Properties

Label 3549.2.a.bh.1.12
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

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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 1.12
Root \(2.07185\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.07185 q^{2} +1.00000 q^{3} +2.29258 q^{4} +3.98491 q^{5} +2.07185 q^{6} -1.00000 q^{7} +0.606176 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.07185 q^{2} +1.00000 q^{3} +2.29258 q^{4} +3.98491 q^{5} +2.07185 q^{6} -1.00000 q^{7} +0.606176 q^{8} +1.00000 q^{9} +8.25616 q^{10} +2.61487 q^{11} +2.29258 q^{12} -2.07185 q^{14} +3.98491 q^{15} -3.32925 q^{16} +2.46321 q^{17} +2.07185 q^{18} +5.30899 q^{19} +9.13572 q^{20} -1.00000 q^{21} +5.41763 q^{22} -8.91513 q^{23} +0.606176 q^{24} +10.8795 q^{25} +1.00000 q^{27} -2.29258 q^{28} -3.55037 q^{29} +8.25616 q^{30} +6.25363 q^{31} -8.11006 q^{32} +2.61487 q^{33} +5.10341 q^{34} -3.98491 q^{35} +2.29258 q^{36} -3.72795 q^{37} +10.9995 q^{38} +2.41556 q^{40} -6.88324 q^{41} -2.07185 q^{42} +7.59739 q^{43} +5.99479 q^{44} +3.98491 q^{45} -18.4709 q^{46} -2.43688 q^{47} -3.32925 q^{48} +1.00000 q^{49} +22.5408 q^{50} +2.46321 q^{51} -10.8574 q^{53} +2.07185 q^{54} +10.4200 q^{55} -0.606176 q^{56} +5.30899 q^{57} -7.35584 q^{58} -0.944885 q^{59} +9.13572 q^{60} +4.95925 q^{61} +12.9566 q^{62} -1.00000 q^{63} -10.1444 q^{64} +5.41763 q^{66} -16.0479 q^{67} +5.64710 q^{68} -8.91513 q^{69} -8.25616 q^{70} +15.8147 q^{71} +0.606176 q^{72} +3.16937 q^{73} -7.72376 q^{74} +10.8795 q^{75} +12.1713 q^{76} -2.61487 q^{77} -5.15670 q^{79} -13.2668 q^{80} +1.00000 q^{81} -14.2611 q^{82} +1.47510 q^{83} -2.29258 q^{84} +9.81567 q^{85} +15.7407 q^{86} -3.55037 q^{87} +1.58507 q^{88} +13.7404 q^{89} +8.25616 q^{90} -20.4386 q^{92} +6.25363 q^{93} -5.04886 q^{94} +21.1559 q^{95} -8.11006 q^{96} -4.52869 q^{97} +2.07185 q^{98} +2.61487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.07185 1.46502 0.732511 0.680755i \(-0.238348\pi\)
0.732511 + 0.680755i \(0.238348\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.29258 1.14629
\(5\) 3.98491 1.78211 0.891054 0.453898i \(-0.149967\pi\)
0.891054 + 0.453898i \(0.149967\pi\)
\(6\) 2.07185 0.845831
\(7\) −1.00000 −0.377964
\(8\) 0.606176 0.214316
\(9\) 1.00000 0.333333
\(10\) 8.25616 2.61083
\(11\) 2.61487 0.788413 0.394207 0.919022i \(-0.371019\pi\)
0.394207 + 0.919022i \(0.371019\pi\)
\(12\) 2.29258 0.661810
\(13\) 0 0
\(14\) −2.07185 −0.553726
\(15\) 3.98491 1.02890
\(16\) −3.32925 −0.832311
\(17\) 2.46321 0.597416 0.298708 0.954345i \(-0.403444\pi\)
0.298708 + 0.954345i \(0.403444\pi\)
\(18\) 2.07185 0.488341
\(19\) 5.30899 1.21797 0.608983 0.793183i \(-0.291578\pi\)
0.608983 + 0.793183i \(0.291578\pi\)
\(20\) 9.13572 2.04281
\(21\) −1.00000 −0.218218
\(22\) 5.41763 1.15504
\(23\) −8.91513 −1.85893 −0.929467 0.368905i \(-0.879733\pi\)
−0.929467 + 0.368905i \(0.879733\pi\)
\(24\) 0.606176 0.123735
\(25\) 10.8795 2.17591
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −2.29258 −0.433256
\(29\) −3.55037 −0.659287 −0.329643 0.944105i \(-0.606929\pi\)
−0.329643 + 0.944105i \(0.606929\pi\)
\(30\) 8.25616 1.50736
\(31\) 6.25363 1.12319 0.561593 0.827414i \(-0.310189\pi\)
0.561593 + 0.827414i \(0.310189\pi\)
\(32\) −8.11006 −1.43367
\(33\) 2.61487 0.455191
\(34\) 5.10341 0.875227
\(35\) −3.98491 −0.673573
\(36\) 2.29258 0.382096
\(37\) −3.72795 −0.612871 −0.306435 0.951891i \(-0.599136\pi\)
−0.306435 + 0.951891i \(0.599136\pi\)
\(38\) 10.9995 1.78435
\(39\) 0 0
\(40\) 2.41556 0.381934
\(41\) −6.88324 −1.07498 −0.537490 0.843270i \(-0.680628\pi\)
−0.537490 + 0.843270i \(0.680628\pi\)
\(42\) −2.07185 −0.319694
\(43\) 7.59739 1.15859 0.579296 0.815117i \(-0.303328\pi\)
0.579296 + 0.815117i \(0.303328\pi\)
\(44\) 5.99479 0.903749
\(45\) 3.98491 0.594036
\(46\) −18.4709 −2.72338
\(47\) −2.43688 −0.355455 −0.177728 0.984080i \(-0.556875\pi\)
−0.177728 + 0.984080i \(0.556875\pi\)
\(48\) −3.32925 −0.480535
\(49\) 1.00000 0.142857
\(50\) 22.5408 3.18775
\(51\) 2.46321 0.344918
\(52\) 0 0
\(53\) −10.8574 −1.49138 −0.745690 0.666293i \(-0.767880\pi\)
−0.745690 + 0.666293i \(0.767880\pi\)
\(54\) 2.07185 0.281944
\(55\) 10.4200 1.40504
\(56\) −0.606176 −0.0810037
\(57\) 5.30899 0.703193
\(58\) −7.35584 −0.965870
\(59\) −0.944885 −0.123014 −0.0615068 0.998107i \(-0.519591\pi\)
−0.0615068 + 0.998107i \(0.519591\pi\)
\(60\) 9.13572 1.17942
\(61\) 4.95925 0.634967 0.317483 0.948264i \(-0.397162\pi\)
0.317483 + 0.948264i \(0.397162\pi\)
\(62\) 12.9566 1.64549
\(63\) −1.00000 −0.125988
\(64\) −10.1444 −1.26805
\(65\) 0 0
\(66\) 5.41763 0.666864
\(67\) −16.0479 −1.96056 −0.980281 0.197609i \(-0.936682\pi\)
−0.980281 + 0.197609i \(0.936682\pi\)
\(68\) 5.64710 0.684811
\(69\) −8.91513 −1.07326
\(70\) −8.25616 −0.986799
\(71\) 15.8147 1.87686 0.938429 0.345471i \(-0.112281\pi\)
0.938429 + 0.345471i \(0.112281\pi\)
\(72\) 0.606176 0.0714386
\(73\) 3.16937 0.370947 0.185473 0.982649i \(-0.440618\pi\)
0.185473 + 0.982649i \(0.440618\pi\)
\(74\) −7.72376 −0.897869
\(75\) 10.8795 1.25626
\(76\) 12.1713 1.39614
\(77\) −2.61487 −0.297992
\(78\) 0 0
\(79\) −5.15670 −0.580174 −0.290087 0.957000i \(-0.593684\pi\)
−0.290087 + 0.957000i \(0.593684\pi\)
\(80\) −13.2668 −1.48327
\(81\) 1.00000 0.111111
\(82\) −14.2611 −1.57487
\(83\) 1.47510 0.161913 0.0809567 0.996718i \(-0.474202\pi\)
0.0809567 + 0.996718i \(0.474202\pi\)
\(84\) −2.29258 −0.250141
\(85\) 9.81567 1.06466
\(86\) 15.7407 1.69736
\(87\) −3.55037 −0.380639
\(88\) 1.58507 0.168969
\(89\) 13.7404 1.45648 0.728241 0.685321i \(-0.240338\pi\)
0.728241 + 0.685321i \(0.240338\pi\)
\(90\) 8.25616 0.870275
\(91\) 0 0
\(92\) −20.4386 −2.13087
\(93\) 6.25363 0.648472
\(94\) −5.04886 −0.520750
\(95\) 21.1559 2.17055
\(96\) −8.11006 −0.827730
\(97\) −4.52869 −0.459819 −0.229910 0.973212i \(-0.573843\pi\)
−0.229910 + 0.973212i \(0.573843\pi\)
\(98\) 2.07185 0.209289
\(99\) 2.61487 0.262804
\(100\) 24.9422 2.49422
\(101\) −2.65442 −0.264125 −0.132062 0.991241i \(-0.542160\pi\)
−0.132062 + 0.991241i \(0.542160\pi\)
\(102\) 5.10341 0.505313
\(103\) −10.9414 −1.07809 −0.539044 0.842278i \(-0.681214\pi\)
−0.539044 + 0.842278i \(0.681214\pi\)
\(104\) 0 0
\(105\) −3.98491 −0.388888
\(106\) −22.4950 −2.18490
\(107\) 5.83503 0.564094 0.282047 0.959401i \(-0.408987\pi\)
0.282047 + 0.959401i \(0.408987\pi\)
\(108\) 2.29258 0.220603
\(109\) 14.4487 1.38393 0.691965 0.721931i \(-0.256745\pi\)
0.691965 + 0.721931i \(0.256745\pi\)
\(110\) 21.5888 2.05841
\(111\) −3.72795 −0.353841
\(112\) 3.32925 0.314584
\(113\) −9.37283 −0.881721 −0.440861 0.897576i \(-0.645327\pi\)
−0.440861 + 0.897576i \(0.645327\pi\)
\(114\) 10.9995 1.03019
\(115\) −35.5260 −3.31282
\(116\) −8.13949 −0.755733
\(117\) 0 0
\(118\) −1.95766 −0.180218
\(119\) −2.46321 −0.225802
\(120\) 2.41556 0.220509
\(121\) −4.16245 −0.378405
\(122\) 10.2748 0.930240
\(123\) −6.88324 −0.620640
\(124\) 14.3369 1.28749
\(125\) 23.4294 2.09559
\(126\) −2.07185 −0.184575
\(127\) −3.25452 −0.288792 −0.144396 0.989520i \(-0.546124\pi\)
−0.144396 + 0.989520i \(0.546124\pi\)
\(128\) −4.79752 −0.424045
\(129\) 7.59739 0.668913
\(130\) 0 0
\(131\) 1.26410 0.110445 0.0552224 0.998474i \(-0.482413\pi\)
0.0552224 + 0.998474i \(0.482413\pi\)
\(132\) 5.99479 0.521780
\(133\) −5.30899 −0.460348
\(134\) −33.2489 −2.87227
\(135\) 3.98491 0.342967
\(136\) 1.49314 0.128036
\(137\) −16.0982 −1.37536 −0.687682 0.726012i \(-0.741371\pi\)
−0.687682 + 0.726012i \(0.741371\pi\)
\(138\) −18.4709 −1.57234
\(139\) 20.8156 1.76556 0.882778 0.469791i \(-0.155671\pi\)
0.882778 + 0.469791i \(0.155671\pi\)
\(140\) −9.13572 −0.772109
\(141\) −2.43688 −0.205222
\(142\) 32.7657 2.74964
\(143\) 0 0
\(144\) −3.32925 −0.277437
\(145\) −14.1479 −1.17492
\(146\) 6.56647 0.543445
\(147\) 1.00000 0.0824786
\(148\) −8.54661 −0.702527
\(149\) −14.5215 −1.18965 −0.594823 0.803856i \(-0.702778\pi\)
−0.594823 + 0.803856i \(0.702778\pi\)
\(150\) 22.5408 1.84045
\(151\) −10.2052 −0.830489 −0.415245 0.909710i \(-0.636304\pi\)
−0.415245 + 0.909710i \(0.636304\pi\)
\(152\) 3.21819 0.261029
\(153\) 2.46321 0.199139
\(154\) −5.41763 −0.436565
\(155\) 24.9202 2.00164
\(156\) 0 0
\(157\) 5.86827 0.468339 0.234170 0.972196i \(-0.424763\pi\)
0.234170 + 0.972196i \(0.424763\pi\)
\(158\) −10.6839 −0.849968
\(159\) −10.8574 −0.861048
\(160\) −32.3179 −2.55495
\(161\) 8.91513 0.702611
\(162\) 2.07185 0.162780
\(163\) −0.697676 −0.0546462 −0.0273231 0.999627i \(-0.508698\pi\)
−0.0273231 + 0.999627i \(0.508698\pi\)
\(164\) −15.7803 −1.23224
\(165\) 10.4200 0.811199
\(166\) 3.05620 0.237207
\(167\) −25.1020 −1.94245 −0.971224 0.238169i \(-0.923453\pi\)
−0.971224 + 0.238169i \(0.923453\pi\)
\(168\) −0.606176 −0.0467675
\(169\) 0 0
\(170\) 20.3366 1.55975
\(171\) 5.30899 0.405989
\(172\) 17.4176 1.32808
\(173\) 5.26644 0.400400 0.200200 0.979755i \(-0.435841\pi\)
0.200200 + 0.979755i \(0.435841\pi\)
\(174\) −7.35584 −0.557645
\(175\) −10.8795 −0.822415
\(176\) −8.70555 −0.656205
\(177\) −0.944885 −0.0710219
\(178\) 28.4681 2.13378
\(179\) 11.4454 0.855469 0.427734 0.903904i \(-0.359312\pi\)
0.427734 + 0.903904i \(0.359312\pi\)
\(180\) 9.13572 0.680936
\(181\) −13.2259 −0.983072 −0.491536 0.870857i \(-0.663564\pi\)
−0.491536 + 0.870857i \(0.663564\pi\)
\(182\) 0 0
\(183\) 4.95925 0.366598
\(184\) −5.40414 −0.398399
\(185\) −14.8556 −1.09220
\(186\) 12.9566 0.950025
\(187\) 6.44097 0.471011
\(188\) −5.58673 −0.407454
\(189\) −1.00000 −0.0727393
\(190\) 43.8319 3.17990
\(191\) 2.77448 0.200754 0.100377 0.994949i \(-0.467995\pi\)
0.100377 + 0.994949i \(0.467995\pi\)
\(192\) −10.1444 −0.732107
\(193\) −16.6422 −1.19793 −0.598965 0.800776i \(-0.704421\pi\)
−0.598965 + 0.800776i \(0.704421\pi\)
\(194\) −9.38279 −0.673645
\(195\) 0 0
\(196\) 2.29258 0.163755
\(197\) −0.164331 −0.0117081 −0.00585404 0.999983i \(-0.501863\pi\)
−0.00585404 + 0.999983i \(0.501863\pi\)
\(198\) 5.41763 0.385014
\(199\) 1.73169 0.122756 0.0613780 0.998115i \(-0.480450\pi\)
0.0613780 + 0.998115i \(0.480450\pi\)
\(200\) 6.59492 0.466331
\(201\) −16.0479 −1.13193
\(202\) −5.49957 −0.386948
\(203\) 3.55037 0.249187
\(204\) 5.64710 0.395376
\(205\) −27.4291 −1.91573
\(206\) −22.6690 −1.57942
\(207\) −8.91513 −0.619645
\(208\) 0 0
\(209\) 13.8823 0.960261
\(210\) −8.25616 −0.569729
\(211\) 14.7885 1.01808 0.509039 0.860743i \(-0.330001\pi\)
0.509039 + 0.860743i \(0.330001\pi\)
\(212\) −24.8914 −1.70955
\(213\) 15.8147 1.08361
\(214\) 12.0893 0.826409
\(215\) 30.2749 2.06473
\(216\) 0.606176 0.0412451
\(217\) −6.25363 −0.424524
\(218\) 29.9355 2.02749
\(219\) 3.16937 0.214166
\(220\) 23.8887 1.61058
\(221\) 0 0
\(222\) −7.72376 −0.518385
\(223\) 16.6943 1.11793 0.558966 0.829191i \(-0.311198\pi\)
0.558966 + 0.829191i \(0.311198\pi\)
\(224\) 8.11006 0.541876
\(225\) 10.8795 0.725302
\(226\) −19.4191 −1.29174
\(227\) −15.2365 −1.01128 −0.505640 0.862745i \(-0.668743\pi\)
−0.505640 + 0.862745i \(0.668743\pi\)
\(228\) 12.1713 0.806062
\(229\) −19.2701 −1.27341 −0.636703 0.771109i \(-0.719702\pi\)
−0.636703 + 0.771109i \(0.719702\pi\)
\(230\) −73.6047 −4.85335
\(231\) −2.61487 −0.172046
\(232\) −2.15215 −0.141296
\(233\) 6.58317 0.431278 0.215639 0.976473i \(-0.430817\pi\)
0.215639 + 0.976473i \(0.430817\pi\)
\(234\) 0 0
\(235\) −9.71075 −0.633460
\(236\) −2.16622 −0.141009
\(237\) −5.15670 −0.334964
\(238\) −5.10341 −0.330805
\(239\) −27.0508 −1.74977 −0.874885 0.484331i \(-0.839063\pi\)
−0.874885 + 0.484331i \(0.839063\pi\)
\(240\) −13.2668 −0.856365
\(241\) 24.4670 1.57606 0.788029 0.615638i \(-0.211102\pi\)
0.788029 + 0.615638i \(0.211102\pi\)
\(242\) −8.62399 −0.554371
\(243\) 1.00000 0.0641500
\(244\) 11.3695 0.727855
\(245\) 3.98491 0.254587
\(246\) −14.2611 −0.909252
\(247\) 0 0
\(248\) 3.79080 0.240716
\(249\) 1.47510 0.0934808
\(250\) 48.5424 3.07009
\(251\) 2.93895 0.185505 0.0927524 0.995689i \(-0.470433\pi\)
0.0927524 + 0.995689i \(0.470433\pi\)
\(252\) −2.29258 −0.144419
\(253\) −23.3119 −1.46561
\(254\) −6.74288 −0.423086
\(255\) 9.81567 0.614681
\(256\) 10.3490 0.646811
\(257\) 5.57830 0.347965 0.173982 0.984749i \(-0.444336\pi\)
0.173982 + 0.984749i \(0.444336\pi\)
\(258\) 15.7407 0.979972
\(259\) 3.72795 0.231643
\(260\) 0 0
\(261\) −3.55037 −0.219762
\(262\) 2.61903 0.161804
\(263\) 21.2240 1.30873 0.654365 0.756179i \(-0.272936\pi\)
0.654365 + 0.756179i \(0.272936\pi\)
\(264\) 1.58507 0.0975545
\(265\) −43.2658 −2.65780
\(266\) −10.9995 −0.674420
\(267\) 13.7404 0.840900
\(268\) −36.7910 −2.24737
\(269\) −1.92240 −0.117211 −0.0586054 0.998281i \(-0.518665\pi\)
−0.0586054 + 0.998281i \(0.518665\pi\)
\(270\) 8.25616 0.502454
\(271\) 2.56202 0.155632 0.0778159 0.996968i \(-0.475205\pi\)
0.0778159 + 0.996968i \(0.475205\pi\)
\(272\) −8.20063 −0.497236
\(273\) 0 0
\(274\) −33.3531 −2.01494
\(275\) 28.4486 1.71551
\(276\) −20.4386 −1.23026
\(277\) −9.31382 −0.559613 −0.279807 0.960056i \(-0.590270\pi\)
−0.279807 + 0.960056i \(0.590270\pi\)
\(278\) 43.1269 2.58658
\(279\) 6.25363 0.374395
\(280\) −2.41556 −0.144357
\(281\) 14.0421 0.837682 0.418841 0.908060i \(-0.362436\pi\)
0.418841 + 0.908060i \(0.362436\pi\)
\(282\) −5.04886 −0.300655
\(283\) 12.6395 0.751342 0.375671 0.926753i \(-0.377412\pi\)
0.375671 + 0.926753i \(0.377412\pi\)
\(284\) 36.2564 2.15142
\(285\) 21.1559 1.25317
\(286\) 0 0
\(287\) 6.88324 0.406305
\(288\) −8.11006 −0.477890
\(289\) −10.9326 −0.643094
\(290\) −29.3124 −1.72128
\(291\) −4.52869 −0.265477
\(292\) 7.26603 0.425212
\(293\) −22.0692 −1.28930 −0.644648 0.764480i \(-0.722996\pi\)
−0.644648 + 0.764480i \(0.722996\pi\)
\(294\) 2.07185 0.120833
\(295\) −3.76529 −0.219223
\(296\) −2.25979 −0.131348
\(297\) 2.61487 0.151730
\(298\) −30.0864 −1.74286
\(299\) 0 0
\(300\) 24.9422 1.44004
\(301\) −7.59739 −0.437906
\(302\) −21.1437 −1.21668
\(303\) −2.65442 −0.152492
\(304\) −17.6749 −1.01373
\(305\) 19.7622 1.13158
\(306\) 5.10341 0.291742
\(307\) 3.30193 0.188451 0.0942255 0.995551i \(-0.469963\pi\)
0.0942255 + 0.995551i \(0.469963\pi\)
\(308\) −5.99479 −0.341585
\(309\) −10.9414 −0.622434
\(310\) 51.6310 2.93244
\(311\) 16.1831 0.917658 0.458829 0.888525i \(-0.348269\pi\)
0.458829 + 0.888525i \(0.348269\pi\)
\(312\) 0 0
\(313\) 2.50394 0.141531 0.0707656 0.997493i \(-0.477456\pi\)
0.0707656 + 0.997493i \(0.477456\pi\)
\(314\) 12.1582 0.686127
\(315\) −3.98491 −0.224524
\(316\) −11.8221 −0.665047
\(317\) 24.1074 1.35401 0.677005 0.735979i \(-0.263278\pi\)
0.677005 + 0.735979i \(0.263278\pi\)
\(318\) −22.4950 −1.26145
\(319\) −9.28376 −0.519791
\(320\) −40.4244 −2.25979
\(321\) 5.83503 0.325680
\(322\) 18.4709 1.02934
\(323\) 13.0772 0.727632
\(324\) 2.29258 0.127365
\(325\) 0 0
\(326\) −1.44548 −0.0800579
\(327\) 14.4487 0.799012
\(328\) −4.17245 −0.230385
\(329\) 2.43688 0.134350
\(330\) 21.5888 1.18842
\(331\) −5.36044 −0.294637 −0.147318 0.989089i \(-0.547064\pi\)
−0.147318 + 0.989089i \(0.547064\pi\)
\(332\) 3.38178 0.185600
\(333\) −3.72795 −0.204290
\(334\) −52.0076 −2.84573
\(335\) −63.9495 −3.49393
\(336\) 3.32925 0.181625
\(337\) −16.4659 −0.896952 −0.448476 0.893795i \(-0.648033\pi\)
−0.448476 + 0.893795i \(0.648033\pi\)
\(338\) 0 0
\(339\) −9.37283 −0.509062
\(340\) 22.5032 1.22041
\(341\) 16.3524 0.885534
\(342\) 10.9995 0.594782
\(343\) −1.00000 −0.0539949
\(344\) 4.60536 0.248304
\(345\) −35.5260 −1.91266
\(346\) 10.9113 0.586595
\(347\) −20.9577 −1.12507 −0.562534 0.826774i \(-0.690173\pi\)
−0.562534 + 0.826774i \(0.690173\pi\)
\(348\) −8.13949 −0.436323
\(349\) −22.9993 −1.23112 −0.615562 0.788088i \(-0.711071\pi\)
−0.615562 + 0.788088i \(0.711071\pi\)
\(350\) −22.5408 −1.20486
\(351\) 0 0
\(352\) −21.2068 −1.13032
\(353\) −27.4204 −1.45944 −0.729722 0.683744i \(-0.760350\pi\)
−0.729722 + 0.683744i \(0.760350\pi\)
\(354\) −1.95766 −0.104049
\(355\) 63.0202 3.34476
\(356\) 31.5010 1.66955
\(357\) −2.46321 −0.130367
\(358\) 23.7132 1.25328
\(359\) −21.3329 −1.12591 −0.562953 0.826489i \(-0.690335\pi\)
−0.562953 + 0.826489i \(0.690335\pi\)
\(360\) 2.41556 0.127311
\(361\) 9.18541 0.483442
\(362\) −27.4021 −1.44022
\(363\) −4.16245 −0.218472
\(364\) 0 0
\(365\) 12.6297 0.661067
\(366\) 10.2748 0.537074
\(367\) −16.9232 −0.883385 −0.441692 0.897167i \(-0.645622\pi\)
−0.441692 + 0.897167i \(0.645622\pi\)
\(368\) 29.6807 1.54721
\(369\) −6.88324 −0.358327
\(370\) −30.7785 −1.60010
\(371\) 10.8574 0.563689
\(372\) 14.3369 0.743335
\(373\) 17.0966 0.885228 0.442614 0.896712i \(-0.354051\pi\)
0.442614 + 0.896712i \(0.354051\pi\)
\(374\) 13.3448 0.690041
\(375\) 23.4294 1.20989
\(376\) −1.47718 −0.0761797
\(377\) 0 0
\(378\) −2.07185 −0.106565
\(379\) 9.18462 0.471782 0.235891 0.971779i \(-0.424199\pi\)
0.235891 + 0.971779i \(0.424199\pi\)
\(380\) 48.5015 2.48807
\(381\) −3.25452 −0.166734
\(382\) 5.74831 0.294109
\(383\) −38.9057 −1.98799 −0.993995 0.109427i \(-0.965098\pi\)
−0.993995 + 0.109427i \(0.965098\pi\)
\(384\) −4.79752 −0.244822
\(385\) −10.4200 −0.531054
\(386\) −34.4801 −1.75499
\(387\) 7.59739 0.386197
\(388\) −10.3824 −0.527086
\(389\) 24.3185 1.23299 0.616497 0.787357i \(-0.288551\pi\)
0.616497 + 0.787357i \(0.288551\pi\)
\(390\) 0 0
\(391\) −21.9598 −1.11056
\(392\) 0.606176 0.0306165
\(393\) 1.26410 0.0637654
\(394\) −0.340469 −0.0171526
\(395\) −20.5490 −1.03393
\(396\) 5.99479 0.301250
\(397\) −39.0819 −1.96146 −0.980732 0.195356i \(-0.937414\pi\)
−0.980732 + 0.195356i \(0.937414\pi\)
\(398\) 3.58780 0.179840
\(399\) −5.30899 −0.265782
\(400\) −36.2206 −1.81103
\(401\) 27.9732 1.39692 0.698458 0.715651i \(-0.253870\pi\)
0.698458 + 0.715651i \(0.253870\pi\)
\(402\) −33.2489 −1.65830
\(403\) 0 0
\(404\) −6.08546 −0.302763
\(405\) 3.98491 0.198012
\(406\) 7.35584 0.365064
\(407\) −9.74810 −0.483196
\(408\) 1.49314 0.0739214
\(409\) 0.558520 0.0276171 0.0138085 0.999905i \(-0.495604\pi\)
0.0138085 + 0.999905i \(0.495604\pi\)
\(410\) −56.8291 −2.80659
\(411\) −16.0982 −0.794066
\(412\) −25.0840 −1.23580
\(413\) 0.944885 0.0464948
\(414\) −18.4709 −0.907793
\(415\) 5.87815 0.288547
\(416\) 0 0
\(417\) 20.8156 1.01934
\(418\) 28.7622 1.40680
\(419\) −8.74541 −0.427241 −0.213621 0.976917i \(-0.568526\pi\)
−0.213621 + 0.976917i \(0.568526\pi\)
\(420\) −9.13572 −0.445777
\(421\) 25.1952 1.22794 0.613969 0.789330i \(-0.289572\pi\)
0.613969 + 0.789330i \(0.289572\pi\)
\(422\) 30.6395 1.49151
\(423\) −2.43688 −0.118485
\(424\) −6.58150 −0.319626
\(425\) 26.7986 1.29992
\(426\) 32.7657 1.58750
\(427\) −4.95925 −0.239995
\(428\) 13.3773 0.646614
\(429\) 0 0
\(430\) 62.7253 3.02488
\(431\) 1.18445 0.0570532 0.0285266 0.999593i \(-0.490918\pi\)
0.0285266 + 0.999593i \(0.490918\pi\)
\(432\) −3.32925 −0.160178
\(433\) −8.48096 −0.407569 −0.203785 0.979016i \(-0.565324\pi\)
−0.203785 + 0.979016i \(0.565324\pi\)
\(434\) −12.9566 −0.621937
\(435\) −14.1479 −0.678340
\(436\) 33.1246 1.58638
\(437\) −47.3304 −2.26412
\(438\) 6.56647 0.313758
\(439\) 32.5677 1.55437 0.777186 0.629271i \(-0.216647\pi\)
0.777186 + 0.629271i \(0.216647\pi\)
\(440\) 6.31638 0.301121
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 23.3749 1.11057 0.555287 0.831659i \(-0.312608\pi\)
0.555287 + 0.831659i \(0.312608\pi\)
\(444\) −8.54661 −0.405604
\(445\) 54.7544 2.59561
\(446\) 34.5881 1.63779
\(447\) −14.5215 −0.686843
\(448\) 10.1444 0.479276
\(449\) −22.5296 −1.06324 −0.531618 0.846984i \(-0.678416\pi\)
−0.531618 + 0.846984i \(0.678416\pi\)
\(450\) 22.5408 1.06258
\(451\) −17.9988 −0.847529
\(452\) −21.4879 −1.01071
\(453\) −10.2052 −0.479483
\(454\) −31.5677 −1.48155
\(455\) 0 0
\(456\) 3.21819 0.150705
\(457\) 14.5781 0.681933 0.340966 0.940075i \(-0.389246\pi\)
0.340966 + 0.940075i \(0.389246\pi\)
\(458\) −39.9249 −1.86557
\(459\) 2.46321 0.114973
\(460\) −81.4462 −3.79745
\(461\) −26.0945 −1.21534 −0.607670 0.794189i \(-0.707896\pi\)
−0.607670 + 0.794189i \(0.707896\pi\)
\(462\) −5.41763 −0.252051
\(463\) 25.6187 1.19060 0.595301 0.803502i \(-0.297033\pi\)
0.595301 + 0.803502i \(0.297033\pi\)
\(464\) 11.8200 0.548732
\(465\) 24.9202 1.15565
\(466\) 13.6394 0.631831
\(467\) 33.3200 1.54187 0.770933 0.636917i \(-0.219790\pi\)
0.770933 + 0.636917i \(0.219790\pi\)
\(468\) 0 0
\(469\) 16.0479 0.741023
\(470\) −20.1193 −0.928032
\(471\) 5.86827 0.270396
\(472\) −0.572767 −0.0263637
\(473\) 19.8662 0.913449
\(474\) −10.6839 −0.490729
\(475\) 57.7594 2.65018
\(476\) −5.64710 −0.258834
\(477\) −10.8574 −0.497127
\(478\) −56.0453 −2.56345
\(479\) 6.09069 0.278291 0.139145 0.990272i \(-0.455564\pi\)
0.139145 + 0.990272i \(0.455564\pi\)
\(480\) −32.3179 −1.47510
\(481\) 0 0
\(482\) 50.6920 2.30896
\(483\) 8.91513 0.405653
\(484\) −9.54274 −0.433761
\(485\) −18.0465 −0.819447
\(486\) 2.07185 0.0939812
\(487\) 29.1782 1.32219 0.661095 0.750302i \(-0.270092\pi\)
0.661095 + 0.750302i \(0.270092\pi\)
\(488\) 3.00618 0.136083
\(489\) −0.697676 −0.0315500
\(490\) 8.25616 0.372975
\(491\) 31.2594 1.41072 0.705359 0.708850i \(-0.250786\pi\)
0.705359 + 0.708850i \(0.250786\pi\)
\(492\) −15.7803 −0.711433
\(493\) −8.74530 −0.393868
\(494\) 0 0
\(495\) 10.4200 0.468346
\(496\) −20.8199 −0.934840
\(497\) −15.8147 −0.709386
\(498\) 3.05620 0.136951
\(499\) 12.5804 0.563177 0.281588 0.959535i \(-0.409139\pi\)
0.281588 + 0.959535i \(0.409139\pi\)
\(500\) 53.7138 2.40215
\(501\) −25.1020 −1.12147
\(502\) 6.08907 0.271769
\(503\) 39.2710 1.75101 0.875504 0.483211i \(-0.160530\pi\)
0.875504 + 0.483211i \(0.160530\pi\)
\(504\) −0.606176 −0.0270012
\(505\) −10.5776 −0.470698
\(506\) −48.2989 −2.14715
\(507\) 0 0
\(508\) −7.46123 −0.331039
\(509\) 32.2548 1.42967 0.714835 0.699293i \(-0.246502\pi\)
0.714835 + 0.699293i \(0.246502\pi\)
\(510\) 20.3366 0.900521
\(511\) −3.16937 −0.140205
\(512\) 31.0366 1.37164
\(513\) 5.30899 0.234398
\(514\) 11.5574 0.509776
\(515\) −43.6005 −1.92127
\(516\) 17.4176 0.766767
\(517\) −6.37213 −0.280246
\(518\) 7.72376 0.339363
\(519\) 5.26644 0.231171
\(520\) 0 0
\(521\) −14.2921 −0.626149 −0.313075 0.949728i \(-0.601359\pi\)
−0.313075 + 0.949728i \(0.601359\pi\)
\(522\) −7.35584 −0.321957
\(523\) 15.6499 0.684322 0.342161 0.939641i \(-0.388841\pi\)
0.342161 + 0.939641i \(0.388841\pi\)
\(524\) 2.89804 0.126602
\(525\) −10.8795 −0.474822
\(526\) 43.9731 1.91732
\(527\) 15.4040 0.671009
\(528\) −8.70555 −0.378860
\(529\) 56.4796 2.45564
\(530\) −89.6405 −3.89373
\(531\) −0.944885 −0.0410045
\(532\) −12.1713 −0.527692
\(533\) 0 0
\(534\) 28.4681 1.23194
\(535\) 23.2521 1.00528
\(536\) −9.72785 −0.420179
\(537\) 11.4454 0.493905
\(538\) −3.98293 −0.171716
\(539\) 2.61487 0.112630
\(540\) 9.13572 0.393139
\(541\) −23.5020 −1.01043 −0.505216 0.862993i \(-0.668587\pi\)
−0.505216 + 0.862993i \(0.668587\pi\)
\(542\) 5.30814 0.228004
\(543\) −13.2259 −0.567577
\(544\) −19.9768 −0.856497
\(545\) 57.5766 2.46631
\(546\) 0 0
\(547\) −12.5884 −0.538242 −0.269121 0.963106i \(-0.586733\pi\)
−0.269121 + 0.963106i \(0.586733\pi\)
\(548\) −36.9064 −1.57656
\(549\) 4.95925 0.211656
\(550\) 58.9413 2.51326
\(551\) −18.8489 −0.802989
\(552\) −5.40414 −0.230016
\(553\) 5.15670 0.219285
\(554\) −19.2969 −0.819845
\(555\) −14.8556 −0.630583
\(556\) 47.7213 2.02384
\(557\) 7.12504 0.301898 0.150949 0.988542i \(-0.451767\pi\)
0.150949 + 0.988542i \(0.451767\pi\)
\(558\) 12.9566 0.548497
\(559\) 0 0
\(560\) 13.2668 0.560623
\(561\) 6.44097 0.271938
\(562\) 29.0932 1.22722
\(563\) −37.5881 −1.58415 −0.792074 0.610425i \(-0.790999\pi\)
−0.792074 + 0.610425i \(0.790999\pi\)
\(564\) −5.58673 −0.235244
\(565\) −37.3499 −1.57132
\(566\) 26.1872 1.10073
\(567\) −1.00000 −0.0419961
\(568\) 9.58649 0.402240
\(569\) −15.9721 −0.669584 −0.334792 0.942292i \(-0.608666\pi\)
−0.334792 + 0.942292i \(0.608666\pi\)
\(570\) 43.8319 1.83592
\(571\) 1.19947 0.0501961 0.0250980 0.999685i \(-0.492010\pi\)
0.0250980 + 0.999685i \(0.492010\pi\)
\(572\) 0 0
\(573\) 2.77448 0.115906
\(574\) 14.2611 0.595245
\(575\) −96.9925 −4.04487
\(576\) −10.1444 −0.422682
\(577\) 31.0326 1.29190 0.645952 0.763378i \(-0.276461\pi\)
0.645952 + 0.763378i \(0.276461\pi\)
\(578\) −22.6508 −0.942147
\(579\) −16.6422 −0.691625
\(580\) −32.4352 −1.34680
\(581\) −1.47510 −0.0611975
\(582\) −9.38279 −0.388929
\(583\) −28.3907 −1.17582
\(584\) 1.92120 0.0794997
\(585\) 0 0
\(586\) −45.7241 −1.88885
\(587\) 9.60481 0.396433 0.198216 0.980158i \(-0.436485\pi\)
0.198216 + 0.980158i \(0.436485\pi\)
\(588\) 2.29258 0.0945443
\(589\) 33.2005 1.36800
\(590\) −7.80112 −0.321167
\(591\) −0.164331 −0.00675966
\(592\) 12.4113 0.510099
\(593\) −30.7042 −1.26087 −0.630435 0.776242i \(-0.717123\pi\)
−0.630435 + 0.776242i \(0.717123\pi\)
\(594\) 5.41763 0.222288
\(595\) −9.81567 −0.402403
\(596\) −33.2916 −1.36368
\(597\) 1.73169 0.0708732
\(598\) 0 0
\(599\) −25.9999 −1.06233 −0.531163 0.847269i \(-0.678245\pi\)
−0.531163 + 0.847269i \(0.678245\pi\)
\(600\) 6.59492 0.269236
\(601\) 9.31463 0.379952 0.189976 0.981789i \(-0.439159\pi\)
0.189976 + 0.981789i \(0.439159\pi\)
\(602\) −15.7407 −0.641542
\(603\) −16.0479 −0.653521
\(604\) −23.3963 −0.951980
\(605\) −16.5870 −0.674358
\(606\) −5.49957 −0.223405
\(607\) −15.3649 −0.623641 −0.311821 0.950141i \(-0.600939\pi\)
−0.311821 + 0.950141i \(0.600939\pi\)
\(608\) −43.0563 −1.74616
\(609\) 3.55037 0.143868
\(610\) 40.9443 1.65779
\(611\) 0 0
\(612\) 5.64710 0.228270
\(613\) −4.71856 −0.190581 −0.0952904 0.995450i \(-0.530378\pi\)
−0.0952904 + 0.995450i \(0.530378\pi\)
\(614\) 6.84111 0.276085
\(615\) −27.4291 −1.10605
\(616\) −1.58507 −0.0638644
\(617\) 16.7054 0.672533 0.336267 0.941767i \(-0.390836\pi\)
0.336267 + 0.941767i \(0.390836\pi\)
\(618\) −22.6690 −0.911879
\(619\) 10.8625 0.436603 0.218301 0.975881i \(-0.429948\pi\)
0.218301 + 0.975881i \(0.429948\pi\)
\(620\) 57.1314 2.29445
\(621\) −8.91513 −0.357752
\(622\) 33.5290 1.34439
\(623\) −13.7404 −0.550498
\(624\) 0 0
\(625\) 38.9666 1.55866
\(626\) 5.18780 0.207346
\(627\) 13.8823 0.554407
\(628\) 13.4535 0.536852
\(629\) −9.18271 −0.366139
\(630\) −8.25616 −0.328933
\(631\) −19.8405 −0.789837 −0.394918 0.918716i \(-0.629227\pi\)
−0.394918 + 0.918716i \(0.629227\pi\)
\(632\) −3.12587 −0.124340
\(633\) 14.7885 0.587788
\(634\) 49.9471 1.98365
\(635\) −12.9690 −0.514658
\(636\) −24.8914 −0.987010
\(637\) 0 0
\(638\) −19.2346 −0.761504
\(639\) 15.8147 0.625620
\(640\) −19.1177 −0.755694
\(641\) −25.7779 −1.01817 −0.509083 0.860717i \(-0.670015\pi\)
−0.509083 + 0.860717i \(0.670015\pi\)
\(642\) 12.0893 0.477128
\(643\) 25.4048 1.00187 0.500935 0.865485i \(-0.332990\pi\)
0.500935 + 0.865485i \(0.332990\pi\)
\(644\) 20.4386 0.805395
\(645\) 30.2749 1.19207
\(646\) 27.0940 1.06600
\(647\) −19.5858 −0.769997 −0.384999 0.922917i \(-0.625798\pi\)
−0.384999 + 0.922917i \(0.625798\pi\)
\(648\) 0.606176 0.0238129
\(649\) −2.47075 −0.0969855
\(650\) 0 0
\(651\) −6.25363 −0.245099
\(652\) −1.59948 −0.0626403
\(653\) −13.7217 −0.536971 −0.268486 0.963284i \(-0.586523\pi\)
−0.268486 + 0.963284i \(0.586523\pi\)
\(654\) 29.9355 1.17057
\(655\) 5.03733 0.196825
\(656\) 22.9160 0.894719
\(657\) 3.16937 0.123649
\(658\) 5.04886 0.196825
\(659\) 26.6231 1.03709 0.518544 0.855051i \(-0.326474\pi\)
0.518544 + 0.855051i \(0.326474\pi\)
\(660\) 23.8887 0.929867
\(661\) −35.1844 −1.36852 −0.684258 0.729240i \(-0.739874\pi\)
−0.684258 + 0.729240i \(0.739874\pi\)
\(662\) −11.1061 −0.431649
\(663\) 0 0
\(664\) 0.894172 0.0347006
\(665\) −21.1559 −0.820390
\(666\) −7.72376 −0.299290
\(667\) 31.6520 1.22557
\(668\) −57.5482 −2.22661
\(669\) 16.6943 0.645438
\(670\) −132.494 −5.11869
\(671\) 12.9678 0.500616
\(672\) 8.11006 0.312852
\(673\) −2.12183 −0.0817905 −0.0408953 0.999163i \(-0.513021\pi\)
−0.0408953 + 0.999163i \(0.513021\pi\)
\(674\) −34.1148 −1.31405
\(675\) 10.8795 0.418753
\(676\) 0 0
\(677\) −14.8001 −0.568813 −0.284406 0.958704i \(-0.591797\pi\)
−0.284406 + 0.958704i \(0.591797\pi\)
\(678\) −19.4191 −0.745787
\(679\) 4.52869 0.173795
\(680\) 5.95003 0.228173
\(681\) −15.2365 −0.583862
\(682\) 33.8799 1.29733
\(683\) 17.8128 0.681590 0.340795 0.940138i \(-0.389304\pi\)
0.340795 + 0.940138i \(0.389304\pi\)
\(684\) 12.1713 0.465380
\(685\) −64.1500 −2.45104
\(686\) −2.07185 −0.0791037
\(687\) −19.2701 −0.735202
\(688\) −25.2936 −0.964309
\(689\) 0 0
\(690\) −73.6047 −2.80208
\(691\) −11.7835 −0.448264 −0.224132 0.974559i \(-0.571955\pi\)
−0.224132 + 0.974559i \(0.571955\pi\)
\(692\) 12.0737 0.458974
\(693\) −2.61487 −0.0993307
\(694\) −43.4212 −1.64825
\(695\) 82.9483 3.14641
\(696\) −2.15215 −0.0815770
\(697\) −16.9548 −0.642211
\(698\) −47.6512 −1.80362
\(699\) 6.58317 0.248998
\(700\) −24.9422 −0.942725
\(701\) −10.5499 −0.398465 −0.199233 0.979952i \(-0.563845\pi\)
−0.199233 + 0.979952i \(0.563845\pi\)
\(702\) 0 0
\(703\) −19.7917 −0.746456
\(704\) −26.5262 −0.999744
\(705\) −9.71075 −0.365728
\(706\) −56.8112 −2.13812
\(707\) 2.65442 0.0998297
\(708\) −2.16622 −0.0814116
\(709\) −20.0085 −0.751435 −0.375717 0.926734i \(-0.622604\pi\)
−0.375717 + 0.926734i \(0.622604\pi\)
\(710\) 130.569 4.90015
\(711\) −5.15670 −0.193391
\(712\) 8.32912 0.312147
\(713\) −55.7520 −2.08793
\(714\) −5.10341 −0.190990
\(715\) 0 0
\(716\) 26.2394 0.980614
\(717\) −27.0508 −1.01023
\(718\) −44.1986 −1.64948
\(719\) 2.64264 0.0985539 0.0492770 0.998785i \(-0.484308\pi\)
0.0492770 + 0.998785i \(0.484308\pi\)
\(720\) −13.2668 −0.494423
\(721\) 10.9414 0.407479
\(722\) 19.0308 0.708254
\(723\) 24.4670 0.909937
\(724\) −30.3213 −1.12688
\(725\) −38.6264 −1.43455
\(726\) −8.62399 −0.320066
\(727\) 23.9042 0.886557 0.443279 0.896384i \(-0.353815\pi\)
0.443279 + 0.896384i \(0.353815\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 26.1668 0.968478
\(731\) 18.7140 0.692161
\(732\) 11.3695 0.420227
\(733\) −33.1800 −1.22553 −0.612766 0.790265i \(-0.709943\pi\)
−0.612766 + 0.790265i \(0.709943\pi\)
\(734\) −35.0624 −1.29418
\(735\) 3.98491 0.146986
\(736\) 72.3023 2.66510
\(737\) −41.9632 −1.54573
\(738\) −14.2611 −0.524957
\(739\) −1.27739 −0.0469894 −0.0234947 0.999724i \(-0.507479\pi\)
−0.0234947 + 0.999724i \(0.507479\pi\)
\(740\) −34.0575 −1.25198
\(741\) 0 0
\(742\) 22.4950 0.825816
\(743\) 39.2019 1.43818 0.719088 0.694919i \(-0.244560\pi\)
0.719088 + 0.694919i \(0.244560\pi\)
\(744\) 3.79080 0.138978
\(745\) −57.8669 −2.12008
\(746\) 35.4216 1.29688
\(747\) 1.47510 0.0539712
\(748\) 14.7664 0.539914
\(749\) −5.83503 −0.213207
\(750\) 48.5424 1.77252
\(751\) −4.89411 −0.178589 −0.0892943 0.996005i \(-0.528461\pi\)
−0.0892943 + 0.996005i \(0.528461\pi\)
\(752\) 8.11297 0.295850
\(753\) 2.93895 0.107101
\(754\) 0 0
\(755\) −40.6669 −1.48002
\(756\) −2.29258 −0.0833802
\(757\) −38.0701 −1.38368 −0.691841 0.722050i \(-0.743200\pi\)
−0.691841 + 0.722050i \(0.743200\pi\)
\(758\) 19.0292 0.691171
\(759\) −23.3119 −0.846169
\(760\) 12.8242 0.465182
\(761\) 31.9088 1.15669 0.578346 0.815792i \(-0.303698\pi\)
0.578346 + 0.815792i \(0.303698\pi\)
\(762\) −6.74288 −0.244269
\(763\) −14.4487 −0.523076
\(764\) 6.36071 0.230122
\(765\) 9.81567 0.354886
\(766\) −80.6070 −2.91245
\(767\) 0 0
\(768\) 10.3490 0.373436
\(769\) −20.1643 −0.727143 −0.363571 0.931566i \(-0.618443\pi\)
−0.363571 + 0.931566i \(0.618443\pi\)
\(770\) −21.5888 −0.778006
\(771\) 5.57830 0.200897
\(772\) −38.1534 −1.37317
\(773\) −27.6159 −0.993274 −0.496637 0.867958i \(-0.665432\pi\)
−0.496637 + 0.867958i \(0.665432\pi\)
\(774\) 15.7407 0.565787
\(775\) 68.0366 2.44395
\(776\) −2.74519 −0.0985465
\(777\) 3.72795 0.133739
\(778\) 50.3843 1.80636
\(779\) −36.5430 −1.30929
\(780\) 0 0
\(781\) 41.3534 1.47974
\(782\) −45.4976 −1.62699
\(783\) −3.55037 −0.126880
\(784\) −3.32925 −0.118902
\(785\) 23.3846 0.834631
\(786\) 2.61903 0.0934176
\(787\) −14.5494 −0.518631 −0.259315 0.965793i \(-0.583497\pi\)
−0.259315 + 0.965793i \(0.583497\pi\)
\(788\) −0.376741 −0.0134208
\(789\) 21.2240 0.755596
\(790\) −42.5745 −1.51473
\(791\) 9.37283 0.333259
\(792\) 1.58507 0.0563231
\(793\) 0 0
\(794\) −80.9720 −2.87359
\(795\) −43.2658 −1.53448
\(796\) 3.97003 0.140714
\(797\) −12.9466 −0.458592 −0.229296 0.973357i \(-0.573642\pi\)
−0.229296 + 0.973357i \(0.573642\pi\)
\(798\) −10.9995 −0.389377
\(799\) −6.00254 −0.212355
\(800\) −88.2337 −3.11953
\(801\) 13.7404 0.485494
\(802\) 57.9564 2.04651
\(803\) 8.28750 0.292459
\(804\) −36.7910 −1.29752
\(805\) 35.5260 1.25213
\(806\) 0 0
\(807\) −1.92240 −0.0676717
\(808\) −1.60905 −0.0566060
\(809\) −9.93693 −0.349364 −0.174682 0.984625i \(-0.555890\pi\)
−0.174682 + 0.984625i \(0.555890\pi\)
\(810\) 8.25616 0.290092
\(811\) −21.6049 −0.758650 −0.379325 0.925263i \(-0.623844\pi\)
−0.379325 + 0.925263i \(0.623844\pi\)
\(812\) 8.13949 0.285640
\(813\) 2.56202 0.0898541
\(814\) −20.1966 −0.707892
\(815\) −2.78018 −0.0973854
\(816\) −8.20063 −0.287079
\(817\) 40.3345 1.41113
\(818\) 1.15717 0.0404596
\(819\) 0 0
\(820\) −62.8833 −2.19598
\(821\) −7.37066 −0.257238 −0.128619 0.991694i \(-0.541054\pi\)
−0.128619 + 0.991694i \(0.541054\pi\)
\(822\) −33.3531 −1.16332
\(823\) 39.7759 1.38650 0.693250 0.720697i \(-0.256178\pi\)
0.693250 + 0.720697i \(0.256178\pi\)
\(824\) −6.63241 −0.231051
\(825\) 28.4486 0.990452
\(826\) 1.95766 0.0681158
\(827\) −2.35530 −0.0819019 −0.0409510 0.999161i \(-0.513039\pi\)
−0.0409510 + 0.999161i \(0.513039\pi\)
\(828\) −20.4386 −0.710292
\(829\) −0.942767 −0.0327436 −0.0163718 0.999866i \(-0.505212\pi\)
−0.0163718 + 0.999866i \(0.505212\pi\)
\(830\) 12.1787 0.422728
\(831\) −9.31382 −0.323093
\(832\) 0 0
\(833\) 2.46321 0.0853451
\(834\) 43.1269 1.49336
\(835\) −100.029 −3.46165
\(836\) 31.8263 1.10074
\(837\) 6.25363 0.216157
\(838\) −18.1192 −0.625918
\(839\) −22.0266 −0.760442 −0.380221 0.924896i \(-0.624152\pi\)
−0.380221 + 0.924896i \(0.624152\pi\)
\(840\) −2.41556 −0.0833447
\(841\) −16.3949 −0.565341
\(842\) 52.2007 1.79896
\(843\) 14.0421 0.483636
\(844\) 33.9037 1.16701
\(845\) 0 0
\(846\) −5.04886 −0.173583
\(847\) 4.16245 0.143023
\(848\) 36.1470 1.24129
\(849\) 12.6395 0.433787
\(850\) 55.5227 1.90441
\(851\) 33.2352 1.13929
\(852\) 36.2564 1.24212
\(853\) 25.5160 0.873652 0.436826 0.899546i \(-0.356103\pi\)
0.436826 + 0.899546i \(0.356103\pi\)
\(854\) −10.2748 −0.351598
\(855\) 21.1559 0.723516
\(856\) 3.53706 0.120894
\(857\) 11.1140 0.379646 0.189823 0.981818i \(-0.439209\pi\)
0.189823 + 0.981818i \(0.439209\pi\)
\(858\) 0 0
\(859\) 8.03548 0.274167 0.137083 0.990560i \(-0.456227\pi\)
0.137083 + 0.990560i \(0.456227\pi\)
\(860\) 69.4076 2.36678
\(861\) 6.88324 0.234580
\(862\) 2.45402 0.0835841
\(863\) −3.40081 −0.115765 −0.0578825 0.998323i \(-0.518435\pi\)
−0.0578825 + 0.998323i \(0.518435\pi\)
\(864\) −8.11006 −0.275910
\(865\) 20.9863 0.713556
\(866\) −17.5713 −0.597098
\(867\) −10.9326 −0.371291
\(868\) −14.3369 −0.486627
\(869\) −13.4841 −0.457417
\(870\) −29.3124 −0.993783
\(871\) 0 0
\(872\) 8.75843 0.296598
\(873\) −4.52869 −0.153273
\(874\) −98.0616 −3.31698
\(875\) −23.4294 −0.792059
\(876\) 7.26603 0.245496
\(877\) 22.1250 0.747110 0.373555 0.927608i \(-0.378139\pi\)
0.373555 + 0.927608i \(0.378139\pi\)
\(878\) 67.4755 2.27719
\(879\) −22.0692 −0.744375
\(880\) −34.6908 −1.16943
\(881\) 24.5254 0.826281 0.413141 0.910667i \(-0.364432\pi\)
0.413141 + 0.910667i \(0.364432\pi\)
\(882\) 2.07185 0.0697629
\(883\) −3.60395 −0.121282 −0.0606412 0.998160i \(-0.519315\pi\)
−0.0606412 + 0.998160i \(0.519315\pi\)
\(884\) 0 0
\(885\) −3.76529 −0.126569
\(886\) 48.4293 1.62701
\(887\) 28.8486 0.968642 0.484321 0.874890i \(-0.339067\pi\)
0.484321 + 0.874890i \(0.339067\pi\)
\(888\) −2.25979 −0.0758337
\(889\) 3.25452 0.109153
\(890\) 113.443 3.80262
\(891\) 2.61487 0.0876015
\(892\) 38.2729 1.28147
\(893\) −12.9374 −0.432933
\(894\) −30.0864 −1.00624
\(895\) 45.6089 1.52454
\(896\) 4.79752 0.160274
\(897\) 0 0
\(898\) −46.6779 −1.55766
\(899\) −22.2027 −0.740502
\(900\) 24.9422 0.831406
\(901\) −26.7441 −0.890974
\(902\) −37.2908 −1.24165
\(903\) −7.59739 −0.252825
\(904\) −5.68159 −0.188967
\(905\) −52.7040 −1.75194
\(906\) −21.1437 −0.702453
\(907\) −5.15964 −0.171323 −0.0856615 0.996324i \(-0.527300\pi\)
−0.0856615 + 0.996324i \(0.527300\pi\)
\(908\) −34.9308 −1.15922
\(909\) −2.65442 −0.0880415
\(910\) 0 0
\(911\) 38.1096 1.26263 0.631313 0.775528i \(-0.282516\pi\)
0.631313 + 0.775528i \(0.282516\pi\)
\(912\) −17.6749 −0.585276
\(913\) 3.85720 0.127655
\(914\) 30.2036 0.999046
\(915\) 19.7622 0.653317
\(916\) −44.1783 −1.45969
\(917\) −1.26410 −0.0417442
\(918\) 5.10341 0.168438
\(919\) 2.13480 0.0704205 0.0352103 0.999380i \(-0.488790\pi\)
0.0352103 + 0.999380i \(0.488790\pi\)
\(920\) −21.5350 −0.709989
\(921\) 3.30193 0.108802
\(922\) −54.0639 −1.78050
\(923\) 0 0
\(924\) −5.99479 −0.197214
\(925\) −40.5583 −1.33355
\(926\) 53.0782 1.74426
\(927\) −10.9414 −0.359362
\(928\) 28.7937 0.945200
\(929\) 40.8343 1.33973 0.669865 0.742483i \(-0.266352\pi\)
0.669865 + 0.742483i \(0.266352\pi\)
\(930\) 51.6310 1.69305
\(931\) 5.30899 0.173995
\(932\) 15.0924 0.494369
\(933\) 16.1831 0.529810
\(934\) 69.0342 2.25887
\(935\) 25.6667 0.839391
\(936\) 0 0
\(937\) 45.9925 1.50251 0.751255 0.660012i \(-0.229449\pi\)
0.751255 + 0.660012i \(0.229449\pi\)
\(938\) 33.2489 1.08561
\(939\) 2.50394 0.0817130
\(940\) −22.2626 −0.726128
\(941\) 9.55992 0.311645 0.155822 0.987785i \(-0.450197\pi\)
0.155822 + 0.987785i \(0.450197\pi\)
\(942\) 12.1582 0.396136
\(943\) 61.3650 1.99832
\(944\) 3.14575 0.102386
\(945\) −3.98491 −0.129629
\(946\) 41.1599 1.33822
\(947\) −30.1550 −0.979905 −0.489952 0.871749i \(-0.662986\pi\)
−0.489952 + 0.871749i \(0.662986\pi\)
\(948\) −11.8221 −0.383965
\(949\) 0 0
\(950\) 119.669 3.88257
\(951\) 24.1074 0.781738
\(952\) −1.49314 −0.0483929
\(953\) 8.11627 0.262912 0.131456 0.991322i \(-0.458035\pi\)
0.131456 + 0.991322i \(0.458035\pi\)
\(954\) −22.4950 −0.728301
\(955\) 11.0561 0.357766
\(956\) −62.0160 −2.00574
\(957\) −9.28376 −0.300101
\(958\) 12.6190 0.407702
\(959\) 16.0982 0.519838
\(960\) −40.4244 −1.30469
\(961\) 8.10792 0.261546
\(962\) 0 0
\(963\) 5.83503 0.188031
\(964\) 56.0925 1.80662
\(965\) −66.3176 −2.13484
\(966\) 18.4709 0.594290
\(967\) 32.9173 1.05855 0.529274 0.848451i \(-0.322464\pi\)
0.529274 + 0.848451i \(0.322464\pi\)
\(968\) −2.52318 −0.0810980
\(969\) 13.0772 0.420099
\(970\) −37.3896 −1.20051
\(971\) 21.6879 0.695997 0.347999 0.937495i \(-0.386861\pi\)
0.347999 + 0.937495i \(0.386861\pi\)
\(972\) 2.29258 0.0735344
\(973\) −20.8156 −0.667317
\(974\) 60.4529 1.93704
\(975\) 0 0
\(976\) −16.5106 −0.528490
\(977\) 13.2955 0.425360 0.212680 0.977122i \(-0.431781\pi\)
0.212680 + 0.977122i \(0.431781\pi\)
\(978\) −1.44548 −0.0462214
\(979\) 35.9294 1.14831
\(980\) 9.13572 0.291830
\(981\) 14.4487 0.461310
\(982\) 64.7650 2.06673
\(983\) 53.4883 1.70601 0.853006 0.521902i \(-0.174777\pi\)
0.853006 + 0.521902i \(0.174777\pi\)
\(984\) −4.17245 −0.133013
\(985\) −0.654844 −0.0208651
\(986\) −18.1190 −0.577026
\(987\) 2.43688 0.0775667
\(988\) 0 0
\(989\) −67.7318 −2.15374
\(990\) 21.5888 0.686137
\(991\) −23.0550 −0.732367 −0.366183 0.930543i \(-0.619336\pi\)
−0.366183 + 0.930543i \(0.619336\pi\)
\(992\) −50.7173 −1.61028
\(993\) −5.36044 −0.170109
\(994\) −32.7657 −1.03927
\(995\) 6.90062 0.218764
\(996\) 3.38178 0.107156
\(997\) −12.6450 −0.400470 −0.200235 0.979748i \(-0.564171\pi\)
−0.200235 + 0.979748i \(0.564171\pi\)
\(998\) 26.0648 0.825066
\(999\) −3.72795 −0.117947
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.1.12 yes 15
13.12 even 2 3549.2.a.bg.1.4 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.4 15 13.12 even 2
3549.2.a.bh.1.12 yes 15 1.1 even 1 trivial