Properties

Label 912.2.bo.f.289.1
Level $912$
Weight $2$
Character 912.289
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 289.1
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 912.289
Dual form 912.2.bo.f.385.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.173648 + 0.984808i) q^{3} +(0.907604 - 0.761570i) q^{5} +(0.266044 - 0.460802i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\) \(q+(0.173648 + 0.984808i) q^{3} +(0.907604 - 0.761570i) q^{5} +(0.266044 - 0.460802i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.939693 + 1.62760i) q^{11} +(-0.673648 + 3.82045i) q^{13} +(0.907604 + 0.761570i) q^{15} +(-1.09240 - 0.397600i) q^{17} +(3.93969 - 1.86516i) q^{19} +(0.500000 + 0.181985i) q^{21} +(5.13429 + 4.30818i) q^{23} +(-0.624485 + 3.54163i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(3.77972 - 1.37570i) q^{29} +(-0.979055 + 1.69577i) q^{31} +(-1.43969 + 1.20805i) q^{33} +(-0.109470 - 0.620838i) q^{35} +6.88713 q^{37} -3.87939 q^{39} +(-1.56031 - 8.84894i) q^{41} +(-1.85844 + 1.55942i) q^{43} +(-0.592396 + 1.02606i) q^{45} +(1.91875 - 0.698367i) q^{47} +(3.35844 + 5.81699i) q^{49} +(0.201867 - 1.14484i) q^{51} +(9.93629 + 8.33754i) q^{53} +(2.09240 + 0.761570i) q^{55} +(2.52094 + 3.55596i) q^{57} +(-2.51842 - 0.916629i) q^{59} +(-8.69253 - 7.29390i) q^{61} +(-0.0923963 + 0.524005i) q^{63} +(2.29813 + 3.98048i) q^{65} +(-10.4966 + 3.82045i) q^{67} +(-3.35117 + 5.80439i) q^{69} +(-4.65136 + 3.90295i) q^{71} +(-0.0569038 - 0.322718i) q^{73} -3.59627 q^{75} +1.00000 q^{77} +(2.80154 + 15.8883i) q^{79} +(0.766044 - 0.642788i) q^{81} +(5.78699 - 10.0234i) q^{83} +(-1.29426 + 0.471073i) q^{85} +(2.01114 + 3.48340i) q^{87} +(-0.618089 + 3.50535i) q^{89} +(1.58125 + 1.32683i) q^{91} +(-1.84002 - 0.669713i) q^{93} +(2.15523 - 4.69318i) q^{95} +(-5.52481 - 2.01087i) q^{97} +(-1.43969 - 1.20805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 9q^{5} - 3q^{7} + O(q^{10}) \) \( 6q + 9q^{5} - 3q^{7} - 3q^{13} + 9q^{15} - 3q^{17} + 18q^{19} + 3q^{21} + 21q^{23} + 9q^{25} - 3q^{27} - 3q^{29} - 9q^{31} - 3q^{33} - 18q^{35} - 18q^{37} - 12q^{39} - 15q^{41} - 3q^{43} + 9q^{47} + 12q^{49} + 15q^{51} + 12q^{53} + 9q^{55} + 12q^{57} - 27q^{59} + 3q^{61} + 3q^{63} - 21q^{67} + 6q^{69} - 39q^{71} + 36q^{73} + 6q^{75} + 6q^{77} + 45q^{79} + 27q^{83} - 18q^{85} + 6q^{87} - 30q^{89} + 12q^{91} + 9q^{93} - 6q^{97} - 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.173648 + 0.984808i 0.100256 + 0.568579i
\(4\) 0 0
\(5\) 0.907604 0.761570i 0.405893 0.340584i −0.416873 0.908965i \(-0.636874\pi\)
0.822766 + 0.568380i \(0.192430\pi\)
\(6\) 0 0
\(7\) 0.266044 0.460802i 0.100555 0.174167i −0.811358 0.584549i \(-0.801271\pi\)
0.911914 + 0.410382i \(0.134605\pi\)
\(8\) 0 0
\(9\) −0.939693 + 0.342020i −0.313231 + 0.114007i
\(10\) 0 0
\(11\) 0.939693 + 1.62760i 0.283328 + 0.490738i 0.972202 0.234142i \(-0.0752282\pi\)
−0.688874 + 0.724881i \(0.741895\pi\)
\(12\) 0 0
\(13\) −0.673648 + 3.82045i −0.186836 + 1.05960i 0.736737 + 0.676180i \(0.236366\pi\)
−0.923573 + 0.383422i \(0.874745\pi\)
\(14\) 0 0
\(15\) 0.907604 + 0.761570i 0.234342 + 0.196637i
\(16\) 0 0
\(17\) −1.09240 0.397600i −0.264945 0.0964321i 0.206132 0.978524i \(-0.433912\pi\)
−0.471077 + 0.882092i \(0.656135\pi\)
\(18\) 0 0
\(19\) 3.93969 1.86516i 0.903827 0.427897i
\(20\) 0 0
\(21\) 0.500000 + 0.181985i 0.109109 + 0.0397124i
\(22\) 0 0
\(23\) 5.13429 + 4.30818i 1.07057 + 0.898317i 0.995104 0.0988312i \(-0.0315104\pi\)
0.0754683 + 0.997148i \(0.475955\pi\)
\(24\) 0 0
\(25\) −0.624485 + 3.54163i −0.124897 + 0.708326i
\(26\) 0 0
\(27\) −0.500000 0.866025i −0.0962250 0.166667i
\(28\) 0 0
\(29\) 3.77972 1.37570i 0.701875 0.255462i 0.0336640 0.999433i \(-0.489282\pi\)
0.668211 + 0.743971i \(0.267060\pi\)
\(30\) 0 0
\(31\) −0.979055 + 1.69577i −0.175844 + 0.304570i −0.940453 0.339924i \(-0.889599\pi\)
0.764609 + 0.644494i \(0.222932\pi\)
\(32\) 0 0
\(33\) −1.43969 + 1.20805i −0.250618 + 0.210294i
\(34\) 0 0
\(35\) −0.109470 0.620838i −0.0185039 0.104941i
\(36\) 0 0
\(37\) 6.88713 1.13224 0.566118 0.824324i \(-0.308445\pi\)
0.566118 + 0.824324i \(0.308445\pi\)
\(38\) 0 0
\(39\) −3.87939 −0.621199
\(40\) 0 0
\(41\) −1.56031 8.84894i −0.243679 1.38197i −0.823540 0.567258i \(-0.808004\pi\)
0.579861 0.814715i \(-0.303107\pi\)
\(42\) 0 0
\(43\) −1.85844 + 1.55942i −0.283410 + 0.237809i −0.773399 0.633919i \(-0.781445\pi\)
0.489989 + 0.871728i \(0.337001\pi\)
\(44\) 0 0
\(45\) −0.592396 + 1.02606i −0.0883092 + 0.152956i
\(46\) 0 0
\(47\) 1.91875 0.698367i 0.279878 0.101867i −0.198267 0.980148i \(-0.563531\pi\)
0.478145 + 0.878281i \(0.341309\pi\)
\(48\) 0 0
\(49\) 3.35844 + 5.81699i 0.479777 + 0.830999i
\(50\) 0 0
\(51\) 0.201867 1.14484i 0.0282670 0.160310i
\(52\) 0 0
\(53\) 9.93629 + 8.33754i 1.36485 + 1.14525i 0.974450 + 0.224605i \(0.0721093\pi\)
0.390404 + 0.920643i \(0.372335\pi\)
\(54\) 0 0
\(55\) 2.09240 + 0.761570i 0.282139 + 0.102690i
\(56\) 0 0
\(57\) 2.52094 + 3.55596i 0.333907 + 0.470998i
\(58\) 0 0
\(59\) −2.51842 0.916629i −0.327870 0.119335i 0.172840 0.984950i \(-0.444706\pi\)
−0.500710 + 0.865615i \(0.666928\pi\)
\(60\) 0 0
\(61\) −8.69253 7.29390i −1.11296 0.933888i −0.114737 0.993396i \(-0.536603\pi\)
−0.998228 + 0.0595075i \(0.981047\pi\)
\(62\) 0 0
\(63\) −0.0923963 + 0.524005i −0.0116408 + 0.0660185i
\(64\) 0 0
\(65\) 2.29813 + 3.98048i 0.285048 + 0.493718i
\(66\) 0 0
\(67\) −10.4966 + 3.82045i −1.28236 + 0.466742i −0.891213 0.453585i \(-0.850145\pi\)
−0.391150 + 0.920327i \(0.627923\pi\)
\(68\) 0 0
\(69\) −3.35117 + 5.80439i −0.403433 + 0.698767i
\(70\) 0 0
\(71\) −4.65136 + 3.90295i −0.552015 + 0.463195i −0.875623 0.482996i \(-0.839549\pi\)
0.323608 + 0.946191i \(0.395104\pi\)
\(72\) 0 0
\(73\) −0.0569038 0.322718i −0.00666009 0.0377712i 0.981297 0.192502i \(-0.0616601\pi\)
−0.987957 + 0.154731i \(0.950549\pi\)
\(74\) 0 0
\(75\) −3.59627 −0.415261
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 2.80154 + 15.8883i 0.315198 + 1.78757i 0.571109 + 0.820874i \(0.306513\pi\)
−0.255912 + 0.966700i \(0.582376\pi\)
\(80\) 0 0
\(81\) 0.766044 0.642788i 0.0851160 0.0714208i
\(82\) 0 0
\(83\) 5.78699 10.0234i 0.635205 1.10021i −0.351267 0.936275i \(-0.614249\pi\)
0.986472 0.163931i \(-0.0524175\pi\)
\(84\) 0 0
\(85\) −1.29426 + 0.471073i −0.140383 + 0.0510951i
\(86\) 0 0
\(87\) 2.01114 + 3.48340i 0.215617 + 0.373460i
\(88\) 0 0
\(89\) −0.618089 + 3.50535i −0.0655173 + 0.371567i 0.934366 + 0.356314i \(0.115967\pi\)
−0.999884 + 0.0152532i \(0.995145\pi\)
\(90\) 0 0
\(91\) 1.58125 + 1.32683i 0.165760 + 0.139089i
\(92\) 0 0
\(93\) −1.84002 0.669713i −0.190801 0.0694460i
\(94\) 0 0
\(95\) 2.15523 4.69318i 0.221122 0.481510i
\(96\) 0 0
\(97\) −5.52481 2.01087i −0.560960 0.204173i 0.0459494 0.998944i \(-0.485369\pi\)
−0.606909 + 0.794771i \(0.707591\pi\)
\(98\) 0 0
\(99\) −1.43969 1.20805i −0.144695 0.121413i
\(100\) 0 0
\(101\) 2.19594 12.4538i 0.218504 1.23920i −0.656218 0.754572i \(-0.727845\pi\)
0.874722 0.484626i \(-0.161044\pi\)
\(102\) 0 0
\(103\) 1.48158 + 2.56617i 0.145985 + 0.252853i 0.929740 0.368217i \(-0.120032\pi\)
−0.783755 + 0.621070i \(0.786698\pi\)
\(104\) 0 0
\(105\) 0.592396 0.215615i 0.0578120 0.0210418i
\(106\) 0 0
\(107\) 9.55690 16.5530i 0.923901 1.60024i 0.130581 0.991438i \(-0.458316\pi\)
0.793320 0.608805i \(-0.208351\pi\)
\(108\) 0 0
\(109\) −12.5719 + 10.5491i −1.20417 + 1.01042i −0.204670 + 0.978831i \(0.565612\pi\)
−0.999501 + 0.0315888i \(0.989943\pi\)
\(110\) 0 0
\(111\) 1.19594 + 6.78250i 0.113513 + 0.643766i
\(112\) 0 0
\(113\) −5.73648 −0.539643 −0.269821 0.962910i \(-0.586965\pi\)
−0.269821 + 0.962910i \(0.586965\pi\)
\(114\) 0 0
\(115\) 7.94087 0.740490
\(116\) 0 0
\(117\) −0.673648 3.82045i −0.0622788 0.353201i
\(118\) 0 0
\(119\) −0.473841 + 0.397600i −0.0434369 + 0.0364479i
\(120\) 0 0
\(121\) 3.73396 6.46740i 0.339451 0.587946i
\(122\) 0 0
\(123\) 8.44356 3.07321i 0.761330 0.277102i
\(124\) 0 0
\(125\) 5.09240 + 8.82029i 0.455478 + 0.788911i
\(126\) 0 0
\(127\) 0.327696 1.85846i 0.0290783 0.164911i −0.966811 0.255494i \(-0.917762\pi\)
0.995889 + 0.0905828i \(0.0288730\pi\)
\(128\) 0 0
\(129\) −1.85844 1.55942i −0.163627 0.137299i
\(130\) 0 0
\(131\) 10.0569 + 3.66041i 0.878676 + 0.319812i 0.741675 0.670759i \(-0.234032\pi\)
0.137001 + 0.990571i \(0.456254\pi\)
\(132\) 0 0
\(133\) 0.188663 2.31164i 0.0163592 0.200444i
\(134\) 0 0
\(135\) −1.11334 0.405223i −0.0958211 0.0348760i
\(136\) 0 0
\(137\) −8.62314 7.23567i −0.736725 0.618185i 0.195231 0.980757i \(-0.437454\pi\)
−0.931956 + 0.362572i \(0.881899\pi\)
\(138\) 0 0
\(139\) 2.11334 11.9854i 0.179251 1.01658i −0.753870 0.657023i \(-0.771815\pi\)
0.933122 0.359561i \(-0.117074\pi\)
\(140\) 0 0
\(141\) 1.02094 + 1.76833i 0.0859790 + 0.148920i
\(142\) 0 0
\(143\) −6.85117 + 2.49362i −0.572923 + 0.208527i
\(144\) 0 0
\(145\) 2.38279 4.12711i 0.197880 0.342738i
\(146\) 0 0
\(147\) −5.14543 + 4.31753i −0.424388 + 0.356104i
\(148\) 0 0
\(149\) −2.84002 16.1066i −0.232664 1.31950i −0.847478 0.530830i \(-0.821880\pi\)
0.614815 0.788672i \(-0.289231\pi\)
\(150\) 0 0
\(151\) −20.5226 −1.67010 −0.835052 0.550170i \(-0.814563\pi\)
−0.835052 + 0.550170i \(0.814563\pi\)
\(152\) 0 0
\(153\) 1.16250 0.0939829
\(154\) 0 0
\(155\) 0.402856 + 2.28471i 0.0323582 + 0.183512i
\(156\) 0 0
\(157\) −2.45084 + 2.05650i −0.195598 + 0.164126i −0.735327 0.677713i \(-0.762971\pi\)
0.539729 + 0.841839i \(0.318527\pi\)
\(158\) 0 0
\(159\) −6.48545 + 11.2331i −0.514330 + 0.890845i
\(160\) 0 0
\(161\) 3.35117 1.21972i 0.264109 0.0961278i
\(162\) 0 0
\(163\) −12.0039 20.7913i −0.940216 1.62850i −0.765058 0.643961i \(-0.777290\pi\)
−0.175157 0.984540i \(-0.556043\pi\)
\(164\) 0 0
\(165\) −0.386659 + 2.19285i −0.0301014 + 0.170713i
\(166\) 0 0
\(167\) −2.80406 2.35289i −0.216985 0.182072i 0.527816 0.849359i \(-0.323011\pi\)
−0.744801 + 0.667287i \(0.767456\pi\)
\(168\) 0 0
\(169\) −1.92602 0.701015i −0.148156 0.0539242i
\(170\) 0 0
\(171\) −3.06418 + 3.10013i −0.234324 + 0.237073i
\(172\) 0 0
\(173\) 5.01114 + 1.82391i 0.380990 + 0.138669i 0.525414 0.850847i \(-0.323911\pi\)
−0.144424 + 0.989516i \(0.546133\pi\)
\(174\) 0 0
\(175\) 1.46585 + 1.23000i 0.110808 + 0.0929789i
\(176\) 0 0
\(177\) 0.465385 2.63933i 0.0349805 0.198384i
\(178\) 0 0
\(179\) −12.6284 21.8730i −0.943888 1.63486i −0.757963 0.652297i \(-0.773805\pi\)
−0.185924 0.982564i \(-0.559528\pi\)
\(180\) 0 0
\(181\) 16.2626 5.91912i 1.20879 0.439965i 0.342508 0.939515i \(-0.388724\pi\)
0.866285 + 0.499550i \(0.166501\pi\)
\(182\) 0 0
\(183\) 5.67365 9.82705i 0.419408 0.726436i
\(184\) 0 0
\(185\) 6.25078 5.24503i 0.459567 0.385622i
\(186\) 0 0
\(187\) −0.379385 2.15160i −0.0277434 0.157341i
\(188\) 0 0
\(189\) −0.532089 −0.0387038
\(190\) 0 0
\(191\) 15.1780 1.09824 0.549120 0.835743i \(-0.314963\pi\)
0.549120 + 0.835743i \(0.314963\pi\)
\(192\) 0 0
\(193\) 2.25877 + 12.8101i 0.162590 + 0.922093i 0.951515 + 0.307603i \(0.0995269\pi\)
−0.788925 + 0.614490i \(0.789362\pi\)
\(194\) 0 0
\(195\) −3.52094 + 2.95442i −0.252140 + 0.211571i
\(196\) 0 0
\(197\) 4.47431 7.74973i 0.318781 0.552145i −0.661453 0.749987i \(-0.730060\pi\)
0.980234 + 0.197842i \(0.0633931\pi\)
\(198\) 0 0
\(199\) −4.23308 + 1.54071i −0.300075 + 0.109218i −0.487670 0.873028i \(-0.662153\pi\)
0.187595 + 0.982246i \(0.439931\pi\)
\(200\) 0 0
\(201\) −5.58512 9.67372i −0.393944 0.682331i
\(202\) 0 0
\(203\) 0.371644 2.10770i 0.0260843 0.147932i
\(204\) 0 0
\(205\) −8.15523 6.84305i −0.569586 0.477939i
\(206\) 0 0
\(207\) −6.29813 2.29233i −0.437751 0.159328i
\(208\) 0 0
\(209\) 6.73783 + 4.65955i 0.466065 + 0.322308i
\(210\) 0 0
\(211\) −6.01754 2.19021i −0.414265 0.150780i 0.126475 0.991970i \(-0.459634\pi\)
−0.540740 + 0.841190i \(0.681856\pi\)
\(212\) 0 0
\(213\) −4.65136 3.90295i −0.318706 0.267426i
\(214\) 0 0
\(215\) −0.499123 + 2.83067i −0.0340399 + 0.193050i
\(216\) 0 0
\(217\) 0.520945 + 0.902302i 0.0353640 + 0.0612523i
\(218\) 0 0
\(219\) 0.307934 0.112079i 0.0208082 0.00757357i
\(220\) 0 0
\(221\) 2.25490 3.90560i 0.151681 0.262719i
\(222\) 0 0
\(223\) −2.48886 + 2.08840i −0.166666 + 0.139849i −0.722306 0.691574i \(-0.756918\pi\)
0.555640 + 0.831423i \(0.312473\pi\)
\(224\) 0 0
\(225\) −0.624485 3.54163i −0.0416323 0.236109i
\(226\) 0 0
\(227\) 11.7023 0.776711 0.388356 0.921510i \(-0.373043\pi\)
0.388356 + 0.921510i \(0.373043\pi\)
\(228\) 0 0
\(229\) −22.9067 −1.51372 −0.756860 0.653578i \(-0.773267\pi\)
−0.756860 + 0.653578i \(0.773267\pi\)
\(230\) 0 0
\(231\) 0.173648 + 0.984808i 0.0114252 + 0.0647956i
\(232\) 0 0
\(233\) −2.45084 + 2.05650i −0.160560 + 0.134726i −0.719528 0.694463i \(-0.755642\pi\)
0.558968 + 0.829189i \(0.311197\pi\)
\(234\) 0 0
\(235\) 1.20961 2.09510i 0.0789061 0.136669i
\(236\) 0 0
\(237\) −15.1604 + 5.51795i −0.984777 + 0.358429i
\(238\) 0 0
\(239\) 3.08647 + 5.34592i 0.199647 + 0.345799i 0.948414 0.317035i \(-0.102687\pi\)
−0.748767 + 0.662833i \(0.769354\pi\)
\(240\) 0 0
\(241\) 0.266922 1.51379i 0.0171939 0.0975117i −0.975003 0.222191i \(-0.928679\pi\)
0.992197 + 0.124679i \(0.0397902\pi\)
\(242\) 0 0
\(243\) 0.766044 + 0.642788i 0.0491418 + 0.0412348i
\(244\) 0 0
\(245\) 7.47818 + 2.72183i 0.477763 + 0.173892i
\(246\) 0 0
\(247\) 4.47178 + 16.3079i 0.284533 + 1.03764i
\(248\) 0 0
\(249\) 10.8760 + 3.95853i 0.689237 + 0.250862i
\(250\) 0 0
\(251\) −13.7456 11.5339i −0.867612 0.728013i 0.0959815 0.995383i \(-0.469401\pi\)
−0.963594 + 0.267370i \(0.913845\pi\)
\(252\) 0 0
\(253\) −2.18732 + 12.4049i −0.137516 + 0.779889i
\(254\) 0 0
\(255\) −0.688663 1.19280i −0.0431257 0.0746960i
\(256\) 0 0
\(257\) −27.6386 + 10.0596i −1.72405 + 0.627503i −0.998179 0.0603277i \(-0.980785\pi\)
−0.725871 + 0.687831i \(0.758563\pi\)
\(258\) 0 0
\(259\) 1.83228 3.17360i 0.113852 0.197198i
\(260\) 0 0
\(261\) −3.08125 + 2.58548i −0.190725 + 0.160037i
\(262\) 0 0
\(263\) −1.85504 10.5204i −0.114386 0.648718i −0.987052 0.160400i \(-0.948722\pi\)
0.872666 0.488318i \(-0.162389\pi\)
\(264\) 0 0
\(265\) 15.3678 0.944038
\(266\) 0 0
\(267\) −3.55943 −0.217834
\(268\) 0 0
\(269\) −3.57310 20.2641i −0.217856 1.23552i −0.875882 0.482526i \(-0.839719\pi\)
0.658026 0.752995i \(-0.271392\pi\)
\(270\) 0 0
\(271\) −1.43763 + 1.20632i −0.0873300 + 0.0732786i −0.685408 0.728160i \(-0.740376\pi\)
0.598078 + 0.801438i \(0.295931\pi\)
\(272\) 0 0
\(273\) −1.03209 + 1.78763i −0.0624649 + 0.108192i
\(274\) 0 0
\(275\) −6.35117 + 2.31164i −0.382990 + 0.139397i
\(276\) 0 0
\(277\) −2.43629 4.21978i −0.146382 0.253542i 0.783505 0.621385i \(-0.213430\pi\)
−0.929888 + 0.367843i \(0.880096\pi\)
\(278\) 0 0
\(279\) 0.340022 1.92836i 0.0203566 0.115448i
\(280\) 0 0
\(281\) −0.309278 0.259515i −0.0184500 0.0154814i 0.633516 0.773730i \(-0.281611\pi\)
−0.651966 + 0.758248i \(0.726056\pi\)
\(282\) 0 0
\(283\) 16.5287 + 6.01595i 0.982528 + 0.357611i 0.782823 0.622245i \(-0.213779\pi\)
0.199706 + 0.979856i \(0.436001\pi\)
\(284\) 0 0
\(285\) 4.99613 + 1.30753i 0.295945 + 0.0774511i
\(286\) 0 0
\(287\) −4.49273 1.63522i −0.265197 0.0965239i
\(288\) 0 0
\(289\) −11.9875 10.0587i −0.705148 0.591689i
\(290\) 0 0
\(291\) 1.02094 5.79006i 0.0598488 0.339420i
\(292\) 0 0
\(293\) 6.58765 + 11.4101i 0.384855 + 0.666588i 0.991749 0.128195i \(-0.0409183\pi\)
−0.606894 + 0.794782i \(0.707585\pi\)
\(294\) 0 0
\(295\) −2.98380 + 1.08602i −0.173724 + 0.0632303i
\(296\) 0 0
\(297\) 0.939693 1.62760i 0.0545265 0.0944427i
\(298\) 0 0
\(299\) −19.9179 + 16.7131i −1.15188 + 0.966542i
\(300\) 0 0
\(301\) 0.224155 + 1.27125i 0.0129201 + 0.0732735i
\(302\) 0 0
\(303\) 12.6459 0.726488
\(304\) 0 0
\(305\) −13.4442 −0.769812
\(306\) 0 0
\(307\) −2.93494 16.6449i −0.167506 0.949975i −0.946443 0.322872i \(-0.895352\pi\)
0.778937 0.627103i \(-0.215759\pi\)
\(308\) 0 0
\(309\) −2.26991 + 1.90468i −0.129131 + 0.108354i
\(310\) 0 0
\(311\) −1.19072 + 2.06239i −0.0675197 + 0.116947i −0.897809 0.440385i \(-0.854842\pi\)
0.830289 + 0.557333i \(0.188175\pi\)
\(312\) 0 0
\(313\) 28.0621 10.2138i 1.58616 0.577317i 0.609632 0.792685i \(-0.291317\pi\)
0.976533 + 0.215368i \(0.0690951\pi\)
\(314\) 0 0
\(315\) 0.315207 + 0.545955i 0.0177599 + 0.0307611i
\(316\) 0 0
\(317\) −1.21941 + 6.91560i −0.0684888 + 0.388419i 0.931224 + 0.364448i \(0.118742\pi\)
−0.999713 + 0.0239714i \(0.992369\pi\)
\(318\) 0 0
\(319\) 5.79086 + 4.85911i 0.324226 + 0.272058i
\(320\) 0 0
\(321\) 17.9611 + 6.53731i 1.00249 + 0.364877i
\(322\) 0 0
\(323\) −5.04529 + 0.471073i −0.280728 + 0.0262112i
\(324\) 0 0
\(325\) −13.1099 4.77163i −0.727208 0.264682i
\(326\) 0 0
\(327\) −12.5719 10.5491i −0.695229 0.583366i
\(328\) 0 0
\(329\) 0.188663 1.06996i 0.0104013 0.0589888i
\(330\) 0 0
\(331\) 13.5993 + 23.5546i 0.747483 + 1.29468i 0.949026 + 0.315199i \(0.102071\pi\)
−0.201543 + 0.979480i \(0.564596\pi\)
\(332\) 0 0
\(333\) −6.47178 + 2.35554i −0.354651 + 0.129083i
\(334\) 0 0
\(335\) −6.61721 + 11.4613i −0.361537 + 0.626200i
\(336\) 0 0
\(337\) −8.59286 + 7.21027i −0.468083 + 0.392768i −0.846095 0.533032i \(-0.821052\pi\)
0.378012 + 0.925801i \(0.376608\pi\)
\(338\) 0 0
\(339\) −0.996130 5.64933i −0.0541023 0.306830i
\(340\) 0 0
\(341\) −3.68004 −0.199286
\(342\) 0 0
\(343\) 7.29860 0.394087
\(344\) 0 0
\(345\) 1.37892 + 7.82023i 0.0742385 + 0.421027i
\(346\) 0 0
\(347\) −1.48293 + 1.24432i −0.0796076 + 0.0667987i −0.681723 0.731610i \(-0.738769\pi\)
0.602115 + 0.798409i \(0.294325\pi\)
\(348\) 0 0
\(349\) −7.19846 + 12.4681i −0.385325 + 0.667402i −0.991814 0.127689i \(-0.959244\pi\)
0.606489 + 0.795092i \(0.292577\pi\)
\(350\) 0 0
\(351\) 3.64543 1.32683i 0.194579 0.0708208i
\(352\) 0 0
\(353\) −7.86184 13.6171i −0.418444 0.724766i 0.577339 0.816504i \(-0.304091\pi\)
−0.995783 + 0.0917384i \(0.970758\pi\)
\(354\) 0 0
\(355\) −1.24922 + 7.08467i −0.0663016 + 0.376015i
\(356\) 0 0
\(357\) −0.473841 0.397600i −0.0250783 0.0210432i
\(358\) 0 0
\(359\) 14.5817 + 5.30731i 0.769594 + 0.280109i 0.696826 0.717240i \(-0.254595\pi\)
0.0727672 + 0.997349i \(0.476817\pi\)
\(360\) 0 0
\(361\) 12.0424 14.6963i 0.633808 0.773490i
\(362\) 0 0
\(363\) 7.01754 + 2.55418i 0.368325 + 0.134059i
\(364\) 0 0
\(365\) −0.297418 0.249563i −0.0155676 0.0130627i
\(366\) 0 0
\(367\) 2.73396 15.5050i 0.142711 0.809356i −0.826465 0.562988i \(-0.809652\pi\)
0.969176 0.246368i \(-0.0792372\pi\)
\(368\) 0 0
\(369\) 4.49273 + 7.78163i 0.233882 + 0.405095i
\(370\) 0 0
\(371\) 6.48545 2.36051i 0.336708 0.122552i
\(372\) 0 0
\(373\) 14.8143 25.6592i 0.767057 1.32858i −0.172095 0.985080i \(-0.555054\pi\)
0.939152 0.343501i \(-0.111613\pi\)
\(374\) 0 0
\(375\) −7.80200 + 6.54666i −0.402894 + 0.338068i
\(376\) 0 0
\(377\) 2.70961 + 15.3669i 0.139552 + 0.791438i
\(378\) 0 0
\(379\) −4.72462 −0.242688 −0.121344 0.992611i \(-0.538720\pi\)
−0.121344 + 0.992611i \(0.538720\pi\)
\(380\) 0 0
\(381\) 1.88713 0.0966804
\(382\) 0 0
\(383\) 0.910130 + 5.16160i 0.0465055 + 0.263746i 0.999191 0.0402115i \(-0.0128032\pi\)
−0.952686 + 0.303957i \(0.901692\pi\)
\(384\) 0 0
\(385\) 0.907604 0.761570i 0.0462558 0.0388132i
\(386\) 0 0
\(387\) 1.21301 2.10100i 0.0616608 0.106800i
\(388\) 0 0
\(389\) 14.1677 5.15663i 0.718332 0.261451i 0.0431144 0.999070i \(-0.486272\pi\)
0.675217 + 0.737619i \(0.264050\pi\)
\(390\) 0 0
\(391\) −3.89574 6.74763i −0.197016 0.341242i
\(392\) 0 0
\(393\) −1.85844 + 10.5397i −0.0937459 + 0.531660i
\(394\) 0 0
\(395\) 14.6427 + 12.2867i 0.736756 + 0.618212i
\(396\) 0 0
\(397\) 13.6677 + 4.97464i 0.685963 + 0.249670i 0.661406 0.750028i \(-0.269960\pi\)
0.0245573 + 0.999698i \(0.492182\pi\)
\(398\) 0 0
\(399\) 2.30928 0.215615i 0.115608 0.0107942i
\(400\) 0 0
\(401\) −2.68257 0.976376i −0.133961 0.0487579i 0.274170 0.961681i \(-0.411597\pi\)
−0.408131 + 0.912923i \(0.633819\pi\)
\(402\) 0 0
\(403\) −5.81908 4.88279i −0.289869 0.243229i
\(404\) 0 0
\(405\) 0.205737 1.16679i 0.0102232 0.0579784i
\(406\) 0 0
\(407\) 6.47178 + 11.2095i 0.320794 + 0.555632i
\(408\) 0 0
\(409\) −32.1634 + 11.7065i −1.59038 + 0.578851i −0.977428 0.211269i \(-0.932240\pi\)
−0.612952 + 0.790120i \(0.710018\pi\)
\(410\) 0 0
\(411\) 5.62836 9.74860i 0.277626 0.480863i
\(412\) 0 0
\(413\) −1.09240 + 0.916629i −0.0537533 + 0.0451044i
\(414\) 0 0
\(415\) −2.38120 13.5044i −0.116888 0.662907i
\(416\) 0 0
\(417\) 12.1702 0.595979
\(418\) 0 0
\(419\) 7.91891 0.386864 0.193432 0.981114i \(-0.438038\pi\)
0.193432 + 0.981114i \(0.438038\pi\)
\(420\) 0 0
\(421\) 2.81480 + 15.9635i 0.137185 + 0.778014i 0.973313 + 0.229480i \(0.0737026\pi\)
−0.836129 + 0.548534i \(0.815186\pi\)
\(422\) 0 0
\(423\) −1.56418 + 1.31250i −0.0760529 + 0.0638160i
\(424\) 0 0
\(425\) 2.09034 3.62057i 0.101396 0.175623i
\(426\) 0 0
\(427\) −5.67365 + 2.06504i −0.274567 + 0.0999342i
\(428\) 0 0
\(429\) −3.64543 6.31407i −0.176003 0.304846i
\(430\) 0 0
\(431\) −4.41622 + 25.0456i −0.212722 + 1.20641i 0.672094 + 0.740466i \(0.265395\pi\)
−0.884816 + 0.465940i \(0.845716\pi\)
\(432\) 0 0
\(433\) 9.07604 + 7.61570i 0.436167 + 0.365987i 0.834273 0.551352i \(-0.185888\pi\)
−0.398106 + 0.917339i \(0.630332\pi\)
\(434\) 0 0
\(435\) 4.47818 + 1.62992i 0.214712 + 0.0781489i
\(436\) 0 0
\(437\) 28.2629 + 7.39663i 1.35200 + 0.353829i
\(438\) 0 0
\(439\) 24.3002 + 8.84457i 1.15979 + 0.422128i 0.849022 0.528358i \(-0.177192\pi\)
0.310766 + 0.950486i \(0.399414\pi\)
\(440\) 0 0
\(441\) −5.14543 4.31753i −0.245020 0.205597i
\(442\) 0 0
\(443\) −0.160282 + 0.909006i −0.00761524 + 0.0431882i −0.988379 0.152012i \(-0.951425\pi\)
0.980763 + 0.195201i \(0.0625358\pi\)
\(444\) 0 0
\(445\) 2.10859 + 3.65219i 0.0999569 + 0.173130i
\(446\) 0 0
\(447\) 15.3687 5.59375i 0.726915 0.264575i
\(448\) 0 0
\(449\) −4.67230 + 8.09267i −0.220500 + 0.381917i −0.954960 0.296735i \(-0.904102\pi\)
0.734460 + 0.678652i \(0.237435\pi\)
\(450\) 0 0
\(451\) 12.9363 10.8548i 0.609146 0.511134i
\(452\) 0 0
\(453\) −3.56371 20.2108i −0.167438 0.949587i
\(454\) 0 0
\(455\) 2.44562 0.114653
\(456\) 0 0
\(457\) 30.9009 1.44548 0.722740 0.691120i \(-0.242882\pi\)
0.722740 + 0.691120i \(0.242882\pi\)
\(458\) 0 0
\(459\) 0.201867 + 1.14484i 0.00942233 + 0.0534367i
\(460\) 0 0
\(461\) −22.7422 + 19.0829i −1.05921 + 0.888781i −0.994032 0.109093i \(-0.965205\pi\)
−0.0651765 + 0.997874i \(0.520761\pi\)
\(462\) 0 0
\(463\) −5.91534 + 10.2457i −0.274909 + 0.476157i −0.970112 0.242657i \(-0.921981\pi\)
0.695203 + 0.718814i \(0.255315\pi\)
\(464\) 0 0
\(465\) −2.18004 + 0.793471i −0.101097 + 0.0367964i
\(466\) 0 0
\(467\) 19.1591 + 33.1845i 0.886577 + 1.53560i 0.843895 + 0.536508i \(0.180257\pi\)
0.0426825 + 0.999089i \(0.486410\pi\)
\(468\) 0 0
\(469\) −1.03209 + 5.85327i −0.0476574 + 0.270279i
\(470\) 0 0
\(471\) −2.45084 2.05650i −0.112929 0.0947584i
\(472\) 0 0
\(473\) −4.28446 1.55942i −0.197000 0.0717021i
\(474\) 0 0
\(475\) 4.14543 + 15.1177i 0.190205 + 0.693648i
\(476\) 0 0
\(477\) −12.1887 4.43631i −0.558081 0.203125i
\(478\) 0 0
\(479\) −28.5612 23.9657i −1.30500 1.09502i −0.989259 0.146176i \(-0.953304\pi\)
−0.315738 0.948846i \(-0.602252\pi\)
\(480\) 0 0
\(481\) −4.63950 + 26.3119i −0.211543 + 1.19972i
\(482\) 0 0
\(483\) 1.78312 + 3.08845i 0.0811347 + 0.140529i
\(484\) 0 0
\(485\) −6.54576 + 2.38246i −0.297228 + 0.108182i
\(486\) 0 0
\(487\) 16.4893 28.5603i 0.747203 1.29419i −0.201956 0.979395i \(-0.564730\pi\)
0.949159 0.314798i \(-0.101937\pi\)
\(488\) 0 0
\(489\) 18.3910 15.4319i 0.831670 0.697854i
\(490\) 0 0
\(491\) −3.07027 17.4124i −0.138559 0.785809i −0.972315 0.233675i \(-0.924925\pi\)
0.833755 0.552134i \(-0.186186\pi\)
\(492\) 0 0
\(493\) −4.67593 −0.210593
\(494\) 0 0
\(495\) −2.22668 −0.100082
\(496\) 0 0
\(497\) 0.561023 + 3.18172i 0.0251653 + 0.142720i
\(498\) 0 0
\(499\) −20.7781 + 17.4349i −0.930157 + 0.780494i −0.975846 0.218462i \(-0.929896\pi\)
0.0456890 + 0.998956i \(0.485452\pi\)
\(500\) 0 0
\(501\) 1.83022 3.17004i 0.0817683 0.141627i
\(502\) 0 0
\(503\) 0.536837 0.195393i 0.0239364 0.00871212i −0.330024 0.943972i \(-0.607057\pi\)
0.353961 + 0.935260i \(0.384835\pi\)
\(504\) 0 0
\(505\) −7.49138 12.9755i −0.333362 0.577400i
\(506\) 0 0
\(507\) 0.355914 2.01849i 0.0158067 0.0896443i
\(508\) 0 0
\(509\) 31.0638 + 26.0656i 1.37688 + 1.15534i 0.970352 + 0.241698i \(0.0777043\pi\)
0.406526 + 0.913639i \(0.366740\pi\)
\(510\) 0 0
\(511\) −0.163848 0.0596358i −0.00724821 0.00263813i
\(512\) 0 0
\(513\) −3.58512 2.47929i −0.158287 0.109463i
\(514\) 0 0
\(515\) 3.29901 + 1.20074i 0.145372 + 0.0529110i
\(516\) 0 0
\(517\) 2.93969 + 2.46669i 0.129288 + 0.108485i
\(518\) 0 0
\(519\) −0.926022 + 5.25173i −0.0406479 + 0.230525i
\(520\) 0 0
\(521\) −9.44996 16.3678i −0.414010 0.717087i 0.581314 0.813680i \(-0.302539\pi\)
−0.995324 + 0.0965927i \(0.969206\pi\)
\(522\) 0 0
\(523\) −4.45589 + 1.62181i −0.194842 + 0.0709168i −0.437598 0.899171i \(-0.644171\pi\)
0.242756 + 0.970087i \(0.421949\pi\)
\(524\) 0 0
\(525\) −0.956767 + 1.65717i −0.0417567 + 0.0723248i
\(526\) 0 0
\(527\) 1.74376 1.46318i 0.0759592 0.0637373i
\(528\) 0 0
\(529\) 3.80659 + 21.5882i 0.165504 + 0.938619i
\(530\) 0 0
\(531\) 2.68004 0.116304
\(532\) 0 0
\(533\) 34.8580 1.50987
\(534\) 0 0
\(535\) −3.93242 22.3019i −0.170013 0.964193i
\(536\) 0 0
\(537\) 19.3478 16.2347i 0.834918 0.700579i
\(538\) 0 0
\(539\) −6.31180 + 10.9324i −0.271869 + 0.470890i
\(540\) 0 0
\(541\) 26.6506 9.70004i 1.14580 0.417037i 0.301796 0.953373i \(-0.402414\pi\)
0.844005 + 0.536335i \(0.180192\pi\)
\(542\) 0 0
\(543\) 8.65317 + 14.9877i 0.371343 + 0.643185i
\(544\) 0 0
\(545\) −3.37645 + 19.1488i −0.144631 + 0.820244i
\(546\) 0 0
\(547\) 5.27063 + 4.42258i 0.225356 + 0.189096i 0.748474 0.663164i \(-0.230787\pi\)
−0.523118 + 0.852260i \(0.675231\pi\)
\(548\) 0 0
\(549\) 10.6630 + 3.88100i 0.455084 + 0.165637i
\(550\) 0 0
\(551\) 12.3250 12.4696i 0.525063 0.531224i
\(552\) 0 0
\(553\) 8.06670 + 2.93604i 0.343031 + 0.124853i
\(554\) 0 0
\(555\) 6.25078 + 5.24503i 0.265331 + 0.222639i
\(556\) 0 0
\(557\) −2.45929 + 13.9473i −0.104204 + 0.590968i 0.887332 + 0.461131i \(0.152556\pi\)
−0.991535 + 0.129836i \(0.958555\pi\)
\(558\) 0 0
\(559\) −4.70574 8.15058i −0.199031 0.344733i
\(560\) 0 0
\(561\) 2.05303 0.747243i 0.0866791 0.0315486i
\(562\) 0 0
\(563\) −18.1275 + 31.3977i −0.763982 + 1.32326i 0.176801 + 0.984247i \(0.443425\pi\)
−0.940783 + 0.339009i \(0.889908\pi\)
\(564\) 0 0
\(565\) −5.20645 + 4.36873i −0.219037 + 0.183794i
\(566\) 0 0
\(567\) −0.0923963 0.524005i −0.00388028 0.0220062i
\(568\) 0 0
\(569\) −30.2918 −1.26990 −0.634949 0.772554i \(-0.718979\pi\)
−0.634949 + 0.772554i \(0.718979\pi\)
\(570\) 0 0
\(571\) −3.39094 −0.141906 −0.0709532 0.997480i \(-0.522604\pi\)
−0.0709532 + 0.997480i \(0.522604\pi\)
\(572\) 0 0
\(573\) 2.63563 + 14.9474i 0.110105 + 0.624436i
\(574\) 0 0
\(575\) −18.4643 + 15.4934i −0.770013 + 0.646117i
\(576\) 0 0
\(577\) 11.1514 19.3147i 0.464237 0.804082i −0.534930 0.844897i \(-0.679662\pi\)
0.999167 + 0.0408143i \(0.0129952\pi\)
\(578\) 0 0
\(579\) −12.2233 + 4.44891i −0.507982 + 0.184890i
\(580\) 0 0
\(581\) −3.07919 5.33332i −0.127746 0.221263i
\(582\) 0 0
\(583\) −4.23308 + 24.0070i −0.175316 + 0.994268i
\(584\) 0 0
\(585\) −3.52094 2.95442i −0.145573 0.122150i
\(586\) 0 0
\(587\) −27.0164 9.83315i −1.11508 0.405858i −0.282228 0.959347i \(-0.591074\pi\)
−0.832856 + 0.553490i \(0.813296\pi\)
\(588\) 0 0
\(589\) −0.694288 + 8.50692i −0.0286076 + 0.350522i
\(590\) 0 0
\(591\) 8.40895 + 3.06061i 0.345898 + 0.125897i
\(592\) 0 0
\(593\) 9.02094 + 7.56947i 0.370446 + 0.310841i 0.808938 0.587894i \(-0.200043\pi\)
−0.438492 + 0.898735i \(0.644487\pi\)
\(594\) 0 0
\(595\) −0.127260 + 0.721726i −0.00521714 + 0.0295879i
\(596\) 0 0
\(597\) −2.25237 3.90123i −0.0921835 0.159667i
\(598\) 0 0
\(599\) −20.3268 + 7.39836i −0.830531 + 0.302289i −0.722077 0.691813i \(-0.756812\pi\)
−0.108454 + 0.994101i \(0.534590\pi\)
\(600\) 0 0
\(601\) 13.0967 22.6842i 0.534227 0.925308i −0.464973 0.885325i \(-0.653936\pi\)
0.999200 0.0399835i \(-0.0127305\pi\)
\(602\) 0 0
\(603\) 8.55690 7.18009i 0.348464 0.292396i
\(604\) 0 0
\(605\) −1.53643 8.71351i −0.0624646 0.354254i
\(606\) 0 0
\(607\) 13.2249 0.536783 0.268392 0.963310i \(-0.413508\pi\)
0.268392 + 0.963310i \(0.413508\pi\)
\(608\) 0 0
\(609\) 2.14022 0.0867259
\(610\) 0 0
\(611\) 1.37551 + 7.80093i 0.0556474 + 0.315592i
\(612\) 0 0
\(613\) −4.30722 + 3.61419i −0.173967 + 0.145976i −0.725614 0.688102i \(-0.758444\pi\)
0.551647 + 0.834078i \(0.314000\pi\)
\(614\) 0 0
\(615\) 5.32295 9.21962i 0.214642 0.371771i
\(616\) 0 0
\(617\) −8.90673 + 3.24178i −0.358571 + 0.130509i −0.515023 0.857176i \(-0.672217\pi\)
0.156452 + 0.987686i \(0.449994\pi\)
\(618\) 0 0
\(619\) −7.37464 12.7732i −0.296412 0.513400i 0.678901 0.734230i \(-0.262457\pi\)
−0.975312 + 0.220830i \(0.929123\pi\)
\(620\) 0 0
\(621\) 1.16385 6.60051i 0.0467036 0.264869i
\(622\) 0 0
\(623\) 1.45084 + 1.21740i 0.0581266 + 0.0487740i
\(624\) 0 0
\(625\) −5.55778 2.02287i −0.222311 0.0809147i
\(626\) 0 0
\(627\) −3.41875 + 7.44459i −0.136532 + 0.297308i
\(628\) 0 0
\(629\) −7.52347 2.73832i −0.299980 0.109184i
\(630\) 0 0
\(631\) −19.1518 16.0703i −0.762422 0.639748i 0.176334 0.984330i \(-0.443576\pi\)
−0.938756 + 0.344582i \(0.888021\pi\)
\(632\) 0 0
\(633\) 1.11200 6.30645i 0.0441979 0.250659i
\(634\) 0 0
\(635\) −1.11793 1.93631i −0.0443636 0.0768399i
\(636\) 0 0
\(637\) −24.4859 + 8.91215i −0.970167 + 0.353112i
\(638\) 0 0
\(639\) 3.03596 5.25844i 0.120101 0.208021i
\(640\) 0 0
\(641\) −33.4996 + 28.1095i −1.32315 + 1.11026i −0.337528 + 0.941315i \(0.609591\pi\)
−0.985626 + 0.168943i \(0.945965\pi\)
\(642\) 0 0
\(643\) 5.80912 + 32.9451i 0.229089 + 1.29923i 0.854712 + 0.519103i \(0.173734\pi\)
−0.625622 + 0.780126i \(0.715155\pi\)
\(644\) 0 0
\(645\) −2.87433 −0.113177
\(646\) 0 0
\(647\) 32.1266 1.26303 0.631514 0.775365i \(-0.282434\pi\)
0.631514 + 0.775365i \(0.282434\pi\)
\(648\) 0 0
\(649\) −0.874638 4.96032i −0.0343325 0.194709i
\(650\) 0 0
\(651\) −0.798133 + 0.669713i −0.0312813 + 0.0262481i
\(652\) 0 0
\(653\) −1.44815 + 2.50827i −0.0566704 + 0.0981561i −0.892969 0.450118i \(-0.851382\pi\)
0.836298 + 0.548275i \(0.184715\pi\)
\(654\) 0 0
\(655\) 11.9153 4.33683i 0.465571 0.169454i
\(656\) 0 0
\(657\) 0.163848 + 0.283793i 0.00639232 + 0.0110718i
\(658\) 0 0
\(659\) −3.15926 + 17.9171i −0.123067 + 0.697950i 0.859370 + 0.511355i \(0.170856\pi\)
−0.982437 + 0.186595i \(0.940255\pi\)
\(660\) 0 0
\(661\) 16.4081 + 13.7680i 0.638200 + 0.535513i 0.903465 0.428662i \(-0.141015\pi\)
−0.265265 + 0.964176i \(0.585459\pi\)
\(662\) 0 0
\(663\) 4.23783 + 1.54244i 0.164584 + 0.0599035i
\(664\) 0 0
\(665\) −1.58924 2.24173i −0.0616281 0.0869305i
\(666\) 0 0
\(667\) 25.3329 + 9.22043i 0.980894 + 0.357016i
\(668\) 0 0
\(669\) −2.48886 2.08840i −0.0962247 0.0807421i
\(670\) 0 0
\(671\) 3.70321 21.0020i 0.142961 0.810771i
\(672\) 0 0
\(673\) −20.3457 35.2398i −0.784269 1.35839i −0.929435 0.368987i \(-0.879705\pi\)
0.145165 0.989407i \(-0.453629\pi\)
\(674\) 0 0
\(675\) 3.37939 1.23000i 0.130073 0.0473426i
\(676\) 0 0
\(677\) 0.0680482 0.117863i 0.00261530 0.00452984i −0.864715 0.502263i \(-0.832501\pi\)
0.867330 + 0.497733i \(0.165834\pi\)
\(678\) 0 0
\(679\) −2.39646 + 2.01087i −0.0919677 + 0.0771700i
\(680\) 0 0
\(681\) 2.03209 + 11.5245i 0.0778698 + 0.441622i
\(682\) 0 0
\(683\) 43.6459 1.67006 0.835032 0.550202i \(-0.185449\pi\)
0.835032 + 0.550202i \(0.185449\pi\)
\(684\) 0 0
\(685\) −13.3369 −0.509576
\(686\) 0 0
\(687\) −3.97771 22.5587i −0.151759 0.860669i
\(688\) 0 0
\(689\) −38.5467 + 32.3445i −1.46851 + 1.23223i
\(690\) 0 0
\(691\) 7.93376 13.7417i 0.301815 0.522758i −0.674732 0.738062i \(-0.735741\pi\)
0.976547 + 0.215304i \(0.0690743\pi\)
\(692\) 0 0
\(693\) −0.939693 + 0.342020i −0.0356960 + 0.0129923i
\(694\) 0 0
\(695\) −7.20961 12.4874i −0.273476 0.473674i
\(696\) 0 0
\(697\) −1.81386 + 10.2869i −0.0687050 + 0.389645i
\(698\) 0 0
\(699\) −2.45084 2.05650i −0.0926992 0.0777838i
\(700\) 0 0
\(701\) −18.0513 6.57013i −0.681787 0.248150i −0.0221726 0.999754i \(-0.507058\pi\)
−0.659615 + 0.751604i \(0.729281\pi\)
\(702\) 0 0
\(703\) 27.1332 12.8456i 1.02335 0.484481i
\(704\) 0 0
\(705\) 2.27332 + 0.827420i 0.0856181 + 0.0311624i
\(706\) 0 0
\(707\) −5.15451 4.32515i −0.193855 0.162664i
\(708\) 0 0
\(709\) 5.73489 32.5242i 0.215378 1.22147i −0.664871 0.746959i \(-0.731513\pi\)
0.880249 0.474512i \(-0.157376\pi\)
\(710\) 0 0
\(711\) −8.06670 13.9719i −0.302525 0.523989i
\(712\) 0 0
\(713\) −12.3324 + 4.48864i −0.461854 + 0.168101i
\(714\) 0 0
\(715\) −4.31908 + 7.48086i −0.161524 + 0.279768i
\(716\) 0 0
\(717\) −4.72874 + 3.96788i −0.176598 + 0.148183i
\(718\) 0 0
\(719\) −6.84952 38.8455i −0.255444 1.44869i −0.794931 0.606700i \(-0.792493\pi\)
0.539487 0.841994i \(-0.318618\pi\)
\(720\) 0 0
\(721\) 1.57667 0.0587181
\(722\) 0 0
\(723\) 1.53714 0.0571669
\(724\) 0 0
\(725\) 2.51186 + 14.2455i 0.0932881 + 0.529063i
\(726\) 0 0
\(727\) −13.9816 + 11.7319i −0.518548 + 0.435114i −0.864125 0.503277i \(-0.832128\pi\)
0.345577 + 0.938390i \(0.387683\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) 2.65018 0.964586i 0.0980204 0.0356765i
\(732\) 0 0
\(733\) −7.69640 13.3306i −0.284273 0.492376i 0.688160 0.725559i \(-0.258419\pi\)
−0.972433 + 0.233184i \(0.925086\pi\)
\(734\) 0 0
\(735\) −1.38191 + 7.83721i −0.0509726 + 0.289080i
\(736\) 0 0
\(737\) −16.0817 13.4942i −0.592378 0.497064i
\(738\) 0 0
\(739\) 14.2618 + 5.19086i 0.524627 + 0.190949i 0.590738 0.806864i \(-0.298837\pi\)
−0.0661104 + 0.997812i \(0.521059\pi\)
\(740\) 0 0
\(741\) −15.2836 + 7.23567i −0.561457 + 0.265809i
\(742\) 0 0
\(743\) −9.27156 3.37457i −0.340141 0.123801i 0.166302 0.986075i \(-0.446817\pi\)
−0.506442 + 0.862274i \(0.669040\pi\)
\(744\) 0 0
\(745\) −14.8439 12.4555i −0.543838 0.456334i
\(746\) 0 0
\(747\) −2.00980 + 11.3981i −0.0735347 + 0.417036i
\(748\) 0 0
\(749\) −5.08512 8.80769i −0.185806 0.321826i
\(750\) 0 0
\(751\) −9.17024 + 3.33770i −0.334627 + 0.121794i −0.503869 0.863780i \(-0.668090\pi\)
0.169242 + 0.985575i \(0.445868\pi\)
\(752\) 0 0
\(753\) 8.97178 15.5396i 0.326950 0.566294i
\(754\) 0 0
\(755\) −18.6264 + 15.6294i −0.677883 + 0.568812i
\(756\) 0 0
\(757\) −7.55438 42.8430i −0.274569 1.55716i −0.740329 0.672245i \(-0.765330\pi\)
0.465761 0.884911i \(-0.345781\pi\)
\(758\) 0 0
\(759\) −12.5963 −0.457216
\(760\) 0 0
\(761\) 44.7137 1.62087 0.810435 0.585828i \(-0.199231\pi\)
0.810435 + 0.585828i \(0.199231\pi\)
\(762\) 0 0
\(763\) 1.51636 + 8.59970i 0.0548959 + 0.311330i
\(764\) 0 0
\(765\) 1.05509 0.885328i 0.0381470 0.0320091i
\(766\) 0 0
\(767\) 5.19846 9.00400i 0.187706 0.325116i
\(768\) 0 0
\(769\) −20.7690 + 7.55931i −0.748951 + 0.272596i −0.688164 0.725555i \(-0.741583\pi\)
−0.0607865 + 0.998151i \(0.519361\pi\)
\(770\) 0 0
\(771\) −14.7062 25.4719i −0.529631 0.917348i
\(772\) 0 0
\(773\) 7.32429 41.5381i 0.263436 1.49402i −0.510014 0.860166i \(-0.670360\pi\)
0.773451 0.633857i \(-0.218529\pi\)
\(774\) 0 0
\(775\) −5.39440 4.52644i −0.193773 0.162594i
\(776\) 0 0
\(777\) 3.44356 + 1.25335i 0.123537 + 0.0449638i
\(778\) 0 0
\(779\) −22.6518 31.9519i −0.811586 1.14480i
\(780\) 0 0
\(781\) −10.7233 3.90295i −0.383709 0.139659i
\(782\) 0 0
\(783\) −3.08125 2.58548i −0.110115 0.0923974i
\(784\) 0 0
\(785\) −0.658223 + 3.73297i −0.0234930 + 0.133235i
\(786\) 0 0
\(787\) −14.2396 24.6638i −0.507588 0.879169i −0.999961 0.00878442i \(-0.997204\pi\)
0.492373 0.870384i \(-0.336130\pi\)
\(788\) 0 0
\(789\) 10.0385 3.65371i 0.357380 0.130076i
\(790\) 0 0
\(791\) −1.52616 + 2.64339i −0.0542640 + 0.0939880i
\(792\) 0 0
\(793\) 33.7217 28.2959i 1.19749 1.00482i