Properties

Label 624.2.cn.f.305.4
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.4
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31722 + 1.12469i) q^{3} +(1.72616 + 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(0.470140 - 2.96293i) q^{9} +O(q^{10})\) \(q+(-1.31722 + 1.12469i) q^{3} +(1.72616 + 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(0.470140 - 2.96293i) q^{9} +(-1.47004 - 5.48627i) q^{11} +(2.76028 - 2.31967i) q^{13} +(-4.21513 - 0.332337i) q^{15} +(-1.40933 - 2.44104i) q^{17} +(7.85833 + 2.10563i) q^{19} +(1.65527 + 3.47161i) q^{21} +(-1.84516 + 3.19592i) q^{23} +0.959270i q^{25} +(2.71311 + 4.43160i) q^{27} +(-1.95737 - 1.13009i) q^{29} +(-3.13483 + 3.13483i) q^{31} +(8.10673 + 5.57328i) q^{33} +(4.69440 - 2.71031i) q^{35} +(7.36333 - 1.97300i) q^{37} +(-1.02699 + 6.15998i) q^{39} +(-7.02869 + 1.88333i) q^{41} +(0.416760 - 0.240616i) q^{43} +(5.92604 - 4.30296i) q^{45} +(9.57953 - 9.57953i) q^{47} +(1.79209 + 1.03466i) q^{49} +(4.60181 + 1.63032i) q^{51} +0.617097i q^{53} +(6.93266 - 12.0077i) q^{55} +(-12.7193 + 6.06461i) q^{57} +(1.94720 + 0.521752i) q^{59} +(0.667748 + 1.15657i) q^{61} +(-6.08485 - 2.71121i) q^{63} +(8.76881 + 0.760564i) q^{65} +(0.667631 + 2.49163i) q^{67} +(-1.16393 - 6.28497i) q^{69} +(-1.81372 + 6.76890i) q^{71} +(-6.75039 - 6.75039i) q^{73} +(-1.07888 - 1.26357i) q^{75} -12.6121 q^{77} +0.372617 q^{79} +(-8.55794 - 2.78599i) q^{81} +(4.99123 + 4.99123i) q^{83} +(1.78089 - 6.64636i) q^{85} +(3.84930 - 0.712863i) q^{87} +(2.17011 + 8.09895i) q^{89} +(-3.38898 - 7.25352i) q^{91} +(0.603546 - 7.65497i) q^{93} +(9.93009 + 17.1994i) q^{95} +(3.03688 + 0.813729i) q^{97} +(-16.9466 + 1.77632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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
\(3\) −1.31722 + 1.12469i −0.760498 + 0.649341i
\(4\) 0 0
\(5\) 1.72616 + 1.72616i 0.771963 + 0.771963i 0.978449 0.206486i \(-0.0662029\pi\)
−0.206486 + 0.978449i \(0.566203\pi\)
\(6\) 0 0
\(7\) 0.574711 2.14485i 0.217220 0.810677i −0.768153 0.640266i \(-0.778824\pi\)
0.985373 0.170411i \(-0.0545094\pi\)
\(8\) 0 0
\(9\) 0.470140 2.96293i 0.156713 0.987644i
\(10\) 0 0
\(11\) −1.47004 5.48627i −0.443234 1.65417i −0.720557 0.693396i \(-0.756114\pi\)
0.277323 0.960777i \(-0.410553\pi\)
\(12\) 0 0
\(13\) 2.76028 2.31967i 0.765564 0.643360i
\(14\) 0 0
\(15\) −4.21513 0.332337i −1.08834 0.0858091i
\(16\) 0 0
\(17\) −1.40933 2.44104i −0.341813 0.592038i 0.642956 0.765903i \(-0.277708\pi\)
−0.984770 + 0.173865i \(0.944374\pi\)
\(18\) 0 0
\(19\) 7.85833 + 2.10563i 1.80282 + 0.483065i 0.994414 0.105553i \(-0.0336613\pi\)
0.808411 + 0.588618i \(0.200328\pi\)
\(20\) 0 0
\(21\) 1.65527 + 3.47161i 0.361210 + 0.757568i
\(22\) 0 0
\(23\) −1.84516 + 3.19592i −0.384743 + 0.666395i −0.991734 0.128314i \(-0.959043\pi\)
0.606990 + 0.794709i \(0.292377\pi\)
\(24\) 0 0
\(25\) 0.959270i 0.191854i
\(26\) 0 0
\(27\) 2.71311 + 4.43160i 0.522137 + 0.852861i
\(28\) 0 0
\(29\) −1.95737 1.13009i −0.363475 0.209853i 0.307129 0.951668i \(-0.400632\pi\)
−0.670604 + 0.741815i \(0.733965\pi\)
\(30\) 0 0
\(31\) −3.13483 + 3.13483i −0.563031 + 0.563031i −0.930167 0.367136i \(-0.880338\pi\)
0.367136 + 0.930167i \(0.380338\pi\)
\(32\) 0 0
\(33\) 8.10673 + 5.57328i 1.41120 + 0.970184i
\(34\) 0 0
\(35\) 4.69440 2.71031i 0.793499 0.458127i
\(36\) 0 0
\(37\) 7.36333 1.97300i 1.21052 0.324359i 0.403557 0.914955i \(-0.367774\pi\)
0.806968 + 0.590596i \(0.201107\pi\)
\(38\) 0 0
\(39\) −1.02699 + 6.15998i −0.164449 + 0.986386i
\(40\) 0 0
\(41\) −7.02869 + 1.88333i −1.09770 + 0.294127i −0.761826 0.647781i \(-0.775697\pi\)
−0.335870 + 0.941908i \(0.609030\pi\)
\(42\) 0 0
\(43\) 0.416760 0.240616i 0.0635553 0.0366937i −0.467886 0.883789i \(-0.654984\pi\)
0.531441 + 0.847095i \(0.321651\pi\)
\(44\) 0 0
\(45\) 5.92604 4.30296i 0.883402 0.641448i
\(46\) 0 0
\(47\) 9.57953 9.57953i 1.39732 1.39732i 0.589685 0.807633i \(-0.299252\pi\)
0.807633 0.589685i \(-0.200748\pi\)
\(48\) 0 0
\(49\) 1.79209 + 1.03466i 0.256013 + 0.147809i
\(50\) 0 0
\(51\) 4.60181 + 1.63032i 0.644383 + 0.228290i
\(52\) 0 0
\(53\) 0.617097i 0.0847648i 0.999101 + 0.0423824i \(0.0134948\pi\)
−0.999101 + 0.0423824i \(0.986505\pi\)
\(54\) 0 0
\(55\) 6.93266 12.0077i 0.934800 1.61912i
\(56\) 0 0
\(57\) −12.7193 + 6.06461i −1.68472 + 0.803277i
\(58\) 0 0
\(59\) 1.94720 + 0.521752i 0.253504 + 0.0679263i 0.383333 0.923610i \(-0.374776\pi\)
−0.129829 + 0.991536i \(0.541443\pi\)
\(60\) 0 0
\(61\) 0.667748 + 1.15657i 0.0854964 + 0.148084i 0.905603 0.424127i \(-0.139419\pi\)
−0.820106 + 0.572211i \(0.806086\pi\)
\(62\) 0 0
\(63\) −6.08485 2.71121i −0.766619 0.341580i
\(64\) 0 0
\(65\) 8.76881 + 0.760564i 1.08764 + 0.0943364i
\(66\) 0 0
\(67\) 0.667631 + 2.49163i 0.0815641 + 0.304401i 0.994641 0.103385i \(-0.0329674\pi\)
−0.913077 + 0.407787i \(0.866301\pi\)
\(68\) 0 0
\(69\) −1.16393 6.28497i −0.140121 0.756621i
\(70\) 0 0
\(71\) −1.81372 + 6.76890i −0.215249 + 0.803320i 0.770830 + 0.637041i \(0.219842\pi\)
−0.986079 + 0.166279i \(0.946825\pi\)
\(72\) 0 0
\(73\) −6.75039 6.75039i −0.790073 0.790073i 0.191432 0.981506i \(-0.438687\pi\)
−0.981506 + 0.191432i \(0.938687\pi\)
\(74\) 0 0
\(75\) −1.07888 1.26357i −0.124579 0.145904i
\(76\) 0 0
\(77\) −12.6121 −1.43728
\(78\) 0 0
\(79\) 0.372617 0.0419226 0.0209613 0.999780i \(-0.493327\pi\)
0.0209613 + 0.999780i \(0.493327\pi\)
\(80\) 0 0
\(81\) −8.55794 2.78599i −0.950882 0.309554i
\(82\) 0 0
\(83\) 4.99123 + 4.99123i 0.547858 + 0.547858i 0.925821 0.377963i \(-0.123375\pi\)
−0.377963 + 0.925821i \(0.623375\pi\)
\(84\) 0 0
\(85\) 1.78089 6.64636i 0.193164 0.720899i
\(86\) 0 0
\(87\) 3.84930 0.712863i 0.412688 0.0764269i
\(88\) 0 0
\(89\) 2.17011 + 8.09895i 0.230031 + 0.858487i 0.980326 + 0.197384i \(0.0632446\pi\)
−0.750295 + 0.661103i \(0.770089\pi\)
\(90\) 0 0
\(91\) −3.38898 7.25352i −0.355261 0.760376i
\(92\) 0 0
\(93\) 0.603546 7.65497i 0.0625849 0.793783i
\(94\) 0 0
\(95\) 9.93009 + 17.1994i 1.01881 + 1.76462i
\(96\) 0 0
\(97\) 3.03688 + 0.813729i 0.308348 + 0.0826217i 0.409675 0.912232i \(-0.365642\pi\)
−0.101327 + 0.994853i \(0.532309\pi\)
\(98\) 0 0
\(99\) −16.9466 + 1.77632i −1.70319 + 0.178527i
\(100\) 0 0
\(101\) 0.672751 1.16524i 0.0669412 0.115946i −0.830612 0.556851i \(-0.812009\pi\)
0.897553 + 0.440906i \(0.145343\pi\)
\(102\) 0 0
\(103\) 10.0519i 0.990446i −0.868766 0.495223i \(-0.835086\pi\)
0.868766 0.495223i \(-0.164914\pi\)
\(104\) 0 0
\(105\) −3.13530 + 8.84983i −0.305974 + 0.863655i
\(106\) 0 0
\(107\) −12.9381 7.46982i −1.25077 0.722135i −0.279511 0.960143i \(-0.590172\pi\)
−0.971263 + 0.238008i \(0.923506\pi\)
\(108\) 0 0
\(109\) −5.96629 + 5.96629i −0.571467 + 0.571467i −0.932538 0.361071i \(-0.882411\pi\)
0.361071 + 0.932538i \(0.382411\pi\)
\(110\) 0 0
\(111\) −7.48012 + 10.8803i −0.709981 + 1.03272i
\(112\) 0 0
\(113\) −15.1400 + 8.74110i −1.42425 + 0.822294i −0.996659 0.0816760i \(-0.973973\pi\)
−0.427596 + 0.903970i \(0.640639\pi\)
\(114\) 0 0
\(115\) −8.70173 + 2.33162i −0.811440 + 0.217425i
\(116\) 0 0
\(117\) −5.57530 9.26909i −0.515437 0.856927i
\(118\) 0 0
\(119\) −6.04561 + 1.61992i −0.554200 + 0.148498i
\(120\) 0 0
\(121\) −18.4119 + 10.6301i −1.67380 + 0.966372i
\(122\) 0 0
\(123\) 7.14017 10.3859i 0.643807 0.936462i
\(124\) 0 0
\(125\) 6.97495 6.97495i 0.623859 0.623859i
\(126\) 0 0
\(127\) 1.06716 + 0.616127i 0.0946954 + 0.0546724i 0.546600 0.837394i \(-0.315922\pi\)
−0.451904 + 0.892066i \(0.649255\pi\)
\(128\) 0 0
\(129\) −0.278346 + 0.785671i −0.0245070 + 0.0691745i
\(130\) 0 0
\(131\) 7.17983i 0.627305i 0.949538 + 0.313652i \(0.101553\pi\)
−0.949538 + 0.313652i \(0.898447\pi\)
\(132\) 0 0
\(133\) 9.03253 15.6448i 0.783220 1.35658i
\(134\) 0 0
\(135\) −2.96640 + 12.3329i −0.255307 + 1.06145i
\(136\) 0 0
\(137\) 11.6202 + 3.11363i 0.992783 + 0.266015i 0.718419 0.695611i \(-0.244866\pi\)
0.274364 + 0.961626i \(0.411533\pi\)
\(138\) 0 0
\(139\) −1.16445 2.01689i −0.0987677 0.171071i 0.812407 0.583091i \(-0.198157\pi\)
−0.911175 + 0.412020i \(0.864823\pi\)
\(140\) 0 0
\(141\) −1.84434 + 23.3924i −0.155322 + 1.96999i
\(142\) 0 0
\(143\) −16.7841 11.7336i −1.40355 0.981215i
\(144\) 0 0
\(145\) −1.42803 5.32947i −0.118591 0.442588i
\(146\) 0 0
\(147\) −3.52425 + 0.652667i −0.290676 + 0.0538311i
\(148\) 0 0
\(149\) 5.04901 18.8432i 0.413631 1.54369i −0.373930 0.927457i \(-0.621990\pi\)
0.787562 0.616236i \(-0.211343\pi\)
\(150\) 0 0
\(151\) −0.712411 0.712411i −0.0579752 0.0579752i 0.677525 0.735500i \(-0.263053\pi\)
−0.735500 + 0.677525i \(0.763053\pi\)
\(152\) 0 0
\(153\) −7.89521 + 3.02813i −0.638290 + 0.244810i
\(154\) 0 0
\(155\) −10.8224 −0.869279
\(156\) 0 0
\(157\) 17.0306 1.35919 0.679594 0.733588i \(-0.262156\pi\)
0.679594 + 0.733588i \(0.262156\pi\)
\(158\) 0 0
\(159\) −0.694044 0.812853i −0.0550413 0.0644635i
\(160\) 0 0
\(161\) 5.79433 + 5.79433i 0.456657 + 0.456657i
\(162\) 0 0
\(163\) −2.57138 + 9.59651i −0.201406 + 0.751657i 0.789109 + 0.614253i \(0.210542\pi\)
−0.990515 + 0.137404i \(0.956124\pi\)
\(164\) 0 0
\(165\) 4.37313 + 23.6139i 0.340448 + 1.83834i
\(166\) 0 0
\(167\) −2.68928 10.0365i −0.208102 0.776649i −0.988481 0.151342i \(-0.951640\pi\)
0.780379 0.625307i \(-0.215026\pi\)
\(168\) 0 0
\(169\) 2.23828 12.8059i 0.172175 0.985066i
\(170\) 0 0
\(171\) 9.93336 22.2938i 0.759623 1.70485i
\(172\) 0 0
\(173\) 6.65624 + 11.5289i 0.506064 + 0.876529i 0.999975 + 0.00701675i \(0.00223352\pi\)
−0.493911 + 0.869512i \(0.664433\pi\)
\(174\) 0 0
\(175\) 2.05749 + 0.551303i 0.155532 + 0.0416746i
\(176\) 0 0
\(177\) −3.15171 + 1.50274i −0.236897 + 0.112953i
\(178\) 0 0
\(179\) −0.225490 + 0.390560i −0.0168539 + 0.0291918i −0.874329 0.485333i \(-0.838698\pi\)
0.857475 + 0.514525i \(0.172032\pi\)
\(180\) 0 0
\(181\) 0.572791i 0.0425752i −0.999773 0.0212876i \(-0.993223\pi\)
0.999773 0.0212876i \(-0.00677657\pi\)
\(182\) 0 0
\(183\) −2.18036 0.772452i −0.161177 0.0571013i
\(184\) 0 0
\(185\) 16.1160 + 9.30459i 1.18487 + 0.684087i
\(186\) 0 0
\(187\) −11.3204 + 11.3204i −0.827830 + 0.827830i
\(188\) 0 0
\(189\) 11.0644 3.27232i 0.804814 0.238026i
\(190\) 0 0
\(191\) 7.87896 4.54892i 0.570102 0.329148i −0.187088 0.982343i \(-0.559905\pi\)
0.757190 + 0.653195i \(0.226572\pi\)
\(192\) 0 0
\(193\) −13.9688 + 3.74292i −1.00549 + 0.269421i −0.723745 0.690067i \(-0.757581\pi\)
−0.281748 + 0.959488i \(0.590914\pi\)
\(194\) 0 0
\(195\) −12.4059 + 8.86037i −0.888402 + 0.634504i
\(196\) 0 0
\(197\) 6.22190 1.66715i 0.443292 0.118780i −0.0302668 0.999542i \(-0.509636\pi\)
0.473559 + 0.880762i \(0.342969\pi\)
\(198\) 0 0
\(199\) 0.683303 0.394505i 0.0484381 0.0279657i −0.475585 0.879670i \(-0.657764\pi\)
0.524023 + 0.851704i \(0.324430\pi\)
\(200\) 0 0
\(201\) −3.68173 2.53115i −0.259689 0.178534i
\(202\) 0 0
\(203\) −3.54880 + 3.54880i −0.249077 + 0.249077i
\(204\) 0 0
\(205\) −15.3836 8.88172i −1.07444 0.620326i
\(206\) 0 0
\(207\) 8.60181 + 6.96963i 0.597867 + 0.484423i
\(208\) 0 0
\(209\) 46.2083i 3.19629i
\(210\) 0 0
\(211\) −11.5246 + 19.9611i −0.793383 + 1.37418i 0.130478 + 0.991451i \(0.458349\pi\)
−0.923861 + 0.382729i \(0.874984\pi\)
\(212\) 0 0
\(213\) −5.22385 10.9560i −0.357932 0.750693i
\(214\) 0 0
\(215\) 1.13474 + 0.304052i 0.0773885 + 0.0207362i
\(216\) 0 0
\(217\) 4.92211 + 8.52535i 0.334135 + 0.578738i
\(218\) 0 0
\(219\) 16.4839 + 1.29965i 1.11388 + 0.0878221i
\(220\) 0 0
\(221\) −9.55254 3.46875i −0.642574 0.233334i
\(222\) 0 0
\(223\) −3.35292 12.5133i −0.224528 0.837950i −0.982593 0.185771i \(-0.940522\pi\)
0.758065 0.652179i \(-0.226145\pi\)
\(224\) 0 0
\(225\) 2.84225 + 0.450991i 0.189483 + 0.0300661i
\(226\) 0 0
\(227\) −2.62037 + 9.77935i −0.173920 + 0.649079i 0.822813 + 0.568312i \(0.192403\pi\)
−0.996733 + 0.0807663i \(0.974263\pi\)
\(228\) 0 0
\(229\) 6.04210 + 6.04210i 0.399273 + 0.399273i 0.877977 0.478703i \(-0.158893\pi\)
−0.478703 + 0.877977i \(0.658893\pi\)
\(230\) 0 0
\(231\) 16.6129 14.1847i 1.09305 0.933284i
\(232\) 0 0
\(233\) 9.52224 0.623823 0.311911 0.950111i \(-0.399031\pi\)
0.311911 + 0.950111i \(0.399031\pi\)
\(234\) 0 0
\(235\) 33.0716 2.15736
\(236\) 0 0
\(237\) −0.490818 + 0.419079i −0.0318821 + 0.0272221i
\(238\) 0 0
\(239\) −0.346997 0.346997i −0.0224454 0.0224454i 0.695795 0.718240i \(-0.255052\pi\)
−0.718240 + 0.695795i \(0.755052\pi\)
\(240\) 0 0
\(241\) −6.84098 + 25.5309i −0.440667 + 1.64459i 0.286464 + 0.958091i \(0.407520\pi\)
−0.727131 + 0.686499i \(0.759147\pi\)
\(242\) 0 0
\(243\) 14.4061 5.95528i 0.924149 0.382031i
\(244\) 0 0
\(245\) 1.30744 + 4.87943i 0.0835293 + 0.311736i
\(246\) 0 0
\(247\) 26.5756 12.4166i 1.69096 0.790049i
\(248\) 0 0
\(249\) −12.1881 0.960958i −0.772392 0.0608983i
\(250\) 0 0
\(251\) 6.74616 + 11.6847i 0.425814 + 0.737531i 0.996496 0.0836399i \(-0.0266545\pi\)
−0.570682 + 0.821171i \(0.693321\pi\)
\(252\) 0 0
\(253\) 20.2461 + 5.42494i 1.27286 + 0.341063i
\(254\) 0 0
\(255\) 5.12928 + 10.7577i 0.321208 + 0.673671i
\(256\) 0 0
\(257\) −1.24981 + 2.16473i −0.0779610 + 0.135032i −0.902370 0.430962i \(-0.858174\pi\)
0.824409 + 0.565994i \(0.191508\pi\)
\(258\) 0 0
\(259\) 16.9271i 1.05180i
\(260\) 0 0
\(261\) −4.26862 + 5.26827i −0.264221 + 0.326098i
\(262\) 0 0
\(263\) −8.32134 4.80433i −0.513116 0.296248i 0.220998 0.975274i \(-0.429069\pi\)
−0.734114 + 0.679027i \(0.762402\pi\)
\(264\) 0 0
\(265\) −1.06521 + 1.06521i −0.0654353 + 0.0654353i
\(266\) 0 0
\(267\) −11.9673 8.22740i −0.732388 0.503509i
\(268\) 0 0
\(269\) −14.4109 + 8.32012i −0.878646 + 0.507286i −0.870212 0.492678i \(-0.836018\pi\)
−0.00843422 + 0.999964i \(0.502685\pi\)
\(270\) 0 0
\(271\) −30.2838 + 8.11452i −1.83961 + 0.492922i −0.998826 0.0484469i \(-0.984573\pi\)
−0.840785 + 0.541369i \(0.817906\pi\)
\(272\) 0 0
\(273\) 12.6220 + 5.74293i 0.763918 + 0.347578i
\(274\) 0 0
\(275\) 5.26281 1.41017i 0.317360 0.0850362i
\(276\) 0 0
\(277\) −6.36855 + 3.67688i −0.382649 + 0.220923i −0.678970 0.734166i \(-0.737573\pi\)
0.296321 + 0.955088i \(0.404240\pi\)
\(278\) 0 0
\(279\) 7.81447 + 10.7621i 0.467840 + 0.644309i
\(280\) 0 0
\(281\) −5.52193 + 5.52193i −0.329411 + 0.329411i −0.852362 0.522952i \(-0.824831\pi\)
0.522952 + 0.852362i \(0.324831\pi\)
\(282\) 0 0
\(283\) −8.91761 5.14859i −0.530097 0.306052i 0.210959 0.977495i \(-0.432341\pi\)
−0.741056 + 0.671443i \(0.765675\pi\)
\(284\) 0 0
\(285\) −32.4241 11.4871i −1.92064 0.680440i
\(286\) 0 0
\(287\) 16.1578i 0.953768i
\(288\) 0 0
\(289\) 4.52756 7.84197i 0.266327 0.461292i
\(290\) 0 0
\(291\) −4.91543 + 2.34369i −0.288148 + 0.137390i
\(292\) 0 0
\(293\) −27.2842 7.31077i −1.59396 0.427100i −0.650748 0.759294i \(-0.725544\pi\)
−0.943211 + 0.332194i \(0.892211\pi\)
\(294\) 0 0
\(295\) 2.46056 + 4.26182i 0.143259 + 0.248133i
\(296\) 0 0
\(297\) 20.3246 21.3995i 1.17935 1.24172i
\(298\) 0 0
\(299\) 2.32030 + 13.1018i 0.134187 + 0.757696i
\(300\) 0 0
\(301\) −0.276570 1.03217i −0.0159412 0.0594934i
\(302\) 0 0
\(303\) 0.424372 + 2.29151i 0.0243796 + 0.131644i
\(304\) 0 0
\(305\) −0.843792 + 3.14907i −0.0483154 + 0.180315i
\(306\) 0 0
\(307\) 0.0722051 + 0.0722051i 0.00412096 + 0.00412096i 0.709164 0.705043i \(-0.249072\pi\)
−0.705043 + 0.709164i \(0.749072\pi\)
\(308\) 0 0
\(309\) 11.3053 + 13.2406i 0.643137 + 0.753232i
\(310\) 0 0
\(311\) 20.0161 1.13501 0.567504 0.823370i \(-0.307909\pi\)
0.567504 + 0.823370i \(0.307909\pi\)
\(312\) 0 0
\(313\) 0.626697 0.0354230 0.0177115 0.999843i \(-0.494362\pi\)
0.0177115 + 0.999843i \(0.494362\pi\)
\(314\) 0 0
\(315\) −5.82345 15.1834i −0.328114 0.855489i
\(316\) 0 0
\(317\) 14.4492 + 14.4492i 0.811546 + 0.811546i 0.984866 0.173320i \(-0.0554493\pi\)
−0.173320 + 0.984866i \(0.555449\pi\)
\(318\) 0 0
\(319\) −3.32256 + 12.4000i −0.186028 + 0.694265i
\(320\) 0 0
\(321\) 25.4436 4.71197i 1.42012 0.262997i
\(322\) 0 0
\(323\) −5.93508 22.1500i −0.330236 1.23246i
\(324\) 0 0
\(325\) 2.22519 + 2.64785i 0.123431 + 0.146876i
\(326\) 0 0
\(327\) 1.14869 14.5692i 0.0635226 0.805677i
\(328\) 0 0
\(329\) −15.0412 26.0521i −0.829248 1.43630i
\(330\) 0 0
\(331\) 9.05445 + 2.42613i 0.497678 + 0.133352i 0.498922 0.866647i \(-0.333729\pi\)
−0.00124426 + 0.999999i \(0.500396\pi\)
\(332\) 0 0
\(333\) −2.38407 22.7446i −0.130646 1.24640i
\(334\) 0 0
\(335\) −3.14852 + 5.45340i −0.172022 + 0.297951i
\(336\) 0 0
\(337\) 20.6022i 1.12227i −0.827724 0.561136i \(-0.810365\pi\)
0.827724 0.561136i \(-0.189635\pi\)
\(338\) 0 0
\(339\) 10.1117 28.5418i 0.549194 1.55018i
\(340\) 0 0
\(341\) 21.8068 + 12.5902i 1.18091 + 0.681796i
\(342\) 0 0
\(343\) 14.2401 14.2401i 0.768893 0.768893i
\(344\) 0 0
\(345\) 8.83974 12.8580i 0.475916 0.692252i
\(346\) 0 0
\(347\) 20.7808 11.9978i 1.11557 0.644076i 0.175306 0.984514i \(-0.443909\pi\)
0.940267 + 0.340437i \(0.110575\pi\)
\(348\) 0 0
\(349\) −29.5949 + 7.92992i −1.58418 + 0.424479i −0.940216 0.340579i \(-0.889377\pi\)
−0.643961 + 0.765058i \(0.722710\pi\)
\(350\) 0 0
\(351\) 17.7688 + 5.93894i 0.948427 + 0.316997i
\(352\) 0 0
\(353\) −28.6149 + 7.66733i −1.52302 + 0.408091i −0.920733 0.390193i \(-0.872408\pi\)
−0.602282 + 0.798283i \(0.705742\pi\)
\(354\) 0 0
\(355\) −14.8150 + 8.55343i −0.786298 + 0.453969i
\(356\) 0 0
\(357\) 6.14150 8.93324i 0.325043 0.472797i
\(358\) 0 0
\(359\) −9.69605 + 9.69605i −0.511738 + 0.511738i −0.915059 0.403321i \(-0.867856\pi\)
0.403321 + 0.915059i \(0.367856\pi\)
\(360\) 0 0
\(361\) 40.8652 + 23.5935i 2.15080 + 1.24176i
\(362\) 0 0
\(363\) 12.2969 34.7098i 0.645420 1.82179i
\(364\) 0 0
\(365\) 23.3045i 1.21981i
\(366\) 0 0
\(367\) 5.92261 10.2583i 0.309158 0.535477i −0.669020 0.743244i \(-0.733286\pi\)
0.978178 + 0.207767i \(0.0666195\pi\)
\(368\) 0 0
\(369\) 2.27572 + 21.7110i 0.118469 + 1.13023i
\(370\) 0 0
\(371\) 1.32358 + 0.354652i 0.0687169 + 0.0184126i
\(372\) 0 0
\(373\) 12.5599 + 21.7543i 0.650325 + 1.12640i 0.983044 + 0.183369i \(0.0587004\pi\)
−0.332719 + 0.943026i \(0.607966\pi\)
\(374\) 0 0
\(375\) −1.34288 + 17.0322i −0.0693463 + 0.879540i
\(376\) 0 0
\(377\) −8.02434 + 1.42109i −0.413274 + 0.0731901i
\(378\) 0 0
\(379\) 7.78147 + 29.0409i 0.399707 + 1.49173i 0.813612 + 0.581408i \(0.197498\pi\)
−0.413904 + 0.910320i \(0.635835\pi\)
\(380\) 0 0
\(381\) −2.09864 + 0.388654i −0.107517 + 0.0199113i
\(382\) 0 0
\(383\) 3.42225 12.7720i 0.174869 0.652620i −0.821705 0.569913i \(-0.806977\pi\)
0.996574 0.0827069i \(-0.0263565\pi\)
\(384\) 0 0
\(385\) −21.7705 21.7705i −1.10953 1.10953i
\(386\) 0 0
\(387\) −0.516995 1.34795i −0.0262803 0.0685204i
\(388\) 0 0
\(389\) 35.5709 1.80352 0.901759 0.432239i \(-0.142276\pi\)
0.901759 + 0.432239i \(0.142276\pi\)
\(390\) 0 0
\(391\) 10.4018 0.526042
\(392\) 0 0
\(393\) −8.07509 9.45742i −0.407334 0.477064i
\(394\) 0 0
\(395\) 0.643197 + 0.643197i 0.0323627 + 0.0323627i
\(396\) 0 0
\(397\) 0.0698912 0.260837i 0.00350774 0.0130911i −0.964150 0.265359i \(-0.914510\pi\)
0.967658 + 0.252268i \(0.0811763\pi\)
\(398\) 0 0
\(399\) 5.69774 + 30.7665i 0.285244 + 1.54025i
\(400\) 0 0
\(401\) 3.32674 + 12.4156i 0.166130 + 0.620004i 0.997893 + 0.0648745i \(0.0206647\pi\)
−0.831764 + 0.555130i \(0.812669\pi\)
\(402\) 0 0
\(403\) −1.38124 + 15.9248i −0.0688043 + 0.793268i
\(404\) 0 0
\(405\) −9.96332 19.5814i −0.495081 0.973010i
\(406\) 0 0
\(407\) −21.6488 37.4968i −1.07309 1.85865i
\(408\) 0 0
\(409\) −14.0337 3.76033i −0.693924 0.185936i −0.105417 0.994428i \(-0.533618\pi\)
−0.588508 + 0.808492i \(0.700284\pi\)
\(410\) 0 0
\(411\) −18.8083 + 8.96782i −0.927743 + 0.442350i
\(412\) 0 0
\(413\) 2.23816 3.87660i 0.110133 0.190755i
\(414\) 0 0
\(415\) 17.2313i 0.845853i
\(416\) 0 0
\(417\) 3.80223 + 1.34704i 0.186196 + 0.0659650i
\(418\) 0 0
\(419\) 28.4856 + 16.4462i 1.39161 + 0.803448i 0.993494 0.113887i \(-0.0363301\pi\)
0.398118 + 0.917334i \(0.369663\pi\)
\(420\) 0 0
\(421\) −12.6319 + 12.6319i −0.615641 + 0.615641i −0.944410 0.328769i \(-0.893366\pi\)
0.328769 + 0.944410i \(0.393366\pi\)
\(422\) 0 0
\(423\) −23.8798 32.8872i −1.16107 1.59903i
\(424\) 0 0
\(425\) 2.34161 1.35193i 0.113585 0.0655782i
\(426\) 0 0
\(427\) 2.86444 0.767524i 0.138620 0.0371431i
\(428\) 0 0
\(429\) 35.3050 3.42110i 1.70454 0.165172i
\(430\) 0 0
\(431\) −21.3199 + 5.71266i −1.02694 + 0.275169i −0.732693 0.680559i \(-0.761737\pi\)
−0.294252 + 0.955728i \(0.595070\pi\)
\(432\) 0 0
\(433\) 32.4780 18.7512i 1.56079 0.901125i 0.563618 0.826035i \(-0.309409\pi\)
0.997177 0.0750900i \(-0.0239244\pi\)
\(434\) 0 0
\(435\) 7.87503 + 5.41399i 0.377579 + 0.259581i
\(436\) 0 0
\(437\) −21.2293 + 21.2293i −1.01554 + 1.01554i
\(438\) 0 0
\(439\) −18.7404 10.8198i −0.894431 0.516400i −0.0190419 0.999819i \(-0.506062\pi\)
−0.875389 + 0.483419i \(0.839395\pi\)
\(440\) 0 0
\(441\) 3.90817 4.82340i 0.186103 0.229686i
\(442\) 0 0
\(443\) 7.66009i 0.363942i −0.983304 0.181971i \(-0.941752\pi\)
0.983304 0.181971i \(-0.0582477\pi\)
\(444\) 0 0
\(445\) −10.2341 + 17.7260i −0.485145 + 0.840295i
\(446\) 0 0
\(447\) 14.5421 + 30.4992i 0.687817 + 1.44256i
\(448\) 0 0
\(449\) 8.38164 + 2.24585i 0.395554 + 0.105988i 0.451113 0.892467i \(-0.351027\pi\)
−0.0555585 + 0.998455i \(0.517694\pi\)
\(450\) 0 0
\(451\) 20.6649 + 35.7927i 0.973073 + 1.68541i
\(452\) 0 0
\(453\) 1.73964 + 0.137160i 0.0817356 + 0.00644434i
\(454\) 0 0
\(455\) 6.67083 18.3707i 0.312733 0.861231i
\(456\) 0 0
\(457\) 10.2516 + 38.2595i 0.479550 + 1.78970i 0.603439 + 0.797409i \(0.293796\pi\)
−0.123890 + 0.992296i \(0.539537\pi\)
\(458\) 0 0
\(459\) 6.99402 12.8684i 0.326453 0.600645i
\(460\) 0 0
\(461\) −2.25094 + 8.40062i −0.104837 + 0.391256i −0.998327 0.0578275i \(-0.981583\pi\)
0.893490 + 0.449083i \(0.148249\pi\)
\(462\) 0 0
\(463\) −13.9840 13.9840i −0.649893 0.649893i 0.303074 0.952967i \(-0.401987\pi\)
−0.952967 + 0.303074i \(0.901987\pi\)
\(464\) 0 0
\(465\) 14.2555 12.1719i 0.661085 0.564458i
\(466\) 0 0
\(467\) −29.4617 −1.36333 −0.681663 0.731666i \(-0.738743\pi\)
−0.681663 + 0.731666i \(0.738743\pi\)
\(468\) 0 0
\(469\) 5.72787 0.264489
\(470\) 0 0
\(471\) −22.4330 + 19.1541i −1.03366 + 0.882576i
\(472\) 0 0
\(473\) −1.93274 1.93274i −0.0888675 0.0888675i
\(474\) 0 0
\(475\) −2.01987 + 7.53826i −0.0926780 + 0.345879i
\(476\) 0 0
\(477\) 1.82842 + 0.290122i 0.0837175 + 0.0132838i
\(478\) 0 0
\(479\) 8.50742 + 31.7501i 0.388714 + 1.45070i 0.832228 + 0.554433i \(0.187065\pi\)
−0.443514 + 0.896267i \(0.646268\pi\)
\(480\) 0 0
\(481\) 15.7481 22.5265i 0.718054 1.02712i
\(482\) 0 0
\(483\) −14.1492 1.11558i −0.643813 0.0507606i
\(484\) 0 0
\(485\) 3.83752 + 6.64677i 0.174253 + 0.301814i
\(486\) 0 0
\(487\) −11.0631 2.96434i −0.501316 0.134327i −0.000705427 1.00000i \(-0.500225\pi\)
−0.500611 + 0.865672i \(0.666891\pi\)
\(488\) 0 0
\(489\) −7.40604 15.5327i −0.334913 0.702414i
\(490\) 0 0
\(491\) −0.607370 + 1.05200i −0.0274102 + 0.0474759i −0.879405 0.476074i \(-0.842059\pi\)
0.851995 + 0.523550i \(0.175393\pi\)
\(492\) 0 0
\(493\) 6.37070i 0.286922i
\(494\) 0 0
\(495\) −32.3187 26.1863i −1.45262 1.17699i
\(496\) 0 0
\(497\) 13.4759 + 7.78031i 0.604477 + 0.348995i
\(498\) 0 0
\(499\) −21.3336 + 21.3336i −0.955024 + 0.955024i −0.999031 0.0440068i \(-0.985988\pi\)
0.0440068 + 0.999031i \(0.485988\pi\)
\(500\) 0 0
\(501\) 14.8304 + 10.1957i 0.662571 + 0.455510i
\(502\) 0 0
\(503\) 19.6423 11.3405i 0.875808 0.505648i 0.00653389 0.999979i \(-0.497920\pi\)
0.869274 + 0.494331i \(0.164587\pi\)
\(504\) 0 0
\(505\) 3.17267 0.850114i 0.141182 0.0378296i
\(506\) 0 0
\(507\) 11.4543 + 19.3855i 0.508705 + 0.860941i
\(508\) 0 0
\(509\) 19.3215 5.17719i 0.856412 0.229475i 0.196209 0.980562i \(-0.437137\pi\)
0.660203 + 0.751087i \(0.270470\pi\)
\(510\) 0 0
\(511\) −18.3581 + 10.5991i −0.812114 + 0.468874i
\(512\) 0 0
\(513\) 11.9892 + 40.5378i 0.529334 + 1.78979i
\(514\) 0 0
\(515\) 17.3513 17.3513i 0.764588 0.764588i
\(516\) 0 0
\(517\) −66.6382 38.4736i −2.93075 1.69207i
\(518\) 0 0
\(519\) −21.7342 7.69995i −0.954027 0.337990i
\(520\) 0 0
\(521\) 19.4238i 0.850973i 0.904965 + 0.425486i \(0.139897\pi\)
−0.904965 + 0.425486i \(0.860103\pi\)
\(522\) 0 0
\(523\) 10.1755 17.6244i 0.444942 0.770663i −0.553106 0.833111i \(-0.686557\pi\)
0.998048 + 0.0624482i \(0.0198908\pi\)
\(524\) 0 0
\(525\) −3.33021 + 1.58785i −0.145342 + 0.0692996i
\(526\) 0 0
\(527\) 12.0702 + 3.23421i 0.525788 + 0.140884i
\(528\) 0 0
\(529\) 4.69074 + 8.12459i 0.203945 + 0.353243i
\(530\) 0 0
\(531\) 2.46137 5.52414i 0.106814 0.239727i
\(532\) 0 0
\(533\) −15.0324 + 21.5027i −0.651127 + 0.931387i
\(534\) 0 0
\(535\) −9.43915 35.2274i −0.408090 1.52301i
\(536\) 0 0
\(537\) −0.142239 0.768060i −0.00613808 0.0331442i
\(538\) 0 0
\(539\) 3.04200 11.3529i 0.131028 0.489003i
\(540\) 0 0
\(541\) 5.28291 + 5.28291i 0.227130 + 0.227130i 0.811493 0.584363i \(-0.198655\pi\)
−0.584363 + 0.811493i \(0.698655\pi\)
\(542\) 0 0
\(543\) 0.644213 + 0.754492i 0.0276458 + 0.0323784i
\(544\) 0 0
\(545\) −20.5976 −0.882303
\(546\) 0 0
\(547\) −15.2518 −0.652122 −0.326061 0.945349i \(-0.605721\pi\)
−0.326061 + 0.945349i \(0.605721\pi\)
\(548\) 0 0
\(549\) 3.74078 1.43474i 0.159653 0.0612332i
\(550\) 0 0
\(551\) −13.0021 13.0021i −0.553910 0.553910i
\(552\) 0 0
\(553\) 0.214147 0.799207i 0.00910645 0.0339857i
\(554\) 0 0
\(555\) −31.6931 + 5.86935i −1.34530 + 0.249140i
\(556\) 0 0
\(557\) −1.77202 6.61326i −0.0750828 0.280213i 0.918169 0.396188i \(-0.129667\pi\)
−0.993252 + 0.115975i \(0.963001\pi\)
\(558\) 0 0
\(559\) 0.592223 1.63091i 0.0250484 0.0689803i
\(560\) 0 0
\(561\) 2.17951 27.6434i 0.0920190 1.16711i
\(562\) 0 0
\(563\) 9.52928 + 16.5052i 0.401611 + 0.695611i 0.993921 0.110099i \(-0.0351169\pi\)
−0.592309 + 0.805711i \(0.701784\pi\)
\(564\) 0 0
\(565\) −41.2227 11.0456i −1.73425 0.464692i
\(566\) 0 0
\(567\) −10.8939 + 16.7544i −0.457499 + 0.703617i
\(568\) 0 0
\(569\) −3.18974 + 5.52479i −0.133721 + 0.231611i −0.925108 0.379704i \(-0.876026\pi\)
0.791387 + 0.611315i \(0.209359\pi\)
\(570\) 0 0
\(571\) 4.64342i 0.194321i 0.995269 + 0.0971605i \(0.0309760\pi\)
−0.995269 + 0.0971605i \(0.969024\pi\)
\(572\) 0 0
\(573\) −5.26220 + 14.8533i −0.219832 + 0.620507i
\(574\) 0 0
\(575\) −3.06575 1.77001i −0.127851 0.0738145i
\(576\) 0 0
\(577\) −16.3269 + 16.3269i −0.679699 + 0.679699i −0.959932 0.280233i \(-0.909588\pi\)
0.280233 + 0.959932i \(0.409588\pi\)
\(578\) 0 0
\(579\) 14.1903 20.6408i 0.589729 0.857802i
\(580\) 0 0
\(581\) 13.5739 7.83692i 0.563142 0.325130i
\(582\) 0 0
\(583\) 3.38556 0.907159i 0.140216 0.0375707i
\(584\) 0 0
\(585\) 6.37607 25.6238i 0.263618 1.05941i
\(586\) 0 0
\(587\) −17.6852 + 4.73874i −0.729948 + 0.195589i −0.604606 0.796525i \(-0.706669\pi\)
−0.125342 + 0.992114i \(0.540003\pi\)
\(588\) 0 0
\(589\) −31.2353 + 18.0337i −1.28703 + 0.743066i
\(590\) 0 0
\(591\) −6.32059 + 9.19373i −0.259994 + 0.378179i
\(592\) 0 0
\(593\) −11.8285 + 11.8285i −0.485739 + 0.485739i −0.906959 0.421220i \(-0.861602\pi\)
0.421220 + 0.906959i \(0.361602\pi\)
\(594\) 0 0
\(595\) −13.2319 7.63947i −0.542457 0.313188i
\(596\) 0 0
\(597\) −0.456364 + 1.28816i −0.0186777 + 0.0527207i
\(598\) 0 0
\(599\) 36.6793i 1.49867i 0.662188 + 0.749337i \(0.269628\pi\)
−0.662188 + 0.749337i \(0.730372\pi\)
\(600\) 0 0
\(601\) −2.04984 + 3.55043i −0.0836147 + 0.144825i −0.904800 0.425837i \(-0.859980\pi\)
0.821185 + 0.570662i \(0.193313\pi\)
\(602\) 0 0
\(603\) 7.69642 0.806729i 0.313422 0.0328525i
\(604\) 0 0
\(605\) −50.1311 13.4326i −2.03812 0.546112i
\(606\) 0 0
\(607\) −4.15357 7.19419i −0.168588 0.292003i 0.769336 0.638845i \(-0.220587\pi\)
−0.937924 + 0.346842i \(0.887254\pi\)
\(608\) 0 0
\(609\) 0.683249 8.66585i 0.0276866 0.351158i
\(610\) 0 0
\(611\) 4.22084 48.6635i 0.170757 1.96872i
\(612\) 0 0
\(613\) −1.42881 5.33239i −0.0577091 0.215373i 0.931050 0.364892i \(-0.118894\pi\)
−0.988759 + 0.149519i \(0.952227\pi\)
\(614\) 0 0
\(615\) 30.2528 5.60260i 1.21991 0.225919i
\(616\) 0 0
\(617\) 6.17063 23.0291i 0.248420 0.927117i −0.723213 0.690625i \(-0.757336\pi\)
0.971633 0.236492i \(-0.0759978\pi\)
\(618\) 0 0
\(619\) −19.4317 19.4317i −0.781028 0.781028i 0.198976 0.980004i \(-0.436238\pi\)
−0.980004 + 0.198976i \(0.936238\pi\)
\(620\) 0 0
\(621\) −19.1692 + 0.493838i −0.769232 + 0.0198170i
\(622\) 0 0
\(623\) 18.6182 0.745923
\(624\) 0 0
\(625\) 28.8762 1.15505
\(626\) 0 0
\(627\) 51.9701 + 60.8665i 2.07548 + 2.43077i
\(628\) 0 0
\(629\) −15.1935 15.1935i −0.605806 0.605806i
\(630\) 0 0
\(631\) 3.00162 11.2022i 0.119493 0.445953i −0.880091 0.474805i \(-0.842519\pi\)
0.999584 + 0.0288524i \(0.00918527\pi\)
\(632\) 0 0
\(633\) −7.26971 39.2548i −0.288945 1.56024i
\(634\) 0 0
\(635\) 0.778561 + 2.90563i 0.0308963 + 0.115306i
\(636\) 0 0
\(637\) 7.34674 1.30109i 0.291089 0.0515512i
\(638\) 0 0
\(639\) 19.2031 + 8.55626i 0.759662 + 0.338480i
\(640\) 0 0
\(641\) −9.29977 16.1077i −0.367319 0.636215i 0.621826 0.783155i \(-0.286391\pi\)
−0.989145 + 0.146940i \(0.953058\pi\)
\(642\) 0 0
\(643\) −28.9091 7.74616i −1.14006 0.305479i −0.361086 0.932532i \(-0.617594\pi\)
−0.778976 + 0.627054i \(0.784261\pi\)
\(644\) 0 0
\(645\) −1.83667 + 0.875726i −0.0723186 + 0.0344817i
\(646\) 0 0
\(647\) −10.6735 + 18.4871i −0.419619 + 0.726802i −0.995901 0.0904492i \(-0.971170\pi\)
0.576282 + 0.817251i \(0.304503\pi\)
\(648\) 0 0
\(649\) 11.4499i 0.449447i
\(650\) 0 0
\(651\) −16.0719 5.69391i −0.629907 0.223162i
\(652\) 0 0
\(653\) −18.3357 10.5861i −0.717533 0.414268i 0.0963112 0.995351i \(-0.469296\pi\)
−0.813844 + 0.581084i \(0.802629\pi\)
\(654\) 0 0
\(655\) −12.3936 + 12.3936i −0.484256 + 0.484256i
\(656\) 0 0
\(657\) −23.1746 + 16.8273i −0.904126 + 0.656496i
\(658\) 0 0
\(659\) −30.9228 + 17.8533i −1.20458 + 0.695464i −0.961570 0.274559i \(-0.911468\pi\)
−0.243010 + 0.970024i \(0.578135\pi\)
\(660\) 0 0
\(661\) −17.7357 + 4.75228i −0.689840 + 0.184842i −0.586675 0.809822i \(-0.699564\pi\)
−0.103165 + 0.994664i \(0.532897\pi\)
\(662\) 0 0
\(663\) 16.4841 6.17455i 0.640189 0.239800i
\(664\) 0 0
\(665\) 42.5971 11.4139i 1.65184 0.442610i
\(666\) 0 0
\(667\) 7.22336 4.17041i 0.279690 0.161479i
\(668\) 0 0
\(669\) 18.4901 + 12.7117i 0.714868 + 0.491464i
\(670\) 0 0
\(671\) 5.36366 5.36366i 0.207062 0.207062i
\(672\) 0 0
\(673\) −25.8577 14.9289i −0.996740 0.575468i −0.0894579 0.995991i \(-0.528513\pi\)
−0.907282 + 0.420522i \(0.861847\pi\)
\(674\) 0 0
\(675\) −4.25110 + 2.60260i −0.163625 + 0.100174i
\(676\) 0 0
\(677\) 21.5956i 0.829988i 0.909824 + 0.414994i \(0.136216\pi\)
−0.909824 + 0.414994i \(0.863784\pi\)
\(678\) 0 0
\(679\) 3.49065 6.04599i 0.133959 0.232024i
\(680\) 0 0
\(681\) −7.54715 15.8287i −0.289207 0.606556i
\(682\) 0 0
\(683\) 33.6457 + 9.01534i 1.28742 + 0.344962i 0.836679 0.547694i \(-0.184494\pi\)
0.450738 + 0.892656i \(0.351161\pi\)
\(684\) 0 0
\(685\) 14.6838 + 25.4330i 0.561038 + 0.971746i
\(686\) 0 0
\(687\) −14.7543 1.16328i −0.562911 0.0443820i
\(688\) 0 0
\(689\) 1.43146 + 1.70336i 0.0545343 + 0.0648929i
\(690\) 0 0
\(691\) 7.05147 + 26.3164i 0.268250 + 1.00112i 0.960231 + 0.279208i \(0.0900718\pi\)
−0.691980 + 0.721916i \(0.743262\pi\)
\(692\) 0 0
\(693\) −5.92944 + 37.3687i −0.225241 + 1.41952i
\(694\) 0 0
\(695\) 1.47145 5.49152i 0.0558152 0.208305i
\(696\) 0 0
\(697\) 14.5030 + 14.5030i 0.549342 + 0.549342i
\(698\) 0 0
\(699\) −12.5429 + 10.7096i −0.474416 + 0.405073i
\(700\) 0 0
\(701\) 7.80915 0.294948 0.147474 0.989066i \(-0.452886\pi\)
0.147474 + 0.989066i \(0.452886\pi\)
\(702\) 0 0
\(703\) 62.0179 2.33905
\(704\) 0 0
\(705\) −43.5627 + 37.1954i −1.64066 + 1.40086i
\(706\) 0 0
\(707\) −2.11262 2.11262i −0.0794534 0.0794534i
\(708\) 0 0
\(709\) 8.07769 30.1463i 0.303364 1.13217i −0.630981 0.775799i \(-0.717347\pi\)
0.934345 0.356371i \(-0.115986\pi\)
\(710\) 0 0
\(711\) 0.175182 1.10404i 0.00656984 0.0414047i
\(712\) 0 0
\(713\) −4.23438 15.8029i −0.158579 0.591824i
\(714\) 0 0
\(715\) −8.71785 49.2261i −0.326029 1.84095i
\(716\) 0 0
\(717\) 0.847337 + 0.0668072i 0.0316444 + 0.00249496i
\(718\) 0 0
\(719\) 2.01546 + 3.49089i 0.0751641 + 0.130188i 0.901158 0.433492i \(-0.142719\pi\)
−0.825993 + 0.563680i \(0.809385\pi\)
\(720\) 0 0
\(721\) −21.5599 5.77695i −0.802932 0.215145i
\(722\) 0 0
\(723\) −19.7033 41.3238i −0.732773 1.53685i
\(724\) 0 0
\(725\) 1.08406 1.87765i 0.0402611 0.0697342i
\(726\) 0 0
\(727\) 26.5507i 0.984711i 0.870394 + 0.492356i \(0.163864\pi\)
−0.870394 + 0.492356i \(0.836136\pi\)
\(728\) 0 0
\(729\) −12.2781 + 24.0468i −0.454745 + 0.890622i
\(730\) 0 0
\(731\) −1.17471 0.678217i −0.0434481 0.0250848i
\(732\) 0 0
\(733\) 15.7035 15.7035i 0.580021 0.580021i −0.354888 0.934909i \(-0.615481\pi\)
0.934909 + 0.354888i \(0.115481\pi\)
\(734\) 0 0
\(735\) −7.21004 4.95682i −0.265946 0.182835i
\(736\) 0 0
\(737\) 12.6883 7.32561i 0.467380 0.269842i
\(738\) 0 0
\(739\) 6.55841 1.75732i 0.241255 0.0646441i −0.136165 0.990686i \(-0.543478\pi\)
0.377420 + 0.926042i \(0.376811\pi\)
\(740\) 0 0
\(741\) −21.0410 + 46.2447i −0.772962 + 1.69884i
\(742\) 0 0
\(743\) 40.6931 10.9037i 1.49288 0.400017i 0.582174 0.813064i \(-0.302202\pi\)
0.910709 + 0.413047i \(0.135536\pi\)
\(744\) 0 0
\(745\) 41.2418 23.8110i 1.51098 0.872366i
\(746\) 0 0
\(747\) 17.1352 12.4421i 0.626946 0.455232i
\(748\) 0 0
\(749\) −23.4573 + 23.4573i −0.857112 + 0.857112i
\(750\) 0 0
\(751\) 31.3813 + 18.1180i 1.14512 + 0.661135i 0.947693 0.319183i \(-0.103408\pi\)
0.197426 + 0.980318i \(0.436742\pi\)
\(752\) 0 0
\(753\) −22.0278 7.80397i −0.802739 0.284392i
\(754\) 0 0
\(755\) 2.45947i 0.0895093i
\(756\) 0 0
\(757\) −3.17824 + 5.50487i −0.115515 + 0.200078i −0.917986 0.396614i \(-0.870185\pi\)
0.802470 + 0.596692i \(0.203519\pi\)
\(758\) 0 0
\(759\) −32.7700 + 15.6248i −1.18948 + 0.567145i
\(760\) 0 0
\(761\) −21.0411 5.63796i −0.762741 0.204376i −0.143579 0.989639i \(-0.545861\pi\)
−0.619162 + 0.785263i \(0.712528\pi\)
\(762\) 0 0
\(763\) 9.36791 + 16.2257i 0.339141 + 0.587410i
\(764\) 0 0
\(765\) −18.8554 8.40137i −0.681720 0.303752i
\(766\) 0 0
\(767\) 6.58512 3.07669i 0.237775 0.111093i
\(768\) 0 0
\(769\) −3.69721 13.7982i −0.133325 0.497575i 0.866674 0.498874i \(-0.166253\pi\)
−0.999999 + 0.00129915i \(0.999586\pi\)
\(770\) 0 0
\(771\) −0.788382 4.25708i −0.0283929 0.153315i
\(772\) 0 0
\(773\) −2.17937 + 8.13353i −0.0783866 + 0.292543i −0.993980 0.109563i \(-0.965055\pi\)
0.915593 + 0.402106i \(0.131722\pi\)
\(774\) 0 0
\(775\) −3.00714 3.00714i −0.108020 0.108020i
\(776\) 0 0
\(777\) 19.0378 + 22.2968i 0.682978 + 0.799893i
\(778\) 0 0
\(779\) −59.1994 −2.12104
\(780\) 0 0
\(781\) 39.8022 1.42424
\(782\) 0 0
\(783\) −0.302456 11.7404i −0.0108089 0.419566i
\(784\) 0 0
\(785\) 29.3975 + 29.3975i 1.04924 + 1.04924i
\(786\) 0 0
\(787\) −8.57267 + 31.9936i −0.305583 + 1.14045i 0.626860 + 0.779132i \(0.284340\pi\)
−0.932443 + 0.361318i \(0.882327\pi\)
\(788\) 0 0
\(789\) 16.3644 3.03058i 0.582589 0.107891i
\(790\) 0 0
\(791\) 10.0472 + 37.4967i 0.357238 + 1.33323i
\(792\) 0 0
\(793\) 4.52604 + 1.64351i 0.160724 + 0.0583628i
\(794\) 0 0
\(795\) 0.205084 2.60115i 0.00727359 0.0922532i
\(796\) 0 0
\(797\) 27.4840 +