Properties

Label 1050.2.bc.d.607.1
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.d.493.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(0.258819 + 0.965926i) q^{12} +(1.60368 + 1.60368i) q^{13} +(-2.59808 + 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.517638 + 0.138701i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.86603 - 4.96410i) q^{19} +(-0.866025 + 2.50000i) q^{21} +(0.707107 + 0.707107i) q^{22} +(2.05197 + 7.65806i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.96410 - 1.13397i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.38014 - 1.15539i) q^{28} -6.92820i q^{29} +(-0.464102 + 0.267949i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.965926 - 0.258819i) q^{33} -0.535898 q^{34} -1.00000 q^{36} +(9.58991 - 2.56961i) q^{37} +(-1.48356 + 5.53674i) q^{38} +(-1.96410 + 1.13397i) q^{39} +5.73205i q^{41} +(0.189469 - 2.63896i) q^{42} +(-3.48477 + 3.48477i) q^{43} +(-0.866025 - 0.500000i) q^{44} +(-3.96410 - 6.86603i) q^{46} +(-2.38014 - 8.88280i) q^{47} +(0.707107 + 0.707107i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-0.267949 + 0.464102i) q^{51} +(2.19067 + 0.586988i) q^{52} +(-0.965926 - 0.258819i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} +(4.05317 + 4.05317i) q^{57} +(1.79315 + 6.69213i) q^{58} +(2.26795 + 3.92820i) q^{59} +(3.92820 + 2.26795i) q^{61} +(0.378937 - 0.378937i) q^{62} +(-2.19067 - 1.48356i) q^{63} -1.00000i q^{64} +(-0.866025 + 0.500000i) q^{66} +(-0.517638 + 1.93185i) q^{67} +(0.517638 - 0.138701i) q^{68} -7.92820 q^{69} +4.92820 q^{71} +(0.965926 - 0.258819i) q^{72} +(-1.03528 + 3.86370i) q^{73} +(-8.59808 + 4.96410i) q^{74} -5.73205i q^{76} +(-1.15539 - 2.38014i) q^{77} +(1.60368 - 1.60368i) q^{78} +(14.6603 + 8.46410i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-1.48356 - 5.53674i) q^{82} +(7.34847 + 7.34847i) q^{83} +(0.500000 + 2.59808i) q^{84} +(2.46410 - 4.26795i) q^{86} +(6.69213 + 1.79315i) q^{87} +(0.965926 + 0.258819i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(3.92820 + 4.53590i) q^{91} +(5.60609 + 5.60609i) q^{92} +(-0.138701 - 0.517638i) q^{93} +(4.59808 + 7.96410i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(-7.72741 + 7.72741i) q^{97} +(-6.95095 + 0.827225i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 4q^{11} + 4q^{16} + 16q^{19} - 4q^{24} + 12q^{26} + 24q^{31} - 32q^{34} - 8q^{36} + 12q^{39} - 4q^{46} - 16q^{51} - 4q^{54} - 16q^{56} + 32q^{59} - 24q^{61} - 8q^{69} - 16q^{71} - 48q^{74} + 48q^{79} + 4q^{81} + 4q^{84} - 8q^{86} - 24q^{91} + 16q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.63896 + 0.189469i 0.997433 + 0.0716124i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) 1.60368 + 1.60368i 0.444781 + 0.444781i 0.893615 0.448834i \(-0.148160\pi\)
−0.448834 + 0.893615i \(0.648160\pi\)
\(14\) −2.59808 + 0.500000i −0.694365 + 0.133631i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.517638 + 0.138701i 0.125546 + 0.0336399i 0.321045 0.947064i \(-0.395966\pi\)
−0.195499 + 0.980704i \(0.562633\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) 2.86603 4.96410i 0.657511 1.13884i −0.323747 0.946144i \(-0.604943\pi\)
0.981258 0.192699i \(-0.0617242\pi\)
\(20\) 0 0
\(21\) −0.866025 + 2.50000i −0.188982 + 0.545545i
\(22\) 0.707107 + 0.707107i 0.150756 + 0.150756i
\(23\) 2.05197 + 7.65806i 0.427865 + 1.59682i 0.757585 + 0.652736i \(0.226379\pi\)
−0.329720 + 0.944079i \(0.606954\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −1.96410 1.13397i −0.385192 0.222391i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 2.38014 1.15539i 0.449804 0.218349i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) 0 0
\(31\) −0.464102 + 0.267949i −0.0833551 + 0.0481251i −0.541098 0.840959i \(-0.681991\pi\)
0.457743 + 0.889085i \(0.348658\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) 0.965926 0.258819i 0.168146 0.0450546i
\(34\) −0.535898 −0.0919058
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 9.58991 2.56961i 1.57657 0.422441i 0.638709 0.769449i \(-0.279469\pi\)
0.937862 + 0.347008i \(0.112802\pi\)
\(38\) −1.48356 + 5.53674i −0.240666 + 0.898177i
\(39\) −1.96410 + 1.13397i −0.314508 + 0.181581i
\(40\) 0 0
\(41\) 5.73205i 0.895196i 0.894235 + 0.447598i \(0.147720\pi\)
−0.894235 + 0.447598i \(0.852280\pi\)
\(42\) 0.189469 2.63896i 0.0292357 0.407200i
\(43\) −3.48477 + 3.48477i −0.531422 + 0.531422i −0.920995 0.389574i \(-0.872622\pi\)
0.389574 + 0.920995i \(0.372622\pi\)
\(44\) −0.866025 0.500000i −0.130558 0.0753778i
\(45\) 0 0
\(46\) −3.96410 6.86603i −0.584475 1.01234i
\(47\) −2.38014 8.88280i −0.347179 1.29569i −0.890046 0.455871i \(-0.849328\pi\)
0.542867 0.839819i \(-0.317339\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 0 0
\(51\) −0.267949 + 0.464102i −0.0375204 + 0.0649872i
\(52\) 2.19067 + 0.586988i 0.303791 + 0.0814007i
\(53\) −0.965926 0.258819i −0.132680 0.0355515i 0.191868 0.981421i \(-0.438546\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 4.05317 + 4.05317i 0.536856 + 0.536856i
\(58\) 1.79315 + 6.69213i 0.235452 + 0.878720i
\(59\) 2.26795 + 3.92820i 0.295262 + 0.511409i 0.975046 0.222004i \(-0.0712598\pi\)
−0.679784 + 0.733412i \(0.737926\pi\)
\(60\) 0 0
\(61\) 3.92820 + 2.26795i 0.502955 + 0.290381i 0.729933 0.683519i \(-0.239551\pi\)
−0.226978 + 0.973900i \(0.572885\pi\)
\(62\) 0.378937 0.378937i 0.0481251 0.0481251i
\(63\) −2.19067 1.48356i −0.275999 0.186911i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −0.866025 + 0.500000i −0.106600 + 0.0615457i
\(67\) −0.517638 + 1.93185i −0.0632396 + 0.236013i −0.990310 0.138874i \(-0.955652\pi\)
0.927071 + 0.374887i \(0.122318\pi\)
\(68\) 0.517638 0.138701i 0.0627728 0.0168199i
\(69\) −7.92820 −0.954444
\(70\) 0 0
\(71\) 4.92820 0.584870 0.292435 0.956285i \(-0.405534\pi\)
0.292435 + 0.956285i \(0.405534\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) −1.03528 + 3.86370i −0.121170 + 0.452212i −0.999674 0.0255221i \(-0.991875\pi\)
0.878504 + 0.477734i \(0.158542\pi\)
\(74\) −8.59808 + 4.96410i −0.999506 + 0.577065i
\(75\) 0 0
\(76\) 5.73205i 0.657511i
\(77\) −1.15539 2.38014i −0.131669 0.271242i
\(78\) 1.60368 1.60368i 0.181581 0.181581i
\(79\) 14.6603 + 8.46410i 1.64941 + 0.952286i 0.977308 + 0.211825i \(0.0679408\pi\)
0.672100 + 0.740460i \(0.265393\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −1.48356 5.53674i −0.163832 0.611430i
\(83\) 7.34847 + 7.34847i 0.806599 + 0.806599i 0.984118 0.177518i \(-0.0568069\pi\)
−0.177518 + 0.984118i \(0.556807\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) 0 0
\(86\) 2.46410 4.26795i 0.265711 0.460225i
\(87\) 6.69213 + 1.79315i 0.717472 + 0.192246i
\(88\) 0.965926 + 0.258819i 0.102968 + 0.0275902i
\(89\) −3.46410 + 6.00000i −0.367194 + 0.635999i −0.989126 0.147073i \(-0.953015\pi\)
0.621932 + 0.783072i \(0.286348\pi\)
\(90\) 0 0
\(91\) 3.92820 + 4.53590i 0.411788 + 0.475491i
\(92\) 5.60609 + 5.60609i 0.584475 + 0.584475i
\(93\) −0.138701 0.517638i −0.0143826 0.0536766i
\(94\) 4.59808 + 7.96410i 0.474255 + 0.821434i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) −7.72741 + 7.72741i −0.784599 + 0.784599i −0.980603 0.196004i \(-0.937203\pi\)
0.196004 + 0.980603i \(0.437203\pi\)
\(98\) −6.95095 + 0.827225i −0.702152 + 0.0835624i
\(99\) 1.00000i 0.100504i
\(100\) 0 0
\(101\) −12.9282 + 7.46410i −1.28640 + 0.742706i −0.978011 0.208553i \(-0.933125\pi\)
−0.308393 + 0.951259i \(0.599791\pi\)
\(102\) 0.138701 0.517638i 0.0137334 0.0512538i
\(103\) −2.31079 + 0.619174i −0.227689 + 0.0610090i −0.370860 0.928689i \(-0.620937\pi\)
0.143171 + 0.989698i \(0.454270\pi\)
\(104\) −2.26795 −0.222391
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) −1.03528 + 0.277401i −0.100084 + 0.0268174i −0.308513 0.951220i \(-0.599831\pi\)
0.208430 + 0.978037i \(0.433165\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) 2.66025 1.53590i 0.254806 0.147112i −0.367157 0.930159i \(-0.619669\pi\)
0.621963 + 0.783047i \(0.286335\pi\)
\(110\) 0 0
\(111\) 9.92820i 0.942343i
\(112\) 1.48356 2.19067i 0.140184 0.206999i
\(113\) −0.656339 + 0.656339i −0.0617432 + 0.0617432i −0.737304 0.675561i \(-0.763902\pi\)
0.675561 + 0.737304i \(0.263902\pi\)
\(114\) −4.96410 2.86603i −0.464931 0.268428i
\(115\) 0 0
\(116\) −3.46410 6.00000i −0.321634 0.557086i
\(117\) −0.586988 2.19067i −0.0542671 0.202528i
\(118\) −3.20736 3.20736i −0.295262 0.295262i
\(119\) 1.33975 + 0.464102i 0.122814 + 0.0425441i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) −4.38134 1.17398i −0.396668 0.106287i
\(123\) −5.53674 1.48356i −0.499231 0.133768i
\(124\) −0.267949 + 0.464102i −0.0240625 + 0.0416776i
\(125\) 0 0
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) 3.53553 + 3.53553i 0.313728 + 0.313728i 0.846352 0.532624i \(-0.178794\pi\)
−0.532624 + 0.846352i \(0.678794\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −2.46410 4.26795i −0.216952 0.375772i
\(130\) 0 0
\(131\) 17.4282 + 10.0622i 1.52271 + 0.879137i 0.999640 + 0.0268466i \(0.00854657\pi\)
0.523070 + 0.852290i \(0.324787\pi\)
\(132\) 0.707107 0.707107i 0.0615457 0.0615457i
\(133\) 8.50386 12.5570i 0.737379 1.08883i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) −0.464102 + 0.267949i −0.0397964 + 0.0229765i
\(137\) 1.31268 4.89898i 0.112150 0.418548i −0.886908 0.461946i \(-0.847152\pi\)
0.999058 + 0.0433975i \(0.0138182\pi\)
\(138\) 7.65806 2.05197i 0.651897 0.174675i
\(139\) 10.3923 0.881464 0.440732 0.897639i \(-0.354719\pi\)
0.440732 + 0.897639i \(0.354719\pi\)
\(140\) 0 0
\(141\) 9.19615 0.774456
\(142\) −4.76028 + 1.27551i −0.399474 + 0.107039i
\(143\) 0.586988 2.19067i 0.0490864 0.183193i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 4.00000i 0.331042i
\(147\) −2.75908 + 6.43331i −0.227565 + 0.530611i
\(148\) 7.02030 7.02030i 0.577065 0.577065i
\(149\) −11.1962 6.46410i −0.917225 0.529560i −0.0344760 0.999406i \(-0.510976\pi\)
−0.882749 + 0.469846i \(0.844310\pi\)
\(150\) 0 0
\(151\) −11.9282 20.6603i −0.970703 1.68131i −0.693441 0.720513i \(-0.743906\pi\)
−0.277262 0.960794i \(-0.589427\pi\)
\(152\) 1.48356 + 5.53674i 0.120333 + 0.449089i
\(153\) −0.378937 0.378937i −0.0306353 0.0306353i
\(154\) 1.73205 + 2.00000i 0.139573 + 0.161165i
\(155\) 0 0
\(156\) −1.13397 + 1.96410i −0.0907906 + 0.157254i
\(157\) −12.2289 3.27671i −0.975970 0.261510i −0.264623 0.964352i \(-0.585248\pi\)
−0.711346 + 0.702842i \(0.751914\pi\)
\(158\) −16.3514 4.38134i −1.30085 0.348561i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) 0 0
\(161\) 3.96410 + 20.5981i 0.312415 + 1.62336i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 3.10583 + 11.5911i 0.243267 + 0.907886i 0.974246 + 0.225486i \(0.0723970\pi\)
−0.730979 + 0.682400i \(0.760936\pi\)
\(164\) 2.86603 + 4.96410i 0.223799 + 0.387631i
\(165\) 0 0
\(166\) −9.00000 5.19615i −0.698535 0.403300i
\(167\) −12.1595 + 12.1595i −0.940932 + 0.940932i −0.998350 0.0574186i \(-0.981713\pi\)
0.0574186 + 0.998350i \(0.481713\pi\)
\(168\) −1.15539 2.38014i −0.0891406 0.183632i
\(169\) 7.85641i 0.604339i
\(170\) 0 0
\(171\) −4.96410 + 2.86603i −0.379614 + 0.219170i
\(172\) −1.27551 + 4.76028i −0.0972569 + 0.362968i
\(173\) 22.7847 6.10514i 1.73229 0.464165i 0.751580 0.659642i \(-0.229292\pi\)
0.980708 + 0.195476i \(0.0626253\pi\)
\(174\) −6.92820 −0.525226
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −4.38134 + 1.17398i −0.329322 + 0.0882415i
\(178\) 1.79315 6.69213i 0.134402 0.501596i
\(179\) −7.79423 + 4.50000i −0.582568 + 0.336346i −0.762153 0.647397i \(-0.775858\pi\)
0.179585 + 0.983742i \(0.442524\pi\)
\(180\) 0 0
\(181\) 6.39230i 0.475136i −0.971371 0.237568i \(-0.923650\pi\)
0.971371 0.237568i \(-0.0763503\pi\)
\(182\) −4.96833 3.36465i −0.368277 0.249404i
\(183\) −3.20736 + 3.20736i −0.237095 + 0.237095i
\(184\) −6.86603 3.96410i −0.506170 0.292237i
\(185\) 0 0
\(186\) 0.267949 + 0.464102i 0.0196470 + 0.0340296i
\(187\) −0.138701 0.517638i −0.0101428 0.0378534i
\(188\) −6.50266 6.50266i −0.474255 0.474255i
\(189\) 2.00000 1.73205i 0.145479 0.125988i
\(190\) 0 0
\(191\) 5.46410 9.46410i 0.395369 0.684798i −0.597780 0.801660i \(-0.703950\pi\)
0.993148 + 0.116862i \(0.0372836\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) −18.1445 4.86181i −1.30607 0.349961i −0.462329 0.886708i \(-0.652986\pi\)
−0.843743 + 0.536747i \(0.819653\pi\)
\(194\) 5.46410 9.46410i 0.392300 0.679483i
\(195\) 0 0
\(196\) 6.50000 2.59808i 0.464286 0.185577i
\(197\) −7.67664 7.67664i −0.546938 0.546938i 0.378616 0.925554i \(-0.376400\pi\)
−0.925554 + 0.378616i \(0.876400\pi\)
\(198\) −0.258819 0.965926i −0.0183935 0.0686454i
\(199\) 9.73205 + 16.8564i 0.689887 + 1.19492i 0.971874 + 0.235501i \(0.0756730\pi\)
−0.281987 + 0.959418i \(0.590994\pi\)
\(200\) 0 0
\(201\) −1.73205 1.00000i −0.122169 0.0705346i
\(202\) 10.5558 10.5558i 0.742706 0.742706i
\(203\) 1.31268 18.2832i 0.0921319 1.28323i
\(204\) 0.535898i 0.0375204i
\(205\) 0 0
\(206\) 2.07180 1.19615i 0.144349 0.0833399i
\(207\) 2.05197 7.65806i 0.142622 0.532272i
\(208\) 2.19067 0.586988i 0.151896 0.0407003i
\(209\) −5.73205 −0.396494
\(210\) 0 0
\(211\) 21.7846 1.49971 0.749857 0.661600i \(-0.230122\pi\)
0.749857 + 0.661600i \(0.230122\pi\)
\(212\) −0.965926 + 0.258819i −0.0663401 + 0.0177758i
\(213\) −1.27551 + 4.76028i −0.0873967 + 0.326169i
\(214\) 0.928203 0.535898i 0.0634507 0.0366333i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −1.27551 + 0.619174i −0.0865875 + 0.0420323i
\(218\) −2.17209 + 2.17209i −0.147112 + 0.147112i
\(219\) −3.46410 2.00000i −0.234082 0.135147i
\(220\) 0 0
\(221\) 0.607695 + 1.05256i 0.0408780 + 0.0708028i
\(222\) −2.56961 9.58991i −0.172461 0.643632i
\(223\) −17.9043 17.9043i −1.19896 1.19896i −0.974478 0.224483i \(-0.927931\pi\)
−0.224483 0.974478i \(-0.572069\pi\)
\(224\) −0.866025 + 2.50000i −0.0578638 + 0.167038i
\(225\) 0 0
\(226\) 0.464102 0.803848i 0.0308716 0.0534711i
\(227\) 3.34607 + 0.896575i 0.222086 + 0.0595078i 0.368146 0.929768i \(-0.379993\pi\)
−0.146060 + 0.989276i \(0.546659\pi\)
\(228\) 5.53674 + 1.48356i 0.366679 + 0.0982514i
\(229\) 5.46410 9.46410i 0.361078 0.625405i −0.627061 0.778971i \(-0.715742\pi\)
0.988139 + 0.153565i \(0.0490755\pi\)
\(230\) 0 0
\(231\) 2.59808 0.500000i 0.170941 0.0328976i
\(232\) 4.89898 + 4.89898i 0.321634 + 0.321634i
\(233\) −6.69213 24.9754i −0.438416 1.63619i −0.732757 0.680490i \(-0.761767\pi\)
0.294341 0.955700i \(-0.404900\pi\)
\(234\) 1.13397 + 1.96410i 0.0741302 + 0.128397i
\(235\) 0 0
\(236\) 3.92820 + 2.26795i 0.255704 + 0.147631i
\(237\) −11.9700 + 11.9700i −0.777538 + 0.777538i
\(238\) −1.41421 0.101536i −0.0916698 0.00658160i
\(239\) 24.0000i 1.55243i −0.630468 0.776215i \(-0.717137\pi\)
0.630468 0.776215i \(-0.282863\pi\)
\(240\) 0 0
\(241\) −22.2846 + 12.8660i −1.43548 + 0.828774i −0.997531 0.0702273i \(-0.977628\pi\)
−0.437947 + 0.899001i \(0.644294\pi\)
\(242\) −2.58819 + 9.65926i −0.166375 + 0.620921i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) 4.53590 0.290381
\(245\) 0 0
\(246\) 5.73205 0.365462
\(247\) 12.5570 3.36465i 0.798985 0.214087i
\(248\) 0.138701 0.517638i 0.00880750 0.0328701i
\(249\) −9.00000 + 5.19615i −0.570352 + 0.329293i
\(250\) 0 0
\(251\) 24.6603i 1.55654i −0.627929 0.778271i \(-0.716097\pi\)
0.627929 0.778271i \(-0.283903\pi\)
\(252\) −2.63896 0.189469i −0.166239 0.0119354i
\(253\) 5.60609 5.60609i 0.352452 0.352452i
\(254\) −4.33013 2.50000i −0.271696 0.156864i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.76028 17.7656i −0.296938 1.10819i −0.939666 0.342093i \(-0.888864\pi\)
0.642728 0.766094i \(-0.277803\pi\)
\(258\) 3.48477 + 3.48477i 0.216952 + 0.216952i
\(259\) 25.7942 4.96410i 1.60278 0.308454i
\(260\) 0 0
\(261\) −3.46410 + 6.00000i −0.214423 + 0.371391i
\(262\) −19.4386 5.20857i −1.20092 0.321786i
\(263\) 2.07055 + 0.554803i 0.127676 + 0.0342106i 0.322091 0.946709i \(-0.395614\pi\)
−0.194415 + 0.980919i \(0.562281\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 0 0
\(266\) −4.96410 + 14.3301i −0.304369 + 0.878636i
\(267\) −4.89898 4.89898i −0.299813 0.299813i
\(268\) 0.517638 + 1.93185i 0.0316198 + 0.118007i
\(269\) 4.66025 + 8.07180i 0.284141 + 0.492146i 0.972400 0.233318i \(-0.0749584\pi\)
−0.688260 + 0.725464i \(0.741625\pi\)
\(270\) 0 0
\(271\) −6.92820 4.00000i −0.420858 0.242983i 0.274586 0.961563i \(-0.411459\pi\)
−0.695444 + 0.718580i \(0.744792\pi\)
\(272\) 0.378937 0.378937i 0.0229765 0.0229765i
\(273\) −5.39804 + 2.62038i −0.326704 + 0.158592i
\(274\) 5.07180i 0.306398i
\(275\) 0 0
\(276\) −6.86603 + 3.96410i −0.413286 + 0.238611i
\(277\) −5.69402 + 21.2504i −0.342120 + 1.27681i 0.553820 + 0.832636i \(0.313170\pi\)
−0.895940 + 0.444174i \(0.853497\pi\)
\(278\) −10.0382 + 2.68973i −0.602051 + 0.161319i
\(279\) 0.535898 0.0320834
\(280\) 0 0
\(281\) −14.0718 −0.839453 −0.419727 0.907651i \(-0.637874\pi\)
−0.419727 + 0.907651i \(0.637874\pi\)
\(282\) −8.88280 + 2.38014i −0.528963 + 0.141735i
\(283\) 5.03768 18.8009i 0.299459 1.11760i −0.638152 0.769910i \(-0.720301\pi\)
0.937611 0.347686i \(-0.113032\pi\)
\(284\) 4.26795 2.46410i 0.253256 0.146218i
\(285\) 0 0
\(286\) 2.26795i 0.134107i
\(287\) −1.08604 + 15.1266i −0.0641072 + 0.892898i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) −14.4737 8.35641i −0.851395 0.491553i
\(290\) 0 0
\(291\) −5.46410 9.46410i −0.320311 0.554795i
\(292\) 1.03528 + 3.86370i 0.0605850 + 0.226106i
\(293\) 1.22474 + 1.22474i 0.0715504 + 0.0715504i 0.741976 0.670426i \(-0.233889\pi\)
−0.670426 + 0.741976i \(0.733889\pi\)
\(294\) 1.00000 6.92820i 0.0583212 0.404061i
\(295\) 0 0
\(296\) −4.96410 + 8.59808i −0.288533 + 0.499753i
\(297\) −0.965926 0.258819i −0.0560487 0.0150182i
\(298\) 12.4877 + 3.34607i 0.723392 + 0.193832i
\(299\) −8.99038 + 15.5718i −0.519927 + 0.900540i
\(300\) 0 0
\(301\) −9.85641 + 8.53590i −0.568114 + 0.492001i
\(302\) 16.8690 + 16.8690i 0.970703 + 0.970703i
\(303\) −3.86370 14.4195i −0.221964 0.828381i
\(304\) −2.86603 4.96410i −0.164378 0.284711i
\(305\) 0 0
\(306\) 0.464102 + 0.267949i 0.0265309 + 0.0153176i
\(307\) −1.13681 + 1.13681i −0.0648813 + 0.0648813i −0.738803 0.673922i \(-0.764609\pi\)
0.673922 + 0.738803i \(0.264609\pi\)
\(308\) −2.19067 1.48356i −0.124825 0.0845339i
\(309\) 2.39230i 0.136093i
\(310\) 0 0
\(311\) −23.7846 + 13.7321i −1.34870 + 0.778673i −0.988066 0.154034i \(-0.950774\pi\)
−0.360636 + 0.932707i \(0.617440\pi\)
\(312\) 0.586988 2.19067i 0.0332317 0.124022i
\(313\) −30.1146 + 8.06918i −1.70218 + 0.456097i −0.973486 0.228746i \(-0.926538\pi\)
−0.728691 + 0.684843i \(0.759871\pi\)
\(314\) 12.6603 0.714459
\(315\) 0 0
\(316\) 16.9282 0.952286
\(317\) 13.5230 3.62347i 0.759525 0.203514i 0.141786 0.989897i \(-0.454715\pi\)
0.617739 + 0.786383i \(0.288049\pi\)
\(318\) −0.258819 + 0.965926i −0.0145139 + 0.0541664i
\(319\) −6.00000 + 3.46410i −0.335936 + 0.193952i
\(320\) 0 0
\(321\) 1.07180i 0.0598219i
\(322\) −9.16020 18.8702i −0.510478 1.05160i
\(323\) 2.17209 2.17209i 0.120858 0.120858i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) 0.795040 + 2.96713i 0.0439658 + 0.164083i
\(328\) −4.05317 4.05317i −0.223799 0.223799i
\(329\) −4.59808 23.8923i −0.253500 1.31723i
\(330\) 0 0
\(331\) 7.89230 13.6699i 0.433800 0.751364i −0.563397 0.826187i \(-0.690506\pi\)
0.997197 + 0.0748224i \(0.0238390\pi\)
\(332\) 10.0382 + 2.68973i 0.550918 + 0.147618i
\(333\) −9.58991 2.56961i −0.525524 0.140814i
\(334\) 8.59808 14.8923i 0.470466 0.814871i
\(335\) 0 0
\(336\) 1.73205 + 2.00000i 0.0944911 + 0.109109i
\(337\) −17.6269 17.6269i −0.960199 0.960199i 0.0390392 0.999238i \(-0.487570\pi\)
−0.999238 + 0.0390392i \(0.987570\pi\)
\(338\) 2.03339 + 7.58871i 0.110602 + 0.412771i
\(339\) −0.464102 0.803848i −0.0252065 0.0436590i
\(340\) 0 0
\(341\) 0.464102 + 0.267949i 0.0251325 + 0.0145103i
\(342\) 4.05317 4.05317i 0.219170 0.219170i
\(343\) 18.0938 + 3.95164i 0.976972 + 0.213368i
\(344\) 4.92820i 0.265711i
\(345\) 0 0
\(346\) −20.4282 + 11.7942i −1.09823 + 0.634062i
\(347\) 2.82843 10.5558i 0.151838 0.566667i −0.847517 0.530767i \(-0.821904\pi\)
0.999355 0.0358994i \(-0.0114296\pi\)
\(348\) 6.69213 1.79315i 0.358736 0.0961230i
\(349\) −25.8564 −1.38406 −0.692031 0.721868i \(-0.743284\pi\)
−0.692031 + 0.721868i \(0.743284\pi\)
\(350\) 0 0
\(351\) 2.26795 0.121054
\(352\) 0.965926 0.258819i 0.0514840 0.0137951i
\(353\) 1.79315 6.69213i 0.0954398 0.356186i −0.901646 0.432475i \(-0.857640\pi\)
0.997086 + 0.0762887i \(0.0243071\pi\)
\(354\) 3.92820 2.26795i 0.208782 0.120540i
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) −0.795040 + 1.17398i −0.0420780 + 0.0621334i
\(358\) 6.36396 6.36396i 0.336346 0.336346i
\(359\) 16.3923 + 9.46410i 0.865153 + 0.499496i 0.865734 0.500504i \(-0.166852\pi\)
−0.000581665 1.00000i \(0.500185\pi\)
\(360\) 0 0
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 1.65445 + 6.17449i 0.0869560 + 0.324524i
\(363\) 7.07107 + 7.07107i 0.371135 + 0.371135i
\(364\) 5.66987 + 1.96410i 0.297182 + 0.102947i
\(365\) 0 0
\(366\) 2.26795 3.92820i 0.118548 0.205330i
\(367\) −14.0220 3.75719i −0.731943 0.196124i −0.126449 0.991973i \(-0.540358\pi\)
−0.605494 + 0.795849i \(0.707025\pi\)
\(368\) 7.65806 + 2.05197i 0.399204 + 0.106966i
\(369\) 2.86603 4.96410i 0.149199 0.258421i
\(370\) 0 0
\(371\) −2.50000 0.866025i −0.129794 0.0449618i
\(372\) −0.378937 0.378937i −0.0196470 0.0196470i
\(373\) 6.72930 + 25.1141i 0.348430 + 1.30036i 0.888554 + 0.458772i \(0.151711\pi\)
−0.540124 + 0.841585i \(0.681623\pi\)
\(374\) 0.267949 + 0.464102i 0.0138553 + 0.0239981i
\(375\) 0 0
\(376\) 7.96410 + 4.59808i 0.410717 + 0.237128i
\(377\) 11.1106 11.1106i 0.572227 0.572227i
\(378\) −1.48356 + 2.19067i −0.0763063 + 0.112676i
\(379\) 9.92820i 0.509978i 0.966944 + 0.254989i \(0.0820718\pi\)
−0.966944 + 0.254989i \(0.917928\pi\)
\(380\) 0 0
\(381\) −4.33013 + 2.50000i −0.221839 + 0.128079i
\(382\) −2.82843 + 10.5558i −0.144715 + 0.540083i
\(383\) 28.9592 7.75959i 1.47975 0.396497i 0.573485 0.819216i \(-0.305591\pi\)
0.906261 + 0.422719i \(0.138924\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 18.7846 0.956111
\(387\) 4.76028 1.27551i 0.241979 0.0648380i
\(388\) −2.82843 + 10.5558i −0.143592 + 0.535891i
\(389\) −28.2679 + 16.3205i −1.43324 + 0.827483i −0.997367 0.0725245i \(-0.976894\pi\)
−0.435875 + 0.900007i \(0.643561\pi\)
\(390\) 0 0
\(391\) 4.24871i 0.214867i
\(392\) −5.60609 + 4.19187i −0.283150 + 0.211722i
\(393\) −14.2301 + 14.2301i −0.717812 + 0.717812i
\(394\) 9.40192 + 5.42820i 0.473662 + 0.273469i
\(395\) 0 0
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) 3.30890 + 12.3490i 0.166069 + 0.619778i 0.997901 + 0.0647510i \(0.0206253\pi\)
−0.831832 + 0.555027i \(0.812708\pi\)
\(398\) −13.7632 13.7632i −0.689887 0.689887i
\(399\) 9.92820 + 11.4641i 0.497032 + 0.573923i
\(400\) 0 0
\(401\) 5.96410 10.3301i 0.297833 0.515862i −0.677807 0.735240i \(-0.737069\pi\)
0.975640 + 0.219378i \(0.0704028\pi\)
\(402\) 1.93185 + 0.517638i 0.0963520 + 0.0258174i
\(403\) −1.17398 0.314566i −0.0584800 0.0156697i
\(404\) −7.46410 + 12.9282i −0.371353 + 0.643202i
\(405\) 0 0
\(406\) 3.46410 + 18.0000i 0.171920 + 0.893325i
\(407\) −7.02030 7.02030i −0.347983 0.347983i
\(408\) −0.138701 0.517638i −0.00686671 0.0256269i
\(409\) −6.39230 11.0718i −0.316079 0.547465i 0.663587 0.748099i \(-0.269033\pi\)
−0.979666 + 0.200634i \(0.935700\pi\)
\(410\) 0 0
\(411\) 4.39230 + 2.53590i 0.216656 + 0.125087i
\(412\) −1.69161 + 1.69161i −0.0833399 + 0.0833399i
\(413\) 5.24075 + 10.7961i 0.257881 + 0.531240i
\(414\) 7.92820i 0.389650i
\(415\) 0 0
\(416\) −1.96410 + 1.13397i −0.0962980 + 0.0555977i
\(417\) −2.68973 + 10.0382i −0.131716 + 0.491573i
\(418\) 5.53674 1.48356i 0.270811 0.0725635i
\(419\) 27.0526 1.32160 0.660802 0.750560i \(-0.270216\pi\)
0.660802 + 0.750560i \(0.270216\pi\)
\(420\) 0 0
\(421\) 13.8564 0.675320 0.337660 0.941268i \(-0.390365\pi\)
0.337660 + 0.941268i \(0.390365\pi\)
\(422\) −21.0423 + 5.63827i −1.02432 + 0.274467i
\(423\) −2.38014 + 8.88280i −0.115726 + 0.431897i
\(424\) 0.866025 0.500000i 0.0420579 0.0242821i
\(425\) 0 0
\(426\) 4.92820i 0.238772i
\(427\) 9.93666 + 6.72930i 0.480869 + 0.325653i
\(428\) −0.757875 + 0.757875i −0.0366333 + 0.0366333i
\(429\) 1.96410 + 1.13397i 0.0948277 + 0.0547488i
\(430\) 0 0
\(431\) −10.8564 18.8038i −0.522935 0.905749i −0.999644 0.0266884i \(-0.991504\pi\)
0.476709 0.879061i \(-0.341830\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) 11.3137 + 11.3137i 0.543702 + 0.543702i 0.924612 0.380910i \(-0.124389\pi\)
−0.380910 + 0.924612i \(0.624389\pi\)
\(434\) 1.07180 0.928203i 0.0514479 0.0445552i
\(435\) 0 0
\(436\) 1.53590 2.66025i 0.0735562 0.127403i
\(437\) 43.8964 + 11.7620i 2.09985 + 0.562653i
\(438\) 3.86370 + 1.03528i 0.184615 + 0.0494674i
\(439\) −10.0000 + 17.3205i −0.477274 + 0.826663i −0.999661 0.0260459i \(-0.991708\pi\)
0.522387 + 0.852709i \(0.325042\pi\)
\(440\) 0 0
\(441\) −5.50000 4.33013i −0.261905 0.206197i
\(442\) −0.859411 0.859411i −0.0408780 0.0408780i
\(443\) −0.0371647 0.138701i −0.00176575 0.00658987i 0.965037 0.262112i \(-0.0844191\pi\)
−0.966803 + 0.255523i \(0.917752\pi\)
\(444\) 4.96410 + 8.59808i 0.235586 + 0.408047i
\(445\) 0 0
\(446\) 21.9282 + 12.6603i 1.03833 + 0.599480i
\(447\) 9.14162 9.14162i 0.432384 0.432384i
\(448\) 0.189469 2.63896i 0.00895155 0.124679i
\(449\) 0.0717968i 0.00338830i −0.999999 0.00169415i \(-0.999461\pi\)
0.999999 0.00169415i \(-0.000539265\pi\)
\(450\) 0 0
\(451\) 4.96410 2.86603i 0.233750 0.134956i
\(452\) −0.240237 + 0.896575i −0.0112998 + 0.0421714i
\(453\) 23.0435 6.17449i 1.08268 0.290103i
\(454\) −3.46410 −0.162578
\(455\) 0 0
\(456\) −5.73205 −0.268428
\(457\) 11.4524 3.06866i 0.535721 0.143546i 0.0191922 0.999816i \(-0.493891\pi\)
0.516529 + 0.856270i \(0.327224\pi\)
\(458\) −2.82843 + 10.5558i −0.132164 + 0.493242i
\(459\) 0.464102 0.267949i 0.0216624 0.0125068i
\(460\) 0 0
\(461\) 30.6410i 1.42709i −0.700607 0.713547i \(-0.747087\pi\)
0.700607 0.713547i \(-0.252913\pi\)
\(462\) −2.38014 + 1.15539i −0.110734 + 0.0537538i
\(463\) −23.1315 + 23.1315i −1.07501 + 1.07501i −0.0780612 + 0.996949i \(0.524873\pi\)
−0.996949 + 0.0780612i \(0.975127\pi\)
\(464\) −6.00000 3.46410i −0.278543 0.160817i
\(465\) 0 0
\(466\) 12.9282 + 22.3923i 0.598887 + 1.03730i
\(467\) 3.72500 + 13.9019i 0.172373 + 0.643303i 0.996984 + 0.0776040i \(0.0247270\pi\)
−0.824612 + 0.565699i \(0.808606\pi\)
\(468\) −1.60368 1.60368i −0.0741302 0.0741302i
\(469\) −1.73205 + 5.00000i −0.0799787 + 0.230879i
\(470\) 0 0
\(471\) 6.33013 10.9641i 0.291677 0.505199i
\(472\) −4.38134 1.17398i −0.201668 0.0540367i
\(473\) 4.76028 + 1.27551i 0.218878 + 0.0586481i
\(474\) 8.46410 14.6603i 0.388769 0.673368i
\(475\) 0 0
\(476\) 1.39230 0.267949i 0.0638162 0.0122814i
\(477\) 0.707107 + 0.707107i 0.0323762 + 0.0323762i
\(478\) 6.21166 + 23.1822i 0.284115 + 1.06033i
\(479\) 21.4641 + 37.1769i 0.980720 + 1.69866i 0.659598 + 0.751619i \(0.270727\pi\)
0.321122 + 0.947038i \(0.395940\pi\)
\(480\) 0 0
\(481\) 19.5000 + 11.2583i 0.889123 + 0.513336i
\(482\) 18.1953 18.1953i 0.828774 0.828774i
\(483\) −20.9222 1.50215i −0.951993 0.0683500i
\(484\) 10.0000i 0.454545i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 5.65685 21.1117i 0.256337 0.956661i −0.711006 0.703186i \(-0.751760\pi\)
0.967342 0.253475i \(-0.0815734\pi\)
\(488\) −4.38134 + 1.17398i −0.198334 + 0.0531434i
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 43.7128 1.97273 0.986366 0.164568i \(-0.0526229\pi\)
0.986366 + 0.164568i \(0.0526229\pi\)
\(492\) −5.53674 + 1.48356i −0.249615 + 0.0668842i
\(493\) 0.960947 3.58630i 0.0432789 0.161519i
\(494\) −11.2583 + 6.50000i −0.506536 + 0.292449i
\(495\) 0 0
\(496\) 0.535898i 0.0240625i
\(497\) 13.0053 + 0.933740i 0.583368 + 0.0418840i
\(498\) 7.34847 7.34847i 0.329293 0.329293i
\(499\) −24.2487 14.0000i −1.08552 0.626726i −0.153141 0.988204i \(-0.548939\pi\)
−0.932381 + 0.361478i \(0.882272\pi\)
\(500\) 0 0
\(501\) −8.59808 14.8923i −0.384134 0.665339i
\(502\) 6.38254 + 23.8200i 0.284867 + 1.06314i
\(503\) 24.3190 + 24.3190i 1.08433 + 1.08433i 0.996100 + 0.0882321i \(0.0281217\pi\)
0.0882321 + 0.996100i \(0.471878\pi\)
\(504\) 2.59808 0.500000i 0.115728 0.0222718i
\(505\) 0 0
\(506\) −3.96410 + 6.86603i −0.176226 + 0.305232i
\(507\) 7.58871 + 2.03339i 0.337026 + 0.0903059i
\(508\) 4.82963 + 1.29410i 0.214280 + 0.0574162i
\(509\) 5.19615 9.00000i 0.230315 0.398918i −0.727586 0.686017i \(-0.759358\pi\)
0.957901 + 0.287099i \(0.0926909\pi\)
\(510\) 0 0
\(511\) −3.46410 + 10.0000i −0.153243 + 0.442374i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −1.48356 5.53674i −0.0655009 0.244453i
\(514\) 9.19615 + 15.9282i 0.405625 + 0.702563i
\(515\) 0 0
\(516\) −4.26795 2.46410i −0.187886 0.108476i
\(517\) −6.50266 + 6.50266i −0.285987 + 0.285987i
\(518\) −23.6305 + 11.4710i −1.03826 + 0.504006i
\(519\) 23.5885i 1.03542i
\(520\) 0 0
\(521\) −6.82051 + 3.93782i −0.298812 + 0.172519i −0.641909 0.766781i \(-0.721857\pi\)
0.343097 + 0.939300i \(0.388524\pi\)
\(522\) 1.79315 6.69213i 0.0784841 0.292907i
\(523\) −32.7028 + 8.76268i −1.42999 + 0.383165i −0.889017 0.457873i \(-0.848611\pi\)
−0.540975 + 0.841039i \(0.681945\pi\)
\(524\) 20.1244 0.879137
\(525\) 0 0
\(526\) −2.14359 −0.0934651
\(527\) −0.277401 + 0.0743295i −0.0120838 + 0.00323784i
\(528\) 0.258819 0.965926i 0.0112637 0.0420365i
\(529\) −34.5167 + 19.9282i −1.50072 + 0.866444i
\(530\) 0 0
\(531\) 4.53590i 0.196841i
\(532\) 1.08604 15.1266i 0.0470860 0.655823i
\(533\) −9.19239 + 9.19239i −0.398167 + 0.398167i
\(534\) 6.00000 + 3.46410i 0.259645 + 0.149906i
\(535\) 0 0
\(536\) −1.00000 1.73205i −0.0431934 0.0748132i
\(537\) −2.32937 8.69333i −0.100520 0.375145i
\(538\) −6.59059 6.59059i −0.284141 0.284141i
\(539\) −2.59808 6.50000i −0.111907 0.279975i
\(540\) 0 0
\(541\) −8.53590 + 14.7846i −0.366987 + 0.635640i −0.989093 0.147293i \(-0.952944\pi\)
0.622106 + 0.782933i \(0.286277\pi\)
\(542\) 7.72741 + 2.07055i 0.331921 + 0.0889378i
\(543\) 6.17449 + 1.65445i 0.264973 + 0.0709993i
\(544\) −0.267949 + 0.464102i −0.0114882 + 0.0198982i
\(545\) 0 0
\(546\) 4.53590 3.92820i 0.194119 0.168112i
\(547\) −21.0101 21.0101i −0.898328 0.898328i 0.0969599 0.995288i \(-0.469088\pi\)
−0.995288 + 0.0969599i \(0.969088\pi\)
\(548\) −1.31268 4.89898i −0.0560748 0.209274i
\(549\) −2.26795 3.92820i −0.0967937 0.167652i
\(550\) 0 0
\(551\) −34.3923 19.8564i −1.46516 0.845911i
\(552\) 5.60609 5.60609i 0.238611 0.238611i
\(553\) 37.0841 + 25.1141i 1.57698 + 1.06796i
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) 9.00000 5.19615i 0.381685 0.220366i
\(557\) 5.91567 22.0776i 0.250655 0.935458i −0.719801 0.694180i \(-0.755767\pi\)
0.970456 0.241277i \(-0.0775663\pi\)
\(558\) −0.517638 + 0.138701i −0.0219134 + 0.00587167i
\(559\) −11.1769 −0.472733
\(560\) 0 0
\(561\) 0.535898 0.0226256
\(562\) 13.5923 3.64205i 0.573357 0.153631i
\(563\) −4.76028 + 17.7656i −0.200622 + 0.748731i 0.790118 + 0.612955i \(0.210019\pi\)
−0.990740 + 0.135776i \(0.956647\pi\)
\(564\) 7.96410 4.59808i 0.335349 0.193614i
\(565\) 0 0
\(566\) 19.4641i 0.818137i
\(567\) 1.15539 + 2.38014i 0.0485220 + 0.0999565i
\(568\) −3.48477 + 3.48477i −0.146218 + 0.146218i
\(569\) −8.47372 4.89230i −0.355237 0.205096i 0.311752 0.950163i \(-0.399084\pi\)
−0.666989 + 0.745067i \(0.732417\pi\)
\(570\) 0 0
\(571\) −6.92820 12.0000i −0.289936 0.502184i 0.683858 0.729615i \(-0.260301\pi\)
−0.973794 + 0.227431i \(0.926967\pi\)
\(572\) −0.586988 2.19067i −0.0245432 0.0915965i
\(573\) 7.72741 + 7.72741i 0.322817 + 0.322817i
\(574\) −2.86603 14.8923i −0.119626 0.621593i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 33.7381 + 9.04008i 1.40453 + 0.376344i 0.879971 0.475028i \(-0.157562\pi\)
0.524563 + 0.851372i \(0.324229\pi\)
\(578\) 16.1433 + 4.32559i 0.671474 + 0.179921i
\(579\) 9.39230 16.2679i 0.390331 0.676073i
\(580\) 0 0
\(581\) 18.0000 + 20.7846i 0.746766 + 0.862291i
\(582\) 7.72741 + 7.72741i 0.320311 + 0.320311i
\(583\) 0.258819 + 0.965926i 0.0107192 + 0.0400046i
\(584\) −2.00000 3.46410i −0.0827606 0.143346i
\(585\) 0 0
\(586\) −1.50000 0.866025i −0.0619644 0.0357752i
\(587\) −9.41902 + 9.41902i −0.388765 + 0.388765i −0.874247 0.485482i \(-0.838644\pi\)
0.485482 + 0.874247i \(0.338644\pi\)
\(588\) 0.827225 + 6.95095i 0.0341142 + 0.286652i
\(589\) 3.07180i 0.126571i
\(590\) 0 0
\(591\) 9.40192 5.42820i 0.386743 0.223286i
\(592\) 2.56961 9.58991i 0.105610 0.394143i
\(593\) −20.8714 + 5.59248i −0.857087 + 0.229656i −0.660496 0.750830i \(-0.729654\pi\)
−0.196591 + 0.980486i \(0.562987\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −12.9282 −0.529560
\(597\) −18.8009 + 5.03768i −0.769469 + 0.206179i
\(598\) 4.65376 17.3681i 0.190307 0.710234i
\(599\) 12.2487 7.07180i 0.500469 0.288946i −0.228438 0.973558i \(-0.573362\pi\)
0.728907 + 0.684613i \(0.240029\pi\)
\(600\) 0 0
\(601\) 12.7846i 0.521495i 0.965407 + 0.260748i \(0.0839690\pi\)
−0.965407 + 0.260748i \(0.916031\pi\)
\(602\) 7.31130 10.7961i 0.297987 0.440015i
\(603\) 1.41421 1.41421i 0.0575912 0.0575912i
\(604\) −20.6603 11.9282i −0.840654 0.485352i
\(605\) 0 0
\(606\) 7.46410 + 12.9282i 0.303208 + 0.525172i
\(607\) 4.93117 + 18.4034i 0.200150 + 0.746969i 0.990873 + 0.134796i \(0.0430379\pi\)
−0.790724 + 0.612173i \(0.790295\pi\)
\(608\) 4.05317 + 4.05317i 0.164378 + 0.164378i
\(609\) 17.3205 + 6.00000i 0.701862 + 0.243132i
\(610\) 0 0
\(611\) 10.4282 18.0622i 0.421880 0.730718i
\(612\) −0.517638 0.138701i −0.0209243 0.00560664i
\(613\) 3.93305 + 1.05386i 0.158855 + 0.0425649i 0.337370 0.941372i \(-0.390463\pi\)
−0.178515 + 0.983937i \(0.557129\pi\)
\(614\) 0.803848 1.39230i 0.0324406 0.0561889i
\(615\) 0 0
\(616\) 2.50000 + 0.866025i 0.100728 + 0.0348932i
\(617\) −11.9700 11.9700i −0.481896 0.481896i 0.423841 0.905737i \(-0.360682\pi\)
−0.905737 + 0.423841i \(0.860682\pi\)
\(618\) 0.619174 + 2.31079i 0.0249068 + 0.0929536i
\(619\) −9.79423 16.9641i −0.393663 0.681845i 0.599266 0.800550i \(-0.295459\pi\)
−0.992930 + 0.118705i \(0.962126\pi\)
\(620\) 0 0
\(621\) 6.86603 + 3.96410i 0.275524 + 0.159074i
\(622\) 19.4201 19.4201i 0.778673 0.778673i
\(623\) −10.2784 + 15.1774i −0.411797 + 0.608070i
\(624\) 2.26795i 0.0907906i
\(625\) 0 0
\(626\) 27.0000 15.5885i 1.07914 0.623040i
\(627\) 1.48356 5.53674i 0.0592478 0.221116i
\(628\) −12.2289 + 3.27671i −0.487985 + 0.130755i
\(629\) 5.32051 0.212143
\(630\) 0 0
\(631\) 1.21539 0.0483839 0.0241920 0.999707i \(-0.492299\pi\)
0.0241920 + 0.999707i \(0.492299\pi\)
\(632\) −16.3514 + 4.38134i −0.650423 + 0.174280i
\(633\) −5.63827 + 21.0423i −0.224101 + 0.836357i
\(634\) −12.1244 + 7.00000i −0.481520 + 0.278006i
\(635\) 0 0
\(636\) 1.00000i 0.0396526i
\(637\) 9.50695 + 12.7143i 0.376679 + 0.503760i
\(638\) 4.89898 4.89898i 0.193952 0.193952i
\(639\) −4.26795 2.46410i −0.168837 0.0974784i
\(640\) 0 0
\(641\) −9.03590 15.6506i −0.356897 0.618163i 0.630544 0.776153i \(-0.282832\pi\)
−0.987441 + 0.157991i \(0.949498\pi\)
\(642\) 0.277401 + 1.03528i 0.0109482 + 0.0408591i
\(643\) 4.72311 + 4.72311i 0.186261 + 0.186261i 0.794078 0.607816i \(-0.207954\pi\)
−0.607816 + 0.794078i \(0.707954\pi\)
\(644\) 13.7321 + 15.8564i 0.541119 + 0.624830i
\(645\) 0 0
\(646\) −1.53590 + 2.66025i −0.0604291 + 0.104666i
\(647\) −34.3758 9.21097i −1.35145 0.362121i −0.490782 0.871283i \(-0.663289\pi\)
−0.860671 + 0.509162i \(0.829955\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) 2.26795 3.92820i 0.0890248 0.154195i
\(650\) 0 0
\(651\) −0.267949 1.39230i −0.0105018 0.0545687i
\(652\) 8.48528 + 8.48528i 0.332309 + 0.332309i
\(653\) −7.94906 29.6663i −0.311071 1.16093i −0.927592 0.373594i \(-0.878125\pi\)
0.616522 0.787338i \(-0.288541\pi\)
\(654\) −1.53590 2.66025i −0.0600584 0.104024i
\(655\) 0 0
\(656\) 4.96410 + 2.86603i 0.193816 + 0.111899i
\(657\) 2.82843 2.82843i 0.110347 0.110347i
\(658\) 10.6252 + 21.8881i 0.414213 + 0.853288i
\(659\) 15.7128i 0.612084i −0.952018 0.306042i \(-0.900995\pi\)
0.952018 0.306042i \(-0.0990048\pi\)
\(660\) 0 0
\(661\) −19.8564 + 11.4641i −0.772325 + 0.445902i −0.833703 0.552213i \(-0.813784\pi\)
0.0613786 + 0.998115i \(0.480450\pi\)
\(662\) −4.08536 + 15.2468i −0.158782 + 0.592582i
\(663\) −1.17398 + 0.314566i −0.0455935 + 0.0122167i
\(664\) −10.3923 −0.403300
\(665\) 0 0
\(666\) 9.92820 0.384710
\(667\) 53.0566 14.2165i 2.05436 0.550464i
\(668\) −4.45069 + 16.6102i −0.172202 + 0.642668i
\(669\) 21.9282 12.6603i 0.847793 0.489474i
\(670\) 0 0
\(671\) 4.53590i 0.175106i
\(672\) −2.19067 1.48356i −0.0845070 0.0572297i
\(673\) 11.8685 11.8685i 0.457497 0.457497i −0.440336 0.897833i \(-0.645141\pi\)
0.897833 + 0.440336i \(0.145141\pi\)
\(674\) 21.5885 + 12.4641i 0.831556 + 0.480099i
\(675\) 0 0
\(676\) −3.92820 6.80385i −0.151085 0.261686i
\(677\) −0.512659 1.91327i −0.0197031 0.0735329i 0.955374 0.295398i \(-0.0954522\pi\)
−0.975077 + 0.221865i \(0.928786\pi\)
\(678\) 0.656339 + 0.656339i 0.0252065 + 0.0252065i
\(679\) −21.8564 + 18.9282i −0.838772 + 0.726398i
\(680\) 0 0
\(681\) −1.73205 + 3.00000i −0.0663723 + 0.114960i
\(682\) −0.517638 0.138701i −0.0198214 0.00531112i
\(683\) 40.4302 + 10.8332i 1.54702 + 0.414522i 0.928526 0.371269i \(-0.121077\pi\)
0.618492 + 0.785791i \(0.287744\pi\)
\(684\) −2.86603 + 4.96410i −0.109585 + 0.189807i
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 7.72741 + 7.72741i 0.294819 + 0.294819i
\(688\) 1.27551 + 4.76028i 0.0486285 + 0.181484i
\(689\) −1.13397 1.96410i −0.0432010 0.0748263i
\(690\) 0 0
\(691\) −7.14359 4.12436i −0.271755 0.156898i 0.357930 0.933748i \(-0.383483\pi\)
−0.629685 + 0.776851i \(0.716816\pi\)
\(692\) 16.6796 16.6796i 0.634062 0.634062i
\(693\) −0.189469 + 2.63896i −0.00719732 + 0.100246i
\(694\) 10.9282i 0.414829i
\(695\) 0 0
\(696\) −6.00000 + 3.46410i −0.227429 + 0.131306i
\(697\) −0.795040 + 2.96713i −0.0301143 + 0.112388i
\(698\) 24.9754 6.69213i 0.945332 0.253301i
\(699\) 25.8564 0.977979
\(700\) 0 0
\(701\) −31.8564 −1.20320 −0.601600 0.798798i \(-0.705470\pi\)
−0.601600 + 0.798798i \(0.705470\pi\)
\(702\) −2.19067 + 0.586988i −0.0826815 + 0.0221545i
\(703\) 14.7291 54.9698i 0.555519 2.07323i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 6.92820i 0.260746i
\(707\) −35.5312 + 17.2480i −1.33629 + 0.648676i
\(708\) −3.20736 + 3.20736i −0.120540 + 0.120540i
\(709\) −11.3205 6.53590i −0.425151 0.245461i 0.272128 0.962261i \(-0.412273\pi\)
−0.697279 + 0.716800i \(0.745606\pi\)
\(710\) 0 0
\(711\) −8.46410 14.6603i −0.317429 0.549802i
\(712\) −1.79315 6.69213i −0.0672012 0.250798i
\(713\) −3.00429 3.00429i −0.112512 0.112512i
\(714\) 0.464102 1.33975i 0.0173686 0.0501387i
\(715\) 0 0
\(716\) −4.50000 + 7.79423i −0.168173 + 0.291284i
\(717\) 23.1822 + 6.21166i 0.865756 + 0.231979i
\(718\) −18.2832 4.89898i −0.682324 0.182828i
\(719\) −7.19615 + 12.4641i −0.268371 + 0.464833i −0.968441 0.249242i \(-0.919819\pi\)
0.700070 + 0.714074i \(0.253152\pi\)
\(720\) 0 0
\(721\) −6.21539 + 1.19615i −0.231473 + 0.0445470i
\(722\) 9.79796 + 9.79796i 0.364642 + 0.364642i
\(723\) −6.65994 24.8553i −0.247686 0.924377i
\(724\) −3.19615 5.53590i −0.118784 0.205740i
\(725\) 0 0
\(726\) −8.66025 5.00000i −0.321412 0.185567i
\(727\) −23.0943 + 23.0943i −0.856520 + 0.856520i −0.990926 0.134407i \(-0.957087\pi\)
0.134407 + 0.990926i \(0.457087\pi\)
\(728\) −5.98502 0.429705i −0.221820 0.0159259i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −2.28719 + 1.32051i −0.0845947 + 0.0488408i
\(732\) −1.17398 + 4.38134i −0.0433914 + 0.161939i
\(733\) −22.2671 + 5.96644i −0.822453 + 0.220376i −0.645418 0.763829i \(-0.723317\pi\)
−0.177034 + 0.984205i \(0.556650\pi\)
\(734\) 14.5167 0.535820
\(735\) 0 0
\(736\) −7.92820 −0.292237
\(737\) 1.93185 0.517638i 0.0711607 0.0190674i
\(738\) −1.48356 + 5.53674i −0.0546107 + 0.203810i
\(739\) −5.25833 + 3.03590i −0.193431 + 0.111677i −0.593588 0.804769i \(-0.702289\pi\)
0.400157 + 0.916447i \(0.368956\pi\)
\(740\) 0 0
\(741\) 13.0000i 0.477567i
\(742\) 2.63896 + 0.189469i 0.0968792 + 0.00695561i
\(743\) −23.8893 + 23.8893i −0.876414 + 0.876414i −0.993162 0.116747i \(-0.962753\pi\)
0.116747 + 0.993162i \(0.462753\pi\)
\(744\) 0.464102 + 0.267949i 0.0170148 + 0.00982349i
\(745\) 0 0
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) −2.68973 10.0382i −0.0984119 0.367278i
\(748\) −0.378937 0.378937i −0.0138553 0.0138553i
\(749\) −2.78461 + 0.535898i −0.101747 + 0.0195813i
\(750\) 0 0
\(751\) −6.92820 + 12.0000i −0.252814 + 0.437886i −0.964299 0.264814i \(-0.914689\pi\)
0.711486 + 0.702701i \(0.248023\pi\)
\(752\) −8.88280 2.38014i −0.323922 0.0867948i
\(753\) 23.8200 + 6.38254i 0.868048 + 0.232593i
\(754\) −7.85641 + 13.6077i −0.286113 + 0.495563i
\(755\) 0 0
\(756\) 0.866025 2.50000i 0.0314970 0.0909241i
\(757\) −12.5249 12.5249i −0.455223 0.455223i 0.441860 0.897084i \(-0.354319\pi\)
−0.897084 + 0.441860i \(0.854319\pi\)
\(758\) −2.56961 9.58991i −0.0933324 0.348321i
\(759\) 3.96410 + 6.86603i 0.143888 + 0.249221i
\(760\) 0 0
\(761\) 21.1077 + 12.1865i 0.765153 + 0.441761i 0.831143 0.556059i \(-0.187687\pi\)
−0.0659896 + 0.997820i \(0.521020\pi\)
\(762\) 3.53553 3.53553i 0.128079 0.128079i
\(763\) 7.31130 3.54914i 0.264687 0.128487i
\(764\) 10.9282i 0.395369i
\(765\) 0 0
\(766\) −25.9641 + 14.9904i −0.938121 + 0.541624i
\(767\) −2.66252 + 9.93666i −0.0961380 + 0.358792i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) −21.1962 −0.764353 −0.382176 0.924089i \(-0.624825\pi\)
−0.382176 + 0.924089i \(0.624825\pi\)
\(770\) 0 0
\(771\) 18.3923 0.662383
\(772\) −18.1445 + 4.86181i −0.653036 + 0.174981i
\(773\) −9.41404 + 35.1337i −0.338600 + 1.26367i 0.561314 + 0.827603i \(0.310296\pi\)
−0.899914 + 0.436068i \(0.856371\pi\)
\(774\) −4.26795 + 2.46410i −0.153408 + 0.0885703i
\(775\) 0 0
\(776\) 10.9282i 0.392300i
\(777\) −1.88108 + 26.2001i −0.0674835 + 0.939924i
\(778\) 23.0807 23.0807i 0.827483 0.827483i
\(779\) 28.4545 + 16.4282i 1.01949 + 0.588601i
\(780\) 0 0
\(781\) −2.46410 4.26795i −0.0881725 0.152719i
\(782\) −1.09965