Properties

Label 3150.2.bp.f.899.2
Level 3150
Weight 2
Character 3150.899
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.2
Root \(-0.258819 - 0.965926i\)
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.f.1349.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} -1.00000 q^{8} +(1.32697 + 0.766125i) q^{11} +1.48236 q^{13} +(2.19067 - 1.48356i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.10342 + 1.21441i) q^{17} +(-4.21209 + 2.43185i) q^{19} +1.53225i q^{22} +(-0.133975 - 0.232051i) q^{23} +(0.741181 + 1.28376i) q^{26} +(2.38014 + 1.15539i) q^{28} +0.898979i q^{29} +(-0.717439 - 0.414214i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.42883i q^{34} +(4.74786 - 2.74118i) q^{37} +(-4.21209 - 2.43185i) q^{38} +8.76028 q^{41} +1.86370i q^{43} +(-1.32697 + 0.766125i) q^{44} +(0.133975 - 0.232051i) q^{46} +(6.46008 - 3.72973i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(-0.741181 + 1.28376i) q^{52} +(1.73508 - 3.00524i) q^{53} +(0.189469 + 2.63896i) q^{56} +(-0.778539 + 0.449490i) q^{58} +(3.12837 - 5.41849i) q^{59} +(5.73445 - 3.31079i) q^{61} -0.828427i q^{62} +1.00000 q^{64} +(13.8859 + 8.01702i) q^{67} +(-2.10342 + 1.21441i) q^{68} -12.7627i q^{71} +(-0.171573 + 0.297173i) q^{73} +(4.74786 + 2.74118i) q^{74} -4.86370i q^{76} +(1.77035 - 3.64697i) q^{77} +(-5.22438 - 9.04889i) q^{79} +(4.38014 + 7.58662i) q^{82} +5.45001i q^{83} +(-1.61401 + 0.931852i) q^{86} +(-1.32697 - 0.766125i) q^{88} +(7.98502 + 13.8305i) q^{89} +(-0.280861 - 3.91189i) q^{91} +0.267949 q^{92} +(6.46008 + 3.72973i) q^{94} +14.9481 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} + 24q^{11} + 16q^{13} - 4q^{16} + 24q^{17} - 8q^{23} + 8q^{26} + 4q^{32} + 32q^{41} - 24q^{44} + 8q^{46} + 12q^{47} - 8q^{52} + 4q^{53} + 24q^{59} + 8q^{64} + 48q^{67} - 24q^{68} - 24q^{73} - 4q^{77} + 24q^{79} + 16q^{82} - 24q^{88} + 16q^{89} - 20q^{91} + 16q^{92} + 12q^{94} - 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.189469 2.63896i −0.0716124 0.997433i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 1.32697 + 0.766125i 0.400096 + 0.230995i 0.686525 0.727106i \(-0.259135\pi\)
−0.286430 + 0.958101i \(0.592468\pi\)
\(12\) 0 0
\(13\) 1.48236 0.411133 0.205567 0.978643i \(-0.434096\pi\)
0.205567 + 0.978643i \(0.434096\pi\)
\(14\) 2.19067 1.48356i 0.585481 0.396499i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.10342 + 1.21441i 0.510155 + 0.294538i 0.732898 0.680339i \(-0.238167\pi\)
−0.222742 + 0.974877i \(0.571501\pi\)
\(18\) 0 0
\(19\) −4.21209 + 2.43185i −0.966320 + 0.557905i −0.898112 0.439766i \(-0.855061\pi\)
−0.0682075 + 0.997671i \(0.521728\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.53225i 0.326677i
\(23\) −0.133975 0.232051i −0.0279356 0.0483859i 0.851720 0.523998i \(-0.175560\pi\)
−0.879655 + 0.475612i \(0.842227\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.741181 + 1.28376i 0.145358 + 0.251767i
\(27\) 0 0
\(28\) 2.38014 + 1.15539i 0.449804 + 0.218349i
\(29\) 0.898979i 0.166936i 0.996510 + 0.0834681i \(0.0265997\pi\)
−0.996510 + 0.0834681i \(0.973400\pi\)
\(30\) 0 0
\(31\) −0.717439 0.414214i −0.128856 0.0743950i 0.434187 0.900823i \(-0.357036\pi\)
−0.563042 + 0.826428i \(0.690369\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.42883i 0.416540i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.74786 2.74118i 0.780544 0.450647i −0.0560790 0.998426i \(-0.517860\pi\)
0.836623 + 0.547779i \(0.184527\pi\)
\(38\) −4.21209 2.43185i −0.683291 0.394498i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.76028 1.36813 0.684063 0.729423i \(-0.260211\pi\)
0.684063 + 0.729423i \(0.260211\pi\)
\(42\) 0 0
\(43\) 1.86370i 0.284212i 0.989851 + 0.142106i \(0.0453874\pi\)
−0.989851 + 0.142106i \(0.954613\pi\)
\(44\) −1.32697 + 0.766125i −0.200048 + 0.115498i
\(45\) 0 0
\(46\) 0.133975 0.232051i 0.0197535 0.0342140i
\(47\) 6.46008 3.72973i 0.942299 0.544037i 0.0516191 0.998667i \(-0.483562\pi\)
0.890680 + 0.454630i \(0.150229\pi\)
\(48\) 0 0
\(49\) −6.92820 + 1.00000i −0.989743 + 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.741181 + 1.28376i −0.102783 + 0.178026i
\(53\) 1.73508 3.00524i 0.238331 0.412802i −0.721904 0.691993i \(-0.756733\pi\)
0.960236 + 0.279191i \(0.0900663\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.189469 + 2.63896i 0.0253188 + 0.352646i
\(57\) 0 0
\(58\) −0.778539 + 0.449490i −0.102227 + 0.0590209i
\(59\) 3.12837 5.41849i 0.407279 0.705428i −0.587305 0.809366i \(-0.699811\pi\)
0.994584 + 0.103938i \(0.0331444\pi\)
\(60\) 0 0
\(61\) 5.73445 3.31079i 0.734222 0.423903i −0.0857429 0.996317i \(-0.527326\pi\)
0.819965 + 0.572414i \(0.193993\pi\)
\(62\) 0.828427i 0.105210i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 13.8859 + 8.01702i 1.69643 + 0.979434i 0.949097 + 0.314985i \(0.102000\pi\)
0.747334 + 0.664449i \(0.231334\pi\)
\(68\) −2.10342 + 1.21441i −0.255078 + 0.147269i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7627i 1.51465i −0.653037 0.757326i \(-0.726505\pi\)
0.653037 0.757326i \(-0.273495\pi\)
\(72\) 0 0
\(73\) −0.171573 + 0.297173i −0.0200811 + 0.0347815i −0.875891 0.482508i \(-0.839726\pi\)
0.855810 + 0.517290i \(0.173059\pi\)
\(74\) 4.74786 + 2.74118i 0.551928 + 0.318656i
\(75\) 0 0
\(76\) 4.86370i 0.557905i
\(77\) 1.77035 3.64697i 0.201750 0.415611i
\(78\) 0 0
\(79\) −5.22438 9.04889i −0.587789 1.01808i −0.994521 0.104533i \(-0.966665\pi\)
0.406733 0.913547i \(-0.366668\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 4.38014 + 7.58662i 0.483705 + 0.837802i
\(83\) 5.45001i 0.598216i 0.954219 + 0.299108i \(0.0966891\pi\)
−0.954219 + 0.299108i \(0.903311\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.61401 + 0.931852i −0.174044 + 0.100484i
\(87\) 0 0
\(88\) −1.32697 0.766125i −0.141455 0.0816692i
\(89\) 7.98502 + 13.8305i 0.846411 + 1.46603i 0.884390 + 0.466748i \(0.154574\pi\)
−0.0379795 + 0.999279i \(0.512092\pi\)
\(90\) 0 0
\(91\) −0.280861 3.91189i −0.0294423 0.410078i
\(92\) 0.267949 0.0279356
\(93\) 0 0
\(94\) 6.46008 + 3.72973i 0.666306 + 0.384692i
\(95\) 0 0
\(96\) 0 0
\(97\) 14.9481 1.51775 0.758877 0.651234i \(-0.225748\pi\)
0.758877 + 0.651234i \(0.225748\pi\)
\(98\) −4.33013 5.50000i −0.437409 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) 1.36773 2.36897i 0.136094 0.235721i −0.789921 0.613209i \(-0.789878\pi\)
0.926015 + 0.377487i \(0.123212\pi\)
\(102\) 0 0
\(103\) −3.08845 5.34935i −0.304314 0.527087i 0.672794 0.739829i \(-0.265094\pi\)
−0.977108 + 0.212742i \(0.931760\pi\)
\(104\) −1.48236 −0.145358
\(105\) 0 0
\(106\) 3.47015 0.337051
\(107\) 2.28497 + 3.95768i 0.220896 + 0.382603i 0.955080 0.296347i \(-0.0957686\pi\)
−0.734184 + 0.678950i \(0.762435\pi\)
\(108\) 0 0
\(109\) −2.97934 + 5.16036i −0.285369 + 0.494273i −0.972699 0.232072i \(-0.925449\pi\)
0.687330 + 0.726345i \(0.258783\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.19067 + 1.48356i −0.206999 + 0.140184i
\(113\) 19.8977 1.87182 0.935911 0.352237i \(-0.114579\pi\)
0.935911 + 0.352237i \(0.114579\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.778539 0.449490i −0.0722855 0.0417341i
\(117\) 0 0
\(118\) 6.25674 0.575979
\(119\) 2.80625 5.78094i 0.257249 0.529938i
\(120\) 0 0
\(121\) −4.32611 7.49303i −0.393282 0.681185i
\(122\) 5.73445 + 3.31079i 0.519173 + 0.299745i
\(123\) 0 0
\(124\) 0.717439 0.414214i 0.0644279 0.0371975i
\(125\) 0 0
\(126\) 0 0
\(127\) 21.2025i 1.88142i 0.339219 + 0.940708i \(0.389837\pi\)
−0.339219 + 0.940708i \(0.610163\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.73085 6.46202i −0.325966 0.564589i 0.655742 0.754985i \(-0.272356\pi\)
−0.981707 + 0.190396i \(0.939023\pi\)
\(132\) 0 0
\(133\) 7.21561 + 10.6548i 0.625673 + 0.923886i
\(134\) 16.0340i 1.38513i
\(135\) 0 0
\(136\) −2.10342 1.21441i −0.180367 0.104135i
\(137\) 0.310789 0.538302i 0.0265525 0.0459903i −0.852444 0.522819i \(-0.824880\pi\)
0.878996 + 0.476829i \(0.158214\pi\)
\(138\) 0 0
\(139\) 18.5334i 1.57198i 0.618237 + 0.785992i \(0.287847\pi\)
−0.618237 + 0.785992i \(0.712153\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 11.0528 6.38134i 0.927531 0.535510i
\(143\) 1.96705 + 1.13567i 0.164493 + 0.0949699i
\(144\) 0 0
\(145\) 0 0
\(146\) −0.343146 −0.0283989
\(147\) 0 0
\(148\) 5.48236i 0.450647i
\(149\) 12.1100 6.99171i 0.992089 0.572783i 0.0861911 0.996279i \(-0.472530\pi\)
0.905898 + 0.423496i \(0.139197\pi\)
\(150\) 0 0
\(151\) −9.83839 + 17.0406i −0.800637 + 1.38674i 0.118560 + 0.992947i \(0.462172\pi\)
−0.919197 + 0.393797i \(0.871161\pi\)
\(152\) 4.21209 2.43185i 0.341646 0.197249i
\(153\) 0 0
\(154\) 4.04354 0.290313i 0.325838 0.0233941i
\(155\) 0 0
\(156\) 0 0
\(157\) −4.53005 + 7.84628i −0.361538 + 0.626201i −0.988214 0.153078i \(-0.951081\pi\)
0.626677 + 0.779279i \(0.284415\pi\)
\(158\) 5.22438 9.04889i 0.415629 0.719891i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.586988 + 0.397520i −0.0462612 + 0.0313289i
\(162\) 0 0
\(163\) 10.2368 5.91019i 0.801804 0.462922i −0.0422974 0.999105i \(-0.513468\pi\)
0.844102 + 0.536183i \(0.180134\pi\)
\(164\) −4.38014 + 7.58662i −0.342031 + 0.592416i
\(165\) 0 0
\(166\) −4.71984 + 2.72500i −0.366331 + 0.211501i
\(167\) 15.7778i 1.22092i −0.792046 0.610462i \(-0.790984\pi\)
0.792046 0.610462i \(-0.209016\pi\)
\(168\) 0 0
\(169\) −10.8026 −0.830969
\(170\) 0 0
\(171\) 0 0
\(172\) −1.61401 0.931852i −0.123067 0.0710530i
\(173\) 17.5129 10.1111i 1.33148 0.768730i 0.345954 0.938252i \(-0.387555\pi\)
0.985527 + 0.169521i \(0.0542221\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.53225i 0.115498i
\(177\) 0 0
\(178\) −7.98502 + 13.8305i −0.598503 + 1.03664i
\(179\) 5.94667 + 3.43331i 0.444475 + 0.256618i 0.705494 0.708716i \(-0.250725\pi\)
−0.261019 + 0.965334i \(0.584059\pi\)
\(180\) 0 0
\(181\) 16.3066i 1.21206i −0.795441 0.606031i \(-0.792761\pi\)
0.795441 0.606031i \(-0.207239\pi\)
\(182\) 3.24737 2.19918i 0.240711 0.163014i
\(183\) 0 0
\(184\) 0.133975 + 0.232051i 0.00987674 + 0.0171070i
\(185\) 0 0
\(186\) 0 0
\(187\) 1.86078 + 3.22297i 0.136074 + 0.235687i
\(188\) 7.45946i 0.544037i
\(189\) 0 0
\(190\) 0 0
\(191\) −14.8630 + 8.58114i −1.07545 + 0.620910i −0.929665 0.368407i \(-0.879903\pi\)
−0.145782 + 0.989317i \(0.546570\pi\)
\(192\) 0 0
\(193\) −7.84204 4.52761i −0.564483 0.325904i 0.190460 0.981695i \(-0.439002\pi\)
−0.754943 + 0.655791i \(0.772335\pi\)
\(194\) 7.47407 + 12.9455i 0.536607 + 0.929430i
\(195\) 0 0
\(196\) 2.59808 6.50000i 0.185577 0.464286i
\(197\) −21.7379 −1.54876 −0.774380 0.632720i \(-0.781938\pi\)
−0.774380 + 0.632720i \(0.781938\pi\)
\(198\) 0 0
\(199\) 7.21101 + 4.16328i 0.511175 + 0.295127i 0.733317 0.679887i \(-0.237971\pi\)
−0.222141 + 0.975014i \(0.571305\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.73545 0.192466
\(203\) 2.37237 0.170328i 0.166508 0.0119547i
\(204\) 0 0
\(205\) 0 0
\(206\) 3.08845 5.34935i 0.215182 0.372707i
\(207\) 0 0
\(208\) −0.741181 1.28376i −0.0513917 0.0890130i
\(209\) −7.45241 −0.515494
\(210\) 0 0
\(211\) −19.9330 −1.37225 −0.686123 0.727486i \(-0.740689\pi\)
−0.686123 + 0.727486i \(0.740689\pi\)
\(212\) 1.73508 + 3.00524i 0.119166 + 0.206401i
\(213\) 0 0
\(214\) −2.28497 + 3.95768i −0.156197 + 0.270541i
\(215\) 0 0
\(216\) 0 0
\(217\) −0.957160 + 1.97177i −0.0649763 + 0.133853i
\(218\) −5.95867 −0.403572
\(219\) 0 0
\(220\) 0 0
\(221\) 3.11804 + 1.80020i 0.209742 + 0.121094i
\(222\) 0 0
\(223\) 7.16604 0.479873 0.239937 0.970789i \(-0.422873\pi\)
0.239937 + 0.970789i \(0.422873\pi\)
\(224\) −2.38014 1.15539i −0.159030 0.0771980i
\(225\) 0 0
\(226\) 9.94887 + 17.2319i 0.661789 + 1.14625i
\(227\) 13.7303 + 7.92721i 0.911314 + 0.526147i 0.880854 0.473389i \(-0.156969\pi\)
0.0304601 + 0.999536i \(0.490303\pi\)
\(228\) 0 0
\(229\) −24.4371 + 14.1087i −1.61485 + 0.932332i −0.626622 + 0.779323i \(0.715563\pi\)
−0.988225 + 0.153009i \(0.951104\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.898979i 0.0590209i
\(233\) −12.1487 21.0421i −0.795886 1.37851i −0.922275 0.386534i \(-0.873672\pi\)
0.126390 0.991981i \(-0.459661\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.12837 + 5.41849i 0.203639 + 0.352714i
\(237\) 0 0
\(238\) 6.40957 0.460186i 0.415471 0.0298295i
\(239\) 19.9081i 1.28774i −0.765133 0.643872i \(-0.777327\pi\)
0.765133 0.643872i \(-0.222673\pi\)
\(240\) 0 0
\(241\) 17.7755 + 10.2627i 1.14502 + 0.661078i 0.947669 0.319255i \(-0.103433\pi\)
0.197351 + 0.980333i \(0.436766\pi\)
\(242\) 4.32611 7.49303i 0.278093 0.481670i
\(243\) 0 0
\(244\) 6.62158i 0.423903i
\(245\) 0 0
\(246\) 0 0
\(247\) −6.24384 + 3.60488i −0.397286 + 0.229373i
\(248\) 0.717439 + 0.414214i 0.0455574 + 0.0263026i
\(249\) 0 0
\(250\) 0 0
\(251\) 5.86787 0.370376 0.185188 0.982703i \(-0.440711\pi\)
0.185188 + 0.982703i \(0.440711\pi\)
\(252\) 0 0
\(253\) 0.410565i 0.0258120i
\(254\) −18.3619 + 10.6012i −1.15213 + 0.665181i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.63519 3.83083i 0.413892 0.238961i −0.278569 0.960416i \(-0.589860\pi\)
0.692461 + 0.721456i \(0.256527\pi\)
\(258\) 0 0
\(259\) −8.13343 12.0100i −0.505387 0.746268i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.73085 6.46202i 0.230493 0.399225i
\(263\) −4.23143 + 7.32905i −0.260921 + 0.451929i −0.966487 0.256716i \(-0.917360\pi\)
0.705566 + 0.708644i \(0.250693\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −5.61950 + 11.5763i −0.344553 + 0.709788i
\(267\) 0 0
\(268\) −13.8859 + 8.01702i −0.848215 + 0.489717i
\(269\) 8.52155 14.7598i 0.519568 0.899919i −0.480173 0.877174i \(-0.659426\pi\)
0.999741 0.0227449i \(-0.00724054\pi\)
\(270\) 0 0
\(271\) −9.12436 + 5.26795i −0.554265 + 0.320005i −0.750840 0.660484i \(-0.770351\pi\)
0.196575 + 0.980489i \(0.437018\pi\)
\(272\) 2.42883i 0.147269i
\(273\) 0 0
\(274\) 0.621578 0.0375509
\(275\) 0 0
\(276\) 0 0
\(277\) −7.00720 4.04561i −0.421022 0.243077i 0.274493 0.961589i \(-0.411490\pi\)
−0.695514 + 0.718512i \(0.744823\pi\)
\(278\) −16.0504 + 9.26670i −0.962639 + 0.555780i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1684i 0.666253i 0.942882 + 0.333127i \(0.108104\pi\)
−0.942882 + 0.333127i \(0.891896\pi\)
\(282\) 0 0
\(283\) 3.60796 6.24917i 0.214471 0.371475i −0.738638 0.674103i \(-0.764531\pi\)
0.953109 + 0.302628i \(0.0978639\pi\)
\(284\) 11.0528 + 6.38134i 0.655863 + 0.378663i
\(285\) 0 0
\(286\) 2.27135i 0.134308i
\(287\) −1.65980 23.1180i −0.0979748 1.36461i
\(288\) 0 0
\(289\) −5.55040 9.61358i −0.326494 0.565505i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.171573 0.297173i −0.0100405 0.0173907i
\(293\) 18.2573i 1.06660i 0.845926 + 0.533300i \(0.179048\pi\)
−0.845926 + 0.533300i \(0.820952\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.74786 + 2.74118i −0.275964 + 0.159328i
\(297\) 0 0
\(298\) 12.1100 + 6.99171i 0.701513 + 0.405019i
\(299\) −0.198599 0.343983i −0.0114853 0.0198931i
\(300\) 0 0
\(301\) 4.91824 0.353113i 0.283482 0.0203531i
\(302\) −19.6768 −1.13227
\(303\) 0 0
\(304\) 4.21209 + 2.43185i 0.241580 + 0.139476i
\(305\) 0 0
\(306\) 0 0
\(307\) −3.42078 −0.195234 −0.0976172 0.995224i \(-0.531122\pi\)
−0.0976172 + 0.995224i \(0.531122\pi\)
\(308\) 2.27319 + 3.35666i 0.129527 + 0.191263i
\(309\) 0 0
\(310\) 0 0
\(311\) −2.84544 + 4.92845i −0.161350 + 0.279467i −0.935353 0.353715i \(-0.884918\pi\)
0.774003 + 0.633182i \(0.218252\pi\)
\(312\) 0 0
\(313\) −6.67335 11.5586i −0.377200 0.653330i 0.613453 0.789731i \(-0.289780\pi\)
−0.990654 + 0.136401i \(0.956447\pi\)
\(314\) −9.06010 −0.511291
\(315\) 0 0
\(316\) 10.4488 0.587789
\(317\) 6.26330 + 10.8484i 0.351782 + 0.609305i 0.986562 0.163389i \(-0.0522424\pi\)
−0.634780 + 0.772693i \(0.718909\pi\)
\(318\) 0 0
\(319\) −0.688731 + 1.19292i −0.0385615 + 0.0667905i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.637756 0.309587i −0.0355408 0.0172526i
\(323\) −11.8131 −0.657298
\(324\) 0 0
\(325\) 0 0
\(326\) 10.2368 + 5.91019i 0.566961 + 0.327335i
\(327\) 0 0
\(328\) −8.76028 −0.483705
\(329\) −11.0666 16.3412i −0.610120 0.900920i
\(330\) 0 0
\(331\) 0.640916 + 1.11010i 0.0352279 + 0.0610166i 0.883102 0.469181i \(-0.155451\pi\)
−0.847874 + 0.530198i \(0.822118\pi\)
\(332\) −4.71984 2.72500i −0.259035 0.149554i
\(333\) 0 0
\(334\) 13.6640 7.88891i 0.747660 0.431662i
\(335\) 0 0
\(336\) 0 0
\(337\) 13.1058i 0.713920i 0.934120 + 0.356960i \(0.116187\pi\)
−0.934120 + 0.356960i \(0.883813\pi\)
\(338\) −5.40130 9.35533i −0.293792 0.508863i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.634679 1.09930i −0.0343698 0.0595302i
\(342\) 0 0
\(343\) 3.95164 + 18.0938i 0.213368 + 0.976972i
\(344\) 1.86370i 0.100484i
\(345\) 0 0
\(346\) 17.5129 + 10.1111i 0.941499 + 0.543574i
\(347\) 7.14262 12.3714i 0.383436 0.664130i −0.608115 0.793849i \(-0.708074\pi\)
0.991551 + 0.129719i \(0.0414074\pi\)
\(348\) 0 0
\(349\) 13.2713i 0.710399i 0.934791 + 0.355200i \(0.115587\pi\)
−0.934791 + 0.355200i \(0.884413\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.32697 0.766125i 0.0707276 0.0408346i
\(353\) 28.2725 + 16.3232i 1.50480 + 0.868794i 0.999985 + 0.00556437i \(0.00177120\pi\)
0.504811 + 0.863230i \(0.331562\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −15.9700 −0.846411
\(357\) 0 0
\(358\) 6.86662i 0.362912i
\(359\) −5.40692 + 3.12168i −0.285366 + 0.164756i −0.635850 0.771812i \(-0.719350\pi\)
0.350484 + 0.936569i \(0.386017\pi\)
\(360\) 0 0
\(361\) 2.32780 4.03188i 0.122516 0.212204i
\(362\) 14.1220 8.15331i 0.742233 0.428529i
\(363\) 0 0
\(364\) 3.52823 + 1.71271i 0.184929 + 0.0897705i
\(365\) 0 0
\(366\) 0 0
\(367\) 6.29461 10.9026i 0.328576 0.569110i −0.653654 0.756794i \(-0.726765\pi\)
0.982230 + 0.187684i \(0.0600980\pi\)
\(368\) −0.133975 + 0.232051i −0.00698391 + 0.0120965i
\(369\) 0 0
\(370\) 0 0
\(371\) −8.25945 4.00940i −0.428809 0.208158i
\(372\) 0 0
\(373\) 31.1408 17.9791i 1.61241 0.930924i 0.623598 0.781745i \(-0.285670\pi\)
0.988810 0.149179i \(-0.0476631\pi\)
\(374\) −1.86078 + 3.22297i −0.0962188 + 0.166656i
\(375\) 0 0
\(376\) −6.46008 + 3.72973i −0.333153 + 0.192346i
\(377\) 1.33261i 0.0686331i
\(378\) 0 0
\(379\) 11.5899 0.595331 0.297666 0.954670i \(-0.403792\pi\)
0.297666 + 0.954670i \(0.403792\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −14.8630 8.58114i −0.760456 0.439049i
\(383\) −3.86897 + 2.23375i −0.197695 + 0.114139i −0.595580 0.803296i \(-0.703078\pi\)
0.397885 + 0.917435i \(0.369744\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.05521i 0.460898i
\(387\) 0 0
\(388\) −7.47407 + 12.9455i −0.379438 + 0.657207i
\(389\) 11.2197 + 6.47772i 0.568863 + 0.328433i 0.756695 0.653768i \(-0.226813\pi\)
−0.187832 + 0.982201i \(0.560146\pi\)
\(390\) 0 0
\(391\) 0.650802i 0.0329125i
\(392\) 6.92820 1.00000i 0.349927 0.0505076i
\(393\) 0 0
\(394\) −10.8689 18.8256i −0.547570 0.948418i
\(395\) 0 0
\(396\) 0 0
\(397\) −4.63995 8.03664i −0.232873 0.403347i 0.725780 0.687927i \(-0.241479\pi\)
−0.958652 + 0.284580i \(0.908146\pi\)
\(398\) 8.32656i 0.417373i
\(399\) 0 0
\(400\) 0 0
\(401\) −6.44260 + 3.71964i −0.321728 + 0.185750i −0.652163 0.758079i \(-0.726138\pi\)
0.330434 + 0.943829i \(0.392805\pi\)
\(402\) 0 0
\(403\) −1.06350 0.614014i −0.0529769 0.0305862i
\(404\) 1.36773 + 2.36897i 0.0680469 + 0.117861i
\(405\) 0 0
\(406\) 1.33369 + 1.96937i 0.0661901 + 0.0977381i
\(407\) 8.40035 0.416390
\(408\) 0 0
\(409\) 13.8647 + 8.00481i 0.685567 + 0.395812i 0.801949 0.597392i \(-0.203796\pi\)
−0.116382 + 0.993204i \(0.537130\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 6.17690 0.304314
\(413\) −14.8919 7.22900i −0.732783 0.355716i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.741181 1.28376i 0.0363394 0.0629417i
\(417\) 0 0
\(418\) −3.72620 6.45398i −0.182255 0.315674i
\(419\) −28.4419 −1.38948 −0.694738 0.719263i \(-0.744480\pi\)
−0.694738 + 0.719263i \(0.744480\pi\)
\(420\) 0 0
\(421\) 17.8345 0.869199 0.434600 0.900624i \(-0.356890\pi\)
0.434600 + 0.900624i \(0.356890\pi\)
\(422\) −9.96651 17.2625i −0.485162 0.840325i
\(423\) 0 0
\(424\) −1.73508 + 3.00524i −0.0842628 + 0.145947i
\(425\) 0 0
\(426\) 0 0
\(427\) −9.82353 14.5057i −0.475394 0.701980i
\(428\) −4.56993 −0.220896
\(429\) 0 0
\(430\) 0 0
\(431\) −26.7539 15.4464i −1.28869 0.744025i −0.310268 0.950649i \(-0.600419\pi\)
−0.978420 + 0.206624i \(0.933752\pi\)
\(432\) 0 0
\(433\) −15.2207 −0.731462 −0.365731 0.930721i \(-0.619181\pi\)
−0.365731 + 0.930721i \(0.619181\pi\)
\(434\) −2.18618 + 0.156961i −0.104940 + 0.00753437i
\(435\) 0 0
\(436\) −2.97934 5.16036i −0.142684 0.247136i
\(437\) 1.12863 + 0.651613i 0.0539895 + 0.0311709i
\(438\) 0 0
\(439\) −12.4054 + 7.16228i −0.592079 + 0.341837i −0.765919 0.642937i \(-0.777716\pi\)
0.173840 + 0.984774i \(0.444382\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3.60040i 0.171253i
\(443\) −2.57874 4.46651i −0.122520 0.212210i 0.798241 0.602338i \(-0.205764\pi\)
−0.920761 + 0.390128i \(0.872431\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3.58302 + 6.20597i 0.169661 + 0.293861i
\(447\) 0 0
\(448\) −0.189469 2.63896i −0.00895155 0.124679i
\(449\) 19.9377i 0.940918i −0.882422 0.470459i \(-0.844088\pi\)
0.882422 0.470459i \(-0.155912\pi\)
\(450\) 0 0
\(451\) 11.6246 + 6.71147i 0.547381 + 0.316031i
\(452\) −9.94887 + 17.2319i −0.467955 + 0.810522i
\(453\) 0 0
\(454\) 15.8544i 0.744085i
\(455\) 0 0
\(456\) 0 0
\(457\) −9.82065 + 5.66995i −0.459391 + 0.265229i −0.711788 0.702394i \(-0.752114\pi\)
0.252397 + 0.967624i \(0.418781\pi\)
\(458\) −24.4371 14.1087i −1.14187 0.659258i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.01890 0.0940298 0.0470149 0.998894i \(-0.485029\pi\)
0.0470149 + 0.998894i \(0.485029\pi\)
\(462\) 0 0
\(463\) 27.2844i 1.26801i −0.773327 0.634007i \(-0.781409\pi\)
0.773327 0.634007i \(-0.218591\pi\)
\(464\) 0.778539 0.449490i 0.0361428 0.0208670i
\(465\) 0 0
\(466\) 12.1487 21.0421i 0.562776 0.974757i
\(467\) −0.599403 + 0.346065i −0.0277370 + 0.0160140i −0.513804 0.857907i \(-0.671764\pi\)
0.486067 + 0.873921i \(0.338431\pi\)
\(468\) 0 0
\(469\) 18.5256 38.1632i 0.855434 1.76221i
\(470\) 0 0
\(471\) 0 0
\(472\) −3.12837 + 5.41849i −0.143995 + 0.249406i
\(473\) −1.42783 + 2.47307i −0.0656517 + 0.113712i
\(474\) 0 0
\(475\) 0 0
\(476\) 3.60332 + 5.32076i 0.165158 + 0.243876i
\(477\) 0 0
\(478\) 17.2409 9.95403i 0.788580 0.455287i
\(479\) 7.95403 13.7768i 0.363429 0.629477i −0.625094 0.780550i \(-0.714939\pi\)
0.988523 + 0.151072i \(0.0482727\pi\)
\(480\) 0 0
\(481\) 7.03805 4.06342i 0.320908 0.185276i
\(482\) 20.5254i 0.934905i
\(483\) 0 0
\(484\) 8.65221 0.393282
\(485\) 0 0
\(486\) 0 0
\(487\) −24.8981 14.3749i −1.12824 0.651390i −0.184749 0.982786i \(-0.559147\pi\)
−0.943492 + 0.331396i \(0.892480\pi\)
\(488\) −5.73445 + 3.31079i −0.259587 + 0.149872i
\(489\) 0 0
\(490\) 0 0
\(491\) 5.45753i 0.246295i −0.992388 0.123148i \(-0.960701\pi\)
0.992388 0.123148i \(-0.0392988\pi\)
\(492\) 0 0
\(493\) −1.09173 + 1.89094i −0.0491691 + 0.0851635i
\(494\) −6.24384 3.60488i −0.280924 0.162191i
\(495\) 0 0
\(496\) 0.828427i 0.0371975i
\(497\) −33.6802 + 2.41813i −1.51076 + 0.108468i
\(498\) 0 0
\(499\) −4.43148 7.67555i −0.198380 0.343605i 0.749623 0.661865i \(-0.230235\pi\)
−0.948003 + 0.318260i \(0.896901\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 2.93393 + 5.08172i 0.130948 + 0.226808i
\(503\) 9.36536i 0.417581i −0.977960 0.208790i \(-0.933047\pi\)
0.977960 0.208790i \(-0.0669526\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.355560 0.205283i 0.0158066 0.00912592i
\(507\) 0 0
\(508\) −18.3619 10.6012i −0.814677 0.470354i
\(509\) 17.5164 + 30.3393i 0.776400 + 1.34477i 0.934004 + 0.357263i \(0.116290\pi\)
−0.157603 + 0.987502i \(0.550377\pi\)
\(510\) 0 0
\(511\) 0.816735 + 0.396469i 0.0361302 + 0.0175387i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.63519 + 3.83083i 0.292666 + 0.168971i
\(515\) 0 0
\(516\) 0 0
\(517\) 11.4298 0.502680
\(518\) 6.33429 13.0488i 0.278313 0.573331i
\(519\) 0 0
\(520\) 0 0
\(521\) 9.99807 17.3172i 0.438023 0.758679i −0.559514 0.828821i \(-0.689012\pi\)
0.997537 + 0.0701424i \(0.0223454\pi\)
\(522\) 0 0
\(523\) −16.7515 29.0144i −0.732491 1.26871i −0.955816 0.293967i \(-0.905024\pi\)
0.223325 0.974744i \(-0.428309\pi\)
\(524\) 7.46170 0.325966
\(525\) 0 0
\(526\) −8.46286 −0.368998
\(527\) −1.00605 1.74253i −0.0438243 0.0759060i
\(528\) 0 0
\(529\) 11.4641 19.8564i 0.498439 0.863322i
\(530\) 0 0
\(531\) 0 0
\(532\) −12.8351 + 0.921519i −0.556473 + 0.0399529i
\(533\) 12.9859 0.562482
\(534\) 0 0
\(535\) 0 0
\(536\) −13.8859 8.01702i −0.599779 0.346282i
\(537\) 0 0
\(538\) 17.0431 0.734781
\(539\) −9.95962 3.98090i −0.428991 0.171470i
\(540\) 0 0
\(541\) −18.8766 32.6952i −0.811568 1.40568i −0.911766 0.410710i \(-0.865281\pi\)
0.100198 0.994967i \(-0.468052\pi\)
\(542\) −9.12436 5.26795i −0.391925 0.226278i
\(543\) 0 0
\(544\) 2.10342 1.21441i 0.0901836 0.0520675i
\(545\) 0 0
\(546\) 0 0
\(547\) 5.07130i 0.216833i −0.994106 0.108417i \(-0.965422\pi\)
0.994106 0.108417i \(-0.0345780\pi\)
\(548\) 0.310789 + 0.538302i 0.0132762 + 0.0229951i
\(549\) 0 0
\(550\) 0 0
\(551\) −2.18618 3.78658i −0.0931346 0.161314i
\(552\) 0 0
\(553\) −22.8898 + 15.5014i −0.973373 + 0.659187i
\(554\) 8.09122i 0.343763i
\(555\) 0 0
\(556\) −16.0504 9.26670i −0.680689 0.392996i
\(557\) −17.1778 + 29.7528i −0.727846 + 1.26067i 0.229946 + 0.973203i \(0.426145\pi\)
−0.957792 + 0.287463i \(0.907188\pi\)
\(558\) 0 0
\(559\) 2.76268i 0.116849i
\(560\) 0 0
\(561\) 0 0
\(562\) −9.67215 + 5.58422i −0.407995 + 0.235556i
\(563\) 40.7539 + 23.5293i 1.71757 + 0.991641i 0.923300 + 0.384079i \(0.125481\pi\)
0.794272 + 0.607562i \(0.207852\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 7.21592 0.303308
\(567\) 0 0
\(568\) 12.7627i 0.535510i
\(569\) −38.2670 + 22.0934i −1.60424 + 0.926206i −0.613608 + 0.789611i \(0.710283\pi\)
−0.990627 + 0.136595i \(0.956384\pi\)
\(570\) 0 0
\(571\) −20.5804 + 35.6463i −0.861263 + 1.49175i 0.00944654 + 0.999955i \(0.496993\pi\)
−0.870710 + 0.491797i \(0.836340\pi\)
\(572\) −1.96705 + 1.13567i −0.0822463 + 0.0474849i
\(573\) 0 0
\(574\) 19.1909 12.9964i 0.801012 0.542461i
\(575\) 0 0
\(576\) 0 0
\(577\) 7.06058 12.2293i 0.293936 0.509112i −0.680801 0.732469i \(-0.738368\pi\)
0.974737 + 0.223357i \(0.0717014\pi\)
\(578\) 5.55040 9.61358i 0.230866 0.399872i
\(579\) 0 0
\(580\) 0 0
\(581\) 14.3823 1.03261i 0.596680 0.0428397i
\(582\) 0 0
\(583\) 4.60478 2.65857i 0.190711 0.110107i
\(584\) 0.171573 0.297173i 0.00709974 0.0122971i
\(585\) 0 0
\(586\) −15.8112 + 9.12863i −0.653156 + 0.377100i
\(587\) 37.7819i 1.55942i 0.626138 + 0.779712i \(0.284635\pi\)
−0.626138 + 0.779712i \(0.715365\pi\)
\(588\) 0 0
\(589\) 4.02922 0.166021
\(590\) 0 0
\(591\) 0 0
\(592\) −4.74786 2.74118i −0.195136 0.112662i
\(593\) −22.6865 + 13.0981i −0.931623 + 0.537873i −0.887324 0.461146i \(-0.847438\pi\)
−0.0442982 + 0.999018i \(0.514105\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 13.9834i 0.572783i
\(597\) 0 0
\(598\) 0.198599 0.343983i 0.00812131 0.0140665i
\(599\) −4.15712 2.40012i −0.169856 0.0980661i 0.412662 0.910884i \(-0.364599\pi\)
−0.582518 + 0.812818i \(0.697932\pi\)
\(600\) 0 0
\(601\) 37.3722i 1.52444i 0.647317 + 0.762221i \(0.275891\pi\)
−0.647317 + 0.762221i \(0.724109\pi\)
\(602\) 2.76492 + 4.08276i 0.112690 + 0.166401i
\(603\) 0 0
\(604\) −9.83839 17.0406i −0.400319 0.693372i
\(605\) 0 0
\(606\) 0 0
\(607\) −18.6195 32.2499i −0.755742 1.30898i −0.945005 0.327057i \(-0.893943\pi\)
0.189263 0.981927i \(-0.439390\pi\)
\(608\) 4.86370i 0.197249i
\(609\) 0 0
\(610\) 0 0
\(611\) 9.57618 5.52881i 0.387411 0.223672i
\(612\) 0 0
\(613\) 8.53861 + 4.92977i 0.344871 + 0.199112i 0.662424 0.749129i \(-0.269528\pi\)
−0.317553 + 0.948241i \(0.602861\pi\)
\(614\) −1.71039 2.96248i −0.0690258 0.119556i
\(615\) 0 0
\(616\) −1.77035 + 3.64697i −0.0713296 + 0.146941i
\(617\) −31.3545 −1.26229 −0.631143 0.775666i \(-0.717414\pi\)
−0.631143 + 0.775666i \(0.717414\pi\)
\(618\) 0 0
\(619\) 13.1943 + 7.61774i 0.530325 + 0.306183i 0.741149 0.671341i \(-0.234281\pi\)
−0.210824 + 0.977524i \(0.567615\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −5.69089 −0.228184
\(623\) 34.9851 23.6926i 1.40165 0.949223i
\(624\) 0 0
\(625\) 0 0
\(626\) 6.67335 11.5586i 0.266721 0.461974i
\(627\) 0 0
\(628\) −4.53005 7.84628i −0.180769 0.313101i
\(629\) 13.3157 0.530932
\(630\) 0 0
\(631\) −1.00406 −0.0399710 −0.0199855 0.999800i \(-0.506362\pi\)
−0.0199855 + 0.999800i \(0.506362\pi\)
\(632\) 5.22438 + 9.04889i 0.207815 + 0.359946i
\(633\) 0 0
\(634\) −6.26330 + 10.8484i −0.248748 + 0.430844i
\(635\) 0 0
\(636\) 0 0
\(637\) −10.2701 + 1.48236i −0.406916 + 0.0587333i
\(638\) −1.37746 −0.0545342
\(639\) 0 0
\(640\) 0 0
\(641\) 20.2689 + 11.7023i 0.800574 + 0.462211i 0.843672 0.536860i \(-0.180389\pi\)
−0.0430981 + 0.999071i \(0.513723\pi\)
\(642\) 0 0
\(643\) −33.4475 −1.31904 −0.659521 0.751686i \(-0.729241\pi\)
−0.659521 + 0.751686i \(0.729241\pi\)
\(644\) −0.0507680 0.707107i −0.00200054 0.0278639i
\(645\) 0 0
\(646\) −5.90654 10.2304i −0.232390 0.402511i
\(647\) −14.3507 8.28540i −0.564185 0.325733i 0.190638 0.981660i \(-0.438944\pi\)
−0.754824 + 0.655928i \(0.772278\pi\)
\(648\) 0 0
\(649\) 8.30249 4.79344i 0.325901 0.188159i
\(650\) 0 0
\(651\) 0 0
\(652\) 11.8204i 0.462922i
\(653\) −3.01453 5.22132i −0.117968 0.204326i 0.800994 0.598672i \(-0.204305\pi\)
−0.918962 + 0.394346i \(0.870971\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.38014 7.58662i −0.171016 0.296208i
\(657\) 0 0
\(658\) 8.61862 17.7545i 0.335989 0.692144i
\(659\) 36.3672i 1.41666i −0.705880 0.708332i \(-0.749448\pi\)
0.705880 0.708332i \(-0.250552\pi\)
\(660\) 0 0
\(661\) −9.90289 5.71744i −0.385178 0.222383i 0.294891 0.955531i \(-0.404717\pi\)
−0.680069 + 0.733148i \(0.738050\pi\)
\(662\) −0.640916 + 1.11010i −0.0249099 + 0.0431452i
\(663\) 0 0
\(664\) 5.45001i 0.211501i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.208609 0.120440i 0.00807737 0.00466347i
\(668\) 13.6640 + 7.88891i 0.528675 + 0.305231i
\(669\) 0 0
\(670\) 0 0
\(671\) 10.1459 0.391679
\(672\) 0 0
\(673\) 10.8070i 0.416581i 0.978067 + 0.208290i \(0.0667899\pi\)
−0.978067 + 0.208290i \(0.933210\pi\)
\(674\) −11.3500 + 6.55291i −0.437185 + 0.252409i
\(675\) 0 0
\(676\) 5.40130 9.35533i 0.207742 0.359820i
\(677\) −12.1638 + 7.02280i −0.467494 + 0.269908i −0.715190 0.698930i \(-0.753660\pi\)
0.247696 + 0.968838i \(0.420327\pi\)
\(678\) 0 0
\(679\) −2.83220 39.4475i −0.108690 1.51386i
\(680\) 0 0
\(681\) 0 0
\(682\) 0.634679 1.09930i 0.0243031 0.0420942i
\(683\) −18.2385 + 31.5900i −0.697877 + 1.20876i 0.271324 + 0.962488i \(0.412539\pi\)
−0.969201 + 0.246271i \(0.920795\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −13.6938 + 12.4691i −0.522834 + 0.476073i
\(687\) 0 0
\(688\) 1.61401 0.931852i 0.0615337 0.0355265i
\(689\) 2.57201 4.45486i 0.0979859 0.169716i
\(690\) 0 0
\(691\) −20.5831 + 11.8836i −0.783017 + 0.452075i −0.837498 0.546440i \(-0.815983\pi\)
0.0544816 + 0.998515i \(0.482649\pi\)
\(692\) 20.2221i 0.768730i
\(693\) 0 0
\(694\) 14.2852 0.542260
\(695\) 0 0
\(696\) 0 0
\(697\) 18.4266 + 10.6386i 0.697957 + 0.402965i
\(698\) −11.4933 + 6.63567i −0.435029 + 0.251164i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.74502i 0.0659086i −0.999457 0.0329543i \(-0.989508\pi\)
0.999457 0.0329543i \(-0.0104916\pi\)
\(702\) 0 0
\(703\) −13.3323 + 23.0922i −0.502837 + 0.870939i
\(704\) 1.32697 + 0.766125i 0.0500120 + 0.0288744i
\(705\) 0 0
\(706\) 32.6463i 1.22866i
\(707\) −6.51075 3.16052i −0.244862 0.118864i
\(708\) 0 0
\(709\) −6.06162 10.4990i −0.227649 0.394299i 0.729462 0.684021i \(-0.239770\pi\)
−0.957111 + 0.289722i \(0.906437\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −7.98502 13.8305i −0.299251 0.518319i
\(713\) 0.221976i 0.00831308i
\(714\) 0 0
\(715\) 0 0
\(716\) −5.94667 + 3.43331i −0.222237 + 0.128309i
\(717\) 0 0
\(718\) −5.40692 3.12168i −0.201784 0.116500i
\(719\) −0.893176 1.54703i −0.0333098 0.0576943i 0.848890 0.528570i \(-0.177271\pi\)
−0.882200 + 0.470875i \(0.843938\pi\)
\(720\) 0 0
\(721\) −13.5315 + 9.16382i −0.503941 + 0.341279i
\(722\) 4.65561 0.173264
\(723\) 0 0
\(724\) 14.1220 + 8.15331i 0.524838 + 0.303015i
\(725\) 0 0
\(726\) 0 0
\(727\) −29.8785 −1.10813 −0.554066 0.832472i \(-0.686925\pi\)
−0.554066 + 0.832472i \(0.686925\pi\)
\(728\) 0.280861 + 3.91189i 0.0104094 + 0.144984i
\(729\) 0 0
\(730\) 0 0
\(731\) −2.26330 + 3.92016i −0.0837114 + 0.144992i
\(732\) 0 0
\(733\) −6.89554 11.9434i −0.254692 0.441140i 0.710119 0.704081i \(-0.248641\pi\)
−0.964812 + 0.262941i \(0.915308\pi\)
\(734\) 12.5892 0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) 12.2841 + 21.2766i 0.452490 + 0.783735i
\(738\) 0 0
\(739\) 3.68349 6.37999i 0.135499 0.234692i −0.790289 0.612735i \(-0.790069\pi\)
0.925788 + 0.378043i \(0.123403\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.657486 9.15759i −0.0241371 0.336186i
\(743\) −11.0774 −0.406389 −0.203194 0.979138i \(-0.565132\pi\)
−0.203194 + 0.979138i \(0.565132\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 31.1408 + 17.9791i 1.14014 + 0.658263i
\(747\) 0 0
\(748\) −3.72157 −0.136074
\(749\) 10.0112 6.77978i 0.365802 0.247728i
\(750\) 0 0
\(751\) −12.1879 21.1100i −0.444741 0.770315i 0.553293 0.832987i \(-0.313371\pi\)
−0.998034 + 0.0626722i \(0.980038\pi\)
\(752\) −6.46008 3.72973i −0.235575 0.136009i
\(753\) 0 0
\(754\) −1.15408 + 0.666306i −0.0420290 + 0.0242655i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.6761i 0.715139i −0.933887 0.357569i \(-0.883606\pi\)
0.933887 0.357569i \(-0.116394\pi\)
\(758\) 5.79493 + 10.0371i 0.210481 + 0.364565i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.9168 + 43.1572i 0.903234 + 1.56445i 0.823270 + 0.567650i \(0.192147\pi\)
0.0799647 + 0.996798i \(0.474519\pi\)
\(762\) 0 0
\(763\) 14.1825 + 6.88462i 0.513440 + 0.249240i
\(764\) 17.1623i 0.620910i
\(765\) 0 0
\(766\) −3.86897 2.23375i −0.139792 0.0807087i
\(767\) 4.63737 8.03217i 0.167446 0.290025i
\(768\) 0 0
\(769\) 31.0584i 1.12000i −0.828494 0.559998i \(-0.810802\pi\)
0.828494 0.559998i \(-0.189198\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.84204 4.52761i 0.282241 0.162952i
\(773\) 3.43855 + 1.98525i 0.123676 + 0.0714043i 0.560562 0.828113i \(-0.310585\pi\)
−0.436886 + 0.899517i \(0.643919\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −14.9481 −0.536607
\(777\) 0 0
\(778\) 12.9554i 0.464475i
\(779\) −36.8991 + 21.3037i −1.32205 + 0.763284i
\(780\) 0 0
\(781\) 9.77781 16.9357i 0.349878 0.606006i
\(782\) 0.563611 0.325401i 0.0201547 0.0116363i
\(783\) 0 0
\(784\) 4.33013 + 5.50000i 0.154647 + 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) 22.4013 38.8001i 0.798519 1.38308i −0.122061 0.992523i \(-0.538950\pi\)
0.920580 0.390553i \(-0.127716\pi\)
\(788\) 10.8689 18.8256i 0.387190 0.670633i
\(789\) 0 0
\(790\) 0 0
\(791\) −3.77000 52.5093i −0.134046 1.86702i
\(792\) 0 0
\(793\) 8.50054 4.90779i 0.301863 0.174281i
\(794\) 4.63995 8.03664i 0.164666 0.285210i
\(795\) 0 0
\(796\) −7.21101 + 4.16328i −0.255588 + 0.147564i