Properties

Label 261.3.s.a.10.1
Level $261$
Weight $3$
Character 261.10
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 10.1
Character \(\chi\) \(=\) 261.10
Dual form 261.3.s.a.235.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.05804 + 1.29315i) q^{2} +(0.827740 - 1.71882i) q^{4} +(-5.87720 - 1.34143i) q^{5} +(-9.36468 + 4.50979i) q^{7} +(-0.569384 - 5.05343i) q^{8} +O(q^{10})\) \(q+(-2.05804 + 1.29315i) q^{2} +(0.827740 - 1.71882i) q^{4} +(-5.87720 - 1.34143i) q^{5} +(-9.36468 + 4.50979i) q^{7} +(-0.569384 - 5.05343i) q^{8} +(13.8301 - 4.83938i) q^{10} +(-0.977326 + 8.67401i) q^{11} +(8.98997 - 7.16926i) q^{13} +(13.4410 - 21.3913i) q^{14} +(12.4645 + 15.6300i) q^{16} +(9.77422 + 9.77422i) q^{17} +(-4.49203 - 12.8375i) q^{19} +(-7.17047 + 8.99148i) q^{20} +(-9.20542 - 19.1153i) q^{22} +(-6.44949 - 28.2571i) q^{23} +(10.2178 + 4.92062i) q^{25} +(-9.23075 + 26.3800i) q^{26} +19.8291i q^{28} +(28.9618 - 1.48885i) q^{29} +(32.8240 - 20.6247i) q^{31} +(-26.6642 - 9.33019i) q^{32} +(-32.7552 - 7.47617i) q^{34} +(61.0877 - 13.9429i) q^{35} +(6.61609 + 58.7194i) q^{37} +(25.8456 + 20.6112i) q^{38} +(-3.43244 + 30.4638i) q^{40} +(-28.8990 + 28.8990i) q^{41} +(23.3701 - 37.1932i) q^{43} +(14.1001 + 8.85967i) q^{44} +(49.8139 + 49.8139i) q^{46} +(16.5298 + 1.86246i) q^{47} +(36.8081 - 46.1559i) q^{49} +(-27.3916 + 3.08629i) q^{50} +(-4.88131 - 21.3864i) q^{52} +(12.8958 - 56.5002i) q^{53} +(17.3795 - 49.6678i) q^{55} +(28.1220 + 44.7559i) q^{56} +(-57.6790 + 40.5160i) q^{58} +34.0756 q^{59} +(5.90275 + 2.06546i) q^{61} +(-40.8822 + 84.8927i) q^{62} +(-11.0199 + 2.51523i) q^{64} +(-62.4529 + 30.0757i) q^{65} +(-53.1751 - 42.4058i) q^{67} +(24.8906 - 8.70961i) q^{68} +(-107.690 + 107.690i) q^{70} +(24.4740 - 19.5174i) q^{71} +(-43.4053 - 27.2734i) q^{73} +(-89.5491 - 112.291i) q^{74} +(-25.7836 - 2.90511i) q^{76} +(-29.9657 - 85.6369i) q^{77} +(36.9784 - 4.16647i) q^{79} +(-52.2897 - 108.581i) q^{80} +(22.1045 - 96.8459i) q^{82} +(-62.9075 - 30.2947i) q^{83} +(-44.3336 - 70.5565i) q^{85} +106.766i q^{86} +44.3899 q^{88} +(-23.7527 + 14.9248i) q^{89} +(-51.8564 + 107.681i) q^{91} +(-53.9073 - 12.3040i) q^{92} +(-36.4274 + 17.5425i) q^{94} +(9.17994 + 81.4742i) q^{95} +(-33.9244 + 11.8707i) q^{97} +(-16.0659 + 142.589i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{23}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05804 + 1.29315i −1.02902 + 0.646575i −0.937053 0.349188i \(-0.886458\pi\)
−0.0919649 + 0.995762i \(0.529315\pi\)
\(3\) 0 0
\(4\) 0.827740 1.71882i 0.206935 0.429705i
\(5\) −5.87720 1.34143i −1.17544 0.268286i −0.410177 0.912006i \(-0.634533\pi\)
−0.765262 + 0.643719i \(0.777390\pi\)
\(6\) 0 0
\(7\) −9.36468 + 4.50979i −1.33781 + 0.644256i −0.959575 0.281452i \(-0.909184\pi\)
−0.378237 + 0.925709i \(0.623470\pi\)
\(8\) −0.569384 5.05343i −0.0711730 0.631678i
\(9\) 0 0
\(10\) 13.8301 4.83938i 1.38301 0.483938i
\(11\) −0.977326 + 8.67401i −0.0888478 + 0.788546i 0.867723 + 0.497048i \(0.165583\pi\)
−0.956571 + 0.291499i \(0.905846\pi\)
\(12\) 0 0
\(13\) 8.98997 7.16926i 0.691536 0.551482i −0.213433 0.976958i \(-0.568465\pi\)
0.904970 + 0.425476i \(0.139893\pi\)
\(14\) 13.4410 21.3913i 0.960073 1.52795i
\(15\) 0 0
\(16\) 12.4645 + 15.6300i 0.779031 + 0.976873i
\(17\) 9.77422 + 9.77422i 0.574954 + 0.574954i 0.933509 0.358554i \(-0.116730\pi\)
−0.358554 + 0.933509i \(0.616730\pi\)
\(18\) 0 0
\(19\) −4.49203 12.8375i −0.236423 0.675658i −0.999567 0.0294292i \(-0.990631\pi\)
0.763144 0.646228i \(-0.223655\pi\)
\(20\) −7.17047 + 8.99148i −0.358523 + 0.449574i
\(21\) 0 0
\(22\) −9.20542 19.1153i −0.418428 0.868875i
\(23\) −6.44949 28.2571i −0.280413 1.22857i −0.897266 0.441490i \(-0.854450\pi\)
0.616853 0.787078i \(-0.288407\pi\)
\(24\) 0 0
\(25\) 10.2178 + 4.92062i 0.408711 + 0.196825i
\(26\) −9.23075 + 26.3800i −0.355029 + 1.01461i
\(27\) 0 0
\(28\) 19.8291i 0.708184i
\(29\) 28.9618 1.48885i 0.998681 0.0513395i
\(30\) 0 0
\(31\) 32.8240 20.6247i 1.05884 0.665313i 0.114212 0.993456i \(-0.463566\pi\)
0.944628 + 0.328144i \(0.106423\pi\)
\(32\) −26.6642 9.33019i −0.833255 0.291568i
\(33\) 0 0
\(34\) −32.7552 7.47617i −0.963389 0.219887i
\(35\) 61.0877 13.9429i 1.74536 0.398367i
\(36\) 0 0
\(37\) 6.61609 + 58.7194i 0.178813 + 1.58701i 0.687581 + 0.726107i \(0.258672\pi\)
−0.508768 + 0.860904i \(0.669899\pi\)
\(38\) 25.8456 + 20.6112i 0.680146 + 0.542399i
\(39\) 0 0
\(40\) −3.43244 + 30.4638i −0.0858110 + 0.761594i
\(41\) −28.8990 + 28.8990i −0.704854 + 0.704854i −0.965448 0.260594i \(-0.916081\pi\)
0.260594 + 0.965448i \(0.416081\pi\)
\(42\) 0 0
\(43\) 23.3701 37.1932i 0.543490 0.864959i −0.456200 0.889877i \(-0.650790\pi\)
0.999689 + 0.0249182i \(0.00793254\pi\)
\(44\) 14.1001 + 8.85967i 0.320457 + 0.201356i
\(45\) 0 0
\(46\) 49.8139 + 49.8139i 1.08291 + 1.08291i
\(47\) 16.5298 + 1.86246i 0.351698 + 0.0396269i 0.286047 0.958216i \(-0.407659\pi\)
0.0656518 + 0.997843i \(0.479087\pi\)
\(48\) 0 0
\(49\) 36.8081 46.1559i 0.751185 0.941956i
\(50\) −27.3916 + 3.08629i −0.547832 + 0.0617259i
\(51\) 0 0
\(52\) −4.88131 21.3864i −0.0938714 0.411278i
\(53\) 12.8958 56.5002i 0.243317 1.06604i −0.694659 0.719340i \(-0.744445\pi\)
0.937975 0.346702i \(-0.112698\pi\)
\(54\) 0 0
\(55\) 17.3795 49.6678i 0.315991 0.903052i
\(56\) 28.1220 + 44.7559i 0.502179 + 0.799213i
\(57\) 0 0
\(58\) −57.6790 + 40.5160i −0.994466 + 0.698551i
\(59\) 34.0756 0.577552 0.288776 0.957397i \(-0.406752\pi\)
0.288776 + 0.957397i \(0.406752\pi\)
\(60\) 0 0
\(61\) 5.90275 + 2.06546i 0.0967664 + 0.0338600i 0.378228 0.925712i \(-0.376534\pi\)
−0.281462 + 0.959572i \(0.590819\pi\)
\(62\) −40.8822 + 84.8927i −0.659390 + 1.36924i
\(63\) 0 0
\(64\) −11.0199 + 2.51523i −0.172186 + 0.0393004i
\(65\) −62.4529 + 30.0757i −0.960814 + 0.462704i
\(66\) 0 0
\(67\) −53.1751 42.4058i −0.793659 0.632922i 0.140378 0.990098i \(-0.455168\pi\)
−0.934037 + 0.357176i \(0.883740\pi\)
\(68\) 24.8906 8.70961i 0.366039 0.128083i
\(69\) 0 0
\(70\) −107.690 + 107.690i −1.53843 + 1.53843i
\(71\) 24.4740 19.5174i 0.344704 0.274893i −0.435799 0.900044i \(-0.643534\pi\)
0.780504 + 0.625151i \(0.214963\pi\)
\(72\) 0 0
\(73\) −43.4053 27.2734i −0.594593 0.373608i 0.200862 0.979619i \(-0.435626\pi\)
−0.795456 + 0.606012i \(0.792768\pi\)
\(74\) −89.5491 112.291i −1.21012 1.51745i
\(75\) 0 0
\(76\) −25.7836 2.90511i −0.339258 0.0382252i
\(77\) −29.9657 85.6369i −0.389164 1.11217i
\(78\) 0 0
\(79\) 36.9784 4.16647i 0.468081 0.0527401i 0.125226 0.992128i \(-0.460034\pi\)
0.342855 + 0.939388i \(0.388606\pi\)
\(80\) −52.2897 108.581i −0.653621 1.35726i
\(81\) 0 0
\(82\) 22.1045 96.8459i 0.269566 1.18105i
\(83\) −62.9075 30.2947i −0.757922 0.364996i 0.0146754 0.999892i \(-0.495329\pi\)
−0.772597 + 0.634896i \(0.781043\pi\)
\(84\) 0 0
\(85\) −44.3336 70.5565i −0.521571 0.830076i
\(86\) 106.766i 1.24147i
\(87\) 0 0
\(88\) 44.3899 0.504431
\(89\) −23.7527 + 14.9248i −0.266885 + 0.167695i −0.658826 0.752296i \(-0.728947\pi\)
0.391941 + 0.919990i \(0.371804\pi\)
\(90\) 0 0
\(91\) −51.8564 + 107.681i −0.569850 + 1.18331i
\(92\) −53.9073 12.3040i −0.585949 0.133739i
\(93\) 0 0
\(94\) −36.4274 + 17.5425i −0.387526 + 0.186623i
\(95\) 9.17994 + 81.4742i 0.0966310 + 0.857623i
\(96\) 0 0
\(97\) −33.9244 + 11.8707i −0.349736 + 0.122378i −0.499430 0.866354i \(-0.666457\pi\)
0.149693 + 0.988732i \(0.452171\pi\)
\(98\) −16.0659 + 142.589i −0.163938 + 1.45499i
\(99\) 0 0
\(100\) 16.9153 13.4895i 0.169153 0.134895i
\(101\) 33.1691 52.7883i 0.328407 0.522657i −0.641184 0.767387i \(-0.721557\pi\)
0.969591 + 0.244730i \(0.0786994\pi\)
\(102\) 0 0
\(103\) −73.2496 91.8521i −0.711161 0.891768i 0.286641 0.958038i \(-0.407461\pi\)
−0.997802 + 0.0662704i \(0.978890\pi\)
\(104\) −41.3481 41.3481i −0.397578 0.397578i
\(105\) 0 0
\(106\) 46.5232 + 132.956i 0.438898 + 1.25430i
\(107\) 42.6207 53.4447i 0.398324 0.499483i −0.541709 0.840566i \(-0.682222\pi\)
0.940033 + 0.341083i \(0.110794\pi\)
\(108\) 0 0
\(109\) 5.04985 + 10.4861i 0.0463289 + 0.0962029i 0.922848 0.385163i \(-0.125855\pi\)
−0.876519 + 0.481366i \(0.840141\pi\)
\(110\) 28.4603 + 124.693i 0.258730 + 1.13357i
\(111\) 0 0
\(112\) −187.214 90.1575i −1.67155 0.804978i
\(113\) 14.1909 40.5554i 0.125584 0.358897i −0.863876 0.503704i \(-0.831970\pi\)
0.989460 + 0.144807i \(0.0462560\pi\)
\(114\) 0 0
\(115\) 174.724i 1.51934i
\(116\) 21.4137 51.0124i 0.184601 0.439762i
\(117\) 0 0
\(118\) −70.1287 + 44.0648i −0.594311 + 0.373431i
\(119\) −135.612 47.4528i −1.13960 0.398763i
\(120\) 0 0
\(121\) 43.6830 + 9.97036i 0.361016 + 0.0823996i
\(122\) −14.8190 + 3.38234i −0.121467 + 0.0277241i
\(123\) 0 0
\(124\) −8.28039 73.4905i −0.0667773 0.592665i
\(125\) 64.3775 + 51.3393i 0.515020 + 0.410715i
\(126\) 0 0
\(127\) 14.8633 131.916i 0.117034 1.03871i −0.788676 0.614809i \(-0.789233\pi\)
0.905710 0.423897i \(-0.139338\pi\)
\(128\) 99.3283 99.3283i 0.776002 0.776002i
\(129\) 0 0
\(130\) 89.6379 142.658i 0.689522 1.09737i
\(131\) −66.7432 41.9375i −0.509490 0.320134i 0.252637 0.967561i \(-0.418702\pi\)
−0.762127 + 0.647427i \(0.775845\pi\)
\(132\) 0 0
\(133\) 99.9609 + 99.9609i 0.751586 + 0.751586i
\(134\) 164.273 + 18.5092i 1.22592 + 0.138128i
\(135\) 0 0
\(136\) 43.8280 54.9586i 0.322265 0.404107i
\(137\) 160.789 18.1166i 1.17364 0.132238i 0.496465 0.868057i \(-0.334631\pi\)
0.677179 + 0.735819i \(0.263202\pi\)
\(138\) 0 0
\(139\) 24.4796 + 107.252i 0.176112 + 0.771599i 0.983401 + 0.181443i \(0.0580767\pi\)
−0.807289 + 0.590156i \(0.799066\pi\)
\(140\) 26.5994 116.540i 0.189996 0.832427i
\(141\) 0 0
\(142\) −25.1295 + 71.8160i −0.176968 + 0.505747i
\(143\) 53.4001 + 84.9858i 0.373428 + 0.594306i
\(144\) 0 0
\(145\) −172.211 30.1000i −1.18766 0.207586i
\(146\) 124.598 0.853412
\(147\) 0 0
\(148\) 106.404 + 37.2325i 0.718949 + 0.251571i
\(149\) −62.5002 + 129.783i −0.419464 + 0.871027i 0.578984 + 0.815339i \(0.303449\pi\)
−0.998448 + 0.0556878i \(0.982265\pi\)
\(150\) 0 0
\(151\) 279.422 63.7763i 1.85048 0.422359i 0.855105 0.518454i \(-0.173492\pi\)
0.995372 + 0.0960946i \(0.0306351\pi\)
\(152\) −62.3156 + 30.0096i −0.409971 + 0.197432i
\(153\) 0 0
\(154\) 172.412 + 137.494i 1.11956 + 0.892817i
\(155\) −220.580 + 77.1842i −1.42310 + 0.497963i
\(156\) 0 0
\(157\) 181.866 181.866i 1.15838 1.15838i 0.173555 0.984824i \(-0.444474\pi\)
0.984824 0.173555i \(-0.0555255\pi\)
\(158\) −70.7150 + 56.3934i −0.447564 + 0.356920i
\(159\) 0 0
\(160\) 144.195 + 90.6035i 0.901216 + 0.566272i
\(161\) 187.831 + 235.533i 1.16665 + 1.46294i
\(162\) 0 0
\(163\) 59.4854 + 6.70239i 0.364941 + 0.0411190i 0.292531 0.956256i \(-0.405502\pi\)
0.0724098 + 0.997375i \(0.476931\pi\)
\(164\) 25.7513 + 73.5931i 0.157020 + 0.448738i
\(165\) 0 0
\(166\) 168.641 19.0013i 1.01591 0.114466i
\(167\) −79.8635 165.838i −0.478225 0.993044i −0.990917 0.134472i \(-0.957066\pi\)
0.512693 0.858572i \(-0.328648\pi\)
\(168\) 0 0
\(169\) −8.18478 + 35.8598i −0.0484306 + 0.212188i
\(170\) 182.480 + 87.8778i 1.07341 + 0.516928i
\(171\) 0 0
\(172\) −44.5842 70.9553i −0.259210 0.412531i
\(173\) 24.3883i 0.140973i 0.997513 + 0.0704864i \(0.0224551\pi\)
−0.997513 + 0.0704864i \(0.977545\pi\)
\(174\) 0 0
\(175\) −117.877 −0.673584
\(176\) −147.756 + 92.8415i −0.839525 + 0.527509i
\(177\) 0 0
\(178\) 29.5840 61.4317i 0.166202 0.345122i
\(179\) 109.960 + 25.0977i 0.614303 + 0.140211i 0.518340 0.855174i \(-0.326550\pi\)
0.0959623 + 0.995385i \(0.469407\pi\)
\(180\) 0 0
\(181\) −181.835 + 87.5671i −1.00461 + 0.483796i −0.862501 0.506055i \(-0.831103\pi\)
−0.142111 + 0.989851i \(0.545389\pi\)
\(182\) −32.5252 288.669i −0.178710 1.58609i
\(183\) 0 0
\(184\) −139.123 + 48.6812i −0.756102 + 0.264572i
\(185\) 39.8840 353.980i 0.215589 1.91341i
\(186\) 0 0
\(187\) −94.3343 + 75.2291i −0.504462 + 0.402295i
\(188\) 16.8836 26.8702i 0.0898066 0.142926i
\(189\) 0 0
\(190\) −124.251 155.806i −0.653953 0.820031i
\(191\) 9.18326 + 9.18326i 0.0480799 + 0.0480799i 0.730738 0.682658i \(-0.239176\pi\)
−0.682658 + 0.730738i \(0.739176\pi\)
\(192\) 0 0
\(193\) −38.7349 110.698i −0.200699 0.573564i 0.798912 0.601447i \(-0.205409\pi\)
−0.999611 + 0.0278831i \(0.991123\pi\)
\(194\) 54.4671 68.2996i 0.280758 0.352060i
\(195\) 0 0
\(196\) −48.8661 101.471i −0.249317 0.517712i
\(197\) 42.3417 + 185.511i 0.214932 + 0.941681i 0.961160 + 0.275990i \(0.0890057\pi\)
−0.746228 + 0.665690i \(0.768137\pi\)
\(198\) 0 0
\(199\) 134.765 + 64.8992i 0.677209 + 0.326127i 0.740681 0.671857i \(-0.234503\pi\)
−0.0634720 + 0.997984i \(0.520217\pi\)
\(200\) 19.0481 54.4364i 0.0952407 0.272182i
\(201\) 0 0
\(202\) 151.533i 0.750163i
\(203\) −264.503 + 144.554i −1.30297 + 0.712089i
\(204\) 0 0
\(205\) 208.611 131.079i 1.01762 0.639410i
\(206\) 269.529 + 94.3122i 1.30839 + 0.457826i
\(207\) 0 0
\(208\) 224.111 + 51.1518i 1.07746 + 0.245922i
\(209\) 115.743 26.4175i 0.553793 0.126400i
\(210\) 0 0
\(211\) −6.26902 55.6391i −0.0297110 0.263692i −0.999782 0.0208716i \(-0.993356\pi\)
0.970071 0.242821i \(-0.0780727\pi\)
\(212\) −86.4393 68.9330i −0.407732 0.325156i
\(213\) 0 0
\(214\) −18.6030 + 165.106i −0.0869298 + 0.771523i
\(215\) −187.243 + 187.243i −0.870896 + 0.870896i
\(216\) 0 0
\(217\) −214.373 + 341.173i −0.987896 + 1.57223i
\(218\) −23.9529 15.0506i −0.109876 0.0690394i
\(219\) 0 0
\(220\) −70.9843 70.9843i −0.322656 0.322656i
\(221\) 157.944 + 17.7960i 0.714679 + 0.0805250i
\(222\) 0 0
\(223\) 83.8099 105.094i 0.375829 0.471275i −0.557562 0.830135i \(-0.688263\pi\)
0.933391 + 0.358860i \(0.116835\pi\)
\(224\) 291.779 32.8756i 1.30258 0.146766i
\(225\) 0 0
\(226\) 23.2387 + 101.815i 0.102826 + 0.450511i
\(227\) 37.6983 165.167i 0.166072 0.727609i −0.821470 0.570252i \(-0.806846\pi\)
0.987542 0.157357i \(-0.0502973\pi\)
\(228\) 0 0
\(229\) 51.6406 147.580i 0.225505 0.644456i −0.774426 0.632665i \(-0.781961\pi\)
0.999930 0.0117911i \(-0.00375331\pi\)
\(230\) −225.944 359.588i −0.982366 1.56343i
\(231\) 0 0
\(232\) −24.0141 145.508i −0.103509 0.627191i
\(233\) −296.039 −1.27055 −0.635276 0.772285i \(-0.719114\pi\)
−0.635276 + 0.772285i \(0.719114\pi\)
\(234\) 0 0
\(235\) −94.6506 33.1197i −0.402769 0.140935i
\(236\) 28.2057 58.5698i 0.119516 0.248177i
\(237\) 0 0
\(238\) 340.458 77.7074i 1.43050 0.326502i
\(239\) 231.857 111.656i 0.970113 0.467182i 0.119420 0.992844i \(-0.461897\pi\)
0.850693 + 0.525662i \(0.176182\pi\)
\(240\) 0 0
\(241\) −18.6581 14.8793i −0.0774196 0.0617400i 0.584015 0.811743i \(-0.301481\pi\)
−0.661435 + 0.750003i \(0.730052\pi\)
\(242\) −102.794 + 35.9693i −0.424770 + 0.148633i
\(243\) 0 0
\(244\) 8.43610 8.43610i 0.0345742 0.0345742i
\(245\) −278.243 + 221.892i −1.13569 + 0.905680i
\(246\) 0 0
\(247\) −132.419 83.2042i −0.536108 0.336859i
\(248\) −122.915 154.130i −0.495625 0.621493i
\(249\) 0 0
\(250\) −198.881 22.4085i −0.795522 0.0896338i
\(251\) −47.2947 135.160i −0.188425 0.538487i 0.810455 0.585801i \(-0.199220\pi\)
−0.998880 + 0.0473132i \(0.984934\pi\)
\(252\) 0 0
\(253\) 251.405 28.3266i 0.993697 0.111963i
\(254\) 139.997 + 290.708i 0.551171 + 1.14452i
\(255\) 0 0
\(256\) −65.9139 + 288.788i −0.257476 + 1.12808i
\(257\) −78.7944 37.9454i −0.306593 0.147647i 0.274261 0.961655i \(-0.411567\pi\)
−0.580854 + 0.814008i \(0.697281\pi\)
\(258\) 0 0
\(259\) −326.770 520.051i −1.26166 2.00792i
\(260\) 132.240i 0.508616i
\(261\) 0 0
\(262\) 191.591 0.731265
\(263\) 82.7439 51.9914i 0.314615 0.197686i −0.365462 0.930826i \(-0.619089\pi\)
0.680077 + 0.733140i \(0.261946\pi\)
\(264\) 0 0
\(265\) −151.582 + 314.764i −0.572009 + 1.18779i
\(266\) −334.988 76.4587i −1.25935 0.287439i
\(267\) 0 0
\(268\) −116.903 + 56.2975i −0.436205 + 0.210065i
\(269\) 2.99923 + 26.6189i 0.0111496 + 0.0989551i 0.998054 0.0623480i \(-0.0198589\pi\)
−0.986905 + 0.161303i \(0.948430\pi\)
\(270\) 0 0
\(271\) −164.750 + 57.6486i −0.607935 + 0.212725i −0.616651 0.787237i \(-0.711511\pi\)
0.00871663 + 0.999962i \(0.497225\pi\)
\(272\) −30.9402 + 274.602i −0.113751 + 1.00956i
\(273\) 0 0
\(274\) −307.482 + 245.209i −1.12220 + 0.894924i
\(275\) −52.6676 + 83.8200i −0.191518 + 0.304800i
\(276\) 0 0
\(277\) 270.444 + 339.126i 0.976331 + 1.22428i 0.974524 + 0.224282i \(0.0720037\pi\)
0.00180677 + 0.999998i \(0.499425\pi\)
\(278\) −189.073 189.073i −0.680119 0.680119i
\(279\) 0 0
\(280\) −105.242 300.763i −0.375863 1.07415i
\(281\) −246.662 + 309.305i −0.877802 + 1.10073i 0.116400 + 0.993202i \(0.462864\pi\)
−0.994202 + 0.107526i \(0.965707\pi\)
\(282\) 0 0
\(283\) 70.0980 + 145.560i 0.247696 + 0.514346i 0.987333 0.158660i \(-0.0507172\pi\)
−0.739637 + 0.673006i \(0.765003\pi\)
\(284\) −13.2887 58.2217i −0.0467913 0.205006i
\(285\) 0 0
\(286\) −219.799 105.849i −0.768527 0.370103i
\(287\) 140.302 400.959i 0.488855 1.39707i
\(288\) 0 0
\(289\) 97.9291i 0.338855i
\(290\) 393.340 160.748i 1.35635 0.554303i
\(291\) 0 0
\(292\) −82.8063 + 52.0307i −0.283583 + 0.178187i
\(293\) 497.689 + 174.149i 1.69860 + 0.594365i 0.993406 0.114653i \(-0.0365756\pi\)
0.705191 + 0.709018i \(0.250861\pi\)
\(294\) 0 0
\(295\) −200.269 45.7100i −0.678877 0.154949i
\(296\) 292.967 66.8678i 0.989754 0.225905i
\(297\) 0 0
\(298\) −39.2012 347.920i −0.131548 1.16752i
\(299\) −260.563 207.792i −0.871449 0.694957i
\(300\) 0 0
\(301\) −51.1194 + 453.697i −0.169832 + 1.50730i
\(302\) −492.588 + 492.588i −1.63109 + 1.63109i
\(303\) 0 0
\(304\) 144.659 230.223i 0.475851 0.757313i
\(305\) −31.9209 20.0573i −0.104659 0.0657615i
\(306\) 0 0
\(307\) −263.183 263.183i −0.857275 0.857275i 0.133742 0.991016i \(-0.457301\pi\)
−0.991016 + 0.133742i \(0.957301\pi\)
\(308\) −171.998 19.3795i −0.558436 0.0629206i
\(309\) 0 0
\(310\) 354.150 444.091i 1.14242 1.43255i
\(311\) 286.428 32.2726i 0.920989 0.103771i 0.361278 0.932458i \(-0.382341\pi\)
0.559711 + 0.828688i \(0.310912\pi\)
\(312\) 0 0
\(313\) 41.7918 + 183.102i 0.133520 + 0.584990i 0.996777 + 0.0802250i \(0.0255639\pi\)
−0.863257 + 0.504765i \(0.831579\pi\)
\(314\) −139.106 + 609.465i −0.443014 + 1.94097i
\(315\) 0 0
\(316\) 23.4471 67.0080i 0.0741997 0.212051i
\(317\) −299.014 475.878i −0.943261 1.50119i −0.863482 0.504379i \(-0.831721\pi\)
−0.0797787 0.996813i \(-0.525421\pi\)
\(318\) 0 0
\(319\) −15.3908 + 252.670i −0.0482471 + 0.792068i
\(320\) 68.1403 0.212938
\(321\) 0 0
\(322\) −691.142 241.841i −2.14640 0.751059i
\(323\) 81.5704 169.383i 0.252540 0.524405i
\(324\) 0 0
\(325\) 127.135 29.0176i 0.391183 0.0892851i
\(326\) −131.090 + 63.1297i −0.402117 + 0.193649i
\(327\) 0 0
\(328\) 162.494 + 129.584i 0.495407 + 0.395074i
\(329\) −163.196 + 57.1047i −0.496036 + 0.173571i
\(330\) 0 0
\(331\) −301.118 + 301.118i −0.909723 + 0.909723i −0.996250 0.0865265i \(-0.972423\pi\)
0.0865265 + 0.996250i \(0.472423\pi\)
\(332\) −104.142 + 83.0506i −0.313681 + 0.250152i
\(333\) 0 0
\(334\) 378.816 + 238.026i 1.13418 + 0.712652i
\(335\) 255.636 + 320.558i 0.763093 + 0.956889i
\(336\) 0 0
\(337\) 354.089 + 39.8962i 1.05071 + 0.118386i 0.620392 0.784292i \(-0.286973\pi\)
0.430316 + 0.902678i \(0.358402\pi\)
\(338\) −29.5276 84.3850i −0.0873597 0.249660i
\(339\) 0 0
\(340\) −157.971 + 17.7990i −0.464619 + 0.0523500i
\(341\) 146.819 + 304.873i 0.430554 + 0.894056i
\(342\) 0 0
\(343\) −23.2111 + 101.695i −0.0676709 + 0.296485i
\(344\) −201.260 96.9216i −0.585058 0.281749i
\(345\) 0 0
\(346\) −31.5377 50.1920i −0.0911495 0.145064i
\(347\) 8.03629i 0.0231593i 0.999933 + 0.0115797i \(0.00368600\pi\)
−0.999933 + 0.0115797i \(0.996314\pi\)
\(348\) 0 0
\(349\) 635.847 1.82191 0.910956 0.412504i \(-0.135346\pi\)
0.910956 + 0.412504i \(0.135346\pi\)
\(350\) 242.595 152.433i 0.693129 0.435522i
\(351\) 0 0
\(352\) 106.990 222.167i 0.303948 0.631155i
\(353\) 466.124 + 106.390i 1.32047 + 0.301388i 0.823961 0.566646i \(-0.191759\pi\)
0.496505 + 0.868034i \(0.334617\pi\)
\(354\) 0 0
\(355\) −170.020 + 81.8772i −0.478929 + 0.230640i
\(356\) 5.99201 + 53.1806i 0.0168315 + 0.149384i
\(357\) 0 0
\(358\) −258.757 + 90.5430i −0.722785 + 0.252913i
\(359\) −9.68103 + 85.9215i −0.0269666 + 0.239336i 0.972997 + 0.230817i \(0.0741400\pi\)
−0.999964 + 0.00851817i \(0.997289\pi\)
\(360\) 0 0
\(361\) 137.618 109.747i 0.381214 0.304008i
\(362\) 260.985 415.356i 0.720954 1.14739i
\(363\) 0 0
\(364\) 142.160 + 178.263i 0.390550 + 0.489735i
\(365\) 218.516 + 218.516i 0.598674 + 0.598674i
\(366\) 0 0
\(367\) −170.932 488.497i −0.465756 1.33105i −0.902198 0.431322i \(-0.858047\pi\)
0.436442 0.899732i \(-0.356238\pi\)
\(368\) 361.268 453.015i 0.981706 1.23102i
\(369\) 0 0
\(370\) 375.667 + 780.080i 1.01532 + 2.10833i
\(371\) 134.039 + 587.264i 0.361291 + 1.58292i
\(372\) 0 0
\(373\) −148.476 71.5023i −0.398059 0.191695i 0.224135 0.974558i \(-0.428044\pi\)
−0.622194 + 0.782863i \(0.713759\pi\)
\(374\) 96.8609 276.813i 0.258986 0.740141i
\(375\) 0 0
\(376\) 84.5927i 0.224981i
\(377\) 249.691 221.019i 0.662312 0.586258i
\(378\) 0 0
\(379\) −385.472 + 242.208i −1.01708 + 0.639072i −0.933927 0.357465i \(-0.883641\pi\)
−0.0831508 + 0.996537i \(0.526498\pi\)
\(380\) 147.638 + 51.6608i 0.388521 + 0.135950i
\(381\) 0 0
\(382\) −30.7748 7.02415i −0.0805623 0.0183878i
\(383\) −280.279 + 63.9719i −0.731799 + 0.167028i −0.572154 0.820146i \(-0.693892\pi\)
−0.159645 + 0.987174i \(0.551035\pi\)
\(384\) 0 0
\(385\) 61.2379 + 543.502i 0.159060 + 1.41169i
\(386\) 222.867 + 177.730i 0.577375 + 0.460441i
\(387\) 0 0
\(388\) −7.67706 + 68.1358i −0.0197862 + 0.175608i
\(389\) 60.4535 60.4535i 0.155408 0.155408i −0.625121 0.780528i \(-0.714950\pi\)
0.780528 + 0.625121i \(0.214950\pi\)
\(390\) 0 0
\(391\) 213.152 339.230i 0.545146 0.867595i
\(392\) −254.203 159.726i −0.648477 0.407465i
\(393\) 0 0
\(394\) −327.034 327.034i −0.830036 0.830036i
\(395\) −222.918 25.1169i −0.564350 0.0635870i
\(396\) 0 0
\(397\) −303.313 + 380.342i −0.764012 + 0.958040i −0.999906 0.0137384i \(-0.995627\pi\)
0.235894 + 0.971779i \(0.424198\pi\)
\(398\) −361.275 + 40.7059i −0.907725 + 0.102276i
\(399\) 0 0
\(400\) 50.4501 + 221.036i 0.126125 + 0.552591i
\(401\) 122.942 538.643i 0.306588 1.34325i −0.553392 0.832921i \(-0.686667\pi\)
0.859980 0.510328i \(-0.170476\pi\)
\(402\) 0 0
\(403\) 147.223 420.740i 0.365318 1.04402i
\(404\) −63.2782 100.707i −0.156629 0.249274i
\(405\) 0 0
\(406\) 357.427 639.540i 0.880362 1.57522i
\(407\) −515.799 −1.26732
\(408\) 0 0
\(409\) 137.784 + 48.2128i 0.336881 + 0.117880i 0.493418 0.869792i \(-0.335747\pi\)
−0.156537 + 0.987672i \(0.550033\pi\)
\(410\) −259.824 + 539.531i −0.633718 + 1.31593i
\(411\) 0 0
\(412\) −218.509 + 49.8732i −0.530361 + 0.121051i
\(413\) −319.107 + 153.674i −0.772656 + 0.372092i
\(414\) 0 0
\(415\) 329.082 + 262.434i 0.792968 + 0.632371i
\(416\) −306.601 + 107.284i −0.737021 + 0.257895i
\(417\) 0 0
\(418\) −204.041 + 204.041i −0.488136 + 0.488136i
\(419\) 148.931 118.769i 0.355444 0.283457i −0.429445 0.903093i \(-0.641291\pi\)
0.784890 + 0.619635i \(0.212720\pi\)
\(420\) 0 0
\(421\) −357.054 224.352i −0.848108 0.532902i 0.0364479 0.999336i \(-0.488396\pi\)
−0.884556 + 0.466434i \(0.845539\pi\)
\(422\) 84.8515 + 106.400i 0.201070 + 0.252134i
\(423\) 0 0
\(424\) −292.862 32.9976i −0.690713 0.0778246i
\(425\) 51.7755 + 147.966i 0.121825 + 0.348155i
\(426\) 0 0
\(427\) −64.5922 + 7.27779i −0.151270 + 0.0170440i
\(428\) −56.5829 117.496i −0.132203 0.274522i
\(429\) 0 0
\(430\) 143.219 627.485i 0.333068 1.45927i
\(431\) 95.2983 + 45.8932i 0.221110 + 0.106481i 0.541160 0.840920i \(-0.317985\pi\)
−0.320050 + 0.947401i \(0.603700\pi\)
\(432\) 0 0
\(433\) −408.562 650.223i −0.943562 1.50167i −0.863174 0.504907i \(-0.831527\pi\)
−0.0803883 0.996764i \(-0.525616\pi\)
\(434\) 979.364i 2.25660i
\(435\) 0 0
\(436\) 22.2037 0.0509260
\(437\) −333.779 + 209.727i −0.763796 + 0.479925i
\(438\) 0 0
\(439\) 228.661 474.820i 0.520869 1.08160i −0.460179 0.887826i \(-0.652215\pi\)
0.981047 0.193769i \(-0.0620711\pi\)
\(440\) −260.888 59.5461i −0.592928 0.135332i
\(441\) 0 0
\(442\) −348.067 + 167.620i −0.787483 + 0.379232i
\(443\) −26.7609 237.510i −0.0604084 0.536139i −0.987075 0.160256i \(-0.948768\pi\)
0.926667 0.375883i \(-0.122661\pi\)
\(444\) 0 0
\(445\) 159.620 55.8535i 0.358697 0.125514i
\(446\) −36.5811 + 324.666i −0.0820204 + 0.727952i
\(447\) 0 0
\(448\) 91.8550 73.2519i 0.205034 0.163509i
\(449\) −162.359 + 258.393i −0.361601 + 0.575485i −0.977133 0.212627i \(-0.931798\pi\)
0.615532 + 0.788112i \(0.288941\pi\)
\(450\) 0 0
\(451\) −222.427 278.914i −0.493185 0.618435i
\(452\) −57.9610 57.9610i −0.128232 0.128232i
\(453\) 0 0
\(454\) 136.001 + 388.670i 0.299563 + 0.856100i
\(455\) 449.216 563.299i 0.987289 1.23802i
\(456\) 0 0
\(457\) 181.449 + 376.783i 0.397045 + 0.824472i 0.999651 + 0.0264327i \(0.00841477\pi\)
−0.602606 + 0.798039i \(0.705871\pi\)
\(458\) 84.5653 + 370.505i 0.184640 + 0.808963i
\(459\) 0 0
\(460\) 300.319 + 144.626i 0.652867 + 0.314404i
\(461\) 196.436 561.383i 0.426109 1.21775i −0.508185 0.861248i \(-0.669683\pi\)
0.934294 0.356502i \(-0.116031\pi\)
\(462\) 0 0
\(463\) 903.693i 1.95182i 0.218171 + 0.975910i \(0.429991\pi\)
−0.218171 + 0.975910i \(0.570009\pi\)
\(464\) 384.264 + 434.114i 0.828155 + 0.935590i
\(465\) 0 0
\(466\) 609.258 382.822i 1.30742 0.821507i
\(467\) −674.139 235.892i −1.44355 0.505121i −0.508945 0.860799i \(-0.669964\pi\)
−0.934609 + 0.355678i \(0.884250\pi\)
\(468\) 0 0
\(469\) 689.210 + 157.308i 1.46953 + 0.335411i
\(470\) 237.623 54.2359i 0.505581 0.115396i
\(471\) 0 0
\(472\) −19.4021 172.198i −0.0411061 0.364827i
\(473\) 299.774 + 239.062i 0.633773 + 0.505417i
\(474\) 0 0
\(475\) 17.2698 153.274i 0.0363576 0.322682i
\(476\) −193.814 + 193.814i −0.407173 + 0.407173i
\(477\) 0 0
\(478\) −332.781 + 529.619i −0.696196 + 1.10799i
\(479\) −9.59607 6.02961i −0.0200336 0.0125879i 0.521978 0.852959i \(-0.325194\pi\)
−0.542012 + 0.840371i \(0.682337\pi\)
\(480\) 0 0
\(481\) 480.453 + 480.453i 0.998863 + 0.998863i
\(482\) 57.6403 + 6.49450i 0.119586 + 0.0134741i
\(483\) 0 0
\(484\) 53.2954 66.8303i 0.110114 0.138079i
\(485\) 215.304 24.2589i 0.443926 0.0500185i
\(486\) 0 0
\(487\) −178.718 783.016i −0.366978 1.60784i −0.735033 0.678031i \(-0.762833\pi\)
0.368055 0.929804i \(-0.380024\pi\)
\(488\) 7.07672 31.0051i 0.0145015 0.0635351i
\(489\) 0 0
\(490\) 285.695 816.471i 0.583052 1.66627i
\(491\) −197.816 314.823i −0.402885 0.641187i 0.582242 0.813015i \(-0.302176\pi\)
−0.985127 + 0.171828i \(0.945033\pi\)
\(492\) 0 0
\(493\) 297.631 + 268.526i 0.603714 + 0.544678i
\(494\) 380.118 0.769469
\(495\) 0 0
\(496\) 731.498 + 255.962i 1.47479 + 0.516053i
\(497\) −141.172 + 293.147i −0.284048 + 0.589833i
\(498\) 0 0
\(499\) 468.476 106.927i 0.938830 0.214282i 0.274386 0.961620i \(-0.411526\pi\)
0.664444 + 0.747338i \(0.268668\pi\)
\(500\) 141.531 68.1577i 0.283062 0.136315i
\(501\) 0 0
\(502\) 272.117 + 217.006i 0.542065 + 0.432282i
\(503\) 344.807 120.653i 0.685501 0.239867i 0.0350167 0.999387i \(-0.488852\pi\)
0.650485 + 0.759519i \(0.274566\pi\)
\(504\) 0 0
\(505\) −265.753 + 265.753i −0.526244 + 0.526244i
\(506\) −480.771 + 383.402i −0.950140 + 0.757711i
\(507\) 0 0
\(508\) −214.436 134.739i −0.422119 0.265235i
\(509\) −525.388 658.816i −1.03220 1.29433i −0.954773 0.297335i \(-0.903902\pi\)
−0.0774230 0.996998i \(-0.524669\pi\)
\(510\) 0 0
\(511\) 529.474 + 59.6574i 1.03615 + 0.116746i
\(512\) −52.2135 149.217i −0.101979 0.291440i
\(513\) 0 0
\(514\) 211.231 23.8000i 0.410955 0.0463035i
\(515\) 307.289 + 638.092i 0.596677 + 1.23901i
\(516\) 0 0
\(517\) −32.3101 + 141.560i −0.0624953 + 0.273810i
\(518\) 1345.01 + 647.722i 2.59654 + 1.25043i
\(519\) 0 0
\(520\) 187.545 + 298.476i 0.360664 + 0.573993i
\(521\) 150.865i 0.289569i −0.989463 0.144784i \(-0.953751\pi\)
0.989463 0.144784i \(-0.0462489\pi\)
\(522\) 0 0
\(523\) −792.504 −1.51530 −0.757652 0.652659i \(-0.773653\pi\)
−0.757652 + 0.652659i \(0.773653\pi\)
\(524\) −127.329 + 80.0062i −0.242994 + 0.152684i
\(525\) 0 0
\(526\) −103.057 + 214.000i −0.195926 + 0.406845i
\(527\) 522.420 + 119.239i 0.991309 + 0.226260i
\(528\) 0 0
\(529\) −280.254 + 134.963i −0.529781 + 0.255129i
\(530\) −95.0750 843.814i −0.179387 1.59210i
\(531\) 0 0
\(532\) 254.557 89.0732i 0.478490 0.167431i
\(533\) −52.6167 + 466.986i −0.0987180 + 0.876146i
\(534\) 0 0
\(535\) −322.183 + 256.932i −0.602210 + 0.480247i
\(536\) −184.017 + 292.862i −0.343316 + 0.546384i
\(537\) 0 0
\(538\) −40.5948 50.9042i −0.0754550 0.0946176i
\(539\) 364.383 + 364.383i 0.676035 + 0.676035i
\(540\) 0 0
\(541\) −71.8125 205.228i −0.132740 0.379350i 0.858259 0.513217i \(-0.171546\pi\)
−0.990999 + 0.133867i \(0.957261\pi\)
\(542\) 264.514 331.690i 0.488033 0.611973i
\(543\) 0 0
\(544\) −169.426 351.817i −0.311445 0.646722i
\(545\) −15.6125 68.4030i −0.0286469 0.125510i
\(546\) 0 0
\(547\) −396.400 190.896i −0.724680 0.348987i 0.0349094 0.999390i \(-0.488886\pi\)
−0.759589 + 0.650403i \(0.774600\pi\)
\(548\) 101.952 291.363i 0.186045 0.531685i
\(549\) 0 0
\(550\) 240.611i 0.437475i
\(551\) −149.210 365.108i −0.270799 0.662629i
\(552\) 0 0
\(553\) −327.501 + 205.783i −0.592227 + 0.372121i
\(554\) −995.123 348.209i −1.79625 0.628535i
\(555\) 0 0
\(556\) 204.610 + 46.7009i 0.368004 + 0.0839945i
\(557\) −593.083 + 135.367i −1.06478 + 0.243029i −0.718803 0.695214i \(-0.755310\pi\)
−0.345977 + 0.938243i \(0.612453\pi\)
\(558\) 0 0
\(559\) −56.5520 501.912i −0.101166 0.897876i
\(560\) 979.353 + 781.008i 1.74884 + 1.39466i
\(561\) 0 0
\(562\) 107.663 955.532i 0.191570 1.70023i
\(563\) −498.815 + 498.815i −0.885995 + 0.885995i −0.994136 0.108141i \(-0.965510\pi\)
0.108141 + 0.994136i \(0.465510\pi\)
\(564\) 0 0
\(565\) −137.805 + 219.316i −0.243903 + 0.388170i
\(566\) −332.495 208.920i −0.587447 0.369117i
\(567\) 0 0
\(568\) −112.565 112.565i −0.198177 0.198177i
\(569\) 315.227 + 35.5176i 0.554002 + 0.0624210i 0.384527 0.923114i \(-0.374364\pi\)
0.169474 + 0.985535i \(0.445793\pi\)
\(570\) 0 0
\(571\) −321.408 + 403.033i −0.562886 + 0.705836i −0.979088 0.203436i \(-0.934789\pi\)
0.416203 + 0.909272i \(0.363361\pi\)
\(572\) 190.277 21.4390i 0.332652 0.0374808i
\(573\) 0 0
\(574\) 229.754 + 1006.62i 0.400268 + 1.75369i
\(575\) 73.1428 320.460i 0.127205 0.557321i
\(576\) 0 0
\(577\) 325.366 929.842i 0.563892 1.61151i −0.209657 0.977775i \(-0.567235\pi\)
0.773549 0.633736i \(-0.218480\pi\)
\(578\) 126.637 + 201.542i 0.219095 + 0.348688i
\(579\) 0 0
\(580\) −194.282 + 271.085i −0.334970 + 0.467388i
\(581\) 725.732 1.24911
\(582\) 0 0
\(583\) 477.480 + 167.077i 0.819005 + 0.286582i
\(584\) −113.110 + 234.875i −0.193681 + 0.402182i
\(585\) 0 0
\(586\) −1249.46 + 285.181i −2.13219 + 0.486658i
\(587\) −758.249 + 365.153i −1.29174 + 0.622067i −0.948379 0.317138i \(-0.897278\pi\)
−0.343356 + 0.939205i \(0.611564\pi\)
\(588\) 0 0
\(589\) −412.216 328.731i −0.699858 0.558118i
\(590\) 471.270 164.905i 0.798763 0.279499i
\(591\) 0 0
\(592\) −835.317 + 835.317i −1.41101 + 1.41101i
\(593\) 27.0486 21.5706i 0.0456132 0.0363753i −0.600418 0.799686i \(-0.704999\pi\)
0.646031 + 0.763311i \(0.276428\pi\)
\(594\) 0 0
\(595\) 733.365 + 460.804i 1.23255 + 0.774460i
\(596\) 171.340 + 214.853i 0.287483 + 0.360492i
\(597\) 0 0
\(598\) 804.955 + 90.6966i 1.34608 + 0.151667i
\(599\) −3.54858 10.1412i −0.00592417 0.0169303i 0.940883 0.338731i \(-0.109998\pi\)
−0.946807 + 0.321801i \(0.895712\pi\)
\(600\) 0 0
\(601\) 368.282 41.4954i 0.612783 0.0690440i 0.199882 0.979820i \(-0.435944\pi\)
0.412901 + 0.910776i \(0.364516\pi\)
\(602\) −481.493 999.830i −0.799822 1.66085i
\(603\) 0 0
\(604\) 121.669 533.067i 0.201439 0.882560i
\(605\) −243.359 117.195i −0.402246 0.193712i
\(606\) 0 0
\(607\) −219.680 349.619i −0.361912 0.575979i 0.615288 0.788302i \(-0.289040\pi\)
−0.977199 + 0.212324i \(0.931897\pi\)
\(608\) 384.212i 0.631928i
\(609\) 0 0
\(610\) 91.6314 0.150215
\(611\) 161.955 101.763i 0.265066 0.166552i
\(612\) 0 0
\(613\) −443.542 + 921.025i −0.723560 + 1.50249i 0.135591 + 0.990765i \(0.456707\pi\)
−0.859151 + 0.511722i \(0.829008\pi\)
\(614\) 881.976 + 201.305i 1.43644 + 0.327859i
\(615\) 0 0
\(616\) −415.698 + 200.190i −0.674834 + 0.324983i
\(617\) −12.9759 115.164i −0.0210306 0.186652i 0.978805 0.204795i \(-0.0656529\pi\)
−0.999835 + 0.0181438i \(0.994224\pi\)
\(618\) 0 0
\(619\) 36.6784 12.8343i 0.0592543 0.0207340i −0.300489 0.953785i \(-0.597150\pi\)
0.359743 + 0.933051i \(0.382864\pi\)
\(620\) −49.9170 + 443.025i −0.0805113 + 0.714557i
\(621\) 0 0
\(622\) −547.745 + 436.812i −0.880619 + 0.702270i
\(623\) 155.129 246.886i 0.249003 0.396286i
\(624\) 0 0
\(625\) −486.264 609.755i −0.778022 0.975609i
\(626\) −322.787 322.787i −0.515635 0.515635i
\(627\) 0 0
\(628\) −162.057 463.132i −0.258052 0.737471i
\(629\) −509.269 + 638.604i −0.809649 + 1.01527i
\(630\) 0 0
\(631\) 116.281 + 241.460i 0.184280 + 0.382662i 0.972559 0.232656i \(-0.0747417\pi\)
−0.788279 + 0.615318i \(0.789027\pi\)
\(632\) −42.1099 184.495i −0.0666295 0.291923i
\(633\) 0 0
\(634\) 1230.76 + 592.704i 1.94127 + 0.934864i
\(635\) −264.310 + 755.356i −0.416237 + 1.18954i
\(636\) 0 0
\(637\) 678.827i 1.06566i
\(638\) −295.065 539.906i −0.462484 0.846247i
\(639\) 0 0
\(640\) −717.014 + 450.530i −1.12033 + 0.703952i
\(641\) 937.367 + 327.999i 1.46235 + 0.511699i 0.940043 0.341057i \(-0.110785\pi\)
0.522309 + 0.852756i \(0.325071\pi\)
\(642\) 0 0
\(643\) 311.987 + 71.2090i 0.485206 + 0.110745i 0.458124 0.888888i \(-0.348522\pi\)
0.0270814 + 0.999633i \(0.491379\pi\)
\(644\) 560.314 127.888i 0.870052 0.198584i
\(645\) 0 0
\(646\) 51.1623 + 454.078i 0.0791987 + 0.702908i
\(647\) 288.416 + 230.004i 0.445774 + 0.355493i 0.820504 0.571641i \(-0.193693\pi\)
−0.374730 + 0.927134i \(0.622264\pi\)
\(648\) 0 0
\(649\) −33.3029 + 295.572i −0.0513142 + 0.455427i
\(650\) −224.123 + 224.123i −0.344805 + 0.344805i
\(651\) 0 0
\(652\) 60.7586 96.6968i 0.0931881 0.148308i
\(653\) 257.346 + 161.701i 0.394098 + 0.247628i 0.714474 0.699662i \(-0.246666\pi\)
−0.320375 + 0.947291i \(0.603809\pi\)
\(654\) 0 0
\(655\) 336.007 + 336.007i 0.512987 + 0.512987i
\(656\) −811.902 91.4794i −1.23766 0.139450i
\(657\) 0 0
\(658\) 262.018 328.560i 0.398204 0.499332i
\(659\) 331.819 37.3870i 0.503518 0.0567329i 0.143448 0.989658i \(-0.454181\pi\)
0.360071 + 0.932925i \(0.382753\pi\)
\(660\) 0 0
\(661\) −231.074 1012.40i −0.349583 1.53162i −0.778131 0.628103i \(-0.783832\pi\)
0.428548 0.903519i \(-0.359025\pi\)
\(662\) 230.321 1009.10i 0.347917 1.52433i
\(663\) 0 0
\(664\) −117.273 + 335.148i −0.176616 + 0.504741i
\(665\) −453.399 721.581i −0.681803 1.08508i
\(666\) 0 0
\(667\) −228.859 808.772i −0.343117 1.21255i
\(668\) −351.152 −0.525677
\(669\) 0 0
\(670\) −940.638 329.143i −1.40394 0.491259i
\(671\) −23.6847 + 49.1819i −0.0352977 + 0.0732964i
\(672\) 0 0
\(673\) 145.913 33.3038i 0.216810 0.0494856i −0.112736 0.993625i \(-0.535961\pi\)
0.329546 + 0.944139i \(0.393104\pi\)
\(674\) −780.319 + 375.782i −1.15774 + 0.557540i
\(675\) 0 0
\(676\) 54.8617 + 43.7508i 0.0811564 + 0.0647201i
\(677\) −458.596 + 160.470i −0.677395 + 0.237031i −0.646980 0.762507i \(-0.723968\pi\)
−0.0304143 + 0.999537i \(0.509683\pi\)
\(678\) 0 0
\(679\) 264.157 264.157i 0.389039 0.389039i
\(680\) −331.309 + 264.210i −0.487219 + 0.388544i
\(681\) 0 0
\(682\) −696.405 437.580i −1.02112 0.641613i
\(683\) −431.703 541.338i −0.632069 0.792589i 0.357918 0.933753i \(-0.383487\pi\)
−0.989986 + 0.141164i \(0.954915\pi\)
\(684\) 0 0
\(685\) −969.292 109.213i −1.41502 0.159435i
\(686\) −83.7369 239.306i −0.122065 0.348843i
\(687\) 0 0
\(688\) 872.626 98.3213i 1.26835 0.142909i
\(689\) −289.132 600.389i −0.419640 0.871391i
\(690\) 0 0
\(691\) 126.440 553.969i 0.182981 0.801691i −0.797221 0.603688i \(-0.793697\pi\)
0.980201 0.198003i \(-0.0634456\pi\)
\(692\) 41.9191 + 20.1872i 0.0605767 + 0.0291722i
\(693\) 0 0
\(694\) −10.3921 16.5390i −0.0149742 0.0238314i
\(695\) 663.180i 0.954216i
\(696\) 0 0
\(697\) −564.931 −0.810518
\(698\) −1308.60 + 822.245i −1.87478 + 1.17800i
\(699\) 0 0
\(700\) −97.5716 + 202.610i −0.139388 + 0.289442i
\(701\) −669.767 152.870i −0.955445 0.218074i −0.283747 0.958899i \(-0.591578\pi\)
−0.671698 + 0.740825i \(0.734435\pi\)
\(702\) 0 0
\(703\) 724.090 348.704i 1.03000 0.496022i
\(704\) −11.0470 98.0452i −0.0156918 0.139269i
\(705\) 0 0
\(706\) −1096.88 + 383.814i −1.55365 + 0.543646i
\(707\) −72.5537 + 643.932i −0.102622 + 0.910795i
\(708\) 0 0
\(709\) 361.110 287.976i 0.509324 0.406172i −0.334826 0.942280i \(-0.608677\pi\)
0.844149 + 0.536108i \(0.180106\pi\)
\(710\) 244.027 388.367i 0.343700 0.546996i
\(711\) 0 0
\(712\) 88.9460 + 111.535i 0.124924 + 0.156650i
\(713\) −794.492 794.492i −1.11429 1.11429i
\(714\) 0 0
\(715\) −199.840 571.111i −0.279497 0.798757i
\(716\) 134.157 168.227i 0.187370 0.234954i
\(717\) 0 0
\(718\) −91.1854 189.349i −0.126999 0.263717i
\(719\) 115.701 + 506.920i 0.160920 + 0.705035i 0.989424 + 0.145052i \(0.0463350\pi\)
−0.828504 + 0.559983i \(0.810808\pi\)
\(720\) 0 0
\(721\) 1100.19 + 529.825i 1.52593 + 0.734848i
\(722\) −141.304 + 403.824i −0.195712 + 0.559313i
\(723\) 0 0
\(724\) 385.024i 0.531801i
\(725\) 303.250 + 127.297i 0.418276 + 0.175582i
\(726\) 0 0
\(727\) −1047.82 + 658.389i −1.44129 + 0.905624i −0.441327 + 0.897346i \(0.645492\pi\)
−0.999966 + 0.00827820i \(0.997365\pi\)
\(728\) 573.683 + 200.740i 0.788026 + 0.275742i
\(729\) 0 0
\(730\) −732.288 167.140i −1.00313 0.228959i
\(731\) 591.959 135.111i 0.809794 0.184830i
\(732\) 0 0
\(733\) 11.3513 + 100.746i 0.0154861 + 0.137443i 0.999076 0.0429750i \(-0.0136836\pi\)
−0.983590 + 0.180418i \(0.942255\pi\)
\(734\) 983.484 + 784.303i 1.33990 + 1.06853i
\(735\) 0 0
\(736\) −91.6736 + 813.626i −0.124557 + 1.10547i
\(737\) 419.797 419.797i 0.569603 0.569603i
\(738\) 0 0
\(739\) −408.803 + 650.606i −0.553184 + 0.880387i −0.999898 0.0142895i \(-0.995451\pi\)
0.446714 + 0.894677i \(0.352594\pi\)
\(740\) −575.415 361.557i −0.777588 0.488591i
\(741\) 0 0
\(742\) −1035.28 1035.28i −1.39525 1.39525i
\(743\) 576.403 + 64.9450i 0.775778 + 0.0874091i 0.490971 0.871176i \(-0.336642\pi\)
0.284807 + 0.958585i \(0.408071\pi\)
\(744\) 0 0
\(745\) 541.421 678.920i 0.726739 0.911302i
\(746\) 398.032 44.8475i 0.533555 0.0601172i
\(747\) 0 0
\(748\) 51.2210 + 224.414i 0.0684773 + 0.300019i
\(749\) −158.105 + 692.703i −0.211088 + 0.924837i
\(750\) 0 0
\(751\) −322.426 + 921.441i −0.429329 + 1.22695i 0.502666 + 0.864481i \(0.332353\pi\)
−0.931995 + 0.362471i \(0.881933\pi\)
\(752\) 176.926 + 281.575i 0.235273 + 0.374435i
\(753\) 0 0
\(754\) −228.063 + 777.754i −0.302471 + 1.03150i
\(755\) −1727.77 −2.28844
\(756\) 0 0
\(757\) 804.590 + 281.538i 1.06287 + 0.371913i 0.804388 0.594104i \(-0.202493\pi\)
0.258478 + 0.966017i \(0.416779\pi\)
\(758\) 480.104 996.947i 0.633383 1.31523i
\(759\) 0 0
\(760\) 406.497 92.7803i 0.534865 0.122079i
\(761\) −327.551 + 157.740i −0.430422 + 0.207280i −0.636535 0.771248i \(-0.719633\pi\)
0.206113 + 0.978528i \(0.433919\pi\)
\(762\) 0 0
\(763\) −94.5805 75.4254i −0.123959 0.0988538i
\(764\) 23.3857 8.18302i 0.0306096 0.0107108i
\(765\) 0 0
\(766\) 494.099 494.099i 0.645038 0.645038i
\(767\) 306.338 244.297i 0.399398 0.318509i
\(768\) 0 0
\(769\) −350.812 220.430i −0.456192 0.286644i 0.284268 0.958745i \(-0.408249\pi\)
−0.740460 + 0.672100i \(0.765392\pi\)
\(770\) −828.859 1039.36i −1.07644 1.34981i
\(771\) 0 0
\(772\) −222.332 25.0508i −0.287995 0.0324493i
\(773\) 229.136 + 654.833i 0.296424 + 0.847132i 0.991721 + 0.128409i \(0.0409871\pi\)
−0.695297 + 0.718722i \(0.744727\pi\)
\(774\) 0 0
\(775\) 436.874 49.2239i 0.563709 0.0635147i
\(776\) 79.3036 + 164.676i 0.102195 + 0.212211i
\(777\) 0 0
\(778\) −46.2401 + 202.591i −0.0594345 + 0.260400i
\(779\) 500.806 + 241.176i 0.642883 + 0.309596i
\(780\) 0 0
\(781\) 145.375 + 231.363i 0.186139 + 0.296239i
\(782\) 973.785i 1.24525i
\(783\) 0 0
\(784\) 1180.21 1.50537
\(785\) −1312.82 + 824.899i −1.67238 + 1.05083i
\(786\) 0 0
\(787\) −266.444 + 553.276i −0.338556 + 0.703019i −0.998848 0.0479904i \(-0.984718\pi\)