Properties

Label 98.4.c.h.79.1
Level $98$
Weight $4$
Character 98.79
Analytic conductor $5.782$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.78218718056\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.4.c.h.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-3.53553 - 6.12372i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-9.89949 + 17.1464i) q^{5} -14.1421 q^{6} -8.00000 q^{8} +(-11.5000 + 19.9186i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-3.53553 - 6.12372i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-9.89949 + 17.1464i) q^{5} -14.1421 q^{6} -8.00000 q^{8} +(-11.5000 + 19.9186i) q^{9} +(19.7990 + 34.2929i) q^{10} +(7.00000 + 12.1244i) q^{11} +(-14.1421 + 24.4949i) q^{12} -50.9117 q^{13} +140.000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(0.707107 + 1.22474i) q^{17} +(23.0000 + 39.8372i) q^{18} +(-0.707107 + 1.22474i) q^{19} +79.1960 q^{20} +28.0000 q^{22} +(-70.0000 + 121.244i) q^{23} +(28.2843 + 48.9898i) q^{24} +(-133.500 - 231.229i) q^{25} +(-50.9117 + 88.1816i) q^{26} -28.2843 q^{27} -286.000 q^{29} +(140.000 - 242.487i) q^{30} +(-46.6690 - 80.8332i) q^{31} +(16.0000 + 27.7128i) q^{32} +(49.4975 - 85.7321i) q^{33} +2.82843 q^{34} +92.0000 q^{36} +(19.0000 - 32.9090i) q^{37} +(1.41421 + 2.44949i) q^{38} +(180.000 + 311.769i) q^{39} +(79.1960 - 137.171i) q^{40} +125.865 q^{41} -34.0000 q^{43} +(28.0000 - 48.4974i) q^{44} +(-227.688 - 394.368i) q^{45} +(140.000 + 242.487i) q^{46} +(261.630 - 453.156i) q^{47} +113.137 q^{48} -534.000 q^{50} +(5.00000 - 8.66025i) q^{51} +(101.823 + 176.363i) q^{52} +(37.0000 + 64.0859i) q^{53} +(-28.2843 + 48.9898i) q^{54} -277.186 q^{55} +10.0000 q^{57} +(-286.000 + 495.367i) q^{58} +(217.082 + 375.997i) q^{59} +(-280.000 - 484.974i) q^{60} +(7.07107 - 12.2474i) q^{61} -186.676 q^{62} +64.0000 q^{64} +(504.000 - 872.954i) q^{65} +(-98.9949 - 171.464i) q^{66} +(-342.000 - 592.361i) q^{67} +(2.82843 - 4.89898i) q^{68} +989.949 q^{69} +588.000 q^{71} +(92.0000 - 159.349i) q^{72} +(-135.057 - 233.926i) q^{73} +(-38.0000 - 65.8179i) q^{74} +(-943.988 + 1635.03i) q^{75} +5.65685 q^{76} +720.000 q^{78} +(-610.000 + 1056.55i) q^{79} +(-158.392 - 274.343i) q^{80} +(410.500 + 711.007i) q^{81} +(125.865 - 218.005i) q^{82} -422.850 q^{83} -28.0000 q^{85} +(-34.0000 + 58.8897i) q^{86} +(1011.16 + 1751.39i) q^{87} +(-56.0000 - 96.9948i) q^{88} +(309.006 - 535.214i) q^{89} -910.754 q^{90} +560.000 q^{92} +(-330.000 + 571.577i) q^{93} +(-523.259 - 906.311i) q^{94} +(-14.0000 - 24.2487i) q^{95} +(113.137 - 195.959i) q^{96} -1483.51 q^{97} -322.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} - 46q^{9} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} - 46q^{9} + 28q^{11} + 560q^{15} - 32q^{16} + 92q^{18} + 112q^{22} - 280q^{23} - 534q^{25} - 1144q^{29} + 560q^{30} + 64q^{32} + 368q^{36} + 76q^{37} + 720q^{39} - 136q^{43} + 112q^{44} + 560q^{46} - 2136q^{50} + 20q^{51} + 148q^{53} + 40q^{57} - 1144q^{58} - 1120q^{60} + 256q^{64} + 2016q^{65} - 1368q^{67} + 2352q^{71} + 368q^{72} - 152q^{74} + 2880q^{78} - 2440q^{79} + 1642q^{81} - 112q^{85} - 136q^{86} - 224q^{88} + 2240q^{92} - 1320q^{93} - 56q^{95} - 1288q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) −3.53553 6.12372i −0.680414 1.17851i −0.974855 0.222842i \(-0.928467\pi\)
0.294441 0.955670i \(-0.404867\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −9.89949 + 17.1464i −0.885438 + 1.53362i −0.0402266 + 0.999191i \(0.512808\pi\)
−0.845211 + 0.534433i \(0.820525\pi\)
\(6\) −14.1421 −0.962250
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −11.5000 + 19.9186i −0.425926 + 0.737725i
\(10\) 19.7990 + 34.2929i 0.626099 + 1.08444i
\(11\) 7.00000 + 12.1244i 0.191871 + 0.332330i 0.945870 0.324545i \(-0.105211\pi\)
−0.753999 + 0.656875i \(0.771878\pi\)
\(12\) −14.1421 + 24.4949i −0.340207 + 0.589256i
\(13\) −50.9117 −1.08618 −0.543091 0.839674i \(-0.682746\pi\)
−0.543091 + 0.839674i \(0.682746\pi\)
\(14\) 0 0
\(15\) 140.000 2.40986
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 0.707107 + 1.22474i 0.0100882 + 0.0174732i 0.871025 0.491238i \(-0.163455\pi\)
−0.860937 + 0.508711i \(0.830122\pi\)
\(18\) 23.0000 + 39.8372i 0.301175 + 0.521651i
\(19\) −0.707107 + 1.22474i −0.00853797 + 0.0147882i −0.870263 0.492588i \(-0.836051\pi\)
0.861725 + 0.507376i \(0.169384\pi\)
\(20\) 79.1960 0.885438
\(21\) 0 0
\(22\) 28.0000 0.271346
\(23\) −70.0000 + 121.244i −0.634609 + 1.09918i 0.351989 + 0.936004i \(0.385506\pi\)
−0.986598 + 0.163171i \(0.947828\pi\)
\(24\) 28.2843 + 48.9898i 0.240563 + 0.416667i
\(25\) −133.500 231.229i −1.06800 1.84983i
\(26\) −50.9117 + 88.1816i −0.384023 + 0.665148i
\(27\) −28.2843 −0.201604
\(28\) 0 0
\(29\) −286.000 −1.83134 −0.915670 0.401931i \(-0.868339\pi\)
−0.915670 + 0.401931i \(0.868339\pi\)
\(30\) 140.000 242.487i 0.852013 1.47573i
\(31\) −46.6690 80.8332i −0.270387 0.468325i 0.698574 0.715538i \(-0.253818\pi\)
−0.968961 + 0.247213i \(0.920485\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 49.4975 85.7321i 0.261103 0.452244i
\(34\) 2.82843 0.0142668
\(35\) 0 0
\(36\) 92.0000 0.425926
\(37\) 19.0000 32.9090i 0.0844211 0.146222i −0.820723 0.571326i \(-0.806429\pi\)
0.905144 + 0.425104i \(0.139763\pi\)
\(38\) 1.41421 + 2.44949i 0.00603726 + 0.0104568i
\(39\) 180.000 + 311.769i 0.739053 + 1.28008i
\(40\) 79.1960 137.171i 0.313050 0.542218i
\(41\) 125.865 0.479434 0.239717 0.970843i \(-0.422945\pi\)
0.239717 + 0.970843i \(0.422945\pi\)
\(42\) 0 0
\(43\) −34.0000 −0.120580 −0.0602901 0.998181i \(-0.519203\pi\)
−0.0602901 + 0.998181i \(0.519203\pi\)
\(44\) 28.0000 48.4974i 0.0959354 0.166165i
\(45\) −227.688 394.368i −0.754262 1.30642i
\(46\) 140.000 + 242.487i 0.448736 + 0.777234i
\(47\) 261.630 453.156i 0.811970 1.40637i −0.0995134 0.995036i \(-0.531729\pi\)
0.911483 0.411337i \(-0.134938\pi\)
\(48\) 113.137 0.340207
\(49\) 0 0
\(50\) −534.000 −1.51038
\(51\) 5.00000 8.66025i 0.0137282 0.0237780i
\(52\) 101.823 + 176.363i 0.271545 + 0.470330i
\(53\) 37.0000 + 64.0859i 0.0958932 + 0.166092i 0.909981 0.414650i \(-0.136096\pi\)
−0.814088 + 0.580742i \(0.802763\pi\)
\(54\) −28.2843 + 48.9898i −0.0712778 + 0.123457i
\(55\) −277.186 −0.679559
\(56\) 0 0
\(57\) 10.0000 0.0232374
\(58\) −286.000 + 495.367i −0.647477 + 1.12146i
\(59\) 217.082 + 375.997i 0.479011 + 0.829671i 0.999710 0.0240689i \(-0.00766211\pi\)
−0.520699 + 0.853740i \(0.674329\pi\)
\(60\) −280.000 484.974i −0.602464 1.04350i
\(61\) 7.07107 12.2474i 0.0148419 0.0257070i −0.858509 0.512798i \(-0.828609\pi\)
0.873351 + 0.487091i \(0.161942\pi\)
\(62\) −186.676 −0.382385
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 504.000 872.954i 0.961746 1.66579i
\(66\) −98.9949 171.464i −0.184628 0.319785i
\(67\) −342.000 592.361i −0.623611 1.08013i −0.988808 0.149196i \(-0.952332\pi\)
0.365196 0.930930i \(-0.381002\pi\)
\(68\) 2.82843 4.89898i 0.00504408 0.00873660i
\(69\) 989.949 1.72719
\(70\) 0 0
\(71\) 588.000 0.982856 0.491428 0.870918i \(-0.336475\pi\)
0.491428 + 0.870918i \(0.336475\pi\)
\(72\) 92.0000 159.349i 0.150588 0.260825i
\(73\) −135.057 233.926i −0.216538 0.375055i 0.737209 0.675664i \(-0.236143\pi\)
−0.953747 + 0.300610i \(0.902810\pi\)
\(74\) −38.0000 65.8179i −0.0596947 0.103394i
\(75\) −943.988 + 1635.03i −1.45336 + 2.51730i
\(76\) 5.65685 0.00853797
\(77\) 0 0
\(78\) 720.000 1.04518
\(79\) −610.000 + 1056.55i −0.868739 + 1.50470i −0.00545246 + 0.999985i \(0.501736\pi\)
−0.863286 + 0.504715i \(0.831598\pi\)
\(80\) −158.392 274.343i −0.221359 0.383406i
\(81\) 410.500 + 711.007i 0.563100 + 0.975318i
\(82\) 125.865 218.005i 0.169506 0.293592i
\(83\) −422.850 −0.559202 −0.279601 0.960116i \(-0.590202\pi\)
−0.279601 + 0.960116i \(0.590202\pi\)
\(84\) 0 0
\(85\) −28.0000 −0.0357297
\(86\) −34.0000 + 58.8897i −0.0426316 + 0.0738400i
\(87\) 1011.16 + 1751.39i 1.24607 + 2.15826i
\(88\) −56.0000 96.9948i −0.0678366 0.117496i
\(89\) 309.006 535.214i 0.368028 0.637444i −0.621229 0.783629i \(-0.713366\pi\)
0.989257 + 0.146185i \(0.0466996\pi\)
\(90\) −910.754 −1.06669
\(91\) 0 0
\(92\) 560.000 0.634609
\(93\) −330.000 + 571.577i −0.367951 + 0.637309i
\(94\) −523.259 906.311i −0.574149 0.994456i
\(95\) −14.0000 24.2487i −0.0151197 0.0261881i
\(96\) 113.137 195.959i 0.120281 0.208333i
\(97\) −1483.51 −1.55286 −0.776431 0.630202i \(-0.782972\pi\)
−0.776431 + 0.630202i \(0.782972\pi\)
\(98\) 0 0
\(99\) −322.000 −0.326891
\(100\) −534.000 + 924.915i −0.534000 + 0.924915i
\(101\) 564.271 + 977.346i 0.555912 + 0.962867i 0.997832 + 0.0658130i \(0.0209641\pi\)
−0.441920 + 0.897054i \(0.645703\pi\)
\(102\) −10.0000 17.3205i −0.00970733 0.0168136i
\(103\) −434.164 + 751.993i −0.415334 + 0.719380i −0.995463 0.0951446i \(-0.969669\pi\)
0.580129 + 0.814524i \(0.303002\pi\)
\(104\) 407.294 0.384023
\(105\) 0 0
\(106\) 148.000 0.135613
\(107\) 842.000 1458.39i 0.760740 1.31764i −0.181729 0.983349i \(-0.558169\pi\)
0.942469 0.334292i \(-0.108497\pi\)
\(108\) 56.5685 + 97.9796i 0.0504010 + 0.0872971i
\(109\) 409.000 + 708.409i 0.359405 + 0.622507i 0.987861 0.155337i \(-0.0496465\pi\)
−0.628457 + 0.777844i \(0.716313\pi\)
\(110\) −277.186 + 480.100i −0.240260 + 0.416143i
\(111\) −268.701 −0.229765
\(112\) 0 0
\(113\) −540.000 −0.449548 −0.224774 0.974411i \(-0.572164\pi\)
−0.224774 + 0.974411i \(0.572164\pi\)
\(114\) 10.0000 17.3205i 0.00821567 0.0142299i
\(115\) −1385.93 2400.50i −1.12381 1.94650i
\(116\) 572.000 + 990.733i 0.457835 + 0.792994i
\(117\) 585.484 1014.09i 0.462633 0.801304i
\(118\) 868.327 0.677424
\(119\) 0 0
\(120\) −1120.00 −0.852013
\(121\) 567.500 982.939i 0.426371 0.738496i
\(122\) −14.1421 24.4949i −0.0104948 0.0181776i
\(123\) −445.000 770.763i −0.326214 0.565019i
\(124\) −186.676 + 323.333i −0.135194 + 0.234162i
\(125\) 2811.46 2.01171
\(126\) 0 0
\(127\) 1720.00 1.20177 0.600887 0.799334i \(-0.294814\pi\)
0.600887 + 0.799334i \(0.294814\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 120.208 + 208.207i 0.0820445 + 0.142105i
\(130\) −1008.00 1745.91i −0.680057 1.17789i
\(131\) −867.620 + 1502.76i −0.578659 + 1.00227i 0.416975 + 0.908918i \(0.363090\pi\)
−0.995634 + 0.0933484i \(0.970243\pi\)
\(132\) −395.980 −0.261103
\(133\) 0 0
\(134\) −1368.00 −0.881919
\(135\) 280.000 484.974i 0.178508 0.309185i
\(136\) −5.65685 9.79796i −0.00356670 0.00617771i
\(137\) −414.000 717.069i −0.258178 0.447178i 0.707576 0.706638i \(-0.249789\pi\)
−0.965754 + 0.259460i \(0.916455\pi\)
\(138\) 989.949 1714.64i 0.610653 1.05768i
\(139\) 425.678 0.259752 0.129876 0.991530i \(-0.458542\pi\)
0.129876 + 0.991530i \(0.458542\pi\)
\(140\) 0 0
\(141\) −3700.00 −2.20990
\(142\) 588.000 1018.45i 0.347492 0.601874i
\(143\) −356.382 617.271i −0.208407 0.360971i
\(144\) −184.000 318.697i −0.106481 0.184431i
\(145\) 2831.26 4903.88i 1.62154 2.80859i
\(146\) −540.230 −0.306231
\(147\) 0 0
\(148\) −152.000 −0.0844211
\(149\) −1025.00 + 1775.35i −0.563566 + 0.976124i 0.433616 + 0.901098i \(0.357237\pi\)
−0.997182 + 0.0750264i \(0.976096\pi\)
\(150\) 1887.98 + 3270.07i 1.02768 + 1.78000i
\(151\) 236.000 + 408.764i 0.127188 + 0.220296i 0.922586 0.385791i \(-0.126071\pi\)
−0.795398 + 0.606087i \(0.792738\pi\)
\(152\) 5.65685 9.79796i 0.00301863 0.00522842i
\(153\) −32.5269 −0.0171872
\(154\) 0 0
\(155\) 1848.00 0.957645
\(156\) 720.000 1247.08i 0.369527 0.640039i
\(157\) −1105.92 1915.50i −0.562176 0.973717i −0.997306 0.0733498i \(-0.976631\pi\)
0.435130 0.900367i \(-0.356702\pi\)
\(158\) 1220.00 + 2113.10i 0.614291 + 1.06398i
\(159\) 261.630 453.156i 0.130494 0.226022i
\(160\) −633.568 −0.313050
\(161\) 0 0
\(162\) 1642.00 0.796344
\(163\) −1643.00 + 2845.76i −0.789507 + 1.36747i 0.136762 + 0.990604i \(0.456331\pi\)
−0.926269 + 0.376863i \(0.877003\pi\)
\(164\) −251.730 436.009i −0.119859 0.207601i
\(165\) 980.000 + 1697.41i 0.462381 + 0.800868i
\(166\) −422.850 + 732.397i −0.197708 + 0.342440i
\(167\) 1490.58 0.690686 0.345343 0.938476i \(-0.387763\pi\)
0.345343 + 0.938476i \(0.387763\pi\)
\(168\) 0 0
\(169\) 395.000 0.179791
\(170\) −28.0000 + 48.4974i −0.0126324 + 0.0218799i
\(171\) −16.2635 28.1691i −0.00727309 0.0125974i
\(172\) 68.0000 + 117.779i 0.0301451 + 0.0522128i
\(173\) −1035.20 + 1793.03i −0.454943 + 0.787984i −0.998685 0.0512682i \(-0.983674\pi\)
0.543742 + 0.839252i \(0.317007\pi\)
\(174\) 4044.65 1.76221
\(175\) 0 0
\(176\) −224.000 −0.0959354
\(177\) 1535.00 2658.70i 0.651851 1.12904i
\(178\) −618.011 1070.43i −0.260235 0.450741i
\(179\) −270.000 467.654i −0.112742 0.195274i 0.804133 0.594449i \(-0.202630\pi\)
−0.916875 + 0.399175i \(0.869297\pi\)
\(180\) −910.754 + 1577.47i −0.377131 + 0.653210i
\(181\) −3784.44 −1.55412 −0.777058 0.629429i \(-0.783289\pi\)
−0.777058 + 0.629429i \(0.783289\pi\)
\(182\) 0 0
\(183\) −100.000 −0.0403946
\(184\) 560.000 969.948i 0.224368 0.388617i
\(185\) 376.181 + 651.564i 0.149499 + 0.258940i
\(186\) 660.000 + 1143.15i 0.260180 + 0.450646i
\(187\) −9.89949 + 17.1464i −0.00387124 + 0.00670519i
\(188\) −2093.04 −0.811970
\(189\) 0 0
\(190\) −56.0000 −0.0213825
\(191\) −514.000 + 890.274i −0.194721 + 0.337267i −0.946809 0.321796i \(-0.895714\pi\)
0.752088 + 0.659063i \(0.229047\pi\)
\(192\) −226.274 391.918i −0.0850517 0.147314i
\(193\) −2296.00 3976.79i −0.856320 1.48319i −0.875415 0.483372i \(-0.839412\pi\)
0.0190956 0.999818i \(-0.493921\pi\)
\(194\) −1483.51 + 2569.51i −0.549020 + 0.950930i
\(195\) −7127.64 −2.61754
\(196\) 0 0
\(197\) 794.000 0.287158 0.143579 0.989639i \(-0.454139\pi\)
0.143579 + 0.989639i \(0.454139\pi\)
\(198\) −322.000 + 557.720i −0.115573 + 0.200179i
\(199\) 1243.09 + 2153.10i 0.442817 + 0.766981i 0.997897 0.0648153i \(-0.0206458\pi\)
−0.555080 + 0.831797i \(0.687312\pi\)
\(200\) 1068.00 + 1849.83i 0.377595 + 0.654014i
\(201\) −2418.31 + 4188.63i −0.848627 + 1.46987i
\(202\) 2257.08 0.786178
\(203\) 0 0
\(204\) −40.0000 −0.0137282
\(205\) −1246.00 + 2158.14i −0.424509 + 0.735272i
\(206\) 868.327 + 1503.99i 0.293686 + 0.508678i
\(207\) −1610.00 2788.60i −0.540593 0.936334i
\(208\) 407.294 705.453i 0.135773 0.235165i
\(209\) −19.7990 −0.00655275
\(210\) 0 0
\(211\) −2748.00 −0.896588 −0.448294 0.893886i \(-0.647968\pi\)
−0.448294 + 0.893886i \(0.647968\pi\)
\(212\) 148.000 256.344i 0.0479466 0.0830460i
\(213\) −2078.89 3600.75i −0.668749 1.15831i
\(214\) −1684.00 2916.77i −0.537925 0.931713i
\(215\) 336.583 582.979i 0.106766 0.184925i
\(216\) 226.274 0.0712778
\(217\) 0 0
\(218\) 1636.00 0.508275
\(219\) −955.000 + 1654.11i −0.294671 + 0.510385i
\(220\) 554.372 + 960.200i 0.169890 + 0.294258i
\(221\) −36.0000 62.3538i −0.0109576 0.0189791i
\(222\) −268.701 + 465.403i −0.0812342 + 0.140702i
\(223\) 3428.05 1.02941 0.514707 0.857366i \(-0.327901\pi\)
0.514707 + 0.857366i \(0.327901\pi\)
\(224\) 0 0
\(225\) 6141.00 1.81956
\(226\) −540.000 + 935.307i −0.158939 + 0.275291i
\(227\) 2645.29 + 4581.77i 0.773453 + 1.33966i 0.935660 + 0.352903i \(0.114805\pi\)
−0.162207 + 0.986757i \(0.551861\pi\)
\(228\) −20.0000 34.6410i −0.00580935 0.0100621i
\(229\) −1374.62 + 2380.90i −0.396669 + 0.687051i −0.993313 0.115456i \(-0.963167\pi\)
0.596644 + 0.802506i \(0.296501\pi\)
\(230\) −5543.72 −1.58931
\(231\) 0 0
\(232\) 2288.00 0.647477
\(233\) −36.0000 + 62.3538i −0.0101221 + 0.0175319i −0.871042 0.491208i \(-0.836555\pi\)
0.860920 + 0.508740i \(0.169889\pi\)
\(234\) −1170.97 2028.18i −0.327131 0.566607i
\(235\) 5180.00 + 8972.02i 1.43790 + 2.49051i
\(236\) 868.327 1503.99i 0.239505 0.414836i
\(237\) 8626.70 2.36441
\(238\) 0 0
\(239\) 4308.00 1.16595 0.582974 0.812491i \(-0.301889\pi\)
0.582974 + 0.812491i \(0.301889\pi\)
\(240\) −1120.00 + 1939.90i −0.301232 + 0.521749i
\(241\) −770.039 1333.75i −0.205820 0.356490i 0.744574 0.667540i \(-0.232653\pi\)
−0.950394 + 0.311050i \(0.899319\pi\)
\(242\) −1135.00 1965.88i −0.301490 0.522196i
\(243\) 2520.84 4366.22i 0.665480 1.15265i
\(244\) −56.5685 −0.0148419
\(245\) 0 0
\(246\) −1780.00 −0.461336
\(247\) 36.0000 62.3538i 0.00927379 0.0160627i
\(248\) 373.352 + 646.665i 0.0955964 + 0.165578i
\(249\) 1495.00 + 2589.42i 0.380489 + 0.659026i
\(250\) 2811.46 4869.59i 0.711249 1.23192i
\(251\) −931.967 −0.234363 −0.117182 0.993110i \(-0.537386\pi\)
−0.117182 + 0.993110i \(0.537386\pi\)
\(252\) 0 0
\(253\) −1960.00 −0.487052
\(254\) 1720.00 2979.13i 0.424891 0.735933i
\(255\) 98.9949 + 171.464i 0.0243110 + 0.0421079i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 468.812 812.006i 0.113789 0.197088i −0.803506 0.595296i \(-0.797035\pi\)
0.917295 + 0.398209i \(0.130368\pi\)
\(258\) 480.833 0.116028
\(259\) 0 0
\(260\) −4032.00 −0.961746
\(261\) 3289.00 5696.72i 0.780015 1.35103i
\(262\) 1735.24 + 3005.52i 0.409174 + 0.708709i
\(263\) −3570.00 6183.42i −0.837018 1.44976i −0.892377 0.451291i \(-0.850964\pi\)
0.0553595 0.998466i \(-0.482370\pi\)
\(264\) −395.980 + 685.857i −0.0923139 + 0.159892i
\(265\) −1465.13 −0.339630
\(266\) 0 0
\(267\) −4370.00 −1.00165
\(268\) −1368.00 + 2369.45i −0.311806 + 0.540063i
\(269\) 2305.17 + 3992.67i 0.522485 + 0.904971i 0.999658 + 0.0261615i \(0.00832843\pi\)
−0.477172 + 0.878810i \(0.658338\pi\)
\(270\) −560.000 969.948i −0.126224 0.218627i
\(271\) −1182.28 + 2047.77i −0.265013 + 0.459016i −0.967567 0.252614i \(-0.918710\pi\)
0.702554 + 0.711630i \(0.252043\pi\)
\(272\) −22.6274 −0.00504408
\(273\) 0 0
\(274\) −1656.00 −0.365119
\(275\) 1869.00 3237.20i 0.409836 0.709857i
\(276\) −1979.90 3429.29i −0.431797 0.747894i
\(277\) −2003.00 3469.30i −0.434472 0.752527i 0.562781 0.826606i \(-0.309731\pi\)
−0.997252 + 0.0740794i \(0.976398\pi\)
\(278\) 425.678 737.296i 0.0918363 0.159065i
\(279\) 2146.78 0.460660
\(280\) 0 0
\(281\) −5984.00 −1.27038 −0.635188 0.772358i \(-0.719077\pi\)
−0.635188 + 0.772358i \(0.719077\pi\)
\(282\) −3700.00 + 6408.59i −0.781318 + 1.35328i
\(283\) −2464.27 4268.24i −0.517617 0.896538i −0.999791 0.0204627i \(-0.993486\pi\)
0.482174 0.876075i \(-0.339847\pi\)
\(284\) −1176.00 2036.89i −0.245714 0.425589i
\(285\) −98.9949 + 171.464i −0.0205753 + 0.0356374i
\(286\) −1425.53 −0.294731
\(287\) 0 0
\(288\) −736.000 −0.150588
\(289\) 2455.50 4253.05i 0.499796 0.865673i
\(290\) −5662.51 9807.76i −1.14660 1.98597i
\(291\) 5245.00 + 9084.61i 1.05659 + 1.83007i
\(292\) −540.230 + 935.705i −0.108269 + 0.187527i
\(293\) −1971.41 −0.393076 −0.196538 0.980496i \(-0.562970\pi\)
−0.196538 + 0.980496i \(0.562970\pi\)
\(294\) 0 0
\(295\) −8596.00 −1.69654
\(296\) −152.000 + 263.272i −0.0298474 + 0.0516972i
\(297\) −197.990 342.929i −0.0386820 0.0669991i
\(298\) 2050.00 + 3550.70i 0.398501 + 0.690224i
\(299\) 3563.82 6172.71i 0.689301 1.19390i
\(300\) 7551.90 1.45336
\(301\) 0 0
\(302\) 944.000 0.179871
\(303\) 3990.00 6910.88i 0.756500 1.31030i
\(304\) −11.3137 19.5959i −0.00213449 0.00369705i
\(305\) 140.000 + 242.487i 0.0262832 + 0.0455238i
\(306\) −32.5269 + 56.3383i −0.00607660 + 0.0105250i
\(307\) 4767.31 0.886270 0.443135 0.896455i \(-0.353866\pi\)
0.443135 + 0.896455i \(0.353866\pi\)
\(308\) 0 0
\(309\) 6140.00 1.13040
\(310\) 1848.00 3200.83i 0.338579 0.586435i
\(311\) −3388.46 5868.98i −0.617819 1.07009i −0.989883 0.141887i \(-0.954683\pi\)
0.372064 0.928207i \(-0.378650\pi\)
\(312\) −1440.00 2494.15i −0.261295 0.452576i
\(313\) −3095.01 + 5360.71i −0.558914 + 0.968068i 0.438673 + 0.898647i \(0.355449\pi\)
−0.997587 + 0.0694210i \(0.977885\pi\)
\(314\) −4423.66 −0.795037
\(315\) 0 0
\(316\) 4880.00 0.868739
\(317\) −4913.00 + 8509.57i −0.870478 + 1.50771i −0.00897524 + 0.999960i \(0.502857\pi\)
−0.861503 + 0.507753i \(0.830476\pi\)
\(318\) −523.259 906.311i −0.0922733 0.159822i
\(319\) −2002.00 3467.57i −0.351381 0.608609i
\(320\) −633.568 + 1097.37i −0.110680 + 0.191703i
\(321\) −11907.7 −2.07047
\(322\) 0 0
\(323\) −2.00000 −0.000344529
\(324\) 1642.00 2844.03i 0.281550 0.487659i
\(325\) 6796.71 + 11772.2i 1.16004 + 2.00925i
\(326\) 3286.00 + 5691.52i 0.558266 + 0.966945i
\(327\) 2892.07 5009.21i 0.489088 0.847125i
\(328\) −1006.92 −0.169506
\(329\) 0 0
\(330\) 3920.00 0.653906
\(331\) 2869.00 4969.25i 0.476418 0.825181i −0.523216 0.852200i \(-0.675268\pi\)
0.999635 + 0.0270189i \(0.00860142\pi\)
\(332\) 845.700 + 1464.79i 0.139801 + 0.242142i
\(333\) 437.000 + 756.906i 0.0719143 + 0.124559i
\(334\) 1490.58 2581.76i 0.244195 0.422957i
\(335\) 13542.5 2.20868
\(336\) 0 0
\(337\) −2254.00 −0.364342 −0.182171 0.983267i \(-0.558312\pi\)
−0.182171 + 0.983267i \(0.558312\pi\)
\(338\) 395.000 684.160i 0.0635656 0.110099i
\(339\) 1909.19 + 3306.81i 0.305879 + 0.529797i
\(340\) 56.0000 + 96.9948i 0.00893243 + 0.0154714i
\(341\) 653.367 1131.66i 0.103759 0.179716i
\(342\) −65.0538 −0.0102857
\(343\) 0 0
\(344\) 272.000 0.0426316
\(345\) −9800.00 + 16974.1i −1.52932 + 2.64885i
\(346\) 2070.41 + 3586.05i 0.321693 + 0.557189i
\(347\) 993.000 + 1719.93i 0.153623 + 0.266082i 0.932557 0.361024i \(-0.117573\pi\)
−0.778934 + 0.627106i \(0.784239\pi\)
\(348\) 4044.65 7005.54i 0.623035 1.07913i
\(349\) −6771.25 −1.03856 −0.519279 0.854605i \(-0.673800\pi\)
−0.519279 + 0.854605i \(0.673800\pi\)
\(350\) 0 0
\(351\) 1440.00 0.218979
\(352\) −224.000 + 387.979i −0.0339183 + 0.0587482i
\(353\) 3496.64 + 6056.36i 0.527217 + 0.913166i 0.999497 + 0.0317177i \(0.0100978\pi\)
−0.472280 + 0.881449i \(0.656569\pi\)
\(354\) −3070.00 5317.40i −0.460928 0.798351i
\(355\) −5820.90 + 10082.1i −0.870258 + 1.50733i
\(356\) −2472.05 −0.368028
\(357\) 0 0
\(358\) −1080.00 −0.159441
\(359\) −2972.00 + 5147.66i −0.436925 + 0.756777i −0.997451 0.0713606i \(-0.977266\pi\)
0.560525 + 0.828137i \(0.310599\pi\)
\(360\) 1821.51 + 3154.94i 0.266672 + 0.461889i
\(361\) 3428.50 + 5938.34i 0.499854 + 0.865773i
\(362\) −3784.44 + 6554.83i −0.549463 + 0.951697i
\(363\) −8025.66 −1.16044
\(364\) 0 0
\(365\) 5348.00 0.766924
\(366\) −100.000 + 173.205i −0.0142816 + 0.0247365i
\(367\) −421.436 729.948i −0.0599421 0.103823i 0.834497 0.551012i \(-0.185758\pi\)
−0.894439 + 0.447190i \(0.852425\pi\)
\(368\) −1120.00 1939.90i −0.158652 0.274794i
\(369\) −1447.45 + 2507.05i −0.204204 + 0.353691i
\(370\) 1504.72 0.211424
\(371\) 0 0
\(372\) 2640.00 0.367951
\(373\) 2863.00 4958.86i 0.397428 0.688365i −0.595980 0.802999i \(-0.703236\pi\)
0.993408 + 0.114634i \(0.0365696\pi\)
\(374\) 19.7990 + 34.2929i 0.00273738 + 0.00474129i
\(375\) −9940.00 17216.6i −1.36880 2.37083i
\(376\) −2093.04 + 3625.24i −0.287075 + 0.497228i
\(377\) 14560.7 1.98917
\(378\) 0 0
\(379\) 10330.0 1.40004 0.700022 0.714122i \(-0.253174\pi\)
0.700022 + 0.714122i \(0.253174\pi\)
\(380\) −56.0000 + 96.9948i −0.00755984 + 0.0130940i
\(381\) −6081.12 10532.8i −0.817704 1.41630i
\(382\) 1028.00 + 1780.55i 0.137689 + 0.238484i
\(383\) 502.046 869.569i 0.0669800 0.116013i −0.830591 0.556884i \(-0.811997\pi\)
0.897571 + 0.440871i \(0.145330\pi\)
\(384\) −905.097 −0.120281
\(385\) 0 0
\(386\) −9184.00 −1.21102
\(387\) 391.000 677.232i 0.0513583 0.0889551i
\(388\) 2967.02 + 5139.03i 0.388216 + 0.672409i
\(389\) −2605.00 4511.99i −0.339534 0.588090i 0.644811 0.764342i \(-0.276936\pi\)
−0.984345 + 0.176252i \(0.943603\pi\)
\(390\) −7127.64 + 12345.4i −0.925441 + 1.60291i
\(391\) −197.990 −0.0256081
\(392\) 0 0
\(393\) 12270.0 1.57491
\(394\) 794.000 1375.25i 0.101526 0.175848i
\(395\) −12077.4 20918.6i −1.53843 2.66464i
\(396\) 644.000 + 1115.44i 0.0817228 + 0.141548i
\(397\) −36.7696 + 63.6867i −0.00464839 + 0.00805125i −0.868340 0.495969i \(-0.834813\pi\)
0.863692 + 0.504020i \(0.168146\pi\)
\(398\) 4972.37 0.626238
\(399\) 0 0
\(400\) 4272.00 0.534000
\(401\) 249.000 431.281i 0.0310086 0.0537085i −0.850105 0.526614i \(-0.823461\pi\)
0.881113 + 0.472905i \(0.156795\pi\)
\(402\) 4836.61 + 8377.25i 0.600070 + 1.03935i
\(403\) 2376.00 + 4115.35i 0.293690 + 0.508686i
\(404\) 2257.08 3909.39i 0.277956 0.481434i
\(405\) −16255.0 −1.99436
\(406\) 0 0
\(407\) 532.000 0.0647918
\(408\) −40.0000 + 69.2820i −0.00485366 + 0.00840679i
\(409\) 1677.96 + 2906.32i 0.202861 + 0.351365i 0.949449 0.313921i \(-0.101643\pi\)
−0.746588 + 0.665286i \(0.768309\pi\)
\(410\) 2492.00 + 4316.27i 0.300173 + 0.519916i
\(411\) −2927.42 + 5070.44i −0.351336 + 0.608532i
\(412\) 3473.31 0.415334
\(413\) 0 0
\(414\) −6440.00 −0.764514
\(415\) 4186.00 7250.36i 0.495139 0.857606i
\(416\) −814.587 1410.91i −0.0960058 0.166287i
\(417\) −1505.00 2606.74i −0.176739 0.306121i
\(418\) −19.7990 + 34.2929i −0.00231675 + 0.00401272i
\(419\) −14545.2 −1.69589 −0.847946 0.530082i \(-0.822161\pi\)
−0.847946 + 0.530082i \(0.822161\pi\)
\(420\) 0 0
\(421\) 10854.0 1.25651 0.628256 0.778007i \(-0.283769\pi\)
0.628256 + 0.778007i \(0.283769\pi\)
\(422\) −2748.00 + 4759.68i −0.316992 + 0.549046i
\(423\) 6017.48 + 10422.6i 0.691678 + 1.19802i
\(424\) −296.000 512.687i −0.0339034 0.0587224i
\(425\) 188.798 327.007i 0.0215483 0.0373227i
\(426\) −8315.58 −0.945753
\(427\) 0 0
\(428\) −6736.00 −0.760740
\(429\) −2520.00 + 4364.77i −0.283605 + 0.491219i
\(430\) −673.166 1165.96i −0.0754952 0.130762i
\(431\) 2682.00 + 4645.36i 0.299739 + 0.519163i 0.976076 0.217429i \(-0.0697672\pi\)
−0.676337 + 0.736592i \(0.736434\pi\)
\(432\) 226.274 391.918i 0.0252005 0.0436486i
\(433\) 6487.00 0.719966 0.359983 0.932959i \(-0.382783\pi\)
0.359983 + 0.932959i \(0.382783\pi\)
\(434\) 0 0
\(435\) −40040.0 −4.41327
\(436\) 1636.00 2833.64i 0.179702 0.311253i
\(437\) −98.9949 171.464i −0.0108365 0.0187694i
\(438\) 1910.00 + 3308.22i 0.208364 + 0.360897i
\(439\) 6966.42 12066.2i 0.757378 1.31182i −0.186806 0.982397i \(-0.559813\pi\)
0.944183 0.329420i \(-0.106853\pi\)
\(440\) 2217.49 0.240260
\(441\) 0 0
\(442\) −144.000 −0.0154963
\(443\) −2998.00 + 5192.69i −0.321533 + 0.556912i −0.980805 0.194993i \(-0.937532\pi\)
0.659271 + 0.751905i \(0.270865\pi\)
\(444\) 537.401 + 930.806i 0.0574413 + 0.0994912i
\(445\) 6118.00 + 10596.7i 0.651733 + 1.12883i
\(446\) 3428.05 5937.56i 0.363953 0.630385i
\(447\) 14495.7 1.53383
\(448\) 0 0
\(449\) 2622.00 0.275590 0.137795 0.990461i \(-0.455999\pi\)
0.137795 + 0.990461i \(0.455999\pi\)
\(450\) 6141.00 10636.5i 0.643310 1.11425i
\(451\) 881.055 + 1526.03i 0.0919895 + 0.159330i
\(452\) 1080.00 + 1870.61i 0.112387 + 0.194660i
\(453\) 1668.77 2890.40i 0.173081 0.299785i
\(454\) 10581.1 1.09383
\(455\) 0 0
\(456\) −80.0000 −0.00821567
\(457\) −5604.00 + 9706.41i −0.573619 + 0.993538i 0.422571 + 0.906330i \(0.361128\pi\)
−0.996190 + 0.0872080i \(0.972206\pi\)
\(458\) 2749.23 + 4761.81i 0.280487 + 0.485818i
\(459\) −20.0000 34.6410i −0.00203381 0.00352267i
\(460\) −5543.72 + 9602.00i −0.561907 + 0.973251i
\(461\) −9786.36 −0.988712 −0.494356 0.869260i \(-0.664596\pi\)
−0.494356 + 0.869260i \(0.664596\pi\)
\(462\) 0 0
\(463\) 3952.00 0.396685 0.198342 0.980133i \(-0.436444\pi\)
0.198342 + 0.980133i \(0.436444\pi\)
\(464\) 2288.00 3962.93i 0.228918 0.396497i
\(465\) −6533.67 11316.6i −0.651595 1.12860i
\(466\) 72.0000 + 124.708i 0.00715737 + 0.0123969i
\(467\) 8753.27 15161.1i 0.867352 1.50230i 0.00265876 0.999996i \(-0.499154\pi\)
0.864693 0.502301i \(-0.167513\pi\)
\(468\) −4683.88 −0.462633
\(469\) 0 0
\(470\) 20720.0 2.03349
\(471\) −7820.00 + 13544.6i −0.765025 + 1.32506i
\(472\) −1736.65 3007.97i −0.169356 0.293333i
\(473\) −238.000 412.228i −0.0231358 0.0400724i
\(474\) 8626.70 14941.9i 0.835944 1.44790i
\(475\) 377.595 0.0364742
\(476\) 0 0
\(477\) −1702.00 −0.163374
\(478\) 4308.00 7461.67i 0.412225 0.713994i
\(479\) 1144.10 + 1981.64i 0.109134 + 0.189026i 0.915420 0.402501i \(-0.131859\pi\)
−0.806286 + 0.591526i \(0.798526\pi\)
\(480\) 2240.00 + 3879.79i 0.213003 + 0.368932i
\(481\) −967.322 + 1675.45i −0.0916967 + 0.158823i
\(482\) −3080.16 −0.291073
\(483\) 0 0
\(484\) −4540.00 −0.426371
\(485\) 14686.0 25436.9i 1.37496 2.38151i
\(486\) −5041.67 8732.43i −0.470566 0.815043i
\(487\) −486.000 841.777i −0.0452213 0.0783256i 0.842529 0.538651i \(-0.181066\pi\)
−0.887750 + 0.460326i \(0.847733\pi\)
\(488\) −56.5685 + 97.9796i −0.00524741 + 0.00908879i
\(489\) 23235.5 2.14877
\(490\) 0 0
\(491\) −7404.00 −0.680525 −0.340263 0.940330i \(-0.610516\pi\)
−0.340263 + 0.940330i \(0.610516\pi\)
\(492\) −1780.00 + 3083.05i −0.163107 + 0.282509i
\(493\) −202.233 350.277i −0.0184748 0.0319994i
\(494\) −72.0000 124.708i −0.00655756 0.0113580i
\(495\) 3187.64 5521.15i 0.289442 0.501328i
\(496\) 1493.41 0.135194
\(497\) 0 0
\(498\) 5980.00 0.538093
\(499\) 6122.00 10603.6i 0.549215 0.951269i −0.449113 0.893475i \(-0.648260\pi\)
0.998329 0.0577938i \(-0.0184066\pi\)
\(500\) −5622.91 9739.17i −0.502929 0.871098i
\(501\) −5270.00 9127.91i −0.469953 0.813982i
\(502\) −931.967 + 1614.21i −0.0828600 + 0.143518i
\(503\) 2415.48 0.214117 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(504\) 0 0
\(505\) −22344.0 −1.96890
\(506\) −1960.00 + 3394.82i −0.172199 + 0.298257i
\(507\) −1396.54 2418.87i −0.122332 0.211885i
\(508\) −3440.00 5958.25i −0.300444 0.520383i
\(509\) −2853.88 + 4943.07i −0.248519 + 0.430447i −0.963115 0.269090i \(-0.913277\pi\)
0.714596 + 0.699537i \(0.246610\pi\)
\(510\) 395.980 0.0343809
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 20.0000 34.6410i 0.00172129 0.00298136i
\(514\) −937.624 1624.01i −0.0804607 0.139362i
\(515\) −8596.00 14888.7i −0.735505 1.27393i
\(516\) 480.833 832.827i 0.0410222 0.0710526i
\(517\) 7325.63 0.623173
\(518\) 0 0
\(519\) 14640.0 1.23820
\(520\) −4032.00 + 6983.63i −0.340029 + 0.588947i
\(521\) 0.707107 + 1.22474i 5.94605e−5 + 0.000102989i 0.866055 0.499949i \(-0.166648\pi\)
−0.865996 + 0.500051i \(0.833314\pi\)
\(522\) −6578.00 11393.4i −0.551554 0.955320i
\(523\) −6128.49 + 10614.9i −0.512391 + 0.887487i 0.487506 + 0.873120i \(0.337907\pi\)
−0.999897 + 0.0143672i \(0.995427\pi\)
\(524\) 6940.96 0.578659
\(525\) 0 0
\(526\) −14280.0 −1.18372
\(527\) 66.0000 114.315i 0.00545542 0.00944906i
\(528\) 791.960 + 1371.71i 0.0652758 + 0.113061i
\(529\) −3716.50 6437.17i −0.305457 0.529068i
\(530\) −1465.13 + 2537.67i −0.120077 + 0.207980i
\(531\) −9985.76 −0.816093
\(532\) 0 0
\(533\) −6408.00 −0.520753
\(534\) −4370.00 + 7569.06i −0.354136 + 0.613381i
\(535\) 16670.7 + 28874.6i 1.34718 + 2.33338i
\(536\) 2736.00 + 4738.89i 0.220480 + 0.381882i
\(537\) −1909.19 + 3306.81i −0.153422 + 0.265735i
\(538\) 9220.67 0.738906
\(539\) 0 0
\(540\) −2240.00 −0.178508
\(541\) −1025.00 + 1775.35i −0.0814569 + 0.141088i −0.903876 0.427795i \(-0.859291\pi\)
0.822419 + 0.568882i \(0.192624\pi\)
\(542\) 2364.57 + 4095.55i 0.187393 + 0.324573i
\(543\) 13380.0 + 23174.8i 1.05744 + 1.83154i
\(544\) −22.6274 + 39.1918i −0.00178335 + 0.00308885i
\(545\) −16195.6 −1.27292
\(546\) 0 0
\(547\) 14554.0 1.13763 0.568815 0.822465i \(-0.307402\pi\)
0.568815 + 0.822465i \(0.307402\pi\)
\(548\) −1656.00 + 2868.28i −0.129089 + 0.223589i
\(549\) 162.635 + 281.691i 0.0126431 + 0.0218985i
\(550\) −3738.00 6474.41i −0.289798 0.501945i
\(551\) 202.233 350.277i 0.0156359 0.0270822i
\(552\) −7919.60 −0.610653
\(553\) 0 0
\(554\) −8012.00 −0.614435
\(555\) 2660.00 4607.26i 0.203443 0.352373i
\(556\) −851.357 1474.59i −0.0649381 0.112476i
\(557\) −3477.00 6022.34i −0.264498 0.458123i 0.702934 0.711255i \(-0.251873\pi\)
−0.967432 + 0.253131i \(0.918539\pi\)
\(558\) 2146.78 3718.33i 0.162868 0.282095i
\(559\) 1731.00 0.130972
\(560\) 0 0
\(561\) 140.000 0.0105362
\(562\) −5984.00 + 10364.6i −0.449146 + 0.777943i
\(563\) −818.123 1417.03i −0.0612429 0.106076i 0.833778 0.552099i \(-0.186173\pi\)
−0.895021 + 0.446024i \(0.852840\pi\)
\(564\) 7400.00 + 12817.2i 0.552476 + 0.956916i
\(565\) 5345.73 9259.07i 0.398047 0.689437i
\(566\) −9857.07 −0.732020
\(567\) 0 0
\(568\) −4704.00 −0.347492
\(569\) 3571.00 6185.15i 0.263100 0.455703i −0.703964 0.710236i \(-0.748588\pi\)
0.967064 + 0.254533i \(0.0819216\pi\)
\(570\) 197.990 + 342.929i 0.0145489 + 0.0251995i
\(571\) 10303.0 + 17845.3i 0.755109 + 1.30789i 0.945320 + 0.326144i \(0.105749\pi\)
−0.190211 + 0.981743i \(0.560917\pi\)
\(572\) −1425.53 + 2469.09i −0.104203 + 0.180485i
\(573\) 7269.06 0.529964
\(574\) 0 0
\(575\) 37380.0 2.71105
\(576\) −736.000 + 1274.79i −0.0532407 + 0.0922157i
\(577\) −4401.74 7624.04i −0.317585 0.550074i 0.662398 0.749152i \(-0.269539\pi\)
−0.979984 + 0.199078i \(0.936205\pi\)
\(578\) −4911.00 8506.10i −0.353409 0.612123i
\(579\) −16235.2 + 28120.1i −1.16530 + 2.01836i
\(580\) −22650.0 −1.62154
\(581\) 0 0
\(582\) 20980.0 1.49424
\(583\) −518.000 + 897.202i −0.0367982 + 0.0637364i
\(584\) 1080.46 + 1871.41i 0.0765577 + 0.132602i
\(585\) 11592.0 + 20077.9i 0.819265 + 1.41901i
\(586\) −1971.41 + 3414.59i −0.138973 + 0.240709i
\(587\) −6503.97 −0.457321 −0.228661 0.973506i \(-0.573435\pi\)
−0.228661 + 0.973506i \(0.573435\pi\)
\(588\) 0 0
\(589\) 132.000 0.00923424
\(590\) −8596.00 + 14888.7i −0.599816 + 1.03891i
\(591\) −2807.21 4862.24i −0.195386 0.338419i
\(592\) 304.000 + 526.543i 0.0211053 + 0.0365554i
\(593\) −11570.4 + 20040.5i −0.801246 + 1.38780i 0.117550 + 0.993067i \(0.462496\pi\)
−0.918796 + 0.394732i \(0.870837\pi\)
\(594\) −791.960 −0.0547045
\(595\) 0 0
\(596\) 8200.00 0.563566
\(597\) 8790.00 15224.7i 0.602598 1.04373i
\(598\) −7127.64 12345.4i −0.487409 0.844218i
\(599\) 5648.00 + 9782.62i 0.385260 + 0.667291i 0.991805 0.127759i \(-0.0407783\pi\)
−0.606545 + 0.795049i \(0.707445\pi\)
\(600\) 7551.90 13080.3i 0.513842 0.890000i
\(601\) −8727.11 −0.592323 −0.296162 0.955138i \(-0.595707\pi\)
−0.296162 + 0.955138i \(0.595707\pi\)
\(602\) 0 0
\(603\) 15732.0 1.06245
\(604\) 944.000 1635.06i 0.0635941 0.110148i
\(605\) 11235.9 + 19461.2i 0.755050 + 1.30779i
\(606\) −7980.00 13821.8i −0.534926 0.926520i
\(607\) 9868.38 17092.5i 0.659877 1.14294i −0.320770 0.947157i \(-0.603942\pi\)
0.980647 0.195783i \(-0.0627249\pi\)
\(608\) −45.2548 −0.00301863
\(609\) 0 0
\(610\) 560.000 0.0371701
\(611\) −13320.0 + 23070.9i −0.881947 + 1.52758i
\(612\) 65.0538 + 112.677i 0.00429681 + 0.00744229i
\(613\) −8481.00 14689.5i −0.558800 0.967870i −0.997597 0.0692837i \(-0.977929\pi\)
0.438797 0.898586i \(-0.355405\pi\)
\(614\) 4767.31 8257.23i 0.313344 0.542727i
\(615\) 17621.1 1.15537
\(616\) 0 0
\(617\) −19034.0 −1.24194 −0.620972 0.783832i \(-0.713262\pi\)
−0.620972 + 0.783832i \(0.713262\pi\)
\(618\) 6140.00 10634.8i 0.399655 0.692223i
\(619\) −9338.76 16175.2i −0.606392 1.05030i −0.991830 0.127568i \(-0.959283\pi\)
0.385438 0.922734i \(-0.374050\pi\)
\(620\) −3696.00 6401.66i −0.239411 0.414672i
\(621\) 1979.90 3429.29i 0.127940 0.221598i
\(622\) −13553.8 −0.873728
\(623\) 0 0
\(624\) −5760.00 −0.369527
\(625\) −11144.5 + 19302.8i −0.713248 + 1.23538i
\(626\) 6190.01 + 10721.4i 0.395212 + 0.684527i
\(627\) 70.0000 + 121.244i 0.00445858 + 0.00772249i
\(628\) −4423.66 + 7662.00i −0.281088 + 0.486859i
\(629\) 53.7401 0.00340661
\(630\) 0 0
\(631\) −14716.0 −0.928423 −0.464211 0.885724i \(-0.653662\pi\)
−0.464211 + 0.885724i \(0.653662\pi\)
\(632\) 4880.00 8452.41i 0.307146 0.531992i
\(633\) 9715.65 + 16828.0i 0.610051 + 1.05664i
\(634\) 9826.00 + 17019.1i 0.615521 + 1.06611i
\(635\) −17027.1 + 29491.9i −1.06410 + 1.84307i
\(636\) −2093.04 −0.130494
\(637\) 0 0
\(638\) −8008.00 −0.496928
\(639\) −6762.00 + 11712.1i −0.418624 + 0.725078i
\(640\) 1267.14 + 2194.74i 0.0782624 + 0.135554i
\(641\) −2365.00 4096.30i −0.145728 0.252409i 0.783916 0.620867i \(-0.213219\pi\)
−0.929644 + 0.368458i \(0.879886\pi\)
\(642\) −11907.7 + 20624.7i −0.732023 + 1.26790i
\(643\) −19056.5 −1.16877 −0.584383 0.811478i \(-0.698663\pi\)
−0.584383 + 0.811478i \(0.698663\pi\)
\(644\) 0 0
\(645\) −4760.00 −0.290581
\(646\) −2.00000 + 3.46410i −0.000121810 + 0.000210980i
\(647\) 4671.15 + 8090.66i 0.283836 + 0.491618i 0.972326 0.233627i \(-0.0750596\pi\)
−0.688490 + 0.725245i \(0.741726\pi\)
\(648\) −3284.00 5688.05i −0.199086 0.344827i
\(649\) −3039.14 + 5263.95i −0.183816 + 0.318379i
\(650\) 27186.8 1.64055
\(651\) 0 0
\(652\) 13144.0 0.789507
\(653\) −1887.00 + 3268.38i −0.113084 + 0.195868i −0.917012 0.398859i \(-0.869406\pi\)
0.803928 + 0.594727i \(0.202740\pi\)
\(654\) −5784.13 10018.4i −0.345837 0.599008i
\(655\) −17178.0 29753.2i −1.02473 1.77489i
\(656\) −1006.92 + 1744.04i −0.0599293 + 0.103801i
\(657\) 6212.64 0.368917
\(658\) 0 0
\(659\) −21150.0 −1.25021 −0.625104 0.780541i \(-0.714943\pi\)
−0.625104 + 0.780541i \(0.714943\pi\)
\(660\) 3920.00 6789.64i 0.231191 0.400434i
\(661\) −5188.75 8987.18i −0.305324 0.528836i 0.672010 0.740542i \(-0.265431\pi\)
−0.977333 + 0.211706i \(0.932098\pi\)
\(662\) −5738.00 9938.51i −0.336879 0.583491i
\(663\) −254.558 + 440.908i −0.0149114 + 0.0258272i
\(664\) 3382.80 0.197708
\(665\) 0 0
\(666\) 1748.00 0.101702
\(667\) 20020.0 34675.7i 1.16219 2.01296i
\(668\) −2981.16 5163.52i −0.172672 0.299076i
\(669\) −12120.0 20992.5i −0.700428 1.21318i
\(670\) 13542.5 23456.3i 0.780885 1.35253i
\(671\) 197.990 0.0113909
\(672\) 0 0
\(673\) −1164.00 −0.0666700 −0.0333350 0.999444i \(-0.510613\pi\)
−0.0333350 + 0.999444i \(0.510613\pi\)
\(674\) −2254.00 + 3904.04i −0.128814 + 0.223113i
\(675\) 3775.95 + 6540.14i 0.215313 + 0.372933i
\(676\) −790.000 1368.32i −0.0449477 0.0778516i
\(677\) 13576.5 23515.1i 0.770732 1.33495i −0.166431 0.986053i \(-0.553224\pi\)
0.937162 0.348893i \(-0.113442\pi\)
\(678\) 7636.75 0.432578
\(679\) 0 0
\(680\) 224.000 0.0126324
\(681\) 18705.0 32398.0i 1.05254 1.82305i
\(682\) −1306.73 2263.33i −0.0733686 0.127078i
\(683\) 8298.00 + 14372.6i 0.464882 + 0.805199i 0.999196 0.0400871i \(-0.0127636\pi\)
−0.534315 + 0.845286i \(0.679430\pi\)
\(684\) −65.0538 + 112.677i −0.00363654 + 0.00629868i
\(685\) 16393.6 0.914403
\(686\) 0 0
\(687\) 19440.0 1.07960
\(688\) 272.000 471.118i 0.0150725 0.0261064i
\(689\) −1883.73 3262.72i −0.104157 0.180406i
\(690\) 19600.0 + 33948.2i 1.08139 + 1.87302i
\(691\) 5649.08 9784.49i 0.311000 0.538668i −0.667579 0.744539i \(-0.732669\pi\)
0.978579 + 0.205871i \(0.0660028\pi\)
\(692\) 8281.63 0.454943
\(693\) 0 0
\(694\) 3972.00 0.217255
\(695\) −4214.00 + 7298.86i −0.229994 + 0.398362i
\(696\) −8089.30 14011.1i −0.440552 0.763058i
\(697\) 89.0000 + 154.153i 0.00483661 + 0.00837725i
\(698\) −6771.25 + 11728.2i −0.367186 + 0.635985i
\(699\) 509.117 0.0275487
\(700\) 0 0
\(701\) −2754.00 −0.148384 −0.0741920 0.997244i \(-0.523638\pi\)
−0.0741920 + 0.997244i \(0.523638\pi\)
\(702\) 1440.00 2494.15i 0.0774207 0.134097i
\(703\) 26.8701 + 46.5403i 0.00144157 + 0.00249687i
\(704\) 448.000 + 775.959i 0.0239839 + 0.0415413i
\(705\) 36628.1 63441.8i 1.95673 3.38916i
\(706\) 13986.6 0.745597
\(707\) 0 0
\(708\) −12280.0 −0.651851
\(709\) −14717.0 + 25490.6i −0.779561 + 1.35024i 0.152634 + 0.988283i \(0.451224\pi\)
−0.932195 + 0.361956i \(0.882109\pi\)
\(710\) 11641.8 + 20164.2i 0.615365 + 1.06584i
\(711\) −14030.0 24300.7i −0.740037 1.28178i
\(712\) −2472.05 + 4281.71i −0.130118 + 0.225370i
\(713\) 13067.3 0.686361
\(714\) 0 0
\(715\) 14112.0 0.738124
\(716\) −1080.00 + 1870.61i −0.0563708 + 0.0976371i
\(717\) −15231.1 26381.0i −0.793327 1.37408i
\(718\) 5944.00 + 10295.3i 0.308953 + 0.535122i
\(719\) −8834.59 + 15302.0i −0.458240 + 0.793695i −0.998868 0.0475666i \(-0.984853\pi\)
0.540628 + 0.841262i \(0.318187\pi\)
\(720\) 7286.03 0.377131
\(721\) 0 0
\(722\) 13714.0 0.706901
\(723\) −5445.00 + 9431.02i −0.280085 + 0.485122i
\(724\) 7568.87 + 13109.7i 0.388529 + 0.672952i
\(725\) 38181.0 + 66131.4i 1.95587 + 3.38767i
\(726\) −8025.66 + 13900.9i −0.410276 + 0.710619i
\(727\) −28445.5 −1.45115 −0.725574 0.688144i \(-0.758426\pi\)
−0.725574 + 0.688144i \(0.758426\pi\)
\(728\) 0 0
\(729\) −13483.0 −0.685007
\(730\) 5348.00 9263.01i 0.271148 0.469643i
\(731\) −24.0416 41.6413i −0.00121643 0.00210692i
\(732\) 200.000 + 346.410i 0.0100987 + 0.0174914i
\(733\) 11170.9 19348.5i 0.562900 0.974971i −0.434342 0.900748i \(-0.643019\pi\)
0.997242 0.0742230i \(-0.0236477\pi\)
\(734\) −1685.74 −0.0847710
\(735\) 0 0
\(736\) −4480.00 −0.224368
\(737\) 4788.00 8293.06i 0.239306 0.414490i
\(738\) 2894.90 + 5014.11i 0.144394 + 0.250097i
\(739\) −10335.0 17900.7i −0.514451 0.891055i −0.999859 0.0167675i \(-0.994662\pi\)
0.485409 0.874287i \(-0.338671\pi\)
\(740\) 1504.72 2606.26i 0.0747496 0.129470i
\(741\) −509.117 −0.0252400
\(742\) 0 0
\(743\) −25400.0 −1.25415 −0.627076 0.778958i \(-0.715749\pi\)
−0.627076 + 0.778958i \(0.715749\pi\)
\(744\) 2640.00 4572.61i 0.130090 0.225323i
\(745\) −20294.0 35150.2i −0.998004 1.72859i
\(746\) −5726.00 9917.72i −0.281024 0.486748i
\(747\) 4862.77 8422.57i 0.238179 0.412538i
\(748\) 79.1960 0.00387124
\(749\) 0 0
\(750\) −39760.0 −1.93577
\(751\) −14590.0 + 25270.6i −0.708917 + 1.22788i 0.256342 + 0.966586i \(0.417483\pi\)
−0.965259 + 0.261294i \(0.915851\pi\)
\(752\) 4186.07 + 7250.49i 0.202992 + 0.351593i
\(753\) 3295.00 + 5707.11i 0.159464 + 0.276200i
\(754\) 14560.7 25219.9i 0.703277 1.21811i
\(755\) −9345.12 −0.450469
\(756\) 0 0
\(757\) −26206.0 −1.25822 −0.629110 0.777316i \(-0.716581\pi\)
−0.629110 + 0.777316i \(0.716581\pi\)
\(758\) 10330.0 17892.1i 0.494990 0.857348i
\(759\) 6929.65 + 12002.5i 0.331397 + 0.573996i
\(760\) 112.000 + 193.990i 0.00534561 + 0.00925888i
\(761\) 3431.59 5943.69i 0.163463 0.283125i −0.772646 0.634838i \(-0.781067\pi\)
0.936108 + 0.351712i \(0.114400\pi\)
\(762\) −24324.5 −1.15641
\(763\) 0 0
\(764\) 4112.00 0.194721
\(765\) 322.000 557.720i 0.0152182 0.0263587i
\(766\) −1004.09 1739.14i −0.0473620 0.0820334i
\(767\) −11052.0 19142.6i −0.520293 0.901174i
\(768\) −905.097 + 1567.67i −0.0425259 + 0.0736570i
\(769\) 9058.04 0.424761 0.212380 0.977187i \(-0.431878\pi\)
0.212380 + 0.977187i \(0.431878\pi\)
\(770\) 0 0
\(771\) −6630.00 −0.309693
\(772\) −9184.00 + 15907.2i −0.428160 + 0.741595i
\(773\) −66.4680 115.126i −0.00309274 0.00535679i 0.864475 0.502676i \(-0.167651\pi\)
−0.867568 + 0.497319i \(0.834318\pi\)
\(774\) −782.000 1354.46i −0.0363158 0.0629008i
\(775\) −12460.6 + 21582.5i −0.577547 + 1.00034i
\(776\) 11868.1 0.549020
\(777\) 0 0
\(778\) −10420.0 −0.480174
\(779\) −89.0000 + 154.153i −0.00409340 + 0.00708997i
\(780\) 14255.3 + 24690.9i