Properties

Label 74.5.d.a.43.3
Level $74$
Weight $5$
Character 74.43
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 43.3
Root \(-1.77388i\) of defining polynomial
Character \(\chi\) \(=\) 74.43
Dual form 74.5.d.a.31.5

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 28q^{2} - 12q^{5} - 40q^{6} + 48q^{7} + 224q^{8} - 346q^{9} + O(q^{10}) \) \( 14q - 28q^{2} - 12q^{5} - 40q^{6} + 48q^{7} + 224q^{8} - 346q^{9} + 48q^{10} + 160q^{12} - 56q^{13} - 96q^{14} - 378q^{15} - 896q^{16} - 348q^{17} + 692q^{18} - 184q^{19} - 96q^{20} - 320q^{22} - 502q^{23} - 320q^{24} + 224q^{26} - 474q^{29} - 630q^{31} + 1792q^{32} + 632q^{33} + 1392q^{34} + 1826q^{35} - 2544q^{37} + 736q^{38} - 798q^{39} - 224q^{42} + 1936q^{43} + 1280q^{44} + 6162q^{45} + 2008q^{46} + 5716q^{47} + 7862q^{49} - 1372q^{50} - 2422q^{51} - 448q^{52} - 20228q^{53} - 656q^{54} + 14006q^{55} + 768q^{56} - 2270q^{57} - 4502q^{59} + 3024q^{60} - 11906q^{61} - 2588q^{63} - 1264q^{66} - 2784q^{68} + 21440q^{69} - 7304q^{70} - 11224q^{71} - 5536q^{72} + 4924q^{74} - 18652q^{75} - 1472q^{76} + 20488q^{79} + 768q^{80} - 1706q^{81} + 9808q^{82} - 20224q^{83} + 896q^{84} - 7744q^{86} + 19636q^{87} - 2560q^{88} + 13864q^{89} - 24648q^{90} - 6070q^{91} - 4016q^{92} - 13800q^{93} - 11432q^{94} + 2560q^{96} + 16622q^{97} - 15724q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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 \(-0.986311\pi\)
0.999075 0.0429935i \(-0.0136895\pi\)
\(4\) 8.00000i 0.500000i
\(5\) 2.70834 + 2.70834i 0.108334 + 0.108334i 0.759196 0.650862i \(-0.225592\pi\)
−0.650862 + 0.759196i \(0.725592\pi\)
\(6\) 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 \(-0.815886\pi\)
0.837332 0.546695i \(-0.184114\pi\)
\(12\) −6.19106 −0.0429935
\(13\) 181.780 + 181.780i 1.07562 + 1.07562i 0.996896 + 0.0787272i \(0.0250856\pi\)
0.0787272 + 0.996896i \(0.474914\pi\)
\(14\) 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 0.995741 0.0921990i \(-0.0293896\pi\)
−0.0921990 + 0.995741i \(0.529390\pi\)
\(18\) −160.802 + 160.802i −0.496303 + 0.496303i
\(19\) 137.325 + 137.325i 0.380402 + 0.380402i 0.871247 0.490845i \(-0.163312\pi\)
−0.490845 + 0.871247i \(0.663312\pi\)
\(20\) 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 0.999621 + 0.0275216i \(0.00876152\pi\)
0.0275216 + 0.999621i \(0.491238\pi\)
\(24\) 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 −0.973183 0.230034i \(-0.926116\pi\)
0.230034 + 0.973183i \(0.426116\pi\)
\(30\) 8.38374i 0.00931527i
\(31\) 833.169 833.169i 0.866982 0.866982i −0.125156 0.992137i \(-0.539943\pi\)
0.992137 + 0.125156i \(0.0399430\pi\)
\(32\) 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 \(-0.908227\pi\)
0.958724 0.284337i \(-0.0917734\pi\)
\(42\) −26.5595 26.5595i −0.0150564 0.0150564i
\(43\) −1509.63 1509.63i −0.816458 0.816458i 0.169135 0.985593i \(-0.445903\pi\)
−0.985593 + 0.169135i \(0.945903\pi\)
\(44\) −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 0.919051 0.394139i \(-0.128957\pi\)
−0.394139 + 0.919051i \(0.628957\pi\)
\(60\) −16.7675 16.7675i −0.00465763 0.00465763i
\(61\) −4096.05 + 4096.05i −1.10079 + 1.10079i −0.106477 + 0.994315i \(0.533957\pi\)
−0.994315 + 0.106477i \(0.966043\pi\)
\(62\) 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 \(-0.911806\pi\)
0.961861 0.273538i \(-0.0881939\pi\)
\(68\) 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 \(0.0984869\pi\)
−0.952515 + 0.304493i \(0.901513\pi\)
\(74\) −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 0.550634 0.834747i \(-0.314386\pi\)
−0.834747 + 0.550634i \(0.814386\pi\)
\(80\) −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 −0.981890 0.189450i \(-0.939330\pi\)
0.189450 + 0.981890i \(0.439330\pi\)
\(90\) −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 0.729635 0.683836i \(-0.239690\pi\)
−0.683836 + 0.729635i \(0.739690\pi\)
\(98\) 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 \(0.158392\pi\)
−0.878729 + 0.477321i \(0.841608\pi\)
\(102\) 808.315i 0.0776928i
\(103\) 6805.12 6805.12i 0.641448 0.641448i −0.309463 0.950911i \(-0.600149\pi\)
0.950911 + 0.309463i \(0.100149\pi\)
\(104\) 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 −0.996833 0.0795192i \(-0.974662\pi\)
−0.0795192 0.996833i \(-0.525338\pi\)
\(110\) 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 −0.865367 0.501139i \(-0.832915\pi\)
0.501139 + 0.865367i \(0.332915\pi\)
\(114\) 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 −0.919483 0.393131i \(-0.871392\pi\)
0.393131 + 0.919483i \(0.371392\pi\)
\(132\) 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 \(-0.906092\pi\)
0.956796 0.290759i \(-0.0939079\pi\)
\(140\) −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 \(-0.748827\pi\)
0.704497 0.709707i \(-0.251173\pi\)
\(152\) 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 −0.145347 0.989381i \(-0.546430\pi\)
0.989381 + 0.145347i \(0.0464299\pi\)
\(164\) −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 0.965319 0.261074i \(-0.0840767\pi\)
−0.261074 + 0.965319i \(0.584077\pi\)
\(168\) −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 \(0.0545837\pi\)
−0.985333 + 0.170641i \(0.945416\pi\)
\(174\) −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 −0.939270 0.343178i \(-0.888497\pi\)
0.343178 + 0.939270i \(0.388497\pi\)
\(180\) 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 0.438454 0.898754i \(-0.355526\pi\)
−0.898754 + 0.438454i \(0.855526\pi\)
\(192\) 396.228 0.0107484
\(193\) 22755.7 + 22755.7i 0.610907 + 0.610907i 0.943183 0.332275i \(-0.107816\pi\)
−0.332275 + 0.943183i \(0.607816\pi\)
\(194\) −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 −0.917539 0.397645i \(-0.869828\pi\)
0.397645 + 0.917539i \(0.369828\pi\)
\(200\) 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 −0.997353 0.0727155i \(-0.976834\pi\)
−0.0727155 0.997353i \(-0.523166\pi\)
\(228\) −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 \(-0.763088\pi\)
0.735576 0.677443i \(-0.236912\pi\)
\(234\) −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 0.728567 0.684974i \(-0.240187\pi\)
−0.684974 + 0.728567i \(0.740187\pi\)
\(240\) −134.140 + 134.140i −0.00232882 + 0.00232882i
\(241\) −45627.5 45627.5i −0.785584 0.785584i 0.195182 0.980767i \(-0.437470\pi\)
−0.980767 + 0.195182i \(0.937470\pi\)
\(242\) 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 −0.0343813 + 0.999409i \(0.510946\pi\)
−0.999409 + 0.0343813i \(0.989054\pi\)
\(252\) 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 −0.994220 0.107367i \(-0.965758\pi\)
−0.107367 0.994220i \(-0.534242\pi\)
\(258\) 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 \(-0.881671\pi\)
0.931696 0.363240i \(-0.118329\pi\)
\(264\) −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 −0.426031 0.904708i \(-0.640089\pi\)
0.904708 + 0.426031i \(0.140089\pi\)
\(278\) 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 0.995051 + 0.0993620i \(0.0316802\pi\)
0.0993620 + 0.995051i \(0.468320\pi\)
\(282\) −4788.98 4788.98i −0.0602205 0.0602205i
\(283\) 17514.8 17514.8i 0.218691 0.218691i −0.589256 0.807947i \(-0.700579\pi\)
0.807947 + 0.589256i \(0.200579\pi\)
\(284\) 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 \(0.205690\pi\)
−0.798381 + 0.602153i \(0.794310\pi\)
\(308\) 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 0.308998 0.951063i \(-0.400006\pi\)
0.951063 0.308998i \(-0.0999936\pi\)
\(312\) 4501.65 0.0462448
\(313\) −37218.8 37218.8i −0.379904 0.379904i 0.491164 0.871067i \(-0.336572\pi\)
−0.871067 + 0.491164i \(0.836572\pi\)
\(314\) 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 \(0.0184763\pi\)
−0.998316 + 0.0580125i \(0.981524\pi\)
\(318\) 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 0.286480 0.958086i \(-0.407515\pi\)
−0.958086 + 0.286480i \(0.907515\pi\)
\(332\) 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 \(0.243571\pi\)
−0.721243 + 0.692682i \(0.756429\pi\)
\(338\) −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 −0.0815002 + 0.996673i \(0.525971\pi\)
−0.996673 + 0.0815002i \(0.974029\pi\)
\(348\) 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 −0.0669291 0.997758i \(-0.521320\pi\)
0.997758 + 0.0669291i \(0.0213201\pi\)
\(354\) 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 \(-0.710769\pi\)
0.614813 0.788673i \(-0.289231\pi\)
\(374\) 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 0.897623 0.440765i \(-0.145293\pi\)
−0.440765 + 0.897623i \(0.645293\pi\)
\(384\) −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 0.114348 0.993441i \(-0.463522\pi\)
−0.993441 + 0.114348i \(0.963522\pi\)
\(390\) −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 \(0.142903\pi\)
−0.900906 + 0.434015i \(0.857097\pi\)
\(398\) 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 −0.955977 0.293443i \(-0.905199\pi\)
0.293443 + 0.955977i \(0.405199\pi\)
\(402\) 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 −0.499134 0.866525i \(-0.666349\pi\)
0.866525 + 0.499134i \(0.166349\pi\)
\(410\) 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 −0.877653 0.479296i \(-0.840892\pi\)
0.479296 + 0.877653i \(0.340892\pi\)
\(422\) 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 −0.995715 0.0924783i \(-0.970521\pi\)
0.0924783 + 0.995715i \(0.470521\pi\)
\(432\) 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 −0.529648 0.848218i \(-0.677676\pi\)
0.848218 + 0.529648i \(0.177676\pi\)
\(440\) 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 \(0.0268289\pi\)
−0.996450 + 0.0841858i \(0.973171\pi\)
\(444\) −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 0.702892 0.711296i \(-0.251892\pi\)
−0.711296 + 0.702892i \(0.751892\pi\)
\(450\) 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 0.456132 0.889912i \(-0.349234\pi\)
−0.889912 + 0.456132i \(0.849234\pi\)
\(458\) 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 0.858460 0.512881i \(-0.171422\pi\)
−0.512881 + 0.858460i \(0.671422\pi\)
\(462\) −3513.83 + 3513.83i −0.0164625 + 0.0164625i
\(463\) −120453. 120453.i −0.561896 0.561896i 0.367949 0.929846i \(-0.380060\pi\)
−0.929846 + 0.367949i \(0.880060\pi\)
\(464\) 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 0.609774 0.792575i \(-0.291260\pi\)
−0.792575 + 0.609774i \(0.791260\pi\)
\(468\) 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 0.653078 0.757291i \(-0.273477\pi\)
−0.757291 + 0.653078i \(0.773477\pi\)
\(480\) 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 0.961311 + 0.275464i \(0.0888316\pi\)
0.275464 + 0.961311i \(0.411168\pi\)
\(488\) −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 −0.929892 0.367832i \(-0.880100\pi\)
0.367832 + 0.929892i \(0.380100\pi\)
\(500\) −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 0.973062 + 0.230542i \(0.0740499\pi\)
0.230542 + 0.973062i \(0.425950\pi\)
\(504\) −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 \(-0.691594\pi\)
0.566217 0.824256i \(-0.308406\pi\)
\(510\) −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 \(-0.806429\pi\)
0.820723 0.571326i \(-0.193571\pi\)
\(522\) 200999.i 0.737654i
\(523\) −296372. 296372.i −1.08351 1.08351i −0.996179 0.0873340i \(-0.972165\pi\)
−0.0873340 0.996179i \(-0.527835\pi\)
\(524\) 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 0.725496 0.688226i \(-0.241610\pi\)
−0.688226 + 0.725496i \(0.741610\pi\)
\(542\) −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 −0.999959 0.00909537i \(-0.997105\pi\)
0.00909537 + 0.999959i \(0.497105\pi\)
\(548\) 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 −0.829071 0.559143i \(-0.811130\pi\)
0.559143 + 0.829071i \(0.311130\pi\)
\(558\) 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 0.0484933 0.998824i \(-0.484558\pi\)
−0.998824 + 0.0484933i \(0.984558\pi\)
\(564\) 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 −0.761409 0.648272i \(-0.775492\pi\)
0.648272 + 0.761409i \(0.275492\pi\)
\(570\) −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 0.989929 + 0.141562i \(0.0452124\pi\)
0.141562 + 0.989929i \(0.454788\pi\)
\(578\) −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 −0.811954 0.583722i \(-0.801596\pi\)
0.583722 + 0.811954i \(0.301596\pi\)
\(588\) 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 −0.573523 0.819190i \(-0.694424\pi\)
0.819190 + 0.573523i \(0.194424\pi\)
\(608\) 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 \(0.210522\pi\)
−0.789149 + 0.614201i \(0.789478\pi\)
\(614\) −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 \(-0.938982\pi\)
0.981683 0.190522i \(-0.0610179\pi\)
\(618\) 21065.5 0.0551561
\(619\) 353899.i 0.923629i 0.886977 + 0.461814i \(0.152801\pi\)
−0.886977 + 0.461814i \(0.847199\pi\)
\(620\) 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 −0.183887 0.982947i \(-0.558868\pi\)
0.982947 + 0.183887i \(0.0588681\pi\)
\(632\) 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 −0.217805 0.975992i \(-0.569890\pi\)
0.975992 + 0.217805i \(0.0698895\pi\)
\(644\) −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 −0.349011 0.937119i \(-0.613482\pi\)
0.937119 + 0.349011i \(0.113482\pi\)
\(648\) 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 −0.828919 0.559369i \(-0.811044\pi\)
0.559369 + 0.828919i \(0.311044\pi\)
\(654\) 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 \(0.244392\pi\)
−0.719454 + 0.694540i \(0.755608\pi\)
\(660\) −2218.34 + 2218.34i −0.00509261 + 0.00509261i
\(661\) 147885. 147885.i 0.338471 0.338471i −0.517320 0.855792i \(-0.673070\pi\)
0.855792 + 0.517320i \(0.173070\pi\)
\(662\) 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 \(0.202933\pi\)
−0.803567 + 0.595214i \(0.797067\pi\)
\(678\) −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 0.973517 0.228614i \(-0.0734194\pi\)
−0.228614 + 0.973517i \(0.573419\pi\)
\(684\) 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 \(0.149787\pi\)
−0.891310 + 0.453395i \(0.850213\pi\)
\(692\) 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 0.0110742 0.999939i \(-0.496475\pi\)
−0.999939 + 0.0110742i \(0.996475\pi\)
\(702\) 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 0.620951 0.783849i \(-0.286746\pi\)
−0.783849 + 0.620951i \(0.786746\pi\)
\(710\) −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 −0.807695 0.589600i \(-0.799285\pi\)
0.589600 + 0.807695i \(0.299285\pi\)
\(728\) 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 \(0.159072\pi\)
−0.877708 + 0.479196i \(0.840928\pi\)
\(734\) −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 \(-0.651995\pi\)
0.459567 0.888143i \(-0.348005\pi\)
\(740\) 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 \(0.0313806\pi\)
−0.995144 + 0.0984255i \(0.968619\pi\)
\(744\) 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 \(0.107024\pi\)
−0.944007 + 0.329927i \(0.892976\pi\)
\(752\) 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 0.434648 0.900600i \(-0.356873\pi\)
−0.900600 + 0.434648i \(0.856873\pi\)
\(758\) 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 \(-0.923466\pi\)
0.971233 0.238130i \(-0.0765345\pi\)
\(762\) −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 −0.939345 0.342974i \(-0.888566\pi\)
0.342974 + 0.939345i \(0.388566\pi\)
\(770\) 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
\(775\)