Properties

Label 74.5.d.a.31.5
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 31.5
Root \(1.77388i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.5.d.a.43.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 2.00000i) q^{2} +0.773882i q^{3} +8.00000i q^{4} +(2.70834 - 2.70834i) q^{5} +(1.54776 - 1.54776i) q^{6} -17.1599 q^{7} +(16.0000 - 16.0000i) q^{8} +80.4011 q^{9} +O(q^{10})\) \(q+(-2.00000 - 2.00000i) q^{2} +0.773882i q^{3} +8.00000i q^{4} +(2.70834 - 2.70834i) q^{5} +(1.54776 - 1.54776i) q^{6} -17.1599 q^{7} +(16.0000 - 16.0000i) q^{8} +80.4011 q^{9} -10.8334 q^{10} +132.300i q^{11} -6.19106 q^{12} +(181.780 - 181.780i) q^{13} +(34.3199 + 34.3199i) q^{14} +(2.09593 + 2.09593i) q^{15} -64.0000 q^{16} +(261.124 - 261.124i) q^{17} +(-160.802 - 160.802i) q^{18} +(137.325 - 137.325i) q^{19} +(21.6667 + 21.6667i) q^{20} -13.2798i q^{21} +(264.600 - 264.600i) q^{22} +(543.359 - 543.359i) q^{23} +(12.3821 + 12.3821i) q^{24} +610.330i q^{25} -727.121 q^{26} +124.905i q^{27} -137.279i q^{28} +(-624.988 - 624.988i) q^{29} -8.38374i q^{30} +(833.169 + 833.169i) q^{31} +(128.000 + 128.000i) q^{32} -102.385 q^{33} -1044.49 q^{34} +(-46.4749 + 46.4749i) q^{35} +643.209i q^{36} +(1049.56 + 878.973i) q^{37} -549.301 q^{38} +(140.677 + 140.677i) q^{39} -86.6668i q^{40} +955.940i q^{41} +(-26.5595 + 26.5595i) q^{42} +(-1509.63 + 1509.63i) q^{43} -1058.40 q^{44} +(217.753 - 217.753i) q^{45} -2173.43 q^{46} -3094.13 q^{47} -49.5285i q^{48} -2106.54 q^{49} +(1220.66 - 1220.66i) q^{50} +(202.079 + 202.079i) q^{51} +(1454.24 + 1454.24i) q^{52} +4409.63 q^{53} +(249.811 - 249.811i) q^{54} +(358.313 + 358.313i) q^{55} +(-274.559 + 274.559i) q^{56} +(106.274 + 106.274i) q^{57} +2499.95i q^{58} +(1827.22 - 1827.22i) q^{59} +(-16.7675 + 16.7675i) q^{60} +(-4096.05 - 4096.05i) q^{61} -3332.68i q^{62} -1379.68 q^{63} -512.000i q^{64} -984.645i q^{65} +(204.769 + 204.769i) q^{66} +2455.82i q^{67} +(2088.99 + 2088.99i) q^{68} +(420.495 + 420.495i) q^{69} +185.900 q^{70} +6687.04 q^{71} +(1286.42 - 1286.42i) q^{72} -3245.28i q^{73} +(-341.165 - 3857.06i) q^{74} -472.323 q^{75} +(1098.60 + 1098.60i) q^{76} -2270.26i q^{77} -562.706i q^{78} +(-1773.15 + 1773.15i) q^{79} +(-173.334 + 173.334i) q^{80} +6415.83 q^{81} +(1911.88 - 1911.88i) q^{82} -5356.85 q^{83} +106.238 q^{84} -1414.42i q^{85} +6038.52 q^{86} +(483.667 - 483.667i) q^{87} +(2116.80 + 2116.80i) q^{88} +(-6276.92 - 6276.92i) q^{89} -871.014 q^{90} +(-3119.34 + 3119.34i) q^{91} +(4346.87 + 4346.87i) q^{92} +(-644.775 + 644.775i) q^{93} +(6188.25 + 6188.25i) q^{94} -743.847i q^{95} +(-99.0569 + 99.0569i) q^{96} +(430.923 - 430.923i) q^{97} +(4213.07 + 4213.07i) q^{98} +10637.1i 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
\(3\) 0.773882i 0.0859869i 0.999075 + 0.0429935i \(0.0136895\pi\)
−0.999075 + 0.0429935i \(0.986311\pi\)
\(4\) 8.00000i 0.500000i
\(5\) 2.70834 2.70834i 0.108334 0.108334i −0.650862 0.759196i \(-0.725592\pi\)
0.759196 + 0.650862i \(0.225592\pi\)
\(6\) 1.54776 1.54776i 0.0429935 0.0429935i
\(7\) −17.1599 −0.350203 −0.175101 0.984550i \(-0.556025\pi\)
−0.175101 + 0.984550i \(0.556025\pi\)
\(8\) 16.0000 16.0000i 0.250000 0.250000i
\(9\) 80.4011 0.992606
\(10\) −10.8334 −0.108334
\(11\) 132.300i 1.09339i 0.837332 + 0.546695i \(0.184114\pi\)
−0.837332 + 0.546695i \(0.815886\pi\)
\(12\) −6.19106 −0.0429935
\(13\) 181.780 181.780i 1.07562 1.07562i 0.0787272 0.996896i \(-0.474914\pi\)
0.996896 0.0787272i \(-0.0250856\pi\)
\(14\) 34.3199 + 34.3199i 0.175101 + 0.175101i
\(15\) 2.09593 + 2.09593i 0.00931527 + 0.00931527i
\(16\) −64.0000 −0.250000
\(17\) 261.124 261.124i 0.903542 0.903542i −0.0921990 0.995741i \(-0.529390\pi\)
0.995741 + 0.0921990i \(0.0293896\pi\)
\(18\) −160.802 160.802i −0.496303 0.496303i
\(19\) 137.325 137.325i 0.380402 0.380402i −0.490845 0.871247i \(-0.663312\pi\)
0.871247 + 0.490845i \(0.163312\pi\)
\(20\) 21.6667 + 21.6667i 0.0541668 + 0.0541668i
\(21\) 13.2798i 0.0301128i
\(22\) 264.600 264.600i 0.546695 0.546695i
\(23\) 543.359 543.359i 1.02714 1.02714i 0.0275216 0.999621i \(-0.491238\pi\)
0.999621 0.0275216i \(-0.00876152\pi\)
\(24\) 12.3821 + 12.3821i 0.0214967 + 0.0214967i
\(25\) 610.330i 0.976528i
\(26\) −727.121 −1.07562
\(27\) 124.905i 0.171338i
\(28\) 137.279i 0.175101i
\(29\) −624.988 624.988i −0.743148 0.743148i 0.230034 0.973183i \(-0.426116\pi\)
−0.973183 + 0.230034i \(0.926116\pi\)
\(30\) 8.38374i 0.00931527i
\(31\) 833.169 + 833.169i 0.866982 + 0.866982i 0.992137 0.125156i \(-0.0399430\pi\)
−0.125156 + 0.992137i \(0.539943\pi\)
\(32\) 128.000 + 128.000i 0.125000 + 0.125000i
\(33\) −102.385 −0.0940172
\(34\) −1044.49 −0.903542
\(35\) −46.4749 + 46.4749i −0.0379387 + 0.0379387i
\(36\) 643.209i 0.496303i
\(37\) 1049.56 + 878.973i 0.766659 + 0.642055i
\(38\) −549.301 −0.380402
\(39\) 140.677 + 140.677i 0.0924895 + 0.0924895i
\(40\) 86.6668i 0.0541668i
\(41\) 955.940i 0.568674i 0.958724 + 0.284337i \(0.0917734\pi\)
−0.958724 + 0.284337i \(0.908227\pi\)
\(42\) −26.5595 + 26.5595i −0.0150564 + 0.0150564i
\(43\) −1509.63 + 1509.63i −0.816458 + 0.816458i −0.985593 0.169135i \(-0.945903\pi\)
0.169135 + 0.985593i \(0.445903\pi\)
\(44\) −1058.40 −0.546695
\(45\) 217.753 217.753i 0.107533 0.107533i
\(46\) −2173.43 −1.02714
\(47\) −3094.13 −1.40069 −0.700346 0.713804i \(-0.746971\pi\)
−0.700346 + 0.713804i \(0.746971\pi\)
\(48\) 49.5285i 0.0214967i
\(49\) −2106.54 −0.877358
\(50\) 1220.66 1220.66i 0.488264 0.488264i
\(51\) 202.079 + 202.079i 0.0776928 + 0.0776928i
\(52\) 1454.24 + 1454.24i 0.537812 + 0.537812i
\(53\) 4409.63 1.56982 0.784911 0.619609i \(-0.212709\pi\)
0.784911 + 0.619609i \(0.212709\pi\)
\(54\) 249.811 249.811i 0.0856690 0.0856690i
\(55\) 358.313 + 358.313i 0.118451 + 0.118451i
\(56\) −274.559 + 274.559i −0.0875507 + 0.0875507i
\(57\) 106.274 + 106.274i 0.0327096 + 0.0327096i
\(58\) 2499.95i 0.743148i
\(59\) 1827.22 1827.22i 0.524912 0.524912i −0.394139 0.919051i \(-0.628957\pi\)
0.919051 + 0.394139i \(0.128957\pi\)
\(60\) −16.7675 + 16.7675i −0.00465763 + 0.00465763i
\(61\) −4096.05 4096.05i −1.10079 1.10079i −0.994315 0.106477i \(-0.966043\pi\)
−0.106477 0.994315i \(-0.533957\pi\)
\(62\) 3332.68i 0.866982i
\(63\) −1379.68 −0.347613
\(64\) 512.000i 0.125000i
\(65\) 984.645i 0.233052i
\(66\) 204.769 + 204.769i 0.0470086 + 0.0470086i
\(67\) 2455.82i 0.547076i 0.961861 + 0.273538i \(0.0881939\pi\)
−0.961861 + 0.273538i \(0.911806\pi\)
\(68\) 2088.99 + 2088.99i 0.451771 + 0.451771i
\(69\) 420.495 + 420.495i 0.0883208 + 0.0883208i
\(70\) 185.900 0.0379387
\(71\) 6687.04 1.32653 0.663265 0.748385i \(-0.269170\pi\)
0.663265 + 0.748385i \(0.269170\pi\)
\(72\) 1286.42 1286.42i 0.248152 0.248152i
\(73\) 3245.28i 0.608985i −0.952515 0.304493i \(-0.901513\pi\)
0.952515 0.304493i \(-0.0984869\pi\)
\(74\) −341.165 3857.06i −0.0623019 0.704357i
\(75\) −472.323 −0.0839686
\(76\) 1098.60 + 1098.60i 0.190201 + 0.190201i
\(77\) 2270.26i 0.382908i
\(78\) 562.706i 0.0924895i
\(79\) −1773.15 + 1773.15i −0.284113 + 0.284113i −0.834747 0.550634i \(-0.814386\pi\)
0.550634 + 0.834747i \(0.314386\pi\)
\(80\) −173.334 + 173.334i −0.0270834 + 0.0270834i
\(81\) 6415.83 0.977873
\(82\) 1911.88 1911.88i 0.284337 0.284337i
\(83\) −5356.85 −0.777595 −0.388798 0.921323i \(-0.627109\pi\)
−0.388798 + 0.921323i \(0.627109\pi\)
\(84\) 106.238 0.0150564
\(85\) 1414.42i 0.195768i
\(86\) 6038.52 0.816458
\(87\) 483.667 483.667i 0.0639010 0.0639010i
\(88\) 2116.80 + 2116.80i 0.273347 + 0.273347i
\(89\) −6276.92 6276.92i −0.792441 0.792441i 0.189450 0.981890i \(-0.439330\pi\)
−0.981890 + 0.189450i \(0.939330\pi\)
\(90\) −871.014 −0.107533
\(91\) −3119.34 + 3119.34i −0.376686 + 0.376686i
\(92\) 4346.87 + 4346.87i 0.513571 + 0.513571i
\(93\) −644.775 + 644.775i −0.0745491 + 0.0745491i
\(94\) 6188.25 + 6188.25i 0.700346 + 0.700346i
\(95\) 743.847i 0.0824207i
\(96\) −99.0569 + 99.0569i −0.0107484 + 0.0107484i
\(97\) 430.923 430.923i 0.0457990 0.0457990i −0.683836 0.729635i \(-0.739690\pi\)
0.729635 + 0.683836i \(0.239690\pi\)
\(98\) 4213.07 + 4213.07i 0.438679 + 0.438679i
\(99\) 10637.1i 1.08531i
\(100\) −4882.64 −0.488264
\(101\) 9738.29i 0.954641i −0.878729 0.477321i \(-0.841608\pi\)
0.878729 0.477321i \(-0.158392\pi\)
\(102\) 808.315i 0.0776928i
\(103\) 6805.12 + 6805.12i 0.641448 + 0.641448i 0.950911 0.309463i \(-0.100149\pi\)
−0.309463 + 0.950911i \(0.600149\pi\)
\(104\) 5816.97i 0.537812i
\(105\) −35.9661 35.9661i −0.00326223 0.00326223i
\(106\) −8819.26 8819.26i −0.784911 0.784911i
\(107\) −2128.30 −0.185894 −0.0929468 0.995671i \(-0.529629\pi\)
−0.0929468 + 0.995671i \(0.529629\pi\)
\(108\) −999.243 −0.0856690
\(109\) −12788.1 + 12788.1i −1.07635 + 1.07635i −0.0795192 + 0.996833i \(0.525338\pi\)
−0.996833 + 0.0795192i \(0.974662\pi\)
\(110\) 1433.25i 0.118451i
\(111\) −680.222 + 812.232i −0.0552083 + 0.0659226i
\(112\) 1098.24 0.0875507
\(113\) −4650.83 4650.83i −0.364228 0.364228i 0.501139 0.865367i \(-0.332915\pi\)
−0.865367 + 0.501139i \(0.832915\pi\)
\(114\) 425.094i 0.0327096i
\(115\) 2943.20i 0.222548i
\(116\) 4999.90 4999.90i 0.371574 0.371574i
\(117\) 14615.3 14615.3i 1.06767 1.06767i
\(118\) −7308.88 −0.524912
\(119\) −4480.86 + 4480.86i −0.316423 + 0.316423i
\(120\) 67.0699 0.00465763
\(121\) −2862.32 −0.195500
\(122\) 16384.2i 1.10079i
\(123\) −739.785 −0.0488985
\(124\) −6665.35 + 6665.35i −0.433491 + 0.433491i
\(125\) 3345.69 + 3345.69i 0.214124 + 0.214124i
\(126\) 2759.35 + 2759.35i 0.173807 + 0.173807i
\(127\) −27171.0 −1.68460 −0.842302 0.539006i \(-0.818800\pi\)
−0.842302 + 0.539006i \(0.818800\pi\)
\(128\) −1024.00 + 1024.00i −0.0625000 + 0.0625000i
\(129\) −1168.28 1168.28i −0.0702047 0.0702047i
\(130\) −1969.29 + 1969.29i −0.116526 + 0.116526i
\(131\) −9032.72 9032.72i −0.526352 0.526352i 0.393131 0.919483i \(-0.371392\pi\)
−0.919483 + 0.393131i \(0.871392\pi\)
\(132\) 819.078i 0.0470086i
\(133\) −2356.49 + 2356.49i −0.133218 + 0.133218i
\(134\) 4911.65 4911.65i 0.273538 0.273538i
\(135\) 338.286 + 338.286i 0.0185617 + 0.0185617i
\(136\) 8355.95i 0.451771i
\(137\) 10999.0 0.586019 0.293010 0.956109i \(-0.405343\pi\)
0.293010 + 0.956109i \(0.405343\pi\)
\(138\) 1681.98i 0.0883208i
\(139\) 11235.5i 0.581518i 0.956796 + 0.290759i \(0.0939079\pi\)
−0.956796 + 0.290759i \(0.906092\pi\)
\(140\) −371.799 371.799i −0.0189693 0.0189693i
\(141\) 2394.49i 0.120441i
\(142\) −13374.1 13374.1i −0.663265 0.663265i
\(143\) 24049.6 + 24049.6i 1.17608 + 1.17608i
\(144\) −5145.67 −0.248152
\(145\) −3385.36 −0.161016
\(146\) −6490.56 + 6490.56i −0.304493 + 0.304493i
\(147\) 1630.21i 0.0754413i
\(148\) −7031.79 + 8396.45i −0.321027 + 0.383329i
\(149\) 4400.81 0.198226 0.0991128 0.995076i \(-0.468400\pi\)
0.0991128 + 0.995076i \(0.468400\pi\)
\(150\) 944.647 + 944.647i 0.0419843 + 0.0419843i
\(151\) 32364.0i 1.41941i 0.704497 + 0.709707i \(0.251173\pi\)
−0.704497 + 0.709707i \(0.748827\pi\)
\(152\) 4394.41i 0.190201i
\(153\) 20994.6 20994.6i 0.896861 0.896861i
\(154\) −4540.52 + 4540.52i −0.191454 + 0.191454i
\(155\) 4513.01 0.187846
\(156\) −1125.41 + 1125.41i −0.0462448 + 0.0462448i
\(157\) −5571.36 −0.226028 −0.113014 0.993593i \(-0.536050\pi\)
−0.113014 + 0.993593i \(0.536050\pi\)
\(158\) 7092.61 0.284113
\(159\) 3412.53i 0.134984i
\(160\) 693.335 0.0270834
\(161\) −9324.00 + 9324.00i −0.359708 + 0.359708i
\(162\) −12831.7 12831.7i −0.488937 0.488937i
\(163\) 22425.1 + 22425.1i 0.844034 + 0.844034i 0.989381 0.145347i \(-0.0464299\pi\)
−0.145347 + 0.989381i \(0.546430\pi\)
\(164\) −7647.52 −0.284337
\(165\) −277.292 + 277.292i −0.0101852 + 0.0101852i
\(166\) 10713.7 + 10713.7i 0.388798 + 0.388798i
\(167\) 19640.7 19640.7i 0.704245 0.704245i −0.261074 0.965319i \(-0.584077\pi\)
0.965319 + 0.261074i \(0.0840767\pi\)
\(168\) −212.476 212.476i −0.00752821 0.00752821i
\(169\) 37527.2i 1.31393i
\(170\) −2828.84 + 2828.84i −0.0978839 + 0.0978839i
\(171\) 11041.1 11041.1i 0.377590 0.377590i
\(172\) −12077.0 12077.0i −0.408229 0.408229i
\(173\) 10214.2i 0.341281i −0.985333 0.170641i \(-0.945416\pi\)
0.985333 0.170641i \(-0.0545837\pi\)
\(174\) −1934.67 −0.0639010
\(175\) 10473.2i 0.341983i
\(176\) 8467.21i 0.273347i
\(177\) 1414.05 + 1414.05i 0.0451356 + 0.0451356i
\(178\) 25107.7i 0.792441i
\(179\) −19099.4 19099.4i −0.596092 0.596092i 0.343178 0.939270i \(-0.388497\pi\)
−0.939270 + 0.343178i \(0.888497\pi\)
\(180\) 1742.03 + 1742.03i 0.0537663 + 0.0537663i
\(181\) 34247.7 1.04538 0.522691 0.852522i \(-0.324928\pi\)
0.522691 + 0.852522i \(0.324928\pi\)
\(182\) 12477.4 0.376686
\(183\) 3169.86 3169.86i 0.0946537 0.0946537i
\(184\) 17387.5i 0.513571i
\(185\) 5223.11 461.995i 0.152611 0.0134988i
\(186\) 2579.10 0.0745491
\(187\) 34546.7 + 34546.7i 0.987923 + 0.987923i
\(188\) 24753.0i 0.700346i
\(189\) 2143.37i 0.0600030i
\(190\) −1487.69 + 1487.69i −0.0412103 + 0.0412103i
\(191\) −16792.2 + 16792.2i −0.460300 + 0.460300i −0.898754 0.438454i \(-0.855526\pi\)
0.438454 + 0.898754i \(0.355526\pi\)
\(192\) 396.228 0.0107484
\(193\) 22755.7 22755.7i 0.610907 0.610907i −0.332275 0.943183i \(-0.607816\pi\)
0.943183 + 0.332275i \(0.107816\pi\)
\(194\) −1723.69 −0.0457990
\(195\) 762.000 0.0200394
\(196\) 16852.3i 0.438679i
\(197\) −8512.13 −0.219334 −0.109667 0.993968i \(-0.534978\pi\)
−0.109667 + 0.993968i \(0.534978\pi\)
\(198\) 21274.2 21274.2i 0.542653 0.542653i
\(199\) −20588.3 20588.3i −0.519894 0.519894i 0.397645 0.917539i \(-0.369828\pi\)
−0.917539 + 0.397645i \(0.869828\pi\)
\(200\) 9765.28 + 9765.28i 0.244132 + 0.244132i
\(201\) −1900.52 −0.0470414
\(202\) −19476.6 + 19476.6i −0.477321 + 0.477321i
\(203\) 10724.7 + 10724.7i 0.260253 + 0.260253i
\(204\) −1616.63 + 1616.63i −0.0388464 + 0.0388464i
\(205\) 2589.01 + 2589.01i 0.0616064 + 0.0616064i
\(206\) 27220.5i 0.641448i
\(207\) 43686.6 43686.6i 1.01955 1.01955i
\(208\) −11633.9 + 11633.9i −0.268906 + 0.268906i
\(209\) 18168.1 + 18168.1i 0.415928 + 0.415928i
\(210\) 143.864i 0.00326223i
\(211\) −42994.6 −0.965715 −0.482857 0.875699i \(-0.660401\pi\)
−0.482857 + 0.875699i \(0.660401\pi\)
\(212\) 35277.0i 0.784911i
\(213\) 5174.98i 0.114064i
\(214\) 4256.59 + 4256.59i 0.0929468 + 0.0929468i
\(215\) 8177.18i 0.176900i
\(216\) 1998.49 + 1998.49i 0.0428345 + 0.0428345i
\(217\) −14297.1 14297.1i −0.303619 0.303619i
\(218\) 51152.6 1.07635
\(219\) 2511.47 0.0523647
\(220\) −2866.51 + 2866.51i −0.0592254 + 0.0592254i
\(221\) 94934.3i 1.94374i
\(222\) 2984.91 264.021i 0.0605655 0.00535714i
\(223\) −35757.6 −0.719048 −0.359524 0.933136i \(-0.617061\pi\)
−0.359524 + 0.933136i \(0.617061\pi\)
\(224\) −2196.47 2196.47i −0.0437753 0.0437753i
\(225\) 49071.2i 0.969307i
\(226\) 18603.3i 0.364228i
\(227\) −55139.5 + 55139.5i −1.07007 + 1.07007i −0.0727155 + 0.997353i \(0.523166\pi\)
−0.997353 + 0.0727155i \(0.976834\pi\)
\(228\) −850.189 + 850.189i −0.0163548 + 0.0163548i
\(229\) −72343.2 −1.37952 −0.689758 0.724040i \(-0.742283\pi\)
−0.689758 + 0.724040i \(0.742283\pi\)
\(230\) −5886.40 + 5886.40i −0.111274 + 0.111274i
\(231\) 1756.91 0.0329251
\(232\) −19999.6 −0.371574
\(233\) 73555.4i 1.35489i 0.735576 + 0.677443i \(0.236912\pi\)
−0.735576 + 0.677443i \(0.763088\pi\)
\(234\) −58461.4 −1.06767
\(235\) −8379.94 + 8379.94i −0.151742 + 0.151742i
\(236\) 14617.8 + 14617.8i 0.262456 + 0.262456i
\(237\) −1372.21 1372.21i −0.0244300 0.0244300i
\(238\) 17923.4 0.316423
\(239\) 2490.09 2490.09i 0.0435932 0.0435932i −0.684974 0.728567i \(-0.740187\pi\)
0.728567 + 0.684974i \(0.240187\pi\)
\(240\) −134.140 134.140i −0.00232882 0.00232882i
\(241\) −45627.5 + 45627.5i −0.785584 + 0.785584i −0.980767 0.195182i \(-0.937470\pi\)
0.195182 + 0.980767i \(0.437470\pi\)
\(242\) 5724.64 + 5724.64i 0.0977502 + 0.0977502i
\(243\) 15082.4i 0.255422i
\(244\) 32768.4 32768.4i 0.550396 0.550396i
\(245\) −5705.21 + 5705.21i −0.0950473 + 0.0950473i
\(246\) 1479.57 + 1479.57i 0.0244492 + 0.0244492i
\(247\) 49926.1i 0.818339i
\(248\) 26661.4 0.433491
\(249\) 4145.57i 0.0668630i
\(250\) 13382.8i 0.214124i
\(251\) −65129.8 65129.8i −1.03379 1.03379i −0.999409 0.0343813i \(-0.989054\pi\)
−0.0343813 0.999409i \(-0.510946\pi\)
\(252\) 11037.4i 0.173807i
\(253\) 71886.4 + 71886.4i 1.12307 + 1.12307i
\(254\) 54342.0 + 54342.0i 0.842302 + 0.842302i
\(255\) 1094.60 0.0168335
\(256\) 4096.00 0.0625000
\(257\) −72758.7 + 72758.7i −1.10159 + 1.10159i −0.107367 + 0.994220i \(0.534242\pi\)
−0.994220 + 0.107367i \(0.965758\pi\)
\(258\) 4673.10i 0.0702047i
\(259\) −18010.3 15083.1i −0.268486 0.224849i
\(260\) 7877.16 0.116526
\(261\) −50249.7 50249.7i −0.737654 0.737654i
\(262\) 36130.9i 0.526352i
\(263\) 50249.8i 0.726479i 0.931696 + 0.363240i \(0.118329\pi\)
−0.931696 + 0.363240i \(0.881671\pi\)
\(264\) −1638.16 + 1638.16i −0.0235043 + 0.0235043i
\(265\) 11942.8 11942.8i 0.170064 0.170064i
\(266\) 9425.97 0.133218
\(267\) 4857.60 4857.60i 0.0681395 0.0681395i
\(268\) −19646.6 −0.273538
\(269\) −101495. −1.40262 −0.701309 0.712857i \(-0.747401\pi\)
−0.701309 + 0.712857i \(0.747401\pi\)
\(270\) 1353.14i 0.0185617i
\(271\) 63036.3 0.858326 0.429163 0.903227i \(-0.358809\pi\)
0.429163 + 0.903227i \(0.358809\pi\)
\(272\) −16711.9 + 16711.9i −0.225885 + 0.225885i
\(273\) −2414.00 2414.00i −0.0323901 0.0323901i
\(274\) −21998.0 21998.0i −0.293010 0.293010i
\(275\) −80746.7 −1.06773
\(276\) −3363.96 + 3363.96i −0.0441604 + 0.0441604i
\(277\) 36728.4 + 36728.4i 0.478677 + 0.478677i 0.904708 0.426031i \(-0.140089\pi\)
−0.426031 + 0.904708i \(0.640089\pi\)
\(278\) 22471.0 22471.0i 0.290759 0.290759i
\(279\) 66987.7 + 66987.7i 0.860571 + 0.860571i
\(280\) 1487.20i 0.0189693i
\(281\) 86416.0 86416.0i 1.09441 1.09441i 0.0993620 0.995051i \(-0.468320\pi\)
0.995051 0.0993620i \(-0.0316802\pi\)
\(282\) −4788.98 + 4788.98i −0.0602205 + 0.0602205i
\(283\) 17514.8 + 17514.8i 0.218691 + 0.218691i 0.807947 0.589256i \(-0.200579\pi\)
−0.589256 + 0.807947i \(0.700579\pi\)
\(284\) 53496.3i 0.663265i
\(285\) 575.650 0.00708710
\(286\) 96198.2i 1.17608i
\(287\) 16403.9i 0.199151i
\(288\) 10291.3 + 10291.3i 0.124076 + 0.124076i
\(289\) 52850.0i 0.632775i
\(290\) 6770.71 + 6770.71i 0.0805079 + 0.0805079i
\(291\) 333.484 + 333.484i 0.00393812 + 0.00393812i
\(292\) 25962.3 0.304493
\(293\) 29076.8 0.338697 0.169349 0.985556i \(-0.445834\pi\)
0.169349 + 0.985556i \(0.445834\pi\)
\(294\) −3260.42 + 3260.42i −0.0377207 + 0.0377207i
\(295\) 9897.46i 0.113731i
\(296\) 30856.5 2729.32i 0.352178 0.0311509i
\(297\) −16525.0 −0.187339
\(298\) −8801.61 8801.61i −0.0991128 0.0991128i
\(299\) 197544.i 2.20964i
\(300\) 3778.59i 0.0419843i
\(301\) 25905.2 25905.2i 0.285926 0.285926i
\(302\) 64728.1 64728.1i 0.709707 0.709707i
\(303\) 7536.29 0.0820866
\(304\) −8788.82 + 8788.82i −0.0951006 + 0.0951006i
\(305\) −22187.0 −0.238505
\(306\) −83978.5 −0.896861
\(307\) 113505.i 1.20431i −0.798381 0.602153i \(-0.794310\pi\)
0.798381 0.602153i \(-0.205690\pi\)
\(308\) 18162.1 0.191454
\(309\) −5266.36 + 5266.36i −0.0551561 + 0.0551561i
\(310\) −9026.02 9026.02i −0.0939232 0.0939232i
\(311\) 121874. + 121874.i 1.26006 + 1.26006i 0.951063 + 0.308998i \(0.0999936\pi\)
0.308998 + 0.951063i \(0.400006\pi\)
\(312\) 4501.65 0.0462448
\(313\) −37218.8 + 37218.8i −0.379904 + 0.379904i −0.871067 0.491164i \(-0.836572\pi\)
0.491164 + 0.871067i \(0.336572\pi\)
\(314\) 11142.7 + 11142.7i 0.113014 + 0.113014i
\(315\) −3736.63 + 3736.63i −0.0376582 + 0.0376582i
\(316\) −14185.2 14185.2i −0.142057 0.142057i
\(317\) 11659.2i 0.116025i −0.998316 0.0580125i \(-0.981524\pi\)
0.998316 0.0580125i \(-0.0184763\pi\)
\(318\) 6825.07 6825.07i 0.0674921 0.0674921i
\(319\) 82686.0 82686.0i 0.812551 0.812551i
\(320\) −1386.67 1386.67i −0.0135417 0.0135417i
\(321\) 1647.05i 0.0159844i
\(322\) 37296.0 0.359708
\(323\) 71717.7i 0.687419i
\(324\) 51326.6i 0.488937i
\(325\) 110946. + 110946.i 1.05038 + 1.05038i
\(326\) 89700.5i 0.844034i
\(327\) −9896.52 9896.52i −0.0925522 0.0925522i
\(328\) 15295.0 + 15295.0i 0.142168 + 0.142168i
\(329\) 53095.0 0.490526
\(330\) 1109.17 0.0101852
\(331\) −73581.9 + 73581.9i −0.671607 + 0.671607i −0.958086 0.286480i \(-0.907515\pi\)
0.286480 + 0.958086i \(0.407515\pi\)
\(332\) 42854.8i 0.388798i
\(333\) 84385.4 + 70670.4i 0.760990 + 0.637308i
\(334\) −78562.7 −0.704245
\(335\) 6651.20 + 6651.20i 0.0592667 + 0.0592667i
\(336\) 849.905i 0.00752821i
\(337\) 157334.i 1.38536i −0.721243 0.692682i \(-0.756429\pi\)
0.721243 0.692682i \(-0.243571\pi\)
\(338\) −75054.4 + 75054.4i −0.656966 + 0.656966i
\(339\) 3599.19 3599.19i 0.0313188 0.0313188i
\(340\) 11315.4 0.0978839
\(341\) −110228. + 110228.i −0.947949 + 0.947949i
\(342\) −44164.4 −0.377590
\(343\) 77349.0 0.657456
\(344\) 48308.2i 0.408229i
\(345\) 2277.69 0.0191362
\(346\) −20428.4 + 20428.4i −0.170641 + 0.170641i
\(347\) −129822. 129822.i −1.07817 1.07817i −0.996673 0.0815002i \(-0.974029\pi\)
−0.0815002 0.996673i \(-0.525971\pi\)
\(348\) 3869.34 + 3869.34i 0.0319505 + 0.0319505i
\(349\) 81437.9 0.668615 0.334307 0.942464i \(-0.391498\pi\)
0.334307 + 0.942464i \(0.391498\pi\)
\(350\) −20946.4 + 20946.4i −0.170991 + 0.170991i
\(351\) 22705.4 + 22705.4i 0.184295 + 0.184295i
\(352\) −16934.4 + 16934.4i −0.136674 + 0.136674i
\(353\) 115990. + 115990.i 0.930829 + 0.930829i 0.997758 0.0669291i \(-0.0213201\pi\)
−0.0669291 + 0.997758i \(0.521320\pi\)
\(354\) 5656.21i 0.0451356i
\(355\) 18110.8 18110.8i 0.143708 0.143708i
\(356\) 50215.4 50215.4i 0.396220 0.396220i
\(357\) −3467.66 3467.66i −0.0272082 0.0272082i
\(358\) 76397.6i 0.596092i
\(359\) 92091.4 0.714546 0.357273 0.934000i \(-0.383707\pi\)
0.357273 + 0.934000i \(0.383707\pi\)
\(360\) 6968.11i 0.0537663i
\(361\) 92604.5i 0.710588i
\(362\) −68495.5 68495.5i −0.522691 0.522691i
\(363\) 2215.10i 0.0168105i
\(364\) −24954.7 24954.7i −0.188343 0.188343i
\(365\) −8789.32 8789.32i −0.0659735 0.0659735i
\(366\) −12679.4 −0.0946537
\(367\) 244475. 1.81511 0.907553 0.419937i \(-0.137948\pi\)
0.907553 + 0.419937i \(0.137948\pi\)
\(368\) −34774.9 + 34774.9i −0.256786 + 0.256786i
\(369\) 76858.7i 0.564469i
\(370\) −11370.2 9522.23i −0.0830548 0.0695561i
\(371\) −75668.9 −0.549756
\(372\) −5158.20 5158.20i −0.0372745 0.0372745i
\(373\) 219454.i 1.57735i 0.614813 + 0.788673i \(0.289231\pi\)
−0.614813 + 0.788673i \(0.710769\pi\)
\(374\) 138187.i 0.987923i
\(375\) −2589.17 + 2589.17i −0.0184119 + 0.0184119i
\(376\) −49506.0 + 49506.0i −0.350173 + 0.350173i
\(377\) −227221. −1.59870
\(378\) −4286.74 + 4286.74i −0.0300015 + 0.0300015i
\(379\) −198641. −1.38290 −0.691450 0.722424i \(-0.743028\pi\)
−0.691450 + 0.722424i \(0.743028\pi\)
\(380\) 5950.77 0.0412103
\(381\) 21027.1i 0.144854i
\(382\) 67168.7 0.460300
\(383\) 67016.0 67016.0i 0.456858 0.456858i −0.440765 0.897623i \(-0.645293\pi\)
0.897623 + 0.440765i \(0.145293\pi\)
\(384\) −792.455 792.455i −0.00537418 0.00537418i
\(385\) −6148.63 6148.63i −0.0414818 0.0414818i
\(386\) −91022.8 −0.610907
\(387\) −121376. + 121376.i −0.810421 + 0.810421i
\(388\) 3447.38 + 3447.38i 0.0228995 + 0.0228995i
\(389\) −133025. + 133025.i −0.879092 + 0.879092i −0.993441 0.114348i \(-0.963522\pi\)
0.114348 + 0.993441i \(0.463522\pi\)
\(390\) −1524.00 1524.00i −0.0100197 0.0100197i
\(391\) 283767.i 1.85613i
\(392\) −33704.6 + 33704.6i −0.219340 + 0.219340i
\(393\) 6990.26 6990.26i 0.0452594 0.0452594i
\(394\) 17024.3 + 17024.3i 0.109667 + 0.109667i
\(395\) 9604.59i 0.0615580i
\(396\) −85096.6 −0.542653
\(397\) 136809.i 0.868029i −0.900906 0.434015i \(-0.857097\pi\)
0.900906 0.434015i \(-0.142903\pi\)
\(398\) 82353.3i 0.519894i
\(399\) −1823.65 1823.65i −0.0114550 0.0114550i
\(400\) 39061.1i 0.244132i
\(401\) −106536. 106536.i −0.662534 0.662534i 0.293443 0.955977i \(-0.405199\pi\)
−0.955977 + 0.293443i \(0.905199\pi\)
\(402\) 3801.04 + 3801.04i 0.0235207 + 0.0235207i
\(403\) 302908. 1.86509
\(404\) 77906.4 0.477321
\(405\) 17376.2 17376.2i 0.105936 0.105936i
\(406\) 42899.0i 0.260253i
\(407\) −116288. + 138856.i −0.702016 + 0.838256i
\(408\) 6466.52 0.0388464
\(409\) 61457.4 + 61457.4i 0.367390 + 0.367390i 0.866525 0.499134i \(-0.166349\pi\)
−0.499134 + 0.866525i \(0.666349\pi\)
\(410\) 10356.0i 0.0616064i
\(411\) 8511.93i 0.0503900i
\(412\) −54441.0 + 54441.0i −0.320724 + 0.320724i
\(413\) −31355.0 + 31355.0i −0.183826 + 0.183826i
\(414\) −174747. −1.01955
\(415\) −14508.2 + 14508.2i −0.0842396 + 0.0842396i
\(416\) 46535.8 0.268906
\(417\) −8694.97 −0.0500030
\(418\) 72672.6i 0.415928i
\(419\) 137264. 0.781857 0.390929 0.920421i \(-0.372154\pi\)
0.390929 + 0.920421i \(0.372154\pi\)
\(420\) 287.729 287.729i 0.00163112 0.00163112i
\(421\) −70605.1 70605.1i −0.398357 0.398357i 0.479296 0.877653i \(-0.340892\pi\)
−0.877653 + 0.479296i \(0.840892\pi\)
\(422\) 85989.2 + 85989.2i 0.482857 + 0.482857i
\(423\) −248771. −1.39033
\(424\) 70554.1 70554.1i 0.392455 0.392455i
\(425\) 159371. + 159371.i 0.882333 + 0.882333i
\(426\) 10350.0 10350.0i 0.0570321 0.0570321i
\(427\) 70287.9 + 70287.9i 0.385500 + 0.385500i
\(428\) 17026.4i 0.0929468i
\(429\) −18611.5 + 18611.5i −0.101127 + 0.101127i
\(430\) 16354.4 16354.4i 0.0884498 0.0884498i
\(431\) −167786. 167786.i −0.903236 0.903236i 0.0924783 0.995715i \(-0.470521\pi\)
−0.995715 + 0.0924783i \(0.970521\pi\)
\(432\) 7993.95i 0.0428345i
\(433\) 181141. 0.966143 0.483071 0.875581i \(-0.339521\pi\)
0.483071 + 0.875581i \(0.339521\pi\)
\(434\) 57188.5i 0.303619i
\(435\) 2619.87i 0.0138452i
\(436\) −102305. 102305.i −0.538176 0.538176i
\(437\) 149234.i 0.781455i
\(438\) −5022.93 5022.93i −0.0261824 0.0261824i
\(439\) 61395.2 + 61395.2i 0.318570 + 0.318570i 0.848218 0.529648i \(-0.177676\pi\)
−0.529648 + 0.848218i \(0.677676\pi\)
\(440\) 11466.0 0.0592254
\(441\) −169368. −0.870871
\(442\) −189869. + 189869.i −0.971871 + 0.971871i
\(443\) 33042.7i 0.168372i −0.996450 0.0841858i \(-0.973171\pi\)
0.996450 0.0841858i \(-0.0268289\pi\)
\(444\) −6497.86 5441.77i −0.0329613 0.0276042i
\(445\) −34000.1 −0.171696
\(446\) 71515.1 + 71515.1i 0.359524 + 0.359524i
\(447\) 3405.71i 0.0170448i
\(448\) 8785.88i 0.0437753i
\(449\) −1694.29 + 1694.29i −0.00840419 + 0.00840419i −0.711296 0.702892i \(-0.751892\pi\)
0.702892 + 0.711296i \(0.251892\pi\)
\(450\) 98142.4 98142.4i 0.484654 0.484654i
\(451\) −126471. −0.621782
\(452\) 37206.6 37206.6i 0.182114 0.182114i
\(453\) −25046.0 −0.122051
\(454\) 220558. 1.07007
\(455\) 16896.4i 0.0816155i
\(456\) 3400.75 0.0163548
\(457\) −90594.5 + 90594.5i −0.433780 + 0.433780i −0.889912 0.456132i \(-0.849234\pi\)
0.456132 + 0.889912i \(0.349234\pi\)
\(458\) 144686. + 144686.i 0.689758 + 0.689758i
\(459\) 32615.7 + 32615.7i 0.154811 + 0.154811i
\(460\) 23545.6 0.111274
\(461\) 73442.7 73442.7i 0.345579 0.345579i −0.512881 0.858460i \(-0.671422\pi\)
0.858460 + 0.512881i \(0.171422\pi\)
\(462\) −3513.83 3513.83i −0.0164625 0.0164625i
\(463\) −120453. + 120453.i −0.561896 + 0.561896i −0.929846 0.367949i \(-0.880060\pi\)
0.367949 + 0.929846i \(0.380060\pi\)
\(464\) 39999.2 + 39999.2i 0.185787 + 0.185787i
\(465\) 3492.54i 0.0161523i
\(466\) 147111. 147111.i 0.677443 0.677443i
\(467\) −39866.8 + 39866.8i −0.182801 + 0.182801i −0.792575 0.609774i \(-0.791260\pi\)
0.609774 + 0.792575i \(0.291260\pi\)
\(468\) 116923. + 116923.i 0.533835 + 0.533835i
\(469\) 42141.8i 0.191587i
\(470\) 33519.8 0.151742
\(471\) 4311.57i 0.0194354i
\(472\) 58471.0i 0.262456i
\(473\) −199724. 199724.i −0.892706 0.892706i
\(474\) 5488.84i 0.0244300i
\(475\) 83813.7 + 83813.7i 0.371473 + 0.371473i
\(476\) −35846.9 35846.9i −0.158211 0.158211i
\(477\) 354539. 1.55821
\(478\) −9960.35 −0.0435932
\(479\) −23910.7 + 23910.7i −0.104213 + 0.104213i −0.757291 0.653078i \(-0.773477\pi\)
0.653078 + 0.757291i \(0.273477\pi\)
\(480\) 536.559i 0.00232882i
\(481\) 350569. 31008.5i 1.51525 0.134027i
\(482\) 182510. 0.785584
\(483\) −7215.67 7215.67i −0.0309302 0.0309302i
\(484\) 22898.6i 0.0977502i
\(485\) 2334.17i 0.00992314i
\(486\) 30164.9 30164.9i 0.127711 0.127711i
\(487\) 293325. 293325.i 1.23678 1.23678i 0.275464 0.961311i \(-0.411168\pi\)
0.961311 0.275464i \(-0.0888316\pi\)
\(488\) −131074. −0.550396
\(489\) −17354.4 + 17354.4i −0.0725758 + 0.0725758i
\(490\) 22820.9 0.0950473
\(491\) −300745. −1.24748 −0.623742 0.781630i \(-0.714388\pi\)
−0.623742 + 0.781630i \(0.714388\pi\)
\(492\) 5918.28i 0.0244492i
\(493\) −326398. −1.34293
\(494\) −99852.1 + 99852.1i −0.409170 + 0.409170i
\(495\) 28808.8 + 28808.8i 0.117575 + 0.117575i
\(496\) −53322.8 53322.8i −0.216745 0.216745i
\(497\) −114749. −0.464554
\(498\) −8291.15 + 8291.15i −0.0334315 + 0.0334315i
\(499\) −139954. 139954.i −0.562061 0.562061i 0.367832 0.929892i \(-0.380100\pi\)
−0.929892 + 0.367832i \(0.880100\pi\)
\(500\) −26765.5 + 26765.5i −0.107062 + 0.107062i
\(501\) 15199.6 + 15199.6i 0.0605558 + 0.0605558i
\(502\) 260519.i 1.03379i
\(503\) 304523. 304523.i 1.20360 1.20360i 0.230542 0.973062i \(-0.425950\pi\)
0.973062 0.230542i \(-0.0740499\pi\)
\(504\) −22074.8 + 22074.8i −0.0869033 + 0.0869033i
\(505\) −26374.6 26374.6i −0.103420 0.103420i
\(506\) 287546.i 1.12307i
\(507\) 29041.6 0.112981
\(508\) 217368.i 0.842302i
\(509\) 427098.i 1.64851i 0.566217 + 0.824256i \(0.308406\pi\)
−0.566217 + 0.824256i \(0.691594\pi\)
\(510\) −2189.19 2189.19i −0.00841673 0.00841673i
\(511\) 55688.8i 0.213268i
\(512\) −8192.00 8192.00i −0.0312500 0.0312500i
\(513\) 17152.7 + 17152.7i 0.0651774 + 0.0651774i
\(514\) 291035. 1.10159
\(515\) 36861.2 0.138981
\(516\) 9346.21 9346.21i 0.0351023 0.0351023i
\(517\) 409353.i 1.53150i
\(518\) 5854.37 + 66186.8i 0.0218183 + 0.246668i
\(519\) 7904.59 0.0293457
\(520\) −15754.3 15754.3i −0.0582630 0.0582630i
\(521\) 310162.i 1.14265i 0.820723 + 0.571326i \(0.193571\pi\)
−0.820723 + 0.571326i \(0.806429\pi\)
\(522\) 200999.i 0.737654i
\(523\) −296372. + 296372.i −1.08351 + 1.08351i −0.0873340 + 0.996179i \(0.527835\pi\)
−0.996179 + 0.0873340i \(0.972165\pi\)
\(524\) 72261.8 72261.8i 0.263176 0.263176i
\(525\) 8105.04 0.0294060
\(526\) 100500. 100500.i 0.363240 0.363240i
\(527\) 435120. 1.56671
\(528\) 6552.62 0.0235043
\(529\) 310636.i 1.11004i
\(530\) −47771.1 −0.170064
\(531\) 146911. 146911.i 0.521031 0.521031i
\(532\) −18851.9 18851.9i −0.0666090 0.0666090i
\(533\) 173771. + 173771.i 0.611679 + 0.611679i
\(534\) −19430.4 −0.0681395
\(535\) −5764.14 + 5764.14i −0.0201385 + 0.0201385i
\(536\) 39293.2 + 39293.2i 0.136769 + 0.136769i
\(537\) 14780.7 14780.7i 0.0512561 0.0512561i
\(538\) 202990. + 202990.i 0.701309 + 0.701309i
\(539\) 278695.i 0.959294i
\(540\) −2706.29 + 2706.29i −0.00928083 + 0.00928083i
\(541\) 10908.2 10908.2i 0.0372699 0.0372699i −0.688226 0.725496i \(-0.741610\pi\)
0.725496 + 0.688226i \(0.241610\pi\)
\(542\) −126073. 126073.i −0.429163 0.429163i
\(543\) 26503.7i 0.0898891i
\(544\) 66847.6 0.225885
\(545\) 69269.2i 0.233210i
\(546\) 9656.00i 0.0323901i
\(547\) −296475. 296475.i −0.990863 0.990863i 0.00909537 0.999959i \(-0.497105\pi\)
−0.999959 + 0.00909537i \(0.997105\pi\)
\(548\) 87992.0i 0.293010i
\(549\) −329327. 329327.i −1.09265 1.09265i
\(550\) 161493. + 161493.i 0.533863 + 0.533863i
\(551\) −171653. −0.565391
\(552\) 13455.9 0.0441604
\(553\) 30427.2 30427.2i 0.0994973 0.0994973i
\(554\) 146914.i 0.478677i
\(555\) 357.530 + 4042.07i 0.00116072 + 0.0131225i
\(556\) −89884.1 −0.290759
\(557\) −83744.8 83744.8i −0.269928 0.269928i 0.559143 0.829071i \(-0.311130\pi\)
−0.829071 + 0.559143i \(0.811130\pi\)
\(558\) 267951.i 0.860571i
\(559\) 548842.i 1.75640i
\(560\) 2974.39 2974.39i 0.00948467 0.00948467i
\(561\) −26735.1 + 26735.1i −0.0849484 + 0.0849484i
\(562\) −345664. −1.09441
\(563\) −301225. + 301225.i −0.950330 + 0.950330i −0.998824 0.0484933i \(-0.984558\pi\)
0.0484933 + 0.998824i \(0.484558\pi\)
\(564\) 19155.9 0.0602205
\(565\) −25192.0 −0.0789162
\(566\) 70059.0i 0.218691i
\(567\) −110095. −0.342454
\(568\) 106993. 106993.i 0.331633 0.331633i
\(569\) −36629.3 36629.3i −0.113137 0.113137i 0.648272 0.761409i \(-0.275492\pi\)
−0.761409 + 0.648272i \(0.775492\pi\)
\(570\) −1151.30 1151.30i −0.00354355 0.00354355i
\(571\) −316415. −0.970476 −0.485238 0.874382i \(-0.661267\pi\)
−0.485238 + 0.874382i \(0.661267\pi\)
\(572\) −192396. + 192396.i −0.588038 + 0.588038i
\(573\) −12995.2 12995.2i −0.0395797 0.0395797i
\(574\) −32807.7 + 32807.7i −0.0995755 + 0.0995755i
\(575\) 331628. + 331628.i 1.00303 + 1.00303i
\(576\) 41165.4i 0.124076i
\(577\) 376706. 376706.i 1.13149 1.13149i 0.141562 0.989929i \(-0.454788\pi\)
0.989929 0.141562i \(-0.0452124\pi\)
\(578\) −105700. + 105700.i −0.316388 + 0.316388i
\(579\) 17610.2 + 17610.2i 0.0525300 + 0.0525300i
\(580\) 27082.9i 0.0805079i
\(581\) 91923.2 0.272316
\(582\) 1333.93i 0.00393812i
\(583\) 583394.i 1.71643i
\(584\) −51924.5 51924.5i −0.152246 0.152246i
\(585\) 79166.6i 0.231329i
\(586\) −58153.7 58153.7i −0.169349 0.169349i
\(587\) −78641.6 78641.6i −0.228232 0.228232i 0.583722 0.811954i \(-0.301596\pi\)
−0.811954 + 0.583722i \(0.801596\pi\)
\(588\) 13041.7 0.0377207
\(589\) 228830. 0.659604
\(590\) −19794.9 + 19794.9i −0.0568656 + 0.0568656i
\(591\) 6587.38i 0.0188598i
\(592\) −67171.6 56254.3i −0.191665 0.160514i
\(593\) 30267.7 0.0860736 0.0430368 0.999073i \(-0.486297\pi\)
0.0430368 + 0.999073i \(0.486297\pi\)
\(594\) 33050.0 + 33050.0i 0.0936696 + 0.0936696i
\(595\) 24271.4i 0.0685584i
\(596\) 35206.5i 0.0991128i
\(597\) 15932.9 15932.9i 0.0447041 0.0447041i
\(598\) −395088. + 395088.i −1.10482 + 1.10482i
\(599\) 103433. 0.288273 0.144137 0.989558i \(-0.453960\pi\)
0.144137 + 0.989558i \(0.453960\pi\)
\(600\) −7557.17 + 7557.17i −0.0209921 + 0.0209921i
\(601\) −322765. −0.893589 −0.446795 0.894637i \(-0.647435\pi\)
−0.446795 + 0.894637i \(0.647435\pi\)
\(602\) −103621. −0.285926
\(603\) 197451.i 0.543031i
\(604\) −258912. −0.709707
\(605\) −7752.13 + 7752.13i −0.0211792 + 0.0211792i
\(606\) −15072.6 15072.6i −0.0410433 0.0410433i
\(607\) 90515.7 + 90515.7i 0.245667 + 0.245667i 0.819190 0.573523i \(-0.194424\pi\)
−0.573523 + 0.819190i \(0.694424\pi\)
\(608\) 35155.3 0.0951006
\(609\) −8299.69 + 8299.69i −0.0223783 + 0.0223783i
\(610\) 44373.9 + 44373.9i 0.119253 + 0.119253i
\(611\) −562451. + 562451.i −1.50662 + 1.50662i
\(612\) 167957. + 167957.i 0.448431 + 0.448431i
\(613\) 461596.i 1.22840i −0.789149 0.614201i \(-0.789478\pi\)
0.789149 0.614201i \(-0.210522\pi\)
\(614\) −227009. + 227009.i −0.602153 + 0.602153i
\(615\) −2003.59 + 2003.59i −0.00529735 + 0.00529735i
\(616\) −36324.2 36324.2i −0.0957270 0.0957270i
\(617\) 145059.i 0.381043i 0.981683 + 0.190522i \(0.0610179\pi\)
−0.981683 + 0.190522i \(0.938982\pi\)
\(618\) 21065.5 0.0551561
\(619\) 353899.i 0.923629i −0.886977 0.461814i \(-0.847199\pi\)
0.886977 0.461814i \(-0.152801\pi\)
\(620\) 36104.1i 0.0939232i
\(621\) 67868.4 + 67868.4i 0.175989 + 0.175989i
\(622\) 487497.i 1.26006i
\(623\) 107712. + 107712.i 0.277515 + 0.277515i
\(624\) −9003.30 9003.30i −0.0231224 0.0231224i
\(625\) −363334. −0.930134
\(626\) 148875. 0.379904
\(627\) −14060.0 + 14060.0i −0.0357644 + 0.0357644i
\(628\) 44570.8i 0.113014i
\(629\) 503584. 44543.1i 1.27283 0.112585i
\(630\) 14946.5 0.0376582
\(631\) 318155. + 318155.i 0.799060 + 0.799060i 0.982947 0.183887i \(-0.0588681\pi\)
−0.183887 + 0.982947i \(0.558868\pi\)
\(632\) 56740.9i 0.142057i
\(633\) 33272.7i 0.0830388i
\(634\) −23318.5 + 23318.5i −0.0580125 + 0.0580125i
\(635\) −73588.2 + 73588.2i −0.182499 + 0.182499i
\(636\) −27300.3 −0.0674921
\(637\) −382927. + 382927.i −0.943707 + 0.943707i
\(638\) −330744. −0.812551
\(639\) 537645. 1.31672
\(640\) 5546.68i 0.0135417i
\(641\) 57302.6 0.139463 0.0697313 0.997566i \(-0.477786\pi\)
0.0697313 + 0.997566i \(0.477786\pi\)
\(642\) −3294.10 + 3294.10i −0.00799221 + 0.00799221i
\(643\) 313472. + 313472.i 0.758188 + 0.758188i 0.975992 0.217805i \(-0.0698895\pi\)
−0.217805 + 0.975992i \(0.569890\pi\)
\(644\) −74592.0 74592.0i −0.179854 0.179854i
\(645\) −6328.17 −0.0152110
\(646\) −143435. + 143435.i −0.343709 + 0.343709i
\(647\) 246187. + 246187.i 0.588108 + 0.588108i 0.937119 0.349011i \(-0.113482\pi\)
−0.349011 + 0.937119i \(0.613482\pi\)
\(648\) 102653. 102653.i 0.244468 0.244468i
\(649\) 241741. + 241741.i 0.573934 + 0.573934i
\(650\) 443784.i 1.05038i
\(651\) 11064.3 11064.3i 0.0261073 0.0261073i
\(652\) −179401. + 179401.i −0.422017 + 0.422017i
\(653\) −114939. 114939.i −0.269550 0.269550i 0.559369 0.828919i \(-0.311044\pi\)
−0.828919 + 0.559369i \(0.811044\pi\)
\(654\) 39586.1i 0.0925522i
\(655\) −48927.3 −0.114043
\(656\) 61180.2i 0.142168i
\(657\) 260924.i 0.604482i
\(658\) −106190. 106190.i −0.245263 0.245263i
\(659\) 603251.i 1.38908i −0.719454 0.694540i \(-0.755608\pi\)
0.719454 0.694540i \(-0.244392\pi\)
\(660\) −2218.34 2218.34i −0.00509261 0.00509261i
\(661\) 147885. + 147885.i 0.338471 + 0.338471i 0.855792 0.517320i \(-0.173070\pi\)
−0.517320 + 0.855792i \(0.673070\pi\)
\(662\) 294328. 0.671607
\(663\) 73467.9 0.167136
\(664\) −85709.7 + 85709.7i −0.194399 + 0.194399i
\(665\) 12764.4i 0.0288639i
\(666\) −27430.0 310112.i −0.0618412 0.699149i
\(667\) −679185. −1.52664
\(668\) 157125. + 157125.i 0.352122 + 0.352122i
\(669\) 27672.1i 0.0618288i
\(670\) 26604.8i 0.0592667i
\(671\) 541908. 541908.i 1.20359 1.20359i
\(672\) 1699.81 1699.81i 0.00376411 0.00376411i
\(673\) −338568. −0.747509 −0.373754 0.927528i \(-0.621930\pi\)
−0.373754 + 0.927528i \(0.621930\pi\)
\(674\) −314669. + 314669.i −0.692682 + 0.692682i
\(675\) −76233.5 −0.167316
\(676\) 300218. 0.656966
\(677\) 545608.i 1.19043i −0.803567 0.595214i \(-0.797067\pi\)
0.803567 0.595214i \(-0.202933\pi\)
\(678\) −14396.8 −0.0313188
\(679\) −7394.61 + 7394.61i −0.0160389 + 0.0160389i
\(680\) −22630.7 22630.7i −0.0489419 0.0489419i
\(681\) −42671.5 42671.5i −0.0920119 0.0920119i
\(682\) 440914. 0.947949
\(683\) 347489. 347489.i 0.744903 0.744903i −0.228614 0.973517i \(-0.573419\pi\)
0.973517 + 0.228614i \(0.0734194\pi\)
\(684\) 88328.8 + 88328.8i 0.188795 + 0.188795i
\(685\) 29789.0 29789.0i 0.0634855 0.0634855i
\(686\) −154698. 154698.i −0.328728 0.328728i
\(687\) 55985.1i 0.118620i
\(688\) 96616.4 96616.4i 0.204114 0.204114i
\(689\) 801584. 801584.i 1.68854 1.68854i
\(690\) −4555.38 4555.38i −0.00956811 0.00956811i
\(691\) 432975.i 0.906790i −0.891310 0.453395i \(-0.850213\pi\)
0.891310 0.453395i \(-0.149787\pi\)
\(692\) 81713.7 0.170641
\(693\) 182531.i 0.380077i
\(694\) 519287.i 1.07817i
\(695\) 30429.6 + 30429.6i 0.0629979 + 0.0629979i
\(696\) 15477.3i 0.0319505i
\(697\) 249619. + 249619.i 0.513820 + 0.513820i
\(698\) −162876. 162876.i −0.334307 0.334307i
\(699\) −56923.2 −0.116502
\(700\) 83785.7 0.170991
\(701\) −485929. + 485929.i −0.988864 + 0.988864i −0.999939 0.0110742i \(-0.996475\pi\)
0.0110742 + 0.999939i \(0.496475\pi\)
\(702\) 90821.4i 0.184295i
\(703\) 264836. 23425.3i 0.535878 0.0473995i
\(704\) 67737.7 0.136674
\(705\) −6485.09 6485.09i −0.0130478 0.0130478i
\(706\) 463959.i 0.930829i
\(707\) 167108.i 0.334318i
\(708\) −11312.4 + 11312.4i −0.0225678 + 0.0225678i
\(709\) −81885.6 + 81885.6i −0.162898 + 0.162898i −0.783849 0.620951i \(-0.786746\pi\)
0.620951 + 0.783849i \(0.286746\pi\)
\(710\) −72443.0 −0.143708
\(711\) −142563. + 142563.i −0.282013 + 0.282013i
\(712\) −200862. −0.396220
\(713\) 905419. 1.78103
\(714\) 13870.6i 0.0272082i
\(715\) 130269. 0.254817
\(716\) 152795. 152795.i 0.298046 0.298046i
\(717\) 1927.03 + 1927.03i 0.00374844 + 0.00374844i
\(718\) −184183. 184183.i −0.357273 0.357273i
\(719\) −430384. −0.832526 −0.416263 0.909244i \(-0.636661\pi\)
−0.416263 + 0.909244i \(0.636661\pi\)
\(720\) −13936.2 + 13936.2i −0.0268831 + 0.0268831i
\(721\) −116775. 116775.i −0.224637 0.224637i
\(722\) 185209. 185209.i 0.355294 0.355294i
\(723\) −35310.3 35310.3i −0.0675500 0.0675500i
\(724\) 273982.i 0.522691i
\(725\) 381449. 381449.i 0.725705 0.725705i
\(726\) −4430.20 + 4430.20i −0.00840524 + 0.00840524i
\(727\) −115270. 115270.i −0.218095 0.218095i 0.589600 0.807695i \(-0.299285\pi\)
−0.807695 + 0.589600i \(0.799285\pi\)
\(728\) 99818.8i 0.188343i
\(729\) 508010. 0.955910
\(730\) 35157.3i 0.0659735i
\(731\) 788400.i 1.47541i
\(732\) 25358.9 + 25358.9i 0.0473269 + 0.0473269i
\(733\) 514933.i 0.958391i −0.877708 0.479196i \(-0.840928\pi\)
0.877708 0.479196i \(-0.159072\pi\)
\(734\) −488950. 488950.i −0.907553 0.907553i
\(735\) −4415.16 4415.16i −0.00817282 0.00817282i
\(736\) 139100. 0.256786
\(737\) −324906. −0.598167
\(738\) 153717. 153717.i 0.282235 0.282235i
\(739\) 970067.i 1.77629i 0.459567 + 0.888143i \(0.348005\pi\)
−0.459567 + 0.888143i \(0.651995\pi\)
\(740\) 3695.96 + 41784.9i 0.00674938 + 0.0763055i
\(741\) 38636.9 0.0703665
\(742\) 151338. + 151338.i 0.274878 + 0.274878i
\(743\) 108671.i 0.196851i −0.995144 0.0984255i \(-0.968619\pi\)
0.995144 0.0984255i \(-0.0313806\pi\)
\(744\) 20632.8i 0.0372745i
\(745\) 11918.9 11918.9i 0.0214745 0.0214745i
\(746\) 438909. 438909.i 0.788673 0.788673i
\(747\) −430697. −0.771846
\(748\) −276373. + 276373.i −0.493961 + 0.493961i
\(749\) 36521.4 0.0651004
\(750\) 10356.7 0.0184119
\(751\) 372158.i 0.659853i −0.944007 0.329927i \(-0.892976\pi\)
0.944007 0.329927i \(-0.107024\pi\)
\(752\) 198024. 0.350173
\(753\) 50402.8 50402.8i 0.0888924 0.0888924i
\(754\) 454442. + 454442.i 0.799348 + 0.799348i
\(755\) 87652.8 + 87652.8i 0.153770 + 0.153770i
\(756\) 17146.9 0.0300015
\(757\) −267014. + 267014.i −0.465953 + 0.465953i −0.900600 0.434648i \(-0.856873\pi\)
0.434648 + 0.900600i \(0.356873\pi\)
\(758\) 397282. + 397282.i 0.691450 + 0.691450i
\(759\) −55631.6 + 55631.6i −0.0965691 + 0.0965691i
\(760\) −11901.5 11901.5i −0.0206052 0.0206052i
\(761\) 275812.i 0.476260i 0.971233 + 0.238130i \(0.0765345\pi\)
−0.971233 + 0.238130i \(0.923466\pi\)
\(762\) −42054.3 + 42054.3i −0.0724270 + 0.0724270i
\(763\) 219444. 219444.i 0.376942 0.376942i
\(764\) −134337. 134337.i −0.230150 0.230150i
\(765\) 113721.i 0.194320i
\(766\) −268064. −0.456858
\(767\) 664305.i 1.12922i
\(768\) 3169.82i 0.00537418i
\(769\) −352671. 352671.i −0.596372 0.596372i 0.342974 0.939345i \(-0.388566\pi\)
−0.939345 + 0.342974i \(0.888566\pi\)
\(770\) 24594.5i 0.0414818i
\(771\) −56306.6 56306.6i −0.0947220 0.0947220i
\(772\) 182046. + 182046.i 0.305454 + 0.305454i
\(773\) −294289. −0.492511 −0.246255 0.969205i \(-0.579200\pi\)
−0.246255 + 0.969205i \(0.579200\pi\)
\(774\) 485504. 0.810421