Properties

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

$q$-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 \(0.218373\pi\)
−0.773762 + 0.633476i \(0.781627\pi\)
\(12\) −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 \(0.0359971\pi\)
−0.993612 + 0.112847i \(0.964003\pi\)
\(24\) −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 \(-0.789878\pi\)
0.789919 0.613211i \(-0.210122\pi\)
\(32\) 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 \(-0.938435\pi\)
0.981354 0.192209i \(-0.0615652\pi\)
\(42\) −4.98653 2.48273i −0.769438 0.383094i
\(43\) 8.70626i 1.32769i 0.747869 + 0.663846i \(0.231077\pi\)
−0.747869 + 0.663846i \(0.768923\pi\)
\(44\) −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 \(-0.974846\pi\)
0.996879 0.0789416i \(-0.0251541\pi\)
\(48\) −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 \(0.275501\pi\)
−0.648250 + 0.761428i \(0.724499\pi\)
\(54\) 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 \(-0.911810\pi\)
0.961864 0.273527i \(-0.0881904\pi\)
\(60\) 2.14130 + 7.44411i 0.276440 + 0.961031i
\(61\) 8.48528i 1.08643i 0.839594 + 0.543214i \(0.182793\pi\)
−0.839594 + 0.543214i \(0.817207\pi\)
\(62\) 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 \(0.0443609\pi\)
−0.990305 + 0.138913i \(0.955639\pi\)
\(68\) −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 \(-0.914244\pi\)
0.963928 0.266164i \(-0.0857564\pi\)
\(74\) 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 \(-0.991309\pi\)
0.999627 0.0272992i \(-0.00869069\pi\)
\(80\) −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 \(0.146943\pi\)
−0.895326 + 0.445412i \(0.853057\pi\)
\(90\) 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 \(-0.811782\pi\)
0.830215 0.557444i \(-0.188218\pi\)
\(98\) −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 \(-0.710339\pi\)
0.613748 0.789502i \(-0.289661\pi\)
\(110\) −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 \(-0.837834\pi\)
0.873008 0.487707i \(-0.162166\pi\)
\(132\) −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 \(-0.963285\pi\)
0.993355 0.115087i \(-0.0367147\pi\)
\(152\) 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 \(-0.889247\pi\)
0.940077 0.340964i \(-0.110753\pi\)
\(164\) 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 \(0.0624786\pi\)
−0.980798 + 0.195024i \(0.937521\pi\)
\(168\) 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 \(0.00317799\pi\)
−0.999950 + 0.00998379i \(0.996822\pi\)
\(174\) 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 \(0.0927010\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(180\) 11.2621 + 7.29143i 0.839428 + 0.543471i
\(181\) 21.6569i 1.60974i 0.593450 + 0.804871i \(0.297765\pi\)
−0.593450 + 0.804871i \(0.702235\pi\)
\(182\) 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 \(0.163398\pi\)
−0.871113 + 0.491082i \(0.836602\pi\)
\(194\) 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 \(0.0922865\pi\)
−0.958265 + 0.285882i \(0.907713\pi\)
\(198\) 4.48288 + 17.2548i 0.318584 + 1.22624i
\(199\) 14.8284i 1.05116i −0.850744 0.525580i \(-0.823848\pi\)
0.850744 0.525580i \(-0.176152\pi\)
\(200\) −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 \(-0.965079\pi\)
0.993988 0.109488i \(-0.0349211\pi\)
\(230\) −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 \(0.344340\pi\)
−0.469762 + 0.882793i \(0.655660\pi\)
\(252\) −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 \(-0.676309\pi\)
0.526001 0.850484i \(-0.323691\pi\)
\(264\) −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 \(0.141323\pi\)
−0.903049 + 0.429537i \(0.858677\pi\)
\(272\) 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 \(-0.943280\pi\)
0.984166 0.177251i \(-0.0567204\pi\)
\(282\) 1.18169 2.37340i 0.0703685 0.141334i
\(283\) 26.1188i 1.55260i −0.630363 0.776300i \(-0.717094\pi\)
0.630363 0.776300i \(-0.282906\pi\)
\(284\) −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 \(0.158096\pi\)
−0.879173 + 0.476502i \(0.841904\pi\)
\(294\) −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 \(-0.830375\pi\)
0.861341 0.508027i \(-0.169625\pi\)
\(308\) 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 \(-0.754986\pi\)
0.718096 0.695944i \(-0.245014\pi\)
\(314\) −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 \(-0.911081\pi\)
0.961235 0.275730i \(-0.0889194\pi\)
\(318\) −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 \(0.176149\pi\)
−0.850749 + 0.525572i \(0.823851\pi\)
\(338\) −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 \(0.119108\pi\)
−0.930805 + 0.365517i \(0.880892\pi\)
\(350\) −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 \(-0.842793\pi\)
0.880500 0.474046i \(-0.157207\pi\)
\(384\) 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 \(0.216746\pi\)
−0.776989 + 0.629514i \(0.783254\pi\)
\(402\) −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 \(0.0327292\pi\)
−0.994718 + 0.102641i \(0.967271\pi\)
\(420\) −4.86955 16.9287i −0.237610 0.826037i
\(421\) 29.1716i 1.42174i −0.703326 0.710868i \(-0.748302\pi\)
0.703326 0.710868i \(-0.251698\pi\)
\(422\) 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 \(0.247258\pi\)
−0.713173 + 0.700988i \(0.752742\pi\)
\(434\) −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 \(0.0886063\pi\)
−0.961506 + 0.274784i \(0.911394\pi\)
\(440\) 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 \(0.198886\pi\)
−0.811070 + 0.584949i \(0.801114\pi\)
\(450\) 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 \(-0.902719\pi\)
0.953661 0.300883i \(-0.0972815\pi\)
\(458\) 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 \(-0.897329\pi\)
0.948430 0.316987i \(-0.102671\pi\)
\(492\) 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 \(0.218987\pi\)
−0.772537 + 0.634969i \(0.781013\pi\)
\(504\) 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 \(0.0691964\pi\)
−0.976464 + 0.215679i \(0.930804\pi\)
\(522\) 7.14716 1.85687i 0.312823 0.0812729i
\(523\) 4.15804i 0.181819i 0.995859 + 0.0909093i \(0.0289773\pi\)
−0.995859 + 0.0909093i \(0.971023\pi\)
\(524\) 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 \(-0.888236\pi\)
0.938989 0.343947i \(-0.111764\pi\)
\(542\) −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 \(0.252470\pi\)
−0.701600 + 0.712571i \(0.747530\pi\)
\(548\) −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 \(0.134631\pi\)
−0.911880 + 0.410457i \(0.865369\pi\)
\(558\) −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 \(0.0632916\pi\)
−0.980297 + 0.197529i \(0.936708\pi\)
\(570\) −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 \(-0.895231\pi\)
0.946320 0.323232i \(-0.104769\pi\)
\(578\) −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 \(0.174199\pi\)
−0.853952 + 0.520351i \(0.825801\pi\)
\(632\) −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 \(-0.837155\pi\)
0.871965 0.489567i \(-0.162845\pi\)
\(642\) 12.4429 + 6.19516i 0.491082 + 0.244504i
\(643\) 1.49376i 0.0589081i 0.999566 + 0.0294540i \(0.00937687\pi\)
−0.999566 + 0.0294540i \(0.990623\pi\)
\(644\) 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 \(-0.686729\pi\)
0.553556 0.832812i \(-0.313271\pi\)
\(648\) 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 \(0.263048\pi\)
−0.677535 + 0.735490i \(0.736952\pi\)
\(654\) 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 \(0.00446989\pi\)
−0.999901 + 0.0140421i \(0.995530\pi\)
\(660\) −31.2802 + 8.99775i −1.21758 + 0.350237i
\(661\) 28.7696i 1.11901i −0.828828 0.559503i \(-0.810992\pi\)
0.828828 0.559503i \(-0.189008\pi\)
\(662\) −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 \(-0.965257\pi\)
0.994049 0.108930i \(-0.0347426\pi\)
\(674\) −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 \(-0.726763\pi\)
0.653649 0.756798i \(-0.273237\pi\)
\(678\) −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 \(0.124384\pi\)
−0.924618 + 0.380896i \(0.875616\pi\)
\(710\) 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 \(-0.998916\pi\)
0.999994 0.00340650i \(-0.00108433\pi\)
\(744\) 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 \(-0.835286\pi\)
0.869076 0.494678i \(-0.164714\pi\)
\(752\) −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 \(-0.971560\pi\)
0.996011 0.0892285i \(-0.0284401\pi\)
\(762\) 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 \(-0.759609\pi\)
0.728128 0.685442i \(-0.240391\pi\)
\(774\) 9.28821 + 35.7507i 0.333858