Properties

Label 2520.2.t.j.1009.4
Level $2520$
Weight $2$
Character 2520.1009
Analytic conductor $20.122$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.t (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 840)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1009.4
Root \(1.45161 - 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1009
Dual form 2520.2.t.j.1009.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.311108 + 2.21432i) q^{5} +1.00000i q^{7} +O(q^{10})\) \(q+(0.311108 + 2.21432i) q^{5} +1.00000i q^{7} +3.80642 q^{11} -0.622216i q^{13} +4.42864i q^{17} -0.622216 q^{19} +2.62222i q^{23} +(-4.80642 + 1.37778i) q^{25} +9.61285 q^{29} -0.622216 q^{31} +(-2.21432 + 0.311108i) q^{35} -1.24443i q^{37} -4.62222 q^{41} +4.85728i q^{43} -11.6128i q^{47} -1.00000 q^{49} +13.4795i q^{53} +(1.18421 + 8.42864i) q^{55} +11.6128 q^{59} -8.10171 q^{61} +(1.37778 - 0.193576i) q^{65} -2.56199 q^{71} -10.9906i q^{73} +3.80642i q^{77} +6.75557 q^{79} +11.6128i q^{83} +(-9.80642 + 1.37778i) q^{85} -8.23506 q^{89} +0.622216 q^{91} +(-0.193576 - 1.37778i) q^{95} +4.23506i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} + O(q^{10}) \) \( 6 q + 2 q^{5} - 4 q^{11} - 4 q^{19} - 2 q^{25} + 4 q^{29} - 4 q^{31} - 28 q^{41} - 6 q^{49} - 20 q^{55} + 16 q^{59} + 4 q^{61} + 8 q^{65} + 12 q^{71} + 40 q^{79} - 32 q^{85} + 4 q^{89} + 4 q^{91} - 28 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(1\) \(-1\)

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 0
\(4\) 0 0
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.80642 1.14768 0.573840 0.818967i \(-0.305453\pi\)
0.573840 + 0.818967i \(0.305453\pi\)
\(12\) 0 0
\(13\) 0.622216i 0.172572i −0.996270 0.0862858i \(-0.972500\pi\)
0.996270 0.0862858i \(-0.0274998\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.42864i 1.07410i 0.843550 + 0.537051i \(0.180462\pi\)
−0.843550 + 0.537051i \(0.819538\pi\)
\(18\) 0 0
\(19\) −0.622216 −0.142746 −0.0713730 0.997450i \(-0.522738\pi\)
−0.0713730 + 0.997450i \(0.522738\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.62222i 0.546770i 0.961905 + 0.273385i \(0.0881433\pi\)
−0.961905 + 0.273385i \(0.911857\pi\)
\(24\) 0 0
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.61285 1.78506 0.892531 0.450987i \(-0.148928\pi\)
0.892531 + 0.450987i \(0.148928\pi\)
\(30\) 0 0
\(31\) −0.622216 −0.111753 −0.0558766 0.998438i \(-0.517795\pi\)
−0.0558766 + 0.998438i \(0.517795\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.21432 + 0.311108i −0.374288 + 0.0525868i
\(36\) 0 0
\(37\) 1.24443i 0.204583i −0.994754 0.102292i \(-0.967383\pi\)
0.994754 0.102292i \(-0.0326175\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.62222 −0.721869 −0.360934 0.932591i \(-0.617542\pi\)
−0.360934 + 0.932591i \(0.617542\pi\)
\(42\) 0 0
\(43\) 4.85728i 0.740728i 0.928887 + 0.370364i \(0.120767\pi\)
−0.928887 + 0.370364i \(0.879233\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.6128i 1.69391i −0.531666 0.846954i \(-0.678434\pi\)
0.531666 0.846954i \(-0.321566\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 13.4795i 1.85155i 0.378074 + 0.925775i \(0.376587\pi\)
−0.378074 + 0.925775i \(0.623413\pi\)
\(54\) 0 0
\(55\) 1.18421 + 8.42864i 0.159679 + 1.13652i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.6128 1.51186 0.755932 0.654650i \(-0.227184\pi\)
0.755932 + 0.654650i \(0.227184\pi\)
\(60\) 0 0
\(61\) −8.10171 −1.03732 −0.518659 0.854981i \(-0.673569\pi\)
−0.518659 + 0.854981i \(0.673569\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.37778 0.193576i 0.170893 0.0240102i
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.56199 −0.304053 −0.152026 0.988376i \(-0.548580\pi\)
−0.152026 + 0.988376i \(0.548580\pi\)
\(72\) 0 0
\(73\) 10.9906i 1.28636i −0.765717 0.643178i \(-0.777615\pi\)
0.765717 0.643178i \(-0.222385\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.80642i 0.433782i
\(78\) 0 0
\(79\) 6.75557 0.760061 0.380030 0.924974i \(-0.375914\pi\)
0.380030 + 0.924974i \(0.375914\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.6128i 1.27468i 0.770585 + 0.637338i \(0.219964\pi\)
−0.770585 + 0.637338i \(0.780036\pi\)
\(84\) 0 0
\(85\) −9.80642 + 1.37778i −1.06366 + 0.149442i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.23506 −0.872915 −0.436457 0.899725i \(-0.643767\pi\)
−0.436457 + 0.899725i \(0.643767\pi\)
\(90\) 0 0
\(91\) 0.622216 0.0652259
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.193576 1.37778i −0.0198605 0.141358i
\(96\) 0 0
\(97\) 4.23506i 0.430006i 0.976613 + 0.215003i \(0.0689761\pi\)
−0.976613 + 0.215003i \(0.931024\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.7239 −1.86310 −0.931550 0.363613i \(-0.881543\pi\)
−0.931550 + 0.363613i \(0.881543\pi\)
\(102\) 0 0
\(103\) 0.857279i 0.0844702i 0.999108 + 0.0422351i \(0.0134479\pi\)
−0.999108 + 0.0422351i \(0.986552\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0923i 1.07234i 0.844111 + 0.536169i \(0.180129\pi\)
−0.844111 + 0.536169i \(0.819871\pi\)
\(108\) 0 0
\(109\) −5.61285 −0.537613 −0.268807 0.963194i \(-0.586629\pi\)
−0.268807 + 0.963194i \(0.586629\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.2351i 1.52727i 0.645650 + 0.763633i \(0.276586\pi\)
−0.645650 + 0.763633i \(0.723414\pi\)
\(114\) 0 0
\(115\) −5.80642 + 0.815792i −0.541452 + 0.0760730i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.42864 −0.405973
\(120\) 0 0
\(121\) 3.48886 0.317169
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) 0 0
\(127\) 15.3461i 1.36175i 0.732400 + 0.680875i \(0.238400\pi\)
−0.732400 + 0.680875i \(0.761600\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) 0.622216i 0.0539529i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.0923i 1.46030i 0.683288 + 0.730149i \(0.260549\pi\)
−0.683288 + 0.730149i \(0.739451\pi\)
\(138\) 0 0
\(139\) 13.4795 1.14332 0.571658 0.820492i \(-0.306300\pi\)
0.571658 + 0.820492i \(0.306300\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.36842i 0.198057i
\(144\) 0 0
\(145\) 2.99063 + 21.2859i 0.248358 + 1.76770i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.34614 −0.765666 −0.382833 0.923818i \(-0.625051\pi\)
−0.382833 + 0.923818i \(0.625051\pi\)
\(150\) 0 0
\(151\) −7.14272 −0.581266 −0.290633 0.956835i \(-0.593866\pi\)
−0.290633 + 0.956835i \(0.593866\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.193576 1.37778i −0.0155484 0.110666i
\(156\) 0 0
\(157\) 6.99063i 0.557913i −0.960304 0.278957i \(-0.910011\pi\)
0.960304 0.278957i \(-0.0899886\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.62222 −0.206660
\(162\) 0 0
\(163\) 15.6128i 1.22289i −0.791286 0.611446i \(-0.790588\pi\)
0.791286 0.611446i \(-0.209412\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.51114i 0.116935i 0.998289 + 0.0584677i \(0.0186215\pi\)
−0.998289 + 0.0584677i \(0.981379\pi\)
\(168\) 0 0
\(169\) 12.6128 0.970219
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.53035i 0.496493i −0.968697 0.248247i \(-0.920146\pi\)
0.968697 0.248247i \(-0.0798543\pi\)
\(174\) 0 0
\(175\) −1.37778 4.80642i −0.104151 0.363331i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.29529 −0.470532 −0.235266 0.971931i \(-0.575596\pi\)
−0.235266 + 0.971931i \(0.575596\pi\)
\(180\) 0 0
\(181\) −6.85728 −0.509698 −0.254849 0.966981i \(-0.582026\pi\)
−0.254849 + 0.966981i \(0.582026\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.75557 0.387152i 0.202593 0.0284640i
\(186\) 0 0
\(187\) 16.8573i 1.23273i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.5620 0.764239 0.382119 0.924113i \(-0.375194\pi\)
0.382119 + 0.924113i \(0.375194\pi\)
\(192\) 0 0
\(193\) 5.24443i 0.377502i −0.982025 0.188751i \(-0.939556\pi\)
0.982025 0.188751i \(-0.0604440\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.7462i 1.26436i −0.774820 0.632182i \(-0.782159\pi\)
0.774820 0.632182i \(-0.217841\pi\)
\(198\) 0 0
\(199\) 20.2351 1.43443 0.717213 0.696854i \(-0.245418\pi\)
0.717213 + 0.696854i \(0.245418\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.61285i 0.674690i
\(204\) 0 0
\(205\) −1.43801 10.2351i −0.100435 0.714848i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.36842 −0.163827
\(210\) 0 0
\(211\) 21.3274 1.46824 0.734120 0.679020i \(-0.237595\pi\)
0.734120 + 0.679020i \(0.237595\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −10.7556 + 1.51114i −0.733524 + 0.103059i
\(216\) 0 0
\(217\) 0.622216i 0.0422387i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.75557 0.185360
\(222\) 0 0
\(223\) 9.71456i 0.650535i 0.945622 + 0.325267i \(0.105454\pi\)
−0.945622 + 0.325267i \(0.894546\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.3461i 0.753070i 0.926402 + 0.376535i \(0.122885\pi\)
−0.926402 + 0.376535i \(0.877115\pi\)
\(228\) 0 0
\(229\) −1.34614 −0.0889555 −0.0444778 0.999010i \(-0.514162\pi\)
−0.0444778 + 0.999010i \(0.514162\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.3778i 1.00743i 0.863869 + 0.503716i \(0.168034\pi\)
−0.863869 + 0.503716i \(0.831966\pi\)
\(234\) 0 0
\(235\) 25.7146 3.61285i 1.67743 0.235676i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.53972 0.487704 0.243852 0.969812i \(-0.421589\pi\)
0.243852 + 0.969812i \(0.421589\pi\)
\(240\) 0 0
\(241\) 23.9813 1.54477 0.772385 0.635155i \(-0.219064\pi\)
0.772385 + 0.635155i \(0.219064\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.311108 2.21432i −0.0198759 0.141468i
\(246\) 0 0
\(247\) 0.387152i 0.0246339i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −14.1017 −0.890092 −0.445046 0.895508i \(-0.646813\pi\)
−0.445046 + 0.895508i \(0.646813\pi\)
\(252\) 0 0
\(253\) 9.98126i 0.627517i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.0192i 1.06163i −0.847488 0.530815i \(-0.821886\pi\)
0.847488 0.530815i \(-0.178114\pi\)
\(258\) 0 0
\(259\) 1.24443 0.0773252
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.6035i 0.777164i 0.921414 + 0.388582i \(0.127035\pi\)
−0.921414 + 0.388582i \(0.872965\pi\)
\(264\) 0 0
\(265\) −29.8479 + 4.19358i −1.83354 + 0.257609i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.76494 0.229552 0.114776 0.993391i \(-0.463385\pi\)
0.114776 + 0.993391i \(0.463385\pi\)
\(270\) 0 0
\(271\) −17.8666 −1.08532 −0.542661 0.839952i \(-0.682583\pi\)
−0.542661 + 0.839952i \(0.682583\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −18.2953 + 5.24443i −1.10325 + 0.316251i
\(276\) 0 0
\(277\) 1.24443i 0.0747706i −0.999301 0.0373853i \(-0.988097\pi\)
0.999301 0.0373853i \(-0.0119029\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.95899 0.534448 0.267224 0.963634i \(-0.413894\pi\)
0.267224 + 0.963634i \(0.413894\pi\)
\(282\) 0 0
\(283\) 30.5718i 1.81731i −0.417551 0.908654i \(-0.637111\pi\)
0.417551 0.908654i \(-0.362889\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.62222i 0.272841i
\(288\) 0 0
\(289\) −2.61285 −0.153697
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.67307i 0.331424i −0.986174 0.165712i \(-0.947008\pi\)
0.986174 0.165712i \(-0.0529923\pi\)
\(294\) 0 0
\(295\) 3.61285 + 25.7146i 0.210348 + 1.49716i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.63158 0.0943569
\(300\) 0 0
\(301\) −4.85728 −0.279969
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.52051 17.9398i −0.144324 1.02723i
\(306\) 0 0
\(307\) 4.85728i 0.277220i −0.990347 0.138610i \(-0.955737\pi\)
0.990347 0.138610i \(-0.0442634\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 34.5718 1.96039 0.980195 0.198037i \(-0.0634567\pi\)
0.980195 + 0.198037i \(0.0634567\pi\)
\(312\) 0 0
\(313\) 6.33677i 0.358176i 0.983833 + 0.179088i \(0.0573146\pi\)
−0.983833 + 0.179088i \(0.942685\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 15.9684i 0.896872i −0.893815 0.448436i \(-0.851981\pi\)
0.893815 0.448436i \(-0.148019\pi\)
\(318\) 0 0
\(319\) 36.5906 2.04868
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.75557i 0.153324i
\(324\) 0 0
\(325\) 0.857279 + 2.99063i 0.0475533 + 0.165890i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11.6128 0.640237
\(330\) 0 0
\(331\) −27.6128 −1.51774 −0.758870 0.651243i \(-0.774248\pi\)
−0.758870 + 0.651243i \(0.774248\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 16.0000i 0.871576i 0.900049 + 0.435788i \(0.143530\pi\)
−0.900049 + 0.435788i \(0.856470\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.36842 −0.128257
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.8666i 0.637035i 0.947917 + 0.318517i \(0.103185\pi\)
−0.947917 + 0.318517i \(0.896815\pi\)
\(348\) 0 0
\(349\) −21.8163 −1.16780 −0.583899 0.811826i \(-0.698474\pi\)
−0.583899 + 0.811826i \(0.698474\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.79706i 0.148872i −0.997226 0.0744361i \(-0.976284\pi\)
0.997226 0.0744361i \(-0.0237157\pi\)
\(354\) 0 0
\(355\) −0.797056 5.67307i −0.0423033 0.301095i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.0509 −0.688798 −0.344399 0.938823i \(-0.611917\pi\)
−0.344399 + 0.938823i \(0.611917\pi\)
\(360\) 0 0
\(361\) −18.6128 −0.979624
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 24.3368 3.41927i 1.27384 0.178973i
\(366\) 0 0
\(367\) 10.4889i 0.547514i −0.961799 0.273757i \(-0.911734\pi\)
0.961799 0.273757i \(-0.0882664\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −13.4795 −0.699820
\(372\) 0 0
\(373\) 30.1847i 1.56290i −0.623966 0.781452i \(-0.714479\pi\)
0.623966 0.781452i \(-0.285521\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.98126i 0.308051i
\(378\) 0 0
\(379\) 12.8573 0.660434 0.330217 0.943905i \(-0.392878\pi\)
0.330217 + 0.943905i \(0.392878\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 24.4701i 1.25037i −0.780479 0.625183i \(-0.785025\pi\)
0.780479 0.625183i \(-0.214975\pi\)
\(384\) 0 0
\(385\) −8.42864 + 1.18421i −0.429563 + 0.0603528i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.61285 −0.0817746 −0.0408873 0.999164i \(-0.513018\pi\)
−0.0408873 + 0.999164i \(0.513018\pi\)
\(390\) 0 0
\(391\) −11.6128 −0.587287
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.10171 + 14.9590i 0.105749 + 0.752668i
\(396\) 0 0
\(397\) 22.2163i 1.11501i 0.830175 + 0.557503i \(0.188240\pi\)
−0.830175 + 0.557503i \(0.811760\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.9813 −0.997817 −0.498908 0.866655i \(-0.666266\pi\)
−0.498908 + 0.866655i \(0.666266\pi\)
\(402\) 0 0
\(403\) 0.387152i 0.0192854i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.73683i 0.234796i
\(408\) 0 0
\(409\) 5.73329 0.283493 0.141747 0.989903i \(-0.454728\pi\)
0.141747 + 0.989903i \(0.454728\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.6128i 0.571431i
\(414\) 0 0
\(415\) −25.7146 + 3.61285i −1.26228 + 0.177348i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 26.3684 1.28818 0.644091 0.764949i \(-0.277236\pi\)
0.644091 + 0.764949i \(0.277236\pi\)
\(420\) 0 0
\(421\) −19.3274 −0.941960 −0.470980 0.882144i \(-0.656100\pi\)
−0.470980 + 0.882144i \(0.656100\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.10171 21.2859i −0.295976 1.03252i
\(426\) 0 0
\(427\) 8.10171i 0.392069i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 26.9491 1.29809 0.649047 0.760748i \(-0.275168\pi\)
0.649047 + 0.760748i \(0.275168\pi\)
\(432\) 0 0
\(433\) 2.13335i 0.102522i 0.998685 + 0.0512612i \(0.0163241\pi\)
−0.998685 + 0.0512612i \(0.983676\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.63158i 0.0780492i
\(438\) 0 0
\(439\) 10.5205 0.502116 0.251058 0.967972i \(-0.419221\pi\)
0.251058 + 0.967972i \(0.419221\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.88892i 0.327303i −0.986518 0.163651i \(-0.947673\pi\)
0.986518 0.163651i \(-0.0523272\pi\)
\(444\) 0 0
\(445\) −2.56199 18.2351i −0.121450 0.864425i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 39.9180 1.88385 0.941923 0.335829i \(-0.109016\pi\)
0.941923 + 0.335829i \(0.109016\pi\)
\(450\) 0 0
\(451\) −17.5941 −0.828474
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.193576 + 1.37778i 0.00907499 + 0.0645915i
\(456\) 0 0
\(457\) 8.47013i 0.396216i −0.980180 0.198108i \(-0.936520\pi\)
0.980180 0.198108i \(-0.0634796\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −40.1146 −1.86832 −0.934162 0.356849i \(-0.883851\pi\)
−0.934162 + 0.356849i \(0.883851\pi\)
\(462\) 0 0
\(463\) 33.5941i 1.56125i −0.624999 0.780625i \(-0.714901\pi\)
0.624999 0.780625i \(-0.285099\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.3461i 0.525037i −0.964927 0.262518i \(-0.915447\pi\)
0.964927 0.262518i \(-0.0845530\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 18.4889i 0.850119i
\(474\) 0 0
\(475\) 2.99063 0.857279i 0.137220 0.0393347i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 36.2864 1.65797 0.828984 0.559273i \(-0.188919\pi\)
0.828984 + 0.559273i \(0.188919\pi\)
\(480\) 0 0
\(481\) −0.774305 −0.0353053
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9.37778 + 1.31756i −0.425823 + 0.0598274i
\(486\) 0 0
\(487\) 38.8385i 1.75994i −0.475027 0.879971i \(-0.657562\pi\)
0.475027 0.879971i \(-0.342438\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 28.7467 1.29732 0.648660 0.761079i \(-0.275330\pi\)
0.648660 + 0.761079i \(0.275330\pi\)
\(492\) 0 0
\(493\) 42.5718i 1.91734i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.56199i 0.114921i
\(498\) 0 0
\(499\) 5.63158 0.252104 0.126052 0.992024i \(-0.459769\pi\)
0.126052 + 0.992024i \(0.459769\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 34.9590i 1.55874i −0.626561 0.779372i \(-0.715538\pi\)
0.626561 0.779372i \(-0.284462\pi\)
\(504\) 0 0
\(505\) −5.82516 41.4608i −0.259216 1.84498i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.9906 −0.487151 −0.243576 0.969882i \(-0.578320\pi\)
−0.243576 + 0.969882i \(0.578320\pi\)
\(510\) 0 0
\(511\) 10.9906 0.486197
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.89829 + 0.266706i −0.0836486 + 0.0117525i
\(516\) 0 0
\(517\) 44.2034i 1.94406i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.90766 −0.302630 −0.151315 0.988486i \(-0.548351\pi\)
−0.151315 + 0.988486i \(0.548351\pi\)
\(522\) 0 0
\(523\) 37.7146i 1.64914i −0.565758 0.824571i \(-0.691416\pi\)
0.565758 0.824571i \(-0.308584\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.75557i 0.120034i
\(528\) 0 0
\(529\) 16.1240 0.701043
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.87601i 0.124574i
\(534\) 0 0
\(535\) −24.5620 + 3.45091i −1.06191 + 0.149196i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.80642 −0.163954
\(540\) 0 0
\(541\) −3.12399 −0.134311 −0.0671553 0.997743i \(-0.521392\pi\)
−0.0671553 + 0.997743i \(0.521392\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.74620 12.4286i −0.0747990 0.532384i
\(546\) 0 0
\(547\) 5.51114i 0.235639i −0.993035 0.117820i \(-0.962410\pi\)
0.993035 0.117820i \(-0.0375905\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.98126 −0.254810
\(552\) 0 0
\(553\) 6.75557i 0.287276i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 36.7052i 1.55525i −0.628729 0.777624i \(-0.716425\pi\)
0.628729 0.777624i \(-0.283575\pi\)
\(558\) 0 0
\(559\) 3.02227 0.127829
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.4924i 1.15867i −0.815091 0.579333i \(-0.803313\pi\)
0.815091 0.579333i \(-0.196687\pi\)
\(564\) 0 0
\(565\) −35.9496 + 5.05086i −1.51241 + 0.212491i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.2444 0.974457 0.487229 0.873274i \(-0.338008\pi\)
0.487229 + 0.873274i \(0.338008\pi\)
\(570\) 0 0
\(571\) −25.5111 −1.06761 −0.533804 0.845608i \(-0.679238\pi\)
−0.533804 + 0.845608i \(0.679238\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.61285 12.6035i −0.150666 0.525601i
\(576\) 0 0
\(577\) 26.0701i 1.08531i 0.839955 + 0.542656i \(0.182581\pi\)
−0.839955 + 0.542656i \(0.817419\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.6128 −0.481782
\(582\) 0 0
\(583\) 51.3087i 2.12499i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.2667i 0.506301i 0.967427 + 0.253151i \(0.0814668\pi\)
−0.967427 + 0.253151i \(0.918533\pi\)
\(588\) 0 0
\(589\) 0.387152 0.0159523
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.9175i 0.612588i −0.951937 0.306294i \(-0.900911\pi\)
0.951937 0.306294i \(-0.0990891\pi\)
\(594\) 0 0
\(595\) −1.37778 9.80642i −0.0564837 0.402024i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −26.5620 −1.08529 −0.542647 0.839961i \(-0.682578\pi\)
−0.542647 + 0.839961i \(0.682578\pi\)
\(600\) 0 0
\(601\) 39.7146 1.61999 0.809995 0.586436i \(-0.199470\pi\)
0.809995 + 0.586436i \(0.199470\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.08541 + 7.72546i 0.0441283 + 0.314084i
\(606\) 0 0
\(607\) 6.28544i 0.255118i 0.991831 + 0.127559i \(0.0407143\pi\)
−0.991831 + 0.127559i \(0.959286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.22570 −0.292320
\(612\) 0 0
\(613\) 45.7146i 1.84639i 0.384328 + 0.923197i \(0.374433\pi\)
−0.384328 + 0.923197i \(0.625567\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.88892i 0.196821i −0.995146 0.0984103i \(-0.968624\pi\)
0.995146 0.0984103i \(-0.0313758\pi\)
\(618\) 0 0
\(619\) −12.2351 −0.491769 −0.245884 0.969299i \(-0.579078\pi\)
−0.245884 + 0.969299i \(0.579078\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.23506i 0.329931i
\(624\) 0 0
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.51114 0.219743
\(630\) 0 0
\(631\) 1.24443 0.0495400 0.0247700 0.999693i \(-0.492115\pi\)
0.0247700 + 0.999693i \(0.492115\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −33.9813 + 4.77430i −1.34851 + 0.189462i
\(636\) 0 0
\(637\) 0.622216i 0.0246531i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 48.1847 1.90318 0.951590 0.307369i \(-0.0994487\pi\)
0.951590 + 0.307369i \(0.0994487\pi\)
\(642\) 0 0
\(643\) 4.85728i 0.191552i −0.995403 0.0957762i \(-0.969467\pi\)
0.995403 0.0957762i \(-0.0305333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.203420i 0.00799728i −0.999992 0.00399864i \(-0.998727\pi\)
0.999992 0.00399864i \(-0.00127281\pi\)
\(648\) 0 0
\(649\) 44.2034 1.73514
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.3145i 1.06890i −0.845200 0.534449i \(-0.820519\pi\)
0.845200 0.534449i \(-0.179481\pi\)
\(654\) 0 0
\(655\) 1.24443 + 8.85728i 0.0486240 + 0.346083i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 33.3176 1.29787 0.648934 0.760845i \(-0.275215\pi\)
0.648934 + 0.760845i \(0.275215\pi\)
\(660\) 0 0
\(661\) 14.5906 0.567508 0.283754 0.958897i \(-0.408420\pi\)
0.283754 + 0.958897i \(0.408420\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.37778 0.193576i 0.0534282 0.00750656i
\(666\) 0 0
\(667\) 25.2070i 0.976017i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −30.8385 −1.19051
\(672\) 0 0
\(673\) 4.53341i 0.174750i −0.996175 0.0873751i \(-0.972152\pi\)
0.996175 0.0873751i \(-0.0278479\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 27.2672i 1.04796i 0.851730 + 0.523981i \(0.175554\pi\)
−0.851730 + 0.523981i \(0.824446\pi\)
\(678\) 0 0
\(679\) −4.23506 −0.162527
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 29.5812i 1.13189i −0.824442 0.565947i \(-0.808511\pi\)
0.824442 0.565947i \(-0.191489\pi\)
\(684\) 0 0
\(685\) −37.8479 + 5.31756i −1.44609 + 0.203174i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.38715 0.319525
\(690\) 0 0
\(691\) 2.99063 0.113769 0.0568845 0.998381i \(-0.481883\pi\)
0.0568845 + 0.998381i \(0.481883\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.19358 + 29.8479i 0.159071 + 1.13220i
\(696\) 0 0
\(697\) 20.4701i 0.775361i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 41.0420 1.55013 0.775067 0.631879i \(-0.217716\pi\)
0.775067 + 0.631879i \(0.217716\pi\)
\(702\) 0 0
\(703\) 0.774305i 0.0292035i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.7239i 0.704186i
\(708\) 0 0
\(709\) 41.4291 1.55590 0.777952 0.628324i \(-0.216259\pi\)
0.777952 + 0.628324i \(0.216259\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.63158i 0.0611033i
\(714\) 0 0
\(715\) 5.24443 0.736833i 0.196131 0.0275560i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18.9590 −0.707051 −0.353525 0.935425i \(-0.615017\pi\)
−0.353525 + 0.935425i \(0.615017\pi\)
\(720\) 0 0
\(721\) −0.857279 −0.0319267
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −46.2034 + 13.2444i −1.71595 + 0.491886i
\(726\) 0 0
\(727\) 41.7975i 1.55018i 0.631848 + 0.775092i \(0.282297\pi\)
−0.631848 + 0.775092i \(0.717703\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −21.5111 −0.795618
\(732\) 0 0
\(733\) 15.3145i 0.565654i −0.959171 0.282827i \(-0.908728\pi\)
0.959171 0.282827i \(-0.0912722\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 32.7368 1.20424 0.602122 0.798404i \(-0.294322\pi\)
0.602122 + 0.798404i \(0.294322\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 37.3778i 1.37126i −0.727951 0.685629i \(-0.759527\pi\)
0.727951 0.685629i \(-0.240473\pi\)
\(744\) 0 0
\(745\) −2.90766 20.6953i −0.106528 0.758219i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −11.0923 −0.405305
\(750\) 0 0
\(751\) 20.3497 0.742570 0.371285 0.928519i \(-0.378917\pi\)
0.371285 + 0.928519i \(0.378917\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.22216 15.8163i −0.0808725 0.575613i
\(756\) 0 0
\(757\) 6.95899i 0.252929i −0.991971 0.126464i \(-0.959637\pi\)
0.991971 0.126464i \(-0.0403629\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −48.6419 −1.76327 −0.881634 0.471934i \(-0.843556\pi\)
−0.881634 + 0.471934i \(0.843556\pi\)
\(762\) 0 0
\(763\) 5.61285i 0.203199i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.22570i 0.260905i
\(768\) 0 0
\(769\) 24.6923 0.890426 0.445213 0.895425i \(-0.353128\pi\)
0.445213 + 0.895425i \(0.353128\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.0415i 1.29632i 0.761503 + 0.648161i \(0.224462\pi\)
−0.761503 + 0.648161i \(0.775538\pi\)
\(774\) 0 0
\(775\) 2.99063 0.857279i 0.107427 0.0307944i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.87601 0.103044
\(780\) 0 0
\(781\) −9.75203 −0.348955
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15.4795 2.17484i 0.552487 0.0776234i
\(786\) 0 0
\(787\) 32.2034i 1.14793i −0.818881 0.573964i \(-0.805405\pi\)
0.818881 0.573964i \(-0.194595\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −16.2351 −0.577252
\(792\) 0 0
\(793\) 5.04101i 0.179012i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.5526i 0.621746i 0.950451 + 0.310873i \(0.100621\pi\)
−0.950451 + 0.310873i \(0.899379\pi\)
\(798\) 0 0
\(799\) 51.4291 1.81943
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 41.8350i 1.47633i
\(804\) 0 0
\(805\) −0.815792 5.80642i −0.0287529 0.204650i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0