Properties

Label 60.2.e.a.11.3
Level $60$
Weight $2$
Character 60.11
Analytic conductor $0.479$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 60.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.479102412128\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
Defining polynomial: \(x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.3
Root \(-0.599676 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 60.11
Dual form 60.2.e.a.11.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.599676 - 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(-1.85500 + 1.59968i) q^{6} -0.936426i q^{7} +(2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})\) \(q+(-0.599676 - 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(-1.85500 + 1.59968i) q^{6} -0.936426i q^{7} +(2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +(-1.28078 + 0.599676i) q^{10} +4.27156 q^{11} +(3.16123 + 1.41656i) q^{12} +3.12311 q^{13} +(-1.19935 + 0.561553i) q^{14} +(-1.66757 + 0.468213i) q^{15} +(-0.719224 - 3.93481i) q^{16} +2.00000i q^{17} +(3.53610 + 2.34435i) q^{18} +4.27156i q^{19} +(1.53610 + 1.28078i) q^{20} +(-1.56155 + 0.438447i) q^{21} +(-2.56155 - 5.47091i) q^{22} -7.60669 q^{23} +(-0.0814236 - 4.89830i) q^{24} -1.00000 q^{25} +(-1.87285 - 4.00000i) q^{26} +(3.80335 + 3.54042i) q^{27} +(1.43845 + 1.19935i) q^{28} -5.12311i q^{29} +(1.59968 + 1.85500i) q^{30} +2.39871i q^{31} +(-4.60831 + 3.28078i) q^{32} +(-2.00000 - 7.12311i) q^{33} +(2.56155 - 1.19935i) q^{34} -0.936426 q^{35} +(0.882071 - 5.93481i) q^{36} -3.12311 q^{37} +(5.47091 - 2.56155i) q^{38} +(-1.46228 - 5.20798i) q^{39} +(0.719224 - 2.73546i) q^{40} +7.12311i q^{41} +(1.49798 + 1.73707i) q^{42} -1.46228i q^{43} +(-5.47091 + 6.56155i) q^{44} +(1.56155 + 2.56155i) q^{45} +(4.56155 + 9.74247i) q^{46} +0.936426 q^{47} +(-6.22480 + 3.04168i) q^{48} +6.12311 q^{49} +(0.599676 + 1.28078i) q^{50} +(3.33513 - 0.936426i) q^{51} +(-4.00000 + 4.79741i) q^{52} +4.24621i q^{53} +(2.25371 - 6.99434i) q^{54} -4.27156i q^{55} +(0.673500 - 2.56155i) q^{56} +(7.12311 - 2.00000i) q^{57} +(-6.56155 + 3.07221i) q^{58} +7.19612 q^{59} +(1.41656 - 3.16123i) q^{60} -5.12311 q^{61} +(3.07221 - 1.43845i) q^{62} +(1.46228 + 2.39871i) q^{63} +(6.96543 + 3.93481i) q^{64} -3.12311i q^{65} +(-7.92375 + 6.83311i) q^{66} -5.20798i q^{67} +(-3.07221 - 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +(0.561553 + 1.19935i) q^{70} -6.67026 q^{71} +(-8.13012 + 2.42923i) q^{72} -8.24621 q^{73} +(1.87285 + 4.00000i) q^{74} +(0.468213 + 1.66757i) q^{75} +(-6.56155 - 5.47091i) q^{76} -4.00000i q^{77} +(-5.79337 + 4.99596i) q^{78} -9.06897i q^{79} +(-3.93481 + 0.719224i) q^{80} +(4.12311 - 8.00000i) q^{81} +(9.12311 - 4.27156i) q^{82} +4.68213 q^{83} +(1.32650 - 2.96026i) q^{84} +2.00000 q^{85} +(-1.87285 + 0.876894i) q^{86} +(-8.54312 + 2.39871i) q^{87} +(11.6847 + 3.07221i) q^{88} -6.24621i q^{89} +(2.34435 - 3.53610i) q^{90} -2.92456i q^{91} +(9.74247 - 11.6847i) q^{92} +(4.00000 - 1.12311i) q^{93} +(-0.561553 - 1.19935i) q^{94} +4.27156 q^{95} +(7.62858 + 6.14856i) q^{96} -6.00000 q^{97} +(-3.67188 - 7.84233i) q^{98} +(-10.9418 + 6.67026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{4} - 6q^{6} - 4q^{9} - 2q^{10} + 4q^{12} - 8q^{13} - 14q^{16} + 16q^{18} + 4q^{21} - 4q^{22} - 2q^{24} - 8q^{25} + 28q^{28} + 8q^{30} - 16q^{33} + 4q^{34} + 18q^{36} + 8q^{37} + 14q^{40} - 12q^{42} - 4q^{45} + 20q^{46} - 36q^{48} + 16q^{49} - 32q^{52} - 10q^{54} + 24q^{57} - 36q^{58} - 14q^{60} - 8q^{61} - 2q^{64} - 40q^{66} + 12q^{69} - 12q^{70} + 24q^{72} - 36q^{76} + 40q^{78} + 40q^{82} + 16q^{84} + 16q^{85} + 44q^{88} + 18q^{90} + 32q^{93} + 12q^{94} + 42q^{96} - 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.599676 1.28078i −0.424035 0.905646i
\(3\) −0.468213 1.66757i −0.270323 0.962770i
\(4\) −1.28078 + 1.53610i −0.640388 + 0.768051i
\(5\) 1.00000i 0.447214i
\(6\) −1.85500 + 1.59968i −0.757302 + 0.653065i
\(7\) 0.936426i 0.353936i −0.984217 0.176968i \(-0.943371\pi\)
0.984217 0.176968i \(-0.0566289\pi\)
\(8\) 2.73546 + 0.719224i 0.967130 + 0.254284i
\(9\) −2.56155 + 1.56155i −0.853851 + 0.520518i
\(10\) −1.28078 + 0.599676i −0.405017 + 0.189634i
\(11\) 4.27156 1.28792 0.643962 0.765058i \(-0.277290\pi\)
0.643962 + 0.765058i \(0.277290\pi\)
\(12\) 3.16123 + 1.41656i 0.912568 + 0.408924i
\(13\) 3.12311 0.866194 0.433097 0.901347i \(-0.357421\pi\)
0.433097 + 0.901347i \(0.357421\pi\)
\(14\) −1.19935 + 0.561553i −0.320541 + 0.150081i
\(15\) −1.66757 + 0.468213i −0.430564 + 0.120892i
\(16\) −0.719224 3.93481i −0.179806 0.983702i
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 3.53610 + 2.34435i 0.833467 + 0.552569i
\(19\) 4.27156i 0.979963i 0.871733 + 0.489981i \(0.162996\pi\)
−0.871733 + 0.489981i \(0.837004\pi\)
\(20\) 1.53610 + 1.28078i 0.343483 + 0.286390i
\(21\) −1.56155 + 0.438447i −0.340759 + 0.0956770i
\(22\) −2.56155 5.47091i −0.546125 1.16640i
\(23\) −7.60669 −1.58610 −0.793052 0.609154i \(-0.791509\pi\)
−0.793052 + 0.609154i \(0.791509\pi\)
\(24\) −0.0814236 4.89830i −0.0166205 0.999862i
\(25\) −1.00000 −0.200000
\(26\) −1.87285 4.00000i −0.367297 0.784465i
\(27\) 3.80335 + 3.54042i 0.731954 + 0.681354i
\(28\) 1.43845 + 1.19935i 0.271841 + 0.226656i
\(29\) 5.12311i 0.951337i −0.879625 0.475668i \(-0.842206\pi\)
0.879625 0.475668i \(-0.157794\pi\)
\(30\) 1.59968 + 1.85500i 0.292060 + 0.338676i
\(31\) 2.39871i 0.430820i 0.976524 + 0.215410i \(0.0691088\pi\)
−0.976524 + 0.215410i \(0.930891\pi\)
\(32\) −4.60831 + 3.28078i −0.814642 + 0.579965i
\(33\) −2.00000 7.12311i −0.348155 1.23997i
\(34\) 2.56155 1.19935i 0.439303 0.205687i
\(35\) −0.936426 −0.158285
\(36\) 0.882071 5.93481i 0.147012 0.989135i
\(37\) −3.12311 −0.513435 −0.256718 0.966486i \(-0.582641\pi\)
−0.256718 + 0.966486i \(0.582641\pi\)
\(38\) 5.47091 2.56155i 0.887499 0.415539i
\(39\) −1.46228 5.20798i −0.234152 0.833945i
\(40\) 0.719224 2.73546i 0.113719 0.432514i
\(41\) 7.12311i 1.11244i 0.831034 + 0.556221i \(0.187749\pi\)
−0.831034 + 0.556221i \(0.812251\pi\)
\(42\) 1.49798 + 1.73707i 0.231143 + 0.268036i
\(43\) 1.46228i 0.222995i −0.993765 0.111498i \(-0.964435\pi\)
0.993765 0.111498i \(-0.0355648\pi\)
\(44\) −5.47091 + 6.56155i −0.824771 + 0.989191i
\(45\) 1.56155 + 2.56155i 0.232783 + 0.381854i
\(46\) 4.56155 + 9.74247i 0.672564 + 1.43645i
\(47\) 0.936426 0.136592 0.0682959 0.997665i \(-0.478244\pi\)
0.0682959 + 0.997665i \(0.478244\pi\)
\(48\) −6.22480 + 3.04168i −0.898473 + 0.439029i
\(49\) 6.12311 0.874729
\(50\) 0.599676 + 1.28078i 0.0848071 + 0.181129i
\(51\) 3.33513 0.936426i 0.467012 0.131126i
\(52\) −4.00000 + 4.79741i −0.554700 + 0.665281i
\(53\) 4.24621i 0.583262i 0.956531 + 0.291631i \(0.0941979\pi\)
−0.956531 + 0.291631i \(0.905802\pi\)
\(54\) 2.25371 6.99434i 0.306691 0.951809i
\(55\) 4.27156i 0.575977i
\(56\) 0.673500 2.56155i 0.0900002 0.342302i
\(57\) 7.12311 2.00000i 0.943478 0.264906i
\(58\) −6.56155 + 3.07221i −0.861574 + 0.403400i
\(59\) 7.19612 0.936855 0.468427 0.883502i \(-0.344821\pi\)
0.468427 + 0.883502i \(0.344821\pi\)
\(60\) 1.41656 3.16123i 0.182877 0.408113i
\(61\) −5.12311 −0.655946 −0.327973 0.944687i \(-0.606366\pi\)
−0.327973 + 0.944687i \(0.606366\pi\)
\(62\) 3.07221 1.43845i 0.390171 0.182683i
\(63\) 1.46228 + 2.39871i 0.184230 + 0.302209i
\(64\) 6.96543 + 3.93481i 0.870679 + 0.491851i
\(65\) 3.12311i 0.387374i
\(66\) −7.92375 + 6.83311i −0.975347 + 0.841098i
\(67\) 5.20798i 0.636257i −0.948048 0.318128i \(-0.896946\pi\)
0.948048 0.318128i \(-0.103054\pi\)
\(68\) −3.07221 2.56155i −0.372560 0.310634i
\(69\) 3.56155 + 12.6847i 0.428761 + 1.52705i
\(70\) 0.561553 + 1.19935i 0.0671184 + 0.143350i
\(71\) −6.67026 −0.791615 −0.395807 0.918334i \(-0.629535\pi\)
−0.395807 + 0.918334i \(0.629535\pi\)
\(72\) −8.13012 + 2.42923i −0.958144 + 0.286287i
\(73\) −8.24621 −0.965146 −0.482573 0.875856i \(-0.660298\pi\)
−0.482573 + 0.875856i \(0.660298\pi\)
\(74\) 1.87285 + 4.00000i 0.217715 + 0.464991i
\(75\) 0.468213 + 1.66757i 0.0540646 + 0.192554i
\(76\) −6.56155 5.47091i −0.752662 0.627557i
\(77\) 4.00000i 0.455842i
\(78\) −5.79337 + 4.99596i −0.655970 + 0.565681i
\(79\) 9.06897i 1.02034i −0.860074 0.510169i \(-0.829583\pi\)
0.860074 0.510169i \(-0.170417\pi\)
\(80\) −3.93481 + 0.719224i −0.439925 + 0.0804116i
\(81\) 4.12311 8.00000i 0.458123 0.888889i
\(82\) 9.12311 4.27156i 1.00748 0.471715i
\(83\) 4.68213 0.513931 0.256965 0.966421i \(-0.417277\pi\)
0.256965 + 0.966421i \(0.417277\pi\)
\(84\) 1.32650 2.96026i 0.144733 0.322991i
\(85\) 2.00000 0.216930
\(86\) −1.87285 + 0.876894i −0.201955 + 0.0945580i
\(87\) −8.54312 + 2.39871i −0.915918 + 0.257168i
\(88\) 11.6847 + 3.07221i 1.24559 + 0.327498i
\(89\) 6.24621i 0.662097i −0.943614 0.331049i \(-0.892598\pi\)
0.943614 0.331049i \(-0.107402\pi\)
\(90\) 2.34435 3.53610i 0.247116 0.372738i
\(91\) 2.92456i 0.306577i
\(92\) 9.74247 11.6847i 1.01572 1.21821i
\(93\) 4.00000 1.12311i 0.414781 0.116461i
\(94\) −0.561553 1.19935i −0.0579198 0.123704i
\(95\) 4.27156 0.438253
\(96\) 7.62858 + 6.14856i 0.778589 + 0.627534i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −3.67188 7.84233i −0.370916 0.792195i
\(99\) −10.9418 + 6.67026i −1.09969 + 0.670387i
\(100\) 1.28078 1.53610i 0.128078 0.153610i
\(101\) 9.12311i 0.907783i −0.891057 0.453891i \(-0.850035\pi\)
0.891057 0.453891i \(-0.149965\pi\)
\(102\) −3.19935 3.71001i −0.316783 0.367345i
\(103\) 12.4041i 1.22221i 0.791549 + 0.611106i \(0.209275\pi\)
−0.791549 + 0.611106i \(0.790725\pi\)
\(104\) 8.54312 + 2.24621i 0.837722 + 0.220259i
\(105\) 0.438447 + 1.56155i 0.0427881 + 0.152392i
\(106\) 5.43845 2.54635i 0.528229 0.247324i
\(107\) −0.936426 −0.0905278 −0.0452639 0.998975i \(-0.514413\pi\)
−0.0452639 + 0.998975i \(0.514413\pi\)
\(108\) −10.3097 + 1.30784i −0.992050 + 0.125847i
\(109\) −9.12311 −0.873835 −0.436918 0.899502i \(-0.643930\pi\)
−0.436918 + 0.899502i \(0.643930\pi\)
\(110\) −5.47091 + 2.56155i −0.521631 + 0.244234i
\(111\) 1.46228 + 5.20798i 0.138793 + 0.494320i
\(112\) −3.68466 + 0.673500i −0.348167 + 0.0636398i
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) −6.83311 7.92375i −0.639980 0.742127i
\(115\) 7.60669i 0.709328i
\(116\) 7.86962 + 6.56155i 0.730676 + 0.609225i
\(117\) −8.00000 + 4.87689i −0.739600 + 0.450869i
\(118\) −4.31534 9.21662i −0.397259 0.848458i
\(119\) 1.87285 0.171684
\(120\) −4.89830 + 0.0814236i −0.447152 + 0.00743292i
\(121\) 7.24621 0.658746
\(122\) 3.07221 + 6.56155i 0.278144 + 0.594055i
\(123\) 11.8782 3.33513i 1.07103 0.300719i
\(124\) −3.68466 3.07221i −0.330892 0.275892i
\(125\) 1.00000i 0.0894427i
\(126\) 2.19531 3.31130i 0.195574 0.294994i
\(127\) 4.68213i 0.415472i 0.978185 + 0.207736i \(0.0666095\pi\)
−0.978185 + 0.207736i \(0.933391\pi\)
\(128\) 0.862603 11.2808i 0.0762440 0.997089i
\(129\) −2.43845 + 0.684658i −0.214693 + 0.0602808i
\(130\) −4.00000 + 1.87285i −0.350823 + 0.164260i
\(131\) −17.6121 −1.53878 −0.769388 0.638782i \(-0.779438\pi\)
−0.769388 + 0.638782i \(0.779438\pi\)
\(132\) 13.5034 + 6.05090i 1.17532 + 0.526663i
\(133\) 4.00000 0.346844
\(134\) −6.67026 + 3.12311i −0.576223 + 0.269795i
\(135\) 3.54042 3.80335i 0.304711 0.327340i
\(136\) −1.43845 + 5.47091i −0.123346 + 0.469127i
\(137\) 8.24621i 0.704521i 0.935902 + 0.352261i \(0.114587\pi\)
−0.935902 + 0.352261i \(0.885413\pi\)
\(138\) 14.1104 12.1682i 1.20116 1.03583i
\(139\) 13.8664i 1.17613i 0.808813 + 0.588066i \(0.200110\pi\)
−0.808813 + 0.588066i \(0.799890\pi\)
\(140\) 1.19935 1.43845i 0.101364 0.121571i
\(141\) −0.438447 1.56155i −0.0369239 0.131506i
\(142\) 4.00000 + 8.54312i 0.335673 + 0.716922i
\(143\) 13.3405 1.11559
\(144\) 7.98674 + 8.95611i 0.665562 + 0.746343i
\(145\) −5.12311 −0.425451
\(146\) 4.94506 + 10.5616i 0.409256 + 0.874080i
\(147\) −2.86692 10.2107i −0.236459 0.842163i
\(148\) 4.00000 4.79741i 0.328798 0.394345i
\(149\) 14.0000i 1.14692i −0.819232 0.573462i \(-0.805600\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) 1.85500 1.59968i 0.151460 0.130613i
\(151\) 6.14441i 0.500025i −0.968243 0.250013i \(-0.919565\pi\)
0.968243 0.250013i \(-0.0804347\pi\)
\(152\) −3.07221 + 11.6847i −0.249189 + 0.947751i
\(153\) −3.12311 5.12311i −0.252488 0.414179i
\(154\) −5.12311 + 2.39871i −0.412832 + 0.193293i
\(155\) 2.39871 0.192669
\(156\) 9.87285 + 4.42405i 0.790461 + 0.354208i
\(157\) 21.3693 1.70546 0.852729 0.522354i \(-0.174946\pi\)
0.852729 + 0.522354i \(0.174946\pi\)
\(158\) −11.6153 + 5.43845i −0.924065 + 0.432660i
\(159\) 7.08084 1.98813i 0.561547 0.157669i
\(160\) 3.28078 + 4.60831i 0.259368 + 0.364319i
\(161\) 7.12311i 0.561379i
\(162\) −12.7187 0.483365i −0.999279 0.0379768i
\(163\) 24.1671i 1.89291i −0.322834 0.946456i \(-0.604636\pi\)
0.322834 0.946456i \(-0.395364\pi\)
\(164\) −10.9418 9.12311i −0.854413 0.712395i
\(165\) −7.12311 + 2.00000i −0.554533 + 0.155700i
\(166\) −2.80776 5.99676i −0.217925 0.465439i
\(167\) −2.80928 −0.217389 −0.108694 0.994075i \(-0.534667\pi\)
−0.108694 + 0.994075i \(0.534667\pi\)
\(168\) −4.58690 + 0.0762472i −0.353887 + 0.00588260i
\(169\) −3.24621 −0.249709
\(170\) −1.19935 2.56155i −0.0919862 0.196462i
\(171\) −6.67026 10.9418i −0.510088 0.836742i
\(172\) 2.24621 + 1.87285i 0.171272 + 0.142804i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 8.19531 + 9.50338i 0.621285 + 0.720449i
\(175\) 0.936426i 0.0707872i
\(176\) −3.07221 16.8078i −0.231576 1.26693i
\(177\) −3.36932 12.0000i −0.253253 0.901975i
\(178\) −8.00000 + 3.74571i −0.599625 + 0.280752i
\(179\) −14.6875 −1.09780 −0.548899 0.835889i \(-0.684953\pi\)
−0.548899 + 0.835889i \(0.684953\pi\)
\(180\) −5.93481 0.882071i −0.442355 0.0657457i
\(181\) 4.24621 0.315618 0.157809 0.987470i \(-0.449557\pi\)
0.157809 + 0.987470i \(0.449557\pi\)
\(182\) −3.74571 + 1.75379i −0.277650 + 0.129999i
\(183\) 2.39871 + 8.54312i 0.177317 + 0.631525i
\(184\) −20.8078 5.47091i −1.53397 0.403321i
\(185\) 3.12311i 0.229615i
\(186\) −3.83715 4.44961i −0.281354 0.326261i
\(187\) 8.54312i 0.624735i
\(188\) −1.19935 + 1.43845i −0.0874718 + 0.104910i
\(189\) 3.31534 3.56155i 0.241156 0.259065i
\(190\) −2.56155 5.47091i −0.185835 0.396902i
\(191\) 7.72197 0.558742 0.279371 0.960183i \(-0.409874\pi\)
0.279371 + 0.960183i \(0.409874\pi\)
\(192\) 3.30024 13.4577i 0.238175 0.971222i
\(193\) 16.2462 1.16943 0.584714 0.811240i \(-0.301207\pi\)
0.584714 + 0.811240i \(0.301207\pi\)
\(194\) 3.59806 + 7.68466i 0.258326 + 0.551726i
\(195\) −5.20798 + 1.46228i −0.372952 + 0.104716i
\(196\) −7.84233 + 9.40572i −0.560166 + 0.671837i
\(197\) 12.2462i 0.872506i −0.899824 0.436253i \(-0.856305\pi\)
0.899824 0.436253i \(-0.143695\pi\)
\(198\) 15.1047 + 10.0140i 1.07344 + 0.711666i
\(199\) 17.6121i 1.24849i −0.781230 0.624244i \(-0.785407\pi\)
0.781230 0.624244i \(-0.214593\pi\)
\(200\) −2.73546 0.719224i −0.193426 0.0508568i
\(201\) −8.68466 + 2.43845i −0.612569 + 0.171995i
\(202\) −11.6847 + 5.47091i −0.822130 + 0.384932i
\(203\) −4.79741 −0.336712
\(204\) −2.83311 + 6.32246i −0.198357 + 0.442661i
\(205\) 7.12311 0.497499
\(206\) 15.8869 7.43845i 1.10689 0.518261i
\(207\) 19.4849 11.8782i 1.35430 0.825595i
\(208\) −2.24621 12.2888i −0.155747 0.852077i
\(209\) 18.2462i 1.26212i
\(210\) 1.73707 1.49798i 0.119869 0.103370i
\(211\) 1.34700i 0.0927313i −0.998925 0.0463656i \(-0.985236\pi\)
0.998925 0.0463656i \(-0.0147639\pi\)
\(212\) −6.52262 5.43845i −0.447975 0.373514i
\(213\) 3.12311 + 11.1231i 0.213992 + 0.762143i
\(214\) 0.561553 + 1.19935i 0.0383870 + 0.0819861i
\(215\) −1.46228 −0.0997266
\(216\) 7.85753 + 12.4201i 0.534637 + 0.845082i
\(217\) 2.24621 0.152483
\(218\) 5.47091 + 11.6847i 0.370537 + 0.791385i
\(219\) 3.86098 + 13.7511i 0.260901 + 0.929213i
\(220\) 6.56155 + 5.47091i 0.442380 + 0.368849i
\(221\) 6.24621i 0.420166i
\(222\) 5.79337 4.99596i 0.388826 0.335307i
\(223\) 18.0227i 1.20689i 0.797406 + 0.603443i \(0.206205\pi\)
−0.797406 + 0.603443i \(0.793795\pi\)
\(224\) 3.07221 + 4.31534i 0.205270 + 0.288331i
\(225\) 2.56155 1.56155i 0.170770 0.104104i
\(226\) 17.9309 8.39547i 1.19274 0.558458i
\(227\) −8.65840 −0.574678 −0.287339 0.957829i \(-0.592771\pi\)
−0.287339 + 0.957829i \(0.592771\pi\)
\(228\) −6.05090 + 13.5034i −0.400731 + 0.894283i
\(229\) 0.246211 0.0162701 0.00813505 0.999967i \(-0.497411\pi\)
0.00813505 + 0.999967i \(0.497411\pi\)
\(230\) 9.74247 4.56155i 0.642399 0.300780i
\(231\) −6.67026 + 1.87285i −0.438871 + 0.123225i
\(232\) 3.68466 14.0140i 0.241910 0.920066i
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) 11.0436 + 7.32165i 0.721944 + 0.478631i
\(235\) 0.936426i 0.0610857i
\(236\) −9.21662 + 11.0540i −0.599951 + 0.719553i
\(237\) −15.1231 + 4.24621i −0.982351 + 0.275821i
\(238\) −1.12311 2.39871i −0.0728001 0.155485i
\(239\) 20.8319 1.34751 0.673753 0.738957i \(-0.264681\pi\)
0.673753 + 0.738957i \(0.264681\pi\)
\(240\) 3.04168 + 6.22480i 0.196340 + 0.401809i
\(241\) −11.3693 −0.732362 −0.366181 0.930544i \(-0.619335\pi\)
−0.366181 + 0.930544i \(0.619335\pi\)
\(242\) −4.34538 9.28078i −0.279332 0.596591i
\(243\) −15.2710 3.12985i −0.979636 0.200780i
\(244\) 6.56155 7.86962i 0.420060 0.503801i
\(245\) 6.12311i 0.391191i
\(246\) −11.3947 13.2134i −0.726497 0.842454i
\(247\) 13.3405i 0.848837i
\(248\) −1.72521 + 6.56155i −0.109551 + 0.416659i
\(249\) −2.19224 7.80776i −0.138927 0.494797i
\(250\) 1.28078 0.599676i 0.0810034 0.0379269i
\(251\) 25.1035 1.58452 0.792259 0.610184i \(-0.208905\pi\)
0.792259 + 0.610184i \(0.208905\pi\)
\(252\) −5.55751 0.825994i −0.350090 0.0520328i
\(253\) −32.4924 −2.04278
\(254\) 5.99676 2.80776i 0.376270 0.176175i
\(255\) −0.936426 3.33513i −0.0586413 0.208854i
\(256\) −14.9654 + 5.66001i −0.935340 + 0.353751i
\(257\) 2.49242i 0.155473i −0.996974 0.0777365i \(-0.975231\pi\)
0.996974 0.0777365i \(-0.0247693\pi\)
\(258\) 2.33917 + 2.71253i 0.145631 + 0.168875i
\(259\) 2.92456i 0.181723i
\(260\) 4.79741 + 4.00000i 0.297523 + 0.248069i
\(261\) 8.00000 + 13.1231i 0.495188 + 0.812300i
\(262\) 10.5616 + 22.5571i 0.652495 + 1.39359i
\(263\) −15.0981 −0.930989 −0.465494 0.885051i \(-0.654123\pi\)
−0.465494 + 0.885051i \(0.654123\pi\)
\(264\) −0.347806 20.9234i −0.0214060 1.28775i
\(265\) 4.24621 0.260843
\(266\) −2.39871 5.12311i −0.147074 0.314118i
\(267\) −10.4160 + 2.92456i −0.637447 + 0.178980i
\(268\) 8.00000 + 6.67026i 0.488678 + 0.407451i
\(269\) 14.0000i 0.853595i 0.904347 + 0.426798i \(0.140358\pi\)
−0.904347 + 0.426798i \(0.859642\pi\)
\(270\) −6.99434 2.25371i −0.425662 0.137156i
\(271\) 31.7738i 1.93012i 0.262032 + 0.965059i \(0.415608\pi\)
−0.262032 + 0.965059i \(0.584392\pi\)
\(272\) 7.86962 1.43845i 0.477166 0.0872187i
\(273\) −4.87689 + 1.36932i −0.295163 + 0.0828748i
\(274\) 10.5616 4.94506i 0.638047 0.298742i
\(275\) −4.27156 −0.257585
\(276\) −24.0465 10.7753i −1.44743 0.648597i
\(277\) −1.36932 −0.0822743 −0.0411371 0.999154i \(-0.513098\pi\)
−0.0411371 + 0.999154i \(0.513098\pi\)
\(278\) 17.7597 8.31534i 1.06516 0.498721i
\(279\) −3.74571 6.14441i −0.224250 0.367856i
\(280\) −2.56155 0.673500i −0.153082 0.0402493i
\(281\) 27.6155i 1.64740i −0.567023 0.823702i \(-0.691905\pi\)
0.567023 0.823702i \(-0.308095\pi\)
\(282\) −1.73707 + 1.49798i −0.103441 + 0.0892034i
\(283\) 4.38684i 0.260770i −0.991463 0.130385i \(-0.958379\pi\)
0.991463 0.130385i \(-0.0416214\pi\)
\(284\) 8.54312 10.2462i 0.506941 0.608001i
\(285\) −2.00000 7.12311i −0.118470 0.421936i
\(286\) −8.00000 17.0862i −0.473050 1.01033i
\(287\) 6.67026 0.393733
\(288\) 6.68132 15.6000i 0.393701 0.919239i
\(289\) 13.0000 0.764706
\(290\) 3.07221 + 6.56155i 0.180406 + 0.385308i
\(291\) 2.80928 + 10.0054i 0.164683 + 0.586527i
\(292\) 10.5616 12.6670i 0.618068 0.741282i
\(293\) 30.4924i 1.78139i −0.454605 0.890693i \(-0.650220\pi\)
0.454605 0.890693i \(-0.349780\pi\)
\(294\) −11.3584 + 9.79499i −0.662434 + 0.571255i
\(295\) 7.19612i 0.418974i
\(296\) −8.54312 2.24621i −0.496559 0.130558i
\(297\) 16.2462 + 15.1231i 0.942701 + 0.877532i
\(298\) −17.9309 + 8.39547i −1.03871 + 0.486337i
\(299\) −23.7565 −1.37387
\(300\) −3.16123 1.41656i −0.182514 0.0817849i
\(301\) −1.36932 −0.0789261
\(302\) −7.86962 + 3.68466i −0.452846 + 0.212028i
\(303\) −15.2134 + 4.27156i −0.873986 + 0.245395i
\(304\) 16.8078 3.07221i 0.963991 0.176203i
\(305\) 5.12311i 0.293348i
\(306\) −4.68870 + 7.07221i −0.268035 + 0.404291i
\(307\) 8.13254i 0.464149i −0.972698 0.232074i \(-0.925449\pi\)
0.972698 0.232074i \(-0.0745513\pi\)
\(308\) 6.14441 + 5.12311i 0.350110 + 0.291916i
\(309\) 20.6847 5.80776i 1.17671 0.330392i
\(310\) −1.43845 3.07221i −0.0816983 0.174490i
\(311\) 14.1617 0.803035 0.401517 0.915851i \(-0.368483\pi\)
0.401517 + 0.915851i \(0.368483\pi\)
\(312\) −0.254294 15.2979i −0.0143966 0.866074i
\(313\) 10.4924 0.593067 0.296533 0.955022i \(-0.404169\pi\)
0.296533 + 0.955022i \(0.404169\pi\)
\(314\) −12.8147 27.3693i −0.723174 1.54454i
\(315\) 2.39871 1.46228i 0.135152 0.0823901i
\(316\) 13.9309 + 11.6153i 0.783673 + 0.653413i
\(317\) 32.7386i 1.83878i 0.393342 + 0.919392i \(0.371319\pi\)
−0.393342 + 0.919392i \(0.628681\pi\)
\(318\) −6.79256 7.87673i −0.380908 0.441705i
\(319\) 21.8836i 1.22525i
\(320\) 3.93481 6.96543i 0.219962 0.389380i
\(321\) 0.438447 + 1.56155i 0.0244717 + 0.0871574i
\(322\) 9.12311 4.27156i 0.508411 0.238045i
\(323\) −8.54312 −0.475352
\(324\) 7.00805 + 16.5797i 0.389336 + 0.921096i
\(325\) −3.12311 −0.173239
\(326\) −30.9526 + 14.4924i −1.71431 + 0.802661i
\(327\) 4.27156 + 15.2134i 0.236218 + 0.841302i
\(328\) −5.12311 + 19.4849i −0.282876 + 1.07588i
\(329\) 0.876894i 0.0483448i
\(330\) 6.83311 + 7.92375i 0.376150 + 0.436188i
\(331\) 28.0281i 1.54056i −0.637705 0.770281i \(-0.720116\pi\)
0.637705 0.770281i \(-0.279884\pi\)
\(332\) −5.99676 + 7.19224i −0.329115 + 0.394725i
\(333\) 8.00000 4.87689i 0.438397 0.267252i
\(334\) 1.68466 + 3.59806i 0.0921804 + 0.196877i
\(335\) −5.20798 −0.284543
\(336\) 2.84831 + 5.82907i 0.155388 + 0.318002i
\(337\) −34.4924 −1.87892 −0.939461 0.342656i \(-0.888674\pi\)
−0.939461 + 0.342656i \(0.888674\pi\)
\(338\) 1.94668 + 4.15767i 0.105885 + 0.226147i
\(339\) 23.3459 6.55498i 1.26798 0.356018i
\(340\) −2.56155 + 3.07221i −0.138920 + 0.166614i
\(341\) 10.2462i 0.554863i
\(342\) −10.0140 + 15.1047i −0.541497 + 0.816767i
\(343\) 12.2888i 0.663534i
\(344\) 1.05171 4.00000i 0.0567042 0.215666i
\(345\) 12.6847 3.56155i 0.682919 0.191748i
\(346\) 2.56155 1.19935i 0.137710 0.0644776i
\(347\) 23.8718 1.28150 0.640752 0.767748i \(-0.278623\pi\)
0.640752 + 0.767748i \(0.278623\pi\)
\(348\) 7.25716 16.1953i 0.389025 0.868160i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 1.19935 0.561553i 0.0641081 0.0300163i
\(351\) 11.8782 + 11.0571i 0.634014 + 0.590184i
\(352\) −19.6847 + 14.0140i −1.04920 + 0.746950i
\(353\) 3.75379i 0.199794i −0.994998 0.0998970i \(-0.968149\pi\)
0.994998 0.0998970i \(-0.0318513\pi\)
\(354\) −13.3488 + 11.5115i −0.709482 + 0.611827i
\(355\) 6.67026i 0.354021i
\(356\) 9.59482 + 8.00000i 0.508525 + 0.423999i
\(357\) −0.876894 3.12311i −0.0464102 0.165292i
\(358\) 8.80776 + 18.8114i 0.465505 + 0.994215i
\(359\) −1.05171 −0.0555069 −0.0277535 0.999615i \(-0.508835\pi\)
−0.0277535 + 0.999615i \(0.508835\pi\)
\(360\) 2.42923 + 8.13012i 0.128032 + 0.428495i
\(361\) 0.753789 0.0396731
\(362\) −2.54635 5.43845i −0.133833 0.285838i
\(363\) −3.39277 12.0835i −0.178074 0.634221i
\(364\) 4.49242 + 3.74571i 0.235467 + 0.196328i
\(365\) 8.24621i 0.431626i
\(366\) 9.50338 8.19531i 0.496749 0.428376i
\(367\) 26.5658i 1.38672i −0.720590 0.693361i \(-0.756129\pi\)
0.720590 0.693361i \(-0.243871\pi\)
\(368\) 5.47091 + 29.9309i 0.285191 + 1.56025i
\(369\) −11.1231 18.2462i −0.579046 0.949860i
\(370\) 4.00000 1.87285i 0.207950 0.0973650i
\(371\) 3.97626 0.206437
\(372\) −3.39790 + 7.58286i −0.176173 + 0.393153i
\(373\) −0.876894 −0.0454039 −0.0227019 0.999742i \(-0.507227\pi\)
−0.0227019 + 0.999742i \(0.507227\pi\)
\(374\) 10.9418 5.12311i 0.565788 0.264909i
\(375\) 1.66757 0.468213i 0.0861127 0.0241784i
\(376\) 2.56155 + 0.673500i 0.132102 + 0.0347331i
\(377\) 16.0000i 0.824042i
\(378\) −6.54968 2.11043i −0.336879 0.108549i
\(379\) 25.1035i 1.28948i 0.764402 + 0.644740i \(0.223034\pi\)
−0.764402 + 0.644740i \(0.776966\pi\)
\(380\) −5.47091 + 6.56155i −0.280652 + 0.336601i
\(381\) 7.80776 2.19224i 0.400004 0.112312i
\(382\) −4.63068 9.89012i −0.236926 0.506022i
\(383\) −4.68213 −0.239246 −0.119623 0.992819i \(-0.538169\pi\)
−0.119623 + 0.992819i \(0.538169\pi\)
\(384\) −19.2153 + 3.84336i −0.980578 + 0.196131i
\(385\) −4.00000 −0.203859
\(386\) −9.74247 20.8078i −0.495879 1.05909i
\(387\) 2.28343 + 3.74571i 0.116073 + 0.190405i
\(388\) 7.68466 9.21662i 0.390129 0.467903i
\(389\) 28.7386i 1.45711i 0.684989 + 0.728553i \(0.259807\pi\)
−0.684989 + 0.728553i \(0.740193\pi\)
\(390\) 4.99596 + 5.79337i 0.252980 + 0.293359i
\(391\) 15.2134i 0.769374i
\(392\) 16.7495 + 4.40388i 0.845977 + 0.222430i
\(393\) 8.24621 + 29.3693i 0.415966 + 1.48149i
\(394\) −15.6847 + 7.34376i −0.790182 + 0.369973i
\(395\) −9.06897 −0.456309
\(396\) 3.76782 25.3509i 0.189340 1.27393i
\(397\) 23.1231 1.16052 0.580258 0.814433i \(-0.302952\pi\)
0.580258 + 0.814433i \(0.302952\pi\)
\(398\) −22.5571 + 10.5616i −1.13069 + 0.529403i
\(399\) −1.87285 6.67026i −0.0937599 0.333931i
\(400\) 0.719224 + 3.93481i 0.0359612 + 0.196740i
\(401\) 24.0000i 1.19850i 0.800561 + 0.599251i \(0.204535\pi\)
−0.800561 + 0.599251i \(0.795465\pi\)
\(402\) 8.33109 + 9.66083i 0.415517 + 0.481838i
\(403\) 7.49141i 0.373174i
\(404\) 14.0140 + 11.6847i 0.697224 + 0.581333i
\(405\) −8.00000 4.12311i −0.397523 0.204879i
\(406\) 2.87689 + 6.14441i 0.142778 + 0.304942i
\(407\) −13.3405 −0.661265
\(408\) 9.79661 0.162847i 0.485004 0.00806214i
\(409\) 0.630683 0.0311853 0.0155926 0.999878i \(-0.495037\pi\)
0.0155926 + 0.999878i \(0.495037\pi\)
\(410\) −4.27156 9.12311i −0.210957 0.450558i
\(411\) 13.7511 3.86098i 0.678292 0.190448i
\(412\) −19.0540 15.8869i −0.938722 0.782690i
\(413\) 6.73863i 0.331586i
\(414\) −26.8980 17.8327i −1.32197 0.876432i
\(415\) 4.68213i 0.229837i
\(416\) −14.3922 + 10.2462i −0.705637 + 0.502362i
\(417\) 23.1231 6.49242i 1.13234 0.317935i
\(418\) 23.3693 10.9418i 1.14303 0.535182i
\(419\) 6.14441 0.300174 0.150087 0.988673i \(-0.452045\pi\)
0.150087 + 0.988673i \(0.452045\pi\)
\(420\) −2.96026 1.32650i −0.144446 0.0647266i
\(421\) −0.630683 −0.0307376 −0.0153688 0.999882i \(-0.504892\pi\)
−0.0153688 + 0.999882i \(0.504892\pi\)
\(422\) −1.72521 + 0.807764i −0.0839817 + 0.0393213i
\(423\) −2.39871 + 1.46228i −0.116629 + 0.0710985i
\(424\) −3.05398 + 11.6153i −0.148314 + 0.564090i
\(425\) 2.00000i 0.0970143i
\(426\) 12.3734 10.6703i 0.599491 0.516976i
\(427\) 4.79741i 0.232163i
\(428\) 1.19935 1.43845i 0.0579729 0.0695300i
\(429\) −6.24621 22.2462i −0.301570 1.07406i
\(430\) 0.876894 + 1.87285i 0.0422876 + 0.0903170i
\(431\) −36.0453 −1.73624 −0.868121 0.496353i \(-0.834672\pi\)
−0.868121 + 0.496353i \(0.834672\pi\)
\(432\) 11.1954 17.5118i 0.538640 0.842536i
\(433\) 18.0000 0.865025 0.432512 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) −1.34700 2.87689i −0.0646581 0.138095i
\(435\) 2.39871 + 8.54312i 0.115009 + 0.409611i
\(436\) 11.6847 14.0140i 0.559594 0.671150i
\(437\) 32.4924i 1.55432i
\(438\) 15.2967 13.1913i 0.730907 0.630303i
\(439\) 29.9009i 1.42709i 0.700608 + 0.713546i \(0.252912\pi\)
−0.700608 + 0.713546i \(0.747088\pi\)
\(440\) 3.07221 11.6847i 0.146462 0.557044i
\(441\) −15.6847 + 9.56155i −0.746888 + 0.455312i
\(442\) 8.00000 3.74571i 0.380521 0.178165i
\(443\) 25.7446 1.22316 0.611582 0.791181i \(-0.290533\pi\)
0.611582 + 0.791181i \(0.290533\pi\)
\(444\) −9.87285 4.42405i −0.468545 0.209956i
\(445\) −6.24621 −0.296099
\(446\) 23.0830 10.8078i 1.09301 0.511762i
\(447\) −23.3459 + 6.55498i −1.10422 + 0.310040i
\(448\) 3.68466 6.52262i 0.174084 0.308165i
\(449\) 2.63068i 0.124150i −0.998071 0.0620748i \(-0.980228\pi\)
0.998071 0.0620748i \(-0.0197717\pi\)
\(450\) −3.53610 2.34435i −0.166693 0.110514i
\(451\) 30.4268i 1.43274i
\(452\) −21.5054 17.9309i −1.01153 0.843397i
\(453\) −10.2462 + 2.87689i −0.481409 + 0.135168i
\(454\) 5.19224 + 11.0895i 0.243684 + 0.520455i
\(455\) −2.92456 −0.137105
\(456\) 20.9234 0.347806i 0.979827 0.0162875i
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −0.147647 0.315342i −0.00689909 0.0147349i
\(459\) −7.08084 + 7.60669i −0.330505 + 0.355050i
\(460\) −11.6847 9.74247i −0.544800 0.454245i
\(461\) 15.8617i 0.738755i −0.929279 0.369377i \(-0.879571\pi\)
0.929279 0.369377i \(-0.120429\pi\)
\(462\) 6.39871 + 7.42001i 0.297695 + 0.345210i
\(463\) 0.936426i 0.0435194i 0.999763 + 0.0217597i \(0.00692688\pi\)
−0.999763 + 0.0217597i \(0.993073\pi\)
\(464\) −20.1584 + 3.68466i −0.935832 + 0.171056i
\(465\) −1.12311 4.00000i −0.0520828 0.185496i
\(466\) −12.8078 + 5.99676i −0.593308 + 0.277795i
\(467\) 16.1498 0.747324 0.373662 0.927565i \(-0.378102\pi\)
0.373662 + 0.927565i \(0.378102\pi\)
\(468\) 2.75480 18.5350i 0.127341 0.856782i
\(469\) −4.87689 −0.225194
\(470\) −1.19935 + 0.561553i −0.0553220 + 0.0259025i
\(471\) −10.0054 35.6347i −0.461024 1.64196i
\(472\) 19.6847 + 5.17562i 0.906060 + 0.238227i
\(473\) 6.24621i 0.287201i
\(474\) 14.5074 + 16.8230i 0.666348 + 0.772704i
\(475\) 4.27156i 0.195993i
\(476\) −2.39871 + 2.87689i −0.109944 + 0.131862i
\(477\) −6.63068 10.8769i −0.303598 0.498019i
\(478\) −12.4924 26.6811i −0.571390 1.22036i
\(479\) −22.9354 −1.04794 −0.523971 0.851736i \(-0.675550\pi\)
−0.523971 + 0.851736i \(0.675550\pi\)
\(480\) 6.14856 7.62858i 0.280642 0.348196i
\(481\) −9.75379 −0.444734
\(482\) 6.81791 + 14.5616i 0.310547 + 0.663261i
\(483\) 11.8782 3.33513i 0.540479 0.151754i
\(484\) −9.28078 + 11.1309i −0.421853 + 0.505951i
\(485\) 6.00000i 0.272446i
\(486\) 5.14904 + 21.4357i 0.233565 + 0.972341i
\(487\) 15.3287i 0.694608i 0.937753 + 0.347304i \(0.112903\pi\)
−0.937753 + 0.347304i \(0.887097\pi\)
\(488\) −14.0140 3.68466i −0.634385 0.166797i
\(489\) −40.3002 + 11.3153i −1.82244 + 0.511697i
\(490\) −7.84233 + 3.67188i −0.354280 + 0.165879i
\(491\) −18.6638 −0.842285 −0.421143 0.906994i \(-0.638371\pi\)
−0.421143 + 0.906994i \(0.638371\pi\)
\(492\) −10.0903 + 22.5178i −0.454905 + 1.01518i
\(493\) 10.2462 0.461466
\(494\) 17.0862 8.00000i 0.768746 0.359937i
\(495\) 6.67026 + 10.9418i 0.299806 + 0.491798i
\(496\) 9.43845 1.72521i 0.423799 0.0774640i
\(497\) 6.24621i 0.280181i
\(498\) −8.68537 + 7.48990i −0.389201 + 0.335630i
\(499\) 1.57756i 0.0706212i −0.999376 0.0353106i \(-0.988758\pi\)
0.999376 0.0353106i \(-0.0112421\pi\)
\(500\) −1.53610 1.28078i −0.0686966 0.0572781i
\(501\) 1.31534 + 4.68466i 0.0587651 + 0.209295i
\(502\) −15.0540 32.1520i −0.671892 1.43501i
\(503\) 19.8955 0.887097 0.443549 0.896250i \(-0.353719\pi\)
0.443549 + 0.896250i \(0.353719\pi\)
\(504\) 2.27479 + 7.61326i 0.101327 + 0.339121i
\(505\) −9.12311 −0.405973
\(506\) 19.4849 + 41.6155i 0.866211 + 1.85004i
\(507\) 1.51992 + 5.41327i 0.0675020 + 0.240412i
\(508\) −7.19224 5.99676i −0.319104 0.266063i
\(509\) 2.87689i 0.127516i 0.997965 + 0.0637581i \(0.0203086\pi\)
−0.997965 + 0.0637581i \(0.979691\pi\)
\(510\) −3.71001 + 3.19935i −0.164282 + 0.141670i
\(511\) 7.72197i 0.341600i
\(512\) 16.2236 + 15.7732i 0.716990 + 0.697083i
\(513\) −15.1231 + 16.2462i −0.667701 + 0.717288i
\(514\) −3.19224 + 1.49465i −0.140803 + 0.0659261i
\(515\) 12.4041 0.546590
\(516\) 2.07140 4.62260i 0.0911883 0.203499i
\(517\) 4.00000 0.175920
\(518\) 3.74571 1.75379i 0.164577 0.0770571i
\(519\) 3.33513 0.936426i 0.146396 0.0411046i
\(520\) 2.24621 8.54312i 0.0985029 0.374640i
\(521\) 21.7538i 0.953051i −0.879161 0.476525i \(-0.841896\pi\)
0.879161 0.476525i \(-0.158104\pi\)
\(522\) 12.0104 18.1158i 0.525679 0.792908i
\(523\) 0.641132i 0.0280348i 0.999902 + 0.0140174i \(0.00446202\pi\)
−0.999902 + 0.0140174i \(0.995538\pi\)
\(524\) 22.5571 27.0540i 0.985413 1.18186i
\(525\) 1.56155 0.438447i 0.0681518 0.0191354i
\(526\) 9.05398 + 19.3373i 0.394772 + 0.843146i
\(527\) −4.79741 −0.208979
\(528\) −26.5896 + 12.9927i −1.15716 + 0.565436i
\(529\) 34.8617 1.51573
\(530\) −2.54635 5.43845i −0.110606 0.236231i
\(531\) −18.4332 + 11.2371i −0.799934 + 0.487649i
\(532\) −5.12311 + 6.14441i −0.222115 + 0.266394i
\(533\) 22.2462i 0.963590i
\(534\) 9.99192 + 11.5867i 0.432393 + 0.501407i
\(535\) 0.936426i 0.0404852i
\(536\) 3.74571 14.2462i 0.161790 0.615343i
\(537\) 6.87689 + 24.4924i 0.296760 + 1.05693i
\(538\) 17.9309 8.39547i 0.773055 0.361954i
\(539\) 26.1552 1.12658
\(540\) 1.30784 + 10.3097i 0.0562807 + 0.443658i
\(541\) 38.9848 1.67609 0.838045 0.545602i \(-0.183699\pi\)
0.838045 + 0.545602i \(0.183699\pi\)
\(542\) 40.6951 19.0540i 1.74800 0.818438i
\(543\) −1.98813 7.08084i −0.0853189 0.303868i
\(544\) −6.56155 9.21662i −0.281324 0.395159i
\(545\) 9.12311i 0.390791i
\(546\) 4.67835 + 5.42506i 0.200215 + 0.232171i
\(547\) 25.2188i 1.07828i −0.842217 0.539139i \(-0.818750\pi\)
0.842217 0.539139i \(-0.181250\pi\)
\(548\) −12.6670 10.5616i −0.541109 0.451167i
\(549\) 13.1231 8.00000i 0.560080 0.341432i
\(550\) 2.56155 + 5.47091i 0.109225 + 0.233280i
\(551\) 21.8836 0.932275
\(552\) 0.619364 + 37.2599i 0.0263619 + 1.58589i
\(553\) −8.49242 −0.361135
\(554\) 0.821147 + 1.75379i 0.0348872 + 0.0745113i
\(555\) 5.20798 1.46228i 0.221067 0.0620703i
\(556\) −21.3002 17.7597i −0.903329 0.753180i
\(557\) 19.7538i 0.836995i 0.908218 + 0.418497i \(0.137443\pi\)
−0.908218 + 0.418497i \(0.862557\pi\)
\(558\) −5.62341 + 8.48207i −0.238058 + 0.359075i
\(559\) 4.56685i 0.193157i
\(560\) 0.673500 + 3.68466i 0.0284606 + 0.155705i
\(561\) 14.2462 4.00000i 0.601476 0.168880i
\(562\) −35.3693 + 16.5604i −1.49196 + 0.698558i
\(563\) 36.1606 1.52399 0.761994 0.647584i \(-0.224221\pi\)
0.761994 + 0.647584i \(0.224221\pi\)
\(564\) 2.96026 + 1.32650i 0.124649 + 0.0558557i
\(565\) 14.0000 0.588984
\(566\) −5.61856 + 2.63068i −0.236166 + 0.110576i
\(567\) −7.49141 3.86098i −0.314610 0.162146i
\(568\) −18.2462 4.79741i −0.765594 0.201295i
\(569\) 4.87689i 0.204450i −0.994761 0.102225i \(-0.967404\pi\)
0.994761 0.102225i \(-0.0325962\pi\)
\(570\) −7.92375 + 6.83311i −0.331889 + 0.286208i
\(571\) 16.7909i 0.702679i −0.936248 0.351339i \(-0.885726\pi\)
0.936248 0.351339i \(-0.114274\pi\)
\(572\) −17.0862 + 20.4924i −0.714411 + 0.856831i
\(573\) −3.61553 12.8769i −0.151041 0.537940i
\(574\) −4.00000 8.54312i −0.166957 0.356583i
\(575\) 7.60669 0.317221
\(576\) −23.9867 + 0.797675i −0.999448 + 0.0332364i
\(577\) −15.7538 −0.655839 −0.327919 0.944706i \(-0.606347\pi\)
−0.327919 + 0.944706i \(0.606347\pi\)
\(578\) −7.79579 16.6501i −0.324262 0.692553i
\(579\) −7.60669 27.0916i −0.316123 1.12589i
\(580\) 6.56155 7.86962i 0.272454 0.326768i
\(581\) 4.38447i 0.181899i
\(582\) 11.1300 9.59806i 0.461354 0.397852i
\(583\) 18.1379i 0.751197i
\(584\) −22.5571 5.93087i −0.933421 0.245421i
\(585\) 4.87689 + 8.00000i 0.201635 + 0.330759i
\(586\) −39.0540 + 18.2856i −1.61330 + 0.755371i
\(587\) −38.0335 −1.56981 −0.784904 0.619617i \(-0.787288\pi\)
−0.784904 + 0.619617i \(0.787288\pi\)
\(588\) 19.3565 + 8.67372i 0.798250 + 0.357698i
\(589\) −10.2462 −0.422188
\(590\) −9.21662 + 4.31534i −0.379442 + 0.177660i
\(591\) −20.4214 + 5.73384i −0.840023 + 0.235859i
\(592\) 2.24621 + 12.2888i 0.0923187 + 0.505067i
\(593\) 8.24621i 0.338631i −0.985562 0.169316i \(-0.945844\pi\)
0.985562 0.169316i \(-0.0541557\pi\)
\(594\) 9.62685 29.8767i 0.394994 1.22586i
\(595\) 1.87285i 0.0767795i
\(596\) 21.5054 + 17.9309i 0.880897 + 0.734477i
\(597\) −29.3693 + 8.24621i −1.20201 + 0.337495i
\(598\) 14.2462 + 30.4268i 0.582571 + 1.24424i
\(599\) −36.8665 −1.50632 −0.753162 0.657836i \(-0.771472\pi\)
−0.753162 + 0.657836i \(0.771472\pi\)
\(600\) 0.0814236 + 4.89830i 0.00332410 + 0.199972i
\(601\) 14.8769 0.606841 0.303421 0.952857i \(-0.401871\pi\)
0.303421 + 0.952857i \(0.401871\pi\)
\(602\) 0.821147 + 1.75379i 0.0334675 + 0.0714791i
\(603\) 8.13254 + 13.3405i 0.331183 + 0.543268i
\(604\) 9.43845 + 7.86962i 0.384045 + 0.320210i
\(605\) 7.24621i 0.294600i
\(606\) 14.5940 + 16.9234i 0.592841 + 0.687466i
\(607\) 29.4903i 1.19698i −0.801132 0.598488i \(-0.795768\pi\)
0.801132 0.598488i \(-0.204232\pi\)
\(608\) −14.0140 19.6847i −0.568344 0.798318i
\(609\) 2.24621 + 8.00000i 0.0910211 + 0.324176i
\(610\) 6.56155 3.07221i 0.265670 0.124390i
\(611\) 2.92456 0.118315
\(612\) 11.8696 + 1.76414i 0.479801 + 0.0713112i
\(613\) 0.876894 0.0354174 0.0177087 0.999843i \(-0.494363\pi\)
0.0177087 + 0.999843i \(0.494363\pi\)
\(614\) −10.4160 + 4.87689i −0.420354 + 0.196815i
\(615\) −3.33513 11.8782i −0.134486 0.478977i
\(616\) 2.87689 10.9418i 0.115913 0.440859i
\(617\) 14.0000i 0.563619i −0.959470 0.281809i \(-0.909065\pi\)
0.959470 0.281809i \(-0.0909346\pi\)
\(618\) −19.8425 23.0096i −0.798184 0.925584i
\(619\) 20.3061i 0.816171i −0.912944 0.408085i \(-0.866197\pi\)
0.912944 0.408085i \(-0.133803\pi\)
\(620\) −3.07221 + 3.68466i −0.123383 + 0.147979i
\(621\) −28.9309 26.9309i −1.16096 1.08070i
\(622\) −8.49242 18.1379i −0.340515 0.727265i
\(623\) −5.84912 −0.234340
\(624\) −19.4407 + 9.49949i −0.778252 + 0.380284i
\(625\) 1.00000 0.0400000
\(626\) −6.29206 13.4384i −0.251481 0.537108i
\(627\) 30.4268 8.54312i 1.21513 0.341179i
\(628\) −27.3693 + 32.8255i −1.09215 + 1.30988i
\(629\) 6.24621i 0.249053i
\(630\) −3.31130 2.19531i −0.131925 0.0874633i
\(631\) 30.1315i 1.19951i −0.800182 0.599757i \(-0.795264\pi\)
0.800182 0.599757i \(-0.204736\pi\)
\(632\) 6.52262 24.8078i 0.259456 0.986800i
\(633\) −2.24621 + 0.630683i −0.0892789 + 0.0250674i
\(634\) 41.9309 19.6326i 1.66529 0.779710i
\(635\) 4.68213 0.185805
\(636\) −6.01499 + 13.4232i −0.238510 + 0.532266i
\(637\) 19.1231 0.757685
\(638\) −28.0281 + 13.1231i −1.10964 + 0.519549i
\(639\) 17.0862 10.4160i 0.675921 0.412049i
\(640\) −11.2808 0.862603i −0.445912 0.0340974i
\(641\) 47.6155i 1.88070i −0.340208 0.940350i \(-0.610498\pi\)
0.340208 0.940350i \(-0.389502\pi\)
\(642\) 1.73707 1.49798i 0.0685568 0.0591205i
\(643\) 20.4214i 0.805340i 0.915345 + 0.402670i \(0.131918\pi\)
−0.915345 + 0.402670i \(0.868082\pi\)
\(644\) −10.9418 9.12311i −0.431168 0.359501i
\(645\) 0.684658 + 2.43845i 0.0269584 + 0.0960138i
\(646\) 5.12311 + 10.9418i 0.201566 + 0.430500i
\(647\) −3.63043 −0.142727 −0.0713634 0.997450i \(-0.522735\pi\)
−0.0713634 + 0.997450i \(0.522735\pi\)
\(648\) 17.0324 18.9182i 0.669094 0.743177i
\(649\) 30.7386 1.20660
\(650\) 1.87285 + 4.00000i 0.0734593 + 0.156893i
\(651\) −1.05171 3.74571i −0.0412196 0.146806i
\(652\) 37.1231 + 30.9526i 1.45385 + 1.21220i
\(653\) 26.9848i 1.05600i 0.849245 + 0.527999i \(0.177058\pi\)
−0.849245 + 0.527999i \(0.822942\pi\)
\(654\) 16.9234 14.5940i 0.661757 0.570671i
\(655\) 17.6121i 0.688161i
\(656\) 28.0281 5.12311i 1.09431 0.200024i
\(657\) 21.1231 12.8769i 0.824091 0.502375i
\(658\) −1.12311 + 0.525853i −0.0437832 + 0.0204999i
\(659\) 26.9764 1.05085 0.525425 0.850840i \(-0.323906\pi\)
0.525425 + 0.850840i \(0.323906\pi\)
\(660\) 6.05090 13.5034i 0.235531 0.525618i
\(661\) −46.1080 −1.79339 −0.896696 0.442647i \(-0.854039\pi\)
−0.896696 + 0.442647i \(0.854039\pi\)
\(662\) −35.8977 + 16.8078i −1.39520 + 0.653252i
\(663\) 10.4160 2.92456i 0.404523 0.113580i
\(664\) 12.8078 + 3.36750i 0.497038 + 0.130684i
\(665\) 4.00000i 0.155113i
\(666\) −11.0436 7.32165i −0.427932 0.283708i
\(667\) 38.9699i 1.50892i
\(668\) 3.59806 4.31534i 0.139213 0.166966i
\(669\) 30.0540 8.43845i 1.16195 0.326249i
\(670\) 3.12311 + 6.67026i 0.120656 + 0.257695i
\(671\) −21.8836 −0.844809
\(672\) 5.75767 7.14361i 0.222107 0.275571i
\(673\) −10.4924 −0.404453 −0.202227 0.979339i \(-0.564818\pi\)
−0.202227 + 0.979339i \(0.564818\pi\)
\(674\) 20.6843 + 44.1771i 0.796729 + 1.70164i
\(675\) −3.80335 3.54042i −0.146391 0.136271i
\(676\) 4.15767 4.98651i 0.159910 0.191789i
\(677\) 34.4924i 1.32565i 0.748774 + 0.662826i \(0.230643\pi\)
−0.748774 + 0.662826i \(0.769357\pi\)
\(678\) −22.3955 25.9700i −0.860093 0.997373i
\(679\) 5.61856i 0.215620i
\(680\) 5.47091 + 1.43845i 0.209800 + 0.0551619i
\(681\) 4.05398 + 14.4384i 0.155349 + 0.553282i
\(682\) 13.1231 6.14441i 0.502510 0.235282i
\(683\) −36.1606 −1.38365 −0.691823 0.722067i \(-0.743192\pi\)
−0.691823 + 0.722067i \(0.743192\pi\)
\(684\) 25.3509 + 3.76782i 0.969315 + 0.144066i
\(685\) 8.24621 0.315072
\(686\) −15.7392 + 7.36932i −0.600927 + 0.281362i
\(687\) −0.115279 0.410574i −0.00439818 0.0156644i
\(688\) −5.75379 + 1.05171i −0.219361 + 0.0400959i
\(689\) 13.2614i 0.505218i
\(690\) −12.1682 14.1104i −0.463237 0.537175i
\(691\) 29.0798i 1.10625i 0.833100 + 0.553123i \(0.186564\pi\)
−0.833100 + 0.553123i \(0.813436\pi\)
\(692\) −3.07221 2.56155i −0.116788 0.0973756i
\(693\) 6.24621 + 10.2462i 0.237274 + 0.389221i
\(694\) −14.3153 30.5744i −0.543403 1.16059i
\(695\) 13.8664 0.525982
\(696\) −25.0945 + 0.417142i −0.951205 + 0.0158117i
\(697\) −14.2462 −0.539614
\(698\) 8.39547 + 17.9309i 0.317773 + 0.678693i
\(699\) −16.6757 + 4.68213i −0.630731 + 0.177094i
\(700\) −1.43845 1.19935i −0.0543682 0.0453313i
\(701\) 50.4924i 1.90707i 0.301278 + 0.953536i \(0.402587\pi\)
−0.301278 + 0.953536i \(0.597413\pi\)
\(702\) 7.03857 21.8441i 0.265654 0.824451i
\(703\) 13.3405i 0.503148i
\(704\) 29.7533 + 16.8078i 1.12137 + 0.633466i
\(705\) −1.56155 + 0.438447i −0.0588115 + 0.0165129i
\(706\) −4.80776 + 2.25106i −0.180943 + 0.0847197i
\(707\) −8.54312 −0.321297
\(708\) 22.7486 + 10.1937i 0.854944 + 0.383103i
\(709\) −26.4924 −0.994944 −0.497472 0.867480i \(-0.665738\pi\)
−0.497472 + 0.867480i \(0.665738\pi\)
\(710\) 8.54312 4.00000i 0.320617 0.150117i
\(711\) 14.1617 + 23.2306i 0.531104 + 0.871217i
\(712\) 4.49242 17.0862i 0.168361 0.640334i
\(713\) 18.2462i 0.683326i
\(714\) −3.47415 + 2.99596i −0.130017 + 0.112121i
\(715\) 13.3405i 0.498907i
\(716\) 18.8114 22.5616i 0.703016 0.843165i
\(717\) −9.75379 34.7386i −0.364262 1.29734i
\(718\) 0.630683 + 1.34700i 0.0235369 + 0.0502696i
\(719\) 5.84912 0.218135 0.109068 0.994034i \(-0.465213\pi\)
0.109068 + 0.994034i \(0.465213\pi\)
\(720\) 8.95611 7.98674i 0.333775 0.297648i
\(721\) 11.6155 0.432585
\(722\) −0.452029 0.965435i −0.0168228 0.0359298i
\(723\) 5.32326 + 18.9591i 0.197974 + 0.705096i
\(724\) −5.43845 + 6.52262i −0.202118 + 0.242411i
\(725\) 5.12311i 0.190267i
\(726\) −13.4417 + 11.5916i −0.498870 + 0.430204i
\(727\) 26.5658i 0.985270i 0.870236 + 0.492635i \(0.163966\pi\)
−0.870236 + 0.492635i \(0.836034\pi\)
\(728\) 2.10341 8.00000i 0.0779576 0.296500i
\(729\) 1.93087 + 26.9309i 0.0715137 + 0.997440i
\(730\) 10.5616 4.94506i 0.390901 0.183025i
\(731\) 2.92456 0.108169
\(732\) −16.1953 7.25716i −0.598596 0.268233i
\(733\) −35.1231 −1.29730 −0.648651 0.761086i \(-0.724666\pi\)
−0.648651 + 0.761086i \(0.724666\pi\)
\(734\) −34.0248 + 15.9309i −1.25588 + 0.588019i
\(735\) −10.2107 + 2.86692i −0.376627 + 0.105748i
\(736\) 35.0540 24.9559i 1.29211 0.919885i
\(737\) 22.2462i 0.819450i
\(738\) −16.6991 + 25.1880i −0.614701 + 0.927184i
\(739\) 18.6638i 0.686559i −0.939233 0.343279i \(-0.888462\pi\)
0.939233 0.343279i \(-0.111538\pi\)
\(740\) −4.79741 4.00000i −0.176356 0.147043i
\(741\) 22.2462 6.24621i 0.817235 0.229460i
\(742\) −2.38447 5.09271i −0.0875367 0.186959i
\(743\) 12.4041 0.455062 0.227531 0.973771i \(-0.426935\pi\)
0.227531 + 0.973771i \(0.426935\pi\)
\(744\) 11.7496 0.195311i 0.430761 0.00716046i
\(745\) −14.0000 −0.512920
\(746\) 0.525853 + 1.12311i 0.0192528 + 0.0411198i
\(747\) −11.9935 + 7.31140i −0.438820 + 0.267510i
\(748\) −13.1231 10.9418i −0.479828 0.400073i
\(749\) 0.876894i 0.0320410i
\(750\) −1.59968 1.85500i −0.0584119 0.0677351i
\(751\) 15.7392i 0.574333i 0.957881 + 0.287166i \(0.0927133\pi\)
−0.957881 + 0.287166i \(0.907287\pi\)
\(752\) −0.673500 3.68466i −0.0245600 0.134366i
\(753\) −11.7538 41.8617i −0.428332 1.52553i
\(754\) −20.4924 + 9.59482i −0.746290 + 0.349423i
\(755\) −6.14441 −0.223618
\(756\) 1.22470 + 9.65426i 0.0445419 + 0.351122i
\(757\) 19.1231 0.695041 0.347521 0.937672i \(-0.387024\pi\)
0.347521 + 0.937672i \(0.387024\pi\)
\(758\) 32.1520 15.0540i 1.16781 0.546785i
\(759\) 15.2134 + 54.1833i 0.552211 + 1.96673i
\(760\) 11.6847 + 3.07221i 0.423847 + 0.111441i
\(761\) 51.2311i 1.85712i 0.371177 + 0.928562i \(0.378954\pi\)
−0.371177 + 0.928562i \(0.621046\pi\)
\(762\) −7.48990 8.68537i −0.271330 0.314638i
\(763\) 8.54312i 0.309282i
\(764\) −9.89012 + 11.8617i −0.357812 + 0.429143i
\(765\) −5.12311 + 3.12311i −0.185226 + 0.112916i
\(766\) 2.80776 + 5.99676i 0.101449 + 0.216672i
\(767\) 22.4742 0.811498
\(768\) 16.4455 + 22.3058i 0.593424 + 0.804890i
\(769\) −26.9848 −0.973098 −0.486549 0.873653i \(-0.661745\pi\)
−0.486549 + 0.873653i \(0.661745\pi\)
\(770\) 2.39871 + 5.12311i 0.0864434 + 0.184624i
\(771\) −4.15628 + 1.16699i −0.149685 + 0.0420279i
\(772\) −20.8078 + 24.9559i −0.748888 + 0.898181i
\(773\) 16.2462i 0.584336i 0.956367 + 0.292168i \(0.0943766\pi\)
−0.956367 + 0.292168i \(0.905623\pi\)
\(774\) 3.42809 5.17077i 0.123220 0.185859i
\(775\) 2.39871i 0.0861641i
\(776\) −16.4127 4.31534i −0.589183 0.154912i
\(777\) 4.87689 1.36932i 0.174958 0.0491240i
\(778\) 36.8078