Properties

Label 1183.2.e.g.508.2
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
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 508.2
Root \(1.16700 - 2.02131i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.g.170.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.952780 - 1.65026i) q^{2} +(-0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +0.816433 q^{6} +(-1.04402 - 2.43105i) q^{7} -0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})\) \(q+(-0.952780 - 1.65026i) q^{2} +(-0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +0.816433 q^{6} +(-1.04402 - 2.43105i) q^{7} -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} +(-3.01715 + 4.03917i) q^{14} +0.631159 q^{15} +(2.30082 + 3.98514i) q^{16} +(0.601356 - 1.04158i) q^{17} +(2.68344 - 4.64786i) q^{18} +(1.62105 + 2.80773i) q^{19} +2.40291 q^{20} +(1.12569 + 0.133408i) q^{21} +8.37230 q^{22} +(2.21855 + 3.84264i) q^{23} +(0.150567 - 0.260790i) q^{24} +(1.41494 - 2.45075i) q^{25} -2.49204 q^{27} +(4.28565 + 0.507904i) q^{28} +0.167561 q^{29} +(-0.601356 - 1.04158i) q^{30} +(2.62272 - 4.54268i) q^{31} +(3.68150 - 6.37655i) q^{32} +(-0.941217 - 1.63024i) q^{33} -2.29184 q^{34} +(-2.33247 + 3.12256i) q^{35} -4.59405 q^{36} +(3.52527 + 6.10595i) q^{37} +(3.08900 - 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} -5.16390 q^{41} +(-0.852374 - 1.98479i) q^{42} +0.0227504 q^{43} +(-3.58334 - 6.20653i) q^{44} +(2.07449 - 3.59311i) q^{45} +(4.22758 - 7.32239i) q^{46} +(5.84178 + 10.1183i) q^{47} -1.97156 q^{48} +(-4.82003 + 5.07615i) q^{49} -5.39252 q^{50} +(0.257649 + 0.446262i) q^{51} +(0.0708929 - 0.122790i) q^{53} +(2.37436 + 4.11252i) q^{54} +6.47236 q^{55} +(0.733790 + 1.70866i) q^{56} -1.38907 q^{57} +(-0.159649 - 0.276520i) q^{58} +(-2.67177 + 4.62764i) q^{59} +(-0.514760 + 0.891591i) q^{60} +(-5.77287 - 9.99891i) q^{61} -9.99549 q^{62} +(4.45938 - 5.96993i) q^{63} -4.82736 q^{64} +(-1.79355 + 3.10651i) q^{66} +(2.06773 - 3.58141i) q^{67} +(0.980907 + 1.69898i) q^{68} -1.90107 q^{69} +(7.37537 + 0.874075i) q^{70} +9.96971 q^{71} +(-0.989763 - 1.71432i) q^{72} +(7.62080 - 13.1996i) q^{73} +(6.71762 - 11.6353i) q^{74} +(0.606229 + 1.05002i) q^{75} -5.28837 q^{76} +(11.5436 + 1.36807i) q^{77} +(-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} +(-1.10654 + 1.48137i) q^{84} -1.77175 q^{85} +(-0.0216761 - 0.0375441i) 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} +(1.57733 + 2.73202i) q^{96} -3.49166 q^{97} +(12.9694 + 3.11787i) q^{98} -12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + 4q^{10} - 4q^{11} + 5q^{12} - 2q^{14} - 4q^{15} + 8q^{16} + 5q^{17} - 3q^{18} + q^{19} - 2q^{20} + 9q^{21} + 10q^{22} - q^{23} + 11q^{24} + 7q^{25} - 8q^{27} - 8q^{28} - 6q^{29} - 5q^{30} - 16q^{31} - 8q^{32} - 16q^{33} - 32q^{34} - 28q^{35} + 42q^{36} + 13q^{37} - 17q^{38} - 5q^{40} - 16q^{41} - 52q^{42} + 22q^{43} - 21q^{44} + 7q^{45} - 16q^{46} + q^{47} - 42q^{48} + 6q^{49} + 12q^{50} - 20q^{51} - 2q^{53} + 18q^{54} - 18q^{55} + 9q^{56} - 42q^{57} + 8q^{58} - 13q^{59} - 20q^{60} - 5q^{61} - 10q^{62} - 8q^{63} - 30q^{64} + 18q^{66} + 11q^{67} + 29q^{68} - 46q^{69} + 39q^{70} + 12q^{71} - 25q^{72} + 30q^{73} - 3q^{74} - 3q^{75} - 18q^{76} + 11q^{77} + 7q^{79} + 7q^{80} - 6q^{81} + q^{82} + 54q^{83} - 41q^{84} - 2q^{85} + 7q^{86} + 16q^{87} - 4q^{89} - 16q^{90} + 54q^{92} + 7q^{93} + 45q^{94} - 6q^{95} - 19q^{96} - 70q^{97} + 82q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.931363\pi\)
0.303125 0.952951i \(-0.401970\pi\)
\(3\) −0.214224 + 0.371047i −0.123682 + 0.214224i −0.921217 0.389049i \(-0.872804\pi\)
0.797535 + 0.603273i \(0.206137\pi\)
\(4\) −0.815580 + 1.41263i −0.407790 + 0.706313i
\(5\) −0.736565 1.27577i −0.329402 0.570541i 0.652991 0.757365i \(-0.273514\pi\)
−0.982393 + 0.186825i \(0.940180\pi\)
\(6\) 0.816433 0.333307
\(7\) −1.04402 2.43105i −0.394604 0.918851i
\(8\) −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 \(0.397113\pi\)
−0.979993 + 0.199031i \(0.936221\pi\)
\(12\) −0.349433 0.605236i −0.100873 0.174717i
\(13\) 0 0
\(14\) −3.01715 + 4.03917i −0.806368 + 1.07951i
\(15\) 0.631159 0.162965
\(16\) 2.30082 + 3.98514i 0.575205 + 0.996284i
\(17\) 0.601356 1.04158i 0.145850 0.252620i −0.783840 0.620963i \(-0.786742\pi\)
0.929690 + 0.368343i \(0.120075\pi\)
\(18\) 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 \(0.712042\pi\)
\(20\) 2.40291 0.537307
\(21\) 1.12569 + 0.133408i 0.245645 + 0.0291121i
\(22\) 8.37230 1.78498
\(23\) 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
\(25\) 1.41494 2.45075i 0.282989 0.490151i
\(26\) 0 0
\(27\) −2.49204 −0.479593
\(28\) 4.28565 + 0.507904i 0.809912 + 0.0959848i
\(29\) 0.167561 0.0311154 0.0155577 0.999879i \(-0.495048\pi\)
0.0155577 + 0.999879i \(0.495048\pi\)
\(30\) −0.601356 1.04158i −0.109792 0.190165i
\(31\) 2.62272 4.54268i 0.471054 0.815889i −0.528398 0.848997i \(-0.677207\pi\)
0.999452 + 0.0331076i \(0.0105404\pi\)
\(32\) 3.68150 6.37655i 0.650803 1.12722i
\(33\) −0.941217 1.63024i −0.163845 0.283788i
\(34\) −2.29184 −0.393047
\(35\) −2.33247 + 3.12256i −0.394259 + 0.527809i
\(36\) −4.59405 −0.765675
\(37\) 3.52527 + 6.10595i 0.579552 + 1.00381i 0.995531 + 0.0944386i \(0.0301056\pi\)
−0.415979 + 0.909374i \(0.636561\pi\)
\(38\) 3.08900 5.35031i 0.501102 0.867934i
\(39\) 0 0
\(40\) 0.517694 + 0.896672i 0.0818546 + 0.141776i
\(41\) −5.16390 −0.806465 −0.403233 0.915098i \(-0.632113\pi\)
−0.403233 + 0.915098i \(0.632113\pi\)
\(42\) −0.852374 1.98479i −0.131524 0.306260i
\(43\) 0.0227504 0.00346940 0.00173470 0.999998i \(-0.499448\pi\)
0.00173470 + 0.999998i \(0.499448\pi\)
\(44\) −3.58334 6.20653i −0.540209 0.935670i
\(45\) 2.07449 3.59311i 0.309246 0.535630i
\(46\) 4.22758 7.32239i 0.623323 1.07963i
\(47\) 5.84178 + 10.1183i 0.852111 + 1.47590i 0.879300 + 0.476269i \(0.158011\pi\)
−0.0271891 + 0.999630i \(0.508656\pi\)
\(48\) −1.97156 −0.284570
\(49\) −4.82003 + 5.07615i −0.688576 + 0.725164i
\(50\) −5.39252 −0.762618
\(51\) 0.257649 + 0.446262i 0.0360781 + 0.0624892i
\(52\) 0 0
\(53\) 0.0708929 0.122790i 0.00973788 0.0168665i −0.861115 0.508410i \(-0.830234\pi\)
0.870853 + 0.491543i \(0.163567\pi\)
\(54\) 2.37436 + 4.11252i 0.323110 + 0.559643i
\(55\) 6.47236 0.872734
\(56\) 0.733790 + 1.70866i 0.0980568 + 0.228330i
\(57\) −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 \(0.279750\pi\)
\(60\) −0.514760 + 0.891591i −0.0664553 + 0.115104i
\(61\) −5.77287 9.99891i −0.739141 1.28023i −0.952883 0.303339i \(-0.901898\pi\)
0.213742 0.976890i \(-0.431435\pi\)
\(62\) −9.99549 −1.26943
\(63\) 4.45938 5.96993i 0.561829 0.752140i
\(64\) −4.82736 −0.603420
\(65\) 0 0
\(66\) −1.79355 + 3.10651i −0.220770 + 0.382385i
\(67\) 2.06773 3.58141i 0.252613 0.437539i −0.711631 0.702553i \(-0.752043\pi\)
0.964245 + 0.265014i \(0.0853767\pi\)
\(68\) 0.980907 + 1.69898i 0.118952 + 0.206032i
\(69\) −1.90107 −0.228861
\(70\) 7.37537 + 0.874075i 0.881526 + 0.104472i
\(71\) 9.96971 1.18319 0.591594 0.806236i \(-0.298499\pi\)
0.591594 + 0.806236i \(0.298499\pi\)
\(72\) −0.989763 1.71432i −0.116645 0.202035i
\(73\) 7.62080 13.1996i 0.891947 1.54490i 0.0544080 0.998519i \(-0.482673\pi\)
0.837539 0.546378i \(-0.183994\pi\)
\(74\) 6.71762 11.6353i 0.780908 1.35257i
\(75\) 0.606229 + 1.05002i 0.0700013 + 0.121246i
\(76\) −5.28837 −0.606617
\(77\) 11.5436 + 1.36807i 1.31552 + 0.155906i
\(78\) 0 0
\(79\) −0.387251 0.670738i −0.0435691 0.0754639i 0.843418 0.537257i \(-0.180540\pi\)
−0.886988 + 0.461793i \(0.847206\pi\)
\(80\) 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 \(0.158121\pi\)
\(84\) −1.10654 + 1.48137i −0.120734 + 0.161631i
\(85\) −1.77175 −0.192173
\(86\) −0.0216761 0.0375441i −0.00233740 0.00404849i
\(87\) −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
\(96\) 1.57733 + 2.73202i 0.160986 + 0.278835i
\(97\) −3.49166 −0.354524 −0.177262 0.984164i \(-0.556724\pi\)
−0.177262 + 0.984164i \(0.556724\pi\)
\(98\) 12.9694 + 3.11787i 1.31011 + 0.314952i
\(99\) −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 \(-0.874269\pi\)
0.794749 + 0.606939i \(0.207603\pi\)
\(102\) 0.490966 0.850379i 0.0486129 0.0842000i
\(103\) 8.43173 + 14.6042i 0.830803 + 1.43899i 0.897402 + 0.441213i \(0.145452\pi\)
−0.0665997 + 0.997780i \(0.521215\pi\)
\(104\) 0 0
\(105\) −0.658944 1.53438i −0.0643064 0.149740i
\(106\) −0.270181 −0.0262423
\(107\) −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
\(109\) −6.02026 + 10.4274i −0.576637 + 0.998764i 0.419225 + 0.907882i \(0.362302\pi\)
−0.995862 + 0.0908816i \(0.971032\pi\)
\(110\) −6.16674 10.6811i −0.587976 1.01840i
\(111\) −3.02079 −0.286721
\(112\) 7.28597 9.75398i 0.688459 0.921665i
\(113\) 9.37232 0.881674 0.440837 0.897587i \(-0.354682\pi\)
0.440837 + 0.897587i \(0.354682\pi\)
\(114\) 1.32348 + 2.29233i 0.123955 + 0.214696i
\(115\) 3.26821 5.66071i 0.304763 0.527864i
\(116\) −0.136660 + 0.236701i −0.0126885 + 0.0219772i
\(117\) 0 0
\(118\) 10.1824 0.937369
\(119\) −3.15996 0.374495i −0.289673 0.0343299i
\(120\) −0.443609 −0.0404958
\(121\) −4.15192 7.19134i −0.377448 0.653758i
\(122\) −11.0006 + 19.0535i −0.995944 + 1.72503i
\(123\) 1.10623 1.91605i 0.0997453 0.172764i
\(124\) 4.27807 + 7.40983i 0.384182 + 0.665423i
\(125\) −11.5344 −1.03167
\(126\) −14.1008 1.67112i −1.25620 0.148875i
\(127\) 15.8854 1.40960 0.704800 0.709406i \(-0.251037\pi\)
0.704800 + 0.709406i \(0.251037\pi\)
\(128\) −2.76359 4.78667i −0.244269 0.423086i
\(129\) −0.00487367 + 0.00844145i −0.000429103 + 0.000743228i
\(130\) 0 0
\(131\) −0.928725 1.60860i −0.0811430 0.140544i 0.822598 0.568623i \(-0.192524\pi\)
−0.903741 + 0.428079i \(0.859190\pi\)
\(132\) 3.07055 0.267257
\(133\) 5.13334 6.87219i 0.445117 0.595894i
\(134\) −7.88036 −0.680759
\(135\) 1.83555 + 3.17926i 0.157979 + 0.273627i
\(136\) −0.422662 + 0.732072i −0.0362430 + 0.0627747i
\(137\) −6.40011 + 11.0853i −0.546798 + 0.947082i 0.451693 + 0.892173i \(0.350820\pi\)
−0.998491 + 0.0549088i \(0.982513\pi\)
\(138\) 1.81130 + 3.13726i 0.154188 + 0.267061i
\(139\) −0.338729 −0.0287306 −0.0143653 0.999897i \(-0.504573\pi\)
−0.0143653 + 0.999897i \(0.504573\pi\)
\(140\) −2.50869 5.84160i −0.212023 0.493705i
\(141\) −5.00579 −0.421564
\(142\) −9.49894 16.4527i −0.797134 1.38068i
\(143\) 0 0
\(144\) −6.48010 + 11.2239i −0.540009 + 0.935322i
\(145\) −0.123420 0.213769i −0.0102495 0.0177526i
\(146\) −29.0438 −2.40368
\(147\) −0.850922 2.87589i −0.0701828 0.237199i
\(148\) −11.5006 −0.945341
\(149\) 1.96158 + 3.39756i 0.160699 + 0.278339i 0.935120 0.354332i \(-0.115292\pi\)
−0.774421 + 0.632671i \(0.781959\pi\)
\(150\) 1.15521 2.00088i 0.0943222 0.163371i
\(151\) −1.05939 + 1.83492i −0.0862122 + 0.149324i −0.905907 0.423476i \(-0.860810\pi\)
0.819695 + 0.572800i \(0.194143\pi\)
\(152\) −1.13935 1.97341i −0.0924135 0.160065i
\(153\) 3.38736 0.273851
\(154\) −8.74087 20.3535i −0.704359 1.64013i
\(155\) −7.72721 −0.620664
\(156\) 0 0
\(157\) 11.0564 19.1502i 0.882397 1.52836i 0.0337285 0.999431i \(-0.489262\pi\)
0.848668 0.528925i \(-0.177405\pi\)
\(158\) −0.737929 + 1.27813i −0.0587065 + 0.101683i
\(159\) 0.0303739 + 0.0526091i 0.00240881 + 0.00417217i
\(160\) −10.8467 −0.857504
\(161\) 7.02545 9.40522i 0.553683 0.741235i
\(162\) 14.0661 1.10513
\(163\) 1.92607 + 3.33605i 0.150861 + 0.261299i 0.931544 0.363628i \(-0.118462\pi\)
−0.780683 + 0.624927i \(0.785129\pi\)
\(164\) 4.21157 7.29465i 0.328868 0.569616i
\(165\) −1.38653 + 2.40155i −0.107942 + 0.186960i
\(166\) −15.2622 26.4349i −1.18458 2.05175i
\(167\) −2.13894 −0.165516 −0.0827582 0.996570i \(-0.526373\pi\)
−0.0827582 + 0.996570i \(0.526373\pi\)
\(168\) −0.791188 0.0937658i −0.0610415 0.00723419i
\(169\) 0 0
\(170\) 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 \(0.0509110\pi\)
−0.355695 + 0.934602i \(0.615756\pi\)
\(174\) 0.136803 0.0103710
\(175\) −7.43515 0.881159i −0.562044 0.0666094i
\(176\) −20.2178 −1.52398
\(177\) −1.14471 1.98270i −0.0860419 0.149029i
\(178\) 6.24795 10.8218i 0.468303 0.811125i
\(179\) 0.269748 0.467217i 0.0201619 0.0349214i −0.855768 0.517359i \(-0.826915\pi\)
0.875930 + 0.482438i \(0.160248\pi\)
\(180\) 3.38382 + 5.86094i 0.252215 + 0.436849i
\(181\) 2.77164 0.206014 0.103007 0.994681i \(-0.467154\pi\)
0.103007 + 0.994681i \(0.467154\pi\)
\(182\) 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
\(187\) 2.64213 + 4.57629i 0.193211 + 0.334652i
\(188\) −19.0577 −1.38993
\(189\) 2.60174 + 6.05827i 0.189249 + 0.440674i
\(190\) −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 \(0.367312\pi\)
−0.994308 + 0.106546i \(0.966021\pi\)
\(194\) 3.32678 + 5.76216i 0.238849 + 0.413699i
\(195\) 0 0
\(196\) −3.23958 10.9489i −0.231398 0.782064i
\(197\) −19.7335 −1.40595 −0.702977 0.711212i \(-0.748146\pi\)
−0.702977 + 0.711212i \(0.748146\pi\)
\(198\) 11.7900 + 20.4209i 0.837879 + 1.45125i
\(199\) 7.05873 12.2261i 0.500380 0.866683i −0.499620 0.866245i \(-0.666527\pi\)
1.00000 0.000438630i \(-0.000139620\pi\)
\(200\) −0.994491 + 1.72251i −0.0703212 + 0.121800i
\(201\) 0.885913 + 1.53445i 0.0624875 + 0.108232i
\(202\) 4.91214 0.345617
\(203\) −0.174938 0.407351i −0.0122782 0.0285904i
\(204\) −0.840534 −0.0588492
\(205\) 3.80354 + 6.58793i 0.265651 + 0.460121i
\(206\) 16.0672 27.8291i 1.11945 1.93895i
\(207\) −6.24840 + 10.8225i −0.434294 + 0.752219i
\(208\) 0 0
\(209\) −14.2445 −0.985313
\(210\) −1.90430 + 2.54936i −0.131409 + 0.175922i
\(211\) −4.62634 −0.318490 −0.159245 0.987239i \(-0.550906\pi\)
−0.159245 + 0.987239i \(0.550906\pi\)
\(212\) 0.115638 + 0.200290i 0.00794202 + 0.0137560i
\(213\) −2.13575 + 3.69923i −0.146339 + 0.253467i
\(214\) −8.27265 + 14.3287i −0.565507 + 0.979487i
\(215\) −0.0167571 0.0290242i −0.00114283 0.00197943i
\(216\) 1.75152 0.119176
\(217\) −13.7817 1.63330i −0.935561 0.110876i
\(218\) 22.9439 1.55396
\(219\) 3.26511 + 5.65534i 0.220636 + 0.382152i
\(220\) −5.27873 + 9.14303i −0.355892 + 0.616423i
\(221\) 0 0
\(222\) 2.87815 + 4.98510i 0.193169 + 0.334578i
\(223\) 21.3523 1.42985 0.714926 0.699200i \(-0.246460\pi\)
0.714926 + 0.699200i \(0.246460\pi\)
\(224\) −19.3453 2.29266i −1.29256 0.153185i
\(225\) 7.97019 0.531346
\(226\) −8.92976 15.4668i −0.593999 1.02884i
\(227\) −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
\(229\) 7.22901 + 12.5210i 0.477706 + 0.827412i 0.999673 0.0255538i \(-0.00813493\pi\)
−0.521967 + 0.852966i \(0.674802\pi\)
\(230\) −12.4556 −0.821295
\(231\) −2.98054 + 3.99015i −0.196105 + 0.262533i
\(232\) −0.117770 −0.00773200
\(233\) 4.64413 + 8.04388i 0.304247 + 0.526972i 0.977093 0.212811i \(-0.0682617\pi\)
−0.672846 + 0.739783i \(0.734928\pi\)
\(234\) 0 0
\(235\) 8.60570 14.9055i 0.561374 0.972328i
\(236\) −4.35808 7.54842i −0.283687 0.491360i
\(237\) 0.331833 0.0215549
\(238\) 2.39273 + 5.57158i 0.155098 + 0.361152i
\(239\) −19.6332 −1.26997 −0.634983 0.772526i \(-0.718993\pi\)
−0.634983 + 0.772526i \(0.718993\pi\)
\(240\) 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 \(0.0910028\pi\)
\(242\) −7.91174 + 13.7035i −0.508586 + 0.880897i
\(243\) −5.31937 9.21341i −0.341238 0.591041i
\(244\) 18.8330 1.20566
\(245\) 10.0263 + 2.41033i 0.640554 + 0.153990i
\(246\) −4.21597 −0.268801
\(247\) 0 0
\(248\) −1.84337 + 3.19282i −0.117054 + 0.202744i
\(249\) −3.43157 + 5.94365i −0.217467 + 0.376664i
\(250\) 10.9898 + 19.0349i 0.695055 + 1.20387i
\(251\) −11.8638 −0.748837 −0.374419 0.927260i \(-0.622158\pi\)
−0.374419 + 0.927260i \(0.622158\pi\)
\(252\) 4.79629 + 11.1684i 0.302138 + 0.703542i
\(253\) −19.4949 −1.22563
\(254\) −15.1353 26.2151i −0.949672 1.64488i
\(255\) 0.379551 0.657402i 0.0237684 0.0411681i
\(256\) −10.0935 + 17.4825i −0.630846 + 1.09266i
\(257\) 7.58608 + 13.1395i 0.473206 + 0.819618i 0.999530 0.0306670i \(-0.00976315\pi\)
−0.526323 + 0.850285i \(0.676430\pi\)
\(258\) 0.0185742 0.00115638
\(259\) 11.1634 14.9449i 0.693662 0.928630i
\(260\) 0 0
\(261\) 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
\(266\) −16.2319 1.92368i −0.995239 0.117948i
\(267\) −2.80959 −0.171944
\(268\) 3.37279 + 5.84185i 0.206026 + 0.356848i
\(269\) −9.46102 + 16.3870i −0.576849 + 0.999131i 0.418989 + 0.907991i \(0.362384\pi\)
−0.995838 + 0.0911401i \(0.970949\pi\)
\(270\) 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 \(0.980174\pi\)
\(278\) 0.322734 + 0.558992i 0.0193563 + 0.0335261i
\(279\) 14.7734 0.884461
\(280\) 1.63937 2.19469i 0.0979712 0.131158i
\(281\) 14.2252 0.848603 0.424302 0.905521i \(-0.360520\pi\)
0.424302 + 0.905521i \(0.360520\pi\)
\(282\) 4.76942 + 8.26087i 0.284015 + 0.491928i
\(283\) 5.71446 9.89773i 0.339689 0.588359i −0.644685 0.764448i \(-0.723011\pi\)
0.984374 + 0.176089i \(0.0563448\pi\)
\(284\) −8.13109 + 14.0835i −0.482492 + 0.835700i
\(285\) 1.02314 + 1.77213i 0.0606055 + 0.104972i
\(286\) 0 0
\(287\) 5.39123 + 12.5537i 0.318234 + 0.741022i
\(288\) 20.7374 1.22196
\(289\) 7.77674 + 13.4697i 0.457455 + 0.792336i
\(290\) −0.235184 + 0.407351i −0.0138105 + 0.0239205i
\(291\) 0.747997 1.29557i 0.0438483 0.0759476i
\(292\) 12.4307 + 21.5307i 0.727453 + 1.25999i
\(293\) 13.2046 0.771422 0.385711 0.922620i \(-0.373956\pi\)
0.385711 + 0.922620i \(0.373956\pi\)
\(294\) −3.93523 + 4.14433i −0.229507 + 0.241702i
\(295\) 7.87173 0.458310
\(296\) −2.47773 4.29156i −0.144015 0.249442i
\(297\) 5.47452 9.48215i 0.317664 0.550210i
\(298\) 3.73791 6.47425i 0.216531 0.375043i
\(299\) 0 0
\(300\) −1.97771 −0.114183
\(301\) −0.0237519 0.0553074i −0.00136904 0.00318786i
\(302\) 4.03748 0.232331
\(303\) −0.552225 0.956482i −0.0317245 0.0549484i
\(304\) −7.45947 + 12.9202i −0.427830 + 0.741023i
\(305\) −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 \(0.439143\pi\)
\(308\) −11.3473 + 15.1911i −0.646573 + 0.865590i
\(309\) −7.22511 −0.411022
\(310\) 7.36233 + 12.7519i 0.418152 + 0.724261i
\(311\) 1.02298 1.77186i 0.0580081 0.100473i −0.835563 0.549395i \(-0.814858\pi\)
0.893571 + 0.448922i \(0.148192\pi\)
\(312\) 0 0
\(313\) −4.70883 8.15594i −0.266159 0.461001i 0.701708 0.712465i \(-0.252421\pi\)
−0.967867 + 0.251464i \(0.919088\pi\)
\(314\) −42.1373 −2.37794
\(315\) −10.9009 1.29189i −0.614194 0.0727897i
\(316\) 1.26333 0.0710681
\(317\) −16.6856 28.9004i −0.937159 1.62321i −0.770738 0.637153i \(-0.780112\pi\)
−0.166421 0.986055i \(-0.553221\pi\)
\(318\) 0.0578792 0.100250i 0.00324571 0.00562173i
\(319\) −0.368100 + 0.637568i −0.0206097 + 0.0356970i
\(320\) 3.55567 + 6.15860i 0.198768 + 0.344276i
\(321\) 3.72006 0.207634
\(322\) −22.2148 2.63273i −1.23798 0.146717i
\(323\) 3.89930 0.216963
\(324\) −6.02027 10.4274i −0.334460 0.579301i
\(325\) 0 0
\(326\) 3.67024 6.35704i 0.203276 0.352084i
\(327\) −2.57937 4.46760i −0.142639 0.247059i
\(328\) 3.62944 0.200402
\(329\) 18.4991 24.7654i 1.01989 1.36536i
\(330\) 5.28425 0.290888
\(331\) 9.53298 + 16.5116i 0.523980 + 0.907560i 0.999610 + 0.0279144i \(0.00888658\pi\)
−0.475631 + 0.879645i \(0.657780\pi\)
\(332\) −13.0645 + 22.6283i −0.717005 + 1.24189i
\(333\) −9.92870 + 17.1970i −0.544089 + 0.942390i
\(334\) 2.03794 + 3.52982i 0.111511 + 0.193143i
\(335\) −6.09207 −0.332845
\(336\) 2.05835 + 4.79297i 0.112292 + 0.261478i
\(337\) −31.2849 −1.70420 −0.852098 0.523382i \(-0.824670\pi\)
−0.852098 + 0.523382i \(0.824670\pi\)
\(338\) 0 0
\(339\) −2.00777 + 3.47757i −0.109047 + 0.188876i
\(340\) 1.44500 2.50282i 0.0783663 0.135734i
\(341\) 11.5232 + 19.9588i 0.624017 + 1.08083i
\(342\) 17.3999 0.940880
\(343\) 17.3726 + 6.41814i 0.938033 + 0.346547i
\(344\) −0.0159901 −0.000862127
\(345\) 1.40026 + 2.42532i 0.0753874 + 0.130575i
\(346\) 15.8288 27.4163i 0.850961 1.47391i
\(347\) −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
\(349\) −23.9904 −1.28418 −0.642089 0.766631i \(-0.721932\pi\)
−0.642089 + 0.766631i \(0.721932\pi\)
\(350\) 5.62992 + 13.1095i 0.300932 + 0.700732i
\(351\) 0 0
\(352\) 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
\(357\) 0.815894 1.09227i 0.0431817 0.0578089i
\(358\) −1.02804 −0.0543337
\(359\) 6.16986 + 10.6865i 0.325633 + 0.564012i 0.981640 0.190742i \(-0.0610894\pi\)
−0.656008 + 0.754754i \(0.727756\pi\)
\(360\) −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 \(-0.850212\pi\)
0.838307 + 0.545199i \(0.183546\pi\)
\(368\) −10.2090 + 17.6825i −0.532179 + 0.921762i
\(369\) −7.27188 12.5953i −0.378559 0.655684i
\(370\) −19.7919 −1.02893
\(371\) −0.372523 0.0441487i −0.0193404 0.00229208i
\(372\) −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 0
\(378\) 7.51886 10.0658i 0.386728 0.517727i
\(379\) 14.5679 0.748303 0.374152 0.927368i \(-0.377934\pi\)
0.374152 + 0.927368i \(0.377934\pi\)
\(380\) 3.89523 + 6.74673i 0.199821 + 0.346100i
\(381\) −3.40303 + 5.89422i −0.174342 + 0.301970i
\(382\) 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 \(-0.406534\pi\)
\(384\) 2.36810 0.120847
\(385\) −6.75730 15.7347i −0.344384 0.801912i
\(386\) 31.2076 1.58842
\(387\) 0.0320375 + 0.0554905i 0.00162856 + 0.00282074i
\(388\) 2.84773 4.93241i 0.144571 0.250405i
\(389\) −6.00738 + 10.4051i −0.304586 + 0.527559i −0.977169 0.212463i \(-0.931852\pi\)
0.672583 + 0.740022i \(0.265185\pi\)
\(390\) 0 0
\(391\) 5.33655 0.269881
\(392\) 3.38775 3.56776i 0.171107 0.180199i
\(393\) 0.795820 0.0401438
\(394\) 18.8017 + 32.5655i 0.947216 + 1.64063i
\(395\) −0.570470 + 0.988084i −0.0287035 + 0.0497159i
\(396\) 10.0922 17.4803i 0.507154 0.878417i
\(397\) −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
\(399\) 1.45022 + 3.37689i 0.0726017 + 0.169056i
\(400\) 13.0221 0.651106
\(401\) −10.2414 17.7386i −0.511430 0.885823i −0.999912 0.0132488i \(-0.995783\pi\)
0.488482 0.872574i \(-0.337551\pi\)
\(402\) 1.68816 2.92398i 0.0841978 0.145835i
\(403\) 0 0
\(404\) −2.10240 3.64146i −0.104598 0.181169i
\(405\) 10.8740 0.540336
\(406\) −0.505558 + 0.676809i −0.0250904 + 0.0335895i
\(407\) −30.9774 −1.53549
\(408\) −0.181089 0.313655i −0.00896522 0.0155282i
\(409\) 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
\(411\) −2.74211 4.74948i −0.135258 0.234274i
\(412\) −27.5070 −1.35517
\(413\) 14.0394 + 1.66385i 0.690835 + 0.0818727i
\(414\) 23.8134 1.17036
\(415\) −11.7988 20.4360i −0.579178 1.00317i
\(416\) 0 0
\(417\) 0.0725639 0.125684i 0.00355347 0.00615479i
\(418\) 13.5719 + 23.5072i 0.663822 + 1.14977i
\(419\) −23.6175 −1.15379 −0.576895 0.816819i \(-0.695736\pi\)
−0.576895 + 0.816819i \(0.695736\pi\)
\(420\) 2.70493 + 0.320568i 0.131987 + 0.0156421i
\(421\) −26.0822 −1.27117 −0.635585 0.772031i \(-0.719241\pi\)
−0.635585 + 0.772031i \(0.719241\pi\)
\(422\) 4.40788 + 7.63467i 0.214572 + 0.371650i
\(423\) −16.4530 + 28.4974i −0.799971 + 1.38559i
\(424\) −0.0498269 + 0.0863028i −0.00241981 + 0.00419123i
\(425\) −1.70177 2.94755i −0.0825479 0.142977i
\(426\) 8.13960 0.394365
\(427\) −18.2809 + 24.4733i −0.884673 + 1.18434i
\(428\) 14.1628 0.684584
\(429\) 0 0
\(430\) −0.0319317 + 0.0553074i −0.00153988 + 0.00266716i
\(431\) −6.65859 + 11.5330i −0.320733 + 0.555526i −0.980640 0.195822i \(-0.937263\pi\)
0.659906 + 0.751348i \(0.270596\pi\)
\(432\) −5.73373 9.93110i −0.275864 0.477810i
\(433\) 20.4221 0.981422 0.490711 0.871322i \(-0.336737\pi\)
0.490711 + 0.871322i \(0.336737\pi\)
\(434\) 10.4355 + 24.2996i 0.500921 + 1.16642i
\(435\) 0.105758 0.00507070
\(436\) −9.82001 17.0087i −0.470293 0.814571i
\(437\) −7.19275 + 12.4582i −0.344076 + 0.595957i
\(438\) 6.22187 10.7766i 0.297292 0.514925i
\(439\) 4.88537 + 8.46171i 0.233166 + 0.403855i 0.958738 0.284291i \(-0.0917581\pi\)
−0.725572 + 0.688146i \(0.758425\pi\)
\(440\) −4.54909 −0.216869
\(441\) −19.1689 4.60824i −0.912804 0.219440i
\(442\) 0 0
\(443\) −10.5819 18.3285i −0.502763 0.870811i −0.999995 0.00319331i \(-0.998984\pi\)
0.497232 0.867618i \(-0.334350\pi\)
\(444\) 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
\(448\) 5.03988 + 11.7356i 0.238112 + 0.554454i
\(449\) 18.1464 0.856382 0.428191 0.903688i \(-0.359151\pi\)
0.428191 + 0.903688i \(0.359151\pi\)
\(450\) −7.59384 13.1529i −0.357977 0.620034i
\(451\) 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 0.574617 0.818422i \(-0.305151\pi\)
−0.996083 + 0.0884220i \(0.971818\pi\)
\(458\) 13.7753 23.8595i 0.643678 1.11488i
\(459\) −1.49860 + 2.59565i −0.0699487 + 0.121155i
\(460\) 5.33098 + 9.23352i 0.248558 + 0.430515i
\(461\) 29.7746 1.38674 0.693370 0.720582i \(-0.256125\pi\)
0.693370 + 0.720582i \(0.256125\pi\)
\(462\) 9.42459 + 1.11693i 0.438472 + 0.0519645i
\(463\) −17.7067 −0.822900 −0.411450 0.911432i \(-0.634977\pi\)
−0.411450 + 0.911432i \(0.634977\pi\)
\(464\) 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 \(-0.123604\pi\)
−0.790677 + 0.612234i \(0.790271\pi\)
\(468\) 0 0
\(469\) −10.8654 1.28768i −0.501715 0.0594596i
\(470\) −32.7973 −1.51283
\(471\) 4.73709 + 8.20488i 0.218274 + 0.378061i
\(472\) 1.87785 3.25253i 0.0864350 0.149710i
\(473\) −0.0499782 + 0.0865648i −0.00229800 + 0.00398025i
\(474\) −0.316164 0.547612i −0.0145219 0.0251527i
\(475\) 9.17476 0.420967
\(476\) 3.10622 4.15841i 0.142373 0.190600i
\(477\) 0.399330 0.0182841
\(478\) 18.7061 + 32.4000i 0.855598 + 1.48194i
\(479\) 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
\(481\) 0 0
\(482\) −13.9316 −0.634569
\(483\) 1.98476 + 4.62159i 0.0903095 + 0.210290i
\(484\) 13.5449 0.615677
\(485\) 2.57183 + 4.45455i 0.116781 + 0.202271i
\(486\) −10.1364 + 17.5567i −0.459795 + 0.796389i
\(487\) −8.98006 + 15.5539i −0.406926 + 0.704816i −0.994543 0.104323i \(-0.966732\pi\)
0.587618 + 0.809139i \(0.300066\pi\)
\(488\) 4.05746 + 7.02772i 0.183672 + 0.318130i
\(489\) −1.65044 −0.0746354
\(490\) −5.57514 18.8425i −0.251859 0.851216i
\(491\) −36.3009 −1.63824 −0.819119 0.573624i \(-0.805537\pi\)
−0.819119 + 0.573624i \(0.805537\pi\)
\(492\) 1.80444 + 3.12537i 0.0813503 + 0.140903i
\(493\) 0.100764 0.174528i 0.00453818 0.00786036i
\(494\) 0 0
\(495\) 9.11449 + 15.7868i 0.409666 + 0.709562i
\(496\) 24.1376 1.08381
\(497\) −10.4086 24.2369i −0.466890 1.08717i
\(498\) 13.0781 0.586045
\(499\) 11.8538 + 20.5314i 0.530649 + 0.919112i 0.999360 + 0.0357602i \(0.0113853\pi\)
−0.468711 + 0.883352i \(0.655281\pi\)
\(500\) 9.40726 16.2938i 0.420705 0.728683i
\(501\) 0.458213 0.793648i 0.0204714 0.0354576i
\(502\) 11.3036 + 19.5784i 0.504505 + 0.873828i
\(503\) 27.7752 1.23843 0.619217 0.785220i \(-0.287450\pi\)
0.619217 + 0.785220i \(0.287450\pi\)
\(504\) −3.13427 + 4.19595i −0.139611 + 0.186903i
\(505\) 3.79743 0.168983
\(506\) 18.5744 + 32.1717i 0.825731 + 1.43021i
\(507\) 0 0
\(508\) −12.9558 + 22.4401i −0.574820 + 0.995618i
\(509\) 4.35208 + 7.53802i 0.192902 + 0.334117i 0.946211 0.323551i \(-0.104877\pi\)
−0.753308 + 0.657667i \(0.771543\pi\)
\(510\) −1.44651 −0.0640527
\(511\) −40.0452 4.74586i −1.77150 0.209945i
\(512\) 27.4134 1.21151
\(513\) −4.03971 6.99698i −0.178357 0.308924i
\(514\) 14.4557 25.0380i 0.637615 1.10438i
\(515\) 12.4210 21.5139i 0.547336 0.948014i
\(516\) −0.00794974 0.0137693i −0.000349968 0.000606162i
\(517\) −51.3330 −2.25762
\(518\) −35.2993 4.18341i −1.55096 0.183809i
\(519\) −7.11792 −0.312442
\(520\) 0 0
\(521\) 4.28573 7.42310i 0.187761 0.325212i −0.756742 0.653713i \(-0.773210\pi\)
0.944504 + 0.328501i \(0.106544\pi\)
\(522\) 0.449641 0.778801i 0.0196803 0.0340872i
\(523\) −14.9746 25.9369i −0.654796 1.13414i −0.981945 0.189167i \(-0.939421\pi\)
0.327149 0.944973i \(-0.393912\pi\)
\(524\) 3.02980 0.132357
\(525\) 1.91974 2.57002i 0.0837842 0.112165i
\(526\) 32.7688 1.42879
\(527\) −3.15437 5.46353i −0.137407 0.237995i
\(528\) 4.33114 7.50175i 0.188489 0.326472i
\(529\) 1.65606 2.86838i 0.0720027 0.124712i
\(530\) 0.199006 + 0.344689i 0.00864427 + 0.0149723i
\(531\) −15.0497 −0.653102
\(532\) 5.52118 + 12.8563i 0.239373 + 0.557391i
\(533\) 0 0
\(534\) 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
\(539\) −8.72597 29.4915i −0.375854 1.27029i
\(540\) −5.98814 −0.257688
\(541\) 5.24095 + 9.07760i 0.225326 + 0.390276i 0.956417 0.292003i \(-0.0943219\pi\)
−0.731091 + 0.682280i \(0.760989\pi\)
\(542\) 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
\(551\) 0.271625 + 0.470468i 0.0115716 + 0.0200426i
\(552\) 1.33616 0.0568708
\(553\) −1.22630 + 1.64169i −0.0521476 + 0.0698118i
\(554\) 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 \(-0.752490\pi\)
0.963872 + 0.266366i \(0.0858230\pi\)
\(558\) −14.0758 24.3800i −0.595877 1.03209i
\(559\) 0 0
\(560\) −17.8104 2.11076i −0.752627 0.0891958i
\(561\) −2.26402 −0.0955872
\(562\) −13.5535 23.4753i −0.571719 0.990246i
\(563\) −3.84675 + 6.66276i −0.162121 + 0.280802i −0.935629 0.352985i \(-0.885167\pi\)
0.773508 + 0.633786i \(0.218500\pi\)
\(564\) 4.08262 7.07131i 0.171909 0.297756i
\(565\) −6.90332 11.9569i −0.290425 0.503031i
\(566\) −21.7785 −0.915418
\(567\) 19.3941 + 2.29845i 0.814477 + 0.0965258i
\(568\) −7.00720 −0.294016
\(569\) −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
\(571\) −7.08285 + 12.2679i −0.296408 + 0.513394i −0.975311 0.220834i \(-0.929122\pi\)
0.678903 + 0.734228i \(0.262456\pi\)
\(572\) 0 0
\(573\) −8.67209 −0.362282
\(574\) 15.5803 20.8579i 0.650308 0.870590i
\(575\) 12.5565 0.523642
\(576\) −6.79797 11.7744i −0.283249 0.490601i
\(577\) −7.48776 + 12.9692i −0.311720 + 0.539914i −0.978735 0.205130i \(-0.934238\pi\)
0.667015 + 0.745044i \(0.267572\pi\)
\(578\) 14.8190 25.6673i 0.616391 1.06762i
\(579\) −3.50837 6.07667i −0.145803 0.252538i
\(580\) 0.402635 0.0167185
\(581\) −16.7238 38.9421i −0.693820 1.61559i
\(582\) −2.85071 −0.118166
\(583\) 0.311476 + 0.539492i 0.0129000 + 0.0223435i
\(584\) −5.35627 + 9.27732i −0.221644 + 0.383898i
\(585\) 0 0
\(586\) −12.5811 21.7911i −0.519720 0.900182i
\(587\) 13.1764 0.543849 0.271925 0.962319i \(-0.412340\pi\)
0.271925 + 0.962319i \(0.412340\pi\)
\(588\) 4.75655 + 1.14348i 0.196157 + 0.0471564i
\(589\) 17.0062 0.700728
\(590\) −7.50003 12.9904i −0.308771 0.534807i
\(591\) 4.22739 7.32205i 0.173892 0.301189i
\(592\) −16.2220 + 28.0974i −0.666722 + 1.15480i
\(593\) −22.0663 38.2200i −0.906156 1.56951i −0.819357 0.573283i \(-0.805670\pi\)
−0.0867989 0.996226i \(-0.527664\pi\)
\(594\) −20.8641 −0.856063
\(595\) 1.84975 + 4.30722i 0.0758323 + 0.176579i
\(596\) −6.39930 −0.262125
\(597\) 3.02429 + 5.23823i 0.123776 + 0.214387i
\(598\) 0 0
\(599\) 3.01349 5.21952i 0.123128 0.213264i −0.797872 0.602827i \(-0.794041\pi\)
0.921000 + 0.389564i \(0.127374\pi\)
\(600\) −0.426087 0.738005i −0.0173949 0.0301289i
\(601\) 3.72520 0.151954 0.0759770 0.997110i \(-0.475792\pi\)
0.0759770 + 0.997110i \(0.475792\pi\)
\(602\) −0.0686414 + 0.0918927i −0.00279761 + 0.00374527i
\(603\) 11.6472 0.474312
\(604\) −1.72804 2.99305i −0.0703129 0.121786i
\(605\) −6.11632 + 10.5938i −0.248664 + 0.430698i
\(606\) −1.05230 + 1.82263i −0.0427467 + 0.0740394i
\(607\) 3.00825 + 5.21045i 0.122101 + 0.211486i 0.920596 0.390516i \(-0.127703\pi\)
−0.798495 + 0.602002i \(0.794370\pi\)
\(608\) 23.8715 0.968118
\(609\) 0.188622 + 0.0223541i 0.00764335 + 0.000905833i
\(610\) 32.4105 1.31226
\(611\) 0 0
\(612\) −2.76266 + 4.78506i −0.111674 + 0.193425i
\(613\) 4.90413 8.49420i 0.198076 0.343077i −0.749829 0.661632i \(-0.769864\pi\)
0.947904 + 0.318555i \(0.103197\pi\)
\(614\) −6.34459 10.9892i −0.256047 0.443486i
\(615\) −3.25924 −0.131425
\(616\) −8.11342 0.961543i −0.326899 0.0387417i
\(617\) −33.7676 −1.35943 −0.679716 0.733475i \(-0.737897\pi\)
−0.679716 + 0.733475i \(0.737897\pi\)
\(618\) 6.88394 + 11.9233i 0.276913 + 0.479627i
\(619\) 2.04671 3.54501i 0.0822644 0.142486i −0.821958 0.569548i \(-0.807118\pi\)
0.904222 + 0.427062i \(0.140451\pi\)
\(620\) 6.30215 10.9156i 0.253100 0.438383i
\(621\) −5.52871 9.57601i −0.221860 0.384272i
\(622\) −3.89871 −0.156324
\(623\) 10.3829 13.9000i 0.415983 0.556891i
\(624\) 0 0
\(625\) 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
\(630\) 8.25416 + 19.2202i 0.328854 + 0.765750i
\(631\) 26.7736 1.06584 0.532921 0.846165i \(-0.321094\pi\)
0.532921 + 0.846165i \(0.321094\pi\)
\(632\) 0.272179 + 0.471427i 0.0108267 + 0.0187524i
\(633\) 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 \(0.0471273\pi\)
\(642\) −3.54440 6.13908i −0.139886 0.242290i
\(643\) 3.93390 0.155138 0.0775690 0.996987i \(-0.475284\pi\)
0.0775690 + 0.996987i \(0.475284\pi\)
\(644\) 7.55624 + 17.5950i 0.297758 + 0.693341i
\(645\) 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 \(-0.832100\pi\)
0.867956 + 0.496641i \(0.165434\pi\)
\(648\) 2.59407 4.49306i 0.101905 0.176504i
\(649\) −11.7387 20.3321i −0.460785 0.798104i
\(650\) 0 0
\(651\) 3.55839 4.76375i 0.139464 0.186706i
\(652\) −6.28345 −0.246079
\(653\) 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
\(655\) −1.36813 + 2.36967i −0.0534573 + 0.0925908i
\(656\) −11.8812 20.5788i −0.463883 0.803468i
\(657\) 42.9269 1.67474
\(658\) −58.4949 6.93238i −2.28037 0.270252i
\(659\) −23.4132 −0.912048 −0.456024 0.889967i \(-0.650727\pi\)
−0.456024 + 0.889967i \(0.650727\pi\)
\(660\) −2.26166 3.91731i −0.0880349 0.152481i
\(661\) −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
\(663\) 0 0
\(664\) −11.2587 −0.436921
\(665\) −12.5484 1.48714i −0.486604 0.0576688i
\(666\) 37.8395 1.46625
\(667\) 0.371744 + 0.643879i 0.0143940 + 0.0249311i
\(668\) 1.74448 3.02153i 0.0674959 0.116906i
\(669\) −4.57416 + 7.92268i −0.176847 + 0.306309i
\(670\) 5.80440 + 10.0535i 0.224243 + 0.388401i
\(671\) 50.7276 1.95832
\(672\) 4.99491 6.68686i 0.192683 0.257951i
\(673\) 7.29407 0.281166 0.140583 0.990069i \(-0.455102\pi\)
0.140583 + 0.990069i \(0.455102\pi\)
\(674\) 29.8076 + 51.6283i 1.14815 + 1.98865i
\(675\) −3.52609 + 6.10737i −0.135719 + 0.235073i
\(676\) 0 0
\(677\) 7.87553 + 13.6408i 0.302681 + 0.524259i 0.976742 0.214416i \(-0.0687849\pi\)
−0.674061 + 0.738676i \(0.735452\pi\)
\(678\) 7.65187 0.293868
\(679\) 3.64537 + 8.48841i 0.139897 + 0.325755i
\(680\) 1.24527 0.0477540
\(681\) −2.23843 3.87707i −0.0857767 0.148570i
\(682\) 21.9582 38.0327i 0.840822 1.45635i
\(683\) 20.7427 35.9274i 0.793697 1.37472i −0.129967 0.991518i \(-0.541487\pi\)
0.923664 0.383204i \(-0.125180\pi\)
\(684\) −7.44717 12.8989i −0.284750 0.493201i
\(685\) 18.8564 0.720465
\(686\) −5.96066 34.7845i −0.227579 1.32808i
\(687\) −6.19450 −0.236335
\(688\) 0.0523445 + 0.0906634i 0.00199562 + 0.00345651i
\(689\) 0 0
\(690\) 2.66828 4.62159i 0.101580 0.175941i
\(691\) −23.4108 40.5487i −0.890589 1.54255i −0.839171 0.543868i \(-0.816959\pi\)
−0.0514184 0.998677i \(-0.516374\pi\)
\(692\) −27.0989 −1.03015
\(693\) 12.9191 + 30.0826i 0.490755 + 1.14274i
\(694\) 22.2478 0.844514
\(695\) 0.249496 + 0.432140i 0.00946392 + 0.0163920i
\(696\) 0.0252292 0.0436983i 0.000956311 0.00165638i
\(697\) −3.10534 + 5.37860i −0.117623 + 0.203729i
\(698\) 22.8576 + 39.5905i 0.865172 + 1.49852i
\(699\) −3.97954 −0.150520
\(700\) 7.30870 9.78442i 0.276243 0.369816i
\(701\) 29.8626 1.12790 0.563948 0.825810i \(-0.309282\pi\)
0.563948 + 0.825810i \(0.309282\pi\)
\(702\) 0 0
\(703\) −11.4293 + 19.7961i −0.431063 + 0.746623i
\(704\) 10.6048 18.3680i 0.399683 0.692271i
\(705\) 3.68709 + 6.38623i 0.138864 + 0.240519i
\(706\) −24.3785 −0.917497
\(707\) 6.77281 + 0.802663i 0.254718 + 0.0301873i
\(708\) 3.73442 0.140348
\(709\) 13.4666 + 23.3249i 0.505750 + 0.875984i 0.999978 + 0.00665185i \(0.00211737\pi\)
−0.494228 + 0.869332i \(0.664549\pi\)
\(710\) −13.9932 + 24.2369i −0.525155 + 0.909595i
\(711\) 1.09067 1.88909i 0.0409031 0.0708463i
\(712\) −2.30450 3.99151i −0.0863647 0.149588i
\(713\) 23.2745 0.871638
\(714\) −2.57990 0.305750i −0.0965502 0.0114424i
\(715\) 0 0
\(716\) 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 0.968953 0.247245i \(-0.0795252\pi\)
−0.698597 + 0.715516i \(0.746192\pi\)
\(720\) 19.0921 0.711519
\(721\) 26.7006 35.7451i 0.994383 1.33122i
\(722\) −16.1760 −0.602008
\(723\) 1.56620 + 2.71274i 0.0582476 + 0.100888i
\(724\) −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 \(-0.537060\pi\)
−0.116164 + 0.993230i \(0.537060\pi\)
\(728\) 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
\(733\) −5.99189 10.3783i −0.221316 0.383330i 0.733892 0.679266i \(-0.237702\pi\)
−0.955208 + 0.295936i \(0.904368\pi\)
\(734\) 3.86975 0.142835
\(735\) −3.04221 + 3.20386i −0.112213 + 0.118176i
\(736\) 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 \(-0.753307\pi\)
0.963185 + 0.268840i \(0.0866404\pi\)
\(740\) 8.47091 + 14.6721i 0.311397 + 0.539355i
\(741\) 0 0
\(742\) 0.282075 + 0.656825i 0.0103553 + 0.0241128i
\(743\) 38.4598 1.41095 0.705477 0.708733i \(-0.250733\pi\)
0.705477 + 0.708733i \(0.250733\pi\)
\(744\) −0.789789 1.36795i −0.0289551 0.0501516i
\(745\) 2.88966 5.00504i 0.105869 0.183371i
\(746\) 3.69107 6.39312i 0.135140 0.234069i
\(747\) 22.5577 + 39.0710i 0.825342 + 1.42953i
\(748\) −8.61945 −0.315158
\(749\) −13.7476 + 18.4044i −0.502326 + 0.672482i
\(750\) −9.41710 −0.343864
\(751\) −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
\(753\) 2.54151 4.40203i 0.0926178 0.160419i
\(754\) 0 0
\(755\) 3.12125 0.113594
\(756\) −10.6800 1.26571i −0.388428 0.0460336i
\(757\) 9.31582 0.338589 0.169295 0.985566i \(-0.445851\pi\)
0.169295 + 0.985566i \(0.445851\pi\)
\(758\) −13.8800 24.0409i −0.504145 0.873205i
\(759\) 4.17627 7.23352i 0.151589 0.262560i
\(760\) −1.67841 + 2.90709i −0.0608824 + 0.105451i
\(761\) −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
\(763\) 31.6349 + 3.74913i 1.14526 + 0.135728i
\(764\) −33.0159 −1.19447
\(765\) −2.49501 4.32148i −0.0902072 0.156243i
\(766\) −25.5172 + 44.1971i −0.921973 + 1.59690i
\(767\) 0 0
\(768\) −4.32455 7.49035i −0.156049 0.270285i
\(769\) −25.3542 −0.914294 −0.457147 0.889391i \(-0.651129\pi\)
−0.457147 + 0.889391i \(0.651129\pi\)
\(770\) −19.5281 + 26.1430i −0.703744 + 0.942128i
\(771\) −6.50047 −0.234109
\(772\) −13.3568 23.1347i −0.480723 0.832637i
\(773\) −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
\(775\) −7.42200 12.8553i −0.266606 0.461775i
\(776\) 2.45411 0.0880974
\(777\) 3.15377 + 7.34370i 0.113141 + 0.263454i
\(778\) 22.8949 0.820820
\(779\) −8.37091 14.4988i −0.299919 0.519475i
\(780\)