Properties

Label 1755.2.i.b.1171.1
Level $1755$
Weight $2$
Character 1755.1171
Analytic conductor $14.014$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0137455547\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1171.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1755.1171
Dual form 1755.2.i.b.586.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} -2.00000 q^{17} -3.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} -2.00000 q^{28} +(2.50000 + 4.33013i) q^{29} +(0.500000 - 0.866025i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{34} +2.00000 q^{35} -5.00000 q^{37} +(1.50000 + 2.59808i) q^{38} +(1.50000 - 2.59808i) q^{40} +(4.00000 + 6.92820i) q^{43} -1.00000 q^{44} +(-1.00000 - 1.73205i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} -14.0000 q^{53} +1.00000 q^{55} +(3.00000 + 5.19615i) q^{56} +(2.50000 - 4.33013i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} -1.00000 q^{62} +7.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(-7.00000 + 12.1244i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-1.00000 - 1.73205i) q^{70} +6.00000 q^{73} +(2.50000 + 4.33013i) q^{74} +(-1.50000 + 2.59808i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(6.00000 + 10.3923i) q^{79} -1.00000 q^{80} +(-5.00000 - 8.66025i) q^{83} +(1.00000 - 1.73205i) q^{85} +(4.00000 - 6.92820i) q^{86} +(1.50000 + 2.59808i) q^{88} -2.00000 q^{89} -2.00000 q^{91} +(-1.00000 + 1.73205i) q^{94} +(1.50000 - 2.59808i) q^{95} +(-0.500000 - 0.866025i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 2 q^{10} - q^{11} + q^{13} - 2 q^{14} + q^{16} - 4 q^{17} - 6 q^{19} + q^{20} - q^{22} - q^{25} - 2 q^{26} - 4 q^{28} + 5 q^{29} + q^{31} - 5 q^{32} + 2 q^{34} + 4 q^{35} - 10 q^{37} + 3 q^{38} + 3 q^{40} + 8 q^{43} - 2 q^{44} - 2 q^{47} + 3 q^{49} - q^{50} - q^{52} - 28 q^{53} + 2 q^{55} + 6 q^{56} + 5 q^{58} - 9 q^{59} + q^{61} - 2 q^{62} + 14 q^{64} + q^{65} - 14 q^{67} - 2 q^{68} - 2 q^{70} + 12 q^{73} + 5 q^{74} - 3 q^{76} - 2 q^{77} + 12 q^{79} - 2 q^{80} - 10 q^{83} + 2 q^{85} + 8 q^{86} + 3 q^{88} - 4 q^{89} - 4 q^{91} - 2 q^{94} + 3 q^{95} - q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) 0 0
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 0 0
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) 1.50000 + 2.59808i 0.243332 + 0.421464i
\(39\) 0 0
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) −14.0000 −1.92305 −0.961524 0.274721i \(-0.911414\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 3.00000 + 5.19615i 0.400892 + 0.694365i
\(57\) 0 0
\(58\) 2.50000 4.33013i 0.328266 0.568574i
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 0 0
\(67\) −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i \(0.493224\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) −1.00000 1.73205i −0.119523 0.207020i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 2.50000 + 4.33013i 0.290619 + 0.503367i
\(75\) 0 0
\(76\) −1.50000 + 2.59808i −0.172062 + 0.298020i
\(77\) −1.00000 + 1.73205i −0.113961 + 0.197386i
\(78\) 0 0
\(79\) 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 0 0
\(83\) −5.00000 8.66025i −0.548821 0.950586i −0.998356 0.0573233i \(-0.981743\pi\)
0.449534 0.893263i \(-0.351590\pi\)
\(84\) 0 0
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) −1.00000 + 1.73205i −0.103142 + 0.178647i
\(95\) 1.50000 2.59808i 0.153897 0.266557i
\(96\) 0 0
\(97\) −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i \(-0.118979\pi\)
−0.781697 + 0.623658i \(0.785646\pi\)
\(102\) 0 0
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) −1.50000 + 2.59808i −0.147087 + 0.254762i
\(105\) 0 0
\(106\) 7.00000 + 12.1244i 0.679900 + 1.17762i
\(107\) −19.0000 −1.83680 −0.918400 0.395654i \(-0.870518\pi\)
−0.918400 + 0.395654i \(0.870518\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) −0.500000 0.866025i −0.0476731 0.0825723i
\(111\) 0 0
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) 5.00000 8.66025i 0.470360 0.814688i −0.529065 0.848581i \(-0.677457\pi\)
0.999425 + 0.0338931i \(0.0107906\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.00000 0.464238
\(117\) 0 0
\(118\) 9.00000 0.828517
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0.500000 0.866025i 0.0452679 0.0784063i
\(123\) 0 0
\(124\) −0.500000 0.866025i −0.0449013 0.0777714i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 0 0
\(130\) 0.500000 0.866025i 0.0438529 0.0759555i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 0 0
\(133\) 3.00000 + 5.19615i 0.260133 + 0.450564i
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −2.50000 4.33013i −0.213589 0.369948i 0.739246 0.673436i \(-0.235182\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) 1.00000 1.73205i 0.0845154 0.146385i
\(141\) 0 0
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −5.00000 −0.415227
\(146\) −3.00000 5.19615i −0.248282 0.430037i
\(147\) 0 0
\(148\) −2.50000 + 4.33013i −0.205499 + 0.355934i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 9.00000 0.729996
\(153\) 0 0
\(154\) 2.00000 0.161165
\(155\) 0.500000 + 0.866025i 0.0401610 + 0.0695608i
\(156\) 0 0
\(157\) 3.00000 5.19615i 0.239426 0.414698i −0.721124 0.692806i \(-0.756374\pi\)
0.960550 + 0.278108i \(0.0897074\pi\)
\(158\) 6.00000 10.3923i 0.477334 0.826767i
\(159\) 0 0
\(160\) −2.50000 4.33013i −0.197642 0.342327i
\(161\) 0 0
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −5.00000 + 8.66025i −0.388075 + 0.672166i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) 0 0
\(175\) −1.00000 + 1.73205i −0.0755929 + 0.130931i
\(176\) 0.500000 0.866025i 0.0376889 0.0652791i
\(177\) 0 0
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0 0
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) 1.00000 + 1.73205i 0.0741249 + 0.128388i
\(183\) 0 0
\(184\) 0 0
\(185\) 2.50000 4.33013i 0.183804 0.318357i
\(186\) 0 0
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) −3.00000 −0.217643
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0 0
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) −0.500000 + 0.866025i −0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) −1.50000 2.59808i −0.107143 0.185577i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 0 0
\(199\) −22.0000 −1.55954 −0.779769 0.626067i \(-0.784664\pi\)
−0.779769 + 0.626067i \(0.784664\pi\)
\(200\) 1.50000 + 2.59808i 0.106066 + 0.183712i
\(201\) 0 0
\(202\) 1.50000 2.59808i 0.105540 0.182800i
\(203\) 5.00000 8.66025i 0.350931 0.607831i
\(204\) 0 0
\(205\) 0 0
\(206\) −1.00000 −0.0696733
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) 1.50000 + 2.59808i 0.103757 + 0.179713i
\(210\) 0 0
\(211\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(212\) −7.00000 + 12.1244i −0.480762 + 0.832704i
\(213\) 0 0
\(214\) 9.50000 + 16.4545i 0.649407 + 1.12481i
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 0 0
\(220\) 0.500000 0.866025i 0.0337100 0.0583874i
\(221\) −1.00000 + 1.73205i −0.0672673 + 0.116510i
\(222\) 0 0
\(223\) 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i \(0.169566\pi\)
0.00910984 + 0.999959i \(0.497100\pi\)
\(224\) 10.0000 0.668153
\(225\) 0 0
\(226\) −10.0000 −0.665190
\(227\) −13.0000 22.5167i −0.862840 1.49448i −0.869176 0.494503i \(-0.835350\pi\)
0.00633544 0.999980i \(-0.497983\pi\)
\(228\) 0 0
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −7.50000 12.9904i −0.492399 0.852860i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) 2.00000 0.130466
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) 0 0
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) 7.50000 12.9904i 0.485135 0.840278i −0.514719 0.857359i \(-0.672104\pi\)
0.999854 + 0.0170808i \(0.00543724\pi\)
\(240\) 0 0
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) −10.0000 −0.642824
\(243\) 0 0
\(244\) 1.00000 0.0640184
\(245\) 1.50000 + 2.59808i 0.0958315 + 0.165985i
\(246\) 0 0
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) −1.50000 + 2.59808i −0.0952501 + 0.164978i
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 4.00000 + 6.92820i 0.250982 + 0.434714i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −14.0000 + 24.2487i −0.873296 + 1.51259i −0.0147291 + 0.999892i \(0.504689\pi\)
−0.858567 + 0.512702i \(0.828645\pi\)
\(258\) 0 0
\(259\) 5.00000 + 8.66025i 0.310685 + 0.538122i
\(260\) 1.00000 0.0620174
\(261\) 0 0
\(262\) 4.00000 0.247121
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 0 0
\(265\) 7.00000 12.1244i 0.430007 0.744793i
\(266\) 3.00000 5.19615i 0.183942 0.318597i
\(267\) 0 0
\(268\) 7.00000 + 12.1244i 0.427593 + 0.740613i
\(269\) −3.00000 −0.182913 −0.0914566 0.995809i \(-0.529152\pi\)
−0.0914566 + 0.995809i \(0.529152\pi\)
\(270\) 0 0
\(271\) −7.00000 −0.425220 −0.212610 0.977137i \(-0.568196\pi\)
−0.212610 + 0.977137i \(0.568196\pi\)
\(272\) −1.00000 1.73205i −0.0606339 0.105021i
\(273\) 0 0
\(274\) −2.50000 + 4.33013i −0.151031 + 0.261593i
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) −6.00000 −0.358569
\(281\) −6.00000 10.3923i −0.357930 0.619953i 0.629685 0.776851i \(-0.283184\pi\)
−0.987615 + 0.156898i \(0.949851\pi\)
\(282\) 0 0
\(283\) 12.5000 21.6506i 0.743048 1.28700i −0.208053 0.978117i \(-0.566713\pi\)
0.951101 0.308879i \(-0.0999539\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.500000 + 0.866025i 0.0295656 + 0.0512092i
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 2.50000 + 4.33013i 0.146805 + 0.254274i
\(291\) 0 0
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) 0.500000 0.866025i 0.0292103 0.0505937i −0.851051 0.525084i \(-0.824034\pi\)
0.880261 + 0.474490i \(0.157367\pi\)
\(294\) 0 0
\(295\) −4.50000 7.79423i −0.262000 0.453798i
\(296\) 15.0000 0.871857
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) 4.00000 6.92820i 0.230174 0.398673i
\(303\) 0 0
\(304\) −1.50000 2.59808i −0.0860309 0.149010i
\(305\) −1.00000 −0.0572598
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 1.00000 + 1.73205i 0.0569803 + 0.0986928i
\(309\) 0 0
\(310\) 0.500000 0.866025i 0.0283981 0.0491869i
\(311\) −2.00000 + 3.46410i −0.113410 + 0.196431i −0.917143 0.398559i \(-0.869511\pi\)
0.803733 + 0.594990i \(0.202844\pi\)
\(312\) 0 0
\(313\) 14.0000 + 24.2487i 0.791327 + 1.37062i 0.925146 + 0.379612i \(0.123943\pi\)
−0.133819 + 0.991006i \(0.542724\pi\)
\(314\) −6.00000 −0.338600
\(315\) 0 0
\(316\) 12.0000 0.675053
\(317\) −13.5000 23.3827i −0.758236 1.31330i −0.943750 0.330661i \(-0.892728\pi\)
0.185514 0.982642i \(-0.440605\pi\)
\(318\) 0 0
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) −3.50000 + 6.06218i −0.195656 + 0.338886i
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) 0 0
\(328\) 0 0
\(329\) −2.00000 + 3.46410i −0.110264 + 0.190982i
\(330\) 0 0
\(331\) −13.5000 23.3827i −0.742027 1.28523i −0.951571 0.307429i \(-0.900531\pi\)
0.209544 0.977799i \(-0.432802\pi\)
\(332\) −10.0000 −0.548821
\(333\) 0 0
\(334\) 0 0
\(335\) −7.00000 12.1244i −0.382451 0.662424i
\(336\) 0 0
\(337\) 11.0000 19.0526i 0.599208 1.03786i −0.393730 0.919226i \(-0.628816\pi\)
0.992938 0.118633i \(-0.0378512\pi\)
\(338\) −0.500000 + 0.866025i −0.0271964 + 0.0471056i
\(339\) 0 0
\(340\) −1.00000 1.73205i −0.0542326 0.0939336i
\(341\) −1.00000 −0.0541530
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) −12.0000 20.7846i −0.646997 1.12063i
\(345\) 0 0
\(346\) 6.00000 10.3923i 0.322562 0.558694i
\(347\) 8.50000 14.7224i 0.456304 0.790342i −0.542458 0.840083i \(-0.682506\pi\)
0.998762 + 0.0497412i \(0.0158397\pi\)
\(348\) 0 0
\(349\) −6.00000 10.3923i −0.321173 0.556287i 0.659558 0.751654i \(-0.270744\pi\)
−0.980730 + 0.195367i \(0.937410\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.00000 + 1.73205i −0.0529999 + 0.0917985i
\(357\) 0 0
\(358\) −9.00000 15.5885i −0.475665 0.823876i
\(359\) 31.0000 1.63612 0.818059 0.575135i \(-0.195050\pi\)
0.818059 + 0.575135i \(0.195050\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) −8.50000 14.7224i −0.446750 0.773794i
\(363\) 0 0
\(364\) −1.00000 + 1.73205i −0.0524142 + 0.0907841i
\(365\) −3.00000 + 5.19615i −0.157027 + 0.271979i
\(366\) 0 0
\(367\) −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i \(-0.940389\pi\)
0.330021 0.943974i \(-0.392944\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −5.00000 −0.259938
\(371\) 14.0000 + 24.2487i 0.726844 + 1.25893i
\(372\) 0 0
\(373\) 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 5.00000 0.257513
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) −1.50000 2.59808i −0.0769484 0.133278i
\(381\) 0 0
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 0 0
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) 13.0000 0.661683
\(387\) 0 0
\(388\) −1.00000 −0.0507673
\(389\) −11.0000 19.0526i −0.557722 0.966003i −0.997686 0.0679877i \(-0.978342\pi\)
0.439964 0.898015i \(-0.354991\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) 0 0
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) −12.0000 −0.603786
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 11.0000 + 19.0526i 0.551380 + 0.955018i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 14.0000 24.2487i 0.699127 1.21092i −0.269643 0.962960i \(-0.586906\pi\)
0.968770 0.247962i \(-0.0797610\pi\)
\(402\) 0 0
\(403\) −0.500000 0.866025i −0.0249068 0.0431398i
\(404\) 3.00000 0.149256
\(405\) 0 0
\(406\) −10.0000 −0.496292
\(407\) 2.50000 + 4.33013i 0.123920 + 0.214636i
\(408\) 0 0
\(409\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.500000 0.866025i −0.0246332 0.0426660i
\(413\) 18.0000 0.885722
\(414\) 0 0
\(415\) 10.0000 0.490881
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) 0 0
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) 10.0000 17.3205i 0.488532 0.846162i −0.511381 0.859354i \(-0.670866\pi\)
0.999913 + 0.0131919i \(0.00419923\pi\)
\(420\) 0 0
\(421\) −5.00000 8.66025i −0.243685 0.422075i 0.718076 0.695965i \(-0.245023\pi\)
−0.961761 + 0.273890i \(0.911690\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 42.0000 2.03970
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 1.00000 1.73205i 0.0483934 0.0838198i
\(428\) −9.50000 + 16.4545i −0.459200 + 0.795357i
\(429\) 0 0
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) −17.0000 −0.818861 −0.409431 0.912341i \(-0.634273\pi\)
−0.409431 + 0.912341i \(0.634273\pi\)
\(432\) 0 0
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 1.00000 + 1.73205i 0.0480015 + 0.0831411i
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −3.00000 −0.143019
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) −3.50000 6.06218i −0.166290 0.288023i 0.770823 0.637050i \(-0.219845\pi\)
−0.937113 + 0.349027i \(0.886512\pi\)
\(444\) 0 0
\(445\) 1.00000 1.73205i 0.0474045 0.0821071i
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 0 0
\(448\) −7.00000 12.1244i −0.330719 0.572822i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −5.00000 8.66025i −0.235180 0.407344i
\(453\) 0 0
\(454\) −13.0000 + 22.5167i −0.610120 + 1.05676i
\(455\) 1.00000 1.73205i 0.0468807 0.0811998i
\(456\) 0 0
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) −16.0000 −0.747631
\(459\) 0 0
\(460\) 0 0
\(461\) −13.0000 22.5167i −0.605470 1.04871i −0.991977 0.126419i \(-0.959652\pi\)
0.386507 0.922287i \(-0.373682\pi\)
\(462\) 0 0
\(463\) 3.00000 5.19615i 0.139422 0.241486i −0.787856 0.615859i \(-0.788809\pi\)
0.927278 + 0.374374i \(0.122142\pi\)
\(464\) −2.50000 + 4.33013i −0.116060 + 0.201021i
\(465\) 0 0
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 0 0
\(469\) 28.0000 1.29292
\(470\) −1.00000 1.73205i −0.0461266 0.0798935i
\(471\) 0 0
\(472\) 13.5000 23.3827i 0.621388 1.07628i
\(473\) 4.00000 6.92820i 0.183920 0.318559i
\(474\) 0 0
\(475\) 1.50000 + 2.59808i 0.0688247 + 0.119208i
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) −15.0000 −0.686084
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) −2.50000 + 4.33013i −0.113990 + 0.197437i
\(482\) −5.00000 + 8.66025i −0.227744 + 0.394464i
\(483\) 0 0
\(484\) −5.00000 8.66025i −0.227273 0.393648i
\(485\) 1.00000 0.0454077
\(486\) 0 0
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) −1.50000 2.59808i −0.0679018 0.117609i
\(489\) 0 0
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) −3.00000 + 5.19615i −0.135388 + 0.234499i −0.925746 0.378147i \(-0.876561\pi\)
0.790358 + 0.612646i \(0.209895\pi\)
\(492\) 0 0
\(493\) −5.00000 8.66025i −0.225189 0.390038i
\(494\) 3.00000 0.134976
\(495\) 0 0
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 0 0
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) 9.00000 0.401290 0.200645 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) 0 0
\(508\) −4.00000 + 6.92820i −0.177471 + 0.307389i
\(509\) −12.0000 + 20.7846i −0.531891 + 0.921262i 0.467416 + 0.884037i \(0.345185\pi\)
−0.999307 + 0.0372243i \(0.988148\pi\)
\(510\) 0 0
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) 28.0000 1.23503
\(515\) 0.500000 + 0.866025i 0.0220326 + 0.0381616i
\(516\) 0 0
\(517\) −1.00000 + 1.73205i −0.0439799 + 0.0761755i
\(518\) 5.00000 8.66025i 0.219687 0.380510i
\(519\) 0 0
\(520\) −1.50000 2.59808i −0.0657794 0.113933i
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −15.0000 −0.655904 −0.327952 0.944694i \(-0.606358\pi\)
−0.327952 + 0.944694i \(0.606358\pi\)
\(524\) 2.00000 + 3.46410i 0.0873704 + 0.151330i
\(525\) 0 0
\(526\) −8.00000 + 13.8564i −0.348817 + 0.604168i
\(527\) −1.00000 + 1.73205i −0.0435607 + 0.0754493i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −14.0000 −0.608121
\(531\) 0 0
\(532\) 6.00000 0.260133
\(533\) 0 0
\(534\) 0 0
\(535\) 9.50000 16.4545i 0.410721 0.711389i
\(536\) 21.0000 36.3731i 0.907062 1.57108i
\(537\) 0 0
\(538\) 1.50000 + 2.59808i 0.0646696 + 0.112011i
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) 32.0000 1.37579 0.687894 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) 3.50000 + 6.06218i 0.150338 + 0.260393i
\(543\) 0 0
\(544\) 5.00000 8.66025i 0.214373 0.371305i
\(545\) 7.00000 12.1244i 0.299847 0.519350i
\(546\) 0 0
\(547\) 7.50000 + 12.9904i 0.320677 + 0.555429i 0.980628 0.195880i \(-0.0627563\pi\)
−0.659951 + 0.751309i \(0.729423\pi\)
\(548\) −5.00000 −0.213589
\(549\) 0 0
\(550\) 1.00000 0.0426401
\(551\) −7.50000 12.9904i −0.319511 0.553409i
\(552\) 0 0
\(553\) 12.0000 20.7846i 0.510292 0.883852i
\(554\) −5.00000 + 8.66025i −0.212430 + 0.367939i
\(555\) 0 0
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) 5.00000 0.211857 0.105928 0.994374i \(-0.466219\pi\)
0.105928 + 0.994374i \(0.466219\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 1.00000 + 1.73205i 0.0422577 + 0.0731925i
\(561\) 0 0
\(562\) −6.00000 + 10.3923i −0.253095 + 0.438373i
\(563\) −9.50000 + 16.4545i −0.400377 + 0.693474i −0.993771 0.111438i \(-0.964454\pi\)
0.593394 + 0.804912i \(0.297788\pi\)
\(564\) 0 0
\(565\) 5.00000 + 8.66025i 0.210352 + 0.364340i
\(566\) −25.0000 −1.05083
\(567\) 0 0
\(568\) 0 0
\(569\) −5.50000 9.52628i −0.230572 0.399362i 0.727405 0.686209i \(-0.240726\pi\)
−0.957977 + 0.286846i \(0.907393\pi\)
\(570\) 0 0
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) −0.500000 + 0.866025i −0.0209061 + 0.0362103i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 0 0
\(580\) −2.50000 + 4.33013i −0.103807 + 0.179799i
\(581\) −10.0000 + 17.3205i −0.414870 + 0.718576i
\(582\) 0 0
\(583\) 7.00000 + 12.1244i 0.289910 + 0.502140i
\(584\) −18.0000 −0.744845
\(585\) 0 0
\(586\) −1.00000 −0.0413096
\(587\) −7.00000 12.1244i −0.288921 0.500426i 0.684632 0.728889i \(-0.259963\pi\)
−0.973552 + 0.228464i \(0.926630\pi\)
\(588\) 0 0
\(589\) −1.50000 + 2.59808i −0.0618064 + 0.107052i
\(590\) −4.50000 + 7.79423i −0.185262 + 0.320883i
\(591\) 0 0
\(592\) −2.50000 4.33013i −0.102749 0.177967i
\(593\) 31.0000 1.27302 0.636509 0.771270i \(-0.280378\pi\)
0.636509 + 0.771270i \(0.280378\pi\)
\(594\) 0 0
\(595\) −4.00000 −0.163984
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) 7.00000 12.1244i 0.286012 0.495388i −0.686842 0.726807i \(-0.741004\pi\)
0.972854 + 0.231419i \(0.0743369\pi\)
\(600\) 0 0
\(601\) 8.50000 + 14.7224i 0.346722 + 0.600541i 0.985665 0.168714i \(-0.0539613\pi\)
−0.638943 + 0.769254i \(0.720628\pi\)
\(602\) −16.0000 −0.652111
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) 7.50000 12.9904i 0.304165 0.526830i
\(609\) 0 0
\(610\) 0.500000 + 0.866025i 0.0202444 + 0.0350643i
\(611\) −2.00000 −0.0809113
\(612\) 0 0
\(613\) 30.0000 1.21169 0.605844 0.795583i \(-0.292835\pi\)
0.605844 + 0.795583i \(0.292835\pi\)
\(614\) −1.00000 1.73205i −0.0403567 0.0698999i
\(615\) 0 0
\(616\) 3.00000 5.19615i 0.120873 0.209359i
\(617\) 4.50000 7.79423i 0.181163 0.313784i −0.761114 0.648618i \(-0.775347\pi\)
0.942277 + 0.334835i \(0.108680\pi\)
\(618\) 0 0
\(619\) 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i \(-0.0957138\pi\)
−0.734068 + 0.679076i \(0.762380\pi\)
\(620\) 1.00000 0.0401610
\(621\) 0 0
\(622\) 4.00000 0.160385
\(623\) 2.00000 + 3.46410i 0.0801283 + 0.138786i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 14.0000 24.2487i 0.559553 0.969173i
\(627\) 0 0
\(628\) −3.00000 5.19615i −0.119713 0.207349i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) −5.00000 −0.199047 −0.0995234 0.995035i \(-0.531732\pi\)
−0.0995234 + 0.995035i \(0.531732\pi\)
\(632\) −18.0000 31.1769i −0.716002 1.24015i
\(633\) 0 0
\(634\) −13.5000 + 23.3827i −0.536153 + 0.928645i
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) 0 0
\(637\) −1.50000 2.59808i −0.0594322 0.102940i
\(638\) −5.00000 −0.197952
\(639\) 0 0
\(640\) −3.00000 −0.118585
\(641\) 8.50000 + 14.7224i 0.335730 + 0.581501i 0.983625 0.180229i \(-0.0576838\pi\)
−0.647895 + 0.761730i \(0.724350\pi\)
\(642\) 0 0
\(643\) −16.0000 + 27.7128i −0.630978 + 1.09289i 0.356374 + 0.934344i \(0.384013\pi\)
−0.987352 + 0.158543i \(0.949320\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.00000 5.19615i −0.118033 0.204440i
\(647\) −41.0000 −1.61188 −0.805938 0.592000i \(-0.798339\pi\)
−0.805938 + 0.592000i \(0.798339\pi\)
\(648\) 0 0
\(649\) 9.00000 0.353281
\(650\) 0.500000 + 0.866025i 0.0196116 + 0.0339683i
\(651\) 0 0
\(652\) −6.00000 + 10.3923i −0.234978 + 0.406994i
\(653\) 24.0000 41.5692i 0.939193 1.62673i 0.172211 0.985060i \(-0.444909\pi\)
0.766982 0.641669i \(-0.221758\pi\)
\(654\) 0 0
\(655\) −2.00000 3.46410i −0.0781465 0.135354i
\(656\) 0 0
\(657\) 0 0
\(658\) 4.00000 0.155936
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 0 0
\(661\) −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) −13.5000 + 23.3827i −0.524692 + 0.908794i
\(663\) 0 0
\(664\) 15.0000 + 25.9808i 0.582113 + 1.00825i
\(665\) −6.00000 −0.232670
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −7.00000 + 12.1244i −0.270434 + 0.468405i
\(671\) 0.500000 0.866025i 0.0193023 0.0334325i
\(672\) 0 0
\(673\) −12.0000 20.7846i −0.462566 0.801188i 0.536522 0.843886i \(-0.319738\pi\)
−0.999088 + 0.0426985i \(0.986405\pi\)
\(674\) −22.0000 −0.847408
\(675\) 0 0
\(676\) −1.00000 −0.0384615
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 0 0
\(679\) −1.00000 + 1.73205i −0.0383765 + 0.0664700i
\(680\) −3.00000 + 5.19615i −0.115045 + 0.199263i
\(681\) 0 0
\(682\) 0.500000 + 0.866025i 0.0191460 + 0.0331618i
\(683\) 20.0000 0.765279 0.382639 0.923898i \(-0.375015\pi\)
0.382639 + 0.923898i \(0.375015\pi\)
\(684\) 0 0
\(685\) 5.00000 0.191040
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −7.00000 + 12.1244i −0.266679 + 0.461901i
\(690\) 0 0
\(691\) −0.500000 0.866025i −0.0190209 0.0329452i 0.856358 0.516382i \(-0.172722\pi\)
−0.875379 + 0.483437i \(0.839388\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −17.0000 −0.645311
\(695\) −6.00000 10.3923i −0.227593 0.394203i
\(696\) 0 0
\(697\) 0 0
\(698\) −6.00000 + 10.3923i −0.227103 + 0.393355i
\(699\) 0 0
\(700\) 1.00000 + 1.73205i 0.0377964 + 0.0654654i
\(701\) 5.00000 0.188847 0.0944237 0.995532i \(-0.469899\pi\)
0.0944237 + 0.995532i \(0.469899\pi\)
\(702\) 0 0
\(703\) 15.0000 0.565736
\(704\) −3.50000 6.06218i −0.131911 0.228477i
\(705\) 0 0
\(706\) −1.50000 + 2.59808i −0.0564532 + 0.0977799i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 0 0
\(709\) −2.00000 3.46410i −0.0751116 0.130097i 0.826023 0.563636i \(-0.190598\pi\)
−0.901135 + 0.433539i \(0.857265\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) 0.500000 0.866025i 0.0186989 0.0323875i
\(716\) 9.00000 15.5885i 0.336346 0.582568i
\(717\) 0 0
\(718\) −15.5000 26.8468i −0.578455 1.00191i
\(719\) 2.00000 0.0745874 0.0372937 0.999304i \(-0.488126\pi\)
0.0372937 + 0.999304i \(0.488126\pi\)
\(720\) 0 0
\(721\) −2.00000 −0.0744839
\(722\) 5.00000 + 8.66025i 0.186081 + 0.322301i
\(723\) 0 0
\(724\) 8.50000 14.7224i 0.315900 0.547155i
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) 0 0
\(727\) −24.0000 41.5692i −0.890111 1.54172i −0.839742 0.542986i \(-0.817294\pi\)
−0.0503692 0.998731i \(-0.516040\pi\)
\(728\) 6.00000 0.222375
\(729\) 0 0
\(730\) 6.00000 0.222070
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) 0 0
\(733\) −6.50000 + 11.2583i −0.240083 + 0.415836i −0.960738 0.277458i \(-0.910508\pi\)
0.720655 + 0.693294i \(0.243841\pi\)
\(734\) −12.5000 + 21.6506i −0.461383 + 0.799140i
\(735\) 0 0
\(736\) 0 0
\(737\) 14.0000 0.515697
\(738\) 0 0
\(739\) 9.00000 0.331070 0.165535 0.986204i \(-0.447065\pi\)
0.165535 + 0.986204i \(0.447065\pi\)
\(740\) −2.50000 4.33013i −0.0919018 0.159179i
\(741\) 0 0
\(742\) 14.0000 24.2487i 0.513956 0.890198i
\(743\) −24.0000 + 41.5692i −0.880475 + 1.52503i −0.0296605 + 0.999560i \(0.509443\pi\)
−0.850814 + 0.525467i \(0.823891\pi\)
\(744\) 0 0
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) −20.0000 −0.732252
\(747\) 0 0
\(748\) 2.00000 0.0731272
\(749\) 19.0000 + 32.9090i 0.694245 + 1.20247i
\(750\) 0 0
\(751\) −1.00000 + 1.73205i −0.0364905 + 0.0632034i −0.883694 0.468065i \(-0.844951\pi\)
0.847203 + 0.531269i \(0.178285\pi\)
\(752\) 1.00000 1.73205i 0.0364662 0.0631614i
\(753\) 0 0
\(754\) −2.50000 4.33013i −0.0910446 0.157694i
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 11.5000 + 19.9186i 0.417699 + 0.723476i
\(759\) 0 0
\(760\) −4.50000 + 7.79423i −0.163232 + 0.282726i
\(761\) −18.0000 + 31.1769i −0.652499 + 1.13016i 0.330015 + 0.943976i \(0.392946\pi\)
−0.982514 + 0.186187i \(0.940387\pi\)
\(762\) 0 0
\(763\) 14.0000 + 24.2487i 0.506834 + 0.877862i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) 4.50000 + 7.79423i 0.162486 + 0.281433i
\(768\) 0 0
\(769\) 20.0000 34.6410i 0.721218 1.24919i −0.239293 0.970947i \(-0.576916\pi\)
0.960512 0.278240i \(-0.0897509\pi\)
\(770\) −1.00000 + 1.73205i −0.0360375 + 0.0624188i
\(771\) 0 0
\(772\) 6.50000 + 11.2583i 0.233940 + 0.405196i
\(773\) −31.0000 −1.11499 −0.557496 0.830179i \(-0.688238\pi\)
−0.557496 + 0.830179i \(0.688238\pi\)
\(774\) 0 0
\(775\) −1.00000 −0.0359211
\(776\) 1.50000 + 2.59808i 0.0538469 + 0.0932655i
\(777\) 0 0
\(778\) −11.0000 + 19.0526i −0.394369 + 0.683067i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 3.00000 + 5.19615i 0.107075 + 0.185459i
\(786\) 0 0
\(787\) −19.0000 + 32.9090i −0.677277 + 1.17308i 0.298521 + 0.954403i \(0.403507\pi\)
−0.975798 + 0.218675i \(0.929827\pi\)
\(788\) −7.50000 + 12.9904i −0.267176 + 0.462763i
\(789\) 0 0
\(790\) 6.00000 + 10.3923i 0.213470 + 0.369742i