Properties

Label 4032.2.v.e.1583.4
Level 4032
Weight 2
Character 4032.1583
Analytic conductor 32.196
Analytic rank 0
Dimension 40
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1008)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1583.4
Character \(\chi\) = 4032.1583
Dual form 4032.2.v.e.3599.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.12043 - 2.12043i) q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+(-2.12043 - 2.12043i) q^{5} -1.00000 q^{7} +(4.03827 - 4.03827i) q^{11} +(-4.91665 - 4.91665i) q^{13} +4.76253i q^{17} +(2.21762 - 2.21762i) q^{19} -6.91384i q^{23} +3.99241i q^{25} +(-2.61285 + 2.61285i) q^{29} -0.712246i q^{31} +(2.12043 + 2.12043i) q^{35} +(5.73777 - 5.73777i) q^{37} +3.59400 q^{41} +(-3.36325 - 3.36325i) q^{43} +6.04590 q^{47} +1.00000 q^{49} +(-4.53235 - 4.53235i) q^{53} -17.1257 q^{55} +(-4.82118 + 4.82118i) q^{59} +(-6.72581 - 6.72581i) q^{61} +20.8508i q^{65} +(3.87274 - 3.87274i) q^{67} +14.7448i q^{71} +4.61241i q^{73} +(-4.03827 + 4.03827i) q^{77} -7.43429i q^{79} +(2.44737 + 2.44737i) q^{83} +(10.0986 - 10.0986i) q^{85} -4.23689 q^{89} +(4.91665 + 4.91665i) q^{91} -9.40458 q^{95} -6.76292 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{7} + O(q^{10}) \) \( 40q - 40q^{7} - 24q^{13} + 32q^{19} - 8q^{37} - 32q^{43} + 40q^{49} - 48q^{55} - 24q^{61} + 64q^{85} + 24q^{91} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.12043 2.12043i −0.948283 0.948283i 0.0504437 0.998727i \(-0.483936\pi\)
−0.998727 + 0.0504437i \(0.983936\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.03827 4.03827i 1.21759 1.21759i 0.249110 0.968475i \(-0.419862\pi\)
0.968475 0.249110i \(-0.0801380\pi\)
\(12\) 0 0
\(13\) −4.91665 4.91665i −1.36363 1.36363i −0.869237 0.494396i \(-0.835389\pi\)
−0.494396 0.869237i \(-0.664611\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.76253i 1.15508i 0.816361 + 0.577542i \(0.195988\pi\)
−0.816361 + 0.577542i \(0.804012\pi\)
\(18\) 0 0
\(19\) 2.21762 2.21762i 0.508756 0.508756i −0.405388 0.914145i \(-0.632864\pi\)
0.914145 + 0.405388i \(0.132864\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.91384i 1.44164i −0.693125 0.720818i \(-0.743767\pi\)
0.693125 0.720818i \(-0.256233\pi\)
\(24\) 0 0
\(25\) 3.99241i 0.798482i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.61285 + 2.61285i −0.485193 + 0.485193i −0.906786 0.421592i \(-0.861471\pi\)
0.421592 + 0.906786i \(0.361471\pi\)
\(30\) 0 0
\(31\) 0.712246i 0.127923i −0.997952 0.0639615i \(-0.979627\pi\)
0.997952 0.0639615i \(-0.0203735\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.12043 + 2.12043i 0.358417 + 0.358417i
\(36\) 0 0
\(37\) 5.73777 5.73777i 0.943283 0.943283i −0.0551925 0.998476i \(-0.517577\pi\)
0.998476 + 0.0551925i \(0.0175773\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.59400 0.561288 0.280644 0.959812i \(-0.409452\pi\)
0.280644 + 0.959812i \(0.409452\pi\)
\(42\) 0 0
\(43\) −3.36325 3.36325i −0.512891 0.512891i 0.402520 0.915411i \(-0.368134\pi\)
−0.915411 + 0.402520i \(0.868134\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.04590 0.881885 0.440942 0.897535i \(-0.354644\pi\)
0.440942 + 0.897535i \(0.354644\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.53235 4.53235i −0.622566 0.622566i 0.323621 0.946187i \(-0.395100\pi\)
−0.946187 + 0.323621i \(0.895100\pi\)
\(54\) 0 0
\(55\) −17.1257 −2.30923
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.82118 + 4.82118i −0.627664 + 0.627664i −0.947480 0.319815i \(-0.896379\pi\)
0.319815 + 0.947480i \(0.396379\pi\)
\(60\) 0 0
\(61\) −6.72581 6.72581i −0.861151 0.861151i 0.130321 0.991472i \(-0.458399\pi\)
−0.991472 + 0.130321i \(0.958399\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 20.8508i 2.58622i
\(66\) 0 0
\(67\) 3.87274 3.87274i 0.473130 0.473130i −0.429796 0.902926i \(-0.641414\pi\)
0.902926 + 0.429796i \(0.141414\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.7448i 1.74988i 0.484229 + 0.874941i \(0.339100\pi\)
−0.484229 + 0.874941i \(0.660900\pi\)
\(72\) 0 0
\(73\) 4.61241i 0.539842i 0.962882 + 0.269921i \(0.0869976\pi\)
−0.962882 + 0.269921i \(0.913002\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.03827 + 4.03827i −0.460204 + 0.460204i
\(78\) 0 0
\(79\) 7.43429i 0.836423i −0.908350 0.418211i \(-0.862657\pi\)
0.908350 0.418211i \(-0.137343\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.44737 + 2.44737i 0.268633 + 0.268633i 0.828549 0.559916i \(-0.189167\pi\)
−0.559916 + 0.828549i \(0.689167\pi\)
\(84\) 0 0
\(85\) 10.0986 10.0986i 1.09535 1.09535i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.23689 −0.449109 −0.224555 0.974461i \(-0.572093\pi\)
−0.224555 + 0.974461i \(0.572093\pi\)
\(90\) 0 0
\(91\) 4.91665 + 4.91665i 0.515405 + 0.515405i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.40458 −0.964890
\(96\) 0 0
\(97\) −6.76292 −0.686670 −0.343335 0.939213i \(-0.611557\pi\)
−0.343335 + 0.939213i \(0.611557\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.7637 + 12.7637i 1.27003 + 1.27003i 0.946070 + 0.323963i \(0.105015\pi\)
0.323963 + 0.946070i \(0.394985\pi\)
\(102\) 0 0
\(103\) −5.09658 −0.502181 −0.251091 0.967964i \(-0.580789\pi\)
−0.251091 + 0.967964i \(0.580789\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.45316 + 3.45316i −0.333829 + 0.333829i −0.854039 0.520209i \(-0.825854\pi\)
0.520209 + 0.854039i \(0.325854\pi\)
\(108\) 0 0
\(109\) 12.6452 + 12.6452i 1.21119 + 1.21119i 0.970635 + 0.240558i \(0.0773304\pi\)
0.240558 + 0.970635i \(0.422670\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.90657i 0.555644i −0.960633 0.277822i \(-0.910388\pi\)
0.960633 0.277822i \(-0.0896125\pi\)
\(114\) 0 0
\(115\) −14.6603 + 14.6603i −1.36708 + 1.36708i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.76253i 0.436581i
\(120\) 0 0
\(121\) 21.6153i 1.96503i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.13652 + 2.13652i −0.191096 + 0.191096i
\(126\) 0 0
\(127\) 3.07038i 0.272452i 0.990678 + 0.136226i \(0.0434974\pi\)
−0.990678 + 0.136226i \(0.956503\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.95401 6.95401i −0.607575 0.607575i 0.334737 0.942312i \(-0.391353\pi\)
−0.942312 + 0.334737i \(0.891353\pi\)
\(132\) 0 0
\(133\) −2.21762 + 2.21762i −0.192292 + 0.192292i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.5548 −0.987193 −0.493596 0.869691i \(-0.664318\pi\)
−0.493596 + 0.869691i \(0.664318\pi\)
\(138\) 0 0
\(139\) −6.19355 6.19355i −0.525330 0.525330i 0.393846 0.919176i \(-0.371144\pi\)
−0.919176 + 0.393846i \(0.871144\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −39.7095 −3.32068
\(144\) 0 0
\(145\) 11.0807 0.920201
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.38965 2.38965i −0.195767 0.195767i 0.602415 0.798183i \(-0.294205\pi\)
−0.798183 + 0.602415i \(0.794205\pi\)
\(150\) 0 0
\(151\) −12.2639 −0.998018 −0.499009 0.866597i \(-0.666303\pi\)
−0.499009 + 0.866597i \(0.666303\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.51026 + 1.51026i −0.121307 + 0.121307i
\(156\) 0 0
\(157\) −4.81144 4.81144i −0.383995 0.383995i 0.488544 0.872539i \(-0.337528\pi\)
−0.872539 + 0.488544i \(0.837528\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.91384i 0.544887i
\(162\) 0 0
\(163\) 6.02781 6.02781i 0.472134 0.472134i −0.430470 0.902605i \(-0.641652\pi\)
0.902605 + 0.430470i \(0.141652\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.75117i 0.367656i −0.982958 0.183828i \(-0.941151\pi\)
0.982958 0.183828i \(-0.0588490\pi\)
\(168\) 0 0
\(169\) 35.3469i 2.71899i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −13.6615 + 13.6615i −1.03867 + 1.03867i −0.0394449 + 0.999222i \(0.512559\pi\)
−0.999222 + 0.0394449i \(0.987441\pi\)
\(174\) 0 0
\(175\) 3.99241i 0.301798i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.71026 9.71026i −0.725779 0.725779i 0.243997 0.969776i \(-0.421541\pi\)
−0.969776 + 0.243997i \(0.921541\pi\)
\(180\) 0 0
\(181\) −3.99969 + 3.99969i −0.297295 + 0.297295i −0.839953 0.542659i \(-0.817418\pi\)
0.542659 + 0.839953i \(0.317418\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −24.3330 −1.78900
\(186\) 0 0
\(187\) 19.2324 + 19.2324i 1.40641 + 1.40641i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.9802 1.15629 0.578143 0.815936i \(-0.303778\pi\)
0.578143 + 0.815936i \(0.303778\pi\)
\(192\) 0 0
\(193\) −3.55024 −0.255552 −0.127776 0.991803i \(-0.540784\pi\)
−0.127776 + 0.991803i \(0.540784\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.4049 + 10.4049i 0.741320 + 0.741320i 0.972832 0.231512i \(-0.0743671\pi\)
−0.231512 + 0.972832i \(0.574367\pi\)
\(198\) 0 0
\(199\) −20.0463 −1.42104 −0.710521 0.703676i \(-0.751541\pi\)
−0.710521 + 0.703676i \(0.751541\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.61285 2.61285i 0.183386 0.183386i
\(204\) 0 0
\(205\) −7.62081 7.62081i −0.532260 0.532260i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 17.9107i 1.23891i
\(210\) 0 0
\(211\) 14.2434 14.2434i 0.980558 0.980558i −0.0192564 0.999815i \(-0.506130\pi\)
0.999815 + 0.0192564i \(0.00612987\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 14.2630i 0.972731i
\(216\) 0 0
\(217\) 0.712246i 0.0483504i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 23.4157 23.4157i 1.57511 1.57511i
\(222\) 0 0
\(223\) 17.0811i 1.14384i −0.820311 0.571918i \(-0.806199\pi\)
0.820311 0.571918i \(-0.193801\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.8882 + 15.8882i 1.05453 + 1.05453i 0.998425 + 0.0561098i \(0.0178697\pi\)
0.0561098 + 0.998425i \(0.482130\pi\)
\(228\) 0 0
\(229\) −17.2648 + 17.2648i −1.14089 + 1.14089i −0.152605 + 0.988287i \(0.548766\pi\)
−0.988287 + 0.152605i \(0.951234\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.37677 −0.548780 −0.274390 0.961618i \(-0.588476\pi\)
−0.274390 + 0.961618i \(0.588476\pi\)
\(234\) 0 0
\(235\) −12.8199 12.8199i −0.836276 0.836276i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.24270 0.403807 0.201903 0.979405i \(-0.435287\pi\)
0.201903 + 0.979405i \(0.435287\pi\)
\(240\) 0 0
\(241\) −2.39859 −0.154507 −0.0772535 0.997011i \(-0.524615\pi\)
−0.0772535 + 0.997011i \(0.524615\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.12043 2.12043i −0.135469 0.135469i
\(246\) 0 0
\(247\) −21.8065 −1.38751
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.5027 + 10.5027i −0.662927 + 0.662927i −0.956069 0.293142i \(-0.905299\pi\)
0.293142 + 0.956069i \(0.405299\pi\)
\(252\) 0 0
\(253\) −27.9200 27.9200i −1.75531 1.75531i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.99198i 0.124256i −0.998068 0.0621282i \(-0.980211\pi\)
0.998068 0.0621282i \(-0.0197888\pi\)
\(258\) 0 0
\(259\) −5.73777 + 5.73777i −0.356528 + 0.356528i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.76661i 0.293922i −0.989142 0.146961i \(-0.953051\pi\)
0.989142 0.146961i \(-0.0469492\pi\)
\(264\) 0 0
\(265\) 19.2210i 1.18074i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.1764 + 10.1764i −0.620468 + 0.620468i −0.945651 0.325183i \(-0.894574\pi\)
0.325183 + 0.945651i \(0.394574\pi\)
\(270\) 0 0
\(271\) 29.8185i 1.81135i 0.423977 + 0.905673i \(0.360634\pi\)
−0.423977 + 0.905673i \(0.639366\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.1224 + 16.1224i 0.972220 + 0.972220i
\(276\) 0 0
\(277\) 10.3689 10.3689i 0.623007 0.623007i −0.323292 0.946299i \(-0.604790\pi\)
0.946299 + 0.323292i \(0.104790\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.1234 −0.603909 −0.301954 0.953322i \(-0.597639\pi\)
−0.301954 + 0.953322i \(0.597639\pi\)
\(282\) 0 0
\(283\) −13.7990 13.7990i −0.820266 0.820266i 0.165880 0.986146i \(-0.446954\pi\)
−0.986146 + 0.165880i \(0.946954\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.59400 −0.212147
\(288\) 0 0
\(289\) −5.68174 −0.334220
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.85735 + 4.85735i 0.283770 + 0.283770i 0.834610 0.550841i \(-0.185693\pi\)
−0.550841 + 0.834610i \(0.685693\pi\)
\(294\) 0 0
\(295\) 20.4459 1.19041
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −33.9929 + 33.9929i −1.96586 + 1.96586i
\(300\) 0 0
\(301\) 3.36325 + 3.36325i 0.193854 + 0.193854i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 28.5231i 1.63323i
\(306\) 0 0
\(307\) 21.4100 21.4100i 1.22193 1.22193i 0.254989 0.966944i \(-0.417928\pi\)
0.966944 0.254989i \(-0.0820719\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.23033i 0.183175i −0.995797 0.0915876i \(-0.970806\pi\)
0.995797 0.0915876i \(-0.0291941\pi\)
\(312\) 0 0
\(313\) 6.53030i 0.369114i −0.982822 0.184557i \(-0.940915\pi\)
0.982822 0.184557i \(-0.0590851\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.7296 12.7296i 0.714965 0.714965i −0.252605 0.967570i \(-0.581287\pi\)
0.967570 + 0.252605i \(0.0812872\pi\)
\(318\) 0 0
\(319\) 21.1028i 1.18153i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 10.5615 + 10.5615i 0.587656 + 0.587656i
\(324\) 0 0
\(325\) 19.6293 19.6293i 1.08884 1.08884i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.04590 −0.333321
\(330\) 0 0
\(331\) −7.98204 7.98204i −0.438732 0.438732i 0.452853 0.891585i \(-0.350406\pi\)
−0.891585 + 0.452853i \(0.850406\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −16.4237 −0.897323
\(336\) 0 0
\(337\) −1.43831 −0.0783498 −0.0391749 0.999232i \(-0.512473\pi\)
−0.0391749 + 0.999232i \(0.512473\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.87624 2.87624i −0.155757 0.155757i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.3928 + 13.3928i −0.718966 + 0.718966i −0.968393 0.249428i \(-0.919758\pi\)
0.249428 + 0.968393i \(0.419758\pi\)
\(348\) 0 0
\(349\) −2.01384 2.01384i −0.107798 0.107798i 0.651150 0.758949i \(-0.274287\pi\)
−0.758949 + 0.651150i \(0.774287\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.9746i 0.584119i −0.956400 0.292060i \(-0.905659\pi\)
0.956400 0.292060i \(-0.0943406\pi\)
\(354\) 0 0
\(355\) 31.2652 31.2652i 1.65938 1.65938i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13.8112i 0.728926i −0.931218 0.364463i \(-0.881253\pi\)
0.931218 0.364463i \(-0.118747\pi\)
\(360\) 0 0
\(361\) 9.16435i 0.482334i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.78028 9.78028i 0.511923 0.511923i
\(366\) 0 0
\(367\) 1.72353i 0.0899673i 0.998988 + 0.0449837i \(0.0143236\pi\)
−0.998988 + 0.0449837i \(0.985676\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.53235 + 4.53235i 0.235308 + 0.235308i
\(372\) 0 0
\(373\) 5.17122 5.17122i 0.267756 0.267756i −0.560440 0.828195i \(-0.689368\pi\)
0.828195 + 0.560440i \(0.189368\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 25.6929 1.32325
\(378\) 0 0
\(379\) 4.73174 + 4.73174i 0.243053 + 0.243053i 0.818112 0.575059i \(-0.195021\pi\)
−0.575059 + 0.818112i \(0.695021\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11.9260 0.609388 0.304694 0.952450i \(-0.401446\pi\)
0.304694 + 0.952450i \(0.401446\pi\)
\(384\) 0 0
\(385\) 17.1257 0.872807
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21.5999 + 21.5999i 1.09516 + 1.09516i 0.994968 + 0.100189i \(0.0319448\pi\)
0.100189 + 0.994968i \(0.468055\pi\)
\(390\) 0 0
\(391\) 32.9274 1.66521
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −15.7639 + 15.7639i −0.793165 + 0.793165i
\(396\) 0 0
\(397\) −24.1706 24.1706i −1.21309 1.21309i −0.970005 0.243084i \(-0.921841\pi\)
−0.243084 0.970005i \(-0.578159\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 32.3793i 1.61694i 0.588536 + 0.808471i \(0.299705\pi\)
−0.588536 + 0.808471i \(0.700295\pi\)
\(402\) 0 0
\(403\) −3.50186 + 3.50186i −0.174440 + 0.174440i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 46.3413i 2.29706i
\(408\) 0 0
\(409\) 15.5253i 0.767676i 0.923400 + 0.383838i \(0.125398\pi\)
−0.923400 + 0.383838i \(0.874602\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.82118 4.82118i 0.237235 0.237235i
\(414\) 0 0
\(415\) 10.3789i 0.509481i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.1080 + 24.1080i 1.17775 + 1.17775i 0.980315 + 0.197438i \(0.0632622\pi\)
0.197438 + 0.980315i \(0.436738\pi\)
\(420\) 0 0
\(421\) −21.4110 + 21.4110i −1.04351 + 1.04351i −0.0444969 + 0.999010i \(0.514168\pi\)
−0.999010 + 0.0444969i \(0.985832\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −19.0140 −0.922314
\(426\) 0 0
\(427\) 6.72581 + 6.72581i 0.325485 + 0.325485i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.7984 0.905485 0.452742 0.891641i \(-0.350446\pi\)
0.452742 + 0.891641i \(0.350446\pi\)
\(432\) 0 0
\(433\) 26.4453 1.27088 0.635440 0.772150i \(-0.280819\pi\)
0.635440 + 0.772150i \(0.280819\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.3322 15.3322i −0.733441 0.733441i
\(438\) 0 0
\(439\) −7.11296 −0.339483 −0.169742 0.985489i \(-0.554293\pi\)
−0.169742 + 0.985489i \(0.554293\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.0108636 0.0108636i 0.000516147 0.000516147i −0.706849 0.707365i \(-0.749884\pi\)
0.707365 + 0.706849i \(0.249884\pi\)
\(444\) 0 0
\(445\) 8.98401 + 8.98401i 0.425883 + 0.425883i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 32.7577i 1.54593i −0.634448 0.772966i \(-0.718772\pi\)
0.634448 0.772966i \(-0.281228\pi\)
\(450\) 0 0
\(451\) 14.5135 14.5135i 0.683416 0.683416i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 20.8508i 0.977499i
\(456\) 0 0
\(457\) 10.0528i 0.470252i −0.971965 0.235126i \(-0.924450\pi\)
0.971965 0.235126i \(-0.0755502\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.1351 15.1351i 0.704910 0.704910i −0.260550 0.965460i \(-0.583904\pi\)
0.965460 + 0.260550i \(0.0839039\pi\)
\(462\) 0 0
\(463\) 10.6714i 0.495940i −0.968768 0.247970i \(-0.920236\pi\)
0.968768 0.247970i \(-0.0797635\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.67348 3.67348i −0.169989 0.169989i 0.616986 0.786974i \(-0.288354\pi\)
−0.786974 + 0.616986i \(0.788354\pi\)
\(468\) 0 0
\(469\) −3.87274 + 3.87274i −0.178826 + 0.178826i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −27.1634 −1.24898
\(474\) 0 0
\(475\) 8.85363 + 8.85363i 0.406233 + 0.406233i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.41155 0.201569 0.100784 0.994908i \(-0.467865\pi\)
0.100784 + 0.994908i \(0.467865\pi\)
\(480\) 0 0
\(481\) −56.4212 −2.57258
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14.3403 + 14.3403i 0.651158 + 0.651158i
\(486\) 0 0
\(487\) −9.97116 −0.451837 −0.225918 0.974146i \(-0.572538\pi\)
−0.225918 + 0.974146i \(0.572538\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 30.2732 30.2732i 1.36621 1.36621i 0.500440 0.865771i \(-0.333172\pi\)
0.865771 0.500440i \(-0.166828\pi\)
\(492\) 0 0
\(493\) −12.4438 12.4438i −0.560439 0.560439i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14.7448i 0.661394i
\(498\) 0 0
\(499\) −10.4161 + 10.4161i −0.466289 + 0.466289i −0.900710 0.434421i \(-0.856953\pi\)
0.434421 + 0.900710i \(0.356953\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.37172i 0.373277i −0.982429 0.186638i \(-0.940241\pi\)
0.982429 0.186638i \(-0.0597592\pi\)
\(504\) 0 0
\(505\) 54.1288i 2.40870i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.0580 17.0580i 0.756083 0.756083i −0.219524 0.975607i \(-0.570450\pi\)
0.975607 + 0.219524i \(0.0704503\pi\)
\(510\) 0 0
\(511\) 4.61241i 0.204041i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.8069 + 10.8069i 0.476210 + 0.476210i
\(516\) 0 0
\(517\) 24.4150 24.4150i 1.07377 1.07377i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.2025 0.534601 0.267300 0.963613i \(-0.413868\pi\)
0.267300 + 0.963613i \(0.413868\pi\)
\(522\) 0 0
\(523\) 8.77429 + 8.77429i 0.383673 + 0.383673i 0.872423 0.488751i \(-0.162547\pi\)
−0.488751 + 0.872423i \(0.662547\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.39209 0.147762
\(528\) 0 0
\(529\) −24.8012 −1.07831
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −17.6704 17.6704i −0.765391 0.765391i
\(534\) 0 0
\(535\) 14.6443 0.633129
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.03827 4.03827i 0.173941 0.173941i
\(540\) 0 0
\(541\) −23.2625 23.2625i −1.00013 1.00013i −1.00000 0.000132738i \(-0.999958\pi\)
−0.000132738 1.00000i \(-0.500042\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 53.6265i 2.29711i
\(546\) 0 0
\(547\) −24.7224 + 24.7224i −1.05705 + 1.05705i −0.0587833 + 0.998271i \(0.518722\pi\)
−0.998271 + 0.0587833i \(0.981278\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11.5886i 0.493690i
\(552\) 0 0
\(553\) 7.43429i 0.316138i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.9473 15.9473i 0.675708 0.675708i −0.283318 0.959026i \(-0.591435\pi\)
0.959026 + 0.283318i \(0.0914352\pi\)
\(558\) 0 0
\(559\) 33.0718i 1.39879i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.75478 8.75478i −0.368970 0.368970i 0.498132 0.867101i \(-0.334020\pi\)
−0.867101 + 0.498132i \(0.834020\pi\)
\(564\) 0 0
\(565\) −12.5244 + 12.5244i −0.526908 + 0.526908i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −24.3805 −1.02209 −0.511043 0.859555i \(-0.670741\pi\)
−0.511043 + 0.859555i \(0.670741\pi\)
\(570\) 0 0
\(571\) 9.52629 + 9.52629i 0.398663 + 0.398663i 0.877761 0.479098i \(-0.159036\pi\)
−0.479098 + 0.877761i \(0.659036\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 27.6029 1.15112
\(576\) 0 0
\(577\) 1.46394 0.0609448 0.0304724 0.999536i \(-0.490299\pi\)
0.0304724 + 0.999536i \(0.490299\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.44737 2.44737i −0.101534 0.101534i
\(582\) 0 0
\(583\) −36.6057 −1.51605
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.13883 7.13883i 0.294651 0.294651i −0.544263 0.838914i \(-0.683191\pi\)
0.838914 + 0.544263i \(0.183191\pi\)
\(588\) 0 0
\(589\) −1.57949 1.57949i −0.0650816 0.0650816i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.7385i 0.605237i 0.953112 + 0.302619i \(0.0978609\pi\)
−0.953112 + 0.302619i \(0.902139\pi\)
\(594\) 0 0
\(595\) −10.0986 + 10.0986i −0.414002 + 0.414002i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 17.8924i 0.731062i 0.930799 + 0.365531i \(0.119113\pi\)
−0.930799 + 0.365531i \(0.880887\pi\)
\(600\) 0 0
\(601\) 6.69170i 0.272960i 0.990643 + 0.136480i \(0.0435790\pi\)
−0.990643 + 0.136480i \(0.956421\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −45.8336 + 45.8336i −1.86340 + 1.86340i
\(606\) 0 0
\(607\) 27.0776i 1.09904i −0.835479 0.549522i \(-0.814810\pi\)
0.835479 0.549522i \(-0.185190\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −29.7255 29.7255i −1.20257 1.20257i
\(612\) 0 0
\(613\) 22.9059 22.9059i 0.925159 0.925159i −0.0722294 0.997388i \(-0.523011\pi\)
0.997388 + 0.0722294i \(0.0230114\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.3945 0.418466 0.209233 0.977866i \(-0.432903\pi\)
0.209233 + 0.977866i \(0.432903\pi\)
\(618\) 0 0
\(619\) 8.53232 + 8.53232i 0.342943 + 0.342943i 0.857473 0.514530i \(-0.172033\pi\)
−0.514530 + 0.857473i \(0.672033\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.23689 0.169747
\(624\) 0 0
\(625\) 29.0227 1.16091
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 27.3263 + 27.3263i 1.08957 + 1.08957i
\(630\) 0 0
\(631\) 3.74199 0.148966 0.0744831 0.997222i \(-0.476269\pi\)
0.0744831 + 0.997222i \(0.476269\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.51051 6.51051i 0.258362 0.258362i
\(636\) 0 0
\(637\) −4.91665 4.91665i −0.194805 0.194805i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.1283i 0.597531i 0.954326 + 0.298766i \(0.0965749\pi\)
−0.954326 + 0.298766i \(0.903425\pi\)
\(642\) 0 0
\(643\) 0.845317 0.845317i 0.0333361 0.0333361i −0.690242 0.723578i \(-0.742496\pi\)
0.723578 + 0.690242i \(0.242496\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.9117i 0.940064i 0.882649 + 0.470032i \(0.155758\pi\)
−0.882649 + 0.470032i \(0.844242\pi\)
\(648\) 0 0
\(649\) 38.9385i 1.52847i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19.8544 + 19.8544i −0.776964 + 0.776964i −0.979313 0.202350i \(-0.935142\pi\)
0.202350 + 0.979313i \(0.435142\pi\)
\(654\) 0 0
\(655\) 29.4909i 1.15231i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9.03903 9.03903i −0.352111 0.352111i 0.508784 0.860894i \(-0.330095\pi\)
−0.860894 + 0.508784i \(0.830095\pi\)
\(660\) 0 0
\(661\) −31.4210 + 31.4210i −1.22213 + 1.22213i −0.255261 + 0.966872i \(0.582161\pi\)
−0.966872 + 0.255261i \(0.917839\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9.40458 0.364694
\(666\) 0 0
\(667\) 18.0648 + 18.0648i 0.699472 + 0.699472i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −54.3213 −2.09705
\(672\) 0 0
\(673\) 16.8543 0.649684 0.324842 0.945768i \(-0.394689\pi\)
0.324842 + 0.945768i \(0.394689\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −20.8816 20.8816i −0.802545 0.802545i 0.180948 0.983493i \(-0.442084\pi\)
−0.983493 + 0.180948i \(0.942084\pi\)
\(678\) 0 0
\(679\) 6.76292 0.259537
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.9351 18.9351i 0.724533 0.724533i −0.244992 0.969525i \(-0.578785\pi\)
0.969525 + 0.244992i \(0.0787854\pi\)
\(684\) 0 0
\(685\) 24.5011 + 24.5011i 0.936138 + 0.936138i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 44.5679i 1.69790i
\(690\) 0 0
\(691\) 2.24775 2.24775i 0.0855083 0.0855083i −0.663059 0.748567i \(-0.730742\pi\)
0.748567 + 0.663059i \(0.230742\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 26.2659i 0.996323i
\(696\) 0 0
\(697\) 17.1165i 0.648335i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.17318 8.17318i 0.308697 0.308697i −0.535707 0.844404i \(-0.679955\pi\)
0.844404 + 0.535707i \(0.179955\pi\)
\(702\) 0 0
\(703\) 25.4483i 0.959802i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.7637 12.7637i −0.480027 0.480027i
\(708\) 0 0
\(709\) −11.4595 + 11.4595i −0.430372 + 0.430372i −0.888755 0.458383i \(-0.848429\pi\)
0.458383 + 0.888755i \(0.348429\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.92435 −0.184418
\(714\) 0 0
\(715\) 84.2011 + 84.2011i 3.14894 + 3.14894i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 23.6156 0.880714 0.440357 0.897823i \(-0.354852\pi\)
0.440357 + 0.897823i \(0.354852\pi\)
\(720\) 0 0
\(721\) 5.09658 0.189807
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.4316 10.4316i −0.387418 0.387418i
\(726\) 0 0
\(727\) 11.2623 0.417695 0.208848 0.977948i \(-0.433029\pi\)
0.208848 + 0.977948i \(0.433029\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.0176 16.0176i 0.592432 0.592432i
\(732\) 0 0
\(733\) 8.10898 + 8.10898i 0.299512 + 0.299512i 0.840823 0.541311i \(-0.182072\pi\)
−0.541311 + 0.840823i \(0.682072\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.2783i 1.15215i
\(738\) 0 0
\(739\) 35.7952 35.7952i 1.31675 1.31675i 0.400410 0.916336i \(-0.368868\pi\)
0.916336 0.400410i \(-0.131132\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0620i 0.882748i −0.897323 0.441374i \(-0.854491\pi\)
0.897323 0.441374i \(-0.145509\pi\)
\(744\) 0 0
\(745\) 10.1341i 0.371286i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.45316 3.45316i 0.126176 0.126176i
\(750\) 0 0
\(751\) 39.8810i 1.45528i −0.685961 0.727639i \(-0.740618\pi\)
0.685961 0.727639i \(-0.259382\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 26.0046 + 26.0046i 0.946404 + 0.946404i
\(756\) 0 0
\(757\) −11.5955 + 11.5955i −0.421446 + 0.421446i −0.885701 0.464255i \(-0.846322\pi\)
0.464255 + 0.885701i \(0.346322\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.8050 0.645430 0.322715 0.946496i \(-0.395404\pi\)
0.322715 + 0.946496i \(0.395404\pi\)
\(762\) 0 0
\(763\) −12.6452 12.6452i −0.457788 0.457788i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 47.4081 1.71181
\(768\) 0 0
\(769\) −6.78949 −0.244835 −0.122418 0.992479i \(-0.539065\pi\)
−0.122418 + 0.992479i \(0.539065\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.3304 + 20.3304i 0.731235 + 0.731235i 0.970864 0.239629i \(-0.0770259\pi\)
−0.239629 + 0.970864i \(0.577026\pi\)
\(774\) 0 0
\(775\) 2.84358 0.102144
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.97011 7.97011i 0.285559 0.285559i
\(780\) 0 0
\(781\) 59.5434 + 59.5434i 2.13063 + 2.13063i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 20.4046i 0.728272i
\(786\) 0 0
\(787\) 11.8828 11.8828i 0.423577 0.423577i −0.462856 0.886433i \(-0.653175\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.90657i 0.210014i
\(792\) 0 0
\(793\) 66.1368i 2.34859i
\(794\) 0 0