Properties

Label 483.2.a.h.1.3
Level $483$
Weight $2$
Character 483.1
Self dual yes
Analytic conductor $3.857$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.837.1
Defining polynomial: \( x^{3} - 6x - 1 \) Copy content Toggle raw display
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 1.3
Root \(2.52892\) of defining polynomial
Character \(\chi\) \(=\) 483.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.52892 q^{2} +1.00000 q^{3} +4.39543 q^{4} -1.52892 q^{5} +2.52892 q^{6} -1.00000 q^{7} +6.05784 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.52892 q^{2} +1.00000 q^{3} +4.39543 q^{4} -1.52892 q^{5} +2.52892 q^{6} -1.00000 q^{7} +6.05784 q^{8} +1.00000 q^{9} -3.86651 q^{10} +1.86651 q^{11} +4.39543 q^{12} +0.604574 q^{13} -2.52892 q^{14} -1.52892 q^{15} +6.52892 q^{16} -2.92434 q^{17} +2.52892 q^{18} -1.86651 q^{19} -6.72025 q^{20} -1.00000 q^{21} +4.72025 q^{22} -1.00000 q^{23} +6.05784 q^{24} -2.66241 q^{25} +1.52892 q^{26} +1.00000 q^{27} -4.39543 q^{28} +7.19133 q^{29} -3.86651 q^{30} -5.86651 q^{31} +4.39543 q^{32} +1.86651 q^{33} -7.39543 q^{34} +1.52892 q^{35} +4.39543 q^{36} -3.19133 q^{37} -4.72025 q^{38} +0.604574 q^{39} -9.26193 q^{40} -6.65736 q^{41} -2.52892 q^{42} -5.66241 q^{43} +8.20410 q^{44} -1.52892 q^{45} -2.52892 q^{46} +10.7909 q^{47} +6.52892 q^{48} +1.00000 q^{49} -6.73302 q^{50} -2.92434 q^{51} +2.65736 q^{52} -1.52892 q^{53} +2.52892 q^{54} -2.85374 q^{55} -6.05784 q^{56} -1.86651 q^{57} +18.1863 q^{58} -6.31977 q^{59} -6.72025 q^{60} -3.66241 q^{61} -14.8359 q^{62} -1.00000 q^{63} -1.94216 q^{64} -0.924344 q^{65} +4.72025 q^{66} +5.37761 q^{67} -12.8537 q^{68} -1.00000 q^{69} +3.86651 q^{70} +15.2441 q^{71} +6.05784 q^{72} +13.9822 q^{73} -8.07061 q^{74} -2.66241 q^{75} -8.20410 q^{76} -1.86651 q^{77} +1.52892 q^{78} +9.19133 q^{79} -9.98218 q^{80} +1.00000 q^{81} -16.8359 q^{82} -0.924344 q^{83} -4.39543 q^{84} +4.47108 q^{85} -14.3198 q^{86} +7.19133 q^{87} +11.3070 q^{88} +7.39543 q^{89} -3.86651 q^{90} -0.604574 q^{91} -4.39543 q^{92} -5.86651 q^{93} +27.2892 q^{94} +2.85374 q^{95} +4.39543 q^{96} +5.98218 q^{97} +2.52892 q^{98} +1.86651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 12 q^{10} + 6 q^{11} + 6 q^{12} + 9 q^{13} + 3 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} - 12 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 6 q^{36} + 6 q^{37} + 9 q^{38} + 9 q^{39} - 21 q^{40} - 6 q^{41} - 9 q^{43} + 33 q^{44} + 3 q^{45} + 18 q^{47} + 12 q^{48} + 3 q^{49} - 21 q^{50} + 6 q^{51} - 6 q^{52} + 3 q^{53} + 15 q^{55} - 3 q^{56} - 6 q^{57} + 33 q^{58} + 3 q^{59} + 3 q^{60} - 3 q^{61} + 9 q^{62} - 3 q^{63} - 21 q^{64} + 12 q^{65} - 9 q^{66} - 21 q^{67} - 15 q^{68} - 3 q^{69} + 12 q^{70} + 9 q^{71} + 3 q^{72} + 12 q^{73} - 33 q^{74} - 33 q^{76} - 6 q^{77} - 3 q^{78} + 12 q^{79} + 3 q^{81} + 3 q^{82} + 12 q^{83} - 6 q^{84} + 21 q^{85} - 21 q^{86} + 6 q^{87} - 12 q^{88} + 15 q^{89} - 12 q^{90} - 9 q^{91} - 6 q^{92} - 18 q^{93} + 6 q^{94} - 15 q^{95} + 6 q^{96} - 12 q^{97} + 6 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52892 1.78822 0.894108 0.447852i \(-0.147811\pi\)
0.894108 + 0.447852i \(0.147811\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.39543 2.19771
\(5\) −1.52892 −0.683753 −0.341876 0.939745i \(-0.611062\pi\)
−0.341876 + 0.939745i \(0.611062\pi\)
\(6\) 2.52892 1.03243
\(7\) −1.00000 −0.377964
\(8\) 6.05784 2.14177
\(9\) 1.00000 0.333333
\(10\) −3.86651 −1.22270
\(11\) 1.86651 0.562773 0.281387 0.959594i \(-0.409206\pi\)
0.281387 + 0.959594i \(0.409206\pi\)
\(12\) 4.39543 1.26885
\(13\) 0.604574 0.167679 0.0838393 0.996479i \(-0.473282\pi\)
0.0838393 + 0.996479i \(0.473282\pi\)
\(14\) −2.52892 −0.675882
\(15\) −1.52892 −0.394765
\(16\) 6.52892 1.63223
\(17\) −2.92434 −0.709258 −0.354629 0.935007i \(-0.615393\pi\)
−0.354629 + 0.935007i \(0.615393\pi\)
\(18\) 2.52892 0.596072
\(19\) −1.86651 −0.428206 −0.214103 0.976811i \(-0.568683\pi\)
−0.214103 + 0.976811i \(0.568683\pi\)
\(20\) −6.72025 −1.50269
\(21\) −1.00000 −0.218218
\(22\) 4.72025 1.00636
\(23\) −1.00000 −0.208514
\(24\) 6.05784 1.23655
\(25\) −2.66241 −0.532482
\(26\) 1.52892 0.299845
\(27\) 1.00000 0.192450
\(28\) −4.39543 −0.830657
\(29\) 7.19133 1.33540 0.667698 0.744432i \(-0.267280\pi\)
0.667698 + 0.744432i \(0.267280\pi\)
\(30\) −3.86651 −0.705925
\(31\) −5.86651 −1.05366 −0.526828 0.849972i \(-0.676619\pi\)
−0.526828 + 0.849972i \(0.676619\pi\)
\(32\) 4.39543 0.777009
\(33\) 1.86651 0.324917
\(34\) −7.39543 −1.26831
\(35\) 1.52892 0.258434
\(36\) 4.39543 0.732571
\(37\) −3.19133 −0.524651 −0.262326 0.964979i \(-0.584489\pi\)
−0.262326 + 0.964979i \(0.584489\pi\)
\(38\) −4.72025 −0.765725
\(39\) 0.604574 0.0968093
\(40\) −9.26193 −1.46444
\(41\) −6.65736 −1.03970 −0.519852 0.854256i \(-0.674013\pi\)
−0.519852 + 0.854256i \(0.674013\pi\)
\(42\) −2.52892 −0.390221
\(43\) −5.66241 −0.863509 −0.431755 0.901991i \(-0.642105\pi\)
−0.431755 + 0.901991i \(0.642105\pi\)
\(44\) 8.20410 1.23681
\(45\) −1.52892 −0.227918
\(46\) −2.52892 −0.372869
\(47\) 10.7909 1.57401 0.787004 0.616948i \(-0.211631\pi\)
0.787004 + 0.616948i \(0.211631\pi\)
\(48\) 6.52892 0.942368
\(49\) 1.00000 0.142857
\(50\) −6.73302 −0.952192
\(51\) −2.92434 −0.409490
\(52\) 2.65736 0.368510
\(53\) −1.52892 −0.210013 −0.105007 0.994472i \(-0.533486\pi\)
−0.105007 + 0.994472i \(0.533486\pi\)
\(54\) 2.52892 0.344142
\(55\) −2.85374 −0.384798
\(56\) −6.05784 −0.809512
\(57\) −1.86651 −0.247225
\(58\) 18.1863 2.38798
\(59\) −6.31977 −0.822764 −0.411382 0.911463i \(-0.634954\pi\)
−0.411382 + 0.911463i \(0.634954\pi\)
\(60\) −6.72025 −0.867580
\(61\) −3.66241 −0.468924 −0.234462 0.972125i \(-0.575333\pi\)
−0.234462 + 0.972125i \(0.575333\pi\)
\(62\) −14.8359 −1.88416
\(63\) −1.00000 −0.125988
\(64\) −1.94216 −0.242771
\(65\) −0.924344 −0.114651
\(66\) 4.72025 0.581022
\(67\) 5.37761 0.656979 0.328490 0.944508i \(-0.393460\pi\)
0.328490 + 0.944508i \(0.393460\pi\)
\(68\) −12.8537 −1.55874
\(69\) −1.00000 −0.120386
\(70\) 3.86651 0.462136
\(71\) 15.2441 1.80914 0.904572 0.426321i \(-0.140191\pi\)
0.904572 + 0.426321i \(0.140191\pi\)
\(72\) 6.05784 0.713923
\(73\) 13.9822 1.63649 0.818245 0.574869i \(-0.194947\pi\)
0.818245 + 0.574869i \(0.194947\pi\)
\(74\) −8.07061 −0.938189
\(75\) −2.66241 −0.307429
\(76\) −8.20410 −0.941075
\(77\) −1.86651 −0.212708
\(78\) 1.52892 0.173116
\(79\) 9.19133 1.03411 0.517053 0.855954i \(-0.327029\pi\)
0.517053 + 0.855954i \(0.327029\pi\)
\(80\) −9.98218 −1.11604
\(81\) 1.00000 0.111111
\(82\) −16.8359 −1.85922
\(83\) −0.924344 −0.101460 −0.0507300 0.998712i \(-0.516155\pi\)
−0.0507300 + 0.998712i \(0.516155\pi\)
\(84\) −4.39543 −0.479580
\(85\) 4.47108 0.484957
\(86\) −14.3198 −1.54414
\(87\) 7.19133 0.770991
\(88\) 11.3070 1.20533
\(89\) 7.39543 0.783914 0.391957 0.919984i \(-0.371798\pi\)
0.391957 + 0.919984i \(0.371798\pi\)
\(90\) −3.86651 −0.407566
\(91\) −0.604574 −0.0633766
\(92\) −4.39543 −0.458255
\(93\) −5.86651 −0.608329
\(94\) 27.2892 2.81466
\(95\) 2.85374 0.292787
\(96\) 4.39543 0.448606
\(97\) 5.98218 0.607398 0.303699 0.952768i \(-0.401778\pi\)
0.303699 + 0.952768i \(0.401778\pi\)
\(98\) 2.52892 0.255459
\(99\) 1.86651 0.187591
\(100\) −11.7024 −1.17024
\(101\) 4.05279 0.403267 0.201634 0.979461i \(-0.435375\pi\)
0.201634 + 0.979461i \(0.435375\pi\)
\(102\) −7.39543 −0.732256
\(103\) −6.11567 −0.602595 −0.301298 0.953530i \(-0.597420\pi\)
−0.301298 + 0.953530i \(0.597420\pi\)
\(104\) 3.66241 0.359129
\(105\) 1.52892 0.149207
\(106\) −3.86651 −0.375548
\(107\) −2.33759 −0.225983 −0.112992 0.993596i \(-0.536043\pi\)
−0.112992 + 0.993596i \(0.536043\pi\)
\(108\) 4.39543 0.422950
\(109\) −8.58675 −0.822462 −0.411231 0.911531i \(-0.634901\pi\)
−0.411231 + 0.911531i \(0.634901\pi\)
\(110\) −7.21687 −0.688101
\(111\) −3.19133 −0.302907
\(112\) −6.52892 −0.616925
\(113\) 19.3776 1.82289 0.911446 0.411420i \(-0.134967\pi\)
0.911446 + 0.411420i \(0.134967\pi\)
\(114\) −4.72025 −0.442092
\(115\) 1.52892 0.142572
\(116\) 31.6089 2.93482
\(117\) 0.604574 0.0558929
\(118\) −15.9822 −1.47128
\(119\) 2.92434 0.268074
\(120\) −9.26193 −0.845495
\(121\) −7.51615 −0.683286
\(122\) −9.26193 −0.838536
\(123\) −6.65736 −0.600274
\(124\) −25.7858 −2.31563
\(125\) 11.7152 1.04784
\(126\) −2.52892 −0.225294
\(127\) 4.98723 0.442545 0.221273 0.975212i \(-0.428979\pi\)
0.221273 + 0.975212i \(0.428979\pi\)
\(128\) −13.7024 −1.21113
\(129\) −5.66241 −0.498547
\(130\) −2.33759 −0.205020
\(131\) −1.86651 −0.163078 −0.0815388 0.996670i \(-0.525983\pi\)
−0.0815388 + 0.996670i \(0.525983\pi\)
\(132\) 8.20410 0.714075
\(133\) 1.86651 0.161847
\(134\) 13.5995 1.17482
\(135\) −1.52892 −0.131588
\(136\) −17.7152 −1.51907
\(137\) −15.1913 −1.29788 −0.648941 0.760838i \(-0.724788\pi\)
−0.648941 + 0.760838i \(0.724788\pi\)
\(138\) −2.52892 −0.215276
\(139\) −12.4711 −1.05778 −0.528892 0.848689i \(-0.677392\pi\)
−0.528892 + 0.848689i \(0.677392\pi\)
\(140\) 6.72025 0.567964
\(141\) 10.7909 0.908754
\(142\) 38.5511 3.23514
\(143\) 1.12844 0.0943651
\(144\) 6.52892 0.544076
\(145\) −10.9950 −0.913081
\(146\) 35.3598 2.92640
\(147\) 1.00000 0.0824786
\(148\) −14.0272 −1.15303
\(149\) −0.523868 −0.0429170 −0.0214585 0.999770i \(-0.506831\pi\)
−0.0214585 + 0.999770i \(0.506831\pi\)
\(150\) −6.73302 −0.549748
\(151\) −11.3248 −0.921601 −0.460800 0.887504i \(-0.652438\pi\)
−0.460800 + 0.887504i \(0.652438\pi\)
\(152\) −11.3070 −0.917119
\(153\) −2.92434 −0.236419
\(154\) −4.72025 −0.380368
\(155\) 8.96941 0.720440
\(156\) 2.65736 0.212759
\(157\) 21.0222 1.67775 0.838877 0.544321i \(-0.183213\pi\)
0.838877 + 0.544321i \(0.183213\pi\)
\(158\) 23.2441 1.84920
\(159\) −1.52892 −0.121251
\(160\) −6.72025 −0.531282
\(161\) 1.00000 0.0788110
\(162\) 2.52892 0.198691
\(163\) −13.3776 −1.04781 −0.523907 0.851775i \(-0.675526\pi\)
−0.523907 + 0.851775i \(0.675526\pi\)
\(164\) −29.2619 −2.28497
\(165\) −2.85374 −0.222163
\(166\) −2.33759 −0.181432
\(167\) 20.5161 1.58759 0.793794 0.608187i \(-0.208103\pi\)
0.793794 + 0.608187i \(0.208103\pi\)
\(168\) −6.05784 −0.467372
\(169\) −12.6345 −0.971884
\(170\) 11.3070 0.867207
\(171\) −1.86651 −0.142735
\(172\) −24.8887 −1.89775
\(173\) −1.34264 −0.102079 −0.0510395 0.998697i \(-0.516253\pi\)
−0.0510395 + 0.998697i \(0.516253\pi\)
\(174\) 18.1863 1.37870
\(175\) 2.66241 0.201259
\(176\) 12.1863 0.918575
\(177\) −6.31977 −0.475023
\(178\) 18.7024 1.40181
\(179\) −0.204098 −0.0152550 −0.00762751 0.999971i \(-0.502428\pi\)
−0.00762751 + 0.999971i \(0.502428\pi\)
\(180\) −6.72025 −0.500898
\(181\) 17.4482 1.29692 0.648458 0.761251i \(-0.275414\pi\)
0.648458 + 0.761251i \(0.275414\pi\)
\(182\) −1.52892 −0.113331
\(183\) −3.66241 −0.270733
\(184\) −6.05784 −0.446590
\(185\) 4.87928 0.358732
\(186\) −14.8359 −1.08782
\(187\) −5.45831 −0.399151
\(188\) 47.4304 3.45922
\(189\) −1.00000 −0.0727393
\(190\) 7.21687 0.523567
\(191\) 19.3248 1.39829 0.699147 0.714978i \(-0.253563\pi\)
0.699147 + 0.714978i \(0.253563\pi\)
\(192\) −1.94216 −0.140164
\(193\) −1.32482 −0.0953626 −0.0476813 0.998863i \(-0.515183\pi\)
−0.0476813 + 0.998863i \(0.515183\pi\)
\(194\) 15.1284 1.08616
\(195\) −0.924344 −0.0661936
\(196\) 4.39543 0.313959
\(197\) 17.5111 1.24761 0.623807 0.781578i \(-0.285585\pi\)
0.623807 + 0.781578i \(0.285585\pi\)
\(198\) 4.72025 0.335453
\(199\) −22.1786 −1.57220 −0.786098 0.618102i \(-0.787902\pi\)
−0.786098 + 0.618102i \(0.787902\pi\)
\(200\) −16.1284 −1.14045
\(201\) 5.37761 0.379307
\(202\) 10.2492 0.721129
\(203\) −7.19133 −0.504732
\(204\) −12.8537 −0.899942
\(205\) 10.1786 0.710901
\(206\) −15.4660 −1.07757
\(207\) −1.00000 −0.0695048
\(208\) 3.94721 0.273690
\(209\) −3.48385 −0.240983
\(210\) 3.86651 0.266814
\(211\) 2.40048 0.165256 0.0826278 0.996580i \(-0.473669\pi\)
0.0826278 + 0.996580i \(0.473669\pi\)
\(212\) −6.72025 −0.461548
\(213\) 15.2441 1.04451
\(214\) −5.91157 −0.404107
\(215\) 8.65736 0.590427
\(216\) 6.05784 0.412184
\(217\) 5.86651 0.398245
\(218\) −21.7152 −1.47074
\(219\) 13.9822 0.944828
\(220\) −12.5434 −0.845675
\(221\) −1.76798 −0.118927
\(222\) −8.07061 −0.541664
\(223\) −14.0528 −0.941044 −0.470522 0.882388i \(-0.655934\pi\)
−0.470522 + 0.882388i \(0.655934\pi\)
\(224\) −4.39543 −0.293682
\(225\) −2.66241 −0.177494
\(226\) 49.0044 3.25972
\(227\) 14.8537 0.985877 0.492939 0.870064i \(-0.335923\pi\)
0.492939 + 0.870064i \(0.335923\pi\)
\(228\) −8.20410 −0.543330
\(229\) −23.1106 −1.52719 −0.763596 0.645694i \(-0.776568\pi\)
−0.763596 + 0.645694i \(0.776568\pi\)
\(230\) 3.86651 0.254950
\(231\) −1.86651 −0.122807
\(232\) 43.5639 2.86011
\(233\) −21.1207 −1.38366 −0.691832 0.722058i \(-0.743196\pi\)
−0.691832 + 0.722058i \(0.743196\pi\)
\(234\) 1.52892 0.0999485
\(235\) −16.4983 −1.07623
\(236\) −27.7781 −1.80820
\(237\) 9.19133 0.597041
\(238\) 7.39543 0.479374
\(239\) −5.64459 −0.365118 −0.182559 0.983195i \(-0.558438\pi\)
−0.182559 + 0.983195i \(0.558438\pi\)
\(240\) −9.98218 −0.644347
\(241\) −9.44821 −0.608613 −0.304306 0.952574i \(-0.598425\pi\)
−0.304306 + 0.952574i \(0.598425\pi\)
\(242\) −19.0077 −1.22186
\(243\) 1.00000 0.0641500
\(244\) −16.0979 −1.03056
\(245\) −1.52892 −0.0976790
\(246\) −16.8359 −1.07342
\(247\) −1.12844 −0.0718011
\(248\) −35.5383 −2.25669
\(249\) −0.924344 −0.0585779
\(250\) 29.6268 1.87376
\(251\) 0.639540 0.0403674 0.0201837 0.999796i \(-0.493575\pi\)
0.0201837 + 0.999796i \(0.493575\pi\)
\(252\) −4.39543 −0.276886
\(253\) −1.86651 −0.117346
\(254\) 12.6123 0.791366
\(255\) 4.47108 0.279990
\(256\) −30.7680 −1.92300
\(257\) −18.6395 −1.16270 −0.581351 0.813653i \(-0.697476\pi\)
−0.581351 + 0.813653i \(0.697476\pi\)
\(258\) −14.3198 −0.891510
\(259\) 3.19133 0.198299
\(260\) −4.06289 −0.251969
\(261\) 7.19133 0.445132
\(262\) −4.72025 −0.291618
\(263\) −25.1557 −1.55117 −0.775583 0.631246i \(-0.782544\pi\)
−0.775583 + 0.631246i \(0.782544\pi\)
\(264\) 11.3070 0.695898
\(265\) 2.33759 0.143597
\(266\) 4.72025 0.289417
\(267\) 7.39543 0.452593
\(268\) 23.6369 1.44385
\(269\) −4.97713 −0.303461 −0.151730 0.988422i \(-0.548485\pi\)
−0.151730 + 0.988422i \(0.548485\pi\)
\(270\) −3.86651 −0.235308
\(271\) 4.92434 0.299133 0.149566 0.988752i \(-0.452212\pi\)
0.149566 + 0.988752i \(0.452212\pi\)
\(272\) −19.0928 −1.15767
\(273\) −0.604574 −0.0365905
\(274\) −38.4176 −2.32089
\(275\) −4.96941 −0.299667
\(276\) −4.39543 −0.264574
\(277\) 25.1029 1.50829 0.754144 0.656710i \(-0.228052\pi\)
0.754144 + 0.656710i \(0.228052\pi\)
\(278\) −31.5383 −1.89154
\(279\) −5.86651 −0.351219
\(280\) 9.26193 0.553506
\(281\) 26.3726 1.57325 0.786627 0.617428i \(-0.211825\pi\)
0.786627 + 0.617428i \(0.211825\pi\)
\(282\) 27.2892 1.62505
\(283\) 12.4354 0.739210 0.369605 0.929189i \(-0.379493\pi\)
0.369605 + 0.929189i \(0.379493\pi\)
\(284\) 67.0044 3.97598
\(285\) 2.85374 0.169041
\(286\) 2.85374 0.168745
\(287\) 6.65736 0.392972
\(288\) 4.39543 0.259003
\(289\) −8.44821 −0.496954
\(290\) −27.8053 −1.63279
\(291\) 5.98218 0.350682
\(292\) 61.4576 3.59654
\(293\) 24.3827 1.42445 0.712225 0.701951i \(-0.247688\pi\)
0.712225 + 0.701951i \(0.247688\pi\)
\(294\) 2.52892 0.147489
\(295\) 9.66241 0.562567
\(296\) −19.3325 −1.12368
\(297\) 1.86651 0.108306
\(298\) −1.32482 −0.0767447
\(299\) −0.604574 −0.0349634
\(300\) −11.7024 −0.675640
\(301\) 5.66241 0.326376
\(302\) −28.6395 −1.64802
\(303\) 4.05279 0.232826
\(304\) −12.1863 −0.698931
\(305\) 5.59952 0.320628
\(306\) −7.39543 −0.422768
\(307\) −6.13349 −0.350057 −0.175028 0.984563i \(-0.556002\pi\)
−0.175028 + 0.984563i \(0.556002\pi\)
\(308\) −8.20410 −0.467472
\(309\) −6.11567 −0.347908
\(310\) 22.6829 1.28830
\(311\) −1.12844 −0.0639881 −0.0319940 0.999488i \(-0.510186\pi\)
−0.0319940 + 0.999488i \(0.510186\pi\)
\(312\) 3.66241 0.207343
\(313\) 25.4304 1.43741 0.718705 0.695315i \(-0.244735\pi\)
0.718705 + 0.695315i \(0.244735\pi\)
\(314\) 53.1634 3.00018
\(315\) 1.52892 0.0861448
\(316\) 40.3998 2.27267
\(317\) −7.64459 −0.429363 −0.214681 0.976684i \(-0.568871\pi\)
−0.214681 + 0.976684i \(0.568871\pi\)
\(318\) −3.86651 −0.216823
\(319\) 13.4227 0.751525
\(320\) 2.96941 0.165995
\(321\) −2.33759 −0.130472
\(322\) 2.52892 0.140931
\(323\) 5.45831 0.303709
\(324\) 4.39543 0.244190
\(325\) −1.60962 −0.0892859
\(326\) −33.8309 −1.87372
\(327\) −8.58675 −0.474849
\(328\) −40.3292 −2.22681
\(329\) −10.7909 −0.594919
\(330\) −7.21687 −0.397276
\(331\) −10.1513 −0.557967 −0.278983 0.960296i \(-0.589997\pi\)
−0.278983 + 0.960296i \(0.589997\pi\)
\(332\) −4.06289 −0.222980
\(333\) −3.19133 −0.174884
\(334\) 51.8837 2.83895
\(335\) −8.22192 −0.449211
\(336\) −6.52892 −0.356182
\(337\) 4.60457 0.250827 0.125414 0.992105i \(-0.459974\pi\)
0.125414 + 0.992105i \(0.459974\pi\)
\(338\) −31.9516 −1.73794
\(339\) 19.3776 1.05245
\(340\) 19.6523 1.06580
\(341\) −10.9499 −0.592970
\(342\) −4.72025 −0.255242
\(343\) −1.00000 −0.0539949
\(344\) −34.3019 −1.84944
\(345\) 1.52892 0.0823142
\(346\) −3.39543 −0.182539
\(347\) −15.5740 −0.836055 −0.418028 0.908434i \(-0.637278\pi\)
−0.418028 + 0.908434i \(0.637278\pi\)
\(348\) 31.6089 1.69442
\(349\) 25.2263 1.35033 0.675166 0.737666i \(-0.264072\pi\)
0.675166 + 0.737666i \(0.264072\pi\)
\(350\) 6.73302 0.359895
\(351\) 0.604574 0.0322698
\(352\) 8.20410 0.437280
\(353\) 28.5060 1.51722 0.758612 0.651543i \(-0.225878\pi\)
0.758612 + 0.651543i \(0.225878\pi\)
\(354\) −15.9822 −0.849443
\(355\) −23.3070 −1.23701
\(356\) 32.5060 1.72282
\(357\) 2.92434 0.154773
\(358\) −0.516148 −0.0272792
\(359\) −32.4711 −1.71376 −0.856879 0.515517i \(-0.827600\pi\)
−0.856879 + 0.515517i \(0.827600\pi\)
\(360\) −9.26193 −0.488147
\(361\) −15.5161 −0.816639
\(362\) 44.1251 2.31916
\(363\) −7.51615 −0.394495
\(364\) −2.65736 −0.139284
\(365\) −21.3776 −1.11896
\(366\) −9.26193 −0.484129
\(367\) −6.87156 −0.358692 −0.179346 0.983786i \(-0.557398\pi\)
−0.179346 + 0.983786i \(0.557398\pi\)
\(368\) −6.52892 −0.340343
\(369\) −6.65736 −0.346568
\(370\) 12.3393 0.641489
\(371\) 1.52892 0.0793775
\(372\) −25.7858 −1.33693
\(373\) −10.6574 −0.551817 −0.275909 0.961184i \(-0.588979\pi\)
−0.275909 + 0.961184i \(0.588979\pi\)
\(374\) −13.8036 −0.713768
\(375\) 11.7152 0.604970
\(376\) 65.3692 3.37116
\(377\) 4.34769 0.223917
\(378\) −2.52892 −0.130074
\(379\) −35.9287 −1.84553 −0.922767 0.385358i \(-0.874078\pi\)
−0.922767 + 0.385358i \(0.874078\pi\)
\(380\) 12.5434 0.643462
\(381\) 4.98723 0.255504
\(382\) 48.8709 2.50045
\(383\) −0.657360 −0.0335895 −0.0167948 0.999859i \(-0.505346\pi\)
−0.0167948 + 0.999859i \(0.505346\pi\)
\(384\) −13.7024 −0.699249
\(385\) 2.85374 0.145440
\(386\) −3.35036 −0.170529
\(387\) −5.66241 −0.287836
\(388\) 26.2942 1.33489
\(389\) 25.4126 1.28847 0.644234 0.764828i \(-0.277176\pi\)
0.644234 + 0.764828i \(0.277176\pi\)
\(390\) −2.33759 −0.118368
\(391\) 2.92434 0.147890
\(392\) 6.05784 0.305967
\(393\) −1.86651 −0.0941529
\(394\) 44.2841 2.23100
\(395\) −14.0528 −0.707072
\(396\) 8.20410 0.412271
\(397\) 35.7075 1.79211 0.896053 0.443946i \(-0.146422\pi\)
0.896053 + 0.443946i \(0.146422\pi\)
\(398\) −56.0878 −2.81142
\(399\) 1.86651 0.0934423
\(400\) −17.3827 −0.869133
\(401\) 19.0299 0.950309 0.475154 0.879902i \(-0.342392\pi\)
0.475154 + 0.879902i \(0.342392\pi\)
\(402\) 13.5995 0.678283
\(403\) −3.54674 −0.176676
\(404\) 17.8137 0.886266
\(405\) −1.52892 −0.0759725
\(406\) −18.1863 −0.902570
\(407\) −5.95664 −0.295260
\(408\) −17.7152 −0.877033
\(409\) −4.77303 −0.236011 −0.118006 0.993013i \(-0.537650\pi\)
−0.118006 + 0.993013i \(0.537650\pi\)
\(410\) 25.7407 1.27124
\(411\) −15.1913 −0.749333
\(412\) −26.8810 −1.32433
\(413\) 6.31977 0.310976
\(414\) −2.52892 −0.124290
\(415\) 1.41325 0.0693735
\(416\) 2.65736 0.130288
\(417\) −12.4711 −0.610712
\(418\) −8.81038 −0.430930
\(419\) 17.6089 0.860253 0.430127 0.902769i \(-0.358469\pi\)
0.430127 + 0.902769i \(0.358469\pi\)
\(420\) 6.72025 0.327914
\(421\) 40.4075 1.96934 0.984671 0.174422i \(-0.0558056\pi\)
0.984671 + 0.174422i \(0.0558056\pi\)
\(422\) 6.07061 0.295512
\(423\) 10.7909 0.524669
\(424\) −9.26193 −0.449799
\(425\) 7.78580 0.377667
\(426\) 38.5511 1.86781
\(427\) 3.66241 0.177236
\(428\) −10.2747 −0.496647
\(429\) 1.12844 0.0544817
\(430\) 21.8938 1.05581
\(431\) −28.0094 −1.34917 −0.674583 0.738199i \(-0.735677\pi\)
−0.674583 + 0.738199i \(0.735677\pi\)
\(432\) 6.52892 0.314123
\(433\) −30.3726 −1.45961 −0.729806 0.683654i \(-0.760390\pi\)
−0.729806 + 0.683654i \(0.760390\pi\)
\(434\) 14.8359 0.712147
\(435\) −10.9950 −0.527168
\(436\) −37.7424 −1.80754
\(437\) 1.86651 0.0892872
\(438\) 35.3598 1.68956
\(439\) −5.33254 −0.254508 −0.127254 0.991870i \(-0.540616\pi\)
−0.127254 + 0.991870i \(0.540616\pi\)
\(440\) −17.2875 −0.824148
\(441\) 1.00000 0.0476190
\(442\) −4.47108 −0.212668
\(443\) −18.1157 −0.860702 −0.430351 0.902662i \(-0.641610\pi\)
−0.430351 + 0.902662i \(0.641610\pi\)
\(444\) −14.0272 −0.665704
\(445\) −11.3070 −0.536003
\(446\) −35.5383 −1.68279
\(447\) −0.523868 −0.0247781
\(448\) 1.94216 0.0917586
\(449\) −33.7603 −1.59325 −0.796623 0.604477i \(-0.793382\pi\)
−0.796623 + 0.604477i \(0.793382\pi\)
\(450\) −6.73302 −0.317397
\(451\) −12.4260 −0.585118
\(452\) 85.1728 4.00619
\(453\) −11.3248 −0.532086
\(454\) 37.5639 1.76296
\(455\) 0.924344 0.0433339
\(456\) −11.3070 −0.529499
\(457\) −1.29757 −0.0606980 −0.0303490 0.999539i \(-0.509662\pi\)
−0.0303490 + 0.999539i \(0.509662\pi\)
\(458\) −58.4449 −2.73095
\(459\) −2.92434 −0.136497
\(460\) 6.72025 0.313333
\(461\) −27.3420 −1.27344 −0.636721 0.771094i \(-0.719710\pi\)
−0.636721 + 0.771094i \(0.719710\pi\)
\(462\) −4.72025 −0.219606
\(463\) −24.6217 −1.14427 −0.572134 0.820160i \(-0.693884\pi\)
−0.572134 + 0.820160i \(0.693884\pi\)
\(464\) 46.9516 2.17967
\(465\) 8.96941 0.415946
\(466\) −53.4126 −2.47429
\(467\) −12.6574 −0.585713 −0.292856 0.956156i \(-0.594606\pi\)
−0.292856 + 0.956156i \(0.594606\pi\)
\(468\) 2.65736 0.122837
\(469\) −5.37761 −0.248315
\(470\) −41.7229 −1.92453
\(471\) 21.0222 0.968652
\(472\) −38.2841 −1.76217
\(473\) −10.5689 −0.485960
\(474\) 23.2441 1.06764
\(475\) 4.96941 0.228012
\(476\) 12.8537 0.589150
\(477\) −1.52892 −0.0700043
\(478\) −14.2747 −0.652910
\(479\) 7.18123 0.328119 0.164059 0.986450i \(-0.447541\pi\)
0.164059 + 0.986450i \(0.447541\pi\)
\(480\) −6.72025 −0.306736
\(481\) −1.92939 −0.0879728
\(482\) −23.8938 −1.08833
\(483\) 1.00000 0.0455016
\(484\) −33.0367 −1.50167
\(485\) −9.14626 −0.415310
\(486\) 2.52892 0.114714
\(487\) −20.8887 −0.946558 −0.473279 0.880913i \(-0.656930\pi\)
−0.473279 + 0.880913i \(0.656930\pi\)
\(488\) −22.1863 −1.00433
\(489\) −13.3776 −0.604956
\(490\) −3.86651 −0.174671
\(491\) −20.7202 −0.935092 −0.467546 0.883969i \(-0.654862\pi\)
−0.467546 + 0.883969i \(0.654862\pi\)
\(492\) −29.2619 −1.31923
\(493\) −21.0299 −0.947140
\(494\) −2.85374 −0.128396
\(495\) −2.85374 −0.128266
\(496\) −38.3019 −1.71981
\(497\) −15.2441 −0.683792
\(498\) −2.33759 −0.104750
\(499\) −7.22629 −0.323493 −0.161747 0.986832i \(-0.551713\pi\)
−0.161747 + 0.986832i \(0.551713\pi\)
\(500\) 51.4933 2.30285
\(501\) 20.5161 0.916594
\(502\) 1.61734 0.0721856
\(503\) −32.0272 −1.42802 −0.714012 0.700133i \(-0.753124\pi\)
−0.714012 + 0.700133i \(0.753124\pi\)
\(504\) −6.05784 −0.269837
\(505\) −6.19638 −0.275735
\(506\) −4.72025 −0.209841
\(507\) −12.6345 −0.561117
\(508\) 21.9210 0.972587
\(509\) 38.3369 1.69925 0.849627 0.527384i \(-0.176827\pi\)
0.849627 + 0.527384i \(0.176827\pi\)
\(510\) 11.3070 0.500682
\(511\) −13.9822 −0.618535
\(512\) −50.4049 −2.22760
\(513\) −1.86651 −0.0824083
\(514\) −47.1379 −2.07916
\(515\) 9.35036 0.412026
\(516\) −24.8887 −1.09566
\(517\) 20.1412 0.885810
\(518\) 8.07061 0.354602
\(519\) −1.34264 −0.0589353
\(520\) −5.59952 −0.245555
\(521\) −31.2791 −1.37036 −0.685181 0.728373i \(-0.740277\pi\)
−0.685181 + 0.728373i \(0.740277\pi\)
\(522\) 18.1863 0.795992
\(523\) −29.0323 −1.26949 −0.634747 0.772720i \(-0.718896\pi\)
−0.634747 + 0.772720i \(0.718896\pi\)
\(524\) −8.20410 −0.358398
\(525\) 2.66241 0.116197
\(526\) −63.6167 −2.77382
\(527\) 17.1557 0.747313
\(528\) 12.1863 0.530340
\(529\) 1.00000 0.0434783
\(530\) 5.91157 0.256782
\(531\) −6.31977 −0.274255
\(532\) 8.20410 0.355693
\(533\) −4.02487 −0.174336
\(534\) 18.7024 0.809333
\(535\) 3.57398 0.154517
\(536\) 32.5767 1.40710
\(537\) −0.204098 −0.00880749
\(538\) −12.5868 −0.542653
\(539\) 1.86651 0.0803962
\(540\) −6.72025 −0.289193
\(541\) −21.8231 −0.938250 −0.469125 0.883132i \(-0.655431\pi\)
−0.469125 + 0.883132i \(0.655431\pi\)
\(542\) 12.4533 0.534913
\(543\) 17.4482 0.748774
\(544\) −12.8537 −0.551099
\(545\) 13.1284 0.562361
\(546\) −1.52892 −0.0654316
\(547\) 37.7502 1.61408 0.807040 0.590497i \(-0.201068\pi\)
0.807040 + 0.590497i \(0.201068\pi\)
\(548\) −66.7724 −2.85237
\(549\) −3.66241 −0.156308
\(550\) −12.5672 −0.535868
\(551\) −13.4227 −0.571825
\(552\) −6.05784 −0.257839
\(553\) −9.19133 −0.390855
\(554\) 63.4832 2.69714
\(555\) 4.87928 0.207114
\(556\) −54.8157 −2.32470
\(557\) −13.8588 −0.587216 −0.293608 0.955926i \(-0.594856\pi\)
−0.293608 + 0.955926i \(0.594856\pi\)
\(558\) −14.8359 −0.628054
\(559\) −3.42335 −0.144792
\(560\) 9.98218 0.421824
\(561\) −5.45831 −0.230450
\(562\) 66.6940 2.81332
\(563\) −36.5588 −1.54077 −0.770386 0.637578i \(-0.779936\pi\)
−0.770386 + 0.637578i \(0.779936\pi\)
\(564\) 47.4304 1.99718
\(565\) −29.6268 −1.24641
\(566\) 31.4482 1.32187
\(567\) −1.00000 −0.0419961
\(568\) 92.3463 3.87477
\(569\) 11.3147 0.474338 0.237169 0.971468i \(-0.423781\pi\)
0.237169 + 0.971468i \(0.423781\pi\)
\(570\) 7.21687 0.302281
\(571\) 27.2714 1.14127 0.570635 0.821204i \(-0.306697\pi\)
0.570635 + 0.821204i \(0.306697\pi\)
\(572\) 4.95998 0.207387
\(573\) 19.3248 0.807306
\(574\) 16.8359 0.702718
\(575\) 2.66241 0.111030
\(576\) −1.94216 −0.0809235
\(577\) 25.4660 1.06016 0.530082 0.847946i \(-0.322161\pi\)
0.530082 + 0.847946i \(0.322161\pi\)
\(578\) −21.3648 −0.888660
\(579\) −1.32482 −0.0550576
\(580\) −48.3275 −2.00669
\(581\) 0.924344 0.0383483
\(582\) 15.1284 0.627094
\(583\) −2.85374 −0.118190
\(584\) 84.7018 3.50498
\(585\) −0.924344 −0.0382169
\(586\) 61.6617 2.54722
\(587\) −5.16408 −0.213144 −0.106572 0.994305i \(-0.533988\pi\)
−0.106572 + 0.994305i \(0.533988\pi\)
\(588\) 4.39543 0.181264
\(589\) 10.9499 0.451182
\(590\) 24.4354 1.00599
\(591\) 17.5111 0.720310
\(592\) −20.8359 −0.856351
\(593\) −3.20915 −0.131784 −0.0658920 0.997827i \(-0.520989\pi\)
−0.0658920 + 0.997827i \(0.520989\pi\)
\(594\) 4.72025 0.193674
\(595\) −4.47108 −0.183296
\(596\) −2.30262 −0.0943192
\(597\) −22.1786 −0.907708
\(598\) −1.52892 −0.0625221
\(599\) −0.186278 −0.00761112 −0.00380556 0.999993i \(-0.501211\pi\)
−0.00380556 + 0.999993i \(0.501211\pi\)
\(600\) −16.1284 −0.658441
\(601\) 14.1328 0.576490 0.288245 0.957557i \(-0.406928\pi\)
0.288245 + 0.957557i \(0.406928\pi\)
\(602\) 14.3198 0.583630
\(603\) 5.37761 0.218993
\(604\) −49.7774 −2.02541
\(605\) 11.4916 0.467199
\(606\) 10.2492 0.416344
\(607\) −29.8938 −1.21335 −0.606675 0.794950i \(-0.707497\pi\)
−0.606675 + 0.794950i \(0.707497\pi\)
\(608\) −8.20410 −0.332720
\(609\) −7.19133 −0.291407
\(610\) 14.1607 0.573351
\(611\) 6.52387 0.263927
\(612\) −12.8537 −0.519582
\(613\) −27.5282 −1.11186 −0.555928 0.831231i \(-0.687637\pi\)
−0.555928 + 0.831231i \(0.687637\pi\)
\(614\) −15.5111 −0.625977
\(615\) 10.1786 0.410439
\(616\) −11.3070 −0.455572
\(617\) 35.0572 1.41135 0.705674 0.708537i \(-0.250644\pi\)
0.705674 + 0.708537i \(0.250644\pi\)
\(618\) −15.4660 −0.622135
\(619\) 21.1284 0.849224 0.424612 0.905375i \(-0.360411\pi\)
0.424612 + 0.905375i \(0.360411\pi\)
\(620\) 39.4244 1.58332
\(621\) −1.00000 −0.0401286
\(622\) −2.85374 −0.114424
\(623\) −7.39543 −0.296291
\(624\) 3.94721 0.158015
\(625\) −4.59952 −0.183981
\(626\) 64.3114 2.57040
\(627\) −3.48385 −0.139132
\(628\) 92.4015 3.68722
\(629\) 9.33254 0.372113
\(630\) 3.86651 0.154045
\(631\) 37.0145 1.47352 0.736761 0.676153i \(-0.236354\pi\)
0.736761 + 0.676153i \(0.236354\pi\)
\(632\) 55.6796 2.21481
\(633\) 2.40048 0.0954103
\(634\) −19.3325 −0.767793
\(635\) −7.62506 −0.302591
\(636\) −6.72025 −0.266475
\(637\) 0.604574 0.0239541
\(638\) 33.9448 1.34389
\(639\) 15.2441 0.603048
\(640\) 20.9499 0.828117
\(641\) −39.9993 −1.57988 −0.789939 0.613185i \(-0.789888\pi\)
−0.789939 + 0.613185i \(0.789888\pi\)
\(642\) −5.91157 −0.233311
\(643\) −31.9193 −1.25877 −0.629387 0.777092i \(-0.716694\pi\)
−0.629387 + 0.777092i \(0.716694\pi\)
\(644\) 4.39543 0.173204
\(645\) 8.65736 0.340883
\(646\) 13.8036 0.543096
\(647\) −19.1005 −0.750919 −0.375460 0.926839i \(-0.622515\pi\)
−0.375460 + 0.926839i \(0.622515\pi\)
\(648\) 6.05784 0.237974
\(649\) −11.7959 −0.463030
\(650\) −4.07061 −0.159662
\(651\) 5.86651 0.229927
\(652\) −58.8003 −2.30280
\(653\) −26.3998 −1.03310 −0.516552 0.856256i \(-0.672785\pi\)
−0.516552 + 0.856256i \(0.672785\pi\)
\(654\) −21.7152 −0.849131
\(655\) 2.85374 0.111505
\(656\) −43.4654 −1.69704
\(657\) 13.9822 0.545497
\(658\) −27.2892 −1.06384
\(659\) 7.98218 0.310942 0.155471 0.987840i \(-0.450311\pi\)
0.155471 + 0.987840i \(0.450311\pi\)
\(660\) −12.5434 −0.488251
\(661\) 45.6796 1.77673 0.888364 0.459139i \(-0.151842\pi\)
0.888364 + 0.459139i \(0.151842\pi\)
\(662\) −25.6718 −0.997764
\(663\) −1.76798 −0.0686627
\(664\) −5.59952 −0.217304
\(665\) −2.85374 −0.110663
\(666\) −8.07061 −0.312730
\(667\) −7.19133 −0.278449
\(668\) 90.1772 3.48906
\(669\) −14.0528 −0.543312
\(670\) −20.7926 −0.803287
\(671\) −6.83592 −0.263898
\(672\) −4.39543 −0.169557
\(673\) 23.0501 0.888517 0.444258 0.895899i \(-0.353467\pi\)
0.444258 + 0.895899i \(0.353467\pi\)
\(674\) 11.6446 0.448533
\(675\) −2.66241 −0.102476
\(676\) −55.5340 −2.13592
\(677\) 24.0350 0.923739 0.461869 0.886948i \(-0.347179\pi\)
0.461869 + 0.886948i \(0.347179\pi\)
\(678\) 49.0044 1.88200
\(679\) −5.98218 −0.229575
\(680\) 27.0851 1.03867
\(681\) 14.8537 0.569196
\(682\) −27.6914 −1.06036
\(683\) 23.5740 0.902033 0.451017 0.892516i \(-0.351061\pi\)
0.451017 + 0.892516i \(0.351061\pi\)
\(684\) −8.20410 −0.313692
\(685\) 23.2263 0.887431
\(686\) −2.52892 −0.0965545
\(687\) −23.1106 −0.881725
\(688\) −36.9694 −1.40945
\(689\) −0.924344 −0.0352147
\(690\) 3.86651 0.147195
\(691\) −26.2663 −0.999218 −0.499609 0.866251i \(-0.666523\pi\)
−0.499609 + 0.866251i \(0.666523\pi\)
\(692\) −5.90147 −0.224340
\(693\) −1.86651 −0.0709028
\(694\) −39.3853 −1.49505
\(695\) 19.0673 0.723262
\(696\) 43.5639 1.65128
\(697\) 19.4684 0.737419
\(698\) 63.7952 2.41468
\(699\) −21.1207 −0.798859
\(700\) 11.7024 0.442310
\(701\) 34.8282 1.31544 0.657721 0.753261i \(-0.271520\pi\)
0.657721 + 0.753261i \(0.271520\pi\)
\(702\) 1.52892 0.0577053
\(703\) 5.95664 0.224659
\(704\) −3.62506 −0.136625
\(705\) −16.4983 −0.621363
\(706\) 72.0895 2.71312
\(707\) −4.05279 −0.152421
\(708\) −27.7781 −1.04396
\(709\) 10.4176 0.391242 0.195621 0.980680i \(-0.437328\pi\)
0.195621 + 0.980680i \(0.437328\pi\)
\(710\) −58.9415 −2.21203
\(711\) 9.19133 0.344702
\(712\) 44.8003 1.67896
\(713\) 5.86651 0.219702
\(714\) 7.39543 0.276767
\(715\) −1.72530 −0.0645224
\(716\) −0.897099 −0.0335261
\(717\) −5.64459 −0.210801
\(718\) −82.1167 −3.06457
\(719\) 10.2593 0.382606 0.191303 0.981531i \(-0.438729\pi\)
0.191303 + 0.981531i \(0.438729\pi\)
\(720\) −9.98218 −0.372014
\(721\) 6.11567 0.227760
\(722\) −39.2391 −1.46033
\(723\) −9.44821 −0.351383
\(724\) 76.6923 2.85025
\(725\) −19.1463 −0.711074
\(726\) −19.0077 −0.705443
\(727\) −31.4328 −1.16578 −0.582888 0.812552i \(-0.698078\pi\)
−0.582888 + 0.812552i \(0.698078\pi\)
\(728\) −3.66241 −0.135738
\(729\) 1.00000 0.0370370
\(730\) −54.0622 −2.00093
\(731\) 16.5588 0.612451
\(732\) −16.0979 −0.594994
\(733\) 1.32482 0.0489333 0.0244667 0.999701i \(-0.492211\pi\)
0.0244667 + 0.999701i \(0.492211\pi\)
\(734\) −17.3776 −0.641419
\(735\) −1.52892 −0.0563950
\(736\) −4.39543 −0.162018
\(737\) 10.0373 0.369730
\(738\) −16.8359 −0.619739
\(739\) 1.33254 0.0490183 0.0245091 0.999700i \(-0.492198\pi\)
0.0245091 + 0.999700i \(0.492198\pi\)
\(740\) 21.4465 0.788389
\(741\) −1.12844 −0.0414544
\(742\) 3.86651 0.141944
\(743\) 8.06289 0.295799 0.147899 0.989002i \(-0.452749\pi\)
0.147899 + 0.989002i \(0.452749\pi\)
\(744\) −35.5383 −1.30290
\(745\) 0.800952 0.0293446
\(746\) −26.9516 −0.986768
\(747\) −0.924344 −0.0338200
\(748\) −23.9916 −0.877220
\(749\) 2.33759 0.0854137
\(750\) 29.6268 1.08182
\(751\) 8.39980 0.306513 0.153257 0.988186i \(-0.451024\pi\)
0.153257 + 0.988186i \(0.451024\pi\)
\(752\) 70.4526 2.56914
\(753\) 0.639540 0.0233061
\(754\) 10.9950 0.400412
\(755\) 17.3147 0.630147
\(756\) −4.39543 −0.159860
\(757\) 2.95998 0.107582 0.0537912 0.998552i \(-0.482869\pi\)
0.0537912 + 0.998552i \(0.482869\pi\)
\(758\) −90.8608 −3.30021
\(759\) −1.86651 −0.0677500
\(760\) 17.2875 0.627083
\(761\) −47.7774 −1.73193 −0.865965 0.500105i \(-0.833295\pi\)
−0.865965 + 0.500105i \(0.833295\pi\)
\(762\) 12.6123 0.456895
\(763\) 8.58675 0.310861
\(764\) 84.9408 3.07305
\(765\) 4.47108 0.161652
\(766\) −1.66241 −0.0600653
\(767\) −3.82077 −0.137960
\(768\) −30.7680 −1.11024
\(769\) 44.7196 1.61263 0.806315 0.591487i \(-0.201459\pi\)
0.806315 + 0.591487i \(0.201459\pi\)
\(770\) 7.21687 0.260078
\(771\) −18.6395 −0.671287
\(772\) −5.82315 −0.209580
\(773\) 22.2848 0.801529 0.400764 0.916181i \(-0.368745\pi\)
0.400764 + 0.916181i \(0.368745\pi\)
\(774\) −14.3198 −0.514714
\(775\) 15.6190 0.561053
\(776\) 36.2391 1.30091
\(777\) 3.19133 0.114488
\(778\) 64.2663 2.30406
\(779\) 12.4260 0.445208
\(780\) −4.06289 −0.145475
\(781\) 28.4533 1.01814
\(782\) 7.39543 0.264460
\(783\) 7.19133 0.256997
\(784\) 6.52892 0.233176
\(785\) −32.1412 −1.14717
\(786\) −4.72025 −0.168366
\(787\) −13.9472 −0.497164 −0.248582 0.968611i \(-0.579965\pi\)
−0.248582 + 0.968611i \(0.579965\pi\)
\(788\) 76.9687 2.74190
\(789\) −25.1557 −0.895566
\(790\) −35.5383 −1.26440
\(791\) −19.3776 −0.688988
\(792\) 11.3070 0.401777
\(793\) −2.21420 −0.0786285
\(794\) 90.3013 3.20467
\(795\) 2.33759 0.0829058
\(796\) −97.4842 −3.45524
\(797\) −26.3369 −0.932901 −0.466451 0.884547i \(-0.654468\pi\)
−0.466451 + 0.884547i \(0.654468\pi\)
\(798\) 4.72025 0.167095
\(799\) −31.5562 −1.11638
\(800\) −11.7024 −0.413743
\(801\) 7.39543 0.261305
\(802\) 48.1251 1.69936
\(803\) 26.0979 0.920973
\(804\) 23.6369 0.833608
\(805\) −1.52892 −0.0538873
\(806\) −8.96941 −0.315934
\(807\) −4.97713 −0.175203
\(808\) 24.5511 0.863705
\(809\) −36.7101 −1.29066 −0.645330 0.763904i \(-0.723280\pi\)
−0.645330 + 0.763904i \(0.723280\pi\)
\(810\) −3.86651 −0.135855
\(811\) 10.7730 0.378292 0.189146 0.981949i \(-0.439428\pi\)
0.189146 + 0.981949i \(0.439428\pi\)
\(812\) −31.6089 −1.10926
\(813\) 4.92434 0.172704
\(814\) −15.0639 −0.527988
\(815\) 20.4533 0.716447
\(816\) −19.0928 −0.668382
\(817\) 10.5689 0.369760
\(818\) −12.0706 −0.422039
\(819\) −0.604574 −0.0211255
\(820\) 44.7391 1.56236
\(821\) −10.1258 −0.353392 −0.176696 0.984265i \(-0.556541\pi\)
−0.176696 + 0.984265i \(0.556541\pi\)
\(822\) −38.4176 −1.33997
\(823\) 29.6446 1.03335 0.516673 0.856183i \(-0.327170\pi\)
0.516673 + 0.856183i \(0.327170\pi\)
\(824\) −37.0477 −1.29062
\(825\) −4.96941 −0.173013
\(826\) 15.9822 0.556091
\(827\) 42.4253 1.47527 0.737637 0.675198i \(-0.235942\pi\)
0.737637 + 0.675198i \(0.235942\pi\)
\(828\) −4.39543 −0.152752
\(829\) −3.97208 −0.137956 −0.0689780 0.997618i \(-0.521974\pi\)
−0.0689780 + 0.997618i \(0.521974\pi\)
\(830\) 3.57398 0.124055
\(831\) 25.1029 0.870810
\(832\) −1.17418 −0.0407074
\(833\) −2.92434 −0.101323
\(834\) −31.5383 −1.09208
\(835\) −31.3675 −1.08552
\(836\) −15.3130 −0.529612
\(837\) −5.86651 −0.202776
\(838\) 44.5316 1.53832
\(839\) −21.8938 −0.755856 −0.377928 0.925835i \(-0.623363\pi\)
−0.377928 + 0.925835i \(0.623363\pi\)
\(840\) 9.26193 0.319567
\(841\) 22.7152 0.783283
\(842\) 102.187 3.52161
\(843\) 26.3726 0.908319
\(844\) 10.5511 0.363184
\(845\) 19.3171 0.664528
\(846\) 27.2892 0.938221
\(847\) 7.51615 0.258258
\(848\) −9.98218 −0.342789
\(849\) 12.4354 0.426783
\(850\) 19.6897 0.675350
\(851\) 3.19133 0.109397
\(852\) 67.0044 2.29553
\(853\) −1.02220 −0.0349993 −0.0174997 0.999847i \(-0.505571\pi\)
−0.0174997 + 0.999847i \(0.505571\pi\)
\(854\) 9.26193 0.316937
\(855\) 2.85374 0.0975958
\(856\) −14.1607 −0.484004
\(857\) 39.6718 1.35516 0.677582 0.735447i \(-0.263028\pi\)
0.677582 + 0.735447i \(0.263028\pi\)
\(858\) 2.85374 0.0974250
\(859\) 47.1278 1.60798 0.803989 0.594644i \(-0.202707\pi\)
0.803989 + 0.594644i \(0.202707\pi\)
\(860\) 38.0528 1.29759
\(861\) 6.65736 0.226882
\(862\) −70.8335 −2.41260
\(863\) −16.1258 −0.548928 −0.274464 0.961597i \(-0.588500\pi\)
−0.274464 + 0.961597i \(0.588500\pi\)
\(864\) 4.39543 0.149535
\(865\) 2.05279 0.0697968
\(866\) −76.8097 −2.61010
\(867\) −8.44821 −0.286916
\(868\) 25.7858 0.875227
\(869\) 17.1557 0.581967
\(870\) −27.8053 −0.942689
\(871\) 3.25116 0.110161
\(872\) −52.0171 −1.76152
\(873\) 5.98218 0.202466
\(874\) 4.72025 0.159665
\(875\) −11.7152 −0.396046
\(876\) 61.4576 2.07646
\(877\) 34.2670 1.15711 0.578557 0.815642i \(-0.303616\pi\)
0.578557 + 0.815642i \(0.303616\pi\)
\(878\) −13.4856 −0.455116
\(879\) 24.3827 0.822407
\(880\) −18.6318 −0.628079
\(881\) −19.2091 −0.647173 −0.323586 0.946199i \(-0.604889\pi\)
−0.323586 + 0.946199i \(0.604889\pi\)
\(882\) 2.52892 0.0851531
\(883\) 46.4432 1.56294 0.781468 0.623945i \(-0.214471\pi\)
0.781468 + 0.623945i \(0.214471\pi\)
\(884\) −7.77104 −0.261368
\(885\) 9.66241 0.324798
\(886\) −45.8130 −1.53912
\(887\) 42.0350 1.41140 0.705698 0.708513i \(-0.250634\pi\)
0.705698 + 0.708513i \(0.250634\pi\)
\(888\) −19.3325 −0.648758
\(889\) −4.98723 −0.167266
\(890\) −28.5945 −0.958489
\(891\) 1.86651 0.0625304
\(892\) −61.7680 −2.06815
\(893\) −20.1412 −0.674000
\(894\) −1.32482 −0.0443086
\(895\) 0.312049 0.0104307
\(896\) 13.7024 0.457766
\(897\) −0.604574 −0.0201861
\(898\) −85.3769 −2.84907
\(899\) −42.1880 −1.40705
\(900\) −11.7024 −0.390081
\(901\) 4.47108 0.148953
\(902\) −31.4244 −1.04632
\(903\) 5.66241 0.188433
\(904\) 117.386 3.90421
\(905\) −26.6769 −0.886770
\(906\) −28.6395 −0.951485
\(907\) 35.6547 1.18389 0.591947 0.805977i \(-0.298359\pi\)
0.591947 + 0.805977i \(0.298359\pi\)
\(908\) 65.2885 2.16668
\(909\) 4.05279 0.134422
\(910\) 2.33759 0.0774904
\(911\) −3.32482 −0.110156 −0.0550781 0.998482i \(-0.517541\pi\)
−0.0550781 + 0.998482i \(0.517541\pi\)
\(912\) −12.1863 −0.403528
\(913\) −1.72530 −0.0570989
\(914\) −3.28146 −0.108541
\(915\) 5.59952 0.185115
\(916\) −101.581 −3.35633
\(917\) 1.86651 0.0616375
\(918\) −7.39543 −0.244085
\(919\) −29.8665 −0.985205 −0.492603 0.870254i \(-0.663954\pi\)
−0.492603 + 0.870254i \(0.663954\pi\)
\(920\) 9.26193 0.305357
\(921\) −6.13349 −0.202105
\(922\) −69.1456 −2.27719
\(923\) 9.21619 0.303355
\(924\) −8.20410 −0.269895
\(925\) 8.49662 0.279367
\(926\) −62.2663 −2.04620
\(927\) −6.11567 −0.200865
\(928\) 31.6089 1.03761
\(929\) −5.15636 −0.169175 −0.0845874 0.996416i \(-0.526957\pi\)
−0.0845874 + 0.996416i \(0.526957\pi\)
\(930\) 22.6829 0.743802
\(931\) −1.86651 −0.0611723
\(932\) −92.8346 −3.04090
\(933\) −1.12844 −0.0369435
\(934\) −32.0094 −1.04738
\(935\) 8.34531 0.272921
\(936\) 3.66241 0.119710
\(937\) −47.1200 −1.53934 −0.769672 0.638439i \(-0.779580\pi\)
−0.769672 + 0.638439i \(0.779580\pi\)
\(938\) −13.5995 −0.444040
\(939\) 25.4304 0.829889
\(940\) −72.5172 −2.36525
\(941\) −10.7808 −0.351442 −0.175721 0.984440i \(-0.556226\pi\)
−0.175721 + 0.984440i \(0.556226\pi\)
\(942\) 53.1634 1.73216
\(943\) 6.65736 0.216793
\(944\) −41.2613 −1.34294
\(945\) 1.52892 0.0497357
\(946\) −26.7280 −0.869001
\(947\) 42.0800 1.36742 0.683709 0.729755i \(-0.260366\pi\)
0.683709 + 0.729755i \(0.260366\pi\)
\(948\) 40.3998 1.31212
\(949\) 8.45326 0.274404
\(950\) 12.5672 0.407735
\(951\) −7.64459 −0.247893
\(952\) 17.7152 0.574153
\(953\) −28.8716 −0.935241 −0.467621 0.883929i \(-0.654889\pi\)
−0.467621 + 0.883929i \(0.654889\pi\)
\(954\) −3.86651 −0.125183
\(955\) −29.5461 −0.956088
\(956\) −24.8104 −0.802425
\(957\) 13.4227 0.433893
\(958\) 18.1607 0.586747
\(959\) 15.1913 0.490554
\(960\) 2.96941 0.0958373
\(961\) 3.41592 0.110191
\(962\) −4.87928 −0.157314
\(963\) −2.33759 −0.0753278
\(964\) −41.5289 −1.33756
\(965\) 2.02554 0.0652045
\(966\) 2.52892 0.0813666
\(967\) 30.8964 0.993562 0.496781 0.867876i \(-0.334515\pi\)
0.496781 + 0.867876i \(0.334515\pi\)
\(968\) −45.5316 −1.46344
\(969\) 5.45831 0.175346
\(970\) −23.1301 −0.742664
\(971\) −24.4176 −0.783599 −0.391799 0.920051i \(-0.628147\pi\)
−0.391799 + 0.920051i \(0.628147\pi\)
\(972\) 4.39543 0.140983
\(973\) 12.4711 0.399805
\(974\) −52.8258 −1.69265
\(975\) −1.60962 −0.0515492
\(976\) −23.9116 −0.765391
\(977\) 6.86146 0.219518 0.109759 0.993958i \(-0.464992\pi\)
0.109759 + 0.993958i \(0.464992\pi\)
\(978\) −33.8309 −1.08179
\(979\) 13.8036 0.441166
\(980\) −6.72025 −0.214670
\(981\) −8.58675 −0.274154
\(982\) −52.3998 −1.67214
\(983\) 44.9243 1.43286 0.716432 0.697657i \(-0.245774\pi\)
0.716432 + 0.697657i \(0.245774\pi\)
\(984\) −40.3292 −1.28565
\(985\) −26.7730 −0.853060
\(986\) −53.1829 −1.69369
\(987\) −10.7909 −0.343477
\(988\) −4.95998 −0.157798
\(989\) 5.66241 0.180054
\(990\) −7.21687 −0.229367
\(991\) 8.31205 0.264041 0.132020 0.991247i \(-0.457854\pi\)
0.132020 + 0.991247i \(0.457854\pi\)
\(992\) −25.7858 −0.818700
\(993\) −10.1513 −0.322142
\(994\) −38.5511 −1.22277
\(995\) 33.9092 1.07499
\(996\) −4.06289 −0.128737
\(997\) −22.3191 −0.706853 −0.353426 0.935462i \(-0.614984\pi\)
−0.353426 + 0.935462i \(0.614984\pi\)
\(998\) −18.2747 −0.578476
\(999\) −3.19133 −0.100969
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 483.2.a.h.1.3 3
3.2 odd 2 1449.2.a.l.1.1 3
4.3 odd 2 7728.2.a.bt.1.1 3
7.6 odd 2 3381.2.a.v.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.h.1.3 3 1.1 even 1 trivial
1449.2.a.l.1.1 3 3.2 odd 2
3381.2.a.v.1.3 3 7.6 odd 2
7728.2.a.bt.1.1 3 4.3 odd 2