Properties

Label 300.2.o.a.109.5
Level $300$
Weight $2$
Character 300.109
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 109.5
Character \(\chi\) \(=\) 300.109
Dual form 300.2.o.a.289.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.951057 - 0.309017i) q^{3} +(-1.64247 + 1.51733i) q^{5} +3.78808i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.951057 - 0.309017i) q^{3} +(-1.64247 + 1.51733i) q^{5} +3.78808i q^{7} +(0.809017 - 0.587785i) q^{9} +(0.653426 + 0.474742i) q^{11} +(2.79168 + 3.84242i) q^{13} +(-1.09320 + 1.95062i) q^{15} +(-1.09262 - 0.355012i) q^{17} +(-0.00463870 + 0.0142765i) q^{19} +(1.17058 + 3.60268i) q^{21} +(3.68422 - 5.07089i) q^{23} +(0.395416 - 4.98434i) q^{25} +(0.587785 - 0.809017i) q^{27} +(-1.14365 - 3.51978i) q^{29} +(-0.488893 + 1.50466i) q^{31} +(0.768148 + 0.249586i) q^{33} +(-5.74777 - 6.22181i) q^{35} +(5.02074 + 6.91045i) q^{37} +(3.84242 + 2.79168i) q^{39} +(-9.30279 + 6.75887i) q^{41} -10.2458i q^{43} +(-0.436922 + 2.19297i) q^{45} +(0.500524 - 0.162630i) q^{47} -7.34957 q^{49} -1.14884 q^{51} +(-2.80539 + 0.911527i) q^{53} +(-1.79357 + 0.211714i) q^{55} +0.0150112i q^{57} +(9.25803 - 6.72635i) q^{59} +(-2.54203 - 1.84689i) q^{61} +(2.22658 + 3.06462i) q^{63} +(-10.4155 - 2.07516i) q^{65} +(12.6312 + 4.10412i) q^{67} +(1.93691 - 5.96119i) q^{69} +(-1.51826 - 4.67271i) q^{71} +(2.75001 - 3.78507i) q^{73} +(-1.16418 - 4.86258i) q^{75} +(-1.79836 + 2.47523i) q^{77} +(-2.86507 - 8.81777i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-1.35402 - 0.439947i) q^{83} +(2.33326 - 1.07476i) q^{85} +(-2.17534 - 2.99410i) q^{87} +(-13.0306 - 9.46730i) q^{89} +(-14.5554 + 10.5751i) q^{91} +1.58209i q^{93} +(-0.0140432 - 0.0304871i) q^{95} +(-7.66744 + 2.49130i) q^{97} +0.807679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.951057 0.309017i 0.549093 0.178411i
\(4\) 0 0
\(5\) −1.64247 + 1.51733i −0.734535 + 0.678571i
\(6\) 0 0
\(7\) 3.78808i 1.43176i 0.698223 + 0.715880i \(0.253974\pi\)
−0.698223 + 0.715880i \(0.746026\pi\)
\(8\) 0 0
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0 0
\(11\) 0.653426 + 0.474742i 0.197015 + 0.143140i 0.681919 0.731427i \(-0.261145\pi\)
−0.484904 + 0.874567i \(0.661145\pi\)
\(12\) 0 0
\(13\) 2.79168 + 3.84242i 0.774274 + 1.06570i 0.995891 + 0.0905626i \(0.0288665\pi\)
−0.221617 + 0.975134i \(0.571133\pi\)
\(14\) 0 0
\(15\) −1.09320 + 1.95062i −0.282263 + 0.503647i
\(16\) 0 0
\(17\) −1.09262 0.355012i −0.264998 0.0861032i 0.173504 0.984833i \(-0.444491\pi\)
−0.438503 + 0.898730i \(0.644491\pi\)
\(18\) 0 0
\(19\) −0.00463870 + 0.0142765i −0.00106419 + 0.00327524i −0.951587 0.307379i \(-0.900548\pi\)
0.950523 + 0.310654i \(0.100548\pi\)
\(20\) 0 0
\(21\) 1.17058 + 3.60268i 0.255442 + 0.786169i
\(22\) 0 0
\(23\) 3.68422 5.07089i 0.768213 1.05735i −0.228274 0.973597i \(-0.573308\pi\)
0.996486 0.0837569i \(-0.0266919\pi\)
\(24\) 0 0
\(25\) 0.395416 4.98434i 0.0790832 0.996868i
\(26\) 0 0
\(27\) 0.587785 0.809017i 0.113119 0.155695i
\(28\) 0 0
\(29\) −1.14365 3.51978i −0.212370 0.653607i −0.999330 0.0366030i \(-0.988346\pi\)
0.786960 0.617004i \(-0.211654\pi\)
\(30\) 0 0
\(31\) −0.488893 + 1.50466i −0.0878078 + 0.270245i −0.985313 0.170760i \(-0.945378\pi\)
0.897505 + 0.441005i \(0.145378\pi\)
\(32\) 0 0
\(33\) 0.768148 + 0.249586i 0.133717 + 0.0434474i
\(34\) 0 0
\(35\) −5.74777 6.22181i −0.971551 1.05168i
\(36\) 0 0
\(37\) 5.02074 + 6.91045i 0.825404 + 1.13607i 0.988761 + 0.149504i \(0.0477678\pi\)
−0.163357 + 0.986567i \(0.552232\pi\)
\(38\) 0 0
\(39\) 3.84242 + 2.79168i 0.615280 + 0.447027i
\(40\) 0 0
\(41\) −9.30279 + 6.75887i −1.45285 + 1.05556i −0.467697 + 0.883889i \(0.654916\pi\)
−0.985155 + 0.171669i \(0.945084\pi\)
\(42\) 0 0
\(43\) 10.2458i 1.56247i −0.624238 0.781234i \(-0.714591\pi\)
0.624238 0.781234i \(-0.285409\pi\)
\(44\) 0 0
\(45\) −0.436922 + 2.19297i −0.0651324 + 0.326908i
\(46\) 0 0
\(47\) 0.500524 0.162630i 0.0730090 0.0237221i −0.272285 0.962217i \(-0.587779\pi\)
0.345294 + 0.938495i \(0.387779\pi\)
\(48\) 0 0
\(49\) −7.34957 −1.04994
\(50\) 0 0
\(51\) −1.14884 −0.160870
\(52\) 0 0
\(53\) −2.80539 + 0.911527i −0.385350 + 0.125208i −0.495284 0.868731i \(-0.664936\pi\)
0.109934 + 0.993939i \(0.464936\pi\)
\(54\) 0 0
\(55\) −1.79357 + 0.211714i −0.241845 + 0.0285475i
\(56\) 0 0
\(57\) 0.0150112i 0.00198828i
\(58\) 0 0
\(59\) 9.25803 6.72635i 1.20529 0.875696i 0.210498 0.977594i \(-0.432492\pi\)
0.994795 + 0.101898i \(0.0324916\pi\)
\(60\) 0 0
\(61\) −2.54203 1.84689i −0.325473 0.236470i 0.413034 0.910716i \(-0.364469\pi\)
−0.738507 + 0.674245i \(0.764469\pi\)
\(62\) 0 0
\(63\) 2.22658 + 3.06462i 0.280523 + 0.386106i
\(64\) 0 0
\(65\) −10.4155 2.07516i −1.29188 0.257392i
\(66\) 0 0
\(67\) 12.6312 + 4.10412i 1.54314 + 0.501398i 0.952241 0.305346i \(-0.0987722\pi\)
0.590901 + 0.806744i \(0.298772\pi\)
\(68\) 0 0
\(69\) 1.93691 5.96119i 0.233176 0.717643i
\(70\) 0 0
\(71\) −1.51826 4.67271i −0.180184 0.554549i 0.819648 0.572867i \(-0.194169\pi\)
−0.999832 + 0.0183179i \(0.994169\pi\)
\(72\) 0 0
\(73\) 2.75001 3.78507i 0.321865 0.443009i −0.617171 0.786829i \(-0.711721\pi\)
0.939035 + 0.343820i \(0.111721\pi\)
\(74\) 0 0
\(75\) −1.16418 4.86258i −0.134428 0.561482i
\(76\) 0 0
\(77\) −1.79836 + 2.47523i −0.204942 + 0.282079i
\(78\) 0 0
\(79\) −2.86507 8.81777i −0.322345 0.992076i −0.972625 0.232381i \(-0.925348\pi\)
0.650280 0.759695i \(-0.274652\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −1.35402 0.439947i −0.148623 0.0482904i 0.233761 0.972294i \(-0.424897\pi\)
−0.382384 + 0.924004i \(0.624897\pi\)
\(84\) 0 0
\(85\) 2.33326 1.07476i 0.253078 0.116574i
\(86\) 0 0
\(87\) −2.17534 2.99410i −0.233221 0.321002i
\(88\) 0 0
\(89\) −13.0306 9.46730i −1.38124 1.00353i −0.996763 0.0803985i \(-0.974381\pi\)
−0.384480 0.923133i \(-0.625619\pi\)
\(90\) 0 0
\(91\) −14.5554 + 10.5751i −1.52582 + 1.10857i
\(92\) 0 0
\(93\) 1.58209i 0.164055i
\(94\) 0 0
\(95\) −0.0140432 0.0304871i −0.00144080 0.00312791i
\(96\) 0 0
\(97\) −7.66744 + 2.49130i −0.778511 + 0.252954i −0.671204 0.741272i \(-0.734223\pi\)
−0.107307 + 0.994226i \(0.534223\pi\)
\(98\) 0 0
\(99\) 0.807679 0.0811748
\(100\) 0 0
\(101\) 11.6496 1.15918 0.579590 0.814908i \(-0.303213\pi\)
0.579590 + 0.814908i \(0.303213\pi\)
\(102\) 0 0
\(103\) 17.9216 5.82307i 1.76587 0.573764i 0.768084 0.640349i \(-0.221210\pi\)
0.997781 + 0.0665845i \(0.0212102\pi\)
\(104\) 0 0
\(105\) −7.38910 4.14114i −0.721103 0.404133i
\(106\) 0 0
\(107\) 14.3957i 1.39168i −0.718195 0.695842i \(-0.755031\pi\)
0.718195 0.695842i \(-0.244969\pi\)
\(108\) 0 0
\(109\) −4.66144 + 3.38673i −0.446485 + 0.324390i −0.788206 0.615411i \(-0.788990\pi\)
0.341722 + 0.939801i \(0.388990\pi\)
\(110\) 0 0
\(111\) 6.91045 + 5.02074i 0.655911 + 0.476547i
\(112\) 0 0
\(113\) 10.5368 + 14.5027i 0.991223 + 1.36430i 0.930559 + 0.366143i \(0.119322\pi\)
0.0606641 + 0.998158i \(0.480678\pi\)
\(114\) 0 0
\(115\) 1.64300 + 13.9190i 0.153211 + 1.29795i
\(116\) 0 0
\(117\) 4.51704 + 1.46767i 0.417600 + 0.135687i
\(118\) 0 0
\(119\) 1.34482 4.13892i 0.123279 0.379414i
\(120\) 0 0
\(121\) −3.19760 9.84120i −0.290691 0.894655i
\(122\) 0 0
\(123\) −6.75887 + 9.30279i −0.609427 + 0.838804i
\(124\) 0 0
\(125\) 6.91343 + 8.78661i 0.618356 + 0.785898i
\(126\) 0 0
\(127\) −1.34592 + 1.85250i −0.119431 + 0.164382i −0.864547 0.502553i \(-0.832394\pi\)
0.745116 + 0.666935i \(0.232394\pi\)
\(128\) 0 0
\(129\) −3.16612 9.74432i −0.278762 0.857940i
\(130\) 0 0
\(131\) −2.17840 + 6.70444i −0.190328 + 0.585769i −0.999999 0.00111420i \(-0.999645\pi\)
0.809671 + 0.586883i \(0.199645\pi\)
\(132\) 0 0
\(133\) −0.0540804 0.0175718i −0.00468937 0.00152367i
\(134\) 0 0
\(135\) 0.262127 + 2.22065i 0.0225603 + 0.191123i
\(136\) 0 0
\(137\) 12.8918 + 17.7441i 1.10142 + 1.51598i 0.833484 + 0.552544i \(0.186343\pi\)
0.267940 + 0.963436i \(0.413657\pi\)
\(138\) 0 0
\(139\) 7.86171 + 5.71187i 0.666822 + 0.484474i 0.868960 0.494883i \(-0.164789\pi\)
−0.202138 + 0.979357i \(0.564789\pi\)
\(140\) 0 0
\(141\) 0.425771 0.309341i 0.0358564 0.0260512i
\(142\) 0 0
\(143\) 3.83607i 0.320788i
\(144\) 0 0
\(145\) 7.21907 + 4.04584i 0.599512 + 0.335989i
\(146\) 0 0
\(147\) −6.98985 + 2.27114i −0.576513 + 0.187321i
\(148\) 0 0
\(149\) 13.9712 1.14457 0.572284 0.820056i \(-0.306058\pi\)
0.572284 + 0.820056i \(0.306058\pi\)
\(150\) 0 0
\(151\) −20.1871 −1.64280 −0.821400 0.570352i \(-0.806807\pi\)
−0.821400 + 0.570352i \(0.806807\pi\)
\(152\) 0 0
\(153\) −1.09262 + 0.355012i −0.0883328 + 0.0287011i
\(154\) 0 0
\(155\) −1.48007 3.21317i −0.118882 0.258088i
\(156\) 0 0
\(157\) 7.76546i 0.619751i 0.950777 + 0.309876i \(0.100287\pi\)
−0.950777 + 0.309876i \(0.899713\pi\)
\(158\) 0 0
\(159\) −2.38641 + 1.73383i −0.189255 + 0.137502i
\(160\) 0 0
\(161\) 19.2090 + 13.9561i 1.51388 + 1.09990i
\(162\) 0 0
\(163\) −8.16480 11.2379i −0.639517 0.880219i 0.359073 0.933310i \(-0.383093\pi\)
−0.998590 + 0.0530901i \(0.983093\pi\)
\(164\) 0 0
\(165\) −1.64037 + 0.755596i −0.127702 + 0.0588231i
\(166\) 0 0
\(167\) −2.75604 0.895491i −0.213269 0.0692952i 0.200434 0.979707i \(-0.435765\pi\)
−0.413703 + 0.910412i \(0.635765\pi\)
\(168\) 0 0
\(169\) −2.95350 + 9.08992i −0.227192 + 0.699225i
\(170\) 0 0
\(171\) 0.00463870 + 0.0142765i 0.000354730 + 0.00109175i
\(172\) 0 0
\(173\) −8.95423 + 12.3244i −0.680777 + 0.937009i −0.999943 0.0106895i \(-0.996597\pi\)
0.319166 + 0.947699i \(0.396597\pi\)
\(174\) 0 0
\(175\) 18.8811 + 1.49787i 1.42728 + 0.113228i
\(176\) 0 0
\(177\) 6.72635 9.25803i 0.505583 0.695876i
\(178\) 0 0
\(179\) 7.20182 + 22.1649i 0.538290 + 1.65669i 0.736432 + 0.676512i \(0.236509\pi\)
−0.198142 + 0.980173i \(0.563491\pi\)
\(180\) 0 0
\(181\) 5.46913 16.8322i 0.406517 1.25113i −0.513105 0.858326i \(-0.671505\pi\)
0.919622 0.392805i \(-0.128495\pi\)
\(182\) 0 0
\(183\) −2.98833 0.970968i −0.220904 0.0717760i
\(184\) 0 0
\(185\) −18.7319 3.73209i −1.37719 0.274389i
\(186\) 0 0
\(187\) −0.545404 0.750685i −0.0398839 0.0548955i
\(188\) 0 0
\(189\) 3.06462 + 2.22658i 0.222919 + 0.161960i
\(190\) 0 0
\(191\) −7.57575 + 5.50411i −0.548162 + 0.398263i −0.827107 0.562044i \(-0.810015\pi\)
0.278945 + 0.960307i \(0.410015\pi\)
\(192\) 0 0
\(193\) 18.9309i 1.36268i −0.731969 0.681338i \(-0.761398\pi\)
0.731969 0.681338i \(-0.238602\pi\)
\(194\) 0 0
\(195\) −10.5470 + 1.24497i −0.755284 + 0.0891541i
\(196\) 0 0
\(197\) 7.17436 2.33109i 0.511152 0.166083i −0.0420739 0.999114i \(-0.513397\pi\)
0.553226 + 0.833031i \(0.313397\pi\)
\(198\) 0 0
\(199\) −3.58560 −0.254176 −0.127088 0.991891i \(-0.540563\pi\)
−0.127088 + 0.991891i \(0.540563\pi\)
\(200\) 0 0
\(201\) 13.2812 0.936783
\(202\) 0 0
\(203\) 13.3332 4.33223i 0.935808 0.304063i
\(204\) 0 0
\(205\) 5.02411 25.2166i 0.350899 1.76121i
\(206\) 0 0
\(207\) 6.26797i 0.435654i
\(208\) 0 0
\(209\) −0.00980868 + 0.00712642i −0.000678480 + 0.000492945i
\(210\) 0 0
\(211\) −1.68674 1.22549i −0.116120 0.0843663i 0.528210 0.849114i \(-0.322864\pi\)
−0.644330 + 0.764748i \(0.722864\pi\)
\(212\) 0 0
\(213\) −2.88790 3.97485i −0.197875 0.272352i
\(214\) 0 0
\(215\) 15.5462 + 16.8284i 1.06025 + 1.14769i
\(216\) 0 0
\(217\) −5.69977 1.85197i −0.386926 0.125720i
\(218\) 0 0
\(219\) 1.44577 4.44962i 0.0976960 0.300677i
\(220\) 0 0
\(221\) −1.68613 5.18938i −0.113421 0.349075i
\(222\) 0 0
\(223\) −8.25091 + 11.3564i −0.552522 + 0.760481i −0.990352 0.138577i \(-0.955747\pi\)
0.437830 + 0.899058i \(0.355747\pi\)
\(224\) 0 0
\(225\) −2.60982 4.26484i −0.173988 0.284322i
\(226\) 0 0
\(227\) −1.48995 + 2.05074i −0.0988915 + 0.136112i −0.855595 0.517646i \(-0.826809\pi\)
0.756704 + 0.653758i \(0.226809\pi\)
\(228\) 0 0
\(229\) 5.10687 + 15.7173i 0.337472 + 1.03863i 0.965492 + 0.260434i \(0.0838656\pi\)
−0.628020 + 0.778197i \(0.716134\pi\)
\(230\) 0 0
\(231\) −0.945454 + 2.90981i −0.0622063 + 0.191451i
\(232\) 0 0
\(233\) −25.2228 8.19539i −1.65240 0.536898i −0.673143 0.739512i \(-0.735056\pi\)
−0.979259 + 0.202614i \(0.935056\pi\)
\(234\) 0 0
\(235\) −0.575332 + 1.02658i −0.0375305 + 0.0669664i
\(236\) 0 0
\(237\) −5.44968 7.50084i −0.353995 0.487232i
\(238\) 0 0
\(239\) −6.03839 4.38714i −0.390591 0.283781i 0.375107 0.926982i \(-0.377606\pi\)
−0.765698 + 0.643201i \(0.777606\pi\)
\(240\) 0 0
\(241\) −8.33107 + 6.05288i −0.536651 + 0.389900i −0.822840 0.568273i \(-0.807612\pi\)
0.286189 + 0.958173i \(0.407612\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 12.0714 11.1517i 0.771216 0.712458i
\(246\) 0 0
\(247\) −0.0678060 + 0.0220315i −0.00431439 + 0.00140183i
\(248\) 0 0
\(249\) −1.42370 −0.0902231
\(250\) 0 0
\(251\) 19.5809 1.23593 0.617967 0.786204i \(-0.287956\pi\)
0.617967 + 0.786204i \(0.287956\pi\)
\(252\) 0 0
\(253\) 4.81473 1.56440i 0.302699 0.0983530i
\(254\) 0 0
\(255\) 1.88694 1.74318i 0.118165 0.109162i
\(256\) 0 0
\(257\) 5.98030i 0.373041i −0.982451 0.186520i \(-0.940279\pi\)
0.982451 0.186520i \(-0.0597210\pi\)
\(258\) 0 0
\(259\) −26.1774 + 19.0190i −1.62658 + 1.18178i
\(260\) 0 0
\(261\) −2.99410 2.17534i −0.185330 0.134650i
\(262\) 0 0
\(263\) 3.56808 + 4.91104i 0.220017 + 0.302827i 0.904730 0.425985i \(-0.140072\pi\)
−0.684713 + 0.728813i \(0.740072\pi\)
\(264\) 0 0
\(265\) 3.22469 5.75386i 0.198091 0.353457i
\(266\) 0 0
\(267\) −15.3184 4.97725i −0.937472 0.304603i
\(268\) 0 0
\(269\) −2.97152 + 9.14540i −0.181177 + 0.557605i −0.999862 0.0166382i \(-0.994704\pi\)
0.818685 + 0.574243i \(0.194704\pi\)
\(270\) 0 0
\(271\) −9.40263 28.9383i −0.571169 1.75788i −0.648868 0.760901i \(-0.724757\pi\)
0.0776990 0.996977i \(-0.475243\pi\)
\(272\) 0 0
\(273\) −10.5751 + 14.5554i −0.640036 + 0.880934i
\(274\) 0 0
\(275\) 2.62465 3.06918i 0.158272 0.185078i
\(276\) 0 0
\(277\) −4.23436 + 5.82810i −0.254418 + 0.350176i −0.917052 0.398767i \(-0.869438\pi\)
0.662634 + 0.748943i \(0.269438\pi\)
\(278\) 0 0
\(279\) 0.488893 + 1.50466i 0.0292693 + 0.0900815i
\(280\) 0 0
\(281\) 9.20758 28.3380i 0.549278 1.69050i −0.161316 0.986903i \(-0.551574\pi\)
0.710594 0.703602i \(-0.248426\pi\)
\(282\) 0 0
\(283\) −8.39215 2.72677i −0.498861 0.162090i 0.0487693 0.998810i \(-0.484470\pi\)
−0.547631 + 0.836720i \(0.684470\pi\)
\(284\) 0 0
\(285\) −0.0227769 0.0246554i −0.00134919 0.00146046i
\(286\) 0 0
\(287\) −25.6032 35.2397i −1.51131 2.08014i
\(288\) 0 0
\(289\) −12.6855 9.21656i −0.746207 0.542151i
\(290\) 0 0
\(291\) −6.52232 + 4.73874i −0.382345 + 0.277790i
\(292\) 0 0
\(293\) 4.20743i 0.245800i 0.992419 + 0.122900i \(0.0392195\pi\)
−0.992419 + 0.122900i \(0.960780\pi\)
\(294\) 0 0
\(295\) −4.99993 + 25.0953i −0.291107 + 1.46111i
\(296\) 0 0
\(297\) 0.768148 0.249586i 0.0445725 0.0144825i
\(298\) 0 0
\(299\) 29.7697 1.72163
\(300\) 0 0
\(301\) 38.8119 2.23708
\(302\) 0 0
\(303\) 11.0794 3.59993i 0.636497 0.206811i
\(304\) 0 0
\(305\) 6.97755 0.823633i 0.399533 0.0471611i
\(306\) 0 0
\(307\) 4.41109i 0.251754i 0.992046 + 0.125877i \(0.0401745\pi\)
−0.992046 + 0.125877i \(0.959825\pi\)
\(308\) 0 0
\(309\) 15.2450 11.0761i 0.867258 0.630100i
\(310\) 0 0
\(311\) 5.11346 + 3.71514i 0.289958 + 0.210667i 0.723249 0.690587i \(-0.242648\pi\)
−0.433291 + 0.901254i \(0.642648\pi\)
\(312\) 0 0
\(313\) −9.00753 12.3978i −0.509136 0.700765i 0.474638 0.880181i \(-0.342579\pi\)
−0.983773 + 0.179416i \(0.942579\pi\)
\(314\) 0 0
\(315\) −8.30714 1.65510i −0.468054 0.0932541i
\(316\) 0 0
\(317\) −20.2723 6.58686i −1.13860 0.369955i −0.321765 0.946820i \(-0.604276\pi\)
−0.816840 + 0.576864i \(0.804276\pi\)
\(318\) 0 0
\(319\) 0.923699 2.84285i 0.0517172 0.159169i
\(320\) 0 0
\(321\) −4.44851 13.6911i −0.248292 0.764164i
\(322\) 0 0
\(323\) 0.0101366 0.0139519i 0.000564018 0.000776304i
\(324\) 0 0
\(325\) 20.2558 12.3953i 1.12359 0.687570i
\(326\) 0 0
\(327\) −3.38673 + 4.66144i −0.187287 + 0.257778i
\(328\) 0 0
\(329\) 0.616057 + 1.89603i 0.0339643 + 0.104531i
\(330\) 0 0
\(331\) 6.12237 18.8427i 0.336516 1.03569i −0.629454 0.777037i \(-0.716722\pi\)
0.965970 0.258652i \(-0.0832785\pi\)
\(332\) 0 0
\(333\) 8.12372 + 2.63956i 0.445177 + 0.144647i
\(334\) 0 0
\(335\) −26.9736 + 12.4248i −1.47373 + 0.678838i
\(336\) 0 0
\(337\) 5.89780 + 8.11762i 0.321274 + 0.442195i 0.938856 0.344311i \(-0.111888\pi\)
−0.617582 + 0.786507i \(0.711888\pi\)
\(338\) 0 0
\(339\) 14.5027 + 10.5368i 0.787680 + 0.572283i
\(340\) 0 0
\(341\) −1.03378 + 0.751085i −0.0559823 + 0.0406735i
\(342\) 0 0
\(343\) 1.32419i 0.0714997i
\(344\) 0 0
\(345\) 5.86378 + 12.7300i 0.315695 + 0.685361i
\(346\) 0 0
\(347\) −13.1885 + 4.28519i −0.707994 + 0.230041i −0.640810 0.767700i \(-0.721401\pi\)
−0.0671837 + 0.997741i \(0.521401\pi\)
\(348\) 0 0
\(349\) −27.2533 −1.45883 −0.729417 0.684069i \(-0.760209\pi\)
−0.729417 + 0.684069i \(0.760209\pi\)
\(350\) 0 0
\(351\) 4.74950 0.253509
\(352\) 0 0
\(353\) −11.8063 + 3.83609i −0.628384 + 0.204174i −0.605859 0.795572i \(-0.707170\pi\)
−0.0225248 + 0.999746i \(0.507170\pi\)
\(354\) 0 0
\(355\) 9.58374 + 5.37110i 0.508652 + 0.285068i
\(356\) 0 0
\(357\) 4.35192i 0.230328i
\(358\) 0 0
\(359\) −15.3910 + 11.1823i −0.812308 + 0.590177i −0.914499 0.404588i \(-0.867415\pi\)
0.102191 + 0.994765i \(0.467415\pi\)
\(360\) 0 0
\(361\) 15.3711 + 11.1678i 0.809007 + 0.587778i
\(362\) 0 0
\(363\) −6.08220 8.37143i −0.319233 0.439386i
\(364\) 0 0
\(365\) 1.22639 + 10.3895i 0.0641920 + 0.543814i
\(366\) 0 0
\(367\) 0.927465 + 0.301352i 0.0484133 + 0.0157304i 0.333124 0.942883i \(-0.391897\pi\)
−0.284710 + 0.958614i \(0.591897\pi\)
\(368\) 0 0
\(369\) −3.55335 + 10.9361i −0.184980 + 0.569310i
\(370\) 0 0
\(371\) −3.45294 10.6271i −0.179268 0.551729i
\(372\) 0 0
\(373\) −11.0341 + 15.1871i −0.571324 + 0.786360i −0.992711 0.120521i \(-0.961543\pi\)
0.421387 + 0.906881i \(0.361543\pi\)
\(374\) 0 0
\(375\) 9.29028 + 6.22019i 0.479748 + 0.321209i
\(376\) 0 0
\(377\) 10.3318 14.2205i 0.532114 0.732392i
\(378\) 0 0
\(379\) 1.06536 + 3.27883i 0.0547236 + 0.168422i 0.974683 0.223592i \(-0.0717784\pi\)
−0.919959 + 0.392014i \(0.871778\pi\)
\(380\) 0 0
\(381\) −0.707591 + 2.17774i −0.0362510 + 0.111569i
\(382\) 0 0
\(383\) −25.9681 8.43755i −1.32691 0.431139i −0.442046 0.896992i \(-0.645747\pi\)
−0.884862 + 0.465854i \(0.845747\pi\)
\(384\) 0 0
\(385\) −0.801990 6.79420i −0.0408732 0.346264i
\(386\) 0 0
\(387\) −6.02232 8.28902i −0.306132 0.421354i
\(388\) 0 0
\(389\) 7.94232 + 5.77044i 0.402692 + 0.292573i 0.770637 0.637275i \(-0.219938\pi\)
−0.367945 + 0.929848i \(0.619938\pi\)
\(390\) 0 0
\(391\) −5.82567 + 4.23259i −0.294617 + 0.214051i
\(392\) 0 0
\(393\) 7.04946i 0.355598i
\(394\) 0 0
\(395\) 18.0853 + 10.1357i 0.909968 + 0.509981i
\(396\) 0 0
\(397\) 11.0447 3.58865i 0.554319 0.180109i −0.0184443 0.999830i \(-0.505871\pi\)
0.572763 + 0.819721i \(0.305871\pi\)
\(398\) 0 0
\(399\) −0.0568635 −0.00284674
\(400\) 0 0
\(401\) −25.4145 −1.26914 −0.634570 0.772865i \(-0.718823\pi\)
−0.634570 + 0.772865i \(0.718823\pi\)
\(402\) 0 0
\(403\) −7.14637 + 2.32200i −0.355986 + 0.115667i
\(404\) 0 0
\(405\) 0.935516 + 2.03096i 0.0464862 + 0.100919i
\(406\) 0 0
\(407\) 6.89902i 0.341972i
\(408\) 0 0
\(409\) 13.9568 10.1402i 0.690117 0.501399i −0.186582 0.982439i \(-0.559741\pi\)
0.876699 + 0.481040i \(0.159741\pi\)
\(410\) 0 0
\(411\) 17.7441 + 12.8918i 0.875251 + 0.635907i
\(412\) 0 0
\(413\) 25.4800 + 35.0702i 1.25379 + 1.72569i
\(414\) 0 0
\(415\) 2.89148 1.33189i 0.141937 0.0653800i
\(416\) 0 0
\(417\) 9.24200 + 3.00291i 0.452583 + 0.147053i
\(418\) 0 0
\(419\) 6.31956 19.4496i 0.308731 0.950176i −0.669528 0.742787i \(-0.733503\pi\)
0.978259 0.207389i \(-0.0664965\pi\)
\(420\) 0 0
\(421\) −6.46100 19.8849i −0.314890 0.969132i −0.975800 0.218666i \(-0.929829\pi\)
0.660910 0.750466i \(-0.270171\pi\)
\(422\) 0 0
\(423\) 0.309341 0.425771i 0.0150407 0.0207017i
\(424\) 0 0
\(425\) −2.20154 + 5.30559i −0.106790 + 0.257359i
\(426\) 0 0
\(427\) 6.99618 9.62941i 0.338569 0.466000i
\(428\) 0 0
\(429\) 1.18541 + 3.64832i 0.0572321 + 0.176142i
\(430\) 0 0
\(431\) −2.85900 + 8.79908i −0.137713 + 0.423837i −0.996002 0.0893294i \(-0.971528\pi\)
0.858289 + 0.513166i \(0.171528\pi\)
\(432\) 0 0
\(433\) 0.223727 + 0.0726932i 0.0107516 + 0.00349341i 0.314388 0.949295i \(-0.398201\pi\)
−0.303636 + 0.952788i \(0.598201\pi\)
\(434\) 0 0
\(435\) 8.11598 + 1.61701i 0.389132 + 0.0775297i
\(436\) 0 0
\(437\) 0.0553044 + 0.0761199i 0.00264557 + 0.00364131i
\(438\) 0 0
\(439\) 25.2424 + 18.3396i 1.20475 + 0.875304i 0.994744 0.102396i \(-0.0326509\pi\)
0.210008 + 0.977700i \(0.432651\pi\)
\(440\) 0 0
\(441\) −5.94593 + 4.31997i −0.283139 + 0.205713i
\(442\) 0 0
\(443\) 24.3862i 1.15862i −0.815106 0.579311i \(-0.803322\pi\)
0.815106 0.579311i \(-0.196678\pi\)
\(444\) 0 0
\(445\) 35.7674 4.22200i 1.69554 0.200142i
\(446\) 0 0
\(447\) 13.2874 4.31735i 0.628474 0.204203i
\(448\) 0 0
\(449\) −23.9483 −1.13019 −0.565096 0.825025i \(-0.691161\pi\)
−0.565096 + 0.825025i \(0.691161\pi\)
\(450\) 0 0
\(451\) −9.28740 −0.437327
\(452\) 0 0
\(453\) −19.1990 + 6.23815i −0.902050 + 0.293094i
\(454\) 0 0
\(455\) 7.86087 39.4547i 0.368523 1.84967i
\(456\) 0 0
\(457\) 3.91244i 0.183016i 0.995804 + 0.0915082i \(0.0291688\pi\)
−0.995804 + 0.0915082i \(0.970831\pi\)
\(458\) 0 0
\(459\) −0.929435 + 0.675274i −0.0433823 + 0.0315191i
\(460\) 0 0
\(461\) 2.09170 + 1.51971i 0.0974202 + 0.0707799i 0.635429 0.772159i \(-0.280823\pi\)
−0.538009 + 0.842939i \(0.680823\pi\)
\(462\) 0 0
\(463\) 12.8777 + 17.7247i 0.598478 + 0.823734i 0.995568 0.0940453i \(-0.0299799\pi\)
−0.397090 + 0.917780i \(0.629980\pi\)
\(464\) 0 0
\(465\) −2.40056 2.59854i −0.111323 0.120504i
\(466\) 0 0
\(467\) 7.79561 + 2.53295i 0.360738 + 0.117211i 0.483778 0.875191i \(-0.339264\pi\)
−0.123040 + 0.992402i \(0.539264\pi\)
\(468\) 0 0
\(469\) −15.5467 + 47.8479i −0.717881 + 2.20941i
\(470\) 0 0
\(471\) 2.39966 + 7.38539i 0.110570 + 0.340301i
\(472\) 0 0
\(473\) 4.86410 6.69486i 0.223652 0.307830i
\(474\) 0 0
\(475\) 0.0693245 + 0.0287660i 0.00318083 + 0.00131987i
\(476\) 0 0
\(477\) −1.73383 + 2.38641i −0.0793865 + 0.109266i
\(478\) 0 0
\(479\) 1.90100 + 5.85067i 0.0868588 + 0.267324i 0.985047 0.172288i \(-0.0551160\pi\)
−0.898188 + 0.439612i \(0.855116\pi\)
\(480\) 0 0
\(481\) −12.5366 + 38.5836i −0.571618 + 1.75926i
\(482\) 0 0
\(483\) 22.5815 + 7.33717i 1.02749 + 0.333853i
\(484\) 0 0
\(485\) 8.81342 15.7259i 0.400197 0.714078i
\(486\) 0 0
\(487\) −3.69230 5.08201i −0.167314 0.230288i 0.717124 0.696945i \(-0.245458\pi\)
−0.884438 + 0.466658i \(0.845458\pi\)
\(488\) 0 0
\(489\) −11.2379 8.16480i −0.508195 0.369225i
\(490\) 0 0
\(491\) 2.22591 1.61722i 0.100454 0.0729840i −0.536424 0.843948i \(-0.680225\pi\)
0.636878 + 0.770964i \(0.280225\pi\)
\(492\) 0 0
\(493\) 4.25178i 0.191490i
\(494\) 0 0
\(495\) −1.32659 + 1.22552i −0.0596257 + 0.0550828i
\(496\) 0 0
\(497\) 17.7006 5.75128i 0.793982 0.257980i
\(498\) 0 0
\(499\) 16.4263 0.735341 0.367670 0.929956i \(-0.380156\pi\)
0.367670 + 0.929956i \(0.380156\pi\)
\(500\) 0 0
\(501\) −2.89787 −0.129467
\(502\) 0 0
\(503\) −11.6860 + 3.79701i −0.521053 + 0.169300i −0.557723 0.830027i \(-0.688325\pi\)
0.0366701 + 0.999327i \(0.488325\pi\)
\(504\) 0 0
\(505\) −19.1341 + 17.6763i −0.851458 + 0.786586i
\(506\) 0 0
\(507\) 9.55771i 0.424473i
\(508\) 0 0
\(509\) −8.50277 + 6.17763i −0.376879 + 0.273818i −0.760058 0.649856i \(-0.774829\pi\)
0.383179 + 0.923674i \(0.374829\pi\)
\(510\) 0 0
\(511\) 14.3382 + 10.4173i 0.634283 + 0.460833i
\(512\) 0 0
\(513\) 0.00882334 + 0.0121443i 0.000389560 + 0.000536183i
\(514\) 0 0
\(515\) −20.6001 + 36.7572i −0.907750 + 1.61971i
\(516\) 0 0
\(517\) 0.404263 + 0.131353i 0.0177795 + 0.00577690i
\(518\) 0 0
\(519\) −4.70752 + 14.4882i −0.206637 + 0.635963i
\(520\) 0 0
\(521\) −2.41778 7.44115i −0.105925 0.326003i 0.884022 0.467446i \(-0.154826\pi\)
−0.989946 + 0.141443i \(0.954826\pi\)
\(522\) 0 0
\(523\) −12.9592 + 17.8368i −0.566665 + 0.779947i −0.992155 0.125016i \(-0.960102\pi\)
0.425490 + 0.904963i \(0.360102\pi\)
\(524\) 0 0
\(525\) 18.4199 4.41002i 0.803908 0.192469i
\(526\) 0 0
\(527\) 1.06834 1.47045i 0.0465378 0.0640538i
\(528\) 0 0
\(529\) −5.03308 15.4902i −0.218830 0.673489i
\(530\) 0 0
\(531\) 3.53625 10.8835i 0.153460 0.472302i
\(532\) 0 0
\(533\) −51.9409 16.8766i −2.24981 0.731007i
\(534\) 0 0
\(535\) 21.8430 + 23.6445i 0.944357 + 1.02224i
\(536\) 0 0
\(537\) 13.6987 + 18.8546i 0.591142 + 0.813637i
\(538\) 0 0
\(539\) −4.80240 3.48915i −0.206854 0.150288i
\(540\) 0 0
\(541\) −10.0860 + 7.32791i −0.433631 + 0.315052i −0.783099 0.621897i \(-0.786362\pi\)
0.349468 + 0.936948i \(0.386362\pi\)
\(542\) 0 0
\(543\) 17.6985i 0.759514i
\(544\) 0 0
\(545\) 2.51748 12.6356i 0.107837 0.541248i
\(546\) 0 0
\(547\) −2.39292 + 0.777505i −0.102314 + 0.0332437i −0.359726 0.933058i \(-0.617130\pi\)
0.257413 + 0.966302i \(0.417130\pi\)
\(548\) 0 0
\(549\) −3.14212 −0.134102
\(550\) 0 0
\(551\) 0.0555550 0.00236672
\(552\) 0 0
\(553\) 33.4024 10.8531i 1.42042 0.461521i
\(554\) 0 0
\(555\) −18.9683 + 2.23903i −0.805161 + 0.0950415i
\(556\) 0 0
\(557\) 0.262544i 0.0111244i −0.999985 0.00556218i \(-0.998229\pi\)
0.999985 0.00556218i \(-0.00177051\pi\)
\(558\) 0 0
\(559\) 39.3687 28.6030i 1.66512 1.20978i
\(560\) 0 0
\(561\) −0.750685 0.545404i −0.0316939 0.0230270i
\(562\) 0 0
\(563\) 19.0928 + 26.2790i 0.804666 + 1.10753i 0.992125 + 0.125255i \(0.0399748\pi\)
−0.187459 + 0.982272i \(0.560025\pi\)
\(564\) 0 0
\(565\) −39.3119 7.83241i −1.65386 0.329512i
\(566\) 0 0
\(567\) 3.60268 + 1.17058i 0.151298 + 0.0491598i
\(568\) 0 0
\(569\) 11.9892 36.8991i 0.502615 1.54689i −0.302128 0.953267i \(-0.597697\pi\)
0.804743 0.593623i \(-0.202303\pi\)
\(570\) 0 0
\(571\) −11.0258 33.9338i −0.461414 1.42009i −0.863437 0.504456i \(-0.831693\pi\)
0.402023 0.915629i \(-0.368307\pi\)
\(572\) 0 0
\(573\) −5.50411 + 7.57575i −0.229937 + 0.316482i
\(574\) 0 0
\(575\) −23.8182 20.3685i −0.993290 0.849425i
\(576\) 0 0
\(577\) −14.8962 + 20.5029i −0.620139 + 0.853548i −0.997363 0.0725741i \(-0.976879\pi\)
0.377224 + 0.926122i \(0.376879\pi\)
\(578\) 0 0
\(579\) −5.84997 18.0044i −0.243116 0.748236i
\(580\) 0 0
\(581\) 1.66655 5.12913i 0.0691403 0.212792i
\(582\) 0 0
\(583\) −2.26586 0.736221i −0.0938422 0.0304912i
\(584\) 0 0
\(585\) −9.64605 + 4.44323i −0.398815 + 0.183705i
\(586\) 0 0
\(587\) −0.303103 0.417186i −0.0125104 0.0172191i 0.802716 0.596362i \(-0.203388\pi\)
−0.815226 + 0.579142i \(0.803388\pi\)
\(588\) 0 0
\(589\) −0.0192134 0.0139593i −0.000791673 0.000575184i
\(590\) 0 0
\(591\) 6.10288 4.43400i 0.251039 0.182390i
\(592\) 0 0
\(593\) 7.14389i 0.293364i −0.989184 0.146682i \(-0.953141\pi\)
0.989184 0.146682i \(-0.0468595\pi\)
\(594\) 0 0
\(595\) 4.07129 + 8.83858i 0.166907 + 0.362347i
\(596\) 0 0
\(597\) −3.41011 + 1.10801i −0.139566 + 0.0453479i
\(598\) 0 0
\(599\) −23.6627 −0.966833 −0.483417 0.875390i \(-0.660604\pi\)
−0.483417 + 0.875390i \(0.660604\pi\)
\(600\) 0 0
\(601\) −7.98023 −0.325520 −0.162760 0.986666i \(-0.552040\pi\)
−0.162760 + 0.986666i \(0.552040\pi\)
\(602\) 0 0
\(603\) 12.6312 4.10412i 0.514381 0.167133i
\(604\) 0 0
\(605\) 20.1843 + 11.3121i 0.820610 + 0.459901i
\(606\) 0 0
\(607\) 17.2004i 0.698144i −0.937096 0.349072i \(-0.886497\pi\)
0.937096 0.349072i \(-0.113503\pi\)
\(608\) 0 0
\(609\) 11.3419 8.24038i 0.459597 0.333917i
\(610\) 0 0
\(611\) 2.02220 + 1.46921i 0.0818094 + 0.0594380i
\(612\) 0 0
\(613\) 8.67810 + 11.9444i 0.350505 + 0.482429i 0.947473 0.319836i \(-0.103628\pi\)
−0.596968 + 0.802265i \(0.703628\pi\)
\(614\) 0 0
\(615\) −3.01416 25.5350i −0.121543 1.02967i
\(616\) 0 0
\(617\) 14.7142 + 4.78092i 0.592370 + 0.192473i 0.589834 0.807524i \(-0.299193\pi\)
0.00253529 + 0.999997i \(0.499193\pi\)
\(618\) 0 0
\(619\) 11.5792 35.6370i 0.465406 1.43237i −0.393066 0.919510i \(-0.628586\pi\)
0.858471 0.512861i \(-0.171414\pi\)
\(620\) 0 0
\(621\) −1.93691 5.96119i −0.0777254 0.239214i
\(622\) 0 0
\(623\) 35.8629 49.3611i 1.43682 1.97761i
\(624\) 0 0
\(625\) −24.6873 3.94177i −0.987492 0.157671i
\(626\) 0 0
\(627\) −0.00712642 + 0.00980868i −0.000284602 + 0.000391721i
\(628\) 0 0
\(629\) −3.03244 9.33290i −0.120911 0.372127i
\(630\) 0 0
\(631\) −0.468691 + 1.44248i −0.0186583 + 0.0574244i −0.959952 0.280164i \(-0.909611\pi\)
0.941294 + 0.337588i \(0.109611\pi\)
\(632\) 0 0
\(633\) −1.98289 0.644279i −0.0788126 0.0256078i
\(634\) 0 0
\(635\) −0.600220 5.08487i −0.0238190 0.201787i
\(636\) 0 0
\(637\) −20.5177 28.2401i −0.812940 1.11892i
\(638\) 0 0
\(639\) −3.97485 2.88790i −0.157243 0.114243i
\(640\) 0 0
\(641\) 3.12903 2.27338i 0.123589 0.0897930i −0.524273 0.851550i \(-0.675663\pi\)
0.647863 + 0.761757i \(0.275663\pi\)
\(642\) 0 0
\(643\) 23.2212i 0.915756i −0.889015 0.457878i \(-0.848610\pi\)
0.889015 0.457878i \(-0.151390\pi\)
\(644\) 0 0
\(645\) 19.9856 + 11.2007i 0.786933 + 0.441027i
\(646\) 0 0
\(647\) −24.8795 + 8.08384i −0.978114 + 0.317808i −0.754087 0.656775i \(-0.771920\pi\)
−0.224027 + 0.974583i \(0.571920\pi\)
\(648\) 0 0
\(649\) 9.24271 0.362808
\(650\) 0 0
\(651\) −5.99309 −0.234888
\(652\) 0 0
\(653\) −8.13602 + 2.64355i −0.318387 + 0.103450i −0.463851 0.885913i \(-0.653533\pi\)
0.145464 + 0.989364i \(0.453533\pi\)
\(654\) 0 0
\(655\) −6.59488 14.3172i −0.257683 0.559419i
\(656\) 0 0
\(657\) 4.67860i 0.182530i
\(658\) 0 0
\(659\) −33.9288 + 24.6507i −1.32168 + 0.960255i −0.321767 + 0.946819i \(0.604277\pi\)
−0.999910 + 0.0134358i \(0.995723\pi\)
\(660\) 0 0
\(661\) 14.1713 + 10.2961i 0.551201 + 0.400471i 0.828228 0.560391i \(-0.189349\pi\)
−0.277027 + 0.960862i \(0.589349\pi\)
\(662\) 0 0
\(663\) −3.20721 4.41435i −0.124558 0.171439i
\(664\) 0 0
\(665\) 0.115488 0.0531967i 0.00447842 0.00206288i
\(666\) 0 0
\(667\) −22.0619 7.16833i −0.854239 0.277559i
\(668\) 0 0
\(669\) −4.33776 + 13.3503i −0.167708 + 0.516151i
\(670\) 0 0
\(671\) −0.784230 2.41361i −0.0302749 0.0931765i
\(672\) 0 0
\(673\) 17.1017 23.5385i 0.659223 0.907343i −0.340232 0.940341i \(-0.610506\pi\)
0.999455 + 0.0329986i \(0.0105057\pi\)
\(674\) 0 0
\(675\) −3.80000 3.24962i −0.146262 0.125078i
\(676\) 0 0
\(677\) −17.5667 + 24.1785i −0.675143 + 0.929255i −0.999863 0.0165555i \(-0.994730\pi\)
0.324720 + 0.945810i \(0.394730\pi\)
\(678\) 0 0
\(679\) −9.43726 29.0449i −0.362169 1.11464i
\(680\) 0 0
\(681\) −0.783313 + 2.41079i −0.0300166 + 0.0923817i
\(682\) 0 0
\(683\) 35.3984 + 11.5016i 1.35448 + 0.440097i 0.894197 0.447674i \(-0.147748\pi\)
0.460284 + 0.887772i \(0.347748\pi\)
\(684\) 0 0
\(685\) −48.0981 9.58296i −1.83773 0.366146i
\(686\) 0 0
\(687\) 9.71385 + 13.3700i 0.370607 + 0.510096i
\(688\) 0 0
\(689\) −11.3342 8.23481i −0.431800 0.313721i
\(690\) 0 0
\(691\) −13.6397 + 9.90980i −0.518877 + 0.376986i −0.816181 0.577797i \(-0.803913\pi\)
0.297303 + 0.954783i \(0.403913\pi\)
\(692\) 0 0
\(693\) 3.05955i 0.116223i
\(694\) 0 0
\(695\) −21.5794 + 2.54724i −0.818554 + 0.0966225i
\(696\) 0 0
\(697\) 12.5639 4.08225i 0.475890 0.154626i
\(698\) 0 0
\(699\) −26.5208 −1.00311
\(700\) 0 0
\(701\) −23.3495 −0.881898 −0.440949 0.897532i \(-0.645358\pi\)
−0.440949 + 0.897532i \(0.645358\pi\)
\(702\) 0 0
\(703\) −0.121947 + 0.0396228i −0.00459930 + 0.00149440i
\(704\) 0 0
\(705\) −0.229944 + 1.15412i −0.00866020 + 0.0434666i
\(706\) 0 0
\(707\) 44.1297i 1.65967i
\(708\) 0 0
\(709\) 15.4019 11.1901i 0.578429 0.420253i −0.259728 0.965682i \(-0.583633\pi\)
0.838157 + 0.545428i \(0.183633\pi\)
\(710\) 0 0
\(711\) −7.50084 5.44968i −0.281303 0.204379i
\(712\) 0 0
\(713\) 5.82877 + 8.02261i 0.218289 + 0.300449i
\(714\) 0 0
\(715\) −5.82058 6.30063i −0.217677 0.235630i
\(716\) 0 0
\(717\) −7.09855 2.30646i −0.265100 0.0861363i
\(718\) 0 0
\(719\) 4.55488 14.0185i 0.169868 0.522801i −0.829494 0.558516i \(-0.811371\pi\)
0.999362 + 0.0357149i \(0.0113708\pi\)
\(720\) 0 0
\(721\) 22.0583 + 67.8884i 0.821493 + 2.52830i
\(722\) 0 0
\(723\) −6.05288 + 8.33107i −0.225109 + 0.309836i
\(724\) 0 0
\(725\) −17.9960 + 4.30854i −0.668355 + 0.160015i
\(726\) 0 0
\(727\) 17.6698 24.3204i 0.655336 0.901993i −0.343979 0.938977i \(-0.611775\pi\)
0.999316 + 0.0369839i \(0.0117750\pi\)
\(728\) 0 0
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) 0 0
\(731\) −3.63738 + 11.1947i −0.134533 + 0.414051i
\(732\) 0 0
\(733\) 21.5355 + 6.99732i 0.795433 + 0.258452i 0.678416 0.734678i \(-0.262667\pi\)
0.117017 + 0.993130i \(0.462667\pi\)
\(734\) 0 0
\(735\) 8.03455 14.3362i 0.296359 0.528799i
\(736\) 0 0
\(737\) 6.30514 + 8.67828i 0.232253 + 0.319668i
\(738\) 0 0
\(739\) −20.7764 15.0949i −0.764272 0.555276i 0.135946 0.990716i \(-0.456593\pi\)
−0.900218 + 0.435440i \(0.856593\pi\)
\(740\) 0 0
\(741\) −0.0576792 + 0.0419064i −0.00211890 + 0.00153947i
\(742\) 0 0
\(743\) 24.9796i 0.916411i 0.888846 + 0.458205i \(0.151508\pi\)
−0.888846 + 0.458205i \(0.848492\pi\)
\(744\) 0 0
\(745\) −22.9473 + 21.1990i −0.840725 + 0.776670i
\(746\) 0 0
\(747\) −1.35402 + 0.439947i −0.0495409 + 0.0160968i
\(748\) 0 0
\(749\) 54.5321 1.99256
\(750\) 0 0
\(751\) 17.9383 0.654580 0.327290 0.944924i \(-0.393865\pi\)
0.327290 + 0.944924i \(0.393865\pi\)
\(752\) 0 0
\(753\) 18.6225 6.05083i 0.678643 0.220504i
\(754\) 0 0
\(755\) 33.1567 30.6305i 1.20669 1.11476i
\(756\) 0 0
\(757\) 9.91474i 0.360357i −0.983634 0.180179i \(-0.942332\pi\)
0.983634 0.180179i \(-0.0576676\pi\)
\(758\) 0 0
\(759\) 4.09565 2.97566i 0.148663 0.108010i
\(760\) 0 0
\(761\) 25.6076 + 18.6050i 0.928273 + 0.674430i 0.945569 0.325420i \(-0.105506\pi\)
−0.0172961 + 0.999850i \(0.505506\pi\)
\(762\) 0 0
\(763\) −12.8292 17.6579i −0.464449 0.639259i
\(764\) 0 0
\(765\) 1.25592 2.24096i 0.0454078 0.0810220i
\(766\) 0 0
\(767\) 51.6910 + 16.7954i 1.86645 + 0.606447i
\(768\) 0 0
\(769\) −6.91430 + 21.2800i −0.249336 + 0.767377i 0.745557 + 0.666442i \(0.232184\pi\)
−0.994893 + 0.100935i \(0.967816\pi\)
\(770\) 0 0
\(771\) −1.84801 5.68760i −0.0665546 0.204834i
\(772\) 0 0
\(773\) 28.1148 38.6967i 1.01122 1.39182i 0.0930367 0.995663i \(-0.470343\pi\)
0.918182 0.396160i \(-0.129657\pi\)
\(774\) 0 0
\(775\) 7.30641 + 3.03178i 0.262454 + 0.108905i
\(776\) 0 0
\(777\) −19.0190 + 26.1774i −0.682302 + 0.939108i
\(778\) 0 0
\(779\) −0.0533399 0.164163i −0.00191110 0.00588176i
\(780\) 0 0
\(781\) 1.22626 3.77405i 0.0438792 0.135046i
\(782\) 0 0
\(783\) −3.51978 1.14365i −0.125787 0.0408706i
\(784\) 0 0
\(785\) −11.7828 12.7545i −0.420545 0.455229i
\(786\) 0 0
\(787\) 16.2038 + 22.3026i 0.577603 + 0.795002i 0.993430 0.114442i \(-0.0365079\pi\)
−0.415827 + 0.909444i \(0.636508\pi\)
\(788\) 0 0
\(789\) 4.91104 + 3.56808i 0.174838 + 0.127027i
\(790\) 0 0
\(791\) −54.9375 + 39.9144i −1.95335 + 1.41919i
\(792\) 0 0
\(793\) 14.9235i 0.529948i
\(794\) 0 0
\(795\) 1.28882 6.46873i 0.0457096 0.229422i
\(796\) 0 0
\(797\) 21.9712 7.13887i 0.778260