Properties

Label 252.2.x.a.41.1
Level $252$
Weight $2$
Character 252.41
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 3 x^{14} - 9 x^{12} - 9 x^{10} + 225 x^{8} - 81 x^{6} - 729 x^{4} - 2187 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.1
Root \(0.744857 - 1.56371i\) of defining polynomial
Character \(\chi\) \(=\) 252.41
Dual form 252.2.x.a.209.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.72664 + 0.136790i) q^{3} +(-0.276914 + 0.479629i) q^{5} +(-0.519138 - 2.59432i) q^{7} +(2.96258 - 0.472374i) q^{9} +O(q^{10})\) \(q+(-1.72664 + 0.136790i) q^{3} +(-0.276914 + 0.479629i) q^{5} +(-0.519138 - 2.59432i) q^{7} +(2.96258 - 0.472374i) q^{9} +(4.03478 - 2.32948i) q^{11} +(-3.58265 - 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} +7.24527 q^{17} -6.71715i q^{19} +(1.25124 + 4.40845i) q^{21} +(-4.85295 - 2.80185i) q^{23} +(2.34664 + 4.06450i) q^{25} +(-5.05069 + 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +(0.830741 + 0.479629i) q^{31} +(-6.64796 + 4.57409i) q^{33} +(1.38807 + 0.469409i) q^{35} -7.06956 q^{37} +(6.46889 + 3.08139i) q^{39} +(2.39152 - 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(-0.593814 + 1.55174i) q^{45} +(4.90301 + 8.49226i) q^{47} +(-6.46099 + 2.69362i) q^{49} +(-12.5100 + 0.991080i) q^{51} +8.43202i q^{53} +2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} +(-3.89955 + 6.75422i) q^{59} +(5.37336 - 3.10231i) q^{61} +(-2.76348 - 7.44065i) q^{63} +(1.98417 - 1.14556i) q^{65} +(1.68814 - 2.92394i) q^{67} +(8.76257 + 4.17396i) q^{69} +0.407556i q^{71} -8.63566i q^{73} +(-4.60778 - 6.69693i) q^{75} +(-8.13802 - 9.25818i) q^{77} +(-0.318176 - 0.551097i) q^{79} +(8.55373 - 2.79889i) q^{81} +(-2.78840 - 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(-1.92117 + 1.32185i) q^{87} +6.93137 q^{89} +(-3.50632 + 10.3683i) q^{91} +(-1.50000 - 0.714509i) q^{93} +(3.22174 + 1.86007i) q^{95} +(-7.48798 + 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + O(q^{10}) \) \( 16q - q^{7} + 6q^{11} - 12q^{15} + 9q^{21} + 6q^{23} - 8q^{25} - 12q^{29} + 4q^{37} + 18q^{39} + 4q^{43} - 5q^{49} - 18q^{51} - 42q^{57} - 27q^{63} - 24q^{65} + 14q^{67} - 21q^{77} + 20q^{79} - 36q^{81} + 6q^{85} - 18q^{91} - 24q^{93} - 60q^{95} + 90q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.72664 + 0.136790i −0.996877 + 0.0789757i
\(4\) 0 0
\(5\) −0.276914 + 0.479629i −0.123840 + 0.214496i −0.921279 0.388903i \(-0.872854\pi\)
0.797439 + 0.603399i \(0.206187\pi\)
\(6\) 0 0
\(7\) −0.519138 2.59432i −0.196216 0.980561i
\(8\) 0 0
\(9\) 2.96258 0.472374i 0.987526 0.157458i
\(10\) 0 0
\(11\) 4.03478 2.32948i 1.21653 0.702365i 0.252357 0.967634i \(-0.418794\pi\)
0.964174 + 0.265270i \(0.0854610\pi\)
\(12\) 0 0
\(13\) −3.58265 2.06844i −0.993648 0.573683i −0.0872856 0.996183i \(-0.527819\pi\)
−0.906363 + 0.422500i \(0.861153\pi\)
\(14\) 0 0
\(15\) 0.412522 0.866025i 0.106513 0.223607i
\(16\) 0 0
\(17\) 7.24527 1.75724 0.878619 0.477524i \(-0.158466\pi\)
0.878619 + 0.477524i \(0.158466\pi\)
\(18\) 0 0
\(19\) 6.71715i 1.54102i −0.637428 0.770510i \(-0.720002\pi\)
0.637428 0.770510i \(-0.279998\pi\)
\(20\) 0 0
\(21\) 1.25124 + 4.40845i 0.273043 + 0.962002i
\(22\) 0 0
\(23\) −4.85295 2.80185i −1.01191 0.584227i −0.100160 0.994971i \(-0.531936\pi\)
−0.911751 + 0.410744i \(0.865269\pi\)
\(24\) 0 0
\(25\) 2.34664 + 4.06450i 0.469328 + 0.812899i
\(26\) 0 0
\(27\) −5.05069 + 1.22087i −0.972006 + 0.234957i
\(28\) 0 0
\(29\) 1.16599 0.673187i 0.216520 0.125008i −0.387818 0.921736i \(-0.626771\pi\)
0.604338 + 0.796728i \(0.293438\pi\)
\(30\) 0 0
\(31\) 0.830741 + 0.479629i 0.149206 + 0.0861438i 0.572744 0.819734i \(-0.305879\pi\)
−0.423539 + 0.905878i \(0.639212\pi\)
\(32\) 0 0
\(33\) −6.64796 + 4.57409i −1.15726 + 0.796247i
\(34\) 0 0
\(35\) 1.38807 + 0.469409i 0.234626 + 0.0793447i
\(36\) 0 0
\(37\) −7.06956 −1.16223 −0.581114 0.813822i \(-0.697383\pi\)
−0.581114 + 0.813822i \(0.697383\pi\)
\(38\) 0 0
\(39\) 6.46889 + 3.08139i 1.03585 + 0.493417i
\(40\) 0 0
\(41\) 2.39152 4.14224i 0.373493 0.646909i −0.616607 0.787271i \(-0.711493\pi\)
0.990100 + 0.140362i \(0.0448265\pi\)
\(42\) 0 0
\(43\) −1.02846 1.78135i −0.156839 0.271653i 0.776888 0.629639i \(-0.216797\pi\)
−0.933727 + 0.357986i \(0.883464\pi\)
\(44\) 0 0
\(45\) −0.593814 + 1.55174i −0.0885206 + 0.231320i
\(46\) 0 0
\(47\) 4.90301 + 8.49226i 0.715177 + 1.23872i 0.962891 + 0.269890i \(0.0869874\pi\)
−0.247714 + 0.968833i \(0.579679\pi\)
\(48\) 0 0
\(49\) −6.46099 + 2.69362i −0.922999 + 0.384803i
\(50\) 0 0
\(51\) −12.5100 + 0.991080i −1.75175 + 0.138779i
\(52\) 0 0
\(53\) 8.43202i 1.15823i 0.815247 + 0.579114i \(0.196601\pi\)
−0.815247 + 0.579114i \(0.803399\pi\)
\(54\) 0 0
\(55\) 2.58026i 0.347922i
\(56\) 0 0
\(57\) 0.918838 + 11.5981i 0.121703 + 1.53621i
\(58\) 0 0
\(59\) −3.89955 + 6.75422i −0.507678 + 0.879325i 0.492282 + 0.870436i \(0.336163\pi\)
−0.999960 + 0.00888893i \(0.997171\pi\)
\(60\) 0 0
\(61\) 5.37336 3.10231i 0.687989 0.397211i −0.114869 0.993381i \(-0.536645\pi\)
0.802858 + 0.596170i \(0.203312\pi\)
\(62\) 0 0
\(63\) −2.76348 7.44065i −0.348165 0.937433i
\(64\) 0 0
\(65\) 1.98417 1.14556i 0.246106 0.142089i
\(66\) 0 0
\(67\) 1.68814 2.92394i 0.206239 0.357217i −0.744288 0.667859i \(-0.767211\pi\)
0.950527 + 0.310642i \(0.100544\pi\)
\(68\) 0 0
\(69\) 8.76257 + 4.17396i 1.05489 + 0.502486i
\(70\) 0 0
\(71\) 0.407556i 0.0483680i 0.999708 + 0.0241840i \(0.00769875\pi\)
−0.999708 + 0.0241840i \(0.992301\pi\)
\(72\) 0 0
\(73\) 8.63566i 1.01073i −0.862906 0.505364i \(-0.831358\pi\)
0.862906 0.505364i \(-0.168642\pi\)
\(74\) 0 0
\(75\) −4.60778 6.69693i −0.532061 0.773295i
\(76\) 0 0
\(77\) −8.13802 9.25818i −0.927414 1.05507i
\(78\) 0 0
\(79\) −0.318176 0.551097i −0.0357976 0.0620032i 0.847572 0.530681i \(-0.178064\pi\)
−0.883369 + 0.468678i \(0.844730\pi\)
\(80\) 0 0
\(81\) 8.55373 2.79889i 0.950414 0.310988i
\(82\) 0 0
\(83\) −2.78840 4.82965i −0.306066 0.530123i 0.671432 0.741066i \(-0.265680\pi\)
−0.977498 + 0.210944i \(0.932346\pi\)
\(84\) 0 0
\(85\) −2.00632 + 3.47504i −0.217616 + 0.376921i
\(86\) 0 0
\(87\) −1.92117 + 1.32185i −0.205971 + 0.141717i
\(88\) 0 0
\(89\) 6.93137 0.734723 0.367362 0.930078i \(-0.380261\pi\)
0.367362 + 0.930078i \(0.380261\pi\)
\(90\) 0 0
\(91\) −3.50632 + 10.3683i −0.367562 + 1.08690i
\(92\) 0 0
\(93\) −1.50000 0.714509i −0.155543 0.0740912i
\(94\) 0 0
\(95\) 3.22174 + 1.86007i 0.330543 + 0.190839i
\(96\) 0 0
\(97\) −7.48798 + 4.32318i −0.760289 + 0.438953i −0.829399 0.558656i \(-0.811317\pi\)
0.0691107 + 0.997609i \(0.477984\pi\)
\(98\) 0 0
\(99\) 10.8530 8.80719i 1.09076 0.885156i
\(100\) 0 0
\(101\) −2.34227 4.05692i −0.233064 0.403679i 0.725644 0.688070i \(-0.241542\pi\)
−0.958708 + 0.284391i \(0.908209\pi\)
\(102\) 0 0
\(103\) 6.40804 + 3.69969i 0.631403 + 0.364541i 0.781295 0.624162i \(-0.214559\pi\)
−0.149892 + 0.988702i \(0.547893\pi\)
\(104\) 0 0
\(105\) −2.46090 0.620628i −0.240160 0.0605671i
\(106\) 0 0
\(107\) 5.06059i 0.489225i 0.969621 + 0.244613i \(0.0786608\pi\)
−0.969621 + 0.244613i \(0.921339\pi\)
\(108\) 0 0
\(109\) 11.7628 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(110\) 0 0
\(111\) 12.2066 0.967044i 1.15860 0.0917877i
\(112\) 0 0
\(113\) −1.51895 0.876965i −0.142891 0.0824979i 0.426850 0.904322i \(-0.359623\pi\)
−0.569741 + 0.821824i \(0.692956\pi\)
\(114\) 0 0
\(115\) 2.68770 1.55174i 0.250629 0.144701i
\(116\) 0 0
\(117\) −11.5910 4.43557i −1.07158 0.410069i
\(118\) 0 0
\(119\) −3.76130 18.7966i −0.344798 1.72308i
\(120\) 0 0
\(121\) 5.35295 9.27159i 0.486632 0.842872i
\(122\) 0 0
\(123\) −3.56269 + 7.47930i −0.321237 + 0.674386i
\(124\) 0 0
\(125\) −5.36840 −0.480164
\(126\) 0 0
\(127\) 11.0822 0.983385 0.491693 0.870769i \(-0.336378\pi\)
0.491693 + 0.870769i \(0.336378\pi\)
\(128\) 0 0
\(129\) 2.01945 + 2.93506i 0.177803 + 0.258418i
\(130\) 0 0
\(131\) −9.23643 + 15.9980i −0.806990 + 1.39775i 0.107949 + 0.994156i \(0.465572\pi\)
−0.914939 + 0.403592i \(0.867762\pi\)
\(132\) 0 0
\(133\) −17.4264 + 3.48713i −1.51106 + 0.302372i
\(134\) 0 0
\(135\) 0.813041 2.76053i 0.0699754 0.237589i
\(136\) 0 0
\(137\) 19.0537 11.0007i 1.62787 0.939851i 0.643142 0.765747i \(-0.277630\pi\)
0.984727 0.174104i \(-0.0557030\pi\)
\(138\) 0 0
\(139\) 8.55986 + 4.94204i 0.726038 + 0.419178i 0.816971 0.576679i \(-0.195652\pi\)
−0.0909332 + 0.995857i \(0.528985\pi\)
\(140\) 0 0
\(141\) −9.62739 13.9924i −0.810773 1.17837i
\(142\) 0 0
\(143\) −19.2736 −1.61174
\(144\) 0 0
\(145\) 0.745659i 0.0619236i
\(146\) 0 0
\(147\) 10.7874 5.53471i 0.889726 0.456495i
\(148\) 0 0
\(149\) −6.36677 3.67585i −0.521586 0.301138i 0.215997 0.976394i \(-0.430700\pi\)
−0.737583 + 0.675256i \(0.764033\pi\)
\(150\) 0 0
\(151\) 2.16599 + 3.75161i 0.176266 + 0.305302i 0.940599 0.339520i \(-0.110265\pi\)
−0.764333 + 0.644822i \(0.776931\pi\)
\(152\) 0 0
\(153\) 21.4647 3.42248i 1.73532 0.276691i
\(154\) 0 0
\(155\) −0.460087 + 0.265632i −0.0369551 + 0.0213360i
\(156\) 0 0
\(157\) 1.54152 + 0.889998i 0.123027 + 0.0710296i 0.560251 0.828323i \(-0.310705\pi\)
−0.437224 + 0.899353i \(0.644038\pi\)
\(158\) 0 0
\(159\) −1.15342 14.5591i −0.0914718 1.15461i
\(160\) 0 0
\(161\) −4.74955 + 14.0447i −0.374317 + 1.10687i
\(162\) 0 0
\(163\) −5.63635 −0.441473 −0.220737 0.975333i \(-0.570846\pi\)
−0.220737 + 0.975333i \(0.570846\pi\)
\(164\) 0 0
\(165\) −0.352954 4.45518i −0.0274774 0.346835i
\(166\) 0 0
\(167\) 2.38803 4.13618i 0.184791 0.320067i −0.758715 0.651423i \(-0.774173\pi\)
0.943506 + 0.331355i \(0.107506\pi\)
\(168\) 0 0
\(169\) 2.05692 + 3.56270i 0.158225 + 0.274054i
\(170\) 0 0
\(171\) −3.17301 19.9001i −0.242646 1.52180i
\(172\) 0 0
\(173\) 2.83766 + 4.91497i 0.215743 + 0.373678i 0.953502 0.301386i \(-0.0974493\pi\)
−0.737759 + 0.675064i \(0.764116\pi\)
\(174\) 0 0
\(175\) 9.32637 8.19796i 0.705008 0.619708i
\(176\) 0 0
\(177\) 5.80921 12.1955i 0.436647 0.916672i
\(178\) 0 0
\(179\) 12.6305i 0.944048i 0.881586 + 0.472024i \(0.156476\pi\)
−0.881586 + 0.472024i \(0.843524\pi\)
\(180\) 0 0
\(181\) 22.7424i 1.69043i 0.534426 + 0.845215i \(0.320528\pi\)
−0.534426 + 0.845215i \(0.679472\pi\)
\(182\) 0 0
\(183\) −8.85351 + 6.09160i −0.654470 + 0.450304i
\(184\) 0 0
\(185\) 1.95766 3.39076i 0.143930 0.249294i
\(186\) 0 0
\(187\) 29.2331 16.8777i 2.13773 1.23422i
\(188\) 0 0
\(189\) 5.78934 + 12.4693i 0.421112 + 0.907009i
\(190\) 0 0
\(191\) −10.0537 + 5.80452i −0.727462 + 0.420000i −0.817493 0.575939i \(-0.804637\pi\)
0.0900309 + 0.995939i \(0.471303\pi\)
\(192\) 0 0
\(193\) −3.16599 + 5.48366i −0.227893 + 0.394723i −0.957184 0.289482i \(-0.906517\pi\)
0.729290 + 0.684204i \(0.239850\pi\)
\(194\) 0 0
\(195\) −3.26925 + 2.24939i −0.234116 + 0.161082i
\(196\) 0 0
\(197\) 3.10030i 0.220888i 0.993882 + 0.110444i \(0.0352272\pi\)
−0.993882 + 0.110444i \(0.964773\pi\)
\(198\) 0 0
\(199\) 15.7268i 1.11484i 0.830229 + 0.557422i \(0.188210\pi\)
−0.830229 + 0.557422i \(0.811790\pi\)
\(200\) 0 0
\(201\) −2.51485 + 5.27952i −0.177384 + 0.372389i
\(202\) 0 0
\(203\) −2.35177 2.67549i −0.165062 0.187782i
\(204\) 0 0
\(205\) 1.32449 + 2.29409i 0.0925065 + 0.160226i
\(206\) 0 0
\(207\) −15.7008 6.00830i −1.09128 0.417606i
\(208\) 0 0
\(209\) −15.6475 27.1022i −1.08236 1.87470i
\(210\) 0 0
\(211\) 3.51263 6.08406i 0.241820 0.418844i −0.719413 0.694582i \(-0.755589\pi\)
0.961233 + 0.275739i \(0.0889225\pi\)
\(212\) 0 0
\(213\) −0.0557495 0.703702i −0.00381989 0.0482169i
\(214\) 0 0
\(215\) 1.13918 0.0776915
\(216\) 0 0
\(217\) 0.813041 2.40420i 0.0551928 0.163208i
\(218\) 0 0
\(219\) 1.18127 + 14.9107i 0.0798229 + 1.00757i
\(220\) 0 0
\(221\) −25.9573 14.9864i −1.74608 1.00810i
\(222\) 0 0
\(223\) −21.3477 + 12.3251i −1.42955 + 0.825350i −0.997085 0.0763008i \(-0.975689\pi\)
−0.432464 + 0.901651i \(0.642356\pi\)
\(224\) 0 0
\(225\) 8.87206 + 10.9329i 0.591470 + 0.728859i
\(226\) 0 0
\(227\) 10.0372 + 17.3849i 0.666190 + 1.15388i 0.978961 + 0.204047i \(0.0654095\pi\)
−0.312771 + 0.949829i \(0.601257\pi\)
\(228\) 0 0
\(229\) −6.75865 3.90211i −0.446624 0.257859i 0.259779 0.965668i \(-0.416350\pi\)
−0.706403 + 0.707809i \(0.749684\pi\)
\(230\) 0 0
\(231\) 15.3179 + 14.8724i 1.00784 + 0.978529i
\(232\) 0 0
\(233\) 7.96562i 0.521845i −0.965360 0.260922i \(-0.915973\pi\)
0.965360 0.260922i \(-0.0840267\pi\)
\(234\) 0 0
\(235\) −5.43084 −0.354269
\(236\) 0 0
\(237\) 0.624760 + 0.908023i 0.0405825 + 0.0589824i
\(238\) 0 0
\(239\) 23.2059 + 13.3979i 1.50107 + 0.866640i 0.999999 + 0.00123146i \(0.000391987\pi\)
0.501066 + 0.865409i \(0.332941\pi\)
\(240\) 0 0
\(241\) −0.757259 + 0.437203i −0.0487793 + 0.0281628i −0.524191 0.851601i \(-0.675632\pi\)
0.475412 + 0.879763i \(0.342299\pi\)
\(242\) 0 0
\(243\) −14.3864 + 6.00274i −0.922885 + 0.385076i
\(244\) 0 0
\(245\) 0.497200 3.84478i 0.0317649 0.245634i
\(246\) 0 0
\(247\) −13.8940 + 24.0652i −0.884057 + 1.53123i
\(248\) 0 0
\(249\) 5.47521 + 7.95764i 0.346977 + 0.504295i
\(250\) 0 0
\(251\) 2.32082 0.146489 0.0732445 0.997314i \(-0.476665\pi\)
0.0732445 + 0.997314i \(0.476665\pi\)
\(252\) 0 0
\(253\) −26.1075 −1.64136
\(254\) 0 0
\(255\) 2.98884 6.27459i 0.187168 0.392930i
\(256\) 0 0
\(257\) −12.3017 + 21.3072i −0.767361 + 1.32911i 0.171628 + 0.985162i \(0.445097\pi\)
−0.938989 + 0.343947i \(0.888236\pi\)
\(258\) 0 0
\(259\) 3.67007 + 18.3407i 0.228047 + 1.13963i
\(260\) 0 0
\(261\) 3.13635 2.54515i 0.194135 0.157541i
\(262\) 0 0
\(263\) −20.5268 + 11.8512i −1.26574 + 0.730775i −0.974179 0.225778i \(-0.927508\pi\)
−0.291560 + 0.956552i \(0.594174\pi\)
\(264\) 0 0
\(265\) −4.04424 2.33494i −0.248436 0.143434i
\(266\) 0 0
\(267\) −11.9680 + 0.948141i −0.732429 + 0.0580253i
\(268\) 0 0
\(269\) 20.6212 1.25730 0.628648 0.777690i \(-0.283609\pi\)
0.628648 + 0.777690i \(0.283609\pi\)
\(270\) 0 0
\(271\) 13.9454i 0.847123i −0.905867 0.423562i \(-0.860780\pi\)
0.905867 0.423562i \(-0.139220\pi\)
\(272\) 0 0
\(273\) 4.63586 18.3820i 0.280575 1.11253i
\(274\) 0 0
\(275\) 18.9363 + 10.9329i 1.14190 + 0.659278i
\(276\) 0 0
\(277\) −10.3940 18.0030i −0.624518 1.08170i −0.988634 0.150343i \(-0.951962\pi\)
0.364116 0.931354i \(-0.381371\pi\)
\(278\) 0 0
\(279\) 2.68770 + 1.02852i 0.160908 + 0.0615757i
\(280\) 0 0
\(281\) −20.3371 + 11.7416i −1.21321 + 0.700448i −0.963457 0.267862i \(-0.913683\pi\)
−0.249754 + 0.968309i \(0.580350\pi\)
\(282\) 0 0
\(283\) 11.1906 + 6.46089i 0.665211 + 0.384060i 0.794260 0.607578i \(-0.207859\pi\)
−0.129048 + 0.991638i \(0.541192\pi\)
\(284\) 0 0
\(285\) −5.81722 2.77097i −0.344582 0.164138i
\(286\) 0 0
\(287\) −11.9878 4.05398i −0.707619 0.239299i
\(288\) 0 0
\(289\) 35.4940 2.08788
\(290\) 0 0
\(291\) 12.3377 8.48887i 0.723247 0.497626i
\(292\) 0 0
\(293\) 1.99115 3.44878i 0.116324 0.201480i −0.801984 0.597346i \(-0.796222\pi\)
0.918308 + 0.395866i \(0.129555\pi\)
\(294\) 0 0
\(295\) −2.15968 3.74067i −0.125741 0.217790i
\(296\) 0 0
\(297\) −17.5344 + 16.6914i −1.01745 + 0.968535i
\(298\) 0 0
\(299\) 11.5910 + 20.0761i 0.670322 + 1.16103i
\(300\) 0 0
\(301\) −4.08747 + 3.59292i −0.235598 + 0.207093i
\(302\) 0 0
\(303\) 4.59920 + 6.68445i 0.264217 + 0.384012i
\(304\) 0 0
\(305\) 3.43629i 0.196762i
\(306\) 0 0
\(307\) 22.3162i 1.27365i −0.771008 0.636825i \(-0.780247\pi\)
0.771008 0.636825i \(-0.219753\pi\)
\(308\) 0 0
\(309\) −11.5705 5.51147i −0.658221 0.313537i
\(310\) 0 0
\(311\) 8.18371 14.1746i 0.464056 0.803768i −0.535103 0.844787i \(-0.679727\pi\)
0.999158 + 0.0410190i \(0.0130604\pi\)
\(312\) 0 0
\(313\) 16.5547 9.55785i 0.935726 0.540242i 0.0471079 0.998890i \(-0.485000\pi\)
0.888618 + 0.458648i \(0.151666\pi\)
\(314\) 0 0
\(315\) 4.33399 + 0.734975i 0.244193 + 0.0414111i
\(316\) 0 0
\(317\) 20.8798 12.0550i 1.17273 0.677074i 0.218405 0.975858i \(-0.429914\pi\)
0.954321 + 0.298784i \(0.0965811\pi\)
\(318\) 0 0
\(319\) 3.13635 5.43232i 0.175602 0.304152i
\(320\) 0 0
\(321\) −0.692237 8.73781i −0.0386369 0.487697i
\(322\) 0 0
\(323\) 48.6676i 2.70794i
\(324\) 0 0
\(325\) 19.4156i 1.07698i
\(326\) 0 0
\(327\) −20.3102 + 1.60904i −1.12316 + 0.0889799i
\(328\) 0 0
\(329\) 19.4863 17.1286i 1.07431 0.944332i
\(330\) 0 0
\(331\) −5.70077 9.87403i −0.313343 0.542726i 0.665741 0.746183i \(-0.268116\pi\)
−0.979084 + 0.203457i \(0.934782\pi\)
\(332\) 0 0
\(333\) −20.9441 + 3.33947i −1.14773 + 0.183002i
\(334\) 0 0
\(335\) 0.934938 + 1.61936i 0.0510811 + 0.0884751i
\(336\) 0 0
\(337\) 2.16599 3.75161i 0.117989 0.204363i −0.800981 0.598689i \(-0.795689\pi\)
0.918971 + 0.394326i \(0.129022\pi\)
\(338\) 0 0
\(339\) 2.74264 + 1.30643i 0.148960 + 0.0709554i
\(340\) 0 0
\(341\) 4.46914 0.242018
\(342\) 0 0
\(343\) 10.3423 + 15.3635i 0.558429 + 0.829552i
\(344\) 0 0
\(345\) −4.42843 + 3.04695i −0.238419 + 0.164042i
\(346\) 0 0
\(347\) −4.62254 2.66882i −0.248151 0.143270i 0.370766 0.928726i \(-0.379095\pi\)
−0.618917 + 0.785456i \(0.712428\pi\)
\(348\) 0 0
\(349\) −8.78031 + 5.06931i −0.469999 + 0.271354i −0.716239 0.697855i \(-0.754138\pi\)
0.246240 + 0.969209i \(0.420805\pi\)
\(350\) 0 0
\(351\) 20.6202 + 6.07312i 1.10062 + 0.324159i
\(352\) 0 0
\(353\) 7.67564 + 13.2946i 0.408533 + 0.707600i 0.994726 0.102571i \(-0.0327070\pi\)
−0.586192 + 0.810172i \(0.699374\pi\)
\(354\) 0 0
\(355\) −0.195475 0.112858i −0.0103748 0.00598987i
\(356\) 0 0
\(357\) 9.06559 + 31.9404i 0.479802 + 1.69047i
\(358\) 0 0
\(359\) 1.74800i 0.0922559i −0.998936 0.0461280i \(-0.985312\pi\)
0.998936 0.0461280i \(-0.0146882\pi\)
\(360\) 0 0
\(361\) −26.1201 −1.37474
\(362\) 0 0
\(363\) −7.97437 + 16.7409i −0.418546 + 0.878671i
\(364\) 0 0
\(365\) 4.14191 + 2.39133i 0.216798 + 0.125168i
\(366\) 0 0
\(367\) 11.1720 6.45018i 0.583176 0.336697i −0.179219 0.983809i \(-0.557357\pi\)
0.762394 + 0.647113i \(0.224024\pi\)
\(368\) 0 0
\(369\) 5.12839 13.4014i 0.266973 0.697649i
\(370\) 0 0
\(371\) 21.8754 4.37738i 1.13571 0.227262i
\(372\) 0 0
\(373\) 5.34782 9.26269i 0.276900 0.479604i −0.693713 0.720251i \(-0.744026\pi\)
0.970613 + 0.240647i \(0.0773597\pi\)
\(374\) 0 0
\(375\) 9.26930 0.734343i 0.478665 0.0379213i
\(376\) 0 0
\(377\) −5.56980 −0.286859
\(378\) 0 0
\(379\) 0.566797 0.0291144 0.0145572 0.999894i \(-0.495366\pi\)
0.0145572 + 0.999894i \(0.495366\pi\)
\(380\) 0 0
\(381\) −19.1350 + 1.51593i −0.980314 + 0.0776635i
\(382\) 0 0
\(383\) 9.43059 16.3343i 0.481880 0.834641i −0.517903 0.855439i \(-0.673287\pi\)
0.999784 + 0.0207978i \(0.00662061\pi\)
\(384\) 0 0
\(385\) 6.69402 1.33951i 0.341159 0.0682678i
\(386\) 0 0
\(387\) −3.88836 4.79156i −0.197656 0.243569i
\(388\) 0 0
\(389\) 14.3182 8.26660i 0.725960 0.419133i −0.0909822 0.995853i \(-0.529001\pi\)
0.816943 + 0.576719i \(0.195667\pi\)
\(390\) 0 0
\(391\) −35.1610 20.3002i −1.77817 1.02663i
\(392\) 0 0
\(393\) 13.7596 28.8862i 0.694082 1.45712i
\(394\) 0 0
\(395\) 0.352429 0.0177326
\(396\) 0 0
\(397\) 34.1080i 1.71183i −0.517114 0.855917i \(-0.672994\pi\)
0.517114 0.855917i \(-0.327006\pi\)
\(398\) 0 0
\(399\) 29.6122 8.40478i 1.48246 0.420765i
\(400\) 0 0
\(401\) 18.6395 + 10.7615i 0.930811 + 0.537404i 0.887068 0.461639i \(-0.152738\pi\)
0.0437428 + 0.999043i \(0.486072\pi\)
\(402\) 0 0
\(403\) −1.98417 3.43668i −0.0988386 0.171193i
\(404\) 0 0
\(405\) −1.02622 + 4.87766i −0.0509931 + 0.242373i
\(406\) 0 0
\(407\) −28.5241 + 16.4684i −1.41389 + 0.816308i
\(408\) 0 0
\(409\) −19.2516 11.1149i −0.951933 0.549599i −0.0582520 0.998302i \(-0.518553\pi\)
−0.893681 + 0.448703i \(0.851886\pi\)
\(410\) 0 0
\(411\) −31.3942 + 21.6006i −1.54856 + 1.06548i
\(412\) 0 0
\(413\) 19.5470 + 6.61031i 0.961846 + 0.325272i
\(414\) 0 0
\(415\) 3.08858 0.151613
\(416\) 0 0
\(417\) −15.4558 7.36222i −0.756875 0.360529i
\(418\) 0 0
\(419\) 6.81490 11.8038i 0.332930 0.576651i −0.650155 0.759802i \(-0.725296\pi\)
0.983085 + 0.183150i \(0.0586294\pi\)
\(420\) 0 0
\(421\) 13.7071 + 23.7414i 0.668043 + 1.15708i 0.978451 + 0.206480i \(0.0662009\pi\)
−0.310408 + 0.950603i \(0.600466\pi\)
\(422\) 0 0
\(423\) 18.5371 + 22.8429i 0.901303 + 1.11066i
\(424\) 0 0
\(425\) 17.0020 + 29.4484i 0.824720 + 1.42846i
\(426\) 0 0
\(427\) −10.8379 12.3297i −0.524483 0.596676i
\(428\) 0 0
\(429\) 33.2786 2.63643i 1.60670 0.127288i
\(430\) 0 0
\(431\) 34.8331i 1.67785i −0.544248 0.838925i \(-0.683185\pi\)
0.544248 0.838925i \(-0.316815\pi\)
\(432\) 0 0
\(433\) 19.5648i 0.940223i 0.882607 + 0.470112i \(0.155786\pi\)
−0.882607 + 0.470112i \(0.844214\pi\)
\(434\) 0 0
\(435\) −0.101999 1.28749i −0.00489046 0.0617302i
\(436\) 0 0
\(437\) −18.8205 + 32.5980i −0.900305 + 1.55937i
\(438\) 0 0
\(439\) −24.7361 + 14.2814i −1.18059 + 0.681614i −0.956151 0.292874i \(-0.905388\pi\)
−0.224439 + 0.974488i \(0.572055\pi\)
\(440\) 0 0
\(441\) −17.8688 + 11.0321i −0.850895 + 0.525336i
\(442\) 0 0
\(443\) −21.8612 + 12.6216i −1.03866 + 0.599669i −0.919453 0.393201i \(-0.871368\pi\)
−0.119205 + 0.992870i \(0.538034\pi\)
\(444\) 0 0
\(445\) −1.91939 + 3.32448i −0.0909878 + 0.157596i
\(446\) 0 0
\(447\) 11.4959 + 5.47597i 0.543739 + 0.259005i
\(448\) 0 0
\(449\) 15.1042i 0.712811i −0.934331 0.356405i \(-0.884002\pi\)
0.934331 0.356405i \(-0.115998\pi\)
\(450\) 0 0
\(451\) 22.2840i 1.04931i
\(452\) 0 0
\(453\) −4.25308 6.18140i −0.199827 0.290428i
\(454\) 0 0
\(455\) −4.00201 4.55287i −0.187617 0.213442i
\(456\) 0 0
\(457\) −1.75138 3.03348i −0.0819261 0.141900i 0.822151 0.569269i \(-0.192774\pi\)
−0.904077 + 0.427369i \(0.859440\pi\)
\(458\) 0 0
\(459\) −36.5936 + 8.84555i −1.70804 + 0.412875i
\(460\) 0 0
\(461\) −1.98765 3.44272i −0.0925743 0.160343i 0.816019 0.578025i \(-0.196176\pi\)
−0.908594 + 0.417681i \(0.862843\pi\)
\(462\) 0 0
\(463\) −5.18494 + 8.98058i −0.240965 + 0.417363i −0.960989 0.276585i \(-0.910797\pi\)
0.720025 + 0.693948i \(0.244130\pi\)
\(464\) 0 0
\(465\) 0.758070 0.521586i 0.0351546 0.0241879i
\(466\) 0 0
\(467\) 19.6190 0.907860 0.453930 0.891037i \(-0.350022\pi\)
0.453930 + 0.891037i \(0.350022\pi\)
\(468\) 0 0
\(469\) −8.46202 2.86164i −0.390740 0.132138i
\(470\) 0 0
\(471\) −2.78340 1.32584i −0.128252 0.0610916i
\(472\) 0 0
\(473\) −8.29923 4.79156i −0.381599 0.220316i
\(474\) 0 0
\(475\) 27.3018 15.7627i 1.25269 0.723243i
\(476\) 0 0
\(477\) 3.98307 + 24.9805i 0.182372 + 1.14378i
\(478\) 0 0
\(479\) −15.8237 27.4074i −0.723002 1.25228i −0.959791 0.280715i \(-0.909428\pi\)
0.236789 0.971561i \(-0.423905\pi\)
\(480\) 0 0
\(481\) 25.3277 + 14.6230i 1.15485 + 0.666751i
\(482\) 0 0
\(483\) 6.27960 24.8998i 0.285732 1.13298i
\(484\) 0 0
\(485\) 4.78860i 0.217439i
\(486\) 0 0
\(487\) −19.4585 −0.881747 −0.440874 0.897569i \(-0.645331\pi\)
−0.440874 + 0.897569i \(0.645331\pi\)
\(488\) 0 0
\(489\) 9.73196 0.770996i 0.440094 0.0348656i
\(490\) 0 0
\(491\) 23.9525 + 13.8290i 1.08096 + 0.624094i 0.931156 0.364622i \(-0.118802\pi\)
0.149806 + 0.988715i \(0.452135\pi\)
\(492\) 0 0
\(493\) 8.44795 4.87743i 0.380476 0.219668i
\(494\) 0 0
\(495\) 1.21885 + 7.64422i 0.0547831 + 0.343582i
\(496\) 0 0
\(497\) 1.05733 0.211578i 0.0474277 0.00949055i
\(498\) 0 0
\(499\) 4.50632 7.80517i 0.201730 0.349407i −0.747356 0.664424i \(-0.768677\pi\)
0.949086 + 0.315017i \(0.102010\pi\)
\(500\) 0 0
\(501\) −3.55748 + 7.46836i −0.158936 + 0.333662i
\(502\) 0 0
\(503\) 27.1572 1.21088 0.605440 0.795891i \(-0.292997\pi\)
0.605440 + 0.795891i \(0.292997\pi\)
\(504\) 0 0
\(505\) 2.59442 0.115450
\(506\) 0 0
\(507\) −4.03891 5.87013i −0.179374 0.260702i
\(508\) 0 0
\(509\) 6.56799 11.3761i 0.291121 0.504236i −0.682954 0.730461i \(-0.739305\pi\)
0.974075 + 0.226225i \(0.0726384\pi\)
\(510\) 0 0
\(511\) −22.4037 + 4.48310i −0.991080 + 0.198321i
\(512\) 0 0
\(513\) 8.20077 + 33.9262i 0.362073 + 1.49788i
\(514\) 0 0
\(515\) −3.54895 + 2.04899i −0.156385 + 0.0902892i
\(516\) 0 0
\(517\) 39.5651 + 22.8429i 1.74007 + 1.00463i
\(518\) 0 0
\(519\) −5.57193 8.09822i −0.244581 0.355472i
\(520\) 0 0
\(521\) −4.03219 −0.176653 −0.0883266 0.996092i \(-0.528152\pi\)
−0.0883266 + 0.996092i \(0.528152\pi\)
\(522\) 0 0
\(523\) 0.595961i 0.0260595i −0.999915 0.0130298i \(-0.995852\pi\)
0.999915 0.0130298i \(-0.00414762\pi\)
\(524\) 0 0
\(525\) −14.9819 + 15.4307i −0.653864 + 0.673451i
\(526\) 0 0
\(527\) 6.01895 + 3.47504i 0.262189 + 0.151375i
\(528\) 0 0
\(529\) 4.20077 + 7.27595i 0.182642 + 0.316346i
\(530\) 0 0
\(531\) −8.36220 + 21.8519i −0.362889 + 0.948294i
\(532\) 0 0
\(533\) −17.1360 + 9.89347i −0.742242 + 0.428534i
\(534\) 0 0
\(535\) −2.42720 1.40135i −0.104937 0.0605855i
\(536\) 0 0
\(537\) −1.72773 21.8083i −0.0745569 0.941100i
\(538\) 0 0
\(539\) −19.7939 + 25.9189i −0.852585 + 1.11641i
\(540\) 0 0
\(541\) −14.1012 −0.606259 −0.303129 0.952949i \(-0.598031\pi\)
−0.303129 + 0.952949i \(0.598031\pi\)
\(542\) 0 0
\(543\) −3.11093 39.2680i −0.133503 1.68515i
\(544\) 0 0
\(545\) −3.25729 + 5.64179i −0.139527 + 0.241668i
\(546\) 0 0
\(547\) −18.9921 32.8952i −0.812042 1.40650i −0.911433 0.411450i \(-0.865023\pi\)
0.0993905 0.995049i \(-0.468311\pi\)
\(548\) 0 0
\(549\) 14.4536 11.7291i 0.616863 0.500585i
\(550\) 0 0
\(551\) −4.52190 7.83216i −0.192639 0.333661i
\(552\) 0 0
\(553\) −1.26454 + 1.11155i −0.0537739 + 0.0472677i
\(554\) 0 0
\(555\) −2.91635 + 6.12241i −0.123792 + 0.259882i
\(556\) 0 0
\(557\) 41.7056i 1.76712i 0.468313 + 0.883562i \(0.344862\pi\)
−0.468313 + 0.883562i \(0.655138\pi\)
\(558\) 0 0
\(559\) 8.50926i 0.359903i
\(560\) 0 0
\(561\) −48.1663 + 33.1406i −2.03358 + 1.39920i
\(562\) 0 0
\(563\) 0.938436 1.62542i 0.0395504 0.0685033i −0.845573 0.533860i \(-0.820741\pi\)
0.885123 + 0.465357i \(0.154074\pi\)
\(564\) 0 0
\(565\) 0.841235 0.485687i 0.0353910 0.0204330i
\(566\) 0 0
\(567\) −11.7018 20.7381i −0.491428 0.870918i
\(568\) 0 0
\(569\) −20.6391 + 11.9160i −0.865237 + 0.499545i −0.865762 0.500455i \(-0.833166\pi\)
0.000525844 1.00000i \(0.499833\pi\)
\(570\) 0 0
\(571\) −14.8719 + 25.7589i −0.622370 + 1.07798i 0.366674 + 0.930350i \(0.380497\pi\)
−0.989043 + 0.147626i \(0.952837\pi\)
\(572\) 0 0
\(573\) 16.5652 11.3976i 0.692020 0.476140i
\(574\) 0 0
\(575\) 26.2997i 1.09678i
\(576\) 0 0
\(577\) 14.6589i 0.610260i 0.952311 + 0.305130i \(0.0986999\pi\)
−0.952311 + 0.305130i \(0.901300\pi\)
\(578\) 0 0
\(579\) 4.71643 9.90139i 0.196008 0.411488i
\(580\) 0 0
\(581\) −11.0821 + 9.74125i −0.459762 + 0.404135i
\(582\) 0 0
\(583\) 19.6422 + 34.0213i 0.813498 + 1.40902i
\(584\) 0 0
\(585\) 5.33712 4.33108i 0.220663 0.179068i
\(586\) 0 0
\(587\) 22.2189 + 38.4843i 0.917074 + 1.58842i 0.803836 + 0.594851i \(0.202789\pi\)
0.113238 + 0.993568i \(0.463878\pi\)
\(588\) 0 0
\(589\) 3.22174 5.58021i 0.132749 0.229929i
\(590\) 0 0
\(591\) −0.424090 5.35311i −0.0174447 0.220198i
\(592\) 0 0
\(593\) −37.1186 −1.52428 −0.762140 0.647412i \(-0.775851\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(594\) 0 0
\(595\) 10.0569 + 3.40100i 0.412294 + 0.139427i
\(596\) 0 0
\(597\) −2.15127 27.1546i −0.0880456 1.11136i
\(598\) 0 0
\(599\) −12.0534 6.95901i −0.492487 0.284338i 0.233119 0.972448i \(-0.425107\pi\)
−0.725606 + 0.688111i \(0.758440\pi\)
\(600\) 0 0
\(601\) −0.377613 + 0.218015i −0.0154032 + 0.00889301i −0.507682 0.861545i \(-0.669497\pi\)
0.492279 + 0.870438i \(0.336164\pi\)
\(602\) 0 0
\(603\) 3.62005 9.45984i 0.147420 0.385235i
\(604\) 0 0
\(605\) 2.96461 + 5.13486i 0.120529 + 0.208762i
\(606\) 0 0
\(607\) −1.92117 1.10919i −0.0779778 0.0450205i 0.460504 0.887658i \(-0.347669\pi\)
−0.538482 + 0.842637i \(0.681002\pi\)
\(608\) 0 0
\(609\) 4.42665 + 4.29790i 0.179377 + 0.174160i
\(610\) 0 0
\(611\) 40.5664i 1.64114i
\(612\) 0 0
\(613\) 38.2023 1.54298 0.771488 0.636244i \(-0.219513\pi\)
0.771488 + 0.636244i \(0.219513\pi\)
\(614\) 0 0
\(615\) −2.60073 3.77989i −0.104872 0.152420i
\(616\) 0 0
\(617\) 21.1043 + 12.1846i 0.849628 + 0.490533i 0.860525 0.509407i \(-0.170135\pi\)
−0.0108970 + 0.999941i \(0.503469\pi\)
\(618\) 0 0
\(619\) −25.4477 + 14.6922i −1.02283 + 0.590531i −0.914922 0.403630i \(-0.867748\pi\)
−0.107907 + 0.994161i \(0.534415\pi\)
\(620\) 0 0
\(621\) 27.9315 + 8.22647i 1.12085 + 0.330117i
\(622\) 0 0
\(623\) −3.59834 17.9822i −0.144164 0.720441i
\(624\) 0 0
\(625\) −10.2466 + 17.7476i −0.409864 + 0.709906i
\(626\) 0 0
\(627\) 30.7249 + 44.6553i 1.22703 + 1.78336i
\(628\) 0 0
\(629\) −51.2209 −2.04231
\(630\) 0 0
\(631\) 5.17077 0.205845 0.102923 0.994689i \(-0.467181\pi\)
0.102923 + 0.994689i \(0.467181\pi\)
\(632\) 0 0
\(633\) −5.23282 + 10.9855i −0.207986 + 0.436633i
\(634\) 0 0
\(635\) −3.06881 + 5.31533i −0.121782 + 0.210933i
\(636\) 0 0
\(637\) 28.7191 + 3.71390i 1.13789 + 0.147150i
\(638\) 0 0
\(639\) 0.192519 + 1.20741i 0.00761592 + 0.0477646i
\(640\) 0 0
\(641\) −5.32405 + 3.07384i −0.210287 + 0.121410i −0.601445 0.798914i \(-0.705408\pi\)
0.391158 + 0.920324i \(0.372075\pi\)
\(642\) 0 0
\(643\) −23.9599 13.8333i −0.944886 0.545530i −0.0533976 0.998573i \(-0.517005\pi\)
−0.891489 + 0.453043i \(0.850338\pi\)
\(644\) 0 0
\(645\) −1.96696 + 0.155828i −0.0774488 + 0.00613574i
\(646\) 0 0
\(647\) −4.81457 −0.189280 −0.0946402 0.995512i \(-0.530170\pi\)
−0.0946402 + 0.995512i \(0.530170\pi\)
\(648\) 0 0
\(649\) 36.3357i 1.42630i
\(650\) 0 0
\(651\) −1.07496 + 4.26241i −0.0421310 + 0.167057i
\(652\) 0 0
\(653\) 21.1759 + 12.2259i 0.828677 + 0.478437i 0.853400 0.521257i \(-0.174537\pi\)
−0.0247223 + 0.999694i \(0.507870\pi\)
\(654\) 0 0
\(655\) −5.11539 8.86011i −0.199875 0.346193i
\(656\) 0 0
\(657\) −4.07926 25.5838i −0.159147 0.998120i
\(658\) 0 0
\(659\) −20.7514 + 11.9808i −0.808359 + 0.466706i −0.846386 0.532570i \(-0.821226\pi\)
0.0380267 + 0.999277i \(0.487893\pi\)
\(660\) 0 0
\(661\) 6.73275 + 3.88715i 0.261874 + 0.151193i 0.625189 0.780473i \(-0.285022\pi\)
−0.363315 + 0.931666i \(0.618355\pi\)
\(662\) 0 0
\(663\) 46.8689 + 22.3255i 1.82024 + 0.867051i
\(664\) 0 0
\(665\) 3.15309 9.32385i 0.122272 0.361563i
\(666\) 0 0
\(667\) −7.54469 −0.292131
\(668\) 0 0
\(669\) 35.1739 24.2012i 1.35990 0.935672i
\(670\) 0 0
\(671\) 14.4536 25.0343i 0.557973 0.966438i
\(672\) 0 0
\(673\) −14.7281 25.5097i −0.567725 0.983328i −0.996790 0.0800548i \(-0.974490\pi\)
0.429066 0.903273i \(-0.358843\pi\)
\(674\) 0 0
\(675\) −16.8144 17.6636i −0.647185 0.679871i
\(676\) 0 0
\(677\) −17.8293 30.8812i −0.685235 1.18686i −0.973363 0.229270i \(-0.926366\pi\)
0.288128 0.957592i \(-0.406967\pi\)
\(678\) 0 0
\(679\) 15.1030 + 17.1819i 0.579601 + 0.659380i
\(680\) 0 0
\(681\) −19.7087 28.6445i −0.755238 1.09766i
\(682\) 0 0
\(683\) 13.0969i 0.501139i 0.968099 + 0.250570i \(0.0806179\pi\)
−0.968099 + 0.250570i \(0.919382\pi\)
\(684\) 0 0
\(685\) 12.1850i 0.465563i
\(686\) 0 0
\(687\) 12.2035 + 5.81302i 0.465594 + 0.221781i
\(688\) 0 0
\(689\) 17.4412 30.2090i 0.664456 1.15087i
\(690\) 0 0
\(691\) −7.81992 + 4.51483i −0.297484 + 0.171752i −0.641312 0.767280i \(-0.721610\pi\)
0.343828 + 0.939033i \(0.388276\pi\)
\(692\) 0 0
\(693\) −28.4828 23.5839i −1.08197 0.895878i
\(694\) 0 0
\(695\) −4.74068 + 2.73704i −0.179824 + 0.103822i
\(696\) 0 0
\(697\) 17.3273 30.0117i 0.656316 1.13677i
\(698\) 0 0
\(699\) 1.08962 + 13.7538i 0.0412131 + 0.520215i
\(700\) 0 0
\(701\) 0.259274i 0.00979264i −0.999988 0.00489632i \(-0.998441\pi\)
0.999988 0.00489632i \(-0.00155855\pi\)
\(702\) 0 0
\(703\) 47.4873i 1.79102i
\(704\) 0 0
\(705\) 9.37711 0.742884i 0.353163 0.0279786i
\(706\) 0 0
\(707\) −9.30900 + 8.18269i −0.350101 + 0.307742i
\(708\) 0 0
\(709\) −3.08574 5.34467i −0.115888 0.200723i 0.802247 0.596993i \(-0.203638\pi\)
−0.918134 + 0.396270i \(0.870305\pi\)
\(710\) 0 0
\(711\) −1.20294 1.48237i −0.0451139 0.0555932i
\(712\) 0 0
\(713\) −2.68770 4.65523i −0.100655 0.174340i
\(714\) 0 0
\(715\) 5.33712 9.24417i 0.199597 0.345712i
\(716\) 0 0
\(717\) −41.9010 19.9591i −1.56482 0.745386i
\(718\) 0 0
\(719\) −19.5275 −0.728253 −0.364127 0.931349i \(-0.618632\pi\)
−0.364127 + 0.931349i \(0.618632\pi\)
\(720\) 0 0
\(721\) 6.27151 18.5452i 0.233563 0.690658i
\(722\) 0 0
\(723\) 1.24771 0.858479i 0.0464028 0.0319272i
\(724\) 0 0
\(725\) 5.47233 + 3.15945i 0.203237 + 0.117339i
\(726\) 0 0
\(727\) −0.425312 + 0.245554i −0.0157740 + 0.00910710i −0.507866 0.861436i \(-0.669566\pi\)
0.492092 + 0.870543i \(0.336232\pi\)
\(728\) 0 0
\(729\) 24.0189 12.3325i 0.889591 0.456759i
\(730\) 0 0
\(731\) −7.45149 12.9064i −0.275603 0.477359i
\(732\) 0 0
\(733\) −6.68424 3.85915i −0.246888 0.142541i 0.371450 0.928453i \(-0.378861\pi\)
−0.618338 + 0.785912i \(0.712194\pi\)
\(734\) 0 0
\(735\) −0.332559 + 6.70656i −0.0122666 + 0.247375i
\(736\) 0 0
\(737\) 15.7300i 0.579420i
\(738\) 0 0
\(739\) 10.9083 0.401270 0.200635 0.979666i \(-0.435700\pi\)
0.200635 + 0.979666i \(0.435700\pi\)
\(740\) 0 0
\(741\) 20.6982 43.4525i 0.760366 1.59627i
\(742\) 0 0
\(743\) 27.0051 + 15.5914i 0.990722 + 0.571994i 0.905490 0.424367i \(-0.139503\pi\)
0.0852322 + 0.996361i \(0.472837\pi\)
\(744\) 0 0
\(745\) 3.52609 2.03579i 0.129186 0.0745855i
\(746\) 0 0
\(747\) −10.5422 12.9910i −0.385721 0.475317i
\(748\) 0 0
\(749\) 13.1288 2.62714i 0.479715 0.0959937i
\(750\) 0 0
\(751\) 23.0367 39.9008i 0.840622 1.45600i −0.0487482 0.998811i \(-0.515523\pi\)
0.889370 0.457188i \(-0.151143\pi\)
\(752\) 0 0
\(753\) −4.00723 + 0.317465i −0.146032 + 0.0115691i
\(754\) 0 0
\(755\) −2.39917 −0.0873149
\(756\) 0 0
\(757\) 40.6419 1.47715 0.738577 0.674169i \(-0.235498\pi\)
0.738577 + 0.674169i \(0.235498\pi\)
\(758\) 0 0
\(759\) 45.0782 3.57124i 1.63623 0.129628i
\(760\) 0 0
\(761\) −3.64190 + 6.30795i −0.132019 + 0.228663i −0.924455 0.381292i \(-0.875479\pi\)
0.792436 + 0.609955i \(0.208813\pi\)
\(762\) 0 0
\(763\) −6.10653 30.5165i −0.221071 1.10477i
\(764\) 0 0
\(765\) −4.30235 + 11.2428i −0.155552 + 0.406485i
\(766\) 0 0
\(767\) 27.9415 16.1320i 1.00891 0.582493i
\(768\) 0 0
\(769\) 35.8261 + 20.6842i 1.29192 + 0.745892i 0.978995 0.203886i \(-0.0653570\pi\)
0.312927 + 0.949777i \(0.398690\pi\)
\(770\) 0 0
\(771\) 18.3261 38.4727i 0.659997 1.38556i
\(772\) 0 0
\(773\) −17.1183 −0.615702 −0.307851 0.951435i \(-0.599610\pi\)
−0.307851 + 0.951435i \(0.599610\pi\)
\(774\) 0 0
\(775\) 4.50206i 0.161719i
\(776\) 0 0
\(777\) −8.84572 31.1658i −0.317339 1.11807i
\(778\) 0 0
\(779\) −27.8241 16.0642i −0.996900 0.575561i
\(780\) 0 0
\(781\) 0.949393 + 1.64440i 0.0339719 + 0.0588411i
\(782\) 0 0
\(783\) −5.06720 + 4.82359i −0.181087 + 0.172381i
\(784\) 0 0
\(785\) −0.853737 + 0.492906i −0.0304712 + 0.0175926i
\(786\) 0 0
\(787\) 25.7426 + 14.8625i 0.917623 + 0.529790i 0.882876 0.469606i \(-0.155604\pi\)
0.0347472 + 0.999396i \(0.488937\pi\)
\(788\) 0 0
\(789\) 33.8214 23.2706i 1.20407 0.828455i
\(790\) 0 0
\(791\) −1.48658 + 4.39590i −0.0528568 + 0.156300i
\(792\) 0 0
\(793\) −25.6679 −0.911492
\(794\) 0 0
\(795\) 7.30235 + 3.47840i 0.258988 + 0.123366i
\(796\) 0