Properties

Label 120.2.m.b.59.5
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 59.5
Root \(0.886177i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.541196 - 1.30656i) q^{2} +(-1.30656 - 1.13705i) q^{3} +(-1.41421 + 1.41421i) q^{4} +(-2.10100 + 0.765367i) q^{5} +(-0.778527 + 2.32248i) q^{6} -2.27411 q^{7} +(2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +O(q^{10})\) \(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} +(-0.778527 + 2.32248i) 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} +(3.45580 - 0.239721i) 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} +(3.65798 - 2.14923i) 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} +(-2.18347 - 4.38548i) 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} +(-0.141860 - 5.47539i) 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} +(-4.78779 - 3.61622i) 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} +(1.77045 - 5.28156i) 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} +(-6.27394 - 3.26155i) q^{50} +(2.00000 + 1.74053i) q^{51} +(4.54822 - 4.54822i) q^{52} -11.0866i q^{53} +(-7.22317 - 1.35121i) 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} +(-7.07717 + 3.14861i) 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} +(9.75906 + 3.27137i) 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} +(-2.13368 + 8.21264i) 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} +(2.50380 - 7.46926i) 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} +(-7.85886 + 0.545152i) 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} +(-6.04047 + 7.31524i) 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} +(9.28991 + 3.11411i) 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
\(6\) −0.778527 + 2.32248i −0.317832 + 0.948147i
\(7\) −2.27411 −0.859533 −0.429766 0.902940i \(-0.641404\pi\)
−0.429766 + 0.902940i \(0.641404\pi\)
\(8\) 2.61313 + 1.08239i 0.923880 + 0.382683i
\(9\) 0.414214 + 2.97127i 0.138071 + 0.990422i
\(10\) 2.13705 + 2.33088i 0.675796 + 0.737089i
\(11\) 4.20201i 1.26695i −0.773762 0.633476i \(-0.781627\pi\)
0.773762 0.633476i \(-0.218373\pi\)
\(12\) 3.45580 0.239721i 0.997603 0.0692015i
\(13\) −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
\(15\) 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 \(0.559432\pi\)
\(18\) 3.65798 2.14923i 0.862193 0.506579i
\(19\) −4.82843 −1.10772 −0.553859 0.832611i \(-0.686845\pi\)
−0.553859 + 0.832611i \(0.686845\pi\)
\(20\) 1.88887 4.05366i 0.422365 0.906426i
\(21\) 2.97127 + 2.58579i 0.648384 + 0.564265i
\(22\) −5.49019 + 2.27411i −1.17051 + 0.484842i
\(23\) 1.08239i 0.225694i −0.993612 0.112847i \(-0.964003\pi\)
0.993612 0.112847i \(-0.0359971\pi\)
\(24\) −2.18347 4.38548i −0.445700 0.895182i
\(25\) 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 \(-0.551667\pi\)
−0.161604 + 0.986856i \(0.551667\pi\)
\(30\) −0.141860 5.47539i −0.0258999 0.999665i
\(31\) 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
\(36\) −4.78779 3.61622i −0.797965 0.602703i
\(37\) 7.76429 1.27644 0.638221 0.769853i \(-0.279671\pi\)
0.638221 + 0.769853i \(0.279671\pi\)
\(38\) 2.61313 + 6.30864i 0.423905 + 1.02340i
\(39\) 4.20201 + 3.65685i 0.672859 + 0.585565i
\(40\) −6.31861 0.274109i −0.999060 0.0433405i
\(41\) 2.46148i 0.384418i 0.981354 + 0.192209i \(0.0615652\pi\)
−0.981354 + 0.192209i \(0.938435\pi\)
\(42\) 1.77045 5.28156i 0.273187 0.814963i
\(43\) 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 \(0.0251541\pi\)
−0.996879 + 0.0789416i \(0.974846\pi\)
\(48\) −4.54822 + 5.22625i −0.656479 + 0.754344i
\(49\) −1.82843 −0.261204
\(50\) −6.27394 3.26155i −0.887269 0.461253i
\(51\) 2.00000 + 1.74053i 0.280056 + 0.243723i
\(52\) 4.54822 4.54822i 0.630724 0.630724i
\(53\) 11.0866i 1.52286i −0.648250 0.761428i \(-0.724499\pi\)
0.648250 0.761428i \(-0.275501\pi\)
\(54\) −7.22317 1.35121i −0.982949 0.183876i
\(55\) 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 \(0.911810\pi\)
\(60\) −7.07717 + 3.14861i −0.913658 + 0.406483i
\(61\) 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
\(66\) 9.75906 + 3.27137i 1.20126 + 0.402678i
\(67\) 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 \(-0.749165\pi\)
−0.705249 + 0.708960i \(0.749165\pi\)
\(72\) −2.13368 + 8.21264i −0.251457 + 0.967868i
\(73\) 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
\(78\) 2.50380 7.46926i 0.283500 0.845727i
\(79\) 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 \(-0.624431\pi\)
−0.381030 + 0.924563i \(0.624431\pi\)
\(84\) −7.85886 + 0.545152i −0.857472 + 0.0594809i
\(85\) 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 \(-0.146943\pi\)
\(90\) −6.04047 + 7.31524i −0.636721 + 0.771094i
\(91\) 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
\(96\) 9.28991 + 3.11411i 0.948147 + 0.317832i
\(97\) 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 \(-0.262891\pi\)
0.677899 + 0.735155i \(0.262891\pi\)
\(102\) 1.19172 3.55509i 0.117998 0.352007i
\(103\) −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
\(105\) −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 \(0.588443\pi\)
\(108\) 2.14371 + 10.1688i 0.206279 + 0.978493i
\(109\) 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 \(-0.490506\pi\)
0.0298232 + 0.999555i \(0.490506\pi\)
\(114\) 3.75906 11.2139i 0.352068 1.05028i
\(115\) 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
\(120\) 7.94399 + 7.54275i 0.725184 + 0.688556i
\(121\) −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
\(126\) −8.31864 + 4.88759i −0.741083 + 0.435421i
\(127\) 2.27411 0.201795 0.100897 0.994897i \(-0.467829\pi\)
0.100897 + 0.994897i \(0.467829\pi\)
\(128\) 4.32957 10.4525i 0.382683 0.923880i
\(129\) 9.89949 11.3753i 0.871602 1.00154i
\(130\) −6.87293 7.49628i −0.602796 0.657468i
\(131\) 11.1641i 0.975413i 0.873008 + 0.487707i \(0.162166\pi\)
−0.873008 + 0.487707i \(0.837834\pi\)
\(132\) −1.00731 14.5213i −0.0876750 1.26392i
\(133\) 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 \(0.611380\pi\)
\(138\) 2.51383 + 0.842671i 0.213991 + 0.0717329i
\(139\) −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 \(-0.509401\pi\)
−0.0295313 + 0.999564i \(0.509401\pi\)
\(150\) 4.48873 + 11.3952i 0.366503 + 0.930417i
\(151\) 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
\(156\) −11.1141 + 0.770961i −0.889841 + 0.0617263i
\(157\) −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
\(162\) 7.90113 + 9.97858i 0.620772 + 0.783992i
\(163\) 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 \(-0.937521\pi\)
0.980798 0.195024i \(-0.0624786\pi\)
\(168\) 4.96546 + 9.97306i 0.383094 + 0.769438i
\(169\) −2.65685 −0.204373
\(170\) −3.27126 3.56796i −0.250894 0.273650i
\(171\) −2.00000 14.3465i −0.152944 1.09711i
\(172\) −12.3125 12.3125i −0.938820 0.938820i
\(173\) 0.262632i 0.0199676i −0.999950 0.00998379i \(-0.996822\pi\)
0.999950 0.00998379i \(-0.00317799\pi\)
\(174\) 1.35505 4.04233i 0.102726 0.306449i
\(175\) −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 \(-0.0927010\pi\)
\(180\) 12.8269 + 3.93327i 0.956061 + 0.293169i
\(181\) 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
\(186\) 15.8589 + 5.31611i 1.16283 + 0.389796i
\(187\) 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 \(-0.401662\pi\)
0.304046 + 0.952657i \(0.401662\pi\)
\(192\) −0.958884 13.8232i −0.0692015 0.997603i
\(193\) 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 \(-0.907713\pi\)
0.958265 0.285882i \(-0.0922865\pi\)
\(198\) −9.03109 15.3708i −0.641812 1.09236i
\(199\) 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
\(204\) −5.28991 + 0.366949i −0.370367 + 0.0256916i
\(205\) −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
\(210\) 0.322604 + 12.4516i 0.0222618 + 0.859244i
\(211\) 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
\(216\) 12.1260 8.30421i 0.825070 0.565030i
\(217\) 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
\(222\) −6.04471 + 18.0324i −0.405694 + 1.21025i
\(223\) 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
\(225\) 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 \(0.449315\pi\)
\(228\) −16.6861 + 1.15748i −1.10506 + 0.0766557i
\(229\) 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 \(-0.129590\pi\)
0.918265 + 0.395967i \(0.129590\pi\)
\(234\) −11.7643 + 6.91210i −0.769058 + 0.451858i
\(235\) −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 \(-0.358152\pi\)
0.431025 + 0.902340i \(0.358152\pi\)
\(240\) 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
\(246\) −5.71672 1.91633i −0.364485 0.122181i
\(247\) 15.5286 0.988060
\(248\) 7.39104 17.8435i 0.469331 1.13307i
\(249\) 9.07107 + 7.89422i 0.574856 + 0.500276i
\(250\) 15.6778 + 2.05067i 0.991554 + 0.129696i
\(251\) 27.9721i 1.76559i −0.469762 0.882793i \(-0.655660\pi\)
0.469762 0.882793i \(-0.344340\pi\)
\(252\) 10.8880 + 8.22368i 0.685877 + 0.518043i
\(253\) −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 \(0.475878\pi\)
\(258\) −20.2201 6.77806i −1.25885 0.421983i
\(259\) −17.6569 −1.09714
\(260\) −6.07476 + 13.0369i −0.376741 + 0.808513i
\(261\) −0.720950 5.17157i −0.0446257 0.320112i
\(262\) 14.5866 6.04198i 0.901165 0.373275i
\(263\) 27.5851i 1.70097i 0.526001 + 0.850484i \(0.323691\pi\)
−0.526001 + 0.850484i \(0.676309\pi\)
\(264\) −18.4278 + 9.17497i −1.13415 + 0.564681i
\(265\) 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 \(-0.575254\pi\)
−0.234222 + 0.972183i \(0.575254\pi\)
\(270\) 16.2101 2.68948i 0.986514 0.163677i
\(271\) 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
\(276\) −0.259472 3.74053i −0.0156184 0.225153i
\(277\) 16.8607 1.01306 0.506532 0.862221i \(-0.330927\pi\)
0.506532 + 0.862221i \(0.330927\pi\)
\(278\) 1.34502 + 3.24718i 0.0806692 + 0.194753i
\(279\) 20.2891 2.82843i 1.21468 0.169334i
\(280\) 14.3692 + 0.623354i 0.858725 + 0.0372525i
\(281\) 5.94253i 0.354502i 0.984166 + 0.177251i \(0.0567204\pi\)
−0.984166 + 0.177251i \(0.943280\pi\)
\(282\) −2.51383 0.842671i −0.149696 0.0501803i
\(283\) 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
\(288\) −8.59694 14.6319i −0.506579 0.862193i
\(289\) −14.6569 −0.862168
\(290\) −3.71960 4.05696i −0.218423 0.238233i
\(291\) −12.4853 + 14.3465i −0.731900 + 0.841009i
\(292\) 6.43215 + 6.43215i 0.376413 + 0.376413i
\(293\) 16.3128i 0.953004i −0.879173 0.476502i \(-0.841904\pi\)
0.879173 0.476502i \(-0.158096\pi\)
\(294\) 1.42348 4.24648i 0.0830190 0.247660i
\(295\) −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
\(300\) 12.4593 12.0319i 0.719338 0.694660i
\(301\) 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
\(306\) −5.59939 + 3.28991i −0.320096 + 0.188071i
\(307\) 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 \(-0.590054\pi\)
−0.279155 + 0.960246i \(0.590054\pi\)
\(312\) 7.02222 + 14.1040i 0.397555 + 0.798484i
\(313\) 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 \(0.0889194\pi\)
−0.961235 + 0.275730i \(0.911081\pi\)
\(318\) 25.7483 + 8.63118i 1.44389 + 0.484012i
\(319\) 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
\(324\) 8.76158 15.7237i 0.486755 0.873539i
\(325\) −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
\(330\) −23.0076 + 0.596095i −1.26653 + 0.0328139i
\(331\) −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
\(342\) −17.6623 + 10.3774i −0.955066 + 0.561147i
\(343\) 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 \(0.365945\pi\)
\(348\) −6.01491 + 0.417241i −0.322433 + 0.0223665i
\(349\) 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 \(-0.747889\pi\)
−0.702403 + 0.711780i \(0.747889\pi\)
\(354\) −9.75906 3.27137i −0.518688 0.173872i
\(355\) 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 \(-0.822821\pi\)
−0.849043 + 0.528323i \(0.822821\pi\)
\(360\) −1.80280 18.8878i −0.0950161 0.995476i
\(361\) 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
\(366\) −19.7069 6.60602i −1.03009 0.345302i
\(367\) −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
\(372\) −1.63692 23.5977i −0.0848702 1.22348i
\(373\) −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
\(375\) 18.3081 6.30975i 0.945427 0.325834i
\(376\) −1.17157 + 2.82843i −0.0604193 + 0.145865i
\(377\) 5.59767 0.288295
\(378\) 16.4263 + 3.07280i 0.844877 + 0.158048i
\(379\) 15.1716 0.779311 0.389656 0.920961i \(-0.372594\pi\)
0.389656 + 0.920961i \(0.372594\pi\)
\(380\) −9.12029 + 19.5728i −0.467861 + 1.00406i
\(381\) −2.97127 2.58579i −0.152223 0.132474i
\(382\) −4.54822 10.9804i −0.232707 0.561805i
\(383\) 18.5545i 0.948091i 0.880500 + 0.474046i \(0.157207\pi\)
−0.880500 + 0.474046i \(0.842793\pi\)
\(384\) −17.5419 + 8.73390i −0.895182 + 0.445700i
\(385\) −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 \(-0.396460\pi\)
0.319575 + 0.947561i \(0.396460\pi\)
\(390\) 0.456231 + 17.6093i 0.0231022 + 0.891680i
\(391\) 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
\(396\) −15.1954 + 20.1183i −0.763596 + 1.01098i
\(397\) 0.551791 0.0276936 0.0138468 0.999904i \(-0.495592\pi\)
0.0138468 + 0.999904i \(0.495592\pi\)
\(398\) −19.3743 + 8.02509i −0.971145 + 0.402261i
\(399\) −14.3465 12.4853i −0.718226 0.625046i
\(400\) −12.8643 15.3137i −0.643215 0.765685i
\(401\) 25.2120i 1.25903i −0.776989 0.629514i \(-0.783254\pi\)
0.776989 0.629514i \(-0.216746\pi\)
\(402\) −5.28156 1.77045i −0.263421 0.0883023i
\(403\) 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
\(408\) 3.34232 + 6.71300i 0.165469 + 0.332343i
\(409\) −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
\(414\) −2.32631 3.95937i −0.114332 0.194592i
\(415\) 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 \(-0.0327292\pi\)
\(420\) 16.0942 7.16028i 0.785319 0.349386i
\(421\) 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
\(426\) 9.25284 27.6028i 0.448302 1.33736i
\(427\) 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 \(-0.324674\pi\)
0.523372 + 0.852104i \(0.324674\pi\)
\(432\) −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
\(438\) 10.5631 + 3.54091i 0.504726 + 0.169191i
\(439\) 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 \(-0.911126\pi\)
−0.961275 + 0.275591i \(0.911126\pi\)
\(444\) 26.8318 1.86126i 1.27338 0.0883317i
\(445\) 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 \(-0.198886\pi\)
\(450\) 7.09220 19.9925i 0.334329 0.942456i
\(451\) 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
\(456\) 10.5427 + 21.1750i 0.493709 + 0.991609i
\(457\) 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 \(-0.642173\pi\)
−0.431946 + 0.901899i \(0.642173\pi\)
\(462\) −22.1932 7.43946i −1.03252 0.346115i
\(463\) 4.93839 0.229507 0.114753 0.993394i \(-0.463392\pi\)
0.114753 + 0.993394i \(0.463392\pi\)
\(464\) 6.96211i 0.323208i
\(465\) 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 \(0.435214\pi\)
\(468\) 15.3979 + 11.6300i 0.711768 + 0.537599i
\(469\) 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
\(474\) 1.12705 + 0.377804i 0.0517673 + 0.0173531i
\(475\) −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 \(-0.385825\pi\)
0.351048 + 0.936357i \(0.385825\pi\)
\(480\) −21.9016 + 0.567438i −0.999665 + 0.0258999i
\(481\) −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
\(486\) 1.02287 22.0217i 0.0463982 0.998923i
\(487\) −19.6866 −0.892086 −0.446043 0.895011i \(-0.647167\pi\)
−0.446043 + 0.895011i \(0.647167\pi\)
\(488\) −9.18440 + 22.1731i −0.415758 + 1.00373i
\(489\) −9.89949 + 11.3753i −0.447671 + 0.514408i
\(490\) −3.90745 4.26184i −0.176521 0.192530i
\(491\) 14.0479i 0.633974i 0.948430 + 0.316987i \(0.102671\pi\)
−0.948430 + 0.316987i \(0.897329\pi\)
\(492\) 0.590068 + 8.50637i 0.0266023 + 0.383497i
\(493\) 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
\(498\) 5.40507 16.1242i 0.242207 0.722545i
\(499\) 25.1127 1.12420 0.562099 0.827070i \(-0.309994\pi\)
0.562099 + 0.827070i \(0.309994\pi\)
\(500\) −5.80546 21.5939i −0.259628 0.965709i
\(501\) −5.73137 + 6.58579i −0.256059 + 0.294231i
\(502\) −36.5474 + 15.1384i −1.63119 + 0.675660i
\(503\) 28.4818i 1.26994i −0.772537 0.634969i \(-0.781013\pi\)
0.772537 0.634969i \(-0.218987\pi\)
\(504\) 4.85223 18.6764i 0.216136 0.831914i
\(505\) −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 \(-0.402355\pi\)
0.301972 + 0.953317i \(0.402355\pi\)
\(510\) 0.217149 + 8.38136i 0.00961553 + 0.371133i
\(511\) 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
\(516\) 2.08707 + 30.0871i 0.0918783 + 1.32451i
\(517\) 4.54822 0.200030
\(518\) 9.55582 + 23.0698i 0.419859 + 1.01363i
\(519\) −0.298627 + 0.343146i −0.0131083 + 0.0150624i
\(520\) 20.3211 + 0.881556i 0.891141 + 0.0386588i
\(521\) 9.84591i 0.431357i −0.976464 0.215679i \(-0.930804\pi\)
0.976464 0.215679i \(-0.0691964\pi\)
\(522\) −6.36681 + 3.74080i −0.278668 + 0.163730i
\(523\) 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
\(530\) 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
\(534\) 19.5181 + 6.54275i 0.844632 + 0.283132i
\(535\) 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
\(540\) −12.2868 19.7240i −0.528740 0.848784i
\(541\) 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
\(546\) −5.69392 + 16.9859i −0.243677 + 0.726930i
\(547\) 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
\(552\) −4.74681 + 2.36338i −0.202038 + 0.100592i
\(553\) 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 \(-0.865369\pi\)
0.911880 0.410457i \(-0.134631\pi\)
\(558\) −14.6759 24.9782i −0.621280 1.05741i
\(559\) 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 \(0.540665\pi\)
\(564\) 0.259472 + 3.74053i 0.0109257 + 0.157505i
\(565\) −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 \(-0.0632916\pi\)
\(570\) 0.684958 + 26.4375i 0.0286898 + 1.10735i
\(571\) −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
\(576\) −14.4649 + 19.1512i −0.602703 + 0.797965i
\(577\) 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
\(582\) 25.5017 + 8.54851i 1.05708 + 0.354347i
\(583\) −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 \(0.419197\pi\)
\(588\) −6.31867 + 0.438312i −0.260578 + 0.0180757i
\(589\) 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 \(-0.799788\pi\)
−0.808625 + 0.588325i \(0.799788\pi\)
\(594\) −5.67779 + 30.3518i −0.232963 + 1.24535i
\(595\) −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 \(-0.711103\pi\)
−0.615641 + 0.788027i \(0.711103\pi\)
\(600\) −22.4633 9.76727i −0.917061 0.398747i
\(601\) 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
\(606\) −10.6079 + 31.6451i −0.430916 + 1.28550i
\(607\) 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
\(612\) 7.32884 + 5.53547i 0.296251 + 0.223758i
\(613\) −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
\(615\) −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 \(0.715275\pi\)
\(618\) 6.77806 20.2201i 0.272653 0.813371i
\(619\) 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
\(630\) 13.7367 16.6357i 0.547283 0.662780i
\(631\) 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
\(636\) −2.65768 38.3129i −0.105384 1.51920i
\(637\) 5.88036 0.232988
\(638\) 9.55582 3.95815i 0.378319 0.156705i
\(639\) −4.92296 35.3137i −0.194749 1.39699i
\(640\) −1.09644 + 25.2745i −0.0433405 + 0.999060i
\(641\) 24.7897i 0.979135i 0.871965 + 0.489567i \(0.162845\pi\)
−0.871965 + 0.489567i \(0.837155\pi\)
\(642\) 4.41782 13.1791i 0.174358 0.520138i
\(643\) 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 \(0.313271\pi\)
−0.553556 + 0.832812i \(0.686729\pi\)
\(648\) −25.2857 2.93796i −0.993317 0.115414i
\(649\) 17.6569 0.693092
\(650\) 20.1775 + 10.4894i 0.791425 + 0.411428i
\(651\) 17.6569 20.2891i 0.692027 0.795192i
\(652\) 12.3125 + 12.3125i 0.482195 + 0.482195i
\(653\) 37.5892i 1.47098i −0.677535 0.735490i \(-0.736952\pi\)
0.677535 0.735490i \(-0.263048\pi\)
\(654\) 38.2867 + 12.8342i 1.49713 + 0.501858i
\(655\) −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 \(-0.00446989\pi\)
\(660\) 13.2305 + 29.7383i 0.514995 + 1.15756i
\(661\) 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
\(666\) 28.4016 16.6873i 1.10054 0.646619i
\(667\) 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
\(672\) −21.1263 7.08182i −0.814963 0.273187i
\(673\) 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 \(0.273237\pi\)
−0.653649 + 0.756798i \(0.726763\pi\)
\(678\) −0.493625 + 1.47257i −0.0189576 + 0.0565536i
\(679\) 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 \(-0.366041\pi\)
0.408532 + 0.912744i \(0.366041\pi\)
\(684\) 23.1175 + 17.4607i 0.883920 + 0.667625i
\(685\) 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
\(690\) −5.92652 + 0.153548i −0.225619 + 0.00584546i
\(691\) −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
\(696\) 3.80040 + 7.63305i 0.144054 + 0.289330i
\(697\) 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 \(-0.483401\pi\)
0.0521239 + 0.998641i \(0.483401\pi\)
\(702\) 23.2303 + 4.34559i 0.876770 + 0.164014i
\(703\) −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
\(708\) 1.00731 + 14.5213i 0.0378570 + 0.545743i
\(709\) 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
\(714\) −2.71009 + 8.08467i −0.101423 + 0.302561i
\(715\) −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 \(-0.320298\pi\)
0.535036 + 0.844829i \(0.320298\pi\)
\(720\) −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
\(726\) 5.18254 15.4604i 0.192342 0.573789i
\(727\) 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
\(732\) 2.03410 + 29.3234i 0.0751825 + 1.08382i
\(733\) 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
\(735\) −6.61042 2.53960i −0.243829 0.0936747i
\(736\) 2.34315 + 5.65685i 0.0863695 + 0.208514i
\(737\) 9.55582 0.351993
\(738\) 5.29029 + 9.00403i 0.194738 + 0.331443i
\(739\) −32.8284 −1.20761 −0.603807 0.797131i \(-0.706350\pi\)
−0.603807 + 0.797131i \(0.706350\pi\)
\(740\) 14.6658 31.4738i 0.539125 1.15700i
\(741\) −20.2891 17.6569i −0.745338 0.648641i
\(742\) 32.9411 13.6447i 1.20931 0.500911i
\(743\) 0.185709i 0.00681301i 0.999994 + 0.00340650i \(0.00108433\pi\)
−0.999994 + 0.00340650i \(0.998916\pi\)
\(744\) −29.9459 + 14.9097i −1.09787 + 0.546616i
\(745\) 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
\(750\) −18.1524 20.5059i −0.662831 0.748769i
\(751\) 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
\(756\) −4.87504 23.1250i −0.177303 0.841047i
\(757\) −36.1572 −1.31416 −0.657078 0.753823i \(-0.728208\pi\)
−0.657078 + 0.753823i \(0.728208\pi\)
\(758\) −8.21080 19.8226i −0.298230 0.719990i
\(759\) 5.94253 + 5.17157i 0.215700 + 0.187716i
\(760\) 30.5090 + 1.32352i 1.10668 + 0.0480090i
\(761\) 4.92296i 0.178457i 0.996011 + 0.0892285i \(0.0284401\pi\)
−0.996011 + 0.0892285i \(0.971560\pi\)
\(762\) −1.77045 + 5.28156i −0.0641368 + 0.191331i
\(763\) 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 \(0.320814\pi\)
\(770\) −22.2735 + 20.4213i −0.802680 + 0.735933i
\(771\) −3.17157 2.76011i −0.114221 0.0994028i
\(772\) −19.2965 19.2965i −0.694495 0.694495i
\(773\) 38.1145i 1.37088i 0.728128 + 0.685442i \(0.240391\pi\)
−0.728128 + 0.685442i \(0.759609\pi\)
\(774\) 18.7118 + 31.8473i 0.672582 + 1.14473i