071i 0.0626796 0.998034i \(-0.480035\pi\)
0.998034 0.0626796i \(-0.0199646\pi\)
\(192\) −5385.61 −0.146094
\(193\) 42591.4 42591.4i 1.14342 1.14342i 0.155605 0.987819i \(-0.450267\pi\)
0.987819 0.155605i \(-0.0497326\pi\)
\(194\) 16065.7 0.426871
\(195\) −50915.8 −1.33901
\(196\) 18932.7i 0.492835i
\(197\) −38271.7 −0.986154 −0.493077 0.869986i \(-0.664128\pi\)
−0.493077 + 0.869986i \(0.664128\pi\)
\(198\) −651.896 + 651.896i −0.0166283 + 0.0166283i
\(199\) −2855.95 2855.95i −0.0721181 0.0721181i 0.670128 0.742246i \(-0.266239\pi\)
−0.742246 + 0.670128i \(0.766239\pi\)
\(200\) −19278.6 19278.6i −0.481966 0.481966i
\(201\) −39302.3 −0.972804
\(202\) −2231.78 + 2231.78i −0.0546952 + 0.0546952i
\(203\) 3449.24 + 3449.24i 0.0837012 + 0.0837012i
\(204\) −29034.9 + 29034.9i −0.697686 + 0.697686i
\(205\) 94606.6 + 94606.6i 2.25120 + 2.25120i
\(206\) 51334.9i 1.20970i
\(207\) 17503.2 17503.2i 0.408486 0.408486i
\(208\) −5120.80 + 5120.80i −0.118362 + 0.118362i
\(209\) 1335.77 + 1335.77i 0.0305802 + 0.0305802i
\(210\) 87876.9i 1.99267i
\(211\) −70101.5 −1.57457 −0.787285 0.616589i \(-0.788514\pi\)
−0.787285 + 0.616589i \(0.788514\pi\)
\(212\) 31542.2i 0.701811i
\(213\) 12570.0i 0.277062i
\(214\) −22945.5 22945.5i −0.501038 0.501038i
\(215\) 31596.9i 0.683547i
\(216\) −8643.17 8643.17i −0.185253 0.185253i
\(217\) 65441.3 + 65441.3i 1.38974 + 1.38974i
\(218\) −2112.43 −0.0444498
\(219\) −12749.1 −0.265823
\(220\) −2660.71 + 2660.71i −0.0549733 + 0.0549733i
\(221\) 55214.6i 1.13050i
\(222\) −2088.68 40676.3i −0.0423805 0.825344i
\(223\) 24775.0 0.498201 0.249101 0.968478i \(-0.419865\pi\)
0.249101 + 0.968478i \(0.419865\pi\)
\(224\) 8838.11 + 8838.11i 0.176142 + 0.176142i
\(225\) 35718.9i 0.705559i
\(226\) 15723.8i 0.307850i
\(227\) −14116.9 + 14116.9i −0.273960 + 0.273960i −0.830692 0.556732i \(-0.812055\pi\)
0.556732 + 0.830692i \(0.312055\pi\)
\(228\) 10223.0 10223.0i 0.196658 0.196658i
\(229\) 14224.9 0.271255 0.135628 0.990760i \(-0.456695\pi\)
0.135628 + 0.990760i \(0.456695\pi\)
\(230\) 71439.3 71439.3i 1.35046 1.35046i
\(231\) 7985.85 0.149657
\(232\) 1598.54 0.0296994
\(233\) 49309.5i 0.908277i −0.890931 0.454139i \(-0.849947\pi\)
0.890931 0.454139i \(-0.150053\pi\)
\(234\) 9487.66 0.173272
\(235\) 9539.32 9539.32i 0.172735 0.172735i
\(236\) 28407.8 + 28407.8i 0.510051 + 0.510051i
\(237\) 19343.9 + 19343.9i 0.344388 + 0.344388i
\(238\) 95296.2 1.68237
\(239\) −38382.7 + 38382.7i −0.671954 + 0.671954i −0.958166 0.286212i \(-0.907604\pi\)
0.286212 + 0.958166i \(0.407604\pi\)
\(240\) 20363.2 + 20363.2i 0.353527 + 0.353527i
\(241\) −36762.8 + 36762.8i −0.632957 + 0.632957i −0.948809 0.315851i \(-0.897710\pi\)
0.315851 + 0.948809i \(0.397710\pi\)
\(242\) −29040.2 29040.2i −0.495871 0.495871i
\(243\) 41271.3i 0.698934i
\(244\) 4155.59 4155.59i 0.0697996 0.0697996i
\(245\) 71585.3 71585.3i 1.19259 1.19259i
\(246\) −65798.4 65798.4i −1.08729 1.08729i
\(247\) 19440.8i 0.318654i
\(248\) 30328.6 0.493116
\(249\) 16097.3i 0.259630i
\(250\) 70165.8i 1.12265i
\(251\) 77326.3 + 77326.3i 1.22738 + 1.22738i 0.964951 + 0.262430i \(0.0845240\pi\)
0.262430 + 0.964951i \(0.415476\pi\)
\(252\) 16375.0i 0.257858i
\(253\) −6492.07 6492.07i −0.101424 0.101424i
\(254\) −30865.8 30865.8i −0.478421 0.478421i
\(255\) 219564. 3.37661
\(256\) 4096.00 0.0625000
\(257\) −54239.9 + 54239.9i −0.821206 + 0.821206i −0.986281 0.165075i \(-0.947213\pi\)
0.165075 + 0.986281i \(0.447213\pi\)
\(258\) 21975.5i 0.330141i
\(259\) −63324.6 + 70180.0i −0.944003 + 1.04620i
\(260\) 38723.8 0.572838
\(261\) −1480.87 1480.87i −0.0217388 0.0217388i
\(262\) 55759.9i 0.812306i
\(263\) 112716.i 1.62957i −0.579762 0.814786i \(-0.696855\pi\)
0.579762 0.814786i \(-0.303145\pi\)
\(264\) 1850.51 1850.51i 0.0265512 0.0265512i
\(265\) −119262. + 119262.i −1.69829 + 1.69829i
\(266\) −33553.3 −0.474212
\(267\) −53803.4 + 53803.4i −0.754723 + 0.754723i
\(268\) 29891.2 0.416173
\(269\) −4250.50 −0.0587402 −0.0293701 0.999569i \(-0.509350\pi\)
−0.0293701 + 0.999569i \(0.509350\pi\)
\(270\) 65360.2i 0.896574i
\(271\) −77055.1 −1.04921 −0.524605 0.851346i \(-0.675787\pi\)
−0.524605 + 0.851346i \(0.675787\pi\)
\(272\) 22082.4 22082.4i 0.298475 0.298475i
\(273\) −58112.8 58112.8i −0.779734 0.779734i
\(274\) 67646.6 + 67646.6i 0.901042 + 0.901042i
\(275\) 13248.4 0.175185
\(276\) −49685.6 + 49685.6i −0.652248 + 0.652248i
\(277\) 41531.0 + 41531.0i 0.541269 + 0.541269i 0.923901 0.382632i \(-0.124982\pi\)
−0.382632 + 0.923901i \(0.624982\pi\)
\(278\) −32848.2 + 32848.2i −0.425033 + 0.425033i
\(279\) −28096.0 28096.0i −0.360940 0.360940i
\(280\) 66834.4i 0.852480i
\(281\) 93101.9 93101.9i 1.17909 1.17909i 0.199110 0.979977i \(-0.436195\pi\)
0.979977 0.199110i \(-0.0638051\pi\)
\(282\) −6634.55 + 6634.55i −0.0834282 + 0.0834282i
\(283\) −44952.4 44952.4i −0.561281 0.561281i 0.368390 0.929671i \(-0.379909\pi\)
−0.929671 + 0.368390i \(0.879909\pi\)
\(284\) 9560.09i 0.118529i
\(285\) −77307.4 −0.951768
\(286\) 3519.04i 0.0430222i
\(287\) 215959.i 2.62184i
\(288\) −3794.47 3794.47i −0.0457474 0.0457474i
\(289\) 154580.i 1.85080i
\(290\) −6044.14 6044.14i −0.0718685 0.0718685i
\(291\) 42247.9 + 42247.9i 0.498906 + 0.498906i
\(292\) 9696.30 0.113721
\(293\) −54120.6 −0.630416 −0.315208 0.949023i \(-0.602074\pi\)
−0.315208 + 0.949023i \(0.602074\pi\)
\(294\) −49787.2 + 49787.2i −0.576001 + 0.576001i
\(295\) 214822.i 2.46850i
\(296\) 1588.54 + 30936.2i 0.0181307 + 0.353088i
\(297\) 5939.64 0.0673360
\(298\) −42812.3 42812.3i −0.482099 0.482099i
\(299\) 94485.3i 1.05687i
\(300\) 101394.i 1.12660i
\(301\) 36063.2 36063.2i 0.398044 0.398044i
\(302\) −23379.5 + 23379.5i −0.256342 + 0.256342i
\(303\) −11737.8 −0.127850
\(304\) −7775.10 + 7775.10i −0.0841315 + 0.0841315i
\(305\) −31424.9 −0.337811
\(306\) −40913.6 −0.436943
\(307\) 2227.91i 0.0236385i −0.999930 0.0118193i \(-0.996238\pi\)
0.999930 0.0118193i \(-0.00376228\pi\)
\(308\) −6073.60 −0.0640243
\(309\) 134995. 134995.i 1.41384 1.41384i
\(310\) −114673. 114673.i −1.19327 1.19327i
\(311\) −39146.1 39146.1i −0.404732 0.404732i 0.475165 0.879897i \(-0.342389\pi\)
−0.879897 + 0.475165i \(0.842389\pi\)
\(312\) −26932.2 −0.276671
\(313\) 37424.8 37424.8i 0.382007 0.382007i −0.489818 0.871825i \(-0.662937\pi\)
0.871825 + 0.489818i \(0.162937\pi\)
\(314\) 49113.9 + 49113.9i 0.498132 + 0.498132i
\(315\) −61914.4 + 61914.4i −0.623980 + 0.623980i
\(316\) −14711.9 14711.9i −0.147331 0.147331i
\(317\) 152147.i 1.51407i 0.653376 + 0.757034i \(0.273352\pi\)
−0.653376 + 0.757034i \(0.726648\pi\)
\(318\) 82946.2 82946.2i 0.820243 0.820243i
\(319\) −549.264 + 549.264i −0.00539759 + 0.00539759i
\(320\) −15487.1 15487.1i −0.151241 0.151241i
\(321\) 120679.i 1.17118i
\(322\) 163074. 1.57280
\(323\) 83834.3i 0.803557i
\(324\) 64667.2i 0.616019i
\(325\) −96408.3 96408.3i −0.912741 0.912741i
\(326\) 38246.7i 0.359881i
\(327\) −5555.05 5555.05i −0.0519508 0.0519508i
\(328\) 50042.7 + 50042.7i 0.465150 + 0.465150i
\(329\) 21775.4 0.201175
\(330\) −13993.7 −0.128500
\(331\) −81389.5 + 81389.5i −0.742869 + 0.742869i −0.973129 0.230260i \(-0.926042\pi\)
0.230260 + 0.973129i \(0.426042\pi\)
\(332\) 12242.7i 0.111071i
\(333\) 27187.2 30130.4i 0.245175 0.271717i
\(334\) 59307.1 0.531635
\(335\) −113020. 113020.i −1.00708 1.00708i
\(336\) 46483.0i 0.411733i
\(337\) 120061.i 1.05716i −0.848883 0.528580i \(-0.822725\pi\)
0.848883 0.528580i \(-0.177275\pi\)
\(338\) 31514.0 31514.0i 0.275848 0.275848i
\(339\) 41348.6 41348.6i 0.359800 0.359800i
\(340\) −166988. −1.44454
\(341\) −10421.0 + 10421.0i −0.0896191 + 0.0896191i
\(342\) 14405.5 0.123162
\(343\) −2375.75 −0.0201936
\(344\) 16713.4i 0.141237i
\(345\) 375726. 3.15670
\(346\) −105167. + 105167.i −0.878473 + 0.878473i
\(347\) −124619. 124619.i −1.03497 1.03497i −0.999366 0.0355998i \(-0.988666\pi\)
−0.0355998 0.999366i \(-0.511334\pi\)
\(348\) 4203.67 + 4203.67i 0.0347112 + 0.0347112i
\(349\) −117331. −0.963303 −0.481652 0.876363i \(-0.659963\pi\)
−0.481652 + 0.876363i \(0.659963\pi\)
\(350\) −166393. + 166393.i −1.35831 + 1.35831i
\(351\) −43222.6 43222.6i −0.350830 0.350830i
\(352\) −1407.40 + 1407.40i −0.0113588 + 0.0113588i
\(353\) 48307.3 + 48307.3i 0.387671 + 0.387671i 0.873856 0.486185i \(-0.161612\pi\)
−0.486185 + 0.873856i \(0.661612\pi\)
\(354\) 149407.i 1.19224i
\(355\) −36147.0 + 36147.0i −0.286824 + 0.286824i
\(356\) 40920.0 40920.0i 0.322876 0.322876i
\(357\) 250599. + 250599.i 1.96627 + 1.96627i
\(358\) 26573.8i 0.207342i
\(359\) 219239. 1.70110 0.850549 0.525895i \(-0.176270\pi\)
0.850549 + 0.525895i \(0.176270\pi\)
\(360\) 28694.1i 0.221405i
\(361\) 100803.i 0.773500i
\(362\) 10113.8 + 10113.8i 0.0771783 + 0.0771783i
\(363\) 152733.i 1.15910i
\(364\) 44197.5 + 44197.5i 0.333576 + 0.333576i
\(365\) −36662.1 36662.1i −0.275189 0.275189i
\(366\) 21855.8 0.163157
\(367\) 66951.0 0.497078 0.248539 0.968622i \(-0.420050\pi\)
0.248539 + 0.968622i \(0.420050\pi\)
\(368\) 37788.2 37788.2i 0.279036 0.279036i
\(369\) 92717.6i 0.680941i
\(370\) 110964. 122977.i 0.810551 0.898298i
\(371\) −272240. −1.97790
\(372\) 79754.8 + 79754.8i 0.576330 + 0.576330i
\(373\) 133716.i 0.961094i 0.876969 + 0.480547i \(0.159562\pi\)
−0.876969 + 0.480547i \(0.840438\pi\)
\(374\) 15175.1i 0.108490i
\(375\) −184514. + 184514.i −1.31210 + 1.31210i
\(376\) 5045.88 5045.88i 0.0356912 0.0356912i
\(377\) 7993.96 0.0562444
\(378\) −74598.9 + 74598.9i −0.522094 + 0.522094i
\(379\) 156448. 1.08916 0.544580 0.838709i \(-0.316689\pi\)
0.544580 + 0.838709i \(0.316689\pi\)
\(380\) 58795.8 0.407173
\(381\) 162335.i 1.11831i
\(382\) −154784. −1.06071
\(383\) −26425.8 + 26425.8i −0.180149 + 0.180149i −0.791421 0.611272i \(-0.790658\pi\)
0.611272 + 0.791421i \(0.290658\pi\)
\(384\) 10771.2 + 10771.2i 0.0730469 + 0.0730469i
\(385\) 22964.5 + 22964.5i 0.154930 + 0.154930i
\(386\) −170366. −1.14342
\(387\) −15483.0 + 15483.0i −0.103379 + 0.103379i
\(388\) −32131.5 32131.5i −0.213436 0.213436i
\(389\) −124197. + 124197.i −0.820754 + 0.820754i −0.986216 0.165462i \(-0.947088\pi\)
0.165462 + 0.986216i \(0.447088\pi\)
\(390\) 101832. + 101832.i 0.669505 + 0.669505i
\(391\) 407448.i 2.66513i
\(392\) 37865.5 37865.5i 0.246417 0.246417i
\(393\) 146631. 146631.i 0.949384 0.949384i
\(394\) 76543.3 + 76543.3i 0.493077 + 0.493077i
\(395\) 111253.i 0.713043i
\(396\) 2607.58 0.0166283
\(397\) 216499.i 1.37365i −0.726824 0.686823i \(-0.759005\pi\)
0.726824 0.686823i \(-0.240995\pi\)
\(398\) 11423.8i 0.0721181i
\(399\) −88234.8 88234.8i −0.554235 0.554235i
\(400\) 77114.6i 0.481966i
\(401\) 161025. + 161025.i 1.00139 + 1.00139i 0.999999 + 0.00139254i \(0.000443259\pi\)
0.00139254 + 0.999999i \(0.499557\pi\)
\(402\) 78604.5 + 78604.5i 0.486402 + 0.486402i
\(403\) 151667. 0.933856
\(404\) 8927.14 0.0546952
\(405\) −244509. + 244509.i −1.49068 + 1.49068i
\(406\) 13797.0i 0.0837012i
\(407\) −11175.6 10083.9i −0.0674655 0.0608753i
\(408\) 116140. 0.697686
\(409\) 9905.97 + 9905.97i 0.0592175 + 0.0592175i 0.736095 0.676878i \(-0.236667\pi\)
−0.676878 + 0.736095i \(0.736667\pi\)
\(410\) 378426.i 2.25120i
\(411\) 355779.i 2.10619i
\(412\) −102670. + 102670.i −0.604851 + 0.604851i
\(413\) 245187. 245187.i 1.43746 1.43746i
\(414\) −70012.9 −0.408486
\(415\) −46290.2 + 46290.2i −0.268777 + 0.268777i
\(416\) 20483.2 0.118362
\(417\) −172761. −0.993515
\(418\) 5343.09i 0.0305802i
\(419\) −282949. −1.61168 −0.805842 0.592131i \(-0.798287\pi\)
−0.805842 + 0.592131i \(0.798287\pi\)
\(420\) 175754. 175754.i 0.996337 0.996337i
\(421\) 40193.9 + 40193.9i 0.226775 + 0.226775i 0.811344 0.584569i \(-0.198736\pi\)
−0.584569 + 0.811344i \(0.698736\pi\)
\(422\) 140203. + 140203.i 0.787285 + 0.787285i
\(423\) −9348.85 −0.0522489
\(424\) −63084.4 + 63084.4i −0.350906 + 0.350906i
\(425\) 415741. + 415741.i 2.30168 + 2.30168i
\(426\) 25140.1 25140.1i 0.138531 0.138531i
\(427\) −35866.8 35866.8i −0.196715 0.196715i
\(428\) 91782.1i 0.501038i
\(429\) 9253.99 9253.99i 0.0502822 0.0502822i
\(430\) −63193.9 + 63193.9i −0.341773 + 0.341773i
\(431\) −17448.6 17448.6i −0.0939305 0.0939305i 0.658580 0.752511i \(-0.271157\pi\)
−0.752511 + 0.658580i \(0.771157\pi\)
\(432\) 34572.7i 0.185253i
\(433\) 169891. 0.906138 0.453069 0.891476i \(-0.350329\pi\)
0.453069 + 0.891476i \(0.350329\pi\)
\(434\) 261765.i 1.38974i
\(435\) 31788.4i 0.167993i
\(436\) 4224.87 + 4224.87i 0.0222249 + 0.0222249i
\(437\) 143460.i 0.751224i
\(438\) 25498.3 + 25498.3i 0.132911 + 0.132911i
\(439\) 158221. + 158221.i 0.820985 + 0.820985i 0.986249 0.165265i \(-0.0528478\pi\)
−0.165265 + 0.986249i \(0.552848\pi\)
\(440\) 10642.8 0.0549733
\(441\) −70156.0 −0.360735
\(442\) 110429. 110429.i 0.565248 0.565248i
\(443\) 173144.i 0.882266i −0.897442 0.441133i \(-0.854577\pi\)
0.897442 0.441133i \(-0.145423\pi\)
\(444\) −77175.2 + 85529.9i −0.391482 + 0.433862i
\(445\) −309440. −1.56263
\(446\) −49550.1 49550.1i −0.249101 0.249101i
\(447\) 225166.i 1.12691i
\(448\) 35352.5i 0.176142i
\(449\) −246154. + 246154.i −1.22099 + 1.22099i −0.253716 + 0.967279i \(0.581653\pi\)
−0.967279 + 0.253716i \(0.918347\pi\)
\(450\) 71437.8 71437.8i 0.352779 0.352779i
\(451\) −34389.6 −0.169073
\(452\) −31447.5 + 31447.5i −0.153925 + 0.153925i
\(453\) −122961. −0.599201
\(454\) 56467.6 0.273960
\(455\) 334224.i 1.61441i
\(456\) −40892.2 −0.196658
\(457\) −146814. + 146814.i −0.702965 + 0.702965i −0.965046 0.262081i \(-0.915591\pi\)
0.262081 + 0.965046i \(0.415591\pi\)
\(458\) −28449.8 28449.8i −0.135628 0.135628i
\(459\) 186388. + 186388.i 0.884695 + 0.884695i
\(460\) −285757. −1.35046
\(461\) 55295.6 55295.6i 0.260189 0.260189i −0.564942 0.825131i \(-0.691101\pi\)
0.825131 + 0.564942i \(0.191101\pi\)
\(462\) −15971.7 15971.7i −0.0748285 0.0748285i
\(463\) 123996. 123996.i 0.578425 0.578425i −0.356044 0.934469i \(-0.615875\pi\)
0.934469 + 0.356044i \(0.115875\pi\)
\(464\) −3197.08 3197.08i −0.0148497 0.0148497i
\(465\) 603111.i 2.78928i
\(466\) −98618.9 + 98618.9i −0.454139 + 0.454139i
\(467\) −36279.1 + 36279.1i −0.166350 + 0.166350i −0.785373 0.619023i \(-0.787529\pi\)
0.619023 + 0.785373i \(0.287529\pi\)
\(468\) −18975.3 18975.3i −0.0866358 0.0866358i
\(469\) 257990.i 1.17289i
\(470\) −38157.3 −0.172735
\(471\) 258308.i 1.16439i
\(472\) 113631.i 0.510051i
\(473\) 5742.77 + 5742.77i 0.0256684 + 0.0256684i
\(474\) 77375.6i 0.344388i
\(475\) −146380. 146380.i −0.648777 0.648777i
\(476\) −190592. 190592.i −0.841185 0.841185i
\(477\) 116881. 0.513697
\(478\) 153531. 0.671954
\(479\) 2.68921 2.68921i 1.17207e−5 1.17207e-5i −0.707101 0.707113i \(-0.749997\pi\)
0.707113 + 0.707101i \(0.249997\pi\)
\(480\) 81452.6i 0.353527i
\(481\) 7943.93 + 154705.i 0.0343356 + 0.668674i
\(482\) 147051. 0.632957
\(483\) 428835. + 428835.i 1.83821 + 1.83821i
\(484\) 116161.i 0.495871i
\(485\) 242980.i 1.03297i
\(486\) 82542.7 82542.7i 0.349467 0.349467i
\(487\) −94175.6 + 94175.6i −0.397082 + 0.397082i −0.877203 0.480120i \(-0.840593\pi\)
0.480120 + 0.877203i \(0.340593\pi\)
\(488\) −16622.4 −0.0697996
\(489\) −100577. + 100577.i −0.420612 + 0.420612i
\(490\) −286341. −1.19259
\(491\) −93918.8 −0.389573 −0.194787 0.980846i \(-0.562401\pi\)
−0.194787 + 0.980846i \(0.562401\pi\)
\(492\) 263194.i 1.08729i
\(493\) −34472.3 −0.141833
\(494\) −38881.6 + 38881.6i −0.159327 + 0.159327i
\(495\) −9859.36 9859.36i −0.0402382 0.0402382i
\(496\) −60657.2 60657.2i −0.246558 0.246558i
\(497\) −82512.8 −0.334048
\(498\) 32194.6 32194.6i 0.129815 0.129815i
\(499\) 26209.4 + 26209.4i 0.105258 + 0.105258i 0.757775 0.652516i \(-0.226287\pi\)
−0.652516 + 0.757775i \(0.726287\pi\)
\(500\) 140332. 140332.i 0.561326 0.561326i
\(501\) 155959. + 155959.i 0.621350 + 0.621350i
\(502\) 309305.i 1.22738i
\(503\) 85511.3 85511.3i 0.337977 0.337977i −0.517628 0.855606i \(-0.673185\pi\)
0.855606 + 0.517628i \(0.173185\pi\)
\(504\) −32750.0 + 32750.0i −0.128929 + 0.128929i
\(505\) −33753.8 33753.8i −0.132355 0.132355i
\(506\) 25968.3i 0.101424i
\(507\) 165744. 0.644796
\(508\) 123463.i 0.478421i
\(509\) 151332.i 0.584112i −0.956401 0.292056i \(-0.905661\pi\)
0.956401 0.292056i \(-0.0943394\pi\)
\(510\) −439128. 439128.i −1.68830 1.68830i
\(511\) 83688.5i 0.320497i
\(512\) −8192.00 8192.00i −0.0312500 0.0312500i
\(513\) −65626.5 65626.5i −0.249370 0.249370i
\(514\) 216959. 0.821206
\(515\) 776396. 2.92731
\(516\) 43951.0 43951.0i 0.165071 0.165071i
\(517\) 3467.56i 0.0129731i
\(518\) 267009. 13710.6i 0.995100 0.0510972i
\(519\) −553115. −2.05343
\(520\) −77447.6 77447.6i −0.286419 0.286419i
\(521\) 196551.i 0.724102i −0.932158 0.362051i \(-0.882077\pi\)
0.932158 0.362051i \(-0.117923\pi\)
\(522\) 5923.46i 0.0217388i
\(523\) 245504. 245504.i 0.897542 0.897542i −0.0976765 0.995218i \(-0.531141\pi\)
0.995218 + 0.0976765i \(0.0311410\pi\)
\(524\) −111520. + 111520.i −0.406153 + 0.406153i
\(525\) −875126. −3.17506
\(526\) −225432. + 225432.i −0.814786 + 0.814786i
\(527\) −654031. −2.35493
\(528\) −7402.04 −0.0265512
\(529\) 417400.i 1.49156i
\(530\) 477049. 1.69829
\(531\) −105266. + 105266.i −0.373336 + 0.373336i
\(532\) 67106.6 + 67106.6i 0.237106 + 0.237106i
\(533\) 250253. + 250253.i 0.880895 + 0.880895i
\(534\) 215214. 0.754723
\(535\) 347031. 347031.i 1.21244 1.21244i
\(536\) −59782.4 59782.4i −0.208086 0.208086i
\(537\) −69880.8 + 69880.8i −0.242331 + 0.242331i
\(538\) 8501.00 + 8501.00i 0.0293701 + 0.0293701i
\(539\) 26021.4i 0.0895680i
\(540\) 130720. 130720.i 0.448287 0.448287i
\(541\) −210674. + 210674.i −0.719807 + 0.719807i −0.968566 0.248758i \(-0.919978\pi\)
0.248758 + 0.968566i \(0.419978\pi\)
\(542\) 154110. + 154110.i 0.524605 + 0.524605i
\(543\) 53192.1i 0.180404i
\(544\) −88329.5 −0.298475
\(545\) 31948.7i 0.107562i
\(546\) 232451.i 0.779734i
\(547\) −23718.7 23718.7i −0.0792713 0.0792713i 0.666359 0.745631i \(-0.267852\pi\)
−0.745631 + 0.666359i \(0.767852\pi\)
\(548\) 270587.i 0.901042i
\(549\) 15398.7 + 15398.7i 0.0510904 + 0.0510904i
\(550\) −26496.8 26496.8i −0.0875927 0.0875927i
\(551\) 12137.5 0.0399785
\(552\) 198743. 0.652248
\(553\) −126978. + 126978.i −0.415221 + 0.415221i
\(554\) 166124.i 0.541269i
\(555\) 615193. 31589.5i 1.99722 0.102555i
\(556\) 131393. 0.425033
\(557\) −105334. 105334.i −0.339513 0.339513i 0.516671 0.856184i \(-0.327171\pi\)
−0.856184 + 0.516671i \(0.827171\pi\)
\(558\) 112384.i 0.360940i
\(559\) 83580.0i 0.267472i
\(560\) −133669. + 133669.i −0.426240 + 0.426240i
\(561\) −39905.9 + 39905.9i −0.126798 + 0.126798i
\(562\) −372408. −1.17909
\(563\) −248718. + 248718.i −0.784675 + 0.784675i −0.980616 0.195940i \(-0.937224\pi\)
0.195940 + 0.980616i \(0.437224\pi\)
\(564\) 26538.2 0.0834282
\(565\) 237808. 0.744955
\(566\) 179810.i 0.561281i
\(567\) −558141. −1.73611
\(568\) −19120.2 + 19120.2i −0.0592646 + 0.0592646i
\(569\) 420587. + 420587.i 1.29907 + 1.29907i 0.929010 + 0.370055i \(0.120661\pi\)
0.370055 + 0.929010i \(0.379339\pi\)
\(570\) 154615. + 154615.i 0.475884 + 0.475884i
\(571\) −496254. −1.52206 −0.761030 0.648717i \(-0.775306\pi\)
−0.761030 + 0.648717i \(0.775306\pi\)
\(572\) −7038.09 + 7038.09i −0.0215111 + 0.0215111i
\(573\) −407033. 407033.i −1.23971 1.23971i
\(574\) 431917. 431917.i 1.31092 1.31092i
\(575\) 711431. + 711431.i 2.15178 + 2.15178i
\(576\) 15177.9i 0.0457474i
\(577\) −101034. + 101034.i −0.303469 + 0.303469i −0.842369 0.538901i \(-0.818840\pi\)
0.538901 + 0.842369i \(0.318840\pi\)
\(578\) −309161. + 309161.i −0.925398 + 0.925398i
\(579\) −448009. 448009.i −1.33638 1.33638i
\(580\) 24176.6i 0.0718685i
\(581\) −105667. −0.313030
\(582\) 168992.i 0.498906i
\(583\) 43352.0i 0.127547i
\(584\) −19392.6 19392.6i −0.0568605 0.0568605i
\(585\) 143493.i 0.419293i
\(586\) 108241. + 108241.i 0.315208 + 0.315208i
\(587\) −315193. 315193.i −0.914746 0.914746i 0.0818952 0.996641i \(-0.473903\pi\)
−0.996641 + 0.0818952i \(0.973903\pi\)
\(588\) 199149. 0.576001
\(589\) 230281. 0.663786
\(590\) −429643. + 429643.i −1.23425 + 1.23425i
\(591\) 402570.i 1.15257i
\(592\) 58695.3 65049.4i 0.167479 0.185609i
\(593\) 549407. 1.56237 0.781186 0.624298i \(-0.214615\pi\)
0.781186 + 0.624298i \(0.214615\pi\)
\(594\) −11879.3 11879.3i −0.0336680 0.0336680i
\(595\) 1.44127e6i 4.07110i
\(596\) 171249.i 0.482099i
\(597\) −30041.0 + 30041.0i −0.0842881 + 0.0842881i
\(598\) 188971. 188971.i 0.528435 0.528435i
\(599\) 172763. 0.481501 0.240750 0.970587i \(-0.422606\pi\)
0.240750 + 0.970587i \(0.422606\pi\)
\(600\) −202787. + 202787.i −0.563299 + 0.563299i
\(601\) 190910. 0.528543 0.264272 0.964448i \(-0.414868\pi\)
0.264272 + 0.964448i \(0.414868\pi\)
\(602\) −144253. −0.398044
\(603\) 110763.i 0.304621i
\(604\) 93517.8 0.256342
\(605\) 439208. 439208.i 1.19994 1.19994i
\(606\) 23475.6 + 23475.6i 0.0639251 + 0.0639251i
\(607\) 201474. + 201474.i 0.546816 + 0.546816i 0.925519 0.378702i \(-0.123630\pi\)
−0.378702 + 0.925519i \(0.623630\pi\)
\(608\) 31100.4 0.0841315
\(609\) 36281.8 36281.8i 0.0978259 0.0978259i
\(610\) 62849.7 + 62849.7i 0.168905 + 0.168905i
\(611\) 25233.3 25233.3i 0.0675915 0.0675915i
\(612\) 81827.2 + 81827.2i 0.218471 + 0.218471i
\(613\) 171480.i 0.456344i −0.973621 0.228172i \(-0.926725\pi\)
0.973621 0.228172i \(-0.0732749\pi\)
\(614\) −4455.82 + 4455.82i −0.0118193 + 0.0118193i
\(615\) 995144. 995144.i 2.63109 2.63109i
\(616\) 12147.2 + 12147.2i 0.0320122 + 0.0320122i
\(617\) 75449.0i 0.198191i −0.995078 0.0990953i \(-0.968405\pi\)
0.995078 0.0990953i \(-0.0315949\pi\)
\(618\) −539979. −1.41384
\(619\) 40455.4i 0.105583i 0.998606 + 0.0527917i \(0.0168119\pi\)
−0.998606 + 0.0527917i \(0.983188\pi\)
\(620\) 458694.i 1.19327i
\(621\) 318955. + 318955.i 0.827078 + 0.827078i
\(622\) 156584.i 0.404732i
\(623\) −353179. 353179.i −0.909953 0.909953i
\(624\) 53864.4 + 53864.4i 0.138335 + 0.138335i
\(625\) −308124. −0.788798
\(626\) −149699. −0.382007
\(627\) 14050.7 14050.7i 0.0357406 0.0357406i
\(628\) 196455.i 0.498132i
\(629\) −34256.5 667133.i −0.0865849 1.68621i
\(630\) 247658. 0.623980
\(631\) 35252.8 + 35252.8i 0.0885391 + 0.0885391i 0.749989 0.661450i \(-0.230059\pi\)
−0.661450 + 0.749989i \(0.730059\pi\)
\(632\) 58847.7i 0.147331i
\(633\) 737380.i 1.84028i
\(634\) 304294. 304294.i 0.757034 0.757034i
\(635\) 466819. 466819.i 1.15771 1.15771i
\(636\) −331785. −0.820243
\(637\) 189357. 189357.i 0.466662 0.466662i
\(638\) 2197.06 0.00539759
\(639\) 35425.3 0.0867584
\(640\) 61948.5i 0.151241i
\(641\) 30042.1 0.0731164 0.0365582 0.999332i \(-0.488361\pi\)
0.0365582 + 0.999332i \(0.488361\pi\)
\(642\) −241359. + 241359.i −0.585589 + 0.585589i
\(643\) 288466. + 288466.i 0.697706 + 0.697706i 0.963915 0.266209i \(-0.0857713\pi\)
−0.266209 + 0.963915i \(0.585771\pi\)
\(644\) −326149. 326149.i −0.786401 0.786401i
\(645\) −332361. −0.798896
\(646\) 167669. 167669.i 0.401779 0.401779i
\(647\) −398994. 398994.i −0.953142 0.953142i 0.0458081 0.998950i \(-0.485414\pi\)
−0.998950 + 0.0458081i \(0.985414\pi\)
\(648\) −129334. + 129334.i −0.308010 + 0.308010i
\(649\) 39044.0 + 39044.0i 0.0926968 + 0.0926968i
\(650\) 385633.i 0.912741i
\(651\) 688362. 688362.i 1.62426 1.62426i
\(652\) 76493.5 76493.5i 0.179941 0.179941i
\(653\) −187012. 187012.i −0.438575 0.438575i 0.452957 0.891532i \(-0.350369\pi\)
−0.891532 + 0.452957i \(0.850369\pi\)
\(654\) 22220.2i 0.0519508i
\(655\) 843321. 1.96567
\(656\) 200171.i 0.465150i
\(657\) 35930.0i 0.0832390i
\(658\) −43550.8 43550.8i −0.100588 0.100588i
\(659\) 199346.i 0.459024i −0.973306 0.229512i \(-0.926287\pi\)
0.973306 0.229512i \(-0.0737131\pi\)
\(660\) 27987.4 + 27987.4i 0.0642501 + 0.0642501i
\(661\) −43738.2 43738.2i −0.100106 0.100106i 0.655280 0.755386i \(-0.272551\pi\)
−0.755386 + 0.655280i \(0.772551\pi\)
\(662\) 325558. 0.742869
\(663\) 580789. 1.32127
\(664\) −24485.5 + 24485.5i −0.0555357 + 0.0555357i
\(665\) 507465.i 1.14753i
\(666\) −114635. + 5886.39i −0.258446 + 0.0132709i
\(667\) −58990.3 −0.132596
\(668\) −118614. 118614.i −0.265818 0.265818i
\(669\) 260603.i 0.582273i
\(670\) 452078.i 1.00708i
\(671\) 5711.50 5711.50i 0.0126854 0.0126854i
\(672\) 92966.0 92966.0i 0.205866 0.205866i
\(673\) −725075. −1.60086 −0.800429 0.599427i \(-0.795395\pi\)
−0.800429 + 0.599427i \(0.795395\pi\)
\(674\) −240121. + 240121.i −0.528580 + 0.528580i
\(675\) −650893. −1.42857
\(676\) −126056. −0.275848
\(677\) 661665.i 1.44365i −0.692078 0.721823i \(-0.743304\pi\)
0.692078 0.721823i \(-0.256696\pi\)
\(678\) −165394. −0.359800
\(679\) −277326. + 277326.i −0.601521 + 0.601521i
\(680\) 333977. + 333977.i 0.722268 + 0.722268i
\(681\) 148492. + 148492.i 0.320192 + 0.320192i
\(682\) 41684.0 0.0896191
\(683\) −529677. + 529677.i −1.13545 + 1.13545i −0.146198 + 0.989255i \(0.546704\pi\)
−0.989255 + 0.146198i \(0.953296\pi\)
\(684\) −28810.9 28810.9i −0.0615808 0.0615808i
\(685\) −1.02310e6 + 1.02310e6i −2.18040 + 2.18040i
\(686\) 4751.51 + 4751.51i 0.0100968 + 0.0100968i
\(687\) 149628.i 0.317030i
\(688\) −33426.8 + 33426.8i −0.0706184 + 0.0706184i
\(689\) −315471. + 315471.i −0.664540 + 0.664540i
\(690\) −751452. 751452.i −1.57835 1.57835i
\(691\) 580294.i 1.21532i 0.794196 + 0.607662i \(0.207892\pi\)
−0.794196 + 0.607662i \(0.792108\pi\)
\(692\) 420669. 0.878473
\(693\) 22506.0i 0.0468632i
\(694\) 498477.i 1.03497i
\(695\) −496801. 496801.i −1.02852 1.02852i
\(696\) 16814.7i 0.0347112i
\(697\) −1.07916e6 1.07916e6i −2.22137 2.22137i
\(698\) 234663. + 234663.i 0.481652 + 0.481652i
\(699\) −518675. −1.06155
\(700\) 665574. 1.35831
\(701\) −235973. + 235973.i −0.480205 + 0.480205i −0.905197 0.424992i \(-0.860277\pi\)
0.424992 + 0.905197i \(0.360277\pi\)
\(702\) 172890.i 0.350830i
\(703\) 12061.6 + 234894.i 0.0244058 + 0.475294i
\(704\) 5629.59 0.0113588
\(705\) −100342. 100342.i −0.201885 0.201885i
\(706\) 193229.i 0.387671i
\(707\) 77049.8i 0.154146i
\(708\) 298815. 298815.i 0.596122 0.596122i
\(709\) 263351. 263351.i 0.523892 0.523892i −0.394852 0.918745i \(-0.629204\pi\)
0.918745 + 0.394852i \(0.129204\pi\)
\(710\) 144588. 0.286824
\(711\) 54515.6 54515.6i 0.107840 0.107840i
\(712\) −163680. −0.322876
\(713\) −1.11920e6 −2.20156
\(714\) 1.00240e6i 1.96627i
\(715\) 53222.5 0.104108
\(716\) 53147.6 53147.6i 0.103671 0.103671i
\(717\) 403738. + 403738.i 0.785347 + 0.785347i
\(718\) −438479. 438479.i −0.850549 0.850549i
\(719\) 64557.5 0.124879 0.0624394 0.998049i \(-0.480112\pi\)
0.0624394 + 0.998049i \(0.480112\pi\)
\(720\) 57388.1 57388.1i 0.110702 0.110702i
\(721\) 886140. + 886140.i 1.70464 + 1.70464i
\(722\) 201607. 201607.i 0.386750 0.386750i
\(723\) 386699. + 386699.i 0.739769 + 0.739769i
\(724\) 40455.0i 0.0771783i
\(725\) 60190.9 60190.9i 0.114513 0.114513i
\(726\) −305467. + 305467.i −0.579550 + 0.579550i
\(727\) 164676. + 164676.i 0.311575 + 0.311575i 0.845520 0.533944i \(-0.179291\pi\)
−0.533944 + 0.845520i \(0.679291\pi\)
\(728\) 176790.i 0.333576i
\(729\) −220632. −0.415159
\(730\) 146648.i 0.275189i
\(731\) 360421.i 0.674491i
\(732\) −43711.7 43711.7i −0.0815784 0.0815784i
\(733\) 274893.i 0.511630i −0.966726 0.255815i \(-0.917656\pi\)
0.966726 0.255815i \(-0.0823437\pi\)
\(734\) −133902. 133902.i −0.248539 0.248539i
\(735\) −752989. 752989.i −1.39384 1.39384i
\(736\) −151153. −0.279036
\(737\) 41082.8 0.0756354
\(738\) −185435. + 185435.i −0.340471 + 0.340471i
\(739\) 308699.i 0.565257i 0.959229 + 0.282629i \(0.0912064\pi\)
−0.959229 + 0.282629i \(0.908794\pi\)
\(740\) −467883. + 24025.3i −0.854425 + 0.0438737i
\(741\) −204493. −0.372427
\(742\) 544480. + 544480.i 0.988949 + 0.988949i
\(743\) 61344.7i 0.111122i 0.998455 + 0.0555609i \(0.0176947\pi\)
−0.998455 + 0.0555609i \(0.982305\pi\)
\(744\) 319019.i 0.576330i
\(745\) 647499. 647499.i 1.16661 1.16661i
\(746\) 267432. 267432.i 0.480547 0.480547i
\(747\) 45365.9 0.0812997
\(748\) 30350.3 30350.3i 0.0542450 0.0542450i
\(749\) 792169. 1.41206
\(750\) 738057. 1.31210
\(751\) 685483.i 1.21539i 0.794169 + 0.607697i \(0.207906\pi\)
−0.794169 + 0.607697i \(0.792094\pi\)
\(752\) −20183.5 −0.0356912
\(753\) 813376. 813376.i 1.43450 1.43450i
\(754\) −15987.9 15987.9i −0.0281222 0.0281222i
\(755\) −353594. 353594.i −0.620313 0.620313i
\(756\) 298396. 0.522094
\(757\) −68334.1 + 68334.1i −0.119246 + 0.119246i −0.764212 0.644965i \(-0.776872\pi\)
0.644965 + 0.764212i \(0.276872\pi\)
\(758\) −312896. 312896.i −0.544580 0.544580i
\(759\) −68288.6 + 68288.6i −0.118540 + 0.118540i
\(760\) −117592. 117592.i −0.203587 0.203587i
\(761\) 1.05937e6i 1.82928i −0.404273 0.914639i \(-0.632475\pi\)
0.404273 0.914639i \(-0.367525\pi\)
\(762\) −324670. + 324670.i −0.559155 + 0.559155i
\(763\) 36464.7 36464.7i 0.0626359 0.0626359i
\(764\) 309567. + 309567.i 0.530357 + 0.530357i
\(765\) 618782.i 1.05734i
\(766\) 105703. 0.180149
\(767\) 568244.i 0.965927i
\(768\) 43084.8i 0.0730469i
\(769\) −240561. 240561.i −0.406793 0.406793i 0.473826 0.880619i \(-0.342873\pi\)
−0.880619 + 0.473826i \(0.842873\pi\)
\(770\) 91858.0i 0.154930i
\(771\) 570536. + 570536.i 0.959786 + 0.959786i
\(772\) 340731. + 340731.i 0.571712 + 0.571712i
\(773\) −374643. −0.626987 −0.313493 0.949590i \(-0.601499\pi\)
−0.313493 + 0.949590i \(0.601499\pi\)
\(774\) 61932.1 0.103379
\(775\) 1.14198e6 1.14198e6i