Properties

Label 261.3.s.a.10.4
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 10.4
Character \(\chi\) \(=\) 261.10
Dual form 261.3.s.a.235.4

$q$-expansion

\(f(q)\) \(=\) \(q+(3.24379 - 2.03821i) q^{2} +(4.63233 - 9.61914i) q^{4} +(5.12808 + 1.17045i) q^{5} +(-6.56728 + 3.16264i) q^{7} +(-2.86375 - 25.4165i) q^{8} +O(q^{10})\) \(q+(3.24379 - 2.03821i) q^{2} +(4.63233 - 9.61914i) q^{4} +(5.12808 + 1.17045i) q^{5} +(-6.56728 + 3.16264i) q^{7} +(-2.86375 - 25.4165i) q^{8} +(19.0200 - 6.65539i) q^{10} +(0.480789 - 4.26712i) q^{11} +(2.73044 - 2.17745i) q^{13} +(-14.8568 + 23.6444i) q^{14} +(-34.4669 - 43.2201i) q^{16} +(6.15599 + 6.15599i) q^{17} +(5.18330 + 14.8130i) q^{19} +(35.0137 - 43.9058i) q^{20} +(-7.13770 - 14.8216i) q^{22} +(3.58915 + 15.7251i) q^{23} +(2.40304 + 1.15724i) q^{25} +(4.41886 - 12.6284i) q^{26} +77.8220i q^{28} +(0.661611 + 28.9925i) q^{29} +(-34.6988 + 21.8027i) q^{31} +(-103.327 - 36.1556i) q^{32} +(32.5159 + 7.42154i) q^{34} +(-37.3793 + 8.53157i) q^{35} +(-5.62751 - 49.9455i) q^{37} +(47.0056 + 37.4857i) q^{38} +(15.0632 - 133.690i) q^{40} +(0.940907 - 0.940907i) q^{41} +(-10.2578 + 16.3252i) q^{43} +(-38.8189 - 24.3915i) q^{44} +(43.6934 + 43.6934i) q^{46} +(59.1758 + 6.66751i) q^{47} +(2.57590 - 3.23008i) q^{49} +(10.1536 - 1.14404i) q^{50} +(-8.29691 - 36.3511i) q^{52} +(8.89009 - 38.9500i) q^{53} +(7.45998 - 21.3194i) q^{55} +(99.1903 + 157.860i) q^{56} +(61.2387 + 92.6968i) q^{58} -6.74786 q^{59} +(74.0694 + 25.9180i) q^{61} +(-68.1170 + 141.446i) q^{62} +(-193.284 + 44.1159i) q^{64} +(16.5505 - 7.97030i) q^{65} +(29.6632 + 23.6556i) q^{67} +(87.7319 - 30.6987i) q^{68} +(-103.861 + 103.861i) q^{70} +(-65.3239 + 52.0941i) q^{71} +(-38.0089 - 23.8825i) q^{73} +(-120.054 - 150.543i) q^{74} +(166.499 + 18.7600i) q^{76} +(10.3379 + 29.5439i) q^{77} +(-120.957 + 13.6286i) q^{79} +(-126.162 - 261.978i) q^{80} +(1.13434 - 4.96987i) q^{82} +(-7.07418 - 3.40675i) q^{83} +(24.3631 + 38.7737i) q^{85} +73.8632i q^{86} -109.832 q^{88} +(94.3960 - 59.3130i) q^{89} +(-11.0451 + 22.9353i) q^{91} +(167.888 + 38.3193i) q^{92} +(205.543 - 98.9845i) q^{94} +(9.24248 + 82.0292i) q^{95} +(-13.0335 + 4.56061i) q^{97} +(1.77211 - 15.7279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.24379 2.03821i 1.62189 1.01910i 0.657926 0.753082i \(-0.271434\pi\)
0.963967 0.266021i \(-0.0857091\pi\)
\(3\) 0 0
\(4\) 4.63233 9.61914i 1.15808 2.40479i
\(5\) 5.12808 + 1.17045i 1.02562 + 0.234090i 0.702059 0.712119i \(-0.252264\pi\)
0.323557 + 0.946209i \(0.395121\pi\)
\(6\) 0 0
\(7\) −6.56728 + 3.16264i −0.938183 + 0.451805i −0.839528 0.543317i \(-0.817168\pi\)
−0.0986550 + 0.995122i \(0.531454\pi\)
\(8\) −2.86375 25.4165i −0.357969 3.17707i
\(9\) 0 0
\(10\) 19.0200 6.65539i 1.90200 0.665539i
\(11\) 0.480789 4.26712i 0.0437081 0.387920i −0.952745 0.303771i \(-0.901754\pi\)
0.996453 0.0841491i \(-0.0268172\pi\)
\(12\) 0 0
\(13\) 2.73044 2.17745i 0.210034 0.167496i −0.512823 0.858494i \(-0.671400\pi\)
0.722856 + 0.690998i \(0.242829\pi\)
\(14\) −14.8568 + 23.6444i −1.06120 + 1.68888i
\(15\) 0 0
\(16\) −34.4669 43.2201i −2.15418 2.70126i
\(17\) 6.15599 + 6.15599i 0.362117 + 0.362117i 0.864592 0.502475i \(-0.167577\pi\)
−0.502475 + 0.864592i \(0.667577\pi\)
\(18\) 0 0
\(19\) 5.18330 + 14.8130i 0.272806 + 0.779633i 0.996030 + 0.0890201i \(0.0283736\pi\)
−0.723224 + 0.690613i \(0.757341\pi\)
\(20\) 35.0137 43.9058i 1.75069 2.19529i
\(21\) 0 0
\(22\) −7.13770 14.8216i −0.324441 0.673708i
\(23\) 3.58915 + 15.7251i 0.156050 + 0.683699i 0.991055 + 0.133457i \(0.0426077\pi\)
−0.835005 + 0.550243i \(0.814535\pi\)
\(24\) 0 0
\(25\) 2.40304 + 1.15724i 0.0961215 + 0.0462897i
\(26\) 4.41886 12.6284i 0.169956 0.485707i
\(27\) 0 0
\(28\) 77.8220i 2.77936i
\(29\) 0.661611 + 28.9925i 0.0228142 + 0.999740i
\(30\) 0 0
\(31\) −34.6988 + 21.8027i −1.11931 + 0.703312i −0.958902 0.283738i \(-0.908425\pi\)
−0.160413 + 0.987050i \(0.551283\pi\)
\(32\) −103.327 36.1556i −3.22896 1.12986i
\(33\) 0 0
\(34\) 32.5159 + 7.42154i 0.956350 + 0.218281i
\(35\) −37.3793 + 8.53157i −1.06798 + 0.243759i
\(36\) 0 0
\(37\) −5.62751 49.9455i −0.152095 1.34988i −0.805376 0.592764i \(-0.798037\pi\)
0.653281 0.757115i \(-0.273392\pi\)
\(38\) 47.0056 + 37.4857i 1.23699 + 0.986465i
\(39\) 0 0
\(40\) 15.0632 133.690i 0.376581 3.34225i
\(41\) 0.940907 0.940907i 0.0229490 0.0229490i −0.695539 0.718488i \(-0.744834\pi\)
0.718488 + 0.695539i \(0.244834\pi\)
\(42\) 0 0
\(43\) −10.2578 + 16.3252i −0.238554 + 0.379657i −0.944448 0.328661i \(-0.893403\pi\)
0.705894 + 0.708318i \(0.250546\pi\)
\(44\) −38.8189 24.3915i −0.882247 0.554352i
\(45\) 0 0
\(46\) 43.6934 + 43.6934i 0.949857 + 0.949857i
\(47\) 59.1758 + 6.66751i 1.25906 + 0.141862i 0.716160 0.697936i \(-0.245898\pi\)
0.542899 + 0.839798i \(0.317327\pi\)
\(48\) 0 0
\(49\) 2.57590 3.23008i 0.0525694 0.0659199i
\(50\) 10.1536 1.14404i 0.203073 0.0228808i
\(51\) 0 0
\(52\) −8.29691 36.3511i −0.159556 0.699060i
\(53\) 8.89009 38.9500i 0.167738 0.734906i −0.819161 0.573564i \(-0.805561\pi\)
0.986898 0.161342i \(-0.0515823\pi\)
\(54\) 0 0
\(55\) 7.45998 21.3194i 0.135636 0.387625i
\(56\) 99.1903 + 157.860i 1.77125 + 2.81894i
\(57\) 0 0
\(58\) 61.2387 + 92.6968i 1.05584 + 1.59822i
\(59\) −6.74786 −0.114371 −0.0571853 0.998364i \(-0.518213\pi\)
−0.0571853 + 0.998364i \(0.518213\pi\)
\(60\) 0 0
\(61\) 74.0694 + 25.9180i 1.21425 + 0.424885i 0.860014 0.510270i \(-0.170454\pi\)
0.354238 + 0.935155i \(0.384740\pi\)
\(62\) −68.1170 + 141.446i −1.09866 + 2.28139i
\(63\) 0 0
\(64\) −193.284 + 44.1159i −3.02007 + 0.689311i
\(65\) 16.5505 7.97030i 0.254623 0.122620i
\(66\) 0 0
\(67\) 29.6632 + 23.6556i 0.442735 + 0.353069i 0.819343 0.573303i \(-0.194338\pi\)
−0.376609 + 0.926373i \(0.622910\pi\)
\(68\) 87.7319 30.6987i 1.29018 0.451452i
\(69\) 0 0
\(70\) −103.861 + 103.861i −1.48373 + 1.48373i
\(71\) −65.3239 + 52.0941i −0.920055 + 0.733719i −0.964164 0.265308i \(-0.914526\pi\)
0.0441092 + 0.999027i \(0.485955\pi\)
\(72\) 0 0
\(73\) −38.0089 23.8825i −0.520669 0.327158i 0.245926 0.969289i \(-0.420908\pi\)
−0.766595 + 0.642130i \(0.778051\pi\)
\(74\) −120.054 150.543i −1.62235 2.03436i
\(75\) 0 0
\(76\) 166.499 + 18.7600i 2.19078 + 0.246842i
\(77\) 10.3379 + 29.5439i 0.134258 + 0.383687i
\(78\) 0 0
\(79\) −120.957 + 13.6286i −1.53111 + 0.172514i −0.836938 0.547298i \(-0.815656\pi\)
−0.694169 + 0.719813i \(0.744228\pi\)
\(80\) −126.162 261.978i −1.57703 3.27473i
\(81\) 0 0
\(82\) 1.13434 4.96987i 0.0138334 0.0606081i
\(83\) −7.07418 3.40675i −0.0852311 0.0410451i 0.390783 0.920483i \(-0.372204\pi\)
−0.476014 + 0.879438i \(0.657919\pi\)
\(84\) 0 0
\(85\) 24.3631 + 38.7737i 0.286625 + 0.456161i
\(86\) 73.8632i 0.858875i
\(87\) 0 0
\(88\) −109.832 −1.24809
\(89\) 94.3960 59.3130i 1.06063 0.666438i 0.115558 0.993301i \(-0.463134\pi\)
0.945072 + 0.326863i \(0.105992\pi\)
\(90\) 0 0
\(91\) −11.0451 + 22.9353i −0.121374 + 0.252036i
\(92\) 167.888 + 38.3193i 1.82487 + 0.416515i
\(93\) 0 0
\(94\) 205.543 98.9845i 2.18663 1.05303i
\(95\) 9.24248 + 82.0292i 0.0972892 + 0.863466i
\(96\) 0 0
\(97\) −13.0335 + 4.56061i −0.134366 + 0.0470166i −0.396624 0.917981i \(-0.629818\pi\)
0.262259 + 0.964998i \(0.415533\pi\)
\(98\) 1.77211 15.7279i 0.0180827 0.160489i
\(99\) 0 0
\(100\) 22.2633 17.7544i 0.222633 0.177544i
\(101\) 63.8690 101.647i 0.632366 1.00640i −0.364794 0.931088i \(-0.618860\pi\)
0.997160 0.0753164i \(-0.0239967\pi\)
\(102\) 0 0
\(103\) −26.7668 33.5645i −0.259872 0.325869i 0.634729 0.772734i \(-0.281112\pi\)
−0.894601 + 0.446866i \(0.852540\pi\)
\(104\) −63.1625 63.1625i −0.607332 0.607332i
\(105\) 0 0
\(106\) −50.5506 144.465i −0.476893 1.36288i
\(107\) −3.07678 + 3.85816i −0.0287549 + 0.0360575i −0.796001 0.605295i \(-0.793055\pi\)
0.767246 + 0.641353i \(0.221626\pi\)
\(108\) 0 0
\(109\) −91.6589 190.332i −0.840907 1.74616i −0.642883 0.765964i \(-0.722262\pi\)
−0.198024 0.980197i \(-0.563452\pi\)
\(110\) −19.2548 84.3606i −0.175043 0.766914i
\(111\) 0 0
\(112\) 363.043 + 174.833i 3.24146 + 1.56100i
\(113\) −32.9621 + 94.2003i −0.291700 + 0.833631i 0.701015 + 0.713146i \(0.252730\pi\)
−0.992715 + 0.120484i \(0.961555\pi\)
\(114\) 0 0
\(115\) 84.8404i 0.737743i
\(116\) 281.947 + 127.939i 2.43058 + 1.10292i
\(117\) 0 0
\(118\) −21.8886 + 13.7535i −0.185497 + 0.116555i
\(119\) −59.8973 20.9590i −0.503338 0.176126i
\(120\) 0 0
\(121\) 99.9891 + 22.8219i 0.826356 + 0.188610i
\(122\) 293.092 66.8963i 2.40239 0.548330i
\(123\) 0 0
\(124\) 48.9868 + 434.770i 0.395055 + 3.50621i
\(125\) −91.8416 73.2412i −0.734733 0.585930i
\(126\) 0 0
\(127\) 12.5115 111.043i 0.0985161 0.874355i −0.843121 0.537724i \(-0.819284\pi\)
0.941637 0.336630i \(-0.109287\pi\)
\(128\) −227.428 + 227.428i −1.77678 + 1.77678i
\(129\) 0 0
\(130\) 37.4412 59.5873i 0.288009 0.458364i
\(131\) −162.714 102.240i −1.24209 0.780456i −0.259409 0.965768i \(-0.583528\pi\)
−0.982680 + 0.185311i \(0.940671\pi\)
\(132\) 0 0
\(133\) −80.8884 80.8884i −0.608184 0.608184i
\(134\) 144.436 + 16.2741i 1.07788 + 0.121448i
\(135\) 0 0
\(136\) 138.835 174.093i 1.02084 1.28010i
\(137\) −211.263 + 23.8036i −1.54206 + 0.173749i −0.841664 0.540002i \(-0.818424\pi\)
−0.700400 + 0.713750i \(0.746995\pi\)
\(138\) 0 0
\(139\) −44.5635 195.245i −0.320601 1.40464i −0.836487 0.547986i \(-0.815395\pi\)
0.515887 0.856657i \(-0.327463\pi\)
\(140\) −91.0868 + 399.077i −0.650620 + 2.85055i
\(141\) 0 0
\(142\) −105.718 + 302.126i −0.744495 + 2.12764i
\(143\) −7.97868 12.6980i −0.0557950 0.0887972i
\(144\) 0 0
\(145\) −30.5414 + 149.450i −0.210631 + 1.03069i
\(146\) −171.970 −1.17788
\(147\) 0 0
\(148\) −506.502 177.233i −3.42231 1.19752i
\(149\) 113.849 236.410i 0.764087 1.58664i −0.0450238 0.998986i \(-0.514336\pi\)
0.809110 0.587657i \(-0.199949\pi\)
\(150\) 0 0
\(151\) 126.068 28.7742i 0.834887 0.190558i 0.216353 0.976315i \(-0.430584\pi\)
0.618534 + 0.785758i \(0.287727\pi\)
\(152\) 361.652 174.162i 2.37929 1.14581i
\(153\) 0 0
\(154\) 93.7505 + 74.7635i 0.608769 + 0.485477i
\(155\) −203.457 + 71.1927i −1.31263 + 0.459308i
\(156\) 0 0
\(157\) −68.2720 + 68.2720i −0.434854 + 0.434854i −0.890276 0.455422i \(-0.849488\pi\)
0.455422 + 0.890276i \(0.349488\pi\)
\(158\) −364.582 + 290.744i −2.30748 + 1.84016i
\(159\) 0 0
\(160\) −487.550 306.348i −3.04719 1.91467i
\(161\) −73.3037 91.9199i −0.455302 0.570931i
\(162\) 0 0
\(163\) −91.2607 10.2826i −0.559882 0.0630835i −0.172511 0.985008i \(-0.555188\pi\)
−0.387371 + 0.921924i \(0.626617\pi\)
\(164\) −4.69212 13.4093i −0.0286105 0.0817641i
\(165\) 0 0
\(166\) −29.8908 + 3.36788i −0.180065 + 0.0202885i
\(167\) 49.7396 + 103.285i 0.297842 + 0.618475i 0.995158 0.0982887i \(-0.0313368\pi\)
−0.697316 + 0.716764i \(0.745623\pi\)
\(168\) 0 0
\(169\) −34.8920 + 152.872i −0.206462 + 0.904568i
\(170\) 158.058 + 76.1165i 0.929751 + 0.447744i
\(171\) 0 0
\(172\) 109.517 + 174.296i 0.636728 + 1.01335i
\(173\) 85.8359i 0.496161i 0.968739 + 0.248081i \(0.0797998\pi\)
−0.968739 + 0.248081i \(0.920200\pi\)
\(174\) 0 0
\(175\) −19.4414 −0.111093
\(176\) −200.997 + 126.295i −1.14203 + 0.717584i
\(177\) 0 0
\(178\) 185.309 384.797i 1.04106 2.16178i
\(179\) 82.0781 + 18.7338i 0.458537 + 0.104658i 0.445549 0.895258i \(-0.353009\pi\)
0.0129880 + 0.999916i \(0.495866\pi\)
\(180\) 0 0
\(181\) −34.3159 + 16.5257i −0.189591 + 0.0913021i −0.526271 0.850317i \(-0.676410\pi\)
0.336680 + 0.941619i \(0.390696\pi\)
\(182\) 10.9191 + 96.9094i 0.0599949 + 0.532469i
\(183\) 0 0
\(184\) 389.399 136.256i 2.11630 0.740524i
\(185\) 29.6005 262.712i 0.160003 1.42006i
\(186\) 0 0
\(187\) 29.2281 23.3086i 0.156300 0.124645i
\(188\) 338.258 538.334i 1.79924 2.86348i
\(189\) 0 0
\(190\) 197.173 + 247.247i 1.03775 + 1.30130i
\(191\) 189.648 + 189.648i 0.992922 + 0.992922i 0.999975 0.00705344i \(-0.00224520\pi\)
−0.00705344 + 0.999975i \(0.502245\pi\)
\(192\) 0 0
\(193\) 58.8988 + 168.323i 0.305175 + 0.872141i 0.989701 + 0.143152i \(0.0457237\pi\)
−0.684525 + 0.728989i \(0.739991\pi\)
\(194\) −32.9823 + 41.3585i −0.170012 + 0.213188i
\(195\) 0 0
\(196\) −19.1381 39.7408i −0.0976436 0.202759i
\(197\) 32.7329 + 143.412i 0.166157 + 0.727980i 0.987509 + 0.157560i \(0.0503626\pi\)
−0.821353 + 0.570421i \(0.806780\pi\)
\(198\) 0 0
\(199\) −192.699 92.7988i −0.968335 0.466326i −0.118257 0.992983i \(-0.537731\pi\)
−0.850078 + 0.526657i \(0.823445\pi\)
\(200\) 22.5314 64.3909i 0.112657 0.321955i
\(201\) 0 0
\(202\) 459.899i 2.27673i
\(203\) −96.0375 188.309i −0.473091 0.927631i
\(204\) 0 0
\(205\) 5.92633 3.72376i 0.0289089 0.0181647i
\(206\) −155.237 54.3198i −0.753578 0.263688i
\(207\) 0 0
\(208\) −188.220 42.9599i −0.904901 0.206538i
\(209\) 65.7011 14.9958i 0.314359 0.0717504i
\(210\) 0 0
\(211\) −1.09661 9.73273i −0.00519723 0.0461267i 0.990846 0.134998i \(-0.0431027\pi\)
−0.996043 + 0.0888710i \(0.971674\pi\)
\(212\) −333.484 265.945i −1.57304 1.25446i
\(213\) 0 0
\(214\) −2.11669 + 18.7861i −0.00989107 + 0.0877857i
\(215\) −71.7109 + 71.7109i −0.333539 + 0.333539i
\(216\) 0 0
\(217\) 158.923 252.924i 0.732362 1.16555i
\(218\) −685.257 430.576i −3.14338 1.97512i
\(219\) 0 0
\(220\) −170.517 170.517i −0.775078 0.775078i
\(221\) 30.2129 + 3.40418i 0.136710 + 0.0154035i
\(222\) 0 0
\(223\) −200.825 + 251.827i −0.900562 + 1.12927i 0.0905034 + 0.995896i \(0.471152\pi\)
−0.991066 + 0.133373i \(0.957419\pi\)
\(224\) 792.923 89.3410i 3.53984 0.398844i
\(225\) 0 0
\(226\) 85.0776 + 372.749i 0.376449 + 1.64933i
\(227\) 57.8450 253.436i 0.254824 1.11646i −0.671879 0.740661i \(-0.734512\pi\)
0.926703 0.375796i \(-0.122630\pi\)
\(228\) 0 0
\(229\) 96.5555 275.940i 0.421640 1.20498i −0.515764 0.856731i \(-0.672492\pi\)
0.937403 0.348246i \(-0.113223\pi\)
\(230\) 172.922 + 275.204i 0.751836 + 1.19654i
\(231\) 0 0
\(232\) 734.993 99.8431i 3.16807 0.430358i
\(233\) 8.24553 0.0353885 0.0176943 0.999843i \(-0.494367\pi\)
0.0176943 + 0.999843i \(0.494367\pi\)
\(234\) 0 0
\(235\) 295.654 + 103.454i 1.25810 + 0.440229i
\(236\) −31.2584 + 64.9086i −0.132451 + 0.275037i
\(237\) 0 0
\(238\) −237.013 + 54.0966i −0.995851 + 0.227297i
\(239\) 144.107 69.3984i 0.602959 0.290370i −0.107392 0.994217i \(-0.534250\pi\)
0.710352 + 0.703847i \(0.248536\pi\)
\(240\) 0 0
\(241\) −85.1309 67.8896i −0.353240 0.281700i 0.430752 0.902470i \(-0.358248\pi\)
−0.783992 + 0.620771i \(0.786820\pi\)
\(242\) 370.859 129.769i 1.53248 0.536236i
\(243\) 0 0
\(244\) 592.423 592.423i 2.42796 2.42796i
\(245\) 16.9901 13.5491i 0.0693472 0.0553026i
\(246\) 0 0
\(247\) 46.4073 + 29.1597i 0.187884 + 0.118055i
\(248\) 653.517 + 819.484i 2.63515 + 3.30437i
\(249\) 0 0
\(250\) −447.195 50.3868i −1.78878 0.201547i
\(251\) −3.89158 11.1215i −0.0155043 0.0443088i 0.935871 0.352342i \(-0.114615\pi\)
−0.951375 + 0.308034i \(0.900329\pi\)
\(252\) 0 0
\(253\) 68.8265 7.75488i 0.272041 0.0306517i
\(254\) −185.744 385.701i −0.731275 1.51851i
\(255\) 0 0
\(256\) −97.7195 + 428.137i −0.381717 + 1.67241i
\(257\) −63.5682 30.6128i −0.247347 0.119116i 0.306103 0.951998i \(-0.400975\pi\)
−0.553450 + 0.832882i \(0.686689\pi\)
\(258\) 0 0
\(259\) 194.917 + 310.209i 0.752575 + 1.19772i
\(260\) 196.123i 0.754318i
\(261\) 0 0
\(262\) −736.194 −2.80990
\(263\) 50.8493 31.9507i 0.193343 0.121486i −0.431881 0.901930i \(-0.642150\pi\)
0.625225 + 0.780445i \(0.285007\pi\)
\(264\) 0 0
\(265\) 91.1782 189.333i 0.344069 0.714466i
\(266\) −427.252 97.5175i −1.60621 0.366607i
\(267\) 0 0
\(268\) 364.957 175.754i 1.36178 0.655798i
\(269\) 18.2957 + 162.379i 0.0680138 + 0.603640i 0.980774 + 0.195145i \(0.0625176\pi\)
−0.912761 + 0.408495i \(0.866054\pi\)
\(270\) 0 0
\(271\) −198.079 + 69.3110i −0.730920 + 0.255760i −0.669978 0.742381i \(-0.733696\pi\)
−0.0609426 + 0.998141i \(0.519411\pi\)
\(272\) 53.8848 478.241i 0.198106 1.75824i
\(273\) 0 0
\(274\) −636.775 + 507.811i −2.32400 + 1.85332i
\(275\) 6.09344 9.69766i 0.0221580 0.0352642i
\(276\) 0 0
\(277\) 35.9969 + 45.1387i 0.129953 + 0.162956i 0.842551 0.538617i \(-0.181053\pi\)
−0.712598 + 0.701573i \(0.752482\pi\)
\(278\) −542.505 542.505i −1.95146 1.95146i
\(279\) 0 0
\(280\) 323.888 + 925.618i 1.15674 + 3.30578i
\(281\) −176.539 + 221.372i −0.628251 + 0.787802i −0.989479 0.144675i \(-0.953786\pi\)
0.361228 + 0.932478i \(0.382358\pi\)
\(282\) 0 0
\(283\) 96.2836 + 199.935i 0.340225 + 0.706484i 0.998946 0.0459032i \(-0.0146166\pi\)
−0.658721 + 0.752387i \(0.728902\pi\)
\(284\) 198.498 + 869.677i 0.698937 + 3.06224i
\(285\) 0 0
\(286\) −51.7623 24.9274i −0.180987 0.0871588i
\(287\) −3.20345 + 9.15495i −0.0111619 + 0.0318988i
\(288\) 0 0
\(289\) 213.208i 0.737742i
\(290\) 205.540 + 547.034i 0.708759 + 1.88632i
\(291\) 0 0
\(292\) −405.799 + 254.981i −1.38972 + 0.873221i
\(293\) −23.2034 8.11923i −0.0791926 0.0277107i 0.290392 0.956908i \(-0.406214\pi\)
−0.369585 + 0.929197i \(0.620500\pi\)
\(294\) 0 0
\(295\) −34.6036 7.89804i −0.117300 0.0267730i
\(296\) −1253.33 + 286.064i −4.23421 + 0.966431i
\(297\) 0 0
\(298\) −112.550 998.910i −0.377685 3.35205i
\(299\) 44.0406 + 35.1212i 0.147293 + 0.117462i
\(300\) 0 0
\(301\) 15.7353 139.654i 0.0522766 0.463968i
\(302\) 350.290 350.290i 1.15990 1.15990i
\(303\) 0 0
\(304\) 461.569 734.583i 1.51832 2.41639i
\(305\) 349.498 + 219.604i 1.14590 + 0.720014i
\(306\) 0 0
\(307\) −96.2745 96.2745i −0.313598 0.313598i 0.532704 0.846302i \(-0.321176\pi\)
−0.846302 + 0.532704i \(0.821176\pi\)
\(308\) 332.076 + 37.4160i 1.07817 + 0.121480i
\(309\) 0 0
\(310\) −514.866 + 645.621i −1.66086 + 2.08265i
\(311\) 305.576 34.4302i 0.982561 0.110708i 0.393956 0.919129i \(-0.371106\pi\)
0.588604 + 0.808421i \(0.299678\pi\)
\(312\) 0 0
\(313\) 77.7372 + 340.589i 0.248362 + 1.08814i 0.933174 + 0.359424i \(0.117027\pi\)
−0.684813 + 0.728719i \(0.740116\pi\)
\(314\) −82.3074 + 360.612i −0.262126 + 1.14845i
\(315\) 0 0
\(316\) −429.219 + 1226.64i −1.35829 + 3.88177i
\(317\) 158.784 + 252.704i 0.500896 + 0.797172i 0.997490 0.0708112i \(-0.0225588\pi\)
−0.496593 + 0.867983i \(0.665416\pi\)
\(318\) 0 0
\(319\) 124.032 + 11.1161i 0.388816 + 0.0348466i
\(320\) −1042.81 −3.25879
\(321\) 0 0
\(322\) −425.133 148.761i −1.32029 0.461989i
\(323\) −59.2805 + 123.097i −0.183531 + 0.381106i
\(324\) 0 0
\(325\) 9.08118 2.07272i 0.0279421 0.00637760i
\(326\) −316.988 + 152.654i −0.972357 + 0.468262i
\(327\) 0 0
\(328\) −26.6091 21.2201i −0.0811254 0.0646953i
\(329\) −409.711 + 143.364i −1.24532 + 0.435757i
\(330\) 0 0
\(331\) −26.9231 + 26.9231i −0.0813386 + 0.0813386i −0.746606 0.665267i \(-0.768318\pi\)
0.665267 + 0.746606i \(0.268318\pi\)
\(332\) −65.5400 + 52.2664i −0.197410 + 0.157429i
\(333\) 0 0
\(334\) 371.862 + 233.656i 1.11336 + 0.699569i
\(335\) 124.428 + 156.027i 0.371426 + 0.465753i
\(336\) 0 0
\(337\) 68.6759 + 7.73791i 0.203786 + 0.0229612i 0.213267 0.976994i \(-0.431589\pi\)
−0.00948132 + 0.999955i \(0.503018\pi\)
\(338\) 198.402 + 567.002i 0.586989 + 1.67752i
\(339\) 0 0
\(340\) 485.828 54.7397i 1.42891 0.160999i
\(341\) 76.3519 + 158.546i 0.223906 + 0.464945i
\(342\) 0 0
\(343\) 72.7761 318.853i 0.212175 0.929601i
\(344\) 444.307 + 213.967i 1.29159 + 0.621997i
\(345\) 0 0
\(346\) 174.951 + 278.433i 0.505639 + 0.804720i
\(347\) 255.048i 0.735009i −0.930022 0.367505i \(-0.880212\pi\)
0.930022 0.367505i \(-0.119788\pi\)
\(348\) 0 0
\(349\) 402.926 1.15451 0.577257 0.816562i \(-0.304123\pi\)
0.577257 + 0.816562i \(0.304123\pi\)
\(350\) −63.0636 + 39.6255i −0.180182 + 0.113216i
\(351\) 0 0
\(352\) −203.959 + 423.525i −0.579428 + 1.20320i
\(353\) 630.205 + 143.840i 1.78528 + 0.407479i 0.982116 0.188274i \(-0.0602894\pi\)
0.803167 + 0.595754i \(0.203147\pi\)
\(354\) 0 0
\(355\) −395.960 + 190.684i −1.11538 + 0.537138i
\(356\) −133.266 1182.77i −0.374342 3.32238i
\(357\) 0 0
\(358\) 304.427 106.524i 0.850356 0.297552i
\(359\) 1.72924 15.3474i 0.00481682 0.0427505i −0.991074 0.133314i \(-0.957438\pi\)
0.995891 + 0.0905633i \(0.0288668\pi\)
\(360\) 0 0
\(361\) 89.6819 71.5189i 0.248426 0.198113i
\(362\) −77.6308 + 123.549i −0.214450 + 0.341295i
\(363\) 0 0
\(364\) 169.454 + 212.488i 0.465532 + 0.583758i
\(365\) −166.959 166.959i −0.457422 0.457422i
\(366\) 0 0
\(367\) 218.637 + 624.829i 0.595741 + 1.70253i 0.705624 + 0.708586i \(0.250667\pi\)
−0.109883 + 0.993945i \(0.535048\pi\)
\(368\) 555.934 697.119i 1.51069 1.89434i
\(369\) 0 0
\(370\) −439.443 912.512i −1.18768 2.46625i
\(371\) 64.8010 + 283.912i 0.174666 + 0.765261i
\(372\) 0 0
\(373\) 398.567 + 191.940i 1.06854 + 0.514584i 0.883637 0.468173i \(-0.155087\pi\)
0.184907 + 0.982756i \(0.440802\pi\)
\(374\) 47.3019 135.181i 0.126476 0.361447i
\(375\) 0 0
\(376\) 1523.14i 4.05090i
\(377\) 64.9361 + 77.7214i 0.172244 + 0.206158i
\(378\) 0 0
\(379\) −78.5862 + 49.3790i −0.207352 + 0.130288i −0.631705 0.775209i \(-0.717644\pi\)
0.424353 + 0.905497i \(0.360502\pi\)
\(380\) 831.865 + 291.082i 2.18912 + 0.766006i
\(381\) 0 0
\(382\) 1001.72 + 228.636i 2.62230 + 0.598524i
\(383\) −52.6752 + 12.0228i −0.137533 + 0.0313911i −0.290733 0.956804i \(-0.593899\pi\)
0.153200 + 0.988195i \(0.451042\pi\)
\(384\) 0 0
\(385\) 18.4337 + 163.604i 0.0478798 + 0.424945i
\(386\) 534.133 + 425.957i 1.38376 + 1.10351i
\(387\) 0 0
\(388\) −16.5062 + 146.497i −0.0425419 + 0.377570i
\(389\) 220.798 220.798i 0.567605 0.567605i −0.363852 0.931457i \(-0.618539\pi\)
0.931457 + 0.363852i \(0.118539\pi\)
\(390\) 0 0
\(391\) −74.7087 + 118.898i −0.191071 + 0.304088i
\(392\) −89.4741 56.2203i −0.228250 0.143419i
\(393\) 0 0
\(394\) 398.482 + 398.482i 1.01138 + 1.01138i
\(395\) −636.231 71.6860i −1.61071 0.181484i
\(396\) 0 0
\(397\) 487.205 610.936i 1.22722 1.53888i 0.474965 0.880005i \(-0.342461\pi\)
0.752251 0.658876i \(-0.228968\pi\)
\(398\) −814.217 + 91.7402i −2.04577 + 0.230503i
\(399\) 0 0
\(400\) −32.8091 143.746i −0.0820228 0.359366i
\(401\) 28.0626 122.950i 0.0699815 0.306609i −0.927808 0.373057i \(-0.878310\pi\)
0.997790 + 0.0664482i \(0.0211667\pi\)
\(402\) 0 0
\(403\) −47.2685 + 135.086i −0.117292 + 0.335200i
\(404\) −681.893 1085.23i −1.68785 2.68621i
\(405\) 0 0
\(406\) −695.338 415.090i −1.71266 1.02239i
\(407\) −215.829 −0.530293
\(408\) 0 0
\(409\) −115.947 40.5715i −0.283488 0.0991968i 0.184790 0.982778i \(-0.440840\pi\)
−0.468278 + 0.883581i \(0.655125\pi\)
\(410\) 11.6340 24.1582i 0.0283755 0.0589224i
\(411\) 0 0
\(412\) −446.854 + 101.992i −1.08460 + 0.247552i
\(413\) 44.3151 21.3410i 0.107300 0.0516732i
\(414\) 0 0
\(415\) −32.2896 25.7501i −0.0778061 0.0620483i
\(416\) −360.854 + 126.268i −0.867439 + 0.303530i
\(417\) 0 0
\(418\) 182.556 182.556i 0.436736 0.436736i
\(419\) 209.191 166.825i 0.499263 0.398149i −0.341223 0.939983i \(-0.610841\pi\)
0.840486 + 0.541833i \(0.182270\pi\)
\(420\) 0 0
\(421\) −301.780 189.621i −0.716818 0.450407i 0.123609 0.992331i \(-0.460553\pi\)
−0.840427 + 0.541924i \(0.817696\pi\)
\(422\) −23.3945 29.3358i −0.0554372 0.0695160i
\(423\) 0 0
\(424\) −1015.43 114.412i −2.39489 0.269839i
\(425\) 7.66911 + 21.9170i 0.0180450 + 0.0515695i
\(426\) 0 0
\(427\) −568.404 + 64.0437i −1.33116 + 0.149985i
\(428\) 22.8595 + 47.4682i 0.0534100 + 0.110907i
\(429\) 0 0
\(430\) −86.4533 + 378.777i −0.201054 + 0.880876i
\(431\) −124.980 60.1870i −0.289976 0.139645i 0.283241 0.959049i \(-0.408590\pi\)
−0.573217 + 0.819404i \(0.694305\pi\)
\(432\) 0 0
\(433\) 107.372 + 170.882i 0.247973 + 0.394647i 0.947397 0.320060i \(-0.103703\pi\)
−0.699424 + 0.714707i \(0.746560\pi\)
\(434\) 1144.35i 2.63675i
\(435\) 0 0
\(436\) −2255.42 −5.17298
\(437\) −214.333 + 134.674i −0.490464 + 0.308179i
\(438\) 0 0
\(439\) 70.9416 147.312i 0.161598 0.335562i −0.804410 0.594075i \(-0.797518\pi\)
0.966008 + 0.258513i \(0.0832325\pi\)
\(440\) −563.228 128.553i −1.28006 0.292166i
\(441\) 0 0
\(442\) 104.943 50.5377i 0.237427 0.114339i
\(443\) 71.6573 + 635.976i 0.161755 + 1.43561i 0.768059 + 0.640379i \(0.221223\pi\)
−0.606304 + 0.795233i \(0.707349\pi\)
\(444\) 0 0
\(445\) 553.493 193.676i 1.24381 0.435226i
\(446\) −138.159 + 1226.20i −0.309774 + 2.74932i
\(447\) 0 0
\(448\) 1129.83 901.009i 2.52194 2.01118i
\(449\) 149.510 237.943i 0.332984 0.529941i −0.637705 0.770281i \(-0.720116\pi\)
0.970689 + 0.240340i \(0.0772589\pi\)
\(450\) 0 0
\(451\) −3.56259 4.46734i −0.00789931 0.00990542i
\(452\) 753.434 + 753.434i 1.66689 + 1.66689i
\(453\) 0 0
\(454\) −328.917 939.992i −0.724487 2.07047i
\(455\) −83.4846 + 104.686i −0.183483 + 0.230080i
\(456\) 0 0
\(457\) 209.594 + 435.225i 0.458629 + 0.952353i 0.994168 + 0.107843i \(0.0343943\pi\)
−0.535539 + 0.844511i \(0.679891\pi\)
\(458\) −249.217 1091.89i −0.544141 2.38404i
\(459\) 0 0
\(460\) 816.092 + 393.009i 1.77411 + 0.854368i
\(461\) 107.774 308.000i 0.233783 0.668114i −0.765901 0.642959i \(-0.777707\pi\)
0.999684 0.0251545i \(-0.00800777\pi\)
\(462\) 0 0
\(463\) 332.607i 0.718374i 0.933266 + 0.359187i \(0.116946\pi\)
−0.933266 + 0.359187i \(0.883054\pi\)
\(464\) 1230.25 1027.88i 2.65141 2.21525i
\(465\) 0 0
\(466\) 26.7467 16.8061i 0.0573965 0.0360646i
\(467\) 182.053 + 63.7030i 0.389835 + 0.136409i 0.518077 0.855334i \(-0.326648\pi\)
−0.128243 + 0.991743i \(0.540934\pi\)
\(468\) 0 0
\(469\) −269.621 61.5392i −0.574884 0.131214i
\(470\) 1169.90 267.022i 2.48915 0.568132i
\(471\) 0 0
\(472\) 19.3242 + 171.507i 0.0409411 + 0.363363i
\(473\) 64.7299 + 51.6204i 0.136850 + 0.109134i
\(474\) 0 0
\(475\) −4.68659 + 41.5946i −0.00986650 + 0.0875676i
\(476\) −479.071 + 479.071i −1.00645 + 1.00645i
\(477\) 0 0
\(478\) 326.005 518.834i 0.682019 1.08543i
\(479\) −149.906 94.1921i −0.312956 0.196643i 0.366390 0.930461i \(-0.380594\pi\)
−0.679346 + 0.733818i \(0.737736\pi\)
\(480\) 0 0
\(481\) −124.120 124.120i −0.258045 0.258045i
\(482\) −414.520 46.7052i −0.859999 0.0968987i
\(483\) 0 0
\(484\) 682.710 856.091i 1.41056 1.76878i
\(485\) −72.1746 + 8.13213i −0.148814 + 0.0167673i
\(486\) 0 0
\(487\) 10.4608 + 45.8320i 0.0214802 + 0.0941108i 0.984532 0.175206i \(-0.0560592\pi\)
−0.963052 + 0.269317i \(0.913202\pi\)
\(488\) 446.629 1956.81i 0.915223 4.00986i
\(489\) 0 0
\(490\) 27.4963 78.5798i 0.0561148 0.160367i
\(491\) 308.602 + 491.137i 0.628517 + 1.00028i 0.997488 + 0.0708376i \(0.0225672\pi\)
−0.368971 + 0.929441i \(0.620290\pi\)
\(492\) 0 0
\(493\) −174.404 + 182.550i −0.353761 + 0.370284i
\(494\) 209.969 0.425038
\(495\) 0 0
\(496\) 2138.27 + 748.214i 4.31104 + 1.50850i
\(497\) 264.246 548.712i 0.531681 1.10405i
\(498\) 0 0
\(499\) −927.838 + 211.773i −1.85939 + 0.424395i −0.996689 0.0813113i \(-0.974089\pi\)
−0.862706 + 0.505706i \(0.831232\pi\)
\(500\) −1129.96 + 544.159i −2.25992 + 1.08832i
\(501\) 0 0
\(502\) −35.2914 28.1439i −0.0703016 0.0560636i
\(503\) 199.435 69.7852i 0.396490 0.138738i −0.124667 0.992199i \(-0.539786\pi\)
0.521157 + 0.853461i \(0.325501\pi\)
\(504\) 0 0
\(505\) 446.498 446.498i 0.884154 0.884154i
\(506\) 207.452 165.438i 0.409985 0.326952i
\(507\) 0 0
\(508\) −1010.18 634.739i −1.98855 1.24949i
\(509\) −41.2535 51.7302i −0.0810481 0.101631i 0.739654 0.672987i \(-0.234989\pi\)
−0.820702 + 0.571356i \(0.806418\pi\)
\(510\) 0 0
\(511\) 325.147 + 36.6352i 0.636295 + 0.0716932i
\(512\) 130.737 + 373.625i 0.255346 + 0.729737i
\(513\) 0 0
\(514\) −268.597 + 30.2636i −0.522562 + 0.0588786i
\(515\) −97.9766 203.451i −0.190246 0.395050i
\(516\) 0 0
\(517\) 56.9021 249.305i 0.110062 0.482214i
\(518\) 1264.54 + 608.970i 2.44119 + 1.17562i
\(519\) 0 0
\(520\) −249.974 397.831i −0.480719 0.765060i
\(521\) 926.186i 1.77771i 0.458190 + 0.888854i \(0.348498\pi\)
−0.458190 + 0.888854i \(0.651502\pi\)
\(522\) 0 0
\(523\) 711.936 1.36125 0.680627 0.732630i \(-0.261707\pi\)
0.680627 + 0.732630i \(0.261707\pi\)
\(524\) −1737.20 + 1091.56i −3.31527 + 2.08312i
\(525\) 0 0
\(526\) 99.8221 207.283i 0.189776 0.394074i
\(527\) −347.822 79.3882i −0.660004 0.150642i
\(528\) 0 0
\(529\) 242.216 116.645i 0.457875 0.220501i
\(530\) −90.1381 799.997i −0.170072 1.50943i
\(531\) 0 0
\(532\) −1152.78 + 403.375i −2.16688 + 0.758224i
\(533\) 0.520309 4.61787i 0.000976189 0.00866392i
\(534\) 0 0
\(535\) −20.2937 + 16.1837i −0.0379322 + 0.0302499i
\(536\) 516.296 821.680i 0.963238 1.53298i
\(537\) 0 0
\(538\) 390.309 + 489.433i 0.725482 + 0.909726i
\(539\) −12.5447 12.5447i −0.0232740 0.0232740i
\(540\) 0 0
\(541\) 51.9016 + 148.326i 0.0959364 + 0.274170i 0.981844 0.189692i \(-0.0607489\pi\)
−0.885907 + 0.463862i \(0.846463\pi\)
\(542\) −501.257 + 628.557i −0.924829 + 1.15970i
\(543\) 0 0
\(544\) −413.505 858.652i −0.760120 1.57841i
\(545\) −247.260 1083.32i −0.453689 1.98774i
\(546\) 0 0
\(547\) 249.900 + 120.346i 0.456856 + 0.220010i 0.648135 0.761525i \(-0.275549\pi\)
−0.191279 + 0.981536i \(0.561263\pi\)
\(548\) −749.670 + 2142.43i −1.36801 + 3.90955i
\(549\) 0 0
\(550\) 43.8768i 0.0797761i
\(551\) −426.037 + 160.077i −0.773207 + 0.290521i
\(552\) 0 0
\(553\) 751.259 472.047i 1.35851 0.853611i
\(554\) 208.768 + 73.0512i 0.376838 + 0.131861i
\(555\) 0 0
\(556\) −2084.53 475.780i −3.74915 0.855719i
\(557\) −114.217 + 26.0694i −0.205058 + 0.0468032i −0.323816 0.946120i \(-0.604966\pi\)
0.118758 + 0.992923i \(0.462109\pi\)
\(558\) 0 0
\(559\) 7.53906 + 66.9110i 0.0134867 + 0.119698i
\(560\) 1657.08 + 1321.48i 2.95908 + 2.35979i
\(561\) 0 0
\(562\) −121.451 + 1077.91i −0.216105 + 1.91798i
\(563\) −544.911 + 544.911i −0.967871 + 0.967871i −0.999500 0.0316292i \(-0.989930\pi\)
0.0316292 + 0.999500i \(0.489930\pi\)
\(564\) 0 0
\(565\) −279.289 + 444.486i −0.494317 + 0.786701i
\(566\) 719.832 + 452.301i 1.27179 + 0.799118i
\(567\) 0 0
\(568\) 1511.12 + 1511.12i 2.66042 + 2.66042i
\(569\) −877.995 98.9262i −1.54305 0.173860i −0.700960 0.713200i \(-0.747245\pi\)
−0.842088 + 0.539340i \(0.818674\pi\)
\(570\) 0 0
\(571\) −118.851 + 149.035i −0.208146 + 0.261007i −0.874936 0.484239i \(-0.839096\pi\)
0.666790 + 0.745246i \(0.267668\pi\)
\(572\) −159.104 + 17.9267i −0.278153 + 0.0313404i
\(573\) 0 0
\(574\) 8.26835 + 36.2260i 0.0144048 + 0.0631115i
\(575\) −9.57287 + 41.9415i −0.0166485 + 0.0729417i
\(576\) 0 0
\(577\) 105.425 301.288i 0.182713 0.522163i −0.815701 0.578474i \(-0.803648\pi\)
0.998413 + 0.0563115i \(0.0179340\pi\)
\(578\) −434.561 691.600i −0.751836 1.19654i
\(579\) 0 0
\(580\) 1296.10 + 986.085i 2.23466 + 1.70015i
\(581\) 57.2324 0.0985068
\(582\) 0 0
\(583\) −161.930 56.6618i −0.277753 0.0971901i
\(584\) −498.163 + 1034.45i −0.853019 + 1.77131i
\(585\) 0 0
\(586\) −91.8156 + 20.9563i −0.156682 + 0.0357616i
\(587\) 927.516 446.668i 1.58009 0.760934i 0.581481 0.813560i \(-0.302474\pi\)
0.998614 + 0.0526268i \(0.0167594\pi\)
\(588\) 0 0
\(589\) −502.818 400.984i −0.853681 0.680788i
\(590\) −128.345 + 44.9097i −0.217533 + 0.0761181i
\(591\) 0 0
\(592\) −1964.69 + 1964.69i −3.31873 + 3.31873i
\(593\) 720.843 574.853i 1.21559 0.969398i 0.215612 0.976479i \(-0.430826\pi\)
0.999975 + 0.00708137i \(0.00225409\pi\)
\(594\) 0 0
\(595\) −282.627 177.586i −0.475003 0.298464i
\(596\) −1746.67 2190.26i −2.93066 3.67493i
\(597\) 0 0
\(598\) 214.442 + 24.1619i 0.358599 + 0.0404044i
\(599\) −53.8833 153.989i −0.0899553 0.257078i 0.890112 0.455741i \(-0.150626\pi\)
−0.980068 + 0.198663i \(0.936340\pi\)
\(600\) 0 0
\(601\) −863.514 + 97.2947i −1.43680 + 0.161888i −0.795755 0.605619i \(-0.792926\pi\)
−0.641041 + 0.767507i \(0.721497\pi\)
\(602\) −233.602 485.080i −0.388044 0.805781i
\(603\) 0 0
\(604\) 307.206 1345.96i 0.508619 2.22841i
\(605\) 486.040 + 234.065i 0.803373 + 0.386884i
\(606\) 0 0
\(607\) −310.491 494.143i −0.511517 0.814075i 0.486712 0.873562i \(-0.338196\pi\)
−0.998229 + 0.0594878i \(0.981053\pi\)
\(608\) 1717.99i 2.82564i
\(609\) 0 0
\(610\) 1581.30 2.59229
\(611\) 176.094 110.647i 0.288206 0.181092i
\(612\) 0 0
\(613\) −246.942 + 512.779i −0.402841 + 0.836508i 0.596582 + 0.802552i \(0.296525\pi\)
−0.999423 + 0.0339560i \(0.989189\pi\)
\(614\) −508.521 116.067i −0.828211 0.189034i
\(615\) 0 0
\(616\) 721.299 347.359i 1.17094 0.563895i
\(617\) −30.7744 273.130i −0.0498775 0.442675i −0.993687 0.112186i \(-0.964215\pi\)
0.943810 0.330489i \(-0.107214\pi\)
\(618\) 0 0
\(619\) −477.311 + 167.018i −0.771100 + 0.269820i −0.687019 0.726639i \(-0.741081\pi\)
−0.0840811 + 0.996459i \(0.526795\pi\)
\(620\) −257.668 + 2286.87i −0.415594 + 3.68850i
\(621\) 0 0
\(622\) 921.049 734.512i 1.48079 1.18089i
\(623\) −432.340 + 688.065i −0.693965 + 1.10444i
\(624\) 0 0
\(625\) −426.820 535.215i −0.682911 0.856344i
\(626\) 946.353 + 946.353i 1.51175 + 1.51175i
\(627\) 0 0
\(628\) 340.459 + 972.977i 0.542133 + 1.54933i
\(629\) 272.821 342.107i 0.433738 0.543891i
\(630\) 0 0
\(631\) −251.062 521.335i −0.397879 0.826205i −0.999621 0.0275142i \(-0.991241\pi\)
0.601742 0.798690i \(-0.294473\pi\)
\(632\) 692.784 + 3035.29i 1.09618 + 4.80267i
\(633\) 0 0
\(634\) 1030.12 + 496.082i 1.62480 + 0.782463i
\(635\) 194.131 554.794i 0.305718 0.873691i
\(636\) 0 0
\(637\) 14.4284i 0.0226506i
\(638\) 424.992 216.745i 0.666131 0.339726i
\(639\) 0 0
\(640\) −1432.46 + 900.076i −2.23822 + 1.40637i
\(641\) 354.797 + 124.149i 0.553505 + 0.193680i 0.592516 0.805559i \(-0.298135\pi\)
−0.0390104 + 0.999239i \(0.512421\pi\)
\(642\) 0 0
\(643\) −13.7935 3.14829i −0.0214519 0.00489625i 0.211782 0.977317i \(-0.432073\pi\)
−0.233233 + 0.972421i \(0.574931\pi\)
\(644\) −1223.76 + 279.315i −1.90024 + 0.433718i
\(645\) 0 0
\(646\) 58.6043 + 520.127i 0.0907187 + 0.805151i
\(647\) −778.933 621.178i −1.20391 0.960090i −0.204092 0.978952i \(-0.565424\pi\)
−0.999822 + 0.0188619i \(0.993996\pi\)
\(648\) 0 0
\(649\) −3.24430 + 28.7939i −0.00499892 + 0.0443666i
\(650\) 25.2328 25.2328i 0.0388197 0.0388197i
\(651\) 0 0
\(652\) −521.660 + 830.217i −0.800092 + 1.27334i
\(653\) 240.927 + 151.384i 0.368954 + 0.231829i 0.703728 0.710469i \(-0.251517\pi\)
−0.334774 + 0.942298i \(0.608660\pi\)
\(654\) 0 0
\(655\) −714.742 714.742i −1.09121 1.09121i
\(656\) −73.0963 8.23598i −0.111427 0.0125548i
\(657\) 0 0
\(658\) −1036.81 + 1300.12i −1.57570 + 1.97586i
\(659\) −1062.63 + 119.729i −1.61249 + 0.181684i −0.871694 0.490050i \(-0.836978\pi\)
−0.740792 + 0.671734i \(0.765550\pi\)
\(660\) 0 0
\(661\) 100.223 + 439.106i 0.151624 + 0.664306i 0.992414 + 0.122945i \(0.0392337\pi\)
−0.840790 + 0.541361i \(0.817909\pi\)
\(662\) −32.4579 + 142.207i −0.0490301 + 0.214815i
\(663\) 0 0
\(664\) −66.3289 + 189.557i −0.0998930 + 0.285478i
\(665\) −320.126 509.478i −0.481393 0.766133i
\(666\) 0 0
\(667\) −453.534 + 114.462i −0.679961 + 0.171607i
\(668\) 1223.93 1.83223
\(669\) 0 0
\(670\) 721.633 + 252.510i 1.07706 + 0.376881i
\(671\) 146.207 303.602i 0.217894 0.452462i
\(672\) 0 0
\(673\) −665.540 + 151.905i −0.988915 + 0.225713i −0.686236 0.727379i \(-0.740738\pi\)
−0.302679 + 0.953092i \(0.597881\pi\)
\(674\) 238.541 114.875i 0.353919 0.170438i
\(675\) 0 0
\(676\) 1308.87 + 1043.79i 1.93619 + 1.54406i
\(677\) −140.624 + 49.2065i −0.207716 + 0.0726831i −0.432132 0.901810i \(-0.642238\pi\)
0.224415 + 0.974494i \(0.427953\pi\)
\(678\) 0 0
\(679\) 71.1709 71.1709i 0.104817 0.104817i
\(680\) 915.722 730.264i 1.34665 1.07392i
\(681\) 0 0
\(682\) 570.819 + 358.670i 0.836978 + 0.525908i
\(683\) 562.476 + 705.323i 0.823538 + 1.03268i 0.998839 + 0.0481690i \(0.0153386\pi\)
−0.175301 + 0.984515i \(0.556090\pi\)
\(684\) 0 0
\(685\) −1111.23 125.206i −1.62224 0.182782i
\(686\) −413.818 1182.62i −0.603233 1.72394i
\(687\) 0 0
\(688\) 1059.14 119.336i 1.53944 0.173453i
\(689\) −60.5379 125.708i −0.0878635 0.182450i
\(690\) 0 0
\(691\) 174.983 766.650i 0.253231 1.10948i −0.675101 0.737726i \(-0.735900\pi\)
0.928332 0.371753i \(-0.121243\pi\)
\(692\) 825.667 + 397.620i 1.19316 + 0.574596i
\(693\) 0 0
\(694\) −519.841 827.322i −0.749050 1.19211i
\(695\) 1053.39i 1.51567i
\(696\) 0 0
\(697\) 11.5844 0.0166204
\(698\) 1307.01 821.246i 1.87250 1.17657i
\(699\) 0 0
\(700\) −90.0589 + 187.009i −0.128656 + 0.267156i
\(701\) −1133.94 258.815i −1.61761 0.369208i −0.684557 0.728959i \(-0.740005\pi\)
−0.933048 + 0.359751i \(0.882862\pi\)
\(702\) 0 0
\(703\) 710.676 342.243i 1.01092 0.486833i
\(704\) 95.3188 + 845.978i 0.135396 + 1.20167i
\(705\) 0 0
\(706\) 2337.43 817.901i 3.31080 1.15850i
\(707\) −97.9734 + 869.538i −0.138576 + 1.22990i
\(708\) 0 0
\(709\) 70.9559 56.5854i 0.100079 0.0798102i −0.572172 0.820134i \(-0.693899\pi\)
0.672251 + 0.740323i \(0.265328\pi\)
\(710\) −895.755 + 1425.59i −1.26163 + 2.00787i
\(711\) 0 0
\(712\) −1777.86 2229.36i −2.49699 3.13112i
\(713\) −467.388 467.388i −0.655523 0.655523i
\(714\) 0 0
\(715\) −26.0529 74.4550i −0.0364377 0.104133i
\(716\) 560.416 702.740i 0.782704 0.981480i
\(717\) 0 0
\(718\) −25.6719 53.3083i −0.0357548 0.0742456i
\(719\) −8.99364 39.4037i −0.0125085 0.0548035i 0.968288 0.249835i \(-0.0803763\pi\)
−0.980797 + 0.195031i \(0.937519\pi\)
\(720\) 0 0
\(721\) 281.937 + 135.774i 0.391036 + 0.188313i
\(722\) 145.139 414.782i 0.201023 0.574491i
\(723\) 0 0
\(724\) 406.642i 0.561661i
\(725\) −31.9614 + 70.4356i −0.0440847 + 0.0971525i
\(726\) 0 0
\(727\) −358.094 + 225.005i −0.492564 + 0.309498i −0.755311 0.655366i \(-0.772514\pi\)
0.262747 + 0.964865i \(0.415371\pi\)
\(728\) 614.566 + 215.046i 0.844184 + 0.295393i
\(729\) 0 0
\(730\) −881.877 201.283i −1.20805 0.275730i
\(731\) −163.645 + 37.3509i −0.223865 + 0.0510957i
\(732\) 0 0
\(733\) −14.7149 130.599i −0.0200749 0.178170i 0.979673 0.200599i \(-0.0642887\pi\)
−0.999748 + 0.0224286i \(0.992860\pi\)
\(734\) 1982.74 + 1581.18i 2.70128 + 2.15420i
\(735\) 0 0
\(736\) 197.695 1754.59i 0.268607 2.38396i
\(737\) 115.203 115.203i 0.156314 0.156314i
\(738\) 0 0
\(739\) −152.535 + 242.758i −0.206407 + 0.328495i −0.933845 0.357679i \(-0.883568\pi\)
0.727438 + 0.686174i \(0.240711\pi\)
\(740\) −2389.94 1501.70i −3.22965 2.02932i
\(741\) 0 0
\(742\) 788.872 + 788.872i 1.06317 + 1.06317i
\(743\) −286.805 32.3151i −0.386009 0.0434928i −0.0831723 0.996535i \(-0.526505\pi\)
−0.302837 + 0.953042i \(0.597934\pi\)
\(744\) 0 0
\(745\) 860.533 1079.07i 1.15508 1.44842i
\(746\) 1684.08 189.750i 2.25748 0.254357i
\(747\) 0 0
\(748\) −88.8146 389.122i −0.118736 0.520217i
\(749\) 8.00411 35.0683i 0.0106864 0.0468202i
\(750\) 0 0
\(751\) 14.9942 42.8510i 0.0199657 0.0570586i −0.933469 0.358657i \(-0.883235\pi\)
0.953435 + 0.301599i \(0.0975203\pi\)
\(752\) −1751.44 2787.40i −2.32904 3.70664i
\(753\) 0 0
\(754\) 369.051 + 119.759i 0.489458 + 0.158831i
\(755\) 680.165 0.900881
\(756\) 0 0
\(757\) −467.425 163.559i −0.617470 0.216062i 0.00337645 0.999994i \(-0.498925\pi\)
−0.620846 + 0.783932i \(0.713211\pi\)
\(758\) −154.272 + 320.350i −0.203526 + 0.422625i
\(759\) 0 0
\(760\) 2058.43 469.823i 2.70846 0.618188i
\(761\) −1035.64 + 498.740i −1.36090 + 0.655375i −0.964837 0.262849i \(-0.915338\pi\)
−0.396062 + 0.918224i \(0.629624\pi\)
\(762\) 0 0
\(763\) 1203.90 + 960.077i 1.57785 + 1.25829i
\(764\) 2702.76 945.738i 3.53765 1.23788i
\(765\) 0 0
\(766\) −146.362 + 146.362i −0.191074 + 0.191074i
\(767\) −18.4246 + 14.6931i −0.0240217 + 0.0191566i
\(768\) 0 0
\(769\) 1078.65 + 677.762i 1.40267 + 0.881355i 0.999431 0.0337394i \(-0.0107416\pi\)
0.403239 + 0.915095i \(0.367884\pi\)
\(770\) 393.253 + 493.124i 0.510718 + 0.640420i
\(771\) 0 0
\(772\) 1891.96 + 213.173i 2.45073 + 0.276131i
\(773\) 101.777 + 290.863i 0.131666 + 0.376279i 0.990776 0.135512i \(-0.0432680\pi\)
−0.859110 + 0.511791i \(0.828982\pi\)
\(774\) 0 0
\(775\) −108.613 + 12.2378i −0.140146 + 0.0157907i
\(776\) 153.239 + 318.205i 0.197473 + 0.410058i
\(777\) 0 0
\(778\) 266.190 1166.26i 0.342147 1.49904i
\(779\) 18.8147 + 9.06068i 0.0241524 + 0.0116312i
\(780\) 0 0
\(781\) 190.885 + 303.791i 0.244410 + 0.388977i
\(782\) 537.952i 0.687919i
\(783\) 0 0
\(784\) −228.388 −0.291311
\(785\) −430.013 + 270.195i −0.547788 + 0.344198i
\(786\) 0 0
\(787\) 418.692 869.423i 0.532010 1.10473i −0.445780 0.895143i \(-0.647074\pi\)
0.977790 0.209588i