Properties

Label 3150.2.bf.b.1601.1
Level 3150
Weight 2
Character 3150.1601
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.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 1601.1
Root \(0.258819 - 0.965926i\)
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.b.1151.1

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 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 −0.686525 0.727106i \(-0.740865\pi\)
0.286430 + 0.958101i \(0.407532\pi\)
\(12\) 0 0
\(13\) 1.48236i 0.411133i −0.978643 0.205567i \(-0.934096\pi\)
0.978643 0.205567i \(-0.0659037\pi\)
\(14\) 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 0.680339 0.732898i \(-0.261833\pi\)
−0.974877 + 0.222742i \(0.928499\pi\)
\(18\) 0 0
\(19\) 4.21209 + 2.43185i 0.966320 + 0.557905i 0.898112 0.439766i \(-0.144939\pi\)
0.0682075 + 0.997671i \(0.478272\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.53225 0.326677
\(23\) −0.232051 0.133975i −0.0483859 0.0279356i 0.475612 0.879655i \(-0.342227\pi\)
−0.523998 + 0.851720i \(0.675560\pi\)
\(24\) 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 \(-0.973400\pi\)
0.996510 0.0834681i \(-0.0265997\pi\)
\(30\) 0 0
\(31\) −0.717439 + 0.414214i −0.128856 + 0.0743950i −0.563042 0.826428i \(-0.690369\pi\)
0.434187 + 0.900823i \(0.357036\pi\)
\(32\) 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 −0.998426 0.0560790i \(-0.982140\pi\)
0.547779 + 0.836623i \(0.315473\pi\)
\(38\) −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 −0.454630 0.890680i \(-0.650229\pi\)
0.998667 0.0516191i \(-0.0164382\pi\)
\(48\) 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 −0.691993 0.721904i \(-0.743267\pi\)
0.279191 + 0.960236i \(0.409934\pi\)
\(54\) 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 0.994584 0.103938i \(-0.0331444\pi\)
−0.587305 + 0.809366i \(0.699811\pi\)
\(60\) 0 0
\(61\) 5.73445 + 3.31079i 0.734222 + 0.423903i 0.819965 0.572414i \(-0.193993\pi\)
−0.0857429 + 0.996317i \(0.527326\pi\)
\(62\) 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 0.664449 + 0.747334i \(0.268666\pi\)
0.314985 + 0.949097i \(0.398000\pi\)
\(68\) 1.21441 2.10342i 0.147269 0.255078i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7627i 1.51465i −0.653037 0.757326i \(-0.726505\pi\)
0.653037 0.757326i \(-0.273495\pi\)
\(72\) 0 0
\(73\) −0.297173 + 0.171573i −0.0347815 + 0.0200811i −0.517290 0.855810i \(-0.673059\pi\)
0.482508 + 0.875891i \(0.339726\pi\)
\(74\) 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 −0.406733 0.913547i \(-0.633332\pi\)
0.994521 0.104533i \(-0.0333347\pi\)
\(80\) 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 −0.0379795 0.999279i \(-0.512092\pi\)
0.884390 0.466748i \(-0.154574\pi\)
\(90\) 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 \(0.274252\pi\)
−0.651234 + 0.758877i \(0.725748\pi\)
\(98\) −5.50000 4.33013i −0.555584 0.437409i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.36773 2.36897i −0.136094 0.235721i 0.789921 0.613209i \(-0.210122\pi\)
−0.926015 + 0.377487i \(0.876788\pi\)
\(102\) 0 0
\(103\) 5.34935 + 3.08845i 0.527087 + 0.304314i 0.739829 0.672794i \(-0.234906\pi\)
−0.212742 + 0.977108i \(0.568240\pi\)
\(104\) −1.48236 −0.145358
\(105\) 0 0
\(106\) 3.47015 0.337051
\(107\) −3.95768 2.28497i −0.382603 0.220896i 0.296347 0.955080i \(-0.404231\pi\)
−0.678950 + 0.734184i \(0.737565\pi\)
\(108\) 0 0
\(109\) 2.97934 + 5.16036i 0.285369 + 0.494273i 0.972699 0.232072i \(-0.0745506\pi\)
−0.687330 + 0.726345i \(0.741217\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.48356 2.19067i 0.140184 0.206999i
\(113\) 19.8977i 1.87182i 0.352237 + 0.935911i \(0.385421\pi\)
−0.352237 + 0.935911i \(0.614579\pi\)
\(114\) 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 −0.655742 0.754985i \(-0.727644\pi\)
0.981707 + 0.190396i \(0.0609772\pi\)
\(132\) 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 −0.476829 0.878996i \(-0.658214\pi\)
0.522819 + 0.852444i \(0.324880\pi\)
\(138\) 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
\(142\) −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 0.905898 0.423496i \(-0.139197\pi\)
0.0861911 + 0.996279i \(0.472530\pi\)
\(150\) 0 0
\(151\) −9.83839 17.0406i −0.800637 1.38674i −0.919197 0.393797i \(-0.871161\pi\)
0.118560 0.992947i \(-0.462172\pi\)
\(152\) 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 −0.153078 0.988214i \(-0.548919\pi\)
0.779279 + 0.626677i \(0.215585\pi\)
\(158\) −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 −0.536183 0.844102i \(-0.680134\pi\)
0.999105 + 0.0422974i \(0.0134677\pi\)
\(164\) −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 0.169521 + 0.985527i \(0.445778\pi\)
−0.938252 + 0.345954i \(0.887555\pi\)
\(174\) 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 −0.261019 0.965334i \(-0.584059\pi\)
0.705494 + 0.708716i \(0.250725\pi\)
\(180\) 0 0
\(181\) 16.3066i 1.21206i 0.795441 + 0.606031i \(0.207239\pi\)
−0.795441 + 0.606031i \(0.792761\pi\)
\(182\) 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 0.929665 0.368407i \(-0.120097\pi\)
0.145782 + 0.989317i \(0.453430\pi\)
\(192\) 0 0
\(193\) 4.52761 + 7.84204i 0.325904 + 0.564483i 0.981695 0.190460i \(-0.0609980\pi\)
−0.655791 + 0.754943i \(0.727665\pi\)
\(194\) 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 \(0.281938\pi\)
−0.632720 + 0.774380i \(0.718062\pi\)
\(198\) 0 0
\(199\) −7.21101 + 4.16328i −0.511175 + 0.295127i −0.733317 0.679887i \(-0.762029\pi\)
0.222141 + 0.975014i \(0.428695\pi\)
\(200\) 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 \(-0.922873\pi\)
0.970789 0.239937i \(-0.0771267\pi\)
\(224\) −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 −0.999536 0.0304601i \(-0.990303\pi\)
0.473389 0.880854i \(-0.343031\pi\)
\(228\) 0 0
\(229\) 24.4371 + 14.1087i 1.61485 + 0.932332i 0.988225 + 0.153009i \(0.0488964\pi\)
0.626622 + 0.779323i \(0.284437\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.898979 −0.0590209
\(233\) −21.0421 12.1487i −1.37851 0.795886i −0.386534 0.922275i \(-0.626328\pi\)
−0.991981 + 0.126390i \(0.959661\pi\)
\(234\) 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 \(0.222673\pi\)
−0.765133 + 0.643872i \(0.777327\pi\)
\(240\) 0 0
\(241\) 17.7755 10.2627i 1.14502 0.661078i 0.197351 0.980333i \(-0.436766\pi\)
0.947669 + 0.319255i \(0.103433\pi\)
\(242\) 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 −0.721456 0.692461i \(-0.756527\pi\)
0.960416 + 0.278569i \(0.0898600\pi\)
\(258\) 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 −0.256716 0.966487i \(-0.582640\pi\)
0.708644 + 0.705566i \(0.249307\pi\)
\(264\) 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 0.999741 + 0.0227449i \(0.00724054\pi\)
−0.480173 + 0.877174i \(0.659426\pi\)
\(270\) 0 0
\(271\) −9.12436 5.26795i −0.554265 0.320005i 0.196575 0.980489i \(-0.437018\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(272\) 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 0.718512 0.695514i \(-0.244823\pi\)
−0.961589 + 0.274493i \(0.911490\pi\)
\(278\) 9.26670 16.0504i 0.555780 0.962639i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1684i 0.666253i 0.942882 + 0.333127i \(0.108104\pi\)
−0.942882 + 0.333127i \(0.891896\pi\)
\(282\) 0 0
\(283\) 6.24917 3.60796i 0.371475 0.214471i −0.302628 0.953109i \(-0.597864\pi\)
0.674103 + 0.738638i \(0.264531\pi\)
\(284\) 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 \(-0.968878\pi\)
0.995224 0.0976172i \(-0.0311221\pi\)
\(308\) 3.35666 + 2.27319i 0.191263 + 0.129527i
\(309\) 0 0
\(310\) 0 0
\(311\) 2.84544 + 4.92845i 0.161350 + 0.279467i 0.935353 0.353715i \(-0.115082\pi\)
−0.774003 + 0.633182i \(0.781748\pi\)
\(312\) 0 0
\(313\) 11.5586 + 6.67335i 0.653330 + 0.377200i 0.789731 0.613453i \(-0.210220\pi\)
−0.136401 + 0.990654i \(0.543553\pi\)
\(314\) −9.06010 −0.511291
\(315\) 0 0
\(316\) 10.4488 0.587789
\(317\) −10.8484 6.26330i −0.609305 0.351782i 0.163389 0.986562i \(-0.447758\pi\)
−0.772693 + 0.634780i \(0.781091\pi\)
\(318\) 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 −0.847874 0.530198i \(-0.822118\pi\)
0.883102 + 0.469181i \(0.155451\pi\)
\(332\) 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 −0.129719 0.991551i \(-0.541407\pi\)
0.793849 + 0.608115i \(0.208074\pi\)
\(348\) 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
\(352\) −0.766125 + 1.32697i −0.0408346 + 0.0707276i
\(353\) 16.3232 + 28.2725i 0.868794 + 1.50480i 0.863230 + 0.504811i \(0.168438\pi\)
0.00556437 + 0.999985i \(0.498229\pi\)
\(354\) 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 0.350484 0.936569i \(-0.386017\pi\)
−0.635850 + 0.771812i \(0.719350\pi\)
\(360\) 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 −0.756794 0.653654i \(-0.773235\pi\)
0.187684 + 0.982230i \(0.439902\pi\)
\(368\) 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 0.149179 0.988810i \(-0.452337\pi\)
0.781745 0.623598i \(-0.214330\pi\)
\(374\) −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 −0.803296 0.595580i \(-0.796922\pi\)
0.917435 + 0.397885i \(0.130256\pi\)
\(384\) 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 −0.187832 0.982201i \(-0.560146\pi\)
0.756695 + 0.653768i \(0.226813\pi\)
\(390\) 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 0.284580 0.958652i \(-0.408146\pi\)
−0.687927 + 0.725780i \(0.741479\pi\)
\(398\) 8.32656 0.417373
\(399\) 0 0
\(400\) 0 0
\(401\) 6.44260 + 3.71964i 0.321728 + 0.185750i 0.652163 0.758079i \(-0.273862\pi\)
−0.330434 + 0.943829i \(0.607195\pi\)
\(402\) 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 −0.801949 0.597392i \(-0.796204\pi\)
0.116382 + 0.993204i \(0.462870\pi\)
\(410\) 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 0.310268 0.950649i \(-0.399581\pi\)
0.978420 + 0.206624i \(0.0662477\pi\)
\(432\) 0 0
\(433\) 15.2207i 0.731462i 0.930721 + 0.365731i \(0.119181\pi\)
−0.930721 + 0.365731i \(0.880819\pi\)
\(434\) −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 0.765919 0.642937i \(-0.222284\pi\)
−0.173840 + 0.984774i \(0.555618\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3.60040 0.171253
\(443\) −4.46651 2.57874i −0.212210 0.122520i 0.390128 0.920761i \(-0.372431\pi\)
−0.602338 + 0.798241i \(0.705764\pi\)
\(444\) 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 \(0.155912\pi\)
−0.882422 + 0.470459i \(0.844088\pi\)
\(450\) 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 −0.702394 0.711788i \(-0.747886\pi\)
0.967624 + 0.252397i \(0.0812190\pi\)
\(458\) −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 −0.873921 0.486067i \(-0.838431\pi\)
0.857907 + 0.513804i \(0.171764\pi\)
\(468\) 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 0.988523 0.151072i \(-0.0482727\pi\)
−0.625094 + 0.780550i \(0.714939\pi\)
\(480\) 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 −0.982786 0.184749i \(-0.940853\pi\)
0.331396 0.943492i \(-0.392480\pi\)
\(488\) 3.31079 5.73445i 0.149872 0.259587i
\(489\) 0 0
\(490\) 0 0
\(491\) 5.45753i 0.246295i −0.992388 0.123148i \(-0.960701\pi\)
0.992388 0.123148i \(-0.0392988\pi\)
\(492\) 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 −0.749623 0.661865i \(-0.769765\pi\)
0.948003 + 0.318260i \(0.103099\pi\)
\(500\) 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 −0.157603 0.987502i \(-0.550377\pi\)
0.934004 0.357263i \(-0.116290\pi\)
\(510\) 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 0.559514 0.828821i \(-0.310988\pi\)
−0.997537 + 0.0701424i \(0.977655\pi\)
\(522\) 0 0
\(523\) 29.0144 + 16.7515i 1.26871 + 0.732491i 0.974744 0.223325i \(-0.0716911\pi\)
0.293967 + 0.955816i \(0.405024\pi\)
\(524\) 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 0.100198 + 0.994967i \(0.468052\pi\)
−0.911766 + 0.410710i \(0.865281\pi\)
\(542\) 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 −0.973203 0.229946i \(-0.926145\pi\)
−0.287463 + 0.957792i \(0.592812\pi\)
\(558\) 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 0.607562 + 0.794272i \(0.292148\pi\)
0.384079 + 0.923300i \(0.374519\pi\)
\(564\) 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 −0.990627 0.136595i \(-0.956384\pi\)
−0.613608 0.789611i \(-0.710283\pi\)
\(570\) 0 0
\(571\) −20.5804 35.6463i −0.861263 1.49175i −0.870710 0.491797i \(-0.836340\pi\)
0.00944654 0.999955i \(-0.496993\pi\)
\(572\) −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 −0.732469 0.680801i \(-0.761632\pi\)
0.223357 + 0.974737i \(0.428299\pi\)
\(578\) −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 −0.461146 0.887324i \(-0.652562\pi\)
0.999018 0.0442982i \(-0.0141052\pi\)
\(594\) 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 −0.582518 0.812818i \(-0.697932\pi\)
0.412662 + 0.910884i \(0.364599\pi\)
\(600\) 0 0
\(601\) 37.3722i 1.52444i −0.647317 0.762221i \(-0.724109\pi\)
0.647317 0.762221i \(-0.275891\pi\)
\(602\) −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 −0.327057 0.945005i \(-0.606057\pi\)
−0.981927 + 0.189263i \(0.939390\pi\)
\(608\) 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 0.749129 0.662424i \(-0.230472\pi\)
−0.948241 + 0.317553i \(0.897139\pi\)
\(614\) −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 \(0.217414\pi\)
−0.775666 + 0.631143i \(0.782586\pi\)
\(618\) 0 0
\(619\) −13.1943 + 7.61774i −0.530325 + 0.306183i −0.741149 0.671341i \(-0.765719\pi\)
0.210824 + 0.977524i \(0.432385\pi\)
\(620\) 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 −0.843672 0.536860i \(-0.819611\pi\)
0.0430981 + 0.999071i \(0.486277\pi\)
\(642\) 0 0
\(643\) 33.4475i 1.31904i 0.751686 + 0.659521i \(0.229241\pi\)
−0.751686 + 0.659521i \(0.770759\pi\)
\(644\) −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 0.981660 0.190638i \(-0.0610557\pi\)
−0.655928 + 0.754824i \(0.727722\pi\)
\(648\) 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 0.394346 0.918962i \(-0.370971\pi\)
−0.598672 + 0.800994i \(0.704305\pi\)
\(654\) 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 \(0.250552\pi\)
−0.705880 + 0.708332i \(0.749448\pi\)
\(660\) 0 0
\(661\) −9.90289 + 5.71744i −0.385178 + 0.222383i −0.680069 0.733148i \(-0.738050\pi\)
0.294891 + 0.955531i \(0.404717\pi\)
\(662\) −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 −0.968838 0.247696i \(-0.920327\pi\)
0.698930 + 0.715190i \(0.253660\pi\)
\(678\) 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 0.246271 0.969201i \(-0.420795\pi\)
0.962488 + 0.271324i \(0.0874614\pi\)
\(684\) 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 0.0544816 0.998515i \(-0.482649\pi\)
−0.837498 + 0.546440i \(0.815983\pi\)
\(692\) −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 \(-0.989508\pi\)
0.999457 0.0329543i \(-0.0104916\pi\)
\(702\) 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 −0.729462 0.684021i \(-0.760230\pi\)
0.957111 + 0.289722i \(0.0935629\pi\)
\(710\) 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 −0.882200 0.470875i \(-0.843938\pi\)
0.848890 + 0.528570i \(0.177271\pi\)
\(720\) 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 \(-0.813075\pi\)
0.832472 0.554066i \(-0.186925\pi\)
\(728\) 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 0.704081 0.710119i \(-0.251359\pi\)
−0.262941 + 0.964812i \(0.584692\pi\)
\(734\) 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 0.790289 0.612735i \(-0.209931\pi\)
−0.925788 + 0.378043i \(0.876597\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −9.15759 0.657486i −0.336186 0.0241371i
\(743\) 11.0774i 0.406389i −0.979138 0.203194i \(-0.934868\pi\)
0.979138 0.203194i \(-0.0651323\pi\)
\(744\) 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 −0.998034 0.0626722i \(-0.980038\pi\)
0.553293 + 0.832987i \(0.313371\pi\)
\(752\) 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 −0.0799647 + 0.996798i \(0.525481\pi\)
−0.823270 + 0.567650i \(0.807853\pi\)
\(762\) 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 \(-0.810802\pi\)
0.828494 0.559998i \(-0.189198\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.52761 + 7.84204i −0.162952 + 0.282241i
\(773\) 1.98525 + 3.43855i 0.0714043 + 0.123676i 0.899517 0.436886i \(-0.143919\pi\)
−0.828113 + 0.560562i \(0.810585\pi\)
\(774\) 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 −0.992523 0.122061i \(-0.961050\pi\)
−0.390553 + 0.920580i \(0.627716\pi\)
\(788\) −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