Properties

Label 525.2.r.f.424.2
Level $525$
Weight $2$
Character 525.424
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 424.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.424
Dual form 525.2.r.f.499.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.36603 - 1.36603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.73205 - 4.73205i) q^{4} +2.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} -9.46410i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(2.36603 - 1.36603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.73205 - 4.73205i) q^{4} +2.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} -9.46410i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.366025 + 0.633975i) q^{11} +(4.73205 - 2.73205i) q^{12} +2.26795i q^{13} +(-7.09808 + 1.36603i) q^{14} +(-7.46410 - 12.9282i) q^{16} +(2.83013 + 1.63397i) q^{17} +(2.36603 + 1.36603i) q^{18} +(2.23205 + 3.86603i) q^{19} +(-1.73205 - 2.00000i) q^{21} +2.00000i q^{22} +(-4.09808 + 2.36603i) q^{23} +(4.73205 - 8.19615i) q^{24} +(3.09808 + 5.36603i) q^{26} +1.00000i q^{27} +(-10.9282 + 9.46410i) q^{28} +4.19615 q^{29} +(0.232051 - 0.401924i) q^{31} +(-18.9282 - 10.9282i) q^{32} +(-0.633975 + 0.366025i) q^{33} +8.92820 q^{34} +5.46410 q^{36} +(2.76795 - 1.59808i) q^{37} +(10.5622 + 6.09808i) q^{38} +(-1.13397 + 1.96410i) q^{39} -0.732051 q^{41} +(-6.83013 - 2.36603i) q^{42} +3.19615i q^{43} +(2.00000 + 3.46410i) q^{44} +(-6.46410 + 11.1962i) q^{46} +(-1.73205 + 1.00000i) q^{47} -14.9282i q^{48} +(5.50000 + 4.33013i) q^{49} +(1.63397 + 2.83013i) q^{51} +(10.7321 + 6.19615i) q^{52} +(-10.7321 - 6.19615i) q^{53} +(1.36603 + 2.36603i) q^{54} +(-8.19615 + 23.6603i) q^{56} +4.46410i q^{57} +(9.92820 - 5.73205i) q^{58} +(-0.0980762 + 0.169873i) q^{59} +(-2.00000 - 3.46410i) q^{61} -1.26795i q^{62} +(-0.500000 - 2.59808i) q^{63} -29.8564 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-12.6962 - 7.33013i) q^{67} +(15.4641 - 8.92820i) q^{68} -4.73205 q^{69} +6.19615 q^{71} +(8.19615 - 4.73205i) q^{72} +(-10.9641 - 6.33013i) q^{73} +(4.36603 - 7.56218i) q^{74} +24.3923 q^{76} +(1.46410 - 1.26795i) q^{77} +6.19615i q^{78} +(-3.69615 - 6.40192i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.73205 + 1.00000i) q^{82} +15.1244i q^{83} +(-14.1962 + 2.73205i) q^{84} +(4.36603 + 7.56218i) q^{86} +(3.63397 + 2.09808i) q^{87} +(6.00000 + 3.46410i) q^{88} +(7.56218 + 13.0981i) q^{89} +(1.96410 - 5.66987i) q^{91} +25.8564i q^{92} +(0.401924 - 0.232051i) q^{93} +(-2.73205 + 4.73205i) q^{94} +(-10.9282 - 18.9282i) q^{96} -14.9282i q^{97} +(18.9282 + 2.73205i) q^{98} -0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{2} + 4q^{4} + 4q^{6} - 10q^{7} + 2q^{9} + O(q^{10}) \) \( 4q + 6q^{2} + 4q^{4} + 4q^{6} - 10q^{7} + 2q^{9} + 2q^{11} + 12q^{12} - 18q^{14} - 16q^{16} - 6q^{17} + 6q^{18} + 2q^{19} - 6q^{23} + 12q^{24} + 2q^{26} - 16q^{28} - 4q^{29} - 6q^{31} - 48q^{32} - 6q^{33} + 8q^{34} + 8q^{36} + 18q^{37} + 18q^{38} - 8q^{39} + 4q^{41} - 10q^{42} + 8q^{44} - 12q^{46} + 22q^{49} + 10q^{51} + 36q^{52} - 36q^{53} + 2q^{54} - 12q^{56} + 12q^{58} + 10q^{59} - 8q^{61} - 2q^{63} - 64q^{64} - 4q^{66} - 30q^{67} + 48q^{68} - 12q^{69} + 4q^{71} + 12q^{72} - 30q^{73} + 14q^{74} + 56q^{76} - 8q^{77} + 6q^{79} - 2q^{81} - 36q^{84} + 14q^{86} + 18q^{87} + 24q^{88} + 6q^{89} - 6q^{91} + 12q^{93} - 4q^{94} - 16q^{96} + 48q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.36603 1.36603i 1.67303 0.965926i 0.707107 0.707107i \(-0.250000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 2.73205 4.73205i 1.36603 2.36603i
\(5\) 0 0
\(6\) 2.73205 1.11536
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 9.46410i 3.34607i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.366025 + 0.633975i −0.110361 + 0.191151i −0.915916 0.401371i \(-0.868534\pi\)
0.805555 + 0.592521i \(0.201867\pi\)
\(12\) 4.73205 2.73205i 1.36603 0.788675i
\(13\) 2.26795i 0.629016i 0.949255 + 0.314508i \(0.101840\pi\)
−0.949255 + 0.314508i \(0.898160\pi\)
\(14\) −7.09808 + 1.36603i −1.89704 + 0.365086i
\(15\) 0 0
\(16\) −7.46410 12.9282i −1.86603 3.23205i
\(17\) 2.83013 + 1.63397i 0.686407 + 0.396297i 0.802264 0.596969i \(-0.203628\pi\)
−0.115858 + 0.993266i \(0.536962\pi\)
\(18\) 2.36603 + 1.36603i 0.557678 + 0.321975i
\(19\) 2.23205 + 3.86603i 0.512068 + 0.886927i 0.999902 + 0.0139909i \(0.00445360\pi\)
−0.487835 + 0.872936i \(0.662213\pi\)
\(20\) 0 0
\(21\) −1.73205 2.00000i −0.377964 0.436436i
\(22\) 2.00000i 0.426401i
\(23\) −4.09808 + 2.36603i −0.854508 + 0.493350i −0.862169 0.506620i \(-0.830895\pi\)
0.00766135 + 0.999971i \(0.497561\pi\)
\(24\) 4.73205 8.19615i 0.965926 1.67303i
\(25\) 0 0
\(26\) 3.09808 + 5.36603i 0.607583 + 1.05236i
\(27\) 1.00000i 0.192450i
\(28\) −10.9282 + 9.46410i −2.06524 + 1.78855i
\(29\) 4.19615 0.779206 0.389603 0.920983i \(-0.372612\pi\)
0.389603 + 0.920983i \(0.372612\pi\)
\(30\) 0 0
\(31\) 0.232051 0.401924i 0.0416776 0.0721876i −0.844434 0.535659i \(-0.820063\pi\)
0.886112 + 0.463472i \(0.153396\pi\)
\(32\) −18.9282 10.9282i −3.34607 1.93185i
\(33\) −0.633975 + 0.366025i −0.110361 + 0.0637168i
\(34\) 8.92820 1.53117
\(35\) 0 0
\(36\) 5.46410 0.910684
\(37\) 2.76795 1.59808i 0.455048 0.262722i −0.254912 0.966964i \(-0.582046\pi\)
0.709960 + 0.704242i \(0.248713\pi\)
\(38\) 10.5622 + 6.09808i 1.71341 + 0.989239i
\(39\) −1.13397 + 1.96410i −0.181581 + 0.314508i
\(40\) 0 0
\(41\) −0.732051 −0.114327 −0.0571636 0.998365i \(-0.518206\pi\)
−0.0571636 + 0.998365i \(0.518206\pi\)
\(42\) −6.83013 2.36603i −1.05391 0.365086i
\(43\) 3.19615i 0.487409i 0.969850 + 0.243704i \(0.0783627\pi\)
−0.969850 + 0.243704i \(0.921637\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 0 0
\(46\) −6.46410 + 11.1962i −0.953080 + 1.65078i
\(47\) −1.73205 + 1.00000i −0.252646 + 0.145865i −0.620975 0.783830i \(-0.713263\pi\)
0.368329 + 0.929695i \(0.379930\pi\)
\(48\) 14.9282i 2.15470i
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 1.63397 + 2.83013i 0.228802 + 0.396297i
\(52\) 10.7321 + 6.19615i 1.48827 + 0.859252i
\(53\) −10.7321 6.19615i −1.47416 0.851107i −0.474584 0.880210i \(-0.657402\pi\)
−0.999576 + 0.0291032i \(0.990735\pi\)
\(54\) 1.36603 + 2.36603i 0.185893 + 0.321975i
\(55\) 0 0
\(56\) −8.19615 + 23.6603i −1.09526 + 3.16173i
\(57\) 4.46410i 0.591285i
\(58\) 9.92820 5.73205i 1.30364 0.752655i
\(59\) −0.0980762 + 0.169873i −0.0127684 + 0.0221156i −0.872339 0.488901i \(-0.837398\pi\)
0.859571 + 0.511017i \(0.170731\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 1.26795i 0.161030i
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) −29.8564 −3.73205
\(65\) 0 0
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) −12.6962 7.33013i −1.55108 0.895518i −0.998054 0.0623548i \(-0.980139\pi\)
−0.553028 0.833163i \(-0.686528\pi\)
\(68\) 15.4641 8.92820i 1.87530 1.08270i
\(69\) −4.73205 −0.569672
\(70\) 0 0
\(71\) 6.19615 0.735348 0.367674 0.929955i \(-0.380154\pi\)
0.367674 + 0.929955i \(0.380154\pi\)
\(72\) 8.19615 4.73205i 0.965926 0.557678i
\(73\) −10.9641 6.33013i −1.28325 0.740885i −0.305810 0.952093i \(-0.598927\pi\)
−0.977441 + 0.211207i \(0.932260\pi\)
\(74\) 4.36603 7.56218i 0.507540 0.879085i
\(75\) 0 0
\(76\) 24.3923 2.79799
\(77\) 1.46410 1.26795i 0.166850 0.144496i
\(78\) 6.19615i 0.701576i
\(79\) −3.69615 6.40192i −0.415850 0.720273i 0.579668 0.814853i \(-0.303182\pi\)
−0.995517 + 0.0945803i \(0.969849\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.73205 + 1.00000i −0.191273 + 0.110432i
\(83\) 15.1244i 1.66011i 0.557679 + 0.830057i \(0.311692\pi\)
−0.557679 + 0.830057i \(0.688308\pi\)
\(84\) −14.1962 + 2.73205i −1.54893 + 0.298091i
\(85\) 0 0
\(86\) 4.36603 + 7.56218i 0.470801 + 0.815451i
\(87\) 3.63397 + 2.09808i 0.389603 + 0.224937i
\(88\) 6.00000 + 3.46410i 0.639602 + 0.369274i
\(89\) 7.56218 + 13.0981i 0.801589 + 1.38839i 0.918570 + 0.395259i \(0.129345\pi\)
−0.116980 + 0.993134i \(0.537321\pi\)
\(90\) 0 0
\(91\) 1.96410 5.66987i 0.205894 0.594364i
\(92\) 25.8564i 2.69572i
\(93\) 0.401924 0.232051i 0.0416776 0.0240625i
\(94\) −2.73205 + 4.73205i −0.281790 + 0.488074i
\(95\) 0 0
\(96\) −10.9282 18.9282i −1.11536 1.93185i
\(97\) 14.9282i 1.51573i −0.652412 0.757865i \(-0.726243\pi\)
0.652412 0.757865i \(-0.273757\pi\)
\(98\) 18.9282 + 2.73205i 1.91204 + 0.275979i
\(99\) −0.732051 −0.0735739
\(100\) 0 0
\(101\) 3.63397 6.29423i 0.361594 0.626299i −0.626629 0.779317i \(-0.715566\pi\)
0.988223 + 0.153018i \(0.0488993\pi\)
\(102\) 7.73205 + 4.46410i 0.765587 + 0.442012i
\(103\) −7.96410 + 4.59808i −0.784726 + 0.453062i −0.838103 0.545513i \(-0.816335\pi\)
0.0533764 + 0.998574i \(0.483002\pi\)
\(104\) 21.4641 2.10473
\(105\) 0 0
\(106\) −33.8564 −3.28842
\(107\) −1.90192 + 1.09808i −0.183866 + 0.106155i −0.589108 0.808054i \(-0.700521\pi\)
0.405242 + 0.914210i \(0.367187\pi\)
\(108\) 4.73205 + 2.73205i 0.455342 + 0.262892i
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) 3.19615 0.303365
\(112\) 7.46410 + 38.7846i 0.705291 + 3.66480i
\(113\) 8.92820i 0.839895i 0.907548 + 0.419947i \(0.137951\pi\)
−0.907548 + 0.419947i \(0.862049\pi\)
\(114\) 6.09808 + 10.5622i 0.571137 + 0.989239i
\(115\) 0 0
\(116\) 11.4641 19.8564i 1.06442 1.84362i
\(117\) −1.96410 + 1.13397i −0.181581 + 0.104836i
\(118\) 0.535898i 0.0493334i
\(119\) −5.66025 6.53590i −0.518875 0.599145i
\(120\) 0 0
\(121\) 5.23205 + 9.06218i 0.475641 + 0.823834i
\(122\) −9.46410 5.46410i −0.856840 0.494697i
\(123\) −0.633975 0.366025i −0.0571636 0.0330034i
\(124\) −1.26795 2.19615i −0.113865 0.197220i
\(125\) 0 0
\(126\) −4.73205 5.46410i −0.421565 0.486781i
\(127\) 4.80385i 0.426273i −0.977022 0.213136i \(-0.931632\pi\)
0.977022 0.213136i \(-0.0683678\pi\)
\(128\) −32.7846 + 18.9282i −2.89778 + 1.67303i
\(129\) −1.59808 + 2.76795i −0.140703 + 0.243704i
\(130\) 0 0
\(131\) −7.73205 13.3923i −0.675552 1.17009i −0.976307 0.216390i \(-0.930572\pi\)
0.300755 0.953702i \(-0.402761\pi\)
\(132\) 4.00000i 0.348155i
\(133\) −2.23205 11.5981i −0.193543 1.00568i
\(134\) −40.0526 −3.46001
\(135\) 0 0
\(136\) 15.4641 26.7846i 1.32604 2.29676i
\(137\) 1.90192 + 1.09808i 0.162492 + 0.0938150i 0.579041 0.815298i \(-0.303427\pi\)
−0.416549 + 0.909113i \(0.636760\pi\)
\(138\) −11.1962 + 6.46410i −0.953080 + 0.550261i
\(139\) −5.92820 −0.502824 −0.251412 0.967880i \(-0.580895\pi\)
−0.251412 + 0.967880i \(0.580895\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 14.6603 8.46410i 1.23026 0.710292i
\(143\) −1.43782 0.830127i −0.120237 0.0694187i
\(144\) 7.46410 12.9282i 0.622008 1.07735i
\(145\) 0 0
\(146\) −34.5885 −2.86256
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 17.4641i 1.43554i
\(149\) 2.92820 + 5.07180i 0.239888 + 0.415498i 0.960682 0.277651i \(-0.0895560\pi\)
−0.720794 + 0.693149i \(0.756223\pi\)
\(150\) 0 0
\(151\) 4.46410 7.73205i 0.363283 0.629225i −0.625216 0.780452i \(-0.714989\pi\)
0.988499 + 0.151227i \(0.0483223\pi\)
\(152\) 36.5885 21.1244i 2.96772 1.71341i
\(153\) 3.26795i 0.264198i
\(154\) 1.73205 5.00000i 0.139573 0.402911i
\(155\) 0 0
\(156\) 6.19615 + 10.7321i 0.496089 + 0.859252i
\(157\) 5.53590 + 3.19615i 0.441813 + 0.255081i 0.704366 0.709837i \(-0.251231\pi\)
−0.262553 + 0.964917i \(0.584565\pi\)
\(158\) −17.4904 10.0981i −1.39146 0.803360i
\(159\) −6.19615 10.7321i −0.491387 0.851107i
\(160\) 0 0
\(161\) 12.2942 2.36603i 0.968921 0.186469i
\(162\) 2.73205i 0.214650i
\(163\) 18.9282 10.9282i 1.48257 0.855963i 0.482767 0.875749i \(-0.339632\pi\)
0.999804 + 0.0197859i \(0.00629845\pi\)
\(164\) −2.00000 + 3.46410i −0.156174 + 0.270501i
\(165\) 0 0
\(166\) 20.6603 + 35.7846i 1.60355 + 2.77742i
\(167\) 17.6603i 1.36659i 0.730142 + 0.683296i \(0.239454\pi\)
−0.730142 + 0.683296i \(0.760546\pi\)
\(168\) −18.9282 + 16.3923i −1.46034 + 1.26469i
\(169\) 7.85641 0.604339
\(170\) 0 0
\(171\) −2.23205 + 3.86603i −0.170689 + 0.295642i
\(172\) 15.1244 + 8.73205i 1.15322 + 0.665813i
\(173\) 12.5885 7.26795i 0.957083 0.552572i 0.0618087 0.998088i \(-0.480313\pi\)
0.895274 + 0.445516i \(0.146980\pi\)
\(174\) 11.4641 0.869091
\(175\) 0 0
\(176\) 10.9282 0.823744
\(177\) −0.169873 + 0.0980762i −0.0127684 + 0.00737186i
\(178\) 35.7846 + 20.6603i 2.68217 + 1.54855i
\(179\) −5.00000 + 8.66025i −0.373718 + 0.647298i −0.990134 0.140122i \(-0.955250\pi\)
0.616417 + 0.787420i \(0.288584\pi\)
\(180\) 0 0
\(181\) −24.3205 −1.80773 −0.903865 0.427819i \(-0.859282\pi\)
−0.903865 + 0.427819i \(0.859282\pi\)
\(182\) −3.09808 16.0981i −0.229645 1.19327i
\(183\) 4.00000i 0.295689i
\(184\) 22.3923 + 38.7846i 1.65078 + 2.85924i
\(185\) 0 0
\(186\) 0.633975 1.09808i 0.0464853 0.0805149i
\(187\) −2.07180 + 1.19615i −0.151505 + 0.0874713i
\(188\) 10.9282i 0.797021i
\(189\) 0.866025 2.50000i 0.0629941 0.181848i
\(190\) 0 0
\(191\) 4.46410 + 7.73205i 0.323011 + 0.559472i 0.981108 0.193462i \(-0.0619716\pi\)
−0.658097 + 0.752933i \(0.728638\pi\)
\(192\) −25.8564 14.9282i −1.86603 1.07735i
\(193\) −1.03590 0.598076i −0.0745656 0.0430505i 0.462254 0.886748i \(-0.347041\pi\)
−0.536819 + 0.843697i \(0.680374\pi\)
\(194\) −20.3923 35.3205i −1.46408 2.53586i
\(195\) 0 0
\(196\) 35.5167 14.1962i 2.53690 1.01401i
\(197\) 0.339746i 0.0242059i 0.999927 + 0.0121029i \(0.00385258\pi\)
−0.999927 + 0.0121029i \(0.996147\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) 11.0000 19.0526i 0.779769 1.35060i −0.152305 0.988334i \(-0.548670\pi\)
0.932075 0.362267i \(-0.117997\pi\)
\(200\) 0 0
\(201\) −7.33013 12.6962i −0.517027 0.895518i
\(202\) 19.8564i 1.39709i
\(203\) −10.4904 3.63397i −0.736280 0.255055i
\(204\) 17.8564 1.25020
\(205\) 0 0
\(206\) −12.5622 + 21.7583i −0.875248 + 1.51597i
\(207\) −4.09808 2.36603i −0.284836 0.164450i
\(208\) 29.3205 16.9282i 2.03301 1.17376i
\(209\) −3.26795 −0.226049
\(210\) 0 0
\(211\) 7.07180 0.486843 0.243421 0.969921i \(-0.421730\pi\)
0.243421 + 0.969921i \(0.421730\pi\)
\(212\) −58.6410 + 33.8564i −4.02748 + 2.32527i
\(213\) 5.36603 + 3.09808i 0.367674 + 0.212277i
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 0 0
\(216\) 9.46410 0.643951
\(217\) −0.928203 + 0.803848i −0.0630105 + 0.0545687i
\(218\) 30.0526i 2.03542i
\(219\) −6.33013 10.9641i −0.427750 0.740885i
\(220\) 0 0
\(221\) −3.70577 + 6.41858i −0.249277 + 0.431761i
\(222\) 7.56218 4.36603i 0.507540 0.293028i
\(223\) 20.3923i 1.36557i −0.730619 0.682785i \(-0.760769\pi\)
0.730619 0.682785i \(-0.239231\pi\)
\(224\) 37.8564 + 43.7128i 2.52939 + 2.92069i
\(225\) 0 0
\(226\) 12.1962 + 21.1244i 0.811276 + 1.40517i
\(227\) −1.43782 0.830127i −0.0954316 0.0550975i 0.451525 0.892259i \(-0.350880\pi\)
−0.546956 + 0.837161i \(0.684214\pi\)
\(228\) 21.1244 + 12.1962i 1.39899 + 0.807710i
\(229\) −1.50000 2.59808i −0.0991228 0.171686i 0.812199 0.583380i \(-0.198270\pi\)
−0.911322 + 0.411695i \(0.864937\pi\)
\(230\) 0 0
\(231\) 1.90192 0.366025i 0.125137 0.0240827i
\(232\) 39.7128i 2.60727i
\(233\) 15.0000 8.66025i 0.982683 0.567352i 0.0796037 0.996827i \(-0.474635\pi\)
0.903079 + 0.429474i \(0.141301\pi\)
\(234\) −3.09808 + 5.36603i −0.202528 + 0.350788i
\(235\) 0 0
\(236\) 0.535898 + 0.928203i 0.0348840 + 0.0604209i
\(237\) 7.39230i 0.480182i
\(238\) −22.3205 7.73205i −1.44682 0.501194i
\(239\) −7.07180 −0.457437 −0.228718 0.973493i \(-0.573453\pi\)
−0.228718 + 0.973493i \(0.573453\pi\)
\(240\) 0 0
\(241\) −6.73205 + 11.6603i −0.433650 + 0.751103i −0.997184 0.0749893i \(-0.976108\pi\)
0.563535 + 0.826092i \(0.309441\pi\)
\(242\) 24.7583 + 14.2942i 1.59153 + 0.918868i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −21.8564 −1.39921
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −8.76795 + 5.06218i −0.557891 + 0.322099i
\(248\) −3.80385 2.19615i −0.241545 0.139456i
\(249\) −7.56218 + 13.0981i −0.479234 + 0.830057i
\(250\) 0 0
\(251\) −24.5885 −1.55201 −0.776005 0.630727i \(-0.782757\pi\)
−0.776005 + 0.630727i \(0.782757\pi\)
\(252\) −13.6603 4.73205i −0.860515 0.298091i
\(253\) 3.46410i 0.217786i
\(254\) −6.56218 11.3660i −0.411748 0.713168i
\(255\) 0 0
\(256\) −21.8564 + 37.8564i −1.36603 + 2.36603i
\(257\) 4.90192 2.83013i 0.305774 0.176538i −0.339260 0.940693i \(-0.610177\pi\)
0.645034 + 0.764154i \(0.276843\pi\)
\(258\) 8.73205i 0.543634i
\(259\) −8.30385 + 1.59808i −0.515976 + 0.0992996i
\(260\) 0 0
\(261\) 2.09808 + 3.63397i 0.129868 + 0.224937i
\(262\) −36.5885 21.1244i −2.26044 1.30507i
\(263\) −7.26795 4.19615i −0.448161 0.258746i 0.258892 0.965906i \(-0.416643\pi\)
−0.707053 + 0.707160i \(0.749976\pi\)
\(264\) 3.46410 + 6.00000i 0.213201 + 0.369274i
\(265\) 0 0
\(266\) −21.1244 24.3923i −1.29522 1.49559i
\(267\) 15.1244i 0.925596i
\(268\) −69.3731 + 40.0526i −4.23763 + 2.44660i
\(269\) −6.26795 + 10.8564i −0.382164 + 0.661927i −0.991371 0.131084i \(-0.958154\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(270\) 0 0
\(271\) −1.53590 2.66025i −0.0932992 0.161599i 0.815598 0.578619i \(-0.196408\pi\)
−0.908897 + 0.417020i \(0.863075\pi\)
\(272\) 48.7846i 2.95800i
\(273\) 4.53590 3.92820i 0.274525 0.237746i
\(274\) 6.00000 0.362473
\(275\) 0 0
\(276\) −12.9282 + 22.3923i −0.778186 + 1.34786i
\(277\) −12.6962 7.33013i −0.762838 0.440425i 0.0674759 0.997721i \(-0.478505\pi\)
−0.830314 + 0.557296i \(0.811839\pi\)
\(278\) −14.0263 + 8.09808i −0.841240 + 0.485690i
\(279\) 0.464102 0.0277850
\(280\) 0 0
\(281\) 13.8564 0.826604 0.413302 0.910594i \(-0.364375\pi\)
0.413302 + 0.910594i \(0.364375\pi\)
\(282\) −4.73205 + 2.73205i −0.281790 + 0.162691i
\(283\) 20.8923 + 12.0622i 1.24192 + 0.717022i 0.969485 0.245152i \(-0.0788380\pi\)
0.272434 + 0.962174i \(0.412171\pi\)
\(284\) 16.9282 29.3205i 1.00450 1.73985i
\(285\) 0 0
\(286\) −4.53590 −0.268213
\(287\) 1.83013 + 0.633975i 0.108029 + 0.0374223i
\(288\) 21.8564i 1.28790i
\(289\) −3.16025 5.47372i −0.185897 0.321984i
\(290\) 0 0
\(291\) 7.46410 12.9282i 0.437553 0.757865i
\(292\) −59.9090 + 34.5885i −3.50591 + 2.02414i
\(293\) 18.9282i 1.10580i 0.833248 + 0.552899i \(0.186478\pi\)
−0.833248 + 0.552899i \(0.813522\pi\)
\(294\) 15.0263 + 11.8301i 0.876350 + 0.689947i
\(295\) 0 0
\(296\) −15.1244 26.1962i −0.879085 1.52262i
\(297\) −0.633975 0.366025i −0.0367869 0.0212389i
\(298\) 13.8564 + 8.00000i 0.802680 + 0.463428i
\(299\) −5.36603 9.29423i −0.310325 0.537499i
\(300\) 0 0
\(301\) 2.76795 7.99038i 0.159542 0.460558i
\(302\) 24.3923i 1.40362i
\(303\) 6.29423 3.63397i 0.361594 0.208766i
\(304\) 33.3205 57.7128i 1.91106 3.31006i
\(305\) 0 0
\(306\) 4.46410 + 7.73205i 0.255196 + 0.442012i
\(307\) 32.1244i 1.83343i 0.399537 + 0.916717i \(0.369171\pi\)
−0.399537 + 0.916717i \(0.630829\pi\)
\(308\) −2.00000 10.3923i −0.113961 0.592157i
\(309\) −9.19615 −0.523151
\(310\) 0 0
\(311\) −4.56218 + 7.90192i −0.258697 + 0.448077i −0.965893 0.258941i \(-0.916627\pi\)
0.707196 + 0.707018i \(0.249960\pi\)
\(312\) 18.5885 + 10.7321i 1.05236 + 0.607583i
\(313\) −10.9641 + 6.33013i −0.619728 + 0.357800i −0.776763 0.629793i \(-0.783140\pi\)
0.157035 + 0.987593i \(0.449806\pi\)
\(314\) 17.4641 0.985556
\(315\) 0 0
\(316\) −40.3923 −2.27224
\(317\) 24.6340 14.2224i 1.38358 0.798811i 0.391000 0.920391i \(-0.372129\pi\)
0.992582 + 0.121579i \(0.0387959\pi\)
\(318\) −29.3205 16.9282i −1.64421 0.949286i
\(319\) −1.53590 + 2.66025i −0.0859938 + 0.148946i
\(320\) 0 0
\(321\) −2.19615 −0.122577
\(322\) 25.8564 22.3923i 1.44092 1.24787i
\(323\) 14.5885i 0.811723i
\(324\) 2.73205 + 4.73205i 0.151781 + 0.262892i
\(325\) 0 0
\(326\) 29.8564 51.7128i 1.65359 2.86411i
\(327\) 9.52628 5.50000i 0.526804 0.304151i
\(328\) 6.92820i 0.382546i
\(329\) 5.19615 1.00000i 0.286473 0.0551318i
\(330\) 0 0
\(331\) −4.03590 6.99038i −0.221833 0.384226i 0.733532 0.679655i \(-0.237871\pi\)
−0.955365 + 0.295429i \(0.904537\pi\)
\(332\) 71.5692 + 41.3205i 3.92787 + 2.26776i
\(333\) 2.76795 + 1.59808i 0.151683 + 0.0875740i
\(334\) 24.1244 + 41.7846i 1.32003 + 2.28635i
\(335\) 0 0
\(336\) −12.9282 + 37.3205i −0.705291 + 2.03600i
\(337\) 17.9808i 0.979475i −0.871870 0.489737i \(-0.837093\pi\)
0.871870 0.489737i \(-0.162907\pi\)
\(338\) 18.5885 10.7321i 1.01108 0.583747i
\(339\) −4.46410 + 7.73205i −0.242457 + 0.419947i
\(340\) 0 0
\(341\) 0.169873 + 0.294229i 0.00919914 + 0.0159334i
\(342\) 12.1962i 0.659492i
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 30.2487 1.63090
\(345\) 0 0
\(346\) 19.8564 34.3923i 1.06749 1.84894i
\(347\) −18.2487 10.5359i −0.979642 0.565597i −0.0774801 0.996994i \(-0.524687\pi\)
−0.902162 + 0.431397i \(0.858021\pi\)
\(348\) 19.8564 11.4641i 1.06442 0.614540i
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) −2.26795 −0.121054
\(352\) 13.8564 8.00000i 0.738549 0.426401i
\(353\) 2.70577 + 1.56218i 0.144014 + 0.0831463i 0.570276 0.821453i \(-0.306836\pi\)
−0.426262 + 0.904600i \(0.640170\pi\)
\(354\) −0.267949 + 0.464102i −0.0142413 + 0.0246667i
\(355\) 0 0
\(356\) 82.6410 4.37997
\(357\) −1.63397 8.49038i −0.0864791 0.449359i
\(358\) 27.3205i 1.44393i
\(359\) −0.633975 1.09808i −0.0334599 0.0579542i 0.848811 0.528697i \(-0.177319\pi\)
−0.882270 + 0.470743i \(0.843986\pi\)
\(360\) 0 0
\(361\) −0.464102 + 0.803848i −0.0244264 + 0.0423078i
\(362\) −57.5429 + 33.2224i −3.02439 + 1.74613i
\(363\) 10.4641i 0.549223i
\(364\) −21.4641 24.7846i −1.12502 1.29907i
\(365\) 0 0
\(366\) −5.46410 9.46410i −0.285613 0.494697i
\(367\) 9.69615 + 5.59808i 0.506135 + 0.292217i 0.731244 0.682117i \(-0.238940\pi\)
−0.225108 + 0.974334i \(0.572274\pi\)
\(368\) 61.1769 + 35.3205i 3.18907 + 1.84121i
\(369\) −0.366025 0.633975i −0.0190545 0.0330034i
\(370\) 0 0
\(371\) 21.4641 + 24.7846i 1.11436 + 1.28675i
\(372\) 2.53590i 0.131480i
\(373\) 22.9641 13.2583i 1.18904 0.686490i 0.230949 0.972966i \(-0.425817\pi\)
0.958088 + 0.286476i \(0.0924837\pi\)
\(374\) −3.26795 + 5.66025i −0.168982 + 0.292685i
\(375\) 0 0
\(376\) 9.46410 + 16.3923i 0.488074 + 0.845369i
\(377\) 9.51666i 0.490133i
\(378\) −1.36603 7.09808i −0.0702608 0.365086i
\(379\) −6.32051 −0.324663 −0.162331 0.986736i \(-0.551901\pi\)
−0.162331 + 0.986736i \(0.551901\pi\)
\(380\) 0 0
\(381\) 2.40192 4.16025i 0.123054 0.213136i
\(382\) 21.1244 + 12.1962i 1.08082 + 0.624009i
\(383\) −20.1962 + 11.6603i −1.03198 + 0.595811i −0.917550 0.397621i \(-0.869836\pi\)
−0.114425 + 0.993432i \(0.536503\pi\)
\(384\) −37.8564 −1.93185
\(385\) 0 0
\(386\) −3.26795 −0.166334
\(387\) −2.76795 + 1.59808i −0.140703 + 0.0812348i
\(388\) −70.6410 40.7846i −3.58625 2.07052i
\(389\) 2.70577 4.68653i 0.137188 0.237617i −0.789243 0.614081i \(-0.789527\pi\)
0.926431 + 0.376464i \(0.122860\pi\)
\(390\) 0 0
\(391\) −15.4641 −0.782053
\(392\) 40.9808 52.0526i 2.06984 2.62905i
\(393\) 15.4641i 0.780061i
\(394\) 0.464102 + 0.803848i 0.0233811 + 0.0404973i
\(395\) 0 0
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) 27.0167 15.5981i 1.35593 0.782845i 0.366855 0.930278i \(-0.380434\pi\)
0.989072 + 0.147433i \(0.0471011\pi\)
\(398\) 60.1051i 3.01280i
\(399\) 3.86603 11.1603i 0.193543 0.558712i
\(400\) 0 0
\(401\) 8.19615 + 14.1962i 0.409296 + 0.708922i 0.994811 0.101740i \(-0.0324409\pi\)
−0.585515 + 0.810662i \(0.699108\pi\)
\(402\) −34.6865 20.0263i −1.73001 0.998820i
\(403\) 0.911543 + 0.526279i 0.0454072 + 0.0262158i
\(404\) −19.8564 34.3923i −0.987893 1.71108i
\(405\) 0 0
\(406\) −29.7846 + 5.73205i −1.47819 + 0.284477i
\(407\) 2.33975i 0.115977i
\(408\) 26.7846 15.4641i 1.32604 0.765587i
\(409\) 1.57180 2.72243i 0.0777203 0.134616i −0.824546 0.565795i \(-0.808569\pi\)
0.902266 + 0.431180i \(0.141903\pi\)
\(410\) 0 0
\(411\) 1.09808 + 1.90192i 0.0541641 + 0.0938150i
\(412\) 50.2487i 2.47558i
\(413\) 0.392305 0.339746i 0.0193041 0.0167178i
\(414\) −12.9282 −0.635387
\(415\) 0 0
\(416\) 24.7846 42.9282i 1.21517 2.10473i
\(417\) −5.13397 2.96410i −0.251412 0.145153i
\(418\) −7.73205 + 4.46410i −0.378187 + 0.218346i
\(419\) 35.4641 1.73253 0.866267 0.499581i \(-0.166513\pi\)
0.866267 + 0.499581i \(0.166513\pi\)
\(420\) 0 0
\(421\) 0.0717968 0.00349916 0.00174958 0.999998i \(-0.499443\pi\)
0.00174958 + 0.999998i \(0.499443\pi\)
\(422\) 16.7321 9.66025i 0.814503 0.470254i
\(423\) −1.73205 1.00000i −0.0842152 0.0486217i
\(424\) −58.6410 + 101.569i −2.84786 + 4.93264i
\(425\) 0 0
\(426\) 16.9282 0.820174
\(427\) 2.00000 + 10.3923i 0.0967868 + 0.502919i
\(428\) 12.0000i 0.580042i
\(429\) −0.830127 1.43782i −0.0400789 0.0694187i
\(430\) 0 0
\(431\) −8.66025 + 15.0000i −0.417150 + 0.722525i −0.995651 0.0931566i \(-0.970304\pi\)
0.578502 + 0.815681i \(0.303638\pi\)
\(432\) 12.9282 7.46410i 0.622008 0.359117i
\(433\) 15.1962i 0.730280i 0.930953 + 0.365140i \(0.118979\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(434\) −1.09808 + 3.16987i −0.0527093 + 0.152159i
\(435\) 0 0
\(436\) −30.0526 52.0526i −1.43926 2.49287i
\(437\) −18.2942 10.5622i −0.875132 0.505257i
\(438\) −29.9545 17.2942i −1.43128 0.826350i
\(439\) 0.267949 + 0.464102i 0.0127885 + 0.0221504i 0.872349 0.488884i \(-0.162596\pi\)
−0.859560 + 0.511034i \(0.829263\pi\)
\(440\) 0 0
\(441\) −1.00000 + 6.92820i −0.0476190 + 0.329914i
\(442\) 20.2487i 0.963133i
\(443\) 8.19615 4.73205i 0.389411 0.224827i −0.292494 0.956267i \(-0.594485\pi\)
0.681905 + 0.731441i \(0.261152\pi\)
\(444\) 8.73205 15.1244i 0.414405 0.717770i
\(445\) 0 0
\(446\) −27.8564 48.2487i −1.31904 2.28464i
\(447\) 5.85641i 0.276999i
\(448\) 74.6410 + 25.8564i 3.52646 + 1.22160i
\(449\) 35.8564 1.69217 0.846084 0.533049i \(-0.178954\pi\)
0.846084 + 0.533049i \(0.178954\pi\)
\(450\) 0 0
\(451\) 0.267949 0.464102i 0.0126172 0.0218537i
\(452\) 42.2487 + 24.3923i 1.98721 + 1.14732i
\(453\) 7.73205 4.46410i 0.363283 0.209742i
\(454\) −4.53590 −0.212880
\(455\) 0 0
\(456\) 42.2487 1.97848
\(457\) 14.4282 8.33013i 0.674923 0.389667i −0.123016 0.992405i \(-0.539257\pi\)
0.797939 + 0.602738i \(0.205923\pi\)
\(458\) −7.09808 4.09808i −0.331671 0.191491i
\(459\) −1.63397 + 2.83013i −0.0762674 + 0.132099i
\(460\) 0 0
\(461\) 16.9808 0.790873 0.395436 0.918493i \(-0.370593\pi\)
0.395436 + 0.918493i \(0.370593\pi\)
\(462\) 4.00000 3.46410i 0.186097 0.161165i
\(463\) 25.7321i 1.19587i 0.801545 + 0.597935i \(0.204012\pi\)
−0.801545 + 0.597935i \(0.795988\pi\)
\(464\) −31.3205 54.2487i −1.45402 2.51843i
\(465\) 0 0
\(466\) 23.6603 40.9808i 1.09604 1.89840i
\(467\) 0.124356 0.0717968i 0.00575449 0.00332236i −0.497120 0.867682i \(-0.665609\pi\)
0.502874 + 0.864359i \(0.332276\pi\)
\(468\) 12.3923i 0.572834i
\(469\) 25.3923 + 29.3205i 1.17251 + 1.35390i
\(470\) 0 0
\(471\) 3.19615 + 5.53590i 0.147271 + 0.255081i
\(472\) 1.60770 + 0.928203i 0.0740002 + 0.0427240i
\(473\) −2.02628 1.16987i −0.0931684 0.0537908i
\(474\) −10.0981 17.4904i −0.463820 0.803360i
\(475\) 0 0
\(476\) −46.3923 + 8.92820i −2.12639 + 0.409224i
\(477\) 12.3923i 0.567405i
\(478\) −16.7321 + 9.66025i −0.765306 + 0.441850i
\(479\) 4.39230 7.60770i 0.200690 0.347604i −0.748061 0.663630i \(-0.769015\pi\)
0.948751 + 0.316025i \(0.102348\pi\)
\(480\) 0 0
\(481\) 3.62436 + 6.27757i 0.165256 + 0.286232i
\(482\) 36.7846i 1.67549i
\(483\) 11.8301 + 4.09808i 0.538289 + 0.186469i
\(484\) 57.1769 2.59895
\(485\) 0 0
\(486\) −1.36603 + 2.36603i −0.0619642 + 0.107325i
\(487\) −0.356406 0.205771i −0.0161503 0.00932439i 0.491903 0.870650i \(-0.336301\pi\)
−0.508053 + 0.861326i \(0.669635\pi\)
\(488\) −32.7846 + 18.9282i −1.48409 + 0.856840i
\(489\) 21.8564 0.988381
\(490\) 0 0
\(491\) −38.2487 −1.72614 −0.863070 0.505084i \(-0.831461\pi\)
−0.863070 + 0.505084i \(0.831461\pi\)
\(492\) −3.46410 + 2.00000i −0.156174 + 0.0901670i
\(493\) 11.8756 + 6.85641i 0.534852 + 0.308797i
\(494\) −13.8301 + 23.9545i −0.622247 + 1.07776i
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) −15.4904 5.36603i −0.694839 0.240699i
\(498\) 41.3205i 1.85162i
\(499\) −6.76795 11.7224i −0.302975 0.524768i 0.673833 0.738883i \(-0.264647\pi\)
−0.976808 + 0.214115i \(0.931313\pi\)
\(500\) 0 0
\(501\) −8.83013 + 15.2942i −0.394501 + 0.683296i
\(502\) −58.1769 + 33.5885i −2.59656 + 1.49913i
\(503\) 14.3923i 0.641721i 0.947126 + 0.320861i \(0.103972\pi\)
−0.947126 + 0.320861i \(0.896028\pi\)
\(504\) −24.5885 + 4.73205i −1.09526 + 0.210782i
\(505\) 0 0
\(506\) −4.73205 8.19615i −0.210365 0.364363i
\(507\) 6.80385 + 3.92820i 0.302169 + 0.174458i
\(508\) −22.7321 13.1244i −1.00857 0.582299i
\(509\) 2.26795 + 3.92820i 0.100525 + 0.174115i 0.911901 0.410410i \(-0.134614\pi\)
−0.811376 + 0.584525i \(0.801281\pi\)
\(510\) 0 0
\(511\) 21.9282 + 25.3205i 0.970047 + 1.12011i
\(512\) 43.7128i 1.93185i
\(513\) −3.86603 + 2.23205i −0.170689 + 0.0985475i
\(514\) 7.73205 13.3923i 0.341046 0.590709i
\(515\) 0 0
\(516\) 8.73205 + 15.1244i 0.384407 + 0.665813i
\(517\) 1.46410i 0.0643911i
\(518\) −17.4641 + 15.1244i −0.767329 + 0.664526i
\(519\) 14.5359 0.638055
\(520\) 0 0
\(521\) 2.73205 4.73205i 0.119693 0.207315i −0.799953 0.600063i \(-0.795142\pi\)
0.919646 + 0.392748i \(0.128476\pi\)
\(522\) 9.92820 + 5.73205i 0.434546 + 0.250885i
\(523\) −24.0167 + 13.8660i −1.05018 + 0.606319i −0.922698 0.385523i \(-0.874021\pi\)
−0.127477 + 0.991842i \(0.540688\pi\)
\(524\) −84.4974 −3.69129
\(525\) 0 0
\(526\) −22.9282 −0.999717
\(527\) 1.31347 0.758330i 0.0572155 0.0330334i
\(528\) 9.46410 + 5.46410i 0.411872 + 0.237795i
\(529\) −0.303848 + 0.526279i −0.0132108 + 0.0228817i
\(530\) 0 0
\(531\) −0.196152 −0.00851229
\(532\) −60.9808 21.1244i −2.64385 0.915857i
\(533\) 1.66025i 0.0719136i
\(534\) 20.6603 + 35.7846i 0.894057 + 1.54855i
\(535\) 0 0
\(536\) −69.3731 + 120.158i −2.99646 + 5.19002i
\(537\) −8.66025 + 5.00000i −0.373718 + 0.215766i
\(538\) 34.2487i 1.47657i
\(539\) −4.75833 + 1.90192i −0.204956 + 0.0819217i
\(540\) 0 0
\(541\) −2.89230 5.00962i −0.124350 0.215380i 0.797129 0.603809i \(-0.206351\pi\)
−0.921479 + 0.388429i \(0.873018\pi\)
\(542\) −7.26795 4.19615i −0.312185 0.180240i
\(543\) −21.0622 12.1603i −0.903865 0.521846i
\(544\) −35.7128 61.8564i −1.53117 2.65207i
\(545\) 0 0
\(546\) 5.36603 15.4904i 0.229645 0.662927i
\(547\) 26.2487i 1.12231i 0.827709 + 0.561157i \(0.189644\pi\)
−0.827709 + 0.561157i \(0.810356\pi\)
\(548\) 10.3923 6.00000i 0.443937 0.256307i
\(549\) 2.00000 3.46410i 0.0853579 0.147844i
\(550\) 0 0
\(551\) 9.36603 + 16.2224i 0.399006 + 0.691099i
\(552\) 44.7846i 1.90616i
\(553\) 3.69615 + 19.2058i 0.157176 + 0.816712i
\(554\) −40.0526 −1.70167
\(555\) 0 0
\(556\) −16.1962 + 28.0526i −0.686870 + 1.18969i
\(557\) 12.8038 + 7.39230i 0.542516 + 0.313222i 0.746098 0.665836i \(-0.231925\pi\)
−0.203582 + 0.979058i \(0.565258\pi\)
\(558\) 1.09808 0.633975i 0.0464853 0.0268383i
\(559\) −7.24871 −0.306588
\(560\) 0 0
\(561\) −2.39230 −0.101003
\(562\) 32.7846 18.9282i 1.38294 0.798438i
\(563\) 15.5885 + 9.00000i 0.656975 + 0.379305i 0.791123 0.611656i \(-0.209497\pi\)
−0.134148 + 0.990961i \(0.542830\pi\)
\(564\) −5.46410 + 9.46410i −0.230080 + 0.398511i
\(565\) 0 0
\(566\) 65.9090 2.77036
\(567\) 2.00000 1.73205i 0.0839921 0.0727393i
\(568\) 58.6410i 2.46052i
\(569\) 16.2224 + 28.0981i 0.680080 + 1.17793i 0.974956 + 0.222397i \(0.0713882\pi\)
−0.294876 + 0.955535i \(0.595278\pi\)
\(570\) 0 0
\(571\) −9.30385 + 16.1147i −0.389354 + 0.674381i −0.992363 0.123354i \(-0.960635\pi\)
0.603009 + 0.797734i \(0.293968\pi\)
\(572\) −7.85641 + 4.53590i −0.328493 + 0.189655i
\(573\) 8.92820i 0.372981i
\(574\) 5.19615 1.00000i 0.216883 0.0417392i
\(575\) 0 0
\(576\) −14.9282 25.8564i −0.622008 1.07735i
\(577\) 24.8205 + 14.3301i 1.03329 + 0.596571i 0.917926 0.396752i \(-0.129863\pi\)
0.115365 + 0.993323i \(0.463196\pi\)
\(578\) −14.9545 8.63397i −0.622024 0.359126i
\(579\) −0.598076 1.03590i −0.0248552 0.0430505i
\(580\) 0 0
\(581\) 13.0981 37.8109i 0.543400 1.56866i
\(582\) 40.7846i 1.69058i
\(583\) 7.85641 4.53590i 0.325379 0.187858i
\(584\) −59.9090 + 103.765i −2.47905 + 4.29384i
\(585\) 0 0
\(586\) 25.8564 + 44.7846i 1.06812 + 1.85004i
\(587\) 40.7321i 1.68119i −0.541663 0.840596i \(-0.682205\pi\)
0.541663 0.840596i \(-0.317795\pi\)
\(588\) 37.8564 + 5.46410i 1.56117 + 0.225336i
\(589\) 2.07180 0.0853669
\(590\) 0 0
\(591\) −0.169873 + 0.294229i −0.00698764 + 0.0121029i
\(592\) −41.3205 23.8564i −1.69826 0.980492i
\(593\) 24.1699 13.9545i 0.992538 0.573042i 0.0865058 0.996251i \(-0.472430\pi\)
0.906032 + 0.423209i \(0.139097\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 32.0000 1.31077
\(597\) 19.0526 11.0000i 0.779769 0.450200i
\(598\) −25.3923 14.6603i −1.03837 0.599502i
\(599\) −19.1244 + 33.1244i −0.781400 + 1.35342i 0.149726 + 0.988727i \(0.452161\pi\)
−0.931126 + 0.364697i \(0.881173\pi\)
\(600\) 0 0
\(601\) −0.0717968 −0.00292865 −0.00146433 0.999999i \(-0.500466\pi\)
−0.00146433 + 0.999999i \(0.500466\pi\)
\(602\) −4.36603 22.6865i −0.177946 0.924634i
\(603\) 14.6603i 0.597012i
\(604\) −24.3923 42.2487i −0.992509 1.71908i
\(605\) 0 0
\(606\) 9.92820 17.1962i 0.403306 0.698546i
\(607\) −2.76795 + 1.59808i −0.112348 + 0.0648639i −0.555121 0.831770i \(-0.687328\pi\)
0.442773 + 0.896634i \(0.353995\pi\)
\(608\) 97.5692i 3.95695i
\(609\) −7.26795 8.39230i −0.294512 0.340073i
\(610\) 0 0
\(611\) −2.26795 3.92820i −0.0917514 0.158918i
\(612\) 15.4641 + 8.92820i 0.625099 + 0.360901i
\(613\) 23.3205 + 13.4641i 0.941906 + 0.543810i 0.890557 0.454871i \(-0.150315\pi\)
0.0513490 + 0.998681i \(0.483648\pi\)
\(614\) 43.8827 + 76.0070i 1.77096 + 3.06739i
\(615\) 0 0
\(616\) −12.0000 13.8564i −0.483494 0.558291i
\(617\) 36.2487i 1.45932i 0.683811 + 0.729659i \(0.260321\pi\)
−0.683811 + 0.729659i \(0.739679\pi\)
\(618\) −21.7583 + 12.5622i −0.875248 + 0.505325i
\(619\) −15.0359 + 26.0429i −0.604344 + 1.04675i 0.387811 + 0.921739i \(0.373231\pi\)
−0.992155 + 0.125015i \(0.960102\pi\)
\(620\) 0 0
\(621\) −2.36603 4.09808i −0.0949453 0.164450i
\(622\) 24.9282i 0.999530i
\(623\) −7.56218 39.2942i −0.302972 1.57429i
\(624\) 33.8564 1.35534
\(625\) 0 0
\(626\) −17.2942 + 29.9545i −0.691216 + 1.19722i
\(627\) −2.83013 1.63397i −0.113024 0.0652547i
\(628\) 30.2487 17.4641i 1.20705 0.696894i
\(629\) 10.4449 0.416464
\(630\) 0 0
\(631\) 48.7846 1.94208 0.971042 0.238908i \(-0.0767893\pi\)
0.971042 + 0.238908i \(0.0767893\pi\)
\(632\) −60.5885 + 34.9808i −2.41008 + 1.39146i
\(633\) 6.12436 + 3.53590i 0.243421 + 0.140539i
\(634\) 38.8564 67.3013i 1.54319 2.67287i
\(635\) 0 0
\(636\) −67.7128 −2.68499
\(637\) −9.82051 + 12.4737i −0.389103 + 0.494227i
\(638\) 8.39230i 0.332255i
\(639\) 3.09808 + 5.36603i 0.122558 + 0.212277i
\(640\) 0 0
\(641\) −1.90192 + 3.29423i −0.0751215 + 0.130114i −0.901139 0.433530i \(-0.857268\pi\)
0.826018 + 0.563644i \(0.190601\pi\)
\(642\) −5.19615 + 3.00000i −0.205076 + 0.118401i
\(643\) 4.51666i 0.178120i 0.996026 + 0.0890599i \(0.0283862\pi\)
−0.996026 + 0.0890599i \(0.971614\pi\)
\(644\) 22.3923 64.6410i 0.882380 2.54721i
\(645\) 0 0
\(646\) 19.9282 + 34.5167i 0.784065 + 1.35804i
\(647\) −24.1699 13.9545i −0.950216 0.548607i −0.0570678 0.998370i \(-0.518175\pi\)
−0.893148 + 0.449763i \(0.851508\pi\)
\(648\) 8.19615 + 4.73205i 0.321975 + 0.185893i
\(649\) −0.0717968 0.124356i −0.00281827 0.00488139i
\(650\) 0 0
\(651\) −1.20577 + 0.232051i −0.0472579 + 0.00909479i
\(652\) 119.426i 4.67707i
\(653\) −38.6147 + 22.2942i −1.51111 + 0.872441i −0.511196 + 0.859464i \(0.670797\pi\)
−0.999916 + 0.0129762i \(0.995869\pi\)
\(654\) 15.0263 26.0263i 0.587574 1.01771i
\(655\) 0 0
\(656\) 5.46410 + 9.46410i 0.213337 + 0.369511i
\(657\) 12.6603i 0.493924i
\(658\) 10.9282 9.46410i 0.426026 0.368949i
\(659\) −2.92820 −0.114067 −0.0570333 0.998372i \(-0.518164\pi\)
−0.0570333 + 0.998372i \(0.518164\pi\)
\(660\) 0 0
\(661\) −5.23205 + 9.06218i −0.203503 + 0.352478i −0.949655 0.313298i \(-0.898566\pi\)
0.746152 + 0.665776i \(0.231899\pi\)
\(662\) −19.0981 11.0263i −0.742268 0.428549i
\(663\) −6.41858 + 3.70577i −0.249277 + 0.143920i
\(664\) 143.138 5.55485
\(665\) 0 0
\(666\) 8.73205 0.338360
\(667\) −17.1962 + 9.92820i −0.665838 + 0.384422i
\(668\) 83.5692 + 48.2487i 3.23339 + 1.86680i
\(669\) 10.1962 17.6603i 0.394206 0.682785i
\(670\) 0 0
\(671\) 2.92820 0.113042
\(672\) 10.9282 + 56.7846i 0.421565 + 2.19051i
\(673\) 27.3397i 1.05387i −0.849906 0.526935i \(-0.823341\pi\)
0.849906 0.526935i \(-0.176659\pi\)
\(674\) −24.5622 42.5429i −0.946100 1.63869i
\(675\) 0 0
\(676\) 21.4641 37.1769i 0.825542 1.42988i
\(677\) 28.6865 16.5622i 1.10251 0.636536i 0.165633 0.986187i \(-0.447033\pi\)
0.936880 + 0.349651i \(0.113700\pi\)
\(678\) 24.3923i 0.936781i
\(679\) −12.9282 + 37.3205i −0.496139 + 1.43223i
\(680\) 0 0
\(681\) −0.830127 1.43782i −0.0318105 0.0550975i
\(682\) 0.803848 + 0.464102i 0.0307809 + 0.0177714i
\(683\) 24.2942 + 14.0263i 0.929593 + 0.536701i 0.886683 0.462378i \(-0.153004\pi\)
0.0429101 + 0.999079i \(0.486337\pi\)
\(684\) 12.1962 + 21.1244i 0.466332 + 0.807710i
\(685\) 0 0
\(686\) −44.9545 23.2224i −1.71637 0.886637i
\(687\) 3.00000i 0.114457i
\(688\) 41.3205 23.8564i 1.57533 0.909517i
\(689\) 14.0526 24.3397i 0.535360 0.927270i
\(690\) 0 0
\(691\) −4.42820 7.66987i −0.168457 0.291776i 0.769421 0.638742i \(-0.220545\pi\)
−0.937877 + 0.346967i \(0.887212\pi\)
\(692\) 79.4256i 3.01931i
\(693\) 1.83013 + 0.633975i 0.0695208 + 0.0240827i
\(694\) −57.5692 −2.18530
\(695\) 0 0
\(696\) 19.8564 34.3923i 0.752655 1.30364i
\(697\) −2.07180 1.19615i −0.0784749 0.0453075i
\(698\) −52.0526 + 30.0526i −1.97022 + 1.13751i
\(699\) 17.3205 0.655122
\(700\) 0 0
\(701\) −8.58846 −0.324382 −0.162191 0.986759i \(-0.551856\pi\)
−0.162191 + 0.986759i \(0.551856\pi\)
\(702\) −5.36603 + 3.09808i −0.202528 + 0.116929i
\(703\) 12.3564 + 7.13397i 0.466031 + 0.269063i
\(704\) 10.9282 18.9282i 0.411872 0.713384i
\(705\) 0 0
\(706\) 8.53590 0.321253
\(707\) −14.5359 + 12.5885i −0.546679 + 0.473438i
\(708\) 1.07180i 0.0402806i
\(709\) −0.535898 0.928203i −0.0201261 0.0348594i 0.855787 0.517328i \(-0.173073\pi\)
−0.875913 + 0.482469i \(0.839740\pi\)
\(710\) 0 0
\(711\) 3.69615 6.40192i 0.138617 0.240091i
\(712\) 123.962 71.5692i 4.64565 2.68217i
\(713\) 2.19615i 0.0822466i
\(714\) −15.4641 17.8564i −0.578729 0.668259i
\(715\) 0 0
\(716\) 27.3205 + 47.3205i 1.02102 + 1.76845i
\(717\) −6.12436 3.53590i −0.228718 0.132051i
\(718\) −3.00000 1.73205i −0.111959 0.0646396i
\(719\) −10.2679 17.7846i −0.382930 0.663254i 0.608550 0.793516i \(-0.291752\pi\)
−0.991480 + 0.130262i \(0.958418\pi\)
\(720\) 0 0
\(721\) 23.8923 4.59808i 0.889796 0.171241i
\(722\) 2.53590i 0.0943764i
\(723\) −11.6603 + 6.73205i −0.433650 + 0.250368i
\(724\) −66.4449 + 115.086i −2.46940 + 4.27713i
\(725\) 0 0
\(726\) 14.2942 + 24.7583i 0.530509 + 0.918868i
\(727\) 13.3397i 0.494744i 0.968921 + 0.247372i \(0.0795669\pi\)
−0.968921 + 0.247372i \(0.920433\pi\)
\(728\) −53.6603 18.5885i −1.98878 0.688934i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −5.22243 + 9.04552i −0.193159 + 0.334561i
\(732\) −18.9282 10.9282i −0.699607 0.403918i
\(733\) −1.16025 + 0.669873i −0.0428550 + 0.0247423i −0.521274 0.853389i \(-0.674543\pi\)
0.478419 + 0.878131i \(0.341210\pi\)
\(734\) 30.5885 1.12904
\(735\) 0 0
\(736\) 103.426 3.81232
\(737\) 9.29423 5.36603i 0.342357 0.197660i
\(738\) −1.73205 1.00000i −0.0637577 0.0368105i
\(739\) 13.8923 24.0622i 0.511037 0.885142i −0.488881 0.872350i \(-0.662595\pi\)
0.999918 0.0127913i \(-0.00407171\pi\)
\(740\) 0 0
\(741\) −10.1244 −0.371927
\(742\) 84.6410 + 29.3205i 3.10727 + 1.07639i
\(743\) 15.9090i 0.583643i −0.956473 0.291822i \(-0.905739\pi\)
0.956473 0.291822i \(-0.0942614\pi\)
\(744\) −2.19615 3.80385i −0.0805149 0.139456i
\(745\) 0 0
\(746\) 36.2224 62.7391i 1.32620 2.29704i
\(747\) −13.0981 + 7.56218i −0.479234 + 0.276686i
\(748\) 13.0718i 0.477952i
\(749\) 5.70577 1.09808i 0.208484 0.0401228i
\(750\) 0 0
\(751\) −9.03590 15.6506i −0.329725 0.571100i 0.652732 0.757588i \(-0.273623\pi\)
−0.982457 + 0.186489i \(0.940289\pi\)
\(752\) 25.8564 + 14.9282i 0.942886 + 0.544376i
\(753\) −21.2942 12.2942i −0.776005 0.448027i
\(754\) 13.0000 + 22.5167i 0.473432 + 0.820008i
\(755\) 0 0
\(756\) −9.46410 10.9282i −0.344206 0.397455i
\(757\) 27.8564i 1.01246i 0.862399 + 0.506229i \(0.168961\pi\)
−0.862399 + 0.506229i \(0.831039\pi\)
\(758\) −14.9545 + 8.63397i −0.543171 + 0.313600i
\(759\) 1.73205 3.00000i 0.0628695 0.108893i
\(760\) 0 0
\(761\) −23.3660 40.4711i −0.847018 1.46708i −0.883857 0.467757i \(-0.845062\pi\)
0.0368396 0.999321i \(-0.488271\pi\)
\(762\) 13.1244i 0.475445i
\(763\) −22.0000 + 19.0526i −0.796453 + 0.689749i
\(764\) 48.7846 1.76497
\(765\) 0 0
\(766\) −31.8564 + 55.1769i −1.15102 + 1.99362i
\(767\) −0.385263 0.222432i −0.0139111 0.00803155i
\(768\) −37.8564 + 21.8564i −1.36603 + 0.788675i
\(769\) −52.3205 −1.88673 −0.943363 0.331763i \(-0.892357\pi\)
−0.943363 + 0.331763i \(0.892357\pi\)
\(770\) 0 0
\(771\) 5.66025 0.203849
\(772\) −5.66025 + 3.26795i −0.203717 + 0.117616i
\(773\) −37.6865 21.7583i −1.35549 0.782593i −0.366478 0.930427i \(-0.619437\pi\)
−0.989012 + 0.147834i \(0.952770\pi\)
\(774\) −4.36603 + 7.56218i −0.156934 + 0.271817i
\(775\) 0 0
\(776\) −141.282 −5.07173
\(777\) −7.99038 2.76795i −0.286653 0.0992996i
\(778\) 14.7846i 0.530054i
\(779\) −1.63397 2.83013i −0.0585432 0.101400i
\(780\) 0 0
\(781\) −2.26795 + 3.92820i −0.0811536 + 0.140562i
\(782\) −36.5885 + 21.1244i −1.30840