Properties

Label 4025.2.a.p.1.3
Level 4025
Weight 2
Character 4025.1
Self dual yes
Analytic conductor 32.140
Analytic rank 0
Dimension 5
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.3
Root \(1.23828\)
Character \(\chi\) = 4025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.23828 q^{2} -2.68857 q^{3} -0.466664 q^{4} +3.32920 q^{6} -1.00000 q^{7} +3.05442 q^{8} +4.22838 q^{9} +O(q^{10})\) \(q-1.23828 q^{2} -2.68857 q^{3} -0.466664 q^{4} +3.32920 q^{6} -1.00000 q^{7} +3.05442 q^{8} +4.22838 q^{9} -0.846153 q^{11} +1.25466 q^{12} -2.55110 q^{13} +1.23828 q^{14} -2.84890 q^{16} +7.07080 q^{17} -5.23592 q^{18} -0.476559 q^{19} +2.68857 q^{21} +1.04777 q^{22} +1.00000 q^{23} -8.21201 q^{24} +3.15897 q^{26} -3.30259 q^{27} +0.466664 q^{28} +8.63827 q^{29} +3.31143 q^{31} -2.58111 q^{32} +2.27494 q^{33} -8.75562 q^{34} -1.97324 q^{36} -7.85369 q^{37} +0.590113 q^{38} +6.85879 q^{39} +2.82603 q^{41} -3.32920 q^{42} +0.274938 q^{43} +0.394869 q^{44} -1.23828 q^{46} +13.4756 q^{47} +7.65944 q^{48} +1.00000 q^{49} -19.0103 q^{51} +1.19051 q^{52} -8.93333 q^{53} +4.08953 q^{54} -3.05442 q^{56} +1.28126 q^{57} -10.6966 q^{58} +1.66091 q^{59} -11.7162 q^{61} -4.10048 q^{62} -4.22838 q^{63} +8.89393 q^{64} -2.81701 q^{66} +2.82636 q^{67} -3.29969 q^{68} -2.68857 q^{69} +9.92823 q^{71} +12.9153 q^{72} -7.31556 q^{73} +9.72506 q^{74} +0.222393 q^{76} +0.846153 q^{77} -8.49310 q^{78} +11.7795 q^{79} -3.80592 q^{81} -3.49942 q^{82} -3.72506 q^{83} -1.25466 q^{84} -0.340450 q^{86} -23.2246 q^{87} -2.58451 q^{88} -8.76310 q^{89} +2.55110 q^{91} -0.466664 q^{92} -8.90301 q^{93} -16.6865 q^{94} +6.93948 q^{96} -1.82229 q^{97} -1.23828 q^{98} -3.57786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 2q^{2} + 12q^{4} - 3q^{6} - 5q^{7} - 3q^{8} + 11q^{9} + O(q^{10}) \) \( 5q - 2q^{2} + 12q^{4} - 3q^{6} - 5q^{7} - 3q^{8} + 11q^{9} - 4q^{11} - 3q^{12} + 6q^{13} + 2q^{14} + 10q^{16} + 12q^{17} + 19q^{18} + 6q^{19} - 14q^{22} + 5q^{23} - 36q^{24} + q^{26} - 12q^{28} - 4q^{29} + 30q^{31} - 8q^{32} + 22q^{33} + 6q^{34} - q^{36} - 4q^{37} + 40q^{38} + 16q^{39} + 6q^{41} + 3q^{42} + 12q^{43} - 26q^{44} - 2q^{46} - 10q^{47} - 25q^{48} + 5q^{49} - 4q^{51} + 21q^{52} - 16q^{53} + 33q^{54} + 3q^{56} - 6q^{57} - 13q^{58} + 22q^{59} - 18q^{61} - 15q^{62} - 11q^{63} + 25q^{64} + 4q^{66} + 2q^{67} - 12q^{68} + 4q^{71} + 41q^{72} + 2q^{73} + 38q^{74} + 10q^{76} + 4q^{77} - 41q^{78} + 30q^{79} - 3q^{81} + 7q^{82} - 8q^{83} + 3q^{84} + 8q^{86} + 12q^{87} - 4q^{88} - 20q^{89} - 6q^{91} + 12q^{92} + 26q^{93} - 25q^{94} - q^{96} + 12q^{97} - 2q^{98} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23828 −0.875596 −0.437798 0.899073i \(-0.644241\pi\)
−0.437798 + 0.899073i \(0.644241\pi\)
\(3\) −2.68857 −1.55224 −0.776122 0.630583i \(-0.782816\pi\)
−0.776122 + 0.630583i \(0.782816\pi\)
\(4\) −0.466664 −0.233332
\(5\) 0 0
\(6\) 3.32920 1.35914
\(7\) −1.00000 −0.377964
\(8\) 3.05442 1.07990
\(9\) 4.22838 1.40946
\(10\) 0 0
\(11\) −0.846153 −0.255125 −0.127562 0.991831i \(-0.540715\pi\)
−0.127562 + 0.991831i \(0.540715\pi\)
\(12\) 1.25466 0.362188
\(13\) −2.55110 −0.707547 −0.353773 0.935331i \(-0.615102\pi\)
−0.353773 + 0.935331i \(0.615102\pi\)
\(14\) 1.23828 0.330944
\(15\) 0 0
\(16\) −2.84890 −0.712224
\(17\) 7.07080 1.71492 0.857460 0.514550i \(-0.172041\pi\)
0.857460 + 0.514550i \(0.172041\pi\)
\(18\) −5.23592 −1.23412
\(19\) −0.476559 −0.109330 −0.0546650 0.998505i \(-0.517409\pi\)
−0.0546650 + 0.998505i \(0.517409\pi\)
\(20\) 0 0
\(21\) 2.68857 0.586693
\(22\) 1.04777 0.223386
\(23\) 1.00000 0.208514
\(24\) −8.21201 −1.67627
\(25\) 0 0
\(26\) 3.15897 0.619525
\(27\) −3.30259 −0.635584
\(28\) 0.466664 0.0881912
\(29\) 8.63827 1.60409 0.802043 0.597266i \(-0.203746\pi\)
0.802043 + 0.597266i \(0.203746\pi\)
\(30\) 0 0
\(31\) 3.31143 0.594751 0.297376 0.954761i \(-0.403889\pi\)
0.297376 + 0.954761i \(0.403889\pi\)
\(32\) −2.58111 −0.456280
\(33\) 2.27494 0.396016
\(34\) −8.75562 −1.50158
\(35\) 0 0
\(36\) −1.97324 −0.328873
\(37\) −7.85369 −1.29114 −0.645569 0.763702i \(-0.723380\pi\)
−0.645569 + 0.763702i \(0.723380\pi\)
\(38\) 0.590113 0.0957289
\(39\) 6.85879 1.09829
\(40\) 0 0
\(41\) 2.82603 0.441352 0.220676 0.975347i \(-0.429174\pi\)
0.220676 + 0.975347i \(0.429174\pi\)
\(42\) −3.32920 −0.513706
\(43\) 0.274938 0.0419276 0.0209638 0.999780i \(-0.493327\pi\)
0.0209638 + 0.999780i \(0.493327\pi\)
\(44\) 0.394869 0.0595288
\(45\) 0 0
\(46\) −1.23828 −0.182574
\(47\) 13.4756 1.96562 0.982808 0.184631i \(-0.0591089\pi\)
0.982808 + 0.184631i \(0.0591089\pi\)
\(48\) 7.65944 1.10555
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −19.0103 −2.66197
\(52\) 1.19051 0.165093
\(53\) −8.93333 −1.22709 −0.613544 0.789661i \(-0.710256\pi\)
−0.613544 + 0.789661i \(0.710256\pi\)
\(54\) 4.08953 0.556515
\(55\) 0 0
\(56\) −3.05442 −0.408164
\(57\) 1.28126 0.169707
\(58\) −10.6966 −1.40453
\(59\) 1.66091 0.216232 0.108116 0.994138i \(-0.465518\pi\)
0.108116 + 0.994138i \(0.465518\pi\)
\(60\) 0 0
\(61\) −11.7162 −1.50011 −0.750054 0.661376i \(-0.769973\pi\)
−0.750054 + 0.661376i \(0.769973\pi\)
\(62\) −4.10048 −0.520762
\(63\) −4.22838 −0.532726
\(64\) 8.89393 1.11174
\(65\) 0 0
\(66\) −2.81701 −0.346750
\(67\) 2.82636 0.345295 0.172648 0.984984i \(-0.444768\pi\)
0.172648 + 0.984984i \(0.444768\pi\)
\(68\) −3.29969 −0.400146
\(69\) −2.68857 −0.323665
\(70\) 0 0
\(71\) 9.92823 1.17826 0.589132 0.808037i \(-0.299470\pi\)
0.589132 + 0.808037i \(0.299470\pi\)
\(72\) 12.9153 1.52208
\(73\) −7.31556 −0.856222 −0.428111 0.903726i \(-0.640821\pi\)
−0.428111 + 0.903726i \(0.640821\pi\)
\(74\) 9.72506 1.13052
\(75\) 0 0
\(76\) 0.222393 0.0255102
\(77\) 0.846153 0.0964281
\(78\) −8.49310 −0.961654
\(79\) 11.7795 1.32530 0.662648 0.748931i \(-0.269433\pi\)
0.662648 + 0.748931i \(0.269433\pi\)
\(80\) 0 0
\(81\) −3.80592 −0.422880
\(82\) −3.49942 −0.386446
\(83\) −3.72506 −0.408879 −0.204439 0.978879i \(-0.565537\pi\)
−0.204439 + 0.978879i \(0.565537\pi\)
\(84\) −1.25466 −0.136894
\(85\) 0 0
\(86\) −0.340450 −0.0367117
\(87\) −23.2246 −2.48993
\(88\) −2.58451 −0.275509
\(89\) −8.76310 −0.928887 −0.464444 0.885603i \(-0.653746\pi\)
−0.464444 + 0.885603i \(0.653746\pi\)
\(90\) 0 0
\(91\) 2.55110 0.267428
\(92\) −0.466664 −0.0486531
\(93\) −8.90301 −0.923199
\(94\) −16.6865 −1.72108
\(95\) 0 0
\(96\) 6.93948 0.708258
\(97\) −1.82229 −0.185026 −0.0925130 0.995711i \(-0.529490\pi\)
−0.0925130 + 0.995711i \(0.529490\pi\)
\(98\) −1.23828 −0.125085
\(99\) −3.57786 −0.359589
\(100\) 0 0
\(101\) −14.7870 −1.47136 −0.735682 0.677327i \(-0.763138\pi\)
−0.735682 + 0.677327i \(0.763138\pi\)
\(102\) 23.5401 2.33081
\(103\) −10.9333 −1.07729 −0.538646 0.842532i \(-0.681064\pi\)
−0.538646 + 0.842532i \(0.681064\pi\)
\(104\) −7.79212 −0.764080
\(105\) 0 0
\(106\) 11.0620 1.07443
\(107\) 17.2636 1.66893 0.834466 0.551059i \(-0.185776\pi\)
0.834466 + 0.551059i \(0.185776\pi\)
\(108\) 1.54120 0.148302
\(109\) −13.2438 −1.26852 −0.634262 0.773118i \(-0.718696\pi\)
−0.634262 + 0.773118i \(0.718696\pi\)
\(110\) 0 0
\(111\) 21.1152 2.00416
\(112\) 2.84890 0.269195
\(113\) 7.10219 0.668118 0.334059 0.942552i \(-0.391581\pi\)
0.334059 + 0.942552i \(0.391581\pi\)
\(114\) −1.58656 −0.148595
\(115\) 0 0
\(116\) −4.03117 −0.374285
\(117\) −10.7870 −0.997260
\(118\) −2.05667 −0.189332
\(119\) −7.07080 −0.648179
\(120\) 0 0
\(121\) −10.2840 −0.934911
\(122\) 14.5080 1.31349
\(123\) −7.59798 −0.685087
\(124\) −1.54533 −0.138775
\(125\) 0 0
\(126\) 5.23592 0.466453
\(127\) −16.1101 −1.42954 −0.714768 0.699361i \(-0.753468\pi\)
−0.714768 + 0.699361i \(0.753468\pi\)
\(128\) −5.85095 −0.517156
\(129\) −0.739189 −0.0650819
\(130\) 0 0
\(131\) −0.854665 −0.0746724 −0.0373362 0.999303i \(-0.511887\pi\)
−0.0373362 + 0.999303i \(0.511887\pi\)
\(132\) −1.06163 −0.0924032
\(133\) 0.476559 0.0413229
\(134\) −3.49983 −0.302339
\(135\) 0 0
\(136\) 21.5972 1.85194
\(137\) −7.11516 −0.607889 −0.303945 0.952690i \(-0.598304\pi\)
−0.303945 + 0.952690i \(0.598304\pi\)
\(138\) 3.32920 0.283400
\(139\) 10.7111 0.908505 0.454253 0.890873i \(-0.349906\pi\)
0.454253 + 0.890873i \(0.349906\pi\)
\(140\) 0 0
\(141\) −36.2300 −3.05112
\(142\) −12.2939 −1.03168
\(143\) 2.15862 0.180513
\(144\) −12.0462 −1.00385
\(145\) 0 0
\(146\) 9.05871 0.749704
\(147\) −2.68857 −0.221749
\(148\) 3.66504 0.301264
\(149\) −6.43632 −0.527284 −0.263642 0.964621i \(-0.584924\pi\)
−0.263642 + 0.964621i \(0.584924\pi\)
\(150\) 0 0
\(151\) 0.803480 0.0653863 0.0326931 0.999465i \(-0.489592\pi\)
0.0326931 + 0.999465i \(0.489592\pi\)
\(152\) −1.45561 −0.118066
\(153\) 29.8981 2.41711
\(154\) −1.04777 −0.0844320
\(155\) 0 0
\(156\) −3.20075 −0.256265
\(157\) 14.7959 1.18084 0.590419 0.807097i \(-0.298962\pi\)
0.590419 + 0.807097i \(0.298962\pi\)
\(158\) −14.5863 −1.16042
\(159\) 24.0178 1.90474
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 4.71279 0.370272
\(163\) −3.13373 −0.245453 −0.122726 0.992441i \(-0.539164\pi\)
−0.122726 + 0.992441i \(0.539164\pi\)
\(164\) −1.31881 −0.102982
\(165\) 0 0
\(166\) 4.61267 0.358012
\(167\) 23.4168 1.81204 0.906022 0.423230i \(-0.139104\pi\)
0.906022 + 0.423230i \(0.139104\pi\)
\(168\) 8.21201 0.633570
\(169\) −6.49191 −0.499377
\(170\) 0 0
\(171\) −2.01507 −0.154097
\(172\) −0.128304 −0.00978306
\(173\) 0.645424 0.0490706 0.0245353 0.999699i \(-0.492189\pi\)
0.0245353 + 0.999699i \(0.492189\pi\)
\(174\) 28.7585 2.18018
\(175\) 0 0
\(176\) 2.41060 0.181706
\(177\) −4.46547 −0.335645
\(178\) 10.8512 0.813330
\(179\) −16.9141 −1.26422 −0.632110 0.774879i \(-0.717811\pi\)
−0.632110 + 0.774879i \(0.717811\pi\)
\(180\) 0 0
\(181\) −4.61403 −0.342958 −0.171479 0.985188i \(-0.554855\pi\)
−0.171479 + 0.985188i \(0.554855\pi\)
\(182\) −3.15897 −0.234158
\(183\) 31.4998 2.32853
\(184\) 3.05442 0.225175
\(185\) 0 0
\(186\) 11.0244 0.808349
\(187\) −5.98298 −0.437519
\(188\) −6.28857 −0.458641
\(189\) 3.30259 0.240228
\(190\) 0 0
\(191\) 6.44380 0.466257 0.233129 0.972446i \(-0.425104\pi\)
0.233129 + 0.972446i \(0.425104\pi\)
\(192\) −23.9119 −1.72569
\(193\) −10.1400 −0.729897 −0.364948 0.931028i \(-0.618913\pi\)
−0.364948 + 0.931028i \(0.618913\pi\)
\(194\) 2.25651 0.162008
\(195\) 0 0
\(196\) −0.466664 −0.0333332
\(197\) 2.37475 0.169194 0.0845970 0.996415i \(-0.473040\pi\)
0.0845970 + 0.996415i \(0.473040\pi\)
\(198\) 4.43039 0.314854
\(199\) 18.6052 1.31889 0.659443 0.751754i \(-0.270792\pi\)
0.659443 + 0.751754i \(0.270792\pi\)
\(200\) 0 0
\(201\) −7.59887 −0.535983
\(202\) 18.3105 1.28832
\(203\) −8.63827 −0.606288
\(204\) 8.87143 0.621124
\(205\) 0 0
\(206\) 13.5385 0.943273
\(207\) 4.22838 0.293893
\(208\) 7.26781 0.503932
\(209\) 0.403242 0.0278928
\(210\) 0 0
\(211\) −21.1247 −1.45429 −0.727144 0.686485i \(-0.759153\pi\)
−0.727144 + 0.686485i \(0.759153\pi\)
\(212\) 4.16886 0.286319
\(213\) −26.6927 −1.82895
\(214\) −21.3771 −1.46131
\(215\) 0 0
\(216\) −10.0875 −0.686368
\(217\) −3.31143 −0.224795
\(218\) 16.3995 1.11071
\(219\) 19.6684 1.32906
\(220\) 0 0
\(221\) −18.0383 −1.21339
\(222\) −26.1465 −1.75484
\(223\) 21.5426 1.44260 0.721301 0.692622i \(-0.243544\pi\)
0.721301 + 0.692622i \(0.243544\pi\)
\(224\) 2.58111 0.172458
\(225\) 0 0
\(226\) −8.79450 −0.585001
\(227\) −12.9135 −0.857102 −0.428551 0.903518i \(-0.640976\pi\)
−0.428551 + 0.903518i \(0.640976\pi\)
\(228\) −0.597918 −0.0395981
\(229\) 28.4835 1.88224 0.941120 0.338074i \(-0.109775\pi\)
0.941120 + 0.338074i \(0.109775\pi\)
\(230\) 0 0
\(231\) −2.27494 −0.149680
\(232\) 26.3849 1.73225
\(233\) −2.58296 −0.169215 −0.0846077 0.996414i \(-0.526964\pi\)
−0.0846077 + 0.996414i \(0.526964\pi\)
\(234\) 13.3573 0.873197
\(235\) 0 0
\(236\) −0.775087 −0.0504539
\(237\) −31.6699 −2.05718
\(238\) 8.75562 0.567543
\(239\) 11.9610 0.773692 0.386846 0.922144i \(-0.373565\pi\)
0.386846 + 0.922144i \(0.373565\pi\)
\(240\) 0 0
\(241\) 2.03140 0.130854 0.0654269 0.997857i \(-0.479159\pi\)
0.0654269 + 0.997857i \(0.479159\pi\)
\(242\) 12.7345 0.818604
\(243\) 20.1402 1.29200
\(244\) 5.46754 0.350023
\(245\) 0 0
\(246\) 9.40842 0.599859
\(247\) 1.21575 0.0773562
\(248\) 10.1145 0.642272
\(249\) 10.0151 0.634680
\(250\) 0 0
\(251\) 27.4454 1.73234 0.866169 0.499750i \(-0.166575\pi\)
0.866169 + 0.499750i \(0.166575\pi\)
\(252\) 1.97324 0.124302
\(253\) −0.846153 −0.0531972
\(254\) 19.9488 1.25170
\(255\) 0 0
\(256\) −10.5427 −0.658922
\(257\) 25.1645 1.56972 0.784860 0.619673i \(-0.212735\pi\)
0.784860 + 0.619673i \(0.212735\pi\)
\(258\) 0.915322 0.0569855
\(259\) 7.85369 0.488005
\(260\) 0 0
\(261\) 36.5259 2.26090
\(262\) 1.05831 0.0653828
\(263\) −10.8612 −0.669732 −0.334866 0.942266i \(-0.608691\pi\)
−0.334866 + 0.942266i \(0.608691\pi\)
\(264\) 6.94861 0.427658
\(265\) 0 0
\(266\) −0.590113 −0.0361821
\(267\) 23.5602 1.44186
\(268\) −1.31896 −0.0805685
\(269\) −2.02133 −0.123243 −0.0616215 0.998100i \(-0.519627\pi\)
−0.0616215 + 0.998100i \(0.519627\pi\)
\(270\) 0 0
\(271\) −4.05733 −0.246465 −0.123233 0.992378i \(-0.539326\pi\)
−0.123233 + 0.992378i \(0.539326\pi\)
\(272\) −20.1440 −1.22141
\(273\) −6.85879 −0.415113
\(274\) 8.81056 0.532265
\(275\) 0 0
\(276\) 1.25466 0.0755215
\(277\) 31.6071 1.89909 0.949544 0.313634i \(-0.101546\pi\)
0.949544 + 0.313634i \(0.101546\pi\)
\(278\) −13.2634 −0.795483
\(279\) 14.0020 0.838279
\(280\) 0 0
\(281\) 25.4680 1.51929 0.759646 0.650337i \(-0.225372\pi\)
0.759646 + 0.650337i \(0.225372\pi\)
\(282\) 44.8629 2.67154
\(283\) 8.06860 0.479629 0.239814 0.970819i \(-0.422913\pi\)
0.239814 + 0.970819i \(0.422913\pi\)
\(284\) −4.63315 −0.274927
\(285\) 0 0
\(286\) −2.67297 −0.158056
\(287\) −2.82603 −0.166816
\(288\) −10.9139 −0.643109
\(289\) 32.9962 1.94095
\(290\) 0 0
\(291\) 4.89936 0.287205
\(292\) 3.41391 0.199784
\(293\) 12.5766 0.734730 0.367365 0.930077i \(-0.380260\pi\)
0.367365 + 0.930077i \(0.380260\pi\)
\(294\) 3.32920 0.194163
\(295\) 0 0
\(296\) −23.9885 −1.39430
\(297\) 2.79450 0.162153
\(298\) 7.96996 0.461688
\(299\) −2.55110 −0.147534
\(300\) 0 0
\(301\) −0.274938 −0.0158472
\(302\) −0.994933 −0.0572519
\(303\) 39.7559 2.28391
\(304\) 1.35767 0.0778675
\(305\) 0 0
\(306\) −37.0221 −2.11641
\(307\) −0.588753 −0.0336019 −0.0168009 0.999859i \(-0.505348\pi\)
−0.0168009 + 0.999859i \(0.505348\pi\)
\(308\) −0.394869 −0.0224998
\(309\) 29.3950 1.67222
\(310\) 0 0
\(311\) 2.32490 0.131833 0.0659165 0.997825i \(-0.479003\pi\)
0.0659165 + 0.997825i \(0.479003\pi\)
\(312\) 20.9496 1.18604
\(313\) 8.02863 0.453805 0.226903 0.973917i \(-0.427140\pi\)
0.226903 + 0.973917i \(0.427140\pi\)
\(314\) −18.3214 −1.03394
\(315\) 0 0
\(316\) −5.49706 −0.309234
\(317\) −27.0431 −1.51889 −0.759445 0.650572i \(-0.774529\pi\)
−0.759445 + 0.650572i \(0.774529\pi\)
\(318\) −29.7408 −1.66778
\(319\) −7.30930 −0.409242
\(320\) 0 0
\(321\) −46.4143 −2.59059
\(322\) 1.23828 0.0690066
\(323\) −3.36965 −0.187492
\(324\) 1.77608 0.0986714
\(325\) 0 0
\(326\) 3.88043 0.214917
\(327\) 35.6068 1.96906
\(328\) 8.63189 0.476617
\(329\) −13.4756 −0.742933
\(330\) 0 0
\(331\) 22.7555 1.25075 0.625377 0.780323i \(-0.284945\pi\)
0.625377 + 0.780323i \(0.284945\pi\)
\(332\) 1.73835 0.0954045
\(333\) −33.2084 −1.81981
\(334\) −28.9965 −1.58662
\(335\) 0 0
\(336\) −7.65944 −0.417857
\(337\) 1.05919 0.0576978 0.0288489 0.999584i \(-0.490816\pi\)
0.0288489 + 0.999584i \(0.490816\pi\)
\(338\) 8.03879 0.437253
\(339\) −19.0947 −1.03708
\(340\) 0 0
\(341\) −2.80198 −0.151736
\(342\) 2.49522 0.134926
\(343\) −1.00000 −0.0539949
\(344\) 0.839776 0.0452777
\(345\) 0 0
\(346\) −0.799215 −0.0429660
\(347\) −14.2245 −0.763611 −0.381806 0.924243i \(-0.624698\pi\)
−0.381806 + 0.924243i \(0.624698\pi\)
\(348\) 10.8381 0.580982
\(349\) −23.4865 −1.25721 −0.628603 0.777727i \(-0.716373\pi\)
−0.628603 + 0.777727i \(0.716373\pi\)
\(350\) 0 0
\(351\) 8.42523 0.449706
\(352\) 2.18401 0.116408
\(353\) 1.19652 0.0636843 0.0318422 0.999493i \(-0.489863\pi\)
0.0318422 + 0.999493i \(0.489863\pi\)
\(354\) 5.52949 0.293889
\(355\) 0 0
\(356\) 4.08943 0.216739
\(357\) 19.0103 1.00613
\(358\) 20.9444 1.10695
\(359\) 8.62376 0.455145 0.227572 0.973761i \(-0.426921\pi\)
0.227572 + 0.973761i \(0.426921\pi\)
\(360\) 0 0
\(361\) −18.7729 −0.988047
\(362\) 5.71346 0.300293
\(363\) 27.6493 1.45121
\(364\) −1.19051 −0.0623994
\(365\) 0 0
\(366\) −39.0056 −2.03885
\(367\) −1.40241 −0.0732050 −0.0366025 0.999330i \(-0.511654\pi\)
−0.0366025 + 0.999330i \(0.511654\pi\)
\(368\) −2.84890 −0.148509
\(369\) 11.9496 0.622069
\(370\) 0 0
\(371\) 8.93333 0.463795
\(372\) 4.15472 0.215412
\(373\) −5.38461 −0.278805 −0.139402 0.990236i \(-0.544518\pi\)
−0.139402 + 0.990236i \(0.544518\pi\)
\(374\) 7.40860 0.383089
\(375\) 0 0
\(376\) 41.1601 2.12267
\(377\) −22.0371 −1.13497
\(378\) −4.08953 −0.210343
\(379\) 26.3413 1.35306 0.676532 0.736413i \(-0.263482\pi\)
0.676532 + 0.736413i \(0.263482\pi\)
\(380\) 0 0
\(381\) 43.3130 2.21899
\(382\) −7.97923 −0.408253
\(383\) −23.4277 −1.19710 −0.598550 0.801085i \(-0.704256\pi\)
−0.598550 + 0.801085i \(0.704256\pi\)
\(384\) 15.7307 0.802752
\(385\) 0 0
\(386\) 12.5562 0.639094
\(387\) 1.16254 0.0590954
\(388\) 0.850399 0.0431725
\(389\) −13.5760 −0.688330 −0.344165 0.938909i \(-0.611838\pi\)
−0.344165 + 0.938909i \(0.611838\pi\)
\(390\) 0 0
\(391\) 7.07080 0.357586
\(392\) 3.05442 0.154271
\(393\) 2.29782 0.115910
\(394\) −2.94060 −0.148146
\(395\) 0 0
\(396\) 1.66966 0.0839036
\(397\) −3.24696 −0.162960 −0.0814801 0.996675i \(-0.525965\pi\)
−0.0814801 + 0.996675i \(0.525965\pi\)
\(398\) −23.0384 −1.15481
\(399\) −1.28126 −0.0641432
\(400\) 0 0
\(401\) 30.2805 1.51213 0.756067 0.654494i \(-0.227118\pi\)
0.756067 + 0.654494i \(0.227118\pi\)
\(402\) 9.40952 0.469304
\(403\) −8.44779 −0.420814
\(404\) 6.90057 0.343316
\(405\) 0 0
\(406\) 10.6966 0.530863
\(407\) 6.64542 0.329401
\(408\) −58.0654 −2.87467
\(409\) 12.3775 0.612029 0.306014 0.952027i \(-0.401004\pi\)
0.306014 + 0.952027i \(0.401004\pi\)
\(410\) 0 0
\(411\) 19.1296 0.943592
\(412\) 5.10219 0.251367
\(413\) −1.66091 −0.0817280
\(414\) −5.23592 −0.257332
\(415\) 0 0
\(416\) 6.58466 0.322840
\(417\) −28.7975 −1.41022
\(418\) −0.499326 −0.0244228
\(419\) 5.46520 0.266992 0.133496 0.991049i \(-0.457380\pi\)
0.133496 + 0.991049i \(0.457380\pi\)
\(420\) 0 0
\(421\) −6.55232 −0.319340 −0.159670 0.987170i \(-0.551043\pi\)
−0.159670 + 0.987170i \(0.551043\pi\)
\(422\) 26.1583 1.27337
\(423\) 56.9800 2.77046
\(424\) −27.2861 −1.32513
\(425\) 0 0
\(426\) 33.0530 1.60142
\(427\) 11.7162 0.566988
\(428\) −8.05629 −0.389416
\(429\) −5.80359 −0.280200
\(430\) 0 0
\(431\) −7.88645 −0.379877 −0.189938 0.981796i \(-0.560829\pi\)
−0.189938 + 0.981796i \(0.560829\pi\)
\(432\) 9.40874 0.452678
\(433\) 33.7313 1.62102 0.810511 0.585723i \(-0.199189\pi\)
0.810511 + 0.585723i \(0.199189\pi\)
\(434\) 4.10048 0.196829
\(435\) 0 0
\(436\) 6.18040 0.295988
\(437\) −0.476559 −0.0227969
\(438\) −24.3549 −1.16372
\(439\) −13.6800 −0.652909 −0.326455 0.945213i \(-0.605854\pi\)
−0.326455 + 0.945213i \(0.605854\pi\)
\(440\) 0 0
\(441\) 4.22838 0.201352
\(442\) 22.3364 1.06244
\(443\) 17.2726 0.820646 0.410323 0.911940i \(-0.365416\pi\)
0.410323 + 0.911940i \(0.365416\pi\)
\(444\) −9.85369 −0.467635
\(445\) 0 0
\(446\) −26.6758 −1.26314
\(447\) 17.3045 0.818473
\(448\) −8.89393 −0.420199
\(449\) 8.26286 0.389949 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(450\) 0 0
\(451\) −2.39126 −0.112600
\(452\) −3.31434 −0.155893
\(453\) −2.16021 −0.101495
\(454\) 15.9906 0.750475
\(455\) 0 0
\(456\) 3.91350 0.183267
\(457\) −2.80779 −0.131343 −0.0656714 0.997841i \(-0.520919\pi\)
−0.0656714 + 0.997841i \(0.520919\pi\)
\(458\) −35.2705 −1.64808
\(459\) −23.3520 −1.08998
\(460\) 0 0
\(461\) −0.220189 −0.0102552 −0.00512761 0.999987i \(-0.501632\pi\)
−0.00512761 + 0.999987i \(0.501632\pi\)
\(462\) 2.81701 0.131059
\(463\) −25.5262 −1.18630 −0.593152 0.805091i \(-0.702117\pi\)
−0.593152 + 0.805091i \(0.702117\pi\)
\(464\) −24.6095 −1.14247
\(465\) 0 0
\(466\) 3.19843 0.148164
\(467\) −6.43084 −0.297584 −0.148792 0.988869i \(-0.547538\pi\)
−0.148792 + 0.988869i \(0.547538\pi\)
\(468\) 5.03392 0.232693
\(469\) −2.82636 −0.130509
\(470\) 0 0
\(471\) −39.7796 −1.83295
\(472\) 5.07312 0.233509
\(473\) −0.232640 −0.0106968
\(474\) 39.2162 1.80126
\(475\) 0 0
\(476\) 3.29969 0.151241
\(477\) −37.7736 −1.72953
\(478\) −14.8110 −0.677441
\(479\) 25.1810 1.15055 0.575276 0.817960i \(-0.304895\pi\)
0.575276 + 0.817960i \(0.304895\pi\)
\(480\) 0 0
\(481\) 20.0355 0.913541
\(482\) −2.51544 −0.114575
\(483\) 2.68857 0.122334
\(484\) 4.79919 0.218145
\(485\) 0 0
\(486\) −24.9392 −1.13127
\(487\) −37.4074 −1.69509 −0.847545 0.530724i \(-0.821920\pi\)
−0.847545 + 0.530724i \(0.821920\pi\)
\(488\) −35.7863 −1.61997
\(489\) 8.42523 0.381002
\(490\) 0 0
\(491\) −8.61145 −0.388629 −0.194315 0.980939i \(-0.562248\pi\)
−0.194315 + 0.980939i \(0.562248\pi\)
\(492\) 3.54571 0.159853
\(493\) 61.0795 2.75088
\(494\) −1.50543 −0.0677327
\(495\) 0 0
\(496\) −9.43393 −0.423596
\(497\) −9.92823 −0.445342
\(498\) −12.4015 −0.555723
\(499\) −31.2249 −1.39782 −0.698909 0.715211i \(-0.746331\pi\)
−0.698909 + 0.715211i \(0.746331\pi\)
\(500\) 0 0
\(501\) −62.9575 −2.81274
\(502\) −33.9851 −1.51683
\(503\) −12.5421 −0.559223 −0.279612 0.960113i \(-0.590206\pi\)
−0.279612 + 0.960113i \(0.590206\pi\)
\(504\) −12.9153 −0.575291
\(505\) 0 0
\(506\) 1.04777 0.0465792
\(507\) 17.4539 0.775156
\(508\) 7.51799 0.333557
\(509\) 12.5436 0.555986 0.277993 0.960583i \(-0.410331\pi\)
0.277993 + 0.960583i \(0.410331\pi\)
\(510\) 0 0
\(511\) 7.31556 0.323621
\(512\) 24.7568 1.09410
\(513\) 1.57388 0.0694885
\(514\) −31.1607 −1.37444
\(515\) 0 0
\(516\) 0.344953 0.0151857
\(517\) −11.4024 −0.501477
\(518\) −9.72506 −0.427295
\(519\) −1.73526 −0.0761696
\(520\) 0 0
\(521\) 18.3842 0.805426 0.402713 0.915326i \(-0.368067\pi\)
0.402713 + 0.915326i \(0.368067\pi\)
\(522\) −45.2293 −1.97963
\(523\) −21.0572 −0.920769 −0.460384 0.887720i \(-0.652288\pi\)
−0.460384 + 0.887720i \(0.652288\pi\)
\(524\) 0.398841 0.0174235
\(525\) 0 0
\(526\) 13.4492 0.586414
\(527\) 23.4145 1.01995
\(528\) −6.48106 −0.282052
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 7.02297 0.304771
\(532\) −0.222393 −0.00964196
\(533\) −7.20949 −0.312278
\(534\) −29.1741 −1.26249
\(535\) 0 0
\(536\) 8.63290 0.372885
\(537\) 45.4747 1.96238
\(538\) 2.50298 0.107911
\(539\) −0.846153 −0.0364464
\(540\) 0 0
\(541\) 30.0230 1.29079 0.645395 0.763849i \(-0.276693\pi\)
0.645395 + 0.763849i \(0.276693\pi\)
\(542\) 5.02411 0.215804
\(543\) 12.4051 0.532354
\(544\) −18.2505 −0.782484
\(545\) 0 0
\(546\) 8.49310 0.363471
\(547\) 9.39847 0.401849 0.200925 0.979607i \(-0.435605\pi\)
0.200925 + 0.979607i \(0.435605\pi\)
\(548\) 3.32039 0.141840
\(549\) −49.5407 −2.11435
\(550\) 0 0
\(551\) −4.11664 −0.175375
\(552\) −8.21201 −0.349526
\(553\) −11.7795 −0.500915
\(554\) −39.1384 −1.66283
\(555\) 0 0
\(556\) −4.99850 −0.211983
\(557\) 22.6305 0.958885 0.479443 0.877573i \(-0.340839\pi\)
0.479443 + 0.877573i \(0.340839\pi\)
\(558\) −17.3384 −0.733993
\(559\) −0.701393 −0.0296658
\(560\) 0 0
\(561\) 16.0856 0.679136
\(562\) −31.5365 −1.33029
\(563\) 21.0667 0.887854 0.443927 0.896063i \(-0.353585\pi\)
0.443927 + 0.896063i \(0.353585\pi\)
\(564\) 16.9072 0.711923
\(565\) 0 0
\(566\) −9.99118 −0.419961
\(567\) 3.80592 0.159833
\(568\) 30.3250 1.27241
\(569\) −40.2625 −1.68789 −0.843945 0.536430i \(-0.819773\pi\)
−0.843945 + 0.536430i \(0.819773\pi\)
\(570\) 0 0
\(571\) 7.61151 0.318532 0.159266 0.987236i \(-0.449087\pi\)
0.159266 + 0.987236i \(0.449087\pi\)
\(572\) −1.00735 −0.0421194
\(573\) −17.3246 −0.723745
\(574\) 3.49942 0.146063
\(575\) 0 0
\(576\) 37.6069 1.56696
\(577\) −18.6364 −0.775845 −0.387923 0.921692i \(-0.626807\pi\)
−0.387923 + 0.921692i \(0.626807\pi\)
\(578\) −40.8585 −1.69949
\(579\) 27.2622 1.13298
\(580\) 0 0
\(581\) 3.72506 0.154542
\(582\) −6.06677 −0.251476
\(583\) 7.55896 0.313060
\(584\) −22.3448 −0.924634
\(585\) 0 0
\(586\) −15.5733 −0.643327
\(587\) −40.9445 −1.68996 −0.844981 0.534797i \(-0.820388\pi\)
−0.844981 + 0.534797i \(0.820388\pi\)
\(588\) 1.25466 0.0517412
\(589\) −1.57809 −0.0650242
\(590\) 0 0
\(591\) −6.38467 −0.262630
\(592\) 22.3743 0.919580
\(593\) −20.5649 −0.844501 −0.422251 0.906479i \(-0.638760\pi\)
−0.422251 + 0.906479i \(0.638760\pi\)
\(594\) −3.46037 −0.141981
\(595\) 0 0
\(596\) 3.00360 0.123032
\(597\) −50.0213 −2.04723
\(598\) 3.15897 0.129180
\(599\) 2.94630 0.120382 0.0601912 0.998187i \(-0.480829\pi\)
0.0601912 + 0.998187i \(0.480829\pi\)
\(600\) 0 0
\(601\) 37.8860 1.54540 0.772702 0.634769i \(-0.218905\pi\)
0.772702 + 0.634769i \(0.218905\pi\)
\(602\) 0.340450 0.0138757
\(603\) 11.9510 0.486681
\(604\) −0.374955 −0.0152567
\(605\) 0 0
\(606\) −49.2289 −1.99979
\(607\) 7.00707 0.284408 0.142204 0.989837i \(-0.454581\pi\)
0.142204 + 0.989837i \(0.454581\pi\)
\(608\) 1.23005 0.0498851
\(609\) 23.2246 0.941107
\(610\) 0 0
\(611\) −34.3775 −1.39077
\(612\) −13.9524 −0.563990
\(613\) 18.9408 0.765012 0.382506 0.923953i \(-0.375061\pi\)
0.382506 + 0.923953i \(0.375061\pi\)
\(614\) 0.729040 0.0294217
\(615\) 0 0
\(616\) 2.58451 0.104133
\(617\) 2.22511 0.0895797 0.0447898 0.998996i \(-0.485738\pi\)
0.0447898 + 0.998996i \(0.485738\pi\)
\(618\) −36.3992 −1.46419
\(619\) −15.2083 −0.611272 −0.305636 0.952148i \(-0.598869\pi\)
−0.305636 + 0.952148i \(0.598869\pi\)
\(620\) 0 0
\(621\) −3.30259 −0.132529
\(622\) −2.87888 −0.115432
\(623\) 8.76310 0.351086
\(624\) −19.5400 −0.782225
\(625\) 0 0
\(626\) −9.94169 −0.397350
\(627\) −1.08414 −0.0432964
\(628\) −6.90470 −0.275527
\(629\) −55.5319 −2.21420
\(630\) 0 0
\(631\) 6.16049 0.245245 0.122623 0.992453i \(-0.460870\pi\)
0.122623 + 0.992453i \(0.460870\pi\)
\(632\) 35.9795 1.43119
\(633\) 56.7953 2.25741
\(634\) 33.4869 1.32993
\(635\) 0 0
\(636\) −11.2083 −0.444437
\(637\) −2.55110 −0.101078
\(638\) 9.05096 0.358331
\(639\) 41.9804 1.66072
\(640\) 0 0
\(641\) 16.3586 0.646126 0.323063 0.946377i \(-0.395287\pi\)
0.323063 + 0.946377i \(0.395287\pi\)
\(642\) 57.4738 2.26831
\(643\) 30.8553 1.21681 0.608407 0.793625i \(-0.291809\pi\)
0.608407 + 0.793625i \(0.291809\pi\)
\(644\) 0.466664 0.0183891
\(645\) 0 0
\(646\) 4.17257 0.164168
\(647\) −10.3205 −0.405742 −0.202871 0.979206i \(-0.565027\pi\)
−0.202871 + 0.979206i \(0.565027\pi\)
\(648\) −11.6249 −0.456668
\(649\) −1.40538 −0.0551662
\(650\) 0 0
\(651\) 8.90301 0.348936
\(652\) 1.46240 0.0572720
\(653\) −1.58679 −0.0620961 −0.0310480 0.999518i \(-0.509884\pi\)
−0.0310480 + 0.999518i \(0.509884\pi\)
\(654\) −44.0912 −1.72410
\(655\) 0 0
\(656\) −8.05108 −0.314342
\(657\) −30.9330 −1.20681
\(658\) 16.6865 0.650509
\(659\) −43.3271 −1.68779 −0.843893 0.536512i \(-0.819742\pi\)
−0.843893 + 0.536512i \(0.819742\pi\)
\(660\) 0 0
\(661\) 18.2262 0.708917 0.354458 0.935072i \(-0.384665\pi\)
0.354458 + 0.935072i \(0.384665\pi\)
\(662\) −28.1776 −1.09516
\(663\) 48.4971 1.88347
\(664\) −11.3779 −0.441548
\(665\) 0 0
\(666\) 41.1213 1.59342
\(667\) 8.63827 0.334475
\(668\) −10.9278 −0.422808
\(669\) −57.9188 −2.23927
\(670\) 0 0
\(671\) 9.91372 0.382715
\(672\) −6.93948 −0.267696
\(673\) −6.47655 −0.249653 −0.124826 0.992179i \(-0.539837\pi\)
−0.124826 + 0.992179i \(0.539837\pi\)
\(674\) −1.31157 −0.0505199
\(675\) 0 0
\(676\) 3.02954 0.116521
\(677\) 8.19344 0.314899 0.157450 0.987527i \(-0.449673\pi\)
0.157450 + 0.987527i \(0.449673\pi\)
\(678\) 23.6446 0.908065
\(679\) 1.82229 0.0699332
\(680\) 0 0
\(681\) 34.7189 1.33043
\(682\) 3.46963 0.132859
\(683\) 7.95826 0.304514 0.152257 0.988341i \(-0.451346\pi\)
0.152257 + 0.988341i \(0.451346\pi\)
\(684\) 0.940363 0.0359557
\(685\) 0 0
\(686\) 1.23828 0.0472777
\(687\) −76.5796 −2.92169
\(688\) −0.783270 −0.0298619
\(689\) 22.7898 0.868222
\(690\) 0 0
\(691\) −3.66850 −0.139556 −0.0697782 0.997563i \(-0.522229\pi\)
−0.0697782 + 0.997563i \(0.522229\pi\)
\(692\) −0.301196 −0.0114498
\(693\) 3.57786 0.135912
\(694\) 17.6139 0.668615
\(695\) 0 0
\(696\) −70.9375 −2.68888
\(697\) 19.9823 0.756884
\(698\) 29.0829 1.10080
\(699\) 6.94446 0.262664
\(700\) 0 0
\(701\) 40.6182 1.53413 0.767063 0.641571i \(-0.221717\pi\)
0.767063 + 0.641571i \(0.221717\pi\)
\(702\) −10.4328 −0.393760
\(703\) 3.74274 0.141160
\(704\) −7.52562 −0.283633
\(705\) 0 0
\(706\) −1.48163 −0.0557617
\(707\) 14.7870 0.556123
\(708\) 2.08387 0.0783168
\(709\) −38.7523 −1.45537 −0.727687 0.685910i \(-0.759405\pi\)
−0.727687 + 0.685910i \(0.759405\pi\)
\(710\) 0 0
\(711\) 49.8082 1.86795
\(712\) −26.7662 −1.00311
\(713\) 3.31143 0.124014
\(714\) −23.5401 −0.880965
\(715\) 0 0
\(716\) 7.89321 0.294983
\(717\) −32.1579 −1.20096
\(718\) −10.6786 −0.398523
\(719\) 34.5902 1.29000 0.644998 0.764184i \(-0.276858\pi\)
0.644998 + 0.764184i \(0.276858\pi\)
\(720\) 0 0
\(721\) 10.9333 0.407178
\(722\) 23.2461 0.865130
\(723\) −5.46154 −0.203117
\(724\) 2.15320 0.0800231
\(725\) 0 0
\(726\) −34.2375 −1.27067
\(727\) 8.51989 0.315985 0.157993 0.987440i \(-0.449498\pi\)
0.157993 + 0.987440i \(0.449498\pi\)
\(728\) 7.79212 0.288795
\(729\) −42.7306 −1.58261
\(730\) 0 0
\(731\) 1.94403 0.0719026
\(732\) −14.6998 −0.543322
\(733\) 35.1739 1.29918 0.649590 0.760285i \(-0.274941\pi\)
0.649590 + 0.760285i \(0.274941\pi\)
\(734\) 1.73657 0.0640980
\(735\) 0 0
\(736\) −2.58111 −0.0951410
\(737\) −2.39154 −0.0880934
\(738\) −14.7969 −0.544681
\(739\) 15.1355 0.556769 0.278384 0.960470i \(-0.410201\pi\)
0.278384 + 0.960470i \(0.410201\pi\)
\(740\) 0 0
\(741\) −3.26862 −0.120076
\(742\) −11.0620 −0.406097
\(743\) 20.2165 0.741670 0.370835 0.928699i \(-0.379072\pi\)
0.370835 + 0.928699i \(0.379072\pi\)
\(744\) −27.1935 −0.996963
\(745\) 0 0
\(746\) 6.66765 0.244120
\(747\) −15.7510 −0.576299
\(748\) 2.79204 0.102087
\(749\) −17.2636 −0.630797
\(750\) 0 0
\(751\) 31.1017 1.13492 0.567459 0.823401i \(-0.307926\pi\)
0.567459 + 0.823401i \(0.307926\pi\)
\(752\) −38.3905 −1.39996
\(753\) −73.7888 −2.68901
\(754\) 27.2880 0.993772
\(755\) 0 0
\(756\) −1.54120 −0.0560530
\(757\) 11.9728 0.435158 0.217579 0.976043i \(-0.430184\pi\)
0.217579 + 0.976043i \(0.430184\pi\)
\(758\) −32.6179 −1.18474
\(759\) 2.27494 0.0825750
\(760\) 0 0
\(761\) 17.8372 0.646597 0.323299 0.946297i \(-0.395208\pi\)
0.323299 + 0.946297i \(0.395208\pi\)
\(762\) −53.6335 −1.94294
\(763\) 13.2438 0.479457
\(764\) −3.00709 −0.108793
\(765\) 0 0
\(766\) 29.0101 1.04818
\(767\) −4.23714 −0.152994
\(768\) 28.3449 1.02281
\(769\) −47.9412 −1.72880 −0.864401 0.502802i \(-0.832302\pi\)
−0.864401 + 0.502802i \(0.832302\pi\)
\(770\) 0 0
\(771\) −67.6565 −2.43659
\(772\) 4.73200 0.170308
\(773\) −22.7079 −0.816748 −0.408374 0.912815i \(-0.633904\pi\)
−0.408374 + 0.912815i \(0.633904\pi\)
\(774\) −1.43955 −0.0517437
\(775\) 0 0
\(776\) −5.56605 −0.199810
\(777\) −21.1152 −0.757502
\(778\) 16.8109 0.602699
\(779\) −1.34677 −0.0482531
\(780\) 0 0
\(781\) −8.40080 −0.300604
\(782\) −8.75562 −0.313100
\(783\) −28.5287 −1.01953
\(784\) −2.84890 −0.101746
\(785\) 0 0
\(786\) −2.84535 −0.101490
\(787\) 20.2521 0.721910 0.360955 0.932583i \(-0.382451\pi\)
0.360955 + 0.932583i \(0.382451\pi\)
\(788\) −1.10821 −0.0394784
\(789\) 29.2011 1.03959
\(790\) 0 0
\(791\) −7.10219 −0.252525
\(792\) −10.9283 −0.388320
\(793\) 29.8892 1.06140
\(794\) 4.02064 0.142687
\(795\) 0 0
\(796\) −8.68237 −0.307739
\(797\) 22.1099 0.783172 0.391586 0.920142i \(-0.371927\pi\)
0.391586 + 0.920142i \(0.371927\pi\)
\(798\) 1.58656 0.0561635
\(799\) 95.2831 3.37087
\(800\) 0 0
\(801\) −37.0538 −1.30923
\(802\) −37.4957 −1.32402
\(803\) 6.19008 0.218443
\(804\) 3.54612 0.125062
\(805\) 0 0
\(806\) 10.4607 0.368463
\(807\) 5.43449 0.191303
\(808\) −45.1658 −1.58893
\(809\) −35.3424 −1.24257 −0.621287 0.783583i \(-0.713390\pi\)
−0.621287 + 0.783583i \(0.713390\pi\)
\(810\) 0 0
\(811\) −15.3968 −0.540654 −0.270327 0.962769i \(-0.587132\pi\)
−0.270327 + 0.962769i \(0.587132\pi\)
\(812\) 4.03117 0.141466
\(813\) 10.9084 0.382574
\(814\) −8.22889 −0.288422
\(815\) 0 0
\(816\) 54.1584 1.89592
\(817\) −0.131024 −0.00458395
\(818\) −15.3268 −0.535890
\(819\) 10.7870 0.376929
\(820\) 0 0
\(821\) −47.6244 −1.66210 −0.831052 0.556195i \(-0.812261\pi\)
−0.831052 + 0.556195i \(0.812261\pi\)
\(822\) −23.6878 −0.826205
\(823\) −24.1554 −0.842006 −0.421003 0.907059i \(-0.638322\pi\)
−0.421003 + 0.907059i \(0.638322\pi\)
\(824\) −33.3950 −1.16337
\(825\) 0 0
\(826\) 2.05667 0.0715607
\(827\) 14.8594 0.516710 0.258355 0.966050i \(-0.416820\pi\)
0.258355 + 0.966050i \(0.416820\pi\)
\(828\) −1.97324 −0.0685747
\(829\) 20.2699 0.704003 0.352001 0.935999i \(-0.385501\pi\)
0.352001 + 0.935999i \(0.385501\pi\)
\(830\) 0 0
\(831\) −84.9778 −2.94785
\(832\) −22.6893 −0.786609
\(833\) 7.07080 0.244989
\(834\) 35.6594 1.23478
\(835\) 0 0
\(836\) −0.188178 −0.00650829
\(837\) −10.9363 −0.378015
\(838\) −6.76744 −0.233777
\(839\) −20.9307 −0.722609 −0.361304 0.932448i \(-0.617668\pi\)
−0.361304 + 0.932448i \(0.617668\pi\)
\(840\) 0 0
\(841\) 45.6197 1.57309
\(842\) 8.11360 0.279613
\(843\) −68.4723 −2.35831
\(844\) 9.85816 0.339332
\(845\) 0 0
\(846\) −70.5571 −2.42580
\(847\) 10.2840 0.353363
\(848\) 25.4501 0.873961
\(849\) −21.6930 −0.744501
\(850\) 0 0
\(851\) −7.85369 −0.269221
\(852\) 12.4565 0.426753
\(853\) 28.3729 0.971470 0.485735 0.874106i \(-0.338552\pi\)
0.485735 + 0.874106i \(0.338552\pi\)
\(854\) −14.5080 −0.496452
\(855\) 0 0
\(856\) 52.7302 1.80228
\(857\) 32.4441 1.10827 0.554134 0.832428i \(-0.313050\pi\)
0.554134 + 0.832428i \(0.313050\pi\)
\(858\) 7.18646 0.245342
\(859\) 32.7552 1.11759 0.558797 0.829305i \(-0.311263\pi\)
0.558797 + 0.829305i \(0.311263\pi\)
\(860\) 0 0
\(861\) 7.59798 0.258938
\(862\) 9.76562 0.332618
\(863\) −5.88556 −0.200347 −0.100173 0.994970i \(-0.531940\pi\)
−0.100173 + 0.994970i \(0.531940\pi\)
\(864\) 8.52436 0.290004
\(865\) 0 0
\(866\) −41.7688 −1.41936
\(867\) −88.7124 −3.01283
\(868\) 1.54533 0.0524518
\(869\) −9.96724 −0.338116
\(870\) 0 0
\(871\) −7.21033 −0.244313
\(872\) −40.4521 −1.36988
\(873\) −7.70536 −0.260787
\(874\) 0.590113 0.0199609
\(875\) 0 0
\(876\) −9.17852 −0.310114
\(877\) 53.7879 1.81629 0.908144 0.418658i \(-0.137499\pi\)
0.908144 + 0.418658i \(0.137499\pi\)
\(878\) 16.9396 0.571685
\(879\) −33.8129 −1.14048
\(880\) 0 0
\(881\) 6.04127 0.203536 0.101768 0.994808i \(-0.467550\pi\)
0.101768 + 0.994808i \(0.467550\pi\)
\(882\) −5.23592 −0.176303
\(883\) −44.1976 −1.48737 −0.743683 0.668532i \(-0.766923\pi\)
−0.743683 + 0.668532i \(0.766923\pi\)
\(884\) 8.41782 0.283122
\(885\) 0 0
\(886\) −21.3883 −0.718554
\(887\) 36.4986 1.22550 0.612752 0.790275i \(-0.290063\pi\)
0.612752 + 0.790275i \(0.290063\pi\)
\(888\) 64.4946 2.16430
\(889\) 16.1101 0.540314
\(890\) 0 0
\(891\) 3.22039 0.107887
\(892\) −10.0532 −0.336605
\(893\) −6.42191 −0.214901
\(894\) −21.4278 −0.716652
\(895\) 0 0
\(896\) 5.85095 0.195466
\(897\) 6.85879 0.229008
\(898\) −10.2317 −0.341437
\(899\) 28.6051 0.954033
\(900\) 0 0
\(901\) −63.1658 −2.10436
\(902\) 2.96105 0.0985920
\(903\) 0.739189 0.0245987
\(904\) 21.6931 0.721501
\(905\) 0 0
\(906\) 2.67494 0.0888690
\(907\) −8.22173 −0.272998 −0.136499 0.990640i \(-0.543585\pi\)
−0.136499 + 0.990640i \(0.543585\pi\)
\(908\) 6.02629 0.199989
\(909\) −62.5252 −2.07383
\(910\) 0 0
\(911\) −21.5853 −0.715154 −0.357577 0.933884i \(-0.616397\pi\)
−0.357577 + 0.933884i \(0.616397\pi\)
\(912\) −3.65017 −0.120869
\(913\) 3.15197 0.104315
\(914\) 3.47683 0.115003
\(915\) 0 0
\(916\) −13.2922 −0.439187
\(917\) 0.854665 0.0282235
\(918\) 28.9163 0.954379
\(919\) −38.0934 −1.25658 −0.628292 0.777978i \(-0.716246\pi\)
−0.628292 + 0.777978i \(0.716246\pi\)
\(920\) 0 0
\(921\) 1.58290 0.0521583
\(922\) 0.272656 0.00897943
\(923\) −25.3279 −0.833677
\(924\) 1.06163 0.0349251
\(925\) 0 0
\(926\) 31.6086 1.03872
\(927\) −46.2303 −1.51840
\(928\) −22.2963 −0.731913
\(929\) −9.15900 −0.300497 −0.150249 0.988648i \(-0.548007\pi\)
−0.150249 + 0.988648i \(0.548007\pi\)
\(930\) 0 0
\(931\) −0.476559 −0.0156186
\(932\) 1.20538 0.0394834
\(933\) −6.25065 −0.204637
\(934\) 7.96317 0.260563
\(935\) 0 0
\(936\) −32.9481 −1.07694
\(937\) 18.8314 0.615194 0.307597 0.951517i \(-0.400475\pi\)
0.307597 + 0.951517i \(0.400475\pi\)
\(938\) 3.49983 0.114273
\(939\) −21.5855 −0.704416
\(940\) 0 0
\(941\) 25.4216 0.828721 0.414360 0.910113i \(-0.364005\pi\)
0.414360 + 0.910113i \(0.364005\pi\)
\(942\) 49.2583 1.60492
\(943\) 2.82603 0.0920283
\(944\) −4.73176 −0.154006
\(945\) 0 0
\(946\) 0.288073 0.00936605
\(947\) −33.3211 −1.08279 −0.541395 0.840768i \(-0.682104\pi\)
−0.541395 + 0.840768i \(0.682104\pi\)
\(948\) 14.7792 0.480007
\(949\) 18.6627 0.605817
\(950\) 0 0
\(951\) 72.7070 2.35769
\(952\) −21.5972 −0.699969
\(953\) −30.5121 −0.988383 −0.494192 0.869353i \(-0.664536\pi\)
−0.494192 + 0.869353i \(0.664536\pi\)
\(954\) 46.7742 1.51437
\(955\) 0 0
\(956\) −5.58176 −0.180527
\(957\) 19.6515 0.635244
\(958\) −31.1812 −1.00742
\(959\) 7.11516 0.229761
\(960\) 0 0
\(961\) −20.0344 −0.646271
\(962\) −24.8096 −0.799893
\(963\) 72.9970 2.35230
\(964\) −0.947980 −0.0305324
\(965\) 0 0
\(966\) −3.32920 −0.107115
\(967\) 23.0298 0.740587 0.370294 0.928915i \(-0.379257\pi\)
0.370294 + 0.928915i \(0.379257\pi\)
\(968\) −31.4117 −1.00961
\(969\) 9.05953 0.291034
\(970\) 0 0
\(971\) 6.95588 0.223225 0.111612 0.993752i \(-0.464398\pi\)
0.111612 + 0.993752i \(0.464398\pi\)
\(972\) −9.39873 −0.301464
\(973\) −10.7111 −0.343383
\(974\) 46.3208 1.48421
\(975\) 0 0
\(976\) 33.3783 1.06841
\(977\) 23.1596 0.740942 0.370471 0.928844i \(-0.379196\pi\)
0.370471 + 0.928844i \(0.379196\pi\)
\(978\) −10.4328 −0.333604
\(979\) 7.41493 0.236982
\(980\) 0 0
\(981\) −55.9998 −1.78794
\(982\) 10.6634 0.340282
\(983\) −11.7384 −0.374397 −0.187198 0.982322i \(-0.559941\pi\)
−0.187198 + 0.982322i \(0.559941\pi\)
\(984\) −23.2074 −0.739825
\(985\) 0 0
\(986\) −75.6334 −2.40866
\(987\) 36.2300 1.15321
\(988\) −0.567346 −0.0180497
\(989\) 0.274938 0.00874252
\(990\) 0 0
\(991\) −14.8198 −0.470766 −0.235383 0.971903i \(-0.575634\pi\)
−0.235383 + 0.971903i \(0.575634\pi\)
\(992\) −8.54718 −0.271373
\(993\) −61.1796 −1.94148
\(994\) 12.2939 0.389939
\(995\) 0 0
\(996\) −4.67368 −0.148091
\(997\) 8.94358 0.283246 0.141623 0.989921i \(-0.454768\pi\)
0.141623 + 0.989921i \(0.454768\pi\)
\(998\) 38.6651 1.22392
\(999\) 25.9375 0.820628
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.1.3 5
5.4 even 2 161.2.a.d.1.3 5
15.14 odd 2 1449.2.a.r.1.3 5
20.19 odd 2 2576.2.a.bd.1.1 5
35.34 odd 2 1127.2.a.h.1.3 5
115.114 odd 2 3703.2.a.j.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.2.a.d.1.3 5 5.4 even 2
1127.2.a.h.1.3 5 35.34 odd 2
1449.2.a.r.1.3 5 15.14 odd 2
2576.2.a.bd.1.1 5 20.19 odd 2
3703.2.a.j.1.3 5 115.114 odd 2
4025.2.a.p.1.3 5 1.1 even 1 trivial