Properties

Label 525.2.r.a.424.1
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 424.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.424
Dual form 525.2.r.a.499.1

$q$-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 \(0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −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 \(-0.898160\pi\)
0.949255 0.314508i \(-0.101840\pi\)
\(14\) −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 0.115858 0.993266i \(-0.463038\pi\)
−0.802264 + 0.596969i \(0.796372\pi\)
\(18\) −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 −0.00766135 0.999971i \(-0.502439\pi\)
0.862169 + 0.506620i \(0.169105\pi\)
\(24\) 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 −0.709960 0.704242i \(-0.751287\pi\)
0.254912 + 0.966964i \(0.417954\pi\)
\(38\) −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 \(-0.921637\pi\)
0.969850 0.243704i \(-0.0783627\pi\)
\(44\) 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 −0.368329 0.929695i \(-0.620070\pi\)
0.620975 + 0.783830i \(0.286737\pi\)
\(48\) 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 0.999576 0.0291032i \(-0.00926513\pi\)
0.474584 + 0.880210i \(0.342598\pi\)
\(54\) 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 \(0.0198610\pi\)
0.553028 + 0.833163i \(0.313472\pi\)
\(68\) −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 0.977441 0.211207i \(-0.0677395\pi\)
0.305810 + 0.952093i \(0.401073\pi\)
\(74\) 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 \(-0.688308\pi\)
0.557679 0.830057i \(-0.311692\pi\)
\(84\) −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 \(0.273757\pi\)
−0.652412 + 0.757865i \(0.726243\pi\)
\(98\) −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 −0.0533764 0.998574i \(-0.516998\pi\)
0.838103 + 0.545513i \(0.183665\pi\)
\(104\) 21.4641 2.10473
\(105\) 0 0
\(106\) −33.8564 −3.28842
\(107\) 1.90192 1.09808i 0.183866 0.106155i −0.405242 0.914210i \(-0.632813\pi\)
0.589108 + 0.808054i \(0.299479\pi\)
\(108\) −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 \(-0.862049\pi\)
0.907548 0.419947i \(-0.137951\pi\)
\(114\) 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 \(0.0683678\pi\)
−0.977022 + 0.213136i \(0.931632\pi\)
\(128\) 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 0.416549 0.909113i \(-0.363240\pi\)
−0.579041 + 0.815298i \(0.696573\pi\)
\(138\) 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 0.262553 0.964917i \(-0.415435\pi\)
−0.704366 + 0.709837i \(0.748769\pi\)
\(158\) 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 −0.999804 0.0197859i \(-0.993702\pi\)
−0.482767 + 0.875749i \(0.660368\pi\)
\(164\) −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 \(-0.760546\pi\)
0.730142 0.683296i \(-0.239454\pi\)
\(168\) 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 −0.895274 0.445516i \(-0.853020\pi\)
−0.0618087 + 0.998088i \(0.519687\pi\)
\(174\) 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 0.536819 0.843697i \(-0.319626\pi\)
−0.462254 + 0.886748i \(0.652959\pi\)
\(194\) −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 \(-0.996147\pi\)
0.999927 0.0121029i \(-0.00385258\pi\)
\(198\) 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 \(0.239231\pi\)
−0.730619 + 0.682785i \(0.760769\pi\)
\(224\) 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 0.546956 0.837161i \(-0.315786\pi\)
−0.451525 + 0.892259i \(0.649120\pi\)
\(228\) −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 −0.903079 0.429474i \(-0.858699\pi\)
−0.0796037 + 0.996827i \(0.525365\pi\)
\(234\) −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 −0.645034 0.764154i \(-0.723157\pi\)
0.339260 + 0.940693i \(0.389823\pi\)
\(258\) 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 0.707053 0.707160i \(-0.250024\pi\)
−0.258892 + 0.965906i \(0.583357\pi\)
\(264\) 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 0.830314 0.557296i \(-0.188161\pi\)
−0.0674759 + 0.997721i \(0.521495\pi\)
\(278\) 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 −0.272434 0.962174i \(-0.587829\pi\)
−0.969485 + 0.245152i \(0.921162\pi\)
\(284\) 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 \(-0.813522\pi\)
0.833248 0.552899i \(-0.186478\pi\)
\(294\) 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 \(-0.630829\pi\)
0.399537 0.916717i \(-0.369171\pi\)
\(308\) 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 −0.157035 0.987593i \(-0.550194\pi\)
0.776763 + 0.629793i \(0.216860\pi\)
\(314\) 17.4641 0.985556
\(315\) 0 0
\(316\) −40.3923 −2.27224
\(317\) −24.6340 + 14.2224i −1.38358 + 0.798811i −0.992582 0.121579i \(-0.961204\pi\)
−0.391000 + 0.920391i \(0.627871\pi\)
\(318\) 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 \(0.162907\pi\)
−0.871870 + 0.489737i \(0.837093\pi\)
\(338\) −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 0.902162 0.431397i \(-0.141979\pi\)
0.0774801 + 0.996994i \(0.475313\pi\)
\(348\) −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 0.426262 0.904600i \(-0.359830\pi\)
−0.570276 + 0.821453i \(0.693164\pi\)
\(354\) −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 0.225108 0.974334i \(-0.427726\pi\)
−0.731244 + 0.682117i \(0.761060\pi\)
\(368\) −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 −0.958088 0.286476i \(-0.907516\pi\)
−0.230949 + 0.972966i \(0.574183\pi\)
\(374\) −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 0.114425 0.993432i \(-0.463497\pi\)
0.917550 + 0.397621i \(0.130164\pi\)
\(384\) −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 −0.989072 0.147433i \(-0.952899\pi\)
−0.366855 + 0.930278i \(0.619566\pi\)
\(398\) 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 \(-0.881021\pi\)
0.930953 0.365140i \(-0.118979\pi\)
\(434\) −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 −0.681905 0.731441i \(-0.738848\pi\)
0.292494 + 0.956267i \(0.405515\pi\)
\(444\) 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 −0.797939 0.602738i \(-0.794077\pi\)
0.123016 + 0.992405i \(0.460743\pi\)
\(458\) 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 \(-0.795988\pi\)
0.801545 0.597935i \(-0.204012\pi\)
\(464\) −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 −0.502874 0.864359i \(-0.667724\pi\)
0.497120 + 0.867682i \(0.334391\pi\)
\(468\) 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 0.508053 0.861326i \(-0.330365\pi\)
−0.491903 + 0.870650i \(0.663699\pi\)
\(488\) 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 \(-0.896028\pi\)
0.947126 0.320861i \(-0.103972\pi\)
\(504\) −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 0.127477 0.991842i \(-0.459312\pi\)
0.922698 + 0.385523i \(0.125979\pi\)
\(524\) −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 \(-0.810356\pi\)
0.827709 0.561157i \(-0.189644\pi\)
\(548\) −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 0.203582 0.979058i \(-0.434742\pi\)
−0.746098 + 0.665836i \(0.768075\pi\)
\(558\) −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 0.134148 0.990961i \(-0.457170\pi\)
−0.791123 + 0.611656i \(0.790503\pi\)
\(564\) −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 −0.115365 0.993323i \(-0.536804\pi\)
−0.917926 + 0.396752i \(0.870137\pi\)
\(578\) 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 \(0.317795\pi\)
−0.541663 + 0.840596i \(0.682205\pi\)
\(588\) −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 −0.906032 0.423209i \(-0.860903\pi\)
−0.0865058 + 0.996251i \(0.527570\pi\)
\(594\) −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 −0.442773 0.896634i \(-0.646005\pi\)
0.555121 + 0.831770i \(0.312672\pi\)
\(608\) 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 −0.0513490 0.998681i \(-0.516352\pi\)
−0.890557 + 0.454871i \(0.849685\pi\)
\(614\) 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 \(-0.739679\pi\)
0.683811 0.729659i \(-0.260321\pi\)
\(618\) 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 \(-0.971614\pi\)
0.996026 0.0890599i \(-0.0283862\pi\)
\(644\) 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 0.893148 0.449763i \(-0.148492\pi\)
0.0570678 + 0.998370i \(0.481825\pi\)
\(648\) −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 \(-0.329203\pi\)
0.999916 0.0129762i \(-0.00413057\pi\)
\(654\) 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 \(0.176659\pi\)
−0.849906 + 0.526935i \(0.823341\pi\)
\(674\) −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 −0.936880 0.349651i \(-0.886300\pi\)
−0.165633 + 0.986187i \(0.552967\pi\)
\(678\) 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 −0.0429101 0.999079i \(-0.513663\pi\)
−0.886683 + 0.462378i \(0.846996\pi\)
\(684\) 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 \(-0.920433\pi\)
0.968921 0.247372i \(-0.0795669\pi\)
\(728\) 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 −0.478419 0.878131i \(-0.658790\pi\)
0.521274 + 0.853389i \(0.325457\pi\)
\(734\) 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 \(0.0942614\pi\)
−0.956473 + 0.291822i \(0.905739\pi\)
\(744\) −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 \(-0.831039\pi\)
0.862399 0.506229i \(-0.168961\pi\)
\(758\) 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 0.989012 0.147834i \(-0.0472301\pi\)
0.366478 + 0.930427i \(0.380563\pi\)
\(774\) −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 0.755405i