Properties

Label 74.5.d.a.31.3
Level $74$
Weight $5$
Character 74.31
Analytic conductor $7.649$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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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 31.3
Root \(-4.34447i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.5.d.a.43.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 2.00000i) q^{2} -5.34447i q^{3} +8.00000i q^{4} +(10.1818 - 10.1818i) q^{5} +(-10.6889 + 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 - 16.0000i) q^{8} +52.4367 q^{9} +O(q^{10})\) \(q+(-2.00000 - 2.00000i) q^{2} -5.34447i q^{3} +8.00000i q^{4} +(10.1818 - 10.1818i) q^{5} +(-10.6889 + 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 - 16.0000i) q^{8} +52.4367 q^{9} -40.7273 q^{10} -104.701i q^{11} +42.7557 q^{12} +(-156.979 + 156.979i) q^{13} +(188.193 + 188.193i) q^{14} +(-54.4165 - 54.4165i) q^{15} -64.0000 q^{16} +(-288.653 + 288.653i) q^{17} +(-104.873 - 104.873i) q^{18} +(-257.997 + 257.997i) q^{19} +(81.4547 + 81.4547i) q^{20} +502.895i q^{21} +(-209.402 + 209.402i) q^{22} +(226.710 - 226.710i) q^{23} +(-85.5115 - 85.5115i) q^{24} +417.660i q^{25} +627.917 q^{26} -713.148i q^{27} -752.771i q^{28} +(-59.2294 - 59.2294i) q^{29} +217.666i q^{30} +(-608.888 - 608.888i) q^{31} +(128.000 + 128.000i) q^{32} -559.571 q^{33} +1154.61 q^{34} +(-958.074 + 958.074i) q^{35} +419.493i q^{36} +(-913.654 - 1019.51i) q^{37} +1031.99 q^{38} +(838.970 + 838.970i) q^{39} -325.819i q^{40} -1818.47i q^{41} +(1005.79 - 1005.79i) q^{42} +(1889.70 - 1889.70i) q^{43} +837.608 q^{44} +(533.902 - 533.902i) q^{45} -906.840 q^{46} -2515.46 q^{47} +342.046i q^{48} +6453.12 q^{49} +(835.321 - 835.321i) q^{50} +(1542.70 + 1542.70i) q^{51} +(-1255.83 - 1255.83i) q^{52} -185.050 q^{53} +(-1426.30 + 1426.30i) q^{54} +(-1066.05 - 1066.05i) q^{55} +(-1505.54 + 1505.54i) q^{56} +(1378.85 + 1378.85i) q^{57} +236.918i q^{58} +(-1987.36 + 1987.36i) q^{59} +(435.332 - 435.332i) q^{60} +(-4805.67 - 4805.67i) q^{61} +2435.55i q^{62} -4934.10 q^{63} -512.000i q^{64} +3196.67i q^{65} +(1119.14 + 1119.14i) q^{66} -2627.87i q^{67} +(-2309.23 - 2309.23i) q^{68} +(-1211.64 - 1211.64i) q^{69} +3832.29 q^{70} +5726.26 q^{71} +(838.987 - 838.987i) q^{72} +7873.75i q^{73} +(-211.711 + 3866.32i) q^{74} +2232.17 q^{75} +(-2063.97 - 2063.97i) q^{76} +9851.98i q^{77} -3355.88i q^{78} +(3214.81 - 3214.81i) q^{79} +(-651.637 + 651.637i) q^{80} +435.978 q^{81} +(-3636.95 + 3636.95i) q^{82} -9870.10 q^{83} -4023.16 q^{84} +5878.04i q^{85} -7558.78 q^{86} +(-316.550 + 316.550i) q^{87} +(-1675.22 - 1675.22i) q^{88} +(3659.89 + 3659.89i) q^{89} -2135.61 q^{90} +(14771.2 - 14771.2i) q^{91} +(1813.68 + 1813.68i) q^{92} +(-3254.18 + 3254.18i) q^{93} +(5030.93 + 5030.93i) q^{94} +5253.76i q^{95} +(684.092 - 684.092i) q^{96} +(945.694 - 945.694i) q^{97} +(-12906.2 - 12906.2i) q^{98} -5490.17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 28q^{2} - 12q^{5} - 40q^{6} + 48q^{7} + 224q^{8} - 346q^{9} + O(q^{10}) \) \( 14q - 28q^{2} - 12q^{5} - 40q^{6} + 48q^{7} + 224q^{8} - 346q^{9} + 48q^{10} + 160q^{12} - 56q^{13} - 96q^{14} - 378q^{15} - 896q^{16} - 348q^{17} + 692q^{18} - 184q^{19} - 96q^{20} - 320q^{22} - 502q^{23} - 320q^{24} + 224q^{26} - 474q^{29} - 630q^{31} + 1792q^{32} + 632q^{33} + 1392q^{34} + 1826q^{35} - 2544q^{37} + 736q^{38} - 798q^{39} - 224q^{42} + 1936q^{43} + 1280q^{44} + 6162q^{45} + 2008q^{46} + 5716q^{47} + 7862q^{49} - 1372q^{50} - 2422q^{51} - 448q^{52} - 20228q^{53} - 656q^{54} + 14006q^{55} + 768q^{56} - 2270q^{57} - 4502q^{59} + 3024q^{60} - 11906q^{61} - 2588q^{63} - 1264q^{66} - 2784q^{68} + 21440q^{69} - 7304q^{70} - 11224q^{71} - 5536q^{72} + 4924q^{74} - 18652q^{75} - 1472q^{76} + 20488q^{79} + 768q^{80} - 1706q^{81} + 9808q^{82} - 20224q^{83} + 896q^{84} - 7744q^{86} + 19636q^{87} - 2560q^{88} + 13864q^{89} - 24648q^{90} - 6070q^{91} - 4016q^{92} - 13800q^{93} - 11432q^{94} + 2560q^{96} + 16622q^{97} - 15724q^{98} + O(q^{100}) \)

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
\(3\) 5.34447i 0.593830i −0.954904 0.296915i \(-0.904042\pi\)
0.954904 0.296915i \(-0.0959577\pi\)
\(4\) 8.00000i 0.500000i
\(5\) 10.1818 10.1818i 0.407273 0.407273i −0.473513 0.880787i \(-0.657014\pi\)
0.880787 + 0.473513i \(0.157014\pi\)
\(6\) −10.6889 + 10.6889i −0.296915 + 0.296915i
\(7\) −94.0964 −1.92033 −0.960167 0.279427i \(-0.909855\pi\)
−0.960167 + 0.279427i \(0.909855\pi\)
\(8\) 16.0000 16.0000i 0.250000 0.250000i
\(9\) 52.4367 0.647366
\(10\) −40.7273 −0.407273
\(11\) 104.701i 0.865297i −0.901563 0.432649i \(-0.857579\pi\)
0.901563 0.432649i \(-0.142421\pi\)
\(12\) 42.7557 0.296915
\(13\) −156.979 + 156.979i −0.928871 + 0.928871i −0.997633 0.0687618i \(-0.978095\pi\)
0.0687618 + 0.997633i \(0.478095\pi\)
\(14\) 188.193 + 188.193i 0.960167 + 0.960167i
\(15\) −54.4165 54.4165i −0.241851 0.241851i
\(16\) −64.0000 −0.250000
\(17\) −288.653 + 288.653i −0.998801 + 0.998801i −0.999999 0.00119826i \(-0.999619\pi\)
0.00119826 + 0.999999i \(0.499619\pi\)
\(18\) −104.873 104.873i −0.323683 0.323683i
\(19\) −257.997 + 257.997i −0.714672 + 0.714672i −0.967509 0.252837i \(-0.918636\pi\)
0.252837 + 0.967509i \(0.418636\pi\)
\(20\) 81.4547 + 81.4547i 0.203637 + 0.203637i
\(21\) 502.895i 1.14035i
\(22\) −209.402 + 209.402i −0.432649 + 0.432649i
\(23\) 226.710 226.710i 0.428563 0.428563i −0.459575 0.888139i \(-0.651998\pi\)
0.888139 + 0.459575i \(0.151998\pi\)
\(24\) −85.5115 85.5115i −0.148457 0.148457i
\(25\) 417.660i 0.668257i
\(26\) 627.917 0.928871
\(27\) 713.148i 0.978255i
\(28\) 752.771i 0.960167i
\(29\) −59.2294 59.2294i −0.0704274 0.0704274i 0.671016 0.741443i \(-0.265858\pi\)
−0.741443 + 0.671016i \(0.765858\pi\)
\(30\) 217.666i 0.241851i
\(31\) −608.888 608.888i −0.633598 0.633598i 0.315371 0.948969i \(-0.397871\pi\)
−0.948969 + 0.315371i \(0.897871\pi\)
\(32\) 128.000 + 128.000i 0.125000 + 0.125000i
\(33\) −559.571 −0.513839
\(34\) 1154.61 0.998801
\(35\) −958.074 + 958.074i −0.782101 + 0.782101i
\(36\) 419.493i 0.323683i
\(37\) −913.654 1019.51i −0.667388 0.744711i
\(38\) 1031.99 0.714672
\(39\) 838.970 + 838.970i 0.551591 + 0.551591i
\(40\) 325.819i 0.203637i
\(41\) 1818.47i 1.08178i −0.841093 0.540891i \(-0.818087\pi\)
0.841093 0.540891i \(-0.181913\pi\)
\(42\) 1005.79 1005.79i 0.570175 0.570175i
\(43\) 1889.70 1889.70i 1.02201 1.02201i 0.0222575 0.999752i \(-0.492915\pi\)
0.999752 0.0222575i \(-0.00708538\pi\)
\(44\) 837.608 0.432649
\(45\) 533.902 533.902i 0.263655 0.263655i
\(46\) −906.840 −0.428563
\(47\) −2515.46 −1.13873 −0.569367 0.822084i \(-0.692812\pi\)
−0.569367 + 0.822084i \(0.692812\pi\)
\(48\) 342.046i 0.148457i
\(49\) 6453.12 2.68768
\(50\) 835.321 835.321i 0.334128 0.334128i
\(51\) 1542.70 + 1542.70i 0.593118 + 0.593118i
\(52\) −1255.83 1255.83i −0.464436 0.464436i
\(53\) −185.050 −0.0658777 −0.0329388 0.999457i \(-0.510487\pi\)
−0.0329388 + 0.999457i \(0.510487\pi\)
\(54\) −1426.30 + 1426.30i −0.489127 + 0.489127i
\(55\) −1066.05 1066.05i −0.352413 0.352413i
\(56\) −1505.54 + 1505.54i −0.480083 + 0.480083i
\(57\) 1378.85 + 1378.85i 0.424393 + 0.424393i
\(58\) 236.918i 0.0704274i
\(59\) −1987.36 + 1987.36i −0.570916 + 0.570916i −0.932384 0.361468i \(-0.882276\pi\)
0.361468 + 0.932384i \(0.382276\pi\)
\(60\) 435.332 435.332i 0.120925 0.120925i
\(61\) −4805.67 4805.67i −1.29150 1.29150i −0.933859 0.357642i \(-0.883581\pi\)
−0.357642 0.933859i \(-0.616419\pi\)
\(62\) 2435.55i 0.633598i
\(63\) −4934.10 −1.24316
\(64\) 512.000i 0.125000i
\(65\) 3196.67i 0.756609i
\(66\) 1119.14 + 1119.14i 0.256920 + 0.256920i
\(67\) 2627.87i 0.585402i −0.956204 0.292701i \(-0.905446\pi\)
0.956204 0.292701i \(-0.0945540\pi\)
\(68\) −2309.23 2309.23i −0.499401 0.499401i
\(69\) −1211.64 1211.64i −0.254494 0.254494i
\(70\) 3832.29 0.782101
\(71\) 5726.26 1.13594 0.567968 0.823050i \(-0.307730\pi\)
0.567968 + 0.823050i \(0.307730\pi\)
\(72\) 838.987 838.987i 0.161842 0.161842i
\(73\) 7873.75i 1.47753i 0.673964 + 0.738764i \(0.264590\pi\)
−0.673964 + 0.738764i \(0.735410\pi\)
\(74\) −211.711 + 3866.32i −0.0386615 + 0.706049i
\(75\) 2232.17 0.396831
\(76\) −2063.97 2063.97i −0.357336 0.357336i
\(77\) 9851.98i 1.66166i
\(78\) 3355.88i 0.551591i
\(79\) 3214.81 3214.81i 0.515112 0.515112i −0.400977 0.916088i \(-0.631329\pi\)
0.916088 + 0.400977i \(0.131329\pi\)
\(80\) −651.637 + 651.637i −0.101818 + 0.101818i
\(81\) 435.978 0.0664499
\(82\) −3636.95 + 3636.95i −0.540891 + 0.540891i
\(83\) −9870.10 −1.43273 −0.716367 0.697724i \(-0.754196\pi\)
−0.716367 + 0.697724i \(0.754196\pi\)
\(84\) −4023.16 −0.570175
\(85\) 5878.04i 0.813570i
\(86\) −7558.78 −1.02201
\(87\) −316.550 + 316.550i −0.0418218 + 0.0418218i
\(88\) −1675.22 1675.22i −0.216324 0.216324i
\(89\) 3659.89 + 3659.89i 0.462049 + 0.462049i 0.899327 0.437278i \(-0.144057\pi\)
−0.437278 + 0.899327i \(0.644057\pi\)
\(90\) −2135.61 −0.263655
\(91\) 14771.2 14771.2i 1.78374 1.78374i
\(92\) 1813.68 + 1813.68i 0.214282 + 0.214282i
\(93\) −3254.18 + 3254.18i −0.376249 + 0.376249i
\(94\) 5030.93 + 5030.93i 0.569367 + 0.569367i
\(95\) 5253.76i 0.582134i
\(96\) 684.092 684.092i 0.0742287 0.0742287i
\(97\) 945.694 945.694i 0.100510 0.100510i −0.655064 0.755573i \(-0.727358\pi\)
0.755573 + 0.655064i \(0.227358\pi\)
\(98\) −12906.2 12906.2i −1.34384 1.34384i
\(99\) 5490.17i 0.560164i
\(100\) −3341.28 −0.334128
\(101\) 18425.6i 1.80625i −0.429378 0.903125i \(-0.641267\pi\)
0.429378 0.903125i \(-0.358733\pi\)
\(102\) 6170.79i 0.593118i
\(103\) −663.465 663.465i −0.0625379 0.0625379i 0.675146 0.737684i \(-0.264081\pi\)
−0.737684 + 0.675146i \(0.764081\pi\)
\(104\) 5023.34i 0.464436i
\(105\) 5120.39 + 5120.39i 0.464435 + 0.464435i
\(106\) 370.101 + 370.101i 0.0329388 + 0.0329388i
\(107\) −1562.94 −0.136513 −0.0682565 0.997668i \(-0.521744\pi\)
−0.0682565 + 0.997668i \(0.521744\pi\)
\(108\) 5705.18 0.489127
\(109\) −10571.0 + 10571.0i −0.889738 + 0.889738i −0.994498 0.104759i \(-0.966593\pi\)
0.104759 + 0.994498i \(0.466593\pi\)
\(110\) 4264.19i 0.352413i
\(111\) −5448.73 + 4882.99i −0.442231 + 0.396314i
\(112\) 6022.17 0.480083
\(113\) 4684.76 + 4684.76i 0.366886 + 0.366886i 0.866340 0.499455i \(-0.166466\pi\)
−0.499455 + 0.866340i \(0.666466\pi\)
\(114\) 5515.42i 0.424393i
\(115\) 4616.65i 0.349085i
\(116\) 473.835 473.835i 0.0352137 0.0352137i
\(117\) −8231.47 + 8231.47i −0.601320 + 0.601320i
\(118\) 7949.43 0.570916
\(119\) 27161.2 27161.2i 1.91803 1.91803i
\(120\) −1741.33 −0.120925
\(121\) 3678.71 0.251261
\(122\) 19222.7i 1.29150i
\(123\) −9718.77 −0.642394
\(124\) 4871.10 4871.10i 0.316799 0.316799i
\(125\) 10616.2 + 10616.2i 0.679437 + 0.679437i
\(126\) 9868.20 + 9868.20i 0.621580 + 0.621580i
\(127\) 860.617 0.0533584 0.0266792 0.999644i \(-0.491507\pi\)
0.0266792 + 0.999644i \(0.491507\pi\)
\(128\) −1024.00 + 1024.00i −0.0625000 + 0.0625000i
\(129\) −10099.4 10099.4i −0.606900 0.606900i
\(130\) 6393.35 6393.35i 0.378305 0.378305i
\(131\) 9264.84 + 9264.84i 0.539878 + 0.539878i 0.923493 0.383615i \(-0.125321\pi\)
−0.383615 + 0.923493i \(0.625321\pi\)
\(132\) 4476.57i 0.256920i
\(133\) 24276.5 24276.5i 1.37241 1.37241i
\(134\) −5255.74 + 5255.74i −0.292701 + 0.292701i
\(135\) −7261.15 7261.15i −0.398417 0.398417i
\(136\) 9236.91i 0.499401i
\(137\) −12740.7 −0.678817 −0.339409 0.940639i \(-0.610227\pi\)
−0.339409 + 0.940639i \(0.610227\pi\)
\(138\) 4846.58i 0.254494i
\(139\) 2561.90i 0.132597i 0.997800 + 0.0662984i \(0.0211189\pi\)
−0.997800 + 0.0662984i \(0.978881\pi\)
\(140\) −7664.59 7664.59i −0.391050 0.391050i
\(141\) 13443.8i 0.676214i
\(142\) −11452.5 11452.5i −0.567968 0.567968i
\(143\) 16435.9 + 16435.9i 0.803750 + 0.803750i
\(144\) −3355.95 −0.161842
\(145\) −1206.13 −0.0573664
\(146\) 15747.5 15747.5i 0.738764 0.738764i
\(147\) 34488.5i 1.59602i
\(148\) 8156.07 7309.23i 0.372355 0.333694i
\(149\) −16513.4 −0.743814 −0.371907 0.928270i \(-0.621296\pi\)
−0.371907 + 0.928270i \(0.621296\pi\)
\(150\) −4464.34 4464.34i −0.198415 0.198415i
\(151\) 3594.24i 0.157635i 0.996889 + 0.0788176i \(0.0251145\pi\)
−0.996889 + 0.0788176i \(0.974886\pi\)
\(152\) 8255.89i 0.357336i
\(153\) −15136.0 + 15136.0i −0.646590 + 0.646590i
\(154\) 19704.0 19704.0i 0.830830 0.830830i
\(155\) −12399.2 −0.516095
\(156\) −6711.76 + 6711.76i −0.275796 + 0.275796i
\(157\) 1308.30 0.0530772 0.0265386 0.999648i \(-0.491552\pi\)
0.0265386 + 0.999648i \(0.491552\pi\)
\(158\) −12859.3 −0.515112
\(159\) 988.995i 0.0391201i
\(160\) 2606.55 0.101818
\(161\) −21332.6 + 21332.6i −0.822985 + 0.822985i
\(162\) −871.955 871.955i −0.0332249 0.0332249i
\(163\) −19856.3 19856.3i −0.747347 0.747347i 0.226633 0.973980i \(-0.427228\pi\)
−0.973980 + 0.226633i \(0.927228\pi\)
\(164\) 14547.8 0.540891
\(165\) −5697.46 + 5697.46i −0.209273 + 0.209273i
\(166\) 19740.2 + 19740.2i 0.716367 + 0.716367i
\(167\) −16420.6 + 16420.6i −0.588786 + 0.588786i −0.937303 0.348517i \(-0.886685\pi\)
0.348517 + 0.937303i \(0.386685\pi\)
\(168\) 8046.32 + 8046.32i 0.285088 + 0.285088i
\(169\) 20724.0i 0.725604i
\(170\) 11756.1 11756.1i 0.406785 0.406785i
\(171\) −13528.5 + 13528.5i −0.462655 + 0.462655i
\(172\) 15117.6 + 15117.6i 0.511005 + 0.511005i
\(173\) 1380.88i 0.0461384i −0.999734 0.0230692i \(-0.992656\pi\)
0.999734 0.0230692i \(-0.00734381\pi\)
\(174\) 1266.20 0.0418218
\(175\) 39300.3i 1.28328i
\(176\) 6700.86i 0.216324i
\(177\) 10621.4 + 10621.4i 0.339027 + 0.339027i
\(178\) 14639.6i 0.462049i
\(179\) −11082.5 11082.5i −0.345886 0.345886i 0.512688 0.858575i \(-0.328650\pi\)
−0.858575 + 0.512688i \(0.828650\pi\)
\(180\) 4271.21 + 4271.21i 0.131828 + 0.131828i
\(181\) 17811.1 0.543667 0.271833 0.962344i \(-0.412370\pi\)
0.271833 + 0.962344i \(0.412370\pi\)
\(182\) −59084.7 −1.78374
\(183\) −25683.8 + 25683.8i −0.766931 + 0.766931i
\(184\) 7254.72i 0.214282i
\(185\) −19683.1 1077.80i −0.575110 0.0314916i
\(186\) 13016.7 0.376249
\(187\) 30222.3 + 30222.3i 0.864260 + 0.864260i
\(188\) 20123.7i 0.569367i
\(189\) 67104.6i 1.87858i
\(190\) 10507.5 10507.5i 0.291067 0.291067i
\(191\) −14170.9 + 14170.9i −0.388446 + 0.388446i −0.874133 0.485687i \(-0.838569\pi\)
0.485687 + 0.874133i \(0.338569\pi\)
\(192\) −2736.37 −0.0742287
\(193\) −31829.7 + 31829.7i −0.854511 + 0.854511i −0.990685 0.136174i \(-0.956519\pi\)
0.136174 + 0.990685i \(0.456519\pi\)
\(194\) −3782.78 −0.100510
\(195\) 17084.5 0.449297
\(196\) 51625.0i 1.34384i
\(197\) 38635.1 0.995520 0.497760 0.867315i \(-0.334156\pi\)
0.497760 + 0.867315i \(0.334156\pi\)
\(198\) −10980.3 + 10980.3i −0.280082 + 0.280082i
\(199\) −42102.2 42102.2i −1.06316 1.06316i −0.997866 0.0652938i \(-0.979202\pi\)
−0.0652938 0.997866i \(-0.520798\pi\)
\(200\) 6682.57 + 6682.57i 0.167064 + 0.167064i
\(201\) −14044.6 −0.347629
\(202\) −36851.1 + 36851.1i −0.903125 + 0.903125i
\(203\) 5573.27 + 5573.27i 0.135244 + 0.135244i
\(204\) −12341.6 + 12341.6i −0.296559 + 0.296559i
\(205\) −18515.4 18515.4i −0.440581 0.440581i
\(206\) 2653.86i 0.0625379i
\(207\) 11887.9 11887.9i 0.277438 0.277438i
\(208\) 10046.7 10046.7i 0.232218 0.232218i
\(209\) 27012.5 + 27012.5i 0.618404 + 0.618404i
\(210\) 20481.6i 0.464435i
\(211\) 3844.31 0.0863483 0.0431742 0.999068i \(-0.486253\pi\)
0.0431742 + 0.999068i \(0.486253\pi\)
\(212\) 1480.40i 0.0329388i
\(213\) 30603.8i 0.674553i
\(214\) 3125.87 + 3125.87i 0.0682565 + 0.0682565i
\(215\) 38481.1i 0.832475i
\(216\) −11410.4 11410.4i −0.244564 0.244564i
\(217\) 57294.1 + 57294.1i 1.21672 + 1.21672i
\(218\) 42283.9 0.889738
\(219\) 42081.0 0.877400
\(220\) 8528.38 8528.38i 0.176206 0.176206i
\(221\) 90625.2i 1.85552i
\(222\) 20663.4 + 1131.48i 0.419273 + 0.0229584i
\(223\) −61406.0 −1.23481 −0.617406 0.786644i \(-0.711817\pi\)
−0.617406 + 0.786644i \(0.711817\pi\)
\(224\) −12044.3 12044.3i −0.240042 0.240042i
\(225\) 21900.7i 0.432607i
\(226\) 18739.0i 0.366886i
\(227\) 27233.3 27233.3i 0.528504 0.528504i −0.391622 0.920126i \(-0.628086\pi\)
0.920126 + 0.391622i \(0.128086\pi\)
\(228\) −11030.8 + 11030.8i −0.212197 + 0.212197i
\(229\) 65938.4 1.25738 0.628691 0.777655i \(-0.283591\pi\)
0.628691 + 0.777655i \(0.283591\pi\)
\(230\) −9233.30 + 9233.30i −0.174542 + 0.174542i
\(231\) 52653.6 0.986742
\(232\) −1895.34 −0.0352137
\(233\) 56189.5i 1.03501i −0.855681 0.517504i \(-0.826861\pi\)
0.855681 0.517504i \(-0.173139\pi\)
\(234\) 32925.9 0.601320
\(235\) −25612.0 + 25612.0i −0.463776 + 0.463776i
\(236\) −15898.9 15898.9i −0.285458 0.285458i
\(237\) −17181.5 17181.5i −0.305889 0.305889i
\(238\) −108645. −1.91803
\(239\) −79431.0 + 79431.0i −1.39057 + 1.39057i −0.566538 + 0.824036i \(0.691718\pi\)
−0.824036 + 0.566538i \(0.808282\pi\)
\(240\) 3482.65 + 3482.65i 0.0604627 + 0.0604627i
\(241\) 21019.1 21019.1i 0.361893 0.361893i −0.502617 0.864509i \(-0.667629\pi\)
0.864509 + 0.502617i \(0.167629\pi\)
\(242\) −7357.42 7357.42i −0.125630 0.125630i
\(243\) 60095.0i 1.01771i
\(244\) 38445.4 38445.4i 0.645750 0.645750i
\(245\) 65704.6 65704.6i 1.09462 1.09462i
\(246\) 19437.5 + 19437.5i 0.321197 + 0.321197i
\(247\) 81000.2i 1.32768i
\(248\) −19484.4 −0.316799
\(249\) 52750.4i 0.850800i
\(250\) 42464.8i 0.679437i
\(251\) 57975.7 + 57975.7i 0.920235 + 0.920235i 0.997046 0.0768107i \(-0.0244737\pi\)
−0.0768107 + 0.997046i \(0.524474\pi\)
\(252\) 39472.8i 0.621580i
\(253\) −23736.8 23736.8i −0.370835 0.370835i
\(254\) −1721.23 1721.23i −0.0266792 0.0266792i
\(255\) 31415.0 0.483122
\(256\) 4096.00 0.0625000
\(257\) −47329.8 + 47329.8i −0.716586 + 0.716586i −0.967904 0.251318i \(-0.919136\pi\)
0.251318 + 0.967904i \(0.419136\pi\)
\(258\) 40397.7i 0.606900i
\(259\) 85971.5 + 95932.1i 1.28161 + 1.43009i
\(260\) −25573.4 −0.378305
\(261\) −3105.79 3105.79i −0.0455923 0.0455923i
\(262\) 37059.4i 0.539878i
\(263\) 75854.7i 1.09666i −0.836263 0.548329i \(-0.815264\pi\)
0.836263 0.548329i \(-0.184736\pi\)
\(264\) −8953.13 + 8953.13i −0.128460 + 0.128460i
\(265\) −1884.15 + 1884.15i −0.0268302 + 0.0268302i
\(266\) −97106.2 −1.37241
\(267\) 19560.2 19560.2i 0.274378 0.274378i
\(268\) 21023.0 0.292701
\(269\) 92814.4 1.28266 0.641329 0.767266i \(-0.278384\pi\)
0.641329 + 0.767266i \(0.278384\pi\)
\(270\) 29044.6i 0.398417i
\(271\) 3154.18 0.0429485 0.0214743 0.999769i \(-0.493164\pi\)
0.0214743 + 0.999769i \(0.493164\pi\)
\(272\) 18473.8 18473.8i 0.249700 0.249700i
\(273\) −78944.0 78944.0i −1.05924 1.05924i
\(274\) 25481.4 + 25481.4i 0.339409 + 0.339409i
\(275\) 43729.5 0.578241
\(276\) 9693.15 9693.15i 0.127247 0.127247i
\(277\) 64846.9 + 64846.9i 0.845142 + 0.845142i 0.989522 0.144380i \(-0.0461188\pi\)
−0.144380 + 0.989522i \(0.546119\pi\)
\(278\) 5123.81 5123.81i 0.0662984 0.0662984i
\(279\) −31928.1 31928.1i −0.410170 0.410170i
\(280\) 30658.4i 0.391050i
\(281\) 65861.6 65861.6i 0.834103 0.834103i −0.153972 0.988075i \(-0.549207\pi\)
0.988075 + 0.153972i \(0.0492066\pi\)
\(282\) 26887.6 26887.6i 0.338107 0.338107i
\(283\) 19240.4 + 19240.4i 0.240238 + 0.240238i 0.816948 0.576711i \(-0.195664\pi\)
−0.576711 + 0.816948i \(0.695664\pi\)
\(284\) 45810.0i 0.567968i
\(285\) 28078.5 0.345688
\(286\) 65743.5i 0.803750i
\(287\) 171112.i 2.07738i
\(288\) 6711.90 + 6711.90i 0.0809208 + 0.0809208i
\(289\) 83120.7i 0.995207i
\(290\) 2412.26 + 2412.26i 0.0286832 + 0.0286832i
\(291\) −5054.23 5054.23i −0.0596855 0.0596855i
\(292\) −62990.0 −0.738764
\(293\) −79617.5 −0.927413 −0.463706 0.885989i \(-0.653481\pi\)
−0.463706 + 0.885989i \(0.653481\pi\)
\(294\) −68977.0 + 68977.0i −0.798012 + 0.798012i
\(295\) 40469.9i 0.465038i
\(296\) −30930.6 1693.69i −0.353025 0.0193308i
\(297\) −74667.3 −0.846481
\(298\) 33026.8 + 33026.8i 0.371907 + 0.371907i
\(299\) 71177.5i 0.796160i
\(300\) 17857.4i 0.198415i
\(301\) −177814. + 177814.i −1.96260 + 1.96260i
\(302\) 7188.48 7188.48i 0.0788176 0.0788176i
\(303\) −98474.7 −1.07260
\(304\) 16511.8 16511.8i 0.178668 0.178668i
\(305\) −97861.2 −1.05199
\(306\) 60544.1 0.646590
\(307\) 65571.3i 0.695725i 0.937546 + 0.347862i \(0.113092\pi\)
−0.937546 + 0.347862i \(0.886908\pi\)
\(308\) −78815.8 −0.830830
\(309\) −3545.86 + 3545.86i −0.0371369 + 0.0371369i
\(310\) 24798.4 + 24798.4i 0.258048 + 0.258048i
\(311\) 48552.1 + 48552.1i 0.501981 + 0.501981i 0.912053 0.410072i \(-0.134497\pi\)
−0.410072 + 0.912053i \(0.634497\pi\)
\(312\) 26847.0 0.275796
\(313\) 16168.1 16168.1i 0.165033 0.165033i −0.619759 0.784792i \(-0.712770\pi\)
0.784792 + 0.619759i \(0.212770\pi\)
\(314\) −2616.60 2616.60i −0.0265386 0.0265386i
\(315\) −50238.2 + 50238.2i −0.506306 + 0.506306i
\(316\) 25718.5 + 25718.5i 0.257556 + 0.257556i
\(317\) 93230.4i 0.927767i −0.885896 0.463884i \(-0.846456\pi\)
0.885896 0.463884i \(-0.153544\pi\)
\(318\) 1977.99 1977.99i 0.0195601 0.0195601i
\(319\) −6201.38 + 6201.38i −0.0609406 + 0.0609406i
\(320\) −5213.10 5213.10i −0.0509092 0.0509092i
\(321\) 8353.07i 0.0810655i
\(322\) 85330.3 0.822985
\(323\) 148943.i 1.42763i
\(324\) 3487.82i 0.0332249i
\(325\) −65564.0 65564.0i −0.620725 0.620725i
\(326\) 79425.1i 0.747347i
\(327\) 56496.2 + 56496.2i 0.528353 + 0.528353i
\(328\) −29095.6 29095.6i −0.270445 0.270445i
\(329\) 236696. 2.18675
\(330\) 22789.8 0.209273
\(331\) −16551.9 + 16551.9i −0.151075 + 0.151075i −0.778598 0.627523i \(-0.784069\pi\)
0.627523 + 0.778598i \(0.284069\pi\)
\(332\) 78960.8i 0.716367i
\(333\) −47909.0 53459.7i −0.432044 0.482101i
\(334\) 65682.6 0.588786
\(335\) −26756.5 26756.5i −0.238419 0.238419i
\(336\) 32185.3i 0.285088i
\(337\) 154951.i 1.36437i −0.731177 0.682187i \(-0.761029\pi\)
0.731177 0.682187i \(-0.238971\pi\)
\(338\) −41447.9 + 41447.9i −0.362802 + 0.362802i
\(339\) 25037.6 25037.6i 0.217868 0.217868i
\(340\) −47024.4 −0.406785
\(341\) −63751.1 + 63751.1i −0.548251 + 0.548251i
\(342\) 54114.0 0.462655
\(343\) −381290. −3.24091
\(344\) 60470.3i 0.511005i
\(345\) −24673.5 −0.207297
\(346\) −2761.75 + 2761.75i −0.0230692 + 0.0230692i
\(347\) 78775.8 + 78775.8i 0.654235 + 0.654235i 0.954010 0.299775i \(-0.0969116\pi\)
−0.299775 + 0.954010i \(0.596912\pi\)
\(348\) −2532.40 2532.40i −0.0209109 0.0209109i
\(349\) −85580.9 −0.702629 −0.351314 0.936258i \(-0.614265\pi\)
−0.351314 + 0.936258i \(0.614265\pi\)
\(350\) −78600.7 + 78600.7i −0.641638 + 0.641638i
\(351\) 111949. + 111949.i 0.908673 + 0.908673i
\(352\) 13401.7 13401.7i 0.108162 0.108162i
\(353\) 142011. + 142011.i 1.13965 + 1.13965i 0.988513 + 0.151136i \(0.0482933\pi\)
0.151136 + 0.988513i \(0.451707\pi\)
\(354\) 42485.5i 0.339027i
\(355\) 58303.8 58303.8i 0.462637 0.462637i
\(356\) −29279.1 + 29279.1i −0.231025 + 0.231025i
\(357\) −145162. 145162.i −1.13898 1.13898i
\(358\) 44330.2i 0.345886i
\(359\) 8356.70 0.0648404 0.0324202 0.999474i \(-0.489679\pi\)
0.0324202 + 0.999474i \(0.489679\pi\)
\(360\) 17084.9i 0.131828i
\(361\) 2803.52i 0.0215124i
\(362\) −35622.1 35622.1i −0.271833 0.271833i
\(363\) 19660.7i 0.149206i
\(364\) 118169. + 118169.i 0.891872 + 0.891872i
\(365\) 80169.2 + 80169.2i 0.601758 + 0.601758i
\(366\) 102735. 0.766931
\(367\) 18123.6 0.134559 0.0672795 0.997734i \(-0.478568\pi\)
0.0672795 + 0.997734i \(0.478568\pi\)
\(368\) −14509.4 + 14509.4i −0.107141 + 0.107141i
\(369\) 95354.8i 0.700309i
\(370\) 37210.7 + 41521.9i 0.271809 + 0.303301i
\(371\) 17412.6 0.126507
\(372\) −26033.4 26033.4i −0.188125 0.188125i
\(373\) 54554.8i 0.392117i −0.980592 0.196058i \(-0.937186\pi\)
0.980592 0.196058i \(-0.0628142\pi\)
\(374\) 120889.i 0.864260i
\(375\) 56737.9 56737.9i 0.403470 0.403470i
\(376\) −40247.4 + 40247.4i −0.284683 + 0.284683i
\(377\) 18595.6 0.130836
\(378\) 134209. 134209.i 0.939288 0.939288i
\(379\) −217488. −1.51411 −0.757053 0.653354i \(-0.773361\pi\)
−0.757053 + 0.653354i \(0.773361\pi\)
\(380\) −42030.1 −0.291067
\(381\) 4599.54i 0.0316858i
\(382\) 56683.5 0.388446
\(383\) 114457. 114457.i 0.780269 0.780269i −0.199607 0.979876i \(-0.563967\pi\)
0.979876 + 0.199607i \(0.0639666\pi\)
\(384\) 5472.73 + 5472.73i 0.0371143 + 0.0371143i
\(385\) 100311. + 100311.i 0.676750 + 0.676750i
\(386\) 127319. 0.854511
\(387\) 99089.4 99089.4i 0.661615 0.661615i
\(388\) 7565.56 + 7565.56i 0.0502548 + 0.0502548i
\(389\) −129419. + 129419.i −0.855260 + 0.855260i −0.990775 0.135515i \(-0.956731\pi\)
0.135515 + 0.990775i \(0.456731\pi\)
\(390\) −34169.0 34169.0i −0.224648 0.224648i
\(391\) 130881.i 0.856099i
\(392\) 103250. 103250.i 0.671920 0.671920i
\(393\) 49515.6 49515.6i 0.320595 0.320595i
\(394\) −77270.2 77270.2i −0.497760 0.497760i
\(395\) 65465.4i 0.419583i
\(396\) 43921.4 0.280082
\(397\) 89391.0i 0.567170i 0.958947 + 0.283585i \(0.0915237\pi\)
−0.958947 + 0.283585i \(0.908476\pi\)
\(398\) 168409.i 1.06316i
\(399\) −129745. 129745.i −0.814977 0.814977i
\(400\) 26730.3i 0.167064i
\(401\) −11590.6 11590.6i −0.0720807 0.0720807i 0.670147 0.742228i \(-0.266231\pi\)
−0.742228 + 0.670147i \(0.766231\pi\)
\(402\) 28089.1 + 28089.1i 0.173814 + 0.173814i
\(403\) 191165. 1.17706
\(404\) 147404. 0.903125
\(405\) 4439.05 4439.05i 0.0270633 0.0270633i
\(406\) 22293.1i 0.135244i
\(407\) −106744. + 95660.4i −0.644396 + 0.577489i
\(408\) 49366.4 0.296559
\(409\) −158731. 158731.i −0.948890 0.948890i 0.0498664 0.998756i \(-0.484120\pi\)
−0.998756 + 0.0498664i \(0.984120\pi\)
\(410\) 74061.6i 0.440581i
\(411\) 68092.3i 0.403102i
\(412\) 5307.72 5307.72i 0.0312690 0.0312690i
\(413\) 187003. 187003.i 1.09635 1.09635i
\(414\) −47551.7 −0.277438
\(415\) −100496. + 100496.i −0.583514 + 0.583514i
\(416\) −40186.7 −0.232218
\(417\) 13692.0 0.0787399
\(418\) 108050.i 0.618404i
\(419\) −53640.6 −0.305538 −0.152769 0.988262i \(-0.548819\pi\)
−0.152769 + 0.988262i \(0.548819\pi\)
\(420\) −40963.1 + 40963.1i −0.232217 + 0.232217i
\(421\) −113029. 113029.i −0.637716 0.637716i 0.312276 0.949992i \(-0.398909\pi\)
−0.949992 + 0.312276i \(0.898909\pi\)
\(422\) −7688.63 7688.63i −0.0431742 0.0431742i
\(423\) −131903. −0.737178
\(424\) −2960.81 + 2960.81i −0.0164694 + 0.0164694i
\(425\) −120559. 120559.i −0.667456 0.667456i
\(426\) −61207.6 + 61207.6i −0.337276 + 0.337276i
\(427\) 452196. + 452196.i 2.48011 + 2.48011i
\(428\) 12503.5i 0.0682565i
\(429\) 87841.0 87841.0i 0.477290 0.477290i
\(430\) −76962.3 + 76962.3i −0.416237 + 0.416237i
\(431\) 208728. + 208728.i 1.12364 + 1.12364i 0.991190 + 0.132448i \(0.0422839\pi\)
0.132448 + 0.991190i \(0.457716\pi\)
\(432\) 45641.5i 0.244564i
\(433\) −75452.6 −0.402437 −0.201219 0.979546i \(-0.564490\pi\)
−0.201219 + 0.979546i \(0.564490\pi\)
\(434\) 229176.i 1.21672i
\(435\) 6446.11i 0.0340658i
\(436\) −84567.9 84567.9i −0.444869 0.444869i
\(437\) 116981.i 0.612565i
\(438\) −84162.0 84162.0i −0.438700 0.438700i
\(439\) −246708. 246708.i −1.28013 1.28013i −0.940593 0.339535i \(-0.889730\pi\)
−0.339535 0.940593i \(-0.610270\pi\)
\(440\) −34113.5 −0.176206
\(441\) 338380. 1.73992
\(442\) −181250. + 181250.i −0.927758 + 0.927758i
\(443\) 68941.1i 0.351294i −0.984453 0.175647i \(-0.943798\pi\)
0.984453 0.175647i \(-0.0562017\pi\)
\(444\) −39063.9 43589.8i −0.198157 0.221116i
\(445\) 74528.8 0.376361
\(446\) 122812. + 122812.i 0.617406 + 0.617406i
\(447\) 88255.4i 0.441699i
\(448\) 48177.3i 0.240042i
\(449\) 143056. 143056.i 0.709600 0.709600i −0.256851 0.966451i \(-0.582685\pi\)
0.966451 + 0.256851i \(0.0826849\pi\)
\(450\) 43801.5 43801.5i 0.216304 0.216304i
\(451\) −190396. −0.936062
\(452\) −37478.1 + 37478.1i −0.183443 + 0.183443i
\(453\) 19209.3 0.0936085
\(454\) −108933. −0.528504
\(455\) 300795.i 1.45294i
\(456\) 44123.3 0.212197
\(457\) 133820. 133820.i 0.640752 0.640752i −0.309988 0.950740i \(-0.600325\pi\)
0.950740 + 0.309988i \(0.100325\pi\)
\(458\) −131877. 131877.i −0.628691 0.628691i
\(459\) 205853. + 205853.i 0.977082 + 0.977082i
\(460\) 36933.2 0.174542
\(461\) 40084.3 40084.3i 0.188613 0.188613i −0.606483 0.795096i \(-0.707420\pi\)
0.795096 + 0.606483i \(0.207420\pi\)
\(462\) −105307. 105307.i −0.493371 0.493371i
\(463\) −230400. + 230400.i −1.07478 + 1.07478i −0.0778161 + 0.996968i \(0.524795\pi\)
−0.996968 + 0.0778161i \(0.975205\pi\)
\(464\) 3790.68 + 3790.68i 0.0176068 + 0.0176068i
\(465\) 66267.0i 0.306473i
\(466\) −112379. + 112379.i −0.517504 + 0.517504i
\(467\) 106600. 106600.i 0.488790 0.488790i −0.419134 0.907924i \(-0.637666\pi\)
0.907924 + 0.419134i \(0.137666\pi\)
\(468\) −65851.8 65851.8i −0.300660 0.300660i
\(469\) 247273.i 1.12417i
\(470\) 102448. 0.463776
\(471\) 6992.16i 0.0315188i
\(472\) 63595.5i 0.285458i
\(473\) −197853. 197853.i −0.884342 0.884342i
\(474\) 68725.8i 0.305889i
\(475\) −107755. 107755.i −0.477584 0.477584i
\(476\) 217290. + 217290.i 0.959016 + 0.959016i
\(477\) −9703.43 −0.0426470
\(478\) 317724. 1.39057
\(479\) −142463. + 142463.i −0.620913 + 0.620913i −0.945765 0.324852i \(-0.894685\pi\)
0.324852 + 0.945765i \(0.394685\pi\)
\(480\) 13930.6i 0.0604627i
\(481\) 303466. + 16617.1i 1.31166 + 0.0718232i
\(482\) −84076.4 −0.361893
\(483\) 114011. + 114011.i 0.488713 + 0.488713i
\(484\) 29429.7i 0.125630i
\(485\) 19257.8i 0.0818697i
\(486\) −120190. + 120190.i −0.508857 + 0.508857i
\(487\) 22476.6 22476.6i 0.0947706 0.0947706i −0.658132 0.752903i \(-0.728653\pi\)
0.752903 + 0.658132i \(0.228653\pi\)
\(488\) −153782. −0.645750
\(489\) −106121. + 106121.i −0.443797 + 0.443797i
\(490\) −262819. −1.09462
\(491\) −132795. −0.550831 −0.275416 0.961325i \(-0.588815\pi\)
−0.275416 + 0.961325i \(0.588815\pi\)
\(492\) 77750.2i 0.321197i
\(493\) 34193.6 0.140686
\(494\) −162000. + 162000.i −0.663838 + 0.663838i
\(495\) −55900.0 55900.0i −0.228140 0.228140i
\(496\) 38968.8 + 38968.8i 0.158399 + 0.158399i
\(497\) −538820. −2.18138
\(498\) 105501. 105501.i 0.425400 0.425400i
\(499\) 206696. + 206696.i 0.830101 + 0.830101i 0.987530 0.157430i \(-0.0503207\pi\)
−0.157430 + 0.987530i \(0.550321\pi\)
\(500\) −84929.6 + 84929.6i −0.339718 + 0.339718i
\(501\) 87759.6 + 87759.6i 0.349638 + 0.349638i
\(502\) 231903.i 0.920235i
\(503\) −119635. + 119635.i −0.472849 + 0.472849i −0.902835 0.429987i \(-0.858518\pi\)
0.429987 + 0.902835i \(0.358518\pi\)
\(504\) −78945.6 + 78945.6i −0.310790 + 0.310790i
\(505\) −187606. 187606.i −0.735637 0.735637i
\(506\) 94947.0i 0.370835i
\(507\) −110759. −0.430885
\(508\) 6884.94i 0.0266792i
\(509\) 78749.6i 0.303957i 0.988384 + 0.151979i \(0.0485645\pi\)
−0.988384 + 0.151979i \(0.951435\pi\)
\(510\) −62830.0 62830.0i −0.241561 0.241561i
\(511\) 740891.i 2.83735i
\(512\) −8192.00 8192.00i −0.0312500 0.0312500i
\(513\) 183990. + 183990.i 0.699131 + 0.699131i
\(514\) 189319. 0.716586
\(515\) −13510.6 −0.0509401
\(516\) 80795.3 80795.3i 0.303450 0.303450i
\(517\) 263371.i 0.985343i
\(518\) 19921.2 363807.i 0.0742431 1.35585i
\(519\) −7380.05 −0.0273984
\(520\) 51146.8 + 51146.8i 0.189152 + 0.189152i
\(521\) 283986.i 1.04622i 0.852266 + 0.523109i \(0.175228\pi\)
−0.852266 + 0.523109i \(0.824772\pi\)
\(522\) 12423.2i 0.0455923i
\(523\) 173621. 173621.i 0.634746 0.634746i −0.314508 0.949255i \(-0.601840\pi\)
0.949255 + 0.314508i \(0.101840\pi\)
\(524\) −74118.7 + 74118.7i −0.269939 + 0.269939i
\(525\) −210039. −0.762047
\(526\) −151709. + 151709.i −0.548329 + 0.548329i
\(527\) 351515. 1.26568
\(528\) 35812.5 0.128460
\(529\) 177046.i 0.632667i
\(530\) 7536.61 0.0268302
\(531\) −104210. + 104210.i −0.369592 + 0.369592i
\(532\) 194212. + 194212.i 0.686204 + 0.686204i
\(533\) 285463. + 285463.i 1.00484 + 1.00484i
\(534\) −78240.6 −0.274378
\(535\) −15913.6 + 15913.6i −0.0555981 + 0.0555981i
\(536\) −42045.9 42045.9i −0.146350 0.146350i
\(537\) −59230.3 + 59230.3i −0.205398 + 0.205398i
\(538\) −185629. 185629.i −0.641329 0.641329i
\(539\) 675648.i 2.32564i
\(540\) 58089.2 58089.2i 0.199209 0.199209i
\(541\) 207308. 207308.i 0.708308 0.708308i −0.257871 0.966179i \(-0.583021\pi\)
0.966179 + 0.257871i \(0.0830210\pi\)
\(542\) −6308.37 6308.37i −0.0214743 0.0214743i
\(543\) 95190.7i 0.322845i
\(544\) −73895.3 −0.249700
\(545\) 215264.i 0.724734i
\(546\) 315776.i 1.05924i
\(547\) 150439. + 150439.i 0.502790 + 0.502790i 0.912304 0.409514i \(-0.134302\pi\)
−0.409514 + 0.912304i \(0.634302\pi\)
\(548\) 101926.i 0.339409i
\(549\) −251994. 251994.i −0.836074 0.836074i
\(550\) −87458.9 87458.9i −0.289120 0.289120i
\(551\) 30562.0 0.100665
\(552\) −38772.6 −0.127247
\(553\) −302502. + 302502.i −0.989187 + 0.989187i
\(554\) 259388.i 0.845142i
\(555\) −5760.27 + 105196.i −0.0187007 + 0.341517i
\(556\) −20495.2 −0.0662984
\(557\) −38740.6 38740.6i −0.124869 0.124869i 0.641910 0.766780i \(-0.278142\pi\)
−0.766780 + 0.641910i \(0.778142\pi\)
\(558\) 127712.i 0.410170i
\(559\) 593286.i 1.89863i
\(560\) 61316.7 61316.7i 0.195525 0.195525i
\(561\) 161522. 161522.i 0.513223 0.513223i
\(562\) −263446. −0.834103
\(563\) 124572. 124572.i 0.393011 0.393011i −0.482748 0.875759i \(-0.660361\pi\)
0.875759 + 0.482748i \(0.160361\pi\)
\(564\) −107550. −0.338107
\(565\) 95399.0 0.298845
\(566\) 76961.6i 0.240238i
\(567\) −41023.9 −0.127606
\(568\) 91620.1 91620.1i 0.283984 0.283984i
\(569\) 101858. + 101858.i 0.314609 + 0.314609i 0.846692 0.532083i \(-0.178591\pi\)
−0.532083 + 0.846692i \(0.678591\pi\)
\(570\) −56157.1 56157.1i −0.172844 0.172844i
\(571\) −110278. −0.338234 −0.169117 0.985596i \(-0.554092\pi\)
−0.169117 + 0.985596i \(0.554092\pi\)
\(572\) −131487. + 131487.i −0.401875 + 0.401875i
\(573\) 75735.8 + 75735.8i 0.230670 + 0.230670i
\(574\) 342224. 342224.i 1.03869 1.03869i
\(575\) 94687.8 + 94687.8i 0.286390 + 0.286390i
\(576\) 26847.6i 0.0809208i
\(577\) 196203. 196203.i 0.589324 0.589324i −0.348124 0.937448i \(-0.613181\pi\)
0.937448 + 0.348124i \(0.113181\pi\)
\(578\) −166241. + 166241.i −0.497603 + 0.497603i
\(579\) 170113. + 170113.i 0.507434 + 0.507434i
\(580\) 9649.02i 0.0286832i
\(581\) 928741. 2.75133
\(582\) 20216.9i 0.0596855i
\(583\) 19375.0i 0.0570038i
\(584\) 125980. + 125980.i 0.369382 + 0.369382i
\(585\) 167623.i 0.489803i
\(586\) 159235. + 159235.i 0.463706 + 0.463706i
\(587\) −189138. 189138.i −0.548913 0.548913i 0.377213 0.926126i \(-0.376882\pi\)
−0.926126 + 0.377213i \(0.876882\pi\)
\(588\) 275908. 0.798012
\(589\) 314182. 0.905630
\(590\) 80939.8 80939.8i 0.232519 0.232519i
\(591\) 206484.i 0.591169i
\(592\) 58473.8 + 65248.6i 0.166847 + 0.186178i
\(593\) −477286. −1.35728 −0.678640 0.734471i \(-0.737430\pi\)
−0.678640 + 0.734471i \(0.737430\pi\)
\(594\) 149335. + 149335.i 0.423241 + 0.423241i
\(595\) 553103.i 1.56233i
\(596\) 132107.i 0.371907i
\(597\) −225014. + 225014.i −0.631336 + 0.631336i
\(598\) 142355. 142355.i 0.398080 0.398080i
\(599\) −693204. −1.93200 −0.966000 0.258540i \(-0.916758\pi\)
−0.966000 + 0.258540i \(0.916758\pi\)
\(600\) 35714.8 35714.8i 0.0992077 0.0992077i
\(601\) −450318. −1.24672 −0.623362 0.781933i \(-0.714234\pi\)
−0.623362 + 0.781933i \(0.714234\pi\)
\(602\) 711254. 1.96260
\(603\) 137797.i 0.378970i
\(604\) −28753.9 −0.0788176
\(605\) 37456.0 37456.0i 0.102332 0.102332i
\(606\) 196949. + 196949.i 0.536302 + 0.536302i
\(607\) −80454.7 80454.7i −0.218360 0.218360i 0.589447 0.807807i \(-0.299346\pi\)
−0.807807 + 0.589447i \(0.799346\pi\)
\(608\) −66047.1 −0.178668
\(609\) 29786.2 29786.2i 0.0803119 0.0803119i
\(610\) 195722. + 195722.i 0.525994 + 0.525994i
\(611\) 394875. 394875.i 1.05774 1.05774i
\(612\) −121088. 121088.i −0.323295 0.323295i
\(613\) 427684.i 1.13816i −0.822283 0.569078i \(-0.807300\pi\)
0.822283 0.569078i \(-0.192700\pi\)
\(614\) 131143. 131143.i 0.347862 0.347862i
\(615\) −98955.0 + 98955.0i −0.261630 + 0.261630i
\(616\) 157632. + 157632.i 0.415415 + 0.415415i
\(617\) 423563.i 1.11262i −0.830974 0.556311i \(-0.812216\pi\)
0.830974 0.556311i \(-0.187784\pi\)
\(618\) 14183.5 0.0371369
\(619\) 704207.i 1.83789i −0.394389 0.918944i \(-0.629044\pi\)
0.394389 0.918944i \(-0.370956\pi\)
\(620\) 99193.5i 0.258048i
\(621\) −161678. 161678.i −0.419244 0.419244i
\(622\) 194208.i 0.501981i
\(623\) −344382. 344382.i −0.887288 0.887288i
\(624\) −53694.1 53694.1i −0.137898 0.137898i
\(625\) −44853.1 −0.114824
\(626\) −64672.5 −0.165033
\(627\) 144367. 144367.i 0.367226 0.367226i
\(628\) 10466.4i 0.0265386i
\(629\) 558014. + 30555.5i 1.41041 + 0.0772304i
\(630\) 200953. 0.506306
\(631\) 187320. + 187320.i 0.470462 + 0.470462i 0.902064 0.431602i \(-0.142051\pi\)
−0.431602 + 0.902064i \(0.642051\pi\)
\(632\) 102874.i 0.257556i
\(633\) 20545.8i 0.0512762i
\(634\) −186461. + 186461.i −0.463884 + 0.463884i
\(635\) 8762.66 8762.66i 0.0217315 0.0217315i
\(636\) −7911.96 −0.0195601
\(637\) −1.01301e6 + 1.01301e6i −2.49651 + 2.49651i
\(638\) 24805.5 0.0609406
\(639\) 300266. 0.735367
\(640\) 20852.4i 0.0509092i
\(641\) −709193. −1.72603 −0.863015 0.505178i \(-0.831427\pi\)
−0.863015 + 0.505178i \(0.831427\pi\)
\(642\) 16706.1 16706.1i 0.0405327 0.0405327i
\(643\) 217277. + 217277.i 0.525522 + 0.525522i 0.919234 0.393712i \(-0.128809\pi\)
−0.393712 + 0.919234i \(0.628809\pi\)
\(644\) −170661. 170661.i −0.411492 0.411492i
\(645\) −205661. −0.494348
\(646\) −297887. + 297887.i −0.713815 + 0.713815i
\(647\) 110695. + 110695.i 0.264435 + 0.264435i 0.826853 0.562418i \(-0.190129\pi\)
−0.562418 + 0.826853i \(0.690129\pi\)
\(648\) 6975.64 6975.64i 0.0166125 0.0166125i
\(649\) 208078. + 208078.i 0.494012 + 0.494012i
\(650\) 262256.i 0.620725i
\(651\) 306206. 306206.i 0.722524 0.722524i
\(652\) 158850. 158850.i 0.373674 0.373674i
\(653\) −239393. 239393.i −0.561417 0.561417i 0.368292 0.929710i \(-0.379943\pi\)
−0.929710 + 0.368292i \(0.879943\pi\)
\(654\) 225985.i 0.528353i
\(655\) 188666. 0.439756
\(656\) 116382.i 0.270445i
\(657\) 412873.i 0.956502i
\(658\) −473392. 473392.i −1.09337 1.09337i
\(659\) 597265.i 1.37530i 0.726044 + 0.687648i \(0.241357\pi\)
−0.726044 + 0.687648i \(0.758643\pi\)
\(660\) −45579.7 45579.7i −0.104636 0.104636i
\(661\) −38924.4 38924.4i −0.0890881 0.0890881i 0.661158 0.750246i \(-0.270065\pi\)
−0.750246 + 0.661158i \(0.770065\pi\)
\(662\) 66207.6 0.151075
\(663\) −484343. −1.10186
\(664\) −157922. + 157922.i −0.358183 + 0.358183i
\(665\) 494359.i 1.11789i
\(666\) −11101.4 + 202737.i −0.0250282 + 0.457073i
\(667\) −26855.8 −0.0603652
\(668\) −131365. 131365.i −0.294393 0.294393i
\(669\) 328182.i 0.733268i
\(670\) 107026.i 0.238419i
\(671\) −503159. + 503159.i −1.11753 + 1.11753i
\(672\) −64370.5 + 64370.5i −0.142544 + 0.142544i
\(673\) 528423. 1.16668 0.583340 0.812228i \(-0.301745\pi\)
0.583340 + 0.812228i \(0.301745\pi\)
\(674\) −309901. + 309901.i −0.682187 + 0.682187i
\(675\) 297854. 0.653725
\(676\) 165792. 0.362802
\(677\) 504764.i 1.10131i −0.834732 0.550657i \(-0.814377\pi\)
0.834732 0.550657i \(-0.185623\pi\)
\(678\) −100150. −0.217868
\(679\) −88986.4 + 88986.4i −0.193012 + 0.193012i
\(680\) 94048.7 + 94048.7i 0.203393 + 0.203393i
\(681\) −145547. 145547.i −0.313841 0.313841i
\(682\) 255004. 0.548251
\(683\) −360139. + 360139.i −0.772020 + 0.772020i −0.978459 0.206440i \(-0.933812\pi\)
0.206440 + 0.978459i \(0.433812\pi\)
\(684\) −108228. 108228.i −0.231327 0.231327i
\(685\) −129724. + 129724.i −0.276464 + 0.276464i
\(686\) 762580. + 762580.i 1.62046 + 1.62046i
\(687\) 352406.i 0.746671i
\(688\) −120941. + 120941.i −0.255502 + 0.255502i
\(689\) 29049.1 29049.1i 0.0611919 0.0611919i
\(690\) 49347.0 + 49347.0i 0.103648 + 0.103648i
\(691\) 850032.i 1.78024i −0.455723 0.890122i \(-0.650619\pi\)
0.455723 0.890122i \(-0.349381\pi\)
\(692\) 11047.0 0.0230692
\(693\) 516605.i 1.07570i
\(694\) 315103.i 0.654235i
\(695\) 26084.9 + 26084.9i 0.0540032 + 0.0540032i
\(696\) 10129.6i 0.0209109i
\(697\) 524909. + 524909.i 1.08048 + 1.08048i
\(698\) 171162. + 171162.i 0.351314 + 0.351314i
\(699\) −300303. −0.614618
\(700\) 314403. 0.641638
\(701\) −67567.6 + 67567.6i −0.137500 + 0.137500i −0.772507 0.635007i \(-0.780997\pi\)
0.635007 + 0.772507i \(0.280997\pi\)
\(702\) 447798.i 0.908673i
\(703\) 498749. + 27310.3i 1.00919 + 0.0552607i
\(704\) −53606.9 −0.108162
\(705\) 136883. + 136883.i 0.275404 + 0.275404i
\(706\) 568042.i 1.13965i
\(707\) 1.73378e6i 3.46860i
\(708\) −84971.0 + 84971.0i −0.169513 + 0.169513i
\(709\) −223391. + 223391.i −0.444399 + 0.444399i −0.893487 0.449089i \(-0.851749\pi\)
0.449089 + 0.893487i \(0.351749\pi\)
\(710\) −233215. −0.462637
\(711\) 168574. 168574.i 0.333466 0.333466i
\(712\) 117117. 0.231025
\(713\) −276082. −0.543074
\(714\) 580649.i 1.13898i
\(715\) 334695. 0.654692
\(716\) 88660.4 88660.4i 0.172943 0.172943i
\(717\) 424516. + 424516.i 0.825764 + 0.825764i
\(718\) −16713.4 16713.4i −0.0324202 0.0324202i
\(719\) −964220. −1.86517 −0.932585 0.360950i \(-0.882452\pi\)
−0.932585 + 0.360950i \(0.882452\pi\)
\(720\) −34169.7 + 34169.7i −0.0659138 + 0.0659138i
\(721\) 62429.6 + 62429.6i 0.120094 + 0.120094i
\(722\) −5607.04 + 5607.04i −0.0107562 + 0.0107562i
\(723\) −112336. 112336.i −0.214903 0.214903i
\(724\) 142489.i 0.271833i
\(725\) 24737.8 24737.8i 0.0470636 0.0470636i
\(726\) −39321.5 + 39321.5i −0.0746030 + 0.0746030i
\(727\) −223895. 223895.i −0.423620 0.423620i 0.462828 0.886448i \(-0.346835\pi\)
−0.886448 + 0.462828i \(0.846835\pi\)
\(728\) 472678.i 0.891872i
\(729\) −285862. −0.537899
\(730\) 320677.i 0.601758i
\(731\) 1.09093e6i 2.04157i
\(732\) −205470. 205470.i −0.383466 0.383466i
\(733\) 551842.i 1.02709i −0.858064 0.513543i \(-0.828333\pi\)
0.858064 0.513543i \(-0.171667\pi\)
\(734\) −36247.2 36247.2i −0.0672795 0.0672795i
\(735\) −351156. 351156.i −0.650018 0.650018i
\(736\) 58037.8 0.107141
\(737\) −275140. −0.506547
\(738\) −190710. + 190710.i −0.350155 + 0.350155i
\(739\) 137775.i 0.252278i 0.992013 + 0.126139i \(0.0402586\pi\)
−0.992013 + 0.126139i \(0.959741\pi\)
\(740\) 8622.41 157465.i 0.0157458 0.287555i
\(741\) −432903. −0.788414
\(742\) −34825.1 34825.1i −0.0632536 0.0632536i
\(743\) 352194.i 0.637977i 0.947759 + 0.318988i \(0.103343\pi\)
−0.947759 + 0.318988i \(0.896657\pi\)
\(744\) 104134.i 0.188125i
\(745\) −168137. + 168137.i −0.302936 + 0.302936i
\(746\) −109110. + 109110.i −0.196058 + 0.196058i
\(747\) −517555. −0.927504
\(748\) −241778. + 241778.i −0.432130 + 0.432130i
\(749\) 147067. 0.262151
\(750\) −226952. −0.403470
\(751\) 1.08959e6i 1.93190i −0.258737 0.965948i \(-0.583306\pi\)
0.258737 0.965948i \(-0.416694\pi\)
\(752\) 160990. 0.284683
\(753\) 309849. 309849.i 0.546463 0.546463i
\(754\) −37191.2 37191.2i −0.0654180 0.0654180i
\(755\) 36596.0 + 36596.0i 0.0642006 + 0.0642006i
\(756\) −536837. −0.939288
\(757\) 103856. 103856.i 0.181233 0.181233i −0.610660 0.791893i \(-0.709096\pi\)
0.791893 + 0.610660i \(0.209096\pi\)
\(758\) 434975. + 434975.i 0.757053 + 0.757053i
\(759\) −126860. + 126860.i −0.220213 + 0.220213i
\(760\) 84060.1 + 84060.1i 0.145533 + 0.145533i
\(761\) 357264.i 0.616908i −0.951239 0.308454i \(-0.900188\pi\)
0.951239 0.308454i \(-0.0998116\pi\)
\(762\) −9199.08 + 9199.08i −0.0158429 + 0.0158429i
\(763\) 994691. 994691.i 1.70859 1.70859i
\(764\) −113367. 113367.i −0.194223 0.194223i
\(765\) 308225.i 0.526678i
\(766\) −457827. −0.780269
\(767\) 623948.i 1.06061i
\(768\) 21890.9i 0.0371143i
\(769\) 305401. + 305401.i 0.516438 + 0.516438i 0.916492 0.400054i \(-0.131009\pi\)
−0.400054 + 0.916492i \(0.631009\pi\)
\(770\) 401245.i 0.676750i
\(771\) 252952. + 252952.i 0.425530 + 0.425530i
\(772\) −254637. 254637.i −0.427255 0.427255i
\(773\) −199611. −0.334060 −0.167030 0.985952i \(-0.553418\pi\)
−0.167030 + 0.985952i \(0.553418\pi\)
\(774\) −396358. −0.661615
\(775\) 254308.