Properties

Label 3330.2.d.p.1999.10
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 51 x^{6} - 124 x^{5} + 154 x^{4} - 46 x^{3} + x^{2} + 4 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 370)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.10
Root \(1.51933 - 1.51933i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.p.1999.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(1.42149 + 1.72608i) q^{5} +4.14336i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(1.42149 + 1.72608i) q^{5} +4.14336i q^{7} -1.00000i q^{8} +(-1.72608 + 1.42149i) q^{10} +4.76853 q^{11} -3.91744i q^{13} -4.14336 q^{14} +1.00000 q^{16} +3.31637i q^{17} +1.85109 q^{19} +(-1.42149 - 1.72608i) q^{20} +4.76853i q^{22} +1.54229i q^{23} +(-0.958719 + 4.90723i) q^{25} +3.91744 q^{26} -4.14336i q^{28} +8.87323 q^{29} +9.75286 q^{31} +1.00000i q^{32} -3.31637 q^{34} +(-7.15179 + 5.88976i) q^{35} -1.00000i q^{37} +1.85109i q^{38} +(1.72608 - 1.42149i) q^{40} +5.06977 q^{41} -9.99446i q^{43} -4.76853 q^{44} -1.54229 q^{46} +4.82700i q^{47} -10.1675 q^{49} +(-4.90723 - 0.958719i) q^{50} +3.91744i q^{52} +5.13611i q^{53} +(6.77843 + 8.23088i) q^{55} +4.14336 q^{56} +8.87323i q^{58} -1.05324 q^{59} -4.14422 q^{61} +9.75286i q^{62} -1.00000 q^{64} +(6.76182 - 5.56861i) q^{65} -1.00811i q^{67} -3.31637i q^{68} +(-5.88976 - 7.15179i) q^{70} -6.45248 q^{71} +10.7714i q^{73} +1.00000 q^{74} -1.85109 q^{76} +19.7578i q^{77} +1.19856 q^{79} +(1.42149 + 1.72608i) q^{80} +5.06977i q^{82} -10.6932i q^{83} +(-5.72432 + 4.71419i) q^{85} +9.99446 q^{86} -4.76853i q^{88} +7.29569 q^{89} +16.2314 q^{91} -1.54229i q^{92} -4.82700 q^{94} +(2.63131 + 3.19514i) q^{95} -14.8988i q^{97} -10.1675i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{4} - 6 q^{5} + O(q^{10}) \) \( 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.42149 + 1.72608i 0.635711 + 0.771927i
\(6\) 0 0
\(7\) 4.14336i 1.56604i 0.621994 + 0.783022i \(0.286323\pi\)
−0.621994 + 0.783022i \(0.713677\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.72608 + 1.42149i −0.545835 + 0.449515i
\(11\) 4.76853 1.43777 0.718883 0.695131i \(-0.244654\pi\)
0.718883 + 0.695131i \(0.244654\pi\)
\(12\) 0 0
\(13\) 3.91744i 1.08650i −0.839570 0.543251i \(-0.817193\pi\)
0.839570 0.543251i \(-0.182807\pi\)
\(14\) −4.14336 −1.10736
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.31637i 0.804337i 0.915566 + 0.402169i \(0.131743\pi\)
−0.915566 + 0.402169i \(0.868257\pi\)
\(18\) 0 0
\(19\) 1.85109 0.424670 0.212335 0.977197i \(-0.431893\pi\)
0.212335 + 0.977197i \(0.431893\pi\)
\(20\) −1.42149 1.72608i −0.317855 0.385964i
\(21\) 0 0
\(22\) 4.76853i 1.01665i
\(23\) 1.54229i 0.321590i 0.986988 + 0.160795i \(0.0514058\pi\)
−0.986988 + 0.160795i \(0.948594\pi\)
\(24\) 0 0
\(25\) −0.958719 + 4.90723i −0.191744 + 0.981445i
\(26\) 3.91744 0.768273
\(27\) 0 0
\(28\) 4.14336i 0.783022i
\(29\) 8.87323 1.64772 0.823859 0.566795i \(-0.191817\pi\)
0.823859 + 0.566795i \(0.191817\pi\)
\(30\) 0 0
\(31\) 9.75286 1.75166 0.875832 0.482615i \(-0.160313\pi\)
0.875832 + 0.482615i \(0.160313\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −3.31637 −0.568752
\(35\) −7.15179 + 5.88976i −1.20887 + 0.995551i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 1.85109i 0.300287i
\(39\) 0 0
\(40\) 1.72608 1.42149i 0.272918 0.224758i
\(41\) 5.06977 0.791764 0.395882 0.918301i \(-0.370439\pi\)
0.395882 + 0.918301i \(0.370439\pi\)
\(42\) 0 0
\(43\) 9.99446i 1.52414i −0.647494 0.762070i \(-0.724183\pi\)
0.647494 0.762070i \(-0.275817\pi\)
\(44\) −4.76853 −0.718883
\(45\) 0 0
\(46\) −1.54229 −0.227399
\(47\) 4.82700i 0.704090i 0.935983 + 0.352045i \(0.114514\pi\)
−0.935983 + 0.352045i \(0.885486\pi\)
\(48\) 0 0
\(49\) −10.1675 −1.45249
\(50\) −4.90723 0.958719i −0.693986 0.135583i
\(51\) 0 0
\(52\) 3.91744i 0.543251i
\(53\) 5.13611i 0.705499i 0.935718 + 0.352750i \(0.114753\pi\)
−0.935718 + 0.352750i \(0.885247\pi\)
\(54\) 0 0
\(55\) 6.77843 + 8.23088i 0.914003 + 1.10985i
\(56\) 4.14336 0.553680
\(57\) 0 0
\(58\) 8.87323i 1.16511i
\(59\) −1.05324 −0.137120 −0.0685598 0.997647i \(-0.521840\pi\)
−0.0685598 + 0.997647i \(0.521840\pi\)
\(60\) 0 0
\(61\) −4.14422 −0.530613 −0.265306 0.964164i \(-0.585473\pi\)
−0.265306 + 0.964164i \(0.585473\pi\)
\(62\) 9.75286i 1.23861i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 6.76182 5.56861i 0.838701 0.690701i
\(66\) 0 0
\(67\) 1.00811i 0.123160i −0.998102 0.0615800i \(-0.980386\pi\)
0.998102 0.0615800i \(-0.0196139\pi\)
\(68\) 3.31637i 0.402169i
\(69\) 0 0
\(70\) −5.88976 7.15179i −0.703961 0.854802i
\(71\) −6.45248 −0.765768 −0.382884 0.923796i \(-0.625069\pi\)
−0.382884 + 0.923796i \(0.625069\pi\)
\(72\) 0 0
\(73\) 10.7714i 1.26070i 0.776312 + 0.630349i \(0.217088\pi\)
−0.776312 + 0.630349i \(0.782912\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −1.85109 −0.212335
\(77\) 19.7578i 2.25161i
\(78\) 0 0
\(79\) 1.19856 0.134849 0.0674243 0.997724i \(-0.478522\pi\)
0.0674243 + 0.997724i \(0.478522\pi\)
\(80\) 1.42149 + 1.72608i 0.158928 + 0.192982i
\(81\) 0 0
\(82\) 5.06977i 0.559862i
\(83\) 10.6932i 1.17373i −0.809683 0.586867i \(-0.800361\pi\)
0.809683 0.586867i \(-0.199639\pi\)
\(84\) 0 0
\(85\) −5.72432 + 4.71419i −0.620890 + 0.511326i
\(86\) 9.99446 1.07773
\(87\) 0 0
\(88\) 4.76853i 0.508327i
\(89\) 7.29569 0.773342 0.386671 0.922218i \(-0.373625\pi\)
0.386671 + 0.922218i \(0.373625\pi\)
\(90\) 0 0
\(91\) 16.2314 1.70151
\(92\) 1.54229i 0.160795i
\(93\) 0 0
\(94\) −4.82700 −0.497867
\(95\) 2.63131 + 3.19514i 0.269967 + 0.327814i
\(96\) 0 0
\(97\) 14.8988i 1.51274i −0.654143 0.756371i \(-0.726970\pi\)
0.654143 0.756371i \(-0.273030\pi\)
\(98\) 10.1675i 1.02707i
\(99\) 0 0
\(100\) 0.958719 4.90723i 0.0958719 0.490723i
\(101\) −18.5903 −1.84980 −0.924902 0.380206i \(-0.875853\pi\)
−0.924902 + 0.380206i \(0.875853\pi\)
\(102\) 0 0
\(103\) 13.3033i 1.31081i −0.755278 0.655404i \(-0.772498\pi\)
0.755278 0.655404i \(-0.227502\pi\)
\(104\) −3.91744 −0.384136
\(105\) 0 0
\(106\) −5.13611 −0.498863
\(107\) 12.4763i 1.20613i 0.797691 + 0.603066i \(0.206054\pi\)
−0.797691 + 0.603066i \(0.793946\pi\)
\(108\) 0 0
\(109\) 4.35447 0.417083 0.208541 0.978014i \(-0.433128\pi\)
0.208541 + 0.978014i \(0.433128\pi\)
\(110\) −8.23088 + 6.77843i −0.784783 + 0.646298i
\(111\) 0 0
\(112\) 4.14336i 0.391511i
\(113\) 9.54261i 0.897693i −0.893609 0.448846i \(-0.851835\pi\)
0.893609 0.448846i \(-0.148165\pi\)
\(114\) 0 0
\(115\) −2.66212 + 2.19236i −0.248244 + 0.204438i
\(116\) −8.87323 −0.823859
\(117\) 0 0
\(118\) 1.05324i 0.0969582i
\(119\) −13.7409 −1.25963
\(120\) 0 0
\(121\) 11.7389 1.06717
\(122\) 4.14422i 0.375200i
\(123\) 0 0
\(124\) −9.75286 −0.875832
\(125\) −9.83309 + 5.32076i −0.879498 + 0.475903i
\(126\) 0 0
\(127\) 8.33492i 0.739605i −0.929110 0.369802i \(-0.879425\pi\)
0.929110 0.369802i \(-0.120575\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 5.56861 + 6.76182i 0.488399 + 0.593051i
\(131\) −3.68597 −0.322045 −0.161022 0.986951i \(-0.551479\pi\)
−0.161022 + 0.986951i \(0.551479\pi\)
\(132\) 0 0
\(133\) 7.66975i 0.665052i
\(134\) 1.00811 0.0870873
\(135\) 0 0
\(136\) 3.31637 0.284376
\(137\) 12.3027i 1.05109i −0.850765 0.525546i \(-0.823861\pi\)
0.850765 0.525546i \(-0.176139\pi\)
\(138\) 0 0
\(139\) 0.842442 0.0714550 0.0357275 0.999362i \(-0.488625\pi\)
0.0357275 + 0.999362i \(0.488625\pi\)
\(140\) 7.15179 5.88976i 0.604436 0.497776i
\(141\) 0 0
\(142\) 6.45248i 0.541480i
\(143\) 18.6804i 1.56214i
\(144\) 0 0
\(145\) 12.6132 + 15.3159i 1.04747 + 1.27192i
\(146\) −10.7714 −0.891448
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −16.7723 −1.37404 −0.687019 0.726640i \(-0.741081\pi\)
−0.687019 + 0.726640i \(0.741081\pi\)
\(150\) 0 0
\(151\) −7.59755 −0.618280 −0.309140 0.951017i \(-0.600041\pi\)
−0.309140 + 0.951017i \(0.600041\pi\)
\(152\) 1.85109i 0.150143i
\(153\) 0 0
\(154\) −19.7578 −1.59213
\(155\) 13.8636 + 16.8342i 1.11355 + 1.35216i
\(156\) 0 0
\(157\) 4.45631i 0.355652i −0.984062 0.177826i \(-0.943094\pi\)
0.984062 0.177826i \(-0.0569065\pi\)
\(158\) 1.19856i 0.0953523i
\(159\) 0 0
\(160\) −1.72608 + 1.42149i −0.136459 + 0.112379i
\(161\) −6.39028 −0.503624
\(162\) 0 0
\(163\) 19.4599i 1.52422i 0.647447 + 0.762110i \(0.275837\pi\)
−0.647447 + 0.762110i \(0.724163\pi\)
\(164\) −5.06977 −0.395882
\(165\) 0 0
\(166\) 10.6932 0.829955
\(167\) 7.13813i 0.552365i 0.961105 + 0.276183i \(0.0890695\pi\)
−0.961105 + 0.276183i \(0.910931\pi\)
\(168\) 0 0
\(169\) −2.34632 −0.180486
\(170\) −4.71419 5.72432i −0.361562 0.439035i
\(171\) 0 0
\(172\) 9.99446i 0.762070i
\(173\) 11.6199i 0.883448i 0.897151 + 0.441724i \(0.145633\pi\)
−0.897151 + 0.441724i \(0.854367\pi\)
\(174\) 0 0
\(175\) −20.3324 3.97232i −1.53699 0.300279i
\(176\) 4.76853 0.359442
\(177\) 0 0
\(178\) 7.29569i 0.546835i
\(179\) −17.2224 −1.28726 −0.643631 0.765336i \(-0.722573\pi\)
−0.643631 + 0.765336i \(0.722573\pi\)
\(180\) 0 0
\(181\) −23.5098 −1.74747 −0.873733 0.486405i \(-0.838308\pi\)
−0.873733 + 0.486405i \(0.838308\pi\)
\(182\) 16.2314i 1.20315i
\(183\) 0 0
\(184\) 1.54229 0.113699
\(185\) 1.72608 1.42149i 0.126904 0.104510i
\(186\) 0 0
\(187\) 15.8142i 1.15645i
\(188\) 4.82700i 0.352045i
\(189\) 0 0
\(190\) −3.19514 + 2.63131i −0.231800 + 0.190896i
\(191\) −1.16660 −0.0844125 −0.0422063 0.999109i \(-0.513439\pi\)
−0.0422063 + 0.999109i \(0.513439\pi\)
\(192\) 0 0
\(193\) 9.36727i 0.674271i −0.941456 0.337135i \(-0.890542\pi\)
0.941456 0.337135i \(-0.109458\pi\)
\(194\) 14.8988 1.06967
\(195\) 0 0
\(196\) 10.1675 0.726247
\(197\) 3.21836i 0.229299i 0.993406 + 0.114649i \(0.0365744\pi\)
−0.993406 + 0.114649i \(0.963426\pi\)
\(198\) 0 0
\(199\) 2.99104 0.212029 0.106014 0.994365i \(-0.466191\pi\)
0.106014 + 0.994365i \(0.466191\pi\)
\(200\) 4.90723 + 0.958719i 0.346993 + 0.0677917i
\(201\) 0 0
\(202\) 18.5903i 1.30801i
\(203\) 36.7650i 2.58040i
\(204\) 0 0
\(205\) 7.20663 + 8.75083i 0.503333 + 0.611185i
\(206\) 13.3033 0.926882
\(207\) 0 0
\(208\) 3.91744i 0.271625i
\(209\) 8.82700 0.610576
\(210\) 0 0
\(211\) 4.75340 0.327237 0.163619 0.986524i \(-0.447683\pi\)
0.163619 + 0.986524i \(0.447683\pi\)
\(212\) 5.13611i 0.352750i
\(213\) 0 0
\(214\) −12.4763 −0.852864
\(215\) 17.2513 14.2070i 1.17653 0.968912i
\(216\) 0 0
\(217\) 40.4096i 2.74318i
\(218\) 4.35447i 0.294922i
\(219\) 0 0
\(220\) −6.77843 8.23088i −0.457002 0.554926i
\(221\) 12.9917 0.873914
\(222\) 0 0
\(223\) 6.95635i 0.465832i −0.972497 0.232916i \(-0.925173\pi\)
0.972497 0.232916i \(-0.0748267\pi\)
\(224\) −4.14336 −0.276840
\(225\) 0 0
\(226\) 9.54261 0.634765
\(227\) 22.2980i 1.47997i −0.672622 0.739986i \(-0.734832\pi\)
0.672622 0.739986i \(-0.265168\pi\)
\(228\) 0 0
\(229\) −12.9648 −0.856739 −0.428370 0.903604i \(-0.640912\pi\)
−0.428370 + 0.903604i \(0.640912\pi\)
\(230\) −2.19236 2.66212i −0.144560 0.175535i
\(231\) 0 0
\(232\) 8.87323i 0.582556i
\(233\) 10.4327i 0.683468i 0.939797 + 0.341734i \(0.111014\pi\)
−0.939797 + 0.341734i \(0.888986\pi\)
\(234\) 0 0
\(235\) −8.33179 + 6.86154i −0.543506 + 0.447597i
\(236\) 1.05324 0.0685598
\(237\) 0 0
\(238\) 13.7409i 0.890691i
\(239\) 1.58711 0.102661 0.0513307 0.998682i \(-0.483654\pi\)
0.0513307 + 0.998682i \(0.483654\pi\)
\(240\) 0 0
\(241\) 16.2576 1.04724 0.523622 0.851951i \(-0.324581\pi\)
0.523622 + 0.851951i \(0.324581\pi\)
\(242\) 11.7389i 0.754604i
\(243\) 0 0
\(244\) 4.14422 0.265306
\(245\) −14.4530 17.5499i −0.923366 1.12122i
\(246\) 0 0
\(247\) 7.25154i 0.461405i
\(248\) 9.75286i 0.619307i
\(249\) 0 0
\(250\) −5.32076 9.83309i −0.336514 0.621899i
\(251\) −14.9486 −0.943547 −0.471774 0.881720i \(-0.656386\pi\)
−0.471774 + 0.881720i \(0.656386\pi\)
\(252\) 0 0
\(253\) 7.35447i 0.462372i
\(254\) 8.33492 0.522979
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 14.9968i 0.935474i 0.883868 + 0.467737i \(0.154931\pi\)
−0.883868 + 0.467737i \(0.845069\pi\)
\(258\) 0 0
\(259\) 4.14336 0.257456
\(260\) −6.76182 + 5.56861i −0.419350 + 0.345350i
\(261\) 0 0
\(262\) 3.68597i 0.227720i
\(263\) 22.9610i 1.41583i −0.706295 0.707917i \(-0.749635\pi\)
0.706295 0.707917i \(-0.250365\pi\)
\(264\) 0 0
\(265\) −8.86535 + 7.30094i −0.544594 + 0.448493i
\(266\) −7.66975 −0.470263
\(267\) 0 0
\(268\) 1.00811i 0.0615800i
\(269\) 10.0896 0.615175 0.307588 0.951520i \(-0.400478\pi\)
0.307588 + 0.951520i \(0.400478\pi\)
\(270\) 0 0
\(271\) 3.30678 0.200872 0.100436 0.994943i \(-0.467976\pi\)
0.100436 + 0.994943i \(0.467976\pi\)
\(272\) 3.31637i 0.201084i
\(273\) 0 0
\(274\) 12.3027 0.743234
\(275\) −4.57168 + 23.4003i −0.275683 + 1.41109i
\(276\) 0 0
\(277\) 15.9046i 0.955617i 0.878464 + 0.477809i \(0.158569\pi\)
−0.878464 + 0.477809i \(0.841431\pi\)
\(278\) 0.842442i 0.0505263i
\(279\) 0 0
\(280\) 5.88976 + 7.15179i 0.351980 + 0.427401i
\(281\) −11.3609 −0.677732 −0.338866 0.940835i \(-0.610043\pi\)
−0.338866 + 0.940835i \(0.610043\pi\)
\(282\) 0 0
\(283\) 20.1530i 1.19797i 0.800761 + 0.598984i \(0.204429\pi\)
−0.800761 + 0.598984i \(0.795571\pi\)
\(284\) 6.45248 0.382884
\(285\) 0 0
\(286\) 18.6804 1.10460
\(287\) 21.0059i 1.23994i
\(288\) 0 0
\(289\) 6.00171 0.353042
\(290\) −15.3159 + 12.6132i −0.899382 + 0.740674i
\(291\) 0 0
\(292\) 10.7714i 0.630349i
\(293\) 21.0517i 1.22986i 0.788583 + 0.614928i \(0.210815\pi\)
−0.788583 + 0.614928i \(0.789185\pi\)
\(294\) 0 0
\(295\) −1.49717 1.81797i −0.0871684 0.105846i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 16.7723i 0.971591i
\(299\) 6.04184 0.349408
\(300\) 0 0
\(301\) 41.4107 2.38687
\(302\) 7.59755i 0.437190i
\(303\) 0 0
\(304\) 1.85109 0.106167
\(305\) −5.89098 7.15326i −0.337316 0.409595i
\(306\) 0 0
\(307\) 17.0946i 0.975638i −0.872945 0.487819i \(-0.837793\pi\)
0.872945 0.487819i \(-0.162207\pi\)
\(308\) 19.7578i 1.12580i
\(309\) 0 0
\(310\) −16.8342 + 13.8636i −0.956120 + 0.787400i
\(311\) −20.0503 −1.13695 −0.568473 0.822702i \(-0.692466\pi\)
−0.568473 + 0.822702i \(0.692466\pi\)
\(312\) 0 0
\(313\) 13.3400i 0.754019i 0.926209 + 0.377010i \(0.123048\pi\)
−0.926209 + 0.377010i \(0.876952\pi\)
\(314\) 4.45631 0.251484
\(315\) 0 0
\(316\) −1.19856 −0.0674243
\(317\) 12.8528i 0.721885i 0.932588 + 0.360943i \(0.117545\pi\)
−0.932588 + 0.360943i \(0.882455\pi\)
\(318\) 0 0
\(319\) 42.3123 2.36903
\(320\) −1.42149 1.72608i −0.0794638 0.0964909i
\(321\) 0 0
\(322\) 6.39028i 0.356116i
\(323\) 6.13890i 0.341578i
\(324\) 0 0
\(325\) 19.2238 + 3.75572i 1.06634 + 0.208330i
\(326\) −19.4599 −1.07779
\(327\) 0 0
\(328\) 5.06977i 0.279931i
\(329\) −20.0000 −1.10264
\(330\) 0 0
\(331\) −23.5835 −1.29627 −0.648134 0.761526i \(-0.724451\pi\)
−0.648134 + 0.761526i \(0.724451\pi\)
\(332\) 10.6932i 0.586867i
\(333\) 0 0
\(334\) −7.13813 −0.390581
\(335\) 1.74008 1.43302i 0.0950706 0.0782942i
\(336\) 0 0
\(337\) 26.6074i 1.44940i −0.689067 0.724698i \(-0.741979\pi\)
0.689067 0.724698i \(-0.258021\pi\)
\(338\) 2.34632i 0.127623i
\(339\) 0 0
\(340\) 5.72432 4.71419i 0.310445 0.255663i
\(341\) 46.5068 2.51848
\(342\) 0 0
\(343\) 13.1239i 0.708626i
\(344\) −9.99446 −0.538865
\(345\) 0 0
\(346\) −11.6199 −0.624692
\(347\) 17.2626i 0.926707i −0.886174 0.463353i \(-0.846646\pi\)
0.886174 0.463353i \(-0.153354\pi\)
\(348\) 0 0
\(349\) −11.1619 −0.597484 −0.298742 0.954334i \(-0.596567\pi\)
−0.298742 + 0.954334i \(0.596567\pi\)
\(350\) 3.97232 20.3324i 0.212330 1.08681i
\(351\) 0 0
\(352\) 4.76853i 0.254164i
\(353\) 12.6563i 0.673628i 0.941571 + 0.336814i \(0.109349\pi\)
−0.941571 + 0.336814i \(0.890651\pi\)
\(354\) 0 0
\(355\) −9.17215 11.1375i −0.486807 0.591117i
\(356\) −7.29569 −0.386671
\(357\) 0 0
\(358\) 17.2224i 0.910232i
\(359\) −23.2778 −1.22855 −0.614277 0.789091i \(-0.710552\pi\)
−0.614277 + 0.789091i \(0.710552\pi\)
\(360\) 0 0
\(361\) −15.5735 −0.819655
\(362\) 23.5098i 1.23565i
\(363\) 0 0
\(364\) −16.2314 −0.850755
\(365\) −18.5923 + 15.3115i −0.973167 + 0.801439i
\(366\) 0 0
\(367\) 9.09417i 0.474712i 0.971423 + 0.237356i \(0.0762808\pi\)
−0.971423 + 0.237356i \(0.923719\pi\)
\(368\) 1.54229i 0.0803976i
\(369\) 0 0
\(370\) 1.42149 + 1.72608i 0.0738999 + 0.0897347i
\(371\) −21.2808 −1.10484
\(372\) 0 0
\(373\) 5.75976i 0.298229i 0.988820 + 0.149114i \(0.0476423\pi\)
−0.988820 + 0.149114i \(0.952358\pi\)
\(374\) −15.8142 −0.817733
\(375\) 0 0
\(376\) 4.82700 0.248933
\(377\) 34.7603i 1.79025i
\(378\) 0 0
\(379\) −18.0902 −0.929229 −0.464614 0.885513i \(-0.653807\pi\)
−0.464614 + 0.885513i \(0.653807\pi\)
\(380\) −2.63131 3.19514i −0.134984 0.163907i
\(381\) 0 0
\(382\) 1.16660i 0.0596887i
\(383\) 3.54752i 0.181270i −0.995884 0.0906350i \(-0.971110\pi\)
0.995884 0.0906350i \(-0.0288896\pi\)
\(384\) 0 0
\(385\) −34.1035 + 28.0855i −1.73808 + 1.43137i
\(386\) 9.36727 0.476781
\(387\) 0 0
\(388\) 14.8988i 0.756371i
\(389\) 25.6053 1.29824 0.649119 0.760687i \(-0.275138\pi\)
0.649119 + 0.760687i \(0.275138\pi\)
\(390\) 0 0
\(391\) −5.11481 −0.258667
\(392\) 10.1675i 0.513534i
\(393\) 0 0
\(394\) −3.21836 −0.162139
\(395\) 1.70374 + 2.06881i 0.0857247 + 0.104093i
\(396\) 0 0
\(397\) 31.4597i 1.57892i −0.613803 0.789459i \(-0.710361\pi\)
0.613803 0.789459i \(-0.289639\pi\)
\(398\) 2.99104i 0.149927i
\(399\) 0 0
\(400\) −0.958719 + 4.90723i −0.0479360 + 0.245361i
\(401\) 22.9940 1.14826 0.574132 0.818763i \(-0.305340\pi\)
0.574132 + 0.818763i \(0.305340\pi\)
\(402\) 0 0
\(403\) 38.2062i 1.90319i
\(404\) 18.5903 0.924902
\(405\) 0 0
\(406\) −36.7650 −1.82462
\(407\) 4.76853i 0.236367i
\(408\) 0 0
\(409\) 33.3828 1.65067 0.825337 0.564640i \(-0.190985\pi\)
0.825337 + 0.564640i \(0.190985\pi\)
\(410\) −8.75083 + 7.20663i −0.432173 + 0.355910i
\(411\) 0 0
\(412\) 13.3033i 0.655404i
\(413\) 4.36394i 0.214735i
\(414\) 0 0
\(415\) 18.4574 15.2003i 0.906037 0.746155i
\(416\) 3.91744 0.192068
\(417\) 0 0
\(418\) 8.82700i 0.431743i
\(419\) 8.32565 0.406734 0.203367 0.979103i \(-0.434811\pi\)
0.203367 + 0.979103i \(0.434811\pi\)
\(420\) 0 0
\(421\) −8.41521 −0.410132 −0.205066 0.978748i \(-0.565741\pi\)
−0.205066 + 0.978748i \(0.565741\pi\)
\(422\) 4.75340i 0.231392i
\(423\) 0 0
\(424\) 5.13611 0.249432
\(425\) −16.2742 3.17946i −0.789413 0.154227i
\(426\) 0 0
\(427\) 17.1710i 0.830963i
\(428\) 12.4763i 0.603066i
\(429\) 0 0
\(430\) 14.2070 + 17.2513i 0.685124 + 0.831929i
\(431\) −3.04769 −0.146802 −0.0734011 0.997303i \(-0.523385\pi\)
−0.0734011 + 0.997303i \(0.523385\pi\)
\(432\) 0 0
\(433\) 22.9439i 1.10262i 0.834302 + 0.551308i \(0.185871\pi\)
−0.834302 + 0.551308i \(0.814129\pi\)
\(434\) −40.4096 −1.93972
\(435\) 0 0
\(436\) −4.35447 −0.208541
\(437\) 2.85493i 0.136570i
\(438\) 0 0
\(439\) −10.3033 −0.491751 −0.245875 0.969301i \(-0.579075\pi\)
−0.245875 + 0.969301i \(0.579075\pi\)
\(440\) 8.23088 6.77843i 0.392392 0.323149i
\(441\) 0 0
\(442\) 12.9917i 0.617950i
\(443\) 4.84236i 0.230067i 0.993362 + 0.115034i \(0.0366976\pi\)
−0.993362 + 0.115034i \(0.963302\pi\)
\(444\) 0 0
\(445\) 10.3708 + 12.5930i 0.491622 + 0.596964i
\(446\) 6.95635 0.329393
\(447\) 0 0
\(448\) 4.14336i 0.195756i
\(449\) 25.3149 1.19468 0.597341 0.801987i \(-0.296224\pi\)
0.597341 + 0.801987i \(0.296224\pi\)
\(450\) 0 0
\(451\) 24.1753 1.13837
\(452\) 9.54261i 0.448846i
\(453\) 0 0
\(454\) 22.2980 1.04650
\(455\) 23.0728 + 28.0167i 1.08167 + 1.31344i
\(456\) 0 0
\(457\) 11.9945i 0.561077i −0.959843 0.280539i \(-0.909487\pi\)
0.959843 0.280539i \(-0.0905130\pi\)
\(458\) 12.9648i 0.605806i
\(459\) 0 0
\(460\) 2.66212 2.19236i 0.124122 0.102219i
\(461\) 23.6570 1.10182 0.550909 0.834565i \(-0.314281\pi\)
0.550909 + 0.834565i \(0.314281\pi\)
\(462\) 0 0
\(463\) 17.3667i 0.807099i −0.914958 0.403550i \(-0.867776\pi\)
0.914958 0.403550i \(-0.132224\pi\)
\(464\) 8.87323 0.411929
\(465\) 0 0
\(466\) −10.4327 −0.483285
\(467\) 20.4476i 0.946200i −0.881009 0.473100i \(-0.843135\pi\)
0.881009 0.473100i \(-0.156865\pi\)
\(468\) 0 0
\(469\) 4.17696 0.192874
\(470\) −6.86154 8.33179i −0.316499 0.384317i
\(471\) 0 0
\(472\) 1.05324i 0.0484791i
\(473\) 47.6589i 2.19136i
\(474\) 0 0
\(475\) −1.77468 + 9.08373i −0.0814278 + 0.416790i
\(476\) 13.7409 0.629814
\(477\) 0 0
\(478\) 1.58711i 0.0725925i
\(479\) −34.1325 −1.55955 −0.779777 0.626057i \(-0.784668\pi\)
−0.779777 + 0.626057i \(0.784668\pi\)
\(480\) 0 0
\(481\) −3.91744 −0.178620
\(482\) 16.2576i 0.740513i
\(483\) 0 0
\(484\) −11.7389 −0.533586
\(485\) 25.7165 21.1785i 1.16773 0.961667i
\(486\) 0 0
\(487\) 6.16917i 0.279552i −0.990183 0.139776i \(-0.955362\pi\)
0.990183 0.139776i \(-0.0446382\pi\)
\(488\) 4.14422i 0.187600i
\(489\) 0 0
\(490\) 17.5499 14.4530i 0.792822 0.652918i
\(491\) 11.8290 0.533836 0.266918 0.963719i \(-0.413995\pi\)
0.266918 + 0.963719i \(0.413995\pi\)
\(492\) 0 0
\(493\) 29.4269i 1.32532i
\(494\) 7.25154 0.326262
\(495\) 0 0
\(496\) 9.75286 0.437916
\(497\) 26.7350i 1.19923i
\(498\) 0 0
\(499\) −31.4004 −1.40568 −0.702839 0.711349i \(-0.748084\pi\)
−0.702839 + 0.711349i \(0.748084\pi\)
\(500\) 9.83309 5.32076i 0.439749 0.237951i
\(501\) 0 0
\(502\) 14.9486i 0.667189i
\(503\) 39.7743i 1.77345i −0.462299 0.886724i \(-0.652975\pi\)
0.462299 0.886724i \(-0.347025\pi\)
\(504\) 0 0
\(505\) −26.4260 32.0884i −1.17594 1.42791i
\(506\) −7.35447 −0.326946
\(507\) 0 0
\(508\) 8.33492i 0.369802i
\(509\) −6.82812 −0.302651 −0.151326 0.988484i \(-0.548354\pi\)
−0.151326 + 0.988484i \(0.548354\pi\)
\(510\) 0 0
\(511\) −44.6299 −1.97431
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −14.9968 −0.661480
\(515\) 22.9625 18.9105i 1.01185 0.833295i
\(516\) 0 0
\(517\) 23.0177i 1.01232i
\(518\) 4.14336i 0.182049i
\(519\) 0 0
\(520\) −5.56861 6.76182i −0.244200 0.296525i
\(521\) 30.6638 1.34341 0.671703 0.740821i \(-0.265563\pi\)
0.671703 + 0.740821i \(0.265563\pi\)
\(522\) 0 0
\(523\) 12.1618i 0.531800i 0.964001 + 0.265900i \(0.0856690\pi\)
−0.964001 + 0.265900i \(0.914331\pi\)
\(524\) 3.68597 0.161022
\(525\) 0 0
\(526\) 22.9610 1.00115
\(527\) 32.3441i 1.40893i
\(528\) 0 0
\(529\) 20.6213 0.896580
\(530\) −7.30094 8.86535i −0.317133 0.385086i
\(531\) 0 0
\(532\) 7.66975i 0.332526i
\(533\) 19.8605i 0.860253i
\(534\) 0 0
\(535\) −21.5352 + 17.7350i −0.931046 + 0.766751i
\(536\) −1.00811 −0.0435437
\(537\) 0 0
\(538\) 10.0896i 0.434995i
\(539\) −48.4839 −2.08835
\(540\) 0 0
\(541\) 10.5469 0.453446 0.226723 0.973959i \(-0.427199\pi\)
0.226723 + 0.973959i \(0.427199\pi\)
\(542\) 3.30678i 0.142038i
\(543\) 0 0
\(544\) −3.31637 −0.142188
\(545\) 6.18985 + 7.51617i 0.265144 + 0.321957i
\(546\) 0 0
\(547\) 4.09517i 0.175097i −0.996160 0.0875484i \(-0.972097\pi\)
0.996160 0.0875484i \(-0.0279032\pi\)
\(548\) 12.3027i 0.525546i
\(549\) 0 0
\(550\) −23.4003 4.57168i −0.997790 0.194937i
\(551\) 16.4252 0.699736
\(552\) 0 0
\(553\) 4.96607i 0.211179i
\(554\) −15.9046 −0.675723
\(555\) 0 0
\(556\) −0.842442 −0.0357275
\(557\) 2.50711i 0.106230i −0.998588 0.0531149i \(-0.983085\pi\)
0.998588 0.0531149i \(-0.0169149\pi\)
\(558\) 0 0
\(559\) −39.1527 −1.65598
\(560\) −7.15179 + 5.88976i −0.302218 + 0.248888i
\(561\) 0 0
\(562\) 11.3609i 0.479229i
\(563\) 9.87532i 0.416195i −0.978108 0.208097i \(-0.933273\pi\)
0.978108 0.208097i \(-0.0667271\pi\)
\(564\) 0 0
\(565\) 16.4713 13.5647i 0.692954 0.570673i
\(566\) −20.1530 −0.847092
\(567\) 0 0
\(568\) 6.45248i 0.270740i
\(569\) 12.5198 0.524858 0.262429 0.964951i \(-0.415477\pi\)
0.262429 + 0.964951i \(0.415477\pi\)
\(570\) 0 0
\(571\) 20.3156 0.850179 0.425090 0.905151i \(-0.360243\pi\)
0.425090 + 0.905151i \(0.360243\pi\)
\(572\) 18.6804i 0.781068i
\(573\) 0 0
\(574\) −21.0059 −0.876769
\(575\) −7.56838 1.47863i −0.315623 0.0616629i
\(576\) 0 0
\(577\) 20.0756i 0.835759i −0.908502 0.417880i \(-0.862773\pi\)
0.908502 0.417880i \(-0.137227\pi\)
\(578\) 6.00171i 0.249638i
\(579\) 0 0
\(580\) −12.6132 15.3159i −0.523736 0.635959i
\(581\) 44.3059 1.83812
\(582\) 0 0
\(583\) 24.4917i 1.01434i
\(584\) 10.7714 0.445724
\(585\) 0 0
\(586\) −21.0517 −0.869639
\(587\) 3.71178i 0.153201i 0.997062 + 0.0766007i \(0.0244067\pi\)
−0.997062 + 0.0766007i \(0.975593\pi\)
\(588\) 0 0
\(589\) 18.0534 0.743879
\(590\) 1.81797 1.49717i 0.0748447 0.0616373i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 36.2899i 1.49025i −0.666926 0.745124i \(-0.732390\pi\)
0.666926 0.745124i \(-0.267610\pi\)
\(594\) 0 0
\(595\) −19.5326 23.7179i −0.800759 0.972341i
\(596\) 16.7723 0.687019
\(597\) 0 0
\(598\) 6.04184i 0.247069i
\(599\) 23.7528 0.970515 0.485257 0.874371i \(-0.338726\pi\)
0.485257 + 0.874371i \(0.338726\pi\)
\(600\) 0 0
\(601\) 15.9718 0.651502 0.325751 0.945456i \(-0.394383\pi\)
0.325751 + 0.945456i \(0.394383\pi\)
\(602\) 41.4107i 1.68777i
\(603\) 0 0
\(604\) 7.59755 0.309140
\(605\) 16.6867 + 20.2623i 0.678413 + 0.823779i
\(606\) 0 0
\(607\) 38.0139i 1.54294i −0.636267 0.771469i \(-0.719522\pi\)
0.636267 0.771469i \(-0.280478\pi\)
\(608\) 1.85109i 0.0750717i
\(609\) 0 0
\(610\) 7.15326 5.89098i 0.289627 0.238519i
\(611\) 18.9095 0.764995
\(612\) 0 0
\(613\) 8.40204i 0.339355i −0.985500 0.169678i \(-0.945727\pi\)
0.985500 0.169678i \(-0.0542726\pi\)
\(614\) 17.0946 0.689880
\(615\) 0 0
\(616\) 19.7578 0.796063
\(617\) 6.72707i 0.270822i −0.990790 0.135411i \(-0.956765\pi\)
0.990790 0.135411i \(-0.0432354\pi\)
\(618\) 0 0
\(619\) −24.3689 −0.979470 −0.489735 0.871871i \(-0.662906\pi\)
−0.489735 + 0.871871i \(0.662906\pi\)
\(620\) −13.8636 16.8342i −0.556776 0.676079i
\(621\) 0 0
\(622\) 20.0503i 0.803943i
\(623\) 30.2287i 1.21109i
\(624\) 0 0
\(625\) −23.1617 9.40930i −0.926469 0.376372i
\(626\) −13.3400 −0.533172
\(627\) 0 0
\(628\) 4.45631i 0.177826i
\(629\) 3.31637 0.132232
\(630\) 0 0
\(631\) 34.7737 1.38432 0.692160 0.721744i \(-0.256659\pi\)
0.692160 + 0.721744i \(0.256659\pi\)
\(632\) 1.19856i 0.0476762i
\(633\) 0 0
\(634\) −12.8528 −0.510450
\(635\) 14.3868 11.8480i 0.570921 0.470175i
\(636\) 0 0
\(637\) 39.8304i 1.57814i
\(638\) 42.3123i 1.67516i
\(639\) 0 0
\(640\) 1.72608 1.42149i 0.0682294 0.0561894i
\(641\) 27.8544 1.10018 0.550091 0.835105i \(-0.314593\pi\)
0.550091 + 0.835105i \(0.314593\pi\)
\(642\) 0 0
\(643\) 35.4013i 1.39609i −0.716054 0.698045i \(-0.754053\pi\)
0.716054 0.698045i \(-0.245947\pi\)
\(644\) 6.39028 0.251812
\(645\) 0 0
\(646\) −6.13890 −0.241532
\(647\) 16.1343i 0.634305i 0.948375 + 0.317152i \(0.102727\pi\)
−0.948375 + 0.317152i \(0.897273\pi\)
\(648\) 0 0
\(649\) −5.02239 −0.197146
\(650\) −3.75572 + 19.2238i −0.147312 + 0.754018i
\(651\) 0 0
\(652\) 19.4599i 0.762110i
\(653\) 11.9146i 0.466256i −0.972446 0.233128i \(-0.925104\pi\)
0.972446 0.233128i \(-0.0748961\pi\)
\(654\) 0 0
\(655\) −5.23958 6.36229i −0.204727 0.248595i
\(656\) 5.06977 0.197941
\(657\) 0 0
\(658\) 20.0000i 0.779681i
\(659\) −30.5124 −1.18859 −0.594297 0.804246i \(-0.702569\pi\)
−0.594297 + 0.804246i \(0.702569\pi\)
\(660\) 0 0
\(661\) 42.0973 1.63740 0.818698 0.574224i \(-0.194696\pi\)
0.818698 + 0.574224i \(0.194696\pi\)
\(662\) 23.5835i 0.916600i
\(663\) 0 0
\(664\) −10.6932 −0.414977
\(665\) −13.2386 + 10.9025i −0.513372 + 0.422781i
\(666\) 0 0
\(667\) 13.6851i 0.529890i
\(668\) 7.13813i 0.276183i
\(669\) 0 0
\(670\) 1.43302 + 1.74008i 0.0553623 + 0.0672251i
\(671\) −19.7618 −0.762897
\(672\) 0 0
\(673\) 41.1540i 1.58637i −0.608982 0.793184i \(-0.708422\pi\)
0.608982 0.793184i \(-0.291578\pi\)
\(674\) 26.6074 1.02488
\(675\) 0 0
\(676\) 2.34632 0.0902431
\(677\) 10.3914i 0.399373i −0.979860 0.199686i \(-0.936008\pi\)
0.979860 0.199686i \(-0.0639923\pi\)
\(678\) 0 0
\(679\) 61.7311 2.36902
\(680\) 4.71419 + 5.72432i 0.180781 + 0.219518i
\(681\) 0 0
\(682\) 46.5068i 1.78084i
\(683\) 5.05345i 0.193365i −0.995315 0.0966824i \(-0.969177\pi\)
0.995315 0.0966824i \(-0.0308231\pi\)
\(684\) 0 0
\(685\) 21.2355 17.4882i 0.811367 0.668190i
\(686\) 13.1239 0.501074
\(687\) 0 0
\(688\) 9.99446i 0.381035i
\(689\) 20.1204 0.766526
\(690\) 0 0
\(691\) 13.7857 0.524432 0.262216 0.965009i \(-0.415547\pi\)
0.262216 + 0.965009i \(0.415547\pi\)
\(692\) 11.6199i 0.441724i
\(693\) 0 0
\(694\) 17.2626 0.655280
\(695\) 1.19753 + 1.45412i 0.0454247 + 0.0551581i
\(696\) 0 0
\(697\) 16.8132i 0.636846i
\(698\) 11.1619i 0.422485i
\(699\) 0 0
\(700\) 20.3324 + 3.97232i 0.768493 + 0.150140i
\(701\) 2.20512 0.0832862 0.0416431 0.999133i \(-0.486741\pi\)
0.0416431 + 0.999133i \(0.486741\pi\)
\(702\) 0 0
\(703\) 1.85109i 0.0698153i
\(704\) −4.76853 −0.179721
\(705\) 0 0
\(706\) −12.6563 −0.476327
\(707\) 77.0264i 2.89687i
\(708\) 0 0
\(709\) 12.7194 0.477687 0.238843 0.971058i \(-0.423232\pi\)
0.238843 + 0.971058i \(0.423232\pi\)
\(710\) 11.1375 9.17215i 0.417983 0.344225i
\(711\) 0 0
\(712\) 7.29569i 0.273418i
\(713\) 15.0418i 0.563318i
\(714\) 0 0
\(715\) 32.2439 26.5541i 1.20586 0.993066i
\(716\) 17.2224 0.643631
\(717\) 0 0
\(718\) 23.2778i 0.868718i
\(719\) 34.9654 1.30399 0.651996 0.758223i \(-0.273932\pi\)
0.651996 + 0.758223i \(0.273932\pi\)
\(720\) 0 0
\(721\) 55.1202 2.05278
\(722\) 15.5735i 0.579584i
\(723\) 0 0
\(724\) 23.5098 0.873733
\(725\) −8.50693 + 43.5429i −0.315940 + 1.61714i
\(726\) 0 0
\(727\) 9.90635i 0.367406i 0.982982 + 0.183703i \(0.0588085\pi\)
−0.982982 + 0.183703i \(0.941191\pi\)
\(728\) 16.2314i 0.601575i
\(729\) 0 0
\(730\) −15.3115 18.5923i −0.566703 0.688133i
\(731\) 33.1453 1.22592
\(732\) 0 0
\(733\) 37.3826i 1.38076i 0.723448 + 0.690379i \(0.242556\pi\)
−0.723448 + 0.690379i \(0.757444\pi\)
\(734\) −9.09417 −0.335672
\(735\) 0 0
\(736\) −1.54229 −0.0568497
\(737\) 4.80720i 0.177075i
\(738\) 0 0
\(739\) −14.4487 −0.531506 −0.265753 0.964041i \(-0.585620\pi\)
−0.265753 + 0.964041i \(0.585620\pi\)
\(740\) −1.72608 + 1.42149i −0.0634520 + 0.0522551i
\(741\) 0 0
\(742\) 21.2808i 0.781242i
\(743\) 45.1826i 1.65759i −0.559553 0.828794i \(-0.689027\pi\)
0.559553 0.828794i \(-0.310973\pi\)
\(744\) 0 0
\(745\) −23.8416 28.9503i −0.873490 1.06066i
\(746\) −5.75976 −0.210880
\(747\) 0 0
\(748\) 15.8142i 0.578224i
\(749\) −51.6939 −1.88886
\(750\) 0 0
\(751\) 49.3127 1.79945 0.899723 0.436461i \(-0.143768\pi\)
0.899723 + 0.436461i \(0.143768\pi\)
\(752\) 4.82700i 0.176022i
\(753\) 0 0
\(754\) 34.7603 1.26590
\(755\) −10.7999 13.1140i −0.393047 0.477267i
\(756\) 0 0
\(757\) 21.5911i 0.784741i −0.919807 0.392370i \(-0.871655\pi\)
0.919807 0.392370i \(-0.128345\pi\)
\(758\) 18.0902i 0.657064i
\(759\) 0 0
\(760\) 3.19514 2.63131i 0.115900 0.0954478i
\(761\) −18.4253 −0.667917 −0.333959 0.942588i \(-0.608385\pi\)
−0.333959 + 0.942588i \(0.608385\pi\)
\(762\) 0 0
\(763\) 18.0422i 0.653170i
\(764\) 1.16660 0.0422063
\(765\) 0 0
\(766\) 3.54752 0.128177
\(767\) 4.12598i 0.148981i
\(768\) 0 0
\(769\) −6.50829 −0.234695 −0.117348 0.993091i \(-0.537439\pi\)
−0.117348 + 0.993091i \(0.537439\pi\)
\(770\) −28.0855 34.1035i −1.01213 1.22901i
\(771\) 0 0
\(772\) 9.36727i 0.337135i
\(773\) 40.5853i 1.45975i 0.683581 + 0.729875i \(0.260422\pi\)
−0.683581 + 0.729875i \(0.739578\pi\)
\(774\) 0 0
\(775\) −9.35025 + 47.8595i −0.335871 + 1.71916i
\(776\) −14.8988 −0.534835
\(777\) 0 0
\(778\) 25.6053i 0.917993i
\(779\) 9.38461 0.336239
\(780\) 0 0
\(781\) −30.7688 −1.10100
\(782\) 5.11481i 0.182905i
\(783\) 0 0
\(784\) −10.1675 −0.363124
\(785\) 7.69196 6.33461i 0.274538 0.226092i
\(786\) 0 0
\(787\) 37.5389i 1.33812i 0.743210 + 0.669059i \(0.233302\pi\)
−0.743210 + 0.669059i \(0.766698\pi\)
\(788\) 3.21836i 0.114649i
\(789\) 0 0
\(790\) −2.06881 + 1.70374i −0.0736051 + 0.0606165i
\(791\) 39.5385 1.40583
\(792\) 0 0
\(793\) 16.2347i 0.576512i
\(794\) 31.4597 1.11646
\(795\) 0 0
\(796\) −2.99104 −0.106014
\(797\) 28.8746i 1.02279i 0.859345 + 0.511396i \(0.170871\pi\)