Properties

Label 252.2.e.a.71.2
Level 252
Weight 2
Character 252.71
Analytic conductor 2.012
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 252.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.653473922154496.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 71.2
Root \(-1.35489 + 0.405301i\)
Character \(\chi\) = 252.71
Dual form 252.2.e.a.71.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.35489 + 0.405301i) q^{2} +(1.67146 - 1.09828i) q^{4} -3.31339i q^{5} -1.00000i q^{7} +(-1.81951 + 2.16549i) q^{8} +O(q^{10})\) \(q+(-1.35489 + 0.405301i) q^{2} +(1.67146 - 1.09828i) q^{4} -3.31339i q^{5} -1.00000i q^{7} +(-1.81951 + 2.16549i) q^{8} +(1.34292 + 4.48929i) q^{10} -4.72761 q^{11} -4.97858 q^{13} +(0.405301 + 1.35489i) q^{14} +(1.58757 - 3.67146i) q^{16} -0.484966i q^{17} -2.29273i q^{19} +(-3.63903 - 5.53821i) q^{20} +(6.40539 - 1.91611i) q^{22} +7.97002 q^{23} -5.97858 q^{25} +(6.74543 - 2.01782i) q^{26} +(-1.09828 - 1.67146i) q^{28} -1.41421i q^{29} -7.66442i q^{31} +(-0.662933 + 5.61788i) q^{32} +(0.196558 + 0.657077i) q^{34} -3.31339 q^{35} -2.39312 q^{37} +(0.929247 + 3.10640i) q^{38} +(7.17513 + 6.02877i) q^{40} -6.55580i q^{41} +5.37169i q^{43} +(-7.90201 + 5.19223i) q^{44} +(-10.7985 + 3.23026i) q^{46} +6.21280 q^{47} -1.00000 q^{49} +(8.10032 - 2.42313i) q^{50} +(-8.32150 + 5.46787i) q^{52} +1.00023i q^{53} +15.6644i q^{55} +(2.16549 + 1.81951i) q^{56} +(0.573183 + 1.91611i) q^{58} +1.38392 q^{59} +13.6644 q^{61} +(3.10640 + 10.3845i) q^{62} +(-1.37873 - 7.88030i) q^{64} +16.4960i q^{65} +3.27131i q^{67} +(-0.532628 - 0.810603i) q^{68} +(4.48929 - 1.34292i) q^{70} +3.34369 q^{71} -2.10038 q^{73} +(3.24241 - 0.969933i) q^{74} +(-2.51806 - 3.83221i) q^{76} +4.72761i q^{77} -12.0575i q^{79} +(-12.1650 - 5.26024i) q^{80} +(2.65708 + 8.88240i) q^{82} -3.24241 q^{83} -1.60688 q^{85} +(-2.17715 - 7.27806i) q^{86} +(8.60195 - 10.2376i) q^{88} -5.72784i q^{89} +4.97858i q^{91} +(13.3216 - 8.75330i) q^{92} +(-8.41767 + 2.51806i) q^{94} -7.59672 q^{95} +12.0575 q^{97} +(1.35489 - 0.405301i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{4} + O(q^{10}) \) \( 12q + 8q^{4} - 8q^{10} - 20q^{16} + 20q^{22} - 12q^{25} - 4q^{28} - 16q^{34} + 8q^{37} + 8q^{40} - 36q^{46} - 12q^{49} - 16q^{52} + 4q^{58} + 56q^{61} - 16q^{64} + 24q^{70} + 72q^{76} + 56q^{82} - 56q^{85} + 28q^{88} - 24q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35489 + 0.405301i −0.958053 + 0.286591i
\(3\) 0 0
\(4\) 1.67146 1.09828i 0.835731 0.549139i
\(5\) 3.31339i 1.48179i −0.671618 0.740897i \(-0.734400\pi\)
0.671618 0.740897i \(-0.265600\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) −1.81951 + 2.16549i −0.643296 + 0.765618i
\(9\) 0 0
\(10\) 1.34292 + 4.48929i 0.424670 + 1.41964i
\(11\) −4.72761 −1.42543 −0.712714 0.701455i \(-0.752534\pi\)
−0.712714 + 0.701455i \(0.752534\pi\)
\(12\) 0 0
\(13\) −4.97858 −1.38081 −0.690404 0.723424i \(-0.742567\pi\)
−0.690404 + 0.723424i \(0.742567\pi\)
\(14\) 0.405301 + 1.35489i 0.108321 + 0.362110i
\(15\) 0 0
\(16\) 1.58757 3.67146i 0.396892 0.917865i
\(17\) 0.484966i 0.117622i −0.998269 0.0588108i \(-0.981269\pi\)
0.998269 0.0588108i \(-0.0187309\pi\)
\(18\) 0 0
\(19\) 2.29273i 0.525989i −0.964797 0.262994i \(-0.915290\pi\)
0.964797 0.262994i \(-0.0847100\pi\)
\(20\) −3.63903 5.53821i −0.813712 1.23838i
\(21\) 0 0
\(22\) 6.40539 1.91611i 1.36563 0.408515i
\(23\) 7.97002 1.66186 0.830932 0.556374i \(-0.187808\pi\)
0.830932 + 0.556374i \(0.187808\pi\)
\(24\) 0 0
\(25\) −5.97858 −1.19572
\(26\) 6.74543 2.01782i 1.32289 0.395728i
\(27\) 0 0
\(28\) −1.09828 1.67146i −0.207555 0.315877i
\(29\) 1.41421i 0.262613i −0.991342 0.131306i \(-0.958083\pi\)
0.991342 0.131306i \(-0.0419172\pi\)
\(30\) 0 0
\(31\) 7.66442i 1.37657i −0.725440 0.688286i \(-0.758364\pi\)
0.725440 0.688286i \(-0.241636\pi\)
\(32\) −0.662933 + 5.61788i −0.117191 + 0.993109i
\(33\) 0 0
\(34\) 0.196558 + 0.657077i 0.0337093 + 0.112688i
\(35\) −3.31339 −0.560066
\(36\) 0 0
\(37\) −2.39312 −0.393426 −0.196713 0.980461i \(-0.563027\pi\)
−0.196713 + 0.980461i \(0.563027\pi\)
\(38\) 0.929247 + 3.10640i 0.150744 + 0.503925i
\(39\) 0 0
\(40\) 7.17513 + 6.02877i 1.13449 + 0.953232i
\(41\) 6.55580i 1.02384i −0.859032 0.511922i \(-0.828934\pi\)
0.859032 0.511922i \(-0.171066\pi\)
\(42\) 0 0
\(43\) 5.37169i 0.819175i 0.912271 + 0.409588i \(0.134327\pi\)
−0.912271 + 0.409588i \(0.865673\pi\)
\(44\) −7.90201 + 5.19223i −1.19127 + 0.782758i
\(45\) 0 0
\(46\) −10.7985 + 3.23026i −1.59215 + 0.476276i
\(47\) 6.21280 0.906230 0.453115 0.891452i \(-0.350313\pi\)
0.453115 + 0.891452i \(0.350313\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 8.10032 2.42313i 1.14556 0.342682i
\(51\) 0 0
\(52\) −8.32150 + 5.46787i −1.15398 + 0.758257i
\(53\) 1.00023i 0.137392i 0.997638 + 0.0686960i \(0.0218839\pi\)
−0.997638 + 0.0686960i \(0.978116\pi\)
\(54\) 0 0
\(55\) 15.6644i 2.11219i
\(56\) 2.16549 + 1.81951i 0.289376 + 0.243143i
\(57\) 0 0
\(58\) 0.573183 + 1.91611i 0.0752626 + 0.251597i
\(59\) 1.38392 0.180171 0.0900853 0.995934i \(-0.471286\pi\)
0.0900853 + 0.995934i \(0.471286\pi\)
\(60\) 0 0
\(61\) 13.6644 1.74955 0.874775 0.484529i \(-0.161009\pi\)
0.874775 + 0.484529i \(0.161009\pi\)
\(62\) 3.10640 + 10.3845i 0.394513 + 1.31883i
\(63\) 0 0
\(64\) −1.37873 7.88030i −0.172341 0.985037i
\(65\) 16.4960i 2.04608i
\(66\) 0 0
\(67\) 3.27131i 0.399654i 0.979831 + 0.199827i \(0.0640380\pi\)
−0.979831 + 0.199827i \(0.935962\pi\)
\(68\) −0.532628 0.810603i −0.0645907 0.0983000i
\(69\) 0 0
\(70\) 4.48929 1.34292i 0.536573 0.160510i
\(71\) 3.34369 0.396823 0.198412 0.980119i \(-0.436422\pi\)
0.198412 + 0.980119i \(0.436422\pi\)
\(72\) 0 0
\(73\) −2.10038 −0.245831 −0.122916 0.992417i \(-0.539224\pi\)
−0.122916 + 0.992417i \(0.539224\pi\)
\(74\) 3.24241 0.969933i 0.376923 0.112752i
\(75\) 0 0
\(76\) −2.51806 3.83221i −0.288841 0.439585i
\(77\) 4.72761i 0.538761i
\(78\) 0 0
\(79\) 12.0575i 1.35658i −0.734795 0.678290i \(-0.762722\pi\)
0.734795 0.678290i \(-0.237278\pi\)
\(80\) −12.1650 5.26024i −1.36009 0.588112i
\(81\) 0 0
\(82\) 2.65708 + 8.88240i 0.293425 + 0.980897i
\(83\) −3.24241 −0.355901 −0.177950 0.984039i \(-0.556947\pi\)
−0.177950 + 0.984039i \(0.556947\pi\)
\(84\) 0 0
\(85\) −1.60688 −0.174291
\(86\) −2.17715 7.27806i −0.234769 0.784813i
\(87\) 0 0
\(88\) 8.60195 10.2376i 0.916971 1.09133i
\(89\) 5.72784i 0.607149i −0.952808 0.303575i \(-0.901820\pi\)
0.952808 0.303575i \(-0.0981802\pi\)
\(90\) 0 0
\(91\) 4.97858i 0.521897i
\(92\) 13.3216 8.75330i 1.38887 0.912595i
\(93\) 0 0
\(94\) −8.41767 + 2.51806i −0.868217 + 0.259718i
\(95\) −7.59672 −0.779407
\(96\) 0 0
\(97\) 12.0575 1.22426 0.612129 0.790758i \(-0.290313\pi\)
0.612129 + 0.790758i \(0.290313\pi\)
\(98\) 1.35489 0.405301i 0.136865 0.0409416i
\(99\) 0 0
\(100\) −9.99296 + 6.56614i −0.999296 + 0.656614i
\(101\) 14.5665i 1.44942i 0.689053 + 0.724711i \(0.258027\pi\)
−0.689053 + 0.724711i \(0.741973\pi\)
\(102\) 0 0
\(103\) 5.70727i 0.562354i 0.959656 + 0.281177i \(0.0907248\pi\)
−0.959656 + 0.281177i \(0.909275\pi\)
\(104\) 9.05860 10.7811i 0.888268 1.05717i
\(105\) 0 0
\(106\) −0.405394 1.35520i −0.0393754 0.131629i
\(107\) −16.0413 −1.55077 −0.775386 0.631487i \(-0.782445\pi\)
−0.775386 + 0.631487i \(0.782445\pi\)
\(108\) 0 0
\(109\) 1.37169 0.131384 0.0656921 0.997840i \(-0.479074\pi\)
0.0656921 + 0.997840i \(0.479074\pi\)
\(110\) −6.34881 21.2236i −0.605336 2.02359i
\(111\) 0 0
\(112\) −3.67146 1.58757i −0.346921 0.150011i
\(113\) 11.2834i 1.06145i −0.847543 0.530727i \(-0.821919\pi\)
0.847543 0.530727i \(-0.178081\pi\)
\(114\) 0 0
\(115\) 26.4078i 2.46254i
\(116\) −1.55320 2.36380i −0.144211 0.219474i
\(117\) 0 0
\(118\) −1.87506 + 0.560904i −0.172613 + 0.0516354i
\(119\) −0.484966 −0.0444568
\(120\) 0 0
\(121\) 11.3503 1.03184
\(122\) −18.5138 + 5.53821i −1.67616 + 0.501406i
\(123\) 0 0
\(124\) −8.41767 12.8108i −0.755929 1.15044i
\(125\) 3.24241i 0.290010i
\(126\) 0 0
\(127\) 16.6430i 1.47683i 0.674348 + 0.738414i \(0.264425\pi\)
−0.674348 + 0.738414i \(0.735575\pi\)
\(128\) 5.06193 + 10.1181i 0.447415 + 0.894326i
\(129\) 0 0
\(130\) −6.68585 22.3503i −0.586387 1.96025i
\(131\) 7.59672 0.663729 0.331864 0.943327i \(-0.392322\pi\)
0.331864 + 0.943327i \(0.392322\pi\)
\(132\) 0 0
\(133\) −2.29273 −0.198805
\(134\) −1.32587 4.43227i −0.114537 0.382890i
\(135\) 0 0
\(136\) 1.05019 + 0.882404i 0.0900532 + 0.0756655i
\(137\) 9.42492i 0.805225i 0.915370 + 0.402613i \(0.131898\pi\)
−0.915370 + 0.402613i \(0.868102\pi\)
\(138\) 0 0
\(139\) 16.0000i 1.35710i −0.734553 0.678551i \(-0.762608\pi\)
0.734553 0.678551i \(-0.237392\pi\)
\(140\) −5.53821 + 3.63903i −0.468064 + 0.307554i
\(141\) 0 0
\(142\) −4.53034 + 1.35520i −0.380177 + 0.113726i
\(143\) 23.5368 1.96824
\(144\) 0 0
\(145\) −4.68585 −0.389138
\(146\) 2.84579 0.851289i 0.235519 0.0704532i
\(147\) 0 0
\(148\) −4.00000 + 2.62831i −0.328798 + 0.216046i
\(149\) 18.4661i 1.51281i −0.654106 0.756403i \(-0.726955\pi\)
0.654106 0.756403i \(-0.273045\pi\)
\(150\) 0 0
\(151\) 23.3288i 1.89847i 0.314561 + 0.949237i \(0.398143\pi\)
−0.314561 + 0.949237i \(0.601857\pi\)
\(152\) 4.96490 + 4.17166i 0.402706 + 0.338366i
\(153\) 0 0
\(154\) −1.91611 6.40539i −0.154404 0.516161i
\(155\) −25.3953 −2.03980
\(156\) 0 0
\(157\) 22.2499 1.77573 0.887867 0.460100i \(-0.152186\pi\)
0.887867 + 0.460100i \(0.152186\pi\)
\(158\) 4.88694 + 16.3367i 0.388784 + 1.29967i
\(159\) 0 0
\(160\) 18.6142 + 2.19656i 1.47158 + 0.173653i
\(161\) 7.97002i 0.628125i
\(162\) 0 0
\(163\) 16.6430i 1.30358i −0.758399 0.651790i \(-0.774018\pi\)
0.758399 0.651790i \(-0.225982\pi\)
\(164\) −7.20010 10.9578i −0.562233 0.855659i
\(165\) 0 0
\(166\) 4.39312 1.31415i 0.340972 0.101998i
\(167\) −8.98064 −0.694943 −0.347471 0.937691i \(-0.612960\pi\)
−0.347471 + 0.937691i \(0.612960\pi\)
\(168\) 0 0
\(169\) 11.7862 0.906633
\(170\) 2.17715 0.651273i 0.166980 0.0499503i
\(171\) 0 0
\(172\) 5.89962 + 8.97858i 0.449841 + 0.684610i
\(173\) 2.75744i 0.209645i −0.994491 0.104822i \(-0.966573\pi\)
0.994491 0.104822i \(-0.0334274\pi\)
\(174\) 0 0
\(175\) 5.97858i 0.451938i
\(176\) −7.50539 + 17.3572i −0.565740 + 1.30835i
\(177\) 0 0
\(178\) 2.32150 + 7.76060i 0.174004 + 0.581681i
\(179\) −4.72761 −0.353358 −0.176679 0.984269i \(-0.556535\pi\)
−0.176679 + 0.984269i \(0.556535\pi\)
\(180\) 0 0
\(181\) −8.39312 −0.623855 −0.311928 0.950106i \(-0.600975\pi\)
−0.311928 + 0.950106i \(0.600975\pi\)
\(182\) −2.01782 6.74543i −0.149571 0.500005i
\(183\) 0 0
\(184\) −14.5016 + 17.2590i −1.06907 + 1.27235i
\(185\) 7.92933i 0.582976i
\(186\) 0 0
\(187\) 2.29273i 0.167661i
\(188\) 10.3845 6.82339i 0.757365 0.497647i
\(189\) 0 0
\(190\) 10.2927 3.07896i 0.746713 0.223371i
\(191\) 1.48520 0.107465 0.0537325 0.998555i \(-0.482888\pi\)
0.0537325 + 0.998555i \(0.482888\pi\)
\(192\) 0 0
\(193\) −8.35027 −0.601066 −0.300533 0.953771i \(-0.597164\pi\)
−0.300533 + 0.953771i \(0.597164\pi\)
\(194\) −16.3367 + 4.88694i −1.17290 + 0.350862i
\(195\) 0 0
\(196\) −1.67146 + 1.09828i −0.119390 + 0.0784485i
\(197\) 3.82866i 0.272780i 0.990655 + 0.136390i \(0.0435501\pi\)
−0.990655 + 0.136390i \(0.956450\pi\)
\(198\) 0 0
\(199\) 6.04285i 0.428366i 0.976794 + 0.214183i \(0.0687089\pi\)
−0.976794 + 0.214183i \(0.931291\pi\)
\(200\) 10.8781 12.9466i 0.769199 0.915461i
\(201\) 0 0
\(202\) −5.90383 19.7360i −0.415392 1.38862i
\(203\) −1.41421 −0.0992583
\(204\) 0 0
\(205\) −21.7220 −1.51713
\(206\) −2.31316 7.73273i −0.161166 0.538765i
\(207\) 0 0
\(208\) −7.90383 + 18.2787i −0.548032 + 1.26740i
\(209\) 10.8391i 0.749758i
\(210\) 0 0
\(211\) 9.95715i 0.685479i 0.939431 + 0.342739i \(0.111355\pi\)
−0.939431 + 0.342739i \(0.888645\pi\)
\(212\) 1.09853 + 1.67185i 0.0754474 + 0.114823i
\(213\) 0 0
\(214\) 21.7342 6.50157i 1.48572 0.444438i
\(215\) 17.7985 1.21385
\(216\) 0 0
\(217\) −7.66442 −0.520295
\(218\) −1.85849 + 0.555949i −0.125873 + 0.0376536i
\(219\) 0 0
\(220\) 17.2039 + 26.1825i 1.15989 + 1.76522i
\(221\) 2.41444i 0.162413i
\(222\) 0 0
\(223\) 0.786230i 0.0526499i 0.999653 + 0.0263249i \(0.00838046\pi\)
−0.999653 + 0.0263249i \(0.991620\pi\)
\(224\) 5.61788 + 0.662933i 0.375360 + 0.0442941i
\(225\) 0 0
\(226\) 4.57318 + 15.2878i 0.304204 + 1.01693i
\(227\) 20.2943 1.34698 0.673492 0.739195i \(-0.264794\pi\)
0.673492 + 0.739195i \(0.264794\pi\)
\(228\) 0 0
\(229\) −4.97858 −0.328994 −0.164497 0.986378i \(-0.552600\pi\)
−0.164497 + 0.986378i \(0.552600\pi\)
\(230\) 10.7031 + 35.7797i 0.705743 + 2.35924i
\(231\) 0 0
\(232\) 3.06247 + 2.57318i 0.201061 + 0.168938i
\(233\) 0.383688i 0.0251362i −0.999921 0.0125681i \(-0.995999\pi\)
0.999921 0.0125681i \(-0.00400066\pi\)
\(234\) 0 0
\(235\) 20.5855i 1.34285i
\(236\) 2.31316 1.51993i 0.150574 0.0989388i
\(237\) 0 0
\(238\) 0.657077 0.196558i 0.0425920 0.0127409i
\(239\) −1.48520 −0.0960693 −0.0480347 0.998846i \(-0.515296\pi\)
−0.0480347 + 0.998846i \(0.515296\pi\)
\(240\) 0 0
\(241\) −23.4721 −1.51197 −0.755985 0.654589i \(-0.772842\pi\)
−0.755985 + 0.654589i \(0.772842\pi\)
\(242\) −15.3784 + 4.60028i −0.988560 + 0.295717i
\(243\) 0 0
\(244\) 22.8396 15.0073i 1.46215 0.960747i
\(245\) 3.31339i 0.211685i
\(246\) 0 0
\(247\) 11.4145i 0.726290i
\(248\) 16.5973 + 13.9455i 1.05393 + 0.885542i
\(249\) 0 0
\(250\) −1.31415 4.39312i −0.0831144 0.277845i
\(251\) 4.62633 0.292011 0.146006 0.989284i \(-0.453358\pi\)
0.146006 + 0.989284i \(0.453358\pi\)
\(252\) 0 0
\(253\) −37.6791 −2.36887
\(254\) −6.74543 22.5495i −0.423246 1.41488i
\(255\) 0 0
\(256\) −10.9593 11.6574i −0.684954 0.728587i
\(257\) 3.78797i 0.236287i 0.992997 + 0.118144i \(0.0376943\pi\)
−0.992997 + 0.118144i \(0.962306\pi\)
\(258\) 0 0
\(259\) 2.39312i 0.148701i
\(260\) 18.1172 + 27.5724i 1.12358 + 1.70997i
\(261\) 0 0
\(262\) −10.2927 + 3.07896i −0.635887 + 0.190219i
\(263\) 12.7989 0.789214 0.394607 0.918850i \(-0.370881\pi\)
0.394607 + 0.918850i \(0.370881\pi\)
\(264\) 0 0
\(265\) 3.31415 0.203587
\(266\) 3.10640 0.929247i 0.190466 0.0569758i
\(267\) 0 0
\(268\) 3.59281 + 5.46787i 0.219466 + 0.334003i
\(269\) 25.4662i 1.55270i −0.630300 0.776352i \(-0.717068\pi\)
0.630300 0.776352i \(-0.282932\pi\)
\(270\) 0 0
\(271\) 21.0361i 1.27785i −0.769268 0.638927i \(-0.779379\pi\)
0.769268 0.638927i \(-0.220621\pi\)
\(272\) −1.78054 0.769917i −0.107961 0.0466831i
\(273\) 0 0
\(274\) −3.81993 12.7697i −0.230771 0.771448i
\(275\) 28.2644 1.70441
\(276\) 0 0
\(277\) 8.39312 0.504293 0.252147 0.967689i \(-0.418863\pi\)
0.252147 + 0.967689i \(0.418863\pi\)
\(278\) 6.48482 + 21.6783i 0.388934 + 1.30018i
\(279\) 0 0
\(280\) 6.02877 7.17513i 0.360288 0.428796i
\(281\) 0.111668i 0.00666157i 0.999994 + 0.00333078i \(0.00106022\pi\)
−0.999994 + 0.00333078i \(0.998940\pi\)
\(282\) 0 0
\(283\) 11.4637i 0.681444i −0.940164 0.340722i \(-0.889329\pi\)
0.940164 0.340722i \(-0.110671\pi\)
\(284\) 5.58885 3.67230i 0.331637 0.217911i
\(285\) 0 0
\(286\) −31.8898 + 9.53948i −1.88568 + 0.564081i
\(287\) −6.55580 −0.386977
\(288\) 0 0
\(289\) 16.7648 0.986165
\(290\) 6.34881 1.89918i 0.372815 0.111524i
\(291\) 0 0
\(292\) −3.51071 + 2.30681i −0.205449 + 0.134996i
\(293\) 17.8089i 1.04041i −0.854042 0.520204i \(-0.825856\pi\)
0.854042 0.520204i \(-0.174144\pi\)
\(294\) 0 0
\(295\) 4.58546i 0.266976i
\(296\) 4.35431 5.18228i 0.253089 0.301214i
\(297\) 0 0
\(298\) 7.48436 + 25.0196i 0.433557 + 1.44935i
\(299\) −39.6794 −2.29472
\(300\) 0 0
\(301\) 5.37169 0.309619
\(302\) −9.45521 31.6081i −0.544086 1.81884i
\(303\) 0 0
\(304\) −8.41767 3.63986i −0.482787 0.208761i
\(305\) 45.2756i 2.59247i
\(306\) 0 0
\(307\) 20.2499i 1.15572i 0.816135 + 0.577861i \(0.196112\pi\)
−0.816135 + 0.577861i \(0.803888\pi\)
\(308\) 5.19223 + 7.90201i 0.295855 + 0.450259i
\(309\) 0 0
\(310\) 34.4078 10.2927i 1.95423 0.584588i
\(311\) −1.38392 −0.0784747 −0.0392374 0.999230i \(-0.512493\pi\)
−0.0392374 + 0.999230i \(0.512493\pi\)
\(312\) 0 0
\(313\) −30.1151 −1.70220 −0.851102 0.525000i \(-0.824065\pi\)
−0.851102 + 0.525000i \(0.824065\pi\)
\(314\) −30.1462 + 9.01791i −1.70125 + 0.508910i
\(315\) 0 0
\(316\) −13.2425 20.1537i −0.744951 1.13373i
\(317\) 5.27317i 0.296171i −0.988975 0.148085i \(-0.952689\pi\)
0.988975 0.148085i \(-0.0473110\pi\)
\(318\) 0 0
\(319\) 6.68585i 0.374336i
\(320\) −26.1105 + 4.56828i −1.45962 + 0.255374i
\(321\) 0 0
\(322\) 3.23026 + 10.7985i 0.180015 + 0.601777i
\(323\) −1.11190 −0.0618676
\(324\) 0 0
\(325\) 29.7648 1.65105
\(326\) 6.74543 + 22.5495i 0.373595 + 1.24890i
\(327\) 0 0
\(328\) 14.1966 + 11.9284i 0.783874 + 0.658635i
\(329\) 6.21280i 0.342523i
\(330\) 0 0
\(331\) 9.95715i 0.547295i 0.961830 + 0.273647i \(0.0882301\pi\)
−0.961830 + 0.273647i \(0.911770\pi\)
\(332\) −5.41957 + 3.56107i −0.297437 + 0.195439i
\(333\) 0 0
\(334\) 12.1678 3.63986i 0.665792 0.199165i
\(335\) 10.8391 0.592205
\(336\) 0 0
\(337\) −13.3717 −0.728402 −0.364201 0.931320i \(-0.618658\pi\)
−0.364201 + 0.931320i \(0.618658\pi\)
\(338\) −15.9691 + 4.77698i −0.868602 + 0.259833i
\(339\) 0 0
\(340\) −2.68585 + 1.76481i −0.145660 + 0.0957101i
\(341\) 36.2344i 1.96220i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −11.6324 9.77387i −0.627175 0.526972i
\(345\) 0 0
\(346\) 1.11760 + 3.73604i 0.0600823 + 0.200851i
\(347\) −11.2124 −0.601915 −0.300957 0.953638i \(-0.597306\pi\)
−0.300957 + 0.953638i \(0.597306\pi\)
\(348\) 0 0
\(349\) −4.29273 −0.229785 −0.114892 0.993378i \(-0.536652\pi\)
−0.114892 + 0.993378i \(0.536652\pi\)
\(350\) −2.42313 8.10032i −0.129522 0.432980i
\(351\) 0 0
\(352\) 3.13409 26.5591i 0.167047 1.41561i
\(353\) 1.78751i 0.0951397i 0.998868 + 0.0475698i \(0.0151477\pi\)
−0.998868 + 0.0475698i \(0.984852\pi\)
\(354\) 0 0
\(355\) 11.0790i 0.588010i
\(356\) −6.29076 9.57386i −0.333410 0.507413i
\(357\) 0 0
\(358\) 6.40539 1.91611i 0.338536 0.101269i
\(359\) 12.7989 0.675500 0.337750 0.941236i \(-0.390334\pi\)
0.337750 + 0.941236i \(0.390334\pi\)
\(360\) 0 0
\(361\) 13.7434 0.723336
\(362\) 11.3718 3.40174i 0.597686 0.178792i
\(363\) 0 0
\(364\) 5.46787 + 8.32150i 0.286594 + 0.436165i
\(365\) 6.95940i 0.364272i
\(366\) 0 0
\(367\) 30.1579i 1.57423i −0.616806 0.787115i \(-0.711574\pi\)
0.616806 0.787115i \(-0.288426\pi\)
\(368\) 12.6529 29.2616i 0.659580 1.52537i
\(369\) 0 0
\(370\) −3.21377 10.7434i −0.167076 0.558522i
\(371\) 1.00023 0.0519293
\(372\) 0 0
\(373\) 5.21377 0.269959 0.134979 0.990848i \(-0.456903\pi\)
0.134979 + 0.990848i \(0.456903\pi\)
\(374\) −0.929247 3.10640i −0.0480502 0.160628i
\(375\) 0 0
\(376\) −11.3043 + 13.4538i −0.582974 + 0.693826i
\(377\) 7.04077i 0.362618i
\(378\) 0 0
\(379\) 16.7862i 0.862251i −0.902292 0.431125i \(-0.858117\pi\)
0.902292 0.431125i \(-0.141883\pi\)
\(380\) −12.6976 + 8.34332i −0.651374 + 0.428003i
\(381\) 0 0
\(382\) −2.01228 + 0.601952i −0.102957 + 0.0307985i
\(383\) −23.7393 −1.21302 −0.606511 0.795075i \(-0.707431\pi\)
−0.606511 + 0.795075i \(0.707431\pi\)
\(384\) 0 0
\(385\) 15.6644 0.798333
\(386\) 11.3137 3.38438i 0.575853 0.172260i
\(387\) 0 0
\(388\) 20.1537 13.2425i 1.02315 0.672288i
\(389\) 17.7682i 0.900885i 0.892805 + 0.450443i \(0.148734\pi\)
−0.892805 + 0.450443i \(0.851266\pi\)
\(390\) 0 0
\(391\) 3.86519i 0.195471i
\(392\) 1.81951 2.16549i 0.0918994 0.109374i
\(393\) 0 0
\(394\) −1.55176 5.18741i −0.0781765 0.261338i
\(395\) −39.9514 −2.01017
\(396\) 0 0
\(397\) 24.4078 1.22499 0.612496 0.790473i \(-0.290165\pi\)
0.612496 + 0.790473i \(0.290165\pi\)
\(398\) −2.44917 8.18740i −0.122766 0.410397i
\(399\) 0 0
\(400\) −9.49139 + 21.9501i −0.474570 + 1.09751i
\(401\) 29.1633i 1.45635i 0.685393 + 0.728173i \(0.259630\pi\)
−0.685393 + 0.728173i \(0.740370\pi\)
\(402\) 0 0
\(403\) 38.1579i 1.90078i
\(404\) 15.9981 + 24.3474i 0.795935 + 1.21133i
\(405\) 0 0
\(406\) 1.91611 0.573183i 0.0950947 0.0284466i
\(407\) 11.3137 0.560800
\(408\) 0 0
\(409\) −10.4851 −0.518454 −0.259227 0.965816i \(-0.583468\pi\)
−0.259227 + 0.965816i \(0.583468\pi\)
\(410\) 29.4309 8.80394i 1.45349 0.434796i
\(411\) 0 0
\(412\) 6.26817 + 9.53948i 0.308811 + 0.469976i
\(413\) 1.38392i 0.0680981i
\(414\) 0 0
\(415\) 10.7434i 0.527372i
\(416\) 3.30046 27.9690i 0.161818 1.37129i
\(417\) 0 0
\(418\) −4.39312 14.6858i −0.214874 0.718308i
\(419\) −31.1335 −1.52097 −0.760485 0.649356i \(-0.775039\pi\)
−0.760485 + 0.649356i \(0.775039\pi\)
\(420\) 0 0
\(421\) 30.2646 1.47501 0.737503 0.675344i \(-0.236005\pi\)
0.737503 + 0.675344i \(0.236005\pi\)
\(422\) −4.03565 13.4909i −0.196452 0.656725i
\(423\) 0 0
\(424\) −2.16599 1.81993i −0.105190 0.0883837i
\(425\) 2.89941i 0.140642i
\(426\) 0 0
\(427\) 13.6644i 0.661268i
\(428\) −26.8124 + 17.6178i −1.29603 + 0.851590i
\(429\) 0 0
\(430\) −24.1151 + 7.21377i −1.16293 + 0.347879i
\(431\) −2.23179 −0.107502 −0.0537508 0.998554i \(-0.517118\pi\)
−0.0537508 + 0.998554i \(0.517118\pi\)
\(432\) 0 0
\(433\) −8.54262 −0.410532 −0.205266 0.978706i \(-0.565806\pi\)
−0.205266 + 0.978706i \(0.565806\pi\)
\(434\) 10.3845 3.10640i 0.498470 0.149112i
\(435\) 0 0
\(436\) 2.29273 1.50650i 0.109802 0.0721483i
\(437\) 18.2731i 0.874121i
\(438\) 0 0
\(439\) 1.17092i 0.0558851i 0.999610 + 0.0279426i \(0.00889556\pi\)
−0.999610 + 0.0279426i \(0.991104\pi\)
\(440\) −33.9212 28.5017i −1.61713 1.35876i
\(441\) 0 0
\(442\) −0.978577 3.27131i −0.0465462 0.155600i
\(443\) 6.58610 0.312915 0.156458 0.987685i \(-0.449993\pi\)
0.156458 + 0.987685i \(0.449993\pi\)
\(444\) 0 0
\(445\) −18.9786 −0.899671
\(446\) −0.318660 1.06526i −0.0150890 0.0504414i
\(447\) 0 0
\(448\) −7.88030 + 1.37873i −0.372309 + 0.0651389i
\(449\) 11.2228i 0.529638i 0.964298 + 0.264819i \(0.0853121\pi\)
−0.964298 + 0.264819i \(0.914688\pi\)
\(450\) 0 0
\(451\) 30.9933i 1.45942i
\(452\) −12.3923 18.8598i −0.582886 0.887090i
\(453\) 0 0
\(454\) −27.4966 + 8.22533i −1.29048 + 0.386034i
\(455\) 16.4960 0.773344
\(456\) 0 0
\(457\) 11.9143 0.557328 0.278664 0.960389i \(-0.410108\pi\)
0.278664 + 0.960389i \(0.410108\pi\)
\(458\) 6.74543 2.01782i 0.315193 0.0942867i
\(459\) 0 0
\(460\) −29.0031 44.1396i −1.35228 2.05802i
\(461\) 18.4255i 0.858159i 0.903267 + 0.429080i \(0.141162\pi\)
−0.903267 + 0.429080i \(0.858838\pi\)
\(462\) 0 0
\(463\) 7.47208i 0.347257i −0.984811 0.173628i \(-0.944451\pi\)
0.984811 0.173628i \(-0.0555492\pi\)
\(464\) −5.19223 2.24516i −0.241043 0.104229i
\(465\) 0 0
\(466\) 0.155509 + 0.519855i 0.00720382 + 0.0240818i
\(467\) 5.57548 0.258003 0.129001 0.991644i \(-0.458823\pi\)
0.129001 + 0.991644i \(0.458823\pi\)
\(468\) 0 0
\(469\) 3.27131 0.151055
\(470\) 8.34332 + 27.8911i 0.384849 + 1.28652i
\(471\) 0 0
\(472\) −2.51806 + 2.99686i −0.115903 + 0.137942i
\(473\) 25.3953i 1.16767i
\(474\) 0 0
\(475\) 13.7073i 0.628933i
\(476\) −0.810603 + 0.532628i −0.0371539 + 0.0244130i
\(477\) 0 0
\(478\) 2.01228 0.601952i 0.0920395 0.0275326i
\(479\) −15.9400 −0.728319 −0.364159 0.931337i \(-0.618644\pi\)
−0.364159 + 0.931337i \(0.618644\pi\)
\(480\) 0 0
\(481\) 11.9143 0.543246
\(482\) 31.8021 9.51327i 1.44855 0.433317i
\(483\) 0 0
\(484\) 18.9715 12.4658i 0.862343 0.566625i
\(485\) 39.9514i 1.81410i
\(486\) 0 0
\(487\) 34.0722i 1.54396i −0.635647 0.771980i \(-0.719266\pi\)
0.635647 0.771980i \(-0.280734\pi\)
\(488\) −24.8626 + 29.5902i −1.12548 + 1.33949i
\(489\) 0 0
\(490\) −1.34292 4.48929i −0.0606671 0.202805i
\(491\) 34.0026 1.53452 0.767258 0.641339i \(-0.221621\pi\)
0.767258 + 0.641339i \(0.221621\pi\)
\(492\) 0 0
\(493\) −0.685846 −0.0308890
\(494\) −4.62633 15.4655i −0.208148 0.695824i
\(495\) 0 0
\(496\) −28.1396 12.1678i −1.26351 0.546350i
\(497\) 3.34369i 0.149985i
\(498\) 0 0
\(499\) 5.37169i 0.240470i 0.992745 + 0.120235i \(0.0383648\pi\)
−0.992745 + 0.120235i \(0.961635\pi\)
\(500\) 3.56107 + 5.41957i 0.159256 + 0.242370i
\(501\) 0 0
\(502\) −6.26817 + 1.87506i −0.279762 + 0.0836879i
\(503\) 37.3463 1.66519 0.832594 0.553884i \(-0.186855\pi\)
0.832594 + 0.553884i \(0.186855\pi\)
\(504\) 0 0
\(505\) 48.2646 2.14775
\(506\) 51.0511 15.2714i 2.26950 0.678896i
\(507\) 0 0
\(508\) 18.2787 + 27.8181i 0.810984 + 1.23423i
\(509\) 0.403595i 0.0178890i −0.999960 0.00894451i \(-0.997153\pi\)
0.999960 0.00894451i \(-0.00284716\pi\)
\(510\) 0 0
\(511\) 2.10038i 0.0929155i
\(512\) 19.5734 + 11.3527i 0.865029 + 0.501723i
\(513\) 0 0
\(514\) −1.53527 5.13229i −0.0677179 0.226376i
\(515\) 18.9104 0.833293
\(516\) 0 0
\(517\) −29.3717 −1.29177
\(518\) −0.969933 3.24241i −0.0426164 0.142463i
\(519\) 0 0
\(520\) −35.7220 30.0147i −1.56651 1.31623i
\(521\) 42.9927i 1.88355i 0.336249 + 0.941773i \(0.390842\pi\)
−0.336249 + 0.941773i \(0.609158\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) 12.6976 8.34332i 0.554698 0.364479i
\(525\) 0 0
\(526\) −17.3411 + 5.18741i −0.756109 + 0.226182i
\(527\) −3.71699 −0.161915
\(528\) 0 0
\(529\) 40.5212 1.76179
\(530\) −4.49032 + 1.34323i −0.195047 + 0.0583462i
\(531\) 0 0
\(532\) −3.83221 + 2.51806i −0.166147 + 0.109172i
\(533\) 32.6386i 1.41373i
\(534\) 0 0
\(535\) 53.1512i 2.29793i
\(536\) −7.08400 5.95219i −0.305982 0.257096i
\(537\) 0 0
\(538\) 10.3215 + 34.5040i 0.444991 + 1.48757i
\(539\) 4.72761 0.203632
\(540\) 0 0
\(541\) 19.1365 0.822742 0.411371 0.911468i \(-0.365050\pi\)
0.411371 + 0.911468i \(0.365050\pi\)
\(542\) 8.52597 + 28.5017i 0.366222 + 1.22425i
\(543\) 0 0
\(544\) 2.72448 + 0.321500i 0.116811 + 0.0137842i
\(545\) 4.54496i 0.194685i
\(546\) 0 0
\(547\) 8.14323i 0.348179i 0.984730 + 0.174090i \(0.0556983\pi\)
−0.984730 + 0.174090i \(0.944302\pi\)
\(548\) 10.3512 + 15.7534i 0.442181 + 0.672951i
\(549\) 0 0
\(550\) −38.2951 + 11.4556i −1.63291 + 0.488468i
\(551\) −3.24241 −0.138131
\(552\) 0 0
\(553\) −12.0575 −0.512739
\(554\) −11.3718 + 3.40174i −0.483140 + 0.144526i
\(555\) 0 0
\(556\) −17.5725 26.7434i −0.745238 1.13417i
\(557\) 39.0931i 1.65643i 0.560412 + 0.828214i \(0.310643\pi\)
−0.560412 + 0.828214i \(0.689357\pi\)
\(558\) 0 0
\(559\) 26.7434i 1.13112i
\(560\) −5.26024 + 12.1650i −0.222286 + 0.514065i
\(561\) 0 0
\(562\) −0.0452593 0.151298i −0.00190915 0.00638213i
\(563\) 13.6468 0.575143 0.287572 0.957759i \(-0.407152\pi\)
0.287572 + 0.957759i \(0.407152\pi\)
\(564\) 0 0
\(565\) −37.3864 −1.57286
\(566\) 4.64624 + 15.5320i 0.195296 + 0.652859i
\(567\) 0 0
\(568\) −6.08389 + 7.24074i −0.255275 + 0.303815i
\(569\) 2.32355i 0.0974084i −0.998813 0.0487042i \(-0.984491\pi\)
0.998813 0.0487042i \(-0.0155092\pi\)
\(570\) 0 0
\(571\) 2.88661i 0.120801i −0.998174 0.0604005i \(-0.980762\pi\)
0.998174 0.0604005i \(-0.0192378\pi\)
\(572\) 39.3408 25.8499i 1.64492 1.08084i
\(573\) 0 0
\(574\) 8.88240 2.65708i 0.370744 0.110904i
\(575\) −47.6494 −1.98712
\(576\) 0 0
\(577\) −18.5855 −0.773723 −0.386861 0.922138i \(-0.626441\pi\)
−0.386861 + 0.922138i \(0.626441\pi\)
\(578\) −22.7145 + 6.79480i −0.944798 + 0.282626i
\(579\) 0 0
\(580\) −7.83221 + 5.14637i −0.325215 + 0.213691i
\(581\) 3.24241i 0.134518i
\(582\) 0 0
\(583\) 4.72869i 0.195842i
\(584\) 3.82168 4.54837i 0.158142 0.188213i
\(585\) 0 0
\(586\) 7.21798 + 24.1292i 0.298172 + 0.996766i
\(587\) −9.92979 −0.409846 −0.204923 0.978778i \(-0.565694\pi\)
−0.204923 + 0.978778i \(0.565694\pi\)
\(588\) 0 0
\(589\) −17.5725 −0.724061
\(590\) 1.85849 + 6.21280i 0.0765130 + 0.255777i
\(591\) 0 0
\(592\) −3.79923 + 8.78623i −0.156147 + 0.361112i
\(593\) 24.0823i 0.988942i 0.869194 + 0.494471i \(0.164638\pi\)
−0.869194 + 0.494471i \(0.835362\pi\)
\(594\) 0 0
\(595\) 1.60688i 0.0658759i
\(596\) −20.2810 30.8655i −0.830741 1.26430i
\(597\) 0 0
\(598\) 53.7612 16.0821i 2.19846 0.657646i
\(599\) 19.2837 0.787912 0.393956 0.919129i \(-0.371106\pi\)
0.393956 + 0.919129i \(0.371106\pi\)
\(600\) 0 0
\(601\) 10.5855 0.431790 0.215895 0.976417i \(-0.430733\pi\)
0.215895 + 0.976417i \(0.430733\pi\)
\(602\) −7.27806 + 2.17715i −0.296632 + 0.0887342i
\(603\) 0 0
\(604\) 25.6216 + 38.9933i 1.04253 + 1.58661i
\(605\) 37.6079i 1.52898i
\(606\) 0 0
\(607\) 34.0722i 1.38295i 0.722401 + 0.691475i \(0.243039\pi\)
−0.722401 + 0.691475i \(0.756961\pi\)
\(608\) 12.8803 + 1.51993i 0.522364 + 0.0616412i
\(609\) 0 0
\(610\) 18.3503 + 61.3435i 0.742981 + 2.48373i
\(611\) −30.9309 −1.25133
\(612\) 0 0
\(613\) −17.3288 −0.699906 −0.349953 0.936767i \(-0.613802\pi\)
−0.349953 + 0.936767i \(0.613802\pi\)
\(614\) −8.20731 27.4364i −0.331220 1.10724i
\(615\) 0 0
\(616\) −10.2376 8.60195i −0.412485 0.346583i
\(617\) 1.76760i 0.0711611i 0.999367 + 0.0355805i \(0.0113280\pi\)
−0.999367 + 0.0355805i \(0.988672\pi\)
\(618\) 0 0
\(619\) 47.0424i 1.89079i 0.325922 + 0.945397i \(0.394325\pi\)
−0.325922 + 0.945397i \(0.605675\pi\)
\(620\) −42.4472 + 27.8911i −1.70472 + 1.12013i
\(621\) 0 0
\(622\) 1.87506 0.560904i 0.0751830 0.0224902i
\(623\) −5.72784 −0.229481
\(624\) 0 0
\(625\) −19.1495 −0.765980
\(626\) 40.8027 12.2057i 1.63080 0.487837i
\(627\) 0 0
\(628\) 37.1898 24.4366i 1.48404 0.975126i
\(629\) 1.16058i 0.0462754i
\(630\) 0 0
\(631\) 14.0147i 0.557916i −0.960303 0.278958i \(-0.910011\pi\)
0.960303 0.278958i \(-0.0899890\pi\)
\(632\) 26.1105 + 21.9389i 1.03862 + 0.872681i
\(633\) 0 0
\(634\) 2.13722 + 7.14457i 0.0848799 + 0.283747i
\(635\) 55.1448 2.18836
\(636\) 0 0
\(637\) 4.97858 0.197258
\(638\) −2.70978 9.05860i −0.107281 0.358633i
\(639\) 0 0
\(640\) 33.5254 16.7722i 1.32521 0.662978i
\(641\) 8.92956i 0.352696i −0.984328 0.176348i \(-0.943572\pi\)
0.984328 0.176348i \(-0.0564285\pi\)
\(642\) 0 0
\(643\) 4.53635i 0.178896i 0.995991 + 0.0894480i \(0.0285103\pi\)
−0.995991 + 0.0894480i \(0.971490\pi\)
\(644\) −8.75330 13.3216i −0.344928 0.524944i
\(645\) 0 0
\(646\) 1.50650 0.450654i 0.0592725 0.0177307i
\(647\) 5.10091 0.200537 0.100269 0.994960i \(-0.468030\pi\)
0.100269 + 0.994960i \(0.468030\pi\)
\(648\) 0 0
\(649\) −6.54262 −0.256820
\(650\) −40.3281 + 12.0637i −1.58180 + 0.473178i
\(651\) 0 0
\(652\) −18.2787 27.8181i −0.715847 1.08944i
\(653\) 26.2535i 1.02738i 0.857976 + 0.513690i \(0.171722\pi\)
−0.857976 + 0.513690i \(0.828278\pi\)
\(654\) 0 0
\(655\) 25.1709i 0.983509i
\(656\) −24.0694 10.4078i −0.939752 0.406356i
\(657\) 0 0
\(658\) 2.51806 + 8.41767i 0.0981641 + 0.328155i
\(659\) 16.0413 0.624881 0.312440 0.949937i \(-0.398854\pi\)
0.312440 + 0.949937i \(0.398854\pi\)
\(660\) 0 0
\(661\) 29.8652 1.16162 0.580811 0.814039i \(-0.302736\pi\)
0.580811 + 0.814039i \(0.302736\pi\)
\(662\) −4.03565 13.4909i −0.156850 0.524337i
\(663\) 0 0
\(664\) 5.89962 7.02142i 0.228949 0.272484i
\(665\) 7.59672i 0.294588i
\(666\) 0 0
\(667\) 11.2713i 0.436427i
\(668\) −15.0108 + 9.86324i −0.580785 + 0.381620i
\(669\) 0 0
\(670\) −14.6858 + 4.39312i −0.567364 + 0.169721i
\(671\) −64.6000 −2.49386
\(672\) 0 0
\(673\) −35.0080 −1.34946 −0.674729 0.738066i \(-0.735739\pi\)
−0.674729 + 0.738066i \(0.735739\pi\)
\(674\) 18.1172 5.41957i 0.697848 0.208754i
\(675\) 0 0
\(676\) 19.7002 12.9446i 0.757701 0.497868i
\(677\) 37.6893i 1.44852i −0.689529 0.724258i \(-0.742182\pi\)
0.689529 0.724258i \(-0.257818\pi\)
\(678\) 0 0
\(679\) 12.0575i 0.462726i
\(680\) 2.92375 3.47970i 0.112121 0.133440i
\(681\) 0 0
\(682\) −14.6858 49.0937i −0.562350 1.87989i
\(683\) 21.5770 0.825620 0.412810 0.910817i \(-0.364547\pi\)
0.412810 + 0.910817i \(0.364547\pi\)
\(684\) 0 0
\(685\) 31.2285 1.19318
\(686\) −0.405301 1.35489i −0.0154745 0.0517300i
\(687\) 0 0
\(688\) 19.7220 + 8.52792i 0.751893 + 0.325124i
\(689\) 4.97972i 0.189712i
\(690\) 0 0
\(691\) 14.0428i 0.534215i 0.963667 + 0.267108i \(0.0860679\pi\)
−0.963667 + 0.267108i \(0.913932\pi\)
\(692\) −3.02844 4.60896i −0.115124 0.175206i
\(693\) 0 0
\(694\) 15.1916 4.54441i 0.576666 0.172504i
\(695\) −53.0143 −2.01095
\(696\) 0 0
\(697\) −3.17935 −0.120426
\(698\) 5.81618 1.73985i 0.220146 0.0658543i
\(699\) 0 0
\(700\) 6.56614 + 9.99296i 0.248177 + 0.377698i
\(701\) 27.9214i 1.05458i −0.849687 0.527288i \(-0.823209\pi\)
0.849687 0.527288i \(-0.176791\pi\)
\(702\) 0 0
\(703\) 5.48677i 0.206937i
\(704\) 6.51810 + 37.2550i 0.245660 + 1.40410i
\(705\) 0 0
\(706\) −0.724481 2.42188i −0.0272662 0.0911488i
\(707\) 14.5665 0.547830
\(708\) 0 0
\(709\) −10.5426 −0.395936 −0.197968 0.980208i \(-0.563434\pi\)
−0.197968 + 0.980208i \(0.563434\pi\)
\(710\) 4.49032 + 15.0108i 0.168519 + 0.563345i
\(711\) 0 0
\(712\) 12.4036 + 10.4219i 0.464844 + 0.390577i
\(713\) 61.0856i 2.28767i
\(714\) 0 0
\(715\) 77.9865i 2.91653i
\(716\) −7.90201 + 5.19223i −0.295312 + 0.194043i
\(717\) 0 0
\(718\) −17.3411 + 5.18741i −0.647165 + 0.193593i
\(719\) −31.8801 −1.18893 −0.594463 0.804123i \(-0.702635\pi\)
−0.594463 + 0.804123i \(0.702635\pi\)
\(720\) 0 0
\(721\) 5.70727 0.212550
\(722\) −18.6208 + 5.57021i −0.692994 + 0.207302i
\(723\) 0 0
\(724\) −14.0288 + 9.21798i −0.521375 + 0.342584i
\(725\) 8.45498i 0.314010i
\(726\) 0 0
\(727\) 46.2070i 1.71372i −0.515546 0.856862i \(-0.672411\pi\)
0.515546 0.856862i \(-0.327589\pi\)
\(728\) −10.7811 9.05860i −0.399573 0.335734i
\(729\) 0 0
\(730\) −2.82065 9.42923i −0.104397 0.348991i
\(731\) 2.60509 0.0963528
\(732\) 0 0
\(733\) 22.4360 0.828691 0.414346 0.910120i \(-0.364010\pi\)
0.414346 + 0.910120i \(0.364010\pi\)
\(734\) 12.2230 + 40.8607i 0.451161 + 1.50820i
\(735\) 0 0
\(736\) −5.28359 + 44.7746i −0.194756 + 1.65041i
\(737\) 15.4655i 0.569678i
\(738\) 0 0
\(739\) 14.0147i 0.515539i −0.966206 0.257769i \(-0.917013\pi\)
0.966206 0.257769i \(-0.0829875\pi\)
\(740\) 8.70862 + 13.2536i 0.320135 + 0.487211i
\(741\) 0 0
\(742\) −1.35520 + 0.405394i −0.0497510 + 0.0148825i
\(743\) 25.9313 0.951327 0.475663 0.879627i \(-0.342208\pi\)
0.475663 + 0.879627i \(0.342208\pi\)
\(744\) 0 0
\(745\) −61.1856 −2.24167
\(746\) −7.06409 + 2.11315i −0.258635 + 0.0773679i
\(747\) 0 0
\(748\) 2.51806 + 3.83221i 0.0920693 + 0.140120i
\(749\) 16.0413i 0.586137i
\(750\) 0 0
\(751\) 2.74338i 0.100108i 0.998747 + 0.0500538i \(0.0159393\pi\)
−0.998747 + 0.0500538i \(0.984061\pi\)
\(752\) 9.86324 22.8101i 0.359675 0.831798i
\(753\) 0 0
\(754\) −2.85363 9.53948i −0.103923 0.347407i
\(755\) 77.2977 2.81315
\(756\) 0 0
\(757\) −15.7992 −0.574233 −0.287116 0.957896i \(-0.592697\pi\)
−0.287116 + 0.957896i \(0.592697\pi\)
\(758\) 6.80348 + 22.7435i 0.247114 + 0.826082i
\(759\) 0 0
\(760\) 13.8223 16.4507i 0.501389 0.596728i
\(761\) 27.0527i 0.980660i −0.871537 0.490330i \(-0.836876\pi\)
0.871537 0.490330i \(-0.163124\pi\)
\(762\) 0 0
\(763\) 1.37169i 0.0496586i
\(764\) 2.48245 1.63116i 0.0898118 0.0590133i
\(765\) 0 0
\(766\) 32.1642 9.62158i 1.16214 0.347642i
\(767\) −6.88994 −0.248781
\(768\) 0 0
\(769\) 39.8715 1.43780 0.718901 0.695113i \(-0.244646\pi\)
0.718901 + 0.695113i \(0.244646\pi\)
\(770\) −21.2236 + 6.34881i −0.764845 + 0.228795i
\(771\) 0 0
\(772\) −13.9572 + 9.17092i −0.502329 + 0.330069i
\(773\) 34.4261i 1.23822i −0.785304 0.619110i \(-0.787493\pi\)
0.785304 0.619110i \(-0.212507\pi\)
\(774\) 0 0
\(775\) 45.8223i 1.64599i
\(776\) −21.9389 + 26.1105i −0.787560 + 0.937313i
\(777\) 0 0
\(778\) −7.20149 24.0740i −0.258186 0.863096i
\(779\) −15.0307 −0.538531
\(780\) 0 0
\(781\) −15.8077 −0.565642
\(782\) 1.56657 + 5.23692i 0.0560203 + 0.187272i
\(783\) 0 0
\(784\) −1.58757 + 3.67146i −0.0566988 + 0.131124i
\(785\) 73.7226i 2.63127i
\(786\) 0 0
\(787\) 24.1151i 0.859610i 0.902922 + 0.429805i \(0.141418\pi\)
−0.902922 + 0.429805i \(0.858582\pi\)
\(788\) 4.20493 + 6.39945i 0.149795 + 0.227971i
\(789\) 0 0
\(790\) 54.1298 16.1923i 1.92585 0.576098i
\(791\)