Properties

Label 3549.2.a.bh.1.2
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + 4553 x^{7} - 6393 x^{6} - 6785 x^{5} + 7806 x^{4} + 4632 x^{3} - 3811 x^{2} - 1041 x + 281\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.60515\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60515 q^{2} +1.00000 q^{3} +4.78683 q^{4} -1.51368 q^{5} -2.60515 q^{6} -1.00000 q^{7} -7.26012 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.60515 q^{2} +1.00000 q^{3} +4.78683 q^{4} -1.51368 q^{5} -2.60515 q^{6} -1.00000 q^{7} -7.26012 q^{8} +1.00000 q^{9} +3.94338 q^{10} -0.949498 q^{11} +4.78683 q^{12} +2.60515 q^{14} -1.51368 q^{15} +9.34008 q^{16} +5.20785 q^{17} -2.60515 q^{18} +5.53387 q^{19} -7.24575 q^{20} -1.00000 q^{21} +2.47359 q^{22} -3.94826 q^{23} -7.26012 q^{24} -2.70876 q^{25} +1.00000 q^{27} -4.78683 q^{28} +5.11085 q^{29} +3.94338 q^{30} +9.26508 q^{31} -9.81211 q^{32} -0.949498 q^{33} -13.5673 q^{34} +1.51368 q^{35} +4.78683 q^{36} +7.19721 q^{37} -14.4166 q^{38} +10.9895 q^{40} -2.01650 q^{41} +2.60515 q^{42} -10.1790 q^{43} -4.54509 q^{44} -1.51368 q^{45} +10.2858 q^{46} -6.97453 q^{47} +9.34008 q^{48} +1.00000 q^{49} +7.05674 q^{50} +5.20785 q^{51} -11.2203 q^{53} -2.60515 q^{54} +1.43724 q^{55} +7.26012 q^{56} +5.53387 q^{57} -13.3146 q^{58} -6.64104 q^{59} -7.24575 q^{60} -3.07927 q^{61} -24.1370 q^{62} -1.00000 q^{63} +6.88190 q^{64} +2.47359 q^{66} +12.8973 q^{67} +24.9291 q^{68} -3.94826 q^{69} -3.94338 q^{70} -7.77833 q^{71} -7.26012 q^{72} -8.64459 q^{73} -18.7499 q^{74} -2.70876 q^{75} +26.4897 q^{76} +0.949498 q^{77} +15.2689 q^{79} -14.1379 q^{80} +1.00000 q^{81} +5.25329 q^{82} -11.7165 q^{83} -4.78683 q^{84} -7.88304 q^{85} +26.5178 q^{86} +5.11085 q^{87} +6.89347 q^{88} +8.13994 q^{89} +3.94338 q^{90} -18.8997 q^{92} +9.26508 q^{93} +18.1697 q^{94} -8.37653 q^{95} -9.81211 q^{96} +14.8803 q^{97} -2.60515 q^{98} -0.949498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60515 −1.84212 −0.921061 0.389418i \(-0.872676\pi\)
−0.921061 + 0.389418i \(0.872676\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.78683 2.39342
\(5\) −1.51368 −0.676940 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(6\) −2.60515 −1.06355
\(7\) −1.00000 −0.377964
\(8\) −7.26012 −2.56684
\(9\) 1.00000 0.333333
\(10\) 3.94338 1.24701
\(11\) −0.949498 −0.286284 −0.143142 0.989702i \(-0.545721\pi\)
−0.143142 + 0.989702i \(0.545721\pi\)
\(12\) 4.78683 1.38184
\(13\) 0 0
\(14\) 2.60515 0.696257
\(15\) −1.51368 −0.390832
\(16\) 9.34008 2.33502
\(17\) 5.20785 1.26309 0.631545 0.775340i \(-0.282421\pi\)
0.631545 + 0.775340i \(0.282421\pi\)
\(18\) −2.60515 −0.614041
\(19\) 5.53387 1.26956 0.634778 0.772695i \(-0.281092\pi\)
0.634778 + 0.772695i \(0.281092\pi\)
\(20\) −7.24575 −1.62020
\(21\) −1.00000 −0.218218
\(22\) 2.47359 0.527371
\(23\) −3.94826 −0.823269 −0.411635 0.911349i \(-0.635042\pi\)
−0.411635 + 0.911349i \(0.635042\pi\)
\(24\) −7.26012 −1.48197
\(25\) −2.70876 −0.541752
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −4.78683 −0.904626
\(29\) 5.11085 0.949062 0.474531 0.880239i \(-0.342618\pi\)
0.474531 + 0.880239i \(0.342618\pi\)
\(30\) 3.94338 0.719960
\(31\) 9.26508 1.66406 0.832028 0.554733i \(-0.187180\pi\)
0.832028 + 0.554733i \(0.187180\pi\)
\(32\) −9.81211 −1.73455
\(33\) −0.949498 −0.165286
\(34\) −13.5673 −2.32676
\(35\) 1.51368 0.255859
\(36\) 4.78683 0.797805
\(37\) 7.19721 1.18321 0.591607 0.806226i \(-0.298494\pi\)
0.591607 + 0.806226i \(0.298494\pi\)
\(38\) −14.4166 −2.33868
\(39\) 0 0
\(40\) 10.9895 1.73760
\(41\) −2.01650 −0.314924 −0.157462 0.987525i \(-0.550331\pi\)
−0.157462 + 0.987525i \(0.550331\pi\)
\(42\) 2.60515 0.401984
\(43\) −10.1790 −1.55228 −0.776138 0.630563i \(-0.782824\pi\)
−0.776138 + 0.630563i \(0.782824\pi\)
\(44\) −4.54509 −0.685197
\(45\) −1.51368 −0.225647
\(46\) 10.2858 1.51656
\(47\) −6.97453 −1.01734 −0.508670 0.860962i \(-0.669863\pi\)
−0.508670 + 0.860962i \(0.669863\pi\)
\(48\) 9.34008 1.34812
\(49\) 1.00000 0.142857
\(50\) 7.05674 0.997973
\(51\) 5.20785 0.729245
\(52\) 0 0
\(53\) −11.2203 −1.54123 −0.770615 0.637301i \(-0.780051\pi\)
−0.770615 + 0.637301i \(0.780051\pi\)
\(54\) −2.60515 −0.354517
\(55\) 1.43724 0.193797
\(56\) 7.26012 0.970175
\(57\) 5.53387 0.732979
\(58\) −13.3146 −1.74829
\(59\) −6.64104 −0.864590 −0.432295 0.901732i \(-0.642296\pi\)
−0.432295 + 0.901732i \(0.642296\pi\)
\(60\) −7.24575 −0.935422
\(61\) −3.07927 −0.394260 −0.197130 0.980377i \(-0.563162\pi\)
−0.197130 + 0.980377i \(0.563162\pi\)
\(62\) −24.1370 −3.06540
\(63\) −1.00000 −0.125988
\(64\) 6.88190 0.860238
\(65\) 0 0
\(66\) 2.47359 0.304478
\(67\) 12.8973 1.57565 0.787826 0.615898i \(-0.211207\pi\)
0.787826 + 0.615898i \(0.211207\pi\)
\(68\) 24.9291 3.02310
\(69\) −3.94826 −0.475315
\(70\) −3.94338 −0.471324
\(71\) −7.77833 −0.923118 −0.461559 0.887110i \(-0.652710\pi\)
−0.461559 + 0.887110i \(0.652710\pi\)
\(72\) −7.26012 −0.855614
\(73\) −8.64459 −1.01177 −0.505886 0.862600i \(-0.668834\pi\)
−0.505886 + 0.862600i \(0.668834\pi\)
\(74\) −18.7499 −2.17963
\(75\) −2.70876 −0.312781
\(76\) 26.4897 3.03857
\(77\) 0.949498 0.108205
\(78\) 0 0
\(79\) 15.2689 1.71788 0.858941 0.512075i \(-0.171123\pi\)
0.858941 + 0.512075i \(0.171123\pi\)
\(80\) −14.1379 −1.58067
\(81\) 1.00000 0.111111
\(82\) 5.25329 0.580129
\(83\) −11.7165 −1.28605 −0.643024 0.765846i \(-0.722321\pi\)
−0.643024 + 0.765846i \(0.722321\pi\)
\(84\) −4.78683 −0.522286
\(85\) −7.88304 −0.855036
\(86\) 26.5178 2.85948
\(87\) 5.11085 0.547941
\(88\) 6.89347 0.734847
\(89\) 8.13994 0.862832 0.431416 0.902153i \(-0.358014\pi\)
0.431416 + 0.902153i \(0.358014\pi\)
\(90\) 3.94338 0.415669
\(91\) 0 0
\(92\) −18.8997 −1.97043
\(93\) 9.26508 0.960744
\(94\) 18.1697 1.87406
\(95\) −8.37653 −0.859414
\(96\) −9.81211 −1.00144
\(97\) 14.8803 1.51086 0.755431 0.655229i \(-0.227428\pi\)
0.755431 + 0.655229i \(0.227428\pi\)
\(98\) −2.60515 −0.263160
\(99\) −0.949498 −0.0954281
\(100\) −12.9664 −1.29664
\(101\) −0.878824 −0.0874463 −0.0437231 0.999044i \(-0.513922\pi\)
−0.0437231 + 0.999044i \(0.513922\pi\)
\(102\) −13.5673 −1.34336
\(103\) 4.72585 0.465652 0.232826 0.972518i \(-0.425203\pi\)
0.232826 + 0.972518i \(0.425203\pi\)
\(104\) 0 0
\(105\) 1.51368 0.147720
\(106\) 29.2307 2.83914
\(107\) 14.5988 1.41132 0.705658 0.708553i \(-0.250652\pi\)
0.705658 + 0.708553i \(0.250652\pi\)
\(108\) 4.78683 0.460613
\(109\) −14.4751 −1.38646 −0.693232 0.720714i \(-0.743814\pi\)
−0.693232 + 0.720714i \(0.743814\pi\)
\(110\) −3.74423 −0.356999
\(111\) 7.19721 0.683129
\(112\) −9.34008 −0.882555
\(113\) −0.659804 −0.0620692 −0.0310346 0.999518i \(-0.509880\pi\)
−0.0310346 + 0.999518i \(0.509880\pi\)
\(114\) −14.4166 −1.35024
\(115\) 5.97642 0.557304
\(116\) 24.4648 2.27150
\(117\) 0 0
\(118\) 17.3009 1.59268
\(119\) −5.20785 −0.477403
\(120\) 10.9895 1.00320
\(121\) −10.0985 −0.918041
\(122\) 8.02197 0.726275
\(123\) −2.01650 −0.181822
\(124\) 44.3503 3.98278
\(125\) 11.6686 1.04367
\(126\) 2.60515 0.232086
\(127\) 3.18132 0.282296 0.141148 0.989988i \(-0.454921\pi\)
0.141148 + 0.989988i \(0.454921\pi\)
\(128\) 1.69580 0.149889
\(129\) −10.1790 −0.896207
\(130\) 0 0
\(131\) 22.2245 1.94177 0.970883 0.239555i \(-0.0770016\pi\)
0.970883 + 0.239555i \(0.0770016\pi\)
\(132\) −4.54509 −0.395599
\(133\) −5.53387 −0.479847
\(134\) −33.5994 −2.90254
\(135\) −1.51368 −0.130277
\(136\) −37.8096 −3.24215
\(137\) 13.2437 1.13148 0.565742 0.824583i \(-0.308590\pi\)
0.565742 + 0.824583i \(0.308590\pi\)
\(138\) 10.2858 0.875588
\(139\) 14.4676 1.22713 0.613564 0.789645i \(-0.289735\pi\)
0.613564 + 0.789645i \(0.289735\pi\)
\(140\) 7.24575 0.612378
\(141\) −6.97453 −0.587361
\(142\) 20.2637 1.70050
\(143\) 0 0
\(144\) 9.34008 0.778340
\(145\) −7.73622 −0.642458
\(146\) 22.5205 1.86381
\(147\) 1.00000 0.0824786
\(148\) 34.4518 2.83192
\(149\) 15.5692 1.27548 0.637740 0.770252i \(-0.279869\pi\)
0.637740 + 0.770252i \(0.279869\pi\)
\(150\) 7.05674 0.576180
\(151\) −7.76523 −0.631926 −0.315963 0.948772i \(-0.602327\pi\)
−0.315963 + 0.948772i \(0.602327\pi\)
\(152\) −40.1766 −3.25875
\(153\) 5.20785 0.421030
\(154\) −2.47359 −0.199327
\(155\) −14.0244 −1.12647
\(156\) 0 0
\(157\) −8.41794 −0.671825 −0.335913 0.941893i \(-0.609045\pi\)
−0.335913 + 0.941893i \(0.609045\pi\)
\(158\) −39.7778 −3.16455
\(159\) −11.2203 −0.889830
\(160\) 14.8524 1.17419
\(161\) 3.94826 0.311167
\(162\) −2.60515 −0.204680
\(163\) −6.67148 −0.522551 −0.261275 0.965264i \(-0.584143\pi\)
−0.261275 + 0.965264i \(0.584143\pi\)
\(164\) −9.65264 −0.753744
\(165\) 1.43724 0.111889
\(166\) 30.5232 2.36906
\(167\) 0.768371 0.0594583 0.0297292 0.999558i \(-0.490536\pi\)
0.0297292 + 0.999558i \(0.490536\pi\)
\(168\) 7.26012 0.560131
\(169\) 0 0
\(170\) 20.5365 1.57508
\(171\) 5.53387 0.423185
\(172\) −48.7249 −3.71524
\(173\) −0.606929 −0.0461440 −0.0230720 0.999734i \(-0.507345\pi\)
−0.0230720 + 0.999734i \(0.507345\pi\)
\(174\) −13.3146 −1.00937
\(175\) 2.70876 0.204763
\(176\) −8.86839 −0.668480
\(177\) −6.64104 −0.499171
\(178\) −21.2058 −1.58944
\(179\) 7.43308 0.555575 0.277787 0.960643i \(-0.410399\pi\)
0.277787 + 0.960643i \(0.410399\pi\)
\(180\) −7.24575 −0.540066
\(181\) 18.2820 1.35889 0.679445 0.733727i \(-0.262221\pi\)
0.679445 + 0.733727i \(0.262221\pi\)
\(182\) 0 0
\(183\) −3.07927 −0.227626
\(184\) 28.6649 2.11320
\(185\) −10.8943 −0.800966
\(186\) −24.1370 −1.76981
\(187\) −4.94484 −0.361603
\(188\) −33.3859 −2.43492
\(189\) −1.00000 −0.0727393
\(190\) 21.8222 1.58315
\(191\) 3.80093 0.275026 0.137513 0.990500i \(-0.456089\pi\)
0.137513 + 0.990500i \(0.456089\pi\)
\(192\) 6.88190 0.496659
\(193\) −2.52606 −0.181830 −0.0909149 0.995859i \(-0.528979\pi\)
−0.0909149 + 0.995859i \(0.528979\pi\)
\(194\) −38.7654 −2.78319
\(195\) 0 0
\(196\) 4.78683 0.341916
\(197\) 7.51285 0.535268 0.267634 0.963521i \(-0.413758\pi\)
0.267634 + 0.963521i \(0.413758\pi\)
\(198\) 2.47359 0.175790
\(199\) 8.40900 0.596098 0.298049 0.954550i \(-0.403664\pi\)
0.298049 + 0.954550i \(0.403664\pi\)
\(200\) 19.6659 1.39059
\(201\) 12.8973 0.909703
\(202\) 2.28947 0.161087
\(203\) −5.11085 −0.358712
\(204\) 24.9291 1.74539
\(205\) 3.05234 0.213185
\(206\) −12.3116 −0.857788
\(207\) −3.94826 −0.274423
\(208\) 0 0
\(209\) −5.25439 −0.363454
\(210\) −3.94338 −0.272119
\(211\) −17.0137 −1.17127 −0.585637 0.810573i \(-0.699156\pi\)
−0.585637 + 0.810573i \(0.699156\pi\)
\(212\) −53.7098 −3.68880
\(213\) −7.77833 −0.532962
\(214\) −38.0320 −2.59982
\(215\) 15.4077 1.05080
\(216\) −7.26012 −0.493989
\(217\) −9.26508 −0.628954
\(218\) 37.7099 2.55404
\(219\) −8.64459 −0.584147
\(220\) 6.87982 0.463838
\(221\) 0 0
\(222\) −18.7499 −1.25841
\(223\) 8.43541 0.564877 0.282438 0.959285i \(-0.408857\pi\)
0.282438 + 0.959285i \(0.408857\pi\)
\(224\) 9.81211 0.655599
\(225\) −2.70876 −0.180584
\(226\) 1.71889 0.114339
\(227\) 19.6940 1.30714 0.653569 0.756867i \(-0.273271\pi\)
0.653569 + 0.756867i \(0.273271\pi\)
\(228\) 26.4897 1.75432
\(229\) −8.84860 −0.584732 −0.292366 0.956306i \(-0.594443\pi\)
−0.292366 + 0.956306i \(0.594443\pi\)
\(230\) −15.5695 −1.02662
\(231\) 0.949498 0.0624724
\(232\) −37.1054 −2.43609
\(233\) 0.554530 0.0363285 0.0181642 0.999835i \(-0.494218\pi\)
0.0181642 + 0.999835i \(0.494218\pi\)
\(234\) 0 0
\(235\) 10.5572 0.688678
\(236\) −31.7895 −2.06932
\(237\) 15.2689 0.991820
\(238\) 13.5673 0.879434
\(239\) −0.0284300 −0.00183898 −0.000919490 1.00000i \(-0.500293\pi\)
−0.000919490 1.00000i \(0.500293\pi\)
\(240\) −14.1379 −0.912600
\(241\) 21.0729 1.35742 0.678712 0.734405i \(-0.262538\pi\)
0.678712 + 0.734405i \(0.262538\pi\)
\(242\) 26.3080 1.69114
\(243\) 1.00000 0.0641500
\(244\) −14.7399 −0.943627
\(245\) −1.51368 −0.0967058
\(246\) 5.25329 0.334938
\(247\) 0 0
\(248\) −67.2656 −4.27137
\(249\) −11.7165 −0.742500
\(250\) −30.3986 −1.92258
\(251\) 10.0148 0.632129 0.316064 0.948738i \(-0.397638\pi\)
0.316064 + 0.948738i \(0.397638\pi\)
\(252\) −4.78683 −0.301542
\(253\) 3.74887 0.235689
\(254\) −8.28782 −0.520024
\(255\) −7.88304 −0.493655
\(256\) −18.1816 −1.13635
\(257\) 2.05650 0.128281 0.0641404 0.997941i \(-0.479569\pi\)
0.0641404 + 0.997941i \(0.479569\pi\)
\(258\) 26.5178 1.65092
\(259\) −7.19721 −0.447213
\(260\) 0 0
\(261\) 5.11085 0.316354
\(262\) −57.8983 −3.57697
\(263\) −25.5725 −1.57686 −0.788432 0.615121i \(-0.789107\pi\)
−0.788432 + 0.615121i \(0.789107\pi\)
\(264\) 6.89347 0.424264
\(265\) 16.9840 1.04332
\(266\) 14.4166 0.883937
\(267\) 8.13994 0.498156
\(268\) 61.7370 3.77119
\(269\) 18.2104 1.11031 0.555155 0.831747i \(-0.312659\pi\)
0.555155 + 0.831747i \(0.312659\pi\)
\(270\) 3.94338 0.239987
\(271\) −0.286832 −0.0174238 −0.00871191 0.999962i \(-0.502773\pi\)
−0.00871191 + 0.999962i \(0.502773\pi\)
\(272\) 48.6417 2.94934
\(273\) 0 0
\(274\) −34.5018 −2.08433
\(275\) 2.57196 0.155095
\(276\) −18.8997 −1.13763
\(277\) −26.3811 −1.58509 −0.792543 0.609816i \(-0.791243\pi\)
−0.792543 + 0.609816i \(0.791243\pi\)
\(278\) −37.6904 −2.26052
\(279\) 9.26508 0.554686
\(280\) −10.9895 −0.656750
\(281\) −20.1174 −1.20010 −0.600051 0.799961i \(-0.704853\pi\)
−0.600051 + 0.799961i \(0.704853\pi\)
\(282\) 18.1697 1.08199
\(283\) 27.2020 1.61699 0.808495 0.588503i \(-0.200283\pi\)
0.808495 + 0.588503i \(0.200283\pi\)
\(284\) −37.2335 −2.20940
\(285\) −8.37653 −0.496183
\(286\) 0 0
\(287\) 2.01650 0.119030
\(288\) −9.81211 −0.578184
\(289\) 10.1217 0.595394
\(290\) 20.1540 1.18349
\(291\) 14.8803 0.872296
\(292\) −41.3802 −2.42159
\(293\) 4.80538 0.280733 0.140367 0.990100i \(-0.455172\pi\)
0.140367 + 0.990100i \(0.455172\pi\)
\(294\) −2.60515 −0.151936
\(295\) 10.0524 0.585276
\(296\) −52.2527 −3.03712
\(297\) −0.949498 −0.0550955
\(298\) −40.5602 −2.34959
\(299\) 0 0
\(300\) −12.9664 −0.748614
\(301\) 10.1790 0.586705
\(302\) 20.2296 1.16408
\(303\) −0.878824 −0.0504871
\(304\) 51.6868 2.96444
\(305\) 4.66104 0.266890
\(306\) −13.5673 −0.775588
\(307\) −3.38773 −0.193348 −0.0966739 0.995316i \(-0.530820\pi\)
−0.0966739 + 0.995316i \(0.530820\pi\)
\(308\) 4.54509 0.258980
\(309\) 4.72585 0.268844
\(310\) 36.5357 2.07509
\(311\) −1.19801 −0.0679327 −0.0339664 0.999423i \(-0.510814\pi\)
−0.0339664 + 0.999423i \(0.510814\pi\)
\(312\) 0 0
\(313\) 7.65369 0.432612 0.216306 0.976326i \(-0.430599\pi\)
0.216306 + 0.976326i \(0.430599\pi\)
\(314\) 21.9300 1.23758
\(315\) 1.51368 0.0852865
\(316\) 73.0895 4.11160
\(317\) 16.9899 0.954249 0.477125 0.878836i \(-0.341679\pi\)
0.477125 + 0.878836i \(0.341679\pi\)
\(318\) 29.2307 1.63918
\(319\) −4.85274 −0.271702
\(320\) −10.4170 −0.582330
\(321\) 14.5988 0.814823
\(322\) −10.2858 −0.573207
\(323\) 28.8195 1.60356
\(324\) 4.78683 0.265935
\(325\) 0 0
\(326\) 17.3802 0.962602
\(327\) −14.4751 −0.800476
\(328\) 14.6400 0.808360
\(329\) 6.97453 0.384518
\(330\) −3.74423 −0.206113
\(331\) −29.4213 −1.61714 −0.808571 0.588399i \(-0.799759\pi\)
−0.808571 + 0.588399i \(0.799759\pi\)
\(332\) −56.0847 −3.07805
\(333\) 7.19721 0.394405
\(334\) −2.00172 −0.109529
\(335\) −19.5224 −1.06662
\(336\) −9.34008 −0.509543
\(337\) 11.6689 0.635647 0.317823 0.948150i \(-0.397048\pi\)
0.317823 + 0.948150i \(0.397048\pi\)
\(338\) 0 0
\(339\) −0.659804 −0.0358356
\(340\) −37.7348 −2.04646
\(341\) −8.79717 −0.476393
\(342\) −14.4166 −0.779559
\(343\) −1.00000 −0.0539949
\(344\) 73.9005 3.98445
\(345\) 5.97642 0.321760
\(346\) 1.58114 0.0850028
\(347\) 27.0926 1.45441 0.727203 0.686422i \(-0.240820\pi\)
0.727203 + 0.686422i \(0.240820\pi\)
\(348\) 24.4648 1.31145
\(349\) 11.2409 0.601711 0.300855 0.953670i \(-0.402728\pi\)
0.300855 + 0.953670i \(0.402728\pi\)
\(350\) −7.05674 −0.377198
\(351\) 0 0
\(352\) 9.31658 0.496575
\(353\) −6.14521 −0.327077 −0.163538 0.986537i \(-0.552291\pi\)
−0.163538 + 0.986537i \(0.552291\pi\)
\(354\) 17.3009 0.919534
\(355\) 11.7739 0.624896
\(356\) 38.9645 2.06511
\(357\) −5.20785 −0.275629
\(358\) −19.3643 −1.02344
\(359\) 16.0261 0.845823 0.422911 0.906171i \(-0.361008\pi\)
0.422911 + 0.906171i \(0.361008\pi\)
\(360\) 10.9895 0.579199
\(361\) 11.6237 0.611773
\(362\) −47.6274 −2.50324
\(363\) −10.0985 −0.530031
\(364\) 0 0
\(365\) 13.0852 0.684910
\(366\) 8.02197 0.419315
\(367\) 13.1656 0.687241 0.343620 0.939109i \(-0.388347\pi\)
0.343620 + 0.939109i \(0.388347\pi\)
\(368\) −36.8771 −1.92235
\(369\) −2.01650 −0.104975
\(370\) 28.3814 1.47548
\(371\) 11.2203 0.582530
\(372\) 44.3503 2.29946
\(373\) 20.9338 1.08391 0.541954 0.840408i \(-0.317685\pi\)
0.541954 + 0.840408i \(0.317685\pi\)
\(374\) 12.8821 0.666116
\(375\) 11.6686 0.602565
\(376\) 50.6359 2.61135
\(377\) 0 0
\(378\) 2.60515 0.133995
\(379\) 21.9130 1.12560 0.562798 0.826595i \(-0.309725\pi\)
0.562798 + 0.826595i \(0.309725\pi\)
\(380\) −40.0970 −2.05693
\(381\) 3.18132 0.162984
\(382\) −9.90201 −0.506631
\(383\) 28.2588 1.44396 0.721979 0.691915i \(-0.243233\pi\)
0.721979 + 0.691915i \(0.243233\pi\)
\(384\) 1.69580 0.0865386
\(385\) −1.43724 −0.0732485
\(386\) 6.58078 0.334953
\(387\) −10.1790 −0.517426
\(388\) 71.2293 3.61612
\(389\) −9.13748 −0.463288 −0.231644 0.972801i \(-0.574411\pi\)
−0.231644 + 0.972801i \(0.574411\pi\)
\(390\) 0 0
\(391\) −20.5619 −1.03986
\(392\) −7.26012 −0.366692
\(393\) 22.2245 1.12108
\(394\) −19.5721 −0.986030
\(395\) −23.1122 −1.16290
\(396\) −4.54509 −0.228399
\(397\) −16.6775 −0.837018 −0.418509 0.908213i \(-0.637447\pi\)
−0.418509 + 0.908213i \(0.637447\pi\)
\(398\) −21.9068 −1.09809
\(399\) −5.53387 −0.277040
\(400\) −25.3000 −1.26500
\(401\) 31.7990 1.58796 0.793982 0.607941i \(-0.208004\pi\)
0.793982 + 0.607941i \(0.208004\pi\)
\(402\) −33.5994 −1.67578
\(403\) 0 0
\(404\) −4.20678 −0.209295
\(405\) −1.51368 −0.0752156
\(406\) 13.3146 0.660791
\(407\) −6.83374 −0.338736
\(408\) −37.8096 −1.87186
\(409\) 9.94983 0.491987 0.245994 0.969271i \(-0.420886\pi\)
0.245994 + 0.969271i \(0.420886\pi\)
\(410\) −7.95182 −0.392713
\(411\) 13.2437 0.653262
\(412\) 22.6218 1.11450
\(413\) 6.64104 0.326784
\(414\) 10.2858 0.505521
\(415\) 17.7350 0.870578
\(416\) 0 0
\(417\) 14.4676 0.708482
\(418\) 13.6885 0.669527
\(419\) 25.2181 1.23198 0.615991 0.787753i \(-0.288756\pi\)
0.615991 + 0.787753i \(0.288756\pi\)
\(420\) 7.24575 0.353556
\(421\) 14.6230 0.712683 0.356341 0.934356i \(-0.384024\pi\)
0.356341 + 0.934356i \(0.384024\pi\)
\(422\) 44.3234 2.15763
\(423\) −6.97453 −0.339113
\(424\) 81.4610 3.95609
\(425\) −14.1068 −0.684281
\(426\) 20.2637 0.981782
\(427\) 3.07927 0.149016
\(428\) 69.8818 3.37786
\(429\) 0 0
\(430\) −40.1395 −1.93570
\(431\) 17.5855 0.847063 0.423532 0.905881i \(-0.360790\pi\)
0.423532 + 0.905881i \(0.360790\pi\)
\(432\) 9.34008 0.449375
\(433\) −32.4471 −1.55931 −0.779654 0.626211i \(-0.784605\pi\)
−0.779654 + 0.626211i \(0.784605\pi\)
\(434\) 24.1370 1.15861
\(435\) −7.73622 −0.370923
\(436\) −69.2899 −3.31839
\(437\) −21.8491 −1.04519
\(438\) 22.5205 1.07607
\(439\) 10.0106 0.477781 0.238890 0.971047i \(-0.423216\pi\)
0.238890 + 0.971047i \(0.423216\pi\)
\(440\) −10.4345 −0.497447
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −5.83618 −0.277286 −0.138643 0.990342i \(-0.544274\pi\)
−0.138643 + 0.990342i \(0.544274\pi\)
\(444\) 34.4518 1.63501
\(445\) −12.3213 −0.584086
\(446\) −21.9755 −1.04057
\(447\) 15.5692 0.736399
\(448\) −6.88190 −0.325139
\(449\) 18.4584 0.871105 0.435552 0.900163i \(-0.356553\pi\)
0.435552 + 0.900163i \(0.356553\pi\)
\(450\) 7.05674 0.332658
\(451\) 1.91466 0.0901579
\(452\) −3.15837 −0.148557
\(453\) −7.76523 −0.364842
\(454\) −51.3059 −2.40791
\(455\) 0 0
\(456\) −40.1766 −1.88144
\(457\) −0.831673 −0.0389040 −0.0194520 0.999811i \(-0.506192\pi\)
−0.0194520 + 0.999811i \(0.506192\pi\)
\(458\) 23.0520 1.07715
\(459\) 5.20785 0.243082
\(460\) 28.6081 1.33386
\(461\) −31.3731 −1.46119 −0.730597 0.682809i \(-0.760758\pi\)
−0.730597 + 0.682809i \(0.760758\pi\)
\(462\) −2.47359 −0.115082
\(463\) −23.7154 −1.10215 −0.551074 0.834457i \(-0.685782\pi\)
−0.551074 + 0.834457i \(0.685782\pi\)
\(464\) 47.7358 2.21608
\(465\) −14.0244 −0.650366
\(466\) −1.44464 −0.0669215
\(467\) −4.32173 −0.199986 −0.0999929 0.994988i \(-0.531882\pi\)
−0.0999929 + 0.994988i \(0.531882\pi\)
\(468\) 0 0
\(469\) −12.8973 −0.595541
\(470\) −27.5032 −1.26863
\(471\) −8.41794 −0.387878
\(472\) 48.2148 2.21926
\(473\) 9.66490 0.444393
\(474\) −39.7778 −1.82705
\(475\) −14.9899 −0.687784
\(476\) −24.9291 −1.14262
\(477\) −11.2203 −0.513743
\(478\) 0.0740644 0.00338763
\(479\) −33.2267 −1.51816 −0.759082 0.650995i \(-0.774352\pi\)
−0.759082 + 0.650995i \(0.774352\pi\)
\(480\) 14.8524 0.677918
\(481\) 0 0
\(482\) −54.8981 −2.50054
\(483\) 3.94826 0.179652
\(484\) −48.3396 −2.19725
\(485\) −22.5240 −1.02276
\(486\) −2.60515 −0.118172
\(487\) 38.7278 1.75492 0.877462 0.479646i \(-0.159235\pi\)
0.877462 + 0.479646i \(0.159235\pi\)
\(488\) 22.3559 1.01200
\(489\) −6.67148 −0.301695
\(490\) 3.94338 0.178144
\(491\) −8.21236 −0.370619 −0.185309 0.982680i \(-0.559329\pi\)
−0.185309 + 0.982680i \(0.559329\pi\)
\(492\) −9.65264 −0.435174
\(493\) 26.6166 1.19875
\(494\) 0 0
\(495\) 1.43724 0.0645991
\(496\) 86.5366 3.88561
\(497\) 7.77833 0.348906
\(498\) 30.5232 1.36778
\(499\) −3.44425 −0.154186 −0.0770930 0.997024i \(-0.524564\pi\)
−0.0770930 + 0.997024i \(0.524564\pi\)
\(500\) 55.8557 2.49794
\(501\) 0.768371 0.0343283
\(502\) −26.0901 −1.16446
\(503\) 31.6929 1.41312 0.706559 0.707654i \(-0.250246\pi\)
0.706559 + 0.707654i \(0.250246\pi\)
\(504\) 7.26012 0.323392
\(505\) 1.33026 0.0591959
\(506\) −9.76637 −0.434168
\(507\) 0 0
\(508\) 15.2284 0.675652
\(509\) 5.98899 0.265457 0.132729 0.991152i \(-0.457626\pi\)
0.132729 + 0.991152i \(0.457626\pi\)
\(510\) 20.5365 0.909373
\(511\) 8.64459 0.382414
\(512\) 43.9744 1.94341
\(513\) 5.53387 0.244326
\(514\) −5.35750 −0.236309
\(515\) −7.15344 −0.315218
\(516\) −48.7249 −2.14500
\(517\) 6.62230 0.291248
\(518\) 18.7499 0.823821
\(519\) −0.606929 −0.0266412
\(520\) 0 0
\(521\) 36.0714 1.58032 0.790159 0.612902i \(-0.209998\pi\)
0.790159 + 0.612902i \(0.209998\pi\)
\(522\) −13.3146 −0.582763
\(523\) −16.9852 −0.742710 −0.371355 0.928491i \(-0.621107\pi\)
−0.371355 + 0.928491i \(0.621107\pi\)
\(524\) 106.385 4.64745
\(525\) 2.70876 0.118220
\(526\) 66.6202 2.90478
\(527\) 48.2511 2.10185
\(528\) −8.86839 −0.385947
\(529\) −7.41124 −0.322228
\(530\) −44.2460 −1.92192
\(531\) −6.64104 −0.288197
\(532\) −26.4897 −1.14847
\(533\) 0 0
\(534\) −21.2058 −0.917665
\(535\) −22.0979 −0.955376
\(536\) −93.6358 −4.04445
\(537\) 7.43308 0.320761
\(538\) −47.4410 −2.04533
\(539\) −0.949498 −0.0408978
\(540\) −7.24575 −0.311807
\(541\) 1.76197 0.0757532 0.0378766 0.999282i \(-0.487941\pi\)
0.0378766 + 0.999282i \(0.487941\pi\)
\(542\) 0.747243 0.0320968
\(543\) 18.2820 0.784555
\(544\) −51.1000 −2.19089
\(545\) 21.9108 0.938554
\(546\) 0 0
\(547\) 15.6128 0.667556 0.333778 0.942652i \(-0.391676\pi\)
0.333778 + 0.942652i \(0.391676\pi\)
\(548\) 63.3952 2.70811
\(549\) −3.07927 −0.131420
\(550\) −6.70036 −0.285704
\(551\) 28.2828 1.20489
\(552\) 28.6649 1.22006
\(553\) −15.2689 −0.649298
\(554\) 68.7268 2.91992
\(555\) −10.8943 −0.462438
\(556\) 69.2540 2.93702
\(557\) −42.6449 −1.80692 −0.903461 0.428671i \(-0.858982\pi\)
−0.903461 + 0.428671i \(0.858982\pi\)
\(558\) −24.1370 −1.02180
\(559\) 0 0
\(560\) 14.1379 0.597437
\(561\) −4.94484 −0.208771
\(562\) 52.4089 2.21074
\(563\) 32.6273 1.37507 0.687537 0.726149i \(-0.258692\pi\)
0.687537 + 0.726149i \(0.258692\pi\)
\(564\) −33.3859 −1.40580
\(565\) 0.998735 0.0420171
\(566\) −70.8653 −2.97869
\(567\) −1.00000 −0.0419961
\(568\) 56.4716 2.36950
\(569\) 41.3429 1.73318 0.866592 0.499017i \(-0.166306\pi\)
0.866592 + 0.499017i \(0.166306\pi\)
\(570\) 21.8222 0.914029
\(571\) −42.3972 −1.77427 −0.887135 0.461511i \(-0.847308\pi\)
−0.887135 + 0.461511i \(0.847308\pi\)
\(572\) 0 0
\(573\) 3.80093 0.158786
\(574\) −5.25329 −0.219268
\(575\) 10.6949 0.446008
\(576\) 6.88190 0.286746
\(577\) −26.2118 −1.09121 −0.545606 0.838042i \(-0.683700\pi\)
−0.545606 + 0.838042i \(0.683700\pi\)
\(578\) −26.3686 −1.09679
\(579\) −2.52606 −0.104979
\(580\) −37.0320 −1.53767
\(581\) 11.7165 0.486081
\(582\) −38.7654 −1.60688
\(583\) 10.6537 0.441230
\(584\) 62.7608 2.59706
\(585\) 0 0
\(586\) −12.5188 −0.517145
\(587\) −30.8293 −1.27246 −0.636230 0.771499i \(-0.719507\pi\)
−0.636230 + 0.771499i \(0.719507\pi\)
\(588\) 4.78683 0.197406
\(589\) 51.2717 2.11261
\(590\) −26.1882 −1.07815
\(591\) 7.51285 0.309037
\(592\) 67.2226 2.76283
\(593\) −27.8372 −1.14314 −0.571568 0.820554i \(-0.693665\pi\)
−0.571568 + 0.820554i \(0.693665\pi\)
\(594\) 2.47359 0.101493
\(595\) 7.88304 0.323173
\(596\) 74.5272 3.05275
\(597\) 8.40900 0.344158
\(598\) 0 0
\(599\) −11.0019 −0.449525 −0.224763 0.974414i \(-0.572161\pi\)
−0.224763 + 0.974414i \(0.572161\pi\)
\(600\) 19.6659 0.802858
\(601\) −15.5029 −0.632377 −0.316188 0.948696i \(-0.602403\pi\)
−0.316188 + 0.948696i \(0.602403\pi\)
\(602\) −26.5178 −1.08078
\(603\) 12.8973 0.525217
\(604\) −37.1708 −1.51246
\(605\) 15.2859 0.621459
\(606\) 2.28947 0.0930035
\(607\) −2.16091 −0.0877086 −0.0438543 0.999038i \(-0.513964\pi\)
−0.0438543 + 0.999038i \(0.513964\pi\)
\(608\) −54.2989 −2.20211
\(609\) −5.11085 −0.207102
\(610\) −12.1427 −0.491645
\(611\) 0 0
\(612\) 24.9291 1.00770
\(613\) −18.3854 −0.742578 −0.371289 0.928517i \(-0.621084\pi\)
−0.371289 + 0.928517i \(0.621084\pi\)
\(614\) 8.82555 0.356170
\(615\) 3.05234 0.123082
\(616\) −6.89347 −0.277746
\(617\) 26.0219 1.04760 0.523801 0.851841i \(-0.324514\pi\)
0.523801 + 0.851841i \(0.324514\pi\)
\(618\) −12.3116 −0.495244
\(619\) 13.1006 0.526557 0.263278 0.964720i \(-0.415196\pi\)
0.263278 + 0.964720i \(0.415196\pi\)
\(620\) −67.1324 −2.69610
\(621\) −3.94826 −0.158438
\(622\) 3.12099 0.125140
\(623\) −8.13994 −0.326120
\(624\) 0 0
\(625\) −4.11883 −0.164753
\(626\) −19.9390 −0.796925
\(627\) −5.25439 −0.209840
\(628\) −40.2953 −1.60796
\(629\) 37.4820 1.49451
\(630\) −3.94338 −0.157108
\(631\) 10.3506 0.412052 0.206026 0.978547i \(-0.433947\pi\)
0.206026 + 0.978547i \(0.433947\pi\)
\(632\) −110.854 −4.40953
\(633\) −17.0137 −0.676235
\(634\) −44.2614 −1.75784
\(635\) −4.81551 −0.191098
\(636\) −53.7098 −2.12973
\(637\) 0 0
\(638\) 12.6421 0.500507
\(639\) −7.77833 −0.307706
\(640\) −2.56691 −0.101466
\(641\) 16.7543 0.661754 0.330877 0.943674i \(-0.392655\pi\)
0.330877 + 0.943674i \(0.392655\pi\)
\(642\) −38.0320 −1.50100
\(643\) 28.7346 1.13318 0.566592 0.823999i \(-0.308262\pi\)
0.566592 + 0.823999i \(0.308262\pi\)
\(644\) 18.8997 0.744751
\(645\) 15.4077 0.606679
\(646\) −75.0794 −2.95396
\(647\) −30.0734 −1.18231 −0.591154 0.806559i \(-0.701327\pi\)
−0.591154 + 0.806559i \(0.701327\pi\)
\(648\) −7.26012 −0.285205
\(649\) 6.30565 0.247518
\(650\) 0 0
\(651\) −9.26508 −0.363127
\(652\) −31.9352 −1.25068
\(653\) 2.99613 0.117247 0.0586237 0.998280i \(-0.481329\pi\)
0.0586237 + 0.998280i \(0.481329\pi\)
\(654\) 37.7099 1.47457
\(655\) −33.6409 −1.31446
\(656\) −18.8343 −0.735354
\(657\) −8.64459 −0.337258
\(658\) −18.1697 −0.708330
\(659\) 18.0993 0.705047 0.352524 0.935803i \(-0.385324\pi\)
0.352524 + 0.935803i \(0.385324\pi\)
\(660\) 6.87982 0.267797
\(661\) 39.9992 1.55579 0.777895 0.628395i \(-0.216288\pi\)
0.777895 + 0.628395i \(0.216288\pi\)
\(662\) 76.6471 2.97897
\(663\) 0 0
\(664\) 85.0629 3.30108
\(665\) 8.37653 0.324828
\(666\) −18.7499 −0.726542
\(667\) −20.1790 −0.781333
\(668\) 3.67806 0.142308
\(669\) 8.43541 0.326132
\(670\) 50.8589 1.96485
\(671\) 2.92376 0.112870
\(672\) 9.81211 0.378510
\(673\) 4.21170 0.162349 0.0811745 0.996700i \(-0.474133\pi\)
0.0811745 + 0.996700i \(0.474133\pi\)
\(674\) −30.3994 −1.17094
\(675\) −2.70876 −0.104260
\(676\) 0 0
\(677\) −31.9491 −1.22790 −0.613951 0.789344i \(-0.710421\pi\)
−0.613951 + 0.789344i \(0.710421\pi\)
\(678\) 1.71889 0.0660136
\(679\) −14.8803 −0.571052
\(680\) 57.2319 2.19474
\(681\) 19.6940 0.754676
\(682\) 22.9180 0.877575
\(683\) 41.8402 1.60097 0.800484 0.599353i \(-0.204576\pi\)
0.800484 + 0.599353i \(0.204576\pi\)
\(684\) 26.4897 1.01286
\(685\) −20.0467 −0.765947
\(686\) 2.60515 0.0994653
\(687\) −8.84860 −0.337595
\(688\) −95.0723 −3.62460
\(689\) 0 0
\(690\) −15.5695 −0.592721
\(691\) 22.8484 0.869192 0.434596 0.900625i \(-0.356891\pi\)
0.434596 + 0.900625i \(0.356891\pi\)
\(692\) −2.90527 −0.110442
\(693\) 0.949498 0.0360684
\(694\) −70.5804 −2.67919
\(695\) −21.8994 −0.830692
\(696\) −37.1054 −1.40648
\(697\) −10.5016 −0.397777
\(698\) −29.2842 −1.10842
\(699\) 0.554530 0.0209743
\(700\) 12.9664 0.490083
\(701\) 14.1083 0.532862 0.266431 0.963854i \(-0.414156\pi\)
0.266431 + 0.963854i \(0.414156\pi\)
\(702\) 0 0
\(703\) 39.8284 1.50216
\(704\) −6.53435 −0.246273
\(705\) 10.5572 0.397608
\(706\) 16.0092 0.602515
\(707\) 0.878824 0.0330516
\(708\) −31.7895 −1.19472
\(709\) 39.8609 1.49701 0.748504 0.663130i \(-0.230772\pi\)
0.748504 + 0.663130i \(0.230772\pi\)
\(710\) −30.6729 −1.15113
\(711\) 15.2689 0.572627
\(712\) −59.0970 −2.21475
\(713\) −36.5809 −1.36997
\(714\) 13.5673 0.507742
\(715\) 0 0
\(716\) 35.5809 1.32972
\(717\) −0.0284300 −0.00106174
\(718\) −41.7503 −1.55811
\(719\) −21.0361 −0.784514 −0.392257 0.919856i \(-0.628306\pi\)
−0.392257 + 0.919856i \(0.628306\pi\)
\(720\) −14.1379 −0.526890
\(721\) −4.72585 −0.176000
\(722\) −30.2815 −1.12696
\(723\) 21.0729 0.783709
\(724\) 87.5128 3.25239
\(725\) −13.8441 −0.514156
\(726\) 26.3080 0.976383
\(727\) −12.6534 −0.469288 −0.234644 0.972081i \(-0.575392\pi\)
−0.234644 + 0.972081i \(0.575392\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −34.0889 −1.26169
\(731\) −53.0105 −1.96066
\(732\) −14.7399 −0.544803
\(733\) −14.2854 −0.527643 −0.263821 0.964572i \(-0.584983\pi\)
−0.263821 + 0.964572i \(0.584983\pi\)
\(734\) −34.2985 −1.26598
\(735\) −1.51368 −0.0558331
\(736\) 38.7408 1.42800
\(737\) −12.2459 −0.451085
\(738\) 5.25329 0.193376
\(739\) 8.90875 0.327714 0.163857 0.986484i \(-0.447606\pi\)
0.163857 + 0.986484i \(0.447606\pi\)
\(740\) −52.1492 −1.91704
\(741\) 0 0
\(742\) −29.2307 −1.07309
\(743\) −28.1389 −1.03232 −0.516158 0.856493i \(-0.672638\pi\)
−0.516158 + 0.856493i \(0.672638\pi\)
\(744\) −67.2656 −2.46608
\(745\) −23.5669 −0.863424
\(746\) −54.5357 −1.99669
\(747\) −11.7165 −0.428683
\(748\) −23.6701 −0.865465
\(749\) −14.5988 −0.533427
\(750\) −30.3986 −1.11000
\(751\) 44.6703 1.63004 0.815020 0.579432i \(-0.196726\pi\)
0.815020 + 0.579432i \(0.196726\pi\)
\(752\) −65.1427 −2.37551
\(753\) 10.0148 0.364960
\(754\) 0 0
\(755\) 11.7541 0.427776
\(756\) −4.78683 −0.174095
\(757\) 12.0887 0.439373 0.219686 0.975571i \(-0.429497\pi\)
0.219686 + 0.975571i \(0.429497\pi\)
\(758\) −57.0867 −2.07348
\(759\) 3.74887 0.136075
\(760\) 60.8146 2.20598
\(761\) 17.8391 0.646667 0.323333 0.946285i \(-0.395197\pi\)
0.323333 + 0.946285i \(0.395197\pi\)
\(762\) −8.28782 −0.300236
\(763\) 14.4751 0.524034
\(764\) 18.1944 0.658250
\(765\) −7.88304 −0.285012
\(766\) −73.6185 −2.65995
\(767\) 0 0
\(768\) −18.1816 −0.656073
\(769\) 11.4506 0.412921 0.206460 0.978455i \(-0.433806\pi\)
0.206460 + 0.978455i \(0.433806\pi\)
\(770\) 3.74423 0.134933
\(771\) 2.05650 0.0740630
\(772\) −12.0918 −0.435194
\(773\) −11.1486 −0.400988 −0.200494 0.979695i \(-0.564255\pi\)
−0.200494 + 0.979695i \(0.564255\pi\)
\(774\) 26.5178 0.953161
\(775\) −25.0969 −0.901506
\(776\) −108.032 −3.87814
\(777\) −7.19721 −0.258199
\(778\) 23.8045 0.853434
\(779\) −11.1590 −0.399814
\(780\) 0 0
\(781\) 7.38551 0.264274
\(782\) 53.5671 1.91555
\(783\) 5.11085 0.182647
\(784\) 9.34008 0.333574
\(785\) 12.7421 0.454785
\(786\) −57.8983 −2.06516
\(787\) −49.5139 −1.76498 −0.882489 0.470332i \(-0.844134\pi\)
−0.882489 + 0.470332i \(0.844134\pi\)
\(788\) 35.9627 1.28112
\(789\) −25.5725 −0.910403
\(790\) 60.2110 2.14221
\(791\) 0.659804 0.0234599
\(792\) 6.89347 0.244949
\(793\) 0 0
\(794\) 43.4474 1.54189
\(795\) 16.9840 0.602362
\(796\) 40.2525 1.42671
\(797\) −33.7455 −1.19533 −0.597664 0.801747i \(-0.703904\pi\)
−0.597664 + 0.801747i \(0.703904\pi\)
\(798\) 14.4166 0.510341
\(799\) −36.3223 −1.28499
\(800\) 26.5786 0.939697
\(801\) 8.13994 0.287611
\(802\) −82.8412 −2.92522
\(803\) 8.20802 0.289655
\(804\) 61.7370 2.17730
\(805\) −5.97642 −0.210641
\(806\) 0 0
\(807\) 18.2104 0.641037
\(808\) 6.38037 0.224461
\(809\) 28.4402 0.999906 0.499953 0.866053i \(-0.333351\pi\)
0.499953 + 0.866053i \(0.333351\pi\)
\(810\) 3.94338 0.138556
\(811\) −2.84955 −0.100061 −0.0500306 0.998748i \(-0.515932\pi\)
−0.0500306 + 0.998748i \(0.515932\pi\)
\(812\) −24.4648 −0.858546
\(813\) −0.286832 −0.0100597
\(814\) 17.8029 0.623993
\(815\) 10.0985 0.353736
\(816\) 48.6417 1.70280
\(817\) −56.3290 −1.97070
\(818\) −25.9208 −0.906301
\(819\) 0 0
\(820\) 14.6110 0.510240
\(821\) −34.9336 −1.21919 −0.609596 0.792712i \(-0.708668\pi\)
−0.609596 + 0.792712i \(0.708668\pi\)
\(822\) −34.5018 −1.20339
\(823\) −41.4188 −1.44377 −0.721884 0.692014i \(-0.756723\pi\)
−0.721884 + 0.692014i \(0.756723\pi\)
\(824\) −34.3102 −1.19525
\(825\) 2.57196 0.0895442
\(826\) −17.3009 −0.601976
\(827\) −23.6924 −0.823866 −0.411933 0.911214i \(-0.635146\pi\)
−0.411933 + 0.911214i \(0.635146\pi\)
\(828\) −18.8997 −0.656808
\(829\) −40.0234 −1.39007 −0.695034 0.718977i \(-0.744611\pi\)
−0.695034 + 0.718977i \(0.744611\pi\)
\(830\) −46.2025 −1.60371
\(831\) −26.3811 −0.915150
\(832\) 0 0
\(833\) 5.20785 0.180441
\(834\) −37.6904 −1.30511
\(835\) −1.16307 −0.0402497
\(836\) −25.1519 −0.869896
\(837\) 9.26508 0.320248
\(838\) −65.6969 −2.26946
\(839\) −43.8642 −1.51436 −0.757181 0.653206i \(-0.773424\pi\)
−0.757181 + 0.653206i \(0.773424\pi\)
\(840\) −10.9895 −0.379175
\(841\) −2.87918 −0.0992820
\(842\) −38.0953 −1.31285
\(843\) −20.1174 −0.692880
\(844\) −81.4419 −2.80334
\(845\) 0 0
\(846\) 18.1697 0.624688
\(847\) 10.0985 0.346987
\(848\) −104.799 −3.59880
\(849\) 27.2020 0.933569
\(850\) 36.7504 1.26053
\(851\) −28.4165 −0.974104
\(852\) −37.2335 −1.27560
\(853\) −18.6397 −0.638210 −0.319105 0.947719i \(-0.603382\pi\)
−0.319105 + 0.947719i \(0.603382\pi\)
\(854\) −8.02197 −0.274506
\(855\) −8.37653 −0.286471
\(856\) −105.989 −3.62262
\(857\) −12.2408 −0.418139 −0.209069 0.977901i \(-0.567043\pi\)
−0.209069 + 0.977901i \(0.567043\pi\)
\(858\) 0 0
\(859\) 12.3049 0.419837 0.209919 0.977719i \(-0.432680\pi\)
0.209919 + 0.977719i \(0.432680\pi\)
\(860\) 73.7542 2.51500
\(861\) 2.01650 0.0687221
\(862\) −45.8129 −1.56039
\(863\) 5.55448 0.189077 0.0945383 0.995521i \(-0.469863\pi\)
0.0945383 + 0.995521i \(0.469863\pi\)
\(864\) −9.81211 −0.333815
\(865\) 0.918699 0.0312367
\(866\) 84.5297 2.87244
\(867\) 10.1217 0.343751
\(868\) −44.3503 −1.50535
\(869\) −14.4978 −0.491803
\(870\) 20.1540 0.683286
\(871\) 0 0
\(872\) 105.091 3.55883
\(873\) 14.8803 0.503620
\(874\) 56.9204 1.92536
\(875\) −11.6686 −0.394472
\(876\) −41.3802 −1.39811
\(877\) 2.68227 0.0905739 0.0452869 0.998974i \(-0.485580\pi\)
0.0452869 + 0.998974i \(0.485580\pi\)
\(878\) −26.0792 −0.880130
\(879\) 4.80538 0.162081
\(880\) 13.4239 0.452521
\(881\) −32.4366 −1.09282 −0.546408 0.837519i \(-0.684005\pi\)
−0.546408 + 0.837519i \(0.684005\pi\)
\(882\) −2.60515 −0.0877201
\(883\) 44.7188 1.50491 0.752453 0.658646i \(-0.228870\pi\)
0.752453 + 0.658646i \(0.228870\pi\)
\(884\) 0 0
\(885\) 10.0524 0.337909
\(886\) 15.2042 0.510794
\(887\) −43.8406 −1.47202 −0.736012 0.676968i \(-0.763293\pi\)
−0.736012 + 0.676968i \(0.763293\pi\)
\(888\) −52.2527 −1.75348
\(889\) −3.18132 −0.106698
\(890\) 32.0989 1.07596
\(891\) −0.949498 −0.0318094
\(892\) 40.3789 1.35198
\(893\) −38.5961 −1.29157
\(894\) −40.5602 −1.35654
\(895\) −11.2513 −0.376091
\(896\) −1.69580 −0.0566528
\(897\) 0 0
\(898\) −48.0869 −1.60468
\(899\) 47.3524 1.57929
\(900\) −12.9664 −0.432212
\(901\) −58.4338 −1.94671
\(902\) −4.98799 −0.166082
\(903\) 10.1790 0.338735
\(904\) 4.79026 0.159322
\(905\) −27.6732 −0.919887
\(906\) 20.2296 0.672084
\(907\) −21.3865 −0.710128 −0.355064 0.934842i \(-0.615541\pi\)
−0.355064 + 0.934842i \(0.615541\pi\)
\(908\) 94.2719 3.12852
\(909\) −0.878824 −0.0291488
\(910\) 0 0
\(911\) −20.5969 −0.682406 −0.341203 0.939990i \(-0.610834\pi\)
−0.341203 + 0.939990i \(0.610834\pi\)
\(912\) 51.6868 1.71152
\(913\) 11.1248 0.368176
\(914\) 2.16664 0.0716660
\(915\) 4.66104 0.154089
\(916\) −42.3568 −1.39951
\(917\) −22.2245 −0.733918
\(918\) −13.5673 −0.447786
\(919\) −7.11153 −0.234588 −0.117294 0.993097i \(-0.537422\pi\)
−0.117294 + 0.993097i \(0.537422\pi\)
\(920\) −43.3896 −1.43051
\(921\) −3.38773 −0.111629
\(922\) 81.7319 2.69170
\(923\) 0 0
\(924\) 4.54509 0.149522
\(925\) −19.4955 −0.641009
\(926\) 61.7823 2.03029
\(927\) 4.72585 0.155217
\(928\) −50.1483 −1.64620
\(929\) 13.4954 0.442769 0.221385 0.975187i \(-0.428942\pi\)
0.221385 + 0.975187i \(0.428942\pi\)
\(930\) 36.5357 1.19805
\(931\) 5.53387 0.181365
\(932\) 2.65444 0.0869492
\(933\) −1.19801 −0.0392210
\(934\) 11.2588 0.368398
\(935\) 7.48493 0.244783
\(936\) 0 0
\(937\) −7.61840 −0.248882 −0.124441 0.992227i \(-0.539714\pi\)
−0.124441 + 0.992227i \(0.539714\pi\)
\(938\) 33.5994 1.09706
\(939\) 7.65369 0.249769
\(940\) 50.5357 1.64829
\(941\) 9.15256 0.298365 0.149182 0.988810i \(-0.452336\pi\)
0.149182 + 0.988810i \(0.452336\pi\)
\(942\) 21.9300 0.714520
\(943\) 7.96166 0.259267
\(944\) −62.0278 −2.01883
\(945\) 1.51368 0.0492402
\(946\) −25.1786 −0.818625
\(947\) 2.69459 0.0875623 0.0437812 0.999041i \(-0.486060\pi\)
0.0437812 + 0.999041i \(0.486060\pi\)
\(948\) 73.0895 2.37384
\(949\) 0 0
\(950\) 39.0510 1.26698
\(951\) 16.9899 0.550936
\(952\) 37.8096 1.22542
\(953\) −16.1487 −0.523106 −0.261553 0.965189i \(-0.584235\pi\)
−0.261553 + 0.965189i \(0.584235\pi\)
\(954\) 29.2307 0.946378
\(955\) −5.75341 −0.186176
\(956\) −0.136089 −0.00440144
\(957\) −4.85274 −0.156867
\(958\) 86.5606 2.79665
\(959\) −13.2437 −0.427660
\(960\) −10.4170 −0.336208
\(961\) 54.8416 1.76909
\(962\) 0 0
\(963\) 14.5988 0.470438
\(964\) 100.872 3.24888
\(965\) 3.82366 0.123088
\(966\) −10.2858 −0.330941
\(967\) −47.9571 −1.54220 −0.771098 0.636717i \(-0.780292\pi\)
−0.771098 + 0.636717i \(0.780292\pi\)
\(968\) 73.3160 2.35647
\(969\) 28.8195 0.925817
\(970\) 58.6785 1.88405
\(971\) 19.2626 0.618166 0.309083 0.951035i \(-0.399978\pi\)
0.309083 + 0.951035i \(0.399978\pi\)
\(972\) 4.78683 0.153538
\(973\) −14.4676 −0.463810
\(974\) −100.892 −3.23279
\(975\) 0 0
\(976\) −28.7606 −0.920605
\(977\) 47.9655 1.53455 0.767276 0.641317i \(-0.221612\pi\)
0.767276 + 0.641317i \(0.221612\pi\)
\(978\) 17.3802 0.555759
\(979\) −7.72885 −0.247015
\(980\) −7.24575 −0.231457
\(981\) −14.4751 −0.462155
\(982\) 21.3945 0.682725
\(983\) 36.7956 1.17360 0.586799 0.809733i \(-0.300388\pi\)
0.586799 + 0.809733i \(0.300388\pi\)
\(984\) 14.6400 0.466707
\(985\) −11.3721 −0.362345
\(986\) −69.3402 −2.20824
\(987\) 6.97453 0.222002
\(988\) 0 0
\(989\) 40.1892 1.27794
\(990\) −3.74423 −0.119000
\(991\) 20.0508 0.636935 0.318467 0.947934i \(-0.396832\pi\)
0.318467 + 0.947934i \(0.396832\pi\)
\(992\) −90.9100 −2.88639
\(993\) −29.4213 −0.933657
\(994\) −20.2637 −0.642727
\(995\) −12.7286 −0.403523
\(996\) −56.0847 −1.77711
\(997\) −31.0874 −0.984549 −0.492274 0.870440i \(-0.663834\pi\)
−0.492274 + 0.870440i \(0.663834\pi\)
\(998\) 8.97282 0.284030
\(999\) 7.19721 0.227710
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 3549.2.a.bh.1.2 yes 15
13.12 even 2 3549.2.a.bg.1.14 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.14 15 13.12 even 2
3549.2.a.bh.1.2 yes 15 1.1 even 1 trivial