Properties

Label 637.2.f.g.393.4
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1485512441856.7
Defining polynomial: \(x^{8} + 24 x^{6} + 455 x^{4} + 2904 x^{2} + 14641\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.4
Root \(1.34203 - 2.32446i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.g.295.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.68406 q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.68406 q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.34203 - 2.32446i) q^{10} +(-2.89792 - 5.01934i) q^{11} +1.41421 q^{12} +(-2.75624 - 2.32446i) q^{13} +(1.89792 + 3.28729i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.75624 - 4.77395i) q^{17} -1.00000 q^{18} +(-1.41421 + 2.44949i) q^{19} +(1.34203 - 2.32446i) q^{20} +(-2.89792 + 5.01934i) q^{22} +(-0.897916 - 1.55524i) q^{23} +(-2.12132 - 3.67423i) q^{24} +2.20417 q^{25} +(-0.634922 + 3.54921i) q^{26} +5.65685 q^{27} +(4.39792 + 7.61741i) q^{29} +(1.89792 - 3.28729i) q^{30} +1.41421 q^{31} +(-2.50000 + 4.33013i) q^{32} +(4.09827 - 7.09841i) q^{33} -5.51249 q^{34} +(-0.500000 - 0.866025i) q^{36} +(3.39792 + 5.88536i) q^{37} +2.82843 q^{38} +(0.897916 - 5.01934i) q^{39} -8.05217 q^{40} +(4.87756 + 8.44819i) q^{41} +(0.897916 - 1.55524i) q^{43} -5.79583 q^{44} +(1.34203 - 2.32446i) q^{45} +(-0.897916 + 1.55524i) q^{46} -2.82843 q^{47} +(-0.707107 + 1.22474i) q^{48} +(-1.10208 - 1.90887i) q^{50} +7.79583 q^{51} +(-3.39116 + 1.22474i) q^{52} +6.59166 q^{53} +(-2.82843 - 4.89898i) q^{54} +(-7.77817 - 13.4722i) q^{55} -4.00000 q^{57} +(4.39792 - 7.61741i) q^{58} +(0.562738 - 0.974691i) q^{59} +3.79583 q^{60} +(0.779291 - 1.34977i) q^{61} +(-0.707107 - 1.22474i) q^{62} +7.00000 q^{64} +(-7.39792 - 6.23899i) q^{65} -8.19654 q^{66} +(-2.89792 - 5.01934i) q^{67} +(-2.75624 - 4.77395i) q^{68} +(1.26984 - 2.19944i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +5.80122 q^{73} +(3.39792 - 5.88536i) q^{74} +(1.55858 + 2.69954i) q^{75} +(1.41421 + 2.44949i) q^{76} +(-4.79583 + 1.73205i) q^{78} -11.7958 q^{79} +(1.34203 + 2.32446i) q^{80} +(2.50000 + 4.33013i) q^{81} +(4.87756 - 8.44819i) q^{82} +9.89949 q^{83} +(7.39792 - 12.8136i) q^{85} -1.79583 q^{86} +(-6.21959 + 10.7726i) q^{87} +(8.69375 + 15.0580i) q^{88} +(6.07522 + 10.5226i) q^{89} -2.68406 q^{90} -1.79583 q^{92} +(1.00000 + 1.73205i) q^{93} +(1.41421 + 2.44949i) q^{94} +(-3.79583 + 6.57457i) q^{95} -7.07107 q^{96} +(-2.12132 + 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + 4q^{4} - 24q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + 4q^{4} - 24q^{8} + 4q^{9} - 4q^{11} - 4q^{15} + 4q^{16} - 8q^{18} - 4q^{22} + 12q^{23} + 56q^{25} + 16q^{29} - 4q^{30} - 20q^{32} - 4q^{36} + 8q^{37} - 12q^{39} - 12q^{43} - 8q^{44} + 12q^{46} - 28q^{50} + 24q^{51} - 24q^{53} - 32q^{57} + 16q^{58} - 8q^{60} + 56q^{64} - 40q^{65} - 4q^{67} - 24q^{71} - 12q^{72} + 8q^{74} - 56q^{79} + 20q^{81} + 40q^{85} + 24q^{86} + 12q^{88} + 24q^{92} + 8q^{93} + 8q^{95} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0.707107 + 1.22474i 0.408248 + 0.707107i 0.994694 0.102882i \(-0.0328064\pi\)
−0.586445 + 0.809989i \(0.699473\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.68406 1.20035 0.600174 0.799870i \(-0.295098\pi\)
0.600174 + 0.799870i \(0.295098\pi\)
\(6\) 0.707107 1.22474i 0.288675 0.500000i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −1.34203 2.32446i −0.424387 0.735060i
\(11\) −2.89792 5.01934i −0.873754 1.51339i −0.858084 0.513510i \(-0.828345\pi\)
−0.0156708 0.999877i \(-0.504988\pi\)
\(12\) 1.41421 0.408248
\(13\) −2.75624 2.32446i −0.764444 0.644690i
\(14\) 0 0
\(15\) 1.89792 + 3.28729i 0.490040 + 0.848774i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.75624 4.77395i 0.668487 1.15785i −0.309840 0.950789i \(-0.600276\pi\)
0.978327 0.207065i \(-0.0663911\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.41421 + 2.44949i −0.324443 + 0.561951i −0.981399 0.191977i \(-0.938510\pi\)
0.656957 + 0.753928i \(0.271843\pi\)
\(20\) 1.34203 2.32446i 0.300087 0.519766i
\(21\) 0 0
\(22\) −2.89792 + 5.01934i −0.617838 + 1.07013i
\(23\) −0.897916 1.55524i −0.187228 0.324289i 0.757097 0.653303i \(-0.226617\pi\)
−0.944325 + 0.329014i \(0.893284\pi\)
\(24\) −2.12132 3.67423i −0.433013 0.750000i
\(25\) 2.20417 0.440834
\(26\) −0.634922 + 3.54921i −0.124519 + 0.696057i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) 4.39792 + 7.61741i 0.816672 + 1.41452i 0.908121 + 0.418708i \(0.137517\pi\)
−0.0914483 + 0.995810i \(0.529150\pi\)
\(30\) 1.89792 3.28729i 0.346510 0.600174i
\(31\) 1.41421 0.254000 0.127000 0.991903i \(-0.459465\pi\)
0.127000 + 0.991903i \(0.459465\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 4.09827 7.09841i 0.713418 1.23568i
\(34\) −5.51249 −0.945383
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.39792 + 5.88536i 0.558614 + 0.967548i 0.997613 + 0.0690599i \(0.0220000\pi\)
−0.438999 + 0.898488i \(0.644667\pi\)
\(38\) 2.82843 0.458831
\(39\) 0.897916 5.01934i 0.143782 0.803737i
\(40\) −8.05217 −1.27316
\(41\) 4.87756 + 8.44819i 0.761747 + 1.31939i 0.941949 + 0.335755i \(0.108992\pi\)
−0.180202 + 0.983630i \(0.557675\pi\)
\(42\) 0 0
\(43\) 0.897916 1.55524i 0.136931 0.237171i −0.789403 0.613876i \(-0.789610\pi\)
0.926333 + 0.376705i \(0.122943\pi\)
\(44\) −5.79583 −0.873754
\(45\) 1.34203 2.32446i 0.200058 0.346510i
\(46\) −0.897916 + 1.55524i −0.132390 + 0.229307i
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) −0.707107 + 1.22474i −0.102062 + 0.176777i
\(49\) 0 0
\(50\) −1.10208 1.90887i −0.155858 0.269954i
\(51\) 7.79583 1.09163
\(52\) −3.39116 + 1.22474i −0.470270 + 0.169842i
\(53\) 6.59166 0.905435 0.452717 0.891654i \(-0.350455\pi\)
0.452717 + 0.891654i \(0.350455\pi\)
\(54\) −2.82843 4.89898i −0.384900 0.666667i
\(55\) −7.77817 13.4722i −1.04881 1.81659i
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 4.39792 7.61741i 0.577475 1.00022i
\(59\) 0.562738 0.974691i 0.0732622 0.126894i −0.827067 0.562103i \(-0.809992\pi\)
0.900329 + 0.435209i \(0.143326\pi\)
\(60\) 3.79583 0.490040
\(61\) 0.779291 1.34977i 0.0997780 0.172821i −0.811815 0.583915i \(-0.801520\pi\)
0.911593 + 0.411095i \(0.134853\pi\)
\(62\) −0.707107 1.22474i −0.0898027 0.155543i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −7.39792 6.23899i −0.917599 0.773852i
\(66\) −8.19654 −1.00892
\(67\) −2.89792 5.01934i −0.354037 0.613210i 0.632916 0.774221i \(-0.281858\pi\)
−0.986953 + 0.161011i \(0.948525\pi\)
\(68\) −2.75624 4.77395i −0.334244 0.578927i
\(69\) 1.26984 2.19944i 0.152871 0.264781i
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 5.80122 0.678982 0.339491 0.940609i \(-0.389745\pi\)
0.339491 + 0.940609i \(0.389745\pi\)
\(74\) 3.39792 5.88536i 0.395000 0.684160i
\(75\) 1.55858 + 2.69954i 0.179970 + 0.311716i
\(76\) 1.41421 + 2.44949i 0.162221 + 0.280976i
\(77\) 0 0
\(78\) −4.79583 + 1.73205i −0.543021 + 0.196116i
\(79\) −11.7958 −1.32713 −0.663567 0.748117i \(-0.730958\pi\)
−0.663567 + 0.748117i \(0.730958\pi\)
\(80\) 1.34203 + 2.32446i 0.150043 + 0.259883i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) 4.87756 8.44819i 0.538637 0.932946i
\(83\) 9.89949 1.08661 0.543305 0.839535i \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 0 0
\(85\) 7.39792 12.8136i 0.802417 1.38983i
\(86\) −1.79583 −0.193649
\(87\) −6.21959 + 10.7726i −0.666810 + 1.15495i
\(88\) 8.69375 + 15.0580i 0.926757 + 1.60519i
\(89\) 6.07522 + 10.5226i 0.643972 + 1.11539i 0.984538 + 0.175172i \(0.0560482\pi\)
−0.340565 + 0.940221i \(0.610618\pi\)
\(90\) −2.68406 −0.282925
\(91\) 0 0
\(92\) −1.79583 −0.187228
\(93\) 1.00000 + 1.73205i 0.103695 + 0.179605i
\(94\) 1.41421 + 2.44949i 0.145865 + 0.252646i
\(95\) −3.79583 + 6.57457i −0.389444 + 0.674537i
\(96\) −7.07107 −0.721688
\(97\) −2.12132 + 3.67423i −0.215387 + 0.373062i −0.953392 0.301733i \(-0.902435\pi\)
0.738005 + 0.674795i \(0.235768\pi\)
\(98\) 0 0
\(99\) −5.79583 −0.582503
\(100\) 1.10208 1.90887i 0.110208 0.190887i
\(101\) −1.48640 2.57452i −0.147902 0.256174i 0.782550 0.622588i \(-0.213919\pi\)
−0.930452 + 0.366414i \(0.880585\pi\)
\(102\) −3.89792 6.75139i −0.385951 0.668487i
\(103\) 8.19654 0.807629 0.403815 0.914841i \(-0.367684\pi\)
0.403815 + 0.914841i \(0.367684\pi\)
\(104\) 8.26873 + 6.97339i 0.810815 + 0.683797i
\(105\) 0 0
\(106\) −3.29583 5.70855i −0.320119 0.554463i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 2.82843 4.89898i 0.272166 0.471405i
\(109\) −17.5917 −1.68498 −0.842488 0.538715i \(-0.818910\pi\)
−0.842488 + 0.538715i \(0.818910\pi\)
\(110\) −7.77817 + 13.4722i −0.741620 + 1.28452i
\(111\) −4.80538 + 8.32316i −0.456106 + 0.789999i
\(112\) 0 0
\(113\) 8.29583 14.3688i 0.780406 1.35170i −0.151299 0.988488i \(-0.548346\pi\)
0.931705 0.363215i \(-0.118321\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) −2.41006 4.17434i −0.224739 0.389260i
\(116\) 8.79583 0.816672
\(117\) −3.39116 + 1.22474i −0.313513 + 0.113228i
\(118\) −1.12548 −0.103608
\(119\) 0 0
\(120\) −5.69375 9.86186i −0.519766 0.900260i
\(121\) −11.2958 + 19.5650i −1.02689 + 1.77863i
\(122\) −1.55858 −0.141107
\(123\) −6.89792 + 11.9475i −0.621964 + 1.07727i
\(124\) 0.707107 1.22474i 0.0635001 0.109985i
\(125\) −7.50417 −0.671194
\(126\) 0 0
\(127\) −3.79583 6.57457i −0.336826 0.583399i 0.647008 0.762483i \(-0.276020\pi\)
−0.983834 + 0.179084i \(0.942687\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 2.53969 0.223607
\(130\) −1.70417 + 9.52628i −0.149465 + 0.835510i
\(131\) 8.19654 0.716135 0.358068 0.933696i \(-0.383436\pi\)
0.358068 + 0.933696i \(0.383436\pi\)
\(132\) −4.09827 7.09841i −0.356709 0.617838i
\(133\) 0 0
\(134\) −2.89792 + 5.01934i −0.250342 + 0.433605i
\(135\) 15.1833 1.30677
\(136\) −8.26873 + 14.3219i −0.709038 + 1.22809i
\(137\) 4.60208 7.97104i 0.393183 0.681012i −0.599685 0.800236i \(-0.704707\pi\)
0.992867 + 0.119224i \(0.0380407\pi\)
\(138\) −2.53969 −0.216193
\(139\) −7.63381 + 13.2221i −0.647491 + 1.12149i 0.336229 + 0.941780i \(0.390848\pi\)
−0.983720 + 0.179707i \(0.942485\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 6.00000 0.503509
\(143\) −3.67990 + 20.5706i −0.307729 + 1.72020i
\(144\) 1.00000 0.0833333
\(145\) 11.8043 + 20.4456i 0.980291 + 1.69791i
\(146\) −2.90061 5.02401i −0.240056 0.415790i
\(147\) 0 0
\(148\) 6.79583 0.558614
\(149\) −2.29583 + 3.97650i −0.188082 + 0.325767i −0.944611 0.328193i \(-0.893560\pi\)
0.756529 + 0.653960i \(0.226894\pi\)
\(150\) 1.55858 2.69954i 0.127258 0.220417i
\(151\) −17.5917 −1.43159 −0.715795 0.698311i \(-0.753935\pi\)
−0.715795 + 0.698311i \(0.753935\pi\)
\(152\) 4.24264 7.34847i 0.344124 0.596040i
\(153\) −2.75624 4.77395i −0.222829 0.385951i
\(154\) 0 0
\(155\) 3.79583 0.304889
\(156\) −3.89792 3.28729i −0.312083 0.263194i
\(157\) 6.92670 0.552811 0.276405 0.961041i \(-0.410857\pi\)
0.276405 + 0.961041i \(0.410857\pi\)
\(158\) 5.89792 + 10.2155i 0.469213 + 0.812701i
\(159\) 4.66101 + 8.07311i 0.369642 + 0.640239i
\(160\) −6.71015 + 11.6223i −0.530484 + 0.918825i
\(161\) 0 0
\(162\) 2.50000 4.33013i 0.196419 0.340207i
\(163\) 6.69375 11.5939i 0.524295 0.908105i −0.475305 0.879821i \(-0.657662\pi\)
0.999600 0.0282841i \(-0.00900432\pi\)
\(164\) 9.75513 0.761747
\(165\) 11.0000 19.0526i 0.856349 1.48324i
\(166\) −4.94975 8.57321i −0.384175 0.665410i
\(167\) 7.63381 + 13.2221i 0.590722 + 1.02316i 0.994135 + 0.108142i \(0.0344902\pi\)
−0.403414 + 0.915018i \(0.632176\pi\)
\(168\) 0 0
\(169\) 2.19375 + 12.8136i 0.168750 + 0.985659i
\(170\) −14.7958 −1.13479
\(171\) 1.41421 + 2.44949i 0.108148 + 0.187317i
\(172\) −0.897916 1.55524i −0.0684654 0.118586i
\(173\) 4.66101 8.07311i 0.354370 0.613787i −0.632640 0.774446i \(-0.718029\pi\)
0.987010 + 0.160659i \(0.0513620\pi\)
\(174\) 12.4392 0.943012
\(175\) 0 0
\(176\) 2.89792 5.01934i 0.218439 0.378347i
\(177\) 1.59166 0.119637
\(178\) 6.07522 10.5226i 0.455357 0.788702i
\(179\) 0.204168 + 0.353630i 0.0152603 + 0.0264316i 0.873555 0.486726i \(-0.161809\pi\)
−0.858294 + 0.513158i \(0.828476\pi\)
\(180\) −1.34203 2.32446i −0.100029 0.173255i
\(181\) 16.5375 1.22922 0.614610 0.788831i \(-0.289314\pi\)
0.614610 + 0.788831i \(0.289314\pi\)
\(182\) 0 0
\(183\) 2.20417 0.162937
\(184\) 2.69375 + 4.66571i 0.198586 + 0.343960i
\(185\) 9.12020 + 15.7967i 0.670531 + 1.16139i
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) −31.9494 −2.33637
\(188\) −1.41421 + 2.44949i −0.103142 + 0.178647i
\(189\) 0 0
\(190\) 7.59166 0.550757
\(191\) 12.8979 22.3398i 0.933260 1.61645i 0.155553 0.987827i \(-0.450284\pi\)
0.777707 0.628627i \(-0.216383\pi\)
\(192\) 4.94975 + 8.57321i 0.357217 + 0.618718i
\(193\) −1.70417 2.95171i −0.122669 0.212468i 0.798151 0.602458i \(-0.205812\pi\)
−0.920819 + 0.389990i \(0.872479\pi\)
\(194\) 4.24264 0.304604
\(195\) 2.41006 13.4722i 0.172588 0.964764i
\(196\) 0 0
\(197\) 4.00000 + 6.92820i 0.284988 + 0.493614i 0.972606 0.232458i \(-0.0746770\pi\)
−0.687618 + 0.726073i \(0.741344\pi\)
\(198\) 2.89792 + 5.01934i 0.205946 + 0.356709i
\(199\) −11.0250 + 19.0958i −0.781539 + 1.35367i 0.149505 + 0.988761i \(0.452232\pi\)
−0.931045 + 0.364905i \(0.881101\pi\)
\(200\) −6.61251 −0.467575
\(201\) 4.09827 7.09841i 0.289070 0.500684i
\(202\) −1.48640 + 2.57452i −0.104583 + 0.181142i
\(203\) 0 0
\(204\) 3.89792 6.75139i 0.272909 0.472692i
\(205\) 13.0917 + 22.6754i 0.914361 + 1.58372i
\(206\) −4.09827 7.09841i −0.285540 0.494570i
\(207\) −1.79583 −0.124819
\(208\) 0.634922 3.54921i 0.0440239 0.246093i
\(209\) 16.3931 1.13393
\(210\) 0 0
\(211\) 0.897916 + 1.55524i 0.0618151 + 0.107067i 0.895277 0.445510i \(-0.146978\pi\)
−0.833462 + 0.552577i \(0.813644\pi\)
\(212\) 3.29583 5.70855i 0.226359 0.392065i
\(213\) −8.48528 −0.581402
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 2.41006 4.17434i 0.164365 0.284688i
\(216\) −16.9706 −1.15470
\(217\) 0 0
\(218\) 8.79583 + 15.2348i 0.595729 + 1.03183i
\(219\) 4.10208 + 7.10502i 0.277193 + 0.480113i
\(220\) −15.5563 −1.04881
\(221\) −18.6937 + 6.75139i −1.25748 + 0.454148i
\(222\) 9.61076 0.645032
\(223\) −2.82843 4.89898i −0.189405 0.328060i 0.755647 0.654979i \(-0.227323\pi\)
−0.945052 + 0.326920i \(0.893989\pi\)
\(224\) 0 0
\(225\) 1.10208 1.90887i 0.0734723 0.127258i
\(226\) −16.5917 −1.10366
\(227\) 10.4622 18.1211i 0.694403 1.20274i −0.275979 0.961164i \(-0.589002\pi\)
0.970382 0.241577i \(-0.0776647\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) −12.7279 −0.841085 −0.420542 0.907273i \(-0.638160\pi\)
−0.420542 + 0.907273i \(0.638160\pi\)
\(230\) −2.41006 + 4.17434i −0.158915 + 0.275248i
\(231\) 0 0
\(232\) −13.1937 22.8522i −0.866212 1.50032i
\(233\) −21.1833 −1.38777 −0.693883 0.720088i \(-0.744101\pi\)
−0.693883 + 0.720088i \(0.744101\pi\)
\(234\) 2.75624 + 2.32446i 0.180181 + 0.151955i
\(235\) −7.59166 −0.495225
\(236\) −0.562738 0.974691i −0.0366311 0.0634470i
\(237\) −8.34091 14.4469i −0.541800 0.938426i
\(238\) 0 0
\(239\) −19.7958 −1.28049 −0.640243 0.768172i \(-0.721166\pi\)
−0.640243 + 0.768172i \(0.721166\pi\)
\(240\) −1.89792 + 3.28729i −0.122510 + 0.212193i
\(241\) 2.19350 3.79926i 0.141296 0.244732i −0.786689 0.617350i \(-0.788206\pi\)
0.927985 + 0.372618i \(0.121540\pi\)
\(242\) 22.5917 1.45225
\(243\) 4.94975 8.57321i 0.317526 0.549972i
\(244\) −0.779291 1.34977i −0.0498890 0.0864103i
\(245\) 0 0
\(246\) 13.7958 0.879590
\(247\) 9.59166 3.46410i 0.610303 0.220416i
\(248\) −4.24264 −0.269408
\(249\) 7.00000 + 12.1244i 0.443607 + 0.768350i
\(250\) 3.75209 + 6.49881i 0.237303 + 0.411021i
\(251\) −1.55858 + 2.69954i −0.0983769 + 0.170394i −0.911013 0.412378i \(-0.864698\pi\)
0.812636 + 0.582771i \(0.198032\pi\)
\(252\) 0 0
\(253\) −5.20417 + 9.01388i −0.327183 + 0.566698i
\(254\) −3.79583 + 6.57457i −0.238172 + 0.412525i
\(255\) 20.9245 1.31034
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 7.70599 + 13.3472i 0.480686 + 0.832573i 0.999754 0.0221596i \(-0.00705419\pi\)
−0.519068 + 0.854733i \(0.673721\pi\)
\(258\) −1.26984 2.19944i −0.0790571 0.136931i
\(259\) 0 0
\(260\) −9.10208 + 3.28729i −0.564487 + 0.203869i
\(261\) 8.79583 0.544448
\(262\) −4.09827 7.09841i −0.253192 0.438542i
\(263\) 12.6937 + 21.9862i 0.782730 + 1.35573i 0.930346 + 0.366683i \(0.119507\pi\)
−0.147616 + 0.989045i \(0.547160\pi\)
\(264\) −12.2948 + 21.2952i −0.756694 + 1.31063i
\(265\) 17.6924 1.08684
\(266\) 0 0
\(267\) −8.59166 + 14.8812i −0.525801 + 0.910714i
\(268\) −5.79583 −0.354037
\(269\) −0.562738 + 0.974691i −0.0343107 + 0.0594279i −0.882671 0.469992i \(-0.844257\pi\)
0.848360 + 0.529420i \(0.177590\pi\)
\(270\) −7.59166 13.1491i −0.462014 0.800232i
\(271\) −11.5877 20.0705i −0.703903 1.21920i −0.967086 0.254450i \(-0.918106\pi\)
0.263183 0.964746i \(-0.415228\pi\)
\(272\) 5.51249 0.334244
\(273\) 0 0
\(274\) −9.20417 −0.556044
\(275\) −6.38749 11.0635i −0.385180 0.667152i
\(276\) −1.26984 2.19944i −0.0764357 0.132390i
\(277\) 3.09166 5.35492i 0.185760 0.321746i −0.758072 0.652170i \(-0.773859\pi\)
0.943832 + 0.330425i \(0.107192\pi\)
\(278\) 15.2676 0.915690
\(279\) 0.707107 1.22474i 0.0423334 0.0733236i
\(280\) 0 0
\(281\) 15.2042 0.907005 0.453502 0.891255i \(-0.350174\pi\)
0.453502 + 0.891255i \(0.350174\pi\)
\(282\) −2.00000 + 3.46410i −0.119098 + 0.206284i
\(283\) −14.7049 25.4696i −0.874114 1.51401i −0.857704 0.514145i \(-0.828109\pi\)
−0.0164104 0.999865i \(-0.505224\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) −10.7362 −0.635960
\(286\) 19.6546 7.09841i 1.16220 0.419738i
\(287\) 0 0
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) −6.69375 11.5939i −0.393750 0.681995i
\(290\) 11.8043 20.4456i 0.693170 1.20061i
\(291\) −6.00000 −0.351726
\(292\) 2.90061 5.02401i 0.169745 0.294008i
\(293\) −4.87756 + 8.44819i −0.284950 + 0.493548i −0.972597 0.232497i \(-0.925310\pi\)
0.687647 + 0.726045i \(0.258644\pi\)
\(294\) 0 0
\(295\) 1.51042 2.61613i 0.0879401 0.152317i
\(296\) −10.1937 17.6561i −0.592500 1.02624i
\(297\) −16.3931 28.3937i −0.951223 1.64757i
\(298\) 4.59166 0.265988
\(299\) −1.14021 + 6.37378i −0.0659403 + 0.368605i
\(300\) 3.11716 0.179970
\(301\) 0 0
\(302\) 8.79583 + 15.2348i 0.506143 + 0.876666i
\(303\) 2.10208 3.64092i 0.120762 0.209165i
\(304\) −2.82843 −0.162221
\(305\) 2.09166 3.62287i 0.119768 0.207445i
\(306\) −2.75624 + 4.77395i −0.157564 + 0.272909i
\(307\) −34.2004 −1.95192 −0.975960 0.217951i \(-0.930063\pi\)
−0.975960 + 0.217951i \(0.930063\pi\)
\(308\) 0 0
\(309\) 5.79583 + 10.0387i 0.329713 + 0.571080i
\(310\) −1.89792 3.28729i −0.107794 0.186705i
\(311\) −11.8617 −0.672616 −0.336308 0.941752i \(-0.609178\pi\)
−0.336308 + 0.941752i \(0.609178\pi\)
\(312\) −2.69375 + 15.0580i −0.152503 + 0.852492i
\(313\) −1.70295 −0.0962565 −0.0481283 0.998841i \(-0.515326\pi\)
−0.0481283 + 0.998841i \(0.515326\pi\)
\(314\) −3.46335 5.99870i −0.195448 0.338526i
\(315\) 0 0
\(316\) −5.89792 + 10.2155i −0.331784 + 0.574666i
\(317\) −12.5917 −0.707218 −0.353609 0.935393i \(-0.615046\pi\)
−0.353609 + 0.935393i \(0.615046\pi\)
\(318\) 4.66101 8.07311i 0.261376 0.452717i
\(319\) 25.4896 44.1492i 1.42714 2.47188i
\(320\) 18.7884 1.05030
\(321\) −4.24264 + 7.34847i −0.236801 + 0.410152i
\(322\) 0 0
\(323\) 7.79583 + 13.5028i 0.433772 + 0.751315i
\(324\) 5.00000 0.277778
\(325\) −6.07522 5.12351i −0.336993 0.284201i
\(326\) −13.3875 −0.741465
\(327\) −12.4392 21.5453i −0.687888 1.19146i
\(328\) −14.6327 25.3446i −0.807955 1.39942i
\(329\) 0 0
\(330\) −22.0000 −1.21106
\(331\) −0.306253 + 0.530445i −0.0168332 + 0.0291559i −0.874319 0.485351i \(-0.838692\pi\)
0.857486 + 0.514507i \(0.172025\pi\)
\(332\) 4.94975 8.57321i 0.271653 0.470516i
\(333\) 6.79583 0.372409
\(334\) 7.63381 13.2221i 0.417703 0.723483i
\(335\) −7.77817 13.4722i −0.424967 0.736065i
\(336\) 0 0
\(337\) −29.9792 −1.63307 −0.816534 0.577297i \(-0.804108\pi\)
−0.816534 + 0.577297i \(0.804108\pi\)
\(338\) 10.0000 8.30662i 0.543928 0.451821i
\(339\) 23.4642 1.27440
\(340\) −7.39792 12.8136i −0.401208 0.694913i
\(341\) −4.09827 7.09841i −0.221934 0.384401i
\(342\) 1.41421 2.44949i 0.0764719 0.132453i
\(343\) 0 0
\(344\) −2.69375 + 4.66571i −0.145237 + 0.251558i
\(345\) 3.40834 5.90341i 0.183499 0.317829i
\(346\) −9.32202 −0.501155
\(347\) −7.48958 + 12.9723i −0.402062 + 0.696391i −0.993975 0.109611i \(-0.965040\pi\)
0.591913 + 0.806002i \(0.298373\pi\)
\(348\) 6.21959 + 10.7726i 0.333405 + 0.577475i
\(349\) 6.50833 + 11.2728i 0.348383 + 0.603417i 0.985962 0.166968i \(-0.0533976\pi\)
−0.637579 + 0.770385i \(0.720064\pi\)
\(350\) 0 0
\(351\) −15.5917 13.1491i −0.832221 0.701849i
\(352\) 28.9792 1.54459
\(353\) −7.56162 13.0971i −0.402464 0.697089i 0.591558 0.806262i \(-0.298513\pi\)
−0.994023 + 0.109173i \(0.965180\pi\)
\(354\) −0.795832 1.37842i −0.0422980 0.0732622i
\(355\) −8.05217 + 13.9468i −0.427365 + 0.740218i
\(356\) 12.1504 0.643972
\(357\) 0 0
\(358\) 0.204168 0.353630i 0.0107906 0.0186899i
\(359\) −4.00000 −0.211112 −0.105556 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) −4.02609 + 6.97339i −0.212193 + 0.367530i
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) −8.26873 14.3219i −0.434595 0.752740i
\(363\) −31.9494 −1.67691
\(364\) 0 0
\(365\) 15.5708 0.815014
\(366\) −1.10208 1.90887i −0.0576069 0.0997780i
\(367\) 10.6066 + 18.3712i 0.553660 + 0.958967i 0.998006 + 0.0631123i \(0.0201026\pi\)
−0.444346 + 0.895855i \(0.646564\pi\)
\(368\) 0.897916 1.55524i 0.0468071 0.0810723i
\(369\) 9.75513 0.507832
\(370\) 9.12020 15.7967i 0.474137 0.821229i
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 6.29583 10.9047i 0.325986 0.564624i −0.655726 0.754999i \(-0.727637\pi\)
0.981711 + 0.190375i \(0.0609705\pi\)
\(374\) 15.9747 + 27.6690i 0.826033 + 1.43073i
\(375\) −5.30625 9.19070i −0.274014 0.474606i
\(376\) 8.48528 0.437595
\(377\) 5.58467 31.2182i 0.287625 1.60782i
\(378\) 0 0
\(379\) 1.69375 + 2.93366i 0.0870020 + 0.150692i 0.906243 0.422758i \(-0.138938\pi\)
−0.819241 + 0.573450i \(0.805605\pi\)
\(380\) 3.79583 + 6.57457i 0.194722 + 0.337268i
\(381\) 5.36812 9.29785i 0.275017 0.476343i
\(382\) −25.7958 −1.31983
\(383\) −7.48944 + 12.9721i −0.382692 + 0.662843i −0.991446 0.130517i \(-0.958336\pi\)
0.608754 + 0.793359i \(0.291670\pi\)
\(384\) −2.12132 + 3.67423i −0.108253 + 0.187500i
\(385\) 0 0
\(386\) −1.70417 + 2.95171i −0.0867399 + 0.150238i
\(387\) −0.897916 1.55524i −0.0456436 0.0790571i
\(388\) 2.12132 + 3.67423i 0.107694 + 0.186531i
\(389\) 28.3875 1.43930 0.719652 0.694335i \(-0.244302\pi\)
0.719652 + 0.694335i \(0.244302\pi\)
\(390\) −12.8723 + 4.64893i −0.651814 + 0.235407i
\(391\) −9.89949 −0.500639
\(392\) 0 0
\(393\) 5.79583 + 10.0387i 0.292361 + 0.506384i
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) −31.6607 −1.59302
\(396\) −2.89792 + 5.01934i −0.145626 + 0.252231i
\(397\) 3.53553 6.12372i 0.177443 0.307341i −0.763561 0.645736i \(-0.776551\pi\)
0.941004 + 0.338395i \(0.109884\pi\)
\(398\) 22.0499 1.10526
\(399\) 0 0
\(400\) 1.10208 + 1.90887i 0.0551042 + 0.0954433i
\(401\) −12.1937 21.1202i −0.608927 1.05469i −0.991418 0.130733i \(-0.958267\pi\)
0.382491 0.923959i \(-0.375066\pi\)
\(402\) −8.19654 −0.408806
\(403\) −3.89792 3.28729i −0.194169 0.163751i
\(404\) −2.97280 −0.147902
\(405\) 6.71015 + 11.6223i 0.333430 + 0.577517i
\(406\) 0 0
\(407\) 19.6937 34.1106i 0.976183 1.69080i
\(408\) −23.3875 −1.15785
\(409\) −14.3440 + 24.8445i −0.709263 + 1.22848i 0.255868 + 0.966712i \(0.417639\pi\)
−0.965131 + 0.261767i \(0.915695\pi\)
\(410\) 13.0917 22.6754i 0.646551 1.11986i
\(411\) 13.0167 0.642064
\(412\) 4.09827 7.09841i 0.201907 0.349714i
\(413\) 0 0
\(414\) 0.897916 + 1.55524i 0.0441302 + 0.0764357i
\(415\) 26.5708 1.30431
\(416\) 16.9558 6.12372i 0.831328 0.300240i
\(417\) −21.5917 −1.05735
\(418\) −8.19654 14.1968i −0.400906 0.694390i
\(419\) 14.2718 + 24.7194i 0.697221 + 1.20762i 0.969426 + 0.245384i \(0.0789139\pi\)
−0.272205 + 0.962239i \(0.587753\pi\)
\(420\) 0 0
\(421\) −6.59166 −0.321258 −0.160629 0.987015i \(-0.551352\pi\)
−0.160629 + 0.987015i \(0.551352\pi\)
\(422\) 0.897916 1.55524i 0.0437099 0.0757077i
\(423\) −1.41421 + 2.44949i −0.0687614 + 0.119098i
\(424\) −19.7750 −0.960358
\(425\) 6.07522 10.5226i 0.294692 0.510421i
\(426\) 4.24264 + 7.34847i 0.205557 + 0.356034i
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) −27.7958 + 10.0387i −1.34200 + 0.484672i
\(430\) −4.82012 −0.232447
\(431\) 2.59166 + 4.48889i 0.124836 + 0.216222i 0.921669 0.387978i \(-0.126826\pi\)
−0.796833 + 0.604200i \(0.793493\pi\)
\(432\) 2.82843 + 4.89898i 0.136083 + 0.235702i
\(433\) 6.71015 11.6223i 0.322469 0.558533i −0.658528 0.752556i \(-0.728821\pi\)
0.980997 + 0.194024i \(0.0621539\pi\)
\(434\) 0 0
\(435\) −16.6937 + 28.9144i −0.800404 + 1.38634i
\(436\) −8.79583 + 15.2348i −0.421244 + 0.729616i
\(437\) 5.07938 0.242980
\(438\) 4.10208 7.10502i 0.196005 0.339491i
\(439\) 17.1002 + 29.6184i 0.816148 + 1.41361i 0.908501 + 0.417883i \(0.137228\pi\)
−0.0923531 + 0.995726i \(0.529439\pi\)
\(440\) 23.3345 + 40.4166i 1.11243 + 1.92678i
\(441\) 0 0
\(442\) 15.1937 + 12.8136i 0.722693 + 0.609479i
\(443\) 10.0000 0.475114 0.237557 0.971374i \(-0.423653\pi\)
0.237557 + 0.971374i \(0.423653\pi\)
\(444\) 4.80538 + 8.32316i 0.228053 + 0.395000i
\(445\) 16.3063 + 28.2433i 0.772991 + 1.33886i
\(446\) −2.82843 + 4.89898i −0.133930 + 0.231973i
\(447\) −6.49359 −0.307136
\(448\) 0 0
\(449\) −2.20417 + 3.81773i −0.104021 + 0.180170i −0.913338 0.407203i \(-0.866504\pi\)
0.809317 + 0.587372i \(0.199838\pi\)
\(450\) −2.20417 −0.103905
\(451\) 28.2695 48.9643i 1.33116 2.30564i
\(452\) −8.29583 14.3688i −0.390203 0.675852i
\(453\) −12.4392 21.5453i −0.584444 1.01229i
\(454\) −20.9245 −0.982034
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) 7.29583 + 12.6368i 0.341285 + 0.591122i 0.984672 0.174419i \(-0.0558047\pi\)
−0.643387 + 0.765541i \(0.722471\pi\)
\(458\) 6.36396 + 11.0227i 0.297368 + 0.515057i
\(459\) 15.5917 27.0056i 0.727757 1.26051i
\(460\) −4.82012 −0.224739
\(461\) 15.4842 26.8194i 0.721169 1.24910i −0.239362 0.970930i \(-0.576938\pi\)
0.960531 0.278172i \(-0.0897284\pi\)
\(462\) 0 0
\(463\) 11.3875 0.529222 0.264611 0.964355i \(-0.414756\pi\)
0.264611 + 0.964355i \(0.414756\pi\)
\(464\) −4.39792 + 7.61741i −0.204168 + 0.353630i
\(465\) 2.68406 + 4.64893i 0.124470 + 0.215589i
\(466\) 10.5917 + 18.3453i 0.490649 + 0.849830i
\(467\) 4.82012 0.223048 0.111524 0.993762i \(-0.464427\pi\)
0.111524 + 0.993762i \(0.464427\pi\)
\(468\) −0.634922 + 3.54921i −0.0293493 + 0.164062i
\(469\) 0 0
\(470\) 3.79583 + 6.57457i 0.175089 + 0.303262i
\(471\) 4.89792 + 8.48344i 0.225684 + 0.390896i
\(472\) −1.68821 + 2.92407i −0.0777063 + 0.134591i
\(473\) −10.4083 −0.478576
\(474\) −8.34091 + 14.4469i −0.383111 + 0.663567i
\(475\) −3.11716 + 5.39909i −0.143025 + 0.247727i
\(476\) 0 0
\(477\) 3.29583 5.70855i 0.150906 0.261376i
\(478\) 9.89792 + 17.1437i 0.452720 + 0.784134i
\(479\) −3.67990 6.37378i −0.168139 0.291225i 0.769627 0.638494i \(-0.220442\pi\)
−0.937766 + 0.347269i \(0.887109\pi\)
\(480\) −18.9792 −0.866276
\(481\) 4.31483 24.1198i 0.196739 1.09977i
\(482\) −4.38701 −0.199823
\(483\) 0 0
\(484\) 11.2958 + 19.5650i 0.513447 + 0.889316i
\(485\) −5.69375 + 9.86186i −0.258540 + 0.447804i
\(486\) −9.89949 −0.449050
\(487\) −9.79583 + 16.9669i −0.443891 + 0.768843i −0.997974 0.0636190i \(-0.979736\pi\)
0.554083 + 0.832462i \(0.313069\pi\)
\(488\) −2.33787 + 4.04932i −0.105831 + 0.183304i
\(489\) 18.9328 0.856170
\(490\) 0 0
\(491\) 4.79583 + 8.30662i 0.216433 + 0.374873i 0.953715 0.300712i \(-0.0972244\pi\)
−0.737282 + 0.675585i \(0.763891\pi\)
\(492\) 6.89792 + 11.9475i 0.310982 + 0.538637i
\(493\) 48.4869 2.18374
\(494\) −7.79583 6.57457i −0.350751 0.295804i
\(495\) −15.5563 −0.699206
\(496\) 0.707107 + 1.22474i 0.0317500 + 0.0549927i
\(497\) 0 0
\(498\) 7.00000 12.1244i 0.313678 0.543305i
\(499\) 16.2042 0.725398 0.362699 0.931906i \(-0.381855\pi\)
0.362699 + 0.931906i \(0.381855\pi\)
\(500\) −3.75209 + 6.49881i −0.167798 + 0.290635i
\(501\) −10.7958 + 18.6989i −0.482322 + 0.835407i
\(502\) 3.11716 0.139126
\(503\) −14.2718 + 24.7194i −0.636347 + 1.10218i 0.349881 + 0.936794i \(0.386222\pi\)
−0.986228 + 0.165391i \(0.947111\pi\)
\(504\) 0 0
\(505\) −3.98958 6.91015i −0.177534 0.307498i
\(506\) 10.4083 0.462707
\(507\) −14.1421 + 11.7473i −0.628074 + 0.521718i
\(508\) −7.59166 −0.336826
\(509\) 13.2185 + 22.8951i 0.585899 + 1.01481i 0.994763 + 0.102211i \(0.0325917\pi\)
−0.408864 + 0.912595i \(0.634075\pi\)
\(510\) −10.4622 18.1211i −0.463275 0.802417i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −8.00000 + 13.8564i −0.353209 + 0.611775i
\(514\) 7.70599 13.3472i 0.339897 0.588718i
\(515\) 22.0000 0.969436
\(516\) 1.26984 2.19944i 0.0559018 0.0968247i
\(517\) 8.19654 + 14.1968i 0.360484 + 0.624376i
\(518\) 0 0
\(519\) 13.1833 0.578684
\(520\) 22.1937 + 18.7170i 0.973260 + 0.820794i
\(521\) −25.0227 −1.09627 −0.548133 0.836391i \(-0.684661\pi\)
−0.548133 + 0.836391i \(0.684661\pi\)
\(522\) −4.39792 7.61741i −0.192492 0.333405i
\(523\) 14.2865 + 24.7450i 0.624705 + 1.08202i 0.988598 + 0.150580i \(0.0481142\pi\)
−0.363893 + 0.931441i \(0.618552\pi\)
\(524\) 4.09827 7.09841i 0.179034 0.310096i
\(525\) 0 0
\(526\) 12.6937 21.9862i 0.553474 0.958645i
\(527\) 3.89792 6.75139i 0.169796 0.294095i
\(528\) 8.19654 0.356709
\(529\) 9.88749 17.1256i 0.429891 0.744593i
\(530\) −8.84620 15.3221i −0.384255 0.665548i
\(531\) −0.562738 0.974691i −0.0244207 0.0422980i
\(532\) 0 0
\(533\) 6.19375 34.6230i 0.268281 1.49969i
\(534\) 17.1833 0.743595
\(535\) 8.05217 + 13.9468i 0.348126 + 0.602972i
\(536\) 8.69375 + 15.0580i 0.375513 + 0.650407i
\(537\) −0.288738 + 0.500109i −0.0124600 + 0.0215813i
\(538\) 1.12548 0.0485227
\(539\) 0 0
\(540\) 7.59166 13.1491i 0.326693 0.565849i
\(541\) −12.5917 −0.541358 −0.270679 0.962670i \(-0.587248\pi\)
−0.270679 + 0.962670i \(0.587248\pi\)
\(542\) −11.5877 + 20.0705i −0.497735 + 0.862102i
\(543\) 11.6937 + 20.2542i 0.501827 + 0.869189i
\(544\) 13.7812 + 23.8698i 0.590865 + 1.02341i
\(545\) −47.2170 −2.02256
\(546\) 0 0
\(547\) −36.9792 −1.58111 −0.790557 0.612388i \(-0.790209\pi\)
−0.790557 + 0.612388i \(0.790209\pi\)
\(548\) −4.60208 7.97104i −0.196591 0.340506i
\(549\) −0.779291 1.34977i −0.0332593 0.0576069i
\(550\) −6.38749 + 11.0635i −0.272364 + 0.471748i
\(551\) −24.8784 −1.05985
\(552\) −3.80953 + 6.59831i −0.162145 + 0.280843i
\(553\) 0 0
\(554\) −6.18333 −0.262704
\(555\) −12.8979 + 22.3398i −0.547486 + 0.948274i
\(556\) 7.63381 + 13.2221i 0.323745 + 0.560744i
\(557\) −10.2958 17.8329i −0.436248 0.755604i 0.561148 0.827715i \(-0.310360\pi\)
−0.997397 + 0.0721110i \(0.977026\pi\)
\(558\) −1.41421 −0.0598684
\(559\) −6.08996 + 2.19944i −0.257578 + 0.0930262i
\(560\) 0 0
\(561\) −22.5917 39.1299i −0.953821 1.65207i
\(562\) −7.60208 13.1672i −0.320675 0.555425i
\(563\) −0.562738 + 0.974691i −0.0237166 + 0.0410783i −0.877640 0.479320i \(-0.840883\pi\)
0.853924 + 0.520399i \(0.174217\pi\)
\(564\) −4.00000 −0.168430
\(565\) 22.2665 38.5667i 0.936758 1.62251i
\(566\) −14.7049 + 25.4696i −0.618092 + 1.07057i
\(567\) 0 0
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) −3.20417 5.54978i −0.134326 0.232659i 0.791014 0.611798i \(-0.209554\pi\)
−0.925340 + 0.379139i \(0.876220\pi\)
\(570\) 5.36812 + 9.29785i 0.224846 + 0.389444i
\(571\) 15.1833 0.635402 0.317701 0.948191i \(-0.397089\pi\)
0.317701 + 0.948191i \(0.397089\pi\)
\(572\) 15.9747 + 13.4722i 0.667937 + 0.563301i
\(573\) 36.4808 1.52401
\(574\) 0 0
\(575\) −1.97916 3.42800i −0.0825366 0.142958i
\(576\) 3.50000 6.06218i 0.145833 0.252591i
\(577\) 9.17765 0.382071 0.191035 0.981583i \(-0.438816\pi\)
0.191035 + 0.981583i \(0.438816\pi\)
\(578\) −6.69375 + 11.5939i −0.278423 + 0.482243i
\(579\) 2.41006 4.17434i 0.100159 0.173480i
\(580\) 23.6085 0.980291
\(581\) 0 0
\(582\) 3.00000 + 5.19615i 0.124354 + 0.215387i
\(583\) −19.1021 33.0858i −0.791127 1.37027i
\(584\) −17.4037 −0.720169
\(585\) −9.10208 + 3.28729i −0.376325 + 0.135913i
\(586\) 9.75513 0.402981
\(587\) 1.55858 + 2.69954i 0.0643296 + 0.111422i 0.896396 0.443253i \(-0.146176\pi\)
−0.832067 + 0.554675i \(0.812842\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) −3.02084 −0.124366
\(591\) −5.65685 + 9.79796i −0.232692 + 0.403034i
\(592\) −3.39792 + 5.88536i −0.139653 + 0.241887i
\(593\) 1.55858 0.0640033 0.0320017 0.999488i \(-0.489812\pi\)
0.0320017 + 0.999488i \(0.489812\pi\)
\(594\) −16.3931 + 28.3937i −0.672617 + 1.16501i
\(595\) 0 0
\(596\) 2.29583 + 3.97650i 0.0940409 + 0.162884i
\(597\) −31.1833 −1.27625
\(598\) 6.08996 2.19944i 0.249037 0.0899416i
\(599\) −14.4083 −0.588709 −0.294354 0.955696i \(-0.595105\pi\)
−0.294354 + 0.955696i \(0.595105\pi\)
\(600\) −4.67575 8.09863i −0.190887 0.330625i
\(601\) −15.4842 26.8194i −0.631612 1.09398i −0.987222 0.159350i \(-0.949060\pi\)
0.355610 0.934634i \(-0.384273\pi\)
\(602\) 0 0
\(603\) −5.79583 −0.236025
\(604\) −8.79583 + 15.2348i −0.357897 + 0.619896i
\(605\) −30.3187 + 52.5135i −1.23263 + 2.13498i
\(606\) −4.20417 −0.170783
\(607\) −17.9517 + 31.0932i −0.728636 + 1.26203i 0.228824 + 0.973468i \(0.426512\pi\)
−0.957460 + 0.288566i \(0.906821\pi\)
\(608\) −7.07107 12.2474i −0.286770 0.496700i
\(609\) 0 0
\(610\) −4.18333 −0.169378
\(611\) 7.79583 + 6.57457i 0.315386 + 0.265979i
\(612\) −5.51249 −0.222829
\(613\) 2.98958 + 5.17810i 0.120748 + 0.209142i 0.920063 0.391771i \(-0.128137\pi\)
−0.799315 + 0.600912i \(0.794804\pi\)
\(614\) 17.1002 + 29.6184i 0.690108 + 1.19530i
\(615\) −18.5144 + 32.0679i −0.746573 + 1.29310i
\(616\) 0 0
\(617\) 12.1937 21.1202i 0.490902 0.850267i −0.509043 0.860741i \(-0.670001\pi\)
0.999945 + 0.0104740i \(0.00333405\pi\)
\(618\) 5.79583 10.0387i 0.233143 0.403815i
\(619\) −33.9116 −1.36302 −0.681512 0.731807i \(-0.738677\pi\)
−0.681512 + 0.731807i \(0.738677\pi\)
\(620\) 1.89792 3.28729i 0.0762221 0.132021i
\(621\) −5.07938 8.79774i −0.203828 0.353041i
\(622\) 5.93085 + 10.2725i 0.237806 + 0.411891i
\(623\) 0 0
\(624\) 4.79583 1.73205i 0.191987 0.0693375i
\(625\) −31.1625 −1.24650
\(626\) 0.851476 + 1.47480i 0.0340318 + 0.0589448i
\(627\) 11.5917 + 20.0773i 0.462926 + 0.801812i
\(628\) 3.46335 5.99870i 0.138203 0.239374i
\(629\) 37.4619 1.49370
\(630\) 0 0
\(631\) 10.2042 17.6741i 0.406222 0.703596i −0.588241 0.808685i \(-0.700179\pi\)
0.994463 + 0.105089i \(0.0335128\pi\)
\(632\) 35.3875 1.40764
\(633\) −1.26984 + 2.19944i −0.0504718 + 0.0874197i
\(634\) 6.29583 + 10.9047i 0.250039 + 0.433081i
\(635\) −10.1882 17.6465i −0.404308 0.700281i
\(636\) 9.32202 0.369642
\(637\) 0 0
\(638\) −50.9792 −2.01828
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 4.02609 + 6.97339i 0.159145 + 0.275647i
\(641\) −2.39792 + 4.15331i −0.0947120 + 0.164046i −0.909488 0.415729i \(-0.863526\pi\)
0.814776 + 0.579775i \(0.196860\pi\)
\(642\) 8.48528 0.334887
\(643\) 2.82843 4.89898i 0.111542 0.193197i −0.804850 0.593478i \(-0.797754\pi\)
0.916392 + 0.400281i \(0.131088\pi\)
\(644\) 0 0
\(645\) 6.81667 0.268406
\(646\) 7.79583 13.5028i 0.306723 0.531260i
\(647\) −0.981107 1.69933i −0.0385713 0.0668074i 0.846095 0.533032i \(-0.178947\pi\)
−0.884667 + 0.466224i \(0.845614\pi\)
\(648\) −7.50000 12.9904i −0.294628 0.510310i
\(649\) −6.52307 −0.256053
\(650\) −1.39948 + 7.82305i −0.0548920 + 0.306845i
\(651\) 0 0
\(652\) −6.69375 11.5939i −0.262147 0.454053i
\(653\) −12.5917 21.8094i −0.492750 0.853468i 0.507215 0.861819i \(-0.330675\pi\)
−0.999965 + 0.00835161i \(0.997342\pi\)
\(654\) −12.4392 + 21.5453i −0.486411 + 0.842488i
\(655\) 22.0000 0.859611
\(656\) −4.87756 + 8.44819i −0.190437 + 0.329846i
\(657\) 2.90061 5.02401i 0.113164 0.196005i
\(658\) 0 0
\(659\) 18.7958 32.5553i 0.732182 1.26818i −0.223767 0.974643i \(-0.571836\pi\)
0.955949 0.293533i \(-0.0948311\pi\)
\(660\) −11.0000 19.0526i −0.428174 0.741620i
\(661\) 13.9256 + 24.1198i 0.541642 + 0.938152i 0.998810 + 0.0487715i \(0.0155306\pi\)
−0.457168 + 0.889381i \(0.651136\pi\)
\(662\) 0.612505 0.0238057
\(663\) −21.4872 18.1211i −0.834494 0.703766i
\(664\) −29.6985 −1.15252
\(665\) 0 0
\(666\) −3.39792 5.88536i −0.131667 0.228053i
\(667\) 7.89792 13.6796i 0.305809 0.529676i
\(668\) 15.2676 0.590722
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) −7.77817 + 13.4722i −0.300497 + 0.520476i
\(671\) −9.03328 −0.348726
\(672\) 0 0
\(673\) −11.9896 20.7666i −0.462164 0.800492i 0.536904 0.843643i \(-0.319594\pi\)
−0.999069 + 0.0431511i \(0.986260\pi\)
\(674\) 14.9896 + 25.9627i 0.577377 + 1.00005i
\(675\) 12.4687 0.479919
\(676\) 12.1937 + 4.50694i 0.468990 + 0.173344i
\(677\) −34.7779 −1.33662 −0.668311 0.743882i \(-0.732982\pi\)
−0.668311 + 0.743882i \(0.732982\pi\)
\(678\) −11.7321 20.3206i −0.450568 0.780406i
\(679\) 0 0
\(680\) −22.1937 + 38.4407i −0.851091 + 1.47413i
\(681\) 29.5917 1.13395
\(682\) −4.09827 + 7.09841i −0.156931 + 0.271812i
\(683\) −25.3875 + 43.9724i −0.971425 + 1.68256i −0.280166 + 0.959952i \(0.590390\pi\)
−0.691259 + 0.722607i \(0.742944\pi\)
\(684\) 2.82843 0.108148
\(685\) 12.3523 21.3947i 0.471956 0.817451i
\(686\) 0 0
\(687\) −9.00000 15.5885i −0.343371 0.594737i
\(688\) 1.79583 0.0684654
\(689\) −18.1682 15.3221i −0.692154 0.583725i
\(690\) −6.81667 −0.259506
\(691\) 5.51249 + 9.54790i 0.209705 + 0.363219i 0.951622 0.307273i \(-0.0994164\pi\)
−0.741917 + 0.670492i \(0.766083\pi\)
\(692\) −4.66101 8.07311i −0.177185 0.306893i
\(693\) 0 0
\(694\) 14.9792 0.568601
\(695\) −20.4896 + 35.4890i −0.777214 + 1.34617i
\(696\) 18.6588 32.3179i 0.707259 1.22501i
\(697\) 53.7750 2.03687
\(698\) 6.50833 11.2728i 0.246344 0.426680i
\(699\) −14.9789 25.9442i −0.566553 0.981299i
\(700\) 0 0
\(701\) −10.4083 −0.393117 −0.196559 0.980492i \(-0.562977\pi\)
−0.196559 + 0.980492i \(0.562977\pi\)
\(702\) −3.59166 + 20.0773i −0.135559 + 0.757771i
\(703\) −19.2215 −0.724953
\(704\) −20.2854 35.1354i −0.764535 1.32421i
\(705\) −5.36812 9.29785i −0.202175 0.350177i
\(706\) −7.56162 + 13.0971i −0.284585 + 0.492916i
\(707\) 0 0
\(708\) 0.795832 1.37842i 0.0299092 0.0518042i
\(709\) 9.39792 16.2777i 0.352946 0.611321i −0.633818 0.773482i \(-0.718513\pi\)
0.986764 + 0.162162i \(0.0518466\pi\)
\(710\) 16.1043 0.604385
\(711\) −5.89792 + 10.2155i −0.221189 + 0.383111i
\(712\) −18.2257 31.5678i −0.683036 1.18305i
\(713\) −1.26984 2.19944i −0.0475561 0.0823695i
\(714\) 0 0
\(715\) −9.87707 + 55.2127i −0.369382 + 2.06484i
\(716\) 0.408337 0.0152603
\(717\) −13.9978 24.2448i −0.522756 0.905440i
\(718\) 2.00000 + 3.46410i 0.0746393 + 0.129279i
\(719\) 14.5605 25.2195i 0.543015 0.940530i −0.455714 0.890126i \(-0.650616\pi\)
0.998729 0.0504035i \(-0.0160507\pi\)
\(720\) 2.68406 0.100029
\(721\) 0 0
\(722\) 5.50000 9.52628i 0.204689 0.354531i
\(723\) 6.20417 0.230736
\(724\) 8.26873 14.3219i 0.307305 0.532268i
\(725\) 9.69375 + 16.7901i 0.360017 + 0.623567i
\(726\) 15.9747 + 27.6690i 0.592877 + 1.02689i
\(727\) 35.3259 1.31016 0.655082 0.755558i \(-0.272634\pi\)
0.655082 + 0.755558i \(0.272634\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) −7.78541 13.4847i −0.288151 0.499092i
\(731\) −4.94975 8.57321i −0.183073 0.317092i
\(732\) 1.10208 1.90887i 0.0407342 0.0705537i
\(733\) −0.692369 −0.0255732 −0.0127866 0.999918i \(-0.504070\pi\)
−0.0127866 + 0.999918i \(0.504070\pi\)
\(734\) 10.6066 18.3712i 0.391497 0.678092i
\(735\) 0 0
\(736\) 8.97916 0.330976
\(737\) −16.7958 + 29.0912i −0.618682 + 1.07159i
\(738\) −4.87756 8.44819i −0.179546 0.310982i
\(739\) −7.59166 13.1491i −0.279264 0.483699i 0.691938 0.721957i \(-0.256757\pi\)
−0.971202 + 0.238258i \(0.923424\pi\)
\(740\) 18.2404 0.670531
\(741\) 11.0250 + 9.29785i 0.405012 + 0.341565i
\(742\) 0 0
\(743\) −4.59166 7.95299i −0.168452 0.291767i 0.769424 0.638738i \(-0.220543\pi\)
−0.937876 + 0.346971i \(0.887210\pi\)
\(744\) −3.00000 5.19615i −0.109985 0.190500i
\(745\) −6.16215 + 10.6731i −0.225764 + 0.391034i
\(746\) −12.5917 −0.461014
\(747\) 4.94975 8.57321i 0.181102 0.313678i
\(748\) −15.9747 + 27.6690i −0.584094 + 1.01168i
\(749\) 0 0
\(750\) −5.30625 + 9.19070i −0.193757 + 0.335597i
\(751\) −0.897916 1.55524i −0.0327654 0.0567514i 0.849178 0.528107i \(-0.177098\pi\)
−0.881943 + 0.471356i \(0.843765\pi\)
\(752\) −1.41421 2.44949i −0.0515711 0.0893237i
\(753\) −4.40834 −0.160649
\(754\) −29.8281 + 10.7726i −1.08628 + 0.392317i
\(755\) −47.2170 −1.71840
\(756\) 0 0
\(757\) 12.5917 + 21.8094i 0.457652 + 0.792676i 0.998836 0.0482277i \(-0.0153573\pi\)
−0.541185 + 0.840904i \(0.682024\pi\)
\(758\) 1.69375 2.93366i 0.0615197 0.106555i
\(759\) −14.7196 −0.534288
\(760\) 11.3875 19.7237i 0.413068 0.715454i
\(761\) 4.66101 8.07311i 0.168961 0.292650i −0.769094 0.639136i \(-0.779292\pi\)
0.938055 + 0.346486i \(0.112625\pi\)
\(762\) −10.7362 −0.388933
\(763\) 0 0
\(764\) −12.8979 22.3398i −0.466630 0.808227i
\(765\) −7.39792 12.8136i −0.267472 0.463275i
\(766\) 14.9789 0.541209
\(767\) −3.81667 + 1.37842i −0.137812 + 0.0497719i
\(768\) 24.0416 0.867528
\(769\) 2.12132 + 3.67423i 0.0764968 + 0.132496i 0.901736 0.432287i \(-0.142293\pi\)
−0.825239 + 0.564783i \(0.808960\pi\)
\(770\) 0 0
\(771\) −10.8979 + 18.8757i −0.392479 + 0.679793i
\(772\) −3.40834 −0.122669
\(773\) 3.82427 6.62383i 0.137549 0.238243i −0.789019 0.614369i \(-0.789411\pi\)
0.926568 + 0.376126i \(0.122744\pi\)
\(774\) −0.897916 + 1.55524i −0.0322749 + 0.0559018i
\(775\) 3.11716 0.111972
\(776\) 6.36396 11.0227i 0.228453 0.395692i
\(777\) 0 0
\(778\) −14.1937 24.5843i −0.508870 0.881390i
\(779\) −27.5917 −0.988574
\(780\) −10.4622 8.82327i −0.374608 0.315924i
\(781\) 34.7750 1.24435
\(782\) 4.94975 + 8.57321i 0.177003 + 0.306578i
\(783\) 24.8784 + 43.0906i