Properties

Label 120.2.m.b.59.10
Level $120$
Weight $2$
Character 120.59
Analytic conductor $0.958$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.10
Root \(-0.528036i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.541196 - 1.30656i) q^{2} +(1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(2.10100 + 0.765367i) q^{5} +(2.19274 - 1.09174i) q^{6} -2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +O(q^{10})\) \(q+(0.541196 - 1.30656i) q^{2} +(1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(2.10100 + 0.765367i) q^{5} +(2.19274 - 1.09174i) q^{6} -2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +(2.13705 - 2.33088i) q^{10} -4.20201i q^{11} +(-0.239721 - 3.45580i) q^{12} -3.21608 q^{13} +(-1.23074 + 2.97127i) q^{14} +(1.87483 + 3.38896i) q^{15} +4.00000i q^{16} +1.53073 q^{17} +(4.10632 + 1.06684i) q^{18} -4.82843 q^{19} +(-1.88887 - 4.05366i) q^{20} +(-2.97127 - 2.58579i) q^{21} +(-5.49019 - 2.27411i) q^{22} -1.08239i q^{23} +(-4.64495 - 1.55705i) q^{24} +(3.82843 + 3.21608i) q^{25} +(-1.74053 + 4.20201i) q^{26} +(-2.83730 + 4.35313i) q^{27} +(3.21608 + 3.21608i) q^{28} +1.74053 q^{29} +(5.44253 - 0.615493i) q^{30} +6.82843i q^{31} +(5.22625 + 2.16478i) q^{32} +(4.77791 - 5.49019i) q^{33} +(0.828427 - 2.00000i) q^{34} +(-4.77791 - 1.74053i) q^{35} +(3.61622 - 4.78779i) q^{36} +7.76429 q^{37} +(-2.61313 + 6.30864i) q^{38} +(-4.20201 - 3.65685i) q^{39} +(-6.31861 + 0.274109i) q^{40} +2.46148i q^{41} +(-4.98653 + 2.48273i) q^{42} -8.70626i q^{43} +(-5.94253 + 5.94253i) q^{44} +(-1.40385 + 6.55967i) q^{45} +(-1.41421 - 0.585786i) q^{46} +1.08239i q^{47} +(-4.54822 + 5.22625i) q^{48} -1.82843 q^{49} +(6.27394 - 3.26155i) q^{50} +(2.00000 + 1.74053i) q^{51} +(4.54822 + 4.54822i) q^{52} -11.0866i q^{53} +(4.15211 + 6.06300i) q^{54} +(3.21608 - 8.82843i) q^{55} +(5.94253 - 2.46148i) q^{56} +(-6.30864 - 5.49019i) q^{57} +(0.941967 - 2.27411i) q^{58} +4.20201i q^{59} +(2.14130 - 7.44411i) q^{60} -8.48528i q^{61} +(8.92177 + 3.69552i) q^{62} +(-0.941967 - 6.75699i) q^{63} +(5.65685 - 5.65685i) q^{64} +(-6.75699 - 2.46148i) q^{65} +(-4.58749 - 9.21391i) q^{66} -2.27411i q^{67} +(-2.16478 - 2.16478i) q^{68} +(1.23074 - 1.41421i) q^{69} +(-4.85990 + 5.30067i) q^{70} +11.8851 q^{71} +(-4.29847 - 7.31595i) q^{72} +4.54822i q^{73} +(4.20201 - 10.1445i) q^{74} +(1.34523 + 8.55514i) q^{75} +(6.82843 + 6.82843i) q^{76} +9.55582i q^{77} +(-7.05202 + 3.51111i) q^{78} +0.485281i q^{79} +(-3.06147 + 8.40401i) q^{80} +(-8.65685 + 2.46148i) q^{81} +(3.21608 + 1.33214i) q^{82} +6.94269 q^{83} +(0.545152 + 7.85886i) q^{84} +(3.21608 + 1.17157i) q^{85} +(-11.3753 - 4.71179i) q^{86} +(2.27411 + 1.97908i) q^{87} +(4.54822 + 10.9804i) q^{88} -8.40401i q^{89} +(7.81086 + 5.38428i) q^{90} +7.31371 q^{91} +(-1.53073 + 1.53073i) q^{92} +(-7.76429 + 8.92177i) q^{93} +(1.41421 + 0.585786i) q^{94} +(-10.1445 - 3.69552i) q^{95} +(4.36695 + 8.77096i) q^{96} +10.9804i q^{97} +(-0.989538 + 2.38896i) q^{98} +(12.4853 - 1.74053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.541196 1.30656i 0.382683 0.923880i
\(3\) 1.30656 + 1.13705i 0.754344 + 0.656479i
\(4\) −1.41421 1.41421i −0.707107 0.707107i
\(5\) 2.10100 + 0.765367i 0.939597 + 0.342282i
\(6\) 2.19274 1.09174i 0.895182 0.445700i
\(7\) −2.27411 −0.859533 −0.429766 0.902940i \(-0.641404\pi\)
−0.429766 + 0.902940i \(0.641404\pi\)
\(8\) −2.61313 + 1.08239i −0.923880 + 0.382683i
\(9\) 0.414214 + 2.97127i 0.138071 + 0.990422i
\(10\) 2.13705 2.33088i 0.675796 0.737089i
\(11\) 4.20201i 1.26695i −0.773762 0.633476i \(-0.781627\pi\)
0.773762 0.633476i \(-0.218373\pi\)
\(12\) −0.239721 3.45580i −0.0692015 0.997603i
\(13\) −3.21608 −0.891979 −0.445990 0.895038i \(-0.647148\pi\)
−0.445990 + 0.895038i \(0.647148\pi\)
\(14\) −1.23074 + 2.97127i −0.328929 + 0.794104i
\(15\) 1.87483 + 3.38896i 0.484079 + 0.875024i
\(16\) 4.00000i 1.00000i
\(17\) 1.53073 0.371257 0.185629 0.982620i \(-0.440568\pi\)
0.185629 + 0.982620i \(0.440568\pi\)
\(18\) 4.10632 + 1.06684i 0.967868 + 0.251457i
\(19\) −4.82843 −1.10772 −0.553859 0.832611i \(-0.686845\pi\)
−0.553859 + 0.832611i \(0.686845\pi\)
\(20\) −1.88887 4.05366i −0.422365 0.906426i
\(21\) −2.97127 2.58579i −0.648384 0.564265i
\(22\) −5.49019 2.27411i −1.17051 0.484842i
\(23\) 1.08239i 0.225694i −0.993612 0.112847i \(-0.964003\pi\)
0.993612 0.112847i \(-0.0359971\pi\)
\(24\) −4.64495 1.55705i −0.948147 0.317832i
\(25\) 3.82843 + 3.21608i 0.765685 + 0.643215i
\(26\) −1.74053 + 4.20201i −0.341346 + 0.824081i
\(27\) −2.83730 + 4.35313i −0.546038 + 0.837760i
\(28\) 3.21608 + 3.21608i 0.607781 + 0.607781i
\(29\) 1.74053 0.323208 0.161604 0.986856i \(-0.448333\pi\)
0.161604 + 0.986856i \(0.448333\pi\)
\(30\) 5.44253 0.615493i 0.993666 0.112373i
\(31\) 6.82843i 1.22642i 0.789919 + 0.613211i \(0.210122\pi\)
−0.789919 + 0.613211i \(0.789878\pi\)
\(32\) 5.22625 + 2.16478i 0.923880 + 0.382683i
\(33\) 4.77791 5.49019i 0.831727 0.955719i
\(34\) 0.828427 2.00000i 0.142074 0.342997i
\(35\) −4.77791 1.74053i −0.807614 0.294203i
\(36\) 3.61622 4.78779i 0.602703 0.797965i
\(37\) 7.76429 1.27644 0.638221 0.769853i \(-0.279671\pi\)
0.638221 + 0.769853i \(0.279671\pi\)
\(38\) −2.61313 + 6.30864i −0.423905 + 1.02340i
\(39\) −4.20201 3.65685i −0.672859 0.585565i
\(40\) −6.31861 + 0.274109i −0.999060 + 0.0433405i
\(41\) 2.46148i 0.384418i 0.981354 + 0.192209i \(0.0615652\pi\)
−0.981354 + 0.192209i \(0.938435\pi\)
\(42\) −4.98653 + 2.48273i −0.769438 + 0.383094i
\(43\) 8.70626i 1.32769i −0.747869 0.663846i \(-0.768923\pi\)
0.747869 0.663846i \(-0.231077\pi\)
\(44\) −5.94253 + 5.94253i −0.895871 + 0.895871i
\(45\) −1.40385 + 6.55967i −0.209273 + 0.977857i
\(46\) −1.41421 0.585786i −0.208514 0.0863695i
\(47\) 1.08239i 0.157883i 0.996879 + 0.0789416i \(0.0251541\pi\)
−0.996879 + 0.0789416i \(0.974846\pi\)
\(48\) −4.54822 + 5.22625i −0.656479 + 0.754344i
\(49\) −1.82843 −0.261204
\(50\) 6.27394 3.26155i 0.887269 0.461253i
\(51\) 2.00000 + 1.74053i 0.280056 + 0.243723i
\(52\) 4.54822 + 4.54822i 0.630724 + 0.630724i
\(53\) 11.0866i 1.52286i −0.648250 0.761428i \(-0.724499\pi\)
0.648250 0.761428i \(-0.275501\pi\)
\(54\) 4.15211 + 6.06300i 0.565030 + 0.825070i
\(55\) 3.21608 8.82843i 0.433656 1.19042i
\(56\) 5.94253 2.46148i 0.794104 0.328929i
\(57\) −6.30864 5.49019i −0.835600 0.727193i
\(58\) 0.941967 2.27411i 0.123686 0.298605i
\(59\) 4.20201i 0.547055i 0.961864 + 0.273527i \(0.0881904\pi\)
−0.961864 + 0.273527i \(0.911810\pi\)
\(60\) 2.14130 7.44411i 0.276440 0.961031i
\(61\) 8.48528i 1.08643i −0.839594 0.543214i \(-0.817207\pi\)
0.839594 0.543214i \(-0.182793\pi\)
\(62\) 8.92177 + 3.69552i 1.13307 + 0.469331i
\(63\) −0.941967 6.75699i −0.118677 0.851300i
\(64\) 5.65685 5.65685i 0.707107 0.707107i
\(65\) −6.75699 2.46148i −0.838101 0.305309i
\(66\) −4.58749 9.21391i −0.564681 1.13415i
\(67\) 2.27411i 0.277827i −0.990305 0.138913i \(-0.955639\pi\)
0.990305 0.138913i \(-0.0443609\pi\)
\(68\) −2.16478 2.16478i −0.262519 0.262519i
\(69\) 1.23074 1.41421i 0.148164 0.170251i
\(70\) −4.85990 + 5.30067i −0.580869 + 0.633552i
\(71\) 11.8851 1.41050 0.705249 0.708960i \(-0.250835\pi\)
0.705249 + 0.708960i \(0.250835\pi\)
\(72\) −4.29847 7.31595i −0.506579 0.862193i
\(73\) 4.54822i 0.532329i 0.963928 + 0.266164i \(0.0857564\pi\)
−0.963928 + 0.266164i \(0.914244\pi\)
\(74\) 4.20201 10.1445i 0.488473 1.17928i
\(75\) 1.34523 + 8.55514i 0.155333 + 0.987862i
\(76\) 6.82843 + 6.82843i 0.783274 + 0.783274i
\(77\) 9.55582i 1.08899i
\(78\) −7.05202 + 3.51111i −0.798484 + 0.397555i
\(79\) 0.485281i 0.0545984i 0.999627 + 0.0272992i \(0.00869069\pi\)
−0.999627 + 0.0272992i \(0.991309\pi\)
\(80\) −3.06147 + 8.40401i −0.342282 + 0.939597i
\(81\) −8.65685 + 2.46148i −0.961873 + 0.273498i
\(82\) 3.21608 + 1.33214i 0.355156 + 0.147111i
\(83\) 6.94269 0.762060 0.381030 0.924563i \(-0.375569\pi\)
0.381030 + 0.924563i \(0.375569\pi\)
\(84\) 0.545152 + 7.85886i 0.0594809 + 0.857472i
\(85\) 3.21608 + 1.17157i 0.348832 + 0.127075i
\(86\) −11.3753 4.71179i −1.22663 0.508086i
\(87\) 2.27411 + 1.97908i 0.243810 + 0.212179i
\(88\) 4.54822 + 10.9804i 0.484842 + 1.17051i
\(89\) 8.40401i 0.890823i −0.895326 0.445412i \(-0.853057\pi\)
0.895326 0.445412i \(-0.146943\pi\)
\(90\) 7.81086 + 5.38428i 0.823337 + 0.567553i
\(91\) 7.31371 0.766685
\(92\) −1.53073 + 1.53073i −0.159590 + 0.159590i
\(93\) −7.76429 + 8.92177i −0.805120 + 0.925144i
\(94\) 1.41421 + 0.585786i 0.145865 + 0.0604193i
\(95\) −10.1445 3.69552i −1.04081 0.379152i
\(96\) 4.36695 + 8.77096i 0.445700 + 0.895182i
\(97\) 10.9804i 1.11489i 0.830215 + 0.557444i \(0.188218\pi\)
−0.830215 + 0.557444i \(0.811782\pi\)
\(98\) −0.989538 + 2.38896i −0.0999584 + 0.241321i
\(99\) 12.4853 1.74053i 1.25482 0.174930i
\(100\) −0.865995 9.96243i −0.0865995 0.996243i
\(101\) −13.6256 −1.35580 −0.677899 0.735155i \(-0.737109\pi\)
−0.677899 + 0.735155i \(0.737109\pi\)
\(102\) 3.35650 1.67116i 0.332343 0.165469i
\(103\) −8.70626 −0.857853 −0.428927 0.903339i \(-0.641108\pi\)
−0.428927 + 0.903339i \(0.641108\pi\)
\(104\) 8.40401 3.48106i 0.824081 0.341346i
\(105\) −4.26357 7.70685i −0.416081 0.752112i
\(106\) −14.4853 6.00000i −1.40693 0.582772i
\(107\) 5.67459 0.548584 0.274292 0.961647i \(-0.411557\pi\)
0.274292 + 0.961647i \(0.411557\pi\)
\(108\) 10.1688 2.14371i 0.978493 0.206279i
\(109\) 16.4853i 1.57900i 0.613748 + 0.789502i \(0.289661\pi\)
−0.613748 + 0.789502i \(0.710339\pi\)
\(110\) −9.79437 8.97992i −0.933856 0.856201i
\(111\) 10.1445 + 8.82843i 0.962877 + 0.837957i
\(112\) 9.09644i 0.859533i
\(113\) −0.634051 −0.0596465 −0.0298232 0.999555i \(-0.509494\pi\)
−0.0298232 + 0.999555i \(0.509494\pi\)
\(114\) −10.5875 + 5.27137i −0.991609 + 0.493709i
\(115\) 0.828427 2.27411i 0.0772512 0.212062i
\(116\) −2.46148 2.46148i −0.228543 0.228543i
\(117\) −1.33214 9.55582i −0.123157 0.883436i
\(118\) 5.49019 + 2.27411i 0.505413 + 0.209349i
\(119\) −3.48106 −0.319108
\(120\) −8.56734 6.82647i −0.782088 0.623168i
\(121\) −6.65685 −0.605169
\(122\) −11.0866 4.59220i −1.00373 0.415758i
\(123\) −2.79884 + 3.21608i −0.252362 + 0.289984i
\(124\) 9.65685 9.65685i 0.867211 0.867211i
\(125\) 5.58206 + 9.68714i 0.499275 + 0.866444i
\(126\) −9.33822 2.42612i −0.831914 0.216136i
\(127\) 2.27411 0.201795 0.100897 0.994897i \(-0.467829\pi\)
0.100897 + 0.994897i \(0.467829\pi\)
\(128\) −4.32957 10.4525i −0.382683 0.923880i
\(129\) 9.89949 11.3753i 0.871602 1.00154i
\(130\) −6.87293 + 7.49628i −0.602796 + 0.657468i
\(131\) 11.1641i 0.975413i 0.873008 + 0.487707i \(0.162166\pi\)
−0.873008 + 0.487707i \(0.837834\pi\)
\(132\) −14.5213 + 1.00731i −1.26392 + 0.0876750i
\(133\) 10.9804 0.952119
\(134\) −2.97127 1.23074i −0.256678 0.106320i
\(135\) −9.29291 + 6.97437i −0.799806 + 0.600258i
\(136\) −4.00000 + 1.65685i −0.342997 + 0.142074i
\(137\) 8.02509 0.685629 0.342815 0.939403i \(-0.388620\pi\)
0.342815 + 0.939403i \(0.388620\pi\)
\(138\) −1.18169 2.37340i −0.100592 0.202038i
\(139\) −2.48528 −0.210799 −0.105399 0.994430i \(-0.533612\pi\)
−0.105399 + 0.994430i \(0.533612\pi\)
\(140\) 4.29551 + 9.21846i 0.363037 + 0.779102i
\(141\) −1.23074 + 1.41421i −0.103647 + 0.119098i
\(142\) 6.43215 15.5286i 0.539774 1.30313i
\(143\) 13.5140i 1.13010i
\(144\) −11.8851 + 1.65685i −0.990422 + 0.138071i
\(145\) 3.65685 + 1.33214i 0.303685 + 0.110628i
\(146\) 5.94253 + 2.46148i 0.491808 + 0.203713i
\(147\) −2.38896 2.07902i −0.197038 0.171475i
\(148\) −10.9804 10.9804i −0.902581 0.902581i
\(149\) 0.720950 0.0590625 0.0295313 0.999564i \(-0.490599\pi\)
0.0295313 + 0.999564i \(0.490599\pi\)
\(150\) 11.9059 + 2.87238i 0.972109 + 0.234529i
\(151\) 2.82843i 0.230174i 0.993355 + 0.115087i \(0.0367147\pi\)
−0.993355 + 0.115087i \(0.963285\pi\)
\(152\) 12.6173 5.22625i 1.02340 0.423905i
\(153\) 0.634051 + 4.54822i 0.0512600 + 0.367702i
\(154\) 12.4853 + 5.17157i 1.00609 + 0.416737i
\(155\) −5.22625 + 14.3465i −0.419783 + 1.15234i
\(156\) 0.770961 + 11.1141i 0.0617263 + 0.889841i
\(157\) −23.2929 −1.85897 −0.929487 0.368854i \(-0.879750\pi\)
−0.929487 + 0.368854i \(0.879750\pi\)
\(158\) 0.634051 + 0.262632i 0.0504424 + 0.0208939i
\(159\) 12.6060 14.4853i 0.999722 1.14876i
\(160\) 9.32352 + 8.54822i 0.737089 + 0.675796i
\(161\) 2.46148i 0.193992i
\(162\) −1.46898 + 12.6429i −0.115414 + 0.993317i
\(163\) 8.70626i 0.681927i 0.940077 + 0.340964i \(0.110753\pi\)
−0.940077 + 0.340964i \(0.889247\pi\)
\(164\) 3.48106 3.48106i 0.271825 0.271825i
\(165\) 14.2404 7.87804i 1.10861 0.613305i
\(166\) 3.75736 9.07107i 0.291628 0.704051i
\(167\) 5.04054i 0.390049i −0.980798 0.195024i \(-0.937521\pi\)
0.980798 0.195024i \(-0.0624786\pi\)
\(168\) 10.5631 + 3.54091i 0.814963 + 0.273187i
\(169\) −2.65685 −0.204373
\(170\) 3.27126 3.56796i 0.250894 0.273650i
\(171\) −2.00000 14.3465i −0.152944 1.09711i
\(172\) −12.3125 + 12.3125i −0.938820 + 0.938820i
\(173\) 0.262632i 0.0199676i −0.999950 0.00998379i \(-0.996822\pi\)
0.999950 0.00998379i \(-0.00317799\pi\)
\(174\) 3.81653 1.90020i 0.289330 0.144054i
\(175\) −8.70626 7.31371i −0.658132 0.552864i
\(176\) 16.8080 1.26695
\(177\) −4.77791 + 5.49019i −0.359130 + 0.412668i
\(178\) −10.9804 4.54822i −0.823014 0.340903i
\(179\) 7.68306i 0.574259i −0.957892 0.287129i \(-0.907299\pi\)
0.957892 0.287129i \(-0.0927010\pi\)
\(180\) 11.2621 7.29143i 0.839428 0.543471i
\(181\) 21.6569i 1.60974i −0.593450 0.804871i \(-0.702235\pi\)
0.593450 0.804871i \(-0.297765\pi\)
\(182\) 3.95815 9.55582i 0.293398 0.708325i
\(183\) 9.64823 11.0866i 0.713218 0.819542i
\(184\) 1.17157 + 2.82843i 0.0863695 + 0.208514i
\(185\) 16.3128 + 5.94253i 1.19934 + 0.436904i
\(186\) 7.45485 + 14.9730i 0.546616 + 1.09787i
\(187\) 6.43215i 0.470366i
\(188\) 1.53073 1.53073i 0.111640 0.111640i
\(189\) 6.45232 9.89949i 0.469337 0.720082i
\(190\) −10.3186 + 11.2545i −0.748591 + 0.816486i
\(191\) −8.40401 −0.608093 −0.304046 0.952657i \(-0.598338\pi\)
−0.304046 + 0.952657i \(0.598338\pi\)
\(192\) 13.8232 0.958884i 0.997603 0.0692015i
\(193\) 13.6447i 0.982164i −0.871113 0.491082i \(-0.836602\pi\)
0.871113 0.491082i \(-0.163398\pi\)
\(194\) 14.3465 + 5.94253i 1.03002 + 0.426649i
\(195\) −6.02959 10.8991i −0.431788 0.780503i
\(196\) 2.58579 + 2.58579i 0.184699 + 0.184699i
\(197\) 8.02509i 0.571764i −0.958265 0.285882i \(-0.907713\pi\)
0.958265 0.285882i \(-0.0922865\pi\)
\(198\) 4.48288 17.2548i 0.318584 1.22624i
\(199\) 14.8284i 1.05116i 0.850744 + 0.525580i \(0.176152\pi\)
−0.850744 + 0.525580i \(0.823848\pi\)
\(200\) −13.4852 4.26015i −0.953549 0.301238i
\(201\) 2.58579 2.97127i 0.182387 0.209577i
\(202\) −7.37412 + 17.8027i −0.518841 + 1.25259i
\(203\) −3.95815 −0.277808
\(204\) −0.366949 5.28991i −0.0256916 0.370367i
\(205\) −1.88393 + 5.17157i −0.131580 + 0.361198i
\(206\) −4.71179 + 11.3753i −0.328286 + 0.792553i
\(207\) 3.21608 0.448342i 0.223533 0.0311619i
\(208\) 12.8643i 0.891979i
\(209\) 20.2891i 1.40342i
\(210\) −12.3769 + 1.39970i −0.854088 + 0.0965883i
\(211\) 1.51472 0.104278 0.0521388 0.998640i \(-0.483396\pi\)
0.0521388 + 0.998640i \(0.483396\pi\)
\(212\) −15.6788 + 15.6788i −1.07682 + 1.07682i
\(213\) 15.5286 + 13.5140i 1.06400 + 0.925962i
\(214\) 3.07107 7.41421i 0.209934 0.506825i
\(215\) 6.66348 18.2919i 0.454446 1.24750i
\(216\) 2.70242 14.4463i 0.183876 0.982949i
\(217\) 15.5286i 1.05415i
\(218\) 21.5391 + 8.92177i 1.45881 + 0.604259i
\(219\) −5.17157 + 5.94253i −0.349463 + 0.401559i
\(220\) −17.0335 + 7.93706i −1.14840 + 0.535117i
\(221\) −4.92296 −0.331154
\(222\) 17.0251 8.47657i 1.14265 0.568910i
\(223\) 10.5902 0.709172 0.354586 0.935023i \(-0.384622\pi\)
0.354586 + 0.935023i \(0.384622\pi\)
\(224\) −11.8851 4.92296i −0.794104 0.328929i
\(225\) −7.97003 + 12.7074i −0.531336 + 0.847161i
\(226\) −0.343146 + 0.828427i −0.0228257 + 0.0551062i
\(227\) −4.77791 −0.317121 −0.158561 0.987349i \(-0.550685\pi\)
−0.158561 + 0.987349i \(0.550685\pi\)
\(228\) 1.15748 + 16.6861i 0.0766557 + 1.10506i
\(229\) 3.31371i 0.218976i 0.993988 + 0.109488i \(0.0349211\pi\)
−0.993988 + 0.109488i \(0.965079\pi\)
\(230\) −2.52293 2.31313i −0.166357 0.152523i
\(231\) −10.8655 + 12.4853i −0.714897 + 0.821471i
\(232\) −4.54822 + 1.88393i −0.298605 + 0.123686i
\(233\) −28.0334 −1.83653 −0.918265 0.395967i \(-0.870410\pi\)
−0.918265 + 0.395967i \(0.870410\pi\)
\(234\) −13.2062 3.43105i −0.863318 0.224294i
\(235\) −0.828427 + 2.27411i −0.0540406 + 0.148347i
\(236\) 5.94253 5.94253i 0.386826 0.386826i
\(237\) −0.551791 + 0.634051i −0.0358427 + 0.0411860i
\(238\) −1.88393 + 4.54822i −0.122117 + 0.294817i
\(239\) −13.3270 −0.862050 −0.431025 0.902340i \(-0.641848\pi\)
−0.431025 + 0.902340i \(0.641848\pi\)
\(240\) −13.5558 + 7.49932i −0.875024 + 0.484079i
\(241\) 10.4853 0.675416 0.337708 0.941251i \(-0.390348\pi\)
0.337708 + 0.941251i \(0.390348\pi\)
\(242\) −3.60266 + 8.69760i −0.231588 + 0.559103i
\(243\) −14.1096 6.62724i −0.905129 0.425138i
\(244\) −12.0000 + 12.0000i −0.768221 + 0.768221i
\(245\) −3.84153 1.39942i −0.245426 0.0894055i
\(246\) 2.68729 + 5.39738i 0.171335 + 0.344125i
\(247\) 15.5286 0.988060
\(248\) −7.39104 17.8435i −0.469331 1.13307i
\(249\) 9.07107 + 7.89422i 0.574856 + 0.500276i
\(250\) 15.6778 2.05067i 0.991554 0.129696i
\(251\) 27.9721i 1.76559i −0.469762 0.882793i \(-0.655660\pi\)
0.469762 0.882793i \(-0.344340\pi\)
\(252\) −8.22368 + 10.8880i −0.518043 + 0.685877i
\(253\) −4.54822 −0.285944
\(254\) 1.23074 2.97127i 0.0772234 0.186434i
\(255\) 2.86986 + 5.18759i 0.179718 + 0.324859i
\(256\) −16.0000 −1.00000
\(257\) −2.42742 −0.151418 −0.0757090 0.997130i \(-0.524122\pi\)
−0.0757090 + 0.997130i \(0.524122\pi\)
\(258\) −9.50495 19.0906i −0.591752 1.18853i
\(259\) −17.6569 −1.09714
\(260\) 6.07476 + 13.0369i 0.376741 + 0.808513i
\(261\) 0.720950 + 5.17157i 0.0446257 + 0.320112i
\(262\) 14.5866 + 6.04198i 0.901165 + 0.373275i
\(263\) 27.5851i 1.70097i 0.526001 + 0.850484i \(0.323691\pi\)
−0.526001 + 0.850484i \(0.676309\pi\)
\(264\) −6.54275 + 19.5181i −0.402678 + 1.20126i
\(265\) 8.48528 23.2929i 0.521247 1.43087i
\(266\) 5.94253 14.3465i 0.364360 0.879643i
\(267\) 9.55582 10.9804i 0.584807 0.671988i
\(268\) −3.21608 + 3.21608i −0.196453 + 0.196453i
\(269\) 7.68306 0.468445 0.234222 0.972183i \(-0.424746\pi\)
0.234222 + 0.972183i \(0.424746\pi\)
\(270\) 4.08316 + 15.9163i 0.248493 + 0.968634i
\(271\) 14.1421i 0.859074i −0.903049 0.429537i \(-0.858677\pi\)
0.903049 0.429537i \(-0.141323\pi\)
\(272\) 6.12293i 0.371257i
\(273\) 9.55582 + 8.31609i 0.578345 + 0.503312i
\(274\) 4.34315 10.4853i 0.262379 0.633439i
\(275\) 13.5140 16.0871i 0.814923 0.970087i
\(276\) −3.74053 + 0.259472i −0.225153 + 0.0156184i
\(277\) 16.8607 1.01306 0.506532 0.862221i \(-0.330927\pi\)
0.506532 + 0.862221i \(0.330927\pi\)
\(278\) −1.34502 + 3.24718i −0.0806692 + 0.194753i
\(279\) −20.2891 + 2.82843i −1.21468 + 0.169334i
\(280\) 14.3692 0.623354i 0.858725 0.0372525i
\(281\) 5.94253i 0.354502i 0.984166 + 0.177251i \(0.0567204\pi\)
−0.984166 + 0.177251i \(0.943280\pi\)
\(282\) 1.18169 + 2.37340i 0.0703685 + 0.141334i
\(283\) 26.1188i 1.55260i 0.630363 + 0.776300i \(0.282906\pi\)
−0.630363 + 0.776300i \(0.717094\pi\)
\(284\) −16.8080 16.8080i −0.997373 0.997373i
\(285\) −9.05247 16.3633i −0.536222 0.969280i
\(286\) 17.6569 + 7.31371i 1.04407 + 0.432469i
\(287\) 5.59767i 0.330420i
\(288\) −4.26737 + 16.4253i −0.251457 + 0.967868i
\(289\) −14.6569 −0.862168
\(290\) 3.71960 4.05696i 0.218423 0.238233i
\(291\) −12.4853 + 14.3465i −0.731900 + 0.841009i
\(292\) 6.43215 6.43215i 0.376413 0.376413i
\(293\) 16.3128i 0.953004i −0.879173 0.476502i \(-0.841904\pi\)
0.879173 0.476502i \(-0.158096\pi\)
\(294\) −4.00927 + 1.99616i −0.233825 + 0.116419i
\(295\) −3.21608 + 8.82843i −0.187247 + 0.514011i
\(296\) −20.2891 + 8.40401i −1.17928 + 0.488473i
\(297\) 18.2919 + 11.9223i 1.06140 + 0.691804i
\(298\) 0.390175 0.941967i 0.0226023 0.0545667i
\(299\) 3.48106i 0.201315i
\(300\) 10.1964 14.0012i 0.588687 0.808361i
\(301\) 19.7990i 1.14119i
\(302\) 3.69552 + 1.53073i 0.212653 + 0.0880838i
\(303\) −17.8027 15.4930i −1.02274 0.890052i
\(304\) 19.3137i 1.10772i
\(305\) 6.49435 17.8276i 0.371866 1.02081i
\(306\) 6.28568 + 1.63305i 0.359328 + 0.0933553i
\(307\) 17.8027i 1.01605i 0.861341 + 0.508027i \(0.169625\pi\)
−0.861341 + 0.508027i \(0.830375\pi\)
\(308\) 13.5140 13.5140i 0.770030 0.770030i
\(309\) −11.3753 9.89949i −0.647117 0.563163i
\(310\) 15.9162 + 14.5927i 0.903982 + 0.828811i
\(311\) 9.84591 0.558310 0.279155 0.960246i \(-0.409946\pi\)
0.279155 + 0.960246i \(0.409946\pi\)
\(312\) 14.9385 + 5.00760i 0.845727 + 0.283500i
\(313\) 24.6250i 1.39189i 0.718096 + 0.695944i \(0.245014\pi\)
−0.718096 + 0.695944i \(0.754986\pi\)
\(314\) −12.6060 + 30.4336i −0.711399 + 1.71747i
\(315\) 3.19250 14.9174i 0.179877 0.840500i
\(316\) 0.686292 0.686292i 0.0386069 0.0386069i
\(317\) 9.81845i 0.551459i 0.961235 + 0.275730i \(0.0889194\pi\)
−0.961235 + 0.275730i \(0.911081\pi\)
\(318\) −12.1036 24.3099i −0.678736 1.36323i
\(319\) 7.31371i 0.409489i
\(320\) 16.2146 7.55550i 0.906426 0.422365i
\(321\) 7.41421 + 6.45232i 0.413821 + 0.360134i
\(322\) 3.21608 + 1.33214i 0.179225 + 0.0742374i
\(323\) −7.39104 −0.411248
\(324\) 15.7237 + 8.76158i 0.873539 + 0.486755i
\(325\) −12.3125 10.3431i −0.682975 0.573734i
\(326\) 11.3753 + 4.71179i 0.630018 + 0.260962i
\(327\) −18.7447 + 21.5391i −1.03658 + 1.19111i
\(328\) −2.66428 6.43215i −0.147111 0.355156i
\(329\) 2.46148i 0.135706i
\(330\) −2.58630 22.8696i −0.142371 1.25893i
\(331\) −1.51472 −0.0832565 −0.0416282 0.999133i \(-0.513255\pi\)
−0.0416282 + 0.999133i \(0.513255\pi\)
\(332\) −9.81845 9.81845i −0.538858 0.538858i
\(333\) 3.21608 + 23.0698i 0.176240 + 1.26422i
\(334\) −6.58579 2.72792i −0.360358 0.149265i
\(335\) 1.74053 4.77791i 0.0950952 0.261045i
\(336\) 10.3431 11.8851i 0.564265 0.648384i
\(337\) 19.2965i 1.05114i −0.850749 0.525572i \(-0.823851\pi\)
0.850749 0.525572i \(-0.176149\pi\)
\(338\) −1.43788 + 3.47135i −0.0782103 + 0.188816i
\(339\) −0.828427 0.720950i −0.0449940 0.0391566i
\(340\) −2.89136 6.20507i −0.156806 0.336517i
\(341\) 28.6931 1.55382
\(342\) −19.8271 5.15117i −1.07212 0.278543i
\(343\) 20.0768 1.08405
\(344\) 9.42359 + 22.7506i 0.508086 + 1.22663i
\(345\) 3.66818 2.02930i 0.197488 0.109254i
\(346\) −0.343146 0.142136i −0.0184476 0.00764126i
\(347\) −15.2304 −0.817611 −0.408806 0.912621i \(-0.634055\pi\)
−0.408806 + 0.912621i \(0.634055\pi\)
\(348\) −0.417241 6.01491i −0.0223665 0.322433i
\(349\) 13.6569i 0.731035i −0.930805 0.365517i \(-0.880892\pi\)
0.930805 0.365517i \(-0.119108\pi\)
\(350\) −14.2676 + 7.41713i −0.762636 + 0.396462i
\(351\) 9.12496 14.0000i 0.487054 0.747265i
\(352\) 9.09644 21.9607i 0.484842 1.17051i
\(353\) 26.3939 1.40481 0.702403 0.711780i \(-0.252111\pi\)
0.702403 + 0.711780i \(0.252111\pi\)
\(354\) 4.58749 + 9.21391i 0.243822 + 0.489714i
\(355\) 24.9706 + 9.09644i 1.32530 + 0.482789i
\(356\) −11.8851 + 11.8851i −0.629907 + 0.629907i
\(357\) −4.54822 3.95815i −0.240717 0.209488i
\(358\) −10.0384 4.15804i −0.530546 0.219759i
\(359\) 32.1741 1.69809 0.849043 0.528323i \(-0.177179\pi\)
0.849043 + 0.528323i \(0.177179\pi\)
\(360\) −3.43171 18.6607i −0.180867 0.983508i
\(361\) 4.31371 0.227037
\(362\) −28.2960 11.7206i −1.48721 0.616021i
\(363\) −8.69760 7.56921i −0.456506 0.397280i
\(364\) −10.3431 10.3431i −0.542128 0.542128i
\(365\) −3.48106 + 9.55582i −0.182207 + 0.500175i
\(366\) −9.26370 18.6060i −0.484221 0.972552i
\(367\) −24.2349 −1.26505 −0.632524 0.774540i \(-0.717981\pi\)
−0.632524 + 0.774540i \(0.717981\pi\)
\(368\) 4.32957 0.225694
\(369\) −7.31371 + 1.01958i −0.380736 + 0.0530771i
\(370\) 16.5927 18.0976i 0.862615 0.940851i
\(371\) 25.2120i 1.30894i
\(372\) 23.5977 1.63692i 1.22348 0.0848702i
\(373\) −10.4286 −0.539971 −0.269986 0.962864i \(-0.587019\pi\)
−0.269986 + 0.962864i \(0.587019\pi\)
\(374\) −8.40401 3.48106i −0.434561 0.180001i
\(375\) −3.72149 + 19.0040i −0.192177 + 0.981360i
\(376\) −1.17157 2.82843i −0.0604193 0.145865i
\(377\) −5.59767 −0.288295
\(378\) −9.44234 13.7879i −0.485662 0.709175i
\(379\) 15.1716 0.779311 0.389656 0.920961i \(-0.372594\pi\)
0.389656 + 0.920961i \(0.372594\pi\)
\(380\) 9.12029 + 19.5728i 0.467861 + 1.00406i
\(381\) 2.97127 + 2.58579i 0.152223 + 0.132474i
\(382\) −4.54822 + 10.9804i −0.232707 + 0.561805i
\(383\) 18.5545i 0.948091i 0.880500 + 0.474046i \(0.157207\pi\)
−0.880500 + 0.474046i \(0.842793\pi\)
\(384\) 6.22821 18.5798i 0.317832 0.948147i
\(385\) −7.31371 + 20.0768i −0.372741 + 1.02321i
\(386\) −17.8276 7.38443i −0.907401 0.375858i
\(387\) 25.8686 3.60625i 1.31498 0.183316i
\(388\) 15.5286 15.5286i 0.788345 0.788345i
\(389\) −12.6060 −0.639150 −0.319575 0.947561i \(-0.603540\pi\)
−0.319575 + 0.947561i \(0.603540\pi\)
\(390\) −17.5036 + 1.97947i −0.886329 + 0.100234i
\(391\) 1.65685i 0.0837907i
\(392\) 4.77791 1.97908i 0.241321 0.0999584i
\(393\) −12.6942 + 14.5866i −0.640338 + 0.735798i
\(394\) −10.4853 4.34315i −0.528241 0.218805i
\(395\) −0.371418 + 1.01958i −0.0186881 + 0.0513005i
\(396\) −20.1183 15.1954i −1.01098 0.763596i
\(397\) 0.551791 0.0276936 0.0138468 0.999904i \(-0.495592\pi\)
0.0138468 + 0.999904i \(0.495592\pi\)
\(398\) 19.3743 + 8.02509i 0.971145 + 0.402261i
\(399\) 14.3465 + 12.4853i 0.718226 + 0.625046i
\(400\) −12.8643 + 15.3137i −0.643215 + 0.765685i
\(401\) 25.2120i 1.25903i −0.776989 0.629514i \(-0.783254\pi\)
0.776989 0.629514i \(-0.216746\pi\)
\(402\) −2.48273 4.98653i −0.123827 0.248706i
\(403\) 21.9607i 1.09394i
\(404\) 19.2695 + 19.2695i 0.958694 + 0.958694i
\(405\) −20.0720 1.45410i −0.997386 0.0722546i
\(406\) −2.14214 + 5.17157i −0.106312 + 0.256661i
\(407\) 32.6256i 1.61719i
\(408\) −7.11019 2.38343i −0.352007 0.117998i
\(409\) −7.17157 −0.354611 −0.177306 0.984156i \(-0.556738\pi\)
−0.177306 + 0.984156i \(0.556738\pi\)
\(410\) 5.73741 + 5.26031i 0.283350 + 0.259788i
\(411\) 10.4853 + 9.12496i 0.517201 + 0.450101i
\(412\) 12.3125 + 12.3125i 0.606594 + 0.606594i
\(413\) 9.55582i 0.470211i
\(414\) 1.15474 4.44465i 0.0567524 0.218442i
\(415\) 14.5866 + 5.31371i 0.716029 + 0.260840i
\(416\) −16.8080 6.96211i −0.824081 0.341346i
\(417\) −3.24718 2.82590i −0.159015 0.138385i
\(418\) 26.5090 + 10.9804i 1.29660 + 0.537067i
\(419\) 4.20201i 0.205281i −0.994718 0.102641i \(-0.967271\pi\)
0.994718 0.102641i \(-0.0327292\pi\)
\(420\) −4.86955 + 16.9287i −0.237610 + 0.826037i
\(421\) 29.1716i 1.42174i 0.703326 + 0.710868i \(0.251698\pi\)
−0.703326 + 0.710868i \(0.748302\pi\)
\(422\) 0.819760 1.97908i 0.0399053 0.0963399i
\(423\) −3.21608 + 0.448342i −0.156371 + 0.0217991i
\(424\) 12.0000 + 28.9706i 0.582772 + 1.40693i
\(425\) 5.86030 + 4.92296i 0.284266 + 0.238798i
\(426\) 26.0609 12.9754i 1.26265 0.628659i
\(427\) 19.2965i 0.933821i
\(428\) −8.02509 8.02509i −0.387907 0.387907i
\(429\) −15.3661 + 17.6569i −0.741883 + 0.852481i
\(430\) −20.2932 18.6058i −0.978627 0.897249i
\(431\) −21.7310 −1.04674 −0.523372 0.852104i \(-0.675326\pi\)
−0.523372 + 0.852104i \(0.675326\pi\)
\(432\) −17.4125 11.3492i −0.837760 0.546038i
\(433\) 29.1732i 1.40198i −0.713173 0.700988i \(-0.752742\pi\)
0.713173 0.700988i \(-0.247258\pi\)
\(434\) −20.2891 8.40401i −0.973907 0.403405i
\(435\) 3.26319 + 5.89857i 0.156458 + 0.282815i
\(436\) 23.3137 23.3137i 1.11652 1.11652i
\(437\) 5.22625i 0.250006i
\(438\) 4.96546 + 9.97306i 0.237259 + 0.476531i
\(439\) 11.5147i 0.549568i −0.961506 0.274784i \(-0.911394\pi\)
0.961506 0.274784i \(-0.0886063\pi\)
\(440\) 1.15181 + 26.5508i 0.0549103 + 1.26576i
\(441\) −0.757359 5.43275i −0.0360647 0.258702i
\(442\) −2.66428 + 6.43215i −0.126727 + 0.305946i
\(443\) 40.4650 1.92255 0.961275 0.275591i \(-0.0888737\pi\)
0.961275 + 0.275591i \(0.0888737\pi\)
\(444\) −1.86126 26.8318i −0.0883317 1.27338i
\(445\) 6.43215 17.6569i 0.304913 0.837015i
\(446\) 5.73137 13.8368i 0.271388 0.655189i
\(447\) 0.941967 + 0.819760i 0.0445535 + 0.0387733i
\(448\) −12.8643 + 12.8643i −0.607781 + 0.607781i
\(449\) 24.7897i 1.16990i −0.811070 0.584949i \(-0.801114\pi\)
0.811070 0.584949i \(-0.198886\pi\)
\(450\) 12.2897 + 17.2906i 0.579342 + 0.815085i
\(451\) 10.3431 0.487040
\(452\) 0.896683 + 0.896683i 0.0421764 + 0.0421764i
\(453\) −3.21608 + 3.69552i −0.151104 + 0.173631i
\(454\) −2.58579 + 6.24264i −0.121357 + 0.292982i
\(455\) 15.3661 + 5.59767i 0.720375 + 0.262423i
\(456\) 22.4278 + 7.51812i 1.05028 + 0.352068i
\(457\) 12.8643i 0.601767i 0.953661 + 0.300883i \(0.0972815\pi\)
−0.953661 + 0.300883i \(0.902719\pi\)
\(458\) 4.32957 + 1.79337i 0.202307 + 0.0837985i
\(459\) −4.34315 + 6.66348i −0.202721 + 0.311025i
\(460\) −4.38765 + 2.04450i −0.204575 + 0.0953255i
\(461\) 18.5486 0.863892 0.431946 0.901899i \(-0.357827\pi\)
0.431946 + 0.901899i \(0.357827\pi\)
\(462\) 10.4324 + 20.9534i 0.485361 + 0.974842i
\(463\) 4.93839 0.229507 0.114753 0.993394i \(-0.463392\pi\)
0.114753 + 0.993394i \(0.463392\pi\)
\(464\) 6.96211i 0.323208i
\(465\) −23.1412 + 12.8021i −1.07315 + 0.593685i
\(466\) −15.1716 + 36.6274i −0.702810 + 1.69673i
\(467\) −8.73606 −0.404257 −0.202128 0.979359i \(-0.564786\pi\)
−0.202128 + 0.979359i \(0.564786\pi\)
\(468\) −11.6300 + 15.3979i −0.537599 + 0.711768i
\(469\) 5.17157i 0.238801i
\(470\) 2.52293 + 2.31313i 0.116374 + 0.106697i
\(471\) −30.4336 26.4853i −1.40231 1.22038i
\(472\) −4.54822 10.9804i −0.209349 0.505413i
\(473\) −36.5838 −1.68212
\(474\) 0.529800 + 1.06410i 0.0243345 + 0.0488755i
\(475\) −18.4853 15.5286i −0.848163 0.712501i
\(476\) 4.92296 + 4.92296i 0.225643 + 0.225643i
\(477\) 32.9411 4.59220i 1.50827 0.210262i
\(478\) −7.21250 + 17.4125i −0.329892 + 0.796430i
\(479\) −15.3661 −0.702096 −0.351048 0.936357i \(-0.614175\pi\)
−0.351048 + 0.936357i \(0.614175\pi\)
\(480\) 2.46197 + 21.7701i 0.112373 + 0.993666i
\(481\) −24.9706 −1.13856
\(482\) 5.67459 13.6997i 0.258471 0.624003i
\(483\) −2.79884 + 3.21608i −0.127351 + 0.146337i
\(484\) 9.41421 + 9.41421i 0.427919 + 0.427919i
\(485\) −8.40401 + 23.0698i −0.381607 + 1.04755i
\(486\) −16.2949 + 14.8484i −0.739154 + 0.673537i
\(487\) −19.6866 −0.892086 −0.446043 0.895011i \(-0.647167\pi\)
−0.446043 + 0.895011i \(0.647167\pi\)
\(488\) 9.18440 + 22.1731i 0.415758 + 1.00373i
\(489\) −9.89949 + 11.3753i −0.447671 + 0.514408i
\(490\) −3.90745 + 4.26184i −0.176521 + 0.192530i
\(491\) 14.0479i 0.633974i 0.948430 + 0.316987i \(0.102671\pi\)
−0.948430 + 0.316987i \(0.897329\pi\)
\(492\) 8.50637 0.590068i 0.383497 0.0266023i
\(493\) 2.66428 0.119993
\(494\) 8.40401 20.2891i 0.378114 0.912849i
\(495\) 27.5638 + 5.89897i 1.23890 + 0.265139i
\(496\) −27.3137 −1.22642
\(497\) −27.0279 −1.21237
\(498\) 15.2235 7.57960i 0.682183 0.339650i
\(499\) 25.1127 1.12420 0.562099 0.827070i \(-0.309994\pi\)
0.562099 + 0.827070i \(0.309994\pi\)
\(500\) 5.80546 21.5939i 0.259628 0.965709i
\(501\) 5.73137 6.58579i 0.256059 0.294231i
\(502\) −36.5474 15.1384i −1.63119 0.675660i
\(503\) 28.4818i 1.26994i −0.772537 0.634969i \(-0.781013\pi\)
0.772537 0.634969i \(-0.218987\pi\)
\(504\) 9.77519 + 16.6373i 0.435421 + 0.741083i
\(505\) −28.6274 10.4286i −1.27390 0.464066i
\(506\) −2.46148 + 5.94253i −0.109426 + 0.264178i
\(507\) −3.47135 3.02099i −0.154168 0.134167i
\(508\) −3.21608 3.21608i −0.142690 0.142690i
\(509\) −13.6256 −0.603944 −0.301972 0.953317i \(-0.597645\pi\)
−0.301972 + 0.953317i \(0.597645\pi\)
\(510\) 8.33107 0.942155i 0.368906 0.0417193i
\(511\) 10.3431i 0.457554i
\(512\) −8.65914 + 20.9050i −0.382683 + 0.923880i
\(513\) 13.6997 21.0188i 0.604856 0.928002i
\(514\) −1.31371 + 3.17157i −0.0579452 + 0.139892i
\(515\) −18.2919 6.66348i −0.806037 0.293628i
\(516\) −30.0871 + 2.08707i −1.32451 + 0.0918783i
\(517\) 4.54822 0.200030
\(518\) −9.55582 + 23.0698i −0.419859 + 1.01363i
\(519\) 0.298627 0.343146i 0.0131083 0.0150624i
\(520\) 20.3211 0.881556i 0.891141 0.0386588i
\(521\) 9.84591i 0.431357i −0.976464 0.215679i \(-0.930804\pi\)
0.976464 0.215679i \(-0.0691964\pi\)
\(522\) 7.14716 + 1.85687i 0.312823 + 0.0812729i
\(523\) 4.15804i 0.181819i −0.995859 0.0909093i \(-0.971023\pi\)
0.995859 0.0909093i \(-0.0289773\pi\)
\(524\) 15.7884 15.7884i 0.689721 0.689721i
\(525\) −3.05919 19.4553i −0.133514 0.849100i
\(526\) 36.0416 + 14.9289i 1.57149 + 0.650932i
\(527\) 10.4525i 0.455318i
\(528\) 21.9607 + 19.1116i 0.955719 + 0.831727i
\(529\) 21.8284 0.949062
\(530\) −25.8414 23.6926i −1.12248 1.02914i
\(531\) −12.4853 + 1.74053i −0.541815 + 0.0755325i
\(532\) −15.5286 15.5286i −0.673250 0.673250i
\(533\) 7.91630i 0.342893i
\(534\) −9.17497 18.4278i −0.397040 0.797450i
\(535\) 11.9223 + 4.34315i 0.515448 + 0.187771i
\(536\) 2.46148 + 5.94253i 0.106320 + 0.256678i
\(537\) 8.73606 10.0384i 0.376989 0.433189i
\(538\) 4.15804 10.0384i 0.179266 0.432786i
\(539\) 7.68306i 0.330933i
\(540\) 23.0054 + 3.27891i 0.989995 + 0.141102i
\(541\) 16.0000i 0.687894i 0.938989 + 0.343947i \(0.111764\pi\)
−0.938989 + 0.343947i \(0.888236\pi\)
\(542\) −18.4776 7.65367i −0.793680 0.328753i
\(543\) 24.6250 28.2960i 1.05676 1.21430i
\(544\) 8.00000 + 3.31371i 0.342997 + 0.142074i
\(545\) −12.6173 + 34.6356i −0.540465 + 1.48363i
\(546\) 16.0371 7.98465i 0.686323 0.341711i
\(547\) 33.3313i 1.42514i −0.701600 0.712571i \(-0.747530\pi\)
0.701600 0.712571i \(-0.252470\pi\)
\(548\) −11.3492 11.3492i −0.484813 0.484813i
\(549\) 25.2120 3.51472i 1.07602 0.150005i
\(550\) −13.7051 26.3631i −0.584386 1.12413i
\(551\) −8.40401 −0.358023
\(552\) −1.68534 + 5.02766i −0.0717329 + 0.213991i
\(553\) 1.10358i 0.0469291i
\(554\) 9.12496 22.0296i 0.387682 0.935948i
\(555\) 14.5567 + 26.3128i 0.617898 + 1.11692i
\(556\) 3.51472 + 3.51472i 0.149057 + 0.149057i
\(557\) 19.3743i 0.820914i −0.911880 0.410457i \(-0.865369\pi\)
0.911880 0.410457i \(-0.134631\pi\)
\(558\) −7.28485 + 28.0397i −0.308392 + 1.18701i
\(559\) 28.0000i 1.18427i
\(560\) 6.96211 19.1116i 0.294203 0.807614i
\(561\) 7.31371 8.40401i 0.308785 0.354818i
\(562\) 7.76429 + 3.21608i 0.327517 + 0.135662i
\(563\) 6.04601 0.254809 0.127405 0.991851i \(-0.459335\pi\)
0.127405 + 0.991851i \(0.459335\pi\)
\(564\) 3.74053 0.259472i 0.157505 0.0109257i
\(565\) −1.33214 0.485281i −0.0560437 0.0204159i
\(566\) 34.1258 + 14.1354i 1.43442 + 0.594155i
\(567\) 19.6866 5.59767i 0.826761 0.235080i
\(568\) −31.0572 + 12.8643i −1.30313 + 0.539774i
\(569\) 9.42359i 0.395057i −0.980297 0.197529i \(-0.936708\pi\)
0.980297 0.197529i \(-0.0632916\pi\)
\(570\) −26.2789 + 2.97186i −1.10070 + 0.124478i
\(571\) −41.1127 −1.72051 −0.860256 0.509862i \(-0.829697\pi\)
−0.860256 + 0.509862i \(0.829697\pi\)
\(572\) 19.1116 19.1116i 0.799098 0.799098i
\(573\) −10.9804 9.55582i −0.458712 0.399200i
\(574\) −7.31371 3.02944i −0.305268 0.126446i
\(575\) 3.48106 4.14386i 0.145170 0.172811i
\(576\) 19.1512 + 14.4649i 0.797965 + 0.602703i
\(577\) 15.5286i 0.646464i 0.946320 + 0.323232i \(0.104769\pi\)
−0.946320 + 0.323232i \(0.895231\pi\)
\(578\) −7.93223 + 19.1501i −0.329937 + 0.796539i
\(579\) 15.5147 17.8276i 0.644770 0.740890i
\(580\) −3.28764 7.05551i −0.136512 0.292964i
\(581\) −15.7884 −0.655015
\(582\) 11.9877 + 24.0771i 0.496905 + 0.998028i
\(583\) −46.5858 −1.92939
\(584\) −4.92296 11.8851i −0.203713 0.491808i
\(585\) 4.51487 21.0964i 0.186667 0.872228i
\(586\) −21.3137 8.82843i −0.880461 0.364699i
\(587\) −12.1689 −0.502266 −0.251133 0.967953i \(-0.580803\pi\)
−0.251133 + 0.967953i \(0.580803\pi\)
\(588\) 0.438312 + 6.31867i 0.0180757 + 0.260578i
\(589\) 32.9706i 1.35853i
\(590\) 9.79437 + 8.97992i 0.403228 + 0.369697i
\(591\) 9.12496 10.4853i 0.375351 0.431307i
\(592\) 31.0572i 1.27644i
\(593\) 39.3826 1.61725 0.808625 0.588325i \(-0.200212\pi\)
0.808625 + 0.588325i \(0.200212\pi\)
\(594\) 25.4768 17.4472i 1.04532 0.715866i
\(595\) −7.31371 2.66428i −0.299833 0.109225i
\(596\) −1.01958 1.01958i −0.0417635 0.0417635i
\(597\) −16.8607 + 19.3743i −0.690064 + 0.792936i
\(598\) 4.54822 + 1.88393i 0.185990 + 0.0770398i
\(599\) 30.1350 1.23128 0.615641 0.788027i \(-0.288897\pi\)
0.615641 + 0.788027i \(0.288897\pi\)
\(600\) −12.7753 20.8996i −0.521548 0.853222i
\(601\) 30.4853 1.24352 0.621760 0.783208i \(-0.286418\pi\)
0.621760 + 0.783208i \(0.286418\pi\)
\(602\) 25.8686 + 10.7151i 1.05433 + 0.436716i
\(603\) 6.75699 0.941967i 0.275166 0.0383599i
\(604\) 4.00000 4.00000i 0.162758 0.162758i
\(605\) −13.9861 5.09494i −0.568615 0.207139i
\(606\) −29.8774 + 14.8756i −1.21369 + 0.604279i
\(607\) 35.2152 1.42934 0.714671 0.699461i \(-0.246576\pi\)
0.714671 + 0.699461i \(0.246576\pi\)
\(608\) −25.2346 10.4525i −1.02340 0.423905i
\(609\) −5.17157 4.50063i −0.209563 0.182375i
\(610\) −19.7782 18.1335i −0.800795 0.734204i
\(611\) 3.48106i 0.140828i
\(612\) 5.53547 7.32884i 0.223758 0.296251i
\(613\) −16.0804 −0.649480 −0.324740 0.945803i \(-0.605277\pi\)
−0.324740 + 0.945803i \(0.605277\pi\)
\(614\) 23.2603 + 9.63475i 0.938711 + 0.388827i
\(615\) −8.34184 + 4.61485i −0.336375 + 0.186089i
\(616\) −10.3431 24.9706i −0.416737 1.00609i
\(617\) 31.0949 1.25183 0.625916 0.779890i \(-0.284725\pi\)
0.625916 + 0.779890i \(0.284725\pi\)
\(618\) −19.0906 + 9.50495i −0.767935 + 0.382345i
\(619\) 14.4853 0.582213 0.291106 0.956691i \(-0.405977\pi\)
0.291106 + 0.956691i \(0.405977\pi\)
\(620\) 27.6801 12.8980i 1.11166 0.517998i
\(621\) 4.71179 + 3.07107i 0.189078 + 0.123238i
\(622\) 5.32857 12.8643i 0.213656 0.515812i
\(623\) 19.1116i 0.765692i
\(624\) 14.6274 16.8080i 0.585565 0.672859i
\(625\) 4.31371 + 24.6250i 0.172548 + 0.985001i
\(626\) 32.1741 + 13.3270i 1.28594 + 0.532653i
\(627\) −23.0698 + 26.5090i −0.921319 + 1.05867i
\(628\) 32.9411 + 32.9411i 1.31449 + 1.31449i
\(629\) 11.8851 0.473889
\(630\) −17.7628 12.2444i −0.707685 0.487830i
\(631\) 26.1421i 1.04070i −0.853952 0.520351i \(-0.825801\pi\)
0.853952 0.520351i \(-0.174199\pi\)
\(632\) −0.525265 1.26810i −0.0208939 0.0504424i
\(633\) 1.97908 + 1.72232i 0.0786612 + 0.0684560i
\(634\) 12.8284 + 5.31371i 0.509482 + 0.211034i
\(635\) 4.77791 + 1.74053i 0.189606 + 0.0690707i
\(636\) −38.3129 + 2.65768i −1.51920 + 0.105384i
\(637\) 5.88036 0.232988
\(638\) −9.55582 3.95815i −0.378319 0.156705i
\(639\) 4.92296 + 35.3137i 0.194749 + 1.39699i
\(640\) −1.09644 25.2745i −0.0433405 0.999060i
\(641\) 24.7897i 0.979135i 0.871965 + 0.489567i \(0.162845\pi\)
−0.871965 + 0.489567i \(0.837155\pi\)
\(642\) 12.4429 6.19516i 0.491082 0.244504i
\(643\) 1.49376i 0.0589081i −0.999566 0.0294540i \(-0.990623\pi\)
0.999566 0.0294540i \(-0.00937687\pi\)
\(644\) 3.48106 3.48106i 0.137173 0.137173i
\(645\) 29.5051 16.3227i 1.16176 0.642708i
\(646\) −4.00000 + 9.65685i −0.157378 + 0.379944i
\(647\) 42.3671i 1.66562i 0.553556 + 0.832812i \(0.313271\pi\)
−0.553556 + 0.832812i \(0.686729\pi\)
\(648\) 19.9572 15.8023i 0.783992 0.620772i
\(649\) 17.6569 0.693092
\(650\) −20.1775 + 10.4894i −0.791425 + 0.411428i
\(651\) 17.6569 20.2891i 0.692027 0.795192i
\(652\) 12.3125 12.3125i 0.482195 0.482195i
\(653\) 37.5892i 1.47098i −0.677535 0.735490i \(-0.736952\pi\)
0.677535 0.735490i \(-0.263048\pi\)
\(654\) 17.9976 + 36.1479i 0.703762 + 1.41350i
\(655\) −8.54465 + 23.4558i −0.333867 + 0.916496i
\(656\) −9.84591 −0.384418
\(657\) −13.5140 + 1.88393i −0.527230 + 0.0734993i
\(658\) −3.21608 1.33214i −0.125376 0.0519323i
\(659\) 0.720950i 0.0280842i −0.999901 0.0140421i \(-0.995530\pi\)
0.999901 0.0140421i \(-0.00446989\pi\)
\(660\) −31.2802 8.99775i −1.21758 0.350237i
\(661\) 28.7696i 1.11901i 0.828828 + 0.559503i \(0.189008\pi\)
−0.828828 + 0.559503i \(0.810992\pi\)
\(662\) −0.819760 + 1.97908i −0.0318609 + 0.0769189i
\(663\) −6.43215 5.59767i −0.249804 0.217395i
\(664\) −18.1421 + 7.51472i −0.704051 + 0.291628i
\(665\) 23.0698 + 8.40401i 0.894608 + 0.325894i
\(666\) 31.8827 + 8.28328i 1.23543 + 0.320970i
\(667\) 1.88393i 0.0729462i
\(668\) −7.12840 + 7.12840i −0.275806 + 0.275806i
\(669\) 13.8368 + 12.0416i 0.534960 + 0.465556i
\(670\) −5.30067 4.85990i −0.204783 0.187754i
\(671\) −35.6552 −1.37645
\(672\) −9.93092 19.9461i −0.383094 0.769438i
\(673\) 5.65180i 0.217861i 0.994049 + 0.108930i \(0.0347426\pi\)
−0.994049 + 0.108930i \(0.965257\pi\)
\(674\) −25.2120 10.4432i −0.971131 0.402256i
\(675\) −24.8624 + 7.54068i −0.956954 + 0.290241i
\(676\) 3.75736 + 3.75736i 0.144514 + 0.144514i
\(677\) 39.3826i 1.51360i 0.653649 + 0.756798i \(0.273237\pi\)
−0.653649 + 0.756798i \(0.726763\pi\)
\(678\) −1.39031 + 0.692217i −0.0533945 + 0.0265844i
\(679\) 24.9706i 0.958282i
\(680\) −9.67211 + 0.419588i −0.370909 + 0.0160905i
\(681\) −6.24264 5.43275i −0.239219 0.208183i
\(682\) 15.5286 37.4893i 0.594620 1.43554i
\(683\) −21.3533 −0.817063 −0.408532 0.912744i \(-0.633959\pi\)
−0.408532 + 0.912744i \(0.633959\pi\)
\(684\) −17.4607 + 23.1175i −0.667625 + 0.883920i
\(685\) 16.8607 + 6.14214i 0.644215 + 0.234679i
\(686\) 10.8655 26.2316i 0.414846 1.00153i
\(687\) −3.76787 + 4.32957i −0.143753 + 0.165183i
\(688\) 34.8250 1.32769
\(689\) 35.6552i 1.35836i
\(690\) −0.666204 5.89096i −0.0253620 0.224265i
\(691\) −12.8284 −0.488016 −0.244008 0.969773i \(-0.578462\pi\)
−0.244008 + 0.969773i \(0.578462\pi\)
\(692\) −0.371418 + 0.371418i −0.0141192 + 0.0141192i
\(693\) −28.3929 + 3.95815i −1.07856 + 0.150358i
\(694\) −8.24264 + 19.8995i −0.312886 + 0.755374i
\(695\) −5.22158 1.90215i −0.198066 0.0721527i
\(696\) −8.08467 2.71009i −0.306449 0.102726i
\(697\) 3.76787i 0.142718i
\(698\) −17.8435 7.39104i −0.675388 0.279755i
\(699\) −36.6274 31.8755i −1.38538 1.20564i
\(700\) 1.96937 + 22.6557i 0.0744351 + 0.856303i
\(701\) −2.76011 −0.104248 −0.0521239 0.998641i \(-0.516599\pi\)
−0.0521239 + 0.998641i \(0.516599\pi\)
\(702\) −13.3535 19.4991i −0.503995 0.735945i
\(703\) −37.4893 −1.41394
\(704\) −23.7701 23.7701i −0.895871 0.895871i
\(705\) −3.66818 + 2.02930i −0.138152 + 0.0764279i
\(706\) 14.2843 34.4853i 0.537596 1.29787i
\(707\) 30.9861 1.16535
\(708\) 14.5213 1.00731i 0.545743 0.0378570i
\(709\) 20.2843i 0.761792i −0.924618 0.380896i \(-0.875616\pi\)
0.924618 0.380896i \(-0.124384\pi\)
\(710\) 25.3990 27.7027i 0.953209 1.03966i
\(711\) −1.44190 + 0.201010i −0.0540755 + 0.00753847i
\(712\) 9.09644 + 21.9607i 0.340903 + 0.823014i
\(713\) 7.39104 0.276796
\(714\) −7.63305 + 3.80040i −0.285660 + 0.142226i
\(715\) −10.3431 + 28.3929i −0.386812 + 1.06183i
\(716\) −10.8655 + 10.8655i −0.406062 + 0.406062i
\(717\) −17.4125 15.1535i −0.650283 0.565917i
\(718\) 17.4125 42.0375i 0.649830 1.56883i
\(719\) −28.6931 −1.07007 −0.535036 0.844829i \(-0.679702\pi\)
−0.535036 + 0.844829i \(0.679702\pi\)
\(720\) −26.2387 5.61538i −0.977857 0.209273i
\(721\) 19.7990 0.737353
\(722\) 2.33456 5.63613i 0.0868834 0.209755i
\(723\) 13.6997 + 11.9223i 0.509497 + 0.443397i
\(724\) −30.6274 + 30.6274i −1.13826 + 1.13826i
\(725\) 6.66348 + 5.59767i 0.247476 + 0.207892i
\(726\) −14.5968 + 7.26754i −0.541736 + 0.269724i
\(727\) 18.9063 0.701195 0.350598 0.936526i \(-0.385978\pi\)
0.350598 + 0.936526i \(0.385978\pi\)
\(728\) −19.1116 + 7.91630i −0.708325 + 0.293398i
\(729\) −10.8995 24.7022i −0.403685 0.914898i
\(730\) 10.6013 + 9.71979i 0.392373 + 0.359746i
\(731\) 13.3270i 0.492916i
\(732\) −29.3234 + 2.03410i −1.08382 + 0.0751825i
\(733\) 38.8215 1.43390 0.716952 0.697123i \(-0.245537\pi\)
0.716952 + 0.697123i \(0.245537\pi\)
\(734\) −13.1158 + 31.6644i −0.484113 + 1.16875i
\(735\) −3.42799 6.19646i −0.126443 0.228560i
\(736\) 2.34315 5.65685i 0.0863695 0.208514i
\(737\) −9.55582 −0.351993
\(738\) −2.62601 + 10.1076i −0.0966647 + 0.372066i
\(739\) −32.8284 −1.20761 −0.603807 0.797131i \(-0.706350\pi\)
−0.603807 + 0.797131i \(0.706350\pi\)
\(740\) −14.6658 31.4738i −0.539125 1.15700i
\(741\) 20.2891 + 17.6569i 0.745338 + 0.648641i
\(742\) 32.9411 + 13.6447i 1.20931 + 0.500911i
\(743\) 0.185709i 0.00681301i 0.999994 + 0.00340650i \(0.00108433\pi\)
−0.999994 + 0.00340650i \(0.998916\pi\)
\(744\) 10.6322 31.7177i 0.389796 1.16283i
\(745\) 1.51472 + 0.551791i 0.0554950 + 0.0202161i
\(746\) −5.64391 + 13.6256i −0.206638 + 0.498868i
\(747\) 2.87576 + 20.6286i 0.105218 + 0.754761i
\(748\) −9.09644 + 9.09644i −0.332599 + 0.332599i
\(749\) −12.9046 −0.471525
\(750\) 22.8158 + 15.1472i 0.833116 + 0.553099i
\(751\) 27.1127i 0.989356i 0.869076 + 0.494678i \(0.164714\pi\)
−0.869076 + 0.494678i \(0.835286\pi\)
\(752\) −4.32957 −0.157883
\(753\) 31.8059 36.5474i 1.15907 1.33186i
\(754\) −3.02944 + 7.31371i −0.110326 + 0.266350i
\(755\) −2.16478 + 5.94253i −0.0787846 + 0.216271i
\(756\) −23.1250 + 4.87504i −0.841047 + 0.177303i
\(757\) −36.1572 −1.31416 −0.657078 0.753823i \(-0.728208\pi\)
−0.657078 + 0.753823i \(0.728208\pi\)
\(758\) 8.21080 19.8226i 0.298230 0.719990i
\(759\) −5.94253 5.17157i −0.215700 0.187716i
\(760\) 30.5090 1.32352i 1.10668 0.0480090i
\(761\) 4.92296i 0.178457i 0.996011 + 0.0892285i \(0.0284401\pi\)
−0.996011 + 0.0892285i \(0.971560\pi\)
\(762\) 4.98653 2.48273i 0.180643 0.0899398i
\(763\) 37.4893i 1.35720i
\(764\) 11.8851 + 11.8851i 0.429987 + 0.429987i
\(765\) −2.14891 + 10.0411i −0.0776941 + 0.363037i
\(766\) 24.2426 + 10.0416i 0.875922 + 0.362819i
\(767\) 13.5140i 0.487961i
\(768\) −20.9050 18.1929i −0.754344 0.656479i
\(769\) 29.5980 1.06733 0.533665 0.845696i \(-0.320814\pi\)
0.533665 + 0.845696i \(0.320814\pi\)
\(770\) 22.2735 + 20.4213i 0.802680 + 0.735933i
\(771\) −3.17157 2.76011i −0.114221 0.0994028i
\(772\) −19.2965 + 19.2965i −0.694495 + 0.694495i
\(773\) 38.1145i 1.37088i 0.728128 + 0.685442i \(0.240391\pi\)
−0.728128 + 0.685442i \(0.759609\pi\)
\(774\) 9.28821 35.7507i 0.333858