Properties

Label 108.3.k.a.5.5
Level 108
Weight 3
Character 108.5
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 108.5
Dual form 108.3.k.a.65.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.70588 - 1.29546i) q^{3} +(1.65461 + 4.54600i) q^{5} +(1.68621 + 9.56295i) q^{7} +(5.64356 - 7.01072i) q^{9} +O(q^{10})\) \(q+(2.70588 - 1.29546i) q^{3} +(1.65461 + 4.54600i) q^{5} +(1.68621 + 9.56295i) q^{7} +(5.64356 - 7.01072i) q^{9} +(5.23790 - 14.3910i) q^{11} +(-6.28432 - 5.27317i) q^{13} +(10.3663 + 10.1574i) q^{15} +(-9.01220 - 5.20319i) q^{17} +(7.17439 + 12.4264i) q^{19} +(16.9511 + 23.6918i) q^{21} +(-24.2260 - 4.27170i) q^{23} +(1.22274 - 1.02600i) q^{25} +(6.18868 - 26.2812i) q^{27} +(-20.0134 - 23.8510i) q^{29} +(-10.5226 + 59.6766i) q^{31} +(-4.46987 - 45.7258i) q^{33} +(-40.6832 + 23.4884i) q^{35} +(-0.367254 + 0.636102i) q^{37} +(-23.8358 - 6.12747i) q^{39} +(30.1540 - 35.9362i) q^{41} +(-69.9886 - 25.4738i) q^{43} +(41.2086 + 14.0556i) q^{45} +(-12.5408 + 2.21127i) q^{47} +(-42.5618 + 15.4912i) q^{49} +(-31.1265 - 2.40427i) q^{51} -36.5138i q^{53} +74.0882 q^{55} +(35.5110 + 24.3302i) q^{57} +(30.5258 + 83.8689i) q^{59} +(-7.06212 - 40.0513i) q^{61} +(76.5594 + 42.1476i) q^{63} +(13.5737 - 37.2935i) q^{65} +(61.6114 + 51.6981i) q^{67} +(-71.0865 + 19.8251i) q^{69} +(0.595295 + 0.343694i) q^{71} +(13.7680 + 23.8468i) q^{73} +(1.97944 - 4.36025i) q^{75} +(146.453 + 25.8236i) q^{77} +(97.1709 - 81.5361i) q^{79} +(-17.3004 - 79.1309i) q^{81} +(-8.62013 - 10.2731i) q^{83} +(8.74206 - 49.5787i) q^{85} +(-85.0518 - 38.6114i) q^{87} +(-146.234 + 84.4283i) q^{89} +(39.8304 - 68.9883i) q^{91} +(48.8358 + 175.109i) q^{93} +(-44.6196 + 53.1756i) q^{95} +(-60.2262 - 21.9205i) q^{97} +(-71.3309 - 117.938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.70588 1.29546i 0.901960 0.431820i
\(4\) 0 0
\(5\) 1.65461 + 4.54600i 0.330922 + 0.909200i 0.987873 + 0.155266i \(0.0496236\pi\)
−0.656951 + 0.753933i \(0.728154\pi\)
\(6\) 0 0
\(7\) 1.68621 + 9.56295i 0.240887 + 1.36614i 0.829855 + 0.557980i \(0.188423\pi\)
−0.588968 + 0.808156i \(0.700466\pi\)
\(8\) 0 0
\(9\) 5.64356 7.01072i 0.627063 0.778969i
\(10\) 0 0
\(11\) 5.23790 14.3910i 0.476173 1.30827i −0.436545 0.899682i \(-0.643798\pi\)
0.912718 0.408591i \(-0.133980\pi\)
\(12\) 0 0
\(13\) −6.28432 5.27317i −0.483409 0.405629i 0.368248 0.929728i \(-0.379958\pi\)
−0.851657 + 0.524099i \(0.824402\pi\)
\(14\) 0 0
\(15\) 10.3663 + 10.1574i 0.691089 + 0.677163i
\(16\) 0 0
\(17\) −9.01220 5.20319i −0.530129 0.306070i 0.210940 0.977499i \(-0.432348\pi\)
−0.741069 + 0.671429i \(0.765681\pi\)
\(18\) 0 0
\(19\) 7.17439 + 12.4264i 0.377599 + 0.654021i 0.990712 0.135974i \(-0.0434163\pi\)
−0.613113 + 0.789995i \(0.710083\pi\)
\(20\) 0 0
\(21\) 16.9511 + 23.6918i 0.807195 + 1.12818i
\(22\) 0 0
\(23\) −24.2260 4.27170i −1.05330 0.185726i −0.379921 0.925019i \(-0.624049\pi\)
−0.673384 + 0.739293i \(0.735160\pi\)
\(24\) 0 0
\(25\) 1.22274 1.02600i 0.0489096 0.0410401i
\(26\) 0 0
\(27\) 6.18868 26.2812i 0.229211 0.973377i
\(28\) 0 0
\(29\) −20.0134 23.8510i −0.690116 0.822449i 0.301253 0.953544i \(-0.402595\pi\)
−0.991370 + 0.131095i \(0.958151\pi\)
\(30\) 0 0
\(31\) −10.5226 + 59.6766i −0.339439 + 1.92505i 0.0385845 + 0.999255i \(0.487715\pi\)
−0.378023 + 0.925796i \(0.623396\pi\)
\(32\) 0 0
\(33\) −4.46987 45.7258i −0.135451 1.38563i
\(34\) 0 0
\(35\) −40.6832 + 23.4884i −1.16238 + 0.671098i
\(36\) 0 0
\(37\) −0.367254 + 0.636102i −0.00992578 + 0.0171920i −0.870946 0.491379i \(-0.836493\pi\)
0.861020 + 0.508571i \(0.169826\pi\)
\(38\) 0 0
\(39\) −23.8358 6.12747i −0.611174 0.157115i
\(40\) 0 0
\(41\) 30.1540 35.9362i 0.735465 0.876493i −0.260570 0.965455i \(-0.583911\pi\)
0.996035 + 0.0889623i \(0.0283551\pi\)
\(42\) 0 0
\(43\) −69.9886 25.4738i −1.62764 0.592413i −0.642826 0.766012i \(-0.722238\pi\)
−0.984816 + 0.173599i \(0.944460\pi\)
\(44\) 0 0
\(45\) 41.2086 + 14.0556i 0.915747 + 0.312347i
\(46\) 0 0
\(47\) −12.5408 + 2.21127i −0.266824 + 0.0470484i −0.305460 0.952205i \(-0.598810\pi\)
0.0386351 + 0.999253i \(0.487699\pi\)
\(48\) 0 0
\(49\) −42.5618 + 15.4912i −0.868609 + 0.316148i
\(50\) 0 0
\(51\) −31.1265 2.40427i −0.610323 0.0471425i
\(52\) 0 0
\(53\) 36.5138i 0.688940i −0.938797 0.344470i \(-0.888059\pi\)
0.938797 0.344470i \(-0.111941\pi\)
\(54\) 0 0
\(55\) 74.0882 1.34706
\(56\) 0 0
\(57\) 35.5110 + 24.3302i 0.622999 + 0.426846i
\(58\) 0 0
\(59\) 30.5258 + 83.8689i 0.517386 + 1.42151i 0.873390 + 0.487022i \(0.161917\pi\)
−0.356004 + 0.934484i \(0.615861\pi\)
\(60\) 0 0
\(61\) −7.06212 40.0513i −0.115772 0.656578i −0.986365 0.164573i \(-0.947375\pi\)
0.870592 0.492005i \(-0.163736\pi\)
\(62\) 0 0
\(63\) 76.5594 + 42.1476i 1.21523 + 0.669009i
\(64\) 0 0
\(65\) 13.5737 37.2935i 0.208827 0.573747i
\(66\) 0 0
\(67\) 61.6114 + 51.6981i 0.919573 + 0.771613i 0.973916 0.226909i \(-0.0728621\pi\)
−0.0543434 + 0.998522i \(0.517307\pi\)
\(68\) 0 0
\(69\) −71.0865 + 19.8251i −1.03024 + 0.287321i
\(70\) 0 0
\(71\) 0.595295 + 0.343694i 0.00838443 + 0.00484075i 0.504186 0.863595i \(-0.331792\pi\)
−0.495802 + 0.868436i \(0.665126\pi\)
\(72\) 0 0
\(73\) 13.7680 + 23.8468i 0.188603 + 0.326669i 0.944785 0.327692i \(-0.106271\pi\)
−0.756182 + 0.654361i \(0.772938\pi\)
\(74\) 0 0
\(75\) 1.97944 4.36025i 0.0263926 0.0581366i
\(76\) 0 0
\(77\) 146.453 + 25.8236i 1.90198 + 0.335371i
\(78\) 0 0
\(79\) 97.1709 81.5361i 1.23001 1.03210i 0.231774 0.972770i \(-0.425547\pi\)
0.998238 0.0593327i \(-0.0188973\pi\)
\(80\) 0 0
\(81\) −17.3004 79.1309i −0.213585 0.976924i
\(82\) 0 0
\(83\) −8.62013 10.2731i −0.103857 0.123772i 0.711612 0.702573i \(-0.247965\pi\)
−0.815469 + 0.578801i \(0.803521\pi\)
\(84\) 0 0
\(85\) 8.74206 49.5787i 0.102848 0.583279i
\(86\) 0 0
\(87\) −85.0518 38.6114i −0.977607 0.443809i
\(88\) 0 0
\(89\) −146.234 + 84.4283i −1.64308 + 0.948632i −0.663349 + 0.748310i \(0.730866\pi\)
−0.979730 + 0.200323i \(0.935801\pi\)
\(90\) 0 0
\(91\) 39.8304 68.9883i 0.437697 0.758113i
\(92\) 0 0
\(93\) 48.8358 + 175.109i 0.525116 + 1.88290i
\(94\) 0 0
\(95\) −44.6196 + 53.1756i −0.469680 + 0.559743i
\(96\) 0 0
\(97\) −60.2262 21.9205i −0.620888 0.225985i 0.0123723 0.999923i \(-0.496062\pi\)
−0.633261 + 0.773939i \(0.718284\pi\)
\(98\) 0 0
\(99\) −71.3309 117.938i −0.720514 1.19129i
\(100\) 0 0
\(101\) 182.669 32.2094i 1.80860 0.318905i 0.835537 0.549434i \(-0.185157\pi\)
0.973065 + 0.230529i \(0.0740456\pi\)
\(102\) 0 0
\(103\) −65.2417 + 23.7460i −0.633415 + 0.230544i −0.638717 0.769442i \(-0.720534\pi\)
0.00530214 + 0.999986i \(0.498312\pi\)
\(104\) 0 0
\(105\) −79.6553 + 116.260i −0.758622 + 1.10724i
\(106\) 0 0
\(107\) 44.4428i 0.415353i 0.978198 + 0.207677i \(0.0665902\pi\)
−0.978198 + 0.207677i \(0.933410\pi\)
\(108\) 0 0
\(109\) 5.37221 0.0492863 0.0246432 0.999696i \(-0.492155\pi\)
0.0246432 + 0.999696i \(0.492155\pi\)
\(110\) 0 0
\(111\) −0.169699 + 2.19698i −0.00152882 + 0.0197926i
\(112\) 0 0
\(113\) 20.2350 + 55.5953i 0.179071 + 0.491994i 0.996458 0.0840959i \(-0.0268002\pi\)
−0.817387 + 0.576089i \(0.804578\pi\)
\(114\) 0 0
\(115\) −20.6654 117.199i −0.179699 1.01912i
\(116\) 0 0
\(117\) −72.4347 + 14.2981i −0.619100 + 0.122206i
\(118\) 0 0
\(119\) 34.5615 94.9569i 0.290433 0.797957i
\(120\) 0 0
\(121\) −86.9742 72.9800i −0.718795 0.603141i
\(122\) 0 0
\(123\) 35.0393 136.302i 0.284872 1.10815i
\(124\) 0 0
\(125\) 111.428 + 64.3328i 0.891422 + 0.514663i
\(126\) 0 0
\(127\) −11.7617 20.3718i −0.0926117 0.160408i 0.815998 0.578055i \(-0.196188\pi\)
−0.908609 + 0.417647i \(0.862855\pi\)
\(128\) 0 0
\(129\) −222.381 + 21.7386i −1.72388 + 0.168516i
\(130\) 0 0
\(131\) 98.3090 + 17.3345i 0.750451 + 0.132325i 0.535775 0.844361i \(-0.320019\pi\)
0.214676 + 0.976685i \(0.431131\pi\)
\(132\) 0 0
\(133\) −106.736 + 89.5618i −0.802524 + 0.673397i
\(134\) 0 0
\(135\) 129.714 15.3513i 0.960845 0.113713i
\(136\) 0 0
\(137\) −29.3994 35.0368i −0.214594 0.255743i 0.648000 0.761641i \(-0.275606\pi\)
−0.862594 + 0.505898i \(0.831161\pi\)
\(138\) 0 0
\(139\) −16.9605 + 96.1879i −0.122018 + 0.691999i 0.861016 + 0.508577i \(0.169828\pi\)
−0.983034 + 0.183422i \(0.941283\pi\)
\(140\) 0 0
\(141\) −31.0691 + 22.2295i −0.220348 + 0.157656i
\(142\) 0 0
\(143\) −108.803 + 62.8174i −0.760860 + 0.439282i
\(144\) 0 0
\(145\) 75.3124 130.445i 0.519396 0.899620i
\(146\) 0 0
\(147\) −95.0989 + 97.0546i −0.646931 + 0.660235i
\(148\) 0 0
\(149\) −115.756 + 137.952i −0.776884 + 0.925854i −0.998788 0.0492145i \(-0.984328\pi\)
0.221905 + 0.975068i \(0.428773\pi\)
\(150\) 0 0
\(151\) 52.3251 + 19.0448i 0.346524 + 0.126124i 0.509418 0.860519i \(-0.329861\pi\)
−0.162894 + 0.986644i \(0.552083\pi\)
\(152\) 0 0
\(153\) −87.3390 + 33.8174i −0.570843 + 0.221029i
\(154\) 0 0
\(155\) −288.700 + 50.9057i −1.86258 + 0.328424i
\(156\) 0 0
\(157\) −0.737193 + 0.268316i −0.00469550 + 0.00170902i −0.344367 0.938835i \(-0.611906\pi\)
0.339671 + 0.940544i \(0.389684\pi\)
\(158\) 0 0
\(159\) −47.3023 98.8020i −0.297498 0.621396i
\(160\) 0 0
\(161\) 238.875i 1.48370i
\(162\) 0 0
\(163\) 292.245 1.79292 0.896458 0.443128i \(-0.146131\pi\)
0.896458 + 0.443128i \(0.146131\pi\)
\(164\) 0 0
\(165\) 200.474 95.9783i 1.21499 0.581687i
\(166\) 0 0
\(167\) −86.5719 237.854i −0.518395 1.42428i −0.872288 0.488992i \(-0.837365\pi\)
0.353893 0.935286i \(-0.384858\pi\)
\(168\) 0 0
\(169\) −17.6602 100.156i −0.104498 0.592638i
\(170\) 0 0
\(171\) 127.607 + 19.8316i 0.746241 + 0.115974i
\(172\) 0 0
\(173\) 15.4798 42.5305i 0.0894788 0.245841i −0.886879 0.462002i \(-0.847131\pi\)
0.976358 + 0.216161i \(0.0693535\pi\)
\(174\) 0 0
\(175\) 11.8734 + 9.96296i 0.0678480 + 0.0569312i
\(176\) 0 0
\(177\) 191.248 + 187.394i 1.08050 + 1.05872i
\(178\) 0 0
\(179\) 292.829 + 169.065i 1.63592 + 0.944498i 0.982218 + 0.187745i \(0.0601179\pi\)
0.653701 + 0.756753i \(0.273215\pi\)
\(180\) 0 0
\(181\) 44.0372 + 76.2746i 0.243299 + 0.421407i 0.961652 0.274272i \(-0.0884369\pi\)
−0.718353 + 0.695679i \(0.755104\pi\)
\(182\) 0 0
\(183\) −70.9941 99.2252i −0.387946 0.542214i
\(184\) 0 0
\(185\) −3.49938 0.617035i −0.0189156 0.00333533i
\(186\) 0 0
\(187\) −122.084 + 102.441i −0.652857 + 0.547812i
\(188\) 0 0
\(189\) 261.761 + 14.8666i 1.38498 + 0.0786593i
\(190\) 0 0
\(191\) 73.2854 + 87.3382i 0.383693 + 0.457268i 0.922976 0.384857i \(-0.125749\pi\)
−0.539283 + 0.842125i \(0.681305\pi\)
\(192\) 0 0
\(193\) −28.7710 + 163.168i −0.149073 + 0.845432i 0.814934 + 0.579554i \(0.196773\pi\)
−0.964007 + 0.265878i \(0.914338\pi\)
\(194\) 0 0
\(195\) −11.5834 118.496i −0.0594022 0.607672i
\(196\) 0 0
\(197\) −147.151 + 84.9579i −0.746962 + 0.431259i −0.824595 0.565723i \(-0.808597\pi\)
0.0776334 + 0.996982i \(0.475264\pi\)
\(198\) 0 0
\(199\) −143.965 + 249.355i −0.723444 + 1.25304i 0.236167 + 0.971712i \(0.424109\pi\)
−0.959611 + 0.281329i \(0.909225\pi\)
\(200\) 0 0
\(201\) 233.686 + 60.0736i 1.16262 + 0.298874i
\(202\) 0 0
\(203\) 194.339 231.605i 0.957337 1.14091i
\(204\) 0 0
\(205\) 213.259 + 77.6199i 1.04029 + 0.378634i
\(206\) 0 0
\(207\) −166.669 + 145.734i −0.805163 + 0.704030i
\(208\) 0 0
\(209\) 216.407 38.1584i 1.03544 0.182576i
\(210\) 0 0
\(211\) 167.189 60.8519i 0.792366 0.288398i 0.0860469 0.996291i \(-0.472576\pi\)
0.706319 + 0.707893i \(0.250354\pi\)
\(212\) 0 0
\(213\) 2.05604 + 0.158812i 0.00965276 + 0.000745597i
\(214\) 0 0
\(215\) 360.317i 1.67589i
\(216\) 0 0
\(217\) −588.428 −2.71165
\(218\) 0 0
\(219\) 68.1472 + 46.6908i 0.311174 + 0.213200i
\(220\) 0 0
\(221\) 29.1982 + 80.2214i 0.132119 + 0.362993i
\(222\) 0 0
\(223\) 25.5930 + 145.145i 0.114767 + 0.650874i 0.986865 + 0.161544i \(0.0516475\pi\)
−0.872099 + 0.489330i \(0.837241\pi\)
\(224\) 0 0
\(225\) −0.292394 14.3626i −0.00129953 0.0638338i
\(226\) 0 0
\(227\) −108.612 + 298.408i −0.478465 + 1.31457i 0.432331 + 0.901715i \(0.357691\pi\)
−0.910796 + 0.412857i \(0.864531\pi\)
\(228\) 0 0
\(229\) 71.8167 + 60.2614i 0.313610 + 0.263150i 0.785982 0.618249i \(-0.212158\pi\)
−0.472372 + 0.881399i \(0.656602\pi\)
\(230\) 0 0
\(231\) 429.737 119.848i 1.86033 0.518824i
\(232\) 0 0
\(233\) −198.373 114.531i −0.851387 0.491549i 0.00973138 0.999953i \(-0.496902\pi\)
−0.861119 + 0.508404i \(0.830236\pi\)
\(234\) 0 0
\(235\) −30.8025 53.3514i −0.131074 0.227027i
\(236\) 0 0
\(237\) 157.306 346.508i 0.663738 1.46206i
\(238\) 0 0
\(239\) −397.341 70.0620i −1.66252 0.293147i −0.738146 0.674641i \(-0.764298\pi\)
−0.924371 + 0.381495i \(0.875409\pi\)
\(240\) 0 0
\(241\) 107.338 90.0675i 0.445387 0.373724i −0.392334 0.919823i \(-0.628332\pi\)
0.837721 + 0.546099i \(0.183888\pi\)
\(242\) 0 0
\(243\) −149.324 191.707i −0.614501 0.788916i
\(244\) 0 0
\(245\) −140.846 167.854i −0.574883 0.685118i
\(246\) 0 0
\(247\) 20.4404 115.923i 0.0827547 0.469325i
\(248\) 0 0
\(249\) −36.6334 16.6306i −0.147122 0.0667897i
\(250\) 0 0
\(251\) −189.721 + 109.536i −0.755862 + 0.436397i −0.827808 0.561011i \(-0.810412\pi\)
0.0719458 + 0.997409i \(0.477079\pi\)
\(252\) 0 0
\(253\) −188.367 + 326.262i −0.744535 + 1.28957i
\(254\) 0 0
\(255\) −40.5723 145.479i −0.159107 0.570506i
\(256\) 0 0
\(257\) −57.7595 + 68.8350i −0.224745 + 0.267841i −0.866620 0.498969i \(-0.833712\pi\)
0.641875 + 0.766809i \(0.278157\pi\)
\(258\) 0 0
\(259\) −6.70228 2.43943i −0.0258775 0.00941865i
\(260\) 0 0
\(261\) −280.160 + 5.70350i −1.07341 + 0.0218525i
\(262\) 0 0
\(263\) −159.024 + 28.0401i −0.604652 + 0.106617i −0.467589 0.883946i \(-0.654877\pi\)
−0.137063 + 0.990562i \(0.543766\pi\)
\(264\) 0 0
\(265\) 165.992 60.4161i 0.626384 0.227985i
\(266\) 0 0
\(267\) −286.318 + 417.893i −1.07235 + 1.56514i
\(268\) 0 0
\(269\) 350.503i 1.30299i −0.758655 0.651493i \(-0.774143\pi\)
0.758655 0.651493i \(-0.225857\pi\)
\(270\) 0 0
\(271\) −60.6565 −0.223825 −0.111912 0.993718i \(-0.535698\pi\)
−0.111912 + 0.993718i \(0.535698\pi\)
\(272\) 0 0
\(273\) 18.4046 238.273i 0.0674163 0.872794i
\(274\) 0 0
\(275\) −8.36060 22.9706i −0.0304022 0.0835293i
\(276\) 0 0
\(277\) 70.9181 + 402.197i 0.256022 + 1.45197i 0.793435 + 0.608654i \(0.208290\pi\)
−0.537413 + 0.843319i \(0.680599\pi\)
\(278\) 0 0
\(279\) 358.991 + 410.560i 1.28671 + 1.47154i
\(280\) 0 0
\(281\) 1.62253 4.45786i 0.00577413 0.0158643i −0.936772 0.349940i \(-0.886202\pi\)
0.942546 + 0.334076i \(0.108424\pi\)
\(282\) 0 0
\(283\) −66.7804 56.0354i −0.235973 0.198005i 0.517131 0.855906i \(-0.327000\pi\)
−0.753104 + 0.657901i \(0.771444\pi\)
\(284\) 0 0
\(285\) −51.8484 + 201.690i −0.181924 + 0.707683i
\(286\) 0 0
\(287\) 394.502 + 227.766i 1.37457 + 0.793609i
\(288\) 0 0
\(289\) −90.3535 156.497i −0.312642 0.541512i
\(290\) 0 0
\(291\) −191.362 + 18.7063i −0.657601 + 0.0642829i
\(292\) 0 0
\(293\) −254.252 44.8315i −0.867754 0.153009i −0.277990 0.960584i \(-0.589668\pi\)
−0.589764 + 0.807575i \(0.700779\pi\)
\(294\) 0 0
\(295\) −330.760 + 277.540i −1.12122 + 0.940814i
\(296\) 0 0
\(297\) −345.797 226.720i −1.16430 0.763366i
\(298\) 0 0
\(299\) 129.719 + 154.593i 0.433841 + 0.517032i
\(300\) 0 0
\(301\) 125.589 712.252i 0.417240 2.36629i
\(302\) 0 0
\(303\) 452.554 323.795i 1.49358 1.06863i
\(304\) 0 0
\(305\) 170.388 98.3735i 0.558649 0.322536i
\(306\) 0 0
\(307\) 189.250 327.790i 0.616449 1.06772i −0.373679 0.927558i \(-0.621904\pi\)
0.990128 0.140163i \(-0.0447628\pi\)
\(308\) 0 0
\(309\) −145.774 + 148.772i −0.471761 + 0.481463i
\(310\) 0 0
\(311\) 174.625 208.110i 0.561497 0.669165i −0.408366 0.912818i \(-0.633901\pi\)
0.969863 + 0.243653i \(0.0783457\pi\)
\(312\) 0 0
\(313\) 382.853 + 139.347i 1.22317 + 0.445198i 0.871254 0.490833i \(-0.163307\pi\)
0.351918 + 0.936031i \(0.385530\pi\)
\(314\) 0 0
\(315\) −64.9271 + 417.777i −0.206118 + 1.32627i
\(316\) 0 0
\(317\) −236.114 + 41.6333i −0.744840 + 0.131335i −0.533173 0.846006i \(-0.679000\pi\)
−0.211667 + 0.977342i \(0.567889\pi\)
\(318\) 0 0
\(319\) −448.068 + 163.083i −1.40460 + 0.511233i
\(320\) 0 0
\(321\) 57.5739 + 120.257i 0.179358 + 0.374632i
\(322\) 0 0
\(323\) 149.319i 0.462288i
\(324\) 0 0
\(325\) −13.0944 −0.0402904
\(326\) 0 0
\(327\) 14.5365 6.95948i 0.0444543 0.0212828i
\(328\) 0 0
\(329\) −42.2926 116.198i −0.128549 0.353185i
\(330\) 0 0
\(331\) −33.9255 192.401i −0.102494 0.581272i −0.992192 0.124722i \(-0.960196\pi\)
0.889698 0.456550i \(-0.150915\pi\)
\(332\) 0 0
\(333\) 2.38692 + 6.16460i 0.00716791 + 0.0185123i
\(334\) 0 0
\(335\) −133.077 + 365.625i −0.397244 + 1.09142i
\(336\) 0 0
\(337\) 4.83567 + 4.05761i 0.0143492 + 0.0120404i 0.649934 0.759991i \(-0.274797\pi\)
−0.635585 + 0.772031i \(0.719241\pi\)
\(338\) 0 0
\(339\) 126.775 + 124.220i 0.373968 + 0.366432i
\(340\) 0 0
\(341\) 803.690 + 464.011i 2.35686 + 1.36074i
\(342\) 0 0
\(343\) 17.9967 + 31.1712i 0.0524685 + 0.0908781i
\(344\) 0 0
\(345\) −207.745 290.356i −0.602160 0.841612i
\(346\) 0 0
\(347\) −368.103 64.9065i −1.06082 0.187050i −0.384097 0.923293i \(-0.625487\pi\)
−0.676718 + 0.736242i \(0.736598\pi\)
\(348\) 0 0
\(349\) 370.783 311.123i 1.06241 0.891471i 0.0680703 0.997681i \(-0.478316\pi\)
0.994344 + 0.106209i \(0.0338713\pi\)
\(350\) 0 0
\(351\) −177.477 + 132.525i −0.505632 + 0.377565i
\(352\) 0 0
\(353\) 371.609 + 442.866i 1.05272 + 1.25458i 0.966054 + 0.258340i \(0.0831756\pi\)
0.0866620 + 0.996238i \(0.472380\pi\)
\(354\) 0 0
\(355\) −0.577451 + 3.27489i −0.00162662 + 0.00922503i
\(356\) 0 0
\(357\) −29.4937 301.715i −0.0826155 0.845140i
\(358\) 0 0
\(359\) 305.985 176.661i 0.852326 0.492091i −0.00910901 0.999959i \(-0.502900\pi\)
0.861435 + 0.507868i \(0.169566\pi\)
\(360\) 0 0
\(361\) 77.5563 134.331i 0.214837 0.372109i
\(362\) 0 0
\(363\) −329.884 84.8034i −0.908773 0.233618i
\(364\) 0 0
\(365\) −85.6271 + 102.046i −0.234595 + 0.279579i
\(366\) 0 0
\(367\) −391.598 142.530i −1.06702 0.388365i −0.251962 0.967737i \(-0.581076\pi\)
−0.815063 + 0.579372i \(0.803298\pi\)
\(368\) 0 0
\(369\) −81.7624 414.210i −0.221578 1.12252i
\(370\) 0 0
\(371\) 349.180 61.5699i 0.941186 0.165957i
\(372\) 0 0
\(373\) 529.096 192.575i 1.41849 0.516287i 0.484879 0.874581i \(-0.338864\pi\)
0.933609 + 0.358294i \(0.116641\pi\)
\(374\) 0 0
\(375\) 384.851 + 29.7266i 1.02627 + 0.0792709i
\(376\) 0 0
\(377\) 255.421i 0.677510i
\(378\) 0 0
\(379\) −43.1728 −0.113912 −0.0569562 0.998377i \(-0.518140\pi\)
−0.0569562 + 0.998377i \(0.518140\pi\)
\(380\) 0 0
\(381\) −58.2166 39.8869i −0.152800 0.104690i
\(382\) 0 0
\(383\) 18.4613 + 50.7221i 0.0482019 + 0.132434i 0.961458 0.274953i \(-0.0886623\pi\)
−0.913256 + 0.407387i \(0.866440\pi\)
\(384\) 0 0
\(385\) 124.928 + 708.502i 0.324488 + 1.84026i
\(386\) 0 0
\(387\) −573.575 + 346.908i −1.48211 + 0.896403i
\(388\) 0 0
\(389\) 6.35035 17.4474i 0.0163248 0.0448520i −0.931263 0.364349i \(-0.881292\pi\)
0.947587 + 0.319497i \(0.103514\pi\)
\(390\) 0 0
\(391\) 196.103 + 164.550i 0.501542 + 0.420844i
\(392\) 0 0
\(393\) 288.469 80.4504i 0.734017 0.204708i
\(394\) 0 0
\(395\) 531.443 + 306.829i 1.34542 + 0.776781i
\(396\) 0 0
\(397\) −76.9302 133.247i −0.193779 0.335635i 0.752721 0.658340i \(-0.228741\pi\)
−0.946500 + 0.322705i \(0.895408\pi\)
\(398\) 0 0
\(399\) −172.790 + 380.615i −0.433057 + 0.953923i
\(400\) 0 0
\(401\) 360.952 + 63.6455i 0.900129 + 0.158717i 0.604518 0.796592i \(-0.293366\pi\)
0.295611 + 0.955308i \(0.404477\pi\)
\(402\) 0 0
\(403\) 380.812 319.539i 0.944944 0.792902i
\(404\) 0 0
\(405\) 331.103 209.578i 0.817539 0.517477i
\(406\) 0 0
\(407\) 7.23052 + 8.61699i 0.0177654 + 0.0211720i
\(408\) 0 0
\(409\) 47.8328 271.273i 0.116951 0.663260i −0.868815 0.495136i \(-0.835118\pi\)
0.985766 0.168124i \(-0.0537707\pi\)
\(410\) 0 0
\(411\) −124.940 56.7196i −0.303990 0.138004i
\(412\) 0 0
\(413\) −750.561 + 433.337i −1.81734 + 1.04924i
\(414\) 0 0
\(415\) 32.4384 56.1850i 0.0781648 0.135385i
\(416\) 0 0
\(417\) 78.7145 + 282.244i 0.188764 + 0.676845i
\(418\) 0 0
\(419\) 80.8046 96.2992i 0.192851 0.229831i −0.660951 0.750429i \(-0.729847\pi\)
0.853802 + 0.520598i \(0.174291\pi\)
\(420\) 0 0
\(421\) −137.678 50.1109i −0.327027 0.119028i 0.173289 0.984871i \(-0.444561\pi\)
−0.500316 + 0.865843i \(0.666783\pi\)
\(422\) 0 0
\(423\) −55.2719 + 100.399i −0.130666 + 0.237350i
\(424\) 0 0
\(425\) −16.3581 + 2.88437i −0.0384896 + 0.00678675i
\(426\) 0 0
\(427\) 371.100 135.069i 0.869087 0.316322i
\(428\) 0 0
\(429\) −213.030 + 310.926i −0.496574 + 0.724770i
\(430\) 0 0
\(431\) 534.529i 1.24021i −0.784520 0.620103i \(-0.787091\pi\)
0.784520 0.620103i \(-0.212909\pi\)
\(432\) 0 0
\(433\) −46.7148 −0.107886 −0.0539431 0.998544i \(-0.517179\pi\)
−0.0539431 + 0.998544i \(0.517179\pi\)
\(434\) 0 0
\(435\) 34.8000 450.532i 0.0799999 1.03571i
\(436\) 0 0
\(437\) −120.725 331.689i −0.276258 0.759014i
\(438\) 0 0
\(439\) −56.0382 317.808i −0.127650 0.723937i −0.979699 0.200475i \(-0.935751\pi\)
0.852049 0.523462i \(-0.175360\pi\)
\(440\) 0 0
\(441\) −131.596 + 385.815i −0.298403 + 0.874863i
\(442\) 0 0
\(443\) −2.37683 + 6.53028i −0.00536530 + 0.0147410i −0.942346 0.334639i \(-0.891386\pi\)
0.936981 + 0.349380i \(0.113608\pi\)
\(444\) 0 0
\(445\) −625.771 525.084i −1.40623 1.17996i
\(446\) 0 0
\(447\) −134.509 + 523.239i −0.300915 + 1.17056i
\(448\) 0 0
\(449\) −711.494 410.781i −1.58462 0.914880i −0.994172 0.107804i \(-0.965618\pi\)
−0.590447 0.807076i \(-0.701049\pi\)
\(450\) 0 0
\(451\) −359.214 622.177i −0.796484 1.37955i
\(452\) 0 0
\(453\) 166.257 16.2523i 0.367014 0.0358769i
\(454\) 0 0
\(455\) 379.525 + 66.9204i 0.834120 + 0.147078i
\(456\) 0 0
\(457\) 4.39384 3.68687i 0.00961453 0.00806755i −0.637968 0.770063i \(-0.720225\pi\)
0.647582 + 0.761996i \(0.275780\pi\)
\(458\) 0 0
\(459\) −192.520 + 204.650i −0.419433 + 0.445861i
\(460\) 0 0
\(461\) −75.4026 89.8613i −0.163563 0.194927i 0.678038 0.735027i \(-0.262831\pi\)
−0.841601 + 0.540100i \(0.818386\pi\)
\(462\) 0 0
\(463\) −75.4724 + 428.025i −0.163007 + 0.924460i 0.788088 + 0.615563i \(0.211071\pi\)
−0.951095 + 0.308898i \(0.900040\pi\)
\(464\) 0 0
\(465\) −715.242 + 511.745i −1.53816 + 1.10053i
\(466\) 0 0
\(467\) 419.536 242.219i 0.898365 0.518671i 0.0216955 0.999765i \(-0.493094\pi\)
0.876669 + 0.481093i \(0.159760\pi\)
\(468\) 0 0
\(469\) −390.497 + 676.360i −0.832616 + 1.44213i
\(470\) 0 0
\(471\) −1.64716 + 1.68104i −0.00349716 + 0.00356908i
\(472\) 0 0
\(473\) −733.187 + 873.778i −1.55008 + 1.84731i
\(474\) 0 0
\(475\) 21.5219 + 7.83334i 0.0453093 + 0.0164912i
\(476\) 0 0
\(477\) −255.988 206.068i −0.536663 0.432009i
\(478\) 0 0
\(479\) −168.511 + 29.7130i −0.351798 + 0.0620314i −0.346755 0.937956i \(-0.612716\pi\)
−0.00504299 + 0.999987i \(0.501605\pi\)
\(480\) 0 0
\(481\) 5.66222 2.06088i 0.0117718 0.00428457i
\(482\) 0 0
\(483\) −309.453 646.367i −0.640690 1.33823i
\(484\) 0 0
\(485\) 310.058i 0.639295i
\(486\) 0 0
\(487\) −144.274 −0.296250 −0.148125 0.988969i \(-0.547324\pi\)
−0.148125 + 0.988969i \(0.547324\pi\)
\(488\) 0 0
\(489\) 790.781 378.592i 1.61714 0.774218i
\(490\) 0 0
\(491\) 34.2046 + 93.9763i 0.0696631 + 0.191398i 0.969638 0.244543i \(-0.0786379\pi\)
−0.899975 + 0.435941i \(0.856416\pi\)
\(492\) 0 0
\(493\) 56.2630 + 319.084i 0.114124 + 0.647228i
\(494\) 0 0
\(495\) 418.121 519.411i 0.844689 1.04932i
\(496\) 0 0
\(497\) −2.28294 + 6.27231i −0.00459343 + 0.0126203i
\(498\) 0 0
\(499\) −219.429 184.123i −0.439738 0.368984i 0.395873 0.918305i \(-0.370442\pi\)
−0.835611 + 0.549321i \(0.814886\pi\)
\(500\) 0 0
\(501\) −542.384 531.455i −1.08260 1.06079i
\(502\) 0 0
\(503\) −369.781 213.493i −0.735150 0.424439i 0.0851531 0.996368i \(-0.472862\pi\)
−0.820303 + 0.571929i \(0.806195\pi\)
\(504\) 0 0
\(505\) 448.669 + 777.118i 0.888454 + 1.53885i
\(506\) 0 0
\(507\) −177.534 248.132i −0.350166 0.489412i
\(508\) 0 0
\(509\) 699.518 + 123.344i 1.37430 + 0.242326i 0.811541 0.584296i \(-0.198629\pi\)
0.562758 + 0.826622i \(0.309740\pi\)
\(510\) 0 0
\(511\) −204.831 + 171.873i −0.400843 + 0.336347i
\(512\) 0 0
\(513\) 370.981 111.648i 0.723159 0.217638i
\(514\) 0 0
\(515\) −215.899 257.298i −0.419221 0.499608i
\(516\) 0 0
\(517\) −33.8647 + 192.056i −0.0655024 + 0.371483i
\(518\) 0 0
\(519\) −13.2100 135.136i −0.0254529 0.260378i
\(520\) 0 0
\(521\) −391.760 + 226.183i −0.751939 + 0.434132i −0.826394 0.563092i \(-0.809612\pi\)
0.0744554 + 0.997224i \(0.476278\pi\)
\(522\) 0 0
\(523\) 53.9338 93.4160i 0.103124 0.178616i −0.809846 0.586642i \(-0.800450\pi\)
0.912970 + 0.408026i \(0.133783\pi\)
\(524\) 0 0
\(525\) 45.0346 + 11.5771i 0.0857802 + 0.0220515i
\(526\) 0 0
\(527\) 405.341 483.066i 0.769147 0.916634i
\(528\) 0 0
\(529\) 71.5545 + 26.0437i 0.135264 + 0.0492320i
\(530\) 0 0
\(531\) 760.255 + 259.312i 1.43174 + 0.488346i
\(532\) 0 0
\(533\) −378.995 + 66.8271i −0.711061 + 0.125379i
\(534\) 0 0
\(535\) −202.037 + 73.5354i −0.377639 + 0.137449i
\(536\) 0 0
\(537\) 1011.38 + 78.1208i 1.88339 + 0.145476i
\(538\) 0 0
\(539\) 693.649i 1.28692i
\(540\) 0 0
\(541\) −38.7755 −0.0716738 −0.0358369 0.999358i \(-0.511410\pi\)
−0.0358369 + 0.999358i \(0.511410\pi\)
\(542\) 0 0
\(543\) 217.970 + 149.342i 0.401418 + 0.275030i
\(544\) 0 0
\(545\) 8.88890 + 24.4220i 0.0163099 + 0.0448111i
\(546\) 0 0
\(547\) −92.2064 522.928i −0.168567 0.955994i −0.945310 0.326175i \(-0.894240\pi\)
0.776742 0.629819i \(-0.216871\pi\)
\(548\) 0 0
\(549\) −320.644 176.521i −0.584051 0.321532i
\(550\) 0 0
\(551\) 152.799 419.811i 0.277311 0.761907i
\(552\) 0 0
\(553\) 943.576 + 791.754i 1.70629 + 1.43174i
\(554\) 0 0
\(555\) −10.2682 + 2.86369i −0.0185013 + 0.00515980i
\(556\) 0 0
\(557\) −324.141 187.143i −0.581942 0.335984i 0.179963 0.983673i \(-0.442402\pi\)
−0.761905 + 0.647689i \(0.775736\pi\)
\(558\) 0 0
\(559\) 305.503 + 529.147i 0.546518 + 0.946596i
\(560\) 0 0
\(561\) −197.637 + 435.348i −0.352294 + 0.776021i
\(562\) 0 0
\(563\) −544.864 96.0742i −0.967787 0.170647i −0.332653 0.943049i \(-0.607944\pi\)
−0.635134 + 0.772402i \(0.719055\pi\)
\(564\) 0 0
\(565\) −219.255 + 183.977i −0.388062 + 0.325623i
\(566\) 0 0
\(567\) 727.553 298.874i 1.28316 0.527114i
\(568\) 0 0
\(569\) 109.394 + 130.371i 0.192257 + 0.229123i 0.853558 0.520997i \(-0.174440\pi\)
−0.661301 + 0.750120i \(0.729995\pi\)
\(570\) 0 0
\(571\) −144.904 + 821.794i −0.253773 + 1.43922i 0.545429 + 0.838157i \(0.316367\pi\)
−0.799202 + 0.601062i \(0.794744\pi\)
\(572\) 0 0
\(573\) 311.445 + 141.388i 0.543534 + 0.246751i
\(574\) 0 0
\(575\) −34.0049 + 19.6327i −0.0591389 + 0.0341439i
\(576\) 0 0
\(577\) 312.331 540.973i 0.541301 0.937561i −0.457528 0.889195i \(-0.651265\pi\)
0.998830 0.0483663i \(-0.0154015\pi\)
\(578\) 0 0
\(579\) 133.527 + 478.786i 0.230617 + 0.826918i
\(580\) 0 0
\(581\) 83.7055 99.7564i 0.144071 0.171698i
\(582\) 0 0
\(583\) −525.471 191.256i −0.901323 0.328055i
\(584\) 0 0
\(585\) −184.850 305.630i −0.315984 0.522445i
\(586\) 0 0
\(587\) 594.734 104.868i 1.01318 0.178650i 0.357676 0.933846i \(-0.383569\pi\)
0.655500 + 0.755195i \(0.272458\pi\)
\(588\) 0 0
\(589\) −817.059 + 297.385i −1.38720 + 0.504898i
\(590\) 0 0
\(591\) −288.114 + 420.515i −0.487503 + 0.711531i
\(592\) 0 0
\(593\) 167.598i 0.282628i −0.989965 0.141314i \(-0.954867\pi\)
0.989965 0.141314i \(-0.0451327\pi\)
\(594\) 0 0
\(595\) 488.859 0.821613
\(596\) 0 0
\(597\) −66.5228 + 861.227i −0.111428 + 1.44259i
\(598\) 0 0
\(599\) −191.447 525.998i −0.319612 0.878126i −0.990616 0.136673i \(-0.956359\pi\)
0.671004 0.741453i \(-0.265863\pi\)
\(600\) 0 0
\(601\) −157.626 893.940i −0.262273 1.48742i −0.776691 0.629882i \(-0.783103\pi\)
0.514418 0.857539i \(-0.328008\pi\)
\(602\) 0 0
\(603\) 710.148 140.179i 1.17769 0.232469i
\(604\) 0 0
\(605\) 187.859 516.138i 0.310510 0.853120i
\(606\) 0 0
\(607\) 269.576 + 226.201i 0.444112 + 0.372654i 0.837246 0.546827i \(-0.184165\pi\)
−0.393133 + 0.919481i \(0.628609\pi\)
\(608\) 0 0
\(609\) 225.824 878.453i 0.370811 1.44245i
\(610\) 0 0
\(611\) 90.4705 + 52.2332i 0.148070 + 0.0854880i
\(612\) 0 0
\(613\) −152.261 263.724i −0.248387 0.430219i 0.714691 0.699440i \(-0.246567\pi\)
−0.963078 + 0.269221i \(0.913234\pi\)
\(614\) 0 0
\(615\) 677.607 66.2385i 1.10180 0.107705i
\(616\) 0 0
\(617\) 500.716 + 88.2897i 0.811533 + 0.143095i 0.563990 0.825782i \(-0.309266\pi\)
0.247543 + 0.968877i \(0.420377\pi\)
\(618\) 0 0
\(619\) −52.3325 + 43.9122i −0.0845436 + 0.0709405i −0.684080 0.729407i \(-0.739796\pi\)
0.599536 + 0.800347i \(0.295352\pi\)
\(620\) 0 0
\(621\) −262.192 + 610.252i −0.422210 + 0.982692i
\(622\) 0 0
\(623\) −1053.96 1256.07i −1.69176 2.01616i
\(624\) 0 0
\(625\) −101.158 + 573.698i −0.161853 + 0.917916i
\(626\) 0 0
\(627\) 536.139 383.599i 0.855086 0.611801i
\(628\) 0 0
\(629\) 6.61953 3.82179i 0.0105239 0.00607597i
\(630\) 0 0
\(631\) 62.9443 109.023i 0.0997533 0.172778i −0.811829 0.583895i \(-0.801528\pi\)
0.911582 + 0.411117i \(0.134861\pi\)
\(632\) 0 0
\(633\) 373.563 381.245i 0.590146 0.602283i
\(634\) 0 0
\(635\) 73.1494 87.1760i 0.115196 0.137285i
\(636\) 0 0
\(637\) 349.160 + 127.084i 0.548132 + 0.199504i
\(638\) 0 0
\(639\) 5.76912 2.23379i 0.00902836 0.00349576i
\(640\) 0 0
\(641\) 525.113 92.5916i 0.819209 0.144449i 0.251689 0.967808i \(-0.419014\pi\)
0.567520 + 0.823360i \(0.307903\pi\)
\(642\) 0 0
\(643\) −456.157 + 166.027i −0.709419 + 0.258207i −0.671427 0.741071i \(-0.734318\pi\)
−0.0379920 + 0.999278i \(0.512096\pi\)
\(644\) 0 0
\(645\) −466.777 974.975i −0.723685 1.51159i
\(646\) 0 0
\(647\) 783.796i 1.21143i 0.795682 + 0.605715i \(0.207113\pi\)
−0.795682 + 0.605715i \(0.792887\pi\)
\(648\) 0 0
\(649\) 1366.85 2.10608
\(650\) 0 0
\(651\) −1592.21 + 762.285i −2.44580 + 1.17094i
\(652\) 0 0
\(653\) 116.572 + 320.280i 0.178518 + 0.490475i 0.996387 0.0849302i \(-0.0270667\pi\)
−0.817869 + 0.575405i \(0.804845\pi\)
\(654\) 0 0
\(655\) 83.8602 + 475.595i 0.128031 + 0.726099i
\(656\) 0 0
\(657\) 244.884 + 38.0577i 0.372731 + 0.0579265i
\(658\) 0 0
\(659\) −182.181 + 500.537i −0.276450 + 0.759540i 0.721308 + 0.692614i \(0.243541\pi\)
−0.997758 + 0.0669256i \(0.978681\pi\)
\(660\) 0 0
\(661\) −130.190 109.242i −0.196959 0.165268i 0.538974 0.842322i \(-0.318812\pi\)
−0.735933 + 0.677054i \(0.763256\pi\)
\(662\) 0 0
\(663\) 182.931 + 179.244i 0.275913 + 0.270353i
\(664\) 0 0
\(665\) −583.753 337.030i −0.877825 0.506812i
\(666\) 0 0
\(667\) 382.960 + 663.306i 0.574153 + 0.994462i
\(668\) 0 0
\(669\) 257.281 + 359.590i 0.384576 + 0.537504i
\(670\) 0 0
\(671\) −613.369 108.153i −0.914112 0.161183i
\(672\) 0 0
\(673\) −668.840 + 561.224i −0.993819 + 0.833913i −0.986116 0.166057i \(-0.946896\pi\)
−0.00770313 + 0.999970i \(0.502452\pi\)
\(674\) 0 0
\(675\) −19.3974 38.4847i −0.0287368 0.0570143i
\(676\) 0 0
\(677\) −18.4136 21.9445i −0.0271989 0.0324144i 0.752274 0.658851i \(-0.228957\pi\)
−0.779472 + 0.626437i \(0.784513\pi\)
\(678\) 0 0
\(679\) 108.071 612.903i 0.159162 0.902655i
\(680\) 0 0
\(681\) 92.6859 + 948.158i 0.136103 + 1.39230i
\(682\) 0 0
\(683\) −547.126 + 315.884i −0.801063 + 0.462494i −0.843843 0.536590i \(-0.819712\pi\)
0.0427795 + 0.999085i \(0.486379\pi\)
\(684\) 0 0
\(685\) 110.633 191.622i 0.161508 0.279740i
\(686\) 0 0
\(687\) 272.394 + 70.0242i 0.396497 + 0.101928i
\(688\) 0 0
\(689\) −192.544 + 229.465i −0.279454 + 0.333040i
\(690\) 0 0
\(691\) 209.825 + 76.3702i 0.303655 + 0.110521i 0.489354 0.872085i \(-0.337233\pi\)
−0.185699 + 0.982607i \(0.559455\pi\)
\(692\) 0 0
\(693\) 1007.56 881.002i 1.45391 1.27129i
\(694\) 0 0
\(695\) −465.333 + 82.0507i −0.669544 + 0.118059i
\(696\) 0 0
\(697\) −458.737 + 166.967i −0.658160 + 0.239551i
\(698\) 0 0
\(699\) −685.144 52.9219i −0.980178 0.0757108i
\(700\) 0 0
\(701\) 489.886i 0.698839i 0.936966 + 0.349419i \(0.113621\pi\)
−0.936966 + 0.349419i \(0.886379\pi\)
\(702\) 0 0
\(703\) −10.5393 −0.0149919
\(704\) 0 0
\(705\) −152.462 104.459i −0.216259 0.148169i
\(706\) 0 0
\(707\) 616.035 + 1692.54i 0.871336 + 2.39398i
\(708\) 0 0
\(709\) −170.312 965.890i −0.240215 1.36233i −0.831348 0.555752i \(-0.812430\pi\)
0.591133 0.806574i \(-0.298681\pi\)
\(710\) 0 0
\(711\) −23.2365 1141.39i −0.0326814 1.60533i
\(712\) 0 0
\(713\) 509.841 1400.78i 0.715064 1.96462i
\(714\) 0 0
\(715\) −465.594 390.680i −0.651180 0.546405i
\(716\) 0 0
\(717\) −1165.92 + 325.161i −1.62611 + 0.453502i
\(718\) 0 0
\(719\) −372.521 215.075i −0.518110 0.299131i 0.218051 0.975937i \(-0.430030\pi\)
−0.736161 + 0.676807i \(0.763363\pi\)
\(720\) 0 0
\(721\) −337.093 583.863i −0.467536 0.809796i
\(722\) 0 0
\(723\) 173.766 382.764i 0.240340 0.529411i
\(724\) 0 0
\(725\) −48.9423 8.62986i −0.0675067 0.0119032i
\(726\) 0 0
\(727\) 264.636 222.056i 0.364011 0.305442i −0.442376 0.896830i \(-0.645864\pi\)
0.806387 + 0.591388i \(0.201420\pi\)
\(728\) 0 0
\(729\) −652.400 325.292i −0.894925 0.446216i
\(730\) 0 0
\(731\) 498.206 + 593.739i 0.681541 + 0.812229i
\(732\) 0 0
\(733\) −29.8989 + 169.565i −0.0407898 + 0.231331i −0.998387 0.0567810i \(-0.981916\pi\)
0.957597 + 0.288112i \(0.0930274\pi\)
\(734\) 0 0
\(735\) −598.561 271.732i −0.814369 0.369703i
\(736\) 0 0
\(737\) 1066.70 615.860i 1.44736 0.835631i
\(738\) 0 0
\(739\) 10.3839 17.9855i 0.0140513 0.0243376i −0.858914 0.512119i \(-0.828861\pi\)
0.872966 + 0.487782i \(0.162194\pi\)
\(740\) 0 0
\(741\) −94.8648 340.154i −0.128023 0.459048i
\(742\) 0 0
\(743\) 268.303 319.751i 0.361108 0.430352i −0.554649 0.832084i \(-0.687147\pi\)
0.915757 + 0.401733i \(0.131592\pi\)
\(744\) 0 0
\(745\) −818.661 297.968i −1.09887 0.399957i
\(746\) 0 0
\(747\) −120.670 + 2.45660i −0.161539 + 0.00328862i
\(748\) 0 0
\(749\) −425.004 + 74.9398i −0.567429 + 0.100053i
\(750\) 0 0
\(751\) −641.259 + 233.399i −0.853874 + 0.310785i −0.731619 0.681714i \(-0.761235\pi\)
−0.122255 + 0.992499i \(0.539013\pi\)
\(752\) 0 0
\(753\) −371.464 + 542.167i −0.493312 + 0.720010i
\(754\) 0 0
\(755\) 269.381i 0.356797i
\(756\) 0 0
\(757\) −127.228 −0.168069 −0.0840346 0.996463i \(-0.526781\pi\)
−0.0840346 + 0.996463i \(0.526781\pi\)
\(758\) 0 0
\(759\) −87.0399 + 1126.85i −0.114677 + 1.48465i
\(760\) 0 0
\(761\) 221.043 + 607.312i 0.290464 + 0.798045i 0.995999 + 0.0893686i \(0.0284849\pi\)
−0.705534 + 0.708676i \(0.749293\pi\)
\(762\) 0 0
\(763\) 9.05865 + 51.3742i 0.0118724 + 0.0673318i
\(764\) 0 0
\(765\) −298.246 341.089i −0.389864 0.445867i
\(766\) 0 0
\(767\) 250.421 688.027i 0.326494 0.897036i
\(768\) 0 0
\(769\) −313.457 263.022i −0.407616 0.342031i 0.415812 0.909450i \(-0.363497\pi\)
−0.823429 + 0.567420i \(0.807942\pi\)
\(770\) 0 0
\(771\) −67.1170 + 261.084i −0.0870519 + 0.338631i
\(772\) 0 0
\(773\) −492.676 284.447i −0.637356 0.367978i 0.146239 0.989249i \(-0.453283\pi\)
−0.783595 + 0.621272i \(0.786616\pi\)
\(774\) 0 0
\(775\) 48.3619 + 83.7652i 0.0624024 + 0.108084i
\(776\) 0 0
\(777\) −21.2958 + 2.08174i −0.0274077 + 0.00267920i
\(778\) 0 0
\(779\) 662.895 + 116.886i 0.850956 + 0.150046i
\(780\) 0 0
\(781\) 8.06419 6.76666i 0.0103255 0.00866410i
\(782\) 0 0
\(783\) −750.689 + 378.369i −0.958734 + 0.483229i
\(784\)