Properties

Label 315.2.j.c.226.1
Level $315$
Weight $2$
Character 315.226
Analytic conductor $2.515$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 315.226
Dual form 315.2.j.c.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +9.46410 q^{8} +O(q^{10})\) \(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +9.46410 q^{8} +(1.36603 + 2.36603i) q^{10} +(0.366025 + 0.633975i) q^{11} +2.26795 q^{13} +(-7.09808 - 1.36603i) q^{14} +(-7.46410 + 12.9282i) q^{16} +(1.63397 + 2.83013i) q^{17} +(-2.23205 + 3.86603i) q^{19} -5.46410 q^{20} -2.00000 q^{22} +(-2.36603 + 4.09808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.09808 + 5.36603i) q^{26} +(9.46410 - 10.9282i) q^{28} +4.19615 q^{29} +(0.232051 + 0.401924i) q^{31} +(-10.9282 - 18.9282i) q^{32} -8.92820 q^{34} +(2.59808 + 0.500000i) q^{35} +(1.59808 - 2.76795i) q^{37} +(-6.09808 - 10.5622i) q^{38} +(4.73205 - 8.19615i) q^{40} +0.732051 q^{41} +3.19615 q^{43} +(2.00000 - 3.46410i) q^{44} +(-6.46410 - 11.1962i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-5.50000 + 4.33013i) q^{49} +2.73205 q^{50} +(-6.19615 - 10.7321i) q^{52} +(6.19615 + 10.7321i) q^{53} +0.732051 q^{55} +(8.19615 + 23.6603i) q^{56} +(-5.73205 + 9.92820i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} -1.26795 q^{62} +29.8564 q^{64} +(1.13397 - 1.96410i) q^{65} +(7.33013 + 12.6962i) q^{67} +(8.92820 - 15.4641i) q^{68} +(-4.73205 + 5.46410i) q^{70} -6.19615 q^{71} +(-6.33013 - 10.9641i) q^{73} +(4.36603 + 7.56218i) q^{74} +24.3923 q^{76} +(-1.26795 + 1.46410i) q^{77} +(3.69615 - 6.40192i) q^{79} +(7.46410 + 12.9282i) q^{80} +(-1.00000 + 1.73205i) q^{82} -15.1244 q^{83} +3.26795 q^{85} +(-4.36603 + 7.56218i) q^{86} +(3.46410 + 6.00000i) q^{88} +(7.56218 - 13.0981i) q^{89} +(1.96410 + 5.66987i) q^{91} +25.8564 q^{92} +(2.73205 + 4.73205i) q^{94} +(2.23205 + 3.86603i) q^{95} +14.9282 q^{97} +(-2.73205 - 18.9282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 4q^{4} + 2q^{5} + 24q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 4q^{4} + 2q^{5} + 24q^{8} + 2q^{10} - 2q^{11} + 16q^{13} - 18q^{14} - 16q^{16} + 10q^{17} - 2q^{19} - 8q^{20} - 8q^{22} - 6q^{23} - 2q^{25} - 2q^{26} + 24q^{28} - 4q^{29} - 6q^{31} - 16q^{32} - 8q^{34} - 4q^{37} - 14q^{38} + 12q^{40} - 4q^{41} - 8q^{43} + 8q^{44} - 12q^{46} + 4q^{47} - 22q^{49} + 4q^{50} - 4q^{52} + 4q^{53} - 4q^{55} + 12q^{56} - 16q^{58} + 10q^{59} - 8q^{61} - 12q^{62} + 64q^{64} + 8q^{65} + 12q^{67} + 8q^{68} - 12q^{70} - 4q^{71} - 8q^{73} + 14q^{74} + 56q^{76} - 12q^{77} - 6q^{79} + 16q^{80} - 4q^{82} - 12q^{83} + 20q^{85} - 14q^{86} + 6q^{89} - 6q^{91} + 48q^{92} + 4q^{94} + 2q^{95} + 32q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 2.36603i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 0 0
\(4\) −2.73205 4.73205i −1.36603 2.36603i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0.866025 + 2.50000i 0.327327 + 0.944911i
\(8\) 9.46410 3.34607
\(9\) 0 0
\(10\) 1.36603 + 2.36603i 0.431975 + 0.748203i
\(11\) 0.366025 + 0.633975i 0.110361 + 0.191151i 0.915916 0.401371i \(-0.131466\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(12\) 0 0
\(13\) 2.26795 0.629016 0.314508 0.949255i \(-0.398160\pi\)
0.314508 + 0.949255i \(0.398160\pi\)
\(14\) −7.09808 1.36603i −1.89704 0.365086i
\(15\) 0 0
\(16\) −7.46410 + 12.9282i −1.86603 + 3.23205i
\(17\) 1.63397 + 2.83013i 0.396297 + 0.686407i 0.993266 0.115858i \(-0.0369617\pi\)
−0.596969 + 0.802264i \(0.703628\pi\)
\(18\) 0 0
\(19\) −2.23205 + 3.86603i −0.512068 + 0.886927i 0.487835 + 0.872936i \(0.337787\pi\)
−0.999902 + 0.0139909i \(0.995546\pi\)
\(20\) −5.46410 −1.22181
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −2.36603 + 4.09808i −0.493350 + 0.854508i −0.999971 0.00766135i \(-0.997561\pi\)
0.506620 + 0.862169i \(0.330895\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.09808 + 5.36603i −0.607583 + 1.05236i
\(27\) 0 0
\(28\) 9.46410 10.9282i 1.78855 2.06524i
\(29\) 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 0.886112 0.463472i \(-0.153396\pi\)
−0.844434 + 0.535659i \(0.820063\pi\)
\(32\) −10.9282 18.9282i −1.93185 3.34607i
\(33\) 0 0
\(34\) −8.92820 −1.53117
\(35\) 2.59808 + 0.500000i 0.439155 + 0.0845154i
\(36\) 0 0
\(37\) 1.59808 2.76795i 0.262722 0.455048i −0.704242 0.709960i \(-0.748713\pi\)
0.966964 + 0.254912i \(0.0820464\pi\)
\(38\) −6.09808 10.5622i −0.989239 1.71341i
\(39\) 0 0
\(40\) 4.73205 8.19615i 0.748203 1.29593i
\(41\) 0.732051 0.114327 0.0571636 0.998365i \(-0.481794\pi\)
0.0571636 + 0.998365i \(0.481794\pi\)
\(42\) 0 0
\(43\) 3.19615 0.487409 0.243704 0.969850i \(-0.421637\pi\)
0.243704 + 0.969850i \(0.421637\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 0 0
\(46\) −6.46410 11.1962i −0.953080 1.65078i
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 0 0
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 2.73205 0.386370
\(51\) 0 0
\(52\) −6.19615 10.7321i −0.859252 1.48827i
\(53\) 6.19615 + 10.7321i 0.851107 + 1.47416i 0.880210 + 0.474584i \(0.157402\pi\)
−0.0291032 + 0.999576i \(0.509265\pi\)
\(54\) 0 0
\(55\) 0.732051 0.0987097
\(56\) 8.19615 + 23.6603i 1.09526 + 3.16173i
\(57\) 0 0
\(58\) −5.73205 + 9.92820i −0.752655 + 1.30364i
\(59\) −0.0980762 0.169873i −0.0127684 0.0221156i 0.859571 0.511017i \(-0.170731\pi\)
−0.872339 + 0.488901i \(0.837398\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −1.26795 −0.161030
\(63\) 0 0
\(64\) 29.8564 3.73205
\(65\) 1.13397 1.96410i 0.140652 0.243617i
\(66\) 0 0
\(67\) 7.33013 + 12.6962i 0.895518 + 1.55108i 0.833163 + 0.553028i \(0.186528\pi\)
0.0623548 + 0.998054i \(0.480139\pi\)
\(68\) 8.92820 15.4641i 1.08270 1.87530i
\(69\) 0 0
\(70\) −4.73205 + 5.46410i −0.565588 + 0.653085i
\(71\) −6.19615 −0.735348 −0.367674 0.929955i \(-0.619846\pi\)
−0.367674 + 0.929955i \(0.619846\pi\)
\(72\) 0 0
\(73\) −6.33013 10.9641i −0.740885 1.28325i −0.952093 0.305810i \(-0.901073\pi\)
0.211207 0.977441i \(-0.432260\pi\)
\(74\) 4.36603 + 7.56218i 0.507540 + 0.879085i
\(75\) 0 0
\(76\) 24.3923 2.79799
\(77\) −1.26795 + 1.46410i −0.144496 + 0.166850i
\(78\) 0 0
\(79\) 3.69615 6.40192i 0.415850 0.720273i −0.579668 0.814853i \(-0.696818\pi\)
0.995517 + 0.0945803i \(0.0301509\pi\)
\(80\) 7.46410 + 12.9282i 0.834512 + 1.44542i
\(81\) 0 0
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) −15.1244 −1.66011 −0.830057 0.557679i \(-0.811692\pi\)
−0.830057 + 0.557679i \(0.811692\pi\)
\(84\) 0 0
\(85\) 3.26795 0.354459
\(86\) −4.36603 + 7.56218i −0.470801 + 0.815451i
\(87\) 0 0
\(88\) 3.46410 + 6.00000i 0.369274 + 0.639602i
\(89\) 7.56218 13.0981i 0.801589 1.38839i −0.116980 0.993134i \(-0.537321\pi\)
0.918570 0.395259i \(-0.129345\pi\)
\(90\) 0 0
\(91\) 1.96410 + 5.66987i 0.205894 + 0.594364i
\(92\) 25.8564 2.69572
\(93\) 0 0
\(94\) 2.73205 + 4.73205i 0.281790 + 0.488074i
\(95\) 2.23205 + 3.86603i 0.229004 + 0.396646i
\(96\) 0 0
\(97\) 14.9282 1.51573 0.757865 0.652412i \(-0.226243\pi\)
0.757865 + 0.652412i \(0.226243\pi\)
\(98\) −2.73205 18.9282i −0.275979 1.91204i
\(99\) 0 0
\(100\) −2.73205 + 4.73205i −0.273205 + 0.473205i
\(101\) −3.63397 6.29423i −0.361594 0.626299i 0.626629 0.779317i \(-0.284434\pi\)
−0.988223 + 0.153018i \(0.951101\pi\)
\(102\) 0 0
\(103\) 4.59808 7.96410i 0.453062 0.784726i −0.545513 0.838103i \(-0.683665\pi\)
0.998574 + 0.0533764i \(0.0169983\pi\)
\(104\) 21.4641 2.10473
\(105\) 0 0
\(106\) −33.8564 −3.28842
\(107\) 1.09808 1.90192i 0.106155 0.183866i −0.808054 0.589108i \(-0.799479\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) 0 0
\(112\) −38.7846 7.46410i −3.66480 0.705291i
\(113\) −8.92820 −0.839895 −0.419947 0.907548i \(-0.637951\pi\)
−0.419947 + 0.907548i \(0.637951\pi\)
\(114\) 0 0
\(115\) 2.36603 + 4.09808i 0.220633 + 0.382148i
\(116\) −11.4641 19.8564i −1.06442 1.84362i
\(117\) 0 0
\(118\) 0.535898 0.0493334
\(119\) −5.66025 + 6.53590i −0.518875 + 0.599145i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) −5.46410 9.46410i −0.494697 0.856840i
\(123\) 0 0
\(124\) 1.26795 2.19615i 0.113865 0.197220i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.80385 0.426273 0.213136 0.977022i \(-0.431632\pi\)
0.213136 + 0.977022i \(0.431632\pi\)
\(128\) −18.9282 + 32.7846i −1.67303 + 2.89778i
\(129\) 0 0
\(130\) 3.09808 + 5.36603i 0.271719 + 0.470632i
\(131\) 7.73205 13.3923i 0.675552 1.17009i −0.300755 0.953702i \(-0.597239\pi\)
0.976307 0.216390i \(-0.0694281\pi\)
\(132\) 0 0
\(133\) −11.5981 2.23205i −1.00568 0.193543i
\(134\) −40.0526 −3.46001
\(135\) 0 0
\(136\) 15.4641 + 26.7846i 1.32604 + 2.29676i
\(137\) 1.09808 + 1.90192i 0.0938150 + 0.162492i 0.909113 0.416549i \(-0.136760\pi\)
−0.815298 + 0.579041i \(0.803427\pi\)
\(138\) 0 0
\(139\) 5.92820 0.502824 0.251412 0.967880i \(-0.419105\pi\)
0.251412 + 0.967880i \(0.419105\pi\)
\(140\) −4.73205 13.6603i −0.399931 1.15450i
\(141\) 0 0
\(142\) 8.46410 14.6603i 0.710292 1.23026i
\(143\) 0.830127 + 1.43782i 0.0694187 + 0.120237i
\(144\) 0 0
\(145\) 2.09808 3.63397i 0.174236 0.301785i
\(146\) 34.5885 2.86256
\(147\) 0 0
\(148\) −17.4641 −1.43554
\(149\) 2.92820 5.07180i 0.239888 0.415498i −0.720794 0.693149i \(-0.756223\pi\)
0.960682 + 0.277651i \(0.0895560\pi\)
\(150\) 0 0
\(151\) 4.46410 + 7.73205i 0.363283 + 0.629225i 0.988499 0.151227i \(-0.0483223\pi\)
−0.625216 + 0.780452i \(0.714989\pi\)
\(152\) −21.1244 + 36.5885i −1.71341 + 2.96772i
\(153\) 0 0
\(154\) −1.73205 5.00000i −0.139573 0.402911i
\(155\) 0.464102 0.0372775
\(156\) 0 0
\(157\) −3.19615 5.53590i −0.255081 0.441813i 0.709837 0.704366i \(-0.248769\pi\)
−0.964917 + 0.262553i \(0.915435\pi\)
\(158\) 10.0981 + 17.4904i 0.803360 + 1.39146i
\(159\) 0 0
\(160\) −21.8564 −1.72790
\(161\) −12.2942 2.36603i −0.968921 0.186469i
\(162\) 0 0
\(163\) −10.9282 + 18.9282i −0.855963 + 1.48257i 0.0197859 + 0.999804i \(0.493702\pi\)
−0.875749 + 0.482767i \(0.839632\pi\)
\(164\) −2.00000 3.46410i −0.156174 0.270501i
\(165\) 0 0
\(166\) 20.6603 35.7846i 1.60355 2.77742i
\(167\) 17.6603 1.36659 0.683296 0.730142i \(-0.260546\pi\)
0.683296 + 0.730142i \(0.260546\pi\)
\(168\) 0 0
\(169\) −7.85641 −0.604339
\(170\) −4.46410 + 7.73205i −0.342381 + 0.593021i
\(171\) 0 0
\(172\) −8.73205 15.1244i −0.665813 1.15322i
\(173\) 7.26795 12.5885i 0.552572 0.957083i −0.445516 0.895274i \(-0.646980\pi\)
0.998088 0.0618087i \(-0.0196869\pi\)
\(174\) 0 0
\(175\) 1.73205 2.00000i 0.130931 0.151186i
\(176\) −10.9282 −0.823744
\(177\) 0 0
\(178\) 20.6603 + 35.7846i 1.54855 + 2.68217i
\(179\) −5.00000 8.66025i −0.373718 0.647298i 0.616417 0.787420i \(-0.288584\pi\)
−0.990134 + 0.140122i \(0.955250\pi\)
\(180\) 0 0
\(181\) −24.3205 −1.80773 −0.903865 0.427819i \(-0.859282\pi\)
−0.903865 + 0.427819i \(0.859282\pi\)
\(182\) −16.0981 3.09808i −1.19327 0.229645i
\(183\) 0 0
\(184\) −22.3923 + 38.7846i −1.65078 + 2.85924i
\(185\) −1.59808 2.76795i −0.117493 0.203504i
\(186\) 0 0
\(187\) −1.19615 + 2.07180i −0.0874713 + 0.151505i
\(188\) −10.9282 −0.797021
\(189\) 0 0
\(190\) −12.1962 −0.884802
\(191\) −4.46410 + 7.73205i −0.323011 + 0.559472i −0.981108 0.193462i \(-0.938028\pi\)
0.658097 + 0.752933i \(0.271362\pi\)
\(192\) 0 0
\(193\) −0.598076 1.03590i −0.0430505 0.0745656i 0.843697 0.536819i \(-0.180374\pi\)
−0.886748 + 0.462254i \(0.847041\pi\)
\(194\) −20.3923 + 35.3205i −1.46408 + 2.53586i
\(195\) 0 0
\(196\) 35.5167 + 14.1962i 2.53690 + 1.01401i
\(197\) 0.339746 0.0242059 0.0121029 0.999927i \(-0.496147\pi\)
0.0121029 + 0.999927i \(0.496147\pi\)
\(198\) 0 0
\(199\) −11.0000 19.0526i −0.779769 1.35060i −0.932075 0.362267i \(-0.882003\pi\)
0.152305 0.988334i \(-0.451330\pi\)
\(200\) −4.73205 8.19615i −0.334607 0.579555i
\(201\) 0 0
\(202\) 19.8564 1.39709
\(203\) 3.63397 + 10.4904i 0.255055 + 0.736280i
\(204\) 0 0
\(205\) 0.366025 0.633975i 0.0255643 0.0442787i
\(206\) 12.5622 + 21.7583i 0.875248 + 1.51597i
\(207\) 0 0
\(208\) −16.9282 + 29.3205i −1.17376 + 2.03301i
\(209\) −3.26795 −0.226049
\(210\) 0 0
\(211\) 7.07180 0.486843 0.243421 0.969921i \(-0.421730\pi\)
0.243421 + 0.969921i \(0.421730\pi\)
\(212\) 33.8564 58.6410i 2.32527 4.02748i
\(213\) 0 0
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 1.59808 2.76795i 0.108988 0.188773i
\(216\) 0 0
\(217\) −0.803848 + 0.928203i −0.0545687 + 0.0630105i
\(218\) 30.0526 2.03542
\(219\) 0 0
\(220\) −2.00000 3.46410i −0.134840 0.233550i
\(221\) 3.70577 + 6.41858i 0.249277 + 0.431761i
\(222\) 0 0
\(223\) −20.3923 −1.36557 −0.682785 0.730619i \(-0.739231\pi\)
−0.682785 + 0.730619i \(0.739231\pi\)
\(224\) 37.8564 43.7128i 2.52939 2.92069i
\(225\) 0 0
\(226\) 12.1962 21.1244i 0.811276 1.40517i
\(227\) −0.830127 1.43782i −0.0550975 0.0954316i 0.837161 0.546956i \(-0.184214\pi\)
−0.892259 + 0.451525i \(0.850880\pi\)
\(228\) 0 0
\(229\) 1.50000 2.59808i 0.0991228 0.171686i −0.812199 0.583380i \(-0.801730\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(230\) −12.9282 −0.852460
\(231\) 0 0
\(232\) 39.7128 2.60727
\(233\) 8.66025 15.0000i 0.567352 0.982683i −0.429474 0.903079i \(-0.641301\pi\)
0.996827 0.0796037i \(-0.0253655\pi\)
\(234\) 0 0
\(235\) −1.00000 1.73205i −0.0652328 0.112987i
\(236\) −0.535898 + 0.928203i −0.0348840 + 0.0604209i
\(237\) 0 0
\(238\) −7.73205 22.3205i −0.501194 1.44682i
\(239\) −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 0.563535 0.826092i \(-0.309441\pi\)
−0.997184 + 0.0749893i \(0.976108\pi\)
\(242\) 14.2942 + 24.7583i 0.918868 + 1.59153i
\(243\) 0 0
\(244\) 21.8564 1.39921
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 0 0
\(247\) −5.06218 + 8.76795i −0.322099 + 0.557891i
\(248\) 2.19615 + 3.80385i 0.139456 + 0.241545i
\(249\) 0 0
\(250\) 1.36603 2.36603i 0.0863950 0.149641i
\(251\) 24.5885 1.55201 0.776005 0.630727i \(-0.217243\pi\)
0.776005 + 0.630727i \(0.217243\pi\)
\(252\) 0 0
\(253\) −3.46410 −0.217786
\(254\) −6.56218 + 11.3660i −0.411748 + 0.713168i
\(255\) 0 0
\(256\) −21.8564 37.8564i −1.36603 2.36603i
\(257\) −2.83013 + 4.90192i −0.176538 + 0.305774i −0.940693 0.339260i \(-0.889823\pi\)
0.764154 + 0.645034i \(0.223157\pi\)
\(258\) 0 0
\(259\) 8.30385 + 1.59808i 0.515976 + 0.0992996i
\(260\) −12.3923 −0.768538
\(261\) 0 0
\(262\) 21.1244 + 36.5885i 1.30507 + 2.26044i
\(263\) 4.19615 + 7.26795i 0.258746 + 0.448161i 0.965906 0.258892i \(-0.0833575\pi\)
−0.707160 + 0.707053i \(0.750024\pi\)
\(264\) 0 0
\(265\) 12.3923 0.761253
\(266\) 21.1244 24.3923i 1.29522 1.49559i
\(267\) 0 0
\(268\) 40.0526 69.3731i 2.44660 4.23763i
\(269\) −6.26795 10.8564i −0.382164 0.661927i 0.609208 0.793011i \(-0.291488\pi\)
−0.991371 + 0.131084i \(0.958154\pi\)
\(270\) 0 0
\(271\) −1.53590 + 2.66025i −0.0932992 + 0.161599i −0.908897 0.417020i \(-0.863075\pi\)
0.815598 + 0.578619i \(0.196408\pi\)
\(272\) −48.7846 −2.95800
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 0.366025 0.633975i 0.0220722 0.0382301i
\(276\) 0 0
\(277\) 7.33013 + 12.6962i 0.440425 + 0.762838i 0.997721 0.0674759i \(-0.0214946\pi\)
−0.557296 + 0.830314i \(0.688161\pi\)
\(278\) −8.09808 + 14.0263i −0.485690 + 0.841240i
\(279\) 0 0
\(280\) 24.5885 + 4.73205i 1.46944 + 0.282794i
\(281\) −13.8564 −0.826604 −0.413302 0.910594i \(-0.635625\pi\)
−0.413302 + 0.910594i \(0.635625\pi\)
\(282\) 0 0
\(283\) 12.0622 + 20.8923i 0.717022 + 1.24192i 0.962174 + 0.272434i \(0.0878287\pi\)
−0.245152 + 0.969485i \(0.578838\pi\)
\(284\) 16.9282 + 29.3205i 1.00450 + 1.73985i
\(285\) 0 0
\(286\) −4.53590 −0.268213
\(287\) 0.633975 + 1.83013i 0.0374223 + 0.108029i
\(288\) 0 0
\(289\) 3.16025 5.47372i 0.185897 0.321984i
\(290\) 5.73205 + 9.92820i 0.336598 + 0.583004i
\(291\) 0 0
\(292\) −34.5885 + 59.9090i −2.02414 + 3.50591i
\(293\) −18.9282 −1.10580 −0.552899 0.833248i \(-0.686478\pi\)
−0.552899 + 0.833248i \(0.686478\pi\)
\(294\) 0 0
\(295\) −0.196152 −0.0114204
\(296\) 15.1244 26.1962i 0.879085 1.52262i
\(297\) 0 0
\(298\) 8.00000 + 13.8564i 0.463428 + 0.802680i
\(299\) −5.36603 + 9.29423i −0.310325 + 0.537499i
\(300\) 0 0
\(301\) 2.76795 + 7.99038i 0.159542 + 0.460558i
\(302\) −24.3923 −1.40362
\(303\) 0 0
\(304\) −33.3205 57.7128i −1.91106 3.31006i
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) 0 0
\(307\) −32.1244 −1.83343 −0.916717 0.399537i \(-0.869171\pi\)
−0.916717 + 0.399537i \(0.869171\pi\)
\(308\) 10.3923 + 2.00000i 0.592157 + 0.113961i
\(309\) 0 0
\(310\) −0.633975 + 1.09808i −0.0360073 + 0.0623665i
\(311\) 4.56218 + 7.90192i 0.258697 + 0.448077i 0.965893 0.258941i \(-0.0833734\pi\)
−0.707196 + 0.707018i \(0.750040\pi\)
\(312\) 0 0
\(313\) 6.33013 10.9641i 0.357800 0.619728i −0.629793 0.776763i \(-0.716860\pi\)
0.987593 + 0.157035i \(0.0501936\pi\)
\(314\) 17.4641 0.985556
\(315\) 0 0
\(316\) −40.3923 −2.27224
\(317\) −14.2224 + 24.6340i −0.798811 + 1.38358i 0.121579 + 0.992582i \(0.461204\pi\)
−0.920391 + 0.391000i \(0.872129\pi\)
\(318\) 0 0
\(319\) 1.53590 + 2.66025i 0.0859938 + 0.148946i
\(320\) 14.9282 25.8564i 0.834512 1.44542i
\(321\) 0 0
\(322\) 22.3923 25.8564i 1.24787 1.44092i
\(323\) −14.5885 −0.811723
\(324\) 0 0
\(325\) −1.13397 1.96410i −0.0629016 0.108949i
\(326\) −29.8564 51.7128i −1.65359 2.86411i
\(327\) 0 0
\(328\) 6.92820 0.382546
\(329\) 5.19615 + 1.00000i 0.286473 + 0.0551318i
\(330\) 0 0
\(331\) −4.03590 + 6.99038i −0.221833 + 0.384226i −0.955365 0.295429i \(-0.904537\pi\)
0.733532 + 0.679655i \(0.237871\pi\)
\(332\) 41.3205 + 71.5692i 2.26776 + 3.92787i
\(333\) 0 0
\(334\) −24.1244 + 41.7846i −1.32003 + 2.28635i
\(335\) 14.6603 0.800975
\(336\) 0 0
\(337\) 17.9808 0.979475 0.489737 0.871870i \(-0.337093\pi\)
0.489737 + 0.871870i \(0.337093\pi\)
\(338\) 10.7321 18.5885i 0.583747 1.01108i
\(339\) 0 0
\(340\) −8.92820 15.4641i −0.484200 0.838659i
\(341\) −0.169873 + 0.294229i −0.00919914 + 0.0159334i
\(342\) 0 0
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 30.2487 1.63090
\(345\) 0 0
\(346\) 19.8564 + 34.3923i 1.06749 + 1.84894i
\(347\) −10.5359 18.2487i −0.565597 0.979642i −0.996994 0.0774801i \(-0.975313\pi\)
0.431397 0.902162i \(-0.358021\pi\)
\(348\) 0 0
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 2.36603 + 6.83013i 0.126469 + 0.365086i
\(351\) 0 0
\(352\) 8.00000 13.8564i 0.426401 0.738549i
\(353\) −1.56218 2.70577i −0.0831463 0.144014i 0.821453 0.570276i \(-0.193164\pi\)
−0.904600 + 0.426262i \(0.859830\pi\)
\(354\) 0 0
\(355\) −3.09808 + 5.36603i −0.164429 + 0.284799i
\(356\) −82.6410 −4.37997
\(357\) 0 0
\(358\) 27.3205 1.44393
\(359\) −0.633975 + 1.09808i −0.0334599 + 0.0579542i −0.882270 0.470743i \(-0.843986\pi\)
0.848811 + 0.528697i \(0.177319\pi\)
\(360\) 0 0
\(361\) −0.464102 0.803848i −0.0244264 0.0423078i
\(362\) 33.2224 57.5429i 1.74613 3.02439i
\(363\) 0 0
\(364\) 21.4641 24.7846i 1.12502 1.29907i
\(365\) −12.6603 −0.662668
\(366\) 0 0
\(367\) −5.59808 9.69615i −0.292217 0.506135i 0.682117 0.731244i \(-0.261060\pi\)
−0.974334 + 0.225108i \(0.927726\pi\)
\(368\) −35.3205 61.1769i −1.84121 3.18907i
\(369\) 0 0
\(370\) 8.73205 0.453958
\(371\) −21.4641 + 24.7846i −1.11436 + 1.28675i
\(372\) 0 0
\(373\) −13.2583 + 22.9641i −0.686490 + 1.18904i 0.286476 + 0.958088i \(0.407516\pi\)
−0.972966 + 0.230949i \(0.925817\pi\)
\(374\) −3.26795 5.66025i −0.168982 0.292685i
\(375\) 0 0
\(376\) 9.46410 16.3923i 0.488074 0.845369i
\(377\) 9.51666 0.490133
\(378\) 0 0
\(379\) 6.32051 0.324663 0.162331 0.986736i \(-0.448099\pi\)
0.162331 + 0.986736i \(0.448099\pi\)
\(380\) 12.1962 21.1244i 0.625649 1.08366i
\(381\) 0 0
\(382\) −12.1962 21.1244i −0.624009 1.08082i
\(383\) −11.6603 + 20.1962i −0.595811 + 1.03198i 0.397621 + 0.917550i \(0.369836\pi\)
−0.993432 + 0.114425i \(0.963497\pi\)
\(384\) 0 0
\(385\) 0.633975 + 1.83013i 0.0323103 + 0.0932719i
\(386\) 3.26795 0.166334
\(387\) 0 0
\(388\) −40.7846 70.6410i −2.07052 3.58625i
\(389\) 2.70577 + 4.68653i 0.137188 + 0.237617i 0.926431 0.376464i \(-0.122860\pi\)
−0.789243 + 0.614081i \(0.789527\pi\)
\(390\) 0 0
\(391\) −15.4641 −0.782053
\(392\) −52.0526 + 40.9808i −2.62905 + 2.06984i
\(393\) 0 0
\(394\) −0.464102 + 0.803848i −0.0233811 + 0.0404973i
\(395\) −3.69615 6.40192i −0.185974 0.322116i
\(396\) 0 0
\(397\) 15.5981 27.0167i 0.782845 1.35593i −0.147433 0.989072i \(-0.547101\pi\)
0.930278 0.366855i \(-0.119566\pi\)
\(398\) 60.1051 3.01280
\(399\) 0 0
\(400\) 14.9282 0.746410
\(401\) −8.19615 + 14.1962i −0.409296 + 0.708922i −0.994811 0.101740i \(-0.967559\pi\)
0.585515 + 0.810662i \(0.300892\pi\)
\(402\) 0 0
\(403\) 0.526279 + 0.911543i 0.0262158 + 0.0454072i
\(404\) −19.8564 + 34.3923i −0.987893 + 1.71108i
\(405\) 0 0
\(406\) −29.7846 5.73205i −1.47819 0.284477i
\(407\) 2.33975 0.115977
\(408\) 0 0
\(409\) −1.57180 2.72243i −0.0777203 0.134616i 0.824546 0.565795i \(-0.191431\pi\)
−0.902266 + 0.431180i \(0.858097\pi\)
\(410\) 1.00000 + 1.73205i 0.0493865 + 0.0855399i
\(411\) 0 0
\(412\) −50.2487 −2.47558
\(413\) 0.339746 0.392305i 0.0167178 0.0193041i
\(414\) 0 0
\(415\) −7.56218 + 13.0981i −0.371213 + 0.642959i
\(416\) −24.7846 42.9282i −1.21517 2.10473i
\(417\) 0 0
\(418\) 4.46410 7.73205i 0.218346 0.378187i
\(419\) 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 \(0.499443\pi\)
\(422\) −9.66025 + 16.7321i −0.470254 + 0.814503i
\(423\) 0 0
\(424\) 58.6410 + 101.569i 2.84786 + 4.93264i
\(425\) 1.63397 2.83013i 0.0792594 0.137281i
\(426\) 0 0
\(427\) −10.3923 2.00000i −0.502919 0.0967868i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 4.36603 + 7.56218i 0.210548 + 0.364681i
\(431\) 8.66025 + 15.0000i 0.417150 + 0.722525i 0.995651 0.0931566i \(-0.0296957\pi\)
−0.578502 + 0.815681i \(0.696362\pi\)
\(432\) 0 0
\(433\) 15.1962 0.730280 0.365140 0.930953i \(-0.381021\pi\)
0.365140 + 0.930953i \(0.381021\pi\)
\(434\) −1.09808 3.16987i −0.0527093 0.152159i
\(435\) 0 0
\(436\) −30.0526 + 52.0526i −1.43926 + 2.49287i
\(437\) −10.5622 18.2942i −0.505257 0.875132i
\(438\) 0 0
\(439\) −0.267949 + 0.464102i −0.0127885 + 0.0221504i −0.872349 0.488884i \(-0.837404\pi\)
0.859560 + 0.511034i \(0.170737\pi\)
\(440\) 6.92820 0.330289
\(441\) 0 0
\(442\) −20.2487 −0.963133
\(443\) 4.73205 8.19615i 0.224827 0.389411i −0.731441 0.681905i \(-0.761152\pi\)
0.956267 + 0.292494i \(0.0944851\pi\)
\(444\) 0 0
\(445\) −7.56218 13.0981i −0.358482 0.620908i
\(446\) 27.8564 48.2487i 1.31904 2.28464i
\(447\) 0 0
\(448\) 25.8564 + 74.6410i 1.22160 + 3.52646i
\(449\) 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
\(452\) 24.3923 + 42.2487i 1.14732 + 1.98721i
\(453\) 0 0
\(454\) 4.53590 0.212880
\(455\) 5.89230 + 1.13397i 0.276236 + 0.0531615i
\(456\) 0 0
\(457\) 8.33013 14.4282i 0.389667 0.674923i −0.602738 0.797939i \(-0.705923\pi\)
0.992405 + 0.123016i \(0.0392568\pi\)
\(458\) 4.09808 + 7.09808i 0.191491 + 0.331671i
\(459\) 0 0
\(460\) 12.9282 22.3923i 0.602781 1.04405i
\(461\) −16.9808 −0.790873 −0.395436 0.918493i \(-0.629407\pi\)
−0.395436 + 0.918493i \(0.629407\pi\)
\(462\) 0 0
\(463\) 25.7321 1.19587 0.597935 0.801545i \(-0.295988\pi\)
0.597935 + 0.801545i \(0.295988\pi\)
\(464\) −31.3205 + 54.2487i −1.45402 + 2.51843i
\(465\) 0 0
\(466\) 23.6603 + 40.9808i 1.09604 + 1.89840i
\(467\) −0.0717968 + 0.124356i −0.00332236 + 0.00575449i −0.867682 0.497120i \(-0.834391\pi\)
0.864359 + 0.502874i \(0.167724\pi\)
\(468\) 0 0
\(469\) −25.3923 + 29.3205i −1.17251 + 1.35390i
\(470\) 5.46410 0.252040
\(471\) 0 0
\(472\) −0.928203 1.60770i −0.0427240 0.0740002i
\(473\) 1.16987 + 2.02628i 0.0537908 + 0.0931684i
\(474\) 0 0
\(475\) 4.46410 0.204827
\(476\) 46.3923 + 8.92820i 2.12639 + 0.409224i
\(477\) 0 0
\(478\) 9.66025 16.7321i 0.441850 0.765306i
\(479\) 4.39230 + 7.60770i 0.200690 + 0.347604i 0.948751 0.316025i \(-0.102348\pi\)
−0.748061 + 0.663630i \(0.769015\pi\)
\(480\) 0 0
\(481\) 3.62436 6.27757i 0.165256 0.286232i
\(482\) 36.7846 1.67549
\(483\) 0 0
\(484\) −57.1769 −2.59895
\(485\) 7.46410 12.9282i 0.338927 0.587039i
\(486\) 0 0
\(487\) 0.205771 + 0.356406i 0.00932439 + 0.0161503i 0.870650 0.491903i \(-0.163699\pi\)
−0.861326 + 0.508053i \(0.830365\pi\)
\(488\) −18.9282 + 32.7846i −0.856840 + 1.48409i
\(489\) 0 0
\(490\) −17.7583 7.09808i −0.802240 0.320658i
\(491\) 38.2487 1.72614 0.863070 0.505084i \(-0.168539\pi\)
0.863070 + 0.505084i \(0.168539\pi\)
\(492\) 0 0
\(493\) 6.85641 + 11.8756i 0.308797 + 0.534852i
\(494\) −13.8301 23.9545i −0.622247 1.07776i
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) −5.36603 15.4904i −0.240699 0.694839i
\(498\) 0 0
\(499\) 6.76795 11.7224i 0.302975 0.524768i −0.673833 0.738883i \(-0.735353\pi\)
0.976808 + 0.214115i \(0.0686868\pi\)
\(500\) 2.73205 + 4.73205i 0.122181 + 0.211624i
\(501\) 0 0
\(502\) −33.5885 + 58.1769i −1.49913 + 2.59656i
\(503\) −14.3923 −0.641721 −0.320861 0.947126i \(-0.603972\pi\)
−0.320861 + 0.947126i \(0.603972\pi\)
\(504\) 0 0
\(505\) −7.26795 −0.323419
\(506\) 4.73205 8.19615i 0.210365 0.364363i
\(507\) 0 0
\(508\) −13.1244 22.7321i −0.582299 1.00857i
\(509\) 2.26795 3.92820i 0.100525 0.174115i −0.811376 0.584525i \(-0.801281\pi\)
0.911901 + 0.410410i \(0.134614\pi\)
\(510\) 0 0
\(511\) 21.9282 25.3205i 0.970047 1.12011i
\(512\) 43.7128 1.93185
\(513\) 0 0
\(514\) −7.73205 13.3923i −0.341046 0.590709i
\(515\) −4.59808 7.96410i −0.202615 0.350940i
\(516\) 0 0
\(517\) 1.46410 0.0643911
\(518\) −15.1244 + 17.4641i −0.664526 + 0.767329i
\(519\) 0 0
\(520\) 10.7321 18.5885i 0.470632 0.815158i
\(521\) −2.73205 4.73205i −0.119693 0.207315i 0.799953 0.600063i \(-0.204858\pi\)
−0.919646 + 0.392748i \(0.871524\pi\)
\(522\) 0 0
\(523\) 13.8660 24.0167i 0.606319 1.05018i −0.385523 0.922698i \(-0.625979\pi\)
0.991842 0.127477i \(-0.0406878\pi\)
\(524\) −84.4974 −3.69129
\(525\) 0 0
\(526\) −22.9282 −0.999717
\(527\) −0.758330 + 1.31347i −0.0330334 + 0.0572155i
\(528\) 0 0
\(529\) 0.303848 + 0.526279i 0.0132108 + 0.0228817i
\(530\) −16.9282 + 29.3205i −0.735314 + 1.27360i
\(531\) 0 0
\(532\) 21.1244 + 60.9808i 0.915857 + 2.64385i
\(533\) 1.66025 0.0719136
\(534\) 0 0
\(535\) −1.09808 1.90192i −0.0474740 0.0822273i
\(536\) 69.3731 + 120.158i 2.99646 + 5.19002i
\(537\) 0 0
\(538\) 34.2487 1.47657
\(539\) −4.75833 1.90192i −0.204956 0.0819217i
\(540\) 0 0
\(541\) −2.89230 + 5.00962i −0.124350 + 0.215380i −0.921479 0.388429i \(-0.873018\pi\)
0.797129 + 0.603809i \(0.206351\pi\)
\(542\) −4.19615 7.26795i −0.180240 0.312185i
\(543\) 0 0
\(544\) 35.7128 61.8564i 1.53117 2.65207i
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) −26.2487 −1.12231 −0.561157 0.827709i \(-0.689644\pi\)
−0.561157 + 0.827709i \(0.689644\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) 0 0
\(550\) 1.00000 + 1.73205i 0.0426401 + 0.0738549i
\(551\) −9.36603 + 16.2224i −0.399006 + 0.691099i
\(552\) 0 0
\(553\) 19.2058 + 3.69615i 0.816712 + 0.157176i
\(554\) −40.0526 −1.70167
\(555\) 0 0
\(556\) −16.1962 28.0526i −0.686870 1.18969i
\(557\) 7.39230 + 12.8038i 0.313222 + 0.542516i 0.979058 0.203582i \(-0.0652583\pi\)
−0.665836 + 0.746098i \(0.731925\pi\)
\(558\) 0 0
\(559\) 7.24871 0.306588
\(560\) −25.8564 + 29.8564i −1.09263 + 1.26166i
\(561\) 0 0
\(562\) 18.9282 32.7846i 0.798438 1.38294i
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) 0 0
\(565\) −4.46410 + 7.73205i −0.187806 + 0.325290i
\(566\) −65.9090 −2.77036
\(567\) 0 0
\(568\) −58.6410 −2.46052
\(569\) 16.2224 28.0981i 0.680080 1.17793i −0.294876 0.955535i \(-0.595278\pi\)
0.974956 0.222397i \(-0.0713882\pi\)
\(570\) 0 0
\(571\) −9.30385 16.1147i −0.389354 0.674381i 0.603009 0.797734i \(-0.293968\pi\)
−0.992363 + 0.123354i \(0.960635\pi\)
\(572\) 4.53590 7.85641i 0.189655 0.328493i
\(573\) 0 0
\(574\) −5.19615 1.00000i −0.216883 0.0417392i
\(575\) 4.73205 0.197340
\(576\) 0 0
\(577\) −14.3301 24.8205i −0.596571 1.03329i −0.993323 0.115365i \(-0.963196\pi\)
0.396752 0.917926i \(-0.370137\pi\)
\(578\) 8.63397 + 14.9545i 0.359126 + 0.622024i
\(579\) 0 0
\(580\) −22.9282 −0.952042
\(581\) −13.0981 37.8109i −0.543400 1.56866i
\(582\) 0 0
\(583\) −4.53590 + 7.85641i −0.187858 + 0.325379i
\(584\) −59.9090 103.765i −2.47905 4.29384i
\(585\) 0 0
\(586\) 25.8564 44.7846i 1.06812 1.85004i
\(587\) −40.7321 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(588\) 0 0
\(589\) −2.07180 −0.0853669
\(590\) 0.267949 0.464102i 0.0110313 0.0191068i
\(591\) 0 0
\(592\) 23.8564 + 41.3205i 0.980492 + 1.69826i
\(593\) 13.9545 24.1699i 0.573042 0.992538i −0.423209 0.906032i \(-0.639097\pi\)
0.996251 0.0865058i \(-0.0275701\pi\)
\(594\) 0 0
\(595\) 2.83013 + 8.16987i 0.116024 + 0.334932i
\(596\) −32.0000 −1.31077
\(597\) 0 0
\(598\) −14.6603 25.3923i −0.599502 1.03837i
\(599\) −19.1244 33.1244i −0.781400 1.35342i −0.931126 0.364697i \(-0.881173\pi\)
0.149726 0.988727i \(-0.452161\pi\)
\(600\) 0 0
\(601\) −0.0717968 −0.00292865 −0.00146433 0.999999i \(-0.500466\pi\)
−0.00146433 + 0.999999i \(0.500466\pi\)
\(602\) −22.6865 4.36603i −0.924634 0.177946i
\(603\) 0 0
\(604\) 24.3923 42.2487i 0.992509 1.71908i
\(605\) −5.23205 9.06218i −0.212713 0.368430i
\(606\) 0 0
\(607\) −1.59808 + 2.76795i −0.0648639 + 0.112348i −0.896634 0.442773i \(-0.853995\pi\)
0.831770 + 0.555121i \(0.187328\pi\)
\(608\) 97.5692 3.95695
\(609\) 0 0
\(610\) −10.9282 −0.442470
\(611\) 2.26795 3.92820i 0.0917514 0.158918i
\(612\) 0 0
\(613\) 13.4641 + 23.3205i 0.543810 + 0.941906i 0.998681 + 0.0513490i \(0.0163521\pi\)
−0.454871 + 0.890557i \(0.650315\pi\)
\(614\) 43.8827 76.0070i 1.77096 3.06739i
\(615\) 0 0
\(616\) −12.0000 + 13.8564i −0.483494 + 0.558291i
\(617\) 36.2487 1.45932 0.729659 0.683811i \(-0.239679\pi\)
0.729659 + 0.683811i \(0.239679\pi\)
\(618\) 0 0
\(619\) 15.0359 + 26.0429i 0.604344 + 1.04675i 0.992155 + 0.125015i \(0.0398980\pi\)
−0.387811 + 0.921739i \(0.626769\pi\)
\(620\) −1.26795 2.19615i −0.0509221 0.0881996i
\(621\) 0 0
\(622\) −24.9282 −0.999530
\(623\) 39.2942 + 7.56218i 1.57429 + 0.302972i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 17.2942 + 29.9545i 0.691216 + 1.19722i
\(627\) 0 0
\(628\) −17.4641 + 30.2487i −0.696894 + 1.20705i
\(629\) 10.4449 0.416464
\(630\) 0 0
\(631\) 48.7846 1.94208 0.971042 0.238908i \(-0.0767893\pi\)
0.971042 + 0.238908i \(0.0767893\pi\)
\(632\) 34.9808 60.5885i 1.39146 2.41008i
\(633\) 0 0
\(634\) −38.8564 67.3013i −1.54319 2.67287i
\(635\) 2.40192 4.16025i 0.0953174 0.165095i
\(636\) 0 0
\(637\) −12.4737 + 9.82051i −0.494227 + 0.389103i
\(638\) −8.39230 −0.332255
\(639\) 0 0
\(640\) 18.9282 + 32.7846i 0.748203 + 1.29593i
\(641\) 1.90192 + 3.29423i 0.0751215 + 0.130114i 0.901139 0.433530i \(-0.142732\pi\)
−0.826018 + 0.563644i \(0.809399\pi\)
\(642\) 0 0
\(643\) 4.51666 0.178120 0.0890599 0.996026i \(-0.471614\pi\)
0.0890599 + 0.996026i \(0.471614\pi\)
\(644\) 22.3923 + 64.6410i 0.882380 + 2.54721i
\(645\) 0 0
\(646\) 19.9282 34.5167i 0.784065 1.35804i
\(647\) −13.9545 24.1699i −0.548607 0.950216i −0.998370 0.0570678i \(-0.981825\pi\)
0.449763 0.893148i \(-0.351508\pi\)
\(648\) 0 0
\(649\) 0.0717968 0.124356i 0.00281827 0.00488139i
\(650\) 6.19615 0.243033
\(651\) 0 0
\(652\) 119.426 4.67707
\(653\) −22.2942 + 38.6147i −0.872441 + 1.51111i −0.0129762 + 0.999916i \(0.504131\pi\)
−0.859464 + 0.511196i \(0.829203\pi\)
\(654\) 0 0
\(655\) −7.73205 13.3923i −0.302116 0.523281i
\(656\) −5.46410 + 9.46410i −0.213337 + 0.369511i
\(657\) 0 0
\(658\) −9.46410 + 10.9282i −0.368949 + 0.426026i
\(659\) −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 0.746152 0.665776i \(-0.231899\pi\)
−0.949655 + 0.313298i \(0.898566\pi\)
\(662\) −11.0263 19.0981i −0.428549 0.742268i
\(663\) 0 0
\(664\) −143.138 −5.55485
\(665\) −7.73205 + 8.92820i −0.299836 + 0.346221i
\(666\) 0 0
\(667\) −9.92820 + 17.1962i −0.384422 + 0.665838i
\(668\) −48.2487 83.5692i −1.86680 3.23339i
\(669\) 0 0
\(670\) −20.0263 + 34.6865i −0.773683 + 1.34006i
\(671\) −2.92820 −0.113042
\(672\) 0 0
\(673\) −27.3397 −1.05387 −0.526935 0.849906i \(-0.676659\pi\)
−0.526935 + 0.849906i \(0.676659\pi\)
\(674\) −24.5622 + 42.5429i −0.946100 + 1.63869i
\(675\) 0 0
\(676\) 21.4641 + 37.1769i 0.825542 + 1.42988i
\(677\) −16.5622 + 28.6865i −0.636536 + 1.10251i 0.349651 + 0.936880i \(0.386300\pi\)
−0.986187 + 0.165633i \(0.947033\pi\)
\(678\) 0 0
\(679\) 12.9282 + 37.3205i 0.496139 + 1.43223i
\(680\) 30.9282 1.18604
\(681\) 0 0
\(682\) −0.464102 0.803848i −0.0177714 0.0307809i
\(683\) −14.0263 24.2942i −0.536701 0.929593i −0.999079 0.0429101i \(-0.986337\pi\)
0.462378 0.886683i \(-0.346996\pi\)
\(684\) 0 0
\(685\) 2.19615 0.0839107
\(686\) 44.9545 23.2224i 1.71637 0.886637i
\(687\) 0 0
\(688\) −23.8564 + 41.3205i −0.909517 + 1.57533i
\(689\) 14.0526 + 24.3397i 0.535360 + 0.927270i
\(690\) 0 0
\(691\) −4.42820 + 7.66987i −0.168457 + 0.291776i −0.937877 0.346967i \(-0.887212\pi\)
0.769421 + 0.638742i \(0.220545\pi\)
\(692\) −79.4256 −3.01931
\(693\) 0 0
\(694\) 57.5692 2.18530
\(695\) 2.96410 5.13397i 0.112435 0.194743i
\(696\) 0 0
\(697\) 1.19615 + 2.07180i 0.0453075 + 0.0784749i
\(698\) −30.0526 + 52.0526i −1.13751 + 1.97022i
\(699\) 0 0
\(700\) −14.1962 2.73205i −0.536564 0.103262i
\(701\) 8.58846 0.324382 0.162191 0.986759i \(-0.448144\pi\)
0.162191 + 0.986759i \(0.448144\pi\)
\(702\) 0 0
\(703\) 7.13397 + 12.3564i 0.269063 + 0.466031i
\(704\) 10.9282 + 18.9282i 0.411872 + 0.713384i
\(705\) 0 0
\(706\) 8.53590 0.321253
\(707\) 12.5885 14.5359i 0.473438 0.546679i
\(708\) 0 0
\(709\) 0.535898 0.928203i 0.0201261 0.0348594i −0.855787 0.517328i \(-0.826927\pi\)
0.875913 + 0.482469i \(0.160260\pi\)
\(710\) −8.46410 14.6603i −0.317652 0.550190i
\(711\) 0 0
\(712\) 71.5692 123.962i 2.68217 4.64565i
\(713\) −2.19615 −0.0822466
\(714\) 0 0
\(715\) 1.66025 0.0620900
\(716\) −27.3205 + 47.3205i −1.02102 + 1.76845i
\(717\) 0 0
\(718\) −1.73205 3.00000i −0.0646396 0.111959i
\(719\) −10.2679 + 17.7846i −0.382930 + 0.663254i −0.991480 0.130262i \(-0.958418\pi\)
0.608550 + 0.793516i \(0.291752\pi\)
\(720\) 0 0
\(721\) 23.8923 + 4.59808i 0.889796 + 0.171241i
\(722\) 2.53590 0.0943764
\(723\) 0 0
\(724\) 66.4449 + 115.086i 2.46940 + 4.27713i
\(725\) −2.09808 3.63397i −0.0779206 0.134962i
\(726\) 0 0
\(727\) −13.3397 −0.494744 −0.247372 0.968921i \(-0.579567\pi\)
−0.247372 + 0.968921i \(0.579567\pi\)
\(728\) 18.5885 + 53.6603i 0.688934 + 1.98878i
\(729\) 0 0
\(730\) 17.2942 29.9545i 0.640088 1.10867i
\(731\) 5.22243 + 9.04552i 0.193159 + 0.334561i
\(732\) 0 0
\(733\) 0.669873 1.16025i 0.0247423 0.0428550i −0.853389 0.521274i \(-0.825457\pi\)
0.878131 + 0.478419i \(0.158790\pi\)
\(734\) 30.5885 1.12904
\(735\) 0 0
\(736\) 103.426 3.81232
\(737\) −5.36603 + 9.29423i −0.197660 + 0.342357i
\(738\) 0 0
\(739\) −13.8923 24.0622i −0.511037 0.885142i −0.999918 0.0127913i \(-0.995928\pi\)
0.488881 0.872350i \(-0.337405\pi\)
\(740\) −8.73205 + 15.1244i −0.320997 + 0.555982i
\(741\) 0 0
\(742\) −29.3205 84.6410i −1.07639 3.10727i
\(743\) 15.9090 0.583643 0.291822 0.956473i \(-0.405739\pi\)
0.291822 + 0.956473i \(0.405739\pi\)
\(744\) 0 0
\(745\) −2.92820 5.07180i −0.107281 0.185816i
\(746\) −36.2224 62.7391i −1.32620 2.29704i
\(747\) 0 0
\(748\) 13.0718 0.477952
\(749\) 5.70577 + 1.09808i 0.208484 + 0.0401228i
\(750\) 0 0
\(751\) −9.03590 + 15.6506i −0.329725 + 0.571100i −0.982457 0.186489i \(-0.940289\pi\)
0.652732 + 0.757588i \(0.273623\pi\)
\(752\) 14.9282 + 25.8564i 0.544376 + 0.942886i
\(753\) 0 0
\(754\) −13.0000 + 22.5167i −0.473432 + 0.820008i
\(755\) 8.92820 0.324931
\(756\) 0 0
\(757\) −27.8564 −1.01246 −0.506229 0.862399i \(-0.668961\pi\)
−0.506229 + 0.862399i \(0.668961\pi\)
\(758\) −8.63397 + 14.9545i −0.313600 + 0.543171i
\(759\) 0 0
\(760\) 21.1244 + 36.5885i 0.766261 + 1.32720i
\(761\) 23.3660 40.4711i 0.847018 1.46708i −0.0368396 0.999321i \(-0.511729\pi\)
0.883857 0.467757i \(-0.154938\pi\)
\(762\) 0 0
\(763\) 19.0526 22.0000i 0.689749 0.796453i
\(764\) 48.7846 1.76497
\(765\) 0 0
\(766\) −31.8564 55.1769i −1.15102 1.99362i
\(767\) −0.222432 0.385263i −0.00803155 0.0139111i
\(768\) 0 0
\(769\) 52.3205 1.88673 0.943363 0.331763i \(-0.107643\pi\)
0.943363 + 0.331763i \(0.107643\pi\)
\(770\) −5.19615 1.00000i −0.187256 0.0360375i
\(771\) 0 0
\(772\) −3.26795 + 5.66025i −0.117616 + 0.203717i
\(773\) 21.7583 + 37.6865i 0.782593 + 1.35549i 0.930427 + 0.366478i \(0.119437\pi\)
−0.147834 + 0.989012i \(0.547230\pi\)
\(774\) 0 0
\(775\) 0.232051 0.401924i 0.00833551 0.0144375i
\(776\) 141.282 5.07173
\(777\) 0 0
\(778\) −14.7846 −0.530054
\(779\) −1.63397 + 2.83013i −0.0585432 + 0.101400i
\(780\) 0 0
\(781\) −2.26795 3.92820i −0.0811536 0.140562i
\(782\) 21.1244 36.5885i 0.755405 1.30840i
\(783\) 0 0
\(784\) −14.9282 103.426i −0.533150 3.69377i
\(785\) −6.39230 −0.228151
\(786\) 0 0
\(787\) −6.73205 11.6603i −0.239972 0.415643i 0.720734 0.693212i \(-0.243805\pi\)
−0.960706 + 0.277568i \(0.910471\pi\)
\(788\) −0.928203 1.60770i −0.0330659 0.0572718i