Properties

Label 1800.2.k.j.901.4
Level $1800$
Weight $2$
Character 1800.901
Analytic conductor $14.373$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.k (of order \(2\), degree \(1\), 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 901.4
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1800.901
Dual form 1800.2.k.j.901.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +2.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +2.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +2.00000i q^{11} -3.46410i q^{13} +(1.00000 + 3.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} -3.46410 q^{17} +7.46410i q^{19} +(-2.73205 + 0.732051i) q^{22} +4.19615 q^{23} +(4.73205 - 1.26795i) q^{26} +(-4.73205 + 2.73205i) q^{28} +6.92820i q^{29} +1.46410 q^{31} +(5.46410 + 1.46410i) q^{32} +(-1.26795 - 4.73205i) q^{34} +2.00000i q^{37} +(-10.1962 + 2.73205i) q^{38} +5.46410 q^{41} +8.73205i q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.53590 + 5.73205i) q^{46} +6.73205 q^{47} +0.464102 q^{49} +(3.46410 + 6.00000i) q^{52} +4.53590i q^{53} +(-5.46410 - 5.46410i) q^{56} +(-9.46410 + 2.53590i) q^{58} +0.535898i q^{59} +4.92820i q^{61} +(0.535898 + 2.00000i) q^{62} +8.00000i q^{64} -7.26795i q^{67} +(6.00000 - 3.46410i) q^{68} +1.46410 q^{71} -0.535898 q^{73} +(-2.73205 + 0.732051i) q^{74} +(-7.46410 - 12.9282i) q^{76} +5.46410i q^{77} -14.9282 q^{79} +(2.00000 + 7.46410i) q^{82} +4.73205i q^{83} +(-11.9282 + 3.19615i) q^{86} +(4.00000 - 4.00000i) q^{88} +4.92820 q^{89} -9.46410i q^{91} +(-7.26795 + 4.19615i) q^{92} +(2.46410 + 9.19615i) q^{94} -6.39230 q^{97} +(0.169873 + 0.633975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 4q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 4q^{7} - 8q^{8} + 4q^{14} + 8q^{16} - 4q^{22} - 4q^{23} + 12q^{26} - 12q^{28} - 8q^{31} + 8q^{32} - 12q^{34} - 20q^{38} + 8q^{41} - 8q^{44} + 20q^{46} + 20q^{47} - 12q^{49} - 8q^{56} - 24q^{58} + 16q^{62} + 24q^{68} - 8q^{71} - 16q^{73} - 4q^{74} - 16q^{76} - 32q^{79} + 8q^{82} - 20q^{86} + 16q^{88} - 8q^{89} - 36q^{92} - 4q^{94} + 16q^{97} + 18q^{98} + O(q^{100}) \)

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
\(7\) 2.73205 1.03262 0.516309 0.856402i \(-0.327306\pi\)
0.516309 + 0.856402i \(0.327306\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) 1.00000 + 3.73205i 0.267261 + 0.997433i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −3.46410 −0.840168 −0.420084 0.907485i \(-0.637999\pi\)
−0.420084 + 0.907485i \(0.637999\pi\)
\(18\) 0 0
\(19\) 7.46410i 1.71238i 0.516659 + 0.856191i \(0.327175\pi\)
−0.516659 + 0.856191i \(0.672825\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.73205 + 0.732051i −0.582475 + 0.156074i
\(23\) 4.19615 0.874958 0.437479 0.899229i \(-0.355871\pi\)
0.437479 + 0.899229i \(0.355871\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 4.73205 1.26795i 0.928032 0.248665i
\(27\) 0 0
\(28\) −4.73205 + 2.73205i −0.894274 + 0.516309i
\(29\) 6.92820i 1.28654i 0.765641 + 0.643268i \(0.222422\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) 0 0
\(31\) 1.46410 0.262960 0.131480 0.991319i \(-0.458027\pi\)
0.131480 + 0.991319i \(0.458027\pi\)
\(32\) 5.46410 + 1.46410i 0.965926 + 0.258819i
\(33\) 0 0
\(34\) −1.26795 4.73205i −0.217451 0.811540i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) −10.1962 + 2.73205i −1.65403 + 0.443197i
\(39\) 0 0
\(40\) 0 0
\(41\) 5.46410 0.853349 0.426675 0.904405i \(-0.359685\pi\)
0.426675 + 0.904405i \(0.359685\pi\)
\(42\) 0 0
\(43\) 8.73205i 1.33163i 0.746119 + 0.665813i \(0.231915\pi\)
−0.746119 + 0.665813i \(0.768085\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0 0
\(46\) 1.53590 + 5.73205i 0.226456 + 0.845145i
\(47\) 6.73205 0.981971 0.490985 0.871168i \(-0.336637\pi\)
0.490985 + 0.871168i \(0.336637\pi\)
\(48\) 0 0
\(49\) 0.464102 0.0663002
\(50\) 0 0
\(51\) 0 0
\(52\) 3.46410 + 6.00000i 0.480384 + 0.832050i
\(53\) 4.53590i 0.623054i 0.950237 + 0.311527i \(0.100840\pi\)
−0.950237 + 0.311527i \(0.899160\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −5.46410 5.46410i −0.730171 0.730171i
\(57\) 0 0
\(58\) −9.46410 + 2.53590i −1.24270 + 0.332980i
\(59\) 0.535898i 0.0697680i 0.999391 + 0.0348840i \(0.0111062\pi\)
−0.999391 + 0.0348840i \(0.988894\pi\)
\(60\) 0 0
\(61\) 4.92820i 0.630992i 0.948927 + 0.315496i \(0.102171\pi\)
−0.948927 + 0.315496i \(0.897829\pi\)
\(62\) 0.535898 + 2.00000i 0.0680592 + 0.254000i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 7.26795i 0.887921i −0.896046 0.443961i \(-0.853573\pi\)
0.896046 0.443961i \(-0.146427\pi\)
\(68\) 6.00000 3.46410i 0.727607 0.420084i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.46410 0.173757 0.0868784 0.996219i \(-0.472311\pi\)
0.0868784 + 0.996219i \(0.472311\pi\)
\(72\) 0 0
\(73\) −0.535898 −0.0627222 −0.0313611 0.999508i \(-0.509984\pi\)
−0.0313611 + 0.999508i \(0.509984\pi\)
\(74\) −2.73205 + 0.732051i −0.317594 + 0.0850992i
\(75\) 0 0
\(76\) −7.46410 12.9282i −0.856191 1.48297i
\(77\) 5.46410i 0.622692i
\(78\) 0 0
\(79\) −14.9282 −1.67955 −0.839777 0.542931i \(-0.817314\pi\)
−0.839777 + 0.542931i \(0.817314\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.00000 + 7.46410i 0.220863 + 0.824272i
\(83\) 4.73205i 0.519410i 0.965688 + 0.259705i \(0.0836253\pi\)
−0.965688 + 0.259705i \(0.916375\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −11.9282 + 3.19615i −1.28625 + 0.344650i
\(87\) 0 0
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) 4.92820 0.522388 0.261194 0.965286i \(-0.415884\pi\)
0.261194 + 0.965286i \(0.415884\pi\)
\(90\) 0 0
\(91\) 9.46410i 0.992107i
\(92\) −7.26795 + 4.19615i −0.757736 + 0.437479i
\(93\) 0 0
\(94\) 2.46410 + 9.19615i 0.254153 + 0.948511i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.39230 −0.649040 −0.324520 0.945879i \(-0.605203\pi\)
−0.324520 + 0.945879i \(0.605203\pi\)
\(98\) 0.169873 + 0.633975i 0.0171598 + 0.0640411i
\(99\) 0 0
\(100\) 0 0
\(101\) 10.9282i 1.08740i 0.839281 + 0.543698i \(0.182976\pi\)
−0.839281 + 0.543698i \(0.817024\pi\)
\(102\) 0 0
\(103\) 1.66025 0.163590 0.0817948 0.996649i \(-0.473935\pi\)
0.0817948 + 0.996649i \(0.473935\pi\)
\(104\) −6.92820 + 6.92820i −0.679366 + 0.679366i
\(105\) 0 0
\(106\) −6.19615 + 1.66025i −0.601824 + 0.161258i
\(107\) 0.732051i 0.0707700i −0.999374 0.0353850i \(-0.988734\pi\)
0.999374 0.0353850i \(-0.0112658\pi\)
\(108\) 0 0
\(109\) 3.07180i 0.294225i 0.989120 + 0.147112i \(0.0469979\pi\)
−0.989120 + 0.147112i \(0.953002\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 5.46410 9.46410i 0.516309 0.894274i
\(113\) 0.928203 0.0873180 0.0436590 0.999046i \(-0.486098\pi\)
0.0436590 + 0.999046i \(0.486098\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.92820 12.0000i −0.643268 1.11417i
\(117\) 0 0
\(118\) −0.732051 + 0.196152i −0.0673907 + 0.0180573i
\(119\) −9.46410 −0.867573
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) −6.73205 + 1.80385i −0.609491 + 0.163313i
\(123\) 0 0
\(124\) −2.53590 + 1.46410i −0.227730 + 0.131480i
\(125\) 0 0
\(126\) 0 0
\(127\) −13.2679 −1.17734 −0.588670 0.808373i \(-0.700348\pi\)
−0.588670 + 0.808373i \(0.700348\pi\)
\(128\) −10.9282 + 2.92820i −0.965926 + 0.258819i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.85641i 0.686417i −0.939259 0.343209i \(-0.888486\pi\)
0.939259 0.343209i \(-0.111514\pi\)
\(132\) 0 0
\(133\) 20.3923i 1.76824i
\(134\) 9.92820 2.66025i 0.857666 0.229811i
\(135\) 0 0
\(136\) 6.92820 + 6.92820i 0.594089 + 0.594089i
\(137\) −8.92820 −0.762788 −0.381394 0.924413i \(-0.624556\pi\)
−0.381394 + 0.924413i \(0.624556\pi\)
\(138\) 0 0
\(139\) 7.46410i 0.633097i −0.948576 0.316548i \(-0.897476\pi\)
0.948576 0.316548i \(-0.102524\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.535898 + 2.00000i 0.0449716 + 0.167836i
\(143\) 6.92820 0.579365
\(144\) 0 0
\(145\) 0 0
\(146\) −0.196152 0.732051i −0.0162337 0.0605850i
\(147\) 0 0
\(148\) −2.00000 3.46410i −0.164399 0.284747i
\(149\) 19.8564i 1.62670i −0.581775 0.813350i \(-0.697641\pi\)
0.581775 0.813350i \(-0.302359\pi\)
\(150\) 0 0
\(151\) 8.39230 0.682956 0.341478 0.939890i \(-0.389073\pi\)
0.341478 + 0.939890i \(0.389073\pi\)
\(152\) 14.9282 14.9282i 1.21084 1.21084i
\(153\) 0 0
\(154\) −7.46410 + 2.00000i −0.601474 + 0.161165i
\(155\) 0 0
\(156\) 0 0
\(157\) 16.9282i 1.35102i 0.737352 + 0.675509i \(0.236076\pi\)
−0.737352 + 0.675509i \(0.763924\pi\)
\(158\) −5.46410 20.3923i −0.434701 1.62232i
\(159\) 0 0
\(160\) 0 0
\(161\) 11.4641 0.903498
\(162\) 0 0
\(163\) 10.1962i 0.798624i −0.916815 0.399312i \(-0.869249\pi\)
0.916815 0.399312i \(-0.130751\pi\)
\(164\) −9.46410 + 5.46410i −0.739022 + 0.426675i
\(165\) 0 0
\(166\) −6.46410 + 1.73205i −0.501712 + 0.134433i
\(167\) −20.1962 −1.56283 −0.781413 0.624015i \(-0.785501\pi\)
−0.781413 + 0.624015i \(0.785501\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) −8.73205 15.1244i −0.665813 1.15322i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.92820 + 4.00000i 0.522233 + 0.301511i
\(177\) 0 0
\(178\) 1.80385 + 6.73205i 0.135204 + 0.504589i
\(179\) 15.4641i 1.15584i 0.816093 + 0.577921i \(0.196136\pi\)
−0.816093 + 0.577921i \(0.803864\pi\)
\(180\) 0 0
\(181\) 16.0000i 1.18927i 0.803996 + 0.594635i \(0.202704\pi\)
−0.803996 + 0.594635i \(0.797296\pi\)
\(182\) 12.9282 3.46410i 0.958302 0.256776i
\(183\) 0 0
\(184\) −8.39230 8.39230i −0.618689 0.618689i
\(185\) 0 0
\(186\) 0 0
\(187\) 6.92820i 0.506640i
\(188\) −11.6603 + 6.73205i −0.850411 + 0.490985i
\(189\) 0 0
\(190\) 0 0
\(191\) 19.3205 1.39798 0.698991 0.715130i \(-0.253633\pi\)
0.698991 + 0.715130i \(0.253633\pi\)
\(192\) 0 0
\(193\) −7.46410 −0.537278 −0.268639 0.963241i \(-0.586574\pi\)
−0.268639 + 0.963241i \(0.586574\pi\)
\(194\) −2.33975 8.73205i −0.167984 0.626925i
\(195\) 0 0
\(196\) −0.803848 + 0.464102i −0.0574177 + 0.0331501i
\(197\) 12.5359i 0.893146i −0.894747 0.446573i \(-0.852644\pi\)
0.894747 0.446573i \(-0.147356\pi\)
\(198\) 0 0
\(199\) 25.8564 1.83291 0.916456 0.400135i \(-0.131037\pi\)
0.916456 + 0.400135i \(0.131037\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −14.9282 + 4.00000i −1.05034 + 0.281439i
\(203\) 18.9282i 1.32850i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.607695 + 2.26795i 0.0423401 + 0.158016i
\(207\) 0 0
\(208\) −12.0000 6.92820i −0.832050 0.480384i
\(209\) −14.9282 −1.03261
\(210\) 0 0
\(211\) 14.7846i 1.01781i −0.860821 0.508907i \(-0.830050\pi\)
0.860821 0.508907i \(-0.169950\pi\)
\(212\) −4.53590 7.85641i −0.311527 0.539580i
\(213\) 0 0
\(214\) 1.00000 0.267949i 0.0683586 0.0183166i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) −4.19615 + 1.12436i −0.284199 + 0.0761510i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000i 0.807207i
\(222\) 0 0
\(223\) 16.1962 1.08457 0.542287 0.840193i \(-0.317558\pi\)
0.542287 + 0.840193i \(0.317558\pi\)
\(224\) 14.9282 + 4.00000i 0.997433 + 0.267261i
\(225\) 0 0
\(226\) 0.339746 + 1.26795i 0.0225996 + 0.0843427i
\(227\) 28.0526i 1.86191i −0.365129 0.930957i \(-0.618975\pi\)
0.365129 0.930957i \(-0.381025\pi\)
\(228\) 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
\(233\) 29.3205 1.92085 0.960425 0.278538i \(-0.0898499\pi\)
0.960425 + 0.278538i \(0.0898499\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.535898 0.928203i −0.0348840 0.0604209i
\(237\) 0 0
\(238\) −3.46410 12.9282i −0.224544 0.838011i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) −4.39230 −0.282933 −0.141467 0.989943i \(-0.545182\pi\)
−0.141467 + 0.989943i \(0.545182\pi\)
\(242\) 2.56218 + 9.56218i 0.164703 + 0.614680i
\(243\) 0 0
\(244\) −4.92820 8.53590i −0.315496 0.546455i
\(245\) 0 0
\(246\) 0 0
\(247\) 25.8564 1.64520
\(248\) −2.92820 2.92820i −0.185941 0.185941i
\(249\) 0 0
\(250\) 0 0
\(251\) 11.0718i 0.698846i −0.936965 0.349423i \(-0.886378\pi\)
0.936965 0.349423i \(-0.113622\pi\)
\(252\) 0 0
\(253\) 8.39230i 0.527620i
\(254\) −4.85641 18.1244i −0.304718 1.13722i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) 5.46410i 0.339523i
\(260\) 0 0
\(261\) 0 0
\(262\) 10.7321 2.87564i 0.663028 0.177658i
\(263\) 5.66025 0.349026 0.174513 0.984655i \(-0.444165\pi\)
0.174513 + 0.984655i \(0.444165\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −27.8564 + 7.46410i −1.70799 + 0.457653i
\(267\) 0 0
\(268\) 7.26795 + 12.5885i 0.443961 + 0.768962i
\(269\) 4.92820i 0.300478i −0.988650 0.150239i \(-0.951996\pi\)
0.988650 0.150239i \(-0.0480043\pi\)
\(270\) 0 0
\(271\) 15.3205 0.930655 0.465327 0.885139i \(-0.345937\pi\)
0.465327 + 0.885139i \(0.345937\pi\)
\(272\) −6.92820 + 12.0000i −0.420084 + 0.727607i
\(273\) 0 0
\(274\) −3.26795 12.1962i −0.197424 0.736797i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 10.1962 2.73205i 0.611525 0.163858i
\(279\) 0 0
\(280\) 0 0
\(281\) −17.4641 −1.04182 −0.520910 0.853611i \(-0.674407\pi\)
−0.520910 + 0.853611i \(0.674407\pi\)
\(282\) 0 0
\(283\) 7.66025i 0.455355i −0.973737 0.227677i \(-0.926887\pi\)
0.973737 0.227677i \(-0.0731132\pi\)
\(284\) −2.53590 + 1.46410i −0.150478 + 0.0868784i
\(285\) 0 0
\(286\) 2.53590 + 9.46410i 0.149951 + 0.559624i
\(287\) 14.9282 0.881184
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) 0.928203 0.535898i 0.0543190 0.0313611i
\(293\) 11.8564i 0.692659i 0.938113 + 0.346329i \(0.112572\pi\)
−0.938113 + 0.346329i \(0.887428\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.00000 4.00000i 0.232495 0.232495i
\(297\) 0 0
\(298\) 27.1244 7.26795i 1.57127 0.421021i
\(299\) 14.5359i 0.840633i
\(300\) 0 0
\(301\) 23.8564i 1.37506i
\(302\) 3.07180 + 11.4641i 0.176762 + 0.659685i
\(303\) 0 0
\(304\) 25.8564 + 14.9282i 1.48297 + 0.856191i
\(305\) 0 0
\(306\) 0 0
\(307\) 26.9808i 1.53987i −0.638120 0.769937i \(-0.720288\pi\)
0.638120 0.769937i \(-0.279712\pi\)
\(308\) −5.46410 9.46410i −0.311346 0.539267i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.32051 0.188289 0.0941444 0.995559i \(-0.469988\pi\)
0.0941444 + 0.995559i \(0.469988\pi\)
\(312\) 0 0
\(313\) 31.8564 1.80063 0.900315 0.435238i \(-0.143336\pi\)
0.900315 + 0.435238i \(0.143336\pi\)
\(314\) −23.1244 + 6.19615i −1.30498 + 0.349669i
\(315\) 0 0
\(316\) 25.8564 14.9282i 1.45454 0.839777i
\(317\) 15.4641i 0.868550i 0.900780 + 0.434275i \(0.142995\pi\)
−0.900780 + 0.434275i \(0.857005\pi\)
\(318\) 0 0
\(319\) −13.8564 −0.775810
\(320\) 0 0
\(321\) 0 0
\(322\) 4.19615 + 15.6603i 0.233842 + 0.872712i
\(323\) 25.8564i 1.43869i
\(324\) 0 0
\(325\) 0 0
\(326\) 13.9282 3.73205i 0.771412 0.206699i
\(327\) 0 0
\(328\) −10.9282 10.9282i −0.603409 0.603409i
\(329\) 18.3923 1.01400
\(330\) 0 0
\(331\) 14.0000i 0.769510i −0.923019 0.384755i \(-0.874286\pi\)
0.923019 0.384755i \(-0.125714\pi\)
\(332\) −4.73205 8.19615i −0.259705 0.449822i
\(333\) 0 0
\(334\) −7.39230 27.5885i −0.404489 1.50957i
\(335\) 0 0
\(336\) 0 0
\(337\) −7.85641 −0.427966 −0.213983 0.976837i \(-0.568644\pi\)
−0.213983 + 0.976837i \(0.568644\pi\)
\(338\) 0.366025 + 1.36603i 0.0199092 + 0.0743020i
\(339\) 0 0
\(340\) 0 0
\(341\) 2.92820i 0.158571i
\(342\) 0 0
\(343\) −17.8564 −0.964155
\(344\) 17.4641 17.4641i 0.941601 0.941601i
\(345\) 0 0
\(346\) −2.73205 + 0.732051i −0.146876 + 0.0393553i
\(347\) 15.6603i 0.840686i 0.907365 + 0.420343i \(0.138090\pi\)
−0.907365 + 0.420343i \(0.861910\pi\)
\(348\) 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
\(353\) −0.928203 −0.0494033 −0.0247016 0.999695i \(-0.507864\pi\)
−0.0247016 + 0.999695i \(0.507864\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −8.53590 + 4.92820i −0.452402 + 0.261194i
\(357\) 0 0
\(358\) −21.1244 + 5.66025i −1.11646 + 0.299154i
\(359\) −5.07180 −0.267679 −0.133840 0.991003i \(-0.542731\pi\)
−0.133840 + 0.991003i \(0.542731\pi\)
\(360\) 0 0
\(361\) −36.7128 −1.93225
\(362\) −21.8564 + 5.85641i −1.14875 + 0.307806i
\(363\) 0 0
\(364\) 9.46410 + 16.3923i 0.496054 + 0.859190i
\(365\) 0 0
\(366\) 0 0
\(367\) −27.1244 −1.41588 −0.707940 0.706273i \(-0.750375\pi\)
−0.707940 + 0.706273i \(0.750375\pi\)
\(368\) 8.39230 14.5359i 0.437479 0.757736i
\(369\) 0 0
\(370\) 0 0
\(371\) 12.3923i 0.643376i
\(372\) 0 0
\(373\) 29.7128i 1.53847i −0.638965 0.769236i \(-0.720637\pi\)
0.638965 0.769236i \(-0.279363\pi\)
\(374\) 9.46410 2.53590i 0.489377 0.131128i
\(375\) 0 0
\(376\) −13.4641 13.4641i −0.694358 0.694358i
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 12.2487i 0.629174i 0.949229 + 0.314587i \(0.101866\pi\)
−0.949229 + 0.314587i \(0.898134\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7.07180 + 26.3923i 0.361825 + 1.35035i
\(383\) −3.12436 −0.159647 −0.0798236 0.996809i \(-0.525436\pi\)
−0.0798236 + 0.996809i \(0.525436\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.73205 10.1962i −0.139058 0.518970i
\(387\) 0 0
\(388\) 11.0718 6.39230i 0.562085 0.324520i
\(389\) 34.7846i 1.76365i 0.471577 + 0.881825i \(0.343685\pi\)
−0.471577 + 0.881825i \(0.656315\pi\)
\(390\) 0 0
\(391\) −14.5359 −0.735112
\(392\) −0.928203 0.928203i −0.0468813 0.0468813i
\(393\) 0 0
\(394\) 17.1244 4.58846i 0.862713 0.231163i
\(395\) 0 0
\(396\) 0 0
\(397\) 16.2487i 0.815499i 0.913094 + 0.407750i \(0.133686\pi\)
−0.913094 + 0.407750i \(0.866314\pi\)
\(398\) 9.46410 + 35.3205i 0.474393 + 1.77046i
\(399\) 0 0
\(400\) 0 0
\(401\) −19.8564 −0.991582 −0.495791 0.868442i \(-0.665122\pi\)
−0.495791 + 0.868442i \(0.665122\pi\)
\(402\) 0 0
\(403\) 5.07180i 0.252644i
\(404\) −10.9282 18.9282i −0.543698 0.941713i
\(405\) 0 0
\(406\) −25.8564 + 6.92820i −1.28323 + 0.343841i
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) 23.3205 1.15312 0.576562 0.817053i \(-0.304394\pi\)
0.576562 + 0.817053i \(0.304394\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.87564 + 1.66025i −0.141673 + 0.0817948i
\(413\) 1.46410i 0.0720437i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.07180 18.9282i 0.248665 0.928032i
\(417\) 0 0
\(418\) −5.46410 20.3923i −0.267258 0.997420i
\(419\) 2.39230i 0.116872i 0.998291 + 0.0584359i \(0.0186113\pi\)
−0.998291 + 0.0584359i \(0.981389\pi\)
\(420\) 0 0
\(421\) 27.8564i 1.35764i 0.734306 + 0.678819i \(0.237508\pi\)
−0.734306 + 0.678819i \(0.762492\pi\)
\(422\) 20.1962 5.41154i 0.983133 0.263430i
\(423\) 0 0
\(424\) 9.07180 9.07180i 0.440565 0.440565i
\(425\) 0 0
\(426\) 0 0
\(427\) 13.4641i 0.651574i
\(428\) 0.732051 + 1.26795i 0.0353850 + 0.0612886i
\(429\) 0 0
\(430\) 0 0
\(431\) 14.5359 0.700170 0.350085 0.936718i \(-0.386153\pi\)
0.350085 + 0.936718i \(0.386153\pi\)
\(432\) 0 0
\(433\) 12.5359 0.602437 0.301218 0.953555i \(-0.402607\pi\)
0.301218 + 0.953555i \(0.402607\pi\)
\(434\) 1.46410 + 5.46410i 0.0702791 + 0.262285i
\(435\) 0 0
\(436\) −3.07180 5.32051i −0.147112 0.254806i
\(437\) 31.3205i 1.49826i
\(438\) 0 0
\(439\) −0.784610 −0.0374474 −0.0187237 0.999825i \(-0.505960\pi\)
−0.0187237 + 0.999825i \(0.505960\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −16.3923 + 4.39230i −0.779702 + 0.208921i
\(443\) 30.9808i 1.47194i −0.677014 0.735970i \(-0.736726\pi\)
0.677014 0.735970i \(-0.263274\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 5.92820 + 22.1244i 0.280709 + 1.04762i
\(447\) 0 0
\(448\) 21.8564i 1.03262i
\(449\) −11.3205 −0.534248 −0.267124 0.963662i \(-0.586073\pi\)
−0.267124 + 0.963662i \(0.586073\pi\)
\(450\) 0 0
\(451\) 10.9282i 0.514589i
\(452\) −1.60770 + 0.928203i −0.0756196 + 0.0436590i
\(453\) 0 0
\(454\) 38.3205 10.2679i 1.79847 0.481899i
\(455\) 0 0
\(456\) 0 0
\(457\) −14.7846 −0.691595 −0.345797 0.938309i \(-0.612392\pi\)
−0.345797 + 0.938309i \(0.612392\pi\)
\(458\) 5.46410 1.46410i 0.255321 0.0684130i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.92820i 0.136380i −0.997672 0.0681900i \(-0.978278\pi\)
0.997672 0.0681900i \(-0.0217224\pi\)
\(462\) 0 0
\(463\) 14.7321 0.684656 0.342328 0.939580i \(-0.388785\pi\)
0.342328 + 0.939580i \(0.388785\pi\)
\(464\) 24.0000 + 13.8564i 1.11417 + 0.643268i
\(465\) 0 0
\(466\) 10.7321 + 40.0526i 0.497153 + 1.85540i
\(467\) 8.33975i 0.385917i −0.981207 0.192959i \(-0.938192\pi\)
0.981207 0.192959i \(-0.0618083\pi\)
\(468\) 0 0
\(469\) 19.8564i 0.916884i
\(470\) 0 0
\(471\) 0 0
\(472\) 1.07180 1.07180i 0.0493334 0.0493334i
\(473\) −17.4641 −0.803000
\(474\) 0 0
\(475\) 0 0
\(476\) 16.3923 9.46410i 0.751340 0.433786i
\(477\) 0 0
\(478\) 7.32051 + 27.3205i 0.334832 + 1.24961i
\(479\) 21.8564 0.998645 0.499322 0.866416i \(-0.333582\pi\)
0.499322 + 0.866416i \(0.333582\pi\)
\(480\) 0 0
\(481\) 6.92820 0.315899
\(482\) −1.60770 6.00000i −0.0732285 0.273293i
\(483\) 0 0
\(484\) −12.1244 + 7.00000i −0.551107 + 0.318182i
\(485\) 0 0
\(486\) 0 0
\(487\) 24.5885 1.11421 0.557105 0.830442i \(-0.311912\pi\)
0.557105 + 0.830442i \(0.311912\pi\)
\(488\) 9.85641 9.85641i 0.446179 0.446179i
\(489\) 0 0
\(490\) 0 0
\(491\) 3.07180i 0.138628i 0.997595 + 0.0693141i \(0.0220811\pi\)
−0.997595 + 0.0693141i \(0.977919\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) 9.46410 + 35.3205i 0.425810 + 1.58914i
\(495\) 0 0
\(496\) 2.92820 5.07180i 0.131480 0.227730i
\(497\) 4.00000 0.179425
\(498\) 0 0
\(499\) 24.5359i 1.09838i 0.835698 + 0.549189i \(0.185063\pi\)
−0.835698 + 0.549189i \(0.814937\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 15.1244 4.05256i 0.675033 0.180875i
\(503\) −17.6603 −0.787432 −0.393716 0.919232i \(-0.628811\pi\)
−0.393716 + 0.919232i \(0.628811\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −11.4641 + 3.07180i −0.509641 + 0.136558i
\(507\) 0 0
\(508\) 22.9808 13.2679i 1.01961 0.588670i
\(509\) 25.8564i 1.14607i −0.819533 0.573033i \(-0.805767\pi\)
0.819533 0.573033i \(-0.194233\pi\)
\(510\) 0 0
\(511\) −1.46410 −0.0647680
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 0 0
\(514\) −0.732051 2.73205i −0.0322894 0.120506i
\(515\) 0 0
\(516\) 0 0
\(517\) 13.4641i 0.592151i
\(518\) −7.46410 + 2.00000i −0.327954 + 0.0878750i
\(519\) 0 0
\(520\) 0 0
\(521\) 16.1436 0.707264 0.353632 0.935385i \(-0.384947\pi\)
0.353632 + 0.935385i \(0.384947\pi\)
\(522\) 0 0
\(523\) 22.1962i 0.970570i 0.874356 + 0.485285i \(0.161284\pi\)
−0.874356 + 0.485285i \(0.838716\pi\)
\(524\) 7.85641 + 13.6077i 0.343209 + 0.594455i
\(525\) 0 0
\(526\) 2.07180 + 7.73205i 0.0903346 + 0.337133i
\(527\) −5.07180 −0.220931
\(528\) 0 0
\(529\) −5.39230 −0.234448
\(530\) 0 0
\(531\) 0 0
\(532\) −20.3923 35.3205i −0.884119 1.53134i
\(533\) 18.9282i 0.819871i
\(534\) 0 0
\(535\) 0 0
\(536\) −14.5359 + 14.5359i −0.627855 + 0.627855i
\(537\) 0 0
\(538\) 6.73205 1.80385i 0.290239 0.0777694i
\(539\) 0.928203i 0.0399805i
\(540\) 0 0
\(541\) 13.0718i 0.562000i −0.959708 0.281000i \(-0.909334\pi\)
0.959708 0.281000i \(-0.0906662\pi\)
\(542\) 5.60770 + 20.9282i 0.240871 + 0.898943i
\(543\) 0 0
\(544\) −18.9282 5.07180i −0.811540 0.217451i
\(545\) 0 0
\(546\) 0 0
\(547\) 36.7321i 1.57055i −0.619148 0.785275i \(-0.712522\pi\)
0.619148 0.785275i \(-0.287478\pi\)
\(548\) 15.4641 8.92820i 0.660594 0.381394i
\(549\) 0 0
\(550\) 0 0
\(551\) −51.7128 −2.20304
\(552\) 0 0
\(553\) −40.7846 −1.73434
\(554\) 2.73205 0.732051i 0.116074 0.0311019i
\(555\) 0 0
\(556\) 7.46410 + 12.9282i 0.316548 + 0.548278i
\(557\) 26.7846i 1.13490i −0.823408 0.567450i \(-0.807930\pi\)
0.823408 0.567450i \(-0.192070\pi\)
\(558\) 0 0
\(559\) 30.2487 1.27938
\(560\) 0 0
\(561\) 0 0
\(562\) −6.39230 23.8564i −0.269643 1.00632i
\(563\) 16.0526i 0.676535i 0.941050 + 0.338267i \(0.109841\pi\)
−0.941050 + 0.338267i \(0.890159\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 10.4641 2.80385i 0.439839 0.117855i
\(567\) 0 0
\(568\) −2.92820 2.92820i −0.122865 0.122865i
\(569\) 6.53590 0.273999 0.137000 0.990571i \(-0.456254\pi\)
0.137000 + 0.990571i \(0.456254\pi\)
\(570\) 0 0
\(571\) 34.7846i 1.45569i −0.685741 0.727845i \(-0.740522\pi\)
0.685741 0.727845i \(-0.259478\pi\)
\(572\) −12.0000 + 6.92820i −0.501745 + 0.289683i
\(573\) 0 0
\(574\) 5.46410 + 20.3923i 0.228067 + 0.851158i
\(575\) 0 0
\(576\) 0 0
\(577\) 43.5692 1.81381 0.906905 0.421335i \(-0.138438\pi\)
0.906905 + 0.421335i \(0.138438\pi\)
\(578\) −1.83013 6.83013i −0.0761232 0.284096i
\(579\) 0 0
\(580\) 0 0
\(581\) 12.9282i 0.536352i
\(582\) 0 0
\(583\) −9.07180 −0.375715
\(584\) 1.07180 + 1.07180i 0.0443513 + 0.0443513i
\(585\) 0 0
\(586\) −16.1962 + 4.33975i −0.669057 + 0.179273i
\(587\) 14.1962i 0.585938i −0.956122 0.292969i \(-0.905357\pi\)
0.956122 0.292969i \(-0.0946433\pi\)
\(588\) 0 0
\(589\) 10.9282i 0.450289i
\(590\) 0 0
\(591\) 0 0
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) −36.6410 −1.50467 −0.752333 0.658783i \(-0.771072\pi\)
−0.752333 + 0.658783i \(0.771072\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 19.8564 + 34.3923i 0.813350 + 1.40876i
\(597\) 0 0
\(598\) 19.8564 5.32051i 0.811989 0.217572i
\(599\) −34.6410 −1.41539 −0.707697 0.706516i \(-0.750266\pi\)
−0.707697 + 0.706516i \(0.750266\pi\)
\(600\) 0 0
\(601\) 25.4641 1.03870 0.519351 0.854561i \(-0.326174\pi\)
0.519351 + 0.854561i \(0.326174\pi\)
\(602\) −32.5885 + 8.73205i −1.32821 + 0.355892i
\(603\) 0 0
\(604\) −14.5359 + 8.39230i −0.591457 + 0.341478i
\(605\) 0 0
\(606\) 0 0
\(607\) 20.9808 0.851583 0.425791 0.904821i \(-0.359996\pi\)
0.425791 + 0.904821i \(0.359996\pi\)
\(608\) −10.9282 + 40.7846i −0.443197 + 1.65403i
\(609\) 0 0
\(610\) 0 0
\(611\) 23.3205i 0.943447i
\(612\) 0 0
\(613\) 5.60770i 0.226493i −0.993567 0.113246i \(-0.963875\pi\)
0.993567 0.113246i \(-0.0361249\pi\)
\(614\) 36.8564 9.87564i 1.48740 0.398549i
\(615\) 0 0
\(616\) 10.9282 10.9282i 0.440310 0.440310i
\(617\) −27.4641 −1.10566 −0.552832 0.833293i \(-0.686453\pi\)
−0.552832 + 0.833293i \(0.686453\pi\)
\(618\) 0 0
\(619\) 33.3205i 1.33926i −0.742693 0.669632i \(-0.766452\pi\)
0.742693 0.669632i \(-0.233548\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 1.21539 + 4.53590i 0.0487327 + 0.181873i
\(623\) 13.4641 0.539428
\(624\) 0 0
\(625\) 0 0
\(626\) 11.6603 + 43.5167i 0.466037 + 1.73928i
\(627\) 0 0
\(628\) −16.9282 29.3205i −0.675509 1.17002i
\(629\) 6.92820i 0.276246i
\(630\) 0 0
\(631\) 11.3205 0.450662 0.225331 0.974282i \(-0.427654\pi\)
0.225331 + 0.974282i \(0.427654\pi\)
\(632\) 29.8564 + 29.8564i 1.18762 + 1.18762i
\(633\) 0 0
\(634\) −21.1244 + 5.66025i −0.838955 + 0.224797i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.60770i 0.0636992i
\(638\) −5.07180 18.9282i −0.200794 0.749375i
\(639\) 0 0
\(640\) 0 0
\(641\) 20.3923 0.805448 0.402724 0.915322i \(-0.368064\pi\)
0.402724 + 0.915322i \(0.368064\pi\)
\(642\) 0 0
\(643\) 14.8756i 0.586638i −0.956015 0.293319i \(-0.905240\pi\)
0.956015 0.293319i \(-0.0947598\pi\)
\(644\) −19.8564 + 11.4641i −0.782452 + 0.451749i
\(645\) 0 0
\(646\) 35.3205 9.46410i 1.38967 0.372360i
\(647\) 13.2679 0.521617 0.260808 0.965391i \(-0.416011\pi\)
0.260808 + 0.965391i \(0.416011\pi\)
\(648\) 0 0
\(649\) −1.07180 −0.0420717
\(650\) 0 0
\(651\) 0 0
\(652\) 10.1962 + 17.6603i 0.399312 + 0.691629i
\(653\) 36.2487i 1.41852i −0.704946 0.709261i \(-0.749029\pi\)
0.704946 0.709261i \(-0.250971\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 10.9282 18.9282i 0.426675 0.739022i
\(657\) 0 0
\(658\) 6.73205 + 25.1244i 0.262443 + 0.979449i
\(659\) 17.3205i 0.674711i −0.941377 0.337356i \(-0.890468\pi\)
0.941377 0.337356i \(-0.109532\pi\)
\(660\) 0 0
\(661\) 35.8564i 1.39465i −0.716754 0.697326i \(-0.754373\pi\)
0.716754 0.697326i \(-0.245627\pi\)
\(662\) 19.1244 5.12436i 0.743289 0.199164i
\(663\) 0 0
\(664\) 9.46410 9.46410i 0.367278 0.367278i
\(665\) 0 0
\(666\) 0 0
\(667\) 29.0718i 1.12566i
\(668\) 34.9808 20.1962i 1.35345 0.781413i
\(669\) 0 0
\(670\) 0 0
\(671\) −9.85641 −0.380502
\(672\) 0 0
\(673\) −19.4641 −0.750286 −0.375143 0.926967i \(-0.622406\pi\)
−0.375143 + 0.926967i \(0.622406\pi\)
\(674\) −2.87564 10.7321i −0.110766 0.413383i
\(675\) 0 0
\(676\) −1.73205 + 1.00000i −0.0666173 + 0.0384615i
\(677\) 38.3923i 1.47554i 0.675054 + 0.737768i \(0.264120\pi\)
−0.675054 + 0.737768i \(0.735880\pi\)
\(678\) 0 0
\(679\) −17.4641 −0.670211
\(680\) 0 0
\(681\) 0 0
\(682\) −4.00000 + 1.07180i −0.153168 + 0.0410412i
\(683\) 34.9808i 1.33850i 0.743037 + 0.669251i \(0.233385\pi\)
−0.743037 + 0.669251i \(0.766615\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −6.53590 24.3923i −0.249542 0.931303i
\(687\) 0 0
\(688\) 30.2487 + 17.4641i 1.15322 + 0.665813i
\(689\) 15.7128 0.598610
\(690\) 0 0
\(691\) 18.0000i 0.684752i 0.939563 + 0.342376i \(0.111232\pi\)
−0.939563 + 0.342376i \(0.888768\pi\)
\(692\) −2.00000 3.46410i −0.0760286 0.131685i
\(693\) 0 0
\(694\) −21.3923 + 5.73205i −0.812041 + 0.217586i
\(695\) 0 0
\(696\) 0 0
\(697\) −18.9282 −0.716957
\(698\) 38.2487 10.2487i 1.44774 0.387919i
\(699\) 0 0
\(700\) 0 0
\(701\) 32.9282i 1.24368i −0.783144 0.621841i \(-0.786385\pi\)
0.783144 0.621841i \(-0.213615\pi\)
\(702\) 0 0
\(703\) −14.9282 −0.563028
\(704\) −16.0000 −0.603023
\(705\) 0 0
\(706\) −0.339746 1.26795i −0.0127865 0.0477199i
\(707\) 29.8564i 1.12287i
\(708\) 0 0
\(709\) 28.7846i 1.08103i 0.841335 + 0.540514i \(0.181770\pi\)
−0.841335 + 0.540514i \(0.818230\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.85641 9.85641i −0.369384 0.369384i
\(713\) 6.14359 0.230079
\(714\) 0 0
\(715\) 0 0
\(716\) −15.4641 26.7846i −0.577921 1.00099i
\(717\) 0 0
\(718\) −1.85641 6.92820i −0.0692805 0.258558i
\(719\) −25.8564 −0.964281 −0.482141 0.876094i \(-0.660141\pi\)
−0.482141 + 0.876094i \(0.660141\pi\)
\(720\) 0 0
\(721\) 4.53590 0.168926
\(722\) −13.4378 50.1506i −0.500104 1.86641i
\(723\) 0 0
\(724\) −16.0000 27.7128i −0.594635 1.02994i
\(725\) 0 0
\(726\) 0 0
\(727\) −14.0526 −0.521181 −0.260590 0.965449i \(-0.583917\pi\)
−0.260590 + 0.965449i \(0.583917\pi\)
\(728\) −18.9282 + 18.9282i −0.701526 + 0.701526i
\(729\) 0 0
\(730\) 0 0
\(731\) 30.2487i 1.11879i
\(732\) 0 0
\(733\) 48.9282i 1.80720i 0.428373 + 0.903602i \(0.359087\pi\)
−0.428373 + 0.903602i \(0.640913\pi\)
\(734\) −9.92820 37.0526i −0.366457 1.36763i
\(735\) 0 0
\(736\) 22.9282 + 6.14359i 0.845145 + 0.226456i
\(737\) 14.5359 0.535437
\(738\) 0 0
\(739\) 5.32051i 0.195718i −0.995200 0.0978590i \(-0.968801\pi\)
0.995200 0.0978590i \(-0.0311994\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −16.9282 + 4.53590i −0.621454 + 0.166518i
\(743\) −40.9808 −1.50344 −0.751719 0.659483i \(-0.770775\pi\)
−0.751719 + 0.659483i \(0.770775\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 40.5885 10.8756i 1.48605 0.398186i
\(747\) 0 0
\(748\) 6.92820 + 12.0000i 0.253320 + 0.438763i
\(749\) 2.00000i 0.0730784i
\(750\) 0 0
\(751\) −22.2487 −0.811867 −0.405934 0.913903i \(-0.633054\pi\)
−0.405934 + 0.913903i \(0.633054\pi\)
\(752\) 13.4641 23.3205i 0.490985 0.850411i
\(753\) 0 0
\(754\) 8.78461 + 32.7846i 0.319917 + 1.19395i
\(755\) 0 0
\(756\) 0 0
\(757\) 32.9282i 1.19680i 0.801199 + 0.598398i \(0.204196\pi\)
−0.801199 + 0.598398i \(0.795804\pi\)
\(758\) −16.7321 + 4.48334i −0.607735 + 0.162842i
\(759\) 0 0
\(760\) 0 0
\(761\) −49.7128 −1.80209 −0.901044 0.433728i \(-0.857198\pi\)
−0.901044 + 0.433728i \(0.857198\pi\)
\(762\) 0 0
\(763\) 8.39230i 0.303822i
\(764\) −33.4641 + 19.3205i −1.21069 + 0.698991i
\(765\) 0 0
\(766\) −1.14359 4.26795i −0.0413197 0.154207i
\(767\) 1.85641 0.0670310
\(768\) 0 0
\(769\) −0.928203 −0.0334719 −0.0167359 0.999860i \(-0.505327\pi\)
−0.0167359 + 0.999860i \(0.505327\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 12.9282 7.46410i 0.465296 0.268639i
\(773\) 1.60770i 0.0578248i −0.999582 0.0289124i \(-0.990796\pi\)
0.999582 0.0289124i \(-0.00920438\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 12.7846 + 12.7846i 0.458941 + 0.458941i
\(777\) 0 0
\(778\) −47.5167 + 12.7321i −1.70355 + 0.456466i
\(779\) 40.7846i 1.46126i
\(780\) 0 0
\(781\) 2.92820i 0.104779i
\(782\) −5.32051 19.8564i −0.190261 0.710064i
\(783\) 0 0
\(784\) 0.928203 1.60770i 0.0331501 0.0574177i
\(785\) 0 0
\(786\) 0 0
\(787\) 14.5885i 0.520022i 0.965606 + 0.260011i \(0.0837262\pi\)
−0.965606 + 0.260011i \(0.916274\pi\)
\(788\) 12.5359 + 21.7128i 0.446573 + 0.773487i
\(789\) 0 0
\(790\) 0 0
\(791\) 2.53590 0.0901662
\(792\) 0 0
\(793\) 17.0718 0.606237
\(794\) −22.1962 + 5.94744i −0.787712 + 0.211067i
\(795\) 0 0
\(796\) −44.7846 + 25.8564i −1.58735 + 0.916456i
\(797\) 26.1051i