Properties

Label 7098.2.a.cc.1.1
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $0$
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: \(0\)
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 1.1
Root \(1.80194\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.24698 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.24698 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.24698 q^{10} +0.692021 q^{11} -1.00000 q^{12} -1.00000 q^{14} +2.24698 q^{15} +1.00000 q^{16} -2.44504 q^{17} -1.00000 q^{18} +3.40581 q^{19} -2.24698 q^{20} -1.00000 q^{21} -0.692021 q^{22} -0.753020 q^{23} +1.00000 q^{24} +0.0489173 q^{25} -1.00000 q^{27} +1.00000 q^{28} -3.66487 q^{29} -2.24698 q^{30} -4.40581 q^{31} -1.00000 q^{32} -0.692021 q^{33} +2.44504 q^{34} -2.24698 q^{35} +1.00000 q^{36} +6.96077 q^{37} -3.40581 q^{38} +2.24698 q^{40} +5.63102 q^{41} +1.00000 q^{42} -1.64310 q^{43} +0.692021 q^{44} -2.24698 q^{45} +0.753020 q^{46} +2.10992 q^{47} -1.00000 q^{48} +1.00000 q^{49} -0.0489173 q^{50} +2.44504 q^{51} -1.69202 q^{53} +1.00000 q^{54} -1.55496 q^{55} -1.00000 q^{56} -3.40581 q^{57} +3.66487 q^{58} +4.96077 q^{59} +2.24698 q^{60} -5.09783 q^{61} +4.40581 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.692021 q^{66} +7.84117 q^{67} -2.44504 q^{68} +0.753020 q^{69} +2.24698 q^{70} -8.76809 q^{71} -1.00000 q^{72} +11.2131 q^{73} -6.96077 q^{74} -0.0489173 q^{75} +3.40581 q^{76} +0.692021 q^{77} +1.97285 q^{79} -2.24698 q^{80} +1.00000 q^{81} -5.63102 q^{82} -9.22952 q^{83} -1.00000 q^{84} +5.49396 q^{85} +1.64310 q^{86} +3.66487 q^{87} -0.692021 q^{88} -3.44504 q^{89} +2.24698 q^{90} -0.753020 q^{92} +4.40581 q^{93} -2.10992 q^{94} -7.65279 q^{95} +1.00000 q^{96} +4.46681 q^{97} -1.00000 q^{98} +0.692021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{2} - 3q^{3} + 3q^{4} - 2q^{5} + 3q^{6} + 3q^{7} - 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - 3q^{2} - 3q^{3} + 3q^{4} - 2q^{5} + 3q^{6} + 3q^{7} - 3q^{8} + 3q^{9} + 2q^{10} - 3q^{11} - 3q^{12} - 3q^{14} + 2q^{15} + 3q^{16} - 7q^{17} - 3q^{18} - 3q^{19} - 2q^{20} - 3q^{21} + 3q^{22} - 7q^{23} + 3q^{24} - 9q^{25} - 3q^{27} + 3q^{28} - 12q^{29} - 2q^{30} - 3q^{32} + 3q^{33} + 7q^{34} - 2q^{35} + 3q^{36} + 8q^{37} + 3q^{38} + 2q^{40} + 2q^{41} + 3q^{42} - 9q^{43} - 3q^{44} - 2q^{45} + 7q^{46} + 7q^{47} - 3q^{48} + 3q^{49} + 9q^{50} + 7q^{51} + 3q^{54} - 5q^{55} - 3q^{56} + 3q^{57} + 12q^{58} + 2q^{59} + 2q^{60} + 3q^{61} + 3q^{63} + 3q^{64} - 3q^{66} + 32q^{67} - 7q^{68} + 7q^{69} + 2q^{70} - 6q^{71} - 3q^{72} + 13q^{73} - 8q^{74} + 9q^{75} - 3q^{76} - 3q^{77} + 12q^{79} - 2q^{80} + 3q^{81} - 2q^{82} - 7q^{83} - 3q^{84} + 7q^{85} + 9q^{86} + 12q^{87} + 3q^{88} - 10q^{89} + 2q^{90} - 7q^{92} - 7q^{94} - 5q^{95} + 3q^{96} + 10q^{97} - 3q^{98} - 3q^{99} + O(q^{100}) \)

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
\(5\) −2.24698 −1.00488 −0.502440 0.864612i \(-0.667564\pi\)
−0.502440 + 0.864612i \(0.667564\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.24698 0.710557
\(11\) 0.692021 0.208652 0.104326 0.994543i \(-0.466731\pi\)
0.104326 + 0.994543i \(0.466731\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 2.24698 0.580168
\(16\) 1.00000 0.250000
\(17\) −2.44504 −0.593010 −0.296505 0.955031i \(-0.595821\pi\)
−0.296505 + 0.955031i \(0.595821\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.40581 0.781347 0.390674 0.920529i \(-0.372242\pi\)
0.390674 + 0.920529i \(0.372242\pi\)
\(20\) −2.24698 −0.502440
\(21\) −1.00000 −0.218218
\(22\) −0.692021 −0.147539
\(23\) −0.753020 −0.157016 −0.0785078 0.996913i \(-0.525016\pi\)
−0.0785078 + 0.996913i \(0.525016\pi\)
\(24\) 1.00000 0.204124
\(25\) 0.0489173 0.00978347
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) −3.66487 −0.680550 −0.340275 0.940326i \(-0.610520\pi\)
−0.340275 + 0.940326i \(0.610520\pi\)
\(30\) −2.24698 −0.410240
\(31\) −4.40581 −0.791307 −0.395654 0.918400i \(-0.629482\pi\)
−0.395654 + 0.918400i \(0.629482\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.692021 −0.120465
\(34\) 2.44504 0.419321
\(35\) −2.24698 −0.379809
\(36\) 1.00000 0.166667
\(37\) 6.96077 1.14434 0.572172 0.820134i \(-0.306101\pi\)
0.572172 + 0.820134i \(0.306101\pi\)
\(38\) −3.40581 −0.552496
\(39\) 0 0
\(40\) 2.24698 0.355279
\(41\) 5.63102 0.879418 0.439709 0.898140i \(-0.355082\pi\)
0.439709 + 0.898140i \(0.355082\pi\)
\(42\) 1.00000 0.154303
\(43\) −1.64310 −0.250571 −0.125286 0.992121i \(-0.539985\pi\)
−0.125286 + 0.992121i \(0.539985\pi\)
\(44\) 0.692021 0.104326
\(45\) −2.24698 −0.334960
\(46\) 0.753020 0.111027
\(47\) 2.10992 0.307763 0.153881 0.988089i \(-0.450823\pi\)
0.153881 + 0.988089i \(0.450823\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −0.0489173 −0.00691796
\(51\) 2.44504 0.342374
\(52\) 0 0
\(53\) −1.69202 −0.232417 −0.116209 0.993225i \(-0.537074\pi\)
−0.116209 + 0.993225i \(0.537074\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.55496 −0.209671
\(56\) −1.00000 −0.133631
\(57\) −3.40581 −0.451111
\(58\) 3.66487 0.481222
\(59\) 4.96077 0.645837 0.322919 0.946427i \(-0.395336\pi\)
0.322919 + 0.946427i \(0.395336\pi\)
\(60\) 2.24698 0.290084
\(61\) −5.09783 −0.652711 −0.326355 0.945247i \(-0.605821\pi\)
−0.326355 + 0.945247i \(0.605821\pi\)
\(62\) 4.40581 0.559539
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.692021 0.0851820
\(67\) 7.84117 0.957951 0.478975 0.877828i \(-0.341008\pi\)
0.478975 + 0.877828i \(0.341008\pi\)
\(68\) −2.44504 −0.296505
\(69\) 0.753020 0.0906530
\(70\) 2.24698 0.268565
\(71\) −8.76809 −1.04058 −0.520290 0.853990i \(-0.674176\pi\)
−0.520290 + 0.853990i \(0.674176\pi\)
\(72\) −1.00000 −0.117851
\(73\) 11.2131 1.31240 0.656199 0.754588i \(-0.272163\pi\)
0.656199 + 0.754588i \(0.272163\pi\)
\(74\) −6.96077 −0.809173
\(75\) −0.0489173 −0.00564849
\(76\) 3.40581 0.390674
\(77\) 0.692021 0.0788632
\(78\) 0 0
\(79\) 1.97285 0.221963 0.110982 0.993822i \(-0.464601\pi\)
0.110982 + 0.993822i \(0.464601\pi\)
\(80\) −2.24698 −0.251220
\(81\) 1.00000 0.111111
\(82\) −5.63102 −0.621842
\(83\) −9.22952 −1.01307 −0.506536 0.862219i \(-0.669074\pi\)
−0.506536 + 0.862219i \(0.669074\pi\)
\(84\) −1.00000 −0.109109
\(85\) 5.49396 0.595904
\(86\) 1.64310 0.177180
\(87\) 3.66487 0.392916
\(88\) −0.692021 −0.0737697
\(89\) −3.44504 −0.365174 −0.182587 0.983190i \(-0.558447\pi\)
−0.182587 + 0.983190i \(0.558447\pi\)
\(90\) 2.24698 0.236852
\(91\) 0 0
\(92\) −0.753020 −0.0785078
\(93\) 4.40581 0.456862
\(94\) −2.10992 −0.217621
\(95\) −7.65279 −0.785160
\(96\) 1.00000 0.102062
\(97\) 4.46681 0.453536 0.226768 0.973949i \(-0.427184\pi\)
0.226768 + 0.973949i \(0.427184\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.692021 0.0695508
\(100\) 0.0489173 0.00489173
\(101\) 6.48858 0.645638 0.322819 0.946461i \(-0.395369\pi\)
0.322819 + 0.946461i \(0.395369\pi\)
\(102\) −2.44504 −0.242095
\(103\) 7.85623 0.774098 0.387049 0.922059i \(-0.373495\pi\)
0.387049 + 0.922059i \(0.373495\pi\)
\(104\) 0 0
\(105\) 2.24698 0.219283
\(106\) 1.69202 0.164344
\(107\) −14.9215 −1.44252 −0.721260 0.692664i \(-0.756437\pi\)
−0.721260 + 0.692664i \(0.756437\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −12.6504 −1.21169 −0.605844 0.795583i \(-0.707165\pi\)
−0.605844 + 0.795583i \(0.707165\pi\)
\(110\) 1.55496 0.148259
\(111\) −6.96077 −0.660687
\(112\) 1.00000 0.0944911
\(113\) −20.5526 −1.93342 −0.966711 0.255869i \(-0.917638\pi\)
−0.966711 + 0.255869i \(0.917638\pi\)
\(114\) 3.40581 0.318984
\(115\) 1.69202 0.157782
\(116\) −3.66487 −0.340275
\(117\) 0 0
\(118\) −4.96077 −0.456676
\(119\) −2.44504 −0.224137
\(120\) −2.24698 −0.205120
\(121\) −10.5211 −0.956464
\(122\) 5.09783 0.461536
\(123\) −5.63102 −0.507732
\(124\) −4.40581 −0.395654
\(125\) 11.1250 0.995049
\(126\) −1.00000 −0.0890871
\(127\) 2.66487 0.236469 0.118235 0.992986i \(-0.462276\pi\)
0.118235 + 0.992986i \(0.462276\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.64310 0.144667
\(130\) 0 0
\(131\) 3.37867 0.295195 0.147598 0.989047i \(-0.452846\pi\)
0.147598 + 0.989047i \(0.452846\pi\)
\(132\) −0.692021 −0.0602327
\(133\) 3.40581 0.295321
\(134\) −7.84117 −0.677374
\(135\) 2.24698 0.193389
\(136\) 2.44504 0.209661
\(137\) 15.5646 1.32978 0.664889 0.746942i \(-0.268479\pi\)
0.664889 + 0.746942i \(0.268479\pi\)
\(138\) −0.753020 −0.0641014
\(139\) −0.405813 −0.0344206 −0.0172103 0.999852i \(-0.505478\pi\)
−0.0172103 + 0.999852i \(0.505478\pi\)
\(140\) −2.24698 −0.189904
\(141\) −2.10992 −0.177687
\(142\) 8.76809 0.735801
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 8.23490 0.683871
\(146\) −11.2131 −0.928005
\(147\) −1.00000 −0.0824786
\(148\) 6.96077 0.572172
\(149\) −8.35019 −0.684074 −0.342037 0.939686i \(-0.611117\pi\)
−0.342037 + 0.939686i \(0.611117\pi\)
\(150\) 0.0489173 0.00399408
\(151\) 5.24160 0.426556 0.213278 0.976992i \(-0.431586\pi\)
0.213278 + 0.976992i \(0.431586\pi\)
\(152\) −3.40581 −0.276248
\(153\) −2.44504 −0.197670
\(154\) −0.692021 −0.0557647
\(155\) 9.89977 0.795169
\(156\) 0 0
\(157\) 10.4940 0.837509 0.418755 0.908099i \(-0.362467\pi\)
0.418755 + 0.908099i \(0.362467\pi\)
\(158\) −1.97285 −0.156952
\(159\) 1.69202 0.134186
\(160\) 2.24698 0.177639
\(161\) −0.753020 −0.0593463
\(162\) −1.00000 −0.0785674
\(163\) −18.6993 −1.46464 −0.732322 0.680959i \(-0.761563\pi\)
−0.732322 + 0.680959i \(0.761563\pi\)
\(164\) 5.63102 0.439709
\(165\) 1.55496 0.121053
\(166\) 9.22952 0.716350
\(167\) −11.9269 −0.922933 −0.461466 0.887158i \(-0.652677\pi\)
−0.461466 + 0.887158i \(0.652677\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) −5.49396 −0.421367
\(171\) 3.40581 0.260449
\(172\) −1.64310 −0.125286
\(173\) −7.10992 −0.540557 −0.270278 0.962782i \(-0.587116\pi\)
−0.270278 + 0.962782i \(0.587116\pi\)
\(174\) −3.66487 −0.277833
\(175\) 0.0489173 0.00369780
\(176\) 0.692021 0.0521631
\(177\) −4.96077 −0.372874
\(178\) 3.44504 0.258217
\(179\) −12.1642 −0.909196 −0.454598 0.890697i \(-0.650217\pi\)
−0.454598 + 0.890697i \(0.650217\pi\)
\(180\) −2.24698 −0.167480
\(181\) 4.83877 0.359663 0.179832 0.983697i \(-0.442445\pi\)
0.179832 + 0.983697i \(0.442445\pi\)
\(182\) 0 0
\(183\) 5.09783 0.376843
\(184\) 0.753020 0.0555134
\(185\) −15.6407 −1.14993
\(186\) −4.40581 −0.323050
\(187\) −1.69202 −0.123733
\(188\) 2.10992 0.153881
\(189\) −1.00000 −0.0727393
\(190\) 7.65279 0.555192
\(191\) −0.664874 −0.0481086 −0.0240543 0.999711i \(-0.507657\pi\)
−0.0240543 + 0.999711i \(0.507657\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 11.3013 0.813483 0.406742 0.913543i \(-0.366665\pi\)
0.406742 + 0.913543i \(0.366665\pi\)
\(194\) −4.46681 −0.320698
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 6.26875 0.446630 0.223315 0.974746i \(-0.428312\pi\)
0.223315 + 0.974746i \(0.428312\pi\)
\(198\) −0.692021 −0.0491798
\(199\) −12.3937 −0.878568 −0.439284 0.898348i \(-0.644768\pi\)
−0.439284 + 0.898348i \(0.644768\pi\)
\(200\) −0.0489173 −0.00345898
\(201\) −7.84117 −0.553073
\(202\) −6.48858 −0.456535
\(203\) −3.66487 −0.257224
\(204\) 2.44504 0.171187
\(205\) −12.6528 −0.883709
\(206\) −7.85623 −0.547370
\(207\) −0.753020 −0.0523385
\(208\) 0 0
\(209\) 2.35690 0.163030
\(210\) −2.24698 −0.155056
\(211\) 7.65279 0.526840 0.263420 0.964681i \(-0.415150\pi\)
0.263420 + 0.964681i \(0.415150\pi\)
\(212\) −1.69202 −0.116209
\(213\) 8.76809 0.600779
\(214\) 14.9215 1.02002
\(215\) 3.69202 0.251794
\(216\) 1.00000 0.0680414
\(217\) −4.40581 −0.299086
\(218\) 12.6504 0.856793
\(219\) −11.2131 −0.757713
\(220\) −1.55496 −0.104835
\(221\) 0 0
\(222\) 6.96077 0.467176
\(223\) 15.2905 1.02393 0.511964 0.859007i \(-0.328918\pi\)
0.511964 + 0.859007i \(0.328918\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0.0489173 0.00326116
\(226\) 20.5526 1.36714
\(227\) 14.2808 0.947852 0.473926 0.880565i \(-0.342836\pi\)
0.473926 + 0.880565i \(0.342836\pi\)
\(228\) −3.40581 −0.225555
\(229\) 6.30127 0.416400 0.208200 0.978086i \(-0.433240\pi\)
0.208200 + 0.978086i \(0.433240\pi\)
\(230\) −1.69202 −0.111569
\(231\) −0.692021 −0.0455317
\(232\) 3.66487 0.240611
\(233\) 25.9071 1.69723 0.848614 0.529012i \(-0.177437\pi\)
0.848614 + 0.529012i \(0.177437\pi\)
\(234\) 0 0
\(235\) −4.74094 −0.309265
\(236\) 4.96077 0.322919
\(237\) −1.97285 −0.128151
\(238\) 2.44504 0.158489
\(239\) −0.811626 −0.0524997 −0.0262499 0.999655i \(-0.508357\pi\)
−0.0262499 + 0.999655i \(0.508357\pi\)
\(240\) 2.24698 0.145042
\(241\) −6.23490 −0.401625 −0.200813 0.979630i \(-0.564358\pi\)
−0.200813 + 0.979630i \(0.564358\pi\)
\(242\) 10.5211 0.676322
\(243\) −1.00000 −0.0641500
\(244\) −5.09783 −0.326355
\(245\) −2.24698 −0.143554
\(246\) 5.63102 0.359021
\(247\) 0 0
\(248\) 4.40581 0.279769
\(249\) 9.22952 0.584897
\(250\) −11.1250 −0.703606
\(251\) 29.6045 1.86862 0.934309 0.356465i \(-0.116018\pi\)
0.934309 + 0.356465i \(0.116018\pi\)
\(252\) 1.00000 0.0629941
\(253\) −0.521106 −0.0327617
\(254\) −2.66487 −0.167209
\(255\) −5.49396 −0.344045
\(256\) 1.00000 0.0625000
\(257\) −9.24160 −0.576475 −0.288238 0.957559i \(-0.593069\pi\)
−0.288238 + 0.957559i \(0.593069\pi\)
\(258\) −1.64310 −0.102295
\(259\) 6.96077 0.432521
\(260\) 0 0
\(261\) −3.66487 −0.226850
\(262\) −3.37867 −0.208735
\(263\) 1.09246 0.0673638 0.0336819 0.999433i \(-0.489277\pi\)
0.0336819 + 0.999433i \(0.489277\pi\)
\(264\) 0.692021 0.0425910
\(265\) 3.80194 0.233551
\(266\) −3.40581 −0.208824
\(267\) 3.44504 0.210833
\(268\) 7.84117 0.478975
\(269\) −0.916166 −0.0558596 −0.0279298 0.999610i \(-0.508891\pi\)
−0.0279298 + 0.999610i \(0.508891\pi\)
\(270\) −2.24698 −0.136747
\(271\) −30.6655 −1.86279 −0.931397 0.364005i \(-0.881409\pi\)
−0.931397 + 0.364005i \(0.881409\pi\)
\(272\) −2.44504 −0.148252
\(273\) 0 0
\(274\) −15.5646 −0.940295
\(275\) 0.0338518 0.00204134
\(276\) 0.753020 0.0453265
\(277\) 21.8146 1.31071 0.655356 0.755320i \(-0.272518\pi\)
0.655356 + 0.755320i \(0.272518\pi\)
\(278\) 0.405813 0.0243391
\(279\) −4.40581 −0.263769
\(280\) 2.24698 0.134283
\(281\) 6.67994 0.398492 0.199246 0.979950i \(-0.436151\pi\)
0.199246 + 0.979950i \(0.436151\pi\)
\(282\) 2.10992 0.125644
\(283\) 26.2228 1.55878 0.779392 0.626536i \(-0.215528\pi\)
0.779392 + 0.626536i \(0.215528\pi\)
\(284\) −8.76809 −0.520290
\(285\) 7.65279 0.453312
\(286\) 0 0
\(287\) 5.63102 0.332389
\(288\) −1.00000 −0.0589256
\(289\) −11.0218 −0.648339
\(290\) −8.23490 −0.483570
\(291\) −4.46681 −0.261849
\(292\) 11.2131 0.656199
\(293\) 13.2741 0.775483 0.387741 0.921768i \(-0.373255\pi\)
0.387741 + 0.921768i \(0.373255\pi\)
\(294\) 1.00000 0.0583212
\(295\) −11.1468 −0.648989
\(296\) −6.96077 −0.404587
\(297\) −0.692021 −0.0401552
\(298\) 8.35019 0.483714
\(299\) 0 0
\(300\) −0.0489173 −0.00282424
\(301\) −1.64310 −0.0947069
\(302\) −5.24160 −0.301620
\(303\) −6.48858 −0.372759
\(304\) 3.40581 0.195337
\(305\) 11.4547 0.655896
\(306\) 2.44504 0.139774
\(307\) 32.3260 1.84494 0.922472 0.386064i \(-0.126166\pi\)
0.922472 + 0.386064i \(0.126166\pi\)
\(308\) 0.692021 0.0394316
\(309\) −7.85623 −0.446925
\(310\) −9.89977 −0.562269
\(311\) −9.89738 −0.561229 −0.280614 0.959821i \(-0.590538\pi\)
−0.280614 + 0.959821i \(0.590538\pi\)
\(312\) 0 0
\(313\) −2.66786 −0.150796 −0.0753981 0.997154i \(-0.524023\pi\)
−0.0753981 + 0.997154i \(0.524023\pi\)
\(314\) −10.4940 −0.592208
\(315\) −2.24698 −0.126603
\(316\) 1.97285 0.110982
\(317\) −9.68425 −0.543922 −0.271961 0.962308i \(-0.587672\pi\)
−0.271961 + 0.962308i \(0.587672\pi\)
\(318\) −1.69202 −0.0948839
\(319\) −2.53617 −0.141998
\(320\) −2.24698 −0.125610
\(321\) 14.9215 0.832839
\(322\) 0.753020 0.0419642
\(323\) −8.32736 −0.463346
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 18.6993 1.03566
\(327\) 12.6504 0.699569
\(328\) −5.63102 −0.310921
\(329\) 2.10992 0.116323
\(330\) −1.55496 −0.0855976
\(331\) −1.38644 −0.0762054 −0.0381027 0.999274i \(-0.512131\pi\)
−0.0381027 + 0.999274i \(0.512131\pi\)
\(332\) −9.22952 −0.506536
\(333\) 6.96077 0.381448
\(334\) 11.9269 0.652612
\(335\) −17.6189 −0.962626
\(336\) −1.00000 −0.0545545
\(337\) −1.30260 −0.0709572 −0.0354786 0.999370i \(-0.511296\pi\)
−0.0354786 + 0.999370i \(0.511296\pi\)
\(338\) 0 0
\(339\) 20.5526 1.11626
\(340\) 5.49396 0.297952
\(341\) −3.04892 −0.165108
\(342\) −3.40581 −0.184165
\(343\) 1.00000 0.0539949
\(344\) 1.64310 0.0885902
\(345\) −1.69202 −0.0910954
\(346\) 7.10992 0.382231
\(347\) −12.7506 −0.684490 −0.342245 0.939611i \(-0.611187\pi\)
−0.342245 + 0.939611i \(0.611187\pi\)
\(348\) 3.66487 0.196458
\(349\) 26.8267 1.43600 0.718000 0.696043i \(-0.245058\pi\)
0.718000 + 0.696043i \(0.245058\pi\)
\(350\) −0.0489173 −0.00261474
\(351\) 0 0
\(352\) −0.692021 −0.0368849
\(353\) 18.1086 0.963823 0.481911 0.876220i \(-0.339943\pi\)
0.481911 + 0.876220i \(0.339943\pi\)
\(354\) 4.96077 0.263662
\(355\) 19.7017 1.04566
\(356\) −3.44504 −0.182587
\(357\) 2.44504 0.129405
\(358\) 12.1642 0.642898
\(359\) −7.46144 −0.393799 −0.196900 0.980424i \(-0.563087\pi\)
−0.196900 + 0.980424i \(0.563087\pi\)
\(360\) 2.24698 0.118426
\(361\) −7.40044 −0.389497
\(362\) −4.83877 −0.254320
\(363\) 10.5211 0.552215
\(364\) 0 0
\(365\) −25.1957 −1.31880
\(366\) −5.09783 −0.266468
\(367\) 28.0194 1.46260 0.731300 0.682056i \(-0.238914\pi\)
0.731300 + 0.682056i \(0.238914\pi\)
\(368\) −0.753020 −0.0392539
\(369\) 5.63102 0.293139
\(370\) 15.6407 0.813122
\(371\) −1.69202 −0.0878454
\(372\) 4.40581 0.228431
\(373\) −32.2868 −1.67175 −0.835874 0.548922i \(-0.815038\pi\)
−0.835874 + 0.548922i \(0.815038\pi\)
\(374\) 1.69202 0.0874923
\(375\) −11.1250 −0.574492
\(376\) −2.10992 −0.108811
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 27.0465 1.38929 0.694643 0.719354i \(-0.255562\pi\)
0.694643 + 0.719354i \(0.255562\pi\)
\(380\) −7.65279 −0.392580
\(381\) −2.66487 −0.136526
\(382\) 0.664874 0.0340179
\(383\) −6.21552 −0.317598 −0.158799 0.987311i \(-0.550762\pi\)
−0.158799 + 0.987311i \(0.550762\pi\)
\(384\) 1.00000 0.0510310
\(385\) −1.55496 −0.0792480
\(386\) −11.3013 −0.575220
\(387\) −1.64310 −0.0835237
\(388\) 4.46681 0.226768
\(389\) 12.0683 0.611887 0.305943 0.952050i \(-0.401028\pi\)
0.305943 + 0.952050i \(0.401028\pi\)
\(390\) 0 0
\(391\) 1.84117 0.0931118
\(392\) −1.00000 −0.0505076
\(393\) −3.37867 −0.170431
\(394\) −6.26875 −0.315815
\(395\) −4.43296 −0.223046
\(396\) 0.692021 0.0347754
\(397\) −36.3551 −1.82461 −0.912305 0.409512i \(-0.865699\pi\)
−0.912305 + 0.409512i \(0.865699\pi\)
\(398\) 12.3937 0.621242
\(399\) −3.40581 −0.170504
\(400\) 0.0489173 0.00244587
\(401\) 23.9463 1.19582 0.597910 0.801563i \(-0.295998\pi\)
0.597910 + 0.801563i \(0.295998\pi\)
\(402\) 7.84117 0.391082
\(403\) 0 0
\(404\) 6.48858 0.322819
\(405\) −2.24698 −0.111653
\(406\) 3.66487 0.181885
\(407\) 4.81700 0.238770
\(408\) −2.44504 −0.121048
\(409\) 19.6571 0.971981 0.485991 0.873964i \(-0.338459\pi\)
0.485991 + 0.873964i \(0.338459\pi\)
\(410\) 12.6528 0.624877
\(411\) −15.5646 −0.767747
\(412\) 7.85623 0.387049
\(413\) 4.96077 0.244104
\(414\) 0.753020 0.0370089
\(415\) 20.7385 1.01802
\(416\) 0 0
\(417\) 0.405813 0.0198728
\(418\) −2.35690 −0.115280
\(419\) −22.4228 −1.09543 −0.547713 0.836666i \(-0.684501\pi\)
−0.547713 + 0.836666i \(0.684501\pi\)
\(420\) 2.24698 0.109641
\(421\) 19.1317 0.932421 0.466211 0.884674i \(-0.345619\pi\)
0.466211 + 0.884674i \(0.345619\pi\)
\(422\) −7.65279 −0.372532
\(423\) 2.10992 0.102588
\(424\) 1.69202 0.0821718
\(425\) −0.119605 −0.00580169
\(426\) −8.76809 −0.424815
\(427\) −5.09783 −0.246702
\(428\) −14.9215 −0.721260
\(429\) 0 0
\(430\) −3.69202 −0.178045
\(431\) 16.0224 0.771770 0.385885 0.922547i \(-0.373896\pi\)
0.385885 + 0.922547i \(0.373896\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 20.1933 0.970427 0.485213 0.874396i \(-0.338742\pi\)
0.485213 + 0.874396i \(0.338742\pi\)
\(434\) 4.40581 0.211486
\(435\) −8.23490 −0.394833
\(436\) −12.6504 −0.605844
\(437\) −2.56465 −0.122684
\(438\) 11.2131 0.535784
\(439\) 2.28190 0.108909 0.0544545 0.998516i \(-0.482658\pi\)
0.0544545 + 0.998516i \(0.482658\pi\)
\(440\) 1.55496 0.0741297
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −14.1129 −0.670524 −0.335262 0.942125i \(-0.608825\pi\)
−0.335262 + 0.942125i \(0.608825\pi\)
\(444\) −6.96077 −0.330344
\(445\) 7.74094 0.366956
\(446\) −15.2905 −0.724027
\(447\) 8.35019 0.394950
\(448\) 1.00000 0.0472456
\(449\) 21.8732 1.03226 0.516130 0.856510i \(-0.327372\pi\)
0.516130 + 0.856510i \(0.327372\pi\)
\(450\) −0.0489173 −0.00230599
\(451\) 3.89679 0.183493
\(452\) −20.5526 −0.966711
\(453\) −5.24160 −0.246272
\(454\) −14.2808 −0.670233
\(455\) 0 0
\(456\) 3.40581 0.159492
\(457\) 27.8280 1.30174 0.650870 0.759189i \(-0.274404\pi\)
0.650870 + 0.759189i \(0.274404\pi\)
\(458\) −6.30127 −0.294439
\(459\) 2.44504 0.114125
\(460\) 1.69202 0.0788909
\(461\) 5.81833 0.270987 0.135493 0.990778i \(-0.456738\pi\)
0.135493 + 0.990778i \(0.456738\pi\)
\(462\) 0.692021 0.0321958
\(463\) 20.0218 0.930491 0.465245 0.885182i \(-0.345966\pi\)
0.465245 + 0.885182i \(0.345966\pi\)
\(464\) −3.66487 −0.170138
\(465\) −9.89977 −0.459091
\(466\) −25.9071 −1.20012
\(467\) 15.7791 0.730170 0.365085 0.930974i \(-0.381040\pi\)
0.365085 + 0.930974i \(0.381040\pi\)
\(468\) 0 0
\(469\) 7.84117 0.362071
\(470\) 4.74094 0.218683
\(471\) −10.4940 −0.483536
\(472\) −4.96077 −0.228338
\(473\) −1.13706 −0.0522822
\(474\) 1.97285 0.0906161
\(475\) 0.166603 0.00764428
\(476\) −2.44504 −0.112068
\(477\) −1.69202 −0.0774723
\(478\) 0.811626 0.0371229
\(479\) 1.31575 0.0601181 0.0300590 0.999548i \(-0.490430\pi\)
0.0300590 + 0.999548i \(0.490430\pi\)
\(480\) −2.24698 −0.102560
\(481\) 0 0
\(482\) 6.23490 0.283992
\(483\) 0.753020 0.0342636
\(484\) −10.5211 −0.478232
\(485\) −10.0368 −0.455749
\(486\) 1.00000 0.0453609
\(487\) 19.1618 0.868305 0.434152 0.900839i \(-0.357048\pi\)
0.434152 + 0.900839i \(0.357048\pi\)
\(488\) 5.09783 0.230768
\(489\) 18.6993 0.845612
\(490\) 2.24698 0.101508
\(491\) 32.3860 1.46156 0.730779 0.682614i \(-0.239157\pi\)
0.730779 + 0.682614i \(0.239157\pi\)
\(492\) −5.63102 −0.253866
\(493\) 8.96077 0.403573
\(494\) 0 0
\(495\) −1.55496 −0.0698902
\(496\) −4.40581 −0.197827
\(497\) −8.76809 −0.393302
\(498\) −9.22952 −0.413585
\(499\) 8.55363 0.382913 0.191457 0.981501i \(-0.438679\pi\)
0.191457 + 0.981501i \(0.438679\pi\)
\(500\) 11.1250 0.497524
\(501\) 11.9269 0.532855
\(502\) −29.6045 −1.32131
\(503\) −1.30319 −0.0581065 −0.0290532 0.999578i \(-0.509249\pi\)
−0.0290532 + 0.999578i \(0.509249\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −14.5797 −0.648789
\(506\) 0.521106 0.0231660
\(507\) 0 0
\(508\) 2.66487 0.118235
\(509\) −10.3720 −0.459729 −0.229865 0.973223i \(-0.573828\pi\)
−0.229865 + 0.973223i \(0.573828\pi\)
\(510\) 5.49396 0.243277
\(511\) 11.2131 0.496040
\(512\) −1.00000 −0.0441942
\(513\) −3.40581 −0.150370
\(514\) 9.24160 0.407630
\(515\) −17.6528 −0.777875
\(516\) 1.64310 0.0723336
\(517\) 1.46011 0.0642154
\(518\) −6.96077 −0.305839
\(519\) 7.10992 0.312091
\(520\) 0 0
\(521\) 30.0183 1.31513 0.657563 0.753399i \(-0.271587\pi\)
0.657563 + 0.753399i \(0.271587\pi\)
\(522\) 3.66487 0.160407
\(523\) 37.3250 1.63211 0.816053 0.577977i \(-0.196158\pi\)
0.816053 + 0.577977i \(0.196158\pi\)
\(524\) 3.37867 0.147598
\(525\) −0.0489173 −0.00213493
\(526\) −1.09246 −0.0476334
\(527\) 10.7724 0.469253
\(528\) −0.692021 −0.0301164
\(529\) −22.4330 −0.975346
\(530\) −3.80194 −0.165146
\(531\) 4.96077 0.215279
\(532\) 3.40581 0.147661
\(533\) 0 0
\(534\) −3.44504 −0.149082
\(535\) 33.5284 1.44956
\(536\) −7.84117 −0.338687
\(537\) 12.1642 0.524924
\(538\) 0.916166 0.0394987
\(539\) 0.692021 0.0298075
\(540\) 2.24698 0.0966946
\(541\) −1.98015 −0.0851332 −0.0425666 0.999094i \(-0.513553\pi\)
−0.0425666 + 0.999094i \(0.513553\pi\)
\(542\) 30.6655 1.31719
\(543\) −4.83877 −0.207652
\(544\) 2.44504 0.104830
\(545\) 28.4252 1.21760
\(546\) 0 0
\(547\) 18.2862 0.781862 0.390931 0.920420i \(-0.372153\pi\)
0.390931 + 0.920420i \(0.372153\pi\)
\(548\) 15.5646 0.664889
\(549\) −5.09783 −0.217570
\(550\) −0.0338518 −0.00144345
\(551\) −12.4819 −0.531746
\(552\) −0.753020 −0.0320507
\(553\) 1.97285 0.0838942
\(554\) −21.8146 −0.926814
\(555\) 15.6407 0.663911
\(556\) −0.405813 −0.0172103
\(557\) 40.6612 1.72287 0.861434 0.507869i \(-0.169567\pi\)
0.861434 + 0.507869i \(0.169567\pi\)
\(558\) 4.40581 0.186513
\(559\) 0 0
\(560\) −2.24698 −0.0949522
\(561\) 1.69202 0.0714372
\(562\) −6.67994 −0.281776
\(563\) 19.8780 0.837758 0.418879 0.908042i \(-0.362423\pi\)
0.418879 + 0.908042i \(0.362423\pi\)
\(564\) −2.10992 −0.0888435
\(565\) 46.1812 1.94286
\(566\) −26.2228 −1.10223
\(567\) 1.00000 0.0419961
\(568\) 8.76809 0.367901
\(569\) 18.9801 0.795689 0.397845 0.917453i \(-0.369758\pi\)
0.397845 + 0.917453i \(0.369758\pi\)
\(570\) −7.65279 −0.320540
\(571\) −30.2355 −1.26532 −0.632658 0.774431i \(-0.718036\pi\)
−0.632658 + 0.774431i \(0.718036\pi\)
\(572\) 0 0
\(573\) 0.664874 0.0277755
\(574\) −5.63102 −0.235034
\(575\) −0.0368358 −0.00153616
\(576\) 1.00000 0.0416667
\(577\) 16.0707 0.669031 0.334516 0.942390i \(-0.391427\pi\)
0.334516 + 0.942390i \(0.391427\pi\)
\(578\) 11.0218 0.458445
\(579\) −11.3013 −0.469665
\(580\) 8.23490 0.341936
\(581\) −9.22952 −0.382905
\(582\) 4.46681 0.185155
\(583\) −1.17092 −0.0484944
\(584\) −11.2131 −0.464003
\(585\) 0 0
\(586\) −13.2741 −0.548349
\(587\) 26.0793 1.07641 0.538204 0.842814i \(-0.319103\pi\)
0.538204 + 0.842814i \(0.319103\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −15.0054 −0.618286
\(590\) 11.1468 0.458905
\(591\) −6.26875 −0.257862
\(592\) 6.96077 0.286086
\(593\) −46.4131 −1.90596 −0.952979 0.303036i \(-0.902000\pi\)
−0.952979 + 0.303036i \(0.902000\pi\)
\(594\) 0.692021 0.0283940
\(595\) 5.49396 0.225230
\(596\) −8.35019 −0.342037
\(597\) 12.3937 0.507242
\(598\) 0 0
\(599\) 17.9269 0.732474 0.366237 0.930522i \(-0.380646\pi\)
0.366237 + 0.930522i \(0.380646\pi\)
\(600\) 0.0489173 0.00199704
\(601\) −27.6829 −1.12921 −0.564605 0.825361i \(-0.690971\pi\)
−0.564605 + 0.825361i \(0.690971\pi\)
\(602\) 1.64310 0.0669679
\(603\) 7.84117 0.319317
\(604\) 5.24160 0.213278
\(605\) 23.6407 0.961132
\(606\) 6.48858 0.263581
\(607\) −13.8659 −0.562800 −0.281400 0.959591i \(-0.590799\pi\)
−0.281400 + 0.959591i \(0.590799\pi\)
\(608\) −3.40581 −0.138124
\(609\) 3.66487 0.148508
\(610\) −11.4547 −0.463788
\(611\) 0 0
\(612\) −2.44504 −0.0988350
\(613\) −6.21744 −0.251120 −0.125560 0.992086i \(-0.540073\pi\)
−0.125560 + 0.992086i \(0.540073\pi\)
\(614\) −32.3260 −1.30457
\(615\) 12.6528 0.510210
\(616\) −0.692021 −0.0278823
\(617\) −47.5900 −1.91590 −0.957950 0.286934i \(-0.907364\pi\)
−0.957950 + 0.286934i \(0.907364\pi\)
\(618\) 7.85623 0.316024
\(619\) −34.7241 −1.39568 −0.697839 0.716255i \(-0.745855\pi\)
−0.697839 + 0.716255i \(0.745855\pi\)
\(620\) 9.89977 0.397584
\(621\) 0.753020 0.0302177
\(622\) 9.89738 0.396849
\(623\) −3.44504 −0.138023
\(624\) 0 0
\(625\) −25.2422 −1.00969
\(626\) 2.66786 0.106629
\(627\) −2.35690 −0.0941254
\(628\) 10.4940 0.418755
\(629\) −17.0194 −0.678607
\(630\) 2.24698 0.0895218
\(631\) −15.6601 −0.623418 −0.311709 0.950178i \(-0.600901\pi\)
−0.311709 + 0.950178i \(0.600901\pi\)
\(632\) −1.97285 −0.0784759
\(633\) −7.65279 −0.304171
\(634\) 9.68425 0.384611
\(635\) −5.98792 −0.237623
\(636\) 1.69202 0.0670930
\(637\) 0 0
\(638\) 2.53617 0.100408
\(639\) −8.76809 −0.346860
\(640\) 2.24698 0.0888197
\(641\) −27.9869 −1.10541 −0.552707 0.833376i \(-0.686405\pi\)
−0.552707 + 0.833376i \(0.686405\pi\)
\(642\) −14.9215 −0.588906
\(643\) 16.1032 0.635049 0.317524 0.948250i \(-0.397148\pi\)
0.317524 + 0.948250i \(0.397148\pi\)
\(644\) −0.753020 −0.0296732
\(645\) −3.69202 −0.145373
\(646\) 8.32736 0.327635
\(647\) 12.2397 0.481192 0.240596 0.970625i \(-0.422657\pi\)
0.240596 + 0.970625i \(0.422657\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 3.43296 0.134755
\(650\) 0 0
\(651\) 4.40581 0.172677
\(652\) −18.6993 −0.732322
\(653\) −4.60281 −0.180122 −0.0900609 0.995936i \(-0.528706\pi\)
−0.0900609 + 0.995936i \(0.528706\pi\)
\(654\) −12.6504 −0.494670
\(655\) −7.59179 −0.296636
\(656\) 5.63102 0.219854
\(657\) 11.2131 0.437466
\(658\) −2.10992 −0.0822531
\(659\) 7.58450 0.295450 0.147725 0.989028i \(-0.452805\pi\)
0.147725 + 0.989028i \(0.452805\pi\)
\(660\) 1.55496 0.0605267
\(661\) 33.4233 1.30001 0.650007 0.759928i \(-0.274766\pi\)
0.650007 + 0.759928i \(0.274766\pi\)
\(662\) 1.38644 0.0538854
\(663\) 0 0
\(664\) 9.22952 0.358175
\(665\) −7.65279 −0.296763
\(666\) −6.96077 −0.269724
\(667\) 2.75973 0.106857
\(668\) −11.9269 −0.461466
\(669\) −15.2905 −0.591166
\(670\) 17.6189 0.680679
\(671\) −3.52781 −0.136190
\(672\) 1.00000 0.0385758
\(673\) 30.0140 1.15695 0.578477 0.815698i \(-0.303647\pi\)
0.578477 + 0.815698i \(0.303647\pi\)
\(674\) 1.30260 0.0501743
\(675\) −0.0489173 −0.00188283
\(676\) 0 0
\(677\) 43.0780 1.65562 0.827811 0.561008i \(-0.189586\pi\)
0.827811 + 0.561008i \(0.189586\pi\)
\(678\) −20.5526 −0.789317
\(679\) 4.46681 0.171421
\(680\) −5.49396 −0.210684
\(681\) −14.2808 −0.547243
\(682\) 3.04892 0.116749
\(683\) 40.6262 1.55452 0.777260 0.629180i \(-0.216609\pi\)
0.777260 + 0.629180i \(0.216609\pi\)
\(684\) 3.40581 0.130225
\(685\) −34.9734 −1.33627
\(686\) −1.00000 −0.0381802
\(687\) −6.30127 −0.240409
\(688\) −1.64310 −0.0626428
\(689\) 0 0
\(690\) 1.69202 0.0644142
\(691\) −8.62266 −0.328022 −0.164011 0.986459i \(-0.552443\pi\)
−0.164011 + 0.986459i \(0.552443\pi\)
\(692\) −7.10992 −0.270278
\(693\) 0.692021 0.0262877
\(694\) 12.7506 0.484007
\(695\) 0.911854 0.0345886
\(696\) −3.66487 −0.138917
\(697\) −13.7681 −0.521503
\(698\) −26.8267 −1.01541
\(699\) −25.9071 −0.979895
\(700\) 0.0489173 0.00184890
\(701\) −0.259652 −0.00980693 −0.00490346 0.999988i \(-0.501561\pi\)
−0.00490346 + 0.999988i \(0.501561\pi\)
\(702\) 0 0
\(703\) 23.7071 0.894130
\(704\) 0.692021 0.0260815
\(705\) 4.74094 0.178554
\(706\) −18.1086 −0.681526
\(707\) 6.48858 0.244028
\(708\) −4.96077 −0.186437
\(709\) −28.6189 −1.07481 −0.537403 0.843325i \(-0.680595\pi\)
−0.537403 + 0.843325i \(0.680595\pi\)
\(710\) −19.7017 −0.739392
\(711\) 1.97285 0.0739878
\(712\) 3.44504 0.129108
\(713\) 3.31767 0.124248
\(714\) −2.44504 −0.0915034
\(715\) 0 0
\(716\) −12.1642 −0.454598
\(717\) 0.811626 0.0303107
\(718\) 7.46144 0.278458
\(719\) 40.6937 1.51762 0.758809 0.651313i \(-0.225782\pi\)
0.758809 + 0.651313i \(0.225782\pi\)
\(720\) −2.24698 −0.0837400
\(721\) 7.85623 0.292581
\(722\) 7.40044 0.275416
\(723\) 6.23490 0.231878
\(724\) 4.83877 0.179832
\(725\) −0.179276 −0.00665814
\(726\) −10.5211 −0.390475
\(727\) −38.3817 −1.42350 −0.711748 0.702435i \(-0.752096\pi\)
−0.711748 + 0.702435i \(0.752096\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 25.1957 0.932534
\(731\) 4.01746 0.148591
\(732\) 5.09783 0.188421
\(733\) 20.7006 0.764596 0.382298 0.924039i \(-0.375133\pi\)
0.382298 + 0.924039i \(0.375133\pi\)
\(734\) −28.0194 −1.03421
\(735\) 2.24698 0.0828811
\(736\) 0.753020 0.0277567
\(737\) 5.42626 0.199879
\(738\) −5.63102 −0.207281
\(739\) 6.15990 0.226596 0.113298 0.993561i \(-0.463859\pi\)
0.113298 + 0.993561i \(0.463859\pi\)
\(740\) −15.6407 −0.574964
\(741\) 0 0
\(742\) 1.69202 0.0621161
\(743\) −9.15644 −0.335917 −0.167959 0.985794i \(-0.553717\pi\)
−0.167959 + 0.985794i \(0.553717\pi\)
\(744\) −4.40581 −0.161525
\(745\) 18.7627 0.687412
\(746\) 32.2868 1.18210
\(747\) −9.22952 −0.337691
\(748\) −1.69202 −0.0618664
\(749\) −14.9215 −0.545221
\(750\) 11.1250 0.406227
\(751\) 21.5362 0.785866 0.392933 0.919567i \(-0.371460\pi\)
0.392933 + 0.919567i \(0.371460\pi\)
\(752\) 2.10992 0.0769407
\(753\) −29.6045 −1.07885
\(754\) 0 0
\(755\) −11.7778 −0.428637
\(756\) −1.00000 −0.0363696
\(757\) 30.1648 1.09636 0.548179 0.836361i \(-0.315321\pi\)
0.548179 + 0.836361i \(0.315321\pi\)
\(758\) −27.0465 −0.982374
\(759\) 0.521106 0.0189150
\(760\) 7.65279 0.277596
\(761\) −1.03193 −0.0374075 −0.0187038 0.999825i \(-0.505954\pi\)
−0.0187038 + 0.999825i \(0.505954\pi\)
\(762\) 2.66487 0.0965382
\(763\) −12.6504 −0.457975
\(764\) −0.664874 −0.0240543
\(765\) 5.49396 0.198635
\(766\) 6.21552 0.224576
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −32.8605 −1.18498 −0.592491 0.805577i \(-0.701855\pi\)
−0.592491 + 0.805577i \(0.701855\pi\)
\(770\) 1.55496 0.0560368
\(771\) 9.24160 0.332828
\(772\) 11.3013 0.406742
\(773\) 24.2717 0.872994 0.436497 0.899706i \(-0.356219\pi\)
0.436497 + 0.899706i \(0.356219\pi\)
\(774\) 1.64310 0.0590602
\(775\) −0.215521 −0.00774173
\(776\) −4.46681 −0.160349
\(777\) −6.96077 −0.249716
\(778\) −12.0683 −0.432669
\(779\) 19.1782 0.687131
\(780\) 0 0
\(781\) −6.06770 −0.217120
\(782\) −1.84117 −0.0658400
\(783\) 3.66487 0.130972
\(784\) 1.00000 0.0357143
\(785\) −23.5797 −0.841596
\(786\) 3.37867 0.120513
\(787\) 35.9506 1.28150 0.640750 0.767749i \(-0.278623\pi\)
0.640750 + 0.767749i \(0.278623\pi\)
\(788\) 6.26875 0.223315
\(789\) −1.09246 −0.0388925
\(790\) 4.43296 0.157718
\(791\) −20.5526 −0.730765
\(792\) −0.692021 −0.0245899
\(793\) 0 0
\(794\) 36.3551 1.29019
\(795\) −3.80194 −0.134841
\(796\) −12.3937 −0.439284
\(797\) 8.11960 0.287611 0.143806 0.989606i \(-0.454066\pi\)
0.143806 + 0.989606i \(0.454066\pi\)
\(798\) 3.40581 0.120564
\(799\) −5.15883 −0.182506
\(800\) −0.0489173 −0.00172949
\(801\) −3.44504 −0.121725
\(802\) −23.9463 −0.845573
\(803\) 7.75973 0.273835
\(804\) −7.84117 −0.276537
\(805\) 1.69202 0.0596359
\(806\) 0 0
\(807\) 0.916166 0.0322506
\(808\) −6.48858 −0.228268
\(809\) −4.10215 −0.144224 −0.0721119 0.997397i \(-0.522974\pi\)
−0.0721119 + 0.997397i \(0.522974\pi\)
\(810\) 2.24698 0.0789508
\(811\) 24.0358 0.844010 0.422005 0.906593i \(-0.361326\pi\)
0.422005 + 0.906593i \(0.361326\pi\)
\(812\) −3.66487 −0.128612
\(813\) 30.6655 1.07548
\(814\) −4.81700 −0.168836
\(815\) 42.0170 1.47179
\(816\) 2.44504 0.0855936
\(817\) −5.59611 −0.195783
\(818\) −19.6571 −0.687295
\(819\) 0 0
\(820\) −12.6528 −0.441855
\(821\) −2.01102 −0.0701850 −0.0350925 0.999384i \(-0.511173\pi\)
−0.0350925 + 0.999384i \(0.511173\pi\)
\(822\) 15.5646 0.542879
\(823\) 31.1511 1.08586 0.542929 0.839779i \(-0.317315\pi\)
0.542929 + 0.839779i \(0.317315\pi\)
\(824\) −7.85623 −0.273685
\(825\) −0.0338518 −0.00117857
\(826\) −4.96077 −0.172607
\(827\) 16.7646 0.582963 0.291482 0.956576i \(-0.405852\pi\)
0.291482 + 0.956576i \(0.405852\pi\)
\(828\) −0.753020 −0.0261693
\(829\) 25.9842 0.902468 0.451234 0.892406i \(-0.350984\pi\)
0.451234 + 0.892406i \(0.350984\pi\)
\(830\) −20.7385 −0.719845
\(831\) −21.8146 −0.756740
\(832\) 0 0
\(833\) −2.44504 −0.0847157
\(834\) −0.405813 −0.0140522
\(835\) 26.7995 0.927436
\(836\) 2.35690 0.0815149
\(837\) 4.40581 0.152287
\(838\) 22.4228 0.774583
\(839\) −16.1511 −0.557597 −0.278798 0.960350i \(-0.589936\pi\)
−0.278798 + 0.960350i \(0.589936\pi\)
\(840\) −2.24698 −0.0775282
\(841\) −15.5687 −0.536852
\(842\) −19.1317 −0.659321
\(843\) −6.67994 −0.230069
\(844\) 7.65279 0.263420
\(845\) 0 0
\(846\) −2.10992 −0.0725404
\(847\) −10.5211 −0.361509
\(848\) −1.69202 −0.0581043
\(849\) −26.2228 −0.899965
\(850\) 0.119605 0.00410242
\(851\) −5.24160 −0.179680
\(852\) 8.76809 0.300390
\(853\) −5.35450 −0.183335 −0.0916673 0.995790i \(-0.529220\pi\)
−0.0916673 + 0.995790i \(0.529220\pi\)
\(854\) 5.09783 0.174444
\(855\) −7.65279 −0.261720
\(856\) 14.9215 0.510008
\(857\) −36.7948 −1.25689 −0.628443 0.777856i \(-0.716307\pi\)
−0.628443 + 0.777856i \(0.716307\pi\)
\(858\) 0 0
\(859\) −4.73019 −0.161392 −0.0806959 0.996739i \(-0.525714\pi\)
−0.0806959 + 0.996739i \(0.525714\pi\)
\(860\) 3.69202 0.125897
\(861\) −5.63102 −0.191905
\(862\) −16.0224 −0.545724
\(863\) −54.0170 −1.83876 −0.919380 0.393371i \(-0.871309\pi\)
−0.919380 + 0.393371i \(0.871309\pi\)
\(864\) 1.00000 0.0340207
\(865\) 15.9758 0.543195
\(866\) −20.1933 −0.686195
\(867\) 11.0218 0.374319
\(868\) −4.40581 −0.149543
\(869\) 1.36526 0.0463132
\(870\) 8.23490 0.279189
\(871\) 0 0
\(872\) 12.6504 0.428397
\(873\) 4.46681 0.151179
\(874\) 2.56465 0.0867505
\(875\) 11.1250 0.376093
\(876\) −11.2131 −0.378856
\(877\) −50.5368 −1.70651 −0.853253 0.521498i \(-0.825373\pi\)
−0.853253 + 0.521498i \(0.825373\pi\)
\(878\) −2.28190 −0.0770103
\(879\) −13.2741 −0.447725
\(880\) −1.55496 −0.0524176
\(881\) 38.0133 1.28070 0.640350 0.768084i \(-0.278789\pi\)
0.640350 + 0.768084i \(0.278789\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 4.70815 0.158442 0.0792210 0.996857i \(-0.474757\pi\)
0.0792210 + 0.996857i \(0.474757\pi\)
\(884\) 0 0
\(885\) 11.1468 0.374694
\(886\) 14.1129 0.474132
\(887\) 47.4010 1.59157 0.795785 0.605579i \(-0.207058\pi\)
0.795785 + 0.605579i \(0.207058\pi\)
\(888\) 6.96077 0.233588
\(889\) 2.66487 0.0893770
\(890\) −7.74094 −0.259477
\(891\) 0.692021 0.0231836
\(892\) 15.2905 0.511964
\(893\) 7.18598 0.240470
\(894\) −8.35019 −0.279272
\(895\) 27.3327 0.913632
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −21.8732 −0.729919
\(899\) 16.1468 0.538524
\(900\) 0.0489173 0.00163058
\(901\) 4.13706 0.137826
\(902\) −3.89679 −0.129749
\(903\) 1.64310 0.0546791
\(904\) 20.5526 0.683568
\(905\) −10.8726 −0.361418
\(906\) 5.24160 0.174141
\(907\) 12.9317 0.429390 0.214695 0.976681i \(-0.431124\pi\)
0.214695 + 0.976681i \(0.431124\pi\)
\(908\) 14.2808 0.473926
\(909\) 6.48858 0.215213
\(910\) 0 0
\(911\) 0.499336 0.0165437 0.00827187 0.999966i \(-0.497367\pi\)
0.00827187 + 0.999966i \(0.497367\pi\)
\(912\) −3.40581 −0.112778
\(913\) −6.38703 −0.211380
\(914\) −27.8280 −0.920469
\(915\) −11.4547 −0.378682
\(916\) 6.30127 0.208200
\(917\) 3.37867 0.111573
\(918\) −2.44504 −0.0806984
\(919\) −13.5439 −0.446773 −0.223387 0.974730i \(-0.571711\pi\)
−0.223387 + 0.974730i \(0.571711\pi\)
\(920\) −1.69202 −0.0557843
\(921\) −32.3260 −1.06518
\(922\) −5.81833 −0.191617
\(923\) 0 0
\(924\) −0.692021 −0.0227658
\(925\) 0.340502 0.0111957
\(926\) −20.0218 −0.657956
\(927\) 7.85623 0.258033
\(928\) 3.66487 0.120305
\(929\) 12.8278 0.420865 0.210433 0.977608i \(-0.432513\pi\)
0.210433 + 0.977608i \(0.432513\pi\)
\(930\) 9.89977 0.324626
\(931\) 3.40581 0.111621
\(932\) 25.9071 0.848614
\(933\) 9.89738 0.324026
\(934\) −15.7791 −0.516308
\(935\) 3.80194 0.124337
\(936\) 0 0
\(937\) −18.0194 −0.588667 −0.294334 0.955703i \(-0.595098\pi\)
−0.294334 + 0.955703i \(0.595098\pi\)
\(938\) −7.84117 −0.256023
\(939\) 2.66786 0.0870623
\(940\) −4.74094 −0.154632
\(941\) −43.8611 −1.42983 −0.714916 0.699210i \(-0.753535\pi\)
−0.714916 + 0.699210i \(0.753535\pi\)
\(942\) 10.4940 0.341912
\(943\) −4.24027 −0.138082
\(944\) 4.96077 0.161459
\(945\) 2.24698 0.0730943
\(946\) 1.13706 0.0369691
\(947\) 38.7991 1.26080 0.630400 0.776270i \(-0.282891\pi\)
0.630400 + 0.776270i \(0.282891\pi\)
\(948\) −1.97285 −0.0640753
\(949\) 0 0
\(950\) −0.166603 −0.00540533
\(951\) 9.68425 0.314033
\(952\) 2.44504 0.0792443
\(953\) −33.6853 −1.09117 −0.545587 0.838054i \(-0.683693\pi\)
−0.545587 + 0.838054i \(0.683693\pi\)
\(954\) 1.69202 0.0547812
\(955\) 1.49396 0.0483434
\(956\) −0.811626 −0.0262499
\(957\) 2.53617 0.0819828
\(958\) −1.31575 −0.0425099
\(959\) 15.5646 0.502609
\(960\) 2.24698 0.0725210
\(961\) −11.5888 −0.373833
\(962\) 0 0
\(963\) −14.9215 −0.480840
\(964\) −6.23490 −0.200813
\(965\) −25.3937 −0.817453
\(966\) −0.753020 −0.0242280
\(967\) 40.1371 1.29072 0.645360 0.763878i \(-0.276707\pi\)
0.645360 + 0.763878i \(0.276707\pi\)
\(968\) 10.5211 0.338161
\(969\) 8.32736 0.267513
\(970\) 10.0368 0.322263
\(971\) 37.6273 1.20752 0.603759 0.797167i \(-0.293669\pi\)
0.603759 + 0.797167i \(0.293669\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −0.405813 −0.0130098
\(974\) −19.1618 −0.613984
\(975\) 0 0
\(976\) −5.09783 −0.163178
\(977\) −52.5182 −1.68021 −0.840104 0.542426i \(-0.817506\pi\)
−0.840104 + 0.542426i \(0.817506\pi\)
\(978\) −18.6993 −0.597938
\(979\) −2.38404 −0.0761943
\(980\) −2.24698 −0.0717771
\(981\) −12.6504 −0.403896
\(982\) −32.3860 −1.03348
\(983\) 39.6222 1.26375 0.631876 0.775070i \(-0.282285\pi\)
0.631876 + 0.775070i \(0.282285\pi\)
\(984\) 5.63102 0.179510
\(985\) −14.0858 −0.448809
\(986\) −8.96077 −0.285369
\(987\) −2.10992 −0.0671594
\(988\) 0 0
\(989\) 1.23729 0.0393436
\(990\) 1.55496 0.0494198
\(991\) 46.4553 1.47570 0.737851 0.674964i \(-0.235841\pi\)
0.737851 + 0.674964i \(0.235841\pi\)
\(992\) 4.40581 0.139885
\(993\) 1.38644 0.0439972
\(994\) 8.76809 0.278107
\(995\) 27.8485 0.882856
\(996\) 9.22952 0.292449
\(997\) −22.6631 −0.717747 −0.358873 0.933386i \(-0.616839\pi\)
−0.358873 + 0.933386i \(0.616839\pi\)
\(998\) −8.55363 −0.270760
\(999\) −6.96077 −0.220229
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.cc.1.1 3
13.12 even 2 7098.2.a.cj.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cc.1.1 3 1.1 even 1 trivial
7098.2.a.cj.1.3 yes 3 13.12 even 2