Properties

Label 7098.2.a.ch.1.2
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.44504 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.44504 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.44504 q^{10} -3.74094 q^{11} -1.00000 q^{12} +1.00000 q^{14} +1.44504 q^{15} +1.00000 q^{16} +0.692021 q^{17} +1.00000 q^{18} -0.753020 q^{19} -1.44504 q^{20} -1.00000 q^{21} -3.74094 q^{22} +1.82908 q^{23} -1.00000 q^{24} -2.91185 q^{25} -1.00000 q^{27} +1.00000 q^{28} +6.89977 q^{29} +1.44504 q^{30} +0.960771 q^{31} +1.00000 q^{32} +3.74094 q^{33} +0.692021 q^{34} -1.44504 q^{35} +1.00000 q^{36} -3.04892 q^{37} -0.753020 q^{38} -1.44504 q^{40} +1.44504 q^{41} -1.00000 q^{42} +5.82908 q^{43} -3.74094 q^{44} -1.44504 q^{45} +1.82908 q^{46} -3.71379 q^{47} -1.00000 q^{48} +1.00000 q^{49} -2.91185 q^{50} -0.692021 q^{51} -1.57673 q^{53} -1.00000 q^{54} +5.40581 q^{55} +1.00000 q^{56} +0.753020 q^{57} +6.89977 q^{58} +6.65279 q^{59} +1.44504 q^{60} -7.00000 q^{61} +0.960771 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.74094 q^{66} -9.11960 q^{67} +0.692021 q^{68} -1.82908 q^{69} -1.44504 q^{70} +0.219833 q^{71} +1.00000 q^{72} -4.91185 q^{73} -3.04892 q^{74} +2.91185 q^{75} -0.753020 q^{76} -3.74094 q^{77} -7.44504 q^{79} -1.44504 q^{80} +1.00000 q^{81} +1.44504 q^{82} -8.75302 q^{83} -1.00000 q^{84} -1.00000 q^{85} +5.82908 q^{86} -6.89977 q^{87} -3.74094 q^{88} -14.5579 q^{89} -1.44504 q^{90} +1.82908 q^{92} -0.960771 q^{93} -3.71379 q^{94} +1.08815 q^{95} -1.00000 q^{96} -6.06100 q^{97} +1.00000 q^{98} -3.74094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 4q^{5} - 3q^{6} + 3q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 4q^{5} - 3q^{6} + 3q^{7} + 3q^{8} + 3q^{9} - 4q^{10} + 3q^{11} - 3q^{12} + 3q^{14} + 4q^{15} + 3q^{16} - 3q^{17} + 3q^{18} - 7q^{19} - 4q^{20} - 3q^{21} + 3q^{22} - 5q^{23} - 3q^{24} - 5q^{25} - 3q^{27} + 3q^{28} - 2q^{29} + 4q^{30} - 10q^{31} + 3q^{32} - 3q^{33} - 3q^{34} - 4q^{35} + 3q^{36} - 7q^{38} - 4q^{40} + 4q^{41} - 3q^{42} + 7q^{43} + 3q^{44} - 4q^{45} - 5q^{46} - 3q^{47} - 3q^{48} + 3q^{49} - 5q^{50} + 3q^{51} - 2q^{53} - 3q^{54} + 3q^{55} + 3q^{56} + 7q^{57} - 2q^{58} + 2q^{59} + 4q^{60} - 21q^{61} - 10q^{62} + 3q^{63} + 3q^{64} - 3q^{66} - 6q^{67} - 3q^{68} + 5q^{69} - 4q^{70} + 2q^{71} + 3q^{72} - 11q^{73} + 5q^{75} - 7q^{76} + 3q^{77} - 22q^{79} - 4q^{80} + 3q^{81} + 4q^{82} - 31q^{83} - 3q^{84} - 3q^{85} + 7q^{86} + 2q^{87} + 3q^{88} - 4q^{90} - 5q^{92} + 10q^{93} - 3q^{94} + 7q^{95} - 3q^{96} - 28q^{97} + 3q^{98} + 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.44504 −0.646242 −0.323121 0.946358i \(-0.604732\pi\)
−0.323121 + 0.946358i \(0.604732\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.44504 −0.456962
\(11\) −3.74094 −1.12794 −0.563968 0.825797i \(-0.690726\pi\)
−0.563968 + 0.825797i \(0.690726\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) 1.44504 0.373108
\(16\) 1.00000 0.250000
\(17\) 0.692021 0.167840 0.0839199 0.996473i \(-0.473256\pi\)
0.0839199 + 0.996473i \(0.473256\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.753020 −0.172755 −0.0863774 0.996262i \(-0.527529\pi\)
−0.0863774 + 0.996262i \(0.527529\pi\)
\(20\) −1.44504 −0.323121
\(21\) −1.00000 −0.218218
\(22\) −3.74094 −0.797571
\(23\) 1.82908 0.381391 0.190695 0.981649i \(-0.438926\pi\)
0.190695 + 0.981649i \(0.438926\pi\)
\(24\) −1.00000 −0.204124
\(25\) −2.91185 −0.582371
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) 6.89977 1.28126 0.640628 0.767852i \(-0.278674\pi\)
0.640628 + 0.767852i \(0.278674\pi\)
\(30\) 1.44504 0.263827
\(31\) 0.960771 0.172560 0.0862798 0.996271i \(-0.472502\pi\)
0.0862798 + 0.996271i \(0.472502\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.74094 0.651214
\(34\) 0.692021 0.118681
\(35\) −1.44504 −0.244257
\(36\) 1.00000 0.166667
\(37\) −3.04892 −0.501239 −0.250619 0.968086i \(-0.580634\pi\)
−0.250619 + 0.968086i \(0.580634\pi\)
\(38\) −0.753020 −0.122156
\(39\) 0 0
\(40\) −1.44504 −0.228481
\(41\) 1.44504 0.225678 0.112839 0.993613i \(-0.464006\pi\)
0.112839 + 0.993613i \(0.464006\pi\)
\(42\) −1.00000 −0.154303
\(43\) 5.82908 0.888927 0.444464 0.895797i \(-0.353394\pi\)
0.444464 + 0.895797i \(0.353394\pi\)
\(44\) −3.74094 −0.563968
\(45\) −1.44504 −0.215414
\(46\) 1.82908 0.269684
\(47\) −3.71379 −0.541712 −0.270856 0.962620i \(-0.587307\pi\)
−0.270856 + 0.962620i \(0.587307\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −2.91185 −0.411798
\(51\) −0.692021 −0.0969024
\(52\) 0 0
\(53\) −1.57673 −0.216580 −0.108290 0.994119i \(-0.534538\pi\)
−0.108290 + 0.994119i \(0.534538\pi\)
\(54\) −1.00000 −0.136083
\(55\) 5.40581 0.728920
\(56\) 1.00000 0.133631
\(57\) 0.753020 0.0997400
\(58\) 6.89977 0.905985
\(59\) 6.65279 0.866120 0.433060 0.901365i \(-0.357434\pi\)
0.433060 + 0.901365i \(0.357434\pi\)
\(60\) 1.44504 0.186554
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 0.960771 0.122018
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.74094 0.460478
\(67\) −9.11960 −1.11414 −0.557069 0.830467i \(-0.688074\pi\)
−0.557069 + 0.830467i \(0.688074\pi\)
\(68\) 0.692021 0.0839199
\(69\) −1.82908 −0.220196
\(70\) −1.44504 −0.172716
\(71\) 0.219833 0.0260893 0.0130447 0.999915i \(-0.495848\pi\)
0.0130447 + 0.999915i \(0.495848\pi\)
\(72\) 1.00000 0.117851
\(73\) −4.91185 −0.574889 −0.287445 0.957797i \(-0.592806\pi\)
−0.287445 + 0.957797i \(0.592806\pi\)
\(74\) −3.04892 −0.354429
\(75\) 2.91185 0.336232
\(76\) −0.753020 −0.0863774
\(77\) −3.74094 −0.426320
\(78\) 0 0
\(79\) −7.44504 −0.837633 −0.418816 0.908071i \(-0.637555\pi\)
−0.418816 + 0.908071i \(0.637555\pi\)
\(80\) −1.44504 −0.161561
\(81\) 1.00000 0.111111
\(82\) 1.44504 0.159578
\(83\) −8.75302 −0.960769 −0.480384 0.877058i \(-0.659503\pi\)
−0.480384 + 0.877058i \(0.659503\pi\)
\(84\) −1.00000 −0.109109
\(85\) −1.00000 −0.108465
\(86\) 5.82908 0.628566
\(87\) −6.89977 −0.739733
\(88\) −3.74094 −0.398785
\(89\) −14.5579 −1.54314 −0.771569 0.636145i \(-0.780528\pi\)
−0.771569 + 0.636145i \(0.780528\pi\)
\(90\) −1.44504 −0.152321
\(91\) 0 0
\(92\) 1.82908 0.190695
\(93\) −0.960771 −0.0996273
\(94\) −3.71379 −0.383048
\(95\) 1.08815 0.111641
\(96\) −1.00000 −0.102062
\(97\) −6.06100 −0.615401 −0.307701 0.951483i \(-0.599560\pi\)
−0.307701 + 0.951483i \(0.599560\pi\)
\(98\) 1.00000 0.101015
\(99\) −3.74094 −0.375978
\(100\) −2.91185 −0.291185
\(101\) −2.81402 −0.280005 −0.140003 0.990151i \(-0.544711\pi\)
−0.140003 + 0.990151i \(0.544711\pi\)
\(102\) −0.692021 −0.0685203
\(103\) −8.23490 −0.811409 −0.405704 0.914004i \(-0.632974\pi\)
−0.405704 + 0.914004i \(0.632974\pi\)
\(104\) 0 0
\(105\) 1.44504 0.141022
\(106\) −1.57673 −0.153145
\(107\) 10.6039 1.02512 0.512558 0.858653i \(-0.328698\pi\)
0.512558 + 0.858653i \(0.328698\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 8.48858 0.813059 0.406529 0.913638i \(-0.366739\pi\)
0.406529 + 0.913638i \(0.366739\pi\)
\(110\) 5.40581 0.515424
\(111\) 3.04892 0.289390
\(112\) 1.00000 0.0944911
\(113\) −5.92692 −0.557558 −0.278779 0.960355i \(-0.589930\pi\)
−0.278779 + 0.960355i \(0.589930\pi\)
\(114\) 0.753020 0.0705268
\(115\) −2.64310 −0.246471
\(116\) 6.89977 0.640628
\(117\) 0 0
\(118\) 6.65279 0.612439
\(119\) 0.692021 0.0634375
\(120\) 1.44504 0.131914
\(121\) 2.99462 0.272238
\(122\) −7.00000 −0.633750
\(123\) −1.44504 −0.130295
\(124\) 0.960771 0.0862798
\(125\) 11.4330 1.02260
\(126\) 1.00000 0.0890871
\(127\) 9.67994 0.858956 0.429478 0.903077i \(-0.358698\pi\)
0.429478 + 0.903077i \(0.358698\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.82908 −0.513222
\(130\) 0 0
\(131\) 2.25236 0.196789 0.0983946 0.995147i \(-0.468629\pi\)
0.0983946 + 0.995147i \(0.468629\pi\)
\(132\) 3.74094 0.325607
\(133\) −0.753020 −0.0652951
\(134\) −9.11960 −0.787814
\(135\) 1.44504 0.124369
\(136\) 0.692021 0.0593404
\(137\) −12.0489 −1.02941 −0.514704 0.857368i \(-0.672098\pi\)
−0.514704 + 0.857368i \(0.672098\pi\)
\(138\) −1.82908 −0.155702
\(139\) −16.6383 −1.41124 −0.705622 0.708589i \(-0.749332\pi\)
−0.705622 + 0.708589i \(0.749332\pi\)
\(140\) −1.44504 −0.122128
\(141\) 3.71379 0.312758
\(142\) 0.219833 0.0184479
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −9.97046 −0.828002
\(146\) −4.91185 −0.406508
\(147\) −1.00000 −0.0824786
\(148\) −3.04892 −0.250619
\(149\) 8.35690 0.684624 0.342312 0.939586i \(-0.388790\pi\)
0.342312 + 0.939586i \(0.388790\pi\)
\(150\) 2.91185 0.237752
\(151\) −7.63102 −0.621004 −0.310502 0.950573i \(-0.600497\pi\)
−0.310502 + 0.950573i \(0.600497\pi\)
\(152\) −0.753020 −0.0610780
\(153\) 0.692021 0.0559466
\(154\) −3.74094 −0.301453
\(155\) −1.38835 −0.111515
\(156\) 0 0
\(157\) 12.2935 0.981128 0.490564 0.871405i \(-0.336791\pi\)
0.490564 + 0.871405i \(0.336791\pi\)
\(158\) −7.44504 −0.592296
\(159\) 1.57673 0.125043
\(160\) −1.44504 −0.114241
\(161\) 1.82908 0.144152
\(162\) 1.00000 0.0785674
\(163\) −15.0151 −1.17607 −0.588035 0.808835i \(-0.700098\pi\)
−0.588035 + 0.808835i \(0.700098\pi\)
\(164\) 1.44504 0.112839
\(165\) −5.40581 −0.420842
\(166\) −8.75302 −0.679366
\(167\) 18.3153 1.41728 0.708639 0.705571i \(-0.249309\pi\)
0.708639 + 0.705571i \(0.249309\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 0 0
\(170\) −1.00000 −0.0766965
\(171\) −0.753020 −0.0575849
\(172\) 5.82908 0.444464
\(173\) −16.7875 −1.27633 −0.638164 0.769901i \(-0.720306\pi\)
−0.638164 + 0.769901i \(0.720306\pi\)
\(174\) −6.89977 −0.523070
\(175\) −2.91185 −0.220115
\(176\) −3.74094 −0.281984
\(177\) −6.65279 −0.500055
\(178\) −14.5579 −1.09116
\(179\) 4.86725 0.363795 0.181898 0.983317i \(-0.441776\pi\)
0.181898 + 0.983317i \(0.441776\pi\)
\(180\) −1.44504 −0.107707
\(181\) −13.4644 −1.00080 −0.500401 0.865794i \(-0.666814\pi\)
−0.500401 + 0.865794i \(0.666814\pi\)
\(182\) 0 0
\(183\) 7.00000 0.517455
\(184\) 1.82908 0.134842
\(185\) 4.40581 0.323922
\(186\) −0.960771 −0.0704472
\(187\) −2.58881 −0.189313
\(188\) −3.71379 −0.270856
\(189\) −1.00000 −0.0727393
\(190\) 1.08815 0.0789424
\(191\) −5.26444 −0.380921 −0.190461 0.981695i \(-0.560998\pi\)
−0.190461 + 0.981695i \(0.560998\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −22.8713 −1.64631 −0.823156 0.567815i \(-0.807789\pi\)
−0.823156 + 0.567815i \(0.807789\pi\)
\(194\) −6.06100 −0.435154
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 18.8877 1.34569 0.672846 0.739782i \(-0.265072\pi\)
0.672846 + 0.739782i \(0.265072\pi\)
\(198\) −3.74094 −0.265857
\(199\) −3.36898 −0.238820 −0.119410 0.992845i \(-0.538100\pi\)
−0.119410 + 0.992845i \(0.538100\pi\)
\(200\) −2.91185 −0.205899
\(201\) 9.11960 0.643247
\(202\) −2.81402 −0.197994
\(203\) 6.89977 0.484269
\(204\) −0.692021 −0.0484512
\(205\) −2.08815 −0.145842
\(206\) −8.23490 −0.573753
\(207\) 1.82908 0.127130
\(208\) 0 0
\(209\) 2.81700 0.194856
\(210\) 1.44504 0.0997174
\(211\) 17.1511 1.18073 0.590364 0.807137i \(-0.298984\pi\)
0.590364 + 0.807137i \(0.298984\pi\)
\(212\) −1.57673 −0.108290
\(213\) −0.219833 −0.0150627
\(214\) 10.6039 0.724866
\(215\) −8.42327 −0.574462
\(216\) −1.00000 −0.0680414
\(217\) 0.960771 0.0652214
\(218\) 8.48858 0.574919
\(219\) 4.91185 0.331912
\(220\) 5.40581 0.364460
\(221\) 0 0
\(222\) 3.04892 0.204630
\(223\) −25.0911 −1.68023 −0.840113 0.542411i \(-0.817512\pi\)
−0.840113 + 0.542411i \(0.817512\pi\)
\(224\) 1.00000 0.0668153
\(225\) −2.91185 −0.194124
\(226\) −5.92692 −0.394253
\(227\) 5.84415 0.387890 0.193945 0.981012i \(-0.437872\pi\)
0.193945 + 0.981012i \(0.437872\pi\)
\(228\) 0.753020 0.0498700
\(229\) −15.2252 −1.00611 −0.503055 0.864254i \(-0.667791\pi\)
−0.503055 + 0.864254i \(0.667791\pi\)
\(230\) −2.64310 −0.174281
\(231\) 3.74094 0.246136
\(232\) 6.89977 0.452992
\(233\) −25.2000 −1.65091 −0.825453 0.564471i \(-0.809080\pi\)
−0.825453 + 0.564471i \(0.809080\pi\)
\(234\) 0 0
\(235\) 5.36658 0.350077
\(236\) 6.65279 0.433060
\(237\) 7.44504 0.483607
\(238\) 0.692021 0.0448571
\(239\) 6.71379 0.434279 0.217140 0.976141i \(-0.430327\pi\)
0.217140 + 0.976141i \(0.430327\pi\)
\(240\) 1.44504 0.0932771
\(241\) −5.21313 −0.335807 −0.167904 0.985803i \(-0.553700\pi\)
−0.167904 + 0.985803i \(0.553700\pi\)
\(242\) 2.99462 0.192502
\(243\) −1.00000 −0.0641500
\(244\) −7.00000 −0.448129
\(245\) −1.44504 −0.0923203
\(246\) −1.44504 −0.0921325
\(247\) 0 0
\(248\) 0.960771 0.0610090
\(249\) 8.75302 0.554700
\(250\) 11.4330 0.723084
\(251\) 9.22952 0.582562 0.291281 0.956638i \(-0.405919\pi\)
0.291281 + 0.956638i \(0.405919\pi\)
\(252\) 1.00000 0.0629941
\(253\) −6.84249 −0.430184
\(254\) 9.67994 0.607373
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 2.51035 0.156591 0.0782957 0.996930i \(-0.475052\pi\)
0.0782957 + 0.996930i \(0.475052\pi\)
\(258\) −5.82908 −0.362903
\(259\) −3.04892 −0.189451
\(260\) 0 0
\(261\) 6.89977 0.427085
\(262\) 2.25236 0.139151
\(263\) 30.1511 1.85919 0.929597 0.368577i \(-0.120155\pi\)
0.929597 + 0.368577i \(0.120155\pi\)
\(264\) 3.74094 0.230239
\(265\) 2.27844 0.139963
\(266\) −0.753020 −0.0461706
\(267\) 14.5579 0.890932
\(268\) −9.11960 −0.557069
\(269\) −14.6063 −0.890560 −0.445280 0.895391i \(-0.646896\pi\)
−0.445280 + 0.895391i \(0.646896\pi\)
\(270\) 1.44504 0.0879424
\(271\) −22.0978 −1.34235 −0.671174 0.741300i \(-0.734210\pi\)
−0.671174 + 0.741300i \(0.734210\pi\)
\(272\) 0.692021 0.0419600
\(273\) 0 0
\(274\) −12.0489 −0.727902
\(275\) 10.8931 0.656877
\(276\) −1.82908 −0.110098
\(277\) 1.23729 0.0743416 0.0371708 0.999309i \(-0.488165\pi\)
0.0371708 + 0.999309i \(0.488165\pi\)
\(278\) −16.6383 −0.997900
\(279\) 0.960771 0.0575199
\(280\) −1.44504 −0.0863578
\(281\) −8.51035 −0.507685 −0.253843 0.967246i \(-0.581695\pi\)
−0.253843 + 0.967246i \(0.581695\pi\)
\(282\) 3.71379 0.221153
\(283\) −16.3002 −0.968947 −0.484473 0.874806i \(-0.660989\pi\)
−0.484473 + 0.874806i \(0.660989\pi\)
\(284\) 0.219833 0.0130447
\(285\) −1.08815 −0.0644562
\(286\) 0 0
\(287\) 1.44504 0.0852981
\(288\) 1.00000 0.0589256
\(289\) −16.5211 −0.971830
\(290\) −9.97046 −0.585486
\(291\) 6.06100 0.355302
\(292\) −4.91185 −0.287445
\(293\) −29.8853 −1.74592 −0.872959 0.487794i \(-0.837802\pi\)
−0.872959 + 0.487794i \(0.837802\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −9.61356 −0.559723
\(296\) −3.04892 −0.177215
\(297\) 3.74094 0.217071
\(298\) 8.35690 0.484102
\(299\) 0 0
\(300\) 2.91185 0.168116
\(301\) 5.82908 0.335983
\(302\) −7.63102 −0.439116
\(303\) 2.81402 0.161661
\(304\) −0.753020 −0.0431887
\(305\) 10.1153 0.579200
\(306\) 0.692021 0.0395602
\(307\) −24.4547 −1.39571 −0.697853 0.716241i \(-0.745861\pi\)
−0.697853 + 0.716241i \(0.745861\pi\)
\(308\) −3.74094 −0.213160
\(309\) 8.23490 0.468467
\(310\) −1.38835 −0.0788533
\(311\) −22.3177 −1.26552 −0.632759 0.774348i \(-0.718078\pi\)
−0.632759 + 0.774348i \(0.718078\pi\)
\(312\) 0 0
\(313\) −2.47889 −0.140115 −0.0700577 0.997543i \(-0.522318\pi\)
−0.0700577 + 0.997543i \(0.522318\pi\)
\(314\) 12.2935 0.693763
\(315\) −1.44504 −0.0814189
\(316\) −7.44504 −0.418816
\(317\) −5.65710 −0.317735 −0.158867 0.987300i \(-0.550784\pi\)
−0.158867 + 0.987300i \(0.550784\pi\)
\(318\) 1.57673 0.0884185
\(319\) −25.8116 −1.44517
\(320\) −1.44504 −0.0807803
\(321\) −10.6039 −0.591851
\(322\) 1.82908 0.101931
\(323\) −0.521106 −0.0289951
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −15.0151 −0.831608
\(327\) −8.48858 −0.469420
\(328\) 1.44504 0.0797891
\(329\) −3.71379 −0.204748
\(330\) −5.40581 −0.297580
\(331\) 23.1879 1.27452 0.637261 0.770648i \(-0.280067\pi\)
0.637261 + 0.770648i \(0.280067\pi\)
\(332\) −8.75302 −0.480384
\(333\) −3.04892 −0.167080
\(334\) 18.3153 1.00217
\(335\) 13.1782 0.720003
\(336\) −1.00000 −0.0545545
\(337\) 10.4873 0.571277 0.285639 0.958337i \(-0.407794\pi\)
0.285639 + 0.958337i \(0.407794\pi\)
\(338\) 0 0
\(339\) 5.92692 0.321906
\(340\) −1.00000 −0.0542326
\(341\) −3.59419 −0.194636
\(342\) −0.753020 −0.0407187
\(343\) 1.00000 0.0539949
\(344\) 5.82908 0.314283
\(345\) 2.64310 0.142300
\(346\) −16.7875 −0.902500
\(347\) −5.28514 −0.283721 −0.141861 0.989887i \(-0.545309\pi\)
−0.141861 + 0.989887i \(0.545309\pi\)
\(348\) −6.89977 −0.369867
\(349\) 8.19029 0.438416 0.219208 0.975678i \(-0.429653\pi\)
0.219208 + 0.975678i \(0.429653\pi\)
\(350\) −2.91185 −0.155645
\(351\) 0 0
\(352\) −3.74094 −0.199393
\(353\) 35.9758 1.91480 0.957400 0.288764i \(-0.0932443\pi\)
0.957400 + 0.288764i \(0.0932443\pi\)
\(354\) −6.65279 −0.353592
\(355\) −0.317667 −0.0168600
\(356\) −14.5579 −0.771569
\(357\) −0.692021 −0.0366257
\(358\) 4.86725 0.257242
\(359\) −28.7603 −1.51791 −0.758956 0.651142i \(-0.774290\pi\)
−0.758956 + 0.651142i \(0.774290\pi\)
\(360\) −1.44504 −0.0761604
\(361\) −18.4330 −0.970156
\(362\) −13.4644 −0.707674
\(363\) −2.99462 −0.157177
\(364\) 0 0
\(365\) 7.09783 0.371518
\(366\) 7.00000 0.365896
\(367\) −3.61463 −0.188682 −0.0943411 0.995540i \(-0.530074\pi\)
−0.0943411 + 0.995540i \(0.530074\pi\)
\(368\) 1.82908 0.0953476
\(369\) 1.44504 0.0752259
\(370\) 4.40581 0.229047
\(371\) −1.57673 −0.0818597
\(372\) −0.960771 −0.0498137
\(373\) 17.9312 0.928444 0.464222 0.885719i \(-0.346334\pi\)
0.464222 + 0.885719i \(0.346334\pi\)
\(374\) −2.58881 −0.133864
\(375\) −11.4330 −0.590396
\(376\) −3.71379 −0.191524
\(377\) 0 0
\(378\) −1.00000 −0.0514344
\(379\) 22.2338 1.14208 0.571038 0.820924i \(-0.306541\pi\)
0.571038 + 0.820924i \(0.306541\pi\)
\(380\) 1.08815 0.0558207
\(381\) −9.67994 −0.495918
\(382\) −5.26444 −0.269352
\(383\) −25.4330 −1.29956 −0.649782 0.760121i \(-0.725140\pi\)
−0.649782 + 0.760121i \(0.725140\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 5.40581 0.275506
\(386\) −22.8713 −1.16412
\(387\) 5.82908 0.296309
\(388\) −6.06100 −0.307701
\(389\) −14.9855 −0.759796 −0.379898 0.925028i \(-0.624041\pi\)
−0.379898 + 0.925028i \(0.624041\pi\)
\(390\) 0 0
\(391\) 1.26577 0.0640125
\(392\) 1.00000 0.0505076
\(393\) −2.25236 −0.113616
\(394\) 18.8877 0.951548
\(395\) 10.7584 0.541314
\(396\) −3.74094 −0.187989
\(397\) −11.8358 −0.594021 −0.297011 0.954874i \(-0.595990\pi\)
−0.297011 + 0.954874i \(0.595990\pi\)
\(398\) −3.36898 −0.168872
\(399\) 0.753020 0.0376982
\(400\) −2.91185 −0.145593
\(401\) 11.6256 0.580557 0.290279 0.956942i \(-0.406252\pi\)
0.290279 + 0.956942i \(0.406252\pi\)
\(402\) 9.11960 0.454845
\(403\) 0 0
\(404\) −2.81402 −0.140003
\(405\) −1.44504 −0.0718047
\(406\) 6.89977 0.342430
\(407\) 11.4058 0.565365
\(408\) −0.692021 −0.0342602
\(409\) −8.09485 −0.400265 −0.200132 0.979769i \(-0.564137\pi\)
−0.200132 + 0.979769i \(0.564137\pi\)
\(410\) −2.08815 −0.103126
\(411\) 12.0489 0.594329
\(412\) −8.23490 −0.405704
\(413\) 6.65279 0.327363
\(414\) 1.82908 0.0898946
\(415\) 12.6485 0.620890
\(416\) 0 0
\(417\) 16.6383 0.814782
\(418\) 2.81700 0.137784
\(419\) −5.80087 −0.283391 −0.141696 0.989910i \(-0.545255\pi\)
−0.141696 + 0.989910i \(0.545255\pi\)
\(420\) 1.44504 0.0705108
\(421\) 21.9909 1.07177 0.535885 0.844291i \(-0.319978\pi\)
0.535885 + 0.844291i \(0.319978\pi\)
\(422\) 17.1511 0.834901
\(423\) −3.71379 −0.180571
\(424\) −1.57673 −0.0765727
\(425\) −2.01507 −0.0977450
\(426\) −0.219833 −0.0106509
\(427\) −7.00000 −0.338754
\(428\) 10.6039 0.512558
\(429\) 0 0
\(430\) −8.42327 −0.406206
\(431\) 3.34242 0.160999 0.0804994 0.996755i \(-0.474348\pi\)
0.0804994 + 0.996755i \(0.474348\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 14.0344 0.674452 0.337226 0.941424i \(-0.390511\pi\)
0.337226 + 0.941424i \(0.390511\pi\)
\(434\) 0.960771 0.0461185
\(435\) 9.97046 0.478047
\(436\) 8.48858 0.406529
\(437\) −1.37734 −0.0658870
\(438\) 4.91185 0.234697
\(439\) 25.7735 1.23010 0.615050 0.788488i \(-0.289136\pi\)
0.615050 + 0.788488i \(0.289136\pi\)
\(440\) 5.40581 0.257712
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 5.53558 0.263003 0.131502 0.991316i \(-0.458020\pi\)
0.131502 + 0.991316i \(0.458020\pi\)
\(444\) 3.04892 0.144695
\(445\) 21.0368 0.997242
\(446\) −25.0911 −1.18810
\(447\) −8.35690 −0.395268
\(448\) 1.00000 0.0472456
\(449\) −21.0616 −0.993958 −0.496979 0.867763i \(-0.665557\pi\)
−0.496979 + 0.867763i \(0.665557\pi\)
\(450\) −2.91185 −0.137266
\(451\) −5.40581 −0.254550
\(452\) −5.92692 −0.278779
\(453\) 7.63102 0.358537
\(454\) 5.84415 0.274280
\(455\) 0 0
\(456\) 0.753020 0.0352634
\(457\) −39.7506 −1.85946 −0.929728 0.368247i \(-0.879958\pi\)
−0.929728 + 0.368247i \(0.879958\pi\)
\(458\) −15.2252 −0.711427
\(459\) −0.692021 −0.0323008
\(460\) −2.64310 −0.123235
\(461\) −18.7851 −0.874908 −0.437454 0.899241i \(-0.644120\pi\)
−0.437454 + 0.899241i \(0.644120\pi\)
\(462\) 3.74094 0.174044
\(463\) −30.6504 −1.42444 −0.712222 0.701954i \(-0.752311\pi\)
−0.712222 + 0.701954i \(0.752311\pi\)
\(464\) 6.89977 0.320314
\(465\) 1.38835 0.0643834
\(466\) −25.2000 −1.16737
\(467\) 1.57673 0.0729623 0.0364811 0.999334i \(-0.488385\pi\)
0.0364811 + 0.999334i \(0.488385\pi\)
\(468\) 0 0
\(469\) −9.11960 −0.421104
\(470\) 5.36658 0.247542
\(471\) −12.2935 −0.566455
\(472\) 6.65279 0.306220
\(473\) −21.8062 −1.00265
\(474\) 7.44504 0.341962
\(475\) 2.19269 0.100607
\(476\) 0.692021 0.0317188
\(477\) −1.57673 −0.0721934
\(478\) 6.71379 0.307082
\(479\) 23.5907 1.07789 0.538944 0.842342i \(-0.318823\pi\)
0.538944 + 0.842342i \(0.318823\pi\)
\(480\) 1.44504 0.0659568
\(481\) 0 0
\(482\) −5.21313 −0.237451
\(483\) −1.82908 −0.0832262
\(484\) 2.99462 0.136119
\(485\) 8.75840 0.397698
\(486\) −1.00000 −0.0453609
\(487\) −4.42460 −0.200498 −0.100249 0.994962i \(-0.531964\pi\)
−0.100249 + 0.994962i \(0.531964\pi\)
\(488\) −7.00000 −0.316875
\(489\) 15.0151 0.679005
\(490\) −1.44504 −0.0652803
\(491\) 4.27652 0.192997 0.0964983 0.995333i \(-0.469236\pi\)
0.0964983 + 0.995333i \(0.469236\pi\)
\(492\) −1.44504 −0.0651475
\(493\) 4.77479 0.215046
\(494\) 0 0
\(495\) 5.40581 0.242973
\(496\) 0.960771 0.0431399
\(497\) 0.219833 0.00986084
\(498\) 8.75302 0.392232
\(499\) −5.35152 −0.239567 −0.119783 0.992800i \(-0.538220\pi\)
−0.119783 + 0.992800i \(0.538220\pi\)
\(500\) 11.4330 0.511298
\(501\) −18.3153 −0.818266
\(502\) 9.22952 0.411934
\(503\) 12.1806 0.543106 0.271553 0.962423i \(-0.412463\pi\)
0.271553 + 0.962423i \(0.412463\pi\)
\(504\) 1.00000 0.0445435
\(505\) 4.06638 0.180951
\(506\) −6.84249 −0.304186
\(507\) 0 0
\(508\) 9.67994 0.429478
\(509\) 16.4698 0.730011 0.365005 0.931005i \(-0.381067\pi\)
0.365005 + 0.931005i \(0.381067\pi\)
\(510\) 1.00000 0.0442807
\(511\) −4.91185 −0.217288
\(512\) 1.00000 0.0441942
\(513\) 0.753020 0.0332467
\(514\) 2.51035 0.110727
\(515\) 11.8998 0.524367
\(516\) −5.82908 −0.256611
\(517\) 13.8931 0.611016
\(518\) −3.04892 −0.133962
\(519\) 16.7875 0.736888
\(520\) 0 0
\(521\) 1.89440 0.0829950 0.0414975 0.999139i \(-0.486787\pi\)
0.0414975 + 0.999139i \(0.486787\pi\)
\(522\) 6.89977 0.301995
\(523\) 31.7211 1.38707 0.693533 0.720425i \(-0.256053\pi\)
0.693533 + 0.720425i \(0.256053\pi\)
\(524\) 2.25236 0.0983946
\(525\) 2.91185 0.127084
\(526\) 30.1511 1.31465
\(527\) 0.664874 0.0289624
\(528\) 3.74094 0.162803
\(529\) −19.6544 −0.854541
\(530\) 2.27844 0.0989690
\(531\) 6.65279 0.288707
\(532\) −0.753020 −0.0326476
\(533\) 0 0
\(534\) 14.5579 0.629984
\(535\) −15.3230 −0.662473
\(536\) −9.11960 −0.393907
\(537\) −4.86725 −0.210037
\(538\) −14.6063 −0.629721
\(539\) −3.74094 −0.161134
\(540\) 1.44504 0.0621847
\(541\) −7.16362 −0.307988 −0.153994 0.988072i \(-0.549214\pi\)
−0.153994 + 0.988072i \(0.549214\pi\)
\(542\) −22.0978 −0.949183
\(543\) 13.4644 0.577814
\(544\) 0.692021 0.0296702
\(545\) −12.2664 −0.525433
\(546\) 0 0
\(547\) −24.7754 −1.05932 −0.529659 0.848210i \(-0.677680\pi\)
−0.529659 + 0.848210i \(0.677680\pi\)
\(548\) −12.0489 −0.514704
\(549\) −7.00000 −0.298753
\(550\) 10.8931 0.464482
\(551\) −5.19567 −0.221343
\(552\) −1.82908 −0.0778510
\(553\) −7.44504 −0.316595
\(554\) 1.23729 0.0525675
\(555\) −4.40581 −0.187016
\(556\) −16.6383 −0.705622
\(557\) 29.2653 1.24001 0.620005 0.784598i \(-0.287131\pi\)
0.620005 + 0.784598i \(0.287131\pi\)
\(558\) 0.960771 0.0406727
\(559\) 0 0
\(560\) −1.44504 −0.0610642
\(561\) 2.58881 0.109300
\(562\) −8.51035 −0.358988
\(563\) −7.93230 −0.334306 −0.167153 0.985931i \(-0.553457\pi\)
−0.167153 + 0.985931i \(0.553457\pi\)
\(564\) 3.71379 0.156379
\(565\) 8.56465 0.360317
\(566\) −16.3002 −0.685149
\(567\) 1.00000 0.0419961
\(568\) 0.219833 0.00922397
\(569\) 40.7942 1.71018 0.855090 0.518479i \(-0.173502\pi\)
0.855090 + 0.518479i \(0.173502\pi\)
\(570\) −1.08815 −0.0455774
\(571\) 31.7289 1.32781 0.663906 0.747816i \(-0.268898\pi\)
0.663906 + 0.747816i \(0.268898\pi\)
\(572\) 0 0
\(573\) 5.26444 0.219925
\(574\) 1.44504 0.0603149
\(575\) −5.32603 −0.222111
\(576\) 1.00000 0.0416667
\(577\) 3.88471 0.161722 0.0808612 0.996725i \(-0.474233\pi\)
0.0808612 + 0.996725i \(0.474233\pi\)
\(578\) −16.5211 −0.687187
\(579\) 22.8713 0.950499
\(580\) −9.97046 −0.414001
\(581\) −8.75302 −0.363136
\(582\) 6.06100 0.251236
\(583\) 5.89844 0.244289
\(584\) −4.91185 −0.203254
\(585\) 0 0
\(586\) −29.8853 −1.23455
\(587\) −19.2446 −0.794309 −0.397155 0.917752i \(-0.630002\pi\)
−0.397155 + 0.917752i \(0.630002\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −0.723480 −0.0298105
\(590\) −9.61356 −0.395784
\(591\) −18.8877 −0.776936
\(592\) −3.04892 −0.125310
\(593\) −8.85086 −0.363461 −0.181731 0.983348i \(-0.558170\pi\)
−0.181731 + 0.983348i \(0.558170\pi\)
\(594\) 3.74094 0.153493
\(595\) −1.00000 −0.0409960
\(596\) 8.35690 0.342312
\(597\) 3.36898 0.137883
\(598\) 0 0
\(599\) 24.2174 0.989498 0.494749 0.869036i \(-0.335260\pi\)
0.494749 + 0.869036i \(0.335260\pi\)
\(600\) 2.91185 0.118876
\(601\) −13.3575 −0.544863 −0.272432 0.962175i \(-0.587828\pi\)
−0.272432 + 0.962175i \(0.587828\pi\)
\(602\) 5.82908 0.237576
\(603\) −9.11960 −0.371379
\(604\) −7.63102 −0.310502
\(605\) −4.32736 −0.175932
\(606\) 2.81402 0.114312
\(607\) −0.568959 −0.0230933 −0.0115467 0.999933i \(-0.503675\pi\)
−0.0115467 + 0.999933i \(0.503675\pi\)
\(608\) −0.753020 −0.0305390
\(609\) −6.89977 −0.279593
\(610\) 10.1153 0.409556
\(611\) 0 0
\(612\) 0.692021 0.0279733
\(613\) 21.1008 0.852254 0.426127 0.904663i \(-0.359878\pi\)
0.426127 + 0.904663i \(0.359878\pi\)
\(614\) −24.4547 −0.986913
\(615\) 2.08815 0.0842022
\(616\) −3.74094 −0.150727
\(617\) −15.9705 −0.642947 −0.321473 0.946919i \(-0.604178\pi\)
−0.321473 + 0.946919i \(0.604178\pi\)
\(618\) 8.23490 0.331256
\(619\) −37.9657 −1.52597 −0.762985 0.646417i \(-0.776267\pi\)
−0.762985 + 0.646417i \(0.776267\pi\)
\(620\) −1.38835 −0.0557577
\(621\) −1.82908 −0.0733986
\(622\) −22.3177 −0.894857
\(623\) −14.5579 −0.583252
\(624\) 0 0
\(625\) −1.96184 −0.0784735
\(626\) −2.47889 −0.0990765
\(627\) −2.81700 −0.112500
\(628\) 12.2935 0.490564
\(629\) −2.10992 −0.0841279
\(630\) −1.44504 −0.0575718
\(631\) −16.2054 −0.645125 −0.322563 0.946548i \(-0.604544\pi\)
−0.322563 + 0.946548i \(0.604544\pi\)
\(632\) −7.44504 −0.296148
\(633\) −17.1511 −0.681694
\(634\) −5.65710 −0.224672
\(635\) −13.9879 −0.555094
\(636\) 1.57673 0.0625213
\(637\) 0 0
\(638\) −25.8116 −1.02189
\(639\) 0.219833 0.00869644
\(640\) −1.44504 −0.0571203
\(641\) −33.1879 −1.31084 −0.655422 0.755263i \(-0.727509\pi\)
−0.655422 + 0.755263i \(0.727509\pi\)
\(642\) −10.6039 −0.418502
\(643\) −9.71486 −0.383117 −0.191558 0.981481i \(-0.561354\pi\)
−0.191558 + 0.981481i \(0.561354\pi\)
\(644\) 1.82908 0.0720760
\(645\) 8.42327 0.331666
\(646\) −0.521106 −0.0205027
\(647\) −15.5066 −0.609629 −0.304814 0.952412i \(-0.598594\pi\)
−0.304814 + 0.952412i \(0.598594\pi\)
\(648\) 1.00000 0.0392837
\(649\) −24.8877 −0.976927
\(650\) 0 0
\(651\) −0.960771 −0.0376556
\(652\) −15.0151 −0.588035
\(653\) −4.37627 −0.171257 −0.0856284 0.996327i \(-0.527290\pi\)
−0.0856284 + 0.996327i \(0.527290\pi\)
\(654\) −8.48858 −0.331930
\(655\) −3.25475 −0.127174
\(656\) 1.44504 0.0564194
\(657\) −4.91185 −0.191630
\(658\) −3.71379 −0.144779
\(659\) 24.9638 0.972450 0.486225 0.873834i \(-0.338374\pi\)
0.486225 + 0.873834i \(0.338374\pi\)
\(660\) −5.40581 −0.210421
\(661\) −20.2252 −0.786669 −0.393335 0.919395i \(-0.628679\pi\)
−0.393335 + 0.919395i \(0.628679\pi\)
\(662\) 23.1879 0.901223
\(663\) 0 0
\(664\) −8.75302 −0.339683
\(665\) 1.08815 0.0421965
\(666\) −3.04892 −0.118143
\(667\) 12.6203 0.488659
\(668\) 18.3153 0.708639
\(669\) 25.0911 0.970079
\(670\) 13.1782 0.509119
\(671\) 26.1866 1.01092
\(672\) −1.00000 −0.0385758
\(673\) 26.9119 1.03738 0.518688 0.854964i \(-0.326421\pi\)
0.518688 + 0.854964i \(0.326421\pi\)
\(674\) 10.4873 0.403954
\(675\) 2.91185 0.112077
\(676\) 0 0
\(677\) 36.9571 1.42037 0.710187 0.704013i \(-0.248610\pi\)
0.710187 + 0.704013i \(0.248610\pi\)
\(678\) 5.92692 0.227622
\(679\) −6.06100 −0.232600
\(680\) −1.00000 −0.0383482
\(681\) −5.84415 −0.223948
\(682\) −3.59419 −0.137629
\(683\) 4.53212 0.173417 0.0867084 0.996234i \(-0.472365\pi\)
0.0867084 + 0.996234i \(0.472365\pi\)
\(684\) −0.753020 −0.0287925
\(685\) 17.4112 0.665247
\(686\) 1.00000 0.0381802
\(687\) 15.2252 0.580878
\(688\) 5.82908 0.222232
\(689\) 0 0
\(690\) 2.64310 0.100621
\(691\) −24.7670 −0.942182 −0.471091 0.882085i \(-0.656140\pi\)
−0.471091 + 0.882085i \(0.656140\pi\)
\(692\) −16.7875 −0.638164
\(693\) −3.74094 −0.142107
\(694\) −5.28514 −0.200621
\(695\) 24.0431 0.912005
\(696\) −6.89977 −0.261535
\(697\) 1.00000 0.0378777
\(698\) 8.19029 0.310007
\(699\) 25.2000 0.953151
\(700\) −2.91185 −0.110058
\(701\) 38.2965 1.44644 0.723219 0.690619i \(-0.242662\pi\)
0.723219 + 0.690619i \(0.242662\pi\)
\(702\) 0 0
\(703\) 2.29590 0.0865914
\(704\) −3.74094 −0.140992
\(705\) −5.36658 −0.202117
\(706\) 35.9758 1.35397
\(707\) −2.81402 −0.105832
\(708\) −6.65279 −0.250027
\(709\) −44.3256 −1.66468 −0.832341 0.554265i \(-0.813000\pi\)
−0.832341 + 0.554265i \(0.813000\pi\)
\(710\) −0.317667 −0.0119218
\(711\) −7.44504 −0.279211
\(712\) −14.5579 −0.545582
\(713\) 1.75733 0.0658126
\(714\) −0.692021 −0.0258983
\(715\) 0 0
\(716\) 4.86725 0.181898
\(717\) −6.71379 −0.250731
\(718\) −28.7603 −1.07333
\(719\) −24.5773 −0.916579 −0.458290 0.888803i \(-0.651538\pi\)
−0.458290 + 0.888803i \(0.651538\pi\)
\(720\) −1.44504 −0.0538535
\(721\) −8.23490 −0.306684
\(722\) −18.4330 −0.686004
\(723\) 5.21313 0.193878
\(724\) −13.4644 −0.500401
\(725\) −20.0911 −0.746166
\(726\) −2.99462 −0.111141
\(727\) 38.8280 1.44005 0.720026 0.693947i \(-0.244130\pi\)
0.720026 + 0.693947i \(0.244130\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 7.09783 0.262703
\(731\) 4.03385 0.149197
\(732\) 7.00000 0.258727
\(733\) 21.6142 0.798337 0.399169 0.916878i \(-0.369299\pi\)
0.399169 + 0.916878i \(0.369299\pi\)
\(734\) −3.61463 −0.133418
\(735\) 1.44504 0.0533012
\(736\) 1.82908 0.0674210
\(737\) 34.1159 1.25667
\(738\) 1.44504 0.0531927
\(739\) −13.4644 −0.495297 −0.247648 0.968850i \(-0.579658\pi\)
−0.247648 + 0.968850i \(0.579658\pi\)
\(740\) 4.40581 0.161961
\(741\) 0 0
\(742\) −1.57673 −0.0578835
\(743\) 3.90887 0.143403 0.0717013 0.997426i \(-0.477157\pi\)
0.0717013 + 0.997426i \(0.477157\pi\)
\(744\) −0.960771 −0.0352236
\(745\) −12.0761 −0.442433
\(746\) 17.9312 0.656509
\(747\) −8.75302 −0.320256
\(748\) −2.58881 −0.0946563
\(749\) 10.6039 0.387457
\(750\) −11.4330 −0.417473
\(751\) 45.2922 1.65273 0.826367 0.563131i \(-0.190403\pi\)
0.826367 + 0.563131i \(0.190403\pi\)
\(752\) −3.71379 −0.135428
\(753\) −9.22952 −0.336342
\(754\) 0 0
\(755\) 11.0271 0.401319
\(756\) −1.00000 −0.0363696
\(757\) 23.6872 0.860927 0.430464 0.902608i \(-0.358350\pi\)
0.430464 + 0.902608i \(0.358350\pi\)
\(758\) 22.2338 0.807569
\(759\) 6.84249 0.248367
\(760\) 1.08815 0.0394712
\(761\) 9.25667 0.335554 0.167777 0.985825i \(-0.446341\pi\)
0.167777 + 0.985825i \(0.446341\pi\)
\(762\) −9.67994 −0.350667
\(763\) 8.48858 0.307307
\(764\) −5.26444 −0.190461
\(765\) −1.00000 −0.0361551
\(766\) −25.4330 −0.918930
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −36.1390 −1.30321 −0.651603 0.758561i \(-0.725903\pi\)
−0.651603 + 0.758561i \(0.725903\pi\)
\(770\) 5.40581 0.194812
\(771\) −2.51035 −0.0904081
\(772\) −22.8713 −0.823156
\(773\) 14.6552 0.527110 0.263555 0.964644i \(-0.415105\pi\)
0.263555 + 0.964644i \(0.415105\pi\)
\(774\) 5.82908 0.209522
\(775\) −2.79763 −0.100494
\(776\) −6.06100 −0.217577
\(777\) 3.04892 0.109379
\(778\) −14.9855 −0.537257
\(779\) −1.08815 −0.0389869
\(780\) 0 0
\(781\) −0.822380 −0.0294271
\(782\) 1.26577 0.0452637
\(783\) −6.89977 −0.246578
\(784\) 1.00000 0.0357143
\(785\) −17.7646 −0.634047
\(786\) −2.25236 −0.0803389
\(787\) 11.7724 0.419641 0.209820 0.977740i \(-0.432712\pi\)
0.209820 + 0.977740i \(0.432712\pi\)
\(788\) 18.8877 0.672846
\(789\) −30.1511 −1.07341
\(790\) 10.7584 0.382767
\(791\) −5.92692 −0.210737
\(792\) −3.74094 −0.132928
\(793\) 0 0
\(794\) −11.8358 −0.420036
\(795\) −2.27844 −0.0808079
\(796\) −3.36898 −0.119410
\(797\) 40.0431 1.41840 0.709199 0.705008i \(-0.249057\pi\)
0.709199 + 0.705008i \(0.249057\pi\)
\(798\) 0.753020 0.0266566
\(799\) −2.57002 −0.0909209
\(800\) −2.91185 −0.102950
\(801\) −14.5579 −0.514380
\(802\) 11.6256 0.410516
\(803\) 18.3749 0.648438
\(804\) 9.11960 0.321624
\(805\) −2.64310 −0.0931572
\(806\) 0 0
\(807\) 14.6063 0.514165
\(808\) −2.81402 −0.0989969
\(809\) 41.8243 1.47046 0.735232 0.677816i \(-0.237073\pi\)
0.735232 + 0.677816i \(0.237073\pi\)
\(810\) −1.44504 −0.0507736
\(811\) 9.53212 0.334718 0.167359 0.985896i \(-0.446476\pi\)
0.167359 + 0.985896i \(0.446476\pi\)
\(812\) 6.89977 0.242135
\(813\) 22.0978 0.775005
\(814\) 11.4058 0.399774
\(815\) 21.6974 0.760027
\(816\) −0.692021 −0.0242256
\(817\) −4.38942 −0.153566
\(818\) −8.09485 −0.283030
\(819\) 0 0
\(820\) −2.08815 −0.0729212
\(821\) 0.509025 0.0177651 0.00888254 0.999961i \(-0.497173\pi\)
0.00888254 + 0.999961i \(0.497173\pi\)
\(822\) 12.0489 0.420254
\(823\) 35.4233 1.23478 0.617389 0.786658i \(-0.288191\pi\)
0.617389 + 0.786658i \(0.288191\pi\)
\(824\) −8.23490 −0.286876
\(825\) −10.8931 −0.379248
\(826\) 6.65279 0.231480
\(827\) −31.6547 −1.10074 −0.550371 0.834920i \(-0.685514\pi\)
−0.550371 + 0.834920i \(0.685514\pi\)
\(828\) 1.82908 0.0635651
\(829\) −32.3026 −1.12192 −0.560958 0.827844i \(-0.689567\pi\)
−0.560958 + 0.827844i \(0.689567\pi\)
\(830\) 12.6485 0.439035
\(831\) −1.23729 −0.0429211
\(832\) 0 0
\(833\) 0.692021 0.0239771
\(834\) 16.6383 0.576138
\(835\) −26.4663 −0.915905
\(836\) 2.81700 0.0974281
\(837\) −0.960771 −0.0332091
\(838\) −5.80087 −0.200388
\(839\) 19.4896 0.672857 0.336429 0.941709i \(-0.390781\pi\)
0.336429 + 0.941709i \(0.390781\pi\)
\(840\) 1.44504 0.0498587
\(841\) 18.6069 0.641616
\(842\) 21.9909 0.757857
\(843\) 8.51035 0.293112
\(844\) 17.1511 0.590364
\(845\) 0 0
\(846\) −3.71379 −0.127683
\(847\) 2.99462 0.102896
\(848\) −1.57673 −0.0541451
\(849\) 16.3002 0.559422
\(850\) −2.01507 −0.0691162
\(851\) −5.57673 −0.191168
\(852\) −0.219833 −0.00753134
\(853\) −6.02177 −0.206181 −0.103091 0.994672i \(-0.532873\pi\)
−0.103091 + 0.994672i \(0.532873\pi\)
\(854\) −7.00000 −0.239535
\(855\) 1.08815 0.0372138
\(856\) 10.6039 0.362433
\(857\) −41.1172 −1.40454 −0.702269 0.711912i \(-0.747829\pi\)
−0.702269 + 0.711912i \(0.747829\pi\)
\(858\) 0 0
\(859\) 53.3666 1.82084 0.910422 0.413680i \(-0.135757\pi\)
0.910422 + 0.413680i \(0.135757\pi\)
\(860\) −8.42327 −0.287231
\(861\) −1.44504 −0.0492469
\(862\) 3.34242 0.113843
\(863\) −27.5056 −0.936300 −0.468150 0.883649i \(-0.655079\pi\)
−0.468150 + 0.883649i \(0.655079\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 24.2586 0.824817
\(866\) 14.0344 0.476910
\(867\) 16.5211 0.561086
\(868\) 0.960771 0.0326107
\(869\) 27.8514 0.944796
\(870\) 9.97046 0.338030
\(871\) 0 0
\(872\) 8.48858 0.287460
\(873\) −6.06100 −0.205134
\(874\) −1.37734 −0.0465892
\(875\) 11.4330 0.386505
\(876\) 4.91185 0.165956
\(877\) 11.8092 0.398769 0.199385 0.979921i \(-0.436106\pi\)
0.199385 + 0.979921i \(0.436106\pi\)
\(878\) 25.7735 0.869812
\(879\) 29.8853 1.00801
\(880\) 5.40581 0.182230
\(881\) −35.6848 −1.20225 −0.601126 0.799154i \(-0.705281\pi\)
−0.601126 + 0.799154i \(0.705281\pi\)
\(882\) 1.00000 0.0336718
\(883\) 18.0718 0.608163 0.304081 0.952646i \(-0.401650\pi\)
0.304081 + 0.952646i \(0.401650\pi\)
\(884\) 0 0
\(885\) 9.61356 0.323156
\(886\) 5.53558 0.185971
\(887\) −36.9922 −1.24208 −0.621039 0.783780i \(-0.713289\pi\)
−0.621039 + 0.783780i \(0.713289\pi\)
\(888\) 3.04892 0.102315
\(889\) 9.67994 0.324655
\(890\) 21.0368 0.705156
\(891\) −3.74094 −0.125326
\(892\) −25.0911 −0.840113
\(893\) 2.79656 0.0935833
\(894\) −8.35690 −0.279496
\(895\) −7.03338 −0.235100
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −21.0616 −0.702834
\(899\) 6.62910 0.221093
\(900\) −2.91185 −0.0970618
\(901\) −1.09113 −0.0363508
\(902\) −5.40581 −0.179994
\(903\) −5.82908 −0.193980
\(904\) −5.92692 −0.197126
\(905\) 19.4566 0.646761
\(906\) 7.63102 0.253524
\(907\) 24.4902 0.813185 0.406593 0.913610i \(-0.366717\pi\)
0.406593 + 0.913610i \(0.366717\pi\)
\(908\) 5.84415 0.193945
\(909\) −2.81402 −0.0933351
\(910\) 0 0
\(911\) 29.8407 0.988666 0.494333 0.869273i \(-0.335412\pi\)
0.494333 + 0.869273i \(0.335412\pi\)
\(912\) 0.753020 0.0249350
\(913\) 32.7445 1.08369
\(914\) −39.7506 −1.31483
\(915\) −10.1153 −0.334401
\(916\) −15.2252 −0.503055
\(917\) 2.25236 0.0743794
\(918\) −0.692021 −0.0228401
\(919\) 44.0756 1.45392 0.726960 0.686680i \(-0.240933\pi\)
0.726960 + 0.686680i \(0.240933\pi\)
\(920\) −2.64310 −0.0871406
\(921\) 24.4547 0.805811
\(922\) −18.7851 −0.618653
\(923\) 0 0
\(924\) 3.74094 0.123068
\(925\) 8.87800 0.291907
\(926\) −30.6504 −1.00723
\(927\) −8.23490 −0.270470
\(928\) 6.89977 0.226496
\(929\) 2.83340 0.0929607 0.0464804 0.998919i \(-0.485200\pi\)
0.0464804 + 0.998919i \(0.485200\pi\)
\(930\) 1.38835 0.0455259
\(931\) −0.753020 −0.0246792
\(932\) −25.2000 −0.825453
\(933\) 22.3177 0.730648
\(934\) 1.57673 0.0515921
\(935\) 3.74094 0.122342
\(936\) 0 0
\(937\) −40.3129 −1.31696 −0.658482 0.752596i \(-0.728801\pi\)
−0.658482 + 0.752596i \(0.728801\pi\)
\(938\) −9.11960 −0.297766
\(939\) 2.47889 0.0808956
\(940\) 5.36658 0.175039
\(941\) 54.3223 1.77086 0.885428 0.464776i \(-0.153865\pi\)
0.885428 + 0.464776i \(0.153865\pi\)
\(942\) −12.2935 −0.400544
\(943\) 2.64310 0.0860713
\(944\) 6.65279 0.216530
\(945\) 1.44504 0.0470072
\(946\) −21.8062 −0.708982
\(947\) 50.8980 1.65396 0.826981 0.562230i \(-0.190056\pi\)
0.826981 + 0.562230i \(0.190056\pi\)
\(948\) 7.44504 0.241804
\(949\) 0 0
\(950\) 2.19269 0.0711401
\(951\) 5.65710 0.183444
\(952\) 0.692021 0.0224285
\(953\) −4.62266 −0.149743 −0.0748714 0.997193i \(-0.523855\pi\)
−0.0748714 + 0.997193i \(0.523855\pi\)
\(954\) −1.57673 −0.0510485
\(955\) 7.60733 0.246168
\(956\) 6.71379 0.217140
\(957\) 25.8116 0.834371
\(958\) 23.5907 0.762182
\(959\) −12.0489 −0.389080
\(960\) 1.44504 0.0466385
\(961\) −30.0769 −0.970223
\(962\) 0 0
\(963\) 10.6039 0.341705
\(964\) −5.21313 −0.167904
\(965\) 33.0500 1.06392
\(966\) −1.82908 −0.0588498
\(967\) 52.9235 1.70190 0.850952 0.525244i \(-0.176026\pi\)
0.850952 + 0.525244i \(0.176026\pi\)
\(968\) 2.99462 0.0962508
\(969\) 0.521106 0.0167403
\(970\) 8.75840 0.281215
\(971\) 2.78256 0.0892966 0.0446483 0.999003i \(-0.485783\pi\)
0.0446483 + 0.999003i \(0.485783\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −16.6383 −0.533400
\(974\) −4.42460 −0.141773
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) −12.0922 −0.386864 −0.193432 0.981114i \(-0.561962\pi\)
−0.193432 + 0.981114i \(0.561962\pi\)
\(978\) 15.0151 0.480129
\(979\) 54.4604 1.74056
\(980\) −1.44504 −0.0461602
\(981\) 8.48858 0.271020
\(982\) 4.27652 0.136469
\(983\) −22.9474 −0.731907 −0.365954 0.930633i \(-0.619257\pi\)
−0.365954 + 0.930633i \(0.619257\pi\)
\(984\) −1.44504 −0.0460663
\(985\) −27.2935 −0.869643
\(986\) 4.77479 0.152060
\(987\) 3.71379 0.118211
\(988\) 0 0
\(989\) 10.6619 0.339028
\(990\) 5.40581 0.171808
\(991\) −1.44876 −0.0460215 −0.0230107 0.999735i \(-0.507325\pi\)
−0.0230107 + 0.999735i \(0.507325\pi\)
\(992\) 0.960771 0.0305045
\(993\) −23.1879 −0.735846
\(994\) 0.219833 0.00697266
\(995\) 4.86831 0.154336
\(996\) 8.75302 0.277350
\(997\) 39.6491 1.25570 0.627849 0.778335i \(-0.283935\pi\)
0.627849 + 0.778335i \(0.283935\pi\)
\(998\) −5.35152 −0.169399
\(999\) 3.04892 0.0964635
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 7098.2.a.ch.1.2 yes 3
13.12 even 2 7098.2.a.ce.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.ce.1.2 3 13.12 even 2
7098.2.a.ch.1.2 yes 3 1.1 even 1 trivial