Properties

Label 3330.2.d.m.1999.3
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 370)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.3
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.m.1999.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -4.44949i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -4.44949i q^{7} -1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} -4.89898 q^{11} +4.00000i q^{13} +4.44949 q^{14} +1.00000 q^{16} -4.89898i q^{17} -3.55051 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.89898i q^{22} +8.89898i q^{23} +(3.00000 + 4.00000i) q^{25} -4.00000 q^{26} +4.44949i q^{28} -1.55051 q^{31} +1.00000i q^{32} +4.89898 q^{34} +(4.44949 - 8.89898i) q^{35} -1.00000i q^{37} -3.55051i q^{38} +(1.00000 - 2.00000i) q^{40} -2.00000 q^{41} +4.00000i q^{43} +4.89898 q^{44} -8.89898 q^{46} +4.44949i q^{47} -12.7980 q^{49} +(-4.00000 + 3.00000i) q^{50} -4.00000i q^{52} +11.7980i q^{53} +(-9.79796 - 4.89898i) q^{55} -4.44949 q^{56} -3.55051 q^{59} +12.0000 q^{61} -1.55051i q^{62} -1.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +5.55051i q^{67} +4.89898i q^{68} +(8.89898 + 4.44949i) q^{70} -4.89898 q^{71} +4.00000i q^{73} +1.00000 q^{74} +3.55051 q^{76} +21.7980i q^{77} -6.44949 q^{79} +(2.00000 + 1.00000i) q^{80} -2.00000i q^{82} +9.55051i q^{83} +(4.89898 - 9.79796i) q^{85} -4.00000 q^{86} +4.89898i q^{88} +15.7980 q^{89} +17.7980 q^{91} -8.89898i q^{92} -4.44949 q^{94} +(-7.10102 - 3.55051i) q^{95} +2.00000i q^{97} -12.7980i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 8 q^{5} - 4 q^{10} + 8 q^{14} + 4 q^{16} - 24 q^{19} - 8 q^{20} + 12 q^{25} - 16 q^{26} - 16 q^{31} + 8 q^{35} + 4 q^{40} - 8 q^{41} - 16 q^{46} - 12 q^{49} - 16 q^{50} - 8 q^{56} - 24 q^{59} + 48 q^{61} - 4 q^{64} - 16 q^{65} + 16 q^{70} + 4 q^{74} + 24 q^{76} - 16 q^{79} + 8 q^{80} - 16 q^{86} + 24 q^{89} + 32 q^{91} - 8 q^{94} - 48 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) 0 0
\(7\) 4.44949i 1.68175i −0.541230 0.840875i \(-0.682041\pi\)
0.541230 0.840875i \(-0.317959\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) −4.89898 −1.47710 −0.738549 0.674200i \(-0.764489\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 4.44949 1.18918
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.89898i 1.18818i −0.804400 0.594089i \(-0.797513\pi\)
0.804400 0.594089i \(-0.202487\pi\)
\(18\) 0 0
\(19\) −3.55051 −0.814543 −0.407271 0.913307i \(-0.633520\pi\)
−0.407271 + 0.913307i \(0.633520\pi\)
\(20\) −2.00000 1.00000i −0.447214 0.223607i
\(21\) 0 0
\(22\) 4.89898i 1.04447i
\(23\) 8.89898i 1.85557i 0.373121 + 0.927783i \(0.378288\pi\)
−0.373121 + 0.927783i \(0.621712\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 4.44949i 0.840875i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −1.55051 −0.278480 −0.139240 0.990259i \(-0.544466\pi\)
−0.139240 + 0.990259i \(0.544466\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 4.89898 0.840168
\(35\) 4.44949 8.89898i 0.752101 1.50420i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 3.55051i 0.575969i
\(39\) 0 0
\(40\) 1.00000 2.00000i 0.158114 0.316228i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 4.89898 0.738549
\(45\) 0 0
\(46\) −8.89898 −1.31208
\(47\) 4.44949i 0.649025i 0.945881 + 0.324512i \(0.105200\pi\)
−0.945881 + 0.324512i \(0.894800\pi\)
\(48\) 0 0
\(49\) −12.7980 −1.82828
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 11.7980i 1.62057i 0.586033 + 0.810287i \(0.300689\pi\)
−0.586033 + 0.810287i \(0.699311\pi\)
\(54\) 0 0
\(55\) −9.79796 4.89898i −1.32116 0.660578i
\(56\) −4.44949 −0.594588
\(57\) 0 0
\(58\) 0 0
\(59\) −3.55051 −0.462237 −0.231119 0.972926i \(-0.574239\pi\)
−0.231119 + 0.972926i \(0.574239\pi\)
\(60\) 0 0
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 1.55051i 0.196915i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −4.00000 + 8.00000i −0.496139 + 0.992278i
\(66\) 0 0
\(67\) 5.55051i 0.678103i 0.940768 + 0.339051i \(0.110106\pi\)
−0.940768 + 0.339051i \(0.889894\pi\)
\(68\) 4.89898i 0.594089i
\(69\) 0 0
\(70\) 8.89898 + 4.44949i 1.06363 + 0.531816i
\(71\) −4.89898 −0.581402 −0.290701 0.956814i \(-0.593888\pi\)
−0.290701 + 0.956814i \(0.593888\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 3.55051 0.407271
\(77\) 21.7980i 2.48411i
\(78\) 0 0
\(79\) −6.44949 −0.725624 −0.362812 0.931862i \(-0.618183\pi\)
−0.362812 + 0.931862i \(0.618183\pi\)
\(80\) 2.00000 + 1.00000i 0.223607 + 0.111803i
\(81\) 0 0
\(82\) 2.00000i 0.220863i
\(83\) 9.55051i 1.04830i 0.851625 + 0.524152i \(0.175618\pi\)
−0.851625 + 0.524152i \(0.824382\pi\)
\(84\) 0 0
\(85\) 4.89898 9.79796i 0.531369 1.06274i
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 4.89898i 0.522233i
\(89\) 15.7980 1.67458 0.837290 0.546759i \(-0.184139\pi\)
0.837290 + 0.546759i \(0.184139\pi\)
\(90\) 0 0
\(91\) 17.7980 1.86573
\(92\) 8.89898i 0.927783i
\(93\) 0 0
\(94\) −4.44949 −0.458930
\(95\) −7.10102 3.55051i −0.728549 0.364275i
\(96\) 0 0
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 12.7980i 1.29279i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −10.6969 −1.06439 −0.532193 0.846623i \(-0.678632\pi\)
−0.532193 + 0.846623i \(0.678632\pi\)
\(102\) 0 0
\(103\) 9.79796i 0.965422i 0.875780 + 0.482711i \(0.160348\pi\)
−0.875780 + 0.482711i \(0.839652\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) −11.7980 −1.14592
\(107\) 5.55051i 0.536588i −0.963337 0.268294i \(-0.913540\pi\)
0.963337 0.268294i \(-0.0864599\pi\)
\(108\) 0 0
\(109\) 5.79796 0.555344 0.277672 0.960676i \(-0.410437\pi\)
0.277672 + 0.960676i \(0.410437\pi\)
\(110\) 4.89898 9.79796i 0.467099 0.934199i
\(111\) 0 0
\(112\) 4.44949i 0.420437i
\(113\) 3.10102i 0.291719i 0.989305 + 0.145860i \(0.0465948\pi\)
−0.989305 + 0.145860i \(0.953405\pi\)
\(114\) 0 0
\(115\) −8.89898 + 17.7980i −0.829834 + 1.65967i
\(116\) 0 0
\(117\) 0 0
\(118\) 3.55051i 0.326851i
\(119\) −21.7980 −1.99822
\(120\) 0 0
\(121\) 13.0000 1.18182
\(122\) 12.0000i 1.08643i
\(123\) 0 0
\(124\) 1.55051 0.139240
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 2.65153i 0.235285i 0.993056 + 0.117643i \(0.0375337\pi\)
−0.993056 + 0.117643i \(0.962466\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −8.00000 4.00000i −0.701646 0.350823i
\(131\) 10.2474 0.895324 0.447662 0.894203i \(-0.352257\pi\)
0.447662 + 0.894203i \(0.352257\pi\)
\(132\) 0 0
\(133\) 15.7980i 1.36986i
\(134\) −5.55051 −0.479491
\(135\) 0 0
\(136\) −4.89898 −0.420084
\(137\) 19.5959i 1.67419i 0.547056 + 0.837096i \(0.315749\pi\)
−0.547056 + 0.837096i \(0.684251\pi\)
\(138\) 0 0
\(139\) 5.79796 0.491776 0.245888 0.969298i \(-0.420920\pi\)
0.245888 + 0.969298i \(0.420920\pi\)
\(140\) −4.44949 + 8.89898i −0.376051 + 0.752101i
\(141\) 0 0
\(142\) 4.89898i 0.411113i
\(143\) 19.5959i 1.63869i
\(144\) 0 0
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −18.6969 −1.53171 −0.765856 0.643012i \(-0.777685\pi\)
−0.765856 + 0.643012i \(0.777685\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 3.55051i 0.287984i
\(153\) 0 0
\(154\) −21.7980 −1.75653
\(155\) −3.10102 1.55051i −0.249080 0.124540i
\(156\) 0 0
\(157\) 7.79796i 0.622345i 0.950353 + 0.311172i \(0.100722\pi\)
−0.950353 + 0.311172i \(0.899278\pi\)
\(158\) 6.44949i 0.513094i
\(159\) 0 0
\(160\) −1.00000 + 2.00000i −0.0790569 + 0.158114i
\(161\) 39.5959 3.12060
\(162\) 0 0
\(163\) 21.7980i 1.70735i −0.520808 0.853674i \(-0.674369\pi\)
0.520808 0.853674i \(-0.325631\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) −9.55051 −0.741263
\(167\) 8.00000i 0.619059i 0.950890 + 0.309529i \(0.100171\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 9.79796 + 4.89898i 0.751469 + 0.375735i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 19.7980i 1.50521i −0.658472 0.752605i \(-0.728797\pi\)
0.658472 0.752605i \(-0.271203\pi\)
\(174\) 0 0
\(175\) 17.7980 13.3485i 1.34540 1.00905i
\(176\) −4.89898 −0.369274
\(177\) 0 0
\(178\) 15.7980i 1.18411i
\(179\) −9.34847 −0.698737 −0.349369 0.936985i \(-0.613604\pi\)
−0.349369 + 0.936985i \(0.613604\pi\)
\(180\) 0 0
\(181\) 10.6969 0.795097 0.397549 0.917581i \(-0.369861\pi\)
0.397549 + 0.917581i \(0.369861\pi\)
\(182\) 17.7980i 1.31927i
\(183\) 0 0
\(184\) 8.89898 0.656041
\(185\) 1.00000 2.00000i 0.0735215 0.147043i
\(186\) 0 0
\(187\) 24.0000i 1.75505i
\(188\) 4.44949i 0.324512i
\(189\) 0 0
\(190\) 3.55051 7.10102i 0.257581 0.515162i
\(191\) −11.3485 −0.821146 −0.410573 0.911828i \(-0.634671\pi\)
−0.410573 + 0.911828i \(0.634671\pi\)
\(192\) 0 0
\(193\) 14.0000i 1.00774i 0.863779 + 0.503871i \(0.168091\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 12.7980 0.914140
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 0 0
\(199\) −6.44949 −0.457192 −0.228596 0.973521i \(-0.573414\pi\)
−0.228596 + 0.973521i \(0.573414\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 10.6969i 0.752634i
\(203\) 0 0
\(204\) 0 0
\(205\) −4.00000 2.00000i −0.279372 0.139686i
\(206\) −9.79796 −0.682656
\(207\) 0 0
\(208\) 4.00000i 0.277350i
\(209\) 17.3939 1.20316
\(210\) 0 0
\(211\) −6.69694 −0.461036 −0.230518 0.973068i \(-0.574042\pi\)
−0.230518 + 0.973068i \(0.574042\pi\)
\(212\) 11.7980i 0.810287i
\(213\) 0 0
\(214\) 5.55051 0.379425
\(215\) −4.00000 + 8.00000i −0.272798 + 0.545595i
\(216\) 0 0
\(217\) 6.89898i 0.468333i
\(218\) 5.79796i 0.392687i
\(219\) 0 0
\(220\) 9.79796 + 4.89898i 0.660578 + 0.330289i
\(221\) 19.5959 1.31816
\(222\) 0 0
\(223\) 0.449490i 0.0301001i 0.999887 + 0.0150500i \(0.00479075\pi\)
−0.999887 + 0.0150500i \(0.995209\pi\)
\(224\) 4.44949 0.297294
\(225\) 0 0
\(226\) −3.10102 −0.206277
\(227\) 24.8990i 1.65260i −0.563228 0.826302i \(-0.690441\pi\)
0.563228 0.826302i \(-0.309559\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −17.7980 8.89898i −1.17356 0.586781i
\(231\) 0 0
\(232\) 0 0
\(233\) 9.79796i 0.641886i −0.947099 0.320943i \(-0.896000\pi\)
0.947099 0.320943i \(-0.104000\pi\)
\(234\) 0 0
\(235\) −4.44949 + 8.89898i −0.290253 + 0.580505i
\(236\) 3.55051 0.231119
\(237\) 0 0
\(238\) 21.7980i 1.41295i
\(239\) −18.0454 −1.16726 −0.583630 0.812020i \(-0.698368\pi\)
−0.583630 + 0.812020i \(0.698368\pi\)
\(240\) 0 0
\(241\) 7.79796 0.502311 0.251155 0.967947i \(-0.419189\pi\)
0.251155 + 0.967947i \(0.419189\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 0 0
\(244\) −12.0000 −0.768221
\(245\) −25.5959 12.7980i −1.63526 0.817632i
\(246\) 0 0
\(247\) 14.2020i 0.903654i
\(248\) 1.55051i 0.0984575i
\(249\) 0 0
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) −21.3485 −1.34750 −0.673752 0.738958i \(-0.735318\pi\)
−0.673752 + 0.738958i \(0.735318\pi\)
\(252\) 0 0
\(253\) 43.5959i 2.74085i
\(254\) −2.65153 −0.166372
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 4.89898i 0.305590i −0.988258 0.152795i \(-0.951173\pi\)
0.988258 0.152795i \(-0.0488274\pi\)
\(258\) 0 0
\(259\) −4.44949 −0.276478
\(260\) 4.00000 8.00000i 0.248069 0.496139i
\(261\) 0 0
\(262\) 10.2474i 0.633089i
\(263\) 1.75255i 0.108067i −0.998539 0.0540335i \(-0.982792\pi\)
0.998539 0.0540335i \(-0.0172078\pi\)
\(264\) 0 0
\(265\) −11.7980 + 23.5959i −0.724743 + 1.44949i
\(266\) −15.7980 −0.968635
\(267\) 0 0
\(268\) 5.55051i 0.339051i
\(269\) −18.6969 −1.13997 −0.569986 0.821654i \(-0.693051\pi\)
−0.569986 + 0.821654i \(0.693051\pi\)
\(270\) 0 0
\(271\) −32.4949 −1.97392 −0.986962 0.160952i \(-0.948544\pi\)
−0.986962 + 0.160952i \(0.948544\pi\)
\(272\) 4.89898i 0.297044i
\(273\) 0 0
\(274\) −19.5959 −1.18383
\(275\) −14.6969 19.5959i −0.886259 1.18168i
\(276\) 0 0
\(277\) 19.5959i 1.17740i −0.808350 0.588702i \(-0.799639\pi\)
0.808350 0.588702i \(-0.200361\pi\)
\(278\) 5.79796i 0.347738i
\(279\) 0 0
\(280\) −8.89898 4.44949i −0.531816 0.265908i
\(281\) −27.7980 −1.65829 −0.829144 0.559036i \(-0.811171\pi\)
−0.829144 + 0.559036i \(0.811171\pi\)
\(282\) 0 0
\(283\) 15.5959i 0.927081i 0.886076 + 0.463541i \(0.153421\pi\)
−0.886076 + 0.463541i \(0.846579\pi\)
\(284\) 4.89898 0.290701
\(285\) 0 0
\(286\) 19.5959 1.15873
\(287\) 8.89898i 0.525290i
\(288\) 0 0
\(289\) −7.00000 −0.411765
\(290\) 0 0
\(291\) 0 0
\(292\) 4.00000i 0.234082i
\(293\) 25.5959i 1.49533i −0.664076 0.747665i \(-0.731175\pi\)
0.664076 0.747665i \(-0.268825\pi\)
\(294\) 0 0
\(295\) −7.10102 3.55051i −0.413437 0.206719i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 18.6969i 1.08308i
\(299\) −35.5959 −2.05857
\(300\) 0 0
\(301\) 17.7980 1.02586
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −3.55051 −0.203636
\(305\) 24.0000 + 12.0000i 1.37424 + 0.687118i
\(306\) 0 0
\(307\) 13.1464i 0.750306i −0.926963 0.375153i \(-0.877590\pi\)
0.926963 0.375153i \(-0.122410\pi\)
\(308\) 21.7980i 1.24205i
\(309\) 0 0
\(310\) 1.55051 3.10102i 0.0880631 0.176126i
\(311\) 7.34847 0.416693 0.208347 0.978055i \(-0.433192\pi\)
0.208347 + 0.978055i \(0.433192\pi\)
\(312\) 0 0
\(313\) 17.5959i 0.994580i −0.867584 0.497290i \(-0.834328\pi\)
0.867584 0.497290i \(-0.165672\pi\)
\(314\) −7.79796 −0.440064
\(315\) 0 0
\(316\) 6.44949 0.362812
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −2.00000 1.00000i −0.111803 0.0559017i
\(321\) 0 0
\(322\) 39.5959i 2.20659i
\(323\) 17.3939i 0.967821i
\(324\) 0 0
\(325\) −16.0000 + 12.0000i −0.887520 + 0.665640i
\(326\) 21.7980 1.20728
\(327\) 0 0
\(328\) 2.00000i 0.110432i
\(329\) 19.7980 1.09150
\(330\) 0 0
\(331\) 14.2474 0.783111 0.391555 0.920155i \(-0.371937\pi\)
0.391555 + 0.920155i \(0.371937\pi\)
\(332\) 9.55051i 0.524152i
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) −5.55051 + 11.1010i −0.303257 + 0.606514i
\(336\) 0 0
\(337\) 3.59592i 0.195882i 0.995192 + 0.0979411i \(0.0312257\pi\)
−0.995192 + 0.0979411i \(0.968774\pi\)
\(338\) 3.00000i 0.163178i
\(339\) 0 0
\(340\) −4.89898 + 9.79796i −0.265684 + 0.531369i
\(341\) 7.59592 0.411342
\(342\) 0 0
\(343\) 25.7980i 1.39296i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 19.7980 1.06434
\(347\) 2.20204i 0.118212i 0.998252 + 0.0591059i \(0.0188250\pi\)
−0.998252 + 0.0591059i \(0.981175\pi\)
\(348\) 0 0
\(349\) −7.10102 −0.380109 −0.190054 0.981774i \(-0.560866\pi\)
−0.190054 + 0.981774i \(0.560866\pi\)
\(350\) 13.3485 + 17.7980i 0.713506 + 0.951341i
\(351\) 0 0
\(352\) 4.89898i 0.261116i
\(353\) 6.00000i 0.319348i 0.987170 + 0.159674i \(0.0510443\pi\)
−0.987170 + 0.159674i \(0.948956\pi\)
\(354\) 0 0
\(355\) −9.79796 4.89898i −0.520022 0.260011i
\(356\) −15.7980 −0.837290
\(357\) 0 0
\(358\) 9.34847i 0.494082i
\(359\) −12.8990 −0.680782 −0.340391 0.940284i \(-0.610559\pi\)
−0.340391 + 0.940284i \(0.610559\pi\)
\(360\) 0 0
\(361\) −6.39388 −0.336520
\(362\) 10.6969i 0.562219i
\(363\) 0 0
\(364\) −17.7980 −0.932867
\(365\) −4.00000 + 8.00000i −0.209370 + 0.418739i
\(366\) 0 0
\(367\) 2.65153i 0.138409i 0.997603 + 0.0692044i \(0.0220461\pi\)
−0.997603 + 0.0692044i \(0.977954\pi\)
\(368\) 8.89898i 0.463891i
\(369\) 0 0
\(370\) 2.00000 + 1.00000i 0.103975 + 0.0519875i
\(371\) 52.4949 2.72540
\(372\) 0 0
\(373\) 11.7980i 0.610875i −0.952212 0.305438i \(-0.901197\pi\)
0.952212 0.305438i \(-0.0988027\pi\)
\(374\) −24.0000 −1.24101
\(375\) 0 0
\(376\) 4.44949 0.229465
\(377\) 0 0
\(378\) 0 0
\(379\) 31.5959 1.62297 0.811487 0.584371i \(-0.198659\pi\)
0.811487 + 0.584371i \(0.198659\pi\)
\(380\) 7.10102 + 3.55051i 0.364275 + 0.182137i
\(381\) 0 0
\(382\) 11.3485i 0.580638i
\(383\) 34.6969i 1.77293i 0.462795 + 0.886465i \(0.346847\pi\)
−0.462795 + 0.886465i \(0.653153\pi\)
\(384\) 0 0
\(385\) −21.7980 + 43.5959i −1.11093 + 2.22185i
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) 2.00000i 0.101535i
\(389\) −25.7980 −1.30801 −0.654004 0.756491i \(-0.726912\pi\)
−0.654004 + 0.756491i \(0.726912\pi\)
\(390\) 0 0
\(391\) 43.5959 2.20474
\(392\) 12.7980i 0.646395i
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) −12.8990 6.44949i −0.649018 0.324509i
\(396\) 0 0
\(397\) 16.2020i 0.813157i 0.913616 + 0.406579i \(0.133278\pi\)
−0.913616 + 0.406579i \(0.866722\pi\)
\(398\) 6.44949i 0.323284i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 23.7980 1.18841 0.594207 0.804312i \(-0.297466\pi\)
0.594207 + 0.804312i \(0.297466\pi\)
\(402\) 0 0
\(403\) 6.20204i 0.308946i
\(404\) 10.6969 0.532193
\(405\) 0 0
\(406\) 0 0
\(407\) 4.89898i 0.242833i
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 2.00000 4.00000i 0.0987730 0.197546i
\(411\) 0 0
\(412\) 9.79796i 0.482711i
\(413\) 15.7980i 0.777367i
\(414\) 0 0
\(415\) −9.55051 + 19.1010i −0.468816 + 0.937632i
\(416\) −4.00000 −0.196116
\(417\) 0 0
\(418\) 17.3939i 0.850762i
\(419\) 5.79796 0.283249 0.141624 0.989920i \(-0.454767\pi\)
0.141624 + 0.989920i \(0.454767\pi\)
\(420\) 0 0
\(421\) −19.5959 −0.955047 −0.477523 0.878619i \(-0.658465\pi\)
−0.477523 + 0.878619i \(0.658465\pi\)
\(422\) 6.69694i 0.326002i
\(423\) 0 0
\(424\) 11.7980 0.572960
\(425\) 19.5959 14.6969i 0.950542 0.712906i
\(426\) 0 0
\(427\) 53.3939i 2.58391i
\(428\) 5.55051i 0.268294i
\(429\) 0 0
\(430\) −8.00000 4.00000i −0.385794 0.192897i
\(431\) 15.7526 0.758774 0.379387 0.925238i \(-0.376135\pi\)
0.379387 + 0.925238i \(0.376135\pi\)
\(432\) 0 0
\(433\) 21.3939i 1.02812i 0.857753 + 0.514062i \(0.171860\pi\)
−0.857753 + 0.514062i \(0.828140\pi\)
\(434\) −6.89898 −0.331162
\(435\) 0 0
\(436\) −5.79796 −0.277672
\(437\) 31.5959i 1.51144i
\(438\) 0 0
\(439\) −20.6515 −0.985644 −0.492822 0.870130i \(-0.664035\pi\)
−0.492822 + 0.870130i \(0.664035\pi\)
\(440\) −4.89898 + 9.79796i −0.233550 + 0.467099i
\(441\) 0 0
\(442\) 19.5959i 0.932083i
\(443\) 24.6515i 1.17123i −0.810589 0.585615i \(-0.800853\pi\)
0.810589 0.585615i \(-0.199147\pi\)
\(444\) 0 0
\(445\) 31.5959 + 15.7980i 1.49779 + 0.748895i
\(446\) −0.449490 −0.0212840
\(447\) 0 0
\(448\) 4.44949i 0.210219i
\(449\) −15.7980 −0.745552 −0.372776 0.927921i \(-0.621594\pi\)
−0.372776 + 0.927921i \(0.621594\pi\)
\(450\) 0 0
\(451\) 9.79796 0.461368
\(452\) 3.10102i 0.145860i
\(453\) 0 0
\(454\) 24.8990 1.16857
\(455\) 35.5959 + 17.7980i 1.66876 + 0.834381i
\(456\) 0 0
\(457\) 2.00000i 0.0935561i 0.998905 + 0.0467780i \(0.0148953\pi\)
−0.998905 + 0.0467780i \(0.985105\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) 8.89898 17.7980i 0.414917 0.829834i
\(461\) 33.7980 1.57413 0.787064 0.616871i \(-0.211600\pi\)
0.787064 + 0.616871i \(0.211600\pi\)
\(462\) 0 0
\(463\) 20.4949i 0.952479i −0.879316 0.476239i \(-0.842000\pi\)
0.879316 0.476239i \(-0.158000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 9.79796 0.453882
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 0 0
\(469\) 24.6969 1.14040
\(470\) −8.89898 4.44949i −0.410479 0.205240i
\(471\) 0 0
\(472\) 3.55051i 0.163425i
\(473\) 19.5959i 0.901021i
\(474\) 0 0
\(475\) −10.6515 14.2020i −0.488726 0.651634i
\(476\) 21.7980 0.999108
\(477\) 0 0
\(478\) 18.0454i 0.825378i
\(479\) 5.14643 0.235146 0.117573 0.993064i \(-0.462489\pi\)
0.117573 + 0.993064i \(0.462489\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 7.79796i 0.355187i
\(483\) 0 0
\(484\) −13.0000 −0.590909
\(485\) −2.00000 + 4.00000i −0.0908153 + 0.181631i
\(486\) 0 0
\(487\) 29.3939i 1.33196i 0.745968 + 0.665982i \(0.231987\pi\)
−0.745968 + 0.665982i \(0.768013\pi\)
\(488\) 12.0000i 0.543214i
\(489\) 0 0
\(490\) 12.7980 25.5959i 0.578153 1.15631i
\(491\) 9.30306 0.419841 0.209921 0.977718i \(-0.432679\pi\)
0.209921 + 0.977718i \(0.432679\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 14.2020 0.638980
\(495\) 0 0
\(496\) −1.55051 −0.0696200
\(497\) 21.7980i 0.977772i
\(498\) 0 0
\(499\) 10.6515 0.476828 0.238414 0.971164i \(-0.423372\pi\)
0.238414 + 0.971164i \(0.423372\pi\)
\(500\) −2.00000 11.0000i −0.0894427 0.491935i
\(501\) 0 0
\(502\) 21.3485i 0.952829i
\(503\) 1.79796i 0.0801670i 0.999196 + 0.0400835i \(0.0127624\pi\)
−0.999196 + 0.0400835i \(0.987238\pi\)
\(504\) 0 0
\(505\) −21.3939 10.6969i −0.952015 0.476008i
\(506\) 43.5959 1.93807
\(507\) 0 0
\(508\) 2.65153i 0.117643i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 17.7980 0.787335
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 4.89898 0.216085
\(515\) −9.79796 + 19.5959i −0.431750 + 0.863499i
\(516\) 0 0
\(517\) 21.7980i 0.958673i
\(518\) 4.44949i 0.195499i
\(519\) 0 0
\(520\) 8.00000 + 4.00000i 0.350823 + 0.175412i
\(521\) −17.7980 −0.779743 −0.389871 0.920869i \(-0.627481\pi\)
−0.389871 + 0.920869i \(0.627481\pi\)
\(522\) 0 0
\(523\) 8.89898i 0.389125i −0.980890 0.194563i \(-0.937671\pi\)
0.980890 0.194563i \(-0.0623287\pi\)
\(524\) −10.2474 −0.447662
\(525\) 0 0
\(526\) 1.75255 0.0764149
\(527\) 7.59592i 0.330883i
\(528\) 0 0
\(529\) −56.1918 −2.44312
\(530\) −23.5959 11.7980i −1.02494 0.512471i
\(531\) 0 0
\(532\) 15.7980i 0.684928i
\(533\) 8.00000i 0.346518i
\(534\) 0 0
\(535\) 5.55051 11.1010i 0.239969 0.479939i
\(536\) 5.55051 0.239746
\(537\) 0 0
\(538\) 18.6969i 0.806082i
\(539\) 62.6969 2.70055
\(540\) 0 0
\(541\) 0.404082 0.0173728 0.00868642 0.999962i \(-0.497235\pi\)
0.00868642 + 0.999962i \(0.497235\pi\)
\(542\) 32.4949i 1.39578i
\(543\) 0 0
\(544\) 4.89898 0.210042
\(545\) 11.5959 + 5.79796i 0.496715 + 0.248357i
\(546\) 0 0
\(547\) 10.6969i 0.457368i 0.973501 + 0.228684i \(0.0734423\pi\)
−0.973501 + 0.228684i \(0.926558\pi\)
\(548\) 19.5959i 0.837096i
\(549\) 0 0
\(550\) 19.5959 14.6969i 0.835573 0.626680i
\(551\) 0 0
\(552\) 0 0
\(553\) 28.6969i 1.22032i
\(554\) 19.5959 0.832551
\(555\) 0 0
\(556\) −5.79796 −0.245888
\(557\) 12.0000i 0.508456i −0.967144 0.254228i \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 4.44949 8.89898i 0.188025 0.376051i
\(561\) 0 0
\(562\) 27.7980i 1.17259i
\(563\) 34.6969i 1.46230i 0.682216 + 0.731151i \(0.261016\pi\)
−0.682216 + 0.731151i \(0.738984\pi\)
\(564\) 0 0
\(565\) −3.10102 + 6.20204i −0.130461 + 0.260922i
\(566\) −15.5959 −0.655545
\(567\) 0 0
\(568\) 4.89898i 0.205557i
\(569\) 21.5959 0.905348 0.452674 0.891676i \(-0.350470\pi\)
0.452674 + 0.891676i \(0.350470\pi\)
\(570\) 0 0
\(571\) −25.3939 −1.06270 −0.531350 0.847152i \(-0.678315\pi\)
−0.531350 + 0.847152i \(0.678315\pi\)
\(572\) 19.5959i 0.819346i
\(573\) 0 0
\(574\) −8.89898 −0.371436
\(575\) −35.5959 + 26.6969i −1.48445 + 1.11334i
\(576\) 0 0
\(577\) 30.6969i 1.27793i 0.769236 + 0.638965i \(0.220637\pi\)
−0.769236 + 0.638965i \(0.779363\pi\)
\(578\) 7.00000i 0.291162i
\(579\) 0 0
\(580\) 0 0
\(581\) 42.4949 1.76299
\(582\) 0 0
\(583\) 57.7980i 2.39375i
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 25.5959 1.05736
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) 5.50510 0.226834
\(590\) 3.55051 7.10102i 0.146172 0.292344i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) 0 0
\(595\) −43.5959 21.7980i −1.78726 0.893629i
\(596\) 18.6969 0.765856
\(597\) 0 0
\(598\) 35.5959i 1.45563i
\(599\) 11.5959 0.473796 0.236898 0.971534i \(-0.423869\pi\)
0.236898 + 0.971534i \(0.423869\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 17.7980i 0.725391i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 26.0000 + 13.0000i 1.05705 + 0.528525i
\(606\) 0 0
\(607\) 26.6969i 1.08360i −0.840509 0.541798i \(-0.817744\pi\)
0.840509 0.541798i \(-0.182256\pi\)
\(608\) 3.55051i 0.143992i
\(609\) 0 0
\(610\) −12.0000 + 24.0000i −0.485866 + 0.971732i
\(611\) −17.7980 −0.720028
\(612\) 0 0
\(613\) 39.7980i 1.60742i 0.595018 + 0.803712i \(0.297145\pi\)
−0.595018 + 0.803712i \(0.702855\pi\)
\(614\) 13.1464 0.530547
\(615\) 0 0
\(616\) 21.7980 0.878265
\(617\) 19.5959i 0.788902i 0.918917 + 0.394451i \(0.129065\pi\)
−0.918917 + 0.394451i \(0.870935\pi\)
\(618\) 0 0
\(619\) 12.8990 0.518454 0.259227 0.965816i \(-0.416532\pi\)
0.259227 + 0.965816i \(0.416532\pi\)
\(620\) 3.10102 + 1.55051i 0.124540 + 0.0622700i
\(621\) 0 0
\(622\) 7.34847i 0.294647i
\(623\) 70.2929i 2.81622i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 17.5959 0.703274
\(627\) 0 0
\(628\) 7.79796i 0.311172i
\(629\) −4.89898 −0.195335
\(630\) 0 0
\(631\) −20.2474 −0.806038 −0.403019 0.915192i \(-0.632039\pi\)
−0.403019 + 0.915192i \(0.632039\pi\)
\(632\) 6.44949i 0.256547i
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) −2.65153 + 5.30306i −0.105223 + 0.210446i
\(636\) 0 0
\(637\) 51.1918i 2.02829i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 2.00000i 0.0395285 0.0790569i
\(641\) −17.7980 −0.702977 −0.351489 0.936192i \(-0.614324\pi\)
−0.351489 + 0.936192i \(0.614324\pi\)
\(642\) 0 0
\(643\) 23.1010i 0.911015i −0.890232 0.455508i \(-0.849458\pi\)
0.890232 0.455508i \(-0.150542\pi\)
\(644\) −39.5959 −1.56030
\(645\) 0 0
\(646\) −17.3939 −0.684353
\(647\) 32.0000i 1.25805i −0.777385 0.629025i \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 0 0
\(649\) 17.3939 0.682769
\(650\) −12.0000 16.0000i −0.470679 0.627572i
\(651\) 0 0
\(652\) 21.7980i 0.853674i
\(653\) 34.0000i 1.33052i −0.746611 0.665261i \(-0.768320\pi\)
0.746611 0.665261i \(-0.231680\pi\)
\(654\) 0 0
\(655\) 20.4949 + 10.2474i 0.800802 + 0.400401i
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 19.7980i 0.771805i
\(659\) 31.5959 1.23080 0.615401 0.788214i \(-0.288994\pi\)
0.615401 + 0.788214i \(0.288994\pi\)
\(660\) 0 0
\(661\) −31.1918 −1.21322 −0.606611 0.794999i \(-0.707471\pi\)
−0.606611 + 0.794999i \(0.707471\pi\)
\(662\) 14.2474i 0.553743i
\(663\) 0 0
\(664\) 9.55051 0.370632
\(665\) −15.7980 + 31.5959i −0.612619 + 1.22524i
\(666\) 0 0
\(667\) 0 0
\(668\) 8.00000i 0.309529i
\(669\) 0 0
\(670\) −11.1010 5.55051i −0.428870 0.214435i
\(671\) −58.7878 −2.26948
\(672\) 0 0
\(673\) 24.0000i 0.925132i 0.886585 + 0.462566i \(0.153071\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) −3.59592 −0.138510
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 18.0000i 0.691796i 0.938272 + 0.345898i \(0.112426\pi\)
−0.938272 + 0.345898i \(0.887574\pi\)
\(678\) 0 0
\(679\) 8.89898 0.341511
\(680\) −9.79796 4.89898i −0.375735 0.187867i
\(681\) 0 0
\(682\) 7.59592i 0.290863i
\(683\) 15.5959i 0.596761i −0.954447 0.298381i \(-0.903554\pi\)
0.954447 0.298381i \(-0.0964465\pi\)
\(684\) 0 0
\(685\) −19.5959 + 39.1918i −0.748722 + 1.49744i
\(686\) −25.7980 −0.984971
\(687\) 0 0
\(688\) 4.00000i 0.152499i
\(689\) −47.1918 −1.79787
\(690\) 0 0
\(691\) 37.7980 1.43790 0.718951 0.695061i \(-0.244623\pi\)
0.718951 + 0.695061i \(0.244623\pi\)
\(692\) 19.7980i 0.752605i
\(693\) 0 0
\(694\) −2.20204 −0.0835883
\(695\) 11.5959 + 5.79796i 0.439858 + 0.219929i
\(696\) 0 0
\(697\) 9.79796i 0.371124i
\(698\) 7.10102i 0.268778i
\(699\) 0 0
\(700\) −17.7980 + 13.3485i −0.672700 + 0.504525i
\(701\) 13.7980 0.521142 0.260571 0.965455i \(-0.416089\pi\)
0.260571 + 0.965455i \(0.416089\pi\)
\(702\) 0 0
\(703\) 3.55051i 0.133910i
\(704\) 4.89898 0.184637
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 47.5959i 1.79003i
\(708\) 0 0
\(709\) −5.79796 −0.217747 −0.108873 0.994056i \(-0.534724\pi\)
−0.108873 + 0.994056i \(0.534724\pi\)
\(710\) 4.89898 9.79796i 0.183855 0.367711i
\(711\) 0 0
\(712\) 15.7980i 0.592054i
\(713\) 13.7980i 0.516738i
\(714\) 0 0
\(715\) 19.5959 39.1918i 0.732846 1.46569i
\(716\) 9.34847 0.349369
\(717\) 0 0
\(718\) 12.8990i 0.481386i
\(719\) 51.5959 1.92420 0.962102 0.272692i \(-0.0879138\pi\)
0.962102 + 0.272692i \(0.0879138\pi\)
\(720\) 0 0
\(721\) 43.5959 1.62360
\(722\) 6.39388i 0.237955i
\(723\) 0 0
\(724\) −10.6969 −0.397549
\(725\) 0 0
\(726\) 0 0
\(727\) 0.898979i 0.0333413i −0.999861 0.0166707i \(-0.994693\pi\)
0.999861 0.0166707i \(-0.00530668\pi\)
\(728\) 17.7980i 0.659636i
\(729\) 0 0
\(730\) −8.00000 4.00000i −0.296093 0.148047i
\(731\) 19.5959 0.724781
\(732\) 0 0
\(733\) 17.5959i 0.649920i −0.945728 0.324960i \(-0.894649\pi\)
0.945728 0.324960i \(-0.105351\pi\)
\(734\) −2.65153 −0.0978698
\(735\) 0 0
\(736\) −8.89898 −0.328021
\(737\) 27.1918i 1.00162i
\(738\) 0 0
\(739\) 45.7980 1.68471 0.842353 0.538927i \(-0.181170\pi\)
0.842353 + 0.538927i \(0.181170\pi\)
\(740\) −1.00000 + 2.00000i −0.0367607 + 0.0735215i
\(741\) 0 0
\(742\) 52.4949i 1.92715i
\(743\) 13.7526i 0.504532i 0.967658 + 0.252266i \(0.0811758\pi\)
−0.967658 + 0.252266i \(0.918824\pi\)
\(744\) 0 0
\(745\) −37.3939 18.6969i −1.37001 0.685003i
\(746\) 11.7980 0.431954
\(747\) 0 0
\(748\) 24.0000i 0.877527i
\(749\) −24.6969 −0.902406
\(750\) 0 0
\(751\) 30.6969 1.12015 0.560074 0.828443i \(-0.310773\pi\)
0.560074 + 0.828443i \(0.310773\pi\)
\(752\) 4.44949i 0.162256i
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 8.00000i −0.582300 0.291150i
\(756\) 0 0
\(757\) 33.5959i 1.22106i 0.791991 + 0.610532i \(0.209044\pi\)
−0.791991 + 0.610532i \(0.790956\pi\)
\(758\) 31.5959i 1.14762i
\(759\) 0 0
\(760\) −3.55051 + 7.10102i −0.128791 + 0.257581i
\(761\) −25.1918 −0.913203 −0.456602 0.889671i \(-0.650934\pi\)
−0.456602 + 0.889671i \(0.650934\pi\)
\(762\) 0 0
\(763\) 25.7980i 0.933949i
\(764\) 11.3485 0.410573
\(765\) 0 0
\(766\) −34.6969 −1.25365
\(767\) 14.2020i 0.512806i
\(768\) 0 0
\(769\) 35.7980 1.29091 0.645454 0.763799i \(-0.276668\pi\)
0.645454 + 0.763799i \(0.276668\pi\)
\(770\) −43.5959 21.7980i −1.57109 0.785544i
\(771\) 0 0
\(772\) 14.0000i 0.503871i
\(773\) 6.00000i 0.215805i 0.994161 + 0.107903i \(0.0344134\pi\)
−0.994161 + 0.107903i \(0.965587\pi\)
\(774\) 0 0
\(775\) −4.65153 6.20204i −0.167088 0.222784i
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 25.7980i 0.924902i
\(779\) 7.10102 0.254420
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 43.5959i 1.55899i
\(783\) 0 0
\(784\) −12.7980 −0.457070
\(785\) −7.79796 + 15.5959i −0.278321 + 0.556642i
\(786\) 0 0
\(787\) 28.7423i 1.02455i 0.858820 + 0.512277i \(0.171198\pi\)
−0.858820 + 0.512277i \(0.828802\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 0 0
\(790\) 6.44949 12.8990i 0.229463 0.458925i
\(791\) 13.7980 0.490599
\(792\) 0 0
\(793\) 48.0000i 1.70453i
\(794\) −16.2020 −0.574989
\(795\) 0 0
\(796\) 6.44949 0.228596