Properties

Label 3150.2.bf.b.1151.1
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), 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 1151.1
Root \(0.258819 + 0.965926i\)
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.b.1601.1

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.63896 + 0.189469i −0.997433 + 0.0716124i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.32697 0.766125i −0.400096 0.230995i 0.286430 0.958101i \(-0.407532\pi\)
−0.686525 + 0.727106i \(0.740865\pi\)
\(12\) 0 0
\(13\) 1.48236i 0.411133i 0.978643 + 0.205567i \(0.0659037\pi\)
−0.978643 + 0.205567i \(0.934096\pi\)
\(14\) 2.19067 1.48356i 0.585481 0.396499i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.21441 + 2.10342i −0.294538 + 0.510155i −0.974877 0.222742i \(-0.928499\pi\)
0.680339 + 0.732898i \(0.261833\pi\)
\(18\) 0 0
\(19\) 4.21209 2.43185i 0.966320 0.557905i 0.0682075 0.997671i \(-0.478272\pi\)
0.898112 + 0.439766i \(0.144939\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.53225 0.326677
\(23\) −0.232051 + 0.133975i −0.0483859 + 0.0279356i −0.523998 0.851720i \(-0.675560\pi\)
0.475612 + 0.879655i \(0.342227\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −0.741181 1.28376i −0.145358 0.251767i
\(27\) 0 0
\(28\) −1.15539 + 2.38014i −0.218349 + 0.449804i
\(29\) 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 \(0.690369\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 2.42883i 0.416540i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.74118 4.74786i −0.450647 0.780544i 0.547779 0.836623i \(-0.315473\pi\)
−0.998426 + 0.0560790i \(0.982140\pi\)
\(38\) −2.43185 + 4.21209i −0.394498 + 0.683291i
\(39\) 0 0
\(40\) 0 0
\(41\) −8.76028 −1.36813 −0.684063 0.729423i \(-0.739789\pi\)
−0.684063 + 0.729423i \(0.739789\pi\)
\(42\) 0 0
\(43\) −1.86370 −0.284212 −0.142106 0.989851i \(-0.545387\pi\)
−0.142106 + 0.989851i \(0.545387\pi\)
\(44\) −1.32697 + 0.766125i −0.200048 + 0.115498i
\(45\) 0 0
\(46\) 0.133975 0.232051i 0.0197535 0.0342140i
\(47\) 3.72973 + 6.46008i 0.544037 + 0.942299i 0.998667 + 0.0516191i \(0.0164382\pi\)
−0.454630 + 0.890680i \(0.650229\pi\)
\(48\) 0 0
\(49\) 6.92820 1.00000i 0.989743 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.28376 + 0.741181i 0.178026 + 0.102783i
\(53\) −3.00524 1.73508i −0.412802 0.238331i 0.279191 0.960236i \(-0.409934\pi\)
−0.691993 + 0.721904i \(0.743267\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.189469 2.63896i −0.0253188 0.352646i
\(57\) 0 0
\(58\) −0.449490 0.778539i −0.0590209 0.102227i
\(59\) 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 \(0.193993\pi\)
\(62\) 0.828427 0.105210
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.01702 13.8859i 0.979434 1.69643i 0.314985 0.949097i \(-0.398000\pi\)
0.664449 0.747334i \(-0.268666\pi\)
\(68\) 1.21441 + 2.10342i 0.147269 + 0.255078i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7627i 1.51465i 0.653037 + 0.757326i \(0.273495\pi\)
−0.653037 + 0.757326i \(0.726505\pi\)
\(72\) 0 0
\(73\) −0.297173 0.171573i −0.0347815 0.0200811i 0.482508 0.875891i \(-0.339726\pi\)
−0.517290 + 0.855810i \(0.673059\pi\)
\(74\) 4.74786 + 2.74118i 0.551928 + 0.318656i
\(75\) 0 0
\(76\) 4.86370i 0.557905i
\(77\) 3.64697 + 1.77035i 0.415611 + 0.201750i
\(78\) 0 0
\(79\) 5.22438 + 9.04889i 0.587789 + 1.01808i 0.994521 + 0.104533i \(0.0333347\pi\)
−0.406733 + 0.913547i \(0.633332\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.58662 4.38014i 0.837802 0.483705i
\(83\) 5.45001 0.598216 0.299108 0.954219i \(-0.403311\pi\)
0.299108 + 0.954219i \(0.403311\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.61401 0.931852i 0.174044 0.100484i
\(87\) 0 0
\(88\) 0.766125 1.32697i 0.0816692 0.141455i
\(89\) 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
\(92\) 0.267949i 0.0279356i
\(93\) 0 0
\(94\) −6.46008 3.72973i −0.666306 0.384692i
\(95\) 0 0
\(96\) 0 0
\(97\) 14.9481i 1.51775i −0.651234 0.758877i \(-0.725748\pi\)
0.651234 0.758877i \(-0.274252\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.36773 + 2.36897i −0.136094 + 0.235721i −0.926015 0.377487i \(-0.876788\pi\)
0.789921 + 0.613209i \(0.210122\pi\)
\(102\) 0 0
\(103\) 5.34935 3.08845i 0.527087 0.304314i −0.212742 0.977108i \(-0.568240\pi\)
0.739829 + 0.672794i \(0.234906\pi\)
\(104\) −1.48236 −0.145358
\(105\) 0 0
\(106\) 3.47015 0.337051
\(107\) −3.95768 + 2.28497i −0.382603 + 0.220896i −0.678950 0.734184i \(-0.737565\pi\)
0.296347 + 0.955080i \(0.404231\pi\)
\(108\) 0 0
\(109\) 2.97934 5.16036i 0.285369 0.494273i −0.687330 0.726345i \(-0.741217\pi\)
0.972699 + 0.232072i \(0.0745506\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.48356 + 2.19067i 0.140184 + 0.206999i
\(113\) 19.8977i 1.87182i −0.352237 0.935911i \(-0.614579\pi\)
0.352237 0.935911i \(-0.385421\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.778539 + 0.449490i 0.0722855 + 0.0417341i
\(117\) 0 0
\(118\) 6.25674i 0.575979i
\(119\) 2.80625 5.78094i 0.257249 0.529938i
\(120\) 0 0
\(121\) −4.32611 7.49303i −0.393282 0.681185i
\(122\) −3.31079 + 5.73445i −0.299745 + 0.519173i
\(123\) 0 0
\(124\) −0.717439 + 0.414214i −0.0644279 + 0.0371975i
\(125\) 0 0
\(126\) 0 0
\(127\) 21.2025 1.88142 0.940708 0.339219i \(-0.110163\pi\)
0.940708 + 0.339219i \(0.110163\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.73085 + 6.46202i 0.325966 + 0.564589i 0.981707 0.190396i \(-0.0609772\pi\)
−0.655742 + 0.754985i \(0.727644\pi\)
\(132\) 0 0
\(133\) −10.6548 + 7.21561i −0.923886 + 0.625673i
\(134\) 16.0340i 1.38513i
\(135\) 0 0
\(136\) −2.10342 1.21441i −0.180367 0.104135i
\(137\) 0.538302 + 0.310789i 0.0459903 + 0.0265525i 0.522819 0.852444i \(-0.324880\pi\)
−0.476829 + 0.878996i \(0.658214\pi\)
\(138\) 0 0
\(139\) 18.5334i 1.57198i −0.618237 0.785992i \(-0.712153\pi\)
0.618237 0.785992i \(-0.287847\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −6.38134 11.0528i −0.535510 0.927531i
\(143\) 1.13567 1.96705i 0.0949699 0.164493i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.343146 0.0283989
\(147\) 0 0
\(148\) −5.48236 −0.450647
\(149\) 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 \(0.871161\pi\)
\(152\) 2.43185 + 4.21209i 0.197249 + 0.341646i
\(153\) 0 0
\(154\) −4.04354 + 0.290313i −0.325838 + 0.0233941i
\(155\) 0 0
\(156\) 0 0
\(157\) 7.84628 + 4.53005i 0.626201 + 0.361538i 0.779279 0.626677i \(-0.215585\pi\)
−0.153078 + 0.988214i \(0.548919\pi\)
\(158\) −9.04889 5.22438i −0.719891 0.415629i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.586988 0.397520i 0.0462612 0.0313289i
\(162\) 0 0
\(163\) 5.91019 + 10.2368i 0.462922 + 0.801804i 0.999105 0.0422974i \(-0.0134677\pi\)
−0.536183 + 0.844102i \(0.680134\pi\)
\(164\) −4.38014 + 7.58662i −0.342031 + 0.592416i
\(165\) 0 0
\(166\) −4.71984 + 2.72500i −0.366331 + 0.211501i
\(167\) 15.7778 1.22092 0.610462 0.792046i \(-0.290984\pi\)
0.610462 + 0.792046i \(0.290984\pi\)
\(168\) 0 0
\(169\) 10.8026 0.830969
\(170\) 0 0
\(171\) 0 0
\(172\) −0.931852 + 1.61401i −0.0710530 + 0.123067i
\(173\) −10.1111 17.5129i −0.768730 1.33148i −0.938252 0.345954i \(-0.887555\pi\)
0.169521 0.985527i \(-0.445778\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.53225i 0.115498i
\(177\) 0 0
\(178\) −13.8305 7.98502i −1.03664 0.598503i
\(179\) 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 \(-0.207239\pi\)
\(182\) 2.19918 + 3.24737i 0.163014 + 0.240711i
\(183\) 0 0
\(184\) −0.133975 0.232051i −0.00987674 0.0171070i
\(185\) 0 0
\(186\) 0 0
\(187\) 3.22297 1.86078i 0.235687 0.136074i
\(188\) 7.45946 0.544037
\(189\) 0 0
\(190\) 0 0
\(191\) 14.8630 8.58114i 1.07545 0.620910i 0.145782 0.989317i \(-0.453430\pi\)
0.929665 + 0.368407i \(0.120097\pi\)
\(192\) 0 0
\(193\) 4.52761 7.84204i 0.325904 0.564483i −0.655791 0.754943i \(-0.727665\pi\)
0.981695 + 0.190460i \(0.0609980\pi\)
\(194\) 7.47407 + 12.9455i 0.536607 + 0.929430i
\(195\) 0 0
\(196\) 2.59808 6.50000i 0.185577 0.464286i
\(197\) 21.7379i 1.54876i −0.632720 0.774380i \(-0.718062\pi\)
0.632720 0.774380i \(-0.281938\pi\)
\(198\) 0 0
\(199\) −7.21101 4.16328i −0.511175 0.295127i 0.222141 0.975014i \(-0.428695\pi\)
−0.733317 + 0.679887i \(0.762029\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.73545i 0.192466i
\(203\) −0.170328 2.37237i −0.0119547 0.166508i
\(204\) 0 0
\(205\) 0 0
\(206\) −3.08845 + 5.34935i −0.215182 + 0.372707i
\(207\) 0 0
\(208\) 1.28376 0.741181i 0.0890130 0.0513917i
\(209\) −7.45241 −0.515494
\(210\) 0 0
\(211\) −19.9330 −1.37225 −0.686123 0.727486i \(-0.740689\pi\)
−0.686123 + 0.727486i \(0.740689\pi\)
\(212\) −3.00524 + 1.73508i −0.206401 + 0.119166i
\(213\) 0 0
\(214\) 2.28497 3.95768i 0.156197 0.270541i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.97177 + 0.957160i 0.133853 + 0.0649763i
\(218\) 5.95867i 0.403572i
\(219\) 0 0
\(220\) 0 0
\(221\) −3.11804 1.80020i −0.209742 0.121094i
\(222\) 0 0
\(223\) 7.16604i 0.479873i 0.970789 + 0.239937i \(0.0771267\pi\)
−0.970789 + 0.239937i \(0.922873\pi\)
\(224\) −2.38014 1.15539i −0.159030 0.0771980i
\(225\) 0 0
\(226\) 9.94887 + 17.2319i 0.661789 + 1.14625i
\(227\) −7.92721 + 13.7303i −0.526147 + 0.911314i 0.473389 + 0.880854i \(0.343031\pi\)
−0.999536 + 0.0304601i \(0.990303\pi\)
\(228\) 0 0
\(229\) 24.4371 14.1087i 1.61485 0.932332i 0.626622 0.779323i \(-0.284437\pi\)
0.988225 0.153009i \(-0.0488964\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.898979 −0.0590209
\(233\) −21.0421 + 12.1487i −1.37851 + 0.795886i −0.991981 0.126390i \(-0.959661\pi\)
−0.386534 + 0.922275i \(0.626328\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.12837 5.41849i −0.203639 0.352714i
\(237\) 0 0
\(238\) 0.460186 + 6.40957i 0.0298295 + 0.415471i
\(239\) 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 \(0.436766\pi\)
\(242\) 7.49303 + 4.32611i 0.481670 + 0.278093i
\(243\) 0 0
\(244\) 6.62158i 0.423903i
\(245\) 0 0
\(246\) 0 0
\(247\) 3.60488 + 6.24384i 0.229373 + 0.397286i
\(248\) 0.414214 0.717439i 0.0263026 0.0455574i
\(249\) 0 0
\(250\) 0 0
\(251\) −5.86787 −0.370376 −0.185188 0.982703i \(-0.559289\pi\)
−0.185188 + 0.982703i \(0.559289\pi\)
\(252\) 0 0
\(253\) 0.410565 0.0258120
\(254\) −18.3619 + 10.6012i −1.15213 + 0.665181i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.83083 + 6.63519i 0.238961 + 0.413892i 0.960416 0.278569i \(-0.0898600\pi\)
−0.721456 + 0.692461i \(0.756527\pi\)
\(258\) 0 0
\(259\) 8.13343 + 12.0100i 0.505387 + 0.746268i
\(260\) 0 0
\(261\) 0 0
\(262\) −6.46202 3.73085i −0.399225 0.230493i
\(263\) 7.32905 + 4.23143i 0.451929 + 0.260921i 0.708644 0.705566i \(-0.249307\pi\)
−0.256716 + 0.966487i \(0.582640\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 5.61950 11.5763i 0.344553 0.709788i
\(267\) 0 0
\(268\) −8.01702 13.8859i −0.489717 0.848215i
\(269\) 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 \(0.437018\pi\)
\(272\) 2.42883 0.147269
\(273\) 0 0
\(274\) −0.621578 −0.0375509
\(275\) 0 0
\(276\) 0 0
\(277\) −4.04561 + 7.00720i −0.243077 + 0.421022i −0.961589 0.274493i \(-0.911490\pi\)
0.718512 + 0.695514i \(0.244823\pi\)
\(278\) 9.26670 + 16.0504i 0.555780 + 0.962639i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1684i 0.666253i −0.942882 0.333127i \(-0.891896\pi\)
0.942882 0.333127i \(-0.108104\pi\)
\(282\) 0 0
\(283\) 6.24917 + 3.60796i 0.371475 + 0.214471i 0.674103 0.738638i \(-0.264531\pi\)
−0.302628 + 0.953109i \(0.597864\pi\)
\(284\) 11.0528 + 6.38134i 0.655863 + 0.378663i
\(285\) 0 0
\(286\) 2.27135i 0.134308i
\(287\) 23.1180 1.65980i 1.36461 0.0979748i
\(288\) 0 0
\(289\) 5.55040 + 9.61358i 0.326494 + 0.565505i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.297173 + 0.171573i −0.0173907 + 0.0100405i
\(293\) 18.2573 1.06660 0.533300 0.845926i \(-0.320952\pi\)
0.533300 + 0.845926i \(0.320952\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.74786 2.74118i 0.275964 0.159328i
\(297\) 0 0
\(298\) −6.99171 + 12.1100i −0.405019 + 0.701513i
\(299\) −0.198599 0.343983i −0.0114853 0.0198931i
\(300\) 0 0
\(301\) 4.91824 0.353113i 0.283482 0.0203531i
\(302\) 19.6768i 1.13227i
\(303\) 0 0
\(304\) −4.21209 2.43185i −0.241580 0.139476i
\(305\) 0 0
\(306\) 0 0
\(307\) 3.42078i 0.195234i 0.995224 + 0.0976172i \(0.0311221\pi\)
−0.995224 + 0.0976172i \(0.968878\pi\)
\(308\) 3.35666 2.27319i 0.191263 0.129527i
\(309\) 0 0
\(310\) 0 0
\(311\) 2.84544 4.92845i 0.161350 0.279467i −0.774003 0.633182i \(-0.781748\pi\)
0.935353 + 0.353715i \(0.115082\pi\)
\(312\) 0 0
\(313\) 11.5586 6.67335i 0.653330 0.377200i −0.136401 0.990654i \(-0.543553\pi\)
0.789731 + 0.613453i \(0.210220\pi\)
\(314\) −9.06010 −0.511291
\(315\) 0 0
\(316\) 10.4488 0.587789
\(317\) −10.8484 + 6.26330i −0.609305 + 0.351782i −0.772693 0.634780i \(-0.781091\pi\)
0.163389 + 0.986562i \(0.447758\pi\)
\(318\) 0 0
\(319\) 0.688731 1.19292i 0.0385615 0.0667905i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.309587 + 0.637756i −0.0172526 + 0.0355408i
\(323\) 11.8131i 0.657298i
\(324\) 0 0
\(325\) 0 0
\(326\) −10.2368 5.91019i −0.566961 0.327335i
\(327\) 0 0
\(328\) 8.76028i 0.483705i
\(329\) −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 \(0.822118\pi\)
\(332\) 2.72500 4.71984i 0.149554 0.259035i
\(333\) 0 0
\(334\) −13.6640 + 7.88891i −0.747660 + 0.431662i
\(335\) 0 0
\(336\) 0 0
\(337\) 13.1058 0.713920 0.356960 0.934120i \(-0.383813\pi\)
0.356960 + 0.934120i \(0.383813\pi\)
\(338\) −9.35533 + 5.40130i −0.508863 + 0.293792i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.634679 + 1.09930i 0.0343698 + 0.0595302i
\(342\) 0 0
\(343\) −18.0938 + 3.95164i −0.976972 + 0.213368i
\(344\) 1.86370i 0.100484i
\(345\) 0 0
\(346\) 17.5129 + 10.1111i 0.941499 + 0.543574i
\(347\) 12.3714 + 7.14262i 0.664130 + 0.383436i 0.793849 0.608115i \(-0.208074\pi\)
−0.129719 + 0.991551i \(0.541407\pi\)
\(348\) 0 0
\(349\) 13.2713i 0.710399i −0.934791 0.355200i \(-0.884413\pi\)
0.934791 0.355200i \(-0.115587\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.766125 1.32697i −0.0408346 0.0707276i
\(353\) 16.3232 28.2725i 0.868794 1.50480i 0.00556437 0.999985i \(-0.498229\pi\)
0.863230 0.504811i \(-0.168438\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 15.9700 0.846411
\(357\) 0 0
\(358\) −6.86662 −0.362912
\(359\) −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
\(362\) 8.15331 + 14.1220i 0.428529 + 0.742233i
\(363\) 0 0
\(364\) −3.52823 1.71271i −0.184929 0.0897705i
\(365\) 0 0
\(366\) 0 0
\(367\) −10.9026 6.29461i −0.569110 0.328576i 0.187684 0.982230i \(-0.439902\pi\)
−0.756794 + 0.653654i \(0.773235\pi\)
\(368\) 0.232051 + 0.133975i 0.0120965 + 0.00698391i
\(369\) 0 0
\(370\) 0 0
\(371\) 8.25945 + 4.00940i 0.428809 + 0.208158i
\(372\) 0 0
\(373\) 17.9791 + 31.1408i 0.930924 + 1.61241i 0.781745 + 0.623598i \(0.214330\pi\)
0.149179 + 0.988810i \(0.452337\pi\)
\(374\) −1.86078 + 3.22297i −0.0962188 + 0.166656i
\(375\) 0 0
\(376\) −6.46008 + 3.72973i −0.333153 + 0.192346i
\(377\) −1.33261 −0.0686331
\(378\) 0 0
\(379\) −11.5899 −0.595331 −0.297666 0.954670i \(-0.596208\pi\)
−0.297666 + 0.954670i \(0.596208\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −8.58114 + 14.8630i −0.439049 + 0.760456i
\(383\) 2.23375 + 3.86897i 0.114139 + 0.197695i 0.917435 0.397885i \(-0.130256\pi\)
−0.803296 + 0.595580i \(0.796922\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.05521i 0.460898i
\(387\) 0 0
\(388\) −12.9455 7.47407i −0.657207 0.379438i
\(389\) 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
\(392\) 1.00000 + 6.92820i 0.0505076 + 0.349927i
\(393\) 0 0
\(394\) 10.8689 + 18.8256i 0.547570 + 0.948418i
\(395\) 0 0
\(396\) 0 0
\(397\) −8.03664 + 4.63995i −0.403347 + 0.232873i −0.687927 0.725780i \(-0.741479\pi\)
0.284580 + 0.958652i \(0.408146\pi\)
\(398\) 8.32656 0.417373
\(399\) 0 0
\(400\) 0 0
\(401\) 6.44260 3.71964i 0.321728 0.185750i −0.330434 0.943829i \(-0.607195\pi\)
0.652163 + 0.758079i \(0.273862\pi\)
\(402\) 0 0
\(403\) 0.614014 1.06350i 0.0305862 0.0529769i
\(404\) 1.36773 + 2.36897i 0.0680469 + 0.117861i
\(405\) 0 0
\(406\) 1.33369 + 1.96937i 0.0661901 + 0.0977381i
\(407\) 8.40035i 0.416390i
\(408\) 0 0
\(409\) −13.8647 8.00481i −0.685567 0.395812i 0.116382 0.993204i \(-0.462870\pi\)
−0.801949 + 0.597392i \(0.796204\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 6.17690i 0.304314i
\(413\) −7.22900 + 14.8919i −0.355716 + 0.732783i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.741181 + 1.28376i −0.0363394 + 0.0629417i
\(417\) 0 0
\(418\) 6.45398 3.72620i 0.315674 0.182255i
\(419\) −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 \(0.356890\pi\)
\(422\) 17.2625 9.96651i 0.840325 0.485162i
\(423\) 0 0
\(424\) 1.73508 3.00524i 0.0842628 0.145947i
\(425\) 0 0
\(426\) 0 0
\(427\) −14.5057 + 9.82353i −0.701980 + 0.475394i
\(428\) 4.56993i 0.220896i
\(429\) 0 0
\(430\) 0 0
\(431\) 26.7539 + 15.4464i 1.28869 + 0.744025i 0.978420 0.206624i \(-0.0662477\pi\)
0.310268 + 0.950649i \(0.399581\pi\)
\(432\) 0 0
\(433\) 15.2207i 0.731462i −0.930721 0.365731i \(-0.880819\pi\)
0.930721 0.365731i \(-0.119181\pi\)
\(434\) −2.18618 + 0.156961i −0.104940 + 0.00753437i
\(435\) 0 0
\(436\) −2.97934 5.16036i −0.142684 0.247136i
\(437\) −0.651613 + 1.12863i −0.0311709 + 0.0539895i
\(438\) 0 0
\(439\) 12.4054 7.16228i 0.592079 0.341837i −0.173840 0.984774i \(-0.555618\pi\)
0.765919 + 0.642937i \(0.222284\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3.60040 0.171253
\(443\) −4.46651 + 2.57874i −0.212210 + 0.122520i −0.602338 0.798241i \(-0.705764\pi\)
0.390128 + 0.920761i \(0.372431\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.58302 6.20597i −0.169661 0.293861i
\(447\) 0 0
\(448\) 2.63896 0.189469i 0.124679 0.00895155i
\(449\) 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
\(452\) −17.2319 9.94887i −0.810522 0.467955i
\(453\) 0 0
\(454\) 15.8544i 0.744085i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.66995 + 9.82065i 0.265229 + 0.459391i 0.967624 0.252397i \(-0.0812190\pi\)
−0.702394 + 0.711788i \(0.747886\pi\)
\(458\) −14.1087 + 24.4371i −0.659258 + 1.14187i
\(459\) 0 0
\(460\) 0 0
\(461\) −2.01890 −0.0940298 −0.0470149 0.998894i \(-0.514971\pi\)
−0.0470149 + 0.998894i \(0.514971\pi\)
\(462\) 0 0
\(463\) 27.2844 1.26801 0.634007 0.773327i \(-0.281409\pi\)
0.634007 + 0.773327i \(0.281409\pi\)
\(464\) 0.778539 0.449490i 0.0361428 0.0208670i
\(465\) 0 0
\(466\) 12.1487 21.0421i 0.562776 0.974757i
\(467\) −0.346065 0.599403i −0.0160140 0.0277370i 0.857907 0.513804i \(-0.171764\pi\)
−0.873921 + 0.486067i \(0.838431\pi\)
\(468\) 0 0
\(469\) −18.5256 + 38.1632i −0.855434 + 1.76221i
\(470\) 0 0
\(471\) 0 0
\(472\) 5.41849 + 3.12837i 0.249406 + 0.143995i
\(473\) 2.47307 + 1.42783i 0.113712 + 0.0656517i
\(474\) 0 0
\(475\) 0 0
\(476\) −3.60332 5.32076i −0.165158 0.243876i
\(477\) 0 0
\(478\) 9.95403 + 17.2409i 0.455287 + 0.788580i
\(479\) 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
\(482\) −20.5254 −0.934905
\(483\) 0 0
\(484\) −8.65221 −0.393282
\(485\) 0 0
\(486\) 0 0
\(487\) −14.3749 + 24.8981i −0.651390 + 1.12824i 0.331396 + 0.943492i \(0.392480\pi\)
−0.982786 + 0.184749i \(0.940853\pi\)
\(488\) 3.31079 + 5.73445i 0.149872 + 0.259587i
\(489\) 0 0
\(490\) 0 0
\(491\) 5.45753i 0.246295i 0.992388 + 0.123148i \(0.0392988\pi\)
−0.992388 + 0.123148i \(0.960701\pi\)
\(492\) 0 0
\(493\) −1.89094 1.09173i −0.0851635 0.0491691i
\(494\) −6.24384 3.60488i −0.280924 0.162191i
\(495\) 0 0
\(496\) 0.828427i 0.0371975i
\(497\) −2.41813 33.6802i −0.108468 1.51076i
\(498\) 0 0
\(499\) 4.43148 + 7.67555i 0.198380 + 0.343605i 0.948003 0.318260i \(-0.103099\pi\)
−0.749623 + 0.661865i \(0.769765\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 5.08172 2.93393i 0.226808 0.130948i
\(503\) −9.36536 −0.417581 −0.208790 0.977960i \(-0.566953\pi\)
−0.208790 + 0.977960i \(0.566953\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.355560 + 0.205283i −0.0158066 + 0.00912592i
\(507\) 0 0
\(508\) 10.6012 18.3619i 0.470354 0.814677i
\(509\) 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
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.63519 3.83083i −0.292666 0.168971i
\(515\) 0 0
\(516\) 0 0
\(517\) 11.4298i 0.502680i
\(518\) −13.0488 6.33429i −0.573331 0.278313i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.99807 + 17.3172i −0.438023 + 0.758679i −0.997537 0.0701424i \(-0.977655\pi\)
0.559514 + 0.828821i \(0.310988\pi\)
\(522\) 0 0
\(523\) 29.0144 16.7515i 1.26871 0.732491i 0.293967 0.955816i \(-0.405024\pi\)
0.974744 + 0.223325i \(0.0716911\pi\)
\(524\) 7.46170 0.325966
\(525\) 0 0
\(526\) −8.46286 −0.368998
\(527\) 1.74253 1.00605i 0.0759060 0.0438243i
\(528\) 0 0
\(529\) −11.4641 + 19.8564i −0.498439 + 0.863322i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.921519 + 12.8351i 0.0399529 + 0.556473i
\(533\) 12.9859i 0.562482i
\(534\) 0 0
\(535\) 0 0
\(536\) 13.8859 + 8.01702i 0.599779 + 0.346282i
\(537\) 0 0
\(538\) 17.0431i 0.734781i
\(539\) −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 \(-0.468052\pi\)
\(542\) 5.26795 9.12436i 0.226278 0.391925i
\(543\) 0 0
\(544\) −2.10342 + 1.21441i −0.0901836 + 0.0520675i
\(545\) 0 0
\(546\) 0 0
\(547\) −5.07130 −0.216833 −0.108417 0.994106i \(-0.534578\pi\)
−0.108417 + 0.994106i \(0.534578\pi\)
\(548\) 0.538302 0.310789i 0.0229951 0.0132762i
\(549\) 0 0
\(550\) 0 0
\(551\) 2.18618 + 3.78658i 0.0931346 + 0.161314i
\(552\) 0 0
\(553\) −15.5014 22.8898i −0.659187 0.973373i
\(554\) 8.09122i 0.343763i
\(555\) 0 0
\(556\) −16.0504 9.26670i −0.680689 0.392996i
\(557\) −29.7528 17.1778i −1.26067 0.727846i −0.287463 0.957792i \(-0.592812\pi\)
−0.973203 + 0.229946i \(0.926145\pi\)
\(558\) 0 0
\(559\) 2.76268i 0.116849i
\(560\) 0 0
\(561\) 0 0
\(562\) 5.58422 + 9.67215i 0.235556 + 0.407995i
\(563\) 23.5293 40.7539i 0.991641 1.71757i 0.384079 0.923300i \(-0.374519\pi\)
0.607562 0.794272i \(-0.292148\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −7.21592 −0.303308
\(567\) 0 0
\(568\) −12.7627 −0.535510
\(569\) −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 \(0.836340\pi\)
\(572\) −1.13567 1.96705i −0.0474849 0.0822463i
\(573\) 0 0
\(574\) −19.1909 + 12.9964i −0.801012 + 0.542461i
\(575\) 0 0
\(576\) 0 0
\(577\) −12.2293 7.06058i −0.509112 0.293936i 0.223357 0.974737i \(-0.428299\pi\)
−0.732469 + 0.680801i \(0.761632\pi\)
\(578\) −9.61358 5.55040i −0.399872 0.230866i
\(579\) 0 0
\(580\) 0 0
\(581\) −14.3823 + 1.03261i −0.596680 + 0.0428397i
\(582\) 0 0
\(583\) 2.65857 + 4.60478i 0.110107 + 0.190711i
\(584\) 0.171573 0.297173i 0.00709974 0.0122971i
\(585\) 0 0
\(586\) −15.8112 + 9.12863i −0.653156 + 0.377100i
\(587\) −37.7819 −1.55942 −0.779712 0.626138i \(-0.784635\pi\)
−0.779712 + 0.626138i \(0.784635\pi\)
\(588\) 0 0
\(589\) −4.02922 −0.166021
\(590\) 0 0
\(591\) 0 0
\(592\) −2.74118 + 4.74786i −0.112662 + 0.195136i
\(593\) 13.0981 + 22.6865i 0.537873 + 0.931623i 0.999018 + 0.0442982i \(0.0141052\pi\)
−0.461146 + 0.887324i \(0.652562\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 13.9834i 0.572783i
\(597\) 0 0
\(598\) 0.343983 + 0.198599i 0.0140665 + 0.00812131i
\(599\) −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 \(0.724109\pi\)
\(602\) −4.08276 + 2.76492i −0.166401 + 0.112690i
\(603\) 0 0
\(604\) 9.83839 + 17.0406i 0.400319 + 0.693372i
\(605\) 0 0
\(606\) 0 0
\(607\) −32.2499 + 18.6195i −1.30898 + 0.755742i −0.981927 0.189263i \(-0.939390\pi\)
−0.327057 + 0.945005i \(0.606057\pi\)
\(608\) 4.86370 0.197249
\(609\) 0 0
\(610\) 0 0
\(611\) −9.57618 + 5.52881i −0.387411 + 0.223672i
\(612\) 0 0
\(613\) −4.92977 + 8.53861i −0.199112 + 0.344871i −0.948241 0.317553i \(-0.897139\pi\)
0.749129 + 0.662424i \(0.230472\pi\)
\(614\) −1.71039 2.96248i −0.0690258 0.119556i
\(615\) 0 0
\(616\) −1.77035 + 3.64697i −0.0713296 + 0.146941i
\(617\) 31.3545i 1.26229i −0.775666 0.631143i \(-0.782586\pi\)
0.775666 0.631143i \(-0.217414\pi\)
\(618\) 0 0
\(619\) −13.1943 7.61774i −0.530325 0.306183i 0.210824 0.977524i \(-0.432385\pi\)
−0.741149 + 0.671341i \(0.765719\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 5.69089i 0.228184i
\(623\) −23.6926 34.9851i −0.949223 1.40165i
\(624\) 0 0
\(625\) 0 0
\(626\) −6.67335 + 11.5586i −0.266721 + 0.461974i
\(627\) 0 0
\(628\) 7.84628 4.53005i 0.313101 0.180769i
\(629\) 13.3157 0.530932
\(630\) 0 0
\(631\) −1.00406 −0.0399710 −0.0199855 0.999800i \(-0.506362\pi\)
−0.0199855 + 0.999800i \(0.506362\pi\)
\(632\) −9.04889 + 5.22438i −0.359946 + 0.207815i
\(633\) 0 0
\(634\) 6.26330 10.8484i 0.248748 0.430844i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.48236 + 10.2701i 0.0587333 + 0.406916i
\(638\) 1.37746i 0.0545342i
\(639\) 0 0
\(640\) 0 0
\(641\) −20.2689 11.7023i −0.800574 0.462211i 0.0430981 0.999071i \(-0.486277\pi\)
−0.843672 + 0.536860i \(0.819611\pi\)
\(642\) 0 0
\(643\) 33.4475i 1.31904i −0.751686 0.659521i \(-0.770759\pi\)
0.751686 0.659521i \(-0.229241\pi\)
\(644\) −0.0507680 0.707107i −0.00200054 0.0278639i
\(645\) 0 0
\(646\) −5.90654 10.2304i −0.232390 0.402511i
\(647\) 8.28540 14.3507i 0.325733 0.564185i −0.655928 0.754824i \(-0.727722\pi\)
0.981660 + 0.190638i \(0.0610557\pi\)
\(648\) 0 0
\(649\) −8.30249 + 4.79344i −0.325901 + 0.188159i
\(650\) 0 0
\(651\) 0 0
\(652\) 11.8204 0.462922
\(653\) −5.22132 + 3.01453i −0.204326 + 0.117968i −0.598672 0.800994i \(-0.704305\pi\)
0.394346 + 0.918962i \(0.370971\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.38014 + 7.58662i 0.171016 + 0.296208i
\(657\) 0 0
\(658\) 17.7545 + 8.61862i 0.692144 + 0.335989i
\(659\) 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 \(0.738050\pi\)
\(662\) −1.11010 0.640916i −0.0431452 0.0249099i
\(663\) 0 0
\(664\) 5.45001i 0.211501i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.120440 0.208609i −0.00466347 0.00807737i
\(668\) 7.88891 13.6640i 0.305231 0.528675i
\(669\) 0 0
\(670\) 0 0
\(671\) −10.1459 −0.391679
\(672\) 0 0
\(673\) −10.8070 −0.416581 −0.208290 0.978067i \(-0.566790\pi\)
−0.208290 + 0.978067i \(0.566790\pi\)
\(674\) −11.3500 + 6.55291i −0.437185 + 0.252409i
\(675\) 0 0
\(676\) 5.40130 9.35533i 0.207742 0.359820i
\(677\) −7.02280 12.1638i −0.269908 0.467494i 0.698930 0.715190i \(-0.253660\pi\)
−0.968838 + 0.247696i \(0.920327\pi\)
\(678\) 0 0
\(679\) 2.83220 + 39.4475i 0.108690 + 1.51386i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.09930 0.634679i −0.0420942 0.0243031i
\(683\) 31.5900 + 18.2385i 1.20876 + 0.697877i 0.962488 0.271324i \(-0.0874614\pi\)
0.246271 + 0.969201i \(0.420795\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 13.6938 12.4691i 0.522834 0.476073i
\(687\) 0 0
\(688\) 0.931852 + 1.61401i 0.0355265 + 0.0615337i
\(689\) 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 \(0.482649\pi\)
\(692\) −20.2221 −0.768730
\(693\) 0 0
\(694\) −14.2852 −0.542260
\(695\) 0 0
\(696\) 0 0
\(697\) 10.6386 18.4266i 0.402965 0.697957i
\(698\) 6.63567 + 11.4933i 0.251164 + 0.435029i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.74502i 0.0659086i 0.999457 + 0.0329543i \(0.0104916\pi\)
−0.999457 + 0.0329543i \(0.989508\pi\)
\(702\) 0 0
\(703\) −23.0922 13.3323i −0.870939 0.502837i
\(704\) 1.32697 + 0.766125i 0.0500120 + 0.0288744i
\(705\) 0 0
\(706\) 32.6463i 1.22866i
\(707\) 3.16052 6.51075i 0.118864 0.244862i
\(708\) 0 0
\(709\) 6.06162 + 10.4990i 0.227649 + 0.394299i 0.957111 0.289722i \(-0.0935629\pi\)
−0.729462 + 0.684021i \(0.760230\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −13.8305 + 7.98502i −0.518319 + 0.299251i
\(713\) 0.221976 0.00831308
\(714\) 0 0
\(715\) 0 0
\(716\) 5.94667 3.43331i 0.222237 0.128309i
\(717\) 0 0
\(718\) 3.12168 5.40692i 0.116500 0.201784i
\(719\) −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
\(722\) 4.65561i 0.173264i
\(723\) 0 0
\(724\) −14.1220 8.15331i −0.524838 0.303015i
\(725\) 0 0
\(726\) 0 0
\(727\) 29.8785i 1.10813i 0.832472 + 0.554066i \(0.186925\pi\)
−0.832472 + 0.554066i \(0.813075\pi\)
\(728\) 3.91189 0.280861i 0.144984 0.0104094i
\(729\) 0 0
\(730\) 0 0
\(731\) 2.26330 3.92016i 0.0837114 0.144992i
\(732\) 0 0
\(733\) 11.9434 6.89554i 0.441140 0.254692i −0.262941 0.964812i \(-0.584692\pi\)
0.704081 + 0.710119i \(0.251359\pi\)
\(734\) 12.5892 0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) −21.2766 + 12.2841i −0.783735 + 0.452490i
\(738\) 0 0
\(739\) −3.68349 + 6.37999i −0.135499 + 0.234692i −0.925788 0.378043i \(-0.876597\pi\)
0.790289 + 0.612735i \(0.209931\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −9.15759 + 0.657486i −0.336186 + 0.0241371i
\(743\) 11.0774i 0.406389i 0.979138 + 0.203194i \(0.0651323\pi\)
−0.979138 + 0.203194i \(0.934868\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −31.1408 17.9791i −1.14014 0.658263i
\(747\) 0 0
\(748\) 3.72157i 0.136074i
\(749\) 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 \(0.980038\pi\)
\(752\) 3.72973 6.46008i 0.136009 0.235575i
\(753\) 0 0
\(754\) 1.15408 0.666306i 0.0420290 0.0242655i
\(755\) 0 0
\(756\) 0 0
\(757\) −19.6761 −0.715139 −0.357569 0.933887i \(-0.616394\pi\)
−0.357569 + 0.933887i \(0.616394\pi\)
\(758\) 10.0371 5.79493i 0.364565 0.210481i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.9168 43.1572i −0.903234 1.56445i −0.823270 0.567650i \(-0.807853\pi\)
−0.0799647 0.996798i \(-0.525481\pi\)
\(762\) 0 0
\(763\) −6.88462 + 14.1825i −0.249240 + 0.513440i
\(764\) 17.1623i 0.620910i
\(765\) 0 0
\(766\) −3.86897 2.23375i −0.139792 0.0807087i
\(767\) 8.03217 + 4.63737i 0.290025 + 0.167446i
\(768\) 0 0
\(769\) 31.0584i 1.12000i 0.828494 + 0.559998i \(0.189198\pi\)
−0.828494 + 0.559998i \(0.810802\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.52761 7.84204i −0.162952 0.282241i
\(773\) 1.98525 3.43855i 0.0714043 0.123676i −0.828113 0.560562i \(-0.810585\pi\)
0.899517 + 0.436886i \(0.143919\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 14.9481 0.536607
\(777\) 0 0
\(778\) −12.9554 −0.464475
\(779\) −36.8991 + 21.3037i −1.32205 + 0.763284i
\(780\) 0 0
\(781\) 9.77781 16.9357i 0.349878 0.606006i
\(782\) 0.325401 + 0.563611i 0.0116363 + 0.0201547i
\(783\) 0 0
\(784\) −4.33013 5.50000i −0.154647 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −38.8001 22.4013i −1.38308 0.798519i −0.390553 0.920580i \(-0.627716\pi\)
−0.992523 + 0.122061i \(0.961050\pi\)
\(788\) −18.8256 10.8689i −0.670633 0.387190i
\(789\) 0 0
\(790\) 0 0
\(791\) 3.77000 + 52.5093i 0.134046 + 1.86702i
\(792\) 0 0
\(793\) 4.90779 + 8.50054i 0.174281 + 0.301863i
\(794\) 4.63995 8.03664i 0.164666 0.285210i
\(795\) 0 0
\(796\) −7.21101