Properties

Label 1638.2.bj.b.1135.2
Level $1638$
Weight $2$
Character 1638.1135
Analytic conductor $13.079$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1135.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1135
Dual form 1638.2.bj.b.127.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(0.366025 - 0.633975i) q^{10} +(-1.50000 - 0.866025i) q^{11} +(1.59808 - 3.23205i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.86603 - 3.23205i) q^{17} +(0.866025 - 0.500000i) q^{19} +(0.633975 - 0.366025i) q^{20} +(-0.866025 - 1.50000i) q^{22} +(1.73205 - 3.00000i) q^{23} +4.46410 q^{25} +(3.00000 - 2.00000i) q^{26} +(0.866025 + 0.500000i) q^{28} +(3.23205 - 5.59808i) q^{29} +2.19615i q^{31} +(-0.866025 + 0.500000i) q^{32} -3.73205i q^{34} +(-0.366025 - 0.633975i) q^{35} +(5.83013 + 3.36603i) q^{37} +1.00000 q^{38} +0.732051 q^{40} +(-2.59808 - 1.50000i) q^{41} +(1.63397 + 2.83013i) q^{43} -1.73205i q^{44} +(3.00000 - 1.73205i) q^{46} -2.46410i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.86603 + 2.23205i) q^{50} +(3.59808 - 0.232051i) q^{52} -7.00000 q^{53} +(-0.633975 + 1.09808i) q^{55} +(0.500000 + 0.866025i) q^{56} +(5.59808 - 3.23205i) q^{58} +(-0.803848 + 0.464102i) q^{59} +(-2.59808 - 4.50000i) q^{61} +(-1.09808 + 1.90192i) q^{62} -1.00000 q^{64} +(-2.36603 - 1.16987i) q^{65} +(7.73205 + 4.46410i) q^{67} +(1.86603 - 3.23205i) q^{68} -0.732051i q^{70} +(1.90192 - 1.09808i) q^{71} -5.46410i q^{73} +(3.36603 + 5.83013i) q^{74} +(0.866025 + 0.500000i) q^{76} -1.73205 q^{77} +2.07180 q^{79} +(0.633975 + 0.366025i) q^{80} +(-1.50000 - 2.59808i) q^{82} -0.196152i q^{83} +(-2.36603 + 1.36603i) q^{85} +3.26795i q^{86} +(0.866025 - 1.50000i) q^{88} +(9.06218 + 5.23205i) q^{89} +(-0.232051 - 3.59808i) q^{91} +3.46410 q^{92} +(1.23205 - 2.13397i) q^{94} +(-0.366025 - 0.633975i) q^{95} +(13.5622 - 7.83013i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 6 q^{29} + 2 q^{35} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 10 q^{43} + 12 q^{46} + 2 q^{49} + 12 q^{50} + 4 q^{52} - 28 q^{53} - 6 q^{55} + 2 q^{56} + 12 q^{58} - 24 q^{59} + 6 q^{62} - 4 q^{64} - 6 q^{65} + 24 q^{67} + 4 q^{68} + 18 q^{71} + 10 q^{74} + 36 q^{79} + 6 q^{80} - 6 q^{82} - 6 q^{85} + 12 q^{89} + 6 q^{91} - 2 q^{94} + 2 q^{95} + 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.732051i 0.327383i −0.986512 0.163692i \(-0.947660\pi\)
0.986512 0.163692i \(-0.0523402\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.366025 0.633975i 0.115747 0.200480i
\(11\) −1.50000 0.866025i −0.452267 0.261116i 0.256520 0.966539i \(-0.417424\pi\)
−0.708787 + 0.705422i \(0.750757\pi\)
\(12\) 0 0
\(13\) 1.59808 3.23205i 0.443227 0.896410i
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.86603 3.23205i −0.452578 0.783887i 0.545968 0.837806i \(-0.316162\pi\)
−0.998545 + 0.0539188i \(0.982829\pi\)
\(18\) 0 0
\(19\) 0.866025 0.500000i 0.198680 0.114708i −0.397360 0.917663i \(-0.630073\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(20\) 0.633975 0.366025i 0.141761 0.0818458i
\(21\) 0 0
\(22\) −0.866025 1.50000i −0.184637 0.319801i
\(23\) 1.73205 3.00000i 0.361158 0.625543i −0.626994 0.779024i \(-0.715715\pi\)
0.988152 + 0.153481i \(0.0490483\pi\)
\(24\) 0 0
\(25\) 4.46410 0.892820
\(26\) 3.00000 2.00000i 0.588348 0.392232i
\(27\) 0 0
\(28\) 0.866025 + 0.500000i 0.163663 + 0.0944911i
\(29\) 3.23205 5.59808i 0.600177 1.03954i −0.392617 0.919702i \(-0.628430\pi\)
0.992794 0.119835i \(-0.0382364\pi\)
\(30\) 0 0
\(31\) 2.19615i 0.394441i 0.980359 + 0.197220i \(0.0631914\pi\)
−0.980359 + 0.197220i \(0.936809\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.73205i 0.640041i
\(35\) −0.366025 0.633975i −0.0618696 0.107161i
\(36\) 0 0
\(37\) 5.83013 + 3.36603i 0.958467 + 0.553371i 0.895701 0.444657i \(-0.146674\pi\)
0.0627661 + 0.998028i \(0.480008\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) 0.732051 0.115747
\(41\) −2.59808 1.50000i −0.405751 0.234261i 0.283211 0.959058i \(-0.408600\pi\)
−0.688963 + 0.724797i \(0.741934\pi\)
\(42\) 0 0
\(43\) 1.63397 + 2.83013i 0.249179 + 0.431590i 0.963298 0.268434i \(-0.0865060\pi\)
−0.714119 + 0.700024i \(0.753173\pi\)
\(44\) 1.73205i 0.261116i
\(45\) 0 0
\(46\) 3.00000 1.73205i 0.442326 0.255377i
\(47\) 2.46410i 0.359426i −0.983719 0.179713i \(-0.942483\pi\)
0.983719 0.179713i \(-0.0575169\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 3.86603 + 2.23205i 0.546739 + 0.315660i
\(51\) 0 0
\(52\) 3.59808 0.232051i 0.498963 0.0321797i
\(53\) −7.00000 −0.961524 −0.480762 0.876851i \(-0.659640\pi\)
−0.480762 + 0.876851i \(0.659640\pi\)
\(54\) 0 0
\(55\) −0.633975 + 1.09808i −0.0854851 + 0.148065i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 5.59808 3.23205i 0.735063 0.424389i
\(59\) −0.803848 + 0.464102i −0.104652 + 0.0604209i −0.551413 0.834233i \(-0.685911\pi\)
0.446760 + 0.894654i \(0.352578\pi\)
\(60\) 0 0
\(61\) −2.59808 4.50000i −0.332650 0.576166i 0.650381 0.759608i \(-0.274609\pi\)
−0.983030 + 0.183442i \(0.941276\pi\)
\(62\) −1.09808 + 1.90192i −0.139456 + 0.241545i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −2.36603 1.16987i −0.293469 0.145105i
\(66\) 0 0
\(67\) 7.73205 + 4.46410i 0.944620 + 0.545377i 0.891406 0.453206i \(-0.149720\pi\)
0.0532147 + 0.998583i \(0.483053\pi\)
\(68\) 1.86603 3.23205i 0.226289 0.391944i
\(69\) 0 0
\(70\) 0.732051i 0.0874968i
\(71\) 1.90192 1.09808i 0.225717 0.130318i −0.382878 0.923799i \(-0.625067\pi\)
0.608595 + 0.793481i \(0.291734\pi\)
\(72\) 0 0
\(73\) 5.46410i 0.639525i −0.947498 0.319762i \(-0.896397\pi\)
0.947498 0.319762i \(-0.103603\pi\)
\(74\) 3.36603 + 5.83013i 0.391293 + 0.677738i
\(75\) 0 0
\(76\) 0.866025 + 0.500000i 0.0993399 + 0.0573539i
\(77\) −1.73205 −0.197386
\(78\) 0 0
\(79\) 2.07180 0.233095 0.116548 0.993185i \(-0.462817\pi\)
0.116548 + 0.993185i \(0.462817\pi\)
\(80\) 0.633975 + 0.366025i 0.0708805 + 0.0409229i
\(81\) 0 0
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 0.196152i 0.0215305i −0.999942 0.0107653i \(-0.996573\pi\)
0.999942 0.0107653i \(-0.00342676\pi\)
\(84\) 0 0
\(85\) −2.36603 + 1.36603i −0.256631 + 0.148166i
\(86\) 3.26795i 0.352392i
\(87\) 0 0
\(88\) 0.866025 1.50000i 0.0923186 0.159901i
\(89\) 9.06218 + 5.23205i 0.960589 + 0.554596i 0.896354 0.443339i \(-0.146206\pi\)
0.0642347 + 0.997935i \(0.479539\pi\)
\(90\) 0 0
\(91\) −0.232051 3.59808i −0.0243255 0.377181i
\(92\) 3.46410 0.361158
\(93\) 0 0
\(94\) 1.23205 2.13397i 0.127076 0.220103i
\(95\) −0.366025 0.633975i −0.0375534 0.0650444i
\(96\) 0 0
\(97\) 13.5622 7.83013i 1.37703 0.795029i 0.385230 0.922821i \(-0.374122\pi\)
0.991801 + 0.127792i \(0.0407889\pi\)
\(98\) 0.866025 0.500000i 0.0874818 0.0505076i
\(99\) 0 0
\(100\) 2.23205 + 3.86603i 0.223205 + 0.386603i
\(101\) −1.53590 + 2.66025i −0.152828 + 0.264705i −0.932266 0.361774i \(-0.882171\pi\)
0.779438 + 0.626479i \(0.215505\pi\)
\(102\) 0 0
\(103\) −14.7321 −1.45159 −0.725796 0.687910i \(-0.758528\pi\)
−0.725796 + 0.687910i \(0.758528\pi\)
\(104\) 3.23205 + 1.59808i 0.316929 + 0.156704i
\(105\) 0 0
\(106\) −6.06218 3.50000i −0.588811 0.339950i
\(107\) 5.42820 9.40192i 0.524764 0.908918i −0.474820 0.880083i \(-0.657487\pi\)
0.999584 0.0288353i \(-0.00917984\pi\)
\(108\) 0 0
\(109\) 4.73205i 0.453248i 0.973982 + 0.226624i \(0.0727689\pi\)
−0.973982 + 0.226624i \(0.927231\pi\)
\(110\) −1.09808 + 0.633975i −0.104697 + 0.0604471i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 7.63397 + 13.2224i 0.718144 + 1.24386i 0.961734 + 0.273984i \(0.0883414\pi\)
−0.243590 + 0.969878i \(0.578325\pi\)
\(114\) 0 0
\(115\) −2.19615 1.26795i −0.204792 0.118237i
\(116\) 6.46410 0.600177
\(117\) 0 0
\(118\) −0.928203 −0.0854480
\(119\) −3.23205 1.86603i −0.296282 0.171058i
\(120\) 0 0
\(121\) −4.00000 6.92820i −0.363636 0.629837i
\(122\) 5.19615i 0.470438i
\(123\) 0 0
\(124\) −1.90192 + 1.09808i −0.170798 + 0.0986102i
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) −7.73205 + 13.3923i −0.686109 + 1.18837i 0.286978 + 0.957937i \(0.407349\pi\)
−0.973087 + 0.230438i \(0.925984\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −1.46410 2.19615i −0.128410 0.192615i
\(131\) 13.8564 1.21064 0.605320 0.795982i \(-0.293045\pi\)
0.605320 + 0.795982i \(0.293045\pi\)
\(132\) 0 0
\(133\) 0.500000 0.866025i 0.0433555 0.0750939i
\(134\) 4.46410 + 7.73205i 0.385640 + 0.667947i
\(135\) 0 0
\(136\) 3.23205 1.86603i 0.277146 0.160010i
\(137\) −12.4641 + 7.19615i −1.06488 + 0.614809i −0.926778 0.375609i \(-0.877433\pi\)
−0.138102 + 0.990418i \(0.544100\pi\)
\(138\) 0 0
\(139\) −5.79423 10.0359i −0.491460 0.851234i 0.508492 0.861067i \(-0.330203\pi\)
−0.999952 + 0.00983316i \(0.996870\pi\)
\(140\) 0.366025 0.633975i 0.0309348 0.0535806i
\(141\) 0 0
\(142\) 2.19615 0.184297
\(143\) −5.19615 + 3.46410i −0.434524 + 0.289683i
\(144\) 0 0
\(145\) −4.09808 2.36603i −0.340327 0.196488i
\(146\) 2.73205 4.73205i 0.226106 0.391627i
\(147\) 0 0
\(148\) 6.73205i 0.553371i
\(149\) −12.0000 + 6.92820i −0.983078 + 0.567581i −0.903198 0.429224i \(-0.858787\pi\)
−0.0798802 + 0.996804i \(0.525454\pi\)
\(150\) 0 0
\(151\) 5.19615i 0.422857i 0.977393 + 0.211428i \(0.0678115\pi\)
−0.977393 + 0.211428i \(0.932188\pi\)
\(152\) 0.500000 + 0.866025i 0.0405554 + 0.0702439i
\(153\) 0 0
\(154\) −1.50000 0.866025i −0.120873 0.0697863i
\(155\) 1.60770 0.129133
\(156\) 0 0
\(157\) −0.535898 −0.0427693 −0.0213847 0.999771i \(-0.506807\pi\)
−0.0213847 + 0.999771i \(0.506807\pi\)
\(158\) 1.79423 + 1.03590i 0.142741 + 0.0824117i
\(159\) 0 0
\(160\) 0.366025 + 0.633975i 0.0289368 + 0.0501201i
\(161\) 3.46410i 0.273009i
\(162\) 0 0
\(163\) 2.36603 1.36603i 0.185321 0.106995i −0.404469 0.914552i \(-0.632544\pi\)
0.589790 + 0.807556i \(0.299210\pi\)
\(164\) 3.00000i 0.234261i
\(165\) 0 0
\(166\) 0.0980762 0.169873i 0.00761219 0.0131847i
\(167\) 12.0000 + 6.92820i 0.928588 + 0.536120i 0.886365 0.462988i \(-0.153223\pi\)
0.0422232 + 0.999108i \(0.486556\pi\)
\(168\) 0 0
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) −2.73205 −0.209539
\(171\) 0 0
\(172\) −1.63397 + 2.83013i −0.124589 + 0.215795i
\(173\) 4.56218 + 7.90192i 0.346856 + 0.600772i 0.985689 0.168573i \(-0.0539159\pi\)
−0.638833 + 0.769345i \(0.720583\pi\)
\(174\) 0 0
\(175\) 3.86603 2.23205i 0.292244 0.168727i
\(176\) 1.50000 0.866025i 0.113067 0.0652791i
\(177\) 0 0
\(178\) 5.23205 + 9.06218i 0.392159 + 0.679239i
\(179\) −5.73205 + 9.92820i −0.428434 + 0.742069i −0.996734 0.0807523i \(-0.974268\pi\)
0.568301 + 0.822821i \(0.307601\pi\)
\(180\) 0 0
\(181\) 2.66025 0.197735 0.0988676 0.995101i \(-0.468478\pi\)
0.0988676 + 0.995101i \(0.468478\pi\)
\(182\) 1.59808 3.23205i 0.118457 0.239576i
\(183\) 0 0
\(184\) 3.00000 + 1.73205i 0.221163 + 0.127688i
\(185\) 2.46410 4.26795i 0.181164 0.313786i
\(186\) 0 0
\(187\) 6.46410i 0.472702i
\(188\) 2.13397 1.23205i 0.155636 0.0898565i
\(189\) 0 0
\(190\) 0.732051i 0.0531085i
\(191\) 11.5622 + 20.0263i 0.836610 + 1.44905i 0.892713 + 0.450626i \(0.148799\pi\)
−0.0561031 + 0.998425i \(0.517868\pi\)
\(192\) 0 0
\(193\) −1.03590 0.598076i −0.0745656 0.0430505i 0.462254 0.886748i \(-0.347041\pi\)
−0.536819 + 0.843697i \(0.680374\pi\)
\(194\) 15.6603 1.12434
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −23.0885 13.3301i −1.64498 0.949732i −0.979024 0.203745i \(-0.934689\pi\)
−0.665961 0.745987i \(-0.731978\pi\)
\(198\) 0 0
\(199\) −8.09808 14.0263i −0.574057 0.994297i −0.996143 0.0877408i \(-0.972035\pi\)
0.422086 0.906556i \(-0.361298\pi\)
\(200\) 4.46410i 0.315660i
\(201\) 0 0
\(202\) −2.66025 + 1.53590i −0.187175 + 0.108065i
\(203\) 6.46410i 0.453691i
\(204\) 0 0
\(205\) −1.09808 + 1.90192i −0.0766930 + 0.132836i
\(206\) −12.7583 7.36603i −0.888915 0.513215i
\(207\) 0 0
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) −1.73205 −0.119808
\(210\) 0 0
\(211\) −13.0000 + 22.5167i −0.894957 + 1.55011i −0.0610990 + 0.998132i \(0.519461\pi\)
−0.833858 + 0.551979i \(0.813873\pi\)
\(212\) −3.50000 6.06218i −0.240381 0.416352i
\(213\) 0 0
\(214\) 9.40192 5.42820i 0.642702 0.371064i
\(215\) 2.07180 1.19615i 0.141295 0.0815769i
\(216\) 0 0
\(217\) 1.09808 + 1.90192i 0.0745423 + 0.129111i
\(218\) −2.36603 + 4.09808i −0.160247 + 0.277557i
\(219\) 0 0
\(220\) −1.26795 −0.0854851
\(221\) −13.4282 + 0.866025i −0.903279 + 0.0582552i
\(222\) 0 0
\(223\) 21.1244 + 12.1962i 1.41459 + 0.816715i 0.995817 0.0913753i \(-0.0291263\pi\)
0.418775 + 0.908090i \(0.362460\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 15.2679i 1.01561i
\(227\) −15.9282 + 9.19615i −1.05719 + 0.610370i −0.924654 0.380808i \(-0.875646\pi\)
−0.132538 + 0.991178i \(0.542313\pi\)
\(228\) 0 0
\(229\) 19.9282i 1.31689i −0.752628 0.658446i \(-0.771214\pi\)
0.752628 0.658446i \(-0.228786\pi\)
\(230\) −1.26795 2.19615i −0.0836061 0.144810i
\(231\) 0 0
\(232\) 5.59808 + 3.23205i 0.367532 + 0.212195i
\(233\) −9.12436 −0.597756 −0.298878 0.954291i \(-0.596612\pi\)
−0.298878 + 0.954291i \(0.596612\pi\)
\(234\) 0 0
\(235\) −1.80385 −0.117670
\(236\) −0.803848 0.464102i −0.0523260 0.0302104i
\(237\) 0 0
\(238\) −1.86603 3.23205i −0.120956 0.209503i
\(239\) 0.732051i 0.0473524i −0.999720 0.0236762i \(-0.992463\pi\)
0.999720 0.0236762i \(-0.00753708\pi\)
\(240\) 0 0
\(241\) −6.92820 + 4.00000i −0.446285 + 0.257663i −0.706260 0.707953i \(-0.749619\pi\)
0.259975 + 0.965615i \(0.416286\pi\)
\(242\) 8.00000i 0.514259i
\(243\) 0 0
\(244\) 2.59808 4.50000i 0.166325 0.288083i
\(245\) −0.633975 0.366025i −0.0405032 0.0233845i
\(246\) 0 0
\(247\) −0.232051 3.59808i −0.0147650 0.228940i
\(248\) −2.19615 −0.139456
\(249\) 0 0
\(250\) 3.46410 6.00000i 0.219089 0.379473i
\(251\) −6.56218 11.3660i −0.414201 0.717417i 0.581143 0.813801i \(-0.302606\pi\)
−0.995344 + 0.0963841i \(0.969272\pi\)
\(252\) 0 0
\(253\) −5.19615 + 3.00000i −0.326679 + 0.188608i
\(254\) −13.3923 + 7.73205i −0.840308 + 0.485152i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.3301 + 17.8923i −0.644376 + 1.11609i 0.340070 + 0.940400i \(0.389549\pi\)
−0.984445 + 0.175691i \(0.943784\pi\)
\(258\) 0 0
\(259\) 6.73205 0.418309
\(260\) −0.169873 2.63397i −0.0105351 0.163352i
\(261\) 0 0
\(262\) 12.0000 + 6.92820i 0.741362 + 0.428026i
\(263\) −7.56218 + 13.0981i −0.466304 + 0.807662i −0.999259 0.0384813i \(-0.987748\pi\)
0.532955 + 0.846143i \(0.321081\pi\)
\(264\) 0 0
\(265\) 5.12436i 0.314787i
\(266\) 0.866025 0.500000i 0.0530994 0.0306570i
\(267\) 0 0
\(268\) 8.92820i 0.545377i
\(269\) −4.92820 8.53590i −0.300478 0.520443i 0.675766 0.737116i \(-0.263813\pi\)
−0.976244 + 0.216673i \(0.930479\pi\)
\(270\) 0 0
\(271\) −24.2942 14.0263i −1.47577 0.852036i −0.476143 0.879368i \(-0.657965\pi\)
−0.999626 + 0.0273321i \(0.991299\pi\)
\(272\) 3.73205 0.226289
\(273\) 0 0
\(274\) −14.3923 −0.869471
\(275\) −6.69615 3.86603i −0.403793 0.233130i
\(276\) 0 0
\(277\) 4.66025 + 8.07180i 0.280008 + 0.484987i 0.971386 0.237505i \(-0.0763297\pi\)
−0.691379 + 0.722493i \(0.742996\pi\)
\(278\) 11.5885i 0.695029i
\(279\) 0 0
\(280\) 0.633975 0.366025i 0.0378872 0.0218742i
\(281\) 0.339746i 0.0202675i 0.999949 + 0.0101338i \(0.00322574\pi\)
−0.999949 + 0.0101338i \(0.996774\pi\)
\(282\) 0 0
\(283\) −4.92820 + 8.53590i −0.292951 + 0.507406i −0.974506 0.224360i \(-0.927971\pi\)
0.681555 + 0.731767i \(0.261304\pi\)
\(284\) 1.90192 + 1.09808i 0.112858 + 0.0651588i
\(285\) 0 0
\(286\) −6.23205 + 0.401924i −0.368509 + 0.0237663i
\(287\) −3.00000 −0.177084
\(288\) 0 0
\(289\) 1.53590 2.66025i 0.0903470 0.156486i
\(290\) −2.36603 4.09808i −0.138938 0.240647i
\(291\) 0 0
\(292\) 4.73205 2.73205i 0.276922 0.159881i
\(293\) 14.7846 8.53590i 0.863726 0.498673i −0.00153218 0.999999i \(-0.500488\pi\)
0.865258 + 0.501326i \(0.167154\pi\)
\(294\) 0 0
\(295\) 0.339746 + 0.588457i 0.0197808 + 0.0342613i
\(296\) −3.36603 + 5.83013i −0.195646 + 0.338869i
\(297\) 0 0
\(298\) −13.8564 −0.802680
\(299\) −6.92820 10.3923i −0.400668 0.601003i
\(300\) 0 0
\(301\) 2.83013 + 1.63397i 0.163126 + 0.0941807i
\(302\) −2.59808 + 4.50000i −0.149502 + 0.258946i
\(303\) 0 0
\(304\) 1.00000i 0.0573539i
\(305\) −3.29423 + 1.90192i −0.188627 + 0.108904i
\(306\) 0 0
\(307\) 8.60770i 0.491267i 0.969363 + 0.245634i \(0.0789960\pi\)
−0.969363 + 0.245634i \(0.921004\pi\)
\(308\) −0.866025 1.50000i −0.0493464 0.0854704i
\(309\) 0 0
\(310\) 1.39230 + 0.803848i 0.0790776 + 0.0456555i
\(311\) 4.26795 0.242013 0.121007 0.992652i \(-0.461388\pi\)
0.121007 + 0.992652i \(0.461388\pi\)
\(312\) 0 0
\(313\) 13.5167 0.764007 0.382003 0.924161i \(-0.375234\pi\)
0.382003 + 0.924161i \(0.375234\pi\)
\(314\) −0.464102 0.267949i −0.0261908 0.0151212i
\(315\) 0 0
\(316\) 1.03590 + 1.79423i 0.0582738 + 0.100933i
\(317\) 11.8564i 0.665922i −0.942941 0.332961i \(-0.891952\pi\)
0.942941 0.332961i \(-0.108048\pi\)
\(318\) 0 0
\(319\) −9.69615 + 5.59808i −0.542880 + 0.313432i
\(320\) 0.732051i 0.0409229i
\(321\) 0 0
\(322\) 1.73205 3.00000i 0.0965234 0.167183i
\(323\) −3.23205 1.86603i −0.179836 0.103828i
\(324\) 0 0
\(325\) 7.13397 14.4282i 0.395722 0.800333i
\(326\) 2.73205 0.151314
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) −1.23205 2.13397i −0.0679252 0.117650i
\(330\) 0 0
\(331\) 24.1244 13.9282i 1.32599 0.765563i 0.341317 0.939948i \(-0.389127\pi\)
0.984678 + 0.174385i \(0.0557937\pi\)
\(332\) 0.169873 0.0980762i 0.00932299 0.00538263i
\(333\) 0 0
\(334\) 6.92820 + 12.0000i 0.379094 + 0.656611i
\(335\) 3.26795 5.66025i 0.178547 0.309253i
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) −1.66987 12.8923i −0.0908291 0.701249i
\(339\) 0 0
\(340\) −2.36603 1.36603i −0.128316 0.0740831i
\(341\) 1.90192 3.29423i 0.102995 0.178392i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −2.83013 + 1.63397i −0.152590 + 0.0880980i
\(345\) 0 0
\(346\) 9.12436i 0.490528i
\(347\) 2.69615 + 4.66987i 0.144737 + 0.250692i 0.929275 0.369389i \(-0.120433\pi\)
−0.784538 + 0.620081i \(0.787100\pi\)
\(348\) 0 0
\(349\) −20.5359 11.8564i −1.09926 0.634659i −0.163235 0.986587i \(-0.552193\pi\)
−0.936027 + 0.351928i \(0.885526\pi\)
\(350\) 4.46410 0.238616
\(351\) 0 0
\(352\) 1.73205 0.0923186
\(353\) 8.19615 + 4.73205i 0.436237 + 0.251862i 0.702000 0.712177i \(-0.252291\pi\)
−0.265763 + 0.964038i \(0.585624\pi\)
\(354\) 0 0
\(355\) −0.803848 1.39230i −0.0426638 0.0738959i
\(356\) 10.4641i 0.554596i
\(357\) 0 0
\(358\) −9.92820 + 5.73205i −0.524722 + 0.302948i
\(359\) 3.80385i 0.200759i 0.994949 + 0.100380i \(0.0320058\pi\)
−0.994949 + 0.100380i \(0.967994\pi\)
\(360\) 0 0
\(361\) −9.00000 + 15.5885i −0.473684 + 0.820445i
\(362\) 2.30385 + 1.33013i 0.121088 + 0.0699099i
\(363\) 0 0
\(364\) 3.00000 2.00000i 0.157243 0.104828i
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) −12.6603 + 21.9282i −0.660860 + 1.14464i 0.319530 + 0.947576i \(0.396475\pi\)
−0.980390 + 0.197067i \(0.936858\pi\)
\(368\) 1.73205 + 3.00000i 0.0902894 + 0.156386i
\(369\) 0 0
\(370\) 4.26795 2.46410i 0.221880 0.128103i
\(371\) −6.06218 + 3.50000i −0.314733 + 0.181711i
\(372\) 0 0
\(373\) −4.83013 8.36603i −0.250094 0.433176i 0.713457 0.700699i \(-0.247128\pi\)
−0.963552 + 0.267523i \(0.913795\pi\)
\(374\) −3.23205 + 5.59808i −0.167125 + 0.289470i
\(375\) 0 0
\(376\) 2.46410 0.127076
\(377\) −12.9282 19.3923i −0.665836 0.998755i
\(378\) 0 0
\(379\) 24.6340 + 14.2224i 1.26536 + 0.730557i 0.974107 0.226088i \(-0.0725937\pi\)
0.291255 + 0.956645i \(0.405927\pi\)
\(380\) 0.366025 0.633975i 0.0187767 0.0325222i
\(381\) 0 0
\(382\) 23.1244i 1.18314i
\(383\) 4.79423 2.76795i 0.244974 0.141436i −0.372487 0.928037i \(-0.621495\pi\)
0.617461 + 0.786602i \(0.288162\pi\)
\(384\) 0 0
\(385\) 1.26795i 0.0646207i
\(386\) −0.598076 1.03590i −0.0304413 0.0527258i
\(387\) 0 0
\(388\) 13.5622 + 7.83013i 0.688515 + 0.397514i
\(389\) 8.39230 0.425507 0.212753 0.977106i \(-0.431757\pi\)
0.212753 + 0.977106i \(0.431757\pi\)
\(390\) 0 0
\(391\) −12.9282 −0.653807
\(392\) 0.866025 + 0.500000i 0.0437409 + 0.0252538i
\(393\) 0 0
\(394\) −13.3301 23.0885i −0.671562 1.16318i
\(395\) 1.51666i 0.0763115i
\(396\) 0 0
\(397\) 6.99038 4.03590i 0.350837 0.202556i −0.314217 0.949351i \(-0.601742\pi\)
0.665054 + 0.746795i \(0.268409\pi\)
\(398\) 16.1962i 0.811840i
\(399\) 0 0
\(400\) −2.23205 + 3.86603i −0.111603 + 0.193301i
\(401\) 33.5885 + 19.3923i 1.67733 + 0.968405i 0.963354 + 0.268233i \(0.0864396\pi\)
0.713973 + 0.700173i \(0.246894\pi\)
\(402\) 0 0
\(403\) 7.09808 + 3.50962i 0.353580 + 0.174827i
\(404\) −3.07180 −0.152828
\(405\) 0 0
\(406\) 3.23205 5.59808i 0.160404 0.277828i
\(407\) −5.83013 10.0981i −0.288989 0.500543i
\(408\) 0 0
\(409\) −33.5429 + 19.3660i −1.65859 + 0.957588i −0.685226 + 0.728331i \(0.740297\pi\)
−0.973366 + 0.229258i \(0.926370\pi\)
\(410\) −1.90192 + 1.09808i −0.0939293 + 0.0542301i
\(411\) 0 0
\(412\) −7.36603 12.7583i −0.362898 0.628558i
\(413\) −0.464102 + 0.803848i −0.0228369 + 0.0395548i
\(414\) 0 0
\(415\) −0.143594 −0.00704873
\(416\) 0.232051 + 3.59808i 0.0113772 + 0.176410i
\(417\) 0 0
\(418\) −1.50000 0.866025i −0.0733674 0.0423587i
\(419\) 0.366025 0.633975i 0.0178815 0.0309717i −0.856946 0.515406i \(-0.827641\pi\)
0.874828 + 0.484434i \(0.160975\pi\)
\(420\) 0 0
\(421\) 22.3923i 1.09133i 0.838002 + 0.545667i \(0.183724\pi\)
−0.838002 + 0.545667i \(0.816276\pi\)
\(422\) −22.5167 + 13.0000i −1.09609 + 0.632830i
\(423\) 0 0
\(424\) 7.00000i 0.339950i
\(425\) −8.33013 14.4282i −0.404071 0.699871i
\(426\) 0 0
\(427\) −4.50000 2.59808i −0.217770 0.125730i
\(428\) 10.8564 0.524764
\(429\) 0 0
\(430\) 2.39230 0.115367
\(431\) 12.2942 + 7.09808i 0.592192 + 0.341902i 0.765964 0.642884i \(-0.222262\pi\)
−0.173772 + 0.984786i \(0.555595\pi\)
\(432\) 0 0
\(433\) −13.5359 23.4449i −0.650494 1.12669i −0.983003 0.183588i \(-0.941229\pi\)
0.332509 0.943100i \(-0.392105\pi\)
\(434\) 2.19615i 0.105419i
\(435\) 0 0
\(436\) −4.09808 + 2.36603i −0.196262 + 0.113312i
\(437\) 3.46410i 0.165710i
\(438\) 0 0
\(439\) −12.5885 + 21.8038i −0.600814 + 1.04064i 0.391884 + 0.920015i \(0.371824\pi\)
−0.992698 + 0.120626i \(0.961510\pi\)
\(440\) −1.09808 0.633975i −0.0523487 0.0302236i
\(441\) 0 0
\(442\) −12.0622 5.96410i −0.573739 0.283683i
\(443\) 33.6410 1.59833 0.799166 0.601110i \(-0.205275\pi\)
0.799166 + 0.601110i \(0.205275\pi\)
\(444\) 0 0
\(445\) 3.83013 6.63397i 0.181565 0.314481i
\(446\) 12.1962 + 21.1244i 0.577505 + 1.00027i
\(447\) 0 0
\(448\) −0.866025 + 0.500000i −0.0409159 + 0.0236228i
\(449\) −17.8301 + 10.2942i −0.841456 + 0.485815i −0.857759 0.514052i \(-0.828144\pi\)
0.0163031 + 0.999867i \(0.494810\pi\)
\(450\) 0 0
\(451\) 2.59808 + 4.50000i 0.122339 + 0.211897i
\(452\) −7.63397 + 13.2224i −0.359072 + 0.621931i
\(453\) 0 0
\(454\) −18.3923 −0.863194
\(455\) −2.63397 + 0.169873i −0.123483 + 0.00796377i
\(456\) 0 0
\(457\) 10.2679 + 5.92820i 0.480314 + 0.277310i 0.720548 0.693406i \(-0.243891\pi\)
−0.240233 + 0.970715i \(0.577224\pi\)
\(458\) 9.96410 17.2583i 0.465592 0.806429i
\(459\) 0 0
\(460\) 2.53590i 0.118237i
\(461\) 23.3205 13.4641i 1.08614 0.627086i 0.153597 0.988134i \(-0.450914\pi\)
0.932547 + 0.361048i \(0.117581\pi\)
\(462\) 0 0
\(463\) 6.26795i 0.291296i −0.989336 0.145648i \(-0.953473\pi\)
0.989336 0.145648i \(-0.0465267\pi\)
\(464\) 3.23205 + 5.59808i 0.150044 + 0.259884i
\(465\) 0 0
\(466\) −7.90192 4.56218i −0.366050 0.211339i
\(467\) −13.8564 −0.641198 −0.320599 0.947215i \(-0.603884\pi\)
−0.320599 + 0.947215i \(0.603884\pi\)
\(468\) 0 0
\(469\) 8.92820 0.412266
\(470\) −1.56218 0.901924i −0.0720579 0.0416026i
\(471\) 0 0
\(472\) −0.464102 0.803848i −0.0213620 0.0370001i
\(473\) 5.66025i 0.260259i
\(474\) 0 0
\(475\) 3.86603 2.23205i 0.177385 0.102414i
\(476\) 3.73205i 0.171058i
\(477\) 0 0
\(478\) 0.366025 0.633975i 0.0167416 0.0289973i
\(479\) 28.1147 + 16.2321i 1.28460 + 0.741661i 0.977685 0.210077i \(-0.0673715\pi\)
0.306910 + 0.951738i \(0.400705\pi\)
\(480\) 0 0
\(481\) 20.1962 13.4641i 0.920865 0.613910i
\(482\) −8.00000 −0.364390
\(483\) 0 0
\(484\) 4.00000 6.92820i 0.181818 0.314918i
\(485\) −5.73205 9.92820i −0.260279 0.450816i
\(486\) 0 0
\(487\) −14.4282 + 8.33013i −0.653804 + 0.377474i −0.789912 0.613220i \(-0.789874\pi\)
0.136108 + 0.990694i \(0.456541\pi\)
\(488\) 4.50000 2.59808i 0.203705 0.117609i
\(489\) 0 0
\(490\) −0.366025 0.633975i −0.0165353 0.0286401i
\(491\) −17.7321 + 30.7128i −0.800236 + 1.38605i 0.119224 + 0.992867i \(0.461959\pi\)
−0.919460 + 0.393182i \(0.871374\pi\)
\(492\) 0 0
\(493\) −24.1244 −1.08651
\(494\) 1.59808 3.23205i 0.0719008 0.145417i
\(495\) 0 0
\(496\) −1.90192 1.09808i −0.0853989 0.0493051i
\(497\) 1.09808 1.90192i 0.0492554 0.0853129i
\(498\) 0 0
\(499\) 11.5167i 0.515557i −0.966204 0.257778i \(-0.917010\pi\)
0.966204 0.257778i \(-0.0829904\pi\)
\(500\) 6.00000 3.46410i 0.268328 0.154919i
\(501\) 0 0
\(502\) 13.1244i 0.585769i
\(503\) 3.46410 + 6.00000i 0.154457 + 0.267527i 0.932861 0.360236i \(-0.117304\pi\)
−0.778404 + 0.627763i \(0.783971\pi\)
\(504\) 0 0
\(505\) 1.94744 + 1.12436i 0.0866600 + 0.0500332i
\(506\) −6.00000 −0.266733
\(507\) 0 0
\(508\) −15.4641 −0.686109
\(509\) 19.3468 + 11.1699i 0.857531 + 0.495096i 0.863185 0.504888i \(-0.168466\pi\)
−0.00565352 + 0.999984i \(0.501800\pi\)
\(510\) 0 0
\(511\) −2.73205 4.73205i −0.120859 0.209334i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −17.8923 + 10.3301i −0.789196 + 0.455642i
\(515\) 10.7846i 0.475227i
\(516\) 0 0
\(517\) −2.13397 + 3.69615i −0.0938521 + 0.162557i
\(518\) 5.83013 + 3.36603i 0.256161 + 0.147895i
\(519\) 0 0
\(520\) 1.16987 2.36603i 0.0513023 0.103757i
\(521\) −7.05256 −0.308978 −0.154489 0.987994i \(-0.549373\pi\)
−0.154489 + 0.987994i \(0.549373\pi\)
\(522\) 0 0
\(523\) 6.93782 12.0167i 0.303370 0.525452i −0.673527 0.739162i \(-0.735222\pi\)
0.976897 + 0.213711i \(0.0685549\pi\)
\(524\) 6.92820 + 12.0000i 0.302660 + 0.524222i
\(525\) 0 0
\(526\) −13.0981 + 7.56218i −0.571103 + 0.329727i
\(527\) 7.09808 4.09808i 0.309197 0.178515i
\(528\) 0 0
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) −2.56218 + 4.43782i −0.111294 + 0.192767i
\(531\) 0 0
\(532\) 1.00000 0.0433555
\(533\) −9.00000 + 6.00000i −0.389833 + 0.259889i
\(534\) 0 0
\(535\) −6.88269 3.97372i −0.297564 0.171799i
\(536\) −4.46410 + 7.73205i −0.192820 + 0.333974i
\(537\) 0 0
\(538\) 9.85641i 0.424940i
\(539\) −1.50000 + 0.866025i −0.0646096 + 0.0373024i
\(540\) 0 0
\(541\) 24.3397i 1.04645i −0.852195 0.523224i \(-0.824729\pi\)
0.852195 0.523224i \(-0.175271\pi\)
\(542\) −14.0263 24.2942i −0.602480 1.04353i
\(543\) 0 0
\(544\) 3.23205 + 1.86603i 0.138573 + 0.0800052i
\(545\) 3.46410 0.148386
\(546\) 0 0
\(547\) −1.26795 −0.0542136 −0.0271068 0.999633i \(-0.508629\pi\)
−0.0271068 + 0.999633i \(0.508629\pi\)
\(548\) −12.4641 7.19615i −0.532440 0.307404i
\(549\) 0 0
\(550\) −3.86603 6.69615i −0.164848 0.285525i
\(551\) 6.46410i 0.275380i
\(552\) 0 0
\(553\) 1.79423 1.03590i 0.0762984 0.0440509i
\(554\) 9.32051i 0.395990i
\(555\) 0 0
\(556\) 5.79423 10.0359i 0.245730 0.425617i
\(557\) −11.3038 6.52628i −0.478959 0.276527i 0.241023 0.970519i \(-0.422517\pi\)
−0.719983 + 0.693992i \(0.755850\pi\)
\(558\) 0 0
\(559\) 11.7583 0.758330i 0.497324 0.0320740i
\(560\) 0.732051 0.0309348
\(561\) 0 0
\(562\) −0.169873 + 0.294229i −0.00716566 + 0.0124113i
\(563\) 18.0981 + 31.3468i 0.762743 + 1.32111i 0.941432 + 0.337204i \(0.109481\pi\)
−0.178689 + 0.983906i \(0.557185\pi\)
\(564\) 0 0
\(565\) 9.67949 5.58846i 0.407219 0.235108i
\(566\) −8.53590 + 4.92820i −0.358791 + 0.207148i
\(567\) 0 0
\(568\) 1.09808 + 1.90192i 0.0460743 + 0.0798029i
\(569\) 19.2224 33.2942i 0.805846 1.39577i −0.109872 0.993946i \(-0.535044\pi\)
0.915718 0.401821i \(-0.131623\pi\)
\(570\) 0 0
\(571\) −16.9808 −0.710623 −0.355311 0.934748i \(-0.615625\pi\)
−0.355311 + 0.934748i \(0.615625\pi\)
\(572\) −5.59808 2.76795i −0.234067 0.115734i
\(573\) 0 0
\(574\) −2.59808 1.50000i −0.108442 0.0626088i
\(575\) 7.73205 13.3923i 0.322449 0.558498i
\(576\) 0 0
\(577\) 10.3397i 0.430449i −0.976565 0.215225i \(-0.930952\pi\)
0.976565 0.215225i \(-0.0690484\pi\)
\(578\) 2.66025 1.53590i 0.110652 0.0638850i
\(579\) 0 0
\(580\) 4.73205i 0.196488i
\(581\) −0.0980762 0.169873i −0.00406889 0.00704752i
\(582\) 0 0
\(583\) 10.5000 + 6.06218i 0.434866 + 0.251070i
\(584\) 5.46410 0.226106
\(585\) 0 0
\(586\) 17.0718 0.705229
\(587\) −10.6865 6.16987i −0.441080 0.254658i 0.262975 0.964803i \(-0.415296\pi\)
−0.704056 + 0.710145i \(0.748630\pi\)
\(588\) 0 0
\(589\) 1.09808 + 1.90192i 0.0452454 + 0.0783674i
\(590\) 0.679492i 0.0279742i
\(591\) 0 0
\(592\) −5.83013 + 3.36603i −0.239617 + 0.138343i
\(593\) 0.464102i 0.0190584i −0.999955 0.00952918i \(-0.996967\pi\)
0.999955 0.00952918i \(-0.00303328\pi\)
\(594\) 0 0
\(595\) −1.36603 + 2.36603i −0.0560016 + 0.0969976i
\(596\) −12.0000 6.92820i −0.491539 0.283790i
\(597\) 0 0
\(598\) −0.803848 12.4641i −0.0328718 0.509695i
\(599\) 28.6410 1.17024 0.585120 0.810947i \(-0.301047\pi\)
0.585120 + 0.810947i \(0.301047\pi\)
\(600\) 0 0
\(601\) 11.3660 19.6865i 0.463630 0.803030i −0.535509 0.844530i \(-0.679880\pi\)
0.999139 + 0.0414993i \(0.0132134\pi\)
\(602\) 1.63397 + 2.83013i 0.0665958 + 0.115347i
\(603\) 0 0
\(604\) −4.50000 + 2.59808i −0.183102 + 0.105714i
\(605\) −5.07180 + 2.92820i −0.206198 + 0.119048i
\(606\) 0 0
\(607\) 15.7583 + 27.2942i 0.639611 + 1.10784i 0.985518 + 0.169570i \(0.0542378\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(608\) −0.500000 + 0.866025i −0.0202777 + 0.0351220i
\(609\) 0 0
\(610\) −3.80385 −0.154013
\(611\) −7.96410 3.93782i −0.322193 0.159307i
\(612\) 0 0
\(613\) 3.46410 + 2.00000i 0.139914 + 0.0807792i 0.568323 0.822806i \(-0.307592\pi\)
−0.428409 + 0.903585i \(0.640926\pi\)
\(614\) −4.30385 + 7.45448i −0.173689 + 0.300838i
\(615\) 0 0
\(616\) 1.73205i 0.0697863i
\(617\) −1.90192 + 1.09808i −0.0765686 + 0.0442069i −0.537795 0.843075i \(-0.680743\pi\)
0.461227 + 0.887282i \(0.347409\pi\)
\(618\) 0 0
\(619\) 22.0718i 0.887140i 0.896240 + 0.443570i \(0.146288\pi\)
−0.896240 + 0.443570i \(0.853712\pi\)
\(620\) 0.803848 + 1.39230i 0.0322833 + 0.0559163i
\(621\) 0 0
\(622\) 3.69615 + 2.13397i 0.148202 + 0.0855646i
\(623\) 10.4641 0.419235
\(624\) 0 0
\(625\) 17.2487 0.689948
\(626\) 11.7058 + 6.75833i 0.467857 + 0.270117i
\(627\) 0 0
\(628\) −0.267949 0.464102i −0.0106923 0.0185197i
\(629\) 25.1244i 1.00177i
\(630\) 0 0
\(631\) 14.5526 8.40192i 0.579328 0.334475i −0.181538 0.983384i \(-0.558108\pi\)
0.760866 + 0.648909i \(0.224774\pi\)
\(632\) 2.07180i 0.0824117i
\(633\) 0 0
\(634\) 5.92820 10.2679i 0.235439 0.407792i
\(635\) 9.80385 + 5.66025i 0.389054 + 0.224620i
\(636\) 0 0
\(637\) −2.00000 3.00000i −0.0792429 0.118864i
\(638\) −11.1962 −0.443260
\(639\) 0 0
\(640\) −0.366025 + 0.633975i −0.0144684 + 0.0250600i
\(641\) −15.5885 27.0000i −0.615707 1.06644i −0.990260 0.139230i \(-0.955537\pi\)
0.374553 0.927206i \(-0.377796\pi\)
\(642\) 0 0
\(643\) 28.4545 16.4282i 1.12214 0.647865i 0.180190 0.983632i \(-0.442329\pi\)
0.941945 + 0.335767i \(0.108995\pi\)
\(644\) 3.00000 1.73205i 0.118217 0.0682524i
\(645\) 0 0
\(646\) −1.86603 3.23205i −0.0734178 0.127163i
\(647\) −17.9186 + 31.0359i −0.704452 + 1.22015i 0.262437 + 0.964949i \(0.415474\pi\)
−0.966889 + 0.255198i \(0.917859\pi\)
\(648\) 0 0
\(649\) 1.60770 0.0631076
\(650\) 13.3923 8.92820i 0.525289 0.350193i
\(651\) 0 0
\(652\) 2.36603 + 1.36603i 0.0926607 + 0.0534977i
\(653\) 23.3564 40.4545i 0.914007 1.58311i 0.105658 0.994403i \(-0.466305\pi\)
0.808349 0.588704i \(-0.200362\pi\)
\(654\) 0 0
\(655\) 10.1436i 0.396343i
\(656\) 2.59808 1.50000i 0.101438 0.0585652i
\(657\) 0 0
\(658\) 2.46410i 0.0960607i
\(659\) 9.30385 + 16.1147i 0.362426 + 0.627741i 0.988360 0.152136i \(-0.0486151\pi\)
−0.625933 + 0.779877i \(0.715282\pi\)
\(660\) 0 0
\(661\) 10.7321 + 6.19615i 0.417428 + 0.241002i 0.693976 0.719998i \(-0.255857\pi\)
−0.276548 + 0.961000i \(0.589190\pi\)
\(662\) 27.8564 1.08267
\(663\) 0 0
\(664\) 0.196152 0.00761219
\(665\) −0.633975 0.366025i −0.0245845 0.0141939i
\(666\) 0 0
\(667\) −11.1962 19.3923i −0.433517 0.750873i
\(668\) 13.8564i 0.536120i
\(669\) 0 0
\(670\) 5.66025 3.26795i 0.218675 0.126252i
\(671\) 9.00000i 0.347441i
\(672\) 0 0
\(673\) −16.3564 + 28.3301i −0.630493 + 1.09205i 0.356958 + 0.934120i \(0.383814\pi\)
−0.987451 + 0.157926i \(0.949519\pi\)
\(674\) −16.4545 9.50000i −0.633803 0.365926i
\(675\) 0 0
\(676\) 5.00000 12.0000i 0.192308 0.461538i
\(677\) −36.7321 −1.41173 −0.705864 0.708348i \(-0.749441\pi\)
−0.705864 + 0.708348i \(0.749441\pi\)
\(678\) 0 0
\(679\) 7.83013 13.5622i 0.300493 0.520469i
\(680\) −1.36603 2.36603i −0.0523847 0.0907329i
\(681\) 0 0
\(682\) 3.29423 1.90192i 0.126143 0.0728284i
\(683\) −25.6410 + 14.8038i −0.981126 + 0.566453i −0.902610 0.430459i \(-0.858352\pi\)
−0.0785163 + 0.996913i \(0.525018\pi\)
\(684\) 0 0
\(685\) 5.26795 + 9.12436i 0.201278 + 0.348624i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) −3.26795 −0.124589
\(689\) −11.1865 + 22.6244i −0.426173 + 0.861919i
\(690\) 0 0
\(691\) 37.8564 + 21.8564i 1.44013 + 0.831457i 0.997857 0.0654260i \(-0.0208406\pi\)
0.442268 + 0.896883i \(0.354174\pi\)
\(692\) −4.56218 + 7.90192i −0.173428 + 0.300386i
\(693\) 0 0
\(694\) 5.39230i 0.204689i
\(695\) −7.34679 + 4.24167i −0.278680 + 0.160896i
\(696\) 0 0
\(697\) 11.1962i 0.424085i
\(698\) −11.8564 20.5359i −0.448772 0.777295i
\(699\) 0 0
\(700\) 3.86603 + 2.23205i 0.146122 + 0.0843636i
\(701\) 1.14359 0.0431929 0.0215965 0.999767i \(-0.493125\pi\)
0.0215965 + 0.999767i \(0.493125\pi\)
\(702\) 0 0
\(703\) 6.73205 0.253904
\(704\) 1.50000 + 0.866025i 0.0565334 + 0.0326396i
\(705\) 0 0
\(706\) 4.73205 + 8.19615i 0.178093 + 0.308466i
\(707\) 3.07180i 0.115527i
\(708\) 0 0
\(709\) −27.7583 + 16.0263i −1.04249 + 0.601880i −0.920536 0.390657i \(-0.872248\pi\)
−0.121950 + 0.992536i \(0.538915\pi\)
\(710\) 1.60770i 0.0603357i
\(711\) 0 0
\(712\) −5.23205 + 9.06218i −0.196079 + 0.339619i
\(713\) 6.58846 + 3.80385i 0.246740 + 0.142455i
\(714\) 0 0
\(715\) 2.53590 + 3.80385i 0.0948372 + 0.142256i
\(716\) −11.4641 −0.428434
\(717\) 0 0
\(718\) −1.90192 + 3.29423i −0.0709792 + 0.122940i
\(719\) −13.2583 22.9641i −0.494452 0.856416i 0.505527 0.862811i \(-0.331298\pi\)
−0.999980 + 0.00639415i \(0.997965\pi\)
\(720\) 0 0
\(721\) −12.7583 + 7.36603i −0.475145 + 0.274325i
\(722\) −15.5885 + 9.00000i −0.580142 + 0.334945i
\(723\) 0 0
\(724\) 1.33013 + 2.30385i 0.0494338 + 0.0856218i
\(725\) 14.4282 24.9904i 0.535850 0.928119i
\(726\) 0 0
\(727\) 19.3205 0.716558 0.358279 0.933615i \(-0.383364\pi\)
0.358279 + 0.933615i \(0.383364\pi\)
\(728\) 3.59808 0.232051i 0.133354 0.00860038i
\(729\) 0 0
\(730\) −3.46410 2.00000i −0.128212 0.0740233i
\(731\) 6.09808 10.5622i 0.225545 0.390656i
\(732\) 0 0
\(733\) 48.1769i 1.77945i −0.456492 0.889727i \(-0.650894\pi\)
0.456492 0.889727i \(-0.349106\pi\)
\(734\) −21.9282 + 12.6603i −0.809385 + 0.467299i
\(735\) 0 0
\(736\) 3.46410i 0.127688i
\(737\) −7.73205 13.3923i −0.284814 0.493312i
\(738\) 0 0
\(739\) 13.1436 + 7.58846i 0.483495 + 0.279146i 0.721872 0.692027i \(-0.243282\pi\)
−0.238377 + 0.971173i \(0.576615\pi\)
\(740\) 4.92820 0.181164
\(741\) 0 0
\(742\) −7.00000 −0.256978
\(743\) 12.1699 + 7.02628i 0.446469 + 0.257769i 0.706338 0.707875i \(-0.250346\pi\)
−0.259869 + 0.965644i \(0.583679\pi\)
\(744\) 0 0
\(745\) 5.07180 + 8.78461i 0.185816 + 0.321843i
\(746\) 9.66025i 0.353687i
\(747\) 0 0
\(748\) −5.59808 + 3.23205i −0.204686 + 0.118175i
\(749\) 10.8564i 0.396684i
\(750\) 0 0
\(751\) −9.57180 + 16.5788i −0.349280 + 0.604970i −0.986122 0.166024i \(-0.946907\pi\)
0.636842 + 0.770994i \(0.280240\pi\)
\(752\) 2.13397 + 1.23205i 0.0778180 + 0.0449283i
\(753\) 0 0
\(754\) −1.50000 23.2583i −0.0546268 0.847018i
\(755\) 3.80385 0.138436
\(756\) 0 0
\(757\) 0.294229 0.509619i 0.0106939 0.0185224i −0.860629 0.509233i \(-0.829929\pi\)
0.871323 + 0.490710i \(0.163263\pi\)
\(758\) 14.2224 + 24.6340i 0.516582 + 0.894746i
\(759\) 0 0
\(760\) 0.633975 0.366025i 0.0229967 0.0132771i
\(761\) −13.2679 + 7.66025i −0.480963 + 0.277684i −0.720818 0.693125i \(-0.756233\pi\)
0.239855 + 0.970809i \(0.422900\pi\)
\(762\) 0 0
\(763\) 2.36603 + 4.09808i 0.0856559 + 0.148360i
\(764\) −11.5622 + 20.0263i −0.418305 + 0.724525i
\(765\) 0 0
\(766\) 5.53590 0.200020
\(767\) 0.215390 + 3.33975i 0.00777729 + 0.120591i
\(768\) 0 0
\(769\) 36.6340 + 21.1506i 1.32105 + 0.762711i 0.983897 0.178737i \(-0.0572010\pi\)
0.337158 + 0.941448i \(0.390534\pi\)
\(770\) −0.633975 + 1.09808i −0.0228469 + 0.0395719i
\(771\) 0 0
\(772\) 1.19615i 0.0430505i
\(773\) 40.8564 23.5885i 1.46950 0.848418i 0.470088 0.882620i \(-0.344222\pi\)
0.999415 + 0.0342018i \(0.0108889\pi\)
\(774\) 0 0
\(775\) 9.80385i 0.352165i
\(776\) 7.83013 + 13.5622i 0.281085 + 0.486854i
\(777\) 0 0
\(778\) 7.26795 + 4.19615i 0.260569 + 0.150439i
\(779\) −3.00000 −0.107486
\(780\) 0 0
\(781\) −3.80385 −0.136112
\(782\) −11.1962 6.46410i −0.400374 0.231156i
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.0178571 + 0.0309295i
\(785\) 0.392305i 0.0140020i
\(786\) 0 0
\(787\) 3.18653 1.83975i 0.113588 0.0655799i −0.442130 0.896951i \(-0.645777\pi\)
0.555717 + 0.831371i \(0.312444\pi\)