Properties

Label 5265.2.a.ba.1.4
Level $5265$
Weight $2$
Character 5265.1
Self dual yes
Analytic conductor $42.041$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5265.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.0412366642\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 3x^{7} - 8x^{6} + 31x^{5} - x^{4} - 70x^{3} + 66x^{2} - 19x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.655066\) of defining polynomial
Character \(\chi\) \(=\) 5265.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.655066 q^{2} -1.57089 q^{4} +1.00000 q^{5} -0.777184 q^{7} +2.33917 q^{8} +O(q^{10})\) \(q-0.655066 q^{2} -1.57089 q^{4} +1.00000 q^{5} -0.777184 q^{7} +2.33917 q^{8} -0.655066 q^{10} +4.06797 q^{11} -1.00000 q^{13} +0.509106 q^{14} +1.60947 q^{16} -5.29154 q^{17} +6.65042 q^{19} -1.57089 q^{20} -2.66479 q^{22} -2.30567 q^{23} +1.00000 q^{25} +0.655066 q^{26} +1.22087 q^{28} -6.38016 q^{29} -8.94517 q^{31} -5.73264 q^{32} +3.46630 q^{34} -0.777184 q^{35} -2.80592 q^{37} -4.35646 q^{38} +2.33917 q^{40} -7.60986 q^{41} +8.84366 q^{43} -6.39034 q^{44} +1.51036 q^{46} +4.08782 q^{47} -6.39599 q^{49} -0.655066 q^{50} +1.57089 q^{52} +4.78025 q^{53} +4.06797 q^{55} -1.81796 q^{56} +4.17942 q^{58} +4.74099 q^{59} -14.3660 q^{61} +5.85967 q^{62} +0.536314 q^{64} -1.00000 q^{65} +10.7871 q^{67} +8.31242 q^{68} +0.509106 q^{70} -0.307776 q^{71} -7.50636 q^{73} +1.83806 q^{74} -10.4471 q^{76} -3.16156 q^{77} +7.61897 q^{79} +1.60947 q^{80} +4.98496 q^{82} +12.5297 q^{83} -5.29154 q^{85} -5.79318 q^{86} +9.51567 q^{88} +11.7743 q^{89} +0.777184 q^{91} +3.62195 q^{92} -2.67779 q^{94} +6.65042 q^{95} -6.08536 q^{97} +4.18979 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 3 q^{2} + 9 q^{4} + 8 q^{5} - 11 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 3 q^{2} + 9 q^{4} + 8 q^{5} - 11 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 8 q^{13} - 10 q^{14} + 11 q^{16} + 2 q^{17} - 10 q^{19} + 9 q^{20} + 3 q^{22} - 6 q^{23} + 8 q^{25} + 3 q^{26} - 34 q^{28} - 14 q^{29} - 31 q^{31} - q^{32} - 7 q^{34} - 11 q^{35} + q^{37} - 9 q^{38} + 6 q^{40} + 12 q^{41} + 15 q^{43} - 16 q^{44} - 32 q^{46} + 18 q^{47} + 17 q^{49} - 3 q^{50} - 9 q^{52} - 2 q^{53} - 6 q^{55} - 16 q^{56} - 42 q^{58} - 24 q^{59} - 9 q^{61} + 20 q^{62} - 30 q^{64} - 8 q^{65} - 18 q^{67} + 14 q^{68} - 10 q^{70} - 10 q^{71} + 6 q^{73} + 37 q^{74} - 53 q^{76} + 34 q^{77} - 3 q^{79} + 11 q^{80} - 34 q^{82} + 10 q^{83} + 2 q^{85} - 60 q^{86} - 14 q^{88} + 13 q^{89} + 11 q^{91} - 5 q^{92} + 17 q^{94} - 10 q^{95} - 34 q^{97} + 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.655066 −0.463201 −0.231601 0.972811i \(-0.574396\pi\)
−0.231601 + 0.972811i \(0.574396\pi\)
\(3\) 0 0
\(4\) −1.57089 −0.785445
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.777184 −0.293748 −0.146874 0.989155i \(-0.546921\pi\)
−0.146874 + 0.989155i \(0.546921\pi\)
\(8\) 2.33917 0.827020
\(9\) 0 0
\(10\) −0.655066 −0.207150
\(11\) 4.06797 1.22654 0.613270 0.789873i \(-0.289854\pi\)
0.613270 + 0.789873i \(0.289854\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0.509106 0.136064
\(15\) 0 0
\(16\) 1.60947 0.402368
\(17\) −5.29154 −1.28339 −0.641693 0.766961i \(-0.721768\pi\)
−0.641693 + 0.766961i \(0.721768\pi\)
\(18\) 0 0
\(19\) 6.65042 1.52571 0.762855 0.646569i \(-0.223797\pi\)
0.762855 + 0.646569i \(0.223797\pi\)
\(20\) −1.57089 −0.351261
\(21\) 0 0
\(22\) −2.66479 −0.568135
\(23\) −2.30567 −0.480765 −0.240383 0.970678i \(-0.577273\pi\)
−0.240383 + 0.970678i \(0.577273\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.655066 0.128469
\(27\) 0 0
\(28\) 1.22087 0.230723
\(29\) −6.38016 −1.18477 −0.592383 0.805656i \(-0.701813\pi\)
−0.592383 + 0.805656i \(0.701813\pi\)
\(30\) 0 0
\(31\) −8.94517 −1.60660 −0.803300 0.595574i \(-0.796925\pi\)
−0.803300 + 0.595574i \(0.796925\pi\)
\(32\) −5.73264 −1.01340
\(33\) 0 0
\(34\) 3.46630 0.594466
\(35\) −0.777184 −0.131368
\(36\) 0 0
\(37\) −2.80592 −0.461291 −0.230645 0.973038i \(-0.574084\pi\)
−0.230645 + 0.973038i \(0.574084\pi\)
\(38\) −4.35646 −0.706711
\(39\) 0 0
\(40\) 2.33917 0.369855
\(41\) −7.60986 −1.18846 −0.594231 0.804295i \(-0.702543\pi\)
−0.594231 + 0.804295i \(0.702543\pi\)
\(42\) 0 0
\(43\) 8.84366 1.34865 0.674323 0.738437i \(-0.264436\pi\)
0.674323 + 0.738437i \(0.264436\pi\)
\(44\) −6.39034 −0.963379
\(45\) 0 0
\(46\) 1.51036 0.222691
\(47\) 4.08782 0.596270 0.298135 0.954524i \(-0.403635\pi\)
0.298135 + 0.954524i \(0.403635\pi\)
\(48\) 0 0
\(49\) −6.39599 −0.913712
\(50\) −0.655066 −0.0926403
\(51\) 0 0
\(52\) 1.57089 0.217843
\(53\) 4.78025 0.656618 0.328309 0.944570i \(-0.393521\pi\)
0.328309 + 0.944570i \(0.393521\pi\)
\(54\) 0 0
\(55\) 4.06797 0.548525
\(56\) −1.81796 −0.242935
\(57\) 0 0
\(58\) 4.17942 0.548785
\(59\) 4.74099 0.617224 0.308612 0.951188i \(-0.400136\pi\)
0.308612 + 0.951188i \(0.400136\pi\)
\(60\) 0 0
\(61\) −14.3660 −1.83938 −0.919688 0.392651i \(-0.871558\pi\)
−0.919688 + 0.392651i \(0.871558\pi\)
\(62\) 5.85967 0.744179
\(63\) 0 0
\(64\) 0.536314 0.0670393
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 10.7871 1.31785 0.658925 0.752209i \(-0.271011\pi\)
0.658925 + 0.752209i \(0.271011\pi\)
\(68\) 8.31242 1.00803
\(69\) 0 0
\(70\) 0.509106 0.0608498
\(71\) −0.307776 −0.0365262 −0.0182631 0.999833i \(-0.505814\pi\)
−0.0182631 + 0.999833i \(0.505814\pi\)
\(72\) 0 0
\(73\) −7.50636 −0.878553 −0.439277 0.898352i \(-0.644765\pi\)
−0.439277 + 0.898352i \(0.644765\pi\)
\(74\) 1.83806 0.213670
\(75\) 0 0
\(76\) −10.4471 −1.19836
\(77\) −3.16156 −0.360293
\(78\) 0 0
\(79\) 7.61897 0.857201 0.428601 0.903494i \(-0.359007\pi\)
0.428601 + 0.903494i \(0.359007\pi\)
\(80\) 1.60947 0.179944
\(81\) 0 0
\(82\) 4.98496 0.550497
\(83\) 12.5297 1.37531 0.687656 0.726037i \(-0.258640\pi\)
0.687656 + 0.726037i \(0.258640\pi\)
\(84\) 0 0
\(85\) −5.29154 −0.573948
\(86\) −5.79318 −0.624694
\(87\) 0 0
\(88\) 9.51567 1.01437
\(89\) 11.7743 1.24807 0.624037 0.781394i \(-0.285491\pi\)
0.624037 + 0.781394i \(0.285491\pi\)
\(90\) 0 0
\(91\) 0.777184 0.0814710
\(92\) 3.62195 0.377615
\(93\) 0 0
\(94\) −2.67779 −0.276193
\(95\) 6.65042 0.682318
\(96\) 0 0
\(97\) −6.08536 −0.617874 −0.308937 0.951082i \(-0.599973\pi\)
−0.308937 + 0.951082i \(0.599973\pi\)
\(98\) 4.18979 0.423233
\(99\) 0 0
\(100\) −1.57089 −0.157089
\(101\) −9.35209 −0.930568 −0.465284 0.885162i \(-0.654048\pi\)
−0.465284 + 0.885162i \(0.654048\pi\)
\(102\) 0 0
\(103\) −2.21467 −0.218218 −0.109109 0.994030i \(-0.534800\pi\)
−0.109109 + 0.994030i \(0.534800\pi\)
\(104\) −2.33917 −0.229374
\(105\) 0 0
\(106\) −3.13138 −0.304146
\(107\) 15.4985 1.49830 0.749148 0.662403i \(-0.230463\pi\)
0.749148 + 0.662403i \(0.230463\pi\)
\(108\) 0 0
\(109\) −5.88278 −0.563468 −0.281734 0.959493i \(-0.590910\pi\)
−0.281734 + 0.959493i \(0.590910\pi\)
\(110\) −2.66479 −0.254078
\(111\) 0 0
\(112\) −1.25085 −0.118195
\(113\) −10.5758 −0.994888 −0.497444 0.867496i \(-0.665728\pi\)
−0.497444 + 0.867496i \(0.665728\pi\)
\(114\) 0 0
\(115\) −2.30567 −0.215005
\(116\) 10.0225 0.930568
\(117\) 0 0
\(118\) −3.10566 −0.285899
\(119\) 4.11250 0.376992
\(120\) 0 0
\(121\) 5.54841 0.504401
\(122\) 9.41066 0.852001
\(123\) 0 0
\(124\) 14.0519 1.26190
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −11.4873 −1.01934 −0.509668 0.860371i \(-0.670232\pi\)
−0.509668 + 0.860371i \(0.670232\pi\)
\(128\) 11.1140 0.982345
\(129\) 0 0
\(130\) 0.655066 0.0574530
\(131\) −12.5793 −1.09906 −0.549531 0.835473i \(-0.685194\pi\)
−0.549531 + 0.835473i \(0.685194\pi\)
\(132\) 0 0
\(133\) −5.16860 −0.448174
\(134\) −7.06624 −0.610430
\(135\) 0 0
\(136\) −12.3778 −1.06139
\(137\) 1.81204 0.154813 0.0774067 0.997000i \(-0.475336\pi\)
0.0774067 + 0.997000i \(0.475336\pi\)
\(138\) 0 0
\(139\) −20.4105 −1.73119 −0.865597 0.500741i \(-0.833061\pi\)
−0.865597 + 0.500741i \(0.833061\pi\)
\(140\) 1.22087 0.103182
\(141\) 0 0
\(142\) 0.201613 0.0169190
\(143\) −4.06797 −0.340181
\(144\) 0 0
\(145\) −6.38016 −0.529843
\(146\) 4.91716 0.406947
\(147\) 0 0
\(148\) 4.40779 0.362318
\(149\) 0.464119 0.0380221 0.0190111 0.999819i \(-0.493948\pi\)
0.0190111 + 0.999819i \(0.493948\pi\)
\(150\) 0 0
\(151\) −9.96476 −0.810921 −0.405460 0.914113i \(-0.632889\pi\)
−0.405460 + 0.914113i \(0.632889\pi\)
\(152\) 15.5564 1.26179
\(153\) 0 0
\(154\) 2.07103 0.166888
\(155\) −8.94517 −0.718494
\(156\) 0 0
\(157\) −9.31971 −0.743794 −0.371897 0.928274i \(-0.621292\pi\)
−0.371897 + 0.928274i \(0.621292\pi\)
\(158\) −4.99093 −0.397057
\(159\) 0 0
\(160\) −5.73264 −0.453205
\(161\) 1.79193 0.141224
\(162\) 0 0
\(163\) 8.93727 0.700021 0.350010 0.936746i \(-0.386178\pi\)
0.350010 + 0.936746i \(0.386178\pi\)
\(164\) 11.9543 0.933470
\(165\) 0 0
\(166\) −8.20776 −0.637046
\(167\) 16.3450 1.26482 0.632409 0.774635i \(-0.282066\pi\)
0.632409 + 0.774635i \(0.282066\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 3.46630 0.265853
\(171\) 0 0
\(172\) −13.8924 −1.05929
\(173\) −11.0008 −0.836374 −0.418187 0.908361i \(-0.637334\pi\)
−0.418187 + 0.908361i \(0.637334\pi\)
\(174\) 0 0
\(175\) −0.777184 −0.0587496
\(176\) 6.54728 0.493520
\(177\) 0 0
\(178\) −7.71295 −0.578110
\(179\) 2.87227 0.214683 0.107342 0.994222i \(-0.465766\pi\)
0.107342 + 0.994222i \(0.465766\pi\)
\(180\) 0 0
\(181\) −10.8459 −0.806169 −0.403084 0.915163i \(-0.632062\pi\)
−0.403084 + 0.915163i \(0.632062\pi\)
\(182\) −0.509106 −0.0377375
\(183\) 0 0
\(184\) −5.39335 −0.397603
\(185\) −2.80592 −0.206296
\(186\) 0 0
\(187\) −21.5258 −1.57413
\(188\) −6.42151 −0.468337
\(189\) 0 0
\(190\) −4.35646 −0.316051
\(191\) −13.8954 −1.00543 −0.502716 0.864452i \(-0.667666\pi\)
−0.502716 + 0.864452i \(0.667666\pi\)
\(192\) 0 0
\(193\) 21.7868 1.56825 0.784123 0.620606i \(-0.213113\pi\)
0.784123 + 0.620606i \(0.213113\pi\)
\(194\) 3.98631 0.286200
\(195\) 0 0
\(196\) 10.0474 0.717670
\(197\) 3.29282 0.234604 0.117302 0.993096i \(-0.462575\pi\)
0.117302 + 0.993096i \(0.462575\pi\)
\(198\) 0 0
\(199\) −19.7792 −1.40211 −0.701055 0.713107i \(-0.747287\pi\)
−0.701055 + 0.713107i \(0.747287\pi\)
\(200\) 2.33917 0.165404
\(201\) 0 0
\(202\) 6.12623 0.431040
\(203\) 4.95856 0.348022
\(204\) 0 0
\(205\) −7.60986 −0.531496
\(206\) 1.45075 0.101079
\(207\) 0 0
\(208\) −1.60947 −0.111597
\(209\) 27.0537 1.87134
\(210\) 0 0
\(211\) −2.42809 −0.167157 −0.0835783 0.996501i \(-0.526635\pi\)
−0.0835783 + 0.996501i \(0.526635\pi\)
\(212\) −7.50925 −0.515737
\(213\) 0 0
\(214\) −10.1525 −0.694013
\(215\) 8.84366 0.603132
\(216\) 0 0
\(217\) 6.95204 0.471935
\(218\) 3.85361 0.260999
\(219\) 0 0
\(220\) −6.39034 −0.430836
\(221\) 5.29154 0.355947
\(222\) 0 0
\(223\) −9.45726 −0.633305 −0.316652 0.948542i \(-0.602559\pi\)
−0.316652 + 0.948542i \(0.602559\pi\)
\(224\) 4.45532 0.297683
\(225\) 0 0
\(226\) 6.92785 0.460834
\(227\) −24.0821 −1.59839 −0.799193 0.601074i \(-0.794740\pi\)
−0.799193 + 0.601074i \(0.794740\pi\)
\(228\) 0 0
\(229\) 9.97401 0.659101 0.329550 0.944138i \(-0.393103\pi\)
0.329550 + 0.944138i \(0.393103\pi\)
\(230\) 1.51036 0.0995905
\(231\) 0 0
\(232\) −14.9243 −0.979825
\(233\) −18.2730 −1.19710 −0.598552 0.801084i \(-0.704257\pi\)
−0.598552 + 0.801084i \(0.704257\pi\)
\(234\) 0 0
\(235\) 4.08782 0.266660
\(236\) −7.44756 −0.484795
\(237\) 0 0
\(238\) −2.69396 −0.174623
\(239\) 26.5440 1.71699 0.858495 0.512822i \(-0.171400\pi\)
0.858495 + 0.512822i \(0.171400\pi\)
\(240\) 0 0
\(241\) 14.4187 0.928791 0.464396 0.885628i \(-0.346272\pi\)
0.464396 + 0.885628i \(0.346272\pi\)
\(242\) −3.63457 −0.233639
\(243\) 0 0
\(244\) 22.5674 1.44473
\(245\) −6.39599 −0.408625
\(246\) 0 0
\(247\) −6.65042 −0.423156
\(248\) −20.9242 −1.32869
\(249\) 0 0
\(250\) −0.655066 −0.0414300
\(251\) −13.7541 −0.868148 −0.434074 0.900877i \(-0.642924\pi\)
−0.434074 + 0.900877i \(0.642924\pi\)
\(252\) 0 0
\(253\) −9.37940 −0.589678
\(254\) 7.52496 0.472158
\(255\) 0 0
\(256\) −8.35300 −0.522063
\(257\) 4.91358 0.306500 0.153250 0.988187i \(-0.451026\pi\)
0.153250 + 0.988187i \(0.451026\pi\)
\(258\) 0 0
\(259\) 2.18072 0.135503
\(260\) 1.57089 0.0974224
\(261\) 0 0
\(262\) 8.24029 0.509087
\(263\) −26.0723 −1.60769 −0.803843 0.594841i \(-0.797215\pi\)
−0.803843 + 0.594841i \(0.797215\pi\)
\(264\) 0 0
\(265\) 4.78025 0.293649
\(266\) 3.38577 0.207595
\(267\) 0 0
\(268\) −16.9453 −1.03510
\(269\) −29.7277 −1.81253 −0.906263 0.422713i \(-0.861078\pi\)
−0.906263 + 0.422713i \(0.861078\pi\)
\(270\) 0 0
\(271\) 14.2980 0.868540 0.434270 0.900783i \(-0.357006\pi\)
0.434270 + 0.900783i \(0.357006\pi\)
\(272\) −8.51658 −0.516393
\(273\) 0 0
\(274\) −1.18701 −0.0717098
\(275\) 4.06797 0.245308
\(276\) 0 0
\(277\) 1.87861 0.112875 0.0564373 0.998406i \(-0.482026\pi\)
0.0564373 + 0.998406i \(0.482026\pi\)
\(278\) 13.3702 0.801892
\(279\) 0 0
\(280\) −1.81796 −0.108644
\(281\) −3.57185 −0.213079 −0.106539 0.994308i \(-0.533977\pi\)
−0.106539 + 0.994308i \(0.533977\pi\)
\(282\) 0 0
\(283\) −13.7483 −0.817249 −0.408625 0.912703i \(-0.633991\pi\)
−0.408625 + 0.912703i \(0.633991\pi\)
\(284\) 0.483481 0.0286893
\(285\) 0 0
\(286\) 2.66479 0.157572
\(287\) 5.91426 0.349108
\(288\) 0 0
\(289\) 11.0004 0.647081
\(290\) 4.17942 0.245424
\(291\) 0 0
\(292\) 11.7917 0.690055
\(293\) 7.49807 0.438042 0.219021 0.975720i \(-0.429714\pi\)
0.219021 + 0.975720i \(0.429714\pi\)
\(294\) 0 0
\(295\) 4.74099 0.276031
\(296\) −6.56352 −0.381497
\(297\) 0 0
\(298\) −0.304028 −0.0176119
\(299\) 2.30567 0.133340
\(300\) 0 0
\(301\) −6.87315 −0.396162
\(302\) 6.52757 0.375619
\(303\) 0 0
\(304\) 10.7037 0.613897
\(305\) −14.3660 −0.822594
\(306\) 0 0
\(307\) −18.4113 −1.05079 −0.525395 0.850858i \(-0.676082\pi\)
−0.525395 + 0.850858i \(0.676082\pi\)
\(308\) 4.96646 0.282991
\(309\) 0 0
\(310\) 5.85967 0.332807
\(311\) −17.2648 −0.978996 −0.489498 0.872004i \(-0.662820\pi\)
−0.489498 + 0.872004i \(0.662820\pi\)
\(312\) 0 0
\(313\) −9.06061 −0.512136 −0.256068 0.966659i \(-0.582427\pi\)
−0.256068 + 0.966659i \(0.582427\pi\)
\(314\) 6.10502 0.344526
\(315\) 0 0
\(316\) −11.9686 −0.673284
\(317\) −8.03887 −0.451508 −0.225754 0.974184i \(-0.572485\pi\)
−0.225754 + 0.974184i \(0.572485\pi\)
\(318\) 0 0
\(319\) −25.9543 −1.45316
\(320\) 0.536314 0.0299809
\(321\) 0 0
\(322\) −1.17383 −0.0654150
\(323\) −35.1909 −1.95808
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −5.85450 −0.324251
\(327\) 0 0
\(328\) −17.8007 −0.982881
\(329\) −3.17699 −0.175153
\(330\) 0 0
\(331\) −29.8664 −1.64161 −0.820803 0.571212i \(-0.806473\pi\)
−0.820803 + 0.571212i \(0.806473\pi\)
\(332\) −19.6827 −1.08023
\(333\) 0 0
\(334\) −10.7071 −0.585865
\(335\) 10.7871 0.589361
\(336\) 0 0
\(337\) 24.2087 1.31873 0.659366 0.751822i \(-0.270825\pi\)
0.659366 + 0.751822i \(0.270825\pi\)
\(338\) −0.655066 −0.0356309
\(339\) 0 0
\(340\) 8.31242 0.450804
\(341\) −36.3887 −1.97056
\(342\) 0 0
\(343\) 10.4111 0.562149
\(344\) 20.6868 1.11536
\(345\) 0 0
\(346\) 7.20624 0.387410
\(347\) 22.9143 1.23011 0.615053 0.788486i \(-0.289135\pi\)
0.615053 + 0.788486i \(0.289135\pi\)
\(348\) 0 0
\(349\) −12.3575 −0.661481 −0.330740 0.943722i \(-0.607298\pi\)
−0.330740 + 0.943722i \(0.607298\pi\)
\(350\) 0.509106 0.0272129
\(351\) 0 0
\(352\) −23.3202 −1.24297
\(353\) 27.0380 1.43909 0.719544 0.694447i \(-0.244351\pi\)
0.719544 + 0.694447i \(0.244351\pi\)
\(354\) 0 0
\(355\) −0.307776 −0.0163350
\(356\) −18.4961 −0.980294
\(357\) 0 0
\(358\) −1.88152 −0.0994417
\(359\) 28.4894 1.50361 0.751806 0.659384i \(-0.229183\pi\)
0.751806 + 0.659384i \(0.229183\pi\)
\(360\) 0 0
\(361\) 25.2280 1.32779
\(362\) 7.10477 0.373418
\(363\) 0 0
\(364\) −1.22087 −0.0639909
\(365\) −7.50636 −0.392901
\(366\) 0 0
\(367\) −30.3201 −1.58269 −0.791347 0.611367i \(-0.790620\pi\)
−0.791347 + 0.611367i \(0.790620\pi\)
\(368\) −3.71091 −0.193444
\(369\) 0 0
\(370\) 1.83806 0.0955563
\(371\) −3.71514 −0.192880
\(372\) 0 0
\(373\) −9.33620 −0.483410 −0.241705 0.970350i \(-0.577707\pi\)
−0.241705 + 0.970350i \(0.577707\pi\)
\(374\) 14.1008 0.729137
\(375\) 0 0
\(376\) 9.56209 0.493127
\(377\) 6.38016 0.328595
\(378\) 0 0
\(379\) −22.5156 −1.15655 −0.578274 0.815843i \(-0.696274\pi\)
−0.578274 + 0.815843i \(0.696274\pi\)
\(380\) −10.4471 −0.535923
\(381\) 0 0
\(382\) 9.10237 0.465718
\(383\) 3.03380 0.155020 0.0775100 0.996992i \(-0.475303\pi\)
0.0775100 + 0.996992i \(0.475303\pi\)
\(384\) 0 0
\(385\) −3.16156 −0.161128
\(386\) −14.2718 −0.726413
\(387\) 0 0
\(388\) 9.55942 0.485306
\(389\) 18.2987 0.927782 0.463891 0.885892i \(-0.346453\pi\)
0.463891 + 0.885892i \(0.346453\pi\)
\(390\) 0 0
\(391\) 12.2005 0.617008
\(392\) −14.9613 −0.755658
\(393\) 0 0
\(394\) −2.15701 −0.108669
\(395\) 7.61897 0.383352
\(396\) 0 0
\(397\) −29.4753 −1.47932 −0.739661 0.672980i \(-0.765014\pi\)
−0.739661 + 0.672980i \(0.765014\pi\)
\(398\) 12.9567 0.649459
\(399\) 0 0
\(400\) 1.60947 0.0804735
\(401\) 27.7675 1.38664 0.693322 0.720628i \(-0.256146\pi\)
0.693322 + 0.720628i \(0.256146\pi\)
\(402\) 0 0
\(403\) 8.94517 0.445591
\(404\) 14.6911 0.730909
\(405\) 0 0
\(406\) −3.24818 −0.161204
\(407\) −11.4144 −0.565792
\(408\) 0 0
\(409\) −9.80833 −0.484991 −0.242495 0.970153i \(-0.577966\pi\)
−0.242495 + 0.970153i \(0.577966\pi\)
\(410\) 4.98496 0.246190
\(411\) 0 0
\(412\) 3.47900 0.171398
\(413\) −3.68462 −0.181308
\(414\) 0 0
\(415\) 12.5297 0.615058
\(416\) 5.73264 0.281066
\(417\) 0 0
\(418\) −17.7220 −0.866809
\(419\) −14.4829 −0.707535 −0.353768 0.935333i \(-0.615100\pi\)
−0.353768 + 0.935333i \(0.615100\pi\)
\(420\) 0 0
\(421\) −35.8224 −1.74587 −0.872937 0.487832i \(-0.837788\pi\)
−0.872937 + 0.487832i \(0.837788\pi\)
\(422\) 1.59056 0.0774272
\(423\) 0 0
\(424\) 11.1818 0.543037
\(425\) −5.29154 −0.256677
\(426\) 0 0
\(427\) 11.1650 0.540313
\(428\) −24.3464 −1.17683
\(429\) 0 0
\(430\) −5.79318 −0.279372
\(431\) −7.34712 −0.353898 −0.176949 0.984220i \(-0.556623\pi\)
−0.176949 + 0.984220i \(0.556623\pi\)
\(432\) 0 0
\(433\) −6.55302 −0.314918 −0.157459 0.987526i \(-0.550330\pi\)
−0.157459 + 0.987526i \(0.550330\pi\)
\(434\) −4.55404 −0.218601
\(435\) 0 0
\(436\) 9.24119 0.442573
\(437\) −15.3337 −0.733509
\(438\) 0 0
\(439\) −1.71109 −0.0816657 −0.0408329 0.999166i \(-0.513001\pi\)
−0.0408329 + 0.999166i \(0.513001\pi\)
\(440\) 9.51567 0.453642
\(441\) 0 0
\(442\) −3.46630 −0.164875
\(443\) 22.0916 1.04960 0.524801 0.851225i \(-0.324140\pi\)
0.524801 + 0.851225i \(0.324140\pi\)
\(444\) 0 0
\(445\) 11.7743 0.558156
\(446\) 6.19512 0.293348
\(447\) 0 0
\(448\) −0.416815 −0.0196926
\(449\) −35.4082 −1.67102 −0.835508 0.549479i \(-0.814826\pi\)
−0.835508 + 0.549479i \(0.814826\pi\)
\(450\) 0 0
\(451\) −30.9567 −1.45770
\(452\) 16.6134 0.781430
\(453\) 0 0
\(454\) 15.7754 0.740375
\(455\) 0.777184 0.0364349
\(456\) 0 0
\(457\) −2.53430 −0.118550 −0.0592748 0.998242i \(-0.518879\pi\)
−0.0592748 + 0.998242i \(0.518879\pi\)
\(458\) −6.53363 −0.305296
\(459\) 0 0
\(460\) 3.62195 0.168874
\(461\) 2.19744 0.102345 0.0511724 0.998690i \(-0.483704\pi\)
0.0511724 + 0.998690i \(0.483704\pi\)
\(462\) 0 0
\(463\) −25.4537 −1.18294 −0.591468 0.806329i \(-0.701451\pi\)
−0.591468 + 0.806329i \(0.701451\pi\)
\(464\) −10.2687 −0.476712
\(465\) 0 0
\(466\) 11.9700 0.554500
\(467\) 15.4769 0.716187 0.358093 0.933686i \(-0.383427\pi\)
0.358093 + 0.933686i \(0.383427\pi\)
\(468\) 0 0
\(469\) −8.38353 −0.387116
\(470\) −2.67779 −0.123517
\(471\) 0 0
\(472\) 11.0900 0.510457
\(473\) 35.9758 1.65417
\(474\) 0 0
\(475\) 6.65042 0.305142
\(476\) −6.46028 −0.296106
\(477\) 0 0
\(478\) −17.3881 −0.795312
\(479\) 9.62232 0.439655 0.219828 0.975539i \(-0.429451\pi\)
0.219828 + 0.975539i \(0.429451\pi\)
\(480\) 0 0
\(481\) 2.80592 0.127939
\(482\) −9.44521 −0.430217
\(483\) 0 0
\(484\) −8.71593 −0.396179
\(485\) −6.08536 −0.276322
\(486\) 0 0
\(487\) −20.0963 −0.910649 −0.455325 0.890325i \(-0.650477\pi\)
−0.455325 + 0.890325i \(0.650477\pi\)
\(488\) −33.6044 −1.52120
\(489\) 0 0
\(490\) 4.18979 0.189275
\(491\) −2.96672 −0.133886 −0.0669430 0.997757i \(-0.521325\pi\)
−0.0669430 + 0.997757i \(0.521325\pi\)
\(492\) 0 0
\(493\) 33.7609 1.52051
\(494\) 4.35646 0.196006
\(495\) 0 0
\(496\) −14.3970 −0.646444
\(497\) 0.239198 0.0107295
\(498\) 0 0
\(499\) 13.9441 0.624224 0.312112 0.950045i \(-0.398964\pi\)
0.312112 + 0.950045i \(0.398964\pi\)
\(500\) −1.57089 −0.0702523
\(501\) 0 0
\(502\) 9.00981 0.402127
\(503\) 25.1391 1.12090 0.560448 0.828190i \(-0.310629\pi\)
0.560448 + 0.828190i \(0.310629\pi\)
\(504\) 0 0
\(505\) −9.35209 −0.416162
\(506\) 6.14412 0.273140
\(507\) 0 0
\(508\) 18.0453 0.800632
\(509\) 2.08157 0.0922639 0.0461320 0.998935i \(-0.485311\pi\)
0.0461320 + 0.998935i \(0.485311\pi\)
\(510\) 0 0
\(511\) 5.83382 0.258073
\(512\) −16.7562 −0.740525
\(513\) 0 0
\(514\) −3.21871 −0.141971
\(515\) −2.21467 −0.0975899
\(516\) 0 0
\(517\) 16.6291 0.731349
\(518\) −1.42851 −0.0627652
\(519\) 0 0
\(520\) −2.33917 −0.102579
\(521\) 16.7112 0.732130 0.366065 0.930589i \(-0.380705\pi\)
0.366065 + 0.930589i \(0.380705\pi\)
\(522\) 0 0
\(523\) 39.1071 1.71003 0.855016 0.518602i \(-0.173547\pi\)
0.855016 + 0.518602i \(0.173547\pi\)
\(524\) 19.7607 0.863252
\(525\) 0 0
\(526\) 17.0791 0.744683
\(527\) 47.3337 2.06189
\(528\) 0 0
\(529\) −17.6839 −0.768865
\(530\) −3.13138 −0.136018
\(531\) 0 0
\(532\) 8.11929 0.352016
\(533\) 7.60986 0.329620
\(534\) 0 0
\(535\) 15.4985 0.670058
\(536\) 25.2328 1.08989
\(537\) 0 0
\(538\) 19.4736 0.839565
\(539\) −26.0187 −1.12070
\(540\) 0 0
\(541\) 4.87732 0.209692 0.104846 0.994488i \(-0.466565\pi\)
0.104846 + 0.994488i \(0.466565\pi\)
\(542\) −9.36611 −0.402309
\(543\) 0 0
\(544\) 30.3345 1.30058
\(545\) −5.88278 −0.251991
\(546\) 0 0
\(547\) −14.9480 −0.639128 −0.319564 0.947565i \(-0.603537\pi\)
−0.319564 + 0.947565i \(0.603537\pi\)
\(548\) −2.84652 −0.121597
\(549\) 0 0
\(550\) −2.66479 −0.113627
\(551\) −42.4307 −1.80761
\(552\) 0 0
\(553\) −5.92134 −0.251801
\(554\) −1.23061 −0.0522836
\(555\) 0 0
\(556\) 32.0626 1.35976
\(557\) 23.5505 0.997866 0.498933 0.866641i \(-0.333725\pi\)
0.498933 + 0.866641i \(0.333725\pi\)
\(558\) 0 0
\(559\) −8.84366 −0.374047
\(560\) −1.25085 −0.0528583
\(561\) 0 0
\(562\) 2.33980 0.0986983
\(563\) 0.293153 0.0123549 0.00617747 0.999981i \(-0.498034\pi\)
0.00617747 + 0.999981i \(0.498034\pi\)
\(564\) 0 0
\(565\) −10.5758 −0.444928
\(566\) 9.00601 0.378551
\(567\) 0 0
\(568\) −0.719938 −0.0302079
\(569\) −33.8631 −1.41961 −0.709807 0.704396i \(-0.751218\pi\)
−0.709807 + 0.704396i \(0.751218\pi\)
\(570\) 0 0
\(571\) −22.0309 −0.921963 −0.460981 0.887410i \(-0.652503\pi\)
−0.460981 + 0.887410i \(0.652503\pi\)
\(572\) 6.39034 0.267193
\(573\) 0 0
\(574\) −3.87423 −0.161707
\(575\) −2.30567 −0.0961531
\(576\) 0 0
\(577\) 23.7846 0.990165 0.495083 0.868846i \(-0.335138\pi\)
0.495083 + 0.868846i \(0.335138\pi\)
\(578\) −7.20597 −0.299729
\(579\) 0 0
\(580\) 10.0225 0.416163
\(581\) −9.73786 −0.403995
\(582\) 0 0
\(583\) 19.4459 0.805369
\(584\) −17.5586 −0.726581
\(585\) 0 0
\(586\) −4.91173 −0.202902
\(587\) −11.6973 −0.482798 −0.241399 0.970426i \(-0.577606\pi\)
−0.241399 + 0.970426i \(0.577606\pi\)
\(588\) 0 0
\(589\) −59.4891 −2.45121
\(590\) −3.10566 −0.127858
\(591\) 0 0
\(592\) −4.51605 −0.185609
\(593\) −14.5999 −0.599545 −0.299773 0.954011i \(-0.596911\pi\)
−0.299773 + 0.954011i \(0.596911\pi\)
\(594\) 0 0
\(595\) 4.11250 0.168596
\(596\) −0.729080 −0.0298643
\(597\) 0 0
\(598\) −1.51036 −0.0617634
\(599\) −17.4884 −0.714557 −0.357278 0.933998i \(-0.616295\pi\)
−0.357278 + 0.933998i \(0.616295\pi\)
\(600\) 0 0
\(601\) −44.7939 −1.82718 −0.913590 0.406636i \(-0.866702\pi\)
−0.913590 + 0.406636i \(0.866702\pi\)
\(602\) 4.50236 0.183503
\(603\) 0 0
\(604\) 15.6535 0.636933
\(605\) 5.54841 0.225575
\(606\) 0 0
\(607\) −42.3787 −1.72010 −0.860050 0.510209i \(-0.829568\pi\)
−0.860050 + 0.510209i \(0.829568\pi\)
\(608\) −38.1245 −1.54615
\(609\) 0 0
\(610\) 9.41066 0.381026
\(611\) −4.08782 −0.165375
\(612\) 0 0
\(613\) −6.73566 −0.272051 −0.136025 0.990705i \(-0.543433\pi\)
−0.136025 + 0.990705i \(0.543433\pi\)
\(614\) 12.0606 0.486727
\(615\) 0 0
\(616\) −7.39542 −0.297970
\(617\) −14.7847 −0.595211 −0.297606 0.954689i \(-0.596188\pi\)
−0.297606 + 0.954689i \(0.596188\pi\)
\(618\) 0 0
\(619\) 27.3795 1.10048 0.550239 0.835008i \(-0.314537\pi\)
0.550239 + 0.835008i \(0.314537\pi\)
\(620\) 14.0519 0.564337
\(621\) 0 0
\(622\) 11.3096 0.453472
\(623\) −9.15080 −0.366619
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 5.93529 0.237222
\(627\) 0 0
\(628\) 14.6402 0.584209
\(629\) 14.8476 0.592014
\(630\) 0 0
\(631\) 19.2458 0.766162 0.383081 0.923715i \(-0.374863\pi\)
0.383081 + 0.923715i \(0.374863\pi\)
\(632\) 17.8220 0.708923
\(633\) 0 0
\(634\) 5.26599 0.209139
\(635\) −11.4873 −0.455861
\(636\) 0 0
\(637\) 6.39599 0.253418
\(638\) 17.0018 0.673107
\(639\) 0 0
\(640\) 11.1140 0.439318
\(641\) 27.9161 1.10262 0.551310 0.834300i \(-0.314128\pi\)
0.551310 + 0.834300i \(0.314128\pi\)
\(642\) 0 0
\(643\) 3.24764 0.128074 0.0640372 0.997948i \(-0.479602\pi\)
0.0640372 + 0.997948i \(0.479602\pi\)
\(644\) −2.81492 −0.110923
\(645\) 0 0
\(646\) 23.0524 0.906983
\(647\) 1.47061 0.0578155 0.0289077 0.999582i \(-0.490797\pi\)
0.0289077 + 0.999582i \(0.490797\pi\)
\(648\) 0 0
\(649\) 19.2862 0.757050
\(650\) 0.655066 0.0256938
\(651\) 0 0
\(652\) −14.0395 −0.549828
\(653\) 2.39978 0.0939107 0.0469554 0.998897i \(-0.485048\pi\)
0.0469554 + 0.998897i \(0.485048\pi\)
\(654\) 0 0
\(655\) −12.5793 −0.491515
\(656\) −12.2479 −0.478198
\(657\) 0 0
\(658\) 2.08113 0.0811311
\(659\) 3.50745 0.136631 0.0683154 0.997664i \(-0.478238\pi\)
0.0683154 + 0.997664i \(0.478238\pi\)
\(660\) 0 0
\(661\) −20.2946 −0.789369 −0.394685 0.918817i \(-0.629146\pi\)
−0.394685 + 0.918817i \(0.629146\pi\)
\(662\) 19.5644 0.760394
\(663\) 0 0
\(664\) 29.3090 1.13741
\(665\) −5.16860 −0.200430
\(666\) 0 0
\(667\) 14.7105 0.569595
\(668\) −25.6763 −0.993444
\(669\) 0 0
\(670\) −7.06624 −0.272993
\(671\) −58.4404 −2.25607
\(672\) 0 0
\(673\) 9.89110 0.381274 0.190637 0.981661i \(-0.438945\pi\)
0.190637 + 0.981661i \(0.438945\pi\)
\(674\) −15.8583 −0.610838
\(675\) 0 0
\(676\) −1.57089 −0.0604188
\(677\) −8.03421 −0.308780 −0.154390 0.988010i \(-0.549341\pi\)
−0.154390 + 0.988010i \(0.549341\pi\)
\(678\) 0 0
\(679\) 4.72944 0.181499
\(680\) −12.3778 −0.474667
\(681\) 0 0
\(682\) 23.8370 0.912766
\(683\) −0.652224 −0.0249567 −0.0124783 0.999922i \(-0.503972\pi\)
−0.0124783 + 0.999922i \(0.503972\pi\)
\(684\) 0 0
\(685\) 1.81204 0.0692347
\(686\) −6.81998 −0.260388
\(687\) 0 0
\(688\) 14.2336 0.542651
\(689\) −4.78025 −0.182113
\(690\) 0 0
\(691\) 41.1289 1.56462 0.782308 0.622892i \(-0.214042\pi\)
0.782308 + 0.622892i \(0.214042\pi\)
\(692\) 17.2810 0.656926
\(693\) 0 0
\(694\) −15.0104 −0.569786
\(695\) −20.4105 −0.774214
\(696\) 0 0
\(697\) 40.2679 1.52526
\(698\) 8.09496 0.306399
\(699\) 0 0
\(700\) 1.22087 0.0461445
\(701\) −28.9154 −1.09212 −0.546060 0.837746i \(-0.683873\pi\)
−0.546060 + 0.837746i \(0.683873\pi\)
\(702\) 0 0
\(703\) −18.6606 −0.703796
\(704\) 2.18171 0.0822264
\(705\) 0 0
\(706\) −17.7117 −0.666588
\(707\) 7.26829 0.273352
\(708\) 0 0
\(709\) −38.2858 −1.43785 −0.718927 0.695086i \(-0.755366\pi\)
−0.718927 + 0.695086i \(0.755366\pi\)
\(710\) 0.201613 0.00756641
\(711\) 0 0
\(712\) 27.5421 1.03218
\(713\) 20.6246 0.772398
\(714\) 0 0
\(715\) −4.06797 −0.152134
\(716\) −4.51202 −0.168622
\(717\) 0 0
\(718\) −18.6624 −0.696475
\(719\) 31.0939 1.15961 0.579803 0.814757i \(-0.303130\pi\)
0.579803 + 0.814757i \(0.303130\pi\)
\(720\) 0 0
\(721\) 1.72120 0.0641009
\(722\) −16.5260 −0.615035
\(723\) 0 0
\(724\) 17.0377 0.633201
\(725\) −6.38016 −0.236953
\(726\) 0 0
\(727\) −23.3504 −0.866017 −0.433008 0.901390i \(-0.642548\pi\)
−0.433008 + 0.901390i \(0.642548\pi\)
\(728\) 1.81796 0.0673782
\(729\) 0 0
\(730\) 4.91716 0.181992
\(731\) −46.7966 −1.73083
\(732\) 0 0
\(733\) 1.11626 0.0412301 0.0206150 0.999787i \(-0.493438\pi\)
0.0206150 + 0.999787i \(0.493438\pi\)
\(734\) 19.8616 0.733106
\(735\) 0 0
\(736\) 13.2176 0.487206
\(737\) 43.8815 1.61640
\(738\) 0 0
\(739\) 1.73962 0.0639930 0.0319965 0.999488i \(-0.489813\pi\)
0.0319965 + 0.999488i \(0.489813\pi\)
\(740\) 4.40779 0.162034
\(741\) 0 0
\(742\) 2.43366 0.0893424
\(743\) 27.2753 1.00063 0.500317 0.865842i \(-0.333217\pi\)
0.500317 + 0.865842i \(0.333217\pi\)
\(744\) 0 0
\(745\) 0.464119 0.0170040
\(746\) 6.11582 0.223916
\(747\) 0 0
\(748\) 33.8147 1.23639
\(749\) −12.0452 −0.440121
\(750\) 0 0
\(751\) 32.6647 1.19195 0.595977 0.803002i \(-0.296765\pi\)
0.595977 + 0.803002i \(0.296765\pi\)
\(752\) 6.57923 0.239920
\(753\) 0 0
\(754\) −4.17942 −0.152206
\(755\) −9.96476 −0.362655
\(756\) 0 0
\(757\) 43.4319 1.57856 0.789279 0.614035i \(-0.210455\pi\)
0.789279 + 0.614035i \(0.210455\pi\)
\(758\) 14.7492 0.535715
\(759\) 0 0
\(760\) 15.5564 0.564291
\(761\) −49.4890 −1.79397 −0.896987 0.442058i \(-0.854249\pi\)
−0.896987 + 0.442058i \(0.854249\pi\)
\(762\) 0 0
\(763\) 4.57200 0.165518
\(764\) 21.8281 0.789711
\(765\) 0 0
\(766\) −1.98734 −0.0718055
\(767\) −4.74099 −0.171187
\(768\) 0 0
\(769\) −9.04054 −0.326010 −0.163005 0.986625i \(-0.552119\pi\)
−0.163005 + 0.986625i \(0.552119\pi\)
\(770\) 2.07103 0.0746348
\(771\) 0 0
\(772\) −34.2246 −1.23177
\(773\) 8.64817 0.311053 0.155527 0.987832i \(-0.450293\pi\)
0.155527 + 0.987832i \(0.450293\pi\)
\(774\) 0 0
\(775\) −8.94517 −0.321320
\(776\) −14.2347 −0.510995
\(777\) 0 0
\(778\) −11.9869 −0.429750
\(779\) −50.6088 −1.81325
\(780\) 0 0
\(781\) −1.25202 −0.0448009
\(782\) −7.99215 −0.285799
\(783\) 0 0
\(784\) −10.2942 −0.367648
\(785\) −9.31971 −0.332635
\(786\) 0 0
\(787\) 18.3542 0.654258 0.327129 0.944980i \(-0.393919\pi\)
0.327129 + 0.944980i \(0.393919\pi\)
\(788\) −5.17266 −0.184268
\(789\) 0 0
\(790\) −4.99093 −0.177569
\(791\) 8.21935 0.292246
\(792\) 0 0
\(793\) 14.3660 0.510151
\(794\) 19.3082 0.685224
\(795\) 0 0
\(796\) 31.0709 1.10128
\(797\) −14.2529 −0.504862 −0.252431 0.967615i \(-0.581230\pi\)
−0.252431 + 0.967615i \(0.581230\pi\)
\(798\) 0 0
\(799\) −21.6309 −0.765245
\(800\) −5.73264 −0.202679
\(801\) 0 0
\(802\) −18.1896 −0.642295
\(803\) −30.5357 −1.07758
\(804\) 0 0
\(805\) 1.79193 0.0631572
\(806\) −5.85967 −0.206398
\(807\) 0 0
\(808\) −21.8761 −0.769598
\(809\) 2.15221 0.0756676 0.0378338 0.999284i \(-0.487954\pi\)
0.0378338 + 0.999284i \(0.487954\pi\)
\(810\) 0 0
\(811\) −30.3748 −1.06660 −0.533302 0.845925i \(-0.679049\pi\)
−0.533302 + 0.845925i \(0.679049\pi\)
\(812\) −7.78934 −0.273352
\(813\) 0 0
\(814\) 7.47719 0.262075
\(815\) 8.93727 0.313059
\(816\) 0 0
\(817\) 58.8140 2.05764
\(818\) 6.42510 0.224648
\(819\) 0 0
\(820\) 11.9543 0.417461
\(821\) 11.9606 0.417428 0.208714 0.977977i \(-0.433072\pi\)
0.208714 + 0.977977i \(0.433072\pi\)
\(822\) 0 0
\(823\) 3.88386 0.135383 0.0676914 0.997706i \(-0.478437\pi\)
0.0676914 + 0.997706i \(0.478437\pi\)
\(824\) −5.18047 −0.180470
\(825\) 0 0
\(826\) 2.41367 0.0839822
\(827\) 30.4261 1.05802 0.529010 0.848615i \(-0.322563\pi\)
0.529010 + 0.848615i \(0.322563\pi\)
\(828\) 0 0
\(829\) −23.8577 −0.828613 −0.414307 0.910137i \(-0.635976\pi\)
−0.414307 + 0.910137i \(0.635976\pi\)
\(830\) −8.20776 −0.284896
\(831\) 0 0
\(832\) −0.536314 −0.0185934
\(833\) 33.8446 1.17265
\(834\) 0 0
\(835\) 16.3450 0.565644
\(836\) −42.4984 −1.46984
\(837\) 0 0
\(838\) 9.48724 0.327731
\(839\) 19.0333 0.657103 0.328552 0.944486i \(-0.393439\pi\)
0.328552 + 0.944486i \(0.393439\pi\)
\(840\) 0 0
\(841\) 11.7064 0.403671
\(842\) 23.4660 0.808691
\(843\) 0 0
\(844\) 3.81426 0.131292
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −4.31213 −0.148167
\(848\) 7.69368 0.264202
\(849\) 0 0
\(850\) 3.46630 0.118893
\(851\) 6.46953 0.221773
\(852\) 0 0
\(853\) 21.0527 0.720832 0.360416 0.932792i \(-0.382635\pi\)
0.360416 + 0.932792i \(0.382635\pi\)
\(854\) −7.31381 −0.250273
\(855\) 0 0
\(856\) 36.2536 1.23912
\(857\) 9.88134 0.337540 0.168770 0.985655i \(-0.446020\pi\)
0.168770 + 0.985655i \(0.446020\pi\)
\(858\) 0 0
\(859\) −9.82391 −0.335187 −0.167594 0.985856i \(-0.553600\pi\)
−0.167594 + 0.985856i \(0.553600\pi\)
\(860\) −13.8924 −0.473727
\(861\) 0 0
\(862\) 4.81285 0.163926
\(863\) −46.5764 −1.58548 −0.792739 0.609561i \(-0.791346\pi\)
−0.792739 + 0.609561i \(0.791346\pi\)
\(864\) 0 0
\(865\) −11.0008 −0.374038
\(866\) 4.29266 0.145870
\(867\) 0 0
\(868\) −10.9209 −0.370679
\(869\) 30.9938 1.05139
\(870\) 0 0
\(871\) −10.7871 −0.365506
\(872\) −13.7608 −0.465999
\(873\) 0 0
\(874\) 10.0446 0.339762
\(875\) −0.777184 −0.0262736
\(876\) 0 0
\(877\) −55.8285 −1.88520 −0.942598 0.333931i \(-0.891625\pi\)
−0.942598 + 0.333931i \(0.891625\pi\)
\(878\) 1.12087 0.0378277
\(879\) 0 0
\(880\) 6.54728 0.220709
\(881\) −1.22939 −0.0414192 −0.0207096 0.999786i \(-0.506593\pi\)
−0.0207096 + 0.999786i \(0.506593\pi\)
\(882\) 0 0
\(883\) −5.89957 −0.198536 −0.0992681 0.995061i \(-0.531650\pi\)
−0.0992681 + 0.995061i \(0.531650\pi\)
\(884\) −8.31242 −0.279577
\(885\) 0 0
\(886\) −14.4714 −0.486177
\(887\) 42.4663 1.42588 0.712939 0.701226i \(-0.247364\pi\)
0.712939 + 0.701226i \(0.247364\pi\)
\(888\) 0 0
\(889\) 8.92777 0.299428
\(890\) −7.71295 −0.258539
\(891\) 0 0
\(892\) 14.8563 0.497426
\(893\) 27.1857 0.909735
\(894\) 0 0
\(895\) 2.87227 0.0960094
\(896\) −8.63759 −0.288562
\(897\) 0 0
\(898\) 23.1947 0.774016
\(899\) 57.0716 1.90345
\(900\) 0 0
\(901\) −25.2949 −0.842695
\(902\) 20.2787 0.675206
\(903\) 0 0
\(904\) −24.7386 −0.822793
\(905\) −10.8459 −0.360530
\(906\) 0 0
\(907\) −11.1772 −0.371134 −0.185567 0.982632i \(-0.559412\pi\)
−0.185567 + 0.982632i \(0.559412\pi\)
\(908\) 37.8304 1.25544
\(909\) 0 0
\(910\) −0.509106 −0.0168767
\(911\) 28.0289 0.928638 0.464319 0.885668i \(-0.346299\pi\)
0.464319 + 0.885668i \(0.346299\pi\)
\(912\) 0 0
\(913\) 50.9704 1.68687
\(914\) 1.66013 0.0549123
\(915\) 0 0
\(916\) −15.6681 −0.517687
\(917\) 9.77645 0.322847
\(918\) 0 0
\(919\) 43.1860 1.42457 0.712287 0.701888i \(-0.247659\pi\)
0.712287 + 0.701888i \(0.247659\pi\)
\(920\) −5.39335 −0.177813
\(921\) 0 0
\(922\) −1.43946 −0.0474062
\(923\) 0.307776 0.0101306
\(924\) 0 0
\(925\) −2.80592 −0.0922582
\(926\) 16.6739 0.547937
\(927\) 0 0
\(928\) 36.5752 1.20064
\(929\) 18.3836 0.603146 0.301573 0.953443i \(-0.402488\pi\)
0.301573 + 0.953443i \(0.402488\pi\)
\(930\) 0 0
\(931\) −42.5360 −1.39406
\(932\) 28.7049 0.940259
\(933\) 0 0
\(934\) −10.1384 −0.331739
\(935\) −21.5258 −0.703970
\(936\) 0 0
\(937\) −13.2414 −0.432579 −0.216289 0.976329i \(-0.569395\pi\)
−0.216289 + 0.976329i \(0.569395\pi\)
\(938\) 5.49176 0.179312
\(939\) 0 0
\(940\) −6.42151 −0.209447
\(941\) −15.3309 −0.499774 −0.249887 0.968275i \(-0.580394\pi\)
−0.249887 + 0.968275i \(0.580394\pi\)
\(942\) 0 0
\(943\) 17.5458 0.571371
\(944\) 7.63048 0.248351
\(945\) 0 0
\(946\) −23.5665 −0.766213
\(947\) −44.0956 −1.43291 −0.716457 0.697631i \(-0.754237\pi\)
−0.716457 + 0.697631i \(0.754237\pi\)
\(948\) 0 0
\(949\) 7.50636 0.243667
\(950\) −4.35646 −0.141342
\(951\) 0 0
\(952\) 9.61982 0.311780
\(953\) 23.1623 0.750300 0.375150 0.926964i \(-0.377591\pi\)
0.375150 + 0.926964i \(0.377591\pi\)
\(954\) 0 0
\(955\) −13.8954 −0.449643
\(956\) −41.6977 −1.34860
\(957\) 0 0
\(958\) −6.30325 −0.203649
\(959\) −1.40829 −0.0454761
\(960\) 0 0
\(961\) 49.0161 1.58116
\(962\) −1.83806 −0.0592615
\(963\) 0 0
\(964\) −22.6502 −0.729514
\(965\) 21.7868 0.701341
\(966\) 0 0
\(967\) −28.8356 −0.927289 −0.463644 0.886021i \(-0.653458\pi\)
−0.463644 + 0.886021i \(0.653458\pi\)
\(968\) 12.9786 0.417150
\(969\) 0 0
\(970\) 3.98631 0.127993
\(971\) 1.72410 0.0553290 0.0276645 0.999617i \(-0.491193\pi\)
0.0276645 + 0.999617i \(0.491193\pi\)
\(972\) 0 0
\(973\) 15.8627 0.508535
\(974\) 13.1644 0.421814
\(975\) 0 0
\(976\) −23.1216 −0.740105
\(977\) −3.18384 −0.101860 −0.0509301 0.998702i \(-0.516219\pi\)
−0.0509301 + 0.998702i \(0.516219\pi\)
\(978\) 0 0
\(979\) 47.8976 1.53081
\(980\) 10.0474 0.320952
\(981\) 0 0
\(982\) 1.94339 0.0620162
\(983\) −11.7189 −0.373776 −0.186888 0.982381i \(-0.559840\pi\)
−0.186888 + 0.982381i \(0.559840\pi\)
\(984\) 0 0
\(985\) 3.29282 0.104918
\(986\) −22.1156 −0.704304
\(987\) 0 0
\(988\) 10.4471 0.332365
\(989\) −20.3906 −0.648382
\(990\) 0 0
\(991\) 45.8521 1.45654 0.728271 0.685290i \(-0.240324\pi\)
0.728271 + 0.685290i \(0.240324\pi\)
\(992\) 51.2795 1.62812
\(993\) 0 0
\(994\) −0.156690 −0.00496992
\(995\) −19.7792 −0.627043
\(996\) 0 0
\(997\) −24.1678 −0.765402 −0.382701 0.923872i \(-0.625006\pi\)
−0.382701 + 0.923872i \(0.625006\pi\)
\(998\) −9.13431 −0.289141
\(999\) 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 5265.2.a.ba.1.4 8
3.2 odd 2 5265.2.a.bf.1.5 8
9.2 odd 6 585.2.i.e.391.4 yes 16
9.4 even 3 1755.2.i.f.586.5 16
9.5 odd 6 585.2.i.e.196.4 16
9.7 even 3 1755.2.i.f.1171.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.i.e.196.4 16 9.5 odd 6
585.2.i.e.391.4 yes 16 9.2 odd 6
1755.2.i.f.586.5 16 9.4 even 3
1755.2.i.f.1171.5 16 9.7 even 3
5265.2.a.ba.1.4 8 1.1 even 1 trivial
5265.2.a.bf.1.5 8 3.2 odd 2