Properties

Label 882.4.g.bd.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: no (minimal twist has level 294)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bd.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.94975 + 3.37706i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.94975 + 3.37706i) q^{5} +8.00000 q^{8} +(-3.89949 - 6.75412i) q^{10} +(-30.6985 - 53.1713i) q^{11} +53.6985 q^{13} +(-8.00000 + 13.8564i) q^{16} +(16.0503 + 27.7999i) q^{17} +(27.8995 - 48.3233i) q^{19} +15.5980 q^{20} +122.794 q^{22} +(-47.3015 + 81.9286i) q^{23} +(54.8970 + 95.0843i) q^{25} +(-53.6985 + 93.0085i) q^{26} -138.191 q^{29} +(-66.3015 - 114.838i) q^{31} +(-16.0000 - 27.7128i) q^{32} -64.2010 q^{34} +(-74.6030 + 129.216i) q^{37} +(55.7990 + 96.6467i) q^{38} +(-15.5980 + 27.0165i) q^{40} -427.497 q^{41} +437.588 q^{43} +(-122.794 + 212.685i) q^{44} +(-94.6030 - 163.857i) q^{46} +(28.5025 - 49.3678i) q^{47} -219.588 q^{50} +(-107.397 - 186.017i) q^{52} +(-131.794 - 228.274i) q^{53} +239.417 q^{55} +(138.191 - 239.354i) q^{58} +(225.899 + 391.269i) q^{59} +(-289.653 + 501.694i) q^{61} +265.206 q^{62} +64.0000 q^{64} +(-104.698 + 181.343i) q^{65} +(-154.794 - 268.111i) q^{67} +(64.2010 - 111.199i) q^{68} +1058.98 q^{71} +(-596.829 - 1033.74i) q^{73} +(-149.206 - 258.432i) q^{74} -223.196 q^{76} +(-659.779 + 1142.77i) q^{79} +(-31.1960 - 54.0330i) q^{80} +(427.497 - 740.447i) q^{82} -1190.33 q^{83} -125.176 q^{85} +(-437.588 + 757.924i) q^{86} +(-245.588 - 425.371i) q^{88} +(-116.543 + 201.858i) q^{89} +378.412 q^{92} +(57.0051 + 98.7356i) q^{94} +(108.794 + 188.437i) q^{95} -1609.44 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} + 12q^{5} + 32q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} + 12q^{5} + 32q^{8} + 24q^{10} - 4q^{11} + 96q^{13} - 32q^{16} + 84q^{17} + 72q^{19} - 96q^{20} + 16q^{22} - 308q^{23} - 18q^{25} - 96q^{26} + 160q^{29} - 384q^{31} - 64q^{32} - 336q^{34} - 536q^{37} + 144q^{38} + 96q^{40} - 1512q^{41} + 800q^{43} - 16q^{44} - 616q^{46} + 312q^{47} + 72q^{50} - 192q^{52} - 52q^{53} + 2304q^{55} - 160q^{58} + 864q^{59} - 1416q^{61} + 1536q^{62} + 256q^{64} - 300q^{65} - 144q^{67} + 336q^{68} + 3048q^{71} - 744q^{73} - 1072q^{74} - 576q^{76} - 976q^{79} + 192q^{80} + 1512q^{82} + 624q^{83} + 1400q^{85} - 800q^{86} - 32q^{88} + 108q^{89} + 2464q^{92} + 624q^{94} - 40q^{95} - 1488q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −1.94975 + 3.37706i −0.174391 + 0.302054i −0.939950 0.341311i \(-0.889129\pi\)
0.765560 + 0.643365i \(0.222462\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −3.89949 6.75412i −0.123313 0.213584i
\(11\) −30.6985 53.1713i −0.841449 1.45743i −0.888669 0.458548i \(-0.848370\pi\)
0.0472203 0.998885i \(-0.484964\pi\)
\(12\) 0 0
\(13\) 53.6985 1.14564 0.572818 0.819682i \(-0.305850\pi\)
0.572818 + 0.819682i \(0.305850\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 16.0503 + 27.7999i 0.228986 + 0.396615i 0.957508 0.288407i \(-0.0931257\pi\)
−0.728522 + 0.685022i \(0.759792\pi\)
\(18\) 0 0
\(19\) 27.8995 48.3233i 0.336873 0.583481i −0.646970 0.762515i \(-0.723964\pi\)
0.983843 + 0.179035i \(0.0572974\pi\)
\(20\) 15.5980 0.174391
\(21\) 0 0
\(22\) 122.794 1.18999
\(23\) −47.3015 + 81.9286i −0.428828 + 0.742752i −0.996769 0.0803170i \(-0.974407\pi\)
0.567941 + 0.823069i \(0.307740\pi\)
\(24\) 0 0
\(25\) 54.8970 + 95.0843i 0.439176 + 0.760675i
\(26\) −53.6985 + 93.0085i −0.405044 + 0.701556i
\(27\) 0 0
\(28\) 0 0
\(29\) −138.191 −0.884876 −0.442438 0.896799i \(-0.645886\pi\)
−0.442438 + 0.896799i \(0.645886\pi\)
\(30\) 0 0
\(31\) −66.3015 114.838i −0.384132 0.665337i 0.607516 0.794307i \(-0.292166\pi\)
−0.991648 + 0.128971i \(0.958833\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −64.2010 −0.323835
\(35\) 0 0
\(36\) 0 0
\(37\) −74.6030 + 129.216i −0.331477 + 0.574136i −0.982802 0.184664i \(-0.940880\pi\)
0.651324 + 0.758799i \(0.274214\pi\)
\(38\) 55.7990 + 96.6467i 0.238205 + 0.412583i
\(39\) 0 0
\(40\) −15.5980 + 27.0165i −0.0616564 + 0.106792i
\(41\) −427.497 −1.62839 −0.814194 0.580593i \(-0.802821\pi\)
−0.814194 + 0.580593i \(0.802821\pi\)
\(42\) 0 0
\(43\) 437.588 1.55190 0.775948 0.630797i \(-0.217272\pi\)
0.775948 + 0.630797i \(0.217272\pi\)
\(44\) −122.794 + 212.685i −0.420725 + 0.728716i
\(45\) 0 0
\(46\) −94.6030 163.857i −0.303227 0.525205i
\(47\) 28.5025 49.3678i 0.0884579 0.153214i −0.818402 0.574647i \(-0.805139\pi\)
0.906859 + 0.421433i \(0.138473\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −219.588 −0.621088
\(51\) 0 0
\(52\) −107.397 186.017i −0.286409 0.496075i
\(53\) −131.794 228.274i −0.341572 0.591619i 0.643153 0.765737i \(-0.277626\pi\)
−0.984725 + 0.174118i \(0.944292\pi\)
\(54\) 0 0
\(55\) 239.417 0.586964
\(56\) 0 0
\(57\) 0 0
\(58\) 138.191 239.354i 0.312851 0.541874i
\(59\) 225.899 + 391.269i 0.498468 + 0.863372i 0.999998 0.00176815i \(-0.000562821\pi\)
−0.501530 + 0.865140i \(0.667229\pi\)
\(60\) 0 0
\(61\) −289.653 + 501.694i −0.607972 + 1.05304i 0.383602 + 0.923499i \(0.374683\pi\)
−0.991574 + 0.129540i \(0.958650\pi\)
\(62\) 265.206 0.543245
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −104.698 + 181.343i −0.199788 + 0.346044i
\(66\) 0 0
\(67\) −154.794 268.111i −0.282255 0.488880i 0.689685 0.724110i \(-0.257749\pi\)
−0.971940 + 0.235230i \(0.924416\pi\)
\(68\) 64.2010 111.199i 0.114493 0.198307i
\(69\) 0 0
\(70\) 0 0
\(71\) 1058.98 1.77012 0.885059 0.465479i \(-0.154118\pi\)
0.885059 + 0.465479i \(0.154118\pi\)
\(72\) 0 0
\(73\) −596.829 1033.74i −0.956898 1.65740i −0.729964 0.683486i \(-0.760463\pi\)
−0.226934 0.973910i \(-0.572870\pi\)
\(74\) −149.206 258.432i −0.234390 0.405975i
\(75\) 0 0
\(76\) −223.196 −0.336873
\(77\) 0 0
\(78\) 0 0
\(79\) −659.779 + 1142.77i −0.939632 + 1.62749i −0.173473 + 0.984839i \(0.555499\pi\)
−0.766159 + 0.642651i \(0.777834\pi\)
\(80\) −31.1960 54.0330i −0.0435977 0.0755134i
\(81\) 0 0
\(82\) 427.497 740.447i 0.575722 0.997180i
\(83\) −1190.33 −1.57417 −0.787083 0.616847i \(-0.788410\pi\)
−0.787083 + 0.616847i \(0.788410\pi\)
\(84\) 0 0
\(85\) −125.176 −0.159732
\(86\) −437.588 + 757.924i −0.548678 + 0.950338i
\(87\) 0 0
\(88\) −245.588 425.371i −0.297497 0.515280i
\(89\) −116.543 + 201.858i −0.138803 + 0.240414i −0.927044 0.374953i \(-0.877659\pi\)
0.788241 + 0.615367i \(0.210992\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 378.412 0.428828
\(93\) 0 0
\(94\) 57.0051 + 98.7356i 0.0625492 + 0.108338i
\(95\) 108.794 + 188.437i 0.117495 + 0.203507i
\(96\) 0 0
\(97\) −1609.44 −1.68468 −0.842338 0.538950i \(-0.818821\pi\)
−0.842338 + 0.538950i \(0.818821\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 219.588 380.337i 0.219588 0.380337i
\(101\) −739.628 1281.07i −0.728671 1.26209i −0.957445 0.288615i \(-0.906805\pi\)
0.228774 0.973479i \(-0.426528\pi\)
\(102\) 0 0
\(103\) 572.673 991.899i 0.547837 0.948881i −0.450586 0.892733i \(-0.648785\pi\)
0.998422 0.0561477i \(-0.0178818\pi\)
\(104\) 429.588 0.405044
\(105\) 0 0
\(106\) 527.176 0.483055
\(107\) 218.477 378.414i 0.197392 0.341894i −0.750290 0.661109i \(-0.770086\pi\)
0.947682 + 0.319215i \(0.103419\pi\)
\(108\) 0 0
\(109\) 83.1758 + 144.065i 0.0730898 + 0.126595i 0.900254 0.435365i \(-0.143381\pi\)
−0.827164 + 0.561960i \(0.810047\pi\)
\(110\) −239.417 + 414.683i −0.207523 + 0.359440i
\(111\) 0 0
\(112\) 0 0
\(113\) −490.824 −0.408609 −0.204305 0.978907i \(-0.565493\pi\)
−0.204305 + 0.978907i \(0.565493\pi\)
\(114\) 0 0
\(115\) −184.452 319.480i −0.149567 0.259058i
\(116\) 276.382 + 478.707i 0.221219 + 0.383163i
\(117\) 0 0
\(118\) −903.598 −0.704940
\(119\) 0 0
\(120\) 0 0
\(121\) −1219.29 + 2111.88i −0.916074 + 1.58669i
\(122\) −579.307 1003.39i −0.429901 0.744611i
\(123\) 0 0
\(124\) −265.206 + 459.350i −0.192066 + 0.332668i
\(125\) −915.578 −0.655134
\(126\) 0 0
\(127\) −2616.70 −1.82831 −0.914153 0.405369i \(-0.867143\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −209.397 362.686i −0.141272 0.244690i
\(131\) 88.7939 153.796i 0.0592211 0.102574i −0.834895 0.550409i \(-0.814472\pi\)
0.894116 + 0.447835i \(0.147805\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 619.176 0.399169
\(135\) 0 0
\(136\) 128.402 + 222.399i 0.0809587 + 0.140225i
\(137\) 13.5076 + 23.3958i 0.00842358 + 0.0145901i 0.870206 0.492687i \(-0.163985\pi\)
−0.861783 + 0.507277i \(0.830652\pi\)
\(138\) 0 0
\(139\) −922.754 −0.563071 −0.281536 0.959551i \(-0.590844\pi\)
−0.281536 + 0.959551i \(0.590844\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1058.98 + 1834.22i −0.625831 + 1.08397i
\(143\) −1648.46 2855.22i −0.963995 1.66969i
\(144\) 0 0
\(145\) 269.437 466.679i 0.154314 0.267280i
\(146\) 2387.32 1.35326
\(147\) 0 0
\(148\) 596.824 0.331477
\(149\) 373.352 646.664i 0.205276 0.355549i −0.744945 0.667126i \(-0.767524\pi\)
0.950221 + 0.311578i \(0.100857\pi\)
\(150\) 0 0
\(151\) −1036.57 1795.40i −0.558643 0.967598i −0.997610 0.0690949i \(-0.977989\pi\)
0.438967 0.898503i \(-0.355344\pi\)
\(152\) 223.196 386.587i 0.119103 0.206292i
\(153\) 0 0
\(154\) 0 0
\(155\) 517.085 0.267956
\(156\) 0 0
\(157\) −783.110 1356.39i −0.398083 0.689500i 0.595407 0.803425i \(-0.296991\pi\)
−0.993489 + 0.113925i \(0.963658\pi\)
\(158\) −1319.56 2285.54i −0.664420 1.15081i
\(159\) 0 0
\(160\) 124.784 0.0616564
\(161\) 0 0
\(162\) 0 0
\(163\) −49.3667 + 85.5056i −0.0237221 + 0.0410878i −0.877643 0.479315i \(-0.840885\pi\)
0.853921 + 0.520403i \(0.174218\pi\)
\(164\) 854.995 + 1480.89i 0.407097 + 0.705112i
\(165\) 0 0
\(166\) 1190.33 2061.71i 0.556552 0.963976i
\(167\) 2231.36 1.03394 0.516969 0.856004i \(-0.327060\pi\)
0.516969 + 0.856004i \(0.327060\pi\)
\(168\) 0 0
\(169\) 686.527 0.312484
\(170\) 125.176 216.811i 0.0564738 0.0978155i
\(171\) 0 0
\(172\) −875.176 1515.85i −0.387974 0.671991i
\(173\) 1050.42 1819.38i 0.461631 0.799568i −0.537412 0.843320i \(-0.680598\pi\)
0.999042 + 0.0437522i \(0.0139312\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 982.352 0.420725
\(177\) 0 0
\(178\) −233.085 403.716i −0.0981488 0.169999i
\(179\) 861.271 + 1491.77i 0.359634 + 0.622904i 0.987900 0.155095i \(-0.0495683\pi\)
−0.628266 + 0.777999i \(0.716235\pi\)
\(180\) 0 0
\(181\) 1655.00 0.679644 0.339822 0.940490i \(-0.389633\pi\)
0.339822 + 0.940490i \(0.389633\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −378.412 + 655.429i −0.151614 + 0.262603i
\(185\) −290.914 503.878i −0.115613 0.200248i
\(186\) 0 0
\(187\) 985.437 1706.83i 0.385360 0.667463i
\(188\) −228.020 −0.0884579
\(189\) 0 0
\(190\) −435.176 −0.166163
\(191\) −503.844 + 872.683i −0.190874 + 0.330603i −0.945540 0.325506i \(-0.894465\pi\)
0.754666 + 0.656109i \(0.227799\pi\)
\(192\) 0 0
\(193\) 3.82424 + 6.62378i 0.00142630 + 0.00247042i 0.866738 0.498764i \(-0.166213\pi\)
−0.865311 + 0.501235i \(0.832879\pi\)
\(194\) 1609.44 2787.63i 0.595623 1.03165i
\(195\) 0 0
\(196\) 0 0
\(197\) −2689.88 −0.972822 −0.486411 0.873730i \(-0.661694\pi\)
−0.486411 + 0.873730i \(0.661694\pi\)
\(198\) 0 0
\(199\) −433.748 751.274i −0.154511 0.267620i 0.778370 0.627806i \(-0.216047\pi\)
−0.932881 + 0.360185i \(0.882713\pi\)
\(200\) 439.176 + 760.675i 0.155272 + 0.268939i
\(201\) 0 0
\(202\) 2958.51 1.03050
\(203\) 0 0
\(204\) 0 0
\(205\) 833.512 1443.69i 0.283976 0.491860i
\(206\) 1145.35 + 1983.80i 0.387379 + 0.670960i
\(207\) 0 0
\(208\) −429.588 + 744.068i −0.143205 + 0.248038i
\(209\) −3425.89 −1.13385
\(210\) 0 0
\(211\) 162.030 0.0528655 0.0264328 0.999651i \(-0.491585\pi\)
0.0264328 + 0.999651i \(0.491585\pi\)
\(212\) −527.176 + 913.095i −0.170786 + 0.295810i
\(213\) 0 0
\(214\) 436.955 + 756.827i 0.139578 + 0.241755i
\(215\) −853.186 + 1477.76i −0.270636 + 0.468756i
\(216\) 0 0
\(217\) 0 0
\(218\) −332.703 −0.103365
\(219\) 0 0
\(220\) −478.834 829.365i −0.146741 0.254163i
\(221\) 861.874 + 1492.81i 0.262335 + 0.454377i
\(222\) 0 0
\(223\) −4577.85 −1.37469 −0.687344 0.726332i \(-0.741223\pi\)
−0.687344 + 0.726332i \(0.741223\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 490.824 850.133i 0.144465 0.250221i
\(227\) −1109.10 1921.01i −0.324287 0.561682i 0.657080 0.753820i \(-0.271791\pi\)
−0.981368 + 0.192138i \(0.938458\pi\)
\(228\) 0 0
\(229\) −392.608 + 680.018i −0.113294 + 0.196231i −0.917096 0.398665i \(-0.869473\pi\)
0.803803 + 0.594896i \(0.202807\pi\)
\(230\) 737.808 0.211520
\(231\) 0 0
\(232\) −1105.53 −0.312851
\(233\) −2684.56 + 4649.80i −0.754813 + 1.30738i 0.190654 + 0.981657i \(0.438939\pi\)
−0.945467 + 0.325718i \(0.894394\pi\)
\(234\) 0 0
\(235\) 111.145 + 192.510i 0.0308525 + 0.0534380i
\(236\) 903.598 1565.08i 0.249234 0.431686i
\(237\) 0 0
\(238\) 0 0
\(239\) −3713.28 −1.00499 −0.502493 0.864581i \(-0.667584\pi\)
−0.502493 + 0.864581i \(0.667584\pi\)
\(240\) 0 0
\(241\) −3499.31 6060.99i −0.935313 1.62001i −0.774075 0.633094i \(-0.781785\pi\)
−0.161238 0.986915i \(-0.551549\pi\)
\(242\) −2438.59 4223.76i −0.647762 1.12196i
\(243\) 0 0
\(244\) 2317.23 0.607972
\(245\) 0 0
\(246\) 0 0
\(247\) 1498.16 2594.89i 0.385934 0.668457i
\(248\) −530.412 918.701i −0.135811 0.235232i
\(249\) 0 0
\(250\) 915.578 1585.83i 0.231625 0.401186i
\(251\) −3722.75 −0.936168 −0.468084 0.883684i \(-0.655055\pi\)
−0.468084 + 0.883684i \(0.655055\pi\)
\(252\) 0 0
\(253\) 5808.34 1.44335
\(254\) 2616.70 4532.26i 0.646404 1.11960i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 615.075 1065.34i 0.149289 0.258576i −0.781676 0.623685i \(-0.785635\pi\)
0.930965 + 0.365109i \(0.118968\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 837.588 0.199788
\(261\) 0 0
\(262\) 177.588 + 307.591i 0.0418756 + 0.0725307i
\(263\) 1194.32 + 2068.62i 0.280018 + 0.485005i 0.971389 0.237495i \(-0.0763262\pi\)
−0.691371 + 0.722500i \(0.742993\pi\)
\(264\) 0 0
\(265\) 1027.86 0.238268
\(266\) 0 0
\(267\) 0 0
\(268\) −619.176 + 1072.44i −0.141128 + 0.244440i
\(269\) 3351.16 + 5804.37i 0.759567 + 1.31561i 0.943071 + 0.332590i \(0.107923\pi\)
−0.183504 + 0.983019i \(0.558744\pi\)
\(270\) 0 0
\(271\) −2475.19 + 4287.15i −0.554822 + 0.960980i 0.443095 + 0.896475i \(0.353880\pi\)
−0.997917 + 0.0645056i \(0.979453\pi\)
\(272\) −513.608 −0.114493
\(273\) 0 0
\(274\) −54.0303 −0.0119127
\(275\) 3370.51 5837.89i 0.739088 1.28014i
\(276\) 0 0
\(277\) 1852.59 + 3208.78i 0.401846 + 0.696017i 0.993949 0.109845i \(-0.0350355\pi\)
−0.592103 + 0.805862i \(0.701702\pi\)
\(278\) 922.754 1598.26i 0.199076 0.344809i
\(279\) 0 0
\(280\) 0 0
\(281\) −9324.74 −1.97960 −0.989800 0.142465i \(-0.954497\pi\)
−0.989800 + 0.142465i \(0.954497\pi\)
\(282\) 0 0
\(283\) 2784.74 + 4823.32i 0.584932 + 1.01313i 0.994884 + 0.101025i \(0.0322122\pi\)
−0.409952 + 0.912107i \(0.634454\pi\)
\(284\) −2117.97 3668.43i −0.442530 0.766484i
\(285\) 0 0
\(286\) 6593.85 1.36330
\(287\) 0 0
\(288\) 0 0
\(289\) 1941.28 3362.39i 0.395131 0.684387i
\(290\) 538.875 + 933.358i 0.109117 + 0.188996i
\(291\) 0 0
\(292\) −2387.32 + 4134.95i −0.478449 + 0.828698i
\(293\) 1665.31 0.332042 0.166021 0.986122i \(-0.446908\pi\)
0.166021 + 0.986122i \(0.446908\pi\)
\(294\) 0 0
\(295\) −1761.79 −0.347713
\(296\) −596.824 + 1033.73i −0.117195 + 0.202988i
\(297\) 0 0
\(298\) 746.703 + 1293.33i 0.145152 + 0.251411i
\(299\) −2540.02 + 4399.44i −0.491281 + 0.850924i
\(300\) 0 0
\(301\) 0 0
\(302\) 4146.29 0.790040
\(303\) 0 0
\(304\) 446.392 + 773.173i 0.0842182 + 0.145870i
\(305\) −1129.50 1956.35i −0.212049 0.367280i
\(306\) 0 0
\(307\) −5303.32 −0.985916 −0.492958 0.870053i \(-0.664084\pi\)
−0.492958 + 0.870053i \(0.664084\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −517.085 + 895.617i −0.0947369 + 0.164089i
\(311\) 562.994 + 975.135i 0.102651 + 0.177797i 0.912776 0.408460i \(-0.133934\pi\)
−0.810125 + 0.586257i \(0.800601\pi\)
\(312\) 0 0
\(313\) 4149.75 7187.58i 0.749386 1.29798i −0.198731 0.980054i \(-0.563682\pi\)
0.948117 0.317921i \(-0.102985\pi\)
\(314\) 3132.44 0.562974
\(315\) 0 0
\(316\) 5278.23 0.939632
\(317\) −2139.38 + 3705.52i −0.379053 + 0.656538i −0.990925 0.134418i \(-0.957083\pi\)
0.611872 + 0.790957i \(0.290417\pi\)
\(318\) 0 0
\(319\) 4242.25 + 7347.80i 0.744578 + 1.28965i
\(320\) −124.784 + 216.132i −0.0217988 + 0.0377567i
\(321\) 0 0
\(322\) 0 0
\(323\) 1791.18 0.308556
\(324\) 0 0
\(325\) 2947.88 + 5105.89i 0.503136 + 0.871457i
\(326\) −98.7333 171.011i −0.0167740 0.0290535i
\(327\) 0 0
\(328\) −3419.98 −0.575722
\(329\) 0 0
\(330\) 0 0
\(331\) 853.558 1478.41i 0.141739 0.245500i −0.786412 0.617702i \(-0.788064\pi\)
0.928152 + 0.372202i \(0.121397\pi\)
\(332\) 2380.66 + 4123.43i 0.393542 + 0.681634i
\(333\) 0 0
\(334\) −2231.36 + 3864.82i −0.365552 + 0.633155i
\(335\) 1207.24 0.196891
\(336\) 0 0
\(337\) 1710.67 0.276517 0.138259 0.990396i \(-0.455849\pi\)
0.138259 + 0.990396i \(0.455849\pi\)
\(338\) −686.527 + 1189.10i −0.110480 + 0.191357i
\(339\) 0 0
\(340\) 250.352 + 433.622i 0.0399330 + 0.0691660i
\(341\) −4070.71 + 7050.68i −0.646456 + 1.11969i
\(342\) 0 0
\(343\) 0 0
\(344\) 3500.70 0.548678
\(345\) 0 0
\(346\) 2100.84 + 3638.77i 0.326422 + 0.565380i
\(347\) 4455.15 + 7716.55i 0.689236 + 1.19379i 0.972085 + 0.234628i \(0.0753871\pi\)
−0.282849 + 0.959164i \(0.591280\pi\)
\(348\) 0 0
\(349\) 5378.68 0.824969 0.412485 0.910965i \(-0.364661\pi\)
0.412485 + 0.910965i \(0.364661\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −982.352 + 1701.48i −0.148749 + 0.257640i
\(353\) −2126.28 3682.83i −0.320596 0.555289i 0.660015 0.751253i \(-0.270550\pi\)
−0.980611 + 0.195963i \(0.937217\pi\)
\(354\) 0 0
\(355\) −2064.75 + 3576.26i −0.308692 + 0.534670i
\(356\) 932.341 0.138803
\(357\) 0 0
\(358\) −3445.08 −0.508599
\(359\) 2451.94 4246.89i 0.360470 0.624352i −0.627568 0.778561i \(-0.715950\pi\)
0.988038 + 0.154209i \(0.0492831\pi\)
\(360\) 0 0
\(361\) 1872.74 + 3243.67i 0.273033 + 0.472908i
\(362\) −1655.00 + 2866.55i −0.240290 + 0.416195i
\(363\) 0 0
\(364\) 0 0
\(365\) 4654.66 0.667497
\(366\) 0 0
\(367\) 2020.78 + 3500.10i 0.287423 + 0.497830i 0.973194 0.229987i \(-0.0738683\pi\)
−0.685771 + 0.727817i \(0.740535\pi\)
\(368\) −756.824 1310.86i −0.107207 0.185688i
\(369\) 0 0
\(370\) 1163.66 0.163502
\(371\) 0 0
\(372\) 0 0
\(373\) 3725.67 6453.05i 0.517180 0.895781i −0.482621 0.875829i \(-0.660315\pi\)
0.999801 0.0199523i \(-0.00635144\pi\)
\(374\) 1970.87 + 3413.65i 0.272491 + 0.471967i
\(375\) 0 0
\(376\) 228.020 394.943i 0.0312746 0.0541692i
\(377\) −7420.64 −1.01375
\(378\) 0 0
\(379\) −12564.4 −1.70288 −0.851438 0.524456i \(-0.824269\pi\)
−0.851438 + 0.524456i \(0.824269\pi\)
\(380\) 435.176 753.747i 0.0587475 0.101754i
\(381\) 0 0
\(382\) −1007.69 1745.37i −0.134968 0.233772i
\(383\) −2144.96 + 3715.19i −0.286169 + 0.495659i −0.972892 0.231260i \(-0.925715\pi\)
0.686723 + 0.726919i \(0.259048\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −15.2970 −0.00201709
\(387\) 0 0
\(388\) 3218.87 + 5575.25i 0.421169 + 0.729486i
\(389\) 2831.39 + 4904.11i 0.369041 + 0.639198i 0.989416 0.145108i \(-0.0463528\pi\)
−0.620375 + 0.784306i \(0.713019\pi\)
\(390\) 0 0
\(391\) −3036.81 −0.392782
\(392\) 0 0
\(393\) 0 0
\(394\) 2689.88 4659.01i 0.343945 0.595729i
\(395\) −2572.80 4456.23i −0.327726 0.567638i
\(396\) 0 0
\(397\) −7280.69 + 12610.5i −0.920421 + 1.59422i −0.121657 + 0.992572i \(0.538821\pi\)
−0.798764 + 0.601644i \(0.794513\pi\)
\(398\) 1734.99 0.218511
\(399\) 0 0
\(400\) −1756.70 −0.219588
\(401\) −1871.10 + 3240.83i −0.233013 + 0.403590i −0.958693 0.284442i \(-0.908192\pi\)
0.725681 + 0.688032i \(0.241525\pi\)
\(402\) 0 0
\(403\) −3560.29 6166.60i −0.440076 0.762234i
\(404\) −2958.51 + 5124.29i −0.364335 + 0.631047i
\(405\) 0 0
\(406\) 0 0
\(407\) 9160.80 1.11569
\(408\) 0 0
\(409\) 1758.59 + 3045.96i 0.212608 + 0.368247i 0.952530 0.304445i \(-0.0984710\pi\)
−0.739922 + 0.672692i \(0.765138\pi\)
\(410\) 1667.02 + 2887.37i 0.200801 + 0.347798i
\(411\) 0 0
\(412\) −4581.39 −0.547837
\(413\) 0 0
\(414\) 0 0
\(415\) 2320.85 4019.82i 0.274520 0.475483i
\(416\) −859.176 1488.14i −0.101261 0.175389i
\(417\) 0 0
\(418\) 3425.89 5933.81i 0.400875 0.694336i
\(419\) 7579.52 0.883732 0.441866 0.897081i \(-0.354317\pi\)
0.441866 + 0.897081i \(0.354317\pi\)
\(420\) 0 0
\(421\) −4980.87 −0.576610 −0.288305 0.957539i \(-0.593092\pi\)
−0.288305 + 0.957539i \(0.593092\pi\)
\(422\) −162.030 + 280.645i −0.0186908 + 0.0323734i
\(423\) 0 0
\(424\) −1054.35 1826.19i −0.120764 0.209169i
\(425\) −1762.22 + 3052.26i −0.201130 + 0.348367i
\(426\) 0 0
\(427\) 0 0
\(428\) −1747.82 −0.197392
\(429\) 0 0
\(430\) −1706.37 2955.52i −0.191369 0.331460i
\(431\) 7101.66 + 12300.4i 0.793678 + 1.37469i 0.923676 + 0.383176i \(0.125170\pi\)
−0.129998 + 0.991514i \(0.541497\pi\)
\(432\) 0 0
\(433\) 3874.82 0.430051 0.215026 0.976608i \(-0.431017\pi\)
0.215026 + 0.976608i \(0.431017\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 332.703 576.259i 0.0365449 0.0632977i
\(437\) 2639.38 + 4571.53i 0.288921 + 0.500426i
\(438\) 0 0
\(439\) −3881.91 + 6723.66i −0.422035 + 0.730986i −0.996138 0.0877966i \(-0.972017\pi\)
0.574103 + 0.818783i \(0.305351\pi\)
\(440\) 1915.34 0.207523
\(441\) 0 0
\(442\) −3447.50 −0.370997
\(443\) 4831.12 8367.74i 0.518134 0.897435i −0.481644 0.876367i \(-0.659960\pi\)
0.999778 0.0210676i \(-0.00670653\pi\)
\(444\) 0 0
\(445\) −454.458 787.144i −0.0484120 0.0838521i
\(446\) 4577.85 7929.07i 0.486026 0.841821i
\(447\) 0 0
\(448\) 0 0
\(449\) 10942.6 1.15014 0.575069 0.818105i \(-0.304975\pi\)
0.575069 + 0.818105i \(0.304975\pi\)
\(450\) 0 0
\(451\) 13123.5 + 22730.6i 1.37021 + 2.37327i
\(452\) 981.648 + 1700.27i 0.102152 + 0.176933i
\(453\) 0 0
\(454\) 4436.38 0.458612
\(455\) 0 0
\(456\) 0 0
\(457\) −6809.17 + 11793.8i −0.696979 + 1.20720i 0.272530 + 0.962147i \(0.412140\pi\)
−0.969509 + 0.245056i \(0.921194\pi\)
\(458\) −785.217 1360.04i −0.0801108 0.138756i
\(459\) 0 0
\(460\) −737.808 + 1277.92i −0.0747836 + 0.129529i
\(461\) −11955.8 −1.20789 −0.603947 0.797025i \(-0.706406\pi\)
−0.603947 + 0.797025i \(0.706406\pi\)
\(462\) 0 0
\(463\) 648.503 0.0650939 0.0325470 0.999470i \(-0.489638\pi\)
0.0325470 + 0.999470i \(0.489638\pi\)
\(464\) 1105.53 1914.83i 0.110610 0.191581i
\(465\) 0 0
\(466\) −5369.12 9299.60i −0.533734 0.924454i
\(467\) 1392.37 2411.66i 0.137969 0.238969i −0.788759 0.614703i \(-0.789276\pi\)
0.926728 + 0.375734i \(0.122609\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −444.582 −0.0436320
\(471\) 0 0
\(472\) 1807.20 + 3130.16i 0.176235 + 0.305248i
\(473\) −13433.3 23267.1i −1.30584 2.26178i
\(474\) 0 0
\(475\) 6126.39 0.591785
\(476\) 0 0
\(477\) 0 0
\(478\) 3713.28 6431.58i 0.355316 0.615426i
\(479\) 5556.70 + 9624.49i 0.530046 + 0.918067i 0.999386 + 0.0350493i \(0.0111588\pi\)
−0.469339 + 0.883018i \(0.655508\pi\)
\(480\) 0 0
\(481\) −4006.07 + 6938.72i −0.379753 + 0.657751i
\(482\) 13997.2 1.32273
\(483\) 0 0
\(484\) 9754.35 0.916074
\(485\) 3138.00 5435.17i 0.293792 0.508862i
\(486\) 0 0
\(487\) 1893.14 + 3279.01i 0.176152 + 0.305105i 0.940559 0.339629i \(-0.110302\pi\)
−0.764407 + 0.644734i \(0.776968\pi\)
\(488\) −2317.23 + 4013.55i −0.214951 + 0.372305i
\(489\) 0 0
\(490\) 0 0
\(491\) 9582.12 0.880723 0.440361 0.897821i \(-0.354850\pi\)
0.440361 + 0.897821i \(0.354850\pi\)
\(492\) 0 0
\(493\) −2218.00 3841.69i −0.202624 0.350955i
\(494\) 2996.32 + 5189.78i 0.272896 + 0.472671i
\(495\) 0 0
\(496\) 2121.65 0.192066
\(497\) 0 0
\(498\) 0 0
\(499\) −2790.77 + 4833.76i −0.250365 + 0.433645i −0.963626 0.267253i \(-0.913884\pi\)
0.713261 + 0.700898i \(0.247217\pi\)
\(500\) 1831.16 + 3171.65i 0.163784 + 0.283681i
\(501\) 0 0
\(502\) 3722.75 6448.00i 0.330985 0.573283i
\(503\) 14116.3 1.25132 0.625661 0.780095i \(-0.284829\pi\)
0.625661 + 0.780095i \(0.284829\pi\)
\(504\) 0 0
\(505\) 5768.35 0.508294
\(506\) −5808.34 + 10060.3i −0.510301 + 0.883867i
\(507\) 0 0
\(508\) 5233.41 + 9064.53i 0.457076 + 0.791680i
\(509\) 8393.81 14538.5i 0.730941 1.26603i −0.225540 0.974234i \(-0.572415\pi\)
0.956481 0.291793i \(-0.0942519\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 1230.15 + 2130.68i 0.105563 + 0.182841i
\(515\) 2233.14 + 3867.91i 0.191075 + 0.330952i
\(516\) 0 0
\(517\) −3499.94 −0.297731
\(518\) 0 0
\(519\) 0 0
\(520\) −837.588 + 1450.74i −0.0706359 + 0.122345i
\(521\) −2799.31 4848.54i −0.235393 0.407713i 0.723994 0.689807i \(-0.242304\pi\)
−0.959387 + 0.282094i \(0.908971\pi\)
\(522\) 0 0
\(523\) 6635.37 11492.8i 0.554769 0.960889i −0.443152 0.896446i \(-0.646140\pi\)
0.997921 0.0644422i \(-0.0205268\pi\)
\(524\) −710.352 −0.0592211
\(525\) 0 0
\(526\) −4777.27 −0.396005
\(527\) 2128.31 3686.34i 0.175922 0.304705i
\(528\) 0 0
\(529\) 1608.63 + 2786.23i 0.132213 + 0.228999i
\(530\) −1027.86 + 1780.31i −0.0842403 + 0.145909i
\(531\) 0 0
\(532\) 0 0
\(533\) −22956.0 −1.86554
\(534\) 0 0
\(535\) 851.951 + 1475.62i 0.0688468 + 0.119246i
\(536\) −1238.35 2144.89i −0.0997922 0.172845i
\(537\) 0 0
\(538\) −13404.6 −1.07419
\(539\) 0 0
\(540\) 0 0
\(541\) 11508.8 19933.8i 0.914603 1.58414i 0.107121 0.994246i \(-0.465837\pi\)
0.807482 0.589893i \(-0.200830\pi\)
\(542\) −4950.37 8574.29i −0.392319 0.679516i
\(543\) 0 0
\(544\) 513.608 889.595i 0.0404793 0.0701123i
\(545\) −648.687 −0.0509848
\(546\) 0 0
\(547\) 4475.84 0.349859 0.174930 0.984581i \(-0.444030\pi\)
0.174930 + 0.984581i \(0.444030\pi\)
\(548\) 54.0303 93.5832i 0.00421179 0.00729503i
\(549\) 0 0
\(550\) 6741.02 + 11675.8i 0.522614 + 0.905194i
\(551\) −3855.46 + 6677.85i −0.298091 + 0.516308i
\(552\) 0 0
\(553\) 0 0
\(554\) −7410.35 −0.568295
\(555\) 0 0
\(556\) 1845.51 + 3196.51i 0.140768 + 0.243817i
\(557\) 770.848 + 1335.15i 0.0586390 + 0.101566i 0.893855 0.448357i \(-0.147991\pi\)
−0.835216 + 0.549922i \(0.814657\pi\)
\(558\) 0 0
\(559\) 23497.8 1.77791
\(560\) 0 0
\(561\) 0 0
\(562\) 9324.74 16150.9i 0.699894 1.21225i
\(563\) 6539.83 + 11327.3i 0.489557 + 0.847938i 0.999928 0.0120164i \(-0.00382502\pi\)
−0.510370 + 0.859955i \(0.670492\pi\)
\(564\) 0 0
\(565\) 956.983 1657.54i 0.0712577 0.123422i
\(566\) −11139.0 −0.827219
\(567\) 0 0
\(568\) 8471.88 0.625831
\(569\) 5705.59 9882.37i 0.420370 0.728102i −0.575605 0.817728i \(-0.695234\pi\)
0.995976 + 0.0896251i \(0.0285669\pi\)
\(570\) 0 0
\(571\) −1155.87 2002.03i −0.0847139 0.146729i 0.820555 0.571567i \(-0.193664\pi\)
−0.905269 + 0.424838i \(0.860331\pi\)
\(572\) −6593.85 + 11420.9i −0.481998 + 0.834844i
\(573\) 0 0
\(574\) 0 0
\(575\) −10386.8 −0.753324
\(576\) 0 0
\(577\) −12548.5 21734.6i −0.905373 1.56815i −0.820415 0.571768i \(-0.806258\pi\)
−0.0849578 0.996385i \(-0.527076\pi\)
\(578\) 3882.56 + 6724.79i 0.279400 + 0.483935i
\(579\) 0 0
\(580\) −2155.50 −0.154314
\(581\) 0 0
\(582\) 0 0
\(583\) −8091.75 + 14015.3i −0.574830 + 0.995635i
\(584\) −4774.63 8269.91i −0.338315 0.585978i
\(585\) 0 0
\(586\) −1665.31 + 2884.40i −0.117395 + 0.203333i
\(587\) −19789.1 −1.39145 −0.695726 0.718307i \(-0.744917\pi\)
−0.695726 + 0.718307i \(0.744917\pi\)
\(588\) 0 0
\(589\) −7399.12 −0.517615
\(590\) 1761.79 3051.51i 0.122935 0.212930i
\(591\) 0 0
\(592\) −1193.65 2067.46i −0.0828693 0.143534i
\(593\) −1387.07 + 2402.47i −0.0960540 + 0.166370i −0.910048 0.414503i \(-0.863955\pi\)
0.813994 + 0.580873i \(0.197289\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2986.81 −0.205276
\(597\) 0 0
\(598\) −5080.04 8798.89i −0.347388 0.601694i
\(599\) −13095.2 22681.5i −0.893245 1.54715i −0.835962 0.548788i \(-0.815090\pi\)
−0.0572831 0.998358i \(-0.518244\pi\)
\(600\) 0 0
\(601\) −11038.6 −0.749211 −0.374605 0.927184i \(-0.622222\pi\)
−0.374605 + 0.927184i \(0.622222\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4146.29 + 7181.59i −0.279321 + 0.483799i
\(605\) −4754.63 8235.26i −0.319509 0.553407i
\(606\) 0 0
\(607\) 927.197 1605.95i 0.0619996 0.107386i −0.833360 0.552731i \(-0.813586\pi\)
0.895359 + 0.445345i \(0.146919\pi\)
\(608\) −1785.57 −0.119103
\(609\) 0 0
\(610\) 4518.01 0.299883
\(611\) 1530.54 2650.98i 0.101341 0.175527i
\(612\) 0 0
\(613\) 7428.42 + 12866.4i 0.489447 + 0.847747i 0.999926 0.0121428i \(-0.00386527\pi\)
−0.510479 + 0.859890i \(0.670532\pi\)
\(614\) 5303.32 9185.61i 0.348574 0.603748i
\(615\) 0 0
\(616\) 0 0
\(617\) −7600.00 −0.495890 −0.247945 0.968774i \(-0.579755\pi\)
−0.247945 + 0.968774i \(0.579755\pi\)
\(618\) 0 0
\(619\) −11342.6 19646.0i −0.736509 1.27567i −0.954058 0.299622i \(-0.903139\pi\)
0.217549 0.976049i \(-0.430194\pi\)
\(620\) −1034.17 1791.23i −0.0669891 0.116029i
\(621\) 0 0
\(622\) −2251.98 −0.145171
\(623\) 0 0
\(624\) 0 0
\(625\) −5076.98 + 8793.58i −0.324926 + 0.562789i
\(626\) 8299.51 + 14375.2i 0.529896 + 0.917807i
\(627\) 0 0
\(628\) −3132.44 + 5425.55i −0.199041 + 0.344750i
\(629\) −4789.59 −0.303614
\(630\) 0 0
\(631\) −12024.1 −0.758595 −0.379297 0.925275i \(-0.623834\pi\)
−0.379297 + 0.925275i \(0.623834\pi\)
\(632\) −5278.23 + 9142.16i −0.332210 + 0.575405i
\(633\) 0 0
\(634\) −4278.76 7411.04i −0.268031 0.464243i
\(635\) 5101.91 8836.77i 0.318840 0.552246i
\(636\) 0 0
\(637\) 0 0
\(638\) −16969.0 −1.05299
\(639\) 0 0
\(640\) −249.568 432.264i −0.0154141 0.0266980i
\(641\) 5660.28 + 9803.89i 0.348779 + 0.604104i 0.986033 0.166551i \(-0.0532629\pi\)
−0.637253 + 0.770654i \(0.719930\pi\)
\(642\) 0 0
\(643\) 16843.6 1.03304 0.516521 0.856275i \(-0.327227\pi\)
0.516521 + 0.856275i \(0.327227\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1791.18 + 3102.41i −0.109091 + 0.188951i
\(647\) 3859.66 + 6685.13i 0.234527 + 0.406212i 0.959135 0.282949i \(-0.0913126\pi\)
−0.724608 + 0.689161i \(0.757979\pi\)
\(648\) 0 0
\(649\) 13869.5 24022.8i 0.838871 1.45297i
\(650\) −11791.5 −0.711542
\(651\) 0 0
\(652\) 394.933 0.0237221
\(653\) −15401.6 + 26676.3i −0.922987 + 1.59866i −0.128219 + 0.991746i \(0.540926\pi\)
−0.794768 + 0.606914i \(0.792407\pi\)
\(654\) 0 0
\(655\) 346.252 + 599.725i 0.0206552 + 0.0357759i
\(656\) 3419.98 5923.58i 0.203548 0.352556i
\(657\) 0 0
\(658\) 0 0
\(659\) −9760.68 −0.576968 −0.288484 0.957485i \(-0.593151\pi\)
−0.288484 + 0.957485i \(0.593151\pi\)
\(660\) 0 0
\(661\) −9035.53 15650.0i −0.531682 0.920899i −0.999316 0.0369775i \(-0.988227\pi\)
0.467635 0.883922i \(-0.345106\pi\)
\(662\) 1707.12 + 2956.81i 0.100225 + 0.173595i
\(663\) 0 0
\(664\) −9522.65 −0.556552
\(665\) 0 0
\(666\) 0 0
\(667\) 6536.64 11321.8i 0.379460 0.657244i
\(668\) −4462.71 7729.65i −0.258484 0.447708i
\(669\) 0 0
\(670\) −1207.24 + 2090.99i −0.0696114 + 0.120570i
\(671\) 35567.7 2.04631
\(672\) 0 0
\(673\) 26591.1 1.52305 0.761524 0.648137i \(-0.224451\pi\)
0.761524 + 0.648137i \(0.224451\pi\)
\(674\) −1710.67 + 2962.97i −0.0977636 + 0.169331i
\(675\) 0 0
\(676\) −1373.05 2378.20i −0.0781210 0.135310i
\(677\) 16540.1 28648.3i 0.938979 1.62636i 0.171599 0.985167i \(-0.445107\pi\)
0.767380 0.641192i \(-0.221560\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1001.41 −0.0564738
\(681\) 0 0
\(682\) −8141.42 14101.4i −0.457113 0.791743i
\(683\) −5233.04 9063.89i −0.293172 0.507789i 0.681386 0.731924i \(-0.261378\pi\)
−0.974558 + 0.224135i \(0.928044\pi\)
\(684\) 0 0
\(685\) −105.345 −0.00587597
\(686\) 0 0
\(687\) 0 0
\(688\) −3500.70 + 6063.40i −0.193987 + 0.335995i
\(689\) −7077.13 12258.0i −0.391317 0.677781i
\(690\) 0 0
\(691\) −6634.95 + 11492.1i −0.365275 + 0.632675i −0.988820 0.149112i \(-0.952358\pi\)
0.623545 + 0.781787i \(0.285692\pi\)
\(692\) −8403.38 −0.461631
\(693\) 0 0
\(694\) −17820.6 −0.974727
\(695\) 1799.14 3116.20i 0.0981944 0.170078i
\(696\) 0 0
\(697\) −6861.44 11884.4i −0.372878 0.645843i
\(698\) −5378.68 + 9316.15i −0.291671 + 0.505189i
\(699\) 0 0
\(700\) 0 0
\(701\) 15169.9 0.817344 0.408672 0.912681i \(-0.365992\pi\)
0.408672 + 0.912681i \(0.365992\pi\)
\(702\) 0 0
\(703\) 4162.77 + 7210.14i 0.223331 + 0.386821i
\(704\) −1964.70 3402.97i −0.105181 0.182179i
\(705\) 0 0
\(706\) 8505.13 0.453392
\(707\) 0 0
\(708\) 0 0
\(709\) −13158.9 + 22791.8i −0.697026 + 1.20728i 0.272467 + 0.962165i \(0.412160\pi\)
−0.969493 + 0.245119i \(0.921173\pi\)
\(710\) −4129.51 7152.51i −0.218278 0.378069i
\(711\) 0 0
\(712\) −932.341 + 1614.86i −0.0490744 + 0.0849994i
\(713\) 12544.6 0.658907
\(714\) 0 0
\(715\) 12856.3 0.672447
\(716\) 3445.08 5967.06i 0.179817 0.311452i
\(717\) 0 0
\(718\) 4903.89 + 8493.78i 0.254891 + 0.441484i
\(719\) 11506.5 19929.9i 0.596831 1.03374i −0.396455 0.918054i \(-0.629760\pi\)
0.993286 0.115687i \(-0.0369069\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −7490.95 −0.386128
\(723\) 0 0
\(724\) −3310.01 5733.10i −0.169911 0.294294i
\(725\) −7586.26 13139.8i −0.388616 0.673103i
\(726\) 0 0
\(727\) −16265.4 −0.829780 −0.414890 0.909872i \(-0.636180\pi\)
−0.414890 + 0.909872i \(0.636180\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4654.66 + 8062.11i −0.235996 + 0.408756i
\(731\) 7023.40 + 12164.9i 0.355362 + 0.615505i
\(732\) 0 0
\(733\) 433.222 750.362i 0.0218300 0.0378107i −0.854904 0.518786i \(-0.826384\pi\)
0.876734 + 0.480975i \(0.159717\pi\)
\(734\) −8083.14 −0.406477
\(735\) 0 0
\(736\) 3027.30 0.151614
\(737\) −9503.88 + 16461.2i −0.475007 + 0.822736i
\(738\) 0 0
\(739\) −5495.03 9517.68i −0.273529 0.473766i 0.696234 0.717815i \(-0.254858\pi\)
−0.969763 + 0.244049i \(0.921524\pi\)
\(740\) −1163.66 + 2015.51i −0.0578066 + 0.100124i
\(741\) 0 0
\(742\) 0 0
\(743\) 22416.4 1.10683 0.553417 0.832905i \(-0.313324\pi\)
0.553417 + 0.832905i \(0.313324\pi\)
\(744\) 0 0
\(745\) 1455.88 + 2521.66i 0.0715965 + 0.124009i
\(746\) 7451.35 + 12906.1i 0.365701 + 0.633413i
\(747\) 0 0
\(748\) −7883.49 −0.385360
\(749\) 0 0
\(750\) 0 0
\(751\) 9858.97 17076.2i 0.479040 0.829722i −0.520671 0.853757i \(-0.674318\pi\)
0.999711 + 0.0240358i \(0.00765155\pi\)
\(752\) 456.040 + 789.885i 0.0221145 + 0.0383034i
\(753\) 0 0
\(754\) 7420.64 12852.9i 0.358414 0.620791i
\(755\) 8084.22 0.389689
\(756\) 0 0
\(757\) 839.321 0.0402981 0.0201490 0.999797i \(-0.493586\pi\)
0.0201490 + 0.999797i \(0.493586\pi\)
\(758\) 12564.4 21762.2i 0.602057 1.04279i
\(759\) 0 0
\(760\) 870.352 + 1507.49i 0.0415407 + 0.0719507i
\(761\) 9182.25 15904.1i 0.437393 0.757587i −0.560094 0.828429i \(-0.689235\pi\)
0.997488 + 0.0708415i \(0.0225685\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4030.75 0.190874
\(765\) 0 0
\(766\) −4289.93 7430.38i −0.202352 0.350484i
\(767\) 12130.5 + 21010.6i 0.571063 + 0.989111i
\(768\) 0 0
\(769\) −14890.8 −0.698277 −0.349138 0.937071i \(-0.613526\pi\)
−0.349138 + 0.937071i \(0.613526\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15.2970 26.4951i 0.000713148 0.00123521i
\(773\) −8303.10 14381.4i −0.386341 0.669163i 0.605613 0.795759i \(-0.292928\pi\)
−0.991954 + 0.126597i \(0.959595\pi\)
\(774\) 0 0
\(775\) 7279.50 12608.5i 0.337403 0.584400i
\(776\) −12875.5 −0.595623
\(777\) 0 0
\(778\) −11325.5 −0.521903
\(779\) −11927.0 + 20658.1i −0.548559 + 0.950133i
\(780\) 0 0
\(781\) −32509.2 56307.6i −1.48946 2.57983i
\(782\) 3036.81 5259.90i 0.138869 0.240529i
\(783\) 0 0
\(784\) 0 0
\(785\) 6107.47 0.277688
\(786\) 0 0
\(787\) −1578.10 2733.35i −0.0714781 0.123804i 0.828071 0.560623i \(-0.189438\pi\)
−0.899549 + 0.436819i \(0.856105\pi\)
\(788\) 5379.76 + 9318.01i 0.243205 + 0.421244i
\(789\) 0 0
\(790\) 10291.2 0.463475
\(791\) 0