Properties

Label 810.2.e.e.541.1
Level $810$
Weight $2$
Character 810.541
Analytic conductor $6.468$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.541
Dual form 810.2.e.e.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +(3.00000 - 5.19615i) q^{11} +(2.00000 + 3.46410i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} -4.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(3.00000 + 5.19615i) q^{22} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{26} +2.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} -2.00000 q^{35} +8.00000 q^{37} +(2.00000 - 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-4.00000 + 6.92820i) q^{43} -6.00000 q^{44} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.00000 - 3.46410i) q^{52} +6.00000 q^{53} +6.00000 q^{55} +(-1.00000 + 1.73205i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-1.00000 + 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.00000 - 1.73205i) q^{70} +12.0000 q^{71} -10.0000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} +(6.00000 + 10.3923i) q^{77} +(2.00000 - 3.46410i) q^{79} -1.00000 q^{80} +(6.00000 - 10.3923i) q^{83} +(3.00000 + 5.19615i) q^{85} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{88} -12.0000 q^{89} -8.00000 q^{91} +(-2.00000 - 3.46410i) q^{95} +(-1.00000 + 1.73205i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + q^{5} - 2q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + q^{5} - 2q^{7} + 2q^{8} - 2q^{10} + 6q^{11} + 4q^{13} - 2q^{14} - q^{16} + 12q^{17} - 8q^{19} + q^{20} + 6q^{22} - q^{25} - 8q^{26} + 4q^{28} - 6q^{29} + 4q^{31} - q^{32} - 6q^{34} - 4q^{35} + 16q^{37} + 4q^{38} + q^{40} - 8q^{43} - 12q^{44} + 3q^{49} - q^{50} + 4q^{52} + 12q^{53} + 12q^{55} - 2q^{56} - 6q^{58} + 6q^{59} - 2q^{61} - 8q^{62} + 2q^{64} - 4q^{65} + 4q^{67} - 6q^{68} + 2q^{70} + 24q^{71} - 20q^{73} - 8q^{74} + 4q^{76} + 12q^{77} + 4q^{79} - 2q^{80} + 12q^{83} + 6q^{85} - 8q^{86} + 6q^{88} - 24q^{89} - 16q^{91} - 4q^{95} - 2q^{97} - 6q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) −1.00000 1.73205i −0.267261 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0 0
\(22\) 3.00000 + 5.19615i 0.639602 + 1.10782i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 0 0
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) 1.00000 1.73205i 0.119523 0.207020i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 6.00000 + 10.3923i 0.683763 + 1.18431i
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) −12.0000 −1.27200 −0.635999 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.00000 3.46410i −0.205196 0.355409i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) −1.00000 1.73205i −0.0985329 0.170664i 0.812545 0.582899i \(-0.198082\pi\)
−0.911078 + 0.412235i \(0.864748\pi\)
\(104\) 2.00000 + 3.46410i 0.196116 + 0.339683i
\(105\) 0 0
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −3.00000 + 5.19615i −0.286039 + 0.495434i
\(111\) 0 0
\(112\) −1.00000 1.73205i −0.0944911 0.163663i
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −6.00000 −0.552345
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −1.00000 1.73205i −0.0905357 0.156813i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −2.00000 3.46410i −0.175412 0.303822i
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −10.0000 17.3205i −0.848189 1.46911i −0.882823 0.469706i \(-0.844360\pi\)
0.0346338 0.999400i \(-0.488974\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 0 0
\(142\) −6.00000 + 10.3923i −0.503509 + 0.872103i
\(143\) 24.0000 2.00698
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 5.00000 8.66025i 0.413803 0.716728i
\(147\) 0 0
\(148\) −4.00000 6.92820i −0.328798 0.569495i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) −4.00000 −0.324443
\(153\) 0 0
\(154\) −12.0000 −0.966988
\(155\) −2.00000 + 3.46410i −0.160644 + 0.278243i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −12.0000 20.7846i −0.928588 1.60836i −0.785687 0.618624i \(-0.787690\pi\)
−0.142901 0.989737i \(-0.545643\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) −6.00000 −0.460179
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 0 0
\(175\) −1.00000 1.73205i −0.0755929 0.130931i
\(176\) 3.00000 + 5.19615i 0.226134 + 0.391675i
\(177\) 0 0
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 4.00000 6.92820i 0.296500 0.513553i
\(183\) 0 0
\(184\) 0 0
\(185\) 4.00000 + 6.92820i 0.294086 + 0.509372i
\(186\) 0 0
\(187\) 18.0000 31.1769i 1.31629 2.27988i
\(188\) 0 0
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 0 0
\(196\) 1.50000 2.59808i 0.107143 0.185577i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) −3.00000 5.19615i −0.211079 0.365600i
\(203\) −6.00000 10.3923i −0.421117 0.729397i
\(204\) 0 0
\(205\) 0 0
\(206\) 2.00000 0.139347
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) −12.0000 + 20.7846i −0.830057 + 1.43770i
\(210\) 0 0
\(211\) 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 0 0
\(220\) −3.00000 5.19615i −0.202260 0.350325i
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 0 0
\(223\) −13.0000 + 22.5167i −0.870544 + 1.50783i −0.00910984 + 0.999959i \(0.502900\pi\)
−0.861435 + 0.507869i \(0.830434\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 + 5.19615i −0.196960 + 0.341144i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) 0 0
\(238\) −6.00000 10.3923i −0.388922 0.673633i
\(239\) −6.00000 10.3923i −0.388108 0.672222i 0.604087 0.796918i \(-0.293538\pi\)
−0.992195 + 0.124696i \(0.960204\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 25.0000 1.60706
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −1.50000 + 2.59808i −0.0958315 + 0.165985i
\(246\) 0 0
\(247\) −8.00000 13.8564i −0.509028 0.881662i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.00000 + 1.73205i −0.0627456 + 0.108679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) −8.00000 + 13.8564i −0.497096 + 0.860995i
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 0 0
\(265\) 3.00000 + 5.19615i 0.184289 + 0.319197i
\(266\) 4.00000 + 6.92820i 0.245256 + 0.424795i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) 3.00000 + 5.19615i 0.180907 + 0.313340i
\(276\) 0 0
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 20.0000 1.19952
\(279\) 0 0
\(280\) −2.00000 −0.119523
\(281\) 6.00000 10.3923i 0.357930 0.619953i −0.629685 0.776851i \(-0.716816\pi\)
0.987615 + 0.156898i \(0.0501493\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) 0 0
\(286\) −12.0000 + 20.7846i −0.709575 + 1.22902i
\(287\) 0 0
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 3.00000 5.19615i 0.176166 0.305129i
\(291\) 0 0
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) −9.00000 15.5885i −0.525786 0.910687i −0.999549 0.0300351i \(-0.990438\pi\)
0.473763 0.880652i \(-0.342895\pi\)
\(294\) 0 0
\(295\) −3.00000 + 5.19615i −0.174667 + 0.302532i
\(296\) 8.00000 0.464991
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) 8.00000 + 13.8564i 0.460348 + 0.797347i
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 6.00000 10.3923i 0.341882 0.592157i
\(309\) 0 0
\(310\) −2.00000 3.46410i −0.113592 0.196748i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) 18.0000 + 31.1769i 1.00781 + 1.74557i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) −4.00000 −0.221880
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 24.0000 1.31322
\(335\) −2.00000 + 3.46410i −0.109272 + 0.189264i
\(336\) 0 0
\(337\) −7.00000 12.1244i −0.381314 0.660456i 0.609936 0.792451i \(-0.291195\pi\)
−0.991250 + 0.131995i \(0.957862\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) 9.00000 + 15.5885i 0.483843 + 0.838041i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i \(-0.632927\pi\)
0.994388 0.105797i \(-0.0337393\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) −15.0000 + 25.9808i −0.798369 + 1.38282i 0.122308 + 0.992492i \(0.460970\pi\)
−0.920677 + 0.390324i \(0.872363\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 6.00000 + 10.3923i 0.317999 + 0.550791i
\(357\) 0 0
\(358\) 3.00000 5.19615i 0.158555 0.274625i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 4.00000 + 6.92820i 0.209657 + 0.363137i
\(365\) −5.00000 8.66025i −0.261712 0.453298i
\(366\) 0 0
\(367\) −13.0000 + 22.5167i −0.678594 + 1.17536i 0.296810 + 0.954937i \(0.404077\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −8.00000 −0.415900
\(371\) −6.00000 + 10.3923i −0.311504 + 0.539542i
\(372\) 0 0
\(373\) 14.0000 + 24.2487i 0.724893 + 1.25555i 0.959018 + 0.283344i \(0.0914439\pi\)
−0.234126 + 0.972206i \(0.575223\pi\)
\(374\) 18.0000 + 31.1769i 0.930758 + 1.61212i
\(375\) 0 0
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −2.00000 + 3.46410i −0.102598 + 0.177705i
\(381\) 0 0
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) −10.0000 −0.508987
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.50000 + 2.59808i 0.0757614 + 0.131223i
\(393\) 0 0
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) −16.0000 −0.803017 −0.401508 0.915855i \(-0.631514\pi\)
−0.401508 + 0.915855i \(0.631514\pi\)
\(398\) 8.00000 13.8564i 0.401004 0.694559i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i \(-0.811051\pi\)
−0.0699455 0.997551i \(-0.522283\pi\)
\(402\) 0 0
\(403\) −8.00000 + 13.8564i −0.398508 + 0.690237i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) 24.0000 41.5692i 1.18964 2.06051i
\(408\) 0 0
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.00000 + 1.73205i −0.0492665 + 0.0853320i
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 0 0
\(418\) −12.0000 20.7846i −0.586939 1.01661i
\(419\) −3.00000 5.19615i −0.146560 0.253849i 0.783394 0.621525i \(-0.213487\pi\)
−0.929954 + 0.367677i \(0.880153\pi\)
\(420\) 0 0
\(421\) −7.00000 + 12.1244i −0.341159 + 0.590905i −0.984648 0.174550i \(-0.944153\pi\)
0.643489 + 0.765455i \(0.277486\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) −2.00000 3.46410i −0.0967868 0.167640i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 0 0
\(430\) 4.00000 6.92820i 0.192897 0.334108i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 38.0000 1.82616 0.913082 0.407777i \(-0.133696\pi\)
0.913082 + 0.407777i \(0.133696\pi\)
\(434\) 4.00000 6.92820i 0.192006 0.332564i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 0 0
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) −13.0000 22.5167i −0.615568 1.06619i
\(447\) 0 0
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 0 0
\(454\) 0 0
\(455\) −4.00000 6.92820i −0.187523 0.324799i
\(456\) 0 0
\(457\) −13.0000 + 22.5167i −0.608114 + 1.05328i 0.383437 + 0.923567i \(0.374740\pi\)
−0.991551 + 0.129718i \(0.958593\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −9.00000 + 15.5885i −0.419172 + 0.726027i −0.995856 0.0909401i \(-0.971013\pi\)
0.576685 + 0.816967i \(0.304346\pi\)
\(462\) 0 0
\(463\) 17.0000 + 29.4449i 0.790057 + 1.36842i 0.925931 + 0.377693i \(0.123282\pi\)
−0.135874 + 0.990726i \(0.543384\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) 24.0000 + 41.5692i 1.10352 + 1.91135i
\(474\) 0 0
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) 12.0000 0.550019
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) 18.0000 31.1769i 0.822441 1.42451i −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) 5.00000 + 8.66025i 0.227744 + 0.394464i
\(483\) 0 0
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) 0 0
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) −3.00000 5.19615i −0.135388 0.234499i 0.790358 0.612646i \(-0.209895\pi\)
−0.925746 + 0.378147i \(0.876561\pi\)
\(492\) 0 0
\(493\) −18.0000 + 31.1769i −0.810679 + 1.40414i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −12.0000 + 20.7846i −0.538274 + 0.932317i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 9.00000 15.5885i 0.401690 0.695747i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 0 0
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 10.0000 17.3205i 0.442374 0.766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) 1.00000 1.73205i 0.0440653 0.0763233i
\(516\) 0 0
\(517\) 0 0
\(518\) −8.00000 13.8564i −0.351500 0.608816i
\(519\) 0 0
\(520\) −2.00000 + 3.46410i −0.0877058 + 0.151911i
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −3.00000 + 5.19615i −0.131056 + 0.226995i
\(525\) 0 0
\(526\) 12.0000 + 20.7846i 0.523225 + 0.906252i
\(527\) 12.0000 + 20.7846i 0.522728 + 0.905392i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −6.00000 −0.260623
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 0 0
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) −4.00000 + 6.92820i −0.171815 + 0.297592i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) 1.00000 + 1.73205i 0.0428353 + 0.0741929i
\(546\) 0 0
\(547\) 20.0000 34.6410i 0.855138 1.48114i −0.0213785 0.999771i \(-0.506805\pi\)
0.876517 0.481371i \(-0.159861\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) 12.0000 20.7846i 0.511217 0.885454i
\(552\) 0 0
\(553\) 4.00000 + 6.92820i 0.170097 + 0.294617i
\(554\) −4.00000 6.92820i −0.169944 0.294351i
\(555\) 0 0
\(556\) −10.0000 + 17.3205i −0.424094 + 0.734553i
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 0 0
\(559\) −32.0000 −1.35346
\(560\) 1.00000 1.73205i 0.0422577 0.0731925i
\(561\) 0 0
\(562\) 6.00000 + 10.3923i 0.253095 + 0.438373i
\(563\) −12.0000 20.7846i −0.505740 0.875967i −0.999978 0.00664037i \(-0.997886\pi\)
0.494238 0.869326i \(-0.335447\pi\)
\(564\) 0 0
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) −22.0000 38.1051i −0.920671 1.59465i −0.798379 0.602155i \(-0.794309\pi\)
−0.122292 0.992494i \(-0.539025\pi\)
\(572\) −12.0000 20.7846i −0.501745 0.869048i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) 0 0
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) 12.0000 + 20.7846i 0.497844 + 0.862291i
\(582\) 0 0
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) −18.0000 + 31.1769i −0.742940 + 1.28681i 0.208212 + 0.978084i \(0.433236\pi\)
−0.951151 + 0.308725i \(0.900098\pi\)
\(588\) 0 0
\(589\) −8.00000 13.8564i −0.329634 0.570943i
\(590\) −3.00000 5.19615i −0.123508 0.213922i
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 0 0
\(601\) 5.00000 8.66025i 0.203954 0.353259i −0.745845 0.666120i \(-0.767954\pi\)
0.949799 + 0.312861i \(0.101287\pi\)
\(602\) 16.0000 0.652111
\(603\) 0 0
\(604\) −16.0000 −0.651031
\(605\) 12.5000 21.6506i 0.508197 0.880223i
\(606\) 0 0
\(607\) −19.0000 32.9090i −0.771186 1.33573i −0.936913 0.349562i \(-0.886330\pi\)
0.165727 0.986172i \(-0.447003\pi\)
\(608\) 2.00000 + 3.46410i 0.0811107 + 0.140488i
\(609\) 0 0
\(610\) 1.00000 1.73205i 0.0404888 0.0701287i
\(611\) 0 0
\(612\) 0 0
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) 0 0
\(616\) 6.00000 + 10.3923i 0.241747 + 0.418718i
\(617\) −15.0000 25.9808i −0.603877 1.04595i −0.992228 0.124434i \(-0.960288\pi\)
0.388351 0.921512i \(-0.373045\pi\)
\(618\) 0 0
\(619\) −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) 4.00000 0.160644
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 12.0000 20.7846i 0.480770 0.832718i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) 0 0
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 1.00000 + 1.73205i 0.0396838 + 0.0687343i
\(636\) 0 0
\(637\) −6.00000 + 10.3923i −0.237729 + 0.411758i
\(638\) −36.0000 −1.42525
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 12.0000 20.7846i 0.473972 0.820943i −0.525584 0.850741i \(-0.676153\pi\)
0.999556 + 0.0297987i \(0.00948663\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 2.00000 3.46410i 0.0784465 0.135873i
\(651\) 0 0
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 0 0
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15.0000 + 25.9808i −0.584317 + 1.01207i 0.410643 + 0.911796i \(0.365304\pi\)
−0.994960 + 0.100271i \(0.968029\pi\)
\(660\) 0 0
\(661\) −1.00000 1.73205i −0.0388955 0.0673690i 0.845922 0.533306i \(-0.179051\pi\)
−0.884818 + 0.465937i \(0.845717\pi\)
\(662\) 2.00000 + 3.46410i 0.0777322 + 0.134636i
\(663\) 0 0
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) 0 0
\(668\) −12.0000 + 20.7846i −0.464294 + 0.804181i
\(669\) 0 0
\(670\) −2.00000 3.46410i −0.0772667 0.133830i
\(671\) 6.00000 + 10.3923i 0.231627 + 0.401190i
\(672\) 0 0
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 0 0
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) 3.00000 + 5.19615i 0.115045 + 0.199263i
\(681\) 0 0
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 0 0
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 12.0000 + 20.7846i 0.457164 + 0.791831i
\(690\) 0 0
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 0 0
\(695\) 10.0000 17.3205i 0.379322 0.657004i
\(696\) 0 0
\(697\) 0 0
\(698\) 11.0000 + 19.0526i 0.416356 + 0.721150i
\(699\) 0 0
\(700\) −1.00000 + 1.73205i −0.0377964 + 0.0654654i
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) −32.0000 −1.20690
\(704\) 3.00000 5.19615i 0.113067 0.195837i
\(705\) 0 0
\(706\) −15.0000 25.9808i −0.564532 0.977799i
\(707\) −6.00000 10.3923i −0.225653 0.390843i
\(708\) 0 0
\(709\) 17.0000 29.4449i 0.638448 1.10583i −0.347325 0.937745i \(-0.612910\pi\)
0.985773 0.168080i \(-0.0537568\pi\)
\(710\) −12.0000 −0.450352
\(711\) 0 0
\(712\) −12.0000 −0.449719
\(713\) 0 0
\(714\) 0 0
\(715\) 12.0000 + 20.7846i 0.448775 + 0.777300i
\(716\) 3.00000 + 5.19615i 0.112115 + 0.194189i
\(717\) 0 0
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 1.50000 2.59808i 0.0558242 0.0966904i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 0 0
\(727\) 5.00000 8.66025i 0.185440 0.321191i −0.758285 0.651923i \(-0.773962\pi\)
0.943725 + 0.330732i \(0.107296\pi\)
\(728\) −8.00000 −0.296500
\(729\) 0 0
\(730\) 10.0000 0.370117
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) 0 0
\(733\) −16.0000 27.7128i −0.590973 1.02360i −0.994102 0.108453i \(-0.965410\pi\)
0.403128 0.915144i \(-0.367923\pi\)
\(734\) −13.0000 22.5167i −0.479839 0.831105i
\(735\) 0 0
\(736\) 0 0
\(737\) 24.0000 0.884051
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 4.00000 6.92820i 0.147043 0.254686i
\(741\) 0 0
\(742\) −6.00000 10.3923i −0.220267 0.381514i
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) −3.00000 + 5.19615i −0.109911 + 0.190372i
\(746\) −28.0000 −1.02515
\(747\) 0 0
\(748\) −36.0000 −1.31629
\(749\) 12.0000 20.7846i 0.438470 0.759453i
\(750\) 0 0
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 12.0000 20.7846i 0.437014 0.756931i
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) −40.0000 −1.45382 −0.726912 0.686730i \(-0.759045\pi\)
−0.726912 + 0.686730i \(0.759045\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) −2.00000 3.46410i −0.0725476 0.125656i
\(761\) 18.0000 + 31.1769i 0.652499 + 1.13016i 0.982514 + 0.186187i \(0.0596129\pi\)
−0.330015 + 0.943976i \(0.607054\pi\)
\(762\) 0 0
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) 0 0
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) −6.00000 10.3923i −0.216225 0.374513i
\(771\) 0 0
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) −9.00000 15.5885i −0.322666 0.558873i
\(779\) 0 0
\(780\) 0 0
\(781\) 36.0000 62.3538i 1.28818 2.23120i
\(782\) 0 0
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) −2.00000 + 3.46410i −0.0713831 + 0.123639i
\(786\) 0 0
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) −9.00000 15.5885i −0.320612 0.555316i
\(789\) 0 0
\(790\) −2.00000 + 3.46410i −0.0711568 + 0.123247i
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) −8.00000