Properties

Label 120.2.m.b.59.7
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 59.7
Root \(2.08509i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.6

$q$-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} +(-0.137055 + 3.15931i) q^{10} -4.20201i q^{11} +(0.239721 + 3.45580i) q^{12} +3.21608 q^{13} +(-1.23074 + 2.97127i) q^{14} +(-3.61536 - 1.38896i) q^{15} +4.00000i q^{16} -1.53073 q^{17} +(-4.10632 - 1.06684i) q^{18} -4.82843 q^{19} +(-4.05366 - 1.88887i) 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} +(3.77137 - 3.97199i) 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} +(4.66176 - 4.27411i) q^{40} +2.46148i q^{41} +(4.98653 - 2.48273i) q^{42} +8.70626i q^{43} +(-5.94253 + 5.94253i) q^{44} +(3.14437 + 5.92562i) q^{45} +(-1.41421 - 0.585786i) q^{46} -1.08239i q^{47} +(4.54822 - 5.22625i) q^{48} -1.82843 q^{49} +(2.13008 + 6.74261i) 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} +(3.14861 + 7.07717i) 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} +(-0.311677 + 7.18461i) q^{70} +11.8851 q^{71} +(4.29847 + 7.31595i) q^{72} -4.54822i q^{73} +(4.20201 - 10.1445i) q^{74} +(-8.65894 - 0.151125i) 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} +(-9.44391 + 0.901402i) 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 \(-0.358596\pi\)
0.429766 + 0.902940i \(0.358596\pi\)
\(8\) 2.61313 1.08239i 0.923880 0.382683i
\(9\) 0.414214 + 2.97127i 0.138071 + 0.990422i
\(10\) −0.137055 + 3.15931i −0.0433405 + 0.999060i
\(11\) 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 \(-0.352852\pi\)
0.445990 + 0.895038i \(0.352852\pi\)
\(14\) −1.23074 + 2.97127i −0.328929 + 0.794104i
\(15\) −3.61536 1.38896i −0.933481 0.358627i
\(16\) 4.00000i 1.00000i
\(17\) −1.53073 −0.371257 −0.185629 0.982620i \(-0.559432\pi\)
−0.185629 + 0.982620i \(0.559432\pi\)
\(18\) −4.10632 1.06684i −0.967868 0.251457i
\(19\) −4.82843 −1.10772 −0.553859 0.832611i \(-0.686845\pi\)
−0.553859 + 0.832611i \(0.686845\pi\)
\(20\) −4.05366 1.88887i −0.906426 0.422365i
\(21\) −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 \(0.448333\pi\)
\(30\) 3.77137 3.97199i 0.688556 0.725184i
\(31\) 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 \(-0.720329\pi\)
−0.638221 + 0.769853i \(0.720329\pi\)
\(38\) 2.61313 6.30864i 0.423905 1.02340i
\(39\) −4.20201 3.65685i −0.672859 0.585565i
\(40\) 4.66176 4.27411i 0.737089 0.675796i
\(41\) 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 \(0.231077\pi\)
−0.747869 + 0.663846i \(0.768923\pi\)
\(44\) −5.94253 + 5.94253i −0.895871 + 0.895871i
\(45\) 3.14437 + 5.92562i 0.468735 + 0.883339i
\(46\) −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
\(50\) 2.13008 + 6.74261i 0.301238 + 0.953549i
\(51\) 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 \(0.0881904\pi\)
−0.961864 + 0.273527i \(0.911810\pi\)
\(60\) 3.14861 + 7.07717i 0.406483 + 0.913658i
\(61\) 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 \(0.0443609\pi\)
−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
\(70\) −0.311677 + 7.18461i −0.0372525 + 0.858725i
\(71\) 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
\(75\) −8.65894 0.151125i −0.999848 0.0174504i
\(76\) 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 \(-0.624431\pi\)
−0.381030 + 0.924563i \(0.624431\pi\)
\(84\) 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 \(-0.146943\pi\)
\(90\) −9.44391 + 0.901402i −0.995476 + 0.0950161i
\(91\) 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
\(100\) −9.96243 0.865995i −0.996243 0.0865995i
\(101\) −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 \(-0.358892\pi\)
0.428927 + 0.903339i \(0.358892\pi\)
\(104\) 8.40401 3.48106i 0.824081 0.341346i
\(105\) −8.22172 3.15864i −0.802357 0.308251i
\(106\) −14.4853 6.00000i −1.40693 0.582772i
\(107\) −5.67459 −0.548584 −0.274292 0.961647i \(-0.588443\pi\)
−0.274292 + 0.961647i \(0.588443\pi\)
\(108\) −10.1688 + 2.14371i −0.978493 + 0.206279i
\(109\) 16.4853i 1.57900i 0.613748 + 0.789502i \(0.289661\pi\)
−0.613748 + 0.789502i \(0.710339\pi\)
\(110\) 13.2754 + 0.575904i 1.26576 + 0.0549103i
\(111\) 10.1445 + 8.82843i 0.962877 + 0.837957i
\(112\) 9.09644i 0.859533i
\(113\) 0.634051 0.0596465 0.0298232 0.999555i \(-0.490506\pi\)
0.0298232 + 0.999555i \(0.490506\pi\)
\(114\) −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
\(120\) −10.9508 + 0.283719i −0.999665 + 0.0258999i
\(121\) −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 \(-0.532171\pi\)
−0.100897 + 0.994897i \(0.532171\pi\)
\(128\) 4.32957 + 10.4525i 0.382683 + 0.923880i
\(129\) 9.89949 11.3753i 0.871602 1.00154i
\(130\) −0.440778 + 10.1606i −0.0386588 + 0.891141i
\(131\) 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
\(135\) 2.62943 11.3175i 0.226305 0.974056i
\(136\) −4.00000 + 1.65685i −0.342997 + 0.142074i
\(137\) −8.02509 −0.685629 −0.342815 0.939403i \(-0.611380\pi\)
−0.342815 + 0.939403i \(0.611380\pi\)
\(138\) 1.18169 + 2.37340i 0.100592 + 0.202038i
\(139\) −2.48528 −0.210799 −0.105399 0.994430i \(-0.533612\pi\)
−0.105399 + 0.994430i \(0.533612\pi\)
\(140\) −9.21846 4.29551i −0.779102 0.363037i
\(141\) −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 \(0.490599\pi\)
\(150\) 4.88364 11.2317i 0.398747 0.917061i
\(151\) 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 \(-0.120250\pi\)
0.929487 + 0.368854i \(0.120250\pi\)
\(158\) −0.634051 0.262632i −0.0504424 0.0208939i
\(159\) 12.6060 14.4853i 0.999722 1.14876i
\(160\) −12.6372 0.548218i −0.999060 0.0433405i
\(161\) 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
\(165\) −5.83640 + 15.1918i −0.454363 + 1.18268i
\(166\) 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
\(170\) 0.209794 4.83606i 0.0160905 0.370909i
\(171\) −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 \(-0.907299\pi\)
0.957892 0.287129i \(-0.0927010\pi\)
\(180\) 3.93327 12.8269i 0.293169 0.956061i
\(181\) 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
\(190\) 0.661758 15.2545i 0.0480090 1.10668i
\(191\) −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
\(195\) −11.6273 4.46699i −0.832646 0.319887i
\(196\) 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 \(0.176152\pi\)
−0.850744 + 0.525580i \(0.823848\pi\)
\(200\) 6.52311 12.5479i 0.461253 0.887269i
\(201\) 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
\(210\) 8.57652 9.03275i 0.591836 0.623319i
\(211\) 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
\(220\) −7.93706 + 17.0335i −0.535117 + 1.14840i
\(221\) −4.92296 −0.331154
\(222\) −17.0251 + 8.47657i −1.14265 + 0.568910i
\(223\) −10.5902 −0.709172 −0.354586 0.935023i \(-0.615378\pi\)
−0.354586 + 0.935023i \(0.615378\pi\)
\(224\) −11.8851 4.92296i −0.794104 0.328929i
\(225\) 11.1416 + 10.0431i 0.742774 + 0.669542i
\(226\) −0.343146 + 0.828427i −0.0228257 + 0.0551062i
\(227\) 4.77791 0.317121 0.158561 0.987349i \(-0.449315\pi\)
0.158561 + 0.987349i \(0.449315\pi\)
\(228\) −1.15748 16.6861i −0.0766557 1.10506i
\(229\) 3.31371i 0.218976i 0.993988 + 0.109488i \(0.0349211\pi\)
−0.993988 + 0.109488i \(0.965079\pi\)
\(230\) −3.41961 0.148347i −0.225482 0.00978170i
\(231\) −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 \(-0.129590\pi\)
0.918265 + 0.395967i \(0.129590\pi\)
\(234\) −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 \(0.641848\pi\)
\(240\) 5.55582 14.4614i 0.358627 0.933481i
\(241\) 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
\(250\) 9.63587 + 12.5360i 0.609426 + 0.792843i
\(251\) 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
\(255\) 5.53415 + 2.12612i 0.346562 + 0.133143i
\(256\) −16.0000 −1.00000
\(257\) 2.42742 0.151418 0.0757090 0.997130i \(-0.475878\pi\)
0.0757090 + 0.997130i \(0.475878\pi\)
\(258\) 9.50495 + 19.0906i 0.591752 + 1.18853i
\(259\) −17.6569 −1.09714
\(260\) −13.0369 6.07476i −0.808513 0.376741i
\(261\) 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 \(0.424746\pi\)
\(270\) 13.3640 + 9.56051i 0.813308 + 0.581834i
\(271\) 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 \(-0.669073\pi\)
−0.506532 + 0.862221i \(0.669073\pi\)
\(278\) 1.34502 3.24718i 0.0806692 0.194753i
\(279\) −20.2891 + 2.82843i −1.21468 + 0.169334i
\(280\) 10.6013 9.71979i 0.633552 0.580869i
\(281\) 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 \(-0.717094\pi\)
0.630363 0.776300i \(-0.282906\pi\)
\(284\) −16.8080 16.8080i −0.997373 0.997373i
\(285\) 17.4565 + 6.70647i 1.03403 + 0.397257i
\(286\) 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
\(290\) −0.238547 + 5.49886i −0.0140080 + 0.322904i
\(291\) −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
\(300\) 12.0319 + 12.4593i 0.694660 + 0.719338i
\(301\) 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
\(310\) −21.5731 0.935868i −1.22527 0.0531537i
\(311\) 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
\(315\) 7.15065 + 13.4755i 0.402893 + 0.759258i
\(316\) 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
\(320\) 7.55550 16.2146i 0.422365 0.906426i
\(321\) 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
\(330\) −16.6903 15.8473i −0.918773 0.872367i
\(331\) −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
\(340\) 6.20507 + 2.89136i 0.336517 + 0.156806i
\(341\) 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
\(345\) 1.50339 3.91323i 0.0809400 0.210681i
\(346\) −0.343146 0.142136i −0.0184476 0.00764126i
\(347\) 15.2304 0.817611 0.408806 0.912621i \(-0.365945\pi\)
0.408806 + 0.912621i \(0.365945\pi\)
\(348\) 0.417241 + 6.01491i 0.0223665 + 0.322433i
\(349\) 13.6569i 0.731035i −0.930805 0.365517i \(-0.880892\pi\)
0.930805 0.365517i \(-0.119108\pi\)
\(350\) 4.84403 + 15.3334i 0.258924 + 0.819606i
\(351\) 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 \(-0.747889\pi\)
−0.702403 + 0.711780i \(0.747889\pi\)
\(354\) 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 \(0.177179\pi\)
\(360\) 14.6305 + 12.0809i 0.771094 + 0.636721i
\(361\) 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 \(-0.282019\pi\)
0.632524 + 0.774540i \(0.282019\pi\)
\(368\) −4.32957 −0.225694
\(369\) −7.31371 + 1.01958i −0.380736 + 0.0530771i
\(370\) 1.06413 24.5298i 0.0553216 1.27524i
\(371\) 25.2120i 1.30894i
\(372\) −23.5977 + 1.63692i −1.22348 + 0.0848702i
\(373\) 10.4286 0.539971 0.269986 0.962864i \(-0.412981\pi\)
0.269986 + 0.962864i \(0.412981\pi\)
\(374\) −8.40401 3.48106i −0.434561 0.180001i
\(375\) −18.3081 + 6.30975i −0.945427 + 0.325834i
\(376\) −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 \(0.372594\pi\)
\(380\) 19.5728 + 9.12029i 1.00406 + 0.467861i
\(381\) 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 \(0.603540\pi\)
\(390\) 12.1290 12.7742i 0.614177 0.646849i
\(391\) 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 \(-0.504408\pi\)
−0.0138468 + 0.999904i \(0.504408\pi\)
\(398\) −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
\(405\) −16.3041 + 11.7972i −0.810159 + 0.586210i
\(406\) −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 \(0.556738\pi\)
\(410\) −7.77656 0.337357i −0.384057 0.0166609i
\(411\) 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 \(-0.0327292\pi\)
\(420\) 7.16028 + 16.0942i 0.349386 + 0.785319i
\(421\) 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
\(430\) −27.5057 1.19323i −1.32644 0.0575428i
\(431\) −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
\(435\) −6.29263 2.41752i −0.301708 0.115911i
\(436\) 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 \(-0.0886063\pi\)
\(440\) −17.9598 19.5887i −0.856201 0.933856i
\(441\) −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 \(-0.911126\pi\)
−0.961275 + 0.275591i \(0.911126\pi\)
\(444\) −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 \(-0.198886\pi\)
\(450\) −19.1518 + 9.12190i −0.902824 + 0.430011i
\(451\) 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
\(460\) 2.04450 4.38765i 0.0953255 0.204575i
\(461\) 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 \(-0.536608\pi\)
−0.114753 + 0.993394i \(0.536608\pi\)
\(464\) 6.96211i 0.323208i
\(465\) 9.48438 24.6872i 0.439828 1.14484i
\(466\) −15.1716 + 36.6274i −0.702810 + 1.69673i
\(467\) 8.73606 0.404257 0.202128 0.979359i \(-0.435214\pi\)
0.202128 + 0.979359i \(0.435214\pi\)
\(468\) 11.6300 15.3979i 0.537599 0.711768i
\(469\) 5.17157i 0.238801i
\(470\) 3.41961 + 0.148347i 0.157735 + 0.00684273i
\(471\) −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 \(0.614175\pi\)
\(480\) 15.8880 + 15.0855i 0.725184 + 0.688556i
\(481\) −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 \(-0.352833\pi\)
0.446043 + 0.895011i \(0.352833\pi\)
\(488\) −9.18440 22.1731i −0.415758 1.00373i
\(489\) −9.89949 + 11.3753i −0.447671 + 0.514408i
\(490\) 0.250594 5.77656i 0.0113207 0.260958i
\(491\) 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
\(495\) 24.8995 13.2127i 1.11915 0.593866i
\(496\) −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 \(0.309994\pi\)
\(500\) −21.5939 + 5.80546i −0.965709 + 0.259628i
\(501\) 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 \(0.597645\pi\)
\(510\) −5.77297 + 6.08007i −0.255631 + 0.269230i
\(511\) 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
\(520\) 14.9926 13.7459i 0.657468 0.602796i
\(521\) 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 \(0.0289773\pi\)
−0.995859 + 0.0909093i \(0.971023\pi\)
\(524\) 15.7884 15.7884i 0.689721 0.689721i
\(525\) −19.6914 0.343674i −0.859402 0.0149992i
\(526\) 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
\(530\) −35.0258 1.51946i −1.52142 0.0660013i
\(531\) −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
\(540\) −19.7240 + 12.2868i −0.848784 + 0.528740i
\(541\) 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 \(0.252470\pi\)
−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
\(550\) 28.3325 8.95059i 1.20810 0.381655i
\(551\) −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
\(555\) 28.0707 + 10.7843i 1.19153 + 0.457766i
\(556\) 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 \(-0.540665\pi\)
−0.127405 + 0.991851i \(0.540665\pi\)
\(564\) 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 \(-0.0632916\pi\)
\(570\) −18.2098 + 19.1785i −0.762725 + 0.803298i
\(571\) −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
\(580\) −7.05551 3.28764i −0.292964 0.136512i
\(581\) −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
\(585\) 10.1125 + 19.0572i 0.418102 + 0.787919i
\(586\) −21.3137 8.82843i −0.880461 0.364699i
\(587\) 12.1689 0.502266 0.251133 0.967953i \(-0.419197\pi\)
0.251133 + 0.967953i \(0.419197\pi\)
\(588\) −0.438312 6.31867i −0.0180757 0.260578i
\(589\) 32.9706i 1.35853i
\(590\) −13.2754 0.575904i −0.546541 0.0237096i
\(591\) 9.12496 10.4853i 0.375351 0.431307i
\(592\) 31.0572i 1.27644i
\(593\) −39.3826 −1.61725 −0.808625 0.588325i \(-0.799788\pi\)
−0.808625 + 0.588325i \(0.799788\pi\)
\(594\) 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 \(0.288897\pi\)
\(600\) −22.7905 + 8.97746i −0.930417 + 0.366503i
\(601\) 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 \(-0.753424\pi\)
−0.714671 + 0.699461i \(0.753424\pi\)
\(608\) 25.2346 + 10.4525i 1.02340 + 0.423905i
\(609\) −5.17157 4.50063i −0.209563 0.182375i
\(610\) 26.8076 + 1.16295i 1.08541 + 0.0470863i
\(611\) 3.48106i 0.140828i
\(612\) −5.53547 + 7.32884i −0.223758 + 0.296251i
\(613\) 16.0804 0.649480 0.324740 0.945803i \(-0.394723\pi\)
0.324740 + 0.945803i \(0.394723\pi\)
\(614\) 23.2603 + 9.63475i 0.938711 + 0.388827i
\(615\) 3.41888 8.89912i 0.137863 0.358847i
\(616\) −10.3431 24.9706i −0.416737 1.00609i
\(617\) −31.0949 −1.25183 −0.625916 0.779890i \(-0.715275\pi\)
−0.625916 + 0.779890i \(0.715275\pi\)
\(618\) 19.0906 9.50495i 0.767935 0.382345i
\(619\) 14.4853 0.582213 0.291106 0.956691i \(-0.405977\pi\)
0.291106 + 0.956691i \(0.405977\pi\)
\(620\) 12.8980 27.6801i 0.517998 1.11166i
\(621\) 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
\(630\) −21.4765 + 2.04989i −0.855644 + 0.0816694i
\(631\) 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
\(640\) 17.0964 + 18.6470i 0.675796 + 0.737089i
\(641\) 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 \(0.00937687\pi\)
−0.999566 + 0.0294540i \(0.990623\pi\)
\(644\) 3.48106 3.48106i 0.137173 0.137173i
\(645\) 12.0926 31.4762i 0.476146 1.23938i
\(646\) −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
\(650\) 6.85049 + 21.6847i 0.268698 + 0.850546i
\(651\) 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 \(-0.995530\pi\)
0.999901 0.0140421i \(-0.00446989\pi\)
\(660\) 29.7383 13.2305i 1.15756 0.514995i
\(661\) 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
\(670\) −7.18461 0.311677i −0.277566 0.0120411i
\(671\) −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
\(675\) −3.13762 25.7906i −0.120767 0.992681i
\(676\) 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
\(680\) −7.13591 + 6.54252i −0.273650 + 0.250894i
\(681\) −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 \(-0.366041\pi\)
0.408532 + 0.912744i \(0.366041\pi\)
\(684\) −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
\(690\) 4.29926 + 4.08211i 0.163670 + 0.155403i
\(691\) −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
\(700\) −22.6557 1.96937i −0.856303 0.0744351i
\(701\) −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
\(705\) −1.50339 + 3.91323i −0.0566211 + 0.147381i
\(706\) 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 \(-0.124384\pi\)
\(710\) −1.62890 + 37.5486i −0.0611317 + 1.40917i
\(711\) −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 \(0.679702\pi\)
\(720\) −23.7025 + 12.5775i −0.883339 + 0.468735i
\(721\) 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 \(-0.614022\pi\)
−0.350598 + 0.936526i \(0.614022\pi\)
\(728\) 19.1116 7.91630i 0.708325 0.293398i
\(729\) −10.8995 24.7022i −0.403685 0.914898i
\(730\) 14.3692 + 0.623354i 0.531829 + 0.0230714i
\(731\) 13.3270i 0.492916i
\(732\) 29.3234 2.03410i 1.08382 0.0751825i
\(733\) −38.8215 −1.43390 −0.716952 0.697123i \(-0.754463\pi\)
−0.716952 + 0.697123i \(0.754463\pi\)
\(734\) −13.1158 + 31.6644i −0.484113 + 1.16875i
\(735\) 6.61042 + 2.53960i 0.243829 + 0.0936747i
\(736\) 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 \(0.706350\pi\)
\(740\) 31.4738 + 14.6658i 1.15700 + 0.539125i
\(741\) 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
\(750\) 1.66420 27.3355i 0.0607679 0.998152i
\(751\) 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 \(-0.271792\pi\)
0.657078 + 0.753823i \(0.271792\pi\)
\(758\) −8.21080 + 19.8226i −0.298230 + 0.719990i
\(759\) −5.94253 5.17157i −0.215700 0.187716i
\(760\) −22.5090 + 20.6372i −0.816486 + 0.748591i
\(761\) 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
\(765\) −4.81320 9.07054i −0.174022 0.327946i
\(766\) 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 \(0.320814\pi\)
\(770\) 30.1898 + 1.30967i 1.08796 + 0.0471972i
\(771\) −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 1.28503i