Properties

Label 75.3.f.c.7.2
Level $75$
Weight $3$
Character 75.7
Analytic conductor $2.044$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04360198270\)
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: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.2
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 75.7
Dual form 75.3.f.c.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.22474 + 2.22474i) q^{2} +(-1.22474 + 1.22474i) q^{3} +5.89898i q^{4} -5.44949 q^{6} +(1.44949 + 1.44949i) q^{7} +(-4.22474 + 4.22474i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(2.22474 + 2.22474i) q^{2} +(-1.22474 + 1.22474i) q^{3} +5.89898i q^{4} -5.44949 q^{6} +(1.44949 + 1.44949i) q^{7} +(-4.22474 + 4.22474i) q^{8} -3.00000i q^{9} -3.34847 q^{11} +(-7.22474 - 7.22474i) q^{12} +(10.4495 - 10.4495i) q^{13} +6.44949i q^{14} +4.79796 q^{16} +(2.65153 + 2.65153i) q^{17} +(6.67423 - 6.67423i) q^{18} -20.6969i q^{19} -3.55051 q^{21} +(-7.44949 - 7.44949i) q^{22} +(-16.4495 + 16.4495i) q^{23} -10.3485i q^{24} +46.4949 q^{26} +(3.67423 + 3.67423i) q^{27} +(-8.55051 + 8.55051i) q^{28} +0.853572i q^{29} -18.6969 q^{31} +(27.5732 + 27.5732i) q^{32} +(4.10102 - 4.10102i) q^{33} +11.7980i q^{34} +17.6969 q^{36} +(-38.0454 - 38.0454i) q^{37} +(46.0454 - 46.0454i) q^{38} +25.5959i q^{39} -28.6969 q^{41} +(-7.89898 - 7.89898i) q^{42} +(-22.4949 + 22.4949i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(-19.7526 - 19.7526i) q^{47} +(-5.87628 + 5.87628i) q^{48} -44.7980i q^{49} -6.49490 q^{51} +(61.6413 + 61.6413i) q^{52} +(-28.6969 + 28.6969i) q^{53} +16.3485i q^{54} -12.2474 q^{56} +(25.3485 + 25.3485i) q^{57} +(-1.89898 + 1.89898i) q^{58} +111.934i q^{59} +94.0908 q^{61} +(-41.5959 - 41.5959i) q^{62} +(4.34847 - 4.34847i) q^{63} +103.495i q^{64} +18.2474 q^{66} +(54.8990 + 54.8990i) q^{67} +(-15.6413 + 15.6413i) q^{68} -40.2929i q^{69} -68.0000 q^{71} +(12.6742 + 12.6742i) q^{72} +(39.7878 - 39.7878i) q^{73} -169.283i q^{74} +122.091 q^{76} +(-4.85357 - 4.85357i) q^{77} +(-56.9444 + 56.9444i) q^{78} +24.4949i q^{79} -9.00000 q^{81} +(-63.8434 - 63.8434i) q^{82} +(21.1464 - 21.1464i) q^{83} -20.9444i q^{84} -100.091 q^{86} +(-1.04541 - 1.04541i) q^{87} +(14.1464 - 14.1464i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(-97.0352 - 97.0352i) q^{92} +(22.8990 - 22.8990i) q^{93} -87.8888i q^{94} -67.5403 q^{96} +(-14.5959 - 14.5959i) q^{97} +(99.6640 - 99.6640i) q^{98} +10.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 12q^{6} - 4q^{7} - 12q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 12q^{6} - 4q^{7} - 12q^{8} + 16q^{11} - 24q^{12} + 32q^{13} - 20q^{16} + 40q^{17} + 12q^{18} - 24q^{21} - 20q^{22} - 56q^{23} + 88q^{26} - 44q^{28} - 16q^{31} + 76q^{32} + 36q^{33} + 12q^{36} - 64q^{37} + 96q^{38} - 56q^{41} - 12q^{42} + 8q^{43} - 136q^{46} - 128q^{47} - 48q^{48} + 72q^{51} + 80q^{52} - 56q^{53} + 72q^{57} + 12q^{58} + 200q^{61} - 88q^{62} - 12q^{63} + 24q^{66} + 200q^{67} + 104q^{68} - 272q^{71} + 36q^{72} - 76q^{73} + 312q^{76} - 88q^{77} - 120q^{78} - 36q^{81} - 128q^{82} + 16q^{83} - 224q^{86} + 84q^{87} - 12q^{88} - 16q^{91} - 104q^{92} + 72q^{93} - 84q^{96} + 20q^{97} + 188q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.22474 + 2.22474i 1.11237 + 1.11237i 0.992829 + 0.119543i \(0.0381431\pi\)
0.119543 + 0.992829i \(0.461857\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 5.89898i 1.47474i
\(5\) 0 0
\(6\) −5.44949 −0.908248
\(7\) 1.44949 + 1.44949i 0.207070 + 0.207070i 0.803021 0.595951i \(-0.203225\pi\)
−0.595951 + 0.803021i \(0.703225\pi\)
\(8\) −4.22474 + 4.22474i −0.528093 + 0.528093i
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −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 −0.179881 0.983688i \(-0.557571\pi\)
0.983688 + 0.179881i \(0.0575714\pi\)
\(14\) 6.44949i 0.460678i
\(15\) 0 0
\(16\) 4.79796 0.299872
\(17\) 2.65153 + 2.65153i 0.155972 + 0.155972i 0.780779 0.624807i \(-0.214822\pi\)
−0.624807 + 0.780779i \(0.714822\pi\)
\(18\) 6.67423 6.67423i 0.370791 0.370791i
\(19\) 20.6969i 1.08931i −0.838659 0.544656i \(-0.816660\pi\)
0.838659 0.544656i \(-0.183340\pi\)
\(20\) 0 0
\(21\) −3.55051 −0.169072
\(22\) −7.44949 7.44949i −0.338613 0.338613i
\(23\) −16.4495 + 16.4495i −0.715195 + 0.715195i −0.967617 0.252422i \(-0.918773\pi\)
0.252422 + 0.967617i \(0.418773\pi\)
\(24\) 10.3485i 0.431186i
\(25\) 0 0
\(26\) 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 \(0.995315\pi\)
\(30\) 0 0
\(31\) −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
\(35\) 0 0
\(36\) 17.6969 0.491582
\(37\) −38.0454 38.0454i −1.02825 1.02825i −0.999589 0.0286652i \(-0.990874\pi\)
−0.0286652 0.999589i \(-0.509126\pi\)
\(38\) 46.0454 46.0454i 1.21172 1.21172i
\(39\) 25.5959i 0.656306i
\(40\) 0 0
\(41\) −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 −0.918517 0.395380i \(-0.870613\pi\)
0.395380 + 0.918517i \(0.370613\pi\)
\(44\) 19.7526i 0.448922i
\(45\) 0 0
\(46\) −73.1918 −1.59113
\(47\) −19.7526 19.7526i −0.420267 0.420267i 0.465029 0.885296i \(-0.346044\pi\)
−0.885296 + 0.465029i \(0.846044\pi\)
\(48\) −5.87628 + 5.87628i −0.122422 + 0.122422i
\(49\) 44.7980i 0.914244i
\(50\) 0 0
\(51\) −6.49490 −0.127351
\(52\) 61.6413 + 61.6413i 1.18541 + 1.18541i
\(53\) −28.6969 + 28.6969i −0.541452 + 0.541452i −0.923954 0.382503i \(-0.875062\pi\)
0.382503 + 0.923954i \(0.375062\pi\)
\(54\) 16.3485i 0.302749i
\(55\) 0 0
\(56\) −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 \(0.602505\pi\)
\(60\) 0 0
\(61\) 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
\(65\) 0 0
\(66\) 18.2474 0.276476
\(67\) 54.8990 + 54.8990i 0.819388 + 0.819388i 0.986019 0.166631i \(-0.0532890\pi\)
−0.166631 + 0.986019i \(0.553289\pi\)
\(68\) −15.6413 + 15.6413i −0.230019 + 0.230019i
\(69\) 40.2929i 0.583954i
\(70\) 0 0
\(71\) −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 −0.379964 0.925001i \(-0.624064\pi\)
0.925001 + 0.379964i \(0.124064\pi\)
\(74\) 169.283i 2.28760i
\(75\) 0 0
\(76\) 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 \(0.950452\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) −63.8434 63.8434i −0.778578 0.778578i
\(83\) 21.1464 21.1464i 0.254776 0.254776i −0.568149 0.822926i \(-0.692340\pi\)
0.822926 + 0.568149i \(0.192340\pi\)
\(84\) 20.9444i 0.249338i
\(85\) 0 0
\(86\) −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 \(-0.177474\pi\)
\(90\) 0 0
\(91\) 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
\(95\) 0 0
\(96\) −67.5403 −0.703545
\(97\) −14.5959 14.5959i −0.150473 0.150473i 0.627856 0.778329i \(-0.283933\pi\)
−0.778329 + 0.627856i \(0.783933\pi\)
\(98\) 99.6640 99.6640i 1.01698 1.01698i
\(99\) 10.0454i 0.101469i
\(100\) 0 0
\(101\) 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 −0.319067 0.947732i \(-0.603369\pi\)
0.947732 + 0.319067i \(0.103369\pi\)
\(104\) 88.2929i 0.848970i
\(105\) 0 0
\(106\) −127.687 −1.20459
\(107\) 4.74235 + 4.74235i 0.0443210 + 0.0443210i 0.728920 0.684599i \(-0.240023\pi\)
−0.684599 + 0.728920i \(0.740023\pi\)
\(108\) −21.6742 + 21.6742i −0.200687 + 0.200687i
\(109\) 39.3031i 0.360579i 0.983614 + 0.180289i \(0.0577034\pi\)
−0.983614 + 0.180289i \(0.942297\pi\)
\(110\) 0 0
\(111\) 93.1918 0.839566
\(112\) 6.95459 + 6.95459i 0.0620946 + 0.0620946i
\(113\) −14.3587 + 14.3587i −0.127068 + 0.127068i −0.767781 0.640713i \(-0.778639\pi\)
0.640713 + 0.767781i \(0.278639\pi\)
\(114\) 112.788i 0.989366i
\(115\) 0 0
\(116\) −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
\(120\) 0 0
\(121\) −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
\(125\) 0 0
\(126\) 19.3485 0.153559
\(127\) 114.621 + 114.621i 0.902527 + 0.902527i 0.995654 0.0931273i \(-0.0296864\pi\)
−0.0931273 + 0.995654i \(0.529686\pi\)
\(128\) −119.957 + 119.957i −0.937163 + 0.937163i
\(129\) 55.1010i 0.427140i
\(130\) 0 0
\(131\) −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
\(135\) 0 0
\(136\) −22.4041 −0.164736
\(137\) −14.6311 14.6311i −0.106796 0.106796i 0.651689 0.758486i \(-0.274061\pi\)
−0.758486 + 0.651689i \(0.774061\pi\)
\(138\) 89.6413 89.6413i 0.649575 0.649575i
\(139\) 83.1714i 0.598356i 0.954197 + 0.299178i \(0.0967124\pi\)
−0.954197 + 0.299178i \(0.903288\pi\)
\(140\) 0 0
\(141\) 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
\(145\) 0 0
\(146\) 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 \(0.869073\pi\)
\(150\) 0 0
\(151\) −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
\(155\) 0 0
\(156\) −150.990 −0.967883
\(157\) −51.1464 51.1464i −0.325773 0.325773i 0.525203 0.850977i \(-0.323989\pi\)
−0.850977 + 0.525203i \(0.823989\pi\)
\(158\) −54.4949 + 54.4949i −0.344904 + 0.344904i
\(159\) 70.2929i 0.442093i
\(160\) 0 0
\(161\) −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 \(0.556921\pi\)
−0.984054 + 0.177872i \(0.943079\pi\)
\(164\) 169.283i 1.03221i
\(165\) 0 0
\(166\) 94.0908 0.566812
\(167\) −97.0352 97.0352i −0.581049 0.581049i 0.354142 0.935192i \(-0.384773\pi\)
−0.935192 + 0.354142i \(0.884773\pi\)
\(168\) 15.0000 15.0000i 0.0892857 0.0892857i
\(169\) 49.3837i 0.292211i
\(170\) 0 0
\(171\) −62.0908 −0.363104
\(172\) −132.697 132.697i −0.771494 0.771494i
\(173\) 34.6311 34.6311i 0.200180 0.200180i −0.599897 0.800077i \(-0.704792\pi\)
0.800077 + 0.599897i \(0.204792\pi\)
\(174\) 4.65153i 0.0267329i
\(175\) 0 0
\(176\) −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 \(-0.171526\pi\)
\(180\) 0 0
\(181\) −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
\(185\) 0 0
\(186\) 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
\(190\) 0 0
\(191\) −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 −0.878900 0.477007i \(-0.841722\pi\)
0.477007 + 0.878900i \(0.341722\pi\)
\(194\) 64.9444i 0.334765i
\(195\) 0 0
\(196\) 264.262 1.34828
\(197\) 67.3031 + 67.3031i 0.341640 + 0.341640i 0.856984 0.515344i \(-0.172336\pi\)
−0.515344 + 0.856984i \(0.672336\pi\)
\(198\) −22.3485 + 22.3485i −0.112871 + 0.112871i
\(199\) 251.394i 1.26329i 0.775259 + 0.631643i \(0.217619\pi\)
−0.775259 + 0.631643i \(0.782381\pi\)
\(200\) 0 0
\(201\) −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
\(205\) 0 0
\(206\) 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
\(210\) 0 0
\(211\) 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
\(215\) 0 0
\(216\) −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
\(220\) 0 0
\(221\) 55.4143 0.250743
\(222\) 207.328 + 207.328i 0.933910 + 0.933910i
\(223\) 33.4291 33.4291i 0.149906 0.149906i −0.628170 0.778076i \(-0.716196\pi\)
0.778076 + 0.628170i \(0.216196\pi\)
\(224\) 79.9342i 0.356849i
\(225\) 0 0
\(226\) −63.8888 −0.282694
\(227\) 21.1714 + 21.1714i 0.0932662 + 0.0932662i 0.752200 0.658934i \(-0.228992\pi\)
−0.658934 + 0.752200i \(0.728992\pi\)
\(228\) −149.530 + 149.530i −0.655834 + 0.655834i
\(229\) 243.798i 1.06462i −0.846550 0.532310i \(-0.821324\pi\)
0.846550 0.532310i \(-0.178676\pi\)
\(230\) 0 0
\(231\) 11.8888 0.0514666
\(232\) −3.60612 3.60612i −0.0155436 0.0155436i
\(233\) −161.712 + 161.712i −0.694042 + 0.694042i −0.963119 0.269077i \(-0.913281\pi\)
0.269077 + 0.963119i \(0.413281\pi\)
\(234\) 139.485i 0.596088i
\(235\) 0 0
\(236\) −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 \(-0.239077\pi\)
\(240\) 0 0
\(241\) −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
\(245\) 0 0
\(246\) 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
\(250\) 0 0
\(251\) −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
\(255\) 0 0
\(256\) −119.767 −0.467841
\(257\) 89.2372 + 89.2372i 0.347227 + 0.347227i 0.859076 0.511849i \(-0.171039\pi\)
−0.511849 + 0.859076i \(0.671039\pi\)
\(258\) 122.586 122.586i 0.475138 0.475138i
\(259\) 110.293i 0.425841i
\(260\) 0 0
\(261\) 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 \(-0.378928\pi\)
0.928532 0.371253i \(-0.121072\pi\)
\(264\) 34.6515i 0.131256i
\(265\) 0 0
\(266\) 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 \(-0.00207111\pi\)
\(270\) 0 0
\(271\) −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
\(275\) 0 0
\(276\) 237.687 0.861184
\(277\) 285.510 + 285.510i 1.03072 + 1.03072i 0.999513 + 0.0312080i \(0.00993542\pi\)
0.0312080 + 0.999513i \(0.490065\pi\)
\(278\) −185.035 + 185.035i −0.665594 + 0.665594i
\(279\) 56.0908i 0.201042i
\(280\) 0 0
\(281\) 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 −0.557449 0.830211i \(-0.688220\pi\)
0.830211 + 0.557449i \(0.188220\pi\)
\(284\) 401.131i 1.41243i
\(285\) 0 0
\(286\) −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
\(290\) 0 0
\(291\) 35.7526 0.122861
\(292\) 234.707 + 234.707i 0.803792 + 0.803792i
\(293\) 236.565 236.565i 0.807390 0.807390i −0.176848 0.984238i \(-0.556590\pi\)
0.984238 + 0.176848i \(0.0565901\pi\)
\(294\) 244.126i 0.830361i
\(295\) 0 0
\(296\) 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
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) 35.3939 0.115666
\(307\) −168.969 168.969i −0.550389 0.550389i 0.376164 0.926553i \(-0.377243\pi\)
−0.926553 + 0.376164i \(0.877243\pi\)
\(308\) 28.6311 28.6311i 0.0929582 0.0929582i
\(309\) 158.611i 0.513303i
\(310\) 0 0
\(311\) 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 −0.907300 0.420484i \(-0.861860\pi\)
0.420484 + 0.907300i \(0.361860\pi\)
\(314\) 227.576i 0.724763i
\(315\) 0 0
\(316\) −144.495 −0.457262
\(317\) 427.217 + 427.217i 1.34769 + 1.34769i 0.888168 + 0.459519i \(0.151978\pi\)
0.459519 + 0.888168i \(0.348022\pi\)
\(318\) 156.384 156.384i 0.491773 0.491773i
\(319\) 2.85816i 0.00895975i
\(320\) 0 0
\(321\) −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
\(325\) 0 0
\(326\) −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
\(330\) 0 0
\(331\) 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
\(335\) 0 0
\(336\) −17.0352 −0.0507000
\(337\) −292.192 292.192i −0.867038 0.867038i 0.125105 0.992143i \(-0.460073\pi\)
−0.992143 + 0.125105i \(0.960073\pi\)
\(338\) 109.866 109.866i 0.325048 0.325048i
\(339\) 35.1714i 0.103751i
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) 154.091 0.445349
\(347\) −320.050 320.050i −0.922334 0.922334i 0.0748598 0.997194i \(-0.476149\pi\)
−0.997194 + 0.0748598i \(0.976149\pi\)
\(348\) 6.16684 6.16684i 0.0177208 0.0177208i
\(349\) 574.009i 1.64473i 0.568964 + 0.822363i \(0.307345\pi\)
−0.568964 + 0.822363i \(0.692655\pi\)
\(350\) 0 0
\(351\) 76.7878 0.218769
\(352\) −92.3281 92.3281i −0.262296 0.262296i
\(353\) −266.520 + 266.520i −0.755014 + 0.755014i −0.975410 0.220396i \(-0.929265\pi\)
0.220396 + 0.975410i \(0.429265\pi\)
\(354\) 609.984i 1.72312i
\(355\) 0 0
\(356\) 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 \(-0.0973922\pi\)
\(360\) 0 0
\(361\) −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
\(365\) 0 0
\(366\) −512.747 −1.40095
\(367\) 240.510 + 240.510i 0.655340 + 0.655340i 0.954274 0.298934i \(-0.0966311\pi\)
−0.298934 + 0.954274i \(0.596631\pi\)
\(368\) −78.9240 + 78.9240i −0.214467 + 0.214467i
\(369\) 86.0908i 0.233308i
\(370\) 0 0
\(371\) −83.1918 −0.224237
\(372\) 135.081 + 135.081i 0.363120 + 0.363120i
\(373\) 330.207 330.207i 0.885272 0.885272i −0.108792 0.994065i \(-0.534698\pi\)
0.994065 + 0.108792i \(0.0346983\pi\)
\(374\) 39.5051i 0.105629i
\(375\) 0 0
\(376\) 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 \(-0.0893551\pi\)
\(380\) 0 0
\(381\) −280.763 −0.736910
\(382\) −89.1918 89.1918i −0.233486 0.233486i
\(383\) −170.631 + 170.631i −0.445512 + 0.445512i −0.893859 0.448347i \(-0.852013\pi\)
0.448347 + 0.893859i \(0.352013\pi\)
\(384\) 293.833i 0.765191i
\(385\) 0 0
\(386\) −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 \(0.751611\pi\)
\(390\) 0 0
\(391\) −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
\(395\) 0 0
\(396\) −59.2577 −0.149641
\(397\) −45.2577 45.2577i −0.113999 0.113999i 0.647806 0.761805i \(-0.275687\pi\)
−0.761805 + 0.647806i \(0.775687\pi\)
\(398\) −559.287 + 559.287i −1.40524 + 1.40524i
\(399\) 73.4847i 0.184172i
\(400\) 0 0
\(401\) −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
\(405\) 0 0
\(406\) −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 \(0.860506\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) 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 \(-0.245118\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 0 0
\(426\) 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
\(430\) 0 0
\(431\) 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 −0.862934 0.505317i \(-0.831376\pi\)
0.505317 + 0.862934i \(0.331376\pi\)
\(434\) 120.586i 0.277847i
\(435\) 0 0
\(436\) −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 \(-0.0930148\pi\)
\(440\) 0 0
\(441\) −134.394 −0.304748
\(442\) 123.283 + 123.283i 0.278920 + 0.278920i
\(443\) 421.131 421.131i 0.950633 0.950633i −0.0482041 0.998838i \(-0.515350\pi\)
0.998838 + 0.0482041i \(0.0153498\pi\)
\(444\) 549.737i 1.23815i
\(445\) 0 0
\(446\) 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 \(0.892362\pi\)
\(450\) 0 0
\(451\) 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
\(455\) 0 0
\(456\) −214.182 −0.469697
\(457\) −285.747 285.747i −0.625267 0.625267i 0.321607 0.946873i \(-0.395777\pi\)
−0.946873 + 0.321607i \(0.895777\pi\)
\(458\) 542.388 542.388i 1.18425 1.18425i
\(459\) 19.4847i 0.0424503i
\(460\) 0 0
\(461\) 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 −0.969631 0.244573i \(-0.921352\pi\)
0.244573 + 0.969631i \(0.421352\pi\)
\(464\) 4.09540i 0.00882630i
\(465\) 0 0
\(466\) −719.535 −1.54407
\(467\) −488.742 488.742i −1.04656 1.04656i −0.998862 0.0476956i \(-0.984812\pi\)
−0.0476956 0.998862i \(-0.515188\pi\)
\(468\) 184.924 184.924i 0.395137 0.395137i
\(469\) 159.151i 0.339341i
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) −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 \(-0.0618404\pi\)
\(480\) 0 0
\(481\) −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
\(485\) 0 0
\(486\) 49.0454 0.100916
\(487\) 120.682 + 120.682i 0.247807 + 0.247807i 0.820070 0.572263i \(-0.193934\pi\)
−0.572263 + 0.820070i \(0.693934\pi\)
\(488\) −397.510 + 397.510i −0.814569 + 0.814569i
\(489\) 463.918i 0.948708i
\(490\) 0 0
\(491\) −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
\(495\) 0 0
\(496\) −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 \(-0.265680\pi\)
\(500\) 0 0
\(501\) 237.687 0.474425
\(502\) −900.448 900.448i −1.79372 1.79372i
\(503\) 406.409 406.409i 0.807970 0.807970i −0.176357 0.984326i \(-0.556431\pi\)
0.984326 + 0.176357i \(0.0564312\pi\)
\(504\) 36.7423i 0.0729015i
\(505\) 0 0
\(506\) 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 \(0.938804\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) −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 −0.558716 0.829359i \(-0.688706\pi\)
0.829359 + 0.558716i \(0.188706\pi\)
\(524\) 154.177i 0.294231i
\(525\) 0 0
\(526\) 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
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) −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
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) −165.081 −0.302345
\(547\) 446.222 + 446.222i 0.815763 + 0.815763i 0.985491 0.169728i \(-0.0542889\pi\)
−0.169728 + 0.985491i \(0.554289\pi\)
\(548\) 86.3087 86.3087i 0.157498 0.157498i
\(549\) 282.272i 0.514157i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) −490.627 −0.882422
\(557\) −214.091 214.091i −0.384364 0.384364i 0.488308 0.872672i \(-0.337614\pi\)
−0.872672 + 0.488308i \(0.837614\pi\)
\(558\) −124.788 + 124.788i −0.223634 + 0.223634i
\(559\) 470.120i 0.841003i
\(560\) 0 0
\(561\) 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 \(0.569816\pi\)
−0.976043 + 0.217579i \(0.930184\pi\)
\(564\) 285.414i 0.506054i
\(565\) 0 0
\(566\) 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 \(-0.325997\pi\)
\(570\) 0 0
\(571\) −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
\(575\) 0 0
\(576\) 310.485 0.539036
\(577\) 497.879 + 497.879i 0.862874 + 0.862874i 0.991671 0.128797i \(-0.0411114\pi\)
−0.128797 + 0.991671i \(0.541111\pi\)
\(578\) 611.669 611.669i 1.05825 1.05825i
\(579\) 189.995i 0.328144i
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) 1052.59 1.79624
\(587\) −292.783 292.783i −0.498779 0.498779i 0.412279 0.911058i \(-0.364733\pi\)
−0.911058 + 0.412279i \(0.864733\pi\)
\(588\) −323.654 + 323.654i −0.550432 + 0.550432i
\(589\) 386.969i 0.656994i
\(590\) 0 0
\(591\) −164.858 −0.278948
\(592\) −182.540 182.540i −0.308345 0.308345i
\(593\) −451.258 + 451.258i −0.760974 + 0.760974i −0.976498 0.215524i \(-0.930854\pi\)
0.215524 + 0.976498i \(0.430854\pi\)
\(594\) 54.7423i 0.0921588i
\(595\) 0 0
\(596\) −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 \(0.991268\pi\)
\(600\) 0 0
\(601\) −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
\(605\) 0 0
\(606\) −946.145 −1.56130
\(607\) −136.389 136.389i −0.224694 0.224694i 0.585778 0.810472i \(-0.300789\pi\)
−0.810472 + 0.585778i \(0.800789\pi\)
\(608\) 570.681 570.681i 0.938620 0.938620i
\(609\) 3.03062i 0.00497638i
\(610\) 0 0
\(611\) −412.808 −0.675627
\(612\) 46.9240 + 46.9240i 0.0766732 + 0.0766732i
\(613\) 12.7128 12.7128i 0.0207386 0.0207386i −0.696661 0.717400i \(-0.745332\pi\)
0.717400 + 0.696661i \(0.245332\pi\)
\(614\) 751.828i 1.22447i
\(615\) 0 0
\(616\) 41.0102 0.0665750
\(617\) 398.752 + 398.752i 0.646275 + 0.646275i 0.952091 0.305816i \(-0.0989292\pi\)
−0.305816 + 0.952091i \(0.598929\pi\)
\(618\) −352.868 + 352.868i −0.570984 + 0.570984i
\(619\) 819.131i 1.32331i 0.749807 + 0.661656i \(0.230146\pi\)
−0.749807 + 0.661656i \(0.769854\pi\)
\(620\) 0 0
\(621\) −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
\(625\) 0 0
\(626\) −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
\(630\) 0 0
\(631\) 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
\(635\) 0 0
\(636\) 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
\(640\) 0 0
\(641\) 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 \(-0.432214\pi\)
0.977411 0.211349i \(-0.0677856\pi\)
\(644\) 281.303i 0.436806i
\(645\) 0 0
\(646\) 244.182 0.377990
\(647\) −321.287 321.287i −0.496580 0.496580i 0.413792 0.910372i \(-0.364204\pi\)
−0.910372 + 0.413792i \(0.864204\pi\)
\(648\) 38.0227 38.0227i 0.0586770 0.0586770i
\(649\) 374.808i 0.577516i
\(650\) 0 0
\(651\) 66.3837 0.101972
\(652\) −1117.23 1117.23i −1.71354 1.71354i
\(653\) 169.823 169.823i 0.260066 0.260066i −0.565015 0.825081i \(-0.691130\pi\)
0.825081 + 0.565015i \(0.191130\pi\)
\(654\) 214.182i 0.327495i
\(655\) 0 0
\(656\) −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 \(0.740711\pi\)
\(660\) 0 0
\(661\) 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
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) −315.060 −0.469538
\(672\) −97.8990 97.8990i −0.145683 0.145683i
\(673\) −164.707 + 164.707i −0.244736 + 0.244736i −0.818806 0.574070i \(-0.805364\pi\)
0.574070 + 0.818806i \(0.305364\pi\)
\(674\) 1300.10i 1.92894i
\(675\) 0 0
\(676\) 291.313 0.430937
\(677\) −544.388 544.388i −0.804119 0.804119i 0.179618 0.983736i \(-0.442514\pi\)
−0.983736 + 0.179618i \(0.942514\pi\)
\(678\) 78.2474 78.2474i 0.115409 0.115409i
\(679\) 42.3133i 0.0623170i
\(680\) 0 0
\(681\) −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 \(0.552908\pi\)
−0.986218 + 0.165452i \(0.947092\pi\)
\(684\) 366.272i 0.535486i
\(685\) 0 0
\(686\) 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
\(690\) 0 0
\(691\) 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
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) 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
\(705\) 0 0
\(706\) −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 \(-0.172412\pi\)
\(710\) 0 0
\(711\) 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
\(715\) 0 0
\(716\) 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 \(0.855828\pi\)
\(720\) 0 0
\(721\) 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
\(725\) 0 0
\(726\) 598.287 0.824087
\(727\) 15.8740 + 15.8740i 0.0218349 + 0.0218349i 0.717940 0.696105i \(-0.245085\pi\)
−0.696105 + 0.717940i \(0.745085\pi\)
\(728\) −127.980 + 127.980i −0.175796 + 0.175796i
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −119.292 −0.163190
\(732\) −679.782 679.782i −0.928664 0.928664i
\(733\) 393.237 393.237i 0.536476 0.536476i −0.386016 0.922492i \(-0.626149\pi\)
0.922492 + 0.386016i \(0.126149\pi\)
\(734\) 1070.15i 1.45796i
\(735\) 0 0
\(736\) −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 \(-0.0415398\pi\)
\(740\) 0 0
\(741\) 529.757 0.714922
\(742\) −185.081 185.081i −0.249435 0.249435i
\(743\) 44.7015 44.7015i 0.0601636 0.0601636i −0.676385 0.736548i \(-0.736454\pi\)
0.736548 + 0.676385i \(0.236454\pi\)
\(744\) 193.485i 0.260060i
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) 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
\(755\) 0 0
\(756\) −62.8332 −0.0831126
\(757\) 235.925 + 235.925i 0.311658 + 0.311658i 0.845552 0.533894i \(-0.179272\pi\)
−0.533894 + 0.845552i \(0.679272\pi\)
\(758\) 467.196 467.196i 0.616354 0.616354i
\(759\) 134.919i 0.177759i
\(760\) 0 0
\(761\) −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
\(765\) 0 0
\(766\) −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 \(-0.287696\pi\)
\(770\) 0 0
\(771\) −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 \(-0.482099\pi\)
0.998419 0.0562070i \(-0.0179007\pi\)
\(774\) 300.272i 0.387949i
\(775\) 0 0
\(776\) 123.328 0.158928
\(777\) 135.081 + 135.081i 0.173849 + 0.173849i
\(778\) −1217.69 + 1217.69i −1.56515 + 1.56515i
\(779\) 593.939i 0.762437i
\(780\) 0 0
\(781\) 227.696 0.291544
\(782\) −194.070 194.070i −0.248172 0.248172i
\(783\) −3.13622 + 3.13622i −0.00400539 + 0.00400539i
\(784\) 214.939i 0.274157i
\(785\) 0 0
\(786\) 142.429