Properties

Label 6025.2.a.h.1.2
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.49073\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49073 q^{2}\) \(-1.22208 q^{3}\) \(+4.20371 q^{4}\) \(+3.04385 q^{6}\) \(-0.136122 q^{7}\) \(-5.48885 q^{8}\) \(-1.50653 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49073 q^{2}\) \(-1.22208 q^{3}\) \(+4.20371 q^{4}\) \(+3.04385 q^{6}\) \(-0.136122 q^{7}\) \(-5.48885 q^{8}\) \(-1.50653 q^{9}\) \(-0.905365 q^{11}\) \(-5.13726 q^{12}\) \(+0.123706 q^{13}\) \(+0.339044 q^{14}\) \(+5.26378 q^{16}\) \(-1.26034 q^{17}\) \(+3.75236 q^{18}\) \(-2.13460 q^{19}\) \(+0.166352 q^{21}\) \(+2.25502 q^{22}\) \(-6.64978 q^{23}\) \(+6.70778 q^{24}\) \(-0.308118 q^{26}\) \(+5.50732 q^{27}\) \(-0.572220 q^{28}\) \(+5.36862 q^{29}\) \(-9.78467 q^{31}\) \(-2.13295 q^{32}\) \(+1.10642 q^{33}\) \(+3.13917 q^{34}\) \(-6.33303 q^{36}\) \(-5.76688 q^{37}\) \(+5.31669 q^{38}\) \(-0.151178 q^{39}\) \(+6.43642 q^{41}\) \(-0.414337 q^{42}\) \(+3.18712 q^{43}\) \(-3.80590 q^{44}\) \(+16.5628 q^{46}\) \(-12.9849 q^{47}\) \(-6.43274 q^{48}\) \(-6.98147 q^{49}\) \(+1.54023 q^{51}\) \(+0.520025 q^{52}\) \(-3.90862 q^{53}\) \(-13.7172 q^{54}\) \(+0.747155 q^{56}\) \(+2.60864 q^{57}\) \(-13.3718 q^{58}\) \(+8.15085 q^{59}\) \(-14.3712 q^{61}\) \(+24.3709 q^{62}\) \(+0.205073 q^{63}\) \(-5.21498 q^{64}\) \(-2.75580 q^{66}\) \(+4.89534 q^{67}\) \(-5.29812 q^{68}\) \(+8.12653 q^{69}\) \(+4.32869 q^{71}\) \(+8.26912 q^{72}\) \(-5.64935 q^{73}\) \(+14.3637 q^{74}\) \(-8.97323 q^{76}\) \(+0.123241 q^{77}\) \(+0.376543 q^{78}\) \(+1.43490 q^{79}\) \(-2.21077 q^{81}\) \(-16.0314 q^{82}\) \(+11.7625 q^{83}\) \(+0.699296 q^{84}\) \(-7.93825 q^{86}\) \(-6.56086 q^{87}\) \(+4.96941 q^{88}\) \(-13.7381 q^{89}\) \(-0.0168392 q^{91}\) \(-27.9538 q^{92}\) \(+11.9576 q^{93}\) \(+32.3419 q^{94}\) \(+2.60662 q^{96}\) \(-13.6204 q^{97}\) \(+17.3889 q^{98}\) \(+1.36396 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49073 −1.76121 −0.880604 0.473852i \(-0.842863\pi\)
−0.880604 + 0.473852i \(0.842863\pi\)
\(3\) −1.22208 −0.705566 −0.352783 0.935705i \(-0.614765\pi\)
−0.352783 + 0.935705i \(0.614765\pi\)
\(4\) 4.20371 2.10186
\(5\) 0 0
\(6\) 3.04385 1.24265
\(7\) −0.136122 −0.0514495 −0.0257247 0.999669i \(-0.508189\pi\)
−0.0257247 + 0.999669i \(0.508189\pi\)
\(8\) −5.48885 −1.94060
\(9\) −1.50653 −0.502177
\(10\) 0 0
\(11\) −0.905365 −0.272978 −0.136489 0.990642i \(-0.543582\pi\)
−0.136489 + 0.990642i \(0.543582\pi\)
\(12\) −5.13726 −1.48300
\(13\) 0.123706 0.0343099 0.0171549 0.999853i \(-0.494539\pi\)
0.0171549 + 0.999853i \(0.494539\pi\)
\(14\) 0.339044 0.0906133
\(15\) 0 0
\(16\) 5.26378 1.31595
\(17\) −1.26034 −0.305678 −0.152839 0.988251i \(-0.548842\pi\)
−0.152839 + 0.988251i \(0.548842\pi\)
\(18\) 3.75236 0.884439
\(19\) −2.13460 −0.489710 −0.244855 0.969560i \(-0.578740\pi\)
−0.244855 + 0.969560i \(0.578740\pi\)
\(20\) 0 0
\(21\) 0.166352 0.0363010
\(22\) 2.25502 0.480771
\(23\) −6.64978 −1.38657 −0.693287 0.720661i \(-0.743838\pi\)
−0.693287 + 0.720661i \(0.743838\pi\)
\(24\) 6.70778 1.36922
\(25\) 0 0
\(26\) −0.308118 −0.0604269
\(27\) 5.50732 1.05988
\(28\) −0.572220 −0.108139
\(29\) 5.36862 0.996928 0.498464 0.866911i \(-0.333898\pi\)
0.498464 + 0.866911i \(0.333898\pi\)
\(30\) 0 0
\(31\) −9.78467 −1.75738 −0.878689 0.477395i \(-0.841581\pi\)
−0.878689 + 0.477395i \(0.841581\pi\)
\(32\) −2.13295 −0.377055
\(33\) 1.10642 0.192604
\(34\) 3.13917 0.538363
\(35\) 0 0
\(36\) −6.33303 −1.05550
\(37\) −5.76688 −0.948070 −0.474035 0.880506i \(-0.657203\pi\)
−0.474035 + 0.880506i \(0.657203\pi\)
\(38\) 5.31669 0.862481
\(39\) −0.151178 −0.0242079
\(40\) 0 0
\(41\) 6.43642 1.00520 0.502600 0.864519i \(-0.332377\pi\)
0.502600 + 0.864519i \(0.332377\pi\)
\(42\) −0.414337 −0.0639336
\(43\) 3.18712 0.486032 0.243016 0.970022i \(-0.421863\pi\)
0.243016 + 0.970022i \(0.421863\pi\)
\(44\) −3.80590 −0.573761
\(45\) 0 0
\(46\) 16.5628 2.44205
\(47\) −12.9849 −1.89404 −0.947022 0.321168i \(-0.895925\pi\)
−0.947022 + 0.321168i \(0.895925\pi\)
\(48\) −6.43274 −0.928486
\(49\) −6.98147 −0.997353
\(50\) 0 0
\(51\) 1.54023 0.215676
\(52\) 0.520025 0.0721145
\(53\) −3.90862 −0.536890 −0.268445 0.963295i \(-0.586510\pi\)
−0.268445 + 0.963295i \(0.586510\pi\)
\(54\) −13.7172 −1.86668
\(55\) 0 0
\(56\) 0.747155 0.0998429
\(57\) 2.60864 0.345522
\(58\) −13.3718 −1.75580
\(59\) 8.15085 1.06115 0.530575 0.847638i \(-0.321976\pi\)
0.530575 + 0.847638i \(0.321976\pi\)
\(60\) 0 0
\(61\) −14.3712 −1.84004 −0.920021 0.391870i \(-0.871828\pi\)
−0.920021 + 0.391870i \(0.871828\pi\)
\(62\) 24.3709 3.09511
\(63\) 0.205073 0.0258368
\(64\) −5.21498 −0.651873
\(65\) 0 0
\(66\) −2.75580 −0.339216
\(67\) 4.89534 0.598062 0.299031 0.954243i \(-0.403337\pi\)
0.299031 + 0.954243i \(0.403337\pi\)
\(68\) −5.29812 −0.642491
\(69\) 8.12653 0.978319
\(70\) 0 0
\(71\) 4.32869 0.513720 0.256860 0.966449i \(-0.417312\pi\)
0.256860 + 0.966449i \(0.417312\pi\)
\(72\) 8.26912 0.974525
\(73\) −5.64935 −0.661206 −0.330603 0.943770i \(-0.607252\pi\)
−0.330603 + 0.943770i \(0.607252\pi\)
\(74\) 14.3637 1.66975
\(75\) 0 0
\(76\) −8.97323 −1.02930
\(77\) 0.123241 0.0140446
\(78\) 0.376543 0.0426351
\(79\) 1.43490 0.161439 0.0807195 0.996737i \(-0.474278\pi\)
0.0807195 + 0.996737i \(0.474278\pi\)
\(80\) 0 0
\(81\) −2.21077 −0.245641
\(82\) −16.0314 −1.77037
\(83\) 11.7625 1.29110 0.645549 0.763718i \(-0.276628\pi\)
0.645549 + 0.763718i \(0.276628\pi\)
\(84\) 0.699296 0.0762994
\(85\) 0 0
\(86\) −7.93825 −0.856004
\(87\) −6.56086 −0.703398
\(88\) 4.96941 0.529741
\(89\) −13.7381 −1.45624 −0.728118 0.685452i \(-0.759605\pi\)
−0.728118 + 0.685452i \(0.759605\pi\)
\(90\) 0 0
\(91\) −0.0168392 −0.00176523
\(92\) −27.9538 −2.91438
\(93\) 11.9576 1.23995
\(94\) 32.3419 3.33581
\(95\) 0 0
\(96\) 2.60662 0.266037
\(97\) −13.6204 −1.38294 −0.691472 0.722404i \(-0.743037\pi\)
−0.691472 + 0.722404i \(0.743037\pi\)
\(98\) 17.3889 1.75655
\(99\) 1.36396 0.137083
\(100\) 0 0
\(101\) −0.0787660 −0.00783751 −0.00391876 0.999992i \(-0.501247\pi\)
−0.00391876 + 0.999992i \(0.501247\pi\)
\(102\) −3.83630 −0.379850
\(103\) 6.36701 0.627360 0.313680 0.949529i \(-0.398438\pi\)
0.313680 + 0.949529i \(0.398438\pi\)
\(104\) −0.679004 −0.0665818
\(105\) 0 0
\(106\) 9.73529 0.945575
\(107\) 1.99570 0.192932 0.0964660 0.995336i \(-0.469246\pi\)
0.0964660 + 0.995336i \(0.469246\pi\)
\(108\) 23.1512 2.22773
\(109\) 14.8223 1.41972 0.709861 0.704341i \(-0.248758\pi\)
0.709861 + 0.704341i \(0.248758\pi\)
\(110\) 0 0
\(111\) 7.04756 0.668925
\(112\) −0.716519 −0.0677047
\(113\) 12.3669 1.16338 0.581690 0.813410i \(-0.302392\pi\)
0.581690 + 0.813410i \(0.302392\pi\)
\(114\) −6.49740 −0.608537
\(115\) 0 0
\(116\) 22.5681 2.09540
\(117\) −0.186367 −0.0172296
\(118\) −20.3015 −1.86891
\(119\) 0.171561 0.0157270
\(120\) 0 0
\(121\) −10.1803 −0.925483
\(122\) 35.7947 3.24070
\(123\) −7.86579 −0.709234
\(124\) −41.1319 −3.69376
\(125\) 0 0
\(126\) −0.510780 −0.0455039
\(127\) −15.9678 −1.41691 −0.708456 0.705754i \(-0.750608\pi\)
−0.708456 + 0.705754i \(0.750608\pi\)
\(128\) 17.2550 1.52514
\(129\) −3.89491 −0.342927
\(130\) 0 0
\(131\) −12.1390 −1.06059 −0.530293 0.847814i \(-0.677918\pi\)
−0.530293 + 0.847814i \(0.677918\pi\)
\(132\) 4.65109 0.404826
\(133\) 0.290566 0.0251953
\(134\) −12.1930 −1.05331
\(135\) 0 0
\(136\) 6.91783 0.593199
\(137\) −0.846052 −0.0722831 −0.0361416 0.999347i \(-0.511507\pi\)
−0.0361416 + 0.999347i \(0.511507\pi\)
\(138\) −20.2410 −1.72302
\(139\) 15.6472 1.32717 0.663587 0.748099i \(-0.269033\pi\)
0.663587 + 0.748099i \(0.269033\pi\)
\(140\) 0 0
\(141\) 15.8685 1.33637
\(142\) −10.7816 −0.904769
\(143\) −0.111999 −0.00936584
\(144\) −7.93006 −0.660838
\(145\) 0 0
\(146\) 14.0710 1.16452
\(147\) 8.53188 0.703698
\(148\) −24.2423 −1.99271
\(149\) −0.542212 −0.0444198 −0.0222099 0.999753i \(-0.507070\pi\)
−0.0222099 + 0.999753i \(0.507070\pi\)
\(150\) 0 0
\(151\) 8.53046 0.694199 0.347100 0.937828i \(-0.387167\pi\)
0.347100 + 0.937828i \(0.387167\pi\)
\(152\) 11.7165 0.950331
\(153\) 1.89875 0.153505
\(154\) −0.306958 −0.0247354
\(155\) 0 0
\(156\) −0.635510 −0.0508815
\(157\) 16.2204 1.29453 0.647263 0.762267i \(-0.275914\pi\)
0.647263 + 0.762267i \(0.275914\pi\)
\(158\) −3.57394 −0.284328
\(159\) 4.77662 0.378811
\(160\) 0 0
\(161\) 0.905184 0.0713385
\(162\) 5.50641 0.432625
\(163\) −1.36363 −0.106808 −0.0534039 0.998573i \(-0.517007\pi\)
−0.0534039 + 0.998573i \(0.517007\pi\)
\(164\) 27.0569 2.11279
\(165\) 0 0
\(166\) −29.2971 −2.27389
\(167\) −13.4045 −1.03727 −0.518636 0.854995i \(-0.673560\pi\)
−0.518636 + 0.854995i \(0.673560\pi\)
\(168\) −0.913080 −0.0704457
\(169\) −12.9847 −0.998823
\(170\) 0 0
\(171\) 3.21584 0.245921
\(172\) 13.3978 1.02157
\(173\) 13.6007 1.03404 0.517022 0.855972i \(-0.327041\pi\)
0.517022 + 0.855972i \(0.327041\pi\)
\(174\) 16.3413 1.23883
\(175\) 0 0
\(176\) −4.76565 −0.359224
\(177\) −9.96096 −0.748711
\(178\) 34.2179 2.56474
\(179\) 23.9070 1.78689 0.893445 0.449172i \(-0.148281\pi\)
0.893445 + 0.449172i \(0.148281\pi\)
\(180\) 0 0
\(181\) −11.6044 −0.862545 −0.431273 0.902222i \(-0.641935\pi\)
−0.431273 + 0.902222i \(0.641935\pi\)
\(182\) 0.0419418 0.00310893
\(183\) 17.5627 1.29827
\(184\) 36.4996 2.69079
\(185\) 0 0
\(186\) −29.7831 −2.18380
\(187\) 1.14107 0.0834433
\(188\) −54.5849 −3.98101
\(189\) −0.749670 −0.0545305
\(190\) 0 0
\(191\) −4.85929 −0.351606 −0.175803 0.984425i \(-0.556252\pi\)
−0.175803 + 0.984425i \(0.556252\pi\)
\(192\) 6.37310 0.459939
\(193\) −25.6451 −1.84597 −0.922987 0.384831i \(-0.874260\pi\)
−0.922987 + 0.384831i \(0.874260\pi\)
\(194\) 33.9247 2.43565
\(195\) 0 0
\(196\) −29.3481 −2.09629
\(197\) −1.46990 −0.104726 −0.0523629 0.998628i \(-0.516675\pi\)
−0.0523629 + 0.998628i \(0.516675\pi\)
\(198\) −3.39725 −0.241432
\(199\) 7.46714 0.529332 0.264666 0.964340i \(-0.414738\pi\)
0.264666 + 0.964340i \(0.414738\pi\)
\(200\) 0 0
\(201\) −5.98248 −0.421972
\(202\) 0.196185 0.0138035
\(203\) −0.730790 −0.0512914
\(204\) 6.47470 0.453320
\(205\) 0 0
\(206\) −15.8585 −1.10491
\(207\) 10.0181 0.696306
\(208\) 0.651162 0.0451500
\(209\) 1.93259 0.133680
\(210\) 0 0
\(211\) −20.1549 −1.38752 −0.693759 0.720208i \(-0.744047\pi\)
−0.693759 + 0.720208i \(0.744047\pi\)
\(212\) −16.4307 −1.12847
\(213\) −5.28998 −0.362463
\(214\) −4.97075 −0.339793
\(215\) 0 0
\(216\) −30.2288 −2.05681
\(217\) 1.33191 0.0904162
\(218\) −36.9184 −2.50043
\(219\) 6.90393 0.466524
\(220\) 0 0
\(221\) −0.155912 −0.0104878
\(222\) −17.5535 −1.17812
\(223\) 8.91317 0.596870 0.298435 0.954430i \(-0.403535\pi\)
0.298435 + 0.954430i \(0.403535\pi\)
\(224\) 0.290342 0.0193993
\(225\) 0 0
\(226\) −30.8026 −2.04896
\(227\) 17.2725 1.14642 0.573209 0.819409i \(-0.305698\pi\)
0.573209 + 0.819409i \(0.305698\pi\)
\(228\) 10.9660 0.726239
\(229\) −12.9392 −0.855044 −0.427522 0.904005i \(-0.640613\pi\)
−0.427522 + 0.904005i \(0.640613\pi\)
\(230\) 0 0
\(231\) −0.150609 −0.00990936
\(232\) −29.4675 −1.93464
\(233\) 24.8301 1.62668 0.813338 0.581791i \(-0.197648\pi\)
0.813338 + 0.581791i \(0.197648\pi\)
\(234\) 0.464189 0.0303450
\(235\) 0 0
\(236\) 34.2639 2.23039
\(237\) −1.75356 −0.113906
\(238\) −0.427311 −0.0276985
\(239\) 7.52122 0.486507 0.243254 0.969963i \(-0.421785\pi\)
0.243254 + 0.969963i \(0.421785\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 25.3564 1.62997
\(243\) −13.8202 −0.886569
\(244\) −60.4123 −3.86750
\(245\) 0 0
\(246\) 19.5915 1.24911
\(247\) −0.264062 −0.0168019
\(248\) 53.7065 3.41037
\(249\) −14.3746 −0.910955
\(250\) 0 0
\(251\) −30.0279 −1.89534 −0.947671 0.319250i \(-0.896569\pi\)
−0.947671 + 0.319250i \(0.896569\pi\)
\(252\) 0.862068 0.0543052
\(253\) 6.02048 0.378504
\(254\) 39.7714 2.49548
\(255\) 0 0
\(256\) −32.5475 −2.03422
\(257\) 9.93458 0.619702 0.309851 0.950785i \(-0.399721\pi\)
0.309851 + 0.950785i \(0.399721\pi\)
\(258\) 9.70114 0.603967
\(259\) 0.785002 0.0487777
\(260\) 0 0
\(261\) −8.08800 −0.500634
\(262\) 30.2348 1.86791
\(263\) −18.4575 −1.13814 −0.569069 0.822290i \(-0.692696\pi\)
−0.569069 + 0.822290i \(0.692696\pi\)
\(264\) −6.07300 −0.373767
\(265\) 0 0
\(266\) −0.723721 −0.0443742
\(267\) 16.7890 1.02747
\(268\) 20.5786 1.25704
\(269\) −1.14902 −0.0700569 −0.0350285 0.999386i \(-0.511152\pi\)
−0.0350285 + 0.999386i \(0.511152\pi\)
\(270\) 0 0
\(271\) 12.2034 0.741303 0.370651 0.928772i \(-0.379134\pi\)
0.370651 + 0.928772i \(0.379134\pi\)
\(272\) −6.63417 −0.402256
\(273\) 0.0205787 0.00124548
\(274\) 2.10728 0.127306
\(275\) 0 0
\(276\) 34.1616 2.05629
\(277\) 4.31327 0.259159 0.129580 0.991569i \(-0.458637\pi\)
0.129580 + 0.991569i \(0.458637\pi\)
\(278\) −38.9728 −2.33743
\(279\) 14.7409 0.882515
\(280\) 0 0
\(281\) −17.1399 −1.02248 −0.511240 0.859438i \(-0.670814\pi\)
−0.511240 + 0.859438i \(0.670814\pi\)
\(282\) −39.5242 −2.35363
\(283\) −13.8905 −0.825704 −0.412852 0.910798i \(-0.635467\pi\)
−0.412852 + 0.910798i \(0.635467\pi\)
\(284\) 18.1966 1.07977
\(285\) 0 0
\(286\) 0.278959 0.0164952
\(287\) −0.876142 −0.0517170
\(288\) 3.21335 0.189349
\(289\) −15.4115 −0.906561
\(290\) 0 0
\(291\) 16.6452 0.975757
\(292\) −23.7482 −1.38976
\(293\) 0.325090 0.0189920 0.00949598 0.999955i \(-0.496977\pi\)
0.00949598 + 0.999955i \(0.496977\pi\)
\(294\) −21.2506 −1.23936
\(295\) 0 0
\(296\) 31.6535 1.83982
\(297\) −4.98614 −0.289325
\(298\) 1.35050 0.0782325
\(299\) −0.822618 −0.0475732
\(300\) 0 0
\(301\) −0.433839 −0.0250061
\(302\) −21.2470 −1.22263
\(303\) 0.0962580 0.00552988
\(304\) −11.2360 −0.644432
\(305\) 0 0
\(306\) −4.72926 −0.270354
\(307\) 14.3600 0.819566 0.409783 0.912183i \(-0.365604\pi\)
0.409783 + 0.912183i \(0.365604\pi\)
\(308\) 0.518068 0.0295197
\(309\) −7.78096 −0.442644
\(310\) 0 0
\(311\) −11.2072 −0.635502 −0.317751 0.948174i \(-0.602928\pi\)
−0.317751 + 0.948174i \(0.602928\pi\)
\(312\) 0.829794 0.0469778
\(313\) −19.3860 −1.09576 −0.547879 0.836557i \(-0.684565\pi\)
−0.547879 + 0.836557i \(0.684565\pi\)
\(314\) −40.4005 −2.27993
\(315\) 0 0
\(316\) 6.03191 0.339322
\(317\) −5.19578 −0.291824 −0.145912 0.989298i \(-0.546612\pi\)
−0.145912 + 0.989298i \(0.546612\pi\)
\(318\) −11.8973 −0.667165
\(319\) −4.86056 −0.272139
\(320\) 0 0
\(321\) −2.43890 −0.136126
\(322\) −2.25457 −0.125642
\(323\) 2.69032 0.149693
\(324\) −9.29343 −0.516302
\(325\) 0 0
\(326\) 3.39643 0.188111
\(327\) −18.1140 −1.00171
\(328\) −35.3285 −1.95069
\(329\) 1.76754 0.0974476
\(330\) 0 0
\(331\) 0.0173250 0.000952268 0 0.000476134 1.00000i \(-0.499848\pi\)
0.000476134 1.00000i \(0.499848\pi\)
\(332\) 49.4461 2.71371
\(333\) 8.68799 0.476099
\(334\) 33.3869 1.82685
\(335\) 0 0
\(336\) 0.875641 0.0477701
\(337\) −0.347899 −0.0189513 −0.00947563 0.999955i \(-0.503016\pi\)
−0.00947563 + 0.999955i \(0.503016\pi\)
\(338\) 32.3413 1.75914
\(339\) −15.1133 −0.820841
\(340\) 0 0
\(341\) 8.85870 0.479725
\(342\) −8.00976 −0.433118
\(343\) 1.90319 0.102763
\(344\) −17.4936 −0.943194
\(345\) 0 0
\(346\) −33.8756 −1.82117
\(347\) −6.37601 −0.342282 −0.171141 0.985247i \(-0.554745\pi\)
−0.171141 + 0.985247i \(0.554745\pi\)
\(348\) −27.5800 −1.47844
\(349\) −0.970720 −0.0519614 −0.0259807 0.999662i \(-0.508271\pi\)
−0.0259807 + 0.999662i \(0.508271\pi\)
\(350\) 0 0
\(351\) 0.681289 0.0363645
\(352\) 1.93110 0.102928
\(353\) −30.5488 −1.62595 −0.812975 0.582299i \(-0.802153\pi\)
−0.812975 + 0.582299i \(0.802153\pi\)
\(354\) 24.8100 1.31864
\(355\) 0 0
\(356\) −57.7511 −3.06080
\(357\) −0.209660 −0.0110964
\(358\) −59.5457 −3.14709
\(359\) 8.22124 0.433901 0.216950 0.976183i \(-0.430389\pi\)
0.216950 + 0.976183i \(0.430389\pi\)
\(360\) 0 0
\(361\) −14.4435 −0.760184
\(362\) 28.9033 1.51912
\(363\) 12.4411 0.652989
\(364\) −0.0707871 −0.00371025
\(365\) 0 0
\(366\) −43.7438 −2.28652
\(367\) −25.1108 −1.31077 −0.655387 0.755294i \(-0.727494\pi\)
−0.655387 + 0.755294i \(0.727494\pi\)
\(368\) −35.0030 −1.82466
\(369\) −9.69667 −0.504789
\(370\) 0 0
\(371\) 0.532051 0.0276227
\(372\) 50.2663 2.60619
\(373\) 27.0231 1.39920 0.699601 0.714534i \(-0.253361\pi\)
0.699601 + 0.714534i \(0.253361\pi\)
\(374\) −2.84209 −0.146961
\(375\) 0 0
\(376\) 71.2722 3.67558
\(377\) 0.664131 0.0342045
\(378\) 1.86722 0.0960396
\(379\) 22.9961 1.18123 0.590616 0.806953i \(-0.298885\pi\)
0.590616 + 0.806953i \(0.298885\pi\)
\(380\) 0 0
\(381\) 19.5139 0.999725
\(382\) 12.1032 0.619252
\(383\) −3.72670 −0.190425 −0.0952126 0.995457i \(-0.530353\pi\)
−0.0952126 + 0.995457i \(0.530353\pi\)
\(384\) −21.0869 −1.07609
\(385\) 0 0
\(386\) 63.8749 3.25115
\(387\) −4.80151 −0.244074
\(388\) −57.2563 −2.90675
\(389\) 4.72525 0.239580 0.119790 0.992799i \(-0.461778\pi\)
0.119790 + 0.992799i \(0.461778\pi\)
\(390\) 0 0
\(391\) 8.38100 0.423845
\(392\) 38.3202 1.93546
\(393\) 14.8347 0.748313
\(394\) 3.66111 0.184444
\(395\) 0 0
\(396\) 5.73370 0.288129
\(397\) −32.2227 −1.61721 −0.808606 0.588350i \(-0.799778\pi\)
−0.808606 + 0.588350i \(0.799778\pi\)
\(398\) −18.5986 −0.932264
\(399\) −0.355094 −0.0177769
\(400\) 0 0
\(401\) −6.02370 −0.300809 −0.150405 0.988625i \(-0.548058\pi\)
−0.150405 + 0.988625i \(0.548058\pi\)
\(402\) 14.9007 0.743180
\(403\) −1.21042 −0.0602955
\(404\) −0.331110 −0.0164733
\(405\) 0 0
\(406\) 1.82020 0.0903349
\(407\) 5.22113 0.258802
\(408\) −8.45411 −0.418541
\(409\) 18.5405 0.916767 0.458384 0.888754i \(-0.348429\pi\)
0.458384 + 0.888754i \(0.348429\pi\)
\(410\) 0 0
\(411\) 1.03394 0.0510005
\(412\) 26.7651 1.31862
\(413\) −1.10951 −0.0545956
\(414\) −24.9523 −1.22634
\(415\) 0 0
\(416\) −0.263858 −0.0129367
\(417\) −19.1220 −0.936409
\(418\) −4.81355 −0.235438
\(419\) 29.7394 1.45286 0.726432 0.687238i \(-0.241177\pi\)
0.726432 + 0.687238i \(0.241177\pi\)
\(420\) 0 0
\(421\) 2.65516 0.129405 0.0647023 0.997905i \(-0.479390\pi\)
0.0647023 + 0.997905i \(0.479390\pi\)
\(422\) 50.2002 2.44371
\(423\) 19.5622 0.951146
\(424\) 21.4538 1.04189
\(425\) 0 0
\(426\) 13.1759 0.638374
\(427\) 1.95624 0.0946691
\(428\) 8.38937 0.405515
\(429\) 0.136871 0.00660822
\(430\) 0 0
\(431\) 27.9512 1.34636 0.673181 0.739478i \(-0.264927\pi\)
0.673181 + 0.739478i \(0.264927\pi\)
\(432\) 28.9893 1.39475
\(433\) −13.5815 −0.652687 −0.326344 0.945251i \(-0.605817\pi\)
−0.326344 + 0.945251i \(0.605817\pi\)
\(434\) −3.31743 −0.159242
\(435\) 0 0
\(436\) 62.3089 2.98405
\(437\) 14.1946 0.679019
\(438\) −17.1958 −0.821647
\(439\) 27.3113 1.30350 0.651748 0.758435i \(-0.274036\pi\)
0.651748 + 0.758435i \(0.274036\pi\)
\(440\) 0 0
\(441\) 10.5178 0.500848
\(442\) 0.388334 0.0184712
\(443\) −4.06001 −0.192897 −0.0964484 0.995338i \(-0.530748\pi\)
−0.0964484 + 0.995338i \(0.530748\pi\)
\(444\) 29.6259 1.40599
\(445\) 0 0
\(446\) −22.2003 −1.05121
\(447\) 0.662624 0.0313410
\(448\) 0.709876 0.0335385
\(449\) −1.53571 −0.0724746 −0.0362373 0.999343i \(-0.511537\pi\)
−0.0362373 + 0.999343i \(0.511537\pi\)
\(450\) 0 0
\(451\) −5.82731 −0.274397
\(452\) 51.9869 2.44526
\(453\) −10.4249 −0.489803
\(454\) −43.0211 −2.01908
\(455\) 0 0
\(456\) −14.3184 −0.670521
\(457\) 4.50705 0.210831 0.105415 0.994428i \(-0.466383\pi\)
0.105415 + 0.994428i \(0.466383\pi\)
\(458\) 32.2279 1.50591
\(459\) −6.94111 −0.323983
\(460\) 0 0
\(461\) 17.5820 0.818875 0.409438 0.912338i \(-0.365725\pi\)
0.409438 + 0.912338i \(0.365725\pi\)
\(462\) 0.375126 0.0174525
\(463\) 42.1082 1.95693 0.978466 0.206407i \(-0.0661772\pi\)
0.978466 + 0.206407i \(0.0661772\pi\)
\(464\) 28.2592 1.31190
\(465\) 0 0
\(466\) −61.8451 −2.86492
\(467\) −10.6368 −0.492210 −0.246105 0.969243i \(-0.579151\pi\)
−0.246105 + 0.969243i \(0.579151\pi\)
\(468\) −0.783434 −0.0362143
\(469\) −0.666367 −0.0307699
\(470\) 0 0
\(471\) −19.8225 −0.913373
\(472\) −44.7388 −2.05927
\(473\) −2.88551 −0.132676
\(474\) 4.36763 0.200612
\(475\) 0 0
\(476\) 0.721193 0.0330558
\(477\) 5.88845 0.269614
\(478\) −18.7333 −0.856841
\(479\) 24.3303 1.11168 0.555839 0.831290i \(-0.312397\pi\)
0.555839 + 0.831290i \(0.312397\pi\)
\(480\) 0 0
\(481\) −0.713398 −0.0325282
\(482\) −2.49073 −0.113449
\(483\) −1.10620 −0.0503340
\(484\) −42.7951 −1.94523
\(485\) 0 0
\(486\) 34.4224 1.56143
\(487\) −15.1777 −0.687768 −0.343884 0.939012i \(-0.611743\pi\)
−0.343884 + 0.939012i \(0.611743\pi\)
\(488\) 78.8812 3.57079
\(489\) 1.66646 0.0753598
\(490\) 0 0
\(491\) 10.0194 0.452169 0.226084 0.974108i \(-0.427408\pi\)
0.226084 + 0.974108i \(0.427408\pi\)
\(492\) −33.0655 −1.49071
\(493\) −6.76630 −0.304739
\(494\) 0.657707 0.0295916
\(495\) 0 0
\(496\) −51.5044 −2.31261
\(497\) −0.589231 −0.0264306
\(498\) 35.8032 1.60438
\(499\) −7.82989 −0.350514 −0.175257 0.984523i \(-0.556076\pi\)
−0.175257 + 0.984523i \(0.556076\pi\)
\(500\) 0 0
\(501\) 16.3813 0.731863
\(502\) 74.7911 3.33809
\(503\) 7.39455 0.329707 0.164853 0.986318i \(-0.447285\pi\)
0.164853 + 0.986318i \(0.447285\pi\)
\(504\) −1.12561 −0.0501388
\(505\) 0 0
\(506\) −14.9954 −0.666625
\(507\) 15.8683 0.704735
\(508\) −67.1241 −2.97815
\(509\) 13.7526 0.609572 0.304786 0.952421i \(-0.401415\pi\)
0.304786 + 0.952421i \(0.401415\pi\)
\(510\) 0 0
\(511\) 0.769003 0.0340187
\(512\) 46.5568 2.05754
\(513\) −11.7559 −0.519036
\(514\) −24.7443 −1.09143
\(515\) 0 0
\(516\) −16.3731 −0.720784
\(517\) 11.7561 0.517032
\(518\) −1.95523 −0.0859077
\(519\) −16.6211 −0.729585
\(520\) 0 0
\(521\) −14.2825 −0.625730 −0.312865 0.949798i \(-0.601289\pi\)
−0.312865 + 0.949798i \(0.601289\pi\)
\(522\) 20.1450 0.881722
\(523\) 29.4674 1.28852 0.644260 0.764806i \(-0.277165\pi\)
0.644260 + 0.764806i \(0.277165\pi\)
\(524\) −51.0287 −2.22920
\(525\) 0 0
\(526\) 45.9726 2.00450
\(527\) 12.3320 0.537192
\(528\) 5.82398 0.253456
\(529\) 21.2195 0.922589
\(530\) 0 0
\(531\) −12.2795 −0.532886
\(532\) 1.22146 0.0529569
\(533\) 0.796224 0.0344883
\(534\) −41.8168 −1.80959
\(535\) 0 0
\(536\) −26.8698 −1.16060
\(537\) −29.2161 −1.26077
\(538\) 2.86189 0.123385
\(539\) 6.32078 0.272255
\(540\) 0 0
\(541\) 31.6583 1.36110 0.680549 0.732703i \(-0.261741\pi\)
0.680549 + 0.732703i \(0.261741\pi\)
\(542\) −30.3953 −1.30559
\(543\) 14.1814 0.608582
\(544\) 2.68824 0.115257
\(545\) 0 0
\(546\) −0.0512560 −0.00219355
\(547\) 31.5186 1.34764 0.673820 0.738896i \(-0.264652\pi\)
0.673820 + 0.738896i \(0.264652\pi\)
\(548\) −3.55656 −0.151929
\(549\) 21.6506 0.924027
\(550\) 0 0
\(551\) −11.4598 −0.488205
\(552\) −44.6053 −1.89853
\(553\) −0.195322 −0.00830595
\(554\) −10.7432 −0.456434
\(555\) 0 0
\(556\) 65.7762 2.78953
\(557\) 32.3589 1.37109 0.685545 0.728030i \(-0.259564\pi\)
0.685545 + 0.728030i \(0.259564\pi\)
\(558\) −36.7156 −1.55429
\(559\) 0.394267 0.0166757
\(560\) 0 0
\(561\) −1.39447 −0.0588747
\(562\) 42.6907 1.80080
\(563\) −20.8428 −0.878419 −0.439209 0.898385i \(-0.644741\pi\)
−0.439209 + 0.898385i \(0.644741\pi\)
\(564\) 66.7068 2.80886
\(565\) 0 0
\(566\) 34.5974 1.45424
\(567\) 0.300935 0.0126381
\(568\) −23.7595 −0.996926
\(569\) 26.6787 1.11843 0.559215 0.829022i \(-0.311103\pi\)
0.559215 + 0.829022i \(0.311103\pi\)
\(570\) 0 0
\(571\) 0.500659 0.0209519 0.0104760 0.999945i \(-0.496665\pi\)
0.0104760 + 0.999945i \(0.496665\pi\)
\(572\) −0.470813 −0.0196857
\(573\) 5.93842 0.248081
\(574\) 2.18223 0.0910844
\(575\) 0 0
\(576\) 7.85654 0.327356
\(577\) 9.59281 0.399354 0.199677 0.979862i \(-0.436011\pi\)
0.199677 + 0.979862i \(0.436011\pi\)
\(578\) 38.3859 1.59664
\(579\) 31.3402 1.30246
\(580\) 0 0
\(581\) −1.60114 −0.0664263
\(582\) −41.4586 −1.71851
\(583\) 3.53873 0.146559
\(584\) 31.0084 1.28314
\(585\) 0 0
\(586\) −0.809710 −0.0334488
\(587\) −19.6676 −0.811770 −0.405885 0.913924i \(-0.633037\pi\)
−0.405885 + 0.913924i \(0.633037\pi\)
\(588\) 35.8656 1.47907
\(589\) 20.8863 0.860605
\(590\) 0 0
\(591\) 1.79632 0.0738909
\(592\) −30.3556 −1.24761
\(593\) −35.9622 −1.47679 −0.738394 0.674369i \(-0.764416\pi\)
−0.738394 + 0.674369i \(0.764416\pi\)
\(594\) 12.4191 0.509562
\(595\) 0 0
\(596\) −2.27931 −0.0933640
\(597\) −9.12541 −0.373478
\(598\) 2.04892 0.0837864
\(599\) −8.60123 −0.351437 −0.175718 0.984440i \(-0.556225\pi\)
−0.175718 + 0.984440i \(0.556225\pi\)
\(600\) 0 0
\(601\) 36.8567 1.50342 0.751708 0.659496i \(-0.229230\pi\)
0.751708 + 0.659496i \(0.229230\pi\)
\(602\) 1.08057 0.0440409
\(603\) −7.37499 −0.300333
\(604\) 35.8596 1.45911
\(605\) 0 0
\(606\) −0.239752 −0.00973927
\(607\) 38.6665 1.56942 0.784712 0.619861i \(-0.212811\pi\)
0.784712 + 0.619861i \(0.212811\pi\)
\(608\) 4.55298 0.184648
\(609\) 0.893080 0.0361894
\(610\) 0 0
\(611\) −1.60631 −0.0649845
\(612\) 7.98179 0.322645
\(613\) 38.3341 1.54830 0.774150 0.633002i \(-0.218178\pi\)
0.774150 + 0.633002i \(0.218178\pi\)
\(614\) −35.7667 −1.44343
\(615\) 0 0
\(616\) −0.676449 −0.0272549
\(617\) 44.3829 1.78679 0.893395 0.449272i \(-0.148317\pi\)
0.893395 + 0.449272i \(0.148317\pi\)
\(618\) 19.3802 0.779588
\(619\) −15.6150 −0.627619 −0.313810 0.949486i \(-0.601605\pi\)
−0.313810 + 0.949486i \(0.601605\pi\)
\(620\) 0 0
\(621\) −36.6225 −1.46961
\(622\) 27.9141 1.11925
\(623\) 1.87007 0.0749226
\(624\) −0.795769 −0.0318563
\(625\) 0 0
\(626\) 48.2851 1.92986
\(627\) −2.36177 −0.0943200
\(628\) 68.1858 2.72091
\(629\) 7.26825 0.289804
\(630\) 0 0
\(631\) −7.52472 −0.299555 −0.149777 0.988720i \(-0.547856\pi\)
−0.149777 + 0.988720i \(0.547856\pi\)
\(632\) −7.87595 −0.313288
\(633\) 24.6307 0.978984
\(634\) 12.9413 0.513963
\(635\) 0 0
\(636\) 20.0796 0.796206
\(637\) −0.863650 −0.0342191
\(638\) 12.1063 0.479294
\(639\) −6.52130 −0.257979
\(640\) 0 0
\(641\) 2.42509 0.0957851 0.0478926 0.998852i \(-0.484749\pi\)
0.0478926 + 0.998852i \(0.484749\pi\)
\(642\) 6.07463 0.239747
\(643\) −12.1224 −0.478061 −0.239030 0.971012i \(-0.576830\pi\)
−0.239030 + 0.971012i \(0.576830\pi\)
\(644\) 3.80514 0.149943
\(645\) 0 0
\(646\) −6.70085 −0.263642
\(647\) −12.4628 −0.489964 −0.244982 0.969528i \(-0.578782\pi\)
−0.244982 + 0.969528i \(0.578782\pi\)
\(648\) 12.1346 0.476691
\(649\) −7.37950 −0.289671
\(650\) 0 0
\(651\) −1.62770 −0.0637945
\(652\) −5.73231 −0.224495
\(653\) 49.4695 1.93589 0.967945 0.251163i \(-0.0808131\pi\)
0.967945 + 0.251163i \(0.0808131\pi\)
\(654\) 45.1171 1.76422
\(655\) 0 0
\(656\) 33.8799 1.32279
\(657\) 8.51092 0.332043
\(658\) −4.40245 −0.171626
\(659\) 19.5067 0.759874 0.379937 0.925012i \(-0.375946\pi\)
0.379937 + 0.925012i \(0.375946\pi\)
\(660\) 0 0
\(661\) 33.2398 1.29288 0.646439 0.762966i \(-0.276258\pi\)
0.646439 + 0.762966i \(0.276258\pi\)
\(662\) −0.0431518 −0.00167714
\(663\) 0.190536 0.00739982
\(664\) −64.5624 −2.50551
\(665\) 0 0
\(666\) −21.6394 −0.838510
\(667\) −35.7001 −1.38231
\(668\) −56.3487 −2.18020
\(669\) −10.8926 −0.421131
\(670\) 0 0
\(671\) 13.0112 0.502291
\(672\) −0.354820 −0.0136875
\(673\) −28.8764 −1.11310 −0.556552 0.830813i \(-0.687876\pi\)
−0.556552 + 0.830813i \(0.687876\pi\)
\(674\) 0.866521 0.0333771
\(675\) 0 0
\(676\) −54.5840 −2.09938
\(677\) −29.4480 −1.13178 −0.565889 0.824482i \(-0.691467\pi\)
−0.565889 + 0.824482i \(0.691467\pi\)
\(678\) 37.6431 1.44567
\(679\) 1.85404 0.0711517
\(680\) 0 0
\(681\) −21.1083 −0.808873
\(682\) −22.0646 −0.844897
\(683\) −19.6959 −0.753643 −0.376821 0.926286i \(-0.622983\pi\)
−0.376821 + 0.926286i \(0.622983\pi\)
\(684\) 13.5185 0.516891
\(685\) 0 0
\(686\) −4.74033 −0.180987
\(687\) 15.8126 0.603289
\(688\) 16.7763 0.639592
\(689\) −0.483520 −0.0184206
\(690\) 0 0
\(691\) 15.6587 0.595683 0.297842 0.954615i \(-0.403733\pi\)
0.297842 + 0.954615i \(0.403733\pi\)
\(692\) 57.1735 2.17341
\(693\) −0.185666 −0.00705286
\(694\) 15.8809 0.602830
\(695\) 0 0
\(696\) 36.0115 1.36501
\(697\) −8.11209 −0.307267
\(698\) 2.41780 0.0915149
\(699\) −30.3443 −1.14773
\(700\) 0 0
\(701\) 32.6726 1.23403 0.617014 0.786952i \(-0.288342\pi\)
0.617014 + 0.786952i \(0.288342\pi\)
\(702\) −1.69690 −0.0640455
\(703\) 12.3100 0.464279
\(704\) 4.72146 0.177947
\(705\) 0 0
\(706\) 76.0887 2.86364
\(707\) 0.0107218 0.000403236 0
\(708\) −41.8730 −1.57368
\(709\) −5.63690 −0.211698 −0.105849 0.994382i \(-0.533756\pi\)
−0.105849 + 0.994382i \(0.533756\pi\)
\(710\) 0 0
\(711\) −2.16172 −0.0810710
\(712\) 75.4064 2.82597
\(713\) 65.0659 2.43674
\(714\) 0.522207 0.0195431
\(715\) 0 0
\(716\) 100.498 3.75579
\(717\) −9.19150 −0.343263
\(718\) −20.4769 −0.764190
\(719\) 13.2196 0.493006 0.246503 0.969142i \(-0.420718\pi\)
0.246503 + 0.969142i \(0.420718\pi\)
\(720\) 0 0
\(721\) −0.866693 −0.0322773
\(722\) 35.9748 1.33884
\(723\) −1.22208 −0.0454495
\(724\) −48.7814 −1.81295
\(725\) 0 0
\(726\) −30.9874 −1.15005
\(727\) −21.6517 −0.803018 −0.401509 0.915855i \(-0.631514\pi\)
−0.401509 + 0.915855i \(0.631514\pi\)
\(728\) 0.0924277 0.00342560
\(729\) 23.5217 0.871173
\(730\) 0 0
\(731\) −4.01687 −0.148569
\(732\) 73.8284 2.72878
\(733\) 37.5385 1.38651 0.693257 0.720690i \(-0.256175\pi\)
0.693257 + 0.720690i \(0.256175\pi\)
\(734\) 62.5441 2.30855
\(735\) 0 0
\(736\) 14.1836 0.522815
\(737\) −4.43208 −0.163258
\(738\) 24.1517 0.889038
\(739\) −28.8751 −1.06219 −0.531093 0.847313i \(-0.678219\pi\)
−0.531093 + 0.847313i \(0.678219\pi\)
\(740\) 0 0
\(741\) 0.322704 0.0118548
\(742\) −1.32519 −0.0486493
\(743\) 24.5272 0.899817 0.449909 0.893075i \(-0.351457\pi\)
0.449909 + 0.893075i \(0.351457\pi\)
\(744\) −65.6334 −2.40624
\(745\) 0 0
\(746\) −67.3070 −2.46429
\(747\) −17.7205 −0.648361
\(748\) 4.79673 0.175386
\(749\) −0.271660 −0.00992624
\(750\) 0 0
\(751\) 38.3355 1.39888 0.699442 0.714689i \(-0.253432\pi\)
0.699442 + 0.714689i \(0.253432\pi\)
\(752\) −68.3498 −2.49246
\(753\) 36.6963 1.33729
\(754\) −1.65417 −0.0602412
\(755\) 0 0
\(756\) −3.15140 −0.114615
\(757\) −31.6239 −1.14939 −0.574694 0.818368i \(-0.694879\pi\)
−0.574694 + 0.818368i \(0.694879\pi\)
\(758\) −57.2771 −2.08040
\(759\) −7.35748 −0.267060
\(760\) 0 0
\(761\) −28.4924 −1.03285 −0.516424 0.856333i \(-0.672737\pi\)
−0.516424 + 0.856333i \(0.672737\pi\)
\(762\) −48.6037 −1.76072
\(763\) −2.01765 −0.0730440
\(764\) −20.4271 −0.739026
\(765\) 0 0
\(766\) 9.28218 0.335379
\(767\) 1.00831 0.0364080
\(768\) 39.7755 1.43527
\(769\) −8.72245 −0.314539 −0.157270 0.987556i \(-0.550269\pi\)
−0.157270 + 0.987556i \(0.550269\pi\)
\(770\) 0 0
\(771\) −12.1408 −0.437241
\(772\) −107.805 −3.87997
\(773\) 42.2655 1.52019 0.760093 0.649814i \(-0.225153\pi\)
0.760093 + 0.649814i \(0.225153\pi\)
\(774\) 11.9592 0.429866
\(775\) 0 0
\(776\) 74.7604 2.68374
\(777\) −0.959332 −0.0344158
\(778\) −11.7693 −0.421950
\(779\) −13.7392 −0.492256
\(780\) 0 0
\(781\) −3.91904 −0.140234
\(782\) −20.8748 −0.746480
\(783\) 29.5667 1.05663
\(784\) −36.7490 −1.31246
\(785\) 0 0
\(786\) −36.9492 −1.31794
\(787\) −17.5127 −0.624261 −0.312130 0.950039i \(-0.601043\pi\)
−0.312130 + 0.950039i \(0.601043\pi\)
\(788\) −6.17903 −0.220119
\(789\) 22.5565 0.803031
\(790\) 0 0
\(791\) −1.68341 −0.0598553
\(792\) −7.48658 −0.266024
\(793\) −1.77780 −0.0631316
\(794\) 80.2580 2.84825
\(795\) 0 0
\(796\) 31.3897 1.11258
\(797\) 44.6851 1.58283 0.791413 0.611281i \(-0.209346\pi\)
0.791413 + 0.611281i \(0.209346\pi\)
\(798\) 0.884442 0.0313089
\(799\) 16.3654 0.578968
\(800\) 0 0
\(801\) 20.6969 0.731289
\(802\) 15.0034 0.529788
\(803\) 5.11472 0.180495
\(804\) −25.1486 −0.886924
\(805\) 0 0
\(806\) 3.01483 0.106193
\(807\) 1.40419 0.0494297
\(808\) 0.432335 0.0152095
\(809\) 37.7898 1.32862 0.664309 0.747458i \(-0.268726\pi\)
0.664309 + 0.747458i \(0.268726\pi\)
\(810\) 0 0
\(811\) 17.5453 0.616097 0.308049 0.951371i \(-0.400324\pi\)
0.308049 + 0.951371i \(0.400324\pi\)
\(812\) −3.07203 −0.107807
\(813\) −14.9135 −0.523038
\(814\) −13.0044 −0.455804
\(815\) 0 0
\(816\) 8.10746 0.283818
\(817\) −6.80322 −0.238015
\(818\) −46.1792 −1.61462
\(819\) 0.0253688 0.000886456 0
\(820\) 0 0
\(821\) −21.1741 −0.738980 −0.369490 0.929235i \(-0.620468\pi\)
−0.369490 + 0.929235i \(0.620468\pi\)
\(822\) −2.57526 −0.0898225
\(823\) 47.1268 1.64274 0.821369 0.570397i \(-0.193211\pi\)
0.821369 + 0.570397i \(0.193211\pi\)
\(824\) −34.9475 −1.21746
\(825\) 0 0
\(826\) 2.76350 0.0961543
\(827\) 13.3177 0.463103 0.231552 0.972823i \(-0.425620\pi\)
0.231552 + 0.972823i \(0.425620\pi\)
\(828\) 42.1132 1.46354
\(829\) −41.6063 −1.44505 −0.722523 0.691347i \(-0.757017\pi\)
−0.722523 + 0.691347i \(0.757017\pi\)
\(830\) 0 0
\(831\) −5.27114 −0.182854
\(832\) −0.645125 −0.0223657
\(833\) 8.79904 0.304869
\(834\) 47.6277 1.64921
\(835\) 0 0
\(836\) 8.12405 0.280976
\(837\) −53.8873 −1.86262
\(838\) −74.0726 −2.55880
\(839\) 20.2863 0.700359 0.350180 0.936683i \(-0.386121\pi\)
0.350180 + 0.936683i \(0.386121\pi\)
\(840\) 0 0
\(841\) −0.177928 −0.00613546
\(842\) −6.61327 −0.227908
\(843\) 20.9462 0.721426
\(844\) −84.7252 −2.91636
\(845\) 0 0
\(846\) −48.7240 −1.67517
\(847\) 1.38577 0.0476156
\(848\) −20.5741 −0.706518
\(849\) 16.9752 0.582588
\(850\) 0 0
\(851\) 38.3485 1.31457
\(852\) −22.2376 −0.761846
\(853\) 26.7153 0.914715 0.457358 0.889283i \(-0.348796\pi\)
0.457358 + 0.889283i \(0.348796\pi\)
\(854\) −4.87246 −0.166732
\(855\) 0 0
\(856\) −10.9541 −0.374404
\(857\) 1.26642 0.0432602 0.0216301 0.999766i \(-0.493114\pi\)
0.0216301 + 0.999766i \(0.493114\pi\)
\(858\) −0.340909 −0.0116385
\(859\) −45.0089 −1.53569 −0.767843 0.640638i \(-0.778670\pi\)
−0.767843 + 0.640638i \(0.778670\pi\)
\(860\) 0 0
\(861\) 1.07071 0.0364897
\(862\) −69.6188 −2.37122
\(863\) −26.1118 −0.888855 −0.444428 0.895815i \(-0.646593\pi\)
−0.444428 + 0.895815i \(0.646593\pi\)
\(864\) −11.7468 −0.399635
\(865\) 0 0
\(866\) 33.8279 1.14952
\(867\) 18.8341 0.639638
\(868\) 5.59898 0.190042
\(869\) −1.29911 −0.0440693
\(870\) 0 0
\(871\) 0.605584 0.0205194
\(872\) −81.3576 −2.75511
\(873\) 20.5196 0.694483
\(874\) −35.3548 −1.19589
\(875\) 0 0
\(876\) 29.0222 0.980568
\(877\) −18.2107 −0.614931 −0.307466 0.951559i \(-0.599481\pi\)
−0.307466 + 0.951559i \(0.599481\pi\)
\(878\) −68.0249 −2.29573
\(879\) −0.397285 −0.0134001
\(880\) 0 0
\(881\) 7.40050 0.249329 0.124665 0.992199i \(-0.460214\pi\)
0.124665 + 0.992199i \(0.460214\pi\)
\(882\) −26.1970 −0.882098
\(883\) 1.57266 0.0529243 0.0264621 0.999650i \(-0.491576\pi\)
0.0264621 + 0.999650i \(0.491576\pi\)
\(884\) −0.655410 −0.0220438
\(885\) 0 0
\(886\) 10.1124 0.339732
\(887\) 1.08367 0.0363861 0.0181930 0.999834i \(-0.494209\pi\)
0.0181930 + 0.999834i \(0.494209\pi\)
\(888\) −38.6830 −1.29812
\(889\) 2.17358 0.0728994
\(890\) 0 0
\(891\) 2.00155 0.0670545
\(892\) 37.4684 1.25453
\(893\) 27.7175 0.927532
\(894\) −1.65042 −0.0551981
\(895\) 0 0
\(896\) −2.34879 −0.0784676
\(897\) 1.00530 0.0335660
\(898\) 3.82503 0.127643
\(899\) −52.5301 −1.75198
\(900\) 0 0
\(901\) 4.92620 0.164115
\(902\) 14.5142 0.483271
\(903\) 0.530184 0.0176434
\(904\) −67.8801 −2.25766
\(905\) 0 0
\(906\) 25.9655 0.862646
\(907\) −39.1868 −1.30118 −0.650588 0.759431i \(-0.725478\pi\)
−0.650588 + 0.759431i \(0.725478\pi\)
\(908\) 72.6088 2.40961
\(909\) 0.118664 0.00393582
\(910\) 0 0
\(911\) 11.8818 0.393662 0.196831 0.980437i \(-0.436935\pi\)
0.196831 + 0.980437i \(0.436935\pi\)
\(912\) 13.7313 0.454689
\(913\) −10.6493 −0.352441
\(914\) −11.2258 −0.371317
\(915\) 0 0
\(916\) −54.3925 −1.79718
\(917\) 1.65239 0.0545666
\(918\) 17.2884 0.570602
\(919\) −28.1347 −0.928077 −0.464039 0.885815i \(-0.653600\pi\)
−0.464039 + 0.885815i \(0.653600\pi\)
\(920\) 0 0
\(921\) −17.5490 −0.578258
\(922\) −43.7919 −1.44221
\(923\) 0.535485 0.0176257
\(924\) −0.633118 −0.0208281
\(925\) 0 0
\(926\) −104.880 −3.44657
\(927\) −9.59210 −0.315046
\(928\) −11.4510 −0.375897
\(929\) 59.5689 1.95439 0.977197 0.212335i \(-0.0681068\pi\)
0.977197 + 0.212335i \(0.0681068\pi\)
\(930\) 0 0
\(931\) 14.9026 0.488413
\(932\) 104.379 3.41904
\(933\) 13.6961 0.448389
\(934\) 26.4932 0.866885
\(935\) 0 0
\(936\) 1.02294 0.0334359
\(937\) −25.8722 −0.845209 −0.422605 0.906314i \(-0.638884\pi\)
−0.422605 + 0.906314i \(0.638884\pi\)
\(938\) 1.65974 0.0541923
\(939\) 23.6911 0.773130
\(940\) 0 0
\(941\) −43.2143 −1.40875 −0.704373 0.709830i \(-0.748772\pi\)
−0.704373 + 0.709830i \(0.748772\pi\)
\(942\) 49.3724 1.60864
\(943\) −42.8008 −1.39378
\(944\) 42.9043 1.39642
\(945\) 0 0
\(946\) 7.18702 0.233670
\(947\) 53.0980 1.72545 0.862726 0.505672i \(-0.168755\pi\)
0.862726 + 0.505672i \(0.168755\pi\)
\(948\) −7.37145 −0.239414
\(949\) −0.698859 −0.0226859
\(950\) 0 0
\(951\) 6.34963 0.205901
\(952\) −0.941672 −0.0305198
\(953\) 28.8397 0.934210 0.467105 0.884202i \(-0.345297\pi\)
0.467105 + 0.884202i \(0.345297\pi\)
\(954\) −14.6665 −0.474846
\(955\) 0 0
\(956\) 31.6171 1.02257
\(957\) 5.93997 0.192012
\(958\) −60.6000 −1.95790
\(959\) 0.115167 0.00371893
\(960\) 0 0
\(961\) 64.7397 2.08838
\(962\) 1.77688 0.0572889
\(963\) −3.00659 −0.0968860
\(964\) 4.20371 0.135393
\(965\) 0 0
\(966\) 2.75525 0.0886487
\(967\) −6.08196 −0.195583 −0.0977914 0.995207i \(-0.531178\pi\)
−0.0977914 + 0.995207i \(0.531178\pi\)
\(968\) 55.8782 1.79599
\(969\) −3.28778 −0.105619
\(970\) 0 0
\(971\) 2.57155 0.0825251 0.0412626 0.999148i \(-0.486862\pi\)
0.0412626 + 0.999148i \(0.486862\pi\)
\(972\) −58.0963 −1.86344
\(973\) −2.12993 −0.0682824
\(974\) 37.8035 1.21130
\(975\) 0 0
\(976\) −75.6468 −2.42139
\(977\) −52.2605 −1.67196 −0.835980 0.548760i \(-0.815100\pi\)
−0.835980 + 0.548760i \(0.815100\pi\)
\(978\) −4.15069 −0.132724
\(979\) 12.4380 0.397520
\(980\) 0 0
\(981\) −22.3303 −0.712953
\(982\) −24.9555 −0.796363
\(983\) −5.96528 −0.190263 −0.0951314 0.995465i \(-0.530327\pi\)
−0.0951314 + 0.995465i \(0.530327\pi\)
\(984\) 43.1741 1.37634
\(985\) 0 0
\(986\) 16.8530 0.536709
\(987\) −2.16007 −0.0687557
\(988\) −1.11004 −0.0353152
\(989\) −21.1937 −0.673920
\(990\) 0 0
\(991\) 1.36771 0.0434466 0.0217233 0.999764i \(-0.493085\pi\)
0.0217233 + 0.999764i \(0.493085\pi\)
\(992\) 20.8702 0.662629
\(993\) −0.0211725 −0.000671888 0
\(994\) 1.46761 0.0465499
\(995\) 0 0
\(996\) −60.4268 −1.91470
\(997\) 17.2016 0.544780 0.272390 0.962187i \(-0.412186\pi\)
0.272390 + 0.962187i \(0.412186\pi\)
\(998\) 19.5021 0.617329
\(999\) −31.7601 −1.00484
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 \(a_p\))