Properties

Label 405.4.e.w.271.4
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.4
Root \(3.41462 + 3.41462i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.w.136.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0745751 + 0.129168i) q^{2} +(3.98888 - 6.90894i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-10.0712 - 17.4439i) q^{7} +2.38308 q^{8} +O(q^{10})\) \(q+(0.0745751 + 0.129168i) q^{2} +(3.98888 - 6.90894i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-10.0712 - 17.4439i) q^{7} +2.38308 q^{8} -0.745751 q^{10} +(4.94688 + 8.56825i) q^{11} +(5.91394 - 10.2432i) q^{13} +(1.50212 - 2.60176i) q^{14} +(-31.7333 - 54.9637i) q^{16} -6.09177 q^{17} -62.6618 q^{19} +(19.9444 + 34.5447i) q^{20} +(-0.737829 + 1.27796i) q^{22} +(-6.03804 + 10.4582i) q^{23} +(-12.5000 - 21.6506i) q^{25} +1.76413 q^{26} -160.691 q^{28} +(-70.2925 - 121.750i) q^{29} +(-89.0513 + 154.241i) q^{31} +(14.2654 - 24.7083i) q^{32} +(-0.454294 - 0.786861i) q^{34} +100.712 q^{35} -216.112 q^{37} +(-4.67301 - 8.09389i) q^{38} +(-5.95771 + 10.3191i) q^{40} +(-205.885 + 356.603i) q^{41} +(24.4588 + 42.3639i) q^{43} +78.9300 q^{44} -1.80115 q^{46} +(-307.710 - 532.969i) q^{47} +(-31.3590 + 54.3153i) q^{49} +(1.86438 - 3.22920i) q^{50} +(-47.1800 - 81.7181i) q^{52} +705.120 q^{53} -49.4688 q^{55} +(-24.0006 - 41.5702i) q^{56} +(10.4841 - 18.1590i) q^{58} +(-247.270 + 428.284i) q^{59} +(-333.101 - 576.948i) q^{61} -26.5640 q^{62} -503.477 q^{64} +(29.5697 + 51.2162i) q^{65} +(-138.909 + 240.598i) q^{67} +(-24.2993 + 42.0877i) q^{68} +(7.51062 + 13.0088i) q^{70} -239.308 q^{71} -919.015 q^{73} +(-16.1166 - 27.9147i) q^{74} +(-249.950 + 432.926i) q^{76} +(99.6423 - 172.586i) q^{77} +(-258.111 - 447.062i) q^{79} +317.333 q^{80} -61.4155 q^{82} +(326.081 + 564.788i) q^{83} +(15.2294 - 26.3781i) q^{85} +(-3.64803 + 6.31858i) q^{86} +(11.7888 + 20.4189i) q^{88} -543.003 q^{89} -238.242 q^{91} +(48.1700 + 83.4329i) q^{92} +(45.8949 - 79.4924i) q^{94} +(156.654 - 271.333i) q^{95} +(-566.695 - 981.545i) q^{97} -9.35439 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + O(q^{10}) \) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0745751 + 0.129168i 0.0263663 + 0.0456677i 0.878907 0.476992i \(-0.158273\pi\)
−0.852541 + 0.522660i \(0.824940\pi\)
\(3\) 0 0
\(4\) 3.98888 6.90894i 0.498610 0.863617i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −10.0712 17.4439i −0.543795 0.941880i −0.998682 0.0513310i \(-0.983654\pi\)
0.454887 0.890549i \(-0.349680\pi\)
\(8\) 2.38308 0.105318
\(9\) 0 0
\(10\) −0.745751 −0.0235827
\(11\) 4.94688 + 8.56825i 0.135595 + 0.234857i 0.925824 0.377954i \(-0.123372\pi\)
−0.790230 + 0.612811i \(0.790039\pi\)
\(12\) 0 0
\(13\) 5.91394 10.2432i 0.126172 0.218536i −0.796019 0.605272i \(-0.793064\pi\)
0.922190 + 0.386736i \(0.126398\pi\)
\(14\) 1.50212 2.60176i 0.0286757 0.0496677i
\(15\) 0 0
\(16\) −31.7333 54.9637i −0.495833 0.858808i
\(17\) −6.09177 −0.0869101 −0.0434550 0.999055i \(-0.513837\pi\)
−0.0434550 + 0.999055i \(0.513837\pi\)
\(18\) 0 0
\(19\) −62.6618 −0.756610 −0.378305 0.925681i \(-0.623493\pi\)
−0.378305 + 0.925681i \(0.623493\pi\)
\(20\) 19.9444 + 34.5447i 0.222985 + 0.386221i
\(21\) 0 0
\(22\) −0.737829 + 1.27796i −0.00715025 + 0.0123846i
\(23\) −6.03804 + 10.4582i −0.0547399 + 0.0948123i −0.892097 0.451844i \(-0.850766\pi\)
0.837357 + 0.546656i \(0.184100\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 1.76413 0.0133067
\(27\) 0 0
\(28\) −160.691 −1.08457
\(29\) −70.2925 121.750i −0.450103 0.779601i 0.548289 0.836289i \(-0.315279\pi\)
−0.998392 + 0.0566879i \(0.981946\pi\)
\(30\) 0 0
\(31\) −89.0513 + 154.241i −0.515938 + 0.893631i 0.483891 + 0.875129i \(0.339223\pi\)
−0.999829 + 0.0185027i \(0.994110\pi\)
\(32\) 14.2654 24.7083i 0.0788058 0.136496i
\(33\) 0 0
\(34\) −0.454294 0.786861i −0.00229149 0.00396899i
\(35\) 100.712 0.486385
\(36\) 0 0
\(37\) −216.112 −0.960231 −0.480116 0.877205i \(-0.659405\pi\)
−0.480116 + 0.877205i \(0.659405\pi\)
\(38\) −4.67301 8.09389i −0.0199490 0.0345527i
\(39\) 0 0
\(40\) −5.95771 + 10.3191i −0.0235499 + 0.0407897i
\(41\) −205.885 + 356.603i −0.784239 + 1.35834i 0.145213 + 0.989400i \(0.453613\pi\)
−0.929453 + 0.368942i \(0.879720\pi\)
\(42\) 0 0
\(43\) 24.4588 + 42.3639i 0.0867425 + 0.150242i 0.906132 0.422994i \(-0.139021\pi\)
−0.819390 + 0.573237i \(0.805688\pi\)
\(44\) 78.9300 0.270435
\(45\) 0 0
\(46\) −1.80115 −0.00577315
\(47\) −307.710 532.969i −0.954980 1.65407i −0.734414 0.678702i \(-0.762543\pi\)
−0.220566 0.975372i \(-0.570790\pi\)
\(48\) 0 0
\(49\) −31.3590 + 54.3153i −0.0914255 + 0.158354i
\(50\) 1.86438 3.22920i 0.00527325 0.00913354i
\(51\) 0 0
\(52\) −47.1800 81.7181i −0.125821 0.217928i
\(53\) 705.120 1.82746 0.913732 0.406316i \(-0.133187\pi\)
0.913732 + 0.406316i \(0.133187\pi\)
\(54\) 0 0
\(55\) −49.4688 −0.121280
\(56\) −24.0006 41.5702i −0.0572716 0.0991974i
\(57\) 0 0
\(58\) 10.4841 18.1590i 0.0237351 0.0411103i
\(59\) −247.270 + 428.284i −0.545624 + 0.945049i 0.452943 + 0.891539i \(0.350374\pi\)
−0.998567 + 0.0535095i \(0.982959\pi\)
\(60\) 0 0
\(61\) −333.101 576.948i −0.699167 1.21099i −0.968755 0.248018i \(-0.920221\pi\)
0.269588 0.962976i \(-0.413112\pi\)
\(62\) −26.5640 −0.0544135
\(63\) 0 0
\(64\) −503.477 −0.983354
\(65\) 29.5697 + 51.2162i 0.0564257 + 0.0977322i
\(66\) 0 0
\(67\) −138.909 + 240.598i −0.253290 + 0.438712i −0.964430 0.264339i \(-0.914846\pi\)
0.711139 + 0.703051i \(0.248179\pi\)
\(68\) −24.2993 + 42.0877i −0.0433342 + 0.0750570i
\(69\) 0 0
\(70\) 7.51062 + 13.0088i 0.0128242 + 0.0222121i
\(71\) −239.308 −0.400009 −0.200005 0.979795i \(-0.564096\pi\)
−0.200005 + 0.979795i \(0.564096\pi\)
\(72\) 0 0
\(73\) −919.015 −1.47346 −0.736730 0.676187i \(-0.763631\pi\)
−0.736730 + 0.676187i \(0.763631\pi\)
\(74\) −16.1166 27.9147i −0.0253177 0.0438516i
\(75\) 0 0
\(76\) −249.950 + 432.926i −0.377253 + 0.653422i
\(77\) 99.6423 172.586i 0.147471 0.255428i
\(78\) 0 0
\(79\) −258.111 447.062i −0.367592 0.636688i 0.621596 0.783338i \(-0.286484\pi\)
−0.989189 + 0.146649i \(0.953151\pi\)
\(80\) 317.333 0.443486
\(81\) 0 0
\(82\) −61.4155 −0.0827099
\(83\) 326.081 + 564.788i 0.431229 + 0.746910i 0.996979 0.0776662i \(-0.0247469\pi\)
−0.565751 + 0.824576i \(0.691414\pi\)
\(84\) 0 0
\(85\) 15.2294 26.3781i 0.0194337 0.0336601i
\(86\) −3.64803 + 6.31858i −0.00457415 + 0.00792267i
\(87\) 0 0
\(88\) 11.7888 + 20.4189i 0.0142806 + 0.0247348i
\(89\) −543.003 −0.646721 −0.323361 0.946276i \(-0.604813\pi\)
−0.323361 + 0.946276i \(0.604813\pi\)
\(90\) 0 0
\(91\) −238.242 −0.274446
\(92\) 48.1700 + 83.4329i 0.0545877 + 0.0945487i
\(93\) 0 0
\(94\) 45.8949 79.4924i 0.0503585 0.0872235i
\(95\) 156.654 271.333i 0.169183 0.293034i
\(96\) 0 0
\(97\) −566.695 981.545i −0.593188 1.02743i −0.993800 0.111183i \(-0.964536\pi\)
0.400612 0.916248i \(-0.368797\pi\)
\(98\) −9.35439 −0.00964220
\(99\) 0 0
\(100\) −199.444 −0.199444
\(101\) −599.618 1038.57i −0.590735 1.02318i −0.994134 0.108158i \(-0.965505\pi\)
0.403399 0.915024i \(-0.367829\pi\)
\(102\) 0 0
\(103\) 622.967 1079.01i 0.595949 1.03221i −0.397463 0.917618i \(-0.630109\pi\)
0.993412 0.114596i \(-0.0365574\pi\)
\(104\) 14.0934 24.4105i 0.0132882 0.0230159i
\(105\) 0 0
\(106\) 52.5844 + 91.0788i 0.0481834 + 0.0834562i
\(107\) 1159.14 1.04728 0.523638 0.851941i \(-0.324574\pi\)
0.523638 + 0.851941i \(0.324574\pi\)
\(108\) 0 0
\(109\) −118.618 −0.104234 −0.0521171 0.998641i \(-0.516597\pi\)
−0.0521171 + 0.998641i \(0.516597\pi\)
\(110\) −3.68914 6.38978i −0.00319769 0.00553856i
\(111\) 0 0
\(112\) −639.186 + 1107.10i −0.539263 + 0.934030i
\(113\) −191.641 + 331.932i −0.159541 + 0.276333i −0.934703 0.355429i \(-0.884335\pi\)
0.775162 + 0.631762i \(0.217668\pi\)
\(114\) 0 0
\(115\) −30.1902 52.2910i −0.0244804 0.0424014i
\(116\) −1121.55 −0.897702
\(117\) 0 0
\(118\) −73.7608 −0.0575443
\(119\) 61.3516 + 106.264i 0.0472612 + 0.0818589i
\(120\) 0 0
\(121\) 616.557 1067.91i 0.463228 0.802335i
\(122\) 49.6821 86.0519i 0.0368689 0.0638588i
\(123\) 0 0
\(124\) 710.429 + 1230.50i 0.514504 + 0.891146i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 2570.69 1.79616 0.898079 0.439834i \(-0.144963\pi\)
0.898079 + 0.439834i \(0.144963\pi\)
\(128\) −151.670 262.700i −0.104733 0.181403i
\(129\) 0 0
\(130\) −4.41033 + 7.63891i −0.00297547 + 0.00515367i
\(131\) 329.029 569.894i 0.219446 0.380091i −0.735193 0.677858i \(-0.762908\pi\)
0.954639 + 0.297767i \(0.0962418\pi\)
\(132\) 0 0
\(133\) 631.081 + 1093.06i 0.411441 + 0.712636i
\(134\) −41.4367 −0.0267133
\(135\) 0 0
\(136\) −14.5172 −0.00915323
\(137\) 313.367 + 542.767i 0.195421 + 0.338480i 0.947039 0.321120i \(-0.104059\pi\)
−0.751617 + 0.659600i \(0.770726\pi\)
\(138\) 0 0
\(139\) 486.872 843.288i 0.297093 0.514581i −0.678376 0.734715i \(-0.737316\pi\)
0.975470 + 0.220134i \(0.0706494\pi\)
\(140\) 401.729 695.814i 0.242516 0.420050i
\(141\) 0 0
\(142\) −17.8464 30.9109i −0.0105468 0.0182675i
\(143\) 117.022 0.0684329
\(144\) 0 0
\(145\) 702.925 0.402584
\(146\) −68.5357 118.707i −0.0388497 0.0672896i
\(147\) 0 0
\(148\) −862.043 + 1493.10i −0.478780 + 0.829272i
\(149\) −1487.92 + 2577.16i −0.818089 + 1.41697i 0.0889994 + 0.996032i \(0.471633\pi\)
−0.907088 + 0.420940i \(0.861700\pi\)
\(150\) 0 0
\(151\) 1038.22 + 1798.24i 0.559529 + 0.969133i 0.997536 + 0.0701611i \(0.0223513\pi\)
−0.438007 + 0.898972i \(0.644315\pi\)
\(152\) −149.328 −0.0796850
\(153\) 0 0
\(154\) 29.7233 0.0155531
\(155\) −445.256 771.207i −0.230735 0.399644i
\(156\) 0 0
\(157\) −176.175 + 305.144i −0.0895559 + 0.155115i −0.907324 0.420433i \(-0.861878\pi\)
0.817768 + 0.575549i \(0.195211\pi\)
\(158\) 38.4973 66.6793i 0.0193841 0.0335742i
\(159\) 0 0
\(160\) 71.3268 + 123.542i 0.0352430 + 0.0610427i
\(161\) 243.242 0.119069
\(162\) 0 0
\(163\) 2772.05 1.33205 0.666023 0.745931i \(-0.267995\pi\)
0.666023 + 0.745931i \(0.267995\pi\)
\(164\) 1642.50 + 2844.89i 0.782058 + 1.35456i
\(165\) 0 0
\(166\) −48.6350 + 84.2382i −0.0227398 + 0.0393865i
\(167\) 1917.72 3321.59i 0.888608 1.53912i 0.0470874 0.998891i \(-0.485006\pi\)
0.841521 0.540224i \(-0.181661\pi\)
\(168\) 0 0
\(169\) 1028.55 + 1781.50i 0.468161 + 0.810879i
\(170\) 4.54294 0.00204958
\(171\) 0 0
\(172\) 390.252 0.173003
\(173\) 567.727 + 983.332i 0.249500 + 0.432146i 0.963387 0.268114i \(-0.0864005\pi\)
−0.713887 + 0.700261i \(0.753067\pi\)
\(174\) 0 0
\(175\) −251.781 + 436.097i −0.108759 + 0.188376i
\(176\) 313.962 543.798i 0.134465 0.232900i
\(177\) 0 0
\(178\) −40.4945 70.1385i −0.0170516 0.0295343i
\(179\) −3192.57 −1.33309 −0.666546 0.745464i \(-0.732228\pi\)
−0.666546 + 0.745464i \(0.732228\pi\)
\(180\) 0 0
\(181\) 990.641 0.406816 0.203408 0.979094i \(-0.434798\pi\)
0.203408 + 0.979094i \(0.434798\pi\)
\(182\) −17.7670 30.7733i −0.00723612 0.0125333i
\(183\) 0 0
\(184\) −14.3892 + 24.9228i −0.00576513 + 0.00998549i
\(185\) 540.279 935.791i 0.214714 0.371896i
\(186\) 0 0
\(187\) −30.1353 52.1958i −0.0117845 0.0204114i
\(188\) −4909.66 −1.90465
\(189\) 0 0
\(190\) 46.7301 0.0178429
\(191\) 1641.86 + 2843.79i 0.621994 + 1.07733i 0.989114 + 0.147152i \(0.0470105\pi\)
−0.367120 + 0.930174i \(0.619656\pi\)
\(192\) 0 0
\(193\) 1184.00 2050.76i 0.441588 0.764853i −0.556219 0.831035i \(-0.687749\pi\)
0.997808 + 0.0661824i \(0.0210819\pi\)
\(194\) 84.5227 146.398i 0.0312803 0.0541790i
\(195\) 0 0
\(196\) 250.174 + 433.314i 0.0911713 + 0.157913i
\(197\) 3754.00 1.35767 0.678836 0.734290i \(-0.262485\pi\)
0.678836 + 0.734290i \(0.262485\pi\)
\(198\) 0 0
\(199\) 1905.82 0.678894 0.339447 0.940625i \(-0.389760\pi\)
0.339447 + 0.940625i \(0.389760\pi\)
\(200\) −29.7886 51.5953i −0.0105318 0.0182417i
\(201\) 0 0
\(202\) 89.4331 154.903i 0.0311509 0.0539550i
\(203\) −1415.86 + 2452.34i −0.489527 + 0.847886i
\(204\) 0 0
\(205\) −1029.42 1783.01i −0.350722 0.607469i
\(206\) 185.831 0.0628518
\(207\) 0 0
\(208\) −750.676 −0.250240
\(209\) −309.981 536.902i −0.102592 0.177695i
\(210\) 0 0
\(211\) 1844.59 3194.93i 0.601834 1.04241i −0.390709 0.920514i \(-0.627770\pi\)
0.992543 0.121893i \(-0.0388966\pi\)
\(212\) 2812.64 4871.63i 0.911192 1.57823i
\(213\) 0 0
\(214\) 86.4431 + 149.724i 0.0276128 + 0.0478267i
\(215\) −244.588 −0.0775849
\(216\) 0 0
\(217\) 3587.42 1.12226
\(218\) −8.84593 15.3216i −0.00274826 0.00476013i
\(219\) 0 0
\(220\) −197.325 + 341.777i −0.0604712 + 0.104739i
\(221\) −36.0264 + 62.3995i −0.0109656 + 0.0189930i
\(222\) 0 0
\(223\) −84.8583 146.979i −0.0254822 0.0441365i 0.853003 0.521906i \(-0.174779\pi\)
−0.878485 + 0.477769i \(0.841445\pi\)
\(224\) −574.679 −0.171417
\(225\) 0 0
\(226\) −57.1667 −0.0168260
\(227\) −1803.73 3124.15i −0.527391 0.913468i −0.999490 0.0319228i \(-0.989837\pi\)
0.472099 0.881545i \(-0.343496\pi\)
\(228\) 0 0
\(229\) 3046.95 5277.47i 0.879250 1.52290i 0.0270836 0.999633i \(-0.491378\pi\)
0.852166 0.523272i \(-0.175289\pi\)
\(230\) 4.50287 7.79921i 0.00129092 0.00223593i
\(231\) 0 0
\(232\) −167.513 290.141i −0.0474041 0.0821064i
\(233\) −3930.28 −1.10507 −0.552534 0.833490i \(-0.686339\pi\)
−0.552534 + 0.833490i \(0.686339\pi\)
\(234\) 0 0
\(235\) 3077.10 0.854160
\(236\) 1972.66 + 3416.75i 0.544107 + 0.942421i
\(237\) 0 0
\(238\) −9.15059 + 15.8493i −0.00249221 + 0.00431663i
\(239\) −1831.12 + 3171.59i −0.495587 + 0.858382i −0.999987 0.00508843i \(-0.998380\pi\)
0.504400 + 0.863470i \(0.331714\pi\)
\(240\) 0 0
\(241\) −111.414 192.976i −0.0297794 0.0515795i 0.850752 0.525568i \(-0.176147\pi\)
−0.880531 + 0.473989i \(0.842814\pi\)
\(242\) 183.919 0.0488544
\(243\) 0 0
\(244\) −5314.80 −1.39445
\(245\) −156.795 271.577i −0.0408867 0.0708179i
\(246\) 0 0
\(247\) −370.578 + 641.860i −0.0954629 + 0.165347i
\(248\) −212.217 + 367.570i −0.0543378 + 0.0941159i
\(249\) 0 0
\(250\) 9.32189 + 16.1460i 0.00235827 + 0.00408465i
\(251\) 4748.92 1.19422 0.597110 0.802159i \(-0.296316\pi\)
0.597110 + 0.802159i \(0.296316\pi\)
\(252\) 0 0
\(253\) −119.478 −0.0296898
\(254\) 191.710 + 332.051i 0.0473580 + 0.0820264i
\(255\) 0 0
\(256\) −1991.29 + 3449.01i −0.486154 + 0.842044i
\(257\) 2826.07 4894.90i 0.685936 1.18808i −0.287205 0.957869i \(-0.592726\pi\)
0.973142 0.230208i \(-0.0739405\pi\)
\(258\) 0 0
\(259\) 2176.51 + 3769.82i 0.522169 + 0.904423i
\(260\) 471.800 0.112538
\(261\) 0 0
\(262\) 98.1494 0.0231438
\(263\) −1644.93 2849.11i −0.385669 0.667998i 0.606193 0.795318i \(-0.292696\pi\)
−0.991862 + 0.127320i \(0.959363\pi\)
\(264\) 0 0
\(265\) −1762.80 + 3053.26i −0.408634 + 0.707774i
\(266\) −94.1258 + 163.031i −0.0216963 + 0.0375791i
\(267\) 0 0
\(268\) 1108.18 + 1919.43i 0.252586 + 0.437492i
\(269\) −5452.66 −1.23589 −0.617945 0.786221i \(-0.712035\pi\)
−0.617945 + 0.786221i \(0.712035\pi\)
\(270\) 0 0
\(271\) −238.923 −0.0535555 −0.0267778 0.999641i \(-0.508525\pi\)
−0.0267778 + 0.999641i \(0.508525\pi\)
\(272\) 193.312 + 334.826i 0.0430929 + 0.0746390i
\(273\) 0 0
\(274\) −46.7387 + 80.9539i −0.0103051 + 0.0178489i
\(275\) 123.672 214.206i 0.0271189 0.0469714i
\(276\) 0 0
\(277\) −1878.87 3254.30i −0.407547 0.705892i 0.587067 0.809538i \(-0.300282\pi\)
−0.994614 + 0.103646i \(0.966949\pi\)
\(278\) 145.234 0.0313330
\(279\) 0 0
\(280\) 240.006 0.0512253
\(281\) 236.491 + 409.615i 0.0502060 + 0.0869593i 0.890036 0.455890i \(-0.150679\pi\)
−0.839830 + 0.542849i \(0.817346\pi\)
\(282\) 0 0
\(283\) −1176.94 + 2038.52i −0.247215 + 0.428190i −0.962752 0.270385i \(-0.912849\pi\)
0.715537 + 0.698575i \(0.246182\pi\)
\(284\) −954.571 + 1653.37i −0.199449 + 0.345455i
\(285\) 0 0
\(286\) 8.72695 + 15.1155i 0.00180432 + 0.00312517i
\(287\) 8294.05 1.70586
\(288\) 0 0
\(289\) −4875.89 −0.992447
\(290\) 52.4207 + 90.7952i 0.0106146 + 0.0183851i
\(291\) 0 0
\(292\) −3665.84 + 6349.42i −0.734682 + 1.27251i
\(293\) −2071.53 + 3587.99i −0.413038 + 0.715402i −0.995220 0.0976560i \(-0.968866\pi\)
0.582183 + 0.813058i \(0.302199\pi\)
\(294\) 0 0
\(295\) −1236.35 2141.42i −0.244011 0.422639i
\(296\) −515.013 −0.101130
\(297\) 0 0
\(298\) −443.847 −0.0862798
\(299\) 71.4172 + 123.698i 0.0138133 + 0.0239253i
\(300\) 0 0
\(301\) 492.660 853.311i 0.0943403 0.163402i
\(302\) −154.850 + 268.208i −0.0295054 + 0.0511048i
\(303\) 0 0
\(304\) 1988.47 + 3444.12i 0.375152 + 0.649783i
\(305\) 3331.01 0.625354
\(306\) 0 0
\(307\) 224.413 0.0417196 0.0208598 0.999782i \(-0.493360\pi\)
0.0208598 + 0.999782i \(0.493360\pi\)
\(308\) −794.922 1376.85i −0.147061 0.254718i
\(309\) 0 0
\(310\) 66.4101 115.026i 0.0121672 0.0210742i
\(311\) −3038.06 + 5262.08i −0.553931 + 0.959437i 0.444055 + 0.896000i \(0.353540\pi\)
−0.997986 + 0.0634374i \(0.979794\pi\)
\(312\) 0 0
\(313\) −1728.17 2993.27i −0.312082 0.540542i 0.666731 0.745299i \(-0.267693\pi\)
−0.978813 + 0.204757i \(0.934360\pi\)
\(314\) −52.5530 −0.00944502
\(315\) 0 0
\(316\) −4118.30 −0.733140
\(317\) −3816.02 6609.54i −0.676117 1.17107i −0.976141 0.217137i \(-0.930328\pi\)
0.300025 0.953931i \(-0.403005\pi\)
\(318\) 0 0
\(319\) 695.457 1204.57i 0.122063 0.211419i
\(320\) 1258.69 2180.12i 0.219885 0.380851i
\(321\) 0 0
\(322\) 18.1398 + 31.4190i 0.00313941 + 0.00543762i
\(323\) 381.721 0.0657571
\(324\) 0 0
\(325\) −295.697 −0.0504687
\(326\) 206.726 + 358.059i 0.0351211 + 0.0608315i
\(327\) 0 0
\(328\) −490.641 + 849.815i −0.0825949 + 0.143058i
\(329\) −6198.02 + 10735.3i −1.03863 + 1.79895i
\(330\) 0 0
\(331\) −595.190 1030.90i −0.0988357 0.171188i 0.812367 0.583146i \(-0.198178\pi\)
−0.911203 + 0.411958i \(0.864845\pi\)
\(332\) 5202.78 0.860059
\(333\) 0 0
\(334\) 572.056 0.0937172
\(335\) −694.546 1202.99i −0.113275 0.196198i
\(336\) 0 0
\(337\) −347.609 + 602.076i −0.0561883 + 0.0973209i −0.892751 0.450550i \(-0.851228\pi\)
0.836563 + 0.547871i \(0.184561\pi\)
\(338\) −153.408 + 265.711i −0.0246873 + 0.0427597i
\(339\) 0 0
\(340\) −121.497 210.438i −0.0193796 0.0335665i
\(341\) −1762.11 −0.279834
\(342\) 0 0
\(343\) −5645.57 −0.888723
\(344\) 58.2873 + 100.957i 0.00913559 + 0.0158233i
\(345\) 0 0
\(346\) −84.6765 + 146.664i −0.0131568 + 0.0227882i
\(347\) 5116.21 8861.54i 0.791506 1.37093i −0.133528 0.991045i \(-0.542631\pi\)
0.925034 0.379884i \(-0.124036\pi\)
\(348\) 0 0
\(349\) −3998.80 6926.12i −0.613326 1.06231i −0.990676 0.136241i \(-0.956498\pi\)
0.377350 0.926071i \(-0.376835\pi\)
\(350\) −75.1062 −0.0114703
\(351\) 0 0
\(352\) 282.276 0.0427426
\(353\) 2718.35 + 4708.32i 0.409867 + 0.709911i 0.994875 0.101117i \(-0.0322416\pi\)
−0.585007 + 0.811028i \(0.698908\pi\)
\(354\) 0 0
\(355\) 598.271 1036.24i 0.0894448 0.154923i
\(356\) −2165.97 + 3751.57i −0.322461 + 0.558520i
\(357\) 0 0
\(358\) −238.086 412.377i −0.0351487 0.0608793i
\(359\) 4767.51 0.700890 0.350445 0.936583i \(-0.386030\pi\)
0.350445 + 0.936583i \(0.386030\pi\)
\(360\) 0 0
\(361\) −2932.50 −0.427541
\(362\) 73.8771 + 127.959i 0.0107262 + 0.0185784i
\(363\) 0 0
\(364\) −950.320 + 1646.00i −0.136841 + 0.237016i
\(365\) 2297.54 3979.45i 0.329476 0.570669i
\(366\) 0 0
\(367\) −6360.69 11017.0i −0.904701 1.56699i −0.821317 0.570471i \(-0.806761\pi\)
−0.0833840 0.996517i \(-0.526573\pi\)
\(368\) 766.428 0.108567
\(369\) 0 0
\(370\) 161.166 0.0226449
\(371\) −7101.42 12300.0i −0.993766 1.72125i
\(372\) 0 0
\(373\) 4653.06 8059.34i 0.645915 1.11876i −0.338174 0.941084i \(-0.609809\pi\)
0.984089 0.177675i \(-0.0568574\pi\)
\(374\) 4.49468 7.78502i 0.000621429 0.00107635i
\(375\) 0 0
\(376\) −733.298 1270.11i −0.100577 0.174204i
\(377\) −1662.82 −0.227161
\(378\) 0 0
\(379\) −11623.8 −1.57539 −0.787694 0.616067i \(-0.788725\pi\)
−0.787694 + 0.616067i \(0.788725\pi\)
\(380\) −1249.75 2164.63i −0.168713 0.292219i
\(381\) 0 0
\(382\) −244.884 + 424.151i −0.0327993 + 0.0568101i
\(383\) −5821.46 + 10083.1i −0.776664 + 1.34522i 0.157190 + 0.987568i \(0.449757\pi\)
−0.933854 + 0.357654i \(0.883577\pi\)
\(384\) 0 0
\(385\) 498.212 + 862.928i 0.0659512 + 0.114231i
\(386\) 353.189 0.0465721
\(387\) 0 0
\(388\) −9041.91 −1.18308
\(389\) 3489.65 + 6044.26i 0.454839 + 0.787805i 0.998679 0.0513843i \(-0.0163633\pi\)
−0.543840 + 0.839189i \(0.683030\pi\)
\(390\) 0 0
\(391\) 36.7824 63.7089i 0.00475745 0.00824015i
\(392\) −74.7310 + 129.438i −0.00962880 + 0.0166776i
\(393\) 0 0
\(394\) 279.955 + 484.896i 0.0357967 + 0.0620018i
\(395\) 2581.11 0.328785
\(396\) 0 0
\(397\) 2884.53 0.364661 0.182330 0.983237i \(-0.441636\pi\)
0.182330 + 0.983237i \(0.441636\pi\)
\(398\) 142.127 + 246.170i 0.0178999 + 0.0310035i
\(399\) 0 0
\(400\) −793.332 + 1374.09i −0.0991666 + 0.171762i
\(401\) 5497.18 9521.40i 0.684579 1.18573i −0.288990 0.957332i \(-0.593319\pi\)
0.973569 0.228393i \(-0.0733472\pi\)
\(402\) 0 0
\(403\) 1053.29 + 1824.35i 0.130194 + 0.225502i
\(404\) −9567.21 −1.17818
\(405\) 0 0
\(406\) −422.352 −0.0516280
\(407\) −1069.08 1851.70i −0.130202 0.225517i
\(408\) 0 0
\(409\) 1423.27 2465.17i 0.172069 0.298031i −0.767074 0.641558i \(-0.778288\pi\)
0.939143 + 0.343527i \(0.111622\pi\)
\(410\) 153.539 265.937i 0.0184945 0.0320334i
\(411\) 0 0
\(412\) −4969.88 8608.08i −0.594292 1.02934i
\(413\) 9961.25 1.18683
\(414\) 0 0
\(415\) −3260.81 −0.385703
\(416\) −168.729 292.247i −0.0198861 0.0344438i
\(417\) 0 0
\(418\) 46.2337 80.0790i 0.00540996 0.00937032i
\(419\) −4152.56 + 7192.44i −0.484167 + 0.838601i −0.999835 0.0181874i \(-0.994210\pi\)
0.515668 + 0.856788i \(0.327544\pi\)
\(420\) 0 0
\(421\) −1785.74 3092.99i −0.206726 0.358060i 0.743955 0.668229i \(-0.232947\pi\)
−0.950681 + 0.310170i \(0.899614\pi\)
\(422\) 550.243 0.0634725
\(423\) 0 0
\(424\) 1680.36 0.192466
\(425\) 76.1471 + 131.891i 0.00869101 + 0.0150533i
\(426\) 0 0
\(427\) −6709.47 + 11621.1i −0.760407 + 1.31706i
\(428\) 4623.68 8008.44i 0.522182 0.904445i
\(429\) 0 0
\(430\) −18.2402 31.5929i −0.00204562 0.00354313i
\(431\) −13408.7 −1.49854 −0.749272 0.662262i \(-0.769597\pi\)
−0.749272 + 0.662262i \(0.769597\pi\)
\(432\) 0 0
\(433\) −1698.17 −0.188473 −0.0942364 0.995550i \(-0.530041\pi\)
−0.0942364 + 0.995550i \(0.530041\pi\)
\(434\) 267.532 + 463.379i 0.0295898 + 0.0512510i
\(435\) 0 0
\(436\) −473.152 + 819.523i −0.0519721 + 0.0900184i
\(437\) 378.354 655.329i 0.0414168 0.0717360i
\(438\) 0 0
\(439\) 5365.08 + 9292.59i 0.583283 + 1.01028i 0.995087 + 0.0990034i \(0.0315655\pi\)
−0.411804 + 0.911272i \(0.635101\pi\)
\(440\) −117.888 −0.0127730
\(441\) 0 0
\(442\) −10.7467 −0.00115649
\(443\) 4219.76 + 7308.84i 0.452566 + 0.783868i 0.998545 0.0539314i \(-0.0171752\pi\)
−0.545978 + 0.837799i \(0.683842\pi\)
\(444\) 0 0
\(445\) 1357.51 2351.27i 0.144611 0.250474i
\(446\) 12.6566 21.9219i 0.00134374 0.00232743i
\(447\) 0 0
\(448\) 5070.63 + 8782.59i 0.534743 + 0.926202i
\(449\) −3860.69 −0.405784 −0.202892 0.979201i \(-0.565034\pi\)
−0.202892 + 0.979201i \(0.565034\pi\)
\(450\) 0 0
\(451\) −4073.95 −0.425355
\(452\) 1528.87 + 2648.08i 0.159097 + 0.275564i
\(453\) 0 0
\(454\) 269.027 465.968i 0.0278107 0.0481695i
\(455\) 595.606 1031.62i 0.0613680 0.106293i
\(456\) 0 0
\(457\) 1736.43 + 3007.59i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763366 + 0.645966i \(0.776455\pi\)
\(458\) 908.906 0.0927301
\(459\) 0 0
\(460\) −481.700 −0.0488247
\(461\) −3420.95 5925.27i −0.345618 0.598627i 0.639848 0.768501i \(-0.278997\pi\)
−0.985466 + 0.169874i \(0.945664\pi\)
\(462\) 0 0
\(463\) −3090.27 + 5352.50i −0.310188 + 0.537261i −0.978403 0.206707i \(-0.933725\pi\)
0.668215 + 0.743968i \(0.267059\pi\)
\(464\) −4461.22 + 7727.06i −0.446351 + 0.773103i
\(465\) 0 0
\(466\) −293.101 507.665i −0.0291365 0.0504660i
\(467\) 10977.3 1.08772 0.543861 0.839175i \(-0.316962\pi\)
0.543861 + 0.839175i \(0.316962\pi\)
\(468\) 0 0
\(469\) 5595.94 0.550952
\(470\) 229.475 + 397.462i 0.0225210 + 0.0390075i
\(471\) 0 0
\(472\) −589.266 + 1020.64i −0.0574643 + 0.0995311i
\(473\) −241.990 + 419.138i −0.0235237 + 0.0407442i
\(474\) 0 0
\(475\) 783.272 + 1356.67i 0.0756610 + 0.131049i
\(476\) 978.895 0.0942596
\(477\) 0 0
\(478\) −546.223 −0.0522671
\(479\) −2642.83 4577.51i −0.252096 0.436643i 0.712007 0.702172i \(-0.247786\pi\)
−0.964103 + 0.265530i \(0.914453\pi\)
\(480\) 0 0
\(481\) −1278.07 + 2213.69i −0.121154 + 0.209845i
\(482\) 16.6175 28.7823i 0.00157034 0.00271992i
\(483\) 0 0
\(484\) −4918.74 8519.50i −0.461940 0.800104i
\(485\) 5666.95 0.530563
\(486\) 0 0
\(487\) 15418.1 1.43462 0.717312 0.696752i \(-0.245372\pi\)
0.717312 + 0.696752i \(0.245372\pi\)
\(488\) −793.808 1374.92i −0.0736352 0.127540i
\(489\) 0 0
\(490\) 23.3860 40.5057i 0.00215606 0.00373441i
\(491\) −6891.19 + 11935.9i −0.633392 + 1.09707i 0.353462 + 0.935449i \(0.385004\pi\)
−0.986853 + 0.161617i \(0.948329\pi\)
\(492\) 0 0
\(493\) 428.205 + 741.674i 0.0391185 + 0.0677552i
\(494\) −110.544 −0.0100680
\(495\) 0 0
\(496\) 11303.6 1.02328
\(497\) 2410.13 + 4174.46i 0.217523 + 0.376761i
\(498\) 0 0
\(499\) 1151.32 1994.14i 0.103287 0.178898i −0.809750 0.586775i \(-0.800397\pi\)
0.913037 + 0.407877i \(0.133731\pi\)
\(500\) 498.610 863.617i 0.0445970 0.0772443i
\(501\) 0 0
\(502\) 354.151 + 613.408i 0.0314871 + 0.0545373i
\(503\) 830.769 0.0736425 0.0368213 0.999322i \(-0.488277\pi\)
0.0368213 + 0.999322i \(0.488277\pi\)
\(504\) 0 0
\(505\) 5996.18 0.528369
\(506\) −8.91008 15.4327i −0.000782809 0.00135586i
\(507\) 0 0
\(508\) 10254.2 17760.8i 0.895582 1.55119i
\(509\) 6932.15 12006.8i 0.603658 1.04557i −0.388604 0.921405i \(-0.627042\pi\)
0.992262 0.124162i \(-0.0396242\pi\)
\(510\) 0 0
\(511\) 9255.61 + 16031.2i 0.801260 + 1.38782i
\(512\) −3020.72 −0.260739
\(513\) 0 0
\(514\) 843.019 0.0723423
\(515\) 3114.84 + 5395.05i 0.266517 + 0.461620i
\(516\) 0 0
\(517\) 3044.41 5273.07i 0.258980 0.448567i
\(518\) −324.627 + 562.270i −0.0275353 + 0.0476925i
\(519\) 0 0
\(520\) 70.4671 + 122.053i 0.00594267 + 0.0102930i
\(521\) −2262.83 −0.190281 −0.0951403 0.995464i \(-0.530330\pi\)
−0.0951403 + 0.995464i \(0.530330\pi\)
\(522\) 0 0
\(523\) 8379.47 0.700590 0.350295 0.936639i \(-0.386081\pi\)
0.350295 + 0.936639i \(0.386081\pi\)
\(524\) −2624.91 4546.48i −0.218835 0.379034i
\(525\) 0 0
\(526\) 245.342 424.945i 0.0203373 0.0352252i
\(527\) 542.480 939.603i 0.0448402 0.0776656i
\(528\) 0 0
\(529\) 6010.58 + 10410.6i 0.494007 + 0.855645i
\(530\) −525.844 −0.0430966
\(531\) 0 0
\(532\) 10069.2 0.820593
\(533\) 2435.18 + 4217.86i 0.197898 + 0.342769i
\(534\) 0 0
\(535\) −2897.86 + 5019.23i −0.234178 + 0.405608i
\(536\) −331.032 + 573.365i −0.0266762 + 0.0462045i
\(537\) 0 0
\(538\) −406.633 704.308i −0.0325858 0.0564403i
\(539\) −620.517 −0.0495873
\(540\) 0 0
\(541\) 11880.6 0.944155 0.472078 0.881557i \(-0.343504\pi\)
0.472078 + 0.881557i \(0.343504\pi\)
\(542\) −17.8177 30.8612i −0.00141206 0.00244576i
\(543\) 0 0
\(544\) −86.9013 + 150.518i −0.00684901 + 0.0118628i
\(545\) 296.544 513.630i 0.0233075 0.0403697i
\(546\) 0 0
\(547\) 4334.23 + 7507.11i 0.338791 + 0.586803i 0.984206 0.177030i \(-0.0566488\pi\)
−0.645415 + 0.763832i \(0.723316\pi\)
\(548\) 4999.93 0.389756
\(549\) 0 0
\(550\) 36.8914 0.00286010
\(551\) 4404.65 + 7629.08i 0.340553 + 0.589854i
\(552\) 0 0
\(553\) −5198.99 + 9004.92i −0.399790 + 0.692456i
\(554\) 280.234 485.380i 0.0214910 0.0372235i
\(555\) 0 0
\(556\) −3884.15 6727.54i −0.296267 0.513150i
\(557\) −19918.2 −1.51519 −0.757594 0.652726i \(-0.773625\pi\)
−0.757594 + 0.652726i \(0.773625\pi\)
\(558\) 0 0
\(559\) 578.591 0.0437778
\(560\) −3195.93 5535.51i −0.241166 0.417711i
\(561\) 0 0
\(562\) −35.2727 + 61.0941i −0.00264749 + 0.00458558i
\(563\) 7241.12 12542.0i 0.542055 0.938866i −0.456731 0.889605i \(-0.650980\pi\)
0.998786 0.0492616i \(-0.0156868\pi\)
\(564\) 0 0
\(565\) −958.207 1659.66i −0.0713488 0.123580i
\(566\) −351.082 −0.0260726
\(567\) 0 0
\(568\) −570.292 −0.0421284
\(569\) 8316.59 + 14404.8i 0.612741 + 1.06130i 0.990776 + 0.135508i \(0.0432665\pi\)
−0.378035 + 0.925791i \(0.623400\pi\)
\(570\) 0 0
\(571\) −415.181 + 719.114i −0.0304287 + 0.0527040i −0.880839 0.473416i \(-0.843021\pi\)
0.850410 + 0.526120i \(0.176354\pi\)
\(572\) 466.788 808.500i 0.0341213 0.0590998i
\(573\) 0 0
\(574\) 618.529 + 1071.32i 0.0449772 + 0.0779028i
\(575\) 301.902 0.0218960
\(576\) 0 0
\(577\) −21152.6 −1.52616 −0.763080 0.646305i \(-0.776314\pi\)
−0.763080 + 0.646305i \(0.776314\pi\)
\(578\) −363.620 629.808i −0.0261671 0.0453228i
\(579\) 0 0
\(580\) 2803.88 4856.46i 0.200732 0.347679i
\(581\) 6568.06 11376.2i 0.469000 0.812332i
\(582\) 0 0
\(583\) 3488.15 + 6041.65i 0.247795 + 0.429193i
\(584\) −2190.09 −0.155183
\(585\) 0 0
\(586\) −617.938 −0.0435610
\(587\) −8527.26 14769.7i −0.599587 1.03852i −0.992882 0.119103i \(-0.961998\pi\)
0.393294 0.919413i \(-0.371335\pi\)
\(588\) 0 0
\(589\) 5580.11 9665.04i 0.390364 0.676131i
\(590\) 184.402 319.393i 0.0128673 0.0222868i
\(591\) 0 0
\(592\) 6857.94 + 11878.3i 0.476114 + 0.824654i
\(593\) −24693.4 −1.71001 −0.855006 0.518619i \(-0.826446\pi\)
−0.855006 + 0.518619i \(0.826446\pi\)
\(594\) 0 0
\(595\) −613.516 −0.0422717
\(596\) 11870.3 + 20559.9i 0.815814 + 1.41303i
\(597\) 0 0
\(598\) −10.6519 + 18.4496i −0.000728409 + 0.00126164i
\(599\) 7320.59 12679.6i 0.499351 0.864901i −0.500649 0.865650i \(-0.666905\pi\)
1.00000 0.000749436i \(0.000238553\pi\)
\(600\) 0 0
\(601\) −6561.87 11365.5i −0.445365 0.771394i 0.552713 0.833372i \(-0.313593\pi\)
−0.998078 + 0.0619774i \(0.980259\pi\)
\(602\) 146.961 0.00994961
\(603\) 0 0
\(604\) 16565.3 1.11595
\(605\) 3082.78 + 5339.54i 0.207162 + 0.358815i
\(606\) 0 0
\(607\) 5292.76 9167.33i 0.353915 0.612999i −0.633016 0.774138i \(-0.718183\pi\)
0.986932 + 0.161139i \(0.0515168\pi\)
\(608\) −893.893 + 1548.27i −0.0596253 + 0.103274i
\(609\) 0 0
\(610\) 248.410 + 430.259i 0.0164883 + 0.0285585i
\(611\) −7279.11 −0.481966
\(612\) 0 0
\(613\) 17835.2 1.17513 0.587566 0.809176i \(-0.300086\pi\)
0.587566 + 0.809176i \(0.300086\pi\)
\(614\) 16.7356 + 28.9869i 0.00109999 + 0.00190524i
\(615\) 0 0
\(616\) 237.456 411.286i 0.0155315 0.0269013i
\(617\) 9389.81 16263.6i 0.612674 1.06118i −0.378114 0.925759i \(-0.623427\pi\)
0.990788 0.135423i \(-0.0432393\pi\)
\(618\) 0 0
\(619\) −1645.15 2849.48i −0.106824 0.185024i 0.807658 0.589651i \(-0.200735\pi\)
−0.914482 + 0.404627i \(0.867401\pi\)
\(620\) −7104.29 −0.460186
\(621\) 0 0
\(622\) −906.255 −0.0584204
\(623\) 5468.70 + 9472.07i 0.351684 + 0.609134i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 257.756 446.447i 0.0164569 0.0285041i
\(627\) 0 0
\(628\) 1405.48 + 2434.36i 0.0893069 + 0.154684i
\(629\) 1316.50 0.0834538
\(630\) 0 0
\(631\) 2094.43 0.132136 0.0660682 0.997815i \(-0.478955\pi\)
0.0660682 + 0.997815i \(0.478955\pi\)
\(632\) −615.101 1065.39i −0.0387142 0.0670550i
\(633\) 0 0
\(634\) 569.160 985.814i 0.0356533 0.0617534i
\(635\) −6426.73 + 11131.4i −0.401633 + 0.695649i
\(636\) 0 0
\(637\) 370.910 + 642.435i 0.0230706 + 0.0399595i
\(638\) 207.455 0.0128734
\(639\) 0 0
\(640\) 1516.70 0.0936762
\(641\) 2102.87 + 3642.27i 0.129576 + 0.224432i 0.923512 0.383569i \(-0.125305\pi\)
−0.793936 + 0.608001i \(0.791972\pi\)
\(642\) 0 0
\(643\) −3517.09 + 6091.78i −0.215709 + 0.373618i −0.953492 0.301420i \(-0.902539\pi\)
0.737783 + 0.675038i \(0.235873\pi\)
\(644\) 970.261 1680.54i 0.0593690 0.102830i
\(645\) 0 0
\(646\) 28.4669 + 49.3061i 0.00173377 + 0.00300298i
\(647\) −11051.7 −0.671543 −0.335772 0.941943i \(-0.608997\pi\)
−0.335772 + 0.941943i \(0.608997\pi\)
\(648\) 0 0
\(649\) −4892.87 −0.295935
\(650\) −22.0516 38.1946i −0.00133067 0.00230479i
\(651\) 0 0
\(652\) 11057.4 19151.9i 0.664171 1.15038i
\(653\) −1277.76 + 2213.14i −0.0765734 + 0.132629i −0.901769 0.432217i \(-0.857731\pi\)
0.825196 + 0.564846i \(0.191065\pi\)
\(654\) 0 0
\(655\) 1645.14 + 2849.47i 0.0981390 + 0.169982i
\(656\) 26133.6 1.55541
\(657\) 0 0
\(658\) −1848.87 −0.109539
\(659\) −2333.59 4041.90i −0.137942 0.238922i 0.788775 0.614681i \(-0.210715\pi\)
−0.926717 + 0.375759i \(0.877382\pi\)
\(660\) 0 0
\(661\) 2267.41 3927.28i 0.133422 0.231094i −0.791571 0.611077i \(-0.790737\pi\)
0.924994 + 0.379982i \(0.124070\pi\)
\(662\) 88.7727 153.759i 0.00521186 0.00902720i
\(663\) 0 0
\(664\) 777.077 + 1345.94i 0.0454163 + 0.0786634i
\(665\) −6310.81 −0.368004
\(666\) 0 0
\(667\) 1697.71 0.0985544
\(668\) −15299.1 26498.8i −0.886137 1.53484i
\(669\) 0 0
\(670\) 103.592 179.426i 0.00597328 0.0103460i
\(671\) 3295.62 5708.19i 0.189607 0.328409i
\(672\) 0 0
\(673\) −13710.0 23746.4i −0.785262 1.36011i −0.928842 0.370475i \(-0.879195\pi\)
0.143581 0.989639i \(-0.454138\pi\)
\(674\) −103.692 −0.00592590
\(675\) 0 0
\(676\) 16411.0 0.933719
\(677\) 13259.9 + 22966.9i 0.752764 + 1.30383i 0.946478 + 0.322767i \(0.104613\pi\)
−0.193715 + 0.981058i \(0.562054\pi\)
\(678\) 0 0
\(679\) −11414.6 + 19770.7i −0.645145 + 1.11742i
\(680\) 36.2930 62.8613i 0.00204673 0.00354503i
\(681\) 0 0
\(682\) −131.409 227.607i −0.00737818 0.0127794i
\(683\) −4297.61 −0.240767 −0.120383 0.992727i \(-0.538412\pi\)
−0.120383 + 0.992727i \(0.538412\pi\)
\(684\) 0 0
\(685\) −3133.67 −0.174790
\(686\) −421.018 729.225i −0.0234323 0.0405859i
\(687\) 0 0
\(688\) 1552.32 2688.69i 0.0860196 0.148990i
\(689\) 4170.04 7222.72i 0.230574 0.399367i
\(690\) 0 0
\(691\) 10950.6 + 18967.0i 0.602866 + 1.04419i 0.992385 + 0.123176i \(0.0393080\pi\)
−0.389519 + 0.921019i \(0.627359\pi\)
\(692\) 9058.37 0.497612
\(693\) 0 0
\(694\) 1526.17 0.0834763
\(695\) 2434.36 + 4216.44i 0.132864 + 0.230128i
\(696\) 0 0
\(697\) 1254.20 2172.34i 0.0681583 0.118054i
\(698\) 596.421 1033.03i 0.0323422 0.0560184i
\(699\) 0 0
\(700\) 2008.64 + 3479.07i 0.108457 + 0.187852i
\(701\) 11225.3 0.604814 0.302407 0.953179i \(-0.402210\pi\)
0.302407 + 0.953179i \(0.402210\pi\)
\(702\) 0 0
\(703\) 13541.9 0.726521
\(704\) −2490.64 4313.92i −0.133338 0.230948i
\(705\) 0 0
\(706\) −405.442 + 702.247i −0.0216133 + 0.0374354i
\(707\) −12077.8 + 20919.3i −0.642477 + 1.11280i
\(708\) 0 0
\(709\) −5779.38 10010.2i −0.306134 0.530240i 0.671379 0.741114i \(-0.265702\pi\)
−0.977513 + 0.210874i \(0.932369\pi\)
\(710\) 178.464 0.00943331
\(711\) 0 0
\(712\) −1294.02 −0.0681117
\(713\) −1075.39 1862.63i −0.0564848 0.0978346i
\(714\) 0 0
\(715\) −292.556 + 506.722i −0.0153021 + 0.0265039i
\(716\) −12734.8 + 22057.2i −0.664693 + 1.15128i
\(717\) 0 0
\(718\) 355.538 + 615.809i 0.0184799 + 0.0320081i
\(719\) 17315.4 0.898128 0.449064 0.893500i \(-0.351757\pi\)
0.449064 + 0.893500i \(0.351757\pi\)
\(720\) 0 0
\(721\) −25096.2 −1.29630
\(722\) −218.691 378.785i −0.0112727 0.0195248i
\(723\) 0 0
\(724\) 3951.54 6844.27i 0.202842 0.351333i
\(725\) −1757.31 + 3043.75i −0.0900206 + 0.155920i
\(726\) 0 0
\(727\) 15728.5 + 27242.5i 0.802390 + 1.38978i 0.918039 + 0.396490i \(0.129772\pi\)
−0.115649 + 0.993290i \(0.536895\pi\)
\(728\) −567.752 −0.0289042
\(729\) 0 0
\(730\) 685.357 0.0347482
\(731\) −148.997 258.071i −0.00753880 0.0130576i
\(732\) 0 0
\(733\) −8046.18 + 13936.4i −0.405447 + 0.702254i −0.994373 0.105932i \(-0.966217\pi\)
0.588927 + 0.808186i \(0.299551\pi\)
\(734\) 948.698 1643.19i 0.0477072 0.0826313i
\(735\) 0 0
\(736\) 172.270 + 298.380i 0.00862764 + 0.0149435i
\(737\) −2748.67 −0.137379
\(738\) 0 0
\(739\) 13798.5 0.686857 0.343429 0.939179i \(-0.388412\pi\)
0.343429 + 0.939179i \(0.388412\pi\)
\(740\) −4310.22 7465.51i −0.214117 0.370862i
\(741\) 0 0
\(742\) 1059.18 1834.55i 0.0524038 0.0907661i
\(743\) −9684.40 + 16773.9i −0.478178 + 0.828228i −0.999687 0.0250174i \(-0.992036\pi\)
0.521509 + 0.853246i \(0.325369\pi\)
\(744\) 0 0
\(745\) −7439.61 12885.8i −0.365861 0.633689i
\(746\) 1388.01 0.0681215
\(747\) 0 0
\(748\) −480.824 −0.0235035
\(749\) −11674.0 20219.9i −0.569503 0.986408i
\(750\) 0 0
\(751\) −1175.45 + 2035.94i −0.0571141 + 0.0989246i −0.893169 0.449722i \(-0.851523\pi\)
0.836055 + 0.548646i \(0.184857\pi\)
\(752\) −19529.3 + 33825.7i −0.947021 + 1.64029i
\(753\) 0 0
\(754\) −124.005 214.783i −0.00598939 0.0103739i
\(755\) −10382.2 −0.500458
\(756\) 0 0
\(757\) −32608.1 −1.56560 −0.782801 0.622272i \(-0.786210\pi\)
−0.782801 + 0.622272i \(0.786210\pi\)
\(758\) −866.842 1501.41i −0.0415371 0.0719444i
\(759\) 0 0
\(760\) 373.321 646.611i 0.0178181 0.0308619i
\(761\) 16488.6 28559.2i 0.785431 1.36041i −0.143310 0.989678i \(-0.545775\pi\)
0.928741 0.370728i \(-0.120892\pi\)
\(762\) 0 0
\(763\) 1194.63 + 2069.15i 0.0566820 + 0.0981760i
\(764\) 26196.7 1.24053
\(765\) 0 0
\(766\) −1736.54 −0.0819110
\(767\) 2924.68 + 5065.70i 0.137685 + 0.238477i
\(768\) 0 0
\(769\) −13393.9 + 23198.9i −0.628082 + 1.08787i 0.359854 + 0.933009i \(0.382827\pi\)
−0.987936 + 0.154862i \(0.950507\pi\)
\(770\) −74.3083 + 128.706i −0.00347777 + 0.00602368i
\(771\) 0 0
\(772\) −9445.70 16360.4i −0.440360 0.762726i
\(773\) −1474.56 −0.0686108 −0.0343054 0.999411i \(-0.510922\pi\)
−0.0343054 + 0.999411i \(0.510922\pi\)
\(774\) 0 0
\(775\) 4452.56 0.206375
\(776\) −1350.48 2339.10i −0.0624736 0.108207i
\(777\) 0 0
\(778\) −520.483 + 901.502i −0.0239848 + 0.0415430i
\(779\) 12901.1 22345.4i 0.593364 1.02774i
\(780\) 0 0
\(781\) −1183.83 2050.45i −0.0542391 0.0939450i
\(782\) 10.9722 0.000501745
\(783\) 0 0
\(784\) 3980.49 0.181327
\(785\) −880.874 1525.72i −0.0400506 0.0693697i
\(786\) 0 0
\(787\) −8632.17