Properties

Label 252.4.x.a.41.4
Level $252$
Weight $4$
Character 252.41
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 41.4
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.66323 + 2.29222i) q^{3} +(-5.16485 + 8.94579i) q^{5} +(14.4986 - 11.5234i) q^{7} +(16.4915 - 21.3783i) q^{9} +O(q^{10})\) \(q+(-4.66323 + 2.29222i) q^{3} +(-5.16485 + 8.94579i) q^{5} +(14.4986 - 11.5234i) q^{7} +(16.4915 - 21.3783i) q^{9} +(27.1307 - 15.6639i) q^{11} +(39.0052 + 22.5196i) q^{13} +(3.57919 - 53.5552i) q^{15} -62.4900 q^{17} +132.928i q^{19} +(-41.1963 + 86.9705i) q^{21} +(-58.8009 - 33.9487i) q^{23} +(9.14862 + 15.8459i) q^{25} +(-27.8997 + 137.494i) q^{27} +(-116.665 + 67.3568i) q^{29} +(25.9914 + 15.0061i) q^{31} +(-90.6116 + 135.234i) q^{33} +(28.2028 + 189.219i) q^{35} +40.4778 q^{37} +(-233.510 - 15.6059i) q^{39} +(-39.7514 + 68.8515i) q^{41} +(161.452 + 279.643i) q^{43} +(106.070 + 257.945i) q^{45} +(171.268 + 296.644i) q^{47} +(77.4212 - 334.148i) q^{49} +(291.405 - 143.241i) q^{51} +64.9125i q^{53} +323.607i q^{55} +(-304.700 - 619.874i) q^{57} +(-79.3800 + 137.490i) q^{59} +(-493.640 + 285.003i) q^{61} +(-7.24774 - 499.994i) q^{63} +(-402.912 + 232.621i) q^{65} +(150.833 - 261.251i) q^{67} +(352.020 + 23.5261i) q^{69} +719.100i q^{71} -558.706i q^{73} +(-78.9843 - 52.9223i) q^{75} +(212.856 - 539.744i) q^{77} +(456.676 + 790.986i) q^{79} +(-185.064 - 705.119i) q^{81} +(352.348 + 610.285i) q^{83} +(322.751 - 559.022i) q^{85} +(389.641 - 581.524i) q^{87} -700.133 q^{89} +(825.026 - 122.969i) q^{91} +(-155.601 - 10.3991i) q^{93} +(-1189.15 - 686.554i) q^{95} +(202.787 - 117.079i) q^{97} +(112.557 - 838.329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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 \(-0.986186\pi\)
0.537100 + 0.843518i \(0.319520\pi\)
\(6\) 0 0
\(7\) 14.4986 11.5234i 0.782853 0.622207i
\(8\) 0 0
\(9\) 16.4915 21.3783i 0.610794 0.791789i
\(10\) 0 0
\(11\) 27.1307 15.6639i 0.743656 0.429350i −0.0797412 0.996816i \(-0.525409\pi\)
0.823397 + 0.567466i \(0.192076\pi\)
\(12\) 0 0
\(13\) 39.0052 + 22.5196i 0.832161 + 0.480448i 0.854592 0.519300i \(-0.173807\pi\)
−0.0224312 + 0.999748i \(0.507141\pi\)
\(14\) 0 0
\(15\) 3.57919 53.5552i 0.0616095 0.921860i
\(16\) 0 0
\(17\) −62.4900 −0.891532 −0.445766 0.895150i \(-0.647069\pi\)
−0.445766 + 0.895150i \(0.647069\pi\)
\(18\) 0 0
\(19\) 132.928i 1.60504i 0.596624 + 0.802521i \(0.296508\pi\)
−0.596624 + 0.802521i \(0.703492\pi\)
\(20\) 0 0
\(21\) −41.1963 + 86.9705i −0.428084 + 0.903739i
\(22\) 0 0
\(23\) −58.8009 33.9487i −0.533080 0.307774i 0.209190 0.977875i \(-0.432917\pi\)
−0.742270 + 0.670101i \(0.766251\pi\)
\(24\) 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 −0.824624 0.565681i \(-0.808613\pi\)
0.0775817 + 0.996986i \(0.475280\pi\)
\(30\) 0 0
\(31\) 25.9914 + 15.0061i 0.150587 + 0.0869413i 0.573400 0.819275i \(-0.305624\pi\)
−0.422813 + 0.906217i \(0.638957\pi\)
\(32\) 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 \(-0.881717\pi\)
0.780331 + 0.625367i \(0.215051\pi\)
\(42\) 0 0
\(43\) 161.452 + 279.643i 0.572586 + 0.991749i 0.996299 + 0.0859521i \(0.0273932\pi\)
−0.423713 + 0.905797i \(0.639273\pi\)
\(44\) 0 0
\(45\) 106.070 + 257.945i 0.351377 + 0.854492i
\(46\) 0 0
\(47\) 171.268 + 296.644i 0.531531 + 0.920638i 0.999323 + 0.0367994i \(0.0117163\pi\)
−0.467792 + 0.883839i \(0.654950\pi\)
\(48\) 0 0
\(49\) 77.4212 334.148i 0.225718 0.974193i
\(50\) 0 0
\(51\) 291.405 143.241i 0.800096 0.393289i
\(52\) 0 0
\(53\) 64.9125i 0.168234i 0.996456 + 0.0841172i \(0.0268070\pi\)
−0.996456 + 0.0841172i \(0.973193\pi\)
\(54\) 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 \(-0.889377\pi\)
0.765057 + 0.643962i \(0.222711\pi\)
\(60\) 0 0
\(61\) −493.640 + 285.003i −1.03613 + 0.598212i −0.918736 0.394873i \(-0.870788\pi\)
−0.117397 + 0.993085i \(0.537455\pi\)
\(62\) 0 0
\(63\) −7.24774 499.994i −0.0144941 0.999895i
\(64\) 0 0
\(65\) −402.912 + 232.621i −0.768847 + 0.443894i
\(66\) 0 0
\(67\) 150.833 261.251i 0.275033 0.476372i −0.695110 0.718903i \(-0.744644\pi\)
0.970144 + 0.242531i \(0.0779778\pi\)
\(68\) 0 0
\(69\) 352.020 + 23.5261i 0.614178 + 0.0410465i
\(70\) 0 0
\(71\) 719.100i 1.20199i 0.799252 + 0.600996i \(0.205229\pi\)
−0.799252 + 0.600996i \(0.794771\pi\)
\(72\) 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
\(77\) 212.856 539.744i 0.315029 0.798825i
\(78\) 0 0
\(79\) 456.676 + 790.986i 0.650381 + 1.12649i 0.983031 + 0.183442i \(0.0587239\pi\)
−0.332650 + 0.943050i \(0.607943\pi\)
\(80\) 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 \(-0.0123733\pi\)
−0.533278 + 0.845940i \(0.679040\pi\)
\(84\) 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 \(-0.636895\pi\)
−0.416932 + 0.908938i \(0.636895\pi\)
\(90\) 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 \(-0.627559\pi\)
0.602364 + 0.798221i \(0.294225\pi\)
\(98\) 0 0
\(99\) 112.557 838.329i 0.114266 0.851063i
\(100\) 0 0
\(101\) −938.098 1624.83i −0.924200 1.60076i −0.792843 0.609427i \(-0.791400\pi\)
−0.131358 0.991335i \(-0.541934\pi\)
\(102\) 0 0
\(103\) 524.507 + 302.824i 0.501759 + 0.289691i 0.729440 0.684045i \(-0.239781\pi\)
−0.227681 + 0.973736i \(0.573114\pi\)
\(104\) 0 0
\(105\) −565.247 817.723i −0.525356 0.760015i
\(106\) 0 0
\(107\) 1299.63i 1.17420i 0.809513 + 0.587102i \(0.199731\pi\)
−0.809513 + 0.587102i \(0.800269\pi\)
\(108\) 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 0.879742 0.475451i \(-0.157715\pi\)
0.0281181 + 0.999605i \(0.491049\pi\)
\(114\) 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
\(119\) −906.020 + 720.099i −0.697939 + 0.554717i
\(120\) 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 0.0792242 0.996857i \(-0.474756\pi\)
0.823691 0.567039i \(-0.191911\pi\)
\(132\) 0 0
\(133\) 1531.79 + 1927.28i 0.998668 + 1.25651i
\(134\) 0 0
\(135\) −1085.89 959.721i −0.692288 0.611849i
\(136\) 0 0
\(137\) −2713.91 + 1566.88i −1.69245 + 0.977135i −0.739915 + 0.672700i \(0.765134\pi\)
−0.952533 + 0.304435i \(0.901532\pi\)
\(138\) 0 0
\(139\) −86.5871 49.9911i −0.0528361 0.0305049i 0.473349 0.880875i \(-0.343045\pi\)
−0.526185 + 0.850370i \(0.676378\pi\)
\(140\) 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
\(147\) 404.908 + 1735.68i 0.227185 + 0.973852i
\(148\) 0 0
\(149\) 2280.20 + 1316.47i 1.25370 + 0.723823i 0.971842 0.235634i \(-0.0757167\pi\)
0.281856 + 0.959457i \(0.409050\pi\)
\(150\) 0 0
\(151\) −944.432 1635.80i −0.508985 0.881588i −0.999946 0.0104066i \(-0.996687\pi\)
0.490961 0.871182i \(-0.336646\pi\)
\(152\) 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 \(-0.438998\pi\)
−0.754935 + 0.655800i \(0.772331\pi\)
\(158\) 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 \(-0.763209\pi\)
0.954357 + 0.298667i \(0.0965420\pi\)
\(168\) 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 \(-0.0976099\pi\)
−0.738100 + 0.674692i \(0.764277\pi\)
\(174\) 0 0
\(175\) 315.241 + 124.320i 0.136171 + 0.0537013i
\(176\) 0 0
\(177\) 55.0095 823.105i 0.0233602 0.349539i
\(178\) 0 0
\(179\) 3739.96i 1.56166i −0.624742 0.780831i \(-0.714796\pi\)
0.624742 0.780831i \(-0.285204\pi\)
\(180\) 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
\(189\) 1179.90 + 2314.98i 0.454099 + 0.890951i
\(190\) 0 0
\(191\) −649.672 + 375.088i −0.246118 + 0.142097i −0.617986 0.786189i \(-0.712051\pi\)
0.371867 + 0.928286i \(0.378718\pi\)
\(192\) 0 0
\(193\) 2026.03 3509.19i 0.755632 1.30879i −0.189428 0.981895i \(-0.560663\pi\)
0.945060 0.326898i \(-0.106003\pi\)
\(194\) 0 0
\(195\) 1345.65 2008.33i 0.494175 0.737536i
\(196\) 0 0
\(197\) 807.631i 0.292088i 0.989278 + 0.146044i \(0.0466541\pi\)
−0.989278 + 0.146044i \(0.953346\pi\)
\(198\) 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
\(203\) −915.309 + 2320.97i −0.316464 + 0.802463i
\(204\) 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 0.274095 + 0.961702i \(0.411622\pi\)
−0.969907 + 0.243478i \(0.921712\pi\)
\(212\) 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 \(-0.567273\pi\)
0.741870 + 0.670544i \(0.233939\pi\)
\(224\) 0 0
\(225\) 489.632 + 65.7394i 0.145076 + 0.0194784i
\(226\) 0 0
\(227\) 2797.06 + 4844.65i 0.817830 + 1.41652i 0.907278 + 0.420532i \(0.138157\pi\)
−0.0894471 + 0.995992i \(0.528510\pi\)
\(228\) 0 0
\(229\) 318.820 + 184.071i 0.0920009 + 0.0531168i 0.545295 0.838244i \(-0.316418\pi\)
−0.453294 + 0.891361i \(0.649751\pi\)
\(230\) 0 0
\(231\) 244.615 + 3004.87i 0.0696730 + 0.855868i
\(232\) 0 0
\(233\) 3900.42i 1.09667i 0.836258 + 0.548336i \(0.184739\pi\)
−0.836258 + 0.548336i \(0.815261\pi\)
\(234\) 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 0.150783 0.988567i \(-0.451820\pi\)
−0.780732 + 0.624866i \(0.785154\pi\)
\(240\) 0 0
\(241\) −2125.83 + 1227.35i −0.568203 + 0.328052i −0.756431 0.654073i \(-0.773059\pi\)
0.188228 + 0.982125i \(0.439726\pi\)
\(242\) 0 0
\(243\) 2479.28 + 2863.92i 0.654511 + 0.756053i
\(244\) 0 0
\(245\) 2589.35 + 2418.42i 0.675214 + 0.630641i
\(246\) 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 \(-0.627291\pi\)
−0.389324 + 0.921101i \(0.627291\pi\)
\(252\) 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 \(-0.730246\pi\)
0.980118 + 0.198415i \(0.0635794\pi\)
\(258\) 0 0
\(259\) 586.874 466.443i 0.140798 0.111905i
\(260\) 0 0
\(261\) −484.008 + 3604.92i −0.114787 + 0.854939i
\(262\) 0 0
\(263\) 6179.60 3567.79i 1.44886 0.836500i 0.450447 0.892803i \(-0.351265\pi\)
0.998414 + 0.0563032i \(0.0179313\pi\)
\(264\) 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 \(-0.643582\pi\)
−0.435934 + 0.899978i \(0.643582\pi\)
\(270\) 0 0
\(271\) 446.364i 0.100054i 0.998748 + 0.0500271i \(0.0159308\pi\)
−0.998748 + 0.0500271i \(0.984069\pi\)
\(272\) 0 0
\(273\) −3565.41 + 2464.57i −0.790434 + 0.546384i
\(274\) 0 0
\(275\) 496.417 + 286.606i 0.108855 + 0.0628473i
\(276\) 0 0
\(277\) −3405.06 5897.74i −0.738593 1.27928i −0.953129 0.302565i \(-0.902157\pi\)
0.214535 0.976716i \(-0.431176\pi\)
\(278\) 0 0
\(279\) 749.441 308.179i 0.160817 0.0661297i
\(280\) 0 0
\(281\) 2970.96 1715.29i 0.630722 0.364147i −0.150310 0.988639i \(-0.548027\pi\)
0.781031 + 0.624492i \(0.214694\pi\)
\(282\) 0 0
\(283\) −275.171 158.870i −0.0577993 0.0333705i 0.470822 0.882228i \(-0.343957\pi\)
−0.528621 + 0.848858i \(0.677291\pi\)
\(284\) 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 −0.215262 0.976556i \(-0.569061\pi\)
0.953354 0.301856i \(-0.0976060\pi\)
\(294\) 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
\(301\) 5563.28 + 2193.97i 1.06532 + 0.420126i
\(302\) 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 −0.238873 0.971051i \(-0.576778\pi\)
0.960391 0.278655i \(-0.0898886\pi\)
\(312\) 0 0
\(313\) −4644.88 + 2681.72i −0.838799 + 0.484281i −0.856856 0.515556i \(-0.827585\pi\)
0.0180566 + 0.999837i \(0.494252\pi\)
\(314\) 0 0
\(315\) 4510.28 + 2517.56i 0.806747 + 0.450313i
\(316\) 0 0
\(317\) 3741.29 2160.03i 0.662876 0.382712i −0.130496 0.991449i \(-0.541657\pi\)
0.793372 + 0.608737i \(0.208324\pi\)
\(318\) 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
\(329\) 5901.50 + 2327.35i 0.988937 + 0.390002i
\(330\) 0 0
\(331\) 371.714 + 643.828i 0.0617259 + 0.106912i 0.895237 0.445590i \(-0.147006\pi\)
−0.833511 + 0.552503i \(0.813673\pi\)
\(332\) 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 −0.139338 0.990245i \(-0.544497\pi\)
0.927246 0.374452i \(-0.122169\pi\)
\(338\) 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 0.253857 0.967242i \(-0.418301\pi\)
−0.710727 + 0.703468i \(0.751634\pi\)
\(348\) 0 0
\(349\) 8157.38 4709.67i 1.25116 0.722357i 0.279820 0.960053i \(-0.409725\pi\)
0.971340 + 0.237695i \(0.0763919\pi\)
\(350\) 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 \(-0.100774\pi\)
−0.744770 + 0.667321i \(0.767441\pi\)
\(354\) 0 0
\(355\) −6432.91 3714.04i −0.961756 0.555270i
\(356\) 0 0
\(357\) 2574.35 5434.78i 0.381651 0.805712i
\(358\) 0 0
\(359\) 8978.19i 1.31992i −0.751302 0.659959i \(-0.770574\pi\)
0.751302 0.659959i \(-0.229426\pi\)
\(360\) 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 \(-0.484287\pi\)
0.889643 + 0.456657i \(0.150953\pi\)
\(368\) 0 0
\(369\) 816.370 + 1985.28i 0.115172 + 0.280080i
\(370\) 0 0
\(371\) 748.015 + 941.143i 0.104677 + 0.131703i
\(372\) 0 0
\(373\) −1255.32 + 2174.28i −0.174258 + 0.301823i −0.939904 0.341438i \(-0.889086\pi\)
0.765646 + 0.643262i \(0.222419\pi\)
\(374\) 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 −0.0685562 0.997647i \(-0.521839\pi\)
0.898266 0.439452i \(-0.144827\pi\)
\(384\) 0 0
\(385\) 3729.06 + 4691.86i 0.493638 + 0.621090i
\(386\) 0 0
\(387\) 8640.88 + 1160.15i 1.13499 + 0.152387i
\(388\) 0 0
\(389\) −2593.05 + 1497.10i −0.337976 + 0.195131i −0.659377 0.751813i \(-0.729180\pi\)
0.321400 + 0.946943i \(0.395846\pi\)
\(390\) 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
\(399\) −11560.8 5476.14i −1.45054 0.687093i
\(400\) 0 0
\(401\) 2674.32 + 1544.02i 0.333040 + 0.192281i 0.657190 0.753725i \(-0.271745\pi\)
−0.324150 + 0.946006i \(0.605078\pi\)
\(402\) 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 \(-0.547395\pi\)
−0.930617 + 0.365995i \(0.880729\pi\)
\(410\) 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 0.309701 + 0.950834i \(0.399771\pi\)
−0.978297 + 0.207208i \(0.933562\pi\)
\(420\) 0 0
\(421\) −3002.26 5200.07i −0.347557 0.601986i 0.638258 0.769822i \(-0.279655\pi\)
−0.985815 + 0.167837i \(0.946322\pi\)
\(422\) 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
\(427\) −3872.89 + 9820.58i −0.438929 + 1.11300i
\(428\) 0 0
\(429\) −6579.74 + 3234.29i −0.740496 + 0.363992i
\(430\) 0 0
\(431\) 8312.17i 0.928963i −0.885583 0.464481i \(-0.846241\pi\)
0.885583 0.464481i \(-0.153759\pi\)
\(432\) 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 −0.523918 + 0.851769i \(0.675530\pi\)
−0.999612 + 0.0278416i \(0.991137\pi\)
\(440\) 0 0
\(441\) −5866.73 7165.72i −0.633488 0.773752i
\(442\) 0 0
\(443\) 2983.47 1722.51i 0.319976 0.184738i −0.331406 0.943488i \(-0.607523\pi\)
0.651382 + 0.758750i \(0.274190\pi\)
\(444\) 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 \(0.0562634\pi\)
−0.984419 + 0.175838i \(0.943737\pi\)
\(450\) 0 0
\(451\) 2490.65i 0.260045i
\(452\) 0 0
\(453\) 8153.73 + 5463.29i 0.845686 + 0.566639i
\(454\) 0 0
\(455\) −3161.08 + 8015.62i −0.325701 + 0.825886i
\(456\) 0 0
\(457\) 2817.23 + 4879.58i 0.288368 + 0.499469i 0.973420 0.229025i \(-0.0735539\pi\)
−0.685052 + 0.728494i \(0.740221\pi\)
\(458\) 0 0
\(459\) 1743.45 8592.00i 0.177292 0.873726i
\(460\) 0 0
\(461\) 8810.53 + 15260.3i 0.890124 + 1.54174i 0.839726 + 0.543011i \(0.182716\pi\)
0.0503981 + 0.998729i \(0.483951\pi\)
\(462\) 0 0
\(463\) 1050.86 1820.15i 0.105481 0.182699i −0.808454 0.588560i \(-0.799695\pi\)
0.913935 + 0.405861i \(0.133028\pi\)
\(464\) 0 0
\(465\) 896.685 1338.27i 0.0894253 0.133464i
\(466\) 0 0
\(467\) 4439.19 0.439874 0.219937 0.975514i \(-0.429415\pi\)
0.219937 + 0.975514i \(0.429415\pi\)
\(468\) 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 \(-0.130372\pi\)
−0.803513 + 0.595287i \(0.797039\pi\)
\(480\) 0 0
\(481\) 1578.85 + 911.547i 0.149666 + 0.0864095i
\(482\) 0 0
\(483\) 5374.92 3715.38i 0.506350 0.350012i
\(484\) 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 −0.958899 0.283748i \(-0.908422\pi\)
−0.725183 0.688556i \(-0.758245\pi\)
\(492\) 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
\(497\) 8286.49 + 10426.0i 0.747887 + 0.940983i
\(498\) 0 0
\(499\) 5302.31 9183.86i 0.475679 0.823900i −0.523933 0.851760i \(-0.675536\pi\)
0.999612 + 0.0278593i \(0.00886904\pi\)
\(500\) 0 0
\(501\) −326.816 + 4890.14i −0.0291438 + 0.436078i
\(502\) 0 0
\(503\) 4721.95 0.418572 0.209286 0.977855i \(-0.432886\pi\)
0.209286 + 0.977855i \(0.432886\pi\)
\(504\) 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 −0.450135 0.892961i \(-0.648624\pi\)
0.998394 0.0566522i \(-0.0180426\pi\)
\(510\) 0 0
\(511\) −6438.21 8100.48i −0.557357 0.701261i
\(512\) 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 \(-0.661935\pi\)
−0.487072 + 0.873362i \(0.661935\pi\)
\(522\) 0 0
\(523\) 3526.37i 0.294833i 0.989075 + 0.147416i \(0.0470957\pi\)
−0.989075 + 0.147416i \(0.952904\pi\)
\(524\) 0 0
\(525\) −1755.01 + 142.869i −0.145895 + 0.0118768i
\(526\) 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 0.990732 + 0.135833i \(0.0433710\pi\)
−0.377731 + 0.925915i \(0.623296\pi\)
\(548\) 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
\(553\) 15736.1 + 6205.75i 1.21006 + 0.477207i
\(554\) 0 0
\(555\) 144.878 2167.80i 0.0110806 0.165798i
\(556\) 0 0
\(557\) 21036.4i 1.60025i 0.599833 + 0.800126i \(0.295234\pi\)
−0.599833 + 0.800126i \(0.704766\pi\)
\(558\) 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 \(-0.675736\pi\)
0.999594 + 0.0284899i \(0.00906983\pi\)
\(564\) 0 0
\(565\) −11264.8 + 6503.75i −0.838787 + 0.484274i
\(566\) 0 0
\(567\) −10808.6 8090.69i −0.800559 0.599254i
\(568\) 0 0
\(569\) −15753.0 + 9095.03i −1.16064 + 0.670094i −0.951456 0.307783i \(-0.900413\pi\)
−0.209180 + 0.977877i \(0.567079\pi\)
\(570\) 0 0
\(571\) −10146.0 + 17573.3i −0.743599 + 1.28795i 0.207247 + 0.978289i \(0.433550\pi\)
−0.950846 + 0.309663i \(0.899784\pi\)
\(572\) 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
\(581\) 12141.1 + 4788.05i 0.866953 + 0.341896i
\(582\) 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 \(-0.134507\pi\)
−0.811179 + 0.584798i \(0.801174\pi\)
\(588\) 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 \(-0.536007\pi\)
−0.112877 + 0.993609i \(0.536007\pi\)
\(594\) 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 0.989926 0.141584i \(-0.0452195\pi\)
0.372348 + 0.928093i \(0.378553\pi\)
\(600\) 0 0
\(601\) 10827.8 6251.41i 0.734897 0.424293i −0.0853138 0.996354i \(-0.527189\pi\)
0.820211 + 0.572061i \(0.193856\pi\)
\(602\) 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 \(-0.415836\pi\)
−0.705260 + 0.708949i \(0.749170\pi\)
\(608\) 0 0
\(609\) −1051.87 12921.3i −0.0699903 0.859766i
\(610\) 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 −0.0396720 0.999213i \(-0.512631\pi\)
−0.885180 + 0.465249i \(0.845965\pi\)
\(618\) 0 0
\(619\) −6056.80 + 3496.90i −0.393285 + 0.227063i −0.683583 0.729873i \(-0.739579\pi\)
0.290298 + 0.956936i \(0.406246\pi\)
\(620\) 0 0
\(621\) 6308.28 7137.62i 0.407637 0.461228i
\(622\) 0 0
\(623\) −10151.0 + 8067.93i −0.652793 + 0.518836i
\(624\) 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
\(637\) 10544.7 11290.0i 0.655883 0.702239i
\(638\) 0 0
\(639\) 15373.1 + 11859.0i 0.951724 + 0.734170i
\(640\) 0 0
\(641\) −2562.09 + 1479.23i −0.157873 + 0.0911481i −0.576855 0.816846i \(-0.695720\pi\)
0.418982 + 0.907994i \(0.362387\pi\)
\(642\) 0 0
\(643\) 11590.6 + 6691.85i 0.710870 + 0.410421i 0.811383 0.584515i \(-0.198715\pi\)
−0.100513 + 0.994936i \(0.532048\pi\)
\(644\) 0 0
\(645\) 15554.2 7645.71i 0.949530 0.466744i
\(646\) 0 0
\(647\) 20353.0 1.23672 0.618362 0.785893i \(-0.287797\pi\)
0.618362 + 0.785893i \(0.287797\pi\)
\(648\) 0 0
\(649\) 4973.61i 0.300818i
\(650\) 0 0
\(651\) −2375.84 + 1642.29i −0.143036 + 0.0988730i
\(652\) 0 0
\(653\) −13525.8 7809.11i −0.810574 0.467985i 0.0365814 0.999331i \(-0.488353\pi\)
−0.847155 + 0.531346i \(0.821687\pi\)
\(654\) 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 −0.662778 0.748816i \(-0.730623\pi\)
0.317105 + 0.948390i \(0.397289\pi\)
\(660\) 0 0
\(661\) 8658.65 + 4999.07i 0.509504 + 0.294162i 0.732630 0.680627i \(-0.238293\pi\)
−0.223126 + 0.974790i \(0.571626\pi\)
\(662\) 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 0.865116 0.501572i \(-0.167245\pi\)
−0.866932 + 0.498426i \(0.833911\pi\)
\(674\) 0 0
\(675\) −2433.96 + 815.786i −0.138790 + 0.0465180i
\(676\) 0 0
\(677\) −8874.33 15370.8i −0.503793 0.872596i −0.999990 0.00438565i \(-0.998604\pi\)
0.496197 0.868210i \(-0.334729\pi\)
\(678\) 0 0
\(679\) 1590.98 4034.28i 0.0899208 0.228014i
\(680\) 0 0
\(681\) −24148.4 16180.3i −1.35884 0.910468i
\(682\) 0 0
\(683\) 8356.42i 0.468155i 0.972218 + 0.234077i \(0.0752069\pi\)
−0.972218 + 0.234077i \(0.924793\pi\)
\(684\) 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 \(-0.962996\pi\)
−0.396174 + 0.918175i \(0.629662\pi\)
\(692\) 0 0
\(693\) −8028.51 13451.7i −0.440083 0.737355i
\(694\) 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 \(0.304846\pi\)
−0.575400 + 0.817872i \(0.695154\pi\)
\(702\) 0 0
\(703\) 5380.64i 0.288670i
\(704\) 0 0
\(705\) 16499.8 8110.53i 0.881447 0.433277i
\(706\) 0 0
\(707\) −32324.8 12747.8i −1.71952 0.678118i
\(708\) 0 0
\(709\) −6063.83 10502.9i −0.321202 0.556338i 0.659535 0.751674i \(-0.270753\pi\)
−0.980736 + 0.195337i \(0.937420\pi\)
\(710\) 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 \(-0.582893\pi\)
−0.257482 + 0.966283i \(0.582893\pi\)
\(720\) 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 \(-0.385319\pi\)
0.986693 + 0.162594i \(0.0519860\pi\)
\(728\) 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 \(-0.491071\pi\)
−0.851661 + 0.524093i \(0.824404\pi\)
\(734\) 0 0
\(735\) −17618.3 5342.29i −0.884163 0.268100i
\(736\) 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 0.940340 0.340236i \(-0.110507\pi\)
0.175517 + 0.984476i \(0.443840\pi\)
\(744\) 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
\(749\) 14976.2 + 18842.9i 0.730598 + 0.919230i
\(750\) 0 0
\(751\) 13211.2 22882.5i 0.641922 1.11184i −0.343081 0.939306i \(-0.611470\pi\)
0.985003 0.172536i \(-0.0551962\pi\)
\(752\) 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 0.106545 0.994308i \(-0.466021\pi\)
0.807823 0.589425i \(-0.200646\pi\)
\(762\) 0 0
\(763\) 30146.1 23959.9i 1.43036 1.13684i
\(764\) 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 \(-0.592016\pi\)
−0.972625 + 0.232378i \(0.925349\pi\)
\(770\) 0 0
\(771\) −908.579 + 13595.0i −0.0424405 + 0.635037i
\(772\) 0 0
\(773\) 28691.6 1.33501 0.667507 0.744604i \(-0.267362\pi\)
0.667507 + 0.744604i \(0.267362\pi\)
\(774\) 0 0
\(775\) 549.142i 0.0254526i
\(776\) 0 0
\(777\) −1667.54 + 3520.38i −0.0769917 + 0.162539i
\(778\) 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 \(-0.505196\pi\)
−0.874071 + 0.485798i \(0.838529\pi\)
\(788\) 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
\(796\)