Properties

Label 4025.2.a.p.1.2
Level 4025
Weight 2
Character 4025.1
Self dual yes
Analytic conductor 32.140
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.2147108.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 161)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.11948\)
Character \(\chi\) = 4025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.11948 q^{2} +1.84074 q^{3} +2.49221 q^{4} -3.90141 q^{6} -1.00000 q^{7} -1.04322 q^{8} +0.388311 q^{9} +O(q^{10})\) \(q-2.11948 q^{2} +1.84074 q^{3} +2.49221 q^{4} -3.90141 q^{6} -1.00000 q^{7} -1.04322 q^{8} +0.388311 q^{9} +5.87722 q^{11} +4.58750 q^{12} +6.24994 q^{13} +2.11948 q^{14} -2.77332 q^{16} +5.42479 q^{17} -0.823019 q^{18} -2.23897 q^{19} -1.84074 q^{21} -12.4567 q^{22} +1.00000 q^{23} -1.92030 q^{24} -13.2466 q^{26} -4.80743 q^{27} -2.49221 q^{28} +0.642864 q^{29} +7.84074 q^{31} +7.96445 q^{32} +10.8184 q^{33} -11.4977 q^{34} +0.967751 q^{36} -0.557492 q^{37} +4.74545 q^{38} +11.5045 q^{39} +2.56847 q^{41} +3.90141 q^{42} +8.81841 q^{43} +14.6472 q^{44} -2.11948 q^{46} -4.26766 q^{47} -5.10495 q^{48} +1.00000 q^{49} +9.98561 q^{51} +15.5761 q^{52} -3.01559 q^{53} +10.1893 q^{54} +1.04322 q^{56} -4.12134 q^{57} -1.36254 q^{58} +4.17024 q^{59} -0.148289 q^{61} -16.6183 q^{62} -0.388311 q^{63} -11.3339 q^{64} -22.9294 q^{66} -13.3396 q^{67} +13.5197 q^{68} +1.84074 q^{69} -7.93141 q^{71} -0.405095 q^{72} -4.28111 q^{73} +1.18159 q^{74} -5.57996 q^{76} -5.87722 q^{77} -24.3836 q^{78} -0.861628 q^{79} -10.0141 q^{81} -5.44382 q^{82} +4.81841 q^{83} -4.58750 q^{84} -18.6905 q^{86} +1.18334 q^{87} -6.13125 q^{88} +6.32964 q^{89} -6.24994 q^{91} +2.49221 q^{92} +14.4327 q^{93} +9.04523 q^{94} +14.6605 q^{96} -10.4822 q^{97} -2.11948 q^{98} +2.28219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 2q^{2} + 12q^{4} - 3q^{6} - 5q^{7} - 3q^{8} + 11q^{9} + O(q^{10}) \) \( 5q - 2q^{2} + 12q^{4} - 3q^{6} - 5q^{7} - 3q^{8} + 11q^{9} - 4q^{11} - 3q^{12} + 6q^{13} + 2q^{14} + 10q^{16} + 12q^{17} + 19q^{18} + 6q^{19} - 14q^{22} + 5q^{23} - 36q^{24} + q^{26} - 12q^{28} - 4q^{29} + 30q^{31} - 8q^{32} + 22q^{33} + 6q^{34} - q^{36} - 4q^{37} + 40q^{38} + 16q^{39} + 6q^{41} + 3q^{42} + 12q^{43} - 26q^{44} - 2q^{46} - 10q^{47} - 25q^{48} + 5q^{49} - 4q^{51} + 21q^{52} - 16q^{53} + 33q^{54} + 3q^{56} - 6q^{57} - 13q^{58} + 22q^{59} - 18q^{61} - 15q^{62} - 11q^{63} + 25q^{64} + 4q^{66} + 2q^{67} - 12q^{68} + 4q^{71} + 41q^{72} + 2q^{73} + 38q^{74} + 10q^{76} + 4q^{77} - 41q^{78} + 30q^{79} - 3q^{81} + 7q^{82} - 8q^{83} + 3q^{84} + 8q^{86} + 12q^{87} - 4q^{88} - 20q^{89} - 6q^{91} + 12q^{92} + 26q^{93} - 25q^{94} - q^{96} + 12q^{97} - 2q^{98} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11948 −1.49870 −0.749350 0.662174i \(-0.769634\pi\)
−0.749350 + 0.662174i \(0.769634\pi\)
\(3\) 1.84074 1.06275 0.531375 0.847137i \(-0.321676\pi\)
0.531375 + 0.847137i \(0.321676\pi\)
\(4\) 2.49221 1.24610
\(5\) 0 0
\(6\) −3.90141 −1.59274
\(7\) −1.00000 −0.377964
\(8\) −1.04322 −0.368835
\(9\) 0.388311 0.129437
\(10\) 0 0
\(11\) 5.87722 1.77205 0.886024 0.463640i \(-0.153457\pi\)
0.886024 + 0.463640i \(0.153457\pi\)
\(12\) 4.58750 1.32430
\(13\) 6.24994 1.73342 0.866711 0.498811i \(-0.166230\pi\)
0.866711 + 0.498811i \(0.166230\pi\)
\(14\) 2.11948 0.566456
\(15\) 0 0
\(16\) −2.77332 −0.693330
\(17\) 5.42479 1.31570 0.657852 0.753147i \(-0.271465\pi\)
0.657852 + 0.753147i \(0.271465\pi\)
\(18\) −0.823019 −0.193987
\(19\) −2.23897 −0.513654 −0.256827 0.966457i \(-0.582677\pi\)
−0.256827 + 0.966457i \(0.582677\pi\)
\(20\) 0 0
\(21\) −1.84074 −0.401682
\(22\) −12.4567 −2.65577
\(23\) 1.00000 0.208514
\(24\) −1.92030 −0.391979
\(25\) 0 0
\(26\) −13.2466 −2.59788
\(27\) −4.80743 −0.925191
\(28\) −2.49221 −0.470983
\(29\) 0.642864 0.119377 0.0596884 0.998217i \(-0.480989\pi\)
0.0596884 + 0.998217i \(0.480989\pi\)
\(30\) 0 0
\(31\) 7.84074 1.40824 0.704119 0.710082i \(-0.251342\pi\)
0.704119 + 0.710082i \(0.251342\pi\)
\(32\) 7.96445 1.40793
\(33\) 10.8184 1.88324
\(34\) −11.4977 −1.97185
\(35\) 0 0
\(36\) 0.967751 0.161292
\(37\) −0.557492 −0.0916511 −0.0458256 0.998949i \(-0.514592\pi\)
−0.0458256 + 0.998949i \(0.514592\pi\)
\(38\) 4.74545 0.769813
\(39\) 11.5045 1.84219
\(40\) 0 0
\(41\) 2.56847 0.401127 0.200564 0.979681i \(-0.435723\pi\)
0.200564 + 0.979681i \(0.435723\pi\)
\(42\) 3.90141 0.602000
\(43\) 8.81841 1.34479 0.672397 0.740191i \(-0.265265\pi\)
0.672397 + 0.740191i \(0.265265\pi\)
\(44\) 14.6472 2.20815
\(45\) 0 0
\(46\) −2.11948 −0.312501
\(47\) −4.26766 −0.622502 −0.311251 0.950328i \(-0.600748\pi\)
−0.311251 + 0.950328i \(0.600748\pi\)
\(48\) −5.10495 −0.736836
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 9.98561 1.39826
\(52\) 15.5761 2.16002
\(53\) −3.01559 −0.414223 −0.207111 0.978317i \(-0.566406\pi\)
−0.207111 + 0.978317i \(0.566406\pi\)
\(54\) 10.1893 1.38658
\(55\) 0 0
\(56\) 1.04322 0.139407
\(57\) −4.12134 −0.545885
\(58\) −1.36254 −0.178910
\(59\) 4.17024 0.542919 0.271459 0.962450i \(-0.412494\pi\)
0.271459 + 0.962450i \(0.412494\pi\)
\(60\) 0 0
\(61\) −0.148289 −0.0189865 −0.00949325 0.999955i \(-0.503022\pi\)
−0.00949325 + 0.999955i \(0.503022\pi\)
\(62\) −16.6183 −2.11053
\(63\) −0.388311 −0.0489226
\(64\) −11.3339 −1.41673
\(65\) 0 0
\(66\) −22.9294 −2.82242
\(67\) −13.3396 −1.62969 −0.814843 0.579681i \(-0.803177\pi\)
−0.814843 + 0.579681i \(0.803177\pi\)
\(68\) 13.5197 1.63950
\(69\) 1.84074 0.221599
\(70\) 0 0
\(71\) −7.93141 −0.941285 −0.470643 0.882324i \(-0.655978\pi\)
−0.470643 + 0.882324i \(0.655978\pi\)
\(72\) −0.405095 −0.0477409
\(73\) −4.28111 −0.501066 −0.250533 0.968108i \(-0.580606\pi\)
−0.250533 + 0.968108i \(0.580606\pi\)
\(74\) 1.18159 0.137358
\(75\) 0 0
\(76\) −5.57996 −0.640066
\(77\) −5.87722 −0.669771
\(78\) −24.3836 −2.76090
\(79\) −0.861628 −0.0969407 −0.0484704 0.998825i \(-0.515435\pi\)
−0.0484704 + 0.998825i \(0.515435\pi\)
\(80\) 0 0
\(81\) −10.0141 −1.11268
\(82\) −5.44382 −0.601169
\(83\) 4.81841 0.528889 0.264444 0.964401i \(-0.414811\pi\)
0.264444 + 0.964401i \(0.414811\pi\)
\(84\) −4.58750 −0.500537
\(85\) 0 0
\(86\) −18.6905 −2.01544
\(87\) 1.18334 0.126868
\(88\) −6.13125 −0.653593
\(89\) 6.32964 0.670941 0.335470 0.942051i \(-0.391105\pi\)
0.335470 + 0.942051i \(0.391105\pi\)
\(90\) 0 0
\(91\) −6.24994 −0.655172
\(92\) 2.49221 0.259830
\(93\) 14.4327 1.49660
\(94\) 9.04523 0.932944
\(95\) 0 0
\(96\) 14.6605 1.49628
\(97\) −10.4822 −1.06430 −0.532151 0.846649i \(-0.678616\pi\)
−0.532151 + 0.846649i \(0.678616\pi\)
\(98\) −2.11948 −0.214100
\(99\) 2.28219 0.229369
\(100\) 0 0
\(101\) −1.57308 −0.156527 −0.0782636 0.996933i \(-0.524938\pi\)
−0.0782636 + 0.996933i \(0.524938\pi\)
\(102\) −21.1643 −2.09558
\(103\) −5.01559 −0.494201 −0.247100 0.968990i \(-0.579478\pi\)
−0.247100 + 0.968990i \(0.579478\pi\)
\(104\) −6.52008 −0.639346
\(105\) 0 0
\(106\) 6.39148 0.620796
\(107\) 5.81204 0.561872 0.280936 0.959727i \(-0.409355\pi\)
0.280936 + 0.959727i \(0.409355\pi\)
\(108\) −11.9811 −1.15288
\(109\) 7.65030 0.732766 0.366383 0.930464i \(-0.380596\pi\)
0.366383 + 0.930464i \(0.380596\pi\)
\(110\) 0 0
\(111\) −1.02620 −0.0974022
\(112\) 2.77332 0.262054
\(113\) −10.4999 −0.987745 −0.493873 0.869534i \(-0.664419\pi\)
−0.493873 + 0.869534i \(0.664419\pi\)
\(114\) 8.73512 0.818119
\(115\) 0 0
\(116\) 1.60215 0.148756
\(117\) 2.42692 0.224369
\(118\) −8.83875 −0.813673
\(119\) −5.42479 −0.497290
\(120\) 0 0
\(121\) 23.5417 2.14015
\(122\) 0.314297 0.0284551
\(123\) 4.72787 0.426298
\(124\) 19.5407 1.75481
\(125\) 0 0
\(126\) 0.823019 0.0733203
\(127\) 17.9732 1.59486 0.797432 0.603409i \(-0.206191\pi\)
0.797432 + 0.603409i \(0.206191\pi\)
\(128\) 8.09304 0.715331
\(129\) 16.2324 1.42918
\(130\) 0 0
\(131\) −13.0641 −1.14142 −0.570708 0.821153i \(-0.693331\pi\)
−0.570708 + 0.821153i \(0.693331\pi\)
\(132\) 26.9617 2.34671
\(133\) 2.23897 0.194143
\(134\) 28.2730 2.44241
\(135\) 0 0
\(136\) −5.65926 −0.485278
\(137\) 15.0262 1.28377 0.641887 0.766799i \(-0.278152\pi\)
0.641887 + 0.766799i \(0.278152\pi\)
\(138\) −3.90141 −0.332110
\(139\) −12.7987 −1.08557 −0.542786 0.839871i \(-0.682631\pi\)
−0.542786 + 0.839871i \(0.682631\pi\)
\(140\) 0 0
\(141\) −7.85563 −0.661564
\(142\) 16.8105 1.41071
\(143\) 36.7322 3.07170
\(144\) −1.07691 −0.0897426
\(145\) 0 0
\(146\) 9.07375 0.750949
\(147\) 1.84074 0.151821
\(148\) −1.38939 −0.114207
\(149\) −21.1303 −1.73106 −0.865532 0.500854i \(-0.833019\pi\)
−0.865532 + 0.500854i \(0.833019\pi\)
\(150\) 0 0
\(151\) 19.5264 1.58904 0.794520 0.607239i \(-0.207723\pi\)
0.794520 + 0.607239i \(0.207723\pi\)
\(152\) 2.33574 0.189453
\(153\) 2.10651 0.170301
\(154\) 12.4567 1.00379
\(155\) 0 0
\(156\) 28.6716 2.29556
\(157\) 4.60638 0.367630 0.183815 0.982961i \(-0.441155\pi\)
0.183815 + 0.982961i \(0.441155\pi\)
\(158\) 1.82621 0.145285
\(159\) −5.55090 −0.440215
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 21.2248 1.66758
\(163\) −16.3229 −1.27851 −0.639254 0.768996i \(-0.720757\pi\)
−0.639254 + 0.768996i \(0.720757\pi\)
\(164\) 6.40115 0.499846
\(165\) 0 0
\(166\) −10.2125 −0.792646
\(167\) −16.7254 −1.29425 −0.647125 0.762384i \(-0.724029\pi\)
−0.647125 + 0.762384i \(0.724029\pi\)
\(168\) 1.92030 0.148154
\(169\) 26.0617 2.00475
\(170\) 0 0
\(171\) −0.869415 −0.0664858
\(172\) 21.9773 1.67575
\(173\) −9.27650 −0.705279 −0.352640 0.935759i \(-0.614716\pi\)
−0.352640 + 0.935759i \(0.614716\pi\)
\(174\) −2.50807 −0.190137
\(175\) 0 0
\(176\) −16.2994 −1.22861
\(177\) 7.67631 0.576987
\(178\) −13.4156 −1.00554
\(179\) −7.48254 −0.559272 −0.279636 0.960106i \(-0.590214\pi\)
−0.279636 + 0.960106i \(0.590214\pi\)
\(180\) 0 0
\(181\) −10.6482 −0.791472 −0.395736 0.918364i \(-0.629510\pi\)
−0.395736 + 0.918364i \(0.629510\pi\)
\(182\) 13.2466 0.981906
\(183\) −0.272962 −0.0201779
\(184\) −1.04322 −0.0769074
\(185\) 0 0
\(186\) −30.5899 −2.24296
\(187\) 31.8827 2.33149
\(188\) −10.6359 −0.775701
\(189\) 4.80743 0.349689
\(190\) 0 0
\(191\) 3.30294 0.238992 0.119496 0.992835i \(-0.461872\pi\)
0.119496 + 0.992835i \(0.461872\pi\)
\(192\) −20.8627 −1.50563
\(193\) −9.38315 −0.675414 −0.337707 0.941251i \(-0.609651\pi\)
−0.337707 + 0.941251i \(0.609651\pi\)
\(194\) 22.2168 1.59507
\(195\) 0 0
\(196\) 2.49221 0.178015
\(197\) 23.0929 1.64530 0.822651 0.568547i \(-0.192494\pi\)
0.822651 + 0.568547i \(0.192494\pi\)
\(198\) −4.83706 −0.343755
\(199\) 21.6149 1.53224 0.766118 0.642699i \(-0.222186\pi\)
0.766118 + 0.642699i \(0.222186\pi\)
\(200\) 0 0
\(201\) −24.5546 −1.73195
\(202\) 3.33411 0.234587
\(203\) −0.642864 −0.0451202
\(204\) 24.8862 1.74238
\(205\) 0 0
\(206\) 10.6304 0.740659
\(207\) 0.388311 0.0269895
\(208\) −17.3331 −1.20183
\(209\) −13.1589 −0.910219
\(210\) 0 0
\(211\) 15.4579 1.06416 0.532081 0.846693i \(-0.321410\pi\)
0.532081 + 0.846693i \(0.321410\pi\)
\(212\) −7.51547 −0.516164
\(213\) −14.5996 −1.00035
\(214\) −12.3185 −0.842077
\(215\) 0 0
\(216\) 5.01522 0.341243
\(217\) −7.84074 −0.532264
\(218\) −16.2147 −1.09820
\(219\) −7.88040 −0.532508
\(220\) 0 0
\(221\) 33.9046 2.28067
\(222\) 2.17500 0.145977
\(223\) 11.0708 0.741357 0.370679 0.928761i \(-0.379125\pi\)
0.370679 + 0.928761i \(0.379125\pi\)
\(224\) −7.96445 −0.532147
\(225\) 0 0
\(226\) 22.2543 1.48033
\(227\) 2.44676 0.162397 0.0811984 0.996698i \(-0.474125\pi\)
0.0811984 + 0.996698i \(0.474125\pi\)
\(228\) −10.2712 −0.680230
\(229\) −5.74097 −0.379374 −0.189687 0.981845i \(-0.560747\pi\)
−0.189687 + 0.981845i \(0.560747\pi\)
\(230\) 0 0
\(231\) −10.8184 −0.711799
\(232\) −0.670650 −0.0440303
\(233\) −8.66481 −0.567651 −0.283825 0.958876i \(-0.591604\pi\)
−0.283825 + 0.958876i \(0.591604\pi\)
\(234\) −5.14382 −0.336262
\(235\) 0 0
\(236\) 10.3931 0.676533
\(237\) −1.58603 −0.103024
\(238\) 11.4977 0.745288
\(239\) −0.995387 −0.0643862 −0.0321931 0.999482i \(-0.510249\pi\)
−0.0321931 + 0.999482i \(0.510249\pi\)
\(240\) 0 0
\(241\) −13.9247 −0.896967 −0.448483 0.893791i \(-0.648036\pi\)
−0.448483 + 0.893791i \(0.648036\pi\)
\(242\) −49.8961 −3.20745
\(243\) −4.01111 −0.257313
\(244\) −0.369568 −0.0236591
\(245\) 0 0
\(246\) −10.0206 −0.638892
\(247\) −13.9934 −0.890378
\(248\) −8.17963 −0.519407
\(249\) 8.86941 0.562076
\(250\) 0 0
\(251\) −0.229739 −0.0145010 −0.00725049 0.999974i \(-0.502308\pi\)
−0.00725049 + 0.999974i \(0.502308\pi\)
\(252\) −0.967751 −0.0609626
\(253\) 5.87722 0.369497
\(254\) −38.0939 −2.39022
\(255\) 0 0
\(256\) 5.51468 0.344667
\(257\) 4.24568 0.264838 0.132419 0.991194i \(-0.457726\pi\)
0.132419 + 0.991194i \(0.457726\pi\)
\(258\) −34.4042 −2.14191
\(259\) 0.557492 0.0346409
\(260\) 0 0
\(261\) 0.249631 0.0154518
\(262\) 27.6892 1.71064
\(263\) −2.99220 −0.184507 −0.0922535 0.995736i \(-0.529407\pi\)
−0.0922535 + 0.995736i \(0.529407\pi\)
\(264\) −11.2860 −0.694606
\(265\) 0 0
\(266\) −4.74545 −0.290962
\(267\) 11.6512 0.713042
\(268\) −33.2449 −2.03076
\(269\) −8.92878 −0.544397 −0.272199 0.962241i \(-0.587751\pi\)
−0.272199 + 0.962241i \(0.587751\pi\)
\(270\) 0 0
\(271\) 20.9773 1.27428 0.637140 0.770748i \(-0.280117\pi\)
0.637140 + 0.770748i \(0.280117\pi\)
\(272\) −15.0447 −0.912218
\(273\) −11.5045 −0.696284
\(274\) −31.8478 −1.92399
\(275\) 0 0
\(276\) 4.58750 0.276135
\(277\) −5.82584 −0.350041 −0.175020 0.984565i \(-0.555999\pi\)
−0.175020 + 0.984565i \(0.555999\pi\)
\(278\) 27.1266 1.62695
\(279\) 3.04464 0.182278
\(280\) 0 0
\(281\) −21.1877 −1.26395 −0.631976 0.774988i \(-0.717756\pi\)
−0.631976 + 0.774988i \(0.717756\pi\)
\(282\) 16.6499 0.991486
\(283\) 12.8049 0.761173 0.380587 0.924745i \(-0.375722\pi\)
0.380587 + 0.924745i \(0.375722\pi\)
\(284\) −19.7667 −1.17294
\(285\) 0 0
\(286\) −77.8533 −4.60356
\(287\) −2.56847 −0.151612
\(288\) 3.09268 0.182238
\(289\) 12.4283 0.731079
\(290\) 0 0
\(291\) −19.2949 −1.13109
\(292\) −10.6694 −0.624381
\(293\) 3.11921 0.182226 0.0911132 0.995841i \(-0.470957\pi\)
0.0911132 + 0.995841i \(0.470957\pi\)
\(294\) −3.90141 −0.227535
\(295\) 0 0
\(296\) 0.581588 0.0338041
\(297\) −28.2543 −1.63948
\(298\) 44.7854 2.59435
\(299\) 6.24994 0.361443
\(300\) 0 0
\(301\) −8.81841 −0.508284
\(302\) −41.3859 −2.38149
\(303\) −2.89562 −0.166349
\(304\) 6.20937 0.356132
\(305\) 0 0
\(306\) −4.46470 −0.255230
\(307\) 16.1152 0.919746 0.459873 0.887985i \(-0.347895\pi\)
0.459873 + 0.887985i \(0.347895\pi\)
\(308\) −14.6472 −0.834604
\(309\) −9.23237 −0.525211
\(310\) 0 0
\(311\) 30.2428 1.71491 0.857457 0.514556i \(-0.172043\pi\)
0.857457 + 0.514556i \(0.172043\pi\)
\(312\) −12.0017 −0.679465
\(313\) 20.4956 1.15848 0.579241 0.815156i \(-0.303349\pi\)
0.579241 + 0.815156i \(0.303349\pi\)
\(314\) −9.76315 −0.550967
\(315\) 0 0
\(316\) −2.14736 −0.120798
\(317\) −2.95042 −0.165712 −0.0828559 0.996562i \(-0.526404\pi\)
−0.0828559 + 0.996562i \(0.526404\pi\)
\(318\) 11.7650 0.659751
\(319\) 3.77825 0.211541
\(320\) 0 0
\(321\) 10.6984 0.597129
\(322\) 2.11948 0.118114
\(323\) −12.1459 −0.675817
\(324\) −24.9573 −1.38652
\(325\) 0 0
\(326\) 34.5961 1.91610
\(327\) 14.0822 0.778747
\(328\) −2.67948 −0.147950
\(329\) 4.26766 0.235284
\(330\) 0 0
\(331\) −21.2497 −1.16799 −0.583994 0.811758i \(-0.698511\pi\)
−0.583994 + 0.811758i \(0.698511\pi\)
\(332\) 12.0085 0.659050
\(333\) −0.216480 −0.0118630
\(334\) 35.4492 1.93969
\(335\) 0 0
\(336\) 5.10495 0.278498
\(337\) 24.8118 1.35158 0.675792 0.737092i \(-0.263802\pi\)
0.675792 + 0.737092i \(0.263802\pi\)
\(338\) −55.2374 −3.00452
\(339\) −19.3275 −1.04973
\(340\) 0 0
\(341\) 46.0817 2.49546
\(342\) 1.84271 0.0996423
\(343\) −1.00000 −0.0539949
\(344\) −9.19956 −0.496007
\(345\) 0 0
\(346\) 19.6614 1.05700
\(347\) −11.8158 −0.634304 −0.317152 0.948375i \(-0.602726\pi\)
−0.317152 + 0.948375i \(0.602726\pi\)
\(348\) 2.94913 0.158090
\(349\) −12.1614 −0.650984 −0.325492 0.945545i \(-0.605530\pi\)
−0.325492 + 0.945545i \(0.605530\pi\)
\(350\) 0 0
\(351\) −30.0462 −1.60375
\(352\) 46.8088 2.49492
\(353\) −17.5264 −0.932838 −0.466419 0.884564i \(-0.654456\pi\)
−0.466419 + 0.884564i \(0.654456\pi\)
\(354\) −16.2698 −0.864730
\(355\) 0 0
\(356\) 15.7748 0.836061
\(357\) −9.98561 −0.528494
\(358\) 15.8591 0.838181
\(359\) 7.70275 0.406535 0.203268 0.979123i \(-0.434844\pi\)
0.203268 + 0.979123i \(0.434844\pi\)
\(360\) 0 0
\(361\) −13.9870 −0.736160
\(362\) 22.5686 1.18618
\(363\) 43.3340 2.27445
\(364\) −15.5761 −0.816411
\(365\) 0 0
\(366\) 0.578537 0.0302406
\(367\) −15.0819 −0.787271 −0.393635 0.919267i \(-0.628783\pi\)
−0.393635 + 0.919267i \(0.628783\pi\)
\(368\) −2.77332 −0.144569
\(369\) 0.997364 0.0519207
\(370\) 0 0
\(371\) 3.01559 0.156561
\(372\) 35.9693 1.86492
\(373\) 21.5089 1.11369 0.556843 0.830618i \(-0.312012\pi\)
0.556843 + 0.830618i \(0.312012\pi\)
\(374\) −67.5747 −3.49421
\(375\) 0 0
\(376\) 4.45212 0.229600
\(377\) 4.01786 0.206930
\(378\) −10.1893 −0.524079
\(379\) 34.7117 1.78302 0.891511 0.452999i \(-0.149646\pi\)
0.891511 + 0.452999i \(0.149646\pi\)
\(380\) 0 0
\(381\) 33.0839 1.69494
\(382\) −7.00052 −0.358178
\(383\) 10.2963 0.526119 0.263059 0.964780i \(-0.415268\pi\)
0.263059 + 0.964780i \(0.415268\pi\)
\(384\) 14.8972 0.760218
\(385\) 0 0
\(386\) 19.8874 1.01224
\(387\) 3.42428 0.174066
\(388\) −26.1237 −1.32623
\(389\) −26.1594 −1.32633 −0.663167 0.748471i \(-0.730788\pi\)
−0.663167 + 0.748471i \(0.730788\pi\)
\(390\) 0 0
\(391\) 5.42479 0.274343
\(392\) −1.04322 −0.0526907
\(393\) −24.0476 −1.21304
\(394\) −48.9450 −2.46582
\(395\) 0 0
\(396\) 5.68768 0.285817
\(397\) 4.52380 0.227043 0.113522 0.993536i \(-0.463787\pi\)
0.113522 + 0.993536i \(0.463787\pi\)
\(398\) −45.8123 −2.29636
\(399\) 4.12134 0.206325
\(400\) 0 0
\(401\) −18.0222 −0.899987 −0.449994 0.893032i \(-0.648574\pi\)
−0.449994 + 0.893032i \(0.648574\pi\)
\(402\) 52.0431 2.59567
\(403\) 49.0041 2.44107
\(404\) −3.92044 −0.195049
\(405\) 0 0
\(406\) 1.36254 0.0676216
\(407\) −3.27650 −0.162410
\(408\) −10.4172 −0.515729
\(409\) 4.67260 0.231045 0.115523 0.993305i \(-0.463146\pi\)
0.115523 + 0.993305i \(0.463146\pi\)
\(410\) 0 0
\(411\) 27.6593 1.36433
\(412\) −12.4999 −0.615825
\(413\) −4.17024 −0.205204
\(414\) −0.823019 −0.0404492
\(415\) 0 0
\(416\) 49.7773 2.44053
\(417\) −23.5591 −1.15369
\(418\) 27.8900 1.36415
\(419\) −12.7674 −0.623728 −0.311864 0.950127i \(-0.600953\pi\)
−0.311864 + 0.950127i \(0.600953\pi\)
\(420\) 0 0
\(421\) 28.1367 1.37130 0.685649 0.727932i \(-0.259518\pi\)
0.685649 + 0.727932i \(0.259518\pi\)
\(422\) −32.7626 −1.59486
\(423\) −1.65718 −0.0805748
\(424\) 3.14593 0.152780
\(425\) 0 0
\(426\) 30.9437 1.49923
\(427\) 0.148289 0.00717622
\(428\) 14.4848 0.700150
\(429\) 67.6144 3.26445
\(430\) 0 0
\(431\) −5.49352 −0.264613 −0.132307 0.991209i \(-0.542238\pi\)
−0.132307 + 0.991209i \(0.542238\pi\)
\(432\) 13.3325 0.641462
\(433\) 21.0177 1.01005 0.505023 0.863106i \(-0.331484\pi\)
0.505023 + 0.863106i \(0.331484\pi\)
\(434\) 16.6183 0.797704
\(435\) 0 0
\(436\) 19.0661 0.913102
\(437\) −2.23897 −0.107104
\(438\) 16.7024 0.798070
\(439\) 39.2674 1.87413 0.937066 0.349153i \(-0.113531\pi\)
0.937066 + 0.349153i \(0.113531\pi\)
\(440\) 0 0
\(441\) 0.388311 0.0184910
\(442\) −71.8602 −3.41804
\(443\) −14.5489 −0.691240 −0.345620 0.938375i \(-0.612331\pi\)
−0.345620 + 0.938375i \(0.612331\pi\)
\(444\) −2.55749 −0.121373
\(445\) 0 0
\(446\) −23.4644 −1.11107
\(447\) −38.8954 −1.83969
\(448\) 11.3339 0.535475
\(449\) 11.3660 0.536395 0.268197 0.963364i \(-0.413572\pi\)
0.268197 + 0.963364i \(0.413572\pi\)
\(450\) 0 0
\(451\) 15.0954 0.710816
\(452\) −26.1679 −1.23083
\(453\) 35.9430 1.68875
\(454\) −5.18586 −0.243384
\(455\) 0 0
\(456\) 4.29948 0.201342
\(457\) 9.42744 0.440997 0.220499 0.975387i \(-0.429232\pi\)
0.220499 + 0.975387i \(0.429232\pi\)
\(458\) 12.1679 0.568568
\(459\) −26.0793 −1.21728
\(460\) 0 0
\(461\) −28.7697 −1.33994 −0.669968 0.742390i \(-0.733692\pi\)
−0.669968 + 0.742390i \(0.733692\pi\)
\(462\) 22.9294 1.06677
\(463\) 4.65928 0.216535 0.108268 0.994122i \(-0.465470\pi\)
0.108268 + 0.994122i \(0.465470\pi\)
\(464\) −1.78287 −0.0827675
\(465\) 0 0
\(466\) 18.3649 0.850738
\(467\) −7.82926 −0.362295 −0.181147 0.983456i \(-0.557981\pi\)
−0.181147 + 0.983456i \(0.557981\pi\)
\(468\) 6.04839 0.279587
\(469\) 13.3396 0.615964
\(470\) 0 0
\(471\) 8.47914 0.390698
\(472\) −4.35049 −0.200247
\(473\) 51.8277 2.38304
\(474\) 3.36156 0.154402
\(475\) 0 0
\(476\) −13.5197 −0.619674
\(477\) −1.17099 −0.0536158
\(478\) 2.10971 0.0964957
\(479\) −33.9427 −1.55088 −0.775440 0.631421i \(-0.782472\pi\)
−0.775440 + 0.631421i \(0.782472\pi\)
\(480\) 0 0
\(481\) −3.48429 −0.158870
\(482\) 29.5131 1.34428
\(483\) −1.84074 −0.0837564
\(484\) 58.6707 2.66685
\(485\) 0 0
\(486\) 8.50149 0.385635
\(487\) 11.6880 0.529633 0.264817 0.964299i \(-0.414689\pi\)
0.264817 + 0.964299i \(0.414689\pi\)
\(488\) 0.154699 0.00700289
\(489\) −30.0462 −1.35873
\(490\) 0 0
\(491\) −19.6742 −0.887885 −0.443943 0.896055i \(-0.646421\pi\)
−0.443943 + 0.896055i \(0.646421\pi\)
\(492\) 11.7828 0.531211
\(493\) 3.48740 0.157065
\(494\) 29.6588 1.33441
\(495\) 0 0
\(496\) −21.7449 −0.976374
\(497\) 7.93141 0.355772
\(498\) −18.7986 −0.842384
\(499\) −30.1698 −1.35059 −0.675294 0.737549i \(-0.735983\pi\)
−0.675294 + 0.737549i \(0.735983\pi\)
\(500\) 0 0
\(501\) −30.7870 −1.37546
\(502\) 0.486927 0.0217326
\(503\) −24.1110 −1.07506 −0.537529 0.843246i \(-0.680642\pi\)
−0.537529 + 0.843246i \(0.680642\pi\)
\(504\) 0.405095 0.0180444
\(505\) 0 0
\(506\) −12.4567 −0.553766
\(507\) 47.9728 2.13055
\(508\) 44.7929 1.98736
\(509\) 21.5774 0.956404 0.478202 0.878250i \(-0.341289\pi\)
0.478202 + 0.878250i \(0.341289\pi\)
\(510\) 0 0
\(511\) 4.28111 0.189385
\(512\) −27.8744 −1.23188
\(513\) 10.7637 0.475228
\(514\) −8.99864 −0.396913
\(515\) 0 0
\(516\) 40.4544 1.78091
\(517\) −25.0819 −1.10310
\(518\) −1.18159 −0.0519163
\(519\) −17.0756 −0.749535
\(520\) 0 0
\(521\) −22.0862 −0.967613 −0.483807 0.875175i \(-0.660746\pi\)
−0.483807 + 0.875175i \(0.660746\pi\)
\(522\) −0.529089 −0.0231576
\(523\) −5.79856 −0.253553 −0.126777 0.991931i \(-0.540463\pi\)
−0.126777 + 0.991931i \(0.540463\pi\)
\(524\) −32.5585 −1.42232
\(525\) 0 0
\(526\) 6.34191 0.276521
\(527\) 42.5343 1.85283
\(528\) −30.0029 −1.30571
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 1.61935 0.0702738
\(532\) 5.57996 0.241922
\(533\) 16.0528 0.695322
\(534\) −24.6945 −1.06864
\(535\) 0 0
\(536\) 13.9161 0.601085
\(537\) −13.7734 −0.594366
\(538\) 18.9244 0.815888
\(539\) 5.87722 0.253150
\(540\) 0 0
\(541\) 29.6582 1.27511 0.637553 0.770407i \(-0.279947\pi\)
0.637553 + 0.770407i \(0.279947\pi\)
\(542\) −44.4610 −1.90976
\(543\) −19.6005 −0.841137
\(544\) 43.2055 1.85242
\(545\) 0 0
\(546\) 24.3836 1.04352
\(547\) 7.24730 0.309872 0.154936 0.987924i \(-0.450483\pi\)
0.154936 + 0.987924i \(0.450483\pi\)
\(548\) 37.4484 1.59972
\(549\) −0.0575824 −0.00245756
\(550\) 0 0
\(551\) −1.43935 −0.0613183
\(552\) −1.92030 −0.0817333
\(553\) 0.861628 0.0366402
\(554\) 12.3478 0.524606
\(555\) 0 0
\(556\) −31.8970 −1.35274
\(557\) −21.7634 −0.922146 −0.461073 0.887362i \(-0.652535\pi\)
−0.461073 + 0.887362i \(0.652535\pi\)
\(558\) −6.45307 −0.273180
\(559\) 55.1145 2.33109
\(560\) 0 0
\(561\) 58.6876 2.47779
\(562\) 44.9070 1.89429
\(563\) 26.9844 1.13726 0.568629 0.822594i \(-0.307474\pi\)
0.568629 + 0.822594i \(0.307474\pi\)
\(564\) −19.5779 −0.824377
\(565\) 0 0
\(566\) −27.1398 −1.14077
\(567\) 10.0141 0.420555
\(568\) 8.27423 0.347179
\(569\) 37.4420 1.56965 0.784826 0.619717i \(-0.212752\pi\)
0.784826 + 0.619717i \(0.212752\pi\)
\(570\) 0 0
\(571\) −3.32489 −0.139142 −0.0695711 0.997577i \(-0.522163\pi\)
−0.0695711 + 0.997577i \(0.522163\pi\)
\(572\) 91.5443 3.82766
\(573\) 6.07984 0.253989
\(574\) 5.44382 0.227221
\(575\) 0 0
\(576\) −4.40107 −0.183378
\(577\) 41.0573 1.70924 0.854618 0.519257i \(-0.173791\pi\)
0.854618 + 0.519257i \(0.173791\pi\)
\(578\) −26.3417 −1.09567
\(579\) −17.2719 −0.717796
\(580\) 0 0
\(581\) −4.81841 −0.199901
\(582\) 40.8952 1.69516
\(583\) −17.7233 −0.734022
\(584\) 4.46616 0.184811
\(585\) 0 0
\(586\) −6.61112 −0.273103
\(587\) 31.9182 1.31741 0.658703 0.752403i \(-0.271105\pi\)
0.658703 + 0.752403i \(0.271105\pi\)
\(588\) 4.58750 0.189185
\(589\) −17.5551 −0.723347
\(590\) 0 0
\(591\) 42.5080 1.74854
\(592\) 1.54610 0.0635445
\(593\) −36.5062 −1.49913 −0.749566 0.661930i \(-0.769738\pi\)
−0.749566 + 0.661930i \(0.769738\pi\)
\(594\) 59.8845 2.45709
\(595\) 0 0
\(596\) −52.6611 −2.15708
\(597\) 39.7873 1.62838
\(598\) −13.2466 −0.541695
\(599\) −7.51073 −0.306880 −0.153440 0.988158i \(-0.549035\pi\)
−0.153440 + 0.988158i \(0.549035\pi\)
\(600\) 0 0
\(601\) −6.05329 −0.246919 −0.123460 0.992350i \(-0.539399\pi\)
−0.123460 + 0.992350i \(0.539399\pi\)
\(602\) 18.6905 0.761766
\(603\) −5.17990 −0.210942
\(604\) 48.6639 1.98011
\(605\) 0 0
\(606\) 6.13723 0.249308
\(607\) −24.4047 −0.990557 −0.495278 0.868734i \(-0.664934\pi\)
−0.495278 + 0.868734i \(0.664934\pi\)
\(608\) −17.8321 −0.723188
\(609\) −1.18334 −0.0479515
\(610\) 0 0
\(611\) −26.6726 −1.07906
\(612\) 5.24985 0.212213
\(613\) −4.81180 −0.194347 −0.0971734 0.995267i \(-0.530980\pi\)
−0.0971734 + 0.995267i \(0.530980\pi\)
\(614\) −34.1560 −1.37842
\(615\) 0 0
\(616\) 6.13125 0.247035
\(617\) 38.1414 1.53552 0.767758 0.640740i \(-0.221372\pi\)
0.767758 + 0.640740i \(0.221372\pi\)
\(618\) 19.5679 0.787135
\(619\) −17.8340 −0.716809 −0.358404 0.933566i \(-0.616679\pi\)
−0.358404 + 0.933566i \(0.616679\pi\)
\(620\) 0 0
\(621\) −4.80743 −0.192916
\(622\) −64.0992 −2.57014
\(623\) −6.32964 −0.253592
\(624\) −31.9056 −1.27725
\(625\) 0 0
\(626\) −43.4402 −1.73622
\(627\) −24.2220 −0.967335
\(628\) 11.4801 0.458104
\(629\) −3.02428 −0.120586
\(630\) 0 0
\(631\) 22.2906 0.887377 0.443688 0.896181i \(-0.353670\pi\)
0.443688 + 0.896181i \(0.353670\pi\)
\(632\) 0.898870 0.0357551
\(633\) 28.4538 1.13094
\(634\) 6.25336 0.248352
\(635\) 0 0
\(636\) −13.8340 −0.548553
\(637\) 6.24994 0.247632
\(638\) −8.00793 −0.317037
\(639\) −3.07986 −0.121837
\(640\) 0 0
\(641\) 28.4927 1.12540 0.562698 0.826663i \(-0.309763\pi\)
0.562698 + 0.826663i \(0.309763\pi\)
\(642\) −22.6752 −0.894917
\(643\) −0.975186 −0.0384576 −0.0192288 0.999815i \(-0.506121\pi\)
−0.0192288 + 0.999815i \(0.506121\pi\)
\(644\) −2.49221 −0.0982067
\(645\) 0 0
\(646\) 25.7431 1.01285
\(647\) 27.5193 1.08190 0.540948 0.841056i \(-0.318065\pi\)
0.540948 + 0.841056i \(0.318065\pi\)
\(648\) 10.4470 0.410396
\(649\) 24.5094 0.962078
\(650\) 0 0
\(651\) −14.4327 −0.565663
\(652\) −40.6800 −1.59315
\(653\) 26.1590 1.02368 0.511840 0.859081i \(-0.328964\pi\)
0.511840 + 0.859081i \(0.328964\pi\)
\(654\) −29.8469 −1.16711
\(655\) 0 0
\(656\) −7.12318 −0.278113
\(657\) −1.66240 −0.0648566
\(658\) −9.04523 −0.352620
\(659\) −2.67085 −0.104042 −0.0520208 0.998646i \(-0.516566\pi\)
−0.0520208 + 0.998646i \(0.516566\pi\)
\(660\) 0 0
\(661\) −18.4928 −0.719285 −0.359643 0.933090i \(-0.617101\pi\)
−0.359643 + 0.933090i \(0.617101\pi\)
\(662\) 45.0384 1.75047
\(663\) 62.4095 2.42378
\(664\) −5.02667 −0.195073
\(665\) 0 0
\(666\) 0.458826 0.0177792
\(667\) 0.642864 0.0248918
\(668\) −41.6831 −1.61277
\(669\) 20.3785 0.787877
\(670\) 0 0
\(671\) −0.871528 −0.0336450
\(672\) −14.6605 −0.565539
\(673\) −47.5002 −1.83100 −0.915499 0.402321i \(-0.868203\pi\)
−0.915499 + 0.402321i \(0.868203\pi\)
\(674\) −52.5882 −2.02562
\(675\) 0 0
\(676\) 64.9512 2.49812
\(677\) −33.4288 −1.28477 −0.642386 0.766381i \(-0.722056\pi\)
−0.642386 + 0.766381i \(0.722056\pi\)
\(678\) 40.9643 1.57323
\(679\) 10.4822 0.402268
\(680\) 0 0
\(681\) 4.50383 0.172587
\(682\) −97.6694 −3.73995
\(683\) −46.7168 −1.78757 −0.893784 0.448498i \(-0.851959\pi\)
−0.893784 + 0.448498i \(0.851959\pi\)
\(684\) −2.16676 −0.0828482
\(685\) 0 0
\(686\) 2.11948 0.0809222
\(687\) −10.5676 −0.403180
\(688\) −24.4563 −0.932386
\(689\) −18.8472 −0.718023
\(690\) 0 0
\(691\) −22.8670 −0.869903 −0.434952 0.900454i \(-0.643235\pi\)
−0.434952 + 0.900454i \(0.643235\pi\)
\(692\) −23.1190 −0.878851
\(693\) −2.28219 −0.0866931
\(694\) 25.0433 0.950631
\(695\) 0 0
\(696\) −1.23449 −0.0467932
\(697\) 13.9334 0.527765
\(698\) 25.7758 0.975630
\(699\) −15.9496 −0.603271
\(700\) 0 0
\(701\) 39.0885 1.47635 0.738177 0.674607i \(-0.235687\pi\)
0.738177 + 0.674607i \(0.235687\pi\)
\(702\) 63.6823 2.40353
\(703\) 1.24821 0.0470769
\(704\) −66.6116 −2.51052
\(705\) 0 0
\(706\) 37.1470 1.39805
\(707\) 1.57308 0.0591617
\(708\) 19.1309 0.718985
\(709\) 18.3762 0.690132 0.345066 0.938578i \(-0.387856\pi\)
0.345066 + 0.938578i \(0.387856\pi\)
\(710\) 0 0
\(711\) −0.334580 −0.0125477
\(712\) −6.60323 −0.247466
\(713\) 7.84074 0.293638
\(714\) 21.1643 0.792055
\(715\) 0 0
\(716\) −18.6480 −0.696910
\(717\) −1.83224 −0.0684264
\(718\) −16.3258 −0.609275
\(719\) −11.2232 −0.418553 −0.209276 0.977857i \(-0.567111\pi\)
−0.209276 + 0.977857i \(0.567111\pi\)
\(720\) 0 0
\(721\) 5.01559 0.186790
\(722\) 29.6453 1.10328
\(723\) −25.6316 −0.953251
\(724\) −26.5374 −0.986256
\(725\) 0 0
\(726\) −91.8457 −3.40871
\(727\) −7.71953 −0.286302 −0.143151 0.989701i \(-0.545723\pi\)
−0.143151 + 0.989701i \(0.545723\pi\)
\(728\) 6.52008 0.241650
\(729\) 22.6590 0.839224
\(730\) 0 0
\(731\) 47.8380 1.76935
\(732\) −0.680277 −0.0251437
\(733\) 23.2083 0.857217 0.428609 0.903490i \(-0.359004\pi\)
0.428609 + 0.903490i \(0.359004\pi\)
\(734\) 31.9659 1.17988
\(735\) 0 0
\(736\) 7.96445 0.293573
\(737\) −78.3995 −2.88788
\(738\) −2.11390 −0.0778136
\(739\) 8.36545 0.307728 0.153864 0.988092i \(-0.450828\pi\)
0.153864 + 0.988092i \(0.450828\pi\)
\(740\) 0 0
\(741\) −25.7582 −0.946249
\(742\) −6.39148 −0.234639
\(743\) −9.54735 −0.350258 −0.175129 0.984545i \(-0.556034\pi\)
−0.175129 + 0.984545i \(0.556034\pi\)
\(744\) −15.0566 −0.552000
\(745\) 0 0
\(746\) −45.5877 −1.66908
\(747\) 1.87104 0.0684578
\(748\) 79.4582 2.90528
\(749\) −5.81204 −0.212367
\(750\) 0 0
\(751\) 2.83381 0.103407 0.0517035 0.998662i \(-0.483535\pi\)
0.0517035 + 0.998662i \(0.483535\pi\)
\(752\) 11.8356 0.431599
\(753\) −0.422889 −0.0154109
\(754\) −8.51578 −0.310126
\(755\) 0 0
\(756\) 11.9811 0.435749
\(757\) −49.7767 −1.80916 −0.904582 0.426300i \(-0.859817\pi\)
−0.904582 + 0.426300i \(0.859817\pi\)
\(758\) −73.5709 −2.67222
\(759\) 10.8184 0.392683
\(760\) 0 0
\(761\) 48.7458 1.76704 0.883518 0.468398i \(-0.155169\pi\)
0.883518 + 0.468398i \(0.155169\pi\)
\(762\) −70.1208 −2.54021
\(763\) −7.65030 −0.276959
\(764\) 8.23161 0.297809
\(765\) 0 0
\(766\) −21.8229 −0.788495
\(767\) 26.0637 0.941107
\(768\) 10.1511 0.366295
\(769\) −13.3190 −0.480296 −0.240148 0.970736i \(-0.577196\pi\)
−0.240148 + 0.970736i \(0.577196\pi\)
\(770\) 0 0
\(771\) 7.81517 0.281457
\(772\) −23.3847 −0.841635
\(773\) 13.9252 0.500855 0.250427 0.968135i \(-0.419429\pi\)
0.250427 + 0.968135i \(0.419429\pi\)
\(774\) −7.25771 −0.260873
\(775\) 0 0
\(776\) 10.9352 0.392552
\(777\) 1.02620 0.0368146
\(778\) 55.4444 1.98778
\(779\) −5.75071 −0.206040
\(780\) 0 0
\(781\) −46.6146 −1.66800
\(782\) −11.4977 −0.411159
\(783\) −3.09052 −0.110446
\(784\) −2.77332 −0.0990472
\(785\) 0 0
\(786\) 50.9685 1.81798
\(787\) −45.7185 −1.62969 −0.814844 0.579680i \(-0.803178\pi\)
−0.814844 + 0.579680i \(0.803178\pi\)
\(788\) 57.5523 2.05022
\(789\) −5.50785 −0.196085
\(790\) 0 0
\(791\) 10.4999 0.373333
\(792\) −2.38083 −0.0845991
\(793\) −0.926799 −0.0329116
\(794\) −9.58812 −0.340270
\(795\) 0 0
\(796\) 53.8687 1.90933
\(797\) 11.4211 0.404555 0.202277 0.979328i \(-0.435166\pi\)
0.202277 + 0.979328i \(0.435166\pi\)
\(798\) −8.73512 −0.309220
\(799\) −23.1511 −0.819029
\(800\) 0 0
\(801\) 2.45787 0.0868446
\(802\) 38.1978 1.34881
\(803\) −25.1610 −0.887913
\(804\) −61.1952 −2.15819
\(805\) 0 0
\(806\) −103.863 −3.65843
\(807\) −16.4355 −0.578558
\(808\) 1.64107 0.0577327
\(809\) 17.6307 0.619864 0.309932 0.950759i \(-0.399694\pi\)
0.309932 + 0.950759i \(0.399694\pi\)
\(810\) 0 0
\(811\) 30.9666 1.08738 0.543692 0.839285i \(-0.317026\pi\)
0.543692 + 0.839285i \(0.317026\pi\)
\(812\) −1.60215 −0.0562244
\(813\) 38.6137 1.35424
\(814\) 6.94449 0.243404
\(815\) 0 0
\(816\) −27.6933 −0.969459
\(817\) −19.7441 −0.690759
\(818\) −9.90349 −0.346267
\(819\) −2.42692 −0.0848035
\(820\) 0 0
\(821\) 25.3060 0.883187 0.441593 0.897215i \(-0.354413\pi\)
0.441593 + 0.897215i \(0.354413\pi\)
\(822\) −58.6233 −2.04472
\(823\) −45.6057 −1.58972 −0.794858 0.606795i \(-0.792455\pi\)
−0.794858 + 0.606795i \(0.792455\pi\)
\(824\) 5.23237 0.182278
\(825\) 0 0
\(826\) 8.83875 0.307539
\(827\) 25.4338 0.884420 0.442210 0.896912i \(-0.354195\pi\)
0.442210 + 0.896912i \(0.354195\pi\)
\(828\) 0.967751 0.0336317
\(829\) −5.12771 −0.178093 −0.0890463 0.996027i \(-0.528382\pi\)
−0.0890463 + 0.996027i \(0.528382\pi\)
\(830\) 0 0
\(831\) −10.7238 −0.372006
\(832\) −70.8360 −2.45580
\(833\) 5.42479 0.187958
\(834\) 49.9330 1.72904
\(835\) 0 0
\(836\) −32.7946 −1.13423
\(837\) −37.6938 −1.30289
\(838\) 27.0603 0.934782
\(839\) −7.81839 −0.269921 −0.134960 0.990851i \(-0.543091\pi\)
−0.134960 + 0.990851i \(0.543091\pi\)
\(840\) 0 0
\(841\) −28.5867 −0.985749
\(842\) −59.6352 −2.05517
\(843\) −39.0010 −1.34327
\(844\) 38.5242 1.32606
\(845\) 0 0
\(846\) 3.51236 0.120757
\(847\) −23.5417 −0.808901
\(848\) 8.36319 0.287193
\(849\) 23.5705 0.808937
\(850\) 0 0
\(851\) −0.557492 −0.0191106
\(852\) −36.3853 −1.24654
\(853\) 36.6540 1.25501 0.627505 0.778613i \(-0.284076\pi\)
0.627505 + 0.778613i \(0.284076\pi\)
\(854\) −0.314297 −0.0107550
\(855\) 0 0
\(856\) −6.06326 −0.207238
\(857\) −44.0599 −1.50506 −0.752529 0.658559i \(-0.771166\pi\)
−0.752529 + 0.658559i \(0.771166\pi\)
\(858\) −143.307 −4.89244
\(859\) −6.04906 −0.206391 −0.103196 0.994661i \(-0.532907\pi\)
−0.103196 + 0.994661i \(0.532907\pi\)
\(860\) 0 0
\(861\) −4.72787 −0.161125
\(862\) 11.6434 0.396576
\(863\) 25.7890 0.877867 0.438933 0.898520i \(-0.355356\pi\)
0.438933 + 0.898520i \(0.355356\pi\)
\(864\) −38.2885 −1.30260
\(865\) 0 0
\(866\) −44.5467 −1.51376
\(867\) 22.8773 0.776954
\(868\) −19.5407 −0.663256
\(869\) −5.06397 −0.171784
\(870\) 0 0
\(871\) −83.3714 −2.82493
\(872\) −7.98097 −0.270270
\(873\) −4.07034 −0.137760
\(874\) 4.74545 0.160517
\(875\) 0 0
\(876\) −19.6396 −0.663560
\(877\) −9.59839 −0.324114 −0.162057 0.986781i \(-0.551813\pi\)
−0.162057 + 0.986781i \(0.551813\pi\)
\(878\) −83.2266 −2.80876
\(879\) 5.74165 0.193661
\(880\) 0 0
\(881\) −9.38385 −0.316150 −0.158075 0.987427i \(-0.550529\pi\)
−0.158075 + 0.987427i \(0.550529\pi\)
\(882\) −0.823019 −0.0277125
\(883\) 4.98842 0.167874 0.0839368 0.996471i \(-0.473251\pi\)
0.0839368 + 0.996471i \(0.473251\pi\)
\(884\) 84.4973 2.84195
\(885\) 0 0
\(886\) 30.8362 1.03596
\(887\) −36.6169 −1.22948 −0.614738 0.788732i \(-0.710738\pi\)
−0.614738 + 0.788732i \(0.710738\pi\)
\(888\) 1.07055 0.0359253
\(889\) −17.9732 −0.602802
\(890\) 0 0
\(891\) −58.8553 −1.97173
\(892\) 27.5908 0.923808
\(893\) 9.55514 0.319750
\(894\) 82.4381 2.75714
\(895\) 0 0
\(896\) −8.09304 −0.270370
\(897\) 11.5045 0.384124
\(898\) −24.0900 −0.803895
\(899\) 5.04052 0.168111
\(900\) 0 0
\(901\) −16.3589 −0.544995
\(902\) −31.9945 −1.06530
\(903\) −16.2324 −0.540179
\(904\) 10.9537 0.364315
\(905\) 0 0
\(906\) −76.1806 −2.53093
\(907\) −34.2361 −1.13679 −0.568395 0.822756i \(-0.692436\pi\)
−0.568395 + 0.822756i \(0.692436\pi\)
\(908\) 6.09782 0.202363
\(909\) −0.610844 −0.0202604
\(910\) 0 0
\(911\) 2.10958 0.0698934 0.0349467 0.999389i \(-0.488874\pi\)
0.0349467 + 0.999389i \(0.488874\pi\)
\(912\) 11.4298 0.378479
\(913\) 28.3188 0.937216
\(914\) −19.9813 −0.660923
\(915\) 0 0
\(916\) −14.3077 −0.472739
\(917\) 13.0641 0.431415
\(918\) 55.2746 1.82433
\(919\) 49.7639 1.64156 0.820779 0.571245i \(-0.193539\pi\)
0.820779 + 0.571245i \(0.193539\pi\)
\(920\) 0 0
\(921\) 29.6639 0.977460
\(922\) 60.9768 2.00816
\(923\) −49.5708 −1.63164
\(924\) −26.9617 −0.886975
\(925\) 0 0
\(926\) −9.87527 −0.324521
\(927\) −1.94761 −0.0639678
\(928\) 5.12005 0.168074
\(929\) −45.0863 −1.47923 −0.739617 0.673028i \(-0.764993\pi\)
−0.739617 + 0.673028i \(0.764993\pi\)
\(930\) 0 0
\(931\) −2.23897 −0.0733791
\(932\) −21.5945 −0.707351
\(933\) 55.6691 1.82252
\(934\) 16.5940 0.542971
\(935\) 0 0
\(936\) −2.53182 −0.0827551
\(937\) −14.8779 −0.486040 −0.243020 0.970021i \(-0.578138\pi\)
−0.243020 + 0.970021i \(0.578138\pi\)
\(938\) −28.2730 −0.923145
\(939\) 37.7271 1.23118
\(940\) 0 0
\(941\) 30.3917 0.990742 0.495371 0.868681i \(-0.335032\pi\)
0.495371 + 0.868681i \(0.335032\pi\)
\(942\) −17.9714 −0.585540
\(943\) 2.56847 0.0836408
\(944\) −11.5654 −0.376422
\(945\) 0 0
\(946\) −109.848 −3.57146
\(947\) 26.5595 0.863068 0.431534 0.902097i \(-0.357972\pi\)
0.431534 + 0.902097i \(0.357972\pi\)
\(948\) −3.95272 −0.128378
\(949\) −26.7567 −0.868559
\(950\) 0 0
\(951\) −5.43094 −0.176110
\(952\) 5.65926 0.183418
\(953\) −8.75467 −0.283592 −0.141796 0.989896i \(-0.545288\pi\)
−0.141796 + 0.989896i \(0.545288\pi\)
\(954\) 2.48188 0.0803540
\(955\) 0 0
\(956\) −2.48071 −0.0802319
\(957\) 6.95476 0.224815
\(958\) 71.9409 2.32430
\(959\) −15.0262 −0.485221
\(960\) 0 0
\(961\) 30.4771 0.983134
\(962\) 7.38489 0.238099
\(963\) 2.25688 0.0727270
\(964\) −34.7031 −1.11771
\(965\) 0 0
\(966\) 3.90141 0.125526
\(967\) 19.3848 0.623372 0.311686 0.950185i \(-0.399106\pi\)
0.311686 + 0.950185i \(0.399106\pi\)
\(968\) −24.5592 −0.789363
\(969\) −22.3574 −0.718224
\(970\) 0 0
\(971\) −17.9424 −0.575799 −0.287899 0.957661i \(-0.592957\pi\)
−0.287899 + 0.957661i \(0.592957\pi\)
\(972\) −9.99652 −0.320639
\(973\) 12.7987 0.410308
\(974\) −24.7725 −0.793762
\(975\) 0 0
\(976\) 0.411254 0.0131639
\(977\) −5.12609 −0.163998 −0.0819991 0.996632i \(-0.526130\pi\)
−0.0819991 + 0.996632i \(0.526130\pi\)
\(978\) 63.6823 2.03634
\(979\) 37.2007 1.18894
\(980\) 0 0
\(981\) 2.97070 0.0948470
\(982\) 41.6992 1.33067
\(983\) 48.1332 1.53521 0.767606 0.640922i \(-0.221448\pi\)
0.767606 + 0.640922i \(0.221448\pi\)
\(984\) −4.93222 −0.157233
\(985\) 0 0
\(986\) −7.39148 −0.235393
\(987\) 7.85563 0.250048
\(988\) −34.8744 −1.10950
\(989\) 8.81841 0.280409
\(990\) 0 0
\(991\) −6.50910 −0.206769 −0.103384 0.994641i \(-0.532967\pi\)
−0.103384 + 0.994641i \(0.532967\pi\)
\(992\) 62.4471 1.98270
\(993\) −39.1151 −1.24128
\(994\) −16.8105 −0.533196
\(995\) 0 0
\(996\) 22.1044 0.700405
\(997\) −43.2321 −1.36917 −0.684587 0.728931i \(-0.740018\pi\)
−0.684587 + 0.728931i \(0.740018\pi\)
\(998\) 63.9445 2.02413
\(999\) 2.68010 0.0847948
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 4025.2.a.p.1.2 5
5.4 even 2 161.2.a.d.1.4 5
15.14 odd 2 1449.2.a.r.1.2 5
20.19 odd 2 2576.2.a.bd.1.4 5
35.34 odd 2 1127.2.a.h.1.4 5
115.114 odd 2 3703.2.a.j.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.2.a.d.1.4 5 5.4 even 2
1127.2.a.h.1.4 5 35.34 odd 2
1449.2.a.r.1.2 5 15.14 odd 2
2576.2.a.bd.1.4 5 20.19 odd 2
3703.2.a.j.1.4 5 115.114 odd 2
4025.2.a.p.1.2 5 1.1 even 1 trivial