Properties

Label 225.4.k.c.124.2
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 23 x^{10} + 198 x^{8} - 719 x^{6} + 886 x^{4} + 585 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.2
Root \(-0.0378788 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.c.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.24635 - 1.87428i) q^{2} +(-3.24635 + 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(27.1492 + 15.6746i) q^{7} +7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +O(q^{10})\) \(q+(-3.24635 - 1.87428i) q^{2} +(-3.24635 + 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(27.1492 + 15.6746i) q^{7} +7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +(10.4166 - 18.0422i) q^{11} +(-31.0869 - 4.73733i) q^{12} +(-51.9018 + 29.9655i) q^{13} +(-58.7572 - 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} -74.0460i q^{17} +(-30.1471 + 96.6172i) q^{18} +63.8390 q^{19} +(-151.731 + 59.2655i) q^{21} +(-67.6322 + 39.0475i) q^{22} +(28.4484 - 16.4247i) q^{23} +(-29.6307 - 23.7087i) q^{24} +224.655 q^{26} +(126.104 + 61.4884i) q^{27} +189.717i q^{28} +(-80.0044 + 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(-195.444 + 112.840i) q^{32} +(39.3853 + 100.834i) q^{33} +(-138.783 + 240.379i) q^{34} +(120.139 - 110.748i) q^{36} +215.365i q^{37} +(-207.244 - 119.652i) q^{38} +(46.9143 - 307.857i) q^{39} +(-70.8407 - 122.700i) q^{41} +(603.654 + 91.9908i) q^{42} +(119.430 + 68.9529i) q^{43} +126.078 q^{44} -123.138 q^{46} +(-29.0803 - 16.7895i) q^{47} +(143.281 + 366.829i) q^{48} +(319.885 + 554.058i) q^{49} +(300.422 + 240.379i) q^{51} +(-314.096 - 181.344i) q^{52} +41.9914i q^{53} +(-294.131 - 435.967i) q^{54} +(-114.474 + 198.275i) q^{56} +(-207.244 + 259.010i) q^{57} +(519.445 - 299.902i) q^{58} +(307.571 + 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} -953.535i q^{62} +(252.119 - 808.007i) q^{63} +239.652 q^{64} +(61.1331 - 401.162i) q^{66} +(-742.646 + 428.767i) q^{67} +(388.072 - 224.054i) q^{68} +(-25.7146 + 168.742i) q^{69} +588.665 q^{71} +(192.384 - 43.2522i) q^{72} +618.191i q^{73} +(403.655 - 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(565.607 - 326.553i) q^{77} +(-729.311 + 911.481i) q^{78} +(-172.644 + 299.029i) q^{79} +(-658.851 + 312.021i) q^{81} +531.102i q^{82} +(-946.711 - 546.584i) q^{83} +(-769.728 - 615.889i) q^{84} +(-258.474 - 447.691i) q^{86} +(-302.496 - 774.450i) q^{87} +(131.765 + 76.0746i) q^{88} -414.849 q^{89} -1878.79 q^{91} +(172.162 + 99.3979i) q^{92} +(-1306.68 - 199.125i) q^{93} +(62.9366 + 109.009i) q^{94} +(176.663 - 1159.28i) q^{96} +(174.427 + 100.705i) q^{97} -2398.22i q^{98} +(-536.967 - 167.547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} + O(q^{10}) \) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.24635 1.87428i −1.14776 0.662659i −0.199419 0.979914i \(-0.563905\pi\)
−0.948340 + 0.317255i \(0.897239\pi\)
\(3\) −3.24635 + 4.05724i −0.624761 + 0.780816i
\(4\) 3.02587 + 5.24096i 0.378234 + 0.655120i
\(5\) 0 0
\(6\) 18.1432 7.08665i 1.23449 0.482185i
\(7\) 27.1492 + 15.6746i 1.46592 + 0.846348i 0.999274 0.0380969i \(-0.0121296\pi\)
0.466644 + 0.884445i \(0.345463\pi\)
\(8\) 7.30318i 0.322758i
\(9\) −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 \(0.0744998\pi\)
\(12\) −31.0869 4.73733i −0.747834 0.113962i
\(13\) −51.9018 + 29.9655i −1.10731 + 0.639303i −0.938130 0.346283i \(-0.887444\pi\)
−0.169175 + 0.985586i \(0.554110\pi\)
\(14\) −58.7572 101.770i −1.12168 1.94281i
\(15\) 0 0
\(16\) 37.8952 65.6364i 0.592112 1.02557i
\(17\) 74.0460i 1.05640i −0.849120 0.528200i \(-0.822867\pi\)
0.849120 0.528200i \(-0.177133\pi\)
\(18\) −30.1471 + 96.6172i −0.394763 + 1.26516i
\(19\) 63.8390 0.770825 0.385413 0.922744i \(-0.374059\pi\)
0.385413 + 0.922744i \(0.374059\pi\)
\(20\) 0 0
\(21\) −151.731 + 59.2655i −1.57669 + 0.615847i
\(22\) −67.6322 + 39.0475i −0.655420 + 0.378407i
\(23\) 28.4484 16.4247i 0.257909 0.148904i −0.365472 0.930823i \(-0.619092\pi\)
0.623380 + 0.781919i \(0.285759\pi\)
\(24\) −29.6307 23.7087i −0.252015 0.201646i
\(25\) 0 0
\(26\) 224.655 1.69456
\(27\) 126.104 + 61.4884i 0.898841 + 0.438276i
\(28\) 189.717i 1.28047i
\(29\) −80.0044 + 138.572i −0.512291 + 0.887314i 0.487607 + 0.873063i \(0.337870\pi\)
−0.999898 + 0.0142513i \(0.995464\pi\)
\(30\) 0 0
\(31\) 127.187 + 220.294i 0.736884 + 1.27632i 0.953892 + 0.300151i \(0.0970371\pi\)
−0.217007 + 0.976170i \(0.569630\pi\)
\(32\) −195.444 + 112.840i −1.07969 + 0.623358i
\(33\) 39.3853 + 100.834i 0.207760 + 0.531908i
\(34\) −138.783 + 240.379i −0.700033 + 1.21249i
\(35\) 0 0
\(36\) 120.139 110.748i 0.556201 0.512722i
\(37\) 215.365i 0.956914i 0.878111 + 0.478457i \(0.158804\pi\)
−0.878111 + 0.478457i \(0.841196\pi\)
\(38\) −207.244 119.652i −0.884722 0.510794i
\(39\) 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 \(0.920304\pi\)
\(42\) 603.654 + 91.9908i 2.21776 + 0.337964i
\(43\) 119.430 + 68.9529i 0.423556 + 0.244540i 0.696597 0.717462i \(-0.254696\pi\)
−0.273042 + 0.962002i \(0.588030\pi\)
\(44\) 126.078 0.431976
\(45\) 0 0
\(46\) −123.138 −0.394689
\(47\) −29.0803 16.7895i −0.0902509 0.0521064i 0.454195 0.890902i \(-0.349927\pi\)
−0.544446 + 0.838796i \(0.683260\pi\)
\(48\) 143.281 + 366.829i 0.430852 + 1.10307i
\(49\) 319.885 + 554.058i 0.932611 + 1.61533i
\(50\) 0 0
\(51\) 300.422 + 240.379i 0.824854 + 0.659997i
\(52\) −314.096 181.344i −0.837641 0.483612i
\(53\) 41.9914i 0.108829i 0.998518 + 0.0544147i \(0.0173293\pi\)
−0.998518 + 0.0544147i \(0.982671\pi\)
\(54\) −294.131 435.967i −0.741225 1.09866i
\(55\) 0 0
\(56\) −114.474 + 198.275i −0.273166 + 0.473137i
\(57\) −207.244 + 259.010i −0.481581 + 0.601873i
\(58\) 519.445 299.902i 1.17597 0.678949i
\(59\) 307.571 + 532.728i 0.678683 + 1.17551i 0.975378 + 0.220541i \(0.0707824\pi\)
−0.296694 + 0.954973i \(0.595884\pi\)
\(60\) 0 0
\(61\) 67.1535 116.313i 0.140953 0.244137i −0.786903 0.617077i \(-0.788317\pi\)
0.927856 + 0.372939i \(0.121650\pi\)
\(62\) 953.535i 1.95321i
\(63\) 252.119 808.007i 0.504191 1.61586i
\(64\) 239.652 0.468071
\(65\) 0 0
\(66\) 61.1331 401.162i 0.114015 0.748176i
\(67\) −742.646 + 428.767i −1.35416 + 0.781824i −0.988829 0.149055i \(-0.952377\pi\)
−0.365329 + 0.930878i \(0.619044\pi\)
\(68\) 388.072 224.054i 0.692069 0.399566i
\(69\) −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 \(0.336272\pi\)
\(72\) 192.384 43.2522i 0.314898 0.0707962i
\(73\) 618.191i 0.991148i 0.868566 + 0.495574i \(0.165042\pi\)
−0.868566 + 0.495574i \(0.834958\pi\)
\(74\) 403.655 699.152i 0.634108 1.09831i
\(75\) 0 0
\(76\) 193.169 + 334.578i 0.291552 + 0.504983i
\(77\) 565.607 326.553i 0.837103 0.483301i
\(78\) −729.311 + 911.481i −1.05869 + 1.32314i
\(79\) −172.644 + 299.029i −0.245873 + 0.425865i −0.962377 0.271718i \(-0.912408\pi\)
0.716503 + 0.697584i \(0.245741\pi\)
\(80\) 0 0
\(81\) −658.851 + 312.021i −0.903773 + 0.428012i
\(82\) 531.102i 0.715249i
\(83\) −946.711 546.584i −1.25199 0.722836i −0.280484 0.959859i \(-0.590495\pi\)
−0.971504 + 0.237023i \(0.923828\pi\)
\(84\) −769.728 615.889i −0.999812 0.799988i
\(85\) 0 0
\(86\) −258.474 447.691i −0.324093 0.561346i
\(87\) −302.496 774.450i −0.372770 0.954365i
\(88\) 131.765 + 76.0746i 0.159616 + 0.0921543i
\(89\) −414.849 −0.494089 −0.247045 0.969004i \(-0.579459\pi\)
−0.247045 + 0.969004i \(0.579459\pi\)
\(90\) 0 0
\(91\) −1878.79 −2.16429
\(92\) 172.162 + 99.3979i 0.195100 + 0.112641i
\(93\) −1306.68 199.125i −1.45695 0.222024i
\(94\) 62.9366 + 109.009i 0.0690576 + 0.119611i
\(95\) 0 0
\(96\) 176.663 1159.28i 0.187819 1.23249i
\(97\) 174.427 + 100.705i 0.182581 + 0.105413i 0.588505 0.808494i \(-0.299717\pi\)
−0.405924 + 0.913907i \(0.633050\pi\)
\(98\) 2398.22i 2.47201i
\(99\) −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 \(0.208397\pi\)
\(102\) −524.738 1343.43i −0.509380 1.30411i
\(103\) 456.931 263.809i 0.437114 0.252368i −0.265259 0.964177i \(-0.585457\pi\)
0.702373 + 0.711810i \(0.252124\pi\)
\(104\) −218.843 379.048i −0.206340 0.357391i
\(105\) 0 0
\(106\) 78.7038 136.319i 0.0721168 0.124910i
\(107\) 2084.24i 1.88310i 0.336877 + 0.941549i \(0.390629\pi\)
−0.336877 + 0.941549i \(0.609371\pi\)
\(108\) 59.3157 + 846.961i 0.0528487 + 0.754619i
\(109\) −925.651 −0.813406 −0.406703 0.913560i \(-0.633322\pi\)
−0.406703 + 0.913560i \(0.633322\pi\)
\(110\) 0 0
\(111\) −873.788 699.152i −0.747174 0.597843i
\(112\) 2057.65 1187.98i 1.73598 1.00227i
\(113\) −472.866 + 273.009i −0.393659 + 0.227279i −0.683745 0.729721i \(-0.739650\pi\)
0.290085 + 0.957001i \(0.406316\pi\)
\(114\) 1158.25 452.405i 0.951576 0.371681i
\(115\) 0 0
\(116\) −968.332 −0.775063
\(117\) 1096.75 + 1189.75i 0.866619 + 0.940109i
\(118\) 2305.90i 1.79894i
\(119\) 1160.64 2010.29i 0.894082 1.54860i
\(120\) 0 0
\(121\) 448.487 + 776.802i 0.336955 + 0.583623i
\(122\) −436.008 + 251.729i −0.323560 + 0.186807i
\(123\) 727.796 + 110.909i 0.533522 + 0.0813033i
\(124\) −769.701 + 1333.16i −0.557429 + 0.965495i
\(125\) 0 0
\(126\) −2332.90 + 2150.53i −1.64946 + 1.52051i
\(127\) 975.972i 0.681918i −0.940078 0.340959i \(-0.889248\pi\)
0.940078 0.340959i \(-0.110752\pi\)
\(128\) 785.559 + 453.543i 0.542455 + 0.313187i
\(129\) −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 \(0.650505\pi\)
\(132\) −409.293 + 511.528i −0.269882 + 0.337294i
\(133\) 1733.18 + 1000.65i 1.12997 + 0.652387i
\(134\) 3214.52 2.07233
\(135\) 0 0
\(136\) 540.771 0.340961
\(137\) −572.833 330.725i −0.357229 0.206246i 0.310635 0.950529i \(-0.399458\pi\)
−0.667865 + 0.744283i \(0.732792\pi\)
\(138\) 399.749 499.600i 0.246586 0.308180i
\(139\) 691.495 + 1197.70i 0.421955 + 0.730848i 0.996131 0.0878842i \(-0.0280105\pi\)
−0.574175 + 0.818732i \(0.694677\pi\)
\(140\) 0 0
\(141\) 162.524 63.4810i 0.0970708 0.0379153i
\(142\) −1911.02 1103.33i −1.12936 0.652035i
\(143\) 1248.56i 0.730139i
\(144\) −1953.45 609.528i −1.13047 0.352736i
\(145\) 0 0
\(146\) 1158.66 2006.87i 0.656793 1.13760i
\(147\) −3286.41 500.815i −1.84393 0.280997i
\(148\) −1128.72 + 651.667i −0.626894 + 0.361937i
\(149\) 1581.75 + 2739.66i 0.869676 + 1.50632i 0.862328 + 0.506349i \(0.169005\pi\)
0.00734719 + 0.999973i \(0.497661\pi\)
\(150\) 0 0
\(151\) 1279.40 2215.98i 0.689509 1.19427i −0.282488 0.959271i \(-0.591160\pi\)
0.971997 0.234994i \(-0.0755071\pi\)
\(152\) 466.228i 0.248790i
\(153\) −1950.55 + 438.529i −1.03067 + 0.231719i
\(154\) −2448.21 −1.28106
\(155\) 0 0
\(156\) 1755.42 685.659i 0.900937 0.351901i
\(157\) 3031.92 1750.48i 1.54123 0.889832i 0.542474 0.840073i \(-0.317488\pi\)
0.998761 0.0497594i \(-0.0158454\pi\)
\(158\) 1120.93 647.168i 0.564407 0.325860i
\(159\) −170.369 136.319i −0.0849758 0.0679924i
\(160\) 0 0
\(161\) 1029.80 0.504097
\(162\) 2723.68 + 221.943i 1.32094 + 0.107639i
\(163\) 263.950i 0.126835i −0.997987 0.0634176i \(-0.979800\pi\)
0.997987 0.0634176i \(-0.0202000\pi\)
\(164\) 428.710 742.547i 0.204126 0.353556i
\(165\) 0 0
\(166\) 2048.90 + 3548.81i 0.957987 + 1.65928i
\(167\) −3108.21 + 1794.53i −1.44024 + 0.831524i −0.997865 0.0653054i \(-0.979198\pi\)
−0.442377 + 0.896829i \(0.645865\pi\)
\(168\) −432.826 1108.12i −0.198770 0.508889i
\(169\) 697.365 1207.87i 0.317417 0.549782i
\(170\) 0 0
\(171\) −378.080 1681.68i −0.169079 0.752053i
\(172\) 834.570i 0.369973i
\(173\) 320.824 + 185.228i 0.140993 + 0.0814024i 0.568837 0.822450i \(-0.307393\pi\)
−0.427844 + 0.903853i \(0.640727\pi\)
\(174\) −469.529 + 3081.10i −0.204568 + 1.34240i
\(175\) 0 0
\(176\) −789.482 1367.42i −0.338122 0.585644i
\(177\) −3159.89 481.535i −1.34188 0.204488i
\(178\) 1346.75 + 777.545i 0.567095 + 0.327413i
\(179\) −446.898 −0.186607 −0.0933036 0.995638i \(-0.529743\pi\)
−0.0933036 + 0.995638i \(0.529743\pi\)
\(180\) 0 0
\(181\) −904.046 −0.371255 −0.185628 0.982620i \(-0.559432\pi\)
−0.185628 + 0.982620i \(0.559432\pi\)
\(182\) 6099.21 + 3521.38i 2.48409 + 1.43419i
\(183\) 253.907 + 650.051i 0.102565 + 0.262586i
\(184\) 119.952 + 207.764i 0.0480598 + 0.0832420i
\(185\) 0 0
\(186\) 3868.72 + 3095.51i 1.52510 + 1.22029i
\(187\) −1335.95 771.311i −0.522430 0.301625i
\(188\) 203.211i 0.0788336i
\(189\) 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 \(0.130437\pi\)
\(192\) −777.995 + 972.326i −0.292432 + 0.365477i
\(193\) 3822.40 2206.87i 1.42561 0.823076i 0.428839 0.903381i \(-0.358923\pi\)
0.996770 + 0.0803048i \(0.0255894\pi\)
\(194\) −377.500 653.850i −0.139706 0.241978i
\(195\) 0 0
\(196\) −1935.86 + 3353.01i −0.705490 + 1.22194i
\(197\) 4807.15i 1.73855i −0.494325 0.869277i \(-0.664585\pi\)
0.494325 0.869277i \(-0.335415\pi\)
\(198\) 1429.15 + 1550.35i 0.512956 + 0.556456i
\(199\) −313.833 −0.111794 −0.0558970 0.998437i \(-0.517802\pi\)
−0.0558970 + 0.998437i \(0.517802\pi\)
\(200\) 0 0
\(201\) 671.281 4405.02i 0.235565 1.54580i
\(202\) 861.527 497.403i 0.300083 0.173253i
\(203\) −4344.11 + 2508.07i −1.50195 + 0.867153i
\(204\) −350.780 + 2301.86i −0.120390 + 0.790012i
\(205\) 0 0
\(206\) −1977.81 −0.668935
\(207\) −601.149 652.127i −0.201849 0.218966i
\(208\) 4542.20i 1.51416i
\(209\) 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 \(0.963579\pi\)
\(212\) −220.075 + 127.061i −0.0712964 + 0.0411630i
\(213\) −1911.02 + 2388.36i −0.614745 + 0.768298i
\(214\) 3906.46 6766.19i 1.24785 2.16134i
\(215\) 0 0
\(216\) −449.060 + 920.959i −0.141457 + 0.290108i
\(217\) 7974.40i 2.49464i
\(218\) 3004.99 + 1734.93i 0.933594 + 0.539011i
\(219\) −2508.15 2006.87i −0.773904 0.619230i
\(220\) 0 0
\(221\) 2218.83 + 3843.12i 0.675360 + 1.16976i
\(222\) 1526.22 + 3907.42i 0.461410 + 1.18130i
\(223\) −2020.79 1166.71i −0.606827 0.350352i 0.164896 0.986311i \(-0.447271\pi\)
−0.771722 + 0.635959i \(0.780605\pi\)
\(224\) −7074.87 −2.11031
\(225\) 0 0
\(226\) 2046.79 0.602435
\(227\) 2358.79 + 1361.85i 0.689684 + 0.398189i 0.803494 0.595313i \(-0.202972\pi\)
−0.113810 + 0.993503i \(0.536305\pi\)
\(228\) −1984.56 302.426i −0.576449 0.0878451i
\(229\) −1657.08 2870.15i −0.478179 0.828230i 0.521508 0.853246i \(-0.325370\pi\)
−0.999687 + 0.0250162i \(0.992036\pi\)
\(230\) 0 0
\(231\) −511.255 + 3354.91i −0.145619 + 0.955571i
\(232\) −1012.01 584.286i −0.286388 0.165346i
\(233\) 3175.44i 0.892833i 0.894825 + 0.446416i \(0.147300\pi\)
−0.894825 + 0.446416i \(0.852700\pi\)
\(234\) −1330.50 5917.98i −0.371698 1.65329i
\(235\) 0 0
\(236\) −1861.34 + 3223.93i −0.513402 + 0.889238i
\(237\) −652.767 1671.21i −0.178910 0.458046i
\(238\) −7535.70 + 4350.74i −2.05238 + 1.18494i
\(239\) −123.062 213.150i −0.0333064 0.0576884i 0.848892 0.528567i \(-0.177270\pi\)
−0.882198 + 0.470878i \(0.843937\pi\)
\(240\) 0 0
\(241\) 2643.87 4579.31i 0.706666 1.22398i −0.259421 0.965764i \(-0.583532\pi\)
0.966087 0.258217i \(-0.0831349\pi\)
\(242\) 3362.36i 0.893144i
\(243\) 872.919 3686.04i 0.230444 0.973086i
\(244\) 812.791 0.213252
\(245\) 0 0
\(246\) −2154.81 1724.14i −0.558478 0.446860i
\(247\) −3313.36 + 1912.97i −0.853539 + 0.492791i
\(248\) −1608.84 + 928.867i −0.411943 + 0.237835i
\(249\) 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 \(0.384573\pi\)
\(252\) 4997.62 1123.58i 1.24929 0.280868i
\(253\) 684.361i 0.170061i
\(254\) −1829.25 + 3168.35i −0.451879 + 0.782677i
\(255\) 0 0
\(256\) −2658.74 4605.08i −0.649107 1.12429i
\(257\) −1631.76 + 942.096i −0.396056 + 0.228663i −0.684781 0.728749i \(-0.740102\pi\)
0.288725 + 0.957412i \(0.406769\pi\)
\(258\) 2655.49 + 404.670i 0.640789 + 0.0976497i
\(259\) −3375.76 + 5846.99i −0.809883 + 1.40276i
\(260\) 0 0
\(261\) 4124.14 + 1286.84i 0.978075 + 0.305185i
\(262\) 6107.27i 1.44011i
\(263\) 478.922 + 276.506i 0.112287 + 0.0648292i 0.555092 0.831789i \(-0.312683\pi\)
−0.442804 + 0.896618i \(0.646016\pi\)
\(264\) −736.409 + 287.638i −0.171677 + 0.0670563i
\(265\) 0 0
\(266\) −3751.00 6496.93i −0.864620 1.49757i
\(267\) 1346.75 1683.14i 0.308688 0.385793i
\(268\) −4494.30 2594.78i −1.02438 0.591424i
\(269\) −3363.48 −0.762361 −0.381180 0.924501i \(-0.624482\pi\)
−0.381180 + 0.924501i \(0.624482\pi\)
\(270\) 0 0
\(271\) −3333.85 −0.747295 −0.373648 0.927571i \(-0.621893\pi\)
−0.373648 + 0.927571i \(0.621893\pi\)
\(272\) −4860.11 2805.99i −1.08341 0.625507i
\(273\) 6099.21 7622.70i 1.35217 1.68991i
\(274\) 1239.75 + 2147.30i 0.273342 + 0.473443i
\(275\) 0 0
\(276\) −962.181 + 375.823i −0.209842 + 0.0819633i
\(277\) 4665.50 + 2693.63i 1.01199 + 0.584275i 0.911775 0.410690i \(-0.134712\pi\)
0.100220 + 0.994965i \(0.468045\pi\)
\(278\) 5184.23i 1.11845i
\(279\) 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 \(0.295755\pi\)
\(282\) −646.591 98.5340i −0.136539 0.0208071i
\(283\) −2397.81 + 1384.38i −0.503658 + 0.290787i −0.730223 0.683209i \(-0.760584\pi\)
0.226565 + 0.973996i \(0.427250\pi\)
\(284\) 1781.23 + 3085.17i 0.372170 + 0.644617i
\(285\) 0 0
\(286\) 2340.16 4053.27i 0.483833 0.838024i
\(287\) 4441.60i 0.913516i
\(288\) 4129.98 + 4480.20i 0.845004 + 0.916662i
\(289\) −569.810 −0.115980
\(290\) 0 0
\(291\) −974.836 + 380.766i −0.196378 + 0.0767041i
\(292\) −3239.91 + 1870.57i −0.649321 + 0.374886i
\(293\) 3013.76 1740.00i 0.600907 0.346934i −0.168491 0.985703i \(-0.553890\pi\)
0.769398 + 0.638769i \(0.220556\pi\)
\(294\) 9730.17 + 7785.48i 1.93019 + 1.54442i
\(295\) 0 0
\(296\) −1572.85 −0.308852
\(297\) 2422.96 1634.68i 0.473382 0.319374i
\(298\) 11858.6i 2.30519i
\(299\) −984.348 + 1704.94i −0.190389 + 0.329764i
\(300\) 0 0
\(301\) 2161.62 + 3744.03i 0.413932 + 0.716951i
\(302\) −8306.75 + 4795.91i −1.58278 + 0.913819i
\(303\) −501.705 1284.47i −0.0951229 0.243533i
\(304\) 2419.19 4190.16i 0.456415 0.790534i
\(305\) 0 0
\(306\) 7154.11 + 2232.27i 1.33651 + 0.417027i
\(307\) 1810.36i 0.336555i −0.985740 0.168278i \(-0.946179\pi\)
0.985740 0.168278i \(-0.0538205\pi\)
\(308\) 3422.91 + 1976.22i 0.633241 + 0.365602i
\(309\) −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 \(0.807557\pi\)
\(312\) 2248.33 + 342.623i 0.407970 + 0.0621706i
\(313\) −1918.36 1107.57i −0.346429 0.200011i 0.316682 0.948532i \(-0.397431\pi\)
−0.663111 + 0.748521i \(0.730764\pi\)
\(314\) −13123.6 −2.35862
\(315\) 0 0
\(316\) −2089.60 −0.371990
\(317\) 569.884 + 329.023i 0.100971 + 0.0582958i 0.549635 0.835405i \(-0.314767\pi\)
−0.448664 + 0.893700i \(0.648100\pi\)
\(318\) 297.578 + 761.859i 0.0524760 + 0.134349i
\(319\) 1666.76 + 2886.91i 0.292540 + 0.506695i
\(320\) 0 0
\(321\) −8456.28 6766.19i −1.47035 1.17649i
\(322\) −3343.10 1930.14i −0.578582 0.334045i
\(323\) 4727.03i 0.814299i
\(324\) −3628.88 2508.88i −0.622237 0.430192i
\(325\) 0 0
\(326\) −494.717 + 856.875i −0.0840485 + 0.145576i
\(327\) 3004.99 3755.59i 0.508184 0.635121i
\(328\) 896.098 517.362i 0.150850 0.0870931i
\(329\) −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 \(0.311014\pi\)
\(332\) 6615.57i 1.09360i
\(333\) 5673.25 1275.48i 0.933610 0.209897i
\(334\) 13453.8 2.20407
\(335\) 0 0
\(336\) −1859.92 + 12205.0i −0.301984 + 1.98165i
\(337\) −2910.95 + 1680.64i −0.470532 + 0.271662i −0.716462 0.697626i \(-0.754240\pi\)
0.245930 + 0.969288i \(0.420907\pi\)
\(338\) −4527.78 + 2614.12i −0.728636 + 0.420678i
\(339\) 427.426 2804.82i 0.0684796 0.449371i
\(340\) 0 0
\(341\) 5299.44 0.841586
\(342\) −1924.56 + 6167.95i −0.304293 + 0.975217i
\(343\) 9303.52i 1.46456i
\(344\) −503.575 + 872.218i −0.0789272 + 0.136706i
\(345\) 0 0
\(346\) −694.339 1202.63i −0.107884 0.186861i
\(347\) 8102.13 4677.77i 1.25344 0.723677i 0.281653 0.959516i \(-0.409117\pi\)
0.971792 + 0.235840i \(0.0757841\pi\)
\(348\) 3143.55 3928.75i 0.484229 0.605182i
\(349\) 3519.65 6096.22i 0.539836 0.935023i −0.459077 0.888397i \(-0.651820\pi\)
0.998912 0.0466263i \(-0.0148470\pi\)
\(350\) 0 0
\(351\) −8387.55 + 587.410i −1.27548 + 0.0893266i
\(352\) 4701.65i 0.711929i
\(353\) 3639.19 + 2101.09i 0.548710 + 0.316798i 0.748602 0.663020i \(-0.230726\pi\)
−0.199891 + 0.979818i \(0.564059\pi\)
\(354\) 9355.58 + 7485.76i 1.40464 + 1.12391i
\(355\) 0 0
\(356\) −1255.28 2174.21i −0.186881 0.323688i
\(357\) 4388.37 + 11235.1i 0.650581 + 1.66562i
\(358\) 1450.79 + 837.612i 0.214180 + 0.123657i
\(359\) −588.013 −0.0864461 −0.0432230 0.999065i \(-0.513763\pi\)
−0.0432230 + 0.999065i \(0.513763\pi\)
\(360\) 0 0
\(361\) −2783.58 −0.405828
\(362\) 2934.85 + 1694.44i 0.426112 + 0.246016i
\(363\) −4607.62 702.155i −0.666218 0.101525i
\(364\) −5684.97 9846.66i −0.818608 1.41787i
\(365\) 0 0
\(366\) 394.109 2586.19i 0.0562853 0.369350i
\(367\) 6742.10 + 3892.55i 0.958950 + 0.553650i 0.895850 0.444357i \(-0.146568\pi\)
0.0631004 + 0.998007i \(0.479901\pi\)
\(368\) 2489.67i 0.352671i
\(369\) −2812.67 + 2592.79i −0.396806 + 0.365787i
\(370\) 0 0
\(371\) −658.198 + 1140.03i −0.0921077 + 0.159535i
\(372\) −2910.23 7450.77i −0.405615 1.03845i
\(373\) 6775.81 3912.02i 0.940585 0.543047i 0.0504412 0.998727i \(-0.483937\pi\)
0.890144 + 0.455680i \(0.150604\pi\)
\(374\) 2891.31 + 5007.90i 0.399749 + 0.692385i
\(375\) 0 0
\(376\) 122.617 212.378i 0.0168177 0.0291292i
\(377\) 9589.49i 1.31004i
\(378\) −1151.81 16446.5i −0.156727 2.23788i
\(379\) 4679.90 0.634275 0.317138 0.948379i \(-0.397278\pi\)
0.317138 + 0.948379i \(0.397278\pi\)
\(380\) 0 0
\(381\) 3959.75 + 3168.35i 0.532452 + 0.426036i
\(382\) −1946.47 + 1123.79i −0.260707 + 0.150519i
\(383\) 5826.31 3363.82i 0.777313 0.448782i −0.0581644 0.998307i \(-0.518525\pi\)
0.835477 + 0.549525i \(0.185191\pi\)
\(384\) −4390.33 + 1714.84i −0.583446 + 0.227891i
\(385\) 0 0
\(386\) −16545.2 −2.18167
\(387\) 1109.08 3554.44i 0.145679 0.466880i
\(388\) 1218.89i 0.159483i
\(389\) −2386.44 + 4133.43i −0.311047 + 0.538749i −0.978589 0.205823i \(-0.934013\pi\)
0.667542 + 0.744572i \(0.267346\pi\)
\(390\) 0 0
\(391\) −1216.18 2106.49i −0.157302 0.272455i
\(392\) −4046.38 + 2336.18i −0.521360 + 0.301007i
\(393\) −8369.10 1275.37i −1.07421 0.163699i
\(394\) −9009.95 + 15605.7i −1.15207 + 1.99544i
\(395\) 0 0
\(396\) −746.681 3321.20i −0.0947529 0.421456i
\(397\) 4688.95i 0.592775i −0.955068 0.296388i \(-0.904218\pi\)
0.955068 0.296388i \(-0.0957820\pi\)
\(398\) 1018.81 + 588.211i 0.128313 + 0.0740813i
\(399\) −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 \(0.863780\pi\)
\(402\) −10435.5 + 13042.1i −1.29471 + 1.61811i
\(403\) −13202.4 7622.43i −1.63191 0.942185i
\(404\) −1606.03 −0.197780
\(405\) 0 0
\(406\) 18803.3 2.29851
\(407\) 3885.66 + 2243.38i 0.473230 + 0.273220i
\(408\) −1755.53 + 2194.04i −0.213019 + 0.266228i
\(409\) −4389.41 7602.68i −0.530666 0.919140i −0.999360 0.0357796i \(-0.988609\pi\)
0.468694 0.883361i \(-0.344725\pi\)
\(410\) 0 0
\(411\) 3201.45 1250.47i 0.384224 0.150076i
\(412\) 2765.23 + 1596.50i 0.330662 + 0.190908i
\(413\) 19284.2i 2.29761i
\(414\) 729.271 + 3243.76i 0.0865742 + 0.385077i
\(415\) 0 0
\(416\) 6762.61 11713.2i 0.797029 1.38050i
\(417\) −7104.21 1082.61i −0.834279 0.127136i
\(418\) −4317.58 + 2492.75i −0.505214 + 0.291686i
\(419\) −2138.02 3703.17i −0.249282 0.431770i 0.714044 0.700100i \(-0.246861\pi\)
−0.963327 + 0.268330i \(0.913528\pi\)
\(420\) 0 0
\(421\) −7231.64 + 12525.6i −0.837169 + 1.45002i 0.0550823 + 0.998482i \(0.482458\pi\)
−0.892252 + 0.451538i \(0.850875\pi\)
\(422\) 9142.07i 1.05457i
\(423\) −270.052 + 865.480i −0.0310411 + 0.0994825i
\(424\) −306.671 −0.0351256
\(425\) 0 0
\(426\) 10680.3 4171.66i 1.21470 0.474455i
\(427\) 3646.32 2105.21i 0.413250 0.238590i
\(428\) −10923.4 + 6306.65i −1.23366 + 0.712251i
\(429\) −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 \(0.539376\pi\)
\(432\) 8814.60 5946.89i 0.981696 0.662314i
\(433\) 10062.3i 1.11677i 0.829581 + 0.558386i \(0.188579\pi\)
−0.829581 + 0.558386i \(0.811421\pi\)
\(434\) 14946.3 25887.7i 1.65310 2.86325i
\(435\) 0 0
\(436\) −2800.90 4851.30i −0.307658 0.532879i
\(437\) 1816.12 1048.54i 0.198803 0.114779i
\(438\) 4380.90 + 11216.0i 0.477917 + 1.22356i
\(439\) 6658.62 11533.1i 0.723915 1.25386i −0.235504 0.971873i \(-0.575674\pi\)
0.959419 0.281984i \(-0.0909925\pi\)
\(440\) 0 0
\(441\) 12700.8 11707.9i 1.37142 1.26422i
\(442\) 16634.8i 1.79013i
\(443\) −12362.6 7137.55i −1.32588 0.765497i −0.341220 0.939983i \(-0.610840\pi\)
−0.984660 + 0.174486i \(0.944174\pi\)
\(444\) 1020.26 6695.03i 0.109052 0.715613i
\(445\) 0 0
\(446\) 4373.47 + 7575.08i 0.464327 + 0.804238i
\(447\) −16250.4 2476.39i −1.71950 0.262034i
\(448\) 6506.36 + 3756.45i 0.686153 + 0.396151i
\(449\) 1690.02 0.177632 0.0888162 0.996048i \(-0.471692\pi\)
0.0888162 + 0.996048i \(0.471692\pi\)
\(450\) 0 0
\(451\) −2951.69 −0.308181
\(452\) −2861.66 1652.18i −0.297791 0.171929i
\(453\) 4837.39 + 12384.7i 0.501723 + 1.28451i
\(454\) −5104.97 8842.07i −0.527727 0.914051i
\(455\) 0 0
\(456\) −1891.60 1513.54i −0.194259 0.155434i
\(457\) 5771.53 + 3332.19i 0.590767 + 0.341080i 0.765401 0.643554i \(-0.222541\pi\)
−0.174633 + 0.984634i \(0.555874\pi\)
\(458\) 12423.3i 1.26748i
\(459\) 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 \(0.193510\pi\)
\(462\) 7947.76 9932.99i 0.800354 1.00027i
\(463\) 5050.68 2916.01i 0.506966 0.292697i −0.224620 0.974446i \(-0.572114\pi\)
0.731585 + 0.681750i \(0.238781\pi\)
\(464\) 6063.56 + 10502.4i 0.606668 + 1.05078i
\(465\) 0 0
\(466\) 5951.67 10308.6i 0.591644 1.02476i
\(467\) 17410.6i 1.72519i 0.505892 + 0.862597i \(0.331163\pi\)
−0.505892 + 0.862597i \(0.668837\pi\)
\(468\) −2916.84 + 9348.06i −0.288100 + 0.923321i
\(469\) −26883.0 −2.64678
\(470\) 0 0
\(471\) −2740.57 + 17983.9i −0.268108 + 1.75935i
\(472\) −3890.61 + 2246.24i −0.379406 + 0.219050i
\(473\) 2488.12 1436.52i 0.241869 0.139643i
\(474\) −1013.21 + 6648.81i −0.0981822 + 0.644283i
\(475\) 0 0
\(476\) 14047.8 1.35269
\(477\) 1106.16 248.689i 0.106179 0.0238715i
\(478\) 922.614i 0.0882832i
\(479\) −1639.67 + 2839.99i −0.156406 + 0.270903i −0.933570 0.358395i \(-0.883324\pi\)
0.777164 + 0.629298i \(0.216657\pi\)
\(480\) 0 0
\(481\) −6453.53 11177.8i −0.611758 1.05960i
\(482\) −17165.9 + 9910.71i −1.62216 + 0.936557i
\(483\) −3343.10 + 4178.15i −0.314940 + 0.393607i
\(484\) −2714.13 + 4701.00i −0.254895 + 0.441492i
\(485\) 0 0
\(486\) −9742.49 + 10330.1i −0.909318 + 0.964162i
\(487\) 10506.7i 0.977624i −0.872389 0.488812i \(-0.837430\pi\)
0.872389 0.488812i \(-0.162570\pi\)
\(488\) 849.456 + 490.433i 0.0787972 + 0.0454936i
\(489\) 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 \(0.605771\pi\)
\(492\) 1620.95 + 4149.95i 0.148532 + 0.380272i
\(493\) 10260.7 + 5924.01i 0.937359 + 0.541184i
\(494\) 14341.8 1.30621
\(495\) 0 0
\(496\) 19279.1 1.74527
\(497\) 15981.8 + 9227.09i 1.44242 + 0.832780i
\(498\) −21049.8 3207.78i −1.89411 0.288643i
\(499\) 4723.70 + 8181.68i 0.423771 + 0.733993i 0.996305 0.0858882i \(-0.0273728\pi\)
−0.572534 + 0.819881i \(0.694039\pi\)
\(500\) 0 0
\(501\) 2809.52 18436.4i 0.250539 1.64407i
\(502\) −9158.70 5287.78i −0.814288 0.470130i
\(503\) 14579.2i 1.29235i −0.763188 0.646177i \(-0.776367\pi\)
0.763188 0.646177i \(-0.223633\pi\)
\(504\) 5901.02 + 1841.27i 0.521532 + 0.162732i
\(505\) 0 0
\(506\) −1282.69 + 2221.68i −0.112692 + 0.195189i
\(507\) 2636.73 + 6750.55i 0.230969 + 0.591327i
\(508\) 5115.03 2953.17i 0.446738 0.257924i
\(509\) 4205.32 + 7283.83i 0.366204 + 0.634283i 0.988969 0.148126i \(-0.0473240\pi\)
−0.622765 + 0.782409i \(0.713991\pi\)
\(510\) 0 0
\(511\) −9689.89 + 16783.4i −0.838856 + 1.45294i
\(512\) 12676.3i 1.09417i
\(513\) 8050.35 + 3925.36i 0.692849 + 0.337834i
\(514\) 7063.02 0.606102
\(515\) 0 0
\(516\) −3386.05 2709.31i −0.288881 0.231145i
\(517\) −605.838 + 349.781i −0.0515372 + 0.0297550i
\(518\) 21917.8 12654.3i 1.85910 1.07335i
\(519\) −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 \(0.361016\pi\)
\(522\) −10976.5 11907.3i −0.920361 0.998409i
\(523\) 20006.3i 1.67269i −0.548205 0.836344i \(-0.684688\pi\)
0.548205 0.836344i \(-0.315312\pi\)
\(524\) −4929.83 + 8538.72i −0.410994 + 0.711862i
\(525\) 0 0
\(526\) −1036.50 1795.27i −0.0859192 0.148817i
\(527\) 16311.9 9417.67i 1.34830 0.778444i
\(528\) 8110.90 + 1236.02i 0.668525 + 0.101877i
\(529\) −5543.96 + 9602.42i −0.455655 + 0.789218i
\(530\) 0 0
\(531\) 12211.8 11257.2i 0.998019 0.920001i
\(532\) 12111.4i 0.987019i
\(533\) 7353.52 + 4245.56i 0.597592 + 0.345020i
\(534\) −7526.70 + 2939.89i −0.609948 + 0.238243i
\(535\) 0 0
\(536\) −3131.36 5423.67i −0.252340 0.437065i
\(537\) 1450.79 1813.17i 0.116585 0.145706i
\(538\) 10919.0 + 6304.11i 0.875006 + 0.505185i
\(539\) 13328.5 1.06512
\(540\) 0 0
\(541\) −1884.15 −0.149734 −0.0748668 0.997194i \(-0.523853\pi\)
−0.0748668 + 0.997194i \(0.523853\pi\)
\(542\) 10822.9 + 6248.58i 0.857715 + 0.495202i
\(543\) 2934.85 3667.93i 0.231946 0.289882i
\(544\) 8355.34 + 14471.9i 0.658515 + 1.14058i
\(545\) 0 0
\(546\) −34087.3 + 13314.3i −2.67180 + 1.04359i
\(547\) 15585.4 + 8998.24i 1.21825 + 0.703358i 0.964544 0.263922i \(-0.0850163\pi\)
0.253708 + 0.967281i \(0.418350\pi\)
\(548\) 4002.93i 0.312038i
\(549\) −3461.68 1080.14i −0.269109 0.0839691i
\(550\) 0 0
\(551\) −5107.40 + 8846.28i −0.394887 + 0.683964i
\(552\) −1232.35 187.798i −0.0950226 0.0144805i
\(553\) −9374.30 + 5412.25i −0.720860 + 0.416189i
\(554\) −10097.2 17488.9i −0.774351 1.34121i
\(555\) 0 0
\(556\) −4184.75 + 7248.19i −0.319196 + 0.552863i
\(557\) 3615.76i 0.275054i −0.990498 0.137527i \(-0.956085\pi\)
0.990498 0.137527i \(-0.0439153\pi\)
\(558\) −25118.5 + 5647.21i −1.90564 + 0.428433i
\(559\) −8264.84 −0.625341
\(560\) 0 0
\(561\) 7466.36 2916.32i 0.561907 0.219478i
\(562\) 12065.7 6966.14i 0.905625 0.522863i
\(563\) −12836.1 + 7410.91i −0.960881 + 0.554765i −0.896444 0.443157i \(-0.853858\pi\)
−0.0644370 + 0.997922i \(0.520525\pi\)
\(564\) 824.478 + 659.696i 0.0615546 + 0.0492522i
\(565\) 0 0
\(566\) 10378.9 0.770771
\(567\) −22778.1 1856.11i −1.68710 0.137477i
\(568\) 4299.13i 0.317583i
\(569\) 11224.7 19441.8i 0.827005 1.43241i −0.0733726 0.997305i \(-0.523376\pi\)
0.900377 0.435110i \(-0.143290\pi\)
\(570\) 0 0
\(571\) 8006.75 + 13868.1i 0.586817 + 1.01640i 0.994646 + 0.103338i \(0.0329523\pi\)
−0.407830 + 0.913058i \(0.633714\pi\)
\(572\) −6543.66 + 3777.98i −0.478329 + 0.276163i
\(573\) 1133.52 + 2902.03i 0.0826410 + 0.211577i
\(574\) −8324.81 + 14419.0i −0.605350 + 1.04850i
\(575\) 0 0
\(576\) −1419.31 6313.03i −0.102670 0.456672i
\(577\) 3096.97i 0.223446i 0.993739 + 0.111723i \(0.0356370\pi\)
−0.993739 + 0.111723i \(0.964363\pi\)
\(578\) 1849.81 + 1067.99i 0.133117 + 0.0768553i
\(579\) −3455.09 + 22672.7i −0.247994 + 1.62736i
\(580\) 0 0
\(581\) −17135.0 29678.6i −1.22354 2.11924i
\(582\) 3878.33 + 591.018i 0.276223 + 0.0420936i
\(583\) 757.616 + 437.410i 0.0538203 + 0.0310732i
\(584\) −4514.76 −0.319901
\(585\) 0 0
\(586\) −13045.0 −0.919595
\(587\) −21325.7 12312.4i −1.49950 0.865734i −0.499496 0.866316i \(-0.666481\pi\)
−1.00000 0.000582275i \(0.999815\pi\)
\(588\) −7319.49 18739.3i −0.513351 1.31428i
\(589\) 8119.48 + 14063.3i 0.568009 + 0.983820i
\(590\) 0 0
\(591\) 19503.8 + 15605.7i 1.35749 + 1.08618i
\(592\) 14135.8 + 8161.30i 0.981381 + 0.566601i
\(593\) 27128.8i 1.87866i −0.343014 0.939330i \(-0.611448\pi\)
0.343014 0.939330i \(-0.388552\pi\)
\(594\) −10929.7 + 765.442i −0.754965 + 0.0528729i
\(595\) 0 0
\(596\) −9572.32 + 16579.7i −0.657881 + 1.13948i
\(597\) 1018.81 1273.29i 0.0698445 0.0872906i
\(598\) 6391.08 3689.89i 0.437042 0.252326i
\(599\) 2815.87 + 4877.24i 0.192076 + 0.332685i 0.945938 0.324347i \(-0.105145\pi\)
−0.753862 + 0.657033i \(0.771811\pi\)
\(600\) 0 0
\(601\) 7375.88 12775.4i 0.500613 0.867087i −0.499387 0.866379i \(-0.666441\pi\)
1.00000 0.000707853i \(-0.000225317\pi\)
\(602\) 16205.9i 1.09718i
\(603\) 15693.0 + 17023.8i 1.05982 + 1.14969i
\(604\) 15485.2 1.04318
\(605\) 0 0
\(606\) −778.738 + 5110.16i −0.0522014 + 0.342552i
\(607\) −12801.7 + 7391.04i −0.856018 + 0.494222i −0.862677 0.505756i \(-0.831214\pi\)
0.00665872 + 0.999978i \(0.497880\pi\)
\(608\) −12477.0 + 7203.59i −0.832251 + 0.480500i
\(609\) 3926.66 25767.2i 0.261275 1.71451i
\(610\) 0 0
\(611\) 2012.43 0.133247
\(612\) −8200.44 8895.85i −0.541639 0.587571i
\(613\) 4947.28i 0.325969i −0.986629 0.162984i \(-0.947888\pi\)
0.986629 0.162984i \(-0.0521120\pi\)
\(614\) −3393.12 + 5877.06i −0.223021 + 0.386284i
\(615\) 0 0
\(616\) 2384.88 + 4130.73i 0.155989 + 0.270181i
\(617\) −3242.09 + 1871.82i −0.211543 + 0.122134i −0.602028 0.798475i \(-0.705640\pi\)
0.390485 + 0.920609i \(0.372307\pi\)
\(618\) 6420.67 8024.45i 0.417924 0.522315i
\(619\) 3069.37 5316.30i 0.199303 0.345202i −0.749000 0.662570i \(-0.769466\pi\)
0.948303 + 0.317368i \(0.102799\pi\)
\(620\) 0 0
\(621\) 4597.38 321.971i 0.297080 0.0208055i
\(622\) 3326.09i 0.214412i
\(623\) −11262.8 6502.59i −0.724294 0.418171i
\(624\) −18428.8 14745.6i −1.18228 0.945986i
\(625\) 0 0
\(626\) 4151.79 + 7191.11i 0.265078 + 0.459128i
\(627\) 2514.32 + 6437.15i 0.160147 + 0.410008i
\(628\) 18348.4 + 10593.5i 1.16589 + 0.673129i
\(629\) 15946.9 1.01088
\(630\) 0 0
\(631\) −5548.00 −0.350019 −0.175010 0.984567i \(-0.555996\pi\)
−0.175010 + 0.984567i \(0.555996\pi\)
\(632\) −2183.86 1260.85i −0.137451 0.0793575i
\(633\) 12527.8 + 1909.12i 0.786630 + 0.119874i
\(634\) −1233.36 2136.25i −0.0772605 0.133819i
\(635\) 0 0
\(636\) 198.927 1305.38i 0.0124025 0.0813864i
\(637\) −33205.3 19171.1i −2.06537 1.19244i
\(638\) 12495.9i 0.775418i
\(639\) −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 \(0.0502487\pi\)
\(642\) 14770.3 + 37814.9i 0.908002 + 2.32466i
\(643\) 11017.3 6360.85i 0.675708 0.390120i −0.122528 0.992465i \(-0.539100\pi\)
0.798236 + 0.602345i \(0.205767\pi\)
\(644\) 3116.04 + 5397.15i 0.190667 + 0.330244i
\(645\) 0 0
\(646\) −8859.78 + 15345.6i −0.539603 + 0.934620i
\(647\) 28203.7i 1.71376i −0.515518 0.856879i \(-0.672400\pi\)
0.515518 0.856879i \(-0.327600\pi\)
\(648\) −2278.74 4811.70i −0.138144 0.291700i
\(649\) 12815.4 0.775115
\(650\) 0 0
\(651\) −32354.0 25887.7i −1.94786 1.55856i
\(652\) 1383.35 798.678i 0.0830924 0.0479734i
\(653\) 19652.5 11346.4i 1.17774 0.679966i 0.222247 0.974991i \(-0.428661\pi\)
0.955490 + 0.295024i \(0.0953277\pi\)
\(654\) −16794.3 + 6559.76i −1.00414 + 0.392213i
\(655\) 0 0
\(656\) −10738.1 −0.639103
\(657\) 16284.7 3661.17i 0.967010 0.217406i
\(658\) 3946.02i 0.233787i
\(659\) 3002.00 5199.61i 0.177453 0.307357i −0.763555 0.645743i \(-0.776548\pi\)
0.941007 + 0.338386i \(0.109881\pi\)
\(660\) 0 0
\(661\) −5958.18 10319.9i −0.350600 0.607256i 0.635755 0.771891i \(-0.280689\pi\)
−0.986355 + 0.164635i \(0.947356\pi\)
\(662\) 17129.2 9889.54i 1.00566 0.580616i
\(663\) −22795.6 3473.81i −1.33530 0.203487i
\(664\) 3991.80 6914.00i 0.233301 0.404089i
\(665\) 0 0
\(666\) −20808.0 6492.63i −1.21065 0.377754i
\(667\) 5256.19i 0.305128i
\(668\) −18810.1 10860.0i −1.08950 0.629021i
\(669\) 11293.8 4411.31i 0.652682 0.254934i
\(670\) 0 0
\(671\) −1399.03 2423.19i −0.0804901 0.139413i
\(672\) 22967.5 28704.5i 1.31844 1.64777i
\(673\) −13885.6 8016.85i −0.795319 0.459178i 0.0465125 0.998918i \(-0.485189\pi\)
−0.841832 + 0.539740i \(0.818523\pi\)
\(674\) 12599.9 0.720077
\(675\) 0 0
\(676\) 8440.54 0.480231
\(677\) −9796.38 5655.94i −0.556138 0.321086i 0.195456 0.980712i \(-0.437381\pi\)
−0.751594 + 0.659626i \(0.770715\pi\)
\(678\) −6644.59 + 8304.31i −0.376378 + 0.470391i
\(679\) 3157.03 + 5468.14i 0.178432 + 0.309054i
\(680\) 0 0
\(681\) −13182.8 + 5149.13i −0.741800 + 0.289743i
\(682\) −17203.8 9932.64i −0.965937 0.557684i
\(683\) 652.395i 0.0365493i 0.999833 + 0.0182747i \(0.00581733\pi\)
−0.999833 + 0.0182747i \(0.994183\pi\)
\(684\) 7669.59 7070.04i 0.428734 0.395219i
\(685\) 0 0
\(686\) 17437.4 30202.5i 0.970502 1.68096i
\(687\) 17024.3 + 2594.34i 0.945443 + 0.144076i
\(688\) 9051.64 5225.96i 0.501585 0.289590i
\(689\) −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 \(0.278830\pi\)
\(692\) 2241.90i 0.123157i
\(693\) −11952.0 12965.5i −0.655148 0.710705i
\(694\) −35069.8 −1.91820
\(695\) 0 0
\(696\) 5655.94 2209.18i 0.308029 0.120314i
\(697\) −9085.42 + 5245.47i −0.493737 + 0.285059i
\(698\) −22852.1 + 13193.6i −1.23920 + 0.715454i
\(699\) −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 \(0.449359\pi\)
\(702\) 28329.9 + 13813.7i 1.52314 + 0.742684i
\(703\) 13748.7i 0.737614i
\(704\) 2496.37 4323.84i 0.133644 0.231479i
\(705\) 0 0
\(706\) −7876.07 13641.8i −0.419858 0.727216i
\(707\) −7204.93 + 4159.77i −0.383266 + 0.221279i
\(708\) −7037.71 18017.9i −0.373578 0.956434i
\(709\) 3203.33 5548.33i 0.169681 0.293895i −0.768627 0.639697i \(-0.779060\pi\)
0.938308 + 0.345802i \(0.112393\pi\)
\(710\) 0 0
\(711\) 8899.62 + 2776.91i 0.469426 + 0.146473i
\(712\) 3029.72i 0.159471i
\(713\) 7236.52 + 4178.00i 0.380098 + 0.219449i
\(714\) 6811.55 44698.2i 0.357025 2.34284i
\(715\) 0 0
\(716\) −1352.25 2342.17i −0.0705812 0.122250i
\(717\) 1264.30 + 192.667i 0.0658526 + 0.0100353i
\(718\) 1908.90 + 1102.10i 0.0992193 + 0.0572843i
\(719\) −21907.0 −1.13629 −0.568144 0.822929i \(-0.692338\pi\)
−0.568144 + 0.822929i \(0.692338\pi\)
\(720\) 0 0
\(721\) 16540.4 0.854364
\(722\) 9036.47 + 5217.21i 0.465793 + 0.268926i
\(723\) 9996.44 + 25592.9i 0.514207 + 1.31647i
\(724\) −2735.53 4738.07i −0.140421 0.243217i
\(725\) 0 0
\(726\) 13641.9 + 10915.4i 0.697382 + 0.558002i
\(727\) −11579.6 6685.46i −0.590732 0.341059i 0.174655 0.984630i \(-0.444119\pi\)
−0.765387 + 0.643571i \(0.777452\pi\)
\(728\) 13721.1i 0.698542i
\(729\) 12121.4 + 15507.8i 0.615829 + 0.787880i
\(730\) 0 0
\(731\) 5105.69 8843.31i 0.258332 0.447444i
\(732\) −2638.61 + 3297.69i −0.133232 + 0.166511i
\(733\) −26146.2 + 15095.5i −1.31751 + 0.760663i −0.983327 0.181846i \(-0.941793\pi\)
−0.334181 + 0.942509i \(0.608460\pi\)
\(734\) −14591.5 25273.2i −0.733762 1.27091i
\(735\) 0 0
\(736\) −3706.72 + 6420.22i −0.185641 + 0.321539i
\(737\) 17865.2i 0.892910i
\(738\) 13990.5 3145.39i 0.697830 0.156888i
\(739\) 11624.7 0.578650 0.289325 0.957231i \(-0.406569\pi\)
0.289325 + 0.957231i \(0.406569\pi\)
\(740\) 0 0
\(741\) 2994.96 19653.3i 0.148479 0.974334i
\(742\) 4273.49 2467.30i 0.211435 0.122072i
\(743\) 4550.42 2627.19i 0.224682 0.129720i −0.383434 0.923568i \(-0.625259\pi\)
0.608116 + 0.793848i \(0.291925\pi\)
\(744\) 1454.24 9542.90i 0.0716601 0.470241i
\(745\) 0 0
\(746\) −29328.9 −1.43942
\(747\) −8791.57 + 28175.8i −0.430612 + 1.38005i
\(748\) 9335.55i 0.456339i
\(749\) −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 \(0.581982\pi\)
\(752\) −2204.00 + 1272.48i −0.106877 + 0.0617057i
\(753\) −9158.70 + 11446.4i −0.443242 + 0.553957i
\(754\) −17973.4 + 31130.9i −0.868108 + 1.50361i
\(755\) 0 0
\(756\) −11665.4 + 23924.1i −0.561199 + 1.15094i
\(757\) 32885.9i 1.57894i 0.613789 + 0.789470i \(0.289645\pi\)
−0.613789 + 0.789470i \(0.710355\pi\)
\(758\) −15192.6 8771.46i −0.727995 0.420308i
\(759\) 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 \(0.730989\pi\)
\(762\) −6916.37 17707.3i −0.328811 0.841820i
\(763\) −25130.7 14509.2i −1.19239 0.688425i
\(764\) 3628.54 0.171827
\(765\) 0 0
\(766\) −25219.0 −1.18956
\(767\) −31927.0 18433.0i −1.50302 0.867769i
\(768\) 27315.1 + 4162.55i 1.28340 + 0.195577i
\(769\) 17142.9 + 29692.4i 0.803887 + 1.39237i 0.917040 + 0.398796i \(0.130572\pi\)
−0.113153 + 0.993578i \(0.536095\pi\)
\(770\) 0 0
\(771\) 1474.95 9678.81i 0.0688964 0.452106i
\(772\) 23132.2 + 13355.4i 1.07843 + 0.622630i
\(773\) 27987.1i 1.30223i 0.758978 + 0.651117i \(0.225699\pi\)
−0.758978 + 0.651117i \(0.774301\pi\)
\(774\) −10262.5 + 9460.25i −0.476586 + 0.439330i
\(775\) 0 0
\(776\) −735.469 + 1273.87i −0.0340229 + 0.0589294i
\(777\) −12763.7 32677.7i −0.589313 1.50876i
\(778\)