Properties

Label 1800.2.d.p.1549.1
Level $1800$
Weight $2$
Character 1800.1549
Analytic conductor $14.373$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3730723638\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1549.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1800.1549
Dual form 1800.2.d.p.1549.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} -0.732051i q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} -0.732051i q^{7} +(2.00000 + 2.00000i) q^{8} -2.00000i q^{11} -3.46410 q^{13} +(-1.00000 + 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} +3.46410i q^{17} +0.535898i q^{19} +(-2.73205 + 0.732051i) q^{22} +6.19615i q^{23} +(1.26795 + 4.73205i) q^{26} +(0.732051 + 1.26795i) q^{28} -6.92820i q^{29} -5.46410 q^{31} +(-5.46410 - 1.46410i) q^{32} +(4.73205 - 1.26795i) q^{34} +2.00000 q^{37} +(0.732051 - 0.196152i) q^{38} -1.46410 q^{41} -5.26795 q^{43} +(2.00000 + 3.46410i) q^{44} +(8.46410 - 2.26795i) q^{46} +3.26795i q^{47} +6.46410 q^{49} +(6.00000 - 3.46410i) q^{52} -11.4641 q^{53} +(1.46410 - 1.46410i) q^{56} +(-9.46410 + 2.53590i) q^{58} +7.46410i q^{59} +8.92820i q^{61} +(2.00000 + 7.46410i) q^{62} +8.00000i q^{64} -10.7321 q^{67} +(-3.46410 - 6.00000i) q^{68} -5.46410 q^{71} +7.46410i q^{73} +(-0.732051 - 2.73205i) q^{74} +(-0.535898 - 0.928203i) q^{76} -1.46410 q^{77} +1.07180 q^{79} +(0.535898 + 2.00000i) q^{82} -1.26795 q^{83} +(1.92820 + 7.19615i) q^{86} +(4.00000 - 4.00000i) q^{88} +8.92820 q^{89} +2.53590i q^{91} +(-6.19615 - 10.7321i) q^{92} +(4.46410 - 1.19615i) q^{94} +14.3923i q^{97} +(-2.36603 - 8.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 8 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} + 8 q^{8} - 4 q^{14} + 8 q^{16} - 4 q^{22} + 12 q^{26} - 4 q^{28} - 8 q^{31} - 8 q^{32} + 12 q^{34} + 8 q^{37} - 4 q^{38} + 8 q^{41} - 28 q^{43} + 8 q^{44} + 20 q^{46} + 12 q^{49} + 24 q^{52} - 32 q^{53} - 8 q^{56} - 24 q^{58} + 8 q^{62} - 36 q^{67} - 8 q^{71} + 4 q^{74} - 16 q^{76} + 8 q^{77} + 32 q^{79} + 16 q^{82} - 12 q^{83} - 20 q^{86} + 16 q^{88} + 8 q^{89} - 4 q^{92} + 4 q^{94} - 6 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.36603i −0.258819 0.965926i
\(3\) 0 0
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.732051i 0.276689i −0.990384 0.138345i \(-0.955822\pi\)
0.990384 0.138345i \(-0.0441781\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 0 0
\(13\) −3.46410 −0.960769 −0.480384 0.877058i \(-0.659503\pi\)
−0.480384 + 0.877058i \(0.659503\pi\)
\(14\) −1.00000 + 0.267949i −0.267261 + 0.0716124i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 3.46410i 0.840168i 0.907485 + 0.420084i \(0.137999\pi\)
−0.907485 + 0.420084i \(0.862001\pi\)
\(18\) 0 0
\(19\) 0.535898i 0.122944i 0.998109 + 0.0614718i \(0.0195794\pi\)
−0.998109 + 0.0614718i \(0.980421\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.73205 + 0.732051i −0.582475 + 0.156074i
\(23\) 6.19615i 1.29199i 0.763343 + 0.645994i \(0.223557\pi\)
−0.763343 + 0.645994i \(0.776443\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.26795 + 4.73205i 0.248665 + 0.928032i
\(27\) 0 0
\(28\) 0.732051 + 1.26795i 0.138345 + 0.239620i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) 0 0
\(31\) −5.46410 −0.981382 −0.490691 0.871334i \(-0.663256\pi\)
−0.490691 + 0.871334i \(0.663256\pi\)
\(32\) −5.46410 1.46410i −0.965926 0.258819i
\(33\) 0 0
\(34\) 4.73205 1.26795i 0.811540 0.217451i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0.732051 0.196152i 0.118754 0.0318201i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.46410 −0.228654 −0.114327 0.993443i \(-0.536471\pi\)
−0.114327 + 0.993443i \(0.536471\pi\)
\(42\) 0 0
\(43\) −5.26795 −0.803355 −0.401677 0.915781i \(-0.631573\pi\)
−0.401677 + 0.915781i \(0.631573\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 0 0
\(46\) 8.46410 2.26795i 1.24796 0.334391i
\(47\) 3.26795i 0.476679i 0.971182 + 0.238340i \(0.0766032\pi\)
−0.971182 + 0.238340i \(0.923397\pi\)
\(48\) 0 0
\(49\) 6.46410 0.923443
\(50\) 0 0
\(51\) 0 0
\(52\) 6.00000 3.46410i 0.832050 0.480384i
\(53\) −11.4641 −1.57472 −0.787358 0.616496i \(-0.788551\pi\)
−0.787358 + 0.616496i \(0.788551\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.46410 1.46410i 0.195649 0.195649i
\(57\) 0 0
\(58\) −9.46410 + 2.53590i −1.24270 + 0.332980i
\(59\) 7.46410i 0.971743i 0.874030 + 0.485872i \(0.161498\pi\)
−0.874030 + 0.485872i \(0.838502\pi\)
\(60\) 0 0
\(61\) 8.92820i 1.14314i 0.820554 + 0.571570i \(0.193665\pi\)
−0.820554 + 0.571570i \(0.806335\pi\)
\(62\) 2.00000 + 7.46410i 0.254000 + 0.947942i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) −10.7321 −1.31113 −0.655564 0.755139i \(-0.727569\pi\)
−0.655564 + 0.755139i \(0.727569\pi\)
\(68\) −3.46410 6.00000i −0.420084 0.727607i
\(69\) 0 0
\(70\) 0 0
\(71\) −5.46410 −0.648470 −0.324235 0.945977i \(-0.605107\pi\)
−0.324235 + 0.945977i \(0.605107\pi\)
\(72\) 0 0
\(73\) 7.46410i 0.873607i 0.899557 + 0.436804i \(0.143889\pi\)
−0.899557 + 0.436804i \(0.856111\pi\)
\(74\) −0.732051 2.73205i −0.0850992 0.317594i
\(75\) 0 0
\(76\) −0.535898 0.928203i −0.0614718 0.106472i
\(77\) −1.46410 −0.166850
\(78\) 0 0
\(79\) 1.07180 0.120587 0.0602933 0.998181i \(-0.480796\pi\)
0.0602933 + 0.998181i \(0.480796\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0.535898 + 2.00000i 0.0591801 + 0.220863i
\(83\) −1.26795 −0.139176 −0.0695878 0.997576i \(-0.522168\pi\)
−0.0695878 + 0.997576i \(0.522168\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.92820 + 7.19615i 0.207924 + 0.775981i
\(87\) 0 0
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) 8.92820 0.946388 0.473194 0.880958i \(-0.343101\pi\)
0.473194 + 0.880958i \(0.343101\pi\)
\(90\) 0 0
\(91\) 2.53590i 0.265834i
\(92\) −6.19615 10.7321i −0.645994 1.11889i
\(93\) 0 0
\(94\) 4.46410 1.19615i 0.460437 0.123374i
\(95\) 0 0
\(96\) 0 0
\(97\) 14.3923i 1.46132i 0.682743 + 0.730659i \(0.260787\pi\)
−0.682743 + 0.730659i \(0.739213\pi\)
\(98\) −2.36603 8.83013i −0.239005 0.891978i
\(99\) 0 0
\(100\) 0 0
\(101\) 2.92820i 0.291367i 0.989331 + 0.145684i \(0.0465381\pi\)
−0.989331 + 0.145684i \(0.953462\pi\)
\(102\) 0 0
\(103\) 15.6603i 1.54305i 0.636199 + 0.771525i \(0.280506\pi\)
−0.636199 + 0.771525i \(0.719494\pi\)
\(104\) −6.92820 6.92820i −0.679366 0.679366i
\(105\) 0 0
\(106\) 4.19615 + 15.6603i 0.407566 + 1.52106i
\(107\) 2.73205 0.264117 0.132059 0.991242i \(-0.457841\pi\)
0.132059 + 0.991242i \(0.457841\pi\)
\(108\) 0 0
\(109\) 16.9282i 1.62143i 0.585443 + 0.810714i \(0.300921\pi\)
−0.585443 + 0.810714i \(0.699079\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.53590 1.46410i −0.239620 0.138345i
\(113\) 12.9282i 1.21618i 0.793867 + 0.608092i \(0.208065\pi\)
−0.793867 + 0.608092i \(0.791935\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.92820 + 12.0000i 0.643268 + 1.11417i
\(117\) 0 0
\(118\) 10.1962 2.73205i 0.938632 0.251506i
\(119\) 2.53590 0.232465
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 12.1962 3.26795i 1.10419 0.295866i
\(123\) 0 0
\(124\) 9.46410 5.46410i 0.849901 0.490691i
\(125\) 0 0
\(126\) 0 0
\(127\) 16.7321i 1.48473i −0.669996 0.742365i \(-0.733704\pi\)
0.669996 0.742365i \(-0.266296\pi\)
\(128\) 10.9282 2.92820i 0.965926 0.258819i
\(129\) 0 0
\(130\) 0 0
\(131\) 19.8564i 1.73486i −0.497557 0.867431i \(-0.665770\pi\)
0.497557 0.867431i \(-0.334230\pi\)
\(132\) 0 0
\(133\) 0.392305 0.0340171
\(134\) 3.92820 + 14.6603i 0.339345 + 1.26645i
\(135\) 0 0
\(136\) −6.92820 + 6.92820i −0.594089 + 0.594089i
\(137\) 4.92820i 0.421045i 0.977589 + 0.210522i \(0.0675165\pi\)
−0.977589 + 0.210522i \(0.932484\pi\)
\(138\) 0 0
\(139\) 0.535898i 0.0454543i −0.999742 0.0227272i \(-0.992765\pi\)
0.999742 0.0227272i \(-0.00723490\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.00000 + 7.46410i 0.167836 + 0.626373i
\(143\) 6.92820i 0.579365i
\(144\) 0 0
\(145\) 0 0
\(146\) 10.1962 2.73205i 0.843840 0.226106i
\(147\) 0 0
\(148\) −3.46410 + 2.00000i −0.284747 + 0.164399i
\(149\) 7.85641i 0.643622i 0.946804 + 0.321811i \(0.104292\pi\)
−0.946804 + 0.321811i \(0.895708\pi\)
\(150\) 0 0
\(151\) −12.3923 −1.00847 −0.504236 0.863566i \(-0.668226\pi\)
−0.504236 + 0.863566i \(0.668226\pi\)
\(152\) −1.07180 + 1.07180i −0.0869342 + 0.0869342i
\(153\) 0 0
\(154\) 0.535898 + 2.00000i 0.0431839 + 0.161165i
\(155\) 0 0
\(156\) 0 0
\(157\) 3.07180 0.245156 0.122578 0.992459i \(-0.460884\pi\)
0.122578 + 0.992459i \(0.460884\pi\)
\(158\) −0.392305 1.46410i −0.0312101 0.116478i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.53590 0.357479
\(162\) 0 0
\(163\) −0.196152 −0.0153638 −0.00768192 0.999970i \(-0.502445\pi\)
−0.00768192 + 0.999970i \(0.502445\pi\)
\(164\) 2.53590 1.46410i 0.198020 0.114327i
\(165\) 0 0
\(166\) 0.464102 + 1.73205i 0.0360213 + 0.134433i
\(167\) 9.80385i 0.758645i −0.925265 0.379322i \(-0.876157\pi\)
0.925265 0.379322i \(-0.123843\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 9.12436 5.26795i 0.695726 0.401677i
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.92820 4.00000i −0.522233 0.301511i
\(177\) 0 0
\(178\) −3.26795 12.1962i −0.244943 0.914140i
\(179\) 8.53590i 0.638003i 0.947754 + 0.319002i \(0.103348\pi\)
−0.947754 + 0.319002i \(0.896652\pi\)
\(180\) 0 0
\(181\) 16.0000i 1.18927i −0.803996 0.594635i \(-0.797296\pi\)
0.803996 0.594635i \(-0.202704\pi\)
\(182\) 3.46410 0.928203i 0.256776 0.0688030i
\(183\) 0 0
\(184\) −12.3923 + 12.3923i −0.913573 + 0.913573i
\(185\) 0 0
\(186\) 0 0
\(187\) 6.92820 0.506640
\(188\) −3.26795 5.66025i −0.238340 0.412816i
\(189\) 0 0
\(190\) 0 0
\(191\) −15.3205 −1.10855 −0.554277 0.832333i \(-0.687005\pi\)
−0.554277 + 0.832333i \(0.687005\pi\)
\(192\) 0 0
\(193\) 0.535898i 0.0385748i 0.999814 + 0.0192874i \(0.00613975\pi\)
−0.999814 + 0.0192874i \(0.993860\pi\)
\(194\) 19.6603 5.26795i 1.41152 0.378217i
\(195\) 0 0
\(196\) −11.1962 + 6.46410i −0.799725 + 0.461722i
\(197\) −19.4641 −1.38676 −0.693380 0.720572i \(-0.743879\pi\)
−0.693380 + 0.720572i \(0.743879\pi\)
\(198\) 0 0
\(199\) 1.85641 0.131597 0.0657986 0.997833i \(-0.479041\pi\)
0.0657986 + 0.997833i \(0.479041\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 4.00000 1.07180i 0.281439 0.0754114i
\(203\) −5.07180 −0.355970
\(204\) 0 0
\(205\) 0 0
\(206\) 21.3923 5.73205i 1.49047 0.399371i
\(207\) 0 0
\(208\) −6.92820 + 12.0000i −0.480384 + 0.832050i
\(209\) 1.07180 0.0741377
\(210\) 0 0
\(211\) 26.7846i 1.84393i −0.387275 0.921964i \(-0.626584\pi\)
0.387275 0.921964i \(-0.373416\pi\)
\(212\) 19.8564 11.4641i 1.36374 0.787358i
\(213\) 0 0
\(214\) −1.00000 3.73205i −0.0683586 0.255118i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.00000i 0.271538i
\(218\) 23.1244 6.19615i 1.56618 0.419656i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000i 0.807207i
\(222\) 0 0
\(223\) 5.80385i 0.388654i −0.980937 0.194327i \(-0.937748\pi\)
0.980937 0.194327i \(-0.0622523\pi\)
\(224\) −1.07180 + 4.00000i −0.0716124 + 0.267261i
\(225\) 0 0
\(226\) 17.6603 4.73205i 1.17474 0.314771i
\(227\) 10.0526 0.667212 0.333606 0.942713i \(-0.391735\pi\)
0.333606 + 0.942713i \(0.391735\pi\)
\(228\) 0 0
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 13.8564 13.8564i 0.909718 0.909718i
\(233\) 5.32051i 0.348558i 0.984696 + 0.174279i \(0.0557595\pi\)
−0.984696 + 0.174279i \(0.944241\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −7.46410 12.9282i −0.485872 0.841554i
\(237\) 0 0
\(238\) −0.928203 3.46410i −0.0601665 0.224544i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) 16.3923 1.05592 0.527961 0.849269i \(-0.322957\pi\)
0.527961 + 0.849269i \(0.322957\pi\)
\(242\) −2.56218 9.56218i −0.164703 0.614680i
\(243\) 0 0
\(244\) −8.92820 15.4641i −0.571570 0.989988i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.85641i 0.118120i
\(248\) −10.9282 10.9282i −0.693942 0.693942i
\(249\) 0 0
\(250\) 0 0
\(251\) 24.9282i 1.57345i 0.617301 + 0.786727i \(0.288226\pi\)
−0.617301 + 0.786727i \(0.711774\pi\)
\(252\) 0 0
\(253\) 12.3923 0.779098
\(254\) −22.8564 + 6.12436i −1.43414 + 0.384276i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 2.00000i 0.124757i −0.998053 0.0623783i \(-0.980131\pi\)
0.998053 0.0623783i \(-0.0198685\pi\)
\(258\) 0 0
\(259\) 1.46410i 0.0909748i
\(260\) 0 0
\(261\) 0 0
\(262\) −27.1244 + 7.26795i −1.67575 + 0.449015i
\(263\) 11.6603i 0.719002i 0.933145 + 0.359501i \(0.117053\pi\)
−0.933145 + 0.359501i \(0.882947\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.143594 0.535898i −0.00880428 0.0328580i
\(267\) 0 0
\(268\) 18.5885 10.7321i 1.13547 0.655564i
\(269\) 8.92820i 0.544362i 0.962246 + 0.272181i \(0.0877450\pi\)
−0.962246 + 0.272181i \(0.912255\pi\)
\(270\) 0 0
\(271\) −19.3205 −1.17364 −0.586819 0.809718i \(-0.699620\pi\)
−0.586819 + 0.809718i \(0.699620\pi\)
\(272\) 12.0000 + 6.92820i 0.727607 + 0.420084i
\(273\) 0 0
\(274\) 6.73205 1.80385i 0.406698 0.108974i
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −0.732051 + 0.196152i −0.0439055 + 0.0117644i
\(279\) 0 0
\(280\) 0 0
\(281\) −10.5359 −0.628519 −0.314260 0.949337i \(-0.601756\pi\)
−0.314260 + 0.949337i \(0.601756\pi\)
\(282\) 0 0
\(283\) −9.66025 −0.574242 −0.287121 0.957894i \(-0.592698\pi\)
−0.287121 + 0.957894i \(0.592698\pi\)
\(284\) 9.46410 5.46410i 0.561591 0.324235i
\(285\) 0 0
\(286\) 9.46410 2.53590i 0.559624 0.149951i
\(287\) 1.07180i 0.0632662i
\(288\) 0 0
\(289\) 5.00000 0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) −7.46410 12.9282i −0.436804 0.756566i
\(293\) 15.8564 0.926341 0.463171 0.886269i \(-0.346712\pi\)
0.463171 + 0.886269i \(0.346712\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.00000 + 4.00000i 0.232495 + 0.232495i
\(297\) 0 0
\(298\) 10.7321 2.87564i 0.621691 0.166582i
\(299\) 21.4641i 1.24130i
\(300\) 0 0
\(301\) 3.85641i 0.222280i
\(302\) 4.53590 + 16.9282i 0.261012 + 0.974109i
\(303\) 0 0
\(304\) 1.85641 + 1.07180i 0.106472 + 0.0614718i
\(305\) 0 0
\(306\) 0 0
\(307\) 24.9808 1.42573 0.712864 0.701303i \(-0.247398\pi\)
0.712864 + 0.701303i \(0.247398\pi\)
\(308\) 2.53590 1.46410i 0.144496 0.0834249i
\(309\) 0 0
\(310\) 0 0
\(311\) −31.3205 −1.77602 −0.888012 0.459821i \(-0.847914\pi\)
−0.888012 + 0.459821i \(0.847914\pi\)
\(312\) 0 0
\(313\) 4.14359i 0.234210i −0.993120 0.117105i \(-0.962639\pi\)
0.993120 0.117105i \(-0.0373614\pi\)
\(314\) −1.12436 4.19615i −0.0634511 0.236803i
\(315\) 0 0
\(316\) −1.85641 + 1.07180i −0.104431 + 0.0602933i
\(317\) 8.53590 0.479424 0.239712 0.970844i \(-0.422947\pi\)
0.239712 + 0.970844i \(0.422947\pi\)
\(318\) 0 0
\(319\) −13.8564 −0.775810
\(320\) 0 0
\(321\) 0 0
\(322\) −1.66025 6.19615i −0.0925223 0.345298i
\(323\) −1.85641 −0.103293
\(324\) 0 0
\(325\) 0 0
\(326\) 0.0717968 + 0.267949i 0.00397646 + 0.0148403i
\(327\) 0 0
\(328\) −2.92820 2.92820i −0.161683 0.161683i
\(329\) 2.39230 0.131892
\(330\) 0 0
\(331\) 14.0000i 0.769510i 0.923019 + 0.384755i \(0.125714\pi\)
−0.923019 + 0.384755i \(0.874286\pi\)
\(332\) 2.19615 1.26795i 0.120530 0.0695878i
\(333\) 0 0
\(334\) −13.3923 + 3.58846i −0.732794 + 0.196352i
\(335\) 0 0
\(336\) 0 0
\(337\) 19.8564i 1.08165i 0.841136 + 0.540824i \(0.181887\pi\)
−0.841136 + 0.540824i \(0.818113\pi\)
\(338\) 0.366025 + 1.36603i 0.0199092 + 0.0743020i
\(339\) 0 0
\(340\) 0 0
\(341\) 10.9282i 0.591795i
\(342\) 0 0
\(343\) 9.85641i 0.532196i
\(344\) −10.5359 10.5359i −0.568058 0.568058i
\(345\) 0 0
\(346\) 0.732051 + 2.73205i 0.0393553 + 0.146876i
\(347\) −1.66025 −0.0891271 −0.0445636 0.999007i \(-0.514190\pi\)
−0.0445636 + 0.999007i \(0.514190\pi\)
\(348\) 0 0
\(349\) 28.0000i 1.49881i −0.662114 0.749403i \(-0.730341\pi\)
0.662114 0.749403i \(-0.269659\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.92820 + 10.9282i −0.156074 + 0.582475i
\(353\) 12.9282i 0.688099i −0.938952 0.344049i \(-0.888201\pi\)
0.938952 0.344049i \(-0.111799\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −15.4641 + 8.92820i −0.819596 + 0.473194i
\(357\) 0 0
\(358\) 11.6603 3.12436i 0.616264 0.165127i
\(359\) 18.9282 0.998992 0.499496 0.866316i \(-0.333518\pi\)
0.499496 + 0.866316i \(0.333518\pi\)
\(360\) 0 0
\(361\) 18.7128 0.984885
\(362\) −21.8564 + 5.85641i −1.14875 + 0.307806i
\(363\) 0 0
\(364\) −2.53590 4.39230i −0.132917 0.230219i
\(365\) 0 0
\(366\) 0 0
\(367\) 2.87564i 0.150107i −0.997179 0.0750537i \(-0.976087\pi\)
0.997179 0.0750537i \(-0.0239128\pi\)
\(368\) 21.4641 + 12.3923i 1.11889 + 0.645994i
\(369\) 0 0
\(370\) 0 0
\(371\) 8.39230i 0.435707i
\(372\) 0 0
\(373\) −25.7128 −1.33136 −0.665679 0.746238i \(-0.731858\pi\)
−0.665679 + 0.746238i \(0.731858\pi\)
\(374\) −2.53590 9.46410i −0.131128 0.489377i
\(375\) 0 0
\(376\) −6.53590 + 6.53590i −0.337063 + 0.337063i
\(377\) 24.0000i 1.23606i
\(378\) 0 0
\(379\) 36.2487i 1.86197i −0.365056 0.930986i \(-0.618950\pi\)
0.365056 0.930986i \(-0.381050\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 5.60770 + 20.9282i 0.286915 + 1.07078i
\(383\) 21.1244i 1.07940i −0.841856 0.539702i \(-0.818537\pi\)
0.841856 0.539702i \(-0.181463\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.732051 0.196152i 0.0372604 0.00998390i
\(387\) 0 0
\(388\) −14.3923 24.9282i −0.730659 1.26554i
\(389\) 6.78461i 0.343993i −0.985098 0.171997i \(-0.944978\pi\)
0.985098 0.171997i \(-0.0550218\pi\)
\(390\) 0 0
\(391\) −21.4641 −1.08549
\(392\) 12.9282 + 12.9282i 0.652973 + 0.652973i
\(393\) 0 0
\(394\) 7.12436 + 26.5885i 0.358920 + 1.33951i
\(395\) 0 0
\(396\) 0 0
\(397\) −32.2487 −1.61852 −0.809258 0.587453i \(-0.800131\pi\)
−0.809258 + 0.587453i \(0.800131\pi\)
\(398\) −0.679492 2.53590i −0.0340599 0.127113i
\(399\) 0 0
\(400\) 0 0
\(401\) 7.85641 0.392330 0.196165 0.980571i \(-0.437151\pi\)
0.196165 + 0.980571i \(0.437151\pi\)
\(402\) 0 0
\(403\) 18.9282 0.942881
\(404\) −2.92820 5.07180i −0.145684 0.252331i
\(405\) 0 0
\(406\) 1.85641 + 6.92820i 0.0921319 + 0.343841i
\(407\) 4.00000i 0.198273i
\(408\) 0 0
\(409\) 11.3205 0.559763 0.279882 0.960035i \(-0.409705\pi\)
0.279882 + 0.960035i \(0.409705\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −15.6603 27.1244i −0.771525 1.33632i
\(413\) 5.46410 0.268871
\(414\) 0 0
\(415\) 0 0
\(416\) 18.9282 + 5.07180i 0.928032 + 0.248665i
\(417\) 0 0
\(418\) −0.392305 1.46410i −0.0191883 0.0716116i
\(419\) 18.3923i 0.898523i −0.893400 0.449261i \(-0.851687\pi\)
0.893400 0.449261i \(-0.148313\pi\)
\(420\) 0 0
\(421\) 0.143594i 0.00699832i −0.999994 0.00349916i \(-0.998886\pi\)
0.999994 0.00349916i \(-0.00111382\pi\)
\(422\) −36.5885 + 9.80385i −1.78110 + 0.477244i
\(423\) 0 0
\(424\) −22.9282 22.9282i −1.11349 1.11349i
\(425\) 0 0
\(426\) 0 0
\(427\) 6.53590 0.316294
\(428\) −4.73205 + 2.73205i −0.228732 + 0.132059i
\(429\) 0 0
\(430\) 0 0
\(431\) 21.4641 1.03389 0.516945 0.856019i \(-0.327069\pi\)
0.516945 + 0.856019i \(0.327069\pi\)
\(432\) 0 0
\(433\) 19.4641i 0.935385i −0.883891 0.467693i \(-0.845085\pi\)
0.883891 0.467693i \(-0.154915\pi\)
\(434\) 5.46410 1.46410i 0.262285 0.0702791i
\(435\) 0 0
\(436\) −16.9282 29.3205i −0.810714 1.40420i
\(437\) −3.32051 −0.158841
\(438\) 0 0
\(439\) −40.7846 −1.94654 −0.973272 0.229657i \(-0.926240\pi\)
−0.973272 + 0.229657i \(0.926240\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −16.3923 + 4.39230i −0.779702 + 0.208921i
\(443\) −20.9808 −0.996826 −0.498413 0.866940i \(-0.666084\pi\)
−0.498413 + 0.866940i \(0.666084\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −7.92820 + 2.12436i −0.375411 + 0.100591i
\(447\) 0 0
\(448\) 5.85641 0.276689
\(449\) −23.3205 −1.10056 −0.550281 0.834979i \(-0.685480\pi\)
−0.550281 + 0.834979i \(0.685480\pi\)
\(450\) 0 0
\(451\) 2.92820i 0.137884i
\(452\) −12.9282 22.3923i −0.608092 1.05325i
\(453\) 0 0
\(454\) −3.67949 13.7321i −0.172687 0.644477i
\(455\) 0 0
\(456\) 0 0
\(457\) 26.7846i 1.25293i 0.779449 + 0.626466i \(0.215499\pi\)
−0.779449 + 0.626466i \(0.784501\pi\)
\(458\) −5.46410 + 1.46410i −0.255321 + 0.0684130i
\(459\) 0 0
\(460\) 0 0
\(461\) 10.9282i 0.508977i −0.967076 0.254489i \(-0.918093\pi\)
0.967076 0.254489i \(-0.0819071\pi\)
\(462\) 0 0
\(463\) 11.2679i 0.523666i −0.965113 0.261833i \(-0.915673\pi\)
0.965113 0.261833i \(-0.0843270\pi\)
\(464\) −24.0000 13.8564i −1.11417 0.643268i
\(465\) 0 0
\(466\) 7.26795 1.94744i 0.336681 0.0902135i
\(467\) −25.6603 −1.18741 −0.593707 0.804681i \(-0.702336\pi\)
−0.593707 + 0.804681i \(0.702336\pi\)
\(468\) 0 0
\(469\) 7.85641i 0.362775i
\(470\) 0 0
\(471\) 0 0
\(472\) −14.9282 + 14.9282i −0.687126 + 0.687126i
\(473\) 10.5359i 0.484441i
\(474\) 0 0
\(475\) 0 0
\(476\) −4.39230 + 2.53590i −0.201321 + 0.116233i
\(477\) 0 0
\(478\) 7.32051 + 27.3205i 0.334832 + 1.24961i
\(479\) 5.85641 0.267586 0.133793 0.991009i \(-0.457284\pi\)
0.133793 + 0.991009i \(0.457284\pi\)
\(480\) 0 0
\(481\) −6.92820 −0.315899
\(482\) −6.00000 22.3923i −0.273293 1.01994i
\(483\) 0 0
\(484\) −12.1244 + 7.00000i −0.551107 + 0.318182i
\(485\) 0 0
\(486\) 0 0
\(487\) 6.58846i 0.298551i −0.988796 0.149276i \(-0.952306\pi\)
0.988796 0.149276i \(-0.0476942\pi\)
\(488\) −17.8564 + 17.8564i −0.808322 + 0.808322i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.9282i 0.763959i −0.924171 0.381980i \(-0.875242\pi\)
0.924171 0.381980i \(-0.124758\pi\)
\(492\) 0 0
\(493\) 24.0000 1.08091
\(494\) −2.53590 + 0.679492i −0.114095 + 0.0305718i
\(495\) 0 0
\(496\) −10.9282 + 18.9282i −0.490691 + 0.849901i
\(497\) 4.00000i 0.179425i
\(498\) 0 0
\(499\) 31.4641i 1.40853i 0.709939 + 0.704263i \(0.248723\pi\)
−0.709939 + 0.704263i \(0.751277\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 34.0526 9.12436i 1.51984 0.407240i
\(503\) 0.339746i 0.0151485i 0.999971 + 0.00757426i \(0.00241099\pi\)
−0.999971 + 0.00757426i \(0.997589\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.53590 16.9282i −0.201645 0.752550i
\(507\) 0 0
\(508\) 16.7321 + 28.9808i 0.742365 + 1.28581i
\(509\) 1.85641i 0.0822838i 0.999153 + 0.0411419i \(0.0130996\pi\)
−0.999153 + 0.0411419i \(0.986900\pi\)
\(510\) 0 0
\(511\) 5.46410 0.241718
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 0 0
\(514\) −2.73205 + 0.732051i −0.120506 + 0.0322894i
\(515\) 0 0
\(516\) 0 0
\(517\) 6.53590 0.287448
\(518\) −2.00000 + 0.535898i −0.0878750 + 0.0235460i
\(519\) 0 0
\(520\) 0 0
\(521\) 43.8564 1.92138 0.960692 0.277616i \(-0.0895444\pi\)
0.960692 + 0.277616i \(0.0895444\pi\)
\(522\) 0 0
\(523\) −11.8038 −0.516146 −0.258073 0.966125i \(-0.583088\pi\)
−0.258073 + 0.966125i \(0.583088\pi\)
\(524\) 19.8564 + 34.3923i 0.867431 + 1.50243i
\(525\) 0 0
\(526\) 15.9282 4.26795i 0.694503 0.186091i
\(527\) 18.9282i 0.824525i
\(528\) 0 0
\(529\) −15.3923 −0.669231
\(530\) 0 0
\(531\) 0 0
\(532\) −0.679492 + 0.392305i −0.0294597 + 0.0170086i
\(533\) 5.07180 0.219684
\(534\) 0 0
\(535\) 0 0
\(536\) −21.4641 21.4641i −0.927108 0.927108i
\(537\) 0 0
\(538\) 12.1962 3.26795i 0.525813 0.140891i
\(539\) 12.9282i 0.556857i
\(540\) 0 0
\(541\) 26.9282i 1.15773i 0.815422 + 0.578867i \(0.196505\pi\)
−0.815422 + 0.578867i \(0.803495\pi\)
\(542\) 7.07180 + 26.3923i 0.303760 + 1.13365i
\(543\) 0 0
\(544\) 5.07180 18.9282i 0.217451 0.811540i
\(545\) 0 0
\(546\) 0 0
\(547\) −33.2679 −1.42243 −0.711217 0.702972i \(-0.751856\pi\)
−0.711217 + 0.702972i \(0.751856\pi\)
\(548\) −4.92820 8.53590i −0.210522 0.364636i
\(549\) 0 0
\(550\) 0 0
\(551\) 3.71281 0.158171
\(552\) 0 0
\(553\) 0.784610i 0.0333650i
\(554\) 0.732051 + 2.73205i 0.0311019 + 0.116074i
\(555\) 0 0
\(556\) 0.535898 + 0.928203i 0.0227272 + 0.0393646i
\(557\) 14.7846 0.626444 0.313222 0.949680i \(-0.398592\pi\)
0.313222 + 0.949680i \(0.398592\pi\)
\(558\) 0 0
\(559\) 18.2487 0.771838
\(560\) 0 0
\(561\) 0 0
\(562\) 3.85641 + 14.3923i 0.162673 + 0.607103i
\(563\) 22.0526 0.929405 0.464702 0.885467i \(-0.346161\pi\)
0.464702 + 0.885467i \(0.346161\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 3.53590 + 13.1962i 0.148625 + 0.554676i
\(567\) 0 0
\(568\) −10.9282 10.9282i −0.458537 0.458537i
\(569\) −13.4641 −0.564445 −0.282222 0.959349i \(-0.591072\pi\)
−0.282222 + 0.959349i \(0.591072\pi\)
\(570\) 0 0
\(571\) 6.78461i 0.283927i −0.989872 0.141964i \(-0.954658\pi\)
0.989872 0.141964i \(-0.0453416\pi\)
\(572\) −6.92820 12.0000i −0.289683 0.501745i
\(573\) 0 0
\(574\) 1.46410 0.392305i 0.0611104 0.0163745i
\(575\) 0 0
\(576\) 0 0
\(577\) 39.5692i 1.64729i −0.567107 0.823644i \(-0.691937\pi\)
0.567107 0.823644i \(-0.308063\pi\)
\(578\) −1.83013 6.83013i −0.0761232 0.284096i
\(579\) 0 0
\(580\) 0 0
\(581\) 0.928203i 0.0385084i
\(582\) 0 0
\(583\) 22.9282i 0.949589i
\(584\) −14.9282 + 14.9282i −0.617733 + 0.617733i
\(585\) 0 0
\(586\) −5.80385 21.6603i −0.239755 0.894777i
\(587\) −3.80385 −0.157002 −0.0785008 0.996914i \(-0.525013\pi\)
−0.0785008 + 0.996914i \(0.525013\pi\)
\(588\) 0 0
\(589\) 2.92820i 0.120655i
\(590\) 0 0
\(591\) 0 0
\(592\) 4.00000 6.92820i 0.164399 0.284747i
\(593\) 32.6410i 1.34041i −0.742178 0.670203i \(-0.766207\pi\)
0.742178 0.670203i \(-0.233793\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −7.85641 13.6077i −0.321811 0.557393i
\(597\) 0 0
\(598\) −29.3205 + 7.85641i −1.19900 + 0.321272i
\(599\) −34.6410 −1.41539 −0.707697 0.706516i \(-0.750266\pi\)
−0.707697 + 0.706516i \(0.750266\pi\)
\(600\) 0 0
\(601\) 18.5359 0.756095 0.378048 0.925786i \(-0.376596\pi\)
0.378048 + 0.925786i \(0.376596\pi\)
\(602\) 5.26795 1.41154i 0.214706 0.0575302i
\(603\) 0 0
\(604\) 21.4641 12.3923i 0.873362 0.504236i
\(605\) 0 0
\(606\) 0 0
\(607\) 30.9808i 1.25747i −0.777619 0.628735i \(-0.783573\pi\)
0.777619 0.628735i \(-0.216427\pi\)
\(608\) 0.784610 2.92820i 0.0318201 0.118754i
\(609\) 0 0
\(610\) 0 0
\(611\) 11.3205i 0.457979i
\(612\) 0 0
\(613\) 26.3923 1.06598 0.532988 0.846123i \(-0.321069\pi\)
0.532988 + 0.846123i \(0.321069\pi\)
\(614\) −9.14359 34.1244i −0.369005 1.37715i
\(615\) 0 0
\(616\) −2.92820 2.92820i −0.117981 0.117981i
\(617\) 20.5359i 0.826744i −0.910562 0.413372i \(-0.864351\pi\)
0.910562 0.413372i \(-0.135649\pi\)
\(618\) 0 0
\(619\) 1.32051i 0.0530757i 0.999648 + 0.0265379i \(0.00844825\pi\)
−0.999648 + 0.0265379i \(0.991552\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.4641 + 42.7846i 0.459669 + 1.71551i
\(623\) 6.53590i 0.261855i
\(624\) 0 0
\(625\) 0 0
\(626\) −5.66025 + 1.51666i −0.226229 + 0.0606179i
\(627\) 0 0
\(628\) −5.32051 + 3.07180i −0.212311 + 0.122578i
\(629\) 6.92820i 0.276246i
\(630\) 0 0
\(631\) −23.3205 −0.928375 −0.464187 0.885737i \(-0.653654\pi\)
−0.464187 + 0.885737i \(0.653654\pi\)
\(632\) 2.14359 + 2.14359i 0.0852676 + 0.0852676i
\(633\) 0 0
\(634\) −3.12436 11.6603i −0.124084 0.463088i
\(635\) 0 0
\(636\) 0 0
\(637\) −22.3923 −0.887215
\(638\) 5.07180 + 18.9282i 0.200794 + 0.749375i
\(639\) 0 0
\(640\) 0 0
\(641\) −0.392305 −0.0154951 −0.00774755 0.999970i \(-0.502466\pi\)
−0.00774755 + 0.999970i \(0.502466\pi\)
\(642\) 0 0
\(643\) 39.1244 1.54291 0.771457 0.636281i \(-0.219528\pi\)
0.771457 + 0.636281i \(0.219528\pi\)
\(644\) −7.85641 + 4.53590i −0.309586 + 0.178739i
\(645\) 0 0
\(646\) 0.679492 + 2.53590i 0.0267343 + 0.0997736i
\(647\) 16.7321i 0.657805i 0.944364 + 0.328902i \(0.106679\pi\)
−0.944364 + 0.328902i \(0.893321\pi\)
\(648\) 0 0
\(649\) 14.9282 0.585983
\(650\) 0 0
\(651\) 0 0
\(652\) 0.339746 0.196152i 0.0133055 0.00768192i
\(653\) −12.2487 −0.479329 −0.239665 0.970856i \(-0.577037\pi\)
−0.239665 + 0.970856i \(0.577037\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.92820 + 5.07180i −0.114327 + 0.198020i
\(657\) 0 0
\(658\) −0.875644 3.26795i −0.0341362 0.127398i
\(659\) 17.3205i 0.674711i 0.941377 + 0.337356i \(0.109532\pi\)
−0.941377 + 0.337356i \(0.890468\pi\)
\(660\) 0 0
\(661\) 8.14359i 0.316749i 0.987379 + 0.158375i \(0.0506253\pi\)
−0.987379 + 0.158375i \(0.949375\pi\)
\(662\) 19.1244 5.12436i 0.743289 0.199164i
\(663\) 0 0
\(664\) −2.53590 2.53590i −0.0984119 0.0984119i
\(665\) 0 0
\(666\) 0 0
\(667\) 42.9282 1.66219
\(668\) 9.80385 + 16.9808i 0.379322 + 0.657005i
\(669\) 0 0
\(670\) 0 0
\(671\) 17.8564 0.689339
\(672\) 0 0
\(673\) 12.5359i 0.483223i 0.970373 + 0.241612i \(0.0776760\pi\)
−0.970373 + 0.241612i \(0.922324\pi\)
\(674\) 27.1244 7.26795i 1.04479 0.279951i
\(675\) 0 0
\(676\) 1.73205 1.00000i 0.0666173 0.0384615i
\(677\) 17.6077 0.676719 0.338359 0.941017i \(-0.390128\pi\)
0.338359 + 0.941017i \(0.390128\pi\)
\(678\) 0 0
\(679\) 10.5359 0.404331
\(680\) 0 0
\(681\) 0 0
\(682\) 14.9282 4.00000i 0.571630 0.153168i
\(683\) 16.9808 0.649751 0.324875 0.945757i \(-0.394678\pi\)
0.324875 + 0.945757i \(0.394678\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −13.4641 + 3.60770i −0.514062 + 0.137742i
\(687\) 0 0
\(688\) −10.5359 + 18.2487i −0.401677 + 0.695726i
\(689\) 39.7128 1.51294
\(690\) 0 0
\(691\) 18.0000i 0.684752i −0.939563 0.342376i \(-0.888768\pi\)
0.939563 0.342376i \(-0.111232\pi\)
\(692\) 3.46410 2.00000i 0.131685 0.0760286i
\(693\) 0 0
\(694\) 0.607695 + 2.26795i 0.0230678 + 0.0860902i
\(695\) 0 0
\(696\) 0 0
\(697\) 5.07180i 0.192108i
\(698\) −38.2487 + 10.2487i −1.44774 + 0.387919i
\(699\) 0 0
\(700\) 0 0
\(701\) 19.0718i 0.720332i 0.932888 + 0.360166i \(0.117280\pi\)
−0.932888 + 0.360166i \(0.882720\pi\)
\(702\) 0 0
\(703\) 1.07180i 0.0404236i
\(704\) 16.0000 0.603023
\(705\) 0 0
\(706\) −17.6603 + 4.73205i −0.664652 + 0.178093i
\(707\) 2.14359 0.0806181
\(708\) 0 0
\(709\) 12.7846i 0.480136i −0.970756 0.240068i \(-0.922830\pi\)
0.970756 0.240068i \(-0.0771698\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 17.8564 + 17.8564i 0.669197 + 0.669197i
\(713\) 33.8564i 1.26793i
\(714\) 0 0
\(715\) 0 0
\(716\) −8.53590 14.7846i −0.319002 0.552527i
\(717\) 0 0
\(718\) −6.92820 25.8564i −0.258558 0.964953i
\(719\) −1.85641 −0.0692323 −0.0346161 0.999401i \(-0.511021\pi\)
−0.0346161 + 0.999401i \(0.511021\pi\)
\(720\) 0 0
\(721\) 11.4641 0.426945
\(722\) −6.84936 25.5622i −0.254907 0.951326i
\(723\) 0 0
\(724\) 16.0000 + 27.7128i 0.594635 + 1.02994i
\(725\) 0 0
\(726\) 0 0
\(727\) 24.0526i 0.892060i 0.895018 + 0.446030i \(0.147163\pi\)
−0.895018 + 0.446030i \(0.852837\pi\)
\(728\) −5.07180 + 5.07180i −0.187973 + 0.187973i
\(729\) 0 0
\(730\) 0 0
\(731\) 18.2487i 0.674953i
\(732\) 0 0
\(733\) −35.0718 −1.29541 −0.647703 0.761893i \(-0.724270\pi\)
−0.647703 + 0.761893i \(0.724270\pi\)
\(734\) −3.92820 + 1.05256i −0.144993 + 0.0388507i
\(735\) 0 0
\(736\) 9.07180 33.8564i 0.334391 1.24796i
\(737\) 21.4641i 0.790640i
\(738\) 0 0
\(739\) 29.3205i 1.07857i 0.842123 + 0.539286i \(0.181306\pi\)
−0.842123 + 0.539286i \(0.818694\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 11.4641 3.07180i 0.420860 0.112769i
\(743\) 10.9808i 0.402845i −0.979504 0.201423i \(-0.935444\pi\)
0.979504 0.201423i \(-0.0645564\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 9.41154 + 35.1244i 0.344581 + 1.28599i
\(747\) 0 0
\(748\) −12.0000 + 6.92820i −0.438763 + 0.253320i
\(749\) 2.00000i 0.0730784i
\(750\) 0 0
\(751\) 26.2487 0.957829 0.478915 0.877862i \(-0.341030\pi\)
0.478915 + 0.877862i \(0.341030\pi\)
\(752\) 11.3205 + 6.53590i 0.412816 + 0.238340i
\(753\) 0 0
\(754\) 32.7846 8.78461i 1.19395 0.319917i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.0718 0.693176 0.346588 0.938017i \(-0.387340\pi\)
0.346588 + 0.938017i \(0.387340\pi\)
\(758\) −49.5167 + 13.2679i −1.79853 + 0.481914i
\(759\) 0 0
\(760\) 0 0
\(761\) 5.71281 0.207089 0.103545 0.994625i \(-0.466982\pi\)
0.103545 + 0.994625i \(0.466982\pi\)
\(762\) 0 0
\(763\) 12.3923 0.448632
\(764\) 26.5359 15.3205i 0.960035 0.554277i
\(765\) 0 0
\(766\) −28.8564 + 7.73205i −1.04262 + 0.279370i
\(767\) 25.8564i 0.933621i
\(768\) 0 0
\(769\) −12.9282 −0.466203 −0.233101 0.972452i \(-0.574887\pi\)
−0.233101 + 0.972452i \(0.574887\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.535898 0.928203i −0.0192874 0.0334068i
\(773\) 22.3923 0.805395 0.402698 0.915333i \(-0.368073\pi\)
0.402698 + 0.915333i \(0.368073\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −28.7846 + 28.7846i −1.03331 + 1.03331i
\(777\) 0 0
\(778\) −9.26795 + 2.48334i −0.332272 + 0.0890320i
\(779\) 0.784610i 0.0281116i
\(780\) 0 0
\(781\) 10.9282i 0.391042i
\(782\) 7.85641 + 29.3205i 0.280945 + 1.04850i
\(783\) 0 0
\(784\) 12.9282 22.3923i 0.461722 0.799725i
\(785\) 0 0
\(786\) 0 0
\(787\) −16.5885 −0.591315 −0.295657 0.955294i \(-0.595539\pi\)
−0.295657 + 0.955294i \(0.595539\pi\)
\(788\) 33.7128 19.4641i 1.20097 0.693380i
\(789\) 0 0
\(790\) 0 0
\(791\) 9.46410 0.336505
\(792\) 0 0
\(793\) 30.9282i 1.09829i
\(794\) 11.8038 + 44.0526i 0.418903 + 1.56337i
\(795\) 0 0
\(796\) −3.21539 + 1.85641i −0.113966 + 0.0657986i
\(797\) 50.1051