Properties

Label 864.2.v.b.109.2
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.2
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.39831 + 0.211463i) q^{2} +(1.91057 - 0.591382i) q^{4} +(-1.77214 + 0.734044i) q^{5} +(-0.0355868 + 0.0355868i) q^{7} +(-2.54652 + 1.23095i) q^{8} +O(q^{10})\) \(q+(-1.39831 + 0.211463i) q^{2} +(1.91057 - 0.591382i) q^{4} +(-1.77214 + 0.734044i) q^{5} +(-0.0355868 + 0.0355868i) q^{7} +(-2.54652 + 1.23095i) q^{8} +(2.32278 - 1.40116i) q^{10} +(1.04798 + 2.53004i) q^{11} +(1.82513 + 0.755995i) q^{13} +(0.0422362 - 0.0572867i) q^{14} +(3.30053 - 2.25975i) q^{16} -2.92843i q^{17} +(-1.55044 - 0.642214i) q^{19} +(-2.95169 + 2.45045i) q^{20} +(-2.00041 - 3.31619i) q^{22} +(-0.146574 - 0.146574i) q^{23} +(-0.933880 + 0.933880i) q^{25} +(-2.71198 - 0.671172i) q^{26} +(-0.0469455 + 0.0890363i) q^{28} +(-2.17892 + 5.26037i) q^{29} -4.28852 q^{31} +(-4.13733 + 3.85778i) q^{32} +(0.619253 + 4.09486i) q^{34} +(0.0369424 - 0.0891869i) q^{35} +(-1.92396 + 0.796930i) q^{37} +(2.30381 + 0.570157i) q^{38} +(3.60921 - 4.05067i) q^{40} +(-4.22763 - 4.22763i) q^{41} +(1.29855 + 3.13498i) q^{43} +(3.49846 + 4.21406i) q^{44} +(0.235952 + 0.173962i) q^{46} +5.33727i q^{47} +6.99747i q^{49} +(1.10838 - 1.50334i) q^{50} +(3.93412 + 0.365028i) q^{52} +(-1.48773 - 3.59170i) q^{53} +(-3.71433 - 3.71433i) q^{55} +(0.0468168 - 0.134428i) q^{56} +(1.93444 - 7.81641i) q^{58} +(-1.27834 + 0.529507i) q^{59} +(-5.58246 + 13.4772i) q^{61} +(5.99670 - 0.906861i) q^{62} +(4.96952 - 6.26928i) q^{64} -3.78932 q^{65} +(1.11670 - 2.69596i) q^{67} +(-1.73182 - 5.59496i) q^{68} +(-0.0327974 + 0.132523i) q^{70} +(-3.73700 + 3.73700i) q^{71} +(-10.8405 - 10.8405i) q^{73} +(2.52178 - 1.52120i) q^{74} +(-3.34202 - 0.310089i) q^{76} +(-0.127330 - 0.0527419i) q^{77} +9.94610i q^{79} +(-4.19025 + 6.42733i) q^{80} +(6.80554 + 5.01757i) q^{82} +(11.2462 + 4.65832i) q^{83} +(2.14959 + 5.18958i) q^{85} +(-2.47871 - 4.10909i) q^{86} +(-5.78306 - 5.15279i) q^{88} +(-6.00227 + 6.00227i) q^{89} +(-0.0918540 + 0.0380472i) q^{91} +(-0.366721 - 0.193358i) q^{92} +(-1.12863 - 7.46318i) q^{94} +3.21901 q^{95} -3.69111 q^{97} +(-1.47970 - 9.78466i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39831 + 0.211463i −0.988758 + 0.149527i
\(3\) 0 0
\(4\) 1.91057 0.591382i 0.955284 0.295691i
\(5\) −1.77214 + 0.734044i −0.792524 + 0.328274i −0.741958 0.670446i \(-0.766103\pi\)
−0.0505664 + 0.998721i \(0.516103\pi\)
\(6\) 0 0
\(7\) −0.0355868 + 0.0355868i −0.0134505 + 0.0134505i −0.713800 0.700350i \(-0.753027\pi\)
0.700350 + 0.713800i \(0.253027\pi\)
\(8\) −2.54652 + 1.23095i −0.900330 + 0.435207i
\(9\) 0 0
\(10\) 2.32278 1.40116i 0.734529 0.443087i
\(11\) 1.04798 + 2.53004i 0.315977 + 0.762837i 0.999460 + 0.0328698i \(0.0104647\pi\)
−0.683482 + 0.729967i \(0.739535\pi\)
\(12\) 0 0
\(13\) 1.82513 + 0.755995i 0.506201 + 0.209675i 0.621144 0.783697i \(-0.286668\pi\)
−0.114942 + 0.993372i \(0.536668\pi\)
\(14\) 0.0422362 0.0572867i 0.0112881 0.0153105i
\(15\) 0 0
\(16\) 3.30053 2.25975i 0.825134 0.564938i
\(17\) 2.92843i 0.710248i −0.934819 0.355124i \(-0.884439\pi\)
0.934819 0.355124i \(-0.115561\pi\)
\(18\) 0 0
\(19\) −1.55044 0.642214i −0.355696 0.147334i 0.197678 0.980267i \(-0.436660\pi\)
−0.553374 + 0.832933i \(0.686660\pi\)
\(20\) −2.95169 + 2.45045i −0.660018 + 0.547937i
\(21\) 0 0
\(22\) −2.00041 3.31619i −0.426490 0.707014i
\(23\) −0.146574 0.146574i −0.0305628 0.0305628i 0.691660 0.722223i \(-0.256880\pi\)
−0.722223 + 0.691660i \(0.756880\pi\)
\(24\) 0 0
\(25\) −0.933880 + 0.933880i −0.186776 + 0.186776i
\(26\) −2.71198 0.671172i −0.531862 0.131628i
\(27\) 0 0
\(28\) −0.0469455 + 0.0890363i −0.00887187 + 0.0168263i
\(29\) −2.17892 + 5.26037i −0.404614 + 0.976826i 0.581916 + 0.813249i \(0.302303\pi\)
−0.986531 + 0.163577i \(0.947697\pi\)
\(30\) 0 0
\(31\) −4.28852 −0.770241 −0.385120 0.922866i \(-0.625840\pi\)
−0.385120 + 0.922866i \(0.625840\pi\)
\(32\) −4.13733 + 3.85778i −0.731384 + 0.681966i
\(33\) 0 0
\(34\) 0.619253 + 4.09486i 0.106201 + 0.702263i
\(35\) 0.0369424 0.0891869i 0.00624441 0.0150753i
\(36\) 0 0
\(37\) −1.92396 + 0.796930i −0.316297 + 0.131014i −0.535183 0.844736i \(-0.679758\pi\)
0.218887 + 0.975750i \(0.429758\pi\)
\(38\) 2.30381 + 0.570157i 0.373727 + 0.0924916i
\(39\) 0 0
\(40\) 3.60921 4.05067i 0.570666 0.640468i
\(41\) −4.22763 4.22763i −0.660244 0.660244i 0.295193 0.955438i \(-0.404616\pi\)
−0.955438 + 0.295193i \(0.904616\pi\)
\(42\) 0 0
\(43\) 1.29855 + 3.13498i 0.198027 + 0.478080i 0.991433 0.130613i \(-0.0416944\pi\)
−0.793406 + 0.608692i \(0.791694\pi\)
\(44\) 3.49846 + 4.21406i 0.527412 + 0.635294i
\(45\) 0 0
\(46\) 0.235952 + 0.173962i 0.0347892 + 0.0256493i
\(47\) 5.33727i 0.778520i 0.921128 + 0.389260i \(0.127269\pi\)
−0.921128 + 0.389260i \(0.872731\pi\)
\(48\) 0 0
\(49\) 6.99747i 0.999638i
\(50\) 1.10838 1.50334i 0.156748 0.212604i
\(51\) 0 0
\(52\) 3.93412 + 0.365028i 0.545565 + 0.0506203i
\(53\) −1.48773 3.59170i −0.204355 0.493357i 0.788161 0.615469i \(-0.211033\pi\)
−0.992516 + 0.122112i \(0.961033\pi\)
\(54\) 0 0
\(55\) −3.71433 3.71433i −0.500840 0.500840i
\(56\) 0.0468168 0.134428i 0.00625615 0.0179637i
\(57\) 0 0
\(58\) 1.93444 7.81641i 0.254004 1.02634i
\(59\) −1.27834 + 0.529507i −0.166426 + 0.0689359i −0.464341 0.885657i \(-0.653709\pi\)
0.297915 + 0.954592i \(0.403709\pi\)
\(60\) 0 0
\(61\) −5.58246 + 13.4772i −0.714761 + 1.72558i −0.0270124 + 0.999635i \(0.508599\pi\)
−0.687748 + 0.725949i \(0.741401\pi\)
\(62\) 5.99670 0.906861i 0.761581 0.115171i
\(63\) 0 0
\(64\) 4.96952 6.26928i 0.621190 0.783660i
\(65\) −3.78932 −0.470008
\(66\) 0 0
\(67\) 1.11670 2.69596i 0.136427 0.329364i −0.840870 0.541237i \(-0.817956\pi\)
0.977297 + 0.211873i \(0.0679562\pi\)
\(68\) −1.73182 5.59496i −0.210014 0.678488i
\(69\) 0 0
\(70\) −0.0327974 + 0.132523i −0.00392004 + 0.0158396i
\(71\) −3.73700 + 3.73700i −0.443501 + 0.443501i −0.893187 0.449686i \(-0.851536\pi\)
0.449686 + 0.893187i \(0.351536\pi\)
\(72\) 0 0
\(73\) −10.8405 10.8405i −1.26878 1.26878i −0.946718 0.322065i \(-0.895623\pi\)
−0.322065 0.946718i \(-0.604377\pi\)
\(74\) 2.52178 1.52120i 0.293151 0.176836i
\(75\) 0 0
\(76\) −3.34202 0.310089i −0.383355 0.0355697i
\(77\) −0.127330 0.0527419i −0.0145106 0.00601050i
\(78\) 0 0
\(79\) 9.94610i 1.11902i 0.828822 + 0.559512i \(0.189011\pi\)
−0.828822 + 0.559512i \(0.810989\pi\)
\(80\) −4.19025 + 6.42733i −0.468484 + 0.718597i
\(81\) 0 0
\(82\) 6.80554 + 5.01757i 0.751546 + 0.554098i
\(83\) 11.2462 + 4.65832i 1.23443 + 0.511318i 0.901970 0.431800i \(-0.142121\pi\)
0.332460 + 0.943117i \(0.392121\pi\)
\(84\) 0 0
\(85\) 2.14959 + 5.18958i 0.233156 + 0.562889i
\(86\) −2.47871 4.10909i −0.267286 0.443095i
\(87\) 0 0
\(88\) −5.78306 5.15279i −0.616476 0.549290i
\(89\) −6.00227 + 6.00227i −0.636239 + 0.636239i −0.949626 0.313386i \(-0.898537\pi\)
0.313386 + 0.949626i \(0.398537\pi\)
\(90\) 0 0
\(91\) −0.0918540 + 0.0380472i −0.00962892 + 0.00398843i
\(92\) −0.366721 0.193358i −0.0382333 0.0201590i
\(93\) 0 0
\(94\) −1.12863 7.46318i −0.116409 0.769768i
\(95\) 3.21901 0.330263
\(96\) 0 0
\(97\) −3.69111 −0.374776 −0.187388 0.982286i \(-0.560002\pi\)
−0.187388 + 0.982286i \(0.560002\pi\)
\(98\) −1.47970 9.78466i −0.149472 0.988400i
\(99\) 0 0
\(100\) −1.23196 + 2.33652i −0.123196 + 0.233652i
\(101\) −13.0062 + 5.38735i −1.29417 + 0.536062i −0.920225 0.391390i \(-0.871994\pi\)
−0.373943 + 0.927452i \(0.621994\pi\)
\(102\) 0 0
\(103\) −14.1391 + 14.1391i −1.39317 + 1.39317i −0.575041 + 0.818124i \(0.695014\pi\)
−0.818124 + 0.575041i \(0.804986\pi\)
\(104\) −5.57833 + 0.321496i −0.547000 + 0.0315252i
\(105\) 0 0
\(106\) 2.83982 + 4.70772i 0.275828 + 0.457254i
\(107\) 3.17772 + 7.67170i 0.307202 + 0.741652i 0.999793 + 0.0203215i \(0.00646897\pi\)
−0.692591 + 0.721330i \(0.743531\pi\)
\(108\) 0 0
\(109\) −2.82294 1.16930i −0.270388 0.111999i 0.243370 0.969934i \(-0.421747\pi\)
−0.513758 + 0.857935i \(0.671747\pi\)
\(110\) 5.97924 + 4.40836i 0.570098 + 0.420320i
\(111\) 0 0
\(112\) −0.0370381 + 0.197873i −0.00349977 + 0.0186972i
\(113\) 13.9959i 1.31662i −0.752745 0.658312i \(-0.771271\pi\)
0.752745 0.658312i \(-0.228729\pi\)
\(114\) 0 0
\(115\) 0.367342 + 0.152158i 0.0342548 + 0.0141888i
\(116\) −1.05208 + 11.3389i −0.0976829 + 1.05279i
\(117\) 0 0
\(118\) 1.67555 1.01074i 0.154247 0.0930460i
\(119\) 0.104213 + 0.104213i 0.00955321 + 0.00955321i
\(120\) 0 0
\(121\) 2.47531 2.47531i 0.225028 0.225028i
\(122\) 4.95610 20.0259i 0.448704 1.81306i
\(123\) 0 0
\(124\) −8.19350 + 2.53615i −0.735798 + 0.227753i
\(125\) 4.63967 11.2012i 0.414985 1.00186i
\(126\) 0 0
\(127\) −3.85566 −0.342135 −0.171067 0.985259i \(-0.554722\pi\)
−0.171067 + 0.985259i \(0.554722\pi\)
\(128\) −5.62323 + 9.81730i −0.497028 + 0.867735i
\(129\) 0 0
\(130\) 5.29867 0.801300i 0.464724 0.0702786i
\(131\) 2.42590 5.85663i 0.211952 0.511697i −0.781771 0.623565i \(-0.785684\pi\)
0.993723 + 0.111869i \(0.0356836\pi\)
\(132\) 0 0
\(133\) 0.0780295 0.0323209i 0.00676601 0.00280257i
\(134\) −0.991409 + 4.00595i −0.0856447 + 0.346061i
\(135\) 0 0
\(136\) 3.60475 + 7.45730i 0.309105 + 0.639458i
\(137\) −1.91013 1.91013i −0.163193 0.163193i 0.620786 0.783980i \(-0.286813\pi\)
−0.783980 + 0.620786i \(0.786813\pi\)
\(138\) 0 0
\(139\) 6.94133 + 16.7578i 0.588756 + 1.42138i 0.884693 + 0.466175i \(0.154368\pi\)
−0.295937 + 0.955207i \(0.595632\pi\)
\(140\) 0.0178374 0.192245i 0.00150754 0.0162476i
\(141\) 0 0
\(142\) 4.43527 6.01574i 0.372200 0.504830i
\(143\) 5.40994i 0.452402i
\(144\) 0 0
\(145\) 10.9215i 0.906983i
\(146\) 17.4508 + 12.8660i 1.44424 + 1.06480i
\(147\) 0 0
\(148\) −3.20456 + 2.66038i −0.263413 + 0.218682i
\(149\) −5.07715 12.2573i −0.415937 1.00416i −0.983513 0.180839i \(-0.942119\pi\)
0.567576 0.823321i \(-0.307881\pi\)
\(150\) 0 0
\(151\) −5.21158 5.21158i −0.424112 0.424112i 0.462505 0.886617i \(-0.346951\pi\)
−0.886617 + 0.462505i \(0.846951\pi\)
\(152\) 4.73876 0.273109i 0.384364 0.0221520i
\(153\) 0 0
\(154\) 0.189201 + 0.0468242i 0.0152462 + 0.00377320i
\(155\) 7.59985 3.14796i 0.610434 0.252850i
\(156\) 0 0
\(157\) −1.66632 + 4.02285i −0.132987 + 0.321059i −0.976320 0.216333i \(-0.930590\pi\)
0.843333 + 0.537392i \(0.180590\pi\)
\(158\) −2.10323 13.9078i −0.167324 1.10644i
\(159\) 0 0
\(160\) 4.50014 9.87351i 0.355768 0.780569i
\(161\) 0.0104322 0.000822173
\(162\) 0 0
\(163\) 5.91014 14.2683i 0.462918 1.11758i −0.504276 0.863542i \(-0.668241\pi\)
0.967194 0.254039i \(-0.0817593\pi\)
\(164\) −10.5773 5.57702i −0.825949 0.435492i
\(165\) 0 0
\(166\) −16.7108 4.13566i −1.29701 0.320989i
\(167\) 9.14462 9.14462i 0.707632 0.707632i −0.258405 0.966037i \(-0.583197\pi\)
0.966037 + 0.258405i \(0.0831969\pi\)
\(168\) 0 0
\(169\) −6.43280 6.43280i −0.494831 0.494831i
\(170\) −4.10321 6.80210i −0.314702 0.521698i
\(171\) 0 0
\(172\) 4.33494 + 5.22165i 0.330536 + 0.398147i
\(173\) 1.32896 + 0.550474i 0.101039 + 0.0418518i 0.432630 0.901571i \(-0.357585\pi\)
−0.331591 + 0.943423i \(0.607585\pi\)
\(174\) 0 0
\(175\) 0.0664675i 0.00502447i
\(176\) 9.17616 + 5.98233i 0.691679 + 0.450935i
\(177\) 0 0
\(178\) 7.12381 9.66232i 0.533952 0.724221i
\(179\) 18.9912 + 7.86639i 1.41947 + 0.587962i 0.954726 0.297486i \(-0.0961481\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(180\) 0 0
\(181\) 3.31249 + 7.99706i 0.246215 + 0.594417i 0.997877 0.0651328i \(-0.0207471\pi\)
−0.751661 + 0.659549i \(0.770747\pi\)
\(182\) 0.120395 0.0726256i 0.00892429 0.00538337i
\(183\) 0 0
\(184\) 0.553680 + 0.192828i 0.0408178 + 0.0142155i
\(185\) 2.82454 2.82454i 0.207664 0.207664i
\(186\) 0 0
\(187\) 7.40905 3.06893i 0.541803 0.224422i
\(188\) 3.15636 + 10.1972i 0.230202 + 0.743708i
\(189\) 0 0
\(190\) −4.50119 + 0.680700i −0.326550 + 0.0493831i
\(191\) 23.4508 1.69684 0.848422 0.529321i \(-0.177553\pi\)
0.848422 + 0.529321i \(0.177553\pi\)
\(192\) 0 0
\(193\) −2.58287 −0.185919 −0.0929594 0.995670i \(-0.529633\pi\)
−0.0929594 + 0.995670i \(0.529633\pi\)
\(194\) 5.16134 0.780532i 0.370563 0.0560390i
\(195\) 0 0
\(196\) 4.13818 + 13.3691i 0.295584 + 0.954938i
\(197\) 11.6273 4.81619i 0.828412 0.343139i 0.0721379 0.997395i \(-0.477018\pi\)
0.756274 + 0.654255i \(0.227018\pi\)
\(198\) 0 0
\(199\) −7.74779 + 7.74779i −0.549226 + 0.549226i −0.926217 0.376991i \(-0.876959\pi\)
0.376991 + 0.926217i \(0.376959\pi\)
\(200\) 1.22858 3.52770i 0.0868738 0.249446i
\(201\) 0 0
\(202\) 17.0476 10.2835i 1.19946 0.723548i
\(203\) −0.109659 0.264740i −0.00769655 0.0185811i
\(204\) 0 0
\(205\) 10.5952 + 4.38868i 0.740001 + 0.306518i
\(206\) 16.7810 22.7608i 1.16919 1.58582i
\(207\) 0 0
\(208\) 7.73228 1.62916i 0.536137 0.112962i
\(209\) 4.59571i 0.317892i
\(210\) 0 0
\(211\) 14.7043 + 6.09070i 1.01228 + 0.419301i 0.826287 0.563249i \(-0.190449\pi\)
0.185996 + 0.982551i \(0.440449\pi\)
\(212\) −4.96647 5.98236i −0.341099 0.410870i
\(213\) 0 0
\(214\) −6.06574 10.0555i −0.414645 0.687379i
\(215\) −4.60242 4.60242i −0.313883 0.313883i
\(216\) 0 0
\(217\) 0.152614 0.152614i 0.0103601 0.0103601i
\(218\) 4.19462 + 1.03810i 0.284095 + 0.0703092i
\(219\) 0 0
\(220\) −9.29306 4.89988i −0.626538 0.330350i
\(221\) 2.21388 5.34477i 0.148922 0.359528i
\(222\) 0 0
\(223\) 8.09618 0.542160 0.271080 0.962557i \(-0.412619\pi\)
0.271080 + 0.962557i \(0.412619\pi\)
\(224\) 0.00994830 0.284520i 0.000664699 0.0190103i
\(225\) 0 0
\(226\) 2.95961 + 19.5707i 0.196870 + 1.30182i
\(227\) 3.70788 8.95160i 0.246100 0.594139i −0.751766 0.659430i \(-0.770798\pi\)
0.997866 + 0.0652913i \(0.0207977\pi\)
\(228\) 0 0
\(229\) 11.3986 4.72144i 0.753238 0.312002i 0.0271762 0.999631i \(-0.491348\pi\)
0.726062 + 0.687629i \(0.241348\pi\)
\(230\) −0.545835 0.135086i −0.0359913 0.00890728i
\(231\) 0 0
\(232\) −0.926609 16.0778i −0.0608348 1.05556i
\(233\) 8.59855 + 8.59855i 0.563310 + 0.563310i 0.930246 0.366936i \(-0.119593\pi\)
−0.366936 + 0.930246i \(0.619593\pi\)
\(234\) 0 0
\(235\) −3.91779 9.45837i −0.255568 0.616996i
\(236\) −2.12922 + 1.76765i −0.138600 + 0.115064i
\(237\) 0 0
\(238\) −0.167760 0.123686i −0.0108743 0.00801735i
\(239\) 25.8457i 1.67182i 0.548868 + 0.835909i \(0.315059\pi\)
−0.548868 + 0.835909i \(0.684941\pi\)
\(240\) 0 0
\(241\) 25.5757i 1.64748i −0.566971 0.823738i \(-0.691885\pi\)
0.566971 0.823738i \(-0.308115\pi\)
\(242\) −2.93783 + 3.98470i −0.188851 + 0.256146i
\(243\) 0 0
\(244\) −2.69546 + 29.0506i −0.172559 + 1.85977i
\(245\) −5.13645 12.4005i −0.328156 0.792238i
\(246\) 0 0
\(247\) −2.34425 2.34425i −0.149161 0.149161i
\(248\) 10.9208 5.27896i 0.693471 0.335214i
\(249\) 0 0
\(250\) −4.11910 + 16.6439i −0.260515 + 1.05265i
\(251\) −25.5297 + 10.5748i −1.61142 + 0.667473i −0.992972 0.118350i \(-0.962240\pi\)
−0.618451 + 0.785823i \(0.712240\pi\)
\(252\) 0 0
\(253\) 0.217233 0.524446i 0.0136573 0.0329716i
\(254\) 5.39143 0.815328i 0.338288 0.0511582i
\(255\) 0 0
\(256\) 5.78705 14.9168i 0.361691 0.932298i
\(257\) 6.54897 0.408513 0.204257 0.978917i \(-0.434522\pi\)
0.204257 + 0.978917i \(0.434522\pi\)
\(258\) 0 0
\(259\) 0.0401073 0.0968276i 0.00249215 0.00601657i
\(260\) −7.23976 + 2.24094i −0.448991 + 0.138977i
\(261\) 0 0
\(262\) −2.15371 + 8.70240i −0.133057 + 0.537636i
\(263\) 17.3589 17.3589i 1.07040 1.07040i 0.0730702 0.997327i \(-0.476720\pi\)
0.997327 0.0730702i \(-0.0232797\pi\)
\(264\) 0 0
\(265\) 5.27292 + 5.27292i 0.323913 + 0.323913i
\(266\) −0.102275 + 0.0616950i −0.00627089 + 0.00378277i
\(267\) 0 0
\(268\) 0.539194 5.81122i 0.0329365 0.354977i
\(269\) 1.98257 + 0.821205i 0.120879 + 0.0500698i 0.442303 0.896866i \(-0.354162\pi\)
−0.321424 + 0.946935i \(0.604162\pi\)
\(270\) 0 0
\(271\) 19.0040i 1.15441i −0.816600 0.577204i \(-0.804144\pi\)
0.816600 0.577204i \(-0.195856\pi\)
\(272\) −6.61752 9.66537i −0.401246 0.586049i
\(273\) 0 0
\(274\) 3.07488 + 2.26704i 0.185760 + 0.136957i
\(275\) −3.34144 1.38407i −0.201497 0.0834626i
\(276\) 0 0
\(277\) 2.76578 + 6.67719i 0.166180 + 0.401193i 0.984929 0.172957i \(-0.0553323\pi\)
−0.818750 + 0.574151i \(0.805332\pi\)
\(278\) −13.2498 21.9649i −0.794671 1.31737i
\(279\) 0 0
\(280\) 0.0157102 + 0.272590i 0.000938863 + 0.0162904i
\(281\) −20.5080 + 20.5080i −1.22341 + 1.22341i −0.256992 + 0.966413i \(0.582732\pi\)
−0.966413 + 0.256992i \(0.917268\pi\)
\(282\) 0 0
\(283\) 26.5696 11.0055i 1.57940 0.654209i 0.591082 0.806612i \(-0.298701\pi\)
0.988319 + 0.152403i \(0.0487010\pi\)
\(284\) −4.92980 + 9.34979i −0.292530 + 0.554808i
\(285\) 0 0
\(286\) −1.14400 7.56479i −0.0676461 0.447316i
\(287\) 0.300895 0.0177613
\(288\) 0 0
\(289\) 8.42431 0.495548
\(290\) 2.30949 + 15.2717i 0.135618 + 0.896786i
\(291\) 0 0
\(292\) −27.1223 14.3006i −1.58721 0.836879i
\(293\) −25.9576 + 10.7520i −1.51646 + 0.628138i −0.976878 0.213797i \(-0.931417\pi\)
−0.539580 + 0.841934i \(0.681417\pi\)
\(294\) 0 0
\(295\) 1.87672 1.87672i 0.109267 0.109267i
\(296\) 3.91841 4.39770i 0.227753 0.255611i
\(297\) 0 0
\(298\) 9.69143 + 16.0660i 0.561409 + 0.930677i
\(299\) −0.156708 0.378327i −0.00906267 0.0218792i
\(300\) 0 0
\(301\) −0.157775 0.0653525i −0.00909399 0.00376686i
\(302\) 8.38948 + 6.18538i 0.482761 + 0.355928i
\(303\) 0 0
\(304\) −6.56853 + 1.38396i −0.376731 + 0.0793757i
\(305\) 27.9813i 1.60221i
\(306\) 0 0
\(307\) 14.8458 + 6.14934i 0.847296 + 0.350961i 0.763726 0.645540i \(-0.223368\pi\)
0.0835699 + 0.996502i \(0.473368\pi\)
\(308\) −0.274464 0.0254661i −0.0156390 0.00145107i
\(309\) 0 0
\(310\) −9.96130 + 6.00892i −0.565764 + 0.341284i
\(311\) −0.108964 0.108964i −0.00617877 0.00617877i 0.704011 0.710189i \(-0.251391\pi\)
−0.710189 + 0.704011i \(0.751391\pi\)
\(312\) 0 0
\(313\) 17.7967 17.7967i 1.00593 1.00593i 0.00594408 0.999982i \(-0.498108\pi\)
0.999982 0.00594408i \(-0.00189207\pi\)
\(314\) 1.47936 5.97758i 0.0834850 0.337334i
\(315\) 0 0
\(316\) 5.88195 + 19.0027i 0.330885 + 1.06898i
\(317\) −0.847035 + 2.04492i −0.0475742 + 0.114854i −0.945880 0.324516i \(-0.894798\pi\)
0.898306 + 0.439371i \(0.144798\pi\)
\(318\) 0 0
\(319\) −15.5924 −0.873008
\(320\) −4.20474 + 14.7579i −0.235052 + 0.824991i
\(321\) 0 0
\(322\) −0.0145875 + 0.00220602i −0.000812929 + 0.000122937i
\(323\) −1.88068 + 4.54035i −0.104644 + 0.252632i
\(324\) 0 0
\(325\) −2.41046 + 0.998447i −0.133709 + 0.0553839i
\(326\) −5.24701 + 21.2014i −0.290605 + 1.17424i
\(327\) 0 0
\(328\) 15.9697 + 5.56173i 0.881781 + 0.307095i
\(329\) −0.189936 0.189936i −0.0104715 0.0104715i
\(330\) 0 0
\(331\) −8.40430 20.2898i −0.461942 1.11523i −0.967599 0.252492i \(-0.918750\pi\)
0.505657 0.862735i \(-0.331250\pi\)
\(332\) 24.2415 + 2.24925i 1.33042 + 0.123443i
\(333\) 0 0
\(334\) −10.8533 + 14.7208i −0.593867 + 0.805486i
\(335\) 5.59733i 0.305815i
\(336\) 0 0
\(337\) 0.515293i 0.0280698i 0.999902 + 0.0140349i \(0.00446760\pi\)
−0.999902 + 0.0140349i \(0.995532\pi\)
\(338\) 10.3554 + 7.63479i 0.563258 + 0.415278i
\(339\) 0 0
\(340\) 7.17597 + 8.64381i 0.389171 + 0.468776i
\(341\) −4.49428 10.8501i −0.243379 0.587568i
\(342\) 0 0
\(343\) −0.498124 0.498124i −0.0268962 0.0268962i
\(344\) −7.16579 6.38483i −0.386353 0.344247i
\(345\) 0 0
\(346\) −1.97471 0.488711i −0.106161 0.0262732i
\(347\) −21.0299 + 8.71086i −1.12894 + 0.467623i −0.867421 0.497574i \(-0.834224\pi\)
−0.261521 + 0.965198i \(0.584224\pi\)
\(348\) 0 0
\(349\) −9.27157 + 22.3835i −0.496296 + 1.19816i 0.455169 + 0.890405i \(0.349579\pi\)
−0.951465 + 0.307758i \(0.900421\pi\)
\(350\) 0.0140554 + 0.0929425i 0.000751292 + 0.00496798i
\(351\) 0 0
\(352\) −14.0962 6.42476i −0.751330 0.342441i
\(353\) −19.4215 −1.03370 −0.516851 0.856076i \(-0.672896\pi\)
−0.516851 + 0.856076i \(0.672896\pi\)
\(354\) 0 0
\(355\) 3.87936 9.36561i 0.205895 0.497075i
\(356\) −7.91811 + 15.0174i −0.419659 + 0.795920i
\(357\) 0 0
\(358\) −28.2191 6.98378i −1.49142 0.369104i
\(359\) −11.9259 + 11.9259i −0.629423 + 0.629423i −0.947923 0.318500i \(-0.896821\pi\)
0.318500 + 0.947923i \(0.396821\pi\)
\(360\) 0 0
\(361\) −11.4436 11.4436i −0.602295 0.602295i
\(362\) −6.32298 10.4819i −0.332328 0.550918i
\(363\) 0 0
\(364\) −0.152993 + 0.127013i −0.00801901 + 0.00665727i
\(365\) 27.1682 + 11.2534i 1.42205 + 0.589032i
\(366\) 0 0
\(367\) 6.36872i 0.332445i 0.986088 + 0.166222i \(0.0531569\pi\)
−0.986088 + 0.166222i \(0.946843\pi\)
\(368\) −0.814994 0.152552i −0.0424845 0.00795232i
\(369\) 0 0
\(370\) −3.35231 + 4.54688i −0.174278 + 0.236381i
\(371\) 0.180760 + 0.0748733i 0.00938460 + 0.00388723i
\(372\) 0 0
\(373\) 6.20853 + 14.9887i 0.321465 + 0.776086i 0.999169 + 0.0407511i \(0.0129751\pi\)
−0.677704 + 0.735335i \(0.737025\pi\)
\(374\) −9.71122 + 5.85806i −0.502155 + 0.302913i
\(375\) 0 0
\(376\) −6.56992 13.5914i −0.338818 0.700925i
\(377\) −7.95363 + 7.95363i −0.409633 + 0.409633i
\(378\) 0 0
\(379\) −0.643556 + 0.266570i −0.0330573 + 0.0136928i −0.399151 0.916885i \(-0.630695\pi\)
0.366094 + 0.930578i \(0.380695\pi\)
\(380\) 6.15013 1.90366i 0.315495 0.0976559i
\(381\) 0 0
\(382\) −32.7917 + 4.95897i −1.67777 + 0.253723i
\(383\) 5.97320 0.305216 0.152608 0.988287i \(-0.451233\pi\)
0.152608 + 0.988287i \(0.451233\pi\)
\(384\) 0 0
\(385\) 0.264362 0.0134731
\(386\) 3.61166 0.546179i 0.183829 0.0277998i
\(387\) 0 0
\(388\) −7.05212 + 2.18286i −0.358017 + 0.110818i
\(389\) −17.5487 + 7.26889i −0.889752 + 0.368547i −0.780271 0.625441i \(-0.784919\pi\)
−0.109481 + 0.993989i \(0.534919\pi\)
\(390\) 0 0
\(391\) −0.429232 + 0.429232i −0.0217072 + 0.0217072i
\(392\) −8.61354 17.8192i −0.435050 0.900005i
\(393\) 0 0
\(394\) −15.2402 + 9.19329i −0.767790 + 0.463151i
\(395\) −7.30087 17.6259i −0.367347 0.886854i
\(396\) 0 0
\(397\) 9.55093 + 3.95613i 0.479348 + 0.198552i 0.609256 0.792974i \(-0.291468\pi\)
−0.129908 + 0.991526i \(0.541468\pi\)
\(398\) 9.19548 12.4722i 0.460928 0.625176i
\(399\) 0 0
\(400\) −0.971967 + 5.19264i −0.0485983 + 0.259632i
\(401\) 16.0262i 0.800308i 0.916448 + 0.400154i \(0.131043\pi\)
−0.916448 + 0.400154i \(0.868957\pi\)
\(402\) 0 0
\(403\) −7.82712 3.24210i −0.389897 0.161500i
\(404\) −21.6633 + 17.9846i −1.07779 + 0.894765i
\(405\) 0 0
\(406\) 0.209320 + 0.347001i 0.0103884 + 0.0172214i
\(407\) −4.03253 4.03253i −0.199885 0.199885i
\(408\) 0 0
\(409\) −14.9468 + 14.9468i −0.739071 + 0.739071i −0.972398 0.233327i \(-0.925039\pi\)
0.233327 + 0.972398i \(0.425039\pi\)
\(410\) −15.7435 3.89626i −0.777514 0.192423i
\(411\) 0 0
\(412\) −18.6521 + 35.3753i −0.918922 + 1.74282i
\(413\) 0.0266486 0.0643355i 0.00131129 0.00316574i
\(414\) 0 0
\(415\) −23.3492 −1.14617
\(416\) −10.4677 + 3.91317i −0.513219 + 0.191859i
\(417\) 0 0
\(418\) 0.971820 + 6.42625i 0.0475333 + 0.314318i
\(419\) 5.09708 12.3054i 0.249009 0.601160i −0.749112 0.662444i \(-0.769519\pi\)
0.998120 + 0.0612837i \(0.0195194\pi\)
\(420\) 0 0
\(421\) 12.6398 5.23558i 0.616027 0.255167i −0.0527763 0.998606i \(-0.516807\pi\)
0.668803 + 0.743440i \(0.266807\pi\)
\(422\) −21.8491 5.40732i −1.06360 0.263224i
\(423\) 0 0
\(424\) 8.20973 + 7.31500i 0.398700 + 0.355248i
\(425\) 2.73480 + 2.73480i 0.132657 + 0.132657i
\(426\) 0 0
\(427\) −0.280950 0.678273i −0.0135961 0.0328239i
\(428\) 10.6082 + 12.7781i 0.512765 + 0.617651i
\(429\) 0 0
\(430\) 7.40887 + 5.46239i 0.357288 + 0.263420i
\(431\) 10.9212i 0.526058i 0.964788 + 0.263029i \(0.0847215\pi\)
−0.964788 + 0.263029i \(0.915279\pi\)
\(432\) 0 0
\(433\) 15.4198i 0.741030i −0.928826 0.370515i \(-0.879181\pi\)
0.928826 0.370515i \(-0.120819\pi\)
\(434\) −0.181131 + 0.245675i −0.00869456 + 0.0117928i
\(435\) 0 0
\(436\) −6.08491 0.564589i −0.291415 0.0270389i
\(437\) 0.133123 + 0.321387i 0.00636812 + 0.0153740i
\(438\) 0 0
\(439\) −2.51199 2.51199i −0.119891 0.119891i 0.644616 0.764507i \(-0.277017\pi\)
−0.764507 + 0.644616i \(0.777017\pi\)
\(440\) 14.0308 + 4.88645i 0.668890 + 0.232952i
\(441\) 0 0
\(442\) −1.96548 + 7.94183i −0.0934882 + 0.377754i
\(443\) −17.3256 + 7.17648i −0.823162 + 0.340965i −0.754192 0.656654i \(-0.771971\pi\)
−0.0689698 + 0.997619i \(0.521971\pi\)
\(444\) 0 0
\(445\) 6.23093 15.0428i 0.295374 0.713096i
\(446\) −11.3210 + 1.71204i −0.536065 + 0.0810674i
\(447\) 0 0
\(448\) 0.0462545 + 0.399952i 0.00218532 + 0.0188960i
\(449\) 28.5759 1.34858 0.674291 0.738466i \(-0.264449\pi\)
0.674291 + 0.738466i \(0.264449\pi\)
\(450\) 0 0
\(451\) 6.26562 15.1265i 0.295036 0.712281i
\(452\) −8.27693 26.7401i −0.389314 1.25775i
\(453\) 0 0
\(454\) −3.29185 + 13.3012i −0.154494 + 0.624258i
\(455\) 0.134850 0.134850i 0.00632185 0.00632185i
\(456\) 0 0
\(457\) −0.438434 0.438434i −0.0205091 0.0205091i 0.696778 0.717287i \(-0.254616\pi\)
−0.717287 + 0.696778i \(0.754616\pi\)
\(458\) −14.9404 + 9.01243i −0.698118 + 0.421123i
\(459\) 0 0
\(460\) 0.791814 + 0.0734686i 0.0369185 + 0.00342549i
\(461\) 11.9681 + 4.95734i 0.557409 + 0.230886i 0.643560 0.765396i \(-0.277457\pi\)
−0.0861508 + 0.996282i \(0.527457\pi\)
\(462\) 0 0
\(463\) 7.85370i 0.364993i 0.983207 + 0.182496i \(0.0584178\pi\)
−0.983207 + 0.182496i \(0.941582\pi\)
\(464\) 4.69553 + 22.2858i 0.217985 + 1.03459i
\(465\) 0 0
\(466\) −13.8417 10.2052i −0.641206 0.472747i
\(467\) 5.86660 + 2.43003i 0.271474 + 0.112448i 0.514268 0.857630i \(-0.328064\pi\)
−0.242794 + 0.970078i \(0.578064\pi\)
\(468\) 0 0
\(469\) 0.0562007 + 0.135680i 0.00259511 + 0.00626514i
\(470\) 7.47839 + 12.3973i 0.344952 + 0.571846i
\(471\) 0 0
\(472\) 2.60352 2.92198i 0.119837 0.134495i
\(473\) −6.57078 + 6.57078i −0.302125 + 0.302125i
\(474\) 0 0
\(475\) 2.04768 0.848175i 0.0939538 0.0389169i
\(476\) 0.260736 + 0.137477i 0.0119508 + 0.00630123i
\(477\) 0 0
\(478\) −5.46539 36.1404i −0.249981 1.65302i
\(479\) 1.98328 0.0906184 0.0453092 0.998973i \(-0.485573\pi\)
0.0453092 + 0.998973i \(0.485573\pi\)
\(480\) 0 0
\(481\) −4.11396 −0.187580
\(482\) 5.40830 + 35.7629i 0.246341 + 1.62895i
\(483\) 0 0
\(484\) 3.26539 6.19310i 0.148427 0.281505i
\(485\) 6.54117 2.70944i 0.297019 0.123029i
\(486\) 0 0
\(487\) 4.91751 4.91751i 0.222834 0.222834i −0.586857 0.809691i \(-0.699635\pi\)
0.809691 + 0.586857i \(0.199635\pi\)
\(488\) −2.37400 41.1918i −0.107466 1.86466i
\(489\) 0 0
\(490\) 9.80461 + 16.2536i 0.442927 + 0.734263i
\(491\) 12.9562 + 31.2791i 0.584706 + 1.41160i 0.888504 + 0.458868i \(0.151745\pi\)
−0.303798 + 0.952736i \(0.598255\pi\)
\(492\) 0 0
\(493\) 15.4046 + 6.38080i 0.693789 + 0.287377i
\(494\) 3.77372 + 2.78228i 0.169788 + 0.125181i
\(495\) 0 0
\(496\) −14.1544 + 9.69098i −0.635551 + 0.435138i
\(497\) 0.265976i 0.0119306i
\(498\) 0 0
\(499\) 33.8042 + 14.0021i 1.51328 + 0.626822i 0.976232 0.216728i \(-0.0695384\pi\)
0.537051 + 0.843550i \(0.319538\pi\)
\(500\) 2.24024 24.1444i 0.100187 1.07977i
\(501\) 0 0
\(502\) 33.4624 20.1854i 1.49350 0.900920i
\(503\) −27.9286 27.9286i −1.24528 1.24528i −0.957782 0.287494i \(-0.907178\pi\)
−0.287494 0.957782i \(-0.592822\pi\)
\(504\) 0 0
\(505\) 19.0943 19.0943i 0.849684 0.849684i
\(506\) −0.192859 + 0.779277i −0.00857362 + 0.0346431i
\(507\) 0 0
\(508\) −7.36650 + 2.28017i −0.326836 + 0.101166i
\(509\) −2.11556 + 5.10740i −0.0937704 + 0.226382i −0.963805 0.266610i \(-0.914097\pi\)
0.870034 + 0.492991i \(0.164097\pi\)
\(510\) 0 0
\(511\) 0.771555 0.0341316
\(512\) −4.93778 + 22.0821i −0.218221 + 0.975899i
\(513\) 0 0
\(514\) −9.15752 + 1.38486i −0.403921 + 0.0610836i
\(515\) 14.6777 35.4351i 0.646777 1.56146i
\(516\) 0 0
\(517\) −13.5035 + 5.59334i −0.593884 + 0.245995i
\(518\) −0.0356072 + 0.143877i −0.00156449 + 0.00632157i
\(519\) 0 0
\(520\) 9.64958 4.66447i 0.423162 0.204551i
\(521\) 13.8505 + 13.8505i 0.606802 + 0.606802i 0.942109 0.335307i \(-0.108840\pi\)
−0.335307 + 0.942109i \(0.608840\pi\)
\(522\) 0 0
\(523\) −0.594708 1.43575i −0.0260048 0.0627810i 0.910344 0.413853i \(-0.135817\pi\)
−0.936348 + 0.351072i \(0.885817\pi\)
\(524\) 1.17133 12.6241i 0.0511698 0.551488i
\(525\) 0 0
\(526\) −20.6025 + 27.9440i −0.898311 + 1.21842i
\(527\) 12.5586i 0.547062i
\(528\) 0 0
\(529\) 22.9570i 0.998132i
\(530\) −8.48823 6.25818i −0.368705 0.271838i
\(531\) 0 0
\(532\) 0.129967 0.107896i 0.00563477 0.00467790i
\(533\) −4.51992 10.9120i −0.195779 0.472653i
\(534\) 0 0
\(535\) −11.2627 11.2627i −0.486930 0.486930i
\(536\) 0.474891 + 8.23993i 0.0205122 + 0.355911i
\(537\) 0 0
\(538\) −2.94590 0.729065i −0.127007 0.0314322i
\(539\) −17.7039 + 7.33320i −0.762561 + 0.315863i
\(540\) 0 0
\(541\) 7.61913 18.3942i 0.327572 0.790829i −0.671199 0.741277i \(-0.734221\pi\)
0.998772 0.0495523i \(-0.0157795\pi\)
\(542\) 4.01863 + 26.5735i 0.172615 + 1.14143i
\(543\) 0 0
\(544\) 11.2972 + 12.1159i 0.484365 + 0.519464i
\(545\) 5.86095 0.251056
\(546\) 0 0
\(547\) −6.58120 + 15.8884i −0.281392 + 0.679340i −0.999869 0.0162112i \(-0.994840\pi\)
0.718477 + 0.695551i \(0.244840\pi\)
\(548\) −4.77904 2.51981i −0.204151 0.107641i
\(549\) 0 0
\(550\) 4.96507 + 1.22878i 0.211711 + 0.0523952i
\(551\) 6.75656 6.75656i 0.287839 0.287839i
\(552\) 0 0
\(553\) −0.353949 0.353949i −0.0150515 0.0150515i
\(554\) −5.27941 8.75195i −0.224301 0.371835i
\(555\) 0 0
\(556\) 23.1722 + 27.9120i 0.982719 + 1.18373i
\(557\) 15.9135 + 6.59160i 0.674278 + 0.279295i 0.693433 0.720521i \(-0.256097\pi\)
−0.0191546 + 0.999817i \(0.506097\pi\)
\(558\) 0 0
\(559\) 6.70345i 0.283526i
\(560\) −0.0796104 0.377845i −0.00336416 0.0159669i
\(561\) 0 0
\(562\) 24.3400 33.0133i 1.02672 1.39258i
\(563\) −6.34626 2.62871i −0.267463 0.110787i 0.244922 0.969543i \(-0.421238\pi\)
−0.512385 + 0.858756i \(0.671238\pi\)
\(564\) 0 0
\(565\) 10.2736 + 24.8027i 0.432214 + 1.04346i
\(566\) −34.8254 + 21.0076i −1.46382 + 0.883017i
\(567\) 0 0
\(568\) 4.91628 14.1164i 0.206282 0.592312i
\(569\) −19.2504 + 19.2504i −0.807017 + 0.807017i −0.984181 0.177164i \(-0.943308\pi\)
0.177164 + 0.984181i \(0.443308\pi\)
\(570\) 0 0
\(571\) 30.2725 12.5393i 1.26686 0.524752i 0.354855 0.934921i \(-0.384530\pi\)
0.912010 + 0.410169i \(0.134530\pi\)
\(572\) 3.19934 + 10.3360i 0.133771 + 0.432172i
\(573\) 0 0
\(574\) −0.420746 + 0.0636280i −0.0175616 + 0.00265578i
\(575\) 0.273765 0.0114168
\(576\) 0 0
\(577\) −11.8128 −0.491775 −0.245887 0.969298i \(-0.579079\pi\)
−0.245887 + 0.969298i \(0.579079\pi\)
\(578\) −11.7798 + 1.78143i −0.489977 + 0.0740976i
\(579\) 0 0
\(580\) −6.45879 20.8663i −0.268187 0.866426i
\(581\) −0.565990 + 0.234441i −0.0234812 + 0.00972624i
\(582\) 0 0
\(583\) 7.52804 7.52804i 0.311780 0.311780i
\(584\) 40.9496 + 14.2614i 1.69451 + 0.590140i
\(585\) 0 0
\(586\) 34.0232 20.5237i 1.40549 0.847827i
\(587\) −4.40174 10.6267i −0.181679 0.438613i 0.806634 0.591052i \(-0.201287\pi\)
−0.988313 + 0.152439i \(0.951287\pi\)
\(588\) 0 0
\(589\) 6.64909 + 2.75415i 0.273971 + 0.113483i
\(590\) −2.22739 + 3.02110i −0.0917000 + 0.124377i
\(591\) 0 0
\(592\) −4.54923 + 6.97796i −0.186972 + 0.286792i
\(593\) 39.4599i 1.62042i −0.586138 0.810211i \(-0.699352\pi\)
0.586138 0.810211i \(-0.300648\pi\)
\(594\) 0 0
\(595\) −0.261177 0.108183i −0.0107072 0.00443508i
\(596\) −16.9490 20.4159i −0.694259 0.836269i
\(597\) 0 0
\(598\) 0.299129 + 0.495882i 0.0122323 + 0.0202781i
\(599\) −28.7816 28.7816i −1.17598 1.17598i −0.980758 0.195226i \(-0.937456\pi\)
−0.195226 0.980758i \(-0.562544\pi\)
\(600\) 0 0
\(601\) 15.1839 15.1839i 0.619365 0.619365i −0.326003 0.945369i \(-0.605702\pi\)
0.945369 + 0.326003i \(0.105702\pi\)
\(602\) 0.234439 + 0.0580199i 0.00955500 + 0.00236471i
\(603\) 0 0
\(604\) −13.0391 6.87504i −0.530554 0.279741i
\(605\) −2.56961 + 6.20358i −0.104469 + 0.252211i
\(606\) 0 0
\(607\) −26.6639 −1.08226 −0.541128 0.840940i \(-0.682002\pi\)
−0.541128 + 0.840940i \(0.682002\pi\)
\(608\) 8.89221 3.32421i 0.360627 0.134815i
\(609\) 0 0
\(610\) 5.91700 + 39.1267i 0.239572 + 1.58419i
\(611\) −4.03495 + 9.74123i −0.163237 + 0.394088i
\(612\) 0 0
\(613\) −14.1048 + 5.84240i −0.569687 + 0.235972i −0.648885 0.760887i \(-0.724764\pi\)
0.0791973 + 0.996859i \(0.474764\pi\)
\(614\) −22.0595 5.45938i −0.890249 0.220323i
\(615\) 0 0
\(616\) 0.389172 0.0224291i 0.0156802 0.000903694i
\(617\) 14.1525 + 14.1525i 0.569758 + 0.569758i 0.932061 0.362302i \(-0.118009\pi\)
−0.362302 + 0.932061i \(0.618009\pi\)
\(618\) 0 0
\(619\) 5.05235 + 12.1975i 0.203071 + 0.490257i 0.992302 0.123839i \(-0.0395206\pi\)
−0.789231 + 0.614096i \(0.789521\pi\)
\(620\) 12.6584 10.5088i 0.508372 0.422044i
\(621\) 0 0
\(622\) 0.175407 + 0.129324i 0.00703319 + 0.00518541i
\(623\) 0.427203i 0.0171155i
\(624\) 0 0
\(625\) 16.6522i 0.666088i
\(626\) −21.1220 + 28.6486i −0.844205 + 1.14503i
\(627\) 0 0
\(628\) −0.804574 + 8.67137i −0.0321060 + 0.346025i
\(629\) 2.33375 + 5.63417i 0.0930527 + 0.224649i
\(630\) 0 0
\(631\) 23.2407 + 23.2407i 0.925199 + 0.925199i 0.997391 0.0721919i \(-0.0229994\pi\)
−0.0721919 + 0.997391i \(0.522999\pi\)
\(632\) −12.2432 25.3279i −0.487007 1.00749i
\(633\) 0 0
\(634\) 0.751997 3.03856i 0.0298656 0.120677i
\(635\) 6.83277 2.83023i 0.271150 0.112314i
\(636\) 0 0
\(637\) −5.29005 + 12.7713i −0.209599 + 0.506018i
\(638\) 21.8031 3.29721i 0.863193 0.130538i
\(639\) 0 0
\(640\) 2.75881 21.5253i 0.109052 0.850862i
\(641\) 33.3063 1.31552 0.657760 0.753227i \(-0.271504\pi\)
0.657760 + 0.753227i \(0.271504\pi\)
\(642\) 0 0
\(643\) −1.26433 + 3.05237i −0.0498605 + 0.120374i −0.946847 0.321684i \(-0.895751\pi\)
0.896987 + 0.442057i \(0.145751\pi\)
\(644\) 0.0199314 0.00616942i 0.000785408 0.000243109i
\(645\) 0 0
\(646\) 1.66966 6.74654i 0.0656920 0.265439i
\(647\) −22.1668 + 22.1668i −0.871465 + 0.871465i −0.992632 0.121167i \(-0.961336\pi\)
0.121167 + 0.992632i \(0.461336\pi\)
\(648\) 0 0
\(649\) −2.67935 2.67935i −0.105174 0.105174i
\(650\) 3.15945 1.90587i 0.123924 0.0747542i
\(651\) 0 0
\(652\) 2.85368 30.7558i 0.111759 1.20449i
\(653\) 43.2891 + 17.9309i 1.69403 + 0.701692i 0.999836 0.0180930i \(-0.00575950\pi\)
0.694197 + 0.719785i \(0.255759\pi\)
\(654\) 0 0
\(655\) 12.1595i 0.475110i
\(656\) −23.5068 4.40004i −0.917787 0.171793i
\(657\) 0 0
\(658\) 0.305755 + 0.225426i 0.0119196 + 0.00878802i
\(659\) 17.3613 + 7.19128i 0.676299 + 0.280132i 0.694279 0.719706i \(-0.255723\pi\)
−0.0179797 + 0.999838i \(0.505723\pi\)
\(660\) 0 0
\(661\) −19.0882 46.0829i −0.742444 1.79242i −0.595637 0.803254i \(-0.703100\pi\)
−0.146807 0.989165i \(-0.546900\pi\)
\(662\) 16.0424 + 26.5943i 0.623505 + 1.03362i
\(663\) 0 0
\(664\) −34.3728 + 1.98101i −1.33392 + 0.0768779i
\(665\) −0.114554 + 0.114554i −0.00444222 + 0.00444222i
\(666\) 0 0
\(667\) 1.09041 0.451661i 0.0422207 0.0174884i
\(668\) 12.0634 22.8794i 0.466749 0.885229i
\(669\) 0 0
\(670\) −1.18363 7.82683i −0.0457274 0.302377i
\(671\) −39.9483 −1.54219
\(672\) 0 0
\(673\) −26.2374 −1.01138 −0.505689 0.862716i \(-0.668762\pi\)
−0.505689 + 0.862716i \(0.668762\pi\)
\(674\) −0.108965 0.720542i −0.00419718 0.0277543i
\(675\) 0 0
\(676\) −16.0945 8.48606i −0.619021 0.326387i
\(677\) −28.0984 + 11.6387i −1.07991 + 0.447313i −0.850477 0.526012i \(-0.823687\pi\)
−0.229432 + 0.973325i \(0.573687\pi\)
\(678\) 0 0
\(679\) 0.131355 0.131355i 0.00504093 0.00504093i
\(680\) −11.8621 10.5693i −0.454891 0.405315i
\(681\) 0 0
\(682\) 8.57881 + 14.2215i 0.328500 + 0.544571i
\(683\) −11.2340 27.1214i −0.429859 1.03777i −0.979332 0.202259i \(-0.935172\pi\)
0.549473 0.835511i \(-0.314828\pi\)
\(684\) 0 0
\(685\) 4.78713 + 1.98289i 0.182907 + 0.0757625i
\(686\) 0.801869 + 0.591200i 0.0306155 + 0.0225721i
\(687\) 0 0
\(688\) 11.3702 + 7.41270i 0.433484 + 0.282607i
\(689\) 7.68004i 0.292586i
\(690\) 0 0
\(691\) −35.4669 14.6909i −1.34922 0.558867i −0.413148 0.910664i \(-0.635571\pi\)
−0.936076 + 0.351797i \(0.885571\pi\)
\(692\) 2.86461 + 0.265793i 0.108896 + 0.0101039i
\(693\) 0 0
\(694\) 27.5644 16.6275i 1.04633 0.631173i
\(695\) −24.6020 24.6020i −0.933207 0.933207i
\(696\) 0 0
\(697\) −12.3803 + 12.3803i −0.468937 + 0.468937i
\(698\) 8.23129 33.2598i 0.311559 1.25890i
\(699\) 0 0
\(700\) −0.0393077 0.126991i −0.00148569 0.00479980i
\(701\) −12.8945 + 31.1300i −0.487017 + 1.17576i 0.469197 + 0.883094i \(0.344543\pi\)
−0.956214 + 0.292669i \(0.905457\pi\)
\(702\) 0 0
\(703\) 3.49478 0.131808
\(704\) 21.0695 + 6.00302i 0.794087 + 0.226247i
\(705\) 0 0
\(706\) 27.1573 4.10692i 1.02208 0.154566i
\(707\) 0.271131 0.654568i 0.0101969 0.0246176i
\(708\) 0 0
\(709\) −37.5458 + 15.5520i −1.41006 + 0.584067i −0.952343 0.305029i \(-0.901334\pi\)
−0.457720 + 0.889096i \(0.651334\pi\)
\(710\) −3.44409 + 13.9164i −0.129255 + 0.522274i
\(711\) 0 0
\(712\) 7.89639 22.6734i 0.295930 0.849722i
\(713\) 0.628586 + 0.628586i 0.0235407 + 0.0235407i
\(714\) 0 0
\(715\) −3.97113 9.58716i −0.148512 0.358539i
\(716\) 40.9359 + 3.79824i 1.52985 + 0.141947i
\(717\) 0 0
\(718\) 14.1542 19.1980i 0.528231 0.716462i
\(719\) 17.6448i 0.658041i −0.944323 0.329020i \(-0.893282\pi\)
0.944323 0.329020i \(-0.106718\pi\)
\(720\) 0 0
\(721\) 1.00633i 0.0374776i
\(722\) 18.4216 + 13.5819i 0.685583 + 0.505464i
\(723\) 0 0
\(724\) 11.0581 + 13.3200i 0.410969 + 0.495033i
\(725\) −2.87771 6.94740i −0.106875 0.258020i
\(726\) 0 0
\(727\) 22.5497 + 22.5497i 0.836323 + 0.836323i 0.988373 0.152050i \(-0.0485874\pi\)
−0.152050 + 0.988373i \(0.548587\pi\)
\(728\) 0.187074 0.209956i 0.00693341 0.00778148i
\(729\) 0 0
\(730\) −40.3694 9.99080i −1.49414 0.369776i
\(731\) 9.18055 3.80271i 0.339555 0.140648i
\(732\) 0 0
\(733\) 16.6634 40.2290i 0.615476 1.48589i −0.241430 0.970418i \(-0.577616\pi\)
0.856906 0.515473i \(-0.172384\pi\)
\(734\) −1.34675 8.90548i −0.0497093 0.328707i
\(735\) 0 0
\(736\) 1.17188 + 0.0409749i 0.0431960 + 0.00151036i
\(737\) 7.99119 0.294359
\(738\) 0 0
\(739\) −8.54690 + 20.6340i −0.314403 + 0.759036i 0.685128 + 0.728422i \(0.259746\pi\)
−0.999531 + 0.0306134i \(0.990254\pi\)
\(740\) 3.72609 7.06685i 0.136974 0.259783i
\(741\) 0 0
\(742\) −0.268593 0.0664725i −0.00986034 0.00244028i
\(743\) 15.7640 15.7640i 0.578324 0.578324i −0.356118 0.934441i \(-0.615900\pi\)
0.934441 + 0.356118i \(0.115900\pi\)
\(744\) 0 0
\(745\) 17.9948 + 17.9948i 0.659280 + 0.659280i
\(746\) −11.8510 19.6461i −0.433897 0.719293i
\(747\) 0 0
\(748\) 12.3406 10.2450i 0.451216 0.374593i
\(749\) −0.386096 0.159926i −0.0141076 0.00584358i
\(750\) 0 0
\(751\) 6.97779i 0.254623i −0.991863 0.127312i \(-0.959365\pi\)
0.991863 0.127312i \(-0.0406348\pi\)
\(752\) 12.0609 + 17.6158i 0.439815 + 0.642383i
\(753\) 0 0
\(754\) 9.43978 12.8036i 0.343776 0.466278i
\(755\) 13.0612 + 5.41011i 0.475345 + 0.196894i
\(756\) 0 0
\(757\) 10.7333 + 25.9125i 0.390108 + 0.941805i 0.989915 + 0.141660i \(0.0452440\pi\)
−0.599807 + 0.800145i \(0.704756\pi\)
\(758\) 0.843525 0.508836i 0.0306382 0.0184818i
\(759\) 0 0
\(760\) −8.19727 + 3.96244i −0.297346 + 0.143733i
\(761\) −6.32305 + 6.32305i −0.229210 + 0.229210i −0.812363 0.583152i \(-0.801819\pi\)
0.583152 + 0.812363i \(0.301819\pi\)
\(762\) 0 0
\(763\) 0.142071 0.0588476i 0.00514331 0.00213043i
\(764\) 44.8044 13.8684i 1.62097 0.501742i
\(765\) 0 0
\(766\) −8.35241 + 1.26311i −0.301785 + 0.0456379i
\(767\) −2.73345 −0.0986992
\(768\) 0 0
\(769\) 9.25313 0.333676 0.166838 0.985984i \(-0.446644\pi\)
0.166838 + 0.985984i \(0.446644\pi\)
\(770\) −0.369661 + 0.0559026i −0.0133216 + 0.00201459i
\(771\) 0 0
\(772\) −4.93474 + 1.52746i −0.177605 + 0.0549745i
\(773\) 31.3565 12.9883i 1.12782 0.467157i 0.260778 0.965399i \(-0.416021\pi\)
0.867038 + 0.498242i \(0.166021\pi\)
\(774\) 0 0
\(775\) 4.00496 4.00496i 0.143862 0.143862i
\(776\) 9.39949 4.54358i 0.337422 0.163105i
\(777\) 0 0
\(778\) 23.0014 13.8751i 0.824642 0.497446i
\(779\) 3.83965 + 9.26972i 0.137570 + 0.332122i
\(780\) 0 0
\(781\) −13.3711 5.53848i −0.478455 0.198183i
\(782\) 0.509435 0.690968i 0.0182173 0.0247090i
\(783\) 0 0
\(784\) 15.8125 + 23.0954i 0.564733 + 0.824835i
\(785\) 8.35221i 0.298103i
\(786\) 0 0
\(787\) 16.1053 + 6.67103i 0.574092 + 0.237797i 0.650790 0.759258i \(-0.274438\pi\)
−0.0766981 + 0.997054i \(0.524438\pi\)
\(788\) 19.3666 16.0778i 0.689905 0.572749i