Properties

Label 1260.2.f.a.629.1
Level $1260$
Weight $2$
Character 1260.629
Analytic conductor $10.061$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.10070523904.11
Defining polynomial: \(x^{8} - 10 x^{4} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 629.1
Root \(0.420861 - 1.68014i\) of defining polynomial
Character \(\chi\) \(=\) 1260.629
Dual form 1260.2.f.a.629.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.95522 - 1.08495i) q^{5} +(2.37608 + 1.16372i) q^{7} +O(q^{10})\) \(q+(-1.95522 - 1.08495i) q^{5} +(2.37608 + 1.16372i) q^{7} +3.74166i q^{11} +0.841723 q^{13} +3.36028i q^{17} -4.55066i q^{19} -7.64575 q^{23} +(2.64575 + 4.24264i) q^{25} +1.41421i q^{29} +0.979531i q^{31} +(-3.38317 - 4.85326i) q^{35} +2.32744i q^{37} +10.3460 q^{41} +10.8127i q^{43} +7.91094i q^{47} +(4.29150 + 5.53019i) q^{49} +4.35425 q^{53} +(4.05952 - 7.31575i) q^{55} -1.38527 q^{59} +(-1.64575 - 0.913230i) q^{65} +13.1402i q^{67} +3.74166i q^{71} +8.66259 q^{73} +(-4.35425 + 8.89047i) q^{77} +14.5830 q^{79} -3.14944i q^{83} +(3.64575 - 6.57008i) q^{85} +3.91044 q^{89} +(2.00000 + 0.979531i) q^{91} +(-4.93725 + 8.89753i) q^{95} -14.8000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 40q^{23} - 16q^{35} - 8q^{49} + 56q^{53} + 8q^{65} - 56q^{77} + 32q^{79} + 8q^{85} + 16q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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
\(5\) −1.95522 1.08495i −0.874400 0.485206i
\(6\) 0 0
\(7\) 2.37608 + 1.16372i 0.898073 + 0.439846i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.74166i 1.12815i 0.825723 + 0.564076i \(0.190768\pi\)
−0.825723 + 0.564076i \(0.809232\pi\)
\(12\) 0 0
\(13\) 0.841723 0.233452 0.116726 0.993164i \(-0.462760\pi\)
0.116726 + 0.993164i \(0.462760\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.36028i 0.814988i 0.913208 + 0.407494i \(0.133597\pi\)
−0.913208 + 0.407494i \(0.866403\pi\)
\(18\) 0 0
\(19\) 4.55066i 1.04399i −0.852948 0.521996i \(-0.825187\pi\)
0.852948 0.521996i \(-0.174813\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.64575 −1.59425 −0.797125 0.603815i \(-0.793647\pi\)
−0.797125 + 0.603815i \(0.793647\pi\)
\(24\) 0 0
\(25\) 2.64575 + 4.24264i 0.529150 + 0.848528i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.41421i 0.262613i 0.991342 + 0.131306i \(0.0419172\pi\)
−0.991342 + 0.131306i \(0.958083\pi\)
\(30\) 0 0
\(31\) 0.979531i 0.175929i 0.996124 + 0.0879645i \(0.0280362\pi\)
−0.996124 + 0.0879645i \(0.971964\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.38317 4.85326i −0.571860 0.820352i
\(36\) 0 0
\(37\) 2.32744i 0.382629i 0.981529 + 0.191315i \(0.0612751\pi\)
−0.981529 + 0.191315i \(0.938725\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.3460 1.61578 0.807890 0.589333i \(-0.200610\pi\)
0.807890 + 0.589333i \(0.200610\pi\)
\(42\) 0 0
\(43\) 10.8127i 1.64893i 0.565916 + 0.824463i \(0.308522\pi\)
−0.565916 + 0.824463i \(0.691478\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.91094i 1.15393i 0.816769 + 0.576965i \(0.195763\pi\)
−0.816769 + 0.576965i \(0.804237\pi\)
\(48\) 0 0
\(49\) 4.29150 + 5.53019i 0.613072 + 0.790027i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.35425 0.598102 0.299051 0.954237i \(-0.403330\pi\)
0.299051 + 0.954237i \(0.403330\pi\)
\(54\) 0 0
\(55\) 4.05952 7.31575i 0.547386 0.986456i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.38527 −0.180346 −0.0901732 0.995926i \(-0.528742\pi\)
−0.0901732 + 0.995926i \(0.528742\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.64575 0.913230i −0.204130 0.113272i
\(66\) 0 0
\(67\) 13.1402i 1.60533i 0.596432 + 0.802664i \(0.296585\pi\)
−0.596432 + 0.802664i \(0.703415\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.74166i 0.444053i 0.975041 + 0.222027i \(0.0712672\pi\)
−0.975041 + 0.222027i \(0.928733\pi\)
\(72\) 0 0
\(73\) 8.66259 1.01388 0.506940 0.861981i \(-0.330777\pi\)
0.506940 + 0.861981i \(0.330777\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.35425 + 8.89047i −0.496213 + 1.01316i
\(78\) 0 0
\(79\) 14.5830 1.64072 0.820358 0.571850i \(-0.193774\pi\)
0.820358 + 0.571850i \(0.193774\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.14944i 0.345696i −0.984949 0.172848i \(-0.944703\pi\)
0.984949 0.172848i \(-0.0552969\pi\)
\(84\) 0 0
\(85\) 3.64575 6.57008i 0.395437 0.712626i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.91044 0.414505 0.207253 0.978287i \(-0.433548\pi\)
0.207253 + 0.978287i \(0.433548\pi\)
\(90\) 0 0
\(91\) 2.00000 + 0.979531i 0.209657 + 0.102683i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.93725 + 8.89753i −0.506552 + 0.912867i
\(96\) 0 0
\(97\) −14.8000 −1.50271 −0.751357 0.659896i \(-0.770600\pi\)
−0.751357 + 0.659896i \(0.770600\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.3460 −1.02947 −0.514735 0.857350i \(-0.672110\pi\)
−0.514735 + 0.857350i \(0.672110\pi\)
\(102\) 0 0
\(103\) 3.36689 0.331750 0.165875 0.986147i \(-0.446955\pi\)
0.165875 + 0.986147i \(0.446955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.06275 −0.102740 −0.0513698 0.998680i \(-0.516359\pi\)
−0.0513698 + 0.998680i \(0.516359\pi\)
\(108\) 0 0
\(109\) −13.8745 −1.32894 −0.664468 0.747316i \(-0.731342\pi\)
−0.664468 + 0.747316i \(0.731342\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.9373 −1.02889 −0.514445 0.857523i \(-0.672002\pi\)
−0.514445 + 0.857523i \(0.672002\pi\)
\(114\) 0 0
\(115\) 14.9491 + 8.29529i 1.39401 + 0.773539i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.91044 + 7.98430i −0.358469 + 0.731919i
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.569951 11.1658i −0.0509780 0.998700i
\(126\) 0 0
\(127\) 4.65489i 0.413054i 0.978441 + 0.206527i \(0.0662162\pi\)
−0.978441 + 0.206527i \(0.933784\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.43560 0.562281 0.281141 0.959667i \(-0.409287\pi\)
0.281141 + 0.959667i \(0.409287\pi\)
\(132\) 0 0
\(133\) 5.29570 10.8127i 0.459196 0.937582i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.2288 1.21564 0.607822 0.794073i \(-0.292043\pi\)
0.607822 + 0.794073i \(0.292043\pi\)
\(138\) 0 0
\(139\) 21.1412i 1.79318i −0.442866 0.896588i \(-0.646038\pi\)
0.442866 0.896588i \(-0.353962\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.14944i 0.263369i
\(144\) 0 0
\(145\) 1.53436 2.76510i 0.127421 0.229629i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.41618i 0.197941i −0.995090 0.0989706i \(-0.968445\pi\)
0.995090 0.0989706i \(-0.0315550\pi\)
\(150\) 0 0
\(151\) 5.29150 0.430616 0.215308 0.976546i \(-0.430924\pi\)
0.215308 + 0.976546i \(0.430924\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.06275 1.91520i 0.0853618 0.153832i
\(156\) 0 0
\(157\) −18.4651 −1.47367 −0.736837 0.676070i \(-0.763682\pi\)
−0.736837 + 0.676070i \(0.763682\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −18.1669 8.89753i −1.43175 0.701223i
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.4821i 0.888509i 0.895901 + 0.444255i \(0.146531\pi\)
−0.895901 + 0.444255i \(0.853469\pi\)
\(168\) 0 0
\(169\) −12.2915 −0.945500
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 20.3725i 1.54890i −0.632638 0.774448i \(-0.718028\pi\)
0.632638 0.774448i \(-0.281972\pi\)
\(174\) 0 0
\(175\) 1.34926 + 13.1598i 0.101994 + 0.994785i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.0534i 1.05040i −0.850979 0.525200i \(-0.823990\pi\)
0.850979 0.525200i \(-0.176010\pi\)
\(180\) 0 0
\(181\) 18.5496i 1.37878i −0.724389 0.689392i \(-0.757878\pi\)
0.724389 0.689392i \(-0.242122\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.52517 4.55066i 0.185654 0.334571i
\(186\) 0 0
\(187\) −12.5730 −0.919431
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.56812i 0.402895i −0.979499 0.201447i \(-0.935435\pi\)
0.979499 0.201447i \(-0.0645645\pi\)
\(192\) 0 0
\(193\) 6.98233i 0.502599i −0.967909 0.251300i \(-0.919142\pi\)
0.967909 0.251300i \(-0.0808579\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 20.8118 1.48278 0.741388 0.671076i \(-0.234168\pi\)
0.741388 + 0.671076i \(0.234168\pi\)
\(198\) 0 0
\(199\) 26.6714i 1.89069i 0.326076 + 0.945343i \(0.394273\pi\)
−0.326076 + 0.945343i \(0.605727\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.64575 + 3.36028i −0.115509 + 0.235846i
\(204\) 0 0
\(205\) −20.2288 11.2250i −1.41284 0.783986i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 17.0270 1.17778
\(210\) 0 0
\(211\) 5.29150 0.364282 0.182141 0.983272i \(-0.441697\pi\)
0.182141 + 0.983272i \(0.441697\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.7313 21.1412i 0.800068 1.44182i
\(216\) 0 0
\(217\) −1.13990 + 2.32744i −0.0773816 + 0.157997i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.82843i 0.190261i
\(222\) 0 0
\(223\) −18.7105 −1.25294 −0.626472 0.779444i \(-0.715502\pi\)
−0.626472 + 0.779444i \(0.715502\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.9304i 1.38920i 0.719397 + 0.694599i \(0.244418\pi\)
−0.719397 + 0.694599i \(0.755582\pi\)
\(228\) 0 0
\(229\) 12.6724i 0.837419i 0.908120 + 0.418709i \(0.137517\pi\)
−0.908120 + 0.418709i \(0.862483\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.3542 1.07140 0.535701 0.844408i \(-0.320047\pi\)
0.535701 + 0.844408i \(0.320047\pi\)
\(234\) 0 0
\(235\) 8.58301 15.4676i 0.559894 1.00900i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.57205i 0.489795i 0.969549 + 0.244898i \(0.0787544\pi\)
−0.969549 + 0.244898i \(0.921246\pi\)
\(240\) 0 0
\(241\) 14.6315i 0.942498i 0.882000 + 0.471249i \(0.156197\pi\)
−0.882000 + 0.471249i \(0.843803\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.39082 15.4688i −0.152744 0.988266i
\(246\) 0 0
\(247\) 3.83039i 0.243722i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 9.20614 0.581086 0.290543 0.956862i \(-0.406164\pi\)
0.290543 + 0.956862i \(0.406164\pi\)
\(252\) 0 0
\(253\) 28.6078i 1.79856i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.5220i 1.46726i 0.679549 + 0.733630i \(0.262176\pi\)
−0.679549 + 0.733630i \(0.737824\pi\)
\(258\) 0 0
\(259\) −2.70850 + 5.53019i −0.168298 + 0.343629i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.35425 −0.268494 −0.134247 0.990948i \(-0.542862\pi\)
−0.134247 + 0.990948i \(0.542862\pi\)
\(264\) 0 0
\(265\) −8.51350 4.72416i −0.522980 0.290203i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −15.3964 −0.938734 −0.469367 0.883003i \(-0.655518\pi\)
−0.469367 + 0.883003i \(0.655518\pi\)
\(270\) 0 0
\(271\) 12.0399i 0.731373i −0.930738 0.365686i \(-0.880834\pi\)
0.930738 0.365686i \(-0.119166\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −15.8745 + 9.89949i −0.957269 + 0.596962i
\(276\) 0 0
\(277\) 25.4558i 1.52949i −0.644331 0.764747i \(-0.722864\pi\)
0.644331 0.764747i \(-0.277136\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.8661i 1.48339i −0.670738 0.741694i \(-0.734023\pi\)
0.670738 0.741694i \(-0.265977\pi\)
\(282\) 0 0
\(283\) 15.3436 0.912080 0.456040 0.889959i \(-0.349267\pi\)
0.456040 + 0.889959i \(0.349267\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 24.5830 + 12.0399i 1.45109 + 0.710694i
\(288\) 0 0
\(289\) 5.70850 0.335794
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 29.8209i 1.74215i −0.491147 0.871077i \(-0.663422\pi\)
0.491147 0.871077i \(-0.336578\pi\)
\(294\) 0 0
\(295\) 2.70850 + 1.50295i 0.157695 + 0.0875051i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.43560 −0.372181
\(300\) 0 0
\(301\) −12.5830 + 25.6919i −0.725272 + 1.48086i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −26.5313 −1.51422 −0.757111 0.653286i \(-0.773390\pi\)
−0.757111 + 0.653286i \(0.773390\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −17.0270 −0.965513 −0.482756 0.875755i \(-0.660364\pi\)
−0.482756 + 0.875755i \(0.660364\pi\)
\(312\) 0 0
\(313\) −5.59388 −0.316185 −0.158092 0.987424i \(-0.550534\pi\)
−0.158092 + 0.987424i \(0.550534\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 32.8118 1.84289 0.921446 0.388506i \(-0.127009\pi\)
0.921446 + 0.388506i \(0.127009\pi\)
\(318\) 0 0
\(319\) −5.29150 −0.296267
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.2915 0.850842
\(324\) 0 0
\(325\) 2.22699 + 3.57113i 0.123531 + 0.198091i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9.20614 + 18.7970i −0.507551 + 1.03631i
\(330\) 0 0
\(331\) −19.8745 −1.09240 −0.546201 0.837654i \(-0.683926\pi\)
−0.546201 + 0.837654i \(0.683926\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 14.2565 25.6919i 0.778914 1.40370i
\(336\) 0 0
\(337\) 1.50295i 0.0818709i −0.999162 0.0409354i \(-0.986966\pi\)
0.999162 0.0409354i \(-0.0130338\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.66507 −0.198475
\(342\) 0 0
\(343\) 3.76135 + 18.1343i 0.203094 + 0.979159i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.0627 −0.701245 −0.350622 0.936517i \(-0.614030\pi\)
−0.350622 + 0.936517i \(0.614030\pi\)
\(348\) 0 0
\(349\) 24.0798i 1.28896i −0.764620 0.644482i \(-0.777073\pi\)
0.764620 0.644482i \(-0.222927\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 20.3725i 1.08432i −0.840275 0.542161i \(-0.817606\pi\)
0.840275 0.542161i \(-0.182394\pi\)
\(354\) 0 0
\(355\) 4.05952 7.31575i 0.215457 0.388280i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 21.7142i 1.14603i −0.819545 0.573015i \(-0.805773\pi\)
0.819545 0.573015i \(-0.194227\pi\)
\(360\) 0 0
\(361\) −1.70850 −0.0899209
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −16.9373 9.39851i −0.886536 0.491941i
\(366\) 0 0
\(367\) 15.3436 0.800927 0.400464 0.916313i \(-0.368849\pi\)
0.400464 + 0.916313i \(0.368849\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.3460 + 5.06713i 0.537140 + 0.263073i
\(372\) 0 0
\(373\) 13.9647i 0.723063i −0.932360 0.361531i \(-0.882254\pi\)
0.932360 0.361531i \(-0.117746\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.19038i 0.0613075i
\(378\) 0 0
\(379\) −13.2915 −0.682739 −0.341369 0.939929i \(-0.610891\pi\)
−0.341369 + 0.939929i \(0.610891\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11.4821i 0.586706i 0.956004 + 0.293353i \(0.0947712\pi\)
−0.956004 + 0.293353i \(0.905229\pi\)
\(384\) 0 0
\(385\) 18.1593 12.6587i 0.925481 0.645145i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 24.8661i 1.26076i −0.776286 0.630381i \(-0.782899\pi\)
0.776286 0.630381i \(-0.217101\pi\)
\(390\) 0 0
\(391\) 25.6919i 1.29929i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −28.5129 15.8219i −1.43464 0.796085i
\(396\) 0 0
\(397\) −26.2860 −1.31925 −0.659627 0.751593i \(-0.729286\pi\)
−0.659627 + 0.751593i \(0.729286\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 32.3494i 1.61545i 0.589557 + 0.807727i \(0.299302\pi\)
−0.589557 + 0.807727i \(0.700698\pi\)
\(402\) 0 0
\(403\) 0.824494i 0.0410710i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.70850 −0.431664
\(408\) 0 0
\(409\) 3.57113i 0.176581i −0.996095 0.0882904i \(-0.971860\pi\)
0.996095 0.0882904i \(-0.0281404\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3.29150 1.61206i −0.161964 0.0793245i
\(414\) 0 0
\(415\) −3.41699 + 6.15784i −0.167734 + 0.302276i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28.5129 1.39295 0.696474 0.717582i \(-0.254751\pi\)
0.696474 + 0.717582i \(0.254751\pi\)
\(420\) 0 0
\(421\) −7.87451 −0.383780 −0.191890 0.981416i \(-0.561462\pi\)
−0.191890 + 0.981416i \(0.561462\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −14.2565 + 8.89047i −0.691541 + 0.431251i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 14.0534i 0.676928i −0.940979 0.338464i \(-0.890093\pi\)
0.940979 0.338464i \(-0.109907\pi\)
\(432\) 0 0
\(433\) 4.50679 0.216583 0.108291 0.994119i \(-0.465462\pi\)
0.108291 + 0.994119i \(0.465462\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 34.7932i 1.66438i
\(438\) 0 0
\(439\) 35.7727i 1.70734i −0.520815 0.853670i \(-0.674372\pi\)
0.520815 0.853670i \(-0.325628\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.35425 −0.206877 −0.103438 0.994636i \(-0.532984\pi\)
−0.103438 + 0.994636i \(0.532984\pi\)
\(444\) 0 0
\(445\) −7.64575 4.24264i −0.362443 0.201120i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.7299i 0.647954i 0.946065 + 0.323977i \(0.105020\pi\)
−0.946065 + 0.323977i \(0.894980\pi\)
\(450\) 0 0
\(451\) 38.7113i 1.82285i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.84769 4.08510i −0.133502 0.191513i
\(456\) 0 0
\(457\) 32.4382i 1.51739i 0.651444 + 0.758697i \(0.274164\pi\)
−0.651444 + 0.758697i \(0.725836\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.5018 0.675418 0.337709 0.941251i \(-0.390348\pi\)
0.337709 + 0.941251i \(0.390348\pi\)
\(462\) 0 0
\(463\) 16.9706i 0.788689i −0.918963 0.394344i \(-0.870972\pi\)
0.918963 0.394344i \(-0.129028\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.2098i 0.657552i −0.944408 0.328776i \(-0.893364\pi\)
0.944408 0.328776i \(-0.106636\pi\)
\(468\) 0 0
\(469\) −15.2915 + 31.2221i −0.706096 + 1.44170i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −40.4575 −1.86024
\(474\) 0 0
\(475\) 19.3068 12.0399i 0.885857 0.552429i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.0270 −0.777984 −0.388992 0.921241i \(-0.627177\pi\)
−0.388992 + 0.921241i \(0.627177\pi\)
\(480\) 0 0
\(481\) 1.95906i 0.0893256i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 28.9373 + 16.0573i 1.31397 + 0.729126i
\(486\) 0 0
\(487\) 15.4676i 0.700904i 0.936581 + 0.350452i \(0.113972\pi\)
−0.936581 + 0.350452i \(0.886028\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 26.1916i 1.18201i 0.806668 + 0.591005i \(0.201269\pi\)
−0.806668 + 0.591005i \(0.798731\pi\)
\(492\) 0 0
\(493\) −4.75216 −0.214026
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.35425 + 8.89047i −0.195315 + 0.398792i
\(498\) 0 0
\(499\) 29.2915 1.31127 0.655634 0.755079i \(-0.272401\pi\)
0.655634 + 0.755079i \(0.272401\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.33981i 0.193503i 0.995309 + 0.0967514i \(0.0308452\pi\)
−0.995309 + 0.0967514i \(0.969155\pi\)
\(504\) 0 0
\(505\) 20.2288 + 11.2250i 0.900168 + 0.499505i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.57551 0.335778 0.167889 0.985806i \(-0.446305\pi\)
0.167889 + 0.985806i \(0.446305\pi\)
\(510\) 0 0
\(511\) 20.5830 + 10.0808i 0.910539 + 0.445951i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.58301 3.65292i −0.290082 0.160967i
\(516\) 0 0
\(517\) −29.6000 −1.30181
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 31.0381 1.35980 0.679902 0.733303i \(-0.262022\pi\)
0.679902 + 0.733303i \(0.262022\pi\)
\(522\) 0 0
\(523\) 3.36689 0.147224 0.0736119 0.997287i \(-0.476547\pi\)
0.0736119 + 0.997287i \(0.476547\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.29150 −0.143380
\(528\) 0 0
\(529\) 35.4575 1.54163
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.70850 0.377207
\(534\) 0 0
\(535\) 2.07790 + 1.15303i 0.0898354 + 0.0498498i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −20.6921 + 16.0573i −0.891271 + 0.691638i
\(540\) 0 0
\(541\) 11.8745 0.510525 0.255262 0.966872i \(-0.417838\pi\)
0.255262 + 0.966872i \(0.417838\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 27.1277 + 15.0532i 1.16202 + 0.644808i
\(546\) 0 0
\(547\) 25.4558i 1.08841i 0.838951 + 0.544207i \(0.183169\pi\)
−0.838951 + 0.544207i \(0.816831\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.43560 0.274166
\(552\) 0 0
\(553\) 34.6504 + 16.9706i 1.47348 + 0.721662i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.5203 0.742357 0.371179 0.928561i \(-0.378954\pi\)
0.371179 + 0.928561i \(0.378954\pi\)
\(558\) 0 0
\(559\) 9.10132i 0.384945i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 44.6632i 1.88233i 0.337947 + 0.941165i \(0.390267\pi\)
−0.337947 + 0.941165i \(0.609733\pi\)
\(564\) 0 0
\(565\) 21.3847 + 11.8664i 0.899662 + 0.499224i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 37.1818i 1.55874i −0.626563 0.779371i \(-0.715539\pi\)
0.626563 0.779371i \(-0.284461\pi\)
\(570\) 0 0
\(571\) 1.41699 0.0592994 0.0296497 0.999560i \(-0.490561\pi\)
0.0296497 + 0.999560i \(0.490561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −20.2288 32.4382i −0.843597 1.35277i
\(576\) 0 0
\(577\) 20.1485 0.838794 0.419397 0.907803i \(-0.362241\pi\)
0.419397 + 0.907803i \(0.362241\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.66507 7.48331i 0.152053 0.310460i
\(582\) 0 0
\(583\) 16.2921i 0.674750i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.6387i 0.439106i −0.975601 0.219553i \(-0.929540\pi\)
0.975601 0.219553i \(-0.0704599\pi\)
\(588\) 0 0
\(589\) 4.45751 0.183669
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.1894i 0.623752i −0.950123 0.311876i \(-0.899043\pi\)
0.950123 0.311876i \(-0.100957\pi\)
\(594\) 0 0
\(595\) 16.3083 11.3684i 0.668577 0.466059i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26.1916i 1.07016i 0.844801 + 0.535080i \(0.179719\pi\)
−0.844801 + 0.535080i \(0.820281\pi\)
\(600\) 0 0
\(601\) 38.3643i 1.56491i −0.622705 0.782457i \(-0.713966\pi\)
0.622705 0.782457i \(-0.286034\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.86565 + 3.25486i 0.238473 + 0.132329i
\(606\) 0 0
\(607\) −13.6601 −0.554447 −0.277223 0.960805i \(-0.589414\pi\)
−0.277223 + 0.960805i \(0.589414\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.65882i 0.269387i
\(612\) 0 0
\(613\) 12.3157i 0.497425i 0.968577 + 0.248713i \(0.0800075\pi\)
−0.968577 + 0.248713i \(0.919992\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.5203 −1.18844 −0.594220 0.804302i \(-0.702539\pi\)
−0.594220 + 0.804302i \(0.702539\pi\)
\(618\) 0 0
\(619\) 23.1003i 0.928479i 0.885710 + 0.464240i \(0.153672\pi\)
−0.885710 + 0.464240i \(0.846328\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9.29150 + 4.55066i 0.372256 + 0.182318i
\(624\) 0 0
\(625\) −11.0000 + 22.4499i −0.440000 + 0.897998i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.82087 −0.311839
\(630\) 0 0
\(631\) 21.1660 0.842606 0.421303 0.906920i \(-0.361573\pi\)
0.421303 + 0.906920i \(0.361573\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.05034 9.10132i 0.200417 0.361175i
\(636\) 0 0
\(637\) 3.61226 + 4.65489i 0.143123 + 0.184433i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 27.6946i 1.09387i 0.837175 + 0.546935i \(0.184205\pi\)
−0.837175 + 0.546935i \(0.815795\pi\)
\(642\) 0 0
\(643\) −5.83925 −0.230277 −0.115139 0.993349i \(-0.536731\pi\)
−0.115139 + 0.993349i \(0.536731\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.29888i 0.247634i 0.992305 + 0.123817i \(0.0395136\pi\)
−0.992305 + 0.123817i \(0.960486\pi\)
\(648\) 0 0
\(649\) 5.18319i 0.203458i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −36.1033 −1.41283 −0.706415 0.707798i \(-0.749689\pi\)
−0.706415 + 0.707798i \(0.749689\pi\)
\(654\) 0 0
\(655\) −12.5830 6.98233i −0.491659 0.272822i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 38.5073i 1.50003i 0.661421 + 0.750015i \(0.269954\pi\)
−0.661421 + 0.750015i \(0.730046\pi\)
\(660\) 0 0
\(661\) 11.0604i 0.430199i −0.976592 0.215099i \(-0.930992\pi\)
0.976592 0.215099i \(-0.0690076\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −22.0856 + 15.3956i −0.856441 + 0.597017i
\(666\) 0 0
\(667\) 10.8127i 0.418670i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 45.5783i 1.75692i 0.477820 + 0.878458i \(0.341427\pi\)
−0.477820 + 0.878458i \(0.658573\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.27841i 0.279732i 0.990170 + 0.139866i \(0.0446672\pi\)
−0.990170 + 0.139866i \(0.955333\pi\)
\(678\) 0 0
\(679\) −35.1660 17.2231i −1.34955 0.660962i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 17.5203 0.670394 0.335197 0.942148i \(-0.391197\pi\)
0.335197 + 0.942148i \(0.391197\pi\)
\(684\) 0 0
\(685\) −27.8203 15.4375i −1.06296 0.589838i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.66507 0.139628
\(690\) 0 0
\(691\) 10.0808i 0.383494i −0.981444 0.191747i \(-0.938585\pi\)
0.981444 0.191747i \(-0.0614152\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −22.9373 + 41.3357i −0.870060 + 1.56795i
\(696\) 0 0
\(697\) 34.7656i 1.31684i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 28.6965i 1.08385i −0.840426 0.541926i \(-0.817695\pi\)
0.840426 0.541926i \(-0.182305\pi\)
\(702\) 0 0
\(703\) 10.5914 0.399462
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −24.5830 12.0399i −0.924539 0.452807i
\(708\) 0 0
\(709\) 6.83399 0.256656 0.128328 0.991732i \(-0.459039\pi\)
0.128328 + 0.991732i \(0.459039\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.48925i 0.280475i
\(714\) 0 0
\(715\) 3.41699 6.15784i 0.127788 0.230290i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 48.3105 1.80168 0.900839 0.434154i \(-0.142953\pi\)
0.900839 + 0.434154i \(0.142953\pi\)
\(720\) 0 0
\(721\) 8.00000 + 3.91813i 0.297936 + 0.145919i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 + 3.74166i −0.222834 + 0.138962i
\(726\) 0 0
\(727\) 34.6504 1.28511 0.642556 0.766239i \(-0.277874\pi\)
0.642556 + 0.766239i \(0.277874\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −36.3338 −1.34385
\(732\) 0 0
\(733\) 32.1252 1.18657 0.593286 0.804992i \(-0.297830\pi\)
0.593286 + 0.804992i \(0.297830\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −49.1660 −1.81105
\(738\) 0 0
\(739\) 33.1660 1.22003 0.610016 0.792389i \(-0.291163\pi\)
0.610016 + 0.792389i \(0.291163\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13.0627 −0.479226 −0.239613 0.970869i \(-0.577021\pi\)
−0.239613 + 0.970869i \(0.577021\pi\)
\(744\) 0 0
\(745\) −2.62144 + 4.72416i −0.0960423 + 0.173080i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.52517 1.23674i −0.0922677 0.0451895i
\(750\) 0 0
\(751\) −18.7085 −0.682683 −0.341341 0.939939i \(-0.610881\pi\)
−0.341341 + 0.939939i \(0.610881\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10.3460 5.74103i −0.376531 0.208938i
\(756\) 0 0
\(757\) 6.15784i 0.223810i −0.993719 0.111905i \(-0.964305\pi\)
0.993719 0.111905i \(-0.0356953\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.45150 −0.342617 −0.171308 0.985217i \(-0.554799\pi\)
−0.171308 + 0.985217i \(0.554799\pi\)
\(762\) 0 0
\(763\) −32.9669 16.1461i −1.19348 0.584527i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.16601 −0.0421022
\(768\) 0 0
\(769\) 38.3643i 1.38345i −0.722159 0.691727i \(-0.756850\pi\)
0.722159 0.691727i \(-0.243150\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 44.4524i 1.59884i −0.600772 0.799420i \(-0.705140\pi\)
0.600772 0.799420i \(-0.294860\pi\)
\(774\) 0 0
\(775\) −4.15580 + 2.59160i −0.149281 + 0.0930929i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 47.0813i 1.68686i
\(780\) 0 0
\(781\) −14.0000 −0.500959
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 36.1033 + 20.0338i 1.28858 + 0.715036i
\(786\) 0 0
\(787\) 29.6000 1.05513 0.527564 0.849516i \(-0.323106\pi\)
0.527564 + 0.849516i \(0.323106\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −25.9878 12.7279i −0.924019 0.452553i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.0327i 0.567908i 0.958838 + 0.283954i \(0.0916464\pi\)
−0.958838 + 0.283954i \(0.908354\pi\)
\(798\) 0 0
\(799\) −26.5830 −0.940439
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 32.4125i 1.14381i
\(804\) 0 0
\(805\) 25.8669 + 37.1069i 0.911687 + 1.30784i
\(806\) 0 0
\(807\) 0 0
\(808\)