Properties

Label 1900.2.i.f.201.6
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + 14 x^{3} + 145 x^{2} + 33 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.6
Root \(-1.08347 + 1.87662i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.f.501.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.58347 - 2.74265i) q^{3} +3.03607 q^{7} +(-3.51475 - 6.08773i) q^{9} +O(q^{10})\) \(q+(1.58347 - 2.74265i) q^{3} +3.03607 q^{7} +(-3.51475 - 6.08773i) q^{9} +2.71642 q^{11} +(1.95668 + 3.38907i) q^{13} +(-0.944962 + 1.63672i) q^{17} +(1.83281 - 3.95485i) q^{19} +(4.80753 - 8.32689i) q^{21} +(-3.57611 - 6.19400i) q^{23} -12.7612 q^{27} +(1.45668 + 2.52305i) q^{29} +7.40548 q^{31} +(4.30137 - 7.45019i) q^{33} -3.43284 q^{37} +12.3934 q^{39} +(-5.16090 + 8.93895i) q^{41} +(5.37852 - 9.31587i) q^{43} +(2.63731 + 4.56795i) q^{47} +2.21774 q^{49} +(2.99264 + 5.18340i) q^{51} +(0.843574 + 1.46111i) q^{53} +(-7.94456 - 11.2891i) q^{57} +(0.347967 - 0.602697i) q^{59} +(-6.28553 - 10.8869i) q^{61} +(-10.6710 - 18.4828i) q^{63} +(0.365572 + 0.633189i) q^{67} -22.6506 q^{69} +(1.75274 - 3.03584i) q^{71} +(-5.55396 + 9.61973i) q^{73} +8.24725 q^{77} +(6.03374 - 10.4507i) q^{79} +(-9.66273 + 16.7363i) q^{81} -11.4181 q^{83} +9.22645 q^{87} +(4.34057 + 7.51809i) q^{89} +(5.94063 + 10.2895i) q^{91} +(11.7264 - 20.3106i) q^{93} +(-3.43468 + 5.94905i) q^{97} +(-9.54754 - 16.5368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} - 3 q^{9} + O(q^{10}) \) \( 12 q + 3 q^{3} - 3 q^{9} + 2 q^{11} + 7 q^{13} - q^{17} + q^{21} - 2 q^{23} - 24 q^{27} + q^{29} + 2 q^{31} + 10 q^{33} + 20 q^{37} + 36 q^{39} - 7 q^{41} + 19 q^{43} - 14 q^{47} + 8 q^{49} + 11 q^{51} + 6 q^{53} - 28 q^{57} - 5 q^{61} - 11 q^{63} + 14 q^{67} - 14 q^{69} + 8 q^{71} - 9 q^{73} + 2 q^{77} + q^{79} + 2 q^{81} - 26 q^{83} + 30 q^{87} - 8 q^{89} + 3 q^{91} + 9 q^{93} - 11 q^{97} - 18 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.58347 2.74265i 0.914217 1.58347i 0.106173 0.994348i \(-0.466140\pi\)
0.808044 0.589122i \(-0.200526\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.03607 1.14753 0.573764 0.819021i \(-0.305483\pi\)
0.573764 + 0.819021i \(0.305483\pi\)
\(8\) 0 0
\(9\) −3.51475 6.08773i −1.17158 2.02924i
\(10\) 0 0
\(11\) 2.71642 0.819031 0.409516 0.912303i \(-0.365698\pi\)
0.409516 + 0.912303i \(0.365698\pi\)
\(12\) 0 0
\(13\) 1.95668 + 3.38907i 0.542686 + 0.939960i 0.998749 + 0.0500123i \(0.0159261\pi\)
−0.456062 + 0.889948i \(0.650741\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.944962 + 1.63672i −0.229187 + 0.396963i −0.957567 0.288210i \(-0.906940\pi\)
0.728380 + 0.685173i \(0.240273\pi\)
\(18\) 0 0
\(19\) 1.83281 3.95485i 0.420476 0.907304i
\(20\) 0 0
\(21\) 4.80753 8.32689i 1.04909 1.81708i
\(22\) 0 0
\(23\) −3.57611 6.19400i −0.745670 1.29154i −0.949881 0.312611i \(-0.898796\pi\)
0.204211 0.978927i \(-0.434537\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −12.7612 −2.45590
\(28\) 0 0
\(29\) 1.45668 + 2.52305i 0.270499 + 0.468518i 0.968990 0.247101i \(-0.0794779\pi\)
−0.698491 + 0.715619i \(0.746145\pi\)
\(30\) 0 0
\(31\) 7.40548 1.33006 0.665032 0.746815i \(-0.268418\pi\)
0.665032 + 0.746815i \(0.268418\pi\)
\(32\) 0 0
\(33\) 4.30137 7.45019i 0.748772 1.29691i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.43284 −0.564355 −0.282178 0.959362i \(-0.591057\pi\)
−0.282178 + 0.959362i \(0.591057\pi\)
\(38\) 0 0
\(39\) 12.3934 1.98453
\(40\) 0 0
\(41\) −5.16090 + 8.93895i −0.805998 + 1.39603i 0.109618 + 0.993974i \(0.465037\pi\)
−0.915616 + 0.402055i \(0.868296\pi\)
\(42\) 0 0
\(43\) 5.37852 9.31587i 0.820217 1.42066i −0.0853036 0.996355i \(-0.527186\pi\)
0.905521 0.424302i \(-0.139481\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.63731 + 4.56795i 0.384691 + 0.666304i 0.991726 0.128371i \(-0.0409747\pi\)
−0.607035 + 0.794675i \(0.707641\pi\)
\(48\) 0 0
\(49\) 2.21774 0.316820
\(50\) 0 0
\(51\) 2.99264 + 5.18340i 0.419053 + 0.725821i
\(52\) 0 0
\(53\) 0.843574 + 1.46111i 0.115874 + 0.200699i 0.918129 0.396282i \(-0.129700\pi\)
−0.802255 + 0.596982i \(0.796367\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −7.94456 11.2891i −1.05228 1.49528i
\(58\) 0 0
\(59\) 0.347967 0.602697i 0.0453015 0.0784644i −0.842486 0.538719i \(-0.818908\pi\)
0.887787 + 0.460254i \(0.152242\pi\)
\(60\) 0 0
\(61\) −6.28553 10.8869i −0.804780 1.39392i −0.916440 0.400173i \(-0.868950\pi\)
0.111660 0.993747i \(-0.464383\pi\)
\(62\) 0 0
\(63\) −10.6710 18.4828i −1.34443 2.32861i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.365572 + 0.633189i 0.0446617 + 0.0773564i 0.887492 0.460823i \(-0.152446\pi\)
−0.842830 + 0.538179i \(0.819112\pi\)
\(68\) 0 0
\(69\) −22.6506 −2.72682
\(70\) 0 0
\(71\) 1.75274 3.03584i 0.208012 0.360288i −0.743076 0.669207i \(-0.766634\pi\)
0.951088 + 0.308919i \(0.0999673\pi\)
\(72\) 0 0
\(73\) −5.55396 + 9.61973i −0.650041 + 1.12590i 0.333071 + 0.942902i \(0.391915\pi\)
−0.983112 + 0.183003i \(0.941418\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.24725 0.939861
\(78\) 0 0
\(79\) 6.03374 10.4507i 0.678849 1.17580i −0.296479 0.955039i \(-0.595812\pi\)
0.975328 0.220761i \(-0.0708542\pi\)
\(80\) 0 0
\(81\) −9.66273 + 16.7363i −1.07364 + 1.85959i
\(82\) 0 0
\(83\) −11.4181 −1.25330 −0.626650 0.779301i \(-0.715575\pi\)
−0.626650 + 0.779301i \(0.715575\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 9.22645 0.989180
\(88\) 0 0
\(89\) 4.34057 + 7.51809i 0.460099 + 0.796916i 0.998965 0.0454758i \(-0.0144804\pi\)
−0.538866 + 0.842392i \(0.681147\pi\)
\(90\) 0 0
\(91\) 5.94063 + 10.2895i 0.622747 + 1.07863i
\(92\) 0 0
\(93\) 11.7264 20.3106i 1.21597 2.10612i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.43468 + 5.94905i −0.348739 + 0.604034i −0.986026 0.166593i \(-0.946724\pi\)
0.637286 + 0.770627i \(0.280057\pi\)
\(98\) 0 0
\(99\) −9.54754 16.5368i −0.959564 1.66201i
\(100\) 0 0
\(101\) 6.96831 + 12.0695i 0.693373 + 1.20096i 0.970726 + 0.240189i \(0.0772093\pi\)
−0.277354 + 0.960768i \(0.589457\pi\)
\(102\) 0 0
\(103\) −9.81071 −0.966678 −0.483339 0.875433i \(-0.660576\pi\)
−0.483339 + 0.875433i \(0.660576\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.6908 1.22687 0.613434 0.789746i \(-0.289788\pi\)
0.613434 + 0.789746i \(0.289788\pi\)
\(108\) 0 0
\(109\) −3.85085 + 6.66986i −0.368844 + 0.638857i −0.989385 0.145317i \(-0.953580\pi\)
0.620541 + 0.784174i \(0.286913\pi\)
\(110\) 0 0
\(111\) −5.43580 + 9.41507i −0.515943 + 0.893639i
\(112\) 0 0
\(113\) −12.8536 −1.20917 −0.604583 0.796542i \(-0.706660\pi\)
−0.604583 + 0.796542i \(0.706660\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 13.7545 23.8235i 1.27161 2.20249i
\(118\) 0 0
\(119\) −2.86897 + 4.96921i −0.262998 + 0.455526i
\(120\) 0 0
\(121\) −3.62107 −0.329188
\(122\) 0 0
\(123\) 16.3443 + 28.3091i 1.47371 + 2.55255i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.735934 1.27468i −0.0653036 0.113109i 0.831525 0.555487i \(-0.187468\pi\)
−0.896829 + 0.442378i \(0.854135\pi\)
\(128\) 0 0
\(129\) −17.0335 29.5028i −1.49971 2.59758i
\(130\) 0 0
\(131\) −8.76584 + 15.1829i −0.765875 + 1.32653i 0.173907 + 0.984762i \(0.444361\pi\)
−0.939783 + 0.341773i \(0.888973\pi\)
\(132\) 0 0
\(133\) 5.56455 12.0072i 0.482507 1.04116i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.49344 6.05081i −0.298464 0.516955i 0.677321 0.735688i \(-0.263141\pi\)
−0.975785 + 0.218733i \(0.929808\pi\)
\(138\) 0 0
\(139\) 7.52394 + 13.0318i 0.638172 + 1.10535i 0.985834 + 0.167727i \(0.0536426\pi\)
−0.347661 + 0.937620i \(0.613024\pi\)
\(140\) 0 0
\(141\) 16.7044 1.40676
\(142\) 0 0
\(143\) 5.31517 + 9.20615i 0.444477 + 0.769857i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.51172 6.08248i 0.289642 0.501674i
\(148\) 0 0
\(149\) 0.664435 1.15084i 0.0544326 0.0942801i −0.837525 0.546399i \(-0.815998\pi\)
0.891958 + 0.452119i \(0.149332\pi\)
\(150\) 0 0
\(151\) −1.88336 −0.153266 −0.0766328 0.997059i \(-0.524417\pi\)
−0.0766328 + 0.997059i \(0.524417\pi\)
\(152\) 0 0
\(153\) 13.2852 1.07405
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 4.40932 7.63717i 0.351902 0.609512i −0.634681 0.772775i \(-0.718868\pi\)
0.986583 + 0.163262i \(0.0522017\pi\)
\(158\) 0 0
\(159\) 5.34310 0.423735
\(160\) 0 0
\(161\) −10.8573 18.8054i −0.855677 1.48208i
\(162\) 0 0
\(163\) −19.9424 −1.56201 −0.781004 0.624526i \(-0.785292\pi\)
−0.781004 + 0.624526i \(0.785292\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.43395 12.8760i −0.575256 0.996373i −0.996014 0.0892000i \(-0.971569\pi\)
0.420757 0.907173i \(-0.361764\pi\)
\(168\) 0 0
\(169\) −1.15722 + 2.00436i −0.0890167 + 0.154181i
\(170\) 0 0
\(171\) −30.5179 + 2.74265i −2.33376 + 0.209736i
\(172\) 0 0
\(173\) −5.61271 + 9.72149i −0.426726 + 0.739111i −0.996580 0.0826348i \(-0.973667\pi\)
0.569854 + 0.821746i \(0.307000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.10199 1.90870i −0.0828307 0.143467i
\(178\) 0 0
\(179\) 17.2702 1.29084 0.645419 0.763828i \(-0.276683\pi\)
0.645419 + 0.763828i \(0.276683\pi\)
\(180\) 0 0
\(181\) 8.87048 + 15.3641i 0.659338 + 1.14201i 0.980787 + 0.195080i \(0.0624965\pi\)
−0.321450 + 0.946927i \(0.604170\pi\)
\(182\) 0 0
\(183\) −39.8118 −2.94297
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.56691 + 4.44602i −0.187711 + 0.325125i
\(188\) 0 0
\(189\) −38.7440 −2.81821
\(190\) 0 0
\(191\) −25.1341 −1.81864 −0.909321 0.416096i \(-0.863398\pi\)
−0.909321 + 0.416096i \(0.863398\pi\)
\(192\) 0 0
\(193\) 7.61627 13.1918i 0.548231 0.949564i −0.450165 0.892945i \(-0.648635\pi\)
0.998396 0.0566184i \(-0.0180318\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.15878 −0.581289 −0.290644 0.956831i \(-0.593870\pi\)
−0.290644 + 0.956831i \(0.593870\pi\)
\(198\) 0 0
\(199\) 6.96105 + 12.0569i 0.493456 + 0.854690i 0.999972 0.00754036i \(-0.00240020\pi\)
−0.506516 + 0.862231i \(0.669067\pi\)
\(200\) 0 0
\(201\) 2.31549 0.163322
\(202\) 0 0
\(203\) 4.42260 + 7.66016i 0.310405 + 0.537638i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −25.1383 + 43.5408i −1.74723 + 3.02629i
\(208\) 0 0
\(209\) 4.97868 10.7430i 0.344383 0.743110i
\(210\) 0 0
\(211\) 2.79305 4.83770i 0.192281 0.333041i −0.753725 0.657190i \(-0.771745\pi\)
0.946006 + 0.324149i \(0.105078\pi\)
\(212\) 0 0
\(213\) −5.55083 9.61431i −0.380336 0.658762i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 22.4836 1.52629
\(218\) 0 0
\(219\) 17.5890 + 30.4651i 1.18856 + 2.05864i
\(220\) 0 0
\(221\) −7.39596 −0.497506
\(222\) 0 0
\(223\) −2.43684 + 4.22074i −0.163183 + 0.282641i −0.936009 0.351977i \(-0.885509\pi\)
0.772825 + 0.634619i \(0.218843\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −26.7800 −1.77745 −0.888727 0.458438i \(-0.848409\pi\)
−0.888727 + 0.458438i \(0.848409\pi\)
\(228\) 0 0
\(229\) 21.4407 1.41684 0.708422 0.705789i \(-0.249407\pi\)
0.708422 + 0.705789i \(0.249407\pi\)
\(230\) 0 0
\(231\) 13.0593 22.6193i 0.859237 1.48824i
\(232\) 0 0
\(233\) 0.0459183 0.0795329i 0.00300821 0.00521037i −0.864517 0.502603i \(-0.832376\pi\)
0.867526 + 0.497393i \(0.165709\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −19.1085 33.0969i −1.24123 2.14987i
\(238\) 0 0
\(239\) 20.9290 1.35378 0.676892 0.736082i \(-0.263326\pi\)
0.676892 + 0.736082i \(0.263326\pi\)
\(240\) 0 0
\(241\) 0.937689 + 1.62412i 0.0604019 + 0.104619i 0.894645 0.446778i \(-0.147428\pi\)
−0.834243 + 0.551397i \(0.814095\pi\)
\(242\) 0 0
\(243\) 11.4595 + 19.8484i 0.735125 + 1.27327i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 16.9895 1.52685i 1.08102 0.0971511i
\(248\) 0 0
\(249\) −18.0802 + 31.3159i −1.14579 + 1.98456i
\(250\) 0 0
\(251\) 8.93088 + 15.4687i 0.563712 + 0.976378i 0.997168 + 0.0752035i \(0.0239606\pi\)
−0.433456 + 0.901175i \(0.642706\pi\)
\(252\) 0 0
\(253\) −9.71421 16.8255i −0.610727 1.05781i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.0988 + 26.1518i 0.941836 + 1.63131i 0.761967 + 0.647616i \(0.224234\pi\)
0.179869 + 0.983691i \(0.442433\pi\)
\(258\) 0 0
\(259\) −10.4223 −0.647613
\(260\) 0 0
\(261\) 10.2398 17.7358i 0.633826 1.09782i
\(262\) 0 0
\(263\) 10.6687 18.4788i 0.657863 1.13945i −0.323305 0.946295i \(-0.604794\pi\)
0.981168 0.193157i \(-0.0618726\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 27.4926 1.68252
\(268\) 0 0
\(269\) 15.1825 26.2969i 0.925694 1.60335i 0.135253 0.990811i \(-0.456815\pi\)
0.790441 0.612538i \(-0.209851\pi\)
\(270\) 0 0
\(271\) 5.20262 9.01119i 0.316036 0.547391i −0.663621 0.748069i \(-0.730981\pi\)
0.979657 + 0.200678i \(0.0643145\pi\)
\(272\) 0 0
\(273\) 37.6272 2.27730
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 13.5757 0.815683 0.407842 0.913053i \(-0.366282\pi\)
0.407842 + 0.913053i \(0.366282\pi\)
\(278\) 0 0
\(279\) −26.0284 45.0826i −1.55828 2.69902i
\(280\) 0 0
\(281\) 2.30763 + 3.99693i 0.137661 + 0.238437i 0.926611 0.376021i \(-0.122708\pi\)
−0.788950 + 0.614458i \(0.789375\pi\)
\(282\) 0 0
\(283\) 7.38676 12.7942i 0.439097 0.760539i −0.558523 0.829489i \(-0.688632\pi\)
0.997620 + 0.0689504i \(0.0219650\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −15.6689 + 27.1393i −0.924905 + 1.60198i
\(288\) 0 0
\(289\) 6.71409 + 11.6292i 0.394947 + 0.684068i
\(290\) 0 0
\(291\) 10.8774 + 18.8403i 0.637647 + 1.10444i
\(292\) 0 0
\(293\) −16.5565 −0.967240 −0.483620 0.875278i \(-0.660678\pi\)
−0.483620 + 0.875278i \(0.660678\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −34.6648 −2.01146
\(298\) 0 0
\(299\) 13.9946 24.2394i 0.809330 1.40180i
\(300\) 0 0
\(301\) 16.3296 28.2837i 0.941222 1.63024i
\(302\) 0 0
\(303\) 44.1364 2.53557
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.07134 12.2479i 0.403583 0.699026i −0.590573 0.806984i \(-0.701098\pi\)
0.994155 + 0.107959i \(0.0344315\pi\)
\(308\) 0 0
\(309\) −15.5350 + 26.9074i −0.883754 + 1.53071i
\(310\) 0 0
\(311\) 23.1773 1.31427 0.657133 0.753775i \(-0.271769\pi\)
0.657133 + 0.753775i \(0.271769\pi\)
\(312\) 0 0
\(313\) 12.4209 + 21.5136i 0.702068 + 1.21602i 0.967739 + 0.251954i \(0.0810732\pi\)
−0.265671 + 0.964064i \(0.585593\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.9737 + 24.2031i 0.784840 + 1.35938i 0.929095 + 0.369842i \(0.120588\pi\)
−0.144255 + 0.989541i \(0.546078\pi\)
\(318\) 0 0
\(319\) 3.95696 + 6.85366i 0.221547 + 0.383731i
\(320\) 0 0
\(321\) 20.0955 34.8065i 1.12162 1.94271i
\(322\) 0 0
\(323\) 4.74105 + 6.73698i 0.263799 + 0.374856i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 12.1954 + 21.1231i 0.674407 + 1.16811i
\(328\) 0 0
\(329\) 8.00706 + 13.8686i 0.441443 + 0.764602i
\(330\) 0 0
\(331\) 15.3670 0.844649 0.422324 0.906445i \(-0.361214\pi\)
0.422324 + 0.906445i \(0.361214\pi\)
\(332\) 0 0
\(333\) 12.0656 + 20.8982i 0.661190 + 1.14521i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2.85108 + 4.93822i −0.155308 + 0.269002i −0.933171 0.359432i \(-0.882970\pi\)
0.777863 + 0.628434i \(0.216304\pi\)
\(338\) 0 0
\(339\) −20.3533 + 35.2529i −1.10544 + 1.91468i
\(340\) 0 0
\(341\) 20.1164 1.08936
\(342\) 0 0
\(343\) −14.5193 −0.783968
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.48887 6.04290i 0.187292 0.324400i −0.757054 0.653352i \(-0.773362\pi\)
0.944347 + 0.328952i \(0.106696\pi\)
\(348\) 0 0
\(349\) −16.9017 −0.904729 −0.452364 0.891833i \(-0.649419\pi\)
−0.452364 + 0.891833i \(0.649419\pi\)
\(350\) 0 0
\(351\) −24.9696 43.2487i −1.33278 2.30844i
\(352\) 0 0
\(353\) −30.5814 −1.62768 −0.813842 0.581086i \(-0.802628\pi\)
−0.813842 + 0.581086i \(0.802628\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 9.08586 + 15.7372i 0.480875 + 0.832900i
\(358\) 0 0
\(359\) −7.95750 + 13.7828i −0.419981 + 0.727428i −0.995937 0.0900527i \(-0.971296\pi\)
0.575956 + 0.817480i \(0.304630\pi\)
\(360\) 0 0
\(361\) −12.2816 14.4970i −0.646401 0.762998i
\(362\) 0 0
\(363\) −5.73385 + 9.93132i −0.300949 + 0.521259i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8.91470 + 15.4407i 0.465343 + 0.805998i 0.999217 0.0395659i \(-0.0125975\pi\)
−0.533874 + 0.845564i \(0.679264\pi\)
\(368\) 0 0
\(369\) 72.5572 3.77718
\(370\) 0 0
\(371\) 2.56115 + 4.43605i 0.132968 + 0.230308i
\(372\) 0 0
\(373\) 10.3643 0.536645 0.268323 0.963329i \(-0.413531\pi\)
0.268323 + 0.963329i \(0.413531\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.70053 + 9.87361i −0.293592 + 0.508517i
\(378\) 0 0
\(379\) −13.1604 −0.676002 −0.338001 0.941146i \(-0.609751\pi\)
−0.338001 + 0.941146i \(0.609751\pi\)
\(380\) 0 0
\(381\) −4.66132 −0.238807
\(382\) 0 0
\(383\) −10.1227 + 17.5330i −0.517244 + 0.895894i 0.482555 + 0.875866i \(0.339709\pi\)
−0.999799 + 0.0200280i \(0.993624\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −75.6167 −3.84381
\(388\) 0 0
\(389\) −0.347599 0.602059i −0.0176240 0.0305256i 0.857079 0.515185i \(-0.172277\pi\)
−0.874703 + 0.484660i \(0.838944\pi\)
\(390\) 0 0
\(391\) 13.5171 0.683591
\(392\) 0 0
\(393\) 27.7609 + 48.0833i 1.40035 + 2.42548i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.16274 14.1383i 0.409676 0.709580i −0.585177 0.810906i \(-0.698975\pi\)
0.994853 + 0.101325i \(0.0323083\pi\)
\(398\) 0 0
\(399\) −24.1203 34.2746i −1.20752 1.71588i
\(400\) 0 0
\(401\) 4.19765 7.27055i 0.209621 0.363074i −0.741974 0.670428i \(-0.766110\pi\)
0.951595 + 0.307354i \(0.0994437\pi\)
\(402\) 0 0
\(403\) 14.4902 + 25.0977i 0.721807 + 1.25021i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.32503 −0.462224
\(408\) 0 0
\(409\) −2.21536 3.83711i −0.109542 0.189733i 0.806043 0.591858i \(-0.201605\pi\)
−0.915585 + 0.402125i \(0.868272\pi\)
\(410\) 0 0
\(411\) −22.1270 −1.09144
\(412\) 0 0
\(413\) 1.05645 1.82983i 0.0519847 0.0900401i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 47.6557 2.33371
\(418\) 0 0
\(419\) −2.05906 −0.100592 −0.0502958 0.998734i \(-0.516016\pi\)
−0.0502958 + 0.998734i \(0.516016\pi\)
\(420\) 0 0
\(421\) 6.71640 11.6331i 0.327337 0.566965i −0.654645 0.755936i \(-0.727182\pi\)
0.981983 + 0.188971i \(0.0605154\pi\)
\(422\) 0 0
\(423\) 18.5390 32.1104i 0.901396 1.56126i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −19.0833 33.0533i −0.923507 1.59956i
\(428\) 0 0
\(429\) 33.6657 1.62539
\(430\) 0 0
\(431\) −19.4194 33.6353i −0.935398 1.62016i −0.773923 0.633280i \(-0.781708\pi\)
−0.161475 0.986877i \(-0.551625\pi\)
\(432\) 0 0
\(433\) 1.51526 + 2.62451i 0.0728188 + 0.126126i 0.900136 0.435610i \(-0.143467\pi\)
−0.827317 + 0.561736i \(0.810134\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −31.0506 + 2.79053i −1.48535 + 0.133489i
\(438\) 0 0
\(439\) 12.6233 21.8642i 0.602477 1.04352i −0.389968 0.920829i \(-0.627514\pi\)
0.992445 0.122692i \(-0.0391529\pi\)
\(440\) 0 0
\(441\) −7.79480 13.5010i −0.371181 0.642904i
\(442\) 0 0
\(443\) 10.7494 + 18.6185i 0.510718 + 0.884590i 0.999923 + 0.0124209i \(0.00395381\pi\)
−0.489205 + 0.872169i \(0.662713\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.10423 3.64463i −0.0995265 0.172385i
\(448\) 0 0
\(449\) 24.7928 1.17004 0.585022 0.811018i \(-0.301086\pi\)
0.585022 + 0.811018i \(0.301086\pi\)
\(450\) 0 0
\(451\) −14.0192 + 24.2819i −0.660137 + 1.14339i
\(452\) 0 0
\(453\) −2.98224 + 5.16539i −0.140118 + 0.242691i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.55913 −0.166489 −0.0832444 0.996529i \(-0.526528\pi\)
−0.0832444 + 0.996529i \(0.526528\pi\)
\(458\) 0 0
\(459\) 12.0589 20.8866i 0.562859 0.974901i
\(460\) 0 0
\(461\) −4.73320 + 8.19814i −0.220447 + 0.381826i −0.954944 0.296787i \(-0.904085\pi\)
0.734497 + 0.678612i \(0.237418\pi\)
\(462\) 0 0
\(463\) −20.7465 −0.964171 −0.482085 0.876124i \(-0.660121\pi\)
−0.482085 + 0.876124i \(0.660121\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.36791 0.0632992 0.0316496 0.999499i \(-0.489924\pi\)
0.0316496 + 0.999499i \(0.489924\pi\)
\(468\) 0 0
\(469\) 1.10990 + 1.92241i 0.0512506 + 0.0887686i
\(470\) 0 0
\(471\) −13.9641 24.1864i −0.643430 1.11445i
\(472\) 0 0
\(473\) 14.6103 25.3058i 0.671783 1.16356i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.92991 10.2709i 0.271512 0.470272i
\(478\) 0 0
\(479\) −2.40085 4.15840i −0.109698 0.190002i 0.805950 0.591984i \(-0.201655\pi\)
−0.915648 + 0.401981i \(0.868322\pi\)
\(480\) 0 0
\(481\) −6.71698 11.6341i −0.306268 0.530471i
\(482\) 0 0
\(483\) −68.7690 −3.12910
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 15.1236 0.685315 0.342657 0.939460i \(-0.388673\pi\)
0.342657 + 0.939460i \(0.388673\pi\)
\(488\) 0 0
\(489\) −31.5781 + 54.6950i −1.42801 + 2.47339i
\(490\) 0 0
\(491\) −20.0731 + 34.7676i −0.905885 + 1.56904i −0.0861613 + 0.996281i \(0.527460\pi\)
−0.819724 + 0.572759i \(0.805873\pi\)
\(492\) 0 0
\(493\) −5.50604 −0.247980
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.32145 9.21702i 0.238700 0.413440i
\(498\) 0 0
\(499\) −18.2320 + 31.5788i −0.816178 + 1.41366i 0.0923011 + 0.995731i \(0.470578\pi\)
−0.908479 + 0.417930i \(0.862756\pi\)
\(500\) 0 0
\(501\) −47.0857 −2.10364
\(502\) 0 0
\(503\) −6.09897 10.5637i −0.271939 0.471013i 0.697419 0.716664i \(-0.254332\pi\)
−0.969358 + 0.245651i \(0.920998\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.66484 + 6.34768i 0.162761 + 0.281910i
\(508\) 0 0
\(509\) −4.94830 8.57071i −0.219330 0.379890i 0.735274 0.677770i \(-0.237054\pi\)
−0.954603 + 0.297880i \(0.903720\pi\)
\(510\) 0 0
\(511\) −16.8622 + 29.2062i −0.745940 + 1.29201i
\(512\) 0 0
\(513\) −23.3889 + 50.4686i −1.03264 + 2.22824i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.16403 + 12.4085i 0.315074 + 0.545724i
\(518\) 0 0
\(519\) 17.7751 + 30.7874i 0.780240 + 1.35142i
\(520\) 0 0
\(521\) 37.7004 1.65169 0.825843 0.563900i \(-0.190700\pi\)
0.825843 + 0.563900i \(0.190700\pi\)
\(522\) 0 0
\(523\) 4.49459 + 7.78487i 0.196535 + 0.340408i 0.947403 0.320044i \(-0.103698\pi\)
−0.750868 + 0.660453i \(0.770364\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.99790 + 12.1207i −0.304833 + 0.527987i
\(528\) 0 0
\(529\) −14.0771 + 24.3822i −0.612047 + 1.06010i
\(530\) 0 0
\(531\) −4.89208 −0.212298
\(532\) 0 0
\(533\) −40.3930 −1.74962
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 27.3469 47.3662i 1.18011 2.04400i
\(538\) 0 0
\(539\) 6.02431 0.259485
\(540\) 0 0
\(541\) 7.49491 + 12.9816i 0.322231 + 0.558121i 0.980948 0.194270i \(-0.0622338\pi\)
−0.658717 + 0.752391i \(0.728900\pi\)
\(542\) 0 0
\(543\) 56.1846 2.41111
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −13.9344 24.1350i −0.595790 1.03194i −0.993435 0.114400i \(-0.963506\pi\)
0.397644 0.917540i \(-0.369828\pi\)
\(548\) 0 0
\(549\) −44.1842 + 76.5293i −1.88574 + 3.26619i
\(550\) 0 0
\(551\) 12.6481 1.13669i 0.538827 0.0484245i
\(552\) 0 0
\(553\) 18.3189 31.7292i 0.778998 1.34926i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.9869 + 20.7620i 0.507903 + 0.879714i 0.999958 + 0.00914996i \(0.00291256\pi\)
−0.492055 + 0.870564i \(0.663754\pi\)
\(558\) 0 0
\(559\) 42.0963 1.78048
\(560\) 0 0
\(561\) 8.12926 + 14.0803i 0.343217 + 0.594470i
\(562\) 0 0
\(563\) 28.6346 1.20681 0.603403 0.797436i \(-0.293811\pi\)
0.603403 + 0.797436i \(0.293811\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −29.3367 + 50.8127i −1.23203 + 2.13393i
\(568\) 0 0
\(569\) −14.5588 −0.610338 −0.305169 0.952298i \(-0.598713\pi\)
−0.305169 + 0.952298i \(0.598713\pi\)
\(570\) 0 0
\(571\) 21.5089 0.900121 0.450061 0.892998i \(-0.351402\pi\)
0.450061 + 0.892998i \(0.351402\pi\)
\(572\) 0 0
\(573\) −39.7991 + 68.9341i −1.66263 + 2.87976i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 42.3885 1.76466 0.882329 0.470634i \(-0.155975\pi\)
0.882329 + 0.470634i \(0.155975\pi\)
\(578\) 0 0
\(579\) −24.1203 41.7775i −1.00240 1.73621i
\(580\) 0 0
\(581\) −34.6662 −1.43820
\(582\) 0 0
\(583\) 2.29150 + 3.96900i 0.0949042 + 0.164379i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.2971 + 24.7634i −0.590106 + 1.02209i 0.404112 + 0.914710i \(0.367581\pi\)
−0.994218 + 0.107384i \(0.965753\pi\)
\(588\) 0 0
\(589\) 13.5728 29.2875i 0.559259 1.20677i
\(590\) 0 0
\(591\) −12.9192 + 22.3767i −0.531424 + 0.920454i
\(592\) 0 0
\(593\) −3.33107 5.76958i −0.136791 0.236928i 0.789489 0.613764i \(-0.210345\pi\)
−0.926280 + 0.376836i \(0.877012\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 44.0904 1.80450
\(598\) 0 0
\(599\) −2.78523 4.82416i −0.113801 0.197110i 0.803499 0.595307i \(-0.202969\pi\)
−0.917300 + 0.398197i \(0.869636\pi\)
\(600\) 0 0
\(601\) 2.78840 0.113741 0.0568706 0.998382i \(-0.481888\pi\)
0.0568706 + 0.998382i \(0.481888\pi\)
\(602\) 0 0
\(603\) 2.56979 4.45101i 0.104650 0.181259i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 31.6698 1.28544 0.642718 0.766102i \(-0.277807\pi\)
0.642718 + 0.766102i \(0.277807\pi\)
\(608\) 0 0
\(609\) 28.0122 1.13511
\(610\) 0 0
\(611\) −10.3207 + 17.8761i −0.417533 + 0.723188i
\(612\) 0 0
\(613\) −2.75765 + 4.77639i −0.111380 + 0.192916i −0.916327 0.400431i \(-0.868861\pi\)
0.804947 + 0.593347i \(0.202194\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.21546 + 5.56934i 0.129450 + 0.224213i 0.923463 0.383686i \(-0.125346\pi\)
−0.794014 + 0.607900i \(0.792012\pi\)
\(618\) 0 0
\(619\) −40.7761 −1.63893 −0.819465 0.573130i \(-0.805729\pi\)
−0.819465 + 0.573130i \(0.805729\pi\)
\(620\) 0 0
\(621\) 45.6355 + 79.0429i 1.83129 + 3.17188i
\(622\) 0 0
\(623\) 13.1783 + 22.8255i 0.527977 + 0.914483i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −21.5808 30.6660i −0.861852 1.22468i
\(628\) 0 0
\(629\) 3.24390 5.61860i 0.129343 0.224028i
\(630\) 0 0
\(631\) 3.83753 + 6.64680i 0.152770 + 0.264605i 0.932245 0.361828i \(-0.117847\pi\)
−0.779475 + 0.626433i \(0.784514\pi\)
\(632\) 0 0
\(633\) −8.84541 15.3207i −0.351574 0.608943i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.33941 + 7.51608i 0.171934 + 0.297798i
\(638\) 0 0
\(639\) −24.6418 −0.974815
\(640\) 0 0
\(641\) 8.21362 14.2264i 0.324419 0.561910i −0.656976 0.753912i \(-0.728165\pi\)
0.981395 + 0.192002i \(0.0614980\pi\)
\(642\) 0 0
\(643\) −1.14488 + 1.98298i −0.0451495 + 0.0782013i −0.887717 0.460389i \(-0.847710\pi\)
0.842568 + 0.538591i \(0.181043\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −37.0509 −1.45662 −0.728311 0.685247i \(-0.759694\pi\)
−0.728311 + 0.685247i \(0.759694\pi\)
\(648\) 0 0
\(649\) 0.945225 1.63718i 0.0371033 0.0642648i
\(650\) 0 0
\(651\) 35.6021 61.6646i 1.39536 2.41683i
\(652\) 0 0
\(653\) −11.6500 −0.455900 −0.227950 0.973673i \(-0.573202\pi\)
−0.227950 + 0.973673i \(0.573202\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 78.0832 3.04631
\(658\) 0 0
\(659\) −6.74906 11.6897i −0.262906 0.455366i 0.704107 0.710094i \(-0.251348\pi\)
−0.967013 + 0.254728i \(0.918014\pi\)
\(660\) 0 0
\(661\) −5.57990 9.66468i −0.217033 0.375912i 0.736867 0.676038i \(-0.236305\pi\)
−0.953900 + 0.300126i \(0.902971\pi\)
\(662\) 0 0
\(663\) −11.7113 + 20.2845i −0.454829 + 0.787786i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.4185 18.0454i 0.403406 0.698720i
\(668\) 0 0
\(669\) 7.71734 + 13.3668i 0.298369 + 0.516791i
\(670\) 0 0
\(671\) −17.0741 29.5733i −0.659140 1.14166i
\(672\) 0 0
\(673\) 24.4257 0.941541 0.470770 0.882256i \(-0.343976\pi\)
0.470770 + 0.882256i \(0.343976\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −40.4552 −1.55482 −0.777409 0.628995i \(-0.783466\pi\)
−0.777409 + 0.628995i \(0.783466\pi\)
\(678\) 0 0
\(679\) −10.4280 + 18.0617i −0.400188 + 0.693146i
\(680\) 0 0
\(681\) −42.4054 + 73.4483i −1.62498 + 2.81454i
\(682\) 0 0
\(683\) 43.7736 1.67495 0.837474 0.546477i \(-0.184031\pi\)
0.837474 + 0.546477i \(0.184031\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 33.9508 58.8044i 1.29530 2.24353i
\(688\) 0 0
\(689\) −3.30121 + 5.71787i −0.125766 + 0.217833i
\(690\) 0 0
\(691\) −24.3966 −0.928091 −0.464045 0.885811i \(-0.653603\pi\)
−0.464045 + 0.885811i \(0.653603\pi\)
\(692\) 0 0
\(693\) −28.9870 50.2070i −1.10113 1.90721i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.75371 16.8939i −0.369448 0.639903i
\(698\) 0 0
\(699\) −0.145421 0.251876i −0.00550031 0.00952682i
\(700\) 0 0
\(701\) −17.0204 + 29.4802i −0.642853 + 1.11345i 0.341940 + 0.939722i \(0.388916\pi\)
−0.984793 + 0.173732i \(0.944417\pi\)
\(702\) 0 0
\(703\) −6.29174 + 13.5763i −0.237298 + 0.512042i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 21.1563 + 36.6438i 0.795664 + 1.37813i
\(708\) 0 0
\(709\) 7.29226 + 12.6306i 0.273867 + 0.474351i 0.969849 0.243708i \(-0.0783640\pi\)
−0.695982 + 0.718059i \(0.745031\pi\)
\(710\) 0 0
\(711\) −84.8285 −3.18132
\(712\) 0 0
\(713\) −26.4828 45.8696i −0.991789 1.71783i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 33.1404 57.4009i 1.23765 2.14368i
\(718\) 0 0
\(719\) 12.8694 22.2904i 0.479946 0.831291i −0.519789 0.854294i \(-0.673990\pi\)
0.999735 + 0.0230037i \(0.00732294\pi\)
\(720\) 0 0
\(721\) −29.7860 −1.10929
\(722\) 0 0
\(723\) 5.93921 0.220882
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −7.54728 + 13.0723i −0.279913 + 0.484824i −0.971363 0.237601i \(-0.923639\pi\)
0.691450 + 0.722425i \(0.256972\pi\)
\(728\) 0 0
\(729\) 14.6065 0.540982
\(730\) 0 0
\(731\) 10.1650 + 17.6063i 0.375966 + 0.651192i
\(732\) 0 0
\(733\) −47.3268 −1.74806 −0.874028 0.485875i \(-0.838501\pi\)
−0.874028 + 0.485875i \(0.838501\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.993047 + 1.72001i 0.0365794 + 0.0633573i
\(738\) 0 0
\(739\) −6.80350 + 11.7840i −0.250271 + 0.433482i −0.963600 0.267347i \(-0.913853\pi\)
0.713330 + 0.700829i \(0.247186\pi\)
\(740\) 0 0
\(741\) 22.7147 49.0140i 0.834447 1.80057i
\(742\) 0 0
\(743\) −18.7359 + 32.4514i −0.687352 + 1.19053i 0.285340 + 0.958426i \(0.407894\pi\)
−0.972692 + 0.232102i \(0.925440\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 40.1319 + 69.5104i 1.46835 + 2.54325i
\(748\) 0 0
\(749\) 38.5302 1.40786
\(750\) 0 0
\(751\) 6.17270 + 10.6914i 0.225245 + 0.390136i 0.956393 0.292083i \(-0.0943484\pi\)
−0.731148 + 0.682219i \(0.761015\pi\)
\(752\) 0 0
\(753\) 56.5671 2.06142
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −15.1799 + 26.2923i −0.551722 + 0.955610i 0.446429 + 0.894819i \(0.352696\pi\)
−0.998151 + 0.0607908i \(0.980638\pi\)
\(758\) 0 0
\(759\) −61.5286 −2.23335
\(760\) 0 0
\(761\) 7.80837 0.283053 0.141527 0.989934i \(-0.454799\pi\)
0.141527 + 0.989934i \(0.454799\pi\)
\(762\) 0 0
\(763\) −11.6915 + 20.2502i −0.423259 + 0.733106i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.72345 0.0983379
\(768\) 0 0
\(769\) −21.5971 37.4073i −0.778811 1.34894i −0.932627 0.360841i \(-0.882490\pi\)
0.153816 0.988099i \(-0.450844\pi\)
\(770\) 0 0
\(771\) 95.6338 3.44417
\(772\) 0 0
\(773\) −9.12048 15.7971i −0.328041 0.568183i 0.654082 0.756423i \(-0.273055\pi\)
−0.982123 + 0.188240i \(0.939722\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −16.5035 + 28.5849i −0.592059 + 1.02548i
\(778\) 0 0
\(779\) 25.8932 + 36.7940i 0.927720 + 1.31828i
\(780\) 0 0
\(781\) 4.76118 8.24661i 0.170368 0.295087i
\(782\) 0 0
\(783\) −18.5890 32.1972i −0.664318 1.15063i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −42.8266 −1.52660 −0.763302 0.646042i \(-0.776423\pi\)
−0.763302 + 0.646042i \(0.776423\pi\)
\(788\) 0 0
\(789\) −33.7872 58.5212i −1.20286 2.08341i
\(790\) 0 0
\(791\) −39.0245 −1.38755
\(792\) 0 0
\(793\) 24.5976 42.6043i 0.873486 1.51292i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −51.5064 −1.82445 −0.912225 0.409689i \(-0.865637\pi\)
−0.912225 + 0.409689i \(0.865637\pi\)
\(798\) 0 0
\(799\) −9.96862 −0.352664
\(800\) 0 0
\(801\) 30.5121 52.8485i 1.07809 1.86731i
\(802\) 0 0