Properties

Label 27.3.d.a.8.1
Level 27
Weight 3
Character 27.8
Analytic conductor 0.736
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 27.d (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.735696713773\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 8.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 27.8
Dual form 27.3.d.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(1.50000 + 0.866025i) q^{2}\) \(+(-0.500000 - 0.866025i) q^{4}\) \(+(-3.00000 + 1.73205i) q^{5}\) \(+(-1.00000 + 1.73205i) q^{7}\) \(-8.66025i q^{8}\) \(+O(q^{10})\) \(q\)\(+(1.50000 + 0.866025i) q^{2}\) \(+(-0.500000 - 0.866025i) q^{4}\) \(+(-3.00000 + 1.73205i) q^{5}\) \(+(-1.00000 + 1.73205i) q^{7}\) \(-8.66025i q^{8}\) \(-6.00000 q^{10}\) \(+(1.50000 + 0.866025i) q^{11}\) \(+(2.00000 + 3.46410i) q^{13}\) \(+(-3.00000 + 1.73205i) q^{14}\) \(+(5.50000 - 9.52628i) q^{16}\) \(+15.5885i q^{17}\) \(+11.0000 q^{19}\) \(+(3.00000 + 1.73205i) q^{20}\) \(+(1.50000 + 2.59808i) q^{22}\) \(+(24.0000 - 13.8564i) q^{23}\) \(+(-6.50000 + 11.2583i) q^{25}\) \(+6.92820i q^{26}\) \(+2.00000 q^{28}\) \(+(-39.0000 - 22.5167i) q^{29}\) \(+(-16.0000 - 27.7128i) q^{31}\) \(+(-13.5000 + 7.79423i) q^{32}\) \(+(-13.5000 + 23.3827i) q^{34}\) \(-6.92820i q^{35}\) \(-34.0000 q^{37}\) \(+(16.5000 + 9.52628i) q^{38}\) \(+(15.0000 + 25.9808i) q^{40}\) \(+(10.5000 - 6.06218i) q^{41}\) \(+(30.5000 - 52.8275i) q^{43}\) \(-1.73205i q^{44}\) \(+48.0000 q^{46}\) \(+(42.0000 + 24.2487i) q^{47}\) \(+(22.5000 + 38.9711i) q^{49}\) \(+(-19.5000 + 11.2583i) q^{50}\) \(+(2.00000 - 3.46410i) q^{52}\) \(-6.00000 q^{55}\) \(+(15.0000 + 8.66025i) q^{56}\) \(+(-39.0000 - 67.5500i) q^{58}\) \(+(-43.5000 + 25.1147i) q^{59}\) \(+(-28.0000 + 48.4974i) q^{61}\) \(-55.4256i q^{62}\) \(-71.0000 q^{64}\) \(+(-12.0000 - 6.92820i) q^{65}\) \(+(15.5000 + 26.8468i) q^{67}\) \(+(13.5000 - 7.79423i) q^{68}\) \(+(6.00000 - 10.3923i) q^{70}\) \(-31.1769i q^{71}\) \(+65.0000 q^{73}\) \(+(-51.0000 - 29.4449i) q^{74}\) \(+(-5.50000 - 9.52628i) q^{76}\) \(+(-3.00000 + 1.73205i) q^{77}\) \(+(-19.0000 + 32.9090i) q^{79}\) \(+38.1051i q^{80}\) \(+21.0000 q^{82}\) \(+(42.0000 + 24.2487i) q^{83}\) \(+(-27.0000 - 46.7654i) q^{85}\) \(+(91.5000 - 52.8275i) q^{86}\) \(+(7.50000 - 12.9904i) q^{88}\) \(+124.708i q^{89}\) \(-8.00000 q^{91}\) \(+(-24.0000 - 13.8564i) q^{92}\) \(+(42.0000 + 72.7461i) q^{94}\) \(+(-33.0000 + 19.0526i) q^{95}\) \(+(57.5000 - 99.5929i) q^{97}\) \(+77.9423i q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 48q^{23} \) \(\mathstrut -\mathstrut 13q^{25} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 78q^{29} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut -\mathstrut 27q^{32} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 68q^{37} \) \(\mathstrut +\mathstrut 33q^{38} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 21q^{41} \) \(\mathstrut +\mathstrut 61q^{43} \) \(\mathstrut +\mathstrut 96q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut +\mathstrut 45q^{49} \) \(\mathstrut -\mathstrut 39q^{50} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut -\mathstrut 78q^{58} \) \(\mathstrut -\mathstrut 87q^{59} \) \(\mathstrut -\mathstrut 56q^{61} \) \(\mathstrut -\mathstrut 142q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 31q^{67} \) \(\mathstrut +\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 130q^{73} \) \(\mathstrut -\mathstrut 102q^{74} \) \(\mathstrut -\mathstrut 11q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 38q^{79} \) \(\mathstrut +\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 54q^{85} \) \(\mathstrut +\mathstrut 183q^{86} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 84q^{94} \) \(\mathstrut -\mathstrut 66q^{95} \) \(\mathstrut +\mathstrut 115q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 + 0.866025i 0.750000 + 0.433013i 0.825694 0.564118i \(-0.190784\pi\)
−0.0756939 + 0.997131i \(0.524117\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.125000 0.216506i
\(5\) −3.00000 + 1.73205i −0.600000 + 0.346410i −0.769042 0.639199i \(-0.779266\pi\)
0.169042 + 0.985609i \(0.445933\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.142857 + 0.247436i −0.928571 0.371154i \(-0.878962\pi\)
0.785714 + 0.618590i \(0.212296\pi\)
\(8\) 8.66025i 1.08253i
\(9\) 0 0
\(10\) −6.00000 −0.600000
\(11\) 1.50000 + 0.866025i 0.136364 + 0.0787296i 0.566630 0.823972i \(-0.308247\pi\)
−0.430266 + 0.902702i \(0.641580\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.153846 + 0.266469i 0.932638 0.360813i \(-0.117501\pi\)
−0.778792 + 0.627282i \(0.784167\pi\)
\(14\) −3.00000 + 1.73205i −0.214286 + 0.123718i
\(15\) 0 0
\(16\) 5.50000 9.52628i 0.343750 0.595392i
\(17\) 15.5885i 0.916968i 0.888703 + 0.458484i \(0.151607\pi\)
−0.888703 + 0.458484i \(0.848393\pi\)
\(18\) 0 0
\(19\) 11.0000 0.578947 0.289474 0.957186i \(-0.406520\pi\)
0.289474 + 0.957186i \(0.406520\pi\)
\(20\) 3.00000 + 1.73205i 0.150000 + 0.0866025i
\(21\) 0 0
\(22\) 1.50000 + 2.59808i 0.0681818 + 0.118094i
\(23\) 24.0000 13.8564i 1.04348 0.602452i 0.122662 0.992449i \(-0.460857\pi\)
0.920817 + 0.389996i \(0.127524\pi\)
\(24\) 0 0
\(25\) −6.50000 + 11.2583i −0.260000 + 0.450333i
\(26\) 6.92820i 0.266469i
\(27\) 0 0
\(28\) 2.00000 0.0714286
\(29\) −39.0000 22.5167i −1.34483 0.776437i −0.357316 0.933984i \(-0.616308\pi\)
−0.987511 + 0.157547i \(0.949641\pi\)
\(30\) 0 0
\(31\) −16.0000 27.7128i −0.516129 0.893962i −0.999825 0.0187254i \(-0.994039\pi\)
0.483696 0.875236i \(-0.339294\pi\)
\(32\) −13.5000 + 7.79423i −0.421875 + 0.243570i
\(33\) 0 0
\(34\) −13.5000 + 23.3827i −0.397059 + 0.687726i
\(35\) 6.92820i 0.197949i
\(36\) 0 0
\(37\) −34.0000 −0.918919 −0.459459 0.888199i \(-0.651957\pi\)
−0.459459 + 0.888199i \(0.651957\pi\)
\(38\) 16.5000 + 9.52628i 0.434211 + 0.250692i
\(39\) 0 0
\(40\) 15.0000 + 25.9808i 0.375000 + 0.649519i
\(41\) 10.5000 6.06218i 0.256098 0.147858i −0.366456 0.930436i \(-0.619429\pi\)
0.622553 + 0.782578i \(0.286095\pi\)
\(42\) 0 0
\(43\) 30.5000 52.8275i 0.709302 1.22855i −0.255814 0.966726i \(-0.582343\pi\)
0.965116 0.261822i \(-0.0843232\pi\)
\(44\) 1.73205i 0.0393648i
\(45\) 0 0
\(46\) 48.0000 1.04348
\(47\) 42.0000 + 24.2487i 0.893617 + 0.515930i 0.875124 0.483899i \(-0.160780\pi\)
0.0184931 + 0.999829i \(0.494113\pi\)
\(48\) 0 0
\(49\) 22.5000 + 38.9711i 0.459184 + 0.795329i
\(50\) −19.5000 + 11.2583i −0.390000 + 0.225167i
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.0384615 0.0666173i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.109091
\(56\) 15.0000 + 8.66025i 0.267857 + 0.154647i
\(57\) 0 0
\(58\) −39.0000 67.5500i −0.672414 1.16465i
\(59\) −43.5000 + 25.1147i −0.737288 + 0.425674i −0.821082 0.570810i \(-0.806629\pi\)
0.0837943 + 0.996483i \(0.473296\pi\)
\(60\) 0 0
\(61\) −28.0000 + 48.4974i −0.459016 + 0.795040i −0.998909 0.0466940i \(-0.985131\pi\)
0.539893 + 0.841734i \(0.318465\pi\)
\(62\) 55.4256i 0.893962i
\(63\) 0 0
\(64\) −71.0000 −1.10938
\(65\) −12.0000 6.92820i −0.184615 0.106588i
\(66\) 0 0
\(67\) 15.5000 + 26.8468i 0.231343 + 0.400698i 0.958204 0.286087i \(-0.0923546\pi\)
−0.726860 + 0.686785i \(0.759021\pi\)
\(68\) 13.5000 7.79423i 0.198529 0.114621i
\(69\) 0 0
\(70\) 6.00000 10.3923i 0.0857143 0.148461i
\(71\) 31.1769i 0.439111i −0.975600 0.219556i \(-0.929539\pi\)
0.975600 0.219556i \(-0.0704608\pi\)
\(72\) 0 0
\(73\) 65.0000 0.890411 0.445205 0.895428i \(-0.353131\pi\)
0.445205 + 0.895428i \(0.353131\pi\)
\(74\) −51.0000 29.4449i −0.689189 0.397904i
\(75\) 0 0
\(76\) −5.50000 9.52628i −0.0723684 0.125346i
\(77\) −3.00000 + 1.73205i −0.0389610 + 0.0224942i
\(78\) 0 0
\(79\) −19.0000 + 32.9090i −0.240506 + 0.416569i −0.960859 0.277039i \(-0.910647\pi\)
0.720352 + 0.693608i \(0.243980\pi\)
\(80\) 38.1051i 0.476314i
\(81\) 0 0
\(82\) 21.0000 0.256098
\(83\) 42.0000 + 24.2487i 0.506024 + 0.292153i 0.731198 0.682165i \(-0.238962\pi\)
−0.225174 + 0.974319i \(0.572295\pi\)
\(84\) 0 0
\(85\) −27.0000 46.7654i −0.317647 0.550181i
\(86\) 91.5000 52.8275i 1.06395 0.614274i
\(87\) 0 0
\(88\) 7.50000 12.9904i 0.0852273 0.147618i
\(89\) 124.708i 1.40121i 0.713549 + 0.700605i \(0.247086\pi\)
−0.713549 + 0.700605i \(0.752914\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.0879121
\(92\) −24.0000 13.8564i −0.260870 0.150613i
\(93\) 0 0
\(94\) 42.0000 + 72.7461i 0.446809 + 0.773895i
\(95\) −33.0000 + 19.0526i −0.347368 + 0.200553i
\(96\) 0 0
\(97\) 57.5000 99.5929i 0.592784 1.02673i −0.401072 0.916047i \(-0.631362\pi\)
0.993856 0.110685i \(-0.0353044\pi\)
\(98\) 77.9423i 0.795329i
\(99\) 0 0
\(100\) 13.0000 0.130000
\(101\) −39.0000 22.5167i −0.386139 0.222937i 0.294347 0.955699i \(-0.404898\pi\)
−0.680486 + 0.732761i \(0.738231\pi\)
\(102\) 0 0
\(103\) 20.0000 + 34.6410i 0.194175 + 0.336321i 0.946630 0.322323i \(-0.104464\pi\)
−0.752455 + 0.658644i \(0.771130\pi\)
\(104\) 30.0000 17.3205i 0.288462 0.166543i
\(105\) 0 0
\(106\) 0 0
\(107\) 140.296i 1.31118i −0.755118 0.655589i \(-0.772420\pi\)
0.755118 0.655589i \(-0.227580\pi\)
\(108\) 0 0
\(109\) −52.0000 −0.477064 −0.238532 0.971135i \(-0.576666\pi\)
−0.238532 + 0.971135i \(0.576666\pi\)
\(110\) −9.00000 5.19615i −0.0818182 0.0472377i
\(111\) 0 0
\(112\) 11.0000 + 19.0526i 0.0982143 + 0.170112i
\(113\) 78.0000 45.0333i 0.690265 0.398525i −0.113446 0.993544i \(-0.536189\pi\)
0.803711 + 0.595019i \(0.202856\pi\)
\(114\) 0 0
\(115\) −48.0000 + 83.1384i −0.417391 + 0.722943i
\(116\) 45.0333i 0.388218i
\(117\) 0 0
\(118\) −87.0000 −0.737288
\(119\) −27.0000 15.5885i −0.226891 0.130995i
\(120\) 0 0
\(121\) −59.0000 102.191i −0.487603 0.844554i
\(122\) −84.0000 + 48.4974i −0.688525 + 0.397520i
\(123\) 0 0
\(124\) −16.0000 + 27.7128i −0.129032 + 0.223490i
\(125\) 131.636i 1.05309i
\(126\) 0 0
\(127\) −16.0000 −0.125984 −0.0629921 0.998014i \(-0.520064\pi\)
−0.0629921 + 0.998014i \(0.520064\pi\)
\(128\) −52.5000 30.3109i −0.410156 0.236804i
\(129\) 0 0
\(130\) −12.0000 20.7846i −0.0923077 0.159882i
\(131\) −138.000 + 79.6743i −1.05344 + 0.608201i −0.923609 0.383336i \(-0.874775\pi\)
−0.129826 + 0.991537i \(0.541442\pi\)
\(132\) 0 0
\(133\) −11.0000 + 19.0526i −0.0827068 + 0.143252i
\(134\) 53.6936i 0.400698i
\(135\) 0 0
\(136\) 135.000 0.992647
\(137\) 163.500 + 94.3968i 1.19343 + 0.689028i 0.959083 0.283125i \(-0.0913712\pi\)
0.234348 + 0.972153i \(0.424705\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.0179856 0.0311520i 0.856893 0.515495i \(-0.172392\pi\)
−0.874878 + 0.484343i \(0.839059\pi\)
\(140\) −6.00000 + 3.46410i −0.0428571 + 0.0247436i
\(141\) 0 0
\(142\) 27.0000 46.7654i 0.190141 0.329334i
\(143\) 6.92820i 0.0484490i
\(144\) 0 0
\(145\) 156.000 1.07586
\(146\) 97.5000 + 56.2917i 0.667808 + 0.385559i
\(147\) 0 0
\(148\) 17.0000 + 29.4449i 0.114865 + 0.198952i
\(149\) 132.000 76.2102i 0.885906 0.511478i 0.0133049 0.999911i \(-0.495765\pi\)
0.872601 + 0.488433i \(0.162431\pi\)
\(150\) 0 0
\(151\) −10.0000 + 17.3205i −0.0662252 + 0.114705i −0.897237 0.441550i \(-0.854429\pi\)
0.831012 + 0.556255i \(0.187762\pi\)
\(152\) 95.2628i 0.626729i
\(153\) 0 0
\(154\) −6.00000 −0.0389610
\(155\) 96.0000 + 55.4256i 0.619355 + 0.357585i
\(156\) 0 0
\(157\) 20.0000 + 34.6410i 0.127389 + 0.220643i 0.922664 0.385605i \(-0.126007\pi\)
−0.795276 + 0.606248i \(0.792674\pi\)
\(158\) −57.0000 + 32.9090i −0.360759 + 0.208285i
\(159\) 0 0
\(160\) 27.0000 46.7654i 0.168750 0.292284i
\(161\) 55.4256i 0.344259i
\(162\) 0 0
\(163\) −106.000 −0.650307 −0.325153 0.945661i \(-0.605416\pi\)
−0.325153 + 0.945661i \(0.605416\pi\)
\(164\) −10.5000 6.06218i −0.0640244 0.0369645i
\(165\) 0 0
\(166\) 42.0000 + 72.7461i 0.253012 + 0.438230i
\(167\) −165.000 + 95.2628i −0.988024 + 0.570436i −0.904683 0.426085i \(-0.859892\pi\)
−0.0833409 + 0.996521i \(0.526559\pi\)
\(168\) 0 0
\(169\) 76.5000 132.502i 0.452663 0.784035i
\(170\) 93.5307i 0.550181i
\(171\) 0 0
\(172\) −61.0000 −0.354651
\(173\) −201.000 116.047i −1.16185 0.670794i −0.210103 0.977679i \(-0.567380\pi\)
−0.951747 + 0.306885i \(0.900713\pi\)
\(174\) 0 0
\(175\) −13.0000 22.5167i −0.0742857 0.128667i
\(176\) 16.5000 9.52628i 0.0937500 0.0541266i
\(177\) 0 0
\(178\) −108.000 + 187.061i −0.606742 + 1.05091i
\(179\) 62.3538i 0.348345i 0.984715 + 0.174173i \(0.0557251\pi\)
−0.984715 + 0.174173i \(0.944275\pi\)
\(180\) 0 0
\(181\) −232.000 −1.28177 −0.640884 0.767638i \(-0.721432\pi\)
−0.640884 + 0.767638i \(0.721432\pi\)
\(182\) −12.0000 6.92820i −0.0659341 0.0380671i
\(183\) 0 0
\(184\) −120.000 207.846i −0.652174 1.12960i
\(185\) 102.000 58.8897i 0.551351 0.318323i
\(186\) 0 0
\(187\) −13.5000 + 23.3827i −0.0721925 + 0.125041i
\(188\) 48.4974i 0.257965i
\(189\) 0 0
\(190\) −66.0000 −0.347368
\(191\) −201.000 116.047i −1.05236 0.607578i −0.129048 0.991638i \(-0.541192\pi\)
−0.923308 + 0.384060i \(0.874525\pi\)
\(192\) 0 0
\(193\) 132.500 + 229.497i 0.686528 + 1.18910i 0.972954 + 0.231000i \(0.0741996\pi\)
−0.286425 + 0.958103i \(0.592467\pi\)
\(194\) 172.500 99.5929i 0.889175 0.513366i
\(195\) 0 0
\(196\) 22.5000 38.9711i 0.114796 0.198832i
\(197\) 124.708i 0.633034i 0.948587 + 0.316517i \(0.102513\pi\)
−0.948587 + 0.316517i \(0.897487\pi\)
\(198\) 0 0
\(199\) 290.000 1.45729 0.728643 0.684893i \(-0.240151\pi\)
0.728643 + 0.684893i \(0.240151\pi\)
\(200\) 97.5000 + 56.2917i 0.487500 + 0.281458i
\(201\) 0 0
\(202\) −39.0000 67.5500i −0.193069 0.334406i
\(203\) 78.0000 45.0333i 0.384236 0.221839i
\(204\) 0 0
\(205\) −21.0000 + 36.3731i −0.102439 + 0.177430i
\(206\) 69.2820i 0.336321i
\(207\) 0 0
\(208\) 44.0000 0.211538
\(209\) 16.5000 + 9.52628i 0.0789474 + 0.0455803i
\(210\) 0 0
\(211\) 47.0000 + 81.4064i 0.222749 + 0.385812i 0.955642 0.294532i \(-0.0951637\pi\)
−0.732893 + 0.680344i \(0.761830\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 121.500 210.444i 0.567757 0.983384i
\(215\) 211.310i 0.982838i
\(216\) 0 0
\(217\) 64.0000 0.294931
\(218\) −78.0000 45.0333i −0.357798 0.206575i
\(219\) 0 0
\(220\) 3.00000 + 5.19615i 0.0136364 + 0.0236189i
\(221\) −54.0000 + 31.1769i −0.244344 + 0.141072i
\(222\) 0 0
\(223\) 26.0000 45.0333i 0.116592 0.201943i −0.801823 0.597562i \(-0.796136\pi\)
0.918415 + 0.395618i \(0.129470\pi\)
\(224\) 31.1769i 0.139183i
\(225\) 0 0
\(226\) 156.000 0.690265
\(227\) 163.500 + 94.3968i 0.720264 + 0.415845i 0.814850 0.579672i \(-0.196819\pi\)
−0.0945856 + 0.995517i \(0.530153\pi\)
\(228\) 0 0
\(229\) −133.000 230.363i −0.580786 1.00595i −0.995386 0.0959473i \(-0.969412\pi\)
0.414600 0.910004i \(-0.363921\pi\)
\(230\) −144.000 + 83.1384i −0.626087 + 0.361471i
\(231\) 0 0
\(232\) −195.000 + 337.750i −0.840517 + 1.45582i
\(233\) 202.650i 0.869742i 0.900493 + 0.434871i \(0.143206\pi\)
−0.900493 + 0.434871i \(0.856794\pi\)
\(234\) 0 0
\(235\) −168.000 −0.714894
\(236\) 43.5000 + 25.1147i 0.184322 + 0.106418i
\(237\) 0 0
\(238\) −27.0000 46.7654i −0.113445 0.196493i
\(239\) 348.000 200.918i 1.45607 0.840661i 0.457252 0.889337i \(-0.348834\pi\)
0.998815 + 0.0486764i \(0.0155003\pi\)
\(240\) 0 0
\(241\) −59.5000 + 103.057i −0.246888 + 0.427623i −0.962661 0.270711i \(-0.912741\pi\)
0.715773 + 0.698333i \(0.246075\pi\)
\(242\) 204.382i 0.844554i
\(243\) 0 0
\(244\) 56.0000 0.229508
\(245\) −135.000 77.9423i −0.551020 0.318132i
\(246\) 0 0
\(247\) 22.0000 + 38.1051i 0.0890688 + 0.154272i
\(248\) −240.000 + 138.564i −0.967742 + 0.558726i
\(249\) 0 0
\(250\) 114.000 197.454i 0.456000 0.789815i
\(251\) 389.711i 1.55264i −0.630342 0.776318i \(-0.717085\pi\)
0.630342 0.776318i \(-0.282915\pi\)
\(252\) 0 0
\(253\) 48.0000 0.189723
\(254\) −24.0000 13.8564i −0.0944882 0.0545528i
\(255\) 0 0
\(256\) 89.5000 + 155.019i 0.349609 + 0.605541i
\(257\) −151.500 + 87.4686i −0.589494 + 0.340345i −0.764897 0.644152i \(-0.777210\pi\)
0.175403 + 0.984497i \(0.443877\pi\)
\(258\) 0 0
\(259\) 34.0000 58.8897i 0.131274 0.227373i
\(260\) 13.8564i 0.0532939i
\(261\) 0 0
\(262\) −276.000 −1.05344
\(263\) −39.0000 22.5167i −0.148289 0.0856147i 0.424020 0.905653i \(-0.360619\pi\)
−0.572309 + 0.820038i \(0.693952\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −33.0000 + 19.0526i −0.124060 + 0.0716262i
\(267\) 0 0
\(268\) 15.5000 26.8468i 0.0578358 0.100175i
\(269\) 187.061i 0.695396i −0.937607 0.347698i \(-0.886963\pi\)
0.937607 0.347698i \(-0.113037\pi\)
\(270\) 0 0
\(271\) −268.000 −0.988930 −0.494465 0.869198i \(-0.664636\pi\)
−0.494465 + 0.869198i \(0.664636\pi\)
\(272\) 148.500 + 85.7365i 0.545956 + 0.315208i
\(273\) 0 0
\(274\) 163.500 + 283.190i 0.596715 + 1.03354i
\(275\) −19.5000 + 11.2583i −0.0709091 + 0.0409394i
\(276\) 0 0
\(277\) −28.0000 + 48.4974i −0.101083 + 0.175081i −0.912131 0.409899i \(-0.865564\pi\)
0.811048 + 0.584979i \(0.198897\pi\)
\(278\) 8.66025i 0.0311520i
\(279\) 0 0
\(280\) −60.0000 −0.214286
\(281\) 42.0000 + 24.2487i 0.149466 + 0.0862943i 0.572868 0.819648i \(-0.305831\pi\)
−0.423402 + 0.905942i \(0.639164\pi\)
\(282\) 0 0
\(283\) −187.000 323.894i −0.660777 1.14450i −0.980412 0.196959i \(-0.936893\pi\)
0.319634 0.947541i \(-0.396440\pi\)
\(284\) −27.0000 + 15.5885i −0.0950704 + 0.0548889i
\(285\) 0 0
\(286\) −6.00000 + 10.3923i −0.0209790 + 0.0363367i
\(287\) 24.2487i 0.0844903i
\(288\) 0 0
\(289\) 46.0000 0.159170
\(290\) 234.000 + 135.100i 0.806897 + 0.465862i
\(291\) 0 0
\(292\) −32.5000 56.2917i −0.111301 0.192780i
\(293\) −219.000 + 126.440i −0.747440 + 0.431535i −0.824768 0.565471i \(-0.808694\pi\)
0.0773280 + 0.997006i \(0.475361\pi\)
\(294\) 0 0
\(295\) 87.0000 150.688i 0.294915 0.510808i
\(296\) 294.449i 0.994759i
\(297\) 0 0
\(298\) 264.000 0.885906
\(299\) 96.0000 + 55.4256i 0.321070 + 0.185370i
\(300\) 0 0
\(301\) 61.0000 + 105.655i 0.202658 + 0.351014i
\(302\) −30.0000 + 17.3205i −0.0993377 + 0.0573527i
\(303\) 0 0
\(304\) 60.5000 104.789i 0.199013 0.344701i
\(305\) 193.990i 0.636032i
\(306\) 0 0
\(307\) 533.000 1.73616 0.868078 0.496428i \(-0.165355\pi\)
0.868078 + 0.496428i \(0.165355\pi\)
\(308\) 3.00000 + 1.73205i 0.00974026 + 0.00562354i
\(309\) 0 0
\(310\) 96.0000 + 166.277i 0.309677 + 0.536377i
\(311\) 213.000 122.976i 0.684887 0.395420i −0.116806 0.993155i \(-0.537266\pi\)
0.801694 + 0.597735i \(0.203932\pi\)
\(312\) 0 0
\(313\) −77.5000 + 134.234i −0.247604 + 0.428862i −0.962860 0.269999i \(-0.912976\pi\)
0.715257 + 0.698862i \(0.246310\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 0 0
\(316\) 38.0000 0.120253
\(317\) 42.0000 + 24.2487i 0.132492 + 0.0764944i 0.564781 0.825241i \(-0.308961\pi\)
−0.432289 + 0.901735i \(0.642294\pi\)
\(318\) 0 0
\(319\) −39.0000 67.5500i −0.122257 0.211755i
\(320\) 213.000 122.976i 0.665625 0.384299i
\(321\) 0 0
\(322\) −48.0000 + 83.1384i −0.149068 + 0.258194i
\(323\) 171.473i 0.530876i
\(324\) 0 0
\(325\) −52.0000 −0.160000
\(326\) −159.000 91.7987i −0.487730 0.281591i
\(327\) 0 0
\(328\) −52.5000 90.9327i −0.160061 0.277234i
\(329\) −84.0000 + 48.4974i −0.255319 + 0.147409i
\(330\) 0 0
\(331\) −1.00000 + 1.73205i −0.00302115 + 0.00523278i −0.867532 0.497381i \(-0.834295\pi\)
0.864511 + 0.502614i \(0.167628\pi\)
\(332\) 48.4974i 0.146077i
\(333\) 0 0
\(334\) −330.000 −0.988024
\(335\) −93.0000 53.6936i −0.277612 0.160279i
\(336\) 0 0
\(337\) −38.5000 66.6840i −0.114243 0.197875i 0.803234 0.595664i \(-0.203111\pi\)
−0.917477 + 0.397789i \(0.869778\pi\)
\(338\) 229.500 132.502i 0.678994 0.392017i
\(339\) 0 0
\(340\) −27.0000 + 46.7654i −0.0794118 + 0.137545i
\(341\) 55.4256i 0.162538i
\(342\) 0 0
\(343\) −188.000 −0.548105
\(344\) −457.500 264.138i −1.32994 0.767842i
\(345\) 0 0
\(346\) −201.000 348.142i −0.580925 1.00619i
\(347\) −97.5000 + 56.2917i −0.280980 + 0.162224i −0.633867 0.773442i \(-0.718533\pi\)
0.352887 + 0.935666i \(0.385200\pi\)
\(348\) 0 0
\(349\) −208.000 + 360.267i −0.595989 + 1.03228i 0.397418 + 0.917638i \(0.369906\pi\)
−0.993407 + 0.114645i \(0.963427\pi\)
\(350\) 45.0333i 0.128667i
\(351\) 0 0
\(352\) −27.0000 −0.0767045
\(353\) 1.50000 + 0.866025i 0.00424929 + 0.00245333i 0.502123 0.864796i \(-0.332552\pi\)
−0.497874 + 0.867249i \(0.665886\pi\)
\(354\) 0 0
\(355\) 54.0000 + 93.5307i 0.152113 + 0.263467i
\(356\) 108.000 62.3538i 0.303371 0.175151i
\(357\) 0 0
\(358\) −54.0000 + 93.5307i −0.150838 + 0.261259i
\(359\) 592.361i 1.65003i 0.565110 + 0.825016i \(0.308834\pi\)
−0.565110 + 0.825016i \(0.691166\pi\)
\(360\) 0 0
\(361\) −240.000 −0.664820
\(362\) −348.000 200.918i −0.961326 0.555022i
\(363\) 0 0
\(364\) 4.00000 + 6.92820i 0.0109890 + 0.0190335i
\(365\) −195.000 + 112.583i −0.534247 + 0.308447i
\(366\) 0 0
\(367\) 179.000 310.037i 0.487738 0.844788i −0.512162 0.858889i \(-0.671155\pi\)
0.999901 + 0.0141011i \(0.00448865\pi\)
\(368\) 304.841i 0.828372i
\(369\) 0 0
\(370\) 204.000 0.551351
\(371\) 0 0
\(372\) 0 0
\(373\) 290.000 + 502.295i 0.777480 + 1.34663i 0.933390 + 0.358863i \(0.116836\pi\)
−0.155910 + 0.987771i \(0.549831\pi\)
\(374\) −40.5000 + 23.3827i −0.108289 + 0.0625206i
\(375\) 0 0
\(376\) 210.000 363.731i 0.558511 0.967369i
\(377\) 180.133i 0.477807i
\(378\) 0 0
\(379\) 83.0000 0.218997 0.109499 0.993987i \(-0.465075\pi\)
0.109499 + 0.993987i \(0.465075\pi\)
\(380\) 33.0000 + 19.0526i 0.0868421 + 0.0501383i
\(381\) 0 0
\(382\) −201.000 348.142i −0.526178 0.911367i
\(383\) 483.000 278.860i 1.26110 0.728094i 0.287810 0.957688i \(-0.407073\pi\)
0.973287 + 0.229593i \(0.0737395\pi\)
\(384\) 0 0
\(385\) 6.00000 10.3923i 0.0155844 0.0269930i
\(386\) 458.993i 1.18910i
\(387\) 0 0
\(388\) −115.000 −0.296392
\(389\) 447.000 + 258.076i 1.14910 + 0.663433i 0.948668 0.316274i \(-0.102432\pi\)
0.200432 + 0.979708i \(0.435765\pi\)
\(390\) 0 0
\(391\) 216.000 + 374.123i 0.552430 + 0.956836i
\(392\) 337.500 194.856i 0.860969 0.497081i
\(393\) 0 0
\(394\) −108.000 + 187.061i −0.274112 + 0.474775i
\(395\) 131.636i 0.333255i
\(396\) 0 0
\(397\) 362.000 0.911839 0.455919 0.890021i \(-0.349311\pi\)
0.455919 + 0.890021i \(0.349311\pi\)
\(398\) 435.000 + 251.147i 1.09296 + 0.631024i
\(399\) 0 0
\(400\) 71.5000 + 123.842i 0.178750 + 0.309604i
\(401\) −340.500 + 196.588i −0.849127 + 0.490244i −0.860356 0.509693i \(-0.829759\pi\)
0.0112291 + 0.999937i \(0.496426\pi\)
\(402\) 0 0
\(403\) 64.0000 110.851i 0.158809 0.275065i
\(404\) 45.0333i 0.111469i
\(405\) 0 0
\(406\) 156.000 0.384236
\(407\) −51.0000 29.4449i −0.125307 0.0723461i
\(408\) 0 0
\(409\) −110.500 191.392i −0.270171 0.467950i 0.698734 0.715381i \(-0.253747\pi\)
−0.968905 + 0.247431i \(0.920414\pi\)
\(410\) −63.0000 + 36.3731i −0.153659 + 0.0887148i
\(411\) 0 0
\(412\) 20.0000 34.6410i 0.0485437 0.0840801i
\(413\) 100.459i 0.243242i
\(414\) 0 0
\(415\) −168.000 −0.404819
\(416\) −54.0000 31.1769i −0.129808 0.0749445i
\(417\) 0 0
\(418\) 16.5000 + 28.5788i 0.0394737 + 0.0683704i
\(419\) −678.000 + 391.443i −1.61814 + 0.934233i −0.630737 + 0.775997i \(0.717247\pi\)
−0.987401 + 0.158236i \(0.949419\pi\)
\(420\) 0 0
\(421\) 341.000 590.629i 0.809976 1.40292i −0.102903 0.994691i \(-0.532813\pi\)
0.912880 0.408229i \(-0.133853\pi\)
\(422\) 162.813i 0.385812i
\(423\) 0 0
\(424\) 0 0
\(425\) −175.500 101.325i −0.412941 0.238412i
\(426\) 0 0
\(427\) −56.0000 96.9948i −0.131148 0.227154i
\(428\) −121.500 + 70.1481i −0.283879 + 0.163897i
\(429\) 0 0
\(430\) −183.000 + 316.965i −0.425581 + 0.737129i
\(431\) 280.592i 0.651026i −0.945538 0.325513i \(-0.894463\pi\)
0.945538 0.325513i \(-0.105537\pi\)
\(432\) 0 0
\(433\) −295.000 −0.681293 −0.340647 0.940191i \(-0.610646\pi\)
−0.340647 + 0.940191i \(0.610646\pi\)
\(434\) 96.0000 + 55.4256i 0.221198 + 0.127709i
\(435\) 0 0
\(436\) 26.0000 + 45.0333i 0.0596330 + 0.103287i
\(437\) 264.000 152.420i 0.604119 0.348788i
\(438\) 0 0
\(439\) −406.000 + 703.213i −0.924829 + 1.60185i −0.132993 + 0.991117i \(0.542459\pi\)
−0.791836 + 0.610734i \(0.790874\pi\)
\(440\) 51.9615i 0.118094i
\(441\) 0 0
\(442\) −108.000 −0.244344
\(443\) −79.5000 45.8993i −0.179458 0.103610i 0.407580 0.913170i \(-0.366373\pi\)
−0.587038 + 0.809559i \(0.699706\pi\)
\(444\) 0 0
\(445\) −216.000 374.123i −0.485393 0.840726i
\(446\) 78.0000 45.0333i 0.174888 0.100972i
\(447\) 0 0
\(448\) 71.0000 122.976i 0.158482 0.274499i
\(449\) 639.127i 1.42344i −0.702461 0.711722i \(-0.747915\pi\)
0.702461 0.711722i \(-0.252085\pi\)
\(450\) 0 0
\(451\) 21.0000 0.0465632
\(452\) −78.0000 45.0333i −0.172566 0.0996312i
\(453\) 0 0
\(454\) 163.500 + 283.190i 0.360132 + 0.623767i
\(455\) 24.0000 13.8564i 0.0527473 0.0304536i
\(456\) 0 0
\(457\) −32.5000 + 56.2917i −0.0711160 + 0.123176i −0.899391 0.437146i \(-0.855989\pi\)
0.828275 + 0.560322i \(0.189323\pi\)
\(458\) 460.726i 1.00595i
\(459\) 0 0
\(460\) 96.0000 0.208696
\(461\) 690.000 + 398.372i 1.49675 + 0.864147i 0.999993 0.00374501i \(-0.00119208\pi\)
0.496753 + 0.867892i \(0.334525\pi\)
\(462\) 0 0
\(463\) −367.000 635.663i −0.792657 1.37292i −0.924317 0.381627i \(-0.875364\pi\)
0.131660 0.991295i \(-0.457969\pi\)
\(464\) −429.000 + 247.683i −0.924569 + 0.533800i
\(465\) 0 0
\(466\) −175.500 + 303.975i −0.376609 + 0.652307i
\(467\) 202.650i 0.433940i −0.976178 0.216970i \(-0.930383\pi\)
0.976178 0.216970i \(-0.0696174\pi\)
\(468\) 0 0
\(469\) −62.0000 −0.132196
\(470\) −252.000 145.492i −0.536170 0.309558i
\(471\) 0 0
\(472\) 217.500 + 376.721i 0.460805 + 0.798138i
\(473\) 91.5000 52.8275i 0.193446 0.111686i
\(474\) 0 0
\(475\) −71.5000 + 123.842i −0.150526 + 0.260719i
\(476\) 31.1769i 0.0654977i
\(477\) 0 0
\(478\) 696.000 1.45607
\(479\) −525.000 303.109i −1.09603 0.632795i −0.160857 0.986978i \(-0.551426\pi\)
−0.935176 + 0.354183i \(0.884759\pi\)
\(480\) 0 0
\(481\) −68.0000 117.779i −0.141372 0.244864i
\(482\) −178.500 + 103.057i −0.370332 + 0.213811i
\(483\) 0 0
\(484\) −59.0000 + 102.191i −0.121901 + 0.211138i
\(485\) 398.372i 0.821385i
\(486\) 0 0
\(487\) −106.000 −0.217659 −0.108830 0.994060i \(-0.534710\pi\)
−0.108830 + 0.994060i \(0.534710\pi\)
\(488\) 420.000 + 242.487i 0.860656 + 0.496900i
\(489\) 0 0
\(490\) −135.000 233.827i −0.275510 0.477198i
\(491\) 199.500 115.181i 0.406314 0.234585i −0.282891 0.959152i \(-0.591293\pi\)
0.689205 + 0.724567i \(0.257960\pi\)
\(492\) 0 0
\(493\) 351.000 607.950i 0.711968 1.23316i
\(494\) 76.2102i 0.154272i
\(495\) 0 0
\(496\) −352.000 −0.709677
\(497\) 54.0000 + 31.1769i 0.108652 + 0.0627302i
\(498\) 0 0
\(499\) 393.500 + 681.562i 0.788577 + 1.36586i 0.926839 + 0.375460i \(0.122515\pi\)
−0.138261 + 0.990396i \(0.544151\pi\)
\(500\) −114.000 + 65.8179i −0.228000 + 0.131636i
\(501\) 0 0
\(502\) 337.500 584.567i 0.672311 1.16448i
\(503\) 623.538i 1.23964i 0.784745 + 0.619819i \(0.212794\pi\)
−0.784745 + 0.619819i \(0.787206\pi\)
\(504\) 0 0
\(505\) 156.000 0.308911
\(506\) 72.0000 + 41.5692i 0.142292 + 0.0821526i
\(507\) 0 0
\(508\) 8.00000 + 13.8564i 0.0157480 + 0.0272764i
\(509\) 186.000 107.387i 0.365422 0.210977i −0.306034 0.952020i \(-0.599002\pi\)
0.671457 + 0.741044i \(0.265669\pi\)
\(510\) 0 0
\(511\) −65.0000 + 112.583i −0.127202 + 0.220320i
\(512\) 552.524i 1.07915i
\(513\) 0 0
\(514\) −303.000 −0.589494
\(515\) −120.000 69.2820i −0.233010 0.134528i
\(516\) 0 0
\(517\) 42.0000 + 72.7461i 0.0812379 + 0.140708i
\(518\) 102.000 58.8897i 0.196911 0.113687i
\(519\) 0 0
\(520\) −60.0000 + 103.923i −0.115385 + 0.199852i
\(521\) 202.650i 0.388963i −0.980906 0.194482i \(-0.937698\pi\)
0.980906 0.194482i \(-0.0623025\pi\)
\(522\) 0 0
\(523\) −250.000 −0.478011 −0.239006 0.971018i \(-0.576821\pi\)
−0.239006 + 0.971018i \(0.576821\pi\)
\(524\) 138.000 + 79.6743i 0.263359 + 0.152050i
\(525\) 0 0
\(526\) −39.0000 67.5500i −0.0741445 0.128422i
\(527\) 432.000 249.415i 0.819734 0.473274i
\(528\) 0 0
\(529\) 119.500 206.980i 0.225898 0.391267i
\(530\) 0 0
\(531\) 0 0
\(532\) 22.0000 0.0413534
\(533\) 42.0000 + 24.2487i 0.0787992 + 0.0454948i
\(534\) 0 0
\(535\) 243.000 + 420.888i 0.454206 + 0.786707i
\(536\) 232.500 134.234i 0.433769 0.250436i
\(537\) 0 0
\(538\) 162.000 280.592i 0.301115 0.521547i
\(539\) 77.9423i 0.144605i
\(540\) 0 0
\(541\) 650.000 1.20148 0.600739 0.799445i \(-0.294873\pi\)
0.600739 + 0.799445i \(0.294873\pi\)
\(542\) −402.000 232.095i −0.741697 0.428219i
\(543\) 0 0
\(544\) −121.500 210.444i −0.223346 0.386846i
\(545\) 156.000 90.0666i 0.286239 0.165260i
\(546\) 0 0
\(547\) −311.500 + 539.534i −0.569470 + 0.986351i 0.427149 + 0.904181i \(0.359518\pi\)
−0.996618 + 0.0821692i \(0.973815\pi\)
\(548\) 188.794i 0.344514i
\(549\) 0 0
\(550\) −39.0000 −0.0709091
\(551\) −429.000 247.683i −0.778584 0.449516i
\(552\) 0 0
\(553\) −38.0000 65.8179i −0.0687161 0.119020i
\(554\) −84.0000 + 48.4974i −0.151625 + 0.0875405i
\(555\) 0 0
\(556\) −2.50000 + 4.33013i −0.00449640 + 0.00778800i
\(557\) 530.008i 0.951540i 0.879570 + 0.475770i \(0.157830\pi\)
−0.879570 + 0.475770i \(0.842170\pi\)
\(558\) 0 0
\(559\) 244.000 0.436494
\(560\) −66.0000 38.1051i −0.117857 0.0680449i
\(561\) 0 0
\(562\) 42.0000 + 72.7461i 0.0747331 + 0.129442i
\(563\) −97.5000 + 56.2917i −0.173179 + 0.0999852i −0.584084 0.811693i \(-0.698546\pi\)
0.410905 + 0.911678i \(0.365213\pi\)
\(564\) 0 0
\(565\) −156.000 + 270.200i −0.276106 + 0.478230i
\(566\) 647.787i 1.14450i
\(567\) 0 0
\(568\) −270.000 −0.475352
\(569\) −565.500 326.492i −0.993849 0.573799i −0.0874263 0.996171i \(-0.527864\pi\)
−0.906423 + 0.422372i \(0.861198\pi\)
\(570\) 0 0
\(571\) −272.500 471.984i −0.477233 0.826592i 0.522427 0.852684i \(-0.325027\pi\)
−0.999660 + 0.0260926i \(0.991694\pi\)
\(572\) 6.00000 3.46410i 0.0104895 0.00605612i
\(573\) 0 0
\(574\) −21.0000 + 36.3731i −0.0365854 + 0.0633677i
\(575\) 360.267i 0.626551i
\(576\) 0 0
\(577\) −871.000 −1.50953 −0.754766 0.655994i \(-0.772250\pi\)
−0.754766 + 0.655994i \(0.772250\pi\)
\(578\) 69.0000 + 39.8372i 0.119377 + 0.0689224i
\(579\) 0 0
\(580\) −78.0000 135.100i −0.134483 0.232931i
\(581\) −84.0000 + 48.4974i −0.144578 + 0.0834723i
\(582\) 0 0
\(583\) 0 0
\(584\) 562.917i 0.963898i
\(585\) 0 0
\(586\) −438.000 −0.747440
\(587\) 1.50000 + 0.866025i 0.00255537 + 0.00147534i 0.501277 0.865287i \(-0.332864\pi\)
−0.498722 + 0.866762i \(0.666197\pi\)
\(588\) 0 0
\(589\) −176.000 304.841i −0.298812 0.517557i
\(590\) 261.000 150.688i 0.442373 0.255404i
\(591\) 0 0
\(592\) −187.000 + 323.894i −0.315878 + 0.547117i
\(593\) 187.061i 0.315449i 0.987483 + 0.157725i \(0.0504159\pi\)
−0.987483 + 0.157725i \(0.949584\pi\)
\(594\) 0 0
\(595\) 108.000 0.181513
\(596\) −132.000 76.2102i −0.221477 0.127870i
\(597\) 0 0
\(598\) 96.0000 + 166.277i 0.160535 + 0.278055i
\(599\) −489.000 + 282.324i −0.816361 + 0.471326i −0.849160 0.528136i \(-0.822891\pi\)
0.0327992 + 0.999462i \(0.489558\pi\)
\(600\) 0 0
\(601\) −230.500 + 399.238i −0.383527 + 0.664289i −0.991564 0.129620i \(-0.958624\pi\)
0.608036 + 0.793909i \(0.291958\pi\)
\(602\) 211.310i 0.351014i
\(603\) 0 0
\(604\) 20.0000 0.0331126
\(605\) 354.000 + 204.382i 0.585124 + 0.337821i
\(606\) 0 0
\(607\) 56.0000 + 96.9948i 0.0922570 + 0.159794i 0.908461 0.417971i \(-0.137259\pi\)
−0.816204 + 0.577765i \(0.803925\pi\)
\(608\) −148.500 + 85.7365i −0.244243 + 0.141014i
\(609\) 0 0
\(610\) 168.000 290.985i 0.275410 0.477024i
\(611\) 193.990i 0.317495i
\(612\) 0 0
\(613\) 902.000 1.47145 0.735726 0.677279i \(-0.236841\pi\)
0.735726 + 0.677279i \(0.236841\pi\)
\(614\) 799.500 + 461.592i 1.30212 + 0.751778i
\(615\) 0 0
\(616\) 15.0000 + 25.9808i 0.0243506 + 0.0421766i
\(617\) 307.500 177.535i 0.498379 0.287739i −0.229665 0.973270i \(-0.573763\pi\)
0.728044 + 0.685530i \(0.240430\pi\)
\(618\) 0 0
\(619\) 399.500 691.954i 0.645396 1.11786i −0.338814 0.940853i \(-0.610026\pi\)
0.984210 0.177005i \(-0.0566409\pi\)
\(620\) 110.851i 0.178792i
\(621\) 0 0
\(622\) 426.000 0.684887
\(623\) −216.000 124.708i −0.346709 0.200173i
\(624\) 0 0
\(625\) 65.5000 + 113.449i 0.104800 + 0.181519i
\(626\) −232.500 + 134.234i −0.371406 + 0.214431i
\(627\) 0 0
\(628\) 20.0000 34.6410i 0.0318471 0.0551609i
\(629\) 530.008i 0.842619i
\(630\) 0 0
\(631\) 830.000 1.31537 0.657686 0.753292i \(-0.271535\pi\)
0.657686 + 0.753292i \(0.271535\pi\)
\(632\) 285.000 + 164.545i 0.450949 + 0.260356i
\(633\) 0 0
\(634\) 42.0000 + 72.7461i 0.0662461 + 0.114742i
\(635\) 48.0000 27.7128i 0.0755906 0.0436422i
\(636\) 0 0
\(637\) −90.0000 + 155.885i −0.141287 + 0.244717i
\(638\) 135.100i 0.211755i
\(639\) 0 0
\(640\) 210.000 0.328125
\(641\) 325.500 + 187.928i 0.507800 + 0.293179i 0.731929 0.681381i \(-0.238620\pi\)
−0.224129 + 0.974560i \(0.571954\pi\)
\(642\) 0 0
\(643\) 6.50000 + 11.2583i 0.0101089 + 0.0175091i 0.871036 0.491220i \(-0.163449\pi\)
−0.860927 + 0.508729i \(0.830116\pi\)
\(644\) 48.0000 27.7128i 0.0745342 0.0430323i
\(645\) 0 0
\(646\) −148.500 + 257.210i −0.229876 + 0.398157i
\(647\) 467.654i 0.722803i 0.932410 + 0.361402i \(0.117702\pi\)
−0.932410 + 0.361402i \(0.882298\pi\)
\(648\) 0 0
\(649\) −87.0000 −0.134052
\(650\) −78.0000 45.0333i −0.120000 0.0692820i
\(651\) 0 0
\(652\) 53.0000 + 91.7987i 0.0812883 + 0.140796i
\(653\) −327.000 + 188.794i −0.500766 + 0.289117i −0.729030 0.684482i \(-0.760028\pi\)
0.228264 + 0.973599i \(0.426695\pi\)
\(654\) 0 0
\(655\) 276.000 478.046i 0.421374 0.729841i
\(656\) 133.368i 0.203305i
\(657\) 0 0
\(658\) −168.000 −0.255319
\(659\) 852.000 + 491.902i 1.29287 + 0.746438i 0.979162 0.203082i \(-0.0650959\pi\)
0.313706 + 0.949520i \(0.398429\pi\)
\(660\) 0 0
\(661\) 191.000 + 330.822i 0.288956 + 0.500487i 0.973561 0.228428i \(-0.0733585\pi\)
−0.684605 + 0.728915i \(0.740025\pi\)
\(662\) −3.00000 + 1.73205i −0.00453172 + 0.00261639i
\(663\) 0 0
\(664\) 210.000 363.731i 0.316265 0.547787i
\(665\) 76.2102i 0.114602i
\(666\) 0 0
\(667\) −1248.00 −1.87106
\(668\) 165.000 + 95.2628i 0.247006 + 0.142609i
\(669\) 0 0
\(670\) −93.0000 161.081i −0.138806 0.240419i
\(671\) −84.0000 + 48.4974i −0.125186 + 0.0722763i
\(672\) 0 0
\(673\) −289.000 + 500.563i −0.429421 + 0.743778i −0.996822 0.0796633i \(-0.974615\pi\)
0.567401 + 0.823441i \(0.307949\pi\)
\(674\) 133.368i 0.197875i
\(675\) 0 0
\(676\) −153.000 −0.226331
\(677\) −606.000 349.874i −0.895126 0.516801i −0.0195100 0.999810i \(-0.506211\pi\)
−0.875616 + 0.483009i \(0.839544\pi\)
\(678\) 0 0
\(679\) 115.000 + 199.186i 0.169367 + 0.293352i
\(680\) −405.000 + 233.827i −0.595588 + 0.343863i
\(681\) 0 0
\(682\) 48.0000 83.1384i 0.0703812 0.121904i
\(683\) 1044.43i 1.52918i −0.644520 0.764588i \(-0.722943\pi\)
0.644520 0.764588i \(-0.277057\pi\)
\(684\) 0 0
\(685\) −654.000 −0.954745
\(686\) −282.000 162.813i −0.411079 0.237336i
\(687\) 0 0
\(688\) −335.500 581.103i −0.487645 0.844627i
\(689\) 0 0
\(690\) 0 0
\(691\) −91.0000 + 157.617i −0.131693 + 0.228099i −0.924329 0.381596i \(-0.875375\pi\)
0.792636 + 0.609695i \(0.208708\pi\)
\(692\) 232.095i 0.335397i
\(693\) 0 0
\(694\) −195.000 −0.280980
\(695\) 15.0000 + 8.66025i 0.0215827 + 0.0124608i
\(696\) 0 0
\(697\) 94.5000 + 163.679i 0.135581 + 0.234833i
\(698\) −624.000 + 360.267i −0.893983 + 0.516141i
\(699\) 0 0
\(700\) −13.0000 + 22.5167i −0.0185714 + 0.0321667i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −374.000 −0.532006
\(704\) −106.500 61.4878i −0.151278 0.0873406i
\(705\) 0 0
\(706\) 1.50000 + 2.59808i 0.00212465 + 0.00367999i
\(707\) 78.0000 45.0333i 0.110325 0.0636964i
\(708\) 0 0
\(709\) 350.000 606.218i 0.493653 0.855032i −0.506320 0.862346i \(-0.668995\pi\)
0.999973 + 0.00731341i \(0.00232795\pi\)
\(710\) 187.061i 0.263467i
\(711\) 0 0
\(712\) 1080.00 1.51685
\(713\) −768.000 443.405i −1.07714 0.621886i
\(714\) 0 0
\(715\) −12.0000 20.7846i −0.0167832 0.0290694i
\(716\) 54.0000 31.1769i 0.0754190 0.0435432i
\(717\) 0 0
\(718\) −513.000 + 888.542i −0.714485 + 1.23752i
\(719\) 592.361i 0.823868i −0.911214 0.411934i \(-0.864853\pi\)
0.911214 0.411934i \(-0.135147\pi\)
\(720\) 0 0
\(721\) −80.0000 −0.110957
\(722\) −360.000 207.846i −0.498615 0.287875i
\(723\) 0 0
\(724\) 116.000 + 200.918i 0.160221 + 0.277511i
\(725\) 507.000 292.717i 0.699310 0.403747i
\(726\) 0 0
\(727\) 332.000 575.041i 0.456671 0.790978i −0.542111 0.840307i \(-0.682375\pi\)
0.998783 + 0.0493289i \(0.0157082\pi\)
\(728\) 69.2820i 0.0951676i
\(729\) 0 0
\(730\) −390.000 −0.534247
\(731\) 823.500 + 475.448i 1.12654 + 0.650408i
\(732\) 0 0
\(733\) 335.000 + 580.237i 0.457026 + 0.791592i 0.998802 0.0489306i \(-0.0155813\pi\)
−0.541776 + 0.840523i \(0.682248\pi\)
\(734\) 537.000 310.037i 0.731608 0.422394i
\(735\) 0 0
\(736\) −216.000 + 374.123i −0.293478 + 0.508319i
\(737\) 53.6936i 0.0728542i
\(738\) 0 0
\(739\) 317.000 0.428958 0.214479 0.976729i \(-0.431195\pi\)
0.214479 + 0.976729i \(0.431195\pi\)
\(740\) −102.000 58.8897i −0.137838 0.0795807i
\(741\) 0 0
\(742\) 0 0
\(743\) 537.000 310.037i 0.722746 0.417277i −0.0930168 0.995665i \(-0.529651\pi\)
0.815762 + 0.578387i \(0.196318\pi\)
\(744\) 0 0
\(745\) −264.000 + 457.261i −0.354362 + 0.613774i
\(746\) 1004.59i 1.34663i
\(747\) 0 0
\(748\) 27.0000 0.0360963
\(749\) 243.000 + 140.296i 0.324433 + 0.187311i
\(750\) 0 0
\(751\) −655.000 1134.49i −0.872170 1.51064i −0.859747 0.510721i \(-0.829379\pi\)
−0.0124237 0.999923i \(-0.503955\pi\)
\(752\) 462.000 266.736i 0.614362 0.354702i
\(753\) 0 0
\(754\) 156.000 270.200i 0.206897 0.358355i
\(755\) 69.2820i 0.0917643i
\(756\) 0 0
\(757\) 218.000 0.287979 0.143989 0.989579i \(-0.454007\pi\)
0.143989 + 0.989579i \(0.454007\pi\)
\(758\) 124.500 + 71.8801i 0.164248 + 0.0948286i
\(759\) 0 0
\(760\) 165.000 + 285.788i 0.217105 + 0.376037i
\(761\) −570.000 + 329.090i −0.749014 + 0.432444i −0.825338 0.564639i \(-0.809015\pi\)
0.0763232 + 0.997083i \(0.475682\pi\)
\(762\) 0 0
\(763\) 52.0000 90.0666i 0.0681520 0.118043i
\(764\) 232.095i 0.303789i
\(765\) 0 0
\(766\) 966.000 1.26110
\(767\) −174.000 100.459i −0.226858 0.130976i
\(768\) 0 0
\(769\) −511.000 885.078i −0.664499 1.15095i −0.979421 0.201829i \(-0.935312\pi\)
0.314921 0.949118i \(-0.398022\pi\)
\(770\) 18.0000 10.3923i 0.0233766 0.0134965i
\(771\) 0 0
\(772\) 132.500 229.497i 0.171632 0.297276i
\(773\) 1184.72i 1.53263i 0.642465 + 0.766315i \(0.277912\pi\)
−0.642465 + 0.766315i \(0.722088\pi\)
\(774\) 0 0
\(775\) 416.000 0.536774
\(776\) −862.500 497.965i −1.11147 0.641707i
\(777\) 0 0
\(778\) 447.000 + 774.227i 0.574550 + 0.995150i
\(779\) 115.500 66.6840i 0.148267 0.0856020i
\(780\) 0 0
\(781\) 27.0000 46.7654i 0.0345711 0.0598788i
\(782\) 748.246i 0.956836i
\(783\) 0 0
\(784\) 495.000 0.631378
\(785\) −120.000 69.2820i −0.152866 0.0882574i
\(786\) 0 0
\(787\) 65.0000 + 112.583i 0.0825921 + 0.143054i 0.904363 0.426765i \(-0.140347\pi\)
−0.821771 + 0.569819i \(0.807013\pi\)
\(788\) 108.000 62.3538i 0.137056 0.0791292i
\(789\) 0 0
\(790\) 114.000 197.454i 0.144304 0.249942i
\(791\) 180.133i 0.227729i
\(792\) 0 0
\(793\) −224.000 −0.282472
\(794\) 543.000 + 313.501i 0.683879 + 0.394838i
\(795\) 0 0
\(796\) −145.000 251.147i −0.182161 0.315512i
\(797\) −273.000 + 157.617i −0.342535 + 0.197762i −0.661392 0.750040i \(-0.730034\pi\)
0.318858 + 0.947803i \(0.396701\pi\)
\(798\) 0 0
\(799\) −378.000 + 654.715i −0.473091 + 0.819418i
\(800\) 202.650i 0.253312i
\(801\)