Properties

Label 1050.2.bc.d.607.2
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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 607.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.d.493.2

$q$-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 0.448834 0.893615i \(-0.351840\pi\)
−0.893615 + 0.448834i \(0.851840\pi\)
\(14\) −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 0.195499 0.980704i \(-0.437367\pi\)
−0.321045 + 0.947064i \(0.604034\pi\)
\(18\) −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 \(-0.773621\pi\)
0.329720 0.944079i \(-0.393046\pi\)
\(24\) −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 −0.937862 0.347008i \(-0.887198\pi\)
−0.638709 + 0.769449i \(0.720531\pi\)
\(38\) 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 −0.389574 0.920995i \(-0.627378\pi\)
0.920995 + 0.389574i \(0.127378\pi\)
\(44\) −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 \(0.150672\pi\)
−0.542867 + 0.839819i \(0.682661\pi\)
\(48\) −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 0.324548 0.945869i \(-0.394788\pi\)
−0.191868 + 0.981421i \(0.561454\pi\)
\(54\) −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 −0.927071 0.374887i \(-0.877682\pi\)
0.990310 + 0.138874i \(0.0443482\pi\)
\(68\) −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 −0.878504 0.477734i \(-0.841458\pi\)
0.999674 + 0.0255221i \(0.00812481\pi\)
\(74\) −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 0.177518 0.984118i \(-0.443193\pi\)
−0.984118 + 0.177518i \(0.943193\pi\)
\(84\) 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 −0.196004 0.980603i \(-0.562797\pi\)
0.980603 + 0.196004i \(0.0627965\pi\)
\(98\) 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 −0.143171 0.989698i \(-0.545730\pi\)
0.370860 + 0.928689i \(0.379063\pi\)
\(104\) −2.26795 −0.222391
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 1.03528 0.277401i 0.100084 0.0268174i −0.208430 0.978037i \(-0.566835\pi\)
0.308513 + 0.951220i \(0.400169\pi\)
\(108\) −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 −0.675561 0.737304i \(-0.736098\pi\)
0.737304 + 0.675561i \(0.236098\pi\)
\(114\) −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 0.532624 0.846352i \(-0.321206\pi\)
−0.846352 + 0.532624i \(0.821206\pi\)
\(128\) −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 −0.999058 0.0433975i \(-0.986182\pi\)
0.886908 + 0.461946i \(0.152848\pi\)
\(138\) −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 0.711346 0.702842i \(-0.248086\pi\)
0.264623 + 0.964352i \(0.414752\pi\)
\(158\) 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 \(-0.927603\pi\)
0.730979 0.682400i \(-0.239064\pi\)
\(164\) 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 −0.0574186 0.998350i \(-0.518287\pi\)
0.998350 + 0.0574186i \(0.0182870\pi\)
\(168\) 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 −0.980708 0.195476i \(-0.937375\pi\)
−0.751580 + 0.659642i \(0.770708\pi\)
\(174\) −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 0.843743 0.536747i \(-0.180347\pi\)
0.462329 + 0.886708i \(0.347014\pi\)
\(194\) 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 0.925554 0.378616i \(-0.123600\pi\)
−0.378616 + 0.925554i \(0.623600\pi\)
\(198\) 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 \(0.0720692\pi\)
0.224483 + 0.974478i \(0.427931\pi\)
\(224\) −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 0.146060 0.989276i \(-0.453341\pi\)
−0.368146 + 0.929768i \(0.620007\pi\)
\(228\) −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 \(0.238233\pi\)
−0.294341 + 0.955700i \(0.595100\pi\)
\(234\) 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 \(0.111136\pi\)
−0.642728 + 0.766094i \(0.722197\pi\)
\(258\) −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 0.194415 0.980919i \(-0.437719\pi\)
−0.322091 + 0.946709i \(0.604386\pi\)
\(264\) −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 \(-0.686830\pi\)
0.895940 0.444174i \(-0.146503\pi\)
\(278\) 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 \(0.279699\pi\)
−0.937611 + 0.347686i \(0.886968\pi\)
\(284\) 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 0.670426 0.741976i \(-0.266111\pi\)
−0.741976 + 0.670426i \(0.766111\pi\)
\(294\) 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 −0.673922 0.738803i \(-0.735391\pi\)
0.738803 + 0.673922i \(0.235391\pi\)
\(308\) 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 0.728691 0.684843i \(-0.240129\pi\)
0.973486 + 0.228746i \(0.0734624\pi\)
\(314\) 12.6603 0.714459
\(315\) 0 0
\(316\) 16.9282 0.952286
\(317\) −13.5230 + 3.62347i −0.759525 + 0.203514i −0.617739 0.786383i \(-0.711951\pi\)
−0.141786 + 0.989897i \(0.545285\pi\)
\(318\) 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 0.999238 0.0390392i \(-0.0124297\pi\)
−0.0390392 + 0.999238i \(0.512430\pi\)
\(338\) −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 \(0.178096\pi\)
−0.999355 + 0.0358994i \(0.988570\pi\)
\(348\) −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 −0.997086 0.0762887i \(-0.975693\pi\)
0.901646 + 0.432475i \(0.142360\pi\)
\(354\) 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 0.605494 0.795849i \(-0.292975\pi\)
0.126449 + 0.991973i \(0.459642\pi\)
\(368\) −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 \(-0.848289\pi\)
0.540124 0.841585i \(-0.318377\pi\)
\(374\) 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 −0.906261 0.422719i \(-0.861076\pi\)
−0.573485 + 0.819216i \(0.694409\pi\)
\(384\) −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 \(-0.979375\pi\)
0.831832 0.555027i \(-0.187292\pi\)
\(398\) 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 0.380910 0.924612i \(-0.375611\pi\)
−0.924612 + 0.380910i \(0.875611\pi\)
\(434\) 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 0.966803 0.255523i \(-0.0822475\pi\)
−0.965037 + 0.262112i \(0.915581\pi\)
\(444\) 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 −0.516529 0.856270i \(-0.672776\pi\)
−0.0191922 + 0.999816i \(0.506109\pi\)
\(458\) 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 \(-0.475127\pi\)
0.996949 0.0780612i \(-0.0248729\pi\)
\(464\) −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 \(-0.975273\pi\)
0.824612 0.565699i \(-0.191394\pi\)
\(468\) 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 \(0.248240\pi\)
−0.967342 + 0.253475i \(0.918427\pi\)
\(488\) 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 \(-0.971878\pi\)
−0.0882321 0.996100i \(-0.528122\pi\)
\(504\) 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 0.540975 0.841039i \(-0.318055\pi\)
0.889017 + 0.457873i \(0.151389\pi\)
\(524\) 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 0.995288 0.0969599i \(-0.0309119\pi\)
−0.0969599 + 0.995288i \(0.530912\pi\)
\(548\) 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 \(0.244233\pi\)
−0.970456 + 0.241277i \(0.922434\pi\)
\(558\) 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 \(-0.789981\pi\)
0.990740 0.135776i \(-0.0433527\pi\)
\(564\) 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 −0.524563 0.851372i \(-0.675771\pi\)
−0.879971 + 0.475028i \(0.842438\pi\)
\(578\) −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 −0.485482 0.874247i \(-0.661356\pi\)
0.874247 + 0.485482i \(0.161356\pi\)
\(588\) −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 0.196591 0.980486i \(-0.437013\pi\)
0.660496 + 0.750830i \(0.270346\pi\)
\(594\) 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 \(-0.956962\pi\)
0.790724 0.612173i \(-0.209705\pi\)
\(608\) −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 0.178515 0.983937i \(-0.442871\pi\)
−0.337370 + 0.941372i \(0.609537\pi\)
\(614\) 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 0.905737 0.423841i \(-0.139318\pi\)
−0.423841 + 0.905737i \(0.639318\pi\)
\(618\) −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 0.607816 0.794078i \(-0.292046\pi\)
−0.794078 + 0.607816i \(0.792046\pi\)
\(644\) 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 0.860671 0.509162i \(-0.170045\pi\)
0.490782 + 0.871283i \(0.336711\pi\)
\(648\) 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 \(0.121875\pi\)
−0.616522 + 0.787338i \(0.711459\pi\)
\(654\) −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 −0.897833 0.440336i \(-0.854859\pi\)
0.440336 + 0.897833i \(0.354859\pi\)
\(674\) 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 0.975077 0.221865i \(-0.0712144\pi\)
−0.955374 + 0.295398i \(0.904548\pi\)
\(678\) −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 −0.618492 0.785791i \(-0.712256\pi\)
−0.928526 + 0.371269i \(0.878923\pi\)
\(684\) −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 −0.134407 0.990926i \(-0.542913\pi\)
0.990926 + 0.134407i \(0.0429128\pi\)
\(728\) 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 0.177034 0.984205i \(-0.443350\pi\)
0.645418 + 0.763829i \(0.276683\pi\)
\(734\) 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 −0.116747 0.993162i \(-0.537247\pi\)
0.993162 + 0.116747i \(0.0372467\pi\)
\(744\) 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 0.897084 0.441860i \(-0.145681\pi\)
−0.441860 + 0.897084i \(0.645681\pi\)
\(758\) 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 \(-0.689704\pi\)
0.899914 0.436068i \(-0.143629\pi\)
\(774\) −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
\(782\)