Properties

Label 261.3.s.a.37.3
Level $261$
Weight $3$
Character 261.37
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 37.3
Character \(\chi\) \(=\) 261.37
Dual form 261.3.s.a.127.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.20133 + 0.770280i) q^{2} +(1.12521 + 0.897324i) q^{4} +(-2.64264 - 5.48750i) q^{5} +(-3.22936 - 4.04949i) q^{7} +(-3.17747 - 5.05691i) q^{8} +O(q^{10})\) \(q+(2.20133 + 0.770280i) q^{2} +(1.12521 + 0.897324i) q^{4} +(-2.64264 - 5.48750i) q^{5} +(-3.22936 - 4.04949i) q^{7} +(-3.17747 - 5.05691i) q^{8} +(-1.59042 - 14.1154i) q^{10} +(-3.16517 + 5.03734i) q^{11} +(14.6839 - 3.35151i) q^{13} +(-3.98966 - 11.4018i) q^{14} +(-4.38044 - 19.1919i) q^{16} +(-22.0898 - 22.0898i) q^{17} +(-0.835449 + 0.0941325i) q^{19} +(1.95054 - 8.54589i) q^{20} +(-10.8478 + 8.65079i) q^{22} +(21.1449 + 10.1828i) q^{23} +(-7.54184 + 9.45717i) q^{25} +(34.9058 + 3.93294i) q^{26} -7.45431i q^{28} +(18.7362 + 22.1350i) q^{29} +(21.3525 + 7.47156i) q^{31} +(2.46561 - 21.8829i) q^{32} +(-31.6117 - 65.6424i) q^{34} +(-13.6875 + 28.4225i) q^{35} +(4.25720 + 6.77529i) q^{37} +(-1.91161 - 0.436313i) q^{38} +(-19.3529 + 30.8000i) q^{40} +(8.24028 - 8.24028i) q^{41} +(-3.09691 - 8.85047i) q^{43} +(-8.08161 + 2.82788i) q^{44} +(38.7033 + 38.7033i) q^{46} +(22.1022 + 13.8877i) q^{47} +(4.93392 - 21.6169i) q^{49} +(-23.8868 + 15.0091i) q^{50} +(19.5299 + 9.40509i) q^{52} +(-47.7265 + 22.9839i) q^{53} +(36.0068 + 4.05699i) q^{55} +(-10.2167 + 29.1977i) q^{56} +(24.1944 + 63.1585i) q^{58} -17.4148 q^{59} +(6.87260 - 60.9960i) q^{61} +(41.2488 + 32.8948i) q^{62} +(-11.8813 + 24.6717i) q^{64} +(-57.1957 - 71.7211i) q^{65} +(-26.2055 - 5.98124i) q^{67} +(-5.03393 - 44.6774i) q^{68} +(-52.0241 + 52.0241i) q^{70} +(4.93086 - 1.12544i) q^{71} +(-53.0793 + 18.5732i) q^{73} +(4.15264 + 18.1939i) q^{74} +(-1.02452 - 0.643750i) q^{76} +(30.6201 - 3.45006i) q^{77} +(74.2026 - 46.6246i) q^{79} +(-93.7398 + 74.7550i) q^{80} +(24.4869 - 11.7923i) q^{82} +(48.3929 - 60.6827i) q^{83} +(-62.8424 + 179.593i) q^{85} -21.8683i q^{86} +35.5306 q^{88} +(138.036 + 48.3009i) q^{89} +(-60.9916 - 48.6392i) q^{91} +(14.6551 + 30.4317i) q^{92} +(37.9568 + 47.5963i) q^{94} +(2.72434 + 4.33577i) q^{95} +(0.115126 + 1.02177i) q^{97} +(27.5123 - 43.7855i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.20133 + 0.770280i 1.10067 + 0.385140i 0.818663 0.574274i \(-0.194715\pi\)
0.282003 + 0.959414i \(0.409001\pi\)
\(3\) 0 0
\(4\) 1.12521 + 0.897324i 0.281302 + 0.224331i
\(5\) −2.64264 5.48750i −0.528528 1.09750i −0.978840 0.204628i \(-0.934401\pi\)
0.450312 0.892871i \(-0.351313\pi\)
\(6\) 0 0
\(7\) −3.22936 4.04949i −0.461337 0.578499i 0.495689 0.868500i \(-0.334916\pi\)
−0.957026 + 0.290001i \(0.906344\pi\)
\(8\) −3.17747 5.05691i −0.397184 0.632114i
\(9\) 0 0
\(10\) −1.59042 14.1154i −0.159042 1.41154i
\(11\) −3.16517 + 5.03734i −0.287743 + 0.457940i −0.959049 0.283240i \(-0.908591\pi\)
0.671306 + 0.741180i \(0.265734\pi\)
\(12\) 0 0
\(13\) 14.6839 3.35151i 1.12953 0.257808i 0.383385 0.923589i \(-0.374758\pi\)
0.746148 + 0.665780i \(0.231901\pi\)
\(14\) −3.98966 11.4018i −0.284976 0.814414i
\(15\) 0 0
\(16\) −4.38044 19.1919i −0.273777 1.19950i
\(17\) −22.0898 22.0898i −1.29940 1.29940i −0.928787 0.370615i \(-0.879147\pi\)
−0.370615 0.928787i \(-0.620853\pi\)
\(18\) 0 0
\(19\) −0.835449 + 0.0941325i −0.0439710 + 0.00495434i −0.133923 0.990992i \(-0.542757\pi\)
0.0899516 + 0.995946i \(0.471329\pi\)
\(20\) 1.95054 8.54589i 0.0975272 0.427294i
\(21\) 0 0
\(22\) −10.8478 + 8.65079i −0.493080 + 0.393218i
\(23\) 21.1449 + 10.1828i 0.919344 + 0.442733i 0.832837 0.553519i \(-0.186715\pi\)
0.0865068 + 0.996251i \(0.472430\pi\)
\(24\) 0 0
\(25\) −7.54184 + 9.45717i −0.301674 + 0.378287i
\(26\) 34.9058 + 3.93294i 1.34253 + 0.151267i
\(27\) 0 0
\(28\) 7.45431i 0.266225i
\(29\) 18.7362 + 22.1350i 0.646074 + 0.763274i
\(30\) 0 0
\(31\) 21.3525 + 7.47156i 0.688790 + 0.241018i 0.651904 0.758301i \(-0.273970\pi\)
0.0368860 + 0.999319i \(0.488256\pi\)
\(32\) 2.46561 21.8829i 0.0770504 0.683841i
\(33\) 0 0
\(34\) −31.6117 65.6424i −0.929756 1.93066i
\(35\) −13.6875 + 28.4225i −0.391073 + 0.812070i
\(36\) 0 0
\(37\) 4.25720 + 6.77529i 0.115059 + 0.183116i 0.899289 0.437355i \(-0.144085\pi\)
−0.784230 + 0.620470i \(0.786942\pi\)
\(38\) −1.91161 0.436313i −0.0503055 0.0114819i
\(39\) 0 0
\(40\) −19.3529 + 30.8000i −0.483822 + 0.769999i
\(41\) 8.24028 8.24028i 0.200982 0.200982i −0.599438 0.800421i \(-0.704609\pi\)
0.800421 + 0.599438i \(0.204609\pi\)
\(42\) 0 0
\(43\) −3.09691 8.85047i −0.0720212 0.205825i 0.902246 0.431222i \(-0.141918\pi\)
−0.974267 + 0.225398i \(0.927632\pi\)
\(44\) −8.08161 + 2.82788i −0.183673 + 0.0642699i
\(45\) 0 0
\(46\) 38.7033 + 38.7033i 0.841377 + 0.841377i
\(47\) 22.1022 + 13.8877i 0.470259 + 0.295483i 0.746237 0.665681i \(-0.231859\pi\)
−0.275978 + 0.961164i \(0.589002\pi\)
\(48\) 0 0
\(49\) 4.93392 21.6169i 0.100692 0.441162i
\(50\) −23.8868 + 15.0091i −0.477735 + 0.300181i
\(51\) 0 0
\(52\) 19.5299 + 9.40509i 0.375574 + 0.180867i
\(53\) −47.7265 + 22.9839i −0.900501 + 0.433658i −0.826070 0.563568i \(-0.809428\pi\)
−0.0744311 + 0.997226i \(0.523714\pi\)
\(54\) 0 0
\(55\) 36.0068 + 4.05699i 0.654669 + 0.0737635i
\(56\) −10.2167 + 29.1977i −0.182442 + 0.521388i
\(57\) 0 0
\(58\) 24.1944 + 63.1585i 0.417145 + 1.08894i
\(59\) −17.4148 −0.295166 −0.147583 0.989050i \(-0.547149\pi\)
−0.147583 + 0.989050i \(0.547149\pi\)
\(60\) 0 0
\(61\) 6.87260 60.9960i 0.112666 0.999935i −0.802443 0.596728i \(-0.796467\pi\)
0.915109 0.403207i \(-0.132104\pi\)
\(62\) 41.2488 + 32.8948i 0.665303 + 0.530561i
\(63\) 0 0
\(64\) −11.8813 + 24.6717i −0.185645 + 0.385496i
\(65\) −57.1957 71.7211i −0.879934 1.10340i
\(66\) 0 0
\(67\) −26.2055 5.98124i −0.391127 0.0892722i 0.0224346 0.999748i \(-0.492858\pi\)
−0.413562 + 0.910476i \(0.635715\pi\)
\(68\) −5.03393 44.6774i −0.0740285 0.657021i
\(69\) 0 0
\(70\) −52.0241 + 52.0241i −0.743201 + 0.743201i
\(71\) 4.93086 1.12544i 0.0694487 0.0158512i −0.187655 0.982235i \(-0.560089\pi\)
0.257104 + 0.966384i \(0.417232\pi\)
\(72\) 0 0
\(73\) −53.0793 + 18.5732i −0.727113 + 0.254428i −0.668353 0.743844i \(-0.733000\pi\)
−0.0587602 + 0.998272i \(0.518715\pi\)
\(74\) 4.15264 + 18.1939i 0.0561167 + 0.245863i
\(75\) 0 0
\(76\) −1.02452 0.643750i −0.0134806 0.00847040i
\(77\) 30.6201 3.45006i 0.397664 0.0448060i
\(78\) 0 0
\(79\) 74.2026 46.6246i 0.939274 0.590185i 0.0269421 0.999637i \(-0.491423\pi\)
0.912332 + 0.409452i \(0.134280\pi\)
\(80\) −93.7398 + 74.7550i −1.17175 + 0.934438i
\(81\) 0 0
\(82\) 24.4869 11.7923i 0.298621 0.143808i
\(83\) 48.3929 60.6827i 0.583047 0.731117i −0.399583 0.916697i \(-0.630845\pi\)
0.982629 + 0.185580i \(0.0594164\pi\)
\(84\) 0 0
\(85\) −62.8424 + 179.593i −0.739322 + 2.11286i
\(86\) 21.8683i 0.254283i
\(87\) 0 0
\(88\) 35.5306 0.403757
\(89\) 138.036 + 48.3009i 1.55097 + 0.542707i 0.963769 0.266737i \(-0.0859455\pi\)
0.587197 + 0.809444i \(0.300231\pi\)
\(90\) 0 0
\(91\) −60.9916 48.6392i −0.670237 0.534497i
\(92\) 14.6551 + 30.4317i 0.159295 + 0.330779i
\(93\) 0 0
\(94\) 37.9568 + 47.5963i 0.403796 + 0.506344i
\(95\) 2.72434 + 4.33577i 0.0286773 + 0.0456397i
\(96\) 0 0
\(97\) 0.115126 + 1.02177i 0.00118686 + 0.0105337i 0.994292 0.106696i \(-0.0340272\pi\)
−0.993105 + 0.117230i \(0.962599\pi\)
\(98\) 27.5123 43.7855i 0.280737 0.446791i
\(99\) 0 0
\(100\) −16.9723 + 3.87382i −0.169723 + 0.0387382i
\(101\) −43.9053 125.474i −0.434706 1.24232i −0.928040 0.372479i \(-0.878508\pi\)
0.493334 0.869840i \(-0.335778\pi\)
\(102\) 0 0
\(103\) 1.55354 + 6.80648i 0.0150829 + 0.0660824i 0.981909 0.189352i \(-0.0606387\pi\)
−0.966826 + 0.255434i \(0.917782\pi\)
\(104\) −63.6060 63.6060i −0.611596 0.611596i
\(105\) 0 0
\(106\) −122.766 + 13.8324i −1.15817 + 0.130494i
\(107\) −14.9676 + 65.5774i −0.139884 + 0.612873i 0.855574 + 0.517680i \(0.173204\pi\)
−0.995459 + 0.0951935i \(0.969653\pi\)
\(108\) 0 0
\(109\) 139.358 111.134i 1.27851 1.01958i 0.280291 0.959915i \(-0.409569\pi\)
0.998219 0.0596621i \(-0.0190023\pi\)
\(110\) 76.1379 + 36.6661i 0.692163 + 0.333328i
\(111\) 0 0
\(112\) −63.5716 + 79.7163i −0.567604 + 0.711752i
\(113\) −14.1294 1.59200i −0.125039 0.0140885i 0.0492231 0.998788i \(-0.484325\pi\)
−0.174262 + 0.984699i \(0.555754\pi\)
\(114\) 0 0
\(115\) 142.942i 1.24298i
\(116\) 1.21986 + 41.7189i 0.0105161 + 0.359645i
\(117\) 0 0
\(118\) −38.3357 13.4143i −0.324879 0.113680i
\(119\) −18.1165 + 160.789i −0.152240 + 1.35116i
\(120\) 0 0
\(121\) 37.1435 + 77.1292i 0.306971 + 0.637431i
\(122\) 62.1129 128.979i 0.509122 1.05720i
\(123\) 0 0
\(124\) 17.3216 + 27.5672i 0.139690 + 0.222316i
\(125\) −76.6224 17.4886i −0.612979 0.139908i
\(126\) 0 0
\(127\) −56.8872 + 90.5354i −0.447931 + 0.712877i −0.992010 0.126156i \(-0.959736\pi\)
0.544080 + 0.839033i \(0.316879\pi\)
\(128\) −107.445 + 107.445i −0.839411 + 0.839411i
\(129\) 0 0
\(130\) −70.6614 201.939i −0.543550 1.55338i
\(131\) 15.0564 5.26846i 0.114934 0.0402172i −0.272199 0.962241i \(-0.587751\pi\)
0.387133 + 0.922024i \(0.373465\pi\)
\(132\) 0 0
\(133\) 3.07916 + 3.07916i 0.0231516 + 0.0231516i
\(134\) −53.0798 33.3523i −0.396118 0.248897i
\(135\) 0 0
\(136\) −41.5166 + 181.896i −0.305269 + 1.33747i
\(137\) 120.235 75.5488i 0.877630 0.551451i −0.0161943 0.999869i \(-0.505155\pi\)
0.893824 + 0.448417i \(0.148012\pi\)
\(138\) 0 0
\(139\) 199.013 + 95.8394i 1.43174 + 0.689492i 0.979321 0.202311i \(-0.0648453\pi\)
0.452423 + 0.891803i \(0.350560\pi\)
\(140\) −40.9055 + 19.6991i −0.292182 + 0.140708i
\(141\) 0 0
\(142\) 11.7214 + 1.32068i 0.0825448 + 0.00930057i
\(143\) −29.5944 + 84.5760i −0.206954 + 0.591440i
\(144\) 0 0
\(145\) 71.9526 161.309i 0.496225 1.11248i
\(146\) −131.152 −0.898299
\(147\) 0 0
\(148\) −1.28940 + 11.4437i −0.00871213 + 0.0773223i
\(149\) 122.156 + 97.4158i 0.819836 + 0.653797i 0.940839 0.338855i \(-0.110040\pi\)
−0.121003 + 0.992652i \(0.538611\pi\)
\(150\) 0 0
\(151\) 81.9702 170.213i 0.542849 1.12724i −0.431483 0.902121i \(-0.642009\pi\)
0.974332 0.225117i \(-0.0722764\pi\)
\(152\) 3.13064 + 3.92569i 0.0205963 + 0.0258269i
\(153\) 0 0
\(154\) 70.0626 + 15.9913i 0.454952 + 0.103840i
\(155\) −15.4268 136.916i −0.0995276 0.883332i
\(156\) 0 0
\(157\) −108.735 + 108.735i −0.692577 + 0.692577i −0.962798 0.270221i \(-0.912903\pi\)
0.270221 + 0.962798i \(0.412903\pi\)
\(158\) 199.259 45.4795i 1.26113 0.287845i
\(159\) 0 0
\(160\) −126.598 + 44.2986i −0.791239 + 0.276866i
\(161\) −27.0492 118.510i −0.168007 0.736088i
\(162\) 0 0
\(163\) −194.774 122.385i −1.19493 0.750826i −0.220474 0.975393i \(-0.570760\pi\)
−0.974459 + 0.224567i \(0.927903\pi\)
\(164\) 16.6662 1.87783i 0.101623 0.0114502i
\(165\) 0 0
\(166\) 153.271 96.3068i 0.923322 0.580162i
\(167\) 96.4643 76.9277i 0.577631 0.460645i −0.290573 0.956853i \(-0.593846\pi\)
0.868204 + 0.496208i \(0.165275\pi\)
\(168\) 0 0
\(169\) 52.1212 25.1002i 0.308409 0.148522i
\(170\) −276.674 + 346.938i −1.62749 + 2.04081i
\(171\) 0 0
\(172\) 4.45707 12.7376i 0.0259132 0.0740556i
\(173\) 32.3262i 0.186857i −0.995626 0.0934283i \(-0.970217\pi\)
0.995626 0.0934283i \(-0.0297826\pi\)
\(174\) 0 0
\(175\) 62.6521 0.358012
\(176\) 110.541 + 38.6800i 0.628075 + 0.219773i
\(177\) 0 0
\(178\) 266.658 + 212.653i 1.49808 + 1.19468i
\(179\) 116.664 + 242.255i 0.651754 + 1.35338i 0.920717 + 0.390231i \(0.127605\pi\)
−0.268963 + 0.963151i \(0.586681\pi\)
\(180\) 0 0
\(181\) −66.4061 83.2706i −0.366884 0.460058i 0.563784 0.825922i \(-0.309345\pi\)
−0.930668 + 0.365864i \(0.880774\pi\)
\(182\) −96.7970 154.052i −0.531852 0.846437i
\(183\) 0 0
\(184\) −15.6935 139.284i −0.0852908 0.756976i
\(185\) 25.9291 41.2660i 0.140158 0.223059i
\(186\) 0 0
\(187\) 181.192 41.3559i 0.968941 0.221154i
\(188\) 12.4078 + 35.4594i 0.0659988 + 0.188614i
\(189\) 0 0
\(190\) 2.65743 + 11.6430i 0.0139865 + 0.0612788i
\(191\) −72.7058 72.7058i −0.380659 0.380659i 0.490681 0.871339i \(-0.336748\pi\)
−0.871339 + 0.490681i \(0.836748\pi\)
\(192\) 0 0
\(193\) −190.040 + 21.4124i −0.984665 + 0.110945i −0.589589 0.807703i \(-0.700710\pi\)
−0.395076 + 0.918649i \(0.629282\pi\)
\(194\) −0.533617 + 2.33793i −0.00275061 + 0.0120512i
\(195\) 0 0
\(196\) 24.9491 19.8962i 0.127291 0.101511i
\(197\) −46.6020 22.4423i −0.236558 0.113920i 0.311849 0.950132i \(-0.399052\pi\)
−0.548408 + 0.836211i \(0.684766\pi\)
\(198\) 0 0
\(199\) 0.321680 0.403373i 0.00161648 0.00202700i −0.781023 0.624503i \(-0.785302\pi\)
0.782639 + 0.622476i \(0.213873\pi\)
\(200\) 71.7881 + 8.08857i 0.358940 + 0.0404429i
\(201\) 0 0
\(202\) 310.030i 1.53480i
\(203\) 29.1295 147.354i 0.143495 0.725880i
\(204\) 0 0
\(205\) −66.9946 23.4424i −0.326803 0.114353i
\(206\) −1.82305 + 16.1800i −0.00884974 + 0.0785437i
\(207\) 0 0
\(208\) −128.644 267.132i −0.618480 1.28429i
\(209\) 2.17016 4.50639i 0.0103835 0.0215617i
\(210\) 0 0
\(211\) 81.6700 + 129.977i 0.387062 + 0.616005i 0.982249 0.187582i \(-0.0600650\pi\)
−0.595187 + 0.803587i \(0.702922\pi\)
\(212\) −74.3264 16.9645i −0.350596 0.0800213i
\(213\) 0 0
\(214\) −83.4617 + 132.829i −0.390008 + 0.620694i
\(215\) −40.3829 + 40.3829i −0.187827 + 0.187827i
\(216\) 0 0
\(217\) −38.6989 110.595i −0.178336 0.509655i
\(218\) 392.376 137.298i 1.79989 0.629810i
\(219\) 0 0
\(220\) 36.8747 + 36.8747i 0.167612 + 0.167612i
\(221\) −398.399 250.331i −1.80271 1.13272i
\(222\) 0 0
\(223\) −17.7211 + 77.6414i −0.0794670 + 0.348168i −0.998993 0.0448610i \(-0.985716\pi\)
0.919526 + 0.393029i \(0.128573\pi\)
\(224\) −96.5770 + 60.6834i −0.431148 + 0.270908i
\(225\) 0 0
\(226\) −29.8773 14.3881i −0.132200 0.0636643i
\(227\) 379.261 182.642i 1.67075 0.804592i 0.672855 0.739774i \(-0.265068\pi\)
0.997897 0.0648180i \(-0.0206467\pi\)
\(228\) 0 0
\(229\) −196.110 22.0963i −0.856378 0.0964906i −0.327152 0.944972i \(-0.606089\pi\)
−0.529226 + 0.848481i \(0.677518\pi\)
\(230\) 110.105 314.663i 0.478719 1.36810i
\(231\) 0 0
\(232\) 52.4010 165.080i 0.225866 0.711553i
\(233\) −122.019 −0.523687 −0.261843 0.965110i \(-0.584330\pi\)
−0.261843 + 0.965110i \(0.584330\pi\)
\(234\) 0 0
\(235\) 17.8007 157.986i 0.0757477 0.672280i
\(236\) −19.5953 15.6267i −0.0830308 0.0662149i
\(237\) 0 0
\(238\) −163.733 + 339.994i −0.687952 + 1.42855i
\(239\) −191.297 239.879i −0.800405 1.00368i −0.999718 0.0237404i \(-0.992442\pi\)
0.199313 0.979936i \(-0.436129\pi\)
\(240\) 0 0
\(241\) −133.954 30.5741i −0.555826 0.126864i −0.0646245 0.997910i \(-0.520585\pi\)
−0.491201 + 0.871046i \(0.663442\pi\)
\(242\) 22.3541 + 198.398i 0.0923722 + 0.819826i
\(243\) 0 0
\(244\) 62.4663 62.4663i 0.256010 0.256010i
\(245\) −131.661 + 30.0508i −0.537393 + 0.122656i
\(246\) 0 0
\(247\) −11.9522 + 4.18225i −0.0483894 + 0.0169322i
\(248\) −30.0639 131.718i −0.121225 0.531123i
\(249\) 0 0
\(250\) −155.200 97.5188i −0.620801 0.390075i
\(251\) 330.590 37.2486i 1.31709 0.148401i 0.574699 0.818365i \(-0.305119\pi\)
0.742393 + 0.669964i \(0.233691\pi\)
\(252\) 0 0
\(253\) −118.222 + 74.2836i −0.467279 + 0.293611i
\(254\) −194.965 + 155.480i −0.767580 + 0.612124i
\(255\) 0 0
\(256\) −220.597 + 106.234i −0.861707 + 0.414976i
\(257\) −44.4882 + 55.7865i −0.173106 + 0.217068i −0.860814 0.508919i \(-0.830045\pi\)
0.687709 + 0.725987i \(0.258617\pi\)
\(258\) 0 0
\(259\) 13.6885 39.1193i 0.0528512 0.151040i
\(260\) 132.024i 0.507786i
\(261\) 0 0
\(262\) 37.2023 0.141993
\(263\) −220.348 77.1032i −0.837826 0.293168i −0.122944 0.992414i \(-0.539234\pi\)
−0.714882 + 0.699246i \(0.753519\pi\)
\(264\) 0 0
\(265\) 252.248 + 201.161i 0.951880 + 0.759099i
\(266\) 4.40644 + 9.15006i 0.0165656 + 0.0343987i
\(267\) 0 0
\(268\) −24.1196 30.2450i −0.0899984 0.112854i
\(269\) 176.731 + 281.266i 0.656993 + 1.04560i 0.994547 + 0.104293i \(0.0332578\pi\)
−0.337553 + 0.941306i \(0.609599\pi\)
\(270\) 0 0
\(271\) 14.5758 + 129.364i 0.0537851 + 0.477356i 0.991515 + 0.129991i \(0.0414949\pi\)
−0.937730 + 0.347365i \(0.887077\pi\)
\(272\) −327.184 + 520.710i −1.20288 + 1.91437i
\(273\) 0 0
\(274\) 322.872 73.6933i 1.17836 0.268954i
\(275\) −23.7678 67.9244i −0.0864282 0.246998i
\(276\) 0 0
\(277\) 10.5344 + 46.1541i 0.0380303 + 0.166621i 0.990377 0.138396i \(-0.0441948\pi\)
−0.952347 + 0.305018i \(0.901338\pi\)
\(278\) 364.270 + 364.270i 1.31032 + 1.31032i
\(279\) 0 0
\(280\) 187.222 21.0948i 0.668649 0.0753386i
\(281\) −15.5090 + 67.9492i −0.0551921 + 0.241812i −0.994998 0.0998970i \(-0.968149\pi\)
0.939806 + 0.341709i \(0.111006\pi\)
\(282\) 0 0
\(283\) 430.103 342.995i 1.51980 1.21200i 0.613253 0.789887i \(-0.289861\pi\)
0.906544 0.422111i \(-0.138711\pi\)
\(284\) 6.55813 + 3.15823i 0.0230920 + 0.0111205i
\(285\) 0 0
\(286\) −130.294 + 163.384i −0.455574 + 0.571272i
\(287\) −59.9798 6.75810i −0.208989 0.0235474i
\(288\) 0 0
\(289\) 686.921i 2.37689i
\(290\) 282.645 299.672i 0.974638 1.03335i
\(291\) 0 0
\(292\) −76.3915 26.7305i −0.261615 0.0915430i
\(293\) −35.7040 + 316.882i −0.121857 + 1.08151i 0.772768 + 0.634689i \(0.218872\pi\)
−0.894624 + 0.446819i \(0.852557\pi\)
\(294\) 0 0
\(295\) 46.0210 + 95.5636i 0.156003 + 0.323944i
\(296\) 20.7349 43.0566i 0.0700505 0.145461i
\(297\) 0 0
\(298\) 193.868 + 308.538i 0.650562 + 1.03536i
\(299\) 344.618 + 78.6568i 1.15257 + 0.263066i
\(300\) 0 0
\(301\) −25.8389 + 41.1223i −0.0858434 + 0.136619i
\(302\) 311.555 311.555i 1.03164 1.03164i
\(303\) 0 0
\(304\) 5.46622 + 15.6216i 0.0179810 + 0.0513867i
\(305\) −352.877 + 123.477i −1.15698 + 0.404843i
\(306\) 0 0
\(307\) 361.966 + 361.966i 1.17904 + 1.17904i 0.979989 + 0.199053i \(0.0637867\pi\)
0.199053 + 0.979989i \(0.436213\pi\)
\(308\) 37.5499 + 23.5942i 0.121915 + 0.0766044i
\(309\) 0 0
\(310\) 71.5045 313.282i 0.230660 1.01059i
\(311\) −409.769 + 257.475i −1.31758 + 0.827893i −0.993017 0.117970i \(-0.962361\pi\)
−0.324567 + 0.945863i \(0.605218\pi\)
\(312\) 0 0
\(313\) 276.742 + 133.272i 0.884159 + 0.425789i 0.820142 0.572160i \(-0.193894\pi\)
0.0640173 + 0.997949i \(0.479609\pi\)
\(314\) −323.117 + 155.605i −1.02903 + 0.495557i
\(315\) 0 0
\(316\) 125.331 + 14.1214i 0.396617 + 0.0446880i
\(317\) −184.663 + 527.737i −0.582534 + 1.66479i 0.153747 + 0.988110i \(0.450866\pi\)
−0.736281 + 0.676676i \(0.763420\pi\)
\(318\) 0 0
\(319\) −170.804 + 24.3195i −0.535437 + 0.0762366i
\(320\) 166.784 0.521200
\(321\) 0 0
\(322\) 31.7418 281.716i 0.0985769 0.874894i
\(323\) 20.5343 + 16.3756i 0.0635737 + 0.0506983i
\(324\) 0 0
\(325\) −79.0480 + 164.145i −0.243225 + 0.505061i
\(326\) −334.492 419.440i −1.02605 1.28663i
\(327\) 0 0
\(328\) −67.8536 15.4871i −0.206871 0.0472169i
\(329\) −15.1377 134.351i −0.0460113 0.408362i
\(330\) 0 0
\(331\) −418.557 + 418.557i −1.26452 + 1.26452i −0.315645 + 0.948877i \(0.602221\pi\)
−0.948877 + 0.315645i \(0.897779\pi\)
\(332\) 108.904 24.8567i 0.328025 0.0748695i
\(333\) 0 0
\(334\) 271.606 95.0390i 0.813191 0.284548i
\(335\) 36.4297 + 159.609i 0.108745 + 0.476445i
\(336\) 0 0
\(337\) −535.661 336.578i −1.58950 0.998748i −0.978281 0.207285i \(-0.933537\pi\)
−0.611218 0.791463i \(-0.709320\pi\)
\(338\) 134.070 15.1061i 0.396657 0.0446926i
\(339\) 0 0
\(340\) −231.864 + 145.690i −0.681954 + 0.428500i
\(341\) −105.221 + 83.9110i −0.308566 + 0.246073i
\(342\) 0 0
\(343\) −332.133 + 159.947i −0.968316 + 0.466317i
\(344\) −34.9157 + 43.7829i −0.101499 + 0.127276i
\(345\) 0 0
\(346\) 24.9002 71.1607i 0.0719659 0.205667i
\(347\) 141.419i 0.407547i 0.979018 + 0.203774i \(0.0653207\pi\)
−0.979018 + 0.203774i \(0.934679\pi\)
\(348\) 0 0
\(349\) −571.537 −1.63764 −0.818821 0.574048i \(-0.805372\pi\)
−0.818821 + 0.574048i \(0.805372\pi\)
\(350\) 137.918 + 48.2596i 0.394052 + 0.137885i
\(351\) 0 0
\(352\) 102.428 + 81.6833i 0.290987 + 0.232055i
\(353\) −6.08107 12.6275i −0.0172268 0.0357719i 0.892178 0.451684i \(-0.149177\pi\)
−0.909405 + 0.415912i \(0.863462\pi\)
\(354\) 0 0
\(355\) −19.2063 24.0840i −0.0541023 0.0678421i
\(356\) 111.978 + 178.212i 0.314545 + 0.500595i
\(357\) 0 0
\(358\) 70.2120 + 623.148i 0.196123 + 1.74064i
\(359\) −8.23661 + 13.1085i −0.0229432 + 0.0365139i −0.857999 0.513651i \(-0.828292\pi\)
0.835056 + 0.550165i \(0.185435\pi\)
\(360\) 0 0
\(361\) −351.260 + 80.1728i −0.973019 + 0.222085i
\(362\) −82.0402 234.457i −0.226630 0.647672i
\(363\) 0 0
\(364\) −24.9832 109.459i −0.0686351 0.300710i
\(365\) 242.190 + 242.190i 0.663534 + 0.663534i
\(366\) 0 0
\(367\) 281.948 31.7679i 0.768249 0.0865609i 0.280864 0.959748i \(-0.409379\pi\)
0.487386 + 0.873187i \(0.337951\pi\)
\(368\) 102.805 450.417i 0.279361 1.22396i
\(369\) 0 0
\(370\) 88.8650 70.8675i 0.240176 0.191534i
\(371\) 247.199 + 119.045i 0.666306 + 0.320876i
\(372\) 0 0
\(373\) 146.301 183.455i 0.392227 0.491837i −0.546035 0.837762i \(-0.683863\pi\)
0.938262 + 0.345925i \(0.112435\pi\)
\(374\) 430.719 + 48.5304i 1.15166 + 0.129760i
\(375\) 0 0
\(376\) 155.896i 0.414618i
\(377\) 349.306 + 262.234i 0.926541 + 0.695580i
\(378\) 0 0
\(379\) 549.482 + 192.272i 1.44982 + 0.507314i 0.936434 0.350844i \(-0.114105\pi\)
0.513386 + 0.858158i \(0.328391\pi\)
\(380\) −0.825134 + 7.32327i −0.00217140 + 0.0192718i
\(381\) 0 0
\(382\) −104.046 216.054i −0.272371 0.565585i
\(383\) 177.905 369.424i 0.464504 0.964553i −0.528770 0.848765i \(-0.677346\pi\)
0.993274 0.115788i \(-0.0369393\pi\)
\(384\) 0 0
\(385\) −99.8502 158.911i −0.259351 0.412755i
\(386\) −434.835 99.2484i −1.12652 0.257120i
\(387\) 0 0
\(388\) −0.787317 + 1.25301i −0.00202917 + 0.00322940i
\(389\) −57.4399 + 57.4399i −0.147661 + 0.147661i −0.777072 0.629412i \(-0.783296\pi\)
0.629412 + 0.777072i \(0.283296\pi\)
\(390\) 0 0
\(391\) −242.150 692.024i −0.619309 1.76988i
\(392\) −124.992 + 43.7367i −0.318858 + 0.111573i
\(393\) 0 0
\(394\) −85.2996 85.2996i −0.216496 0.216496i
\(395\) −451.943 283.975i −1.14416 0.718923i
\(396\) 0 0
\(397\) 22.5451 98.7767i 0.0567887 0.248808i −0.938564 0.345106i \(-0.887843\pi\)
0.995353 + 0.0962980i \(0.0307002\pi\)
\(398\) 1.01883 0.640176i 0.00255988 0.00160848i
\(399\) 0 0
\(400\) 214.538 + 103.316i 0.536345 + 0.258290i
\(401\) −107.974 + 51.9976i −0.269262 + 0.129670i −0.563643 0.826018i \(-0.690601\pi\)
0.294381 + 0.955688i \(0.404887\pi\)
\(402\) 0 0
\(403\) 338.579 + 38.1487i 0.840147 + 0.0946619i
\(404\) 63.1884 180.582i 0.156407 0.446985i
\(405\) 0 0
\(406\) 177.627 301.937i 0.437506 0.743687i
\(407\) −47.6042 −0.116964
\(408\) 0 0
\(409\) −42.0942 + 373.596i −0.102920 + 0.913438i 0.831077 + 0.556157i \(0.187725\pi\)
−0.933997 + 0.357281i \(0.883704\pi\)
\(410\) −129.420 103.209i −0.315659 0.251730i
\(411\) 0 0
\(412\) −4.35957 + 9.05274i −0.0105815 + 0.0219727i
\(413\) 56.2386 + 70.5210i 0.136171 + 0.170753i
\(414\) 0 0
\(415\) −460.881 105.193i −1.11056 0.253477i
\(416\) −37.1359 329.590i −0.0892691 0.792285i
\(417\) 0 0
\(418\) 8.24843 8.24843i 0.0197331 0.0197331i
\(419\) 231.325 52.7983i 0.552087 0.126010i 0.0626288 0.998037i \(-0.480052\pi\)
0.489459 + 0.872027i \(0.337194\pi\)
\(420\) 0 0
\(421\) 120.085 42.0197i 0.285238 0.0998092i −0.183868 0.982951i \(-0.558862\pi\)
0.469106 + 0.883142i \(0.344576\pi\)
\(422\) 79.6642 + 349.032i 0.188778 + 0.827089i
\(423\) 0 0
\(424\) 267.877 + 168.318i 0.631786 + 0.396977i
\(425\) 375.505 42.3093i 0.883542 0.0995512i
\(426\) 0 0
\(427\) −269.197 + 169.148i −0.630438 + 0.396131i
\(428\) −75.6860 + 60.3575i −0.176836 + 0.141022i
\(429\) 0 0
\(430\) −120.002 + 57.7901i −0.279075 + 0.134396i
\(431\) −102.073 + 127.996i −0.236828 + 0.296973i −0.886016 0.463655i \(-0.846538\pi\)
0.649187 + 0.760629i \(0.275109\pi\)
\(432\) 0 0
\(433\) −29.3711 + 83.9378i −0.0678316 + 0.193852i −0.972809 0.231607i \(-0.925602\pi\)
0.904978 + 0.425459i \(0.139887\pi\)
\(434\) 273.266i 0.629644i
\(435\) 0 0
\(436\) 256.530 0.588371
\(437\) −18.6240 6.51683i −0.0426179 0.0149127i
\(438\) 0 0
\(439\) 377.689 + 301.197i 0.860340 + 0.686098i 0.950801 0.309802i \(-0.100263\pi\)
−0.0904611 + 0.995900i \(0.528834\pi\)
\(440\) −93.8946 194.974i −0.213397 0.443123i
\(441\) 0 0
\(442\) −684.185 857.941i −1.54793 1.94104i
\(443\) 33.5662 + 53.4203i 0.0757703 + 0.120588i 0.882460 0.470388i \(-0.155886\pi\)
−0.806690 + 0.590975i \(0.798743\pi\)
\(444\) 0 0
\(445\) −99.7284 885.114i −0.224109 1.98902i
\(446\) −98.8157 + 157.264i −0.221560 + 0.352610i
\(447\) 0 0
\(448\) 138.277 31.5608i 0.308654 0.0704482i
\(449\) −224.975 642.941i −0.501058 1.43194i −0.865592 0.500751i \(-0.833057\pi\)
0.364534 0.931190i \(-0.381228\pi\)
\(450\) 0 0
\(451\) 15.4272 + 67.5910i 0.0342066 + 0.149869i
\(452\) −14.4700 14.4700i −0.0320133 0.0320133i
\(453\) 0 0
\(454\) 975.565 109.920i 2.14882 0.242114i
\(455\) −105.729 + 463.227i −0.232370 + 1.01808i
\(456\) 0 0
\(457\) −81.2493 + 64.7942i −0.177788 + 0.141782i −0.708341 0.705871i \(-0.750556\pi\)
0.530552 + 0.847652i \(0.321985\pi\)
\(458\) −414.684 199.701i −0.905424 0.436029i
\(459\) 0 0
\(460\) 128.266 160.840i 0.278838 0.349652i
\(461\) −286.769 32.3111i −0.622058 0.0700891i −0.204690 0.978827i \(-0.565619\pi\)
−0.417368 + 0.908738i \(0.637047\pi\)
\(462\) 0 0
\(463\) 377.960i 0.816329i 0.912908 + 0.408164i \(0.133831\pi\)
−0.912908 + 0.408164i \(0.866169\pi\)
\(464\) 342.740 456.544i 0.738664 0.983931i
\(465\) 0 0
\(466\) −268.604 93.9888i −0.576404 0.201693i
\(467\) 89.7450 796.509i 0.192173 1.70559i −0.414019 0.910268i \(-0.635875\pi\)
0.606193 0.795318i \(-0.292696\pi\)
\(468\) 0 0
\(469\) 60.4061 + 125.435i 0.128798 + 0.267451i
\(470\) 160.879 334.068i 0.342295 0.710782i
\(471\) 0 0
\(472\) 55.3349 + 88.0650i 0.117235 + 0.186578i
\(473\) 54.3851 + 12.4130i 0.114979 + 0.0262432i
\(474\) 0 0
\(475\) 5.41060 8.61092i 0.0113907 0.0181283i
\(476\) −164.664 + 164.664i −0.345934 + 0.345934i
\(477\) 0 0
\(478\) −236.334 675.405i −0.494423 1.41298i
\(479\) 392.771 137.436i 0.819981 0.286924i 0.112496 0.993652i \(-0.464115\pi\)
0.707485 + 0.706729i \(0.249830\pi\)
\(480\) 0 0
\(481\) 85.2198 + 85.2198i 0.177172 + 0.177172i
\(482\) −271.327 170.486i −0.562919 0.353705i
\(483\) 0 0
\(484\) −27.4157 + 120.116i −0.0566441 + 0.248174i
\(485\) 5.30271 3.33192i 0.0109334 0.00686993i
\(486\) 0 0
\(487\) −642.025 309.183i −1.31833 0.634873i −0.363378 0.931642i \(-0.618377\pi\)
−0.954949 + 0.296769i \(0.904091\pi\)
\(488\) −330.289 + 159.059i −0.676822 + 0.325940i
\(489\) 0 0
\(490\) −312.978 35.2641i −0.638731 0.0719676i
\(491\) 16.0776 45.9471i 0.0327446 0.0935786i −0.926351 0.376662i \(-0.877072\pi\)
0.959095 + 0.283084i \(0.0913574\pi\)
\(492\) 0 0
\(493\) 75.0788 902.836i 0.152290 1.83131i
\(494\) −29.5322 −0.0597819
\(495\) 0 0
\(496\) 49.8605 442.525i 0.100525 0.892187i
\(497\) −20.4810 16.3330i −0.0412092 0.0328632i
\(498\) 0 0
\(499\) 336.600 698.958i 0.674550 1.40072i −0.229508 0.973307i \(-0.573712\pi\)
0.904058 0.427410i \(-0.140574\pi\)
\(500\) −70.5233 88.4334i −0.141047 0.176867i
\(501\) 0 0
\(502\) 756.431 + 172.650i 1.50683 + 0.343925i
\(503\) 52.8932 + 469.440i 0.105156 + 0.933281i 0.929909 + 0.367789i \(0.119885\pi\)
−0.824754 + 0.565492i \(0.808686\pi\)
\(504\) 0 0
\(505\) −572.514 + 572.514i −1.13369 + 1.13369i
\(506\) −317.464 + 72.4592i −0.627400 + 0.143200i
\(507\) 0 0
\(508\) −145.250 + 50.8250i −0.285924 + 0.100049i
\(509\) 171.270 + 750.383i 0.336483 + 1.47423i 0.806322 + 0.591477i \(0.201455\pi\)
−0.469838 + 0.882753i \(0.655688\pi\)
\(510\) 0 0
\(511\) 246.624 + 154.964i 0.482631 + 0.303257i
\(512\) 36.5399 4.11706i 0.0713670 0.00804114i
\(513\) 0 0
\(514\) −140.905 + 88.5362i −0.274133 + 0.172249i
\(515\) 33.2451 26.5121i 0.0645537 0.0514798i
\(516\) 0 0
\(517\) −139.914 + 67.3791i −0.270627 + 0.130327i
\(518\) 60.2657 75.5708i 0.116343 0.145890i
\(519\) 0 0
\(520\) −180.950 + 517.126i −0.347981 + 0.994472i
\(521\) 306.568i 0.588421i −0.955741 0.294211i \(-0.904943\pi\)
0.955741 0.294211i \(-0.0950567\pi\)
\(522\) 0 0
\(523\) 789.078 1.50875 0.754377 0.656442i \(-0.227939\pi\)
0.754377 + 0.656442i \(0.227939\pi\)
\(524\) 21.6691 + 7.58234i 0.0413532 + 0.0144701i
\(525\) 0 0
\(526\) −425.669 339.459i −0.809256 0.645360i
\(527\) −306.627 636.718i −0.581836 1.20819i
\(528\) 0 0
\(529\) 13.5904 + 17.0418i 0.0256907 + 0.0322151i
\(530\) 400.332 + 637.124i 0.755343 + 1.20212i
\(531\) 0 0
\(532\) 0.701693 + 6.22770i 0.00131897 + 0.0117062i
\(533\) 93.3822 148.617i 0.175201 0.278831i
\(534\) 0 0
\(535\) 399.410 91.1628i 0.746561 0.170398i
\(536\) 53.0206 + 151.524i 0.0989191 + 0.282694i
\(537\) 0 0
\(538\) 172.391 + 755.293i 0.320429 + 1.40389i
\(539\) 93.2750 + 93.2750i 0.173052 + 0.173052i
\(540\) 0 0
\(541\) 231.201 26.0502i 0.427359 0.0481518i 0.104334 0.994542i \(-0.466729\pi\)
0.323025 + 0.946390i \(0.395300\pi\)
\(542\) −67.5600 + 296.000i −0.124649 + 0.546125i
\(543\) 0 0
\(544\) −537.855 + 428.925i −0.988703 + 0.788465i
\(545\) −978.119 471.037i −1.79471 0.864288i
\(546\) 0 0
\(547\) 5.46184 6.84892i 0.00998507 0.0125209i −0.776814 0.629730i \(-0.783165\pi\)
0.786799 + 0.617209i \(0.211737\pi\)
\(548\) 203.082 + 22.8818i 0.370587 + 0.0417551i
\(549\) 0 0
\(550\) 167.832i 0.305149i
\(551\) −17.7367 16.7290i −0.0321901 0.0303611i
\(552\) 0 0
\(553\) −428.433 149.915i −0.774743 0.271094i
\(554\) −12.3619 + 109.715i −0.0223139 + 0.198042i
\(555\) 0 0
\(556\) 137.932 + 286.418i 0.248079 + 0.515141i
\(557\) 184.669 383.470i 0.331543 0.688456i −0.666846 0.745195i \(-0.732356\pi\)
0.998389 + 0.0567395i \(0.0180704\pi\)
\(558\) 0 0
\(559\) −75.1373 119.580i −0.134414 0.213918i
\(560\) 605.440 + 138.188i 1.08114 + 0.246764i
\(561\) 0 0
\(562\) −86.4803 + 137.633i −0.153880 + 0.244898i
\(563\) −493.000 + 493.000i −0.875666 + 0.875666i −0.993083 0.117416i \(-0.962539\pi\)
0.117416 + 0.993083i \(0.462539\pi\)
\(564\) 0 0
\(565\) 28.6029 + 81.7423i 0.0506245 + 0.144677i
\(566\) 1211.00 423.748i 2.13958 0.748671i
\(567\) 0 0
\(568\) −21.3589 21.3589i −0.0376037 0.0376037i
\(569\) 267.135 + 167.852i 0.469482 + 0.294995i 0.745919 0.666037i \(-0.232011\pi\)
−0.276436 + 0.961032i \(0.589154\pi\)
\(570\) 0 0
\(571\) −136.850 + 599.581i −0.239668 + 1.05005i 0.701647 + 0.712525i \(0.252448\pi\)
−0.941315 + 0.337529i \(0.890409\pi\)
\(572\) −109.192 + 68.6099i −0.190895 + 0.119947i
\(573\) 0 0
\(574\) −126.830 61.0780i −0.220958 0.106408i
\(575\) −255.772 + 123.174i −0.444822 + 0.214215i
\(576\) 0 0
\(577\) −468.624 52.8013i −0.812173 0.0915100i −0.303898 0.952705i \(-0.598288\pi\)
−0.508275 + 0.861195i \(0.669717\pi\)
\(578\) −529.121 + 1512.14i −0.915434 + 2.61616i
\(579\) 0 0
\(580\) 225.709 116.942i 0.389153 0.201624i
\(581\) −402.012 −0.691932
\(582\) 0 0
\(583\) 35.2850 313.163i 0.0605231 0.537157i
\(584\) 262.581 + 209.401i 0.449625 + 0.358564i
\(585\) 0 0
\(586\) −322.684 + 670.061i −0.550656 + 1.14345i
\(587\) 125.247 + 157.054i 0.213367 + 0.267554i 0.876985 0.480518i \(-0.159551\pi\)
−0.663618 + 0.748072i \(0.730980\pi\)
\(588\) 0 0
\(589\) −18.5422 4.23215i −0.0314809 0.00718531i
\(590\) 27.6968 + 245.816i 0.0469438 + 0.416638i
\(591\) 0 0
\(592\) 111.383 111.383i 0.188146 0.188146i
\(593\) 372.413 85.0008i 0.628015 0.143340i 0.103344 0.994646i \(-0.467046\pi\)
0.524671 + 0.851305i \(0.324188\pi\)
\(594\) 0 0
\(595\) 930.202 325.492i 1.56337 0.547045i
\(596\) 50.0370 + 219.226i 0.0839546 + 0.367829i
\(597\) 0 0
\(598\) 698.031 + 438.602i 1.16728 + 0.733448i
\(599\) 289.961 32.6708i 0.484076 0.0545422i 0.133445 0.991056i \(-0.457396\pi\)
0.350630 + 0.936514i \(0.385967\pi\)
\(600\) 0 0
\(601\) 434.543 273.041i 0.723033 0.454312i −0.119585 0.992824i \(-0.538156\pi\)
0.842618 + 0.538512i \(0.181013\pi\)
\(602\) −88.5556 + 70.6207i −0.147102 + 0.117310i
\(603\) 0 0
\(604\) 244.970 117.971i 0.405579 0.195317i
\(605\) 325.089 407.649i 0.537338 0.673800i
\(606\) 0 0
\(607\) 182.154 520.567i 0.300090 0.857607i −0.690814 0.723033i \(-0.742748\pi\)
0.990904 0.134574i \(-0.0429667\pi\)
\(608\) 18.5142i 0.0304509i
\(609\) 0 0
\(610\) −871.912 −1.42936
\(611\) 371.091 + 129.850i 0.607350 + 0.212521i
\(612\) 0 0
\(613\) 280.338 + 223.562i 0.457321 + 0.364701i 0.824888 0.565295i \(-0.191238\pi\)
−0.367567 + 0.929997i \(0.619809\pi\)
\(614\) 517.992 + 1075.62i 0.843636 + 1.75183i
\(615\) 0 0
\(616\) −114.741 143.881i −0.186268 0.233573i
\(617\) 279.227 + 444.387i 0.452555 + 0.720238i 0.992604 0.121396i \(-0.0387371\pi\)
−0.540049 + 0.841634i \(0.681594\pi\)
\(618\) 0 0
\(619\) 112.177 + 995.602i 0.181224 + 1.60840i 0.674327 + 0.738433i \(0.264434\pi\)
−0.493103 + 0.869971i \(0.664137\pi\)
\(620\) 105.500 167.902i 0.170161 0.270810i
\(621\) 0 0
\(622\) −1100.36 + 251.151i −1.76907 + 0.403780i
\(623\) −250.174 714.957i −0.401564 1.14760i
\(624\) 0 0
\(625\) 173.808 + 761.503i 0.278093 + 1.21841i
\(626\) 506.544 + 506.544i 0.809176 + 0.809176i
\(627\) 0 0
\(628\) −219.919 + 24.7790i −0.350190 + 0.0394569i
\(629\) 55.6242 243.706i 0.0884328 0.387449i
\(630\) 0 0
\(631\) −434.398 + 346.421i −0.688427 + 0.549002i −0.904025 0.427480i \(-0.859401\pi\)
0.215598 + 0.976482i \(0.430830\pi\)
\(632\) −471.553 227.088i −0.746128 0.359317i
\(633\) 0 0
\(634\) −813.011 + 1019.48i −1.28235 + 1.60802i
\(635\) 647.145 + 72.9158i 1.01913 + 0.114828i
\(636\) 0 0
\(637\) 333.957i 0.524266i
\(638\) −394.730 78.0319i −0.618699 0.122307i
\(639\) 0 0
\(640\) 873.540 + 305.665i 1.36491 + 0.477601i
\(641\) 75.0000 665.643i 0.117005 1.03845i −0.788771 0.614687i \(-0.789282\pi\)
0.905775 0.423758i \(-0.139289\pi\)
\(642\) 0 0
\(643\) 38.4657 + 79.8749i 0.0598223 + 0.124222i 0.928737 0.370740i \(-0.120896\pi\)
−0.868914 + 0.494963i \(0.835182\pi\)
\(644\) 75.9061 157.621i 0.117867 0.244753i
\(645\) 0 0
\(646\) 32.5891 + 51.8652i 0.0504475 + 0.0802867i
\(647\) 399.560 + 91.1970i 0.617558 + 0.140954i 0.519844 0.854261i \(-0.325990\pi\)
0.0977136 + 0.995215i \(0.468847\pi\)
\(648\) 0 0
\(649\) 55.1207 87.7241i 0.0849318 0.135168i
\(650\) −300.448 + 300.448i −0.462228 + 0.462228i
\(651\) 0 0
\(652\) −109.343 312.484i −0.167704 0.479270i
\(653\) 28.0410 9.81196i 0.0429418 0.0150260i −0.308723 0.951152i \(-0.599902\pi\)
0.351664 + 0.936126i \(0.385616\pi\)
\(654\) 0 0
\(655\) −68.6992 68.6992i −0.104884 0.104884i
\(656\) −194.243 122.051i −0.296102 0.186053i
\(657\) 0 0
\(658\) 70.1647 307.411i 0.106633 0.467191i
\(659\) −839.507 + 527.497i −1.27391 + 0.800451i −0.987494 0.157655i \(-0.949607\pi\)
−0.286416 + 0.958105i \(0.592464\pi\)
\(660\) 0 0
\(661\) 34.7693 + 16.7440i 0.0526010 + 0.0253313i 0.459999 0.887919i \(-0.347850\pi\)
−0.407398 + 0.913251i \(0.633564\pi\)
\(662\) −1243.79 + 598.977i −1.87883 + 0.904799i
\(663\) 0 0
\(664\) −460.634 51.9010i −0.693726 0.0781642i
\(665\) 8.75977 25.0340i 0.0131726 0.0376451i
\(666\) 0 0
\(667\) 170.777 + 658.829i 0.256038 + 0.987750i
\(668\) 177.572 0.265826
\(669\) 0 0
\(670\) −42.7496 + 379.413i −0.0638054 + 0.566289i
\(671\) 285.505 + 227.682i 0.425491 + 0.339318i
\(672\) 0 0
\(673\) 340.019 706.057i 0.505229 1.04912i −0.479903 0.877321i \(-0.659328\pi\)
0.985132 0.171797i \(-0.0549575\pi\)
\(674\) −919.909 1153.53i −1.36485 1.71147i
\(675\) 0 0
\(676\) 81.1703 + 18.5266i 0.120074 + 0.0274062i
\(677\) −72.2705 641.418i −0.106751 0.947442i −0.926904 0.375298i \(-0.877540\pi\)
0.820153 0.572144i \(-0.193888\pi\)
\(678\) 0 0
\(679\) 3.76586 3.76586i 0.00554618 0.00554618i
\(680\) 1107.87 252.864i 1.62922 0.371858i
\(681\) 0 0
\(682\) −296.261 + 103.666i −0.434401 + 0.152003i
\(683\) −196.973 862.994i −0.288393 1.26353i −0.886729 0.462289i \(-0.847028\pi\)
0.598336 0.801245i \(-0.295829\pi\)
\(684\) 0 0
\(685\) −732.313 460.143i −1.06907 0.671741i
\(686\) −854.338 + 96.2608i −1.24539 + 0.140322i
\(687\) 0 0
\(688\) −156.292 + 98.2047i −0.227168 + 0.142739i
\(689\) −623.782 + 497.450i −0.905344 + 0.721988i
\(690\) 0 0
\(691\) 553.507 266.555i 0.801023 0.385752i 0.0118551 0.999930i \(-0.496226\pi\)
0.789168 + 0.614177i \(0.210512\pi\)
\(692\) 29.0071 36.3737i 0.0419177 0.0525632i
\(693\) 0 0
\(694\) −108.932 + 311.310i −0.156963 + 0.448574i
\(695\) 1345.35i 1.93575i
\(696\) 0 0
\(697\) −364.053 −0.522314
\(698\) −1258.14 440.244i −1.80250 0.630721i
\(699\) 0 0
\(700\) 70.4967 + 56.2192i 0.100710 + 0.0803132i
\(701\) −92.4303 191.933i −0.131855 0.273800i 0.824580 0.565745i \(-0.191412\pi\)
−0.956435 + 0.291946i \(0.905697\pi\)
\(702\) 0 0
\(703\) −4.19445 5.25967i −0.00596650 0.00748175i
\(704\) −86.6736 137.940i −0.123116 0.195938i
\(705\) 0 0
\(706\) −3.65977 32.4814i −0.00518381 0.0460076i
\(707\) −366.321 + 582.996i −0.518134 + 0.824606i
\(708\) 0 0
\(709\) 976.236 222.819i 1.37692 0.314273i 0.530904 0.847432i \(-0.321852\pi\)
0.846015 + 0.533159i \(0.178995\pi\)
\(710\) −23.7281 67.8110i −0.0334199 0.0955085i
\(711\) 0 0
\(712\) −194.352 851.511i −0.272966 1.19594i
\(713\) 375.415 + 375.415i 0.526528 + 0.526528i
\(714\) 0 0
\(715\) 542.318 61.1045i 0.758486 0.0854609i
\(716\) −86.1102 + 377.273i −0.120266 + 0.526918i
\(717\) 0 0
\(718\) −28.2287 + 22.5116i −0.0393158 + 0.0313533i
\(719\) 1085.74 + 522.866i 1.51007 + 0.727213i 0.991776 0.127987i \(-0.0408517\pi\)
0.518298 + 0.855200i \(0.326566\pi\)
\(720\) 0 0
\(721\) 22.5459 28.2716i 0.0312703 0.0392117i
\(722\) −834.995 94.0814i −1.15650 0.130307i
\(723\) 0 0
\(724\) 153.285i 0.211719i
\(725\) −350.639 + 10.2527i −0.483640 + 0.0141417i
\(726\) 0 0
\(727\) −984.289 344.418i −1.35391 0.473752i −0.446792 0.894638i \(-0.647433\pi\)
−0.907113 + 0.420886i \(0.861719\pi\)
\(728\) −52.1652 + 462.979i −0.0716555 + 0.635960i
\(729\) 0 0
\(730\) 346.587 + 719.695i 0.474776 + 0.985883i
\(731\) −127.095 + 263.916i −0.173865 + 0.361034i
\(732\) 0 0
\(733\) 365.036 + 580.951i 0.498002 + 0.792566i 0.997267 0.0738833i \(-0.0235392\pi\)
−0.499264 + 0.866450i \(0.666396\pi\)
\(734\) 645.131 + 147.247i 0.878924 + 0.200609i
\(735\) 0 0
\(736\) 274.966 437.605i 0.373594 0.594572i
\(737\) 113.074 113.074i 0.153425 0.153425i
\(738\) 0 0
\(739\) 282.220 + 806.539i 0.381895 + 1.09139i 0.961098 + 0.276209i \(0.0890782\pi\)
−0.579203 + 0.815183i \(0.696636\pi\)
\(740\) 66.2047 23.1660i 0.0894658 0.0313054i
\(741\) 0 0
\(742\) 452.470 + 452.470i 0.609798 + 0.609798i
\(743\) 277.918 + 174.627i 0.374048 + 0.235030i 0.705915 0.708296i \(-0.250536\pi\)
−0.331868 + 0.943326i \(0.607679\pi\)
\(744\) 0 0
\(745\) 211.756 927.763i 0.284236 1.24532i
\(746\) 463.369 291.154i 0.621138 0.390287i
\(747\) 0 0
\(748\) 240.988 + 116.054i 0.322177 + 0.155152i
\(749\) 313.891 151.162i 0.419080 0.201818i
\(750\) 0 0
\(751\) 971.174 + 109.425i 1.29318 + 0.145706i 0.731608 0.681725i \(-0.238770\pi\)
0.561567 + 0.827431i \(0.310199\pi\)
\(752\) 169.715 485.018i 0.225685 0.644970i
\(753\) 0 0
\(754\) 566.945 + 846.326i 0.751917 + 1.12245i
\(755\) −1150.66 −1.52405
\(756\) 0 0
\(757\) −0.974699 + 8.65069i −0.00128758 + 0.0114276i −0.994340 0.106249i \(-0.966116\pi\)
0.993052 + 0.117676i \(0.0375446\pi\)
\(758\) 1061.49 + 846.509i 1.40038 + 1.11677i
\(759\) 0 0
\(760\) 13.2691 27.5535i 0.0174593 0.0362547i
\(761\) 380.683 + 477.361i 0.500240 + 0.627282i 0.966284 0.257480i \(-0.0828923\pi\)
−0.466043 + 0.884762i \(0.654321\pi\)
\(762\) 0 0
\(763\) −900.072 205.436i −1.17965 0.269247i
\(764\) −16.5686 147.050i −0.0216866 0.192474i
\(765\) 0 0
\(766\) 676.188 676.188i 0.882752 0.882752i
\(767\) −255.717 + 58.3658i −0.333399 + 0.0760962i
\(768\) 0 0
\(769\) 61.7689 21.6139i 0.0803237 0.0281065i −0.289818 0.957082i \(-0.593595\pi\)
0.370142 + 0.928975i \(0.379309\pi\)
\(770\) −97.3979 426.728i −0.126491 0.554192i
\(771\) 0 0
\(772\) −233.049 146.434i −0.301877 0.189682i
\(773\) −199.336 + 22.4598i −0.257873 + 0.0290554i −0.239955 0.970784i \(-0.577133\pi\)
−0.0179188 + 0.999839i \(0.505704\pi\)
\(774\) 0 0
\(775\) −231.697 + 145.585i −0.298964 + 0.187851i
\(776\) 4.80119 3.82882i 0.00618709 0.00493404i
\(777\) 0 0
\(778\) −170.689 + 82.1996i −0.219395 + 0.105655i
\(779\) −6.10866 + 7.66001i −0.00784167 + 0.00983314i
\(780\) 0 0
\(781\) −9.93780 + 28.4006i −0.0127245 + 0.0363644i
\(782\) 1709.90i 2.18657i
\(783\) 0 0
\(784\) −436.483 −0.556739
\(785\) 884.027 + 309.334i 1.12615 + 0.394057i
\(786\) 0 0
\(787\) −350.315 279.367i −0.445126 0.354977i 0.375130 0.926972i \(-0.377598\pi\)