Properties

Label 1386.2.k.g.793.1
Level $1386$
Weight $2$
Character 1386.793
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 793.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.g.991.1

$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

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

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 −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 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 −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) 0 0
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i \(0.427054\pi\)
−0.956967 + 0.290196i \(0.906280\pi\)
\(24\) 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 −0.830014 0.557743i \(-0.811667\pi\)
−0.0680129 0.997684i \(-0.521666\pi\)
\(32\) −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 −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 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 −0.827253 0.561830i \(-0.810098\pi\)
0.900185 + 0.435507i \(0.143431\pi\)
\(48\) 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 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 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 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 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 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) −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 −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) 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 −0.493684 0.869641i \(-0.664350\pi\)
0.999974 0.00727784i \(-0.00231663\pi\)
\(80\) 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 −0.350304 0.936636i \(-0.613922\pi\)
0.986303 0.164946i \(-0.0527450\pi\)
\(90\) 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 −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i \(0.368011\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 6.50000 11.2583i 0.628379 1.08838i −0.359498 0.933146i \(-0.617052\pi\)
0.987877 0.155238i \(-0.0496145\pi\)
\(108\) 0 0
\(109\) −9.50000 16.4545i −0.909935 1.57605i −0.814152 0.580651i \(-0.802798\pi\)
−0.0957826 0.995402i \(-0.530535\pi\)
\(110\) −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 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 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 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 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 −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) 0 0
\(151\) −4.50000 7.79423i −0.366205 0.634285i 0.622764 0.782410i \(-0.286010\pi\)
−0.988969 + 0.148124i \(0.952676\pi\)
\(152\) 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 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) 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 0.490825 + 0.871258i \(0.336695\pi\)
−0.999944 + 0.0105623i \(0.996638\pi\)
\(164\) −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 −0.467093 0.884208i \(-0.654699\pi\)
0.999293 0.0375896i \(-0.0119679\pi\)
\(174\) 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 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) 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 0.235983 + 0.971757i \(0.424169\pi\)
−0.959558 + 0.281511i \(0.909164\pi\)
\(192\) 0 0
\(193\) −4.00000 6.92820i −0.287926 0.498703i 0.685388 0.728178i \(-0.259632\pi\)
−0.973315 + 0.229475i \(0.926299\pi\)
\(194\) −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 0.797025 + 0.603947i \(0.206406\pi\)
0.124521 + 0.992217i \(0.460261\pi\)
\(200\) 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 0.997127 + 0.0757500i \(0.0241351\pi\)
−0.432962 + 0.901412i \(0.642532\pi\)
\(228\) 0 0
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) −7.00000 −0.461566
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) −10.5000 + 18.1865i −0.687878 + 1.19144i 0.284645 + 0.958633i \(0.408124\pi\)
−0.972523 + 0.232806i \(0.925209\pi\)
\(234\) 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 0.605481 0.795860i \(-0.292981\pi\)
−0.991975 + 0.126432i \(0.959647\pi\)
\(242\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 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 −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) 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 0.816668 0.577108i \(-0.195819\pi\)
−0.908124 + 0.418701i \(0.862486\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 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 0.998861 + 0.0477206i \(0.0151957\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(278\) −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 −0.963602 0.267342i \(-0.913855\pi\)
0.250276 0.968175i \(-0.419479\pi\)
\(284\) 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 0.517796 0.855504i \(-0.326753\pi\)
−0.999786 + 0.0206719i \(0.993419\pi\)
\(312\) 0 0
\(313\) −11.0000 + 19.0526i −0.621757 + 1.07691i 0.367402 + 0.930062i \(0.380247\pi\)
−0.989158 + 0.146852i \(0.953086\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −9.00000 −0.506290
\(317\) 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i \(-0.806484\pi\)
0.905071 + 0.425261i \(0.139818\pi\)
\(318\) 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 −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 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 0.986061 0.166383i \(-0.0532089\pi\)
−0.637123 + 0.770762i \(0.719876\pi\)
\(348\) 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 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 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 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 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 0.890945 0.454112i \(-0.150043\pi\)
−0.838745 + 0.544524i \(0.816710\pi\)
\(368\) −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 −0.647225 0.762299i \(-0.724071\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) 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 −0.585973 0.810331i \(-0.699287\pi\)
0.994753 + 0.102302i \(0.0326207\pi\)
\(384\) 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 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 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 −0.976392 0.216004i \(-0.930698\pi\)
0.675261 + 0.737579i \(0.264031\pi\)
\(398\) −26.0000 −1.30326
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 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 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 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 0.720113 0.693857i \(-0.244090\pi\)
−0.960954 + 0.276707i \(0.910757\pi\)
\(432\) 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 −0.937380 0.348309i \(-0.886756\pi\)
0.770334 + 0.637641i \(0.220089\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) 10.0000 0.475651
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 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 −0.944286 0.329125i \(-0.893246\pi\)
0.757174 + 0.653213i \(0.226579\pi\)
\(458\) −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 −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 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 0.908093 0.418769i \(-0.137538\pi\)
−0.816711 + 0.577047i \(0.804205\pi\)
\(480\) 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 0.956790 0.290780i \(-0.0939149\pi\)
−0.730218 + 0.683214i \(0.760582\pi\)
\(488\) −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 −0.361478 0.932381i \(-0.617728\pi\)
0.988204 0.153141i \(-0.0489388\pi\)
\(500\) −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 −0.512331 0.858788i \(-0.671218\pi\)
0.999898 + 0.0142980i \(0.00455136\pi\)
\(510\) 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 0.735465 0.677563i \(-0.236964\pi\)
−0.954519 + 0.298150i \(0.903630\pi\)
\(522\) 0 0
\(523\) 17.0000 29.4449i 0.743358 1.28753i −0.207600 0.978214i \(-0.566565\pi\)
0.950958 0.309320i \(-0.100101\pi\)
\(524\) 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 −0.855077 0.518501i \(-0.826490\pi\)
0.876574 + 0.481268i \(0.159824\pi\)
\(542\) −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 0.984239 0.176841i \(-0.0565879\pi\)
−0.645269 + 0.763956i \(0.723255\pi\)
\(558\) 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 0.994228 + 0.107290i \(0.0342173\pi\)
−0.404198 + 0.914671i \(0.632449\pi\)
\(564\) 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 0.0294311 0.999567i \(-0.490630\pi\)
0.850935 0.525271i \(-0.176036\pi\)
\(570\) 0 0
\(571\) −8.00000 13.8564i −0.334790 0.579873i 0.648655 0.761083i \(-0.275332\pi\)
−0.983444 + 0.181210i \(0.941999\pi\)
\(572\) 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 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) −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 −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 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 0.833753 0.552137i \(-0.186188\pi\)
−0.895042 + 0.445983i \(0.852854\pi\)
\(600\) 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 0.405887 + 0.913923i \(0.366962\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) −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 0.955458 0.295126i \(-0.0953615\pi\)
−0.733316 + 0.679888i \(0.762028\pi\)
\(614\) −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 0.927752 0.373198i \(-0.121739\pi\)
−0.787075 + 0.616858i \(0.788405\pi\)
\(620\) 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 0.959848 0.280521i \(-0.0905072\pi\)
−0.722862 + 0.690992i \(0.757174\pi\)
\(642\) 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 0.846210 + 0.532850i \(0.178879\pi\)
0.0383563 + 0.999264i \(0.487788\pi\)
\(648\) 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 −0.964723 0.263268i \(-0.915200\pi\)
0.710358 + 0.703840i \(0.248533\pi\)
\(654\) 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 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −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 −0.884602 0.466347i \(-0.845570\pi\)
0.846169 + 0.532915i \(0.178903\pi\)
\(678\) 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 0.539750 0.841825i \(-0.318519\pi\)
−0.998917 + 0.0465244i \(0.985185\pi\)
\(684\) 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 −0.972685 0.232128i \(-0.925431\pi\)
0.687372 + 0.726306i \(0.258764\pi\)
\(692\) −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 −0.138109 0.990417i \(-0.544103\pi\)
0.926781 0.375602i \(-0.122564\pi\)
\(710\) −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 −0.815636 0.578565i \(-0.803613\pi\)
0.908870 + 0.417079i \(0.136946\pi\)
\(720\) 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 −0.290651 0.956829i \(-0.593872\pi\)
0.973964 0.226704i \(-0.0727949\pi\)
\(734\) −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 0.805557 0.592518i \(-0.201866\pi\)
−0.915914 + 0.401374i \(0.868533\pi\)
\(740\) −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 −0.277424 0.960748i \(-0.589481\pi\)
0.970744 0.240118i \(-0.0771860\pi\)
\(752\) 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 −0.259136 0.965841i \(-0.583438\pi\)
0.966011 0.258502i \(-0.0832288\pi\)
\(762\) 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 0.993762 + 0.111524i \(0.0355733\pi\)
−0.400298 + 0.916385i \(0.631093\pi\)
\(774\) 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 0.713871 0.700278i \(-0.246941\pi\)
−0.963394 + 0.268091i \(0.913607\pi\)
\(788\) 12.0000 + 20.7846i 0.427482 + 0.740421i
\(789\) 0