Properties

Label 252.4.x.a.209.21
Level $252$
Weight $4$
Character 252.209
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 209.21
Character \(\chi\) \(=\) 252.209
Dual form 252.4.x.a.41.21

$q$-expansion

\(f(q)\) \(=\) \(q+(4.66323 + 2.29222i) q^{3} +(5.16485 + 8.94579i) q^{5} +(-17.2289 - 6.79448i) q^{7} +(16.4915 + 21.3783i) q^{9} +O(q^{10})\) \(q+(4.66323 + 2.29222i) q^{3} +(5.16485 + 8.94579i) q^{5} +(-17.2289 - 6.79448i) q^{7} +(16.4915 + 21.3783i) q^{9} +(27.1307 + 15.6639i) q^{11} +(-39.0052 + 22.5196i) q^{13} +(3.57919 + 53.5552i) q^{15} +62.4900 q^{17} +132.928i q^{19} +(-64.7679 - 71.1767i) q^{21} +(-58.8009 + 33.9487i) q^{23} +(9.14862 - 15.8459i) q^{25} +(27.8997 + 137.494i) q^{27} +(-116.665 - 67.3568i) q^{29} +(-25.9914 + 15.0061i) q^{31} +(90.6116 + 135.234i) q^{33} +(-28.2028 - 189.219i) q^{35} +40.4778 q^{37} +(-233.510 + 15.6059i) q^{39} +(39.7514 + 68.8515i) q^{41} +(161.452 - 279.643i) q^{43} +(-106.070 + 257.945i) q^{45} +(-171.268 + 296.644i) q^{47} +(250.670 + 234.123i) q^{49} +(291.405 + 143.241i) q^{51} -64.9125i q^{53} +323.607i q^{55} +(-304.700 + 619.874i) q^{57} +(79.3800 + 137.490i) q^{59} +(493.640 + 285.003i) q^{61} +(-138.875 - 480.376i) q^{63} +(-402.912 - 232.621i) q^{65} +(150.833 + 261.251i) q^{67} +(-352.020 + 23.5261i) q^{69} -719.100i q^{71} -558.706i q^{73} +(78.9843 - 52.9223i) q^{75} +(-361.004 - 454.211i) q^{77} +(456.676 - 790.986i) q^{79} +(-185.064 + 705.119i) q^{81} +(-352.348 + 610.285i) q^{83} +(322.751 + 559.022i) q^{85} +(-389.641 - 581.524i) q^{87} +700.133 q^{89} +(825.026 - 122.969i) q^{91} +(-155.601 + 10.3991i) q^{93} +(-1189.15 + 686.554i) q^{95} +(-202.787 - 117.079i) q^{97} +(112.557 + 838.329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.66323 + 2.29222i 0.897439 + 0.441138i
\(4\) 0 0
\(5\) 5.16485 + 8.94579i 0.461958 + 0.800135i 0.999059 0.0433831i \(-0.0138136\pi\)
−0.537100 + 0.843518i \(0.680480\pi\)
\(6\) 0 0
\(7\) −17.2289 6.79448i −0.930273 0.366867i
\(8\) 0 0
\(9\) 16.4915 + 21.3783i 0.610794 + 0.791789i
\(10\) 0 0
\(11\) 27.1307 + 15.6639i 0.743656 + 0.429350i 0.823397 0.567466i \(-0.192076\pi\)
−0.0797412 + 0.996816i \(0.525409\pi\)
\(12\) 0 0
\(13\) −39.0052 + 22.5196i −0.832161 + 0.480448i −0.854592 0.519300i \(-0.826193\pi\)
0.0224312 + 0.999748i \(0.492859\pi\)
\(14\) 0 0
\(15\) 3.57919 + 53.5552i 0.0616095 + 0.921860i
\(16\) 0 0
\(17\) 62.4900 0.891532 0.445766 0.895150i \(-0.352931\pi\)
0.445766 + 0.895150i \(0.352931\pi\)
\(18\) 0 0
\(19\) 132.928i 1.60504i 0.596624 + 0.802521i \(0.296508\pi\)
−0.596624 + 0.802521i \(0.703492\pi\)
\(20\) 0 0
\(21\) −64.7679 71.1767i −0.673025 0.739620i
\(22\) 0 0
\(23\) −58.8009 + 33.9487i −0.533080 + 0.307774i −0.742270 0.670101i \(-0.766251\pi\)
0.209190 + 0.977875i \(0.432917\pi\)
\(24\) 0 0
\(25\) 9.14862 15.8459i 0.0731889 0.126767i
\(26\) 0 0
\(27\) 27.8997 + 137.494i 0.198863 + 0.980027i
\(28\) 0 0
\(29\) −116.665 67.3568i −0.747043 0.431305i 0.0775817 0.996986i \(-0.475280\pi\)
−0.824624 + 0.565681i \(0.808613\pi\)
\(30\) 0 0
\(31\) −25.9914 + 15.0061i −0.150587 + 0.0869413i −0.573400 0.819275i \(-0.694376\pi\)
0.422813 + 0.906217i \(0.361043\pi\)
\(32\) 0 0
\(33\) 90.6116 + 135.234i 0.477983 + 0.713370i
\(34\) 0 0
\(35\) −28.2028 189.219i −0.136204 0.913822i
\(36\) 0 0
\(37\) 40.4778 0.179852 0.0899259 0.995948i \(-0.471337\pi\)
0.0899259 + 0.995948i \(0.471337\pi\)
\(38\) 0 0
\(39\) −233.510 + 15.6059i −0.958758 + 0.0640754i
\(40\) 0 0
\(41\) 39.7514 + 68.8515i 0.151418 + 0.262263i 0.931749 0.363103i \(-0.118283\pi\)
−0.780331 + 0.625367i \(0.784949\pi\)
\(42\) 0 0
\(43\) 161.452 279.643i 0.572586 0.991749i −0.423713 0.905797i \(-0.639273\pi\)
0.996299 0.0859521i \(-0.0273932\pi\)
\(44\) 0 0
\(45\) −106.070 + 257.945i −0.351377 + 0.854492i
\(46\) 0 0
\(47\) −171.268 + 296.644i −0.531531 + 0.920638i 0.467792 + 0.883839i \(0.345050\pi\)
−0.999323 + 0.0367994i \(0.988284\pi\)
\(48\) 0 0
\(49\) 250.670 + 234.123i 0.730817 + 0.682574i
\(50\) 0 0
\(51\) 291.405 + 143.241i 0.800096 + 0.393289i
\(52\) 0 0
\(53\) 64.9125i 0.168234i −0.996456 0.0841172i \(-0.973193\pi\)
0.996456 0.0841172i \(-0.0268070\pi\)
\(54\) 0 0
\(55\) 323.607i 0.793367i
\(56\) 0 0
\(57\) −304.700 + 619.874i −0.708045 + 1.44043i
\(58\) 0 0
\(59\) 79.3800 + 137.490i 0.175159 + 0.303385i 0.940216 0.340578i \(-0.110623\pi\)
−0.765057 + 0.643962i \(0.777289\pi\)
\(60\) 0 0
\(61\) 493.640 + 285.003i 1.03613 + 0.598212i 0.918736 0.394873i \(-0.129212\pi\)
0.117397 + 0.993085i \(0.462545\pi\)
\(62\) 0 0
\(63\) −138.875 480.376i −0.277724 0.960661i
\(64\) 0 0
\(65\) −402.912 232.621i −0.768847 0.443894i
\(66\) 0 0
\(67\) 150.833 + 261.251i 0.275033 + 0.476372i 0.970144 0.242531i \(-0.0779778\pi\)
−0.695110 + 0.718903i \(0.744644\pi\)
\(68\) 0 0
\(69\) −352.020 + 23.5261i −0.614178 + 0.0410465i
\(70\) 0 0
\(71\) 719.100i 1.20199i −0.799252 0.600996i \(-0.794771\pi\)
0.799252 0.600996i \(-0.205229\pi\)
\(72\) 0 0
\(73\) 558.706i 0.895775i −0.894090 0.447888i \(-0.852176\pi\)
0.894090 0.447888i \(-0.147824\pi\)
\(74\) 0 0
\(75\) 78.9843 52.9223i 0.121604 0.0814792i
\(76\) 0 0
\(77\) −361.004 454.211i −0.534289 0.672236i
\(78\) 0 0
\(79\) 456.676 790.986i 0.650381 1.12649i −0.332650 0.943050i \(-0.607943\pi\)
0.983031 0.183442i \(-0.0587239\pi\)
\(80\) 0 0
\(81\) −185.064 + 705.119i −0.253860 + 0.967241i
\(82\) 0 0
\(83\) −352.348 + 610.285i −0.465967 + 0.807078i −0.999245 0.0388620i \(-0.987627\pi\)
0.533278 + 0.845940i \(0.320960\pi\)
\(84\) 0 0
\(85\) 322.751 + 559.022i 0.411851 + 0.713346i
\(86\) 0 0
\(87\) −389.641 581.524i −0.480160 0.716619i
\(88\) 0 0
\(89\) 700.133 0.833865 0.416932 0.908938i \(-0.363105\pi\)
0.416932 + 0.908938i \(0.363105\pi\)
\(90\) 0 0
\(91\) 825.026 122.969i 0.950398 0.141656i
\(92\) 0 0
\(93\) −155.601 + 10.3991i −0.173496 + 0.0115950i
\(94\) 0 0
\(95\) −1189.15 + 686.554i −1.28425 + 0.741463i
\(96\) 0 0
\(97\) −202.787 117.079i −0.212267 0.122552i 0.390098 0.920773i \(-0.372441\pi\)
−0.602364 + 0.798221i \(0.705775\pi\)
\(98\) 0 0
\(99\) 112.557 + 838.329i 0.114266 + 0.851063i
\(100\) 0 0
\(101\) 938.098 1624.83i 0.924200 1.60076i 0.131358 0.991335i \(-0.458066\pi\)
0.792843 0.609427i \(-0.208600\pi\)
\(102\) 0 0
\(103\) −524.507 + 302.824i −0.501759 + 0.289691i −0.729440 0.684045i \(-0.760219\pi\)
0.227681 + 0.973736i \(0.426886\pi\)
\(104\) 0 0
\(105\) 302.214 947.017i 0.280887 0.880184i
\(106\) 0 0
\(107\) 1299.63i 1.17420i −0.809513 0.587102i \(-0.800269\pi\)
0.809513 0.587102i \(-0.199731\pi\)
\(108\) 0 0
\(109\) 2079.24 1.82711 0.913554 0.406717i \(-0.133326\pi\)
0.913554 + 0.406717i \(0.133326\pi\)
\(110\) 0 0
\(111\) 188.758 + 92.7841i 0.161406 + 0.0793395i
\(112\) 0 0
\(113\) 1090.53 629.616i 0.907860 0.524153i 0.0281181 0.999605i \(-0.491049\pi\)
0.879742 + 0.475451i \(0.157715\pi\)
\(114\) 0 0
\(115\) −607.396 350.680i −0.492522 0.284358i
\(116\) 0 0
\(117\) −1124.68 462.483i −0.888693 0.365441i
\(118\) 0 0
\(119\) −1076.63 424.587i −0.829368 0.327074i
\(120\) 0 0
\(121\) −174.783 302.734i −0.131317 0.227448i
\(122\) 0 0
\(123\) 27.5473 + 412.190i 0.0201940 + 0.302162i
\(124\) 0 0
\(125\) 1480.22 1.05916
\(126\) 0 0
\(127\) −1015.62 −0.709623 −0.354811 0.934938i \(-0.615455\pi\)
−0.354811 + 0.934938i \(0.615455\pi\)
\(128\) 0 0
\(129\) 1393.89 933.957i 0.951359 0.637445i
\(130\) 0 0
\(131\) −1353.80 2344.85i −0.902915 1.56390i −0.823691 0.567039i \(-0.808089\pi\)
−0.0792242 0.996857i \(-0.525244\pi\)
\(132\) 0 0
\(133\) 903.177 2290.21i 0.588837 1.49313i
\(134\) 0 0
\(135\) −1085.89 + 959.721i −0.692288 + 0.611849i
\(136\) 0 0
\(137\) −2713.91 1566.88i −1.69245 0.977135i −0.952533 0.304435i \(-0.901532\pi\)
−0.739915 0.672700i \(-0.765134\pi\)
\(138\) 0 0
\(139\) 86.5871 49.9911i 0.0528361 0.0305049i −0.473349 0.880875i \(-0.656955\pi\)
0.526185 + 0.850370i \(0.323622\pi\)
\(140\) 0 0
\(141\) −1478.63 + 990.737i −0.883145 + 0.591738i
\(142\) 0 0
\(143\) −1410.98 −0.825121
\(144\) 0 0
\(145\) 1391.55i 0.796980i
\(146\) 0 0
\(147\) 632.272 + 1666.36i 0.354754 + 0.934960i
\(148\) 0 0
\(149\) 2280.20 1316.47i 1.25370 0.723823i 0.281856 0.959457i \(-0.409050\pi\)
0.971842 + 0.235634i \(0.0757167\pi\)
\(150\) 0 0
\(151\) −944.432 + 1635.80i −0.508985 + 0.881588i 0.490961 + 0.871182i \(0.336646\pi\)
−0.999946 + 0.0104066i \(0.996687\pi\)
\(152\) 0 0
\(153\) 1030.55 + 1335.93i 0.544543 + 0.705905i
\(154\) 0 0
\(155\) −268.483 155.009i −0.139130 0.0803266i
\(156\) 0 0
\(157\) 1110.41 641.097i 0.564462 0.325892i −0.190472 0.981693i \(-0.561002\pi\)
0.754935 + 0.655800i \(0.227669\pi\)
\(158\) 0 0
\(159\) 148.794 302.702i 0.0742146 0.150980i
\(160\) 0 0
\(161\) 1243.74 185.378i 0.608822 0.0907442i
\(162\) 0 0
\(163\) 3558.63 1.71002 0.855011 0.518610i \(-0.173550\pi\)
0.855011 + 0.518610i \(0.173550\pi\)
\(164\) 0 0
\(165\) −741.779 + 1509.06i −0.349984 + 0.711999i
\(166\) 0 0
\(167\) −471.603 816.841i −0.218526 0.378497i 0.735832 0.677164i \(-0.236791\pi\)
−0.954357 + 0.298667i \(0.903458\pi\)
\(168\) 0 0
\(169\) −84.2309 + 145.892i −0.0383390 + 0.0664052i
\(170\) 0 0
\(171\) −2841.78 + 2192.18i −1.27085 + 0.980351i
\(172\) 0 0
\(173\) −489.793 + 848.347i −0.215250 + 0.372824i −0.953350 0.301867i \(-0.902390\pi\)
0.738100 + 0.674692i \(0.235723\pi\)
\(174\) 0 0
\(175\) −265.285 + 210.847i −0.114592 + 0.0910773i
\(176\) 0 0
\(177\) 55.0095 + 823.105i 0.0233602 + 0.349539i
\(178\) 0 0
\(179\) 3739.96i 1.56166i 0.624742 + 0.780831i \(0.285204\pi\)
−0.624742 + 0.780831i \(0.714796\pi\)
\(180\) 0 0
\(181\) 1540.52i 0.632631i 0.948654 + 0.316316i \(0.102446\pi\)
−0.948654 + 0.316316i \(0.897554\pi\)
\(182\) 0 0
\(183\) 1648.67 + 2460.57i 0.665972 + 0.993936i
\(184\) 0 0
\(185\) 209.062 + 362.106i 0.0830840 + 0.143906i
\(186\) 0 0
\(187\) 1695.40 + 978.838i 0.662993 + 0.382779i
\(188\) 0 0
\(189\) 453.520 2558.43i 0.174543 0.984649i
\(190\) 0 0
\(191\) −649.672 375.088i −0.246118 0.142097i 0.371867 0.928286i \(-0.378718\pi\)
−0.617986 + 0.786189i \(0.712051\pi\)
\(192\) 0 0
\(193\) 2026.03 + 3509.19i 0.755632 + 1.30879i 0.945060 + 0.326898i \(0.106003\pi\)
−0.189428 + 0.981895i \(0.560663\pi\)
\(194\) 0 0
\(195\) −1345.65 2008.33i −0.494175 0.737536i
\(196\) 0 0
\(197\) 807.631i 0.292088i −0.989278 0.146044i \(-0.953346\pi\)
0.989278 0.146044i \(-0.0466541\pi\)
\(198\) 0 0
\(199\) 4386.10i 1.56243i 0.624265 + 0.781213i \(0.285399\pi\)
−0.624265 + 0.781213i \(0.714601\pi\)
\(200\) 0 0
\(201\) 104.526 + 1564.02i 0.0366801 + 0.548842i
\(202\) 0 0
\(203\) 1552.36 + 1953.17i 0.536722 + 0.675297i
\(204\) 0 0
\(205\) −410.621 + 711.216i −0.139897 + 0.242310i
\(206\) 0 0
\(207\) −1695.48 697.201i −0.569295 0.234100i
\(208\) 0 0
\(209\) −2082.17 + 3606.43i −0.689124 + 1.19360i
\(210\) 0 0
\(211\) −2132.63 3693.82i −0.695811 1.20518i −0.969907 0.243478i \(-0.921712\pi\)
0.274095 0.961702i \(-0.411622\pi\)
\(212\) 0 0
\(213\) 1648.34 3353.33i 0.530244 1.07871i
\(214\) 0 0
\(215\) 3335.50 1.05804
\(216\) 0 0
\(217\) 549.762 81.9413i 0.171983 0.0256338i
\(218\) 0 0
\(219\) 1280.68 2605.38i 0.395161 0.803904i
\(220\) 0 0
\(221\) −2437.43 + 1407.25i −0.741898 + 0.428335i
\(222\) 0 0
\(223\) −1771.94 1023.03i −0.532097 0.307206i 0.209773 0.977750i \(-0.432727\pi\)
−0.741870 + 0.670544i \(0.766061\pi\)
\(224\) 0 0
\(225\) 489.632 65.7394i 0.145076 0.0194784i
\(226\) 0 0
\(227\) −2797.06 + 4844.65i −0.817830 + 1.41652i 0.0894471 + 0.995992i \(0.471490\pi\)
−0.907278 + 0.420532i \(0.861843\pi\)
\(228\) 0 0
\(229\) −318.820 + 184.071i −0.0920009 + 0.0531168i −0.545295 0.838244i \(-0.683582\pi\)
0.453294 + 0.891361i \(0.350249\pi\)
\(230\) 0 0
\(231\) −642.293 2945.59i −0.182943 0.838986i
\(232\) 0 0
\(233\) 3900.42i 1.09667i −0.836258 0.548336i \(-0.815261\pi\)
0.836258 0.548336i \(-0.184739\pi\)
\(234\) 0 0
\(235\) −3538.29 −0.982180
\(236\) 0 0
\(237\) 3942.70 2641.75i 1.08062 0.724051i
\(238\) 0 0
\(239\) −2327.57 + 1343.82i −0.629949 + 0.363701i −0.780732 0.624866i \(-0.785154\pi\)
0.150783 + 0.988567i \(0.451820\pi\)
\(240\) 0 0
\(241\) 2125.83 + 1227.35i 0.568203 + 0.328052i 0.756431 0.654073i \(-0.226941\pi\)
−0.188228 + 0.982125i \(0.560274\pi\)
\(242\) 0 0
\(243\) −2479.28 + 2863.92i −0.654511 + 0.756053i
\(244\) 0 0
\(245\) −799.738 + 3451.65i −0.208544 + 0.900073i
\(246\) 0 0
\(247\) −2993.49 5184.88i −0.771139 1.33565i
\(248\) 0 0
\(249\) −3041.99 + 2038.24i −0.774210 + 0.518748i
\(250\) 0 0
\(251\) 3096.36 0.778648 0.389324 0.921101i \(-0.372709\pi\)
0.389324 + 0.921101i \(0.372709\pi\)
\(252\) 0 0
\(253\) −2127.08 −0.528571
\(254\) 0 0
\(255\) 223.663 + 3346.67i 0.0549268 + 0.821868i
\(256\) 0 0
\(257\) −1311.10 2270.89i −0.318227 0.551185i 0.661892 0.749600i \(-0.269754\pi\)
−0.980118 + 0.198415i \(0.936421\pi\)
\(258\) 0 0
\(259\) −697.389 275.026i −0.167311 0.0659817i
\(260\) 0 0
\(261\) −484.008 3604.92i −0.114787 0.854939i
\(262\) 0 0
\(263\) 6179.60 + 3567.79i 1.44886 + 0.836500i 0.998414 0.0563032i \(-0.0179313\pi\)
0.450447 + 0.892803i \(0.351265\pi\)
\(264\) 0 0
\(265\) 580.693 335.263i 0.134610 0.0777173i
\(266\) 0 0
\(267\) 3264.88 + 1604.86i 0.748343 + 0.367849i
\(268\) 0 0
\(269\) 3846.62 0.871869 0.435934 0.899978i \(-0.356418\pi\)
0.435934 + 0.899978i \(0.356418\pi\)
\(270\) 0 0
\(271\) 446.364i 0.100054i 0.998748 + 0.0500271i \(0.0159308\pi\)
−0.998748 + 0.0500271i \(0.984069\pi\)
\(272\) 0 0
\(273\) 4129.16 + 1317.71i 0.915414 + 0.292129i
\(274\) 0 0
\(275\) 496.417 286.606i 0.108855 0.0628473i
\(276\) 0 0
\(277\) −3405.06 + 5897.74i −0.738593 + 1.27928i 0.214535 + 0.976716i \(0.431176\pi\)
−0.953129 + 0.302565i \(0.902157\pi\)
\(278\) 0 0
\(279\) −749.441 308.179i −0.160817 0.0661297i
\(280\) 0 0
\(281\) 2970.96 + 1715.29i 0.630722 + 0.364147i 0.781031 0.624492i \(-0.214694\pi\)
−0.150310 + 0.988639i \(0.548027\pi\)
\(282\) 0 0
\(283\) 275.171 158.870i 0.0577993 0.0333705i −0.470822 0.882228i \(-0.656043\pi\)
0.528621 + 0.848858i \(0.322709\pi\)
\(284\) 0 0
\(285\) −7119.00 + 475.774i −1.47962 + 0.0988857i
\(286\) 0 0
\(287\) −217.064 1456.33i −0.0446441 0.299527i
\(288\) 0 0
\(289\) −1008.00 −0.205171
\(290\) 0 0
\(291\) −677.270 1010.80i −0.136434 0.203622i
\(292\) 0 0
\(293\) −3701.79 6411.69i −0.738091 1.27841i −0.953354 0.301856i \(-0.902394\pi\)
0.215262 0.976556i \(-0.430939\pi\)
\(294\) 0 0
\(295\) −819.972 + 1420.23i −0.161833 + 0.280302i
\(296\) 0 0
\(297\) −1396.76 + 4167.33i −0.272889 + 0.814185i
\(298\) 0 0
\(299\) 1529.03 2648.35i 0.295739 0.512235i
\(300\) 0 0
\(301\) −4681.67 + 3720.96i −0.896502 + 0.712534i
\(302\) 0 0
\(303\) 8099.04 5426.65i 1.53557 1.02889i
\(304\) 0 0
\(305\) 5887.99i 1.10540i
\(306\) 0 0
\(307\) 9692.73i 1.80193i −0.433888 0.900967i \(-0.642859\pi\)
0.433888 0.900967i \(-0.357141\pi\)
\(308\) 0 0
\(309\) −3140.03 + 209.854i −0.578092 + 0.0386348i
\(310\) 0 0
\(311\) −3957.20 6854.07i −0.721518 1.24971i −0.960391 0.278655i \(-0.910111\pi\)
0.238873 0.971051i \(-0.423222\pi\)
\(312\) 0 0
\(313\) 4644.88 + 2681.72i 0.838799 + 0.484281i 0.856856 0.515556i \(-0.172415\pi\)
−0.0180566 + 0.999837i \(0.505748\pi\)
\(314\) 0 0
\(315\) 3580.07 3723.42i 0.640362 0.666002i
\(316\) 0 0
\(317\) 3741.29 + 2160.03i 0.662876 + 0.382712i 0.793372 0.608737i \(-0.208324\pi\)
−0.130496 + 0.991449i \(0.541657\pi\)
\(318\) 0 0
\(319\) −2110.14 3654.88i −0.370362 0.641485i
\(320\) 0 0
\(321\) 2979.04 6060.47i 0.517986 1.05378i
\(322\) 0 0
\(323\) 8306.67i 1.43095i
\(324\) 0 0
\(325\) 824.095i 0.140654i
\(326\) 0 0
\(327\) 9695.97 + 4766.07i 1.63972 + 0.806007i
\(328\) 0 0
\(329\) 4966.29 3947.18i 0.832221 0.661444i
\(330\) 0 0
\(331\) 371.714 643.828i 0.0617259 0.106912i −0.833511 0.552503i \(-0.813673\pi\)
0.895237 + 0.445590i \(0.147006\pi\)
\(332\) 0 0
\(333\) 667.538 + 865.348i 0.109852 + 0.142405i
\(334\) 0 0
\(335\) −1558.06 + 2698.65i −0.254108 + 0.440128i
\(336\) 0 0
\(337\) 4874.39 + 8442.69i 0.787908 + 1.36470i 0.927246 + 0.374452i \(0.122169\pi\)
−0.139338 + 0.990245i \(0.544497\pi\)
\(338\) 0 0
\(339\) 6528.60 436.317i 1.04597 0.0699041i
\(340\) 0 0
\(341\) −940.219 −0.149313
\(342\) 0 0
\(343\) −2728.03 5736.85i −0.429445 0.903093i
\(344\) 0 0
\(345\) −2028.59 3027.59i −0.316567 0.472464i
\(346\) 0 0
\(347\) −2953.16 + 1705.01i −0.456870 + 0.263774i −0.710727 0.703468i \(-0.751634\pi\)
0.253857 + 0.967242i \(0.418301\pi\)
\(348\) 0 0
\(349\) −8157.38 4709.67i −1.25116 0.722357i −0.279820 0.960053i \(-0.590275\pi\)
−0.971340 + 0.237695i \(0.923608\pi\)
\(350\) 0 0
\(351\) −4184.55 4734.69i −0.636338 0.719997i
\(352\) 0 0
\(353\) −1363.14 + 2361.03i −0.205532 + 0.355992i −0.950302 0.311329i \(-0.899226\pi\)
0.744770 + 0.667321i \(0.232559\pi\)
\(354\) 0 0
\(355\) 6432.91 3714.04i 0.961756 0.555270i
\(356\) 0 0
\(357\) −4047.35 4447.83i −0.600023 0.659395i
\(358\) 0 0
\(359\) 8978.19i 1.31992i 0.751302 + 0.659959i \(0.229426\pi\)
−0.751302 + 0.659959i \(0.770574\pi\)
\(360\) 0 0
\(361\) −10810.9 −1.57616
\(362\) 0 0
\(363\) −121.123 1812.36i −0.0175133 0.262050i
\(364\) 0 0
\(365\) 4998.06 2885.63i 0.716742 0.413811i
\(366\) 0 0
\(367\) −6601.74 3811.52i −0.938987 0.542124i −0.0493444 0.998782i \(-0.515713\pi\)
−0.889643 + 0.456657i \(0.849047\pi\)
\(368\) 0 0
\(369\) −816.370 + 1985.28i −0.115172 + 0.280080i
\(370\) 0 0
\(371\) −441.047 + 1118.37i −0.0617197 + 0.156504i
\(372\) 0 0
\(373\) −1255.32 2174.28i −0.174258 0.301823i 0.765646 0.643262i \(-0.222419\pi\)
−0.939904 + 0.341438i \(0.889086\pi\)
\(374\) 0 0
\(375\) 6902.60 + 3392.99i 0.950530 + 0.467235i
\(376\) 0 0
\(377\) 6067.41 0.828879
\(378\) 0 0
\(379\) −7234.68 −0.980529 −0.490265 0.871574i \(-0.663100\pi\)
−0.490265 + 0.871574i \(0.663100\pi\)
\(380\) 0 0
\(381\) −4736.09 2328.04i −0.636844 0.313042i
\(382\) 0 0
\(383\) −6219.05 10771.7i −0.829710 1.43710i −0.898266 0.439452i \(-0.855173\pi\)
0.0685562 0.997647i \(-0.478161\pi\)
\(384\) 0 0
\(385\) 2198.74 5575.40i 0.291060 0.738048i
\(386\) 0 0
\(387\) 8640.88 1160.15i 1.13499 0.152387i
\(388\) 0 0
\(389\) −2593.05 1497.10i −0.337976 0.195131i 0.321400 0.946943i \(-0.395846\pi\)
−0.659377 + 0.751813i \(0.729180\pi\)
\(390\) 0 0
\(391\) −3674.47 + 2121.46i −0.475258 + 0.274390i
\(392\) 0 0
\(393\) −938.168 14037.8i −0.120418 1.80181i
\(394\) 0 0
\(395\) 9434.66 1.20180
\(396\) 0 0
\(397\) 3404.67i 0.430417i 0.976568 + 0.215208i \(0.0690430\pi\)
−0.976568 + 0.215208i \(0.930957\pi\)
\(398\) 0 0
\(399\) 9461.38 8609.48i 1.18712 1.08023i
\(400\) 0 0
\(401\) 2674.32 1544.02i 0.333040 0.192281i −0.324150 0.946006i \(-0.605078\pi\)
0.657190 + 0.753725i \(0.271745\pi\)
\(402\) 0 0
\(403\) 675.866 1170.63i 0.0835416 0.144698i
\(404\) 0 0
\(405\) −7263.67 + 1986.29i −0.891196 + 0.243703i
\(406\) 0 0
\(407\) 1098.19 + 634.041i 0.133748 + 0.0772193i
\(408\) 0 0
\(409\) 8924.66 5152.66i 1.07896 0.622940i 0.148347 0.988935i \(-0.452605\pi\)
0.930617 + 0.365995i \(0.119271\pi\)
\(410\) 0 0
\(411\) −9063.98 13527.6i −1.08782 1.62352i
\(412\) 0 0
\(413\) −433.456 2908.15i −0.0516440 0.346491i
\(414\) 0 0
\(415\) −7279.31 −0.861029
\(416\) 0 0
\(417\) 518.366 34.6433i 0.0608741 0.00406832i
\(418\) 0 0
\(419\) 5734.36 + 9932.20i 0.668596 + 1.15804i 0.978297 + 0.207208i \(0.0664378\pi\)
−0.309701 + 0.950834i \(0.600229\pi\)
\(420\) 0 0
\(421\) −3002.26 + 5200.07i −0.347557 + 0.601986i −0.985815 0.167837i \(-0.946322\pi\)
0.638258 + 0.769822i \(0.279655\pi\)
\(422\) 0 0
\(423\) −9166.20 + 1230.68i −1.05361 + 0.141460i
\(424\) 0 0
\(425\) 571.697 990.208i 0.0652503 0.113017i
\(426\) 0 0
\(427\) −6568.43 8264.32i −0.744422 0.936624i
\(428\) 0 0
\(429\) −6579.74 3234.29i −0.740496 0.363992i
\(430\) 0 0
\(431\) 8312.17i 0.928963i 0.885583 + 0.464481i \(0.153759\pi\)
−0.885583 + 0.464481i \(0.846241\pi\)
\(432\) 0 0
\(433\) 4419.65i 0.490519i 0.969458 + 0.245259i \(0.0788731\pi\)
−0.969458 + 0.245259i \(0.921127\pi\)
\(434\) 0 0
\(435\) 3189.74 6489.13i 0.351578 0.715241i
\(436\) 0 0
\(437\) −4512.74 7816.30i −0.493990 0.855616i
\(438\) 0 0
\(439\) 14013.5 + 8090.72i 1.52353 + 0.879610i 0.999612 + 0.0278416i \(0.00886340\pi\)
0.523918 + 0.851769i \(0.324470\pi\)
\(440\) 0 0
\(441\) −871.235 + 9219.93i −0.0940757 + 0.995565i
\(442\) 0 0
\(443\) 2983.47 + 1722.51i 0.319976 + 0.184738i 0.651382 0.758750i \(-0.274190\pi\)
−0.331406 + 0.943488i \(0.607523\pi\)
\(444\) 0 0
\(445\) 3616.08 + 6263.24i 0.385211 + 0.667205i
\(446\) 0 0
\(447\) 13650.7 912.300i 1.44442 0.0965332i
\(448\) 0 0
\(449\) 3345.89i 0.351675i −0.984419 0.175838i \(-0.943737\pi\)
0.984419 0.175838i \(-0.0562634\pi\)
\(450\) 0 0
\(451\) 2490.65i 0.260045i
\(452\) 0 0
\(453\) −8153.73 + 5463.29i −0.845686 + 0.566639i
\(454\) 0 0
\(455\) 5361.19 + 6745.39i 0.552388 + 0.695008i
\(456\) 0 0
\(457\) 2817.23 4879.58i 0.288368 0.499469i −0.685052 0.728494i \(-0.740221\pi\)
0.973420 + 0.229025i \(0.0735539\pi\)
\(458\) 0 0
\(459\) 1743.45 + 8592.00i 0.177292 + 0.873726i
\(460\) 0 0
\(461\) −8810.53 + 15260.3i −0.890124 + 1.54174i −0.0503981 + 0.998729i \(0.516049\pi\)
−0.839726 + 0.543011i \(0.817284\pi\)
\(462\) 0 0
\(463\) 1050.86 + 1820.15i 0.105481 + 0.182699i 0.913935 0.405861i \(-0.133028\pi\)
−0.808454 + 0.588560i \(0.799695\pi\)
\(464\) 0 0
\(465\) −896.685 1338.27i −0.0894253 0.133464i
\(466\) 0 0
\(467\) −4439.19 −0.439874 −0.219937 0.975514i \(-0.570585\pi\)
−0.219937 + 0.975514i \(0.570585\pi\)
\(468\) 0 0
\(469\) −823.629 5525.91i −0.0810910 0.544057i
\(470\) 0 0
\(471\) 6647.65 444.273i 0.650334 0.0434629i
\(472\) 0 0
\(473\) 8760.62 5057.94i 0.851614 0.491680i
\(474\) 0 0
\(475\) 2106.36 + 1216.11i 0.203466 + 0.117471i
\(476\) 0 0
\(477\) 1387.72 1070.50i 0.133206 0.102757i
\(478\) 0 0
\(479\) −1192.77 + 2065.94i −0.113777 + 0.197067i −0.917290 0.398220i \(-0.869628\pi\)
0.803513 + 0.595287i \(0.202961\pi\)
\(480\) 0 0
\(481\) −1578.85 + 911.547i −0.149666 + 0.0864095i
\(482\) 0 0
\(483\) 6224.77 + 1986.47i 0.586412 + 0.187137i
\(484\) 0 0
\(485\) 2418.78i 0.226456i
\(486\) 0 0
\(487\) −1032.17 −0.0960409 −0.0480205 0.998846i \(-0.515291\pi\)
−0.0480205 + 0.998846i \(0.515291\pi\)
\(488\) 0 0
\(489\) 16594.7 + 8157.17i 1.53464 + 0.754356i
\(490\) 0 0
\(491\) −18322.5 + 10578.5i −1.68408 + 0.972305i −0.725183 + 0.688556i \(0.758245\pi\)
−0.958899 + 0.283748i \(0.908422\pi\)
\(492\) 0 0
\(493\) −7290.42 4209.13i −0.666012 0.384522i
\(494\) 0 0
\(495\) −6918.17 + 5336.75i −0.628179 + 0.484584i
\(496\) 0 0
\(497\) −4885.91 + 12389.3i −0.440972 + 1.11818i
\(498\) 0 0
\(499\) 5302.31 + 9183.86i 0.475679 + 0.823900i 0.999612 0.0278593i \(-0.00886904\pi\)
−0.523933 + 0.851760i \(0.675536\pi\)
\(500\) 0 0
\(501\) −326.816 4890.14i −0.0291438 0.436078i
\(502\) 0 0
\(503\) −4721.95 −0.418572 −0.209286 0.977855i \(-0.567114\pi\)
−0.209286 + 0.977855i \(0.567114\pi\)
\(504\) 0 0
\(505\) 19380.5 1.70777
\(506\) 0 0
\(507\) −727.205 + 487.253i −0.0637008 + 0.0426818i
\(508\) 0 0
\(509\) −6295.97 10904.9i −0.548259 0.949613i −0.998394 0.0566522i \(-0.981957\pi\)
0.450135 0.892961i \(-0.351376\pi\)
\(510\) 0 0
\(511\) −3796.12 + 9625.89i −0.328631 + 0.833316i
\(512\) 0 0
\(513\) −18276.8 + 3708.65i −1.57298 + 0.319183i
\(514\) 0 0
\(515\) −5418.00 3128.08i −0.463583 0.267650i
\(516\) 0 0
\(517\) −9293.22 + 5365.44i −0.790552 + 0.456425i
\(518\) 0 0
\(519\) −4228.62 + 2833.32i −0.357641 + 0.239632i
\(520\) 0 0
\(521\) 11584.6 0.974145 0.487072 0.873362i \(-0.338065\pi\)
0.487072 + 0.873362i \(0.338065\pi\)
\(522\) 0 0
\(523\) 3526.37i 0.294833i 0.989075 + 0.147416i \(0.0470957\pi\)
−0.989075 + 0.147416i \(0.952904\pi\)
\(524\) 0 0
\(525\) −1720.39 + 375.136i −0.143017 + 0.0311853i
\(526\) 0 0
\(527\) −1624.20 + 937.733i −0.134253 + 0.0775110i
\(528\) 0 0
\(529\) −3778.47 + 6544.50i −0.310550 + 0.537889i
\(530\) 0 0
\(531\) −1630.22 + 3964.42i −0.133230 + 0.323995i
\(532\) 0 0
\(533\) −3101.02 1790.38i −0.252008 0.145497i
\(534\) 0 0
\(535\) 11626.2 6712.39i 0.939523 0.542434i
\(536\) 0 0
\(537\) −8572.81 + 17440.3i −0.688909 + 1.40150i
\(538\) 0 0
\(539\) 3133.58 + 10278.4i 0.250413 + 0.821376i
\(540\) 0 0
\(541\) 7849.84 0.623828 0.311914 0.950110i \(-0.399030\pi\)
0.311914 + 0.950110i \(0.399030\pi\)
\(542\) 0 0
\(543\) −3531.22 + 7183.82i −0.279078 + 0.567748i
\(544\) 0 0
\(545\) 10739.0 + 18600.4i 0.844048 + 1.46193i
\(546\) 0 0
\(547\) 7842.27 13583.2i 0.613001 1.06175i −0.377731 0.925915i \(-0.623296\pi\)
0.990732 0.135833i \(-0.0433710\pi\)
\(548\) 0 0
\(549\) 2047.95 + 15253.3i 0.159207 + 1.18578i
\(550\) 0 0
\(551\) 8953.62 15508.1i 0.692263 1.19903i
\(552\) 0 0
\(553\) −13242.4 + 10524.9i −1.01831 + 0.809342i
\(554\) 0 0
\(555\) 144.878 + 2167.80i 0.0110806 + 0.165798i
\(556\) 0 0
\(557\) 21036.4i 1.60025i −0.599833 0.800126i \(-0.704766\pi\)
0.599833 0.800126i \(-0.295234\pi\)
\(558\) 0 0
\(559\) 14543.4i 1.10039i
\(560\) 0 0
\(561\) 5662.32 + 8450.77i 0.426137 + 0.635992i
\(562\) 0 0
\(563\) −6347.02 10993.4i −0.475124 0.822939i 0.524470 0.851429i \(-0.324264\pi\)
−0.999594 + 0.0284899i \(0.990930\pi\)
\(564\) 0 0
\(565\) 11264.8 + 6503.75i 0.838787 + 0.484274i
\(566\) 0 0
\(567\) 7979.36 10891.0i 0.591008 0.806665i
\(568\) 0 0
\(569\) −15753.0 9095.03i −1.16064 0.670094i −0.209180 0.977877i \(-0.567079\pi\)
−0.951456 + 0.307783i \(0.900413\pi\)
\(570\) 0 0
\(571\) −10146.0 17573.3i −0.743599 1.28795i −0.950846 0.309663i \(-0.899784\pi\)
0.207247 0.978289i \(-0.433550\pi\)
\(572\) 0 0
\(573\) −2169.79 3238.32i −0.158192 0.236095i
\(574\) 0 0
\(575\) 1242.34i 0.0901026i
\(576\) 0 0
\(577\) 12356.1i 0.891494i 0.895159 + 0.445747i \(0.147062\pi\)
−0.895159 + 0.445747i \(0.852938\pi\)
\(578\) 0 0
\(579\) 1404.02 + 21008.3i 0.100775 + 1.50790i
\(580\) 0 0
\(581\) 10217.1 8120.52i 0.729567 0.579855i
\(582\) 0 0
\(583\) 1016.78 1761.12i 0.0722314 0.125108i
\(584\) 0 0
\(585\) −1671.55 12449.8i −0.118137 0.879893i
\(586\) 0 0
\(587\) −1434.42 + 2484.50i −0.100860 + 0.174695i −0.912039 0.410103i \(-0.865493\pi\)
0.811179 + 0.584798i \(0.198826\pi\)
\(588\) 0 0
\(589\) −1994.74 3454.99i −0.139544 0.241698i
\(590\) 0 0
\(591\) 1851.27 3766.17i 0.128851 0.262131i
\(592\) 0 0
\(593\) 3259.99 0.225754 0.112877 0.993609i \(-0.463993\pi\)
0.112877 + 0.993609i \(0.463993\pi\)
\(594\) 0 0
\(595\) −1762.39 11824.3i −0.121430 0.814702i
\(596\) 0 0
\(597\) −10053.9 + 20453.4i −0.689245 + 1.40218i
\(598\) 0 0
\(599\) 19971.2 11530.4i 1.36227 0.786509i 0.372348 0.928093i \(-0.378553\pi\)
0.989926 + 0.141584i \(0.0452195\pi\)
\(600\) 0 0
\(601\) −10827.8 6251.41i −0.734897 0.424293i 0.0853138 0.996354i \(-0.472811\pi\)
−0.820211 + 0.572061i \(0.806144\pi\)
\(602\) 0 0
\(603\) −3097.65 + 7532.97i −0.209197 + 0.508734i
\(604\) 0 0
\(605\) 1805.46 3127.15i 0.121326 0.210143i
\(606\) 0 0
\(607\) 6638.81 3832.92i 0.443923 0.256299i −0.261338 0.965247i \(-0.584164\pi\)
0.705260 + 0.708949i \(0.250830\pi\)
\(608\) 0 0
\(609\) 2761.94 + 12666.4i 0.183776 + 0.842807i
\(610\) 0 0
\(611\) 15427.5i 1.02149i
\(612\) 0 0
\(613\) 20585.4 1.35634 0.678170 0.734905i \(-0.262773\pi\)
0.678170 + 0.734905i \(0.262773\pi\)
\(614\) 0 0
\(615\) −3545.08 + 2375.33i −0.232441 + 0.155744i
\(616\) 0 0
\(617\) −14174.2 + 8183.50i −0.924852 + 0.533963i −0.885180 0.465249i \(-0.845965\pi\)
−0.0396720 + 0.999213i \(0.512631\pi\)
\(618\) 0 0
\(619\) 6056.80 + 3496.90i 0.393285 + 0.227063i 0.683583 0.729873i \(-0.260421\pi\)
−0.290298 + 0.956936i \(0.593754\pi\)
\(620\) 0 0
\(621\) −6308.28 7137.62i −0.407637 0.461228i
\(622\) 0 0
\(623\) −12062.5 4757.04i −0.775722 0.305918i
\(624\) 0 0
\(625\) 6501.53 + 11261.0i 0.416098 + 0.720703i
\(626\) 0 0
\(627\) −17976.4 + 12044.8i −1.14499 + 0.767183i
\(628\) 0 0
\(629\) 2529.46 0.160344
\(630\) 0 0
\(631\) 8776.78 0.553721 0.276861 0.960910i \(-0.410706\pi\)
0.276861 + 0.960910i \(0.410706\pi\)
\(632\) 0 0
\(633\) −1477.89 22113.6i −0.0927974 1.38852i
\(634\) 0 0
\(635\) −5245.55 9085.56i −0.327816 0.567794i
\(636\) 0 0
\(637\) −15049.8 3487.00i −0.936098 0.216891i
\(638\) 0 0
\(639\) 15373.1 11859.0i 0.951724 0.734170i
\(640\) 0 0
\(641\) −2562.09 1479.23i −0.157873 0.0911481i 0.418982 0.907994i \(-0.362387\pi\)
−0.576855 + 0.816846i \(0.695720\pi\)
\(642\) 0 0
\(643\) −11590.6 + 6691.85i −0.710870 + 0.410421i −0.811383 0.584515i \(-0.801285\pi\)
0.100513 + 0.994936i \(0.467952\pi\)
\(644\) 0 0
\(645\) 15554.2 + 7645.71i 0.949530 + 0.466744i
\(646\) 0 0
\(647\) −20353.0 −1.23672 −0.618362 0.785893i \(-0.712203\pi\)
−0.618362 + 0.785893i \(0.712203\pi\)
\(648\) 0 0
\(649\) 4973.61i 0.300818i
\(650\) 0 0
\(651\) 2751.49 + 878.064i 0.165652 + 0.0528634i
\(652\) 0 0
\(653\) −13525.8 + 7809.11i −0.810574 + 0.467985i −0.847155 0.531346i \(-0.821687\pi\)
0.0365814 + 0.999331i \(0.488353\pi\)
\(654\) 0 0
\(655\) 13984.3 24221.6i 0.834219 1.44491i
\(656\) 0 0
\(657\) 11944.2 9213.87i 0.709265 0.547135i
\(658\) 0 0
\(659\) −5847.81 3376.24i −0.345673 0.199574i 0.317105 0.948390i \(-0.397289\pi\)
−0.662778 + 0.748816i \(0.730623\pi\)
\(660\) 0 0
\(661\) −8658.65 + 4999.07i −0.509504 + 0.294162i −0.732630 0.680627i \(-0.761707\pi\)
0.223126 + 0.974790i \(0.428374\pi\)
\(662\) 0 0
\(663\) −14592.0 + 975.210i −0.854763 + 0.0571252i
\(664\) 0 0
\(665\) 25152.5 3748.94i 1.46672 0.218613i
\(666\) 0 0
\(667\) 9146.72 0.530978
\(668\) 0 0
\(669\) −5917.94 8832.28i −0.342004 0.510427i
\(670\) 0 0
\(671\) 8928.53 + 15464.7i 0.513684 + 0.889727i
\(672\) 0 0
\(673\) −31.7088 + 54.9213i −0.00181617 + 0.00314570i −0.866932 0.498426i \(-0.833911\pi\)
0.865116 + 0.501572i \(0.167245\pi\)
\(674\) 0 0
\(675\) 2433.96 + 815.786i 0.138790 + 0.0465180i
\(676\) 0 0
\(677\) 8874.33 15370.8i 0.503793 0.872596i −0.496197 0.868210i \(-0.665271\pi\)
0.999990 0.00438565i \(-0.00139600\pi\)
\(678\) 0 0
\(679\) 2698.30 + 3394.97i 0.152506 + 0.191881i
\(680\) 0 0
\(681\) −24148.4 + 16180.3i −1.35884 + 0.910468i
\(682\) 0 0
\(683\) 8356.42i 0.468155i −0.972218 0.234077i \(-0.924793\pi\)
0.972218 0.234077i \(-0.0752069\pi\)
\(684\) 0 0
\(685\) 32370.8i 1.80558i
\(686\) 0 0
\(687\) −1908.66 + 127.559i −0.105997 + 0.00708396i
\(688\) 0 0
\(689\) 1461.81 + 2531.92i 0.0808279 + 0.139998i
\(690\) 0 0
\(691\) 25237.8 + 14571.1i 1.38942 + 0.802185i 0.993250 0.115991i \(-0.0370042\pi\)
0.396174 + 0.918175i \(0.370338\pi\)
\(692\) 0 0
\(693\) 3756.78 15208.3i 0.205928 0.833642i
\(694\) 0 0
\(695\) 894.419 + 516.393i 0.0488162 + 0.0281840i
\(696\) 0 0
\(697\) 2484.07 + 4302.53i 0.134994 + 0.233816i
\(698\) 0 0
\(699\) 8940.61 18188.5i 0.483784 0.984197i
\(700\) 0 0
\(701\) 30359.4i 1.63574i −0.575400 0.817872i \(-0.695154\pi\)
0.575400 0.817872i \(-0.304846\pi\)
\(702\) 0 0
\(703\) 5380.64i 0.288670i
\(704\) 0 0
\(705\) −16499.8 8110.53i −0.881447 0.433277i
\(706\) 0 0
\(707\) −27202.3 + 21620.2i −1.44703 + 1.15009i
\(708\) 0 0
\(709\) −6063.83 + 10502.9i −0.321202 + 0.556338i −0.980736 0.195337i \(-0.937420\pi\)
0.659535 + 0.751674i \(0.270753\pi\)
\(710\) 0 0
\(711\) 24441.2 3281.55i 1.28919 0.173091i
\(712\) 0 0
\(713\) 1018.88 1764.75i 0.0535166 0.0926934i
\(714\) 0 0
\(715\) −7287.52 12622.4i −0.381172 0.660209i
\(716\) 0 0
\(717\) −13934.3 + 931.254i −0.725783 + 0.0485053i
\(718\) 0 0
\(719\) 9928.20 0.514964 0.257482 0.966283i \(-0.417107\pi\)
0.257482 + 0.966283i \(0.417107\pi\)
\(720\) 0 0
\(721\) 11094.2 1653.58i 0.573051 0.0854125i
\(722\) 0 0
\(723\) 7099.90 + 10596.3i 0.365212 + 0.545063i
\(724\) 0 0
\(725\) −2134.66 + 1232.44i −0.109351 + 0.0631335i
\(726\) 0 0
\(727\) −26251.7 15156.4i −1.33923 0.773204i −0.352536 0.935798i \(-0.614681\pi\)
−0.986693 + 0.162594i \(0.948014\pi\)
\(728\) 0 0
\(729\) −18126.2 + 7672.07i −0.920907 + 0.389782i
\(730\) 0 0
\(731\) 10089.1 17474.9i 0.510479 0.884176i
\(732\) 0 0
\(733\) 16344.8 9436.67i 0.823613 0.475513i −0.0280476 0.999607i \(-0.508929\pi\)
0.851661 + 0.524093i \(0.175596\pi\)
\(734\) 0 0
\(735\) −11641.3 + 14262.7i −0.584212 + 0.715764i
\(736\) 0 0
\(737\) 9450.57i 0.472342i
\(738\) 0 0
\(739\) 24825.4 1.23575 0.617873 0.786278i \(-0.287995\pi\)
0.617873 + 0.786278i \(0.287995\pi\)
\(740\) 0 0
\(741\) −2074.46 31040.1i −0.102844 1.53885i
\(742\) 0 0
\(743\) 22599.1 13047.6i 1.11586 0.644241i 0.175517 0.984476i \(-0.443840\pi\)
0.940340 + 0.340236i \(0.110507\pi\)
\(744\) 0 0
\(745\) 23553.7 + 13598.8i 1.15831 + 0.668752i
\(746\) 0 0
\(747\) −18857.6 + 2531.88i −0.923646 + 0.124011i
\(748\) 0 0
\(749\) −8830.30 + 22391.2i −0.430777 + 1.09233i
\(750\) 0 0
\(751\) 13211.2 + 22882.5i 0.641922 + 1.11184i 0.985003 + 0.172536i \(0.0551962\pi\)
−0.343081 + 0.939306i \(0.611470\pi\)
\(752\) 0 0
\(753\) 14439.1 + 7097.54i 0.698789 + 0.343491i
\(754\) 0 0
\(755\) −19511.4 −0.940520
\(756\) 0 0
\(757\) 28263.9 1.35703 0.678513 0.734588i \(-0.262625\pi\)
0.678513 + 0.734588i \(0.262625\pi\)
\(758\) 0 0
\(759\) −9919.07 4875.74i −0.474360 0.233173i
\(760\) 0 0
\(761\) −19195.4 33247.5i −0.914369 1.58373i −0.807823 0.589425i \(-0.799354\pi\)
−0.106545 0.994308i \(-0.533979\pi\)
\(762\) 0 0
\(763\) −35823.0 14127.3i −1.69971 0.670307i
\(764\) 0 0
\(765\) −6628.30 + 16119.0i −0.313264 + 0.761807i
\(766\) 0 0
\(767\) −6192.46 3575.22i −0.291521 0.168310i
\(768\) 0 0
\(769\) 26820.3 15484.7i 1.25769 0.726129i 0.285067 0.958508i \(-0.407984\pi\)
0.972625 + 0.232378i \(0.0746507\pi\)
\(770\) 0 0
\(771\) −908.579 13595.0i −0.0424405 0.635037i
\(772\) 0 0
\(773\) −28691.6 −1.33501 −0.667507 0.744604i \(-0.732638\pi\)
−0.667507 + 0.744604i \(0.732638\pi\)
\(774\) 0 0
\(775\) 549.142i 0.0254526i
\(776\) 0 0
\(777\) −2621.67 2881.08i −0.121045 0.133022i
\(778\) 0 0
\(779\) −9152.30 + 5284.08i −0.420944 + 0.243032i
\(780\) 0 0
\(781\) 11263.9 19509.7i 0.516075 0.893868i
\(782\) 0 0
\(783\) 6006.24 17920.0i 0.274132 0.817893i
\(784\) 0 0
\(785\) 11470.2 + 6622.34i 0.521516 + 0.301097i
\(786\) 0 0
\(787\) 19658.2 11349.7i 0.890392 0.514068i 0.0163216 0.999867i \(-0.494804\pi\)
0.874071 + 0.485798i \(0.161471\pi\)
\(788\) 0 0
\(789\) 20638.7 + 30802.4i 0.931252 + 1.38986i
\(790\) 0 0
\(791\) −23066.5 + 3438.03i −1.03685 + 0.154542i
\(792\) 0 0
\(793\) −25672.7 −1.14964
\(794\) 0 0
\(795\) 3476.41 232.334i 0.155089 0.0103648i