Properties

Label 4600.2.a.bg.1.4
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $0$
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: \(0\)
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 1.4
Root \(-0.514659\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.51466 q^{3} -3.49880 q^{7} -0.705809 q^{9} +O(q^{10})\) \(q+1.51466 q^{3} -3.49880 q^{7} -0.705809 q^{9} -4.35556 q^{11} +3.67906 q^{13} -5.18556 q^{17} +2.08538 q^{19} -5.29949 q^{21} +1.00000 q^{23} -5.61304 q^{27} -1.24902 q^{29} +4.82185 q^{31} -6.59718 q^{33} +1.04471 q^{37} +5.57253 q^{39} +9.05578 q^{41} +10.4964 q^{43} +12.8597 q^{47} +5.24162 q^{49} -7.85436 q^{51} +9.37352 q^{53} +3.15864 q^{57} +14.1570 q^{59} -9.29949 q^{61} +2.46949 q^{63} +4.44274 q^{67} +1.51466 q^{69} +2.45044 q^{71} -13.2197 q^{73} +15.2392 q^{77} +7.72666 q^{79} -6.38441 q^{81} -2.97086 q^{83} -1.89184 q^{87} -14.6241 q^{89} -12.8723 q^{91} +7.30345 q^{93} +9.37991 q^{97} +3.07419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 3q^{3} - q^{7} + 4q^{9} + O(q^{10}) \) \( 5q + 3q^{3} - q^{7} + 4q^{9} - 4q^{11} - q^{13} + 5q^{17} + 4q^{19} - 6q^{21} + 5q^{23} + 6q^{27} - 11q^{29} + 4q^{31} + 13q^{33} + 6q^{37} + 31q^{39} - 8q^{41} + 3q^{43} + 2q^{47} - 2q^{49} - 5q^{51} + 18q^{53} + 27q^{57} + 23q^{59} - 26q^{61} + 5q^{63} + 3q^{67} + 3q^{69} - 2q^{71} + 4q^{73} + 15q^{77} + 43q^{79} - 3q^{81} + 30q^{83} + 27q^{87} + 15q^{89} - 19q^{91} - 15q^{93} + 8q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) 1.51466 0.874489 0.437244 0.899343i \(-0.355954\pi\)
0.437244 + 0.899343i \(0.355954\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.49880 −1.32242 −0.661212 0.750199i \(-0.729957\pi\)
−0.661212 + 0.750199i \(0.729957\pi\)
\(8\) 0 0
\(9\) −0.705809 −0.235270
\(10\) 0 0
\(11\) −4.35556 −1.31325 −0.656625 0.754217i \(-0.728016\pi\)
−0.656625 + 0.754217i \(0.728016\pi\)
\(12\) 0 0
\(13\) 3.67906 1.02039 0.510194 0.860059i \(-0.329573\pi\)
0.510194 + 0.860059i \(0.329573\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.18556 −1.25768 −0.628842 0.777533i \(-0.716471\pi\)
−0.628842 + 0.777533i \(0.716471\pi\)
\(18\) 0 0
\(19\) 2.08538 0.478419 0.239209 0.970968i \(-0.423112\pi\)
0.239209 + 0.970968i \(0.423112\pi\)
\(20\) 0 0
\(21\) −5.29949 −1.15644
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.61304 −1.08023
\(28\) 0 0
\(29\) −1.24902 −0.231937 −0.115968 0.993253i \(-0.536997\pi\)
−0.115968 + 0.993253i \(0.536997\pi\)
\(30\) 0 0
\(31\) 4.82185 0.866029 0.433015 0.901387i \(-0.357450\pi\)
0.433015 + 0.901387i \(0.357450\pi\)
\(32\) 0 0
\(33\) −6.59718 −1.14842
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.04471 0.171749 0.0858745 0.996306i \(-0.472632\pi\)
0.0858745 + 0.996306i \(0.472632\pi\)
\(38\) 0 0
\(39\) 5.57253 0.892318
\(40\) 0 0
\(41\) 9.05578 1.41427 0.707137 0.707076i \(-0.249986\pi\)
0.707137 + 0.707076i \(0.249986\pi\)
\(42\) 0 0
\(43\) 10.4964 1.60069 0.800344 0.599541i \(-0.204650\pi\)
0.800344 + 0.599541i \(0.204650\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.8597 1.87577 0.937887 0.346940i \(-0.112779\pi\)
0.937887 + 0.346940i \(0.112779\pi\)
\(48\) 0 0
\(49\) 5.24162 0.748804
\(50\) 0 0
\(51\) −7.85436 −1.09983
\(52\) 0 0
\(53\) 9.37352 1.28755 0.643776 0.765214i \(-0.277367\pi\)
0.643776 + 0.765214i \(0.277367\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.15864 0.418372
\(58\) 0 0
\(59\) 14.1570 1.84309 0.921543 0.388276i \(-0.126929\pi\)
0.921543 + 0.388276i \(0.126929\pi\)
\(60\) 0 0
\(61\) −9.29949 −1.19068 −0.595339 0.803475i \(-0.702982\pi\)
−0.595339 + 0.803475i \(0.702982\pi\)
\(62\) 0 0
\(63\) 2.46949 0.311126
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.44274 0.542767 0.271384 0.962471i \(-0.412519\pi\)
0.271384 + 0.962471i \(0.412519\pi\)
\(68\) 0 0
\(69\) 1.51466 0.182343
\(70\) 0 0
\(71\) 2.45044 0.290813 0.145407 0.989372i \(-0.453551\pi\)
0.145407 + 0.989372i \(0.453551\pi\)
\(72\) 0 0
\(73\) −13.2197 −1.54725 −0.773625 0.633643i \(-0.781559\pi\)
−0.773625 + 0.633643i \(0.781559\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 15.2392 1.73667
\(78\) 0 0
\(79\) 7.72666 0.869318 0.434659 0.900595i \(-0.356869\pi\)
0.434659 + 0.900595i \(0.356869\pi\)
\(80\) 0 0
\(81\) −6.38441 −0.709379
\(82\) 0 0
\(83\) −2.97086 −0.326095 −0.163047 0.986618i \(-0.552132\pi\)
−0.163047 + 0.986618i \(0.552132\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.89184 −0.202826
\(88\) 0 0
\(89\) −14.6241 −1.55015 −0.775076 0.631868i \(-0.782288\pi\)
−0.775076 + 0.631868i \(0.782288\pi\)
\(90\) 0 0
\(91\) −12.8723 −1.34939
\(92\) 0 0
\(93\) 7.30345 0.757333
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.37991 0.952385 0.476193 0.879341i \(-0.342017\pi\)
0.476193 + 0.879341i \(0.342017\pi\)
\(98\) 0 0
\(99\) 3.07419 0.308968
\(100\) 0 0
\(101\) −1.02674 −0.102165 −0.0510824 0.998694i \(-0.516267\pi\)
−0.0510824 + 0.998694i \(0.516267\pi\)
\(102\) 0 0
\(103\) −1.71127 −0.168617 −0.0843084 0.996440i \(-0.526868\pi\)
−0.0843084 + 0.996440i \(0.526868\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.58418 0.733191 0.366595 0.930380i \(-0.380523\pi\)
0.366595 + 0.930380i \(0.380523\pi\)
\(108\) 0 0
\(109\) −8.95951 −0.858165 −0.429083 0.903265i \(-0.641163\pi\)
−0.429083 + 0.903265i \(0.641163\pi\)
\(110\) 0 0
\(111\) 1.58238 0.150193
\(112\) 0 0
\(113\) 18.8103 1.76952 0.884760 0.466047i \(-0.154322\pi\)
0.884760 + 0.466047i \(0.154322\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.59672 −0.240066
\(118\) 0 0
\(119\) 18.1433 1.66319
\(120\) 0 0
\(121\) 7.97086 0.724624
\(122\) 0 0
\(123\) 13.7164 1.23677
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −15.0385 −1.33445 −0.667227 0.744854i \(-0.732519\pi\)
−0.667227 + 0.744854i \(0.732519\pi\)
\(128\) 0 0
\(129\) 15.8985 1.39978
\(130\) 0 0
\(131\) 20.3503 1.77801 0.889007 0.457893i \(-0.151396\pi\)
0.889007 + 0.457893i \(0.151396\pi\)
\(132\) 0 0
\(133\) −7.29633 −0.632672
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.51494 0.129430 0.0647152 0.997904i \(-0.479386\pi\)
0.0647152 + 0.997904i \(0.479386\pi\)
\(138\) 0 0
\(139\) 13.3658 1.13367 0.566837 0.823830i \(-0.308167\pi\)
0.566837 + 0.823830i \(0.308167\pi\)
\(140\) 0 0
\(141\) 19.4780 1.64034
\(142\) 0 0
\(143\) −16.0244 −1.34002
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 7.93927 0.654820
\(148\) 0 0
\(149\) −10.6307 −0.870901 −0.435450 0.900213i \(-0.643411\pi\)
−0.435450 + 0.900213i \(0.643411\pi\)
\(150\) 0 0
\(151\) −22.2918 −1.81408 −0.907041 0.421042i \(-0.861664\pi\)
−0.907041 + 0.421042i \(0.861664\pi\)
\(152\) 0 0
\(153\) 3.66002 0.295895
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2.95590 −0.235906 −0.117953 0.993019i \(-0.537633\pi\)
−0.117953 + 0.993019i \(0.537633\pi\)
\(158\) 0 0
\(159\) 14.1977 1.12595
\(160\) 0 0
\(161\) −3.49880 −0.275744
\(162\) 0 0
\(163\) 4.40543 0.345060 0.172530 0.985004i \(-0.444806\pi\)
0.172530 + 0.985004i \(0.444806\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.9252 1.15495 0.577474 0.816409i \(-0.304038\pi\)
0.577474 + 0.816409i \(0.304038\pi\)
\(168\) 0 0
\(169\) 0.535514 0.0411934
\(170\) 0 0
\(171\) −1.47188 −0.112557
\(172\) 0 0
\(173\) 18.2696 1.38901 0.694506 0.719487i \(-0.255623\pi\)
0.694506 + 0.719487i \(0.255623\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 21.4430 1.61176
\(178\) 0 0
\(179\) −6.20356 −0.463676 −0.231838 0.972754i \(-0.574474\pi\)
−0.231838 + 0.972754i \(0.574474\pi\)
\(180\) 0 0
\(181\) 5.74043 0.426683 0.213341 0.976978i \(-0.431565\pi\)
0.213341 + 0.976978i \(0.431565\pi\)
\(182\) 0 0
\(183\) −14.0856 −1.04123
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 22.5860 1.65165
\(188\) 0 0
\(189\) 19.6389 1.42852
\(190\) 0 0
\(191\) −13.4671 −0.974445 −0.487222 0.873278i \(-0.661990\pi\)
−0.487222 + 0.873278i \(0.661990\pi\)
\(192\) 0 0
\(193\) −0.295578 −0.0212762 −0.0106381 0.999943i \(-0.503386\pi\)
−0.0106381 + 0.999943i \(0.503386\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.6206 0.827932 0.413966 0.910292i \(-0.364143\pi\)
0.413966 + 0.910292i \(0.364143\pi\)
\(198\) 0 0
\(199\) 4.46949 0.316833 0.158417 0.987372i \(-0.449361\pi\)
0.158417 + 0.987372i \(0.449361\pi\)
\(200\) 0 0
\(201\) 6.72924 0.474644
\(202\) 0 0
\(203\) 4.37007 0.306719
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.705809 −0.0490571
\(208\) 0 0
\(209\) −9.08299 −0.628283
\(210\) 0 0
\(211\) −15.0878 −1.03869 −0.519343 0.854566i \(-0.673823\pi\)
−0.519343 + 0.854566i \(0.673823\pi\)
\(212\) 0 0
\(213\) 3.71158 0.254313
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −16.8707 −1.14526
\(218\) 0 0
\(219\) −20.0234 −1.35305
\(220\) 0 0
\(221\) −19.0780 −1.28333
\(222\) 0 0
\(223\) −25.2033 −1.68774 −0.843870 0.536548i \(-0.819728\pi\)
−0.843870 + 0.536548i \(0.819728\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.1385 −1.33664 −0.668319 0.743875i \(-0.732986\pi\)
−0.668319 + 0.743875i \(0.732986\pi\)
\(228\) 0 0
\(229\) 9.72411 0.642587 0.321294 0.946980i \(-0.395882\pi\)
0.321294 + 0.946980i \(0.395882\pi\)
\(230\) 0 0
\(231\) 23.0822 1.51870
\(232\) 0 0
\(233\) −6.37957 −0.417940 −0.208970 0.977922i \(-0.567011\pi\)
−0.208970 + 0.977922i \(0.567011\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 11.7033 0.760208
\(238\) 0 0
\(239\) −3.07706 −0.199039 −0.0995194 0.995036i \(-0.531731\pi\)
−0.0995194 + 0.995036i \(0.531731\pi\)
\(240\) 0 0
\(241\) −28.6341 −1.84448 −0.922242 0.386612i \(-0.873645\pi\)
−0.922242 + 0.386612i \(0.873645\pi\)
\(242\) 0 0
\(243\) 7.16891 0.459886
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 7.67225 0.488173
\(248\) 0 0
\(249\) −4.49984 −0.285166
\(250\) 0 0
\(251\) 0.728308 0.0459704 0.0229852 0.999736i \(-0.492683\pi\)
0.0229852 + 0.999736i \(0.492683\pi\)
\(252\) 0 0
\(253\) −4.35556 −0.273831
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 29.1681 1.81945 0.909727 0.415206i \(-0.136290\pi\)
0.909727 + 0.415206i \(0.136290\pi\)
\(258\) 0 0
\(259\) −3.65523 −0.227125
\(260\) 0 0
\(261\) 0.881568 0.0545677
\(262\) 0 0
\(263\) 2.79631 0.172428 0.0862139 0.996277i \(-0.472523\pi\)
0.0862139 + 0.996277i \(0.472523\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −22.1505 −1.35559
\(268\) 0 0
\(269\) −0.662454 −0.0403905 −0.0201953 0.999796i \(-0.506429\pi\)
−0.0201953 + 0.999796i \(0.506429\pi\)
\(270\) 0 0
\(271\) 14.5266 0.882428 0.441214 0.897402i \(-0.354548\pi\)
0.441214 + 0.897402i \(0.354548\pi\)
\(272\) 0 0
\(273\) −19.4972 −1.18002
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.15432 −0.0693562 −0.0346781 0.999399i \(-0.511041\pi\)
−0.0346781 + 0.999399i \(0.511041\pi\)
\(278\) 0 0
\(279\) −3.40330 −0.203750
\(280\) 0 0
\(281\) −14.2977 −0.852930 −0.426465 0.904504i \(-0.640241\pi\)
−0.426465 + 0.904504i \(0.640241\pi\)
\(282\) 0 0
\(283\) 31.2654 1.85854 0.929268 0.369407i \(-0.120439\pi\)
0.929268 + 0.369407i \(0.120439\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −31.6844 −1.87027
\(288\) 0 0
\(289\) 9.89006 0.581768
\(290\) 0 0
\(291\) 14.2074 0.832850
\(292\) 0 0
\(293\) 4.59477 0.268429 0.134215 0.990952i \(-0.457149\pi\)
0.134215 + 0.990952i \(0.457149\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 24.4479 1.41861
\(298\) 0 0
\(299\) 3.67906 0.212766
\(300\) 0 0
\(301\) −36.7249 −2.11679
\(302\) 0 0
\(303\) −1.55517 −0.0893420
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.96103 0.568506 0.284253 0.958749i \(-0.408254\pi\)
0.284253 + 0.958749i \(0.408254\pi\)
\(308\) 0 0
\(309\) −2.59200 −0.147453
\(310\) 0 0
\(311\) −12.7520 −0.723102 −0.361551 0.932352i \(-0.617753\pi\)
−0.361551 + 0.932352i \(0.617753\pi\)
\(312\) 0 0
\(313\) −19.5585 −1.10551 −0.552756 0.833343i \(-0.686424\pi\)
−0.552756 + 0.833343i \(0.686424\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 32.5493 1.82815 0.914076 0.405542i \(-0.132917\pi\)
0.914076 + 0.405542i \(0.132917\pi\)
\(318\) 0 0
\(319\) 5.44017 0.304591
\(320\) 0 0
\(321\) 11.4874 0.641167
\(322\) 0 0
\(323\) −10.8139 −0.601700
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −13.5706 −0.750456
\(328\) 0 0
\(329\) −44.9934 −2.48057
\(330\) 0 0
\(331\) 23.9704 1.31753 0.658767 0.752347i \(-0.271078\pi\)
0.658767 + 0.752347i \(0.271078\pi\)
\(332\) 0 0
\(333\) −0.737364 −0.0404073
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 5.88246 0.320438 0.160219 0.987082i \(-0.448780\pi\)
0.160219 + 0.987082i \(0.448780\pi\)
\(338\) 0 0
\(339\) 28.4911 1.54743
\(340\) 0 0
\(341\) −21.0018 −1.13731
\(342\) 0 0
\(343\) 6.15221 0.332188
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 25.7454 1.38209 0.691043 0.722814i \(-0.257151\pi\)
0.691043 + 0.722814i \(0.257151\pi\)
\(348\) 0 0
\(349\) −17.7758 −0.951517 −0.475758 0.879576i \(-0.657826\pi\)
−0.475758 + 0.879576i \(0.657826\pi\)
\(350\) 0 0
\(351\) −20.6507 −1.10225
\(352\) 0 0
\(353\) 20.4426 1.08805 0.544026 0.839068i \(-0.316899\pi\)
0.544026 + 0.839068i \(0.316899\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 27.4809 1.45444
\(358\) 0 0
\(359\) −14.5323 −0.766987 −0.383494 0.923543i \(-0.625279\pi\)
−0.383494 + 0.923543i \(0.625279\pi\)
\(360\) 0 0
\(361\) −14.6512 −0.771115
\(362\) 0 0
\(363\) 12.0731 0.633675
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −12.2205 −0.637906 −0.318953 0.947771i \(-0.603331\pi\)
−0.318953 + 0.947771i \(0.603331\pi\)
\(368\) 0 0
\(369\) −6.39165 −0.332736
\(370\) 0 0
\(371\) −32.7961 −1.70269
\(372\) 0 0
\(373\) −1.78846 −0.0926029 −0.0463015 0.998928i \(-0.514743\pi\)
−0.0463015 + 0.998928i \(0.514743\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.59522 −0.236666
\(378\) 0 0
\(379\) 7.02119 0.360654 0.180327 0.983607i \(-0.442284\pi\)
0.180327 + 0.983607i \(0.442284\pi\)
\(380\) 0 0
\(381\) −22.7782 −1.16697
\(382\) 0 0
\(383\) 13.0896 0.668846 0.334423 0.942423i \(-0.391459\pi\)
0.334423 + 0.942423i \(0.391459\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −7.40846 −0.376593
\(388\) 0 0
\(389\) −21.5395 −1.09210 −0.546048 0.837754i \(-0.683868\pi\)
−0.546048 + 0.837754i \(0.683868\pi\)
\(390\) 0 0
\(391\) −5.18556 −0.262245
\(392\) 0 0
\(393\) 30.8238 1.55485
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −31.2045 −1.56611 −0.783055 0.621953i \(-0.786340\pi\)
−0.783055 + 0.621953i \(0.786340\pi\)
\(398\) 0 0
\(399\) −11.0515 −0.553265
\(400\) 0 0
\(401\) 13.7592 0.687100 0.343550 0.939134i \(-0.388371\pi\)
0.343550 + 0.939134i \(0.388371\pi\)
\(402\) 0 0
\(403\) 17.7399 0.883687
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.55028 −0.225549
\(408\) 0 0
\(409\) 21.9730 1.08649 0.543247 0.839573i \(-0.317195\pi\)
0.543247 + 0.839573i \(0.317195\pi\)
\(410\) 0 0
\(411\) 2.29462 0.113185
\(412\) 0 0
\(413\) −49.5326 −2.43734
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 20.2447 0.991385
\(418\) 0 0
\(419\) −13.3024 −0.649867 −0.324934 0.945737i \(-0.605342\pi\)
−0.324934 + 0.945737i \(0.605342\pi\)
\(420\) 0 0
\(421\) −7.32759 −0.357125 −0.178562 0.983929i \(-0.557145\pi\)
−0.178562 + 0.983929i \(0.557145\pi\)
\(422\) 0 0
\(423\) −9.07646 −0.441313
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 32.5371 1.57458
\(428\) 0 0
\(429\) −24.2715 −1.17184
\(430\) 0 0
\(431\) 29.4301 1.41760 0.708800 0.705409i \(-0.249237\pi\)
0.708800 + 0.705409i \(0.249237\pi\)
\(432\) 0 0
\(433\) 10.5491 0.506960 0.253480 0.967341i \(-0.418425\pi\)
0.253480 + 0.967341i \(0.418425\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.08538 0.0997572
\(438\) 0 0
\(439\) 1.04921 0.0500761 0.0250380 0.999686i \(-0.492029\pi\)
0.0250380 + 0.999686i \(0.492029\pi\)
\(440\) 0 0
\(441\) −3.69958 −0.176171
\(442\) 0 0
\(443\) 9.57098 0.454731 0.227365 0.973810i \(-0.426989\pi\)
0.227365 + 0.973810i \(0.426989\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −16.1019 −0.761593
\(448\) 0 0
\(449\) 8.10079 0.382300 0.191150 0.981561i \(-0.438778\pi\)
0.191150 + 0.981561i \(0.438778\pi\)
\(450\) 0 0
\(451\) −39.4429 −1.85730
\(452\) 0 0
\(453\) −33.7645 −1.58639
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 34.5867 1.61790 0.808948 0.587880i \(-0.200037\pi\)
0.808948 + 0.587880i \(0.200037\pi\)
\(458\) 0 0
\(459\) 29.1068 1.35859
\(460\) 0 0
\(461\) −23.3497 −1.08750 −0.543752 0.839246i \(-0.682997\pi\)
−0.543752 + 0.839246i \(0.682997\pi\)
\(462\) 0 0
\(463\) 36.7512 1.70797 0.853987 0.520295i \(-0.174178\pi\)
0.853987 + 0.520295i \(0.174178\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.5786 1.36874 0.684368 0.729137i \(-0.260078\pi\)
0.684368 + 0.729137i \(0.260078\pi\)
\(468\) 0 0
\(469\) −15.5443 −0.717768
\(470\) 0 0
\(471\) −4.47717 −0.206297
\(472\) 0 0
\(473\) −45.7177 −2.10210
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −6.61591 −0.302922
\(478\) 0 0
\(479\) 7.23409 0.330534 0.165267 0.986249i \(-0.447151\pi\)
0.165267 + 0.986249i \(0.447151\pi\)
\(480\) 0 0
\(481\) 3.84355 0.175251
\(482\) 0 0
\(483\) −5.29949 −0.241135
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.99593 0.407645 0.203822 0.979008i \(-0.434664\pi\)
0.203822 + 0.979008i \(0.434664\pi\)
\(488\) 0 0
\(489\) 6.67272 0.301751
\(490\) 0 0
\(491\) 9.71762 0.438550 0.219275 0.975663i \(-0.429631\pi\)
0.219275 + 0.975663i \(0.429631\pi\)
\(492\) 0 0
\(493\) 6.47686 0.291703
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.57360 −0.384578
\(498\) 0 0
\(499\) 33.3758 1.49410 0.747052 0.664765i \(-0.231468\pi\)
0.747052 + 0.664765i \(0.231468\pi\)
\(500\) 0 0
\(501\) 22.6066 1.00999
\(502\) 0 0
\(503\) 22.1147 0.986046 0.493023 0.870016i \(-0.335892\pi\)
0.493023 + 0.870016i \(0.335892\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.811121 0.0360232
\(508\) 0 0
\(509\) 10.8182 0.479507 0.239753 0.970834i \(-0.422933\pi\)
0.239753 + 0.970834i \(0.422933\pi\)
\(510\) 0 0
\(511\) 46.2532 2.04612
\(512\) 0 0
\(513\) −11.7053 −0.516802
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −56.0110 −2.46336
\(518\) 0 0
\(519\) 27.6722 1.21467
\(520\) 0 0
\(521\) −3.20820 −0.140554 −0.0702770 0.997528i \(-0.522388\pi\)
−0.0702770 + 0.997528i \(0.522388\pi\)
\(522\) 0 0
\(523\) 23.7159 1.03702 0.518512 0.855071i \(-0.326486\pi\)
0.518512 + 0.855071i \(0.326486\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −25.0040 −1.08919
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −9.99214 −0.433622
\(532\) 0 0
\(533\) 33.3168 1.44311
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.39628 −0.405479
\(538\) 0 0
\(539\) −22.8302 −0.983366
\(540\) 0 0
\(541\) −6.46616 −0.278002 −0.139001 0.990292i \(-0.544389\pi\)
−0.139001 + 0.990292i \(0.544389\pi\)
\(542\) 0 0
\(543\) 8.69479 0.373129
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.48526 0.320047 0.160023 0.987113i \(-0.448843\pi\)
0.160023 + 0.987113i \(0.448843\pi\)
\(548\) 0 0
\(549\) 6.56366 0.280130
\(550\) 0 0
\(551\) −2.60468 −0.110963
\(552\) 0 0
\(553\) −27.0341 −1.14961
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22.2922 −0.944553 −0.472276 0.881451i \(-0.656568\pi\)
−0.472276 + 0.881451i \(0.656568\pi\)
\(558\) 0 0
\(559\) 38.6170 1.63332
\(560\) 0 0
\(561\) 34.2101 1.44435
\(562\) 0 0
\(563\) −9.93402 −0.418669 −0.209335 0.977844i \(-0.567130\pi\)
−0.209335 + 0.977844i \(0.567130\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 22.3378 0.938099
\(568\) 0 0
\(569\) −26.8239 −1.12452 −0.562258 0.826962i \(-0.690067\pi\)
−0.562258 + 0.826962i \(0.690067\pi\)
\(570\) 0 0
\(571\) 30.0260 1.25655 0.628274 0.777992i \(-0.283762\pi\)
0.628274 + 0.777992i \(0.283762\pi\)
\(572\) 0 0
\(573\) −20.3981 −0.852141
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −23.5058 −0.978559 −0.489279 0.872127i \(-0.662740\pi\)
−0.489279 + 0.872127i \(0.662740\pi\)
\(578\) 0 0
\(579\) −0.447701 −0.0186058
\(580\) 0 0
\(581\) 10.3945 0.431235
\(582\) 0 0
\(583\) −40.8269 −1.69088
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.05879 −0.208799 −0.104399 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(588\) 0 0
\(589\) 10.0554 0.414325
\(590\) 0 0
\(591\) 17.6012 0.724017
\(592\) 0 0
\(593\) 15.0522 0.618120 0.309060 0.951043i \(-0.399986\pi\)
0.309060 + 0.951043i \(0.399986\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.76975 0.277067
\(598\) 0 0
\(599\) −15.9863 −0.653181 −0.326590 0.945166i \(-0.605900\pi\)
−0.326590 + 0.945166i \(0.605900\pi\)
\(600\) 0 0
\(601\) 32.7941 1.33770 0.668851 0.743397i \(-0.266787\pi\)
0.668851 + 0.743397i \(0.266787\pi\)
\(602\) 0 0
\(603\) −3.13573 −0.127697
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −38.4884 −1.56220 −0.781098 0.624409i \(-0.785340\pi\)
−0.781098 + 0.624409i \(0.785340\pi\)
\(608\) 0 0
\(609\) 6.61916 0.268222
\(610\) 0 0
\(611\) 47.3115 1.91402
\(612\) 0 0
\(613\) 6.47626 0.261574 0.130787 0.991411i \(-0.458250\pi\)
0.130787 + 0.991411i \(0.458250\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 33.8193 1.36152 0.680758 0.732509i \(-0.261651\pi\)
0.680758 + 0.732509i \(0.261651\pi\)
\(618\) 0 0
\(619\) 2.02686 0.0814663 0.0407331 0.999170i \(-0.487031\pi\)
0.0407331 + 0.999170i \(0.487031\pi\)
\(620\) 0 0
\(621\) −5.61304 −0.225243
\(622\) 0 0
\(623\) 51.1669 2.04996
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −13.7576 −0.549427
\(628\) 0 0
\(629\) −5.41740 −0.216006
\(630\) 0 0
\(631\) −3.45649 −0.137601 −0.0688003 0.997630i \(-0.521917\pi\)
−0.0688003 + 0.997630i \(0.521917\pi\)
\(632\) 0 0
\(633\) −22.8529 −0.908319
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 19.2843 0.764071
\(638\) 0 0
\(639\) −1.72954 −0.0684195
\(640\) 0 0
\(641\) 47.2630 1.86678 0.933388 0.358869i \(-0.116837\pi\)
0.933388 + 0.358869i \(0.116837\pi\)
\(642\) 0 0
\(643\) −23.6052 −0.930899 −0.465449 0.885075i \(-0.654107\pi\)
−0.465449 + 0.885075i \(0.654107\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.3090 −0.798430 −0.399215 0.916857i \(-0.630717\pi\)
−0.399215 + 0.916857i \(0.630717\pi\)
\(648\) 0 0
\(649\) −61.6617 −2.42043
\(650\) 0 0
\(651\) −25.5533 −1.00151
\(652\) 0 0
\(653\) −15.8982 −0.622146 −0.311073 0.950386i \(-0.600688\pi\)
−0.311073 + 0.950386i \(0.600688\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 9.33059 0.364021
\(658\) 0 0
\(659\) 13.6170 0.530441 0.265221 0.964188i \(-0.414555\pi\)
0.265221 + 0.964188i \(0.414555\pi\)
\(660\) 0 0
\(661\) 27.8049 1.08148 0.540742 0.841188i \(-0.318143\pi\)
0.540742 + 0.841188i \(0.318143\pi\)
\(662\) 0 0
\(663\) −28.8967 −1.12225
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.24902 −0.0483622
\(668\) 0 0
\(669\) −38.1744 −1.47591
\(670\) 0 0
\(671\) 40.5045 1.56366
\(672\) 0 0
\(673\) −4.92071 −0.189679 −0.0948396 0.995493i \(-0.530234\pi\)
−0.0948396 + 0.995493i \(0.530234\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −48.4096 −1.86053 −0.930266 0.366886i \(-0.880424\pi\)
−0.930266 + 0.366886i \(0.880424\pi\)
\(678\) 0 0
\(679\) −32.8184 −1.25946
\(680\) 0 0
\(681\) −30.5029 −1.16887
\(682\) 0 0
\(683\) −36.1788 −1.38434 −0.692172 0.721732i \(-0.743346\pi\)
−0.692172 + 0.721732i \(0.743346\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 14.7287 0.561935
\(688\) 0 0
\(689\) 34.4858 1.31380
\(690\) 0 0
\(691\) 32.1568 1.22330 0.611651 0.791127i \(-0.290506\pi\)
0.611651 + 0.791127i \(0.290506\pi\)
\(692\) 0 0
\(693\) −10.7560 −0.408586
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −46.9593 −1.77871
\(698\) 0 0
\(699\) −9.66287 −0.365483
\(700\) 0 0
\(701\) 17.9408 0.677614 0.338807 0.940856i \(-0.389977\pi\)
0.338807 + 0.940856i \(0.389977\pi\)
\(702\) 0 0
\(703\) 2.17861 0.0821680
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.59238 0.135105
\(708\) 0 0
\(709\) 45.4153 1.70561 0.852804 0.522231i \(-0.174900\pi\)
0.852804 + 0.522231i \(0.174900\pi\)
\(710\) 0 0
\(711\) −5.45355 −0.204524
\(712\) 0 0
\(713\) 4.82185 0.180580
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −4.66070 −0.174057
\(718\) 0 0
\(719\) 5.90426 0.220192 0.110096 0.993921i \(-0.464884\pi\)
0.110096 + 0.993921i \(0.464884\pi\)
\(720\) 0 0
\(721\) 5.98741 0.222983
\(722\) 0 0
\(723\) −43.3709 −1.61298
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −34.8037 −1.29080 −0.645398 0.763846i \(-0.723309\pi\)
−0.645398 + 0.763846i \(0.723309\pi\)
\(728\) 0 0
\(729\) 30.0117 1.11154
\(730\) 0 0
\(731\) −54.4298 −2.01316
\(732\) 0 0
\(733\) −21.6346 −0.799093 −0.399547 0.916713i \(-0.630832\pi\)
−0.399547 + 0.916713i \(0.630832\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −19.3506 −0.712789
\(738\) 0 0
\(739\) −4.53418 −0.166792 −0.0833962 0.996516i \(-0.526577\pi\)
−0.0833962 + 0.996516i \(0.526577\pi\)
\(740\) 0 0
\(741\) 11.6208 0.426902
\(742\) 0 0
\(743\) 17.9137 0.657192 0.328596 0.944471i \(-0.393425\pi\)
0.328596 + 0.944471i \(0.393425\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.09686 0.0767201
\(748\) 0 0
\(749\) −26.5356 −0.969588
\(750\) 0 0
\(751\) −25.1812 −0.918875 −0.459438 0.888210i \(-0.651949\pi\)
−0.459438 + 0.888210i \(0.651949\pi\)
\(752\) 0 0
\(753\) 1.10314 0.0402006
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 30.7079 1.11610 0.558048 0.829809i \(-0.311550\pi\)
0.558048 + 0.829809i \(0.311550\pi\)
\(758\) 0 0
\(759\) −6.59718 −0.239462
\(760\) 0 0
\(761\) 9.58720 0.347536 0.173768 0.984787i \(-0.444406\pi\)
0.173768 + 0.984787i \(0.444406\pi\)
\(762\) 0 0
\(763\) 31.3476 1.13486
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 52.0846 1.88066
\(768\) 0 0
\(769\) −6.31547 −0.227742 −0.113871 0.993496i \(-0.536325\pi\)
−0.113871 + 0.993496i \(0.536325\pi\)
\(770\) 0 0
\(771\) 44.1797 1.59109
\(772\) 0 0
\(773\) 47.4787 1.70769 0.853845 0.520528i \(-0.174265\pi\)
0.853845 + 0.520528i \(0.174265\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −5.53642 −0.198618
\(778\) 0 0
\(779\) 18.8847 0.676616
\(780\) 0 0
\(781\) −10.6730 −0.381910
\(782\) 0 0
\(783\) 7.01078 0.250545
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −47.0588 −1.67747 −0.838733 0.544543i \(-0.816703\pi\)
−0.838733 + 0.544543i \(0.816703\pi\)
\(788\) 0 0
\(789\) 4.23546 0.150786
\(790\) 0 0
\(791\) −65.8134 −2.34005
\(792\) 0 0
\(793\) −34.2134 −1.21495
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.8819 −0.810517 −0.405259 0.914202i \(-0.632819\pi\)
−0.405259 + 0.914202i \(0.632819\pi\)
\(798\) 0 0
\(799\) −66.6846 −2.35913
\(800\) 0 0
\(801\) 10.3218 0.364704
\(802\) 0 0
\(803\) 57.5792 2.03193
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.00339 −0.0353211
\(808\) 0 0
\(809\) 21.6918 0.762643 0.381322 0.924442i \(-0.375469\pi\)
0.381322 + 0.924442i \(0.375469\pi\)
\(810\) 0 0
\(811\) 5.84992 0.205418 0.102709 0.994711i \(-0.467249\pi\)
0.102709 + 0.994711i \(0.467249\pi\)
\(812\) 0 0
\(813\) 22.0028 0.771674
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 21.8890 0.765799
\(818\) 0 0
\(819\) 9.08540 0.317469
\(820\) 0 0
\(821\) 5.98613 0.208917 0.104459 0.994529i \(-0.466689\pi\)
0.104459 + 0.994529i \(0.466689\pi\)
\(822\) 0 0
\(823\) 27.4906 0.958261 0.479131 0.877744i \(-0.340952\pi\)
0.479131 + 0.877744i \(0.340952\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.85519 −0.0992848 −0.0496424 0.998767i \(-0.515808\pi\)
−0.0496424 + 0.998767i \(0.515808\pi\)
\(828\) 0 0
\(829\) −7.63982 −0.265342 −0.132671 0.991160i \(-0.542355\pi\)
−0.132671 + 0.991160i \(0.542355\pi\)
\(830\) 0 0
\(831\) −1.74840 −0.0606512
\(832\) 0 0
\(833\) −27.1808 −0.941758
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −27.0652 −0.935510
\(838\) 0 0
\(839\) −8.41078 −0.290372 −0.145186 0.989404i \(-0.546378\pi\)
−0.145186 + 0.989404i \(0.546378\pi\)
\(840\) 0 0
\(841\) −27.4400 −0.946205
\(842\) 0 0
\(843\) −21.6561 −0.745877
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −27.8885 −0.958260
\(848\) 0 0
\(849\) 47.3564 1.62527
\(850\) 0 0
\(851\) 1.04471 0.0358121
\(852\) 0 0
\(853\) 35.6430 1.22039 0.610197 0.792250i \(-0.291090\pi\)
0.610197 + 0.792250i \(0.291090\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.66046 0.0908794 0.0454397 0.998967i \(-0.485531\pi\)
0.0454397 + 0.998967i \(0.485531\pi\)
\(858\) 0 0
\(859\) 14.0909 0.480774 0.240387 0.970677i \(-0.422726\pi\)
0.240387 + 0.970677i \(0.422726\pi\)
\(860\) 0 0
\(861\) −47.9910 −1.63553
\(862\) 0 0
\(863\) 48.1228 1.63812 0.819060 0.573708i \(-0.194496\pi\)
0.819060 + 0.573708i \(0.194496\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 14.9801 0.508750
\(868\) 0 0
\(869\) −33.6539 −1.14163
\(870\) 0 0
\(871\) 16.3451 0.553834
\(872\) 0 0
\(873\) −6.62042 −0.224067
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −26.3172 −0.888668 −0.444334 0.895861i \(-0.646560\pi\)
−0.444334 + 0.895861i \(0.646560\pi\)
\(878\) 0 0
\(879\) 6.95951 0.234738
\(880\) 0 0
\(881\) 7.59556 0.255901 0.127951 0.991781i \(-0.459160\pi\)
0.127951 + 0.991781i \(0.459160\pi\)
\(882\) 0 0
\(883\) 11.8772 0.399699 0.199849 0.979827i \(-0.435955\pi\)
0.199849 + 0.979827i \(0.435955\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −35.9421 −1.20682 −0.603409 0.797432i \(-0.706191\pi\)
−0.603409 + 0.797432i \(0.706191\pi\)
\(888\) 0 0
\(889\) 52.6169 1.76471
\(890\) 0 0
\(891\) 27.8076 0.931591
\(892\) 0 0
\(893\) 26.8173 0.897406
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 5.57253 0.186061
\(898\) 0 0
\(899\) −6.02258 −0.200864
\(900\) 0 0
\(901\) −48.6070 −1.61933
\(902\) 0 0
\(903\) −55.6257 −1.85111
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 56.9912 1.89236 0.946181 0.323637i \(-0.104906\pi\)
0.946181 + 0.323637i \(0.104906\pi\)
\(908\) 0 0
\(909\) 0.724685 0.0240363
\(910\) 0 0
\(911\) −36.5339 −1.21042 −0.605212 0.796065i \(-0.706912\pi\)
−0.605212 + 0.796065i \(0.706912\pi\)
\(912\) 0 0
\(913\) 12.9398 0.428243
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −71.2017 −2.35129
\(918\) 0 0
\(919\) −1.65041 −0.0544419 −0.0272210 0.999629i \(-0.508666\pi\)
−0.0272210 + 0.999629i \(0.508666\pi\)
\(920\) 0 0
\(921\) 15.0876 0.497152
\(922\) 0 0
\(923\) 9.01531 0.296743
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.20783 0.0396704
\(928\) 0 0
\(929\) 3.24062 0.106321 0.0531606 0.998586i \(-0.483070\pi\)
0.0531606 + 0.998586i \(0.483070\pi\)
\(930\) 0 0
\(931\) 10.9308 0.358242
\(932\) 0 0
\(933\) −19.3150 −0.632344
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −4.26930 −0.139472 −0.0697360 0.997565i \(-0.522216\pi\)
−0.0697360 + 0.997565i \(0.522216\pi\)
\(938\) 0 0
\(939\) −29.6244 −0.966757
\(940\) 0 0
\(941\) −57.0889 −1.86105 −0.930523 0.366234i \(-0.880647\pi\)
−0.930523 + 0.366234i \(0.880647\pi\)
\(942\) 0 0
\(943\) 9.05578 0.294897
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −50.1371 −1.62924 −0.814618 0.579997i \(-0.803054\pi\)
−0.814618 + 0.579997i \(0.803054\pi\)
\(948\) 0 0
\(949\) −48.6362 −1.57880
\(950\) 0 0
\(951\) 49.3011 1.59870
\(952\) 0 0
\(953\) 6.17257 0.199949 0.0999745 0.994990i \(-0.468124\pi\)
0.0999745 + 0.994990i \(0.468124\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 8.24000 0.266361
\(958\) 0 0
\(959\) −5.30049 −0.171162
\(960\) 0 0
\(961\) −7.74979 −0.249993
\(962\) 0 0
\(963\) −5.35298 −0.172497
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 7.04066 0.226412 0.113206 0.993572i \(-0.463888\pi\)
0.113206 + 0.993572i \(0.463888\pi\)
\(968\) 0 0
\(969\) −16.3793 −0.526180
\(970\) 0 0
\(971\) −5.91622 −0.189861 −0.0949303 0.995484i \(-0.530263\pi\)
−0.0949303 + 0.995484i \(0.530263\pi\)
\(972\) 0 0
\(973\) −46.7644 −1.49920
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −14.7695 −0.472517 −0.236259 0.971690i \(-0.575921\pi\)
−0.236259 + 0.971690i \(0.575921\pi\)
\(978\) 0 0
\(979\) 63.6961 2.03574
\(980\) 0 0
\(981\) 6.32370 0.201900
\(982\) 0 0
\(983\) −22.8892 −0.730054 −0.365027 0.930997i \(-0.618940\pi\)
−0.365027 + 0.930997i \(0.618940\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −68.1497 −2.16923
\(988\) 0 0
\(989\) 10.4964 0.333766
\(990\) 0 0
\(991\) 22.4611 0.713500 0.356750 0.934200i \(-0.383885\pi\)
0.356750 + 0.934200i \(0.383885\pi\)
\(992\) 0 0
\(993\) 36.3070 1.15217
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −43.9293 −1.39125 −0.695627 0.718403i \(-0.744873\pi\)
−0.695627 + 0.718403i \(0.744873\pi\)
\(998\) 0 0
\(999\) −5.86398 −0.185528
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.bg.1.4 yes 5
4.3 odd 2 9200.2.a.cs.1.2 5
5.2 odd 4 4600.2.e.v.4049.3 10
5.3 odd 4 4600.2.e.v.4049.8 10
5.4 even 2 4600.2.a.bc.1.2 5
20.19 odd 2 9200.2.a.cw.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bc.1.2 5 5.4 even 2
4600.2.a.bg.1.4 yes 5 1.1 even 1 trivial
4600.2.e.v.4049.3 10 5.2 odd 4
4600.2.e.v.4049.8 10 5.3 odd 4
9200.2.a.cs.1.2 5 4.3 odd 2
9200.2.a.cw.1.4 5 20.19 odd 2