Properties

Label 27.3.d.a.17.1
Level 27
Weight 3
Character 27.17
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 17.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 27.17
Dual form 27.3.d.a.8.1

$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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 −0.0756939 0.997131i \(-0.524117\pi\)
0.825694 + 0.564118i \(0.190784\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(5\) −3.00000 1.73205i −0.600000 0.346410i 0.169042 0.985609i \(-0.445933\pi\)
−0.769042 + 0.639199i \(0.779266\pi\)
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.142857 0.247436i 0.785714 0.618590i \(-0.212296\pi\)
−0.928571 + 0.371154i \(0.878962\pi\)
\(8\) 8.66025i 1.08253i
\(9\) 0 0
\(10\) −6.00000 −0.600000
\(11\) 1.50000 0.866025i 0.136364 0.0787296i −0.430266 0.902702i \(-0.641580\pi\)
0.566630 + 0.823972i \(0.308247\pi\)
\(12\) 0 0
\(13\) 2.00000 3.46410i 0.153846 0.266469i −0.778792 0.627282i \(-0.784167\pi\)
0.932638 + 0.360813i \(0.117501\pi\)
\(14\) −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 \(-0.848393\pi\)
0.888703 0.458484i \(-0.151607\pi\)
\(18\) 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 0.920817 0.389996i \(-0.127524\pi\)
0.122662 + 0.992449i \(0.460857\pi\)
\(24\) 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 −0.987511 0.157547i \(-0.949641\pi\)
−0.357316 + 0.933984i \(0.616308\pi\)
\(30\) 0 0
\(31\) −16.0000 + 27.7128i −0.516129 + 0.893962i 0.483696 + 0.875236i \(0.339294\pi\)
−0.999825 + 0.0187254i \(0.994039\pi\)
\(32\) −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 0.622553 0.782578i \(-0.286095\pi\)
−0.366456 + 0.930436i \(0.619429\pi\)
\(42\) 0 0
\(43\) 30.5000 + 52.8275i 0.709302 + 1.22855i 0.965116 + 0.261822i \(0.0843232\pi\)
−0.255814 + 0.966726i \(0.582343\pi\)
\(44\) 1.73205i 0.0393648i
\(45\) 0 0
\(46\) 48.0000 1.04348
\(47\) 42.0000 24.2487i 0.893617 0.515930i 0.0184931 0.999829i \(-0.494113\pi\)
0.875124 + 0.483899i \(0.160780\pi\)
\(48\) 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 0.0837943 0.996483i \(-0.473296\pi\)
−0.821082 + 0.570810i \(0.806629\pi\)
\(60\) 0 0
\(61\) −28.0000 48.4974i −0.459016 0.795040i 0.539893 0.841734i \(-0.318465\pi\)
−0.998909 + 0.0466940i \(0.985131\pi\)
\(62\) 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 −0.726860 0.686785i \(-0.759021\pi\)
0.958204 + 0.286087i \(0.0923546\pi\)
\(68\) 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 \(0.0704608\pi\)
−0.975600 + 0.219556i \(0.929539\pi\)
\(72\) 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 0.720352 0.693608i \(-0.243980\pi\)
−0.960859 + 0.277039i \(0.910647\pi\)
\(80\) 38.1051i 0.476314i
\(81\) 0 0
\(82\) 21.0000 0.256098
\(83\) 42.0000 24.2487i 0.506024 0.292153i −0.225174 0.974319i \(-0.572295\pi\)
0.731198 + 0.682165i \(0.238962\pi\)
\(84\) 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 \(-0.752914\pi\)
0.713549 0.700605i \(-0.247086\pi\)
\(90\) 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 0.993856 + 0.110685i \(0.0353044\pi\)
−0.401072 + 0.916047i \(0.631362\pi\)
\(98\) 77.9423i 0.795329i
\(99\) 0 0
\(100\) 13.0000 0.130000
\(101\) −39.0000 + 22.5167i −0.386139 + 0.222937i −0.680486 0.732761i \(-0.738231\pi\)
0.294347 + 0.955699i \(0.404898\pi\)
\(102\) 0 0
\(103\) 20.0000 34.6410i 0.194175 0.336321i −0.752455 0.658644i \(-0.771130\pi\)
0.946630 + 0.322323i \(0.104464\pi\)
\(104\) 30.0000 + 17.3205i 0.288462 + 0.166543i
\(105\) 0 0
\(106\) 0 0
\(107\) 140.296i 1.31118i 0.755118 + 0.655589i \(0.227580\pi\)
−0.755118 + 0.655589i \(0.772420\pi\)
\(108\) 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 0.803711 0.595019i \(-0.202856\pi\)
−0.113446 + 0.993544i \(0.536189\pi\)
\(114\) 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 −0.129826 0.991537i \(-0.541442\pi\)
−0.923609 + 0.383336i \(0.874775\pi\)
\(132\) 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 0.234348 0.972153i \(-0.424705\pi\)
0.959083 + 0.283125i \(0.0913712\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.0179856 + 0.0311520i −0.874878 0.484343i \(-0.839059\pi\)
0.856893 + 0.515495i \(0.172392\pi\)
\(140\) −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 0.872601 0.488433i \(-0.162431\pi\)
0.0133049 + 0.999911i \(0.495765\pi\)
\(150\) 0 0
\(151\) −10.0000 17.3205i −0.0662252 0.114705i 0.831012 0.556255i \(-0.187762\pi\)
−0.897237 + 0.441550i \(0.854429\pi\)
\(152\) 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 −0.795276 0.606248i \(-0.792674\pi\)
0.922664 + 0.385605i \(0.126007\pi\)
\(158\) −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 −0.0833409 0.996521i \(-0.526559\pi\)
−0.904683 + 0.426085i \(0.859892\pi\)
\(168\) 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 −0.951747 0.306885i \(-0.900713\pi\)
−0.210103 + 0.977679i \(0.567380\pi\)
\(174\) 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 \(-0.944275\pi\)
0.984715 0.174173i \(-0.0557251\pi\)
\(180\) 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 −0.923308 0.384060i \(-0.874525\pi\)
−0.129048 + 0.991638i \(0.541192\pi\)
\(192\) 0 0
\(193\) 132.500 229.497i 0.686528 1.18910i −0.286425 0.958103i \(-0.592467\pi\)
0.972954 0.231000i \(-0.0741996\pi\)
\(194\) 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 \(-0.897487\pi\)
0.948587 0.316517i \(-0.102513\pi\)
\(198\) 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 −0.732893 0.680344i \(-0.761830\pi\)
0.955642 + 0.294532i \(0.0951637\pi\)
\(212\) 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 0.918415 0.395618i \(-0.129470\pi\)
−0.801823 + 0.597562i \(0.796136\pi\)
\(224\) 31.1769i 0.139183i
\(225\) 0 0
\(226\) 156.000 0.690265
\(227\) 163.500 94.3968i 0.720264 0.415845i −0.0945856 0.995517i \(-0.530153\pi\)
0.814850 + 0.579672i \(0.196819\pi\)
\(228\) 0 0
\(229\) −133.000 + 230.363i −0.580786 + 1.00595i 0.414600 + 0.910004i \(0.363921\pi\)
−0.995386 + 0.0959473i \(0.969412\pi\)
\(230\) −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 \(-0.856794\pi\)
0.900493 0.434871i \(-0.143206\pi\)
\(234\) 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 0.998815 0.0486764i \(-0.0155003\pi\)
0.457252 + 0.889337i \(0.348834\pi\)
\(240\) 0 0
\(241\) −59.5000 103.057i −0.246888 0.427623i 0.715773 0.698333i \(-0.246075\pi\)
−0.962661 + 0.270711i \(0.912741\pi\)
\(242\) 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 \(0.282915\pi\)
−0.630342 + 0.776318i \(0.717085\pi\)
\(252\) 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 0.175403 0.984497i \(-0.443877\pi\)
−0.764897 + 0.644152i \(0.777210\pi\)
\(258\) 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 −0.572309 0.820038i \(-0.693952\pi\)
0.424020 + 0.905653i \(0.360619\pi\)
\(264\) 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 \(0.113037\pi\)
−0.937607 + 0.347698i \(0.886963\pi\)
\(270\) 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 0.811048 0.584979i \(-0.198897\pi\)
−0.912131 + 0.409899i \(0.865564\pi\)
\(278\) 8.66025i 0.0311520i
\(279\) 0 0
\(280\) −60.0000 −0.214286
\(281\) 42.0000 24.2487i 0.149466 0.0862943i −0.423402 0.905942i \(-0.639164\pi\)
0.572868 + 0.819648i \(0.305831\pi\)
\(282\) 0 0
\(283\) −187.000 + 323.894i −0.660777 + 1.14450i 0.319634 + 0.947541i \(0.396440\pi\)
−0.980412 + 0.196959i \(0.936893\pi\)
\(284\) −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 0.0773280 0.997006i \(-0.475361\pi\)
−0.824768 + 0.565471i \(0.808694\pi\)
\(294\) 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 0.801694 0.597735i \(-0.203932\pi\)
−0.116806 + 0.993155i \(0.537266\pi\)
\(312\) 0 0
\(313\) −77.5000 134.234i −0.247604 0.428862i 0.715257 0.698862i \(-0.246310\pi\)
−0.962860 + 0.269999i \(0.912976\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 0 0
\(316\) 38.0000 0.120253
\(317\) 42.0000 24.2487i 0.132492 0.0764944i −0.432289 0.901735i \(-0.642294\pi\)
0.564781 + 0.825241i \(0.308961\pi\)
\(318\) 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 0.864511 0.502614i \(-0.167628\pi\)
−0.867532 + 0.497381i \(0.834295\pi\)
\(332\) 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 −0.917477 0.397789i \(-0.869778\pi\)
0.803234 + 0.595664i \(0.203111\pi\)
\(338\) 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 0.352887 0.935666i \(-0.385200\pi\)
−0.633867 + 0.773442i \(0.718533\pi\)
\(348\) 0 0
\(349\) −208.000 360.267i −0.595989 1.03228i −0.993407 0.114645i \(-0.963427\pi\)
0.397418 0.917638i \(-0.369906\pi\)
\(350\) 45.0333i 0.128667i
\(351\) 0 0
\(352\) −27.0000 −0.0767045
\(353\) 1.50000 0.866025i 0.00424929 0.00245333i −0.497874 0.867249i \(-0.665886\pi\)
0.502123 + 0.864796i \(0.332552\pi\)
\(354\) 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 \(-0.691166\pi\)
0.565110 0.825016i \(-0.308834\pi\)
\(360\) 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 0.999901 0.0141011i \(-0.00448865\pi\)
−0.512162 + 0.858889i \(0.671155\pi\)
\(368\) 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 −0.155910 0.987771i \(-0.549831\pi\)
0.933390 0.358863i \(-0.116836\pi\)
\(374\) −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 0.973287 0.229593i \(-0.0737395\pi\)
0.287810 + 0.957688i \(0.407073\pi\)
\(384\) 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 0.200432 0.979708i \(-0.435765\pi\)
0.948668 + 0.316274i \(0.102432\pi\)
\(390\) 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 0.0112291 0.999937i \(-0.496426\pi\)
−0.860356 + 0.509693i \(0.829759\pi\)
\(402\) 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 −0.968905 0.247431i \(-0.920414\pi\)
0.698734 + 0.715381i \(0.253747\pi\)
\(410\) −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 −0.987401 0.158236i \(-0.949419\pi\)
−0.630737 0.775997i \(-0.717247\pi\)
\(420\) 0 0
\(421\) 341.000 + 590.629i 0.809976 + 1.40292i 0.912880 + 0.408229i \(0.133853\pi\)
−0.102903 + 0.994691i \(0.532813\pi\)
\(422\) 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 \(0.105537\pi\)
−0.945538 + 0.325513i \(0.894463\pi\)
\(432\) 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 −0.791836 0.610734i \(-0.790874\pi\)
−0.132993 0.991117i \(-0.542459\pi\)
\(440\) 51.9615i 0.118094i
\(441\) 0 0
\(442\) −108.000 −0.244344
\(443\) −79.5000 + 45.8993i −0.179458 + 0.103610i −0.587038 0.809559i \(-0.699706\pi\)
0.407580 + 0.913170i \(0.366373\pi\)
\(444\) 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 \(0.252085\pi\)
−0.702461 + 0.711722i \(0.747915\pi\)
\(450\) 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 0.828275 0.560322i \(-0.189323\pi\)
−0.899391 + 0.437146i \(0.855989\pi\)
\(458\) 460.726i 1.00595i
\(459\) 0 0
\(460\) 96.0000 0.208696
\(461\) 690.000 398.372i 1.49675 0.864147i 0.496753 0.867892i \(-0.334525\pi\)
0.999993 + 0.00374501i \(0.00119208\pi\)
\(462\) 0 0
\(463\) −367.000 + 635.663i −0.792657 + 1.37292i 0.131660 + 0.991295i \(0.457969\pi\)
−0.924317 + 0.381627i \(0.875364\pi\)
\(464\) −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 \(0.0696174\pi\)
−0.976178 + 0.216970i \(0.930383\pi\)
\(468\) 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 −0.935176 0.354183i \(-0.884759\pi\)
−0.160857 + 0.986978i \(0.551426\pi\)
\(480\) 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 0.689205 0.724567i \(-0.257960\pi\)
−0.282891 + 0.959152i \(0.591293\pi\)
\(492\) 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 −0.138261 0.990396i \(-0.544151\pi\)
0.926839 0.375460i \(-0.122515\pi\)
\(500\) −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 \(-0.787206\pi\)
0.784745 0.619819i \(-0.212794\pi\)
\(504\) 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 0.671457 0.741044i \(-0.265669\pi\)
−0.306034 + 0.952020i \(0.599002\pi\)
\(510\) 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 \(0.0623025\pi\)
−0.980906 + 0.194482i \(0.937698\pi\)
\(522\) 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 −0.996618 0.0821692i \(-0.973815\pi\)
0.427149 0.904181i \(-0.359518\pi\)
\(548\) 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 \(-0.842170\pi\)
0.879570 0.475770i \(-0.157830\pi\)
\(558\) 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 0.410905 0.911678i \(-0.365213\pi\)
−0.584084 + 0.811693i \(0.698546\pi\)
\(564\) 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 −0.906423 0.422372i \(-0.861198\pi\)
−0.0874263 + 0.996171i \(0.527864\pi\)
\(570\) 0 0
\(571\) −272.500 + 471.984i −0.477233 + 0.826592i −0.999660 0.0260926i \(-0.991694\pi\)
0.522427 + 0.852684i \(0.325027\pi\)
\(572\) 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 −0.498722 0.866762i \(-0.666197\pi\)
0.501277 + 0.865287i \(0.332864\pi\)
\(588\) 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 \(-0.949584\pi\)
0.987483 0.157725i \(-0.0504159\pi\)
\(594\) 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 0.0327992 0.999462i \(-0.489558\pi\)
−0.849160 + 0.528136i \(0.822891\pi\)
\(600\) 0 0
\(601\) −230.500 399.238i −0.383527 0.664289i 0.608036 0.793909i \(-0.291958\pi\)
−0.991564 + 0.129620i \(0.958624\pi\)
\(602\) 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 −0.816204 0.577765i \(-0.803925\pi\)
0.908461 + 0.417971i \(0.137259\pi\)
\(608\) −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 0.728044 0.685530i \(-0.240430\pi\)
−0.229665 + 0.973270i \(0.573763\pi\)
\(618\) 0 0
\(619\) 399.500 + 691.954i 0.645396 + 1.11786i 0.984210 + 0.177005i \(0.0566409\pi\)
−0.338814 + 0.940853i \(0.610026\pi\)
\(620\) 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 −0.224129 0.974560i \(-0.571954\pi\)
0.731929 + 0.681381i \(0.238620\pi\)
\(642\) 0 0
\(643\) 6.50000 11.2583i 0.0101089 0.0175091i −0.860927 0.508729i \(-0.830116\pi\)
0.871036 + 0.491220i \(0.163449\pi\)
\(644\) 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 \(-0.882298\pi\)
0.932410 0.361402i \(-0.117702\pi\)
\(648\) 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 0.228264 0.973599i \(-0.426695\pi\)
−0.729030 + 0.684482i \(0.760028\pi\)
\(654\) 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 0.313706 0.949520i \(-0.398429\pi\)
0.979162 + 0.203082i \(0.0650959\pi\)
\(660\) 0 0
\(661\) 191.000 330.822i 0.288956 0.500487i −0.684605 0.728915i \(-0.740025\pi\)
0.973561 + 0.228428i \(0.0733585\pi\)
\(662\) −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 0.567401 0.823441i \(-0.307949\pi\)
−0.996822 + 0.0796633i \(0.974615\pi\)
\(674\) 133.368i 0.197875i
\(675\) 0 0
\(676\) −153.000 −0.226331
\(677\) −606.000 + 349.874i −0.895126 + 0.516801i −0.875616 0.483009i \(-0.839544\pi\)
−0.0195100 + 0.999810i \(0.506211\pi\)
\(678\) 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 \(0.277057\pi\)
−0.644520 + 0.764588i \(0.722943\pi\)
\(684\) 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 0.792636 0.609695i \(-0.208708\pi\)
−0.924329 + 0.381596i \(0.875375\pi\)
\(692\) 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 0.999973 0.00731341i \(-0.00232795\pi\)
−0.506320 + 0.862346i \(0.668995\pi\)
\(710\) 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 \(0.135147\pi\)
−0.911214 + 0.411934i \(0.864853\pi\)
\(720\) 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 0.998783 0.0493289i \(-0.0157082\pi\)
−0.542111 + 0.840307i \(0.682375\pi\)
\(728\) 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 −0.541776 0.840523i \(-0.682248\pi\)
0.998802 + 0.0489306i \(0.0155813\pi\)
\(734\) 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 0.815762 0.578387i \(-0.196318\pi\)
−0.0930168 + 0.995665i \(0.529651\pi\)
\(744\) 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 −0.0124237 + 0.999923i \(0.503955\pi\)
−0.859747 + 0.510721i \(0.829379\pi\)
\(752\) 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 0.0763232 0.997083i \(-0.475682\pi\)
−0.825338 + 0.564639i \(0.809015\pi\)
\(762\) 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 0.314921 + 0.949118i \(0.398022\pi\)
−0.979421 + 0.201829i \(0.935312\pi\)
\(770\) 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 \(-0.722088\pi\)
0.642465 0.766315i \(-0.277912\pi\)
\(774\) 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 −0.821771 0.569819i \(-0.807013\pi\)
0.904363 + 0.426765i \(0.140347\pi\)
\(788\) 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 0.318858 0.947803i \(-0.396701\pi\)
−0.661392 + 0.750040i \(0.730034\pi\)
\(798\) 0 0
\(799\) −378.000 654.715i −0.473091 0.819418i
\(800\) 202.650i 0.253312i