Properties

Label 756.2.ck.a.5.13
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.13
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.212510 + 1.71896i) q^{3} +(0.455707 - 2.58444i) q^{5} +(2.64406 - 0.0947211i) q^{7} +(-2.90968 + 0.730593i) q^{9} +O(q^{10})\) \(q+(0.212510 + 1.71896i) q^{3} +(0.455707 - 2.58444i) q^{5} +(2.64406 - 0.0947211i) q^{7} +(-2.90968 + 0.730593i) q^{9} +(0.625382 - 0.110272i) q^{11} +(-2.83064 + 3.37342i) q^{13} +(4.53941 + 0.234125i) q^{15} +8.05877 q^{17} -3.96393i q^{19} +(0.724710 + 4.52491i) q^{21} +(3.59496 - 4.28431i) q^{23} +(-1.77321 - 0.645394i) q^{25} +(-1.87420 - 4.84638i) q^{27} +(4.88838 + 5.82574i) q^{29} +(1.20156 + 3.30125i) q^{31} +(0.322453 + 1.05158i) q^{33} +(0.960113 - 6.87657i) q^{35} +(-3.51540 - 6.08885i) q^{37} +(-6.40033 - 4.14888i) q^{39} +(4.16466 + 3.49456i) q^{41} +(-0.637408 - 0.231997i) q^{43} +(0.562216 + 7.85283i) q^{45} +(-2.65000 - 0.964522i) q^{47} +(6.98206 - 0.500896i) q^{49} +(1.71257 + 13.8527i) q^{51} +(-3.98038 + 2.29807i) q^{53} -1.66652i q^{55} +(6.81386 - 0.842375i) q^{57} +(-0.846158 - 0.710011i) q^{59} +(-0.698819 + 1.91999i) q^{61} +(-7.62415 + 2.20734i) q^{63} +(7.42847 + 8.85290i) q^{65} +(-2.32519 + 13.1868i) q^{67} +(8.12853 + 5.26915i) q^{69} +(6.01970 + 3.47547i) q^{71} +(4.04198 + 2.33364i) q^{73} +(0.732586 - 3.18523i) q^{75} +(1.64310 - 0.350801i) q^{77} +(-2.57678 - 14.6136i) q^{79} +(7.93247 - 4.25159i) q^{81} +(0.855255 - 0.717644i) q^{83} +(3.67243 - 20.8274i) q^{85} +(-8.97542 + 9.64098i) q^{87} -13.9067 q^{89} +(-7.16482 + 9.18763i) q^{91} +(-5.41939 + 2.76698i) q^{93} +(-10.2446 - 1.80639i) q^{95} +(-5.47800 + 15.0507i) q^{97} +(-1.73910 + 0.777756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.212510 + 1.71896i 0.122693 + 0.992445i
\(4\) 0 0
\(5\) 0.455707 2.58444i 0.203798 1.15580i −0.695521 0.718505i \(-0.744827\pi\)
0.899320 0.437292i \(-0.144062\pi\)
\(6\) 0 0
\(7\) 2.64406 0.0947211i 0.999359 0.0358012i
\(8\) 0 0
\(9\) −2.90968 + 0.730593i −0.969893 + 0.243531i
\(10\) 0 0
\(11\) 0.625382 0.110272i 0.188560 0.0332482i −0.0785707 0.996909i \(-0.525036\pi\)
0.267131 + 0.963660i \(0.413925\pi\)
\(12\) 0 0
\(13\) −2.83064 + 3.37342i −0.785077 + 0.935619i −0.999151 0.0411989i \(-0.986882\pi\)
0.214074 + 0.976817i \(0.431327\pi\)
\(14\) 0 0
\(15\) 4.53941 + 0.234125i 1.17207 + 0.0604508i
\(16\) 0 0
\(17\) 8.05877 1.95454 0.977269 0.212003i \(-0.0679986\pi\)
0.977269 + 0.212003i \(0.0679986\pi\)
\(18\) 0 0
\(19\) 3.96393i 0.909389i −0.890647 0.454695i \(-0.849748\pi\)
0.890647 0.454695i \(-0.150252\pi\)
\(20\) 0 0
\(21\) 0.724710 + 4.52491i 0.158145 + 0.987416i
\(22\) 0 0
\(23\) 3.59496 4.28431i 0.749601 0.893339i −0.247542 0.968877i \(-0.579623\pi\)
0.997143 + 0.0755377i \(0.0240673\pi\)
\(24\) 0 0
\(25\) −1.77321 0.645394i −0.354641 0.129079i
\(26\) 0 0
\(27\) −1.87420 4.84638i −0.360690 0.932686i
\(28\) 0 0
\(29\) 4.88838 + 5.82574i 0.907749 + 1.08181i 0.996317 + 0.0857433i \(0.0273265\pi\)
−0.0885680 + 0.996070i \(0.528229\pi\)
\(30\) 0 0
\(31\) 1.20156 + 3.30125i 0.215806 + 0.592922i 0.999605 0.0280923i \(-0.00894324\pi\)
−0.783800 + 0.621014i \(0.786721\pi\)
\(32\) 0 0
\(33\) 0.322453 + 1.05158i 0.0561319 + 0.183056i
\(34\) 0 0
\(35\) 0.960113 6.87657i 0.162289 1.16235i
\(36\) 0 0
\(37\) −3.51540 6.08885i −0.577928 1.00100i −0.995717 0.0924566i \(-0.970528\pi\)
0.417789 0.908544i \(-0.362805\pi\)
\(38\) 0 0
\(39\) −6.40033 4.14888i −1.02487 0.664352i
\(40\) 0 0
\(41\) 4.16466 + 3.49456i 0.650410 + 0.545759i 0.907195 0.420710i \(-0.138219\pi\)
−0.256785 + 0.966468i \(0.582663\pi\)
\(42\) 0 0
\(43\) −0.637408 0.231997i −0.0972038 0.0353793i 0.292960 0.956125i \(-0.405360\pi\)
−0.390164 + 0.920745i \(0.627582\pi\)
\(44\) 0 0
\(45\) 0.562216 + 7.85283i 0.0838102 + 1.17063i
\(46\) 0 0
\(47\) −2.65000 0.964522i −0.386542 0.140690i 0.141437 0.989947i \(-0.454828\pi\)
−0.527979 + 0.849257i \(0.677050\pi\)
\(48\) 0 0
\(49\) 6.98206 0.500896i 0.997437 0.0715565i
\(50\) 0 0
\(51\) 1.71257 + 13.8527i 0.239807 + 1.93977i
\(52\) 0 0
\(53\) −3.98038 + 2.29807i −0.546747 + 0.315665i −0.747809 0.663914i \(-0.768894\pi\)
0.201062 + 0.979579i \(0.435561\pi\)
\(54\) 0 0
\(55\) 1.66652i 0.224713i
\(56\) 0 0
\(57\) 6.81386 0.842375i 0.902518 0.111575i
\(58\) 0 0
\(59\) −0.846158 0.710011i −0.110160 0.0924355i 0.586044 0.810279i \(-0.300685\pi\)
−0.696204 + 0.717844i \(0.745129\pi\)
\(60\) 0 0
\(61\) −0.698819 + 1.91999i −0.0894745 + 0.245829i −0.976356 0.216167i \(-0.930644\pi\)
0.886882 + 0.461996i \(0.152867\pi\)
\(62\) 0 0
\(63\) −7.62415 + 2.20734i −0.960553 + 0.278098i
\(64\) 0 0
\(65\) 7.42847 + 8.85290i 0.921388 + 1.09807i
\(66\) 0 0
\(67\) −2.32519 + 13.1868i −0.284067 + 1.61102i 0.424534 + 0.905412i \(0.360438\pi\)
−0.708601 + 0.705610i \(0.750673\pi\)
\(68\) 0 0
\(69\) 8.12853 + 5.26915i 0.978560 + 0.634331i
\(70\) 0 0
\(71\) 6.01970 + 3.47547i 0.714406 + 0.412463i 0.812690 0.582696i \(-0.198002\pi\)
−0.0982840 + 0.995158i \(0.531335\pi\)
\(72\) 0 0
\(73\) 4.04198 + 2.33364i 0.473078 + 0.273132i 0.717527 0.696530i \(-0.245274\pi\)
−0.244449 + 0.969662i \(0.578607\pi\)
\(74\) 0 0
\(75\) 0.732586 3.18523i 0.0845918 0.367799i
\(76\) 0 0
\(77\) 1.64310 0.350801i 0.187249 0.0399775i
\(78\) 0 0
\(79\) −2.57678 14.6136i −0.289910 1.64416i −0.687199 0.726469i \(-0.741160\pi\)
0.397289 0.917693i \(-0.369951\pi\)
\(80\) 0 0
\(81\) 7.93247 4.25159i 0.881385 0.472398i
\(82\) 0 0
\(83\) 0.855255 0.717644i 0.0938764 0.0787717i −0.594642 0.803991i \(-0.702706\pi\)
0.688518 + 0.725219i \(0.258262\pi\)
\(84\) 0 0
\(85\) 3.67243 20.8274i 0.398331 2.25905i
\(86\) 0 0
\(87\) −8.97542 + 9.64098i −0.962266 + 1.03362i
\(88\) 0 0
\(89\) −13.9067 −1.47411 −0.737055 0.675833i \(-0.763784\pi\)
−0.737055 + 0.675833i \(0.763784\pi\)
\(90\) 0 0
\(91\) −7.16482 + 9.18763i −0.751078 + 0.963125i
\(92\) 0 0
\(93\) −5.41939 + 2.76698i −0.561964 + 0.286922i
\(94\) 0 0
\(95\) −10.2446 1.80639i −1.05107 0.185332i
\(96\) 0 0
\(97\) −5.47800 + 15.0507i −0.556207 + 1.52817i 0.268887 + 0.963172i \(0.413344\pi\)
−0.825095 + 0.564995i \(0.808878\pi\)
\(98\) 0 0
\(99\) −1.73910 + 0.777756i −0.174786 + 0.0781674i
\(100\) 0 0
\(101\) 2.40544 2.01841i 0.239350 0.200839i −0.515220 0.857058i \(-0.672290\pi\)
0.754570 + 0.656219i \(0.227845\pi\)
\(102\) 0 0
\(103\) −9.58707 1.69046i −0.944642 0.166566i −0.319948 0.947435i \(-0.603665\pi\)
−0.624694 + 0.780869i \(0.714776\pi\)
\(104\) 0 0
\(105\) 12.0246 + 0.189061i 1.17348 + 0.0184505i
\(106\) 0 0
\(107\) −11.7794 6.80085i −1.13876 0.657463i −0.192637 0.981270i \(-0.561704\pi\)
−0.946123 + 0.323807i \(0.895037\pi\)
\(108\) 0 0
\(109\) −7.11868 12.3299i −0.681846 1.18099i −0.974417 0.224748i \(-0.927844\pi\)
0.292571 0.956244i \(-0.405489\pi\)
\(110\) 0 0
\(111\) 9.71946 7.33679i 0.922531 0.696377i
\(112\) 0 0
\(113\) −1.74448 4.79293i −0.164107 0.450881i 0.830196 0.557472i \(-0.188229\pi\)
−0.994303 + 0.106591i \(0.966006\pi\)
\(114\) 0 0
\(115\) −9.43429 11.2433i −0.879752 1.04845i
\(116\) 0 0
\(117\) 5.77164 11.8836i 0.533589 1.09864i
\(118\) 0 0
\(119\) 21.3078 0.763335i 1.95329 0.0699748i
\(120\) 0 0
\(121\) −9.95768 + 3.62430i −0.905243 + 0.329482i
\(122\) 0 0
\(123\) −5.12200 + 7.90153i −0.461835 + 0.712457i
\(124\) 0 0
\(125\) 4.08473 7.07496i 0.365349 0.632804i
\(126\) 0 0
\(127\) −4.26064 7.37965i −0.378071 0.654838i 0.612711 0.790307i \(-0.290079\pi\)
−0.990782 + 0.135469i \(0.956746\pi\)
\(128\) 0 0
\(129\) 0.263340 1.14498i 0.0231858 0.100810i
\(130\) 0 0
\(131\) 13.8775 + 11.6446i 1.21248 + 1.01739i 0.999183 + 0.0404024i \(0.0128640\pi\)
0.213295 + 0.976988i \(0.431580\pi\)
\(132\) 0 0
\(133\) −0.375468 10.4809i −0.0325572 0.908806i
\(134\) 0 0
\(135\) −13.3793 + 2.63523i −1.15150 + 0.226805i
\(136\) 0 0
\(137\) −0.318833 + 0.875986i −0.0272397 + 0.0748406i −0.952567 0.304329i \(-0.901568\pi\)
0.925327 + 0.379169i \(0.123790\pi\)
\(138\) 0 0
\(139\) −5.49627 0.969140i −0.466187 0.0822014i −0.0643796 0.997925i \(-0.520507\pi\)
−0.401808 + 0.915724i \(0.631618\pi\)
\(140\) 0 0
\(141\) 1.09483 4.76023i 0.0922011 0.400884i
\(142\) 0 0
\(143\) −1.39824 + 2.42182i −0.116926 + 0.202522i
\(144\) 0 0
\(145\) 17.2840 9.97890i 1.43535 0.828702i
\(146\) 0 0
\(147\) 2.34478 + 11.8955i 0.193394 + 0.981121i
\(148\) 0 0
\(149\) −2.40615 6.61084i −0.197119 0.541581i 0.801271 0.598302i \(-0.204158\pi\)
−0.998390 + 0.0567208i \(0.981936\pi\)
\(150\) 0 0
\(151\) −2.67172 15.1521i −0.217421 1.23306i −0.876655 0.481119i \(-0.840231\pi\)
0.659234 0.751938i \(-0.270881\pi\)
\(152\) 0 0
\(153\) −23.4484 + 5.88768i −1.89569 + 0.475991i
\(154\) 0 0
\(155\) 9.07944 1.60095i 0.729278 0.128591i
\(156\) 0 0
\(157\) −11.5994 + 13.8236i −0.925731 + 1.10324i 0.0686772 + 0.997639i \(0.478122\pi\)
−0.994408 + 0.105604i \(0.966322\pi\)
\(158\) 0 0
\(159\) −4.79618 6.35377i −0.380362 0.503887i
\(160\) 0 0
\(161\) 9.09946 11.6685i 0.717138 0.919603i
\(162\) 0 0
\(163\) 2.76364 4.78676i 0.216465 0.374928i −0.737260 0.675609i \(-0.763881\pi\)
0.953725 + 0.300681i \(0.0972140\pi\)
\(164\) 0 0
\(165\) 2.86468 0.354151i 0.223015 0.0275706i
\(166\) 0 0
\(167\) 0.905887 0.329716i 0.0700996 0.0255142i −0.306732 0.951796i \(-0.599236\pi\)
0.376832 + 0.926282i \(0.377013\pi\)
\(168\) 0 0
\(169\) −1.11004 6.29535i −0.0853877 0.484258i
\(170\) 0 0
\(171\) 2.89602 + 11.5338i 0.221465 + 0.882010i
\(172\) 0 0
\(173\) 0.453368 0.380421i 0.0344690 0.0289229i −0.625390 0.780312i \(-0.715060\pi\)
0.659859 + 0.751389i \(0.270616\pi\)
\(174\) 0 0
\(175\) −4.74959 1.53850i −0.359035 0.116300i
\(176\) 0 0
\(177\) 1.04067 1.60540i 0.0782213 0.120669i
\(178\) 0 0
\(179\) 15.4023i 1.15122i −0.817723 0.575612i \(-0.804764\pi\)
0.817723 0.575612i \(-0.195236\pi\)
\(180\) 0 0
\(181\) −0.932828 + 0.538569i −0.0693366 + 0.0400315i −0.534267 0.845315i \(-0.679412\pi\)
0.464931 + 0.885347i \(0.346079\pi\)
\(182\) 0 0
\(183\) −3.44890 0.793228i −0.254950 0.0586371i
\(184\) 0 0
\(185\) −17.3383 + 6.31061i −1.27474 + 0.463966i
\(186\) 0 0
\(187\) 5.03981 0.888654i 0.368547 0.0649848i
\(188\) 0 0
\(189\) −5.41454 12.6366i −0.393850 0.919175i
\(190\) 0 0
\(191\) 1.82347 0.321527i 0.131942 0.0232649i −0.107287 0.994228i \(-0.534216\pi\)
0.239229 + 0.970963i \(0.423105\pi\)
\(192\) 0 0
\(193\) 8.67241 3.15650i 0.624254 0.227210i −0.0104744 0.999945i \(-0.503334\pi\)
0.634728 + 0.772735i \(0.281112\pi\)
\(194\) 0 0
\(195\) −13.6392 + 14.6506i −0.976724 + 1.04915i
\(196\) 0 0
\(197\) 10.0512 5.80304i 0.716116 0.413450i −0.0972057 0.995264i \(-0.530990\pi\)
0.813321 + 0.581815i \(0.197657\pi\)
\(198\) 0 0
\(199\) 11.0159i 0.780899i 0.920624 + 0.390449i \(0.127680\pi\)
−0.920624 + 0.390449i \(0.872320\pi\)
\(200\) 0 0
\(201\) −23.1617 1.19459i −1.63370 0.0842600i
\(202\) 0 0
\(203\) 13.4770 + 14.9406i 0.945898 + 1.04862i
\(204\) 0 0
\(205\) 10.9294 9.17082i 0.763339 0.640518i
\(206\) 0 0
\(207\) −7.33009 + 15.0924i −0.509477 + 1.04899i
\(208\) 0 0
\(209\) −0.437110 2.47897i −0.0302355 0.171474i
\(210\) 0 0
\(211\) −19.8285 + 7.21697i −1.36505 + 0.496837i −0.917611 0.397479i \(-0.869885\pi\)
−0.447437 + 0.894316i \(0.647663\pi\)
\(212\) 0 0
\(213\) −4.69497 + 11.0862i −0.321694 + 0.759615i
\(214\) 0 0
\(215\) −0.890055 + 1.54162i −0.0607012 + 0.105138i
\(216\) 0 0
\(217\) 3.48968 + 8.61487i 0.236895 + 0.584815i
\(218\) 0 0
\(219\) −3.15248 + 7.44395i −0.213025 + 0.503015i
\(220\) 0 0
\(221\) −22.8114 + 27.1856i −1.53446 + 1.82870i
\(222\) 0 0
\(223\) −23.8990 + 4.21405i −1.60040 + 0.282193i −0.901419 0.432948i \(-0.857473\pi\)
−0.698979 + 0.715142i \(0.746362\pi\)
\(224\) 0 0
\(225\) 5.63098 + 0.582397i 0.375399 + 0.0388265i
\(226\) 0 0
\(227\) −0.446322 2.53122i −0.0296234 0.168003i 0.966407 0.257017i \(-0.0827396\pi\)
−0.996030 + 0.0890139i \(0.971628\pi\)
\(228\) 0 0
\(229\) 4.64890 + 12.7728i 0.307208 + 0.844047i 0.993198 + 0.116436i \(0.0371471\pi\)
−0.685990 + 0.727611i \(0.740631\pi\)
\(230\) 0 0
\(231\) 0.952190 + 2.74988i 0.0626495 + 0.180929i
\(232\) 0 0
\(233\) 13.0968 7.56146i 0.858002 0.495368i −0.00534083 0.999986i \(-0.501700\pi\)
0.863343 + 0.504618i \(0.168367\pi\)
\(234\) 0 0
\(235\) −3.70037 + 6.40923i −0.241386 + 0.418092i
\(236\) 0 0
\(237\) 24.5727 7.53493i 1.59617 0.489446i
\(238\) 0 0
\(239\) −19.9067 3.51009i −1.28766 0.227049i −0.512428 0.858730i \(-0.671254\pi\)
−0.775228 + 0.631681i \(0.782365\pi\)
\(240\) 0 0
\(241\) −4.89339 + 13.4445i −0.315211 + 0.866034i 0.676372 + 0.736560i \(0.263551\pi\)
−0.991583 + 0.129474i \(0.958671\pi\)
\(242\) 0 0
\(243\) 8.99405 + 12.7321i 0.576969 + 0.816766i
\(244\) 0 0
\(245\) 1.88723 18.2730i 0.120571 1.16742i
\(246\) 0 0
\(247\) 13.3720 + 11.2205i 0.850841 + 0.713941i
\(248\) 0 0
\(249\) 1.41535 + 1.31765i 0.0896945 + 0.0835025i
\(250\) 0 0
\(251\) −11.6736 20.2193i −0.736831 1.27623i −0.953916 0.300075i \(-0.902988\pi\)
0.217085 0.976153i \(-0.430345\pi\)
\(252\) 0 0
\(253\) 1.77579 3.07575i 0.111643 0.193371i
\(254\) 0 0
\(255\) 36.5820 + 1.88676i 2.29085 + 0.118153i
\(256\) 0 0
\(257\) −11.2872 + 4.10819i −0.704074 + 0.256262i −0.669149 0.743128i \(-0.733341\pi\)
−0.0349244 + 0.999390i \(0.511119\pi\)
\(258\) 0 0
\(259\) −9.87165 15.7663i −0.613395 0.979669i
\(260\) 0 0
\(261\) −18.4799 13.3796i −1.14387 0.828178i
\(262\) 0 0
\(263\) −19.4451 23.1738i −1.19904 1.42896i −0.875824 0.482630i \(-0.839681\pi\)
−0.323213 0.946326i \(-0.604763\pi\)
\(264\) 0 0
\(265\) 4.12535 + 11.3343i 0.253418 + 0.696261i
\(266\) 0 0
\(267\) −2.95531 23.9052i −0.180862 1.46297i
\(268\) 0 0
\(269\) 12.1233 + 20.9981i 0.739170 + 1.28028i 0.952870 + 0.303380i \(0.0981152\pi\)
−0.213700 + 0.976899i \(0.568551\pi\)
\(270\) 0 0
\(271\) 20.5884 + 11.8867i 1.25066 + 0.722067i 0.971240 0.238103i \(-0.0765255\pi\)
0.279417 + 0.960170i \(0.409859\pi\)
\(272\) 0 0
\(273\) −17.3158 10.3636i −1.04800 0.627235i
\(274\) 0 0
\(275\) −1.18010 0.208084i −0.0711627 0.0125479i
\(276\) 0 0
\(277\) −14.7173 + 12.3493i −0.884278 + 0.741997i −0.967054 0.254571i \(-0.918066\pi\)
0.0827763 + 0.996568i \(0.473621\pi\)
\(278\) 0 0
\(279\) −5.90801 8.72772i −0.353703 0.522515i
\(280\) 0 0
\(281\) −4.71932 + 12.9662i −0.281531 + 0.773500i 0.715649 + 0.698460i \(0.246131\pi\)
−0.997180 + 0.0750405i \(0.976091\pi\)
\(282\) 0 0
\(283\) −24.4150 4.30502i −1.45132 0.255907i −0.608264 0.793735i \(-0.708134\pi\)
−0.843055 + 0.537828i \(0.819245\pi\)
\(284\) 0 0
\(285\) 0.928056 17.9939i 0.0549733 1.06587i
\(286\) 0 0
\(287\) 11.3426 + 8.84533i 0.669532 + 0.522124i
\(288\) 0 0
\(289\) 47.9437 2.82022
\(290\) 0 0
\(291\) −27.0357 6.21808i −1.58486 0.364510i
\(292\) 0 0
\(293\) −1.54464 + 8.76011i −0.0902391 + 0.511771i 0.905864 + 0.423570i \(0.139223\pi\)
−0.996103 + 0.0882016i \(0.971888\pi\)
\(294\) 0 0
\(295\) −2.22058 + 1.86329i −0.129287 + 0.108485i
\(296\) 0 0
\(297\) −1.70651 2.82417i −0.0990217 0.163875i
\(298\) 0 0
\(299\) 4.27674 + 24.2546i 0.247330 + 1.40268i
\(300\) 0 0
\(301\) −1.70732 0.553038i −0.0984081 0.0318766i
\(302\) 0 0
\(303\) 3.98075 + 3.70594i 0.228688 + 0.212901i
\(304\) 0 0
\(305\) 4.64364 + 2.68101i 0.265894 + 0.153514i
\(306\) 0 0
\(307\) 19.1446 + 11.0532i 1.09264 + 0.630837i 0.934279 0.356543i \(-0.116045\pi\)
0.158364 + 0.987381i \(0.449378\pi\)
\(308\) 0 0
\(309\) 0.868494 16.8391i 0.0494069 0.957942i
\(310\) 0 0
\(311\) 4.68231 26.5547i 0.265509 1.50578i −0.502071 0.864826i \(-0.667429\pi\)
0.767581 0.640952i \(-0.221460\pi\)
\(312\) 0 0
\(313\) 14.7236 + 17.5469i 0.832226 + 0.991808i 0.999982 + 0.00597981i \(0.00190344\pi\)
−0.167756 + 0.985829i \(0.553652\pi\)
\(314\) 0 0
\(315\) 2.23036 + 20.7101i 0.125666 + 1.16688i
\(316\) 0 0
\(317\) −1.47509 + 4.05276i −0.0828490 + 0.227626i −0.974199 0.225689i \(-0.927537\pi\)
0.891350 + 0.453315i \(0.149759\pi\)
\(318\) 0 0
\(319\) 3.69952 + 3.10427i 0.207133 + 0.173806i
\(320\) 0 0
\(321\) 9.18719 21.6937i 0.512779 1.21082i
\(322\) 0 0
\(323\) 31.9444i 1.77744i
\(324\) 0 0
\(325\) 7.19649 4.15489i 0.399189 0.230472i
\(326\) 0 0
\(327\) 19.6819 14.8570i 1.08841 0.821593i
\(328\) 0 0
\(329\) −7.09811 2.29924i −0.391331 0.126761i
\(330\) 0 0
\(331\) −24.2303 8.81912i −1.33182 0.484743i −0.424592 0.905385i \(-0.639583\pi\)
−0.907227 + 0.420642i \(0.861805\pi\)
\(332\) 0 0
\(333\) 14.6772 + 15.1483i 0.804303 + 0.830120i
\(334\) 0 0
\(335\) 33.0209 + 12.0186i 1.80412 + 0.656647i
\(336\) 0 0
\(337\) 21.8311 + 18.3185i 1.18922 + 0.997871i 0.999873 + 0.0159600i \(0.00508043\pi\)
0.189344 + 0.981911i \(0.439364\pi\)
\(338\) 0 0
\(339\) 7.86816 4.01725i 0.427340 0.218187i
\(340\) 0 0
\(341\) 1.11547 + 1.93204i 0.0604059 + 0.104626i
\(342\) 0 0
\(343\) 18.4135 1.98574i 0.994235 0.107220i
\(344\) 0 0
\(345\) 17.3220 18.6065i 0.932587 1.00174i
\(346\) 0 0
\(347\) 7.03408 + 19.3260i 0.377609 + 1.03747i 0.972344 + 0.233551i \(0.0750347\pi\)
−0.594735 + 0.803922i \(0.702743\pi\)
\(348\) 0 0
\(349\) −6.15541 7.33574i −0.329492 0.392673i 0.575711 0.817653i \(-0.304725\pi\)
−0.905203 + 0.424980i \(0.860281\pi\)
\(350\) 0 0
\(351\) 21.6540 + 7.39587i 1.15581 + 0.394762i
\(352\) 0 0
\(353\) 8.12157 + 2.95601i 0.432268 + 0.157333i 0.548984 0.835833i \(-0.315015\pi\)
−0.116717 + 0.993165i \(0.537237\pi\)
\(354\) 0 0
\(355\) 11.7254 13.9738i 0.622318 0.741650i
\(356\) 0 0
\(357\) 5.84027 + 36.4652i 0.309100 + 1.92994i
\(358\) 0 0
\(359\) 9.01772i 0.475937i 0.971273 + 0.237969i \(0.0764815\pi\)
−0.971273 + 0.237969i \(0.923518\pi\)
\(360\) 0 0
\(361\) 3.28722 0.173012
\(362\) 0 0
\(363\) −8.34614 16.3467i −0.438059 0.857979i
\(364\) 0 0
\(365\) 7.87312 9.38281i 0.412098 0.491119i
\(366\) 0 0
\(367\) 21.3238 3.75995i 1.11309 0.196268i 0.413286 0.910601i \(-0.364381\pi\)
0.699806 + 0.714333i \(0.253270\pi\)
\(368\) 0 0
\(369\) −14.6709 7.12538i −0.763738 0.370933i
\(370\) 0 0
\(371\) −10.3067 + 6.45326i −0.535096 + 0.335037i
\(372\) 0 0
\(373\) 5.14431 29.1748i 0.266362 1.51062i −0.498766 0.866737i \(-0.666213\pi\)
0.765128 0.643878i \(-0.222676\pi\)
\(374\) 0 0
\(375\) 13.0297 + 5.51801i 0.672848 + 0.284949i
\(376\) 0 0
\(377\) −33.4899 −1.72482
\(378\) 0 0
\(379\) −21.5189 −1.10535 −0.552675 0.833397i \(-0.686393\pi\)
−0.552675 + 0.833397i \(0.686393\pi\)
\(380\) 0 0
\(381\) 11.7799 8.89214i 0.603504 0.455558i
\(382\) 0 0
\(383\) −2.27975 + 12.9291i −0.116490 + 0.660645i 0.869512 + 0.493911i \(0.164433\pi\)
−0.986002 + 0.166734i \(0.946678\pi\)
\(384\) 0 0
\(385\) −0.157854 4.40636i −0.00804499 0.224569i
\(386\) 0 0
\(387\) 2.02415 + 0.209352i 0.102893 + 0.0106420i
\(388\) 0 0
\(389\) 17.4811 3.08238i 0.886325 0.156283i 0.288089 0.957604i \(-0.406980\pi\)
0.598235 + 0.801321i \(0.295869\pi\)
\(390\) 0 0
\(391\) 28.9709 34.5262i 1.46512 1.74607i
\(392\) 0 0
\(393\) −17.0675 + 26.3294i −0.860942 + 1.32814i
\(394\) 0 0
\(395\) −38.9423 −1.95940
\(396\) 0 0
\(397\) 9.43024i 0.473290i −0.971596 0.236645i \(-0.923952\pi\)
0.971596 0.236645i \(-0.0760478\pi\)
\(398\) 0 0
\(399\) 17.9364 2.87270i 0.897945 0.143815i
\(400\) 0 0
\(401\) −17.3157 + 20.6360i −0.864703 + 1.03051i 0.134513 + 0.990912i \(0.457053\pi\)
−0.999216 + 0.0396008i \(0.987391\pi\)
\(402\) 0 0
\(403\) −14.5377 5.29128i −0.724173 0.263577i
\(404\) 0 0
\(405\) −7.37310 22.4385i −0.366372 1.11498i
\(406\) 0 0
\(407\) −2.86990 3.42021i −0.142255 0.169533i
\(408\) 0 0
\(409\) 10.5588 + 29.0100i 0.522097 + 1.43445i 0.868181 + 0.496247i \(0.165289\pi\)
−0.346084 + 0.938204i \(0.612489\pi\)
\(410\) 0 0
\(411\) −1.57354 0.361907i −0.0776172 0.0178516i
\(412\) 0 0
\(413\) −2.30454 1.79716i −0.113399 0.0884324i
\(414\) 0 0
\(415\) −1.46496 2.53739i −0.0719122 0.124556i
\(416\) 0 0
\(417\) 0.497907 9.65384i 0.0243826 0.472751i
\(418\) 0 0
\(419\) −1.30333 1.09362i −0.0636717 0.0534269i 0.610396 0.792096i \(-0.291010\pi\)
−0.674068 + 0.738669i \(0.735455\pi\)
\(420\) 0 0
\(421\) −4.04181 1.47110i −0.196986 0.0716969i 0.241643 0.970365i \(-0.422314\pi\)
−0.438629 + 0.898668i \(0.644536\pi\)
\(422\) 0 0
\(423\) 8.41533 + 0.870375i 0.409167 + 0.0423191i
\(424\) 0 0
\(425\) −14.2899 5.20108i −0.693160 0.252290i
\(426\) 0 0
\(427\) −1.66585 + 5.14275i −0.0806162 + 0.248875i
\(428\) 0 0
\(429\) −4.46016 1.88886i −0.215338 0.0911950i
\(430\) 0 0
\(431\) −3.63284 + 2.09742i −0.174988 + 0.101029i −0.584936 0.811080i \(-0.698880\pi\)
0.409948 + 0.912109i \(0.365547\pi\)
\(432\) 0 0
\(433\) 8.83087i 0.424385i −0.977228 0.212192i \(-0.931940\pi\)
0.977228 0.212192i \(-0.0680603\pi\)
\(434\) 0 0
\(435\) 20.8264 + 27.5899i 0.998549 + 1.32283i
\(436\) 0 0
\(437\) −16.9827 14.2502i −0.812393 0.681679i
\(438\) 0 0
\(439\) 1.68330 4.62482i 0.0803393 0.220730i −0.893019 0.450018i \(-0.851417\pi\)
0.973359 + 0.229288i \(0.0736397\pi\)
\(440\) 0 0
\(441\) −19.9496 + 6.55849i −0.949981 + 0.312309i
\(442\) 0 0
\(443\) 11.1745 + 13.3173i 0.530917 + 0.632722i 0.963126 0.269052i \(-0.0867102\pi\)
−0.432209 + 0.901773i \(0.642266\pi\)
\(444\) 0 0
\(445\) −6.33739 + 35.9411i −0.300421 + 1.70377i
\(446\) 0 0
\(447\) 10.8525 5.54096i 0.513304 0.262078i
\(448\) 0 0
\(449\) 1.41048 + 0.814341i 0.0665647 + 0.0384311i 0.532913 0.846170i \(-0.321097\pi\)
−0.466348 + 0.884601i \(0.654431\pi\)
\(450\) 0 0
\(451\) 2.98985 + 1.72619i 0.140787 + 0.0812832i
\(452\) 0 0
\(453\) 25.4781 7.81254i 1.19706 0.367065i
\(454\) 0 0
\(455\) 20.4798 + 22.7039i 0.960110 + 1.06438i
\(456\) 0 0
\(457\) −5.43057 30.7983i −0.254031 1.44068i −0.798547 0.601933i \(-0.794398\pi\)
0.544515 0.838751i \(-0.316714\pi\)
\(458\) 0 0
\(459\) −15.1037 39.0558i −0.704982 1.82297i
\(460\) 0 0
\(461\) −20.4541 + 17.1630i −0.952641 + 0.799361i −0.979740 0.200272i \(-0.935817\pi\)
0.0270990 + 0.999633i \(0.491373\pi\)
\(462\) 0 0
\(463\) −1.82238 + 10.3352i −0.0846931 + 0.480318i 0.912729 + 0.408565i \(0.133971\pi\)
−0.997422 + 0.0717534i \(0.977141\pi\)
\(464\) 0 0
\(465\) 4.68145 + 15.2670i 0.217097 + 0.707991i
\(466\) 0 0
\(467\) 3.69568 0.171016 0.0855078 0.996338i \(-0.472749\pi\)
0.0855078 + 0.996338i \(0.472749\pi\)
\(468\) 0 0
\(469\) −4.89885 + 35.0868i −0.226208 + 1.62016i
\(470\) 0 0
\(471\) −26.2273 17.0013i −1.20849 0.783377i
\(472\) 0 0
\(473\) −0.424206 0.0747990i −0.0195050 0.00343926i
\(474\) 0 0
\(475\) −2.55830 + 7.02887i −0.117383 + 0.322507i
\(476\) 0 0
\(477\) 9.90268 9.59470i 0.453412 0.439311i
\(478\) 0 0
\(479\) 16.3218 13.6956i 0.745762 0.625768i −0.188617 0.982051i \(-0.560400\pi\)
0.934378 + 0.356283i \(0.115956\pi\)
\(480\) 0 0
\(481\) 30.4911 + 5.37640i 1.39027 + 0.245143i
\(482\) 0 0
\(483\) 21.9914 + 13.1620i 1.00064 + 0.598891i
\(484\) 0 0
\(485\) 36.4013 + 21.0163i 1.65290 + 0.954300i
\(486\) 0 0
\(487\) −4.17289 7.22766i −0.189092 0.327516i 0.755856 0.654738i \(-0.227221\pi\)
−0.944948 + 0.327222i \(0.893888\pi\)
\(488\) 0 0
\(489\) 8.81557 + 3.73336i 0.398654 + 0.168828i
\(490\) 0 0
\(491\) −2.78557 7.65329i −0.125711 0.345388i 0.860832 0.508889i \(-0.169944\pi\)
−0.986543 + 0.163501i \(0.947721\pi\)
\(492\) 0 0
\(493\) 39.3943 + 46.9483i 1.77423 + 2.11445i
\(494\) 0 0
\(495\) 1.21755 + 4.84902i 0.0547246 + 0.217947i
\(496\) 0 0
\(497\) 16.2456 + 8.61915i 0.728715 + 0.386622i
\(498\) 0 0
\(499\) −25.8300 + 9.40134i −1.15631 + 0.420862i −0.847777 0.530353i \(-0.822059\pi\)
−0.308531 + 0.951214i \(0.599837\pi\)
\(500\) 0 0
\(501\) 0.759280 + 1.48712i 0.0339221 + 0.0664396i
\(502\) 0 0
\(503\) 0.341404 0.591329i 0.0152225 0.0263661i −0.858314 0.513125i \(-0.828488\pi\)
0.873536 + 0.486759i \(0.161821\pi\)
\(504\) 0 0
\(505\) −4.12028 7.13653i −0.183350 0.317571i
\(506\) 0 0
\(507\) 10.5856 3.24594i 0.470123 0.144157i
\(508\) 0 0
\(509\) −33.1189 27.7901i −1.46797 1.23177i −0.917995 0.396592i \(-0.870193\pi\)
−0.549975 0.835181i \(-0.685363\pi\)
\(510\) 0 0
\(511\) 10.9083 + 5.78741i 0.482554 + 0.256020i
\(512\) 0 0
\(513\) −19.2107 + 7.42921i −0.848174 + 0.328007i
\(514\) 0 0
\(515\) −8.73779 + 24.0069i −0.385033 + 1.05787i
\(516\) 0 0
\(517\) −1.76362 0.310974i −0.0775640 0.0136766i
\(518\) 0 0
\(519\) 0.750276 + 0.698481i 0.0329335 + 0.0306599i
\(520\) 0 0
\(521\) 16.7897 29.0805i 0.735568 1.27404i −0.218905 0.975746i \(-0.570249\pi\)
0.954474 0.298296i \(-0.0964181\pi\)
\(522\) 0 0
\(523\) −13.7285 + 7.92615i −0.600305 + 0.346586i −0.769162 0.639054i \(-0.779326\pi\)
0.168857 + 0.985641i \(0.445993\pi\)
\(524\) 0 0
\(525\) 1.63529 8.49132i 0.0713699 0.370592i
\(526\) 0 0
\(527\) 9.68306 + 26.6040i 0.421801 + 1.15889i
\(528\) 0 0
\(529\) −1.43763 8.15323i −0.0625058 0.354488i
\(530\) 0 0
\(531\) 2.98078 + 1.44771i 0.129355 + 0.0628251i
\(532\) 0 0
\(533\) −23.5773 + 4.15731i −1.02124 + 0.180073i
\(534\) 0 0
\(535\) −22.9444 + 27.3440i −0.991972 + 1.18219i
\(536\) 0 0
\(537\) 26.4761 3.27314i 1.14253 0.141247i
\(538\) 0 0
\(539\) 4.31122 1.08317i 0.185697 0.0466556i
\(540\) 0 0
\(541\) −8.71319 + 15.0917i −0.374609 + 0.648842i −0.990268 0.139170i \(-0.955556\pi\)
0.615659 + 0.788012i \(0.288890\pi\)
\(542\) 0 0
\(543\) −1.12402 1.48905i −0.0482361 0.0639011i
\(544\) 0 0
\(545\) −35.1100 + 12.7790i −1.50395 + 0.547392i
\(546\) 0 0
\(547\) 5.05757 + 28.6829i 0.216246 + 1.22639i 0.878731 + 0.477317i \(0.158391\pi\)
−0.662485 + 0.749075i \(0.730498\pi\)
\(548\) 0 0
\(549\) 0.630607 6.09710i 0.0269136 0.260218i
\(550\) 0 0
\(551\) 23.0929 19.3772i 0.983789 0.825497i
\(552\) 0 0
\(553\) −8.19736 38.3952i −0.348587 1.63273i
\(554\) 0 0
\(555\) −14.5323 28.4628i −0.616861 1.20818i
\(556\) 0 0
\(557\) 4.54341i 0.192510i 0.995357 + 0.0962552i \(0.0306865\pi\)
−0.995357 + 0.0962552i \(0.969314\pi\)
\(558\) 0 0
\(559\) 2.58689 1.49354i 0.109414 0.0631702i
\(560\) 0 0
\(561\) 2.59857 + 8.47441i 0.109712 + 0.357790i
\(562\) 0 0
\(563\) −4.51721 + 1.64413i −0.190378 + 0.0692918i −0.435450 0.900213i \(-0.643411\pi\)
0.245072 + 0.969505i \(0.421188\pi\)
\(564\) 0 0
\(565\) −13.1820 + 2.32435i −0.554572 + 0.0977860i
\(566\) 0 0
\(567\) 20.5712 11.9928i 0.863908 0.503650i
\(568\) 0 0
\(569\) −35.5964 + 6.27661i −1.49228 + 0.263129i −0.859473 0.511181i \(-0.829208\pi\)
−0.632806 + 0.774310i \(0.718097\pi\)
\(570\) 0 0
\(571\) 12.1039 4.40545i 0.506532 0.184363i −0.0760977 0.997100i \(-0.524246\pi\)
0.582630 + 0.812738i \(0.302024\pi\)
\(572\) 0 0
\(573\) 0.940198 + 3.06615i 0.0392773 + 0.128090i
\(574\) 0 0
\(575\) −9.13967 + 5.27679i −0.381151 + 0.220057i
\(576\) 0 0
\(577\) 6.71260i 0.279449i −0.990190 0.139725i \(-0.955378\pi\)
0.990190 0.139725i \(-0.0446217\pi\)
\(578\) 0 0
\(579\) 7.26889 + 14.2368i 0.302085 + 0.591661i
\(580\) 0 0
\(581\) 2.19336 1.97850i 0.0909961 0.0820821i
\(582\) 0 0
\(583\) −2.23585 + 1.87610i −0.0925993 + 0.0777001i
\(584\) 0 0
\(585\) −28.0823 20.3319i −1.16106 0.840621i
\(586\) 0 0
\(587\) −2.54009 14.4056i −0.104841 0.594581i −0.991284 0.131743i \(-0.957943\pi\)
0.886443 0.462837i \(-0.153169\pi\)
\(588\) 0 0
\(589\) 13.0859 4.76289i 0.539196 0.196251i
\(590\) 0 0
\(591\) 12.1112 + 16.0444i 0.498188 + 0.659978i
\(592\) 0 0
\(593\) −20.4263 + 35.3794i −0.838809 + 1.45286i 0.0520821 + 0.998643i \(0.483414\pi\)
−0.890891 + 0.454217i \(0.849919\pi\)
\(594\) 0 0
\(595\) 7.73732 55.4167i 0.317199 2.27186i
\(596\) 0 0
\(597\) −18.9360 + 2.34099i −0.774999 + 0.0958104i
\(598\) 0 0
\(599\) 21.5274 25.6553i 0.879585 1.04825i −0.118883 0.992908i \(-0.537931\pi\)
0.998468 0.0553401i \(-0.0176243\pi\)
\(600\) 0 0
\(601\) 39.7569 7.01021i 1.62172 0.285953i 0.712312 0.701863i \(-0.247648\pi\)
0.909406 + 0.415911i \(0.136537\pi\)
\(602\) 0 0
\(603\) −2.86863 40.0681i −0.116820 1.63170i
\(604\) 0 0
\(605\) 4.82900 + 27.3866i 0.196327 + 1.11343i
\(606\) 0 0
\(607\) 6.69163 + 18.3851i 0.271605 + 0.746228i 0.998246 + 0.0592102i \(0.0188582\pi\)
−0.726641 + 0.687018i \(0.758920\pi\)
\(608\) 0 0
\(609\) −22.8183 + 26.3414i −0.924644 + 1.06741i
\(610\) 0 0
\(611\) 10.7549 6.20936i 0.435098 0.251204i
\(612\) 0 0
\(613\) −10.5161 + 18.2144i −0.424742 + 0.735675i −0.996396 0.0848199i \(-0.972968\pi\)
0.571654 + 0.820495i \(0.306302\pi\)
\(614\) 0 0
\(615\) 18.0869 + 16.8383i 0.729334 + 0.678985i
\(616\) 0 0
\(617\) −16.9370 2.98646i −0.681859 0.120230i −0.178019 0.984027i \(-0.556969\pi\)
−0.503840 + 0.863797i \(0.668080\pi\)
\(618\) 0 0
\(619\) 3.37863 9.28271i 0.135799 0.373104i −0.853090 0.521764i \(-0.825274\pi\)
0.988888 + 0.148661i \(0.0474962\pi\)
\(620\) 0 0
\(621\) −27.5010 9.39289i −1.10358 0.376924i
\(622\) 0 0
\(623\) −36.7701 + 1.31726i −1.47316 + 0.0527749i
\(624\) 0 0
\(625\) −23.6510 19.8456i −0.946042 0.793823i
\(626\) 0 0
\(627\) 4.16838 1.27818i 0.166469 0.0510457i
\(628\) 0 0
\(629\) −28.3298 49.0686i −1.12958 1.95649i
\(630\) 0 0
\(631\) 13.3688 23.1555i 0.532204 0.921804i −0.467089 0.884210i \(-0.654697\pi\)
0.999293 0.0375939i \(-0.0119693\pi\)
\(632\) 0 0
\(633\) −16.6195 32.5508i −0.660564 1.29378i
\(634\) 0 0
\(635\) −21.0139 + 7.64842i −0.833910 + 0.303518i
\(636\) 0 0
\(637\) −18.0739 + 24.9713i −0.716115 + 0.989398i
\(638\) 0 0
\(639\) −20.0545 5.71456i −0.793345 0.226065i
\(640\) 0 0
\(641\) −12.5657 14.9752i −0.496315 0.591485i 0.458497 0.888696i \(-0.348388\pi\)
−0.954812 + 0.297211i \(0.903944\pi\)
\(642\) 0 0
\(643\) 8.14572 + 22.3802i 0.321236 + 0.882588i 0.990245 + 0.139334i \(0.0444963\pi\)
−0.669010 + 0.743254i \(0.733281\pi\)
\(644\) 0 0
\(645\) −2.83914 1.20236i −0.111791 0.0473430i
\(646\) 0 0
\(647\) −5.30690 9.19182i −0.208636 0.361368i 0.742649 0.669680i \(-0.233569\pi\)
−0.951285 + 0.308313i \(0.900236\pi\)
\(648\) 0 0
\(649\) −0.607466 0.350721i −0.0238451 0.0137670i
\(650\) 0 0
\(651\) −14.0671 + 7.82938i −0.551332 + 0.306857i
\(652\) 0 0
\(653\) 27.6321 + 4.87229i 1.08133 + 0.190667i 0.685803 0.727787i \(-0.259451\pi\)
0.395526 + 0.918455i \(0.370562\pi\)
\(654\) 0 0
\(655\) 36.4187 30.5590i 1.42300 1.19404i
\(656\) 0 0
\(657\) −13.4658 3.83710i −0.525352 0.149699i
\(658\) 0 0
\(659\) 14.7119 40.4206i 0.573094 1.57456i −0.226492 0.974013i \(-0.572726\pi\)
0.799587 0.600551i \(-0.205052\pi\)
\(660\) 0 0
\(661\) −27.1091 4.78007i −1.05442 0.185923i −0.380542 0.924764i \(-0.624263\pi\)
−0.673880 + 0.738840i \(0.735374\pi\)
\(662\) 0 0
\(663\) −51.5788 33.4348i −2.00315 1.29850i
\(664\) 0 0
\(665\) −27.2583 3.80582i −1.05703 0.147584i
\(666\) 0 0
\(667\) 42.5328 1.64688
\(668\) 0 0
\(669\) −12.3226 40.1861i −0.476418 1.55368i
\(670\) 0 0
\(671\) −0.225308 + 1.27779i −0.00869793 + 0.0493284i
\(672\) 0 0
\(673\) −11.0731 + 9.29143i −0.426836 + 0.358158i −0.830757 0.556636i \(-0.812092\pi\)
0.403920 + 0.914794i \(0.367647\pi\)
\(674\) 0 0
\(675\) 0.195518 + 9.80322i 0.00752549 + 0.377326i
\(676\) 0 0
\(677\) 2.52350 + 14.3115i 0.0969858 + 0.550034i 0.994121 + 0.108277i \(0.0345334\pi\)
−0.897135 + 0.441757i \(0.854355\pi\)
\(678\) 0 0
\(679\) −13.0585 + 40.3137i −0.501140 + 1.54710i
\(680\) 0 0
\(681\) 4.25623 1.30512i 0.163099 0.0500123i
\(682\) 0 0
\(683\) 37.7172 + 21.7760i 1.44321 + 0.833236i 0.998062 0.0622218i \(-0.0198186\pi\)
0.445146 + 0.895458i \(0.353152\pi\)
\(684\) 0 0
\(685\) 2.11864 + 1.22320i 0.0809491 + 0.0467360i
\(686\) 0 0
\(687\) −20.9680 + 10.7056i −0.799978 + 0.408445i
\(688\) 0 0
\(689\) 3.51464 19.9325i 0.133897 0.759368i
\(690\) 0 0
\(691\) 2.75307 + 3.28098i 0.104732 + 0.124814i 0.815864 0.578244i \(-0.196262\pi\)
−0.711132 + 0.703058i \(0.751817\pi\)
\(692\) 0 0
\(693\) −4.52460 + 2.22116i −0.171875 + 0.0843748i
\(694\) 0 0
\(695\) −5.00937 + 13.7631i −0.190016 + 0.522065i
\(696\) 0 0
\(697\) 33.5620 + 28.1619i 1.27125 + 1.06671i
\(698\) 0 0
\(699\) 15.7811 + 20.9061i 0.596895 + 0.790741i
\(700\) 0 0
\(701\) 18.9199i 0.714595i −0.933991 0.357297i \(-0.883698\pi\)
0.933991 0.357297i \(-0.116302\pi\)
\(702\) 0 0
\(703\) −24.1358 + 13.9348i −0.910299 + 0.525562i
\(704\) 0 0
\(705\) −11.8036 4.99879i −0.444550 0.188265i
\(706\) 0 0
\(707\) 6.16894 5.56462i 0.232007 0.209279i
\(708\) 0 0
\(709\) −2.84439 1.03527i −0.106823 0.0388805i 0.288056 0.957614i \(-0.406991\pi\)
−0.394879 + 0.918733i \(0.629213\pi\)
\(710\) 0 0
\(711\) 18.1742 + 40.6384i 0.681587 + 1.52406i
\(712\) 0 0
\(713\) 18.4631 + 6.72002i 0.691449 + 0.251667i
\(714\) 0 0
\(715\) 5.62186 + 4.71730i 0.210246 + 0.176417i
\(716\) 0 0
\(717\) 1.80335 34.9648i 0.0673473 1.30579i
\(718\) 0 0
\(719\) 0.271522 + 0.470290i 0.0101261 + 0.0175388i 0.871044 0.491205i \(-0.163443\pi\)
−0.860918 + 0.508744i \(0.830110\pi\)
\(720\) 0 0
\(721\) −25.5089 3.56157i −0.950000 0.132640i
\(722\) 0 0
\(723\) −24.1505 5.55448i −0.898165 0.206573i
\(724\) 0 0
\(725\) −4.90820 13.4852i −0.182286 0.500827i
\(726\) 0 0
\(727\) 24.2349 + 28.8820i 0.898821 + 1.07117i 0.997107 + 0.0760149i \(0.0242197\pi\)
−0.0982857 + 0.995158i \(0.531336\pi\)
\(728\) 0 0
\(729\) −19.9748 + 18.1662i −0.739806 + 0.672821i
\(730\) 0 0
\(731\) −5.13672 1.86961i −0.189988 0.0691501i
\(732\) 0 0
\(733\) −5.80284 + 6.91556i −0.214333 + 0.255432i −0.862489 0.506075i \(-0.831096\pi\)
0.648157 + 0.761507i \(0.275540\pi\)
\(734\) 0 0
\(735\) 31.8117 0.639096i 1.17339 0.0235734i
\(736\) 0 0
\(737\) 8.50318i 0.313219i
\(738\) 0 0
\(739\) 19.6599 0.723200 0.361600 0.932333i \(-0.382231\pi\)
0.361600 + 0.932333i \(0.382231\pi\)
\(740\) 0 0
\(741\) −16.4459 + 25.3705i −0.604155 + 0.932008i
\(742\) 0 0
\(743\) −7.89524 + 9.40918i −0.289648 + 0.345189i −0.891172 0.453665i \(-0.850116\pi\)
0.601524 + 0.798855i \(0.294561\pi\)
\(744\) 0 0
\(745\) −18.1818 + 3.20595i −0.666131 + 0.117457i
\(746\) 0 0
\(747\) −1.96421 + 2.71296i −0.0718667 + 0.0992619i
\(748\) 0 0
\(749\) −31.7896 16.8661i −1.16157 0.616273i
\(750\) 0 0
\(751\) −2.66917 + 15.1376i −0.0973993 + 0.552379i 0.896586 + 0.442869i \(0.146039\pi\)
−0.993986 + 0.109510i \(0.965072\pi\)
\(752\) 0 0
\(753\) 32.2754 24.3633i 1.17618 0.887847i
\(754\) 0 0
\(755\) −40.3771 −1.46947
\(756\) 0 0
\(757\) 19.2152 0.698390 0.349195 0.937050i \(-0.386455\pi\)
0.349195 + 0.937050i \(0.386455\pi\)
\(758\) 0 0
\(759\) 5.66448 + 2.39889i 0.205608 + 0.0870740i
\(760\) 0 0
\(761\) 5.78604 32.8143i 0.209744 1.18952i −0.680054 0.733162i \(-0.738044\pi\)
0.889798 0.456354i \(-0.150845\pi\)
\(762\) 0 0
\(763\) −19.9901 31.9267i −0.723690 1.15582i
\(764\) 0 0
\(765\) 4.53076 + 63.2841i 0.163810 + 2.28804i
\(766\) 0 0
\(767\) 4.79033 0.844664i 0.172969 0.0304991i
\(768\) 0 0
\(769\) 1.96014 2.33600i 0.0706843 0.0842383i −0.729543 0.683934i \(-0.760267\pi\)
0.800228 + 0.599696i \(0.204712\pi\)
\(770\) 0 0
\(771\) −9.46046 18.5292i −0.340710 0.667313i
\(772\) 0 0
\(773\) −23.9908 −0.862890 −0.431445 0.902139i \(-0.641996\pi\)
−0.431445 + 0.902139i \(0.641996\pi\)
\(774\) 0 0
\(775\) 6.62927i 0.238130i
\(776\) 0 0
\(777\) 25.0038 20.3195i 0.897008 0.728958i