Properties

Label 1386.2.k.g.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.g.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(3.00000 + 5.19615i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(2.00000 - 1.73205i) q^{28} -8.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +5.00000 q^{34} +(-0.500000 - 2.59808i) q^{35} +(4.00000 + 6.92820i) q^{37} +(3.00000 - 5.19615i) q^{38} +(0.500000 + 0.866025i) q^{40} +7.00000 q^{41} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-3.50000 + 6.06218i) q^{46} +(0.500000 + 0.866025i) q^{47} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +1.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +(4.00000 + 6.92820i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{61} +10.0000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(-2.00000 + 1.73205i) q^{70} -8.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(4.00000 - 6.92820i) q^{74} -6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(4.50000 + 7.79423i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-3.50000 - 6.06218i) q^{82} -15.0000 q^{83} -5.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(6.00000 + 10.3923i) q^{89} +(-5.00000 - 1.73205i) q^{91} +7.00000 q^{92} +(0.500000 - 0.866025i) q^{94} +(-3.00000 + 5.19615i) q^{95} +13.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} + q^{5} - 5 q^{7} + 2 q^{8} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} + q^{5} - 5 q^{7} + 2 q^{8} + q^{10} + q^{11} + 4 q^{13} + q^{14} - q^{16} - 5 q^{17} + 6 q^{19} - 2 q^{20} - 2 q^{22} - 7 q^{23} + 4 q^{25} - 2 q^{26} + 4 q^{28} - 16 q^{29} - 10 q^{31} - q^{32} + 10 q^{34} - q^{35} + 8 q^{37} + 6 q^{38} + q^{40} + 14 q^{41} + 8 q^{43} + q^{44} - 7 q^{46} + q^{47} + 11 q^{49} - 8 q^{50} - 2 q^{52} - 6 q^{53} + 2 q^{55} - 5 q^{56} + 8 q^{58} - 6 q^{59} - q^{61} + 20 q^{62} + 2 q^{64} + 2 q^{65} - 3 q^{67} - 5 q^{68} - 4 q^{70} - 16 q^{71} - 10 q^{73} + 8 q^{74} - 12 q^{76} - 4 q^{77} + 9 q^{79} + q^{80} - 7 q^{82} - 30 q^{83} - 10 q^{85} - 4 q^{86} + q^{88} + 12 q^{89} - 10 q^{91} + 14 q^{92} + q^{94} - 6 q^{95} + 26 q^{97} + 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.50000 + 4.33013i −0.606339 + 1.05021i 0.385499 + 0.922708i \(0.374029\pi\)
−0.991838 + 0.127502i \(0.959304\pi\)
\(18\) 0 0
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i \(-0.906280\pi\)
0.227167 0.973856i \(-0.427054\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) −5.00000 + 8.66025i −0.898027 + 1.55543i −0.0680129 + 0.997684i \(0.521666\pi\)
−0.830014 + 0.557743i \(0.811667\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 5.00000 0.857493
\(35\) −0.500000 2.59808i −0.0845154 0.439155i
\(36\) 0 0
\(37\) 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i \(0.0617599\pi\)
−0.323640 + 0.946180i \(0.604907\pi\)
\(38\) 3.00000 5.19615i 0.486664 0.842927i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −3.50000 + 6.06218i −0.516047 + 0.893819i
\(47\) 0.500000 + 0.866025i 0.0729325 + 0.126323i 0.900185 0.435507i \(-0.143431\pi\)
−0.827253 + 0.561830i \(0.810098\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) 0 0
\(58\) 4.00000 + 6.92820i 0.525226 + 0.909718i
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 10.0000 1.27000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) −2.50000 4.33013i −0.303170 0.525105i
\(69\) 0 0
\(70\) −2.00000 + 1.73205i −0.239046 + 0.207020i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 4.00000 6.92820i 0.464991 0.805387i
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) 0 0
\(79\) 4.50000 + 7.79423i 0.506290 + 0.876919i 0.999974 + 0.00727784i \(0.00231663\pi\)
−0.493684 + 0.869641i \(0.664350\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 0 0
\(82\) −3.50000 6.06218i −0.386510 0.669456i
\(83\) −15.0000 −1.64646 −0.823232 0.567705i \(-0.807831\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(84\) 0 0
\(85\) −5.00000 −0.542326
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) 0 0
\(91\) −5.00000 1.73205i −0.524142 0.181568i
\(92\) 7.00000 0.729800
\(93\) 0 0
\(94\) 0.500000 0.866025i 0.0515711 0.0893237i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 0 0
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) −6.00000 10.3923i −0.591198 1.02398i −0.994071 0.108729i \(-0.965322\pi\)
0.402874 0.915255i \(-0.368011\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 6.50000 + 11.2583i 0.628379 + 1.08838i 0.987877 + 0.155238i \(0.0496145\pi\)
−0.359498 + 0.933146i \(0.617052\pi\)
\(108\) 0 0
\(109\) −9.50000 + 16.4545i −0.909935 + 1.57605i −0.0957826 + 0.995402i \(0.530535\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −0.500000 0.866025i −0.0476731 0.0825723i
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 3.50000 6.06218i 0.326377 0.565301i
\(116\) 4.00000 6.92820i 0.371391 0.643268i
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 10.0000 8.66025i 0.916698 0.793884i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) 0 0
\(124\) −5.00000 8.66025i −0.449013 0.777714i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 1.00000 1.73205i 0.0877058 0.151911i
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 0 0
\(133\) −3.00000 15.5885i −0.260133 1.35169i
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) −2.50000 + 4.33013i −0.214373 + 0.371305i
\(137\) 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 2.50000 + 0.866025i 0.211289 + 0.0731925i
\(141\) 0 0
\(142\) 4.00000 + 6.92820i 0.335673 + 0.581402i
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) 0 0
\(145\) −4.00000 6.92820i −0.332182 0.575356i
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) −8.00000 −0.657596
\(149\) 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i \(-0.114277\pi\)
−0.772399 + 0.635138i \(0.780943\pi\)
\(150\) 0 0
\(151\) −4.50000 + 7.79423i −0.366205 + 0.634285i −0.988969 0.148124i \(-0.952676\pi\)
0.622764 + 0.782410i \(0.286010\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) 0 0
\(154\) 2.50000 + 0.866025i 0.201456 + 0.0697863i
\(155\) −10.0000 −0.803219
\(156\) 0 0
\(157\) −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i \(-0.884359\pi\)
0.775113 + 0.631822i \(0.217693\pi\)
\(158\) 4.50000 7.79423i 0.358001 0.620076i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 3.50000 + 18.1865i 0.275839 + 1.43330i
\(162\) 0 0
\(163\) −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i \(-0.996638\pi\)
0.490825 0.871258i \(-0.336695\pi\)
\(164\) −3.50000 + 6.06218i −0.273304 + 0.473377i
\(165\) 0 0
\(166\) 7.50000 + 12.9904i 0.582113 + 1.00825i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 2.50000 + 4.33013i 0.191741 + 0.332106i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 7.00000 + 12.1244i 0.532200 + 0.921798i 0.999293 + 0.0375896i \(0.0119679\pi\)
−0.467093 + 0.884208i \(0.654699\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.92820i −0.604743 + 0.523723i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) 1.00000 1.73205i 0.0747435 0.129460i −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 1.00000 + 5.19615i 0.0741249 + 0.385164i
\(183\) 0 0
\(184\) −3.50000 6.06218i −0.258023 0.446910i
\(185\) −4.00000 + 6.92820i −0.294086 + 0.509372i
\(186\) 0 0
\(187\) 2.50000 + 4.33013i 0.182818 + 0.316650i
\(188\) −1.00000 −0.0729325
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i \(-0.909164\pi\)
0.235983 0.971757i \(-0.424169\pi\)
\(192\) 0 0
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) −6.50000 11.2583i −0.466673 0.808301i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 0 0
\(199\) 13.0000 22.5167i 0.921546 1.59616i 0.124521 0.992217i \(-0.460261\pi\)
0.797025 0.603947i \(-0.206406\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 0 0
\(202\) 12.0000 0.844317
\(203\) 20.0000 + 6.92820i 1.40372 + 0.486265i
\(204\) 0 0
\(205\) 3.50000 + 6.06218i 0.244451 + 0.423401i
\(206\) −6.00000 + 10.3923i −0.418040 + 0.724066i
\(207\) 0 0
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) 6.50000 11.2583i 0.444331 0.769604i
\(215\) 2.00000 + 3.46410i 0.136399 + 0.236250i
\(216\) 0 0
\(217\) 20.0000 17.3205i 1.35769 1.17579i
\(218\) 19.0000 1.28684
\(219\) 0 0
\(220\) −0.500000 + 0.866025i −0.0337100 + 0.0583874i
\(221\) −5.00000 + 8.66025i −0.336336 + 0.582552i
\(222\) 0 0
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) 8.50000 14.7224i 0.564165 0.977162i −0.432962 0.901412i \(-0.642532\pi\)
0.997127 0.0757500i \(-0.0241351\pi\)
\(228\) 0 0
\(229\) −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i \(-0.936876\pi\)
0.319582 0.947559i \(-0.396457\pi\)
\(230\) −7.00000 −0.461566
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) −10.5000 18.1865i −0.687878 1.19144i −0.972523 0.232806i \(-0.925209\pi\)
0.284645 0.958633i \(-0.408124\pi\)
\(234\) 0 0
\(235\) −0.500000 + 0.866025i −0.0326164 + 0.0564933i
\(236\) −3.00000 5.19615i −0.195283 0.338241i
\(237\) 0 0
\(238\) −12.5000 4.33013i −0.810255 0.280680i
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −6.00000 + 10.3923i −0.386494 + 0.669427i −0.991975 0.126432i \(-0.959647\pi\)
0.605481 + 0.795860i \(0.292981\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 1.00000 0.0640184
\(245\) −1.00000 + 6.92820i −0.0638877 + 0.442627i
\(246\) 0 0
\(247\) 6.00000 + 10.3923i 0.381771 + 0.661247i
\(248\) −5.00000 + 8.66025i −0.317500 + 0.549927i
\(249\) 0 0
\(250\) −4.50000 7.79423i −0.284605 0.492950i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) −7.00000 −0.440086
\(254\) −8.50000 14.7224i −0.533337 0.923768i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) −4.00000 20.7846i −0.248548 1.29149i
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) −6.00000 + 10.3923i −0.370681 + 0.642039i
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −12.0000 + 10.3923i −0.735767 + 0.637193i
\(267\) 0 0
\(268\) −1.50000 2.59808i −0.0916271 0.158703i
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 5.00000 0.303170
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0 0
\(277\) 9.00000 15.5885i 0.540758 0.936620i −0.458103 0.888899i \(-0.651471\pi\)
0.998861 0.0477206i \(-0.0151957\pi\)
\(278\) −1.00000 1.73205i −0.0599760 0.103882i
\(279\) 0 0
\(280\) −0.500000 2.59808i −0.0298807 0.155265i
\(281\) −19.0000 −1.13344 −0.566722 0.823909i \(-0.691789\pi\)
−0.566722 + 0.823909i \(0.691789\pi\)
\(282\) 0 0
\(283\) −12.0000 + 20.7846i −0.713326 + 1.23552i 0.250276 + 0.968175i \(0.419479\pi\)
−0.963602 + 0.267342i \(0.913855\pi\)
\(284\) 4.00000 6.92820i 0.237356 0.411113i
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) −17.5000 6.06218i −1.03299 0.357839i
\(288\) 0 0
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) −4.00000 + 6.92820i −0.234888 + 0.406838i
\(291\) 0 0
\(292\) −5.00000 8.66025i −0.292603 0.506803i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) 0 0
\(298\) 2.00000 3.46410i 0.115857 0.200670i
\(299\) −7.00000 12.1244i −0.404820 0.701170i
\(300\) 0 0
\(301\) −10.0000 3.46410i −0.576390 0.199667i
\(302\) 9.00000 0.517892
\(303\) 0 0
\(304\) 3.00000 5.19615i 0.172062 0.298020i
\(305\) 0.500000 0.866025i 0.0286299 0.0495885i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −0.500000 2.59808i −0.0284901 0.148039i
\(309\) 0 0
\(310\) 5.00000 + 8.66025i 0.283981 + 0.491869i
\(311\) −8.50000 + 14.7224i −0.481991 + 0.834833i −0.999786 0.0206719i \(-0.993419\pi\)
0.517796 + 0.855504i \(0.326753\pi\)
\(312\) 0 0
\(313\) −11.0000 19.0526i −0.621757 1.07691i −0.989158 0.146852i \(-0.953086\pi\)
0.367402 0.930062i \(-0.380247\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −9.00000 −0.506290
\(317\) 1.50000 + 2.59808i 0.0842484 + 0.145922i 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(318\) 0 0
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 14.0000 12.1244i 0.780189 0.675664i
\(323\) −30.0000 −1.66924
\(324\) 0 0
\(325\) 4.00000 6.92820i 0.221880 0.384308i
\(326\) −6.50000 + 11.2583i −0.360002 + 0.623541i
\(327\) 0 0
\(328\) 7.00000 0.386510
\(329\) −0.500000 2.59808i −0.0275659 0.143237i
\(330\) 0 0
\(331\) −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(332\) 7.50000 12.9904i 0.411616 0.712940i
\(333\) 0 0
\(334\) 4.00000 + 6.92820i 0.218870 + 0.379094i
\(335\) −3.00000 −0.163908
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 0 0
\(340\) 2.50000 4.33013i 0.135582 0.234834i
\(341\) 5.00000 + 8.66025i 0.270765 + 0.468979i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 7.00000 12.1244i 0.376322 0.651809i
\(347\) 6.50000 11.2583i 0.348938 0.604379i −0.637123 0.770762i \(-0.719876\pi\)
0.986061 + 0.166383i \(0.0532089\pi\)
\(348\) 0 0
\(349\) −13.0000 −0.695874 −0.347937 0.937518i \(-0.613118\pi\)
−0.347937 + 0.937518i \(0.613118\pi\)
\(350\) 10.0000 + 3.46410i 0.534522 + 0.185164i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 0 0
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) −12.0000 −0.635999
\(357\) 0 0
\(358\) −2.00000 −0.105703
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −10.0000 17.3205i −0.525588 0.910346i
\(363\) 0 0
\(364\) 4.00000 3.46410i 0.209657 0.181568i
\(365\) −10.0000 −0.523424
\(366\) 0 0
\(367\) 1.00000 1.73205i 0.0521996 0.0904123i −0.838745 0.544524i \(-0.816710\pi\)
0.890945 + 0.454112i \(0.150043\pi\)
\(368\) −3.50000 + 6.06218i −0.182450 + 0.316013i
\(369\) 0 0
\(370\) 8.00000 0.415900
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 2.50000 4.33013i 0.129272 0.223906i
\(375\) 0 0
\(376\) 0.500000 + 0.866025i 0.0257855 + 0.0446619i
\(377\) −16.0000 −0.824042
\(378\) 0 0
\(379\) −17.0000 −0.873231 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 0 0
\(382\) −10.0000 + 17.3205i −0.511645 + 0.886194i
\(383\) 8.00000 + 13.8564i 0.408781 + 0.708029i 0.994753 0.102302i \(-0.0326207\pi\)
−0.585973 + 0.810331i \(0.699287\pi\)
\(384\) 0 0
\(385\) −2.50000 0.866025i −0.127412 0.0441367i
\(386\) 8.00000 0.407189
\(387\) 0 0
\(388\) −6.50000 + 11.2583i −0.329988 + 0.571555i
\(389\) −7.50000 + 12.9904i −0.380265 + 0.658638i −0.991100 0.133120i \(-0.957501\pi\)
0.610835 + 0.791758i \(0.290834\pi\)
\(390\) 0 0
\(391\) 35.0000 1.77003
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) 0 0
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) −4.50000 + 7.79423i −0.226420 + 0.392170i
\(396\) 0 0
\(397\) −6.00000 10.3923i −0.301131 0.521575i 0.675261 0.737579i \(-0.264031\pi\)
−0.976392 + 0.216004i \(0.930698\pi\)
\(398\) −26.0000 −1.30326
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 0 0
\(403\) −10.0000 + 17.3205i −0.498135 + 0.862796i
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) 0 0
\(406\) −4.00000 20.7846i −0.198517 1.03152i
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 3.50000 6.06218i 0.172853 0.299390i
\(411\) 0 0
\(412\) 12.0000 0.591198
\(413\) 12.0000 10.3923i 0.590481 0.511372i
\(414\) 0 0
\(415\) −7.50000 12.9904i −0.368161 0.637673i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 0 0
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) 10.0000 + 17.3205i 0.486792 + 0.843149i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 10.0000 + 17.3205i 0.485071 + 0.840168i
\(426\) 0 0
\(427\) 0.500000 + 2.59808i 0.0241967 + 0.125730i
\(428\) −13.0000 −0.628379
\(429\) 0 0
\(430\) 2.00000 3.46410i 0.0964486 0.167054i
\(431\) −5.00000 + 8.66025i −0.240842 + 0.417150i −0.960954 0.276707i \(-0.910757\pi\)
0.720113 + 0.693857i \(0.244090\pi\)
\(432\) 0 0
\(433\) −13.0000 −0.624740 −0.312370 0.949960i \(-0.601123\pi\)
−0.312370 + 0.949960i \(0.601123\pi\)
\(434\) −25.0000 8.66025i −1.20004 0.415705i
\(435\) 0 0
\(436\) −9.50000 16.4545i −0.454967 0.788027i
\(437\) 21.0000 36.3731i 1.00457 1.73996i
\(438\) 0 0
\(439\) −3.50000 6.06218i −0.167046 0.289332i 0.770334 0.637641i \(-0.220089\pi\)
−0.937380 + 0.348309i \(0.886756\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) 10.0000 0.475651
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −5.00000 8.66025i −0.236757 0.410075i
\(447\) 0 0
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) 3.50000 6.06218i 0.164809 0.285457i
\(452\) −7.00000 + 12.1244i −0.329252 + 0.570282i
\(453\) 0 0
\(454\) −17.0000 −0.797850
\(455\) −1.00000 5.19615i −0.0468807 0.243599i
\(456\) 0 0
\(457\) −4.00000 6.92820i −0.187112 0.324088i 0.757174 0.653213i \(-0.226579\pi\)
−0.944286 + 0.329125i \(0.893246\pi\)
\(458\) −10.0000 + 17.3205i −0.467269 + 0.809334i
\(459\) 0 0
\(460\) 3.50000 + 6.06218i 0.163188 + 0.282650i
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 4.00000 + 6.92820i 0.185695 + 0.321634i
\(465\) 0 0
\(466\) −10.5000 + 18.1865i −0.486403 + 0.842475i
\(467\) −3.00000 5.19615i −0.138823 0.240449i 0.788228 0.615383i \(-0.210999\pi\)
−0.927052 + 0.374934i \(0.877665\pi\)
\(468\) 0 0
\(469\) 6.00000 5.19615i 0.277054 0.239936i
\(470\) 1.00000 0.0461266
\(471\) 0 0
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 0 0
\(475\) 24.0000 1.10120
\(476\) 2.50000 + 12.9904i 0.114587 + 0.595413i
\(477\) 0 0
\(478\) −8.00000 13.8564i −0.365911 0.633777i
\(479\) 2.00000 3.46410i 0.0913823 0.158279i −0.816711 0.577047i \(-0.804205\pi\)
0.908093 + 0.418769i \(0.137538\pi\)
\(480\) 0 0
\(481\) 8.00000 + 13.8564i 0.364769 + 0.631798i
\(482\) 12.0000 0.546585
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 6.50000 + 11.2583i 0.295150 + 0.511214i
\(486\) 0 0
\(487\) 5.00000 8.66025i 0.226572 0.392434i −0.730218 0.683214i \(-0.760582\pi\)
0.956790 + 0.290780i \(0.0939149\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) 0 0
\(490\) 6.50000 2.59808i 0.293640 0.117369i
\(491\) 9.00000 0.406164 0.203082 0.979162i \(-0.434904\pi\)
0.203082 + 0.979162i \(0.434904\pi\)
\(492\) 0 0
\(493\) 20.0000 34.6410i 0.900755 1.56015i
\(494\) 6.00000 10.3923i 0.269953 0.467572i
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 20.0000 + 6.92820i 0.897123 + 0.310772i
\(498\) 0 0
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 0 0
\(502\) −12.0000 20.7846i −0.535586 0.927663i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 3.50000 + 6.06218i 0.155594 + 0.269497i
\(507\) 0 0
\(508\) −8.50000 + 14.7224i −0.377127 + 0.653202i
\(509\) 11.0000 + 19.0526i 0.487566 + 0.844490i 0.999898 0.0142980i \(-0.00455136\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(510\) 0 0
\(511\) 20.0000 17.3205i 0.884748 0.766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0 0
\(515\) 6.00000 10.3923i 0.264392 0.457940i
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) −16.0000 + 13.8564i −0.703000 + 0.608816i
\(519\) 0 0
\(520\) 1.00000 + 1.73205i 0.0438529 + 0.0759555i
\(521\) −5.00000 + 8.66025i −0.219054 + 0.379413i −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) 0 0
\(523\) 17.0000 + 29.4449i 0.743358 + 1.28753i 0.950958 + 0.309320i \(0.100101\pi\)
−0.207600 + 0.978214i \(0.566565\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 18.0000 0.784837
\(527\) −25.0000 43.3013i −1.08902 1.88623i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 3.00000 + 5.19615i 0.130312 + 0.225706i
\(531\) 0 0
\(532\) 15.0000 + 5.19615i 0.650332 + 0.225282i
\(533\) 14.0000 0.606407
\(534\) 0 0
\(535\) −6.50000 + 11.2583i −0.281020 + 0.486740i
\(536\) −1.50000 + 2.59808i −0.0647901 + 0.112220i
\(537\) 0 0
\(538\) 3.00000 0.129339
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) 0 0
\(541\) 0.500000 + 0.866025i 0.0214967 + 0.0372333i 0.876574 0.481268i \(-0.159824\pi\)
−0.855077 + 0.518501i \(0.826490\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 0 0
\(544\) −2.50000 4.33013i −0.107187 0.185653i
\(545\) −19.0000 −0.813871
\(546\) 0 0
\(547\) 6.00000 0.256541 0.128271 0.991739i \(-0.459057\pi\)
0.128271 + 0.991739i \(0.459057\pi\)
\(548\) 9.00000 + 15.5885i 0.384461 + 0.665906i
\(549\) 0 0
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) −24.0000 41.5692i −1.02243 1.77091i
\(552\) 0 0
\(553\) −4.50000 23.3827i −0.191359 0.994333i
\(554\) −18.0000 −0.764747
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 8.00000 13.8564i 0.338971 0.587115i −0.645269 0.763956i \(-0.723255\pi\)
0.984239 + 0.176841i \(0.0565879\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) −2.00000 + 1.73205i −0.0845154 + 0.0731925i
\(561\) 0 0
\(562\) 9.50000 + 16.4545i 0.400733 + 0.694090i
\(563\) 14.0000 24.2487i 0.590030 1.02196i −0.404198 0.914671i \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 0 0
\(565\) 7.00000 + 12.1244i 0.294492 + 0.510075i
\(566\) 24.0000 1.00880
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i \(0.176036\pi\)
0.0294311 + 0.999567i \(0.490630\pi\)
\(570\) 0 0
\(571\) −8.00000 + 13.8564i −0.334790 + 0.579873i −0.983444 0.181210i \(-0.941999\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) 0 0
\(574\) 3.50000 + 18.1865i 0.146087 + 0.759091i
\(575\) −28.0000 −1.16768
\(576\) 0 0
\(577\) 3.50000 6.06218i 0.145707 0.252372i −0.783930 0.620850i \(-0.786788\pi\)
0.929636 + 0.368478i \(0.120121\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 0 0
\(580\) 8.00000 0.332182
\(581\) 37.5000 + 12.9904i 1.55576 + 0.538932i
\(582\) 0 0
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) −5.00000 + 8.66025i −0.206901 + 0.358364i
\(585\) 0 0
\(586\) −3.00000 5.19615i −0.123929 0.214651i
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) 3.00000 + 5.19615i 0.123508 + 0.213922i
\(591\) 0 0
\(592\) 4.00000 6.92820i 0.164399 0.284747i
\(593\) 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 0 0
\(595\) 12.5000 + 4.33013i 0.512450 + 0.177518i
\(596\) −4.00000 −0.163846
\(597\) 0 0
\(598\) −7.00000 + 12.1244i −0.286251 + 0.495802i
\(599\) −1.50000 + 2.59808i −0.0612883 + 0.106155i −0.895042 0.445983i \(-0.852854\pi\)
0.833753 + 0.552137i \(0.186188\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 2.00000 + 10.3923i 0.0815139 + 0.423559i
\(603\) 0 0
\(604\) −4.50000 7.79423i −0.183102 0.317143i
\(605\) 0.500000 0.866025i 0.0203279 0.0352089i
\(606\) 0 0
\(607\) −14.5000 25.1147i −0.588537 1.01938i −0.994424 0.105453i \(-0.966371\pi\)
0.405887 0.913923i \(-0.366962\pi\)
\(608\) −6.00000 −0.243332
\(609\) 0 0
\(610\) −1.00000 −0.0404888
\(611\) 1.00000 + 1.73205i 0.0404557 + 0.0700713i
\(612\) 0 0
\(613\) 5.50000 9.52628i 0.222143 0.384763i −0.733316 0.679888i \(-0.762028\pi\)
0.955458 + 0.295126i \(0.0953615\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) 0 0
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) −24.0000 −0.966204 −0.483102 0.875564i \(-0.660490\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(618\) 0 0
\(619\) 3.50000 6.06218i 0.140677 0.243659i −0.787075 0.616858i \(-0.788405\pi\)
0.927752 + 0.373198i \(0.121739\pi\)
\(620\) 5.00000 8.66025i 0.200805 0.347804i
\(621\) 0 0
\(622\) 17.0000 0.681638
\(623\) −6.00000 31.1769i −0.240385 1.24908i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) −11.0000 + 19.0526i −0.439648 + 0.761493i
\(627\) 0 0
\(628\) −2.00000 3.46410i −0.0798087 0.138233i
\(629\) −40.0000 −1.59490
\(630\) 0 0
\(631\) −42.0000 −1.67199 −0.835997 0.548734i \(-0.815110\pi\)
−0.835997 + 0.548734i \(0.815110\pi\)
\(632\) 4.50000 + 7.79423i 0.179000 + 0.310038i
\(633\) 0 0
\(634\) 1.50000 2.59808i 0.0595726 0.103183i
\(635\) 8.50000 + 14.7224i 0.337312 + 0.584242i
\(636\) 0 0
\(637\) 11.0000 + 8.66025i 0.435836 + 0.343132i
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 6.00000 10.3923i 0.236986 0.410471i −0.722862 0.690992i \(-0.757174\pi\)
0.959848 + 0.280521i \(0.0905072\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −17.5000 6.06218i −0.689597 0.238883i
\(645\) 0 0
\(646\) 15.0000 + 25.9808i 0.590167 + 1.02220i
\(647\) 22.5000 38.9711i 0.884566 1.53211i 0.0383563 0.999264i \(-0.487788\pi\)
0.846210 0.532850i \(-0.178879\pi\)
\(648\) 0 0
\(649\) 3.00000 + 5.19615i 0.117760 + 0.203967i
\(650\) −8.00000 −0.313786
\(651\) 0 0
\(652\) 13.0000 0.509119
\(653\) −6.50000 11.2583i −0.254365 0.440573i 0.710358 0.703840i \(-0.248533\pi\)
−0.964723 + 0.263268i \(0.915200\pi\)
\(654\) 0 0
\(655\) 6.00000 10.3923i 0.234439 0.406061i
\(656\) −3.50000 6.06218i −0.136652 0.236688i
\(657\) 0 0
\(658\) −2.00000 + 1.73205i −0.0779681 + 0.0675224i
\(659\) 19.0000 0.740135 0.370067 0.929005i \(-0.379335\pi\)
0.370067 + 0.929005i \(0.379335\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −6.50000 + 11.2583i −0.252630 + 0.437567i
\(663\) 0 0
\(664\) −15.0000 −0.582113
\(665\) 12.0000 10.3923i 0.465340 0.402996i
\(666\) 0 0
\(667\) 28.0000 + 48.4974i 1.08416 + 1.87783i
\(668\) 4.00000 6.92820i 0.154765 0.268060i
\(669\) 0 0
\(670\) 1.50000 + 2.59808i 0.0579501 + 0.100372i
\(671\) −1.00000 −0.0386046
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −1.00000 1.73205i −0.0384331 0.0665681i 0.846169 0.532915i \(-0.178903\pi\)
−0.884602 + 0.466347i \(0.845570\pi\)
\(678\) 0 0
\(679\) −32.5000 11.2583i −1.24724 0.432055i
\(680\) −5.00000 −0.191741
\(681\) 0 0
\(682\) 5.00000 8.66025i 0.191460 0.331618i
\(683\) −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) −7.50000 12.9904i −0.285313 0.494177i 0.687372 0.726306i \(-0.258764\pi\)
−0.972685 + 0.232128i \(0.925431\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) −13.0000 −0.493473
\(695\) 1.00000 + 1.73205i 0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) −17.5000 + 30.3109i −0.662860 + 1.14811i
\(698\) 6.50000 + 11.2583i 0.246029 + 0.426134i
\(699\) 0 0
\(700\) −2.00000 10.3923i −0.0755929 0.392792i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −24.0000 + 41.5692i −0.905177 + 1.56781i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 24.0000 20.7846i 0.902613 0.781686i
\(708\) 0 0
\(709\) 21.0000 + 36.3731i 0.788672 + 1.36602i 0.926781 + 0.375602i \(0.122564\pi\)
−0.138109 + 0.990417i \(0.544103\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) 0 0
\(712\) 6.00000 + 10.3923i 0.224860 + 0.389468i
\(713\) 70.0000 2.62152
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) 1.00000 + 1.73205i 0.0373718 + 0.0647298i
\(717\) 0 0
\(718\) −10.0000 + 17.3205i −0.373197 + 0.646396i
\(719\) 2.50000 + 4.33013i 0.0932343 + 0.161486i 0.908870 0.417079i \(-0.136946\pi\)
−0.815636 + 0.578565i \(0.803613\pi\)
\(720\) 0 0
\(721\) 6.00000 + 31.1769i 0.223452 + 1.16109i
\(722\) 17.0000 0.632674
\(723\) 0 0
\(724\) −10.0000 + 17.3205i −0.371647 + 0.643712i
\(725\) −16.0000 + 27.7128i −0.594225 + 1.02923i
\(726\) 0 0
\(727\) 20.0000 0.741759 0.370879 0.928681i \(-0.379056\pi\)
0.370879 + 0.928681i \(0.379056\pi\)
\(728\) −5.00000 1.73205i −0.185312 0.0641941i
\(729\) 0 0
\(730\) 5.00000 + 8.66025i 0.185058 + 0.320530i
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 0 0
\(733\) 18.5000 + 32.0429i 0.683313 + 1.18353i 0.973964 + 0.226704i \(0.0727949\pi\)
−0.290651 + 0.956829i \(0.593872\pi\)
\(734\) −2.00000 −0.0738213
\(735\) 0 0
\(736\) 7.00000 0.258023
\(737\) 1.50000 + 2.59808i 0.0552532 + 0.0957014i
\(738\) 0 0
\(739\) −3.00000 + 5.19615i −0.110357 + 0.191144i −0.915914 0.401374i \(-0.868533\pi\)
0.805557 + 0.592518i \(0.201866\pi\)
\(740\) −4.00000 6.92820i −0.147043 0.254686i
\(741\) 0 0
\(742\) −15.0000 5.19615i −0.550667 0.190757i
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) −2.00000 + 3.46410i −0.0732743 + 0.126915i
\(746\) 6.50000 11.2583i 0.237982 0.412197i
\(747\) 0 0
\(748\) −5.00000 −0.182818
\(749\) −6.50000 33.7750i −0.237505 1.23411i
\(750\) 0 0
\(751\) 19.0000 + 32.9090i 0.693320 + 1.20087i 0.970744 + 0.240118i \(0.0771860\pi\)
−0.277424 + 0.960748i \(0.589481\pi\)
\(752\) 0.500000 0.866025i 0.0182331 0.0315807i
\(753\) 0 0
\(754\) 8.00000 + 13.8564i 0.291343 + 0.504621i
\(755\) −9.00000 −0.327544
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 8.50000 + 14.7224i 0.308734 + 0.534743i
\(759\) 0 0
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) 19.5000 + 33.7750i 0.706874 + 1.22434i 0.966011 + 0.258502i \(0.0832288\pi\)
−0.259136 + 0.965841i \(0.583438\pi\)
\(762\) 0 0
\(763\) 38.0000 32.9090i 1.37569 1.19138i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 8.00000 13.8564i 0.289052 0.500652i
\(767\) −6.00000 + 10.3923i −0.216647 + 0.375244i
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0.500000 + 2.59808i 0.0180187 + 0.0936282i
\(771\) 0 0
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) 16.5000 28.5788i 0.593464 1.02791i −0.400298 0.916385i \(-0.631093\pi\)
0.993762 0.111524i \(-0.0355733\pi\)
\(774\) 0 0
\(775\) 20.0000 + 34.6410i 0.718421 + 1.24434i
\(776\) 13.0000 0.466673
\(777\) 0 0
\(778\) 15.0000 0.537776
\(779\) 21.0000 + 36.3731i 0.752403 + 1.30320i
\(780\) 0 0
\(781\) −4.00000 + 6.92820i −0.143131 + 0.247911i
\(782\) −17.5000 30.3109i −0.625799 1.08392i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −7.00000 + 12.1244i −0.249523 + 0.432187i −0.963394 0.268091i \(-0.913607\pi\)
0.713871 + 0.700278i \(0.246941\pi\)
\(788\) 12.0000 20.7846i 0.427482 0.740421i
\(789\) 0