Properties

Label 98.2.c.c.79.1
Level $98$
Weight $2$
Character 98.79
Analytic conductor $0.783$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.782533939809\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.2.c.c.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.41421 - 2.44949i) q^{5} +1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.41421 - 2.44949i) q^{5} +1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.41421 + 2.44949i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-0.707107 + 1.22474i) q^{12} -4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.707107 - 1.22474i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.53553 + 6.12372i) q^{19} -2.82843 q^{20} -2.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.707107 - 1.22474i) q^{24} +(-1.50000 - 2.59808i) q^{25} -5.65685 q^{27} +2.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(4.24264 + 7.34847i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.41421 - 2.44949i) q^{33} +1.41421 q^{34} -1.00000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(-3.53553 - 6.12372i) q^{38} +(1.41421 - 2.44949i) q^{40} +9.89949 q^{41} +2.00000 q^{43} +(1.00000 - 1.73205i) q^{44} +(-1.41421 - 2.44949i) q^{45} +(2.00000 + 3.46410i) q^{46} +(1.41421 - 2.44949i) q^{47} +1.41421 q^{48} +3.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{53} +(2.82843 - 4.89898i) q^{54} +5.65685 q^{55} +10.0000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-0.707107 - 1.22474i) q^{59} +(2.00000 + 3.46410i) q^{60} +(1.41421 - 2.44949i) q^{61} -8.48528 q^{62} +1.00000 q^{64} +(1.41421 + 2.44949i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-0.707107 + 1.22474i) q^{68} -5.65685 q^{69} -12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-2.12132 + 3.67423i) q^{75} +7.07107 q^{76} +(2.00000 - 3.46410i) q^{79} +(1.41421 + 2.44949i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-4.94975 + 8.57321i) q^{82} -9.89949 q^{83} -4.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-3.53553 + 6.12372i) q^{89} +2.82843 q^{90} -4.00000 q^{92} +(6.00000 - 10.3923i) q^{93} +(1.41421 + 2.44949i) q^{94} +(10.0000 + 17.3205i) q^{95} +(-0.707107 + 1.22474i) q^{96} -9.89949 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 4 q^{11} - 16 q^{15} - 2 q^{16} + 2 q^{18} - 8 q^{22} + 8 q^{23} - 6 q^{25} + 8 q^{29} + 8 q^{30} - 2 q^{32} - 4 q^{36} - 20 q^{37} + 8 q^{43} + 4 q^{44} + 8 q^{46} + 12 q^{50} - 4 q^{51} + 4 q^{53} + 40 q^{57} - 4 q^{58} + 8 q^{60} + 4 q^{64} - 24 q^{67} - 48 q^{71} + 2 q^{72} - 20 q^{74} + 8 q^{79} + 10 q^{81} - 16 q^{85} - 4 q^{86} + 4 q^{88} - 16 q^{92} + 24 q^{93} + 40 q^{95} + 8 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.707107 1.22474i −0.408248 0.707107i 0.586445 0.809989i \(-0.300527\pi\)
−0.994694 + 0.102882i \(0.967194\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.41421 2.44949i 0.632456 1.09545i −0.354593 0.935021i \(-0.615380\pi\)
0.987048 0.160424i \(-0.0512862\pi\)
\(6\) 1.41421 0.577350
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.41421 + 2.44949i 0.447214 + 0.774597i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) −0.707107 + 1.22474i −0.204124 + 0.353553i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.707107 1.22474i −0.171499 0.297044i 0.767445 0.641114i \(-0.221528\pi\)
−0.938944 + 0.344070i \(0.888194\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −3.53553 + 6.12372i −0.811107 + 1.40488i 0.100983 + 0.994888i \(0.467801\pi\)
−0.912090 + 0.409991i \(0.865532\pi\)
\(20\) −2.82843 −0.632456
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) −0.707107 1.22474i −0.144338 0.250000i
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 0 0
\(27\) −5.65685 −1.08866
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 2.00000 3.46410i 0.365148 0.632456i
\(31\) 4.24264 + 7.34847i 0.762001 + 1.31982i 0.941818 + 0.336124i \(0.109116\pi\)
−0.179817 + 0.983700i \(0.557551\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.41421 2.44949i 0.246183 0.426401i
\(34\) 1.41421 0.242536
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i \(0.473806\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −3.53553 6.12372i −0.573539 0.993399i
\(39\) 0 0
\(40\) 1.41421 2.44949i 0.223607 0.387298i
\(41\) 9.89949 1.54604 0.773021 0.634381i \(-0.218745\pi\)
0.773021 + 0.634381i \(0.218745\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) −1.41421 2.44949i −0.210819 0.365148i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 1.41421 2.44949i 0.206284 0.357295i −0.744257 0.667893i \(-0.767196\pi\)
0.950541 + 0.310599i \(0.100530\pi\)
\(48\) 1.41421 0.204124
\(49\) 0 0
\(50\) 3.00000 0.424264
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 0 0
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 2.82843 4.89898i 0.384900 0.666667i
\(55\) 5.65685 0.762770
\(56\) 0 0
\(57\) 10.0000 1.32453
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) −0.707107 1.22474i −0.0920575 0.159448i 0.816319 0.577601i \(-0.196011\pi\)
−0.908377 + 0.418153i \(0.862678\pi\)
\(60\) 2.00000 + 3.46410i 0.258199 + 0.447214i
\(61\) 1.41421 2.44949i 0.181071 0.313625i −0.761174 0.648547i \(-0.775377\pi\)
0.942246 + 0.334922i \(0.108710\pi\)
\(62\) −8.48528 −1.07763
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.41421 + 2.44949i 0.174078 + 0.301511i
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) −0.707107 + 1.22474i −0.0857493 + 0.148522i
\(69\) −5.65685 −0.681005
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −0.707107 1.22474i −0.0827606 0.143346i 0.821674 0.569958i \(-0.193040\pi\)
−0.904435 + 0.426612i \(0.859707\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) −2.12132 + 3.67423i −0.244949 + 0.424264i
\(76\) 7.07107 0.811107
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 1.41421 + 2.44949i 0.158114 + 0.273861i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) −4.94975 + 8.57321i −0.546608 + 0.946753i
\(83\) −9.89949 −1.08661 −0.543305 0.839535i \(-0.682827\pi\)
−0.543305 + 0.839535i \(0.682827\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) −1.41421 2.44949i −0.151620 0.262613i
\(88\) 1.00000 + 1.73205i 0.106600 + 0.184637i
\(89\) −3.53553 + 6.12372i −0.374766 + 0.649113i −0.990292 0.139003i \(-0.955610\pi\)
0.615526 + 0.788116i \(0.288944\pi\)
\(90\) 2.82843 0.298142
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 6.00000 10.3923i 0.622171 1.07763i
\(94\) 1.41421 + 2.44949i 0.145865 + 0.252646i
\(95\) 10.0000 + 17.3205i 1.02598 + 1.77705i
\(96\) −0.707107 + 1.22474i −0.0721688 + 0.125000i
\(97\) −9.89949 −1.00514 −0.502571 0.864536i \(-0.667612\pi\)
−0.502571 + 0.864536i \(0.667612\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) −1.50000 + 2.59808i −0.150000 + 0.259808i
\(101\) 4.24264 + 7.34847i 0.422159 + 0.731200i 0.996150 0.0876610i \(-0.0279392\pi\)
−0.573992 + 0.818861i \(0.694606\pi\)
\(102\) −1.00000 1.73205i −0.0990148 0.171499i
\(103\) 1.41421 2.44949i 0.139347 0.241355i −0.787903 0.615800i \(-0.788833\pi\)
0.927249 + 0.374444i \(0.122166\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) 2.82843 + 4.89898i 0.272166 + 0.471405i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −2.82843 + 4.89898i −0.269680 + 0.467099i
\(111\) 14.1421 1.34231
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) −5.00000 + 8.66025i −0.468293 + 0.811107i
\(115\) −5.65685 9.79796i −0.527504 0.913664i
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) 0 0
\(118\) 1.41421 0.130189
\(119\) 0 0
\(120\) −4.00000 −0.365148
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 1.41421 + 2.44949i 0.128037 + 0.221766i
\(123\) −7.00000 12.1244i −0.631169 1.09322i
\(124\) 4.24264 7.34847i 0.381000 0.659912i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.41421 2.44949i −0.124515 0.215666i
\(130\) 0 0
\(131\) 6.36396 11.0227i 0.556022 0.963058i −0.441801 0.897113i \(-0.645660\pi\)
0.997823 0.0659452i \(-0.0210063\pi\)
\(132\) −2.82843 −0.246183
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) −8.00000 + 13.8564i −0.688530 + 1.19257i
\(136\) −0.707107 1.22474i −0.0606339 0.105021i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 2.82843 4.89898i 0.240772 0.417029i
\(139\) −9.89949 −0.839664 −0.419832 0.907602i \(-0.637911\pi\)
−0.419832 + 0.907602i \(0.637911\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 0 0
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 2.82843 4.89898i 0.234888 0.406838i
\(146\) 1.41421 0.117041
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) −2.12132 3.67423i −0.173205 0.300000i
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) −3.53553 + 6.12372i −0.286770 + 0.496700i
\(153\) −1.41421 −0.114332
\(154\) 0 0
\(155\) 24.0000 1.92773
\(156\) 0 0
\(157\) −5.65685 9.79796i −0.451466 0.781962i 0.547011 0.837125i \(-0.315765\pi\)
−0.998477 + 0.0551630i \(0.982432\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) 1.41421 2.44949i 0.112154 0.194257i
\(160\) −2.82843 −0.223607
\(161\) 0 0
\(162\) −5.00000 −0.392837
\(163\) −5.00000 + 8.66025i −0.391630 + 0.678323i −0.992665 0.120900i \(-0.961422\pi\)
0.601035 + 0.799223i \(0.294755\pi\)
\(164\) −4.94975 8.57321i −0.386510 0.669456i
\(165\) −4.00000 6.92820i −0.311400 0.539360i
\(166\) 4.94975 8.57321i 0.384175 0.665410i
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) 3.53553 + 6.12372i 0.270369 + 0.468293i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) −8.48528 + 14.6969i −0.645124 + 1.11739i 0.339149 + 0.940733i \(0.389861\pi\)
−0.984273 + 0.176655i \(0.943472\pi\)
\(174\) 2.82843 0.214423
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) −1.00000 + 1.73205i −0.0751646 + 0.130189i
\(178\) −3.53553 6.12372i −0.264999 0.458993i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −1.41421 + 2.44949i −0.105409 + 0.182574i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 14.1421 + 24.4949i 1.03975 + 1.80090i
\(186\) 6.00000 + 10.3923i 0.439941 + 0.762001i
\(187\) 1.41421 2.44949i 0.103418 0.179124i
\(188\) −2.82843 −0.206284
\(189\) 0 0
\(190\) −20.0000 −1.45095
\(191\) 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i \(-0.787107\pi\)
0.929267 + 0.369410i \(0.120440\pi\)
\(192\) −0.707107 1.22474i −0.0510310 0.0883883i
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 4.94975 8.57321i 0.355371 0.615521i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) 4.24264 + 7.34847i 0.300753 + 0.520919i 0.976307 0.216391i \(-0.0694287\pi\)
−0.675554 + 0.737311i \(0.736095\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) −8.48528 + 14.6969i −0.598506 + 1.03664i
\(202\) −8.48528 −0.597022
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 14.0000 24.2487i 0.977802 1.69360i
\(206\) 1.41421 + 2.44949i 0.0985329 + 0.170664i
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) 0 0
\(209\) −14.1421 −0.978232
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) 8.48528 + 14.6969i 0.581402 + 1.00702i
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) 2.82843 4.89898i 0.192897 0.334108i
\(216\) −5.65685 −0.384900
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) −2.82843 4.89898i −0.190693 0.330289i
\(221\) 0 0
\(222\) −7.07107 + 12.2474i −0.474579 + 0.821995i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) −10.6066 18.3712i −0.703985 1.21934i −0.967057 0.254561i \(-0.918069\pi\)
0.263072 0.964776i \(-0.415264\pi\)
\(228\) −5.00000 8.66025i −0.331133 0.573539i
\(229\) −8.48528 + 14.6969i −0.560723 + 0.971201i 0.436710 + 0.899602i \(0.356143\pi\)
−0.997434 + 0.0715988i \(0.977190\pi\)
\(230\) 11.3137 0.746004
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) −12.0000 + 20.7846i −0.786146 + 1.36165i 0.142166 + 0.989843i \(0.454593\pi\)
−0.928312 + 0.371802i \(0.878740\pi\)
\(234\) 0 0
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) −0.707107 + 1.22474i −0.0460287 + 0.0797241i
\(237\) −5.65685 −0.367452
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 2.00000 3.46410i 0.129099 0.223607i
\(241\) −10.6066 18.3712i −0.683231 1.18339i −0.973989 0.226595i \(-0.927241\pi\)
0.290758 0.956797i \(-0.406093\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) −4.94975 + 8.57321i −0.317526 + 0.549972i
\(244\) −2.82843 −0.181071
\(245\) 0 0
\(246\) 14.0000 0.892607
\(247\) 0 0
\(248\) 4.24264 + 7.34847i 0.269408 + 0.466628i
\(249\) 7.00000 + 12.1244i 0.443607 + 0.768350i
\(250\) −2.82843 + 4.89898i −0.178885 + 0.309839i
\(251\) −9.89949 −0.624851 −0.312425 0.949942i \(-0.601141\pi\)
−0.312425 + 0.949942i \(0.601141\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) 2.82843 + 4.89898i 0.177123 + 0.306786i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.36396 11.0227i 0.396973 0.687577i −0.596378 0.802704i \(-0.703394\pi\)
0.993351 + 0.115126i \(0.0367273\pi\)
\(258\) 2.82843 0.176090
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) 6.36396 + 11.0227i 0.393167 + 0.680985i
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 1.41421 2.44949i 0.0870388 0.150756i
\(265\) 5.65685 0.347498
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) −6.00000 + 10.3923i −0.366508 + 0.634811i
\(269\) −5.65685 9.79796i −0.344904 0.597392i 0.640432 0.768015i \(-0.278755\pi\)
−0.985336 + 0.170623i \(0.945422\pi\)
\(270\) −8.00000 13.8564i −0.486864 0.843274i
\(271\) 11.3137 19.5959i 0.687259 1.19037i −0.285462 0.958390i \(-0.592147\pi\)
0.972721 0.231977i \(-0.0745195\pi\)
\(272\) 1.41421 0.0857493
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) 2.82843 + 4.89898i 0.170251 + 0.294884i
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 4.94975 8.57321i 0.296866 0.514187i
\(279\) 8.48528 0.508001
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 2.00000 3.46410i 0.119098 0.206284i
\(283\) −0.707107 1.22474i −0.0420331 0.0728035i 0.844243 0.535960i \(-0.180050\pi\)
−0.886277 + 0.463156i \(0.846717\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 14.1421 24.4949i 0.837708 1.45095i
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 7.50000 12.9904i 0.441176 0.764140i
\(290\) 2.82843 + 4.89898i 0.166091 + 0.287678i
\(291\) 7.00000 + 12.1244i 0.410347 + 0.710742i
\(292\) −0.707107 + 1.22474i −0.0413803 + 0.0716728i
\(293\) 19.7990 1.15667 0.578335 0.815800i \(-0.303703\pi\)
0.578335 + 0.815800i \(0.303703\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) −5.00000 + 8.66025i −0.290619 + 0.503367i
\(297\) −5.65685 9.79796i −0.328244 0.568535i
\(298\) −5.00000 8.66025i −0.289642 0.501675i
\(299\) 0 0
\(300\) 4.24264 0.244949
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 6.00000 10.3923i 0.344691 0.597022i
\(304\) −3.53553 6.12372i −0.202777 0.351220i
\(305\) −4.00000 6.92820i −0.229039 0.396708i
\(306\) 0.707107 1.22474i 0.0404226 0.0700140i
\(307\) 9.89949 0.564994 0.282497 0.959268i \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) −12.0000 + 20.7846i −0.681554 + 1.18049i
\(311\) −5.65685 9.79796i −0.320771 0.555591i 0.659877 0.751374i \(-0.270609\pi\)
−0.980647 + 0.195783i \(0.937275\pi\)
\(312\) 0 0
\(313\) 6.36396 11.0227i 0.359712 0.623040i −0.628200 0.778052i \(-0.716208\pi\)
0.987913 + 0.155012i \(0.0495415\pi\)
\(314\) 11.3137 0.638470
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) 1.41421 + 2.44949i 0.0793052 + 0.137361i
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) 1.41421 2.44949i 0.0790569 0.136931i
\(321\) −5.65685 −0.315735
\(322\) 0 0
\(323\) 10.0000 0.556415
\(324\) 2.50000 4.33013i 0.138889 0.240563i
\(325\) 0 0
\(326\) −5.00000 8.66025i −0.276924 0.479647i
\(327\) 1.41421 2.44949i 0.0782062 0.135457i
\(328\) 9.89949 0.546608
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) 4.94975 + 8.57321i 0.271653 + 0.470516i
\(333\) 5.00000 + 8.66025i 0.273998 + 0.474579i
\(334\) −9.89949 + 17.1464i −0.541676 + 0.938211i
\(335\) −33.9411 −1.85440
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 6.50000 11.2583i 0.353553 0.612372i
\(339\) 8.48528 + 14.6969i 0.460857 + 0.798228i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) −8.48528 + 14.6969i −0.459504 + 0.795884i
\(342\) −7.07107 −0.382360
\(343\) 0 0
\(344\) 2.00000 0.107833
\(345\) −8.00000 + 13.8564i −0.430706 + 0.746004i
\(346\) −8.48528 14.6969i −0.456172 0.790112i
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) −1.41421 + 2.44949i −0.0758098 + 0.131306i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.00000 1.73205i 0.0533002 0.0923186i
\(353\) −0.707107 1.22474i −0.0376355 0.0651866i 0.846594 0.532239i \(-0.178649\pi\)
−0.884230 + 0.467052i \(0.845316\pi\)
\(354\) −1.00000 1.73205i −0.0531494 0.0920575i
\(355\) −16.9706 + 29.3939i −0.900704 + 1.56007i
\(356\) 7.07107 0.374766
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 16.0000 27.7128i 0.844448 1.46263i −0.0416523 0.999132i \(-0.513262\pi\)
0.886100 0.463494i \(-0.153404\pi\)
\(360\) −1.41421 2.44949i −0.0745356 0.129099i
\(361\) −15.5000 26.8468i −0.815789 1.41299i
\(362\) 0 0
\(363\) −9.89949 −0.519589
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) 14.1421 + 24.4949i 0.738213 + 1.27862i 0.953299 + 0.302028i \(0.0976636\pi\)
−0.215086 + 0.976595i \(0.569003\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 4.94975 8.57321i 0.257674 0.446304i
\(370\) −28.2843 −1.47043
\(371\) 0 0
\(372\) −12.0000 −0.622171
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 1.41421 + 2.44949i 0.0731272 + 0.126660i
\(375\) −4.00000 6.92820i −0.206559 0.357771i
\(376\) 1.41421 2.44949i 0.0729325 0.126323i
\(377\) 0 0
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 10.0000 17.3205i 0.512989 0.888523i
\(381\) −11.3137 19.5959i −0.579619 1.00393i
\(382\) 2.00000 + 3.46410i 0.102329 + 0.177239i
\(383\) −18.3848 + 31.8434i −0.939418 + 1.62712i −0.172859 + 0.984947i \(0.555300\pi\)
−0.766559 + 0.642173i \(0.778033\pi\)
\(384\) 1.41421 0.0721688
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 1.00000 1.73205i 0.0508329 0.0880451i
\(388\) 4.94975 + 8.57321i 0.251285 + 0.435239i
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) −5.65685 −0.286079
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) −5.65685 9.79796i −0.284627 0.492989i
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) 11.3137 19.5959i 0.567819 0.983491i −0.428963 0.903322i \(-0.641121\pi\)
0.996781 0.0801687i \(-0.0255459\pi\)
\(398\) −8.48528 −0.425329
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) −8.48528 14.6969i −0.423207 0.733017i
\(403\) 0 0
\(404\) 4.24264 7.34847i 0.211079 0.365600i
\(405\) 14.1421 0.702728
\(406\) 0 0
\(407\) −20.0000 −0.991363
\(408\) −1.00000 + 1.73205i −0.0495074 + 0.0857493i
\(409\) 19.0919 + 33.0681i 0.944033 + 1.63511i 0.757676 + 0.652631i \(0.226335\pi\)
0.186357 + 0.982482i \(0.440332\pi\)
\(410\) 14.0000 + 24.2487i 0.691411 + 1.19756i
\(411\) −8.48528 + 14.6969i −0.418548 + 0.724947i
\(412\) −2.82843 −0.139347
\(413\) 0 0
\(414\) 4.00000 0.196589
\(415\) −14.0000 + 24.2487i −0.687233 + 1.19032i
\(416\) 0 0
\(417\) 7.00000 + 12.1244i 0.342791 + 0.593732i
\(418\) 7.07107 12.2474i 0.345857 0.599042i
\(419\) 9.89949 0.483622 0.241811 0.970323i \(-0.422259\pi\)
0.241811 + 0.970323i \(0.422259\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 6.00000 10.3923i 0.292075 0.505889i
\(423\) −1.41421 2.44949i −0.0687614 0.119098i
\(424\) 1.00000 + 1.73205i 0.0485643 + 0.0841158i
\(425\) −2.12132 + 3.67423i −0.102899 + 0.178227i
\(426\) −16.9706 −0.822226
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 2.82843 + 4.89898i 0.136399 + 0.236250i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 2.82843 4.89898i 0.136083 0.235702i
\(433\) 29.6985 1.42722 0.713609 0.700544i \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 14.1421 + 24.4949i 0.676510 + 1.17175i
\(438\) −1.00000 1.73205i −0.0477818 0.0827606i
\(439\) −8.48528 + 14.6969i −0.404980 + 0.701447i −0.994319 0.106439i \(-0.966055\pi\)
0.589339 + 0.807886i \(0.299388\pi\)
\(440\) 5.65685 0.269680
\(441\) 0 0
\(442\) 0 0
\(443\) 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i \(-0.803041\pi\)
0.909618 + 0.415445i \(0.136374\pi\)
\(444\) −7.07107 12.2474i −0.335578 0.581238i
\(445\) 10.0000 + 17.3205i 0.474045 + 0.821071i
\(446\) 0 0
\(447\) 14.1421 0.668900
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 1.50000 2.59808i 0.0707107 0.122474i
\(451\) 9.89949 + 17.1464i 0.466149 + 0.807394i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 11.3137 19.5959i 0.531564 0.920697i
\(454\) 21.2132 0.995585
\(455\) 0 0
\(456\) 10.0000 0.468293
\(457\) −12.0000 + 20.7846i −0.561336 + 0.972263i 0.436044 + 0.899925i \(0.356379\pi\)
−0.997380 + 0.0723376i \(0.976954\pi\)
\(458\) −8.48528 14.6969i −0.396491 0.686743i
\(459\) 4.00000 + 6.92820i 0.186704 + 0.323381i
\(460\) −5.65685 + 9.79796i −0.263752 + 0.456832i
\(461\) −39.5980 −1.84426 −0.922131 0.386878i \(-0.873553\pi\)
−0.922131 + 0.386878i \(0.873553\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) −16.9706 29.3939i −0.786991 1.36311i
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) 16.2635 28.1691i 0.752583 1.30351i −0.193984 0.981005i \(-0.562141\pi\)
0.946567 0.322507i \(-0.104526\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) −8.00000 + 13.8564i −0.368621 + 0.638470i
\(472\) −0.707107 1.22474i −0.0325472 0.0563735i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 2.82843 4.89898i 0.129914 0.225018i
\(475\) 21.2132 0.973329
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) −15.5563 26.9444i −0.710788 1.23112i −0.964562 0.263857i \(-0.915005\pi\)
0.253774 0.967264i \(-0.418328\pi\)
\(480\) 2.00000 + 3.46410i 0.0912871 + 0.158114i
\(481\) 0 0
\(482\) 21.2132 0.966235
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) −14.0000 + 24.2487i −0.635707 + 1.10108i
\(486\) −4.94975 8.57321i −0.224525 0.388889i
\(487\) −6.00000 10.3923i −0.271886 0.470920i 0.697459 0.716625i \(-0.254314\pi\)
−0.969345 + 0.245705i \(0.920981\pi\)
\(488\) 1.41421 2.44949i 0.0640184 0.110883i
\(489\) 14.1421 0.639529
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −7.00000 + 12.1244i −0.315584 + 0.546608i
\(493\) −1.41421 2.44949i −0.0636930 0.110319i
\(494\) 0 0
\(495\) 2.82843 4.89898i 0.127128 0.220193i
\(496\) −8.48528 −0.381000
\(497\) 0 0
\(498\) −14.0000 −0.627355
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −2.82843 4.89898i −0.126491 0.219089i
\(501\) −14.0000 24.2487i −0.625474 1.08335i
\(502\) 4.94975 8.57321i 0.220918 0.382641i
\(503\) −39.5980 −1.76559 −0.882793 0.469762i \(-0.844340\pi\)
−0.882793 + 0.469762i \(0.844340\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) −4.00000 + 6.92820i −0.177822 + 0.307996i
\(507\) 9.19239 + 15.9217i 0.408248 + 0.707107i
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) 11.3137 19.5959i 0.501471 0.868574i −0.498527 0.866874i \(-0.666126\pi\)
0.999999 0.00169976i \(-0.000541051\pi\)
\(510\) −5.65685 −0.250490
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 20.0000 34.6410i 0.883022 1.52944i
\(514\) 6.36396 + 11.0227i 0.280702 + 0.486191i
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) −1.41421 + 2.44949i −0.0622573 + 0.107833i
\(517\) 5.65685 0.248788
\(518\) 0 0
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −0.707107 1.22474i −0.0309789 0.0536570i 0.850120 0.526589i \(-0.176529\pi\)
−0.881099 + 0.472931i \(0.843196\pi\)
\(522\) 1.00000 + 1.73205i 0.0437688 + 0.0758098i
\(523\) 6.36396 11.0227i 0.278277 0.481989i −0.692680 0.721245i \(-0.743570\pi\)
0.970957 + 0.239256i \(0.0769035\pi\)
\(524\) −12.7279 −0.556022
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 1.41421 + 2.44949i 0.0615457 + 0.106600i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −2.82843 + 4.89898i −0.122859 + 0.212798i
\(531\) −1.41421 −0.0613716
\(532\) 0 0
\(533\) 0 0
\(534\) −5.00000 + 8.66025i −0.216371 + 0.374766i
\(535\) −5.65685 9.79796i −0.244567 0.423603i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) −8.48528 + 14.6969i −0.366167 + 0.634220i
\(538\) 11.3137 0.487769
\(539\) 0 0
\(540\) 16.0000 0.688530
\(541\) −5.00000 + 8.66025i −0.214967 + 0.372333i −0.953262 0.302144i \(-0.902298\pi\)
0.738296 + 0.674477i \(0.235631\pi\)
\(542\) 11.3137 + 19.5959i 0.485965 + 0.841717i
\(543\) 0 0
\(544\) −0.707107 + 1.22474i −0.0303170 + 0.0525105i
\(545\) 5.65685 0.242313
\(546\) 0 0
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) −1.41421 2.44949i −0.0603572 0.104542i
\(550\) 3.00000 + 5.19615i 0.127920 + 0.221565i
\(551\) −7.07107 + 12.2474i −0.301238 + 0.521759i
\(552\) −5.65685 −0.240772
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 20.0000 34.6410i 0.848953 1.47043i
\(556\) 4.94975 + 8.57321i 0.209916 + 0.363585i
\(557\) 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i \(0.0525683\pi\)
−0.350824 + 0.936442i \(0.614098\pi\)
\(558\) −4.24264 + 7.34847i −0.179605 + 0.311086i
\(559\) 0 0
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −8.00000 + 13.8564i −0.337460 + 0.584497i
\(563\) −0.707107 1.22474i −0.0298010 0.0516168i 0.850740 0.525586i \(-0.176154\pi\)
−0.880541 + 0.473970i \(0.842821\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) −16.9706 + 29.3939i −0.713957 + 1.23661i
\(566\) 1.41421 0.0594438
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) 14.1421 + 24.4949i 0.592349 + 1.02598i
\(571\) 1.00000 + 1.73205i 0.0418487 + 0.0724841i 0.886191 0.463320i \(-0.153342\pi\)
−0.844342 + 0.535804i \(0.820009\pi\)
\(572\) 0 0
\(573\) −5.65685 −0.236318
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −10.6066 18.3712i −0.441559 0.764802i 0.556247 0.831017i \(-0.312241\pi\)
−0.997805 + 0.0662152i \(0.978908\pi\)
\(578\) 7.50000 + 12.9904i 0.311959 + 0.540329i
\(579\) 11.3137 19.5959i 0.470182 0.814379i
\(580\) −5.65685 −0.234888
\(581\) 0 0
\(582\) −14.0000 −0.580319
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) −0.707107 1.22474i −0.0292603 0.0506803i
\(585\) 0 0
\(586\) −9.89949 + 17.1464i −0.408944 + 0.708312i
\(587\) 29.6985 1.22579 0.612894 0.790165i \(-0.290005\pi\)
0.612894 + 0.790165i \(0.290005\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) 2.00000 3.46410i 0.0823387 0.142615i
\(591\) −1.41421 2.44949i −0.0581730 0.100759i
\(592\) −5.00000 8.66025i −0.205499 0.355934i
\(593\) −3.53553 + 6.12372i −0.145187 + 0.251471i −0.929443 0.368967i \(-0.879712\pi\)
0.784256 + 0.620438i \(0.213045\pi\)
\(594\) 11.3137 0.464207
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 6.00000 10.3923i 0.245564 0.425329i
\(598\) 0 0
\(599\) 8.00000 + 13.8564i 0.326871 + 0.566157i 0.981889 0.189456i \(-0.0606724\pi\)
−0.655018 + 0.755613i \(0.727339\pi\)
\(600\) −2.12132 + 3.67423i −0.0866025 + 0.150000i
\(601\) −29.6985 −1.21143 −0.605713 0.795683i \(-0.707112\pi\)
−0.605713 + 0.795683i \(0.707112\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) −9.89949 17.1464i −0.402472 0.697101i
\(606\) 6.00000 + 10.3923i 0.243733 + 0.422159i
\(607\) −8.48528 + 14.6969i −0.344407 + 0.596530i −0.985246 0.171145i \(-0.945253\pi\)
0.640839 + 0.767675i \(0.278587\pi\)
\(608\) 7.07107 0.286770
\(609\) 0 0
\(610\) 8.00000 0.323911
\(611\) 0 0
\(612\) 0.707107 + 1.22474i 0.0285831 + 0.0495074i
\(613\) 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i \(0.0404979\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(614\) −4.94975 + 8.57321i −0.199756 + 0.345987i
\(615\) −39.5980 −1.59674
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 2.00000 3.46410i 0.0804518 0.139347i
\(619\) 9.19239 + 15.9217i 0.369473 + 0.639946i 0.989483 0.144647i \(-0.0462048\pi\)
−0.620010 + 0.784594i \(0.712871\pi\)
\(620\) −12.0000 20.7846i −0.481932 0.834730i
\(621\) −11.3137 + 19.5959i −0.454003 + 0.786357i
\(622\) 11.3137 0.453638
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) 6.36396 + 11.0227i 0.254355 + 0.440556i
\(627\) 10.0000 + 17.3205i 0.399362 + 0.691714i
\(628\) −5.65685 + 9.79796i −0.225733 + 0.390981i
\(629\) 14.1421 0.563884
\(630\) 0 0
\(631\) 44.0000 1.75161 0.875806 0.482663i \(-0.160330\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) 8.48528 + 14.6969i 0.337260 + 0.584151i
\(634\) −5.00000 8.66025i −0.198575 0.343943i
\(635\) 22.6274 39.1918i 0.897942 1.55528i
\(636\) −2.82843 −0.112154
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) 1.41421 + 2.44949i 0.0559017 + 0.0968246i
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) 2.82843 4.89898i 0.111629 0.193347i
\(643\) −9.89949 −0.390398 −0.195199 0.980764i \(-0.562535\pi\)
−0.195199 + 0.980764i \(0.562535\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) −5.00000 + 8.66025i −0.196722 + 0.340733i
\(647\) 4.24264 + 7.34847i 0.166795 + 0.288898i 0.937291 0.348547i \(-0.113325\pi\)
−0.770496 + 0.637445i \(0.779991\pi\)
\(648\) 2.50000 + 4.33013i 0.0982093 + 0.170103i
\(649\) 1.41421 2.44949i 0.0555127 0.0961509i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 1.41421 + 2.44949i 0.0553001 + 0.0957826i
\(655\) −18.0000 31.1769i −0.703318 1.21818i
\(656\) −4.94975 + 8.57321i −0.193255 + 0.334728i
\(657\) −1.41421 −0.0551737
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) −4.00000 + 6.92820i −0.155700 + 0.269680i
\(661\) 4.24264 + 7.34847i 0.165020 + 0.285822i 0.936662 0.350234i \(-0.113898\pi\)
−0.771643 + 0.636056i \(0.780565\pi\)
\(662\) −5.00000 8.66025i −0.194331 0.336590i
\(663\) 0 0
\(664\) −9.89949 −0.384175
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) −9.89949 17.1464i −0.383023 0.663415i
\(669\) 0 0
\(670\) 16.9706 29.3939i 0.655630 1.13558i
\(671\) 5.65685 0.218380
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) 8.48528 + 14.6969i 0.326599 + 0.565685i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −8.48528 + 14.6969i −0.326116 + 0.564849i −0.981738 0.190240i \(-0.939073\pi\)
0.655622 + 0.755090i \(0.272407\pi\)
\(678\) −16.9706 −0.651751
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) −15.0000 + 25.9808i −0.574801 + 0.995585i
\(682\) −8.48528 14.6969i −0.324918 0.562775i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 3.53553 6.12372i 0.135185 0.234146i
\(685\) −33.9411 −1.29682
\(686\) 0 0
\(687\) 24.0000 0.915657
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 0 0
\(690\) −8.00000 13.8564i −0.304555 0.527504i
\(691\) 6.36396 11.0227i 0.242096 0.419323i −0.719215 0.694788i \(-0.755498\pi\)
0.961311 + 0.275464i \(0.0888316\pi\)
\(692\) 16.9706 0.645124
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) −14.0000 + 24.2487i −0.531050 + 0.919806i
\(696\) −1.41421 2.44949i −0.0536056 0.0928477i
\(697\) −7.00000 12.1244i −0.265144 0.459243i
\(698\) 0 0
\(699\) 33.9411 1.28377
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −35.3553 61.2372i −1.33345 2.30961i
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) −5.65685 + 9.79796i −0.213049 + 0.369012i
\(706\) 1.41421 0.0532246
\(707\) 0 0
\(708\) 2.00000 0.0751646
\(709\) −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) −16.9706 29.3939i −0.636894 1.10313i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −3.53553 + 6.12372i −0.132500 + 0.229496i
\(713\) 33.9411 1.27111
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 8.48528 + 14.6969i 0.316889 + 0.548867i
\(718\) 16.0000 + 27.7128i 0.597115 + 1.03423i
\(719\) 1.41421 2.44949i 0.0527413 0.0913506i −0.838449 0.544979i \(-0.816537\pi\)
0.891191 + 0.453629i \(0.149871\pi\)
\(720\) 2.82843 0.105409
\(721\) 0 0
\(722\) 31.0000 1.15370
\(723\) −15.0000 + 25.9808i −0.557856 + 0.966235i
\(724\) 0 0
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 4.94975 8.57321i 0.183702 0.318182i
\(727\) 19.7990 0.734304 0.367152 0.930161i \(-0.380333\pi\)
0.367152 + 0.930161i \(0.380333\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 2.00000 3.46410i 0.0740233 0.128212i
\(731\) −1.41421 2.44949i −0.0523066 0.0905977i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) 21.2132 36.7423i 0.783528 1.35711i −0.146347 0.989233i \(-0.546752\pi\)
0.929875 0.367876i \(-0.119915\pi\)
\(734\) −28.2843 −1.04399
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 12.0000 20.7846i 0.442026 0.765611i
\(738\) 4.94975 + 8.57321i 0.182203 + 0.315584i
\(739\) 15.0000 + 25.9808i 0.551784 + 0.955718i 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) 14.1421 24.4949i 0.519875 0.900450i
\(741\) 0 0
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 6.00000 10.3923i 0.219971 0.381000i
\(745\) 14.1421 + 24.4949i 0.518128 + 0.897424i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) −4.94975 + 8.57321i −0.181102 + 0.313678i
\(748\) −2.82843 −0.103418
\(749\) 0 0
\(750\) 8.00000 0.292119
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) 1.41421 + 2.44949i 0.0515711 + 0.0893237i
\(753\) 7.00000 + 12.1244i 0.255094 + 0.441836i
\(754\) 0 0
\(755\) 45.2548 1.64699
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 13.0000 22.5167i 0.472181 0.817842i
\(759\) −5.65685 9.79796i −0.205331 0.355643i
\(760\) 10.0000 + 17.3205i 0.362738 + 0.628281i
\(761\) −3.53553 + 6.12372i −0.128163 + 0.221985i −0.922965 0.384884i \(-0.874241\pi\)
0.794802 + 0.606869i \(0.207575\pi\)
\(762\) 22.6274 0.819705
\(763\) 0 0
\(764\) −4.00000 −0.144715
\(765\) −2.00000 + 3.46410i −0.0723102 + 0.125245i
\(766\) −18.3848 31.8434i −0.664269 1.15055i
\(767\) 0 0
\(768\) −0.707107 + 1.22474i −0.0255155 + 0.0441942i
\(769\) −29.6985 −1.07095 −0.535477 0.844550i \(-0.679868\pi\)
−0.535477 + 0.844550i \(0.679868\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 8.00000 13.8564i 0.287926 0.498703i
\(773\) 24.0416 + 41.6413i 0.864717 + 1.49773i 0.867328 + 0.497738i \(0.165836\pi\)
−0.00261021 + 0.999997i \(0.500831\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 12.7279 22.0454i 0.457200 0.791894i
\(776\) −9.89949 −0.355371
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) −35.0000 + 60.6218i −1.25401 + 2.17200i
\(780\) 0 0
\(781\) −12.0000 20.7846i −0.429394 0.743732i
\(782\) 2.82843 4.89898i 0.101144 0.175187i
\(783\) −11.3137 −0.404319
\(784\) 0 0
\(785\) −32.0000 −1.14213
\(786\) 9.00000 15.5885i 0.321019 0.556022i
\(787\) −0.707107 1.22474i −0.0252056