Properties

Label 1008.2.r.f.337.1
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.f.673.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.18614 - 1.26217i) q^{3} +(0.686141 - 1.18843i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\) \(q+(-1.18614 - 1.26217i) q^{3} +(0.686141 - 1.18843i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.186141 + 2.99422i) q^{9} +(2.18614 + 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.31386 + 0.543620i) q^{15} -4.37228 q^{17} -5.00000 q^{19} +(0.500000 - 1.65831i) q^{21} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(1.00000 - 1.73205i) q^{31} +(2.18614 - 7.25061i) q^{33} +1.37228 q^{35} +2.00000 q^{37} +(3.37228 - 0.792287i) q^{39} +(-5.18614 + 8.98266i) q^{41} +(4.55842 + 7.89542i) q^{43} +(3.43070 + 2.27567i) q^{45} +(-0.500000 + 0.866025i) q^{49} +(5.18614 + 5.51856i) q^{51} +2.74456 q^{53} +6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} +(3.55842 - 6.16337i) q^{59} +(7.05842 + 12.2255i) q^{61} +(-2.68614 + 1.33591i) q^{63} +(1.37228 + 2.37686i) q^{65} +(7.55842 - 13.0916i) q^{67} +(12.4307 - 2.92048i) q^{69} -10.1168 q^{71} -5.11684 q^{73} +(1.55842 - 5.16870i) q^{75} +(-2.18614 + 3.78651i) q^{77} +(6.05842 + 10.4935i) q^{79} +(-8.93070 - 1.11469i) q^{81} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-1.37228 + 4.55134i) q^{87} +3.25544 q^{89} -2.00000 q^{91} +(-3.37228 + 0.792287i) q^{93} +(-3.43070 + 5.94215i) q^{95} +(-4.55842 - 7.89542i) q^{97} +(-11.7446 + 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} + O(q^{10}) \) \( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} + 3 q^{11} - 4 q^{13} - 15 q^{15} - 6 q^{17} - 20 q^{19} + 2 q^{21} - 9 q^{23} - 11 q^{25} + 16 q^{27} + 6 q^{29} + 4 q^{31} + 3 q^{33} - 6 q^{35} + 8 q^{37} + 2 q^{39} - 15 q^{41} + q^{43} - 15 q^{45} - 2 q^{49} + 15 q^{51} - 12 q^{53} + 24 q^{55} - 5 q^{57} - 3 q^{59} + 11 q^{61} - 5 q^{63} - 6 q^{65} + 13 q^{67} + 21 q^{69} - 6 q^{71} + 14 q^{73} - 11 q^{75} - 3 q^{77} + 7 q^{79} - 7 q^{81} + 12 q^{83} - 12 q^{85} + 6 q^{87} + 36 q^{89} - 8 q^{91} - 2 q^{93} + 15 q^{95} - q^{97} - 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −1.18614 1.26217i −0.684819 0.728714i
\(4\) 0 0
\(5\) 0.686141 1.18843i 0.306851 0.531482i −0.670820 0.741620i \(-0.734058\pi\)
0.977672 + 0.210138i \(0.0673912\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) −0.186141 + 2.99422i −0.0620469 + 0.998073i
\(10\) 0 0
\(11\) 2.18614 + 3.78651i 0.659146 + 1.14167i 0.980837 + 0.194830i \(0.0624155\pi\)
−0.321691 + 0.946845i \(0.604251\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) −2.31386 + 0.543620i −0.597436 + 0.140362i
\(16\) 0 0
\(17\) −4.37228 −1.06043 −0.530217 0.847862i \(-0.677890\pi\)
−0.530217 + 0.847862i \(0.677890\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0.500000 1.65831i 0.109109 0.361873i
\(22\) 0 0
\(23\) −3.68614 + 6.38458i −0.768613 + 1.33128i 0.169701 + 0.985496i \(0.445720\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) 1.55842 + 2.69927i 0.311684 + 0.539853i
\(26\) 0 0
\(27\) 4.00000 3.31662i 0.769800 0.638285i
\(28\) 0 0
\(29\) −1.37228 2.37686i −0.254826 0.441372i 0.710022 0.704179i \(-0.248685\pi\)
−0.964848 + 0.262807i \(0.915352\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0 0
\(33\) 2.18614 7.25061i 0.380558 1.26217i
\(34\) 0 0
\(35\) 1.37228 0.231958
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 3.37228 0.792287i 0.539997 0.126867i
\(40\) 0 0
\(41\) −5.18614 + 8.98266i −0.809939 + 1.40286i 0.102966 + 0.994685i \(0.467167\pi\)
−0.912906 + 0.408171i \(0.866167\pi\)
\(42\) 0 0
\(43\) 4.55842 + 7.89542i 0.695153 + 1.20404i 0.970129 + 0.242589i \(0.0779967\pi\)
−0.274976 + 0.961451i \(0.588670\pi\)
\(44\) 0 0
\(45\) 3.43070 + 2.27567i 0.511419 + 0.339237i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 5.18614 + 5.51856i 0.726205 + 0.772753i
\(52\) 0 0
\(53\) 2.74456 0.376995 0.188497 0.982074i \(-0.439638\pi\)
0.188497 + 0.982074i \(0.439638\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 5.93070 + 6.31084i 0.785541 + 0.835892i
\(58\) 0 0
\(59\) 3.55842 6.16337i 0.463267 0.802402i −0.535854 0.844310i \(-0.680010\pi\)
0.999121 + 0.0419083i \(0.0133437\pi\)
\(60\) 0 0
\(61\) 7.05842 + 12.2255i 0.903738 + 1.56532i 0.822602 + 0.568618i \(0.192522\pi\)
0.0811364 + 0.996703i \(0.474145\pi\)
\(62\) 0 0
\(63\) −2.68614 + 1.33591i −0.338422 + 0.168309i
\(64\) 0 0
\(65\) 1.37228 + 2.37686i 0.170211 + 0.294813i
\(66\) 0 0
\(67\) 7.55842 13.0916i 0.923408 1.59939i 0.129307 0.991605i \(-0.458725\pi\)
0.794101 0.607785i \(-0.207942\pi\)
\(68\) 0 0
\(69\) 12.4307 2.92048i 1.49648 0.351585i
\(70\) 0 0
\(71\) −10.1168 −1.20065 −0.600324 0.799757i \(-0.704962\pi\)
−0.600324 + 0.799757i \(0.704962\pi\)
\(72\) 0 0
\(73\) −5.11684 −0.598881 −0.299441 0.954115i \(-0.596800\pi\)
−0.299441 + 0.954115i \(0.596800\pi\)
\(74\) 0 0
\(75\) 1.55842 5.16870i 0.179951 0.596830i
\(76\) 0 0
\(77\) −2.18614 + 3.78651i −0.249134 + 0.431512i
\(78\) 0 0
\(79\) 6.05842 + 10.4935i 0.681626 + 1.18061i 0.974485 + 0.224455i \(0.0720601\pi\)
−0.292859 + 0.956156i \(0.594607\pi\)
\(80\) 0 0
\(81\) −8.93070 1.11469i −0.992300 0.123855i
\(82\) 0 0
\(83\) −2.74456 4.75372i −0.301255 0.521789i 0.675166 0.737666i \(-0.264072\pi\)
−0.976420 + 0.215877i \(0.930739\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) 0 0
\(87\) −1.37228 + 4.55134i −0.147124 + 0.487955i
\(88\) 0 0
\(89\) 3.25544 0.345076 0.172538 0.985003i \(-0.444803\pi\)
0.172538 + 0.985003i \(0.444803\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) −3.37228 + 0.792287i −0.349689 + 0.0821563i
\(94\) 0 0
\(95\) −3.43070 + 5.94215i −0.351983 + 0.609652i
\(96\) 0 0
\(97\) −4.55842 7.89542i −0.462838 0.801658i 0.536263 0.844051i \(-0.319835\pi\)
−0.999101 + 0.0423924i \(0.986502\pi\)
\(98\) 0 0
\(99\) −11.7446 + 5.84096i −1.18037 + 0.587039i
\(100\) 0 0
\(101\) −3.68614 6.38458i −0.366785 0.635290i 0.622276 0.782798i \(-0.286208\pi\)
−0.989061 + 0.147508i \(0.952875\pi\)
\(102\) 0 0
\(103\) −5.00000 + 8.66025i −0.492665 + 0.853320i −0.999964 0.00844953i \(-0.997310\pi\)
0.507300 + 0.861770i \(0.330644\pi\)
\(104\) 0 0
\(105\) −1.62772 1.73205i −0.158849 0.169031i
\(106\) 0 0
\(107\) 1.62772 0.157358 0.0786788 0.996900i \(-0.474930\pi\)
0.0786788 + 0.996900i \(0.474930\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) −2.37228 2.52434i −0.225167 0.239600i
\(112\) 0 0
\(113\) −0.686141 + 1.18843i −0.0645467 + 0.111798i −0.896493 0.443058i \(-0.853893\pi\)
0.831946 + 0.554856i \(0.187227\pi\)
\(114\) 0 0
\(115\) 5.05842 + 8.76144i 0.471700 + 0.817009i
\(116\) 0 0
\(117\) −5.00000 3.31662i −0.462250 0.306622i
\(118\) 0 0
\(119\) −2.18614 3.78651i −0.200403 0.347108i
\(120\) 0 0
\(121\) −4.05842 + 7.02939i −0.368947 + 0.639036i
\(122\) 0 0
\(123\) 17.4891 4.10891i 1.57694 0.370488i
\(124\) 0 0
\(125\) 11.1386 0.996266
\(126\) 0 0
\(127\) 14.1168 1.25267 0.626334 0.779555i \(-0.284555\pi\)
0.626334 + 0.779555i \(0.284555\pi\)
\(128\) 0 0
\(129\) 4.55842 15.1186i 0.401347 1.33112i
\(130\) 0 0
\(131\) −3.68614 + 6.38458i −0.322060 + 0.557824i −0.980913 0.194448i \(-0.937708\pi\)
0.658853 + 0.752271i \(0.271042\pi\)
\(132\) 0 0
\(133\) −2.50000 4.33013i −0.216777 0.375470i
\(134\) 0 0
\(135\) −1.19702 7.02939i −0.103023 0.604994i
\(136\) 0 0
\(137\) −8.18614 14.1788i −0.699389 1.21138i −0.968678 0.248318i \(-0.920122\pi\)
0.269289 0.963059i \(-0.413211\pi\)
\(138\) 0 0
\(139\) −10.6168 + 18.3889i −0.900509 + 1.55973i −0.0736742 + 0.997282i \(0.523472\pi\)
−0.826835 + 0.562445i \(0.809861\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.74456 −0.731257
\(144\) 0 0
\(145\) −3.76631 −0.312775
\(146\) 0 0
\(147\) 1.68614 0.396143i 0.139071 0.0326734i
\(148\) 0 0
\(149\) −7.37228 + 12.7692i −0.603961 + 1.04609i 0.388254 + 0.921552i \(0.373078\pi\)
−0.992215 + 0.124538i \(0.960255\pi\)
\(150\) 0 0
\(151\) −4.05842 7.02939i −0.330270 0.572044i 0.652295 0.757965i \(-0.273806\pi\)
−0.982565 + 0.185921i \(0.940473\pi\)
\(152\) 0 0
\(153\) 0.813859 13.0916i 0.0657966 1.05839i
\(154\) 0 0
\(155\) −1.37228 2.37686i −0.110224 0.190914i
\(156\) 0 0
\(157\) 4.05842 7.02939i 0.323897 0.561007i −0.657391 0.753549i \(-0.728340\pi\)
0.981289 + 0.192543i \(0.0616734\pi\)
\(158\) 0 0
\(159\) −3.25544 3.46410i −0.258173 0.274721i
\(160\) 0 0
\(161\) −7.37228 −0.581017
\(162\) 0 0
\(163\) −16.2337 −1.27152 −0.635760 0.771887i \(-0.719313\pi\)
−0.635760 + 0.771887i \(0.719313\pi\)
\(164\) 0 0
\(165\) −7.11684 7.57301i −0.554046 0.589558i
\(166\) 0 0
\(167\) 8.74456 15.1460i 0.676675 1.17203i −0.299302 0.954158i \(-0.596754\pi\)
0.975976 0.217876i \(-0.0699129\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 0.930703 14.9711i 0.0711727 1.14487i
\(172\) 0 0
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) −1.55842 + 2.69927i −0.117806 + 0.204045i
\(176\) 0 0
\(177\) −12.0000 + 2.81929i −0.901975 + 0.211911i
\(178\) 0 0
\(179\) −14.7446 −1.10206 −0.551030 0.834485i \(-0.685765\pi\)
−0.551030 + 0.834485i \(0.685765\pi\)
\(180\) 0 0
\(181\) 18.1168 1.34661 0.673307 0.739363i \(-0.264873\pi\)
0.673307 + 0.739363i \(0.264873\pi\)
\(182\) 0 0
\(183\) 7.05842 23.4101i 0.521774 1.73053i
\(184\) 0 0
\(185\) 1.37228 2.37686i 0.100892 0.174750i
\(186\) 0 0
\(187\) −9.55842 16.5557i −0.698981 1.21067i
\(188\) 0 0
\(189\) 4.87228 + 1.80579i 0.354406 + 0.131352i
\(190\) 0 0
\(191\) −0.941578 1.63086i −0.0681302 0.118005i 0.829948 0.557841i \(-0.188370\pi\)
−0.898078 + 0.439836i \(0.855037\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 0 0
\(195\) 1.37228 4.55134i 0.0982711 0.325928i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) −25.4891 + 5.98844i −1.79786 + 0.422392i
\(202\) 0 0
\(203\) 1.37228 2.37686i 0.0963153 0.166823i
\(204\) 0 0
\(205\) 7.11684 + 12.3267i 0.497062 + 0.860937i
\(206\) 0 0
\(207\) −18.4307 12.2255i −1.28102 0.849734i
\(208\) 0 0
\(209\) −10.9307 18.9325i −0.756093 1.30959i
\(210\) 0 0
\(211\) −8.00000 + 13.8564i −0.550743 + 0.953914i 0.447478 + 0.894295i \(0.352322\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 0 0
\(213\) 12.0000 + 12.7692i 0.822226 + 0.874929i
\(214\) 0 0
\(215\) 12.5109 0.853235
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) 6.06930 + 6.45832i 0.410125 + 0.436413i
\(220\) 0 0
\(221\) 4.37228 7.57301i 0.294111 0.509416i
\(222\) 0 0
\(223\) −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 0 0
\(225\) −8.37228 + 4.16381i −0.558152 + 0.277588i
\(226\) 0 0
\(227\) −11.8723 20.5634i −0.787991 1.36484i −0.927196 0.374577i \(-0.877788\pi\)
0.139205 0.990264i \(-0.455545\pi\)
\(228\) 0 0
\(229\) 10.0584 17.4217i 0.664679 1.15126i −0.314693 0.949194i \(-0.601902\pi\)
0.979372 0.202065i \(-0.0647651\pi\)
\(230\) 0 0
\(231\) 7.37228 1.73205i 0.485060 0.113961i
\(232\) 0 0
\(233\) −11.7446 −0.769412 −0.384706 0.923039i \(-0.625697\pi\)
−0.384706 + 0.923039i \(0.625697\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 6.05842 20.0935i 0.393537 1.30521i
\(238\) 0 0
\(239\) −9.43070 + 16.3345i −0.610021 + 1.05659i 0.381215 + 0.924487i \(0.375506\pi\)
−0.991236 + 0.132102i \(0.957827\pi\)
\(240\) 0 0
\(241\) −0.441578 0.764836i −0.0284445 0.0492674i 0.851453 0.524431i \(-0.175722\pi\)
−0.879897 + 0.475164i \(0.842389\pi\)
\(242\) 0 0
\(243\) 9.18614 + 12.5942i 0.589291 + 0.807921i
\(244\) 0 0
\(245\) 0.686141 + 1.18843i 0.0438359 + 0.0759260i
\(246\) 0 0
\(247\) 5.00000 8.66025i 0.318142 0.551039i
\(248\) 0 0
\(249\) −2.74456 + 9.10268i −0.173930 + 0.576859i
\(250\) 0 0
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) −32.2337 −2.02651
\(254\) 0 0
\(255\) 10.1168 2.37686i 0.633541 0.148845i
\(256\) 0 0
\(257\) −10.9307 + 18.9325i −0.681839 + 1.18098i 0.292581 + 0.956241i \(0.405486\pi\)
−0.974419 + 0.224738i \(0.927847\pi\)
\(258\) 0 0
\(259\) 1.00000 + 1.73205i 0.0621370 + 0.107624i
\(260\) 0 0
\(261\) 7.37228 3.66648i 0.456333 0.226949i
\(262\) 0 0
\(263\) 6.68614 + 11.5807i 0.412285 + 0.714099i 0.995139 0.0984781i \(-0.0313974\pi\)
−0.582854 + 0.812577i \(0.698064\pi\)
\(264\) 0 0
\(265\) 1.88316 3.26172i 0.115681 0.200366i
\(266\) 0 0
\(267\) −3.86141 4.10891i −0.236314 0.251461i
\(268\) 0 0
\(269\) −7.37228 −0.449496 −0.224748 0.974417i \(-0.572156\pi\)
−0.224748 + 0.974417i \(0.572156\pi\)
\(270\) 0 0
\(271\) 18.2337 1.10762 0.553809 0.832644i \(-0.313174\pi\)
0.553809 + 0.832644i \(0.313174\pi\)
\(272\) 0 0
\(273\) 2.37228 + 2.52434i 0.143577 + 0.152780i
\(274\) 0 0
\(275\) −6.81386 + 11.8020i −0.410891 + 0.711684i
\(276\) 0 0
\(277\) −11.1168 19.2549i −0.667946 1.15692i −0.978477 0.206354i \(-0.933840\pi\)
0.310531 0.950563i \(-0.399493\pi\)
\(278\) 0 0
\(279\) 5.00000 + 3.31662i 0.299342 + 0.198561i
\(280\) 0 0
\(281\) −5.31386 9.20387i −0.316998 0.549057i 0.662862 0.748742i \(-0.269342\pi\)
−0.979860 + 0.199685i \(0.936008\pi\)
\(282\) 0 0
\(283\) 4.94158 8.55906i 0.293746 0.508784i −0.680946 0.732333i \(-0.738431\pi\)
0.974692 + 0.223550i \(0.0717646\pi\)
\(284\) 0 0
\(285\) 11.5693 2.71810i 0.685306 0.161006i
\(286\) 0 0
\(287\) −10.3723 −0.612256
\(288\) 0 0
\(289\) 2.11684 0.124520
\(290\) 0 0
\(291\) −4.55842 + 15.1186i −0.267219 + 0.886267i
\(292\) 0 0
\(293\) 2.31386 4.00772i 0.135177 0.234134i −0.790488 0.612478i \(-0.790173\pi\)
0.925665 + 0.378344i \(0.123506\pi\)
\(294\) 0 0
\(295\) −4.88316 8.45787i −0.284308 0.492436i
\(296\) 0 0
\(297\) 21.3030 + 7.89542i 1.23612 + 0.458139i
\(298\) 0 0
\(299\) −7.37228 12.7692i −0.426350 0.738460i
\(300\) 0 0
\(301\) −4.55842 + 7.89542i −0.262743 + 0.455084i
\(302\) 0 0
\(303\) −3.68614 + 12.2255i −0.211763 + 0.702339i
\(304\) 0 0
\(305\) 19.3723 1.10925
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) 16.8614 3.96143i 0.959212 0.225358i
\(310\) 0 0
\(311\) −13.1168 + 22.7190i −0.743788 + 1.28828i 0.206971 + 0.978347i \(0.433639\pi\)
−0.950759 + 0.309931i \(0.899694\pi\)
\(312\) 0 0
\(313\) 1.44158 + 2.49689i 0.0814828 + 0.141132i 0.903887 0.427771i \(-0.140701\pi\)
−0.822404 + 0.568904i \(0.807368\pi\)
\(314\) 0 0
\(315\) −0.255437 + 4.10891i −0.0143923 + 0.231511i
\(316\) 0 0
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) −1.93070 2.05446i −0.107761 0.114669i
\(322\) 0 0
\(323\) 21.8614 1.21640
\(324\) 0 0
\(325\) −6.23369 −0.345783
\(326\) 0 0
\(327\) −16.6060 17.6704i −0.918312 0.977173i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.11684 10.5947i −0.336212 0.582337i 0.647505 0.762061i \(-0.275813\pi\)
−0.983717 + 0.179725i \(0.942479\pi\)
\(332\) 0 0
\(333\) −0.372281 + 5.98844i −0.0204009 + 0.328164i
\(334\) 0 0
\(335\) −10.3723 17.9653i −0.566698 0.981550i
\(336\) 0 0
\(337\) −4.55842 + 7.89542i −0.248313 + 0.430091i −0.963058 0.269294i \(-0.913210\pi\)
0.714745 + 0.699385i \(0.246543\pi\)
\(338\) 0 0
\(339\) 2.31386 0.543620i 0.125672 0.0295254i
\(340\) 0 0
\(341\) 8.74456 0.473545
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 5.05842 16.7769i 0.272336 0.903237i
\(346\) 0 0
\(347\) 3.55842 6.16337i 0.191026 0.330867i −0.754564 0.656226i \(-0.772152\pi\)
0.945591 + 0.325359i \(0.105485\pi\)
\(348\) 0 0
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) 0 0
\(351\) 1.74456 + 10.2448i 0.0931179 + 0.546828i
\(352\) 0 0
\(353\) 3.81386 + 6.60580i 0.202991 + 0.351591i 0.949491 0.313795i \(-0.101600\pi\)
−0.746500 + 0.665386i \(0.768267\pi\)
\(354\) 0 0
\(355\) −6.94158 + 12.0232i −0.368421 + 0.638123i
\(356\) 0 0
\(357\) −2.18614 + 7.25061i −0.115703 + 0.383743i
\(358\) 0 0
\(359\) 6.86141 0.362131 0.181066 0.983471i \(-0.442045\pi\)
0.181066 + 0.983471i \(0.442045\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 13.6861 3.21543i 0.718336 0.168767i
\(364\) 0 0
\(365\) −3.51087 + 6.08101i −0.183768 + 0.318295i
\(366\) 0 0
\(367\) 11.1168 + 19.2549i 0.580295 + 1.00510i 0.995444 + 0.0953465i \(0.0303959\pi\)
−0.415150 + 0.909753i \(0.636271\pi\)
\(368\) 0 0
\(369\) −25.9307 17.2005i −1.34990 0.895421i
\(370\) 0 0
\(371\) 1.37228 + 2.37686i 0.0712453 + 0.123400i
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 0 0
\(375\) −13.2119 14.0588i −0.682262 0.725993i
\(376\) 0 0
\(377\) 5.48913 0.282704
\(378\) 0 0
\(379\) −9.11684 −0.468301 −0.234150 0.972200i \(-0.575231\pi\)
−0.234150 + 0.972200i \(0.575231\pi\)
\(380\) 0 0
\(381\) −16.7446 17.8178i −0.857850 0.912836i
\(382\) 0 0
\(383\) −10.6277 + 18.4077i −0.543051 + 0.940592i 0.455676 + 0.890146i \(0.349398\pi\)
−0.998727 + 0.0504462i \(0.983936\pi\)
\(384\) 0 0
\(385\) 3.00000 + 5.19615i 0.152894 + 0.264820i
\(386\) 0 0
\(387\) −24.4891 + 12.1793i −1.24485 + 0.619107i
\(388\) 0 0
\(389\) 17.4891 + 30.2921i 0.886734 + 1.53587i 0.843713 + 0.536794i \(0.180365\pi\)
0.0430204 + 0.999074i \(0.486302\pi\)
\(390\) 0 0
\(391\) 16.1168 27.9152i 0.815064 1.41173i
\(392\) 0 0
\(393\) 12.4307 2.92048i 0.627046 0.147319i
\(394\) 0 0
\(395\) 16.6277 0.836631
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −2.50000 + 8.29156i −0.125157 + 0.415097i
\(400\) 0 0
\(401\) 0.127719 0.221215i 0.00637797 0.0110470i −0.862819 0.505513i \(-0.831303\pi\)
0.869197 + 0.494466i \(0.164636\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) 0 0
\(405\) −7.45245 + 9.84868i −0.370315 + 0.489385i
\(406\) 0 0
\(407\) 4.37228 + 7.57301i 0.216726 + 0.375380i
\(408\) 0 0
\(409\) −14.6753 + 25.4183i −0.725645 + 1.25685i 0.233063 + 0.972462i \(0.425125\pi\)
−0.958708 + 0.284393i \(0.908208\pi\)
\(410\) 0 0
\(411\) −8.18614 + 27.1504i −0.403793 + 1.33923i
\(412\) 0 0
\(413\) 7.11684 0.350197
\(414\) 0 0
\(415\) −7.53262 −0.369762
\(416\) 0 0
\(417\) 35.8030 8.41159i 1.75328 0.411917i
\(418\) 0 0
\(419\) 13.8030 23.9075i 0.674320 1.16796i −0.302347 0.953198i \(-0.597770\pi\)
0.976667 0.214759i \(-0.0688964\pi\)
\(420\) 0 0
\(421\) 0.116844 + 0.202380i 0.00569463 + 0.00986338i 0.868859 0.495060i \(-0.164854\pi\)
−0.863164 + 0.504924i \(0.831521\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.81386 11.8020i −0.330521 0.572479i
\(426\) 0 0
\(427\) −7.05842 + 12.2255i −0.341581 + 0.591636i
\(428\) 0 0
\(429\) 10.3723 + 11.0371i 0.500778 + 0.532877i
\(430\) 0 0
\(431\) 29.4891 1.42044 0.710221 0.703979i \(-0.248595\pi\)
0.710221 + 0.703979i \(0.248595\pi\)
\(432\) 0 0
\(433\) −2.88316 −0.138556 −0.0692778 0.997597i \(-0.522069\pi\)
−0.0692778 + 0.997597i \(0.522069\pi\)
\(434\) 0 0
\(435\) 4.46738 + 4.75372i 0.214194 + 0.227924i
\(436\) 0 0
\(437\) 18.4307 31.9229i 0.881660 1.52708i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 0 0
\(441\) −2.50000 1.65831i −0.119048 0.0789673i
\(442\) 0 0
\(443\) −11.4416 19.8174i −0.543606 0.941553i −0.998693 0.0511061i \(-0.983725\pi\)
0.455087 0.890447i \(-0.349608\pi\)
\(444\) 0 0
\(445\) 2.23369 3.86886i 0.105887 0.183402i
\(446\) 0 0
\(447\) 24.8614 5.84096i 1.17590 0.276268i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) −45.3505 −2.13547
\(452\) 0 0
\(453\) −4.05842 + 13.4603i −0.190681 + 0.632418i
\(454\) 0 0
\(455\) −1.37228 + 2.37686i −0.0643335 + 0.111429i
\(456\) 0 0
\(457\) −16.7337 28.9836i −0.782769 1.35580i −0.930323 0.366742i \(-0.880473\pi\)
0.147554 0.989054i \(-0.452860\pi\)
\(458\) 0 0
\(459\) −17.4891 + 14.5012i −0.816322 + 0.676859i
\(460\) 0 0
\(461\) −15.4307 26.7268i −0.718680 1.24479i −0.961523 0.274724i \(-0.911414\pi\)
0.242844 0.970065i \(-0.421920\pi\)
\(462\) 0 0
\(463\) −2.94158 + 5.09496i −0.136707 + 0.236783i −0.926248 0.376914i \(-0.876985\pi\)
0.789541 + 0.613697i \(0.210318\pi\)
\(464\) 0 0
\(465\) −1.37228 + 4.55134i −0.0636380 + 0.211063i
\(466\) 0 0
\(467\) 30.0951 1.39263 0.696317 0.717734i \(-0.254821\pi\)
0.696317 + 0.717734i \(0.254821\pi\)
\(468\) 0 0
\(469\) 15.1168 0.698031
\(470\) 0 0
\(471\) −13.6861 + 3.21543i −0.630624 + 0.148159i
\(472\) 0 0
\(473\) −19.9307 + 34.5210i −0.916415 + 1.58728i
\(474\) 0 0
\(475\) −7.79211 13.4963i −0.357527 0.619254i
\(476\) 0 0
\(477\) −0.510875 + 8.21782i −0.0233913 + 0.376268i
\(478\) 0 0
\(479\) 10.6277 + 18.4077i 0.485593 + 0.841072i 0.999863 0.0165568i \(-0.00527043\pi\)
−0.514270 + 0.857628i \(0.671937\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) 0 0
\(483\) 8.74456 + 9.30506i 0.397891 + 0.423395i
\(484\) 0 0
\(485\) −12.5109 −0.568090
\(486\) 0 0
\(487\) 16.3505 0.740913 0.370457 0.928850i \(-0.379201\pi\)
0.370457 + 0.928850i \(0.379201\pi\)
\(488\) 0 0
\(489\) 19.2554 + 20.4897i 0.870761 + 0.926574i
\(490\) 0 0
\(491\) −9.81386 + 16.9981i −0.442893 + 0.767114i −0.997903 0.0647303i \(-0.979381\pi\)
0.555010 + 0.831844i \(0.312715\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) 0 0
\(495\) −1.11684 + 17.9653i −0.0501984 + 0.807481i
\(496\) 0 0
\(497\) −5.05842 8.76144i −0.226901 0.393004i
\(498\) 0 0
\(499\) 0.441578 0.764836i 0.0197677 0.0342387i −0.855972 0.517022i \(-0.827041\pi\)
0.875740 + 0.482783i \(0.160374\pi\)
\(500\) 0 0
\(501\) −29.4891 + 6.92820i −1.31748 + 0.309529i
\(502\) 0 0
\(503\) −2.23369 −0.0995952 −0.0497976 0.998759i \(-0.515858\pi\)
−0.0497976 + 0.998759i \(0.515858\pi\)
\(504\) 0 0
\(505\) −10.1168 −0.450194
\(506\) 0 0
\(507\) 4.50000 14.9248i 0.199852 0.662834i
\(508\) 0 0
\(509\) −8.48913 + 14.7036i −0.376274 + 0.651725i −0.990517 0.137392i \(-0.956128\pi\)
0.614243 + 0.789117i \(0.289461\pi\)
\(510\) 0 0
\(511\) −2.55842 4.43132i −0.113178 0.196030i
\(512\) 0 0
\(513\) −20.0000 + 16.5831i −0.883022 + 0.732163i
\(514\) 0 0
\(515\) 6.86141 + 11.8843i 0.302350 + 0.523685i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 9.94987i 0.131685 0.436751i
\(520\) 0 0
\(521\) 3.86141 0.169171 0.0845856 0.996416i \(-0.473043\pi\)
0.0845856 + 0.996416i \(0.473043\pi\)
\(522\) 0 0
\(523\) 17.8832 0.781976 0.390988 0.920396i \(-0.372133\pi\)
0.390988 + 0.920396i \(0.372133\pi\)
\(524\) 0 0
\(525\) 5.25544 1.23472i 0.229366 0.0538875i
\(526\) 0 0
\(527\) −4.37228 + 7.57301i −0.190460 + 0.329886i
\(528\) 0 0
\(529\) −15.6753 27.1504i −0.681533 1.18045i
\(530\) 0 0
\(531\) 17.7921 + 11.8020i 0.772112 + 0.512161i
\(532\) 0 0
\(533\) −10.3723 17.9653i −0.449273 0.778164i
\(534\) 0 0
\(535\) 1.11684 1.93443i 0.0482854 0.0836327i
\(536\) 0 0
\(537\) 17.4891 + 18.6101i 0.754711 + 0.803086i
\(538\) 0 0
\(539\) −4.37228 −0.188327
\(540\) 0 0
\(541\) 28.2337 1.21386 0.606931 0.794755i \(-0.292401\pi\)
0.606931 + 0.794755i \(0.292401\pi\)
\(542\) 0 0
\(543\) −21.4891 22.8665i −0.922187 0.981296i
\(544\) 0 0
\(545\) 9.60597 16.6380i 0.411475 0.712695i
\(546\) 0 0
\(547\) 0.441578 + 0.764836i 0.0188805 + 0.0327020i 0.875311 0.483560i \(-0.160656\pi\)
−0.856431 + 0.516262i \(0.827323\pi\)
\(548\) 0 0
\(549\) −37.9198 + 18.8588i −1.61838 + 0.804874i
\(550\) 0 0
\(551\) 6.86141 + 11.8843i 0.292306 + 0.506288i
\(552\) 0 0
\(553\) −6.05842 + 10.4935i −0.257630 + 0.446229i
\(554\) 0 0
\(555\) −4.62772 + 1.08724i −0.196436 + 0.0461508i
\(556\) 0 0
\(557\) 6.51087 0.275875 0.137937 0.990441i \(-0.455953\pi\)
0.137937 + 0.990441i \(0.455953\pi\)
\(558\) 0 0
\(559\) −18.2337 −0.771203
\(560\) 0 0
\(561\) −9.55842 + 31.7017i −0.403557 + 1.33845i
\(562\) 0 0
\(563\) 1.50000 2.59808i 0.0632175 0.109496i −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 0 0
\(565\) 0.941578 + 1.63086i 0.0396125 + 0.0686108i
\(566\) 0 0
\(567\) −3.50000 8.29156i −0.146986 0.348213i
\(568\) 0 0
\(569\) 0.558422 + 0.967215i 0.0234103 + 0.0405478i 0.877493 0.479589i \(-0.159214\pi\)
−0.854083 + 0.520137i \(0.825881\pi\)
\(570\) 0 0
\(571\) 14.6753 25.4183i 0.614141 1.06372i −0.376394 0.926460i \(-0.622836\pi\)
0.990535 0.137263i \(-0.0438306\pi\)
\(572\) 0 0
\(573\) −0.941578 + 3.12286i −0.0393350 + 0.130459i
\(574\) 0 0
\(575\) −22.9783 −0.958259
\(576\) 0 0
\(577\) 27.1168 1.12889 0.564444 0.825471i \(-0.309090\pi\)
0.564444 + 0.825471i \(0.309090\pi\)
\(578\) 0 0
\(579\) −11.8030 + 2.77300i −0.490515 + 0.115242i
\(580\) 0 0
\(581\) 2.74456 4.75372i 0.113864 0.197218i
\(582\) 0 0
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) 0 0
\(585\) −7.37228 + 3.66648i −0.304806 + 0.151590i
\(586\) 0 0
\(587\) −4.24456 7.35180i −0.175192 0.303441i 0.765036 0.643988i \(-0.222721\pi\)
−0.940228 + 0.340547i \(0.889388\pi\)
\(588\) 0 0
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) 0 0
\(591\) 7.11684 + 7.57301i 0.292748 + 0.311512i
\(592\) 0 0
\(593\) 3.25544 0.133685 0.0668424 0.997764i \(-0.478708\pi\)
0.0668424 + 0.997764i \(0.478708\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) 0 0
\(597\) −11.8614 12.6217i −0.485455 0.516571i
\(598\) 0 0
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) −3.44158 5.96099i −0.140385 0.243154i 0.787257 0.616625i \(-0.211501\pi\)
−0.927642 + 0.373472i \(0.878167\pi\)
\(602\) 0 0
\(603\) 37.7921 + 25.0684i 1.53901 + 1.02087i
\(604\) 0 0
\(605\) 5.56930 + 9.64630i 0.226424 + 0.392178i
\(606\) 0 0
\(607\) −6.11684 + 10.5947i −0.248275 + 0.430025i −0.963047 0.269332i \(-0.913197\pi\)
0.714772 + 0.699357i \(0.246530\pi\)
\(608\) 0 0
\(609\) −4.62772 + 1.08724i −0.187525 + 0.0440572i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.76631 −0.0713407 −0.0356703 0.999364i \(-0.511357\pi\)
−0.0356703 + 0.999364i \(0.511357\pi\)
\(614\) 0 0
\(615\) 7.11684 23.6039i 0.286979 0.951801i
\(616\) 0 0
\(617\) 4.93070 8.54023i 0.198503 0.343817i −0.749540 0.661959i \(-0.769725\pi\)
0.948043 + 0.318142i \(0.103059\pi\)
\(618\) 0 0
\(619\) −11.7337 20.3233i −0.471617 0.816864i 0.527856 0.849334i \(-0.322996\pi\)
−0.999473 + 0.0324697i \(0.989663\pi\)
\(620\) 0 0
\(621\) 6.43070 + 37.7639i 0.258055 + 1.51541i
\(622\) 0 0
\(623\) 1.62772 + 2.81929i 0.0652132 + 0.112953i
\(624\) 0 0
\(625\) −0.149468 + 0.258886i −0.00597872 + 0.0103555i
\(626\) 0 0
\(627\) −10.9307 + 36.2530i −0.436530 + 1.44781i
\(628\) 0 0
\(629\) −8.74456 −0.348669
\(630\) 0 0
\(631\) −14.3505 −0.571286 −0.285643 0.958336i \(-0.592207\pi\)
−0.285643 + 0.958336i \(0.592207\pi\)
\(632\) 0 0
\(633\) 26.9783 6.33830i 1.07229 0.251925i
\(634\) 0 0
\(635\) 9.68614 16.7769i 0.384383 0.665770i
\(636\) 0 0
\(637\) −1.00000 1.73205i −0.0396214 0.0686264i
\(638\) 0 0
\(639\) 1.88316 30.2921i 0.0744965 1.19834i
\(640\) 0 0
\(641\) 23.1060 + 40.0207i 0.912631 + 1.58072i 0.810333 + 0.585969i \(0.199286\pi\)
0.102298 + 0.994754i \(0.467381\pi\)
\(642\) 0 0
\(643\) −12.6753 + 21.9542i −0.499864 + 0.865789i −1.00000 0.000157386i \(-0.999950\pi\)
0.500136 + 0.865947i \(0.333283\pi\)
\(644\) 0 0
\(645\) −14.8397 15.7908i −0.584311 0.621764i
\(646\) 0 0
\(647\) 17.4891 0.687568 0.343784 0.939049i \(-0.388291\pi\)
0.343784 + 0.939049i \(0.388291\pi\)
\(648\) 0 0
\(649\) 31.1168 1.22144
\(650\) 0 0
\(651\) −2.37228 2.52434i −0.0929770 0.0989366i
\(652\) 0 0
\(653\) 7.62772 13.2116i 0.298496 0.517010i −0.677296 0.735710i \(-0.736848\pi\)
0.975792 + 0.218701i \(0.0701818\pi\)
\(654\) 0 0
\(655\) 5.05842 + 8.76144i 0.197649 + 0.342338i
\(656\) 0 0
\(657\) 0.952453 15.3210i 0.0371587 0.597727i
\(658\) 0 0
\(659\) −4.62772 8.01544i −0.180270 0.312237i 0.761702 0.647927i \(-0.224364\pi\)
−0.941973 + 0.335690i \(0.891031\pi\)
\(660\) 0 0
\(661\) −4.94158 + 8.55906i −0.192205 + 0.332909i −0.945981 0.324223i \(-0.894897\pi\)
0.753776 + 0.657132i \(0.228231\pi\)
\(662\) 0 0
\(663\) −14.7446 + 3.46410i −0.572631 + 0.134535i
\(664\) 0 0
\(665\) −6.86141 −0.266074
\(666\) 0 0
\(667\) 20.2337 0.783452
\(668\) 0 0
\(669\) −2.00000 + 6.63325i −0.0773245 + 0.256456i
\(670\) 0 0
\(671\) −30.8614 + 53.4535i −1.19139 + 2.06355i
\(672\) 0 0
\(673\) 10.0584 + 17.4217i 0.387724 + 0.671557i 0.992143 0.125109i \(-0.0399281\pi\)
−0.604419 + 0.796666i \(0.706595\pi\)
\(674\) 0 0
\(675\) 15.1861 + 5.62836i 0.584515 + 0.216636i
\(676\) 0 0
\(677\) 17.2337 + 29.8496i 0.662344 + 1.14721i 0.979998 + 0.199007i \(0.0637718\pi\)
−0.317654 + 0.948207i \(0.602895\pi\)
\(678\) 0 0
\(679\) 4.55842 7.89542i 0.174936 0.302998i
\(680\) 0 0
\(681\) −11.8723 + 39.3759i −0.454947 + 1.50889i
\(682\) 0 0
\(683\) 44.8397 1.71574 0.857871 0.513865i \(-0.171787\pi\)
0.857871 + 0.513865i \(0.171787\pi\)
\(684\) 0 0
\(685\) −22.4674 −0.858434
\(686\) 0 0
\(687\) −33.9198 + 7.96916i −1.29412 + 0.304042i
\(688\) 0 0
\(689\) −2.74456 + 4.75372i −0.104560 + 0.181102i
\(690\) 0 0
\(691\) −2.94158 5.09496i −0.111903 0.193822i 0.804635 0.593770i \(-0.202361\pi\)
−0.916537 + 0.399949i \(0.869028\pi\)
\(692\) 0 0
\(693\) −10.9307 7.25061i −0.415223 0.275428i
\(694\) 0 0
\(695\) 14.5693 + 25.2348i 0.552645 + 0.957209i
\(696\) 0 0
\(697\) 22.6753 39.2747i 0.858887 1.48764i
\(698\) 0 0
\(699\) 13.9307 + 14.8236i 0.526908 + 0.560681i
\(700\) 0 0
\(701\) −3.76631 −0.142252 −0.0711258 0.997467i \(-0.522659\pi\)
−0.0711258 + 0.997467i \(0.522659\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.68614 6.38458i 0.138632 0.240117i
\(708\) 0 0
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) 0 0
\(711\) −32.5475 + 16.1870i −1.22063 + 0.607059i
\(712\) 0 0
\(713\) 7.37228 + 12.7692i 0.276094 + 0.478209i
\(714\) 0 0
\(715\) −6.00000 + 10.3923i −0.224387 + 0.388650i
\(716\) 0 0
\(717\) 31.8030 7.47182i 1.18770 0.279040i
\(718\) 0 0
\(719\) 8.74456 0.326117 0.163059 0.986616i \(-0.447864\pi\)
0.163059 + 0.986616i \(0.447864\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 0 0
\(723\) −0.441578 + 1.46455i −0.0164225 + 0.0544671i
\(724\) 0 0
\(725\) 4.27719 7.40830i 0.158851 0.275138i
\(726\) 0 0
\(727\) −0.883156 1.52967i −0.0327544 0.0567324i 0.849183 0.528098i \(-0.177095\pi\)
−0.881938 + 0.471366i \(0.843761\pi\)
\(728\) 0 0
\(729\) 5.00000 26.5330i 0.185185 0.982704i
\(730\) 0 0
\(731\) −19.9307 34.5210i −0.737164 1.27680i
\(732\) 0 0
\(733\) 11.9416 20.6834i 0.441072 0.763960i −0.556697 0.830716i \(-0.687932\pi\)
0.997769 + 0.0667560i \(0.0212649\pi\)
\(734\) 0 0
\(735\) 0.686141 2.27567i 0.0253087 0.0839394i
\(736\) 0 0
\(737\) 66.0951 2.43464
\(738\) 0 0
\(739\) −9.11684 −0.335369 −0.167684 0.985841i \(-0.553629\pi\)
−0.167684 + 0.985841i \(0.553629\pi\)
\(740\) 0 0
\(741\) −16.8614 + 3.96143i −0.619419 + 0.145527i
\(742\) 0 0
\(743\) 21.8614 37.8651i 0.802017 1.38913i −0.116269 0.993218i \(-0.537094\pi\)
0.918286 0.395917i \(-0.129573\pi\)
\(744\) 0 0
\(745\) 10.1168 + 17.5229i 0.370652 + 0.641989i
\(746\) 0 0
\(747\) 14.7446 7.33296i 0.539475 0.268299i
\(748\) 0 0
\(749\) 0.813859 + 1.40965i 0.0297378 + 0.0515073i
\(750\) 0 0
\(751\) 0.0584220 0.101190i 0.00213185 0.00369247i −0.864958 0.501845i \(-0.832655\pi\)
0.867089 + 0.498153i \(0.165988\pi\)
\(752\) 0 0
\(753\) −10.6753 11.3595i −0.389028 0.413964i
\(754\) 0 0
\(755\) −11.1386 −0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) 0 0
\(759\) 38.2337 + 40.6844i 1.38779 + 1.47675i
\(760\) 0 0
\(761\) −6.25544 + 10.8347i −0.226759 + 0.392759i −0.956846 0.290596i \(-0.906146\pi\)
0.730086 + 0.683355i \(0.239480\pi\)
\(762\) 0 0
\(763\) 7.00000 + 12.1244i 0.253417 + 0.438931i
\(764\) 0 0
\(765\) −15.0000 9.94987i −0.542326 0.359738i
\(766\) 0 0
\(767\) 7.11684 + 12.3267i 0.256974 + 0.445093i
\(768\) 0 0
\(769\) 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 0 0
\(771\) 36.8614 8.66025i 1.32753 0.311891i
\(772\) 0 0
\(773\) −11.1386 −0.400627 −0.200314 0.979732i \(-0.564196\pi\)
−0.200314 + 0.979732i \(0.564196\pi\)
\(774\) 0 0
\(775\) 6.23369 0.223921
\(776\) 0 0
\(777\) 1.00000 3.31662i 0.0358748 0.118983i
\(778\) 0 0
\(779\) 25.9307 44.9133i 0.929064 1.60919i
\(780\) 0 0
\(781\) −22.1168 38.3075i −0.791403 1.37075i
\(782\) 0 0
\(783\) −13.3723 4.95610i −0.477886 0.177117i
\(784\) 0 0
\(785\) −5.56930 9.64630i −0.198777 0.344291i
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) 0 0
\(789\) 6.68614 22.1754i 0.238033 0.789466i
\(790\) 0 0
\(791\) −1.37228 −0.0487927
\(792\) 0 0
\(793\) −28.2337 −1.00261
\(794\) 0 0
\(795\) −6.35053 + 1.49200i −0.225230 + 0.0529158i