Properties

Label 624.2.cn.f.305.10
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 305.10
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19941 + 1.24957i) q^{3} +(1.44076 + 1.44076i) q^{5} +(-0.918532 + 3.42801i) q^{7} +(-0.122851 + 2.99748i) q^{9} +O(q^{10})\) \(q+(1.19941 + 1.24957i) q^{3} +(1.44076 + 1.44076i) q^{5} +(-0.918532 + 3.42801i) q^{7} +(-0.122851 + 2.99748i) q^{9} +(-0.0392149 - 0.146352i) q^{11} +(1.92366 - 3.04952i) q^{13} +(-0.0722747 + 3.52839i) q^{15} +(-1.60706 - 2.78351i) q^{17} +(-1.90607 - 0.510729i) q^{19} +(-5.38523 + 2.96380i) q^{21} +(-4.19640 + 7.26837i) q^{23} -0.848416i q^{25} +(-3.89291 + 3.44169i) q^{27} +(-0.0238088 - 0.0137460i) q^{29} +(5.54595 - 5.54595i) q^{31} +(0.135842 - 0.224537i) q^{33} +(-6.26232 + 3.61555i) q^{35} +(3.84429 - 1.03007i) q^{37} +(6.11783 - 1.25387i) q^{39} +(2.53382 - 0.678935i) q^{41} +(5.90548 - 3.40953i) q^{43} +(-4.49566 + 4.14166i) q^{45} +(4.77303 - 4.77303i) q^{47} +(-4.84536 - 2.79747i) q^{49} +(1.55068 - 5.34670i) q^{51} +13.3755i q^{53} +(0.154359 - 0.267357i) q^{55} +(-1.64796 - 2.99434i) q^{57} +(-8.09489 - 2.16902i) q^{59} +(6.61697 + 11.4609i) q^{61} +(-10.1626 - 3.17442i) q^{63} +(7.16515 - 1.62210i) q^{65} +(-1.18370 - 4.41762i) q^{67} +(-14.1155 + 3.47404i) q^{69} +(-1.29021 + 4.81512i) q^{71} +(6.22036 + 6.22036i) q^{73} +(1.06016 - 1.01760i) q^{75} +0.537715 q^{77} +13.3852 q^{79} +(-8.96982 - 0.736488i) q^{81} +(-1.94085 - 1.94085i) q^{83} +(1.69499 - 6.32577i) q^{85} +(-0.0113798 - 0.0462379i) q^{87} +(-2.87300 - 10.7222i) q^{89} +(8.68683 + 9.39538i) q^{91} +(13.5819 + 0.278209i) q^{93} +(-2.01035 - 3.48203i) q^{95} +(-17.7357 - 4.75227i) q^{97} +(0.443505 - 0.0995664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

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
\(3\) 1.19941 + 1.24957i 0.692477 + 0.721440i
\(4\) 0 0
\(5\) 1.44076 + 1.44076i 0.644328 + 0.644328i 0.951616 0.307289i \(-0.0994217\pi\)
−0.307289 + 0.951616i \(0.599422\pi\)
\(6\) 0 0
\(7\) −0.918532 + 3.42801i −0.347172 + 1.29567i 0.542881 + 0.839809i \(0.317333\pi\)
−0.890054 + 0.455856i \(0.849333\pi\)
\(8\) 0 0
\(9\) −0.122851 + 2.99748i −0.0409503 + 0.999161i
\(10\) 0 0
\(11\) −0.0392149 0.146352i −0.0118237 0.0441267i 0.959762 0.280815i \(-0.0906047\pi\)
−0.971586 + 0.236688i \(0.923938\pi\)
\(12\) 0 0
\(13\) 1.92366 3.04952i 0.533526 0.845784i
\(14\) 0 0
\(15\) −0.0722747 + 3.52839i −0.0186612 + 0.911026i
\(16\) 0 0
\(17\) −1.60706 2.78351i −0.389770 0.675101i 0.602648 0.798007i \(-0.294112\pi\)
−0.992418 + 0.122905i \(0.960779\pi\)
\(18\) 0 0
\(19\) −1.90607 0.510729i −0.437282 0.117169i 0.0334605 0.999440i \(-0.489347\pi\)
−0.470742 + 0.882271i \(0.656014\pi\)
\(20\) 0 0
\(21\) −5.38523 + 2.96380i −1.17515 + 0.646755i
\(22\) 0 0
\(23\) −4.19640 + 7.26837i −0.875009 + 1.51556i −0.0182561 + 0.999833i \(0.505811\pi\)
−0.856753 + 0.515727i \(0.827522\pi\)
\(24\) 0 0
\(25\) 0.848416i 0.169683i
\(26\) 0 0
\(27\) −3.89291 + 3.44169i −0.749192 + 0.662353i
\(28\) 0 0
\(29\) −0.0238088 0.0137460i −0.00442119 0.00255258i 0.497788 0.867299i \(-0.334146\pi\)
−0.502209 + 0.864746i \(0.667479\pi\)
\(30\) 0 0
\(31\) 5.54595 5.54595i 0.996083 0.996083i −0.00390967 0.999992i \(-0.501244\pi\)
0.999992 + 0.00390967i \(0.00124449\pi\)
\(32\) 0 0
\(33\) 0.135842 0.224537i 0.0236471 0.0390869i
\(34\) 0 0
\(35\) −6.26232 + 3.61555i −1.05853 + 0.611140i
\(36\) 0 0
\(37\) 3.84429 1.03007i 0.631997 0.169343i 0.0714212 0.997446i \(-0.477247\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(38\) 0 0
\(39\) 6.11783 1.25387i 0.979637 0.200779i
\(40\) 0 0
\(41\) 2.53382 0.678935i 0.395716 0.106032i −0.0554728 0.998460i \(-0.517667\pi\)
0.451189 + 0.892428i \(0.351000\pi\)
\(42\) 0 0
\(43\) 5.90548 3.40953i 0.900577 0.519948i 0.0231896 0.999731i \(-0.492618\pi\)
0.877387 + 0.479783i \(0.159285\pi\)
\(44\) 0 0
\(45\) −4.49566 + 4.14166i −0.670173 + 0.617402i
\(46\) 0 0
\(47\) 4.77303 4.77303i 0.696218 0.696218i −0.267374 0.963593i \(-0.586156\pi\)
0.963593 + 0.267374i \(0.0861560\pi\)
\(48\) 0 0
\(49\) −4.84536 2.79747i −0.692194 0.399638i
\(50\) 0 0
\(51\) 1.55068 5.34670i 0.217138 0.748688i
\(52\) 0 0
\(53\) 13.3755i 1.83726i 0.395119 + 0.918630i \(0.370703\pi\)
−0.395119 + 0.918630i \(0.629297\pi\)
\(54\) 0 0
\(55\) 0.154359 0.267357i 0.0208137 0.0360504i
\(56\) 0 0
\(57\) −1.64796 2.99434i −0.218277 0.396610i
\(58\) 0 0
\(59\) −8.09489 2.16902i −1.05386 0.282382i −0.310017 0.950731i \(-0.600335\pi\)
−0.743848 + 0.668349i \(0.767001\pi\)
\(60\) 0 0
\(61\) 6.61697 + 11.4609i 0.847216 + 1.46742i 0.883683 + 0.468086i \(0.155056\pi\)
−0.0364673 + 0.999335i \(0.511610\pi\)
\(62\) 0 0
\(63\) −10.1626 3.17442i −1.28036 0.399939i
\(64\) 0 0
\(65\) 7.16515 1.62210i 0.888728 0.201196i
\(66\) 0 0
\(67\) −1.18370 4.41762i −0.144612 0.539698i −0.999772 0.0213353i \(-0.993208\pi\)
0.855161 0.518363i \(-0.173458\pi\)
\(68\) 0 0
\(69\) −14.1155 + 3.47404i −1.69931 + 0.418225i
\(70\) 0 0
\(71\) −1.29021 + 4.81512i −0.153119 + 0.571449i 0.846140 + 0.532961i \(0.178921\pi\)
−0.999259 + 0.0384882i \(0.987746\pi\)
\(72\) 0 0
\(73\) 6.22036 + 6.22036i 0.728038 + 0.728038i 0.970229 0.242191i \(-0.0778660\pi\)
−0.242191 + 0.970229i \(0.577866\pi\)
\(74\) 0 0
\(75\) 1.06016 1.01760i 0.122416 0.117502i
\(76\) 0 0
\(77\) 0.537715 0.0612784
\(78\) 0 0
\(79\) 13.3852 1.50596 0.752979 0.658045i \(-0.228616\pi\)
0.752979 + 0.658045i \(0.228616\pi\)
\(80\) 0 0
\(81\) −8.96982 0.736488i −0.996646 0.0818320i
\(82\) 0 0
\(83\) −1.94085 1.94085i −0.213036 0.213036i 0.592520 0.805556i \(-0.298133\pi\)
−0.805556 + 0.592520i \(0.798133\pi\)
\(84\) 0 0
\(85\) 1.69499 6.32577i 0.183847 0.686126i
\(86\) 0 0
\(87\) −0.0113798 0.0462379i −0.00122005 0.00495722i
\(88\) 0 0
\(89\) −2.87300 10.7222i −0.304537 1.13655i −0.933343 0.358987i \(-0.883122\pi\)
0.628805 0.777563i \(-0.283544\pi\)
\(90\) 0 0
\(91\) 8.68683 + 9.39538i 0.910627 + 0.984904i
\(92\) 0 0
\(93\) 13.5819 + 0.278209i 1.40838 + 0.0288489i
\(94\) 0 0
\(95\) −2.01035 3.48203i −0.206257 0.357248i
\(96\) 0 0
\(97\) −17.7357 4.75227i −1.80079 0.482520i −0.806687 0.590978i \(-0.798742\pi\)
−0.994101 + 0.108458i \(0.965409\pi\)
\(98\) 0 0
\(99\) 0.443505 0.0995664i 0.0445739 0.0100068i
\(100\) 0 0
\(101\) −0.226814 + 0.392853i −0.0225688 + 0.0390903i −0.877089 0.480327i \(-0.840518\pi\)
0.854520 + 0.519418i \(0.173851\pi\)
\(102\) 0 0
\(103\) 10.0525i 0.990499i −0.868751 0.495250i \(-0.835077\pi\)
0.868751 0.495250i \(-0.164923\pi\)
\(104\) 0 0
\(105\) −12.0290 3.48870i −1.17391 0.340462i
\(106\) 0 0
\(107\) 11.4165 + 6.59132i 1.10368 + 0.637207i 0.937184 0.348836i \(-0.113423\pi\)
0.166492 + 0.986043i \(0.446756\pi\)
\(108\) 0 0
\(109\) 4.43289 4.43289i 0.424594 0.424594i −0.462188 0.886782i \(-0.652936\pi\)
0.886782 + 0.462188i \(0.152936\pi\)
\(110\) 0 0
\(111\) 5.89801 + 3.56823i 0.559814 + 0.338681i
\(112\) 0 0
\(113\) 5.33256 3.07875i 0.501645 0.289625i −0.227748 0.973720i \(-0.573136\pi\)
0.729393 + 0.684095i \(0.239803\pi\)
\(114\) 0 0
\(115\) −16.5180 + 4.42598i −1.54031 + 0.412725i
\(116\) 0 0
\(117\) 8.90455 + 6.14076i 0.823226 + 0.567714i
\(118\) 0 0
\(119\) 11.0180 2.95228i 1.01002 0.270635i
\(120\) 0 0
\(121\) 9.50640 5.48852i 0.864218 0.498957i
\(122\) 0 0
\(123\) 3.88746 + 2.35187i 0.350520 + 0.212061i
\(124\) 0 0
\(125\) 8.42617 8.42617i 0.753659 0.753659i
\(126\) 0 0
\(127\) −8.15516 4.70839i −0.723654 0.417802i 0.0924423 0.995718i \(-0.470533\pi\)
−0.816096 + 0.577916i \(0.803866\pi\)
\(128\) 0 0
\(129\) 11.3435 + 3.28990i 0.998740 + 0.289659i
\(130\) 0 0
\(131\) 14.8806i 1.30012i −0.759881 0.650062i \(-0.774743\pi\)
0.759881 0.650062i \(-0.225257\pi\)
\(132\) 0 0
\(133\) 3.50157 6.06489i 0.303624 0.525893i
\(134\) 0 0
\(135\) −10.5674 0.650108i −0.909498 0.0559524i
\(136\) 0 0
\(137\) −8.69061 2.32864i −0.742489 0.198949i −0.132305 0.991209i \(-0.542238\pi\)
−0.610184 + 0.792260i \(0.708905\pi\)
\(138\) 0 0
\(139\) 0.0458925 + 0.0794881i 0.00389255 + 0.00674210i 0.867965 0.496625i \(-0.165428\pi\)
−0.864073 + 0.503367i \(0.832094\pi\)
\(140\) 0 0
\(141\) 11.6890 + 0.239436i 0.984395 + 0.0201641i
\(142\) 0 0
\(143\) −0.521738 0.161944i −0.0436299 0.0135424i
\(144\) 0 0
\(145\) −0.0144981 0.0541076i −0.00120400 0.00449339i
\(146\) 0 0
\(147\) −2.31592 9.40992i −0.191014 0.776117i
\(148\) 0 0
\(149\) −3.50013 + 13.0627i −0.286742 + 1.07014i 0.660815 + 0.750549i \(0.270211\pi\)
−0.947557 + 0.319587i \(0.896456\pi\)
\(150\) 0 0
\(151\) −8.24642 8.24642i −0.671084 0.671084i 0.286882 0.957966i \(-0.407381\pi\)
−0.957966 + 0.286882i \(0.907381\pi\)
\(152\) 0 0
\(153\) 8.54097 4.47519i 0.690496 0.361797i
\(154\) 0 0
\(155\) 15.9808 1.28361
\(156\) 0 0
\(157\) −5.99636 −0.478562 −0.239281 0.970950i \(-0.576912\pi\)
−0.239281 + 0.970950i \(0.576912\pi\)
\(158\) 0 0
\(159\) −16.7136 + 16.0426i −1.32547 + 1.27226i
\(160\) 0 0
\(161\) −21.0615 21.0615i −1.65988 1.65988i
\(162\) 0 0
\(163\) −3.72133 + 13.8882i −0.291477 + 1.08781i 0.652499 + 0.757790i \(0.273721\pi\)
−0.943975 + 0.330016i \(0.892946\pi\)
\(164\) 0 0
\(165\) 0.519220 0.127788i 0.0404213 0.00994826i
\(166\) 0 0
\(167\) −1.36831 5.10660i −0.105883 0.395161i 0.892561 0.450927i \(-0.148906\pi\)
−0.998444 + 0.0557663i \(0.982240\pi\)
\(168\) 0 0
\(169\) −5.59910 11.7324i −0.430700 0.902495i
\(170\) 0 0
\(171\) 1.76506 5.65066i 0.134978 0.432117i
\(172\) 0 0
\(173\) 3.05984 + 5.29979i 0.232635 + 0.402936i 0.958583 0.284814i \(-0.0919319\pi\)
−0.725948 + 0.687750i \(0.758599\pi\)
\(174\) 0 0
\(175\) 2.90838 + 0.779297i 0.219853 + 0.0589093i
\(176\) 0 0
\(177\) −6.99872 12.7167i −0.526056 0.955843i
\(178\) 0 0
\(179\) 10.1144 17.5187i 0.755986 1.30941i −0.188897 0.981997i \(-0.560491\pi\)
0.944883 0.327409i \(-0.106175\pi\)
\(180\) 0 0
\(181\) 4.39016i 0.326318i 0.986600 + 0.163159i \(0.0521683\pi\)
−0.986600 + 0.163159i \(0.947832\pi\)
\(182\) 0 0
\(183\) −6.38480 + 22.0147i −0.471978 + 1.62737i
\(184\) 0 0
\(185\) 7.02279 + 4.05461i 0.516326 + 0.298101i
\(186\) 0 0
\(187\) −0.344352 + 0.344352i −0.0251815 + 0.0251815i
\(188\) 0 0
\(189\) −8.22237 16.5062i −0.598089 1.20065i
\(190\) 0 0
\(191\) −12.3027 + 7.10298i −0.890194 + 0.513954i −0.874006 0.485915i \(-0.838486\pi\)
−0.0161878 + 0.999869i \(0.505153\pi\)
\(192\) 0 0
\(193\) 14.1074 3.78006i 1.01547 0.272095i 0.287558 0.957763i \(-0.407157\pi\)
0.727914 + 0.685668i \(0.240490\pi\)
\(194\) 0 0
\(195\) 10.6208 + 7.00781i 0.760575 + 0.501839i
\(196\) 0 0
\(197\) −0.668505 + 0.179125i −0.0476290 + 0.0127622i −0.282555 0.959251i \(-0.591182\pi\)
0.234926 + 0.972013i \(0.424515\pi\)
\(198\) 0 0
\(199\) 13.8158 7.97656i 0.979377 0.565443i 0.0772948 0.997008i \(-0.475372\pi\)
0.902082 + 0.431565i \(0.142038\pi\)
\(200\) 0 0
\(201\) 4.10039 6.77764i 0.289219 0.478058i
\(202\) 0 0
\(203\) 0.0689907 0.0689907i 0.00484220 0.00484220i
\(204\) 0 0
\(205\) 4.62881 + 2.67245i 0.323290 + 0.186652i
\(206\) 0 0
\(207\) −21.2713 13.4716i −1.47846 0.936338i
\(208\) 0 0
\(209\) 0.298985i 0.0206812i
\(210\) 0 0
\(211\) −3.28525 + 5.69022i −0.226166 + 0.391731i −0.956669 0.291179i \(-0.905952\pi\)
0.730503 + 0.682910i \(0.239286\pi\)
\(212\) 0 0
\(213\) −7.56431 + 4.16308i −0.518298 + 0.285249i
\(214\) 0 0
\(215\) 13.4207 + 3.59607i 0.915284 + 0.245250i
\(216\) 0 0
\(217\) 13.9174 + 24.1057i 0.944777 + 1.63640i
\(218\) 0 0
\(219\) −0.312040 + 15.2335i −0.0210857 + 1.02938i
\(220\) 0 0
\(221\) −11.5798 0.453757i −0.778942 0.0305230i
\(222\) 0 0
\(223\) −1.79575 6.70184i −0.120252 0.448788i 0.879374 0.476132i \(-0.157962\pi\)
−0.999626 + 0.0273441i \(0.991295\pi\)
\(224\) 0 0
\(225\) 2.54311 + 0.104229i 0.169541 + 0.00694859i
\(226\) 0 0
\(227\) −3.00698 + 11.2222i −0.199580 + 0.744843i 0.791453 + 0.611230i \(0.209325\pi\)
−0.991033 + 0.133614i \(0.957342\pi\)
\(228\) 0 0
\(229\) −18.7056 18.7056i −1.23610 1.23610i −0.961580 0.274523i \(-0.911480\pi\)
−0.274523 0.961580i \(-0.588520\pi\)
\(230\) 0 0
\(231\) 0.644939 + 0.671913i 0.0424339 + 0.0442086i
\(232\) 0 0
\(233\) 4.96187 0.325063 0.162531 0.986703i \(-0.448034\pi\)
0.162531 + 0.986703i \(0.448034\pi\)
\(234\) 0 0
\(235\) 13.7536 0.897186
\(236\) 0 0
\(237\) 16.0543 + 16.7258i 1.04284 + 1.08646i
\(238\) 0 0
\(239\) −19.8475 19.8475i −1.28382 1.28382i −0.938473 0.345352i \(-0.887760\pi\)
−0.345352 0.938473i \(-0.612240\pi\)
\(240\) 0 0
\(241\) 1.59927 5.96857i 0.103018 0.384469i −0.895095 0.445876i \(-0.852892\pi\)
0.998113 + 0.0614071i \(0.0195588\pi\)
\(242\) 0 0
\(243\) −9.83816 12.0918i −0.631118 0.775687i
\(244\) 0 0
\(245\) −2.95052 11.0115i −0.188502 0.703498i
\(246\) 0 0
\(247\) −5.22409 + 4.83012i −0.332401 + 0.307333i
\(248\) 0 0
\(249\) 0.0973611 4.75309i 0.00617001 0.301215i
\(250\) 0 0
\(251\) −2.16622 3.75201i −0.136731 0.236825i 0.789526 0.613717i \(-0.210326\pi\)
−0.926257 + 0.376892i \(0.876993\pi\)
\(252\) 0 0
\(253\) 1.22830 + 0.329122i 0.0772226 + 0.0206917i
\(254\) 0 0
\(255\) 9.93747 5.46917i 0.622309 0.342492i
\(256\) 0 0
\(257\) −10.6302 + 18.4120i −0.663093 + 1.14851i 0.316706 + 0.948524i \(0.397423\pi\)
−0.979799 + 0.199986i \(0.935910\pi\)
\(258\) 0 0
\(259\) 14.1244i 0.877648i
\(260\) 0 0
\(261\) 0.0441285 0.0696779i 0.00273148 0.00431295i
\(262\) 0 0
\(263\) 15.0017 + 8.66123i 0.925044 + 0.534074i 0.885241 0.465133i \(-0.153994\pi\)
0.0398032 + 0.999208i \(0.487327\pi\)
\(264\) 0 0
\(265\) −19.2708 + 19.2708i −1.18380 + 1.18380i
\(266\) 0 0
\(267\) 9.95223 16.4503i 0.609067 1.00674i
\(268\) 0 0
\(269\) −27.3500 + 15.7905i −1.66756 + 0.962766i −0.698612 + 0.715500i \(0.746199\pi\)
−0.968948 + 0.247266i \(0.920468\pi\)
\(270\) 0 0
\(271\) 8.18818 2.19402i 0.497397 0.133277i −0.00139487 0.999999i \(-0.500444\pi\)
0.498792 + 0.866722i \(0.333777\pi\)
\(272\) 0 0
\(273\) −1.32116 + 22.1237i −0.0799601 + 1.33899i
\(274\) 0 0
\(275\) −0.124167 + 0.0332705i −0.00748757 + 0.00200629i
\(276\) 0 0
\(277\) −16.6692 + 9.62397i −1.00156 + 0.578248i −0.908708 0.417432i \(-0.862930\pi\)
−0.0928470 + 0.995680i \(0.529597\pi\)
\(278\) 0 0
\(279\) 15.9426 + 17.3052i 0.954457 + 1.03604i
\(280\) 0 0
\(281\) 16.6481 16.6481i 0.993141 0.993141i −0.00683587 0.999977i \(-0.502176\pi\)
0.999977 + 0.00683587i \(0.00217594\pi\)
\(282\) 0 0
\(283\) −8.15184 4.70646i −0.484576 0.279770i 0.237745 0.971328i \(-0.423592\pi\)
−0.722322 + 0.691557i \(0.756925\pi\)
\(284\) 0 0
\(285\) 1.93981 6.68843i 0.114905 0.396189i
\(286\) 0 0
\(287\) 9.30958i 0.549527i
\(288\) 0 0
\(289\) 3.33470 5.77587i 0.196159 0.339757i
\(290\) 0 0
\(291\) −15.3340 27.8619i −0.898896 1.63329i
\(292\) 0 0
\(293\) 25.3285 + 6.78675i 1.47971 + 0.396486i 0.906248 0.422747i \(-0.138934\pi\)
0.573460 + 0.819234i \(0.305601\pi\)
\(294\) 0 0
\(295\) −8.53776 14.7878i −0.497088 0.860981i
\(296\) 0 0
\(297\) 0.656358 + 0.434770i 0.0380857 + 0.0252279i
\(298\) 0 0
\(299\) 14.0926 + 26.7788i 0.814996 + 1.54866i
\(300\) 0 0
\(301\) 6.26352 + 23.3758i 0.361023 + 1.34736i
\(302\) 0 0
\(303\) −0.762939 + 0.187770i −0.0438297 + 0.0107871i
\(304\) 0 0
\(305\) −6.97898 + 26.0459i −0.399615 + 1.49138i
\(306\) 0 0
\(307\) 15.7215 + 15.7215i 0.897271 + 0.897271i 0.995194 0.0979227i \(-0.0312198\pi\)
−0.0979227 + 0.995194i \(0.531220\pi\)
\(308\) 0 0
\(309\) 12.5613 12.0570i 0.714585 0.685898i
\(310\) 0 0
\(311\) 4.34210 0.246218 0.123109 0.992393i \(-0.460714\pi\)
0.123109 + 0.992393i \(0.460714\pi\)
\(312\) 0 0
\(313\) 18.6341 1.05326 0.526630 0.850095i \(-0.323455\pi\)
0.526630 + 0.850095i \(0.323455\pi\)
\(314\) 0 0
\(315\) −10.0682 19.2154i −0.567281 1.08266i
\(316\) 0 0
\(317\) −9.07889 9.07889i −0.509921 0.509921i 0.404581 0.914502i \(-0.367417\pi\)
−0.914502 + 0.404581i \(0.867417\pi\)
\(318\) 0 0
\(319\) −0.00107810 + 0.00402352i −6.03619e−5 + 0.000225274i
\(320\) 0 0
\(321\) 5.45671 + 22.1714i 0.304564 + 1.23749i
\(322\) 0 0
\(323\) 1.64155 + 6.12634i 0.0913382 + 0.340879i
\(324\) 0 0
\(325\) −2.58726 1.63206i −0.143515 0.0905304i
\(326\) 0 0
\(327\) 10.8560 + 0.222372i 0.600340 + 0.0122972i
\(328\) 0 0
\(329\) 11.9778 + 20.7462i 0.660358 + 1.14377i
\(330\) 0 0
\(331\) −11.3587 3.04354i −0.624328 0.167288i −0.0672335 0.997737i \(-0.521417\pi\)
−0.557095 + 0.830449i \(0.688084\pi\)
\(332\) 0 0
\(333\) 2.61535 + 11.6497i 0.143321 + 0.638401i
\(334\) 0 0
\(335\) 4.65931 8.07016i 0.254565 0.440920i
\(336\) 0 0
\(337\) 19.7236i 1.07441i 0.843451 + 0.537206i \(0.180520\pi\)
−0.843451 + 0.537206i \(0.819480\pi\)
\(338\) 0 0
\(339\) 10.2430 + 2.97073i 0.556324 + 0.161348i
\(340\) 0 0
\(341\) −1.02914 0.594177i −0.0557313 0.0321765i
\(342\) 0 0
\(343\) −3.52597 + 3.52597i −0.190384 + 0.190384i
\(344\) 0 0
\(345\) −25.3423 15.3318i −1.36439 0.825438i
\(346\) 0 0
\(347\) −30.5245 + 17.6233i −1.63864 + 0.946071i −0.657342 + 0.753593i \(0.728319\pi\)
−0.981301 + 0.192478i \(0.938348\pi\)
\(348\) 0 0
\(349\) −22.9572 + 6.15136i −1.22887 + 0.329275i −0.814139 0.580670i \(-0.802791\pi\)
−0.414730 + 0.909944i \(0.636124\pi\)
\(350\) 0 0
\(351\) 3.00686 + 18.4921i 0.160494 + 0.987037i
\(352\) 0 0
\(353\) −7.81588 + 2.09426i −0.415997 + 0.111466i −0.460746 0.887532i \(-0.652418\pi\)
0.0447484 + 0.998998i \(0.485751\pi\)
\(354\) 0 0
\(355\) −8.79631 + 5.07855i −0.466860 + 0.269542i
\(356\) 0 0
\(357\) 16.9042 + 10.2268i 0.894665 + 0.541262i
\(358\) 0 0
\(359\) −9.77619 + 9.77619i −0.515968 + 0.515968i −0.916349 0.400381i \(-0.868878\pi\)
0.400381 + 0.916349i \(0.368878\pi\)
\(360\) 0 0
\(361\) −13.0822 7.55303i −0.688539 0.397528i
\(362\) 0 0
\(363\) 18.2603 + 5.29595i 0.958418 + 0.277965i
\(364\) 0 0
\(365\) 17.9241i 0.938190i
\(366\) 0 0
\(367\) −6.84234 + 11.8513i −0.357167 + 0.618632i −0.987486 0.157704i \(-0.949591\pi\)
0.630319 + 0.776336i \(0.282924\pi\)
\(368\) 0 0
\(369\) 1.72382 + 7.67850i 0.0897382 + 0.399727i
\(370\) 0 0
\(371\) −45.8512 12.2858i −2.38047 0.637846i
\(372\) 0 0
\(373\) −1.97549 3.42164i −0.102287 0.177166i 0.810340 0.585960i \(-0.199283\pi\)
−0.912626 + 0.408794i \(0.865949\pi\)
\(374\) 0 0
\(375\) 20.6355 + 0.422692i 1.06561 + 0.0218277i
\(376\) 0 0
\(377\) −0.0877188 + 0.0461628i −0.00451775 + 0.00237751i
\(378\) 0 0
\(379\) 4.23059 + 15.7888i 0.217311 + 0.811014i 0.985340 + 0.170600i \(0.0545706\pi\)
−0.768030 + 0.640414i \(0.778763\pi\)
\(380\) 0 0
\(381\) −3.89789 15.8377i −0.199695 0.811391i
\(382\) 0 0
\(383\) 5.85081 21.8355i 0.298963 1.11574i −0.639057 0.769160i \(-0.720675\pi\)
0.938019 0.346584i \(-0.112658\pi\)
\(384\) 0 0
\(385\) 0.774719 + 0.774719i 0.0394834 + 0.0394834i
\(386\) 0 0
\(387\) 9.49451 + 18.1204i 0.482633 + 0.921114i
\(388\) 0 0
\(389\) −1.80850 −0.0916947 −0.0458474 0.998948i \(-0.514599\pi\)
−0.0458474 + 0.998948i \(0.514599\pi\)
\(390\) 0 0
\(391\) 26.9755 1.36421
\(392\) 0 0
\(393\) 18.5943 17.8479i 0.937961 0.900306i
\(394\) 0 0
\(395\) 19.2849 + 19.2849i 0.970331 + 0.970331i
\(396\) 0 0
\(397\) −1.04738 + 3.90888i −0.0525665 + 0.196181i −0.987216 0.159391i \(-0.949047\pi\)
0.934649 + 0.355572i \(0.115714\pi\)
\(398\) 0 0
\(399\) 11.7783 2.89881i 0.589653 0.145122i
\(400\) 0 0
\(401\) −0.540214 2.01611i −0.0269770 0.100680i 0.951125 0.308807i \(-0.0999298\pi\)
−0.978102 + 0.208128i \(0.933263\pi\)
\(402\) 0 0
\(403\) −6.24398 27.5810i −0.311035 1.37391i
\(404\) 0 0
\(405\) −11.8623 13.9845i −0.589440 0.694894i
\(406\) 0 0
\(407\) −0.301506 0.522224i −0.0149451 0.0258857i
\(408\) 0 0
\(409\) −8.15394 2.18484i −0.403186 0.108033i 0.0515263 0.998672i \(-0.483591\pi\)
−0.454713 + 0.890638i \(0.650258\pi\)
\(410\) 0 0
\(411\) −7.51377 13.6525i −0.370627 0.673429i
\(412\) 0 0
\(413\) 14.8708 25.7570i 0.731746 1.26742i
\(414\) 0 0
\(415\) 5.59259i 0.274529i
\(416\) 0 0
\(417\) −0.0442823 + 0.152684i −0.00216851 + 0.00747699i
\(418\) 0 0
\(419\) −0.585414 0.337989i −0.0285993 0.0165118i 0.485632 0.874163i \(-0.338589\pi\)
−0.514232 + 0.857651i \(0.671923\pi\)
\(420\) 0 0
\(421\) 6.17588 6.17588i 0.300994 0.300994i −0.540409 0.841403i \(-0.681730\pi\)
0.841403 + 0.540409i \(0.181730\pi\)
\(422\) 0 0
\(423\) 13.7207 + 14.8935i 0.667124 + 0.724145i
\(424\) 0 0
\(425\) −2.36158 + 1.36346i −0.114553 + 0.0661374i
\(426\) 0 0
\(427\) −45.3660 + 12.1558i −2.19542 + 0.588260i
\(428\) 0 0
\(429\) −0.423415 0.846185i −0.0204427 0.0408542i
\(430\) 0 0
\(431\) −9.78631 + 2.62223i −0.471390 + 0.126309i −0.486691 0.873574i \(-0.661796\pi\)
0.0153006 + 0.999883i \(0.495129\pi\)
\(432\) 0 0
\(433\) −11.0298 + 6.36809i −0.530061 + 0.306031i −0.741041 0.671460i \(-0.765668\pi\)
0.210980 + 0.977490i \(0.432334\pi\)
\(434\) 0 0
\(435\) 0.0502222 0.0830134i 0.00240797 0.00398019i
\(436\) 0 0
\(437\) 11.7108 11.7108i 0.560203 0.560203i
\(438\) 0 0
\(439\) −3.07428 1.77494i −0.146727 0.0847131i 0.424839 0.905269i \(-0.360331\pi\)
−0.571566 + 0.820556i \(0.693664\pi\)
\(440\) 0 0
\(441\) 8.98063 14.1802i 0.427649 0.675248i
\(442\) 0 0
\(443\) 13.7327i 0.652461i 0.945290 + 0.326231i \(0.105779\pi\)
−0.945290 + 0.326231i \(0.894221\pi\)
\(444\) 0 0
\(445\) 11.3088 19.5874i 0.536088 0.928532i
\(446\) 0 0
\(447\) −20.5208 + 11.2938i −0.970601 + 0.534178i
\(448\) 0 0
\(449\) 12.7370 + 3.41288i 0.601098 + 0.161064i 0.546520 0.837446i \(-0.315952\pi\)
0.0545774 + 0.998510i \(0.482619\pi\)
\(450\) 0 0
\(451\) −0.198727 0.344205i −0.00935769 0.0162080i
\(452\) 0 0
\(453\) 0.413675 20.1953i 0.0194362 0.948857i
\(454\) 0 0
\(455\) −1.02086 + 26.0521i −0.0478586 + 1.22134i
\(456\) 0 0
\(457\) −4.80678 17.9391i −0.224852 0.839157i −0.982464 0.186453i \(-0.940301\pi\)
0.757612 0.652705i \(-0.226366\pi\)
\(458\) 0 0
\(459\) 15.8361 + 5.30497i 0.739168 + 0.247615i
\(460\) 0 0
\(461\) 1.15902 4.32554i 0.0539812 0.201460i −0.933669 0.358138i \(-0.883412\pi\)
0.987650 + 0.156678i \(0.0500784\pi\)
\(462\) 0 0
\(463\) −8.53278 8.53278i −0.396552 0.396552i 0.480463 0.877015i \(-0.340469\pi\)
−0.877015 + 0.480463i \(0.840469\pi\)
\(464\) 0 0
\(465\) 19.1674 + 19.9691i 0.888869 + 0.926045i
\(466\) 0 0
\(467\) 9.69885 0.448809 0.224405 0.974496i \(-0.427956\pi\)
0.224405 + 0.974496i \(0.427956\pi\)
\(468\) 0 0
\(469\) 16.2309 0.749474
\(470\) 0 0
\(471\) −7.19207 7.49288i −0.331393 0.345254i
\(472\) 0 0
\(473\) −0.730573 0.730573i −0.0335918 0.0335918i
\(474\) 0 0
\(475\) −0.433311 + 1.61714i −0.0198817 + 0.0741994i
\(476\) 0 0
\(477\) −40.0927 1.64319i −1.83572 0.0752364i
\(478\) 0 0
\(479\) −6.64461 24.7980i −0.303600 1.13305i −0.934144 0.356897i \(-0.883835\pi\)
0.630544 0.776154i \(-0.282832\pi\)
\(480\) 0 0
\(481\) 4.25386 13.7047i 0.193959 0.624882i
\(482\) 0 0
\(483\) 1.05653 51.5791i 0.0480740 2.34693i
\(484\) 0 0
\(485\) −18.7060 32.3998i −0.849397 1.47120i
\(486\) 0 0
\(487\) 15.4146 + 4.13033i 0.698501 + 0.187163i 0.590559 0.806994i \(-0.298907\pi\)
0.107942 + 0.994157i \(0.465574\pi\)
\(488\) 0 0
\(489\) −21.8176 + 12.0075i −0.986627 + 0.542998i
\(490\) 0 0
\(491\) 6.38912 11.0663i 0.288337 0.499414i −0.685076 0.728472i \(-0.740231\pi\)
0.973413 + 0.229057i \(0.0735643\pi\)
\(492\) 0 0
\(493\) 0.0883630i 0.00397967i
\(494\) 0 0
\(495\) 0.782436 + 0.495533i 0.0351679 + 0.0222726i
\(496\) 0 0
\(497\) −15.3212 8.84568i −0.687248 0.396783i
\(498\) 0 0
\(499\) −26.5255 + 26.5255i −1.18744 + 1.18744i −0.209671 + 0.977772i \(0.567239\pi\)
−0.977772 + 0.209671i \(0.932761\pi\)
\(500\) 0 0
\(501\) 4.73990 7.83468i 0.211763 0.350028i
\(502\) 0 0
\(503\) −3.29946 + 1.90495i −0.147116 + 0.0849374i −0.571751 0.820427i \(-0.693736\pi\)
0.424635 + 0.905365i \(0.360402\pi\)
\(504\) 0 0
\(505\) −0.892792 + 0.239223i −0.0397287 + 0.0106453i
\(506\) 0 0
\(507\) 7.94491 21.0684i 0.352846 0.935682i
\(508\) 0 0
\(509\) 37.5368 10.0580i 1.66379 0.445811i 0.700364 0.713786i \(-0.253021\pi\)
0.963426 + 0.267975i \(0.0863545\pi\)
\(510\) 0 0
\(511\) −27.0370 + 15.6098i −1.19605 + 0.690539i
\(512\) 0 0
\(513\) 9.17793 4.57186i 0.405215 0.201853i
\(514\) 0 0
\(515\) 14.4832 14.4832i 0.638206 0.638206i
\(516\) 0 0
\(517\) −0.885716 0.511368i −0.0389537 0.0224900i
\(518\) 0 0
\(519\) −2.95248 + 10.1801i −0.129599 + 0.446856i
\(520\) 0 0
\(521\) 41.6988i 1.82686i 0.406996 + 0.913430i \(0.366576\pi\)
−0.406996 + 0.913430i \(0.633424\pi\)
\(522\) 0 0
\(523\) 13.1004 22.6906i 0.572842 0.992192i −0.423430 0.905929i \(-0.639174\pi\)
0.996272 0.0862632i \(-0.0274926\pi\)
\(524\) 0 0
\(525\) 2.51454 + 4.56892i 0.109743 + 0.199404i
\(526\) 0 0
\(527\) −24.3499 6.52455i −1.06070 0.284214i
\(528\) 0 0
\(529\) −23.7195 41.0833i −1.03128 1.78623i
\(530\) 0 0
\(531\) 7.49606 23.9978i 0.325301 1.04142i
\(532\) 0 0
\(533\) 2.80377 9.03297i 0.121445 0.391261i
\(534\) 0 0
\(535\) 6.95194 + 25.9450i 0.300558 + 1.12170i
\(536\) 0 0
\(537\) 34.0221 8.37333i 1.46816 0.361336i
\(538\) 0 0
\(539\) −0.219405 + 0.818830i −0.00945043 + 0.0352695i
\(540\) 0 0
\(541\) 14.9894 + 14.9894i 0.644447 + 0.644447i 0.951645 0.307199i \(-0.0993916\pi\)
−0.307199 + 0.951645i \(0.599392\pi\)
\(542\) 0 0
\(543\) −5.48581 + 5.26558i −0.235419 + 0.225968i
\(544\) 0 0
\(545\) 12.7735 0.547155
\(546\) 0 0
\(547\) −23.7046 −1.01354 −0.506768 0.862082i \(-0.669160\pi\)
−0.506768 + 0.862082i \(0.669160\pi\)
\(548\) 0 0
\(549\) −35.1668 + 18.4263i −1.50088 + 0.786414i
\(550\) 0 0
\(551\) 0.0383608 + 0.0383608i 0.00163422 + 0.00163422i
\(552\) 0 0
\(553\) −12.2948 + 45.8847i −0.522827 + 1.95122i
\(554\) 0 0
\(555\) 3.35666 + 13.6386i 0.142482 + 0.578926i
\(556\) 0 0
\(557\) −10.2264 38.1653i −0.433304 1.61711i −0.745091 0.666962i \(-0.767594\pi\)
0.311787 0.950152i \(-0.399072\pi\)
\(558\) 0 0
\(559\) 0.962687 24.5676i 0.0407173 1.03910i
\(560\) 0 0
\(561\) −0.843309 0.0172741i −0.0356045 0.000729315i
\(562\) 0 0
\(563\) −8.48383 14.6944i −0.357551 0.619296i 0.630000 0.776595i \(-0.283055\pi\)
−0.987551 + 0.157299i \(0.949721\pi\)
\(564\) 0 0
\(565\) 12.1187 + 3.24719i 0.509837 + 0.136610i
\(566\) 0 0
\(567\) 10.7637 30.0721i 0.452035 1.26291i
\(568\) 0 0
\(569\) −15.2347 + 26.3873i −0.638674 + 1.10622i 0.347051 + 0.937846i \(0.387183\pi\)
−0.985724 + 0.168369i \(0.946150\pi\)
\(570\) 0 0
\(571\) 5.03996i 0.210916i 0.994424 + 0.105458i \(0.0336309\pi\)
−0.994424 + 0.105458i \(0.966369\pi\)
\(572\) 0 0
\(573\) −23.6316 6.85376i −0.987225 0.286320i
\(574\) 0 0
\(575\) 6.16660 + 3.56029i 0.257165 + 0.148474i
\(576\) 0 0
\(577\) 15.8862 15.8862i 0.661350 0.661350i −0.294348 0.955698i \(-0.595102\pi\)
0.955698 + 0.294348i \(0.0951024\pi\)
\(578\) 0 0
\(579\) 21.6439 + 13.0943i 0.899492 + 0.544182i
\(580\) 0 0
\(581\) 8.43596 4.87051i 0.349983 0.202063i
\(582\) 0 0
\(583\) 1.95752 0.524516i 0.0810723 0.0217233i
\(584\) 0 0
\(585\) 3.98196 + 21.6767i 0.164634 + 0.896221i
\(586\) 0 0
\(587\) 8.06056 2.15982i 0.332695 0.0891453i −0.0886047 0.996067i \(-0.528241\pi\)
0.421300 + 0.906922i \(0.361574\pi\)
\(588\) 0 0
\(589\) −13.4034 + 7.73848i −0.552279 + 0.318859i
\(590\) 0 0
\(591\) −1.02564 0.620500i −0.0421892 0.0255240i
\(592\) 0 0
\(593\) 30.0266 30.0266i 1.23305 1.23305i 0.270257 0.962788i \(-0.412891\pi\)
0.962788 0.270257i \(-0.0871086\pi\)
\(594\) 0 0
\(595\) 20.1279 + 11.6208i 0.825163 + 0.476408i
\(596\) 0 0
\(597\) 26.5380 + 7.69669i 1.08613 + 0.315004i
\(598\) 0 0
\(599\) 17.0119i 0.695088i −0.937664 0.347544i \(-0.887016\pi\)
0.937664 0.347544i \(-0.112984\pi\)
\(600\) 0 0
\(601\) −12.8220 + 22.2084i −0.523022 + 0.905901i 0.476619 + 0.879110i \(0.341862\pi\)
−0.999641 + 0.0267907i \(0.991471\pi\)
\(602\) 0 0
\(603\) 13.3872 3.00541i 0.545168 0.122390i
\(604\) 0 0
\(605\) 21.6041 + 5.78880i 0.878331 + 0.235348i
\(606\) 0 0
\(607\) 8.99964 + 15.5878i 0.365284 + 0.632691i 0.988822 0.149103i \(-0.0476385\pi\)
−0.623537 + 0.781793i \(0.714305\pi\)
\(608\) 0 0
\(609\) 0.168957 + 0.00346087i 0.00684647 + 0.000140241i
\(610\) 0 0
\(611\) −5.37377 23.7371i −0.217400 0.960301i
\(612\) 0 0
\(613\) 6.40516 + 23.9044i 0.258702 + 0.965489i 0.965993 + 0.258567i \(0.0832502\pi\)
−0.707292 + 0.706922i \(0.750083\pi\)
\(614\) 0 0
\(615\) 2.21242 + 8.98938i 0.0892133 + 0.362487i
\(616\) 0 0
\(617\) 9.32585 34.8045i 0.375444 1.40118i −0.477250 0.878768i \(-0.658366\pi\)
0.852694 0.522410i \(-0.174967\pi\)
\(618\) 0 0
\(619\) 8.29611 + 8.29611i 0.333449 + 0.333449i 0.853895 0.520446i \(-0.174234\pi\)
−0.520446 + 0.853895i \(0.674234\pi\)
\(620\) 0 0
\(621\) −8.67926 42.7378i −0.348287 1.71501i
\(622\) 0 0
\(623\) 39.3947 1.57831
\(624\) 0 0
\(625\) 20.0381 0.801524
\(626\) 0 0
\(627\) −0.373602 + 0.358604i −0.0149202 + 0.0143213i
\(628\) 0 0
\(629\) −9.04524 9.04524i −0.360657 0.360657i
\(630\) 0 0
\(631\) −5.40401 + 20.1680i −0.215130 + 0.802877i 0.770990 + 0.636847i \(0.219762\pi\)
−0.986121 + 0.166030i \(0.946905\pi\)
\(632\) 0 0
\(633\) −11.0507 + 2.71973i −0.439225 + 0.108100i
\(634\) 0 0
\(635\) −4.96598 18.5333i −0.197069 0.735471i
\(636\) 0 0
\(637\) −17.8517 + 9.39464i −0.707311 + 0.372229i
\(638\) 0 0
\(639\) −14.2747 4.45892i −0.564700 0.176392i
\(640\) 0 0
\(641\) −5.39416 9.34296i −0.213056 0.369025i 0.739613 0.673032i \(-0.235008\pi\)
−0.952670 + 0.304008i \(0.901675\pi\)
\(642\) 0 0
\(643\) 8.87352 + 2.37765i 0.349937 + 0.0937655i 0.429506 0.903064i \(-0.358688\pi\)
−0.0795687 + 0.996829i \(0.525354\pi\)
\(644\) 0 0
\(645\) 11.6033 + 21.0832i 0.456881 + 0.830152i
\(646\) 0 0
\(647\) −12.5642 + 21.7619i −0.493951 + 0.855549i −0.999976 0.00697039i \(-0.997781\pi\)
0.506024 + 0.862519i \(0.331115\pi\)
\(648\) 0 0
\(649\) 1.26976i 0.0498424i
\(650\) 0 0
\(651\) −13.4291 + 46.3033i −0.526329 + 1.81477i
\(652\) 0 0
\(653\) −12.6456 7.30093i −0.494860 0.285708i 0.231728 0.972781i \(-0.425562\pi\)
−0.726588 + 0.687073i \(0.758895\pi\)
\(654\) 0 0
\(655\) 21.4394 21.4394i 0.837706 0.837706i
\(656\) 0 0
\(657\) −19.4096 + 17.8812i −0.757240 + 0.697614i
\(658\) 0 0
\(659\) −9.24365 + 5.33682i −0.360081 + 0.207893i −0.669116 0.743158i \(-0.733327\pi\)
0.309035 + 0.951051i \(0.399994\pi\)
\(660\) 0 0
\(661\) −39.5548 + 10.5987i −1.53850 + 0.412241i −0.925782 0.378057i \(-0.876592\pi\)
−0.612723 + 0.790298i \(0.709926\pi\)
\(662\) 0 0
\(663\) −13.3219 15.0140i −0.517379 0.583096i
\(664\) 0 0
\(665\) 13.7830 3.69314i 0.534481 0.143214i
\(666\) 0 0
\(667\) 0.199823 0.115368i 0.00773717 0.00446706i
\(668\) 0 0
\(669\) 6.22058 10.2821i 0.240502 0.397531i
\(670\) 0 0
\(671\) 1.41784 1.41784i 0.0547352 0.0547352i
\(672\) 0 0
\(673\) 2.95408 + 1.70554i 0.113871 + 0.0657437i 0.555854 0.831280i \(-0.312391\pi\)
−0.441983 + 0.897024i \(0.645725\pi\)
\(674\) 0 0
\(675\) 2.91998 + 3.30281i 0.112390 + 0.127125i
\(676\) 0 0
\(677\) 9.33387i 0.358730i −0.983783 0.179365i \(-0.942596\pi\)
0.983783 0.179365i \(-0.0574043\pi\)
\(678\) 0 0
\(679\) 32.5816 56.4330i 1.25037 2.16570i
\(680\) 0 0
\(681\) −17.6295 + 9.70254i −0.675564 + 0.371802i
\(682\) 0 0
\(683\) 20.2277 + 5.42001i 0.773993 + 0.207391i 0.624135 0.781317i \(-0.285452\pi\)
0.149858 + 0.988708i \(0.452118\pi\)
\(684\) 0 0
\(685\) −9.16608 15.8761i −0.350218 0.606595i
\(686\) 0 0
\(687\) 0.938354 45.8097i 0.0358005 1.74775i
\(688\) 0 0
\(689\) 40.7887 + 25.7298i 1.55392 + 0.980226i
\(690\) 0 0
\(691\) 0.861578 + 3.21545i 0.0327760 + 0.122322i 0.980376 0.197139i \(-0.0631650\pi\)
−0.947600 + 0.319461i \(0.896498\pi\)
\(692\) 0 0
\(693\) −0.0660589 + 1.61179i −0.00250937 + 0.0612270i
\(694\) 0 0
\(695\) −0.0484033 + 0.180643i −0.00183604 + 0.00685220i
\(696\) 0 0
\(697\) −5.96184 5.96184i −0.225821 0.225821i
\(698\) 0 0
\(699\) 5.95130 + 6.20021i 0.225099 + 0.234513i
\(700\) 0 0
\(701\) −11.9388 −0.450923 −0.225462 0.974252i \(-0.572389\pi\)
−0.225462 + 0.974252i \(0.572389\pi\)
\(702\) 0 0
\(703\) −7.85356 −0.296203
\(704\) 0 0
\(705\) 16.4961 + 17.1861i 0.621281 + 0.647265i
\(706\) 0 0
\(707\) −1.13837 1.13837i −0.0428127 0.0428127i
\(708\) 0 0
\(709\) −1.31499 + 4.90761i −0.0493855 + 0.184309i −0.986212 0.165484i \(-0.947081\pi\)
0.936827 + 0.349793i \(0.113748\pi\)
\(710\) 0 0
\(711\) −1.64439 + 40.1221i −0.0616695 + 1.50469i
\(712\) 0 0
\(713\) 17.0370 + 63.5831i 0.638042 + 2.38120i
\(714\) 0 0
\(715\) −0.518377 0.985023i −0.0193862 0.0368378i
\(716\) 0 0
\(717\) 0.995633 48.6059i 0.0371826 1.81522i
\(718\) 0 0
\(719\) −1.78171 3.08602i −0.0664468 0.115089i 0.830888 0.556440i \(-0.187833\pi\)
−0.897335 + 0.441350i \(0.854500\pi\)
\(720\) 0 0
\(721\) 34.4599 + 9.23351i 1.28336 + 0.343874i
\(722\) 0 0
\(723\) 9.37632 5.16033i 0.348709 0.191915i
\(724\) 0 0
\(725\) −0.0116624 + 0.0201998i −0.000433129 + 0.000750202i
\(726\) 0 0
\(727\) 30.2149i 1.12061i −0.828287 0.560304i \(-0.810684\pi\)
0.828287 0.560304i \(-0.189316\pi\)
\(728\) 0 0
\(729\) 3.30956 26.7964i 0.122576 0.992459i
\(730\) 0 0
\(731\) −18.9809 10.9587i −0.702036 0.405321i
\(732\) 0 0
\(733\) −4.27805 + 4.27805i −0.158013 + 0.158013i −0.781686 0.623672i \(-0.785640\pi\)
0.623672 + 0.781686i \(0.285640\pi\)
\(734\) 0 0
\(735\) 10.2208 16.8941i 0.376998 0.623149i
\(736\) 0 0
\(737\) −0.600109 + 0.346473i −0.0221053 + 0.0127625i
\(738\) 0 0
\(739\) 22.8637 6.12632i 0.841056 0.225360i 0.187525 0.982260i \(-0.439954\pi\)
0.653531 + 0.756900i \(0.273287\pi\)
\(740\) 0 0
\(741\) −12.3014 0.734600i −0.451902 0.0269862i
\(742\) 0 0
\(743\) 45.0215 12.0635i 1.65168 0.442566i 0.691597 0.722284i \(-0.256907\pi\)
0.960082 + 0.279717i \(0.0902408\pi\)
\(744\) 0 0
\(745\) −23.8630 + 13.7773i −0.874274 + 0.504762i
\(746\) 0 0
\(747\) 6.05609 5.57922i 0.221581 0.204133i
\(748\) 0 0
\(749\) −33.0815 + 33.0815i −1.20877 + 1.20877i
\(750\) 0 0
\(751\) −38.1177 22.0072i −1.39093 0.803056i −0.397514 0.917596i \(-0.630127\pi\)
−0.993419 + 0.114540i \(0.963460\pi\)
\(752\) 0 0
\(753\) 2.09022 7.20703i 0.0761718 0.262639i
\(754\) 0 0
\(755\) 23.7622i 0.864796i
\(756\) 0 0
\(757\) 15.5726 26.9726i 0.565996 0.980334i −0.430960 0.902371i \(-0.641825\pi\)
0.996956 0.0779632i \(-0.0248417\pi\)
\(758\) 0 0
\(759\) 1.06197 + 1.92960i 0.0385471 + 0.0700400i
\(760\) 0 0
\(761\) −35.3991 9.48515i −1.28322 0.343836i −0.448136 0.893966i \(-0.647912\pi\)
−0.835080 + 0.550129i \(0.814578\pi\)
\(762\) 0 0
\(763\) 11.1242 + 19.2677i 0.402724 + 0.697538i
\(764\) 0 0
\(765\) 18.7532 + 5.85782i 0.678022 + 0.211790i
\(766\) 0 0
\(767\) −22.1862 + 20.5131i −0.801098 + 0.740683i
\(768\) 0 0
\(769\) −0.493875 1.84317i −0.0178096 0.0664663i 0.956449 0.291899i \(-0.0942871\pi\)
−0.974259 + 0.225433i \(0.927620\pi\)
\(770\) 0 0
\(771\) −35.7570 + 8.80032i −1.28776 + 0.316936i
\(772\) 0 0
\(773\) −7.52425 + 28.0809i −0.270629 + 1.01000i 0.688086 + 0.725629i \(0.258451\pi\)
−0.958714 + 0.284371i \(0.908215\pi\)
\(774\) 0 0
\(775\) −4.70528 4.70528i −0.169019 0.169019i
\(776\) 0 0
\(777\) −17.6494 + 16.9409i −0.633170 + 0.607751i
\(778\) 0 0
\(779\) −5.17639 −0.185463
\(780\) 0 0
\(781\) 0.755297 0.0270266
\(782\) 0 0
\(783\) 0.139995 0.0284305i 0.00500303 0.00101602i
\(784\) 0 0
\(785\) −8.63933 8.63933i −0.308351 0.308351i
\(786\) 0 0
\(787\) 11.8946 44.3912i 0.423996 1.58237i −0.342110 0.939660i \(-0.611142\pi\)
0.766106 0.642714i \(-0.222192\pi\)
\(788\) 0 0
\(789\) 7.17030 + 29.1340i 0.255270 + 1.03720i
\(790\) 0 0
\(791\) 5.65587 + 21.1080i 0.201099 + 0.750513i
\(792\) 0 0
\(793\) 47.6790 + 1.86831i 1.69313 + 0.0663457i
\(794\) 0 0
\(795\) −47.1938 0.966707i −1.67379 0.0342856i
\(796\) 0 0