Properties

Label 1050.2.bc.b.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.b.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.366025 + 0.633975i) q^{11} +(0.258819 + 0.965926i) q^{12} +(1.03528 + 1.03528i) q^{13} +(0.866025 - 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.19067 + 0.586988i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.09808 - 3.63397i) q^{19} +(1.73205 + 2.00000i) q^{21} +(0.517638 + 0.517638i) q^{22} +(0.965926 + 3.60488i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.26795 + 0.732051i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.189469 - 2.63896i) q^{28} -8.19615i q^{29} +(6.86603 - 3.96410i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.707107 + 0.189469i) q^{33} +2.26795 q^{34} -1.00000 q^{36} +(-4.57081 + 1.22474i) q^{37} +(1.08604 - 4.05317i) q^{38} +(-1.26795 + 0.732051i) q^{39} +2.46410i q^{41} +(2.19067 + 1.48356i) q^{42} +(0.138701 - 0.138701i) q^{43} +(0.633975 + 0.366025i) q^{44} +(1.86603 + 3.23205i) q^{46} +(2.84701 + 10.6252i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.59808 - 6.50000i) q^{49} +(-1.13397 + 1.96410i) q^{51} +(1.41421 + 0.378937i) q^{52} +(5.08845 + 1.36345i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(2.96713 + 2.96713i) q^{57} +(-2.12132 - 7.91688i) q^{58} +(0.267949 + 0.464102i) q^{59} +(10.5622 + 6.09808i) q^{61} +(5.60609 - 5.60609i) q^{62} +(-2.38014 + 1.15539i) q^{63} -1.00000i q^{64} +(-0.633975 + 0.366025i) q^{66} +(-1.03528 + 3.86370i) q^{67} +(2.19067 - 0.586988i) q^{68} -3.73205 q^{69} -12.8564 q^{71} +(-0.965926 + 0.258819i) q^{72} +(2.07055 - 7.72741i) q^{73} +(-4.09808 + 2.36603i) q^{74} -4.19615i q^{76} +(1.93185 + 0.138701i) q^{77} +(-1.03528 + 1.03528i) q^{78} +(-7.03590 - 4.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.637756 + 2.38014i) q^{82} +(8.24504 + 8.24504i) q^{83} +(2.50000 + 0.866025i) q^{84} +(0.0980762 - 0.169873i) q^{86} +(7.91688 + 2.12132i) q^{87} +(0.707107 + 0.189469i) q^{88} +(3.23205 - 5.59808i) q^{89} +(3.80385 - 0.732051i) q^{91} +(2.63896 + 2.63896i) q^{92} +(2.05197 + 7.65806i) q^{93} +(5.50000 + 9.52628i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-4.94975 + 4.94975i) q^{97} +(-4.19187 - 5.60609i) q^{98} -0.732051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 4q^{11} + 4q^{16} - 4q^{19} + 4q^{24} + 24q^{26} + 48q^{31} + 32q^{34} - 8q^{36} - 24q^{39} + 12q^{44} + 8q^{46} - 16q^{51} + 4q^{54} - 4q^{56} + 16q^{59} + 36q^{61} - 12q^{66} - 16q^{69} + 8q^{71} - 12q^{74} - 84q^{79} + 4q^{81} + 20q^{84} - 20q^{86} + 12q^{89} + 72q^{91} + 44q^{94} + O(q^{100}) \)

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
\(7\) 1.48356 2.19067i 0.560734 0.827996i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) 0.366025 + 0.633975i 0.110361 + 0.191151i 0.915916 0.401371i \(-0.131466\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) 1.03528 + 1.03528i 0.287134 + 0.287134i 0.835946 0.548812i \(-0.184920\pi\)
−0.548812 + 0.835946i \(0.684920\pi\)
\(14\) 0.866025 2.50000i 0.231455 0.668153i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 2.19067 + 0.586988i 0.531316 + 0.142366i 0.514496 0.857493i \(-0.327979\pi\)
0.0168199 + 0.999859i \(0.494646\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) 2.09808 3.63397i 0.481332 0.833691i −0.518439 0.855115i \(-0.673487\pi\)
0.999770 + 0.0214238i \(0.00681993\pi\)
\(20\) 0 0
\(21\) 1.73205 + 2.00000i 0.377964 + 0.436436i
\(22\) 0.517638 + 0.517638i 0.110361 + 0.110361i
\(23\) 0.965926 + 3.60488i 0.201409 + 0.751670i 0.990514 + 0.137411i \(0.0438783\pi\)
−0.789105 + 0.614259i \(0.789455\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 1.26795 + 0.732051i 0.248665 + 0.143567i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0.189469 2.63896i 0.0358062 0.498716i
\(29\) 8.19615i 1.52199i −0.648759 0.760994i \(-0.724712\pi\)
0.648759 0.760994i \(-0.275288\pi\)
\(30\) 0 0
\(31\) 6.86603 3.96410i 1.23317 0.711974i 0.265484 0.964115i \(-0.414468\pi\)
0.967690 + 0.252142i \(0.0811349\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −0.707107 + 0.189469i −0.123091 + 0.0329823i
\(34\) 2.26795 0.388950
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −4.57081 + 1.22474i −0.751437 + 0.201347i −0.614155 0.789185i \(-0.710503\pi\)
−0.137281 + 0.990532i \(0.543836\pi\)
\(38\) 1.08604 4.05317i 0.176180 0.657511i
\(39\) −1.26795 + 0.732051i −0.203034 + 0.117222i
\(40\) 0 0
\(41\) 2.46410i 0.384828i 0.981314 + 0.192414i \(0.0616316\pi\)
−0.981314 + 0.192414i \(0.938368\pi\)
\(42\) 2.19067 + 1.48356i 0.338028 + 0.228919i
\(43\) 0.138701 0.138701i 0.0211517 0.0211517i −0.696452 0.717604i \(-0.745239\pi\)
0.717604 + 0.696452i \(0.245239\pi\)
\(44\) 0.633975 + 0.366025i 0.0955753 + 0.0551804i
\(45\) 0 0
\(46\) 1.86603 + 3.23205i 0.275130 + 0.476540i
\(47\) 2.84701 + 10.6252i 0.415279 + 1.54984i 0.784276 + 0.620412i \(0.213035\pi\)
−0.368997 + 0.929431i \(0.620299\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) −2.59808 6.50000i −0.371154 0.928571i
\(50\) 0 0
\(51\) −1.13397 + 1.96410i −0.158788 + 0.275029i
\(52\) 1.41421 + 0.378937i 0.196116 + 0.0525492i
\(53\) 5.08845 + 1.36345i 0.698952 + 0.187284i 0.590761 0.806846i \(-0.298828\pi\)
0.108191 + 0.994130i \(0.465494\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 2.96713 + 2.96713i 0.393006 + 0.393006i
\(58\) −2.12132 7.91688i −0.278543 1.03954i
\(59\) 0.267949 + 0.464102i 0.0348840 + 0.0604209i 0.882940 0.469485i \(-0.155560\pi\)
−0.848056 + 0.529906i \(0.822227\pi\)
\(60\) 0 0
\(61\) 10.5622 + 6.09808i 1.35235 + 0.780779i 0.988578 0.150710i \(-0.0481560\pi\)
0.363770 + 0.931489i \(0.381489\pi\)
\(62\) 5.60609 5.60609i 0.711974 0.711974i
\(63\) −2.38014 + 1.15539i −0.299869 + 0.145566i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −0.633975 + 0.366025i −0.0780369 + 0.0450546i
\(67\) −1.03528 + 3.86370i −0.126479 + 0.472026i −0.999888 0.0149610i \(-0.995238\pi\)
0.873409 + 0.486987i \(0.161904\pi\)
\(68\) 2.19067 0.586988i 0.265658 0.0711828i
\(69\) −3.73205 −0.449286
\(70\) 0 0
\(71\) −12.8564 −1.52577 −0.762887 0.646531i \(-0.776219\pi\)
−0.762887 + 0.646531i \(0.776219\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) 2.07055 7.72741i 0.242340 0.904425i −0.732362 0.680915i \(-0.761582\pi\)
0.974702 0.223509i \(-0.0717512\pi\)
\(74\) −4.09808 + 2.36603i −0.476392 + 0.275045i
\(75\) 0 0
\(76\) 4.19615i 0.481332i
\(77\) 1.93185 + 0.138701i 0.220155 + 0.0158064i
\(78\) −1.03528 + 1.03528i −0.117222 + 0.117222i
\(79\) −7.03590 4.06218i −0.791600 0.457031i 0.0489252 0.998802i \(-0.484420\pi\)
−0.840526 + 0.541772i \(0.817754\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 0.637756 + 2.38014i 0.0704284 + 0.262842i
\(83\) 8.24504 + 8.24504i 0.905011 + 0.905011i 0.995864 0.0908531i \(-0.0289594\pi\)
−0.0908531 + 0.995864i \(0.528959\pi\)
\(84\) 2.50000 + 0.866025i 0.272772 + 0.0944911i
\(85\) 0 0
\(86\) 0.0980762 0.169873i 0.0105758 0.0183179i
\(87\) 7.91688 + 2.12132i 0.848778 + 0.227429i
\(88\) 0.707107 + 0.189469i 0.0753778 + 0.0201974i
\(89\) 3.23205 5.59808i 0.342597 0.593395i −0.642317 0.766439i \(-0.722027\pi\)
0.984914 + 0.173044i \(0.0553602\pi\)
\(90\) 0 0
\(91\) 3.80385 0.732051i 0.398752 0.0767398i
\(92\) 2.63896 + 2.63896i 0.275130 + 0.275130i
\(93\) 2.05197 + 7.65806i 0.212779 + 0.794103i
\(94\) 5.50000 + 9.52628i 0.567282 + 0.982561i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) −4.94975 + 4.94975i −0.502571 + 0.502571i −0.912236 0.409665i \(-0.865646\pi\)
0.409665 + 0.912236i \(0.365646\pi\)
\(98\) −4.19187 5.60609i −0.423443 0.566300i
\(99\) 0.732051i 0.0735739i
\(100\) 0 0
\(101\) −0.169873 + 0.0980762i −0.0169030 + 0.00975895i −0.508428 0.861105i \(-0.669773\pi\)
0.491525 + 0.870864i \(0.336440\pi\)
\(102\) −0.586988 + 2.19067i −0.0581205 + 0.216909i
\(103\) −6.43331 + 1.72380i −0.633893 + 0.169851i −0.561436 0.827520i \(-0.689751\pi\)
−0.0724573 + 0.997372i \(0.523084\pi\)
\(104\) 1.46410 0.143567
\(105\) 0 0
\(106\) 5.26795 0.511668
\(107\) −9.65926 + 2.58819i −0.933796 + 0.250210i −0.693472 0.720483i \(-0.743920\pi\)
−0.240323 + 0.970693i \(0.577253\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) −11.8301 + 6.83013i −1.13312 + 0.654208i −0.944718 0.327884i \(-0.893664\pi\)
−0.188403 + 0.982092i \(0.560331\pi\)
\(110\) 0 0
\(111\) 4.73205i 0.449146i
\(112\) −1.15539 2.38014i −0.109175 0.224902i
\(113\) −2.12132 + 2.12132i −0.199557 + 0.199557i −0.799810 0.600253i \(-0.795067\pi\)
0.600253 + 0.799810i \(0.295067\pi\)
\(114\) 3.63397 + 2.09808i 0.340353 + 0.196503i
\(115\) 0 0
\(116\) −4.09808 7.09808i −0.380497 0.659040i
\(117\) −0.378937 1.41421i −0.0350328 0.130744i
\(118\) 0.378937 + 0.378937i 0.0348840 + 0.0348840i
\(119\) 4.53590 3.92820i 0.415805 0.360098i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) 11.7806 + 3.15660i 1.06656 + 0.285785i
\(123\) −2.38014 0.637756i −0.214610 0.0575046i
\(124\) 3.96410 6.86603i 0.355987 0.616587i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) −11.2122 11.2122i −0.994919 0.994919i 0.00506773 0.999987i \(-0.498387\pi\)
−0.999987 + 0.00506773i \(0.998387\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 0.0980762 + 0.169873i 0.00863513 + 0.0149565i
\(130\) 0 0
\(131\) −11.8301 6.83013i −1.03360 0.596751i −0.115588 0.993297i \(-0.536875\pi\)
−0.918015 + 0.396546i \(0.870209\pi\)
\(132\) −0.517638 + 0.517638i −0.0450546 + 0.0450546i
\(133\) −4.84821 9.98743i −0.420393 0.866020i
\(134\) 4.00000i 0.345547i
\(135\) 0 0
\(136\) 1.96410 1.13397i 0.168420 0.0972375i
\(137\) −2.08913 + 7.79676i −0.178487 + 0.666122i 0.817445 + 0.576007i \(0.195390\pi\)
−0.995931 + 0.0901146i \(0.971277\pi\)
\(138\) −3.60488 + 0.965926i −0.306868 + 0.0822251i
\(139\) −12.9282 −1.09656 −0.548278 0.836296i \(-0.684716\pi\)
−0.548278 + 0.836296i \(0.684716\pi\)
\(140\) 0 0
\(141\) −11.0000 −0.926367
\(142\) −12.4183 + 3.32748i −1.04212 + 0.279236i
\(143\) −0.277401 + 1.03528i −0.0231975 + 0.0865741i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 8.00000i 0.662085i
\(147\) 6.95095 0.827225i 0.573305 0.0682284i
\(148\) −3.34607 + 3.34607i −0.275045 + 0.275045i
\(149\) 15.5885 + 9.00000i 1.27706 + 0.737309i 0.976306 0.216394i \(-0.0694297\pi\)
0.300750 + 0.953703i \(0.402763\pi\)
\(150\) 0 0
\(151\) −5.46410 9.46410i −0.444662 0.770178i 0.553366 0.832938i \(-0.313343\pi\)
−0.998029 + 0.0627603i \(0.980010\pi\)
\(152\) −1.08604 4.05317i −0.0880898 0.328756i
\(153\) −1.60368 1.60368i −0.129650 0.129650i
\(154\) 1.90192 0.366025i 0.153261 0.0294952i
\(155\) 0 0
\(156\) −0.732051 + 1.26795i −0.0586110 + 0.101517i
\(157\) −20.0256 5.36585i −1.59822 0.428241i −0.653715 0.756741i \(-0.726790\pi\)
−0.944504 + 0.328500i \(0.893457\pi\)
\(158\) −7.84752 2.10274i −0.624316 0.167285i
\(159\) −2.63397 + 4.56218i −0.208888 + 0.361804i
\(160\) 0 0
\(161\) 9.33013 + 3.23205i 0.735317 + 0.254721i
\(162\) 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 \(0.760936\pi\)
\(164\) 1.23205 + 2.13397i 0.0962070 + 0.166635i
\(165\) 0 0
\(166\) 10.0981 + 5.83013i 0.783763 + 0.452506i
\(167\) 3.58630 3.58630i 0.277516 0.277516i −0.554600 0.832117i \(-0.687129\pi\)
0.832117 + 0.554600i \(0.187129\pi\)
\(168\) 2.63896 + 0.189469i 0.203600 + 0.0146178i
\(169\) 10.8564i 0.835108i
\(170\) 0 0
\(171\) −3.63397 + 2.09808i −0.277897 + 0.160444i
\(172\) 0.0507680 0.189469i 0.00387102 0.0144469i
\(173\) −7.20977 + 1.93185i −0.548149 + 0.146876i −0.522256 0.852789i \(-0.674909\pi\)
−0.0258926 + 0.999665i \(0.508243\pi\)
\(174\) 8.19615 0.621349
\(175\) 0 0
\(176\) 0.732051 0.0551804
\(177\) −0.517638 + 0.138701i −0.0389081 + 0.0104254i
\(178\) 1.67303 6.24384i 0.125399 0.467996i
\(179\) −17.1962 + 9.92820i −1.28530 + 0.742069i −0.977812 0.209483i \(-0.932822\pi\)
−0.307488 + 0.951552i \(0.599489\pi\)
\(180\) 0 0
\(181\) 0.196152i 0.0145799i −0.999973 0.00728995i \(-0.997680\pi\)
0.999973 0.00728995i \(-0.00232048\pi\)
\(182\) 3.48477 1.69161i 0.258308 0.125391i
\(183\) −8.62398 + 8.62398i −0.637503 + 0.637503i
\(184\) 3.23205 + 1.86603i 0.238270 + 0.137565i
\(185\) 0 0
\(186\) 3.96410 + 6.86603i 0.290662 + 0.503441i
\(187\) 0.429705 + 1.60368i 0.0314232 + 0.117273i
\(188\) 7.77817 + 7.77817i 0.567282 + 0.567282i
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 0 0
\(191\) −12.4282 + 21.5263i −0.899273 + 1.55759i −0.0708481 + 0.997487i \(0.522571\pi\)
−0.828425 + 0.560100i \(0.810763\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) 22.9234 + 6.14231i 1.65006 + 0.442133i 0.959630 0.281264i \(-0.0907537\pi\)
0.690432 + 0.723397i \(0.257420\pi\)
\(194\) −3.50000 + 6.06218i −0.251285 + 0.435239i
\(195\) 0 0
\(196\) −5.50000 4.33013i −0.392857 0.309295i
\(197\) −18.2832 18.2832i −1.30263 1.30263i −0.926615 0.376012i \(-0.877295\pi\)
−0.376012 0.926615i \(-0.622705\pi\)
\(198\) −0.189469 0.707107i −0.0134650 0.0502519i
\(199\) 13.2321 + 22.9186i 0.937995 + 1.62466i 0.769204 + 0.639004i \(0.220653\pi\)
0.168791 + 0.985652i \(0.446014\pi\)
\(200\) 0 0
\(201\) −3.46410 2.00000i −0.244339 0.141069i
\(202\) −0.138701 + 0.138701i −0.00975895 + 0.00975895i
\(203\) −17.9551 12.1595i −1.26020 0.853431i
\(204\) 2.26795i 0.158788i
\(205\) 0 0
\(206\) −5.76795 + 3.33013i −0.401872 + 0.232021i
\(207\) 0.965926 3.60488i 0.0671365 0.250557i
\(208\) 1.41421 0.378937i 0.0980581 0.0262746i
\(209\) 3.07180 0.212481
\(210\) 0 0
\(211\) −19.6603 −1.35347 −0.676734 0.736228i \(-0.736605\pi\)
−0.676734 + 0.736228i \(0.736605\pi\)
\(212\) 5.08845 1.36345i 0.349476 0.0936418i
\(213\) 3.32748 12.4183i 0.227995 0.850890i
\(214\) −8.66025 + 5.00000i −0.592003 + 0.341793i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 1.50215 20.9222i 0.101972 1.42029i
\(218\) −9.65926 + 9.65926i −0.654208 + 0.654208i
\(219\) 6.92820 + 4.00000i 0.468165 + 0.270295i
\(220\) 0 0
\(221\) 1.66025 + 2.87564i 0.111681 + 0.193437i
\(222\) −1.22474 4.57081i −0.0821995 0.306773i
\(223\) −8.67475 8.67475i −0.580904 0.580904i 0.354247 0.935152i \(-0.384737\pi\)
−0.935152 + 0.354247i \(0.884737\pi\)
\(224\) −1.73205 2.00000i −0.115728 0.133631i
\(225\) 0 0
\(226\) −1.50000 + 2.59808i −0.0997785 + 0.172821i
\(227\) 5.13922 + 1.37705i 0.341102 + 0.0913979i 0.425304 0.905051i \(-0.360167\pi\)
−0.0842018 + 0.996449i \(0.526834\pi\)
\(228\) 4.05317 + 1.08604i 0.268428 + 0.0719250i
\(229\) 5.90192 10.2224i 0.390010 0.675517i −0.602440 0.798164i \(-0.705805\pi\)
0.992450 + 0.122647i \(0.0391382\pi\)
\(230\) 0 0
\(231\) −0.633975 + 1.83013i −0.0417125 + 0.120414i
\(232\) −5.79555 5.79555i −0.380497 0.380497i
\(233\) 4.89898 + 18.2832i 0.320943 + 1.19777i 0.918328 + 0.395820i \(0.129540\pi\)
−0.597385 + 0.801954i \(0.703794\pi\)
\(234\) −0.732051 1.26795i −0.0478557 0.0828884i
\(235\) 0 0
\(236\) 0.464102 + 0.267949i 0.0302104 + 0.0174420i
\(237\) 5.74479 5.74479i 0.373164 0.373164i
\(238\) 3.36465 4.96833i 0.218098 0.322049i
\(239\) 4.85641i 0.314135i −0.987588 0.157067i \(-0.949796\pi\)
0.987588 0.157067i \(-0.0502040\pi\)
\(240\) 0 0
\(241\) 11.1962 6.46410i 0.721208 0.416389i −0.0939894 0.995573i \(-0.529962\pi\)
0.815197 + 0.579184i \(0.196629\pi\)
\(242\) 2.70831 10.1075i 0.174097 0.649738i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) 12.1962 0.780779
\(245\) 0 0
\(246\) −2.46410 −0.157105
\(247\) 5.93426 1.59008i 0.377588 0.101174i
\(248\) 2.05197 7.65806i 0.130300 0.486287i
\(249\) −10.0981 + 5.83013i −0.639940 + 0.369469i
\(250\) 0 0
\(251\) 17.8564i 1.12709i 0.826087 + 0.563543i \(0.190562\pi\)
−0.826087 + 0.563543i \(0.809438\pi\)
\(252\) −1.48356 + 2.19067i −0.0934557 + 0.137999i
\(253\) −1.93185 + 1.93185i −0.121454 + 0.121454i
\(254\) −13.7321 7.92820i −0.861625 0.497460i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.998111 3.72500i −0.0622605 0.232359i 0.927783 0.373120i \(-0.121712\pi\)
−0.990044 + 0.140760i \(0.955045\pi\)
\(258\) 0.138701 + 0.138701i 0.00863513 + 0.00863513i
\(259\) −4.09808 + 11.8301i −0.254642 + 0.735088i
\(260\) 0 0
\(261\) −4.09808 + 7.09808i −0.253665 + 0.439360i
\(262\) −13.1948 3.53553i −0.815177 0.218426i
\(263\) 17.8857 + 4.79246i 1.10288 + 0.295516i 0.763937 0.645291i \(-0.223264\pi\)
0.338944 + 0.940807i \(0.389930\pi\)
\(264\) −0.366025 + 0.633975i −0.0225273 + 0.0390184i
\(265\) 0 0
\(266\) −7.26795 8.39230i −0.445627 0.514565i
\(267\) 4.57081 + 4.57081i 0.279729 + 0.279729i
\(268\) 1.03528 + 3.86370i 0.0632396 + 0.236013i
\(269\) 12.8301 + 22.2224i 0.782267 + 1.35493i 0.930618 + 0.365991i \(0.119270\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(270\) 0 0
\(271\) 2.13397 + 1.23205i 0.129630 + 0.0748418i 0.563413 0.826176i \(-0.309488\pi\)
−0.433783 + 0.901017i \(0.642821\pi\)
\(272\) 1.60368 1.60368i 0.0972375 0.0972375i
\(273\) −0.277401 + 3.86370i −0.0167891 + 0.233842i
\(274\) 8.07180i 0.487635i
\(275\) 0 0
\(276\) −3.23205 + 1.86603i −0.194547 + 0.112322i
\(277\) 4.29341 16.0232i 0.257966 0.962742i −0.708450 0.705761i \(-0.750605\pi\)
0.966416 0.256981i \(-0.0827279\pi\)
\(278\) −12.4877 + 3.34607i −0.748962 + 0.200684i
\(279\) −7.92820 −0.474649
\(280\) 0 0
\(281\) 19.9808 1.19195 0.595976 0.803002i \(-0.296765\pi\)
0.595976 + 0.803002i \(0.296765\pi\)
\(282\) −10.6252 + 2.84701i −0.632721 + 0.169537i
\(283\) 1.84392 6.88160i 0.109610 0.409069i −0.889218 0.457484i \(-0.848751\pi\)
0.998827 + 0.0484158i \(0.0154172\pi\)
\(284\) −11.1340 + 6.42820i −0.660680 + 0.381444i
\(285\) 0 0
\(286\) 1.07180i 0.0633767i
\(287\) 5.39804 + 3.65565i 0.318636 + 0.215786i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) −10.2679 5.92820i −0.603997 0.348718i
\(290\) 0 0
\(291\) −3.50000 6.06218i −0.205174 0.355371i
\(292\) −2.07055 7.72741i −0.121170 0.452212i
\(293\) −9.38186 9.38186i −0.548094 0.548094i 0.377795 0.925889i \(-0.376682\pi\)
−0.925889 + 0.377795i \(0.876682\pi\)
\(294\) 6.50000 2.59808i 0.379088 0.151523i
\(295\) 0 0
\(296\) −2.36603 + 4.09808i −0.137522 + 0.238196i
\(297\) 0.707107 + 0.189469i 0.0410305 + 0.0109941i
\(298\) 17.3867 + 4.65874i 1.00718 + 0.269874i
\(299\) −2.73205 + 4.73205i −0.157999 + 0.273662i
\(300\) 0 0
\(301\) −0.0980762 0.509619i −0.00565302 0.0293739i
\(302\) −7.72741 7.72741i −0.444662 0.444662i
\(303\) −0.0507680 0.189469i −0.00291654 0.0108847i
\(304\) −2.09808 3.63397i −0.120333 0.208423i
\(305\) 0 0
\(306\) −1.96410 1.13397i −0.112280 0.0648250i
\(307\) −13.3843 + 13.3843i −0.763880 + 0.763880i −0.977021 0.213141i \(-0.931631\pi\)
0.213141 + 0.977021i \(0.431631\pi\)
\(308\) 1.74238 0.845807i 0.0992815 0.0481944i
\(309\) 6.66025i 0.378889i
\(310\) 0 0
\(311\) −11.8923 + 6.86603i −0.674351 + 0.389337i −0.797723 0.603024i \(-0.793962\pi\)
0.123372 + 0.992360i \(0.460629\pi\)
\(312\) −0.378937 + 1.41421i −0.0214531 + 0.0800641i
\(313\) 17.8350 4.77886i 1.00809 0.270117i 0.283260 0.959043i \(-0.408584\pi\)
0.724832 + 0.688926i \(0.241918\pi\)
\(314\) −20.7321 −1.16998
\(315\) 0 0
\(316\) −8.12436 −0.457031
\(317\) −11.4016 + 3.05506i −0.640380 + 0.171589i −0.564376 0.825518i \(-0.690883\pi\)
−0.0760044 + 0.997107i \(0.524216\pi\)
\(318\) −1.36345 + 5.08845i −0.0764582 + 0.285346i
\(319\) 5.19615 3.00000i 0.290929 0.167968i
\(320\) 0 0
\(321\) 10.0000i 0.558146i
\(322\) 9.84873 + 0.707107i 0.548848 + 0.0394055i
\(323\) 6.72930 6.72930i 0.374428 0.374428i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) −3.53553 13.1948i −0.195515 0.729674i
\(328\) 1.74238 + 1.74238i 0.0962070 + 0.0962070i
\(329\) 27.5000 + 9.52628i 1.51612 + 0.525201i
\(330\) 0 0
\(331\) 5.92820 10.2679i 0.325844 0.564378i −0.655839 0.754901i \(-0.727685\pi\)
0.981683 + 0.190523i \(0.0610184\pi\)
\(332\) 11.2629 + 3.01790i 0.618134 + 0.165629i
\(333\) 4.57081 + 1.22474i 0.250479 + 0.0671156i
\(334\) 2.53590 4.39230i 0.138758 0.240336i
\(335\) 0 0
\(336\) 2.59808 0.500000i 0.141737 0.0272772i
\(337\) −13.2963 13.2963i −0.724297 0.724297i 0.245180 0.969477i \(-0.421153\pi\)
−0.969477 + 0.245180i \(0.921153\pi\)
\(338\) −2.80984 10.4865i −0.152835 0.570390i
\(339\) −1.50000 2.59808i −0.0814688 0.141108i
\(340\) 0 0
\(341\) 5.02628 + 2.90192i 0.272188 + 0.157148i
\(342\) −2.96713 + 2.96713i −0.160444 + 0.160444i
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 0.196152i 0.0105758i
\(345\) 0 0
\(346\) −6.46410 + 3.73205i −0.347512 + 0.200636i
\(347\) −7.39924 + 27.6143i −0.397212 + 1.48241i 0.420768 + 0.907168i \(0.361761\pi\)
−0.817980 + 0.575247i \(0.804906\pi\)
\(348\) 7.91688 2.12132i 0.424389 0.113715i
\(349\) −7.26795 −0.389044 −0.194522 0.980898i \(-0.562316\pi\)
−0.194522 + 0.980898i \(0.562316\pi\)
\(350\) 0 0
\(351\) 1.46410 0.0781480
\(352\) 0.707107 0.189469i 0.0376889 0.0100987i
\(353\) 0.928761 3.46618i 0.0494330 0.184486i −0.936795 0.349879i \(-0.886223\pi\)
0.986228 + 0.165393i \(0.0528893\pi\)
\(354\) −0.464102 + 0.267949i −0.0246667 + 0.0142413i
\(355\) 0 0
\(356\) 6.46410i 0.342597i
\(357\) 2.62038 + 5.39804i 0.138685 + 0.285694i
\(358\) −14.0406 + 14.0406i −0.742069 + 0.742069i
\(359\) 18.0000 + 10.3923i 0.950004 + 0.548485i 0.893082 0.449894i \(-0.148538\pi\)
0.0569216 + 0.998379i \(0.481871\pi\)
\(360\) 0 0
\(361\) 0.696152 + 1.20577i 0.0366396 + 0.0634617i
\(362\) −0.0507680 0.189469i −0.00266831 0.00995825i
\(363\) 7.39924 + 7.39924i 0.388359 + 0.388359i
\(364\) 2.92820 2.53590i 0.153480 0.132917i
\(365\) 0 0
\(366\) −6.09808 + 10.5622i −0.318752 + 0.552094i
\(367\) 30.2533 + 8.10634i 1.57921 + 0.423148i 0.938681 0.344787i \(-0.112049\pi\)
0.640528 + 0.767935i \(0.278716\pi\)
\(368\) 3.60488 + 0.965926i 0.187918 + 0.0503524i
\(369\) 1.23205 2.13397i 0.0641380 0.111090i
\(370\) 0 0
\(371\) 10.5359 9.12436i 0.546997 0.473713i
\(372\) 5.60609 + 5.60609i 0.290662 + 0.290662i
\(373\) −1.59008 5.93426i −0.0823312 0.307264i 0.912464 0.409156i \(-0.134177\pi\)
−0.994795 + 0.101892i \(0.967510\pi\)
\(374\) 0.830127 + 1.43782i 0.0429248 + 0.0743480i
\(375\) 0 0
\(376\) 9.52628 + 5.50000i 0.491280 + 0.283641i
\(377\) 8.48528 8.48528i 0.437014 0.437014i
\(378\) −1.15539 2.38014i −0.0594271 0.122421i
\(379\) 10.0526i 0.516365i 0.966096 + 0.258183i \(0.0831236\pi\)
−0.966096 + 0.258183i \(0.916876\pi\)
\(380\) 0 0
\(381\) 13.7321 7.92820i 0.703514 0.406174i
\(382\) −6.43331 + 24.0094i −0.329157 + 1.22843i
\(383\) −25.5624 + 6.84941i −1.30618 + 0.349989i −0.843782 0.536686i \(-0.819676\pi\)
−0.462394 + 0.886675i \(0.653009\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 23.7321 1.20793
\(387\) −0.189469 + 0.0507680i −0.00963123 + 0.00258068i
\(388\) −1.81173 + 6.76148i −0.0919768 + 0.343262i
\(389\) −23.9545 + 13.8301i −1.21454 + 0.701215i −0.963745 0.266825i \(-0.914025\pi\)
−0.250795 + 0.968040i \(0.580692\pi\)
\(390\) 0 0
\(391\) 8.46410i 0.428048i
\(392\) −6.43331 2.75908i −0.324931 0.139354i
\(393\) 9.65926 9.65926i 0.487245 0.487245i
\(394\) −22.3923 12.9282i −1.12811 0.651313i
\(395\) 0 0
\(396\) −0.366025 0.633975i −0.0183935 0.0318584i
\(397\) 5.03768 + 18.8009i 0.252834 + 0.943589i 0.969283 + 0.245949i \(0.0790997\pi\)
−0.716449 + 0.697640i \(0.754234\pi\)
\(398\) 18.7129 + 18.7129i 0.937995 + 0.937995i
\(399\) 10.9019 2.09808i 0.545779 0.105035i
\(400\) 0 0
\(401\) 10.4641 18.1244i 0.522552 0.905087i −0.477103 0.878847i \(-0.658313\pi\)
0.999656 0.0262399i \(-0.00835339\pi\)
\(402\) −3.86370 1.03528i −0.192704 0.0516349i
\(403\) 11.2122 + 3.00429i 0.558518 + 0.149654i
\(404\) −0.0980762 + 0.169873i −0.00487947 + 0.00845150i
\(405\) 0 0
\(406\) −20.4904 7.09808i −1.01692 0.352272i
\(407\) −2.44949 2.44949i −0.121417 0.121417i
\(408\) 0.586988 + 2.19067i 0.0290603 + 0.108454i
\(409\) 16.5981 + 28.7487i 0.820722 + 1.42153i 0.905145 + 0.425102i \(0.139762\pi\)
−0.0844233 + 0.996430i \(0.526905\pi\)
\(410\) 0 0
\(411\) −6.99038 4.03590i −0.344810 0.199076i
\(412\) −4.70951 + 4.70951i −0.232021 + 0.232021i
\(413\) 1.41421 + 0.101536i 0.0695889 + 0.00499626i
\(414\) 3.73205i 0.183420i
\(415\) 0 0
\(416\) 1.26795 0.732051i 0.0621663 0.0358917i
\(417\) 3.34607 12.4877i 0.163858 0.611525i
\(418\) 2.96713 0.795040i 0.145127 0.0388867i
\(419\) 10.5885 0.517280 0.258640 0.965974i \(-0.416726\pi\)
0.258640 + 0.965974i \(0.416726\pi\)
\(420\) 0 0
\(421\) −2.53590 −0.123592 −0.0617961 0.998089i \(-0.519683\pi\)
−0.0617961 + 0.998089i \(0.519683\pi\)
\(422\) −18.9903 + 5.08845i −0.924436 + 0.247702i
\(423\) 2.84701 10.6252i 0.138426 0.516614i
\(424\) 4.56218 2.63397i 0.221559 0.127917i
\(425\) 0 0
\(426\) 12.8564i 0.622895i
\(427\) 29.0285 14.0914i 1.40479 0.681929i
\(428\) −7.07107 + 7.07107i −0.341793 + 0.341793i
\(429\) −0.928203 0.535898i −0.0448141 0.0258734i
\(430\) 0 0
\(431\) −0.232051 0.401924i −0.0111775 0.0193600i 0.860383 0.509649i \(-0.170225\pi\)
−0.871560 + 0.490289i \(0.836891\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) −20.0256 20.0256i −0.962370 0.962370i 0.0369472 0.999317i \(-0.488237\pi\)
−0.999317 + 0.0369472i \(0.988237\pi\)
\(434\) −3.96410 20.5981i −0.190283 0.988739i
\(435\) 0 0
\(436\) −6.83013 + 11.8301i −0.327104 + 0.566560i
\(437\) 15.1266 + 4.05317i 0.723606 + 0.193890i
\(438\) 7.72741 + 2.07055i 0.369230 + 0.0989348i
\(439\) 19.6962 34.1147i 0.940046 1.62821i 0.174667 0.984628i \(-0.444115\pi\)
0.765379 0.643580i \(-0.222552\pi\)
\(440\) 0 0
\(441\) −1.00000 + 6.92820i −0.0476190 + 0.329914i
\(442\) 2.34795 + 2.34795i 0.111681 + 0.111681i
\(443\) 5.56892 + 20.7835i 0.264587 + 0.987454i 0.962502 + 0.271273i \(0.0874447\pi\)
−0.697915 + 0.716181i \(0.745889\pi\)
\(444\) −2.36603 4.09808i −0.112287 0.194486i
\(445\) 0 0
\(446\) −10.6244 6.13397i −0.503078 0.290452i
\(447\) −12.7279 + 12.7279i −0.602010 + 0.602010i
\(448\) −2.19067 1.48356i −0.103499 0.0700918i
\(449\) 29.7321i 1.40314i −0.712599 0.701571i \(-0.752482\pi\)
0.712599 0.701571i \(-0.247518\pi\)
\(450\) 0 0
\(451\) −1.56218 + 0.901924i −0.0735601 + 0.0424699i
\(452\) −0.776457 + 2.89778i −0.0365215 + 0.136300i
\(453\) 10.5558 2.82843i 0.495956 0.132891i
\(454\) 5.32051 0.249704
\(455\) 0 0
\(456\) 4.19615 0.196503
\(457\) 32.7028 8.76268i 1.52977 0.409901i 0.606827 0.794834i \(-0.292442\pi\)
0.922945 + 0.384933i \(0.125775\pi\)
\(458\) 3.05506 11.4016i 0.142754 0.532764i
\(459\) 1.96410 1.13397i 0.0916764 0.0529294i
\(460\) 0 0
\(461\) 19.3205i 0.899846i 0.893067 + 0.449923i \(0.148549\pi\)
−0.893067 + 0.449923i \(0.851451\pi\)
\(462\) −0.138701 + 1.93185i −0.00645294 + 0.0898779i
\(463\) −10.3292 + 10.3292i −0.480039 + 0.480039i −0.905144 0.425105i \(-0.860237\pi\)
0.425105 + 0.905144i \(0.360237\pi\)
\(464\) −7.09808 4.09808i −0.329520 0.190248i
\(465\) 0 0
\(466\) 9.46410 + 16.3923i 0.438416 + 0.759359i
\(467\) 2.08416 + 7.77817i 0.0964432 + 0.359931i 0.997234 0.0743217i \(-0.0236792\pi\)
−0.900791 + 0.434253i \(0.857012\pi\)
\(468\) −1.03528 1.03528i −0.0478557 0.0478557i
\(469\) 6.92820 + 8.00000i 0.319915 + 0.369406i
\(470\) 0 0
\(471\) 10.3660 17.9545i 0.477641 0.827299i
\(472\) 0.517638 + 0.138701i 0.0238262 + 0.00638422i
\(473\) 0.138701 + 0.0371647i 0.00637747 + 0.00170884i
\(474\) 4.06218 7.03590i 0.186582 0.323170i
\(475\) 0 0
\(476\) 1.96410 5.66987i 0.0900244 0.259878i
\(477\) −3.72500 3.72500i −0.170556 0.170556i
\(478\) −1.25693 4.69093i −0.0574907 0.214558i
\(479\) −9.99038 17.3038i −0.456472 0.790633i 0.542299 0.840185i \(-0.317554\pi\)
−0.998772 + 0.0495524i \(0.984221\pi\)
\(480\) 0 0
\(481\) −6.00000 3.46410i −0.273576 0.157949i
\(482\) 9.14162 9.14162i 0.416389 0.416389i
\(483\) −5.53674 + 8.17569i −0.251930 + 0.372007i
\(484\) 10.4641i 0.475641i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) −3.50335 + 13.0747i −0.158752 + 0.592470i 0.840003 + 0.542582i \(0.182553\pi\)
−0.998755 + 0.0498882i \(0.984114\pi\)
\(488\) 11.7806 3.15660i 0.533282 0.142892i
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) −1.66025 −0.0749262 −0.0374631 0.999298i \(-0.511928\pi\)
−0.0374631 + 0.999298i \(0.511928\pi\)
\(492\) −2.38014 + 0.637756i −0.107305 + 0.0287523i
\(493\) 4.81105 17.9551i 0.216679 0.808656i
\(494\) 5.32051 3.07180i 0.239381 0.138207i
\(495\) 0 0
\(496\) 7.92820i 0.355987i
\(497\) −19.0733 + 28.1642i −0.855554 + 1.26333i
\(498\) −8.24504 + 8.24504i −0.369469 + 0.369469i
\(499\) −18.1699 10.4904i −0.813395 0.469614i 0.0347383 0.999396i \(-0.488940\pi\)
−0.848134 + 0.529782i \(0.822274\pi\)
\(500\) 0 0
\(501\) 2.53590 + 4.39230i 0.113296 + 0.196234i
\(502\) 4.62158 + 17.2480i 0.206271 + 0.769814i
\(503\) −30.5307 30.5307i −1.36130 1.36130i −0.872268 0.489028i \(-0.837352\pi\)
−0.489028 0.872268i \(-0.662648\pi\)
\(504\) −0.866025 + 2.50000i −0.0385758 + 0.111359i
\(505\) 0 0
\(506\) −1.36603 + 2.36603i −0.0607272 + 0.105183i
\(507\) 10.4865 + 2.80984i 0.465721 + 0.124790i
\(508\) −15.3161 4.10394i −0.679543 0.182083i
\(509\) 2.02628 3.50962i 0.0898133 0.155561i −0.817619 0.575760i \(-0.804706\pi\)
0.907432 + 0.420199i \(0.138040\pi\)
\(510\) 0 0
\(511\) −13.8564 16.0000i −0.612971 0.707798i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −1.08604 4.05317i −0.0479500 0.178952i
\(514\) −1.92820 3.33975i −0.0850494 0.147310i
\(515\) 0 0
\(516\) 0.169873 + 0.0980762i 0.00747824 + 0.00431756i
\(517\) −5.69402 + 5.69402i −0.250423 + 0.250423i
\(518\) −0.896575 + 12.4877i −0.0393933 + 0.548677i
\(519\) 7.46410i 0.327638i
\(520\) 0 0
\(521\) 27.3109 15.7679i 1.19651 0.690806i 0.236736 0.971574i \(-0.423922\pi\)
0.959776 + 0.280768i \(0.0905890\pi\)
\(522\) −2.12132 + 7.91688i −0.0928477 + 0.346512i
\(523\) −6.50266 + 1.74238i −0.284342 + 0.0761891i −0.398171 0.917311i \(-0.630355\pi\)
0.113829 + 0.993500i \(0.463688\pi\)
\(524\) −13.6603 −0.596751
\(525\) 0 0
\(526\) 18.5167 0.807365
\(527\) 17.3681 4.65376i 0.756566 0.202721i
\(528\) −0.189469 + 0.707107i −0.00824557 + 0.0307729i
\(529\) 7.85641 4.53590i 0.341583 0.197213i
\(530\) 0 0
\(531\) 0.535898i 0.0232560i
\(532\) −9.19239 6.22526i −0.398541 0.269899i
\(533\) −2.55103 + 2.55103i −0.110497 + 0.110497i
\(534\) 5.59808 + 3.23205i 0.242252 + 0.139865i
\(535\) 0 0
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) −5.13922 19.1798i −0.221774 0.827670i
\(538\) 18.1445 + 18.1445i 0.782267 + 0.782267i
\(539\) 3.16987 4.02628i 0.136536 0.173424i
\(540\) 0 0
\(541\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(542\) 2.38014 + 0.637756i 0.102236 + 0.0273940i
\(543\) 0.189469 + 0.0507680i 0.00813088 + 0.00217866i
\(544\) 1.13397 1.96410i 0.0486188 0.0842102i
\(545\) 0 0
\(546\) 0.732051 + 3.80385i 0.0313289 + 0.162790i
\(547\) 31.0483 + 31.0483i 1.32753 + 1.32753i 0.907519 + 0.420012i \(0.137974\pi\)
0.420012 + 0.907519i \(0.362026\pi\)
\(548\) 2.08913 + 7.79676i 0.0892434 + 0.333061i
\(549\) −6.09808 10.5622i −0.260260 0.450783i
\(550\) 0 0
\(551\) −29.7846 17.1962i −1.26887 0.732581i
\(552\) −2.63896 + 2.63896i −0.112322 + 0.112322i
\(553\) −19.3371 + 9.38684i −0.822297 + 0.399169i
\(554\) 16.5885i 0.704776i
\(555\) 0 0
\(556\) −11.1962 + 6.46410i −0.474823 + 0.274139i
\(557\) −3.17020 + 11.8313i −0.134326 + 0.501310i 0.865674 + 0.500608i \(0.166890\pi\)
−1.00000 0.000702224i \(0.999776\pi\)
\(558\) −7.65806 + 2.05197i −0.324191 + 0.0868668i
\(559\) 0.287187 0.0121467
\(560\) 0 0
\(561\) −1.66025 −0.0700960
\(562\) 19.2999 5.17140i 0.814119 0.218142i
\(563\) 10.3292 38.5491i 0.435324 1.62465i −0.304966 0.952363i \(-0.598645\pi\)
0.740290 0.672288i \(-0.234688\pi\)
\(564\) −9.52628 + 5.50000i −0.401129 + 0.231592i
\(565\) 0 0
\(566\) 7.12436i 0.299459i
\(567\) 2.63896 + 0.189469i 0.110826 + 0.00795694i
\(568\) −9.09085 + 9.09085i −0.381444 + 0.381444i
\(569\) −5.55256 3.20577i −0.232775 0.134393i 0.379076 0.925365i \(-0.376242\pi\)
−0.611852 + 0.790972i \(0.709575\pi\)
\(570\) 0 0
\(571\) 3.80385 + 6.58846i 0.159186 + 0.275718i 0.934575 0.355765i \(-0.115780\pi\)
−0.775389 + 0.631483i \(0.782446\pi\)
\(572\) 0.277401 + 1.03528i 0.0115987 + 0.0432871i
\(573\) −17.5761 17.5761i −0.734254 0.734254i
\(574\) 6.16025 + 2.13397i 0.257124 + 0.0890704i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −2.17209 0.582009i −0.0904252 0.0242294i 0.213323 0.976982i \(-0.431571\pi\)
−0.303748 + 0.952752i \(0.598238\pi\)
\(578\) −11.4524 3.06866i −0.476357 0.127640i
\(579\) −11.8660 + 20.5526i −0.493135 + 0.854135i
\(580\) 0 0
\(581\) 30.2942 5.83013i 1.25682 0.241874i
\(582\) −4.94975 4.94975i −0.205174 0.205174i
\(583\) 0.998111 + 3.72500i 0.0413376 + 0.154274i
\(584\) −4.00000 6.92820i −0.165521 0.286691i
\(585\) 0 0
\(586\) −11.4904 6.63397i −0.474663 0.274047i
\(587\) −13.0053 + 13.0053i −0.536787 + 0.536787i −0.922584 0.385797i \(-0.873927\pi\)
0.385797 + 0.922584i \(0.373927\pi\)
\(588\) 5.60609 4.19187i 0.231191 0.172870i
\(589\) 33.2679i 1.37078i
\(590\) 0 0
\(591\) 22.3923 12.9282i 0.921096 0.531795i
\(592\) −1.22474 + 4.57081i −0.0503367 + 0.187859i
\(593\) 16.2313 4.34916i 0.666538 0.178598i 0.0903434 0.995911i \(-0.471204\pi\)
0.576195 + 0.817312i \(0.304537\pi\)
\(594\) 0.732051 0.0300364
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −25.5624 + 6.84941i −1.04620 + 0.280328i
\(598\) −1.41421 + 5.27792i −0.0578315 + 0.215830i
\(599\) 38.0429 21.9641i 1.55439 0.897429i 0.556617 0.830770i \(-0.312099\pi\)
0.997776 0.0666594i \(-0.0212341\pi\)
\(600\) 0 0
\(601\) 20.2487i 0.825962i 0.910740 + 0.412981i \(0.135512\pi\)
−0.910740 + 0.412981i \(0.864488\pi\)
\(602\) −0.226633 0.466870i −0.00923689 0.0190282i
\(603\) 2.82843 2.82843i 0.115182 0.115182i
\(604\) −9.46410 5.46410i −0.385089 0.222331i
\(605\) 0 0
\(606\) −0.0980762 0.169873i −0.00398407 0.00690062i
\(607\) 6.24384 + 23.3023i 0.253430 + 0.945813i 0.968957 + 0.247228i \(0.0795197\pi\)
−0.715528 + 0.698585i \(0.753814\pi\)
\(608\) −2.96713 2.96713i −0.120333 0.120333i
\(609\) 16.3923 14.1962i 0.664250 0.575257i
\(610\) 0 0
\(611\) −8.05256 + 13.9474i −0.325772 + 0.564253i
\(612\) −2.19067 0.586988i −0.0885526 0.0237276i
\(613\) 4.43211 + 1.18758i 0.179011 + 0.0479659i 0.347211 0.937787i \(-0.387129\pi\)
−0.168200 + 0.985753i \(0.553795\pi\)
\(614\) −9.46410 + 16.3923i −0.381940 + 0.661540i
\(615\) 0 0
\(616\) 1.46410 1.26795i 0.0589903 0.0510871i
\(617\) −3.05506 3.05506i −0.122992 0.122992i 0.642932 0.765924i \(-0.277718\pi\)
−0.765924 + 0.642932i \(0.777718\pi\)
\(618\) −1.72380 6.43331i −0.0693414 0.258786i
\(619\) 6.90192 + 11.9545i 0.277412 + 0.480491i 0.970741 0.240130i \(-0.0771901\pi\)
−0.693329 + 0.720621i \(0.743857\pi\)
\(620\) 0 0
\(621\) 3.23205 + 1.86603i 0.129698 + 0.0748810i
\(622\) −9.71003 + 9.71003i −0.389337 + 0.389337i
\(623\) −7.46859 15.3855i −0.299223 0.616406i
\(624\) 1.46410i 0.0586110i
\(625\) 0 0
\(626\) 15.9904 9.23205i 0.639104 0.368987i
\(627\) −0.795040 + 2.96713i −0.0317508 + 0.118496i
\(628\) −20.0256 + 5.36585i −0.799109 + 0.214121i
\(629\) −10.7321 −0.427915
\(630\) 0 0
\(631\) −16.4115 −0.653333 −0.326667 0.945140i \(-0.605925\pi\)
−0.326667 + 0.945140i \(0.605925\pi\)
\(632\) −7.84752 + 2.10274i −0.312158 + 0.0836424i
\(633\) 5.08845 18.9903i 0.202248 0.754799i
\(634\) −10.2224 + 5.90192i −0.405985 + 0.234395i
\(635\) 0 0
\(636\) 5.26795i 0.208888i
\(637\) 4.03957 9.41902i 0.160054 0.373195i
\(638\) 4.24264 4.24264i 0.167968 0.167968i
\(639\) 11.1340 + 6.42820i 0.440453 + 0.254296i
\(640\) 0 0
\(641\) −0.330127 0.571797i −0.0130392 0.0225846i 0.859432 0.511250i \(-0.170817\pi\)
−0.872471 + 0.488665i \(0.837484\pi\)
\(642\) −2.58819 9.65926i −0.102148 0.381221i
\(643\) 24.3190 + 24.3190i 0.959049 + 0.959049i 0.999194 0.0401449i \(-0.0127819\pi\)
−0.0401449 + 0.999194i \(0.512782\pi\)
\(644\) 9.69615 1.86603i 0.382082 0.0735317i
\(645\) 0 0
\(646\) 4.75833 8.24167i 0.187214 0.324264i
\(647\) 18.8009 + 5.03768i 0.739139 + 0.198052i 0.608695 0.793404i \(-0.291693\pi\)
0.130444 + 0.991456i \(0.458360\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) −0.196152 + 0.339746i −0.00769966 + 0.0133362i
\(650\) 0 0
\(651\) 19.8205 + 6.86603i 0.776827 + 0.269101i
\(652\) 8.48528 + 8.48528i 0.332309 + 0.332309i
\(653\) −5.85993 21.8695i −0.229317 0.855821i −0.980629 0.195875i \(-0.937245\pi\)
0.751312 0.659947i \(-0.229421\pi\)
\(654\) −6.83013 11.8301i −0.267079 0.462595i
\(655\) 0 0
\(656\) 2.13397 + 1.23205i 0.0833177 + 0.0481035i
\(657\) −5.65685 + 5.65685i −0.220695 + 0.220695i
\(658\) 29.0285 + 2.08416i 1.13165 + 0.0812488i
\(659\) 14.1962i 0.553004i −0.961013 0.276502i \(-0.910825\pi\)
0.961013 0.276502i \(-0.0891752\pi\)
\(660\) 0 0
\(661\) −34.5167 + 19.9282i −1.34254 + 0.775117i −0.987180 0.159611i \(-0.948976\pi\)
−0.355363 + 0.934729i \(0.615643\pi\)
\(662\) 3.06866 11.4524i 0.119267 0.445111i
\(663\) −3.20736 + 0.859411i −0.124564 + 0.0333767i
\(664\) 11.6603 0.452506
\(665\) 0 0
\(666\) 4.73205 0.183363
\(667\) 29.5462 7.91688i 1.14403 0.306543i
\(668\) 1.31268 4.89898i 0.0507890 0.189547i
\(669\) 10.6244 6.13397i 0.410761 0.237153i
\(670\) 0 0
\(671\) 8.92820i 0.344669i
\(672\) 2.38014 1.15539i 0.0918159 0.0445703i
\(673\) 1.60368 1.60368i 0.0618174 0.0618174i −0.675522 0.737340i \(-0.736082\pi\)
0.737340 + 0.675522i \(0.236082\pi\)
\(674\) −16.2846 9.40192i −0.627260 0.362149i
\(675\) 0 0
\(676\) −5.42820 9.40192i −0.208777 0.361612i
\(677\) −11.0871 41.3775i −0.426111 1.59027i −0.761485 0.648183i \(-0.775529\pi\)
0.335374 0.942085i \(-0.391137\pi\)
\(678\) −2.12132 2.12132i −0.0814688 0.0814688i
\(679\) 3.50000 + 18.1865i 0.134318 + 0.697935i
\(680\) 0 0
\(681\) −2.66025 + 4.60770i −0.101941 + 0.176567i
\(682\) 5.60609 + 1.50215i 0.214668 + 0.0575202i
\(683\) 36.7052 + 9.83512i 1.40448 + 0.376331i 0.879953 0.475060i \(-0.157574\pi\)
0.524532 + 0.851391i \(0.324240\pi\)
\(684\) −2.09808 + 3.63397i −0.0802219 + 0.138948i
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 8.34658 + 8.34658i 0.318442 + 0.318442i
\(688\) −0.0507680 0.189469i −0.00193551 0.00722343i
\(689\) 3.85641 + 6.67949i 0.146917 + 0.254468i
\(690\) 0 0
\(691\) 17.6147 + 10.1699i 0.670096 + 0.386880i 0.796113 0.605148i \(-0.206886\pi\)
−0.126017 + 0.992028i \(0.540219\pi\)
\(692\) −5.27792 + 5.27792i −0.200636 + 0.200636i
\(693\) −1.60368 1.08604i −0.0609189 0.0412554i
\(694\) 28.5885i 1.08520i
\(695\) 0 0
\(696\) 7.09808 4.09808i 0.269052 0.155337i
\(697\) −1.44640 + 5.39804i −0.0547863 + 0.204465i
\(698\) −7.02030 + 1.88108i −0.265722 + 0.0712001i
\(699\) −18.9282 −0.715930
\(700\) 0 0
\(701\) 21.4641 0.810688 0.405344 0.914164i \(-0.367152\pi\)
0.405344 + 0.914164i \(0.367152\pi\)
\(702\) 1.41421 0.378937i 0.0533761 0.0143021i
\(703\) −5.13922 + 19.1798i −0.193829 + 0.723380i
\(704\) 0.633975 0.366025i 0.0238938 0.0137951i
\(705\) 0 0
\(706\) 3.58846i 0.135053i
\(707\) −0.0371647 + 0.517638i −0.00139772 + 0.0194678i
\(708\) −0.378937 + 0.378937i −0.0142413 + 0.0142413i
\(709\) −33.9282 19.5885i −1.27420 0.735660i −0.298425 0.954433i \(-0.596461\pi\)
−0.975776 + 0.218773i \(0.929795\pi\)
\(710\) 0 0
\(711\) 4.06218 + 7.03590i 0.152344 + 0.263867i
\(712\) −1.67303 6.24384i −0.0626995 0.233998i
\(713\) 20.9222 + 20.9222i 0.783543 + 0.783543i
\(714\) 3.92820 + 4.53590i 0.147009 + 0.169752i
\(715\) 0 0
\(716\) −9.92820 + 17.1962i −0.371034 + 0.642650i
\(717\) 4.69093 + 1.25693i 0.175186 + 0.0469409i
\(718\) 20.0764 + 5.37945i 0.749244 + 0.200759i
\(719\) 6.66987 11.5526i 0.248744 0.430838i −0.714433 0.699703i \(-0.753315\pi\)
0.963178 + 0.268866i \(0.0866488\pi\)
\(720\) 0 0
\(721\) −5.76795 + 16.6506i −0.214810 + 0.620102i
\(722\) 0.984508 + 0.984508i 0.0366396 + 0.0366396i
\(723\) 3.34607 + 12.4877i 0.124442 + 0.464422i
\(724\) −0.0980762 0.169873i −0.00364497 0.00631328i
\(725\) 0 0
\(726\) 9.06218 + 5.23205i 0.336329 + 0.194180i
\(727\) 0.0879327 0.0879327i 0.00326124 0.00326124i −0.705474 0.708736i \(-0.749266\pi\)
0.708736 + 0.705474i \(0.249266\pi\)
\(728\) 2.17209 3.20736i 0.0805029 0.118873i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0.385263 0.222432i 0.0142495 0.00822694i
\(732\) −3.15660 + 11.7806i −0.116671 + 0.435423i
\(733\) 26.2509 7.03390i 0.969599 0.259803i 0.260940 0.965355i \(-0.415967\pi\)
0.708658 + 0.705552i \(0.249301\pi\)
\(734\) 31.3205 1.15606
\(735\) 0 0
\(736\) 3.73205 0.137565
\(737\) −2.82843 + 0.757875i −0.104186 + 0.0279167i
\(738\) 0.637756 2.38014i 0.0234761 0.0876141i
\(739\) 11.6147 6.70577i 0.427255 0.246676i −0.270922 0.962601i \(-0.587328\pi\)
0.698177 + 0.715926i \(0.253995\pi\)
\(740\) 0 0
\(741\) 6.14359i 0.225691i
\(742\) 7.81534 11.5403i 0.286910 0.423659i
\(743\) 27.2354 27.2354i 0.999170 0.999170i −0.000830035 1.00000i \(-0.500264\pi\)
1.00000 0.000830035i \(0.000264208\pi\)
\(744\) 6.86603 + 3.96410i 0.251721 + 0.145331i
\(745\) 0 0
\(746\) −3.07180 5.32051i −0.112466 0.194798i
\(747\) −3.01790 11.2629i −0.110419 0.412089i
\(748\) 1.17398 + 1.17398i 0.0429248 + 0.0429248i
\(749\) −8.66025 + 25.0000i −0.316439 + 0.913480i
\(750\) 0 0
\(751\) 12.9282 22.3923i 0.471757 0.817107i −0.527721 0.849418i \(-0.676953\pi\)
0.999478 + 0.0323109i \(0.0102867\pi\)
\(752\) 10.6252 + 2.84701i 0.387461 + 0.103820i
\(753\) −17.2480 4.62158i −0.628551 0.168420i
\(754\) 6.00000 10.3923i 0.218507 0.378465i
\(755\) 0 0
\(756\) −1.73205 2.00000i −0.0629941 0.0727393i
\(757\) 14.9743 + 14.9743i 0.544252 + 0.544252i 0.924772 0.380521i \(-0.124255\pi\)
−0.380521 + 0.924772i \(0.624255\pi\)
\(758\) 2.60179 + 9.71003i 0.0945014 + 0.352684i
\(759\) −1.36603 2.36603i −0.0495836 0.0858813i
\(760\) 0 0
\(761\) −10.7942 6.23205i −0.391290 0.225912i 0.291429 0.956593i \(-0.405869\pi\)
−0.682719 + 0.730681i \(0.739203\pi\)
\(762\) 11.2122 11.2122i 0.406174 0.406174i
\(763\) −2.58819 + 36.0488i −0.0936988 + 1.30506i
\(764\) 24.8564i 0.899273i
\(765\) 0 0
\(766\) −22.9186 + 13.2321i −0.828082 + 0.478093i
\(767\) −0.203072 + 0.757875i −0.00733250 + 0.0273653i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) 9.07180 0.327137 0.163569 0.986532i \(-0.447699\pi\)
0.163569 + 0.986532i \(0.447699\pi\)
\(770\) 0 0
\(771\) 3.85641 0.138885
\(772\) 22.9234 6.14231i 0.825031 0.221066i
\(773\) −9.88589 + 36.8947i −0.355571 + 1.32701i 0.524194 + 0.851599i \(0.324367\pi\)
−0.879765 + 0.475409i \(0.842300\pi\)
\(774\) −0.169873 + 0.0980762i −0.00610596 + 0.00352528i
\(775\) 0 0
\(776\) 7.00000i 0.251285i
\(777\) −10.3664 7.02030i −0.371891 0.251852i
\(778\) −19.5588 + 19.5588i −0.701215 + 0.701215i
\(779\) 8.95448 + 5.16987i 0.320828 + 0.185230i
\(780\) 0 0
\(781\) −4.70577 8.15064i −0.168386 0.291653i
\(782\) 2.19067 + 8.17569i 0.0783382 + 0.292362i