Properties

Label 342.2.g.c.163.1
Level $342$
Weight $2$
Character 342.163
Analytic conductor $2.731$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.73088374913\)
Analytic rank: \(0\)
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 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 342.163
Dual form 342.2.g.c.235.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(2.50000 + 4.33013i) q^{25} -3.00000 q^{26} +(-0.500000 - 0.866025i) q^{28} -3.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} -5.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(2.00000 - 3.46410i) q^{41} +(4.50000 - 7.79423i) q^{43} +(-1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(5.00000 + 8.66025i) q^{47} -6.00000 q^{49} -5.00000 q^{50} +(1.50000 - 2.59808i) q^{52} +(-2.00000 - 3.46410i) q^{53} +1.00000 q^{56} +(-7.00000 + 12.1244i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(1.50000 - 2.59808i) q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{67} -4.00000 q^{68} +(7.00000 - 12.1244i) q^{71} +(5.50000 - 9.52628i) q^{73} +(2.50000 - 4.33013i) q^{74} +(-0.500000 - 4.33013i) q^{76} +2.00000 q^{77} +(-0.500000 + 0.866025i) q^{79} +(2.00000 + 3.46410i) q^{82} -8.00000 q^{83} +(4.50000 + 7.79423i) q^{86} +2.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{91} +(2.00000 - 3.46410i) q^{92} -10.0000 q^{94} +(-1.00000 + 1.73205i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8} + 4 q^{11} + 3 q^{13} - q^{14} - q^{16} + 4 q^{17} + 8 q^{19} - 2 q^{22} + 4 q^{23} + 5 q^{25} - 6 q^{26} - q^{28} - 6 q^{31} - q^{32} + 4 q^{34} - 10 q^{37} - 7 q^{38} + 4 q^{41} + 9 q^{43} - 2 q^{44} - 8 q^{46} + 10 q^{47} - 12 q^{49} - 10 q^{50} + 3 q^{52} - 4 q^{53} + 2 q^{56} - 14 q^{59} - 11 q^{61} + 3 q^{62} + 2 q^{64} - 3 q^{67} - 8 q^{68} + 14 q^{71} + 11 q^{73} + 5 q^{74} - q^{76} + 4 q^{77} - q^{79} + 4 q^{82} - 16 q^{83} + 9 q^{86} + 4 q^{88} - 14 q^{89} + 3 q^{91} + 4 q^{92} - 20 q^{94} - 2 q^{97} + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i \(-0.0300895\pi\)
−0.579510 + 0.814965i \(0.696756\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 0 0
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −3.00000 −0.588348
\(27\) 0 0
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) −3.50000 + 2.59808i −0.567775 + 0.421464i
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 3.46410i 0.312348 0.541002i −0.666523 0.745485i \(-0.732218\pi\)
0.978870 + 0.204483i \(0.0655513\pi\)
\(42\) 0 0
\(43\) 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i \(-0.592592\pi\)
0.973044 0.230618i \(-0.0740749\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 5.00000 + 8.66025i 0.729325 + 1.26323i 0.957169 + 0.289530i \(0.0934991\pi\)
−0.227844 + 0.973698i \(0.573168\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 1.50000 2.59808i 0.208013 0.360288i
\(53\) −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i \(-0.255252\pi\)
−0.970065 + 0.242846i \(0.921919\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 0 0
\(59\) −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i \(0.531604\pi\)
−0.812198 + 0.583382i \(0.801729\pi\)
\(60\) 0 0
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) 1.50000 2.59808i 0.190500 0.329956i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) 7.00000 12.1244i 0.830747 1.43890i −0.0666994 0.997773i \(-0.521247\pi\)
0.897447 0.441123i \(-0.145420\pi\)
\(72\) 0 0
\(73\) 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) 2.50000 4.33013i 0.290619 0.503367i
\(75\) 0 0
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.00000 + 3.46410i 0.220863 + 0.382546i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.50000 + 7.79423i 0.485247 + 0.840473i
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i \(-0.900545\pi\)
0.209585 0.977790i \(-0.432789\pi\)
\(90\) 0 0
\(91\) 1.50000 + 2.59808i 0.157243 + 0.272352i
\(92\) 2.00000 3.46410i 0.208514 0.361158i
\(93\) 0 0
\(94\) −10.0000 −1.03142
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 3.00000 5.19615i 0.303046 0.524891i
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) −3.00000 −0.295599 −0.147799 0.989017i \(-0.547219\pi\)
−0.147799 + 0.989017i \(0.547219\pi\)
\(104\) 1.50000 + 2.59808i 0.147087 + 0.254762i
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 10.0000 0.966736 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.500000 + 0.866025i −0.0472456 + 0.0818317i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −7.00000 12.1244i −0.644402 1.11614i
\(119\) 2.00000 3.46410i 0.183340 0.317554i
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 11.0000 0.995893
\(123\) 0 0
\(124\) 1.50000 + 2.59808i 0.134704 + 0.233314i
\(125\) 0 0
\(126\) 0 0
\(127\) 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) 4.00000 + 1.73205i 0.346844 + 0.150188i
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) 9.50000 + 16.4545i 0.805779 + 1.39565i 0.915764 + 0.401718i \(0.131587\pi\)
−0.109984 + 0.993933i \(0.535080\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.00000 + 12.1244i 0.587427 + 1.01745i
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 5.50000 + 9.52628i 0.455183 + 0.788400i
\(147\) 0 0
\(148\) 2.50000 + 4.33013i 0.205499 + 0.355934i
\(149\) −11.0000 + 19.0526i −0.901155 + 1.56085i −0.0751583 + 0.997172i \(0.523946\pi\)
−0.825997 + 0.563675i \(0.809387\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 4.00000 + 1.73205i 0.324443 + 0.140488i
\(153\) 0 0
\(154\) −1.00000 + 1.73205i −0.0805823 + 0.139573i
\(155\) 0 0
\(156\) 0 0
\(157\) 10.5000 18.1865i 0.837991 1.45144i −0.0535803 0.998564i \(-0.517063\pi\)
0.891572 0.452880i \(-0.149603\pi\)
\(158\) −0.500000 0.866025i −0.0397779 0.0688973i
\(159\) 0 0
\(160\) 0 0
\(161\) 2.00000 + 3.46410i 0.157622 + 0.273009i
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) 3.00000 + 5.19615i 0.232147 + 0.402090i 0.958440 0.285295i \(-0.0920916\pi\)
−0.726293 + 0.687386i \(0.758758\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 0 0
\(171\) 0 0
\(172\) −9.00000 −0.686244
\(173\) −12.0000 + 20.7846i −0.912343 + 1.58022i −0.101598 + 0.994826i \(0.532395\pi\)
−0.810745 + 0.585399i \(0.800938\pi\)
\(174\) 0 0
\(175\) 2.50000 + 4.33013i 0.188982 + 0.327327i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 0 0
\(178\) 14.0000 1.04934
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) 9.00000 + 15.5885i 0.668965 + 1.15868i 0.978194 + 0.207693i \(0.0665956\pi\)
−0.309229 + 0.950988i \(0.600071\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 0 0
\(186\) 0 0
\(187\) 4.00000 6.92820i 0.292509 0.506640i
\(188\) 5.00000 8.66025i 0.364662 0.631614i
\(189\) 0 0
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i \(-0.678351\pi\)
0.999326 + 0.0366998i \(0.0116845\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) −2.50000 4.33013i −0.177220 0.306955i 0.763707 0.645563i \(-0.223377\pi\)
−0.940927 + 0.338608i \(0.890044\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 1.50000 2.59808i 0.104510 0.181017i
\(207\) 0 0
\(208\) −3.00000 −0.208013
\(209\) 8.00000 + 3.46410i 0.553372 + 0.239617i
\(210\) 0 0
\(211\) −12.5000 + 21.6506i −0.860535 + 1.49049i 0.0108774 + 0.999941i \(0.496538\pi\)
−0.871413 + 0.490550i \(0.836796\pi\)
\(212\) −2.00000 + 3.46410i −0.137361 + 0.237915i
\(213\) 0 0
\(214\) −5.00000 + 8.66025i −0.341793 + 0.592003i
\(215\) 0 0
\(216\) 0 0
\(217\) −3.00000 −0.203653
\(218\) −7.00000 12.1244i −0.474100 0.821165i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i \(-0.930768\pi\)
0.675098 + 0.737728i \(0.264101\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 0 0
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 0 0
\(229\) −11.0000 −0.726900 −0.363450 0.931614i \(-0.618401\pi\)
−0.363450 + 0.931614i \(0.618401\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.00000 15.5885i 0.589610 1.02123i −0.404674 0.914461i \(-0.632615\pi\)
0.994283 0.106773i \(-0.0340517\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 14.0000 0.911322
\(237\) 0 0
\(238\) 2.00000 + 3.46410i 0.129641 + 0.224544i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i \(-0.868727\pi\)
0.110963 0.993825i \(-0.464606\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) 0 0
\(244\) −5.50000 + 9.52628i −0.352101 + 0.609858i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.50000 + 12.9904i 0.0954427 + 0.826558i
\(248\) −3.00000 −0.190500
\(249\) 0 0
\(250\) 0 0
\(251\) −9.00000 15.5885i −0.568075 0.983935i −0.996756 0.0804789i \(-0.974355\pi\)
0.428681 0.903456i \(-0.358978\pi\)
\(252\) 0 0
\(253\) 4.00000 + 6.92820i 0.251478 + 0.435572i
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i \(-0.288773\pi\)
−0.990217 + 0.139533i \(0.955440\pi\)
\(258\) 0 0
\(259\) −5.00000 −0.310685
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.50000 + 2.59808i −0.214599 + 0.159298i
\(267\) 0 0
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) 1.00000 1.73205i 0.0609711 0.105605i −0.833929 0.551872i \(-0.813914\pi\)
0.894900 + 0.446267i \(0.147247\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 2.00000 + 3.46410i 0.121268 + 0.210042i
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 5.00000 + 8.66025i 0.301511 + 0.522233i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −19.0000 −1.13954
\(279\) 0 0
\(280\) 0 0
\(281\) −4.00000 6.92820i −0.238620 0.413302i 0.721699 0.692207i \(-0.243362\pi\)
−0.960319 + 0.278906i \(0.910028\pi\)
\(282\) 0 0
\(283\) 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) −14.0000 −0.830747
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 2.00000 3.46410i 0.118056 0.204479i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) −11.0000 −0.643726
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −5.00000 −0.290619
\(297\) 0 0
\(298\) −11.0000 19.0526i −0.637213 1.10369i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 0 0
\(301\) 4.50000 7.79423i 0.259376 0.449252i
\(302\) 10.0000 17.3205i 0.575435 0.996683i
\(303\) 0 0
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) 0 0
\(306\) 0 0
\(307\) 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i \(-0.722081\pi\)
0.984885 + 0.173210i \(0.0554140\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 0 0
\(310\) 0 0
\(311\) −10.0000 −0.567048 −0.283524 0.958965i \(-0.591504\pi\)
−0.283524 + 0.958965i \(0.591504\pi\)
\(312\) 0 0
\(313\) −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i \(-0.220905\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(314\) 10.5000 + 18.1865i 0.592549 + 1.02633i
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −4.00000 −0.222911
\(323\) 14.0000 10.3923i 0.778981 0.578243i
\(324\) 0 0
\(325\) −7.50000 + 12.9904i −0.416025 + 0.720577i
\(326\) −5.50000 + 9.52628i −0.304617 + 0.527612i
\(327\) 0 0
\(328\) 2.00000 3.46410i 0.110432 0.191273i
\(329\) 5.00000 + 8.66025i 0.275659 + 0.477455i
\(330\) 0 0
\(331\) 15.0000 0.824475 0.412237 0.911077i \(-0.364747\pi\)
0.412237 + 0.911077i \(0.364747\pi\)
\(332\) 4.00000 + 6.92820i 0.219529 + 0.380235i
\(333\) 0 0
\(334\) −6.00000 −0.328305
\(335\) 0 0
\(336\) 0 0
\(337\) 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i \(-0.660197\pi\)
0.999793 0.0203242i \(-0.00646983\pi\)
\(338\) 2.00000 + 3.46410i 0.108786 + 0.188422i
\(339\) 0 0
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 4.50000 7.79423i 0.242624 0.420237i
\(345\) 0 0
\(346\) −12.0000 20.7846i −0.645124 1.11739i
\(347\) 8.00000 13.8564i 0.429463 0.743851i −0.567363 0.823468i \(-0.692036\pi\)
0.996826 + 0.0796169i \(0.0253697\pi\)
\(348\) 0 0
\(349\) −29.0000 −1.55233 −0.776167 0.630527i \(-0.782839\pi\)
−0.776167 + 0.630527i \(0.782839\pi\)
\(350\) −5.00000 −0.267261
\(351\) 0 0
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) 12.0000 0.638696 0.319348 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.00000 + 12.1244i −0.370999 + 0.642590i
\(357\) 0 0
\(358\) 2.00000 3.46410i 0.105703 0.183083i
\(359\) −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i \(0.565588\pi\)
−0.745409 + 0.666608i \(0.767746\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) −18.0000 −0.946059
\(363\) 0 0
\(364\) 1.50000 2.59808i 0.0786214 0.136176i
\(365\) 0 0
\(366\) 0 0
\(367\) −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i \(-0.961716\pi\)
0.392481 0.919760i \(-0.371617\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) −2.00000 3.46410i −0.103835 0.179847i
\(372\) 0 0
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 4.00000 + 6.92820i 0.206835 + 0.358249i
\(375\) 0 0
\(376\) 5.00000 + 8.66025i 0.257855 + 0.446619i
\(377\) 0 0
\(378\) 0 0
\(379\) −13.0000 −0.667765 −0.333883 0.942615i \(-0.608359\pi\)
−0.333883 + 0.942615i \(0.608359\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) 7.00000 12.1244i 0.357683 0.619526i −0.629890 0.776684i \(-0.716900\pi\)
0.987573 + 0.157159i \(0.0502334\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.50000 + 11.2583i 0.330841 + 0.573034i
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) −8.00000 13.8564i −0.405616 0.702548i 0.588777 0.808296i \(-0.299610\pi\)
−0.994393 + 0.105748i \(0.966276\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) −6.00000 −0.303046
\(393\) 0 0
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) 0 0
\(397\) −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i \(-0.956176\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(398\) 5.00000 0.250627
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) −4.50000 7.79423i −0.224161 0.388258i
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) 0 0
\(406\) 0 0
\(407\) −10.0000 −0.495682
\(408\) 0 0
\(409\) 15.0000 + 25.9808i 0.741702 + 1.28467i 0.951720 + 0.306968i \(0.0993146\pi\)
−0.210017 + 0.977698i \(0.567352\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.50000 + 2.59808i 0.0738997 + 0.127998i
\(413\) −7.00000 + 12.1244i −0.344447 + 0.596601i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.50000 2.59808i 0.0735436 0.127381i
\(417\) 0 0
\(418\) −7.00000 + 5.19615i −0.342381 + 0.254152i
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i \(-0.911690\pi\)
0.718076 + 0.695965i \(0.245023\pi\)
\(422\) −12.5000 21.6506i −0.608490 1.05394i
\(423\) 0 0
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) 20.0000 0.970143
\(426\) 0 0
\(427\) −5.50000 9.52628i −0.266164 0.461009i
\(428\) −5.00000 8.66025i −0.241684 0.418609i
\(429\) 0 0
\(430\) 0 0
\(431\) −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
\(433\) 4.50000 + 7.79423i 0.216256 + 0.374567i 0.953660 0.300885i \(-0.0972820\pi\)
−0.737404 + 0.675452i \(0.763949\pi\)
\(434\) 1.50000 2.59808i 0.0720023 0.124712i
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) 2.00000 + 17.3205i 0.0956730 + 0.828552i
\(438\) 0 0
\(439\) −9.50000 + 16.4545i −0.453410 + 0.785330i −0.998595 0.0529862i \(-0.983126\pi\)
0.545185 + 0.838316i \(0.316459\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6.00000 + 10.3923i −0.285391 + 0.494312i
\(443\) 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i \(0.0264433\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.50000 7.79423i −0.213081 0.369067i
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) 5.00000 + 8.66025i 0.235180 + 0.407344i
\(453\) 0 0
\(454\) 4.00000 6.92820i 0.187729 0.325157i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) 5.50000 9.52628i 0.256998 0.445134i
\(459\) 0 0
\(460\) 0 0
\(461\) 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i \(-0.788712\pi\)
0.927392 + 0.374091i \(0.122045\pi\)
\(462\) 0 0
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 9.00000 + 15.5885i 0.416917 + 0.722121i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) −1.50000 2.59808i −0.0692636 0.119968i
\(470\) 0 0
\(471\) 0 0
\(472\) −7.00000 + 12.1244i −0.322201 + 0.558069i
\(473\) 9.00000 15.5885i 0.413820 0.716758i
\(474\) 0 0
\(475\) 2.50000 + 21.6506i 0.114708 + 0.993399i
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i \(-0.122897\pi\)
−0.789314 + 0.613990i \(0.789564\pi\)
\(480\) 0 0
\(481\) −7.50000 12.9904i −0.341971 0.592310i
\(482\) 25.0000 1.13872
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 0 0
\(486\) 0 0
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) −5.50000 9.52628i −0.248973 0.431234i
\(489\) 0 0
\(490\) 0 0
\(491\) 15.0000 25.9808i 0.676941 1.17250i −0.298957 0.954267i \(-0.596639\pi\)
0.975898 0.218229i \(-0.0700279\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −12.0000 5.19615i −0.539906 0.233786i
\(495\) 0 0
\(496\) 1.50000 2.59808i 0.0673520 0.116657i
\(497\) 7.00000 12.1244i 0.313993 0.543852i
\(498\) 0 0
\(499\) −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i \(-0.869032\pi\)
0.804627 + 0.593780i \(0.202365\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.0000 0.803379
\(503\) 8.00000 + 13.8564i 0.356702 + 0.617827i 0.987408 0.158196i \(-0.0505677\pi\)
−0.630705 + 0.776022i \(0.717234\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −8.00000 −0.355643
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) 13.0000 + 22.5167i 0.576215 + 0.998033i 0.995908 + 0.0903676i \(0.0288042\pi\)
−0.419694 + 0.907666i \(0.637862\pi\)
\(510\) 0 0
\(511\) 5.50000 9.52628i 0.243306 0.421418i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) 0 0
\(516\) 0 0
\(517\) 10.0000 + 17.3205i 0.439799 + 0.761755i
\(518\) 2.50000 4.33013i 0.109844 0.190255i
\(519\) 0 0
\(520\) 0 0
\(521\) −34.0000 −1.48957 −0.744784 0.667306i \(-0.767447\pi\)
−0.744784 + 0.667306i \(0.767447\pi\)
\(522\) 0 0
\(523\) −18.5000 32.0429i −0.808949 1.40114i −0.913593 0.406630i \(-0.866704\pi\)
0.104644 0.994510i \(-0.466630\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.500000 4.33013i −0.0216777 0.187735i
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) −1.50000 2.59808i −0.0647901 0.112220i
\(537\) 0 0
\(538\) 1.00000 + 1.73205i 0.0431131 + 0.0746740i
\(539\) −12.0000 −0.516877
\(540\) 0 0
\(541\) 15.5000 + 26.8468i 0.666397 + 1.15423i 0.978905 + 0.204318i \(0.0654977\pi\)
−0.312507 + 0.949915i \(0.601169\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) 0 0
\(546\) 0 0
\(547\) −5.50000 9.52628i −0.235163 0.407314i 0.724157 0.689635i \(-0.242229\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) 0 0
\(550\) −10.0000 −0.426401
\(551\) 0 0
\(552\) 0 0
\(553\) −0.500000 + 0.866025i −0.0212622 + 0.0368271i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 0 0
\(556\) 9.50000 16.4545i 0.402890 0.697826i
\(557\) 17.0000 + 29.4449i 0.720313 + 1.24762i 0.960874 + 0.276985i \(0.0893352\pi\)
−0.240561 + 0.970634i \(0.577331\pi\)
\(558\) 0 0
\(559\) 27.0000 1.14198
\(560\) 0 0
\(561\) 0 0
\(562\) 8.00000 0.337460
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 10.0000 + 17.3205i 0.420331 + 0.728035i
\(567\) 0 0
\(568\) 7.00000 12.1244i 0.293713 0.508727i
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) 3.00000 5.19615i 0.125436 0.217262i
\(573\) 0 0
\(574\) 2.00000 + 3.46410i 0.0834784 + 0.144589i
\(575\) −10.0000 + 17.3205i −0.417029 + 0.722315i
\(576\) 0 0
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 0 0
\(580\) 0 0
\(581\) −8.00000 −0.331896
\(582\) 0 0
\(583\) −4.00000 6.92820i −0.165663 0.286937i
\(584\) 5.50000 9.52628i 0.227592 0.394200i
\(585\) 0 0
\(586\) 7.00000 12.1244i 0.289167 0.500853i
\(587\) −1.00000 + 1.73205i −0.0412744 + 0.0714894i −0.885925 0.463829i \(-0.846475\pi\)
0.844650 + 0.535319i \(0.179808\pi\)
\(588\) 0 0
\(589\) −12.0000 5.19615i −0.494451 0.214104i
\(590\) 0 0
\(591\) 0 0
\(592\) 2.50000 4.33013i 0.102749 0.177967i
\(593\) 17.0000 + 29.4449i 0.698106 + 1.20916i 0.969122 + 0.246581i \(0.0793071\pi\)
−0.271016 + 0.962575i \(0.587360\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 22.0000 0.901155
\(597\) 0 0
\(598\) −6.00000 10.3923i −0.245358 0.424973i
\(599\) −23.0000 39.8372i −0.939755 1.62770i −0.765928 0.642926i \(-0.777720\pi\)
−0.173826 0.984776i \(-0.555613\pi\)
\(600\) 0 0
\(601\) 27.0000 1.10135 0.550676 0.834719i \(-0.314370\pi\)
0.550676 + 0.834719i \(0.314370\pi\)
\(602\) 4.50000 + 7.79423i 0.183406 + 0.317669i
\(603\) 0 0
\(604\) 10.0000 + 17.3205i 0.406894 + 0.704761i
\(605\) 0 0
\(606\) 0 0
\(607\) 5.00000 0.202944 0.101472 0.994838i \(-0.467645\pi\)
0.101472 + 0.994838i \(0.467645\pi\)
\(608\) −0.500000 4.33013i −0.0202777 0.175610i
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 + 25.9808i −0.606835 + 1.05107i
\(612\) 0 0
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −21.0000 36.3731i −0.845428 1.46432i −0.885249 0.465118i \(-0.846012\pi\)
0.0398207 0.999207i \(-0.487321\pi\)
\(618\) 0 0
\(619\) 1.00000 0.0401934 0.0200967 0.999798i \(-0.493603\pi\)
0.0200967 + 0.999798i \(0.493603\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 5.00000 8.66025i 0.200482 0.347245i
\(623\) −7.00000 12.1244i −0.280449 0.485752i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) −21.0000 −0.837991
\(629\) −10.0000 + 17.3205i −0.398726 + 0.690614i
\(630\) 0 0
\(631\) −8.50000 14.7224i −0.338380 0.586091i 0.645748 0.763550i \(-0.276545\pi\)
−0.984128 + 0.177459i \(0.943212\pi\)
\(632\) −0.500000 + 0.866025i −0.0198889 + 0.0344486i
\(633\) 0 0
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) 0 0
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.00000 + 12.1244i −0.276483 + 0.478883i −0.970508 0.241068i \(-0.922502\pi\)
0.694025 + 0.719951i \(0.255836\pi\)
\(642\) 0 0
\(643\) −18.5000 + 32.0429i −0.729569 + 1.26365i 0.227497 + 0.973779i \(0.426946\pi\)
−0.957066 + 0.289871i \(0.906387\pi\)
\(644\) 2.00000 3.46410i 0.0788110 0.136505i
\(645\) 0 0
\(646\) 2.00000 + 17.3205i 0.0786889 + 0.681466i
\(647\) −48.0000 −1.88707 −0.943537 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 0 0
\(649\) −14.0000 + 24.2487i −0.549548 + 0.951845i
\(650\) −7.50000 12.9904i −0.294174 0.509525i
\(651\) 0 0
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) 42.0000 1.64359 0.821794 0.569785i \(-0.192974\pi\)
0.821794 + 0.569785i \(0.192974\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.00000 + 3.46410i 0.0780869 + 0.135250i
\(657\) 0 0
\(658\) −10.0000 −0.389841
\(659\) −7.00000 12.1244i −0.272681 0.472298i 0.696866 0.717201i \(-0.254577\pi\)
−0.969548 + 0.244903i \(0.921244\pi\)
\(660\) 0 0
\(661\) −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i \(-0.228968\pi\)
−0.946729 + 0.322031i \(0.895634\pi\)
\(662\) −7.50000 + 12.9904i −0.291496 + 0.504885i
\(663\) 0 0
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 3.00000 5.19615i 0.116073 0.201045i
\(669\) 0 0
\(670\) 0 0
\(671\) −11.0000 19.0526i −0.424650 0.735516i
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 9.50000 + 16.4545i 0.365926 + 0.633803i
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) −1.00000 + 1.73205i −0.0383765 + 0.0664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.00000 5.19615i 0.114876 0.198971i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 6.50000 11.2583i 0.248171 0.429845i
\(687\) 0 0
\(688\) 4.50000 + 7.79423i 0.171561 + 0.297152i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 24.0000 0.912343
\(693\) 0 0
\(694\) 8.00000 + 13.8564i 0.303676 + 0.525982i
\(695\) 0 0
\(696\) 0 0
\(697\) −8.00000 13.8564i −0.303022 0.524849i
\(698\) 14.5000 25.1147i 0.548833 0.950607i
\(699\) 0 0
\(700\) 2.50000 4.33013i 0.0944911 0.163663i
\(701\) −22.0000 + 38.1051i −0.830929 + 1.43921i 0.0663742 + 0.997795i \(0.478857\pi\)
−0.897303 + 0.441416i \(0.854476\pi\)
\(702\) 0 0
\(703\) −20.0000 8.66025i −0.754314 0.326628i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −6.00000 + 10.3923i −0.225813 + 0.391120i
\(707\) −5.00000 8.66025i −0.188044 0.325702i
\(708\) 0 0
\(709\) 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −7.00000 12.1244i −0.262336 0.454379i
\(713\) −6.00000 10.3923i −0.224702 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000 + 3.46410i 0.0747435 + 0.129460i
\(717\) 0 0
\(718\) −18.0000 31.1769i −0.671754 1.16351i
\(719\) 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i \(-0.565365\pi\)
0.949785 0.312903i \(-0.101301\pi\)
\(720\) 0 0
\(721\) −3.00000 −0.111726
\(722\) −18.5000 + 4.33013i −0.688499 + 0.161151i
\(723\) 0 0
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) 0 0
\(726\) 0 0
\(727\) −8.50000 + 14.7224i −0.315248 + 0.546025i −0.979490 0.201492i \(-0.935421\pi\)
0.664243 + 0.747517i \(0.268754\pi\)
\(728\) 1.50000 + 2.59808i 0.0555937 + 0.0962911i
\(729\) 0 0
\(730\) 0 0
\(731\) −18.0000 31.1769i −0.665754 1.15312i
\(732\) 0 0
\(733\) −2.00000 −0.0738717 −0.0369358 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) 23.0000 0.848945
\(735\) 0 0
\(736\) 2.00000 3.46410i 0.0737210 0.127688i
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 0 0
\(739\) 2.50000 4.33013i 0.0919640 0.159286i −0.816373 0.577524i \(-0.804019\pi\)
0.908337 + 0.418238i \(0.137352\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 4.00000 0.146845
\(743\) −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i \(-0.940442\pi\)
0.652369 + 0.757902i \(0.273775\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −13.0000 + 22.5167i −0.475964 + 0.824394i
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) 10.0000 0.365392
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) −10.0000 −0.364662
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.50000 + 4.33013i −0.0908640 + 0.157381i −0.907875 0.419241i \(-0.862296\pi\)
0.817011 + 0.576622i \(0.195630\pi\)
\(758\) 6.50000 11.2583i 0.236091 0.408921i
\(759\) 0 0
\(760\) 0 0
\(761\) 34.0000 1.23250 0.616250 0.787551i \(-0.288651\pi\)
0.616250 + 0.787551i \(0.288651\pi\)
\(762\) 0 0
\(763\) −7.00000 + 12.1244i −0.253417 + 0.438931i
\(764\) −4.00000 6.92820i −0.144715 0.250654i
\(765\) 0 0
\(766\) 7.00000 + 12.1244i 0.252920 + 0.438071i
\(767\) −42.0000 −1.51653
\(768\) 0 0
\(769\) −13.5000 23.3827i −0.486822 0.843201i 0.513063 0.858351i \(-0.328511\pi\)
−0.999885 + 0.0151499i \(0.995177\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −13.0000 −0.467880
\(773\) −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i \(-0.271596\pi\)
−0.981250 + 0.192740i \(0.938263\pi\)
\(774\) 0 0
\(775\) −7.50000 12.9904i −0.269408 0.466628i
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) 16.0000 0.573628
\(779\) 14.0000 10.3923i 0.501602 0.372343i
\(780\) 0 0
\(781\) 14.0000 24.2487i 0.500959 0.867687i
\(782\) −8.00000 + 13.8564i −0.286079 + 0.495504i
\(783\) 0 0
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 0 0
\(786\) 0 0
\(787\) −47.0000 −1.67537 −0.837685 0.546154i \(-0.816091\pi\)
−0.837685 + 0.546154i \(0.816091\pi\)
\(788\) −1.00000 1.73205i −0.0356235 0.0617018i
\(789\) 0 0
\(790\) 0 0
\(791\) −10.0000 −0.355559
\(792\) 0 0
\(793\) 16.5000 28.5788i 0.585932 1.01486i