Properties

Label 624.2.cn.f.305.6
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 305.6
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.315401 + 1.70309i) q^{3} +(-1.72616 - 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(-2.80104 - 1.07431i) q^{9} +O(q^{10})\) \(q+(-0.315401 + 1.70309i) q^{3} +(-1.72616 - 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(-2.80104 - 1.07431i) q^{9} +(1.47004 + 5.48627i) q^{11} +(2.76028 - 2.31967i) q^{13} +(3.48425 - 2.39538i) q^{15} +(1.40933 + 2.44104i) q^{17} +(7.85833 + 2.10563i) q^{19} +(3.47161 + 1.65527i) q^{21} +(1.84516 - 3.19592i) q^{23} +0.959270i q^{25} +(2.71311 - 4.43160i) q^{27} +(1.95737 + 1.13009i) q^{29} +(-3.13483 + 3.13483i) q^{31} +(-9.80727 + 0.773242i) q^{33} +(-4.69440 + 2.71031i) q^{35} +(7.36333 - 1.97300i) q^{37} +(3.08001 + 5.43263i) q^{39} +(7.02869 - 1.88333i) q^{41} +(0.416760 - 0.240616i) q^{43} +(2.98062 + 6.68949i) q^{45} +(-9.57953 + 9.57953i) q^{47} +(1.79209 + 1.03466i) q^{49} +(-4.60181 + 1.63032i) q^{51} -0.617097i q^{53} +(6.93266 - 12.0077i) q^{55} +(-6.06461 + 12.7193i) q^{57} +(-1.94720 - 0.521752i) q^{59} +(0.667748 + 1.15657i) q^{61} +(-3.91403 + 5.39040i) q^{63} +(-8.76881 - 0.760564i) q^{65} +(0.667631 + 2.49163i) q^{67} +(4.86098 + 4.15048i) q^{69} +(1.81372 - 6.76890i) q^{71} +(-6.75039 - 6.75039i) q^{73} +(-1.63372 - 0.302554i) q^{75} +12.6121 q^{77} +0.372617 q^{79} +(6.69170 + 6.01840i) q^{81} +(-4.99123 - 4.99123i) q^{83} +(1.78089 - 6.64636i) q^{85} +(-2.54201 + 2.97716i) q^{87} +(-2.17011 - 8.09895i) q^{89} +(-3.38898 - 7.25352i) q^{91} +(-4.35017 - 6.32762i) q^{93} +(-9.93009 - 17.1994i) q^{95} +(3.03688 + 0.813729i) q^{97} +(1.77632 - 16.9466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

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
\(3\) −0.315401 + 1.70309i −0.182097 + 0.983281i
\(4\) 0 0
\(5\) −1.72616 1.72616i −0.771963 0.771963i 0.206486 0.978449i \(-0.433797\pi\)
−0.978449 + 0.206486i \(0.933797\pi\)
\(6\) 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
\(9\) −2.80104 1.07431i −0.933682 0.358104i
\(10\) 0 0
\(11\) 1.47004 + 5.48627i 0.443234 + 1.65417i 0.720557 + 0.693396i \(0.243886\pi\)
−0.277323 + 0.960777i \(0.589447\pi\)
\(12\) 0 0
\(13\) 2.76028 2.31967i 0.765564 0.643360i
\(14\) 0 0
\(15\) 3.48425 2.39538i 0.899628 0.618484i
\(16\) 0 0
\(17\) 1.40933 + 2.44104i 0.341813 + 0.592038i 0.984770 0.173865i \(-0.0556256\pi\)
−0.642956 + 0.765903i \(0.722292\pi\)
\(18\) 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
\(21\) 3.47161 + 1.65527i 0.757568 + 0.361210i
\(22\) 0 0
\(23\) 1.84516 3.19592i 0.384743 0.666395i −0.606990 0.794709i \(-0.707623\pi\)
0.991734 + 0.128314i \(0.0409566\pi\)
\(24\) 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 0.670604 0.741815i \(-0.266035\pi\)
−0.307129 + 0.951668i \(0.599368\pi\)
\(30\) 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
\(33\) −9.80727 + 0.773242i −1.70723 + 0.134604i
\(34\) 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
\(39\) 3.08001 + 5.43263i 0.493197 + 0.869918i
\(40\) 0 0
\(41\) 7.02869 1.88333i 1.09770 0.294127i 0.335870 0.941908i \(-0.390970\pi\)
0.761826 + 0.647781i \(0.224303\pi\)
\(42\) 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
\(45\) 2.98062 + 6.68949i 0.444324 + 0.997211i
\(46\) 0 0
\(47\) −9.57953 + 9.57953i −1.39732 + 1.39732i −0.589685 + 0.807633i \(0.700748\pi\)
−0.807633 + 0.589685i \(0.799252\pi\)
\(48\) 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 \(-0.986505\pi\)
0.999101 0.0423824i \(-0.0134948\pi\)
\(54\) 0 0
\(55\) 6.93266 12.0077i 0.934800 1.61912i
\(56\) 0 0
\(57\) −6.06461 + 12.7193i −0.803277 + 1.68472i
\(58\) 0 0
\(59\) −1.94720 0.521752i −0.253504 0.0679263i 0.129829 0.991536i \(-0.458557\pi\)
−0.383333 + 0.923610i \(0.625224\pi\)
\(60\) 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
\(63\) −3.91403 + 5.39040i −0.493121 + 0.679127i
\(64\) 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
\(69\) 4.86098 + 4.15048i 0.585193 + 0.499659i
\(70\) 0 0
\(71\) 1.81372 6.76890i 0.215249 0.803320i −0.770830 0.637041i \(-0.780158\pi\)
0.986079 0.166279i \(-0.0531752\pi\)
\(72\) 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
\(75\) −1.63372 0.302554i −0.188646 0.0349360i
\(76\) 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
\(81\) 6.69170 + 6.01840i 0.743523 + 0.668711i
\(82\) 0 0
\(83\) −4.99123 4.99123i −0.547858 0.547858i 0.377963 0.925821i \(-0.376625\pi\)
−0.925821 + 0.377963i \(0.876625\pi\)
\(84\) 0 0
\(85\) 1.78089 6.64636i 0.193164 0.720899i
\(86\) 0 0
\(87\) −2.54201 + 2.97716i −0.272532 + 0.319185i
\(88\) 0 0
\(89\) −2.17011 8.09895i −0.230031 0.858487i −0.980326 0.197384i \(-0.936755\pi\)
0.750295 0.661103i \(-0.229911\pi\)
\(90\) 0 0
\(91\) −3.38898 7.25352i −0.355261 0.760376i
\(92\) 0 0
\(93\) −4.35017 6.32762i −0.451092 0.656144i
\(94\) 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
\(99\) 1.77632 16.9466i 0.178527 1.70319i
\(100\) 0 0
\(101\) −0.672751 + 1.16524i −0.0669412 + 0.115946i −0.897553 0.440906i \(-0.854657\pi\)
0.830612 + 0.556851i \(0.187991\pi\)
\(102\) 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 0.971263 0.238008i \(-0.0764943\pi\)
0.279511 + 0.960143i \(0.409828\pi\)
\(108\) 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
\(111\) 1.03780 + 13.1627i 0.0985034 + 1.24935i
\(112\) 0 0
\(113\) 15.1400 8.74110i 1.42425 0.822294i 0.427596 0.903970i \(-0.359361\pi\)
0.996659 + 0.0816760i \(0.0260273\pi\)
\(114\) 0 0
\(115\) −8.70173 + 2.33162i −0.811440 + 0.217425i
\(116\) 0 0
\(117\) −10.2237 + 3.53209i −0.945183 + 0.326542i
\(118\) 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
\(123\) 0.990633 + 12.5645i 0.0893224 + 1.13290i
\(124\) 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 \(-0.898447\pi\)
0.949538 0.313652i \(-0.101553\pi\)
\(132\) 0 0
\(133\) 9.03253 15.6448i 0.783220 1.35658i
\(134\) 0 0
\(135\) −12.3329 + 2.96640i −1.06145 + 0.255307i
\(136\) 0 0
\(137\) −11.6202 3.11363i −0.992783 0.266015i −0.274364 0.961626i \(-0.588467\pi\)
−0.718419 + 0.695611i \(0.755134\pi\)
\(138\) 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
\(141\) −13.2934 19.3362i −1.11951 1.62840i
\(142\) 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
\(147\) −2.32735 + 2.72576i −0.191957 + 0.224817i
\(148\) 0 0
\(149\) −5.04901 + 18.8432i −0.413631 + 1.54369i 0.373930 + 0.927457i \(0.378010\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(150\) 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
\(153\) −1.32517 8.35151i −0.107133 0.675180i
\(154\) 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
\(159\) 1.05097 + 0.194633i 0.0833476 + 0.0154354i
\(160\) 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
\(165\) 18.2637 + 15.5942i 1.42183 + 1.21401i
\(166\) 0 0
\(167\) 2.68928 + 10.0365i 0.208102 + 0.776649i 0.988481 + 0.151342i \(0.0483595\pi\)
−0.780379 + 0.625307i \(0.784974\pi\)
\(168\) 0 0
\(169\) 2.23828 12.8059i 0.172175 0.985066i
\(170\) 0 0
\(171\) −19.7494 14.3403i −1.51028 1.09663i
\(172\) 0 0
\(173\) −6.65624 11.5289i −0.506064 0.876529i −0.999975 0.00701675i \(-0.997766\pi\)
0.493911 0.869512i \(-0.335567\pi\)
\(174\) 0 0
\(175\) 2.05749 + 0.551303i 0.155532 + 0.0416746i
\(176\) 0 0
\(177\) 1.50274 3.15171i 0.112953 0.236897i
\(178\) 0 0
\(179\) 0.225490 0.390560i 0.0168539 0.0291918i −0.857475 0.514525i \(-0.827968\pi\)
0.874329 + 0.485333i \(0.161302\pi\)
\(180\) 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
\(189\) −7.94586 8.36609i −0.577976 0.608544i
\(190\) 0 0
\(191\) −7.87896 + 4.54892i −0.570102 + 0.329148i −0.757190 0.653195i \(-0.773428\pi\)
0.187088 + 0.982343i \(0.440095\pi\)
\(192\) 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
\(195\) 4.06100 14.6942i 0.290814 1.05227i
\(196\) 0 0
\(197\) −6.22190 + 1.66715i −0.443292 + 0.118780i −0.473559 0.880762i \(-0.657031\pi\)
0.0302668 + 0.999542i \(0.490364\pi\)
\(198\) 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
\(201\) −4.45405 + 0.351174i −0.314164 + 0.0247699i
\(202\) 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
\(213\) 10.9560 + 5.22385i 0.750693 + 0.357932i
\(214\) 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
\(219\) 13.6256 9.36746i 0.920734 0.632994i
\(220\) 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
\(225\) 1.03056 2.68696i 0.0687037 0.179130i
\(226\) 0 0
\(227\) 2.62037 9.77935i 0.173920 0.649079i −0.822813 0.568312i \(-0.807597\pi\)
0.996733 0.0807663i \(-0.0257368\pi\)
\(228\) 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
\(231\) −3.97786 + 21.4795i −0.261724 + 1.41325i
\(232\) 0 0
\(233\) −9.52224 −0.623823 −0.311911 0.950111i \(-0.600969\pi\)
−0.311911 + 0.950111i \(0.600969\pi\)
\(234\) 0 0
\(235\) 33.0716 2.15736
\(236\) 0 0
\(237\) −0.117524 + 0.634600i −0.00763398 + 0.0412217i
\(238\) 0 0
\(239\) 0.346997 + 0.346997i 0.0224454 + 0.0224454i 0.718240 0.695795i \(-0.244948\pi\)
−0.695795 + 0.718240i \(0.744948\pi\)
\(240\) 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
\(243\) −12.3605 + 9.49838i −0.792923 + 0.609321i
\(244\) 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
\(249\) 10.0748 6.92628i 0.638462 0.438935i
\(250\) 0 0
\(251\) −6.74616 11.6847i −0.425814 0.737531i 0.570682 0.821171i \(-0.306679\pi\)
−0.996496 + 0.0836399i \(0.973345\pi\)
\(252\) 0 0
\(253\) 20.2461 + 5.42494i 1.27286 + 0.341063i
\(254\) 0 0
\(255\) 10.7577 + 5.12928i 0.673671 + 0.321208i
\(256\) 0 0
\(257\) 1.24981 2.16473i 0.0779610 0.135032i −0.824409 0.565994i \(-0.808492\pi\)
0.902370 + 0.430962i \(0.141826\pi\)
\(258\) 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 0.734114 0.679027i \(-0.237598\pi\)
−0.220998 + 0.975274i \(0.570931\pi\)
\(264\) 0 0
\(265\) −1.06521 + 1.06521i −0.0654353 + 0.0654353i
\(266\) 0 0
\(267\) 14.4777 1.14148i 0.886021 0.0698572i
\(268\) 0 0
\(269\) 14.4109 8.32012i 0.878646 0.507286i 0.00843422 0.999964i \(-0.497315\pi\)
0.870212 + 0.492678i \(0.163982\pi\)
\(270\) 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
\(273\) 13.4223 3.48398i 0.812355 0.210860i
\(274\) 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
\(279\) 12.1486 5.41300i 0.727316 0.324068i
\(280\) 0 0
\(281\) 5.52193 5.52193i 0.329411 0.329411i −0.522952 0.852362i \(-0.675169\pi\)
0.852362 + 0.522952i \(0.175169\pi\)
\(282\) 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
\(291\) −2.34369 + 4.91543i −0.137390 + 0.288148i
\(292\) 0 0
\(293\) 27.2842 + 7.31077i 1.59396 + 0.427100i 0.943211 0.332194i \(-0.107789\pi\)
0.650748 + 0.759294i \(0.274456\pi\)
\(294\) 0 0
\(295\) 2.46056 + 4.26182i 0.143259 + 0.248133i
\(296\) 0 0
\(297\) 28.3013 + 8.37020i 1.64221 + 0.485688i
\(298\) 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
\(303\) −1.77232 1.51327i −0.101817 0.0869353i
\(304\) 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
\(309\) 17.1194 + 3.17039i 0.973886 + 0.180357i
\(310\) 0 0
\(311\) −20.0161 −1.13501 −0.567504 0.823370i \(-0.692091\pi\)
−0.567504 + 0.823370i \(0.692091\pi\)
\(312\) 0 0
\(313\) 0.626697 0.0354230 0.0177115 0.999843i \(-0.494362\pi\)
0.0177115 + 0.999843i \(0.494362\pi\)
\(314\) 0 0
\(315\) 16.0610 2.54845i 0.904932 0.143589i
\(316\) 0 0
\(317\) −14.4492 14.4492i −0.811546 0.811546i 0.173320 0.984866i \(-0.444551\pi\)
−0.984866 + 0.173320i \(0.944551\pi\)
\(318\) 0 0
\(319\) −3.32256 + 12.4000i −0.186028 + 0.694265i
\(320\) 0 0
\(321\) −16.8025 + 19.6788i −0.937823 + 1.09836i
\(322\) 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
\(327\) −8.27938 12.0429i −0.457850 0.665975i
\(328\) 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
\(333\) −22.7446 2.38407i −1.24640 0.130646i
\(334\) 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
\(345\) −1.22643 15.5552i −0.0660289 0.837466i
\(346\) 0 0
\(347\) −20.7808 + 11.9978i −1.11557 + 0.644076i −0.940267 0.340437i \(-0.889425\pi\)
−0.175306 + 0.984514i \(0.556091\pi\)
\(348\) 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
\(351\) −2.79091 18.5259i −0.148968 0.988842i
\(352\) 0 0
\(353\) 28.6149 7.66733i 1.52302 0.408091i 0.602282 0.798283i \(-0.294258\pi\)
0.920733 + 0.390193i \(0.127592\pi\)
\(354\) 0 0
\(355\) −14.8150 + 8.55343i −0.786298 + 0.453969i
\(356\) 0 0
\(357\) 0.852077 + 10.8072i 0.0450967 + 0.571976i
\(358\) 0 0
\(359\) 9.69605 9.69605i 0.511738 0.511738i −0.403321 0.915059i \(-0.632144\pi\)
0.915059 + 0.403321i \(0.132144\pi\)
\(360\) 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
\(369\) −21.7110 2.27572i −1.13023 0.118469i
\(370\) 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
\(375\) −9.67908 14.0789i −0.499826 0.727031i
\(376\) 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
\(381\) −1.38590 + 1.62315i −0.0710020 + 0.0831565i
\(382\) 0 0
\(383\) −3.42225 + 12.7720i −0.174869 + 0.652620i 0.821705 + 0.569913i \(0.193023\pi\)
−0.996574 + 0.0827069i \(0.973643\pi\)
\(384\) 0 0
\(385\) −21.7705 21.7705i −1.10953 1.10953i
\(386\) 0 0
\(387\) −1.42586 + 0.226247i −0.0724806 + 0.0115008i
\(388\) 0 0
\(389\) −35.5709 −1.80352 −0.901759 0.432239i \(-0.857724\pi\)
−0.901759 + 0.432239i \(0.857724\pi\)
\(390\) 0 0
\(391\) 10.4018 0.526042
\(392\) 0 0
\(393\) 12.2279 + 2.26452i 0.616817 + 0.114230i
\(394\) 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
\(399\) 23.7957 + 20.3176i 1.19127 + 1.01715i
\(400\) 0 0
\(401\) −3.32674 12.4156i −0.166130 0.620004i −0.997893 0.0648745i \(-0.979335\pi\)
0.831764 0.555130i \(-0.187331\pi\)
\(402\) 0 0
\(403\) −1.38124 + 15.9248i −0.0688043 + 0.793268i
\(404\) 0 0
\(405\) −1.16223 21.9397i −0.0577519 1.09019i
\(406\) 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
\(411\) 8.96782 18.8083i 0.442350 0.927743i
\(412\) 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 −0.398118 0.917334i \(-0.630337\pi\)
−0.993494 + 0.113887i \(0.963670\pi\)
\(420\) 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
\(423\) 37.1241 16.5413i 1.80504 0.804265i
\(424\) 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
\(429\) −25.2771 + 24.8840i −1.22039 + 1.20141i
\(430\) 0 0
\(431\) 21.3199 5.71266i 1.02694 0.275169i 0.294252 0.955728i \(-0.404930\pi\)
0.732693 + 0.680559i \(0.238263\pi\)
\(432\) 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
\(435\) 9.52697 0.751142i 0.456783 0.0360145i
\(436\) 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 \(0.0582477\pi\)
−0.983304 + 0.181971i \(0.941752\pi\)
\(444\) 0 0
\(445\) −10.2341 + 17.7260i −0.485145 + 0.840295i
\(446\) 0 0
\(447\) −30.4992 14.5421i −1.44256 0.687817i
\(448\) 0 0
\(449\) −8.38164 2.24585i −0.395554 0.105988i 0.0555585 0.998455i \(-0.482306\pi\)
−0.451113 + 0.892467i \(0.648973\pi\)
\(450\) 0 0
\(451\) 20.6649 + 35.7927i 0.973073 + 1.68541i
\(452\) 0 0
\(453\) 1.43800 0.988606i 0.0675629 0.0464488i
\(454\) 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
\(459\) 14.6414 + 0.377192i 0.683400 + 0.0176058i
\(460\) 0 0
\(461\) 2.25094 8.40062i 0.104837 0.391256i −0.893490 0.449083i \(-0.851751\pi\)
0.998327 + 0.0578275i \(0.0184173\pi\)
\(462\) 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
\(465\) −3.41340 + 18.4316i −0.158293 + 0.854745i
\(466\) 0 0
\(467\) 29.4617 1.36333 0.681663 0.731666i \(-0.261257\pi\)
0.681663 + 0.731666i \(0.261257\pi\)
\(468\) 0 0
\(469\) 5.72787 0.264489
\(470\) 0 0
\(471\) −5.37146 + 29.0047i −0.247504 + 1.33646i
\(472\) 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
\(477\) −0.662956 + 1.72852i −0.0303547 + 0.0791434i
\(478\) 0 0
\(479\) −8.50742 31.7501i −0.388714 1.45070i −0.832228 0.554433i \(-0.812935\pi\)
0.443514 0.896267i \(-0.353732\pi\)
\(480\) 0 0
\(481\) 15.7481 22.5265i 0.718054 1.02712i
\(482\) 0 0
\(483\) 11.6958 8.04074i 0.532178 0.365866i
\(484\) 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
\(489\) −15.5327 7.40604i −0.702414 0.334913i
\(490\) 0 0
\(491\) 0.607370 1.05200i 0.0274102 0.0474759i −0.851995 0.523550i \(-0.824607\pi\)
0.879405 + 0.476074i \(0.157941\pi\)
\(492\) 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
\(501\) −17.9413 + 1.41456i −0.801559 + 0.0631979i
\(502\) 0 0
\(503\) −19.6423 + 11.3405i −0.875808 + 0.505648i −0.869274 0.494331i \(-0.835413\pi\)
−0.00653389 + 0.999979i \(0.502080\pi\)
\(504\) 0 0
\(505\) 3.17267 0.850114i 0.141182 0.0378296i
\(506\) 0 0
\(507\) 21.1036 + 7.85097i 0.937244 + 0.348674i
\(508\) 0 0
\(509\) −19.3215 + 5.17719i −0.856412 + 0.229475i −0.660203 0.751087i \(-0.729530\pi\)
−0.196209 + 0.980562i \(0.562863\pi\)
\(510\) 0 0
\(511\) −18.3581 + 10.5991i −0.812114 + 0.468874i
\(512\) 0 0
\(513\) 30.6518 29.1122i 1.35331 1.28533i
\(514\) 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 \(-0.860103\pi\)
0.904965 0.425486i \(-0.139897\pi\)
\(522\) 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
\(525\) −1.58785 + 3.33021i −0.0692996 + 0.145342i
\(526\) 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
\(531\) 4.89368 + 3.55336i 0.212368 + 0.154203i
\(532\) 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
\(537\) 0.594040 + 0.507213i 0.0256347 + 0.0218879i
\(538\) 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
\(543\) 0.975516 + 0.180659i 0.0418634 + 0.00775281i
\(544\) 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
\(549\) −0.627870 3.95698i −0.0267968 0.168880i
\(550\) 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
\(555\) 20.9296 24.5124i 0.888411 1.04049i
\(556\) 0 0
\(557\) 1.77202 + 6.61326i 0.0750828 + 0.280213i 0.993252 0.115975i \(-0.0369994\pi\)
−0.918169 + 0.396188i \(0.870333\pi\)
\(558\) 0 0
\(559\) 0.592223 1.63091i 0.0250484 0.0689803i
\(560\) 0 0
\(561\) −15.7092 22.8502i −0.663244 0.964734i
\(562\) 0 0
\(563\) −9.52928 16.5052i −0.401611 0.695611i 0.592309 0.805711i \(-0.298216\pi\)
−0.993921 + 0.110099i \(0.964883\pi\)
\(564\) 0 0
\(565\) −41.2227 11.0456i −1.73425 0.464692i
\(566\) 0 0
\(567\) 16.7544 10.8939i 0.703617 0.457499i
\(568\) 0 0
\(569\) 3.18974 5.52479i 0.133721 0.231611i −0.791387 0.611315i \(-0.790641\pi\)
0.925108 + 0.379704i \(0.123974\pi\)
\(570\) 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
\(579\) −1.96878 24.9706i −0.0818195 1.03774i
\(580\) 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
\(585\) 23.7447 + 11.5508i 0.981724 + 0.477568i
\(586\) 0 0
\(587\) 17.6852 4.73874i 0.729948 0.195589i 0.125342 0.992114i \(-0.459997\pi\)
0.604606 + 0.796525i \(0.293331\pi\)
\(588\) 0 0
\(589\) −31.2353 + 18.0337i −1.28703 + 0.743066i
\(590\) 0 0
\(591\) −0.876924 11.1223i −0.0360718 0.457510i
\(592\) 0 0
\(593\) 11.8285 11.8285i 0.485739 0.485739i −0.421220 0.906959i \(-0.638398\pi\)
0.906959 + 0.421220i \(0.138398\pi\)
\(594\) 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 \(-0.730372\pi\)
0.662188 0.749337i \(-0.269628\pi\)
\(600\) 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
\(603\) 0.806729 7.69642i 0.0328525 0.313422i
\(604\) 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
\(609\) 4.92464 + 7.16323i 0.199556 + 0.290269i
\(610\) 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
\(615\) 19.9784 23.3984i 0.805606 0.943513i
\(616\) 0 0
\(617\) −6.17063 + 23.0291i −0.248420 + 0.927117i 0.723213 + 0.690625i \(0.242664\pi\)
−0.971633 + 0.236492i \(0.924002\pi\)
\(618\) 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
\(621\) −9.15690 16.8479i −0.367454 0.676083i
\(622\) 0 0
\(623\) −18.6182 −0.745923
\(624\) 0 0
\(625\) 28.8762 1.15505
\(626\) 0 0
\(627\) −78.6970 14.5741i −3.14285 0.582035i
\(628\) 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
\(633\) −30.3608 25.9231i −1.20673 1.03035i
\(634\) 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
\(639\) −12.3522 + 17.0115i −0.488646 + 0.672964i
\(640\) 0 0
\(641\) 9.29977 + 16.1077i 0.367319 + 0.636215i 0.989145 0.146940i \(-0.0469424\pi\)
−0.621826 + 0.783155i \(0.713609\pi\)
\(642\) 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
\(645\) 0.875726 1.83667i 0.0344817 0.0723186i
\(646\) 0 0
\(647\) 10.6735 18.4871i 0.419619 0.726802i −0.576282 0.817251i \(-0.695497\pi\)
0.995901 + 0.0904492i \(0.0288303\pi\)
\(648\) 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 0.813844 0.581084i \(-0.197371\pi\)
−0.0963112 + 0.995351i \(0.530704\pi\)
\(654\) 0 0
\(655\) −12.3936 + 12.3936i −0.484256 + 0.484256i
\(656\) 0 0
\(657\) 11.6561 + 26.1602i 0.454748 + 1.02061i
\(658\) 0 0
\(659\) 30.9228 17.8533i 1.20458 0.695464i 0.243010 0.970024i \(-0.421865\pi\)
0.961570 + 0.274559i \(0.0885320\pi\)
\(660\) 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
\(663\) −8.92049 + 15.1748i −0.346443 + 0.589341i
\(664\) 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
\(669\) 22.3688 1.76364i 0.864826 0.0681861i
\(670\) 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 \(-0.863784\pi\)
0.909824 0.414994i \(-0.136216\pi\)
\(678\) 0 0
\(679\) 3.49065 6.04599i 0.133959 0.232024i
\(680\) 0 0
\(681\) 15.8287 + 7.54715i 0.606556 + 0.289207i
\(682\) 0 0
\(683\) −33.6457 9.01534i −1.28742 0.344962i −0.450738 0.892656i \(-0.648839\pi\)
−0.836679 + 0.547694i \(0.815506\pi\)
\(684\) 0 0
\(685\) 14.6838 + 25.4330i 0.561038 + 0.971746i
\(686\) 0 0
\(687\) −12.1959 + 8.38457i −0.465304 + 0.319891i
\(688\) 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
\(693\) −35.3270 13.5493i −1.34196 0.514696i
\(694\) 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
\(699\) 3.00332 16.2172i 0.113596 0.613393i
\(700\) 0 0
\(701\) −7.80915 −0.294948 −0.147474 0.989066i \(-0.547114\pi\)
−0.147474 + 0.989066i \(0.547114\pi\)
\(702\) 0 0
\(703\) 62.0179 2.33905
\(704\) 0 0
\(705\) −10.4308 + 56.3241i −0.392848 + 2.12129i
\(706\) 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
\(711\) −1.04372 0.400307i −0.0391424 0.0150127i
\(712\) 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
\(717\) −0.700411 + 0.481525i −0.0261573 + 0.0179829i
\(718\) 0 0
\(719\) −2.01546 3.49089i −0.0751641 0.130188i 0.825993 0.563680i \(-0.190615\pi\)
−0.901158 + 0.433492i \(0.857281\pi\)
\(720\) 0 0
\(721\) −21.5599 5.77695i −0.802932 0.215145i
\(722\) 0 0
\(723\) −41.3238 19.7033i −1.53685 0.732773i
\(724\) 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
\(735\) 8.72249 0.687714i 0.321734 0.0253667i
\(736\) 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
\(741\) 12.7646 + 49.1768i 0.468921 + 1.80656i
\(742\) 0 0
\(743\) −40.6931 + 10.9037i −1.49288 + 0.400017i −0.910709 0.413047i \(-0.864464\pi\)
−0.582174 + 0.813064i \(0.697798\pi\)
\(744\) 0 0
\(745\) 41.2418 23.8110i 1.51098 0.872366i
\(746\) 0 0
\(747\) 8.61851 + 19.3428i 0.315335 + 0.707716i
\(748\) 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
\(759\) −15.6248 + 32.7700i −0.567145 + 1.18948i
\(760\) 0 0
\(761\) 21.0411 + 5.63796i 0.762741 + 0.204376i 0.619162 0.785263i \(-0.287472\pi\)
0.143579 + 0.989639i \(0.454139\pi\)
\(762\) 0 0
\(763\) 9.36791 + 16.2257i 0.339141 + 0.587410i
\(764\) 0 0
\(765\) −12.1286 + 16.7035i −0.438511 + 0.603917i
\(766\) 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
\(771\) 3.29255 + 2.81130i 0.118578 + 0.101246i
\(772\) 0 0
\(773\) 2.17937 8.13353i 0.0783866 0.292543i −0.915593 0.402106i \(-0.868278\pi\)
0.993980 + 0.109563i \(0.0349451\pi\)
\(774\) 0 0
\(775\) −3.00714 3.00714i −0.108020 0.108020i
\(776\) 0 0
\(777\) 28.8285 + 5.33883i 1.03422 + 0.191530i
\(778\) 0 0
\(779\) 59.1994 2.12104
\(780\) 0 0
\(781\) 39.8022 1.42424
\(782\) 0 0
\(783\) 10.3187 5.60824i 0.368759 0.200422i
\(784\) 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
\(789\) −10.8068 + 12.6567i −0.384731 + 0.450591i
\(790\) 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
\(795\) −1.47818 2.15012i −0.0524257 0.0762568i
\(796\) 0 0
\(797\)