Properties

Label 241.2.a.a.1.2
Level $241$
Weight $2$
Character 241.1
Self dual yes
Analytic conductor $1.924$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.92439468871\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.31056073.1
Defining polynomial: \(x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + x^{3} - 9 x^{2} + 1\)
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 1.2
Root \(-0.911223\) of defining polynomial
Character \(\chi\) \(=\) 241.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.91122 q^{2} -0.186202 q^{3} +1.65278 q^{4} -2.25110 q^{5} +0.355874 q^{6} +3.52970 q^{7} +0.663624 q^{8} -2.96533 q^{9} +O(q^{10})\) \(q-1.91122 q^{2} -0.186202 q^{3} +1.65278 q^{4} -2.25110 q^{5} +0.355874 q^{6} +3.52970 q^{7} +0.663624 q^{8} -2.96533 q^{9} +4.30235 q^{10} +0.515564 q^{11} -0.307750 q^{12} -5.38098 q^{13} -6.74604 q^{14} +0.419160 q^{15} -4.57388 q^{16} -4.16566 q^{17} +5.66741 q^{18} +4.92935 q^{19} -3.72056 q^{20} -0.657237 q^{21} -0.985358 q^{22} -7.69193 q^{23} -0.123568 q^{24} +0.0674429 q^{25} +10.2843 q^{26} +1.11076 q^{27} +5.83379 q^{28} -8.93755 q^{29} -0.801107 q^{30} -4.43182 q^{31} +7.41447 q^{32} -0.0959992 q^{33} +7.96151 q^{34} -7.94569 q^{35} -4.90102 q^{36} +5.99816 q^{37} -9.42110 q^{38} +1.00195 q^{39} -1.49388 q^{40} -8.99946 q^{41} +1.25613 q^{42} -1.66336 q^{43} +0.852112 q^{44} +6.67525 q^{45} +14.7010 q^{46} +8.55484 q^{47} +0.851668 q^{48} +5.45876 q^{49} -0.128898 q^{50} +0.775656 q^{51} -8.89356 q^{52} +13.1736 q^{53} -2.12291 q^{54} -1.16059 q^{55} +2.34239 q^{56} -0.917857 q^{57} +17.0817 q^{58} +9.25521 q^{59} +0.692776 q^{60} -10.4203 q^{61} +8.47019 q^{62} -10.4667 q^{63} -5.02293 q^{64} +12.1131 q^{65} +0.183476 q^{66} -3.91715 q^{67} -6.88490 q^{68} +1.43226 q^{69} +15.1860 q^{70} -13.6724 q^{71} -1.96786 q^{72} +11.5529 q^{73} -11.4638 q^{74} -0.0125580 q^{75} +8.14711 q^{76} +1.81979 q^{77} -1.91495 q^{78} -1.43448 q^{79} +10.2963 q^{80} +8.68916 q^{81} +17.2000 q^{82} +1.73047 q^{83} -1.08627 q^{84} +9.37732 q^{85} +3.17906 q^{86} +1.66419 q^{87} +0.342141 q^{88} -1.07999 q^{89} -12.7579 q^{90} -18.9932 q^{91} -12.7130 q^{92} +0.825214 q^{93} -16.3502 q^{94} -11.0965 q^{95} -1.38059 q^{96} -16.0883 q^{97} -10.4329 q^{98} -1.52882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} - 6q^{8} - 2q^{9} + 3q^{10} - 18q^{11} + q^{12} - q^{13} - 6q^{14} - 11q^{15} + 4q^{16} - 2q^{17} + 8q^{18} - 6q^{19} - 8q^{20} - 2q^{21} + 10q^{22} - 22q^{23} - 3q^{24} + 5q^{25} + 8q^{26} + 3q^{27} + 9q^{28} - 16q^{29} + 29q^{30} - 18q^{31} - 6q^{32} + 4q^{33} + 11q^{34} + 7q^{35} - 7q^{36} + 8q^{37} + 16q^{38} - 9q^{39} + 14q^{40} - 15q^{41} + 19q^{42} + 14q^{43} - 4q^{44} + 3q^{45} + 11q^{46} - 10q^{47} + 31q^{48} + 6q^{49} - 4q^{50} + 13q^{51} + 27q^{52} + 15q^{53} + 16q^{54} + 29q^{55} + 13q^{56} + 14q^{57} + 17q^{58} - 18q^{59} + 15q^{60} + 4q^{61} + 13q^{62} - 16q^{63} + 2q^{64} - 7q^{65} + 16q^{66} + 18q^{67} - 15q^{68} + 26q^{69} + 8q^{70} - 50q^{71} + 30q^{72} + 10q^{74} + 16q^{75} - 20q^{76} + 17q^{77} - 32q^{78} - 15q^{79} - 11q^{80} - 9q^{81} + 45q^{82} - 24q^{83} + 6q^{84} - 2q^{85} - 23q^{86} + 12q^{87} + 8q^{88} - 13q^{89} - 39q^{90} - 12q^{91} - 10q^{92} + 14q^{93} - 32q^{94} - 41q^{95} - 15q^{96} + q^{97} + 9q^{98} - 20q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.91122 −1.35144 −0.675720 0.737159i \(-0.736167\pi\)
−0.675720 + 0.737159i \(0.736167\pi\)
\(3\) −0.186202 −0.107504 −0.0537520 0.998554i \(-0.517118\pi\)
−0.0537520 + 0.998554i \(0.517118\pi\)
\(4\) 1.65278 0.826388
\(5\) −2.25110 −1.00672 −0.503361 0.864076i \(-0.667903\pi\)
−0.503361 + 0.864076i \(0.667903\pi\)
\(6\) 0.355874 0.145285
\(7\) 3.52970 1.33410 0.667050 0.745013i \(-0.267557\pi\)
0.667050 + 0.745013i \(0.267557\pi\)
\(8\) 0.663624 0.234627
\(9\) −2.96533 −0.988443
\(10\) 4.30235 1.36052
\(11\) 0.515564 0.155448 0.0777242 0.996975i \(-0.475235\pi\)
0.0777242 + 0.996975i \(0.475235\pi\)
\(12\) −0.307750 −0.0888399
\(13\) −5.38098 −1.49242 −0.746208 0.665712i \(-0.768128\pi\)
−0.746208 + 0.665712i \(0.768128\pi\)
\(14\) −6.74604 −1.80295
\(15\) 0.419160 0.108227
\(16\) −4.57388 −1.14347
\(17\) −4.16566 −1.01032 −0.505161 0.863025i \(-0.668567\pi\)
−0.505161 + 0.863025i \(0.668567\pi\)
\(18\) 5.66741 1.33582
\(19\) 4.92935 1.13087 0.565436 0.824792i \(-0.308708\pi\)
0.565436 + 0.824792i \(0.308708\pi\)
\(20\) −3.72056 −0.831942
\(21\) −0.657237 −0.143421
\(22\) −0.985358 −0.210079
\(23\) −7.69193 −1.60388 −0.801940 0.597405i \(-0.796198\pi\)
−0.801940 + 0.597405i \(0.796198\pi\)
\(24\) −0.123568 −0.0252233
\(25\) 0.0674429 0.0134886
\(26\) 10.2843 2.01691
\(27\) 1.11076 0.213765
\(28\) 5.83379 1.10248
\(29\) −8.93755 −1.65966 −0.829831 0.558015i \(-0.811563\pi\)
−0.829831 + 0.558015i \(0.811563\pi\)
\(30\) −0.801107 −0.146262
\(31\) −4.43182 −0.795978 −0.397989 0.917390i \(-0.630292\pi\)
−0.397989 + 0.917390i \(0.630292\pi\)
\(32\) 7.41447 1.31070
\(33\) −0.0959992 −0.0167113
\(34\) 7.96151 1.36539
\(35\) −7.94569 −1.34307
\(36\) −4.90102 −0.816837
\(37\) 5.99816 0.986091 0.493046 0.870003i \(-0.335884\pi\)
0.493046 + 0.870003i \(0.335884\pi\)
\(38\) −9.42110 −1.52830
\(39\) 1.00195 0.160441
\(40\) −1.49388 −0.236204
\(41\) −8.99946 −1.40548 −0.702740 0.711447i \(-0.748040\pi\)
−0.702740 + 0.711447i \(0.748040\pi\)
\(42\) 1.25613 0.193825
\(43\) −1.66336 −0.253660 −0.126830 0.991924i \(-0.540480\pi\)
−0.126830 + 0.991924i \(0.540480\pi\)
\(44\) 0.852112 0.128461
\(45\) 6.67525 0.995087
\(46\) 14.7010 2.16754
\(47\) 8.55484 1.24785 0.623926 0.781483i \(-0.285537\pi\)
0.623926 + 0.781483i \(0.285537\pi\)
\(48\) 0.851668 0.122928
\(49\) 5.45876 0.779823
\(50\) −0.128898 −0.0182290
\(51\) 0.775656 0.108614
\(52\) −8.89356 −1.23331
\(53\) 13.1736 1.80954 0.904769 0.425903i \(-0.140043\pi\)
0.904769 + 0.425903i \(0.140043\pi\)
\(54\) −2.12291 −0.288891
\(55\) −1.16059 −0.156493
\(56\) 2.34239 0.313015
\(57\) −0.917857 −0.121573
\(58\) 17.0817 2.24293
\(59\) 9.25521 1.20493 0.602463 0.798147i \(-0.294186\pi\)
0.602463 + 0.798147i \(0.294186\pi\)
\(60\) 0.692776 0.0894370
\(61\) −10.4203 −1.33418 −0.667090 0.744978i \(-0.732460\pi\)
−0.667090 + 0.744978i \(0.732460\pi\)
\(62\) 8.47019 1.07572
\(63\) −10.4667 −1.31868
\(64\) −5.02293 −0.627867
\(65\) 12.1131 1.50245
\(66\) 0.183476 0.0225843
\(67\) −3.91715 −0.478555 −0.239278 0.970951i \(-0.576911\pi\)
−0.239278 + 0.970951i \(0.576911\pi\)
\(68\) −6.88490 −0.834917
\(69\) 1.43226 0.172423
\(70\) 15.1860 1.81507
\(71\) −13.6724 −1.62262 −0.811308 0.584619i \(-0.801244\pi\)
−0.811308 + 0.584619i \(0.801244\pi\)
\(72\) −1.96786 −0.231915
\(73\) 11.5529 1.35217 0.676083 0.736825i \(-0.263676\pi\)
0.676083 + 0.736825i \(0.263676\pi\)
\(74\) −11.4638 −1.33264
\(75\) −0.0125580 −0.00145007
\(76\) 8.14711 0.934538
\(77\) 1.81979 0.207384
\(78\) −1.91495 −0.216826
\(79\) −1.43448 −0.161391 −0.0806956 0.996739i \(-0.525714\pi\)
−0.0806956 + 0.996739i \(0.525714\pi\)
\(80\) 10.2963 1.15116
\(81\) 8.68916 0.965462
\(82\) 17.2000 1.89942
\(83\) 1.73047 0.189944 0.0949720 0.995480i \(-0.469724\pi\)
0.0949720 + 0.995480i \(0.469724\pi\)
\(84\) −1.08627 −0.118521
\(85\) 9.37732 1.01711
\(86\) 3.17906 0.342807
\(87\) 1.66419 0.178420
\(88\) 0.342141 0.0364724
\(89\) −1.07999 −0.114478 −0.0572392 0.998360i \(-0.518230\pi\)
−0.0572392 + 0.998360i \(0.518230\pi\)
\(90\) −12.7579 −1.34480
\(91\) −18.9932 −1.99103
\(92\) −12.7130 −1.32543
\(93\) 0.825214 0.0855707
\(94\) −16.3502 −1.68640
\(95\) −11.0965 −1.13847
\(96\) −1.38059 −0.140906
\(97\) −16.0883 −1.63352 −0.816759 0.576979i \(-0.804231\pi\)
−0.816759 + 0.576979i \(0.804231\pi\)
\(98\) −10.4329 −1.05388
\(99\) −1.52882 −0.153652
\(100\) 0.111468 0.0111468
\(101\) −1.23922 −0.123307 −0.0616536 0.998098i \(-0.519637\pi\)
−0.0616536 + 0.998098i \(0.519637\pi\)
\(102\) −1.48245 −0.146785
\(103\) 5.27633 0.519892 0.259946 0.965623i \(-0.416295\pi\)
0.259946 + 0.965623i \(0.416295\pi\)
\(104\) −3.57095 −0.350161
\(105\) 1.47951 0.144385
\(106\) −25.1778 −2.44548
\(107\) 10.7822 1.04236 0.521178 0.853448i \(-0.325493\pi\)
0.521178 + 0.853448i \(0.325493\pi\)
\(108\) 1.83583 0.176653
\(109\) −1.15255 −0.110394 −0.0551972 0.998475i \(-0.517579\pi\)
−0.0551972 + 0.998475i \(0.517579\pi\)
\(110\) 2.21814 0.211491
\(111\) −1.11687 −0.106009
\(112\) −16.1444 −1.52550
\(113\) −8.70999 −0.819367 −0.409684 0.912228i \(-0.634361\pi\)
−0.409684 + 0.912228i \(0.634361\pi\)
\(114\) 1.75423 0.164299
\(115\) 17.3153 1.61466
\(116\) −14.7718 −1.37152
\(117\) 15.9564 1.47517
\(118\) −17.6888 −1.62838
\(119\) −14.7035 −1.34787
\(120\) 0.278165 0.0253928
\(121\) −10.7342 −0.975836
\(122\) 19.9155 1.80306
\(123\) 1.67572 0.151095
\(124\) −7.32480 −0.657786
\(125\) 11.1037 0.993142
\(126\) 20.0042 1.78212
\(127\) −8.22063 −0.729463 −0.364732 0.931113i \(-0.618839\pi\)
−0.364732 + 0.931113i \(0.618839\pi\)
\(128\) −5.22899 −0.462181
\(129\) 0.309722 0.0272695
\(130\) −23.1509 −2.03047
\(131\) −7.30323 −0.638086 −0.319043 0.947740i \(-0.603362\pi\)
−0.319043 + 0.947740i \(0.603362\pi\)
\(132\) −0.158665 −0.0138100
\(133\) 17.3991 1.50870
\(134\) 7.48654 0.646739
\(135\) −2.50042 −0.215202
\(136\) −2.76444 −0.237048
\(137\) 5.95317 0.508614 0.254307 0.967124i \(-0.418153\pi\)
0.254307 + 0.967124i \(0.418153\pi\)
\(138\) −2.73736 −0.233020
\(139\) 14.9650 1.26931 0.634656 0.772795i \(-0.281142\pi\)
0.634656 + 0.772795i \(0.281142\pi\)
\(140\) −13.1324 −1.10989
\(141\) −1.59293 −0.134149
\(142\) 26.1310 2.19287
\(143\) −2.77424 −0.231994
\(144\) 13.5631 1.13026
\(145\) 20.1193 1.67082
\(146\) −22.0802 −1.82737
\(147\) −1.01643 −0.0838340
\(148\) 9.91361 0.814894
\(149\) −0.130576 −0.0106972 −0.00534860 0.999986i \(-0.501703\pi\)
−0.00534860 + 0.999986i \(0.501703\pi\)
\(150\) 0.0240012 0.00195969
\(151\) 0.276102 0.0224688 0.0112344 0.999937i \(-0.496424\pi\)
0.0112344 + 0.999937i \(0.496424\pi\)
\(152\) 3.27124 0.265333
\(153\) 12.3526 0.998645
\(154\) −3.47802 −0.280267
\(155\) 9.97646 0.801328
\(156\) 1.65600 0.132586
\(157\) 16.1044 1.28527 0.642636 0.766172i \(-0.277841\pi\)
0.642636 + 0.766172i \(0.277841\pi\)
\(158\) 2.74160 0.218110
\(159\) −2.45296 −0.194532
\(160\) −16.6907 −1.31952
\(161\) −27.1502 −2.13973
\(162\) −16.6069 −1.30476
\(163\) −18.5215 −1.45071 −0.725357 0.688373i \(-0.758325\pi\)
−0.725357 + 0.688373i \(0.758325\pi\)
\(164\) −14.8741 −1.16147
\(165\) 0.216104 0.0168236
\(166\) −3.30732 −0.256698
\(167\) 15.5017 1.19956 0.599779 0.800166i \(-0.295255\pi\)
0.599779 + 0.800166i \(0.295255\pi\)
\(168\) −0.436159 −0.0336504
\(169\) 15.9550 1.22731
\(170\) −17.9221 −1.37457
\(171\) −14.6172 −1.11780
\(172\) −2.74916 −0.209622
\(173\) −0.366438 −0.0278597 −0.0139299 0.999903i \(-0.504434\pi\)
−0.0139299 + 0.999903i \(0.504434\pi\)
\(174\) −3.18064 −0.241124
\(175\) 0.238053 0.0179951
\(176\) −2.35813 −0.177751
\(177\) −1.72334 −0.129534
\(178\) 2.06410 0.154711
\(179\) 12.8719 0.962090 0.481045 0.876696i \(-0.340257\pi\)
0.481045 + 0.876696i \(0.340257\pi\)
\(180\) 11.0327 0.822327
\(181\) −12.2125 −0.907746 −0.453873 0.891066i \(-0.649958\pi\)
−0.453873 + 0.891066i \(0.649958\pi\)
\(182\) 36.3003 2.69076
\(183\) 1.94028 0.143429
\(184\) −5.10456 −0.376313
\(185\) −13.5024 −0.992719
\(186\) −1.57717 −0.115644
\(187\) −2.14767 −0.157053
\(188\) 14.1392 1.03121
\(189\) 3.92064 0.285184
\(190\) 21.2078 1.53858
\(191\) −3.92400 −0.283930 −0.141965 0.989872i \(-0.545342\pi\)
−0.141965 + 0.989872i \(0.545342\pi\)
\(192\) 0.935281 0.0674981
\(193\) −1.69319 −0.121879 −0.0609393 0.998141i \(-0.519410\pi\)
−0.0609393 + 0.998141i \(0.519410\pi\)
\(194\) 30.7483 2.20760
\(195\) −2.25549 −0.161519
\(196\) 9.02210 0.644436
\(197\) −2.20382 −0.157016 −0.0785080 0.996913i \(-0.525016\pi\)
−0.0785080 + 0.996913i \(0.525016\pi\)
\(198\) 2.92191 0.207651
\(199\) −15.5533 −1.10255 −0.551274 0.834324i \(-0.685858\pi\)
−0.551274 + 0.834324i \(0.685858\pi\)
\(200\) 0.0447567 0.00316478
\(201\) 0.729381 0.0514466
\(202\) 2.36843 0.166642
\(203\) −31.5468 −2.21415
\(204\) 1.28198 0.0897569
\(205\) 20.2587 1.41493
\(206\) −10.0842 −0.702603
\(207\) 22.8091 1.58534
\(208\) 24.6120 1.70654
\(209\) 2.54140 0.175792
\(210\) −2.82767 −0.195128
\(211\) 6.55996 0.451606 0.225803 0.974173i \(-0.427499\pi\)
0.225803 + 0.974173i \(0.427499\pi\)
\(212\) 21.7731 1.49538
\(213\) 2.54583 0.174438
\(214\) −20.6072 −1.40868
\(215\) 3.74439 0.255365
\(216\) 0.737126 0.0501551
\(217\) −15.6430 −1.06191
\(218\) 2.20278 0.149191
\(219\) −2.15118 −0.145363
\(220\) −1.91819 −0.129324
\(221\) 22.4154 1.50782
\(222\) 2.13459 0.143264
\(223\) 6.53800 0.437817 0.218908 0.975745i \(-0.429750\pi\)
0.218908 + 0.975745i \(0.429750\pi\)
\(224\) 26.1708 1.74861
\(225\) −0.199990 −0.0133327
\(226\) 16.6467 1.10732
\(227\) 16.1673 1.07306 0.536530 0.843881i \(-0.319735\pi\)
0.536530 + 0.843881i \(0.319735\pi\)
\(228\) −1.51701 −0.100466
\(229\) 0.0208412 0.00137722 0.000688612 1.00000i \(-0.499781\pi\)
0.000688612 1.00000i \(0.499781\pi\)
\(230\) −33.0934 −2.18211
\(231\) −0.338848 −0.0222946
\(232\) −5.93118 −0.389401
\(233\) −0.651845 −0.0427038 −0.0213519 0.999772i \(-0.506797\pi\)
−0.0213519 + 0.999772i \(0.506797\pi\)
\(234\) −30.4962 −1.99360
\(235\) −19.2578 −1.25624
\(236\) 15.2968 0.995736
\(237\) 0.267103 0.0173502
\(238\) 28.1017 1.82156
\(239\) −8.99997 −0.582160 −0.291080 0.956699i \(-0.594015\pi\)
−0.291080 + 0.956699i \(0.594015\pi\)
\(240\) −1.91719 −0.123754
\(241\) −1.00000 −0.0644157
\(242\) 20.5154 1.31878
\(243\) −4.95021 −0.317556
\(244\) −17.2224 −1.10255
\(245\) −12.2882 −0.785064
\(246\) −3.20268 −0.204195
\(247\) −26.5248 −1.68773
\(248\) −2.94106 −0.186758
\(249\) −0.322218 −0.0204197
\(250\) −21.2216 −1.34217
\(251\) 16.4986 1.04138 0.520691 0.853745i \(-0.325674\pi\)
0.520691 + 0.853745i \(0.325674\pi\)
\(252\) −17.2991 −1.08974
\(253\) −3.96569 −0.249321
\(254\) 15.7115 0.985825
\(255\) −1.74608 −0.109344
\(256\) 20.0396 1.25248
\(257\) 7.99029 0.498420 0.249210 0.968449i \(-0.419829\pi\)
0.249210 + 0.968449i \(0.419829\pi\)
\(258\) −0.591948 −0.0368530
\(259\) 21.1717 1.31554
\(260\) 20.0203 1.24160
\(261\) 26.5028 1.64048
\(262\) 13.9581 0.862335
\(263\) −5.47488 −0.337595 −0.168798 0.985651i \(-0.553988\pi\)
−0.168798 + 0.985651i \(0.553988\pi\)
\(264\) −0.0637074 −0.00392092
\(265\) −29.6551 −1.82170
\(266\) −33.2536 −2.03891
\(267\) 0.201096 0.0123069
\(268\) −6.47416 −0.395472
\(269\) −2.34697 −0.143097 −0.0715486 0.997437i \(-0.522794\pi\)
−0.0715486 + 0.997437i \(0.522794\pi\)
\(270\) 4.77887 0.290833
\(271\) 1.60301 0.0973758 0.0486879 0.998814i \(-0.484496\pi\)
0.0486879 + 0.998814i \(0.484496\pi\)
\(272\) 19.0533 1.15527
\(273\) 3.53658 0.214044
\(274\) −11.3778 −0.687360
\(275\) 0.0347711 0.00209678
\(276\) 2.36720 0.142488
\(277\) −21.6775 −1.30247 −0.651237 0.758875i \(-0.725750\pi\)
−0.651237 + 0.758875i \(0.725750\pi\)
\(278\) −28.6014 −1.71540
\(279\) 13.1418 0.786779
\(280\) −5.27296 −0.315119
\(281\) 26.9010 1.60478 0.802388 0.596802i \(-0.203562\pi\)
0.802388 + 0.596802i \(0.203562\pi\)
\(282\) 3.04445 0.181294
\(283\) 3.89230 0.231373 0.115687 0.993286i \(-0.463093\pi\)
0.115687 + 0.993286i \(0.463093\pi\)
\(284\) −22.5974 −1.34091
\(285\) 2.06619 0.122390
\(286\) 5.30220 0.313526
\(287\) −31.7654 −1.87505
\(288\) −21.9863 −1.29556
\(289\) 0.352752 0.0207501
\(290\) −38.4525 −2.25801
\(291\) 2.99567 0.175610
\(292\) 19.0944 1.11741
\(293\) −5.57389 −0.325630 −0.162815 0.986657i \(-0.552057\pi\)
−0.162815 + 0.986657i \(0.552057\pi\)
\(294\) 1.94263 0.113297
\(295\) −20.8344 −1.21302
\(296\) 3.98053 0.231363
\(297\) 0.572667 0.0332295
\(298\) 0.249560 0.0144566
\(299\) 41.3902 2.39366
\(300\) −0.0207556 −0.00119832
\(301\) −5.87116 −0.338408
\(302\) −0.527692 −0.0303652
\(303\) 0.230746 0.0132560
\(304\) −22.5463 −1.29312
\(305\) 23.4571 1.34315
\(306\) −23.6085 −1.34961
\(307\) 23.0795 1.31722 0.658608 0.752486i \(-0.271146\pi\)
0.658608 + 0.752486i \(0.271146\pi\)
\(308\) 3.00770 0.171379
\(309\) −0.982465 −0.0558905
\(310\) −19.0672 −1.08295
\(311\) −14.9884 −0.849916 −0.424958 0.905213i \(-0.639711\pi\)
−0.424958 + 0.905213i \(0.639711\pi\)
\(312\) 0.664919 0.0376437
\(313\) −2.31082 −0.130615 −0.0653076 0.997865i \(-0.520803\pi\)
−0.0653076 + 0.997865i \(0.520803\pi\)
\(314\) −30.7791 −1.73697
\(315\) 23.5616 1.32755
\(316\) −2.37087 −0.133372
\(317\) −18.3630 −1.03137 −0.515684 0.856779i \(-0.672462\pi\)
−0.515684 + 0.856779i \(0.672462\pi\)
\(318\) 4.68816 0.262899
\(319\) −4.60788 −0.257992
\(320\) 11.3071 0.632087
\(321\) −2.00767 −0.112057
\(322\) 51.8901 2.89172
\(323\) −20.5340 −1.14254
\(324\) 14.3612 0.797846
\(325\) −0.362909 −0.0201306
\(326\) 35.3987 1.96055
\(327\) 0.214608 0.0118678
\(328\) −5.97226 −0.329763
\(329\) 30.1960 1.66476
\(330\) −0.413022 −0.0227361
\(331\) −6.47933 −0.356136 −0.178068 0.984018i \(-0.556985\pi\)
−0.178068 + 0.984018i \(0.556985\pi\)
\(332\) 2.86008 0.156967
\(333\) −17.7865 −0.974695
\(334\) −29.6272 −1.62113
\(335\) 8.81788 0.481772
\(336\) 3.00613 0.163998
\(337\) −3.54257 −0.192976 −0.0964880 0.995334i \(-0.530761\pi\)
−0.0964880 + 0.995334i \(0.530761\pi\)
\(338\) −30.4936 −1.65863
\(339\) 1.62182 0.0880852
\(340\) 15.4986 0.840529
\(341\) −2.28489 −0.123734
\(342\) 27.9366 1.51064
\(343\) −5.44011 −0.293739
\(344\) −1.10385 −0.0595155
\(345\) −3.22415 −0.173582
\(346\) 0.700344 0.0376507
\(347\) −14.4844 −0.777566 −0.388783 0.921329i \(-0.627104\pi\)
−0.388783 + 0.921329i \(0.627104\pi\)
\(348\) 2.75053 0.147444
\(349\) −23.6287 −1.26482 −0.632408 0.774636i \(-0.717933\pi\)
−0.632408 + 0.774636i \(0.717933\pi\)
\(350\) −0.454972 −0.0243193
\(351\) −5.97697 −0.319027
\(352\) 3.82263 0.203747
\(353\) −18.2662 −0.972209 −0.486105 0.873901i \(-0.661583\pi\)
−0.486105 + 0.873901i \(0.661583\pi\)
\(354\) 3.29369 0.175058
\(355\) 30.7779 1.63352
\(356\) −1.78498 −0.0946036
\(357\) 2.73783 0.144901
\(358\) −24.6010 −1.30021
\(359\) −20.3758 −1.07539 −0.537697 0.843138i \(-0.680706\pi\)
−0.537697 + 0.843138i \(0.680706\pi\)
\(360\) 4.42986 0.233474
\(361\) 5.29852 0.278870
\(362\) 23.3408 1.22676
\(363\) 1.99873 0.104906
\(364\) −31.3916 −1.64536
\(365\) −26.0067 −1.36125
\(366\) −3.70830 −0.193836
\(367\) −1.76412 −0.0920862 −0.0460431 0.998939i \(-0.514661\pi\)
−0.0460431 + 0.998939i \(0.514661\pi\)
\(368\) 35.1820 1.83399
\(369\) 26.6864 1.38924
\(370\) 25.8062 1.34160
\(371\) 46.4989 2.41410
\(372\) 1.36389 0.0707146
\(373\) −32.1736 −1.66589 −0.832943 0.553359i \(-0.813346\pi\)
−0.832943 + 0.553359i \(0.813346\pi\)
\(374\) 4.10467 0.212247
\(375\) −2.06753 −0.106767
\(376\) 5.67720 0.292779
\(377\) 48.0928 2.47691
\(378\) −7.49321 −0.385409
\(379\) −31.3680 −1.61126 −0.805632 0.592416i \(-0.798174\pi\)
−0.805632 + 0.592416i \(0.798174\pi\)
\(380\) −18.3399 −0.940820
\(381\) 1.53070 0.0784201
\(382\) 7.49963 0.383715
\(383\) 16.8623 0.861624 0.430812 0.902442i \(-0.358227\pi\)
0.430812 + 0.902442i \(0.358227\pi\)
\(384\) 0.973649 0.0496863
\(385\) −4.09651 −0.208778
\(386\) 3.23607 0.164712
\(387\) 4.93242 0.250729
\(388\) −26.5903 −1.34992
\(389\) −0.816001 −0.0413729 −0.0206864 0.999786i \(-0.506585\pi\)
−0.0206864 + 0.999786i \(0.506585\pi\)
\(390\) 4.31075 0.218283
\(391\) 32.0420 1.62043
\(392\) 3.62257 0.182967
\(393\) 1.35988 0.0685968
\(394\) 4.21200 0.212198
\(395\) 3.22915 0.162476
\(396\) −2.52679 −0.126976
\(397\) −21.8279 −1.09551 −0.547755 0.836639i \(-0.684517\pi\)
−0.547755 + 0.836639i \(0.684517\pi\)
\(398\) 29.7259 1.49003
\(399\) −3.23976 −0.162191
\(400\) −0.308476 −0.0154238
\(401\) −15.4857 −0.773321 −0.386661 0.922222i \(-0.626372\pi\)
−0.386661 + 0.922222i \(0.626372\pi\)
\(402\) −1.39401 −0.0695269
\(403\) 23.8475 1.18793
\(404\) −2.04816 −0.101900
\(405\) −19.5602 −0.971952
\(406\) 60.2931 2.99229
\(407\) 3.09244 0.153286
\(408\) 0.514744 0.0254836
\(409\) 26.0377 1.28748 0.643740 0.765245i \(-0.277382\pi\)
0.643740 + 0.765245i \(0.277382\pi\)
\(410\) −38.7189 −1.91219
\(411\) −1.10849 −0.0546780
\(412\) 8.72059 0.429633
\(413\) 32.6681 1.60749
\(414\) −43.5933 −2.14249
\(415\) −3.89546 −0.191221
\(416\) −39.8971 −1.95612
\(417\) −2.78651 −0.136456
\(418\) −4.85718 −0.237572
\(419\) −33.2204 −1.62292 −0.811462 0.584406i \(-0.801328\pi\)
−0.811462 + 0.584406i \(0.801328\pi\)
\(420\) 2.44529 0.119318
\(421\) 2.90586 0.141623 0.0708115 0.997490i \(-0.477441\pi\)
0.0708115 + 0.997490i \(0.477441\pi\)
\(422\) −12.5375 −0.610318
\(423\) −25.3679 −1.23343
\(424\) 8.74235 0.424566
\(425\) −0.280944 −0.0136278
\(426\) −4.86565 −0.235742
\(427\) −36.7804 −1.77993
\(428\) 17.8206 0.861390
\(429\) 0.516570 0.0249402
\(430\) −7.15637 −0.345111
\(431\) −28.4892 −1.37228 −0.686139 0.727471i \(-0.740696\pi\)
−0.686139 + 0.727471i \(0.740696\pi\)
\(432\) −5.08048 −0.244435
\(433\) −28.9311 −1.39034 −0.695169 0.718846i \(-0.744671\pi\)
−0.695169 + 0.718846i \(0.744671\pi\)
\(434\) 29.8972 1.43511
\(435\) −3.74626 −0.179619
\(436\) −1.90491 −0.0912286
\(437\) −37.9163 −1.81378
\(438\) 4.11138 0.196449
\(439\) −8.92156 −0.425803 −0.212901 0.977074i \(-0.568291\pi\)
−0.212901 + 0.977074i \(0.568291\pi\)
\(440\) −0.770193 −0.0367175
\(441\) −16.1870 −0.770810
\(442\) −42.8408 −2.03773
\(443\) 24.8216 1.17931 0.589656 0.807655i \(-0.299264\pi\)
0.589656 + 0.807655i \(0.299264\pi\)
\(444\) −1.84594 −0.0876042
\(445\) 2.43116 0.115248
\(446\) −12.4956 −0.591683
\(447\) 0.0243136 0.00114999
\(448\) −17.7294 −0.837637
\(449\) 11.9254 0.562793 0.281397 0.959592i \(-0.409202\pi\)
0.281397 + 0.959592i \(0.409202\pi\)
\(450\) 0.382226 0.0180183
\(451\) −4.63980 −0.218480
\(452\) −14.3957 −0.677115
\(453\) −0.0514107 −0.00241549
\(454\) −30.8993 −1.45018
\(455\) 42.7557 2.00442
\(456\) −0.609112 −0.0285243
\(457\) 8.44205 0.394902 0.197451 0.980313i \(-0.436734\pi\)
0.197451 + 0.980313i \(0.436734\pi\)
\(458\) −0.0398321 −0.00186123
\(459\) −4.62704 −0.215972
\(460\) 28.6183 1.33433
\(461\) 23.2925 1.08484 0.542419 0.840108i \(-0.317509\pi\)
0.542419 + 0.840108i \(0.317509\pi\)
\(462\) 0.647614 0.0301297
\(463\) 1.66578 0.0774152 0.0387076 0.999251i \(-0.487676\pi\)
0.0387076 + 0.999251i \(0.487676\pi\)
\(464\) 40.8793 1.89777
\(465\) −1.85764 −0.0861459
\(466\) 1.24582 0.0577116
\(467\) −6.66428 −0.308386 −0.154193 0.988041i \(-0.549278\pi\)
−0.154193 + 0.988041i \(0.549278\pi\)
\(468\) 26.3723 1.21906
\(469\) −13.8263 −0.638441
\(470\) 36.8059 1.69773
\(471\) −2.99868 −0.138172
\(472\) 6.14198 0.282708
\(473\) −0.857570 −0.0394311
\(474\) −0.510493 −0.0234477
\(475\) 0.332450 0.0152538
\(476\) −24.3016 −1.11386
\(477\) −39.0642 −1.78863
\(478\) 17.2010 0.786753
\(479\) −13.6902 −0.625523 −0.312762 0.949832i \(-0.601254\pi\)
−0.312762 + 0.949832i \(0.601254\pi\)
\(480\) 3.10784 0.141853
\(481\) −32.2760 −1.47166
\(482\) 1.91122 0.0870538
\(483\) 5.05543 0.230030
\(484\) −17.7412 −0.806419
\(485\) 36.2163 1.64450
\(486\) 9.46096 0.429158
\(487\) 31.9634 1.44840 0.724200 0.689590i \(-0.242209\pi\)
0.724200 + 0.689590i \(0.242209\pi\)
\(488\) −6.91515 −0.313034
\(489\) 3.44874 0.155957
\(490\) 23.4855 1.06097
\(491\) −10.0550 −0.453777 −0.226889 0.973921i \(-0.572855\pi\)
−0.226889 + 0.973921i \(0.572855\pi\)
\(492\) 2.76959 0.124863
\(493\) 37.2308 1.67679
\(494\) 50.6948 2.28087
\(495\) 3.44152 0.154685
\(496\) 20.2706 0.910178
\(497\) −48.2594 −2.16473
\(498\) 0.615830 0.0275960
\(499\) 9.14295 0.409295 0.204647 0.978836i \(-0.434395\pi\)
0.204647 + 0.978836i \(0.434395\pi\)
\(500\) 18.3519 0.820721
\(501\) −2.88645 −0.128957
\(502\) −31.5325 −1.40736
\(503\) −27.2050 −1.21301 −0.606506 0.795079i \(-0.707429\pi\)
−0.606506 + 0.795079i \(0.707429\pi\)
\(504\) −6.94597 −0.309398
\(505\) 2.78961 0.124136
\(506\) 7.57931 0.336941
\(507\) −2.97086 −0.131940
\(508\) −13.5869 −0.602819
\(509\) 7.79598 0.345551 0.172775 0.984961i \(-0.444726\pi\)
0.172775 + 0.984961i \(0.444726\pi\)
\(510\) 3.33714 0.147771
\(511\) 40.7783 1.80392
\(512\) −27.8422 −1.23046
\(513\) 5.47532 0.241741
\(514\) −15.2712 −0.673585
\(515\) −11.8775 −0.523387
\(516\) 0.511900 0.0225352
\(517\) 4.41057 0.193977
\(518\) −40.4638 −1.77788
\(519\) 0.0682315 0.00299503
\(520\) 8.03857 0.352514
\(521\) 32.6959 1.43243 0.716216 0.697878i \(-0.245872\pi\)
0.716216 + 0.697878i \(0.245872\pi\)
\(522\) −50.6527 −2.21701
\(523\) −7.80136 −0.341129 −0.170565 0.985346i \(-0.554559\pi\)
−0.170565 + 0.985346i \(0.554559\pi\)
\(524\) −12.0706 −0.527307
\(525\) −0.0443260 −0.00193454
\(526\) 10.4637 0.456240
\(527\) 18.4615 0.804194
\(528\) 0.439089 0.0191089
\(529\) 36.1658 1.57243
\(530\) 56.6776 2.46192
\(531\) −27.4447 −1.19100
\(532\) 28.7568 1.24677
\(533\) 48.4260 2.09756
\(534\) −0.384340 −0.0166320
\(535\) −24.2718 −1.04936
\(536\) −2.59951 −0.112282
\(537\) −2.39677 −0.103428
\(538\) 4.48558 0.193387
\(539\) 2.81434 0.121222
\(540\) −4.13264 −0.177840
\(541\) 22.3971 0.962926 0.481463 0.876467i \(-0.340106\pi\)
0.481463 + 0.876467i \(0.340106\pi\)
\(542\) −3.06371 −0.131597
\(543\) 2.27399 0.0975863
\(544\) −30.8862 −1.32423
\(545\) 2.59451 0.111136
\(546\) −6.75920 −0.289267
\(547\) 37.2322 1.59193 0.795966 0.605341i \(-0.206963\pi\)
0.795966 + 0.605341i \(0.206963\pi\)
\(548\) 9.83925 0.420312
\(549\) 30.8995 1.31876
\(550\) −0.0664554 −0.00283367
\(551\) −44.0563 −1.87686
\(552\) 0.950480 0.0404551
\(553\) −5.06326 −0.215312
\(554\) 41.4305 1.76021
\(555\) 2.51419 0.106721
\(556\) 24.7337 1.04894
\(557\) −27.6457 −1.17139 −0.585693 0.810533i \(-0.699177\pi\)
−0.585693 + 0.810533i \(0.699177\pi\)
\(558\) −25.1169 −1.06328
\(559\) 8.95053 0.378567
\(560\) 36.3427 1.53576
\(561\) 0.399900 0.0168838
\(562\) −51.4138 −2.16876
\(563\) −23.3454 −0.983891 −0.491945 0.870626i \(-0.663714\pi\)
−0.491945 + 0.870626i \(0.663714\pi\)
\(564\) −2.63276 −0.110859
\(565\) 19.6070 0.824875
\(566\) −7.43905 −0.312687
\(567\) 30.6701 1.28802
\(568\) −9.07334 −0.380709
\(569\) 2.61346 0.109562 0.0547811 0.998498i \(-0.482554\pi\)
0.0547811 + 0.998498i \(0.482554\pi\)
\(570\) −3.94894 −0.165403
\(571\) 16.9259 0.708326 0.354163 0.935184i \(-0.384766\pi\)
0.354163 + 0.935184i \(0.384766\pi\)
\(572\) −4.58520 −0.191717
\(573\) 0.730657 0.0305236
\(574\) 60.7107 2.53402
\(575\) −0.518766 −0.0216340
\(576\) 14.8946 0.620610
\(577\) 4.67534 0.194637 0.0973185 0.995253i \(-0.468973\pi\)
0.0973185 + 0.995253i \(0.468973\pi\)
\(578\) −0.674188 −0.0280425
\(579\) 0.315276 0.0131024
\(580\) 33.2527 1.38074
\(581\) 6.10804 0.253404
\(582\) −5.72540 −0.237326
\(583\) 6.79185 0.281290
\(584\) 7.66680 0.317254
\(585\) −35.9194 −1.48508
\(586\) 10.6530 0.440069
\(587\) −3.78940 −0.156405 −0.0782027 0.996937i \(-0.524918\pi\)
−0.0782027 + 0.996937i \(0.524918\pi\)
\(588\) −1.67994 −0.0692794
\(589\) −21.8460 −0.900148
\(590\) 39.8192 1.63933
\(591\) 0.410357 0.0168798
\(592\) −27.4349 −1.12757
\(593\) −6.81434 −0.279831 −0.139916 0.990163i \(-0.544683\pi\)
−0.139916 + 0.990163i \(0.544683\pi\)
\(594\) −1.09449 −0.0449076
\(595\) 33.0991 1.35693
\(596\) −0.215813 −0.00884004
\(597\) 2.89607 0.118528
\(598\) −79.1059 −3.23488
\(599\) −39.7739 −1.62512 −0.812559 0.582879i \(-0.801926\pi\)
−0.812559 + 0.582879i \(0.801926\pi\)
\(600\) −0.00833381 −0.000340226 0
\(601\) 27.4256 1.11871 0.559356 0.828927i \(-0.311048\pi\)
0.559356 + 0.828927i \(0.311048\pi\)
\(602\) 11.2211 0.457338
\(603\) 11.6156 0.473025
\(604\) 0.456334 0.0185680
\(605\) 24.1637 0.982395
\(606\) −0.441007 −0.0179147
\(607\) 20.6168 0.836811 0.418405 0.908260i \(-0.362589\pi\)
0.418405 + 0.908260i \(0.362589\pi\)
\(608\) 36.5485 1.48224
\(609\) 5.87409 0.238030
\(610\) −44.8317 −1.81518
\(611\) −46.0335 −1.86232
\(612\) 20.4160 0.825268
\(613\) −12.9127 −0.521540 −0.260770 0.965401i \(-0.583976\pi\)
−0.260770 + 0.965401i \(0.583976\pi\)
\(614\) −44.1100 −1.78014
\(615\) −3.77221 −0.152110
\(616\) 1.20765 0.0486578
\(617\) 26.3856 1.06225 0.531123 0.847295i \(-0.321770\pi\)
0.531123 + 0.847295i \(0.321770\pi\)
\(618\) 1.87771 0.0755326
\(619\) −2.30850 −0.0927866 −0.0463933 0.998923i \(-0.514773\pi\)
−0.0463933 + 0.998923i \(0.514773\pi\)
\(620\) 16.4888 0.662208
\(621\) −8.54387 −0.342854
\(622\) 28.6462 1.14861
\(623\) −3.81203 −0.152726
\(624\) −4.58281 −0.183459
\(625\) −25.3327 −1.01331
\(626\) 4.41649 0.176519
\(627\) −0.473214 −0.0188983
\(628\) 26.6170 1.06213
\(629\) −24.9863 −0.996270
\(630\) −45.0315 −1.79410
\(631\) −8.60820 −0.342687 −0.171343 0.985211i \(-0.554811\pi\)
−0.171343 + 0.985211i \(0.554811\pi\)
\(632\) −0.951953 −0.0378667
\(633\) −1.22148 −0.0485494
\(634\) 35.0958 1.39383
\(635\) 18.5054 0.734366
\(636\) −4.05419 −0.160759
\(637\) −29.3735 −1.16382
\(638\) 8.80669 0.348660
\(639\) 40.5432 1.60386
\(640\) 11.7710 0.465288
\(641\) −11.7479 −0.464014 −0.232007 0.972714i \(-0.574529\pi\)
−0.232007 + 0.972714i \(0.574529\pi\)
\(642\) 3.83711 0.151439
\(643\) 15.0808 0.594729 0.297364 0.954764i \(-0.403892\pi\)
0.297364 + 0.954764i \(0.403892\pi\)
\(644\) −44.8732 −1.76825
\(645\) −0.697214 −0.0274528
\(646\) 39.2451 1.54408
\(647\) −5.68014 −0.223309 −0.111655 0.993747i \(-0.535615\pi\)
−0.111655 + 0.993747i \(0.535615\pi\)
\(648\) 5.76634 0.226523
\(649\) 4.77166 0.187304
\(650\) 0.693600 0.0272052
\(651\) 2.91276 0.114160
\(652\) −30.6118 −1.19885
\(653\) −48.9941 −1.91729 −0.958644 0.284608i \(-0.908137\pi\)
−0.958644 + 0.284608i \(0.908137\pi\)
\(654\) −0.410163 −0.0160387
\(655\) 16.4403 0.642375
\(656\) 41.1625 1.60713
\(657\) −34.2582 −1.33654
\(658\) −57.7113 −2.24982
\(659\) −23.5789 −0.918505 −0.459252 0.888306i \(-0.651883\pi\)
−0.459252 + 0.888306i \(0.651883\pi\)
\(660\) 0.357171 0.0139028
\(661\) −38.6322 −1.50262 −0.751310 0.659949i \(-0.770578\pi\)
−0.751310 + 0.659949i \(0.770578\pi\)
\(662\) 12.3835 0.481296
\(663\) −4.17379 −0.162097
\(664\) 1.14838 0.0445659
\(665\) −39.1671 −1.51884
\(666\) 33.9940 1.31724
\(667\) 68.7470 2.66190
\(668\) 25.6208 0.991300
\(669\) −1.21739 −0.0470670
\(670\) −16.8529 −0.651086
\(671\) −5.37232 −0.207396
\(672\) −4.87306 −0.187983
\(673\) −37.4530 −1.44371 −0.721853 0.692047i \(-0.756709\pi\)
−0.721853 + 0.692047i \(0.756709\pi\)
\(674\) 6.77064 0.260795
\(675\) 0.0749127 0.00288339
\(676\) 26.3700 1.01423
\(677\) 16.0616 0.617297 0.308649 0.951176i \(-0.400123\pi\)
0.308649 + 0.951176i \(0.400123\pi\)
\(678\) −3.09966 −0.119042
\(679\) −56.7868 −2.17928
\(680\) 6.22302 0.238642
\(681\) −3.01038 −0.115358
\(682\) 4.36693 0.167218
\(683\) 13.5819 0.519696 0.259848 0.965649i \(-0.416327\pi\)
0.259848 + 0.965649i \(0.416327\pi\)
\(684\) −24.1589 −0.923737
\(685\) −13.4012 −0.512032
\(686\) 10.3973 0.396970
\(687\) −0.00388067 −0.000148057 0
\(688\) 7.60803 0.290053
\(689\) −70.8871 −2.70058
\(690\) 6.16207 0.234586
\(691\) −5.72328 −0.217724 −0.108862 0.994057i \(-0.534721\pi\)
−0.108862 + 0.994057i \(0.534721\pi\)
\(692\) −0.605639 −0.0230229
\(693\) −5.39626 −0.204987
\(694\) 27.6830 1.05083
\(695\) −33.6876 −1.27784
\(696\) 1.10440 0.0418621
\(697\) 37.4887 1.41999
\(698\) 45.1597 1.70932
\(699\) 0.121375 0.00459083
\(700\) 0.393448 0.0148709
\(701\) −20.2921 −0.766421 −0.383211 0.923661i \(-0.625182\pi\)
−0.383211 + 0.923661i \(0.625182\pi\)
\(702\) 11.4233 0.431146
\(703\) 29.5670 1.11514
\(704\) −2.58964 −0.0976009
\(705\) 3.58584 0.135051
\(706\) 34.9107 1.31388
\(707\) −4.37408 −0.164504
\(708\) −2.84829 −0.107045
\(709\) −31.5398 −1.18450 −0.592251 0.805754i \(-0.701761\pi\)
−0.592251 + 0.805754i \(0.701761\pi\)
\(710\) −58.8235 −2.20761
\(711\) 4.25369 0.159526
\(712\) −0.716706 −0.0268597
\(713\) 34.0892 1.27665
\(714\) −5.23260 −0.195825
\(715\) 6.24509 0.233553
\(716\) 21.2743 0.795059
\(717\) 1.67581 0.0625844
\(718\) 38.9427 1.45333
\(719\) −11.0676 −0.412753 −0.206376 0.978473i \(-0.566167\pi\)
−0.206376 + 0.978473i \(0.566167\pi\)
\(720\) −30.5318 −1.13785
\(721\) 18.6238 0.693588
\(722\) −10.1267 −0.376875
\(723\) 0.186202 0.00692494
\(724\) −20.1845 −0.750150
\(725\) −0.602774 −0.0223865
\(726\) −3.82002 −0.141774
\(727\) −49.5631 −1.83819 −0.919096 0.394033i \(-0.871079\pi\)
−0.919096 + 0.394033i \(0.871079\pi\)
\(728\) −12.6044 −0.467149
\(729\) −25.1457 −0.931324
\(730\) 49.7047 1.83965
\(731\) 6.92901 0.256279
\(732\) 3.20684 0.118528
\(733\) −2.44508 −0.0903110 −0.0451555 0.998980i \(-0.514378\pi\)
−0.0451555 + 0.998980i \(0.514378\pi\)
\(734\) 3.37162 0.124449
\(735\) 2.28809 0.0843975
\(736\) −57.0316 −2.10221
\(737\) −2.01954 −0.0743907
\(738\) −51.0036 −1.87747
\(739\) 36.9067 1.35764 0.678818 0.734307i \(-0.262492\pi\)
0.678818 + 0.734307i \(0.262492\pi\)
\(740\) −22.3165 −0.820371
\(741\) 4.93897 0.181438
\(742\) −88.8699 −3.26252
\(743\) 40.6188 1.49016 0.745079 0.666976i \(-0.232412\pi\)
0.745079 + 0.666976i \(0.232412\pi\)
\(744\) 0.547632 0.0200772
\(745\) 0.293940 0.0107691
\(746\) 61.4909 2.25134
\(747\) −5.13142 −0.187749
\(748\) −3.54961 −0.129787
\(749\) 38.0579 1.39061
\(750\) 3.95151 0.144289
\(751\) −14.0406 −0.512349 −0.256174 0.966631i \(-0.582462\pi\)
−0.256174 + 0.966631i \(0.582462\pi\)
\(752\) −39.1289 −1.42688
\(753\) −3.07207 −0.111953
\(754\) −91.9161 −3.34739
\(755\) −0.621532 −0.0226199
\(756\) 6.47993 0.235673
\(757\) 24.6936 0.897505 0.448752 0.893656i \(-0.351869\pi\)
0.448752 + 0.893656i \(0.351869\pi\)
\(758\) 59.9512 2.17753
\(759\) 0.738419 0.0268029
\(760\) −7.36388 −0.267116
\(761\) 12.6083 0.457051 0.228525 0.973538i \(-0.426610\pi\)
0.228525 + 0.973538i \(0.426610\pi\)
\(762\) −2.92551 −0.105980
\(763\) −4.06816 −0.147277
\(764\) −6.48548 −0.234636
\(765\) −27.8068 −1.00536
\(766\) −32.2276 −1.16443
\(767\) −49.8021 −1.79825
\(768\) −3.73142 −0.134646
\(769\) 42.1413 1.51965 0.759827 0.650125i \(-0.225283\pi\)
0.759827 + 0.650125i \(0.225283\pi\)
\(770\) 7.82936 0.282150
\(771\) −1.48781 −0.0535821
\(772\) −2.79847 −0.100719
\(773\) −9.62659 −0.346244 −0.173122 0.984900i \(-0.555386\pi\)
−0.173122 + 0.984900i \(0.555386\pi\)
\(774\) −9.42695 −0.338845
\(775\) −0.298895 −0.0107366
\(776\) −10.6766 −0.383267
\(777\) −3.94221 −0.141426
\(778\) 1.55956 0.0559129
\(779\) −44.3615 −1.58942
\(780\) −3.72782 −0.133477
\(781\) −7.04900 −0.252233
\(782\) −61.2394 −2.18992
\(783\) −9.92745 −0.354778
\(784\) −24.9677 −0.891705
\(785\) −36.2526 −1.29391
\(786\) −2.59903 −0.0927044
\(787\) 50.4413 1.79804 0.899019 0.437909i \(-0.144281\pi\)
0.899019 + 0.437909i \(0.144281\pi\)
\(788\) −3.64243 −0.129756
\(789\) 1.01943 0.0362928
\(790\) −6.17162 −0.219576
\(791\) −30.7436 −1.09312
\(792\) −1.01456 −0.0360508
\(793\) 56.0713 1.99115
\(794\) 41.7179 1.48051
\(795\) 5.52185 0.195840
\(796\) −25.7062 −0.911131
\(797\) 34.3043 1.21512 0.607561 0.794273i \(-0.292148\pi\)
0.607561 + 0.794273i \(0.292148\pi\)
\(798\) 6.19190 0.219191
\(799\) −35.6366 −1.26073
\(800\) 0.500053 0.0176795
\(801\) 3.20252 0.113155
\(802\) 29.5967 1.04510
\(803\) 5.95627 0.210192
\(804\) 1.20550 0.0425148
\(805\) 61.1177 2.15412
\(806\) −45.5780 −1.60542
\(807\) 0.437011 0.0153835
\(808\) −0.822378 −0.0289312
\(809\) −43.9886 −1.54656 −0.773279 0.634066i \(-0.781385\pi\)
−0.773279 + 0.634066i \(0.781385\pi\)
\(810\) 37.3838 1.31353
\(811\) −43.0270 −1.51088 −0.755440 0.655217i \(-0.772577\pi\)
−0.755440 + 0.655217i \(0.772577\pi\)
\(812\) −52.1398 −1.82975
\(813\) −0.298484 −0.0104683
\(814\) −5.91034 −0.207157
\(815\) 41.6937 1.46047
\(816\) −3.54776 −0.124196
\(817\) −8.19930 −0.286857
\(818\) −49.7638 −1.73995
\(819\) 56.3212 1.96802
\(820\) 33.4830 1.16928
\(821\) 18.7704 0.655090 0.327545 0.944836i \(-0.393779\pi\)
0.327545 + 0.944836i \(0.393779\pi\)
\(822\) 2.11858 0.0738939
\(823\) 27.1588 0.946695 0.473348 0.880876i \(-0.343045\pi\)
0.473348 + 0.880876i \(0.343045\pi\)
\(824\) 3.50150 0.121981
\(825\) −0.00647446 −0.000225412 0
\(826\) −62.4360 −2.17243
\(827\) 41.5157 1.44364 0.721821 0.692079i \(-0.243305\pi\)
0.721821 + 0.692079i \(0.243305\pi\)
\(828\) 37.6983 1.31011
\(829\) −30.6349 −1.06399 −0.531997 0.846746i \(-0.678558\pi\)
−0.531997 + 0.846746i \(0.678558\pi\)
\(830\) 7.44510 0.258423
\(831\) 4.03640 0.140021
\(832\) 27.0283 0.937039
\(833\) −22.7394 −0.787872
\(834\) 5.32565 0.184412
\(835\) −34.8959 −1.20762
\(836\) 4.20036 0.145272
\(837\) −4.92267 −0.170153
\(838\) 63.4916 2.19328
\(839\) 30.2456 1.04419 0.522097 0.852886i \(-0.325150\pi\)
0.522097 + 0.852886i \(0.325150\pi\)
\(840\) 0.981836 0.0338766
\(841\) 50.8798 1.75447
\(842\) −5.55375 −0.191395
\(843\) −5.00902 −0.172520
\(844\) 10.8421 0.373202
\(845\) −35.9163 −1.23556
\(846\) 48.4838 1.66691
\(847\) −37.8884 −1.30186
\(848\) −60.2547 −2.06915
\(849\) −0.724755 −0.0248735
\(850\) 0.536947 0.0184171
\(851\) −46.1374 −1.58157
\(852\) 4.20769 0.144153
\(853\) 42.7734 1.46453 0.732267 0.681018i \(-0.238462\pi\)
0.732267 + 0.681018i \(0.238462\pi\)
\(854\) 70.2956 2.40546
\(855\) 32.9046 1.12532
\(856\) 7.15534 0.244564
\(857\) −18.8048 −0.642361 −0.321181 0.947018i \(-0.604080\pi\)
−0.321181 + 0.947018i \(0.604080\pi\)
\(858\) −0.987281 −0.0337052
\(859\) −8.22676 −0.280693 −0.140347 0.990102i \(-0.544822\pi\)
−0.140347 + 0.990102i \(0.544822\pi\)
\(860\) 6.18864 0.211031
\(861\) 5.91478 0.201575
\(862\) 54.4493 1.85455
\(863\) −41.8464 −1.42447 −0.712235 0.701941i \(-0.752317\pi\)
−0.712235 + 0.701941i \(0.752317\pi\)
\(864\) 8.23567 0.280183
\(865\) 0.824887 0.0280470
\(866\) 55.2937 1.87896
\(867\) −0.0656832 −0.00223072
\(868\) −25.8543 −0.877552
\(869\) −0.739564 −0.0250880
\(870\) 7.15994 0.242745
\(871\) 21.0781 0.714204
\(872\) −0.764862 −0.0259015
\(873\) 47.7071 1.61464
\(874\) 72.4664 2.45121
\(875\) 39.1926 1.32495
\(876\) −3.55541 −0.120126
\(877\) −6.11483 −0.206483 −0.103242 0.994656i \(-0.532921\pi\)
−0.103242 + 0.994656i \(0.532921\pi\)
\(878\) 17.0511 0.575446
\(879\) 1.03787 0.0350065
\(880\) 5.30838 0.178946
\(881\) −13.5157 −0.455355 −0.227678 0.973737i \(-0.573113\pi\)
−0.227678 + 0.973737i \(0.573113\pi\)
\(882\) 30.9370 1.04170
\(883\) 38.5489 1.29727 0.648637 0.761098i \(-0.275339\pi\)
0.648637 + 0.761098i \(0.275339\pi\)
\(884\) 37.0476 1.24604
\(885\) 3.87941 0.130405
\(886\) −47.4397 −1.59377
\(887\) 40.8386 1.37123 0.685613 0.727966i \(-0.259534\pi\)
0.685613 + 0.727966i \(0.259534\pi\)
\(888\) −0.741183 −0.0248725
\(889\) −29.0163 −0.973177
\(890\) −4.64649 −0.155751
\(891\) 4.47982 0.150080
\(892\) 10.8058 0.361806
\(893\) 42.1698 1.41116
\(894\) −0.0464686 −0.00155414
\(895\) −28.9759 −0.968557
\(896\) −18.4567 −0.616596
\(897\) −7.70694 −0.257327
\(898\) −22.7921 −0.760581
\(899\) 39.6096 1.32105
\(900\) −0.330539 −0.0110180
\(901\) −54.8769 −1.82822
\(902\) 8.86770 0.295262
\(903\) 1.09322 0.0363802
\(904\) −5.78016 −0.192245
\(905\) 27.4915 0.913848
\(906\) 0.0982574 0.00326438
\(907\) −34.3321 −1.13998 −0.569989 0.821652i \(-0.693053\pi\)
−0.569989 + 0.821652i \(0.693053\pi\)
\(908\) 26.7209 0.886763
\(909\) 3.67470 0.121882
\(910\) −81.7156 −2.70885
\(911\) 49.0410 1.62480 0.812400 0.583100i \(-0.198160\pi\)
0.812400 + 0.583100i \(0.198160\pi\)
\(912\) 4.19817 0.139015
\(913\) 0.892169 0.0295265
\(914\) −16.1346 −0.533686
\(915\) −4.36776 −0.144394
\(916\) 0.0344458 0.00113812
\(917\) −25.7782 −0.851271
\(918\) 8.84331 0.291873
\(919\) 48.7329 1.60755 0.803775 0.594934i \(-0.202822\pi\)
0.803775 + 0.594934i \(0.202822\pi\)
\(920\) 11.4909 0.378842
\(921\) −4.29745 −0.141606
\(922\) −44.5171 −1.46609
\(923\) 73.5710 2.42162
\(924\) −0.560040 −0.0184240
\(925\) 0.404533 0.0133010
\(926\) −3.18367 −0.104622
\(927\) −15.6461 −0.513884
\(928\) −66.2672 −2.17533
\(929\) 52.9031 1.73569 0.867847 0.496832i \(-0.165504\pi\)
0.867847 + 0.496832i \(0.165504\pi\)
\(930\) 3.55036 0.116421
\(931\) 26.9081 0.881879
\(932\) −1.07735 −0.0352899
\(933\) 2.79088 0.0913693
\(934\) 12.7369 0.416765
\(935\) 4.83461 0.158109
\(936\) 10.5891 0.346114
\(937\) −16.1310 −0.526976 −0.263488 0.964663i \(-0.584873\pi\)
−0.263488 + 0.964663i \(0.584873\pi\)
\(938\) 26.4252 0.862814
\(939\) 0.430280 0.0140416
\(940\) −31.8288 −1.03814
\(941\) 10.7225 0.349544 0.174772 0.984609i \(-0.444081\pi\)
0.174772 + 0.984609i \(0.444081\pi\)
\(942\) 5.73114 0.186731
\(943\) 69.2233 2.25422
\(944\) −42.3323 −1.37780
\(945\) −8.82574 −0.287101
\(946\) 1.63901 0.0532887
\(947\) −21.9984 −0.714851 −0.357426 0.933942i \(-0.616345\pi\)
−0.357426 + 0.933942i \(0.616345\pi\)
\(948\) 0.441460 0.0143380
\(949\) −62.1660 −2.01800
\(950\) −0.635386 −0.0206146
\(951\) 3.41923 0.110876
\(952\) −9.75762 −0.316246
\(953\) −40.5214 −1.31262 −0.656309 0.754492i \(-0.727883\pi\)
−0.656309 + 0.754492i \(0.727883\pi\)
\(954\) 74.6603 2.41722
\(955\) 8.83330 0.285839
\(956\) −14.8749 −0.481090
\(957\) 0.857998 0.0277351
\(958\) 26.1651 0.845356
\(959\) 21.0129 0.678542
\(960\) −2.10541 −0.0679518
\(961\) −11.3590 −0.366419
\(962\) 61.6867 1.98886
\(963\) −31.9728 −1.03031
\(964\) −1.65278 −0.0532323
\(965\) 3.81154 0.122698
\(966\) −9.66205 −0.310871
\(967\) −46.5645 −1.49741 −0.748706 0.662902i \(-0.769324\pi\)
−0.748706 + 0.662902i \(0.769324\pi\)
\(968\) −7.12347 −0.228957
\(969\) 3.82348 0.122828
\(970\) −69.2175 −2.22244
\(971\) 2.03099 0.0651775 0.0325887 0.999469i \(-0.489625\pi\)
0.0325887 + 0.999469i \(0.489625\pi\)
\(972\) −8.18159 −0.262425
\(973\) 52.8218 1.69339
\(974\) −61.0892 −1.95743
\(975\) 0.0675745 0.00216412
\(976\) 47.6611 1.52560
\(977\) −45.7170 −1.46262 −0.731308 0.682047i \(-0.761090\pi\)
−0.731308 + 0.682047i \(0.761090\pi\)
\(978\) −6.59131 −0.210767
\(979\) −0.556803 −0.0177955
\(980\) −20.3096 −0.648767
\(981\) 3.41770 0.109119
\(982\) 19.2174 0.613252
\(983\) −47.0190 −1.49967 −0.749837 0.661623i \(-0.769868\pi\)
−0.749837 + 0.661623i \(0.769868\pi\)
\(984\) 1.11205 0.0354508
\(985\) 4.96103 0.158071
\(986\) −71.1564 −2.26608
\(987\) −5.62256 −0.178968
\(988\) −43.8395 −1.39472
\(989\) 12.7945 0.406841
\(990\) −6.57751 −0.209047
\(991\) 54.4626 1.73006 0.865031 0.501718i \(-0.167298\pi\)
0.865031 + 0.501718i \(0.167298\pi\)
\(992\) −32.8596 −1.04329
\(993\) 1.20647 0.0382860
\(994\) 92.2346 2.92550
\(995\) 35.0121 1.10996
\(996\) −0.532553 −0.0168746
\(997\) 13.5868 0.430297 0.215149 0.976581i \(-0.430976\pi\)
0.215149 + 0.976581i \(0.430976\pi\)
\(998\) −17.4742 −0.553137
\(999\) 6.66250 0.210792
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 241.2.a.a.1.2 7
3.2 odd 2 2169.2.a.e.1.6 7
4.3 odd 2 3856.2.a.j.1.3 7
5.4 even 2 6025.2.a.f.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.2 7 1.1 even 1 trivial
2169.2.a.e.1.6 7 3.2 odd 2
3856.2.a.j.1.3 7 4.3 odd 2
6025.2.a.f.1.6 7 5.4 even 2