Properties

Label 336.2.bl.b.271.1
Level 336
Weight 2
Character 336.271
Analytic conductor 2.683
Analytic rank 1
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.bl (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 336.271
Dual form 336.2.bl.b.31.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-4.50000 + 2.59808i) q^{11} +6.92820i q^{13} +1.73205i q^{15} +(3.00000 - 1.73205i) q^{17} +(1.00000 - 1.73205i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-6.00000 - 3.46410i) q^{23} +(-1.00000 - 1.73205i) q^{25} +1.00000 q^{27} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(4.50000 + 2.59808i) q^{33} +(3.00000 + 3.46410i) q^{35} +(1.00000 - 1.73205i) q^{37} +(6.00000 - 3.46410i) q^{39} -3.46410i q^{41} +3.46410i q^{43} +(1.50000 - 0.866025i) q^{45} +(5.50000 + 4.33013i) q^{49} +(-3.00000 - 1.73205i) q^{51} +(-4.50000 - 7.79423i) q^{53} +9.00000 q^{55} -2.00000 q^{57} +(-1.50000 - 2.59808i) q^{59} +(-6.00000 - 3.46410i) q^{61} +(2.00000 - 1.73205i) q^{63} +(6.00000 - 10.3923i) q^{65} +6.92820i q^{69} +6.92820i q^{71} +(6.00000 - 3.46410i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(13.5000 - 2.59808i) q^{77} +(1.50000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +15.0000 q^{83} -6.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(-9.00000 - 5.19615i) q^{89} +(6.00000 - 17.3205i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-3.00000 + 1.73205i) q^{95} +8.66025i q^{97} -5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 3q^{5} - 5q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - 3q^{5} - 5q^{7} - q^{9} - 9q^{11} + 6q^{17} + 2q^{19} + q^{21} - 12q^{23} - 2q^{25} + 2q^{27} - 18q^{29} + q^{31} + 9q^{33} + 6q^{35} + 2q^{37} + 12q^{39} + 3q^{45} + 11q^{49} - 6q^{51} - 9q^{53} + 18q^{55} - 4q^{57} - 3q^{59} - 12q^{61} + 4q^{63} + 12q^{65} + 12q^{73} - 2q^{75} + 27q^{77} + 3q^{79} - q^{81} + 30q^{83} - 12q^{85} + 9q^{87} - 18q^{89} + 12q^{91} + q^{93} - 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i \(-0.459925\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −4.50000 + 2.59808i −1.35680 + 0.783349i −0.989191 0.146631i \(-0.953157\pi\)
−0.367610 + 0.929980i \(0.619824\pi\)
\(12\) 0 0
\(13\) 6.92820i 1.92154i 0.277350 + 0.960769i \(0.410544\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 1.73205i 0.447214i
\(16\) 0 0
\(17\) 3.00000 1.73205i 0.727607 0.420084i −0.0899392 0.995947i \(-0.528667\pi\)
0.817546 + 0.575863i \(0.195334\pi\)
\(18\) 0 0
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0.500000 + 2.59808i 0.109109 + 0.566947i
\(22\) 0 0
\(23\) −6.00000 3.46410i −1.25109 0.722315i −0.279761 0.960070i \(-0.590255\pi\)
−0.971325 + 0.237754i \(0.923589\pi\)
\(24\) 0 0
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) 4.50000 + 2.59808i 0.783349 + 0.452267i
\(34\) 0 0
\(35\) 3.00000 + 3.46410i 0.507093 + 0.585540i
\(36\) 0 0
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) 6.00000 3.46410i 0.960769 0.554700i
\(40\) 0 0
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i 0.964486 + 0.264135i \(0.0850865\pi\)
−0.964486 + 0.264135i \(0.914913\pi\)
\(44\) 0 0
\(45\) 1.50000 0.866025i 0.223607 0.129099i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) −3.00000 1.73205i −0.420084 0.242536i
\(52\) 0 0
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −6.00000 3.46410i −0.768221 0.443533i 0.0640184 0.997949i \(-0.479608\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 2.00000 1.73205i 0.251976 0.218218i
\(64\) 0 0
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 0 0
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) 6.92820i 0.822226i 0.911584 + 0.411113i \(0.134860\pi\)
−0.911584 + 0.411113i \(0.865140\pi\)
\(72\) 0 0
\(73\) 6.00000 3.46410i 0.702247 0.405442i −0.105937 0.994373i \(-0.533784\pi\)
0.808184 + 0.588930i \(0.200451\pi\)
\(74\) 0 0
\(75\) −1.00000 + 1.73205i −0.115470 + 0.200000i
\(76\) 0 0
\(77\) 13.5000 2.59808i 1.53847 0.296078i
\(78\) 0 0
\(79\) 1.50000 + 0.866025i 0.168763 + 0.0974355i 0.582003 0.813187i \(-0.302269\pi\)
−0.413239 + 0.910622i \(0.635603\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 15.0000 1.64646 0.823232 0.567705i \(-0.192169\pi\)
0.823232 + 0.567705i \(0.192169\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 0 0
\(87\) 4.50000 + 7.79423i 0.482451 + 0.835629i
\(88\) 0 0
\(89\) −9.00000 5.19615i −0.953998 0.550791i −0.0596775 0.998218i \(-0.519007\pi\)
−0.894321 + 0.447427i \(0.852341\pi\)
\(90\) 0 0
\(91\) 6.00000 17.3205i 0.628971 1.81568i
\(92\) 0 0
\(93\) 0.500000 0.866025i 0.0518476 0.0898027i
\(94\) 0 0
\(95\) −3.00000 + 1.73205i −0.307794 + 0.177705i
\(96\) 0 0
\(97\) 8.66025i 0.879316i 0.898165 + 0.439658i \(0.144900\pi\)
−0.898165 + 0.439658i \(0.855100\pi\)
\(98\) 0 0
\(99\) 5.19615i 0.522233i
\(100\) 0 0
\(101\) −12.0000 + 6.92820i −1.19404 + 0.689382i −0.959221 0.282656i \(-0.908784\pi\)
−0.234823 + 0.972038i \(0.575451\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 0 0
\(105\) 1.50000 4.33013i 0.146385 0.422577i
\(106\) 0 0
\(107\) 7.50000 + 4.33013i 0.725052 + 0.418609i 0.816609 0.577191i \(-0.195851\pi\)
−0.0915571 + 0.995800i \(0.529184\pi\)
\(108\) 0 0
\(109\) 2.00000 + 3.46410i 0.191565 + 0.331801i 0.945769 0.324840i \(-0.105310\pi\)
−0.754204 + 0.656640i \(0.771977\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 6.00000 + 10.3923i 0.559503 + 0.969087i
\(116\) 0 0
\(117\) −6.00000 3.46410i −0.554700 0.320256i
\(118\) 0 0
\(119\) −9.00000 + 1.73205i −0.825029 + 0.158777i
\(120\) 0 0
\(121\) 8.00000 13.8564i 0.727273 1.25967i
\(122\) 0 0
\(123\) −3.00000 + 1.73205i −0.270501 + 0.156174i
\(124\) 0 0
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 15.5885i 1.38325i 0.722256 + 0.691626i \(0.243105\pi\)
−0.722256 + 0.691626i \(0.756895\pi\)
\(128\) 0 0
\(129\) 3.00000 1.73205i 0.264135 0.152499i
\(130\) 0 0
\(131\) −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i \(-0.875170\pi\)
0.793028 + 0.609185i \(0.208503\pi\)
\(132\) 0 0
\(133\) −4.00000 + 3.46410i −0.346844 + 0.300376i
\(134\) 0 0
\(135\) −1.50000 0.866025i −0.129099 0.0745356i
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −22.0000 −1.86602 −0.933008 0.359856i \(-0.882826\pi\)
−0.933008 + 0.359856i \(0.882826\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −18.0000 31.1769i −1.50524 2.60714i
\(144\) 0 0
\(145\) 13.5000 + 7.79423i 1.12111 + 0.647275i
\(146\) 0 0
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) 0 0
\(149\) 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
\(151\) 1.50000 0.866025i 0.122068 0.0704761i −0.437723 0.899110i \(-0.644215\pi\)
0.559791 + 0.828634i \(0.310881\pi\)
\(152\) 0 0
\(153\) 3.46410i 0.280056i
\(154\) 0 0
\(155\) 1.73205i 0.139122i
\(156\) 0 0
\(157\) 6.00000 3.46410i 0.478852 0.276465i −0.241086 0.970504i \(-0.577504\pi\)
0.719938 + 0.694038i \(0.244170\pi\)
\(158\) 0 0
\(159\) −4.50000 + 7.79423i −0.356873 + 0.618123i
\(160\) 0 0
\(161\) 12.0000 + 13.8564i 0.945732 + 1.09204i
\(162\) 0 0
\(163\) −18.0000 10.3923i −1.40987 0.813988i −0.414494 0.910052i \(-0.636041\pi\)
−0.995375 + 0.0960641i \(0.969375\pi\)
\(164\) 0 0
\(165\) −4.50000 7.79423i −0.350325 0.606780i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −35.0000 −2.69231
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 0 0
\(173\) 12.0000 + 6.92820i 0.912343 + 0.526742i 0.881184 0.472773i \(-0.156747\pi\)
0.0311588 + 0.999514i \(0.490080\pi\)
\(174\) 0 0
\(175\) 1.00000 + 5.19615i 0.0755929 + 0.392792i
\(176\) 0 0
\(177\) −1.50000 + 2.59808i −0.112747 + 0.195283i
\(178\) 0 0
\(179\) −15.0000 + 8.66025i −1.12115 + 0.647298i −0.941695 0.336468i \(-0.890768\pi\)
−0.179458 + 0.983766i \(0.557434\pi\)
\(180\) 0 0
\(181\) 3.46410i 0.257485i −0.991678 0.128742i \(-0.958906\pi\)
0.991678 0.128742i \(-0.0410940\pi\)
\(182\) 0 0
\(183\) 6.92820i 0.512148i
\(184\) 0 0
\(185\) −3.00000 + 1.73205i −0.220564 + 0.127343i
\(186\) 0 0
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) 0 0
\(189\) −2.50000 0.866025i −0.181848 0.0629941i
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) −9.50000 16.4545i −0.683825 1.18442i −0.973805 0.227387i \(-0.926982\pi\)
0.289980 0.957033i \(-0.406351\pi\)
\(194\) 0 0
\(195\) −12.0000 −0.859338
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(1.64140\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 22.5000 + 7.79423i 1.57919 + 0.547048i
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) 0 0
\(207\) 6.00000 3.46410i 0.417029 0.240772i
\(208\) 0 0
\(209\) 10.3923i 0.718851i
\(210\) 0 0
\(211\) 13.8564i 0.953914i −0.878927 0.476957i \(-0.841740\pi\)
0.878927 0.476957i \(-0.158260\pi\)
\(212\) 0 0
\(213\) 6.00000 3.46410i 0.411113 0.237356i
\(214\) 0 0
\(215\) 3.00000 5.19615i 0.204598 0.354375i
\(216\) 0 0
\(217\) −0.500000 2.59808i −0.0339422 0.176369i
\(218\) 0 0
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 0 0
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 0 0
\(223\) 1.00000 0.0669650 0.0334825 0.999439i \(-0.489340\pi\)
0.0334825 + 0.999439i \(0.489340\pi\)
\(224\) 0 0
\(225\) 2.00000 0.133333
\(226\) 0 0
\(227\) 4.50000 + 7.79423i 0.298675 + 0.517321i 0.975833 0.218517i \(-0.0701218\pi\)
−0.677158 + 0.735838i \(0.736789\pi\)
\(228\) 0 0
\(229\) −3.00000 1.73205i −0.198246 0.114457i 0.397591 0.917563i \(-0.369846\pi\)
−0.595837 + 0.803105i \(0.703180\pi\)
\(230\) 0 0
\(231\) −9.00000 10.3923i −0.592157 0.683763i
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.73205i 0.112509i
\(238\) 0 0
\(239\) 13.8564i 0.896296i −0.893959 0.448148i \(-0.852084\pi\)
0.893959 0.448148i \(-0.147916\pi\)
\(240\) 0 0
\(241\) −4.50000 + 2.59808i −0.289870 + 0.167357i −0.637883 0.770133i \(-0.720190\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −4.50000 11.2583i −0.287494 0.719268i
\(246\) 0 0
\(247\) 12.0000 + 6.92820i 0.763542 + 0.440831i
\(248\) 0 0
\(249\) −7.50000 12.9904i −0.475293 0.823232i
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) 36.0000 2.26330
\(254\) 0 0
\(255\) 3.00000 + 5.19615i 0.187867 + 0.325396i
\(256\) 0 0
\(257\) −3.00000 1.73205i −0.187135 0.108042i 0.403506 0.914977i \(-0.367792\pi\)
−0.590641 + 0.806935i \(0.701125\pi\)
\(258\) 0 0
\(259\) −4.00000 + 3.46410i −0.248548 + 0.215249i
\(260\) 0 0
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) 0 0
\(263\) −15.0000 + 8.66025i −0.924940 + 0.534014i −0.885208 0.465196i \(-0.845984\pi\)
−0.0397320 + 0.999210i \(0.512650\pi\)
\(264\) 0 0
\(265\) 15.5885i 0.957591i
\(266\) 0 0
\(267\) 10.3923i 0.635999i
\(268\) 0 0
\(269\) 1.50000 0.866025i 0.0914566 0.0528025i −0.453574 0.891219i \(-0.649851\pi\)
0.545031 + 0.838416i \(0.316518\pi\)
\(270\) 0 0
\(271\) −8.50000 + 14.7224i −0.516338 + 0.894324i 0.483482 + 0.875354i \(0.339372\pi\)
−0.999820 + 0.0189696i \(0.993961\pi\)
\(272\) 0 0
\(273\) −18.0000 + 3.46410i −1.08941 + 0.209657i
\(274\) 0 0
\(275\) 9.00000 + 5.19615i 0.542720 + 0.313340i
\(276\) 0 0
\(277\) −14.0000 24.2487i −0.841178 1.45696i −0.888899 0.458103i \(-0.848529\pi\)
0.0477206 0.998861i \(-0.484804\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 0 0
\(285\) 3.00000 + 1.73205i 0.177705 + 0.102598i
\(286\) 0 0
\(287\) −3.00000 + 8.66025i −0.177084 + 0.511199i
\(288\) 0 0
\(289\) −2.50000 + 4.33013i −0.147059 + 0.254713i
\(290\) 0 0
\(291\) 7.50000 4.33013i 0.439658 0.253837i
\(292\) 0 0
\(293\) 5.19615i 0.303562i −0.988414 0.151781i \(-0.951499\pi\)
0.988414 0.151781i \(-0.0485009\pi\)
\(294\) 0 0
\(295\) 5.19615i 0.302532i
\(296\) 0 0
\(297\) −4.50000 + 2.59808i −0.261116 + 0.150756i
\(298\) 0 0
\(299\) 24.0000 41.5692i 1.38796 2.40401i
\(300\) 0 0
\(301\) 3.00000 8.66025i 0.172917 0.499169i
\(302\) 0 0
\(303\) 12.0000 + 6.92820i 0.689382 + 0.398015i
\(304\) 0 0
\(305\) 6.00000 + 10.3923i 0.343559 + 0.595062i
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) 0 0
\(313\) −16.5000 9.52628i −0.932635 0.538457i −0.0449911 0.998987i \(-0.514326\pi\)
−0.887644 + 0.460530i \(0.847659\pi\)
\(314\) 0 0
\(315\) −4.50000 + 0.866025i −0.253546 + 0.0487950i
\(316\) 0 0
\(317\) 13.5000 23.3827i 0.758236 1.31330i −0.185514 0.982642i \(-0.559395\pi\)
0.943750 0.330661i \(-0.107272\pi\)
\(318\) 0 0
\(319\) 40.5000 23.3827i 2.26756 1.30918i
\(320\) 0 0
\(321\) 8.66025i 0.483368i
\(322\) 0 0
\(323\) 6.92820i 0.385496i
\(324\) 0 0
\(325\) 12.0000 6.92820i 0.665640 0.384308i
\(326\) 0 0
\(327\) 2.00000 3.46410i 0.110600 0.191565i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 1.00000 + 1.73205i 0.0547997 + 0.0949158i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) −4.50000 2.59808i −0.243689 0.140694i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 6.00000 10.3923i 0.323029 0.559503i
\(346\) 0 0
\(347\) −27.0000 + 15.5885i −1.44944 + 0.836832i −0.998448 0.0556976i \(-0.982262\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(348\) 0 0
\(349\) 20.7846i 1.11257i −0.830990 0.556287i \(-0.812225\pi\)
0.830990 0.556287i \(-0.187775\pi\)
\(350\) 0 0
\(351\) 6.92820i 0.369800i
\(352\) 0 0
\(353\) −6.00000 + 3.46410i −0.319348 + 0.184376i −0.651102 0.758990i \(-0.725693\pi\)
0.331754 + 0.943366i \(0.392360\pi\)
\(354\) 0 0
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) 0 0
\(357\) 6.00000 + 6.92820i 0.317554 + 0.366679i
\(358\) 0 0
\(359\) 24.0000 + 13.8564i 1.26667 + 0.731313i 0.974357 0.225009i \(-0.0722411\pi\)
0.292315 + 0.956322i \(0.405574\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) −16.0000 −0.839782
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) 0 0
\(367\) 11.5000 + 19.9186i 0.600295 + 1.03974i 0.992776 + 0.119982i \(0.0382835\pi\)
−0.392481 + 0.919760i \(0.628383\pi\)
\(368\) 0 0
\(369\) 3.00000 + 1.73205i 0.156174 + 0.0901670i
\(370\) 0 0
\(371\) 4.50000 + 23.3827i 0.233628 + 1.21397i
\(372\) 0 0
\(373\) −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i \(0.401711\pi\)
−0.977016 + 0.213165i \(0.931623\pi\)
\(374\) 0 0
\(375\) 10.5000 6.06218i 0.542218 0.313050i
\(376\) 0 0
\(377\) 62.3538i 3.21139i
\(378\) 0 0
\(379\) 17.3205i 0.889695i −0.895606 0.444847i \(-0.853258\pi\)
0.895606 0.444847i \(-0.146742\pi\)
\(380\) 0 0
\(381\) 13.5000 7.79423i 0.691626 0.399310i
\(382\) 0 0
\(383\) 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i \(-0.784346\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(384\) 0 0
\(385\) −22.5000 7.79423i −1.14671 0.397231i
\(386\) 0 0
\(387\) −3.00000 1.73205i −0.152499 0.0880451i
\(388\) 0 0
\(389\) 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) 0 0
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) 0 0
\(397\) 18.0000 + 10.3923i 0.903394 + 0.521575i 0.878300 0.478110i \(-0.158678\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) 0 0
\(399\) 5.00000 + 1.73205i 0.250313 + 0.0867110i
\(400\) 0 0
\(401\) −18.0000 + 31.1769i −0.898877 + 1.55690i −0.0699455 + 0.997551i \(0.522283\pi\)
−0.828932 + 0.559350i \(0.811051\pi\)
\(402\) 0 0
\(403\) −6.00000 + 3.46410i −0.298881 + 0.172559i
\(404\) 0 0
\(405\) 1.73205i 0.0860663i
\(406\) 0 0
\(407\) 10.3923i 0.515127i
\(408\) 0 0
\(409\) −7.50000 + 4.33013i −0.370851 + 0.214111i −0.673830 0.738886i \(-0.735352\pi\)
0.302979 + 0.952997i \(0.402019\pi\)
\(410\) 0 0
\(411\) 6.00000 10.3923i 0.295958 0.512615i
\(412\) 0 0
\(413\) 1.50000 + 7.79423i 0.0738102 + 0.383529i
\(414\) 0 0
\(415\) −22.5000 12.9904i −1.10448 0.637673i
\(416\) 0 0
\(417\) 11.0000 + 19.0526i 0.538672 + 0.933008i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.00000 3.46410i −0.291043 0.168034i
\(426\) 0 0
\(427\) 12.0000 + 13.8564i 0.580721 + 0.670559i
\(428\) 0 0
\(429\) −18.0000 + 31.1769i −0.869048 + 1.50524i
\(430\) 0 0
\(431\) 21.0000 12.1244i 1.01153 0.584010i 0.0998939 0.994998i \(-0.468150\pi\)
0.911641 + 0.410988i \(0.134816\pi\)
\(432\) 0 0
\(433\) 6.92820i 0.332948i −0.986046 0.166474i \(-0.946762\pi\)
0.986046 0.166474i \(-0.0532382\pi\)
\(434\) 0 0
\(435\) 15.5885i 0.747409i
\(436\) 0 0
\(437\) −12.0000 + 6.92820i −0.574038 + 0.331421i
\(438\) 0 0
\(439\) −12.5000 + 21.6506i −0.596592 + 1.03333i 0.396728 + 0.917936i \(0.370146\pi\)
−0.993320 + 0.115392i \(0.963188\pi\)
\(440\) 0 0
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) −19.5000 11.2583i −0.926473 0.534899i −0.0407786 0.999168i \(-0.512984\pi\)
−0.885694 + 0.464269i \(0.846317\pi\)
\(444\) 0 0
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) 0 0
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 0 0
\(453\) −1.50000 0.866025i −0.0704761 0.0406894i
\(454\) 0 0
\(455\) −24.0000 + 20.7846i −1.12514 + 0.974398i
\(456\) 0 0
\(457\) −8.50000 + 14.7224i −0.397613 + 0.688686i −0.993431 0.114433i \(-0.963495\pi\)
0.595818 + 0.803120i \(0.296828\pi\)
\(458\) 0 0
\(459\) 3.00000 1.73205i 0.140028 0.0808452i
\(460\) 0 0
\(461\) 20.7846i 0.968036i −0.875058 0.484018i \(-0.839177\pi\)
0.875058 0.484018i \(-0.160823\pi\)
\(462\) 0 0
\(463\) 10.3923i 0.482971i 0.970404 + 0.241486i \(0.0776347\pi\)
−0.970404 + 0.241486i \(0.922365\pi\)
\(464\) 0 0
\(465\) −1.50000 + 0.866025i −0.0695608 + 0.0401610i
\(466\) 0 0
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −6.00000 3.46410i −0.276465 0.159617i
\(472\) 0 0
\(473\) −9.00000 15.5885i −0.413820 0.716758i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) 0 0
\(479\) −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i \(-0.757551\pi\)
−0.235833 0.971794i \(1.42422\pi\)
\(480\) 0 0
\(481\) 12.0000 + 6.92820i 0.547153 + 0.315899i
\(482\) 0 0
\(483\) 6.00000 17.3205i 0.273009 0.788110i
\(484\) 0 0
\(485\) 7.50000 12.9904i 0.340557 0.589863i
\(486\) 0 0
\(487\) 13.5000 7.79423i 0.611743 0.353190i −0.161904 0.986807i \(-0.551764\pi\)
0.773647 + 0.633616i \(0.218430\pi\)
\(488\) 0 0
\(489\) 20.7846i 0.939913i
\(490\) 0 0
\(491\) 19.0526i 0.859830i −0.902869 0.429915i \(-0.858544\pi\)
0.902869 0.429915i \(-0.141456\pi\)
\(492\) 0 0
\(493\) −27.0000 + 15.5885i −1.21602 + 0.702069i
\(494\) 0 0
\(495\) −4.50000 + 7.79423i −0.202260 + 0.350325i
\(496\) 0 0
\(497\) 6.00000 17.3205i 0.269137 0.776931i
\(498\) 0 0
\(499\) −15.0000 8.66025i −0.671492 0.387686i 0.125150 0.992138i \(-0.460059\pi\)
−0.796642 + 0.604452i \(0.793392\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 0 0
\(507\) 17.5000 + 30.3109i 0.777202 + 1.34615i
\(508\) 0 0
\(509\) −16.5000 9.52628i −0.731350 0.422245i 0.0875661 0.996159i \(-0.472091\pi\)
−0.818916 + 0.573914i \(0.805424\pi\)
\(510\) 0 0
\(511\) −18.0000 + 3.46410i −0.796273 + 0.153243i
\(512\) 0 0
\(513\) 1.00000 1.73205i 0.0441511 0.0764719i
\(514\) 0 0
\(515\) −6.00000 + 3.46410i −0.264392 + 0.152647i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 13.8564i 0.608229i
\(520\) 0 0
\(521\) −27.0000 + 15.5885i −1.18289 + 0.682943i −0.956682 0.291136i \(-0.905967\pi\)
−0.226210 + 0.974079i \(0.572633\pi\)
\(522\) 0 0
\(523\) 20.0000 34.6410i 0.874539 1.51475i 0.0172859 0.999851i \(-0.494497\pi\)
0.857253 0.514895i \(-0.172169\pi\)
\(524\) 0 0
\(525\) 4.00000 3.46410i 0.174574 0.151186i
\(526\) 0 0
\(527\) 3.00000 + 1.73205i 0.130682 + 0.0754493i
\(528\) 0 0
\(529\) 12.5000 + 21.6506i 0.543478 + 0.941332i
\(530\) 0 0
\(531\) 3.00000 0.130189
\(532\) 0 0
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) −7.50000 12.9904i −0.324253 0.561623i
\(536\) 0 0
\(537\) 15.0000 + 8.66025i 0.647298 + 0.373718i
\(538\) 0 0
\(539\) −36.0000 5.19615i −1.55063 0.223814i
\(540\) 0 0
\(541\) −5.00000 + 8.66025i −0.214967 + 0.372333i −0.953262 0.302144i \(-0.902298\pi\)
0.738296 + 0.674477i \(0.235631\pi\)
\(542\) 0 0
\(543\) −3.00000 + 1.73205i −0.128742 + 0.0743294i
\(544\) 0 0
\(545\) 6.92820i 0.296772i
\(546\) 0 0
\(547\) 24.2487i 1.03680i −0.855138 0.518400i \(-0.826528\pi\)
0.855138 0.518400i \(-0.173472\pi\)
\(548\) 0 0
\(549\) 6.00000 3.46410i 0.256074 0.147844i
\(550\) 0 0
\(551\) −9.00000 + 15.5885i −0.383413 + 0.664091i
\(552\) 0 0
\(553\) −3.00000 3.46410i −0.127573 0.147309i
\(554\) 0 0
\(555\) 3.00000 + 1.73205i 0.127343 + 0.0735215i
\(556\) 0 0
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 18.0000 0.759961
\(562\) 0 0
\(563\) 4.50000 + 7.79423i 0.189652 + 0.328488i 0.945134 0.326682i \(-0.105931\pi\)
−0.755482 + 0.655169i \(0.772597\pi\)
\(564\) 0 0
\(565\) 9.00000 + 5.19615i 0.378633 + 0.218604i
\(566\) 0 0
\(567\) 0.500000 + 2.59808i 0.0209980 + 0.109109i
\(568\) 0 0
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 0 0
\(571\) −24.0000 + 13.8564i −1.00437 + 0.579873i −0.909538 0.415621i \(-0.863564\pi\)
−0.0948308 + 0.995493i \(0.530231\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.8564i 0.577852i
\(576\) 0 0
\(577\) 22.5000 12.9904i 0.936687 0.540797i 0.0477669 0.998859i \(-0.484790\pi\)
0.888920 + 0.458062i \(0.151456\pi\)
\(578\) 0 0
\(579\) −9.50000 + 16.4545i −0.394807 + 0.683825i
\(580\) 0 0
\(581\) −37.5000 12.9904i −1.55576 0.538932i
\(582\) 0 0
\(583\) 40.5000 + 23.3827i 1.67734 + 0.968412i
\(584\) 0 0
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 0 0
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) 0 0
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 0 0
\(593\) −18.0000 10.3923i −0.739171 0.426761i 0.0825966 0.996583i \(-0.473679\pi\)
−0.821768 + 0.569822i \(0.807012\pi\)
\(594\) 0 0
\(595\) 15.0000 + 5.19615i 0.614940 + 0.213021i
\(596\) 0 0
\(597\) −8.00000 + 13.8564i −0.327418 + 0.567105i
\(598\) 0 0
\(599\) −24.0000 + 13.8564i −0.980613 + 0.566157i −0.902455 0.430784i \(-0.858237\pi\)
−0.0781581 + 0.996941i \(0.524904\pi\)
\(600\) 0 0
\(601\) 15.5885i 0.635866i −0.948113 0.317933i \(-0.897011\pi\)
0.948113 0.317933i \(-0.102989\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −24.0000 + 13.8564i −0.975739 + 0.563343i
\(606\) 0 0
\(607\) 11.5000 19.9186i 0.466771 0.808470i −0.532509 0.846424i \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) 0 0
\(609\) −4.50000 23.3827i −0.182349 0.947514i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) 0 0
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) 24.0000 0.966204 0.483102 0.875564i \(-0.339510\pi\)
0.483102 + 0.875564i \(0.339510\pi\)
\(618\) 0 0
\(619\) 8.00000 + 13.8564i 0.321547 + 0.556936i 0.980807 0.194979i \(-0.0624638\pi\)
−0.659260 + 0.751915i \(0.729130\pi\)
\(620\) 0 0
\(621\) −6.00000 3.46410i −0.240772 0.139010i
\(622\) 0 0
\(623\) 18.0000 + 20.7846i 0.721155 + 0.832718i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 0 0
\(627\) 9.00000 5.19615i 0.359425 0.207514i
\(628\) 0 0
\(629\) 6.92820i 0.276246i
\(630\) 0 0
\(631\) 25.9808i 1.03428i −0.855901 0.517139i \(-0.826997\pi\)
0.855901 0.517139i \(-0.173003\pi\)
\(632\) 0 0
\(633\) −12.0000 + 6.92820i −0.476957 + 0.275371i
\(634\) 0 0
\(635\) 13.5000 23.3827i 0.535731 0.927914i
\(636\) 0 0
\(637\) −30.0000 + 38.1051i −1.18864 + 1.50978i
\(638\) 0 0
\(639\) −6.00000 3.46410i −0.237356 0.137038i
\(640\) 0 0
\(641\) −12.0000 20.7846i −0.473972 0.820943i 0.525584 0.850741i \(-0.323847\pi\)
−0.999556 + 0.0297987i \(0.990513\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) 0 0
\(649\) 13.5000 + 7.79423i 0.529921 + 0.305950i
\(650\) 0 0
\(651\) −2.00000 + 1.73205i −0.0783862 + 0.0678844i
\(652\) 0 0
\(653\) 10.5000 18.1865i 0.410897 0.711694i −0.584091 0.811688i \(-0.698549\pi\)
0.994988 + 0.0999939i \(0.0318823\pi\)
\(654\) 0 0
\(655\) 4.50000 2.59808i 0.175830 0.101515i
\(656\) 0 0
\(657\) 6.92820i 0.270295i
\(658\) 0 0
\(659\) 17.3205i 0.674711i −0.941377 0.337356i \(-0.890468\pi\)
0.941377 0.337356i \(-0.109532\pi\)
\(660\) 0 0
\(661\) 33.0000 19.0526i 1.28355 0.741059i 0.306055 0.952014i \(-0.400991\pi\)
0.977496 + 0.210955i \(0.0676574\pi\)
\(662\) 0 0
\(663\) 12.0000 20.7846i 0.466041 0.807207i
\(664\) 0 0
\(665\) 9.00000 1.73205i 0.349005 0.0671660i
\(666\) 0 0
\(667\) 54.0000 + 31.1769i 2.09089 + 1.20717i
\(668\) 0 0
\(669\) −0.500000 0.866025i −0.0193311 0.0334825i
\(670\) 0 0
\(671\) 36.0000 1.38976
\(672\) 0 0
\(673\) −11.0000 −0.424019 −0.212009 0.977268i \(-0.568001\pi\)
−0.212009 + 0.977268i \(0.568001\pi\)
\(674\) 0 0
\(675\) −1.00000 1.73205i −0.0384900 0.0666667i
\(676\) 0 0
\(677\) 22.5000 + 12.9904i 0.864745 + 0.499261i 0.865598 0.500739i \(-0.166938\pi\)
−0.000853228 1.00000i \(0.500272\pi\)
\(678\) 0 0
\(679\) 7.50000 21.6506i 0.287824 0.830875i
\(680\) 0 0
\(681\) 4.50000 7.79423i 0.172440 0.298675i
\(682\) 0 0
\(683\) 7.50000 4.33013i 0.286980 0.165688i −0.349599 0.936899i \(-0.613682\pi\)
0.636579 + 0.771212i \(0.280349\pi\)
\(684\) 0 0
\(685\) 20.7846i 0.794139i
\(686\) 0 0
\(687\) 3.46410i 0.132164i
\(688\) 0 0
\(689\) 54.0000 31.1769i 2.05724 1.18775i
\(690\) 0 0
\(691\) −7.00000 + 12.1244i −0.266293 + 0.461232i −0.967901 0.251330i \(-0.919132\pi\)
0.701609 + 0.712562i \(0.252465\pi\)
\(692\) 0 0
\(693\) −4.50000 + 12.9904i −0.170941 + 0.493464i
\(694\) 0 0
\(695\) 33.0000 + 19.0526i 1.25176 + 0.722705i
\(696\) 0 0
\(697\) −6.00000 10.3923i −0.227266 0.393637i
\(698\) 0 0
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 0 0
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 36.0000 6.92820i 1.35392 0.260562i
\(708\) 0 0
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) −1.50000 + 0.866025i −0.0562544 + 0.0324785i
\(712\) 0 0
\(713\) 6.92820i 0.259463i
\(714\) 0 0
\(715\) 62.3538i 2.33190i
\(716\) 0 0
\(717\) −12.0000 + 6.92820i −0.448148 + 0.258738i
\(718\) 0 0
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) −8.00000 + 6.92820i −0.297936 + 0.258020i
\(722\) 0 0
\(723\) 4.50000 + 2.59808i 0.167357 + 0.0966235i
\(724\) 0 0
\(725\) 9.00000 + 15.5885i 0.334252 + 0.578941i
\(726\) 0 0
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) −27.0000 15.5885i −0.997268 0.575773i −0.0898290 0.995957i \(-0.528632\pi\)
−0.907439 + 0.420184i \(0.861965\pi\)
\(734\) 0 0
\(735\) −7.50000 + 9.52628i −0.276642 + 0.351382i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 27.0000 15.5885i 0.993211 0.573431i 0.0869785 0.996210i \(-0.472279\pi\)
0.906233 + 0.422780i \(0.138946\pi\)
\(740\) 0 0
\(741\) 13.8564i 0.509028i
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −9.00000 + 5.19615i −0.329734 + 0.190372i
\(746\) 0 0
\(747\) −7.50000 + 12.9904i −0.274411 + 0.475293i
\(748\) 0 0
\(749\) −15.0000 17.3205i −0.548088 0.632878i
\(750\) 0 0
\(751\) −10.5000 6.06218i −0.383150 0.221212i 0.296038 0.955176i \(-0.404335\pi\)
−0.679188 + 0.733964i \(0.737668\pi\)
\(752\) 0 0
\(753\) −10.5000 18.1865i −0.382641 0.662754i
\(754\) 0 0
\(755\) −3.00000 −0.109181
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 0 0
\(759\) −18.0000 31.1769i −0.653359 1.13165i
\(760\) 0 0
\(761\) 12.0000 + 6.92820i 0.435000 + 0.251147i 0.701474 0.712695i \(-0.252526\pi\)
−0.266475 + 0.963842i \(0.585859\pi\)
\(762\) 0 0
\(763\) −2.00000 10.3923i −0.0724049 0.376227i
\(764\) 0 0
\(765\) 3.00000 5.19615i 0.108465 0.187867i
\(766\) 0 0
\(767\) 18.0000 10.3923i 0.649942 0.375244i
\(768\) 0 0
\(769\) 5.19615i 0.187378i 0.995602 + 0.0936890i \(0.0298659\pi\)
−0.995602 + 0.0936890i \(0.970134\pi\)
\(770\) 0 0
\(771\) 3.46410i 0.124757i
\(772\) 0 0
\(773\) −24.0000 + 13.8564i −0.863220 + 0.498380i −0.865089 0.501618i \(-0.832738\pi\)
0.00186926 + 0.999998i \(0.499405\pi\)
\(774\) 0 0
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) 0 0
\(777\) 5.00000 + 1.73205i 0.179374 + 0.0621370i
\(778\) 0 0
\(779\) −6.00000 3.46410i −0.214972 0.124114i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) 0 0
\(783\) −9.00000 −0.321634
\(784\) 0 0
\(785\) −12.0000 −0.428298
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(1.64015\pi\)
\(788\) 0 0
\(789\) 15.0000 + 8.66025i 0.534014 + 0.308313i
\(790\) 0 0
\(791\) 15.0000 + 5.19615i 0.533339 + 0.184754i
\(792\) 0 0
\(793\) 24.0000 41.5692i 0.852265 1.47617i
\(794\) 0 0
\(795\) 13.5000 7.79423i 0.478796 0.276433i
\(796\) 0 0
\(797\) 8.66025i 0.306762i 0.988167 + 0.153381i \(0.0490162\pi\)
−0.988167 + 0.153381i \(0.950984\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 9.00000 5.19615i 0.317999 0.183597i
\(802\) 0 0
\(803\) −18.0000 + 31.1769i −0.635206 + 1.10021i
\(804\) 0 0
\(805\) −6.00000 31.1769i −0.211472 1.09884i
\(806\) 0 0
\(807\) −1.50000 0.866025i −0.0528025 0.0304855i
\(808\) 0 0