Properties

Label 547.2.a.b.1.8
Level $547$
Weight $2$
Character 547.1
Self dual yes
Analytic conductor $4.368$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.8
Root \(0.826129\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.826129 q^{2} +2.26041 q^{3} -1.31751 q^{4} -0.786316 q^{5} -1.86739 q^{6} -5.06179 q^{7} +2.74069 q^{8} +2.10946 q^{9} +O(q^{10})\) \(q-0.826129 q^{2} +2.26041 q^{3} -1.31751 q^{4} -0.786316 q^{5} -1.86739 q^{6} -5.06179 q^{7} +2.74069 q^{8} +2.10946 q^{9} +0.649598 q^{10} +3.16492 q^{11} -2.97812 q^{12} -2.09157 q^{13} +4.18169 q^{14} -1.77740 q^{15} +0.370855 q^{16} -0.108946 q^{17} -1.74269 q^{18} -6.43031 q^{19} +1.03598 q^{20} -11.4417 q^{21} -2.61463 q^{22} -2.45365 q^{23} +6.19509 q^{24} -4.38171 q^{25} +1.72790 q^{26} -2.01298 q^{27} +6.66896 q^{28} -6.82278 q^{29} +1.46836 q^{30} -4.03224 q^{31} -5.78776 q^{32} +7.15403 q^{33} +0.0900034 q^{34} +3.98016 q^{35} -2.77924 q^{36} -5.74026 q^{37} +5.31227 q^{38} -4.72780 q^{39} -2.15505 q^{40} +9.42512 q^{41} +9.45235 q^{42} +6.98045 q^{43} -4.16982 q^{44} -1.65870 q^{45} +2.02703 q^{46} +4.86990 q^{47} +0.838285 q^{48} +18.6217 q^{49} +3.61986 q^{50} -0.246263 q^{51} +2.75566 q^{52} -13.4156 q^{53} +1.66299 q^{54} -2.48863 q^{55} -13.8728 q^{56} -14.5351 q^{57} +5.63650 q^{58} +5.35027 q^{59} +2.34174 q^{60} +6.38066 q^{61} +3.33115 q^{62} -10.6776 q^{63} +4.03973 q^{64} +1.64463 q^{65} -5.91015 q^{66} -10.0563 q^{67} +0.143537 q^{68} -5.54626 q^{69} -3.28813 q^{70} +13.7032 q^{71} +5.78138 q^{72} +12.7591 q^{73} +4.74220 q^{74} -9.90446 q^{75} +8.47200 q^{76} -16.0202 q^{77} +3.90578 q^{78} -0.423068 q^{79} -0.291609 q^{80} -10.8786 q^{81} -7.78637 q^{82} +2.31035 q^{83} +15.0746 q^{84} +0.0856659 q^{85} -5.76676 q^{86} -15.4223 q^{87} +8.67408 q^{88} -12.2474 q^{89} +1.37030 q^{90} +10.5871 q^{91} +3.23271 q^{92} -9.11453 q^{93} -4.02317 q^{94} +5.05625 q^{95} -13.0827 q^{96} +0.251761 q^{97} -15.3839 q^{98} +6.67628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.826129 −0.584162 −0.292081 0.956394i \(-0.594348\pi\)
−0.292081 + 0.956394i \(0.594348\pi\)
\(3\) 2.26041 1.30505 0.652525 0.757767i \(-0.273710\pi\)
0.652525 + 0.757767i \(0.273710\pi\)
\(4\) −1.31751 −0.658755
\(5\) −0.786316 −0.351651 −0.175826 0.984421i \(-0.556259\pi\)
−0.175826 + 0.984421i \(0.556259\pi\)
\(6\) −1.86739 −0.762360
\(7\) −5.06179 −1.91318 −0.956588 0.291442i \(-0.905865\pi\)
−0.956588 + 0.291442i \(0.905865\pi\)
\(8\) 2.74069 0.968981
\(9\) 2.10946 0.703154
\(10\) 0.649598 0.205421
\(11\) 3.16492 0.954260 0.477130 0.878833i \(-0.341677\pi\)
0.477130 + 0.878833i \(0.341677\pi\)
\(12\) −2.97812 −0.859708
\(13\) −2.09157 −0.580096 −0.290048 0.957012i \(-0.593671\pi\)
−0.290048 + 0.957012i \(0.593671\pi\)
\(14\) 4.18169 1.11760
\(15\) −1.77740 −0.458922
\(16\) 0.370855 0.0927137
\(17\) −0.108946 −0.0264233 −0.0132116 0.999913i \(-0.504206\pi\)
−0.0132116 + 0.999913i \(0.504206\pi\)
\(18\) −1.74269 −0.410755
\(19\) −6.43031 −1.47521 −0.737607 0.675230i \(-0.764044\pi\)
−0.737607 + 0.675230i \(0.764044\pi\)
\(20\) 1.03598 0.231652
\(21\) −11.4417 −2.49679
\(22\) −2.61463 −0.557442
\(23\) −2.45365 −0.511621 −0.255811 0.966727i \(-0.582342\pi\)
−0.255811 + 0.966727i \(0.582342\pi\)
\(24\) 6.19509 1.26457
\(25\) −4.38171 −0.876342
\(26\) 1.72790 0.338870
\(27\) −2.01298 −0.387399
\(28\) 6.66896 1.26032
\(29\) −6.82278 −1.26696 −0.633480 0.773759i \(-0.718374\pi\)
−0.633480 + 0.773759i \(0.718374\pi\)
\(30\) 1.46836 0.268085
\(31\) −4.03224 −0.724212 −0.362106 0.932137i \(-0.617942\pi\)
−0.362106 + 0.932137i \(0.617942\pi\)
\(32\) −5.78776 −1.02314
\(33\) 7.15403 1.24536
\(34\) 0.0900034 0.0154355
\(35\) 3.98016 0.672771
\(36\) −2.77924 −0.463206
\(37\) −5.74026 −0.943693 −0.471847 0.881681i \(-0.656412\pi\)
−0.471847 + 0.881681i \(0.656412\pi\)
\(38\) 5.31227 0.861764
\(39\) −4.72780 −0.757054
\(40\) −2.15505 −0.340743
\(41\) 9.42512 1.47196 0.735978 0.677005i \(-0.236723\pi\)
0.735978 + 0.677005i \(0.236723\pi\)
\(42\) 9.45235 1.45853
\(43\) 6.98045 1.06451 0.532255 0.846584i \(-0.321345\pi\)
0.532255 + 0.846584i \(0.321345\pi\)
\(44\) −4.16982 −0.628624
\(45\) −1.65870 −0.247265
\(46\) 2.02703 0.298869
\(47\) 4.86990 0.710348 0.355174 0.934800i \(-0.384422\pi\)
0.355174 + 0.934800i \(0.384422\pi\)
\(48\) 0.838285 0.120996
\(49\) 18.6217 2.66025
\(50\) 3.61986 0.511925
\(51\) −0.246263 −0.0344837
\(52\) 2.75566 0.382141
\(53\) −13.4156 −1.84278 −0.921388 0.388645i \(-0.872943\pi\)
−0.921388 + 0.388645i \(0.872943\pi\)
\(54\) 1.66299 0.226304
\(55\) −2.48863 −0.335566
\(56\) −13.8728 −1.85383
\(57\) −14.5351 −1.92523
\(58\) 5.63650 0.740109
\(59\) 5.35027 0.696546 0.348273 0.937393i \(-0.386768\pi\)
0.348273 + 0.937393i \(0.386768\pi\)
\(60\) 2.34174 0.302317
\(61\) 6.38066 0.816959 0.408480 0.912767i \(-0.366059\pi\)
0.408480 + 0.912767i \(0.366059\pi\)
\(62\) 3.33115 0.423057
\(63\) −10.6776 −1.34526
\(64\) 4.03973 0.504966
\(65\) 1.64463 0.203991
\(66\) −5.91015 −0.727489
\(67\) −10.0563 −1.22858 −0.614288 0.789082i \(-0.710557\pi\)
−0.614288 + 0.789082i \(0.710557\pi\)
\(68\) 0.143537 0.0174065
\(69\) −5.54626 −0.667691
\(70\) −3.28813 −0.393007
\(71\) 13.7032 1.62627 0.813133 0.582077i \(-0.197760\pi\)
0.813133 + 0.582077i \(0.197760\pi\)
\(72\) 5.78138 0.681343
\(73\) 12.7591 1.49334 0.746668 0.665196i \(-0.231652\pi\)
0.746668 + 0.665196i \(0.231652\pi\)
\(74\) 4.74220 0.551269
\(75\) −9.90446 −1.14367
\(76\) 8.47200 0.971805
\(77\) −16.0202 −1.82567
\(78\) 3.90578 0.442242
\(79\) −0.423068 −0.0475989 −0.0237994 0.999717i \(-0.507576\pi\)
−0.0237994 + 0.999717i \(0.507576\pi\)
\(80\) −0.291609 −0.0326029
\(81\) −10.8786 −1.20873
\(82\) −7.78637 −0.859860
\(83\) 2.31035 0.253594 0.126797 0.991929i \(-0.459530\pi\)
0.126797 + 0.991929i \(0.459530\pi\)
\(84\) 15.0746 1.64477
\(85\) 0.0856659 0.00929177
\(86\) −5.76676 −0.621845
\(87\) −15.4223 −1.65344
\(88\) 8.67408 0.924660
\(89\) −12.2474 −1.29823 −0.649113 0.760692i \(-0.724860\pi\)
−0.649113 + 0.760692i \(0.724860\pi\)
\(90\) 1.37030 0.144443
\(91\) 10.5871 1.10983
\(92\) 3.23271 0.337033
\(93\) −9.11453 −0.945133
\(94\) −4.02317 −0.414958
\(95\) 5.05625 0.518761
\(96\) −13.0827 −1.33525
\(97\) 0.251761 0.0255625 0.0127812 0.999918i \(-0.495931\pi\)
0.0127812 + 0.999918i \(0.495931\pi\)
\(98\) −15.3839 −1.55401
\(99\) 6.67628 0.670991
\(100\) 5.77295 0.577295
\(101\) −0.761643 −0.0757863 −0.0378931 0.999282i \(-0.512065\pi\)
−0.0378931 + 0.999282i \(0.512065\pi\)
\(102\) 0.203445 0.0201440
\(103\) −8.12573 −0.800652 −0.400326 0.916373i \(-0.631103\pi\)
−0.400326 + 0.916373i \(0.631103\pi\)
\(104\) −5.73234 −0.562102
\(105\) 8.99681 0.877999
\(106\) 11.0830 1.07648
\(107\) 6.91809 0.668797 0.334399 0.942432i \(-0.391467\pi\)
0.334399 + 0.942432i \(0.391467\pi\)
\(108\) 2.65213 0.255201
\(109\) 7.83918 0.750857 0.375428 0.926851i \(-0.377496\pi\)
0.375428 + 0.926851i \(0.377496\pi\)
\(110\) 2.05593 0.196025
\(111\) −12.9754 −1.23157
\(112\) −1.87719 −0.177378
\(113\) −9.98412 −0.939227 −0.469614 0.882872i \(-0.655607\pi\)
−0.469614 + 0.882872i \(0.655607\pi\)
\(114\) 12.0079 1.12464
\(115\) 1.92934 0.179912
\(116\) 8.98909 0.834616
\(117\) −4.41208 −0.407897
\(118\) −4.42002 −0.406896
\(119\) 0.551462 0.0505524
\(120\) −4.87130 −0.444687
\(121\) −0.983273 −0.0893884
\(122\) −5.27125 −0.477236
\(123\) 21.3047 1.92098
\(124\) 5.31252 0.477079
\(125\) 7.37698 0.659817
\(126\) 8.82112 0.785848
\(127\) 19.1377 1.69820 0.849099 0.528234i \(-0.177146\pi\)
0.849099 + 0.528234i \(0.177146\pi\)
\(128\) 8.23818 0.728159
\(129\) 15.7787 1.38924
\(130\) −1.35868 −0.119164
\(131\) −20.0684 −1.75339 −0.876693 0.481051i \(-0.840255\pi\)
−0.876693 + 0.481051i \(0.840255\pi\)
\(132\) −9.42550 −0.820385
\(133\) 32.5489 2.82235
\(134\) 8.30782 0.717686
\(135\) 1.58284 0.136229
\(136\) −0.298587 −0.0256037
\(137\) 0.483338 0.0412944 0.0206472 0.999787i \(-0.493427\pi\)
0.0206472 + 0.999787i \(0.493427\pi\)
\(138\) 4.58192 0.390039
\(139\) 11.7671 0.998071 0.499035 0.866582i \(-0.333688\pi\)
0.499035 + 0.866582i \(0.333688\pi\)
\(140\) −5.24391 −0.443191
\(141\) 11.0080 0.927039
\(142\) −11.3206 −0.950003
\(143\) −6.61964 −0.553563
\(144\) 0.782304 0.0651920
\(145\) 5.36486 0.445528
\(146\) −10.5406 −0.872350
\(147\) 42.0927 3.47175
\(148\) 7.56286 0.621663
\(149\) 3.59414 0.294443 0.147222 0.989104i \(-0.452967\pi\)
0.147222 + 0.989104i \(0.452967\pi\)
\(150\) 8.18237 0.668087
\(151\) −12.3861 −1.00797 −0.503984 0.863713i \(-0.668133\pi\)
−0.503984 + 0.863713i \(0.668133\pi\)
\(152\) −17.6235 −1.42945
\(153\) −0.229817 −0.0185796
\(154\) 13.2347 1.06648
\(155\) 3.17062 0.254670
\(156\) 6.22893 0.498713
\(157\) −22.4520 −1.79187 −0.895933 0.444188i \(-0.853492\pi\)
−0.895933 + 0.444188i \(0.853492\pi\)
\(158\) 0.349509 0.0278054
\(159\) −30.3248 −2.40491
\(160\) 4.55101 0.359789
\(161\) 12.4199 0.978822
\(162\) 8.98709 0.706093
\(163\) −3.40571 −0.266756 −0.133378 0.991065i \(-0.542582\pi\)
−0.133378 + 0.991065i \(0.542582\pi\)
\(164\) −12.4177 −0.969659
\(165\) −5.62532 −0.437931
\(166\) −1.90865 −0.148140
\(167\) −0.617110 −0.0477534 −0.0238767 0.999715i \(-0.507601\pi\)
−0.0238767 + 0.999715i \(0.507601\pi\)
\(168\) −31.3583 −2.41934
\(169\) −8.62535 −0.663488
\(170\) −0.0707711 −0.00542790
\(171\) −13.5645 −1.03730
\(172\) −9.19682 −0.701251
\(173\) 8.12121 0.617444 0.308722 0.951152i \(-0.400099\pi\)
0.308722 + 0.951152i \(0.400099\pi\)
\(174\) 12.7408 0.965879
\(175\) 22.1793 1.67660
\(176\) 1.17373 0.0884730
\(177\) 12.0938 0.909027
\(178\) 10.1180 0.758374
\(179\) −5.38653 −0.402608 −0.201304 0.979529i \(-0.564518\pi\)
−0.201304 + 0.979529i \(0.564518\pi\)
\(180\) 2.18536 0.162887
\(181\) 7.68451 0.571185 0.285593 0.958351i \(-0.407810\pi\)
0.285593 + 0.958351i \(0.407810\pi\)
\(182\) −8.74629 −0.648318
\(183\) 14.4229 1.06617
\(184\) −6.72470 −0.495751
\(185\) 4.51366 0.331851
\(186\) 7.52978 0.552110
\(187\) −0.344805 −0.0252147
\(188\) −6.41615 −0.467946
\(189\) 10.1893 0.741163
\(190\) −4.17712 −0.303040
\(191\) −16.2735 −1.17751 −0.588753 0.808313i \(-0.700381\pi\)
−0.588753 + 0.808313i \(0.700381\pi\)
\(192\) 9.13145 0.659005
\(193\) −1.47963 −0.106506 −0.0532531 0.998581i \(-0.516959\pi\)
−0.0532531 + 0.998581i \(0.516959\pi\)
\(194\) −0.207987 −0.0149326
\(195\) 3.71755 0.266219
\(196\) −24.5343 −1.75245
\(197\) 4.77839 0.340446 0.170223 0.985406i \(-0.445551\pi\)
0.170223 + 0.985406i \(0.445551\pi\)
\(198\) −5.51547 −0.391967
\(199\) 13.8921 0.984784 0.492392 0.870373i \(-0.336123\pi\)
0.492392 + 0.870373i \(0.336123\pi\)
\(200\) −12.0089 −0.849158
\(201\) −22.7314 −1.60335
\(202\) 0.629215 0.0442714
\(203\) 34.5355 2.42392
\(204\) 0.324454 0.0227163
\(205\) −7.41112 −0.517615
\(206\) 6.71291 0.467710
\(207\) −5.17588 −0.359748
\(208\) −0.775668 −0.0537829
\(209\) −20.3514 −1.40774
\(210\) −7.43253 −0.512893
\(211\) −24.6663 −1.69810 −0.849049 0.528314i \(-0.822824\pi\)
−0.849049 + 0.528314i \(0.822824\pi\)
\(212\) 17.6752 1.21394
\(213\) 30.9748 2.12236
\(214\) −5.71524 −0.390686
\(215\) −5.48884 −0.374336
\(216\) −5.51697 −0.375382
\(217\) 20.4104 1.38555
\(218\) −6.47617 −0.438622
\(219\) 28.8408 1.94888
\(220\) 3.27879 0.221056
\(221\) 0.227868 0.0153280
\(222\) 10.7193 0.719434
\(223\) −8.58640 −0.574988 −0.287494 0.957782i \(-0.592822\pi\)
−0.287494 + 0.957782i \(0.592822\pi\)
\(224\) 29.2964 1.95745
\(225\) −9.24304 −0.616203
\(226\) 8.24818 0.548660
\(227\) −25.2376 −1.67508 −0.837540 0.546375i \(-0.816007\pi\)
−0.837540 + 0.546375i \(0.816007\pi\)
\(228\) 19.1502 1.26825
\(229\) −10.2627 −0.678176 −0.339088 0.940755i \(-0.610119\pi\)
−0.339088 + 0.940755i \(0.610119\pi\)
\(230\) −1.59389 −0.105098
\(231\) −36.2122 −2.38259
\(232\) −18.6992 −1.22766
\(233\) 0.393334 0.0257682 0.0128841 0.999917i \(-0.495899\pi\)
0.0128841 + 0.999917i \(0.495899\pi\)
\(234\) 3.64495 0.238278
\(235\) −3.82928 −0.249795
\(236\) −7.04904 −0.458854
\(237\) −0.956308 −0.0621189
\(238\) −0.455578 −0.0295308
\(239\) −4.68089 −0.302782 −0.151391 0.988474i \(-0.548375\pi\)
−0.151391 + 0.988474i \(0.548375\pi\)
\(240\) −0.659156 −0.0425484
\(241\) 15.4761 0.996905 0.498452 0.866917i \(-0.333902\pi\)
0.498452 + 0.866917i \(0.333902\pi\)
\(242\) 0.812310 0.0522173
\(243\) −18.5511 −1.19005
\(244\) −8.40658 −0.538176
\(245\) −14.6425 −0.935478
\(246\) −17.6004 −1.12216
\(247\) 13.4494 0.855766
\(248\) −11.0511 −0.701748
\(249\) 5.22235 0.330953
\(250\) −6.09434 −0.385440
\(251\) 7.93354 0.500761 0.250380 0.968148i \(-0.419444\pi\)
0.250380 + 0.968148i \(0.419444\pi\)
\(252\) 14.0679 0.886195
\(253\) −7.76561 −0.488219
\(254\) −15.8102 −0.992022
\(255\) 0.193640 0.0121262
\(256\) −14.8853 −0.930329
\(257\) −21.8790 −1.36478 −0.682389 0.730990i \(-0.739059\pi\)
−0.682389 + 0.730990i \(0.739059\pi\)
\(258\) −13.0352 −0.811539
\(259\) 29.0560 1.80545
\(260\) −2.16682 −0.134380
\(261\) −14.3924 −0.890867
\(262\) 16.5791 1.02426
\(263\) 16.8492 1.03897 0.519484 0.854480i \(-0.326124\pi\)
0.519484 + 0.854480i \(0.326124\pi\)
\(264\) 19.6070 1.20673
\(265\) 10.5489 0.648014
\(266\) −26.8896 −1.64871
\(267\) −27.6843 −1.69425
\(268\) 13.2493 0.809330
\(269\) 6.42681 0.391849 0.195925 0.980619i \(-0.437229\pi\)
0.195925 + 0.980619i \(0.437229\pi\)
\(270\) −1.30763 −0.0795799
\(271\) 19.9132 1.20964 0.604820 0.796362i \(-0.293245\pi\)
0.604820 + 0.796362i \(0.293245\pi\)
\(272\) −0.0404031 −0.00244980
\(273\) 23.9311 1.44838
\(274\) −0.399300 −0.0241226
\(275\) −13.8678 −0.836257
\(276\) 7.30725 0.439845
\(277\) −2.56259 −0.153971 −0.0769854 0.997032i \(-0.524529\pi\)
−0.0769854 + 0.997032i \(0.524529\pi\)
\(278\) −9.72113 −0.583035
\(279\) −8.50586 −0.509233
\(280\) 10.9084 0.651902
\(281\) −9.17907 −0.547577 −0.273789 0.961790i \(-0.588277\pi\)
−0.273789 + 0.961790i \(0.588277\pi\)
\(282\) −9.09402 −0.541541
\(283\) −16.3038 −0.969158 −0.484579 0.874748i \(-0.661027\pi\)
−0.484579 + 0.874748i \(0.661027\pi\)
\(284\) −18.0541 −1.07131
\(285\) 11.4292 0.677008
\(286\) 5.46868 0.323370
\(287\) −47.7080 −2.81611
\(288\) −12.2091 −0.719425
\(289\) −16.9881 −0.999302
\(290\) −4.43207 −0.260260
\(291\) 0.569084 0.0333603
\(292\) −16.8102 −0.983743
\(293\) −8.66768 −0.506371 −0.253186 0.967418i \(-0.581478\pi\)
−0.253186 + 0.967418i \(0.581478\pi\)
\(294\) −34.7741 −2.02806
\(295\) −4.20700 −0.244941
\(296\) −15.7323 −0.914421
\(297\) −6.37094 −0.369679
\(298\) −2.96922 −0.172002
\(299\) 5.13197 0.296790
\(300\) 13.0492 0.753398
\(301\) −35.3336 −2.03659
\(302\) 10.2325 0.588817
\(303\) −1.72163 −0.0989048
\(304\) −2.38471 −0.136773
\(305\) −5.01721 −0.287285
\(306\) 0.189859 0.0108535
\(307\) 11.3930 0.650233 0.325116 0.945674i \(-0.394597\pi\)
0.325116 + 0.945674i \(0.394597\pi\)
\(308\) 21.1067 1.20267
\(309\) −18.3675 −1.04489
\(310\) −2.61934 −0.148768
\(311\) −14.0569 −0.797096 −0.398548 0.917147i \(-0.630486\pi\)
−0.398548 + 0.917147i \(0.630486\pi\)
\(312\) −12.9575 −0.733571
\(313\) −30.2403 −1.70928 −0.854640 0.519221i \(-0.826222\pi\)
−0.854640 + 0.519221i \(0.826222\pi\)
\(314\) 18.5483 1.04674
\(315\) 8.39600 0.473061
\(316\) 0.557397 0.0313560
\(317\) 31.2545 1.75543 0.877715 0.479184i \(-0.159067\pi\)
0.877715 + 0.479184i \(0.159067\pi\)
\(318\) 25.0522 1.40486
\(319\) −21.5936 −1.20901
\(320\) −3.17650 −0.177572
\(321\) 15.6377 0.872813
\(322\) −10.2604 −0.571790
\(323\) 0.700556 0.0389800
\(324\) 14.3326 0.796256
\(325\) 9.16463 0.508362
\(326\) 2.81356 0.155829
\(327\) 17.7198 0.979905
\(328\) 25.8314 1.42630
\(329\) −24.6504 −1.35902
\(330\) 4.64724 0.255822
\(331\) 34.5967 1.90161 0.950803 0.309797i \(-0.100261\pi\)
0.950803 + 0.309797i \(0.100261\pi\)
\(332\) −3.04391 −0.167056
\(333\) −12.1089 −0.663562
\(334\) 0.509813 0.0278957
\(335\) 7.90744 0.432030
\(336\) −4.24322 −0.231487
\(337\) 1.53217 0.0834625 0.0417312 0.999129i \(-0.486713\pi\)
0.0417312 + 0.999129i \(0.486713\pi\)
\(338\) 7.12565 0.387584
\(339\) −22.5682 −1.22574
\(340\) −0.112866 −0.00612100
\(341\) −12.7617 −0.691087
\(342\) 11.2060 0.605952
\(343\) −58.8267 −3.17634
\(344\) 19.1313 1.03149
\(345\) 4.36111 0.234794
\(346\) −6.70917 −0.360687
\(347\) 16.8369 0.903851 0.451926 0.892056i \(-0.350737\pi\)
0.451926 + 0.892056i \(0.350737\pi\)
\(348\) 20.3190 1.08922
\(349\) −23.7566 −1.27166 −0.635830 0.771829i \(-0.719342\pi\)
−0.635830 + 0.771829i \(0.719342\pi\)
\(350\) −18.3230 −0.979403
\(351\) 4.21029 0.224729
\(352\) −18.3178 −0.976342
\(353\) 1.39136 0.0740545 0.0370273 0.999314i \(-0.488211\pi\)
0.0370273 + 0.999314i \(0.488211\pi\)
\(354\) −9.99106 −0.531019
\(355\) −10.7750 −0.571878
\(356\) 16.1361 0.855213
\(357\) 1.24653 0.0659734
\(358\) 4.44997 0.235188
\(359\) 28.2644 1.49174 0.745868 0.666094i \(-0.232035\pi\)
0.745868 + 0.666094i \(0.232035\pi\)
\(360\) −4.54599 −0.239595
\(361\) 22.3489 1.17626
\(362\) −6.34840 −0.333665
\(363\) −2.22260 −0.116656
\(364\) −13.9486 −0.731104
\(365\) −10.0327 −0.525133
\(366\) −11.9152 −0.622817
\(367\) −3.01566 −0.157416 −0.0787082 0.996898i \(-0.525080\pi\)
−0.0787082 + 0.996898i \(0.525080\pi\)
\(368\) −0.909948 −0.0474343
\(369\) 19.8819 1.03501
\(370\) −3.72887 −0.193854
\(371\) 67.9070 3.52556
\(372\) 12.0085 0.622611
\(373\) −31.1754 −1.61420 −0.807101 0.590413i \(-0.798965\pi\)
−0.807101 + 0.590413i \(0.798965\pi\)
\(374\) 0.284854 0.0147294
\(375\) 16.6750 0.861094
\(376\) 13.3469 0.688314
\(377\) 14.2703 0.734958
\(378\) −8.41768 −0.432959
\(379\) 21.4740 1.10304 0.551522 0.834161i \(-0.314047\pi\)
0.551522 + 0.834161i \(0.314047\pi\)
\(380\) −6.66167 −0.341736
\(381\) 43.2591 2.21623
\(382\) 13.4440 0.687854
\(383\) −28.8202 −1.47265 −0.736323 0.676630i \(-0.763440\pi\)
−0.736323 + 0.676630i \(0.763440\pi\)
\(384\) 18.6217 0.950284
\(385\) 12.5969 0.641998
\(386\) 1.22237 0.0622169
\(387\) 14.7250 0.748514
\(388\) −0.331698 −0.0168394
\(389\) −18.9124 −0.958896 −0.479448 0.877570i \(-0.659163\pi\)
−0.479448 + 0.877570i \(0.659163\pi\)
\(390\) −3.07117 −0.155515
\(391\) 0.267315 0.0135187
\(392\) 51.0364 2.57773
\(393\) −45.3629 −2.28825
\(394\) −3.94756 −0.198875
\(395\) 0.332665 0.0167382
\(396\) −8.79607 −0.442019
\(397\) 8.57041 0.430137 0.215068 0.976599i \(-0.431003\pi\)
0.215068 + 0.976599i \(0.431003\pi\)
\(398\) −11.4767 −0.575273
\(399\) 73.5739 3.68330
\(400\) −1.62498 −0.0812489
\(401\) 8.96307 0.447595 0.223797 0.974636i \(-0.428155\pi\)
0.223797 + 0.974636i \(0.428155\pi\)
\(402\) 18.7791 0.936616
\(403\) 8.43371 0.420113
\(404\) 1.00347 0.0499246
\(405\) 8.55398 0.425051
\(406\) −28.5308 −1.41596
\(407\) −18.1675 −0.900529
\(408\) −0.674930 −0.0334140
\(409\) −3.36946 −0.166609 −0.0833045 0.996524i \(-0.526547\pi\)
−0.0833045 + 0.996524i \(0.526547\pi\)
\(410\) 6.12254 0.302371
\(411\) 1.09254 0.0538912
\(412\) 10.7057 0.527434
\(413\) −27.0820 −1.33262
\(414\) 4.27594 0.210151
\(415\) −1.81667 −0.0891766
\(416\) 12.1055 0.593520
\(417\) 26.5984 1.30253
\(418\) 16.8129 0.822346
\(419\) 21.4455 1.04768 0.523841 0.851816i \(-0.324499\pi\)
0.523841 + 0.851816i \(0.324499\pi\)
\(420\) −11.8534 −0.578386
\(421\) 30.3392 1.47864 0.739321 0.673353i \(-0.235146\pi\)
0.739321 + 0.673353i \(0.235146\pi\)
\(422\) 20.3776 0.991964
\(423\) 10.2729 0.499484
\(424\) −36.7681 −1.78561
\(425\) 0.477369 0.0231558
\(426\) −25.5892 −1.23980
\(427\) −32.2975 −1.56299
\(428\) −9.11466 −0.440574
\(429\) −14.9631 −0.722426
\(430\) 4.53449 0.218673
\(431\) 16.9804 0.817915 0.408958 0.912553i \(-0.365892\pi\)
0.408958 + 0.912553i \(0.365892\pi\)
\(432\) −0.746525 −0.0359172
\(433\) 6.02425 0.289507 0.144753 0.989468i \(-0.453761\pi\)
0.144753 + 0.989468i \(0.453761\pi\)
\(434\) −16.8616 −0.809383
\(435\) 12.1268 0.581435
\(436\) −10.3282 −0.494631
\(437\) 15.7777 0.754751
\(438\) −23.8262 −1.13846
\(439\) 11.3630 0.542328 0.271164 0.962533i \(-0.412592\pi\)
0.271164 + 0.962533i \(0.412592\pi\)
\(440\) −6.82056 −0.325158
\(441\) 39.2818 1.87056
\(442\) −0.188248 −0.00895405
\(443\) 11.0858 0.526703 0.263351 0.964700i \(-0.415172\pi\)
0.263351 + 0.964700i \(0.415172\pi\)
\(444\) 17.0952 0.811301
\(445\) 9.63035 0.456522
\(446\) 7.09348 0.335886
\(447\) 8.12423 0.384263
\(448\) −20.4482 −0.966089
\(449\) −18.5315 −0.874554 −0.437277 0.899327i \(-0.644057\pi\)
−0.437277 + 0.899327i \(0.644057\pi\)
\(450\) 7.63595 0.359962
\(451\) 29.8298 1.40463
\(452\) 13.1542 0.618721
\(453\) −27.9978 −1.31545
\(454\) 20.8496 0.978518
\(455\) −8.32478 −0.390272
\(456\) −39.8364 −1.86551
\(457\) 3.77862 0.176756 0.0883782 0.996087i \(-0.471832\pi\)
0.0883782 + 0.996087i \(0.471832\pi\)
\(458\) 8.47829 0.396165
\(459\) 0.219307 0.0102364
\(460\) −2.54193 −0.118518
\(461\) −12.7036 −0.591665 −0.295833 0.955240i \(-0.595597\pi\)
−0.295833 + 0.955240i \(0.595597\pi\)
\(462\) 29.9159 1.39182
\(463\) −8.23426 −0.382678 −0.191339 0.981524i \(-0.561283\pi\)
−0.191339 + 0.981524i \(0.561283\pi\)
\(464\) −2.53026 −0.117465
\(465\) 7.16690 0.332357
\(466\) −0.324945 −0.0150528
\(467\) 3.12314 0.144521 0.0722607 0.997386i \(-0.476979\pi\)
0.0722607 + 0.997386i \(0.476979\pi\)
\(468\) 5.81296 0.268704
\(469\) 50.9030 2.35048
\(470\) 3.16348 0.145920
\(471\) −50.7508 −2.33847
\(472\) 14.6635 0.674940
\(473\) 22.0926 1.01582
\(474\) 0.790034 0.0362875
\(475\) 28.1757 1.29279
\(476\) −0.726556 −0.0333017
\(477\) −28.2997 −1.29575
\(478\) 3.86702 0.176874
\(479\) −4.21771 −0.192712 −0.0963561 0.995347i \(-0.530719\pi\)
−0.0963561 + 0.995347i \(0.530719\pi\)
\(480\) 10.2871 0.469542
\(481\) 12.0061 0.547433
\(482\) −12.7853 −0.582353
\(483\) 28.0740 1.27741
\(484\) 1.29547 0.0588851
\(485\) −0.197964 −0.00898908
\(486\) 15.3256 0.695182
\(487\) 22.7931 1.03285 0.516427 0.856331i \(-0.327262\pi\)
0.516427 + 0.856331i \(0.327262\pi\)
\(488\) 17.4874 0.791618
\(489\) −7.69831 −0.348130
\(490\) 12.0966 0.546470
\(491\) −6.80067 −0.306910 −0.153455 0.988156i \(-0.549040\pi\)
−0.153455 + 0.988156i \(0.549040\pi\)
\(492\) −28.0691 −1.26545
\(493\) 0.743315 0.0334772
\(494\) −11.1110 −0.499906
\(495\) −5.24966 −0.235955
\(496\) −1.49538 −0.0671444
\(497\) −69.3626 −3.11134
\(498\) −4.31433 −0.193330
\(499\) 5.63452 0.252236 0.126118 0.992015i \(-0.459748\pi\)
0.126118 + 0.992015i \(0.459748\pi\)
\(500\) −9.71925 −0.434658
\(501\) −1.39492 −0.0623206
\(502\) −6.55413 −0.292525
\(503\) −23.7525 −1.05907 −0.529535 0.848288i \(-0.677634\pi\)
−0.529535 + 0.848288i \(0.677634\pi\)
\(504\) −29.2642 −1.30353
\(505\) 0.598892 0.0266503
\(506\) 6.41539 0.285199
\(507\) −19.4968 −0.865885
\(508\) −25.2141 −1.11870
\(509\) −38.4562 −1.70454 −0.852270 0.523101i \(-0.824775\pi\)
−0.852270 + 0.523101i \(0.824775\pi\)
\(510\) −0.159972 −0.00708367
\(511\) −64.5838 −2.85702
\(512\) −4.17922 −0.184697
\(513\) 12.9441 0.571497
\(514\) 18.0749 0.797250
\(515\) 6.38939 0.281550
\(516\) −20.7886 −0.915167
\(517\) 15.4129 0.677857
\(518\) −24.0040 −1.05468
\(519\) 18.3573 0.805795
\(520\) 4.50743 0.197664
\(521\) 14.0011 0.613401 0.306701 0.951806i \(-0.400775\pi\)
0.306701 + 0.951806i \(0.400775\pi\)
\(522\) 11.8900 0.520410
\(523\) −9.02076 −0.394450 −0.197225 0.980358i \(-0.563193\pi\)
−0.197225 + 0.980358i \(0.563193\pi\)
\(524\) 26.4403 1.15505
\(525\) 50.1343 2.18804
\(526\) −13.9197 −0.606926
\(527\) 0.439297 0.0191361
\(528\) 2.65311 0.115462
\(529\) −16.9796 −0.738244
\(530\) −8.71476 −0.378545
\(531\) 11.2862 0.489779
\(532\) −42.8835 −1.85924
\(533\) −19.7133 −0.853876
\(534\) 22.8708 0.989715
\(535\) −5.43980 −0.235183
\(536\) −27.5613 −1.19047
\(537\) −12.1758 −0.525423
\(538\) −5.30937 −0.228903
\(539\) 58.9363 2.53857
\(540\) −2.08541 −0.0897418
\(541\) −40.7851 −1.75349 −0.876743 0.480959i \(-0.840289\pi\)
−0.876743 + 0.480959i \(0.840289\pi\)
\(542\) −16.4509 −0.706626
\(543\) 17.3702 0.745425
\(544\) 0.630553 0.0270347
\(545\) −6.16407 −0.264040
\(546\) −19.7702 −0.846087
\(547\) −1.00000 −0.0427569
\(548\) −0.636803 −0.0272029
\(549\) 13.4597 0.574448
\(550\) 11.4566 0.488509
\(551\) 43.8726 1.86904
\(552\) −15.2006 −0.646980
\(553\) 2.14148 0.0910651
\(554\) 2.11703 0.0899439
\(555\) 10.2027 0.433082
\(556\) −15.5033 −0.657484
\(557\) −35.9029 −1.52125 −0.760627 0.649190i \(-0.775108\pi\)
−0.760627 + 0.649190i \(0.775108\pi\)
\(558\) 7.02694 0.297474
\(559\) −14.6001 −0.617518
\(560\) 1.47606 0.0623751
\(561\) −0.779402 −0.0329064
\(562\) 7.58310 0.319874
\(563\) 15.3436 0.646657 0.323329 0.946287i \(-0.395198\pi\)
0.323329 + 0.946287i \(0.395198\pi\)
\(564\) −14.5031 −0.610692
\(565\) 7.85067 0.330280
\(566\) 13.4690 0.566145
\(567\) 55.0650 2.31251
\(568\) 37.5562 1.57582
\(569\) −5.21447 −0.218602 −0.109301 0.994009i \(-0.534861\pi\)
−0.109301 + 0.994009i \(0.534861\pi\)
\(570\) −9.44201 −0.395482
\(571\) 4.18745 0.175239 0.0876196 0.996154i \(-0.472074\pi\)
0.0876196 + 0.996154i \(0.472074\pi\)
\(572\) 8.72145 0.364662
\(573\) −36.7847 −1.53670
\(574\) 39.4130 1.64507
\(575\) 10.7512 0.448355
\(576\) 8.52165 0.355069
\(577\) 2.13588 0.0889176 0.0444588 0.999011i \(-0.485844\pi\)
0.0444588 + 0.999011i \(0.485844\pi\)
\(578\) 14.0344 0.583754
\(579\) −3.34458 −0.138996
\(580\) −7.06826 −0.293494
\(581\) −11.6945 −0.485170
\(582\) −0.470137 −0.0194878
\(583\) −42.4593 −1.75849
\(584\) 34.9687 1.44702
\(585\) 3.46929 0.143437
\(586\) 7.16062 0.295803
\(587\) −4.54834 −0.187730 −0.0938650 0.995585i \(-0.529922\pi\)
−0.0938650 + 0.995585i \(0.529922\pi\)
\(588\) −55.4576 −2.28703
\(589\) 25.9286 1.06837
\(590\) 3.47553 0.143085
\(591\) 10.8011 0.444299
\(592\) −2.12881 −0.0874933
\(593\) −21.3019 −0.874766 −0.437383 0.899275i \(-0.644095\pi\)
−0.437383 + 0.899275i \(0.644095\pi\)
\(594\) 5.26322 0.215952
\(595\) −0.433623 −0.0177768
\(596\) −4.73531 −0.193966
\(597\) 31.4018 1.28519
\(598\) −4.23967 −0.173373
\(599\) −3.77034 −0.154052 −0.0770260 0.997029i \(-0.524542\pi\)
−0.0770260 + 0.997029i \(0.524542\pi\)
\(600\) −27.1451 −1.10819
\(601\) −3.60143 −0.146905 −0.0734527 0.997299i \(-0.523402\pi\)
−0.0734527 + 0.997299i \(0.523402\pi\)
\(602\) 29.1901 1.18970
\(603\) −21.2134 −0.863877
\(604\) 16.3189 0.664005
\(605\) 0.773163 0.0314335
\(606\) 1.42229 0.0577764
\(607\) 0.723525 0.0293670 0.0146835 0.999892i \(-0.495326\pi\)
0.0146835 + 0.999892i \(0.495326\pi\)
\(608\) 37.2171 1.50935
\(609\) 78.0644 3.16333
\(610\) 4.14486 0.167821
\(611\) −10.1857 −0.412070
\(612\) 0.302787 0.0122394
\(613\) −31.8621 −1.28690 −0.643449 0.765489i \(-0.722497\pi\)
−0.643449 + 0.765489i \(0.722497\pi\)
\(614\) −9.41209 −0.379841
\(615\) −16.7522 −0.675513
\(616\) −43.9064 −1.76904
\(617\) −19.2818 −0.776255 −0.388128 0.921606i \(-0.626878\pi\)
−0.388128 + 0.921606i \(0.626878\pi\)
\(618\) 15.1739 0.610385
\(619\) 22.6679 0.911099 0.455549 0.890210i \(-0.349443\pi\)
0.455549 + 0.890210i \(0.349443\pi\)
\(620\) −4.17732 −0.167765
\(621\) 4.93916 0.198202
\(622\) 11.6129 0.465633
\(623\) 61.9940 2.48374
\(624\) −1.75333 −0.0701893
\(625\) 16.1079 0.644316
\(626\) 24.9824 0.998496
\(627\) −46.0026 −1.83717
\(628\) 29.5808 1.18040
\(629\) 0.625378 0.0249355
\(630\) −6.93618 −0.276344
\(631\) 19.6329 0.781574 0.390787 0.920481i \(-0.372203\pi\)
0.390787 + 0.920481i \(0.372203\pi\)
\(632\) −1.15950 −0.0461224
\(633\) −55.7560 −2.21610
\(634\) −25.8203 −1.02545
\(635\) −15.0483 −0.597173
\(636\) 39.9532 1.58425
\(637\) −38.9486 −1.54320
\(638\) 17.8391 0.706256
\(639\) 28.9063 1.14352
\(640\) −6.47781 −0.256058
\(641\) −1.12354 −0.0443773 −0.0221887 0.999754i \(-0.507063\pi\)
−0.0221887 + 0.999754i \(0.507063\pi\)
\(642\) −12.9188 −0.509864
\(643\) −37.6799 −1.48595 −0.742975 0.669319i \(-0.766586\pi\)
−0.742975 + 0.669319i \(0.766586\pi\)
\(644\) −16.3633 −0.644804
\(645\) −12.4070 −0.488527
\(646\) −0.578750 −0.0227706
\(647\) 20.2406 0.795740 0.397870 0.917442i \(-0.369749\pi\)
0.397870 + 0.917442i \(0.369749\pi\)
\(648\) −29.8148 −1.17124
\(649\) 16.9332 0.664686
\(650\) −7.57117 −0.296966
\(651\) 46.1358 1.80821
\(652\) 4.48706 0.175727
\(653\) −36.3954 −1.42426 −0.712131 0.702046i \(-0.752270\pi\)
−0.712131 + 0.702046i \(0.752270\pi\)
\(654\) −14.6388 −0.572423
\(655\) 15.7801 0.616580
\(656\) 3.49535 0.136471
\(657\) 26.9148 1.05005
\(658\) 20.3644 0.793888
\(659\) 21.1203 0.822729 0.411365 0.911471i \(-0.365052\pi\)
0.411365 + 0.911471i \(0.365052\pi\)
\(660\) 7.41142 0.288489
\(661\) −21.2739 −0.827458 −0.413729 0.910400i \(-0.635774\pi\)
−0.413729 + 0.910400i \(0.635774\pi\)
\(662\) −28.5813 −1.11084
\(663\) 0.515075 0.0200039
\(664\) 6.33197 0.245728
\(665\) −25.5937 −0.992481
\(666\) 10.0035 0.387627
\(667\) 16.7407 0.648203
\(668\) 0.813049 0.0314578
\(669\) −19.4088 −0.750388
\(670\) −6.53257 −0.252375
\(671\) 20.1943 0.779591
\(672\) 66.2220 2.55457
\(673\) −39.9319 −1.53926 −0.769631 0.638489i \(-0.779560\pi\)
−0.769631 + 0.638489i \(0.779560\pi\)
\(674\) −1.26577 −0.0487556
\(675\) 8.82031 0.339494
\(676\) 11.3640 0.437076
\(677\) −42.0748 −1.61706 −0.808532 0.588452i \(-0.799738\pi\)
−0.808532 + 0.588452i \(0.799738\pi\)
\(678\) 18.6443 0.716029
\(679\) −1.27436 −0.0489056
\(680\) 0.234784 0.00900355
\(681\) −57.0475 −2.18606
\(682\) 10.5428 0.403706
\(683\) −24.1077 −0.922454 −0.461227 0.887282i \(-0.652591\pi\)
−0.461227 + 0.887282i \(0.652591\pi\)
\(684\) 17.8714 0.683328
\(685\) −0.380057 −0.0145212
\(686\) 48.5985 1.85550
\(687\) −23.1979 −0.885054
\(688\) 2.58874 0.0986946
\(689\) 28.0596 1.06899
\(690\) −3.60284 −0.137158
\(691\) 1.60780 0.0611638 0.0305819 0.999532i \(-0.490264\pi\)
0.0305819 + 0.999532i \(0.490264\pi\)
\(692\) −10.6998 −0.406745
\(693\) −33.7939 −1.28372
\(694\) −13.9094 −0.527995
\(695\) −9.25264 −0.350973
\(696\) −42.2678 −1.60216
\(697\) −1.02683 −0.0388939
\(698\) 19.6260 0.742854
\(699\) 0.889097 0.0336287
\(700\) −29.2214 −1.10447
\(701\) −3.38942 −0.128017 −0.0640083 0.997949i \(-0.520388\pi\)
−0.0640083 + 0.997949i \(0.520388\pi\)
\(702\) −3.47825 −0.131278
\(703\) 36.9117 1.39215
\(704\) 12.7854 0.481869
\(705\) −8.65575 −0.325994
\(706\) −1.14944 −0.0432598
\(707\) 3.85528 0.144993
\(708\) −15.9337 −0.598827
\(709\) −5.79060 −0.217471 −0.108735 0.994071i \(-0.534680\pi\)
−0.108735 + 0.994071i \(0.534680\pi\)
\(710\) 8.90156 0.334069
\(711\) −0.892446 −0.0334693
\(712\) −33.5665 −1.25796
\(713\) 9.89371 0.370522
\(714\) −1.02979 −0.0385391
\(715\) 5.20513 0.194661
\(716\) 7.09681 0.265220
\(717\) −10.5807 −0.395145
\(718\) −23.3500 −0.871415
\(719\) −22.6574 −0.844980 −0.422490 0.906368i \(-0.638844\pi\)
−0.422490 + 0.906368i \(0.638844\pi\)
\(720\) −0.615138 −0.0229248
\(721\) 41.1308 1.53179
\(722\) −18.4631 −0.687125
\(723\) 34.9824 1.30101
\(724\) −10.1244 −0.376271
\(725\) 29.8954 1.11029
\(726\) 1.83616 0.0681461
\(727\) 16.0566 0.595507 0.297753 0.954643i \(-0.403763\pi\)
0.297753 + 0.954643i \(0.403763\pi\)
\(728\) 29.0159 1.07540
\(729\) −9.29737 −0.344347
\(730\) 8.28827 0.306763
\(731\) −0.760492 −0.0281278
\(732\) −19.0023 −0.702347
\(733\) 33.7217 1.24554 0.622770 0.782405i \(-0.286007\pi\)
0.622770 + 0.782405i \(0.286007\pi\)
\(734\) 2.49133 0.0919566
\(735\) −33.0982 −1.22085
\(736\) 14.2011 0.523461
\(737\) −31.8275 −1.17238
\(738\) −16.4250 −0.604614
\(739\) 28.8700 1.06200 0.530999 0.847372i \(-0.321817\pi\)
0.530999 + 0.847372i \(0.321817\pi\)
\(740\) −5.94679 −0.218608
\(741\) 30.4012 1.11682
\(742\) −56.0999 −2.05949
\(743\) 49.2010 1.80501 0.902505 0.430678i \(-0.141726\pi\)
0.902505 + 0.430678i \(0.141726\pi\)
\(744\) −24.9801 −0.915816
\(745\) −2.82613 −0.103541
\(746\) 25.7549 0.942955
\(747\) 4.87360 0.178316
\(748\) 0.454285 0.0166103
\(749\) −35.0179 −1.27953
\(750\) −13.7757 −0.503018
\(751\) −2.75859 −0.100663 −0.0503313 0.998733i \(-0.516028\pi\)
−0.0503313 + 0.998733i \(0.516028\pi\)
\(752\) 1.80603 0.0658590
\(753\) 17.9331 0.653518
\(754\) −11.7891 −0.429334
\(755\) 9.73941 0.354453
\(756\) −13.4245 −0.488245
\(757\) 4.96288 0.180379 0.0901894 0.995925i \(-0.471253\pi\)
0.0901894 + 0.995925i \(0.471253\pi\)
\(758\) −17.7403 −0.644356
\(759\) −17.5535 −0.637150
\(760\) 13.8576 0.502669
\(761\) 24.3799 0.883772 0.441886 0.897071i \(-0.354310\pi\)
0.441886 + 0.897071i \(0.354310\pi\)
\(762\) −35.7376 −1.29464
\(763\) −39.6803 −1.43652
\(764\) 21.4405 0.775689
\(765\) 0.180709 0.00653354
\(766\) 23.8092 0.860263
\(767\) −11.1905 −0.404064
\(768\) −33.6468 −1.21412
\(769\) −17.9443 −0.647089 −0.323544 0.946213i \(-0.604875\pi\)
−0.323544 + 0.946213i \(0.604875\pi\)
\(770\) −10.4067 −0.375031
\(771\) −49.4556 −1.78110
\(772\) 1.94943 0.0701616
\(773\) −19.3616 −0.696387 −0.348193 0.937423i \(-0.613205\pi\)
−0.348193 + 0.937423i \(0.613205\pi\)
\(774\) −12.1647 −0.437253
\(775\) 17.6681 0.634657
\(776\) 0.690001 0.0247696
\(777\) 65.6785 2.35620
\(778\) 15.6241 0.560150
\(779\) −60.6065 −2.17145
\(780\) −4.89790 −0.175373
\(781\) 43.3694 1.55188
\(782\) −0.220837 −0.00789711
\(783\) 13.7342 0.490819
\(784\) 6.90596 0.246641
\(785\) 17.6544 0.630112
\(786\) 37.4756 1.33671
\(787\) 39.9866 1.42537 0.712684 0.701486i \(-0.247480\pi\)
0.712684 + 0.701486i \(0.247480\pi\)
\(788\) −6.29557 −0.224271
\(789\) 38.0862 1.35591
\(790\) −0.274824 −0.00977781
\(791\) 50.5375 1.79691
\(792\) 18.2976 0.650178
\(793\) −13.3456 −0.473915
\(794\) −7.08027 −0.251269
\(795\) 23.8449 0.845690
\(796\) −18.3030 −0.648732
\(797\) 8.61344 0.305104 0.152552 0.988295i \(-0.451251\pi\)
0.152552 + 0.988295i \(0.451251\pi\)
\(798\) −60.7815 −2.15164
\(799\) −0.530556 −0.0187697
\(800\) 25.3603 0.896621
\(801\) −25.8355 −0.912852
\(802\) −7.40466 −0.261468
\(803\) 40.3815 1.42503
\(804\) 29.9489 1.05622
\(805\) −9.76593 −0.344204
\(806\) −6.96733 −0.245414
\(807\) 14.5272 0.511383
\(808\) −2.08743 −0.0734355
\(809\) 29.8360 1.04898 0.524488 0.851418i \(-0.324257\pi\)
0.524488 + 0.851418i \(0.324257\pi\)
\(810\) −7.06669 −0.248298
\(811\) −41.9510 −1.47310 −0.736549 0.676384i \(-0.763546\pi\)
−0.736549 + 0.676384i \(0.763546\pi\)
\(812\) −45.5009 −1.59677
\(813\) 45.0120 1.57864
\(814\) 15.0087 0.526054
\(815\) 2.67796 0.0938050
\(816\) −0.0913277 −0.00319711
\(817\) −44.8865 −1.57038
\(818\) 2.78361 0.0973266
\(819\) 22.3330 0.780379
\(820\) 9.76423 0.340982
\(821\) 31.0960 1.08526 0.542628 0.839973i \(-0.317429\pi\)
0.542628 + 0.839973i \(0.317429\pi\)
\(822\) −0.902582 −0.0314812
\(823\) 33.1740 1.15637 0.578186 0.815905i \(-0.303761\pi\)
0.578186 + 0.815905i \(0.303761\pi\)
\(824\) −22.2701 −0.775817
\(825\) −31.3468 −1.09136
\(826\) 22.3732 0.778463
\(827\) −38.5228 −1.33957 −0.669785 0.742555i \(-0.733614\pi\)
−0.669785 + 0.742555i \(0.733614\pi\)
\(828\) 6.81927 0.236986
\(829\) 19.7333 0.685366 0.342683 0.939451i \(-0.388664\pi\)
0.342683 + 0.939451i \(0.388664\pi\)
\(830\) 1.50080 0.0520936
\(831\) −5.79250 −0.200940
\(832\) −8.44936 −0.292929
\(833\) −2.02876 −0.0702924
\(834\) −21.9738 −0.760889
\(835\) 0.485243 0.0167925
\(836\) 26.8132 0.927355
\(837\) 8.11685 0.280559
\(838\) −17.7168 −0.612015
\(839\) 46.0637 1.59030 0.795149 0.606415i \(-0.207393\pi\)
0.795149 + 0.606415i \(0.207393\pi\)
\(840\) 24.6575 0.850764
\(841\) 17.5504 0.605185
\(842\) −25.0641 −0.863766
\(843\) −20.7485 −0.714615
\(844\) 32.4981 1.11863
\(845\) 6.78225 0.233316
\(846\) −8.48672 −0.291779
\(847\) 4.97712 0.171016
\(848\) −4.97524 −0.170851
\(849\) −36.8532 −1.26480
\(850\) −0.394369 −0.0135267
\(851\) 14.0846 0.482814
\(852\) −40.8096 −1.39811
\(853\) −28.2328 −0.966672 −0.483336 0.875435i \(-0.660575\pi\)
−0.483336 + 0.875435i \(0.660575\pi\)
\(854\) 26.6819 0.913037
\(855\) 10.6660 0.364769
\(856\) 18.9604 0.648052
\(857\) −14.6620 −0.500845 −0.250422 0.968137i \(-0.580569\pi\)
−0.250422 + 0.968137i \(0.580569\pi\)
\(858\) 12.3615 0.422014
\(859\) 12.2615 0.418356 0.209178 0.977878i \(-0.432921\pi\)
0.209178 + 0.977878i \(0.432921\pi\)
\(860\) 7.23160 0.246596
\(861\) −107.840 −3.67517
\(862\) −14.0280 −0.477795
\(863\) −27.6201 −0.940199 −0.470099 0.882613i \(-0.655782\pi\)
−0.470099 + 0.882613i \(0.655782\pi\)
\(864\) 11.6507 0.396364
\(865\) −6.38584 −0.217125
\(866\) −4.97681 −0.169119
\(867\) −38.4002 −1.30414
\(868\) −26.8909 −0.912736
\(869\) −1.33898 −0.0454217
\(870\) −10.0183 −0.339652
\(871\) 21.0335 0.712692
\(872\) 21.4848 0.727566
\(873\) 0.531081 0.0179744
\(874\) −13.0344 −0.440896
\(875\) −37.3407 −1.26235
\(876\) −37.9980 −1.28383
\(877\) −13.7496 −0.464293 −0.232146 0.972681i \(-0.574575\pi\)
−0.232146 + 0.972681i \(0.574575\pi\)
\(878\) −9.38733 −0.316807
\(879\) −19.5925 −0.660839
\(880\) −0.922920 −0.0311116
\(881\) −38.5777 −1.29972 −0.649858 0.760055i \(-0.725172\pi\)
−0.649858 + 0.760055i \(0.725172\pi\)
\(882\) −32.4518 −1.09271
\(883\) 52.1427 1.75474 0.877371 0.479813i \(-0.159296\pi\)
0.877371 + 0.479813i \(0.159296\pi\)
\(884\) −0.300218 −0.0100974
\(885\) −9.50956 −0.319660
\(886\) −9.15831 −0.307680
\(887\) 3.23758 0.108707 0.0543537 0.998522i \(-0.482690\pi\)
0.0543537 + 0.998522i \(0.482690\pi\)
\(888\) −35.5615 −1.19336
\(889\) −96.8711 −3.24895
\(890\) −7.95592 −0.266683
\(891\) −34.4298 −1.15344
\(892\) 11.3127 0.378776
\(893\) −31.3150 −1.04792
\(894\) −6.71166 −0.224472
\(895\) 4.23551 0.141577
\(896\) −41.6999 −1.39310
\(897\) 11.6004 0.387325
\(898\) 15.3094 0.510881
\(899\) 27.5111 0.917548
\(900\) 12.1778 0.405927
\(901\) 1.46158 0.0486922
\(902\) −24.6432 −0.820530
\(903\) −79.8685 −2.65786
\(904\) −27.3634 −0.910093
\(905\) −6.04245 −0.200858
\(906\) 23.1298 0.768435
\(907\) 25.8082 0.856946 0.428473 0.903555i \(-0.359052\pi\)
0.428473 + 0.903555i \(0.359052\pi\)
\(908\) 33.2509 1.10347
\(909\) −1.60666 −0.0532894
\(910\) 6.87734 0.227982
\(911\) 50.0860 1.65942 0.829712 0.558192i \(-0.188505\pi\)
0.829712 + 0.558192i \(0.188505\pi\)
\(912\) −5.39043 −0.178495
\(913\) 7.31208 0.241995
\(914\) −3.12163 −0.103254
\(915\) −11.3410 −0.374921
\(916\) 13.5212 0.446752
\(917\) 101.582 3.35454
\(918\) −0.181176 −0.00597968
\(919\) −1.51395 −0.0499407 −0.0249703 0.999688i \(-0.507949\pi\)
−0.0249703 + 0.999688i \(0.507949\pi\)
\(920\) 5.28773 0.174331
\(921\) 25.7529 0.848586
\(922\) 10.4948 0.345628
\(923\) −28.6611 −0.943391
\(924\) 47.7099 1.56954
\(925\) 25.1522 0.826998
\(926\) 6.80256 0.223546
\(927\) −17.1409 −0.562982
\(928\) 39.4886 1.29628
\(929\) −23.3902 −0.767408 −0.383704 0.923456i \(-0.625352\pi\)
−0.383704 + 0.923456i \(0.625352\pi\)
\(930\) −5.92078 −0.194150
\(931\) −119.743 −3.92443
\(932\) −0.518222 −0.0169749
\(933\) −31.7745 −1.04025
\(934\) −2.58011 −0.0844239
\(935\) 0.271126 0.00886676
\(936\) −12.0922 −0.395244
\(937\) −1.93988 −0.0633731 −0.0316865 0.999498i \(-0.510088\pi\)
−0.0316865 + 0.999498i \(0.510088\pi\)
\(938\) −42.0524 −1.37306
\(939\) −68.3554 −2.23070
\(940\) 5.04512 0.164554
\(941\) 58.8179 1.91741 0.958705 0.284403i \(-0.0917954\pi\)
0.958705 + 0.284403i \(0.0917954\pi\)
\(942\) 41.9267 1.36605
\(943\) −23.1259 −0.753084
\(944\) 1.98418 0.0645794
\(945\) −8.01201 −0.260631
\(946\) −18.2513 −0.593402
\(947\) 15.6362 0.508107 0.254054 0.967190i \(-0.418236\pi\)
0.254054 + 0.967190i \(0.418236\pi\)
\(948\) 1.25995 0.0409212
\(949\) −26.6865 −0.866279
\(950\) −23.2768 −0.755199
\(951\) 70.6481 2.29092
\(952\) 1.51139 0.0489843
\(953\) 37.3601 1.21021 0.605106 0.796145i \(-0.293131\pi\)
0.605106 + 0.796145i \(0.293131\pi\)
\(954\) 23.3792 0.756930
\(955\) 12.7961 0.414072
\(956\) 6.16713 0.199459
\(957\) −48.8104 −1.57782
\(958\) 3.48438 0.112575
\(959\) −2.44656 −0.0790035
\(960\) −7.18020 −0.231740
\(961\) −14.7410 −0.475516
\(962\) −9.91863 −0.319789
\(963\) 14.5934 0.470267
\(964\) −20.3900 −0.656716
\(965\) 1.16346 0.0374530
\(966\) −23.1927 −0.746214
\(967\) −16.6383 −0.535051 −0.267526 0.963551i \(-0.586206\pi\)
−0.267526 + 0.963551i \(0.586206\pi\)
\(968\) −2.69485 −0.0866157
\(969\) 1.58355 0.0508708
\(970\) 0.163544 0.00525107
\(971\) −4.34862 −0.139554 −0.0697770 0.997563i \(-0.522229\pi\)
−0.0697770 + 0.997563i \(0.522229\pi\)
\(972\) 24.4412 0.783953
\(973\) −59.5625 −1.90949
\(974\) −18.8300 −0.603353
\(975\) 20.7158 0.663438
\(976\) 2.36630 0.0757433
\(977\) 52.0366 1.66480 0.832399 0.554177i \(-0.186967\pi\)
0.832399 + 0.554177i \(0.186967\pi\)
\(978\) 6.35980 0.203364
\(979\) −38.7622 −1.23884
\(980\) 19.2917 0.616251
\(981\) 16.5364 0.527968
\(982\) 5.61823 0.179285
\(983\) 3.76181 0.119983 0.0599916 0.998199i \(-0.480893\pi\)
0.0599916 + 0.998199i \(0.480893\pi\)
\(984\) 58.3895 1.86139
\(985\) −3.75732 −0.119718
\(986\) −0.614074 −0.0195561
\(987\) −55.7201 −1.77359
\(988\) −17.7198 −0.563741
\(989\) −17.1276 −0.544625
\(990\) 4.33690 0.137836
\(991\) −41.0075 −1.30265 −0.651323 0.758801i \(-0.725786\pi\)
−0.651323 + 0.758801i \(0.725786\pi\)
\(992\) 23.3377 0.740971
\(993\) 78.2027 2.48169
\(994\) 57.3024 1.81752
\(995\) −10.9236 −0.346300
\(996\) −6.88050 −0.218017
\(997\) 12.7824 0.404823 0.202411 0.979301i \(-0.435122\pi\)
0.202411 + 0.979301i \(0.435122\pi\)
\(998\) −4.65484 −0.147346
\(999\) 11.5551 0.365586
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.1.8 18
3.2 odd 2 4923.2.a.l.1.11 18
4.3 odd 2 8752.2.a.s.1.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.8 18 1.1 even 1 trivial
4923.2.a.l.1.11 18 3.2 odd 2
8752.2.a.s.1.1 18 4.3 odd 2