Properties

Label 547.2.a.b.1.11
Level $547$
Weight $2$
Character 547.1
Self dual yes
Analytic conductor $4.368$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.36781699056\)
Analytic rank: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + 4048 x^{4} + 3834 x^{3} - 1851 x^{2} - 654 x + 328\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-0.735255\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.735255 q^{2} +0.544167 q^{3} -1.45940 q^{4} +0.962787 q^{5} +0.400102 q^{6} -3.25298 q^{7} -2.54354 q^{8} -2.70388 q^{9} +O(q^{10})\) \(q+0.735255 q^{2} +0.544167 q^{3} -1.45940 q^{4} +0.962787 q^{5} +0.400102 q^{6} -3.25298 q^{7} -2.54354 q^{8} -2.70388 q^{9} +0.707894 q^{10} -0.883096 q^{11} -0.794158 q^{12} -4.48154 q^{13} -2.39177 q^{14} +0.523917 q^{15} +1.04865 q^{16} -3.18294 q^{17} -1.98804 q^{18} +4.12466 q^{19} -1.40509 q^{20} -1.77017 q^{21} -0.649301 q^{22} +3.73970 q^{23} -1.38411 q^{24} -4.07304 q^{25} -3.29508 q^{26} -3.10387 q^{27} +4.74740 q^{28} +6.33388 q^{29} +0.385213 q^{30} -8.47939 q^{31} +5.85811 q^{32} -0.480552 q^{33} -2.34028 q^{34} -3.13193 q^{35} +3.94604 q^{36} +11.0375 q^{37} +3.03268 q^{38} -2.43871 q^{39} -2.44889 q^{40} +1.41138 q^{41} -1.30152 q^{42} -9.31097 q^{43} +1.28879 q^{44} -2.60326 q^{45} +2.74963 q^{46} -5.82191 q^{47} +0.570639 q^{48} +3.58188 q^{49} -2.99473 q^{50} -1.73205 q^{51} +6.54036 q^{52} -7.06826 q^{53} -2.28213 q^{54} -0.850233 q^{55} +8.27409 q^{56} +2.24450 q^{57} +4.65702 q^{58} +12.9274 q^{59} -0.764605 q^{60} -3.04777 q^{61} -6.23452 q^{62} +8.79567 q^{63} +2.20991 q^{64} -4.31477 q^{65} -0.353328 q^{66} -9.15218 q^{67} +4.64518 q^{68} +2.03502 q^{69} -2.30277 q^{70} -4.57601 q^{71} +6.87744 q^{72} -14.4453 q^{73} +8.11538 q^{74} -2.21642 q^{75} -6.01952 q^{76} +2.87269 q^{77} -1.79308 q^{78} +7.20620 q^{79} +1.00962 q^{80} +6.42262 q^{81} +1.03773 q^{82} +7.39056 q^{83} +2.58338 q^{84} -3.06450 q^{85} -6.84594 q^{86} +3.44669 q^{87} +2.24619 q^{88} +0.838265 q^{89} -1.91406 q^{90} +14.5784 q^{91} -5.45771 q^{92} -4.61421 q^{93} -4.28059 q^{94} +3.97117 q^{95} +3.18779 q^{96} +0.475381 q^{97} +2.63360 q^{98} +2.38779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.735255 0.519904 0.259952 0.965622i \(-0.416293\pi\)
0.259952 + 0.965622i \(0.416293\pi\)
\(3\) 0.544167 0.314175 0.157088 0.987585i \(-0.449790\pi\)
0.157088 + 0.987585i \(0.449790\pi\)
\(4\) −1.45940 −0.729700
\(5\) 0.962787 0.430571 0.215286 0.976551i \(-0.430932\pi\)
0.215286 + 0.976551i \(0.430932\pi\)
\(6\) 0.400102 0.163341
\(7\) −3.25298 −1.22951 −0.614755 0.788718i \(-0.710745\pi\)
−0.614755 + 0.788718i \(0.710745\pi\)
\(8\) −2.54354 −0.899278
\(9\) −2.70388 −0.901294
\(10\) 0.707894 0.223856
\(11\) −0.883096 −0.266263 −0.133132 0.991098i \(-0.542503\pi\)
−0.133132 + 0.991098i \(0.542503\pi\)
\(12\) −0.794158 −0.229254
\(13\) −4.48154 −1.24296 −0.621478 0.783431i \(-0.713468\pi\)
−0.621478 + 0.783431i \(0.713468\pi\)
\(14\) −2.39177 −0.639228
\(15\) 0.523917 0.135275
\(16\) 1.04865 0.262161
\(17\) −3.18294 −0.771977 −0.385988 0.922504i \(-0.626140\pi\)
−0.385988 + 0.922504i \(0.626140\pi\)
\(18\) −1.98804 −0.468586
\(19\) 4.12466 0.946261 0.473131 0.880992i \(-0.343124\pi\)
0.473131 + 0.880992i \(0.343124\pi\)
\(20\) −1.40509 −0.314188
\(21\) −1.77017 −0.386282
\(22\) −0.649301 −0.138431
\(23\) 3.73970 0.779781 0.389890 0.920861i \(-0.372513\pi\)
0.389890 + 0.920861i \(0.372513\pi\)
\(24\) −1.38411 −0.282531
\(25\) −4.07304 −0.814608
\(26\) −3.29508 −0.646218
\(27\) −3.10387 −0.597339
\(28\) 4.74740 0.897174
\(29\) 6.33388 1.17617 0.588086 0.808798i \(-0.299881\pi\)
0.588086 + 0.808798i \(0.299881\pi\)
\(30\) 0.385213 0.0703300
\(31\) −8.47939 −1.52294 −0.761472 0.648198i \(-0.775523\pi\)
−0.761472 + 0.648198i \(0.775523\pi\)
\(32\) 5.85811 1.03558
\(33\) −0.480552 −0.0836533
\(34\) −2.34028 −0.401354
\(35\) −3.13193 −0.529392
\(36\) 3.94604 0.657674
\(37\) 11.0375 1.81455 0.907276 0.420535i \(-0.138158\pi\)
0.907276 + 0.420535i \(0.138158\pi\)
\(38\) 3.03268 0.491965
\(39\) −2.43871 −0.390506
\(40\) −2.44889 −0.387203
\(41\) 1.41138 0.220421 0.110210 0.993908i \(-0.464848\pi\)
0.110210 + 0.993908i \(0.464848\pi\)
\(42\) −1.30152 −0.200829
\(43\) −9.31097 −1.41991 −0.709955 0.704247i \(-0.751285\pi\)
−0.709955 + 0.704247i \(0.751285\pi\)
\(44\) 1.28879 0.194292
\(45\) −2.60326 −0.388071
\(46\) 2.74963 0.405411
\(47\) −5.82191 −0.849213 −0.424606 0.905378i \(-0.639587\pi\)
−0.424606 + 0.905378i \(0.639587\pi\)
\(48\) 0.570639 0.0823646
\(49\) 3.58188 0.511697
\(50\) −2.99473 −0.423518
\(51\) −1.73205 −0.242536
\(52\) 6.54036 0.906985
\(53\) −7.06826 −0.970900 −0.485450 0.874264i \(-0.661344\pi\)
−0.485450 + 0.874264i \(0.661344\pi\)
\(54\) −2.28213 −0.310559
\(55\) −0.850233 −0.114645
\(56\) 8.27409 1.10567
\(57\) 2.24450 0.297292
\(58\) 4.65702 0.611497
\(59\) 12.9274 1.68301 0.841503 0.540252i \(-0.181671\pi\)
0.841503 + 0.540252i \(0.181671\pi\)
\(60\) −0.764605 −0.0987100
\(61\) −3.04777 −0.390227 −0.195114 0.980781i \(-0.562508\pi\)
−0.195114 + 0.980781i \(0.562508\pi\)
\(62\) −6.23452 −0.791784
\(63\) 8.79567 1.10815
\(64\) 2.20991 0.276239
\(65\) −4.31477 −0.535182
\(66\) −0.353328 −0.0434917
\(67\) −9.15218 −1.11812 −0.559059 0.829128i \(-0.688837\pi\)
−0.559059 + 0.829128i \(0.688837\pi\)
\(68\) 4.64518 0.563311
\(69\) 2.03502 0.244988
\(70\) −2.30277 −0.275233
\(71\) −4.57601 −0.543072 −0.271536 0.962428i \(-0.587532\pi\)
−0.271536 + 0.962428i \(0.587532\pi\)
\(72\) 6.87744 0.810514
\(73\) −14.4453 −1.69070 −0.845349 0.534215i \(-0.820607\pi\)
−0.845349 + 0.534215i \(0.820607\pi\)
\(74\) 8.11538 0.943393
\(75\) −2.21642 −0.255930
\(76\) −6.01952 −0.690486
\(77\) 2.87269 0.327374
\(78\) −1.79308 −0.203026
\(79\) 7.20620 0.810761 0.405381 0.914148i \(-0.367139\pi\)
0.405381 + 0.914148i \(0.367139\pi\)
\(80\) 1.00962 0.112879
\(81\) 6.42262 0.713625
\(82\) 1.03773 0.114598
\(83\) 7.39056 0.811219 0.405610 0.914046i \(-0.367059\pi\)
0.405610 + 0.914046i \(0.367059\pi\)
\(84\) 2.58338 0.281870
\(85\) −3.06450 −0.332391
\(86\) −6.84594 −0.738217
\(87\) 3.44669 0.369524
\(88\) 2.24619 0.239445
\(89\) 0.838265 0.0888559 0.0444280 0.999013i \(-0.485853\pi\)
0.0444280 + 0.999013i \(0.485853\pi\)
\(90\) −1.91406 −0.201760
\(91\) 14.5784 1.52823
\(92\) −5.45771 −0.569006
\(93\) −4.61421 −0.478471
\(94\) −4.28059 −0.441509
\(95\) 3.97117 0.407433
\(96\) 3.18779 0.325353
\(97\) 0.475381 0.0482676 0.0241338 0.999709i \(-0.492317\pi\)
0.0241338 + 0.999709i \(0.492317\pi\)
\(98\) 2.63360 0.266033
\(99\) 2.38779 0.239982
\(100\) 5.94419 0.594419
\(101\) −3.07939 −0.306411 −0.153205 0.988194i \(-0.548960\pi\)
−0.153205 + 0.988194i \(0.548960\pi\)
\(102\) −1.27350 −0.126095
\(103\) −3.71378 −0.365929 −0.182965 0.983119i \(-0.558569\pi\)
−0.182965 + 0.983119i \(0.558569\pi\)
\(104\) 11.3990 1.11776
\(105\) −1.70429 −0.166322
\(106\) −5.19698 −0.504775
\(107\) 16.1036 1.55680 0.778398 0.627771i \(-0.216032\pi\)
0.778398 + 0.627771i \(0.216032\pi\)
\(108\) 4.52978 0.435878
\(109\) 2.61098 0.250087 0.125043 0.992151i \(-0.460093\pi\)
0.125043 + 0.992151i \(0.460093\pi\)
\(110\) −0.625139 −0.0596046
\(111\) 6.00624 0.570087
\(112\) −3.41122 −0.322330
\(113\) −12.2204 −1.14960 −0.574798 0.818295i \(-0.694919\pi\)
−0.574798 + 0.818295i \(0.694919\pi\)
\(114\) 1.65028 0.154563
\(115\) 3.60053 0.335751
\(116\) −9.24367 −0.858253
\(117\) 12.1176 1.12027
\(118\) 9.50495 0.875002
\(119\) 10.3540 0.949154
\(120\) −1.33261 −0.121650
\(121\) −10.2201 −0.929104
\(122\) −2.24089 −0.202881
\(123\) 0.768028 0.0692508
\(124\) 12.3748 1.11129
\(125\) −8.73541 −0.781318
\(126\) 6.46707 0.576132
\(127\) 5.90845 0.524290 0.262145 0.965028i \(-0.415570\pi\)
0.262145 + 0.965028i \(0.415570\pi\)
\(128\) −10.0914 −0.891959
\(129\) −5.06673 −0.446100
\(130\) −3.17246 −0.278243
\(131\) 4.91027 0.429012 0.214506 0.976723i \(-0.431186\pi\)
0.214506 + 0.976723i \(0.431186\pi\)
\(132\) 0.701317 0.0610418
\(133\) −13.4174 −1.16344
\(134\) −6.72919 −0.581314
\(135\) −2.98836 −0.257197
\(136\) 8.09595 0.694222
\(137\) −8.29905 −0.709036 −0.354518 0.935049i \(-0.615355\pi\)
−0.354518 + 0.935049i \(0.615355\pi\)
\(138\) 1.49626 0.127370
\(139\) 21.0776 1.78778 0.893889 0.448288i \(-0.147966\pi\)
0.893889 + 0.448288i \(0.147966\pi\)
\(140\) 4.57073 0.386297
\(141\) −3.16809 −0.266802
\(142\) −3.36453 −0.282345
\(143\) 3.95763 0.330954
\(144\) −2.83541 −0.236284
\(145\) 6.09818 0.506426
\(146\) −10.6210 −0.879001
\(147\) 1.94914 0.160762
\(148\) −16.1081 −1.32408
\(149\) −20.9236 −1.71413 −0.857063 0.515212i \(-0.827713\pi\)
−0.857063 + 0.515212i \(0.827713\pi\)
\(150\) −1.62963 −0.133059
\(151\) −12.2666 −0.998241 −0.499121 0.866533i \(-0.666344\pi\)
−0.499121 + 0.866533i \(0.666344\pi\)
\(152\) −10.4912 −0.850952
\(153\) 8.60630 0.695778
\(154\) 2.11216 0.170203
\(155\) −8.16385 −0.655736
\(156\) 3.55905 0.284952
\(157\) 9.63793 0.769191 0.384595 0.923085i \(-0.374341\pi\)
0.384595 + 0.923085i \(0.374341\pi\)
\(158\) 5.29840 0.421518
\(159\) −3.84632 −0.305033
\(160\) 5.64011 0.445890
\(161\) −12.1652 −0.958749
\(162\) 4.72227 0.371016
\(163\) 11.8440 0.927693 0.463847 0.885915i \(-0.346469\pi\)
0.463847 + 0.885915i \(0.346469\pi\)
\(164\) −2.05977 −0.160841
\(165\) −0.462669 −0.0360187
\(166\) 5.43395 0.421756
\(167\) −18.8572 −1.45922 −0.729609 0.683865i \(-0.760298\pi\)
−0.729609 + 0.683865i \(0.760298\pi\)
\(168\) 4.50249 0.347375
\(169\) 7.08424 0.544941
\(170\) −2.25319 −0.172812
\(171\) −11.1526 −0.852859
\(172\) 13.5884 1.03611
\(173\) −15.1822 −1.15428 −0.577140 0.816645i \(-0.695831\pi\)
−0.577140 + 0.816645i \(0.695831\pi\)
\(174\) 2.53420 0.192117
\(175\) 13.2495 1.00157
\(176\) −0.926054 −0.0698040
\(177\) 7.03468 0.528759
\(178\) 0.616339 0.0461966
\(179\) −2.57897 −0.192761 −0.0963806 0.995345i \(-0.530727\pi\)
−0.0963806 + 0.995345i \(0.530727\pi\)
\(180\) 3.79920 0.283176
\(181\) −9.50776 −0.706706 −0.353353 0.935490i \(-0.614959\pi\)
−0.353353 + 0.935490i \(0.614959\pi\)
\(182\) 10.7188 0.794532
\(183\) −1.65850 −0.122600
\(184\) −9.51208 −0.701240
\(185\) 10.6268 0.781295
\(186\) −3.39262 −0.248759
\(187\) 2.81084 0.205549
\(188\) 8.49649 0.619670
\(189\) 10.0968 0.734435
\(190\) 2.91982 0.211826
\(191\) 6.20885 0.449257 0.224628 0.974444i \(-0.427883\pi\)
0.224628 + 0.974444i \(0.427883\pi\)
\(192\) 1.20256 0.0867875
\(193\) −19.6307 −1.41305 −0.706526 0.707687i \(-0.749739\pi\)
−0.706526 + 0.707687i \(0.749739\pi\)
\(194\) 0.349526 0.0250945
\(195\) −2.34796 −0.168141
\(196\) −5.22739 −0.373385
\(197\) 26.3638 1.87834 0.939171 0.343449i \(-0.111595\pi\)
0.939171 + 0.343449i \(0.111595\pi\)
\(198\) 1.75563 0.124767
\(199\) −5.17965 −0.367176 −0.183588 0.983003i \(-0.558771\pi\)
−0.183588 + 0.983003i \(0.558771\pi\)
\(200\) 10.3600 0.732559
\(201\) −4.98032 −0.351285
\(202\) −2.26414 −0.159304
\(203\) −20.6040 −1.44612
\(204\) 2.52776 0.176978
\(205\) 1.35886 0.0949069
\(206\) −2.73058 −0.190248
\(207\) −10.1117 −0.702812
\(208\) −4.69955 −0.325855
\(209\) −3.64247 −0.251955
\(210\) −1.25309 −0.0864714
\(211\) 11.3624 0.782217 0.391109 0.920344i \(-0.372092\pi\)
0.391109 + 0.920344i \(0.372092\pi\)
\(212\) 10.3154 0.708466
\(213\) −2.49011 −0.170620
\(214\) 11.8403 0.809385
\(215\) −8.96448 −0.611373
\(216\) 7.89482 0.537174
\(217\) 27.5833 1.87248
\(218\) 1.91974 0.130021
\(219\) −7.86068 −0.531175
\(220\) 1.24083 0.0836567
\(221\) 14.2645 0.959534
\(222\) 4.41612 0.296391
\(223\) 18.9951 1.27201 0.636003 0.771686i \(-0.280587\pi\)
0.636003 + 0.771686i \(0.280587\pi\)
\(224\) −19.0563 −1.27325
\(225\) 11.0130 0.734201
\(226\) −8.98510 −0.597680
\(227\) 11.7708 0.781254 0.390627 0.920549i \(-0.372258\pi\)
0.390627 + 0.920549i \(0.372258\pi\)
\(228\) −3.27563 −0.216934
\(229\) 6.31464 0.417283 0.208641 0.977992i \(-0.433096\pi\)
0.208641 + 0.977992i \(0.433096\pi\)
\(230\) 2.64731 0.174558
\(231\) 1.56323 0.102853
\(232\) −16.1105 −1.05771
\(233\) 20.7839 1.36160 0.680799 0.732470i \(-0.261633\pi\)
0.680799 + 0.732470i \(0.261633\pi\)
\(234\) 8.90951 0.582433
\(235\) −5.60526 −0.365647
\(236\) −18.8663 −1.22809
\(237\) 3.92138 0.254721
\(238\) 7.61287 0.493469
\(239\) −23.8405 −1.54212 −0.771058 0.636765i \(-0.780272\pi\)
−0.771058 + 0.636765i \(0.780272\pi\)
\(240\) 0.549403 0.0354638
\(241\) 1.62031 0.104374 0.0521868 0.998637i \(-0.483381\pi\)
0.0521868 + 0.998637i \(0.483381\pi\)
\(242\) −7.51442 −0.483045
\(243\) 12.8066 0.821543
\(244\) 4.44792 0.284749
\(245\) 3.44859 0.220322
\(246\) 0.564697 0.0360038
\(247\) −18.4848 −1.17616
\(248\) 21.5677 1.36955
\(249\) 4.02170 0.254865
\(250\) −6.42276 −0.406211
\(251\) −10.7109 −0.676064 −0.338032 0.941135i \(-0.609761\pi\)
−0.338032 + 0.941135i \(0.609761\pi\)
\(252\) −12.8364 −0.808617
\(253\) −3.30251 −0.207627
\(254\) 4.34422 0.272581
\(255\) −1.66760 −0.104429
\(256\) −11.8396 −0.739972
\(257\) −28.7954 −1.79621 −0.898105 0.439781i \(-0.855056\pi\)
−0.898105 + 0.439781i \(0.855056\pi\)
\(258\) −3.72534 −0.231929
\(259\) −35.9047 −2.23101
\(260\) 6.29698 0.390522
\(261\) −17.1261 −1.06008
\(262\) 3.61030 0.223045
\(263\) −27.1652 −1.67508 −0.837539 0.546378i \(-0.816006\pi\)
−0.837539 + 0.546378i \(0.816006\pi\)
\(264\) 1.22230 0.0752276
\(265\) −6.80523 −0.418042
\(266\) −9.86523 −0.604876
\(267\) 0.456156 0.0279163
\(268\) 13.3567 0.815890
\(269\) −19.2182 −1.17176 −0.585878 0.810399i \(-0.699250\pi\)
−0.585878 + 0.810399i \(0.699250\pi\)
\(270\) −2.19721 −0.133718
\(271\) −9.73786 −0.591533 −0.295766 0.955260i \(-0.595575\pi\)
−0.295766 + 0.955260i \(0.595575\pi\)
\(272\) −3.33778 −0.202382
\(273\) 7.93308 0.480132
\(274\) −6.10192 −0.368631
\(275\) 3.59689 0.216900
\(276\) −2.96991 −0.178767
\(277\) −26.8931 −1.61585 −0.807925 0.589285i \(-0.799409\pi\)
−0.807925 + 0.589285i \(0.799409\pi\)
\(278\) 15.4974 0.929474
\(279\) 22.9273 1.37262
\(280\) 7.96619 0.476071
\(281\) −4.21282 −0.251316 −0.125658 0.992074i \(-0.540104\pi\)
−0.125658 + 0.992074i \(0.540104\pi\)
\(282\) −2.32936 −0.138711
\(283\) 31.3587 1.86408 0.932039 0.362357i \(-0.118028\pi\)
0.932039 + 0.362357i \(0.118028\pi\)
\(284\) 6.67822 0.396280
\(285\) 2.16098 0.128005
\(286\) 2.90987 0.172064
\(287\) −4.59120 −0.271010
\(288\) −15.8396 −0.933359
\(289\) −6.86888 −0.404052
\(290\) 4.48372 0.263293
\(291\) 0.258687 0.0151645
\(292\) 21.0815 1.23370
\(293\) −15.8890 −0.928244 −0.464122 0.885771i \(-0.653630\pi\)
−0.464122 + 0.885771i \(0.653630\pi\)
\(294\) 1.43312 0.0835811
\(295\) 12.4463 0.724654
\(296\) −28.0743 −1.63179
\(297\) 2.74101 0.159050
\(298\) −15.3842 −0.891181
\(299\) −16.7596 −0.969234
\(300\) 3.23464 0.186752
\(301\) 30.2884 1.74579
\(302\) −9.01908 −0.518990
\(303\) −1.67570 −0.0962667
\(304\) 4.32530 0.248073
\(305\) −2.93436 −0.168021
\(306\) 6.32783 0.361738
\(307\) −13.7030 −0.782070 −0.391035 0.920376i \(-0.627883\pi\)
−0.391035 + 0.920376i \(0.627883\pi\)
\(308\) −4.19241 −0.238884
\(309\) −2.02092 −0.114966
\(310\) −6.00251 −0.340920
\(311\) 6.49422 0.368253 0.184127 0.982903i \(-0.441054\pi\)
0.184127 + 0.982903i \(0.441054\pi\)
\(312\) 6.20296 0.351174
\(313\) 8.26403 0.467111 0.233555 0.972344i \(-0.424964\pi\)
0.233555 + 0.972344i \(0.424964\pi\)
\(314\) 7.08634 0.399905
\(315\) 8.46836 0.477138
\(316\) −10.5167 −0.591612
\(317\) −28.1441 −1.58073 −0.790364 0.612638i \(-0.790108\pi\)
−0.790364 + 0.612638i \(0.790108\pi\)
\(318\) −2.82803 −0.158588
\(319\) −5.59343 −0.313172
\(320\) 2.12768 0.118941
\(321\) 8.76307 0.489107
\(322\) −8.94450 −0.498457
\(323\) −13.1285 −0.730492
\(324\) −9.37317 −0.520732
\(325\) 18.2535 1.01252
\(326\) 8.70836 0.482312
\(327\) 1.42081 0.0785710
\(328\) −3.58991 −0.198220
\(329\) 18.9386 1.04412
\(330\) −0.340180 −0.0187263
\(331\) −1.78319 −0.0980130 −0.0490065 0.998798i \(-0.515606\pi\)
−0.0490065 + 0.998798i \(0.515606\pi\)
\(332\) −10.7858 −0.591947
\(333\) −29.8441 −1.63545
\(334\) −13.8649 −0.758653
\(335\) −8.81160 −0.481429
\(336\) −1.85628 −0.101268
\(337\) 17.5528 0.956160 0.478080 0.878316i \(-0.341333\pi\)
0.478080 + 0.878316i \(0.341333\pi\)
\(338\) 5.20873 0.283317
\(339\) −6.64993 −0.361175
\(340\) 4.47232 0.242546
\(341\) 7.48811 0.405504
\(342\) −8.20000 −0.443405
\(343\) 11.1191 0.600374
\(344\) 23.6829 1.27689
\(345\) 1.95929 0.105485
\(346\) −11.1628 −0.600115
\(347\) 14.8308 0.796160 0.398080 0.917351i \(-0.369677\pi\)
0.398080 + 0.917351i \(0.369677\pi\)
\(348\) −5.03010 −0.269642
\(349\) −34.3697 −1.83977 −0.919884 0.392190i \(-0.871718\pi\)
−0.919884 + 0.392190i \(0.871718\pi\)
\(350\) 9.74178 0.520720
\(351\) 13.9101 0.742467
\(352\) −5.17327 −0.275736
\(353\) −16.1758 −0.860949 −0.430474 0.902603i \(-0.641654\pi\)
−0.430474 + 0.902603i \(0.641654\pi\)
\(354\) 5.17229 0.274904
\(355\) −4.40572 −0.233831
\(356\) −1.22336 −0.0648381
\(357\) 5.63433 0.298201
\(358\) −1.89620 −0.100217
\(359\) 17.7167 0.935053 0.467526 0.883979i \(-0.345145\pi\)
0.467526 + 0.883979i \(0.345145\pi\)
\(360\) 6.62151 0.348984
\(361\) −1.98721 −0.104590
\(362\) −6.99063 −0.367419
\(363\) −5.56147 −0.291901
\(364\) −21.2757 −1.11515
\(365\) −13.9078 −0.727966
\(366\) −1.21942 −0.0637401
\(367\) 7.29148 0.380612 0.190306 0.981725i \(-0.439052\pi\)
0.190306 + 0.981725i \(0.439052\pi\)
\(368\) 3.92162 0.204428
\(369\) −3.81621 −0.198664
\(370\) 7.81338 0.406198
\(371\) 22.9929 1.19373
\(372\) 6.73397 0.349140
\(373\) 19.4135 1.00520 0.502598 0.864520i \(-0.332378\pi\)
0.502598 + 0.864520i \(0.332378\pi\)
\(374\) 2.06669 0.106866
\(375\) −4.75352 −0.245471
\(376\) 14.8083 0.763678
\(377\) −28.3856 −1.46193
\(378\) 7.42374 0.381836
\(379\) 21.5543 1.10717 0.553586 0.832792i \(-0.313259\pi\)
0.553586 + 0.832792i \(0.313259\pi\)
\(380\) −5.79552 −0.297304
\(381\) 3.21519 0.164719
\(382\) 4.56509 0.233571
\(383\) −8.69462 −0.444274 −0.222137 0.975015i \(-0.571303\pi\)
−0.222137 + 0.975015i \(0.571303\pi\)
\(384\) −5.49139 −0.280231
\(385\) 2.76579 0.140958
\(386\) −14.4336 −0.734652
\(387\) 25.1758 1.27976
\(388\) −0.693771 −0.0352209
\(389\) 20.0986 1.01904 0.509520 0.860459i \(-0.329823\pi\)
0.509520 + 0.860459i \(0.329823\pi\)
\(390\) −1.72635 −0.0874171
\(391\) −11.9032 −0.601973
\(392\) −9.11066 −0.460158
\(393\) 2.67201 0.134785
\(394\) 19.3841 0.976558
\(395\) 6.93804 0.349091
\(396\) −3.48473 −0.175114
\(397\) −22.3318 −1.12080 −0.560402 0.828221i \(-0.689353\pi\)
−0.560402 + 0.828221i \(0.689353\pi\)
\(398\) −3.80836 −0.190896
\(399\) −7.30132 −0.365523
\(400\) −4.27118 −0.213559
\(401\) −1.95708 −0.0977321 −0.0488661 0.998805i \(-0.515561\pi\)
−0.0488661 + 0.998805i \(0.515561\pi\)
\(402\) −3.66181 −0.182634
\(403\) 38.0008 1.89295
\(404\) 4.49406 0.223588
\(405\) 6.18362 0.307266
\(406\) −15.1492 −0.751842
\(407\) −9.74716 −0.483149
\(408\) 4.40555 0.218107
\(409\) 14.4716 0.715576 0.357788 0.933803i \(-0.383531\pi\)
0.357788 + 0.933803i \(0.383531\pi\)
\(410\) 0.999110 0.0493425
\(411\) −4.51607 −0.222761
\(412\) 5.41989 0.267019
\(413\) −42.0526 −2.06927
\(414\) −7.43468 −0.365395
\(415\) 7.11554 0.349288
\(416\) −26.2534 −1.28718
\(417\) 11.4697 0.561676
\(418\) −2.67814 −0.130992
\(419\) −4.92102 −0.240408 −0.120204 0.992749i \(-0.538355\pi\)
−0.120204 + 0.992749i \(0.538355\pi\)
\(420\) 2.48724 0.121365
\(421\) 16.7810 0.817857 0.408928 0.912566i \(-0.365903\pi\)
0.408928 + 0.912566i \(0.365903\pi\)
\(422\) 8.35424 0.406678
\(423\) 15.7418 0.765390
\(424\) 17.9784 0.873109
\(425\) 12.9643 0.628859
\(426\) −1.83087 −0.0887059
\(427\) 9.91435 0.479789
\(428\) −23.5016 −1.13599
\(429\) 2.15361 0.103977
\(430\) −6.59119 −0.317855
\(431\) 10.5214 0.506800 0.253400 0.967362i \(-0.418451\pi\)
0.253400 + 0.967362i \(0.418451\pi\)
\(432\) −3.25486 −0.156599
\(433\) −11.8135 −0.567721 −0.283860 0.958866i \(-0.591615\pi\)
−0.283860 + 0.958866i \(0.591615\pi\)
\(434\) 20.2808 0.973508
\(435\) 3.31843 0.159107
\(436\) −3.81047 −0.182488
\(437\) 15.4250 0.737876
\(438\) −5.77961 −0.276160
\(439\) 8.18885 0.390833 0.195416 0.980720i \(-0.437394\pi\)
0.195416 + 0.980720i \(0.437394\pi\)
\(440\) 2.16260 0.103098
\(441\) −9.68497 −0.461189
\(442\) 10.4880 0.498866
\(443\) −15.7119 −0.746496 −0.373248 0.927732i \(-0.621756\pi\)
−0.373248 + 0.927732i \(0.621756\pi\)
\(444\) −8.76551 −0.415993
\(445\) 0.807071 0.0382588
\(446\) 13.9663 0.661321
\(447\) −11.3859 −0.538536
\(448\) −7.18881 −0.339639
\(449\) 9.89465 0.466957 0.233479 0.972362i \(-0.424989\pi\)
0.233479 + 0.972362i \(0.424989\pi\)
\(450\) 8.09738 0.381714
\(451\) −1.24639 −0.0586900
\(452\) 17.8344 0.838860
\(453\) −6.67508 −0.313623
\(454\) 8.65453 0.406177
\(455\) 14.0359 0.658012
\(456\) −5.70899 −0.267348
\(457\) 19.4319 0.908985 0.454492 0.890751i \(-0.349821\pi\)
0.454492 + 0.890751i \(0.349821\pi\)
\(458\) 4.64287 0.216947
\(459\) 9.87943 0.461132
\(460\) −5.25461 −0.244998
\(461\) 28.4760 1.32626 0.663130 0.748504i \(-0.269228\pi\)
0.663130 + 0.748504i \(0.269228\pi\)
\(462\) 1.14937 0.0534735
\(463\) −10.8095 −0.502361 −0.251181 0.967940i \(-0.580819\pi\)
−0.251181 + 0.967940i \(0.580819\pi\)
\(464\) 6.64200 0.308347
\(465\) −4.44250 −0.206016
\(466\) 15.2815 0.707901
\(467\) 26.3662 1.22008 0.610041 0.792369i \(-0.291153\pi\)
0.610041 + 0.792369i \(0.291153\pi\)
\(468\) −17.6844 −0.817460
\(469\) 29.7719 1.37474
\(470\) −4.12130 −0.190101
\(471\) 5.24465 0.241661
\(472\) −32.8814 −1.51349
\(473\) 8.22248 0.378070
\(474\) 2.88322 0.132431
\(475\) −16.7999 −0.770832
\(476\) −15.1107 −0.692597
\(477\) 19.1117 0.875067
\(478\) −17.5289 −0.801752
\(479\) −0.194030 −0.00886547 −0.00443274 0.999990i \(-0.501411\pi\)
−0.00443274 + 0.999990i \(0.501411\pi\)
\(480\) 3.06916 0.140088
\(481\) −49.4650 −2.25541
\(482\) 1.19134 0.0542642
\(483\) −6.61988 −0.301215
\(484\) 14.9153 0.677967
\(485\) 0.457691 0.0207827
\(486\) 9.41611 0.427123
\(487\) −2.65682 −0.120392 −0.0601959 0.998187i \(-0.519173\pi\)
−0.0601959 + 0.998187i \(0.519173\pi\)
\(488\) 7.75214 0.350923
\(489\) 6.44512 0.291458
\(490\) 2.53559 0.114546
\(491\) 11.0398 0.498219 0.249109 0.968475i \(-0.419862\pi\)
0.249109 + 0.968475i \(0.419862\pi\)
\(492\) −1.12086 −0.0505323
\(493\) −20.1604 −0.907978
\(494\) −13.5911 −0.611491
\(495\) 2.29893 0.103329
\(496\) −8.89187 −0.399257
\(497\) 14.8857 0.667713
\(498\) 2.95698 0.132505
\(499\) 30.9966 1.38760 0.693799 0.720168i \(-0.255935\pi\)
0.693799 + 0.720168i \(0.255935\pi\)
\(500\) 12.7484 0.570128
\(501\) −10.2615 −0.458450
\(502\) −7.87523 −0.351489
\(503\) −37.0982 −1.65413 −0.827063 0.562109i \(-0.809990\pi\)
−0.827063 + 0.562109i \(0.809990\pi\)
\(504\) −22.3722 −0.996536
\(505\) −2.96480 −0.131932
\(506\) −2.42819 −0.107946
\(507\) 3.85501 0.171207
\(508\) −8.62279 −0.382575
\(509\) −8.10275 −0.359148 −0.179574 0.983744i \(-0.557472\pi\)
−0.179574 + 0.983744i \(0.557472\pi\)
\(510\) −1.22611 −0.0542931
\(511\) 46.9904 2.07873
\(512\) 11.4776 0.507244
\(513\) −12.8024 −0.565239
\(514\) −21.1720 −0.933857
\(515\) −3.57558 −0.157559
\(516\) 7.39438 0.325519
\(517\) 5.14130 0.226114
\(518\) −26.3992 −1.15991
\(519\) −8.26165 −0.362646
\(520\) 10.9748 0.481277
\(521\) 9.96721 0.436671 0.218336 0.975874i \(-0.429937\pi\)
0.218336 + 0.975874i \(0.429937\pi\)
\(522\) −12.5920 −0.551139
\(523\) −7.12073 −0.311368 −0.155684 0.987807i \(-0.549758\pi\)
−0.155684 + 0.987807i \(0.549758\pi\)
\(524\) −7.16604 −0.313050
\(525\) 7.20996 0.314668
\(526\) −19.9734 −0.870879
\(527\) 26.9894 1.17568
\(528\) −0.503929 −0.0219307
\(529\) −9.01467 −0.391942
\(530\) −5.00358 −0.217342
\(531\) −34.9542 −1.51688
\(532\) 19.5814 0.848961
\(533\) −6.32517 −0.273974
\(534\) 0.335392 0.0145138
\(535\) 15.5044 0.670312
\(536\) 23.2790 1.00550
\(537\) −1.40339 −0.0605608
\(538\) −14.1303 −0.609201
\(539\) −3.16314 −0.136246
\(540\) 4.36121 0.187677
\(541\) 39.1006 1.68107 0.840533 0.541760i \(-0.182242\pi\)
0.840533 + 0.541760i \(0.182242\pi\)
\(542\) −7.15981 −0.307540
\(543\) −5.17381 −0.222030
\(544\) −18.6460 −0.799441
\(545\) 2.51382 0.107680
\(546\) 5.83284 0.249622
\(547\) −1.00000 −0.0427569
\(548\) 12.1116 0.517383
\(549\) 8.24082 0.351710
\(550\) 2.64463 0.112767
\(551\) 26.1251 1.11297
\(552\) −5.17616 −0.220312
\(553\) −23.4416 −0.996840
\(554\) −19.7733 −0.840087
\(555\) 5.78273 0.245463
\(556\) −30.7606 −1.30454
\(557\) 39.1227 1.65768 0.828841 0.559485i \(-0.189001\pi\)
0.828841 + 0.559485i \(0.189001\pi\)
\(558\) 16.8574 0.713631
\(559\) 41.7275 1.76489
\(560\) −3.28428 −0.138786
\(561\) 1.52957 0.0645784
\(562\) −3.09750 −0.130660
\(563\) 32.3381 1.36289 0.681445 0.731869i \(-0.261352\pi\)
0.681445 + 0.731869i \(0.261352\pi\)
\(564\) 4.62351 0.194685
\(565\) −11.7656 −0.494983
\(566\) 23.0566 0.969142
\(567\) −20.8927 −0.877409
\(568\) 11.6393 0.488373
\(569\) 0.316254 0.0132581 0.00662903 0.999978i \(-0.497890\pi\)
0.00662903 + 0.999978i \(0.497890\pi\)
\(570\) 1.58887 0.0665505
\(571\) 4.67642 0.195702 0.0978511 0.995201i \(-0.468803\pi\)
0.0978511 + 0.995201i \(0.468803\pi\)
\(572\) −5.77577 −0.241497
\(573\) 3.37866 0.141145
\(574\) −3.37570 −0.140899
\(575\) −15.2319 −0.635216
\(576\) −5.97535 −0.248973
\(577\) 38.4107 1.59906 0.799529 0.600627i \(-0.205082\pi\)
0.799529 + 0.600627i \(0.205082\pi\)
\(578\) −5.05038 −0.210068
\(579\) −10.6824 −0.443946
\(580\) −8.89968 −0.369539
\(581\) −24.0413 −0.997403
\(582\) 0.190201 0.00788408
\(583\) 6.24195 0.258515
\(584\) 36.7423 1.52041
\(585\) 11.6666 0.482356
\(586\) −11.6825 −0.482598
\(587\) 6.56995 0.271171 0.135586 0.990766i \(-0.456708\pi\)
0.135586 + 0.990766i \(0.456708\pi\)
\(588\) −2.84458 −0.117308
\(589\) −34.9746 −1.44110
\(590\) 9.15125 0.376751
\(591\) 14.3463 0.590129
\(592\) 11.5744 0.475706
\(593\) −0.570902 −0.0234441 −0.0117221 0.999931i \(-0.503731\pi\)
−0.0117221 + 0.999931i \(0.503731\pi\)
\(594\) 2.01534 0.0826905
\(595\) 9.96874 0.408679
\(596\) 30.5359 1.25080
\(597\) −2.81860 −0.115357
\(598\) −12.3226 −0.503909
\(599\) 8.95352 0.365831 0.182915 0.983129i \(-0.441447\pi\)
0.182915 + 0.983129i \(0.441447\pi\)
\(600\) 5.63755 0.230152
\(601\) −12.7284 −0.519202 −0.259601 0.965716i \(-0.583591\pi\)
−0.259601 + 0.965716i \(0.583591\pi\)
\(602\) 22.2697 0.907646
\(603\) 24.7464 1.00775
\(604\) 17.9019 0.728416
\(605\) −9.83982 −0.400046
\(606\) −1.23207 −0.0500495
\(607\) 26.7859 1.08721 0.543603 0.839342i \(-0.317060\pi\)
0.543603 + 0.839342i \(0.317060\pi\)
\(608\) 24.1627 0.979926
\(609\) −11.2120 −0.454334
\(610\) −2.15750 −0.0873547
\(611\) 26.0911 1.05553
\(612\) −12.5600 −0.507709
\(613\) 31.3273 1.26530 0.632649 0.774439i \(-0.281968\pi\)
0.632649 + 0.774439i \(0.281968\pi\)
\(614\) −10.0752 −0.406602
\(615\) 0.739448 0.0298174
\(616\) −7.30682 −0.294400
\(617\) −31.6103 −1.27258 −0.636292 0.771448i \(-0.719533\pi\)
−0.636292 + 0.771448i \(0.719533\pi\)
\(618\) −1.48589 −0.0597713
\(619\) 7.99712 0.321431 0.160716 0.987001i \(-0.448620\pi\)
0.160716 + 0.987001i \(0.448620\pi\)
\(620\) 11.9143 0.478490
\(621\) −11.6075 −0.465794
\(622\) 4.77491 0.191457
\(623\) −2.72686 −0.109249
\(624\) −2.55734 −0.102376
\(625\) 11.9549 0.478195
\(626\) 6.07617 0.242853
\(627\) −1.98211 −0.0791579
\(628\) −14.0656 −0.561278
\(629\) −35.1317 −1.40079
\(630\) 6.22641 0.248066
\(631\) −44.2164 −1.76023 −0.880113 0.474764i \(-0.842534\pi\)
−0.880113 + 0.474764i \(0.842534\pi\)
\(632\) −18.3293 −0.729100
\(633\) 6.18303 0.245753
\(634\) −20.6931 −0.821827
\(635\) 5.68858 0.225744
\(636\) 5.61331 0.222582
\(637\) −16.0523 −0.636017
\(638\) −4.11260 −0.162819
\(639\) 12.3730 0.489468
\(640\) −9.71583 −0.384052
\(641\) −16.8320 −0.664824 −0.332412 0.943134i \(-0.607862\pi\)
−0.332412 + 0.943134i \(0.607862\pi\)
\(642\) 6.44310 0.254289
\(643\) −12.4597 −0.491362 −0.245681 0.969351i \(-0.579012\pi\)
−0.245681 + 0.969351i \(0.579012\pi\)
\(644\) 17.7538 0.699599
\(645\) −4.87818 −0.192078
\(646\) −9.65283 −0.379786
\(647\) −48.1533 −1.89310 −0.946551 0.322555i \(-0.895458\pi\)
−0.946551 + 0.322555i \(0.895458\pi\)
\(648\) −16.3362 −0.641747
\(649\) −11.4161 −0.448123
\(650\) 13.4210 0.526415
\(651\) 15.0099 0.588285
\(652\) −17.2851 −0.676938
\(653\) −12.7505 −0.498967 −0.249484 0.968379i \(-0.580261\pi\)
−0.249484 + 0.968379i \(0.580261\pi\)
\(654\) 1.04466 0.0408494
\(655\) 4.72754 0.184720
\(656\) 1.48004 0.0577858
\(657\) 39.0585 1.52382
\(658\) 13.9247 0.542840
\(659\) −29.8939 −1.16450 −0.582250 0.813010i \(-0.697828\pi\)
−0.582250 + 0.813010i \(0.697828\pi\)
\(660\) 0.675219 0.0262829
\(661\) 22.0815 0.858872 0.429436 0.903097i \(-0.358712\pi\)
0.429436 + 0.903097i \(0.358712\pi\)
\(662\) −1.31110 −0.0509574
\(663\) 7.76227 0.301462
\(664\) −18.7982 −0.729512
\(665\) −12.9181 −0.500943
\(666\) −21.9430 −0.850275
\(667\) 23.6868 0.917157
\(668\) 27.5203 1.06479
\(669\) 10.3365 0.399633
\(670\) −6.47878 −0.250297
\(671\) 2.69148 0.103903
\(672\) −10.3698 −0.400024
\(673\) 24.6133 0.948772 0.474386 0.880317i \(-0.342670\pi\)
0.474386 + 0.880317i \(0.342670\pi\)
\(674\) 12.9058 0.497112
\(675\) 12.6422 0.486598
\(676\) −10.3387 −0.397644
\(677\) 15.1930 0.583913 0.291956 0.956432i \(-0.405694\pi\)
0.291956 + 0.956432i \(0.405694\pi\)
\(678\) −4.88940 −0.187776
\(679\) −1.54640 −0.0593456
\(680\) 7.79467 0.298912
\(681\) 6.40527 0.245451
\(682\) 5.50568 0.210823
\(683\) −23.5519 −0.901189 −0.450594 0.892729i \(-0.648788\pi\)
−0.450594 + 0.892729i \(0.648788\pi\)
\(684\) 16.2761 0.622331
\(685\) −7.99022 −0.305291
\(686\) 8.17537 0.312137
\(687\) 3.43622 0.131100
\(688\) −9.76391 −0.372245
\(689\) 31.6767 1.20679
\(690\) 1.44058 0.0548419
\(691\) −37.0300 −1.40869 −0.704343 0.709860i \(-0.748758\pi\)
−0.704343 + 0.709860i \(0.748758\pi\)
\(692\) 22.1569 0.842278
\(693\) −7.76742 −0.295060
\(694\) 10.9044 0.413927
\(695\) 20.2932 0.769766
\(696\) −8.76681 −0.332305
\(697\) −4.49235 −0.170160
\(698\) −25.2705 −0.956503
\(699\) 11.3099 0.427781
\(700\) −19.3363 −0.730845
\(701\) 35.5829 1.34395 0.671973 0.740576i \(-0.265447\pi\)
0.671973 + 0.740576i \(0.265447\pi\)
\(702\) 10.2275 0.386012
\(703\) 45.5259 1.71704
\(704\) −1.95157 −0.0735524
\(705\) −3.05020 −0.114877
\(706\) −11.8933 −0.447611
\(707\) 10.0172 0.376736
\(708\) −10.2664 −0.385835
\(709\) 40.5125 1.52148 0.760739 0.649058i \(-0.224837\pi\)
0.760739 + 0.649058i \(0.224837\pi\)
\(710\) −3.23933 −0.121570
\(711\) −19.4847 −0.730734
\(712\) −2.13216 −0.0799062
\(713\) −31.7103 −1.18756
\(714\) 4.14267 0.155036
\(715\) 3.81036 0.142499
\(716\) 3.76375 0.140658
\(717\) −12.9732 −0.484494
\(718\) 13.0263 0.486138
\(719\) 6.36743 0.237465 0.118733 0.992926i \(-0.462117\pi\)
0.118733 + 0.992926i \(0.462117\pi\)
\(720\) −2.72990 −0.101737
\(721\) 12.0808 0.449914
\(722\) −1.46111 −0.0543767
\(723\) 0.881722 0.0327916
\(724\) 13.8756 0.515683
\(725\) −25.7982 −0.958120
\(726\) −4.08910 −0.151761
\(727\) −35.1164 −1.30240 −0.651198 0.758908i \(-0.725733\pi\)
−0.651198 + 0.758908i \(0.725733\pi\)
\(728\) −37.0807 −1.37430
\(729\) −12.2989 −0.455516
\(730\) −10.2258 −0.378473
\(731\) 29.6363 1.09614
\(732\) 2.42041 0.0894610
\(733\) 26.1891 0.967315 0.483658 0.875257i \(-0.339308\pi\)
0.483658 + 0.875257i \(0.339308\pi\)
\(734\) 5.36110 0.197882
\(735\) 1.87661 0.0692197
\(736\) 21.9075 0.807523
\(737\) 8.08225 0.297714
\(738\) −2.80589 −0.103286
\(739\) 15.8483 0.582988 0.291494 0.956573i \(-0.405848\pi\)
0.291494 + 0.956573i \(0.405848\pi\)
\(740\) −15.5087 −0.570110
\(741\) −10.0588 −0.369521
\(742\) 16.9057 0.620626
\(743\) 13.1980 0.484189 0.242095 0.970253i \(-0.422166\pi\)
0.242095 + 0.970253i \(0.422166\pi\)
\(744\) 11.7364 0.430278
\(745\) −20.1449 −0.738054
\(746\) 14.2739 0.522605
\(747\) −19.9832 −0.731147
\(748\) −4.10214 −0.149989
\(749\) −52.3848 −1.91410
\(750\) −3.49505 −0.127621
\(751\) −17.3729 −0.633945 −0.316973 0.948435i \(-0.602666\pi\)
−0.316973 + 0.948435i \(0.602666\pi\)
\(752\) −6.10512 −0.222631
\(753\) −5.82851 −0.212403
\(754\) −20.8707 −0.760064
\(755\) −11.8101 −0.429814
\(756\) −14.7353 −0.535917
\(757\) −38.7514 −1.40844 −0.704222 0.709980i \(-0.748704\pi\)
−0.704222 + 0.709980i \(0.748704\pi\)
\(758\) 15.8479 0.575623
\(759\) −1.79712 −0.0652313
\(760\) −10.1008 −0.366396
\(761\) −29.0280 −1.05226 −0.526132 0.850403i \(-0.676358\pi\)
−0.526132 + 0.850403i \(0.676358\pi\)
\(762\) 2.36398 0.0856381
\(763\) −8.49347 −0.307484
\(764\) −9.06120 −0.327823
\(765\) 8.28603 0.299582
\(766\) −6.39277 −0.230980
\(767\) −57.9348 −2.09190
\(768\) −6.44270 −0.232481
\(769\) −8.49451 −0.306320 −0.153160 0.988201i \(-0.548945\pi\)
−0.153160 + 0.988201i \(0.548945\pi\)
\(770\) 2.03356 0.0732845
\(771\) −15.6695 −0.564325
\(772\) 28.6491 1.03110
\(773\) −30.2676 −1.08865 −0.544325 0.838875i \(-0.683214\pi\)
−0.544325 + 0.838875i \(0.683214\pi\)
\(774\) 18.5106 0.665351
\(775\) 34.5369 1.24060
\(776\) −1.20915 −0.0434060
\(777\) −19.5382 −0.700929
\(778\) 14.7776 0.529803
\(779\) 5.82147 0.208576
\(780\) 3.42661 0.122692
\(781\) 4.04105 0.144600
\(782\) −8.75192 −0.312968
\(783\) −19.6595 −0.702574
\(784\) 3.75612 0.134147
\(785\) 9.27927 0.331191
\(786\) 1.96461 0.0700752
\(787\) −25.5339 −0.910185 −0.455093 0.890444i \(-0.650394\pi\)
−0.455093 + 0.890444i \(0.650394\pi\)
\(788\) −38.4753 −1.37063
\(789\) −14.7824 −0.526268
\(790\) 5.10123 0.181494
\(791\) 39.7526 1.41344
\(792\) −6.07344 −0.215810
\(793\) 13.6587 0.485036
\(794\) −16.4196 −0.582710
\(795\) −3.70318 −0.131338
\(796\) 7.55918 0.267928
\(797\) −48.5429 −1.71948 −0.859738 0.510735i \(-0.829373\pi\)
−0.859738 + 0.510735i \(0.829373\pi\)
\(798\) −5.36834 −0.190037
\(799\) 18.5308 0.655573
\(800\) −23.8603 −0.843589
\(801\) −2.26657 −0.0800853
\(802\) −1.43896 −0.0508113
\(803\) 12.7566 0.450171
\(804\) 7.26828 0.256332
\(805\) −11.7125 −0.412810
\(806\) 27.9403 0.984154
\(807\) −10.4579 −0.368137
\(808\) 7.83256 0.275549
\(809\) 30.1082 1.05855 0.529274 0.848451i \(-0.322464\pi\)
0.529274 + 0.848451i \(0.322464\pi\)
\(810\) 4.54654 0.159749
\(811\) −26.6166 −0.934634 −0.467317 0.884090i \(-0.654779\pi\)
−0.467317 + 0.884090i \(0.654779\pi\)
\(812\) 30.0695 1.05523
\(813\) −5.29902 −0.185845
\(814\) −7.16665 −0.251191
\(815\) 11.4032 0.399438
\(816\) −1.81631 −0.0635836
\(817\) −38.4046 −1.34361
\(818\) 10.6403 0.372031
\(819\) −39.4182 −1.37738
\(820\) −1.98312 −0.0692536
\(821\) −52.7820 −1.84210 −0.921052 0.389440i \(-0.872668\pi\)
−0.921052 + 0.389440i \(0.872668\pi\)
\(822\) −3.32047 −0.115815
\(823\) −20.7992 −0.725014 −0.362507 0.931981i \(-0.618079\pi\)
−0.362507 + 0.931981i \(0.618079\pi\)
\(824\) 9.44615 0.329072
\(825\) 1.95731 0.0681447
\(826\) −30.9194 −1.07582
\(827\) 12.6722 0.440654 0.220327 0.975426i \(-0.429287\pi\)
0.220327 + 0.975426i \(0.429287\pi\)
\(828\) 14.7570 0.512841
\(829\) 24.4262 0.848357 0.424179 0.905579i \(-0.360563\pi\)
0.424179 + 0.905579i \(0.360563\pi\)
\(830\) 5.23174 0.181596
\(831\) −14.6343 −0.507660
\(832\) −9.90383 −0.343354
\(833\) −11.4009 −0.395018
\(834\) 8.43319 0.292018
\(835\) −18.1555 −0.628297
\(836\) 5.31581 0.183851
\(837\) 26.3189 0.909714
\(838\) −3.61821 −0.124989
\(839\) 41.6208 1.43691 0.718455 0.695574i \(-0.244850\pi\)
0.718455 + 0.695574i \(0.244850\pi\)
\(840\) 4.33494 0.149570
\(841\) 11.1181 0.383383
\(842\) 12.3383 0.425207
\(843\) −2.29248 −0.0789572
\(844\) −16.5822 −0.570784
\(845\) 6.82061 0.234636
\(846\) 11.5742 0.397930
\(847\) 33.2459 1.14234
\(848\) −7.41210 −0.254533
\(849\) 17.0644 0.585647
\(850\) 9.53204 0.326946
\(851\) 41.2769 1.41495
\(852\) 3.63407 0.124501
\(853\) 11.9436 0.408942 0.204471 0.978873i \(-0.434453\pi\)
0.204471 + 0.978873i \(0.434453\pi\)
\(854\) 7.28958 0.249444
\(855\) −10.7376 −0.367217
\(856\) −40.9603 −1.39999
\(857\) −17.0803 −0.583452 −0.291726 0.956502i \(-0.594229\pi\)
−0.291726 + 0.956502i \(0.594229\pi\)
\(858\) 1.58346 0.0540583
\(859\) −45.1499 −1.54049 −0.770247 0.637745i \(-0.779867\pi\)
−0.770247 + 0.637745i \(0.779867\pi\)
\(860\) 13.0828 0.446118
\(861\) −2.49838 −0.0851446
\(862\) 7.73595 0.263487
\(863\) −42.9192 −1.46099 −0.730494 0.682919i \(-0.760710\pi\)
−0.730494 + 0.682919i \(0.760710\pi\)
\(864\) −18.1828 −0.618591
\(865\) −14.6172 −0.497000
\(866\) −8.68594 −0.295160
\(867\) −3.73782 −0.126943
\(868\) −40.2550 −1.36634
\(869\) −6.36377 −0.215876
\(870\) 2.43990 0.0827202
\(871\) 41.0159 1.38977
\(872\) −6.64114 −0.224897
\(873\) −1.28537 −0.0435033
\(874\) 11.3413 0.383625
\(875\) 28.4161 0.960640
\(876\) 11.4719 0.387598
\(877\) −22.1529 −0.748050 −0.374025 0.927419i \(-0.622023\pi\)
−0.374025 + 0.927419i \(0.622023\pi\)
\(878\) 6.02090 0.203196
\(879\) −8.64627 −0.291631
\(880\) −0.891593 −0.0300556
\(881\) −8.84872 −0.298121 −0.149060 0.988828i \(-0.547625\pi\)
−0.149060 + 0.988828i \(0.547625\pi\)
\(882\) −7.12093 −0.239774
\(883\) 14.6632 0.493455 0.246728 0.969085i \(-0.420645\pi\)
0.246728 + 0.969085i \(0.420645\pi\)
\(884\) −20.8176 −0.700172
\(885\) 6.77290 0.227668
\(886\) −11.5523 −0.388107
\(887\) 17.3973 0.584143 0.292072 0.956396i \(-0.405655\pi\)
0.292072 + 0.956396i \(0.405655\pi\)
\(888\) −15.2771 −0.512667
\(889\) −19.2201 −0.644621
\(890\) 0.593403 0.0198909
\(891\) −5.67179 −0.190012
\(892\) −27.7214 −0.928183
\(893\) −24.0134 −0.803577
\(894\) −8.37157 −0.279987
\(895\) −2.48300 −0.0829975
\(896\) 32.8270 1.09667
\(897\) −9.12004 −0.304509
\(898\) 7.27509 0.242773
\(899\) −53.7075 −1.79124
\(900\) −16.0724 −0.535747
\(901\) 22.4979 0.749512
\(902\) −0.916412 −0.0305132
\(903\) 16.4820 0.548485
\(904\) 31.0830 1.03381
\(905\) −9.15395 −0.304288
\(906\) −4.90789 −0.163054
\(907\) −33.7438 −1.12045 −0.560223 0.828342i \(-0.689285\pi\)
−0.560223 + 0.828342i \(0.689285\pi\)
\(908\) −17.1783 −0.570081
\(909\) 8.32631 0.276166
\(910\) 10.3199 0.342103
\(911\) 12.1001 0.400895 0.200447 0.979704i \(-0.435760\pi\)
0.200447 + 0.979704i \(0.435760\pi\)
\(912\) 2.35369 0.0779384
\(913\) −6.52657 −0.215998
\(914\) 14.2874 0.472585
\(915\) −1.59678 −0.0527880
\(916\) −9.21557 −0.304491
\(917\) −15.9730 −0.527475
\(918\) 7.26390 0.239745
\(919\) −31.4919 −1.03882 −0.519412 0.854524i \(-0.673849\pi\)
−0.519412 + 0.854524i \(0.673849\pi\)
\(920\) −9.15811 −0.301934
\(921\) −7.45671 −0.245707
\(922\) 20.9371 0.689528
\(923\) 20.5076 0.675015
\(924\) −2.28137 −0.0750516
\(925\) −44.9562 −1.47815
\(926\) −7.94777 −0.261180
\(927\) 10.0416 0.329810
\(928\) 37.1046 1.21802
\(929\) 28.6545 0.940123 0.470061 0.882634i \(-0.344232\pi\)
0.470061 + 0.882634i \(0.344232\pi\)
\(930\) −3.26637 −0.107109
\(931\) 14.7740 0.484199
\(932\) −30.3320 −0.993558
\(933\) 3.53394 0.115696
\(934\) 19.3859 0.634326
\(935\) 2.70624 0.0885036
\(936\) −30.8215 −1.00743
\(937\) 6.14354 0.200701 0.100350 0.994952i \(-0.468004\pi\)
0.100350 + 0.994952i \(0.468004\pi\)
\(938\) 21.8899 0.714731
\(939\) 4.49702 0.146755
\(940\) 8.18031 0.266812
\(941\) −25.9528 −0.846038 −0.423019 0.906121i \(-0.639030\pi\)
−0.423019 + 0.906121i \(0.639030\pi\)
\(942\) 3.85616 0.125640
\(943\) 5.27814 0.171880
\(944\) 13.5563 0.441219
\(945\) 9.72108 0.316227
\(946\) 6.04562 0.196560
\(947\) 45.1337 1.46665 0.733324 0.679880i \(-0.237968\pi\)
0.733324 + 0.679880i \(0.237968\pi\)
\(948\) −5.72286 −0.185870
\(949\) 64.7374 2.10146
\(950\) −12.3522 −0.400759
\(951\) −15.3151 −0.496625
\(952\) −26.3360 −0.853553
\(953\) −6.09060 −0.197294 −0.0986469 0.995122i \(-0.531451\pi\)
−0.0986469 + 0.995122i \(0.531451\pi\)
\(954\) 14.0520 0.454951
\(955\) 5.97781 0.193437
\(956\) 34.7929 1.12528
\(957\) −3.04376 −0.0983908
\(958\) −0.142662 −0.00460920
\(959\) 26.9966 0.871767
\(960\) 1.15781 0.0373682
\(961\) 40.9000 1.31936
\(962\) −36.3694 −1.17260
\(963\) −43.5423 −1.40313
\(964\) −2.36468 −0.0761614
\(965\) −18.9002 −0.608420
\(966\) −4.86731 −0.156603
\(967\) −32.8474 −1.05630 −0.528151 0.849150i \(-0.677115\pi\)
−0.528151 + 0.849150i \(0.677115\pi\)
\(968\) 25.9954 0.835523
\(969\) −7.14412 −0.229502
\(970\) 0.336519 0.0108050
\(971\) 45.3642 1.45581 0.727903 0.685680i \(-0.240495\pi\)
0.727903 + 0.685680i \(0.240495\pi\)
\(972\) −18.6899 −0.599479
\(973\) −68.5650 −2.19809
\(974\) −1.95344 −0.0625922
\(975\) 9.93297 0.318110
\(976\) −3.19603 −0.102303
\(977\) 9.96515 0.318813 0.159407 0.987213i \(-0.449042\pi\)
0.159407 + 0.987213i \(0.449042\pi\)
\(978\) 4.73881 0.151530
\(979\) −0.740268 −0.0236591
\(980\) −5.03286 −0.160769
\(981\) −7.05979 −0.225402
\(982\) 8.11707 0.259026
\(983\) −8.37150 −0.267009 −0.133505 0.991048i \(-0.542623\pi\)
−0.133505 + 0.991048i \(0.542623\pi\)
\(984\) −1.95351 −0.0622757
\(985\) 25.3827 0.808761
\(986\) −14.8230 −0.472062
\(987\) 10.3057 0.328035
\(988\) 26.9768 0.858245
\(989\) −34.8202 −1.10722
\(990\) 1.69030 0.0537213
\(991\) 28.8111 0.915215 0.457608 0.889154i \(-0.348706\pi\)
0.457608 + 0.889154i \(0.348706\pi\)
\(992\) −49.6732 −1.57712
\(993\) −0.970354 −0.0307933
\(994\) 10.9448 0.347147
\(995\) −4.98690 −0.158095
\(996\) −5.86927 −0.185975
\(997\) 12.3708 0.391788 0.195894 0.980625i \(-0.437239\pi\)
0.195894 + 0.980625i \(0.437239\pi\)
\(998\) 22.7904 0.721418
\(999\) −34.2589 −1.08390
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 547.2.a.b.1.11 18
3.2 odd 2 4923.2.a.l.1.8 18
4.3 odd 2 8752.2.a.s.1.6 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.11 18 1.1 even 1 trivial
4923.2.a.l.1.8 18 3.2 odd 2
8752.2.a.s.1.6 18 4.3 odd 2