Properties

Label 7623.2.a.cm.1.1
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.7488.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2541)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.326909\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.05896 q^{2} +2.23931 q^{4} +1.05896 q^{5} -1.00000 q^{7} -0.492737 q^{8} +O(q^{10})\) \(q-2.05896 q^{2} +2.23931 q^{4} +1.05896 q^{5} -1.00000 q^{7} -0.492737 q^{8} -2.18035 q^{10} +3.80554 q^{13} +2.05896 q^{14} -3.46410 q^{16} +2.56622 q^{17} -0.180354 q^{19} +2.37134 q^{20} -0.433778 q^{23} -3.87861 q^{25} -7.83544 q^{26} -2.23931 q^{28} +9.03032 q^{29} -0.492737 q^{31} +8.11792 q^{32} -5.28375 q^{34} -1.05896 q^{35} -0.775212 q^{37} +0.371342 q^{38} -0.521789 q^{40} +3.09276 q^{41} -1.61413 q^{43} +0.893131 q^{46} -0.502098 q^{47} +1.00000 q^{49} +7.98589 q^{50} +8.52179 q^{52} +9.94273 q^{53} +0.492737 q^{56} -18.5931 q^{58} -13.4513 q^{59} +5.93756 q^{61} +1.01453 q^{62} -9.78626 q^{64} +4.02991 q^{65} -14.4068 q^{67} +5.74658 q^{68} +2.18035 q^{70} +12.4990 q^{71} -4.27383 q^{73} +1.59613 q^{74} -0.403870 q^{76} +1.37176 q^{79} -3.66834 q^{80} -6.36787 q^{82} +7.47346 q^{83} +2.71753 q^{85} +3.32343 q^{86} +16.1341 q^{89} -3.80554 q^{91} -0.971364 q^{92} +1.03380 q^{94} -0.190988 q^{95} +14.6158 q^{97} -2.05896 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 4q^{4} - 6q^{5} - 4q^{7} + O(q^{10}) \) \( 4q + 2q^{2} + 4q^{4} - 6q^{5} - 4q^{7} - 14q^{10} + 2q^{13} - 2q^{14} + 2q^{17} - 6q^{19} - 8q^{20} - 10q^{23} - 4q^{28} + 14q^{29} + 12q^{32} - 2q^{34} + 6q^{35} - 12q^{37} - 16q^{38} - 8q^{40} + 16q^{41} - 20q^{43} - 8q^{46} - 2q^{47} + 4q^{49} + 24q^{50} + 40q^{52} + 16q^{53} - 8q^{58} - 2q^{59} - 2q^{61} + 8q^{62} - 16q^{64} - 2q^{65} - 20q^{67} + 20q^{68} + 14q^{70} + 10q^{71} + 10q^{73} - 20q^{74} - 28q^{76} - 16q^{79} - 12q^{80} + 28q^{82} + 18q^{83} - 26q^{86} + 14q^{89} - 2q^{91} + 8q^{92} + 18q^{94} + 22q^{95} + 38q^{97} + 2q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05896 −1.45590 −0.727952 0.685628i \(-0.759528\pi\)
−0.727952 + 0.685628i \(0.759528\pi\)
\(3\) 0 0
\(4\) 2.23931 1.11966
\(5\) 1.05896 0.473581 0.236791 0.971561i \(-0.423904\pi\)
0.236791 + 0.971561i \(0.423904\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −0.492737 −0.174209
\(9\) 0 0
\(10\) −2.18035 −0.689489
\(11\) 0 0
\(12\) 0 0
\(13\) 3.80554 1.05547 0.527733 0.849410i \(-0.323042\pi\)
0.527733 + 0.849410i \(0.323042\pi\)
\(14\) 2.05896 0.550280
\(15\) 0 0
\(16\) −3.46410 −0.866025
\(17\) 2.56622 0.622400 0.311200 0.950344i \(-0.399269\pi\)
0.311200 + 0.950344i \(0.399269\pi\)
\(18\) 0 0
\(19\) −0.180354 −0.0413761 −0.0206881 0.999786i \(-0.506586\pi\)
−0.0206881 + 0.999786i \(0.506586\pi\)
\(20\) 2.37134 0.530248
\(21\) 0 0
\(22\) 0 0
\(23\) −0.433778 −0.0904489 −0.0452245 0.998977i \(-0.514400\pi\)
−0.0452245 + 0.998977i \(0.514400\pi\)
\(24\) 0 0
\(25\) −3.87861 −0.775721
\(26\) −7.83544 −1.53666
\(27\) 0 0
\(28\) −2.23931 −0.423191
\(29\) 9.03032 1.67689 0.838445 0.544987i \(-0.183465\pi\)
0.838445 + 0.544987i \(0.183465\pi\)
\(30\) 0 0
\(31\) −0.492737 −0.0884982 −0.0442491 0.999021i \(-0.514090\pi\)
−0.0442491 + 0.999021i \(0.514090\pi\)
\(32\) 8.11792 1.43506
\(33\) 0 0
\(34\) −5.28375 −0.906155
\(35\) −1.05896 −0.178997
\(36\) 0 0
\(37\) −0.775212 −0.127444 −0.0637220 0.997968i \(-0.520297\pi\)
−0.0637220 + 0.997968i \(0.520297\pi\)
\(38\) 0.371342 0.0602397
\(39\) 0 0
\(40\) −0.521789 −0.0825020
\(41\) 3.09276 0.483008 0.241504 0.970400i \(-0.422359\pi\)
0.241504 + 0.970400i \(0.422359\pi\)
\(42\) 0 0
\(43\) −1.61413 −0.246153 −0.123076 0.992397i \(-0.539276\pi\)
−0.123076 + 0.992397i \(0.539276\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.893131 0.131685
\(47\) −0.502098 −0.0732386 −0.0366193 0.999329i \(-0.511659\pi\)
−0.0366193 + 0.999329i \(0.511659\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 7.98589 1.12938
\(51\) 0 0
\(52\) 8.52179 1.18176
\(53\) 9.94273 1.36574 0.682869 0.730540i \(-0.260732\pi\)
0.682869 + 0.730540i \(0.260732\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.492737 0.0658448
\(57\) 0 0
\(58\) −18.5931 −2.44139
\(59\) −13.4513 −1.75121 −0.875603 0.483032i \(-0.839535\pi\)
−0.875603 + 0.483032i \(0.839535\pi\)
\(60\) 0 0
\(61\) 5.93756 0.760227 0.380114 0.924940i \(-0.375885\pi\)
0.380114 + 0.924940i \(0.375885\pi\)
\(62\) 1.01453 0.128845
\(63\) 0 0
\(64\) −9.78626 −1.22328
\(65\) 4.02991 0.499849
\(66\) 0 0
\(67\) −14.4068 −1.76007 −0.880037 0.474905i \(-0.842483\pi\)
−0.880037 + 0.474905i \(0.842483\pi\)
\(68\) 5.74658 0.696875
\(69\) 0 0
\(70\) 2.18035 0.260602
\(71\) 12.4990 1.48336 0.741681 0.670752i \(-0.234029\pi\)
0.741681 + 0.670752i \(0.234029\pi\)
\(72\) 0 0
\(73\) −4.27383 −0.500214 −0.250107 0.968218i \(-0.580466\pi\)
−0.250107 + 0.968218i \(0.580466\pi\)
\(74\) 1.59613 0.185546
\(75\) 0 0
\(76\) −0.403870 −0.0463271
\(77\) 0 0
\(78\) 0 0
\(79\) 1.37176 0.154335 0.0771674 0.997018i \(-0.475412\pi\)
0.0771674 + 0.997018i \(0.475412\pi\)
\(80\) −3.66834 −0.410133
\(81\) 0 0
\(82\) −6.36787 −0.703213
\(83\) 7.47346 0.820319 0.410160 0.912014i \(-0.365473\pi\)
0.410160 + 0.912014i \(0.365473\pi\)
\(84\) 0 0
\(85\) 2.71753 0.294757
\(86\) 3.32343 0.358375
\(87\) 0 0
\(88\) 0 0
\(89\) 16.1341 1.71021 0.855107 0.518451i \(-0.173491\pi\)
0.855107 + 0.518451i \(0.173491\pi\)
\(90\) 0 0
\(91\) −3.80554 −0.398929
\(92\) −0.971364 −0.101272
\(93\) 0 0
\(94\) 1.03380 0.106628
\(95\) −0.190988 −0.0195949
\(96\) 0 0
\(97\) 14.6158 1.48401 0.742006 0.670393i \(-0.233875\pi\)
0.742006 + 0.670393i \(0.233875\pi\)
\(98\) −2.05896 −0.207986
\(99\) 0 0
\(100\) −8.68541 −0.868541
\(101\) 6.10856 0.607824 0.303912 0.952700i \(-0.401707\pi\)
0.303912 + 0.952700i \(0.401707\pi\)
\(102\) 0 0
\(103\) −9.56275 −0.942245 −0.471123 0.882068i \(-0.656151\pi\)
−0.471123 + 0.882068i \(0.656151\pi\)
\(104\) −1.87513 −0.183872
\(105\) 0 0
\(106\) −20.4717 −1.98838
\(107\) 4.59486 0.444202 0.222101 0.975024i \(-0.428709\pi\)
0.222101 + 0.975024i \(0.428709\pi\)
\(108\) 0 0
\(109\) −1.99009 −0.190616 −0.0953079 0.995448i \(-0.530384\pi\)
−0.0953079 + 0.995448i \(0.530384\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 3.46410 0.327327
\(113\) −8.61527 −0.810456 −0.405228 0.914216i \(-0.632808\pi\)
−0.405228 + 0.914216i \(0.632808\pi\)
\(114\) 0 0
\(115\) −0.459353 −0.0428349
\(116\) 20.2217 1.87754
\(117\) 0 0
\(118\) 27.6956 2.54959
\(119\) −2.56622 −0.235245
\(120\) 0 0
\(121\) 0 0
\(122\) −12.2252 −1.10682
\(123\) 0 0
\(124\) −1.10339 −0.0990876
\(125\) −9.40208 −0.840948
\(126\) 0 0
\(127\) 19.1294 1.69746 0.848729 0.528828i \(-0.177368\pi\)
0.848729 + 0.528828i \(0.177368\pi\)
\(128\) 3.91368 0.345923
\(129\) 0 0
\(130\) −8.29742 −0.727732
\(131\) −6.91998 −0.604601 −0.302301 0.953213i \(-0.597755\pi\)
−0.302301 + 0.953213i \(0.597755\pi\)
\(132\) 0 0
\(133\) 0.180354 0.0156387
\(134\) 29.6631 2.56250
\(135\) 0 0
\(136\) −1.26447 −0.108428
\(137\) −6.81197 −0.581986 −0.290993 0.956725i \(-0.593986\pi\)
−0.290993 + 0.956725i \(0.593986\pi\)
\(138\) 0 0
\(139\) −19.6013 −1.66256 −0.831280 0.555854i \(-0.812391\pi\)
−0.831280 + 0.555854i \(0.812391\pi\)
\(140\) −2.37134 −0.200415
\(141\) 0 0
\(142\) −25.7350 −2.15963
\(143\) 0 0
\(144\) 0 0
\(145\) 9.56275 0.794143
\(146\) 8.79965 0.728264
\(147\) 0 0
\(148\) −1.73594 −0.142694
\(149\) −8.18721 −0.670722 −0.335361 0.942090i \(-0.608858\pi\)
−0.335361 + 0.942090i \(0.608858\pi\)
\(150\) 0 0
\(151\) −17.1576 −1.39627 −0.698133 0.715968i \(-0.745986\pi\)
−0.698133 + 0.715968i \(0.745986\pi\)
\(152\) 0.0888673 0.00720809
\(153\) 0 0
\(154\) 0 0
\(155\) −0.521789 −0.0419111
\(156\) 0 0
\(157\) 5.02864 0.401329 0.200664 0.979660i \(-0.435690\pi\)
0.200664 + 0.979660i \(0.435690\pi\)
\(158\) −2.82439 −0.224697
\(159\) 0 0
\(160\) 8.59655 0.679617
\(161\) 0.433778 0.0341865
\(162\) 0 0
\(163\) 15.2469 1.19423 0.597114 0.802156i \(-0.296314\pi\)
0.597114 + 0.802156i \(0.296314\pi\)
\(164\) 6.92566 0.540803
\(165\) 0 0
\(166\) −15.3876 −1.19431
\(167\) −4.43072 −0.342859 −0.171430 0.985196i \(-0.554839\pi\)
−0.171430 + 0.985196i \(0.554839\pi\)
\(168\) 0 0
\(169\) 1.48210 0.114008
\(170\) −5.59527 −0.429138
\(171\) 0 0
\(172\) −3.61455 −0.275607
\(173\) 10.7124 0.814446 0.407223 0.913329i \(-0.366497\pi\)
0.407223 + 0.913329i \(0.366497\pi\)
\(174\) 0 0
\(175\) 3.87861 0.293195
\(176\) 0 0
\(177\) 0 0
\(178\) −33.2195 −2.48991
\(179\) −11.4546 −0.856157 −0.428079 0.903741i \(-0.640809\pi\)
−0.428079 + 0.903741i \(0.640809\pi\)
\(180\) 0 0
\(181\) 16.5252 1.22831 0.614153 0.789187i \(-0.289498\pi\)
0.614153 + 0.789187i \(0.289498\pi\)
\(182\) 7.83544 0.580802
\(183\) 0 0
\(184\) 0.213738 0.0157570
\(185\) −0.820918 −0.0603551
\(186\) 0 0
\(187\) 0 0
\(188\) −1.12436 −0.0820021
\(189\) 0 0
\(190\) 0.393236 0.0285284
\(191\) 2.19794 0.159037 0.0795187 0.996833i \(-0.474662\pi\)
0.0795187 + 0.996833i \(0.474662\pi\)
\(192\) 0 0
\(193\) 25.1481 1.81020 0.905100 0.425198i \(-0.139796\pi\)
0.905100 + 0.425198i \(0.139796\pi\)
\(194\) −30.0934 −2.16058
\(195\) 0 0
\(196\) 2.23931 0.159951
\(197\) −6.13203 −0.436889 −0.218444 0.975849i \(-0.570098\pi\)
−0.218444 + 0.975849i \(0.570098\pi\)
\(198\) 0 0
\(199\) 20.4956 1.45289 0.726446 0.687224i \(-0.241171\pi\)
0.726446 + 0.687224i \(0.241171\pi\)
\(200\) 1.91113 0.135137
\(201\) 0 0
\(202\) −12.5773 −0.884934
\(203\) −9.03032 −0.633804
\(204\) 0 0
\(205\) 3.27511 0.228743
\(206\) 19.6893 1.37182
\(207\) 0 0
\(208\) −13.1828 −0.914060
\(209\) 0 0
\(210\) 0 0
\(211\) −8.82942 −0.607843 −0.303921 0.952697i \(-0.598296\pi\)
−0.303921 + 0.952697i \(0.598296\pi\)
\(212\) 22.2649 1.52916
\(213\) 0 0
\(214\) −9.46063 −0.646715
\(215\) −1.70930 −0.116573
\(216\) 0 0
\(217\) 0.492737 0.0334492
\(218\) 4.09751 0.277518
\(219\) 0 0
\(220\) 0 0
\(221\) 9.76585 0.656922
\(222\) 0 0
\(223\) −20.6012 −1.37956 −0.689778 0.724021i \(-0.742292\pi\)
−0.689778 + 0.724021i \(0.742292\pi\)
\(224\) −8.11792 −0.542401
\(225\) 0 0
\(226\) 17.7385 1.17995
\(227\) 17.4349 1.15720 0.578598 0.815613i \(-0.303600\pi\)
0.578598 + 0.815613i \(0.303600\pi\)
\(228\) 0 0
\(229\) 23.4477 1.54946 0.774732 0.632289i \(-0.217885\pi\)
0.774732 + 0.632289i \(0.217885\pi\)
\(230\) 0.945789 0.0623635
\(231\) 0 0
\(232\) −4.44958 −0.292129
\(233\) −14.8692 −0.974117 −0.487058 0.873369i \(-0.661930\pi\)
−0.487058 + 0.873369i \(0.661930\pi\)
\(234\) 0 0
\(235\) −0.531702 −0.0346844
\(236\) −30.1216 −1.96075
\(237\) 0 0
\(238\) 5.28375 0.342494
\(239\) 22.5721 1.46007 0.730034 0.683411i \(-0.239504\pi\)
0.730034 + 0.683411i \(0.239504\pi\)
\(240\) 0 0
\(241\) −2.20245 −0.141872 −0.0709362 0.997481i \(-0.522599\pi\)
−0.0709362 + 0.997481i \(0.522599\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 13.2961 0.851194
\(245\) 1.05896 0.0676544
\(246\) 0 0
\(247\) −0.686345 −0.0436711
\(248\) 0.242790 0.0154172
\(249\) 0 0
\(250\) 19.3585 1.22434
\(251\) −7.39733 −0.466916 −0.233458 0.972367i \(-0.575004\pi\)
−0.233458 + 0.972367i \(0.575004\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −39.3866 −2.47134
\(255\) 0 0
\(256\) 11.5144 0.719651
\(257\) −6.29786 −0.392850 −0.196425 0.980519i \(-0.562933\pi\)
−0.196425 + 0.980519i \(0.562933\pi\)
\(258\) 0 0
\(259\) 0.775212 0.0481693
\(260\) 9.02423 0.559659
\(261\) 0 0
\(262\) 14.2480 0.880242
\(263\) 32.2131 1.98634 0.993172 0.116659i \(-0.0372185\pi\)
0.993172 + 0.116659i \(0.0372185\pi\)
\(264\) 0 0
\(265\) 10.5289 0.646788
\(266\) −0.371342 −0.0227685
\(267\) 0 0
\(268\) −32.2614 −1.97068
\(269\) −27.6136 −1.68363 −0.841816 0.539765i \(-0.818513\pi\)
−0.841816 + 0.539765i \(0.818513\pi\)
\(270\) 0 0
\(271\) 30.9678 1.88116 0.940580 0.339573i \(-0.110283\pi\)
0.940580 + 0.339573i \(0.110283\pi\)
\(272\) −8.88965 −0.539014
\(273\) 0 0
\(274\) 14.0256 0.847316
\(275\) 0 0
\(276\) 0 0
\(277\) −0.420940 −0.0252919 −0.0126459 0.999920i \(-0.504025\pi\)
−0.0126459 + 0.999920i \(0.504025\pi\)
\(278\) 40.3583 2.42053
\(279\) 0 0
\(280\) 0.521789 0.0311828
\(281\) 19.8996 1.18711 0.593554 0.804794i \(-0.297724\pi\)
0.593554 + 0.804794i \(0.297724\pi\)
\(282\) 0 0
\(283\) −24.3641 −1.44829 −0.724147 0.689645i \(-0.757766\pi\)
−0.724147 + 0.689645i \(0.757766\pi\)
\(284\) 27.9893 1.66086
\(285\) 0 0
\(286\) 0 0
\(287\) −3.09276 −0.182560
\(288\) 0 0
\(289\) −10.4145 −0.612618
\(290\) −19.6893 −1.15620
\(291\) 0 0
\(292\) −9.57046 −0.560069
\(293\) −17.4662 −1.02039 −0.510193 0.860060i \(-0.670426\pi\)
−0.510193 + 0.860060i \(0.670426\pi\)
\(294\) 0 0
\(295\) −14.2443 −0.829338
\(296\) 0.381976 0.0222019
\(297\) 0 0
\(298\) 16.8571 0.976507
\(299\) −1.65076 −0.0954657
\(300\) 0 0
\(301\) 1.61413 0.0930370
\(302\) 35.3268 2.03283
\(303\) 0 0
\(304\) 0.624766 0.0358328
\(305\) 6.28764 0.360029
\(306\) 0 0
\(307\) −10.9239 −0.623458 −0.311729 0.950171i \(-0.600908\pi\)
−0.311729 + 0.950171i \(0.600908\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.07434 0.0610185
\(311\) −3.51662 −0.199409 −0.0997047 0.995017i \(-0.531790\pi\)
−0.0997047 + 0.995017i \(0.531790\pi\)
\(312\) 0 0
\(313\) 25.9789 1.46842 0.734208 0.678924i \(-0.237554\pi\)
0.734208 + 0.678924i \(0.237554\pi\)
\(314\) −10.3538 −0.584296
\(315\) 0 0
\(316\) 3.07180 0.172802
\(317\) 3.72269 0.209087 0.104544 0.994520i \(-0.466662\pi\)
0.104544 + 0.994520i \(0.466662\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −10.3633 −0.579323
\(321\) 0 0
\(322\) −0.893131 −0.0497722
\(323\) −0.462829 −0.0257525
\(324\) 0 0
\(325\) −14.7602 −0.818747
\(326\) −31.3927 −1.73868
\(327\) 0 0
\(328\) −1.52392 −0.0841443
\(329\) 0.502098 0.0276816
\(330\) 0 0
\(331\) 17.7683 0.976632 0.488316 0.872667i \(-0.337611\pi\)
0.488316 + 0.872667i \(0.337611\pi\)
\(332\) 16.7354 0.918476
\(333\) 0 0
\(334\) 9.12267 0.499170
\(335\) −15.2562 −0.833538
\(336\) 0 0
\(337\) −26.1178 −1.42273 −0.711364 0.702824i \(-0.751922\pi\)
−0.711364 + 0.702824i \(0.751922\pi\)
\(338\) −3.05159 −0.165985
\(339\) 0 0
\(340\) 6.08539 0.330027
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0.795343 0.0428820
\(345\) 0 0
\(346\) −22.0563 −1.18575
\(347\) 0.794486 0.0426503 0.0213251 0.999773i \(-0.493211\pi\)
0.0213251 + 0.999773i \(0.493211\pi\)
\(348\) 0 0
\(349\) −11.7816 −0.630657 −0.315329 0.948983i \(-0.602115\pi\)
−0.315329 + 0.948983i \(0.602115\pi\)
\(350\) −7.98589 −0.426864
\(351\) 0 0
\(352\) 0 0
\(353\) −6.45041 −0.343321 −0.171660 0.985156i \(-0.554913\pi\)
−0.171660 + 0.985156i \(0.554913\pi\)
\(354\) 0 0
\(355\) 13.2360 0.702493
\(356\) 36.1294 1.91485
\(357\) 0 0
\(358\) 23.5846 1.24648
\(359\) 5.87916 0.310290 0.155145 0.987892i \(-0.450416\pi\)
0.155145 + 0.987892i \(0.450416\pi\)
\(360\) 0 0
\(361\) −18.9675 −0.998288
\(362\) −34.0246 −1.78830
\(363\) 0 0
\(364\) −8.52179 −0.446663
\(365\) −4.52582 −0.236892
\(366\) 0 0
\(367\) −29.3478 −1.53194 −0.765971 0.642876i \(-0.777741\pi\)
−0.765971 + 0.642876i \(0.777741\pi\)
\(368\) 1.50265 0.0783311
\(369\) 0 0
\(370\) 1.69024 0.0878712
\(371\) −9.94273 −0.516201
\(372\) 0 0
\(373\) 8.83207 0.457307 0.228654 0.973508i \(-0.426568\pi\)
0.228654 + 0.973508i \(0.426568\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.247402 0.0127588
\(377\) 34.3652 1.76990
\(378\) 0 0
\(379\) −11.7171 −0.601867 −0.300934 0.953645i \(-0.597298\pi\)
−0.300934 + 0.953645i \(0.597298\pi\)
\(380\) −0.427682 −0.0219396
\(381\) 0 0
\(382\) −4.52547 −0.231543
\(383\) −30.6516 −1.56622 −0.783112 0.621881i \(-0.786369\pi\)
−0.783112 + 0.621881i \(0.786369\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −51.7789 −2.63548
\(387\) 0 0
\(388\) 32.7294 1.66158
\(389\) 3.61107 0.183089 0.0915443 0.995801i \(-0.470820\pi\)
0.0915443 + 0.995801i \(0.470820\pi\)
\(390\) 0 0
\(391\) −1.11317 −0.0562954
\(392\) −0.492737 −0.0248870
\(393\) 0 0
\(394\) 12.6256 0.636068
\(395\) 1.45264 0.0730901
\(396\) 0 0
\(397\) 3.10339 0.155755 0.0778774 0.996963i \(-0.475186\pi\)
0.0778774 + 0.996963i \(0.475186\pi\)
\(398\) −42.1995 −2.11527
\(399\) 0 0
\(400\) 13.4359 0.671794
\(401\) −29.8141 −1.48884 −0.744422 0.667709i \(-0.767275\pi\)
−0.744422 + 0.667709i \(0.767275\pi\)
\(402\) 0 0
\(403\) −1.87513 −0.0934068
\(404\) 13.6790 0.680555
\(405\) 0 0
\(406\) 18.5931 0.922759
\(407\) 0 0
\(408\) 0 0
\(409\) −19.0348 −0.941212 −0.470606 0.882343i \(-0.655965\pi\)
−0.470606 + 0.882343i \(0.655965\pi\)
\(410\) −6.74331 −0.333028
\(411\) 0 0
\(412\) −21.4140 −1.05499
\(413\) 13.4513 0.661893
\(414\) 0 0
\(415\) 7.91409 0.388488
\(416\) 30.8930 1.51466
\(417\) 0 0
\(418\) 0 0
\(419\) −6.05476 −0.295795 −0.147897 0.989003i \(-0.547250\pi\)
−0.147897 + 0.989003i \(0.547250\pi\)
\(420\) 0 0
\(421\) 29.2007 1.42315 0.711577 0.702608i \(-0.247981\pi\)
0.711577 + 0.702608i \(0.247981\pi\)
\(422\) 18.1794 0.884960
\(423\) 0 0
\(424\) −4.89915 −0.237924
\(425\) −9.95336 −0.482809
\(426\) 0 0
\(427\) −5.93756 −0.287339
\(428\) 10.2893 0.497353
\(429\) 0 0
\(430\) 3.51938 0.169720
\(431\) 15.3401 0.738905 0.369452 0.929250i \(-0.379545\pi\)
0.369452 + 0.929250i \(0.379545\pi\)
\(432\) 0 0
\(433\) 4.47808 0.215203 0.107601 0.994194i \(-0.465683\pi\)
0.107601 + 0.994194i \(0.465683\pi\)
\(434\) −1.01453 −0.0486988
\(435\) 0 0
\(436\) −4.45643 −0.213424
\(437\) 0.0782337 0.00374242
\(438\) 0 0
\(439\) −26.4717 −1.26342 −0.631712 0.775203i \(-0.717647\pi\)
−0.631712 + 0.775203i \(0.717647\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −20.1075 −0.956416
\(443\) 3.86545 0.183653 0.0918266 0.995775i \(-0.470729\pi\)
0.0918266 + 0.995775i \(0.470729\pi\)
\(444\) 0 0
\(445\) 17.0854 0.809925
\(446\) 42.4169 2.00850
\(447\) 0 0
\(448\) 9.78626 0.462357
\(449\) 7.26530 0.342871 0.171435 0.985195i \(-0.445159\pi\)
0.171435 + 0.985195i \(0.445159\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −19.2923 −0.907433
\(453\) 0 0
\(454\) −35.8978 −1.68477
\(455\) −4.02991 −0.188925
\(456\) 0 0
\(457\) 25.7449 1.20430 0.602148 0.798384i \(-0.294312\pi\)
0.602148 + 0.798384i \(0.294312\pi\)
\(458\) −48.2778 −2.25587
\(459\) 0 0
\(460\) −1.02864 −0.0479604
\(461\) 22.9619 1.06944 0.534721 0.845029i \(-0.320417\pi\)
0.534721 + 0.845029i \(0.320417\pi\)
\(462\) 0 0
\(463\) 4.68972 0.217950 0.108975 0.994044i \(-0.465243\pi\)
0.108975 + 0.994044i \(0.465243\pi\)
\(464\) −31.2820 −1.45223
\(465\) 0 0
\(466\) 30.6152 1.41822
\(467\) 32.8849 1.52173 0.760867 0.648908i \(-0.224774\pi\)
0.760867 + 0.648908i \(0.224774\pi\)
\(468\) 0 0
\(469\) 14.4068 0.665246
\(470\) 1.09475 0.0504972
\(471\) 0 0
\(472\) 6.62794 0.305076
\(473\) 0 0
\(474\) 0 0
\(475\) 0.699523 0.0320963
\(476\) −5.74658 −0.263394
\(477\) 0 0
\(478\) −46.4751 −2.12572
\(479\) 10.3796 0.474255 0.237127 0.971479i \(-0.423794\pi\)
0.237127 + 0.971479i \(0.423794\pi\)
\(480\) 0 0
\(481\) −2.95010 −0.134513
\(482\) 4.53476 0.206553
\(483\) 0 0
\(484\) 0 0
\(485\) 15.4776 0.702800
\(486\) 0 0
\(487\) 28.4384 1.28867 0.644334 0.764744i \(-0.277135\pi\)
0.644334 + 0.764744i \(0.277135\pi\)
\(488\) −2.92566 −0.132438
\(489\) 0 0
\(490\) −2.18035 −0.0984984
\(491\) 30.9474 1.39664 0.698318 0.715788i \(-0.253932\pi\)
0.698318 + 0.715788i \(0.253932\pi\)
\(492\) 0 0
\(493\) 23.1738 1.04370
\(494\) 1.41316 0.0635809
\(495\) 0 0
\(496\) 1.70689 0.0766417
\(497\) −12.4990 −0.560658
\(498\) 0 0
\(499\) −34.2751 −1.53436 −0.767182 0.641429i \(-0.778342\pi\)
−0.767182 + 0.641429i \(0.778342\pi\)
\(500\) −21.0542 −0.941573
\(501\) 0 0
\(502\) 15.2308 0.679784
\(503\) 13.0742 0.582950 0.291475 0.956578i \(-0.405854\pi\)
0.291475 + 0.956578i \(0.405854\pi\)
\(504\) 0 0
\(505\) 6.46871 0.287854
\(506\) 0 0
\(507\) 0 0
\(508\) 42.8367 1.90057
\(509\) 32.5765 1.44393 0.721963 0.691932i \(-0.243240\pi\)
0.721963 + 0.691932i \(0.243240\pi\)
\(510\) 0 0
\(511\) 4.27383 0.189063
\(512\) −31.5351 −1.39367
\(513\) 0 0
\(514\) 12.9670 0.571951
\(515\) −10.1266 −0.446230
\(516\) 0 0
\(517\) 0 0
\(518\) −1.59613 −0.0701299
\(519\) 0 0
\(520\) −1.98569 −0.0870781
\(521\) −11.0109 −0.482397 −0.241198 0.970476i \(-0.577540\pi\)
−0.241198 + 0.970476i \(0.577540\pi\)
\(522\) 0 0
\(523\) −9.20204 −0.402377 −0.201189 0.979553i \(-0.564480\pi\)
−0.201189 + 0.979553i \(0.564480\pi\)
\(524\) −15.4960 −0.676946
\(525\) 0 0
\(526\) −66.3254 −2.89193
\(527\) −1.26447 −0.0550813
\(528\) 0 0
\(529\) −22.8118 −0.991819
\(530\) −21.6787 −0.941661
\(531\) 0 0
\(532\) 0.403870 0.0175100
\(533\) 11.7696 0.509798
\(534\) 0 0
\(535\) 4.86577 0.210365
\(536\) 7.09878 0.306621
\(537\) 0 0
\(538\) 56.8553 2.45121
\(539\) 0 0
\(540\) 0 0
\(541\) −9.28585 −0.399230 −0.199615 0.979874i \(-0.563969\pi\)
−0.199615 + 0.979874i \(0.563969\pi\)
\(542\) −63.7614 −2.73879
\(543\) 0 0
\(544\) 20.8324 0.893181
\(545\) −2.10742 −0.0902720
\(546\) 0 0
\(547\) −5.40335 −0.231031 −0.115515 0.993306i \(-0.536852\pi\)
−0.115515 + 0.993306i \(0.536852\pi\)
\(548\) −15.2541 −0.651625
\(549\) 0 0
\(550\) 0 0
\(551\) −1.62866 −0.0693832
\(552\) 0 0
\(553\) −1.37176 −0.0583331
\(554\) 0.866699 0.0368225
\(555\) 0 0
\(556\) −43.8934 −1.86150
\(557\) 23.3870 0.990939 0.495470 0.868625i \(-0.334996\pi\)
0.495470 + 0.868625i \(0.334996\pi\)
\(558\) 0 0
\(559\) −6.14264 −0.259806
\(560\) 3.66834 0.155016
\(561\) 0 0
\(562\) −40.9724 −1.72832
\(563\) −24.5311 −1.03386 −0.516930 0.856028i \(-0.672925\pi\)
−0.516930 + 0.856028i \(0.672925\pi\)
\(564\) 0 0
\(565\) −9.12322 −0.383817
\(566\) 50.1647 2.10858
\(567\) 0 0
\(568\) −6.15874 −0.258415
\(569\) −39.4165 −1.65243 −0.826213 0.563358i \(-0.809509\pi\)
−0.826213 + 0.563358i \(0.809509\pi\)
\(570\) 0 0
\(571\) 41.0006 1.71582 0.857911 0.513798i \(-0.171762\pi\)
0.857911 + 0.513798i \(0.171762\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 6.36787 0.265790
\(575\) 1.68245 0.0701631
\(576\) 0 0
\(577\) −44.1963 −1.83992 −0.919959 0.392015i \(-0.871778\pi\)
−0.919959 + 0.392015i \(0.871778\pi\)
\(578\) 21.4430 0.891913
\(579\) 0 0
\(580\) 21.4140 0.889167
\(581\) −7.47346 −0.310051
\(582\) 0 0
\(583\) 0 0
\(584\) 2.10588 0.0871418
\(585\) 0 0
\(586\) 35.9622 1.48559
\(587\) 2.75552 0.113733 0.0568663 0.998382i \(-0.481889\pi\)
0.0568663 + 0.998382i \(0.481889\pi\)
\(588\) 0 0
\(589\) 0.0888673 0.00366171
\(590\) 29.3285 1.20744
\(591\) 0 0
\(592\) 2.68541 0.110370
\(593\) −30.8619 −1.26735 −0.633673 0.773601i \(-0.718453\pi\)
−0.633673 + 0.773601i \(0.718453\pi\)
\(594\) 0 0
\(595\) −2.71753 −0.111408
\(596\) −18.3337 −0.750979
\(597\) 0 0
\(598\) 3.39884 0.138989
\(599\) 13.3297 0.544638 0.272319 0.962207i \(-0.412209\pi\)
0.272319 + 0.962207i \(0.412209\pi\)
\(600\) 0 0
\(601\) 16.4395 0.670582 0.335291 0.942115i \(-0.391165\pi\)
0.335291 + 0.942115i \(0.391165\pi\)
\(602\) −3.32343 −0.135453
\(603\) 0 0
\(604\) −38.4213 −1.56334
\(605\) 0 0
\(606\) 0 0
\(607\) 24.2669 0.984962 0.492481 0.870323i \(-0.336090\pi\)
0.492481 + 0.870323i \(0.336090\pi\)
\(608\) −1.46410 −0.0593772
\(609\) 0 0
\(610\) −12.9460 −0.524168
\(611\) −1.91075 −0.0773008
\(612\) 0 0
\(613\) 24.5773 0.992668 0.496334 0.868132i \(-0.334679\pi\)
0.496334 + 0.868132i \(0.334679\pi\)
\(614\) 22.4918 0.907695
\(615\) 0 0
\(616\) 0 0
\(617\) 15.4094 0.620358 0.310179 0.950678i \(-0.399611\pi\)
0.310179 + 0.950678i \(0.399611\pi\)
\(618\) 0 0
\(619\) 35.6568 1.43317 0.716583 0.697501i \(-0.245705\pi\)
0.716583 + 0.697501i \(0.245705\pi\)
\(620\) −1.16845 −0.0469260
\(621\) 0 0
\(622\) 7.24059 0.290321
\(623\) −16.1341 −0.646400
\(624\) 0 0
\(625\) 9.43660 0.377464
\(626\) −53.4896 −2.13787
\(627\) 0 0
\(628\) 11.2607 0.449351
\(629\) −1.98937 −0.0793212
\(630\) 0 0
\(631\) 11.6305 0.463003 0.231502 0.972834i \(-0.425636\pi\)
0.231502 + 0.972834i \(0.425636\pi\)
\(632\) −0.675916 −0.0268865
\(633\) 0 0
\(634\) −7.66487 −0.304411
\(635\) 20.2572 0.803884
\(636\) 0 0
\(637\) 3.80554 0.150781
\(638\) 0 0
\(639\) 0 0
\(640\) 4.14443 0.163823
\(641\) −36.8237 −1.45445 −0.727225 0.686399i \(-0.759190\pi\)
−0.727225 + 0.686399i \(0.759190\pi\)
\(642\) 0 0
\(643\) 48.4049 1.90890 0.954452 0.298366i \(-0.0964415\pi\)
0.954452 + 0.298366i \(0.0964415\pi\)
\(644\) 0.971364 0.0382771
\(645\) 0 0
\(646\) 0.952947 0.0374932
\(647\) 26.2987 1.03391 0.516954 0.856013i \(-0.327066\pi\)
0.516954 + 0.856013i \(0.327066\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 30.3906 1.19202
\(651\) 0 0
\(652\) 34.1426 1.33713
\(653\) 23.9772 0.938302 0.469151 0.883118i \(-0.344560\pi\)
0.469151 + 0.883118i \(0.344560\pi\)
\(654\) 0 0
\(655\) −7.32798 −0.286328
\(656\) −10.7136 −0.418297
\(657\) 0 0
\(658\) −1.03380 −0.0403017
\(659\) 5.02206 0.195632 0.0978159 0.995205i \(-0.468814\pi\)
0.0978159 + 0.995205i \(0.468814\pi\)
\(660\) 0 0
\(661\) −13.2645 −0.515928 −0.257964 0.966155i \(-0.583052\pi\)
−0.257964 + 0.966155i \(0.583052\pi\)
\(662\) −36.5841 −1.42188
\(663\) 0 0
\(664\) −3.68245 −0.142907
\(665\) 0.190988 0.00740619
\(666\) 0 0
\(667\) −3.91715 −0.151673
\(668\) −9.92177 −0.383885
\(669\) 0 0
\(670\) 31.4120 1.21355
\(671\) 0 0
\(672\) 0 0
\(673\) 36.2097 1.39578 0.697892 0.716203i \(-0.254122\pi\)
0.697892 + 0.716203i \(0.254122\pi\)
\(674\) 53.7755 2.07136
\(675\) 0 0
\(676\) 3.31889 0.127650
\(677\) −8.90851 −0.342382 −0.171191 0.985238i \(-0.554762\pi\)
−0.171191 + 0.985238i \(0.554762\pi\)
\(678\) 0 0
\(679\) −14.6158 −0.560904
\(680\) −1.33903 −0.0513493
\(681\) 0 0
\(682\) 0 0
\(683\) 23.2377 0.889166 0.444583 0.895738i \(-0.353352\pi\)
0.444583 + 0.895738i \(0.353352\pi\)
\(684\) 0 0
\(685\) −7.21360 −0.275618
\(686\) 2.05896 0.0786114
\(687\) 0 0
\(688\) 5.59152 0.213175
\(689\) 37.8374 1.44149
\(690\) 0 0
\(691\) 29.2034 1.11095 0.555475 0.831533i \(-0.312536\pi\)
0.555475 + 0.831533i \(0.312536\pi\)
\(692\) 23.9883 0.911900
\(693\) 0 0
\(694\) −1.63582 −0.0620947
\(695\) −20.7570 −0.787357
\(696\) 0 0
\(697\) 7.93671 0.300624
\(698\) 24.2579 0.918176
\(699\) 0 0
\(700\) 8.68541 0.328278
\(701\) 45.7062 1.72630 0.863150 0.504947i \(-0.168488\pi\)
0.863150 + 0.504947i \(0.168488\pi\)
\(702\) 0 0
\(703\) 0.139813 0.00527314
\(704\) 0 0
\(705\) 0 0
\(706\) 13.2811 0.499842
\(707\) −6.10856 −0.229736
\(708\) 0 0
\(709\) −5.12487 −0.192469 −0.0962343 0.995359i \(-0.530680\pi\)
−0.0962343 + 0.995359i \(0.530680\pi\)
\(710\) −27.2523 −1.02276
\(711\) 0 0
\(712\) −7.94989 −0.297935
\(713\) 0.213738 0.00800457
\(714\) 0 0
\(715\) 0 0
\(716\) −25.6505 −0.958602
\(717\) 0 0
\(718\) −12.1049 −0.451753
\(719\) −2.68899 −0.100282 −0.0501412 0.998742i \(-0.515967\pi\)
−0.0501412 + 0.998742i \(0.515967\pi\)
\(720\) 0 0
\(721\) 9.56275 0.356135
\(722\) 39.0533 1.45341
\(723\) 0 0
\(724\) 37.0050 1.37528
\(725\) −35.0251 −1.30080
\(726\) 0 0
\(727\) 1.17656 0.0436363 0.0218181 0.999762i \(-0.493055\pi\)
0.0218181 + 0.999762i \(0.493055\pi\)
\(728\) 1.87513 0.0694969
\(729\) 0 0
\(730\) 9.31847 0.344892
\(731\) −4.14222 −0.153206
\(732\) 0 0
\(733\) 16.2128 0.598833 0.299416 0.954123i \(-0.403208\pi\)
0.299416 + 0.954123i \(0.403208\pi\)
\(734\) 60.4259 2.23036
\(735\) 0 0
\(736\) −3.52137 −0.129800
\(737\) 0 0
\(738\) 0 0
\(739\) −37.2564 −1.37050 −0.685249 0.728309i \(-0.740307\pi\)
−0.685249 + 0.728309i \(0.740307\pi\)
\(740\) −1.83829 −0.0675770
\(741\) 0 0
\(742\) 20.4717 0.751539
\(743\) 31.9013 1.17034 0.585172 0.810909i \(-0.301027\pi\)
0.585172 + 0.810909i \(0.301027\pi\)
\(744\) 0 0
\(745\) −8.66992 −0.317641
\(746\) −18.1849 −0.665795
\(747\) 0 0
\(748\) 0 0
\(749\) −4.59486 −0.167892
\(750\) 0 0
\(751\) 22.2186 0.810767 0.405384 0.914147i \(-0.367138\pi\)
0.405384 + 0.914147i \(0.367138\pi\)
\(752\) 1.73932 0.0634265
\(753\) 0 0
\(754\) −70.7566 −2.57680
\(755\) −18.1692 −0.661245
\(756\) 0 0
\(757\) −38.8014 −1.41026 −0.705131 0.709077i \(-0.749112\pi\)
−0.705131 + 0.709077i \(0.749112\pi\)
\(758\) 24.1251 0.876261
\(759\) 0 0
\(760\) 0.0941068 0.00341361
\(761\) 49.4020 1.79082 0.895410 0.445242i \(-0.146882\pi\)
0.895410 + 0.445242i \(0.146882\pi\)
\(762\) 0 0
\(763\) 1.99009 0.0720460
\(764\) 4.92188 0.178067
\(765\) 0 0
\(766\) 63.1104 2.28027
\(767\) −51.1893 −1.84834
\(768\) 0 0
\(769\) 16.2939 0.587575 0.293787 0.955871i \(-0.405084\pi\)
0.293787 + 0.955871i \(0.405084\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 56.3145 2.02680
\(773\) 47.5351 1.70972 0.854860 0.518858i \(-0.173643\pi\)
0.854860 + 0.518858i \(0.173643\pi\)
\(774\) 0 0
\(775\) 1.91113 0.0686499
\(776\) −7.20176 −0.258528
\(777\) 0 0
\(778\) −7.43505 −0.266559
\(779\) −0.557792 −0.0199850
\(780\) 0 0
\(781\) 0 0
\(782\) 2.29197 0.0819608
\(783\) 0 0
\(784\) −3.46410 −0.123718
\(785\) 5.32512 0.190062
\(786\) 0 0
\(787\) −46.8753 −1.67093 −0.835463 0.549547i \(-0.814800\pi\)
−0.835463 + 0.549547i \(0.814800\pi\)
\(788\) −13.7315 −0.489166
\(789\) 0 0
\(790\) −2.99092 −0.106412
\(791\) 8.61527 0.306324
\(792\) 0 0
\(793\) 22.5956 0.802394
\(794\) −6.38976 −0.226764
\(795\) 0 0
\(796\) 45.8960 1.62674
\(797\) 22.5463 0.798631 0.399315 0.916814i \(-0.369248\pi\)
0.399315 + 0.916814i \(0.369248\pi\)
\(798\) 0 0
\(799\) −1.28850 −0.0455837
\(800\) −31.4862 −1.11321
\(801\) 0 0
\(802\) 61.3860 2.16761
\(803\) 0 0
\(804\) 0 0
\(805\) 0.459353 0.0161901
\(806\) 3.86081 0.135991
\(807\) 0 0
\(808\) −3.00991 −0.105888
\(809\) 12.8111 0.450416 0.225208 0.974311i \(-0.427694\pi\)
0.225208 + 0.974311i \(0.427694\pi\)
\(810\) 0 0
\(811\) −4.65327 −0.163398 −0.0816991 0.996657i \(-0.526035\pi\)
−0.0816991 + 0.996657i \(0.526035\pi\)
\(812\) −20.2217 −0.709644
\(813\) 0 0
\(814\) 0 0
\(815\) 16.1458 0.565564
\(816\) 0 0
\(817\) 0.291116 0.0101848
\(818\) 39.1920 1.37031
\(819\) 0 0
\(820\) 7.33399 0.256114
\(821\) 45.9133 1.60238 0.801192 0.598407i \(-0.204199\pi\)
0.801192 + 0.598407i \(0.204199\pi\)
\(822\) 0 0
\(823\) 39.0742 1.36204 0.681021 0.732264i \(-0.261536\pi\)
0.681021 + 0.732264i \(0.261536\pi\)
\(824\) 4.71192 0.164148
\(825\) 0 0
\(826\) −27.6956 −0.963653
\(827\) 43.9735 1.52911 0.764554 0.644560i \(-0.222959\pi\)
0.764554 + 0.644560i \(0.222959\pi\)
\(828\) 0 0
\(829\) 16.9035 0.587082 0.293541 0.955946i \(-0.405166\pi\)
0.293541 + 0.955946i \(0.405166\pi\)
\(830\) −16.2948 −0.565601
\(831\) 0 0
\(832\) −37.2420 −1.29113
\(833\) 2.56622 0.0889143
\(834\) 0 0
\(835\) −4.69195 −0.162372
\(836\) 0 0
\(837\) 0 0
\(838\) 12.4665 0.430648
\(839\) 16.2627 0.561450 0.280725 0.959788i \(-0.409425\pi\)
0.280725 + 0.959788i \(0.409425\pi\)
\(840\) 0 0
\(841\) 52.5467 1.81196
\(842\) −60.1230 −2.07197
\(843\) 0 0
\(844\) −19.7718 −0.680575
\(845\) 1.56949 0.0539920
\(846\) 0 0
\(847\) 0 0
\(848\) −34.4426 −1.18276
\(849\) 0 0
\(850\) 20.4936 0.702924
\(851\) 0.336270 0.0115272
\(852\) 0 0
\(853\) −4.70771 −0.161189 −0.0805945 0.996747i \(-0.525682\pi\)
−0.0805945 + 0.996747i \(0.525682\pi\)
\(854\) 12.2252 0.418338
\(855\) 0 0
\(856\) −2.26406 −0.0773839
\(857\) 27.6135 0.943259 0.471629 0.881797i \(-0.343666\pi\)
0.471629 + 0.881797i \(0.343666\pi\)
\(858\) 0 0
\(859\) 18.1645 0.619763 0.309882 0.950775i \(-0.399711\pi\)
0.309882 + 0.950775i \(0.399711\pi\)
\(860\) −3.82766 −0.130522
\(861\) 0 0
\(862\) −31.5846 −1.07577
\(863\) 31.2285 1.06303 0.531515 0.847049i \(-0.321623\pi\)
0.531515 + 0.847049i \(0.321623\pi\)
\(864\) 0 0
\(865\) 11.3440 0.385706
\(866\) −9.22018 −0.313314
\(867\) 0 0
\(868\) 1.10339 0.0374516
\(869\) 0 0
\(870\) 0 0
\(871\) −54.8257 −1.85770
\(872\) 0.980590 0.0332070
\(873\) 0 0
\(874\) −0.161080 −0.00544861
\(875\) 9.40208 0.317848
\(876\) 0 0
\(877\) −15.4419 −0.521436 −0.260718 0.965415i \(-0.583959\pi\)
−0.260718 + 0.965415i \(0.583959\pi\)
\(878\) 54.5041 1.83942
\(879\) 0 0
\(880\) 0 0
\(881\) 47.5879 1.60328 0.801639 0.597808i \(-0.203962\pi\)
0.801639 + 0.597808i \(0.203962\pi\)
\(882\) 0 0
\(883\) −22.2786 −0.749734 −0.374867 0.927079i \(-0.622312\pi\)
−0.374867 + 0.927079i \(0.622312\pi\)
\(884\) 21.8688 0.735527
\(885\) 0 0
\(886\) −7.95881 −0.267381
\(887\) 25.5643 0.858365 0.429183 0.903218i \(-0.358802\pi\)
0.429183 + 0.903218i \(0.358802\pi\)
\(888\) 0 0
\(889\) −19.1294 −0.641579
\(890\) −35.1781 −1.17917
\(891\) 0 0
\(892\) −46.1325 −1.54463
\(893\) 0.0905556 0.00303033
\(894\) 0 0
\(895\) −12.1300 −0.405460
\(896\) −3.91368 −0.130747
\(897\) 0 0
\(898\) −14.9590 −0.499187
\(899\) −4.44958 −0.148402
\(900\) 0 0
\(901\) 25.5153 0.850036
\(902\) 0 0
\(903\) 0 0
\(904\) 4.24506 0.141189
\(905\) 17.4995 0.581702
\(906\) 0 0
\(907\) 3.08704 0.102504 0.0512518 0.998686i \(-0.483679\pi\)
0.0512518 + 0.998686i \(0.483679\pi\)
\(908\) 39.0422 1.29566
\(909\) 0 0
\(910\) 8.29742 0.275057
\(911\) 5.06946 0.167959 0.0839793 0.996467i \(-0.473237\pi\)
0.0839793 + 0.996467i \(0.473237\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −53.0078 −1.75334
\(915\) 0 0
\(916\) 52.5066 1.73487
\(917\) 6.91998 0.228518
\(918\) 0 0
\(919\) −32.7870 −1.08154 −0.540771 0.841170i \(-0.681868\pi\)
−0.540771 + 0.841170i \(0.681868\pi\)
\(920\) 0.226340 0.00746222
\(921\) 0 0
\(922\) −47.2776 −1.55701
\(923\) 47.5655 1.56564
\(924\) 0 0
\(925\) 3.00674 0.0988610
\(926\) −9.65595 −0.317314
\(927\) 0 0
\(928\) 73.3074 2.40643
\(929\) −22.3901 −0.734595 −0.367298 0.930103i \(-0.619717\pi\)
−0.367298 + 0.930103i \(0.619717\pi\)
\(930\) 0 0
\(931\) −0.180354 −0.00591087
\(932\) −33.2969 −1.09068
\(933\) 0 0
\(934\) −67.7088 −2.21550
\(935\) 0 0
\(936\) 0 0
\(937\) −6.67075 −0.217924 −0.108962 0.994046i \(-0.534753\pi\)
−0.108962 + 0.994046i \(0.534753\pi\)
\(938\) −29.6631 −0.968534
\(939\) 0 0
\(940\) −1.19065 −0.0388346
\(941\) 8.84967 0.288491 0.144245 0.989542i \(-0.453925\pi\)
0.144245 + 0.989542i \(0.453925\pi\)
\(942\) 0 0
\(943\) −1.34157 −0.0436875
\(944\) 46.5965 1.51659
\(945\) 0 0
\(946\) 0 0
\(947\) −34.9296 −1.13506 −0.567530 0.823352i \(-0.692101\pi\)
−0.567530 + 0.823352i \(0.692101\pi\)
\(948\) 0 0
\(949\) −16.2642 −0.527959
\(950\) −1.44029 −0.0467292
\(951\) 0 0
\(952\) 1.26447 0.0409818
\(953\) −3.36257 −0.108924 −0.0544621 0.998516i \(-0.517344\pi\)
−0.0544621 + 0.998516i \(0.517344\pi\)
\(954\) 0 0
\(955\) 2.32753 0.0753171
\(956\) 50.5460 1.63478
\(957\) 0 0
\(958\) −21.3711 −0.690469
\(959\) 6.81197 0.219970
\(960\) 0 0
\(961\) −30.7572 −0.992168
\(962\) 6.07413 0.195838
\(963\) 0 0
\(964\) −4.93198 −0.158849
\(965\) 26.6308 0.857277
\(966\) 0 0
\(967\) 6.65340 0.213959 0.106979 0.994261i \(-0.465882\pi\)
0.106979 + 0.994261i \(0.465882\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −31.8677 −1.02321
\(971\) −13.3090 −0.427106 −0.213553 0.976931i \(-0.568504\pi\)
−0.213553 + 0.976931i \(0.568504\pi\)
\(972\) 0 0
\(973\) 19.6013 0.628389
\(974\) −58.5536 −1.87618
\(975\) 0 0
\(976\) −20.5683 −0.658376
\(977\) −1.37314 −0.0439307 −0.0219654 0.999759i \(-0.506992\pi\)
−0.0219654 + 0.999759i \(0.506992\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 2.37134 0.0757497
\(981\) 0 0
\(982\) −63.7194 −2.03337
\(983\) 10.7743 0.343646 0.171823 0.985128i \(-0.445034\pi\)
0.171823 + 0.985128i \(0.445034\pi\)
\(984\) 0 0
\(985\) −6.49357 −0.206902
\(986\) −47.7139 −1.51952
\(987\) 0 0
\(988\) −1.53694 −0.0488966
\(989\) 0.700175 0.0222643
\(990\) 0 0
\(991\) 5.59499 0.177731 0.0888654 0.996044i \(-0.471676\pi\)
0.0888654 + 0.996044i \(0.471676\pi\)
\(992\) −4.00000 −0.127000
\(993\) 0 0
\(994\) 25.7350 0.816265
\(995\) 21.7040 0.688062
\(996\) 0 0
\(997\) 45.7503 1.44893 0.724463 0.689314i \(-0.242088\pi\)
0.724463 + 0.689314i \(0.242088\pi\)
\(998\) 70.5711 2.23389
\(999\) 0 0
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 7623.2.a.cm.1.1 4
3.2 odd 2 2541.2.a.bk.1.4 4
11.10 odd 2 7623.2.a.cf.1.4 4
33.32 even 2 2541.2.a.bo.1.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2541.2.a.bk.1.4 4 3.2 odd 2
2541.2.a.bo.1.1 yes 4 33.32 even 2
7623.2.a.cf.1.4 4 11.10 odd 2
7623.2.a.cm.1.1 4 1.1 even 1 trivial