Properties

Label 4600.2.a.bc.1.5
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.791953.1
Defining polynomial: \(x^{5} - 2 x^{4} - 7 x^{3} + 7 x^{2} + 9 x + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(3.21042\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.21042 q^{3} -2.22487 q^{7} +1.88594 q^{9} +O(q^{10})\) \(q+2.21042 q^{3} -2.22487 q^{7} +1.88594 q^{9} -1.57300 q^{11} +3.96189 q^{13} +0.294907 q^{17} -7.76572 q^{19} -4.91788 q^{21} -1.00000 q^{23} -2.46253 q^{27} -9.29233 q^{29} +9.18913 q^{31} -3.47698 q^{33} -10.5425 q^{37} +8.75744 q^{39} -2.34251 q^{41} +6.67460 q^{43} -1.38007 q^{47} -2.04998 q^{49} +0.651868 q^{51} -11.0395 q^{53} -17.1655 q^{57} -5.09378 q^{59} -8.91788 q^{61} -4.19597 q^{63} -1.12002 q^{67} -2.21042 q^{69} +7.60168 q^{71} +12.8549 q^{73} +3.49971 q^{77} +11.0211 q^{79} -11.1010 q^{81} -13.5257 q^{83} -20.5399 q^{87} +14.3475 q^{89} -8.81468 q^{91} +20.3118 q^{93} -0.199218 q^{97} -2.96658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 3 q^{3} + q^{7} + 4 q^{9} + O(q^{10}) \) \( 5 q - 3 q^{3} + q^{7} + 4 q^{9} - 4 q^{11} + q^{13} - 5 q^{17} + 4 q^{19} - 6 q^{21} - 5 q^{23} - 6 q^{27} - 11 q^{29} + 4 q^{31} - 13 q^{33} - 6 q^{37} + 31 q^{39} - 8 q^{41} - 3 q^{43} - 2 q^{47} - 2 q^{49} - 5 q^{51} - 18 q^{53} - 27 q^{57} + 23 q^{59} - 26 q^{61} - 5 q^{63} - 3 q^{67} + 3 q^{69} - 2 q^{71} - 4 q^{73} - 15 q^{77} + 43 q^{79} - 3 q^{81} - 30 q^{83} - 27 q^{87} + 15 q^{89} - 19 q^{91} + 15 q^{93} - 8 q^{97} + 37 q^{99} + O(q^{100}) \)

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
\(3\) 2.21042 1.27618 0.638092 0.769960i \(-0.279724\pi\)
0.638092 + 0.769960i \(0.279724\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.22487 −0.840920 −0.420460 0.907311i \(-0.638131\pi\)
−0.420460 + 0.907311i \(0.638131\pi\)
\(8\) 0 0
\(9\) 1.88594 0.628648
\(10\) 0 0
\(11\) −1.57300 −0.474276 −0.237138 0.971476i \(-0.576209\pi\)
−0.237138 + 0.971476i \(0.576209\pi\)
\(12\) 0 0
\(13\) 3.96189 1.09883 0.549416 0.835549i \(-0.314850\pi\)
0.549416 + 0.835549i \(0.314850\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.294907 0.0715256 0.0357628 0.999360i \(-0.488614\pi\)
0.0357628 + 0.999360i \(0.488614\pi\)
\(18\) 0 0
\(19\) −7.76572 −1.78158 −0.890789 0.454418i \(-0.849847\pi\)
−0.890789 + 0.454418i \(0.849847\pi\)
\(20\) 0 0
\(21\) −4.91788 −1.07317
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.46253 −0.473914
\(28\) 0 0
\(29\) −9.29233 −1.72554 −0.862771 0.505595i \(-0.831273\pi\)
−0.862771 + 0.505595i \(0.831273\pi\)
\(30\) 0 0
\(31\) 9.18913 1.65042 0.825208 0.564829i \(-0.191058\pi\)
0.825208 + 0.564829i \(0.191058\pi\)
\(32\) 0 0
\(33\) −3.47698 −0.605264
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.5425 −1.73318 −0.866588 0.499024i \(-0.833692\pi\)
−0.866588 + 0.499024i \(0.833692\pi\)
\(38\) 0 0
\(39\) 8.75744 1.40231
\(40\) 0 0
\(41\) −2.34251 −0.365839 −0.182920 0.983128i \(-0.558555\pi\)
−0.182920 + 0.983128i \(0.558555\pi\)
\(42\) 0 0
\(43\) 6.67460 1.01787 0.508933 0.860806i \(-0.330040\pi\)
0.508933 + 0.860806i \(0.330040\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.38007 −0.201304 −0.100652 0.994922i \(-0.532093\pi\)
−0.100652 + 0.994922i \(0.532093\pi\)
\(48\) 0 0
\(49\) −2.04998 −0.292854
\(50\) 0 0
\(51\) 0.651868 0.0912798
\(52\) 0 0
\(53\) −11.0395 −1.51640 −0.758199 0.652023i \(-0.773920\pi\)
−0.758199 + 0.652023i \(0.773920\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −17.1655 −2.27362
\(58\) 0 0
\(59\) −5.09378 −0.663154 −0.331577 0.943428i \(-0.607581\pi\)
−0.331577 + 0.943428i \(0.607581\pi\)
\(60\) 0 0
\(61\) −8.91788 −1.14182 −0.570909 0.821014i \(-0.693409\pi\)
−0.570909 + 0.821014i \(0.693409\pi\)
\(62\) 0 0
\(63\) −4.19597 −0.528642
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.12002 −0.136832 −0.0684160 0.997657i \(-0.521795\pi\)
−0.0684160 + 0.997657i \(0.521795\pi\)
\(68\) 0 0
\(69\) −2.21042 −0.266103
\(70\) 0 0
\(71\) 7.60168 0.902154 0.451077 0.892485i \(-0.351040\pi\)
0.451077 + 0.892485i \(0.351040\pi\)
\(72\) 0 0
\(73\) 12.8549 1.50455 0.752276 0.658848i \(-0.228956\pi\)
0.752276 + 0.658848i \(0.228956\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.49971 0.398828
\(78\) 0 0
\(79\) 11.0211 1.23997 0.619984 0.784614i \(-0.287139\pi\)
0.619984 + 0.784614i \(0.287139\pi\)
\(80\) 0 0
\(81\) −11.1010 −1.23345
\(82\) 0 0
\(83\) −13.5257 −1.48464 −0.742318 0.670048i \(-0.766274\pi\)
−0.742318 + 0.670048i \(0.766274\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −20.5399 −2.20211
\(88\) 0 0
\(89\) 14.3475 1.52084 0.760418 0.649434i \(-0.224994\pi\)
0.760418 + 0.649434i \(0.224994\pi\)
\(90\) 0 0
\(91\) −8.81468 −0.924030
\(92\) 0 0
\(93\) 20.3118 2.10624
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.199218 −0.0202275 −0.0101137 0.999949i \(-0.503219\pi\)
−0.0101137 + 0.999949i \(0.503219\pi\)
\(98\) 0 0
\(99\) −2.96658 −0.298153
\(100\) 0 0
\(101\) −6.07595 −0.604580 −0.302290 0.953216i \(-0.597751\pi\)
−0.302290 + 0.953216i \(0.597751\pi\)
\(102\) 0 0
\(103\) −11.9423 −1.17671 −0.588353 0.808604i \(-0.700223\pi\)
−0.588353 + 0.808604i \(0.700223\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.99058 0.772479 0.386239 0.922399i \(-0.373774\pi\)
0.386239 + 0.922399i \(0.373774\pi\)
\(108\) 0 0
\(109\) −4.36170 −0.417775 −0.208888 0.977940i \(-0.566984\pi\)
−0.208888 + 0.977940i \(0.566984\pi\)
\(110\) 0 0
\(111\) −23.3033 −2.21185
\(112\) 0 0
\(113\) 12.9156 1.21500 0.607501 0.794319i \(-0.292172\pi\)
0.607501 + 0.794319i \(0.292172\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 7.47191 0.690778
\(118\) 0 0
\(119\) −0.656129 −0.0601473
\(120\) 0 0
\(121\) −8.52568 −0.775062
\(122\) 0 0
\(123\) −5.17793 −0.466878
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 16.3759 1.45313 0.726565 0.687098i \(-0.241116\pi\)
0.726565 + 0.687098i \(0.241116\pi\)
\(128\) 0 0
\(129\) 14.7536 1.29899
\(130\) 0 0
\(131\) 9.62242 0.840715 0.420357 0.907359i \(-0.361905\pi\)
0.420357 + 0.907359i \(0.361905\pi\)
\(132\) 0 0
\(133\) 17.2777 1.49816
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.78721 −0.579871 −0.289935 0.957046i \(-0.593634\pi\)
−0.289935 + 0.957046i \(0.593634\pi\)
\(138\) 0 0
\(139\) 6.55788 0.556232 0.278116 0.960547i \(-0.410290\pi\)
0.278116 + 0.960547i \(0.410290\pi\)
\(140\) 0 0
\(141\) −3.05053 −0.256901
\(142\) 0 0
\(143\) −6.23205 −0.521150
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.53130 −0.373735
\(148\) 0 0
\(149\) −13.8647 −1.13584 −0.567918 0.823085i \(-0.692251\pi\)
−0.567918 + 0.823085i \(0.692251\pi\)
\(150\) 0 0
\(151\) 2.42205 0.197104 0.0985520 0.995132i \(-0.468579\pi\)
0.0985520 + 0.995132i \(0.468579\pi\)
\(152\) 0 0
\(153\) 0.556179 0.0449644
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −20.2638 −1.61723 −0.808613 0.588341i \(-0.799781\pi\)
−0.808613 + 0.588341i \(0.799781\pi\)
\(158\) 0 0
\(159\) −24.4020 −1.93520
\(160\) 0 0
\(161\) 2.22487 0.175344
\(162\) 0 0
\(163\) −6.91982 −0.542002 −0.271001 0.962579i \(-0.587355\pi\)
−0.271001 + 0.962579i \(0.587355\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.8296 −1.45708 −0.728539 0.685005i \(-0.759800\pi\)
−0.728539 + 0.685005i \(0.759800\pi\)
\(168\) 0 0
\(169\) 2.69661 0.207431
\(170\) 0 0
\(171\) −14.6457 −1.11998
\(172\) 0 0
\(173\) −23.2017 −1.76399 −0.881997 0.471255i \(-0.843801\pi\)
−0.881997 + 0.471255i \(0.843801\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −11.2594 −0.846307
\(178\) 0 0
\(179\) −10.7011 −0.799837 −0.399918 0.916551i \(-0.630962\pi\)
−0.399918 + 0.916551i \(0.630962\pi\)
\(180\) 0 0
\(181\) −7.27484 −0.540735 −0.270367 0.962757i \(-0.587145\pi\)
−0.270367 + 0.962757i \(0.587145\pi\)
\(182\) 0 0
\(183\) −19.7122 −1.45717
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.463888 −0.0339229
\(188\) 0 0
\(189\) 5.47880 0.398524
\(190\) 0 0
\(191\) −3.74624 −0.271068 −0.135534 0.990773i \(-0.543275\pi\)
−0.135534 + 0.990773i \(0.543275\pi\)
\(192\) 0 0
\(193\) −11.8470 −0.852763 −0.426381 0.904543i \(-0.640212\pi\)
−0.426381 + 0.904543i \(0.640212\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.0064 0.712924 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(198\) 0 0
\(199\) 6.19597 0.439221 0.219610 0.975588i \(-0.429521\pi\)
0.219610 + 0.975588i \(0.429521\pi\)
\(200\) 0 0
\(201\) −2.47571 −0.174623
\(202\) 0 0
\(203\) 20.6742 1.45104
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.88594 −0.131082
\(208\) 0 0
\(209\) 12.2154 0.844960
\(210\) 0 0
\(211\) −0.825746 −0.0568467 −0.0284234 0.999596i \(-0.509049\pi\)
−0.0284234 + 0.999596i \(0.509049\pi\)
\(212\) 0 0
\(213\) 16.8029 1.15132
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −20.4446 −1.38787
\(218\) 0 0
\(219\) 28.4147 1.92009
\(220\) 0 0
\(221\) 1.16839 0.0785946
\(222\) 0 0
\(223\) −18.2911 −1.22486 −0.612430 0.790525i \(-0.709808\pi\)
−0.612430 + 0.790525i \(0.709808\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.5556 −1.43069 −0.715347 0.698769i \(-0.753732\pi\)
−0.715347 + 0.698769i \(0.753732\pi\)
\(228\) 0 0
\(229\) 9.65960 0.638324 0.319162 0.947700i \(-0.396599\pi\)
0.319162 + 0.947700i \(0.396599\pi\)
\(230\) 0 0
\(231\) 7.73581 0.508979
\(232\) 0 0
\(233\) −0.879774 −0.0576359 −0.0288179 0.999585i \(-0.509174\pi\)
−0.0288179 + 0.999585i \(0.509174\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 24.3612 1.58243
\(238\) 0 0
\(239\) 22.3240 1.44402 0.722010 0.691883i \(-0.243218\pi\)
0.722010 + 0.691883i \(0.243218\pi\)
\(240\) 0 0
\(241\) −7.43761 −0.479098 −0.239549 0.970884i \(-0.577000\pi\)
−0.239549 + 0.970884i \(0.577000\pi\)
\(242\) 0 0
\(243\) −17.1504 −1.10020
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −30.7669 −1.95765
\(248\) 0 0
\(249\) −29.8974 −1.89467
\(250\) 0 0
\(251\) 21.4221 1.35215 0.676074 0.736833i \(-0.263680\pi\)
0.676074 + 0.736833i \(0.263680\pi\)
\(252\) 0 0
\(253\) 1.57300 0.0988935
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.9788 0.684838 0.342419 0.939547i \(-0.388754\pi\)
0.342419 + 0.939547i \(0.388754\pi\)
\(258\) 0 0
\(259\) 23.4556 1.45746
\(260\) 0 0
\(261\) −17.5248 −1.08476
\(262\) 0 0
\(263\) −11.3268 −0.698440 −0.349220 0.937041i \(-0.613553\pi\)
−0.349220 + 0.937041i \(0.613553\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 31.7141 1.94087
\(268\) 0 0
\(269\) 31.1010 1.89626 0.948130 0.317883i \(-0.102972\pi\)
0.948130 + 0.317883i \(0.102972\pi\)
\(270\) 0 0
\(271\) 29.1151 1.76862 0.884308 0.466905i \(-0.154631\pi\)
0.884308 + 0.466905i \(0.154631\pi\)
\(272\) 0 0
\(273\) −19.4841 −1.17923
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −22.6829 −1.36288 −0.681441 0.731873i \(-0.738646\pi\)
−0.681441 + 0.731873i \(0.738646\pi\)
\(278\) 0 0
\(279\) 17.3302 1.03753
\(280\) 0 0
\(281\) 11.2531 0.671305 0.335653 0.941986i \(-0.391043\pi\)
0.335653 + 0.941986i \(0.391043\pi\)
\(282\) 0 0
\(283\) 0.419014 0.0249078 0.0124539 0.999922i \(-0.496036\pi\)
0.0124539 + 0.999922i \(0.496036\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.21177 0.307641
\(288\) 0 0
\(289\) −16.9130 −0.994884
\(290\) 0 0
\(291\) −0.440354 −0.0258140
\(292\) 0 0
\(293\) 1.06844 0.0624190 0.0312095 0.999513i \(-0.490064\pi\)
0.0312095 + 0.999513i \(0.490064\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.87355 0.224766
\(298\) 0 0
\(299\) −3.96189 −0.229122
\(300\) 0 0
\(301\) −14.8501 −0.855944
\(302\) 0 0
\(303\) −13.4304 −0.771555
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 22.3991 1.27838 0.639191 0.769048i \(-0.279269\pi\)
0.639191 + 0.769048i \(0.279269\pi\)
\(308\) 0 0
\(309\) −26.3974 −1.50169
\(310\) 0 0
\(311\) −19.9717 −1.13249 −0.566245 0.824237i \(-0.691604\pi\)
−0.566245 + 0.824237i \(0.691604\pi\)
\(312\) 0 0
\(313\) 14.1975 0.802488 0.401244 0.915971i \(-0.368578\pi\)
0.401244 + 0.915971i \(0.368578\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.48205 −0.420234 −0.210117 0.977676i \(-0.567384\pi\)
−0.210117 + 0.977676i \(0.567384\pi\)
\(318\) 0 0
\(319\) 14.6168 0.818384
\(320\) 0 0
\(321\) 17.6625 0.985826
\(322\) 0 0
\(323\) −2.29017 −0.127428
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −9.64118 −0.533158
\(328\) 0 0
\(329\) 3.07047 0.169280
\(330\) 0 0
\(331\) 6.56494 0.360842 0.180421 0.983590i \(-0.442254\pi\)
0.180421 + 0.983590i \(0.442254\pi\)
\(332\) 0 0
\(333\) −19.8826 −1.08956
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 17.2484 0.939583 0.469791 0.882777i \(-0.344329\pi\)
0.469791 + 0.882777i \(0.344329\pi\)
\(338\) 0 0
\(339\) 28.5490 1.55057
\(340\) 0 0
\(341\) −14.4545 −0.782753
\(342\) 0 0
\(343\) 20.1350 1.08719
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.18016 0.224403 0.112201 0.993685i \(-0.464210\pi\)
0.112201 + 0.993685i \(0.464210\pi\)
\(348\) 0 0
\(349\) 11.6150 0.621736 0.310868 0.950453i \(-0.399380\pi\)
0.310868 + 0.950453i \(0.399380\pi\)
\(350\) 0 0
\(351\) −9.75628 −0.520752
\(352\) 0 0
\(353\) 15.8241 0.842233 0.421117 0.907006i \(-0.361638\pi\)
0.421117 + 0.907006i \(0.361638\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.45032 −0.0767590
\(358\) 0 0
\(359\) −6.25850 −0.330311 −0.165156 0.986268i \(-0.552813\pi\)
−0.165156 + 0.986268i \(0.552813\pi\)
\(360\) 0 0
\(361\) 41.3064 2.17402
\(362\) 0 0
\(363\) −18.8453 −0.989122
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −5.01500 −0.261781 −0.130890 0.991397i \(-0.541784\pi\)
−0.130890 + 0.991397i \(0.541784\pi\)
\(368\) 0 0
\(369\) −4.41785 −0.229984
\(370\) 0 0
\(371\) 24.5615 1.27517
\(372\) 0 0
\(373\) −20.1804 −1.04490 −0.522450 0.852670i \(-0.674982\pi\)
−0.522450 + 0.852670i \(0.674982\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −36.8152 −1.89608
\(378\) 0 0
\(379\) 10.9860 0.564314 0.282157 0.959368i \(-0.408950\pi\)
0.282157 + 0.959368i \(0.408950\pi\)
\(380\) 0 0
\(381\) 36.1977 1.85446
\(382\) 0 0
\(383\) −23.9968 −1.22618 −0.613088 0.790014i \(-0.710073\pi\)
−0.613088 + 0.790014i \(0.710073\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 12.5879 0.639879
\(388\) 0 0
\(389\) 19.3913 0.983180 0.491590 0.870827i \(-0.336416\pi\)
0.491590 + 0.870827i \(0.336416\pi\)
\(390\) 0 0
\(391\) −0.294907 −0.0149141
\(392\) 0 0
\(393\) 21.2696 1.07291
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.0550 −0.504644 −0.252322 0.967643i \(-0.581194\pi\)
−0.252322 + 0.967643i \(0.581194\pi\)
\(398\) 0 0
\(399\) 38.1909 1.91193
\(400\) 0 0
\(401\) −16.6178 −0.829854 −0.414927 0.909855i \(-0.636193\pi\)
−0.414927 + 0.909855i \(0.636193\pi\)
\(402\) 0 0
\(403\) 36.4064 1.81353
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.5833 0.822005
\(408\) 0 0
\(409\) 7.92642 0.391936 0.195968 0.980610i \(-0.437215\pi\)
0.195968 + 0.980610i \(0.437215\pi\)
\(410\) 0 0
\(411\) −15.0026 −0.740022
\(412\) 0 0
\(413\) 11.3330 0.557659
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 14.4956 0.709855
\(418\) 0 0
\(419\) 40.4944 1.97828 0.989141 0.146967i \(-0.0469511\pi\)
0.989141 + 0.146967i \(0.0469511\pi\)
\(420\) 0 0
\(421\) 7.67870 0.374237 0.187118 0.982337i \(-0.440085\pi\)
0.187118 + 0.982337i \(0.440085\pi\)
\(422\) 0 0
\(423\) −2.60273 −0.126549
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 19.8411 0.960177
\(428\) 0 0
\(429\) −13.7754 −0.665084
\(430\) 0 0
\(431\) −36.1674 −1.74212 −0.871061 0.491175i \(-0.836567\pi\)
−0.871061 + 0.491175i \(0.836567\pi\)
\(432\) 0 0
\(433\) −9.42856 −0.453108 −0.226554 0.973999i \(-0.572746\pi\)
−0.226554 + 0.973999i \(0.572746\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.76572 0.371485
\(438\) 0 0
\(439\) 24.4443 1.16666 0.583332 0.812234i \(-0.301749\pi\)
0.583332 + 0.812234i \(0.301749\pi\)
\(440\) 0 0
\(441\) −3.86614 −0.184102
\(442\) 0 0
\(443\) −35.5786 −1.69039 −0.845195 0.534458i \(-0.820516\pi\)
−0.845195 + 0.534458i \(0.820516\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −30.6467 −1.44954
\(448\) 0 0
\(449\) −0.660651 −0.0311780 −0.0155890 0.999878i \(-0.504962\pi\)
−0.0155890 + 0.999878i \(0.504962\pi\)
\(450\) 0 0
\(451\) 3.68476 0.173509
\(452\) 0 0
\(453\) 5.35375 0.251541
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.62187 −0.403314 −0.201657 0.979456i \(-0.564633\pi\)
−0.201657 + 0.979456i \(0.564633\pi\)
\(458\) 0 0
\(459\) −0.726219 −0.0338970
\(460\) 0 0
\(461\) −5.54580 −0.258294 −0.129147 0.991625i \(-0.541224\pi\)
−0.129147 + 0.991625i \(0.541224\pi\)
\(462\) 0 0
\(463\) 6.15748 0.286162 0.143081 0.989711i \(-0.454299\pi\)
0.143081 + 0.989711i \(0.454299\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.93879 0.135991 0.0679954 0.997686i \(-0.478340\pi\)
0.0679954 + 0.997686i \(0.478340\pi\)
\(468\) 0 0
\(469\) 2.49189 0.115065
\(470\) 0 0
\(471\) −44.7914 −2.06388
\(472\) 0 0
\(473\) −10.4991 −0.482750
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −20.8200 −0.953280
\(478\) 0 0
\(479\) 13.4939 0.616550 0.308275 0.951297i \(-0.400248\pi\)
0.308275 + 0.951297i \(0.400248\pi\)
\(480\) 0 0
\(481\) −41.7683 −1.90447
\(482\) 0 0
\(483\) 4.91788 0.223771
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −3.28554 −0.148882 −0.0744410 0.997225i \(-0.523717\pi\)
−0.0744410 + 0.997225i \(0.523717\pi\)
\(488\) 0 0
\(489\) −15.2957 −0.691695
\(490\) 0 0
\(491\) 24.2119 1.09267 0.546335 0.837567i \(-0.316023\pi\)
0.546335 + 0.837567i \(0.316023\pi\)
\(492\) 0 0
\(493\) −2.74038 −0.123420
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.9127 −0.758639
\(498\) 0 0
\(499\) −37.5956 −1.68301 −0.841506 0.540248i \(-0.818331\pi\)
−0.841506 + 0.540248i \(0.818331\pi\)
\(500\) 0 0
\(501\) −41.6212 −1.85950
\(502\) 0 0
\(503\) 11.0448 0.492464 0.246232 0.969211i \(-0.420807\pi\)
0.246232 + 0.969211i \(0.420807\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 5.96062 0.264720
\(508\) 0 0
\(509\) −31.4409 −1.39359 −0.696796 0.717269i \(-0.745392\pi\)
−0.696796 + 0.717269i \(0.745392\pi\)
\(510\) 0 0
\(511\) −28.6004 −1.26521
\(512\) 0 0
\(513\) 19.1233 0.844315
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2.17084 0.0954735
\(518\) 0 0
\(519\) −51.2855 −2.25118
\(520\) 0 0
\(521\) 35.3591 1.54911 0.774555 0.632506i \(-0.217974\pi\)
0.774555 + 0.632506i \(0.217974\pi\)
\(522\) 0 0
\(523\) 41.8119 1.82830 0.914152 0.405371i \(-0.132858\pi\)
0.914152 + 0.405371i \(0.132858\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.70994 0.118047
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −9.60658 −0.416890
\(532\) 0 0
\(533\) −9.28079 −0.401996
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −23.6539 −1.02074
\(538\) 0 0
\(539\) 3.22460 0.138894
\(540\) 0 0
\(541\) 1.43188 0.0615612 0.0307806 0.999526i \(-0.490201\pi\)
0.0307806 + 0.999526i \(0.490201\pi\)
\(542\) 0 0
\(543\) −16.0804 −0.690077
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 44.8700 1.91850 0.959251 0.282555i \(-0.0911821\pi\)
0.959251 + 0.282555i \(0.0911821\pi\)
\(548\) 0 0
\(549\) −16.8186 −0.717801
\(550\) 0 0
\(551\) 72.1616 3.07419
\(552\) 0 0
\(553\) −24.5204 −1.04271
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22.3106 −0.945329 −0.472665 0.881242i \(-0.656708\pi\)
−0.472665 + 0.881242i \(0.656708\pi\)
\(558\) 0 0
\(559\) 26.4440 1.11846
\(560\) 0 0
\(561\) −1.02539 −0.0432919
\(562\) 0 0
\(563\) −1.41928 −0.0598153 −0.0299077 0.999553i \(-0.509521\pi\)
−0.0299077 + 0.999553i \(0.509521\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 24.6983 1.03723
\(568\) 0 0
\(569\) −21.4950 −0.901116 −0.450558 0.892747i \(-0.648775\pi\)
−0.450558 + 0.892747i \(0.648775\pi\)
\(570\) 0 0
\(571\) 41.0272 1.71694 0.858468 0.512868i \(-0.171417\pi\)
0.858468 + 0.512868i \(0.171417\pi\)
\(572\) 0 0
\(573\) −8.28075 −0.345933
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 37.1477 1.54648 0.773239 0.634114i \(-0.218635\pi\)
0.773239 + 0.634114i \(0.218635\pi\)
\(578\) 0 0
\(579\) −26.1867 −1.08828
\(580\) 0 0
\(581\) 30.0928 1.24846
\(582\) 0 0
\(583\) 17.3652 0.719192
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.1838 0.502881 0.251440 0.967873i \(-0.419096\pi\)
0.251440 + 0.967873i \(0.419096\pi\)
\(588\) 0 0
\(589\) −71.3602 −2.94034
\(590\) 0 0
\(591\) 22.1183 0.909823
\(592\) 0 0
\(593\) 40.1421 1.64844 0.824220 0.566270i \(-0.191614\pi\)
0.824220 + 0.566270i \(0.191614\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 13.6957 0.560527
\(598\) 0 0
\(599\) −16.4377 −0.671624 −0.335812 0.941929i \(-0.609011\pi\)
−0.335812 + 0.941929i \(0.609011\pi\)
\(600\) 0 0
\(601\) −4.98809 −0.203469 −0.101734 0.994812i \(-0.532439\pi\)
−0.101734 + 0.994812i \(0.532439\pi\)
\(602\) 0 0
\(603\) −2.11229 −0.0860191
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.09352 −0.0443846 −0.0221923 0.999754i \(-0.507065\pi\)
−0.0221923 + 0.999754i \(0.507065\pi\)
\(608\) 0 0
\(609\) 45.6986 1.85180
\(610\) 0 0
\(611\) −5.46768 −0.221199
\(612\) 0 0
\(613\) −16.4617 −0.664880 −0.332440 0.943124i \(-0.607872\pi\)
−0.332440 + 0.943124i \(0.607872\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −23.9090 −0.962540 −0.481270 0.876572i \(-0.659824\pi\)
−0.481270 + 0.876572i \(0.659824\pi\)
\(618\) 0 0
\(619\) −26.7498 −1.07517 −0.537583 0.843211i \(-0.680663\pi\)
−0.537583 + 0.843211i \(0.680663\pi\)
\(620\) 0 0
\(621\) 2.46253 0.0988179
\(622\) 0 0
\(623\) −31.9213 −1.27890
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 27.0012 1.07833
\(628\) 0 0
\(629\) −3.10906 −0.123966
\(630\) 0 0
\(631\) 0.317634 0.0126448 0.00632241 0.999980i \(-0.497988\pi\)
0.00632241 + 0.999980i \(0.497988\pi\)
\(632\) 0 0
\(633\) −1.82524 −0.0725469
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −8.12179 −0.321797
\(638\) 0 0
\(639\) 14.3363 0.567137
\(640\) 0 0
\(641\) 19.9895 0.789539 0.394769 0.918780i \(-0.370825\pi\)
0.394769 + 0.918780i \(0.370825\pi\)
\(642\) 0 0
\(643\) 20.0837 0.792023 0.396011 0.918246i \(-0.370394\pi\)
0.396011 + 0.918246i \(0.370394\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.0801 −0.868060 −0.434030 0.900898i \(-0.642909\pi\)
−0.434030 + 0.900898i \(0.642909\pi\)
\(648\) 0 0
\(649\) 8.01250 0.314518
\(650\) 0 0
\(651\) −45.1910 −1.77118
\(652\) 0 0
\(653\) −33.2385 −1.30072 −0.650362 0.759625i \(-0.725383\pi\)
−0.650362 + 0.759625i \(0.725383\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 24.2436 0.945833
\(658\) 0 0
\(659\) 17.3023 0.674002 0.337001 0.941504i \(-0.390587\pi\)
0.337001 + 0.941504i \(0.390587\pi\)
\(660\) 0 0
\(661\) −28.9521 −1.12611 −0.563053 0.826421i \(-0.690373\pi\)
−0.563053 + 0.826421i \(0.690373\pi\)
\(662\) 0 0
\(663\) 2.58263 0.100301
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 9.29233 0.359800
\(668\) 0 0
\(669\) −40.4309 −1.56315
\(670\) 0 0
\(671\) 14.0278 0.541537
\(672\) 0 0
\(673\) 10.7860 0.415771 0.207885 0.978153i \(-0.433342\pi\)
0.207885 + 0.978153i \(0.433342\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.1146 −0.619336 −0.309668 0.950845i \(-0.600218\pi\)
−0.309668 + 0.950845i \(0.600218\pi\)
\(678\) 0 0
\(679\) 0.443232 0.0170097
\(680\) 0 0
\(681\) −47.6468 −1.82583
\(682\) 0 0
\(683\) 12.1106 0.463399 0.231699 0.972787i \(-0.425571\pi\)
0.231699 + 0.972787i \(0.425571\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 21.3517 0.814620
\(688\) 0 0
\(689\) −43.7375 −1.66627
\(690\) 0 0
\(691\) −30.1463 −1.14682 −0.573410 0.819269i \(-0.694380\pi\)
−0.573410 + 0.819269i \(0.694380\pi\)
\(692\) 0 0
\(693\) 6.60025 0.250723
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.690824 −0.0261668
\(698\) 0 0
\(699\) −1.94467 −0.0735540
\(700\) 0 0
\(701\) 14.8464 0.560741 0.280371 0.959892i \(-0.409543\pi\)
0.280371 + 0.959892i \(0.409543\pi\)
\(702\) 0 0
\(703\) 81.8701 3.08779
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.5182 0.508403
\(708\) 0 0
\(709\) 37.0163 1.39018 0.695088 0.718924i \(-0.255365\pi\)
0.695088 + 0.718924i \(0.255365\pi\)
\(710\) 0 0
\(711\) 20.7851 0.779503
\(712\) 0 0
\(713\) −9.18913 −0.344136
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 49.3454 1.84284
\(718\) 0 0
\(719\) 7.63459 0.284722 0.142361 0.989815i \(-0.454531\pi\)
0.142361 + 0.989815i \(0.454531\pi\)
\(720\) 0 0
\(721\) 26.5699 0.989515
\(722\) 0 0
\(723\) −16.4402 −0.611418
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −29.1278 −1.08029 −0.540146 0.841571i \(-0.681631\pi\)
−0.540146 + 0.841571i \(0.681631\pi\)
\(728\) 0 0
\(729\) −4.60629 −0.170603
\(730\) 0 0
\(731\) 1.96839 0.0728034
\(732\) 0 0
\(733\) −7.30466 −0.269804 −0.134902 0.990859i \(-0.543072\pi\)
−0.134902 + 0.990859i \(0.543072\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.76178 0.0648962
\(738\) 0 0
\(739\) −10.5109 −0.386649 −0.193324 0.981135i \(-0.561927\pi\)
−0.193324 + 0.981135i \(0.561927\pi\)
\(740\) 0 0
\(741\) −68.0078 −2.49833
\(742\) 0 0
\(743\) 11.4448 0.419869 0.209934 0.977715i \(-0.432675\pi\)
0.209934 + 0.977715i \(0.432675\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −25.5087 −0.933313
\(748\) 0 0
\(749\) −17.7780 −0.649593
\(750\) 0 0
\(751\) −7.62069 −0.278083 −0.139041 0.990287i \(-0.544402\pi\)
−0.139041 + 0.990287i \(0.544402\pi\)
\(752\) 0 0
\(753\) 47.3517 1.72559
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 41.3725 1.50371 0.751855 0.659329i \(-0.229159\pi\)
0.751855 + 0.659329i \(0.229159\pi\)
\(758\) 0 0
\(759\) 3.47698 0.126206
\(760\) 0 0
\(761\) 12.5358 0.454421 0.227211 0.973846i \(-0.427039\pi\)
0.227211 + 0.973846i \(0.427039\pi\)
\(762\) 0 0
\(763\) 9.70420 0.351315
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −20.1810 −0.728694
\(768\) 0 0
\(769\) −25.0182 −0.902180 −0.451090 0.892479i \(-0.648965\pi\)
−0.451090 + 0.892479i \(0.648965\pi\)
\(770\) 0 0
\(771\) 24.2677 0.873980
\(772\) 0 0
\(773\) −37.1948 −1.33781 −0.668903 0.743350i \(-0.733236\pi\)
−0.668903 + 0.743350i \(0.733236\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 51.8467 1.85999
\(778\) 0 0
\(779\) 18.1913 0.651771
\(780\) 0 0
\(781\) −11.9574 −0.427870
\(782\) 0 0
\(783\) 22.8826 0.817759
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −7.64645 −0.272567 −0.136283 0.990670i \(-0.543516\pi\)
−0.136283 + 0.990670i \(0.543516\pi\)
\(788\) 0 0
\(789\) −25.0369 −0.891338
\(790\) 0 0
\(791\) −28.7356 −1.02172
\(792\) 0 0
\(793\) −35.3317 −1.25467
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.38544 −0.0844966 −0.0422483 0.999107i \(-0.513452\pi\)
−0.0422483 + 0.999107i \(0.513452\pi\)
\(798\) 0 0
\(799\) −0.406992 −0.0143984
\(800\) 0 0
\(801\) 27.0586 0.956070
\(802\) 0 0
\(803\) −20.2207 −0.713573
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 68.7461 2.41998
\(808\) 0 0
\(809\) 15.4937 0.544730 0.272365 0.962194i \(-0.412194\pi\)
0.272365 + 0.962194i \(0.412194\pi\)
\(810\) 0 0
\(811\) 55.3850 1.94483 0.972415 0.233259i \(-0.0749389\pi\)
0.972415 + 0.233259i \(0.0749389\pi\)
\(812\) 0 0
\(813\) 64.3565 2.25708
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −51.8330 −1.81341
\(818\) 0 0
\(819\) −16.6240 −0.580889
\(820\) 0 0
\(821\) −38.7241 −1.35148 −0.675740 0.737140i \(-0.736176\pi\)
−0.675740 + 0.737140i \(0.736176\pi\)
\(822\) 0 0
\(823\) −0.237837 −0.00829047 −0.00414524 0.999991i \(-0.501319\pi\)
−0.00414524 + 0.999991i \(0.501319\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −17.5821 −0.611391 −0.305695 0.952129i \(-0.598889\pi\)
−0.305695 + 0.952129i \(0.598889\pi\)
\(828\) 0 0
\(829\) 20.5607 0.714103 0.357051 0.934085i \(-0.383782\pi\)
0.357051 + 0.934085i \(0.383782\pi\)
\(830\) 0 0
\(831\) −50.1386 −1.73929
\(832\) 0 0
\(833\) −0.604553 −0.0209465
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −22.6285 −0.782156
\(838\) 0 0
\(839\) −15.1584 −0.523325 −0.261663 0.965159i \(-0.584271\pi\)
−0.261663 + 0.965159i \(0.584271\pi\)
\(840\) 0 0
\(841\) 57.3474 1.97750
\(842\) 0 0
\(843\) 24.8741 0.856709
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 18.9685 0.651765
\(848\) 0 0
\(849\) 0.926197 0.0317870
\(850\) 0 0
\(851\) 10.5425 0.361392
\(852\) 0 0
\(853\) 18.7788 0.642973 0.321486 0.946914i \(-0.395818\pi\)
0.321486 + 0.946914i \(0.395818\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −29.4670 −1.00657 −0.503286 0.864120i \(-0.667876\pi\)
−0.503286 + 0.864120i \(0.667876\pi\)
\(858\) 0 0
\(859\) −50.7562 −1.73178 −0.865889 0.500236i \(-0.833247\pi\)
−0.865889 + 0.500236i \(0.833247\pi\)
\(860\) 0 0
\(861\) 11.5202 0.392607
\(862\) 0 0
\(863\) 19.5166 0.664351 0.332176 0.943218i \(-0.392217\pi\)
0.332176 + 0.943218i \(0.392217\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −37.3848 −1.26966
\(868\) 0 0
\(869\) −17.3361 −0.588088
\(870\) 0 0
\(871\) −4.43739 −0.150355
\(872\) 0 0
\(873\) −0.375713 −0.0127160
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6.68909 −0.225874 −0.112937 0.993602i \(-0.536026\pi\)
−0.112937 + 0.993602i \(0.536026\pi\)
\(878\) 0 0
\(879\) 2.36170 0.0796582
\(880\) 0 0
\(881\) 47.1211 1.58755 0.793775 0.608212i \(-0.208113\pi\)
0.793775 + 0.608212i \(0.208113\pi\)
\(882\) 0 0
\(883\) −40.5934 −1.36608 −0.683038 0.730383i \(-0.739342\pi\)
−0.683038 + 0.730383i \(0.739342\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −9.89101 −0.332108 −0.166054 0.986117i \(-0.553103\pi\)
−0.166054 + 0.986117i \(0.553103\pi\)
\(888\) 0 0
\(889\) −36.4343 −1.22197
\(890\) 0 0
\(891\) 17.4619 0.584996
\(892\) 0 0
\(893\) 10.7172 0.358638
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −8.75744 −0.292402
\(898\) 0 0
\(899\) −85.3884 −2.84786
\(900\) 0 0
\(901\) −3.25564 −0.108461
\(902\) 0 0
\(903\) −32.8249 −1.09234
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 42.3250 1.40538 0.702689 0.711497i \(-0.251983\pi\)
0.702689 + 0.711497i \(0.251983\pi\)
\(908\) 0 0
\(909\) −11.4589 −0.380068
\(910\) 0 0
\(911\) 5.48129 0.181603 0.0908016 0.995869i \(-0.471057\pi\)
0.0908016 + 0.995869i \(0.471057\pi\)
\(912\) 0 0
\(913\) 21.2759 0.704128
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −21.4086 −0.706974
\(918\) 0 0
\(919\) 16.6386 0.548856 0.274428 0.961608i \(-0.411512\pi\)
0.274428 + 0.961608i \(0.411512\pi\)
\(920\) 0 0
\(921\) 49.5113 1.63145
\(922\) 0 0
\(923\) 30.1171 0.991315
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −22.5224 −0.739733
\(928\) 0 0
\(929\) −30.2326 −0.991900 −0.495950 0.868351i \(-0.665180\pi\)
−0.495950 + 0.868351i \(0.665180\pi\)
\(930\) 0 0
\(931\) 15.9195 0.521741
\(932\) 0 0
\(933\) −44.1457 −1.44527
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −27.8718 −0.910532 −0.455266 0.890356i \(-0.650456\pi\)
−0.455266 + 0.890356i \(0.650456\pi\)
\(938\) 0 0
\(939\) 31.3823 1.02412
\(940\) 0 0
\(941\) 26.8768 0.876159 0.438079 0.898936i \(-0.355659\pi\)
0.438079 + 0.898936i \(0.355659\pi\)
\(942\) 0 0
\(943\) 2.34251 0.0762827
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 23.1773 0.753161 0.376581 0.926384i \(-0.377100\pi\)
0.376581 + 0.926384i \(0.377100\pi\)
\(948\) 0 0
\(949\) 50.9297 1.65325
\(950\) 0 0
\(951\) −16.5384 −0.536296
\(952\) 0 0
\(953\) 4.21870 0.136657 0.0683285 0.997663i \(-0.478233\pi\)
0.0683285 + 0.997663i \(0.478233\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 32.3092 1.04441
\(958\) 0 0
\(959\) 15.1006 0.487625
\(960\) 0 0
\(961\) 53.4401 1.72387
\(962\) 0 0
\(963\) 15.0698 0.485617
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −17.8055 −0.572588 −0.286294 0.958142i \(-0.592423\pi\)
−0.286294 + 0.958142i \(0.592423\pi\)
\(968\) 0 0
\(969\) −5.06223 −0.162622
\(970\) 0 0
\(971\) 17.9741 0.576815 0.288408 0.957508i \(-0.406874\pi\)
0.288408 + 0.957508i \(0.406874\pi\)
\(972\) 0 0
\(973\) −14.5904 −0.467747
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −58.6275 −1.87566 −0.937829 0.347097i \(-0.887167\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(978\) 0 0
\(979\) −22.5686 −0.721297
\(980\) 0 0
\(981\) −8.22592 −0.262633
\(982\) 0 0
\(983\) −7.84103 −0.250090 −0.125045 0.992151i \(-0.539908\pi\)
−0.125045 + 0.992151i \(0.539908\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 6.78701 0.216033
\(988\) 0 0
\(989\) −6.67460 −0.212240
\(990\) 0 0
\(991\) −33.1872 −1.05423 −0.527114 0.849795i \(-0.676726\pi\)
−0.527114 + 0.849795i \(0.676726\pi\)
\(992\) 0 0
\(993\) 14.5112 0.460500
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 60.8220 1.92625 0.963127 0.269049i \(-0.0867092\pi\)
0.963127 + 0.269049i \(0.0867092\pi\)
\(998\) 0 0
\(999\) 25.9612 0.821377
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4600.2.a.bc.1.5 5
4.3 odd 2 9200.2.a.cw.1.1 5
5.2 odd 4 4600.2.e.v.4049.2 10
5.3 odd 4 4600.2.e.v.4049.9 10
5.4 even 2 4600.2.a.bg.1.1 yes 5
20.19 odd 2 9200.2.a.cs.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bc.1.5 5 1.1 even 1 trivial
4600.2.a.bg.1.1 yes 5 5.4 even 2
4600.2.e.v.4049.2 10 5.2 odd 4
4600.2.e.v.4049.9 10 5.3 odd 4
9200.2.a.cs.1.5 5 20.19 odd 2
9200.2.a.cw.1.1 5 4.3 odd 2