Properties

Label 7448.2.a.bn.1.1
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.98211824.1
Defining polynomial: \(x^{6} - 3 x^{5} - 6 x^{4} + 15 x^{3} + 8 x^{2} - 9 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.28578\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.28578 q^{3} +1.50233 q^{5} +2.22478 q^{9} +O(q^{10})\) \(q-2.28578 q^{3} +1.50233 q^{5} +2.22478 q^{9} +2.10336 q^{11} +3.79902 q^{13} -3.43400 q^{15} -2.43400 q^{17} -1.00000 q^{19} +3.12609 q^{23} -2.74300 q^{25} +1.77197 q^{27} -8.00114 q^{29} +8.70171 q^{31} -4.80782 q^{33} +3.59835 q^{37} -8.68371 q^{39} +0.873155 q^{41} +5.89147 q^{43} +3.34236 q^{45} +4.76756 q^{47} +5.56358 q^{51} -11.4157 q^{53} +3.15994 q^{55} +2.28578 q^{57} +1.76374 q^{59} +12.6632 q^{61} +5.70738 q^{65} +1.44840 q^{67} -7.14554 q^{69} -2.47693 q^{71} -1.04070 q^{73} +6.26989 q^{75} +12.9444 q^{79} -10.7247 q^{81} -6.67051 q^{83} -3.65667 q^{85} +18.2888 q^{87} +11.5172 q^{89} -19.8902 q^{93} -1.50233 q^{95} -2.84904 q^{97} +4.67952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} + q^{5} + 3 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{3} + q^{5} + 3 q^{9} + 3 q^{11} + 6 q^{13} - 8 q^{15} - 2 q^{17} - 6 q^{19} + 2 q^{23} + 5 q^{25} + 6 q^{27} - q^{29} + 14 q^{31} + 19 q^{33} - 7 q^{37} + 22 q^{39} - 21 q^{41} + q^{43} - 4 q^{45} + 23 q^{47} + 2 q^{51} - 15 q^{53} + 2 q^{55} - 3 q^{57} + 25 q^{59} + 21 q^{61} + 6 q^{65} + 2 q^{67} - 20 q^{69} + 13 q^{71} - 2 q^{73} + 24 q^{75} - 17 q^{79} - 2 q^{81} + 4 q^{83} + 40 q^{85} + 30 q^{87} - q^{89} + 6 q^{93} - q^{95} - 13 q^{97} + 41 q^{99} + O(q^{100}) \)

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
\(3\) −2.28578 −1.31969 −0.659847 0.751400i \(-0.729379\pi\)
−0.659847 + 0.751400i \(0.729379\pi\)
\(4\) 0 0
\(5\) 1.50233 0.671863 0.335931 0.941886i \(-0.390949\pi\)
0.335931 + 0.941886i \(0.390949\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 2.22478 0.741595
\(10\) 0 0
\(11\) 2.10336 0.634187 0.317093 0.948394i \(-0.397293\pi\)
0.317093 + 0.948394i \(0.397293\pi\)
\(12\) 0 0
\(13\) 3.79902 1.05366 0.526829 0.849971i \(-0.323381\pi\)
0.526829 + 0.849971i \(0.323381\pi\)
\(14\) 0 0
\(15\) −3.43400 −0.886654
\(16\) 0 0
\(17\) −2.43400 −0.590331 −0.295165 0.955446i \(-0.595375\pi\)
−0.295165 + 0.955446i \(0.595375\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.12609 0.651834 0.325917 0.945398i \(-0.394327\pi\)
0.325917 + 0.945398i \(0.394327\pi\)
\(24\) 0 0
\(25\) −2.74300 −0.548600
\(26\) 0 0
\(27\) 1.77197 0.341016
\(28\) 0 0
\(29\) −8.00114 −1.48577 −0.742887 0.669416i \(-0.766544\pi\)
−0.742887 + 0.669416i \(0.766544\pi\)
\(30\) 0 0
\(31\) 8.70171 1.56287 0.781437 0.623984i \(-0.214487\pi\)
0.781437 + 0.623984i \(0.214487\pi\)
\(32\) 0 0
\(33\) −4.80782 −0.836933
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.59835 0.591565 0.295783 0.955255i \(-0.404420\pi\)
0.295783 + 0.955255i \(0.404420\pi\)
\(38\) 0 0
\(39\) −8.68371 −1.39051
\(40\) 0 0
\(41\) 0.873155 0.136364 0.0681820 0.997673i \(-0.478280\pi\)
0.0681820 + 0.997673i \(0.478280\pi\)
\(42\) 0 0
\(43\) 5.89147 0.898441 0.449220 0.893421i \(-0.351702\pi\)
0.449220 + 0.893421i \(0.351702\pi\)
\(44\) 0 0
\(45\) 3.34236 0.498250
\(46\) 0 0
\(47\) 4.76756 0.695420 0.347710 0.937602i \(-0.386959\pi\)
0.347710 + 0.937602i \(0.386959\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 5.56358 0.779057
\(52\) 0 0
\(53\) −11.4157 −1.56806 −0.784032 0.620720i \(-0.786840\pi\)
−0.784032 + 0.620720i \(0.786840\pi\)
\(54\) 0 0
\(55\) 3.15994 0.426087
\(56\) 0 0
\(57\) 2.28578 0.302759
\(58\) 0 0
\(59\) 1.76374 0.229620 0.114810 0.993387i \(-0.463374\pi\)
0.114810 + 0.993387i \(0.463374\pi\)
\(60\) 0 0
\(61\) 12.6632 1.62135 0.810676 0.585495i \(-0.199100\pi\)
0.810676 + 0.585495i \(0.199100\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.70738 0.707914
\(66\) 0 0
\(67\) 1.44840 0.176950 0.0884751 0.996078i \(-0.471801\pi\)
0.0884751 + 0.996078i \(0.471801\pi\)
\(68\) 0 0
\(69\) −7.14554 −0.860222
\(70\) 0 0
\(71\) −2.47693 −0.293957 −0.146979 0.989140i \(-0.546955\pi\)
−0.146979 + 0.989140i \(0.546955\pi\)
\(72\) 0 0
\(73\) −1.04070 −0.121804 −0.0609022 0.998144i \(-0.519398\pi\)
−0.0609022 + 0.998144i \(0.519398\pi\)
\(74\) 0 0
\(75\) 6.26989 0.723985
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 12.9444 1.45635 0.728177 0.685389i \(-0.240368\pi\)
0.728177 + 0.685389i \(0.240368\pi\)
\(80\) 0 0
\(81\) −10.7247 −1.19163
\(82\) 0 0
\(83\) −6.67051 −0.732183 −0.366092 0.930579i \(-0.619304\pi\)
−0.366092 + 0.930579i \(0.619304\pi\)
\(84\) 0 0
\(85\) −3.65667 −0.396621
\(86\) 0 0
\(87\) 18.2888 1.96077
\(88\) 0 0
\(89\) 11.5172 1.22082 0.610409 0.792086i \(-0.291005\pi\)
0.610409 + 0.792086i \(0.291005\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −19.8902 −2.06252
\(94\) 0 0
\(95\) −1.50233 −0.154136
\(96\) 0 0
\(97\) −2.84904 −0.289276 −0.144638 0.989485i \(-0.546202\pi\)
−0.144638 + 0.989485i \(0.546202\pi\)
\(98\) 0 0
\(99\) 4.67952 0.470310
\(100\) 0 0
\(101\) −7.86632 −0.782728 −0.391364 0.920236i \(-0.627997\pi\)
−0.391364 + 0.920236i \(0.627997\pi\)
\(102\) 0 0
\(103\) −6.21795 −0.612672 −0.306336 0.951923i \(-0.599103\pi\)
−0.306336 + 0.951923i \(0.599103\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.57240 0.345357 0.172678 0.984978i \(-0.444758\pi\)
0.172678 + 0.984978i \(0.444758\pi\)
\(108\) 0 0
\(109\) −3.09929 −0.296858 −0.148429 0.988923i \(-0.547422\pi\)
−0.148429 + 0.988923i \(0.547422\pi\)
\(110\) 0 0
\(111\) −8.22503 −0.780686
\(112\) 0 0
\(113\) −11.5136 −1.08311 −0.541556 0.840665i \(-0.682164\pi\)
−0.541556 + 0.840665i \(0.682164\pi\)
\(114\) 0 0
\(115\) 4.69642 0.437943
\(116\) 0 0
\(117\) 8.45199 0.781387
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −6.57588 −0.597807
\(122\) 0 0
\(123\) −1.99584 −0.179959
\(124\) 0 0
\(125\) −11.6326 −1.04045
\(126\) 0 0
\(127\) 8.69629 0.771671 0.385835 0.922568i \(-0.373913\pi\)
0.385835 + 0.922568i \(0.373913\pi\)
\(128\) 0 0
\(129\) −13.4666 −1.18567
\(130\) 0 0
\(131\) 1.15640 0.101035 0.0505176 0.998723i \(-0.483913\pi\)
0.0505176 + 0.998723i \(0.483913\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.66209 0.229116
\(136\) 0 0
\(137\) 14.9033 1.27327 0.636636 0.771164i \(-0.280325\pi\)
0.636636 + 0.771164i \(0.280325\pi\)
\(138\) 0 0
\(139\) 5.69572 0.483105 0.241553 0.970388i \(-0.422343\pi\)
0.241553 + 0.970388i \(0.422343\pi\)
\(140\) 0 0
\(141\) −10.8976 −0.917743
\(142\) 0 0
\(143\) 7.99070 0.668216
\(144\) 0 0
\(145\) −12.0204 −0.998237
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.89970 −0.729092 −0.364546 0.931185i \(-0.618776\pi\)
−0.364546 + 0.931185i \(0.618776\pi\)
\(150\) 0 0
\(151\) −21.1484 −1.72103 −0.860516 0.509424i \(-0.829859\pi\)
−0.860516 + 0.509424i \(0.829859\pi\)
\(152\) 0 0
\(153\) −5.41512 −0.437786
\(154\) 0 0
\(155\) 13.0729 1.05004
\(156\) 0 0
\(157\) 13.6136 1.08649 0.543244 0.839575i \(-0.317196\pi\)
0.543244 + 0.839575i \(0.317196\pi\)
\(158\) 0 0
\(159\) 26.0937 2.06937
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.2106 0.799756 0.399878 0.916568i \(-0.369052\pi\)
0.399878 + 0.916568i \(0.369052\pi\)
\(164\) 0 0
\(165\) −7.22293 −0.562304
\(166\) 0 0
\(167\) 8.15068 0.630718 0.315359 0.948972i \(-0.397875\pi\)
0.315359 + 0.948972i \(0.397875\pi\)
\(168\) 0 0
\(169\) 1.43254 0.110195
\(170\) 0 0
\(171\) −2.22478 −0.170133
\(172\) 0 0
\(173\) 0.659491 0.0501401 0.0250701 0.999686i \(-0.492019\pi\)
0.0250701 + 0.999686i \(0.492019\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.03152 −0.303028
\(178\) 0 0
\(179\) −17.9091 −1.33859 −0.669294 0.742998i \(-0.733403\pi\)
−0.669294 + 0.742998i \(0.733403\pi\)
\(180\) 0 0
\(181\) 2.28178 0.169604 0.0848018 0.996398i \(-0.472974\pi\)
0.0848018 + 0.996398i \(0.472974\pi\)
\(182\) 0 0
\(183\) −28.9452 −2.13969
\(184\) 0 0
\(185\) 5.40592 0.397451
\(186\) 0 0
\(187\) −5.11957 −0.374380
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.5754 0.909924 0.454962 0.890511i \(-0.349653\pi\)
0.454962 + 0.890511i \(0.349653\pi\)
\(192\) 0 0
\(193\) −4.34103 −0.312474 −0.156237 0.987720i \(-0.549936\pi\)
−0.156237 + 0.987720i \(0.549936\pi\)
\(194\) 0 0
\(195\) −13.0458 −0.934230
\(196\) 0 0
\(197\) −18.9665 −1.35131 −0.675655 0.737218i \(-0.736139\pi\)
−0.675655 + 0.737218i \(0.736139\pi\)
\(198\) 0 0
\(199\) 2.07987 0.147438 0.0737192 0.997279i \(-0.476513\pi\)
0.0737192 + 0.997279i \(0.476513\pi\)
\(200\) 0 0
\(201\) −3.31072 −0.233520
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.31177 0.0916179
\(206\) 0 0
\(207\) 6.95487 0.483397
\(208\) 0 0
\(209\) −2.10336 −0.145492
\(210\) 0 0
\(211\) 14.2072 0.978062 0.489031 0.872266i \(-0.337350\pi\)
0.489031 + 0.872266i \(0.337350\pi\)
\(212\) 0 0
\(213\) 5.66171 0.387934
\(214\) 0 0
\(215\) 8.85094 0.603629
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2.37880 0.160745
\(220\) 0 0
\(221\) −9.24680 −0.622007
\(222\) 0 0
\(223\) −18.8650 −1.26330 −0.631648 0.775255i \(-0.717621\pi\)
−0.631648 + 0.775255i \(0.717621\pi\)
\(224\) 0 0
\(225\) −6.10258 −0.406839
\(226\) 0 0
\(227\) 1.24034 0.0823246 0.0411623 0.999152i \(-0.486894\pi\)
0.0411623 + 0.999152i \(0.486894\pi\)
\(228\) 0 0
\(229\) 18.0353 1.19180 0.595902 0.803057i \(-0.296795\pi\)
0.595902 + 0.803057i \(0.296795\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.8402 1.36528 0.682642 0.730753i \(-0.260831\pi\)
0.682642 + 0.730753i \(0.260831\pi\)
\(234\) 0 0
\(235\) 7.16246 0.467227
\(236\) 0 0
\(237\) −29.5880 −1.92194
\(238\) 0 0
\(239\) 5.24639 0.339361 0.169680 0.985499i \(-0.445726\pi\)
0.169680 + 0.985499i \(0.445726\pi\)
\(240\) 0 0
\(241\) 25.6952 1.65518 0.827588 0.561337i \(-0.189713\pi\)
0.827588 + 0.561337i \(0.189713\pi\)
\(242\) 0 0
\(243\) 19.1983 1.23157
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.79902 −0.241726
\(248\) 0 0
\(249\) 15.2473 0.966258
\(250\) 0 0
\(251\) 16.9859 1.07214 0.536070 0.844174i \(-0.319908\pi\)
0.536070 + 0.844174i \(0.319908\pi\)
\(252\) 0 0
\(253\) 6.57528 0.413385
\(254\) 0 0
\(255\) 8.35834 0.523419
\(256\) 0 0
\(257\) 17.0370 1.06274 0.531370 0.847140i \(-0.321677\pi\)
0.531370 + 0.847140i \(0.321677\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −17.8008 −1.10184
\(262\) 0 0
\(263\) −12.6143 −0.777832 −0.388916 0.921273i \(-0.627150\pi\)
−0.388916 + 0.921273i \(0.627150\pi\)
\(264\) 0 0
\(265\) −17.1501 −1.05352
\(266\) 0 0
\(267\) −26.3257 −1.61111
\(268\) 0 0
\(269\) −0.686018 −0.0418273 −0.0209136 0.999781i \(-0.506658\pi\)
−0.0209136 + 0.999781i \(0.506658\pi\)
\(270\) 0 0
\(271\) −27.1831 −1.65126 −0.825628 0.564214i \(-0.809179\pi\)
−0.825628 + 0.564214i \(0.809179\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.76952 −0.347915
\(276\) 0 0
\(277\) 14.8938 0.894881 0.447440 0.894314i \(-0.352336\pi\)
0.447440 + 0.894314i \(0.352336\pi\)
\(278\) 0 0
\(279\) 19.3594 1.15902
\(280\) 0 0
\(281\) −16.2910 −0.971842 −0.485921 0.874003i \(-0.661516\pi\)
−0.485921 + 0.874003i \(0.661516\pi\)
\(282\) 0 0
\(283\) 5.60997 0.333478 0.166739 0.986001i \(-0.446676\pi\)
0.166739 + 0.986001i \(0.446676\pi\)
\(284\) 0 0
\(285\) 3.43400 0.203412
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −11.0757 −0.651509
\(290\) 0 0
\(291\) 6.51227 0.381756
\(292\) 0 0
\(293\) 19.6149 1.14591 0.572957 0.819586i \(-0.305796\pi\)
0.572957 + 0.819586i \(0.305796\pi\)
\(294\) 0 0
\(295\) 2.64972 0.154273
\(296\) 0 0
\(297\) 3.72710 0.216268
\(298\) 0 0
\(299\) 11.8761 0.686810
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 17.9807 1.03296
\(304\) 0 0
\(305\) 19.0243 1.08933
\(306\) 0 0
\(307\) −6.48600 −0.370176 −0.185088 0.982722i \(-0.559257\pi\)
−0.185088 + 0.982722i \(0.559257\pi\)
\(308\) 0 0
\(309\) 14.2128 0.808541
\(310\) 0 0
\(311\) 0.166456 0.00943886 0.00471943 0.999989i \(-0.498498\pi\)
0.00471943 + 0.999989i \(0.498498\pi\)
\(312\) 0 0
\(313\) −1.65711 −0.0936655 −0.0468328 0.998903i \(-0.514913\pi\)
−0.0468328 + 0.998903i \(0.514913\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.65335 0.0928613 0.0464307 0.998922i \(-0.485215\pi\)
0.0464307 + 0.998922i \(0.485215\pi\)
\(318\) 0 0
\(319\) −16.8293 −0.942259
\(320\) 0 0
\(321\) −8.16572 −0.455766
\(322\) 0 0
\(323\) 2.43400 0.135431
\(324\) 0 0
\(325\) −10.4207 −0.578037
\(326\) 0 0
\(327\) 7.08429 0.391762
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −28.0907 −1.54400 −0.772001 0.635621i \(-0.780744\pi\)
−0.772001 + 0.635621i \(0.780744\pi\)
\(332\) 0 0
\(333\) 8.00555 0.438702
\(334\) 0 0
\(335\) 2.17598 0.118886
\(336\) 0 0
\(337\) 1.05092 0.0572472 0.0286236 0.999590i \(-0.490888\pi\)
0.0286236 + 0.999590i \(0.490888\pi\)
\(338\) 0 0
\(339\) 26.3176 1.42938
\(340\) 0 0
\(341\) 18.3028 0.991154
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −10.7350 −0.577951
\(346\) 0 0
\(347\) 25.1323 1.34917 0.674586 0.738196i \(-0.264322\pi\)
0.674586 + 0.738196i \(0.264322\pi\)
\(348\) 0 0
\(349\) 21.4346 1.14737 0.573684 0.819077i \(-0.305514\pi\)
0.573684 + 0.819077i \(0.305514\pi\)
\(350\) 0 0
\(351\) 6.73176 0.359315
\(352\) 0 0
\(353\) 12.1316 0.645699 0.322849 0.946450i \(-0.395359\pi\)
0.322849 + 0.946450i \(0.395359\pi\)
\(354\) 0 0
\(355\) −3.72117 −0.197499
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 19.4220 1.02505 0.512526 0.858672i \(-0.328710\pi\)
0.512526 + 0.858672i \(0.328710\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 15.0310 0.788923
\(364\) 0 0
\(365\) −1.56347 −0.0818359
\(366\) 0 0
\(367\) 11.6956 0.610507 0.305253 0.952271i \(-0.401259\pi\)
0.305253 + 0.952271i \(0.401259\pi\)
\(368\) 0 0
\(369\) 1.94258 0.101127
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −8.66393 −0.448602 −0.224301 0.974520i \(-0.572010\pi\)
−0.224301 + 0.974520i \(0.572010\pi\)
\(374\) 0 0
\(375\) 26.5894 1.37307
\(376\) 0 0
\(377\) −30.3965 −1.56550
\(378\) 0 0
\(379\) 2.71551 0.139487 0.0697433 0.997565i \(-0.477782\pi\)
0.0697433 + 0.997565i \(0.477782\pi\)
\(380\) 0 0
\(381\) −19.8778 −1.01837
\(382\) 0 0
\(383\) −22.1482 −1.13172 −0.565859 0.824502i \(-0.691455\pi\)
−0.565859 + 0.824502i \(0.691455\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 13.1072 0.666279
\(388\) 0 0
\(389\) 29.0037 1.47055 0.735274 0.677770i \(-0.237054\pi\)
0.735274 + 0.677770i \(0.237054\pi\)
\(390\) 0 0
\(391\) −7.60888 −0.384798
\(392\) 0 0
\(393\) −2.64328 −0.133336
\(394\) 0 0
\(395\) 19.4467 0.978471
\(396\) 0 0
\(397\) 31.5938 1.58565 0.792823 0.609452i \(-0.208610\pi\)
0.792823 + 0.609452i \(0.208610\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −27.7045 −1.38350 −0.691748 0.722139i \(-0.743159\pi\)
−0.691748 + 0.722139i \(0.743159\pi\)
\(402\) 0 0
\(403\) 33.0580 1.64673
\(404\) 0 0
\(405\) −16.1120 −0.800613
\(406\) 0 0
\(407\) 7.56863 0.375163
\(408\) 0 0
\(409\) −0.474535 −0.0234643 −0.0117321 0.999931i \(-0.503735\pi\)
−0.0117321 + 0.999931i \(0.503735\pi\)
\(410\) 0 0
\(411\) −34.0656 −1.68033
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −10.0213 −0.491927
\(416\) 0 0
\(417\) −13.0192 −0.637551
\(418\) 0 0
\(419\) 21.0544 1.02857 0.514287 0.857618i \(-0.328057\pi\)
0.514287 + 0.857618i \(0.328057\pi\)
\(420\) 0 0
\(421\) 8.89324 0.433430 0.216715 0.976235i \(-0.430466\pi\)
0.216715 + 0.976235i \(0.430466\pi\)
\(422\) 0 0
\(423\) 10.6068 0.515720
\(424\) 0 0
\(425\) 6.67645 0.323856
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −18.2650 −0.881841
\(430\) 0 0
\(431\) −20.5442 −0.989578 −0.494789 0.869013i \(-0.664755\pi\)
−0.494789 + 0.869013i \(0.664755\pi\)
\(432\) 0 0
\(433\) 11.6228 0.558555 0.279277 0.960210i \(-0.409905\pi\)
0.279277 + 0.960210i \(0.409905\pi\)
\(434\) 0 0
\(435\) 27.4759 1.31737
\(436\) 0 0
\(437\) −3.12609 −0.149541
\(438\) 0 0
\(439\) 39.7296 1.89619 0.948096 0.317986i \(-0.103006\pi\)
0.948096 + 0.317986i \(0.103006\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.2858 0.868782 0.434391 0.900724i \(-0.356964\pi\)
0.434391 + 0.900724i \(0.356964\pi\)
\(444\) 0 0
\(445\) 17.3026 0.820223
\(446\) 0 0
\(447\) 20.3427 0.962179
\(448\) 0 0
\(449\) 26.7431 1.26209 0.631043 0.775748i \(-0.282627\pi\)
0.631043 + 0.775748i \(0.282627\pi\)
\(450\) 0 0
\(451\) 1.83656 0.0864802
\(452\) 0 0
\(453\) 48.3405 2.27124
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 33.3288 1.55905 0.779527 0.626369i \(-0.215460\pi\)
0.779527 + 0.626369i \(0.215460\pi\)
\(458\) 0 0
\(459\) −4.31298 −0.201312
\(460\) 0 0
\(461\) −24.7784 −1.15405 −0.577023 0.816728i \(-0.695786\pi\)
−0.577023 + 0.816728i \(0.695786\pi\)
\(462\) 0 0
\(463\) 13.3230 0.619172 0.309586 0.950872i \(-0.399810\pi\)
0.309586 + 0.950872i \(0.399810\pi\)
\(464\) 0 0
\(465\) −29.8816 −1.38573
\(466\) 0 0
\(467\) 14.9325 0.690994 0.345497 0.938420i \(-0.387710\pi\)
0.345497 + 0.938420i \(0.387710\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −31.1178 −1.43383
\(472\) 0 0
\(473\) 12.3919 0.569779
\(474\) 0 0
\(475\) 2.74300 0.125858
\(476\) 0 0
\(477\) −25.3974 −1.16287
\(478\) 0 0
\(479\) 16.5824 0.757671 0.378836 0.925464i \(-0.376325\pi\)
0.378836 + 0.925464i \(0.376325\pi\)
\(480\) 0 0
\(481\) 13.6702 0.623308
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.28020 −0.194354
\(486\) 0 0
\(487\) 11.9003 0.539252 0.269626 0.962965i \(-0.413100\pi\)
0.269626 + 0.962965i \(0.413100\pi\)
\(488\) 0 0
\(489\) −23.3392 −1.05543
\(490\) 0 0
\(491\) 34.1036 1.53907 0.769537 0.638602i \(-0.220487\pi\)
0.769537 + 0.638602i \(0.220487\pi\)
\(492\) 0 0
\(493\) 19.4748 0.877099
\(494\) 0 0
\(495\) 7.03019 0.315984
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −25.6631 −1.14884 −0.574419 0.818562i \(-0.694772\pi\)
−0.574419 + 0.818562i \(0.694772\pi\)
\(500\) 0 0
\(501\) −18.6306 −0.832356
\(502\) 0 0
\(503\) −0.480489 −0.0214239 −0.0107120 0.999943i \(-0.503410\pi\)
−0.0107120 + 0.999943i \(0.503410\pi\)
\(504\) 0 0
\(505\) −11.8178 −0.525886
\(506\) 0 0
\(507\) −3.27447 −0.145424
\(508\) 0 0
\(509\) −1.82404 −0.0808490 −0.0404245 0.999183i \(-0.512871\pi\)
−0.0404245 + 0.999183i \(0.512871\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.77197 −0.0782345
\(514\) 0 0
\(515\) −9.34141 −0.411632
\(516\) 0 0
\(517\) 10.0279 0.441026
\(518\) 0 0
\(519\) −1.50745 −0.0661697
\(520\) 0 0
\(521\) 2.21626 0.0970961 0.0485481 0.998821i \(-0.484541\pi\)
0.0485481 + 0.998821i \(0.484541\pi\)
\(522\) 0 0
\(523\) 8.84272 0.386665 0.193333 0.981133i \(-0.438070\pi\)
0.193333 + 0.981133i \(0.438070\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.1799 −0.922612
\(528\) 0 0
\(529\) −13.2276 −0.575112
\(530\) 0 0
\(531\) 3.92394 0.170285
\(532\) 0 0
\(533\) 3.31713 0.143681
\(534\) 0 0
\(535\) 5.36693 0.232033
\(536\) 0 0
\(537\) 40.9362 1.76653
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 8.05024 0.346107 0.173053 0.984912i \(-0.444637\pi\)
0.173053 + 0.984912i \(0.444637\pi\)
\(542\) 0 0
\(543\) −5.21565 −0.223825
\(544\) 0 0
\(545\) −4.65616 −0.199448
\(546\) 0 0
\(547\) −6.58372 −0.281500 −0.140750 0.990045i \(-0.544951\pi\)
−0.140750 + 0.990045i \(0.544951\pi\)
\(548\) 0 0
\(549\) 28.1728 1.20239
\(550\) 0 0
\(551\) 8.00114 0.340860
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −12.3567 −0.524514
\(556\) 0 0
\(557\) −5.99440 −0.253991 −0.126995 0.991903i \(-0.540533\pi\)
−0.126995 + 0.991903i \(0.540533\pi\)
\(558\) 0 0
\(559\) 22.3818 0.946649
\(560\) 0 0
\(561\) 11.7022 0.494068
\(562\) 0 0
\(563\) 18.0238 0.759613 0.379807 0.925066i \(-0.375991\pi\)
0.379807 + 0.925066i \(0.375991\pi\)
\(564\) 0 0
\(565\) −17.2973 −0.727702
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25.3279 1.06180 0.530901 0.847434i \(-0.321854\pi\)
0.530901 + 0.847434i \(0.321854\pi\)
\(570\) 0 0
\(571\) 27.7300 1.16046 0.580232 0.814451i \(-0.302962\pi\)
0.580232 + 0.814451i \(0.302962\pi\)
\(572\) 0 0
\(573\) −28.7446 −1.20082
\(574\) 0 0
\(575\) −8.57486 −0.357596
\(576\) 0 0
\(577\) −35.1453 −1.46312 −0.731559 0.681778i \(-0.761207\pi\)
−0.731559 + 0.681778i \(0.761207\pi\)
\(578\) 0 0
\(579\) 9.92263 0.412370
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −24.0113 −0.994446
\(584\) 0 0
\(585\) 12.6977 0.524985
\(586\) 0 0
\(587\) −2.91495 −0.120313 −0.0601564 0.998189i \(-0.519160\pi\)
−0.0601564 + 0.998189i \(0.519160\pi\)
\(588\) 0 0
\(589\) −8.70171 −0.358548
\(590\) 0 0
\(591\) 43.3533 1.78332
\(592\) 0 0
\(593\) −29.9287 −1.22903 −0.614513 0.788907i \(-0.710647\pi\)
−0.614513 + 0.788907i \(0.710647\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.75413 −0.194574
\(598\) 0 0
\(599\) −20.9090 −0.854317 −0.427158 0.904177i \(-0.640485\pi\)
−0.427158 + 0.904177i \(0.640485\pi\)
\(600\) 0 0
\(601\) −37.4286 −1.52674 −0.763372 0.645960i \(-0.776457\pi\)
−0.763372 + 0.645960i \(0.776457\pi\)
\(602\) 0 0
\(603\) 3.22238 0.131225
\(604\) 0 0
\(605\) −9.87914 −0.401644
\(606\) 0 0
\(607\) −4.12339 −0.167363 −0.0836816 0.996493i \(-0.526668\pi\)
−0.0836816 + 0.996493i \(0.526668\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 18.1121 0.732735
\(612\) 0 0
\(613\) −6.01803 −0.243066 −0.121533 0.992587i \(-0.538781\pi\)
−0.121533 + 0.992587i \(0.538781\pi\)
\(614\) 0 0
\(615\) −2.99841 −0.120908
\(616\) 0 0
\(617\) 42.3840 1.70631 0.853157 0.521654i \(-0.174685\pi\)
0.853157 + 0.521654i \(0.174685\pi\)
\(618\) 0 0
\(619\) 37.8235 1.52025 0.760127 0.649774i \(-0.225137\pi\)
0.760127 + 0.649774i \(0.225137\pi\)
\(620\) 0 0
\(621\) 5.53934 0.222286
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −3.76094 −0.150438
\(626\) 0 0
\(627\) 4.80782 0.192006
\(628\) 0 0
\(629\) −8.75838 −0.349219
\(630\) 0 0
\(631\) 34.2901 1.36507 0.682534 0.730854i \(-0.260878\pi\)
0.682534 + 0.730854i \(0.260878\pi\)
\(632\) 0 0
\(633\) −32.4745 −1.29074
\(634\) 0 0
\(635\) 13.0647 0.518457
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −5.51063 −0.217997
\(640\) 0 0
\(641\) −4.82023 −0.190388 −0.0951939 0.995459i \(-0.530347\pi\)
−0.0951939 + 0.995459i \(0.530347\pi\)
\(642\) 0 0
\(643\) −27.2145 −1.07324 −0.536618 0.843825i \(-0.680298\pi\)
−0.536618 + 0.843825i \(0.680298\pi\)
\(644\) 0 0
\(645\) −20.2313 −0.796606
\(646\) 0 0
\(647\) −21.3241 −0.838336 −0.419168 0.907909i \(-0.637678\pi\)
−0.419168 + 0.907909i \(0.637678\pi\)
\(648\) 0 0
\(649\) 3.70978 0.145622
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14.4961 0.567276 0.283638 0.958931i \(-0.408459\pi\)
0.283638 + 0.958931i \(0.408459\pi\)
\(654\) 0 0
\(655\) 1.73730 0.0678818
\(656\) 0 0
\(657\) −2.31533 −0.0903295
\(658\) 0 0
\(659\) 38.5594 1.50206 0.751030 0.660268i \(-0.229557\pi\)
0.751030 + 0.660268i \(0.229557\pi\)
\(660\) 0 0
\(661\) −6.74065 −0.262181 −0.131090 0.991370i \(-0.541848\pi\)
−0.131090 + 0.991370i \(0.541848\pi\)
\(662\) 0 0
\(663\) 21.1361 0.820859
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −25.0123 −0.968479
\(668\) 0 0
\(669\) 43.1213 1.66717
\(670\) 0 0
\(671\) 26.6352 1.02824
\(672\) 0 0
\(673\) 33.8643 1.30537 0.652686 0.757629i \(-0.273642\pi\)
0.652686 + 0.757629i \(0.273642\pi\)
\(674\) 0 0
\(675\) −4.86052 −0.187082
\(676\) 0 0
\(677\) −26.8461 −1.03178 −0.515890 0.856655i \(-0.672539\pi\)
−0.515890 + 0.856655i \(0.672539\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2.83515 −0.108643
\(682\) 0 0
\(683\) 28.2987 1.08282 0.541411 0.840758i \(-0.317890\pi\)
0.541411 + 0.840758i \(0.317890\pi\)
\(684\) 0 0
\(685\) 22.3896 0.855464
\(686\) 0 0
\(687\) −41.2246 −1.57282
\(688\) 0 0
\(689\) −43.3684 −1.65220
\(690\) 0 0
\(691\) −14.6108 −0.555822 −0.277911 0.960607i \(-0.589642\pi\)
−0.277911 + 0.960607i \(0.589642\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.55686 0.324580
\(696\) 0 0
\(697\) −2.12526 −0.0804998
\(698\) 0 0
\(699\) −47.6360 −1.80176
\(700\) 0 0
\(701\) 16.2496 0.613739 0.306869 0.951752i \(-0.400719\pi\)
0.306869 + 0.951752i \(0.400719\pi\)
\(702\) 0 0
\(703\) −3.59835 −0.135714
\(704\) 0 0
\(705\) −16.3718 −0.616597
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 18.5432 0.696404 0.348202 0.937420i \(-0.386792\pi\)
0.348202 + 0.937420i \(0.386792\pi\)
\(710\) 0 0
\(711\) 28.7984 1.08002
\(712\) 0 0
\(713\) 27.2023 1.01873
\(714\) 0 0
\(715\) 12.0047 0.448950
\(716\) 0 0
\(717\) −11.9921 −0.447853
\(718\) 0 0
\(719\) −36.4717 −1.36017 −0.680083 0.733135i \(-0.738056\pi\)
−0.680083 + 0.733135i \(0.738056\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −58.7336 −2.18433
\(724\) 0 0
\(725\) 21.9471 0.815096
\(726\) 0 0
\(727\) 49.4445 1.83380 0.916898 0.399122i \(-0.130685\pi\)
0.916898 + 0.399122i \(0.130685\pi\)
\(728\) 0 0
\(729\) −11.7091 −0.433670
\(730\) 0 0
\(731\) −14.3398 −0.530377
\(732\) 0 0
\(733\) −20.9039 −0.772102 −0.386051 0.922477i \(-0.626161\pi\)
−0.386051 + 0.922477i \(0.626161\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.04651 0.112219
\(738\) 0 0
\(739\) −31.5546 −1.16076 −0.580378 0.814347i \(-0.697095\pi\)
−0.580378 + 0.814347i \(0.697095\pi\)
\(740\) 0 0
\(741\) 8.68371 0.319004
\(742\) 0 0
\(743\) −25.9123 −0.950628 −0.475314 0.879816i \(-0.657666\pi\)
−0.475314 + 0.879816i \(0.657666\pi\)
\(744\) 0 0
\(745\) −13.3703 −0.489850
\(746\) 0 0
\(747\) −14.8404 −0.542983
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 47.0277 1.71607 0.858033 0.513594i \(-0.171686\pi\)
0.858033 + 0.513594i \(0.171686\pi\)
\(752\) 0 0
\(753\) −38.8260 −1.41490
\(754\) 0 0
\(755\) −31.7719 −1.15630
\(756\) 0 0
\(757\) −21.8924 −0.795693 −0.397846 0.917452i \(-0.630242\pi\)
−0.397846 + 0.917452i \(0.630242\pi\)
\(758\) 0 0
\(759\) −15.0296 −0.545542
\(760\) 0 0
\(761\) −11.1869 −0.405527 −0.202763 0.979228i \(-0.564992\pi\)
−0.202763 + 0.979228i \(0.564992\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −8.13530 −0.294132
\(766\) 0 0
\(767\) 6.70049 0.241941
\(768\) 0 0
\(769\) 6.03222 0.217527 0.108764 0.994068i \(-0.465311\pi\)
0.108764 + 0.994068i \(0.465311\pi\)
\(770\) 0 0
\(771\) −38.9428 −1.40249
\(772\) 0 0
\(773\) 28.1013 1.01073 0.505367 0.862905i \(-0.331357\pi\)
0.505367 + 0.862905i \(0.331357\pi\)
\(774\) 0 0
\(775\) −23.8688 −0.857393
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.873155 −0.0312840
\(780\) 0 0
\(781\) −5.20987 −0.186424
\(782\) 0 0
\(783\) −14.1778 −0.506673
\(784\) 0 0
\(785\) 20.4522 0.729970
\(786\) 0 0
\(787\) 39.0182 1.39085 0.695424 0.718599i \(-0.255216\pi\)
0.695424 + 0.718599i \(0.255216\pi\)
\(788\) 0 0
\(789\) 28.8335 1.02650
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 48.1076 1.70835
\(794\) 0 0
\(795\) 39.2014 1.39033
\(796\) 0 0
\(797\) −33.0551 −1.17087 −0.585435 0.810719i \(-0.699076\pi\)
−0.585435 + 0.810719i \(0.699076\pi\)
\(798\) 0 0
\(799\) −11.6042 −0.410528
\(800\) 0 0
\(801\) 25.6232 0.905353
\(802\) 0 0
\(803\) −2.18896 −0.0772468
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.56809 0.0551992
\(808\) 0 0
\(809\) −11.1926 −0.393512 −0.196756 0.980452i \(-0.563041\pi\)
−0.196756 + 0.980452i \(0.563041\pi\)
\(810\) 0 0
\(811\) 41.3203 1.45095 0.725475 0.688248i \(-0.241620\pi\)
0.725475 + 0.688248i \(0.241620\pi\)
\(812\) 0 0
\(813\) 62.1346 2.17916
\(814\) 0 0
\(815\) 15.3397 0.537327
\(816\) 0 0
\(817\) −5.89147 −0.206116
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 37.6569 1.31423 0.657117 0.753789i \(-0.271776\pi\)
0.657117 + 0.753789i \(0.271776\pi\)
\(822\) 0 0
\(823\) −27.6497 −0.963809 −0.481905 0.876224i \(-0.660055\pi\)
−0.481905 + 0.876224i \(0.660055\pi\)
\(824\) 0 0
\(825\) 13.1878 0.459142
\(826\) 0 0
\(827\) 16.2955 0.566651 0.283326 0.959024i \(-0.408562\pi\)
0.283326 + 0.959024i \(0.408562\pi\)
\(828\) 0 0
\(829\) 5.19887 0.180564 0.0902821 0.995916i \(-0.471223\pi\)
0.0902821 + 0.995916i \(0.471223\pi\)
\(830\) 0 0
\(831\) −34.0439 −1.18097
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 12.2450 0.423756
\(836\) 0 0
\(837\) 15.4192 0.532965
\(838\) 0 0
\(839\) −56.8378 −1.96226 −0.981129 0.193356i \(-0.938063\pi\)
−0.981129 + 0.193356i \(0.938063\pi\)
\(840\) 0 0
\(841\) 35.0183 1.20753
\(842\) 0 0
\(843\) 37.2377 1.28254
\(844\) 0 0
\(845\) 2.15215 0.0740362
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −12.8231 −0.440089
\(850\) 0 0
\(851\) 11.2488 0.385602
\(852\) 0 0
\(853\) −6.37920 −0.218420 −0.109210 0.994019i \(-0.534832\pi\)
−0.109210 + 0.994019i \(0.534832\pi\)
\(854\) 0 0
\(855\) −3.34236 −0.114306
\(856\) 0 0
\(857\) −29.0289 −0.991609 −0.495805 0.868434i \(-0.665127\pi\)
−0.495805 + 0.868434i \(0.665127\pi\)
\(858\) 0 0
\(859\) −32.9712 −1.12496 −0.562482 0.826810i \(-0.690153\pi\)
−0.562482 + 0.826810i \(0.690153\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 28.6959 0.976818 0.488409 0.872615i \(-0.337577\pi\)
0.488409 + 0.872615i \(0.337577\pi\)
\(864\) 0 0
\(865\) 0.990773 0.0336873
\(866\) 0 0
\(867\) 25.3165 0.859794
\(868\) 0 0
\(869\) 27.2267 0.923601
\(870\) 0 0
\(871\) 5.50250 0.186445
\(872\) 0 0
\(873\) −6.33849 −0.214526
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 15.8596 0.535540 0.267770 0.963483i \(-0.413713\pi\)
0.267770 + 0.963483i \(0.413713\pi\)
\(878\) 0 0
\(879\) −44.8353 −1.51226
\(880\) 0 0
\(881\) 11.0864 0.373511 0.186755 0.982406i \(-0.440203\pi\)
0.186755 + 0.982406i \(0.440203\pi\)
\(882\) 0 0
\(883\) 38.3939 1.29206 0.646029 0.763313i \(-0.276429\pi\)
0.646029 + 0.763313i \(0.276429\pi\)
\(884\) 0 0
\(885\) −6.05668 −0.203593
\(886\) 0 0
\(887\) 11.8483 0.397827 0.198914 0.980017i \(-0.436259\pi\)
0.198914 + 0.980017i \(0.436259\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −22.5579 −0.755717
\(892\) 0 0
\(893\) −4.76756 −0.159540
\(894\) 0 0
\(895\) −26.9054 −0.899347
\(896\) 0 0
\(897\) −27.1460 −0.906380
\(898\) 0 0
\(899\) −69.6236 −2.32208
\(900\) 0 0
\(901\) 27.7857 0.925677
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.42800 0.113950
\(906\) 0 0
\(907\) 29.6864 0.985720 0.492860 0.870109i \(-0.335951\pi\)
0.492860 + 0.870109i \(0.335951\pi\)
\(908\) 0 0
\(909\) −17.5009 −0.580467
\(910\) 0 0
\(911\) −20.5983 −0.682452 −0.341226 0.939981i \(-0.610842\pi\)
−0.341226 + 0.939981i \(0.610842\pi\)
\(912\) 0 0
\(913\) −14.0305 −0.464341
\(914\) 0 0
\(915\) −43.4853 −1.43758
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −27.4117 −0.904228 −0.452114 0.891960i \(-0.649330\pi\)
−0.452114 + 0.891960i \(0.649330\pi\)
\(920\) 0 0
\(921\) 14.8256 0.488519
\(922\) 0 0
\(923\) −9.40989 −0.309730
\(924\) 0 0
\(925\) −9.87028 −0.324533
\(926\) 0 0
\(927\) −13.8336 −0.454355
\(928\) 0 0
\(929\) 17.3485 0.569187 0.284594 0.958648i \(-0.408141\pi\)
0.284594 + 0.958648i \(0.408141\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.380482 −0.0124564
\(934\) 0 0
\(935\) −7.69129 −0.251532
\(936\) 0 0
\(937\) 41.6883 1.36190 0.680948 0.732332i \(-0.261568\pi\)
0.680948 + 0.732332i \(0.261568\pi\)
\(938\) 0 0
\(939\) 3.78779 0.123610
\(940\) 0 0
\(941\) −17.2816 −0.563363 −0.281681 0.959508i \(-0.590892\pi\)
−0.281681 + 0.959508i \(0.590892\pi\)
\(942\) 0 0
\(943\) 2.72956 0.0888867
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 37.3014 1.21213 0.606066 0.795414i \(-0.292747\pi\)
0.606066 + 0.795414i \(0.292747\pi\)
\(948\) 0 0
\(949\) −3.95363 −0.128340
\(950\) 0 0
\(951\) −3.77919 −0.122549
\(952\) 0 0
\(953\) −42.4534 −1.37520 −0.687600 0.726089i \(-0.741336\pi\)
−0.687600 + 0.726089i \(0.741336\pi\)
\(954\) 0 0
\(955\) 18.8924 0.611344
\(956\) 0 0
\(957\) 38.4680 1.24349
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 44.7198 1.44257
\(962\) 0 0
\(963\) 7.94782 0.256115
\(964\) 0 0
\(965\) −6.52166 −0.209940
\(966\) 0 0
\(967\) −29.1861 −0.938561 −0.469280 0.883049i \(-0.655487\pi\)
−0.469280 + 0.883049i \(0.655487\pi\)
\(968\) 0 0
\(969\) −5.56358 −0.178728
\(970\) 0 0
\(971\) 47.6945 1.53059 0.765294 0.643680i \(-0.222593\pi\)
0.765294 + 0.643680i \(0.222593\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 23.8194 0.762832
\(976\) 0 0
\(977\) 9.91351 0.317161 0.158581 0.987346i \(-0.449308\pi\)
0.158581 + 0.987346i \(0.449308\pi\)
\(978\) 0 0
\(979\) 24.2248 0.774227
\(980\) 0 0
\(981\) −6.89525 −0.220149
\(982\) 0 0
\(983\) 16.9219 0.539725 0.269863 0.962899i \(-0.413022\pi\)
0.269863 + 0.962899i \(0.413022\pi\)
\(984\) 0 0
\(985\) −28.4940 −0.907894
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 18.4172 0.585634
\(990\) 0 0
\(991\) −61.6939 −1.95977 −0.979886 0.199558i \(-0.936049\pi\)
−0.979886 + 0.199558i \(0.936049\pi\)
\(992\) 0 0
\(993\) 64.2090 2.03761
\(994\) 0 0
\(995\) 3.12466 0.0990583
\(996\) 0 0
\(997\) 43.4308 1.37547 0.687733 0.725964i \(-0.258606\pi\)
0.687733 + 0.725964i \(0.258606\pi\)
\(998\) 0 0
\(999\) 6.37618 0.201733
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 7448.2.a.bn.1.1 yes 6
7.6 odd 2 7448.2.a.bm.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7448.2.a.bm.1.6 6 7.6 odd 2
7448.2.a.bn.1.1 yes 6 1.1 even 1 trivial