Properties

Label 6025.2.a.p.1.18
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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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: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.760721 q^{2} +1.12938 q^{3} -1.42130 q^{4} -0.859145 q^{6} +2.53853 q^{7} +2.60266 q^{8} -1.72450 q^{9} +O(q^{10})\) \(q-0.760721 q^{2} +1.12938 q^{3} -1.42130 q^{4} -0.859145 q^{6} +2.53853 q^{7} +2.60266 q^{8} -1.72450 q^{9} -2.06253 q^{11} -1.60519 q^{12} -4.79651 q^{13} -1.93111 q^{14} +0.862709 q^{16} -1.95237 q^{17} +1.31186 q^{18} -1.03825 q^{19} +2.86697 q^{21} +1.56901 q^{22} +2.68585 q^{23} +2.93940 q^{24} +3.64880 q^{26} -5.33576 q^{27} -3.60802 q^{28} +5.84308 q^{29} +7.76074 q^{31} -5.86160 q^{32} -2.32939 q^{33} +1.48521 q^{34} +2.45103 q^{36} +9.08041 q^{37} +0.789817 q^{38} -5.41709 q^{39} +9.18849 q^{41} -2.18096 q^{42} +3.23632 q^{43} +2.93148 q^{44} -2.04318 q^{46} -4.22721 q^{47} +0.974328 q^{48} -0.555881 q^{49} -2.20497 q^{51} +6.81729 q^{52} -6.32114 q^{53} +4.05903 q^{54} +6.60692 q^{56} -1.17258 q^{57} -4.44495 q^{58} +2.97769 q^{59} -11.0977 q^{61} -5.90376 q^{62} -4.37768 q^{63} +2.73362 q^{64} +1.77202 q^{66} -1.40319 q^{67} +2.77490 q^{68} +3.03335 q^{69} -6.51732 q^{71} -4.48827 q^{72} +1.89995 q^{73} -6.90766 q^{74} +1.47566 q^{76} -5.23580 q^{77} +4.12089 q^{78} -13.9020 q^{79} -0.852626 q^{81} -6.98988 q^{82} -6.49943 q^{83} -4.07483 q^{84} -2.46194 q^{86} +6.59906 q^{87} -5.36807 q^{88} -0.236437 q^{89} -12.1761 q^{91} -3.81741 q^{92} +8.76484 q^{93} +3.21573 q^{94} -6.61998 q^{96} -13.5524 q^{97} +0.422870 q^{98} +3.55683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.760721 −0.537911 −0.268956 0.963153i \(-0.586678\pi\)
−0.268956 + 0.963153i \(0.586678\pi\)
\(3\) 1.12938 0.652049 0.326025 0.945361i \(-0.394291\pi\)
0.326025 + 0.945361i \(0.394291\pi\)
\(4\) −1.42130 −0.710652
\(5\) 0 0
\(6\) −0.859145 −0.350745
\(7\) 2.53853 0.959473 0.479737 0.877413i \(-0.340732\pi\)
0.479737 + 0.877413i \(0.340732\pi\)
\(8\) 2.60266 0.920179
\(9\) −1.72450 −0.574832
\(10\) 0 0
\(11\) −2.06253 −0.621877 −0.310939 0.950430i \(-0.600643\pi\)
−0.310939 + 0.950430i \(0.600643\pi\)
\(12\) −1.60519 −0.463380
\(13\) −4.79651 −1.33031 −0.665156 0.746705i \(-0.731635\pi\)
−0.665156 + 0.746705i \(0.731635\pi\)
\(14\) −1.93111 −0.516111
\(15\) 0 0
\(16\) 0.862709 0.215677
\(17\) −1.95237 −0.473518 −0.236759 0.971568i \(-0.576085\pi\)
−0.236759 + 0.971568i \(0.576085\pi\)
\(18\) 1.31186 0.309209
\(19\) −1.03825 −0.238190 −0.119095 0.992883i \(-0.537999\pi\)
−0.119095 + 0.992883i \(0.537999\pi\)
\(20\) 0 0
\(21\) 2.86697 0.625623
\(22\) 1.56901 0.334515
\(23\) 2.68585 0.560039 0.280019 0.959994i \(-0.409659\pi\)
0.280019 + 0.959994i \(0.409659\pi\)
\(24\) 2.93940 0.600002
\(25\) 0 0
\(26\) 3.64880 0.715589
\(27\) −5.33576 −1.02687
\(28\) −3.60802 −0.681851
\(29\) 5.84308 1.08503 0.542516 0.840046i \(-0.317472\pi\)
0.542516 + 0.840046i \(0.317472\pi\)
\(30\) 0 0
\(31\) 7.76074 1.39387 0.696935 0.717134i \(-0.254547\pi\)
0.696935 + 0.717134i \(0.254547\pi\)
\(32\) −5.86160 −1.03619
\(33\) −2.32939 −0.405494
\(34\) 1.48521 0.254711
\(35\) 0 0
\(36\) 2.45103 0.408505
\(37\) 9.08041 1.49281 0.746405 0.665492i \(-0.231778\pi\)
0.746405 + 0.665492i \(0.231778\pi\)
\(38\) 0.789817 0.128125
\(39\) −5.41709 −0.867428
\(40\) 0 0
\(41\) 9.18849 1.43500 0.717501 0.696558i \(-0.245286\pi\)
0.717501 + 0.696558i \(0.245286\pi\)
\(42\) −2.18096 −0.336530
\(43\) 3.23632 0.493534 0.246767 0.969075i \(-0.420632\pi\)
0.246767 + 0.969075i \(0.420632\pi\)
\(44\) 2.93148 0.441938
\(45\) 0 0
\(46\) −2.04318 −0.301251
\(47\) −4.22721 −0.616603 −0.308301 0.951289i \(-0.599761\pi\)
−0.308301 + 0.951289i \(0.599761\pi\)
\(48\) 0.974328 0.140632
\(49\) −0.555881 −0.0794116
\(50\) 0 0
\(51\) −2.20497 −0.308757
\(52\) 6.81729 0.945388
\(53\) −6.32114 −0.868276 −0.434138 0.900846i \(-0.642947\pi\)
−0.434138 + 0.900846i \(0.642947\pi\)
\(54\) 4.05903 0.552364
\(55\) 0 0
\(56\) 6.60692 0.882887
\(57\) −1.17258 −0.155312
\(58\) −4.44495 −0.583651
\(59\) 2.97769 0.387662 0.193831 0.981035i \(-0.437909\pi\)
0.193831 + 0.981035i \(0.437909\pi\)
\(60\) 0 0
\(61\) −11.0977 −1.42091 −0.710456 0.703741i \(-0.751511\pi\)
−0.710456 + 0.703741i \(0.751511\pi\)
\(62\) −5.90376 −0.749778
\(63\) −4.37768 −0.551536
\(64\) 2.73362 0.341703
\(65\) 0 0
\(66\) 1.77202 0.218120
\(67\) −1.40319 −0.171427 −0.0857134 0.996320i \(-0.527317\pi\)
−0.0857134 + 0.996320i \(0.527317\pi\)
\(68\) 2.77490 0.336506
\(69\) 3.03335 0.365173
\(70\) 0 0
\(71\) −6.51732 −0.773464 −0.386732 0.922192i \(-0.626396\pi\)
−0.386732 + 0.922192i \(0.626396\pi\)
\(72\) −4.48827 −0.528948
\(73\) 1.89995 0.222373 0.111186 0.993800i \(-0.464535\pi\)
0.111186 + 0.993800i \(0.464535\pi\)
\(74\) −6.90766 −0.802999
\(75\) 0 0
\(76\) 1.47566 0.169270
\(77\) −5.23580 −0.596674
\(78\) 4.12089 0.466599
\(79\) −13.9020 −1.56410 −0.782050 0.623215i \(-0.785826\pi\)
−0.782050 + 0.623215i \(0.785826\pi\)
\(80\) 0 0
\(81\) −0.852626 −0.0947362
\(82\) −6.98988 −0.771904
\(83\) −6.49943 −0.713405 −0.356703 0.934218i \(-0.616099\pi\)
−0.356703 + 0.934218i \(0.616099\pi\)
\(84\) −4.07483 −0.444600
\(85\) 0 0
\(86\) −2.46194 −0.265477
\(87\) 6.59906 0.707494
\(88\) −5.36807 −0.572238
\(89\) −0.236437 −0.0250623 −0.0125311 0.999921i \(-0.503989\pi\)
−0.0125311 + 0.999921i \(0.503989\pi\)
\(90\) 0 0
\(91\) −12.1761 −1.27640
\(92\) −3.81741 −0.397992
\(93\) 8.76484 0.908871
\(94\) 3.21573 0.331677
\(95\) 0 0
\(96\) −6.61998 −0.675649
\(97\) −13.5524 −1.37604 −0.688020 0.725691i \(-0.741520\pi\)
−0.688020 + 0.725691i \(0.741520\pi\)
\(98\) 0.422870 0.0427164
\(99\) 3.55683 0.357475
\(100\) 0 0
\(101\) −12.0004 −1.19409 −0.597044 0.802209i \(-0.703658\pi\)
−0.597044 + 0.802209i \(0.703658\pi\)
\(102\) 1.67737 0.166084
\(103\) 13.6216 1.34218 0.671088 0.741377i \(-0.265827\pi\)
0.671088 + 0.741377i \(0.265827\pi\)
\(104\) −12.4837 −1.22412
\(105\) 0 0
\(106\) 4.80863 0.467055
\(107\) −13.8286 −1.33686 −0.668432 0.743773i \(-0.733034\pi\)
−0.668432 + 0.743773i \(0.733034\pi\)
\(108\) 7.58373 0.729745
\(109\) 13.7652 1.31846 0.659232 0.751940i \(-0.270882\pi\)
0.659232 + 0.751940i \(0.270882\pi\)
\(110\) 0 0
\(111\) 10.2553 0.973386
\(112\) 2.19001 0.206936
\(113\) 6.68313 0.628696 0.314348 0.949308i \(-0.398214\pi\)
0.314348 + 0.949308i \(0.398214\pi\)
\(114\) 0.892005 0.0835439
\(115\) 0 0
\(116\) −8.30478 −0.771080
\(117\) 8.27155 0.764705
\(118\) −2.26519 −0.208528
\(119\) −4.95613 −0.454328
\(120\) 0 0
\(121\) −6.74596 −0.613269
\(122\) 8.44224 0.764325
\(123\) 10.3773 0.935692
\(124\) −11.0304 −0.990556
\(125\) 0 0
\(126\) 3.33019 0.296677
\(127\) 4.63183 0.411008 0.205504 0.978656i \(-0.434117\pi\)
0.205504 + 0.978656i \(0.434117\pi\)
\(128\) 9.64367 0.852388
\(129\) 3.65504 0.321808
\(130\) 0 0
\(131\) −10.6049 −0.926558 −0.463279 0.886212i \(-0.653327\pi\)
−0.463279 + 0.886212i \(0.653327\pi\)
\(132\) 3.31077 0.288165
\(133\) −2.63562 −0.228537
\(134\) 1.06744 0.0922124
\(135\) 0 0
\(136\) −5.08134 −0.435721
\(137\) −18.3739 −1.56979 −0.784895 0.619629i \(-0.787283\pi\)
−0.784895 + 0.619629i \(0.787283\pi\)
\(138\) −2.30754 −0.196431
\(139\) −5.98608 −0.507733 −0.253866 0.967239i \(-0.581702\pi\)
−0.253866 + 0.967239i \(0.581702\pi\)
\(140\) 0 0
\(141\) −4.77414 −0.402055
\(142\) 4.95787 0.416055
\(143\) 9.89295 0.827290
\(144\) −1.48774 −0.123978
\(145\) 0 0
\(146\) −1.44534 −0.119617
\(147\) −0.627802 −0.0517802
\(148\) −12.9060 −1.06087
\(149\) −6.99343 −0.572924 −0.286462 0.958092i \(-0.592479\pi\)
−0.286462 + 0.958092i \(0.592479\pi\)
\(150\) 0 0
\(151\) −23.3270 −1.89833 −0.949164 0.314783i \(-0.898068\pi\)
−0.949164 + 0.314783i \(0.898068\pi\)
\(152\) −2.70220 −0.219178
\(153\) 3.36685 0.272193
\(154\) 3.98298 0.320958
\(155\) 0 0
\(156\) 7.69932 0.616439
\(157\) −6.99961 −0.558630 −0.279315 0.960200i \(-0.590107\pi\)
−0.279315 + 0.960200i \(0.590107\pi\)
\(158\) 10.5756 0.841347
\(159\) −7.13899 −0.566158
\(160\) 0 0
\(161\) 6.81811 0.537342
\(162\) 0.648610 0.0509596
\(163\) −7.32590 −0.573809 −0.286904 0.957959i \(-0.592626\pi\)
−0.286904 + 0.957959i \(0.592626\pi\)
\(164\) −13.0596 −1.01979
\(165\) 0 0
\(166\) 4.94426 0.383749
\(167\) 10.8149 0.836882 0.418441 0.908244i \(-0.362577\pi\)
0.418441 + 0.908244i \(0.362577\pi\)
\(168\) 7.46174 0.575685
\(169\) 10.0065 0.769728
\(170\) 0 0
\(171\) 1.79045 0.136919
\(172\) −4.59979 −0.350731
\(173\) 8.58809 0.652941 0.326470 0.945207i \(-0.394141\pi\)
0.326470 + 0.945207i \(0.394141\pi\)
\(174\) −5.02005 −0.380569
\(175\) 0 0
\(176\) −1.77936 −0.134125
\(177\) 3.36295 0.252775
\(178\) 0.179863 0.0134813
\(179\) 7.06513 0.528073 0.264036 0.964513i \(-0.414946\pi\)
0.264036 + 0.964513i \(0.414946\pi\)
\(180\) 0 0
\(181\) −22.5251 −1.67427 −0.837137 0.546993i \(-0.815773\pi\)
−0.837137 + 0.546993i \(0.815773\pi\)
\(182\) 9.26259 0.686589
\(183\) −12.5335 −0.926505
\(184\) 6.99035 0.515336
\(185\) 0 0
\(186\) −6.66760 −0.488892
\(187\) 4.02682 0.294470
\(188\) 6.00815 0.438190
\(189\) −13.5450 −0.985252
\(190\) 0 0
\(191\) 16.0033 1.15796 0.578981 0.815341i \(-0.303451\pi\)
0.578981 + 0.815341i \(0.303451\pi\)
\(192\) 3.08731 0.222807
\(193\) −15.9736 −1.14981 −0.574903 0.818221i \(-0.694960\pi\)
−0.574903 + 0.818221i \(0.694960\pi\)
\(194\) 10.3096 0.740188
\(195\) 0 0
\(196\) 0.790075 0.0564339
\(197\) 24.2137 1.72516 0.862579 0.505922i \(-0.168848\pi\)
0.862579 + 0.505922i \(0.168848\pi\)
\(198\) −2.70576 −0.192290
\(199\) −12.3227 −0.873535 −0.436768 0.899574i \(-0.643877\pi\)
−0.436768 + 0.899574i \(0.643877\pi\)
\(200\) 0 0
\(201\) −1.58474 −0.111779
\(202\) 9.12899 0.642313
\(203\) 14.8328 1.04106
\(204\) 3.13393 0.219419
\(205\) 0 0
\(206\) −10.3622 −0.721972
\(207\) −4.63174 −0.321928
\(208\) −4.13799 −0.286918
\(209\) 2.14142 0.148125
\(210\) 0 0
\(211\) 26.5630 1.82867 0.914335 0.404959i \(-0.132714\pi\)
0.914335 + 0.404959i \(0.132714\pi\)
\(212\) 8.98426 0.617042
\(213\) −7.36055 −0.504336
\(214\) 10.5197 0.719114
\(215\) 0 0
\(216\) −13.8872 −0.944902
\(217\) 19.7008 1.33738
\(218\) −10.4715 −0.709216
\(219\) 2.14577 0.144998
\(220\) 0 0
\(221\) 9.36453 0.629927
\(222\) −7.80139 −0.523595
\(223\) −8.33195 −0.557949 −0.278974 0.960299i \(-0.589994\pi\)
−0.278974 + 0.960299i \(0.589994\pi\)
\(224\) −14.8798 −0.994200
\(225\) 0 0
\(226\) −5.08400 −0.338183
\(227\) 4.33870 0.287970 0.143985 0.989580i \(-0.454008\pi\)
0.143985 + 0.989580i \(0.454008\pi\)
\(228\) 1.66659 0.110373
\(229\) 29.3533 1.93972 0.969859 0.243665i \(-0.0783499\pi\)
0.969859 + 0.243665i \(0.0783499\pi\)
\(230\) 0 0
\(231\) −5.91321 −0.389061
\(232\) 15.2075 0.998423
\(233\) −13.0291 −0.853563 −0.426781 0.904355i \(-0.640353\pi\)
−0.426781 + 0.904355i \(0.640353\pi\)
\(234\) −6.29235 −0.411344
\(235\) 0 0
\(236\) −4.23220 −0.275492
\(237\) −15.7007 −1.01987
\(238\) 3.77024 0.244388
\(239\) 7.27224 0.470402 0.235201 0.971947i \(-0.424425\pi\)
0.235201 + 0.971947i \(0.424425\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 5.13179 0.329884
\(243\) 15.0443 0.965095
\(244\) 15.7732 1.00977
\(245\) 0 0
\(246\) −7.89425 −0.503319
\(247\) 4.97996 0.316867
\(248\) 20.1985 1.28261
\(249\) −7.34034 −0.465175
\(250\) 0 0
\(251\) −27.8592 −1.75846 −0.879229 0.476400i \(-0.841941\pi\)
−0.879229 + 0.476400i \(0.841941\pi\)
\(252\) 6.22201 0.391950
\(253\) −5.53966 −0.348275
\(254\) −3.52353 −0.221086
\(255\) 0 0
\(256\) −12.8034 −0.800212
\(257\) −15.9448 −0.994607 −0.497303 0.867577i \(-0.665676\pi\)
−0.497303 + 0.867577i \(0.665676\pi\)
\(258\) −2.78047 −0.173104
\(259\) 23.0509 1.43231
\(260\) 0 0
\(261\) −10.0764 −0.623711
\(262\) 8.06741 0.498406
\(263\) 0.603786 0.0372310 0.0186155 0.999827i \(-0.494074\pi\)
0.0186155 + 0.999827i \(0.494074\pi\)
\(264\) −6.06260 −0.373127
\(265\) 0 0
\(266\) 2.00497 0.122933
\(267\) −0.267028 −0.0163418
\(268\) 1.99436 0.121825
\(269\) −23.5550 −1.43618 −0.718088 0.695952i \(-0.754982\pi\)
−0.718088 + 0.695952i \(0.754982\pi\)
\(270\) 0 0
\(271\) −9.80993 −0.595911 −0.297955 0.954580i \(-0.596305\pi\)
−0.297955 + 0.954580i \(0.596305\pi\)
\(272\) −1.68432 −0.102127
\(273\) −13.7514 −0.832274
\(274\) 13.9774 0.844407
\(275\) 0 0
\(276\) −4.31131 −0.259511
\(277\) 7.76495 0.466551 0.233275 0.972411i \(-0.425056\pi\)
0.233275 + 0.972411i \(0.425056\pi\)
\(278\) 4.55374 0.273115
\(279\) −13.3834 −0.801241
\(280\) 0 0
\(281\) −20.7632 −1.23863 −0.619314 0.785143i \(-0.712589\pi\)
−0.619314 + 0.785143i \(0.712589\pi\)
\(282\) 3.63179 0.216270
\(283\) 8.45091 0.502355 0.251177 0.967941i \(-0.419182\pi\)
0.251177 + 0.967941i \(0.419182\pi\)
\(284\) 9.26309 0.549663
\(285\) 0 0
\(286\) −7.52578 −0.445009
\(287\) 23.3252 1.37685
\(288\) 10.1083 0.595637
\(289\) −13.1883 −0.775781
\(290\) 0 0
\(291\) −15.3059 −0.897246
\(292\) −2.70041 −0.158030
\(293\) −13.4756 −0.787253 −0.393626 0.919271i \(-0.628780\pi\)
−0.393626 + 0.919271i \(0.628780\pi\)
\(294\) 0.477582 0.0278532
\(295\) 0 0
\(296\) 23.6332 1.37365
\(297\) 11.0052 0.638586
\(298\) 5.32005 0.308182
\(299\) −12.8827 −0.745026
\(300\) 0 0
\(301\) 8.21548 0.473533
\(302\) 17.7454 1.02113
\(303\) −13.5531 −0.778604
\(304\) −0.895705 −0.0513722
\(305\) 0 0
\(306\) −2.56123 −0.146416
\(307\) 9.67527 0.552197 0.276099 0.961129i \(-0.410958\pi\)
0.276099 + 0.961129i \(0.410958\pi\)
\(308\) 7.44165 0.424028
\(309\) 15.3840 0.875165
\(310\) 0 0
\(311\) −34.8734 −1.97749 −0.988746 0.149607i \(-0.952199\pi\)
−0.988746 + 0.149607i \(0.952199\pi\)
\(312\) −14.0988 −0.798189
\(313\) 27.2238 1.53878 0.769391 0.638779i \(-0.220560\pi\)
0.769391 + 0.638779i \(0.220560\pi\)
\(314\) 5.32475 0.300493
\(315\) 0 0
\(316\) 19.7590 1.11153
\(317\) 2.90326 0.163063 0.0815316 0.996671i \(-0.474019\pi\)
0.0815316 + 0.996671i \(0.474019\pi\)
\(318\) 5.43078 0.304543
\(319\) −12.0515 −0.674756
\(320\) 0 0
\(321\) −15.6178 −0.871701
\(322\) −5.18668 −0.289042
\(323\) 2.02704 0.112787
\(324\) 1.21184 0.0673244
\(325\) 0 0
\(326\) 5.57297 0.308658
\(327\) 15.5461 0.859703
\(328\) 23.9145 1.32046
\(329\) −10.7309 −0.591614
\(330\) 0 0
\(331\) 4.82961 0.265459 0.132730 0.991152i \(-0.457626\pi\)
0.132730 + 0.991152i \(0.457626\pi\)
\(332\) 9.23766 0.506983
\(333\) −15.6591 −0.858115
\(334\) −8.22712 −0.450168
\(335\) 0 0
\(336\) 2.47336 0.134933
\(337\) −22.1454 −1.20634 −0.603168 0.797614i \(-0.706095\pi\)
−0.603168 + 0.797614i \(0.706095\pi\)
\(338\) −7.61213 −0.414045
\(339\) 7.54781 0.409941
\(340\) 0 0
\(341\) −16.0068 −0.866816
\(342\) −1.36204 −0.0736505
\(343\) −19.1808 −1.03567
\(344\) 8.42303 0.454139
\(345\) 0 0
\(346\) −6.53315 −0.351224
\(347\) −20.1874 −1.08372 −0.541859 0.840470i \(-0.682279\pi\)
−0.541859 + 0.840470i \(0.682279\pi\)
\(348\) −9.37927 −0.502782
\(349\) 4.22280 0.226041 0.113021 0.993593i \(-0.463947\pi\)
0.113021 + 0.993593i \(0.463947\pi\)
\(350\) 0 0
\(351\) 25.5930 1.36605
\(352\) 12.0897 0.644385
\(353\) −20.2277 −1.07661 −0.538305 0.842750i \(-0.680935\pi\)
−0.538305 + 0.842750i \(0.680935\pi\)
\(354\) −2.55826 −0.135970
\(355\) 0 0
\(356\) 0.336048 0.0178105
\(357\) −5.59737 −0.296244
\(358\) −5.37460 −0.284056
\(359\) −23.0788 −1.21805 −0.609027 0.793149i \(-0.708440\pi\)
−0.609027 + 0.793149i \(0.708440\pi\)
\(360\) 0 0
\(361\) −17.9220 −0.943265
\(362\) 17.1353 0.900611
\(363\) −7.61876 −0.399881
\(364\) 17.3059 0.907074
\(365\) 0 0
\(366\) 9.53452 0.498377
\(367\) 15.5656 0.812516 0.406258 0.913758i \(-0.366833\pi\)
0.406258 + 0.913758i \(0.366833\pi\)
\(368\) 2.31711 0.120788
\(369\) −15.8455 −0.824885
\(370\) 0 0
\(371\) −16.0464 −0.833087
\(372\) −12.4575 −0.645891
\(373\) −22.9059 −1.18602 −0.593011 0.805194i \(-0.702061\pi\)
−0.593011 + 0.805194i \(0.702061\pi\)
\(374\) −3.06329 −0.158399
\(375\) 0 0
\(376\) −11.0020 −0.567385
\(377\) −28.0263 −1.44343
\(378\) 10.3040 0.529978
\(379\) −9.63127 −0.494725 −0.247363 0.968923i \(-0.579564\pi\)
−0.247363 + 0.968923i \(0.579564\pi\)
\(380\) 0 0
\(381\) 5.23110 0.267997
\(382\) −12.1741 −0.622880
\(383\) −1.19113 −0.0608640 −0.0304320 0.999537i \(-0.509688\pi\)
−0.0304320 + 0.999537i \(0.509688\pi\)
\(384\) 10.8914 0.555799
\(385\) 0 0
\(386\) 12.1515 0.618494
\(387\) −5.58102 −0.283699
\(388\) 19.2621 0.977885
\(389\) −12.0151 −0.609188 −0.304594 0.952482i \(-0.598521\pi\)
−0.304594 + 0.952482i \(0.598521\pi\)
\(390\) 0 0
\(391\) −5.24376 −0.265189
\(392\) −1.44677 −0.0730728
\(393\) −11.9770 −0.604161
\(394\) −18.4199 −0.927982
\(395\) 0 0
\(396\) −5.05533 −0.254040
\(397\) 1.30174 0.0653324 0.0326662 0.999466i \(-0.489600\pi\)
0.0326662 + 0.999466i \(0.489600\pi\)
\(398\) 9.37416 0.469884
\(399\) −2.97662 −0.149017
\(400\) 0 0
\(401\) 17.7958 0.888680 0.444340 0.895858i \(-0.353438\pi\)
0.444340 + 0.895858i \(0.353438\pi\)
\(402\) 1.20554 0.0601270
\(403\) −37.2244 −1.85428
\(404\) 17.0563 0.848580
\(405\) 0 0
\(406\) −11.2836 −0.559997
\(407\) −18.7286 −0.928345
\(408\) −5.73877 −0.284112
\(409\) 1.21607 0.0601305 0.0300653 0.999548i \(-0.490428\pi\)
0.0300653 + 0.999548i \(0.490428\pi\)
\(410\) 0 0
\(411\) −20.7512 −1.02358
\(412\) −19.3604 −0.953820
\(413\) 7.55894 0.371951
\(414\) 3.52346 0.173169
\(415\) 0 0
\(416\) 28.1152 1.37846
\(417\) −6.76057 −0.331067
\(418\) −1.62902 −0.0796781
\(419\) −23.5246 −1.14925 −0.574626 0.818416i \(-0.694853\pi\)
−0.574626 + 0.818416i \(0.694853\pi\)
\(420\) 0 0
\(421\) 24.1129 1.17519 0.587596 0.809154i \(-0.300074\pi\)
0.587596 + 0.809154i \(0.300074\pi\)
\(422\) −20.2070 −0.983662
\(423\) 7.28982 0.354443
\(424\) −16.4518 −0.798969
\(425\) 0 0
\(426\) 5.59933 0.271288
\(427\) −28.1718 −1.36333
\(428\) 19.6547 0.950045
\(429\) 11.1729 0.539434
\(430\) 0 0
\(431\) 9.23057 0.444621 0.222310 0.974976i \(-0.428640\pi\)
0.222310 + 0.974976i \(0.428640\pi\)
\(432\) −4.60321 −0.221472
\(433\) −40.5437 −1.94841 −0.974203 0.225673i \(-0.927542\pi\)
−0.974203 + 0.225673i \(0.927542\pi\)
\(434\) −14.9869 −0.719392
\(435\) 0 0
\(436\) −19.5645 −0.936968
\(437\) −2.78858 −0.133396
\(438\) −1.63234 −0.0779960
\(439\) 19.5448 0.932823 0.466411 0.884568i \(-0.345547\pi\)
0.466411 + 0.884568i \(0.345547\pi\)
\(440\) 0 0
\(441\) 0.958614 0.0456483
\(442\) −7.12380 −0.338845
\(443\) 38.3533 1.82222 0.911109 0.412165i \(-0.135227\pi\)
0.911109 + 0.412165i \(0.135227\pi\)
\(444\) −14.5758 −0.691738
\(445\) 0 0
\(446\) 6.33829 0.300127
\(447\) −7.89825 −0.373574
\(448\) 6.93938 0.327855
\(449\) −7.15454 −0.337643 −0.168822 0.985647i \(-0.553996\pi\)
−0.168822 + 0.985647i \(0.553996\pi\)
\(450\) 0 0
\(451\) −18.9516 −0.892395
\(452\) −9.49876 −0.446784
\(453\) −26.3451 −1.23780
\(454\) −3.30054 −0.154902
\(455\) 0 0
\(456\) −3.05182 −0.142915
\(457\) −13.2079 −0.617838 −0.308919 0.951088i \(-0.599967\pi\)
−0.308919 + 0.951088i \(0.599967\pi\)
\(458\) −22.3297 −1.04340
\(459\) 10.4174 0.486241
\(460\) 0 0
\(461\) 25.6149 1.19300 0.596502 0.802612i \(-0.296557\pi\)
0.596502 + 0.802612i \(0.296557\pi\)
\(462\) 4.49831 0.209280
\(463\) 36.7408 1.70749 0.853745 0.520691i \(-0.174326\pi\)
0.853745 + 0.520691i \(0.174326\pi\)
\(464\) 5.04087 0.234017
\(465\) 0 0
\(466\) 9.91149 0.459141
\(467\) −11.5404 −0.534028 −0.267014 0.963693i \(-0.586037\pi\)
−0.267014 + 0.963693i \(0.586037\pi\)
\(468\) −11.7564 −0.543439
\(469\) −3.56203 −0.164479
\(470\) 0 0
\(471\) −7.90524 −0.364254
\(472\) 7.74990 0.356718
\(473\) −6.67502 −0.306918
\(474\) 11.9439 0.548600
\(475\) 0 0
\(476\) 7.04417 0.322869
\(477\) 10.9008 0.499113
\(478\) −5.53215 −0.253035
\(479\) 29.9925 1.37039 0.685197 0.728358i \(-0.259716\pi\)
0.685197 + 0.728358i \(0.259716\pi\)
\(480\) 0 0
\(481\) −43.5542 −1.98590
\(482\) −0.760721 −0.0346499
\(483\) 7.70025 0.350373
\(484\) 9.58805 0.435820
\(485\) 0 0
\(486\) −11.4446 −0.519135
\(487\) 8.15043 0.369331 0.184666 0.982801i \(-0.440880\pi\)
0.184666 + 0.982801i \(0.440880\pi\)
\(488\) −28.8835 −1.30749
\(489\) −8.27374 −0.374152
\(490\) 0 0
\(491\) −7.89709 −0.356391 −0.178195 0.983995i \(-0.557026\pi\)
−0.178195 + 0.983995i \(0.557026\pi\)
\(492\) −14.7493 −0.664951
\(493\) −11.4078 −0.513782
\(494\) −3.78836 −0.170446
\(495\) 0 0
\(496\) 6.69526 0.300626
\(497\) −16.5444 −0.742118
\(498\) 5.58396 0.250223
\(499\) −22.4351 −1.00433 −0.502166 0.864771i \(-0.667463\pi\)
−0.502166 + 0.864771i \(0.667463\pi\)
\(500\) 0 0
\(501\) 12.2142 0.545688
\(502\) 21.1931 0.945894
\(503\) 7.14129 0.318415 0.159207 0.987245i \(-0.449106\pi\)
0.159207 + 0.987245i \(0.449106\pi\)
\(504\) −11.3936 −0.507511
\(505\) 0 0
\(506\) 4.21414 0.187341
\(507\) 11.3011 0.501900
\(508\) −6.58323 −0.292084
\(509\) −12.5554 −0.556506 −0.278253 0.960508i \(-0.589755\pi\)
−0.278253 + 0.960508i \(0.589755\pi\)
\(510\) 0 0
\(511\) 4.82308 0.213361
\(512\) −9.54752 −0.421945
\(513\) 5.53984 0.244590
\(514\) 12.1295 0.535010
\(515\) 0 0
\(516\) −5.19492 −0.228694
\(517\) 8.71877 0.383451
\(518\) −17.5353 −0.770456
\(519\) 9.69924 0.425749
\(520\) 0 0
\(521\) 4.94447 0.216621 0.108310 0.994117i \(-0.465456\pi\)
0.108310 + 0.994117i \(0.465456\pi\)
\(522\) 7.66530 0.335501
\(523\) −1.07988 −0.0472200 −0.0236100 0.999721i \(-0.507516\pi\)
−0.0236100 + 0.999721i \(0.507516\pi\)
\(524\) 15.0728 0.658460
\(525\) 0 0
\(526\) −0.459313 −0.0200270
\(527\) −15.1518 −0.660023
\(528\) −2.00958 −0.0874559
\(529\) −15.7862 −0.686357
\(530\) 0 0
\(531\) −5.13501 −0.222840
\(532\) 3.74601 0.162410
\(533\) −44.0727 −1.90900
\(534\) 0.203134 0.00879045
\(535\) 0 0
\(536\) −3.65202 −0.157743
\(537\) 7.97923 0.344329
\(538\) 17.9188 0.772535
\(539\) 1.14652 0.0493842
\(540\) 0 0
\(541\) −15.7184 −0.675785 −0.337892 0.941185i \(-0.609714\pi\)
−0.337892 + 0.941185i \(0.609714\pi\)
\(542\) 7.46262 0.320547
\(543\) −25.4394 −1.09171
\(544\) 11.4440 0.490657
\(545\) 0 0
\(546\) 10.4610 0.447689
\(547\) 18.6002 0.795286 0.397643 0.917540i \(-0.369828\pi\)
0.397643 + 0.917540i \(0.369828\pi\)
\(548\) 26.1149 1.11557
\(549\) 19.1379 0.816786
\(550\) 0 0
\(551\) −6.06656 −0.258444
\(552\) 7.89478 0.336024
\(553\) −35.2907 −1.50071
\(554\) −5.90697 −0.250963
\(555\) 0 0
\(556\) 8.50803 0.360821
\(557\) 1.59319 0.0675055 0.0337528 0.999430i \(-0.489254\pi\)
0.0337528 + 0.999430i \(0.489254\pi\)
\(558\) 10.1810 0.430996
\(559\) −15.5230 −0.656554
\(560\) 0 0
\(561\) 4.54782 0.192009
\(562\) 15.7950 0.666272
\(563\) 30.0999 1.26856 0.634280 0.773103i \(-0.281297\pi\)
0.634280 + 0.773103i \(0.281297\pi\)
\(564\) 6.78550 0.285721
\(565\) 0 0
\(566\) −6.42879 −0.270222
\(567\) −2.16441 −0.0908968
\(568\) −16.9624 −0.711725
\(569\) −1.17755 −0.0493656 −0.0246828 0.999695i \(-0.507858\pi\)
−0.0246828 + 0.999695i \(0.507858\pi\)
\(570\) 0 0
\(571\) −9.39221 −0.393052 −0.196526 0.980499i \(-0.562966\pi\)
−0.196526 + 0.980499i \(0.562966\pi\)
\(572\) −14.0609 −0.587915
\(573\) 18.0739 0.755048
\(574\) −17.7440 −0.740621
\(575\) 0 0
\(576\) −4.71413 −0.196422
\(577\) 38.4047 1.59881 0.799405 0.600792i \(-0.205148\pi\)
0.799405 + 0.600792i \(0.205148\pi\)
\(578\) 10.0326 0.417301
\(579\) −18.0403 −0.749730
\(580\) 0 0
\(581\) −16.4990 −0.684493
\(582\) 11.6435 0.482639
\(583\) 13.0376 0.539961
\(584\) 4.94493 0.204623
\(585\) 0 0
\(586\) 10.2512 0.423472
\(587\) 32.9101 1.35834 0.679172 0.733979i \(-0.262339\pi\)
0.679172 + 0.733979i \(0.262339\pi\)
\(588\) 0.892297 0.0367977
\(589\) −8.05757 −0.332006
\(590\) 0 0
\(591\) 27.3466 1.12489
\(592\) 7.83375 0.321965
\(593\) 25.5785 1.05038 0.525191 0.850984i \(-0.323994\pi\)
0.525191 + 0.850984i \(0.323994\pi\)
\(594\) −8.37188 −0.343502
\(595\) 0 0
\(596\) 9.93978 0.407149
\(597\) −13.9171 −0.569588
\(598\) 9.80015 0.400758
\(599\) −0.739459 −0.0302135 −0.0151067 0.999886i \(-0.504809\pi\)
−0.0151067 + 0.999886i \(0.504809\pi\)
\(600\) 0 0
\(601\) −12.2755 −0.500730 −0.250365 0.968152i \(-0.580551\pi\)
−0.250365 + 0.968152i \(0.580551\pi\)
\(602\) −6.24969 −0.254718
\(603\) 2.41979 0.0985417
\(604\) 33.1548 1.34905
\(605\) 0 0
\(606\) 10.3101 0.418820
\(607\) −13.7567 −0.558368 −0.279184 0.960238i \(-0.590064\pi\)
−0.279184 + 0.960238i \(0.590064\pi\)
\(608\) 6.08579 0.246811
\(609\) 16.7519 0.678821
\(610\) 0 0
\(611\) 20.2759 0.820273
\(612\) −4.78531 −0.193435
\(613\) 32.1681 1.29926 0.649629 0.760251i \(-0.274924\pi\)
0.649629 + 0.760251i \(0.274924\pi\)
\(614\) −7.36019 −0.297033
\(615\) 0 0
\(616\) −13.6270 −0.549047
\(617\) −29.1316 −1.17279 −0.586397 0.810024i \(-0.699454\pi\)
−0.586397 + 0.810024i \(0.699454\pi\)
\(618\) −11.7029 −0.470761
\(619\) 4.25398 0.170982 0.0854909 0.996339i \(-0.472754\pi\)
0.0854909 + 0.996339i \(0.472754\pi\)
\(620\) 0 0
\(621\) −14.3311 −0.575086
\(622\) 26.5290 1.06371
\(623\) −0.600201 −0.0240466
\(624\) −4.67337 −0.187084
\(625\) 0 0
\(626\) −20.7097 −0.827728
\(627\) 2.41848 0.0965848
\(628\) 9.94857 0.396991
\(629\) −17.7283 −0.706873
\(630\) 0 0
\(631\) 8.94679 0.356166 0.178083 0.984015i \(-0.443010\pi\)
0.178083 + 0.984015i \(0.443010\pi\)
\(632\) −36.1822 −1.43925
\(633\) 29.9997 1.19238
\(634\) −2.20857 −0.0877135
\(635\) 0 0
\(636\) 10.1467 0.402341
\(637\) 2.66629 0.105642
\(638\) 9.16786 0.362959
\(639\) 11.2391 0.444612
\(640\) 0 0
\(641\) 11.6413 0.459803 0.229902 0.973214i \(-0.426160\pi\)
0.229902 + 0.973214i \(0.426160\pi\)
\(642\) 11.8808 0.468898
\(643\) 31.5371 1.24370 0.621851 0.783136i \(-0.286381\pi\)
0.621851 + 0.783136i \(0.286381\pi\)
\(644\) −9.69060 −0.381863
\(645\) 0 0
\(646\) −1.54201 −0.0606696
\(647\) −7.63153 −0.300027 −0.150013 0.988684i \(-0.547932\pi\)
−0.150013 + 0.988684i \(0.547932\pi\)
\(648\) −2.21909 −0.0871742
\(649\) −6.14158 −0.241078
\(650\) 0 0
\(651\) 22.2498 0.872038
\(652\) 10.4123 0.407778
\(653\) −25.3578 −0.992328 −0.496164 0.868229i \(-0.665259\pi\)
−0.496164 + 0.868229i \(0.665259\pi\)
\(654\) −11.8263 −0.462444
\(655\) 0 0
\(656\) 7.92699 0.309497
\(657\) −3.27646 −0.127827
\(658\) 8.16322 0.318236
\(659\) −39.0160 −1.51985 −0.759924 0.650011i \(-0.774764\pi\)
−0.759924 + 0.650011i \(0.774764\pi\)
\(660\) 0 0
\(661\) 48.6676 1.89295 0.946474 0.322779i \(-0.104617\pi\)
0.946474 + 0.322779i \(0.104617\pi\)
\(662\) −3.67399 −0.142794
\(663\) 10.5761 0.410743
\(664\) −16.9158 −0.656460
\(665\) 0 0
\(666\) 11.9122 0.461590
\(667\) 15.6936 0.607660
\(668\) −15.3713 −0.594732
\(669\) −9.40995 −0.363810
\(670\) 0 0
\(671\) 22.8893 0.883633
\(672\) −16.8050 −0.648267
\(673\) −20.8488 −0.803664 −0.401832 0.915713i \(-0.631626\pi\)
−0.401832 + 0.915713i \(0.631626\pi\)
\(674\) 16.8465 0.648902
\(675\) 0 0
\(676\) −14.2222 −0.547008
\(677\) 30.6907 1.17954 0.589769 0.807572i \(-0.299219\pi\)
0.589769 + 0.807572i \(0.299219\pi\)
\(678\) −5.74178 −0.220512
\(679\) −34.4032 −1.32027
\(680\) 0 0
\(681\) 4.90005 0.187770
\(682\) 12.1767 0.466270
\(683\) 22.3276 0.854344 0.427172 0.904170i \(-0.359510\pi\)
0.427172 + 0.904170i \(0.359510\pi\)
\(684\) −2.54478 −0.0973020
\(685\) 0 0
\(686\) 14.5912 0.557096
\(687\) 33.1511 1.26479
\(688\) 2.79200 0.106444
\(689\) 30.3194 1.15508
\(690\) 0 0
\(691\) −27.0489 −1.02899 −0.514495 0.857493i \(-0.672021\pi\)
−0.514495 + 0.857493i \(0.672021\pi\)
\(692\) −12.2063 −0.464013
\(693\) 9.02911 0.342987
\(694\) 15.3570 0.582944
\(695\) 0 0
\(696\) 17.1751 0.651021
\(697\) −17.9393 −0.679499
\(698\) −3.21238 −0.121590
\(699\) −14.7148 −0.556565
\(700\) 0 0
\(701\) −39.0100 −1.47339 −0.736693 0.676227i \(-0.763614\pi\)
−0.736693 + 0.676227i \(0.763614\pi\)
\(702\) −19.4691 −0.734816
\(703\) −9.42771 −0.355573
\(704\) −5.63819 −0.212497
\(705\) 0 0
\(706\) 15.3876 0.579121
\(707\) −30.4634 −1.14570
\(708\) −4.77977 −0.179635
\(709\) −12.6642 −0.475612 −0.237806 0.971313i \(-0.576428\pi\)
−0.237806 + 0.971313i \(0.576428\pi\)
\(710\) 0 0
\(711\) 23.9740 0.899095
\(712\) −0.615364 −0.0230618
\(713\) 20.8442 0.780621
\(714\) 4.25804 0.159353
\(715\) 0 0
\(716\) −10.0417 −0.375276
\(717\) 8.21314 0.306725
\(718\) 17.5566 0.655205
\(719\) 18.1316 0.676193 0.338096 0.941111i \(-0.390217\pi\)
0.338096 + 0.941111i \(0.390217\pi\)
\(720\) 0 0
\(721\) 34.5788 1.28778
\(722\) 13.6337 0.507393
\(723\) 1.12938 0.0420022
\(724\) 32.0149 1.18983
\(725\) 0 0
\(726\) 5.79576 0.215101
\(727\) 21.4455 0.795368 0.397684 0.917522i \(-0.369814\pi\)
0.397684 + 0.917522i \(0.369814\pi\)
\(728\) −31.6901 −1.17451
\(729\) 19.5487 0.724026
\(730\) 0 0
\(731\) −6.31848 −0.233697
\(732\) 17.8139 0.658422
\(733\) −0.379985 −0.0140350 −0.00701752 0.999975i \(-0.502234\pi\)
−0.00701752 + 0.999975i \(0.502234\pi\)
\(734\) −11.8411 −0.437061
\(735\) 0 0
\(736\) −15.7434 −0.580309
\(737\) 2.89412 0.106606
\(738\) 12.0540 0.443715
\(739\) 42.6584 1.56921 0.784607 0.619993i \(-0.212865\pi\)
0.784607 + 0.619993i \(0.212865\pi\)
\(740\) 0 0
\(741\) 5.62428 0.206613
\(742\) 12.2068 0.448127
\(743\) 17.0856 0.626810 0.313405 0.949620i \(-0.398530\pi\)
0.313405 + 0.949620i \(0.398530\pi\)
\(744\) 22.8119 0.836324
\(745\) 0 0
\(746\) 17.4250 0.637975
\(747\) 11.2082 0.410088
\(748\) −5.72333 −0.209266
\(749\) −35.1044 −1.28269
\(750\) 0 0
\(751\) −33.7135 −1.23022 −0.615111 0.788441i \(-0.710889\pi\)
−0.615111 + 0.788441i \(0.710889\pi\)
\(752\) −3.64685 −0.132987
\(753\) −31.4637 −1.14660
\(754\) 21.3202 0.776437
\(755\) 0 0
\(756\) 19.2515 0.700171
\(757\) 16.7814 0.609932 0.304966 0.952363i \(-0.401355\pi\)
0.304966 + 0.952363i \(0.401355\pi\)
\(758\) 7.32671 0.266118
\(759\) −6.25639 −0.227093
\(760\) 0 0
\(761\) −29.8307 −1.08136 −0.540681 0.841227i \(-0.681834\pi\)
−0.540681 + 0.841227i \(0.681834\pi\)
\(762\) −3.97941 −0.144159
\(763\) 34.9432 1.26503
\(764\) −22.7456 −0.822907
\(765\) 0 0
\(766\) 0.906120 0.0327394
\(767\) −14.2825 −0.515711
\(768\) −14.4599 −0.521778
\(769\) 7.89994 0.284879 0.142440 0.989803i \(-0.454505\pi\)
0.142440 + 0.989803i \(0.454505\pi\)
\(770\) 0 0
\(771\) −18.0077 −0.648532
\(772\) 22.7034 0.817112
\(773\) −25.4969 −0.917061 −0.458530 0.888679i \(-0.651624\pi\)
−0.458530 + 0.888679i \(0.651624\pi\)
\(774\) 4.24560 0.152605
\(775\) 0 0
\(776\) −35.2723 −1.26620
\(777\) 26.0332 0.933937
\(778\) 9.14012 0.327689
\(779\) −9.53993 −0.341803
\(780\) 0 0
\(781\) 13.4422 0.480999
\(782\) 3.98904 0.142648
\(783\) −31.1773 −1.11418
\(784\) −0.479563 −0.0171273
\(785\) 0 0
\(786\) 9.11119 0.324985
\(787\) −49.0412 −1.74813 −0.874065 0.485809i \(-0.838525\pi\)
−0.874065 + 0.485809i \(0.838525\pi\)
\(788\) −34.4151 −1.22599
\(789\) 0.681905 0.0242764
\(790\) 0 0
\(791\) 16.9653 0.603217
\(792\) 9.25721 0.328941
\(793\) 53.2301 1.89026
\(794\) −0.990260 −0.0351430
\(795\) 0 0
\(796\) 17.5143 0.620779
\(797\) −1.15733 −0.0409948 −0.0204974 0.999790i \(-0.506525\pi\)
−0.0204974 + 0.999790i \(0.506525\pi\)
\(798\) 2.26438 0.0801581
\(799\) 8.25307 0.291973
\(800\) 0 0
\(801\) 0.407734 0.0144066
\(802\) −13.5377 −0.478031
\(803\) −3.91872 −0.138289
\(804\) 2.25239 0.0794357
\(805\) 0 0
\(806\) 28.3174 0.997438
\(807\) −26.6026 −0.936457
\(808\) −31.2330 −1.09877
\(809\) −31.6665 −1.11334 −0.556668 0.830735i \(-0.687920\pi\)
−0.556668 + 0.830735i \(0.687920\pi\)
\(810\) 0 0
\(811\) 36.0360 1.26540 0.632698 0.774398i \(-0.281947\pi\)
0.632698 + 0.774398i \(0.281947\pi\)
\(812\) −21.0819 −0.739830
\(813\) −11.0792 −0.388563
\(814\) 14.2473 0.499367
\(815\) 0 0
\(816\) −1.90224 −0.0665918
\(817\) −3.36010 −0.117555
\(818\) −0.925087 −0.0323449
\(819\) 20.9976 0.733714
\(820\) 0 0
\(821\) 30.1203 1.05121 0.525603 0.850730i \(-0.323840\pi\)
0.525603 + 0.850730i \(0.323840\pi\)
\(822\) 15.7859 0.550595
\(823\) 21.5975 0.752843 0.376421 0.926449i \(-0.377155\pi\)
0.376421 + 0.926449i \(0.377155\pi\)
\(824\) 35.4524 1.23504
\(825\) 0 0
\(826\) −5.75025 −0.200077
\(827\) 2.37687 0.0826519 0.0413259 0.999146i \(-0.486842\pi\)
0.0413259 + 0.999146i \(0.486842\pi\)
\(828\) 6.58311 0.228779
\(829\) −20.4204 −0.709230 −0.354615 0.935012i \(-0.615388\pi\)
−0.354615 + 0.935012i \(0.615388\pi\)
\(830\) 0 0
\(831\) 8.76960 0.304214
\(832\) −13.1118 −0.454571
\(833\) 1.08528 0.0376028
\(834\) 5.14291 0.178084
\(835\) 0 0
\(836\) −3.04361 −0.105265
\(837\) −41.4094 −1.43132
\(838\) 17.8957 0.618196
\(839\) 2.84185 0.0981115 0.0490557 0.998796i \(-0.484379\pi\)
0.0490557 + 0.998796i \(0.484379\pi\)
\(840\) 0 0
\(841\) 5.14153 0.177294
\(842\) −18.3432 −0.632149
\(843\) −23.4496 −0.807646
\(844\) −37.7540 −1.29955
\(845\) 0 0
\(846\) −5.54552 −0.190659
\(847\) −17.1248 −0.588415
\(848\) −5.45330 −0.187267
\(849\) 9.54431 0.327560
\(850\) 0 0
\(851\) 24.3886 0.836032
\(852\) 10.4616 0.358407
\(853\) 13.8008 0.472530 0.236265 0.971689i \(-0.424077\pi\)
0.236265 + 0.971689i \(0.424077\pi\)
\(854\) 21.4309 0.733349
\(855\) 0 0
\(856\) −35.9912 −1.23015
\(857\) −2.06240 −0.0704502 −0.0352251 0.999379i \(-0.511215\pi\)
−0.0352251 + 0.999379i \(0.511215\pi\)
\(858\) −8.49948 −0.290167
\(859\) −22.7067 −0.774742 −0.387371 0.921924i \(-0.626617\pi\)
−0.387371 + 0.921924i \(0.626617\pi\)
\(860\) 0 0
\(861\) 26.3431 0.897771
\(862\) −7.02189 −0.239166
\(863\) −25.2543 −0.859667 −0.429833 0.902908i \(-0.641428\pi\)
−0.429833 + 0.902908i \(0.641428\pi\)
\(864\) 31.2761 1.06403
\(865\) 0 0
\(866\) 30.8425 1.04807
\(867\) −14.8946 −0.505847
\(868\) −28.0009 −0.950411
\(869\) 28.6734 0.972678
\(870\) 0 0
\(871\) 6.73041 0.228051
\(872\) 35.8260 1.21322
\(873\) 23.3711 0.790992
\(874\) 2.12133 0.0717551
\(875\) 0 0
\(876\) −3.04980 −0.103043
\(877\) −23.5255 −0.794401 −0.397200 0.917732i \(-0.630018\pi\)
−0.397200 + 0.917732i \(0.630018\pi\)
\(878\) −14.8681 −0.501776
\(879\) −15.2191 −0.513327
\(880\) 0 0
\(881\) −23.8946 −0.805029 −0.402515 0.915414i \(-0.631864\pi\)
−0.402515 + 0.915414i \(0.631864\pi\)
\(882\) −0.729238 −0.0245547
\(883\) −12.9066 −0.434342 −0.217171 0.976134i \(-0.569683\pi\)
−0.217171 + 0.976134i \(0.569683\pi\)
\(884\) −13.3098 −0.447658
\(885\) 0 0
\(886\) −29.1761 −0.980192
\(887\) 26.6396 0.894471 0.447235 0.894416i \(-0.352409\pi\)
0.447235 + 0.894416i \(0.352409\pi\)
\(888\) 26.6909 0.895689
\(889\) 11.7580 0.394351
\(890\) 0 0
\(891\) 1.75857 0.0589143
\(892\) 11.8422 0.396507
\(893\) 4.38889 0.146869
\(894\) 6.00837 0.200950
\(895\) 0 0
\(896\) 24.4807 0.817843
\(897\) −14.5495 −0.485793
\(898\) 5.44261 0.181622
\(899\) 45.3466 1.51239
\(900\) 0 0
\(901\) 12.3412 0.411144
\(902\) 14.4169 0.480029
\(903\) 9.27842 0.308766
\(904\) 17.3939 0.578513
\(905\) 0 0
\(906\) 20.0413 0.665828
\(907\) −21.2193 −0.704574 −0.352287 0.935892i \(-0.614596\pi\)
−0.352287 + 0.935892i \(0.614596\pi\)
\(908\) −6.16661 −0.204646
\(909\) 20.6947 0.686400
\(910\) 0 0
\(911\) −6.50032 −0.215365 −0.107683 0.994185i \(-0.534343\pi\)
−0.107683 + 0.994185i \(0.534343\pi\)
\(912\) −1.01159 −0.0334972
\(913\) 13.4053 0.443650
\(914\) 10.0475 0.332342
\(915\) 0 0
\(916\) −41.7199 −1.37846
\(917\) −26.9209 −0.889008
\(918\) −7.92471 −0.261554
\(919\) 19.1428 0.631461 0.315731 0.948849i \(-0.397750\pi\)
0.315731 + 0.948849i \(0.397750\pi\)
\(920\) 0 0
\(921\) 10.9271 0.360060
\(922\) −19.4858 −0.641730
\(923\) 31.2604 1.02895
\(924\) 8.40447 0.276487
\(925\) 0 0
\(926\) −27.9495 −0.918478
\(927\) −23.4904 −0.771526
\(928\) −34.2498 −1.12430
\(929\) −58.3414 −1.91412 −0.957059 0.289892i \(-0.906381\pi\)
−0.957059 + 0.289892i \(0.906381\pi\)
\(930\) 0 0
\(931\) 0.577142 0.0189151
\(932\) 18.5183 0.606586
\(933\) −39.3854 −1.28942
\(934\) 8.77906 0.287260
\(935\) 0 0
\(936\) 21.5280 0.703666
\(937\) 15.6711 0.511952 0.255976 0.966683i \(-0.417603\pi\)
0.255976 + 0.966683i \(0.417603\pi\)
\(938\) 2.70972 0.0884753
\(939\) 30.7461 1.00336
\(940\) 0 0
\(941\) 12.8470 0.418799 0.209399 0.977830i \(-0.432849\pi\)
0.209399 + 0.977830i \(0.432849\pi\)
\(942\) 6.01368 0.195936
\(943\) 24.6789 0.803657
\(944\) 2.56888 0.0836098
\(945\) 0 0
\(946\) 5.07783 0.165094
\(947\) 22.7709 0.739954 0.369977 0.929041i \(-0.379366\pi\)
0.369977 + 0.929041i \(0.379366\pi\)
\(948\) 22.3155 0.724772
\(949\) −9.11314 −0.295825
\(950\) 0 0
\(951\) 3.27889 0.106325
\(952\) −12.8991 −0.418063
\(953\) −23.0127 −0.745453 −0.372727 0.927941i \(-0.621577\pi\)
−0.372727 + 0.927941i \(0.621577\pi\)
\(954\) −8.29246 −0.268478
\(955\) 0 0
\(956\) −10.3361 −0.334292
\(957\) −13.6108 −0.439974
\(958\) −22.8160 −0.737150
\(959\) −46.6427 −1.50617
\(960\) 0 0
\(961\) 29.2291 0.942873
\(962\) 33.1326 1.06824
\(963\) 23.8474 0.768472
\(964\) −1.42130 −0.0457771
\(965\) 0 0
\(966\) −5.85774 −0.188470
\(967\) −8.23926 −0.264957 −0.132478 0.991186i \(-0.542294\pi\)
−0.132478 + 0.991186i \(0.542294\pi\)
\(968\) −17.5574 −0.564317
\(969\) 2.28930 0.0735429
\(970\) 0 0
\(971\) −42.6419 −1.36845 −0.684223 0.729273i \(-0.739858\pi\)
−0.684223 + 0.729273i \(0.739858\pi\)
\(972\) −21.3826 −0.685846
\(973\) −15.1958 −0.487156
\(974\) −6.20021 −0.198667
\(975\) 0 0
\(976\) −9.57407 −0.306458
\(977\) 5.17109 0.165438 0.0827189 0.996573i \(-0.473640\pi\)
0.0827189 + 0.996573i \(0.473640\pi\)
\(978\) 6.29401 0.201260
\(979\) 0.487659 0.0155856
\(980\) 0 0
\(981\) −23.7380 −0.757895
\(982\) 6.00749 0.191707
\(983\) 20.8634 0.665438 0.332719 0.943026i \(-0.392034\pi\)
0.332719 + 0.943026i \(0.392034\pi\)
\(984\) 27.0086 0.861003
\(985\) 0 0
\(986\) 8.67817 0.276369
\(987\) −12.1193 −0.385761
\(988\) −7.07803 −0.225182
\(989\) 8.69227 0.276398
\(990\) 0 0
\(991\) 16.2535 0.516311 0.258155 0.966103i \(-0.416885\pi\)
0.258155 + 0.966103i \(0.416885\pi\)
\(992\) −45.4903 −1.44432
\(993\) 5.45448 0.173093
\(994\) 12.5857 0.399193
\(995\) 0 0
\(996\) 10.4329 0.330578
\(997\) 27.4154 0.868254 0.434127 0.900852i \(-0.357057\pi\)
0.434127 + 0.900852i \(0.357057\pi\)
\(998\) 17.0668 0.540241
\(999\) −48.4509 −1.53292
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 6025.2.a.p.1.18 46
5.2 odd 4 1205.2.b.c.724.18 46
5.3 odd 4 1205.2.b.c.724.29 yes 46
5.4 even 2 inner 6025.2.a.p.1.29 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.18 46 5.2 odd 4
1205.2.b.c.724.29 yes 46 5.3 odd 4
6025.2.a.p.1.18 46 1.1 even 1 trivial
6025.2.a.p.1.29 46 5.4 even 2 inner