Properties

Label 637.2.f.j.393.5
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.5
Root \(1.16700 - 2.02131i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.j.295.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.952780 + 1.65026i) q^{2} +(0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +1.47313 q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +O(q^{10})\) \(q+(0.952780 + 1.65026i) q^{2} +(0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +1.47313 q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +(1.40357 + 2.43105i) q^{10} +(2.19681 + 3.80498i) q^{11} -0.698866 q^{12} +(-2.69752 - 2.39236i) q^{13} +(0.315580 + 0.546600i) q^{15} +(2.30082 + 3.98514i) q^{16} +(-0.601356 + 1.04158i) q^{17} +5.36688 q^{18} +(1.62105 - 2.80773i) q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} +(2.21855 + 3.84264i) q^{23} +(0.150567 + 0.260790i) q^{24} -2.82989 q^{25} +(1.37787 - 6.73101i) q^{26} +2.49204 q^{27} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 + 1.04158i) q^{30} -5.24543 q^{31} +(-3.68150 + 6.37655i) q^{32} +(-0.941217 + 1.63024i) q^{33} -2.29184 q^{34} +(2.29702 + 3.97856i) q^{36} +(-3.52527 - 6.10595i) q^{37} +6.17800 q^{38} +(0.309802 - 1.51341i) q^{39} +1.03539 q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} -7.16668 q^{44} +(2.07449 - 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} -11.6836 q^{47} +(-0.985780 + 1.70742i) q^{48} +(-2.69626 - 4.67006i) q^{50} -0.515299 q^{51} +(5.57955 - 1.85943i) q^{52} -0.141786 q^{53} +(2.37436 + 4.11252i) q^{54} +(3.23618 + 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 - 0.276520i) q^{58} +(-2.67177 + 4.62764i) q^{59} -1.02952 q^{60} +(5.77287 - 9.99891i) q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(-3.97380 - 3.52425i) q^{65} -3.58709 q^{66} +(-2.06773 - 3.58141i) q^{67} +(-0.980907 - 1.69898i) q^{68} +(-0.950533 + 1.64637i) q^{69} +(4.98486 - 8.63403i) q^{71} +(0.989763 - 1.71432i) q^{72} -15.2416 q^{73} +(6.71762 - 11.6353i) q^{74} +(-0.606229 - 1.05002i) q^{75} +(2.64418 + 4.57986i) q^{76} +(2.79269 - 0.930689i) q^{78} +0.774501 q^{79} +(3.38941 + 5.87062i) q^{80} +(-3.69080 - 6.39265i) q^{81} +(-4.92006 + 8.52179i) q^{82} +16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} -0.0433522 q^{86} +(0.0358956 - 0.0621731i) q^{87} +(1.54402 + 2.67433i) q^{88} +(3.27880 + 5.67904i) q^{89} +7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +(-11.1319 - 19.2809i) q^{94} +(2.38801 - 4.13616i) q^{95} -3.15466 q^{96} +(1.74583 - 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} + 10q^{12} + 2q^{13} - 2q^{15} + 8q^{16} - 5q^{17} - 6q^{18} + q^{19} + q^{20} - 5q^{22} - q^{23} + 11q^{24} - 14q^{25} - 11q^{26} + 8q^{27} + 3q^{29} - 5q^{30} + 32q^{31} + 8q^{32} - 16q^{33} - 32q^{34} - 21q^{36} - 13q^{37} - 34q^{38} + 43q^{39} - 10q^{40} + 8q^{41} - 11q^{43} - 42q^{44} + 7q^{45} + 16q^{46} - 2q^{47} - 21q^{48} + 6q^{50} + 40q^{51} + 16q^{52} + 4q^{53} + 18q^{54} - 9q^{55} + 42q^{57} - 8q^{58} - 13q^{59} - 40q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 14q^{65} + 36q^{66} - 11q^{67} - 29q^{68} - 23q^{69} + 6q^{71} + 25q^{72} - 60q^{73} - 3q^{74} + 3q^{75} + 9q^{76} + 16q^{78} - 14q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} + 14q^{86} - 16q^{87} - 4q^{89} + 16q^{90} + 54q^{92} - 7q^{93} - 45q^{94} - 6q^{95} + 38q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.952780 + 1.65026i 0.673717 + 1.16691i 0.976842 + 0.213962i \(0.0686367\pi\)
−0.303125 + 0.952951i \(0.598030\pi\)
\(3\) 0.214224 + 0.371047i 0.123682 + 0.214224i 0.921217 0.389049i \(-0.127196\pi\)
−0.797535 + 0.603273i \(0.793863\pi\)
\(4\) −0.815580 + 1.41263i −0.407790 + 0.706313i
\(5\) 1.47313 0.658804 0.329402 0.944190i \(-0.393153\pi\)
0.329402 + 0.944190i \(0.393153\pi\)
\(6\) −0.408216 + 0.707051i −0.166654 + 0.288653i
\(7\) 0 0
\(8\) 0.702849 0.248495
\(9\) 1.40822 2.43910i 0.469405 0.813034i
\(10\) 1.40357 + 2.43105i 0.443847 + 0.768766i
\(11\) 2.19681 + 3.80498i 0.662362 + 1.14725i 0.979993 + 0.199031i \(0.0637794\pi\)
−0.317631 + 0.948214i \(0.602887\pi\)
\(12\) −0.698866 −0.201745
\(13\) −2.69752 2.39236i −0.748158 0.663520i
\(14\) 0 0
\(15\) 0.315580 + 0.546600i 0.0814823 + 0.141131i
\(16\) 2.30082 + 3.98514i 0.575205 + 0.996284i
\(17\) −0.601356 + 1.04158i −0.145850 + 0.252620i −0.929690 0.368343i \(-0.879925\pi\)
0.783840 + 0.620963i \(0.213258\pi\)
\(18\) 5.36688 1.26499
\(19\) 1.62105 2.80773i 0.371893 0.644138i −0.617963 0.786207i \(-0.712042\pi\)
0.989857 + 0.142068i \(0.0453753\pi\)
\(20\) −1.20145 + 2.08098i −0.268653 + 0.465321i
\(21\) 0 0
\(22\) −4.18615 + 7.25062i −0.892490 + 1.54584i
\(23\) 2.21855 + 3.84264i 0.462600 + 0.801246i 0.999090 0.0426603i \(-0.0135833\pi\)
−0.536490 + 0.843907i \(0.680250\pi\)
\(24\) 0.150567 + 0.260790i 0.0307343 + 0.0532334i
\(25\) −2.82989 −0.565978
\(26\) 1.37787 6.73101i 0.270223 1.32006i
\(27\) 2.49204 0.479593
\(28\) 0 0
\(29\) −0.0837807 0.145112i −0.0155577 0.0269467i 0.858142 0.513413i \(-0.171619\pi\)
−0.873699 + 0.486466i \(0.838286\pi\)
\(30\) −0.601356 + 1.04158i −0.109792 + 0.190165i
\(31\) −5.24543 −0.942108 −0.471054 0.882104i \(-0.656126\pi\)
−0.471054 + 0.882104i \(0.656126\pi\)
\(32\) −3.68150 + 6.37655i −0.650803 + 1.12722i
\(33\) −0.941217 + 1.63024i −0.163845 + 0.283788i
\(34\) −2.29184 −0.393047
\(35\) 0 0
\(36\) 2.29702 + 3.97856i 0.382837 + 0.663094i
\(37\) −3.52527 6.10595i −0.579552 1.00381i −0.995531 0.0944386i \(-0.969894\pi\)
0.415979 0.909374i \(-0.363439\pi\)
\(38\) 6.17800 1.00220
\(39\) 0.309802 1.51341i 0.0496080 0.242339i
\(40\) 1.03539 0.163709
\(41\) 2.58195 + 4.47206i 0.403233 + 0.698419i 0.994114 0.108339i \(-0.0345533\pi\)
−0.590881 + 0.806758i \(0.701220\pi\)
\(42\) 0 0
\(43\) −0.0113752 + 0.0197024i −0.00173470 + 0.00300459i −0.866891 0.498497i \(-0.833886\pi\)
0.865157 + 0.501502i \(0.167219\pi\)
\(44\) −7.16668 −1.08042
\(45\) 2.07449 3.59311i 0.309246 0.535630i
\(46\) −4.22758 + 7.32239i −0.623323 + 1.07963i
\(47\) −11.6836 −1.70422 −0.852111 0.523362i \(-0.824678\pi\)
−0.852111 + 0.523362i \(0.824678\pi\)
\(48\) −0.985780 + 1.70742i −0.142285 + 0.246445i
\(49\) 0 0
\(50\) −2.69626 4.67006i −0.381309 0.660446i
\(51\) −0.515299 −0.0721563
\(52\) 5.57955 1.85943i 0.773744 0.257857i
\(53\) −0.141786 −0.0194758 −0.00973788 0.999953i \(-0.503100\pi\)
−0.00973788 + 0.999953i \(0.503100\pi\)
\(54\) 2.37436 + 4.11252i 0.323110 + 0.559643i
\(55\) 3.23618 + 5.60523i 0.436367 + 0.755809i
\(56\) 0 0
\(57\) 1.38907 0.183986
\(58\) 0.159649 0.276520i 0.0209630 0.0363089i
\(59\) −2.67177 + 4.62764i −0.347835 + 0.602468i −0.985865 0.167544i \(-0.946416\pi\)
0.638030 + 0.770012i \(0.279750\pi\)
\(60\) −1.02952 −0.132911
\(61\) 5.77287 9.99891i 0.739141 1.28023i −0.213742 0.976890i \(-0.568565\pi\)
0.952883 0.303339i \(-0.0981016\pi\)
\(62\) −4.99774 8.65635i −0.634714 1.09936i
\(63\) 0 0
\(64\) −4.82736 −0.603420
\(65\) −3.97380 3.52425i −0.492889 0.437130i
\(66\) −3.58709 −0.441540
\(67\) −2.06773 3.58141i −0.252613 0.437539i 0.711631 0.702553i \(-0.247957\pi\)
−0.964245 + 0.265014i \(0.914623\pi\)
\(68\) −0.980907 1.69898i −0.118952 0.206032i
\(69\) −0.950533 + 1.64637i −0.114431 + 0.198200i
\(70\) 0 0
\(71\) 4.98486 8.63403i 0.591594 1.02467i −0.402424 0.915453i \(-0.631832\pi\)
0.994018 0.109217i \(-0.0348344\pi\)
\(72\) 0.989763 1.71432i 0.116645 0.202035i
\(73\) −15.2416 −1.78389 −0.891947 0.452141i \(-0.850660\pi\)
−0.891947 + 0.452141i \(0.850660\pi\)
\(74\) 6.71762 11.6353i 0.780908 1.35257i
\(75\) −0.606229 1.05002i −0.0700013 0.121246i
\(76\) 2.64418 + 4.57986i 0.303309 + 0.525346i
\(77\) 0 0
\(78\) 2.79269 0.930689i 0.316210 0.105380i
\(79\) 0.774501 0.0871382 0.0435691 0.999050i \(-0.486127\pi\)
0.0435691 + 0.999050i \(0.486127\pi\)
\(80\) 3.38941 + 5.87062i 0.378947 + 0.656356i
\(81\) −3.69080 6.39265i −0.410088 0.710294i
\(82\) −4.92006 + 8.52179i −0.543329 + 0.941074i
\(83\) 16.0186 1.75827 0.879136 0.476571i \(-0.158121\pi\)
0.879136 + 0.476571i \(0.158121\pi\)
\(84\) 0 0
\(85\) −0.885875 + 1.53438i −0.0960866 + 0.166427i
\(86\) −0.0433522 −0.00467479
\(87\) 0.0358956 0.0621731i 0.00384842 0.00666565i
\(88\) 1.54402 + 2.67433i 0.164593 + 0.285084i
\(89\) 3.27880 + 5.67904i 0.347552 + 0.601977i 0.985814 0.167842i \(-0.0536797\pi\)
−0.638262 + 0.769819i \(0.720346\pi\)
\(90\) 7.90611 0.833378
\(91\) 0 0
\(92\) −7.23762 −0.754574
\(93\) −1.12370 1.94630i −0.116522 0.201822i
\(94\) −11.1319 19.2809i −1.14816 1.98868i
\(95\) 2.38801 4.13616i 0.245005 0.424361i
\(96\) −3.15466 −0.321971
\(97\) 1.74583 3.02387i 0.177262 0.307027i −0.763680 0.645595i \(-0.776609\pi\)
0.940942 + 0.338568i \(0.109943\pi\)
\(98\) 0 0
\(99\) 12.3743 1.24367
\(100\) 2.30800 3.99757i 0.230800 0.399757i
\(101\) 1.28890 + 2.23244i 0.128250 + 0.222136i 0.922999 0.384803i \(-0.125731\pi\)
−0.794749 + 0.606939i \(0.792397\pi\)
\(102\) −0.490966 0.850379i −0.0486129 0.0842000i
\(103\) 16.8635 1.66161 0.830803 0.556567i \(-0.187882\pi\)
0.830803 + 0.556567i \(0.187882\pi\)
\(104\) −1.89595 1.68146i −0.185913 0.164881i
\(105\) 0 0
\(106\) −0.135091 0.233984i −0.0131212 0.0227265i
\(107\) −4.34132 7.51939i −0.419692 0.726927i 0.576217 0.817297i \(-0.304528\pi\)
−0.995908 + 0.0903697i \(0.971195\pi\)
\(108\) −2.03245 + 3.52031i −0.195573 + 0.338742i
\(109\) −12.0405 −1.15327 −0.576637 0.817001i \(-0.695635\pi\)
−0.576637 + 0.817001i \(0.695635\pi\)
\(110\) −6.16674 + 10.6811i −0.587976 + 1.01840i
\(111\) 1.51040 2.61608i 0.143360 0.248307i
\(112\) 0 0
\(113\) −4.68616 + 8.11667i −0.440837 + 0.763552i −0.997752 0.0670176i \(-0.978652\pi\)
0.556915 + 0.830570i \(0.311985\pi\)
\(114\) 1.32348 + 2.29233i 0.123955 + 0.214696i
\(115\) 3.26821 + 5.66071i 0.304763 + 0.527864i
\(116\) 0.273319 0.0253771
\(117\) −9.63390 + 3.21058i −0.890654 + 0.296818i
\(118\) −10.1824 −0.937369
\(119\) 0 0
\(120\) 0.221805 + 0.384177i 0.0202479 + 0.0350704i
\(121\) −4.15192 + 7.19134i −0.377448 + 0.653758i
\(122\) 22.0011 1.99189
\(123\) −1.10623 + 1.91605i −0.0997453 + 0.172764i
\(124\) 4.27807 7.40983i 0.384182 0.665423i
\(125\) −11.5344 −1.03167
\(126\) 0 0
\(127\) −7.94269 13.7571i −0.704800 1.22075i −0.966764 0.255672i \(-0.917703\pi\)
0.261964 0.965078i \(-0.415630\pi\)
\(128\) 2.76359 + 4.78667i 0.244269 + 0.423086i
\(129\) −0.00974735 −0.000858206
\(130\) 2.02978 9.91566i 0.178024 0.869661i
\(131\) −1.85745 −0.162286 −0.0811430 0.996702i \(-0.525857\pi\)
−0.0811430 + 0.996702i \(0.525857\pi\)
\(132\) −1.53527 2.65917i −0.133628 0.231451i
\(133\) 0 0
\(134\) 3.94018 6.82459i 0.340380 0.589555i
\(135\) 3.67109 0.315957
\(136\) −0.422662 + 0.732072i −0.0362430 + 0.0627747i
\(137\) 6.40011 11.0853i 0.546798 0.947082i −0.451693 0.892173i \(-0.649180\pi\)
0.998491 0.0549088i \(-0.0174868\pi\)
\(138\) −3.62260 −0.308376
\(139\) −0.169365 + 0.293348i −0.0143653 + 0.0248815i −0.873119 0.487508i \(-0.837906\pi\)
0.858753 + 0.512389i \(0.171239\pi\)
\(140\) 0 0
\(141\) −2.50290 4.33514i −0.210782 0.365085i
\(142\) 18.9979 1.59427
\(143\) 3.17693 15.5196i 0.265669 1.29781i
\(144\) 12.9602 1.08002
\(145\) −0.123420 0.213769i −0.0102495 0.0177526i
\(146\) −14.5219 25.1526i −1.20184 2.08165i
\(147\) 0 0
\(148\) 11.5006 0.945341
\(149\) −1.96158 + 3.39756i −0.160699 + 0.278339i −0.935120 0.354332i \(-0.884708\pi\)
0.774421 + 0.632671i \(0.218041\pi\)
\(150\) 1.15521 2.00088i 0.0943222 0.163371i
\(151\) −2.11879 −0.172424 −0.0862122 0.996277i \(-0.527476\pi\)
−0.0862122 + 0.996277i \(0.527476\pi\)
\(152\) 1.13935 1.97341i 0.0924135 0.160065i
\(153\) 1.69368 + 2.93354i 0.136926 + 0.237162i
\(154\) 0 0
\(155\) −7.72721 −0.620664
\(156\) 1.88521 + 1.67194i 0.150937 + 0.133862i
\(157\) 22.1128 1.76479 0.882397 0.470506i \(-0.155929\pi\)
0.882397 + 0.470506i \(0.155929\pi\)
\(158\) 0.737929 + 1.27813i 0.0587065 + 0.101683i
\(159\) −0.0303739 0.0526091i −0.00240881 0.00417217i
\(160\) −5.42333 + 9.39348i −0.428752 + 0.742620i
\(161\) 0 0
\(162\) 7.03303 12.1816i 0.552567 0.957074i
\(163\) −1.92607 + 3.33605i −0.150861 + 0.261299i −0.931544 0.363628i \(-0.881538\pi\)
0.780683 + 0.624927i \(0.214871\pi\)
\(164\) −8.42314 −0.657736
\(165\) −1.38653 + 2.40155i −0.107942 + 0.186960i
\(166\) 15.2622 + 26.4349i 1.18458 + 2.05175i
\(167\) 1.06947 + 1.85238i 0.0827582 + 0.143341i 0.904434 0.426614i \(-0.140294\pi\)
−0.821676 + 0.569956i \(0.806960\pi\)
\(168\) 0 0
\(169\) 1.55326 + 12.9069i 0.119482 + 0.992836i
\(170\) −3.37618 −0.258941
\(171\) −4.56557 7.90779i −0.349138 0.604724i
\(172\) −0.0185547 0.0321378i −0.00141479 0.00245048i
\(173\) −8.30664 + 14.3875i −0.631542 + 1.09386i 0.355695 + 0.934602i \(0.384244\pi\)
−0.987237 + 0.159260i \(0.949089\pi\)
\(174\) 0.136803 0.0103710
\(175\) 0 0
\(176\) −10.1089 + 17.5091i −0.761988 + 1.31980i
\(177\) −2.28943 −0.172084
\(178\) −6.24795 + 10.8218i −0.468303 + 0.811125i
\(179\) 0.269748 + 0.467217i 0.0201619 + 0.0349214i 0.875930 0.482438i \(-0.160248\pi\)
−0.855768 + 0.517359i \(0.826915\pi\)
\(180\) 3.38382 + 5.86094i 0.252215 + 0.436849i
\(181\) −2.77164 −0.206014 −0.103007 0.994681i \(-0.532846\pi\)
−0.103007 + 0.994681i \(0.532846\pi\)
\(182\) 0 0
\(183\) 4.94675 0.365674
\(184\) 1.55931 + 2.70080i 0.114954 + 0.199105i
\(185\) −5.19319 8.99486i −0.381811 0.661316i
\(186\) 2.14127 3.70879i 0.157006 0.271942i
\(187\) −5.28425 −0.386423
\(188\) 9.52887 16.5045i 0.694964 1.20371i
\(189\) 0 0
\(190\) 9.10100 0.660256
\(191\) 10.1204 17.5290i 0.732284 1.26835i −0.223621 0.974676i \(-0.571788\pi\)
0.955905 0.293677i \(-0.0948790\pi\)
\(192\) −1.03414 1.79118i −0.0746323 0.129267i
\(193\) 8.18856 + 14.1830i 0.589425 + 1.02091i 0.994308 + 0.106546i \(0.0339791\pi\)
−0.404882 + 0.914369i \(0.632688\pi\)
\(194\) 6.65357 0.477698
\(195\) 0.456378 2.22944i 0.0326819 0.159654i
\(196\) 0 0
\(197\) −9.86676 17.0897i −0.702977 1.21759i −0.967417 0.253190i \(-0.918520\pi\)
0.264439 0.964402i \(-0.414813\pi\)
\(198\) 11.7900 + 20.4209i 0.837879 + 1.45125i
\(199\) −7.05873 + 12.2261i −0.500380 + 0.866683i 0.499620 + 0.866245i \(0.333473\pi\)
−1.00000 0.000438630i \(0.999860\pi\)
\(200\) −1.98898 −0.140642
\(201\) 0.885913 1.53445i 0.0624875 0.108232i
\(202\) −2.45607 + 4.25404i −0.172809 + 0.299313i
\(203\) 0 0
\(204\) 0.420267 0.727924i 0.0294246 0.0509649i
\(205\) 3.80354 + 6.58793i 0.265651 + 0.460121i
\(206\) 16.0672 + 27.8291i 1.11945 + 1.93895i
\(207\) 12.4968 0.868588
\(208\) 3.32735 16.2544i 0.230710 1.12704i
\(209\) 14.2445 0.985313
\(210\) 0 0
\(211\) 2.31317 + 4.00652i 0.159245 + 0.275820i 0.934597 0.355709i \(-0.115761\pi\)
−0.775352 + 0.631530i \(0.782427\pi\)
\(212\) 0.115638 0.200290i 0.00794202 0.0137560i
\(213\) 4.27150 0.292678
\(214\) 8.27265 14.3287i 0.565507 0.979487i
\(215\) −0.0167571 + 0.0290242i −0.00114283 + 0.00197943i
\(216\) 1.75152 0.119176
\(217\) 0 0
\(218\) −11.4720 19.8700i −0.776980 1.34577i
\(219\) −3.26511 5.65534i −0.220636 0.382152i
\(220\) −10.5575 −0.711784
\(221\) 4.11400 1.37103i 0.276737 0.0922251i
\(222\) 5.75630 0.386337
\(223\) −10.6761 18.4916i −0.714926 1.23829i −0.962988 0.269545i \(-0.913127\pi\)
0.248061 0.968744i \(-0.420207\pi\)
\(224\) 0 0
\(225\) −3.98509 + 6.90239i −0.265673 + 0.460159i
\(226\) −17.8595 −1.18800
\(227\) −5.22451 + 9.04911i −0.346763 + 0.600611i −0.985672 0.168671i \(-0.946052\pi\)
0.638910 + 0.769282i \(0.279386\pi\)
\(228\) −1.13289 + 1.96223i −0.0750278 + 0.129952i
\(229\) −14.4580 −0.955413 −0.477706 0.878520i \(-0.658532\pi\)
−0.477706 + 0.878520i \(0.658532\pi\)
\(230\) −6.22778 + 10.7868i −0.410648 + 0.711262i
\(231\) 0 0
\(232\) −0.0588852 0.101992i −0.00386600 0.00669611i
\(233\) −9.28827 −0.608495 −0.304247 0.952593i \(-0.598405\pi\)
−0.304247 + 0.952593i \(0.598405\pi\)
\(234\) −14.4773 12.8395i −0.946410 0.839344i
\(235\) −17.2114 −1.12275
\(236\) −4.35808 7.54842i −0.283687 0.491360i
\(237\) 0.165917 + 0.287376i 0.0107774 + 0.0186671i
\(238\) 0 0
\(239\) 19.6332 1.26997 0.634983 0.772526i \(-0.281007\pi\)
0.634983 + 0.772526i \(0.281007\pi\)
\(240\) −1.45218 + 2.51525i −0.0937380 + 0.162359i
\(241\) 3.65552 6.33155i 0.235473 0.407851i −0.723937 0.689866i \(-0.757669\pi\)
0.959410 + 0.282015i \(0.0910028\pi\)
\(242\) −15.8235 −1.01717
\(243\) 5.31937 9.21341i 0.341238 0.591041i
\(244\) 9.41648 + 16.3098i 0.602828 + 1.04413i
\(245\) 0 0
\(246\) −4.21597 −0.268801
\(247\) −11.0899 + 3.69581i −0.705634 + 0.235159i
\(248\) −3.68675 −0.234109
\(249\) 3.43157 + 5.94365i 0.217467 + 0.376664i
\(250\) −10.9898 19.0349i −0.695055 1.20387i
\(251\) −5.93191 + 10.2744i −0.374419 + 0.648512i −0.990240 0.139374i \(-0.955491\pi\)
0.615821 + 0.787886i \(0.288824\pi\)
\(252\) 0 0
\(253\) −9.74746 + 16.8831i −0.612817 + 1.06143i
\(254\) 15.1353 26.2151i 0.949672 1.64488i
\(255\) −0.759102 −0.0475368
\(256\) −10.0935 + 17.4825i −0.630846 + 1.09266i
\(257\) −7.58608 13.1395i −0.473206 0.819618i 0.526323 0.850285i \(-0.323570\pi\)
−0.999530 + 0.0306670i \(0.990237\pi\)
\(258\) −0.00928708 0.0160857i −0.000578188 0.00100145i
\(259\) 0 0
\(260\) 8.21940 2.73919i 0.509745 0.169877i
\(261\) −0.471925 −0.0292115
\(262\) −1.76974 3.06528i −0.109335 0.189374i
\(263\) −8.59820 14.8925i −0.530187 0.918312i −0.999380 0.0352156i \(-0.988788\pi\)
0.469192 0.883096i \(-0.344545\pi\)
\(264\) −0.661533 + 1.14581i −0.0407145 + 0.0705196i
\(265\) −0.208869 −0.0128307
\(266\) 0 0
\(267\) −1.40479 + 2.43317i −0.0859719 + 0.148908i
\(268\) 6.74559 0.412052
\(269\) 9.46102 16.3870i 0.576849 0.999131i −0.418989 0.907991i \(-0.637616\pi\)
0.995838 0.0911401i \(-0.0290511\pi\)
\(270\) 3.49774 + 6.05827i 0.212866 + 0.368695i
\(271\) 16.0667 + 27.8283i 0.975982 + 1.69045i 0.676657 + 0.736298i \(0.263428\pi\)
0.299324 + 0.954151i \(0.403239\pi\)
\(272\) −5.53444 −0.335575
\(273\) 0 0
\(274\) 24.3916 1.47355
\(275\) −6.21672 10.7677i −0.374882 0.649315i
\(276\) −1.55047 2.68549i −0.0933273 0.161648i
\(277\) −9.20269 + 15.9395i −0.552936 + 0.957714i 0.445125 + 0.895469i \(0.353159\pi\)
−0.998061 + 0.0622450i \(0.980174\pi\)
\(278\) −0.645469 −0.0387126
\(279\) −7.38671 + 12.7942i −0.442231 + 0.765966i
\(280\) 0 0
\(281\) −14.2252 −0.848603 −0.424302 0.905521i \(-0.639480\pi\)
−0.424302 + 0.905521i \(0.639480\pi\)
\(282\) 4.76942 8.26087i 0.284015 0.491928i
\(283\) −5.71446 9.89773i −0.339689 0.588359i 0.644685 0.764448i \(-0.276989\pi\)
−0.984374 + 0.176089i \(0.943655\pi\)
\(284\) 8.13109 + 14.0835i 0.482492 + 0.835700i
\(285\) 2.04628 0.121211
\(286\) 28.6383 9.54396i 1.69342 0.564346i
\(287\) 0 0
\(288\) 10.3687 + 17.9591i 0.610981 + 1.05825i
\(289\) 7.77674 + 13.4697i 0.457455 + 0.792336i
\(290\) 0.235184 0.407351i 0.0138105 0.0239205i
\(291\) 1.49599 0.0876967
\(292\) 12.4307 21.5307i 0.727453 1.25999i
\(293\) −6.60231 + 11.4355i −0.385711 + 0.668071i −0.991868 0.127274i \(-0.959377\pi\)
0.606156 + 0.795345i \(0.292711\pi\)
\(294\) 0 0
\(295\) −3.93586 + 6.81712i −0.229155 + 0.396908i
\(296\) −2.47773 4.29156i −0.144015 0.249442i
\(297\) 5.47452 + 9.48215i 0.317664 + 0.550210i
\(298\) −7.47582 −0.433062
\(299\) 3.20838 15.6732i 0.185545 0.906404i
\(300\) 1.97771 0.114183
\(301\) 0 0
\(302\) −2.01874 3.49656i −0.116165 0.201204i
\(303\) −0.552225 + 0.956482i −0.0317245 + 0.0549484i
\(304\) 14.9189 0.855660
\(305\) 8.50420 14.7297i 0.486949 0.843420i
\(306\) −3.22740 + 5.59003i −0.184498 + 0.319561i
\(307\) 6.65903 0.380051 0.190026 0.981779i \(-0.439143\pi\)
0.190026 + 0.981779i \(0.439143\pi\)
\(308\) 0 0
\(309\) 3.61255 + 6.25713i 0.205511 + 0.355955i
\(310\) −7.36233 12.7519i −0.418152 0.724261i
\(311\) 2.04597 0.116016 0.0580081 0.998316i \(-0.481525\pi\)
0.0580081 + 0.998316i \(0.481525\pi\)
\(312\) 0.217744 1.06370i 0.0123273 0.0602199i
\(313\) −9.41767 −0.532318 −0.266159 0.963929i \(-0.585755\pi\)
−0.266159 + 0.963929i \(0.585755\pi\)
\(314\) 21.0686 + 36.4919i 1.18897 + 2.05936i
\(315\) 0 0
\(316\) −0.631667 + 1.09408i −0.0355341 + 0.0615468i
\(317\) −33.3713 −1.87432 −0.937159 0.348902i \(-0.886555\pi\)
−0.937159 + 0.348902i \(0.886555\pi\)
\(318\) 0.0578792 0.100250i 0.00324571 0.00562173i
\(319\) 0.368100 0.637568i 0.0206097 0.0356970i
\(320\) −7.11133 −0.397536
\(321\) 1.86003 3.22167i 0.103817 0.179816i
\(322\) 0 0
\(323\) 1.94965 + 3.37689i 0.108481 + 0.187895i
\(324\) 12.0405 0.668919
\(325\) 7.63369 + 6.77010i 0.423441 + 0.375538i
\(326\) −7.34048 −0.406551
\(327\) −2.57937 4.46760i −0.142639 0.247059i
\(328\) 1.81472 + 3.14318i 0.100201 + 0.173553i
\(329\) 0 0
\(330\) −5.28425 −0.290888
\(331\) −9.53298 + 16.5116i −0.523980 + 0.907560i 0.475631 + 0.879645i \(0.342220\pi\)
−0.999610 + 0.0279144i \(0.991113\pi\)
\(332\) −13.0645 + 22.6283i −0.717005 + 1.24189i
\(333\) −19.8574 −1.08818
\(334\) −2.03794 + 3.52982i −0.111511 + 0.193143i
\(335\) −3.04603 5.27588i −0.166423 0.288252i
\(336\) 0 0
\(337\) −31.2849 −1.70420 −0.852098 0.523382i \(-0.824670\pi\)
−0.852098 + 0.523382i \(0.824670\pi\)
\(338\) −19.8198 + 14.8607i −1.07806 + 0.808316i
\(339\) −4.01555 −0.218095
\(340\) −1.44500 2.50282i −0.0783663 0.135734i
\(341\) −11.5232 19.9588i −0.624017 1.08083i
\(342\) 8.69996 15.0688i 0.470440 0.814826i
\(343\) 0 0
\(344\) −0.00799504 + 0.0138478i −0.000431064 + 0.000746624i
\(345\) −1.40026 + 2.42532i −0.0753874 + 0.130575i
\(346\) −31.6576 −1.70192
\(347\) −5.83759 + 10.1110i −0.313378 + 0.542787i −0.979091 0.203420i \(-0.934794\pi\)
0.665713 + 0.746208i \(0.268128\pi\)
\(348\) 0.0585515 + 0.101414i 0.00313869 + 0.00543637i
\(349\) 11.9952 + 20.7763i 0.642089 + 1.11213i 0.984966 + 0.172750i \(0.0552652\pi\)
−0.342877 + 0.939380i \(0.611401\pi\)
\(350\) 0 0
\(351\) −6.72233 5.96184i −0.358811 0.318219i
\(352\) −32.3502 −1.72427
\(353\) 6.39668 + 11.0794i 0.340461 + 0.589696i 0.984518 0.175282i \(-0.0560836\pi\)
−0.644057 + 0.764977i \(0.722750\pi\)
\(354\) −2.18132 3.77816i −0.115936 0.200807i
\(355\) 7.34334 12.7190i 0.389744 0.675057i
\(356\) −10.6965 −0.566912
\(357\) 0 0
\(358\) −0.514021 + 0.890310i −0.0271668 + 0.0470544i
\(359\) 12.3397 0.651265 0.325633 0.945496i \(-0.394423\pi\)
0.325633 + 0.945496i \(0.394423\pi\)
\(360\) 1.45805 2.52542i 0.0768460 0.133101i
\(361\) 4.24442 + 7.35155i 0.223390 + 0.386924i
\(362\) −2.64076 4.57393i −0.138795 0.240401i
\(363\) −3.55776 −0.186734
\(364\) 0 0
\(365\) −22.4528 −1.17524
\(366\) 4.71316 + 8.16344i 0.246361 + 0.426710i
\(367\) 1.01538 + 1.75870i 0.0530026 + 0.0918032i 0.891309 0.453396i \(-0.149788\pi\)
−0.838307 + 0.545199i \(0.816454\pi\)
\(368\) −10.2090 + 17.6825i −0.532179 + 0.921762i
\(369\) 14.5438 0.757118
\(370\) 9.89593 17.1403i 0.514465 0.891079i
\(371\) 0 0
\(372\) 3.66586 0.190066
\(373\) 1.93700 3.35498i 0.100294 0.173714i −0.811512 0.584336i \(-0.801355\pi\)
0.911806 + 0.410622i \(0.134688\pi\)
\(374\) −5.03473 8.72040i −0.260340 0.450921i
\(375\) −2.47095 4.27981i −0.127599 0.221009i
\(376\) −8.21177 −0.423490
\(377\) −0.121160 + 0.591877i −0.00624007 + 0.0304832i
\(378\) 0 0
\(379\) 7.28396 + 12.6162i 0.374152 + 0.648050i 0.990200 0.139659i \(-0.0446006\pi\)
−0.616048 + 0.787709i \(0.711267\pi\)
\(380\) 3.89523 + 6.74673i 0.199821 + 0.346100i
\(381\) 3.40303 5.89422i 0.174342 0.301970i
\(382\) 38.5699 1.97341
\(383\) −13.3909 + 23.1937i −0.684243 + 1.18514i 0.289430 + 0.957199i \(0.406534\pi\)
−0.973674 + 0.227945i \(0.926799\pi\)
\(384\) −1.18405 + 2.05084i −0.0604234 + 0.104656i
\(385\) 0 0
\(386\) −15.6038 + 27.0266i −0.794212 + 1.37562i
\(387\) 0.0320375 + 0.0554905i 0.00162856 + 0.00282074i
\(388\) 2.84773 + 4.93241i 0.144571 + 0.250405i
\(389\) 12.0148 0.609173 0.304586 0.952485i \(-0.401482\pi\)
0.304586 + 0.952485i \(0.401482\pi\)
\(390\) 4.11400 1.37103i 0.208320 0.0694246i
\(391\) −5.33655 −0.269881
\(392\) 0 0
\(393\) −0.397910 0.689200i −0.0200719 0.0347655i
\(394\) 18.8017 32.5655i 0.947216 1.64063i
\(395\) 1.14094 0.0574070
\(396\) −10.0922 + 17.4803i −0.507154 + 0.878417i
\(397\) −0.828825 + 1.43557i −0.0415975 + 0.0720491i −0.886075 0.463543i \(-0.846578\pi\)
0.844477 + 0.535592i \(0.179911\pi\)
\(398\) −26.9017 −1.34846
\(399\) 0 0
\(400\) −6.51106 11.2775i −0.325553 0.563874i
\(401\) 10.2414 + 17.7386i 0.511430 + 0.885823i 0.999912 + 0.0132488i \(0.00421735\pi\)
−0.488482 + 0.872574i \(0.662449\pi\)
\(402\) 3.37632 0.168396
\(403\) 14.1497 + 12.5489i 0.704846 + 0.625108i
\(404\) −4.20479 −0.209196
\(405\) −5.43702 9.41720i −0.270168 0.467944i
\(406\) 0 0
\(407\) 15.4887 26.8272i 0.767746 1.32978i
\(408\) −0.362177 −0.0179304
\(409\) 7.43293 12.8742i 0.367535 0.636589i −0.621645 0.783299i \(-0.713535\pi\)
0.989180 + 0.146710i \(0.0468685\pi\)
\(410\) −7.24788 + 12.5537i −0.357947 + 0.619983i
\(411\) 5.48422 0.270517
\(412\) −13.7535 + 23.8217i −0.677586 + 1.17361i
\(413\) 0 0
\(414\) 11.9067 + 20.6230i 0.585182 + 1.01357i
\(415\) 23.5975 1.15836
\(416\) 25.1859 8.39342i 1.23484 0.411521i
\(417\) −0.145128 −0.00710693
\(418\) 13.5719 + 23.5072i 0.663822 + 1.14977i
\(419\) −11.8087 20.4533i −0.576895 0.999211i −0.995833 0.0911962i \(-0.970931\pi\)
0.418938 0.908015i \(-0.362402\pi\)
\(420\) 0 0
\(421\) 26.0822 1.27117 0.635585 0.772031i \(-0.280759\pi\)
0.635585 + 0.772031i \(0.280759\pi\)
\(422\) −4.40788 + 7.63467i −0.214572 + 0.371650i
\(423\) −16.4530 + 28.4974i −0.799971 + 1.38559i
\(424\) −0.0996539 −0.00483962
\(425\) 1.70177 2.94755i 0.0825479 0.142977i
\(426\) 4.06980 + 7.04910i 0.197182 + 0.341530i
\(427\) 0 0
\(428\) 14.1628 0.684584
\(429\) 6.43906 2.14587i 0.310881 0.103604i
\(430\) −0.0638635 −0.00307977
\(431\) 6.65859 + 11.5330i 0.320733 + 0.555526i 0.980640 0.195822i \(-0.0627374\pi\)
−0.659906 + 0.751348i \(0.729404\pi\)
\(432\) 5.73373 + 9.93110i 0.275864 + 0.477810i
\(433\) 10.2110 17.6860i 0.490711 0.849937i −0.509232 0.860629i \(-0.670070\pi\)
0.999943 + 0.0106929i \(0.00340371\pi\)
\(434\) 0 0
\(435\) 0.0528790 0.0915890i 0.00253535 0.00439136i
\(436\) 9.82001 17.0087i 0.470293 0.814571i
\(437\) 14.3855 0.688152
\(438\) 6.22187 10.7766i 0.297292 0.514925i
\(439\) −4.88537 8.46171i −0.233166 0.403855i 0.725572 0.688146i \(-0.241575\pi\)
−0.958738 + 0.284291i \(0.908242\pi\)
\(440\) 2.27455 + 3.93963i 0.108435 + 0.187814i
\(441\) 0 0
\(442\) 6.18229 + 5.48290i 0.294061 + 0.260795i
\(443\) 21.1639 1.00553 0.502763 0.864424i \(-0.332317\pi\)
0.502763 + 0.864424i \(0.332317\pi\)
\(444\) 2.46370 + 4.26725i 0.116922 + 0.202514i
\(445\) 4.83010 + 8.36597i 0.228968 + 0.396585i
\(446\) 20.3440 35.2368i 0.963317 1.66851i
\(447\) −1.68087 −0.0795023
\(448\) 0 0
\(449\) 9.07320 15.7152i 0.428191 0.741648i −0.568522 0.822668i \(-0.692484\pi\)
0.996712 + 0.0810200i \(0.0258178\pi\)
\(450\) −15.1877 −0.715954
\(451\) −11.3441 + 19.6485i −0.534172 + 0.925213i
\(452\) −7.64387 13.2396i −0.359538 0.622737i
\(453\) −0.453895 0.786168i −0.0213258 0.0369374i
\(454\) −19.9112 −0.934480
\(455\) 0 0
\(456\) 0.976304 0.0457196
\(457\) 9.00991 + 15.6056i 0.421466 + 0.730000i 0.996083 0.0884220i \(-0.0281824\pi\)
−0.574617 + 0.818422i \(0.694849\pi\)
\(458\) −13.7753 23.8595i −0.643678 1.11488i
\(459\) −1.49860 + 2.59565i −0.0699487 + 0.121155i
\(460\) −10.6620 −0.497116
\(461\) −14.8873 + 25.7855i −0.693370 + 1.20095i 0.277357 + 0.960767i \(0.410542\pi\)
−0.970727 + 0.240185i \(0.922792\pi\)
\(462\) 0 0
\(463\) 17.7067 0.822900 0.411450 0.911432i \(-0.365023\pi\)
0.411450 + 0.911432i \(0.365023\pi\)
\(464\) 0.385529 0.667755i 0.0178977 0.0309997i
\(465\) −1.65535 2.86715i −0.0767651 0.132961i
\(466\) −8.84968 15.3281i −0.409953 0.710060i
\(467\) 5.82922 0.269744 0.134872 0.990863i \(-0.456938\pi\)
0.134872 + 0.990863i \(0.456938\pi\)
\(468\) 3.32186 16.2276i 0.153553 0.750120i
\(469\) 0 0
\(470\) −16.3987 28.4033i −0.756414 1.31015i
\(471\) 4.73709 + 8.20488i 0.218274 + 0.378061i
\(472\) −1.87785 + 3.25253i −0.0864350 + 0.149710i
\(473\) −0.0999564 −0.00459600
\(474\) −0.316164 + 0.547612i −0.0145219 + 0.0251527i
\(475\) −4.58738 + 7.94557i −0.210483 + 0.364568i
\(476\) 0 0
\(477\) −0.199665 + 0.345830i −0.00914203 + 0.0158345i
\(478\) 18.7061 + 32.4000i 0.855598 + 1.48194i
\(479\) 7.24565 + 12.5498i 0.331062 + 0.573417i 0.982720 0.185096i \(-0.0592596\pi\)
−0.651658 + 0.758513i \(0.725926\pi\)
\(480\) −4.64722 −0.212116
\(481\) −5.09811 + 24.9047i −0.232454 + 1.13556i
\(482\) 13.9316 0.634569
\(483\) 0 0
\(484\) −6.77245 11.7302i −0.307839 0.533192i
\(485\) 2.57183 4.45455i 0.116781 0.202271i
\(486\) 20.2727 0.919591
\(487\) 8.98006 15.5539i 0.406926 0.704816i −0.587618 0.809139i \(-0.699934\pi\)
0.994543 + 0.104323i \(0.0332675\pi\)
\(488\) 4.05746 7.02772i 0.183672 0.318130i
\(489\) −1.65044 −0.0746354
\(490\) 0 0
\(491\) 18.1505 + 31.4375i 0.819119 + 1.41876i 0.906332 + 0.422566i \(0.138870\pi\)
−0.0872134 + 0.996190i \(0.527796\pi\)
\(492\) −1.80444 3.12537i −0.0813503 0.140903i
\(493\) 0.201528 0.00907637
\(494\) −16.6653 14.7800i −0.749807 0.664983i
\(495\) 18.2290 0.819332
\(496\) −12.0688 20.9038i −0.541905 0.938607i
\(497\) 0 0
\(498\) −6.53906 + 11.3260i −0.293022 + 0.507530i
\(499\) 23.7076 1.06130 0.530649 0.847591i \(-0.321948\pi\)
0.530649 + 0.847591i \(0.321948\pi\)
\(500\) 9.40726 16.2938i 0.420705 0.728683i
\(501\) −0.458213 + 0.793648i −0.0204714 + 0.0354576i
\(502\) −22.6072 −1.00901
\(503\) 13.8876 24.0540i 0.619217 1.07252i −0.370411 0.928868i \(-0.620783\pi\)
0.989629 0.143648i \(-0.0458834\pi\)
\(504\) 0 0
\(505\) 1.89871 + 3.28867i 0.0844916 + 0.146344i
\(506\) −37.1487 −1.65146
\(507\) −4.45630 + 3.34129i −0.197911 + 0.148392i
\(508\) 25.9116 1.14964
\(509\) 4.35208 + 7.53802i 0.192902 + 0.334117i 0.946211 0.323551i \(-0.104877\pi\)
−0.753308 + 0.657667i \(0.771543\pi\)
\(510\) −0.723257 1.25272i −0.0320264 0.0554713i
\(511\) 0 0
\(512\) −27.4134 −1.21151
\(513\) 4.03971 6.99698i 0.178357 0.308924i
\(514\) 14.4557 25.0380i 0.637615 1.10438i
\(515\) 24.8421 1.09467
\(516\) 0.00794974 0.0137693i 0.000349968 0.000606162i
\(517\) −25.6665 44.4557i −1.12881 1.95516i
\(518\) 0 0
\(519\) −7.11792 −0.312442
\(520\) −2.79298 2.47702i −0.122480 0.108624i
\(521\) 8.57146 0.375523 0.187761 0.982215i \(-0.439877\pi\)
0.187761 + 0.982215i \(0.439877\pi\)
\(522\) −0.449641 0.778801i −0.0196803 0.0340872i
\(523\) 14.9746 + 25.9369i 0.654796 + 1.13414i 0.981945 + 0.189167i \(0.0605787\pi\)
−0.327149 + 0.944973i \(0.606088\pi\)
\(524\) 1.51490 2.62388i 0.0661786 0.114625i
\(525\) 0 0
\(526\) 16.3844 28.3786i 0.714393 1.23736i
\(527\) 3.15437 5.46353i 0.137407 0.237995i
\(528\) −8.66228 −0.376977
\(529\) 1.65606 2.86838i 0.0720027 0.124712i
\(530\) −0.199006 0.344689i −0.00864427 0.0149723i
\(531\) 7.52486 + 13.0334i 0.326551 + 0.565603i
\(532\) 0 0
\(533\) 3.73391 18.2404i 0.161734 0.790081i
\(534\) −5.35383 −0.231683
\(535\) −6.39534 11.0770i −0.276494 0.478902i
\(536\) −1.45330 2.51719i −0.0627730 0.108726i
\(537\) −0.115573 + 0.200178i −0.00498734 + 0.00863832i
\(538\) 36.0571 1.55453
\(539\) 0 0
\(540\) −2.99407 + 5.18588i −0.128844 + 0.223165i
\(541\) 10.4819 0.450652 0.225326 0.974283i \(-0.427655\pi\)
0.225326 + 0.974283i \(0.427655\pi\)
\(542\) −30.6160 + 53.0285i −1.31507 + 2.27777i
\(543\) −0.593751 1.02841i −0.0254803 0.0441331i
\(544\) −4.42778 7.66914i −0.189840 0.328812i
\(545\) −17.7373 −0.759781
\(546\) 0 0
\(547\) 15.2216 0.650829 0.325415 0.945571i \(-0.394496\pi\)
0.325415 + 0.945571i \(0.394496\pi\)
\(548\) 10.4396 + 18.0819i 0.445957 + 0.772421i
\(549\) −16.2589 28.1613i −0.693914 1.20189i
\(550\) 11.8463 20.5184i 0.505129 0.874909i
\(551\) −0.543250 −0.0231432
\(552\) −0.668081 + 1.15715i −0.0284354 + 0.0492516i
\(553\) 0 0
\(554\) −35.0726 −1.49009
\(555\) 2.22501 3.85383i 0.0944464 0.163586i
\(556\) −0.276261 0.478497i −0.0117161 0.0202928i
\(557\) −5.92986 10.2708i −0.251256 0.435189i 0.712616 0.701555i \(-0.247510\pi\)
−0.963872 + 0.266366i \(0.914177\pi\)
\(558\) −28.1516 −1.19175
\(559\) 0.0778200 0.0259342i 0.00329144 0.00109690i
\(560\) 0 0
\(561\) −1.13201 1.96070i −0.0477936 0.0827809i
\(562\) −13.5535 23.4753i −0.571719 0.990246i
\(563\) 3.84675 6.66276i 0.162121 0.280802i −0.773508 0.633786i \(-0.781500\pi\)
0.935629 + 0.352985i \(0.114833\pi\)
\(564\) 8.16524 0.343819
\(565\) −6.90332 + 11.9569i −0.290425 + 0.503031i
\(566\) 10.8892 18.8607i 0.457709 0.792775i
\(567\) 0 0
\(568\) 3.50360 6.06841i 0.147008 0.254625i
\(569\) −18.7098 32.4063i −0.784355 1.35854i −0.929384 0.369115i \(-0.879661\pi\)
0.145029 0.989427i \(-0.453673\pi\)
\(570\) 1.94965 + 3.37689i 0.0816619 + 0.141443i
\(571\) 14.1657 0.592816 0.296408 0.955061i \(-0.404211\pi\)
0.296408 + 0.955061i \(0.404211\pi\)
\(572\) 19.3323 + 17.1453i 0.808324 + 0.716879i
\(573\) 8.67209 0.362282
\(574\) 0 0
\(575\) −6.27825 10.8742i −0.261821 0.453488i
\(576\) −6.79797 + 11.7744i −0.283249 + 0.490601i
\(577\) 14.9755 0.623439 0.311720 0.950174i \(-0.399095\pi\)
0.311720 + 0.950174i \(0.399095\pi\)
\(578\) −14.8190 + 25.6673i −0.616391 + 1.06762i
\(579\) −3.50837 + 6.07667i −0.145803 + 0.252538i
\(580\) 0.402635 0.0167185
\(581\) 0 0
\(582\) 1.42535 + 2.46878i 0.0590828 + 0.102334i
\(583\) −0.311476 0.539492i −0.0129000 0.0223435i
\(584\) −10.7125 −0.443288
\(585\) −14.1920 + 4.72960i −0.586766 + 0.195545i
\(586\) −25.1622 −1.03944
\(587\) −6.58821 11.4111i −0.271925 0.470987i 0.697430 0.716653i \(-0.254327\pi\)
−0.969355 + 0.245666i \(0.920993\pi\)
\(588\) 0 0
\(589\) −8.50309 + 14.7278i −0.350364 + 0.606848i
\(590\) −15.0001 −0.617542
\(591\) 4.22739 7.32205i 0.173892 0.301189i
\(592\) 16.2220 28.0974i 0.666722 1.15480i
\(593\) 44.1327 1.81231 0.906156 0.422943i \(-0.139003\pi\)
0.906156 + 0.422943i \(0.139003\pi\)
\(594\) −10.4320 + 18.0688i −0.428032 + 0.741372i
\(595\) 0 0
\(596\) −3.19965 5.54195i −0.131063 0.227007i
\(597\) −6.04859 −0.247552
\(598\) 28.9218 9.63843i 1.18270 0.394145i
\(599\) −6.02698 −0.246256 −0.123128 0.992391i \(-0.539293\pi\)
−0.123128 + 0.992391i \(0.539293\pi\)
\(600\) −0.426087 0.738005i −0.0173949 0.0301289i
\(601\) 1.86260 + 3.22612i 0.0759770 + 0.131596i 0.901511 0.432757i \(-0.142459\pi\)
−0.825534 + 0.564353i \(0.809126\pi\)
\(602\) 0 0
\(603\) −11.6472 −0.474312
\(604\) 1.72804 2.99305i 0.0703129 0.121786i
\(605\) −6.11632 + 10.5938i −0.248664 + 0.430698i
\(606\) −2.10460 −0.0854934
\(607\) −3.00825 + 5.21045i −0.122101 + 0.211486i −0.920596 0.390516i \(-0.872297\pi\)
0.798495 + 0.602002i \(0.205630\pi\)
\(608\) 11.9358 + 20.6733i 0.484059 + 0.838415i
\(609\) 0 0
\(610\) 32.4105 1.31226
\(611\) 31.5167 + 27.9512i 1.27503 + 1.13079i
\(612\) −5.52532 −0.223348
\(613\) −4.90413 8.49420i −0.198076 0.343077i 0.749829 0.661632i \(-0.230136\pi\)
−0.947904 + 0.318555i \(0.896803\pi\)
\(614\) 6.34459 + 10.9892i 0.256047 + 0.443486i
\(615\) −1.62962 + 2.82258i −0.0657126 + 0.113818i
\(616\) 0 0
\(617\) −16.8838 + 29.2436i −0.679716 + 1.17730i 0.295350 + 0.955389i \(0.404564\pi\)
−0.975066 + 0.221914i \(0.928770\pi\)
\(618\) −6.88394 + 11.9233i −0.276913 + 0.479627i
\(619\) −4.09343 −0.164529 −0.0822644 0.996611i \(-0.526215\pi\)
−0.0822644 + 0.996611i \(0.526215\pi\)
\(620\) 6.30215 10.9156i 0.253100 0.438383i
\(621\) 5.52871 + 9.57601i 0.221860 + 0.384272i
\(622\) 1.94936 + 3.37639i 0.0781621 + 0.135381i
\(623\) 0 0
\(624\) 6.74393 2.24747i 0.269973 0.0899709i
\(625\) −2.84229 −0.113692
\(626\) −8.97297 15.5416i −0.358632 0.621169i
\(627\) 3.05151 + 5.28537i 0.121866 + 0.211077i
\(628\) −18.0347 + 31.2371i −0.719665 + 1.24650i
\(629\) 8.47978 0.338111
\(630\) 0 0
\(631\) 13.3868 23.1866i 0.532921 0.923046i −0.466340 0.884605i \(-0.654428\pi\)
0.999261 0.0384402i \(-0.0122389\pi\)
\(632\) 0.544357 0.0216534
\(633\) −0.991071 + 1.71659i −0.0393915 + 0.0682282i
\(634\) −31.7955 55.0714i −1.26276 2.18717i
\(635\) −11.7006 20.2661i −0.464325 0.804234i
\(636\) 0.0990892 0.00392914
\(637\) 0 0
\(638\) 1.40287 0.0555403
\(639\) −14.0395 24.3172i −0.555395 0.961972i
\(640\) 4.07112 + 7.05139i 0.160925 + 0.278731i
\(641\) 9.28610 16.0840i 0.366779 0.635279i −0.622281 0.782794i \(-0.713794\pi\)
0.989060 + 0.147514i \(0.0471273\pi\)
\(642\) 7.08880 0.279773
\(643\) −1.96695 + 3.40686i −0.0775690 + 0.134353i −0.902201 0.431317i \(-0.858049\pi\)
0.824632 + 0.565670i \(0.191382\pi\)
\(644\) 0 0
\(645\) −0.0143591 −0.000565389
\(646\) −3.71518 + 6.43487i −0.146172 + 0.253177i
\(647\) −0.0985378 0.170672i −0.00387392 0.00670983i 0.864082 0.503351i \(-0.167900\pi\)
−0.867956 + 0.496641i \(0.834566\pi\)
\(648\) −2.59407 4.49306i −0.101905 0.176504i
\(649\) −23.4775 −0.921571
\(650\) −3.89922 + 19.0480i −0.152940 + 0.747125i
\(651\) 0 0
\(652\) −3.14172 5.44163i −0.123039 0.213110i
\(653\) 7.23363 + 12.5290i 0.283074 + 0.490298i 0.972140 0.234400i \(-0.0753125\pi\)
−0.689066 + 0.724698i \(0.741979\pi\)
\(654\) 4.91514 8.51327i 0.192197 0.332895i
\(655\) −2.73626 −0.106915
\(656\) −11.8812 + 20.5788i −0.463883 + 0.803468i
\(657\) −21.4635 + 37.1758i −0.837369 + 1.45037i
\(658\) 0 0
\(659\) 11.7066 20.2764i 0.456024 0.789857i −0.542722 0.839912i \(-0.682606\pi\)
0.998746 + 0.0500552i \(0.0159397\pi\)
\(660\) −2.26166 3.91731i −0.0880349 0.152481i
\(661\) −2.02409 3.50582i −0.0787278 0.136361i 0.823973 0.566628i \(-0.191752\pi\)
−0.902701 + 0.430268i \(0.858419\pi\)
\(662\) −36.3313 −1.41206
\(663\) 1.39003 + 1.23278i 0.0539843 + 0.0478771i
\(664\) 11.2587 0.436921
\(665\) 0 0
\(666\) −18.9197 32.7699i −0.733125 1.26981i
\(667\) 0.371744 0.643879i 0.0143940 0.0249311i
\(668\) −3.48896 −0.134992
\(669\) 4.57416 7.92268i 0.176847 0.306309i
\(670\) 5.80440 10.0535i 0.224243 0.388401i
\(671\) 50.7276 1.95832
\(672\) 0 0
\(673\) −3.64704 6.31685i −0.140583 0.243497i 0.787133 0.616783i \(-0.211564\pi\)
−0.927716 + 0.373286i \(0.878231\pi\)
\(674\) −29.8076 51.6283i −1.14815 1.98865i
\(675\) −7.05218 −0.271439
\(676\) −19.4994 8.33241i −0.749976 0.320477i
\(677\) 15.7511 0.605362 0.302681 0.953092i \(-0.402118\pi\)
0.302681 + 0.953092i \(0.402118\pi\)
\(678\) −3.82593 6.62671i −0.146934 0.254497i
\(679\) 0 0
\(680\) −0.622636 + 1.07844i −0.0238770 + 0.0413562i
\(681\) −4.47686 −0.171553
\(682\) 21.9582 38.0327i 0.840822 1.45635i
\(683\) −20.7427 + 35.9274i −0.793697 + 1.37472i 0.129967 + 0.991518i \(0.458513\pi\)
−0.923664 + 0.383204i \(0.874820\pi\)
\(684\) 14.8943 0.569499
\(685\) 9.42819 16.3301i 0.360233 0.623941i
\(686\) 0 0
\(687\) −3.09725 5.36460i −0.118168 0.204672i
\(688\) −0.104689 −0.00399123
\(689\) 0.382470 + 0.339202i 0.0145710 + 0.0129226i
\(690\) −5.33655 −0.203159
\(691\) −23.4108 40.5487i −0.890589 1.54255i −0.839171 0.543868i \(-0.816959\pi\)
−0.0514184 0.998677i \(-0.516374\pi\)
\(692\) −13.5494 23.4683i −0.515073 0.892132i
\(693\) 0 0
\(694\) −22.2478 −0.844514
\(695\) −0.249496 + 0.432140i −0.00946392 + 0.0163920i
\(696\) 0.0252292 0.0436983i 0.000956311 0.00165638i
\(697\) −6.21068 −0.235246
\(698\) −22.8576 + 39.5905i −0.865172 + 1.49852i
\(699\) −1.98977 3.44638i −0.0752600 0.130354i
\(700\) 0 0
\(701\) 29.8626 1.12790 0.563948 0.825810i \(-0.309282\pi\)
0.563948 + 0.825810i \(0.309282\pi\)
\(702\) 3.43371 16.7739i 0.129597 0.633091i
\(703\) −22.8585 −0.862126
\(704\) −10.6048 18.3680i −0.399683 0.692271i
\(705\) −3.68709 6.38623i −0.138864 0.240519i
\(706\) −12.1893 + 21.1124i −0.458749 + 0.794576i
\(707\) 0 0
\(708\) 1.86721 3.23410i 0.0701740 0.121545i
\(709\) −13.4666 + 23.3249i −0.505750 + 0.875984i 0.494228 + 0.869332i \(0.335451\pi\)
−0.999978 + 0.00665185i \(0.997883\pi\)
\(710\) 27.9864 1.05031
\(711\) 1.09067 1.88909i 0.0409031 0.0708463i
\(712\) 2.30450 + 3.99151i 0.0863647 + 0.149588i
\(713\) −11.6373 20.1563i −0.435819 0.754861i
\(714\) 0 0
\(715\) 4.68004 22.8623i 0.175023 0.855003i
\(716\) −0.880004 −0.0328873
\(717\) 4.20590 + 7.28483i 0.157072 + 0.272057i
\(718\) 11.7570 + 20.3638i 0.438769 + 0.759969i
\(719\) −7.24938 + 12.5563i −0.270356 + 0.468271i −0.968953 0.247245i \(-0.920475\pi\)
0.698597 + 0.715516i \(0.253808\pi\)
\(720\) 19.0921 0.711519
\(721\) 0 0
\(722\) −8.08799 + 14.0088i −0.301004 + 0.521354i
\(723\) 3.13240 0.116495
\(724\) 2.26049 3.91528i 0.0840105 0.145510i
\(725\) 0.237090 + 0.410652i 0.00880530 + 0.0152512i
\(726\) −3.38977 5.87125i −0.125806 0.217902i
\(727\) 6.26424 0.232328 0.116164 0.993230i \(-0.462940\pi\)
0.116164 + 0.993230i \(0.462940\pi\)
\(728\) 0 0
\(729\) −17.5866 −0.651357
\(730\) −21.3926 37.0531i −0.791776 1.37140i
\(731\) −0.0136811 0.0236963i −0.000506013 0.000876440i
\(732\) −4.03447 + 6.98790i −0.149118 + 0.258280i
\(733\) 11.9838 0.442631 0.221316 0.975202i \(-0.428965\pi\)
0.221316 + 0.975202i \(0.428965\pi\)
\(734\) −1.93487 + 3.35130i −0.0714175 + 0.123699i
\(735\) 0 0
\(736\) −32.6704 −1.20425
\(737\) 9.08480 15.7353i 0.334643 0.579619i
\(738\) 13.8570 + 24.0010i 0.510084 + 0.883491i
\(739\) −6.76269 11.7133i −0.248770 0.430882i 0.714415 0.699722i \(-0.246693\pi\)
−0.963185 + 0.268840i \(0.913360\pi\)
\(740\) 16.9418 0.622794
\(741\) −3.74704 3.32314i −0.137651 0.122079i
\(742\) 0 0
\(743\) 19.2299 + 33.3072i 0.705477 + 1.22192i 0.966519 + 0.256594i \(0.0826003\pi\)
−0.261043 + 0.965327i \(0.584066\pi\)
\(744\) −0.789789 1.36795i −0.0289551 0.0501516i
\(745\) −2.88966 + 5.00504i −0.105869 + 0.183371i
\(746\) 7.38214 0.270279
\(747\) 22.5577 39.0710i 0.825342 1.42953i
\(748\) 4.30973 7.46466i 0.157579 0.272935i
\(749\) 0 0
\(750\) 4.70855 8.15544i 0.171932 0.297795i
\(751\) −5.85573 10.1424i −0.213679 0.370102i 0.739184 0.673503i \(-0.235211\pi\)
−0.952863 + 0.303401i \(0.901878\pi\)
\(752\) −26.8817 46.5605i −0.980276 1.69789i
\(753\) −5.08302 −0.185236
\(754\) −1.09219 + 0.363983i −0.0397753 + 0.0132555i
\(755\) −3.12125 −0.113594
\(756\) 0 0
\(757\) −4.65791 8.06773i −0.169295 0.293227i 0.768877 0.639396i \(-0.220816\pi\)
−0.938172 + 0.346169i \(0.887482\pi\)
\(758\) −13.8800 + 24.0409i −0.504145 + 0.873205i
\(759\) −8.35255 −0.303178
\(760\) 1.67841 2.90709i 0.0608824 0.105451i
\(761\) −21.9691 + 38.0515i −0.796378 + 1.37937i 0.125582 + 0.992083i \(0.459920\pi\)
−0.921960 + 0.387284i \(0.873413\pi\)
\(762\) 12.9693 0.469830
\(763\) 0 0
\(764\) 16.5079 + 28.5926i 0.597236 + 1.03444i
\(765\) 2.49501 + 4.32148i 0.0902072 + 0.156243i
\(766\) −51.0344 −1.84395
\(767\) 18.2781 6.09134i 0.659985 0.219946i
\(768\) −8.64911 −0.312098
\(769\) 12.6771 + 21.9573i 0.457147 + 0.791802i 0.998809 0.0487946i \(-0.0155380\pi\)
−0.541662 + 0.840597i \(0.682205\pi\)
\(770\) 0 0
\(771\) 3.25024 5.62957i 0.117054 0.202744i
\(772\) −26.7137 −0.961447
\(773\) −11.5542 + 20.0125i −0.415576 + 0.719798i −0.995489 0.0948801i \(-0.969753\pi\)
0.579913 + 0.814678i \(0.303087\pi\)
\(774\) −0.0610493 + 0.105741i −0.00219437 + 0.00380076i
\(775\) 14.8440 0.533212
\(776\) 1.22705 2.12532i 0.0440487 0.0762946i
\(777\) 0 0
\(778\) 11.4474 + 19.8275i 0.410410 + 0.710851i
\(779\) 16.7418 0.599838
\(780\) 2.77716 + 2.46298i 0.0994381 + 0.0881889i
\(781\) 43.8031 1.56740
\(782\) −5.08456 8.80672i −0.181824 0.314928i
\(783\) −0.208785 0.361626i −0.00746135 0.0129234i