Properties

Label 720.2.q.e.241.1
Level $720$
Weight $2$
Character 720.241
Analytic conductor $5.749$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 360)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 241.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 720.241
Dual form 720.2.q.e.481.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{9} +(-2.50000 + 4.33013i) q^{11} +1.73205i q^{15} +3.00000 q^{17} -5.00000 q^{19} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(5.00000 - 8.66025i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-7.50000 + 4.33013i) q^{33} +4.00000 q^{37} +(1.50000 + 2.59808i) q^{41} +(1.50000 - 2.59808i) q^{43} +(-1.50000 + 2.59808i) q^{45} +(2.00000 - 3.46410i) q^{47} +(3.50000 + 6.06218i) q^{49} +(4.50000 + 2.59808i) q^{51} -6.00000 q^{53} -5.00000 q^{55} +(-7.50000 - 4.33013i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-5.50000 - 9.52628i) q^{67} +10.3923i q^{69} +14.0000 q^{71} -15.0000 q^{73} +(-1.50000 + 0.866025i) q^{75} +(5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(1.50000 + 2.59808i) q^{85} +(15.0000 - 8.66025i) q^{87} +14.0000 q^{89} -3.46410i q^{93} +(-2.50000 - 4.33013i) q^{95} +(6.50000 - 11.2583i) q^{97} -15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + q^{5} + 3q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + q^{5} + 3q^{9} - 5q^{11} + 6q^{17} - 10q^{19} + 6q^{23} - q^{25} + 10q^{29} - 2q^{31} - 15q^{33} + 8q^{37} + 3q^{41} + 3q^{43} - 3q^{45} + 4q^{47} + 7q^{49} + 9q^{51} - 12q^{53} - 10q^{55} - 15q^{57} - 3q^{59} - 2q^{61} - 11q^{67} + 28q^{71} - 30q^{73} - 3q^{75} + 10q^{79} - 9q^{81} - 12q^{83} + 3q^{85} + 30q^{87} + 28q^{89} - 5q^{95} + 13q^{97} - 30q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0 0
\(15\) 1.73205i 0.447214i
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 5.00000 8.66025i 0.928477 1.60817i 0.142605 0.989780i \(-0.454452\pi\)
0.785872 0.618389i \(-0.212214\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0 0
\(33\) −7.50000 + 4.33013i −1.30558 + 0.753778i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 1.50000 2.59808i 0.228748 0.396203i −0.728689 0.684844i \(-0.759870\pi\)
0.957437 + 0.288641i \(0.0932035\pi\)
\(44\) 0 0
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 0 0
\(47\) 2.00000 3.46410i 0.291730 0.505291i −0.682489 0.730896i \(-0.739102\pi\)
0.974219 + 0.225605i \(0.0724358\pi\)
\(48\) 0 0
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) 0 0
\(51\) 4.50000 + 2.59808i 0.630126 + 0.363803i
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) −7.50000 4.33013i −0.993399 0.573539i
\(58\) 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
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) 10.3923i 1.25109i
\(70\) 0 0
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 0 0
\(73\) −15.0000 −1.75562 −0.877809 0.479012i \(-0.840995\pi\)
−0.877809 + 0.479012i \(0.840995\pi\)
\(74\) 0 0
\(75\) −1.50000 + 0.866025i −0.173205 + 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 0 0
\(87\) 15.0000 8.66025i 1.60817 0.928477i
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 3.46410i 0.359211i
\(94\) 0 0
\(95\) −2.50000 4.33013i −0.256495 0.444262i
\(96\) 0 0
\(97\) 6.50000 11.2583i 0.659975 1.14311i −0.320647 0.947199i \(-0.603900\pi\)
0.980622 0.195911i \(-0.0627665\pi\)
\(98\) 0 0
\(99\) −15.0000 −1.50756
\(100\) 0 0
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) 0 0
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.0000 1.64345 0.821726 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) 0 0
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) 6.00000 + 3.46410i 0.569495 + 0.328798i
\(112\) 0 0
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 0 0
\(115\) −3.00000 + 5.19615i −0.279751 + 0.484544i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 5.19615i 0.468521i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −10.0000 −0.887357 −0.443678 0.896186i \(-0.646327\pi\)
−0.443678 + 0.896186i \(0.646327\pi\)
\(128\) 0 0
\(129\) 4.50000 2.59808i 0.396203 0.228748i
\(130\) 0 0
\(131\) −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −4.50000 + 2.59808i −0.387298 + 0.223607i
\(136\) 0 0
\(137\) −3.50000 + 6.06218i −0.299025 + 0.517927i −0.975913 0.218159i \(-0.929995\pi\)
0.676888 + 0.736086i \(0.263328\pi\)
\(138\) 0 0
\(139\) 3.50000 + 6.06218i 0.296866 + 0.514187i 0.975417 0.220366i \(-0.0707252\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 6.00000 3.46410i 0.505291 0.291730i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) 0 0
\(147\) 12.1244i 1.00000i
\(148\) 0 0
\(149\) −2.00000 3.46410i −0.163846 0.283790i 0.772399 0.635138i \(-0.219057\pi\)
−0.936245 + 0.351348i \(0.885723\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) 0 0
\(153\) 4.50000 + 7.79423i 0.363803 + 0.630126i
\(154\) 0 0
\(155\) 1.00000 1.73205i 0.0803219 0.139122i
\(156\) 0 0
\(157\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) −9.00000 5.19615i −0.713746 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) −7.50000 4.33013i −0.583874 0.337100i
\(166\) 0 0
\(167\) −11.0000 19.0526i −0.851206 1.47433i −0.880121 0.474749i \(-0.842539\pi\)
0.0289155 0.999582i \(-0.490795\pi\)
\(168\) 0 0
\(169\) 6.50000 11.2583i 0.500000 0.866025i
\(170\) 0 0
\(171\) −7.50000 12.9904i −0.573539 0.993399i
\(172\) 0 0
\(173\) 1.00000 1.73205i 0.0760286 0.131685i −0.825505 0.564396i \(-0.809109\pi\)
0.901533 + 0.432710i \(0.142443\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.19615i 0.390567i
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 0 0
\(183\) −3.00000 + 1.73205i −0.221766 + 0.128037i
\(184\) 0 0
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 0 0
\(187\) −7.50000 + 12.9904i −0.548454 + 0.949951i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 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
\(195\) 0 0
\(196\) 0 0
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 0 0
\(201\) 19.0526i 1.34386i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.50000 + 2.59808i −0.104765 + 0.181458i
\(206\) 0 0
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 0 0
\(209\) 12.5000 21.6506i 0.864643 1.49761i
\(210\) 0 0
\(211\) 6.00000 + 10.3923i 0.413057 + 0.715436i 0.995222 0.0976347i \(-0.0311277\pi\)
−0.582165 + 0.813070i \(0.697794\pi\)
\(212\) 0 0
\(213\) 21.0000 + 12.1244i 1.43890 + 0.830747i
\(214\) 0 0
\(215\) 3.00000 0.204598
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −22.5000 12.9904i −1.52041 0.877809i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.00000 1.73205i 0.0669650 0.115987i −0.830599 0.556871i \(-0.812002\pi\)
0.897564 + 0.440884i \(0.145335\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) 6.50000 11.2583i 0.431420 0.747242i −0.565576 0.824696i \(-0.691346\pi\)
0.996996 + 0.0774548i \(0.0246793\pi\)
\(228\) 0 0
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.0000 −0.720634 −0.360317 0.932830i \(-0.617331\pi\)
−0.360317 + 0.932830i \(0.617331\pi\)
\(234\) 0 0
\(235\) 4.00000 0.260931
\(236\) 0 0
\(237\) 15.0000 8.66025i 0.974355 0.562544i
\(238\) 0 0
\(239\) 3.00000 + 5.19615i 0.194054 + 0.336111i 0.946590 0.322440i \(-0.104503\pi\)
−0.752536 + 0.658551i \(0.771170\pi\)
\(240\) 0 0
\(241\) 11.5000 19.9186i 0.740780 1.28307i −0.211360 0.977408i \(-0.567789\pi\)
0.952141 0.305661i \(-0.0988773\pi\)
\(242\) 0 0
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 0 0
\(245\) −3.50000 + 6.06218i −0.223607 + 0.387298i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −18.0000 + 10.3923i −1.14070 + 0.658586i
\(250\) 0 0
\(251\) −11.0000 −0.694314 −0.347157 0.937807i \(-0.612853\pi\)
−0.347157 + 0.937807i \(0.612853\pi\)
\(252\) 0 0
\(253\) −30.0000 −1.88608
\(254\) 0 0
\(255\) 5.19615i 0.325396i
\(256\) 0 0
\(257\) 15.5000 + 26.8468i 0.966863 + 1.67466i 0.704523 + 0.709681i \(0.251161\pi\)
0.262341 + 0.964975i \(0.415506\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 30.0000 1.85695
\(262\) 0 0
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) −3.00000 5.19615i −0.184289 0.319197i
\(266\) 0 0
\(267\) 21.0000 + 12.1244i 1.28518 + 0.741999i
\(268\) 0 0
\(269\) −30.0000 −1.82913 −0.914566 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) 0 0
\(271\) −24.0000 −1.45790 −0.728948 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.50000 4.33013i −0.150756 0.261116i
\(276\) 0 0
\(277\) 7.00000 12.1244i 0.420589 0.728482i −0.575408 0.817867i \(-0.695157\pi\)
0.995997 + 0.0893846i \(0.0284900\pi\)
\(278\) 0 0
\(279\) 3.00000 5.19615i 0.179605 0.311086i
\(280\) 0 0
\(281\) −5.00000 + 8.66025i −0.298275 + 0.516627i −0.975741 0.218926i \(-0.929745\pi\)
0.677466 + 0.735554i \(0.263078\pi\)
\(282\) 0 0
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 0 0
\(285\) 8.66025i 0.512989i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 19.5000 11.2583i 1.14311 0.659975i
\(292\) 0 0
\(293\) 5.00000 + 8.66025i 0.292103 + 0.505937i 0.974307 0.225225i \(-0.0723116\pi\)
−0.682204 + 0.731162i \(0.738978\pi\)
\(294\) 0 0
\(295\) 1.50000 2.59808i 0.0873334 0.151266i
\(296\) 0 0
\(297\) −22.5000 12.9904i −1.30558 0.753778i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 18.0000 10.3923i 1.03407 0.597022i
\(304\) 0 0
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.00000 + 8.66025i 0.283524 + 0.491078i 0.972250 0.233944i \(-0.0751631\pi\)
−0.688726 + 0.725022i \(0.741830\pi\)
\(312\) 0 0
\(313\) −3.50000 + 6.06218i −0.197832 + 0.342655i −0.947825 0.318791i \(-0.896723\pi\)
0.749993 + 0.661445i \(0.230057\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.0000 + 24.2487i −0.786318 + 1.36194i 0.141890 + 0.989882i \(0.454682\pi\)
−0.928208 + 0.372061i \(0.878651\pi\)
\(318\) 0 0
\(319\) 25.0000 + 43.3013i 1.39973 + 2.42441i
\(320\) 0 0
\(321\) 25.5000 + 14.7224i 1.42327 + 0.821726i
\(322\) 0 0
\(323\) −15.0000 −0.834622
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −18.0000 10.3923i −0.995402 0.574696i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) 0 0
\(333\) 6.00000 + 10.3923i 0.328798 + 0.569495i
\(334\) 0 0
\(335\) 5.50000 9.52628i 0.300497 0.520476i
\(336\) 0 0
\(337\) 15.5000 + 26.8468i 0.844339 + 1.46244i 0.886194 + 0.463314i \(0.153340\pi\)
−0.0418554 + 0.999124i \(0.513327\pi\)
\(338\) 0 0
\(339\) 10.3923i 0.564433i
\(340\) 0 0
\(341\) 10.0000 0.541530
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −9.00000 + 5.19615i −0.484544 + 0.279751i
\(346\) 0 0
\(347\) −1.50000 2.59808i −0.0805242 0.139472i 0.822951 0.568112i \(-0.192326\pi\)
−0.903475 + 0.428640i \(0.858993\pi\)
\(348\) 0 0
\(349\) −16.0000 + 27.7128i −0.856460 + 1.48343i 0.0188232 + 0.999823i \(0.494008\pi\)
−0.875284 + 0.483610i \(0.839325\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.5000 + 21.6506i −0.665308 + 1.15235i 0.313894 + 0.949458i \(0.398366\pi\)
−0.979202 + 0.202889i \(0.934967\pi\)
\(354\) 0 0
\(355\) 7.00000 + 12.1244i 0.371521 + 0.643494i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 24.2487i 1.27273i
\(364\) 0 0
\(365\) −7.50000 12.9904i −0.392568 0.679948i
\(366\) 0 0
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 0 0
\(369\) −4.50000 + 7.79423i −0.234261 + 0.405751i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i \(0.0683772\pi\)
−0.303902 + 0.952703i \(0.598289\pi\)
\(374\) 0 0
\(375\) −1.50000 0.866025i −0.0774597 0.0447214i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 35.0000 1.79783 0.898915 0.438124i \(-0.144357\pi\)
0.898915 + 0.438124i \(0.144357\pi\)
\(380\) 0 0
\(381\) −15.0000 8.66025i −0.768473 0.443678i
\(382\) 0 0
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 9.00000 0.457496
\(388\) 0 0
\(389\) 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i \(-0.625135\pi\)
0.991500 0.130105i \(-0.0415314\pi\)
\(390\) 0 0
\(391\) 9.00000 + 15.5885i 0.455150 + 0.788342i
\(392\) 0 0
\(393\) 6.92820i 0.349482i
\(394\) 0 0
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) 8.00000 0.401508 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.50000 + 6.06218i 0.174782 + 0.302731i 0.940086 0.340938i \(-0.110745\pi\)
−0.765304 + 0.643669i \(0.777411\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −9.00000 −0.447214
\(406\) 0 0
\(407\) −10.0000 + 17.3205i −0.495682 + 0.858546i
\(408\) 0 0
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 0 0
\(411\) −10.5000 + 6.06218i −0.517927 + 0.299025i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 12.1244i 0.593732i
\(418\) 0 0
\(419\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) −19.0000 + 32.9090i −0.926003 + 1.60388i −0.136064 + 0.990700i \(0.543445\pi\)
−0.789940 + 0.613185i \(0.789888\pi\)
\(422\) 0 0
\(423\) 12.0000 0.583460
\(424\) 0 0
\(425\) −1.50000 + 2.59808i −0.0727607 + 0.126025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −28.0000 −1.34871 −0.674356 0.738406i \(-0.735579\pi\)
−0.674356 + 0.738406i \(0.735579\pi\)
\(432\) 0 0
\(433\) 27.0000 1.29754 0.648769 0.760986i \(-0.275284\pi\)
0.648769 + 0.760986i \(0.275284\pi\)
\(434\) 0 0
\(435\) 15.0000 + 8.66025i 0.719195 + 0.415227i
\(436\) 0 0
\(437\) −15.0000 25.9808i −0.717547 1.24283i
\(438\) 0 0
\(439\) −7.00000 + 12.1244i −0.334092 + 0.578664i −0.983310 0.181938i \(-0.941763\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(440\) 0 0
\(441\) −10.5000 + 18.1865i −0.500000 + 0.866025i
\(442\) 0 0
\(443\) −14.5000 + 25.1147i −0.688916 + 1.19324i 0.283273 + 0.959039i \(0.408580\pi\)
−0.972189 + 0.234198i \(0.924754\pi\)
\(444\) 0 0
\(445\) 7.00000 + 12.1244i 0.331832 + 0.574750i
\(446\) 0 0
\(447\) 6.92820i 0.327693i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −15.0000 −0.706322
\(452\) 0 0
\(453\) 33.0000 19.0526i 1.55048 0.895167i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.5000 21.6506i 0.584725 1.01277i −0.410184 0.912003i \(-0.634536\pi\)
0.994910 0.100771i \(-0.0321310\pi\)
\(458\) 0 0
\(459\) 15.5885i 0.727607i
\(460\) 0 0
\(461\) −2.00000 + 3.46410i −0.0931493 + 0.161339i −0.908835 0.417156i \(-0.863027\pi\)
0.815685 + 0.578496i \(0.196360\pi\)
\(462\) 0 0
\(463\) −2.00000 3.46410i −0.0929479 0.160990i 0.815802 0.578331i \(-0.196296\pi\)
−0.908750 + 0.417340i \(0.862962\pi\)
\(464\) 0 0
\(465\) 3.00000 1.73205i 0.139122 0.0803219i
\(466\) 0 0
\(467\) 11.0000 0.509019 0.254510 0.967070i \(-0.418086\pi\)
0.254510 + 0.967070i \(0.418086\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.50000 + 12.9904i 0.344850 + 0.597298i
\(474\) 0 0
\(475\) 2.50000 4.33013i 0.114708 0.198680i
\(476\) 0 0
\(477\) −9.00000 15.5885i −0.412082 0.713746i
\(478\) 0 0
\(479\) 13.0000 22.5167i 0.593985 1.02881i −0.399704 0.916644i \(-0.630887\pi\)
0.993689 0.112168i \(-0.0357796\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 13.0000 0.590300
\(486\) 0 0
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) 0 0
\(489\) −24.0000 13.8564i −1.08532 0.626608i
\(490\) 0 0
\(491\) 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i \(-0.0567572\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(492\) 0 0
\(493\) 15.0000 25.9808i 0.675566 1.17011i
\(494\) 0 0
\(495\) −7.50000 12.9904i −0.337100 0.583874i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −11.5000 19.9186i −0.514811 0.891678i −0.999852 0.0171872i \(-0.994529\pi\)
0.485042 0.874491i \(-0.338804\pi\)
\(500\) 0 0
\(501\) 38.1051i 1.70241i
\(502\) 0 0
\(503\) −34.0000 −1.51599 −0.757993 0.652263i \(-0.773820\pi\)
−0.757993 + 0.652263i \(0.773820\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) 19.5000 11.2583i 0.866025 0.500000i
\(508\) 0 0
\(509\) −22.0000 38.1051i −0.975133 1.68898i −0.679496 0.733679i \(-0.737801\pi\)
−0.295637 0.955300i \(-0.595532\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 25.9808i 1.14708i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.0000 + 17.3205i 0.439799 + 0.761755i
\(518\) 0 0
\(519\) 3.00000 1.73205i 0.131685 0.0760286i
\(520\) 0 0
\(521\) −27.0000 −1.18289 −0.591446 0.806345i \(-0.701443\pi\)
−0.591446 + 0.806345i \(0.701443\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.00000 5.19615i −0.130682 0.226348i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 4.50000 7.79423i 0.195283 0.338241i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 8.50000 + 14.7224i 0.367487 + 0.636506i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −35.0000 −1.50756
\(540\) 0 0
\(541\) 24.0000 1.03184 0.515920 0.856637i \(-0.327450\pi\)
0.515920 + 0.856637i \(0.327450\pi\)
\(542\) 0 0
\(543\) −6.00000 3.46410i −0.257485 0.148659i
\(544\) 0 0
\(545\) −6.00000 10.3923i −0.257012 0.445157i
\(546\) 0 0
\(547\) −4.50000 + 7.79423i −0.192406 + 0.333257i −0.946047 0.324029i \(-0.894962\pi\)
0.753641 + 0.657286i \(0.228296\pi\)
\(548\) 0 0
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) −25.0000 + 43.3013i −1.06504 + 1.84470i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.92820i 0.294086i
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −22.5000 + 12.9904i −0.949951 + 0.548454i
\(562\) 0 0
\(563\) 2.50000 + 4.33013i 0.105362 + 0.182493i 0.913886 0.405970i \(-0.133066\pi\)
−0.808524 + 0.588463i \(0.799733\pi\)
\(564\) 0 0
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i \(-0.731525\pi\)
0.979313 + 0.202350i \(0.0648579\pi\)
\(570\) 0 0
\(571\) −1.50000 2.59808i −0.0627730 0.108726i 0.832931 0.553377i \(-0.186661\pi\)
−0.895704 + 0.444651i \(0.853328\pi\)
\(572\) 0 0
\(573\) 18.0000 10.3923i 0.751961 0.434145i
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) −31.0000 −1.29055 −0.645273 0.763952i \(-0.723257\pi\)
−0.645273 + 0.763952i \(0.723257\pi\)
\(578\) 0 0
\(579\) 32.9090i 1.36765i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 15.0000 25.9808i 0.621237 1.07601i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.50000 + 14.7224i −0.350833 + 0.607660i −0.986396 0.164389i \(-0.947435\pi\)
0.635563 + 0.772049i \(0.280768\pi\)
\(588\) 0 0
\(589\) 5.00000 + 8.66025i 0.206021 + 0.356840i
\(590\) 0 0
\(591\) −12.0000 6.92820i −0.493614 0.284988i
\(592\) 0 0
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 36.0000 + 20.7846i 1.47338 + 0.850657i
\(598\) 0 0
\(599\) 8.00000 + 13.8564i 0.326871 + 0.566157i 0.981889 0.189456i \(-0.0606724\pi\)
−0.655018 + 0.755613i \(0.727339\pi\)
\(600\) 0 0
\(601\) 0.500000 0.866025i 0.0203954 0.0353259i −0.855648 0.517559i \(-0.826841\pi\)
0.876043 + 0.482233i \(0.160174\pi\)
\(602\) 0 0
\(603\) 16.5000 28.5788i 0.671932 1.16382i
\(604\) 0 0
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) 0 0
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 0 0
\(615\) −4.50000 + 2.59808i −0.181458 + 0.104765i
\(616\) 0 0
\(617\) −12.5000 21.6506i −0.503231 0.871622i −0.999993 0.00373492i \(-0.998811\pi\)
0.496762 0.867887i \(-0.334522\pi\)
\(618\) 0 0
\(619\) −9.50000 + 16.4545i −0.381837 + 0.661361i −0.991325 0.131434i \(-0.958042\pi\)
0.609488 + 0.792796i \(0.291375\pi\)
\(620\) 0 0
\(621\) −27.0000 + 15.5885i −1.08347 + 0.625543i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 37.5000 21.6506i 1.49761 0.864643i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −2.00000 −0.0796187 −0.0398094 0.999207i \(-0.512675\pi\)
−0.0398094 + 0.999207i \(0.512675\pi\)
\(632\) 0 0
\(633\) 20.7846i 0.826114i
\(634\) 0 0
\(635\) −5.00000 8.66025i −0.198419 0.343672i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 21.0000 + 36.3731i 0.830747 + 1.43890i
\(640\) 0 0
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 0 0
\(643\) −20.5000 35.5070i −0.808441 1.40026i −0.913943 0.405842i \(-0.866978\pi\)
0.105502 0.994419i \(-0.466355\pi\)
\(644\) 0 0
\(645\) 4.50000 + 2.59808i 0.177187 + 0.102299i
\(646\) 0 0
\(647\) −30.0000 −1.17942 −0.589711 0.807614i \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) 0 0
\(649\) 15.0000 0.588802
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17.0000 29.4449i −0.665261 1.15227i −0.979214 0.202828i \(-0.934987\pi\)
0.313953 0.949439i \(-0.398347\pi\)
\(654\) 0 0
\(655\) 2.00000 3.46410i 0.0781465 0.135354i
\(656\) 0 0
\(657\) −22.5000 38.9711i −0.877809 1.52041i
\(658\) 0 0
\(659\) 22.0000 38.1051i 0.856998 1.48436i −0.0177803 0.999842i \(-0.505660\pi\)
0.874779 0.484523i \(-0.161007\pi\)
\(660\) 0 0
\(661\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 60.0000 2.32321
\(668\) 0 0
\(669\) 3.00000 1.73205i 0.115987 0.0669650i
\(670\) 0 0
\(671\) −5.00000 8.66025i −0.193023 0.334325i
\(672\) 0 0
\(673\) 13.0000 22.5167i 0.501113 0.867953i −0.498886 0.866668i \(-0.666257\pi\)
0.999999 0.00128586i \(-0.000409302\pi\)
\(674\) 0 0
\(675\) −4.50000 2.59808i −0.173205 0.100000i
\(676\) 0 0
\(677\) −14.0000 + 24.2487i −0.538064 + 0.931954i 0.460945 + 0.887429i \(0.347511\pi\)
−0.999008 + 0.0445248i \(0.985823\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 19.5000 11.2583i 0.747242 0.431420i
\(682\) 0 0
\(683\) 13.0000 0.497431 0.248716 0.968577i \(-0.419992\pi\)
0.248716 + 0.968577i \(0.419992\pi\)
\(684\) 0 0
\(685\) −7.00000 −0.267456
\(686\) 0 0
\(687\) 27.7128i 1.05731i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.50000 + 6.06218i −0.132763 + 0.229952i
\(696\) 0 0
\(697\) 4.50000 + 7.79423i 0.170450 + 0.295227i
\(698\) 0 0
\(699\) −16.5000 9.52628i −0.624087 0.360317i
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) 6.00000 + 3.46410i 0.225973 + 0.130466i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 23.0000 39.8372i 0.863783 1.49612i −0.00446726 0.999990i \(-0.501422\pi\)
0.868250 0.496126i \(-0.165245\pi\)
\(710\) 0 0
\(711\) 30.0000 1.12509
\(712\) 0 0
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.3923i 0.388108i
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 34.5000 19.9186i 1.28307 0.740780i
\(724\) 0 0
\(725\) 5.00000 + 8.66025i 0.185695 + 0.321634i
\(726\) 0 0
\(727\) 8.00000 13.8564i 0.296704 0.513906i −0.678676 0.734438i \(-0.737446\pi\)
0.975380 + 0.220532i \(0.0707793\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 4.50000 7.79423i 0.166439 0.288280i
\(732\) 0 0
\(733\) −14.0000 24.2487i −0.517102 0.895647i −0.999803 0.0198613i \(-0.993678\pi\)
0.482701 0.875785i \(-0.339656\pi\)
\(734\) 0 0
\(735\) −10.5000 + 6.06218i −0.387298 + 0.223607i
\(736\) 0 0
\(737\) 55.0000 2.02595
\(738\) 0 0
\(739\) −5.00000 −0.183928 −0.0919640 0.995762i \(-0.529314\pi\)
−0.0919640 + 0.995762i \(0.529314\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 17.0000 + 29.4449i 0.623670 + 1.08023i 0.988797 + 0.149270i \(0.0476922\pi\)
−0.365127 + 0.930958i \(0.618974\pi\)
\(744\) 0 0
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) 0 0
\(747\) −36.0000 −1.31717
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i \(-0.0477681\pi\)
−0.623856 + 0.781540i \(0.714435\pi\)
\(752\) 0 0
\(753\) −16.5000 9.52628i −0.601293 0.347157i
\(754\) 0 0
\(755\) 22.0000 0.800662
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) −45.0000 25.9808i −1.63340 0.943042i
\(760\) 0 0
\(761\) −5.00000 8.66025i −0.181250 0.313934i 0.761057 0.648686i \(-0.224681\pi\)
−0.942306 + 0.334752i \(0.891348\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −4.50000 + 7.79423i −0.162698 + 0.281801i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 27.0000 + 46.7654i 0.973645 + 1.68640i 0.684336 + 0.729167i \(0.260092\pi\)
0.289309 + 0.957236i \(0.406575\pi\)
\(770\) 0 0
\(771\) 53.6936i 1.93373i
\(772\) 0 0
\(773\) −30.0000 −1.07903 −0.539513 0.841978i \(-0.681391\pi\)
−0.539513 + 0.841978i \(0.681391\pi\)
\(774\) 0 0
\(775\) 2.00000 0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.50000 12.9904i −0.268715 0.465429i
\(780\) 0 0
\(781\) −35.0000 + 60.6218i −1.25240 + 2.16922i
\(782\) 0 0
\(783\) 45.0000 + 25.9808i 1.60817 + 0.928477i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) 0 0
\(789\) −18.0000 + 10.3923i −0.640817 + 0.369976i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 10.3923i 0.368577i
\(796\) 0 0
\(797\) −16.0000 27.7128i −0.566749 0.981638i −0.996885 0.0788739i \(-0.974868\pi\)
0.430136 0.902764i \(-0.358466\pi\)
\(798\) 0 0
\(799\) 6.00000 10.3923i 0.212265 0.367653i
\(800\) 0 0
\(801\) 21.0000 + 36.3731i