Properties

Label 15.3.f.a.7.1
Level $15$
Weight $3$
Character 15.7
Analytic conductor $0.409$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 15.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.408720396540\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 15.7
Dual form 15.3.f.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.22474 - 2.22474i) q^{2} +(1.22474 - 1.22474i) q^{3} +5.89898i q^{4} +(2.67423 + 4.22474i) q^{5} -5.44949 q^{6} +(-1.44949 - 1.44949i) q^{7} +(4.22474 - 4.22474i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-2.22474 - 2.22474i) q^{2} +(1.22474 - 1.22474i) q^{3} +5.89898i q^{4} +(2.67423 + 4.22474i) q^{5} -5.44949 q^{6} +(-1.44949 - 1.44949i) q^{7} +(4.22474 - 4.22474i) q^{8} -3.00000i q^{9} +(3.44949 - 15.3485i) q^{10} -3.34847 q^{11} +(7.22474 + 7.22474i) q^{12} +(-10.4495 + 10.4495i) q^{13} +6.44949i q^{14} +(8.44949 + 1.89898i) q^{15} +4.79796 q^{16} +(-2.65153 - 2.65153i) q^{17} +(-6.67423 + 6.67423i) q^{18} -20.6969i q^{19} +(-24.9217 + 15.7753i) q^{20} -3.55051 q^{21} +(7.44949 + 7.44949i) q^{22} +(16.4495 - 16.4495i) q^{23} -10.3485i q^{24} +(-10.6969 + 22.5959i) q^{25} +46.4949 q^{26} +(-3.67423 - 3.67423i) q^{27} +(8.55051 - 8.55051i) q^{28} +0.853572i q^{29} +(-14.5732 - 23.0227i) q^{30} -18.6969 q^{31} +(-27.5732 - 27.5732i) q^{32} +(-4.10102 + 4.10102i) q^{33} +11.7980i q^{34} +(2.24745 - 10.0000i) q^{35} +17.6969 q^{36} +(38.0454 + 38.0454i) q^{37} +(-46.0454 + 46.0454i) q^{38} +25.5959i q^{39} +(29.1464 + 6.55051i) q^{40} -28.6969 q^{41} +(7.89898 + 7.89898i) q^{42} +(22.4949 - 22.4949i) q^{43} -19.7526i q^{44} +(12.6742 - 8.02270i) q^{45} -73.1918 q^{46} +(19.7526 + 19.7526i) q^{47} +(5.87628 - 5.87628i) q^{48} -44.7980i q^{49} +(74.0681 - 26.4722i) q^{50} -6.49490 q^{51} +(-61.6413 - 61.6413i) q^{52} +(28.6969 - 28.6969i) q^{53} +16.3485i q^{54} +(-8.95459 - 14.1464i) q^{55} -12.2474 q^{56} +(-25.3485 - 25.3485i) q^{57} +(1.89898 - 1.89898i) q^{58} +111.934i q^{59} +(-11.2020 + 49.8434i) q^{60} +94.0908 q^{61} +(41.5959 + 41.5959i) q^{62} +(-4.34847 + 4.34847i) q^{63} +103.495i q^{64} +(-72.0908 - 16.2020i) q^{65} +18.2474 q^{66} +(-54.8990 - 54.8990i) q^{67} +(15.6413 - 15.6413i) q^{68} -40.2929i q^{69} +(-27.2474 + 17.2474i) q^{70} -68.0000 q^{71} +(-12.6742 - 12.6742i) q^{72} +(-39.7878 + 39.7878i) q^{73} -169.283i q^{74} +(14.5732 + 40.7753i) q^{75} +122.091 q^{76} +(4.85357 + 4.85357i) q^{77} +(56.9444 - 56.9444i) q^{78} +24.4949i q^{79} +(12.8309 + 20.2702i) q^{80} -9.00000 q^{81} +(63.8434 + 63.8434i) q^{82} +(-21.1464 + 21.1464i) q^{83} -20.9444i q^{84} +(4.11123 - 18.2929i) q^{85} -100.091 q^{86} +(1.04541 + 1.04541i) q^{87} +(-14.1464 + 14.1464i) q^{88} -94.1816i q^{89} +(-46.0454 - 10.3485i) q^{90} +30.2929 q^{91} +(97.0352 + 97.0352i) q^{92} +(-22.8990 + 22.8990i) q^{93} -87.8888i q^{94} +(87.4393 - 55.3485i) q^{95} -67.5403 q^{96} +(14.5959 + 14.5959i) q^{97} +(-99.6640 + 99.6640i) q^{98} +10.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 4q^{5} - 12q^{6} + 4q^{7} + 12q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 4q^{5} - 12q^{6} + 4q^{7} + 12q^{8} + 4q^{10} + 16q^{11} + 24q^{12} - 32q^{13} + 24q^{15} - 20q^{16} - 40q^{17} - 12q^{18} - 36q^{20} - 24q^{21} + 20q^{22} + 56q^{23} + 16q^{25} + 88q^{26} + 44q^{28} - 24q^{30} - 16q^{31} - 76q^{32} - 36q^{33} - 40q^{35} + 12q^{36} + 64q^{37} - 96q^{38} + 48q^{40} - 56q^{41} + 12q^{42} - 8q^{43} + 36q^{45} - 136q^{46} + 128q^{47} + 48q^{48} + 164q^{50} + 72q^{51} - 80q^{52} + 56q^{53} - 124q^{55} - 72q^{57} - 12q^{58} - 84q^{60} + 200q^{61} + 88q^{62} + 12q^{63} - 112q^{65} + 24q^{66} - 200q^{67} - 104q^{68} - 60q^{70} - 272q^{71} - 36q^{72} + 76q^{73} + 24q^{75} + 312q^{76} + 88q^{77} + 120q^{78} + 164q^{80} - 36q^{81} + 128q^{82} - 16q^{83} + 232q^{85} - 224q^{86} - 84q^{87} + 12q^{88} - 96q^{90} - 16q^{91} + 104q^{92} - 72q^{93} + 144q^{95} - 84q^{96} - 20q^{97} - 188q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22474 2.22474i −1.11237 1.11237i −0.992829 0.119543i \(-0.961857\pi\)
−0.119543 0.992829i \(-0.538143\pi\)
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 5.89898i 1.47474i
\(5\) 2.67423 + 4.22474i 0.534847 + 0.844949i
\(6\) −5.44949 −0.908248
\(7\) −1.44949 1.44949i −0.207070 0.207070i 0.595951 0.803021i \(-0.296775\pi\)
−0.803021 + 0.595951i \(0.796775\pi\)
\(8\) 4.22474 4.22474i 0.528093 0.528093i
\(9\) 3.00000i 0.333333i
\(10\) 3.44949 15.3485i 0.344949 1.53485i
\(11\) −3.34847 −0.304406 −0.152203 0.988349i \(-0.548637\pi\)
−0.152203 + 0.988349i \(0.548637\pi\)
\(12\) 7.22474 + 7.22474i 0.602062 + 0.602062i
\(13\) −10.4495 + 10.4495i −0.803807 + 0.803807i −0.983688 0.179881i \(-0.942429\pi\)
0.179881 + 0.983688i \(0.442429\pi\)
\(14\) 6.44949i 0.460678i
\(15\) 8.44949 + 1.89898i 0.563299 + 0.126599i
\(16\) 4.79796 0.299872
\(17\) −2.65153 2.65153i −0.155972 0.155972i 0.624807 0.780779i \(-0.285178\pi\)
−0.780779 + 0.624807i \(0.785178\pi\)
\(18\) −6.67423 + 6.67423i −0.370791 + 0.370791i
\(19\) 20.6969i 1.08931i −0.838659 0.544656i \(-0.816660\pi\)
0.838659 0.544656i \(-0.183340\pi\)
\(20\) −24.9217 + 15.7753i −1.24608 + 0.788763i
\(21\) −3.55051 −0.169072
\(22\) 7.44949 + 7.44949i 0.338613 + 0.338613i
\(23\) 16.4495 16.4495i 0.715195 0.715195i −0.252422 0.967617i \(-0.581227\pi\)
0.967617 + 0.252422i \(0.0812271\pi\)
\(24\) 10.3485i 0.431186i
\(25\) −10.6969 + 22.5959i −0.427878 + 0.903837i
\(26\) 46.4949 1.78827
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 8.55051 8.55051i 0.305375 0.305375i
\(29\) 0.853572i 0.0294335i 0.999892 + 0.0147168i \(0.00468466\pi\)
−0.999892 + 0.0147168i \(0.995315\pi\)
\(30\) −14.5732 23.0227i −0.485774 0.767423i
\(31\) −18.6969 −0.603127 −0.301564 0.953446i \(-0.597509\pi\)
−0.301564 + 0.953446i \(0.597509\pi\)
\(32\) −27.5732 27.5732i −0.861663 0.861663i
\(33\) −4.10102 + 4.10102i −0.124273 + 0.124273i
\(34\) 11.7980i 0.346999i
\(35\) 2.24745 10.0000i 0.0642128 0.285714i
\(36\) 17.6969 0.491582
\(37\) 38.0454 + 38.0454i 1.02825 + 1.02825i 0.999589 + 0.0286652i \(0.00912566\pi\)
0.0286652 + 0.999589i \(0.490874\pi\)
\(38\) −46.0454 + 46.0454i −1.21172 + 1.21172i
\(39\) 25.5959i 0.656306i
\(40\) 29.1464 + 6.55051i 0.728661 + 0.163763i
\(41\) −28.6969 −0.699925 −0.349963 0.936764i \(-0.613806\pi\)
−0.349963 + 0.936764i \(0.613806\pi\)
\(42\) 7.89898 + 7.89898i 0.188071 + 0.188071i
\(43\) 22.4949 22.4949i 0.523137 0.523137i −0.395380 0.918517i \(-0.629387\pi\)
0.918517 + 0.395380i \(0.129387\pi\)
\(44\) 19.7526i 0.448922i
\(45\) 12.6742 8.02270i 0.281650 0.178282i
\(46\) −73.1918 −1.59113
\(47\) 19.7526 + 19.7526i 0.420267 + 0.420267i 0.885296 0.465029i \(-0.153956\pi\)
−0.465029 + 0.885296i \(0.653956\pi\)
\(48\) 5.87628 5.87628i 0.122422 0.122422i
\(49\) 44.7980i 0.914244i
\(50\) 74.0681 26.4722i 1.48136 0.529444i
\(51\) −6.49490 −0.127351
\(52\) −61.6413 61.6413i −1.18541 1.18541i
\(53\) 28.6969 28.6969i 0.541452 0.541452i −0.382503 0.923954i \(-0.624938\pi\)
0.923954 + 0.382503i \(0.124938\pi\)
\(54\) 16.3485i 0.302749i
\(55\) −8.95459 14.1464i −0.162811 0.257208i
\(56\) −12.2474 −0.218704
\(57\) −25.3485 25.3485i −0.444710 0.444710i
\(58\) 1.89898 1.89898i 0.0327410 0.0327410i
\(59\) 111.934i 1.89719i 0.316493 + 0.948595i \(0.397495\pi\)
−0.316493 + 0.948595i \(0.602505\pi\)
\(60\) −11.2020 + 49.8434i −0.186701 + 0.830723i
\(61\) 94.0908 1.54247 0.771236 0.636549i \(-0.219639\pi\)
0.771236 + 0.636549i \(0.219639\pi\)
\(62\) 41.5959 + 41.5959i 0.670902 + 0.670902i
\(63\) −4.34847 + 4.34847i −0.0690233 + 0.0690233i
\(64\) 103.495i 1.61711i
\(65\) −72.0908 16.2020i −1.10909 0.249262i
\(66\) 18.2474 0.276476
\(67\) −54.8990 54.8990i −0.819388 0.819388i 0.166631 0.986019i \(-0.446711\pi\)
−0.986019 + 0.166631i \(0.946711\pi\)
\(68\) 15.6413 15.6413i 0.230019 0.230019i
\(69\) 40.2929i 0.583954i
\(70\) −27.2474 + 17.2474i −0.389249 + 0.246392i
\(71\) −68.0000 −0.957746 −0.478873 0.877884i \(-0.658955\pi\)
−0.478873 + 0.877884i \(0.658955\pi\)
\(72\) −12.6742 12.6742i −0.176031 0.176031i
\(73\) −39.7878 + 39.7878i −0.545038 + 0.545038i −0.925001 0.379964i \(-0.875936\pi\)
0.379964 + 0.925001i \(0.375936\pi\)
\(74\) 169.283i 2.28760i
\(75\) 14.5732 + 40.7753i 0.194310 + 0.543670i
\(76\) 122.091 1.60646
\(77\) 4.85357 + 4.85357i 0.0630334 + 0.0630334i
\(78\) 56.9444 56.9444i 0.730056 0.730056i
\(79\) 24.4949i 0.310062i 0.987910 + 0.155031i \(0.0495477\pi\)
−0.987910 + 0.155031i \(0.950452\pi\)
\(80\) 12.8309 + 20.2702i 0.160386 + 0.253377i
\(81\) −9.00000 −0.111111
\(82\) 63.8434 + 63.8434i 0.778578 + 0.778578i
\(83\) −21.1464 + 21.1464i −0.254776 + 0.254776i −0.822926 0.568149i \(-0.807660\pi\)
0.568149 + 0.822926i \(0.307660\pi\)
\(84\) 20.9444i 0.249338i
\(85\) 4.11123 18.2929i 0.0483674 0.215210i
\(86\) −100.091 −1.16385
\(87\) 1.04541 + 1.04541i 0.0120162 + 0.0120162i
\(88\) −14.1464 + 14.1464i −0.160755 + 0.160755i
\(89\) 94.1816i 1.05822i −0.848553 0.529110i \(-0.822526\pi\)
0.848553 0.529110i \(-0.177474\pi\)
\(90\) −46.0454 10.3485i −0.511616 0.114983i
\(91\) 30.2929 0.332889
\(92\) 97.0352 + 97.0352i 1.05473 + 1.05473i
\(93\) −22.8990 + 22.8990i −0.246226 + 0.246226i
\(94\) 87.8888i 0.934987i
\(95\) 87.4393 55.3485i 0.920414 0.582615i
\(96\) −67.5403 −0.703545
\(97\) 14.5959 + 14.5959i 0.150473 + 0.150473i 0.778329 0.627856i \(-0.216067\pi\)
−0.627856 + 0.778329i \(0.716067\pi\)
\(98\) −99.6640 + 99.6640i −1.01698 + 1.01698i
\(99\) 10.0454i 0.101469i
\(100\) −133.293 63.1010i −1.33293 0.631010i
\(101\) 173.621 1.71902 0.859509 0.511120i \(-0.170769\pi\)
0.859509 + 0.511120i \(0.170769\pi\)
\(102\) 14.4495 + 14.4495i 0.141662 + 0.141662i
\(103\) −64.7526 + 64.7526i −0.628666 + 0.628666i −0.947732 0.319067i \(-0.896631\pi\)
0.319067 + 0.947732i \(0.396631\pi\)
\(104\) 88.2929i 0.848970i
\(105\) −9.49490 15.0000i −0.0904276 0.142857i
\(106\) −127.687 −1.20459
\(107\) −4.74235 4.74235i −0.0443210 0.0443210i 0.684599 0.728920i \(-0.259977\pi\)
−0.728920 + 0.684599i \(0.759977\pi\)
\(108\) 21.6742 21.6742i 0.200687 0.200687i
\(109\) 39.3031i 0.360579i 0.983614 + 0.180289i \(0.0577034\pi\)
−0.983614 + 0.180289i \(0.942297\pi\)
\(110\) −11.5505 + 51.3939i −0.105005 + 0.467217i
\(111\) 93.1918 0.839566
\(112\) −6.95459 6.95459i −0.0620946 0.0620946i
\(113\) 14.3587 14.3587i 0.127068 0.127068i −0.640713 0.767781i \(-0.721361\pi\)
0.767781 + 0.640713i \(0.221361\pi\)
\(114\) 112.788i 0.989366i
\(115\) 113.485 + 25.5051i 0.986823 + 0.221784i
\(116\) −5.03520 −0.0434069
\(117\) 31.3485 + 31.3485i 0.267936 + 0.267936i
\(118\) 249.025 249.025i 2.11038 2.11038i
\(119\) 7.68673i 0.0645944i
\(120\) 43.7196 27.6742i 0.364330 0.230619i
\(121\) −109.788 −0.907337
\(122\) −209.328 209.328i −1.71580 1.71580i
\(123\) −35.1464 + 35.1464i −0.285743 + 0.285743i
\(124\) 110.293i 0.889459i
\(125\) −124.068 + 15.2350i −0.992545 + 0.121880i
\(126\) 19.3485 0.153559
\(127\) −114.621 114.621i −0.902527 0.902527i 0.0931273 0.995654i \(-0.470314\pi\)
−0.995654 + 0.0931273i \(0.970314\pi\)
\(128\) 119.957 119.957i 0.937163 0.937163i
\(129\) 55.1010i 0.427140i
\(130\) 124.338 + 196.429i 0.956448 + 1.51099i
\(131\) −26.1362 −0.199513 −0.0997566 0.995012i \(-0.531806\pi\)
−0.0997566 + 0.995012i \(0.531806\pi\)
\(132\) −24.1918 24.1918i −0.183271 0.183271i
\(133\) −30.0000 + 30.0000i −0.225564 + 0.225564i
\(134\) 244.272i 1.82293i
\(135\) 5.69694 25.3485i 0.0421995 0.187766i
\(136\) −22.4041 −0.164736
\(137\) 14.6311 + 14.6311i 0.106796 + 0.106796i 0.758486 0.651689i \(-0.225939\pi\)
−0.651689 + 0.758486i \(0.725939\pi\)
\(138\) −89.6413 + 89.6413i −0.649575 + 0.649575i
\(139\) 83.1714i 0.598356i 0.954197 + 0.299178i \(0.0967124\pi\)
−0.954197 + 0.299178i \(0.903288\pi\)
\(140\) 58.9898 + 13.2577i 0.421356 + 0.0946975i
\(141\) 48.3837 0.343147
\(142\) 151.283 + 151.283i 1.06537 + 1.06537i
\(143\) 34.9898 34.9898i 0.244684 0.244684i
\(144\) 14.3939i 0.0999575i
\(145\) −3.60612 + 2.28265i −0.0248698 + 0.0157424i
\(146\) 177.035 1.21257
\(147\) −54.8661 54.8661i −0.373239 0.373239i
\(148\) −224.429 + 224.429i −1.51641 + 1.51641i
\(149\) 119.146i 0.799640i 0.916594 + 0.399820i \(0.130927\pi\)
−0.916594 + 0.399820i \(0.869073\pi\)
\(150\) 58.2929 123.136i 0.388619 0.820908i
\(151\) −144.969 −0.960062 −0.480031 0.877251i \(-0.659375\pi\)
−0.480031 + 0.877251i \(0.659375\pi\)
\(152\) −87.4393 87.4393i −0.575258 0.575258i
\(153\) −7.95459 + 7.95459i −0.0519908 + 0.0519908i
\(154\) 21.5959i 0.140233i
\(155\) −50.0000 78.9898i −0.322581 0.509612i
\(156\) −150.990 −0.967883
\(157\) 51.1464 + 51.1464i 0.325773 + 0.325773i 0.850977 0.525203i \(-0.176011\pi\)
−0.525203 + 0.850977i \(0.676011\pi\)
\(158\) 54.4949 54.4949i 0.344904 0.344904i
\(159\) 70.2929i 0.442093i
\(160\) 42.7526 190.227i 0.267203 1.18892i
\(161\) −47.6867 −0.296191
\(162\) 20.0227 + 20.0227i 0.123597 + 0.123597i
\(163\) 189.394 189.394i 1.16193 1.16193i 0.177872 0.984054i \(-0.443079\pi\)
0.984054 0.177872i \(-0.0569213\pi\)
\(164\) 169.283i 1.03221i
\(165\) −28.2929 6.35867i −0.171472 0.0385374i
\(166\) 94.0908 0.566812
\(167\) 97.0352 + 97.0352i 0.581049 + 0.581049i 0.935192 0.354142i \(-0.115227\pi\)
−0.354142 + 0.935192i \(0.615227\pi\)
\(168\) −15.0000 + 15.0000i −0.0892857 + 0.0892857i
\(169\) 49.3837i 0.292211i
\(170\) −49.8434 + 31.5505i −0.293196 + 0.185591i
\(171\) −62.0908 −0.363104
\(172\) 132.697 + 132.697i 0.771494 + 0.771494i
\(173\) −34.6311 + 34.6311i −0.200180 + 0.200180i −0.800077 0.599897i \(-0.795208\pi\)
0.599897 + 0.800077i \(0.295208\pi\)
\(174\) 4.65153i 0.0267329i
\(175\) 48.2577 17.2474i 0.275758 0.0985568i
\(176\) −16.0658 −0.0912831
\(177\) 137.091 + 137.091i 0.774524 + 0.774524i
\(178\) −209.530 + 209.530i −1.17714 + 1.17714i
\(179\) 183.712i 1.02632i −0.858292 0.513161i \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 47.3258 + 74.7650i 0.262921 + 0.415361i
\(181\) −21.7276 −0.120042 −0.0600209 0.998197i \(-0.519117\pi\)
−0.0600209 + 0.998197i \(0.519117\pi\)
\(182\) −67.3939 67.3939i −0.370296 0.370296i
\(183\) 115.237 115.237i 0.629712 0.629712i
\(184\) 138.990i 0.755379i
\(185\) −58.9898 + 262.474i −0.318864 + 1.41878i
\(186\) 101.889 0.547789
\(187\) 8.87857 + 8.87857i 0.0474790 + 0.0474790i
\(188\) −116.520 + 116.520i −0.619787 + 0.619787i
\(189\) 10.6515i 0.0563573i
\(190\) −317.666 71.3939i −1.67193 0.375757i
\(191\) −40.0908 −0.209900 −0.104950 0.994478i \(-0.533468\pi\)
−0.104950 + 0.994478i \(0.533468\pi\)
\(192\) 126.755 + 126.755i 0.660181 + 0.660181i
\(193\) 77.5653 77.5653i 0.401893 0.401893i −0.477007 0.878900i \(-0.658278\pi\)
0.878900 + 0.477007i \(0.158278\pi\)
\(194\) 64.9444i 0.334765i
\(195\) −108.136 + 68.4495i −0.554545 + 0.351023i
\(196\) 264.262 1.34828
\(197\) −67.3031 67.3031i −0.341640 0.341640i 0.515344 0.856984i \(-0.327664\pi\)
−0.856984 + 0.515344i \(0.827664\pi\)
\(198\) 22.3485 22.3485i 0.112871 0.112871i
\(199\) 251.394i 1.26329i 0.775259 + 0.631643i \(0.217619\pi\)
−0.775259 + 0.631643i \(0.782381\pi\)
\(200\) 50.2702 + 140.654i 0.251351 + 0.703269i
\(201\) −134.474 −0.669027
\(202\) −386.262 386.262i −1.91219 1.91219i
\(203\) 1.23724 1.23724i 0.00609480 0.00609480i
\(204\) 38.3133i 0.187810i
\(205\) −76.7423 121.237i −0.374353 0.591401i
\(206\) 288.116 1.39862
\(207\) −49.3485 49.3485i −0.238398 0.238398i
\(208\) −50.1362 + 50.1362i −0.241040 + 0.241040i
\(209\) 69.3031i 0.331594i
\(210\) −12.2474 + 54.4949i −0.0583212 + 0.259500i
\(211\) 264.788 1.25492 0.627459 0.778649i \(-0.284095\pi\)
0.627459 + 0.778649i \(0.284095\pi\)
\(212\) 169.283 + 169.283i 0.798503 + 0.798503i
\(213\) −83.2827 + 83.2827i −0.390998 + 0.390998i
\(214\) 21.1010i 0.0986029i
\(215\) 155.192 + 34.8786i 0.721822 + 0.162226i
\(216\) −31.0454 −0.143729
\(217\) 27.1010 + 27.1010i 0.124889 + 0.124889i
\(218\) 87.4393 87.4393i 0.401098 0.401098i
\(219\) 97.4597i 0.445021i
\(220\) 83.4495 52.8230i 0.379316 0.240104i
\(221\) 55.4143 0.250743
\(222\) −207.328 207.328i −0.933910 0.933910i
\(223\) −33.4291 + 33.4291i −0.149906 + 0.149906i −0.778076 0.628170i \(-0.783804\pi\)
0.628170 + 0.778076i \(0.283804\pi\)
\(224\) 79.9342i 0.356849i
\(225\) 67.7878 + 32.0908i 0.301279 + 0.142626i
\(226\) −63.8888 −0.282694
\(227\) −21.1714 21.1714i −0.0932662 0.0932662i 0.658934 0.752200i \(-0.271008\pi\)
−0.752200 + 0.658934i \(0.771008\pi\)
\(228\) 149.530 149.530i 0.655834 0.655834i
\(229\) 243.798i 1.06462i −0.846550 0.532310i \(-0.821324\pi\)
0.846550 0.532310i \(-0.178676\pi\)
\(230\) −195.732 309.217i −0.851009 1.34442i
\(231\) 11.8888 0.0514666
\(232\) 3.60612 + 3.60612i 0.0155436 + 0.0155436i
\(233\) 161.712 161.712i 0.694042 0.694042i −0.269077 0.963119i \(-0.586719\pi\)
0.963119 + 0.269077i \(0.0867186\pi\)
\(234\) 139.485i 0.596088i
\(235\) −30.6265 + 136.272i −0.130326 + 0.579883i
\(236\) −660.297 −2.79787
\(237\) 30.0000 + 30.0000i 0.126582 + 0.126582i
\(238\) 17.1010 17.1010i 0.0718530 0.0718530i
\(239\) 326.202i 1.36486i −0.730950 0.682431i \(-0.760923\pi\)
0.730950 0.682431i \(-0.239077\pi\)
\(240\) 40.5403 + 9.11123i 0.168918 + 0.0379634i
\(241\) −133.576 −0.554255 −0.277128 0.960833i \(-0.589382\pi\)
−0.277128 + 0.960833i \(0.589382\pi\)
\(242\) 244.250 + 244.250i 1.00930 + 1.00930i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 555.040i 2.27475i
\(245\) 189.260 119.800i 0.772490 0.488981i
\(246\) 156.384 0.635706
\(247\) 216.272 + 216.272i 0.875597 + 0.875597i
\(248\) −78.9898 + 78.9898i −0.318507 + 0.318507i
\(249\) 51.7980i 0.208024i
\(250\) 309.914 + 242.126i 1.23966 + 0.968504i
\(251\) −404.742 −1.61252 −0.806260 0.591562i \(-0.798512\pi\)
−0.806260 + 0.591562i \(0.798512\pi\)
\(252\) −25.6515 25.6515i −0.101792 0.101792i
\(253\) −55.0806 + 55.0806i −0.217710 + 0.217710i
\(254\) 510.005i 2.00789i
\(255\) −17.3689 27.4393i −0.0681133 0.107605i
\(256\) −119.767 −0.467841
\(257\) −89.2372 89.2372i −0.347227 0.347227i 0.511849 0.859076i \(-0.328961\pi\)
−0.859076 + 0.511849i \(0.828961\pi\)
\(258\) −122.586 + 122.586i −0.475138 + 0.475138i
\(259\) 110.293i 0.425841i
\(260\) 95.5755 425.262i 0.367598 1.63562i
\(261\) 2.56072 0.00981117
\(262\) 58.1464 + 58.1464i 0.221933 + 0.221933i
\(263\) −341.843 + 341.843i −1.29978 + 1.29978i −0.371253 + 0.928532i \(0.621072\pi\)
−0.928532 + 0.371253i \(0.878928\pi\)
\(264\) 34.6515i 0.131256i
\(265\) 197.980 + 44.4949i 0.747093 + 0.167905i
\(266\) 133.485 0.501822
\(267\) −115.348 115.348i −0.432017 0.432017i
\(268\) 323.848 323.848i 1.20839 1.20839i
\(269\) 3.50052i 0.0130131i −0.999979 0.00650653i \(-0.997929\pi\)
0.999979 0.00650653i \(-0.00207111\pi\)
\(270\) −69.0681 + 43.7196i −0.255808 + 0.161925i
\(271\) −103.576 −0.382197 −0.191099 0.981571i \(-0.561205\pi\)
−0.191099 + 0.981571i \(0.561205\pi\)
\(272\) −12.7219 12.7219i −0.0467718 0.0467718i
\(273\) 37.1010 37.1010i 0.135901 0.135901i
\(274\) 65.1010i 0.237595i
\(275\) 35.8184 75.6617i 0.130249 0.275134i
\(276\) 237.687 0.861184
\(277\) −285.510 285.510i −1.03072 1.03072i −0.999513 0.0312080i \(-0.990065\pi\)
−0.0312080 0.999513i \(-0.509935\pi\)
\(278\) 185.035 185.035i 0.665594 0.665594i
\(279\) 56.0908i 0.201042i
\(280\) −32.7526 51.7423i −0.116973 0.184794i
\(281\) 372.697 1.32632 0.663162 0.748476i \(-0.269214\pi\)
0.663162 + 0.748476i \(0.269214\pi\)
\(282\) −107.641 107.641i −0.381707 0.381707i
\(283\) −77.1918 + 77.1918i −0.272763 + 0.272763i −0.830211 0.557449i \(-0.811780\pi\)
0.557449 + 0.830211i \(0.311780\pi\)
\(284\) 401.131i 1.41243i
\(285\) 39.3031 174.879i 0.137905 0.613609i
\(286\) −155.687 −0.544359
\(287\) 41.5959 + 41.5959i 0.144934 + 0.144934i
\(288\) −82.7196 + 82.7196i −0.287221 + 0.287221i
\(289\) 274.939i 0.951345i
\(290\) 13.1010 + 2.94439i 0.0451759 + 0.0101531i
\(291\) 35.7526 0.122861
\(292\) −234.707 234.707i −0.803792 0.803792i
\(293\) −236.565 + 236.565i −0.807390 + 0.807390i −0.984238 0.176848i \(-0.943410\pi\)
0.176848 + 0.984238i \(0.443410\pi\)
\(294\) 244.126i 0.830361i
\(295\) −472.893 + 299.338i −1.60303 + 1.01471i
\(296\) 321.464 1.08603
\(297\) 12.3031 + 12.3031i 0.0414244 + 0.0414244i
\(298\) 265.070 265.070i 0.889498 0.889498i
\(299\) 343.778i 1.14976i
\(300\) −240.532 + 85.9671i −0.801775 + 0.286557i
\(301\) −65.2122 −0.216652
\(302\) 322.520 + 322.520i 1.06795 + 1.06795i
\(303\) 212.641 212.641i 0.701787 0.701787i
\(304\) 99.3031i 0.326655i
\(305\) 251.621 + 397.510i 0.824987 + 1.30331i
\(306\) 35.3939 0.115666
\(307\) 168.969 + 168.969i 0.550389 + 0.550389i 0.926553 0.376164i \(-0.122757\pi\)
−0.376164 + 0.926553i \(0.622757\pi\)
\(308\) −28.6311 + 28.6311i −0.0929582 + 0.0929582i
\(309\) 158.611i 0.513303i
\(310\) −64.4949 + 286.969i −0.208048 + 0.925708i
\(311\) 354.302 1.13923 0.569617 0.821910i \(-0.307091\pi\)
0.569617 + 0.821910i \(0.307091\pi\)
\(312\) 108.136 + 108.136i 0.346590 + 0.346590i
\(313\) 152.373 152.373i 0.486816 0.486816i −0.420484 0.907300i \(-0.638140\pi\)
0.907300 + 0.420484i \(0.138140\pi\)
\(314\) 227.576i 0.724763i
\(315\) −30.0000 6.74235i −0.0952381 0.0214043i
\(316\) −144.495 −0.457262
\(317\) −427.217 427.217i −1.34769 1.34769i −0.888168 0.459519i \(-0.848022\pi\)
−0.459519 0.888168i \(-0.651978\pi\)
\(318\) −156.384 + 156.384i −0.491773 + 0.491773i
\(319\) 2.85816i 0.00895975i
\(320\) −437.240 + 276.770i −1.36637 + 0.864905i
\(321\) −11.6163 −0.0361879
\(322\) 106.091 + 106.091i 0.329475 + 0.329475i
\(323\) −54.8786 + 54.8786i −0.169903 + 0.169903i
\(324\) 53.0908i 0.163861i
\(325\) −124.338 347.893i −0.382579 1.07044i
\(326\) −842.706 −2.58499
\(327\) 48.1362 + 48.1362i 0.147206 + 0.147206i
\(328\) −121.237 + 121.237i −0.369626 + 0.369626i
\(329\) 57.2622i 0.174049i
\(330\) 48.7980 + 77.0908i 0.147873 + 0.233609i
\(331\) 489.423 1.47862 0.739310 0.673365i \(-0.235152\pi\)
0.739310 + 0.673365i \(0.235152\pi\)
\(332\) −124.742 124.742i −0.375730 0.375730i
\(333\) 114.136 114.136i 0.342751 0.342751i
\(334\) 431.757i 1.29269i
\(335\) 85.1214 378.747i 0.254094 1.13059i
\(336\) −17.0352 −0.0507000
\(337\) 292.192 + 292.192i 0.867038 + 0.867038i 0.992143 0.125105i \(-0.0399269\pi\)
−0.125105 + 0.992143i \(0.539927\pi\)
\(338\) −109.866 + 109.866i −0.325048 + 0.325048i
\(339\) 35.1714i 0.103751i
\(340\) 107.909 + 24.2520i 0.317380 + 0.0713295i
\(341\) 62.6061 0.183596
\(342\) 138.136 + 138.136i 0.403907 + 0.403907i
\(343\) −135.959 + 135.959i −0.396382 + 0.396382i
\(344\) 190.070i 0.552530i
\(345\) 170.227 107.753i 0.493412 0.312326i
\(346\) 154.091 0.445349
\(347\) 320.050 + 320.050i 0.922334 + 0.922334i 0.997194 0.0748598i \(-0.0238509\pi\)
−0.0748598 + 0.997194i \(0.523851\pi\)
\(348\) −6.16684 + 6.16684i −0.0177208 + 0.0177208i
\(349\) 574.009i 1.64473i 0.568964 + 0.822363i \(0.307345\pi\)
−0.568964 + 0.822363i \(0.692655\pi\)
\(350\) −145.732 68.9898i −0.416378 0.197114i
\(351\) 76.7878 0.218769
\(352\) 92.3281 + 92.3281i 0.262296 + 0.262296i
\(353\) 266.520 266.520i 0.755014 0.755014i −0.220396 0.975410i \(-0.570735\pi\)
0.975410 + 0.220396i \(0.0707351\pi\)
\(354\) 609.984i 1.72312i
\(355\) −181.848 287.283i −0.512248 0.809247i
\(356\) 555.576 1.56061
\(357\) 9.41429 + 9.41429i 0.0263706 + 0.0263706i
\(358\) −408.712 + 408.712i −1.14165 + 1.14165i
\(359\) 216.272i 0.602430i −0.953556 0.301215i \(-0.902608\pi\)
0.953556 0.301215i \(-0.0973922\pi\)
\(360\) 19.6515 87.4393i 0.0545876 0.242887i
\(361\) −67.3633 −0.186602
\(362\) 48.3383 + 48.3383i 0.133531 + 0.133531i
\(363\) −134.462 + 134.462i −0.370419 + 0.370419i
\(364\) 178.697i 0.490926i
\(365\) −274.495 61.6913i −0.752041 0.169017i
\(366\) −512.747 −1.40095
\(367\) −240.510 240.510i −0.655340 0.655340i 0.298934 0.954274i \(-0.403369\pi\)
−0.954274 + 0.298934i \(0.903369\pi\)
\(368\) 78.9240 78.9240i 0.214467 0.214467i
\(369\) 86.0908i 0.233308i
\(370\) 715.176 452.702i 1.93291 1.22352i
\(371\) −83.1918 −0.224237
\(372\) −135.081 135.081i −0.363120 0.363120i
\(373\) −330.207 + 330.207i −0.885272 + 0.885272i −0.994065 0.108792i \(-0.965302\pi\)
0.108792 + 0.994065i \(0.465302\pi\)
\(374\) 39.5051i 0.105629i
\(375\) −133.293 + 170.611i −0.355448 + 0.454962i
\(376\) 166.899 0.443880
\(377\) −8.91939 8.91939i −0.0236589 0.0236589i
\(378\) 23.6969 23.6969i 0.0626903 0.0626903i
\(379\) 210.000i 0.554090i −0.960857 0.277045i \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) 326.499 + 515.803i 0.859209 + 1.35738i
\(381\) −280.763 −0.736910
\(382\) 89.1918 + 89.1918i 0.233486 + 0.233486i
\(383\) 170.631 170.631i 0.445512 0.445512i −0.448347 0.893859i \(-0.647987\pi\)
0.893859 + 0.448347i \(0.147987\pi\)
\(384\) 293.833i 0.765191i
\(385\) −7.52551 + 33.4847i −0.0195468 + 0.0869732i
\(386\) −345.126 −0.894109
\(387\) −67.4847 67.4847i −0.174379 0.174379i
\(388\) −86.1010 + 86.1010i −0.221910 + 0.221910i
\(389\) 547.337i 1.40704i 0.710677 + 0.703518i \(0.248389\pi\)
−0.710677 + 0.703518i \(0.751611\pi\)
\(390\) 392.858 + 88.2929i 1.00733 + 0.226392i
\(391\) −87.2327 −0.223101
\(392\) −189.260 189.260i −0.482806 0.482806i
\(393\) −32.0102 + 32.0102i −0.0814509 + 0.0814509i
\(394\) 299.464i 0.760062i
\(395\) −103.485 + 65.5051i −0.261987 + 0.165836i
\(396\) −59.2577 −0.149641
\(397\) 45.2577 + 45.2577i 0.113999 + 0.113999i 0.761805 0.647806i \(-0.224313\pi\)
−0.647806 + 0.761805i \(0.724313\pi\)
\(398\) 559.287 559.287i 1.40524 1.40524i
\(399\) 73.4847i 0.184172i
\(400\) −51.3235 + 108.414i −0.128309 + 0.271036i
\(401\) −520.302 −1.29751 −0.648756 0.760997i \(-0.724710\pi\)
−0.648756 + 0.760997i \(0.724710\pi\)
\(402\) 299.171 + 299.171i 0.744208 + 0.744208i
\(403\) 195.373 195.373i 0.484798 0.484798i
\(404\) 1024.19i 2.53511i
\(405\) −24.0681 38.0227i −0.0594274 0.0938832i
\(406\) −5.50510 −0.0135594
\(407\) −127.394 127.394i −0.313007 0.313007i
\(408\) −27.4393 + 27.4393i −0.0672531 + 0.0672531i
\(409\) 347.110i 0.848680i 0.905503 + 0.424340i \(0.139494\pi\)
−0.905503 + 0.424340i \(0.860506\pi\)
\(410\) −98.9898 + 440.454i −0.241439 + 1.07428i
\(411\) 35.8388 0.0871990
\(412\) −381.974 381.974i −0.927121 0.927121i
\(413\) 162.247 162.247i 0.392851 0.392851i
\(414\) 219.576i 0.530376i
\(415\) −145.889 32.7878i −0.351539 0.0790066i
\(416\) 576.252 1.38522
\(417\) 101.864 + 101.864i 0.244278 + 0.244278i
\(418\) 154.182 154.182i 0.368856 0.368856i
\(419\) 583.398i 1.39236i −0.717868 0.696180i \(-0.754882\pi\)
0.717868 0.696180i \(-0.245118\pi\)
\(420\) 88.4847 56.0102i 0.210678 0.133358i
\(421\) 213.151 0.506297 0.253148 0.967427i \(-0.418534\pi\)
0.253148 + 0.967427i \(0.418534\pi\)
\(422\) −589.085 589.085i −1.39594 1.39594i
\(423\) 59.2577 59.2577i 0.140089 0.140089i
\(424\) 242.474i 0.571874i
\(425\) 88.2770 31.5505i 0.207711 0.0742365i
\(426\) 370.565 0.869872
\(427\) −136.384 136.384i −0.319400 0.319400i
\(428\) 27.9750 27.9750i 0.0653622 0.0653622i
\(429\) 85.7071i 0.199784i
\(430\) −267.666 422.858i −0.622480 0.983391i
\(431\) 187.364 0.434720 0.217360 0.976092i \(-0.430255\pi\)
0.217360 + 0.976092i \(0.430255\pi\)
\(432\) −17.6288 17.6288i −0.0408075 0.0408075i
\(433\) 154.848 154.848i 0.357617 0.357617i −0.505317 0.862934i \(-0.668624\pi\)
0.862934 + 0.505317i \(0.168624\pi\)
\(434\) 120.586i 0.277847i
\(435\) −1.62092 + 7.21225i −0.00372624 + 0.0165799i
\(436\) −231.848 −0.531761
\(437\) −340.454 340.454i −0.779071 0.779071i
\(438\) 216.823 216.823i 0.495030 0.495030i
\(439\) 252.929i 0.576147i −0.957608 0.288074i \(-0.906985\pi\)
0.957608 0.288074i \(-0.0930148\pi\)
\(440\) −97.5959 21.9342i −0.221809 0.0498504i
\(441\) −134.394 −0.304748
\(442\) −123.283 123.283i −0.278920 0.278920i
\(443\) −421.131 + 421.131i −0.950633 + 0.950633i −0.998838 0.0482041i \(-0.984650\pi\)
0.0482041 + 0.998838i \(0.484650\pi\)
\(444\) 549.737i 1.23815i
\(445\) 397.893 251.864i 0.894142 0.565986i
\(446\) 148.742 0.333503
\(447\) 145.924 + 145.924i 0.326452 + 0.326452i
\(448\) 150.015 150.015i 0.334854 0.334854i
\(449\) 297.909i 0.663495i 0.943368 + 0.331747i \(0.107638\pi\)
−0.943368 + 0.331747i \(0.892362\pi\)
\(450\) −79.4166 222.204i −0.176481 0.493787i
\(451\) 96.0908 0.213062
\(452\) 84.7015 + 84.7015i 0.187393 + 0.187393i
\(453\) −177.551 + 177.551i −0.391944 + 0.391944i
\(454\) 94.2020i 0.207493i
\(455\) 81.0102 + 127.980i 0.178044 + 0.281274i
\(456\) −214.182 −0.469697
\(457\) 285.747 + 285.747i 0.625267 + 0.625267i 0.946873 0.321607i \(-0.104223\pi\)
−0.321607 + 0.946873i \(0.604223\pi\)
\(458\) −542.388 + 542.388i −1.18425 + 1.18425i
\(459\) 19.4847i 0.0424503i
\(460\) −150.454 + 669.444i −0.327074 + 1.45531i
\(461\) 526.620 1.14234 0.571171 0.820831i \(-0.306489\pi\)
0.571171 + 0.820831i \(0.306489\pi\)
\(462\) −26.4495 26.4495i −0.0572500 0.0572500i
\(463\) 335.702 335.702i 0.725057 0.725057i −0.244573 0.969631i \(-0.578648\pi\)
0.969631 + 0.244573i \(0.0786479\pi\)
\(464\) 4.09540i 0.00882630i
\(465\) −157.980 35.5051i −0.339741 0.0763551i
\(466\) −719.535 −1.54407
\(467\) 488.742 + 488.742i 1.04656 + 1.04656i 0.998862 + 0.0476956i \(0.0151877\pi\)
0.0476956 + 0.998862i \(0.484812\pi\)
\(468\) −184.924 + 184.924i −0.395137 + 0.395137i
\(469\) 159.151i 0.339341i
\(470\) 371.308 235.035i 0.790016 0.500075i
\(471\) 125.283 0.265993
\(472\) 472.893 + 472.893i 1.00189 + 1.00189i
\(473\) −75.3235 + 75.3235i −0.159246 + 0.159246i
\(474\) 133.485i 0.281613i
\(475\) 467.666 + 221.394i 0.984561 + 0.466092i
\(476\) −45.3439 −0.0952603
\(477\) −86.0908 86.0908i −0.180484 0.180484i
\(478\) −725.716 + 725.716i −1.51823 + 1.51823i
\(479\) 184.949i 0.386115i −0.981187 0.193057i \(-0.938160\pi\)
0.981187 0.193057i \(-0.0618404\pi\)
\(480\) −180.619 285.341i −0.376289 0.594459i
\(481\) −795.110 −1.65304
\(482\) 297.171 + 297.171i 0.616538 + 0.616538i
\(483\) −58.4041 + 58.4041i −0.120919 + 0.120919i
\(484\) 647.636i 1.33809i
\(485\) −22.6311 + 100.697i −0.0466621 + 0.207623i
\(486\) 49.0454 0.100916
\(487\) −120.682 120.682i −0.247807 0.247807i 0.572263 0.820070i \(-0.306066\pi\)
−0.820070 + 0.572263i \(0.806066\pi\)
\(488\) 397.510 397.510i 0.814569 0.814569i
\(489\) 463.918i 0.948708i
\(490\) −687.580 154.530i −1.40322 0.315368i
\(491\) −105.682 −0.215239 −0.107619 0.994192i \(-0.534323\pi\)
−0.107619 + 0.994192i \(0.534323\pi\)
\(492\) −207.328 207.328i −0.421398 0.421398i
\(493\) 2.26327 2.26327i 0.00459082 0.00459082i
\(494\) 962.302i 1.94798i
\(495\) −42.4393 + 26.8638i −0.0857359 + 0.0542703i
\(496\) −89.7071 −0.180861
\(497\) 98.5653 + 98.5653i 0.198321 + 0.198321i
\(498\) 115.237 115.237i 0.231400 0.231400i
\(499\) 739.585i 1.48213i −0.671431 0.741067i \(-0.734320\pi\)
0.671431 0.741067i \(-0.265680\pi\)
\(500\) −89.8707 731.875i −0.179741 1.46375i
\(501\) 237.687 0.474425
\(502\) 900.448 + 900.448i 1.79372 + 1.79372i
\(503\) −406.409 + 406.409i −0.807970 + 0.807970i −0.984326 0.176357i \(-0.943569\pi\)
0.176357 + 0.984326i \(0.443569\pi\)
\(504\) 36.7423i 0.0729015i
\(505\) 464.303 + 733.504i 0.919412 + 1.45248i
\(506\) 245.081 0.484349
\(507\) −60.4824 60.4824i −0.119295 0.119295i
\(508\) 676.146 676.146i 1.33100 1.33100i
\(509\) 194.511i 0.382143i 0.981576 + 0.191071i \(0.0611962\pi\)
−0.981576 + 0.191071i \(0.938804\pi\)
\(510\) −22.4041 + 99.6867i −0.0439296 + 0.195464i
\(511\) 115.344 0.225722
\(512\) −213.376 213.376i −0.416750 0.416750i
\(513\) −76.0454 + 76.0454i −0.148237 + 0.148237i
\(514\) 397.060i 0.772491i
\(515\) −446.727 100.399i −0.867430 0.194950i
\(516\) 325.040 0.629922
\(517\) −66.1408 66.1408i −0.127932 0.127932i
\(518\) −245.373 + 245.373i −0.473694 + 0.473694i
\(519\) 84.8286i 0.163446i
\(520\) −373.015 + 236.116i −0.717336 + 0.454069i
\(521\) −589.605 −1.13168 −0.565840 0.824515i \(-0.691448\pi\)
−0.565840 + 0.824515i \(0.691448\pi\)
\(522\) −5.69694 5.69694i −0.0109137 0.0109137i
\(523\) −141.546 + 141.546i −0.270642 + 0.270642i −0.829359 0.558716i \(-0.811294\pi\)
0.558716 + 0.829359i \(0.311294\pi\)
\(524\) 154.177i 0.294231i
\(525\) 37.9796 80.2270i 0.0723421 0.152813i
\(526\) 1521.03 2.89169
\(527\) 49.5755 + 49.5755i 0.0940712 + 0.0940712i
\(528\) −19.6765 + 19.6765i −0.0372662 + 0.0372662i
\(529\) 12.1714i 0.0230084i
\(530\) −341.464 539.444i −0.644272 1.01782i
\(531\) 335.803 0.632397
\(532\) −176.969 176.969i −0.332649 0.332649i
\(533\) 299.868 299.868i 0.562605 0.562605i
\(534\) 513.242i 0.961127i
\(535\) 7.35306 32.7173i 0.0137440 0.0611539i
\(536\) −463.868 −0.865426
\(537\) −225.000 225.000i −0.418994 0.418994i
\(538\) −7.78775 + 7.78775i −0.0144754 + 0.0144754i
\(539\) 150.005i 0.278302i
\(540\) 149.530 + 33.6061i 0.276908 + 0.0622336i
\(541\) 431.303 0.797233 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(542\) 230.429 + 230.429i 0.425146 + 0.425146i
\(543\) −26.6107 + 26.6107i −0.0490068 + 0.0490068i
\(544\) 146.222i 0.268791i
\(545\) −166.045 + 105.106i −0.304670 + 0.192854i
\(546\) −165.081 −0.302345
\(547\) −446.222 446.222i −0.815763 0.815763i 0.169728 0.985491i \(-0.445711\pi\)
−0.985491 + 0.169728i \(0.945711\pi\)
\(548\) −86.3087 + 86.3087i −0.157498 + 0.157498i
\(549\) 282.272i 0.514157i
\(550\) −248.015 + 88.6413i −0.450936 + 0.161166i
\(551\) 17.6663 0.0320623
\(552\) −170.227 170.227i −0.308382 0.308382i
\(553\) 35.5051 35.5051i 0.0642045 0.0642045i
\(554\) 1270.37i 2.29309i
\(555\) 249.217 + 393.712i 0.449039 + 0.709391i
\(556\) −490.627 −0.882422
\(557\) 214.091 + 214.091i 0.384364 + 0.384364i 0.872672 0.488308i \(-0.162386\pi\)
−0.488308 + 0.872672i \(0.662386\pi\)
\(558\) 124.788 124.788i 0.223634 0.223634i
\(559\) 470.120i 0.841003i
\(560\) 10.7832 47.9796i 0.0192557 0.0856778i
\(561\) 21.7480 0.0387664
\(562\) −829.156 829.156i −1.47537 1.47537i
\(563\) 672.009 672.009i 1.19362 1.19362i 0.217579 0.976043i \(-0.430184\pi\)
0.976043 0.217579i \(-0.0698161\pi\)
\(564\) 285.414i 0.506054i
\(565\) 99.0602 + 22.2633i 0.175328 + 0.0394040i
\(566\) 343.464 0.606827
\(567\) 13.0454 + 13.0454i 0.0230078 + 0.0230078i
\(568\) −287.283 + 287.283i −0.505779 + 0.505779i
\(569\) 972.161i 1.70854i −0.519827 0.854272i \(-0.674003\pi\)
0.519827 0.854272i \(-0.325997\pi\)
\(570\) −476.499 + 301.621i −0.835964 + 0.529160i
\(571\) −924.030 −1.61827 −0.809133 0.587626i \(-0.800063\pi\)
−0.809133 + 0.587626i \(0.800063\pi\)
\(572\) 206.404 + 206.404i 0.360846 + 0.360846i
\(573\) −49.1010 + 49.1010i −0.0856911 + 0.0856911i
\(574\) 185.081i 0.322440i
\(575\) 195.732 + 547.650i 0.340404 + 0.952436i
\(576\) 310.485 0.539036
\(577\) −497.879 497.879i −0.862874 0.862874i 0.128797 0.991671i \(-0.458889\pi\)
−0.991671 + 0.128797i \(0.958889\pi\)
\(578\) −611.669 + 611.669i −1.05825 + 1.05825i
\(579\) 189.995i 0.328144i
\(580\) −13.4653 21.2724i −0.0232161 0.0366766i
\(581\) 61.3031 0.105513
\(582\) −79.5403 79.5403i −0.136667 0.136667i
\(583\) −96.0908 + 96.0908i −0.164821 + 0.164821i
\(584\) 336.186i 0.575661i
\(585\) −48.6061 + 216.272i −0.0830874 + 0.369696i
\(586\) 1052.59 1.79624
\(587\) 292.783 + 292.783i 0.498779 + 0.498779i 0.911058 0.412279i \(-0.135267\pi\)
−0.412279 + 0.911058i \(0.635267\pi\)
\(588\) 323.654 323.654i 0.550432 0.550432i
\(589\) 386.969i 0.656994i
\(590\) 1718.02 + 386.116i 2.91190 + 0.654434i
\(591\) −164.858 −0.278948
\(592\) 182.540 + 182.540i 0.308345 + 0.308345i
\(593\) 451.258 451.258i 0.760974 0.760974i −0.215524 0.976498i \(-0.569146\pi\)
0.976498 + 0.215524i \(0.0691461\pi\)
\(594\) 54.7423i 0.0921588i
\(595\) −32.4745 + 20.5561i −0.0545790 + 0.0345481i
\(596\) −702.842 −1.17927
\(597\) 307.893 + 307.893i 0.515734 + 0.515734i
\(598\) 764.817 764.817i 1.27896 1.27896i
\(599\) 32.8582i 0.0548550i 0.999624 + 0.0274275i \(0.00873154\pi\)
−0.999624 + 0.0274275i \(0.991268\pi\)
\(600\) 233.833 + 110.697i 0.389722 + 0.184495i
\(601\) −184.484 −0.306961 −0.153481 0.988152i \(-0.549048\pi\)
−0.153481 + 0.988152i \(0.549048\pi\)
\(602\) 145.081 + 145.081i 0.240998 + 0.240998i
\(603\) −164.697 + 164.697i −0.273129 + 0.273129i
\(604\) 855.171i 1.41585i
\(605\) −293.598 463.825i −0.485286 0.766653i
\(606\) −946.145 −1.56130
\(607\) 136.389 + 136.389i 0.224694 + 0.224694i 0.810472 0.585778i \(-0.199211\pi\)
−0.585778 + 0.810472i \(0.699211\pi\)
\(608\) −570.681 + 570.681i −0.938620 + 0.938620i
\(609\) 3.03062i 0.00497638i
\(610\) 324.565 1444.15i 0.532074 2.36746i
\(611\) −412.808 −0.675627
\(612\) −46.9240 46.9240i −0.0766732 0.0766732i
\(613\) −12.7128 + 12.7128i −0.0207386 + 0.0207386i −0.717400 0.696661i \(-0.754668\pi\)
0.696661 + 0.717400i \(0.254668\pi\)
\(614\) 751.828i 1.22447i
\(615\) −242.474 54.4949i −0.394267 0.0886096i
\(616\) 41.0102 0.0665750
\(617\) −398.752 398.752i −0.646275 0.646275i 0.305816 0.952091i \(-0.401071\pi\)
−0.952091 + 0.305816i \(0.901071\pi\)
\(618\) 352.868 352.868i 0.570984 0.570984i
\(619\) 819.131i 1.32331i 0.749807 + 0.661656i \(0.230146\pi\)
−0.749807 + 0.661656i \(0.769854\pi\)
\(620\) 465.959 294.949i 0.751547 0.475724i
\(621\) −120.879 −0.194651
\(622\) −788.232 788.232i −1.26725 1.26725i
\(623\) −136.515 + 136.515i −0.219126 + 0.219126i
\(624\) 122.808i 0.196808i
\(625\) −396.151 483.414i −0.633842 0.773463i
\(626\) −677.984 −1.08304
\(627\) 84.8786 + 84.8786i 0.135373 + 0.135373i
\(628\) −301.712 + 301.712i −0.480433 + 0.480433i
\(629\) 201.757i 0.320759i
\(630\) 51.7423 + 81.7423i 0.0821307 + 0.129750i
\(631\) 105.485 0.167171 0.0835853 0.996501i \(-0.473363\pi\)
0.0835853 + 0.996501i \(0.473363\pi\)
\(632\) 103.485 + 103.485i 0.163742 + 0.163742i
\(633\) 324.297 324.297i 0.512318 0.512318i
\(634\) 1900.90i 2.99826i
\(635\) 177.721 790.767i 0.279875 1.24530i
\(636\) 414.656 0.651975
\(637\) 468.116 + 468.116i 0.734876 + 0.734876i
\(638\) −6.35867 + 6.35867i −0.00996657 + 0.00996657i
\(639\) 204.000i 0.319249i
\(640\) 827.580 + 185.994i 1.29309 + 0.290616i
\(641\) 164.788 0.257079 0.128540 0.991704i \(-0.458971\pi\)
0.128540 + 0.991704i \(0.458971\pi\)
\(642\) 25.8434 + 25.8434i 0.0402545 + 0.0402545i
\(643\) −764.372 + 764.372i −1.18876 + 1.18876i −0.211349 + 0.977411i \(0.567786\pi\)
−0.977411 + 0.211349i \(0.932214\pi\)
\(644\) 281.303i 0.436806i
\(645\) 232.788 147.353i 0.360911 0.228454i
\(646\) 244.182 0.377990
\(647\) 321.287 + 321.287i 0.496580 + 0.496580i 0.910372 0.413792i \(-0.135796\pi\)
−0.413792 + 0.910372i \(0.635796\pi\)
\(648\) −38.0227 + 38.0227i −0.0586770 + 0.0586770i
\(649\) 374.808i 0.577516i
\(650\) −497.353 + 1050.59i −0.765159 + 1.61630i
\(651\) 66.3837 0.101972
\(652\) 1117.23 + 1117.23i 1.71354 + 1.71354i
\(653\) −169.823 + 169.823i −0.260066 + 0.260066i −0.825081 0.565015i \(-0.808870\pi\)
0.565015 + 0.825081i \(0.308870\pi\)
\(654\) 214.182i 0.327495i
\(655\) −69.8944 110.419i −0.106709 0.168578i
\(656\) −137.687 −0.209888
\(657\) 119.363 + 119.363i 0.181679 + 0.181679i
\(658\) −127.394 + 127.394i −0.193608 + 0.193608i
\(659\) 958.763i 1.45488i 0.686174 + 0.727438i \(0.259289\pi\)
−0.686174 + 0.727438i \(0.740711\pi\)
\(660\) 37.5097 166.899i 0.0568329 0.252877i
\(661\) 396.393 0.599687 0.299843 0.953988i \(-0.403066\pi\)
0.299843 + 0.953988i \(0.403066\pi\)
\(662\) −1088.84 1088.84i −1.64478 1.64478i
\(663\) 67.8684 67.8684i 0.102366 0.102366i
\(664\) 178.677i 0.269091i
\(665\) −206.969 46.5153i −0.311232 0.0699478i
\(666\) −507.848 −0.762534
\(667\) 14.0408 + 14.0408i 0.0210507 + 0.0210507i
\(668\) −572.409 + 572.409i −0.856899 + 0.856899i
\(669\) 81.8842i 0.122398i
\(670\) −1031.99 + 653.242i −1.54028 + 0.974988i
\(671\) −315.060 −0.469538
\(672\) 97.8990 + 97.8990i 0.145683 + 0.145683i
\(673\) 164.707 164.707i 0.244736 0.244736i −0.574070 0.818806i \(-0.694636\pi\)
0.818806 + 0.574070i \(0.194636\pi\)
\(674\) 1300.10i 1.92894i
\(675\) 122.326 43.7196i 0.181223 0.0647698i
\(676\) 291.313 0.430937
\(677\) 544.388 + 544.388i 0.804119 + 0.804119i 0.983736 0.179618i \(-0.0574861\pi\)
−0.179618 + 0.983736i \(0.557486\pi\)
\(678\) −78.2474 + 78.2474i −0.115409 + 0.115409i
\(679\) 42.3133i 0.0623170i
\(680\) −59.9138 94.6515i −0.0881085 0.139193i
\(681\) −51.8592 −0.0761515
\(682\) −139.283 139.283i −0.204227 0.204227i
\(683\) 786.590 786.590i 1.15167 1.15167i 0.165452 0.986218i \(-0.447092\pi\)
0.986218 0.165452i \(-0.0529082\pi\)
\(684\) 366.272i 0.535486i
\(685\) −22.6857 + 100.940i −0.0331178 + 0.147357i
\(686\) 604.949 0.881850
\(687\) −298.590 298.590i −0.434629 0.434629i
\(688\) 107.930 107.930i 0.156874 0.156874i
\(689\) 599.737i 0.870445i
\(690\) −618.434 138.990i −0.896281 0.201434i
\(691\) 356.879 0.516467 0.258233 0.966083i \(-0.416860\pi\)
0.258233 + 0.966083i \(0.416860\pi\)
\(692\) −204.288 204.288i −0.295214 0.295214i
\(693\) 14.5607 14.5607i 0.0210111 0.0210111i
\(694\) 1424.06i 2.05196i
\(695\) −351.378 + 222.420i −0.505580 + 0.320029i
\(696\) 8.83316 0.0126913
\(697\) 76.0908 + 76.0908i 0.109169 + 0.109169i
\(698\) 1277.02 1277.02i 1.82955 1.82955i
\(699\) 396.111i 0.566683i
\(700\) 101.742 + 284.671i 0.145346 + 0.406673i
\(701\) 885.680 1.26345 0.631726 0.775192i \(-0.282347\pi\)
0.631726 + 0.775192i \(0.282347\pi\)
\(702\) −170.833 170.833i −0.243352 0.243352i
\(703\) 787.423 787.423i 1.12009 1.12009i
\(704\) 346.549i 0.492258i
\(705\) 129.389 + 204.409i 0.183531 + 0.289941i
\(706\) −1185.88 −1.67971
\(707\) −251.662 251.662i −0.355957 0.355957i
\(708\) −808.696 + 808.696i −1.14223 + 1.14223i
\(709\) 731.049i 1.03110i −0.856860 0.515549i \(-0.827588\pi\)
0.856860 0.515549i \(-0.172412\pi\)
\(710\) −234.565 + 1043.70i −0.330374 + 1.46999i
\(711\) 73.4847 0.103354
\(712\) −397.893 397.893i −0.558839 0.558839i
\(713\) −307.555 + 307.555i −0.431354 + 0.431354i
\(714\) 41.8888i 0.0586678i
\(715\) 241.394 + 54.2520i 0.337614 + 0.0758770i
\(716\) 1083.71 1.51356
\(717\) −399.514 399.514i −0.557203 0.557203i
\(718\) −481.151 + 481.151i −0.670127 + 0.670127i
\(719\) 629.271i 0.875204i 0.899169 + 0.437602i \(0.144172\pi\)
−0.899169 + 0.437602i \(0.855828\pi\)
\(720\) 60.8105 38.4926i 0.0844590 0.0534619i
\(721\) 187.716 0.260356
\(722\) 149.866 + 149.866i 0.207571 + 0.207571i
\(723\) −163.596 + 163.596i −0.226274 + 0.226274i
\(724\) 128.170i 0.177031i
\(725\) −19.2872 9.13061i −0.0266031 0.0125939i
\(726\) 598.287 0.824087
\(727\) −15.8740 15.8740i −0.0218349 0.0218349i 0.696105 0.717940i \(-0.254915\pi\)
−0.717940 + 0.696105i \(0.754915\pi\)
\(728\) 127.980 127.980i 0.175796 0.175796i
\(729\) 27.0000i 0.0370370i
\(730\) 473.434 + 747.929i 0.648539 + 1.02456i
\(731\) −119.292 −0.163190
\(732\) 679.782 + 679.782i 0.928664 + 0.928664i
\(733\) −393.237 + 393.237i −0.536476 + 0.536476i −0.922492 0.386016i \(-0.873851\pi\)
0.386016 + 0.922492i \(0.373851\pi\)
\(734\) 1070.15i 1.45796i
\(735\) 85.0704 378.520i 0.115742 0.514993i
\(736\) −907.131 −1.23251
\(737\) 183.828 + 183.828i 0.249427 + 0.249427i
\(738\) 191.530 191.530i 0.259526 0.259526i
\(739\) 192.334i 0.260262i −0.991497 0.130131i \(-0.958460\pi\)
0.991497 0.130131i \(-0.0415398\pi\)
\(740\) −1548.33 347.980i −2.09234 0.470243i
\(741\) 529.757 0.714922
\(742\) 185.081 + 185.081i 0.249435 + 0.249435i
\(743\) −44.7015 + 44.7015i −0.0601636 + 0.0601636i −0.736548 0.676385i \(-0.763546\pi\)
0.676385 + 0.736548i \(0.263546\pi\)
\(744\) 193.485i 0.260060i
\(745\) −503.363 + 318.626i −0.675655 + 0.427685i
\(746\) 1469.25 1.96951
\(747\) 63.4393 + 63.4393i 0.0849254 + 0.0849254i
\(748\) −52.3745 + 52.3745i −0.0700194 + 0.0700194i
\(749\) 13.7480i 0.0183551i
\(750\) 676.108 83.0227i 0.901477 0.110697i
\(751\) 227.787 0.303311 0.151656 0.988433i \(-0.451540\pi\)
0.151656 + 0.988433i \(0.451540\pi\)
\(752\) 94.7719 + 94.7719i 0.126027 + 0.126027i
\(753\) −495.706 + 495.706i −0.658308 + 0.658308i
\(754\) 39.6867i 0.0526349i
\(755\) −387.682 612.459i −0.513486 0.811204i
\(756\) −62.8332 −0.0831126
\(757\) −235.925 235.925i −0.311658 0.311658i 0.533894 0.845552i \(-0.320728\pi\)
−0.845552 + 0.533894i \(0.820728\pi\)
\(758\) −467.196 + 467.196i −0.616354 + 0.616354i
\(759\) 134.919i 0.177759i
\(760\) 135.576 603.242i 0.178389 0.793739i
\(761\) −881.242 −1.15801 −0.579003 0.815326i \(-0.696558\pi\)
−0.579003 + 0.815326i \(0.696558\pi\)
\(762\) 624.626 + 624.626i 0.819719 + 0.819719i
\(763\) 56.9694 56.9694i 0.0746650 0.0746650i
\(764\) 236.495i 0.309548i
\(765\) −54.8786 12.3337i −0.0717367 0.0161225i
\(766\) −759.221 −0.991151
\(767\) −1169.66 1169.66i −1.52497 1.52497i
\(768\) −146.684 + 146.684i −0.190995 + 0.190995i
\(769\) 1208.40i 1.57139i −0.618612 0.785697i \(-0.712304\pi\)
0.618612 0.785697i \(-0.287696\pi\)
\(770\) 91.2372 57.7526i 0.118490 0.0750033i
\(771\) −218.586 −0.283509
\(772\) 457.556 + 457.556i 0.592689 + 0.592689i
\(773\) −815.226 + 815.226i −1.05463 + 1.05463i −0.0562070 + 0.998419i \(0.517901\pi\)
−0.998419 + 0.0562070i \(0.982099\pi\)
\(774\) 300.272i 0.387949i
\(775\) 200.000 422.474i 0.258065 0.545128i
\(776\) 123.328