Properties

Label 1805.2.a.j.1.4
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4129975648\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.2225.1
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.75660\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.75660 q^{2} +0.0856374 q^{3} +1.08564 q^{4} +1.00000 q^{5} +0.150431 q^{6} -1.86144 q^{7} -1.60617 q^{8} -2.99267 q^{9} +O(q^{10})\) \(q+1.75660 q^{2} +0.0856374 q^{3} +1.08564 q^{4} +1.00000 q^{5} +0.150431 q^{6} -1.86144 q^{7} -1.60617 q^{8} -2.99267 q^{9} +1.75660 q^{10} -1.22420 q^{11} +0.0929712 q^{12} -2.40734 q^{13} -3.26979 q^{14} +0.0856374 q^{15} -4.99267 q^{16} +6.05910 q^{17} -5.25691 q^{18} +1.08564 q^{20} -0.159409 q^{21} -2.15043 q^{22} -7.20500 q^{23} -0.137548 q^{24} +1.00000 q^{25} -4.22873 q^{26} -0.513197 q^{27} -2.02084 q^{28} +1.28446 q^{29} +0.150431 q^{30} -5.87596 q^{31} -5.55777 q^{32} -0.104837 q^{33} +10.6434 q^{34} -1.86144 q^{35} -3.24895 q^{36} -1.59883 q^{37} -0.206159 q^{39} -1.60617 q^{40} -9.72553 q^{41} -0.280017 q^{42} -0.697495 q^{43} -1.32904 q^{44} -2.99267 q^{45} -12.6563 q^{46} -11.6434 q^{47} -0.427559 q^{48} -3.53506 q^{49} +1.75660 q^{50} +0.518886 q^{51} -2.61350 q^{52} +10.2614 q^{53} -0.901480 q^{54} -1.22420 q^{55} +2.98978 q^{56} +2.25628 q^{58} +9.40836 q^{59} +0.0929712 q^{60} +3.73575 q^{61} -10.3217 q^{62} +5.57066 q^{63} +0.222557 q^{64} -2.40734 q^{65} -0.184157 q^{66} +7.41188 q^{67} +6.57799 q^{68} -0.617018 q^{69} -3.26979 q^{70} -8.51320 q^{71} +4.80672 q^{72} -6.21234 q^{73} -2.80851 q^{74} +0.0856374 q^{75} +2.27877 q^{77} -0.362138 q^{78} -7.39383 q^{79} -4.99267 q^{80} +8.93405 q^{81} -17.0839 q^{82} +0.0135105 q^{83} -0.173060 q^{84} +6.05910 q^{85} -1.22522 q^{86} +0.109998 q^{87} +1.96627 q^{88} -1.25527 q^{89} -5.25691 q^{90} +4.48111 q^{91} -7.82202 q^{92} -0.503202 q^{93} -20.4528 q^{94} -0.475953 q^{96} +7.97800 q^{97} -6.20967 q^{98} +3.66363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} + 3 q^{4} + 4 q^{5} - 7 q^{6} - 11 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{3} + 3 q^{4} + 4 q^{5} - 7 q^{6} - 11 q^{7} - 6 q^{8} + 5 q^{9} - q^{10} + 16 q^{12} + 2 q^{13} + 11 q^{14} - q^{15} - 3 q^{16} - 7 q^{17} - 17 q^{18} + 3 q^{20} - 2 q^{21} - q^{22} - 11 q^{23} - 13 q^{24} + 4 q^{25} + 9 q^{26} + 14 q^{27} - 13 q^{28} + 15 q^{29} - 7 q^{30} + q^{31} - 3 q^{32} - 12 q^{33} + 22 q^{34} - 11 q^{35} + 16 q^{36} + 11 q^{37} - 29 q^{39} - 6 q^{40} - 22 q^{41} + 19 q^{42} - 26 q^{43} - 12 q^{44} + 5 q^{45} - 10 q^{46} - 26 q^{47} + 13 q^{48} + 13 q^{49} - q^{50} + 11 q^{51} - 27 q^{52} + 16 q^{53} - 25 q^{54} + 8 q^{56} - 3 q^{58} + 10 q^{59} + 16 q^{60} + 2 q^{61} - 31 q^{62} - 17 q^{63} + 4 q^{64} + 2 q^{65} + 22 q^{66} - 3 q^{67} + 4 q^{68} - 14 q^{69} + 11 q^{70} - 18 q^{71} - 29 q^{72} - 24 q^{73} - 17 q^{74} - q^{75} - 6 q^{77} + 15 q^{78} - 30 q^{79} - 3 q^{80} - 4 q^{81} - 13 q^{82} - 12 q^{83} - 52 q^{84} - 7 q^{85} + 16 q^{86} - q^{87} + 23 q^{88} - 9 q^{89} - 17 q^{90} + 9 q^{91} - 25 q^{92} + 7 q^{93} + 11 q^{94} - 6 q^{96} - 19 q^{97} - 48 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.75660 1.24210 0.621051 0.783770i \(-0.286706\pi\)
0.621051 + 0.783770i \(0.286706\pi\)
\(3\) 0.0856374 0.0494428 0.0247214 0.999694i \(-0.492130\pi\)
0.0247214 + 0.999694i \(0.492130\pi\)
\(4\) 1.08564 0.542819
\(5\) 1.00000 0.447214
\(6\) 0.150431 0.0614130
\(7\) −1.86144 −0.703557 −0.351778 0.936083i \(-0.614423\pi\)
−0.351778 + 0.936083i \(0.614423\pi\)
\(8\) −1.60617 −0.567866
\(9\) −2.99267 −0.997555
\(10\) 1.75660 0.555485
\(11\) −1.22420 −0.369111 −0.184555 0.982822i \(-0.559084\pi\)
−0.184555 + 0.982822i \(0.559084\pi\)
\(12\) 0.0929712 0.0268385
\(13\) −2.40734 −0.667677 −0.333838 0.942630i \(-0.608344\pi\)
−0.333838 + 0.942630i \(0.608344\pi\)
\(14\) −3.26979 −0.873889
\(15\) 0.0856374 0.0221115
\(16\) −4.99267 −1.24817
\(17\) 6.05910 1.46955 0.734774 0.678312i \(-0.237288\pi\)
0.734774 + 0.678312i \(0.237288\pi\)
\(18\) −5.25691 −1.23907
\(19\) 0 0
\(20\) 1.08564 0.242756
\(21\) −0.159409 −0.0347858
\(22\) −2.15043 −0.458473
\(23\) −7.20500 −1.50235 −0.751173 0.660105i \(-0.770512\pi\)
−0.751173 + 0.660105i \(0.770512\pi\)
\(24\) −0.137548 −0.0280769
\(25\) 1.00000 0.200000
\(26\) −4.22873 −0.829323
\(27\) −0.513197 −0.0987647
\(28\) −2.02084 −0.381904
\(29\) 1.28446 0.238519 0.119259 0.992863i \(-0.461948\pi\)
0.119259 + 0.992863i \(0.461948\pi\)
\(30\) 0.150431 0.0274647
\(31\) −5.87596 −1.05535 −0.527677 0.849445i \(-0.676937\pi\)
−0.527677 + 0.849445i \(0.676937\pi\)
\(32\) −5.55777 −0.982485
\(33\) −0.104837 −0.0182499
\(34\) 10.6434 1.82533
\(35\) −1.86144 −0.314640
\(36\) −3.24895 −0.541492
\(37\) −1.59883 −0.262847 −0.131423 0.991326i \(-0.541955\pi\)
−0.131423 + 0.991326i \(0.541955\pi\)
\(38\) 0 0
\(39\) −0.206159 −0.0330118
\(40\) −1.60617 −0.253957
\(41\) −9.72553 −1.51887 −0.759436 0.650581i \(-0.774525\pi\)
−0.759436 + 0.650581i \(0.774525\pi\)
\(42\) −0.280017 −0.0432075
\(43\) −0.697495 −0.106367 −0.0531835 0.998585i \(-0.516937\pi\)
−0.0531835 + 0.998585i \(0.516937\pi\)
\(44\) −1.32904 −0.200360
\(45\) −2.99267 −0.446120
\(46\) −12.6563 −1.86607
\(47\) −11.6434 −1.69837 −0.849183 0.528099i \(-0.822905\pi\)
−0.849183 + 0.528099i \(0.822905\pi\)
\(48\) −0.427559 −0.0617128
\(49\) −3.53506 −0.505008
\(50\) 1.75660 0.248421
\(51\) 0.518886 0.0726586
\(52\) −2.61350 −0.362427
\(53\) 10.2614 1.40952 0.704759 0.709447i \(-0.251055\pi\)
0.704759 + 0.709447i \(0.251055\pi\)
\(54\) −0.901480 −0.122676
\(55\) −1.22420 −0.165071
\(56\) 2.98978 0.399526
\(57\) 0 0
\(58\) 2.25628 0.296265
\(59\) 9.40836 1.22486 0.612432 0.790523i \(-0.290191\pi\)
0.612432 + 0.790523i \(0.290191\pi\)
\(60\) 0.0929712 0.0120025
\(61\) 3.73575 0.478314 0.239157 0.970981i \(-0.423129\pi\)
0.239157 + 0.970981i \(0.423129\pi\)
\(62\) −10.3217 −1.31086
\(63\) 5.57066 0.701837
\(64\) 0.222557 0.0278197
\(65\) −2.40734 −0.298594
\(66\) −0.184157 −0.0226682
\(67\) 7.41188 0.905505 0.452752 0.891636i \(-0.350442\pi\)
0.452752 + 0.891636i \(0.350442\pi\)
\(68\) 6.57799 0.797698
\(69\) −0.617018 −0.0742802
\(70\) −3.26979 −0.390815
\(71\) −8.51320 −1.01033 −0.505165 0.863023i \(-0.668568\pi\)
−0.505165 + 0.863023i \(0.668568\pi\)
\(72\) 4.80672 0.566478
\(73\) −6.21234 −0.727099 −0.363549 0.931575i \(-0.618435\pi\)
−0.363549 + 0.931575i \(0.618435\pi\)
\(74\) −2.80851 −0.326483
\(75\) 0.0856374 0.00988856
\(76\) 0 0
\(77\) 2.27877 0.259690
\(78\) −0.362138 −0.0410040
\(79\) −7.39383 −0.831871 −0.415936 0.909394i \(-0.636546\pi\)
−0.415936 + 0.909394i \(0.636546\pi\)
\(80\) −4.99267 −0.558197
\(81\) 8.93405 0.992672
\(82\) −17.0839 −1.88660
\(83\) 0.0135105 0.00148297 0.000741487 1.00000i \(-0.499764\pi\)
0.000741487 1.00000i \(0.499764\pi\)
\(84\) −0.173060 −0.0188824
\(85\) 6.05910 0.657202
\(86\) −1.22522 −0.132119
\(87\) 0.109998 0.0117930
\(88\) 1.96627 0.209605
\(89\) −1.25527 −0.133058 −0.0665291 0.997784i \(-0.521193\pi\)
−0.0665291 + 0.997784i \(0.521193\pi\)
\(90\) −5.25691 −0.554127
\(91\) 4.48111 0.469748
\(92\) −7.82202 −0.815502
\(93\) −0.503202 −0.0521796
\(94\) −20.4528 −2.10954
\(95\) 0 0
\(96\) −0.475953 −0.0485768
\(97\) 7.97800 0.810043 0.405022 0.914307i \(-0.367264\pi\)
0.405022 + 0.914307i \(0.367264\pi\)
\(98\) −6.20967 −0.627272
\(99\) 3.66363 0.368208
\(100\) 1.08564 0.108564
\(101\) 18.2028 1.81125 0.905625 0.424080i \(-0.139403\pi\)
0.905625 + 0.424080i \(0.139403\pi\)
\(102\) 0.911474 0.0902494
\(103\) 3.41352 0.336344 0.168172 0.985758i \(-0.446214\pi\)
0.168172 + 0.985758i \(0.446214\pi\)
\(104\) 3.86660 0.379151
\(105\) −0.159409 −0.0155567
\(106\) 18.0252 1.75077
\(107\) 1.49515 0.144542 0.0722710 0.997385i \(-0.476975\pi\)
0.0722710 + 0.997385i \(0.476975\pi\)
\(108\) −0.557145 −0.0536113
\(109\) 15.5780 1.49210 0.746050 0.665889i \(-0.231948\pi\)
0.746050 + 0.665889i \(0.231948\pi\)
\(110\) −2.15043 −0.205036
\(111\) −0.136920 −0.0129959
\(112\) 9.29353 0.878156
\(113\) −13.6479 −1.28389 −0.641945 0.766750i \(-0.721872\pi\)
−0.641945 + 0.766750i \(0.721872\pi\)
\(114\) 0 0
\(115\) −7.20500 −0.671870
\(116\) 1.39446 0.129472
\(117\) 7.20437 0.666045
\(118\) 16.5267 1.52141
\(119\) −11.2786 −1.03391
\(120\) −0.137548 −0.0125564
\(121\) −9.50133 −0.863757
\(122\) 6.56222 0.594115
\(123\) −0.832870 −0.0750973
\(124\) −6.37916 −0.572866
\(125\) 1.00000 0.0894427
\(126\) 9.78540 0.871753
\(127\) 19.2055 1.70421 0.852106 0.523370i \(-0.175325\pi\)
0.852106 + 0.523370i \(0.175325\pi\)
\(128\) 11.5065 1.01704
\(129\) −0.0597316 −0.00525908
\(130\) −4.22873 −0.370885
\(131\) −19.3097 −1.68710 −0.843548 0.537054i \(-0.819537\pi\)
−0.843548 + 0.537054i \(0.819537\pi\)
\(132\) −0.113815 −0.00990637
\(133\) 0 0
\(134\) 13.0197 1.12473
\(135\) −0.513197 −0.0441689
\(136\) −9.73194 −0.834507
\(137\) −14.6242 −1.24943 −0.624715 0.780853i \(-0.714785\pi\)
−0.624715 + 0.780853i \(0.714785\pi\)
\(138\) −1.08385 −0.0922636
\(139\) 1.39485 0.118310 0.0591548 0.998249i \(-0.481159\pi\)
0.0591548 + 0.998249i \(0.481159\pi\)
\(140\) −2.02084 −0.170793
\(141\) −0.997112 −0.0839720
\(142\) −14.9543 −1.25493
\(143\) 2.94707 0.246447
\(144\) 14.9414 1.24512
\(145\) 1.28446 0.106669
\(146\) −10.9126 −0.903131
\(147\) −0.302733 −0.0249690
\(148\) −1.73575 −0.142678
\(149\) 14.5340 1.19068 0.595338 0.803476i \(-0.297018\pi\)
0.595338 + 0.803476i \(0.297018\pi\)
\(150\) 0.150431 0.0122826
\(151\) 23.5773 1.91870 0.959348 0.282227i \(-0.0910733\pi\)
0.959348 + 0.282227i \(0.0910733\pi\)
\(152\) 0 0
\(153\) −18.1329 −1.46596
\(154\) 4.00289 0.322562
\(155\) −5.87596 −0.471969
\(156\) −0.223814 −0.0179194
\(157\) −17.0409 −1.36001 −0.680007 0.733206i \(-0.738023\pi\)
−0.680007 + 0.733206i \(0.738023\pi\)
\(158\) −12.9880 −1.03327
\(159\) 0.878764 0.0696905
\(160\) −5.55777 −0.439381
\(161\) 13.4116 1.05699
\(162\) 15.6935 1.23300
\(163\) −9.98080 −0.781757 −0.390878 0.920442i \(-0.627829\pi\)
−0.390878 + 0.920442i \(0.627829\pi\)
\(164\) −10.5584 −0.824473
\(165\) −0.104837 −0.00816159
\(166\) 0.0237326 0.00184200
\(167\) −23.1483 −1.79127 −0.895633 0.444794i \(-0.853277\pi\)
−0.895633 + 0.444794i \(0.853277\pi\)
\(168\) 0.256037 0.0197537
\(169\) −7.20470 −0.554208
\(170\) 10.6434 0.816312
\(171\) 0 0
\(172\) −0.757226 −0.0577380
\(173\) 12.4017 0.942880 0.471440 0.881898i \(-0.343734\pi\)
0.471440 + 0.881898i \(0.343734\pi\)
\(174\) 0.193222 0.0146482
\(175\) −1.86144 −0.140711
\(176\) 6.11203 0.460712
\(177\) 0.805708 0.0605607
\(178\) −2.20500 −0.165272
\(179\) 22.5640 1.68651 0.843254 0.537515i \(-0.180637\pi\)
0.843254 + 0.537515i \(0.180637\pi\)
\(180\) −3.24895 −0.242162
\(181\) 7.13669 0.530466 0.265233 0.964184i \(-0.414551\pi\)
0.265233 + 0.964184i \(0.414551\pi\)
\(182\) 7.87152 0.583476
\(183\) 0.319920 0.0236492
\(184\) 11.5724 0.853132
\(185\) −1.59883 −0.117549
\(186\) −0.883924 −0.0648125
\(187\) −7.41756 −0.542426
\(188\) −12.6405 −0.921905
\(189\) 0.955282 0.0694866
\(190\) 0 0
\(191\) −12.6479 −0.915173 −0.457587 0.889165i \(-0.651286\pi\)
−0.457587 + 0.889165i \(0.651286\pi\)
\(192\) 0.0190592 0.00137548
\(193\) 3.82038 0.274997 0.137498 0.990502i \(-0.456094\pi\)
0.137498 + 0.990502i \(0.456094\pi\)
\(194\) 14.0141 1.00616
\(195\) −0.206159 −0.0147633
\(196\) −3.83779 −0.274128
\(197\) 5.35606 0.381603 0.190802 0.981629i \(-0.438891\pi\)
0.190802 + 0.981629i \(0.438891\pi\)
\(198\) 6.43552 0.457353
\(199\) −7.19251 −0.509863 −0.254932 0.966959i \(-0.582053\pi\)
−0.254932 + 0.966959i \(0.582053\pi\)
\(200\) −1.60617 −0.113573
\(201\) 0.634734 0.0447707
\(202\) 31.9751 2.24976
\(203\) −2.39094 −0.167811
\(204\) 0.563322 0.0394404
\(205\) −9.72553 −0.679261
\(206\) 5.99618 0.417774
\(207\) 21.5622 1.49867
\(208\) 12.0191 0.833372
\(209\) 0 0
\(210\) −0.280017 −0.0193230
\(211\) −23.3668 −1.60863 −0.804317 0.594200i \(-0.797469\pi\)
−0.804317 + 0.594200i \(0.797469\pi\)
\(212\) 11.1402 0.765113
\(213\) −0.729048 −0.0499536
\(214\) 2.62638 0.179536
\(215\) −0.697495 −0.0475687
\(216\) 0.824280 0.0560851
\(217\) 10.9377 0.742501
\(218\) 27.3643 1.85334
\(219\) −0.532008 −0.0359498
\(220\) −1.32904 −0.0896038
\(221\) −14.5863 −0.981183
\(222\) −0.240513 −0.0161422
\(223\) 4.28166 0.286721 0.143361 0.989671i \(-0.454209\pi\)
0.143361 + 0.989671i \(0.454209\pi\)
\(224\) 10.3454 0.691234
\(225\) −2.99267 −0.199511
\(226\) −23.9740 −1.59472
\(227\) −6.60883 −0.438643 −0.219322 0.975653i \(-0.570384\pi\)
−0.219322 + 0.975653i \(0.570384\pi\)
\(228\) 0 0
\(229\) −23.3277 −1.54154 −0.770770 0.637113i \(-0.780128\pi\)
−0.770770 + 0.637113i \(0.780128\pi\)
\(230\) −12.6563 −0.834531
\(231\) 0.195148 0.0128398
\(232\) −2.06306 −0.135447
\(233\) −17.0372 −1.11615 −0.558073 0.829792i \(-0.688459\pi\)
−0.558073 + 0.829792i \(0.688459\pi\)
\(234\) 12.6552 0.827296
\(235\) −11.6434 −0.759532
\(236\) 10.2141 0.664879
\(237\) −0.633189 −0.0411300
\(238\) −19.8120 −1.28422
\(239\) 10.4194 0.673973 0.336986 0.941509i \(-0.390592\pi\)
0.336986 + 0.941509i \(0.390592\pi\)
\(240\) −0.427559 −0.0275988
\(241\) −3.32069 −0.213904 −0.106952 0.994264i \(-0.534109\pi\)
−0.106952 + 0.994264i \(0.534109\pi\)
\(242\) −16.6900 −1.07288
\(243\) 2.30468 0.147845
\(244\) 4.05567 0.259638
\(245\) −3.53506 −0.225847
\(246\) −1.46302 −0.0932786
\(247\) 0 0
\(248\) 9.43778 0.599300
\(249\) 0.00115701 7.33223e−5 0
\(250\) 1.75660 0.111097
\(251\) −25.7802 −1.62723 −0.813616 0.581403i \(-0.802504\pi\)
−0.813616 + 0.581403i \(0.802504\pi\)
\(252\) 6.04771 0.380970
\(253\) 8.82038 0.554532
\(254\) 33.7363 2.11681
\(255\) 0.518886 0.0324939
\(256\) 19.7672 1.23545
\(257\) 5.40015 0.336852 0.168426 0.985714i \(-0.446132\pi\)
0.168426 + 0.985714i \(0.446132\pi\)
\(258\) −0.104925 −0.00653231
\(259\) 2.97613 0.184928
\(260\) −2.61350 −0.162082
\(261\) −3.84397 −0.237936
\(262\) −33.9194 −2.09555
\(263\) 8.76997 0.540779 0.270390 0.962751i \(-0.412847\pi\)
0.270390 + 0.962751i \(0.412847\pi\)
\(264\) 0.168387 0.0103635
\(265\) 10.2614 0.630356
\(266\) 0 0
\(267\) −0.107498 −0.00657877
\(268\) 8.04661 0.491525
\(269\) 19.3500 1.17979 0.589894 0.807481i \(-0.299169\pi\)
0.589894 + 0.807481i \(0.299169\pi\)
\(270\) −0.901480 −0.0548623
\(271\) 8.95871 0.544203 0.272101 0.962269i \(-0.412281\pi\)
0.272101 + 0.962269i \(0.412281\pi\)
\(272\) −30.2511 −1.83424
\(273\) 0.383751 0.0232257
\(274\) −25.6889 −1.55192
\(275\) −1.22420 −0.0738221
\(276\) −0.669858 −0.0403207
\(277\) −10.4586 −0.628398 −0.314199 0.949357i \(-0.601736\pi\)
−0.314199 + 0.949357i \(0.601736\pi\)
\(278\) 2.45019 0.146953
\(279\) 17.5848 1.05277
\(280\) 2.98978 0.178673
\(281\) −10.9107 −0.650878 −0.325439 0.945563i \(-0.605512\pi\)
−0.325439 + 0.945563i \(0.605512\pi\)
\(282\) −1.75152 −0.104302
\(283\) −0.952763 −0.0566359 −0.0283179 0.999599i \(-0.509015\pi\)
−0.0283179 + 0.999599i \(0.509015\pi\)
\(284\) −9.24224 −0.548426
\(285\) 0 0
\(286\) 5.17682 0.306112
\(287\) 18.1035 1.06861
\(288\) 16.6326 0.980083
\(289\) 19.7127 1.15957
\(290\) 2.25628 0.132494
\(291\) 0.683215 0.0400508
\(292\) −6.74434 −0.394683
\(293\) −13.4219 −0.784114 −0.392057 0.919941i \(-0.628236\pi\)
−0.392057 + 0.919941i \(0.628236\pi\)
\(294\) −0.531781 −0.0310141
\(295\) 9.40836 0.547776
\(296\) 2.56800 0.149262
\(297\) 0.628256 0.0364551
\(298\) 25.5305 1.47894
\(299\) 17.3449 1.00308
\(300\) 0.0929712 0.00536769
\(301\) 1.29834 0.0748352
\(302\) 41.4159 2.38322
\(303\) 1.55884 0.0895532
\(304\) 0 0
\(305\) 3.73575 0.213909
\(306\) −31.8522 −1.82087
\(307\) 18.8433 1.07544 0.537721 0.843123i \(-0.319286\pi\)
0.537721 + 0.843123i \(0.319286\pi\)
\(308\) 2.47392 0.140965
\(309\) 0.292325 0.0166298
\(310\) −10.3217 −0.586233
\(311\) −0.912189 −0.0517255 −0.0258628 0.999666i \(-0.508233\pi\)
−0.0258628 + 0.999666i \(0.508233\pi\)
\(312\) 0.331125 0.0187463
\(313\) −18.7665 −1.06074 −0.530371 0.847765i \(-0.677947\pi\)
−0.530371 + 0.847765i \(0.677947\pi\)
\(314\) −29.9340 −1.68928
\(315\) 5.57066 0.313871
\(316\) −8.02702 −0.451555
\(317\) −8.85956 −0.497603 −0.248801 0.968555i \(-0.580037\pi\)
−0.248801 + 0.968555i \(0.580037\pi\)
\(318\) 1.54363 0.0865627
\(319\) −1.57244 −0.0880398
\(320\) 0.222557 0.0124413
\(321\) 0.128041 0.00714656
\(322\) 23.5589 1.31288
\(323\) 0 0
\(324\) 9.69914 0.538841
\(325\) −2.40734 −0.133535
\(326\) −17.5323 −0.971022
\(327\) 1.33406 0.0737736
\(328\) 15.6208 0.862516
\(329\) 21.6735 1.19490
\(330\) −0.184157 −0.0101375
\(331\) −3.96044 −0.217686 −0.108843 0.994059i \(-0.534715\pi\)
−0.108843 + 0.994059i \(0.534715\pi\)
\(332\) 0.0146675 0.000804986 0
\(333\) 4.78478 0.262204
\(334\) −40.6622 −2.22494
\(335\) 7.41188 0.404954
\(336\) 0.795874 0.0434185
\(337\) 5.79148 0.315482 0.157741 0.987481i \(-0.449579\pi\)
0.157741 + 0.987481i \(0.449579\pi\)
\(338\) −12.6558 −0.688383
\(339\) −1.16877 −0.0634791
\(340\) 6.57799 0.356742
\(341\) 7.19336 0.389542
\(342\) 0 0
\(343\) 19.6103 1.05886
\(344\) 1.12029 0.0604022
\(345\) −0.617018 −0.0332191
\(346\) 21.7847 1.17115
\(347\) 14.4126 0.773708 0.386854 0.922141i \(-0.373562\pi\)
0.386854 + 0.922141i \(0.373562\pi\)
\(348\) 0.119418 0.00640148
\(349\) 9.11150 0.487727 0.243864 0.969810i \(-0.421585\pi\)
0.243864 + 0.969810i \(0.421585\pi\)
\(350\) −3.26979 −0.174778
\(351\) 1.23544 0.0659429
\(352\) 6.80384 0.362646
\(353\) −3.59377 −0.191277 −0.0956386 0.995416i \(-0.530489\pi\)
−0.0956386 + 0.995416i \(0.530489\pi\)
\(354\) 1.41530 0.0752226
\(355\) −8.51320 −0.451834
\(356\) −1.36277 −0.0722265
\(357\) −0.965873 −0.0511194
\(358\) 39.6358 2.09482
\(359\) −10.7465 −0.567177 −0.283588 0.958946i \(-0.591525\pi\)
−0.283588 + 0.958946i \(0.591525\pi\)
\(360\) 4.80672 0.253337
\(361\) 0 0
\(362\) 12.5363 0.658893
\(363\) −0.813669 −0.0427066
\(364\) 4.86487 0.254988
\(365\) −6.21234 −0.325168
\(366\) 0.561972 0.0293747
\(367\) 1.68713 0.0880676 0.0440338 0.999030i \(-0.485979\pi\)
0.0440338 + 0.999030i \(0.485979\pi\)
\(368\) 35.9722 1.87518
\(369\) 29.1053 1.51516
\(370\) −2.80851 −0.146007
\(371\) −19.1010 −0.991676
\(372\) −0.546295 −0.0283241
\(373\) −34.2844 −1.77518 −0.887590 0.460635i \(-0.847622\pi\)
−0.887590 + 0.460635i \(0.847622\pi\)
\(374\) −13.0297 −0.673749
\(375\) 0.0856374 0.00442230
\(376\) 18.7013 0.964444
\(377\) −3.09214 −0.159253
\(378\) 1.67805 0.0863094
\(379\) −24.7637 −1.27202 −0.636012 0.771679i \(-0.719417\pi\)
−0.636012 + 0.771679i \(0.719417\pi\)
\(380\) 0 0
\(381\) 1.64471 0.0842610
\(382\) −22.2174 −1.13674
\(383\) −17.2980 −0.883885 −0.441943 0.897043i \(-0.645710\pi\)
−0.441943 + 0.897043i \(0.645710\pi\)
\(384\) 0.985386 0.0502853
\(385\) 2.27877 0.116137
\(386\) 6.71086 0.341574
\(387\) 2.08737 0.106107
\(388\) 8.66121 0.439707
\(389\) 31.5131 1.59778 0.798888 0.601480i \(-0.205422\pi\)
0.798888 + 0.601480i \(0.205422\pi\)
\(390\) −0.362138 −0.0183376
\(391\) −43.6559 −2.20777
\(392\) 5.67789 0.286777
\(393\) −1.65363 −0.0834147
\(394\) 9.40845 0.473991
\(395\) −7.39383 −0.372024
\(396\) 3.97737 0.199870
\(397\) 27.9014 1.40033 0.700166 0.713980i \(-0.253109\pi\)
0.700166 + 0.713980i \(0.253109\pi\)
\(398\) −12.6343 −0.633303
\(399\) 0 0
\(400\) −4.99267 −0.249633
\(401\) 4.73460 0.236434 0.118217 0.992988i \(-0.462282\pi\)
0.118217 + 0.992988i \(0.462282\pi\)
\(402\) 1.11497 0.0556098
\(403\) 14.1455 0.704635
\(404\) 19.7617 0.983180
\(405\) 8.93405 0.443937
\(406\) −4.19993 −0.208439
\(407\) 1.95730 0.0970195
\(408\) −0.833418 −0.0412603
\(409\) −8.34645 −0.412706 −0.206353 0.978478i \(-0.566159\pi\)
−0.206353 + 0.978478i \(0.566159\pi\)
\(410\) −17.0839 −0.843711
\(411\) −1.25238 −0.0617753
\(412\) 3.70584 0.182574
\(413\) −17.5131 −0.861761
\(414\) 37.8761 1.86151
\(415\) 0.0135105 0.000663206 0
\(416\) 13.3795 0.655982
\(417\) 0.119451 0.00584955
\(418\) 0 0
\(419\) 21.5120 1.05093 0.525466 0.850815i \(-0.323891\pi\)
0.525466 + 0.850815i \(0.323891\pi\)
\(420\) −0.173060 −0.00844446
\(421\) 30.6789 1.49520 0.747598 0.664151i \(-0.231207\pi\)
0.747598 + 0.664151i \(0.231207\pi\)
\(422\) −41.0460 −1.99809
\(423\) 34.8448 1.69421
\(424\) −16.4816 −0.800417
\(425\) 6.05910 0.293910
\(426\) −1.28064 −0.0620474
\(427\) −6.95387 −0.336521
\(428\) 1.62319 0.0784601
\(429\) 0.252380 0.0121850
\(430\) −1.22522 −0.0590853
\(431\) −25.5833 −1.23230 −0.616152 0.787627i \(-0.711309\pi\)
−0.616152 + 0.787627i \(0.711309\pi\)
\(432\) 2.56222 0.123275
\(433\) 31.9328 1.53459 0.767295 0.641294i \(-0.221602\pi\)
0.767295 + 0.641294i \(0.221602\pi\)
\(434\) 19.2132 0.922263
\(435\) 0.109998 0.00527400
\(436\) 16.9120 0.809940
\(437\) 0 0
\(438\) −0.934525 −0.0446533
\(439\) 9.45544 0.451283 0.225642 0.974210i \(-0.427552\pi\)
0.225642 + 0.974210i \(0.427552\pi\)
\(440\) 1.96627 0.0937384
\(441\) 10.5792 0.503774
\(442\) −25.6223 −1.21873
\(443\) 9.27713 0.440770 0.220385 0.975413i \(-0.429269\pi\)
0.220385 + 0.975413i \(0.429269\pi\)
\(444\) −0.148645 −0.00705440
\(445\) −1.25527 −0.0595054
\(446\) 7.52116 0.356137
\(447\) 1.24466 0.0588703
\(448\) −0.414276 −0.0195727
\(449\) −27.6454 −1.30467 −0.652335 0.757931i \(-0.726210\pi\)
−0.652335 + 0.757931i \(0.726210\pi\)
\(450\) −5.25691 −0.247813
\(451\) 11.9060 0.560632
\(452\) −14.8167 −0.696920
\(453\) 2.01910 0.0948656
\(454\) −11.6091 −0.544840
\(455\) 4.48111 0.210078
\(456\) 0 0
\(457\) −6.99174 −0.327060 −0.163530 0.986538i \(-0.552288\pi\)
−0.163530 + 0.986538i \(0.552288\pi\)
\(458\) −40.9775 −1.91475
\(459\) −3.10951 −0.145140
\(460\) −7.82202 −0.364704
\(461\) 15.2246 0.709080 0.354540 0.935041i \(-0.384638\pi\)
0.354540 + 0.935041i \(0.384638\pi\)
\(462\) 0.342797 0.0159484
\(463\) −27.7350 −1.28895 −0.644477 0.764623i \(-0.722925\pi\)
−0.644477 + 0.764623i \(0.722925\pi\)
\(464\) −6.41289 −0.297711
\(465\) −0.503202 −0.0233354
\(466\) −29.9276 −1.38637
\(467\) −38.3385 −1.77409 −0.887046 0.461681i \(-0.847246\pi\)
−0.887046 + 0.461681i \(0.847246\pi\)
\(468\) 7.82134 0.361541
\(469\) −13.7967 −0.637074
\(470\) −20.4528 −0.943417
\(471\) −1.45934 −0.0672429
\(472\) −15.1114 −0.695559
\(473\) 0.853874 0.0392612
\(474\) −1.11226 −0.0510877
\(475\) 0 0
\(476\) −12.2445 −0.561226
\(477\) −30.7091 −1.40607
\(478\) 18.3026 0.837144
\(479\) −10.5137 −0.480382 −0.240191 0.970726i \(-0.577210\pi\)
−0.240191 + 0.970726i \(0.577210\pi\)
\(480\) −0.475953 −0.0217242
\(481\) 3.84894 0.175497
\(482\) −5.83312 −0.265691
\(483\) 1.14854 0.0522603
\(484\) −10.3150 −0.468864
\(485\) 7.97800 0.362262
\(486\) 4.04839 0.183639
\(487\) −14.1296 −0.640273 −0.320136 0.947371i \(-0.603729\pi\)
−0.320136 + 0.947371i \(0.603729\pi\)
\(488\) −6.00025 −0.271618
\(489\) −0.854730 −0.0386522
\(490\) −6.20967 −0.280525
\(491\) 18.7427 0.845847 0.422924 0.906165i \(-0.361004\pi\)
0.422924 + 0.906165i \(0.361004\pi\)
\(492\) −0.904194 −0.0407642
\(493\) 7.78269 0.350515
\(494\) 0 0
\(495\) 3.66363 0.164668
\(496\) 29.3367 1.31726
\(497\) 15.8468 0.710825
\(498\) 0.00203240 9.10739e−5 0
\(499\) 16.2646 0.728103 0.364052 0.931379i \(-0.381393\pi\)
0.364052 + 0.931379i \(0.381393\pi\)
\(500\) 1.08564 0.0485512
\(501\) −1.98236 −0.0885652
\(502\) −45.2854 −2.02119
\(503\) −26.1541 −1.16615 −0.583077 0.812417i \(-0.698151\pi\)
−0.583077 + 0.812417i \(0.698151\pi\)
\(504\) −8.94741 −0.398549
\(505\) 18.2028 0.810015
\(506\) 15.4939 0.688786
\(507\) −0.616992 −0.0274016
\(508\) 20.8502 0.925078
\(509\) −17.3725 −0.770025 −0.385012 0.922911i \(-0.625803\pi\)
−0.385012 + 0.922911i \(0.625803\pi\)
\(510\) 0.911474 0.0403608
\(511\) 11.5639 0.511555
\(512\) 11.7100 0.517513
\(513\) 0 0
\(514\) 9.48589 0.418405
\(515\) 3.41352 0.150418
\(516\) −0.0648469 −0.00285473
\(517\) 14.2539 0.626885
\(518\) 5.22786 0.229699
\(519\) 1.06205 0.0466186
\(520\) 3.86660 0.169561
\(521\) −33.7615 −1.47912 −0.739559 0.673092i \(-0.764966\pi\)
−0.739559 + 0.673092i \(0.764966\pi\)
\(522\) −6.75231 −0.295540
\(523\) −28.7361 −1.25654 −0.628271 0.777995i \(-0.716237\pi\)
−0.628271 + 0.777995i \(0.716237\pi\)
\(524\) −20.9633 −0.915787
\(525\) −0.159409 −0.00695716
\(526\) 15.4053 0.671703
\(527\) −35.6031 −1.55089
\(528\) 0.523419 0.0227789
\(529\) 28.9120 1.25705
\(530\) 18.0252 0.782966
\(531\) −28.1561 −1.22187
\(532\) 0 0
\(533\) 23.4127 1.01412
\(534\) −0.188831 −0.00817150
\(535\) 1.49515 0.0646411
\(536\) −11.9047 −0.514205
\(537\) 1.93232 0.0833857
\(538\) 33.9901 1.46542
\(539\) 4.32762 0.186404
\(540\) −0.557145 −0.0239757
\(541\) −17.7661 −0.763823 −0.381911 0.924199i \(-0.624734\pi\)
−0.381911 + 0.924199i \(0.624734\pi\)
\(542\) 15.7369 0.675956
\(543\) 0.611168 0.0262277
\(544\) −33.6751 −1.44381
\(545\) 15.5780 0.667288
\(546\) 0.674096 0.0288487
\(547\) −10.4531 −0.446941 −0.223471 0.974711i \(-0.571739\pi\)
−0.223471 + 0.974711i \(0.571739\pi\)
\(548\) −15.8766 −0.678214
\(549\) −11.1799 −0.477145
\(550\) −2.15043 −0.0916947
\(551\) 0 0
\(552\) 0.991034 0.0421812
\(553\) 13.7631 0.585268
\(554\) −18.3716 −0.780535
\(555\) −0.136920 −0.00581193
\(556\) 1.51430 0.0642206
\(557\) −23.5768 −0.998982 −0.499491 0.866319i \(-0.666480\pi\)
−0.499491 + 0.866319i \(0.666480\pi\)
\(558\) 30.8894 1.30765
\(559\) 1.67911 0.0710187
\(560\) 9.29353 0.392723
\(561\) −0.635221 −0.0268191
\(562\) −19.1657 −0.808457
\(563\) −27.8106 −1.17208 −0.586038 0.810283i \(-0.699313\pi\)
−0.586038 + 0.810283i \(0.699313\pi\)
\(564\) −1.08250 −0.0455815
\(565\) −13.6479 −0.574173
\(566\) −1.67362 −0.0703475
\(567\) −16.6302 −0.698401
\(568\) 13.6736 0.573732
\(569\) 9.72405 0.407653 0.203827 0.979007i \(-0.434662\pi\)
0.203827 + 0.979007i \(0.434662\pi\)
\(570\) 0 0
\(571\) −7.74753 −0.324224 −0.162112 0.986772i \(-0.551831\pi\)
−0.162112 + 0.986772i \(0.551831\pi\)
\(572\) 3.19945 0.133776
\(573\) −1.08314 −0.0452487
\(574\) 31.8005 1.32733
\(575\) −7.20500 −0.300469
\(576\) −0.666040 −0.0277517
\(577\) −21.3536 −0.888964 −0.444482 0.895788i \(-0.646612\pi\)
−0.444482 + 0.895788i \(0.646612\pi\)
\(578\) 34.6274 1.44031
\(579\) 0.327167 0.0135966
\(580\) 1.39446 0.0579018
\(581\) −0.0251490 −0.00104336
\(582\) 1.20013 0.0497472
\(583\) −12.5621 −0.520268
\(584\) 9.97805 0.412895
\(585\) 7.20437 0.297864
\(586\) −23.5768 −0.973950
\(587\) −34.7452 −1.43409 −0.717043 0.697029i \(-0.754505\pi\)
−0.717043 + 0.697029i \(0.754505\pi\)
\(588\) −0.328658 −0.0135536
\(589\) 0 0
\(590\) 16.5267 0.680394
\(591\) 0.458679 0.0188675
\(592\) 7.98244 0.328076
\(593\) −0.557914 −0.0229108 −0.0114554 0.999934i \(-0.503646\pi\)
−0.0114554 + 0.999934i \(0.503646\pi\)
\(594\) 1.10359 0.0452810
\(595\) −11.2786 −0.462379
\(596\) 15.7787 0.646321
\(597\) −0.615948 −0.0252091
\(598\) 30.4680 1.24593
\(599\) −10.1872 −0.416237 −0.208119 0.978104i \(-0.566734\pi\)
−0.208119 + 0.978104i \(0.566734\pi\)
\(600\) −0.137548 −0.00561538
\(601\) −1.46619 −0.0598070 −0.0299035 0.999553i \(-0.509520\pi\)
−0.0299035 + 0.999553i \(0.509520\pi\)
\(602\) 2.28066 0.0929529
\(603\) −22.1813 −0.903291
\(604\) 25.5964 1.04150
\(605\) −9.50133 −0.386284
\(606\) 2.73826 0.111234
\(607\) 37.3950 1.51782 0.758909 0.651197i \(-0.225733\pi\)
0.758909 + 0.651197i \(0.225733\pi\)
\(608\) 0 0
\(609\) −0.204754 −0.00829706
\(610\) 6.56222 0.265696
\(611\) 28.0297 1.13396
\(612\) −19.6857 −0.795748
\(613\) −29.0310 −1.17255 −0.586276 0.810111i \(-0.699407\pi\)
−0.586276 + 0.810111i \(0.699407\pi\)
\(614\) 33.1000 1.33581
\(615\) −0.832870 −0.0335845
\(616\) −3.66009 −0.147469
\(617\) −0.259474 −0.0104460 −0.00522301 0.999986i \(-0.501663\pi\)
−0.00522301 + 0.999986i \(0.501663\pi\)
\(618\) 0.513498 0.0206559
\(619\) 23.2107 0.932917 0.466459 0.884543i \(-0.345530\pi\)
0.466459 + 0.884543i \(0.345530\pi\)
\(620\) −6.37916 −0.256193
\(621\) 3.69758 0.148379
\(622\) −1.60235 −0.0642484
\(623\) 2.33660 0.0936139
\(624\) 1.02928 0.0412042
\(625\) 1.00000 0.0400000
\(626\) −32.9651 −1.31755
\(627\) 0 0
\(628\) −18.5003 −0.738241
\(629\) −9.68750 −0.386266
\(630\) 9.78540 0.389860
\(631\) −1.74339 −0.0694032 −0.0347016 0.999398i \(-0.511048\pi\)
−0.0347016 + 0.999398i \(0.511048\pi\)
\(632\) 11.8757 0.472391
\(633\) −2.00107 −0.0795354
\(634\) −15.5627 −0.618074
\(635\) 19.2055 0.762147
\(636\) 0.954019 0.0378293
\(637\) 8.51009 0.337182
\(638\) −2.76215 −0.109354
\(639\) 25.4772 1.00786
\(640\) 11.5065 0.454834
\(641\) 9.38800 0.370804 0.185402 0.982663i \(-0.440641\pi\)
0.185402 + 0.982663i \(0.440641\pi\)
\(642\) 0.224917 0.00887676
\(643\) −35.4801 −1.39920 −0.699600 0.714535i \(-0.746638\pi\)
−0.699600 + 0.714535i \(0.746638\pi\)
\(644\) 14.5602 0.573752
\(645\) −0.0597316 −0.00235193
\(646\) 0 0
\(647\) −9.61436 −0.377979 −0.188990 0.981979i \(-0.560521\pi\)
−0.188990 + 0.981979i \(0.560521\pi\)
\(648\) −14.3496 −0.563705
\(649\) −11.5177 −0.452110
\(650\) −4.22873 −0.165865
\(651\) 0.936679 0.0367113
\(652\) −10.8355 −0.424352
\(653\) 10.9351 0.427922 0.213961 0.976842i \(-0.431363\pi\)
0.213961 + 0.976842i \(0.431363\pi\)
\(654\) 2.34341 0.0916344
\(655\) −19.3097 −0.754492
\(656\) 48.5563 1.89581
\(657\) 18.5914 0.725321
\(658\) 38.0716 1.48418
\(659\) 30.2427 1.17809 0.589045 0.808100i \(-0.299504\pi\)
0.589045 + 0.808100i \(0.299504\pi\)
\(660\) −0.113815 −0.00443026
\(661\) −17.8243 −0.693284 −0.346642 0.937997i \(-0.612678\pi\)
−0.346642 + 0.937997i \(0.612678\pi\)
\(662\) −6.95691 −0.270388
\(663\) −1.24914 −0.0485124
\(664\) −0.0217002 −0.000842130 0
\(665\) 0 0
\(666\) 8.40493 0.325684
\(667\) −9.25455 −0.358338
\(668\) −25.1306 −0.972333
\(669\) 0.366670 0.0141763
\(670\) 13.0197 0.502994
\(671\) −4.57332 −0.176551
\(672\) 0.885957 0.0341765
\(673\) −16.6638 −0.642341 −0.321171 0.947021i \(-0.604076\pi\)
−0.321171 + 0.947021i \(0.604076\pi\)
\(674\) 10.1733 0.391861
\(675\) −0.513197 −0.0197529
\(676\) −7.82169 −0.300834
\(677\) 36.5254 1.40379 0.701893 0.712283i \(-0.252339\pi\)
0.701893 + 0.712283i \(0.252339\pi\)
\(678\) −2.05307 −0.0788476
\(679\) −14.8505 −0.569911
\(680\) −9.73194 −0.373203
\(681\) −0.565963 −0.0216878
\(682\) 12.6358 0.483852
\(683\) −34.2305 −1.30979 −0.654896 0.755719i \(-0.727288\pi\)
−0.654896 + 0.755719i \(0.727288\pi\)
\(684\) 0 0
\(685\) −14.6242 −0.558762
\(686\) 34.4475 1.31521
\(687\) −1.99773 −0.0762181
\(688\) 3.48236 0.132764
\(689\) −24.7028 −0.941102
\(690\) −1.08385 −0.0412616
\(691\) 4.08362 0.155348 0.0776742 0.996979i \(-0.475251\pi\)
0.0776742 + 0.996979i \(0.475251\pi\)
\(692\) 13.4637 0.511813
\(693\) −6.81961 −0.259055
\(694\) 25.3171 0.961025
\(695\) 1.39485 0.0529096
\(696\) −0.176675 −0.00669686
\(697\) −58.9280 −2.23206
\(698\) 16.0052 0.605808
\(699\) −1.45903 −0.0551854
\(700\) −2.02084 −0.0763807
\(701\) 25.6862 0.970154 0.485077 0.874471i \(-0.338791\pi\)
0.485077 + 0.874471i \(0.338791\pi\)
\(702\) 2.17017 0.0819078
\(703\) 0 0
\(704\) −0.272455 −0.0102685
\(705\) −0.997112 −0.0375534
\(706\) −6.31281 −0.237586
\(707\) −33.8834 −1.27432
\(708\) 0.874706 0.0328735
\(709\) −19.5953 −0.735918 −0.367959 0.929842i \(-0.619943\pi\)
−0.367959 + 0.929842i \(0.619943\pi\)
\(710\) −14.9543 −0.561224
\(711\) 22.1273 0.829838
\(712\) 2.01617 0.0755592
\(713\) 42.3363 1.58551
\(714\) −1.69665 −0.0634956
\(715\) 2.94707 0.110214
\(716\) 24.4963 0.915469
\(717\) 0.892288 0.0333231
\(718\) −18.8772 −0.704492
\(719\) −1.29094 −0.0481439 −0.0240720 0.999710i \(-0.507663\pi\)
−0.0240720 + 0.999710i \(0.507663\pi\)
\(720\) 14.9414 0.556832
\(721\) −6.35405 −0.236637
\(722\) 0 0
\(723\) −0.284375 −0.0105760
\(724\) 7.74786 0.287947
\(725\) 1.28446 0.0477037
\(726\) −1.42929 −0.0530459
\(727\) −3.54012 −0.131296 −0.0656479 0.997843i \(-0.520911\pi\)
−0.0656479 + 0.997843i \(0.520911\pi\)
\(728\) −7.19742 −0.266754
\(729\) −26.6048 −0.985362
\(730\) −10.9126 −0.403893
\(731\) −4.22619 −0.156311
\(732\) 0.347318 0.0128372
\(733\) 17.2078 0.635585 0.317792 0.948160i \(-0.397059\pi\)
0.317792 + 0.948160i \(0.397059\pi\)
\(734\) 2.96361 0.109389
\(735\) −0.302733 −0.0111665
\(736\) 40.0438 1.47603
\(737\) −9.07363 −0.334231
\(738\) 51.1263 1.88198
\(739\) −40.0918 −1.47480 −0.737401 0.675456i \(-0.763947\pi\)
−0.737401 + 0.675456i \(0.763947\pi\)
\(740\) −1.73575 −0.0638076
\(741\) 0 0
\(742\) −33.5528 −1.23176
\(743\) 20.2637 0.743403 0.371702 0.928352i \(-0.378774\pi\)
0.371702 + 0.928352i \(0.378774\pi\)
\(744\) 0.808227 0.0296310
\(745\) 14.5340 0.532486
\(746\) −60.2239 −2.20495
\(747\) −0.0404325 −0.00147935
\(748\) −8.05279 −0.294439
\(749\) −2.78313 −0.101693
\(750\) 0.150431 0.00549295
\(751\) −38.7484 −1.41395 −0.706975 0.707238i \(-0.749941\pi\)
−0.706975 + 0.707238i \(0.749941\pi\)
\(752\) 58.1317 2.11984
\(753\) −2.20775 −0.0804548
\(754\) −5.43165 −0.197809
\(755\) 23.5773 0.858067
\(756\) 1.03709 0.0377186
\(757\) 20.8068 0.756237 0.378118 0.925757i \(-0.376571\pi\)
0.378118 + 0.925757i \(0.376571\pi\)
\(758\) −43.4998 −1.57998
\(759\) 0.755354 0.0274176
\(760\) 0 0
\(761\) 48.6822 1.76473 0.882363 0.470569i \(-0.155951\pi\)
0.882363 + 0.470569i \(0.155951\pi\)
\(762\) 2.88909 0.104661
\(763\) −28.9974 −1.04978
\(764\) −13.7311 −0.496773
\(765\) −18.1329 −0.655595
\(766\) −30.3856 −1.09788
\(767\) −22.6491 −0.817813
\(768\) 1.69281 0.0610840
\(769\) 20.0077 0.721495 0.360748 0.932663i \(-0.382522\pi\)
0.360748 + 0.932663i \(0.382522\pi\)
\(770\) 4.00289 0.144254
\(771\) 0.462455 0.0166549
\(772\) 4.14754 0.149273
\(773\) 1.59040 0.0572026 0.0286013 0.999591i \(-0.490895\pi\)
0.0286013 + 0.999591i \(0.490895\pi\)
\(774\) 3.66667 0.131796
\(775\) −5.87596 −0.211071
\(776\) −12.8140 −0.459996
\(777\) 0.254868 0.00914333
\(778\) 55.3558 1.98460
\(779\) 0 0
\(780\) −0.223814 −0.00801381
\(781\) 10.4219 0.372924
\(782\) −76.6858 −2.74228
\(783\) −0.659182 −0.0235572
\(784\) 17.6494 0.630334
\(785\) −17.0409 −0.608217
\(786\) −2.90477 −0.103610
\(787\) 2.87913 0.102630 0.0513150 0.998683i \(-0.483659\pi\)
0.0513150 + 0.998683i \(0.483659\pi\)
\(788\) 5.81474 0.207142
\(789\) 0.751037 0.0267376
\(790\) −12.9880 −0.462092
\(791\) 25.4048 0.903290
\(792\) −5.88440 −0.209093
\(793\) −8.99324 −0.319359
\(794\) 49.0116 1.73936
\(795\) 0.878764 0.0311665
\(796\) −7.80846 −0.276763
\(797\) 30.6071 1.08416 0.542080 0.840327i \(-0.317637\pi\)
0.542080 + 0.840327i \(0.317637\pi\)
\(798\) 0 0
\(799\) −70.5486 −2.49583
\(800\) −5.55777 −0.196497
\(801\) 3.75660 0.132733
\(802\) 8.31678 0.293676
\(803\) 7.60515 0.268380
\(804\) 0.689091 0.0243024
\(805\) 13.4116 0.472698
\(806\) 24.8479 0.875229
\(807\) 1.65708 0.0583320
\(808\) −29.2368 −1.02855
\(809\) 51.0221 1.79384 0.896920 0.442193i \(-0.145799\pi\)
0.896920 + 0.442193i \(0.145799\pi\)
\(810\) 15.6935 0.551415
\(811\) 34.3444 1.20600 0.602998 0.797743i \(-0.293973\pi\)
0.602998 + 0.797743i \(0.293973\pi\)
\(812\) −2.59570 −0.0910912
\(813\) 0.767201 0.0269069
\(814\) 3.43818 0.120508
\(815\) −9.98080 −0.349612
\(816\) −2.59062 −0.0906900
\(817\) 0 0
\(818\) −14.6614 −0.512623
\(819\) −13.4105 −0.468600
\(820\) −10.5584 −0.368715
\(821\) 40.2464 1.40461 0.702305 0.711876i \(-0.252154\pi\)
0.702305 + 0.711876i \(0.252154\pi\)
\(822\) −2.19993 −0.0767313
\(823\) −23.3478 −0.813853 −0.406927 0.913461i \(-0.633399\pi\)
−0.406927 + 0.913461i \(0.633399\pi\)
\(824\) −5.48268 −0.190998
\(825\) −0.104837 −0.00364997
\(826\) −30.7634 −1.07040
\(827\) −32.7322 −1.13821 −0.569105 0.822265i \(-0.692710\pi\)
−0.569105 + 0.822265i \(0.692710\pi\)
\(828\) 23.4087 0.813508
\(829\) 4.83161 0.167809 0.0839044 0.996474i \(-0.473261\pi\)
0.0839044 + 0.996474i \(0.473261\pi\)
\(830\) 0.0237326 0.000823770 0
\(831\) −0.895650 −0.0310697
\(832\) −0.535772 −0.0185746
\(833\) −21.4193 −0.742134
\(834\) 0.209828 0.00726574
\(835\) −23.1483 −0.801078
\(836\) 0 0
\(837\) 3.01552 0.104232
\(838\) 37.7880 1.30537
\(839\) 37.2171 1.28488 0.642438 0.766338i \(-0.277923\pi\)
0.642438 + 0.766338i \(0.277923\pi\)
\(840\) 0.256037 0.00883411
\(841\) −27.3502 −0.943109
\(842\) 53.8904 1.85719
\(843\) −0.934365 −0.0321812
\(844\) −25.3678 −0.873197
\(845\) −7.20470 −0.247849
\(846\) 61.2084 2.10439
\(847\) 17.6861 0.607702
\(848\) −51.2320 −1.75931
\(849\) −0.0815921 −0.00280024
\(850\) 10.6434 0.365066
\(851\) 11.5196 0.394887
\(852\) −0.791482 −0.0271157
\(853\) −12.1087 −0.414593 −0.207297 0.978278i \(-0.566467\pi\)
−0.207297 + 0.978278i \(0.566467\pi\)
\(854\) −12.2151 −0.417994
\(855\) 0 0
\(856\) −2.40147 −0.0820805
\(857\) −23.8743 −0.815532 −0.407766 0.913086i \(-0.633692\pi\)
−0.407766 + 0.913086i \(0.633692\pi\)
\(858\) 0.443330 0.0151350
\(859\) 35.4892 1.21088 0.605438 0.795893i \(-0.292998\pi\)
0.605438 + 0.795893i \(0.292998\pi\)
\(860\) −0.757226 −0.0258212
\(861\) 1.55033 0.0528352
\(862\) −44.9396 −1.53065
\(863\) −26.9330 −0.916810 −0.458405 0.888743i \(-0.651579\pi\)
−0.458405 + 0.888743i \(0.651579\pi\)
\(864\) 2.85223 0.0970348
\(865\) 12.4017 0.421669
\(866\) 56.0930 1.90612
\(867\) 1.68815 0.0573325
\(868\) 11.8744 0.403044
\(869\) 9.05154 0.307053
\(870\) 0.193222 0.00655085
\(871\) −17.8429 −0.604584
\(872\) −25.0209 −0.847313
\(873\) −23.8755 −0.808063
\(874\) 0 0
\(875\) −1.86144 −0.0629280
\(876\) −0.577568 −0.0195142
\(877\) −24.7625 −0.836170 −0.418085 0.908408i \(-0.637299\pi\)
−0.418085 + 0.908408i \(0.637299\pi\)
\(878\) 16.6094 0.560540
\(879\) −1.14941 −0.0387688
\(880\) 6.11203 0.206037
\(881\) 53.6558 1.80771 0.903855 0.427840i \(-0.140725\pi\)
0.903855 + 0.427840i \(0.140725\pi\)
\(882\) 18.5835 0.625738
\(883\) −0.946198 −0.0318421 −0.0159210 0.999873i \(-0.505068\pi\)
−0.0159210 + 0.999873i \(0.505068\pi\)
\(884\) −15.8355 −0.532605
\(885\) 0.805708 0.0270836
\(886\) 16.2962 0.547481
\(887\) 2.27312 0.0763241 0.0381620 0.999272i \(-0.487850\pi\)
0.0381620 + 0.999272i \(0.487850\pi\)
\(888\) 0.219917 0.00737992
\(889\) −35.7498 −1.19901
\(890\) −2.20500 −0.0739118
\(891\) −10.9371 −0.366406
\(892\) 4.64833 0.155638
\(893\) 0 0
\(894\) 2.18636 0.0731229
\(895\) 22.5640 0.754230
\(896\) −21.4186 −0.715545
\(897\) 1.48537 0.0495952
\(898\) −48.5619 −1.62053
\(899\) −7.54745 −0.251722
\(900\) −3.24895 −0.108298
\(901\) 62.1752 2.07135
\(902\) 20.9141 0.696363
\(903\) 0.111187 0.00370006
\(904\) 21.9209 0.729078
\(905\) 7.13669 0.237232
\(906\) 3.54675 0.117833
\(907\) −12.3800 −0.411070 −0.205535 0.978650i \(-0.565893\pi\)
−0.205535 + 0.978650i \(0.565893\pi\)
\(908\) −7.17479 −0.238104
\(909\) −54.4750 −1.80682
\(910\) 7.87152 0.260938
\(911\) −47.9424 −1.58840 −0.794202 0.607654i \(-0.792111\pi\)
−0.794202 + 0.607654i \(0.792111\pi\)
\(912\) 0 0
\(913\) −0.0165396 −0.000547381 0
\(914\) −12.2817 −0.406242
\(915\) 0.319920 0.0105762
\(916\) −25.3255 −0.836777
\(917\) 35.9438 1.18697
\(918\) −5.46216 −0.180278
\(919\) 43.4053 1.43181 0.715904 0.698199i \(-0.246015\pi\)
0.715904 + 0.698199i \(0.246015\pi\)
\(920\) 11.5724 0.381532
\(921\) 1.61369 0.0531728
\(922\) 26.7435 0.880750
\(923\) 20.4942 0.674574
\(924\) 0.211860 0.00696969
\(925\) −1.59883 −0.0525693
\(926\) −48.7192 −1.60101
\(927\) −10.2155 −0.335522
\(928\) −7.13875 −0.234341
\(929\) −37.9300 −1.24444 −0.622222 0.782841i \(-0.713770\pi\)
−0.622222 + 0.782841i \(0.713770\pi\)
\(930\) −0.883924 −0.0289850
\(931\) 0 0
\(932\) −18.4963 −0.605865
\(933\) −0.0781175 −0.00255745
\(934\) −67.3453 −2.20360
\(935\) −7.41756 −0.242580
\(936\) −11.5714 −0.378224
\(937\) −6.68720 −0.218461 −0.109231 0.994016i \(-0.534839\pi\)
−0.109231 + 0.994016i \(0.534839\pi\)
\(938\) −24.2353 −0.791311
\(939\) −1.60711 −0.0524461
\(940\) −12.6405 −0.412288
\(941\) 4.36774 0.142384 0.0711921 0.997463i \(-0.477320\pi\)
0.0711921 + 0.997463i \(0.477320\pi\)
\(942\) −2.56347 −0.0835225
\(943\) 70.0725 2.28187
\(944\) −46.9728 −1.52883
\(945\) 0.955282 0.0310753
\(946\) 1.49991 0.0487664
\(947\) −1.50804 −0.0490046 −0.0245023 0.999700i \(-0.507800\pi\)
−0.0245023 + 0.999700i \(0.507800\pi\)
\(948\) −0.687413 −0.0223261
\(949\) 14.9552 0.485467
\(950\) 0 0
\(951\) −0.758710 −0.0246029
\(952\) 18.1154 0.587123
\(953\) 16.0555 0.520090 0.260045 0.965596i \(-0.416263\pi\)
0.260045 + 0.965596i \(0.416263\pi\)
\(954\) −53.9435 −1.74649
\(955\) −12.6479 −0.409278
\(956\) 11.3117 0.365845
\(957\) −0.134660 −0.00435293
\(958\) −18.4683 −0.596684
\(959\) 27.2220 0.879045
\(960\) 0.0190592 0.000615135 0
\(961\) 3.52693 0.113772
\(962\) 6.76104 0.217985
\(963\) −4.47450 −0.144189
\(964\) −3.60506 −0.116111
\(965\) 3.82038 0.122982
\(966\) 2.01752 0.0649127
\(967\) −45.0466 −1.44860 −0.724300 0.689485i \(-0.757837\pi\)
−0.724300 + 0.689485i \(0.757837\pi\)
\(968\) 15.2607 0.490498
\(969\) 0 0
\(970\) 14.0141 0.449967
\(971\) 15.2507 0.489417 0.244709 0.969597i \(-0.421308\pi\)
0.244709 + 0.969597i \(0.421308\pi\)
\(972\) 2.50205 0.0802531
\(973\) −2.59642 −0.0832374
\(974\) −24.8200 −0.795284
\(975\) −0.206159 −0.00660236
\(976\) −18.6514 −0.597016
\(977\) −26.8192 −0.858023 −0.429011 0.903299i \(-0.641138\pi\)
−0.429011 + 0.903299i \(0.641138\pi\)
\(978\) −1.50142 −0.0480100
\(979\) 1.53670 0.0491132
\(980\) −3.83779 −0.122594
\(981\) −46.6197 −1.48845
\(982\) 32.9234 1.05063
\(983\) 28.8049 0.918735 0.459367 0.888246i \(-0.348076\pi\)
0.459367 + 0.888246i \(0.348076\pi\)
\(984\) 1.33773 0.0426452
\(985\) 5.35606 0.170658
\(986\) 13.6711 0.435375
\(987\) 1.85606 0.0590790
\(988\) 0 0
\(989\) 5.02545 0.159800
\(990\) 6.43552 0.204534
\(991\) 10.3840 0.329859 0.164929 0.986305i \(-0.447260\pi\)
0.164929 + 0.986305i \(0.447260\pi\)
\(992\) 32.6573 1.03687
\(993\) −0.339162 −0.0107630
\(994\) 27.8364 0.882917
\(995\) −7.19251 −0.228018
\(996\) 0.00125609 3.98007e−5 0
\(997\) 49.9100 1.58066 0.790332 0.612679i \(-0.209908\pi\)
0.790332 + 0.612679i \(0.209908\pi\)
\(998\) 28.5704 0.904379
\(999\) 0.820516 0.0259600
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 1805.2.a.j.1.4 4
5.4 even 2 9025.2.a.bo.1.1 4
19.18 odd 2 1805.2.a.n.1.1 yes 4
95.94 odd 2 9025.2.a.bh.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.j.1.4 4 1.1 even 1 trivial
1805.2.a.n.1.1 yes 4 19.18 odd 2
9025.2.a.bh.1.4 4 95.94 odd 2
9025.2.a.bo.1.1 4 5.4 even 2