Properties

Label 225.4.e.c.151.3
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.15759792.1
Defining polynomial: \(x^{6} - 3 x^{5} + 16 x^{4} - 27 x^{3} + 52 x^{2} - 39 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.3
Root \(0.500000 - 0.0378788i\) of defining polynomial
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.c.76.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.87428 - 3.24635i) q^{2} +(4.05724 + 3.24635i) q^{3} +(-3.02587 - 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(-15.6746 + 27.1492i) q^{7} +7.30318 q^{8} +(5.92239 + 26.3425i) q^{9} +O(q^{10})\) \(q+(1.87428 - 3.24635i) q^{2} +(4.05724 + 3.24635i) q^{3} +(-3.02587 - 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(-15.6746 + 27.1492i) q^{7} +7.30318 q^{8} +(5.92239 + 26.3425i) q^{9} +(10.4166 - 18.0422i) q^{11} +(4.73733 - 31.0869i) q^{12} +(29.9655 + 51.9018i) q^{13} +(58.7572 + 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} +74.0460 q^{17} +(96.6172 + 30.1471i) q^{18} -63.8390 q^{19} +(-151.731 + 59.2655i) q^{21} +(-39.0475 - 67.6322i) q^{22} +(-16.4247 - 28.4484i) q^{23} +(29.6307 + 23.7087i) q^{24} +224.655 q^{26} +(-61.4884 + 126.104i) q^{27} +189.717 q^{28} +(80.0044 - 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(-112.840 - 195.444i) q^{32} +(100.834 - 39.3853i) q^{33} +(138.783 - 240.379i) q^{34} +(120.139 - 110.748i) q^{36} -215.365 q^{37} +(-119.652 + 207.244i) q^{38} +(-46.9143 + 307.857i) q^{39} +(-70.8407 - 122.700i) q^{41} +(-91.9908 + 603.654i) q^{42} +(68.9529 - 119.430i) q^{43} -126.078 q^{44} -123.138 q^{46} +(16.7895 - 29.0803i) q^{47} +(366.829 - 143.281i) q^{48} +(-319.885 - 554.058i) q^{49} +(300.422 + 240.379i) q^{51} +(181.344 - 314.096i) q^{52} +41.9914 q^{53} +(294.131 + 435.967i) q^{54} +(-114.474 + 198.275i) q^{56} +(-259.010 - 207.244i) q^{57} +(-299.902 - 519.445i) q^{58} +(-307.571 - 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} +953.535 q^{62} +(-808.007 - 252.119i) q^{63} -239.652 q^{64} +(61.1331 - 401.162i) q^{66} +(-428.767 - 742.646i) q^{67} +(-224.054 - 388.072i) q^{68} +(25.7146 - 168.742i) q^{69} +588.665 q^{71} +(43.2522 + 192.384i) q^{72} +618.191 q^{73} +(-403.655 + 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(326.553 + 565.607i) q^{77} +(911.481 + 729.311i) q^{78} +(172.644 - 299.029i) q^{79} +(-658.851 + 312.021i) q^{81} -531.102 q^{82} +(-546.584 + 946.711i) q^{83} +(769.728 + 615.889i) q^{84} +(-258.474 - 447.691i) q^{86} +(774.450 - 302.496i) q^{87} +(76.0746 - 131.765i) q^{88} +414.849 q^{89} -1878.79 q^{91} +(-99.3979 + 172.162i) q^{92} +(-199.125 + 1306.68i) q^{93} +(-62.9366 - 109.009i) q^{94} +(176.663 - 1159.28i) q^{96} +(-100.705 + 174.427i) q^{97} -2398.22 q^{98} +(536.967 + 167.547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9} + O(q^{10}) \) \( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9} - 14 q^{11} - 75 q^{12} + 40 q^{13} + 27 q^{14} + 13 q^{16} + 332 q^{17} - 3 q^{18} - 328 q^{19} - 144 q^{21} - 376 q^{22} + 171 q^{23} - 63 q^{24} + 868 q^{26} - 162 q^{27} + 1034 q^{28} + 335 q^{29} + 352 q^{31} - 77 q^{32} + 708 q^{33} + 52 q^{34} + 1086 q^{36} - 804 q^{37} - 178 q^{38} - 390 q^{39} - 187 q^{41} - 513 q^{42} - 602 q^{43} + 1964 q^{44} - 402 q^{46} + 665 q^{47} + 1074 q^{48} - 430 q^{49} - 180 q^{51} - 456 q^{52} + 1460 q^{53} + 639 q^{54} - 705 q^{56} + 486 q^{57} + 217 q^{58} + 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 2205 q^{63} - 3138 q^{64} - 966 q^{66} - 1849 q^{67} - 710 q^{68} - 873 q^{69} + 140 q^{71} - 261 q^{72} + 736 q^{73} + 320 q^{74} - 204 q^{76} - 948 q^{77} + 432 q^{78} + 382 q^{79} - 1251 q^{81} + 1150 q^{82} - 831 q^{83} - 909 q^{84} - 1580 q^{86} - 258 q^{87} - 1428 q^{88} + 3438 q^{89} - 1420 q^{91} - 1623 q^{92} - 2178 q^{93} + 2077 q^{94} + 1155 q^{96} - 282 q^{97} - 4328 q^{98} - 762 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87428 3.24635i 0.662659 1.14776i −0.317255 0.948340i \(-0.602761\pi\)
0.979914 0.199419i \(-0.0639054\pi\)
\(3\) 4.05724 + 3.24635i 0.780816 + 0.624761i
\(4\) −3.02587 5.24096i −0.378234 0.655120i
\(5\) 0 0
\(6\) 18.1432 7.08665i 1.23449 0.482185i
\(7\) −15.6746 + 27.1492i −0.846348 + 1.46592i 0.0380969 + 0.999274i \(0.487870\pi\)
−0.884445 + 0.466644i \(0.845463\pi\)
\(8\) 7.30318 0.322758
\(9\) 5.92239 + 26.3425i 0.219348 + 0.975647i
\(10\) 0 0
\(11\) 10.4166 18.0422i 0.285522 0.494538i −0.687214 0.726455i \(-0.741166\pi\)
0.972736 + 0.231917i \(0.0744998\pi\)
\(12\) 4.73733 31.0869i 0.113962 0.747834i
\(13\) 29.9655 + 51.9018i 0.639303 + 1.10731i 0.985586 + 0.169175i \(0.0541104\pi\)
−0.346283 + 0.938130i \(0.612556\pi\)
\(14\) 58.7572 + 101.770i 1.12168 + 1.94281i
\(15\) 0 0
\(16\) 37.8952 65.6364i 0.592112 1.02557i
\(17\) 74.0460 1.05640 0.528200 0.849120i \(-0.322867\pi\)
0.528200 + 0.849120i \(0.322867\pi\)
\(18\) 96.6172 + 30.1471i 1.26516 + 0.394763i
\(19\) −63.8390 −0.770825 −0.385413 0.922744i \(-0.625941\pi\)
−0.385413 + 0.922744i \(0.625941\pi\)
\(20\) 0 0
\(21\) −151.731 + 59.2655i −1.57669 + 0.615847i
\(22\) −39.0475 67.6322i −0.378407 0.655420i
\(23\) −16.4247 28.4484i −0.148904 0.257909i 0.781919 0.623380i \(-0.214241\pi\)
−0.930823 + 0.365472i \(0.880908\pi\)
\(24\) 29.6307 + 23.7087i 0.252015 + 0.201646i
\(25\) 0 0
\(26\) 224.655 1.69456
\(27\) −61.4884 + 126.104i −0.438276 + 0.898841i
\(28\) 189.717 1.28047
\(29\) 80.0044 138.572i 0.512291 0.887314i −0.487607 0.873063i \(-0.662130\pi\)
0.999898 0.0142513i \(-0.00453647\pi\)
\(30\) 0 0
\(31\) 127.187 + 220.294i 0.736884 + 1.27632i 0.953892 + 0.300151i \(0.0970371\pi\)
−0.217007 + 0.976170i \(0.569630\pi\)
\(32\) −112.840 195.444i −0.623358 1.07969i
\(33\) 100.834 39.3853i 0.531908 0.207760i
\(34\) 138.783 240.379i 0.700033 1.21249i
\(35\) 0 0
\(36\) 120.139 110.748i 0.556201 0.512722i
\(37\) −215.365 −0.956914 −0.478457 0.878111i \(-0.658804\pi\)
−0.478457 + 0.878111i \(0.658804\pi\)
\(38\) −119.652 + 207.244i −0.510794 + 0.884722i
\(39\) −46.9143 + 307.857i −0.192623 + 1.26401i
\(40\) 0 0
\(41\) −70.8407 122.700i −0.269841 0.467377i 0.698980 0.715141i \(-0.253638\pi\)
−0.968820 + 0.247764i \(0.920304\pi\)
\(42\) −91.9908 + 603.654i −0.337964 + 2.21776i
\(43\) 68.9529 119.430i 0.244540 0.423556i −0.717462 0.696597i \(-0.754696\pi\)
0.962002 + 0.273042i \(0.0880297\pi\)
\(44\) −126.078 −0.431976
\(45\) 0 0
\(46\) −123.138 −0.394689
\(47\) 16.7895 29.0803i 0.0521064 0.0902509i −0.838796 0.544446i \(-0.816740\pi\)
0.890902 + 0.454195i \(0.150073\pi\)
\(48\) 366.829 143.281i 1.10307 0.430852i
\(49\) −319.885 554.058i −0.932611 1.61533i
\(50\) 0 0
\(51\) 300.422 + 240.379i 0.824854 + 0.659997i
\(52\) 181.344 314.096i 0.483612 0.837641i
\(53\) 41.9914 0.108829 0.0544147 0.998518i \(-0.482671\pi\)
0.0544147 + 0.998518i \(0.482671\pi\)
\(54\) 294.131 + 435.967i 0.741225 + 1.09866i
\(55\) 0 0
\(56\) −114.474 + 198.275i −0.273166 + 0.473137i
\(57\) −259.010 207.244i −0.601873 0.481581i
\(58\) −299.902 519.445i −0.678949 1.17597i
\(59\) −307.571 532.728i −0.678683 1.17551i −0.975378 0.220541i \(-0.929218\pi\)
0.296694 0.954973i \(-0.404116\pi\)
\(60\) 0 0
\(61\) 67.1535 116.313i 0.140953 0.244137i −0.786903 0.617077i \(-0.788317\pi\)
0.927856 + 0.372939i \(0.121650\pi\)
\(62\) 953.535 1.95321
\(63\) −808.007 252.119i −1.61586 0.504191i
\(64\) −239.652 −0.468071
\(65\) 0 0
\(66\) 61.1331 401.162i 0.114015 0.748176i
\(67\) −428.767 742.646i −0.781824 1.35416i −0.930878 0.365329i \(-0.880956\pi\)
0.149055 0.988829i \(-0.452377\pi\)
\(68\) −224.054 388.072i −0.399566 0.692069i
\(69\) 25.7146 168.742i 0.0448649 0.294408i
\(70\) 0 0
\(71\) 588.665 0.983968 0.491984 0.870604i \(-0.336272\pi\)
0.491984 + 0.870604i \(0.336272\pi\)
\(72\) 43.2522 + 192.384i 0.0707962 + 0.314898i
\(73\) 618.191 0.991148 0.495574 0.868566i \(-0.334958\pi\)
0.495574 + 0.868566i \(0.334958\pi\)
\(74\) −403.655 + 699.152i −0.634108 + 1.09831i
\(75\) 0 0
\(76\) 193.169 + 334.578i 0.291552 + 0.504983i
\(77\) 326.553 + 565.607i 0.483301 + 0.837103i
\(78\) 911.481 + 729.311i 1.32314 + 1.05869i
\(79\) 172.644 299.029i 0.245873 0.425865i −0.716503 0.697584i \(-0.754259\pi\)
0.962377 + 0.271718i \(0.0875919\pi\)
\(80\) 0 0
\(81\) −658.851 + 312.021i −0.903773 + 0.428012i
\(82\) −531.102 −0.715249
\(83\) −546.584 + 946.711i −0.722836 + 1.25199i 0.237023 + 0.971504i \(0.423828\pi\)
−0.959859 + 0.280484i \(0.909505\pi\)
\(84\) 769.728 + 615.889i 0.999812 + 0.799988i
\(85\) 0 0
\(86\) −258.474 447.691i −0.324093 0.561346i
\(87\) 774.450 302.496i 0.954365 0.372770i
\(88\) 76.0746 131.765i 0.0921543 0.159616i
\(89\) 414.849 0.494089 0.247045 0.969004i \(-0.420541\pi\)
0.247045 + 0.969004i \(0.420541\pi\)
\(90\) 0 0
\(91\) −1878.79 −2.16429
\(92\) −99.3979 + 172.162i −0.112641 + 0.195100i
\(93\) −199.125 + 1306.68i −0.222024 + 1.45695i
\(94\) −62.9366 109.009i −0.0690576 0.119611i
\(95\) 0 0
\(96\) 176.663 1159.28i 0.187819 1.23249i
\(97\) −100.705 + 174.427i −0.105413 + 0.182581i −0.913907 0.405924i \(-0.866950\pi\)
0.808494 + 0.588505i \(0.200283\pi\)
\(98\) −2398.22 −2.47201
\(99\) 536.967 + 167.547i 0.545123 + 0.170092i
\(100\) 0 0
\(101\) −132.691 + 229.828i −0.130726 + 0.226424i −0.923957 0.382498i \(-0.875064\pi\)
0.793231 + 0.608921i \(0.208397\pi\)
\(102\) 1343.43 524.738i 1.30411 0.509380i
\(103\) −263.809 456.931i −0.252368 0.437114i 0.711810 0.702373i \(-0.247876\pi\)
−0.964177 + 0.265259i \(0.914543\pi\)
\(104\) 218.843 + 379.048i 0.206340 + 0.357391i
\(105\) 0 0
\(106\) 78.7038 136.319i 0.0721168 0.124910i
\(107\) −2084.24 −1.88310 −0.941549 0.336877i \(-0.890629\pi\)
−0.941549 + 0.336877i \(0.890629\pi\)
\(108\) 846.961 59.3157i 0.754619 0.0528487i
\(109\) 925.651 0.813406 0.406703 0.913560i \(-0.366678\pi\)
0.406703 + 0.913560i \(0.366678\pi\)
\(110\) 0 0
\(111\) −873.788 699.152i −0.747174 0.597843i
\(112\) 1187.98 + 2057.65i 1.00227 + 1.73598i
\(113\) 273.009 + 472.866i 0.227279 + 0.393659i 0.957001 0.290085i \(-0.0936836\pi\)
−0.729721 + 0.683745i \(0.760350\pi\)
\(114\) −1158.25 + 452.405i −0.951576 + 0.371681i
\(115\) 0 0
\(116\) −968.332 −0.775063
\(117\) −1189.75 + 1096.75i −0.940109 + 0.866619i
\(118\) −2305.90 −1.79894
\(119\) −1160.64 + 2010.29i −0.894082 + 1.54860i
\(120\) 0 0
\(121\) 448.487 + 776.802i 0.336955 + 0.583623i
\(122\) −251.729 436.008i −0.186807 0.323560i
\(123\) 110.909 727.796i 0.0813033 0.533522i
\(124\) 769.701 1333.16i 0.557429 0.965495i
\(125\) 0 0
\(126\) −2332.90 + 2150.53i −1.64946 + 1.52051i
\(127\) 975.972 0.681918 0.340959 0.940078i \(-0.389248\pi\)
0.340959 + 0.940078i \(0.389248\pi\)
\(128\) 453.543 785.559i 0.313187 0.542455i
\(129\) 667.470 260.710i 0.455562 0.177940i
\(130\) 0 0
\(131\) 814.614 + 1410.95i 0.543307 + 0.941035i 0.998711 + 0.0507502i \(0.0161612\pi\)
−0.455405 + 0.890285i \(0.650505\pi\)
\(132\) −511.528 409.293i −0.337294 0.269882i
\(133\) 1000.65 1733.18i 0.652387 1.12997i
\(134\) −3214.52 −2.07233
\(135\) 0 0
\(136\) 540.771 0.340961
\(137\) 330.725 572.833i 0.206246 0.357229i −0.744283 0.667865i \(-0.767208\pi\)
0.950529 + 0.310635i \(0.100542\pi\)
\(138\) −499.600 399.749i −0.308180 0.246586i
\(139\) −691.495 1197.70i −0.421955 0.730848i 0.574175 0.818732i \(-0.305323\pi\)
−0.996131 + 0.0878842i \(0.971989\pi\)
\(140\) 0 0
\(141\) 162.524 63.4810i 0.0970708 0.0379153i
\(142\) 1103.33 1911.02i 0.652035 1.12936i
\(143\) 1248.56 0.730139
\(144\) 1953.45 + 609.528i 1.13047 + 0.352736i
\(145\) 0 0
\(146\) 1158.66 2006.87i 0.656793 1.13760i
\(147\) 500.815 3286.41i 0.280997 1.84393i
\(148\) 651.667 + 1128.72i 0.361937 + 0.626894i
\(149\) −1581.75 2739.66i −0.869676 1.50632i −0.862328 0.506349i \(-0.830995\pi\)
−0.00734719 0.999973i \(-0.502339\pi\)
\(150\) 0 0
\(151\) 1279.40 2215.98i 0.689509 1.19427i −0.282488 0.959271i \(-0.591160\pi\)
0.971997 0.234994i \(-0.0755071\pi\)
\(152\) −466.228 −0.248790
\(153\) 438.529 + 1950.55i 0.231719 + 1.03067i
\(154\) 2448.21 1.28106
\(155\) 0 0
\(156\) 1755.42 685.659i 0.900937 0.351901i
\(157\) 1750.48 + 3031.92i 0.889832 + 1.54123i 0.840073 + 0.542474i \(0.182512\pi\)
0.0497594 + 0.998761i \(0.484155\pi\)
\(158\) −647.168 1120.93i −0.325860 0.564407i
\(159\) 170.369 + 136.319i 0.0849758 + 0.0679924i
\(160\) 0 0
\(161\) 1029.80 0.504097
\(162\) −221.943 + 2723.68i −0.107639 + 1.32094i
\(163\) −263.950 −0.126835 −0.0634176 0.997987i \(-0.520200\pi\)
−0.0634176 + 0.997987i \(0.520200\pi\)
\(164\) −428.710 + 742.547i −0.204126 + 0.353556i
\(165\) 0 0
\(166\) 2048.90 + 3548.81i 0.957987 + 1.65928i
\(167\) −1794.53 3108.21i −0.831524 1.44024i −0.896829 0.442377i \(-0.854135\pi\)
0.0653054 0.997865i \(-0.479198\pi\)
\(168\) −1108.12 + 432.826i −0.508889 + 0.198770i
\(169\) −697.365 + 1207.87i −0.317417 + 0.549782i
\(170\) 0 0
\(171\) −378.080 1681.68i −0.169079 0.752053i
\(172\) −834.570 −0.369973
\(173\) 185.228 320.824i 0.0814024 0.140993i −0.822450 0.568837i \(-0.807393\pi\)
0.903853 + 0.427844i \(0.140727\pi\)
\(174\) 469.529 3081.10i 0.204568 1.34240i
\(175\) 0 0
\(176\) −789.482 1367.42i −0.338122 0.585644i
\(177\) 481.535 3159.89i 0.204488 1.34188i
\(178\) 777.545 1346.75i 0.327413 0.567095i
\(179\) 446.898 0.186607 0.0933036 0.995638i \(-0.470257\pi\)
0.0933036 + 0.995638i \(0.470257\pi\)
\(180\) 0 0
\(181\) −904.046 −0.371255 −0.185628 0.982620i \(-0.559432\pi\)
−0.185628 + 0.982620i \(0.559432\pi\)
\(182\) −3521.38 + 6099.21i −1.43419 + 2.48409i
\(183\) 650.051 253.907i 0.262586 0.102565i
\(184\) −119.952 207.764i −0.0480598 0.0832420i
\(185\) 0 0
\(186\) 3868.72 + 3095.51i 1.52510 + 1.22029i
\(187\) 771.311 1335.95i 0.301625 0.522430i
\(188\) −203.211 −0.0788336
\(189\) −2459.81 3645.99i −0.946693 1.40321i
\(190\) 0 0
\(191\) 299.793 519.257i 0.113572 0.196713i −0.803636 0.595121i \(-0.797104\pi\)
0.917208 + 0.398409i \(0.130437\pi\)
\(192\) −972.326 777.995i −0.365477 0.292432i
\(193\) −2206.87 3822.40i −0.823076 1.42561i −0.903381 0.428839i \(-0.858923\pi\)
0.0803048 0.996770i \(-0.474411\pi\)
\(194\) 377.500 + 653.850i 0.139706 + 0.241978i
\(195\) 0 0
\(196\) −1935.86 + 3353.01i −0.705490 + 1.22194i
\(197\) 4807.15 1.73855 0.869277 0.494325i \(-0.164585\pi\)
0.869277 + 0.494325i \(0.164585\pi\)
\(198\) 1550.35 1429.15i 0.556456 0.512956i
\(199\) 313.833 0.111794 0.0558970 0.998437i \(-0.482198\pi\)
0.0558970 + 0.998437i \(0.482198\pi\)
\(200\) 0 0
\(201\) 671.281 4405.02i 0.235565 1.54580i
\(202\) 497.403 + 861.527i 0.173253 + 0.300083i
\(203\) 2508.07 + 4344.11i 0.867153 + 1.50195i
\(204\) 350.780 2301.86i 0.120390 0.790012i
\(205\) 0 0
\(206\) −1977.81 −0.668935
\(207\) 652.127 601.149i 0.218966 0.201849i
\(208\) 4542.20 1.51416
\(209\) −664.989 + 1151.79i −0.220087 + 0.381202i
\(210\) 0 0
\(211\) −1219.41 2112.08i −0.397856 0.689106i 0.595605 0.803277i \(-0.296912\pi\)
−0.993461 + 0.114171i \(0.963579\pi\)
\(212\) −127.061 220.075i −0.0411630 0.0712964i
\(213\) 2388.36 + 1911.02i 0.768298 + 0.614745i
\(214\) −3906.46 + 6766.19i −1.24785 + 2.16134i
\(215\) 0 0
\(216\) −449.060 + 920.959i −0.141457 + 0.290108i
\(217\) −7974.40 −2.49464
\(218\) 1734.93 3004.99i 0.539011 0.933594i
\(219\) 2508.15 + 2006.87i 0.773904 + 0.619230i
\(220\) 0 0
\(221\) 2218.83 + 3843.12i 0.675360 + 1.16976i
\(222\) −3907.42 + 1526.22i −1.18130 + 0.461410i
\(223\) −1166.71 + 2020.79i −0.350352 + 0.606827i −0.986311 0.164896i \(-0.947271\pi\)
0.635959 + 0.771722i \(0.280605\pi\)
\(224\) 7074.87 2.11031
\(225\) 0 0
\(226\) 2046.79 0.602435
\(227\) −1361.85 + 2358.79i −0.398189 + 0.689684i −0.993503 0.113810i \(-0.963695\pi\)
0.595313 + 0.803494i \(0.297028\pi\)
\(228\) −302.426 + 1984.56i −0.0878451 + 0.576449i
\(229\) 1657.08 + 2870.15i 0.478179 + 0.828230i 0.999687 0.0250162i \(-0.00796375\pi\)
−0.521508 + 0.853246i \(0.674630\pi\)
\(230\) 0 0
\(231\) −511.255 + 3354.91i −0.145619 + 0.955571i
\(232\) 584.286 1012.01i 0.165346 0.286388i
\(233\) 3175.44 0.892833 0.446416 0.894825i \(-0.352700\pi\)
0.446416 + 0.894825i \(0.352700\pi\)
\(234\) 1330.50 + 5917.98i 0.371698 + 1.65329i
\(235\) 0 0
\(236\) −1861.34 + 3223.93i −0.513402 + 0.889238i
\(237\) 1671.21 652.767i 0.458046 0.178910i
\(238\) 4350.74 + 7535.70i 1.18494 + 2.05238i
\(239\) 123.062 + 213.150i 0.0333064 + 0.0576884i 0.882198 0.470878i \(-0.156063\pi\)
−0.848892 + 0.528567i \(0.822730\pi\)
\(240\) 0 0
\(241\) 2643.87 4579.31i 0.706666 1.22398i −0.259421 0.965764i \(-0.583532\pi\)
0.966087 0.258217i \(-0.0831349\pi\)
\(242\) 3362.36 0.893144
\(243\) −3686.04 872.919i −0.973086 0.230444i
\(244\) −812.791 −0.213252
\(245\) 0 0
\(246\) −2154.81 1724.14i −0.558478 0.446860i
\(247\) −1912.97 3313.36i −0.492791 0.853539i
\(248\) 928.867 + 1608.84i 0.237835 + 0.411943i
\(249\) −5290.98 + 2066.63i −1.34659 + 0.525973i
\(250\) 0 0
\(251\) 2821.23 0.709459 0.354730 0.934969i \(-0.384573\pi\)
0.354730 + 0.934969i \(0.384573\pi\)
\(252\) 1123.58 + 4997.62i 0.280868 + 1.24929i
\(253\) −684.361 −0.170061
\(254\) 1829.25 3168.35i 0.451879 0.782677i
\(255\) 0 0
\(256\) −2658.74 4605.08i −0.649107 1.12429i
\(257\) −942.096 1631.76i −0.228663 0.396056i 0.728749 0.684781i \(-0.240102\pi\)
−0.957412 + 0.288725i \(0.906769\pi\)
\(258\) 404.670 2655.49i 0.0976497 0.640789i
\(259\) 3375.76 5846.99i 0.809883 1.40276i
\(260\) 0 0
\(261\) 4124.14 + 1286.84i 0.978075 + 0.305185i
\(262\) 6107.27 1.44011
\(263\) 276.506 478.922i 0.0648292 0.112287i −0.831789 0.555092i \(-0.812683\pi\)
0.896618 + 0.442804i \(0.146016\pi\)
\(264\) 736.409 287.638i 0.171677 0.0670563i
\(265\) 0 0
\(266\) −3751.00 6496.93i −0.864620 1.49757i
\(267\) 1683.14 + 1346.75i 0.385793 + 0.308688i
\(268\) −2594.78 + 4494.30i −0.591424 + 1.02438i
\(269\) 3363.48 0.762361 0.381180 0.924501i \(-0.375518\pi\)
0.381180 + 0.924501i \(0.375518\pi\)
\(270\) 0 0
\(271\) −3333.85 −0.747295 −0.373648 0.927571i \(-0.621893\pi\)
−0.373648 + 0.927571i \(0.621893\pi\)
\(272\) 2805.99 4860.11i 0.625507 1.08341i
\(273\) −7622.70 6099.21i −1.68991 1.35217i
\(274\) −1239.75 2147.30i −0.273342 0.473443i
\(275\) 0 0
\(276\) −962.181 + 375.823i −0.209842 + 0.0819633i
\(277\) −2693.63 + 4665.50i −0.584275 + 1.01199i 0.410690 + 0.911775i \(0.365288\pi\)
−0.994965 + 0.100220i \(0.968045\pi\)
\(278\) −5184.23 −1.11845
\(279\) −5049.83 + 4655.08i −1.08360 + 0.998897i
\(280\) 0 0
\(281\) −1858.35 + 3218.76i −0.394519 + 0.683327i −0.993040 0.117781i \(-0.962422\pi\)
0.598521 + 0.801107i \(0.295755\pi\)
\(282\) 98.5340 646.591i 0.0208071 0.136539i
\(283\) 1384.38 + 2397.81i 0.290787 + 0.503658i 0.973996 0.226565i \(-0.0727496\pi\)
−0.683209 + 0.730223i \(0.739416\pi\)
\(284\) −1781.23 3085.17i −0.372170 0.644617i
\(285\) 0 0
\(286\) 2340.16 4053.27i 0.483833 0.838024i
\(287\) 4441.60 0.913516
\(288\) 4480.20 4129.98i 0.916662 0.845004i
\(289\) 569.810 0.115980
\(290\) 0 0
\(291\) −974.836 + 380.766i −0.196378 + 0.0767041i
\(292\) −1870.57 3239.91i −0.374886 0.649321i
\(293\) −1740.00 3013.76i −0.346934 0.600907i 0.638769 0.769398i \(-0.279444\pi\)
−0.985703 + 0.168491i \(0.946110\pi\)
\(294\) −9730.17 7785.48i −1.93019 1.54442i
\(295\) 0 0
\(296\) −1572.85 −0.308852
\(297\) 1634.68 + 2422.96i 0.319374 + 0.473382i
\(298\) −11858.6 −2.30519
\(299\) 984.348 1704.94i 0.190389 0.329764i
\(300\) 0 0
\(301\) 2161.62 + 3744.03i 0.413932 + 0.716951i
\(302\) −4795.91 8306.75i −0.913819 1.58278i
\(303\) −1284.47 + 501.705i −0.243533 + 0.0951229i
\(304\) −2419.19 + 4190.16i −0.456415 + 0.790534i
\(305\) 0 0
\(306\) 7154.11 + 2232.27i 1.33651 + 0.417027i
\(307\) 1810.36 0.336555 0.168278 0.985740i \(-0.446179\pi\)
0.168278 + 0.985740i \(0.446179\pi\)
\(308\) 1976.22 3422.91i 0.365602 0.633241i
\(309\) 413.021 2710.29i 0.0760387 0.498975i
\(310\) 0 0
\(311\) 443.649 + 768.422i 0.0808907 + 0.140107i 0.903633 0.428308i \(-0.140890\pi\)
−0.822742 + 0.568415i \(0.807557\pi\)
\(312\) −342.623 + 2248.33i −0.0621706 + 0.407970i
\(313\) −1107.57 + 1918.36i −0.200011 + 0.346429i −0.948532 0.316682i \(-0.897431\pi\)
0.748521 + 0.663111i \(0.230764\pi\)
\(314\) 13123.6 2.35862
\(315\) 0 0
\(316\) −2089.60 −0.371990
\(317\) −329.023 + 569.884i −0.0582958 + 0.100971i −0.893700 0.448664i \(-0.851900\pi\)
0.835405 + 0.549635i \(0.185233\pi\)
\(318\) 761.859 297.578i 0.134349 0.0524760i
\(319\) −1666.76 2886.91i −0.292540 0.506695i
\(320\) 0 0
\(321\) −8456.28 6766.19i −1.47035 1.17649i
\(322\) 1930.14 3343.10i 0.334045 0.578582i
\(323\) −4727.03 −0.814299
\(324\) 3628.88 + 2508.88i 0.622237 + 0.430192i
\(325\) 0 0
\(326\) −494.717 + 856.875i −0.0840485 + 0.145576i
\(327\) 3755.59 + 3004.99i 0.635121 + 0.508184i
\(328\) −517.362 896.098i −0.0870931 0.150850i
\(329\) 526.337 + 911.643i 0.0882003 + 0.152767i
\(330\) 0 0
\(331\) −2638.22 + 4569.53i −0.438096 + 0.758804i −0.997543 0.0700619i \(-0.977680\pi\)
0.559447 + 0.828866i \(0.311014\pi\)
\(332\) 6615.57 1.09360
\(333\) −1275.48 5673.25i −0.209897 0.933610i
\(334\) −13453.8 −2.20407
\(335\) 0 0
\(336\) −1859.92 + 12205.0i −0.301984 + 1.98165i
\(337\) −1680.64 2910.95i −0.271662 0.470532i 0.697626 0.716462i \(-0.254240\pi\)
−0.969288 + 0.245930i \(0.920907\pi\)
\(338\) 2614.12 + 4527.78i 0.420678 + 0.728636i
\(339\) −427.426 + 2804.82i −0.0684796 + 0.449371i
\(340\) 0 0
\(341\) 5299.44 0.841586
\(342\) −6167.95 1924.56i −0.975217 0.304293i
\(343\) 9303.52 1.46456
\(344\) 503.575 872.218i 0.0789272 0.136706i
\(345\) 0 0
\(346\) −694.339 1202.63i −0.107884 0.186861i
\(347\) 4677.77 + 8102.13i 0.723677 + 1.25344i 0.959516 + 0.281653i \(0.0908826\pi\)
−0.235840 + 0.971792i \(0.575784\pi\)
\(348\) −3928.75 3143.55i −0.605182 0.484229i
\(349\) −3519.65 + 6096.22i −0.539836 + 0.935023i 0.459077 + 0.888397i \(0.348180\pi\)
−0.998912 + 0.0466263i \(0.985153\pi\)
\(350\) 0 0
\(351\) −8387.55 + 587.410i −1.27548 + 0.0893266i
\(352\) −4701.65 −0.711929
\(353\) 2101.09 3639.19i 0.316798 0.548710i −0.663020 0.748602i \(-0.730726\pi\)
0.979818 + 0.199891i \(0.0640589\pi\)
\(354\) −9355.58 7485.76i −1.40464 1.12391i
\(355\) 0 0
\(356\) −1255.28 2174.21i −0.186881 0.323688i
\(357\) −11235.1 + 4388.37i −1.66562 + 0.650581i
\(358\) 837.612 1450.79i 0.123657 0.214180i
\(359\) 588.013 0.0864461 0.0432230 0.999065i \(-0.486237\pi\)
0.0432230 + 0.999065i \(0.486237\pi\)
\(360\) 0 0
\(361\) −2783.58 −0.405828
\(362\) −1694.44 + 2934.85i −0.246016 + 0.426112i
\(363\) −702.155 + 4607.62i −0.101525 + 0.666218i
\(364\) 5684.97 + 9846.66i 0.818608 + 1.41787i
\(365\) 0 0
\(366\) 394.109 2586.19i 0.0562853 0.369350i
\(367\) −3892.55 + 6742.10i −0.553650 + 0.958950i 0.444357 + 0.895850i \(0.353432\pi\)
−0.998007 + 0.0631004i \(0.979901\pi\)
\(368\) −2489.67 −0.352671
\(369\) 2812.67 2592.79i 0.396806 0.365787i
\(370\) 0 0
\(371\) −658.198 + 1140.03i −0.0921077 + 0.159535i
\(372\) 7450.77 2910.23i 1.03845 0.405615i
\(373\) −3912.02 6775.81i −0.543047 0.940585i −0.998727 0.0504412i \(-0.983937\pi\)
0.455680 0.890144i \(-0.349396\pi\)
\(374\) −2891.31 5007.90i −0.399749 0.692385i
\(375\) 0 0
\(376\) 122.617 212.378i 0.0168177 0.0291292i
\(377\) 9589.49 1.31004
\(378\) −16446.5 + 1151.81i −2.23788 + 0.156727i
\(379\) −4679.90 −0.634275 −0.317138 0.948379i \(-0.602722\pi\)
−0.317138 + 0.948379i \(0.602722\pi\)
\(380\) 0 0
\(381\) 3959.75 + 3168.35i 0.532452 + 0.426036i
\(382\) −1123.79 1946.47i −0.150519 0.260707i
\(383\) −3363.82 5826.31i −0.448782 0.777313i 0.549525 0.835477i \(-0.314809\pi\)
−0.998307 + 0.0581644i \(0.981475\pi\)
\(384\) 4390.33 1714.84i 0.583446 0.227891i
\(385\) 0 0
\(386\) −16545.2 −2.18167
\(387\) 3554.44 + 1109.08i 0.466880 + 0.145679i
\(388\) 1218.89 0.159483
\(389\) 2386.44 4133.43i 0.311047 0.538749i −0.667542 0.744572i \(-0.732654\pi\)
0.978589 + 0.205823i \(0.0659871\pi\)
\(390\) 0 0
\(391\) −1216.18 2106.49i −0.157302 0.272455i
\(392\) −2336.18 4046.38i −0.301007 0.521360i
\(393\) −1275.37 + 8369.10i −0.163699 + 1.07421i
\(394\) 9009.95 15605.7i 1.15207 1.99544i
\(395\) 0 0
\(396\) −746.681 3321.20i −0.0947529 0.421456i
\(397\) 4688.95 0.592775 0.296388 0.955068i \(-0.404218\pi\)
0.296388 + 0.955068i \(0.404218\pi\)
\(398\) 588.211 1018.81i 0.0740813 0.128313i
\(399\) 9686.39 3783.45i 1.21535 0.474711i
\(400\) 0 0
\(401\) −766.916 1328.34i −0.0955061 0.165421i 0.814314 0.580425i \(-0.197114\pi\)
−0.909820 + 0.415004i \(0.863780\pi\)
\(402\) −13042.1 10435.5i −1.61811 1.29471i
\(403\) −7622.43 + 13202.4i −0.942185 + 1.63191i
\(404\) 1606.03 0.197780
\(405\) 0 0
\(406\) 18803.3 2.29851
\(407\) −2243.38 + 3885.66i −0.273220 + 0.473230i
\(408\) 2194.04 + 1755.53i 0.266228 + 0.213019i
\(409\) 4389.41 + 7602.68i 0.530666 + 0.919140i 0.999360 + 0.0357796i \(0.0113914\pi\)
−0.468694 + 0.883361i \(0.655275\pi\)
\(410\) 0 0
\(411\) 3201.45 1250.47i 0.384224 0.150076i
\(412\) −1596.50 + 2765.23i −0.190908 + 0.330662i
\(413\) 19284.2 2.29761
\(414\) −729.271 3243.76i −0.0865742 0.385077i
\(415\) 0 0
\(416\) 6762.61 11713.2i 0.797029 1.38050i
\(417\) 1082.61 7104.21i 0.127136 0.834279i
\(418\) 2492.75 + 4317.58i 0.291686 + 0.505214i
\(419\) 2138.02 + 3703.17i 0.249282 + 0.431770i 0.963327 0.268330i \(-0.0864719\pi\)
−0.714044 + 0.700100i \(0.753139\pi\)
\(420\) 0 0
\(421\) −7231.64 + 12525.6i −0.837169 + 1.45002i 0.0550823 + 0.998482i \(0.482458\pi\)
−0.892252 + 0.451538i \(0.850875\pi\)
\(422\) −9142.07 −1.05457
\(423\) 865.480 + 270.052i 0.0994825 + 0.0310411i
\(424\) 306.671 0.0351256
\(425\) 0 0
\(426\) 10680.3 4171.66i 1.21470 0.474455i
\(427\) 2105.21 + 3646.32i 0.238590 + 0.413250i
\(428\) 6306.65 + 10923.4i 0.712251 + 1.23366i
\(429\) 5065.71 + 4053.27i 0.570105 + 0.456163i
\(430\) 0 0
\(431\) −2208.11 −0.246777 −0.123389 0.992358i \(-0.539376\pi\)
−0.123389 + 0.992358i \(0.539376\pi\)
\(432\) 5946.89 + 8814.60i 0.662314 + 0.981696i
\(433\) 10062.3 1.11677 0.558386 0.829581i \(-0.311421\pi\)
0.558386 + 0.829581i \(0.311421\pi\)
\(434\) −14946.3 + 25887.7i −1.65310 + 2.86325i
\(435\) 0 0
\(436\) −2800.90 4851.30i −0.307658 0.532879i
\(437\) 1048.54 + 1816.12i 0.114779 + 0.198803i
\(438\) 11216.0 4380.90i 1.22356 0.477917i
\(439\) −6658.62 + 11533.1i −0.723915 + 1.25386i 0.235504 + 0.971873i \(0.424326\pi\)
−0.959419 + 0.281984i \(0.909008\pi\)
\(440\) 0 0
\(441\) 12700.8 11707.9i 1.37142 1.26422i
\(442\) 16634.8 1.79013
\(443\) −7137.55 + 12362.6i −0.765497 + 1.32588i 0.174486 + 0.984660i \(0.444174\pi\)
−0.939983 + 0.341220i \(0.889160\pi\)
\(444\) −1020.26 + 6695.03i −0.109052 + 0.715613i
\(445\) 0 0
\(446\) 4373.47 + 7575.08i 0.464327 + 0.804238i
\(447\) 2476.39 16250.4i 0.262034 1.71950i
\(448\) 3756.45 6506.36i 0.396151 0.686153i
\(449\) −1690.02 −0.177632 −0.0888162 0.996048i \(-0.528308\pi\)
−0.0888162 + 0.996048i \(0.528308\pi\)
\(450\) 0 0
\(451\) −2951.69 −0.308181
\(452\) 1652.18 2861.66i 0.171929 0.297791i
\(453\) 12384.7 4837.39i 1.28451 0.501723i
\(454\) 5104.97 + 8842.07i 0.527727 + 0.914051i
\(455\) 0 0
\(456\) −1891.60 1513.54i −0.194259 0.155434i
\(457\) −3332.19 + 5771.53i −0.341080 + 0.590767i −0.984634 0.174633i \(-0.944126\pi\)
0.643554 + 0.765401i \(0.277459\pi\)
\(458\) 12423.3 1.26748
\(459\) −4552.97 + 9337.49i −0.462994 + 0.949535i
\(460\) 0 0
\(461\) −833.712 + 1444.03i −0.0842295 + 0.145890i −0.905063 0.425278i \(-0.860176\pi\)
0.820833 + 0.571168i \(0.193510\pi\)
\(462\) 9932.99 + 7947.76i 1.00027 + 0.800354i
\(463\) −2916.01 5050.68i −0.292697 0.506966i 0.681750 0.731585i \(-0.261219\pi\)
−0.974446 + 0.224620i \(0.927886\pi\)
\(464\) −6063.56 10502.4i −0.606668 1.05078i
\(465\) 0 0
\(466\) 5951.67 10308.6i 0.591644 1.02476i
\(467\) −17410.6 −1.72519 −0.862597 0.505892i \(-0.831163\pi\)
−0.862597 + 0.505892i \(0.831163\pi\)
\(468\) 9348.06 + 2916.84i 0.923321 + 0.288100i
\(469\) 26883.0 2.64678
\(470\) 0 0
\(471\) −2740.57 + 17983.9i −0.268108 + 1.75935i
\(472\) −2246.24 3890.61i −0.219050 0.379406i
\(473\) −1436.52 2488.12i −0.139643 0.241869i
\(474\) 1013.21 6648.81i 0.0981822 0.644283i
\(475\) 0 0
\(476\) 14047.8 1.35269
\(477\) 248.689 + 1106.16i 0.0238715 + 0.106179i
\(478\) 922.614 0.0882832
\(479\) 1639.67 2839.99i 0.156406 0.270903i −0.777164 0.629298i \(-0.783343\pi\)
0.933570 + 0.358395i \(0.116676\pi\)
\(480\) 0 0
\(481\) −6453.53 11177.8i −0.611758 1.05960i
\(482\) −9910.71 17165.9i −0.936557 1.62216i
\(483\) 4178.15 + 3343.10i 0.393607 + 0.314940i
\(484\) 2714.13 4701.00i 0.254895 0.441492i
\(485\) 0 0
\(486\) −9742.49 + 10330.1i −0.909318 + 0.964162i
\(487\) 10506.7 0.977624 0.488812 0.872389i \(-0.337430\pi\)
0.488812 + 0.872389i \(0.337430\pi\)
\(488\) 490.433 849.456i 0.0454936 0.0787972i
\(489\) −1070.91 856.875i −0.0990350 0.0792417i
\(490\) 0 0
\(491\) 7132.25 + 12353.4i 0.655548 + 1.13544i 0.981756 + 0.190144i \(0.0608956\pi\)
−0.326208 + 0.945298i \(0.605771\pi\)
\(492\) −4149.95 + 1620.95i −0.380272 + 0.148532i
\(493\) 5924.01 10260.7i 0.541184 0.937359i
\(494\) −14341.8 −1.30621
\(495\) 0 0
\(496\) 19279.1 1.74527
\(497\) −9227.09 + 15981.8i −0.832780 + 1.44242i
\(498\) −3207.78 + 21049.8i −0.288643 + 1.89411i
\(499\) −4723.70 8181.68i −0.423771 0.733993i 0.572534 0.819881i \(-0.305961\pi\)
−0.996305 + 0.0858882i \(0.972627\pi\)
\(500\) 0 0
\(501\) 2809.52 18436.4i 0.250539 1.64407i
\(502\) 5287.78 9158.70i 0.470130 0.814288i
\(503\) −14579.2 −1.29235 −0.646177 0.763188i \(-0.723633\pi\)
−0.646177 + 0.763188i \(0.723633\pi\)
\(504\) −5901.02 1841.27i −0.521532 0.162732i
\(505\) 0 0
\(506\) −1282.69 + 2221.68i −0.112692 + 0.195189i
\(507\) −6750.55 + 2636.73i −0.591327 + 0.230969i
\(508\) −2953.17 5115.03i −0.257924 0.446738i
\(509\) −4205.32 7283.83i −0.366204 0.634283i 0.622765 0.782409i \(-0.286009\pi\)
−0.988969 + 0.148126i \(0.952676\pi\)
\(510\) 0 0
\(511\) −9689.89 + 16783.4i −0.838856 + 1.45294i
\(512\) −12676.3 −1.09417
\(513\) 3925.36 8050.35i 0.337834 0.692849i
\(514\) −7063.02 −0.606102
\(515\) 0 0
\(516\) −3386.05 2709.31i −0.288881 0.231145i
\(517\) −349.781 605.838i −0.0297550 0.0515372i
\(518\) −12654.3 21917.8i −1.07335 1.85910i
\(519\) 1793.02 700.345i 0.151647 0.0592327i
\(520\) 0 0
\(521\) 10058.1 0.845781 0.422890 0.906181i \(-0.361016\pi\)
0.422890 + 0.906181i \(0.361016\pi\)
\(522\) 11907.3 10976.5i 0.998409 0.920361i
\(523\) −20006.3 −1.67269 −0.836344 0.548205i \(-0.815312\pi\)
−0.836344 + 0.548205i \(0.815312\pi\)
\(524\) 4929.83 8538.72i 0.410994 0.711862i
\(525\) 0 0
\(526\) −1036.50 1795.27i −0.0859192 0.148817i
\(527\) 9417.67 + 16311.9i 0.778444 + 1.34830i
\(528\) 1236.02 8110.90i 0.101877 0.668525i
\(529\) 5543.96 9602.42i 0.455655 0.789218i
\(530\) 0 0
\(531\) 12211.8 11257.2i 0.998019 0.920001i
\(532\) −12111.4 −0.987019
\(533\) 4245.56 7353.52i 0.345020 0.597592i
\(534\) 7526.70 2939.89i 0.609948 0.238243i
\(535\) 0 0
\(536\) −3131.36 5423.67i −0.252340 0.437065i
\(537\) 1813.17 + 1450.79i 0.145706 + 0.116585i
\(538\) 6304.11 10919.0i 0.505185 0.875006i
\(539\) −13328.5 −1.06512
\(540\) 0 0
\(541\) −1884.15 −0.149734 −0.0748668 0.997194i \(-0.523853\pi\)
−0.0748668 + 0.997194i \(0.523853\pi\)
\(542\) −6248.58 + 10822.9i −0.495202 + 0.857715i
\(543\) −3667.93 2934.85i −0.289882 0.231946i
\(544\) −8355.34 14471.9i −0.658515 1.14058i
\(545\) 0 0
\(546\) −34087.3 + 13314.3i −2.67180 + 1.04359i
\(547\) −8998.24 + 15585.4i −0.703358 + 1.21825i 0.263922 + 0.964544i \(0.414984\pi\)
−0.967281 + 0.253708i \(0.918350\pi\)
\(548\) −4002.93 −0.312038
\(549\) 3461.68 + 1080.14i 0.269109 + 0.0839691i
\(550\) 0 0
\(551\) −5107.40 + 8846.28i −0.394887 + 0.683964i
\(552\) 187.798 1232.35i 0.0144805 0.0950226i
\(553\) 5412.25 + 9374.30i 0.416189 + 0.720860i
\(554\) 10097.2 + 17488.9i 0.774351 + 1.34121i
\(555\) 0 0
\(556\) −4184.75 + 7248.19i −0.319196 + 0.552863i
\(557\) 3615.76 0.275054 0.137527 0.990498i \(-0.456085\pi\)
0.137527 + 0.990498i \(0.456085\pi\)
\(558\) 5647.21 + 25118.5i 0.428433 + 1.90564i
\(559\) 8264.84 0.625341
\(560\) 0 0
\(561\) 7466.36 2916.32i 0.561907 0.219478i
\(562\) 6966.14 + 12065.7i 0.522863 + 0.905625i
\(563\) 7410.91 + 12836.1i 0.554765 + 0.960881i 0.997922 + 0.0644370i \(0.0205251\pi\)
−0.443157 + 0.896444i \(0.646142\pi\)
\(564\) −824.478 659.696i −0.0615546 0.0492522i
\(565\) 0 0
\(566\) 10378.9 0.770771
\(567\) 1856.11 22778.1i 0.137477 1.68710i
\(568\) 4299.13 0.317583
\(569\) −11224.7 + 19441.8i −0.827005 + 1.43241i 0.0733726 + 0.997305i \(0.476624\pi\)
−0.900377 + 0.435110i \(0.856710\pi\)
\(570\) 0 0
\(571\) 8006.75 + 13868.1i 0.586817 + 1.01640i 0.994646 + 0.103338i \(0.0329523\pi\)
−0.407830 + 0.913058i \(0.633714\pi\)
\(572\) −3777.98 6543.66i −0.276163 0.478329i
\(573\) 2902.03 1133.52i 0.211577 0.0826410i
\(574\) 8324.81 14419.0i 0.605350 1.04850i
\(575\) 0 0
\(576\) −1419.31 6313.03i −0.102670 0.456672i
\(577\) −3096.97 −0.223446 −0.111723 0.993739i \(-0.535637\pi\)
−0.111723 + 0.993739i \(0.535637\pi\)
\(578\) 1067.99 1849.81i 0.0768553 0.133117i
\(579\) 3455.09 22672.7i 0.247994 1.62736i
\(580\) 0 0
\(581\) −17135.0 29678.6i −1.22354 2.11924i
\(582\) −591.018 + 3878.33i −0.0420936 + 0.276223i
\(583\) 437.410 757.616i 0.0310732 0.0538203i
\(584\) 4514.76 0.319901
\(585\) 0 0
\(586\) −13045.0 −0.919595
\(587\) 12312.4 21325.7i 0.865734 1.49950i −0.000582275 1.00000i \(-0.500185\pi\)
0.866316 0.499496i \(-0.166481\pi\)
\(588\) −18739.3 + 7319.49i −1.31428 + 0.513351i
\(589\) −8119.48 14063.3i −0.568009 0.983820i
\(590\) 0 0
\(591\) 19503.8 + 15605.7i 1.35749 + 1.08618i
\(592\) −8161.30 + 14135.8i −0.566601 + 0.981381i
\(593\) −27128.8 −1.87866 −0.939330 0.343014i \(-0.888552\pi\)
−0.939330 + 0.343014i \(0.888552\pi\)
\(594\) 10929.7 765.442i 0.754965 0.0528729i
\(595\) 0 0
\(596\) −9572.32 + 16579.7i −0.657881 + 1.13948i
\(597\) 1273.29 + 1018.81i 0.0872906 + 0.0698445i
\(598\) −3689.89 6391.08i −0.252326 0.437042i
\(599\) −2815.87 4877.24i −0.192076 0.332685i 0.753862 0.657033i \(-0.228189\pi\)
−0.945938 + 0.324347i \(0.894855\pi\)
\(600\) 0 0
\(601\) 7375.88 12775.4i 0.500613 0.867087i −0.499387 0.866379i \(-0.666441\pi\)
1.00000 0.000707853i \(-0.000225317\pi\)
\(602\) 16205.9 1.09718
\(603\) 17023.8 15693.0i 1.14969 1.05982i
\(604\) −15485.2 −1.04318
\(605\) 0 0
\(606\) −778.738 + 5110.16i −0.0522014 + 0.342552i
\(607\) −7391.04 12801.7i −0.494222 0.856018i 0.505756 0.862677i \(-0.331214\pi\)
−0.999978 + 0.00665872i \(0.997880\pi\)
\(608\) 7203.59 + 12477.0i 0.480500 + 0.832251i
\(609\) −3926.66 + 25767.2i −0.261275 + 1.71451i
\(610\) 0 0
\(611\) 2012.43 0.133247
\(612\) 8895.85 8200.44i 0.587571 0.541639i
\(613\) −4947.28 −0.325969 −0.162984 0.986629i \(-0.552112\pi\)
−0.162984 + 0.986629i \(0.552112\pi\)
\(614\) 3393.12 5877.06i 0.223021 0.386284i
\(615\) 0 0
\(616\) 2384.88 + 4130.73i 0.155989 + 0.270181i
\(617\) −1871.82 3242.09i −0.122134 0.211543i 0.798475 0.602028i \(-0.205640\pi\)
−0.920609 + 0.390485i \(0.872307\pi\)
\(618\) −8024.45 6420.67i −0.522315 0.417924i
\(619\) −3069.37 + 5316.30i −0.199303 + 0.345202i −0.948303 0.317368i \(-0.897201\pi\)
0.749000 + 0.662570i \(0.230534\pi\)
\(620\) 0 0
\(621\) 4597.38 321.971i 0.297080 0.0208055i
\(622\) 3326.09 0.214412
\(623\) −6502.59 + 11262.8i −0.418171 + 0.724294i
\(624\) 18428.8 + 14745.6i 1.18228 + 0.945986i
\(625\) 0 0
\(626\) 4151.79 + 7191.11i 0.265078 + 0.459128i
\(627\) −6437.15 + 2514.32i −0.410008 + 0.160147i
\(628\) 10593.5 18348.4i 0.673129 1.16589i
\(629\) −15946.9 −1.01088
\(630\) 0 0
\(631\) −5548.00 −0.350019 −0.175010 0.984567i \(-0.555996\pi\)
−0.175010 + 0.984567i \(0.555996\pi\)
\(632\) 1260.85 2183.86i 0.0793575 0.137451i
\(633\) 1909.12 12527.8i 0.119874 0.786630i
\(634\) 1233.36 + 2136.25i 0.0772605 + 0.133819i
\(635\) 0 0
\(636\) 198.927 1305.38i 0.0124025 0.0813864i
\(637\) 19171.1 33205.3i 1.19244 2.06537i
\(638\) −12495.9 −0.775418
\(639\) 3486.31 + 15506.9i 0.215831 + 0.960005i
\(640\) 0 0
\(641\) 5804.05 10052.9i 0.357639 0.619448i −0.629927 0.776654i \(-0.716915\pi\)
0.987566 + 0.157206i \(0.0502487\pi\)
\(642\) −37814.9 + 14770.3i −2.32466 + 0.908002i
\(643\) −6360.85 11017.3i −0.390120 0.675708i 0.602345 0.798236i \(-0.294233\pi\)
−0.992465 + 0.122528i \(0.960900\pi\)
\(644\) −3116.04 5397.15i −0.190667 0.330244i
\(645\) 0 0
\(646\) −8859.78 + 15345.6i −0.539603 + 0.934620i
\(647\) 28203.7 1.71376 0.856879 0.515518i \(-0.172400\pi\)
0.856879 + 0.515518i \(0.172400\pi\)
\(648\) −4811.70 + 2278.74i −0.291700 + 0.138144i
\(649\) −12815.4 −0.775115
\(650\) 0 0
\(651\) −32354.0 25887.7i −1.94786 1.55856i
\(652\) 798.678 + 1383.35i 0.0479734 + 0.0830924i
\(653\) −11346.4 19652.5i −0.679966 1.17774i −0.974991 0.222247i \(-0.928661\pi\)
0.295024 0.955490i \(-0.404672\pi\)
\(654\) 16794.3 6559.76i 1.00414 0.392213i
\(655\) 0 0
\(656\) −10738.1 −0.639103
\(657\) 3661.17 + 16284.7i 0.217406 + 0.967010i
\(658\) 3946.02 0.233787
\(659\) −3002.00 + 5199.61i −0.177453 + 0.307357i −0.941007 0.338386i \(-0.890119\pi\)
0.763555 + 0.645743i \(0.223452\pi\)
\(660\) 0 0
\(661\) −5958.18 10319.9i −0.350600 0.607256i 0.635755 0.771891i \(-0.280689\pi\)
−0.986355 + 0.164635i \(0.947356\pi\)
\(662\) 9889.54 + 17129.2i 0.580616 + 1.00566i
\(663\) −3473.81 + 22795.6i −0.203487 + 1.33530i
\(664\) −3991.80 + 6914.00i −0.233301 + 0.404089i
\(665\) 0 0
\(666\) −20808.0 6492.63i −1.21065 0.377754i
\(667\) −5256.19 −0.305128
\(668\) −10860.0 + 18810.1i −0.629021 + 1.08950i
\(669\) −11293.8 + 4411.31i −0.652682 + 0.254934i
\(670\) 0 0
\(671\) −1399.03 2423.19i −0.0804901 0.139413i
\(672\) 28704.5 + 22967.5i 1.64777 + 1.31844i
\(673\) −8016.85 + 13885.6i −0.459178 + 0.795319i −0.998918 0.0465125i \(-0.985189\pi\)
0.539740 + 0.841832i \(0.318523\pi\)
\(674\) −12599.9 −0.720077
\(675\) 0 0
\(676\) 8440.54 0.480231
\(677\) 5655.94 9796.38i 0.321086 0.556138i −0.659626 0.751594i \(-0.729285\pi\)
0.980712 + 0.195456i \(0.0626187\pi\)
\(678\) 8304.31 + 6644.59i 0.470391 + 0.376378i
\(679\) −3157.03 5468.14i −0.178432 0.309054i
\(680\) 0 0
\(681\) −13182.8 + 5149.13i −0.741800 + 0.289743i
\(682\) 9932.64 17203.8i 0.557684 0.965937i
\(683\) 652.395 0.0365493 0.0182747 0.999833i \(-0.494183\pi\)
0.0182747 + 0.999833i \(0.494183\pi\)
\(684\) −7669.59 + 7070.04i −0.428734 + 0.395219i
\(685\) 0 0
\(686\) 17437.4 30202.5i 0.970502 1.68096i
\(687\) −2594.34 + 17024.3i −0.144076 + 0.945443i
\(688\) −5225.96 9051.64i −0.289590 0.501585i
\(689\) 1258.29 + 2179.43i 0.0695750 + 0.120507i
\(690\) 0 0
\(691\) −6268.93 + 10858.1i −0.345125 + 0.597774i −0.985376 0.170392i \(-0.945497\pi\)
0.640252 + 0.768165i \(0.278830\pi\)
\(692\) −2241.90 −0.123157
\(693\) −12965.5 + 11952.0i −0.710705 + 0.655148i
\(694\) 35069.8 1.91820
\(695\) 0 0
\(696\) 5655.94 2209.18i 0.308029 0.120314i
\(697\) −5245.47 9085.42i −0.285059 0.493737i
\(698\) 13193.6 + 22852.1i 0.715454 + 1.23920i
\(699\) 12883.5 + 10308.6i 0.697138 + 0.557807i
\(700\) 0 0
\(701\) 5880.60 0.316844 0.158422 0.987372i \(-0.449359\pi\)
0.158422 + 0.987372i \(0.449359\pi\)
\(702\) −13813.7 + 28329.9i −0.742684 + 1.52314i
\(703\) 13748.7 0.737614
\(704\) −2496.37 + 4323.84i −0.133644 + 0.231479i
\(705\) 0 0
\(706\) −7876.07 13641.8i −0.419858 0.727216i
\(707\) −4159.77 7204.93i −0.221279 0.383266i
\(708\) −18017.9 + 7037.71i −0.956434 + 0.373578i
\(709\) −3203.33 + 5548.33i −0.169681 + 0.293895i −0.938308 0.345802i \(-0.887607\pi\)
0.768627 + 0.639697i \(0.220940\pi\)
\(710\) 0 0
\(711\) 8899.62 + 2776.91i 0.469426 + 0.146473i
\(712\) 3029.72 0.159471
\(713\) 4178.00 7236.52i 0.219449 0.380098i
\(714\) −6811.55 + 44698.2i −0.357025 + 2.34284i
\(715\) 0 0
\(716\) −1352.25 2342.17i −0.0705812 0.122250i
\(717\) −192.667 + 1264.30i −0.0100353 + 0.0658526i
\(718\) 1102.10 1908.90i 0.0572843 0.0992193i
\(719\) 21907.0 1.13629 0.568144 0.822929i \(-0.307662\pi\)
0.568144 + 0.822929i \(0.307662\pi\)
\(720\) 0 0
\(721\) 16540.4 0.854364
\(722\) −5217.21 + 9036.47i −0.268926 + 0.465793i
\(723\) 25592.9 9996.44i 1.31647 0.514207i
\(724\) 2735.53 + 4738.07i 0.140421 + 0.243217i
\(725\) 0 0
\(726\) 13641.9 + 10915.4i 0.697382 + 0.558002i
\(727\) 6685.46 11579.6i 0.341059 0.590732i −0.643571 0.765387i \(-0.722548\pi\)
0.984630 + 0.174655i \(0.0558810\pi\)
\(728\) −13721.1 −0.698542
\(729\) −12121.4 15507.8i −0.615829 0.787880i
\(730\) 0 0
\(731\) 5105.69 8843.31i 0.258332 0.447444i
\(732\) −3297.69 2638.61i −0.166511 0.133232i
\(733\) 15095.5 + 26146.2i 0.760663 + 1.31751i 0.942509 + 0.334181i \(0.108460\pi\)
−0.181846 + 0.983327i \(0.558207\pi\)
\(734\) 14591.5 + 25273.2i 0.733762 + 1.27091i
\(735\) 0 0
\(736\) −3706.72 + 6420.22i −0.185641 + 0.321539i
\(737\) −17865.2 −0.892910
\(738\) −3145.39 13990.5i −0.156888 0.697830i
\(739\) −11624.7 −0.578650 −0.289325 0.957231i \(-0.593431\pi\)
−0.289325 + 0.957231i \(0.593431\pi\)
\(740\) 0 0
\(741\) 2994.96 19653.3i 0.148479 0.974334i
\(742\) 2467.30 + 4273.49i 0.122072 + 0.211435i
\(743\) −2627.19 4550.42i −0.129720 0.224682i 0.793848 0.608116i \(-0.208075\pi\)
−0.923568 + 0.383434i \(0.874741\pi\)
\(744\) −1454.24 + 9542.90i −0.0716601 + 0.470241i
\(745\) 0 0
\(746\) −29328.9 −1.43942
\(747\) −28175.8 8791.57i −1.38005 0.430612i
\(748\) −9335.55 −0.456339
\(749\) 32669.7 56585.5i 1.59376 2.76047i
\(750\) 0 0
\(751\) 14614.4 + 25312.9i 0.710102 + 1.22993i 0.964819 + 0.262917i \(0.0846844\pi\)
−0.254717 + 0.967016i \(0.581982\pi\)
\(752\) −1272.48 2204.00i −0.0617057 0.106877i
\(753\) 11446.4 + 9158.70i 0.553957 + 0.443242i
\(754\) 17973.4 31130.9i 0.868108 1.50361i
\(755\) 0 0
\(756\) −11665.4 + 23924.1i −0.561199 + 1.15094i
\(757\) −32885.9 −1.57894 −0.789470 0.613789i \(-0.789645\pi\)
−0.789470 + 0.613789i \(0.789645\pi\)
\(758\) −8771.46 + 15192.6i −0.420308 + 0.727995i
\(759\) −2776.62 2221.68i −0.132786 0.106247i
\(760\) 0 0
\(761\) 6634.11 + 11490.6i 0.316014 + 0.547352i 0.979652 0.200702i \(-0.0643221\pi\)
−0.663639 + 0.748053i \(0.730989\pi\)
\(762\) 17707.3 6916.37i 0.841820 0.328811i
\(763\) −14509.2 + 25130.7i −0.688425 + 1.19239i
\(764\) −3628.54 −0.171827
\(765\) 0 0
\(766\) −25219.0 −1.18956
\(767\) 18433.0 31927.0i 0.867769 1.50302i
\(768\) 4162.55 27315.1i 0.195577 1.28340i
\(769\) −17142.9 29692.4i −0.803887 1.39237i −0.917040 0.398796i \(-0.869428\pi\)
0.113153 0.993578i \(-0.463905\pi\)
\(770\) 0 0
\(771\) 1474.95 9678.81i 0.0688964 0.452106i
\(772\) −13355.4 + 23132.2i −0.622630 + 1.07843i
\(773\) 27987.1 1.30223 0.651117 0.758978i \(-0.274301\pi\)
0.651117 + 0.758978i \(0.274301\pi\)
\(774\) 10262.5 9460.25i 0.476586 0.439330i
\(775\) 0 0
\(776\) −735.469 + 1273.87i −0.0340229 + 0.0589294i
\(777\) 32677.7 12763.7i 1.50876 0.589313i
\(778\) −8945.72 15494.4i &