Properties

Label 261.3.s.a.73.3
Level $261$
Weight $3$
Character 261.73
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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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 73.3
Character \(\chi\) \(=\) 261.73
Dual form 261.3.s.a.118.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68783 - 0.190173i) q^{2} +(-1.08711 + 0.248126i) q^{4} +(-0.141728 - 0.113024i) q^{5} +(-1.55116 + 6.79606i) q^{7} +(-8.20045 + 2.86946i) q^{8} +O(q^{10})\) \(q+(1.68783 - 0.190173i) q^{2} +(-1.08711 + 0.248126i) q^{4} +(-0.141728 - 0.113024i) q^{5} +(-1.55116 + 6.79606i) q^{7} +(-8.20045 + 2.86946i) q^{8} +(-0.260707 - 0.163813i) q^{10} +(12.2566 + 4.28875i) q^{11} +(9.66173 + 20.0628i) q^{13} +(-1.32566 + 11.7656i) q^{14} +(-9.27670 + 4.46742i) q^{16} +(5.90660 + 5.90660i) q^{17} +(-10.7431 + 17.0975i) q^{19} +(0.182118 + 0.0877036i) q^{20} +(21.5026 + 4.90782i) q^{22} +(-15.0384 - 18.8575i) q^{23} +(-5.55571 - 24.3412i) q^{25} +(20.1228 + 32.0252i) q^{26} -7.77294i q^{28} +(-28.5764 + 4.93832i) q^{29} +(35.5909 - 4.01014i) q^{31} +(14.6174 - 9.18473i) q^{32} +(11.0926 + 8.84605i) q^{34} +(0.987964 - 0.787875i) q^{35} +(-23.0925 + 8.08043i) q^{37} +(-14.8810 + 30.9007i) q^{38} +(1.48655 + 0.520168i) q^{40} +(14.1288 - 14.1288i) q^{41} +(-4.31425 + 38.2901i) q^{43} +(-14.3884 - 1.62118i) q^{44} +(-28.9684 - 28.9684i) q^{46} +(-1.53295 + 4.38091i) q^{47} +(0.367152 + 0.176811i) q^{49} +(-14.0061 - 40.0272i) q^{50} +(-15.4815 - 19.4131i) q^{52} +(51.0246 - 63.9828i) q^{53} +(-1.25237 - 1.99313i) q^{55} +(-6.78085 - 60.1817i) q^{56} +(-47.2930 + 13.7695i) q^{58} -28.0326 q^{59} +(-3.26475 + 2.05138i) q^{61} +(59.3088 - 13.5368i) q^{62} +(55.1251 - 43.9608i) q^{64} +(0.898247 - 3.93548i) q^{65} +(-2.88318 + 5.98698i) q^{67} +(-7.88670 - 4.95554i) q^{68} +(1.51768 - 1.51768i) q^{70} +(15.5711 + 32.3337i) q^{71} +(103.524 + 11.6644i) q^{73} +(-37.4396 + 18.0300i) q^{74} +(7.43657 - 21.2525i) q^{76} +(-48.1585 + 76.6437i) q^{77} +(-28.1618 - 80.4819i) q^{79} +(1.81970 + 0.415334i) q^{80} +(21.1601 - 26.5339i) q^{82} +(6.13681 + 26.8871i) q^{83} +(-0.169541 - 1.50472i) q^{85} +65.4475i q^{86} -112.816 q^{88} +(-26.8243 + 3.02237i) q^{89} +(-151.335 + 34.5412i) q^{91} +(21.0274 + 16.7688i) q^{92} +(-1.75422 + 7.68575i) q^{94} +(3.45503 - 1.20897i) q^{95} +(-6.09419 - 3.82923i) q^{97} +(0.653314 + 0.228604i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{27}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.68783 0.190173i 0.843915 0.0950863i 0.320588 0.947219i \(-0.396119\pi\)
0.523326 + 0.852132i \(0.324691\pi\)
\(3\) 0 0
\(4\) −1.08711 + 0.248126i −0.271777 + 0.0620314i
\(5\) −0.141728 0.113024i −0.0283456 0.0226049i 0.609215 0.793005i \(-0.291485\pi\)
−0.637560 + 0.770401i \(0.720056\pi\)
\(6\) 0 0
\(7\) −1.55116 + 6.79606i −0.221594 + 0.970865i 0.734685 + 0.678408i \(0.237330\pi\)
−0.956279 + 0.292457i \(0.905527\pi\)
\(8\) −8.20045 + 2.86946i −1.02506 + 0.358683i
\(9\) 0 0
\(10\) −0.260707 0.163813i −0.0260707 0.0163813i
\(11\) 12.2566 + 4.28875i 1.11423 + 0.389887i 0.823727 0.566987i \(-0.191891\pi\)
0.290505 + 0.956873i \(0.406177\pi\)
\(12\) 0 0
\(13\) 9.66173 + 20.0628i 0.743210 + 1.54329i 0.836694 + 0.547671i \(0.184486\pi\)
−0.0934833 + 0.995621i \(0.529800\pi\)
\(14\) −1.32566 + 11.7656i −0.0946901 + 0.840398i
\(15\) 0 0
\(16\) −9.27670 + 4.46742i −0.579794 + 0.279214i
\(17\) 5.90660 + 5.90660i 0.347447 + 0.347447i 0.859158 0.511711i \(-0.170988\pi\)
−0.511711 + 0.859158i \(0.670988\pi\)
\(18\) 0 0
\(19\) −10.7431 + 17.0975i −0.565425 + 0.899868i −1.00000 0.000767373i \(-0.999756\pi\)
0.434575 + 0.900636i \(0.356899\pi\)
\(20\) 0.182118 + 0.0877036i 0.00910592 + 0.00438518i
\(21\) 0 0
\(22\) 21.5026 + 4.90782i 0.977390 + 0.223083i
\(23\) −15.0384 18.8575i −0.653843 0.819893i 0.338814 0.940853i \(-0.389974\pi\)
−0.992657 + 0.120960i \(0.961403\pi\)
\(24\) 0 0
\(25\) −5.55571 24.3412i −0.222228 0.973646i
\(26\) 20.1228 + 32.0252i 0.773952 + 1.23174i
\(27\) 0 0
\(28\) 7.77294i 0.277605i
\(29\) −28.5764 + 4.93832i −0.985395 + 0.170287i
\(30\) 0 0
\(31\) 35.5909 4.01014i 1.14809 0.129359i 0.482655 0.875811i \(-0.339673\pi\)
0.665440 + 0.746451i \(0.268244\pi\)
\(32\) 14.6174 9.18473i 0.456794 0.287023i
\(33\) 0 0
\(34\) 11.0926 + 8.84605i 0.326253 + 0.260178i
\(35\) 0.987964 0.787875i 0.0282275 0.0225107i
\(36\) 0 0
\(37\) −23.0925 + 8.08043i −0.624123 + 0.218390i −0.623767 0.781610i \(-0.714399\pi\)
−0.000355153 1.00000i \(0.500113\pi\)
\(38\) −14.8810 + 30.9007i −0.391605 + 0.813176i
\(39\) 0 0
\(40\) 1.48655 + 0.520168i 0.0371639 + 0.0130042i
\(41\) 14.1288 14.1288i 0.344605 0.344605i −0.513490 0.858095i \(-0.671648\pi\)
0.858095 + 0.513490i \(0.171648\pi\)
\(42\) 0 0
\(43\) −4.31425 + 38.2901i −0.100331 + 0.890466i 0.838221 + 0.545330i \(0.183596\pi\)
−0.938553 + 0.345136i \(0.887833\pi\)
\(44\) −14.3884 1.62118i −0.327008 0.0368450i
\(45\) 0 0
\(46\) −28.9684 28.9684i −0.629748 0.629748i
\(47\) −1.53295 + 4.38091i −0.0326159 + 0.0932108i −0.959040 0.283271i \(-0.908580\pi\)
0.926424 + 0.376482i \(0.122866\pi\)
\(48\) 0 0
\(49\) 0.367152 + 0.176811i 0.00749289 + 0.00360839i
\(50\) −14.0061 40.0272i −0.280122 0.800544i
\(51\) 0 0
\(52\) −15.4815 19.4131i −0.297720 0.373330i
\(53\) 51.0246 63.9828i 0.962728 1.20722i −0.0155405 0.999879i \(-0.504947\pi\)
0.978268 0.207343i \(-0.0664817\pi\)
\(54\) 0 0
\(55\) −1.25237 1.99313i −0.0227703 0.0362387i
\(56\) −6.78085 60.1817i −0.121087 1.07467i
\(57\) 0 0
\(58\) −47.2930 + 13.7695i −0.815397 + 0.237405i
\(59\) −28.0326 −0.475129 −0.237564 0.971372i \(-0.576349\pi\)
−0.237564 + 0.971372i \(0.576349\pi\)
\(60\) 0 0
\(61\) −3.26475 + 2.05138i −0.0535205 + 0.0336292i −0.558527 0.829487i \(-0.688633\pi\)
0.505006 + 0.863116i \(0.331490\pi\)
\(62\) 59.3088 13.5368i 0.956594 0.218336i
\(63\) 0 0
\(64\) 55.1251 43.9608i 0.861329 0.686887i
\(65\) 0.898247 3.93548i 0.0138192 0.0605458i
\(66\) 0 0
\(67\) −2.88318 + 5.98698i −0.0430325 + 0.0893579i −0.921377 0.388671i \(-0.872934\pi\)
0.878344 + 0.478029i \(0.158649\pi\)
\(68\) −7.88670 4.95554i −0.115981 0.0728756i
\(69\) 0 0
\(70\) 1.51768 1.51768i 0.0216812 0.0216812i
\(71\) 15.5711 + 32.3337i 0.219311 + 0.455404i 0.981376 0.192096i \(-0.0615286\pi\)
−0.762065 + 0.647501i \(0.775814\pi\)
\(72\) 0 0
\(73\) 103.524 + 11.6644i 1.41814 + 0.159786i 0.787511 0.616301i \(-0.211370\pi\)
0.630626 + 0.776087i \(0.282798\pi\)
\(74\) −37.4396 + 18.0300i −0.505940 + 0.243648i
\(75\) 0 0
\(76\) 7.43657 21.2525i 0.0978496 0.279638i
\(77\) −48.1585 + 76.6437i −0.625434 + 0.995373i
\(78\) 0 0
\(79\) −28.1618 80.4819i −0.356479 1.01876i −0.972877 0.231323i \(-0.925694\pi\)
0.616398 0.787435i \(-0.288591\pi\)
\(80\) 1.81970 + 0.415334i 0.0227462 + 0.00519168i
\(81\) 0 0
\(82\) 21.1601 26.5339i 0.258050 0.323584i
\(83\) 6.13681 + 26.8871i 0.0739375 + 0.323941i 0.998348 0.0574578i \(-0.0182995\pi\)
−0.924410 + 0.381399i \(0.875442\pi\)
\(84\) 0 0
\(85\) −0.169541 1.50472i −0.00199461 0.0177026i
\(86\) 65.4475i 0.761018i
\(87\) 0 0
\(88\) −112.816 −1.28200
\(89\) −26.8243 + 3.02237i −0.301397 + 0.0339592i −0.261368 0.965239i \(-0.584174\pi\)
−0.0400288 + 0.999199i \(0.512745\pi\)
\(90\) 0 0
\(91\) −151.335 + 34.5412i −1.66302 + 0.379573i
\(92\) 21.0274 + 16.7688i 0.228559 + 0.182270i
\(93\) 0 0
\(94\) −1.75422 + 7.68575i −0.0186619 + 0.0817633i
\(95\) 3.45503 1.20897i 0.0363688 0.0127260i
\(96\) 0 0
\(97\) −6.09419 3.82923i −0.0628267 0.0394766i 0.500252 0.865880i \(-0.333241\pi\)
−0.563079 + 0.826403i \(0.690383\pi\)
\(98\) 0.653314 + 0.228604i 0.00666647 + 0.00233270i
\(99\) 0 0
\(100\) 12.0793 + 25.0830i 0.120793 + 0.250830i
\(101\) 12.4952 110.898i 0.123715 1.09800i −0.766433 0.642324i \(-0.777970\pi\)
0.890148 0.455672i \(-0.150601\pi\)
\(102\) 0 0
\(103\) 108.481 52.2416i 1.05321 0.507200i 0.174552 0.984648i \(-0.444152\pi\)
0.878660 + 0.477448i \(0.158438\pi\)
\(104\) −136.800 136.800i −1.31538 1.31538i
\(105\) 0 0
\(106\) 73.9530 117.696i 0.697670 1.11033i
\(107\) 127.998 + 61.6404i 1.19624 + 0.576079i 0.922602 0.385754i \(-0.126059\pi\)
0.273638 + 0.961833i \(0.411773\pi\)
\(108\) 0 0
\(109\) 30.7554 + 7.01972i 0.282160 + 0.0644011i 0.361259 0.932466i \(-0.382347\pi\)
−0.0790990 + 0.996867i \(0.525204\pi\)
\(110\) −2.49282 3.12590i −0.0226620 0.0284172i
\(111\) 0 0
\(112\) −15.9713 69.9747i −0.142601 0.624774i
\(113\) 51.3355 + 81.7000i 0.454297 + 0.723009i 0.992822 0.119600i \(-0.0381613\pi\)
−0.538526 + 0.842609i \(0.681018\pi\)
\(114\) 0 0
\(115\) 4.37235i 0.0380205i
\(116\) 29.8404 12.4590i 0.257245 0.107406i
\(117\) 0 0
\(118\) −47.3143 + 5.33104i −0.400968 + 0.0451783i
\(119\) −49.3036 + 30.9795i −0.414316 + 0.260332i
\(120\) 0 0
\(121\) 37.2281 + 29.6884i 0.307671 + 0.245359i
\(122\) −5.12023 + 4.08324i −0.0419691 + 0.0334692i
\(123\) 0 0
\(124\) −37.6962 + 13.1905i −0.304002 + 0.106375i
\(125\) −3.93008 + 8.16089i −0.0314406 + 0.0652871i
\(126\) 0 0
\(127\) 95.5607 + 33.4381i 0.752446 + 0.263292i 0.679132 0.734017i \(-0.262357\pi\)
0.0733147 + 0.997309i \(0.476642\pi\)
\(128\) 35.8531 35.8531i 0.280102 0.280102i
\(129\) 0 0
\(130\) 0.767667 6.81324i 0.00590513 0.0524095i
\(131\) −95.6113 10.7728i −0.729857 0.0822352i −0.260787 0.965396i \(-0.583982\pi\)
−0.469070 + 0.883161i \(0.655411\pi\)
\(132\) 0 0
\(133\) −99.5314 99.5314i −0.748356 0.748356i
\(134\) −3.72775 + 10.6533i −0.0278190 + 0.0795022i
\(135\) 0 0
\(136\) −65.3855 31.4880i −0.480776 0.231529i
\(137\) −60.7818 173.704i −0.443662 1.26791i −0.921127 0.389263i \(-0.872730\pi\)
0.477464 0.878651i \(-0.341556\pi\)
\(138\) 0 0
\(139\) 116.483 + 146.065i 0.838009 + 1.05083i 0.997969 + 0.0637063i \(0.0202921\pi\)
−0.159960 + 0.987124i \(0.551136\pi\)
\(140\) −0.878533 + 1.10165i −0.00627524 + 0.00786890i
\(141\) 0 0
\(142\) 32.4303 + 51.6126i 0.228383 + 0.363469i
\(143\) 32.3752 + 287.338i 0.226400 + 2.00935i
\(144\) 0 0
\(145\) 4.60824 + 2.52994i 0.0317810 + 0.0174479i
\(146\) 176.949 1.21198
\(147\) 0 0
\(148\) 23.0992 14.5142i 0.156075 0.0980687i
\(149\) −112.412 + 25.6572i −0.754440 + 0.172196i −0.582410 0.812896i \(-0.697890\pi\)
−0.172031 + 0.985092i \(0.555033\pi\)
\(150\) 0 0
\(151\) −7.95750 + 6.34590i −0.0526987 + 0.0420258i −0.649485 0.760374i \(-0.725015\pi\)
0.596786 + 0.802400i \(0.296444\pi\)
\(152\) 39.0374 171.034i 0.256825 1.12522i
\(153\) 0 0
\(154\) −66.7077 + 138.520i −0.433167 + 0.899480i
\(155\) −5.49748 3.45430i −0.0354676 0.0222858i
\(156\) 0 0
\(157\) −54.2399 + 54.2399i −0.345477 + 0.345477i −0.858422 0.512945i \(-0.828555\pi\)
0.512945 + 0.858422i \(0.328555\pi\)
\(158\) −62.8378 130.484i −0.397708 0.825849i
\(159\) 0 0
\(160\) −3.10980 0.350390i −0.0194363 0.00218994i
\(161\) 151.484 72.9508i 0.940894 0.453111i
\(162\) 0 0
\(163\) −9.39776 + 26.8573i −0.0576550 + 0.164768i −0.969109 0.246634i \(-0.920675\pi\)
0.911454 + 0.411403i \(0.134961\pi\)
\(164\) −11.8538 + 18.8653i −0.0722795 + 0.115032i
\(165\) 0 0
\(166\) 15.4711 + 44.2138i 0.0931994 + 0.266348i
\(167\) 41.1889 + 9.40109i 0.246640 + 0.0562939i 0.344053 0.938950i \(-0.388200\pi\)
−0.0974137 + 0.995244i \(0.531057\pi\)
\(168\) 0 0
\(169\) −203.797 + 255.553i −1.20590 + 1.51215i
\(170\) −0.572314 2.50747i −0.00336655 0.0147498i
\(171\) 0 0
\(172\) −4.81068 42.6960i −0.0279691 0.248232i
\(173\) 127.036i 0.734309i −0.930160 0.367155i \(-0.880332\pi\)
0.930160 0.367155i \(-0.119668\pi\)
\(174\) 0 0
\(175\) 174.042 0.994524
\(176\) −132.860 + 14.9697i −0.754887 + 0.0850553i
\(177\) 0 0
\(178\) −44.7001 + 10.2025i −0.251124 + 0.0573174i
\(179\) 114.042 + 90.9455i 0.637106 + 0.508075i 0.887943 0.459954i \(-0.152134\pi\)
−0.250836 + 0.968030i \(0.580706\pi\)
\(180\) 0 0
\(181\) 48.4132 212.112i 0.267476 1.17189i −0.645462 0.763792i \(-0.723335\pi\)
0.912938 0.408098i \(-0.133808\pi\)
\(182\) −248.859 + 87.0794i −1.36735 + 0.478458i
\(183\) 0 0
\(184\) 177.433 + 111.488i 0.964307 + 0.605914i
\(185\) 4.18615 + 1.46480i 0.0226278 + 0.00791782i
\(186\) 0 0
\(187\) 47.0626 + 97.7265i 0.251672 + 0.522602i
\(188\) 0.579465 5.14289i 0.00308226 0.0273558i
\(189\) 0 0
\(190\) 5.60159 2.69758i 0.0294821 0.0141978i
\(191\) 140.809 + 140.809i 0.737221 + 0.737221i 0.972039 0.234818i \(-0.0754495\pi\)
−0.234818 + 0.972039i \(0.575450\pi\)
\(192\) 0 0
\(193\) −170.596 + 271.502i −0.883916 + 1.40674i 0.0294336 + 0.999567i \(0.490630\pi\)
−0.913349 + 0.407177i \(0.866513\pi\)
\(194\) −11.0142 5.30414i −0.0567740 0.0273409i
\(195\) 0 0
\(196\) −0.443006 0.101113i −0.00226023 0.000515883i
\(197\) 35.3554 + 44.3343i 0.179469 + 0.225047i 0.863426 0.504475i \(-0.168314\pi\)
−0.683957 + 0.729522i \(0.739742\pi\)
\(198\) 0 0
\(199\) −6.42619 28.1550i −0.0322924 0.141482i 0.956212 0.292676i \(-0.0945456\pi\)
−0.988504 + 0.151193i \(0.951688\pi\)
\(200\) 115.405 + 183.666i 0.577027 + 0.918332i
\(201\) 0 0
\(202\) 189.553i 0.938379i
\(203\) 10.7654 201.867i 0.0530317 0.994420i
\(204\) 0 0
\(205\) −3.59935 + 0.405549i −0.0175578 + 0.00197829i
\(206\) 173.162 108.805i 0.840593 0.528179i
\(207\) 0 0
\(208\) −179.258 142.953i −0.861817 0.687276i
\(209\) −205.000 + 163.482i −0.980861 + 0.782211i
\(210\) 0 0
\(211\) 281.518 98.5074i 1.33421 0.466860i 0.433449 0.901178i \(-0.357296\pi\)
0.900759 + 0.434318i \(0.143011\pi\)
\(212\) −39.5935 + 82.2168i −0.186762 + 0.387815i
\(213\) 0 0
\(214\) 227.761 + 79.6969i 1.06430 + 0.372415i
\(215\) 4.93917 4.93917i 0.0229729 0.0229729i
\(216\) 0 0
\(217\) −27.9540 + 248.098i −0.128820 + 1.14331i
\(218\) 53.2448 + 5.99925i 0.244242 + 0.0275195i
\(219\) 0 0
\(220\) 1.85601 + 1.85601i 0.00843639 + 0.00843639i
\(221\) −61.4349 + 175.571i −0.277986 + 0.794438i
\(222\) 0 0
\(223\) −61.9105 29.8145i −0.277625 0.133697i 0.289890 0.957060i \(-0.406381\pi\)
−0.567516 + 0.823363i \(0.692095\pi\)
\(224\) 39.7461 + 113.588i 0.177438 + 0.507088i
\(225\) 0 0
\(226\) 102.183 + 128.133i 0.452136 + 0.566960i
\(227\) −275.667 + 345.675i −1.21439 + 1.52280i −0.429625 + 0.903007i \(0.641354\pi\)
−0.784766 + 0.619792i \(0.787217\pi\)
\(228\) 0 0
\(229\) −48.7472 77.5808i −0.212870 0.338781i 0.723173 0.690667i \(-0.242683\pi\)
−0.936043 + 0.351887i \(0.885540\pi\)
\(230\) 0.831502 + 7.37979i 0.00361523 + 0.0320860i
\(231\) 0 0
\(232\) 220.169 122.495i 0.949006 0.527997i
\(233\) 115.705 0.496587 0.248294 0.968685i \(-0.420130\pi\)
0.248294 + 0.968685i \(0.420130\pi\)
\(234\) 0 0
\(235\) 0.712412 0.447638i 0.00303154 0.00190484i
\(236\) 30.4745 6.95561i 0.129129 0.0294729i
\(237\) 0 0
\(238\) −77.3247 + 61.6644i −0.324893 + 0.259094i
\(239\) 39.0003 170.872i 0.163181 0.714944i −0.825436 0.564495i \(-0.809071\pi\)
0.988618 0.150449i \(-0.0480719\pi\)
\(240\) 0 0
\(241\) 1.62503 3.37442i 0.00674288 0.0140017i −0.897570 0.440872i \(-0.854669\pi\)
0.904313 + 0.426870i \(0.140384\pi\)
\(242\) 68.4807 + 43.0293i 0.282978 + 0.177807i
\(243\) 0 0
\(244\) 3.04014 3.04014i 0.0124596 0.0124596i
\(245\) −0.0320518 0.0665563i −0.000130824 0.000271658i
\(246\) 0 0
\(247\) −446.820 50.3446i −1.80899 0.203824i
\(248\) −280.355 + 135.012i −1.13046 + 0.544402i
\(249\) 0 0
\(250\) −5.08132 + 14.5216i −0.0203253 + 0.0580863i
\(251\) 101.330 161.266i 0.403705 0.642493i −0.581565 0.813500i \(-0.697559\pi\)
0.985270 + 0.171007i \(0.0547022\pi\)
\(252\) 0 0
\(253\) −103.444 295.625i −0.408868 1.16848i
\(254\) 167.649 + 38.2648i 0.660036 + 0.150649i
\(255\) 0 0
\(256\) −122.148 + 153.168i −0.477139 + 0.598313i
\(257\) −31.9955 140.182i −0.124496 0.545454i −0.998253 0.0590900i \(-0.981180\pi\)
0.873756 0.486364i \(-0.161677\pi\)
\(258\) 0 0
\(259\) −19.0949 169.472i −0.0737256 0.654333i
\(260\) 4.50117i 0.0173122i
\(261\) 0 0
\(262\) −163.424 −0.623757
\(263\) 14.2134 1.60147i 0.0540434 0.00608923i −0.0849014 0.996389i \(-0.527058\pi\)
0.138945 + 0.990300i \(0.455629\pi\)
\(264\) 0 0
\(265\) −14.4632 + 3.30114i −0.0545783 + 0.0124571i
\(266\) −186.920 149.064i −0.702707 0.560390i
\(267\) 0 0
\(268\) 1.64881 7.22389i 0.00615226 0.0269548i
\(269\) −115.482 + 40.4089i −0.429301 + 0.150219i −0.536276 0.844043i \(-0.680169\pi\)
0.106975 + 0.994262i \(0.465884\pi\)
\(270\) 0 0
\(271\) 364.109 + 228.785i 1.34358 + 0.844225i 0.995639 0.0932924i \(-0.0297391\pi\)
0.347938 + 0.937518i \(0.386882\pi\)
\(272\) −81.1810 28.4065i −0.298460 0.104435i
\(273\) 0 0
\(274\) −135.623 281.624i −0.494975 1.02783i
\(275\) 36.2994 322.166i 0.131998 1.17151i
\(276\) 0 0
\(277\) 363.232 174.923i 1.31131 0.631492i 0.358064 0.933697i \(-0.383437\pi\)
0.953243 + 0.302205i \(0.0977227\pi\)
\(278\) 224.381 + 224.381i 0.807127 + 0.807127i
\(279\) 0 0
\(280\) −5.84097 + 9.29585i −0.0208606 + 0.0331995i
\(281\) −55.4249 26.6912i −0.197242 0.0949865i 0.332656 0.943048i \(-0.392055\pi\)
−0.529897 + 0.848062i \(0.677770\pi\)
\(282\) 0 0
\(283\) 172.772 + 39.4340i 0.610501 + 0.139343i 0.516583 0.856237i \(-0.327204\pi\)
0.0939179 + 0.995580i \(0.470061\pi\)
\(284\) −24.9503 31.2867i −0.0878532 0.110164i
\(285\) 0 0
\(286\) 109.288 + 478.820i 0.382124 + 1.67420i
\(287\) 74.1042 + 117.936i 0.258203 + 0.410927i
\(288\) 0 0
\(289\) 219.224i 0.758561i
\(290\) 8.25905 + 3.39374i 0.0284795 + 0.0117026i
\(291\) 0 0
\(292\) −115.436 + 13.0065i −0.395329 + 0.0445429i
\(293\) 42.8502 26.9246i 0.146246 0.0918927i −0.456921 0.889507i \(-0.651048\pi\)
0.603168 + 0.797614i \(0.293905\pi\)
\(294\) 0 0
\(295\) 3.97301 + 3.16837i 0.0134678 + 0.0107402i
\(296\) 166.183 132.526i 0.561428 0.447724i
\(297\) 0 0
\(298\) −184.852 + 64.6826i −0.620310 + 0.217056i
\(299\) 233.038 483.909i 0.779392 1.61842i
\(300\) 0 0
\(301\) −253.529 88.7138i −0.842290 0.294730i
\(302\) −12.2241 + 12.2241i −0.0404771 + 0.0404771i
\(303\) 0 0
\(304\) 23.2785 206.602i 0.0765739 0.679612i
\(305\) 0.694563 + 0.0782585i 0.00227726 + 0.000256585i
\(306\) 0 0
\(307\) 91.5953 + 91.5953i 0.298356 + 0.298356i 0.840370 0.542014i \(-0.182338\pi\)
−0.542014 + 0.840370i \(0.682338\pi\)
\(308\) 33.3362 95.2695i 0.108235 0.309317i
\(309\) 0 0
\(310\) −9.93573 4.78479i −0.0320507 0.0154348i
\(311\) −161.202 460.688i −0.518333 1.48131i −0.844269 0.535919i \(-0.819965\pi\)
0.325936 0.945392i \(-0.394320\pi\)
\(312\) 0 0
\(313\) −331.292 415.427i −1.05844 1.32724i −0.942581 0.333979i \(-0.891609\pi\)
−0.115861 0.993265i \(-0.536963\pi\)
\(314\) −81.2328 + 101.863i −0.258703 + 0.324403i
\(315\) 0 0
\(316\) 50.5846 + 80.5050i 0.160078 + 0.254763i
\(317\) −49.7527 441.567i −0.156948 1.39296i −0.787264 0.616617i \(-0.788503\pi\)
0.630315 0.776339i \(-0.282926\pi\)
\(318\) 0 0
\(319\) −371.428 62.0306i −1.16435 0.194453i
\(320\) −12.7814 −0.0399420
\(321\) 0 0
\(322\) 241.806 151.937i 0.750949 0.471853i
\(323\) −164.443 + 37.5330i −0.509112 + 0.116201i
\(324\) 0 0
\(325\) 434.674 346.641i 1.33746 1.06659i
\(326\) −10.7543 + 47.1177i −0.0329886 + 0.144533i
\(327\) 0 0
\(328\) −75.3204 + 156.404i −0.229635 + 0.476843i
\(329\) −27.3951 17.2135i −0.0832677 0.0523205i
\(330\) 0 0
\(331\) −206.567 + 206.567i −0.624068 + 0.624068i −0.946569 0.322501i \(-0.895477\pi\)
0.322501 + 0.946569i \(0.395477\pi\)
\(332\) −13.3428 27.7066i −0.0401891 0.0834535i
\(333\) 0 0
\(334\) 71.3076 + 8.03443i 0.213496 + 0.0240552i
\(335\) 1.08530 0.522654i 0.00323971 0.00156016i
\(336\) 0 0
\(337\) 156.253 446.546i 0.463659 1.32506i −0.440457 0.897774i \(-0.645184\pi\)
0.904116 0.427287i \(-0.140531\pi\)
\(338\) −295.375 + 470.087i −0.873891 + 1.39079i
\(339\) 0 0
\(340\) 0.557670 + 1.59373i 0.00164021 + 0.00468744i
\(341\) 453.421 + 103.490i 1.32968 + 0.303491i
\(342\) 0 0
\(343\) −214.737 + 269.272i −0.626055 + 0.785049i
\(344\) −74.4930 326.375i −0.216549 0.948765i
\(345\) 0 0
\(346\) −24.1587 214.414i −0.0698228 0.619694i
\(347\) 511.474i 1.47399i 0.675899 + 0.736994i \(0.263755\pi\)
−0.675899 + 0.736994i \(0.736245\pi\)
\(348\) 0 0
\(349\) −482.022 −1.38115 −0.690576 0.723260i \(-0.742643\pi\)
−0.690576 + 0.723260i \(0.742643\pi\)
\(350\) 293.753 33.0980i 0.839293 0.0945657i
\(351\) 0 0
\(352\) 218.550 49.8827i 0.620881 0.141712i
\(353\) −190.763 152.128i −0.540404 0.430958i 0.314869 0.949135i \(-0.398039\pi\)
−0.855273 + 0.518177i \(0.826611\pi\)
\(354\) 0 0
\(355\) 1.44764 6.34252i 0.00407785 0.0178662i
\(356\) 28.4110 9.94145i 0.0798063 0.0279254i
\(357\) 0 0
\(358\) 209.779 + 131.813i 0.585975 + 0.368192i
\(359\) −569.212 199.176i −1.58555 0.554808i −0.613522 0.789677i \(-0.710248\pi\)
−0.972027 + 0.234870i \(0.924534\pi\)
\(360\) 0 0
\(361\) −20.2788 42.1094i −0.0561741 0.116647i
\(362\) 41.3753 367.216i 0.114296 1.01441i
\(363\) 0 0
\(364\) 155.947 75.1001i 0.428426 0.206319i
\(365\) −13.3539 13.3539i −0.0365861 0.0365861i
\(366\) 0 0
\(367\) 137.681 219.118i 0.375153 0.597052i −0.604777 0.796395i \(-0.706738\pi\)
0.979930 + 0.199343i \(0.0638807\pi\)
\(368\) 223.751 + 107.753i 0.608020 + 0.292807i
\(369\) 0 0
\(370\) 7.34407 + 1.67624i 0.0198488 + 0.00453037i
\(371\) 355.684 + 446.013i 0.958716 + 1.20219i
\(372\) 0 0
\(373\) −135.641 594.282i −0.363649 1.59325i −0.743850 0.668347i \(-0.767002\pi\)
0.380201 0.924904i \(-0.375855\pi\)
\(374\) 98.0185 + 155.996i 0.262082 + 0.417101i
\(375\) 0 0
\(376\) 40.3241i 0.107245i
\(377\) −375.174 525.611i −0.995158 1.39419i
\(378\) 0 0
\(379\) −160.764 + 18.1138i −0.424180 + 0.0477936i −0.321475 0.946918i \(-0.604179\pi\)
−0.102706 + 0.994712i \(0.532750\pi\)
\(380\) −3.45602 + 2.17156i −0.00909480 + 0.00571464i
\(381\) 0 0
\(382\) 264.440 + 210.884i 0.692251 + 0.552052i
\(383\) 272.105 216.997i 0.710458 0.566571i −0.200189 0.979757i \(-0.564155\pi\)
0.910647 + 0.413186i \(0.135584\pi\)
\(384\) 0 0
\(385\) 15.4880 5.41950i 0.0402287 0.0140766i
\(386\) −236.304 + 490.691i −0.612187 + 1.27122i
\(387\) 0 0
\(388\) 7.57518 + 2.65067i 0.0195237 + 0.00683163i
\(389\) −254.246 + 254.246i −0.653588 + 0.653588i −0.953855 0.300267i \(-0.902924\pi\)
0.300267 + 0.953855i \(0.402924\pi\)
\(390\) 0 0
\(391\) 22.5582 200.210i 0.0576936 0.512045i
\(392\) −3.51816 0.396401i −0.00897490 0.00101123i
\(393\) 0 0
\(394\) 68.1051 + 68.1051i 0.172856 + 0.172856i
\(395\) −5.10510 + 14.5895i −0.0129243 + 0.0369355i
\(396\) 0 0
\(397\) 110.601 + 53.2627i 0.278592 + 0.134163i 0.567963 0.823054i \(-0.307732\pi\)
−0.289371 + 0.957217i \(0.593446\pi\)
\(398\) −16.2006 46.2987i −0.0407051 0.116328i
\(399\) 0 0
\(400\) 160.281 + 200.986i 0.400702 + 0.502465i
\(401\) −158.554 + 198.821i −0.395398 + 0.495813i −0.939186 0.343410i \(-0.888418\pi\)
0.543788 + 0.839223i \(0.316990\pi\)
\(402\) 0 0
\(403\) 424.325 + 675.309i 1.05292 + 1.67570i
\(404\) 13.9329 + 123.658i 0.0344875 + 0.306085i
\(405\) 0 0
\(406\) −20.2194 342.765i −0.0498015 0.844248i
\(407\) −317.690 −0.780565
\(408\) 0 0
\(409\) −55.7403 + 35.0239i −0.136284 + 0.0856331i −0.598449 0.801161i \(-0.704216\pi\)
0.462164 + 0.886794i \(0.347073\pi\)
\(410\) −5.99796 + 1.36900i −0.0146292 + 0.00333901i
\(411\) 0 0
\(412\) −104.968 + 83.7092i −0.254777 + 0.203178i
\(413\) 43.4830 190.511i 0.105286 0.461286i
\(414\) 0 0
\(415\) 2.16915 4.50428i 0.00522686 0.0108537i
\(416\) 325.501 + 204.526i 0.782454 + 0.491649i
\(417\) 0 0
\(418\) −314.915 + 314.915i −0.753386 + 0.753386i
\(419\) 226.933 + 471.231i 0.541606 + 1.12466i 0.974743 + 0.223329i \(0.0716923\pi\)
−0.433137 + 0.901328i \(0.642593\pi\)
\(420\) 0 0
\(421\) −192.380 21.6760i −0.456960 0.0514871i −0.119515 0.992832i \(-0.538134\pi\)
−0.337445 + 0.941345i \(0.609563\pi\)
\(422\) 456.421 219.801i 1.08157 0.520855i
\(423\) 0 0
\(424\) −234.828 + 671.100i −0.553840 + 1.58278i
\(425\) 110.958 176.589i 0.261078 0.415503i
\(426\) 0 0
\(427\) −8.87715 25.3694i −0.0207896 0.0594132i
\(428\) −154.442 35.2504i −0.360846 0.0823608i
\(429\) 0 0
\(430\) 7.39717 9.27576i 0.0172027 0.0215715i
\(431\) 58.0221 + 254.212i 0.134622 + 0.589818i 0.996565 + 0.0828129i \(0.0263904\pi\)
−0.861943 + 0.507005i \(0.830752\pi\)
\(432\) 0 0
\(433\) 6.90278 + 61.2639i 0.0159418 + 0.141487i 0.999162 0.0409369i \(-0.0130343\pi\)
−0.983220 + 0.182424i \(0.941606\pi\)
\(434\) 424.064i 0.977106i
\(435\) 0 0
\(436\) −35.1763 −0.0806795
\(437\) 483.975 54.5309i 1.10750 0.124785i
\(438\) 0 0
\(439\) −173.225 + 39.5375i −0.394590 + 0.0900626i −0.415212 0.909725i \(-0.636293\pi\)
0.0206218 + 0.999787i \(0.493435\pi\)
\(440\) 15.9892 + 12.7509i 0.0363390 + 0.0289794i
\(441\) 0 0
\(442\) −70.3028 + 308.017i −0.159056 + 0.696871i
\(443\) −632.160 + 221.202i −1.42700 + 0.499328i −0.929721 0.368265i \(-0.879952\pi\)
−0.497276 + 0.867592i \(0.665666\pi\)
\(444\) 0 0
\(445\) 4.14336 + 2.60345i 0.00931093 + 0.00585044i
\(446\) −110.164 38.5481i −0.247005 0.0864308i
\(447\) 0 0
\(448\) 213.252 + 442.823i 0.476010 + 0.988445i
\(449\) −28.7774 + 255.406i −0.0640921 + 0.568834i 0.920094 + 0.391697i \(0.128112\pi\)
−0.984186 + 0.177136i \(0.943317\pi\)
\(450\) 0 0
\(451\) 233.765 112.575i 0.518327 0.249613i
\(452\) −76.0792 76.0792i −0.168317 0.168317i
\(453\) 0 0
\(454\) −399.541 + 635.865i −0.880045 + 1.40058i
\(455\) 25.3524 + 12.2091i 0.0557196 + 0.0268331i
\(456\) 0 0
\(457\) 508.462 + 116.053i 1.11261 + 0.253946i 0.739043 0.673658i \(-0.235278\pi\)
0.373566 + 0.927604i \(0.378135\pi\)
\(458\) −97.0308 121.673i −0.211858 0.265661i
\(459\) 0 0
\(460\) −1.08489 4.75323i −0.00235846 0.0103331i
\(461\) 305.337 + 485.941i 0.662336 + 1.05410i 0.993859 + 0.110655i \(0.0352948\pi\)
−0.331523 + 0.943447i \(0.607562\pi\)
\(462\) 0 0
\(463\) 548.047i 1.18369i 0.806053 + 0.591843i \(0.201600\pi\)
−0.806053 + 0.591843i \(0.798400\pi\)
\(464\) 243.033 173.474i 0.523779 0.373867i
\(465\) 0 0
\(466\) 195.290 22.0039i 0.419077 0.0472187i
\(467\) 696.323 437.528i 1.49105 0.936892i 0.493304 0.869857i \(-0.335789\pi\)
0.997751 0.0670350i \(-0.0213539\pi\)
\(468\) 0 0
\(469\) −36.2156 28.8810i −0.0772187 0.0615799i
\(470\) 1.11730 0.891017i 0.00237724 0.00189578i
\(471\) 0 0
\(472\) 229.880 80.4385i 0.487034 0.170420i
\(473\) −217.095 + 450.801i −0.458974 + 0.953069i
\(474\) 0 0
\(475\) 475.858 + 166.510i 1.00181 + 0.350547i
\(476\) 45.9116 45.9116i 0.0964530 0.0964530i
\(477\) 0 0
\(478\) 33.3308 295.819i 0.0697297 0.618868i
\(479\) −272.204 30.6701i −0.568277 0.0640294i −0.176848 0.984238i \(-0.556590\pi\)
−0.391428 + 0.920209i \(0.628019\pi\)
\(480\) 0 0
\(481\) −385.230 385.230i −0.800894 0.800894i
\(482\) 2.10106 6.00448i 0.00435904 0.0124574i
\(483\) 0 0
\(484\) −47.8375 23.0373i −0.0988379 0.0475978i
\(485\) 0.430922 + 1.23150i 0.000888498 + 0.00253918i
\(486\) 0 0
\(487\) 77.1649 + 96.7617i 0.158449 + 0.198689i 0.854719 0.519091i \(-0.173730\pi\)
−0.696269 + 0.717781i \(0.745158\pi\)
\(488\) 20.8861 26.1903i 0.0427993 0.0536686i
\(489\) 0 0
\(490\) −0.0667551 0.106240i −0.000136235 0.000216817i
\(491\) −11.6732 103.602i −0.0237743 0.211002i 0.976209 0.216833i \(-0.0695727\pi\)
−0.999983 + 0.00583045i \(0.998144\pi\)
\(492\) 0 0
\(493\) −197.958 139.621i −0.401538 0.283207i
\(494\) −763.731 −1.54601
\(495\) 0 0
\(496\) −312.251 + 196.201i −0.629539 + 0.395566i
\(497\) −243.895 + 55.6675i −0.490734 + 0.112007i
\(498\) 0 0
\(499\) −276.912 + 220.830i −0.554935 + 0.442546i −0.860372 0.509666i \(-0.829769\pi\)
0.305437 + 0.952212i \(0.401197\pi\)
\(500\) 2.24750 9.84694i 0.00449500 0.0196939i
\(501\) 0 0
\(502\) 140.359 291.459i 0.279600 0.580596i
\(503\) 437.771 + 275.070i 0.870320 + 0.546858i 0.891553 0.452916i \(-0.149616\pi\)
−0.0212333 + 0.999775i \(0.506759\pi\)
\(504\) 0 0
\(505\) −14.3051 + 14.3051i −0.0283269 + 0.0283269i
\(506\) −230.815 479.292i −0.456155 0.947217i
\(507\) 0 0
\(508\) −112.182 12.6399i −0.220830 0.0248816i
\(509\) −282.331 + 135.964i −0.554679 + 0.267119i −0.690155 0.723661i \(-0.742458\pi\)
0.135477 + 0.990781i \(0.456743\pi\)
\(510\) 0 0
\(511\) −239.853 + 685.462i −0.469381 + 1.34141i
\(512\) −284.940 + 453.480i −0.556524 + 0.885703i
\(513\) 0 0
\(514\) −80.6617 230.518i −0.156929 0.448479i
\(515\) −21.2794 4.85688i −0.0413192 0.00943083i
\(516\) 0 0
\(517\) −37.5773 + 47.1204i −0.0726833 + 0.0911420i
\(518\) −64.4580 282.409i −0.124436 0.545191i
\(519\) 0 0
\(520\) 3.92667 + 34.8502i 0.00755129 + 0.0670195i
\(521\) 903.060i 1.73332i −0.498898 0.866661i \(-0.666262\pi\)
0.498898 0.866661i \(-0.333738\pi\)
\(522\) 0 0
\(523\) 643.715 1.23081 0.615407 0.788210i \(-0.288992\pi\)
0.615407 + 0.788210i \(0.288992\pi\)
\(524\) 106.613 12.0124i 0.203460 0.0229244i
\(525\) 0 0
\(526\) 23.6853 5.40601i 0.0450290 0.0102776i
\(527\) 233.908 + 186.535i 0.443847 + 0.353957i
\(528\) 0 0
\(529\) −11.7403 + 51.4375i −0.0221934 + 0.0972354i
\(530\) −23.7837 + 8.32228i −0.0448749 + 0.0157024i
\(531\) 0 0
\(532\) 132.898 + 83.5053i 0.249808 + 0.156965i
\(533\) 419.972 + 146.955i 0.787940 + 0.275712i
\(534\) 0 0
\(535\) −11.1740 23.2031i −0.0208860 0.0433702i
\(536\) 6.46394 57.3690i 0.0120596 0.107032i
\(537\) 0 0
\(538\) −187.229 + 90.1649i −0.348010 + 0.167593i
\(539\) 3.74172 + 3.74172i 0.00694196 + 0.00694196i
\(540\) 0 0
\(541\) 63.1537 100.509i 0.116735 0.185783i −0.783246 0.621712i \(-0.786437\pi\)
0.899981 + 0.435929i \(0.143580\pi\)
\(542\) 658.063 + 316.906i 1.21414 + 0.584698i
\(543\) 0 0
\(544\) 140.590 + 32.0887i 0.258437 + 0.0589865i
\(545\) −3.56551 4.47101i −0.00654222 0.00820368i
\(546\) 0 0
\(547\) −141.842 621.450i −0.259309 1.13611i −0.921993 0.387206i \(-0.873440\pi\)
0.662684 0.748899i \(-0.269417\pi\)
\(548\) 109.177 + 173.754i 0.199228 + 0.317070i
\(549\) 0 0
\(550\) 550.664i 1.00121i
\(551\) 222.566 541.638i 0.403931 0.983010i
\(552\) 0 0
\(553\) 590.643 66.5495i 1.06807 0.120343i
\(554\) 579.808 364.317i 1.04658 0.657613i
\(555\) 0 0
\(556\) −162.873 129.887i −0.292936 0.233609i
\(557\) −593.908 + 473.626i −1.06626 + 0.850316i −0.989180 0.146709i \(-0.953132\pi\)
−0.0770829 + 0.997025i \(0.524561\pi\)
\(558\) 0 0
\(559\) −809.889 + 283.392i −1.44882 + 0.506963i
\(560\) −5.64527 + 11.7225i −0.0100808 + 0.0209331i
\(561\) 0 0
\(562\) −98.6237 34.5099i −0.175487 0.0614055i
\(563\) 443.544 443.544i 0.787822 0.787822i −0.193315 0.981137i \(-0.561924\pi\)
0.981137 + 0.193315i \(0.0619240\pi\)
\(564\) 0 0
\(565\) 1.95841 17.3814i 0.00346621 0.0307635i
\(566\) 299.109 + 33.7014i 0.528460 + 0.0595432i
\(567\) 0 0
\(568\) −220.470 220.470i −0.388152 0.388152i
\(569\) −92.2750 + 263.707i −0.162170 + 0.463456i −0.996081 0.0884427i \(-0.971811\pi\)
0.833911 + 0.551899i \(0.186097\pi\)
\(570\) 0 0
\(571\) 438.799 + 211.315i 0.768475 + 0.370078i 0.776686 0.629888i \(-0.216899\pi\)
−0.00821061 + 0.999966i \(0.502614\pi\)
\(572\) −106.491 304.334i −0.186173 0.532053i
\(573\) 0 0
\(574\) 147.503 + 184.963i 0.256975 + 0.322236i
\(575\) −375.466 + 470.819i −0.652984 + 0.818816i
\(576\) 0 0
\(577\) 150.219 + 239.072i 0.260345 + 0.414336i 0.951161 0.308694i \(-0.0998918\pi\)
−0.690817 + 0.723030i \(0.742749\pi\)
\(578\) −41.6905 370.013i −0.0721288 0.640161i
\(579\) 0 0
\(580\) −5.63741 1.60690i −0.00971966 0.00277052i
\(581\) −192.246 −0.330888
\(582\) 0 0
\(583\) 899.792 565.377i 1.54338 0.969771i
\(584\) −882.413 + 201.405i −1.51098 + 0.344872i
\(585\) 0 0
\(586\) 67.2035 53.5930i 0.114682 0.0914556i
\(587\) −36.9042 + 161.688i −0.0628691 + 0.275448i −0.996586 0.0825656i \(-0.973689\pi\)
0.933717 + 0.358013i \(0.116546\pi\)
\(588\) 0 0
\(589\) −313.793 + 651.597i −0.532755 + 1.10628i
\(590\) 7.30830 + 4.59211i 0.0123870 + 0.00778324i
\(591\) 0 0
\(592\) 178.124 178.124i 0.300885 0.300885i
\(593\) −464.417 964.372i −0.783165 1.62626i −0.779610 0.626266i \(-0.784582\pi\)
−0.00355571 0.999994i \(-0.501132\pi\)
\(594\) 0 0
\(595\) 10.4892 + 1.18184i 0.0176288 + 0.00198629i
\(596\) 115.838 55.7844i 0.194358 0.0935980i
\(597\) 0 0
\(598\) 301.302 861.073i 0.503850 1.43992i
\(599\) −19.6237 + 31.2310i −0.0327608 + 0.0521385i −0.862703 0.505711i \(-0.831230\pi\)
0.829942 + 0.557849i \(0.188373\pi\)
\(600\) 0 0
\(601\) −165.010 471.571i −0.274559 0.784645i −0.995766 0.0919249i \(-0.970698\pi\)
0.721207 0.692720i \(-0.243588\pi\)
\(602\) −444.785 101.519i −0.738846 0.168637i
\(603\) 0 0
\(604\) 7.07610 8.87315i 0.0117154 0.0146906i
\(605\) −1.92076 8.41538i −0.00317480 0.0139097i
\(606\) 0 0
\(607\) −18.5846 164.942i −0.0306171 0.271734i −0.999689 0.0249540i \(-0.992056\pi\)
0.969072 0.246780i \(-0.0793725\pi\)
\(608\) 348.593i 0.573344i
\(609\) 0 0
\(610\) 1.18719 0.00194621
\(611\) −102.704 + 11.5720i −0.168092 + 0.0189394i
\(612\) 0 0
\(613\) −793.283 + 181.062i −1.29410 + 0.295370i −0.813497 0.581569i \(-0.802439\pi\)
−0.480602 + 0.876939i \(0.659582\pi\)
\(614\) 172.016 + 137.178i 0.280157 + 0.223418i
\(615\) 0 0
\(616\) 174.995 766.702i 0.284082 1.24465i
\(617\) 889.197 311.143i 1.44116 0.504284i 0.507254 0.861797i \(-0.330661\pi\)
0.933908 + 0.357512i \(0.116375\pi\)
\(618\) 0 0
\(619\) −690.219 433.693i −1.11505 0.700635i −0.157108 0.987581i \(-0.550217\pi\)
−0.957947 + 0.286946i \(0.907360\pi\)
\(620\) 6.83347 + 2.39113i 0.0110217 + 0.00385667i
\(621\) 0 0
\(622\) −359.691 746.906i −0.578281 1.20081i
\(623\) 21.0685 186.988i 0.0338177 0.300141i
\(624\) 0 0
\(625\) −560.886 + 270.108i −0.897418 + 0.432174i
\(626\) −638.168 638.168i −1.01944 1.01944i
\(627\) 0 0
\(628\) 45.5064 72.4231i 0.0724625 0.115323i
\(629\) −184.126 88.6705i −0.292728 0.140971i
\(630\) 0 0
\(631\) 430.841 + 98.3366i 0.682791 + 0.155842i 0.549827 0.835278i \(-0.314694\pi\)
0.132963 + 0.991121i \(0.457551\pi\)
\(632\) 461.879 + 579.178i 0.730822 + 0.916421i
\(633\) 0 0
\(634\) −167.948 735.828i −0.264902 1.16061i
\(635\) −9.76432 15.5398i −0.0153769 0.0244722i
\(636\) 0 0
\(637\) 9.07439i 0.0142455i
\(638\) −638.704 34.0616i −1.00110 0.0533881i
\(639\) 0 0
\(640\) −9.13367 + 1.02912i −0.0142714 + 0.00160800i
\(641\) −439.716 + 276.292i −0.685984 + 0.431032i −0.829419 0.558628i \(-0.811328\pi\)
0.143435 + 0.989660i \(0.454185\pi\)
\(642\) 0 0
\(643\) 886.679 + 707.103i 1.37897 + 1.09969i 0.983439 + 0.181241i \(0.0580115\pi\)
0.395533 + 0.918452i \(0.370560\pi\)
\(644\) −146.579 + 116.893i −0.227607 + 0.181510i
\(645\) 0 0
\(646\) −270.414 + 94.6219i −0.418597 + 0.146474i
\(647\) 64.3196 133.561i 0.0994120 0.206431i −0.845331 0.534243i \(-0.820597\pi\)
0.944743 + 0.327812i \(0.106311\pi\)
\(648\) 0 0
\(649\) −343.583 120.225i −0.529404 0.185246i
\(650\) 667.734 667.734i 1.02728 1.02728i
\(651\) 0 0
\(652\) 3.55242 31.5286i 0.00544850 0.0483568i
\(653\) 828.414 + 93.3398i 1.26863 + 0.142940i 0.720500 0.693455i \(-0.243912\pi\)
0.548128 + 0.836395i \(0.315341\pi\)
\(654\) 0 0
\(655\) 12.3332 + 12.3332i 0.0188294 + 0.0188294i
\(656\) −67.9493 + 194.188i −0.103581 + 0.296018i
\(657\) 0 0
\(658\) −49.5117 23.8436i −0.0752458 0.0362365i
\(659\) −30.0943 86.0046i −0.0456666 0.130508i 0.918792 0.394743i \(-0.129166\pi\)
−0.964458 + 0.264235i \(0.914881\pi\)
\(660\) 0 0
\(661\) −17.7926 22.3113i −0.0269177 0.0337538i 0.768190 0.640221i \(-0.221157\pi\)
−0.795108 + 0.606468i \(0.792586\pi\)
\(662\) −309.366 + 387.933i −0.467320 + 0.586001i
\(663\) 0 0
\(664\) −127.476 202.877i −0.191982 0.305538i
\(665\) 2.85692 + 25.3559i 0.00429613 + 0.0381292i
\(666\) 0 0
\(667\) 522.868 + 464.617i 0.783910 + 0.696578i
\(668\) −47.1095 −0.0705231
\(669\) 0 0
\(670\) 1.73241 1.08855i 0.00258569 0.00162470i
\(671\) −48.8125 + 11.1411i −0.0727458 + 0.0166038i
\(672\) 0 0
\(673\) −459.480 + 366.423i −0.682734 + 0.544463i −0.902286 0.431138i \(-0.858112\pi\)
0.219551 + 0.975601i \(0.429541\pi\)
\(674\) 178.808 783.408i 0.265293 1.16233i
\(675\) 0 0
\(676\) 158.140 328.382i 0.233935 0.485772i
\(677\) 104.008 + 65.3523i 0.153630 + 0.0965322i 0.606653 0.794967i \(-0.292512\pi\)
−0.453023 + 0.891499i \(0.649654\pi\)
\(678\) 0 0
\(679\) 35.4767 35.4767i 0.0522485 0.0522485i
\(680\) 5.70806 + 11.8529i 0.00839420 + 0.0174307i
\(681\) 0 0
\(682\) 784.978 + 88.4458i 1.15099 + 0.129686i
\(683\) −909.152 + 437.825i −1.33112 + 0.641032i −0.958004 0.286755i \(-0.907423\pi\)
−0.373112 + 0.927786i \(0.621709\pi\)
\(684\) 0 0
\(685\) −11.0183 + 31.4886i −0.0160852 + 0.0459688i
\(686\) −311.231 + 495.322i −0.453690 + 0.722043i
\(687\) 0 0
\(688\) −131.036 374.479i −0.190459 0.544301i
\(689\) 1776.66 + 405.511i 2.57861 + 0.588550i
\(690\) 0 0
\(691\) −82.1865 + 103.059i −0.118938 + 0.149144i −0.837736 0.546075i \(-0.816121\pi\)
0.718798 + 0.695219i \(0.244693\pi\)
\(692\) 31.5208 + 138.102i 0.0455503 + 0.199569i
\(693\) 0 0
\(694\) 97.2684 + 863.280i 0.140156 + 1.24392i
\(695\) 33.8670i 0.0487296i
\(696\) 0 0
\(697\) 166.906 0.239464
\(698\) −813.571 + 91.6674i −1.16557 + 0.131329i
\(699\) 0 0
\(700\) −189.202 + 43.1842i −0.270289 + 0.0616918i
\(701\) −205.200 163.642i −0.292725 0.233441i 0.466104 0.884730i \(-0.345657\pi\)
−0.758830 + 0.651289i \(0.774229\pi\)
\(702\) 0 0
\(703\) 109.930 481.633i 0.156372 0.685111i
\(704\) 864.181 302.390i 1.22753 0.429531i
\(705\) 0 0
\(706\) −350.905 220.488i −0.497033 0.312307i
\(707\) 734.285 + 256.937i 1.03859 + 0.363419i
\(708\) 0 0
\(709\) 242.106 + 502.738i 0.341475 + 0.709081i 0.999017 0.0443379i \(-0.0141178\pi\)
−0.657541 + 0.753418i \(0.728404\pi\)
\(710\) 1.23719 10.9804i 0.00174252 0.0154653i
\(711\) 0 0
\(712\) 211.299 101.756i 0.296768 0.142916i
\(713\) −610.852 610.852i −0.856735 0.856735i
\(714\) 0 0
\(715\) 27.8877 44.3830i 0.0390038 0.0620742i
\(716\) −146.542 70.5710i −0.204668 0.0985628i
\(717\) 0 0
\(718\) −998.611 227.926i −1.39082 0.317446i
\(719\) −173.291 217.300i −0.241017 0.302225i 0.646581 0.762846i \(-0.276198\pi\)
−0.887597 + 0.460620i \(0.847627\pi\)
\(720\) 0 0
\(721\) 186.766 + 818.277i 0.259038 + 1.13492i
\(722\) −42.2353 67.2171i −0.0584976 0.0930984i
\(723\) 0 0
\(724\) 242.602i 0.335085i
\(725\) 278.967 + 668.148i 0.384782 + 0.921583i
\(726\) 0 0
\(727\) −868.909 + 97.9026i −1.19520 + 0.134667i −0.687055 0.726606i \(-0.741097\pi\)
−0.508144 + 0.861272i \(0.669668\pi\)
\(728\) 1141.90 717.502i 1.56854 0.985580i
\(729\) 0 0
\(730\) −25.0787 19.9996i −0.0343543 0.0273967i
\(731\) −251.647 + 200.681i −0.344250 + 0.274530i
\(732\) 0 0
\(733\) 121.421 42.4869i 0.165649 0.0579631i −0.246181 0.969224i \(-0.579176\pi\)
0.411830 + 0.911261i \(0.364890\pi\)
\(734\) 190.712 396.017i 0.259825 0.539533i
\(735\) 0 0
\(736\) −393.024 137.525i −0.534000 0.186855i
\(737\) −61.0145 + 61.0145i −0.0827876 + 0.0827876i
\(738\) 0 0
\(739\) 61.1890 543.068i 0.0827998 0.734868i −0.881886 0.471463i \(-0.843726\pi\)
0.964685 0.263405i \(-0.0848455\pi\)
\(740\) −4.91426 0.553704i −0.00664089 0.000748249i
\(741\) 0 0
\(742\) 685.153 + 685.153i 0.923387 + 0.923387i
\(743\) −73.3592 + 209.649i −0.0987338 + 0.282165i −0.982647 0.185486i \(-0.940614\pi\)
0.883913 + 0.467651i \(0.154900\pi\)
\(744\) 0 0
\(745\) 18.8318 + 9.06891i 0.0252776 + 0.0121730i
\(746\) −341.955 977.252i −0.458385 1.30999i
\(747\) 0 0
\(748\) −75.4107 94.5620i −0.100816 0.126420i
\(749\) −617.456 + 774.266i −0.824374 + 1.03373i
\(750\) 0 0
\(751\) −4.56022 7.25755i −0.00607220 0.00966385i 0.843674 0.536855i \(-0.180388\pi\)
−0.849747 + 0.527191i \(0.823245\pi\)
\(752\) −5.35069 47.4887i −0.00711528 0.0631498i
\(753\) 0 0
\(754\) −733.187 815.793i −0.972397 1.08195i
\(755\) 1.84504 0.00244377
\(756\) 0 0
\(757\) 642.972 404.006i 0.849368 0.533693i −0.0355886 0.999367i \(-0.511331\pi\)
0.884957 + 0.465673i \(0.154188\pi\)
\(758\) −267.898 + 61.1460i −0.353427 + 0.0806675i
\(759\) 0 0
\(760\) −24.8637 + 19.8282i −0.0327154 + 0.0260897i
\(761\) 61.0011 267.263i 0.0801592 0.351200i −0.918904 0.394482i \(-0.870924\pi\)
0.999063 + 0.0432815i \(0.0137812\pi\)
\(762\) 0 0
\(763\) −95.4128 + 198.127i −0.125050 + 0.259668i
\(764\) −188.013 118.137i −0.246091 0.154629i
\(765\) 0 0
\(766\) 418.001 418.001i 0.545693 0.545693i
\(767\) −270.844 562.413i −0.353121 0.733263i
\(768\) 0 0
\(769\) 1376.20 + 155.060i 1.78959 + 0.201639i 0.943494 0.331390i \(-0.107518\pi\)
0.846097 + 0.533028i \(0.178946\pi\)
\(770\) 25.1105 12.0926i 0.0326111 0.0157047i
\(771\) 0 0
\(772\) 118.090 337.481i 0.152966 0.437152i
\(773\) −566.278 + 901.226i −0.732572 + 1.16588i 0.247817 + 0.968807i \(0.420287\pi\)
−0.980389 + 0.197075i \(0.936856\pi\)
\(774\) 0 0
\(775\) −295.344 844.046i −0.381089 1.08909i
\(776\) 60.9629 + 13.9144i 0.0785604 + 0.0179309i
\(777\) 0 0
\(778\) −380.773 + 477.474i −0.489425 + 0.613720i
\(779\) 89.7804 + 393.354i 0.115251 + 0.504947i
\(780\) 0 0
\(781\) 52.1767 + 463.081i 0.0668075 + 0.592933i
\(782\) 342.210i 0.437608i
\(783\) 0 0
\(784\) −4.19585 −0.00535184
\(785\) 13.8178 1.55689i 0.0176023 0.00198330i
\(786\) 0 0
\(787\) −526.723 + 120.221i −0.669280