Properties

Label 4235.2.a.bb.1.4
Level $4235$
Weight $2$
Character 4235.1
Self dual yes
Analytic conductor $33.817$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.580017.1
Defining polynomial: \(x^{5} - 7 x^{3} - 4 x^{2} + 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.27779\) of defining polynomial
Character \(\chi\) \(=\) 4235.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.27779 q^{2} +2.68935 q^{3} -0.367260 q^{4} -1.00000 q^{5} +3.43642 q^{6} +1.00000 q^{7} -3.02485 q^{8} +4.23262 q^{9} +O(q^{10})\) \(q+1.27779 q^{2} +2.68935 q^{3} -0.367260 q^{4} -1.00000 q^{5} +3.43642 q^{6} +1.00000 q^{7} -3.02485 q^{8} +4.23262 q^{9} -1.27779 q^{10} -0.987692 q^{12} -5.71421 q^{13} +1.27779 q^{14} -2.68935 q^{15} -3.13060 q^{16} +0.114328 q^{17} +5.40839 q^{18} -6.33354 q^{19} +0.367260 q^{20} +2.68935 q^{21} -5.42928 q^{23} -8.13490 q^{24} +1.00000 q^{25} -7.30154 q^{26} +3.31495 q^{27} -0.367260 q^{28} -3.52986 q^{29} -3.43642 q^{30} -7.76248 q^{31} +2.04947 q^{32} +0.146086 q^{34} -1.00000 q^{35} -1.55447 q^{36} +10.9880 q^{37} -8.09291 q^{38} -15.3675 q^{39} +3.02485 q^{40} +2.05057 q^{41} +3.43642 q^{42} -3.25834 q^{43} -4.23262 q^{45} -6.93746 q^{46} -0.743888 q^{47} -8.41929 q^{48} +1.00000 q^{49} +1.27779 q^{50} +0.307468 q^{51} +2.09860 q^{52} +0.656155 q^{53} +4.23580 q^{54} -3.02485 q^{56} -17.0331 q^{57} -4.51041 q^{58} -5.88567 q^{59} +0.987692 q^{60} -7.98055 q^{61} -9.91879 q^{62} +4.23262 q^{63} +8.87998 q^{64} +5.71421 q^{65} +12.0477 q^{67} -0.0419880 q^{68} -14.6012 q^{69} -1.27779 q^{70} -0.829397 q^{71} -12.8031 q^{72} +1.17180 q^{73} +14.0403 q^{74} +2.68935 q^{75} +2.32606 q^{76} -19.6364 q^{78} +0.699582 q^{79} +3.13060 q^{80} -3.78279 q^{81} +2.62019 q^{82} +8.74733 q^{83} -0.987692 q^{84} -0.114328 q^{85} -4.16346 q^{86} -9.49303 q^{87} +8.44787 q^{89} -5.40839 q^{90} -5.71421 q^{91} +1.99396 q^{92} -20.8760 q^{93} -0.950530 q^{94} +6.33354 q^{95} +5.51175 q^{96} -7.68221 q^{97} +1.27779 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} + O(q^{10}) \) \( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} - 23 q^{12} - 10 q^{13} + 2 q^{15} + 10 q^{16} - 2 q^{17} - 5 q^{18} + 3 q^{19} - 4 q^{20} - 2 q^{21} + 3 q^{23} + 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} + 4 q^{28} - q^{29} - 5 q^{30} - 12 q^{31} - 29 q^{32} - 20 q^{34} - 5 q^{35} + 45 q^{36} + 9 q^{38} + 2 q^{39} + 12 q^{40} + 11 q^{41} + 5 q^{42} - 10 q^{43} - 11 q^{45} - 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} - 6 q^{51} - 30 q^{52} + 4 q^{53} + 34 q^{54} - 12 q^{56} - 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} - 40 q^{61} - q^{62} + 11 q^{63} + 38 q^{64} + 10 q^{65} + 7 q^{67} + 19 q^{68} - 24 q^{69} + 10 q^{71} - 72 q^{72} - 11 q^{73} + 37 q^{74} - 2 q^{75} - 3 q^{76} - 87 q^{78} - 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} - 26 q^{83} - 23 q^{84} + 2 q^{85} - 17 q^{86} - 14 q^{87} + 5 q^{89} + 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} - 44 q^{94} - 3 q^{95} + 84 q^{96} - 5 q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27779 0.903532 0.451766 0.892136i \(-0.350794\pi\)
0.451766 + 0.892136i \(0.350794\pi\)
\(3\) 2.68935 1.55270 0.776349 0.630303i \(-0.217069\pi\)
0.776349 + 0.630303i \(0.217069\pi\)
\(4\) −0.367260 −0.183630
\(5\) −1.00000 −0.447214
\(6\) 3.43642 1.40291
\(7\) 1.00000 0.377964
\(8\) −3.02485 −1.06945
\(9\) 4.23262 1.41087
\(10\) −1.27779 −0.404072
\(11\) 0 0
\(12\) −0.987692 −0.285122
\(13\) −5.71421 −1.58484 −0.792418 0.609978i \(-0.791178\pi\)
−0.792418 + 0.609978i \(0.791178\pi\)
\(14\) 1.27779 0.341503
\(15\) −2.68935 −0.694388
\(16\) −3.13060 −0.782650
\(17\) 0.114328 0.0277285 0.0138643 0.999904i \(-0.495587\pi\)
0.0138643 + 0.999904i \(0.495587\pi\)
\(18\) 5.40839 1.27477
\(19\) −6.33354 −1.45301 −0.726507 0.687159i \(-0.758857\pi\)
−0.726507 + 0.687159i \(0.758857\pi\)
\(20\) 0.367260 0.0821219
\(21\) 2.68935 0.586865
\(22\) 0 0
\(23\) −5.42928 −1.13208 −0.566041 0.824377i \(-0.691526\pi\)
−0.566041 + 0.824377i \(0.691526\pi\)
\(24\) −8.13490 −1.66053
\(25\) 1.00000 0.200000
\(26\) −7.30154 −1.43195
\(27\) 3.31495 0.637962
\(28\) −0.367260 −0.0694057
\(29\) −3.52986 −0.655478 −0.327739 0.944768i \(-0.606287\pi\)
−0.327739 + 0.944768i \(0.606287\pi\)
\(30\) −3.43642 −0.627402
\(31\) −7.76248 −1.39418 −0.697091 0.716983i \(-0.745523\pi\)
−0.697091 + 0.716983i \(0.745523\pi\)
\(32\) 2.04947 0.362298
\(33\) 0 0
\(34\) 0.146086 0.0250536
\(35\) −1.00000 −0.169031
\(36\) −1.55447 −0.259079
\(37\) 10.9880 1.80641 0.903204 0.429211i \(-0.141208\pi\)
0.903204 + 0.429211i \(0.141208\pi\)
\(38\) −8.09291 −1.31284
\(39\) −15.3675 −2.46077
\(40\) 3.02485 0.478271
\(41\) 2.05057 0.320245 0.160123 0.987097i \(-0.448811\pi\)
0.160123 + 0.987097i \(0.448811\pi\)
\(42\) 3.43642 0.530251
\(43\) −3.25834 −0.496892 −0.248446 0.968646i \(-0.579920\pi\)
−0.248446 + 0.968646i \(0.579920\pi\)
\(44\) 0 0
\(45\) −4.23262 −0.630962
\(46\) −6.93746 −1.02287
\(47\) −0.743888 −0.108507 −0.0542536 0.998527i \(-0.517278\pi\)
−0.0542536 + 0.998527i \(0.517278\pi\)
\(48\) −8.41929 −1.21522
\(49\) 1.00000 0.142857
\(50\) 1.27779 0.180706
\(51\) 0.307468 0.0430541
\(52\) 2.09860 0.291024
\(53\) 0.656155 0.0901298 0.0450649 0.998984i \(-0.485651\pi\)
0.0450649 + 0.998984i \(0.485651\pi\)
\(54\) 4.23580 0.576419
\(55\) 0 0
\(56\) −3.02485 −0.404213
\(57\) −17.0331 −2.25609
\(58\) −4.51041 −0.592245
\(59\) −5.88567 −0.766249 −0.383125 0.923697i \(-0.625152\pi\)
−0.383125 + 0.923697i \(0.625152\pi\)
\(60\) 0.987692 0.127511
\(61\) −7.98055 −1.02180 −0.510902 0.859639i \(-0.670689\pi\)
−0.510902 + 0.859639i \(0.670689\pi\)
\(62\) −9.91879 −1.25969
\(63\) 4.23262 0.533260
\(64\) 8.87998 1.11000
\(65\) 5.71421 0.708760
\(66\) 0 0
\(67\) 12.0477 1.47187 0.735933 0.677054i \(-0.236744\pi\)
0.735933 + 0.677054i \(0.236744\pi\)
\(68\) −0.0419880 −0.00509179
\(69\) −14.6012 −1.75778
\(70\) −1.27779 −0.152725
\(71\) −0.829397 −0.0984313 −0.0492157 0.998788i \(-0.515672\pi\)
−0.0492157 + 0.998788i \(0.515672\pi\)
\(72\) −12.8031 −1.50885
\(73\) 1.17180 0.137149 0.0685746 0.997646i \(-0.478155\pi\)
0.0685746 + 0.997646i \(0.478155\pi\)
\(74\) 14.0403 1.63215
\(75\) 2.68935 0.310540
\(76\) 2.32606 0.266817
\(77\) 0 0
\(78\) −19.6364 −2.22339
\(79\) 0.699582 0.0787092 0.0393546 0.999225i \(-0.487470\pi\)
0.0393546 + 0.999225i \(0.487470\pi\)
\(80\) 3.13060 0.350012
\(81\) −3.78279 −0.420310
\(82\) 2.62019 0.289352
\(83\) 8.74733 0.960144 0.480072 0.877229i \(-0.340611\pi\)
0.480072 + 0.877229i \(0.340611\pi\)
\(84\) −0.987692 −0.107766
\(85\) −0.114328 −0.0124006
\(86\) −4.16346 −0.448957
\(87\) −9.49303 −1.01776
\(88\) 0 0
\(89\) 8.44787 0.895472 0.447736 0.894166i \(-0.352230\pi\)
0.447736 + 0.894166i \(0.352230\pi\)
\(90\) −5.40839 −0.570094
\(91\) −5.71421 −0.599012
\(92\) 1.99396 0.207884
\(93\) −20.8760 −2.16474
\(94\) −0.950530 −0.0980397
\(95\) 6.33354 0.649807
\(96\) 5.51175 0.562540
\(97\) −7.68221 −0.780010 −0.390005 0.920813i \(-0.627527\pi\)
−0.390005 + 0.920813i \(0.627527\pi\)
\(98\) 1.27779 0.129076
\(99\) 0 0
\(100\) −0.367260 −0.0367260
\(101\) −19.1938 −1.90986 −0.954929 0.296835i \(-0.904069\pi\)
−0.954929 + 0.296835i \(0.904069\pi\)
\(102\) 0.392878 0.0389007
\(103\) −8.84677 −0.871698 −0.435849 0.900020i \(-0.643552\pi\)
−0.435849 + 0.900020i \(0.643552\pi\)
\(104\) 17.2846 1.69490
\(105\) −2.68935 −0.262454
\(106\) 0.838427 0.0814352
\(107\) 15.4018 1.48895 0.744475 0.667650i \(-0.232700\pi\)
0.744475 + 0.667650i \(0.232700\pi\)
\(108\) −1.21745 −0.117149
\(109\) −3.91449 −0.374940 −0.187470 0.982270i \(-0.560029\pi\)
−0.187470 + 0.982270i \(0.560029\pi\)
\(110\) 0 0
\(111\) 29.5505 2.80481
\(112\) −3.13060 −0.295814
\(113\) 17.7729 1.67193 0.835967 0.548780i \(-0.184908\pi\)
0.835967 + 0.548780i \(0.184908\pi\)
\(114\) −21.7647 −2.03845
\(115\) 5.42928 0.506283
\(116\) 1.29638 0.120366
\(117\) −24.1861 −2.23600
\(118\) −7.52064 −0.692331
\(119\) 0.114328 0.0104804
\(120\) 8.13490 0.742612
\(121\) 0 0
\(122\) −10.1974 −0.923233
\(123\) 5.51471 0.497245
\(124\) 2.85085 0.256014
\(125\) −1.00000 −0.0894427
\(126\) 5.40839 0.481817
\(127\) −3.11741 −0.276626 −0.138313 0.990389i \(-0.544168\pi\)
−0.138313 + 0.990389i \(0.544168\pi\)
\(128\) 7.24779 0.640620
\(129\) −8.76282 −0.771523
\(130\) 7.30154 0.640387
\(131\) −12.4579 −1.08845 −0.544225 0.838939i \(-0.683176\pi\)
−0.544225 + 0.838939i \(0.683176\pi\)
\(132\) 0 0
\(133\) −6.33354 −0.549187
\(134\) 15.3945 1.32988
\(135\) −3.31495 −0.285305
\(136\) −0.345825 −0.0296542
\(137\) −20.5066 −1.75200 −0.876000 0.482312i \(-0.839797\pi\)
−0.876000 + 0.482312i \(0.839797\pi\)
\(138\) −18.6573 −1.58821
\(139\) 21.4970 1.82335 0.911675 0.410913i \(-0.134790\pi\)
0.911675 + 0.410913i \(0.134790\pi\)
\(140\) 0.367260 0.0310392
\(141\) −2.00058 −0.168479
\(142\) −1.05979 −0.0889358
\(143\) 0 0
\(144\) −13.2506 −1.10422
\(145\) 3.52986 0.293139
\(146\) 1.49731 0.123919
\(147\) 2.68935 0.221814
\(148\) −4.03544 −0.331711
\(149\) −15.0366 −1.23185 −0.615925 0.787805i \(-0.711217\pi\)
−0.615925 + 0.787805i \(0.711217\pi\)
\(150\) 3.43642 0.280583
\(151\) 18.4655 1.50270 0.751351 0.659903i \(-0.229403\pi\)
0.751351 + 0.659903i \(0.229403\pi\)
\(152\) 19.1580 1.55392
\(153\) 0.483906 0.0391215
\(154\) 0 0
\(155\) 7.76248 0.623497
\(156\) 5.64388 0.451872
\(157\) −3.80016 −0.303286 −0.151643 0.988435i \(-0.548456\pi\)
−0.151643 + 0.988435i \(0.548456\pi\)
\(158\) 0.893917 0.0711162
\(159\) 1.76463 0.139944
\(160\) −2.04947 −0.162025
\(161\) −5.42928 −0.427887
\(162\) −4.83360 −0.379764
\(163\) 4.68279 0.366784 0.183392 0.983040i \(-0.441292\pi\)
0.183392 + 0.983040i \(0.441292\pi\)
\(164\) −0.753093 −0.0588067
\(165\) 0 0
\(166\) 11.1772 0.867521
\(167\) −19.7979 −1.53201 −0.766004 0.642836i \(-0.777758\pi\)
−0.766004 + 0.642836i \(0.777758\pi\)
\(168\) −8.13490 −0.627621
\(169\) 19.6522 1.51171
\(170\) −0.146086 −0.0112043
\(171\) −26.8075 −2.05002
\(172\) 1.19666 0.0912443
\(173\) 5.03852 0.383072 0.191536 0.981486i \(-0.438653\pi\)
0.191536 + 0.981486i \(0.438653\pi\)
\(174\) −12.1301 −0.919579
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −15.8287 −1.18975
\(178\) 10.7946 0.809088
\(179\) 3.48467 0.260457 0.130228 0.991484i \(-0.458429\pi\)
0.130228 + 0.991484i \(0.458429\pi\)
\(180\) 1.55447 0.115864
\(181\) 18.4355 1.37030 0.685149 0.728403i \(-0.259737\pi\)
0.685149 + 0.728403i \(0.259737\pi\)
\(182\) −7.30154 −0.541226
\(183\) −21.4625 −1.58655
\(184\) 16.4228 1.21070
\(185\) −10.9880 −0.807850
\(186\) −26.6751 −1.95592
\(187\) 0 0
\(188\) 0.273200 0.0199252
\(189\) 3.31495 0.241127
\(190\) 8.09291 0.587122
\(191\) 12.3915 0.896618 0.448309 0.893879i \(-0.352026\pi\)
0.448309 + 0.893879i \(0.352026\pi\)
\(192\) 23.8814 1.72349
\(193\) −13.3250 −0.959151 −0.479576 0.877501i \(-0.659209\pi\)
−0.479576 + 0.877501i \(0.659209\pi\)
\(194\) −9.81623 −0.704764
\(195\) 15.3675 1.10049
\(196\) −0.367260 −0.0262329
\(197\) −14.3676 −1.02365 −0.511824 0.859090i \(-0.671030\pi\)
−0.511824 + 0.859090i \(0.671030\pi\)
\(198\) 0 0
\(199\) 4.88790 0.346494 0.173247 0.984878i \(-0.444574\pi\)
0.173247 + 0.984878i \(0.444574\pi\)
\(200\) −3.02485 −0.213890
\(201\) 32.4006 2.28537
\(202\) −24.5256 −1.72562
\(203\) −3.52986 −0.247747
\(204\) −0.112921 −0.00790602
\(205\) −2.05057 −0.143218
\(206\) −11.3043 −0.787607
\(207\) −22.9801 −1.59722
\(208\) 17.8889 1.24037
\(209\) 0 0
\(210\) −3.43642 −0.237136
\(211\) −19.7242 −1.35787 −0.678935 0.734199i \(-0.737558\pi\)
−0.678935 + 0.734199i \(0.737558\pi\)
\(212\) −0.240980 −0.0165506
\(213\) −2.23054 −0.152834
\(214\) 19.6802 1.34531
\(215\) 3.25834 0.222217
\(216\) −10.0272 −0.682267
\(217\) −7.76248 −0.526951
\(218\) −5.00189 −0.338770
\(219\) 3.15139 0.212951
\(220\) 0 0
\(221\) −0.653292 −0.0439452
\(222\) 37.7592 2.53423
\(223\) 18.8686 1.26353 0.631767 0.775159i \(-0.282330\pi\)
0.631767 + 0.775159i \(0.282330\pi\)
\(224\) 2.04947 0.136936
\(225\) 4.23262 0.282175
\(226\) 22.7100 1.51065
\(227\) 14.6125 0.969868 0.484934 0.874551i \(-0.338844\pi\)
0.484934 + 0.874551i \(0.338844\pi\)
\(228\) 6.25559 0.414286
\(229\) 19.1789 1.26738 0.633689 0.773588i \(-0.281540\pi\)
0.633689 + 0.773588i \(0.281540\pi\)
\(230\) 6.93746 0.457443
\(231\) 0 0
\(232\) 10.6773 0.700999
\(233\) −20.6605 −1.35352 −0.676758 0.736206i \(-0.736615\pi\)
−0.676758 + 0.736206i \(0.736615\pi\)
\(234\) −30.9046 −2.02030
\(235\) 0.743888 0.0485259
\(236\) 2.16157 0.140706
\(237\) 1.88142 0.122212
\(238\) 0.146086 0.00946938
\(239\) −18.4967 −1.19645 −0.598227 0.801327i \(-0.704128\pi\)
−0.598227 + 0.801327i \(0.704128\pi\)
\(240\) 8.41929 0.543463
\(241\) −22.3243 −1.43804 −0.719018 0.694992i \(-0.755408\pi\)
−0.719018 + 0.694992i \(0.755408\pi\)
\(242\) 0 0
\(243\) −20.1181 −1.29058
\(244\) 2.93094 0.187634
\(245\) −1.00000 −0.0638877
\(246\) 7.04662 0.449276
\(247\) 36.1912 2.30279
\(248\) 23.4804 1.49100
\(249\) 23.5247 1.49081
\(250\) −1.27779 −0.0808143
\(251\) −29.5965 −1.86812 −0.934058 0.357121i \(-0.883758\pi\)
−0.934058 + 0.357121i \(0.883758\pi\)
\(252\) −1.55447 −0.0979226
\(253\) 0 0
\(254\) −3.98339 −0.249940
\(255\) −0.307468 −0.0192544
\(256\) −8.49884 −0.531177
\(257\) 24.8642 1.55099 0.775494 0.631355i \(-0.217501\pi\)
0.775494 + 0.631355i \(0.217501\pi\)
\(258\) −11.1970 −0.697096
\(259\) 10.9880 0.682758
\(260\) −2.09860 −0.130150
\(261\) −14.9405 −0.924797
\(262\) −15.9185 −0.983449
\(263\) 10.2318 0.630917 0.315459 0.948939i \(-0.397842\pi\)
0.315459 + 0.948939i \(0.397842\pi\)
\(264\) 0 0
\(265\) −0.656155 −0.0403073
\(266\) −8.09291 −0.496208
\(267\) 22.7193 1.39040
\(268\) −4.42466 −0.270279
\(269\) 5.45707 0.332724 0.166362 0.986065i \(-0.446798\pi\)
0.166362 + 0.986065i \(0.446798\pi\)
\(270\) −4.23580 −0.257783
\(271\) −6.88897 −0.418475 −0.209237 0.977865i \(-0.567098\pi\)
−0.209237 + 0.977865i \(0.567098\pi\)
\(272\) −0.357914 −0.0217017
\(273\) −15.3675 −0.930085
\(274\) −26.2031 −1.58299
\(275\) 0 0
\(276\) 5.36246 0.322782
\(277\) −25.1238 −1.50954 −0.754772 0.655988i \(-0.772252\pi\)
−0.754772 + 0.655988i \(0.772252\pi\)
\(278\) 27.4686 1.64745
\(279\) −32.8556 −1.96701
\(280\) 3.02485 0.180770
\(281\) 16.4407 0.980771 0.490386 0.871506i \(-0.336856\pi\)
0.490386 + 0.871506i \(0.336856\pi\)
\(282\) −2.55631 −0.152226
\(283\) −6.27657 −0.373103 −0.186552 0.982445i \(-0.559731\pi\)
−0.186552 + 0.982445i \(0.559731\pi\)
\(284\) 0.304605 0.0180750
\(285\) 17.0331 1.00895
\(286\) 0 0
\(287\) 2.05057 0.121041
\(288\) 8.67463 0.511157
\(289\) −16.9869 −0.999231
\(290\) 4.51041 0.264860
\(291\) −20.6602 −1.21112
\(292\) −0.430357 −0.0251847
\(293\) 5.98463 0.349626 0.174813 0.984602i \(-0.444068\pi\)
0.174813 + 0.984602i \(0.444068\pi\)
\(294\) 3.43642 0.200416
\(295\) 5.88567 0.342677
\(296\) −33.2370 −1.93186
\(297\) 0 0
\(298\) −19.2136 −1.11302
\(299\) 31.0240 1.79417
\(300\) −0.987692 −0.0570245
\(301\) −3.25834 −0.187807
\(302\) 23.5950 1.35774
\(303\) −51.6190 −2.96543
\(304\) 19.8278 1.13720
\(305\) 7.98055 0.456965
\(306\) 0.618328 0.0353475
\(307\) −24.1958 −1.38093 −0.690465 0.723366i \(-0.742594\pi\)
−0.690465 + 0.723366i \(0.742594\pi\)
\(308\) 0 0
\(309\) −23.7921 −1.35348
\(310\) 9.91879 0.563350
\(311\) −8.26385 −0.468600 −0.234300 0.972164i \(-0.575280\pi\)
−0.234300 + 0.972164i \(0.575280\pi\)
\(312\) 46.4845 2.63167
\(313\) −3.32802 −0.188111 −0.0940554 0.995567i \(-0.529983\pi\)
−0.0940554 + 0.995567i \(0.529983\pi\)
\(314\) −4.85580 −0.274029
\(315\) −4.23262 −0.238481
\(316\) −0.256929 −0.0144534
\(317\) −4.42285 −0.248412 −0.124206 0.992256i \(-0.539638\pi\)
−0.124206 + 0.992256i \(0.539638\pi\)
\(318\) 2.25482 0.126444
\(319\) 0 0
\(320\) −8.87998 −0.496406
\(321\) 41.4209 2.31189
\(322\) −6.93746 −0.386610
\(323\) −0.724099 −0.0402899
\(324\) 1.38927 0.0771816
\(325\) −5.71421 −0.316967
\(326\) 5.98360 0.331401
\(327\) −10.5274 −0.582169
\(328\) −6.20268 −0.342486
\(329\) −0.743888 −0.0410119
\(330\) 0 0
\(331\) −35.1681 −1.93301 −0.966506 0.256644i \(-0.917383\pi\)
−0.966506 + 0.256644i \(0.917383\pi\)
\(332\) −3.21255 −0.176311
\(333\) 46.5078 2.54861
\(334\) −25.2975 −1.38422
\(335\) −12.0477 −0.658239
\(336\) −8.41929 −0.459310
\(337\) 14.5648 0.793397 0.396699 0.917949i \(-0.370156\pi\)
0.396699 + 0.917949i \(0.370156\pi\)
\(338\) 25.1113 1.36587
\(339\) 47.7976 2.59601
\(340\) 0.0419880 0.00227712
\(341\) 0 0
\(342\) −34.2542 −1.85226
\(343\) 1.00000 0.0539949
\(344\) 9.85599 0.531399
\(345\) 14.6012 0.786104
\(346\) 6.43816 0.346118
\(347\) 36.7525 1.97298 0.986488 0.163834i \(-0.0523861\pi\)
0.986488 + 0.163834i \(0.0523861\pi\)
\(348\) 3.48641 0.186891
\(349\) −6.07415 −0.325142 −0.162571 0.986697i \(-0.551979\pi\)
−0.162571 + 0.986697i \(0.551979\pi\)
\(350\) 1.27779 0.0683006
\(351\) −18.9423 −1.01107
\(352\) 0 0
\(353\) −25.7569 −1.37090 −0.685451 0.728119i \(-0.740395\pi\)
−0.685451 + 0.728119i \(0.740395\pi\)
\(354\) −20.2256 −1.07498
\(355\) 0.829397 0.0440198
\(356\) −3.10257 −0.164436
\(357\) 0.307468 0.0162729
\(358\) 4.45267 0.235331
\(359\) −24.8162 −1.30975 −0.654876 0.755737i \(-0.727279\pi\)
−0.654876 + 0.755737i \(0.727279\pi\)
\(360\) 12.8031 0.674780
\(361\) 21.1137 1.11125
\(362\) 23.5566 1.23811
\(363\) 0 0
\(364\) 2.09860 0.109997
\(365\) −1.17180 −0.0613350
\(366\) −27.4245 −1.43350
\(367\) −27.3679 −1.42859 −0.714296 0.699844i \(-0.753253\pi\)
−0.714296 + 0.699844i \(0.753253\pi\)
\(368\) 16.9969 0.886024
\(369\) 8.67929 0.451826
\(370\) −14.0403 −0.729919
\(371\) 0.656155 0.0340659
\(372\) 7.66694 0.397512
\(373\) 10.7019 0.554125 0.277063 0.960852i \(-0.410639\pi\)
0.277063 + 0.960852i \(0.410639\pi\)
\(374\) 0 0
\(375\) −2.68935 −0.138878
\(376\) 2.25015 0.116043
\(377\) 20.1703 1.03883
\(378\) 4.23580 0.217866
\(379\) −1.03501 −0.0531647 −0.0265824 0.999647i \(-0.508462\pi\)
−0.0265824 + 0.999647i \(0.508462\pi\)
\(380\) −2.32606 −0.119324
\(381\) −8.38382 −0.429516
\(382\) 15.8337 0.810123
\(383\) −26.0652 −1.33187 −0.665935 0.746010i \(-0.731967\pi\)
−0.665935 + 0.746010i \(0.731967\pi\)
\(384\) 19.4919 0.994690
\(385\) 0 0
\(386\) −17.0265 −0.866624
\(387\) −13.7913 −0.701051
\(388\) 2.82137 0.143233
\(389\) −12.3040 −0.623837 −0.311918 0.950109i \(-0.600972\pi\)
−0.311918 + 0.950109i \(0.600972\pi\)
\(390\) 19.6364 0.994329
\(391\) −0.620717 −0.0313910
\(392\) −3.02485 −0.152778
\(393\) −33.5036 −1.69003
\(394\) −18.3587 −0.924900
\(395\) −0.699582 −0.0351998
\(396\) 0 0
\(397\) 30.3190 1.52167 0.760834 0.648946i \(-0.224790\pi\)
0.760834 + 0.648946i \(0.224790\pi\)
\(398\) 6.24569 0.313068
\(399\) −17.0331 −0.852723
\(400\) −3.13060 −0.156530
\(401\) 5.72615 0.285950 0.142975 0.989726i \(-0.454333\pi\)
0.142975 + 0.989726i \(0.454333\pi\)
\(402\) 41.4011 2.06490
\(403\) 44.3564 2.20955
\(404\) 7.04913 0.350707
\(405\) 3.78279 0.187968
\(406\) −4.51041 −0.223848
\(407\) 0 0
\(408\) −0.930045 −0.0460441
\(409\) 9.18023 0.453933 0.226967 0.973903i \(-0.427119\pi\)
0.226967 + 0.973903i \(0.427119\pi\)
\(410\) −2.62019 −0.129402
\(411\) −55.1496 −2.72033
\(412\) 3.24907 0.160070
\(413\) −5.88567 −0.289615
\(414\) −29.3636 −1.44314
\(415\) −8.74733 −0.429389
\(416\) −11.7111 −0.574184
\(417\) 57.8130 2.83111
\(418\) 0 0
\(419\) 19.3924 0.947380 0.473690 0.880692i \(-0.342922\pi\)
0.473690 + 0.880692i \(0.342922\pi\)
\(420\) 0.987692 0.0481945
\(421\) −17.6613 −0.860759 −0.430379 0.902648i \(-0.641620\pi\)
−0.430379 + 0.902648i \(0.641620\pi\)
\(422\) −25.2033 −1.22688
\(423\) −3.14859 −0.153090
\(424\) −1.98477 −0.0963891
\(425\) 0.114328 0.00554571
\(426\) −2.85016 −0.138091
\(427\) −7.98055 −0.386206
\(428\) −5.65648 −0.273416
\(429\) 0 0
\(430\) 4.16346 0.200780
\(431\) 13.8924 0.669175 0.334588 0.942365i \(-0.391403\pi\)
0.334588 + 0.942365i \(0.391403\pi\)
\(432\) −10.3778 −0.499301
\(433\) 21.5969 1.03788 0.518941 0.854810i \(-0.326326\pi\)
0.518941 + 0.854810i \(0.326326\pi\)
\(434\) −9.91879 −0.476117
\(435\) 9.49303 0.455156
\(436\) 1.43764 0.0688503
\(437\) 34.3865 1.64493
\(438\) 4.02681 0.192408
\(439\) −4.59245 −0.219186 −0.109593 0.993977i \(-0.534955\pi\)
−0.109593 + 0.993977i \(0.534955\pi\)
\(440\) 0 0
\(441\) 4.23262 0.201553
\(442\) −0.834768 −0.0397059
\(443\) 18.0085 0.855609 0.427805 0.903871i \(-0.359287\pi\)
0.427805 + 0.903871i \(0.359287\pi\)
\(444\) −10.8527 −0.515047
\(445\) −8.44787 −0.400467
\(446\) 24.1100 1.14164
\(447\) −40.4388 −1.91269
\(448\) 8.87998 0.419540
\(449\) 14.4902 0.683836 0.341918 0.939730i \(-0.388924\pi\)
0.341918 + 0.939730i \(0.388924\pi\)
\(450\) 5.40839 0.254954
\(451\) 0 0
\(452\) −6.52728 −0.307017
\(453\) 49.6602 2.33324
\(454\) 18.6717 0.876307
\(455\) 5.71421 0.267886
\(456\) 51.5227 2.41277
\(457\) −15.8719 −0.742455 −0.371228 0.928542i \(-0.621063\pi\)
−0.371228 + 0.928542i \(0.621063\pi\)
\(458\) 24.5066 1.14512
\(459\) 0.378990 0.0176898
\(460\) −1.99396 −0.0929687
\(461\) 12.8746 0.599629 0.299815 0.953998i \(-0.403075\pi\)
0.299815 + 0.953998i \(0.403075\pi\)
\(462\) 0 0
\(463\) 24.7254 1.14909 0.574543 0.818475i \(-0.305180\pi\)
0.574543 + 0.818475i \(0.305180\pi\)
\(464\) 11.0506 0.513010
\(465\) 20.8760 0.968103
\(466\) −26.3997 −1.22294
\(467\) 10.6779 0.494116 0.247058 0.969001i \(-0.420536\pi\)
0.247058 + 0.969001i \(0.420536\pi\)
\(468\) 8.88258 0.410597
\(469\) 12.0477 0.556313
\(470\) 0.950530 0.0438447
\(471\) −10.2200 −0.470912
\(472\) 17.8033 0.819463
\(473\) 0 0
\(474\) 2.40406 0.110422
\(475\) −6.33354 −0.290603
\(476\) −0.0419880 −0.00192452
\(477\) 2.77726 0.127162
\(478\) −23.6349 −1.08103
\(479\) 21.0362 0.961169 0.480584 0.876948i \(-0.340425\pi\)
0.480584 + 0.876948i \(0.340425\pi\)
\(480\) −5.51175 −0.251576
\(481\) −62.7874 −2.86286
\(482\) −28.5257 −1.29931
\(483\) −14.6012 −0.664380
\(484\) 0 0
\(485\) 7.68221 0.348831
\(486\) −25.7067 −1.16608
\(487\) 11.4131 0.517176 0.258588 0.965988i \(-0.416743\pi\)
0.258588 + 0.965988i \(0.416743\pi\)
\(488\) 24.1400 1.09277
\(489\) 12.5937 0.569505
\(490\) −1.27779 −0.0577245
\(491\) −3.16966 −0.143045 −0.0715225 0.997439i \(-0.522786\pi\)
−0.0715225 + 0.997439i \(0.522786\pi\)
\(492\) −2.02533 −0.0913091
\(493\) −0.403560 −0.0181755
\(494\) 46.2446 2.08064
\(495\) 0 0
\(496\) 24.3012 1.09116
\(497\) −0.829397 −0.0372035
\(498\) 30.0595 1.34700
\(499\) −1.23960 −0.0554922 −0.0277461 0.999615i \(-0.508833\pi\)
−0.0277461 + 0.999615i \(0.508833\pi\)
\(500\) 0.367260 0.0164244
\(501\) −53.2435 −2.37875
\(502\) −37.8181 −1.68790
\(503\) −1.03614 −0.0461991 −0.0230996 0.999733i \(-0.507353\pi\)
−0.0230996 + 0.999733i \(0.507353\pi\)
\(504\) −12.8031 −0.570294
\(505\) 19.1938 0.854114
\(506\) 0 0
\(507\) 52.8516 2.34722
\(508\) 1.14490 0.0507968
\(509\) 29.4873 1.30700 0.653501 0.756926i \(-0.273300\pi\)
0.653501 + 0.756926i \(0.273300\pi\)
\(510\) −0.392878 −0.0173969
\(511\) 1.17180 0.0518375
\(512\) −25.3553 −1.12056
\(513\) −20.9954 −0.926968
\(514\) 31.7712 1.40137
\(515\) 8.84677 0.389835
\(516\) 3.21823 0.141675
\(517\) 0 0
\(518\) 14.0403 0.616894
\(519\) 13.5504 0.594795
\(520\) −17.2846 −0.757982
\(521\) 14.3644 0.629315 0.314658 0.949205i \(-0.398110\pi\)
0.314658 + 0.949205i \(0.398110\pi\)
\(522\) −19.0908 −0.835583
\(523\) 26.0926 1.14095 0.570475 0.821315i \(-0.306759\pi\)
0.570475 + 0.821315i \(0.306759\pi\)
\(524\) 4.57528 0.199872
\(525\) 2.68935 0.117373
\(526\) 13.0740 0.570054
\(527\) −0.887466 −0.0386586
\(528\) 0 0
\(529\) 6.47705 0.281611
\(530\) −0.838427 −0.0364189
\(531\) −24.9118 −1.08108
\(532\) 2.32606 0.100847
\(533\) −11.7174 −0.507536
\(534\) 29.0304 1.25627
\(535\) −15.4018 −0.665879
\(536\) −36.4427 −1.57408
\(537\) 9.37152 0.404411
\(538\) 6.97298 0.300626
\(539\) 0 0
\(540\) 1.21745 0.0523907
\(541\) 24.4387 1.05070 0.525351 0.850885i \(-0.323934\pi\)
0.525351 + 0.850885i \(0.323934\pi\)
\(542\) −8.80263 −0.378105
\(543\) 49.5795 2.12766
\(544\) 0.234311 0.0100460
\(545\) 3.91449 0.167678
\(546\) −19.6364 −0.840361
\(547\) −9.64267 −0.412291 −0.206145 0.978521i \(-0.566092\pi\)
−0.206145 + 0.978521i \(0.566092\pi\)
\(548\) 7.53127 0.321720
\(549\) −33.7786 −1.44164
\(550\) 0 0
\(551\) 22.3565 0.952419
\(552\) 44.1666 1.87986
\(553\) 0.699582 0.0297493
\(554\) −32.1029 −1.36392
\(555\) −29.5505 −1.25435
\(556\) −7.89498 −0.334822
\(557\) 11.0653 0.468852 0.234426 0.972134i \(-0.424679\pi\)
0.234426 + 0.972134i \(0.424679\pi\)
\(558\) −41.9825 −1.77726
\(559\) 18.6188 0.787492
\(560\) 3.13060 0.132292
\(561\) 0 0
\(562\) 21.0077 0.886158
\(563\) 6.71297 0.282918 0.141459 0.989944i \(-0.454821\pi\)
0.141459 + 0.989944i \(0.454821\pi\)
\(564\) 0.734733 0.0309378
\(565\) −17.7729 −0.747711
\(566\) −8.02012 −0.337111
\(567\) −3.78279 −0.158862
\(568\) 2.50881 0.105267
\(569\) 33.9179 1.42191 0.710955 0.703237i \(-0.248263\pi\)
0.710955 + 0.703237i \(0.248263\pi\)
\(570\) 21.7647 0.911623
\(571\) 20.0707 0.839931 0.419965 0.907540i \(-0.362042\pi\)
0.419965 + 0.907540i \(0.362042\pi\)
\(572\) 0 0
\(573\) 33.3252 1.39218
\(574\) 2.62019 0.109365
\(575\) −5.42928 −0.226416
\(576\) 37.5856 1.56607
\(577\) −36.6983 −1.52777 −0.763884 0.645353i \(-0.776710\pi\)
−0.763884 + 0.645353i \(0.776710\pi\)
\(578\) −21.7057 −0.902837
\(579\) −35.8355 −1.48927
\(580\) −1.29638 −0.0538291
\(581\) 8.74733 0.362900
\(582\) −26.3993 −1.09429
\(583\) 0 0
\(584\) −3.54453 −0.146674
\(585\) 24.1861 0.999971
\(586\) 7.64708 0.315898
\(587\) 0.710389 0.0293209 0.0146604 0.999893i \(-0.495333\pi\)
0.0146604 + 0.999893i \(0.495333\pi\)
\(588\) −0.987692 −0.0407318
\(589\) 49.1639 2.02577
\(590\) 7.52064 0.309620
\(591\) −38.6395 −1.58942
\(592\) −34.3989 −1.41379
\(593\) −3.10847 −0.127650 −0.0638248 0.997961i \(-0.520330\pi\)
−0.0638248 + 0.997961i \(0.520330\pi\)
\(594\) 0 0
\(595\) −0.114328 −0.00468698
\(596\) 5.52236 0.226205
\(597\) 13.1453 0.538000
\(598\) 39.6421 1.62109
\(599\) −10.8079 −0.441600 −0.220800 0.975319i \(-0.570867\pi\)
−0.220800 + 0.975319i \(0.570867\pi\)
\(600\) −8.13490 −0.332106
\(601\) 1.36180 0.0555488 0.0277744 0.999614i \(-0.491158\pi\)
0.0277744 + 0.999614i \(0.491158\pi\)
\(602\) −4.16346 −0.169690
\(603\) 50.9935 2.07662
\(604\) −6.78164 −0.275941
\(605\) 0 0
\(606\) −65.9581 −2.67936
\(607\) −20.6040 −0.836291 −0.418146 0.908380i \(-0.637320\pi\)
−0.418146 + 0.908380i \(0.637320\pi\)
\(608\) −12.9804 −0.526425
\(609\) −9.49303 −0.384677
\(610\) 10.1974 0.412882
\(611\) 4.25073 0.171966
\(612\) −0.177719 −0.00718388
\(613\) −2.68962 −0.108633 −0.0543163 0.998524i \(-0.517298\pi\)
−0.0543163 + 0.998524i \(0.517298\pi\)
\(614\) −30.9171 −1.24771
\(615\) −5.51471 −0.222375
\(616\) 0 0
\(617\) 20.2761 0.816285 0.408143 0.912918i \(-0.366177\pi\)
0.408143 + 0.912918i \(0.366177\pi\)
\(618\) −30.4012 −1.22292
\(619\) −34.1015 −1.37066 −0.685328 0.728234i \(-0.740341\pi\)
−0.685328 + 0.728234i \(0.740341\pi\)
\(620\) −2.85085 −0.114493
\(621\) −17.9978 −0.722226
\(622\) −10.5594 −0.423395
\(623\) 8.44787 0.338457
\(624\) 48.1096 1.92592
\(625\) 1.00000 0.0400000
\(626\) −4.25250 −0.169964
\(627\) 0 0
\(628\) 1.39565 0.0556925
\(629\) 1.25623 0.0500891
\(630\) −5.40839 −0.215475
\(631\) 17.5803 0.699861 0.349930 0.936776i \(-0.386205\pi\)
0.349930 + 0.936776i \(0.386205\pi\)
\(632\) −2.11613 −0.0841753
\(633\) −53.0453 −2.10836
\(634\) −5.65146 −0.224448
\(635\) 3.11741 0.123711
\(636\) −0.648079 −0.0256980
\(637\) −5.71421 −0.226405
\(638\) 0 0
\(639\) −3.51052 −0.138874
\(640\) −7.24779 −0.286494
\(641\) −20.4508 −0.807758 −0.403879 0.914812i \(-0.632338\pi\)
−0.403879 + 0.914812i \(0.632338\pi\)
\(642\) 52.9271 2.08887
\(643\) −17.9192 −0.706665 −0.353332 0.935498i \(-0.614951\pi\)
−0.353332 + 0.935498i \(0.614951\pi\)
\(644\) 1.99396 0.0785729
\(645\) 8.76282 0.345036
\(646\) −0.925244 −0.0364032
\(647\) 27.5048 1.08133 0.540663 0.841239i \(-0.318173\pi\)
0.540663 + 0.841239i \(0.318173\pi\)
\(648\) 11.4424 0.449500
\(649\) 0 0
\(650\) −7.30154 −0.286390
\(651\) −20.8760 −0.818197
\(652\) −1.71980 −0.0673526
\(653\) −44.8740 −1.75606 −0.878028 0.478610i \(-0.841141\pi\)
−0.878028 + 0.478610i \(0.841141\pi\)
\(654\) −13.4518 −0.526008
\(655\) 12.4579 0.486769
\(656\) −6.41952 −0.250640
\(657\) 4.95980 0.193500
\(658\) −0.950530 −0.0370555
\(659\) −33.2963 −1.29704 −0.648521 0.761197i \(-0.724612\pi\)
−0.648521 + 0.761197i \(0.724612\pi\)
\(660\) 0 0
\(661\) −20.7701 −0.807863 −0.403932 0.914789i \(-0.632357\pi\)
−0.403932 + 0.914789i \(0.632357\pi\)
\(662\) −44.9373 −1.74654
\(663\) −1.75693 −0.0682336
\(664\) −26.4594 −1.02682
\(665\) 6.33354 0.245604
\(666\) 59.4271 2.30275
\(667\) 19.1646 0.742055
\(668\) 7.27098 0.281323
\(669\) 50.7443 1.96189
\(670\) −15.3945 −0.594740
\(671\) 0 0
\(672\) 5.51175 0.212620
\(673\) −36.8748 −1.42142 −0.710710 0.703485i \(-0.751626\pi\)
−0.710710 + 0.703485i \(0.751626\pi\)
\(674\) 18.6108 0.716860
\(675\) 3.31495 0.127592
\(676\) −7.21746 −0.277595
\(677\) −13.3892 −0.514588 −0.257294 0.966333i \(-0.582831\pi\)
−0.257294 + 0.966333i \(0.582831\pi\)
\(678\) 61.0752 2.34558
\(679\) −7.68221 −0.294816
\(680\) 0.345825 0.0132618
\(681\) 39.2983 1.50591
\(682\) 0 0
\(683\) −4.46213 −0.170739 −0.0853693 0.996349i \(-0.527207\pi\)
−0.0853693 + 0.996349i \(0.527207\pi\)
\(684\) 9.84531 0.376445
\(685\) 20.5066 0.783518
\(686\) 1.27779 0.0487861
\(687\) 51.5788 1.96786
\(688\) 10.2005 0.388892
\(689\) −3.74941 −0.142841
\(690\) 18.6573 0.710270
\(691\) −32.9632 −1.25398 −0.626990 0.779027i \(-0.715713\pi\)
−0.626990 + 0.779027i \(0.715713\pi\)
\(692\) −1.85045 −0.0703435
\(693\) 0 0
\(694\) 46.9618 1.78265
\(695\) −21.4970 −0.815427
\(696\) 28.7150 1.08844
\(697\) 0.234437 0.00887994
\(698\) −7.76147 −0.293776
\(699\) −55.5634 −2.10160
\(700\) −0.367260 −0.0138811
\(701\) 10.0233 0.378574 0.189287 0.981922i \(-0.439382\pi\)
0.189287 + 0.981922i \(0.439382\pi\)
\(702\) −24.2042 −0.913530
\(703\) −69.5926 −2.62474
\(704\) 0 0
\(705\) 2.00058 0.0753461
\(706\) −32.9118 −1.23865
\(707\) −19.1938 −0.721858
\(708\) 5.81323 0.218475
\(709\) −35.3012 −1.32576 −0.662882 0.748724i \(-0.730667\pi\)
−0.662882 + 0.748724i \(0.730667\pi\)
\(710\) 1.05979 0.0397733
\(711\) 2.96107 0.111049
\(712\) −25.5536 −0.957660
\(713\) 42.1446 1.57833
\(714\) 0.392878 0.0147031
\(715\) 0 0
\(716\) −1.27978 −0.0478277
\(717\) −49.7442 −1.85773
\(718\) −31.7099 −1.18340
\(719\) −15.8441 −0.590886 −0.295443 0.955360i \(-0.595467\pi\)
−0.295443 + 0.955360i \(0.595467\pi\)
\(720\) 13.2506 0.493822
\(721\) −8.84677 −0.329471
\(722\) 26.9788 1.00405
\(723\) −60.0380 −2.23284
\(724\) −6.77062 −0.251628
\(725\) −3.52986 −0.131096
\(726\) 0 0
\(727\) 41.9381 1.55540 0.777699 0.628636i \(-0.216387\pi\)
0.777699 + 0.628636i \(0.216387\pi\)
\(728\) 17.2846 0.640612
\(729\) −42.7563 −1.58357
\(730\) −1.49731 −0.0554181
\(731\) −0.372518 −0.0137781
\(732\) 7.88233 0.291339
\(733\) −15.6164 −0.576806 −0.288403 0.957509i \(-0.593124\pi\)
−0.288403 + 0.957509i \(0.593124\pi\)
\(734\) −34.9703 −1.29078
\(735\) −2.68935 −0.0991983
\(736\) −11.1271 −0.410152
\(737\) 0 0
\(738\) 11.0903 0.408239
\(739\) 2.15862 0.0794060 0.0397030 0.999212i \(-0.487359\pi\)
0.0397030 + 0.999212i \(0.487359\pi\)
\(740\) 4.03544 0.148346
\(741\) 97.3308 3.57554
\(742\) 0.838427 0.0307796
\(743\) 23.1867 0.850638 0.425319 0.905044i \(-0.360162\pi\)
0.425319 + 0.905044i \(0.360162\pi\)
\(744\) 63.1470 2.31508
\(745\) 15.0366 0.550900
\(746\) 13.6748 0.500670
\(747\) 37.0241 1.35464
\(748\) 0 0
\(749\) 15.4018 0.562770
\(750\) −3.43642 −0.125480
\(751\) −32.8301 −1.19799 −0.598993 0.800754i \(-0.704432\pi\)
−0.598993 + 0.800754i \(0.704432\pi\)
\(752\) 2.32882 0.0849232
\(753\) −79.5955 −2.90062
\(754\) 25.7734 0.938612
\(755\) −18.4655 −0.672028
\(756\) −1.21745 −0.0442782
\(757\) 14.5746 0.529722 0.264861 0.964287i \(-0.414674\pi\)
0.264861 + 0.964287i \(0.414674\pi\)
\(758\) −1.32252 −0.0480360
\(759\) 0 0
\(760\) −19.1580 −0.694935
\(761\) 10.0458 0.364159 0.182080 0.983284i \(-0.441717\pi\)
0.182080 + 0.983284i \(0.441717\pi\)
\(762\) −10.7127 −0.388082
\(763\) −3.91449 −0.141714
\(764\) −4.55091 −0.164646
\(765\) −0.483906 −0.0174956
\(766\) −33.3058 −1.20339
\(767\) 33.6320 1.21438
\(768\) −22.8564 −0.824758
\(769\) −21.2784 −0.767320 −0.383660 0.923475i \(-0.625336\pi\)
−0.383660 + 0.923475i \(0.625336\pi\)
\(770\) 0 0
\(771\) 66.8687 2.40822
\(772\) 4.89373 0.176129
\(773\) 6.70714 0.241239 0.120620 0.992699i \(-0.461512\pi\)
0.120620 + 0.992699i \(0.461512\pi\)
\(774\) −17.6223 −0.633422
\(775\) −7.76248 −0.278836
\(776\) 23.2376 0.834180
\(777\) 29.5505 1.06012
\(778\) −15.7219 −0.563657
\(779\) −12.9874 −0.465321
\(780\) −5.64388 −0.202083
\(781\) 0 0
\(782\) −0.793144 −0.0283628
\(783\) −11.7013 −0.418170
\(784\) −3.13060 −0.111807
\(785\) 3.80016 0.135634
\(786\) −42.8105 −1.52700
\(787\) 3.15876 0.112597 0.0562987 0.998414i \(-0.482070\pi\)
0.0562987 + 0.998414i \(0.482070\pi\)
\(788\) 5.27665 0.187973
\(789\) 27.5168 0.979624
\(790\) −0.893917 −0.0318041
\(791\) 17.7729 0.631932
\(792\) 0 0
\(793\) 45.6025 1.61939
\(794\) 38.7413 1.37488
\(795\) −1.76463 −0.0625851
\(796\) −1.79513 −0.0636267
\(797\) −54.6066 −1.93427 −0.967133 0.254270i \(-0.918165\pi\)
−0.967133 + 0.254270i \(0.918165\pi\)
\(798\) −21.7647 −0.770462
\(799\) −0.0850470 −0.00300875
\(800\) 2.04947 0.0724597
\(801\) 35.7566 1.26340
\(802\) 7.31680 0.258365
\(803\) 0 0
\(804\) −11.8995 −0.419662
\(805\) 5.42928 0.191357
\(806\) 56.6780 1.99640
\(807\) 14.6760 0.516619
\(808\) 58.0586 2.04249
\(809\) 22.3195 0.784712 0.392356 0.919814i \(-0.371660\pi\)
0.392356 + 0.919814i \(0.371660\pi\)
\(810\) 4.83360 0.169835
\(811\) 27.7089 0.972990 0.486495 0.873683i \(-0.338275\pi\)
0.486495 + 0.873683i \(0.338275\pi\)
\(812\) 1.29638 0.0454939
\(813\) −18.5269 −0.649765
\(814\) 0 0
\(815\) −4.68279 −0.164031
\(816\) −0.962558 −0.0336963
\(817\) 20.6368 0.721990
\(818\) 11.7304 0.410143
\(819\) −24.1861 −0.845130
\(820\) 0.753093 0.0262992
\(821\) 23.1125 0.806632 0.403316 0.915061i \(-0.367858\pi\)
0.403316 + 0.915061i \(0.367858\pi\)
\(822\) −70.4694 −2.45790
\(823\) 25.2118 0.878827 0.439413 0.898285i \(-0.355186\pi\)
0.439413 + 0.898285i \(0.355186\pi\)
\(824\) 26.7602 0.932235
\(825\) 0 0
\(826\) −7.52064 −0.261676
\(827\) 20.9598 0.728844 0.364422 0.931234i \(-0.381267\pi\)
0.364422 + 0.931234i \(0.381267\pi\)
\(828\) 8.43966 0.293299
\(829\) −0.142169 −0.00493774 −0.00246887 0.999997i \(-0.500786\pi\)
−0.00246887 + 0.999997i \(0.500786\pi\)
\(830\) −11.1772 −0.387967
\(831\) −67.5668 −2.34387
\(832\) −50.7421 −1.75916
\(833\) 0.114328 0.00396122
\(834\) 73.8726 2.55800
\(835\) 19.7979 0.685135
\(836\) 0 0
\(837\) −25.7322 −0.889436
\(838\) 24.7793 0.855988
\(839\) −27.2849 −0.941979 −0.470989 0.882139i \(-0.656103\pi\)
−0.470989 + 0.882139i \(0.656103\pi\)
\(840\) 8.13490 0.280681
\(841\) −16.5401 −0.570348
\(842\) −22.5674 −0.777723
\(843\) 44.2149 1.52284
\(844\) 7.24391 0.249346
\(845\) −19.6522 −0.676055
\(846\) −4.02323 −0.138322
\(847\) 0 0
\(848\) −2.05416 −0.0705401
\(849\) −16.8799 −0.579317
\(850\) 0.146086 0.00501072
\(851\) −59.6566 −2.04500
\(852\) 0.819189 0.0280650
\(853\) −36.8827 −1.26284 −0.631420 0.775441i \(-0.717528\pi\)
−0.631420 + 0.775441i \(0.717528\pi\)
\(854\) −10.1974 −0.348949
\(855\) 26.8075 0.916796
\(856\) −46.5883 −1.59235
\(857\) −18.6949 −0.638606 −0.319303 0.947653i \(-0.603449\pi\)
−0.319303 + 0.947653i \(0.603449\pi\)
\(858\) 0 0
\(859\) −24.6718 −0.841790 −0.420895 0.907109i \(-0.638284\pi\)
−0.420895 + 0.907109i \(0.638284\pi\)
\(860\) −1.19666 −0.0408057
\(861\) 5.51471 0.187941
\(862\) 17.7516 0.604621
\(863\) −35.1893 −1.19786 −0.598930 0.800802i \(-0.704407\pi\)
−0.598930 + 0.800802i \(0.704407\pi\)
\(864\) 6.79389 0.231133
\(865\) −5.03852 −0.171315
\(866\) 27.5963 0.937760
\(867\) −45.6838 −1.55150
\(868\) 2.85085 0.0967641
\(869\) 0 0
\(870\) 12.1301 0.411248
\(871\) −68.8433 −2.33267
\(872\) 11.8408 0.400979
\(873\) −32.5159 −1.10050
\(874\) 43.9387 1.48625
\(875\) −1.00000 −0.0338062
\(876\) −1.15738 −0.0391043
\(877\) −10.6113 −0.358319 −0.179160 0.983820i \(-0.557338\pi\)
−0.179160 + 0.983820i \(0.557338\pi\)
\(878\) −5.86818 −0.198041
\(879\) 16.0948 0.542863
\(880\) 0 0
\(881\) 7.08762 0.238788 0.119394 0.992847i \(-0.461905\pi\)
0.119394 + 0.992847i \(0.461905\pi\)
\(882\) 5.40839 0.182110
\(883\) −33.3327 −1.12174 −0.560868 0.827906i \(-0.689532\pi\)
−0.560868 + 0.827906i \(0.689532\pi\)
\(884\) 0.239928 0.00806966
\(885\) 15.8287 0.532074
\(886\) 23.0110 0.773070
\(887\) 6.54635 0.219805 0.109902 0.993942i \(-0.464946\pi\)
0.109902 + 0.993942i \(0.464946\pi\)
\(888\) −89.3859 −2.99959
\(889\) −3.11741 −0.104555
\(890\) −10.7946 −0.361835
\(891\) 0 0
\(892\) −6.92968 −0.232023
\(893\) 4.71144 0.157662
\(894\) −51.6722 −1.72818
\(895\) −3.48467 −0.116480
\(896\) 7.24779 0.242132
\(897\) 83.4345 2.78580
\(898\) 18.5154 0.617867
\(899\) 27.4004 0.913856
\(900\) −1.55447 −0.0518158
\(901\) 0.0750167 0.00249917
\(902\) 0 0
\(903\) −8.76282 −0.291608
\(904\) −53.7604 −1.78805
\(905\) −18.4355 −0.612816
\(906\) 63.4552 2.10816
\(907\) 48.2558 1.60231 0.801154 0.598458i \(-0.204220\pi\)
0.801154 + 0.598458i \(0.204220\pi\)
\(908\) −5.36661 −0.178097
\(909\) −81.2402 −2.69457
\(910\) 7.30154 0.242044
\(911\) 8.98748 0.297768 0.148884 0.988855i \(-0.452432\pi\)
0.148884 + 0.988855i \(0.452432\pi\)
\(912\) 53.3239 1.76573
\(913\) 0 0
\(914\) −20.2809 −0.670832
\(915\) 21.4625 0.709529
\(916\) −7.04365 −0.232729
\(917\) −12.4579 −0.411395
\(918\) 0.484269 0.0159833
\(919\) 54.8689 1.80996 0.904979 0.425457i \(-0.139887\pi\)
0.904979 + 0.425457i \(0.139887\pi\)
\(920\) −16.4228 −0.541443
\(921\) −65.0711 −2.14417
\(922\) 16.4510 0.541784
\(923\) 4.73935 0.155997
\(924\) 0 0
\(925\) 10.9880 0.361282
\(926\) 31.5938 1.03824
\(927\) −37.4450 −1.22986
\(928\) −7.23434 −0.237479
\(929\) −53.6029 −1.75866 −0.879328 0.476217i \(-0.842008\pi\)
−0.879328 + 0.476217i \(0.842008\pi\)
\(930\) 26.6751 0.874712
\(931\) −6.33354 −0.207573
\(932\) 7.58778 0.248546
\(933\) −22.2244 −0.727595
\(934\) 13.6441 0.446450
\(935\) 0 0
\(936\) 73.1593 2.39129
\(937\) 45.2105 1.47696 0.738482 0.674274i \(-0.235543\pi\)
0.738482 + 0.674274i \(0.235543\pi\)
\(938\) 15.3945 0.502647
\(939\) −8.95022 −0.292079
\(940\) −0.273200 −0.00891082
\(941\) 53.2174 1.73484 0.867419 0.497578i \(-0.165777\pi\)
0.867419 + 0.497578i \(0.165777\pi\)
\(942\) −13.0590 −0.425484
\(943\) −11.1331 −0.362544
\(944\) 18.4257 0.599705
\(945\) −3.31495 −0.107835
\(946\) 0 0
\(947\) 2.16339 0.0703008 0.0351504 0.999382i \(-0.488809\pi\)
0.0351504 + 0.999382i \(0.488809\pi\)
\(948\) −0.690972 −0.0224417
\(949\) −6.69592 −0.217359
\(950\) −8.09291 −0.262569
\(951\) −11.8946 −0.385709
\(952\) −0.345825 −0.0112082
\(953\) 11.5589 0.374431 0.187215 0.982319i \(-0.440054\pi\)
0.187215 + 0.982319i \(0.440054\pi\)
\(954\) 3.54874 0.114895
\(955\) −12.3915 −0.400980
\(956\) 6.79312 0.219705
\(957\) 0 0
\(958\) 26.8798 0.868447
\(959\) −20.5066 −0.662193
\(960\) −23.8814 −0.770769
\(961\) 29.2561 0.943744
\(962\) −80.2290 −2.58669
\(963\) 65.1900 2.10072
\(964\) 8.19883 0.264067
\(965\) 13.3250 0.428946
\(966\) −18.6573 −0.600288
\(967\) 27.8539 0.895721 0.447860 0.894104i \(-0.352186\pi\)
0.447860 + 0.894104i \(0.352186\pi\)
\(968\) 0 0
\(969\) −1.94736 −0.0625581
\(970\) 9.81623 0.315180
\(971\) 33.5681 1.07725 0.538625 0.842545i \(-0.318944\pi\)
0.538625 + 0.842545i \(0.318944\pi\)
\(972\) 7.38858 0.236989
\(973\) 21.4970 0.689161
\(974\) 14.5835 0.467285
\(975\) −15.3675 −0.492155
\(976\) 24.9839 0.799715
\(977\) 29.3005 0.937406 0.468703 0.883356i \(-0.344721\pi\)
0.468703 + 0.883356i \(0.344721\pi\)
\(978\) 16.0920 0.514566
\(979\) 0 0
\(980\) 0.367260 0.0117317
\(981\) −16.5686 −0.528993
\(982\) −4.05016 −0.129246
\(983\) 15.9995 0.510305 0.255153 0.966901i \(-0.417874\pi\)
0.255153 + 0.966901i \(0.417874\pi\)
\(984\) −16.6812 −0.531777
\(985\) 14.3676 0.457790
\(986\) −0.515664 −0.0164221
\(987\) −2.00058 −0.0636791
\(988\) −13.2916 −0.422861
\(989\) 17.6904 0.562522
\(990\) 0 0
\(991\) −22.8782 −0.726749 −0.363375 0.931643i \(-0.618376\pi\)
−0.363375 + 0.931643i \(0.618376\pi\)
\(992\) −15.9090 −0.505110
\(993\) −94.5794 −3.00139
\(994\) −1.05979 −0.0336146
\(995\) −4.88790 −0.154957
\(996\) −8.63967 −0.273758
\(997\) −14.5120 −0.459598 −0.229799 0.973238i \(-0.573807\pi\)
−0.229799 + 0.973238i \(0.573807\pi\)
\(998\) −1.58395 −0.0501389
\(999\) 36.4245 1.15242
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 4235.2.a.bb.1.4 yes 5
11.10 odd 2 4235.2.a.ba.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4235.2.a.ba.1.2 5 11.10 odd 2
4235.2.a.bb.1.4 yes 5 1.1 even 1 trivial