Properties

Label 120.2.m.b.59.12
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 59.12
Root \(3.49930i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.9

$q$-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} +(-0.137055 - 3.15931i) q^{10} -4.20201i q^{11} +(-3.45580 + 0.239721i) q^{12} +3.21608 q^{13} +(1.23074 + 2.97127i) q^{14} +(-1.87483 - 3.38896i) q^{15} -4.00000i q^{16} +1.53073 q^{17} +(-3.65798 + 2.14923i) 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} +(-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} +(3.41323 - 4.28367i) 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} +(4.66176 + 4.27411i) q^{40} +2.46148i q^{41} +(-1.77045 + 5.28156i) q^{42} -8.70626i q^{43} +(5.94253 + 5.94253i) q^{44} +(1.40385 - 6.55967i) q^{45} +(-1.41421 + 0.585786i) q^{46} -1.08239i q^{47} +(4.54822 - 5.22625i) q^{48} -1.82843 q^{49} +(-2.13008 + 6.74261i) 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} +(7.44411 + 2.14130i) 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} +(-0.311677 - 7.18461i) q^{70} -11.8851 q^{71} +(2.13368 - 8.21264i) q^{72} +4.54822i q^{73} +(-4.20201 - 10.1445i) q^{74} +(1.34523 + 8.55514i) q^{75} +(6.82843 - 6.82843i) q^{76} -9.55582i q^{77} +(-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} +(9.33037 - 1.71585i) 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 \(-0.358596\pi\)
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 \(-0.218373\pi\)
\(12\) −3.45580 + 0.239721i −0.997603 + 0.0692015i
\(13\) 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
\(15\) −1.87483 3.38896i −0.484079 0.875024i
\(16\) 4.00000i 1.00000i
\(17\) 1.53073 0.371257 0.185629 0.982620i \(-0.440568\pi\)
0.185629 + 0.982620i \(0.440568\pi\)
\(18\) −3.65798 + 2.14923i −0.862193 + 0.506579i
\(19\) −4.82843 −1.10772 −0.553859 0.832611i \(-0.686845\pi\)
−0.553859 + 0.832611i \(0.686845\pi\)
\(20\) 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 \(0.964003\pi\)
\(24\) −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 \(0.551667\pi\)
\(30\) 3.41323 4.28367i 0.623168 0.782088i
\(31\) 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 \(-0.720329\pi\)
−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 \(0.938435\pi\)
\(42\) −1.77045 + 5.28156i −0.273187 + 0.814963i
\(43\) 8.70626i 1.32769i −0.747869 0.663846i \(-0.768923\pi\)
0.747869 0.663846i \(-0.231077\pi\)
\(44\) 5.94253 + 5.94253i 0.895871 + 0.895871i
\(45\) 1.40385 6.55967i 0.209273 0.977857i
\(46\) −1.41421 + 0.585786i −0.208514 + 0.0863695i
\(47\) 1.08239i 0.157883i −0.996879 0.0789416i \(-0.974846\pi\)
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 \(0.724499\pi\)
\(54\) −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 \(0.911810\pi\)
\(60\) 7.44411 + 2.14130i 0.961031 + 0.276440i
\(61\) 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 \(-0.955639\pi\)
0.990305 0.138913i \(-0.0443609\pi\)
\(68\) −2.16478 + 2.16478i −0.262519 + 0.262519i
\(69\) −1.23074 + 1.41421i −0.148164 + 0.170251i
\(70\) −0.311677 7.18461i −0.0372525 0.858725i
\(71\) −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 \(0.0857564\pi\)
−0.963928 + 0.266164i \(0.914244\pi\)
\(74\) −4.20201 10.1445i −0.488473 1.17928i
\(75\) 1.34523 + 8.55514i 0.155333 + 0.987862i
\(76\) 6.82843 6.82843i 0.783274 0.783274i
\(77\) 9.55582i 1.08899i
\(78\) −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 \(-0.375569\pi\)
0.381030 + 0.924563i \(0.375569\pi\)
\(84\) −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 \(-0.146943\pi\)
\(90\) 9.33037 1.71585i 0.983508 0.180867i
\(91\) 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 \(0.188218\pi\)
−0.830215 + 0.557444i \(0.811782\pi\)
\(98\) −0.989538 2.38896i −0.0999584 0.241321i
\(99\) 12.4853 1.74053i 1.25482 0.174930i
\(100\) −9.96243 + 0.865995i −0.996243 + 0.0865995i
\(101\) 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 \(-0.358892\pi\)
0.428927 + 0.903339i \(0.358892\pi\)
\(104\) −8.40401 3.48106i −0.824081 0.341346i
\(105\) −4.26357 7.70685i −0.416081 0.752112i
\(106\) −14.4853 + 6.00000i −1.40693 + 0.582772i
\(107\) 5.67459 0.548584 0.274292 0.961647i \(-0.411557\pi\)
0.274292 + 0.961647i \(0.411557\pi\)
\(108\) −2.14371 10.1688i −0.206279 0.978493i
\(109\) 16.4853i 1.57900i −0.613748 0.789502i \(-0.710339\pi\)
0.613748 0.789502i \(-0.289661\pi\)
\(110\) −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 \(-0.509494\pi\)
−0.0298232 + 0.999555i \(0.509494\pi\)
\(114\) 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
\(120\) 1.23099 + 10.8851i 0.112373 + 0.993666i
\(121\) −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 \(-0.532171\pi\)
−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 \(0.837834\pi\)
\(132\) 1.00731 + 14.5213i 0.0876750 + 1.26392i
\(133\) −10.9804 −0.952119
\(134\) 2.97127 1.23074i 0.256678 0.106320i
\(135\) 9.29291 6.97437i 0.799806 0.600258i
\(136\) −4.00000 1.65685i −0.342997 0.142074i
\(137\) 8.02509 0.685629 0.342815 0.939403i \(-0.388620\pi\)
0.342815 + 0.939403i \(0.388620\pi\)
\(138\) −2.51383 0.842671i −0.213991 0.0717329i
\(139\) −2.48528 −0.210799 −0.105399 0.994430i \(-0.533612\pi\)
−0.105399 + 0.994430i \(0.533612\pi\)
\(140\) 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 \(-0.509401\pi\)
−0.0295313 + 0.999564i \(0.509401\pi\)
\(150\) −10.4498 + 6.38763i −0.853222 + 0.521548i
\(151\) 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 \(-0.120250\pi\)
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
\(162\) −7.90113 9.97858i −0.620772 0.783992i
\(163\) 8.70626i 0.681927i 0.940077 + 0.340964i \(0.110753\pi\)
−0.940077 + 0.340964i \(0.889247\pi\)
\(164\) −3.48106 3.48106i −0.271825 0.271825i
\(165\) −14.2404 + 7.87804i −1.10861 + 0.613305i
\(166\) 3.75736 + 9.07107i 0.291628 + 0.704051i
\(167\) 5.04054i 0.390049i 0.980798 + 0.195024i \(0.0624786\pi\)
−0.980798 + 0.195024i \(0.937521\pi\)
\(168\) −4.96546 9.97306i −0.383094 0.769438i
\(169\) −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 \(0.996822\pi\)
\(174\) 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 \(-0.0927010\pi\)
\(180\) 7.29143 + 11.2621i 0.543471 + 0.839428i
\(181\) 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
\(190\) 0.661758 + 15.2545i 0.0480090 + 1.10668i
\(191\) 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 \(-0.836602\pi\)
0.871113 0.491082i \(-0.163398\pi\)
\(194\) −14.3465 + 5.94253i −1.03002 + 0.426649i
\(195\) −6.02959 10.8991i −0.431788 0.780503i
\(196\) 2.58579 2.58579i 0.184699 0.184699i
\(197\) 8.02509i 0.571764i 0.958265 + 0.285882i \(0.0922865\pi\)
−0.958265 + 0.285882i \(0.907713\pi\)
\(198\) 9.03109 + 15.3708i 0.641812 + 1.09236i
\(199\) 14.8284i 1.05116i −0.850744 0.525580i \(-0.823848\pi\)
0.850744 0.525580i \(-0.176152\pi\)
\(200\) −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
\(204\) −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
\(210\) 7.76207 9.74154i 0.535633 0.672230i
\(211\) 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
\(220\) −7.93706 17.0335i −0.535117 1.14840i
\(221\) 4.92296 0.331154
\(222\) 6.04471 18.0324i 0.405694 1.21025i
\(223\) −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
\(225\) −7.97003 + 12.7074i −0.531336 + 0.847161i
\(226\) −0.343146 0.828427i −0.0228257 0.0551062i
\(227\) −4.77791 −0.317121 −0.158561 0.987349i \(-0.550685\pi\)
−0.158561 + 0.987349i \(0.550685\pi\)
\(228\) 16.6861 1.15748i 1.10506 0.0766557i
\(229\) 3.31371i 0.218976i −0.993988 0.109488i \(-0.965079\pi\)
0.993988 0.109488i \(-0.0349211\pi\)
\(230\) 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 \(-0.870410\pi\)
−0.918265 + 0.395967i \(0.870410\pi\)
\(234\) −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 \(0.358152\pi\)
\(240\) −13.5558 + 7.49932i −0.875024 + 0.484079i
\(241\) 10.4853 0.675416 0.337708 0.941251i \(-0.390348\pi\)
0.337708 + 0.941251i \(0.390348\pi\)
\(242\) −3.60266 8.69760i −0.231588 0.559103i
\(243\) −14.1096 6.62724i −0.905129 0.425138i
\(244\) −12.0000 12.0000i −0.768221 0.768221i
\(245\) 3.84153 + 1.39942i 0.245426 + 0.0894055i
\(246\) −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
\(250\) 9.63587 12.5360i 0.609426 0.792843i
\(251\) 27.9721i 1.76559i −0.469762 0.882793i \(-0.655660\pi\)
0.469762 0.882793i \(-0.344340\pi\)
\(252\) −10.8880 8.22368i −0.685877 0.518043i
\(253\) 4.54822 0.285944
\(254\) −1.23074 2.97127i −0.0772234 0.186434i
\(255\) −2.86986 5.18759i −0.179718 0.324859i
\(256\) −16.0000 −1.00000
\(257\) −2.42742 −0.151418 −0.0757090 0.997130i \(-0.524122\pi\)
−0.0757090 + 0.997130i \(0.524122\pi\)
\(258\) 20.2201 + 6.77806i 1.25885 + 0.421983i
\(259\) −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 \(-0.323691\pi\)
\(264\) −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 \(0.575254\pi\)
\(270\) 14.1417 + 8.36727i 0.860639 + 0.509216i
\(271\) 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 \(-0.669073\pi\)
−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 \(0.943280\pi\)
\(282\) 2.51383 + 0.842671i 0.149696 + 0.0501803i
\(283\) 26.1188i 1.55260i 0.630363 + 0.776300i \(0.282906\pi\)
−0.630363 + 0.776300i \(0.717094\pi\)
\(284\) 16.8080 16.8080i 0.997373 0.997373i
\(285\) 9.05247 + 16.3633i 0.536222 + 0.969280i
\(286\) 17.6569 7.31371i 1.04407 0.432469i
\(287\) 5.59767i 0.330420i
\(288\) 8.59694 + 14.6319i 0.506579 + 0.862193i
\(289\) −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 \(0.841904\pi\)
\(294\) 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
\(300\) −14.0012 10.1964i −0.808361 0.588687i
\(301\) 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 \(0.169625\pi\)
−0.861341 + 0.508027i \(0.830375\pi\)
\(308\) 13.5140 + 13.5140i 0.770030 + 0.770030i
\(309\) 11.3753 + 9.89949i 0.647117 + 0.563163i
\(310\) −21.5731 + 0.935868i −1.22527 + 0.0531537i
\(311\) −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 \(0.245014\pi\)
−0.718096 + 0.695944i \(0.754986\pi\)
\(314\) 12.6060 + 30.4336i 0.711399 + 1.71747i
\(315\) 3.19250 14.9174i 0.179877 0.840500i
\(316\) 0.686292 + 0.686292i 0.0386069 + 0.0386069i
\(317\) 9.81845i 0.551459i −0.961235 0.275730i \(-0.911081\pi\)
0.961235 0.275730i \(-0.0889194\pi\)
\(318\) −25.7483 8.63118i −1.44389 0.484012i
\(319\) 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
\(324\) 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
\(330\) −18.0000 14.3424i −0.990868 0.789525i
\(331\) −1.51472 −0.0832565 −0.0416282 0.999133i \(-0.513255\pi\)
−0.0416282 + 0.999133i \(0.513255\pi\)
\(332\) −9.81845 + 9.81845i −0.538858 + 0.538858i
\(333\) −3.21608 23.0698i −0.176240 1.26422i
\(334\) −6.58579 + 2.72792i −0.360358 + 0.149265i
\(335\) −1.74053 + 4.77791i −0.0950952 + 0.261045i
\(336\) 10.3431 11.8851i 0.564265 0.648384i
\(337\) 19.2965i 1.05114i −0.850749 0.525572i \(-0.823851\pi\)
0.850749 0.525572i \(-0.176149\pi\)
\(338\) −1.43788 3.47135i −0.0782103 0.188816i
\(339\) −0.828427 0.720950i −0.0449940 0.0391566i
\(340\) 6.20507 2.89136i 0.336517 0.156806i
\(341\) −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
\(345\) 3.66818 2.02930i 0.197488 0.109254i
\(346\) −0.343146 + 0.142136i −0.0184476 + 0.00764126i
\(347\) −15.2304 −0.817611 −0.408806 0.912621i \(-0.634055\pi\)
−0.408806 + 0.912621i \(0.634055\pi\)
\(348\) 6.01491 0.417241i 0.322433 0.0223665i
\(349\) 13.6569i 0.731035i 0.930805 + 0.365517i \(0.119108\pi\)
−0.930805 + 0.365517i \(0.880892\pi\)
\(350\) −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 \(-0.252111\pi\)
0.702403 + 0.711780i \(0.252111\pi\)
\(354\) −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 \(0.822821\pi\)
\(360\) −10.7686 + 15.6217i −0.567553 + 0.823337i
\(361\) 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 \(-0.282019\pi\)
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
\(372\) 1.63692 + 23.5977i 0.0848702 + 1.22348i
\(373\) 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
\(375\) 3.72149 19.0040i 0.192177 0.981360i
\(376\) −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 \(0.372594\pi\)
\(380\) −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 \(-0.157207\pi\)
\(384\) −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 \(0.396460\pi\)
\(390\) 10.9772 13.7766i 0.555853 0.697606i
\(391\) 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 \(-0.504408\pi\)
−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 \(-0.216746\pi\)
\(402\) 5.28156 + 1.77045i 0.263421 + 0.0883023i
\(403\) 21.9607i 1.09394i
\(404\) −19.2695 + 19.2695i −0.958694 + 0.958694i
\(405\) 20.0720 + 1.45410i 0.997386 + 0.0722546i
\(406\) −2.14214 5.17157i −0.106312 0.256661i
\(407\) 32.6256i 1.61719i
\(408\) −3.34232 6.71300i −0.165469 0.332343i
\(409\) −7.17157 −0.354611 −0.177306 0.984156i \(-0.556738\pi\)
−0.177306 + 0.984156i \(0.556738\pi\)
\(410\) 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
\(414\) −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 \(-0.0327292\pi\)
\(420\) 16.9287 + 4.86955i 0.826037 + 0.237610i
\(421\) 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
\(430\) −27.5057 + 1.19323i −1.32644 + 0.0575428i
\(431\) 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 \(-0.752742\pi\)
0.713173 0.700988i \(-0.247258\pi\)
\(434\) 20.2891 8.40401i 0.973907 0.403405i
\(435\) 3.26319 + 5.89857i 0.156458 + 0.282815i
\(436\) 23.3137 + 23.3137i 1.11652 + 1.11652i
\(437\) 5.22625i 0.250006i
\(438\) −10.5631 3.54091i −0.504726 0.169191i
\(439\) 11.5147i 0.549568i 0.961506 + 0.274784i \(0.0886063\pi\)
−0.961506 + 0.274784i \(0.911394\pi\)
\(440\) 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 \(-0.0888737\pi\)
0.961275 + 0.275591i \(0.0888737\pi\)
\(444\) 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 \(-0.198886\pi\)
\(450\) −20.9164 3.53614i −0.986008 0.166695i
\(451\) 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 \(0.0972815\pi\)
−0.953661 + 0.300883i \(0.902719\pi\)
\(458\) 4.32957 1.79337i 0.202307 0.0837985i
\(459\) −4.34315 + 6.66348i −0.202721 + 0.311025i
\(460\) 2.04450 + 4.38765i 0.0953255 + 0.204575i
\(461\) −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 \(-0.536608\pi\)
−0.114753 + 0.993394i \(0.536608\pi\)
\(464\) 6.96211i 0.323208i
\(465\) −23.1412 + 12.8021i −1.07315 + 0.593685i
\(466\) −15.1716 36.6274i −0.702810 1.69673i
\(467\) −8.73606 −0.404257 −0.202128 0.979359i \(-0.564786\pi\)
−0.202128 + 0.979359i \(0.564786\pi\)
\(468\) −15.3979 11.6300i −0.711768 0.537599i
\(469\) 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
\(474\) 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 \(0.385825\pi\)
\(480\) −17.1347 13.6529i −0.782088 0.623168i
\(481\) −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 \(-0.352833\pi\)
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 \(0.897329\pi\)
\(492\) −0.590068 8.50637i −0.0266023 0.383497i
\(493\) −2.66428 −0.119993
\(494\) −8.40401 20.2891i −0.378114 0.912849i
\(495\) −27.5638 5.89897i −1.23890 0.265139i
\(496\) −27.3137 −1.22642
\(497\) −27.0279 −1.21237
\(498\) −5.40507 + 16.1242i −0.242207 + 0.722545i
\(499\) 25.1127 1.12420 0.562099 0.827070i \(-0.309994\pi\)
0.562099 + 0.827070i \(0.309994\pi\)
\(500\) 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 \(0.781013\pi\)
\(504\) 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 \(0.402355\pi\)
\(510\) 5.22475 6.55716i 0.231356 0.290356i
\(511\) 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
\(520\) 14.9926 + 13.7459i 0.657468 + 0.602796i
\(521\) 9.84591i 0.431357i −0.976464 0.215679i \(-0.930804\pi\)
0.976464 0.215679i \(-0.0691964\pi\)
\(522\) 6.36681 3.74080i 0.278668 0.163730i
\(523\) 4.15804i 0.181819i −0.995859 0.0909093i \(-0.971023\pi\)
0.995859 0.0909093i \(-0.0289773\pi\)
\(524\) −15.7884 15.7884i −0.689721 0.689721i
\(525\) 3.05919 + 19.4553i 0.133514 + 0.849100i
\(526\) 36.0416 14.9289i 1.57149 0.650932i
\(527\) 10.4525i 0.455318i
\(528\) −21.9607 19.1116i −0.955719 0.831727i
\(529\) 21.8284 0.949062
\(530\) 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
\(534\) 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
\(540\) −3.27891 + 23.0054i −0.141102 + 0.989995i
\(541\) 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 \(-0.747530\pi\)
0.701600 0.712571i \(-0.252470\pi\)
\(548\) −11.3492 + 11.3492i −0.484813 + 0.484813i
\(549\) −25.2120 + 3.51472i −1.07602 + 0.150005i
\(550\) 28.3325 + 8.95059i 1.20810 + 0.381655i
\(551\) 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
\(555\) 14.5567 + 26.3128i 0.617898 + 1.11692i
\(556\) 3.51472 3.51472i 0.149057 0.149057i
\(557\) 19.3743i 0.820914i 0.911880 + 0.410457i \(0.134631\pi\)
−0.911880 + 0.410457i \(0.865369\pi\)
\(558\) 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 \(-0.459335\pi\)
0.127405 + 0.991851i \(0.459335\pi\)
\(564\) 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 \(-0.0632916\pi\)
\(570\) −16.4805 + 20.6834i −0.690294 + 0.866332i
\(571\) −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 \(0.104769\pi\)
−0.946320 + 0.323232i \(0.895231\pi\)
\(578\) −7.93223 19.1501i −0.329937 0.796539i
\(579\) 15.5147 17.8276i 0.644770 0.740890i
\(580\) −7.05551 + 3.28764i −0.292964 + 0.136512i
\(581\) 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
\(585\) 4.51487 21.0964i 0.186667 0.872228i
\(586\) −21.3137 + 8.82843i −0.880461 + 0.364699i
\(587\) −12.1689 −0.502266 −0.251133 0.967953i \(-0.580803\pi\)
−0.251133 + 0.967953i \(0.580803\pi\)
\(588\) 6.31867 0.438312i 0.260578 0.0180757i
\(589\) 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 \(-0.200212\pi\)
0.808625 + 0.588325i \(0.200212\pi\)
\(594\) −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 \(0.711103\pi\)
\(600\) 5.74477 23.8117i 0.234529 0.972109i
\(601\) 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 \(-0.753424\pi\)
−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
\(612\) −7.32884 5.53547i −0.296251 0.223758i
\(613\) 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
\(615\) 8.34184 4.61485i 0.336375 0.186089i
\(616\) −10.3431 + 24.9706i −0.416737 + 1.00609i
\(617\) 31.0949 1.25183 0.625916 0.779890i \(-0.284725\pi\)
0.625916 + 0.779890i \(0.284725\pi\)
\(618\) −6.77806 + 20.2201i −0.272653 + 0.813371i
\(619\) 14.4853 0.582213 0.291106 0.956691i \(-0.405977\pi\)
0.291106 + 0.956691i \(0.405977\pi\)
\(620\) −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
\(630\) 21.2183 3.90204i 0.845357 0.155461i
\(631\) 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
\(640\) 17.0964 18.6470i 0.675796 0.737089i
\(641\) 24.7897i 0.979135i 0.871965 + 0.489567i \(0.162845\pi\)
−0.871965 + 0.489567i \(0.837155\pi\)
\(642\) −4.41782 + 13.1791i −0.174358 + 0.520138i
\(643\) 1.49376i 0.0589081i −0.999566 0.0294540i \(-0.990623\pi\)
0.999566 0.0294540i \(-0.00937687\pi\)
\(644\) −3.48106 3.48106i −0.137173 0.137173i
\(645\) −29.5051 + 16.3227i −1.16176 + 0.642708i
\(646\) −4.00000 9.65685i −0.157378 0.379944i
\(647\) 42.3671i 1.66562i −0.553556 0.832812i \(-0.686729\pi\)
0.553556 0.832812i \(-0.313271\pi\)
\(648\) 25.2857 + 2.93796i 0.993317 + 0.115414i
\(649\) 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 \(0.736952\pi\)
\(654\) 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 \(-0.00446989\pi\)
\(660\) 8.99775 31.2802i 0.350237 1.21758i
\(661\) 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
\(670\) −7.18461 + 0.311677i −0.277566 + 0.0120411i
\(671\) 35.6552 1.37645
\(672\) 21.1263 + 7.08182i 0.814963 + 0.273187i
\(673\) 5.65180i 0.217861i 0.994049 + 0.108930i \(0.0347426\pi\)
−0.994049 + 0.108930i \(0.965257\pi\)
\(674\) 25.2120 10.4432i 0.971131 0.402256i
\(675\) −24.8624 + 7.54068i −0.956954 + 0.290241i
\(676\) 3.75736 3.75736i 0.144514 0.144514i
\(677\) 39.3826i 1.51360i −0.653649 0.756798i \(-0.726763\pi\)
0.653649 0.756798i \(-0.273237\pi\)
\(678\) 0.493625 1.47257i 0.0189576 0.0565536i
\(679\) 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 \(-0.633959\pi\)
−0.408532 + 0.912744i \(0.633959\pi\)
\(684\) 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
\(690\) 4.63661 + 3.69446i 0.176513 + 0.140646i
\(691\) −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
\(700\) −22.6557 + 1.96937i −0.856303 + 0.0744351i
\(701\) 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
\(705\) −3.66818 + 2.02930i −0.138152 + 0.0764279i
\(706\) 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 \(0.875616\pi\)
\(710\) 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
\(714\) −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 \(0.320298\pi\)
\(720\) −26.2387 5.61538i −0.977857 0.209273i
\(721\) 19.7990 0.737353
\(722\) 2.33456 + 5.63613i 0.0868834 + 0.209755i
\(723\) 13.6997 + 11.9223i 0.509497 + 0.443397i
\(724\) −30.6274 30.6274i −1.13826 1.13826i
\(725\) −6.66348 5.59767i −0.247476 0.207892i
\(726\) 5.18254 15.4604i 0.192342 0.573789i
\(727\) −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
\(732\) −2.03410 29.3234i −0.0751825 1.08382i
\(733\) −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
\(735\) 3.42799 + 6.19646i 0.126443 + 0.228560i
\(736\) 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 \(0.706350\pi\)
\(740\) −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 \(-0.00108433\pi\)
\(744\) −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
\(750\) 26.8439 5.42250i 0.980202 0.198002i
\(751\) 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 \(-0.271792\pi\)
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 \(0.971560\pi\)
\(762\) 1.77045 5.28156i 0.0641368 0.191331i
\(763\) 37.4893i 1.35720i
\(764\) −11.8851 + 11.8851i −0.429987 + 0.429987i
\(765\) 2.14891 10.0411i 0.0776941 0.363037i
\(766\) 24.2426 10.0416i 0.875922 0.362819i
\(767\) 13.5140i 0.487961i
\(768\) −20.9050 18.1929i −0.754344 0.656479i
\(769\) 29.5980 1.06733 0.533665 0.845696i \(-0.320814\pi\)
0.533665 + 0.845696i \(0.320814\pi\)
\(770\) −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 \(-0.240391\pi\)
\(774\) 18.7118 + 31.8473i 0.672582 </