Properties

Label 637.2.h.l.471.2
Level $637$
Weight $2$
Character 637.471
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.h (of order \(3\), degree \(2\), not 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 471.2
Root \(1.16700 + 2.02131i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.l.165.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.90556 q^{2} +(0.214224 - 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})\) \(q-1.90556 q^{2} +(0.214224 - 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 + 1.27577i) 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} +(0.349433 - 0.605236i) q^{12} +(-2.69752 - 2.39236i) q^{13} +(0.315580 + 0.546600i) q^{15} -4.60164 q^{16} +1.20271 q^{17} +(-2.68344 - 4.64786i) q^{18} +(1.62105 + 2.80773i) q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} -4.43710 q^{23} +(0.150567 - 0.260790i) q^{24} +(1.41494 + 2.45075i) q^{25} +(5.14029 + 4.55878i) q^{26} +2.49204 q^{27} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 - 1.04158i) q^{30} +(2.62272 + 4.54268i) q^{31} +7.36300 q^{32} +(-0.941217 - 1.63024i) q^{33} -2.29184 q^{34} +(2.29702 + 3.97856i) q^{36} +7.05055 q^{37} +(-3.08900 - 5.35031i) q^{38} +(-1.46555 + 0.488407i) q^{39} +(-0.517694 + 0.896672i) q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} -4.14897 q^{45} +8.45516 q^{46} +(5.84178 - 10.1183i) q^{47} +(-0.985780 + 1.70742i) q^{48} +(-2.69626 - 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(-4.40009 - 3.90231i) q^{52} +(0.0708929 + 0.122790i) q^{53} -4.74873 q^{54} +(3.23618 + 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} +5.34354 q^{59} +(0.514760 + 0.891591i) q^{60} +(5.77287 + 9.99891i) q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(5.03899 - 1.67929i) q^{65} +(1.79355 + 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} +1.96181 q^{68} +(-0.950533 + 1.64637i) q^{69} +(4.98486 - 8.63403i) q^{71} +(0.989763 + 1.71432i) q^{72} +(7.62080 + 13.1996i) q^{73} -13.4352 q^{74} +1.21246 q^{75} +(2.64418 + 4.57986i) q^{76} +(2.79269 - 0.930689i) q^{78} +(-0.387251 + 0.670738i) 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} +(0.0216761 - 0.0375441i) q^{86} -0.0717913 q^{87} +(1.54402 - 2.67433i) q^{88} -6.55760 q^{89} +7.90611 q^{90} -7.23762 q^{92} +2.24739 q^{93} +(-11.1319 + 19.2809i) q^{94} -4.77602 q^{95} +(1.57733 - 2.73202i) q^{96} +(1.74583 - 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90556 −1.34743 −0.673717 0.738989i \(-0.735303\pi\)
−0.673717 + 0.738989i \(0.735303\pi\)
\(3\) 0.214224 0.371047i 0.123682 0.214224i −0.797535 0.603273i \(-0.793863\pi\)
0.921217 + 0.389049i \(0.127196\pi\)
\(4\) 1.63116 0.815580
\(5\) −0.736565 + 1.27577i −0.329402 + 0.570541i −0.982393 0.186825i \(-0.940180\pi\)
0.652991 + 0.757365i \(0.273514\pi\)
\(6\) −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 −0.317631 0.948214i \(-0.602887\pi\)
0.979993 0.199031i \(-0.0637794\pi\)
\(12\) 0.349433 0.605236i 0.100873 0.174717i
\(13\) −2.69752 2.39236i −0.748158 0.663520i
\(14\) 0 0
\(15\) 0.315580 + 0.546600i 0.0814823 + 0.141131i
\(16\) −4.60164 −1.15041
\(17\) 1.20271 0.291700 0.145850 0.989307i \(-0.453408\pi\)
0.145850 + 0.989307i \(0.453408\pi\)
\(18\) −2.68344 4.64786i −0.632493 1.09551i
\(19\) 1.62105 + 2.80773i 0.371893 + 0.644138i 0.989857 0.142068i \(-0.0453753\pi\)
−0.617963 + 0.786207i \(0.712042\pi\)
\(20\) −1.20145 + 2.08098i −0.268653 + 0.465321i
\(21\) 0 0
\(22\) −4.18615 + 7.25062i −0.892490 + 1.54584i
\(23\) −4.43710 −0.925200 −0.462600 0.886567i \(-0.653083\pi\)
−0.462600 + 0.886567i \(0.653083\pi\)
\(24\) 0.150567 0.260790i 0.0307343 0.0532334i
\(25\) 1.41494 + 2.45075i 0.282989 + 0.490151i
\(26\) 5.14029 + 4.55878i 1.00809 + 0.894050i
\(27\) 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
\(31\) 2.62272 + 4.54268i 0.471054 + 0.815889i 0.999452 0.0331076i \(-0.0105404\pi\)
−0.528398 + 0.848997i \(0.677207\pi\)
\(32\) 7.36300 1.30161
\(33\) −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
\(37\) 7.05055 1.15910 0.579552 0.814936i \(-0.303228\pi\)
0.579552 + 0.814936i \(0.303228\pi\)
\(38\) −3.08900 5.35031i −0.501102 0.867934i
\(39\) −1.46555 + 0.488407i −0.234676 + 0.0782077i
\(40\) −0.517694 + 0.896672i −0.0818546 + 0.141776i
\(41\) 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 \(0.167219\pi\)
\(44\) 3.58334 6.20653i 0.540209 0.935670i
\(45\) −4.14897 −0.618492
\(46\) 8.45516 1.24665
\(47\) 5.84178 10.1183i 0.852111 1.47590i −0.0271891 0.999630i \(-0.508656\pi\)
0.879300 0.476269i \(-0.158011\pi\)
\(48\) −0.985780 + 1.70742i −0.142285 + 0.246445i
\(49\) 0 0
\(50\) −2.69626 4.67006i −0.381309 0.660446i
\(51\) 0.257649 0.446262i 0.0360781 0.0624892i
\(52\) −4.40009 3.90231i −0.610183 0.541154i
\(53\) 0.0708929 + 0.122790i 0.00973788 + 0.0168665i 0.870853 0.491543i \(-0.163567\pi\)
−0.861115 + 0.508410i \(0.830234\pi\)
\(54\) −4.74873 −0.646220
\(55\) 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
\(59\) 5.34354 0.695670 0.347835 0.937556i \(-0.386917\pi\)
0.347835 + 0.937556i \(0.386917\pi\)
\(60\) 0.514760 + 0.891591i 0.0664553 + 0.115104i
\(61\) 5.77287 + 9.99891i 0.739141 + 1.28023i 0.952883 + 0.303339i \(0.0981016\pi\)
−0.213742 + 0.976890i \(0.568565\pi\)
\(62\) −4.99774 8.65635i −0.634714 1.09936i
\(63\) 0 0
\(64\) −4.82736 −0.603420
\(65\) 5.03899 1.67929i 0.625010 0.208290i
\(66\) 1.79355 + 3.10651i 0.220770 + 0.382385i
\(67\) −2.06773 + 3.58141i −0.252613 + 0.437539i −0.964245 0.265014i \(-0.914623\pi\)
0.711631 + 0.702553i \(0.247957\pi\)
\(68\) 1.96181 0.237905
\(69\) −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
\(73\) 7.62080 + 13.1996i 0.891947 + 1.54490i 0.837539 + 0.546378i \(0.183994\pi\)
0.0544080 + 0.998519i \(0.482673\pi\)
\(74\) −13.4352 −1.56182
\(75\) 1.21246 0.140003
\(76\) 2.64418 + 4.57986i 0.303309 + 0.525346i
\(77\) 0 0
\(78\) 2.79269 0.930689i 0.316210 0.105380i
\(79\) −0.387251 + 0.670738i −0.0435691 + 0.0754639i −0.886988 0.461793i \(-0.847206\pi\)
0.843418 + 0.537257i \(0.180540\pi\)
\(80\) 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
\(86\) 0.0216761 0.0375441i 0.00233740 0.00404849i
\(87\) −0.0717913 −0.00769683
\(88\) 1.54402 2.67433i 0.164593 0.285084i
\(89\) −6.55760 −0.695104 −0.347552 0.937661i \(-0.612987\pi\)
−0.347552 + 0.937661i \(0.612987\pi\)
\(90\) 7.90611 0.833378
\(91\) 0 0
\(92\) −7.23762 −0.754574
\(93\) 2.24739 0.233044
\(94\) −11.1319 + 19.2809i −1.14816 + 1.98868i
\(95\) −4.77602 −0.490010
\(96\) 1.57733 2.73202i 0.160986 0.278835i
\(97\) 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 −0.794749 0.606939i \(-0.792397\pi\)
0.922999 + 0.384803i \(0.125731\pi\)
\(102\) −0.490966 + 0.850379i −0.0486129 + 0.0842000i
\(103\) −8.43173 + 14.6042i −0.830803 + 1.43899i 0.0665997 + 0.997780i \(0.478785\pi\)
−0.897402 + 0.441213i \(0.854548\pi\)
\(104\) −1.89595 1.68146i −0.185913 0.164881i
\(105\) 0 0
\(106\) −0.135091 0.233984i −0.0131212 0.0227265i
\(107\) 8.68265 0.839383 0.419692 0.907667i \(-0.362138\pi\)
0.419692 + 0.907667i \(0.362138\pi\)
\(108\) 4.06491 0.391146
\(109\) 6.02026 + 10.4274i 0.576637 + 0.998764i 0.995862 + 0.0908816i \(0.0289685\pi\)
−0.419225 + 0.907882i \(0.637698\pi\)
\(110\) −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 \(0.311985\pi\)
\(114\) −2.64695 −0.247910
\(115\) 3.26821 5.66071i 0.304763 0.527864i
\(116\) −0.136660 0.236701i −0.0126885 0.0219772i
\(117\) 2.03651 9.94849i 0.188275 0.919738i
\(118\) −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
\(122\) −11.0006 19.0535i −0.995944 1.72503i
\(123\) 2.21246 0.199491
\(124\) 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 \(-0.415630\pi\)
\(128\) −5.52717 −0.488537
\(129\) 0.00487367 + 0.00844145i 0.000429103 + 0.000743228i
\(130\) −9.60210 + 3.19998i −0.842160 + 0.280657i
\(131\) 0.928725 1.60860i 0.0811430 0.140544i −0.822598 0.568623i \(-0.807476\pi\)
0.903741 + 0.428079i \(0.140810\pi\)
\(132\) −1.53527 2.65917i −0.133628 0.231451i
\(133\) 0 0
\(134\) 3.94018 6.82459i 0.340380 0.589555i
\(135\) −1.83555 + 3.17926i −0.157979 + 0.273627i
\(136\) 0.845324 0.0724859
\(137\) −12.8002 −1.09360 −0.546798 0.837264i \(-0.684153\pi\)
−0.546798 + 0.837264i \(0.684153\pi\)
\(138\) 1.81130 3.13726i 0.154188 0.267061i
\(139\) −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
\(142\) −9.49894 + 16.4527i −0.797134 + 1.38068i
\(143\) −15.0288 + 5.00848i −1.25677 + 0.418830i
\(144\) −6.48010 11.2239i −0.540009 0.935322i
\(145\) 0.246840 0.0204989
\(146\) −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 0.774421 0.632671i \(-0.218041\pi\)
−0.935120 + 0.354332i \(0.884708\pi\)
\(150\) −2.31041 −0.188644
\(151\) 1.05939 + 1.83492i 0.0862122 + 0.149324i 0.905907 0.423476i \(-0.139190\pi\)
−0.819695 + 0.572800i \(0.805857\pi\)
\(152\) 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
\(156\) −2.39054 + 0.796669i −0.191397 + 0.0637846i
\(157\) −11.0564 19.1502i −0.882397 1.52836i −0.848668 0.528925i \(-0.822595\pi\)
−0.0337285 0.999431i \(-0.510738\pi\)
\(158\) 0.737929 1.27813i 0.0587065 0.101683i
\(159\) 0.0607478 0.00481761
\(160\) −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 0.780683 0.624927i \(-0.214871\pi\)
−0.931544 + 0.363628i \(0.881538\pi\)
\(164\) 4.21157 + 7.29465i 0.328868 + 0.569616i
\(165\) 2.77307 0.215883
\(166\) −30.5244 −2.36916
\(167\) 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
\(170\) 1.68809 2.92385i 0.129470 0.224249i
\(171\) −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 −0.987237 0.159260i \(-0.949089\pi\)
0.355695 0.934602i \(-0.384244\pi\)
\(174\) 0.136803 0.0103710
\(175\) 0 0
\(176\) −10.1089 + 17.5091i −0.761988 + 1.31980i
\(177\) 1.14471 1.98270i 0.0860419 0.149029i
\(178\) 12.4959 0.936607
\(179\) 0.269748 0.467217i 0.0201619 0.0349214i −0.855768 0.517359i \(-0.826915\pi\)
0.875930 + 0.482438i \(0.160248\pi\)
\(180\) −6.76763 −0.504430
\(181\) −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
\(184\) −3.11861 −0.229907
\(185\) −5.19319 + 8.99486i −0.381811 + 0.661316i
\(186\) −4.28254 −0.314011
\(187\) 2.64213 4.57629i 0.193211 0.334652i
\(188\) 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 0.955905 + 0.293677i \(0.0948790\pi\)
−0.223621 + 0.974676i \(0.571788\pi\)
\(192\) −1.03414 + 1.79118i −0.0746323 + 0.129267i
\(193\) 8.18856 14.1830i 0.589425 1.02091i −0.404882 0.914369i \(-0.632688\pi\)
0.994308 0.106546i \(-0.0339791\pi\)
\(194\) −3.32678 + 5.76216i −0.238849 + 0.413699i
\(195\) 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 \(-0.414813\pi\)
\(198\) −23.5800 −1.67576
\(199\) 14.1175 1.00076 0.500380 0.865806i \(-0.333194\pi\)
0.500380 + 0.865806i \(0.333194\pi\)
\(200\) 0.994491 + 1.72251i 0.0703212 + 0.121800i
\(201\) 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
\(205\) −7.60709 −0.531302
\(206\) 16.0672 27.8291i 1.11945 1.93895i
\(207\) −6.24840 10.8225i −0.434294 0.752219i
\(208\) 12.4130 + 11.0088i 0.860688 + 0.763320i
\(209\) 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
\(213\) −2.13575 3.69923i −0.146339 0.253467i
\(214\) −16.5453 −1.13101
\(215\) −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
\(219\) 6.53022 0.441272
\(220\) 5.27873 + 9.14303i 0.355892 + 0.616423i
\(221\) −3.24434 2.87731i −0.218238 0.193549i
\(222\) −2.87815 + 4.98510i −0.193169 + 0.334578i
\(223\) −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
\(226\) 8.92976 15.4668i 0.593999 1.02884i
\(227\) 10.4490 0.693526 0.346763 0.937953i \(-0.387281\pi\)
0.346763 + 0.937953i \(0.387281\pi\)
\(228\) 2.26579 0.150056
\(229\) 7.22901 12.5210i 0.477706 0.827412i −0.521967 0.852966i \(-0.674802\pi\)
0.999673 + 0.0255538i \(0.00813493\pi\)
\(230\) −6.22778 + 10.7868i −0.410648 + 0.711262i
\(231\) 0 0
\(232\) −0.0588852 0.101992i −0.00386600 0.00669611i
\(233\) 4.64413 8.04388i 0.304247 0.526972i −0.672846 0.739783i \(-0.734928\pi\)
0.977093 + 0.212811i \(0.0682617\pi\)
\(234\) −3.88068 + 18.9574i −0.253688 + 1.23929i
\(235\) 8.60570 + 14.9055i 0.561374 + 0.972328i
\(236\) 8.71616 0.567374
\(237\) 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
\(241\) −7.31105 −0.470946 −0.235473 0.971881i \(-0.575664\pi\)
−0.235473 + 0.971881i \(0.575664\pi\)
\(242\) 7.91174 + 13.7035i 0.508586 + 0.880897i
\(243\) 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
\(247\) 2.34429 11.4520i 0.149164 0.728676i
\(248\) 1.84337 + 3.19282i 0.117054 + 0.202744i
\(249\) 3.43157 5.94365i 0.217467 0.376664i
\(250\) 21.9796 1.39011
\(251\) −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
\(255\) 0.379551 + 0.657402i 0.0237684 + 0.0411681i
\(256\) 20.1871 1.26169
\(257\) 15.1722 0.946413 0.473206 0.880952i \(-0.343096\pi\)
0.473206 + 0.880952i \(0.343096\pi\)
\(258\) −0.00928708 0.0160857i −0.000578188 0.00100145i
\(259\) 0 0
\(260\) 8.21940 2.73919i 0.509745 0.169877i
\(261\) 0.235963 0.408699i 0.0146057 0.0252979i
\(262\) −1.76974 + 3.06528i −0.109335 + 0.189374i
\(263\) −8.59820 + 14.8925i −0.530187 + 0.918312i 0.469192 + 0.883096i \(0.344545\pi\)
−0.999380 + 0.0352156i \(0.988788\pi\)
\(264\) −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
\(268\) −3.37279 + 5.84185i −0.206026 + 0.356848i
\(269\) −18.9220 −1.15370 −0.576849 0.816851i \(-0.695718\pi\)
−0.576849 + 0.816851i \(0.695718\pi\)
\(270\) 3.49774 6.05827i 0.212866 0.368695i
\(271\) −32.1334 −1.95196 −0.975982 0.217853i \(-0.930095\pi\)
−0.975982 + 0.217853i \(0.930095\pi\)
\(272\) −5.53444 −0.335575
\(273\) 0 0
\(274\) 24.3916 1.47355
\(275\) 12.4334 0.749764
\(276\) −1.55047 + 2.68549i −0.0933273 + 0.161648i
\(277\) 18.4054 1.10587 0.552936 0.833224i \(-0.313507\pi\)
0.552936 + 0.833224i \(0.313507\pi\)
\(278\) 0.322734 0.558992i 0.0193563 0.0335261i
\(279\) −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 −0.984374 0.176089i \(-0.943655\pi\)
0.644685 + 0.764448i \(0.276989\pi\)
\(284\) 8.13109 14.0835i 0.482492 0.835700i
\(285\) −1.02314 + 1.77213i −0.0606055 + 0.104972i
\(286\) 28.6383 9.54396i 1.69342 0.564346i
\(287\) 0 0
\(288\) 10.3687 + 17.9591i 0.610981 + 1.05825i
\(289\) −15.5535 −0.914911
\(290\) −0.470368 −0.0276210
\(291\) −0.747997 1.29557i −0.0438483 0.0759476i
\(292\) 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
\(296\) 4.95547 0.288031
\(297\) 5.47452 9.48215i 0.317664 0.550210i
\(298\) 3.73791 + 6.47425i 0.216531 + 0.375043i
\(299\) 11.9692 + 10.6151i 0.692196 + 0.613889i
\(300\) 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
\(304\) −7.45947 12.9202i −0.427830 0.741023i
\(305\) −17.0084 −0.973898
\(306\) −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
\(310\) 14.7247 0.836304
\(311\) −1.02298 1.77186i −0.0580081 0.100473i 0.835563 0.549395i \(-0.185142\pi\)
−0.893571 + 0.448922i \(0.851808\pi\)
\(312\) −1.03006 + 0.343276i −0.0583156 + 0.0194342i
\(313\) 4.70883 8.15594i 0.266159 0.461001i −0.701708 0.712465i \(-0.747579\pi\)
0.967867 + 0.251464i \(0.0809120\pi\)
\(314\) 21.0686 + 36.4919i 1.18897 + 2.05936i
\(315\) 0 0
\(316\) −0.631667 + 1.09408i −0.0355341 + 0.0615468i
\(317\) 16.6856 28.9004i 0.937159 1.62321i 0.166421 0.986055i \(-0.446779\pi\)
0.770738 0.637153i \(-0.219888\pi\)
\(318\) −0.115758 −0.00649141
\(319\) −0.736200 −0.0412193
\(320\) 3.55567 6.15860i 0.198768 0.344276i
\(321\) 1.86003 3.22167i 0.103817 0.179816i
\(322\) 0 0
\(323\) 1.94965 + 3.37689i 0.108481 + 0.187895i
\(324\) −6.02027 + 10.4274i −0.334460 + 0.579301i
\(325\) 2.04624 9.99602i 0.113505 0.554479i
\(326\) 3.67024 + 6.35704i 0.203276 + 0.352084i
\(327\) 5.15873 0.285279
\(328\) 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 −0.999610 0.0279144i \(-0.991113\pi\)
0.475631 0.879645i \(-0.342220\pi\)
\(332\) 26.1289 1.43401
\(333\) 9.92870 + 17.1970i 0.544089 + 0.942390i
\(334\) −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 \(0.824670\pi\)
\(338\) −2.95983 24.5948i −0.160994 1.33778i
\(339\) 2.00777 + 3.47757i 0.109047 + 0.188876i
\(340\) −1.44500 + 2.50282i −0.0783663 + 0.135734i
\(341\) 23.0464 1.24803
\(342\) 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
\(346\) 15.8288 + 27.4163i 0.850961 + 1.47391i
\(347\) 11.6752 0.626757 0.313378 0.949628i \(-0.398539\pi\)
0.313378 + 0.949628i \(0.398539\pi\)
\(348\) −0.117103 −0.00627738
\(349\) 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
\(352\) 16.1751 28.0161i 0.862135 1.49326i
\(353\) 6.39668 11.0794i 0.340461 0.589696i −0.644057 0.764977i \(-0.722750\pi\)
0.984518 + 0.175282i \(0.0560836\pi\)
\(354\) −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
\(359\) −6.16986 + 10.6865i −0.325633 + 0.564012i −0.981640 0.190742i \(-0.938911\pi\)
0.656008 + 0.754754i \(0.272244\pi\)
\(360\) −2.91610 −0.153692
\(361\) 4.24442 7.35155i 0.223390 0.386924i
\(362\) 5.28152 0.277591
\(363\) −3.55776 −0.186734
\(364\) 0 0
\(365\) −22.4528 −1.17524
\(366\) −9.42633 −0.492722
\(367\) 1.01538 1.75870i 0.0530026 0.0918032i −0.838307 0.545199i \(-0.816454\pi\)
0.891309 + 0.453396i \(0.149788\pi\)
\(368\) 20.4179 1.06436
\(369\) −7.27188 + 12.5953i −0.378559 + 0.655684i
\(370\) 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 0.911806 0.410622i \(-0.134688\pi\)
−0.811512 + 0.584336i \(0.801355\pi\)
\(374\) −5.03473 + 8.72040i −0.260340 + 0.450921i
\(375\) −2.47095 + 4.27981i −0.127599 + 0.221009i
\(376\) 4.10588 7.11160i 0.211745 0.366753i
\(377\) −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 \(0.711267\pi\)
\(380\) −7.79045 −0.399642
\(381\) −6.80606 −0.348685
\(382\) −19.2850 33.4025i −0.986705 1.70902i
\(383\) −13.3909 23.1937i −0.684243 1.18514i −0.973674 0.227945i \(-0.926799\pi\)
0.289430 0.957199i \(-0.406534\pi\)
\(384\) −1.18405 + 2.05084i −0.0604234 + 0.104656i
\(385\) 0 0
\(386\) −15.6038 + 27.0266i −0.794212 + 1.37562i
\(387\) −0.0640749 −0.00325711
\(388\) 2.84773 4.93241i 0.144571 0.250405i
\(389\) −6.00738 10.4051i −0.304586 0.527559i 0.672583 0.740022i \(-0.265185\pi\)
−0.977169 + 0.212463i \(0.931852\pi\)
\(390\) −0.869656 + 4.24834i −0.0440368 + 0.215123i
\(391\) −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
\(395\) −0.570470 0.988084i −0.0287035 0.0497159i
\(396\) 20.1845 1.01431
\(397\) −0.828825 1.43557i −0.0415975 0.0720491i 0.844477 0.535592i \(-0.179911\pi\)
−0.886075 + 0.463543i \(0.846578\pi\)
\(398\) −26.9017 −1.34846
\(399\) 0 0
\(400\) −6.51106 11.2775i −0.325553 0.563874i
\(401\) −20.4828 −1.02286 −0.511430 0.859325i \(-0.670884\pi\)
−0.511430 + 0.859325i \(0.670884\pi\)
\(402\) −1.68816 2.92398i −0.0841978 0.145835i
\(403\) 3.79287 18.5285i 0.188936 0.922968i
\(404\) 2.10240 3.64146i 0.104598 0.181169i
\(405\) −5.43702 9.41720i −0.270168 0.467944i
\(406\) 0 0
\(407\) 15.4887 26.8272i 0.767746 1.32978i
\(408\) 0.181089 0.313655i 0.00896522 0.0155282i
\(409\) −14.8659 −0.735070 −0.367535 0.930010i \(-0.619798\pi\)
−0.367535 + 0.930010i \(0.619798\pi\)
\(410\) 14.4958 0.715895
\(411\) −2.74211 + 4.74948i −0.135258 + 0.234274i
\(412\) −13.7535 + 23.8217i −0.677586 + 1.17361i
\(413\) 0 0
\(414\) 11.9067 + 20.6230i 0.585182 + 1.01357i
\(415\) −11.7988 + 20.4360i −0.579178 + 1.00317i
\(416\) −19.8619 17.6149i −0.973808 0.863643i
\(417\) 0.0725639 + 0.125684i 0.00355347 + 0.00615479i
\(418\) −27.1438 −1.32764
\(419\) −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
\(423\) 32.9059 1.59994
\(424\) 0.0498269 + 0.0863028i 0.00241981 + 0.00419123i
\(425\) 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
\(429\) −1.36115 + 6.64932i −0.0657169 + 0.321032i
\(430\) 0.0319317 + 0.0553074i 0.00153988 + 0.00266716i
\(431\) 6.65859 11.5330i 0.320733 0.555526i −0.659906 0.751348i \(-0.729404\pi\)
0.980640 + 0.195822i \(0.0627374\pi\)
\(432\) −11.4675 −0.551728
\(433\) 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
\(437\) −7.19275 12.4582i −0.344076 0.595957i
\(438\) −12.4437 −0.594585
\(439\) 9.77074 0.466332 0.233166 0.972437i \(-0.425091\pi\)
0.233166 + 0.972437i \(0.425091\pi\)
\(440\) 2.27455 + 3.93963i 0.108435 + 0.187814i
\(441\) 0 0
\(442\) 6.18229 + 5.48290i 0.294061 + 0.260795i
\(443\) −10.5819 + 18.3285i −0.502763 + 0.870811i 0.497232 + 0.867618i \(0.334350\pi\)
−0.999995 + 0.00319331i \(0.998984\pi\)
\(444\) 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 \(0.0258178\pi\)
\(450\) 7.59384 13.1529i 0.357977 0.620034i
\(451\) 22.6882 1.06834
\(452\) −7.64387 + 13.2396i −0.359538 + 0.622737i
\(453\) 0.907789 0.0426517
\(454\) −19.9112 −0.934480
\(455\) 0 0
\(456\) 0.976304 0.0457196
\(457\) −18.0198 −0.842932 −0.421466 0.906844i \(-0.638484\pi\)
−0.421466 + 0.906844i \(0.638484\pi\)
\(458\) −13.7753 + 23.8595i −0.643678 + 1.11488i
\(459\) 2.99720 0.139897
\(460\) 5.33098 9.23352i 0.248558 0.430515i
\(461\) −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
\(467\) −2.91461 + 5.04825i −0.134872 + 0.233605i −0.925549 0.378629i \(-0.876396\pi\)
0.790677 + 0.612234i \(0.209729\pi\)
\(468\) 3.32186 16.2276i 0.153553 0.750120i
\(469\) 0 0
\(470\) −16.3987 28.4033i −0.756414 1.31015i
\(471\) −9.47418 −0.436547
\(472\) 3.75570 0.172870
\(473\) 0.0499782 + 0.0865648i 0.00229800 + 0.00398025i
\(474\) −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
\(478\) −37.4122 −1.71120
\(479\) 7.24565 12.5498i 0.331062 0.573417i −0.651658 0.758513i \(-0.725926\pi\)
0.982720 + 0.185096i \(0.0592596\pi\)
\(480\) 2.32361 + 4.02461i 0.106058 + 0.183698i
\(481\) −19.0190 16.8674i −0.867193 0.769088i
\(482\) 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
\(486\) −10.1364 17.5567i −0.459795 0.796389i
\(487\) −17.9601 −0.813851 −0.406926 0.913461i \(-0.633399\pi\)
−0.406926 + 0.913461i \(0.633399\pi\)
\(488\) 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 \(0.527796\pi\)
\(492\) 3.60887 0.162701
\(493\) −0.100764 0.174528i −0.00453818 0.00786036i
\(494\) −4.46719 + 21.8226i −0.200988 + 0.981844i
\(495\) −9.11449 + 15.7868i −0.409666 + 0.709562i
\(496\) −12.0688 20.9038i −0.541905 0.938607i
\(497\) 0 0
\(498\) −6.53906 + 11.3260i −0.293022 + 0.507530i
\(499\) −11.8538 + 20.5314i −0.530649 + 0.919112i 0.468711 + 0.883352i \(0.344719\pi\)
−0.999360 + 0.0357602i \(0.988615\pi\)
\(500\) −18.8145 −0.841410
\(501\) 0.916426 0.0409429
\(502\) 11.3036 19.5784i 0.504505 0.873828i
\(503\) 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
\(506\) 18.5744 32.1717i 0.825731 1.43021i
\(507\) 5.12180 + 2.18863i 0.227467 + 0.0972003i
\(508\) −12.9558 22.4401i −0.574820 0.995618i
\(509\) −8.70416 −0.385805 −0.192902 0.981218i \(-0.561790\pi\)
−0.192902 + 0.981218i \(0.561790\pi\)
\(510\) −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
\(514\) −28.9114 −1.27523
\(515\) −12.4210 21.5139i −0.547336 0.948014i
\(516\) 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
\(520\) 3.54165 1.18028i 0.155312 0.0517589i
\(521\) −4.28573 7.42310i −0.187761 0.325212i 0.756742 0.653713i \(-0.226790\pi\)
−0.944504 + 0.328501i \(0.893456\pi\)
\(522\) −0.449641 + 0.778801i −0.0196803 + 0.0340872i
\(523\) −29.9493 −1.30959 −0.654796 0.755806i \(-0.727245\pi\)
−0.654796 + 0.755806i \(0.727245\pi\)
\(524\) 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
\(528\) 4.33114 + 7.50175i 0.188489 + 0.326472i
\(529\) −3.31212 −0.144005
\(530\) 0.398012 0.0172885
\(531\) 7.52486 + 13.0334i 0.326551 + 0.565603i
\(532\) 0 0
\(533\) 3.73391 18.2404i 0.161734 0.790081i
\(534\) 2.67692 4.63656i 0.115842 0.200643i
\(535\) −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
\(541\) −5.24095 + 9.07760i −0.225326 + 0.390276i −0.956417 0.292003i \(-0.905678\pi\)
0.731091 + 0.682280i \(0.239011\pi\)
\(542\) 61.2321 2.63014
\(543\) −0.593751 + 1.02841i −0.0254803 + 0.0441331i
\(544\) 8.85557 0.379679
\(545\) −17.7373 −0.759781
\(546\) 0 0
\(547\) 15.2216 0.650829 0.325415 0.945571i \(-0.394496\pi\)
0.325415 + 0.945571i \(0.394496\pi\)
\(548\) −20.8792 −0.891915
\(549\) −16.2589 + 28.1613i −0.693914 + 1.20189i
\(550\) −23.6927 −1.01026
\(551\) 0.271625 0.470468i 0.0115716 0.0200426i
\(552\) −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 −0.963872 0.266366i \(-0.914177\pi\)
0.712616 + 0.701555i \(0.247510\pi\)
\(558\) 14.0758 24.3800i 0.595877 1.03209i
\(559\) 0.0778200 0.0259342i 0.00329144 0.00109690i
\(560\) 0 0
\(561\) −1.13201 1.96070i −0.0477936 0.0827809i
\(562\) 27.1069 1.14344
\(563\) −7.69349 −0.324242 −0.162121 0.986771i \(-0.551834\pi\)
−0.162121 + 0.986771i \(0.551834\pi\)
\(564\) −4.08262 7.07131i −0.171909 0.297756i
\(565\) −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
\(569\) 37.4196 1.56871 0.784355 0.620312i \(-0.212994\pi\)
0.784355 + 0.620312i \(0.212994\pi\)
\(570\) 1.94965 3.37689i 0.0816619 0.141443i
\(571\) −7.08285 12.2679i −0.296408 0.513394i 0.678903 0.734228i \(-0.262456\pi\)
−0.975311 + 0.220834i \(0.929122\pi\)
\(572\) −24.5144 + 8.16963i −1.02500 + 0.341589i
\(573\) 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
\(577\) −7.48776 12.9692i −0.311720 0.539914i 0.667015 0.745044i \(-0.267572\pi\)
−0.978735 + 0.205130i \(0.934238\pi\)
\(578\) 29.6381 1.23278
\(579\) −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
\(583\) 0.622952 0.0258000
\(584\) 5.35627 + 9.27732i 0.221644 + 0.383898i
\(585\) 11.1919 + 9.92582i 0.462730 + 0.410382i
\(586\) 12.5811 21.7911i 0.519720 0.900182i
\(587\) −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
\(590\) 7.50003 12.9904i 0.308771 0.534807i
\(591\) −8.45478 −0.347783
\(592\) −32.4441 −1.33344
\(593\) −22.0663 + 38.2200i −0.906156 + 1.56951i −0.0867989 + 0.996226i \(0.527664\pi\)
−0.819357 + 0.573283i \(0.805670\pi\)
\(594\) −10.4320 + 18.0688i −0.428032 + 0.741372i
\(595\) 0 0
\(596\) −3.19965 5.54195i −0.131063 0.227007i
\(597\) 3.02429 5.23823i 0.123776 0.214387i
\(598\) −22.8080 20.2278i −0.932689 0.827175i
\(599\) 3.01349 + 5.21952i 0.123128 + 0.213264i 0.921000 0.389564i \(-0.127374\pi\)
−0.797872 + 0.602827i \(0.794041\pi\)
\(600\) 0.852175 0.0347899
\(601\) 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
\(605\) 12.2326 0.497328
\(606\) 1.05230 + 1.82263i 0.0427467 + 0.0740394i
\(607\) −3.00825 5.21045i −0.122101 0.211486i 0.798495 0.602002i \(-0.205630\pi\)
−0.920596 + 0.390516i \(0.872297\pi\)
\(608\) 11.9358 + 20.6733i 0.484059 + 0.838415i
\(609\) 0 0
\(610\) 32.4105 1.31226
\(611\) −39.9648 + 13.3186i −1.61680 + 0.538813i
\(612\) 2.76266 + 4.78506i 0.111674 + 0.193425i
\(613\) −4.90413 + 8.49420i −0.198076 + 0.343077i −0.947904 0.318555i \(-0.896803\pi\)
0.749829 + 0.661632i \(0.230136\pi\)
\(614\) −12.6892 −0.512094
\(615\) −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
\(619\) 2.04671 + 3.54501i 0.0822644 + 0.142486i 0.904222 0.427062i \(-0.140451\pi\)
−0.821958 + 0.569548i \(0.807118\pi\)
\(620\) −12.6043 −0.506201
\(621\) −11.0574 −0.443719
\(622\) 1.94936 + 3.37639i 0.0781621 + 0.135381i
\(623\) 0 0
\(624\) 6.74393 2.24747i 0.269973 0.0899709i
\(625\) 1.42115 2.46150i 0.0568459 0.0984599i
\(626\) −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 \(-0.0122389\pi\)
\(632\) −0.272179 + 0.471427i −0.0108267 + 0.0187524i
\(633\) 1.98214 0.0787831
\(634\) −31.7955 + 55.0714i −1.26276 + 2.18717i
\(635\) 23.4012 0.928650
\(636\) 0.0990892 0.00392914
\(637\) 0 0
\(638\) 1.40287 0.0555403
\(639\) 28.0790 1.11079
\(640\) 4.07112 7.05139i 0.160925 0.278731i
\(641\) −18.5722 −0.733558 −0.366779 0.930308i \(-0.619539\pi\)
−0.366779 + 0.930308i \(0.619539\pi\)
\(642\) −3.54440 + 6.13908i −0.139886 + 0.242290i
\(643\) −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 −0.867956 0.496641i \(-0.834566\pi\)
0.864082 + 0.503351i \(0.167900\pi\)
\(648\) −2.59407 + 4.49306i −0.101905 + 0.176504i
\(649\) 11.7387 20.3321i 0.460785 0.798104i
\(650\) −3.89922 + 19.0480i −0.152940 + 0.747125i
\(651\) 0 0
\(652\) −3.14172 5.44163i −0.123039 0.213110i
\(653\) −14.4673 −0.566148 −0.283074 0.959098i \(-0.591354\pi\)
−0.283074 + 0.959098i \(0.591354\pi\)
\(654\) −9.83028 −0.384394
\(655\) 1.36813 + 2.36967i 0.0534573 + 0.0925908i
\(656\) −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 \(0.0159397\pi\)
\(660\) 4.52332 0.176070
\(661\) −2.02409 + 3.50582i −0.0787278 + 0.136361i −0.902701 0.430268i \(-0.858419\pi\)
0.823973 + 0.566628i \(0.191752\pi\)
\(662\) 18.1657 + 31.4638i 0.706028 + 1.22288i
\(663\) −1.76263 + 0.587412i −0.0684550 + 0.0228132i
\(664\) 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
\(668\) 1.74448 + 3.02153i 0.0674959 + 0.116906i
\(669\) −9.14832 −0.353695
\(670\) 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 \(0.878231\pi\)
\(674\) 59.6152 2.29629
\(675\) 3.52609 + 6.10737i 0.135719 + 0.235073i
\(676\) 2.53362 + 21.0532i 0.0974468 + 0.809737i
\(677\) −7.87553 + 13.6408i −0.302681 + 0.524259i −0.976742 0.214416i \(-0.931215\pi\)
0.674061 + 0.738676i \(0.264548\pi\)
\(678\) −3.82593 6.62671i −0.146934 0.254497i
\(679\) 0 0
\(680\) −0.622636 + 1.07844i −0.0238770 + 0.0413562i
\(681\) 2.23843 3.87707i 0.0857767 0.148570i
\(682\) −43.9163 −1.68164
\(683\) 41.4854 1.58739 0.793697 0.608314i \(-0.208154\pi\)
0.793697 + 0.608314i \(0.208154\pi\)
\(684\) −7.44717 + 12.8989i −0.284750 + 0.493201i
\(685\) 9.42819 16.3301i 0.360233 0.623941i
\(686\) 0 0
\(687\) −3.09725 5.36460i −0.118168 0.204672i
\(688\) 0.0523445 0.0906634i 0.00199562 0.00345651i
\(689\) 0.102522 0.500830i 0.00390579 0.0190801i
\(690\) 2.66828 + 4.62159i 0.101580 + 0.175941i
\(691\) 46.8216 1.78118 0.890589 0.454809i \(-0.150292\pi\)
0.890589 + 0.454809i \(0.150292\pi\)
\(692\) −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
\(696\) −0.0504584 −0.00191262
\(697\) 3.10534 + 5.37860i 0.117623 + 0.203729i
\(698\) −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 \(0.309282\pi\)
\(702\) 12.8098 + 11.3606i 0.483475 + 0.428780i
\(703\) 11.4293 + 19.7961i 0.431063 + 0.746623i
\(704\) −10.6048 + 18.3680i −0.399683 + 0.692271i
\(705\) 7.37418 0.277728
\(706\) −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 −0.999978 0.00665185i \(-0.997883\pi\)
0.494228 0.869332i \(-0.335451\pi\)
\(710\) −13.9932 24.2369i −0.525155 0.909595i
\(711\) −2.18133 −0.0818063
\(712\) −4.60900 −0.172729
\(713\) −11.6373 20.1563i −0.435819 0.754861i
\(714\) 0 0
\(715\) 4.68004 22.8623i 0.175023 0.855003i
\(716\) 0.440002 0.762105i 0.0164436 0.0284812i
\(717\) 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 0.698597 0.715516i \(-0.253808\pi\)
−0.968953 + 0.247245i \(0.920475\pi\)
\(720\) 19.0921 0.711519
\(721\) 0 0
\(722\) −8.08799 + 14.0088i −0.301004 + 0.521354i
\(723\) −1.56620 + 2.71274i −0.0582476 + 0.100888i
\(724\) −4.52098 −0.168021
\(725\) 0.237090 0.410652i 0.00880530 0.0152512i
\(726\) 6.77953 0.251612
\(727\) 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
\(730\) 42.7852 1.58355
\(731\) −0.0136811 + 0.0236963i −0.000506013 + 0.000876440i
\(732\) 8.06893 0.298236
\(733\) −5.99189 + 10.3783i −0.221316 + 0.383330i −0.955208 0.295936i \(-0.904368\pi\)
0.733892 + 0.679266i \(0.237702\pi\)
\(734\) −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 −0.963185 0.268840i \(-0.913360\pi\)
0.714415 + 0.699722i \(0.246693\pi\)
\(740\) −8.47091 + 14.6721i −0.311397 + 0.539355i
\(741\) −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 \(0.584066\pi\)
\(744\) 1.57958 0.0579101
\(745\) 5.77932 0.211738
\(746\) −3.69107 6.39312i −0.135140 0.234069i
\(747\) 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
\(751\) 11.7115 0.427357 0.213679 0.976904i \(-0.431455\pi\)
0.213679 + 0.976904i \(0.431455\pi\)
\(752\) −26.8817 + 46.5605i −0.980276 + 1.69789i
\(753\) 2.54151 + 4.40203i 0.0926178 + 0.160419i
\(754\) 0.230878 1.12786i 0.00840809 0.0410742i
\(755\) −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
\(759\) 4.17627 + 7.23352i 0.151589 + 0.262560i
\(760\) −3.35682 −0.121765
\(761\) −21.9691 38.0515i −0.796378 1.37937i −0.921960 0.387284i \(-0.873413\pi\)
0.125582 0.992083i \(-0.459920\pi\)
\(762\) 12.9693 0.469830
\(763\) 0 0
\(764\) 16.5079 + 28.5926i 0.597236 + 1.03444i
\(765\) −4.99002 −0.180414
\(766\) 25.5172 + 44.1971i 0.921973 + 1.59690i
\(767\) −14.4143 12.7837i −0.520471 0.461591i
\(768\) 4.32455 7.49035i 0.156049 0.270285i
\(769\) 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
\(772\) 13.3568 23.1347i 0.480723 0.832637i
\(773\) 23.1084 0.831152 0.415576 0.909559i \(-0.363580\pi\)
0.415576 + 0.909559i \(0.363580\pi\)
\(774\) 0.122099 0.00438874
\(775\) −7.42200 + 12.8553i −0.266606 + 0.461775i
\(776\) 1.22705 2.12532i 0.0440487 0.0762946i
\(777\) 0 0
\(778\) 11.4474 + 19.8275i 0.410410 + 0.710851i
\(779\) −8.37091 + 14.4988i −0.299919 + 0.519475i
\(780\) 0.744426 3.63658i 0.0266547 0.130210i
\(781\) −21.9015 37.9346i −0.783699 1.35741i
\(782\) 10.1691 0.363647
\(783\) −0.208785 0.361626i