Properties

Label 2028.2.q.h.1837.1
Level $2028$
Weight $2$
Character 2028.1837
Analytic conductor $16.194$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2028.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.1936615299\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 156)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1837.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 2028.1837
Dual form 2028.2.q.h.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} -4.00000i q^{5} +(1.73205 - 1.00000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} -4.00000i q^{5} +(1.73205 - 1.00000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.46410 - 2.00000i) q^{11} +(-3.46410 - 2.00000i) q^{15} +(1.00000 + 1.73205i) q^{17} +(-1.73205 + 1.00000i) q^{19} -2.00000i q^{21} -11.0000 q^{25} -1.00000 q^{27} +(3.00000 - 5.19615i) q^{29} -10.0000i q^{31} +(-3.46410 + 2.00000i) q^{33} +(-4.00000 - 6.92820i) q^{35} +(8.66025 + 5.00000i) q^{37} +(-6.92820 - 4.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} +(-3.46410 + 2.00000i) q^{45} +4.00000i q^{47} +(-1.50000 + 2.59808i) q^{49} +2.00000 q^{51} -10.0000 q^{53} +(-8.00000 + 13.8564i) q^{55} +2.00000i q^{57} +(6.92820 - 4.00000i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-1.73205 - 1.00000i) q^{63} +(-1.73205 - 1.00000i) q^{67} +(13.8564 - 8.00000i) q^{71} +10.0000i q^{73} +(-5.50000 + 9.52628i) q^{75} -8.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(6.92820 - 4.00000i) q^{85} +(-3.00000 - 5.19615i) q^{87} +(-3.46410 - 2.00000i) q^{89} +(-8.66025 - 5.00000i) q^{93} +(4.00000 + 6.92820i) q^{95} +(-1.73205 + 1.00000i) q^{97} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} - 2q^{9} + 4q^{17} - 44q^{25} - 4q^{27} + 12q^{29} - 16q^{35} + 8q^{43} - 6q^{49} + 8q^{51} - 40q^{53} - 32q^{55} + 28q^{61} - 22q^{75} - 32q^{77} - 64q^{79} - 2q^{81} - 12q^{87} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(1015\) \(1861\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) 4.00000i 1.78885i −0.447214 0.894427i \(-0.647584\pi\)
0.447214 0.894427i \(-0.352416\pi\)
\(6\) 0 0
\(7\) 1.73205 1.00000i 0.654654 0.377964i −0.135583 0.990766i \(-0.543291\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.46410 2.00000i −1.04447 0.603023i −0.123371 0.992361i \(-0.539370\pi\)
−0.921095 + 0.389338i \(0.872704\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) −3.46410 2.00000i −0.894427 0.516398i
\(16\) 0 0
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −1.73205 + 1.00000i −0.397360 + 0.229416i −0.685344 0.728219i \(-0.740348\pi\)
0.287984 + 0.957635i \(0.407015\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −11.0000 −2.20000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 10.0000i 1.79605i −0.439941 0.898027i \(-0.645001\pi\)
0.439941 0.898027i \(-0.354999\pi\)
\(32\) 0 0
\(33\) −3.46410 + 2.00000i −0.603023 + 0.348155i
\(34\) 0 0
\(35\) −4.00000 6.92820i −0.676123 1.17108i
\(36\) 0 0
\(37\) 8.66025 + 5.00000i 1.42374 + 0.821995i 0.996616 0.0821995i \(-0.0261945\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.92820 4.00000i −1.08200 0.624695i −0.150567 0.988600i \(-0.548110\pi\)
−0.931436 + 0.363905i \(0.881443\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 0 0
\(45\) −3.46410 + 2.00000i −0.516398 + 0.298142i
\(46\) 0 0
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) 0 0
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) −8.00000 + 13.8564i −1.07872 + 1.86840i
\(56\) 0 0
\(57\) 2.00000i 0.264906i
\(58\) 0 0
\(59\) 6.92820 4.00000i 0.901975 0.520756i 0.0241347 0.999709i \(-0.492317\pi\)
0.877841 + 0.478953i \(0.158984\pi\)
\(60\) 0 0
\(61\) 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 0 0
\(63\) −1.73205 1.00000i −0.218218 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.73205 1.00000i −0.211604 0.122169i 0.390453 0.920623i \(-0.372318\pi\)
−0.602056 + 0.798454i \(0.705652\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.8564 8.00000i 1.64445 0.949425i 0.665230 0.746639i \(-0.268333\pi\)
0.979223 0.202787i \(-0.0649998\pi\)
\(72\) 0 0
\(73\) 10.0000i 1.17041i 0.810885 + 0.585206i \(0.198986\pi\)
−0.810885 + 0.585206i \(0.801014\pi\)
\(74\) 0 0
\(75\) −5.50000 + 9.52628i −0.635085 + 1.10000i
\(76\) 0 0
\(77\) −8.00000 −0.911685
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 6.92820 4.00000i 0.751469 0.433861i
\(86\) 0 0
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) −3.46410 2.00000i −0.367194 0.212000i 0.305038 0.952340i \(-0.401331\pi\)
−0.672232 + 0.740341i \(0.734664\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −8.66025 5.00000i −0.898027 0.518476i
\(94\) 0 0
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) −1.73205 + 1.00000i −0.175863 + 0.101535i −0.585348 0.810782i \(-0.699042\pi\)
0.409484 + 0.912317i \(0.365709\pi\)
\(98\) 0 0
\(99\) 4.00000i 0.402015i
\(100\) 0 0
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 0 0
\(111\) 8.66025 5.00000i 0.821995 0.474579i
\(112\) 0 0
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.46410 + 2.00000i 0.317554 + 0.183340i
\(120\) 0 0
\(121\) 2.50000 + 4.33013i 0.227273 + 0.393648i
\(122\) 0 0
\(123\) −6.92820 + 4.00000i −0.624695 + 0.360668i
\(124\) 0 0
\(125\) 24.0000i 2.14663i
\(126\) 0 0
\(127\) 6.00000 10.3923i 0.532414 0.922168i −0.466870 0.884326i \(-0.654618\pi\)
0.999284 0.0378419i \(-0.0120483\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) 0 0
\(135\) 4.00000i 0.344265i
\(136\) 0 0
\(137\) −6.92820 + 4.00000i −0.591916 + 0.341743i −0.765855 0.643013i \(-0.777684\pi\)
0.173939 + 0.984757i \(0.444351\pi\)
\(138\) 0 0
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 3.46410 + 2.00000i 0.291730 + 0.168430i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −20.7846 12.0000i −1.72607 0.996546i
\(146\) 0 0
\(147\) 1.50000 + 2.59808i 0.123718 + 0.214286i
\(148\) 0 0
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i −0.680864 0.732410i \(-0.738396\pi\)
0.680864 0.732410i \(-0.261604\pi\)
\(152\) 0 0
\(153\) 1.00000 1.73205i 0.0808452 0.140028i
\(154\) 0 0
\(155\) −40.0000 −3.21288
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) −5.00000 + 8.66025i −0.396526 + 0.686803i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.73205 + 1.00000i −0.135665 + 0.0783260i −0.566296 0.824202i \(-0.691624\pi\)
0.430632 + 0.902528i \(0.358291\pi\)
\(164\) 0 0
\(165\) 8.00000 + 13.8564i 0.622799 + 1.07872i
\(166\) 0 0
\(167\) −10.3923 6.00000i −0.804181 0.464294i 0.0407502 0.999169i \(-0.487025\pi\)
−0.844931 + 0.534875i \(0.820359\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 1.73205 + 1.00000i 0.132453 + 0.0764719i
\(172\) 0 0
\(173\) 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i \(-0.142443\pi\)
−0.825505 + 0.564396i \(0.809109\pi\)
\(174\) 0 0
\(175\) −19.0526 + 11.0000i −1.44024 + 0.831522i
\(176\) 0 0
\(177\) 8.00000i 0.601317i
\(178\) 0 0
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) 20.0000 34.6410i 1.47043 2.54686i
\(186\) 0 0
\(187\) 8.00000i 0.585018i
\(188\) 0 0
\(189\) −1.73205 + 1.00000i −0.125988 + 0.0727393i
\(190\) 0 0
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 0 0
\(193\) −12.1244 7.00000i −0.872730 0.503871i −0.00447566 0.999990i \(-0.501425\pi\)
−0.868255 + 0.496119i \(0.834758\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.3923 + 6.00000i 0.740421 + 0.427482i 0.822222 0.569166i \(-0.192734\pi\)
−0.0818013 + 0.996649i \(0.526067\pi\)
\(198\) 0 0
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0 0
\(201\) −1.73205 + 1.00000i −0.122169 + 0.0705346i
\(202\) 0 0
\(203\) 12.0000i 0.842235i
\(204\) 0 0
\(205\) −16.0000 + 27.7128i −1.11749 + 1.93555i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) 0 0
\(213\) 16.0000i 1.09630i
\(214\) 0 0
\(215\) 13.8564 8.00000i 0.944999 0.545595i
\(216\) 0 0
\(217\) −10.0000 17.3205i −0.678844 1.17579i
\(218\) 0 0
\(219\) 8.66025 + 5.00000i 0.585206 + 0.337869i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −12.1244 7.00000i −0.811907 0.468755i 0.0357107 0.999362i \(-0.488630\pi\)
−0.847618 + 0.530607i \(0.821964\pi\)
\(224\) 0 0
\(225\) 5.50000 + 9.52628i 0.366667 + 0.635085i
\(226\) 0 0
\(227\) −3.46410 + 2.00000i −0.229920 + 0.132745i −0.610535 0.791989i \(-0.709046\pi\)
0.380615 + 0.924734i \(0.375712\pi\)
\(228\) 0 0
\(229\) 2.00000i 0.132164i 0.997814 + 0.0660819i \(0.0210498\pi\)
−0.997814 + 0.0660819i \(0.978950\pi\)
\(230\) 0 0
\(231\) −4.00000 + 6.92820i −0.263181 + 0.455842i
\(232\) 0 0
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 0 0
\(237\) −8.00000 + 13.8564i −0.519656 + 0.900070i
\(238\) 0 0
\(239\) 24.0000i 1.55243i −0.630468 0.776215i \(-0.717137\pi\)
0.630468 0.776215i \(-0.282863\pi\)
\(240\) 0 0
\(241\) 1.73205 1.00000i 0.111571 0.0644157i −0.443176 0.896435i \(-0.646148\pi\)
0.554747 + 0.832019i \(0.312815\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 10.3923 + 6.00000i 0.663940 + 0.383326i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.0000 17.3205i −0.631194 1.09326i −0.987308 0.158818i \(-0.949232\pi\)
0.356113 0.934443i \(-0.384102\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 8.00000i 0.500979i
\(256\) 0 0
\(257\) 15.0000 25.9808i 0.935674 1.62064i 0.162247 0.986750i \(-0.448126\pi\)
0.773427 0.633885i \(-0.218541\pi\)
\(258\) 0 0
\(259\) 20.0000 1.24274
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 8.00000 13.8564i 0.493301 0.854423i −0.506669 0.862141i \(-0.669123\pi\)
0.999970 + 0.00771799i \(0.00245674\pi\)
\(264\) 0 0
\(265\) 40.0000i 2.45718i
\(266\) 0 0
\(267\) −3.46410 + 2.00000i −0.212000 + 0.122398i
\(268\) 0 0
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) 0 0
\(271\) −8.66025 5.00000i −0.526073 0.303728i 0.213343 0.976977i \(-0.431565\pi\)
−0.739416 + 0.673249i \(0.764898\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 38.1051 + 22.0000i 2.29783 + 1.32665i
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) 0 0
\(279\) −8.66025 + 5.00000i −0.518476 + 0.299342i
\(280\) 0 0
\(281\) 8.00000i 0.477240i 0.971113 + 0.238620i \(0.0766950\pi\)
−0.971113 + 0.238620i \(0.923305\pi\)
\(282\) 0 0
\(283\) −8.00000 + 13.8564i −0.475551 + 0.823678i −0.999608 0.0280052i \(-0.991084\pi\)
0.524057 + 0.851683i \(0.324418\pi\)
\(284\) 0 0
\(285\) 8.00000 0.473879
\(286\) 0 0
\(287\) −16.0000 −0.944450
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 2.00000i 0.117242i
\(292\) 0 0
\(293\) −6.92820 + 4.00000i −0.404750 + 0.233682i −0.688531 0.725206i \(-0.741744\pi\)
0.283782 + 0.958889i \(0.408411\pi\)
\(294\) 0 0
\(295\) −16.0000 27.7128i −0.931556 1.61350i
\(296\) 0 0
\(297\) 3.46410 + 2.00000i 0.201008 + 0.116052i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 6.92820 + 4.00000i 0.399335 + 0.230556i
\(302\) 0 0
\(303\) −5.00000 8.66025i −0.287242 0.497519i
\(304\) 0 0
\(305\) 48.4974 28.0000i 2.77695 1.60328i
\(306\) 0 0
\(307\) 22.0000i 1.25561i −0.778372 0.627803i \(-0.783954\pi\)
0.778372 0.627803i \(-0.216046\pi\)
\(308\) 0 0
\(309\) 4.00000 6.92820i 0.227552 0.394132i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0 0
\(315\) −4.00000 + 6.92820i −0.225374 + 0.390360i
\(316\) 0 0
\(317\) 12.0000i 0.673987i −0.941507 0.336994i \(-0.890590\pi\)
0.941507 0.336994i \(-0.109410\pi\)
\(318\) 0 0
\(319\) −20.7846 + 12.0000i −1.16371 + 0.671871i
\(320\) 0 0
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 0 0
\(323\) −3.46410 2.00000i −0.192748 0.111283i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.73205 1.00000i −0.0957826 0.0553001i
\(328\) 0 0
\(329\) 4.00000 + 6.92820i 0.220527 + 0.381964i
\(330\) 0 0
\(331\) 1.73205 1.00000i 0.0952021 0.0549650i −0.451643 0.892199i \(-0.649162\pi\)
0.546845 + 0.837234i \(0.315829\pi\)
\(332\) 0 0
\(333\) 10.0000i 0.547997i
\(334\) 0 0
\(335\) −4.00000 + 6.92820i −0.218543 + 0.378528i
\(336\) 0 0
\(337\) 30.0000 1.63420 0.817102 0.576493i \(-0.195579\pi\)
0.817102 + 0.576493i \(0.195579\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −20.0000 + 34.6410i −1.08306 + 1.87592i
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) 15.5885 + 9.00000i 0.834431 + 0.481759i 0.855367 0.518022i \(-0.173331\pi\)
−0.0209364 + 0.999781i \(0.506665\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 13.8564 + 8.00000i 0.737502 + 0.425797i 0.821160 0.570697i \(-0.193327\pi\)
−0.0836583 + 0.996495i \(0.526660\pi\)
\(354\) 0 0
\(355\) −32.0000 55.4256i −1.69838 2.94169i
\(356\) 0 0
\(357\) 3.46410 2.00000i 0.183340 0.105851i
\(358\) 0 0
\(359\) 12.0000i 0.633336i 0.948536 + 0.316668i \(0.102564\pi\)
−0.948536 + 0.316668i \(0.897436\pi\)
\(360\) 0 0
\(361\) −7.50000 + 12.9904i −0.394737 + 0.683704i
\(362\) 0 0
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 40.0000 2.09370
\(366\) 0 0
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 0 0
\(369\) 8.00000i 0.416463i
\(370\) 0 0
\(371\) −17.3205 + 10.0000i −0.899236 + 0.519174i
\(372\) 0 0
\(373\) 9.00000 + 15.5885i 0.466002 + 0.807140i 0.999246 0.0388219i \(-0.0123605\pi\)
−0.533244 + 0.845962i \(0.679027\pi\)
\(374\) 0 0
\(375\) 20.7846 + 12.0000i 1.07331 + 0.619677i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −5.19615 3.00000i −0.266908 0.154100i 0.360573 0.932731i \(-0.382581\pi\)
−0.627482 + 0.778631i \(0.715914\pi\)
\(380\) 0 0
\(381\) −6.00000 10.3923i −0.307389 0.532414i
\(382\) 0 0
\(383\) 10.3923 6.00000i 0.531022 0.306586i −0.210411 0.977613i \(-0.567480\pi\)
0.741433 + 0.671027i \(0.234147\pi\)
\(384\) 0 0
\(385\) 32.0000i 1.63087i
\(386\) 0 0
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 0 0
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 2.00000 3.46410i 0.100887 0.174741i
\(394\) 0 0
\(395\) 64.0000i 3.22019i
\(396\) 0 0
\(397\) −15.5885 + 9.00000i −0.782362 + 0.451697i −0.837267 0.546795i \(-0.815848\pi\)
0.0549046 + 0.998492i \(0.482515\pi\)
\(398\) 0 0
\(399\) 2.00000 + 3.46410i 0.100125 + 0.173422i
\(400\) 0 0
\(401\) −10.3923 6.00000i −0.518967 0.299626i 0.217545 0.976050i \(-0.430195\pi\)
−0.736512 + 0.676425i \(0.763528\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 3.46410 + 2.00000i 0.172133 + 0.0993808i
\(406\) 0 0
\(407\) −20.0000 34.6410i −0.991363 1.71709i
\(408\) 0 0
\(409\) 12.1244 7.00000i 0.599511 0.346128i −0.169338 0.985558i \(-0.554163\pi\)
0.768849 + 0.639430i \(0.220830\pi\)
\(410\) 0 0
\(411\) 8.00000i 0.394611i
\(412\) 0 0
\(413\) 8.00000 13.8564i 0.393654 0.681829i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.0000 17.3205i 0.488532 0.846162i −0.511381 0.859354i \(-0.670866\pi\)
0.999913 + 0.0131919i \(0.00419923\pi\)
\(420\) 0 0
\(421\) 2.00000i 0.0974740i −0.998812 0.0487370i \(-0.984480\pi\)
0.998812 0.0487370i \(-0.0155196\pi\)
\(422\) 0 0
\(423\) 3.46410 2.00000i 0.168430 0.0972433i
\(424\) 0 0
\(425\) −11.0000 19.0526i −0.533578 0.924185i
\(426\) 0 0
\(427\) 24.2487 + 14.0000i 1.17348 + 0.677507i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 17.3205 + 10.0000i 0.834300 + 0.481683i 0.855323 0.518096i \(-0.173359\pi\)
−0.0210230 + 0.999779i \(0.506692\pi\)
\(432\) 0 0
\(433\) −9.00000 15.5885i −0.432512 0.749133i 0.564577 0.825381i \(-0.309039\pi\)
−0.997089 + 0.0762473i \(0.975706\pi\)
\(434\) 0 0
\(435\) −20.7846 + 12.0000i −0.996546 + 0.575356i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) −8.00000 + 13.8564i −0.379236 + 0.656857i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.3923 + 6.00000i −0.490443 + 0.283158i −0.724758 0.689003i \(-0.758049\pi\)
0.234315 + 0.972161i \(0.424715\pi\)
\(450\) 0 0
\(451\) 16.0000 + 27.7128i 0.753411 + 1.30495i
\(452\) 0 0
\(453\) −15.5885 9.00000i −0.732410 0.422857i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 15.5885 + 9.00000i 0.729197 + 0.421002i 0.818128 0.575036i \(-0.195012\pi\)
−0.0889312 + 0.996038i \(0.528345\pi\)
\(458\) 0 0
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 0 0
\(461\) 10.3923 6.00000i 0.484018 0.279448i −0.238071 0.971248i \(-0.576515\pi\)
0.722089 + 0.691800i \(0.243182\pi\)
\(462\) 0 0
\(463\) 22.0000i 1.02243i −0.859454 0.511213i \(-0.829196\pi\)
0.859454 0.511213i \(-0.170804\pi\)
\(464\) 0 0
\(465\) −20.0000 + 34.6410i −0.927478 + 1.60644i
\(466\) 0 0
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) 1.00000 1.73205i 0.0460776 0.0798087i
\(472\) 0 0
\(473\) 16.0000i 0.735681i
\(474\) 0 0
\(475\) 19.0526 11.0000i 0.874191 0.504715i
\(476\) 0 0
\(477\) 5.00000 + 8.66025i 0.228934 + 0.396526i
\(478\) 0 0
\(479\) −13.8564 8.00000i −0.633115 0.365529i 0.148842 0.988861i \(-0.452445\pi\)
−0.781958 + 0.623332i \(0.785779\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.00000 + 6.92820i 0.181631 + 0.314594i
\(486\) 0 0
\(487\) −22.5167 + 13.0000i −1.02033 + 0.589086i −0.914199 0.405266i \(-0.867179\pi\)
−0.106129 + 0.994352i \(0.533846\pi\)
\(488\) 0 0
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 16.0000 0.719147
\(496\) 0 0
\(497\) 16.0000 27.7128i 0.717698 1.24309i
\(498\) 0 0
\(499\) 6.00000i 0.268597i −0.990941 0.134298i \(-0.957122\pi\)
0.990941 0.134298i \(-0.0428781\pi\)
\(500\) 0 0
\(501\) −10.3923 + 6.00000i −0.464294 + 0.268060i
\(502\) 0 0
\(503\) −8.00000 13.8564i −0.356702 0.617827i 0.630705 0.776022i \(-0.282766\pi\)
−0.987408 + 0.158196i \(0.949432\pi\)
\(504\) 0 0
\(505\) −34.6410 20.0000i −1.54150 0.889988i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.3923 6.00000i −0.460631 0.265945i 0.251679 0.967811i \(-0.419017\pi\)
−0.712309 + 0.701866i \(0.752351\pi\)
\(510\) 0 0
\(511\) 10.0000 + 17.3205i 0.442374 + 0.766214i
\(512\) 0 0
\(513\) 1.73205 1.00000i 0.0764719 0.0441511i
\(514\) 0 0
\(515\) 32.0000i 1.41009i
\(516\) 0 0
\(517\) 8.00000 13.8564i 0.351840 0.609404i
\(518\) 0 0
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) −2.00000 −0.0876216 −0.0438108 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) 0 0
\(523\) −8.00000 + 13.8564i −0.349816 + 0.605898i −0.986216 0.165460i \(-0.947089\pi\)
0.636401 + 0.771358i \(0.280422\pi\)
\(524\) 0 0
\(525\) 22.0000i 0.960159i
\(526\) 0 0
\(527\) 17.3205 10.0000i 0.754493 0.435607i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −6.92820 4.00000i −0.300658 0.173585i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 41.5692 + 24.0000i 1.79719 + 1.03761i
\(536\) 0 0
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 0 0
\(539\) 10.3923 6.00000i 0.447628 0.258438i
\(540\) 0 0
\(541\) 38.0000i 1.63375i −0.576816 0.816874i \(-0.695705\pi\)
0.576816 0.816874i \(-0.304295\pi\)
\(542\) 0 0
\(543\) −1.00000 + 1.73205i −0.0429141 + 0.0743294i
\(544\) 0 0
\(545\) −8.00000 −0.342682
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 0 0
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) 0 0
\(553\) −27.7128 + 16.0000i −1.17847 + 0.680389i
\(554\) 0 0
\(555\) −20.0000 34.6410i −0.848953 1.47043i
\(556\) 0 0
\(557\) 20.7846 + 12.0000i 0.880672 + 0.508456i 0.870880 0.491496i \(-0.163550\pi\)
0.00979220 + 0.999952i \(0.496883\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −6.92820 4.00000i −0.292509 0.168880i
\(562\) 0 0
\(563\) 14.0000 + 24.2487i 0.590030 + 1.02196i 0.994228 + 0.107290i \(0.0342173\pi\)
−0.404198 + 0.914671i \(0.632449\pi\)
\(564\) 0 0
\(565\) −20.7846 + 12.0000i −0.874415 + 0.504844i
\(566\) 0 0
\(567\) 2.00000i 0.0839921i
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 30.0000i 1.24892i −0.781058 0.624458i \(-0.785320\pi\)
0.781058 0.624458i \(-0.214680\pi\)
\(578\) 0 0
\(579\) −12.1244 + 7.00000i −0.503871 + 0.290910i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 34.6410 + 20.0000i 1.43468 + 0.828315i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.92820 + 4.00000i 0.285958 + 0.165098i 0.636117 0.771592i \(-0.280539\pi\)
−0.350160 + 0.936690i \(0.613873\pi\)
\(588\) 0 0
\(589\) 10.0000 + 17.3205i 0.412043 + 0.713679i
\(590\) 0 0
\(591\) 10.3923 6.00000i 0.427482 0.246807i
\(592\) 0 0
\(593\) 36.0000i 1.47834i 0.673517 + 0.739171i \(0.264783\pi\)
−0.673517 + 0.739171i \(0.735217\pi\)
\(594\) 0 0
\(595\) 8.00000 13.8564i 0.327968 0.568057i
\(596\) 0 0
\(597\) 4.00000 0.163709
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 11.0000 19.0526i 0.448699 0.777170i −0.549602 0.835426i \(-0.685221\pi\)
0.998302 + 0.0582563i \(0.0185541\pi\)
\(602\) 0 0
\(603\) 2.00000i 0.0814463i
\(604\) 0 0
\(605\) 17.3205 10.0000i 0.704179 0.406558i
\(606\) 0 0
\(607\) 2.00000 + 3.46410i 0.0811775 + 0.140604i 0.903756 0.428048i \(-0.140799\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(608\) 0 0
\(609\) −10.3923 6.00000i −0.421117 0.243132i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 12.1244 + 7.00000i 0.489698 + 0.282727i 0.724449 0.689328i \(-0.242094\pi\)
−0.234751 + 0.972056i \(0.575428\pi\)
\(614\) 0 0
\(615\) 16.0000 + 27.7128i 0.645182 + 1.11749i
\(616\) 0 0
\(617\) −41.5692 + 24.0000i −1.67351 + 0.966204i −0.707867 + 0.706346i \(0.750342\pi\)
−0.965647 + 0.259858i \(0.916324\pi\)
\(618\) 0 0
\(619\) 14.0000i 0.562708i −0.959604 0.281354i \(-0.909217\pi\)
0.959604 0.281354i \(-0.0907834\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 4.00000 6.92820i 0.159745 0.276686i
\(628\) 0 0
\(629\) 20.0000i 0.797452i
\(630\) 0 0
\(631\) 25.9808 15.0000i 1.03428 0.597141i 0.116071 0.993241i \(-0.462970\pi\)
0.918207 + 0.396100i \(0.129637\pi\)
\(632\) 0 0
\(633\) −6.00000 10.3923i −0.238479 0.413057i
\(634\) 0 0
\(635\) −41.5692 24.0000i −1.64962 0.952411i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −13.8564 8.00000i −0.548151 0.316475i
\(640\) 0 0
\(641\) 13.0000 + 22.5167i 0.513469 + 0.889355i 0.999878 + 0.0156233i \(0.00497325\pi\)
−0.486409 + 0.873731i \(0.661693\pi\)
\(642\) 0 0
\(643\) 22.5167 13.0000i 0.887970 0.512670i 0.0146923 0.999892i \(-0.495323\pi\)
0.873278 + 0.487222i \(0.161990\pi\)
\(644\) 0 0
\(645\) 16.0000i 0.629999i
\(646\) 0 0
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) 0 0
\(649\) −32.0000 −1.25611
\(650\) 0 0
\(651\) −20.0000 −0.783862
\(652\) 0 0
\(653\) 23.0000 39.8372i 0.900060 1.55895i 0.0726446 0.997358i \(-0.476856\pi\)
0.827415 0.561591i \(-0.189811\pi\)
\(654\) 0 0
\(655\) 16.0000i 0.625172i
\(656\) 0 0
\(657\) 8.66025 5.00000i 0.337869 0.195069i
\(658\) 0 0
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) 8.66025 + 5.00000i 0.336845 + 0.194477i 0.658876 0.752252i \(-0.271032\pi\)
−0.322031 + 0.946729i \(0.604366\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 13.8564 + 8.00000i 0.537328 + 0.310227i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −12.1244 + 7.00000i −0.468755 + 0.270636i
\(670\) 0 0
\(671\) 56.0000i 2.16186i
\(672\) 0 0
\(673\) 11.0000 19.0526i 0.424019 0.734422i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856156i \(0.0272857\pi\)
\(674\) 0 0
\(675\) 11.0000 0.423390
\(676\) 0 0
\(677\) 38.0000 1.46046 0.730229 0.683202i \(-0.239413\pi\)
0.730229 + 0.683202i \(0.239413\pi\)
\(678\) 0 0
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 0 0
\(681\) 4.00000i 0.153280i
\(682\) 0 0
\(683\) −17.3205 + 10.0000i −0.662751 + 0.382639i −0.793324 0.608799i \(-0.791651\pi\)
0.130573 + 0.991439i \(0.458318\pi\)
\(684\) 0 0
\(685\) 16.0000 + 27.7128i 0.611329 + 1.05885i
\(686\) 0 0
\(687\) 1.73205 + 1.00000i 0.0660819 + 0.0381524i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −8.66025 5.00000i −0.329452 0.190209i 0.326146 0.945319i \(-0.394250\pi\)
−0.655598 + 0.755110i \(0.727583\pi\)
\(692\) 0 0
\(693\) 4.00000 + 6.92820i 0.151947 + 0.263181i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 16.0000i 0.606043i
\(698\) 0 0
\(699\) 9.00000 15.5885i 0.340411 0.589610i
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) 8.00000 13.8564i 0.301297 0.521862i
\(706\) 0 0
\(707\) 20.0000i 0.752177i
\(708\) 0 0
\(709\) −5.19615 + 3.00000i −0.195146 + 0.112667i −0.594389 0.804178i \(-0.702606\pi\)
0.399244 + 0.916845i \(0.369273\pi\)
\(710\) 0 0
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −20.7846 12.0000i −0.776215 0.448148i
\(718\) 0 0
\(719\) −24.0000 41.5692i −0.895049 1.55027i −0.833744 0.552151i \(-0.813807\pi\)
−0.0613050 0.998119i \(-0.519526\pi\)
\(720\) 0 0
\(721\) 13.8564 8.00000i 0.516040 0.297936i
\(722\) 0 0
\(723\) 2.00000i 0.0743808i
\(724\) 0 0
\(725\) −33.0000 + 57.1577i −1.22559 + 2.12278i
\(726\) 0 0
\(727\) −44.0000 −1.63187 −0.815935 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) 0 0
\(733\) 22.0000i 0.812589i 0.913742 + 0.406294i \(0.133179\pi\)
−0.913742 + 0.406294i \(0.866821\pi\)
\(734\) 0 0
\(735\) 10.3923 6.00000i 0.383326 0.221313i
\(736\) 0 0
\(737\) 4.00000 + 6.92820i 0.147342 + 0.255204i
\(738\) 0 0
\(739\) 19.0526 + 11.0000i 0.700860 + 0.404642i 0.807668 0.589638i \(-0.200730\pi\)
−0.106808 + 0.994280i \(0.534063\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −41.5692 24.0000i −1.52503 0.880475i −0.999560 0.0296605i \(-0.990557\pi\)
−0.525467 0.850814i \(-0.676109\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 24.0000i 0.876941i
\(750\) 0 0
\(751\) 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) 0 0
\(753\) −20.0000 −0.728841
\(754\) 0 0
\(755\) −72.0000 −2.62035
\(756\) 0 0
\(757\) −9.00000 + 15.5885i −0.327111 + 0.566572i −0.981937 0.189207i \(-0.939408\pi\)
0.654827 + 0.755779i \(0.272742\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −34.6410 + 20.0000i −1.25574 + 0.724999i −0.972243 0.233975i \(-0.924827\pi\)
−0.283493 + 0.958974i \(0.591493\pi\)
\(762\) 0 0
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) 0 0
\(765\) −6.92820 4.00000i −0.250490 0.144620i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 19.0526 + 11.0000i 0.687053 + 0.396670i 0.802507 0.596643i \(-0.203499\pi\)
−0.115454 + 0.993313i \(0.536832\pi\)
\(770\) 0 0
\(771\) −15.0000 25.9808i −0.540212 0.935674i
\(772\) 0 0
\(773\) −41.5692 + 24.0000i −1.49514 + 0.863220i −0.999984 0.00558380i \(-0.998223\pi\)
−0.495156 + 0.868804i \(0.664889\pi\)
\(774\) 0 0
\(775\) 110.000i 3.95132i
\(776\) 0 0
\(777\) 10.0000 17.3205i 0.358748 0.621370i
\(778\) 0 0
\(779\) 16.0000 0.573259
\(780\) 0 0
\(781\) −64.0000 −2.29010
\(782\) 0 0
\(783\) −3.00000 + 5.19615i −0.107211 + 0.185695i
\(784\) 0 0
\(785\) 8.00000i 0.285532i
\(786\) 0 0
\(787\) 43.3013 25.0000i 1.54352 0.891154i 0.544911 0.838494i \(-0.316563\pi\)
0.998613 0.0526599i \(-0.0167699\pi\)
\(788\) 0 0
\(789\) −8.00000 13.8564i −0.284808 0.493301i
\(790\) 0 0
\(791\) −10.3923 6.00000i −0.369508 0.213335i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 34.6410 + 20.0000i 1.22859 + 0.709327i
\(796\) 0 0
\(797\) −13.0000 22.5167i −0.460484 0.797581i 0.538501 0.842625i \(-0.318991\pi\)
−0.998985 + 0.0450436i \(0.985657\pi\)
\(798\) 0 0
\(799\) −6.92820 + 4.00000i −0.245102 + 0.141510i
\(800\) 0 0