Properties

Label 3525.2.a.be.1.2
Level $3525$
Weight $2$
Character 3525.1
Self dual yes
Analytic conductor $28.147$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.1472667125\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 3 x^{7} - 7 x^{6} + 24 x^{5} + 8 x^{4} - 47 x^{3} + 8 x^{2} + 13 x + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.60641\) of defining polynomial
Character \(\chi\) \(=\) 3525.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.60641 q^{2} -1.00000 q^{3} +0.580562 q^{4} +1.60641 q^{6} +2.35394 q^{7} +2.28020 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.60641 q^{2} -1.00000 q^{3} +0.580562 q^{4} +1.60641 q^{6} +2.35394 q^{7} +2.28020 q^{8} +1.00000 q^{9} +1.21821 q^{11} -0.580562 q^{12} -1.28767 q^{13} -3.78140 q^{14} -4.82407 q^{16} +2.46057 q^{17} -1.60641 q^{18} -0.168892 q^{19} -2.35394 q^{21} -1.95695 q^{22} +8.96026 q^{23} -2.28020 q^{24} +2.06852 q^{26} -1.00000 q^{27} +1.36661 q^{28} -2.39692 q^{29} +6.32953 q^{31} +3.18904 q^{32} -1.21821 q^{33} -3.95270 q^{34} +0.580562 q^{36} +9.44703 q^{37} +0.271311 q^{38} +1.28767 q^{39} -1.59177 q^{41} +3.78140 q^{42} +1.20123 q^{43} +0.707246 q^{44} -14.3939 q^{46} +1.00000 q^{47} +4.82407 q^{48} -1.45896 q^{49} -2.46057 q^{51} -0.747570 q^{52} +5.14255 q^{53} +1.60641 q^{54} +5.36746 q^{56} +0.168892 q^{57} +3.85044 q^{58} -11.9036 q^{59} +14.0274 q^{61} -10.1678 q^{62} +2.35394 q^{63} +4.52522 q^{64} +1.95695 q^{66} +8.76052 q^{67} +1.42852 q^{68} -8.96026 q^{69} -6.83248 q^{71} +2.28020 q^{72} +0.476914 q^{73} -15.1758 q^{74} -0.0980525 q^{76} +2.86759 q^{77} -2.06852 q^{78} -5.18222 q^{79} +1.00000 q^{81} +2.55704 q^{82} -13.6149 q^{83} -1.36661 q^{84} -1.92967 q^{86} +2.39692 q^{87} +2.77776 q^{88} -12.0162 q^{89} -3.03109 q^{91} +5.20199 q^{92} -6.32953 q^{93} -1.60641 q^{94} -3.18904 q^{96} +13.4808 q^{97} +2.34370 q^{98} +1.21821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 3q^{2} - 8q^{3} + 7q^{4} - 3q^{6} + 8q^{7} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + 3q^{2} - 8q^{3} + 7q^{4} - 3q^{6} + 8q^{7} + 6q^{8} + 8q^{9} - 8q^{11} - 7q^{12} + 10q^{13} + q^{14} + 5q^{16} + 6q^{17} + 3q^{18} - 2q^{19} - 8q^{21} + 10q^{23} - 6q^{24} - 14q^{26} - 8q^{27} + 44q^{28} - 13q^{29} + 10q^{32} + 8q^{33} + 28q^{34} + 7q^{36} + 3q^{37} + 36q^{38} - 10q^{39} - 16q^{41} - q^{42} + 25q^{43} - 17q^{44} - 5q^{46} + 8q^{47} - 5q^{48} + 16q^{49} - 6q^{51} - 17q^{52} + 4q^{53} - 3q^{54} + 37q^{56} + 2q^{57} + 15q^{58} - 8q^{59} + 15q^{61} + 6q^{62} + 8q^{63} - 14q^{64} + 27q^{67} + 14q^{68} - 10q^{69} + 14q^{71} + 6q^{72} + 28q^{73} - 21q^{74} + 6q^{76} + 4q^{77} + 14q^{78} + 7q^{79} + 8q^{81} - 53q^{82} + 60q^{83} - 44q^{84} - 3q^{86} + 13q^{87} + 54q^{88} - 34q^{89} + 23q^{91} - 43q^{92} + 3q^{94} - 10q^{96} + 7q^{97} + 40q^{98} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60641 −1.13591 −0.567953 0.823061i \(-0.692264\pi\)
−0.567953 + 0.823061i \(0.692264\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.580562 0.290281
\(5\) 0 0
\(6\) 1.60641 0.655815
\(7\) 2.35394 0.889706 0.444853 0.895604i \(-0.353256\pi\)
0.444853 + 0.895604i \(0.353256\pi\)
\(8\) 2.28020 0.806174
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.21821 0.367304 0.183652 0.982991i \(-0.441208\pi\)
0.183652 + 0.982991i \(0.441208\pi\)
\(12\) −0.580562 −0.167594
\(13\) −1.28767 −0.357134 −0.178567 0.983928i \(-0.557146\pi\)
−0.178567 + 0.983928i \(0.557146\pi\)
\(14\) −3.78140 −1.01062
\(15\) 0 0
\(16\) −4.82407 −1.20602
\(17\) 2.46057 0.596777 0.298388 0.954445i \(-0.403551\pi\)
0.298388 + 0.954445i \(0.403551\pi\)
\(18\) −1.60641 −0.378635
\(19\) −0.168892 −0.0387466 −0.0193733 0.999812i \(-0.506167\pi\)
−0.0193733 + 0.999812i \(0.506167\pi\)
\(20\) 0 0
\(21\) −2.35394 −0.513672
\(22\) −1.95695 −0.417222
\(23\) 8.96026 1.86834 0.934172 0.356823i \(-0.116140\pi\)
0.934172 + 0.356823i \(0.116140\pi\)
\(24\) −2.28020 −0.465445
\(25\) 0 0
\(26\) 2.06852 0.405671
\(27\) −1.00000 −0.192450
\(28\) 1.36661 0.258265
\(29\) −2.39692 −0.445097 −0.222548 0.974922i \(-0.571437\pi\)
−0.222548 + 0.974922i \(0.571437\pi\)
\(30\) 0 0
\(31\) 6.32953 1.13682 0.568409 0.822746i \(-0.307559\pi\)
0.568409 + 0.822746i \(0.307559\pi\)
\(32\) 3.18904 0.563749
\(33\) −1.21821 −0.212063
\(34\) −3.95270 −0.677882
\(35\) 0 0
\(36\) 0.580562 0.0967603
\(37\) 9.44703 1.55308 0.776541 0.630066i \(-0.216972\pi\)
0.776541 + 0.630066i \(0.216972\pi\)
\(38\) 0.271311 0.0440124
\(39\) 1.28767 0.206191
\(40\) 0 0
\(41\) −1.59177 −0.248593 −0.124296 0.992245i \(-0.539667\pi\)
−0.124296 + 0.992245i \(0.539667\pi\)
\(42\) 3.78140 0.583483
\(43\) 1.20123 0.183186 0.0915928 0.995797i \(-0.470804\pi\)
0.0915928 + 0.995797i \(0.470804\pi\)
\(44\) 0.707246 0.106621
\(45\) 0 0
\(46\) −14.3939 −2.12226
\(47\) 1.00000 0.145865
\(48\) 4.82407 0.696295
\(49\) −1.45896 −0.208423
\(50\) 0 0
\(51\) −2.46057 −0.344549
\(52\) −0.747570 −0.103669
\(53\) 5.14255 0.706384 0.353192 0.935551i \(-0.385096\pi\)
0.353192 + 0.935551i \(0.385096\pi\)
\(54\) 1.60641 0.218605
\(55\) 0 0
\(56\) 5.36746 0.717257
\(57\) 0.168892 0.0223703
\(58\) 3.85044 0.505588
\(59\) −11.9036 −1.54972 −0.774861 0.632131i \(-0.782180\pi\)
−0.774861 + 0.632131i \(0.782180\pi\)
\(60\) 0 0
\(61\) 14.0274 1.79602 0.898009 0.439977i \(-0.145013\pi\)
0.898009 + 0.439977i \(0.145013\pi\)
\(62\) −10.1678 −1.29132
\(63\) 2.35394 0.296569
\(64\) 4.52522 0.565653
\(65\) 0 0
\(66\) 1.95695 0.240884
\(67\) 8.76052 1.07027 0.535134 0.844767i \(-0.320261\pi\)
0.535134 + 0.844767i \(0.320261\pi\)
\(68\) 1.42852 0.173233
\(69\) −8.96026 −1.07869
\(70\) 0 0
\(71\) −6.83248 −0.810866 −0.405433 0.914125i \(-0.632879\pi\)
−0.405433 + 0.914125i \(0.632879\pi\)
\(72\) 2.28020 0.268725
\(73\) 0.476914 0.0558185 0.0279093 0.999610i \(-0.491115\pi\)
0.0279093 + 0.999610i \(0.491115\pi\)
\(74\) −15.1758 −1.76415
\(75\) 0 0
\(76\) −0.0980525 −0.0112474
\(77\) 2.86759 0.326792
\(78\) −2.06852 −0.234214
\(79\) −5.18222 −0.583045 −0.291523 0.956564i \(-0.594162\pi\)
−0.291523 + 0.956564i \(0.594162\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.55704 0.282378
\(83\) −13.6149 −1.49443 −0.747214 0.664583i \(-0.768609\pi\)
−0.747214 + 0.664583i \(0.768609\pi\)
\(84\) −1.36661 −0.149109
\(85\) 0 0
\(86\) −1.92967 −0.208082
\(87\) 2.39692 0.256977
\(88\) 2.77776 0.296111
\(89\) −12.0162 −1.27371 −0.636855 0.770984i \(-0.719765\pi\)
−0.636855 + 0.770984i \(0.719765\pi\)
\(90\) 0 0
\(91\) −3.03109 −0.317744
\(92\) 5.20199 0.542345
\(93\) −6.32953 −0.656342
\(94\) −1.60641 −0.165689
\(95\) 0 0
\(96\) −3.18904 −0.325480
\(97\) 13.4808 1.36876 0.684381 0.729124i \(-0.260072\pi\)
0.684381 + 0.729124i \(0.260072\pi\)
\(98\) 2.34370 0.236749
\(99\) 1.21821 0.122435
\(100\) 0 0
\(101\) 5.27825 0.525206 0.262603 0.964904i \(-0.415419\pi\)
0.262603 + 0.964904i \(0.415419\pi\)
\(102\) 3.95270 0.391375
\(103\) −9.08889 −0.895555 −0.447778 0.894145i \(-0.647784\pi\)
−0.447778 + 0.894145i \(0.647784\pi\)
\(104\) −2.93614 −0.287912
\(105\) 0 0
\(106\) −8.26107 −0.802386
\(107\) −5.74384 −0.555278 −0.277639 0.960686i \(-0.589552\pi\)
−0.277639 + 0.960686i \(0.589552\pi\)
\(108\) −0.580562 −0.0558646
\(109\) 5.71806 0.547691 0.273846 0.961774i \(-0.411704\pi\)
0.273846 + 0.961774i \(0.411704\pi\)
\(110\) 0 0
\(111\) −9.44703 −0.896673
\(112\) −11.3556 −1.07300
\(113\) −10.9763 −1.03257 −0.516283 0.856418i \(-0.672685\pi\)
−0.516283 + 0.856418i \(0.672685\pi\)
\(114\) −0.271311 −0.0254106
\(115\) 0 0
\(116\) −1.39156 −0.129203
\(117\) −1.28767 −0.119045
\(118\) 19.1222 1.76034
\(119\) 5.79205 0.530956
\(120\) 0 0
\(121\) −9.51597 −0.865088
\(122\) −22.5337 −2.04011
\(123\) 1.59177 0.143525
\(124\) 3.67468 0.329996
\(125\) 0 0
\(126\) −3.78140 −0.336874
\(127\) −3.75661 −0.333345 −0.166673 0.986012i \(-0.553302\pi\)
−0.166673 + 0.986012i \(0.553302\pi\)
\(128\) −13.6475 −1.20628
\(129\) −1.20123 −0.105762
\(130\) 0 0
\(131\) 6.15566 0.537823 0.268911 0.963165i \(-0.413336\pi\)
0.268911 + 0.963165i \(0.413336\pi\)
\(132\) −0.707246 −0.0615579
\(133\) −0.397563 −0.0344731
\(134\) −14.0730 −1.21572
\(135\) 0 0
\(136\) 5.61061 0.481106
\(137\) 1.52211 0.130043 0.0650213 0.997884i \(-0.479288\pi\)
0.0650213 + 0.997884i \(0.479288\pi\)
\(138\) 14.3939 1.22529
\(139\) 0.241574 0.0204900 0.0102450 0.999948i \(-0.496739\pi\)
0.0102450 + 0.999948i \(0.496739\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) 10.9758 0.921067
\(143\) −1.56865 −0.131177
\(144\) −4.82407 −0.402006
\(145\) 0 0
\(146\) −0.766120 −0.0634046
\(147\) 1.45896 0.120333
\(148\) 5.48459 0.450830
\(149\) −6.91605 −0.566585 −0.283292 0.959034i \(-0.591427\pi\)
−0.283292 + 0.959034i \(0.591427\pi\)
\(150\) 0 0
\(151\) −13.1690 −1.07168 −0.535838 0.844321i \(-0.680004\pi\)
−0.535838 + 0.844321i \(0.680004\pi\)
\(152\) −0.385109 −0.0312365
\(153\) 2.46057 0.198926
\(154\) −4.60654 −0.371205
\(155\) 0 0
\(156\) 0.747570 0.0598535
\(157\) −7.97672 −0.636612 −0.318306 0.947988i \(-0.603114\pi\)
−0.318306 + 0.947988i \(0.603114\pi\)
\(158\) 8.32478 0.662284
\(159\) −5.14255 −0.407831
\(160\) 0 0
\(161\) 21.0919 1.66228
\(162\) −1.60641 −0.126212
\(163\) 18.1440 1.42114 0.710572 0.703624i \(-0.248436\pi\)
0.710572 + 0.703624i \(0.248436\pi\)
\(164\) −0.924122 −0.0721618
\(165\) 0 0
\(166\) 21.8711 1.69753
\(167\) 15.5428 1.20273 0.601367 0.798973i \(-0.294623\pi\)
0.601367 + 0.798973i \(0.294623\pi\)
\(168\) −5.36746 −0.414109
\(169\) −11.3419 −0.872455
\(170\) 0 0
\(171\) −0.168892 −0.0129155
\(172\) 0.697388 0.0531753
\(173\) 9.13465 0.694494 0.347247 0.937774i \(-0.387116\pi\)
0.347247 + 0.937774i \(0.387116\pi\)
\(174\) −3.85044 −0.291901
\(175\) 0 0
\(176\) −5.87673 −0.442975
\(177\) 11.9036 0.894733
\(178\) 19.3029 1.44681
\(179\) −12.1271 −0.906422 −0.453211 0.891403i \(-0.649722\pi\)
−0.453211 + 0.891403i \(0.649722\pi\)
\(180\) 0 0
\(181\) 21.3726 1.58861 0.794305 0.607519i \(-0.207835\pi\)
0.794305 + 0.607519i \(0.207835\pi\)
\(182\) 4.86918 0.360928
\(183\) −14.0274 −1.03693
\(184\) 20.4312 1.50621
\(185\) 0 0
\(186\) 10.1678 0.745542
\(187\) 2.99749 0.219199
\(188\) 0.580562 0.0423418
\(189\) −2.35394 −0.171224
\(190\) 0 0
\(191\) 13.4979 0.976673 0.488336 0.872655i \(-0.337604\pi\)
0.488336 + 0.872655i \(0.337604\pi\)
\(192\) −4.52522 −0.326580
\(193\) 8.03065 0.578059 0.289030 0.957320i \(-0.406667\pi\)
0.289030 + 0.957320i \(0.406667\pi\)
\(194\) −21.6557 −1.55479
\(195\) 0 0
\(196\) −0.847019 −0.0605013
\(197\) 17.2888 1.23178 0.615888 0.787833i \(-0.288797\pi\)
0.615888 + 0.787833i \(0.288797\pi\)
\(198\) −1.95695 −0.139074
\(199\) 5.14079 0.364421 0.182211 0.983260i \(-0.441675\pi\)
0.182211 + 0.983260i \(0.441675\pi\)
\(200\) 0 0
\(201\) −8.76052 −0.617919
\(202\) −8.47905 −0.596584
\(203\) −5.64220 −0.396005
\(204\) −1.42852 −0.100016
\(205\) 0 0
\(206\) 14.6005 1.01727
\(207\) 8.96026 0.622781
\(208\) 6.21179 0.430710
\(209\) −0.205746 −0.0142318
\(210\) 0 0
\(211\) 6.07830 0.418448 0.209224 0.977868i \(-0.432906\pi\)
0.209224 + 0.977868i \(0.432906\pi\)
\(212\) 2.98557 0.205050
\(213\) 6.83248 0.468154
\(214\) 9.22697 0.630743
\(215\) 0 0
\(216\) −2.28020 −0.155148
\(217\) 14.8993 1.01143
\(218\) −9.18557 −0.622125
\(219\) −0.476914 −0.0322268
\(220\) 0 0
\(221\) −3.16840 −0.213129
\(222\) 15.1758 1.01854
\(223\) −12.8780 −0.862372 −0.431186 0.902263i \(-0.641905\pi\)
−0.431186 + 0.902263i \(0.641905\pi\)
\(224\) 7.50682 0.501571
\(225\) 0 0
\(226\) 17.6325 1.17290
\(227\) −13.8756 −0.920957 −0.460478 0.887671i \(-0.652322\pi\)
−0.460478 + 0.887671i \(0.652322\pi\)
\(228\) 0.0980525 0.00649369
\(229\) 24.1014 1.59266 0.796331 0.604861i \(-0.206771\pi\)
0.796331 + 0.604861i \(0.206771\pi\)
\(230\) 0 0
\(231\) −2.86759 −0.188674
\(232\) −5.46546 −0.358825
\(233\) −26.5063 −1.73648 −0.868241 0.496142i \(-0.834750\pi\)
−0.868241 + 0.496142i \(0.834750\pi\)
\(234\) 2.06852 0.135224
\(235\) 0 0
\(236\) −6.91081 −0.449855
\(237\) 5.18222 0.336621
\(238\) −9.30442 −0.603116
\(239\) −5.89635 −0.381403 −0.190702 0.981648i \(-0.561076\pi\)
−0.190702 + 0.981648i \(0.561076\pi\)
\(240\) 0 0
\(241\) 4.50808 0.290391 0.145195 0.989403i \(-0.453619\pi\)
0.145195 + 0.989403i \(0.453619\pi\)
\(242\) 15.2866 0.982658
\(243\) −1.00000 −0.0641500
\(244\) 8.14375 0.521350
\(245\) 0 0
\(246\) −2.55704 −0.163031
\(247\) 0.217477 0.0138377
\(248\) 14.4326 0.916472
\(249\) 13.6149 0.862809
\(250\) 0 0
\(251\) 9.71575 0.613253 0.306626 0.951830i \(-0.400800\pi\)
0.306626 + 0.951830i \(0.400800\pi\)
\(252\) 1.36661 0.0860882
\(253\) 10.9155 0.686250
\(254\) 6.03466 0.378649
\(255\) 0 0
\(256\) 12.8730 0.804563
\(257\) −22.1299 −1.38043 −0.690213 0.723607i \(-0.742483\pi\)
−0.690213 + 0.723607i \(0.742483\pi\)
\(258\) 1.92967 0.120136
\(259\) 22.2378 1.38179
\(260\) 0 0
\(261\) −2.39692 −0.148366
\(262\) −9.88854 −0.610916
\(263\) 24.7388 1.52546 0.762729 0.646719i \(-0.223859\pi\)
0.762729 + 0.646719i \(0.223859\pi\)
\(264\) −2.77776 −0.170960
\(265\) 0 0
\(266\) 0.638650 0.0391581
\(267\) 12.0162 0.735377
\(268\) 5.08602 0.310678
\(269\) 24.4078 1.48817 0.744086 0.668084i \(-0.232885\pi\)
0.744086 + 0.668084i \(0.232885\pi\)
\(270\) 0 0
\(271\) 20.3632 1.23698 0.618488 0.785795i \(-0.287746\pi\)
0.618488 + 0.785795i \(0.287746\pi\)
\(272\) −11.8700 −0.719724
\(273\) 3.03109 0.183450
\(274\) −2.44513 −0.147716
\(275\) 0 0
\(276\) −5.20199 −0.313123
\(277\) −10.2127 −0.613621 −0.306811 0.951771i \(-0.599262\pi\)
−0.306811 + 0.951771i \(0.599262\pi\)
\(278\) −0.388067 −0.0232747
\(279\) 6.32953 0.378939
\(280\) 0 0
\(281\) 9.12961 0.544627 0.272314 0.962209i \(-0.412211\pi\)
0.272314 + 0.962209i \(0.412211\pi\)
\(282\) 1.60641 0.0956605
\(283\) 20.4947 1.21828 0.609141 0.793062i \(-0.291514\pi\)
0.609141 + 0.793062i \(0.291514\pi\)
\(284\) −3.96668 −0.235379
\(285\) 0 0
\(286\) 2.51989 0.149004
\(287\) −3.74694 −0.221175
\(288\) 3.18904 0.187916
\(289\) −10.9456 −0.643857
\(290\) 0 0
\(291\) −13.4808 −0.790256
\(292\) 0.276878 0.0162031
\(293\) 21.4658 1.25405 0.627023 0.779000i \(-0.284273\pi\)
0.627023 + 0.779000i \(0.284273\pi\)
\(294\) −2.34370 −0.136687
\(295\) 0 0
\(296\) 21.5412 1.25205
\(297\) −1.21821 −0.0706877
\(298\) 11.1100 0.643586
\(299\) −11.5378 −0.667249
\(300\) 0 0
\(301\) 2.82762 0.162981
\(302\) 21.1548 1.21732
\(303\) −5.27825 −0.303228
\(304\) 0.814749 0.0467291
\(305\) 0 0
\(306\) −3.95270 −0.225961
\(307\) 11.4104 0.651226 0.325613 0.945503i \(-0.394429\pi\)
0.325613 + 0.945503i \(0.394429\pi\)
\(308\) 1.66482 0.0948616
\(309\) 9.08889 0.517049
\(310\) 0 0
\(311\) 7.47198 0.423697 0.211849 0.977303i \(-0.432052\pi\)
0.211849 + 0.977303i \(0.432052\pi\)
\(312\) 2.93614 0.166226
\(313\) −15.3336 −0.866707 −0.433353 0.901224i \(-0.642670\pi\)
−0.433353 + 0.901224i \(0.642670\pi\)
\(314\) 12.8139 0.723131
\(315\) 0 0
\(316\) −3.00860 −0.169247
\(317\) −18.8478 −1.05860 −0.529298 0.848436i \(-0.677545\pi\)
−0.529298 + 0.848436i \(0.677545\pi\)
\(318\) 8.26107 0.463258
\(319\) −2.91995 −0.163486
\(320\) 0 0
\(321\) 5.74384 0.320590
\(322\) −33.8823 −1.88819
\(323\) −0.415572 −0.0231231
\(324\) 0.580562 0.0322534
\(325\) 0 0
\(326\) −29.1467 −1.61429
\(327\) −5.71806 −0.316210
\(328\) −3.62956 −0.200409
\(329\) 2.35394 0.129777
\(330\) 0 0
\(331\) −3.60922 −0.198380 −0.0991902 0.995068i \(-0.531625\pi\)
−0.0991902 + 0.995068i \(0.531625\pi\)
\(332\) −7.90429 −0.433804
\(333\) 9.44703 0.517694
\(334\) −24.9681 −1.36619
\(335\) 0 0
\(336\) 11.3556 0.619498
\(337\) −18.5074 −1.00816 −0.504082 0.863656i \(-0.668169\pi\)
−0.504082 + 0.863656i \(0.668169\pi\)
\(338\) 18.2198 0.991027
\(339\) 10.9763 0.596152
\(340\) 0 0
\(341\) 7.71069 0.417557
\(342\) 0.271311 0.0146708
\(343\) −19.9119 −1.07514
\(344\) 2.73905 0.147679
\(345\) 0 0
\(346\) −14.6740 −0.788880
\(347\) 1.05799 0.0567958 0.0283979 0.999597i \(-0.490959\pi\)
0.0283979 + 0.999597i \(0.490959\pi\)
\(348\) 1.39156 0.0745954
\(349\) 27.1342 1.45246 0.726230 0.687452i \(-0.241271\pi\)
0.726230 + 0.687452i \(0.241271\pi\)
\(350\) 0 0
\(351\) 1.28767 0.0687305
\(352\) 3.88492 0.207067
\(353\) 4.09521 0.217966 0.108983 0.994044i \(-0.465241\pi\)
0.108983 + 0.994044i \(0.465241\pi\)
\(354\) −19.1222 −1.01633
\(355\) 0 0
\(356\) −6.97612 −0.369734
\(357\) −5.79205 −0.306548
\(358\) 19.4811 1.02961
\(359\) 25.4872 1.34516 0.672580 0.740024i \(-0.265186\pi\)
0.672580 + 0.740024i \(0.265186\pi\)
\(360\) 0 0
\(361\) −18.9715 −0.998499
\(362\) −34.3332 −1.80451
\(363\) 9.51597 0.499459
\(364\) −1.75973 −0.0922352
\(365\) 0 0
\(366\) 22.5337 1.17786
\(367\) 18.1282 0.946284 0.473142 0.880986i \(-0.343120\pi\)
0.473142 + 0.880986i \(0.343120\pi\)
\(368\) −43.2249 −2.25326
\(369\) −1.59177 −0.0828643
\(370\) 0 0
\(371\) 12.1053 0.628474
\(372\) −3.67468 −0.190524
\(373\) 6.22180 0.322153 0.161076 0.986942i \(-0.448503\pi\)
0.161076 + 0.986942i \(0.448503\pi\)
\(374\) −4.81521 −0.248989
\(375\) 0 0
\(376\) 2.28020 0.117593
\(377\) 3.08643 0.158959
\(378\) 3.78140 0.194494
\(379\) 5.23729 0.269021 0.134511 0.990912i \(-0.457054\pi\)
0.134511 + 0.990912i \(0.457054\pi\)
\(380\) 0 0
\(381\) 3.75661 0.192457
\(382\) −21.6832 −1.10941
\(383\) 11.0477 0.564512 0.282256 0.959339i \(-0.408917\pi\)
0.282256 + 0.959339i \(0.408917\pi\)
\(384\) 13.6475 0.696444
\(385\) 0 0
\(386\) −12.9005 −0.656621
\(387\) 1.20123 0.0610619
\(388\) 7.82641 0.397326
\(389\) 9.44478 0.478869 0.239435 0.970913i \(-0.423038\pi\)
0.239435 + 0.970913i \(0.423038\pi\)
\(390\) 0 0
\(391\) 22.0474 1.11498
\(392\) −3.32673 −0.168025
\(393\) −6.15566 −0.310512
\(394\) −27.7730 −1.39918
\(395\) 0 0
\(396\) 0.707246 0.0355404
\(397\) 3.00343 0.150738 0.0753689 0.997156i \(-0.475987\pi\)
0.0753689 + 0.997156i \(0.475987\pi\)
\(398\) −8.25823 −0.413948
\(399\) 0.397563 0.0199030
\(400\) 0 0
\(401\) −29.6585 −1.48107 −0.740537 0.672015i \(-0.765429\pi\)
−0.740537 + 0.672015i \(0.765429\pi\)
\(402\) 14.0730 0.701898
\(403\) −8.15032 −0.405996
\(404\) 3.06435 0.152457
\(405\) 0 0
\(406\) 9.06371 0.449824
\(407\) 11.5085 0.570453
\(408\) −5.61061 −0.277767
\(409\) 10.5918 0.523730 0.261865 0.965105i \(-0.415663\pi\)
0.261865 + 0.965105i \(0.415663\pi\)
\(410\) 0 0
\(411\) −1.52211 −0.0750801
\(412\) −5.27667 −0.259963
\(413\) −28.0205 −1.37880
\(414\) −14.3939 −0.707421
\(415\) 0 0
\(416\) −4.10642 −0.201334
\(417\) −0.241574 −0.0118299
\(418\) 0.330513 0.0161659
\(419\) −21.2794 −1.03957 −0.519783 0.854298i \(-0.673987\pi\)
−0.519783 + 0.854298i \(0.673987\pi\)
\(420\) 0 0
\(421\) −18.4416 −0.898789 −0.449395 0.893333i \(-0.648360\pi\)
−0.449395 + 0.893333i \(0.648360\pi\)
\(422\) −9.76426 −0.475317
\(423\) 1.00000 0.0486217
\(424\) 11.7261 0.569468
\(425\) 0 0
\(426\) −10.9758 −0.531778
\(427\) 33.0195 1.59793
\(428\) −3.33465 −0.161187
\(429\) 1.56865 0.0757349
\(430\) 0 0
\(431\) −1.32450 −0.0637991 −0.0318995 0.999491i \(-0.510156\pi\)
−0.0318995 + 0.999491i \(0.510156\pi\)
\(432\) 4.82407 0.232098
\(433\) 27.9318 1.34232 0.671159 0.741313i \(-0.265797\pi\)
0.671159 + 0.741313i \(0.265797\pi\)
\(434\) −23.9345 −1.14889
\(435\) 0 0
\(436\) 3.31969 0.158984
\(437\) −1.51332 −0.0723919
\(438\) 0.766120 0.0366066
\(439\) 18.3491 0.875756 0.437878 0.899034i \(-0.355730\pi\)
0.437878 + 0.899034i \(0.355730\pi\)
\(440\) 0 0
\(441\) −1.45896 −0.0694745
\(442\) 5.08975 0.242095
\(443\) 13.7771 0.654569 0.327285 0.944926i \(-0.393866\pi\)
0.327285 + 0.944926i \(0.393866\pi\)
\(444\) −5.48459 −0.260287
\(445\) 0 0
\(446\) 20.6873 0.979573
\(447\) 6.91605 0.327118
\(448\) 10.6521 0.503265
\(449\) −9.08241 −0.428625 −0.214313 0.976765i \(-0.568751\pi\)
−0.214313 + 0.976765i \(0.568751\pi\)
\(450\) 0 0
\(451\) −1.93911 −0.0913092
\(452\) −6.37244 −0.299734
\(453\) 13.1690 0.618732
\(454\) 22.2900 1.04612
\(455\) 0 0
\(456\) 0.385109 0.0180344
\(457\) −28.8025 −1.34732 −0.673662 0.739039i \(-0.735280\pi\)
−0.673662 + 0.739039i \(0.735280\pi\)
\(458\) −38.7167 −1.80911
\(459\) −2.46057 −0.114850
\(460\) 0 0
\(461\) −29.5937 −1.37831 −0.689157 0.724612i \(-0.742019\pi\)
−0.689157 + 0.724612i \(0.742019\pi\)
\(462\) 4.60654 0.214315
\(463\) 17.0730 0.793447 0.396724 0.917938i \(-0.370147\pi\)
0.396724 + 0.917938i \(0.370147\pi\)
\(464\) 11.5629 0.536794
\(465\) 0 0
\(466\) 42.5800 1.97248
\(467\) 26.7895 1.23967 0.619834 0.784733i \(-0.287200\pi\)
0.619834 + 0.784733i \(0.287200\pi\)
\(468\) −0.747570 −0.0345564
\(469\) 20.6217 0.952223
\(470\) 0 0
\(471\) 7.97672 0.367548
\(472\) −27.1427 −1.24935
\(473\) 1.46335 0.0672848
\(474\) −8.32478 −0.382370
\(475\) 0 0
\(476\) 3.36264 0.154126
\(477\) 5.14255 0.235461
\(478\) 9.47198 0.433238
\(479\) −30.0981 −1.37522 −0.687609 0.726081i \(-0.741340\pi\)
−0.687609 + 0.726081i \(0.741340\pi\)
\(480\) 0 0
\(481\) −12.1646 −0.554659
\(482\) −7.24184 −0.329857
\(483\) −21.0919 −0.959716
\(484\) −5.52461 −0.251119
\(485\) 0 0
\(486\) 1.60641 0.0728684
\(487\) 10.5069 0.476114 0.238057 0.971251i \(-0.423490\pi\)
0.238057 + 0.971251i \(0.423490\pi\)
\(488\) 31.9852 1.44790
\(489\) −18.1440 −0.820498
\(490\) 0 0
\(491\) 17.5258 0.790928 0.395464 0.918481i \(-0.370584\pi\)
0.395464 + 0.918481i \(0.370584\pi\)
\(492\) 0.924122 0.0416626
\(493\) −5.89780 −0.265623
\(494\) −0.349358 −0.0157183
\(495\) 0 0
\(496\) −30.5341 −1.37102
\(497\) −16.0833 −0.721432
\(498\) −21.8711 −0.980069
\(499\) 3.44802 0.154354 0.0771772 0.997017i \(-0.475409\pi\)
0.0771772 + 0.997017i \(0.475409\pi\)
\(500\) 0 0
\(501\) −15.5428 −0.694399
\(502\) −15.6075 −0.696597
\(503\) −1.65374 −0.0737367 −0.0368684 0.999320i \(-0.511738\pi\)
−0.0368684 + 0.999320i \(0.511738\pi\)
\(504\) 5.36746 0.239086
\(505\) 0 0
\(506\) −17.5348 −0.779515
\(507\) 11.3419 0.503712
\(508\) −2.18094 −0.0967638
\(509\) 23.3010 1.03280 0.516399 0.856348i \(-0.327272\pi\)
0.516399 + 0.856348i \(0.327272\pi\)
\(510\) 0 0
\(511\) 1.12263 0.0496621
\(512\) 6.61555 0.292369
\(513\) 0.168892 0.00745678
\(514\) 35.5498 1.56803
\(515\) 0 0
\(516\) −0.697388 −0.0307008
\(517\) 1.21821 0.0535768
\(518\) −35.7230 −1.56958
\(519\) −9.13465 −0.400967
\(520\) 0 0
\(521\) −12.6319 −0.553415 −0.276707 0.960954i \(-0.589243\pi\)
−0.276707 + 0.960954i \(0.589243\pi\)
\(522\) 3.85044 0.168529
\(523\) 29.1509 1.27468 0.637340 0.770583i \(-0.280035\pi\)
0.637340 + 0.770583i \(0.280035\pi\)
\(524\) 3.57374 0.156120
\(525\) 0 0
\(526\) −39.7407 −1.73278
\(527\) 15.5743 0.678426
\(528\) 5.87673 0.255752
\(529\) 57.2863 2.49071
\(530\) 0 0
\(531\) −11.9036 −0.516574
\(532\) −0.230810 −0.0100069
\(533\) 2.04967 0.0887810
\(534\) −19.3029 −0.835319
\(535\) 0 0
\(536\) 19.9758 0.862821
\(537\) 12.1271 0.523323
\(538\) −39.2091 −1.69042
\(539\) −1.77732 −0.0765547
\(540\) 0 0
\(541\) 26.2586 1.12894 0.564472 0.825452i \(-0.309080\pi\)
0.564472 + 0.825452i \(0.309080\pi\)
\(542\) −32.7117 −1.40509
\(543\) −21.3726 −0.917184
\(544\) 7.84688 0.336432
\(545\) 0 0
\(546\) −4.86918 −0.208382
\(547\) 22.9028 0.979253 0.489626 0.871932i \(-0.337133\pi\)
0.489626 + 0.871932i \(0.337133\pi\)
\(548\) 0.883679 0.0377489
\(549\) 14.0274 0.598673
\(550\) 0 0
\(551\) 0.404821 0.0172460
\(552\) −20.4312 −0.869610
\(553\) −12.1986 −0.518739
\(554\) 16.4058 0.697016
\(555\) 0 0
\(556\) 0.140249 0.00594787
\(557\) −5.02429 −0.212886 −0.106443 0.994319i \(-0.533946\pi\)
−0.106443 + 0.994319i \(0.533946\pi\)
\(558\) −10.1678 −0.430439
\(559\) −1.54678 −0.0654219
\(560\) 0 0
\(561\) −2.99749 −0.126554
\(562\) −14.6659 −0.618645
\(563\) 22.6970 0.956564 0.478282 0.878206i \(-0.341260\pi\)
0.478282 + 0.878206i \(0.341260\pi\)
\(564\) −0.580562 −0.0244461
\(565\) 0 0
\(566\) −32.9229 −1.38385
\(567\) 2.35394 0.0988562
\(568\) −15.5794 −0.653699
\(569\) −17.3367 −0.726791 −0.363395 0.931635i \(-0.618383\pi\)
−0.363395 + 0.931635i \(0.618383\pi\)
\(570\) 0 0
\(571\) −9.39051 −0.392981 −0.196490 0.980506i \(-0.562954\pi\)
−0.196490 + 0.980506i \(0.562954\pi\)
\(572\) −0.910696 −0.0380781
\(573\) −13.4979 −0.563882
\(574\) 6.01913 0.251233
\(575\) 0 0
\(576\) 4.52522 0.188551
\(577\) −18.8942 −0.786576 −0.393288 0.919415i \(-0.628663\pi\)
−0.393288 + 0.919415i \(0.628663\pi\)
\(578\) 17.5831 0.731361
\(579\) −8.03065 −0.333743
\(580\) 0 0
\(581\) −32.0487 −1.32960
\(582\) 21.6557 0.897656
\(583\) 6.26471 0.259458
\(584\) 1.08746 0.0449994
\(585\) 0 0
\(586\) −34.4830 −1.42448
\(587\) 44.8632 1.85170 0.925851 0.377889i \(-0.123350\pi\)
0.925851 + 0.377889i \(0.123350\pi\)
\(588\) 0.847019 0.0349305
\(589\) −1.06901 −0.0440478
\(590\) 0 0
\(591\) −17.2888 −0.711167
\(592\) −45.5732 −1.87305
\(593\) 2.66127 0.109285 0.0546425 0.998506i \(-0.482598\pi\)
0.0546425 + 0.998506i \(0.482598\pi\)
\(594\) 1.95695 0.0802945
\(595\) 0 0
\(596\) −4.01519 −0.164469
\(597\) −5.14079 −0.210399
\(598\) 18.5345 0.757932
\(599\) −12.2072 −0.498771 −0.249386 0.968404i \(-0.580229\pi\)
−0.249386 + 0.968404i \(0.580229\pi\)
\(600\) 0 0
\(601\) −6.16119 −0.251320 −0.125660 0.992073i \(-0.540105\pi\)
−0.125660 + 0.992073i \(0.540105\pi\)
\(602\) −4.54233 −0.185131
\(603\) 8.76052 0.356756
\(604\) −7.64540 −0.311087
\(605\) 0 0
\(606\) 8.47905 0.344438
\(607\) 11.0117 0.446952 0.223476 0.974709i \(-0.428260\pi\)
0.223476 + 0.974709i \(0.428260\pi\)
\(608\) −0.538605 −0.0218433
\(609\) 5.64220 0.228634
\(610\) 0 0
\(611\) −1.28767 −0.0520934
\(612\) 1.42852 0.0577443
\(613\) 24.1631 0.975938 0.487969 0.872861i \(-0.337738\pi\)
0.487969 + 0.872861i \(0.337738\pi\)
\(614\) −18.3298 −0.739731
\(615\) 0 0
\(616\) 6.53869 0.263451
\(617\) 28.8522 1.16155 0.580773 0.814066i \(-0.302750\pi\)
0.580773 + 0.814066i \(0.302750\pi\)
\(618\) −14.6005 −0.587319
\(619\) 1.78397 0.0717037 0.0358519 0.999357i \(-0.488586\pi\)
0.0358519 + 0.999357i \(0.488586\pi\)
\(620\) 0 0
\(621\) −8.96026 −0.359563
\(622\) −12.0031 −0.481280
\(623\) −28.2853 −1.13323
\(624\) −6.21179 −0.248671
\(625\) 0 0
\(626\) 24.6321 0.984497
\(627\) 0.205746 0.00821671
\(628\) −4.63098 −0.184796
\(629\) 23.2451 0.926844
\(630\) 0 0
\(631\) 12.2661 0.488306 0.244153 0.969737i \(-0.421490\pi\)
0.244153 + 0.969737i \(0.421490\pi\)
\(632\) −11.8165 −0.470036
\(633\) −6.07830 −0.241591
\(634\) 30.2773 1.20246
\(635\) 0 0
\(636\) −2.98557 −0.118386
\(637\) 1.87866 0.0744351
\(638\) 4.69064 0.185704
\(639\) −6.83248 −0.270289
\(640\) 0 0
\(641\) −31.0075 −1.22472 −0.612362 0.790578i \(-0.709780\pi\)
−0.612362 + 0.790578i \(0.709780\pi\)
\(642\) −9.22697 −0.364160
\(643\) −23.9013 −0.942574 −0.471287 0.881980i \(-0.656210\pi\)
−0.471287 + 0.881980i \(0.656210\pi\)
\(644\) 12.2452 0.482527
\(645\) 0 0
\(646\) 0.667581 0.0262656
\(647\) −28.8735 −1.13513 −0.567566 0.823328i \(-0.692115\pi\)
−0.567566 + 0.823328i \(0.692115\pi\)
\(648\) 2.28020 0.0895748
\(649\) −14.5011 −0.569219
\(650\) 0 0
\(651\) −14.8993 −0.583951
\(652\) 10.5337 0.412531
\(653\) −36.1118 −1.41316 −0.706582 0.707631i \(-0.749764\pi\)
−0.706582 + 0.707631i \(0.749764\pi\)
\(654\) 9.18557 0.359184
\(655\) 0 0
\(656\) 7.67882 0.299808
\(657\) 0.476914 0.0186062
\(658\) −3.78140 −0.147414
\(659\) 31.4095 1.22354 0.611770 0.791036i \(-0.290458\pi\)
0.611770 + 0.791036i \(0.290458\pi\)
\(660\) 0 0
\(661\) 10.1647 0.395361 0.197681 0.980266i \(-0.436659\pi\)
0.197681 + 0.980266i \(0.436659\pi\)
\(662\) 5.79789 0.225341
\(663\) 3.16840 0.123050
\(664\) −31.0447 −1.20477
\(665\) 0 0
\(666\) −15.1758 −0.588052
\(667\) −21.4770 −0.831593
\(668\) 9.02353 0.349131
\(669\) 12.8780 0.497891
\(670\) 0 0
\(671\) 17.0882 0.659684
\(672\) −7.50682 −0.289582
\(673\) −13.4744 −0.519400 −0.259700 0.965689i \(-0.583624\pi\)
−0.259700 + 0.965689i \(0.583624\pi\)
\(674\) 29.7306 1.14518
\(675\) 0 0
\(676\) −6.58469 −0.253257
\(677\) 1.48122 0.0569281 0.0284640 0.999595i \(-0.490938\pi\)
0.0284640 + 0.999595i \(0.490938\pi\)
\(678\) −17.6325 −0.677172
\(679\) 31.7329 1.21780
\(680\) 0 0
\(681\) 13.8756 0.531715
\(682\) −12.3866 −0.474306
\(683\) −14.5690 −0.557469 −0.278734 0.960368i \(-0.589915\pi\)
−0.278734 + 0.960368i \(0.589915\pi\)
\(684\) −0.0980525 −0.00374913
\(685\) 0 0
\(686\) 31.9867 1.22126
\(687\) −24.1014 −0.919524
\(688\) −5.79481 −0.220925
\(689\) −6.62189 −0.252274
\(690\) 0 0
\(691\) −25.4543 −0.968327 −0.484163 0.874978i \(-0.660876\pi\)
−0.484163 + 0.874978i \(0.660876\pi\)
\(692\) 5.30323 0.201599
\(693\) 2.86759 0.108931
\(694\) −1.69957 −0.0645146
\(695\) 0 0
\(696\) 5.46546 0.207168
\(697\) −3.91667 −0.148355
\(698\) −43.5887 −1.64986
\(699\) 26.5063 1.00256
\(700\) 0 0
\(701\) 47.1753 1.78179 0.890894 0.454211i \(-0.150079\pi\)
0.890894 + 0.454211i \(0.150079\pi\)
\(702\) −2.06852 −0.0780713
\(703\) −1.59553 −0.0601766
\(704\) 5.51267 0.207766
\(705\) 0 0
\(706\) −6.57860 −0.247589
\(707\) 12.4247 0.467279
\(708\) 6.91081 0.259724
\(709\) −37.8007 −1.41964 −0.709818 0.704385i \(-0.751223\pi\)
−0.709818 + 0.704385i \(0.751223\pi\)
\(710\) 0 0
\(711\) −5.18222 −0.194348
\(712\) −27.3993 −1.02683
\(713\) 56.7142 2.12397
\(714\) 9.30442 0.348209
\(715\) 0 0
\(716\) −7.04053 −0.263117
\(717\) 5.89635 0.220203
\(718\) −40.9429 −1.52797
\(719\) −13.3382 −0.497431 −0.248716 0.968577i \(-0.580008\pi\)
−0.248716 + 0.968577i \(0.580008\pi\)
\(720\) 0 0
\(721\) −21.3947 −0.796781
\(722\) 30.4760 1.13420
\(723\) −4.50808 −0.167657
\(724\) 12.4081 0.461143
\(725\) 0 0
\(726\) −15.2866 −0.567338
\(727\) −0.000763187 0 −2.83050e−5 0 −1.41525e−5 1.00000i \(-0.500005\pi\)
−1.41525e−5 1.00000i \(0.500005\pi\)
\(728\) −6.91150 −0.256157
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.95571 0.109321
\(732\) −8.14375 −0.301002
\(733\) −39.7135 −1.46685 −0.733425 0.679770i \(-0.762080\pi\)
−0.733425 + 0.679770i \(0.762080\pi\)
\(734\) −29.1214 −1.07489
\(735\) 0 0
\(736\) 28.5747 1.05328
\(737\) 10.6721 0.393113
\(738\) 2.55704 0.0941260
\(739\) 20.0290 0.736777 0.368389 0.929672i \(-0.379910\pi\)
0.368389 + 0.929672i \(0.379910\pi\)
\(740\) 0 0
\(741\) −0.217477 −0.00798921
\(742\) −19.4461 −0.713887
\(743\) −12.4716 −0.457539 −0.228769 0.973481i \(-0.573470\pi\)
−0.228769 + 0.973481i \(0.573470\pi\)
\(744\) −14.4326 −0.529125
\(745\) 0 0
\(746\) −9.99478 −0.365935
\(747\) −13.6149 −0.498143
\(748\) 1.74023 0.0636292
\(749\) −13.5207 −0.494034
\(750\) 0 0
\(751\) −21.9589 −0.801291 −0.400646 0.916233i \(-0.631214\pi\)
−0.400646 + 0.916233i \(0.631214\pi\)
\(752\) −4.82407 −0.175916
\(753\) −9.71575 −0.354062
\(754\) −4.95808 −0.180563
\(755\) 0 0
\(756\) −1.36661 −0.0497031
\(757\) 26.4162 0.960113 0.480056 0.877238i \(-0.340616\pi\)
0.480056 + 0.877238i \(0.340616\pi\)
\(758\) −8.41325 −0.305583
\(759\) −10.9155 −0.396207
\(760\) 0 0
\(761\) −36.2026 −1.31234 −0.656172 0.754611i \(-0.727826\pi\)
−0.656172 + 0.754611i \(0.727826\pi\)
\(762\) −6.03466 −0.218613
\(763\) 13.4600 0.487284
\(764\) 7.83636 0.283510
\(765\) 0 0
\(766\) −17.7472 −0.641232
\(767\) 15.3279 0.553459
\(768\) −12.8730 −0.464515
\(769\) 34.8533 1.25684 0.628422 0.777873i \(-0.283701\pi\)
0.628422 + 0.777873i \(0.283701\pi\)
\(770\) 0 0
\(771\) 22.1299 0.796989
\(772\) 4.66229 0.167800
\(773\) −9.23266 −0.332076 −0.166038 0.986119i \(-0.553097\pi\)
−0.166038 + 0.986119i \(0.553097\pi\)
\(774\) −1.92967 −0.0693605
\(775\) 0 0
\(776\) 30.7389 1.10346
\(777\) −22.2378 −0.797775
\(778\) −15.1722 −0.543950
\(779\) 0.268838 0.00963212
\(780\) 0 0
\(781\) −8.32339 −0.297834
\(782\) −35.4172 −1.26652
\(783\) 2.39692 0.0856589
\(784\) 7.03814 0.251362
\(785\) 0 0
\(786\) 9.88854 0.352712
\(787\) 17.2217 0.613886 0.306943 0.951728i \(-0.400694\pi\)
0.306943 + 0.951728i \(0.400694\pi\)
\(788\) 10.0372 0.357561
\(789\) −24.7388 −0.880723
\(790\) 0 0
\(791\) −25.8376 −0.918680
\(792\) 2.77776 0.0987036
\(793\) −18.0625 −0.641419
\(794\) −4.82475 −0.171224
\(795\) 0 0
\(796\) 2.98455 0.105785
\(797\) 2.93899 0.104105 0.0520523 0.998644i \(-0.483424\pi\)
0.0520523 + 0.998644i \(0.483424\pi\)
\(798\) −0.638650 −0.0226080
\(799\) 2.46057 0.0870489
\(800\) 0 0
\(801\) −12.0162 −0.424570
\(802\) 47.6438 1.68236
\(803\) 0.580981 0.0205024
\(804\) −5.08602 −0.179370
\(805\) 0 0
\(806\) 13.0928 0.461173
\(807\) −24.4078 −0.859196
\(808\) 12.0355 0.423407
\(809\) −47.0667 −1.65478 −0.827389 0.561629i \(-0.810175\pi\)
−0.827389 + 0.561629i \(0.810175\pi\)
\(810\) 0 0
\(811\) 12.1936 0.428176 0.214088 0.976814i \(-0.431322\pi\)
0.214088 + 0.976814i \(0.431322\pi\)
\(812\) −3.27565 −0.114953
\(813\) −20.3632 −0.714168
\(814\) −18.4873 −0.647981
\(815\) 0 0
\(816\) 11.8700 0.415533
\(817\) −0.202878 −0.00709782
\(818\) −17.0148 −0.594907
\(819\) −3.03109 −0.105915
\(820\) 0 0
\(821\) −27.8694 −0.972647 −0.486324 0.873779i \(-0.661662\pi\)
−0.486324 + 0.873779i \(0.661662\pi\)
\(822\) 2.44513 0.0852839
\(823\) −26.1727 −0.912323 −0.456161 0.889897i \(-0.650776\pi\)
−0.456161 + 0.889897i \(0.650776\pi\)
\(824\) −20.7245 −0.721973
\(825\) 0 0
\(826\) 45.0125 1.56618
\(827\) −6.25176 −0.217395 −0.108697 0.994075i \(-0.534668\pi\)
−0.108697 + 0.994075i \(0.534668\pi\)
\(828\) 5.20199 0.180782
\(829\) −2.54642 −0.0884409 −0.0442205 0.999022i \(-0.514080\pi\)
−0.0442205 + 0.999022i \(0.514080\pi\)
\(830\) 0 0
\(831\) 10.2127 0.354274
\(832\) −5.82697 −0.202014
\(833\) −3.58989 −0.124382
\(834\) 0.388067 0.0134377
\(835\) 0 0
\(836\) −0.119448 −0.00413121
\(837\) −6.32953 −0.218781
\(838\) 34.1835 1.18085
\(839\) 6.20012 0.214052 0.107026 0.994256i \(-0.465867\pi\)
0.107026 + 0.994256i \(0.465867\pi\)
\(840\) 0 0
\(841\) −23.2548 −0.801889
\(842\) 29.6248 1.02094
\(843\) −9.12961 −0.314441
\(844\) 3.52883 0.121467
\(845\) 0 0
\(846\) −1.60641 −0.0552296
\(847\) −22.4000 −0.769674
\(848\) −24.8081 −0.851912
\(849\) −20.4947 −0.703375
\(850\) 0 0
\(851\) 84.6479 2.90169
\(852\) 3.96668 0.135896
\(853\) 30.5276 1.04525 0.522623 0.852564i \(-0.324953\pi\)
0.522623 + 0.852564i \(0.324953\pi\)
\(854\) −53.0430 −1.81509
\(855\) 0 0
\(856\) −13.0971 −0.447650
\(857\) 18.2826 0.624522 0.312261 0.949996i \(-0.398914\pi\)
0.312261 + 0.949996i \(0.398914\pi\)
\(858\) −2.51989 −0.0860277
\(859\) 42.6716 1.45594 0.727969 0.685610i \(-0.240465\pi\)
0.727969 + 0.685610i \(0.240465\pi\)
\(860\) 0 0
\(861\) 3.74694 0.127695
\(862\) 2.12770 0.0724697
\(863\) 3.21332 0.109383 0.0546913 0.998503i \(-0.482583\pi\)
0.0546913 + 0.998503i \(0.482583\pi\)
\(864\) −3.18904 −0.108493
\(865\) 0 0
\(866\) −44.8701 −1.52475
\(867\) 10.9456 0.371731
\(868\) 8.64999 0.293600
\(869\) −6.31303 −0.214155
\(870\) 0 0
\(871\) −11.2806 −0.382229
\(872\) 13.0383 0.441534
\(873\) 13.4808 0.456254
\(874\) 2.43102 0.0822304
\(875\) 0 0
\(876\) −0.276878 −0.00935484
\(877\) −48.8397 −1.64920 −0.824600 0.565717i \(-0.808600\pi\)
−0.824600 + 0.565717i \(0.808600\pi\)
\(878\) −29.4763 −0.994776
\(879\) −21.4658 −0.724024
\(880\) 0 0
\(881\) −29.2473 −0.985367 −0.492684 0.870209i \(-0.663984\pi\)
−0.492684 + 0.870209i \(0.663984\pi\)
\(882\) 2.34370 0.0789164
\(883\) 37.5839 1.26480 0.632400 0.774642i \(-0.282070\pi\)
0.632400 + 0.774642i \(0.282070\pi\)
\(884\) −1.83945 −0.0618674
\(885\) 0 0
\(886\) −22.1317 −0.743529
\(887\) −10.7876 −0.362211 −0.181106 0.983464i \(-0.557968\pi\)
−0.181106 + 0.983464i \(0.557968\pi\)
\(888\) −21.5412 −0.722874
\(889\) −8.84283 −0.296579
\(890\) 0 0
\(891\) 1.21821 0.0408115
\(892\) −7.47645 −0.250330
\(893\) −0.168892 −0.00565177
\(894\) −11.1100 −0.371575
\(895\) 0 0
\(896\) −32.1253 −1.07323
\(897\) 11.5378 0.385237
\(898\) 14.5901 0.486878
\(899\) −15.1714 −0.505993
\(900\) 0 0
\(901\) 12.6536 0.421554
\(902\) 3.11501 0.103719
\(903\) −2.82762 −0.0940973
\(904\) −25.0282 −0.832427
\(905\) 0 0
\(906\) −21.1548 −0.702821
\(907\) −35.2429 −1.17022 −0.585111 0.810953i \(-0.698949\pi\)
−0.585111 + 0.810953i \(0.698949\pi\)
\(908\) −8.05565 −0.267336
\(909\) 5.27825 0.175069
\(910\) 0 0
\(911\) −11.1069 −0.367987 −0.183993 0.982927i \(-0.558903\pi\)
−0.183993 + 0.982927i \(0.558903\pi\)
\(912\) −0.814749 −0.0269790
\(913\) −16.5858 −0.548910
\(914\) 46.2687 1.53043
\(915\) 0 0
\(916\) 13.9923 0.462320
\(917\) 14.4901 0.478504
\(918\) 3.95270 0.130458
\(919\) −47.4809 −1.56625 −0.783126 0.621863i \(-0.786376\pi\)
−0.783126 + 0.621863i \(0.786376\pi\)
\(920\) 0 0
\(921\) −11.4104 −0.375985
\(922\) 47.5396 1.56563
\(923\) 8.79795 0.289588
\(924\) −1.66482 −0.0547684
\(925\) 0 0
\(926\) −27.4262 −0.901281
\(927\) −9.08889 −0.298518
\(928\) −7.64388 −0.250923
\(929\) 32.0236 1.05066 0.525331 0.850898i \(-0.323942\pi\)
0.525331 + 0.850898i \(0.323942\pi\)
\(930\) 0 0
\(931\) 0.246408 0.00807569
\(932\) −15.3885 −0.504068
\(933\) −7.47198 −0.244622
\(934\) −43.0350 −1.40815
\(935\) 0 0
\(936\) −2.93614 −0.0959707
\(937\) 29.3965 0.960342 0.480171 0.877175i \(-0.340575\pi\)
0.480171 + 0.877175i \(0.340575\pi\)
\(938\) −33.1270 −1.08164
\(939\) 15.3336 0.500394
\(940\) 0 0
\(941\) −27.5767 −0.898976 −0.449488 0.893286i \(-0.648393\pi\)
−0.449488 + 0.893286i \(0.648393\pi\)
\(942\) −12.8139 −0.417500
\(943\) −14.2627 −0.464457
\(944\) 57.4240 1.86899
\(945\) 0 0
\(946\) −2.35074 −0.0764292
\(947\) 6.49455 0.211044 0.105522 0.994417i \(-0.466349\pi\)
0.105522 + 0.994417i \(0.466349\pi\)
\(948\) 3.00860 0.0977147
\(949\) −0.614105 −0.0199347
\(950\) 0 0
\(951\) 18.8478 0.611181
\(952\) 13.2070 0.428043
\(953\) 54.1799 1.75506 0.877530 0.479522i \(-0.159190\pi\)
0.877530 + 0.479522i \(0.159190\pi\)
\(954\) −8.26107 −0.267462
\(955\) 0 0
\(956\) −3.42320 −0.110714
\(957\) 2.91995 0.0943885
\(958\) 48.3500 1.56212
\(959\) 3.58295 0.115700
\(960\) 0 0
\(961\) 9.06294 0.292353
\(962\) 19.5414 0.630040
\(963\) −5.74384 −0.185093
\(964\) 2.61722 0.0842950
\(965\) 0 0
\(966\) 33.8823 1.09015
\(967\) 49.7977 1.60139 0.800693 0.599075i \(-0.204465\pi\)
0.800693 + 0.599075i \(0.204465\pi\)
\(968\) −21.6983 −0.697411
\(969\) 0.415572 0.0133501
\(970\) 0 0
\(971\) −43.9456 −1.41028 −0.705140 0.709068i \(-0.749116\pi\)
−0.705140 + 0.709068i \(0.749116\pi\)
\(972\) −0.580562 −0.0186215
\(973\) 0.568651 0.0182301
\(974\) −16.8784 −0.540820
\(975\) 0 0
\(976\) −67.6689 −2.16603
\(977\) 23.1730 0.741371 0.370685 0.928758i \(-0.379123\pi\)
0.370685 + 0.928758i \(0.379123\pi\)
\(978\) 29.1467 0.932008
\(979\) −14.6382 −0.467839
\(980\) 0 0
\(981\) 5.71806 0.182564
\(982\) −28.1537 −0.898420
\(983\) 61.2466 1.95346 0.976732 0.214465i \(-0.0688009\pi\)
0.976732 + 0.214465i \(0.0688009\pi\)
\(984\) 3.62956 0.115706
\(985\) 0 0
\(986\) 9.47429 0.301723
\(987\) −2.35394 −0.0749268
\(988\) 0.126259 0.00401683
\(989\) 10.7633 0.342254
\(990\) 0 0
\(991\) 57.7571 1.83471 0.917357 0.398064i \(-0.130318\pi\)
0.917357 + 0.398064i \(0.130318\pi\)
\(992\) 20.1851 0.640879
\(993\) 3.60922 0.114535
\(994\) 25.8363 0.819479
\(995\) 0 0
\(996\) 7.90429 0.250457
\(997\) −37.2895 −1.18097 −0.590486 0.807048i \(-0.701064\pi\)
−0.590486 + 0.807048i \(0.701064\pi\)
\(998\) −5.53894 −0.175332
\(999\) −9.44703 −0.298891
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 3525.2.a.be.1.2 yes 8
5.4 even 2 3525.2.a.bd.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3525.2.a.bd.1.7 8 5.4 even 2
3525.2.a.be.1.2 yes 8 1.1 even 1 trivial