Properties

Label 9025.2.a.bh.1.1
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.0649878242\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.2225.1
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.43828\) of defining polynomial
Character \(\chi\) \(=\) 9025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43828 q^{2} +2.94523 q^{3} +3.94523 q^{4} -7.18129 q^{6} +3.82025 q^{7} -4.74301 q^{8} +5.67435 q^{9} +O(q^{10})\) \(q-2.43828 q^{2} +2.94523 q^{3} +3.94523 q^{4} -7.18129 q^{6} +3.82025 q^{7} -4.74301 q^{8} +5.67435 q^{9} -2.12498 q^{11} +11.6196 q^{12} -3.65438 q^{13} -9.31485 q^{14} +3.67435 q^{16} +3.04243 q^{17} -13.8357 q^{18} +11.2515 q^{21} +5.18129 q^{22} +4.81167 q^{23} -13.9692 q^{24} +8.91042 q^{26} +7.87657 q^{27} +15.0717 q^{28} -6.03385 q^{29} -3.57184 q^{31} +0.526911 q^{32} -6.25853 q^{33} -7.41831 q^{34} +22.3866 q^{36} +3.93134 q^{37} -10.7630 q^{39} +7.60945 q^{41} -27.4343 q^{42} +5.60415 q^{43} -8.38351 q^{44} -11.7322 q^{46} +8.41831 q^{47} +10.8218 q^{48} +7.59430 q^{49} +8.96065 q^{51} -14.4174 q^{52} +4.80028 q^{53} -19.2053 q^{54} -18.1195 q^{56} +14.7122 q^{58} +5.13510 q^{59} -13.5100 q^{61} +8.70916 q^{62} +21.6774 q^{63} -8.63346 q^{64} +15.2601 q^{66} -5.38101 q^{67} +12.0031 q^{68} +14.1714 q^{69} +0.123434 q^{71} -26.9135 q^{72} +12.4860 q^{73} -9.58572 q^{74} -8.11794 q^{77} +26.2432 q^{78} +4.25699 q^{79} +6.17521 q^{81} -18.5540 q^{82} -4.39739 q^{83} +44.3897 q^{84} -13.6645 q^{86} -17.7711 q^{87} +10.0788 q^{88} +0.0772394 q^{89} -13.9607 q^{91} +18.9831 q^{92} -10.5199 q^{93} -20.5262 q^{94} +1.55187 q^{96} -18.0231 q^{97} -18.5171 q^{98} -12.0579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} + 3 q^{4} - 7 q^{6} + 11 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{3} + 3 q^{4} - 7 q^{6} + 11 q^{7} - 6 q^{8} + 5 q^{9} + 16 q^{12} + 2 q^{13} - 11 q^{14} - 3 q^{16} + 7 q^{17} - 17 q^{18} + 2 q^{21} - q^{22} + 11 q^{23} - 13 q^{24} + 9 q^{26} + 14 q^{27} + 13 q^{28} - 15 q^{29} - q^{31} - 3 q^{32} - 12 q^{33} - 22 q^{34} + 16 q^{36} + 11 q^{37} - 29 q^{39} + 22 q^{41} - 19 q^{42} + 26 q^{43} - 12 q^{44} + 10 q^{46} + 26 q^{47} + 13 q^{48} + 13 q^{49} - 11 q^{51} - 27 q^{52} + 16 q^{53} - 25 q^{54} - 8 q^{56} + 3 q^{58} - 10 q^{59} + 2 q^{61} + 31 q^{62} + 17 q^{63} + 4 q^{64} + 22 q^{66} - 3 q^{67} - 4 q^{68} + 14 q^{69} + 18 q^{71} - 29 q^{72} + 24 q^{73} - 17 q^{74} + 6 q^{77} + 15 q^{78} + 30 q^{79} - 4 q^{81} + 13 q^{82} + 12 q^{83} + 52 q^{84} - 16 q^{86} + q^{87} + 23 q^{88} + 9 q^{89} - 9 q^{91} + 25 q^{92} - 7 q^{93} - 11 q^{94} - 6 q^{96} - 19 q^{97} - 48 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43828 −1.72413 −0.862063 0.506801i \(-0.830828\pi\)
−0.862063 + 0.506801i \(0.830828\pi\)
\(3\) 2.94523 1.70043 0.850213 0.526438i \(-0.176473\pi\)
0.850213 + 0.526438i \(0.176473\pi\)
\(4\) 3.94523 1.97261
\(5\) 0 0
\(6\) −7.18129 −2.93175
\(7\) 3.82025 1.44392 0.721959 0.691936i \(-0.243242\pi\)
0.721959 + 0.691936i \(0.243242\pi\)
\(8\) −4.74301 −1.67691
\(9\) 5.67435 1.89145
\(10\) 0 0
\(11\) −2.12498 −0.640704 −0.320352 0.947299i \(-0.603801\pi\)
−0.320352 + 0.947299i \(0.603801\pi\)
\(12\) 11.6196 3.35428
\(13\) −3.65438 −1.01354 −0.506772 0.862080i \(-0.669161\pi\)
−0.506772 + 0.862080i \(0.669161\pi\)
\(14\) −9.31485 −2.48950
\(15\) 0 0
\(16\) 3.67435 0.918588
\(17\) 3.04243 0.737898 0.368949 0.929450i \(-0.379718\pi\)
0.368949 + 0.929450i \(0.379718\pi\)
\(18\) −13.8357 −3.26110
\(19\) 0 0
\(20\) 0 0
\(21\) 11.2515 2.45528
\(22\) 5.18129 1.10466
\(23\) 4.81167 1.00330 0.501651 0.865070i \(-0.332726\pi\)
0.501651 + 0.865070i \(0.332726\pi\)
\(24\) −13.9692 −2.85146
\(25\) 0 0
\(26\) 8.91042 1.74748
\(27\) 7.87657 1.51585
\(28\) 15.0717 2.84829
\(29\) −6.03385 −1.12046 −0.560229 0.828338i \(-0.689287\pi\)
−0.560229 + 0.828338i \(0.689287\pi\)
\(30\) 0 0
\(31\) −3.57184 −0.641521 −0.320761 0.947160i \(-0.603939\pi\)
−0.320761 + 0.947160i \(0.603939\pi\)
\(32\) 0.526911 0.0931455
\(33\) −6.25853 −1.08947
\(34\) −7.41831 −1.27223
\(35\) 0 0
\(36\) 22.3866 3.73110
\(37\) 3.93134 0.646309 0.323154 0.946346i \(-0.395257\pi\)
0.323154 + 0.946346i \(0.395257\pi\)
\(38\) 0 0
\(39\) −10.7630 −1.72346
\(40\) 0 0
\(41\) 7.60945 1.18840 0.594198 0.804318i \(-0.297469\pi\)
0.594198 + 0.804318i \(0.297469\pi\)
\(42\) −27.4343 −4.23321
\(43\) 5.60415 0.854625 0.427312 0.904104i \(-0.359460\pi\)
0.427312 + 0.904104i \(0.359460\pi\)
\(44\) −8.38351 −1.26386
\(45\) 0 0
\(46\) −11.7322 −1.72982
\(47\) 8.41831 1.22794 0.613969 0.789330i \(-0.289572\pi\)
0.613969 + 0.789330i \(0.289572\pi\)
\(48\) 10.8218 1.56199
\(49\) 7.59430 1.08490
\(50\) 0 0
\(51\) 8.96065 1.25474
\(52\) −14.4174 −1.99933
\(53\) 4.80028 0.659369 0.329685 0.944091i \(-0.393058\pi\)
0.329685 + 0.944091i \(0.393058\pi\)
\(54\) −19.2053 −2.61351
\(55\) 0 0
\(56\) −18.1195 −2.42132
\(57\) 0 0
\(58\) 14.7122 1.93181
\(59\) 5.13510 0.668533 0.334266 0.942479i \(-0.391511\pi\)
0.334266 + 0.942479i \(0.391511\pi\)
\(60\) 0 0
\(61\) −13.5100 −1.72978 −0.864891 0.501960i \(-0.832612\pi\)
−0.864891 + 0.501960i \(0.832612\pi\)
\(62\) 8.70916 1.10606
\(63\) 21.6774 2.73110
\(64\) −8.63346 −1.07918
\(65\) 0 0
\(66\) 15.2601 1.87839
\(67\) −5.38101 −0.657395 −0.328698 0.944435i \(-0.606610\pi\)
−0.328698 + 0.944435i \(0.606610\pi\)
\(68\) 12.0031 1.45559
\(69\) 14.1714 1.70604
\(70\) 0 0
\(71\) 0.123434 0.0146489 0.00732443 0.999973i \(-0.497669\pi\)
0.00732443 + 0.999973i \(0.497669\pi\)
\(72\) −26.9135 −3.17179
\(73\) 12.4860 1.46138 0.730689 0.682710i \(-0.239199\pi\)
0.730689 + 0.682710i \(0.239199\pi\)
\(74\) −9.58572 −1.11432
\(75\) 0 0
\(76\) 0 0
\(77\) −8.11794 −0.925125
\(78\) 26.2432 2.97146
\(79\) 4.25699 0.478949 0.239474 0.970903i \(-0.423025\pi\)
0.239474 + 0.970903i \(0.423025\pi\)
\(80\) 0 0
\(81\) 6.17521 0.686134
\(82\) −18.5540 −2.04895
\(83\) −4.39739 −0.482677 −0.241338 0.970441i \(-0.577586\pi\)
−0.241338 + 0.970441i \(0.577586\pi\)
\(84\) 44.3897 4.84331
\(85\) 0 0
\(86\) −13.6645 −1.47348
\(87\) −17.7711 −1.90526
\(88\) 10.0788 1.07440
\(89\) 0.0772394 0.00818736 0.00409368 0.999992i \(-0.498697\pi\)
0.00409368 + 0.999992i \(0.498697\pi\)
\(90\) 0 0
\(91\) −13.9607 −1.46347
\(92\) 18.9831 1.97913
\(93\) −10.5199 −1.09086
\(94\) −20.5262 −2.11712
\(95\) 0 0
\(96\) 1.55187 0.158387
\(97\) −18.0231 −1.82996 −0.914982 0.403495i \(-0.867795\pi\)
−0.914982 + 0.403495i \(0.867795\pi\)
\(98\) −18.5171 −1.87051
\(99\) −12.0579 −1.21186
\(100\) 0 0
\(101\) 18.6498 1.85573 0.927864 0.372918i \(-0.121643\pi\)
0.927864 + 0.372918i \(0.121643\pi\)
\(102\) −21.8486 −2.16333
\(103\) 0.377423 0.0371886 0.0185943 0.999827i \(-0.494081\pi\)
0.0185943 + 0.999827i \(0.494081\pi\)
\(104\) 17.3328 1.69962
\(105\) 0 0
\(106\) −11.7044 −1.13684
\(107\) 2.76144 0.266958 0.133479 0.991052i \(-0.457385\pi\)
0.133479 + 0.991052i \(0.457385\pi\)
\(108\) 31.0748 2.99018
\(109\) 3.00308 0.287643 0.143822 0.989604i \(-0.454061\pi\)
0.143822 + 0.989604i \(0.454061\pi\)
\(110\) 0 0
\(111\) 11.5787 1.09900
\(112\) 14.0369 1.32637
\(113\) 3.61708 0.340266 0.170133 0.985421i \(-0.445580\pi\)
0.170133 + 0.985421i \(0.445580\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −23.8049 −2.21023
\(117\) −20.7362 −1.91707
\(118\) −12.5208 −1.15264
\(119\) 11.6229 1.06547
\(120\) 0 0
\(121\) −6.48448 −0.589498
\(122\) 32.9413 2.98236
\(123\) 22.4116 2.02078
\(124\) −14.0917 −1.26547
\(125\) 0 0
\(126\) −52.8557 −4.70876
\(127\) 13.6188 1.20847 0.604236 0.796805i \(-0.293478\pi\)
0.604236 + 0.796805i \(0.293478\pi\)
\(128\) 19.9970 1.76750
\(129\) 16.5055 1.45323
\(130\) 0 0
\(131\) 5.67059 0.495442 0.247721 0.968831i \(-0.420318\pi\)
0.247721 + 0.968831i \(0.420318\pi\)
\(132\) −24.6913 −2.14910
\(133\) 0 0
\(134\) 13.1204 1.13343
\(135\) 0 0
\(136\) −14.4303 −1.23739
\(137\) 8.10501 0.692457 0.346229 0.938150i \(-0.387462\pi\)
0.346229 + 0.938150i \(0.387462\pi\)
\(138\) −34.5540 −2.94143
\(139\) −17.5325 −1.48709 −0.743543 0.668688i \(-0.766856\pi\)
−0.743543 + 0.668688i \(0.766856\pi\)
\(140\) 0 0
\(141\) 24.7938 2.08802
\(142\) −0.300966 −0.0252565
\(143\) 7.76547 0.649382
\(144\) 20.8496 1.73746
\(145\) 0 0
\(146\) −30.4445 −2.51960
\(147\) 22.3669 1.84479
\(148\) 15.5100 1.27492
\(149\) 19.1952 1.57253 0.786265 0.617889i \(-0.212012\pi\)
0.786265 + 0.617889i \(0.212012\pi\)
\(150\) 0 0
\(151\) 11.1473 0.907152 0.453576 0.891218i \(-0.350148\pi\)
0.453576 + 0.891218i \(0.350148\pi\)
\(152\) 0 0
\(153\) 17.2638 1.39570
\(154\) 19.7938 1.59503
\(155\) 0 0
\(156\) −42.4624 −3.39971
\(157\) −11.1452 −0.889486 −0.444743 0.895658i \(-0.646705\pi\)
−0.444743 + 0.895658i \(0.646705\pi\)
\(158\) −10.3797 −0.825768
\(159\) 14.1379 1.12121
\(160\) 0 0
\(161\) 18.3818 1.44869
\(162\) −15.0569 −1.18298
\(163\) 6.68669 0.523742 0.261871 0.965103i \(-0.415660\pi\)
0.261871 + 0.965103i \(0.415660\pi\)
\(164\) 30.0210 2.34425
\(165\) 0 0
\(166\) 10.7221 0.832195
\(167\) −18.6569 −1.44371 −0.721856 0.692043i \(-0.756711\pi\)
−0.721856 + 0.692043i \(0.756711\pi\)
\(168\) −53.3659 −4.11727
\(169\) 0.354510 0.0272700
\(170\) 0 0
\(171\) 0 0
\(172\) 22.1096 1.68584
\(173\) 14.7385 1.12054 0.560272 0.828308i \(-0.310696\pi\)
0.560272 + 0.828308i \(0.310696\pi\)
\(174\) 43.3309 3.28490
\(175\) 0 0
\(176\) −7.80791 −0.588543
\(177\) 15.1240 1.13679
\(178\) −0.188331 −0.0141160
\(179\) −12.1961 −0.911582 −0.455791 0.890087i \(-0.650643\pi\)
−0.455791 + 0.890087i \(0.650643\pi\)
\(180\) 0 0
\(181\) −13.1841 −0.979966 −0.489983 0.871732i \(-0.662997\pi\)
−0.489983 + 0.871732i \(0.662997\pi\)
\(182\) 34.0400 2.52321
\(183\) −39.7901 −2.94137
\(184\) −22.8218 −1.68244
\(185\) 0 0
\(186\) 25.6504 1.88078
\(187\) −6.46510 −0.472775
\(188\) 33.2121 2.42224
\(189\) 30.0904 2.18876
\(190\) 0 0
\(191\) 4.61708 0.334080 0.167040 0.985950i \(-0.446579\pi\)
0.167040 + 0.985950i \(0.446579\pi\)
\(192\) −25.4275 −1.83507
\(193\) 5.22468 0.376081 0.188040 0.982161i \(-0.439786\pi\)
0.188040 + 0.982161i \(0.439786\pi\)
\(194\) 43.9453 3.15509
\(195\) 0 0
\(196\) 29.9612 2.14009
\(197\) −21.1783 −1.50889 −0.754445 0.656363i \(-0.772094\pi\)
−0.754445 + 0.656363i \(0.772094\pi\)
\(198\) 29.4005 2.08940
\(199\) 15.3752 1.08992 0.544960 0.838462i \(-0.316545\pi\)
0.544960 + 0.838462i \(0.316545\pi\)
\(200\) 0 0
\(201\) −15.8483 −1.11785
\(202\) −45.4736 −3.19951
\(203\) −23.0508 −1.61785
\(204\) 35.3518 2.47512
\(205\) 0 0
\(206\) −0.920265 −0.0641179
\(207\) 27.3031 1.89770
\(208\) −13.4275 −0.931029
\(209\) 0 0
\(210\) 0 0
\(211\) 20.8659 1.43647 0.718235 0.695800i \(-0.244950\pi\)
0.718235 + 0.695800i \(0.244950\pi\)
\(212\) 18.9382 1.30068
\(213\) 0.363540 0.0249093
\(214\) −6.73316 −0.460270
\(215\) 0 0
\(216\) −37.3586 −2.54193
\(217\) −13.6453 −0.926305
\(218\) −7.32237 −0.495934
\(219\) 36.7741 2.48497
\(220\) 0 0
\(221\) −11.1182 −0.747892
\(222\) −28.2321 −1.89482
\(223\) −13.6759 −0.915806 −0.457903 0.889002i \(-0.651399\pi\)
−0.457903 + 0.889002i \(0.651399\pi\)
\(224\) 2.01293 0.134495
\(225\) 0 0
\(226\) −8.81947 −0.586662
\(227\) −3.71196 −0.246372 −0.123186 0.992384i \(-0.539311\pi\)
−0.123186 + 0.992384i \(0.539311\pi\)
\(228\) 0 0
\(229\) 11.3086 0.747293 0.373646 0.927571i \(-0.378107\pi\)
0.373646 + 0.927571i \(0.378107\pi\)
\(230\) 0 0
\(231\) −23.9092 −1.57311
\(232\) 28.6186 1.87890
\(233\) 10.6753 0.699362 0.349681 0.936869i \(-0.386290\pi\)
0.349681 + 0.936869i \(0.386290\pi\)
\(234\) 50.5608 3.30527
\(235\) 0 0
\(236\) 20.2591 1.31876
\(237\) 12.5378 0.814417
\(238\) −28.3398 −1.83700
\(239\) −17.2813 −1.11783 −0.558916 0.829224i \(-0.688783\pi\)
−0.558916 + 0.829224i \(0.688783\pi\)
\(240\) 0 0
\(241\) 17.4986 1.12719 0.563593 0.826052i \(-0.309419\pi\)
0.563593 + 0.826052i \(0.309419\pi\)
\(242\) 15.8110 1.01637
\(243\) −5.44232 −0.349125
\(244\) −53.3001 −3.41219
\(245\) 0 0
\(246\) −54.6457 −3.48408
\(247\) 0 0
\(248\) 16.9413 1.07577
\(249\) −12.9513 −0.820756
\(250\) 0 0
\(251\) 17.9012 1.12991 0.564956 0.825121i \(-0.308893\pi\)
0.564956 + 0.825121i \(0.308893\pi\)
\(252\) 85.5224 5.38740
\(253\) −10.2247 −0.642820
\(254\) −33.2065 −2.08356
\(255\) 0 0
\(256\) −31.4914 −1.96821
\(257\) 26.7208 1.66680 0.833400 0.552671i \(-0.186391\pi\)
0.833400 + 0.552671i \(0.186391\pi\)
\(258\) −40.2450 −2.50555
\(259\) 15.0187 0.933217
\(260\) 0 0
\(261\) −34.2382 −2.11929
\(262\) −13.8265 −0.854204
\(263\) 19.7817 1.21979 0.609895 0.792482i \(-0.291211\pi\)
0.609895 + 0.792482i \(0.291211\pi\)
\(264\) 29.6843 1.82694
\(265\) 0 0
\(266\) 0 0
\(267\) 0.227487 0.0139220
\(268\) −21.2293 −1.29679
\(269\) 7.04833 0.429744 0.214872 0.976642i \(-0.431067\pi\)
0.214872 + 0.976642i \(0.431067\pi\)
\(270\) 0 0
\(271\) 26.1672 1.58955 0.794773 0.606907i \(-0.207590\pi\)
0.794773 + 0.606907i \(0.207590\pi\)
\(272\) 11.1790 0.677825
\(273\) −41.1173 −2.48853
\(274\) −19.7623 −1.19388
\(275\) 0 0
\(276\) 55.9096 3.36536
\(277\) −2.86953 −0.172413 −0.0862066 0.996277i \(-0.527475\pi\)
−0.0862066 + 0.996277i \(0.527475\pi\)
\(278\) 42.7492 2.56393
\(279\) −20.2679 −1.21341
\(280\) 0 0
\(281\) −22.4401 −1.33866 −0.669332 0.742963i \(-0.733420\pi\)
−0.669332 + 0.742963i \(0.733420\pi\)
\(282\) −60.4544 −3.60001
\(283\) 4.68139 0.278280 0.139140 0.990273i \(-0.455566\pi\)
0.139140 + 0.990273i \(0.455566\pi\)
\(284\) 0.486973 0.0288965
\(285\) 0 0
\(286\) −18.9344 −1.11962
\(287\) 29.0700 1.71595
\(288\) 2.98988 0.176180
\(289\) −7.74360 −0.455506
\(290\) 0 0
\(291\) −53.0820 −3.11172
\(292\) 49.2602 2.88273
\(293\) −3.26229 −0.190585 −0.0952926 0.995449i \(-0.530379\pi\)
−0.0952926 + 0.995449i \(0.530379\pi\)
\(294\) −54.5369 −3.18066
\(295\) 0 0
\(296\) −18.6464 −1.08380
\(297\) −16.7375 −0.971209
\(298\) −46.8033 −2.71124
\(299\) −17.5837 −1.01689
\(300\) 0 0
\(301\) 21.4093 1.23401
\(302\) −27.1802 −1.56404
\(303\) 54.9280 3.15553
\(304\) 0 0
\(305\) 0 0
\(306\) −42.0941 −2.40636
\(307\) 1.71746 0.0980207 0.0490103 0.998798i \(-0.484393\pi\)
0.0490103 + 0.998798i \(0.484393\pi\)
\(308\) −32.0271 −1.82491
\(309\) 1.11160 0.0632365
\(310\) 0 0
\(311\) −0.892946 −0.0506343 −0.0253172 0.999679i \(-0.508060\pi\)
−0.0253172 + 0.999679i \(0.508060\pi\)
\(312\) 51.0489 2.89008
\(313\) −11.5358 −0.652040 −0.326020 0.945363i \(-0.605708\pi\)
−0.326020 + 0.945363i \(0.605708\pi\)
\(314\) 27.1752 1.53359
\(315\) 0 0
\(316\) 16.7948 0.944780
\(317\) −18.8246 −1.05729 −0.528647 0.848842i \(-0.677301\pi\)
−0.528647 + 0.848842i \(0.677301\pi\)
\(318\) −34.4722 −1.93311
\(319\) 12.8218 0.717883
\(320\) 0 0
\(321\) 8.13305 0.453943
\(322\) −44.8200 −2.49772
\(323\) 0 0
\(324\) 24.3626 1.35348
\(325\) 0 0
\(326\) −16.3041 −0.902998
\(327\) 8.84476 0.489116
\(328\) −36.0917 −1.99283
\(329\) 32.1601 1.77304
\(330\) 0 0
\(331\) −15.5779 −0.856240 −0.428120 0.903722i \(-0.640824\pi\)
−0.428120 + 0.903722i \(0.640824\pi\)
\(332\) −17.3487 −0.952134
\(333\) 22.3078 1.22246
\(334\) 45.4908 2.48914
\(335\) 0 0
\(336\) 41.3419 2.25539
\(337\) 6.43425 0.350496 0.175248 0.984524i \(-0.443927\pi\)
0.175248 + 0.984524i \(0.443927\pi\)
\(338\) −0.864396 −0.0470170
\(339\) 10.6531 0.578598
\(340\) 0 0
\(341\) 7.59007 0.411026
\(342\) 0 0
\(343\) 2.27039 0.122590
\(344\) −26.5805 −1.43313
\(345\) 0 0
\(346\) −35.9366 −1.93196
\(347\) 19.3367 1.03805 0.519023 0.854760i \(-0.326296\pi\)
0.519023 + 0.854760i \(0.326296\pi\)
\(348\) −70.1108 −3.75833
\(349\) 7.78870 0.416920 0.208460 0.978031i \(-0.433155\pi\)
0.208460 + 0.978031i \(0.433155\pi\)
\(350\) 0 0
\(351\) −28.7840 −1.53638
\(352\) −1.11967 −0.0596788
\(353\) 24.7007 1.31468 0.657342 0.753593i \(-0.271681\pi\)
0.657342 + 0.753593i \(0.271681\pi\)
\(354\) −36.8767 −1.95997
\(355\) 0 0
\(356\) 0.304727 0.0161505
\(357\) 34.2319 1.81175
\(358\) 29.7376 1.57168
\(359\) 24.8224 1.31008 0.655038 0.755596i \(-0.272653\pi\)
0.655038 + 0.755596i \(0.272653\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 32.1466 1.68959
\(363\) −19.0982 −1.00240
\(364\) −55.0779 −2.88687
\(365\) 0 0
\(366\) 97.0195 5.07129
\(367\) 7.01716 0.366293 0.183146 0.983086i \(-0.441372\pi\)
0.183146 + 0.983086i \(0.441372\pi\)
\(368\) 17.6798 0.921621
\(369\) 43.1787 2.24779
\(370\) 0 0
\(371\) 18.3383 0.952075
\(372\) −41.5033 −2.15184
\(373\) 36.2105 1.87491 0.937455 0.348107i \(-0.113175\pi\)
0.937455 + 0.348107i \(0.113175\pi\)
\(374\) 15.7637 0.815124
\(375\) 0 0
\(376\) −39.9281 −2.05914
\(377\) 22.0500 1.13563
\(378\) −73.3690 −3.77370
\(379\) −28.2455 −1.45087 −0.725437 0.688288i \(-0.758362\pi\)
−0.725437 + 0.688288i \(0.758362\pi\)
\(380\) 0 0
\(381\) 40.1104 2.05492
\(382\) −11.2578 −0.575997
\(383\) −26.4312 −1.35057 −0.675287 0.737555i \(-0.735980\pi\)
−0.675287 + 0.737555i \(0.735980\pi\)
\(384\) 58.8957 3.00551
\(385\) 0 0
\(386\) −12.7392 −0.648411
\(387\) 31.7999 1.61648
\(388\) −71.1050 −3.60981
\(389\) −5.61736 −0.284811 −0.142406 0.989808i \(-0.545484\pi\)
−0.142406 + 0.989808i \(0.545484\pi\)
\(390\) 0 0
\(391\) 14.6392 0.740335
\(392\) −36.0199 −1.81928
\(393\) 16.7012 0.842462
\(394\) 51.6387 2.60152
\(395\) 0 0
\(396\) −47.5710 −2.39053
\(397\) 29.0391 1.45743 0.728715 0.684818i \(-0.240118\pi\)
0.728715 + 0.684818i \(0.240118\pi\)
\(398\) −37.4891 −1.87916
\(399\) 0 0
\(400\) 0 0
\(401\) 25.4613 1.27148 0.635739 0.771904i \(-0.280695\pi\)
0.635739 + 0.771904i \(0.280695\pi\)
\(402\) 38.6426 1.92732
\(403\) 13.0529 0.650210
\(404\) 73.5778 3.66063
\(405\) 0 0
\(406\) 56.2044 2.78938
\(407\) −8.35401 −0.414093
\(408\) −42.5005 −2.10409
\(409\) −19.8024 −0.979166 −0.489583 0.871957i \(-0.662851\pi\)
−0.489583 + 0.871957i \(0.662851\pi\)
\(410\) 0 0
\(411\) 23.8711 1.17747
\(412\) 1.48902 0.0733588
\(413\) 19.6174 0.965307
\(414\) −66.5727 −3.27187
\(415\) 0 0
\(416\) −1.92553 −0.0944070
\(417\) −51.6371 −2.52868
\(418\) 0 0
\(419\) 0.172123 0.00840877 0.00420439 0.999991i \(-0.498662\pi\)
0.00420439 + 0.999991i \(0.498662\pi\)
\(420\) 0 0
\(421\) 17.4056 0.848297 0.424149 0.905593i \(-0.360573\pi\)
0.424149 + 0.905593i \(0.360573\pi\)
\(422\) −50.8771 −2.47666
\(423\) 47.7685 2.32258
\(424\) −22.7678 −1.10570
\(425\) 0 0
\(426\) −0.886412 −0.0429468
\(427\) −51.6117 −2.49766
\(428\) 10.8945 0.526605
\(429\) 22.8711 1.10423
\(430\) 0 0
\(431\) −5.06518 −0.243981 −0.121990 0.992531i \(-0.538928\pi\)
−0.121990 + 0.992531i \(0.538928\pi\)
\(432\) 28.9413 1.39244
\(433\) −12.5169 −0.601524 −0.300762 0.953699i \(-0.597241\pi\)
−0.300762 + 0.953699i \(0.597241\pi\)
\(434\) 33.2712 1.59707
\(435\) 0 0
\(436\) 11.8478 0.567409
\(437\) 0 0
\(438\) −89.6658 −4.28440
\(439\) −14.7581 −0.704367 −0.352183 0.935931i \(-0.614561\pi\)
−0.352183 + 0.935931i \(0.614561\pi\)
\(440\) 0 0
\(441\) 43.0928 2.05204
\(442\) 27.1094 1.28946
\(443\) −5.35950 −0.254638 −0.127319 0.991862i \(-0.540637\pi\)
−0.127319 + 0.991862i \(0.540637\pi\)
\(444\) 45.6805 2.16790
\(445\) 0 0
\(446\) 33.3457 1.57896
\(447\) 56.5341 2.67397
\(448\) −32.9820 −1.55825
\(449\) −7.16065 −0.337932 −0.168966 0.985622i \(-0.554043\pi\)
−0.168966 + 0.985622i \(0.554043\pi\)
\(450\) 0 0
\(451\) −16.1699 −0.761411
\(452\) 14.2702 0.671214
\(453\) 32.8312 1.54255
\(454\) 9.05082 0.424776
\(455\) 0 0
\(456\) 0 0
\(457\) −32.3884 −1.51507 −0.757534 0.652796i \(-0.773596\pi\)
−0.757534 + 0.652796i \(0.773596\pi\)
\(458\) −27.5736 −1.28843
\(459\) 23.9639 1.11854
\(460\) 0 0
\(461\) −25.2124 −1.17426 −0.587130 0.809493i \(-0.699742\pi\)
−0.587130 + 0.809493i \(0.699742\pi\)
\(462\) 58.2973 2.71224
\(463\) 40.8494 1.89843 0.949216 0.314627i \(-0.101879\pi\)
0.949216 + 0.314627i \(0.101879\pi\)
\(464\) −22.1705 −1.02924
\(465\) 0 0
\(466\) −26.0294 −1.20579
\(467\) −14.6209 −0.676577 −0.338288 0.941042i \(-0.609848\pi\)
−0.338288 + 0.941042i \(0.609848\pi\)
\(468\) −81.8092 −3.78163
\(469\) −20.5568 −0.949225
\(470\) 0 0
\(471\) −32.8252 −1.51250
\(472\) −24.3558 −1.12107
\(473\) −11.9087 −0.547562
\(474\) −30.5707 −1.40416
\(475\) 0 0
\(476\) 45.8548 2.10175
\(477\) 27.2385 1.24716
\(478\) 42.1366 1.92729
\(479\) 1.06944 0.0488640 0.0244320 0.999701i \(-0.492222\pi\)
0.0244320 + 0.999701i \(0.492222\pi\)
\(480\) 0 0
\(481\) −14.3666 −0.655062
\(482\) −42.6666 −1.94341
\(483\) 54.1385 2.46339
\(484\) −25.5827 −1.16285
\(485\) 0 0
\(486\) 13.2699 0.601936
\(487\) 6.25304 0.283352 0.141676 0.989913i \(-0.454751\pi\)
0.141676 + 0.989913i \(0.454751\pi\)
\(488\) 64.0782 2.90068
\(489\) 19.6938 0.890585
\(490\) 0 0
\(491\) −0.813681 −0.0367209 −0.0183605 0.999831i \(-0.505845\pi\)
−0.0183605 + 0.999831i \(0.505845\pi\)
\(492\) 88.4186 3.98622
\(493\) −18.3576 −0.826784
\(494\) 0 0
\(495\) 0 0
\(496\) −13.1242 −0.589294
\(497\) 0.471547 0.0211518
\(498\) 31.5790 1.41509
\(499\) 1.57636 0.0705676 0.0352838 0.999377i \(-0.488766\pi\)
0.0352838 + 0.999377i \(0.488766\pi\)
\(500\) 0 0
\(501\) −54.9487 −2.45493
\(502\) −43.6481 −1.94811
\(503\) −3.00182 −0.133845 −0.0669223 0.997758i \(-0.521318\pi\)
−0.0669223 + 0.997758i \(0.521318\pi\)
\(504\) −102.816 −4.57980
\(505\) 0 0
\(506\) 24.9307 1.10830
\(507\) 1.04411 0.0463707
\(508\) 53.7292 2.38385
\(509\) −32.7217 −1.45036 −0.725182 0.688557i \(-0.758245\pi\)
−0.725182 + 0.688557i \(0.758245\pi\)
\(510\) 0 0
\(511\) 47.6997 2.11011
\(512\) 36.7910 1.62595
\(513\) 0 0
\(514\) −65.1529 −2.87377
\(515\) 0 0
\(516\) 65.1179 2.86665
\(517\) −17.8887 −0.786745
\(518\) −36.6199 −1.60898
\(519\) 43.4081 1.90540
\(520\) 0 0
\(521\) −16.4073 −0.718819 −0.359409 0.933180i \(-0.617022\pi\)
−0.359409 + 0.933180i \(0.617022\pi\)
\(522\) 83.4824 3.65393
\(523\) 20.4437 0.893940 0.446970 0.894549i \(-0.352503\pi\)
0.446970 + 0.894549i \(0.352503\pi\)
\(524\) 22.3718 0.977315
\(525\) 0 0
\(526\) −48.2333 −2.10307
\(527\) −10.8671 −0.473378
\(528\) −22.9960 −1.00077
\(529\) 0.152154 0.00661541
\(530\) 0 0
\(531\) 29.1384 1.26450
\(532\) 0 0
\(533\) −27.8079 −1.20449
\(534\) −0.554678 −0.0240033
\(535\) 0 0
\(536\) 25.5222 1.10239
\(537\) −35.9203 −1.55008
\(538\) −17.1858 −0.740933
\(539\) −16.1377 −0.695101
\(540\) 0 0
\(541\) −28.8016 −1.23828 −0.619139 0.785281i \(-0.712518\pi\)
−0.619139 + 0.785281i \(0.712518\pi\)
\(542\) −63.8031 −2.74058
\(543\) −38.8301 −1.66636
\(544\) 1.60309 0.0687320
\(545\) 0 0
\(546\) 100.256 4.29054
\(547\) −26.9553 −1.15253 −0.576264 0.817264i \(-0.695490\pi\)
−0.576264 + 0.817264i \(0.695490\pi\)
\(548\) 31.9761 1.36595
\(549\) −76.6606 −3.27180
\(550\) 0 0
\(551\) 0 0
\(552\) −67.2153 −2.86087
\(553\) 16.2628 0.691563
\(554\) 6.99672 0.297262
\(555\) 0 0
\(556\) −69.1696 −2.93345
\(557\) −7.95439 −0.337039 −0.168519 0.985698i \(-0.553899\pi\)
−0.168519 + 0.985698i \(0.553899\pi\)
\(558\) 49.4188 2.09207
\(559\) −20.4797 −0.866199
\(560\) 0 0
\(561\) −19.0412 −0.803919
\(562\) 54.7153 2.30803
\(563\) 34.0931 1.43685 0.718426 0.695603i \(-0.244863\pi\)
0.718426 + 0.695603i \(0.244863\pi\)
\(564\) 97.8172 4.11885
\(565\) 0 0
\(566\) −11.4146 −0.479789
\(567\) 23.5908 0.990722
\(568\) −0.585446 −0.0245648
\(569\) 25.7236 1.07839 0.539195 0.842181i \(-0.318729\pi\)
0.539195 + 0.842181i \(0.318729\pi\)
\(570\) 0 0
\(571\) −31.6325 −1.32378 −0.661890 0.749601i \(-0.730245\pi\)
−0.661890 + 0.749601i \(0.730245\pi\)
\(572\) 30.6365 1.28098
\(573\) 13.5983 0.568079
\(574\) −70.8809 −2.95851
\(575\) 0 0
\(576\) −48.9893 −2.04122
\(577\) −26.8689 −1.11856 −0.559282 0.828977i \(-0.688923\pi\)
−0.559282 + 0.828977i \(0.688923\pi\)
\(578\) 18.8811 0.785350
\(579\) 15.3879 0.639498
\(580\) 0 0
\(581\) −16.7991 −0.696946
\(582\) 129.429 5.36500
\(583\) −10.2005 −0.422461
\(584\) −59.2213 −2.45060
\(585\) 0 0
\(586\) 7.95439 0.328593
\(587\) −42.5145 −1.75476 −0.877380 0.479796i \(-0.840711\pi\)
−0.877380 + 0.479796i \(0.840711\pi\)
\(588\) 88.2426 3.63906
\(589\) 0 0
\(590\) 0 0
\(591\) −62.3748 −2.56576
\(592\) 14.4451 0.593691
\(593\) 23.2139 0.953280 0.476640 0.879099i \(-0.341855\pi\)
0.476640 + 0.879099i \(0.341855\pi\)
\(594\) 40.8108 1.67449
\(595\) 0 0
\(596\) 75.7293 3.10199
\(597\) 45.2834 1.85333
\(598\) 42.8740 1.75325
\(599\) −0.313115 −0.0127935 −0.00639676 0.999980i \(-0.502036\pi\)
−0.00639676 + 0.999980i \(0.502036\pi\)
\(600\) 0 0
\(601\) −20.9580 −0.854893 −0.427447 0.904041i \(-0.640587\pi\)
−0.427447 + 0.904041i \(0.640587\pi\)
\(602\) −52.2018 −2.12759
\(603\) −30.5338 −1.24343
\(604\) 43.9785 1.78946
\(605\) 0 0
\(606\) −133.930 −5.44053
\(607\) 10.1085 0.410290 0.205145 0.978732i \(-0.434233\pi\)
0.205145 + 0.978732i \(0.434233\pi\)
\(608\) 0 0
\(609\) −67.8899 −2.75104
\(610\) 0 0
\(611\) −30.7637 −1.24457
\(612\) 68.1097 2.75317
\(613\) 36.3560 1.46840 0.734202 0.678931i \(-0.237556\pi\)
0.734202 + 0.678931i \(0.237556\pi\)
\(614\) −4.18766 −0.169000
\(615\) 0 0
\(616\) 38.5035 1.55135
\(617\) −35.3399 −1.42273 −0.711365 0.702822i \(-0.751923\pi\)
−0.711365 + 0.702822i \(0.751923\pi\)
\(618\) −2.71039 −0.109028
\(619\) −32.5878 −1.30982 −0.654908 0.755709i \(-0.727292\pi\)
−0.654908 + 0.755709i \(0.727292\pi\)
\(620\) 0 0
\(621\) 37.8994 1.52085
\(622\) 2.17726 0.0873000
\(623\) 0.295074 0.0118219
\(624\) −39.5470 −1.58315
\(625\) 0 0
\(626\) 28.1275 1.12420
\(627\) 0 0
\(628\) −43.9704 −1.75461
\(629\) 11.9608 0.476910
\(630\) 0 0
\(631\) 1.66950 0.0664616 0.0332308 0.999448i \(-0.489420\pi\)
0.0332308 + 0.999448i \(0.489420\pi\)
\(632\) −20.1909 −0.803153
\(633\) 61.4549 2.44261
\(634\) 45.8997 1.82291
\(635\) 0 0
\(636\) 55.7772 2.21171
\(637\) −27.7525 −1.09959
\(638\) −31.2632 −1.23772
\(639\) 0.700405 0.0277076
\(640\) 0 0
\(641\) 21.3997 0.845238 0.422619 0.906307i \(-0.361111\pi\)
0.422619 + 0.906307i \(0.361111\pi\)
\(642\) −19.8307 −0.782655
\(643\) 8.43473 0.332633 0.166317 0.986072i \(-0.446813\pi\)
0.166317 + 0.986072i \(0.446813\pi\)
\(644\) 72.5202 2.85770
\(645\) 0 0
\(646\) 0 0
\(647\) 29.2025 1.14807 0.574034 0.818831i \(-0.305378\pi\)
0.574034 + 0.818831i \(0.305378\pi\)
\(648\) −29.2891 −1.15058
\(649\) −10.9120 −0.428332
\(650\) 0 0
\(651\) −40.1885 −1.57511
\(652\) 26.3805 1.03314
\(653\) 7.61427 0.297970 0.148985 0.988839i \(-0.452399\pi\)
0.148985 + 0.988839i \(0.452399\pi\)
\(654\) −21.5660 −0.843299
\(655\) 0 0
\(656\) 27.9598 1.09165
\(657\) 70.8501 2.76412
\(658\) −78.4153 −3.05695
\(659\) −18.2941 −0.712637 −0.356318 0.934365i \(-0.615968\pi\)
−0.356318 + 0.934365i \(0.615968\pi\)
\(660\) 0 0
\(661\) −20.3586 −0.791859 −0.395930 0.918281i \(-0.629578\pi\)
−0.395930 + 0.918281i \(0.629578\pi\)
\(662\) 37.9834 1.47627
\(663\) −32.7456 −1.27174
\(664\) 20.8569 0.809404
\(665\) 0 0
\(666\) −54.3928 −2.10768
\(667\) −29.0329 −1.12416
\(668\) −73.6056 −2.84789
\(669\) −40.2786 −1.55726
\(670\) 0 0
\(671\) 28.7085 1.10828
\(672\) 5.92853 0.228698
\(673\) −29.6829 −1.14419 −0.572096 0.820186i \(-0.693870\pi\)
−0.572096 + 0.820186i \(0.693870\pi\)
\(674\) −15.6885 −0.604299
\(675\) 0 0
\(676\) 1.39862 0.0537932
\(677\) −9.17128 −0.352481 −0.176240 0.984347i \(-0.556394\pi\)
−0.176240 + 0.984347i \(0.556394\pi\)
\(678\) −25.9753 −0.997576
\(679\) −68.8526 −2.64232
\(680\) 0 0
\(681\) −10.9326 −0.418937
\(682\) −18.5067 −0.708660
\(683\) 15.6556 0.599043 0.299522 0.954089i \(-0.403173\pi\)
0.299522 + 0.954089i \(0.403173\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −5.53586 −0.211360
\(687\) 33.3064 1.27072
\(688\) 20.5916 0.785048
\(689\) −17.5421 −0.668299
\(690\) 0 0
\(691\) −13.7912 −0.524643 −0.262321 0.964981i \(-0.584488\pi\)
−0.262321 + 0.964981i \(0.584488\pi\)
\(692\) 58.1466 2.21040
\(693\) −46.0640 −1.74983
\(694\) −47.1483 −1.78972
\(695\) 0 0
\(696\) 84.2883 3.19494
\(697\) 23.1513 0.876916
\(698\) −18.9911 −0.718822
\(699\) 31.4412 1.18921
\(700\) 0 0
\(701\) −13.7313 −0.518622 −0.259311 0.965794i \(-0.583496\pi\)
−0.259311 + 0.965794i \(0.583496\pi\)
\(702\) 70.1835 2.64891
\(703\) 0 0
\(704\) 18.3459 0.691437
\(705\) 0 0
\(706\) −60.2272 −2.26668
\(707\) 71.2470 2.67952
\(708\) 59.6677 2.24245
\(709\) −12.3146 −0.462483 −0.231242 0.972896i \(-0.574279\pi\)
−0.231242 + 0.972896i \(0.574279\pi\)
\(710\) 0 0
\(711\) 24.1557 0.905908
\(712\) −0.366347 −0.0137294
\(713\) −17.1865 −0.643640
\(714\) −83.4671 −3.12368
\(715\) 0 0
\(716\) −48.1165 −1.79820
\(717\) −50.8972 −1.90079
\(718\) −60.5240 −2.25874
\(719\) −6.92307 −0.258187 −0.129094 0.991632i \(-0.541207\pi\)
−0.129094 + 0.991632i \(0.541207\pi\)
\(720\) 0 0
\(721\) 1.44185 0.0536973
\(722\) 0 0
\(723\) 51.5374 1.91670
\(724\) −52.0142 −1.93309
\(725\) 0 0
\(726\) 46.5669 1.72826
\(727\) −34.2263 −1.26938 −0.634692 0.772765i \(-0.718873\pi\)
−0.634692 + 0.772765i \(0.718873\pi\)
\(728\) 66.2155 2.45411
\(729\) −34.5545 −1.27980
\(730\) 0 0
\(731\) 17.0503 0.630626
\(732\) −156.981 −5.80218
\(733\) −37.5214 −1.38589 −0.692943 0.720993i \(-0.743686\pi\)
−0.692943 + 0.720993i \(0.743686\pi\)
\(734\) −17.1098 −0.631535
\(735\) 0 0
\(736\) 2.53532 0.0934531
\(737\) 11.4345 0.421196
\(738\) −105.282 −3.87548
\(739\) −38.6683 −1.42244 −0.711218 0.702972i \(-0.751856\pi\)
−0.711218 + 0.702972i \(0.751856\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −44.7139 −1.64150
\(743\) −34.5415 −1.26720 −0.633602 0.773659i \(-0.718424\pi\)
−0.633602 + 0.773659i \(0.718424\pi\)
\(744\) 49.8959 1.82927
\(745\) 0 0
\(746\) −88.2915 −3.23258
\(747\) −24.9523 −0.912959
\(748\) −25.5063 −0.932601
\(749\) 10.5494 0.385466
\(750\) 0 0
\(751\) 33.3178 1.21578 0.607892 0.794020i \(-0.292015\pi\)
0.607892 + 0.794020i \(0.292015\pi\)
\(752\) 30.9318 1.12797
\(753\) 52.7230 1.92133
\(754\) −53.7642 −1.95798
\(755\) 0 0
\(756\) 118.714 4.31757
\(757\) −27.2310 −0.989728 −0.494864 0.868970i \(-0.664782\pi\)
−0.494864 + 0.868970i \(0.664782\pi\)
\(758\) 68.8706 2.50149
\(759\) −30.1140 −1.09307
\(760\) 0 0
\(761\) 20.1113 0.729033 0.364516 0.931197i \(-0.381234\pi\)
0.364516 + 0.931197i \(0.381234\pi\)
\(762\) −97.8006 −3.54294
\(763\) 11.4725 0.415334
\(764\) 18.2154 0.659011
\(765\) 0 0
\(766\) 64.4469 2.32856
\(767\) −18.7656 −0.677587
\(768\) −92.7493 −3.34680
\(769\) −3.25931 −0.117534 −0.0587669 0.998272i \(-0.518717\pi\)
−0.0587669 + 0.998272i \(0.518717\pi\)
\(770\) 0 0
\(771\) 78.6988 2.83427
\(772\) 20.6125 0.741861
\(773\) 49.6874 1.78713 0.893565 0.448933i \(-0.148196\pi\)
0.893565 + 0.448933i \(0.148196\pi\)
\(774\) −77.5372 −2.78702
\(775\) 0 0
\(776\) 85.4835 3.06868
\(777\) 44.2335 1.58687
\(778\) 13.6967 0.491051
\(779\) 0 0
\(780\) 0 0
\(781\) −0.262293 −0.00938559
\(782\) −35.6945 −1.27643
\(783\) −47.5260 −1.69844
\(784\) 27.9041 0.996576
\(785\) 0 0
\(786\) −40.7222 −1.45251
\(787\) 27.1159 0.966578 0.483289 0.875461i \(-0.339442\pi\)
0.483289 + 0.875461i \(0.339442\pi\)
\(788\) −83.5531 −2.97646
\(789\) 58.2615 2.07416
\(790\) 0 0
\(791\) 13.8181 0.491317
\(792\) 57.1905 2.03218
\(793\) 49.3708 1.75321
\(794\) −70.8055 −2.51279
\(795\) 0 0
\(796\) 60.6586 2.14999
\(797\) 27.3573 0.969044 0.484522 0.874779i \(-0.338994\pi\)
0.484522 + 0.874779i \(0.338994\pi\)
\(798\) 0 0
\(799\) 25.6122 0.906093
\(800\) 0 0
\(801\) 0.438283 0.0154860
\(802\) −62.0820 −2.19219
\(803\) −26.5325 −0.936311
\(804\) −62.5251 −2.20509
\(805\) 0 0
\(806\) −31.8266 −1.12104
\(807\) 20.7589 0.730748
\(808\) −88.4564 −3.11188
\(809\) −12.3922 −0.435686 −0.217843 0.975984i \(-0.569902\pi\)
−0.217843 + 0.975984i \(0.569902\pi\)
\(810\) 0 0
\(811\) 14.5389 0.510528 0.255264 0.966871i \(-0.417838\pi\)
0.255264 + 0.966871i \(0.417838\pi\)
\(812\) −90.9407 −3.19139
\(813\) 77.0683 2.70290
\(814\) 20.3694 0.713948
\(815\) 0 0
\(816\) 32.9246 1.15259
\(817\) 0 0
\(818\) 48.2839 1.68821
\(819\) −79.2176 −2.76809
\(820\) 0 0
\(821\) 6.47357 0.225929 0.112965 0.993599i \(-0.463965\pi\)
0.112965 + 0.993599i \(0.463965\pi\)
\(822\) −58.2044 −2.03011
\(823\) −0.210155 −0.00732553 −0.00366276 0.999993i \(-0.501166\pi\)
−0.00366276 + 0.999993i \(0.501166\pi\)
\(824\) −1.79012 −0.0623619
\(825\) 0 0
\(826\) −47.8327 −1.66431
\(827\) −23.1396 −0.804643 −0.402322 0.915498i \(-0.631797\pi\)
−0.402322 + 0.915498i \(0.631797\pi\)
\(828\) 107.717 3.74342
\(829\) 24.6843 0.857321 0.428660 0.903466i \(-0.358986\pi\)
0.428660 + 0.903466i \(0.358986\pi\)
\(830\) 0 0
\(831\) −8.45141 −0.293176
\(832\) 31.5500 1.09380
\(833\) 23.1052 0.800547
\(834\) 125.906 4.35977
\(835\) 0 0
\(836\) 0 0
\(837\) −28.1338 −0.972448
\(838\) −0.419685 −0.0144978
\(839\) 31.2238 1.07797 0.538983 0.842317i \(-0.318809\pi\)
0.538983 + 0.842317i \(0.318809\pi\)
\(840\) 0 0
\(841\) 7.40738 0.255427
\(842\) −42.4398 −1.46257
\(843\) −66.0912 −2.27630
\(844\) 82.3208 2.83360
\(845\) 0 0
\(846\) −116.473 −4.00443
\(847\) −24.7723 −0.851187
\(848\) 17.6379 0.605689
\(849\) 13.7877 0.473194
\(850\) 0 0
\(851\) 18.9163 0.648443
\(852\) 1.43425 0.0491364
\(853\) −27.1366 −0.929140 −0.464570 0.885536i \(-0.653791\pi\)
−0.464570 + 0.885536i \(0.653791\pi\)
\(854\) 125.844 4.30629
\(855\) 0 0
\(856\) −13.0975 −0.447664
\(857\) 47.6457 1.62755 0.813773 0.581183i \(-0.197410\pi\)
0.813773 + 0.581183i \(0.197410\pi\)
\(858\) −55.7661 −1.90382
\(859\) −19.6361 −0.669974 −0.334987 0.942223i \(-0.608732\pi\)
−0.334987 + 0.942223i \(0.608732\pi\)
\(860\) 0 0
\(861\) 85.6177 2.91784
\(862\) 12.3503 0.420654
\(863\) −49.3684 −1.68052 −0.840260 0.542183i \(-0.817598\pi\)
−0.840260 + 0.542183i \(0.817598\pi\)
\(864\) 4.15025 0.141194
\(865\) 0 0
\(866\) 30.5197 1.03710
\(867\) −22.8066 −0.774554
\(868\) −53.8339 −1.82724
\(869\) −9.04600 −0.306865
\(870\) 0 0
\(871\) 19.6643 0.666299
\(872\) −14.2437 −0.482351
\(873\) −102.269 −3.46129
\(874\) 0 0
\(875\) 0 0
\(876\) 145.082 4.90188
\(877\) 41.1968 1.39112 0.695559 0.718469i \(-0.255157\pi\)
0.695559 + 0.718469i \(0.255157\pi\)
\(878\) 35.9845 1.21442
\(879\) −9.60819 −0.324076
\(880\) 0 0
\(881\) −10.4510 −0.352103 −0.176052 0.984381i \(-0.556333\pi\)
−0.176052 + 0.984381i \(0.556333\pi\)
\(882\) −105.072 −3.53797
\(883\) 50.2957 1.69259 0.846293 0.532717i \(-0.178829\pi\)
0.846293 + 0.532717i \(0.178829\pi\)
\(884\) −43.8639 −1.47530
\(885\) 0 0
\(886\) 13.0680 0.439027
\(887\) −0.201711 −0.00677278 −0.00338639 0.999994i \(-0.501078\pi\)
−0.00338639 + 0.999994i \(0.501078\pi\)
\(888\) −54.9178 −1.84292
\(889\) 52.0272 1.74494
\(890\) 0 0
\(891\) −13.1222 −0.439609
\(892\) −53.9545 −1.80653
\(893\) 0 0
\(894\) −137.846 −4.61027
\(895\) 0 0
\(896\) 76.3935 2.55213
\(897\) −51.7879 −1.72915
\(898\) 17.4597 0.582637
\(899\) 21.5520 0.718798
\(900\) 0 0
\(901\) 14.6045 0.486548
\(902\) 39.4268 1.31277
\(903\) 63.0551 2.09834
\(904\) −17.1558 −0.570595
\(905\) 0 0
\(906\) −80.0518 −2.65954
\(907\) 6.11841 0.203158 0.101579 0.994827i \(-0.467610\pi\)
0.101579 + 0.994827i \(0.467610\pi\)
\(908\) −14.6445 −0.485996
\(909\) 105.826 3.51002
\(910\) 0 0
\(911\) 0.960234 0.0318140 0.0159070 0.999873i \(-0.494936\pi\)
0.0159070 + 0.999873i \(0.494936\pi\)
\(912\) 0 0
\(913\) 9.34435 0.309253
\(914\) 78.9722 2.61217
\(915\) 0 0
\(916\) 44.6149 1.47412
\(917\) 21.6631 0.715378
\(918\) −58.4308 −1.92851
\(919\) −51.3264 −1.69310 −0.846551 0.532307i \(-0.821325\pi\)
−0.846551 + 0.532307i \(0.821325\pi\)
\(920\) 0 0
\(921\) 5.05831 0.166677
\(922\) 61.4750 2.02457
\(923\) −0.451073 −0.0148473
\(924\) −94.3270 −3.10313
\(925\) 0 0
\(926\) −99.6023 −3.27314
\(927\) 2.14163 0.0703404
\(928\) −3.17930 −0.104366
\(929\) −46.0177 −1.50979 −0.754896 0.655844i \(-0.772313\pi\)
−0.754896 + 0.655844i \(0.772313\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 42.1165 1.37957
\(933\) −2.62993 −0.0860999
\(934\) 35.6500 1.16650
\(935\) 0 0
\(936\) 98.3522 3.21474
\(937\) 3.79467 0.123966 0.0619832 0.998077i \(-0.480257\pi\)
0.0619832 + 0.998077i \(0.480257\pi\)
\(938\) 50.1233 1.63658
\(939\) −33.9754 −1.10875
\(940\) 0 0
\(941\) −23.1763 −0.755526 −0.377763 0.925902i \(-0.623307\pi\)
−0.377763 + 0.925902i \(0.623307\pi\)
\(942\) 80.0371 2.60775
\(943\) 36.6142 1.19232
\(944\) 18.8682 0.614106
\(945\) 0 0
\(946\) 29.0367 0.944066
\(947\) −18.3891 −0.597565 −0.298783 0.954321i \(-0.596581\pi\)
−0.298783 + 0.954321i \(0.596581\pi\)
\(948\) 49.4644 1.60653
\(949\) −45.6287 −1.48117
\(950\) 0 0
\(951\) −55.4427 −1.79785
\(952\) −55.1273 −1.78669
\(953\) 14.6072 0.473174 0.236587 0.971610i \(-0.423971\pi\)
0.236587 + 0.971610i \(0.423971\pi\)
\(954\) −66.4151 −2.15027
\(955\) 0 0
\(956\) −68.1785 −2.20505
\(957\) 37.7631 1.22071
\(958\) −2.60760 −0.0842477
\(959\) 30.9631 0.999852
\(960\) 0 0
\(961\) −18.2420 −0.588450
\(962\) 35.0299 1.12941
\(963\) 15.6694 0.504938
\(964\) 69.0361 2.22350
\(965\) 0 0
\(966\) −132.005 −4.24719
\(967\) −59.4737 −1.91254 −0.956272 0.292478i \(-0.905520\pi\)
−0.956272 + 0.292478i \(0.905520\pi\)
\(968\) 30.7559 0.988533
\(969\) 0 0
\(970\) 0 0
\(971\) −22.3008 −0.715667 −0.357833 0.933785i \(-0.616484\pi\)
−0.357833 + 0.933785i \(0.616484\pi\)
\(972\) −21.4712 −0.688689
\(973\) −66.9785 −2.14723
\(974\) −15.2467 −0.488535
\(975\) 0 0
\(976\) −49.6406 −1.58896
\(977\) −15.2734 −0.488638 −0.244319 0.969695i \(-0.578564\pi\)
−0.244319 + 0.969695i \(0.578564\pi\)
\(978\) −48.0191 −1.53548
\(979\) −0.164132 −0.00524567
\(980\) 0 0
\(981\) 17.0406 0.544063
\(982\) 1.98398 0.0633115
\(983\) −41.4127 −1.32086 −0.660431 0.750887i \(-0.729626\pi\)
−0.660431 + 0.750887i \(0.729626\pi\)
\(984\) −106.298 −3.38866
\(985\) 0 0
\(986\) 44.7610 1.42548
\(987\) 94.7186 3.01493
\(988\) 0 0
\(989\) 26.9653 0.857447
\(990\) 0 0
\(991\) 18.9609 0.602314 0.301157 0.953575i \(-0.402627\pi\)
0.301157 + 0.953575i \(0.402627\pi\)
\(992\) −1.88204 −0.0597549
\(993\) −45.8805 −1.45597
\(994\) −1.14976 −0.0364683
\(995\) 0 0
\(996\) −51.0958 −1.61903
\(997\) 22.5133 0.713002 0.356501 0.934295i \(-0.383970\pi\)
0.356501 + 0.934295i \(0.383970\pi\)
\(998\) −3.84361 −0.121668
\(999\) 30.9655 0.979704
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 9025.2.a.bh.1.1 4
5.4 even 2 1805.2.a.n.1.4 yes 4
19.18 odd 2 9025.2.a.bo.1.4 4
95.94 odd 2 1805.2.a.j.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.j.1.1 4 95.94 odd 2
1805.2.a.n.1.4 yes 4 5.4 even 2
9025.2.a.bh.1.1 4 1.1 even 1 trivial
9025.2.a.bo.1.4 4 19.18 odd 2