Properties

Label 261.3.s.a.19.2
Level $261$
Weight $3$
Character 261.19
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 19.2
Character \(\chi\) \(=\) 261.19
Dual form 261.3.s.a.55.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.488049 - 0.776726i) q^{2} +(1.37042 - 2.84571i) q^{4} +(1.98497 + 0.453055i) q^{5} +(9.56374 - 4.60566i) q^{7} +(-6.52543 + 0.735239i) q^{8} +O(q^{10})\) \(q+(-0.488049 - 0.776726i) q^{2} +(1.37042 - 2.84571i) q^{4} +(1.98497 + 0.453055i) q^{5} +(9.56374 - 4.60566i) q^{7} +(-6.52543 + 0.735239i) q^{8} +(-0.616861 - 1.76289i) q^{10} +(11.6332 + 1.31075i) q^{11} +(-11.0274 + 8.79408i) q^{13} +(-8.24491 - 5.18062i) q^{14} +(-4.12137 - 5.16804i) q^{16} +(-0.154761 + 0.154761i) q^{17} +(20.3603 - 7.12436i) q^{19} +(4.00951 - 5.02777i) q^{20} +(-4.65948 - 9.67551i) q^{22} +(-1.51251 - 6.62676i) q^{23} +(-18.7894 - 9.04850i) q^{25} +(12.2125 + 4.27334i) q^{26} -33.5274i q^{28} +(15.7913 - 24.3235i) q^{29} +(-0.406230 - 0.646512i) q^{31} +(-10.6781 + 30.5163i) q^{32} +(0.195737 + 0.0446758i) q^{34} +(21.0703 - 4.80916i) q^{35} +(-6.96097 + 0.784313i) q^{37} +(-15.4705 - 12.3373i) q^{38} +(-13.2858 - 1.49696i) q^{40} +(-35.8917 - 35.8917i) q^{41} +(18.2000 + 11.4358i) q^{43} +(19.6724 - 31.3084i) q^{44} +(-4.40899 + 4.40899i) q^{46} +(2.57409 - 22.8457i) q^{47} +(39.7021 - 49.7849i) q^{49} +(2.14195 + 19.0103i) q^{50} +(9.91319 + 43.4325i) q^{52} +(-12.7427 + 55.8292i) q^{53} +(22.4976 + 7.87226i) q^{55} +(-59.0212 + 37.0855i) q^{56} +(-26.5997 - 0.394450i) q^{58} +48.4185 q^{59} +(-24.4350 + 69.8312i) q^{61} +(-0.303902 + 0.631059i) q^{62} +(3.13649 - 0.715883i) q^{64} +(-25.8733 + 12.4599i) q^{65} +(33.7392 + 26.9061i) q^{67} +(0.228317 + 0.652492i) q^{68} +(-14.0188 - 14.0188i) q^{70} +(-78.3788 + 62.5050i) q^{71} +(5.59603 - 8.90604i) q^{73} +(4.00650 + 5.02399i) q^{74} +(7.62828 - 67.7029i) q^{76} +(117.294 - 41.0428i) q^{77} +(4.65001 + 41.2700i) q^{79} +(-5.83937 - 12.1256i) q^{80} +(-10.3611 + 45.3949i) q^{82} +(-85.5238 - 41.1861i) q^{83} +(-0.377310 + 0.237079i) q^{85} -19.7176i q^{86} -76.8752 q^{88} +(89.2455 + 142.033i) q^{89} +(-64.9610 + 134.893i) q^{91} +(-20.9306 - 4.77728i) q^{92} +(-19.0011 + 9.15045i) q^{94} +(43.6421 - 4.91729i) q^{95} +(20.2947 + 57.9990i) q^{97} +(-58.0458 - 6.54019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{9}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.488049 0.776726i −0.244025 0.388363i 0.702145 0.712034i \(-0.252226\pi\)
−0.946170 + 0.323671i \(0.895083\pi\)
\(3\) 0 0
\(4\) 1.37042 2.84571i 0.342606 0.711429i
\(5\) 1.98497 + 0.453055i 0.396993 + 0.0906111i 0.416356 0.909201i \(-0.363307\pi\)
−0.0193635 + 0.999813i \(0.506164\pi\)
\(6\) 0 0
\(7\) 9.56374 4.60566i 1.36625 0.657951i 0.400228 0.916415i \(-0.368931\pi\)
0.966021 + 0.258465i \(0.0832165\pi\)
\(8\) −6.52543 + 0.735239i −0.815678 + 0.0919049i
\(9\) 0 0
\(10\) −0.616861 1.76289i −0.0616861 0.176289i
\(11\) 11.6332 + 1.31075i 1.05756 + 0.119159i 0.623577 0.781762i \(-0.285679\pi\)
0.433985 + 0.900920i \(0.357107\pi\)
\(12\) 0 0
\(13\) −11.0274 + 8.79408i −0.848264 + 0.676468i −0.947904 0.318556i \(-0.896802\pi\)
0.0996406 + 0.995023i \(0.468231\pi\)
\(14\) −8.24491 5.18062i −0.588922 0.370044i
\(15\) 0 0
\(16\) −4.12137 5.16804i −0.257586 0.323002i
\(17\) −0.154761 + 0.154761i −0.00910357 + 0.00910357i −0.711644 0.702540i \(-0.752049\pi\)
0.702540 + 0.711644i \(0.252049\pi\)
\(18\) 0 0
\(19\) 20.3603 7.12436i 1.07159 0.374966i 0.263888 0.964553i \(-0.414995\pi\)
0.807705 + 0.589587i \(0.200710\pi\)
\(20\) 4.00951 5.02777i 0.200475 0.251388i
\(21\) 0 0
\(22\) −4.65948 9.67551i −0.211794 0.439796i
\(23\) −1.51251 6.62676i −0.0657615 0.288120i 0.931345 0.364138i \(-0.118636\pi\)
−0.997106 + 0.0760183i \(0.975779\pi\)
\(24\) 0 0
\(25\) −18.7894 9.04850i −0.751576 0.361940i
\(26\) 12.2125 + 4.27334i 0.469712 + 0.164359i
\(27\) 0 0
\(28\) 33.5274i 1.19741i
\(29\) 15.7913 24.3235i 0.544528 0.838742i
\(30\) 0 0
\(31\) −0.406230 0.646512i −0.0131042 0.0208552i 0.840108 0.542419i \(-0.182492\pi\)
−0.853212 + 0.521564i \(0.825349\pi\)
\(32\) −10.6781 + 30.5163i −0.333691 + 0.953634i
\(33\) 0 0
\(34\) 0.195737 + 0.0446758i 0.00575698 + 0.00131399i
\(35\) 21.0703 4.80916i 0.602009 0.137405i
\(36\) 0 0
\(37\) −6.96097 + 0.784313i −0.188134 + 0.0211977i −0.205529 0.978651i \(-0.565891\pi\)
0.0173945 + 0.999849i \(0.494463\pi\)
\(38\) −15.4705 12.3373i −0.407118 0.324666i
\(39\) 0 0
\(40\) −13.2858 1.49696i −0.332146 0.0374239i
\(41\) −35.8917 35.8917i −0.875407 0.875407i 0.117648 0.993055i \(-0.462464\pi\)
−0.993055 + 0.117648i \(0.962464\pi\)
\(42\) 0 0
\(43\) 18.2000 + 11.4358i 0.423256 + 0.265949i 0.726774 0.686876i \(-0.241019\pi\)
−0.303519 + 0.952825i \(0.598161\pi\)
\(44\) 19.6724 31.3084i 0.447100 0.711556i
\(45\) 0 0
\(46\) −4.40899 + 4.40899i −0.0958477 + 0.0958477i
\(47\) 2.57409 22.8457i 0.0547678 0.486078i −0.936149 0.351603i \(-0.885637\pi\)
0.990917 0.134475i \(-0.0429347\pi\)
\(48\) 0 0
\(49\) 39.7021 49.7849i 0.810247 1.01602i
\(50\) 2.14195 + 19.0103i 0.0428390 + 0.380206i
\(51\) 0 0
\(52\) 9.91319 + 43.4325i 0.190638 + 0.835241i
\(53\) −12.7427 + 55.8292i −0.240427 + 1.05338i 0.700202 + 0.713945i \(0.253093\pi\)
−0.940629 + 0.339436i \(0.889764\pi\)
\(54\) 0 0
\(55\) 22.4976 + 7.87226i 0.409048 + 0.143132i
\(56\) −59.0212 + 37.0855i −1.05395 + 0.662241i
\(57\) 0 0
\(58\) −26.5997 0.394450i −0.458615 0.00680085i
\(59\) 48.4185 0.820652 0.410326 0.911939i \(-0.365415\pi\)
0.410326 + 0.911939i \(0.365415\pi\)
\(60\) 0 0
\(61\) −24.4350 + 69.8312i −0.400574 + 1.14477i 0.550239 + 0.835007i \(0.314537\pi\)
−0.950813 + 0.309766i \(0.899749\pi\)
\(62\) −0.303902 + 0.631059i −0.00490165 + 0.0101784i
\(63\) 0 0
\(64\) 3.13649 0.715883i 0.0490076 0.0111857i
\(65\) −25.8733 + 12.4599i −0.398050 + 0.191691i
\(66\) 0 0
\(67\) 33.7392 + 26.9061i 0.503570 + 0.401584i 0.842058 0.539387i \(-0.181344\pi\)
−0.338488 + 0.940971i \(0.609915\pi\)
\(68\) 0.228317 + 0.652492i 0.00335760 + 0.00959548i
\(69\) 0 0
\(70\) −14.0188 14.0188i −0.200268 0.200268i
\(71\) −78.3788 + 62.5050i −1.10393 + 0.880352i −0.993534 0.113536i \(-0.963782\pi\)
−0.110393 + 0.993888i \(0.535211\pi\)
\(72\) 0 0
\(73\) 5.59603 8.90604i 0.0766580 0.122001i −0.806195 0.591650i \(-0.798477\pi\)
0.882853 + 0.469649i \(0.155620\pi\)
\(74\) 4.00650 + 5.02399i 0.0541418 + 0.0678917i
\(75\) 0 0
\(76\) 7.62828 67.7029i 0.100372 0.890827i
\(77\) 117.294 41.0428i 1.52329 0.533024i
\(78\) 0 0
\(79\) 4.65001 + 41.2700i 0.0588609 + 0.522405i 0.988199 + 0.153175i \(0.0489499\pi\)
−0.929338 + 0.369230i \(0.879622\pi\)
\(80\) −5.83937 12.1256i −0.0729922 0.151570i
\(81\) 0 0
\(82\) −10.3611 + 45.3949i −0.126355 + 0.553597i
\(83\) −85.5238 41.1861i −1.03041 0.496218i −0.159259 0.987237i \(-0.550910\pi\)
−0.871149 + 0.491019i \(0.836625\pi\)
\(84\) 0 0
\(85\) −0.377310 + 0.237079i −0.00443894 + 0.00278917i
\(86\) 19.7176i 0.229275i
\(87\) 0 0
\(88\) −76.8752 −0.873582
\(89\) 89.2455 + 142.033i 1.00276 + 1.59588i 0.784633 + 0.619961i \(0.212852\pi\)
0.218126 + 0.975921i \(0.430006\pi\)
\(90\) 0 0
\(91\) −64.9610 + 134.893i −0.713857 + 1.48234i
\(92\) −20.9306 4.77728i −0.227507 0.0519270i
\(93\) 0 0
\(94\) −19.0011 + 9.15045i −0.202139 + 0.0973452i
\(95\) 43.6421 4.91729i 0.459391 0.0517609i
\(96\) 0 0
\(97\) 20.2947 + 57.9990i 0.209224 + 0.597928i 0.999898 0.0143099i \(-0.00455513\pi\)
−0.790673 + 0.612238i \(0.790269\pi\)
\(98\) −58.0458 6.54019i −0.592304 0.0667367i
\(99\) 0 0
\(100\) −51.4989 + 41.0690i −0.514989 + 0.410690i
\(101\) 119.742 + 75.2390i 1.18557 + 0.744941i 0.972683 0.232137i \(-0.0745717\pi\)
0.212883 + 0.977078i \(0.431715\pi\)
\(102\) 0 0
\(103\) 61.1848 + 76.7234i 0.594028 + 0.744887i 0.984434 0.175756i \(-0.0562368\pi\)
−0.390406 + 0.920643i \(0.627665\pi\)
\(104\) 65.4929 65.4929i 0.629739 0.629739i
\(105\) 0 0
\(106\) 49.5831 17.3499i 0.467765 0.163678i
\(107\) −91.2780 + 114.459i −0.853066 + 1.06971i 0.143722 + 0.989618i \(0.454093\pi\)
−0.996787 + 0.0800922i \(0.974479\pi\)
\(108\) 0 0
\(109\) −8.55158 17.7575i −0.0784549 0.162913i 0.858052 0.513563i \(-0.171675\pi\)
−0.936507 + 0.350650i \(0.885961\pi\)
\(110\) −4.86536 21.3165i −0.0442306 0.193787i
\(111\) 0 0
\(112\) −63.2180 30.4442i −0.564446 0.271823i
\(113\) 36.2240 + 12.6753i 0.320566 + 0.112171i 0.485765 0.874089i \(-0.338541\pi\)
−0.165199 + 0.986260i \(0.552827\pi\)
\(114\) 0 0
\(115\) 13.8391i 0.120340i
\(116\) −47.5770 78.2711i −0.410147 0.674751i
\(117\) 0 0
\(118\) −23.6306 37.6079i −0.200259 0.318711i
\(119\) −0.767317 + 2.19287i −0.00644804 + 0.0184274i
\(120\) 0 0
\(121\) 15.6466 + 3.57125i 0.129311 + 0.0295144i
\(122\) 66.1652 15.1018i 0.542337 0.123785i
\(123\) 0 0
\(124\) −2.39650 + 0.270020i −0.0193266 + 0.00217758i
\(125\) −72.9923 58.2094i −0.583938 0.465675i
\(126\) 0 0
\(127\) 53.9964 + 6.08394i 0.425169 + 0.0479050i 0.321957 0.946754i \(-0.395659\pi\)
0.103212 + 0.994659i \(0.467088\pi\)
\(128\) 89.3579 + 89.3579i 0.698108 + 0.698108i
\(129\) 0 0
\(130\) 22.3054 + 14.0154i 0.171580 + 0.107811i
\(131\) 37.0804 59.0132i 0.283057 0.450482i −0.674687 0.738104i \(-0.735722\pi\)
0.957744 + 0.287621i \(0.0928644\pi\)
\(132\) 0 0
\(133\) 161.908 161.908i 1.21735 1.21735i
\(134\) 4.43229 39.3376i 0.0330768 0.293565i
\(135\) 0 0
\(136\) 0.896093 1.12367i 0.00658892 0.00826224i
\(137\) −10.8849 96.6061i −0.0794518 0.705154i −0.968786 0.247897i \(-0.920260\pi\)
0.889335 0.457257i \(-0.151168\pi\)
\(138\) 0 0
\(139\) −43.7002 191.463i −0.314390 1.37743i −0.847235 0.531219i \(-0.821734\pi\)
0.532845 0.846213i \(-0.321123\pi\)
\(140\) 15.1898 66.5507i 0.108498 0.475362i
\(141\) 0 0
\(142\) 86.8020 + 30.3733i 0.611282 + 0.213897i
\(143\) −139.811 + 87.8490i −0.977698 + 0.614329i
\(144\) 0 0
\(145\) 42.3651 41.1270i 0.292173 0.283635i
\(146\) −9.64869 −0.0660869
\(147\) 0 0
\(148\) −7.30755 + 20.8838i −0.0493754 + 0.141107i
\(149\) −14.9818 + 31.1100i −0.100549 + 0.208792i −0.945175 0.326565i \(-0.894109\pi\)
0.844626 + 0.535357i \(0.179823\pi\)
\(150\) 0 0
\(151\) −84.5495 + 19.2979i −0.559931 + 0.127801i −0.493114 0.869965i \(-0.664141\pi\)
−0.0668168 + 0.997765i \(0.521284\pi\)
\(152\) −127.621 + 61.4591i −0.839613 + 0.404336i
\(153\) 0 0
\(154\) −89.1241 71.0741i −0.578728 0.461520i
\(155\) −0.513447 1.46735i −0.00331256 0.00946676i
\(156\) 0 0
\(157\) −31.5274 31.5274i −0.200812 0.200812i 0.599536 0.800348i \(-0.295352\pi\)
−0.800348 + 0.599536i \(0.795352\pi\)
\(158\) 29.7860 23.7536i 0.188519 0.150339i
\(159\) 0 0
\(160\) −35.0212 + 55.7360i −0.218883 + 0.348350i
\(161\) −44.9859 56.4105i −0.279415 0.350376i
\(162\) 0 0
\(163\) −10.5971 + 94.0522i −0.0650131 + 0.577008i 0.918403 + 0.395646i \(0.129479\pi\)
−0.983416 + 0.181362i \(0.941949\pi\)
\(164\) −151.324 + 52.9507i −0.922709 + 0.322870i
\(165\) 0 0
\(166\) 9.74953 + 86.5295i 0.0587321 + 0.521262i
\(167\) −9.33539 19.3851i −0.0559006 0.116079i 0.871147 0.491022i \(-0.163376\pi\)
−0.927048 + 0.374943i \(0.877662\pi\)
\(168\) 0 0
\(169\) 6.66226 29.1893i 0.0394217 0.172718i
\(170\) 0.368291 + 0.177360i 0.00216642 + 0.00104329i
\(171\) 0 0
\(172\) 57.4848 36.1201i 0.334214 0.210000i
\(173\) 76.1743i 0.440314i −0.975464 0.220157i \(-0.929343\pi\)
0.975464 0.220157i \(-0.0706569\pi\)
\(174\) 0 0
\(175\) −221.371 −1.26498
\(176\) −41.1707 65.5228i −0.233924 0.372289i
\(177\) 0 0
\(178\) 66.7649 138.639i 0.375083 0.778869i
\(179\) −107.104 24.4459i −0.598349 0.136569i −0.0873895 0.996174i \(-0.527852\pi\)
−0.510959 + 0.859605i \(0.670710\pi\)
\(180\) 0 0
\(181\) 267.619 128.879i 1.47856 0.712036i 0.491275 0.871005i \(-0.336531\pi\)
0.987284 + 0.158968i \(0.0508167\pi\)
\(182\) 136.479 15.3775i 0.749884 0.0844917i
\(183\) 0 0
\(184\) 14.7420 + 42.1304i 0.0801198 + 0.228969i
\(185\) −14.1726 1.59687i −0.0766088 0.00863174i
\(186\) 0 0
\(187\) −2.00321 + 1.59751i −0.0107124 + 0.00854282i
\(188\) −61.4846 38.6333i −0.327046 0.205497i
\(189\) 0 0
\(190\) −25.1189 31.4981i −0.132205 0.165779i
\(191\) 131.587 131.587i 0.688937 0.688937i −0.273060 0.961997i \(-0.588036\pi\)
0.961997 + 0.273060i \(0.0880357\pi\)
\(192\) 0 0
\(193\) 10.5516 3.69218i 0.0546717 0.0191304i −0.302805 0.953053i \(-0.597923\pi\)
0.357476 + 0.933922i \(0.383637\pi\)
\(194\) 35.1445 44.0698i 0.181157 0.227164i
\(195\) 0 0
\(196\) −87.2648 181.207i −0.445229 0.924527i
\(197\) 43.6695 + 191.329i 0.221673 + 0.971211i 0.956219 + 0.292652i \(0.0945379\pi\)
−0.734546 + 0.678559i \(0.762605\pi\)
\(198\) 0 0
\(199\) −191.282 92.1164i −0.961214 0.462896i −0.113610 0.993525i \(-0.536241\pi\)
−0.847604 + 0.530629i \(0.821956\pi\)
\(200\) 129.262 + 45.2306i 0.646308 + 0.226153i
\(201\) 0 0
\(202\) 129.727i 0.642214i
\(203\) 38.9983 305.353i 0.192110 1.50420i
\(204\) 0 0
\(205\) −54.9828 87.5047i −0.268209 0.426852i
\(206\) 29.7318 84.9687i 0.144329 0.412469i
\(207\) 0 0
\(208\) 90.8963 + 20.7465i 0.437001 + 0.0997427i
\(209\) 246.193 56.1919i 1.17796 0.268861i
\(210\) 0 0
\(211\) 347.213 39.1215i 1.64556 0.185410i 0.759996 0.649927i \(-0.225201\pi\)
0.885564 + 0.464517i \(0.153772\pi\)
\(212\) 141.411 + 112.772i 0.667034 + 0.531942i
\(213\) 0 0
\(214\) 133.451 + 15.0364i 0.623605 + 0.0702634i
\(215\) 30.9453 + 30.9453i 0.143932 + 0.143932i
\(216\) 0 0
\(217\) −6.86269 4.31212i −0.0316253 0.0198715i
\(218\) −9.61915 + 15.3088i −0.0441246 + 0.0702238i
\(219\) 0 0
\(220\) 53.2335 53.2335i 0.241970 0.241970i
\(221\) 0.345634 3.06759i 0.00156396 0.0138805i
\(222\) 0 0
\(223\) −223.712 + 280.525i −1.00319 + 1.25796i −0.0372207 + 0.999307i \(0.511850\pi\)
−0.965970 + 0.258654i \(0.916721\pi\)
\(224\) 38.4248 + 341.030i 0.171539 + 1.52245i
\(225\) 0 0
\(226\) −7.83384 34.3223i −0.0346630 0.151869i
\(227\) −22.9453 + 100.530i −0.101080 + 0.442862i 0.898908 + 0.438137i \(0.144361\pi\)
−0.999989 + 0.00472574i \(0.998496\pi\)
\(228\) 0 0
\(229\) −143.168 50.0967i −0.625189 0.218763i −0.000953694 1.00000i \(-0.500304\pi\)
−0.624235 + 0.781237i \(0.714589\pi\)
\(230\) −10.7492 + 6.75418i −0.0467357 + 0.0293660i
\(231\) 0 0
\(232\) −85.1615 + 170.332i −0.367075 + 0.734189i
\(233\) −317.385 −1.36217 −0.681083 0.732206i \(-0.738491\pi\)
−0.681083 + 0.732206i \(0.738491\pi\)
\(234\) 0 0
\(235\) 15.4598 44.1816i 0.0657865 0.188007i
\(236\) 66.3538 137.785i 0.281160 0.583835i
\(237\) 0 0
\(238\) 2.07774 0.474232i 0.00873002 0.00199257i
\(239\) −26.5371 + 12.7796i −0.111034 + 0.0534711i −0.488576 0.872521i \(-0.662484\pi\)
0.377542 + 0.925992i \(0.376769\pi\)
\(240\) 0 0
\(241\) 114.945 + 91.6659i 0.476952 + 0.380356i 0.832253 0.554395i \(-0.187050\pi\)
−0.355302 + 0.934752i \(0.615622\pi\)
\(242\) −4.86246 13.8961i −0.0200928 0.0574219i
\(243\) 0 0
\(244\) 165.233 + 165.233i 0.677186 + 0.677186i
\(245\) 101.363 80.8340i 0.413725 0.329935i
\(246\) 0 0
\(247\) −161.869 + 257.613i −0.655340 + 1.04297i
\(248\) 3.12617 + 3.92009i 0.0126055 + 0.0158068i
\(249\) 0 0
\(250\) −9.58893 + 85.1041i −0.0383557 + 0.340416i
\(251\) −77.7163 + 27.1941i −0.309627 + 0.108343i −0.480620 0.876929i \(-0.659588\pi\)
0.170993 + 0.985272i \(0.445302\pi\)
\(252\) 0 0
\(253\) −8.90937 79.0728i −0.0352149 0.312541i
\(254\) −21.6274 44.9097i −0.0851471 0.176810i
\(255\) 0 0
\(256\) 28.6591 125.564i 0.111949 0.490483i
\(257\) 137.519 + 66.2259i 0.535095 + 0.257688i 0.681859 0.731483i \(-0.261172\pi\)
−0.146764 + 0.989171i \(0.546886\pi\)
\(258\) 0 0
\(259\) −62.9607 + 39.5608i −0.243091 + 0.152745i
\(260\) 90.7033i 0.348859i
\(261\) 0 0
\(262\) −63.9342 −0.244024
\(263\) 163.041 + 259.478i 0.619928 + 0.986609i 0.998144 + 0.0608922i \(0.0193946\pi\)
−0.378217 + 0.925717i \(0.623463\pi\)
\(264\) 0 0
\(265\) −50.5875 + 105.046i −0.190896 + 0.396400i
\(266\) −204.777 46.7390i −0.769839 0.175711i
\(267\) 0 0
\(268\) 122.804 59.1394i 0.458225 0.220669i
\(269\) 289.980 32.6729i 1.07799 0.121461i 0.444934 0.895563i \(-0.353227\pi\)
0.633060 + 0.774103i \(0.281799\pi\)
\(270\) 0 0
\(271\) −51.9021 148.328i −0.191521 0.547335i 0.807579 0.589759i \(-0.200777\pi\)
−0.999100 + 0.0424247i \(0.986492\pi\)
\(272\) 1.43764 + 0.161983i 0.00528542 + 0.000595524i
\(273\) 0 0
\(274\) −69.7241 + 55.6031i −0.254468 + 0.202931i
\(275\) −206.720 129.891i −0.751710 0.472331i
\(276\) 0 0
\(277\) −83.4157 104.600i −0.301140 0.377617i 0.608121 0.793844i \(-0.291924\pi\)
−0.909261 + 0.416227i \(0.863352\pi\)
\(278\) −127.386 + 127.386i −0.458225 + 0.458225i
\(279\) 0 0
\(280\) −133.957 + 46.8735i −0.478417 + 0.167405i
\(281\) −233.501 + 292.801i −0.830965 + 1.04200i 0.167459 + 0.985879i \(0.446444\pi\)
−0.998424 + 0.0561179i \(0.982128\pi\)
\(282\) 0 0
\(283\) 61.5039 + 127.714i 0.217328 + 0.451287i 0.980920 0.194413i \(-0.0622801\pi\)
−0.763591 + 0.645700i \(0.776566\pi\)
\(284\) 70.4592 + 308.702i 0.248096 + 1.08698i
\(285\) 0 0
\(286\) 136.469 + 65.7201i 0.477165 + 0.229791i
\(287\) −508.564 177.954i −1.77200 0.620049i
\(288\) 0 0
\(289\) 288.952i 0.999834i
\(290\) −52.6207 12.8341i −0.181451 0.0442555i
\(291\) 0 0
\(292\) −17.6751 28.1298i −0.0605312 0.0963348i
\(293\) 129.389 369.772i 0.441600 1.26202i −0.481156 0.876635i \(-0.659783\pi\)
0.922756 0.385385i \(-0.125931\pi\)
\(294\) 0 0
\(295\) 96.1090 + 21.9362i 0.325793 + 0.0743601i
\(296\) 44.8467 10.2360i 0.151509 0.0345809i
\(297\) 0 0
\(298\) 31.4757 3.54647i 0.105623 0.0119009i
\(299\) 74.9554 + 59.7749i 0.250687 + 0.199916i
\(300\) 0 0
\(301\) 226.729 + 25.5463i 0.753254 + 0.0848713i
\(302\) 56.2535 + 56.2535i 0.186270 + 0.186270i
\(303\) 0 0
\(304\) −120.731 75.8604i −0.397142 0.249541i
\(305\) −80.1400 + 127.542i −0.262754 + 0.418171i
\(306\) 0 0
\(307\) −364.784 + 364.784i −1.18822 + 1.18822i −0.210663 + 0.977559i \(0.567562\pi\)
−0.977559 + 0.210663i \(0.932438\pi\)
\(308\) 43.9459 390.030i 0.142681 1.26633i
\(309\) 0 0
\(310\) −0.889140 + 1.11495i −0.00286819 + 0.00359660i
\(311\) −1.60736 14.2657i −0.00516836 0.0458705i 0.990863 0.134870i \(-0.0430616\pi\)
−0.996032 + 0.0889994i \(0.971633\pi\)
\(312\) 0 0
\(313\) 3.75343 + 16.4449i 0.0119918 + 0.0525395i 0.980570 0.196170i \(-0.0628506\pi\)
−0.968578 + 0.248710i \(0.919993\pi\)
\(314\) −9.10123 + 39.8751i −0.0289848 + 0.126991i
\(315\) 0 0
\(316\) 123.815 + 43.3248i 0.391820 + 0.137104i
\(317\) −45.2757 + 28.4486i −0.142825 + 0.0897432i −0.601549 0.798836i \(-0.705450\pi\)
0.458724 + 0.888579i \(0.348307\pi\)
\(318\) 0 0
\(319\) 215.585 262.262i 0.675816 0.822137i
\(320\) 6.55015 0.0204692
\(321\) 0 0
\(322\) −21.8602 + 62.4728i −0.0678887 + 0.194015i
\(323\) −2.04840 + 4.25354i −0.00634178 + 0.0131688i
\(324\) 0 0
\(325\) 286.772 65.4538i 0.882375 0.201396i
\(326\) 78.2248 37.6711i 0.239953 0.115555i
\(327\) 0 0
\(328\) 260.597 + 207.820i 0.794505 + 0.633596i
\(329\) −80.6013 230.345i −0.244989 0.700138i
\(330\) 0 0
\(331\) −397.745 397.745i −1.20165 1.20165i −0.973666 0.227980i \(-0.926788\pi\)
−0.227980 0.973666i \(-0.573212\pi\)
\(332\) −234.408 + 186.934i −0.706048 + 0.563054i
\(333\) 0 0
\(334\) −10.5008 + 16.7119i −0.0314396 + 0.0500358i
\(335\) 54.7812 + 68.6935i 0.163526 + 0.205055i
\(336\) 0 0
\(337\) −42.6588 + 378.607i −0.126584 + 1.12346i 0.756416 + 0.654091i \(0.226949\pi\)
−0.883000 + 0.469373i \(0.844480\pi\)
\(338\) −25.9236 + 9.07105i −0.0766970 + 0.0268374i
\(339\) 0 0
\(340\) 0.157586 + 1.39861i 0.000463488 + 0.00411357i
\(341\) −3.87834 8.05346i −0.0113734 0.0236172i
\(342\) 0 0
\(343\) 34.6684 151.892i 0.101074 0.442834i
\(344\) −127.171 61.2422i −0.369682 0.178030i
\(345\) 0 0
\(346\) −59.1666 + 37.1768i −0.171002 + 0.107447i
\(347\) 274.022i 0.789689i 0.918748 + 0.394845i \(0.129202\pi\)
−0.918748 + 0.394845i \(0.870798\pi\)
\(348\) 0 0
\(349\) −156.235 −0.447666 −0.223833 0.974628i \(-0.571857\pi\)
−0.223833 + 0.974628i \(0.571857\pi\)
\(350\) 108.040 + 171.945i 0.308686 + 0.491271i
\(351\) 0 0
\(352\) −164.220 + 341.005i −0.466533 + 0.968765i
\(353\) −339.627 77.5177i −0.962117 0.219597i −0.287513 0.957777i \(-0.592828\pi\)
−0.674604 + 0.738180i \(0.735686\pi\)
\(354\) 0 0
\(355\) −183.897 + 88.5603i −0.518021 + 0.249466i
\(356\) 526.491 59.3213i 1.47891 0.166633i
\(357\) 0 0
\(358\) 33.2845 + 95.1216i 0.0929734 + 0.265703i
\(359\) 291.435 + 32.8368i 0.811796 + 0.0914674i 0.508096 0.861300i \(-0.330349\pi\)
0.303700 + 0.952768i \(0.401778\pi\)
\(360\) 0 0
\(361\) 81.5423 65.0278i 0.225879 0.180132i
\(362\) −230.715 144.968i −0.637333 0.400463i
\(363\) 0 0
\(364\) 294.842 + 369.721i 0.810007 + 1.01572i
\(365\) 15.1429 15.1429i 0.0414873 0.0414873i
\(366\) 0 0
\(367\) 94.9299 33.2174i 0.258665 0.0905107i −0.197832 0.980236i \(-0.563390\pi\)
0.456496 + 0.889725i \(0.349104\pi\)
\(368\) −28.0137 + 35.1281i −0.0761242 + 0.0954567i
\(369\) 0 0
\(370\) 5.67661 + 11.7876i 0.0153422 + 0.0318584i
\(371\) 135.263 + 592.625i 0.364589 + 1.59737i
\(372\) 0 0
\(373\) −579.925 279.277i −1.55476 0.748732i −0.558050 0.829807i \(-0.688450\pi\)
−0.996708 + 0.0810749i \(0.974165\pi\)
\(374\) 2.21849 + 0.776284i 0.00593180 + 0.00207563i
\(375\) 0 0
\(376\) 150.970i 0.401516i
\(377\) 39.7654 + 407.096i 0.105478 + 1.07983i
\(378\) 0 0
\(379\) −311.876 496.348i −0.822893 1.30963i −0.948253 0.317515i \(-0.897152\pi\)
0.125361 0.992111i \(-0.459991\pi\)
\(380\) 45.8150 130.932i 0.120566 0.344557i
\(381\) 0 0
\(382\) −166.428 37.9861i −0.435675 0.0994401i
\(383\) 588.492 134.319i 1.53653 0.350704i 0.631272 0.775561i \(-0.282533\pi\)
0.905260 + 0.424858i \(0.139676\pi\)
\(384\) 0 0
\(385\) 251.418 28.3281i 0.653035 0.0735794i
\(386\) −8.01753 6.39376i −0.0207708 0.0165642i
\(387\) 0 0
\(388\) 192.861 + 21.7302i 0.497065 + 0.0560057i
\(389\) −458.331 458.331i −1.17823 1.17823i −0.980195 0.198033i \(-0.936545\pi\)
−0.198033 0.980195i \(-0.563455\pi\)
\(390\) 0 0
\(391\) 1.25964 + 0.791484i 0.00322158 + 0.00202426i
\(392\) −222.469 + 354.058i −0.567524 + 0.903209i
\(393\) 0 0
\(394\) 127.297 127.297i 0.323089 0.323089i
\(395\) −9.46748 + 84.0262i −0.0239683 + 0.212725i
\(396\) 0 0
\(397\) −105.509 + 132.305i −0.265767 + 0.333261i −0.896752 0.442534i \(-0.854080\pi\)
0.630985 + 0.775795i \(0.282651\pi\)
\(398\) 21.8057 + 193.531i 0.0547881 + 0.486258i
\(399\) 0 0
\(400\) 30.6751 + 134.397i 0.0766878 + 0.335991i
\(401\) 127.467 558.467i 0.317872 1.39269i −0.523406 0.852084i \(-0.675339\pi\)
0.841278 0.540603i \(-0.181804\pi\)
\(402\) 0 0
\(403\) 10.1652 + 3.55694i 0.0252237 + 0.00882615i
\(404\) 378.206 237.643i 0.936154 0.588225i
\(405\) 0 0
\(406\) −256.209 + 118.736i −0.631057 + 0.292454i
\(407\) −82.0063 −0.201490
\(408\) 0 0
\(409\) 198.692 567.828i 0.485799 1.38833i −0.396670 0.917961i \(-0.629834\pi\)
0.882468 0.470372i \(-0.155880\pi\)
\(410\) −41.1328 + 85.4132i −0.100324 + 0.208325i
\(411\) 0 0
\(412\) 302.182 68.9711i 0.733451 0.167405i
\(413\) 463.062 222.999i 1.12121 0.539949i
\(414\) 0 0
\(415\) −151.102 120.500i −0.364102 0.290362i
\(416\) −150.611 430.420i −0.362045 1.03466i
\(417\) 0 0
\(418\) −163.800 163.800i −0.391866 0.391866i
\(419\) 447.663 356.999i 1.06841 0.852026i 0.0789538 0.996878i \(-0.474842\pi\)
0.989453 + 0.144852i \(0.0462706\pi\)
\(420\) 0 0
\(421\) −11.6235 + 18.4986i −0.0276092 + 0.0439398i −0.860244 0.509883i \(-0.829689\pi\)
0.832635 + 0.553823i \(0.186832\pi\)
\(422\) −199.844 250.596i −0.473564 0.593830i
\(423\) 0 0
\(424\) 42.1034 373.678i 0.0993005 0.881317i
\(425\) 4.30821 1.50751i 0.0101370 0.00354708i
\(426\) 0 0
\(427\) 87.9284 + 780.387i 0.205921 + 1.82760i
\(428\) 200.628 + 416.608i 0.468757 + 0.973384i
\(429\) 0 0
\(430\) 8.93318 39.1388i 0.0207748 0.0910206i
\(431\) −493.089 237.459i −1.14406 0.550949i −0.236814 0.971555i \(-0.576103\pi\)
−0.907243 + 0.420606i \(0.861817\pi\)
\(432\) 0 0
\(433\) 694.921 436.648i 1.60490 1.00842i 0.632659 0.774430i \(-0.281963\pi\)
0.972238 0.233993i \(-0.0751794\pi\)
\(434\) 7.43496i 0.0171312i
\(435\) 0 0
\(436\) −62.2522 −0.142780
\(437\) −78.0066 124.147i −0.178505 0.284089i
\(438\) 0 0
\(439\) 36.2784 75.3329i 0.0826387 0.171601i −0.855555 0.517712i \(-0.826784\pi\)
0.938193 + 0.346111i \(0.112498\pi\)
\(440\) −152.595 34.8287i −0.346806 0.0791562i
\(441\) 0 0
\(442\) −2.55136 + 1.22867i −0.00577231 + 0.00277980i
\(443\) −596.083 + 67.1625i −1.34556 + 0.151608i −0.755180 0.655517i \(-0.772451\pi\)
−0.590380 + 0.807125i \(0.701022\pi\)
\(444\) 0 0
\(445\) 112.800 + 322.365i 0.253484 + 0.724415i
\(446\) 327.074 + 36.8523i 0.733349 + 0.0826286i
\(447\) 0 0
\(448\) 26.6994 21.2921i 0.0595970 0.0475270i
\(449\) 143.331 + 90.0608i 0.319223 + 0.200581i 0.682105 0.731254i \(-0.261065\pi\)
−0.362883 + 0.931835i \(0.618207\pi\)
\(450\) 0 0
\(451\) −370.490 464.579i −0.821485 1.03011i
\(452\) 85.7126 85.7126i 0.189630 0.189630i
\(453\) 0 0
\(454\) 89.2825 31.2413i 0.196657 0.0688134i
\(455\) −190.059 + 238.327i −0.417712 + 0.523795i
\(456\) 0 0
\(457\) −307.067 637.632i −0.671919 1.39526i −0.906101 0.423062i \(-0.860955\pi\)
0.234181 0.972193i \(-0.424759\pi\)
\(458\) 30.9617 + 135.652i 0.0676020 + 0.296184i
\(459\) 0 0
\(460\) −39.3822 18.9655i −0.0856135 0.0412293i
\(461\) 189.621 + 66.3513i 0.411326 + 0.143929i 0.528006 0.849240i \(-0.322940\pi\)
−0.116681 + 0.993169i \(0.537225\pi\)
\(462\) 0 0
\(463\) 545.754i 1.17873i −0.807865 0.589367i \(-0.799377\pi\)
0.807865 0.589367i \(-0.200623\pi\)
\(464\) −190.787 + 18.6362i −0.411179 + 0.0401642i
\(465\) 0 0
\(466\) 154.899 + 246.521i 0.332402 + 0.529015i
\(467\) 8.31232 23.7552i 0.0177994 0.0508677i −0.934641 0.355593i \(-0.884279\pi\)
0.952440 + 0.304725i \(0.0985646\pi\)
\(468\) 0 0
\(469\) 446.594 + 101.932i 0.952225 + 0.217339i
\(470\) −41.8622 + 9.55477i −0.0890685 + 0.0203293i
\(471\) 0 0
\(472\) −315.951 + 35.5991i −0.669388 + 0.0754219i
\(473\) 196.734 + 156.890i 0.415929 + 0.331692i
\(474\) 0 0
\(475\) −447.022 50.3672i −0.941098 0.106036i
\(476\) 5.18872 + 5.18872i 0.0109007 + 0.0109007i
\(477\) 0 0
\(478\) 22.8776 + 14.3750i 0.0478612 + 0.0300732i
\(479\) −125.217 + 199.282i −0.261414 + 0.416038i −0.951481 0.307707i \(-0.900438\pi\)
0.690067 + 0.723746i \(0.257581\pi\)
\(480\) 0 0
\(481\) 69.8643 69.8643i 0.145248 0.145248i
\(482\) 15.1003 134.019i 0.0313283 0.278047i
\(483\) 0 0
\(484\) 31.6053 39.6318i 0.0653002 0.0818838i
\(485\) 14.0076 + 124.321i 0.0288816 + 0.256331i
\(486\) 0 0
\(487\) 205.721 + 901.323i 0.422425 + 1.85077i 0.518053 + 0.855348i \(0.326657\pi\)
−0.0956278 + 0.995417i \(0.530486\pi\)
\(488\) 108.106 473.644i 0.221529 0.970581i
\(489\) 0 0
\(490\) −112.256 39.2800i −0.229094 0.0801633i
\(491\) −413.153 + 259.601i −0.841452 + 0.528720i −0.882432 0.470440i \(-0.844095\pi\)
0.0409794 + 0.999160i \(0.486952\pi\)
\(492\) 0 0
\(493\) 1.32045 + 6.20820i 0.00267840 + 0.0125927i
\(494\) 279.095 0.564969
\(495\) 0 0
\(496\) −1.66697 + 4.76393i −0.00336083 + 0.00960470i
\(497\) −461.718 + 958.768i −0.929010 + 1.92911i
\(498\) 0 0
\(499\) 464.245 105.961i 0.930351 0.212347i 0.269618 0.962967i \(-0.413103\pi\)
0.660733 + 0.750621i \(0.270245\pi\)
\(500\) −265.678 + 127.944i −0.531355 + 0.255887i
\(501\) 0 0
\(502\) 59.0518 + 47.0922i 0.117633 + 0.0938092i
\(503\) 16.5430 + 47.2773i 0.0328887 + 0.0939906i 0.959157 0.282874i \(-0.0912879\pi\)
−0.926268 + 0.376865i \(0.877002\pi\)
\(504\) 0 0
\(505\) 203.597 + 203.597i 0.403162 + 0.403162i
\(506\) −57.0697 + 45.5116i −0.112786 + 0.0899438i
\(507\) 0 0
\(508\) 91.3111 145.321i 0.179746 0.286065i
\(509\) −484.514 607.562i −0.951895 1.19364i −0.980989 0.194062i \(-0.937834\pi\)
0.0290946 0.999577i \(-0.490738\pi\)
\(510\) 0 0
\(511\) 12.5009 110.948i 0.0244636 0.217120i
\(512\) 365.603 127.930i 0.714068 0.249863i
\(513\) 0 0
\(514\) −15.6769 139.136i −0.0304998 0.270693i
\(515\) 86.6899 + 180.013i 0.168330 + 0.349540i
\(516\) 0 0
\(517\) 59.8897 262.394i 0.115841 0.507531i
\(518\) 61.4558 + 29.5956i 0.118641 + 0.0571343i
\(519\) 0 0
\(520\) 159.673 100.329i 0.307063 0.192941i
\(521\) 368.806i 0.707881i −0.935268 0.353940i \(-0.884842\pi\)
0.935268 0.353940i \(-0.115158\pi\)
\(522\) 0 0
\(523\) 384.561 0.735299 0.367649 0.929964i \(-0.380163\pi\)
0.367649 + 0.929964i \(0.380163\pi\)
\(524\) −117.119 186.393i −0.223509 0.355713i
\(525\) 0 0
\(526\) 121.971 253.276i 0.231885 0.481514i
\(527\) 0.162923 + 0.0371861i 0.000309152 + 7.05619e-5i
\(528\) 0 0
\(529\) 434.986 209.478i 0.822280 0.395989i
\(530\) 106.281 11.9750i 0.200530 0.0225943i
\(531\) 0 0
\(532\) −238.861 682.626i −0.448987 1.28313i
\(533\) 711.427 + 80.1586i 1.33476 + 0.150391i
\(534\) 0 0
\(535\) −233.040 + 185.843i −0.435589 + 0.347370i
\(536\) −239.945 150.768i −0.447659 0.281283i
\(537\) 0 0
\(538\) −166.903 209.289i −0.310228 0.389014i
\(539\) 527.117 527.117i 0.977954 0.977954i
\(540\) 0 0
\(541\) −216.745 + 75.8424i −0.400638 + 0.140189i −0.523074 0.852287i \(-0.675215\pi\)
0.122436 + 0.992476i \(0.460929\pi\)
\(542\) −89.8792 + 112.705i −0.165829 + 0.207943i
\(543\) 0 0
\(544\) −3.07017 6.37527i −0.00564369 0.0117193i
\(545\) −8.92944 39.1224i −0.0163843 0.0717843i
\(546\) 0 0
\(547\) −20.9942 10.1103i −0.0383807 0.0184832i 0.414595 0.910006i \(-0.363923\pi\)
−0.452976 + 0.891523i \(0.649638\pi\)
\(548\) −289.830 101.416i −0.528888 0.185066i
\(549\) 0 0
\(550\) 223.958i 0.407197i
\(551\) 148.226 607.736i 0.269012 1.10297i
\(552\) 0 0
\(553\) 234.547 + 373.279i 0.424136 + 0.675008i
\(554\) −40.5346 + 115.841i −0.0731671 + 0.209099i
\(555\) 0 0
\(556\) −604.737 138.027i −1.08766 0.248250i
\(557\) 1081.10 246.754i 1.94093 0.443005i 0.949197 0.314682i \(-0.101898\pi\)
0.991733 0.128322i \(-0.0409592\pi\)
\(558\) 0 0
\(559\) −301.266 + 33.9446i −0.538938 + 0.0607238i
\(560\) −111.693 89.0718i −0.199451 0.159057i
\(561\) 0 0
\(562\) 341.386 + 38.4650i 0.607449 + 0.0684431i
\(563\) −160.111 160.111i −0.284390 0.284390i 0.550467 0.834857i \(-0.314450\pi\)
−0.834857 + 0.550467i \(0.814450\pi\)
\(564\) 0 0
\(565\) 66.1608 + 41.5716i 0.117099 + 0.0735780i
\(566\) 69.1820 110.103i 0.122230 0.194527i
\(567\) 0 0
\(568\) 465.499 465.499i 0.819540 0.819540i
\(569\) 56.4577 501.076i 0.0992226 0.880625i −0.841225 0.540686i \(-0.818165\pi\)
0.940447 0.339939i \(-0.110407\pi\)
\(570\) 0 0
\(571\) −35.8730 + 44.9834i −0.0628249 + 0.0787800i −0.812251 0.583308i \(-0.801758\pi\)
0.749426 + 0.662088i \(0.230329\pi\)
\(572\) 58.3930 + 518.252i 0.102086 + 0.906035i
\(573\) 0 0
\(574\) 109.983 + 481.865i 0.191607 + 0.839486i
\(575\) −31.5430 + 138.199i −0.0548573 + 0.240346i
\(576\) 0 0
\(577\) −699.675 244.827i −1.21261 0.424310i −0.353175 0.935557i \(-0.614898\pi\)
−0.859434 + 0.511247i \(0.829184\pi\)
\(578\) 224.437 141.023i 0.388299 0.243984i
\(579\) 0 0
\(580\) −58.9776 176.920i −0.101685 0.305035i
\(581\) −1007.62 −1.73428
\(582\) 0 0
\(583\) −221.416 + 632.769i −0.379787 + 1.08537i
\(584\) −29.9684 + 62.2301i −0.0513158 + 0.106558i
\(585\) 0 0
\(586\) −350.359 + 79.9672i −0.597883 + 0.136463i
\(587\) 381.756 183.844i 0.650351 0.313192i −0.0794637 0.996838i \(-0.525321\pi\)
0.729814 + 0.683645i \(0.239607\pi\)
\(588\) 0 0
\(589\) −12.8769 10.2690i −0.0218624 0.0174347i
\(590\) −29.8675 85.3563i −0.0506228 0.144672i
\(591\) 0 0
\(592\) 32.7421 + 32.7421i 0.0553077 + 0.0553077i
\(593\) −491.712 + 392.127i −0.829194 + 0.661260i −0.943202 0.332220i \(-0.892202\pi\)
0.114008 + 0.993480i \(0.463631\pi\)
\(594\) 0 0
\(595\) −2.51659 + 4.00512i −0.00422956 + 0.00673130i
\(596\) 67.9987 + 85.2676i 0.114092 + 0.143067i
\(597\) 0 0
\(598\) 9.84681 87.3929i 0.0164662 0.146142i
\(599\) −1029.67 + 360.297i −1.71898 + 0.601498i −0.995999 0.0893686i \(-0.971515\pi\)
−0.722983 + 0.690866i \(0.757229\pi\)
\(600\) 0 0
\(601\) 2.18327 + 19.3770i 0.00363272 + 0.0322413i 0.995398 0.0958291i \(-0.0305502\pi\)
−0.991765 + 0.128070i \(0.959122\pi\)
\(602\) −90.8127 188.575i −0.150852 0.313247i
\(603\) 0 0
\(604\) −60.9524 + 267.050i −0.100915 + 0.442136i
\(605\) 29.4401 + 14.1776i 0.0486613 + 0.0234340i
\(606\) 0 0
\(607\) −678.738 + 426.479i −1.11818 + 0.702602i −0.958649 0.284591i \(-0.908142\pi\)
−0.159535 + 0.987192i \(0.551000\pi\)
\(608\) 697.394i 1.14703i
\(609\) 0 0
\(610\) 138.177 0.226520
\(611\) 172.521 + 274.566i 0.282358 + 0.449371i
\(612\) 0 0
\(613\) −376.980 + 782.807i −0.614975 + 1.27701i 0.328167 + 0.944620i \(0.393569\pi\)
−0.943142 + 0.332390i \(0.892145\pi\)
\(614\) 461.370 + 105.305i 0.751417 + 0.171506i
\(615\) 0 0
\(616\) −735.215 + 354.061i −1.19353 + 0.574774i
\(617\) −80.6908 + 9.09167i −0.130779 + 0.0147353i −0.177111 0.984191i \(-0.556675\pi\)
0.0463322 + 0.998926i \(0.485247\pi\)
\(618\) 0 0
\(619\) −330.849 945.513i −0.534490 1.52748i −0.821874 0.569669i \(-0.807071\pi\)
0.287384 0.957815i \(-0.407214\pi\)
\(620\) −4.87929 0.549765i −0.00786983 0.000886717i
\(621\) 0 0
\(622\) −10.2961 + 8.21085i −0.0165532 + 0.0132007i
\(623\) 1507.68 + 947.337i 2.42003 + 1.52061i
\(624\) 0 0
\(625\) 206.552 + 259.007i 0.330482 + 0.414412i
\(626\) 10.9413 10.9413i 0.0174781 0.0174781i
\(627\) 0 0
\(628\) −132.924 + 46.5121i −0.211662 + 0.0740639i
\(629\) 0.955904 1.19867i 0.00151972 0.00190567i
\(630\) 0 0
\(631\) 335.980 + 697.669i 0.532456 + 1.10566i 0.977653 + 0.210224i \(0.0674193\pi\)
−0.445197 + 0.895433i \(0.646866\pi\)
\(632\) −60.6866 265.885i −0.0960231 0.420705i
\(633\) 0 0
\(634\) 44.1935 + 21.2825i 0.0697059 + 0.0335686i
\(635\) 104.425 + 36.5398i 0.164448 + 0.0575430i
\(636\) 0 0
\(637\) 898.143i 1.40996i
\(638\) −308.922 39.4541i −0.484203 0.0618403i
\(639\) 0 0
\(640\) 136.888 + 217.856i 0.213888 + 0.340400i
\(641\) −26.7029 + 76.3125i −0.0416582 + 0.119052i −0.962834 0.270095i \(-0.912945\pi\)
0.921175 + 0.389148i \(0.127230\pi\)
\(642\) 0 0
\(643\) −682.001 155.662i −1.06066 0.242088i −0.343609 0.939113i \(-0.611649\pi\)
−0.717047 + 0.697025i \(0.754507\pi\)
\(644\) −222.178 + 50.7106i −0.344997 + 0.0787432i
\(645\) 0 0
\(646\) 4.30355 0.484894i 0.00666184 0.000750610i
\(647\) −854.959 681.807i −1.32142 1.05380i −0.994053 0.108901i \(-0.965267\pi\)
−0.327368 0.944897i \(-0.606162\pi\)
\(648\) 0 0
\(649\) 563.261 + 63.4643i 0.867890 + 0.0977878i
\(650\) −190.798 190.798i −0.293536 0.293536i
\(651\) 0 0
\(652\) 253.123 + 159.048i 0.388226 + 0.243938i
\(653\) −272.229 + 433.250i −0.416889 + 0.663476i −0.987477 0.157761i \(-0.949572\pi\)
0.570588 + 0.821236i \(0.306715\pi\)
\(654\) 0 0
\(655\) 100.340 100.340i 0.153190 0.153190i
\(656\) −37.5666 + 333.413i −0.0572661 + 0.508251i
\(657\) 0 0
\(658\) −139.578 + 175.025i −0.212124 + 0.265996i
\(659\) 105.681 + 937.943i 0.160365 + 1.42328i 0.773746 + 0.633495i \(0.218380\pi\)
−0.613381 + 0.789787i \(0.710191\pi\)
\(660\) 0 0
\(661\) −116.346 509.745i −0.176015 0.771173i −0.983445 0.181209i \(-0.941999\pi\)
0.807429 0.589964i \(-0.200858\pi\)
\(662\) −114.820 + 503.058i −0.173444 + 0.759906i
\(663\) 0 0
\(664\) 588.361 + 205.876i 0.886086 + 0.310055i
\(665\) 394.735 248.028i 0.593586 0.372975i
\(666\) 0 0
\(667\) −185.071 67.8556i −0.277467 0.101733i
\(668\) −67.9580 −0.101734
\(669\) 0 0
\(670\) 26.6201 76.0758i 0.0397314 0.113546i
\(671\) −375.788 + 780.331i −0.560041 + 1.16294i
\(672\) 0 0
\(673\) 734.243 167.586i 1.09100 0.249014i 0.361072 0.932538i \(-0.382411\pi\)
0.729928 + 0.683524i \(0.239554\pi\)
\(674\) 314.894 151.645i 0.467201 0.224992i
\(675\) 0 0
\(676\) −73.9342 58.9606i −0.109370 0.0872198i
\(677\) −84.8727 242.552i −0.125366 0.358275i 0.864045 0.503414i \(-0.167923\pi\)
−0.989411 + 0.145139i \(0.953637\pi\)
\(678\) 0 0
\(679\) 461.217 + 461.217i 0.679260 + 0.679260i
\(680\) 2.28780 1.82446i 0.00336441 0.00268302i
\(681\) 0 0
\(682\) −4.36251 + 6.94289i −0.00639664 + 0.0101802i
\(683\) −765.006 959.287i −1.12007 1.40452i −0.903678 0.428213i \(-0.859143\pi\)
−0.216390 0.976307i \(-0.569428\pi\)
\(684\) 0 0
\(685\) 22.1618 196.691i 0.0323530 0.287141i
\(686\) −134.899 + 47.2030i −0.196645 + 0.0688091i
\(687\) 0 0
\(688\) −15.9082 141.189i −0.0231224 0.205217i
\(689\) −350.448 727.712i −0.508633 1.05619i
\(690\) 0 0
\(691\) −36.0165 + 157.799i −0.0521223 + 0.228363i −0.994280 0.106808i \(-0.965937\pi\)
0.942157 + 0.335171i \(0.108794\pi\)
\(692\) −216.770 104.391i −0.313252 0.150854i
\(693\) 0 0
\(694\) 212.840 133.736i 0.306686 0.192704i
\(695\) 399.846i 0.575318i
\(696\) 0 0
\(697\) 11.1092 0.0159387
\(698\) 76.2506 + 121.352i 0.109241 + 0.173857i
\(699\) 0 0
\(700\) −303.372 + 629.959i −0.433389 + 0.899942i
\(701\) 956.674 + 218.355i 1.36473 + 0.311490i 0.841295 0.540577i \(-0.181794\pi\)
0.523433 + 0.852067i \(0.324651\pi\)
\(702\) 0 0
\(703\) −136.139 + 65.5613i −0.193655 + 0.0932593i
\(704\) 37.4257 4.21686i 0.0531615 0.00598986i
\(705\) 0 0
\(706\) 105.545 + 301.630i 0.149497 + 0.427238i
\(707\) 1491.71 + 168.075i 2.10991 + 0.237730i
\(708\) 0 0
\(709\) −46.3533 + 36.9655i −0.0653784 + 0.0521375i −0.655634 0.755079i \(-0.727598\pi\)
0.590255 + 0.807217i \(0.299027\pi\)
\(710\) 158.538 + 99.6161i 0.223293 + 0.140304i
\(711\) 0 0
\(712\) −686.794 861.212i −0.964598 1.20957i
\(713\) −3.66985 + 3.66985i −0.00514705 + 0.00514705i
\(714\) 0 0
\(715\) −317.320 + 111.035i −0.443804 + 0.155294i
\(716\) −216.344 + 271.287i −0.302157 + 0.378893i
\(717\) 0 0
\(718\) −116.729 242.391i −0.162576 0.337592i
\(719\) 13.6399 + 59.7604i 0.0189707 + 0.0831160i 0.983527 0.180761i \(-0.0578559\pi\)
−0.964556 + 0.263877i \(0.914999\pi\)
\(720\) 0 0
\(721\) 938.518 + 451.966i 1.30169 + 0.626860i
\(722\) −90.3055 31.5992i −0.125077 0.0437663i
\(723\) 0 0
\(724\) 938.186i 1.29584i
\(725\) −516.801 + 314.137i −0.712829 + 0.433292i
\(726\) 0 0
\(727\) 495.191 + 788.091i 0.681142 + 1.08403i 0.991079 + 0.133275i \(0.0425493\pi\)
−0.309937 + 0.950757i \(0.600308\pi\)
\(728\) 324.719 927.995i 0.446043 1.27472i
\(729\) 0 0
\(730\) −19.1523 4.37139i −0.0262361 0.00598821i
\(731\) −4.58646 + 1.04683i −0.00627422 + 0.00143205i
\(732\) 0 0
\(733\) 905.749 102.053i 1.23567 0.139227i 0.530144 0.847907i \(-0.322138\pi\)
0.705530 + 0.708680i \(0.250709\pi\)
\(734\) −72.1313 57.5228i −0.0982716 0.0783690i
\(735\) 0 0
\(736\) 218.375 + 24.6049i 0.296705 + 0.0334306i
\(737\) 357.227 + 357.227i 0.484705 + 0.484705i
\(738\) 0 0
\(739\) 725.917 + 456.124i 0.982297 + 0.617218i 0.924529 0.381112i \(-0.124459\pi\)
0.0577679 + 0.998330i \(0.481602\pi\)
\(740\) −23.9667 + 38.1429i −0.0323875 + 0.0515444i
\(741\) 0 0
\(742\) 394.292 394.292i 0.531391 0.531391i
\(743\) 28.5464 253.356i 0.0384204 0.340991i −0.959766 0.280799i \(-0.909400\pi\)
0.998187 0.0601911i \(-0.0191710\pi\)
\(744\) 0 0
\(745\) −43.8328 + 54.9646i −0.0588360 + 0.0737780i
\(746\) 66.1101 + 586.744i 0.0886195 + 0.786520i
\(747\) 0 0
\(748\) 1.80080 + 7.88983i 0.00240749 + 0.0105479i
\(749\) −345.801 + 1515.05i −0.461683 + 2.02277i
\(750\) 0 0
\(751\) 322.155 + 112.727i 0.428968 + 0.150103i 0.536123 0.844140i \(-0.319888\pi\)
−0.107155 + 0.994242i \(0.534174\pi\)
\(752\) −128.676 + 80.8525i −0.171112 + 0.107517i
\(753\) 0 0
\(754\) 296.795 229.570i 0.393627 0.304469i
\(755\) −176.571 −0.233869
\(756\) 0 0
\(757\) −182.836 + 522.514i −0.241527 + 0.690244i 0.757762 + 0.652531i \(0.226293\pi\)
−0.999289 + 0.0377125i \(0.987993\pi\)
\(758\) −233.316 + 484.485i −0.307804 + 0.639162i
\(759\) 0 0
\(760\) −281.168 + 64.1748i −0.369958 + 0.0844405i
\(761\) 449.183 216.315i 0.590253 0.284251i −0.114819 0.993386i \(-0.536629\pi\)
0.705072 + 0.709135i \(0.250915\pi\)
\(762\) 0 0
\(763\) −163.570 130.443i −0.214378 0.170961i
\(764\) −194.129 554.789i −0.254096 0.726164i
\(765\) 0 0
\(766\) −391.542 391.542i −0.511152 0.511152i
\(767\) −533.931 + 425.796i −0.696129 + 0.555144i
\(768\) 0 0
\(769\) −44.7471 + 71.2146i −0.0581887 + 0.0926068i −0.874552 0.484933i \(-0.838844\pi\)
0.816363 + 0.577539i \(0.195987\pi\)
\(770\) −144.708 181.458i −0.187932 0.235659i
\(771\) 0 0
\(772\) 3.95333 35.0868i 0.00512089 0.0454492i
\(773\) 657.345 230.015i 0.850381 0.297561i 0.130320 0.991472i \(-0.458399\pi\)
0.720061 + 0.693911i \(0.244114\pi\)
\(774\) 0 0
\(775\) 1.78286 + 15.8233i 0.00230047 + 0.0204172i
\(776\) −175.075 363.547i −0.225612 0.468488i
\(777\) 0 0
\(778\) −132.309 + 579.686i −0.170064 + 0.745097i
\(779\) −986.469 475.059i −1.26633 0.609831i
\(780\) 0 0
\(781\) −993.723 + 624.398i −1.27237 + 0.799485i
\(782\) 1.36468i 0.00174511i
\(783\) 0 0
\(784\) −420.917 −0.536884
\(785\) −48.2972 76.8645i −0.0615251 0.0979166i
\(786\) 0 0
\(787\) 380.344 789.793i 0.483284