Properties

Label 2667.2.a.j.1.3
Level $2667$
Weight $2$
Character 2667.1
Self dual yes
Analytic conductor $21.296$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.2961022191\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
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 1.3
Root \(1.20244\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.24280 q^{2} +1.00000 q^{3} -0.455452 q^{4} -3.33400 q^{5} -1.24280 q^{6} +1.00000 q^{7} +3.05163 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.24280 q^{2} +1.00000 q^{3} -0.455452 q^{4} -3.33400 q^{5} -1.24280 q^{6} +1.00000 q^{7} +3.05163 q^{8} +1.00000 q^{9} +4.14349 q^{10} +2.90717 q^{11} -0.455452 q^{12} -4.59254 q^{13} -1.24280 q^{14} -3.33400 q^{15} -2.88166 q^{16} -5.29249 q^{17} -1.24280 q^{18} +1.86822 q^{19} +1.51848 q^{20} +1.00000 q^{21} -3.61302 q^{22} +5.03184 q^{23} +3.05163 q^{24} +6.11557 q^{25} +5.70761 q^{26} +1.00000 q^{27} -0.455452 q^{28} +3.69938 q^{29} +4.14349 q^{30} +0.968597 q^{31} -2.52194 q^{32} +2.90717 q^{33} +6.57750 q^{34} -3.33400 q^{35} -0.455452 q^{36} -10.5381 q^{37} -2.32183 q^{38} -4.59254 q^{39} -10.1741 q^{40} +11.5606 q^{41} -1.24280 q^{42} +2.54868 q^{43} -1.32408 q^{44} -3.33400 q^{45} -6.25356 q^{46} +7.34702 q^{47} -2.88166 q^{48} +1.00000 q^{49} -7.60043 q^{50} -5.29249 q^{51} +2.09168 q^{52} -11.2837 q^{53} -1.24280 q^{54} -9.69250 q^{55} +3.05163 q^{56} +1.86822 q^{57} -4.59758 q^{58} -13.3410 q^{59} +1.51848 q^{60} +0.666722 q^{61} -1.20377 q^{62} +1.00000 q^{63} +8.89758 q^{64} +15.3116 q^{65} -3.61302 q^{66} -14.0335 q^{67} +2.41048 q^{68} +5.03184 q^{69} +4.14349 q^{70} +9.88541 q^{71} +3.05163 q^{72} -2.57222 q^{73} +13.0968 q^{74} +6.11557 q^{75} -0.850887 q^{76} +2.90717 q^{77} +5.70761 q^{78} +14.5706 q^{79} +9.60746 q^{80} +1.00000 q^{81} -14.3675 q^{82} +0.493442 q^{83} -0.455452 q^{84} +17.6452 q^{85} -3.16749 q^{86} +3.69938 q^{87} +8.87160 q^{88} +12.1652 q^{89} +4.14349 q^{90} -4.59254 q^{91} -2.29176 q^{92} +0.968597 q^{93} -9.13087 q^{94} -6.22866 q^{95} -2.52194 q^{96} -14.7006 q^{97} -1.24280 q^{98} +2.90717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24280 −0.878791 −0.439396 0.898294i \(-0.644807\pi\)
−0.439396 + 0.898294i \(0.644807\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.455452 −0.227726
\(5\) −3.33400 −1.49101 −0.745506 0.666499i \(-0.767792\pi\)
−0.745506 + 0.666499i \(0.767792\pi\)
\(6\) −1.24280 −0.507370
\(7\) 1.00000 0.377964
\(8\) 3.05163 1.07891
\(9\) 1.00000 0.333333
\(10\) 4.14349 1.31029
\(11\) 2.90717 0.876544 0.438272 0.898842i \(-0.355591\pi\)
0.438272 + 0.898842i \(0.355591\pi\)
\(12\) −0.455452 −0.131478
\(13\) −4.59254 −1.27374 −0.636871 0.770970i \(-0.719772\pi\)
−0.636871 + 0.770970i \(0.719772\pi\)
\(14\) −1.24280 −0.332152
\(15\) −3.33400 −0.860836
\(16\) −2.88166 −0.720415
\(17\) −5.29249 −1.28362 −0.641809 0.766865i \(-0.721816\pi\)
−0.641809 + 0.766865i \(0.721816\pi\)
\(18\) −1.24280 −0.292930
\(19\) 1.86822 0.428600 0.214300 0.976768i \(-0.431253\pi\)
0.214300 + 0.976768i \(0.431253\pi\)
\(20\) 1.51848 0.339542
\(21\) 1.00000 0.218218
\(22\) −3.61302 −0.770299
\(23\) 5.03184 1.04921 0.524606 0.851345i \(-0.324213\pi\)
0.524606 + 0.851345i \(0.324213\pi\)
\(24\) 3.05163 0.622912
\(25\) 6.11557 1.22311
\(26\) 5.70761 1.11935
\(27\) 1.00000 0.192450
\(28\) −0.455452 −0.0860724
\(29\) 3.69938 0.686957 0.343478 0.939161i \(-0.388395\pi\)
0.343478 + 0.939161i \(0.388395\pi\)
\(30\) 4.14349 0.756495
\(31\) 0.968597 0.173965 0.0869826 0.996210i \(-0.472278\pi\)
0.0869826 + 0.996210i \(0.472278\pi\)
\(32\) −2.52194 −0.445821
\(33\) 2.90717 0.506073
\(34\) 6.57750 1.12803
\(35\) −3.33400 −0.563549
\(36\) −0.455452 −0.0759087
\(37\) −10.5381 −1.73246 −0.866230 0.499645i \(-0.833464\pi\)
−0.866230 + 0.499645i \(0.833464\pi\)
\(38\) −2.32183 −0.376650
\(39\) −4.59254 −0.735395
\(40\) −10.1741 −1.60867
\(41\) 11.5606 1.80546 0.902731 0.430205i \(-0.141559\pi\)
0.902731 + 0.430205i \(0.141559\pi\)
\(42\) −1.24280 −0.191768
\(43\) 2.54868 0.388670 0.194335 0.980935i \(-0.437745\pi\)
0.194335 + 0.980935i \(0.437745\pi\)
\(44\) −1.32408 −0.199612
\(45\) −3.33400 −0.497004
\(46\) −6.25356 −0.922038
\(47\) 7.34702 1.07167 0.535837 0.844322i \(-0.319996\pi\)
0.535837 + 0.844322i \(0.319996\pi\)
\(48\) −2.88166 −0.415932
\(49\) 1.00000 0.142857
\(50\) −7.60043 −1.07486
\(51\) −5.29249 −0.741097
\(52\) 2.09168 0.290064
\(53\) −11.2837 −1.54993 −0.774966 0.632003i \(-0.782233\pi\)
−0.774966 + 0.632003i \(0.782233\pi\)
\(54\) −1.24280 −0.169123
\(55\) −9.69250 −1.30694
\(56\) 3.05163 0.407791
\(57\) 1.86822 0.247452
\(58\) −4.59758 −0.603691
\(59\) −13.3410 −1.73685 −0.868425 0.495820i \(-0.834868\pi\)
−0.868425 + 0.495820i \(0.834868\pi\)
\(60\) 1.51848 0.196035
\(61\) 0.666722 0.0853651 0.0426825 0.999089i \(-0.486410\pi\)
0.0426825 + 0.999089i \(0.486410\pi\)
\(62\) −1.20377 −0.152879
\(63\) 1.00000 0.125988
\(64\) 8.89758 1.11220
\(65\) 15.3116 1.89916
\(66\) −3.61302 −0.444732
\(67\) −14.0335 −1.71447 −0.857233 0.514929i \(-0.827818\pi\)
−0.857233 + 0.514929i \(0.827818\pi\)
\(68\) 2.41048 0.292313
\(69\) 5.03184 0.605763
\(70\) 4.14349 0.495242
\(71\) 9.88541 1.17318 0.586591 0.809883i \(-0.300470\pi\)
0.586591 + 0.809883i \(0.300470\pi\)
\(72\) 3.05163 0.359638
\(73\) −2.57222 −0.301056 −0.150528 0.988606i \(-0.548097\pi\)
−0.150528 + 0.988606i \(0.548097\pi\)
\(74\) 13.0968 1.52247
\(75\) 6.11557 0.706166
\(76\) −0.850887 −0.0976034
\(77\) 2.90717 0.331302
\(78\) 5.70761 0.646259
\(79\) 14.5706 1.63932 0.819661 0.572849i \(-0.194162\pi\)
0.819661 + 0.572849i \(0.194162\pi\)
\(80\) 9.60746 1.07415
\(81\) 1.00000 0.111111
\(82\) −14.3675 −1.58662
\(83\) 0.493442 0.0541623 0.0270811 0.999633i \(-0.491379\pi\)
0.0270811 + 0.999633i \(0.491379\pi\)
\(84\) −0.455452 −0.0496939
\(85\) 17.6452 1.91389
\(86\) −3.16749 −0.341560
\(87\) 3.69938 0.396615
\(88\) 8.87160 0.945716
\(89\) 12.1652 1.28951 0.644754 0.764390i \(-0.276960\pi\)
0.644754 + 0.764390i \(0.276960\pi\)
\(90\) 4.14349 0.436763
\(91\) −4.59254 −0.481429
\(92\) −2.29176 −0.238933
\(93\) 0.968597 0.100439
\(94\) −9.13087 −0.941777
\(95\) −6.22866 −0.639047
\(96\) −2.52194 −0.257395
\(97\) −14.7006 −1.49262 −0.746312 0.665596i \(-0.768177\pi\)
−0.746312 + 0.665596i \(0.768177\pi\)
\(98\) −1.24280 −0.125542
\(99\) 2.90717 0.292181
\(100\) −2.78535 −0.278535
\(101\) −7.69701 −0.765881 −0.382941 0.923773i \(-0.625089\pi\)
−0.382941 + 0.923773i \(0.625089\pi\)
\(102\) 6.57750 0.651269
\(103\) −18.0952 −1.78297 −0.891486 0.453048i \(-0.850337\pi\)
−0.891486 + 0.453048i \(0.850337\pi\)
\(104\) −14.0148 −1.37426
\(105\) −3.33400 −0.325365
\(106\) 14.0233 1.36207
\(107\) −2.30658 −0.222986 −0.111493 0.993765i \(-0.535563\pi\)
−0.111493 + 0.993765i \(0.535563\pi\)
\(108\) −0.455452 −0.0438259
\(109\) −0.892079 −0.0854457 −0.0427228 0.999087i \(-0.513603\pi\)
−0.0427228 + 0.999087i \(0.513603\pi\)
\(110\) 12.0458 1.14852
\(111\) −10.5381 −1.00024
\(112\) −2.88166 −0.272291
\(113\) 4.35699 0.409872 0.204936 0.978775i \(-0.434301\pi\)
0.204936 + 0.978775i \(0.434301\pi\)
\(114\) −2.32183 −0.217459
\(115\) −16.7762 −1.56439
\(116\) −1.68489 −0.156438
\(117\) −4.59254 −0.424581
\(118\) 16.5802 1.52633
\(119\) −5.29249 −0.485162
\(120\) −10.1741 −0.928769
\(121\) −2.54838 −0.231671
\(122\) −0.828601 −0.0750181
\(123\) 11.5606 1.04238
\(124\) −0.441150 −0.0396164
\(125\) −3.71933 −0.332667
\(126\) −1.24280 −0.110717
\(127\) −1.00000 −0.0887357
\(128\) −6.01402 −0.531569
\(129\) 2.54868 0.224399
\(130\) −19.0292 −1.66897
\(131\) 8.71812 0.761706 0.380853 0.924636i \(-0.375630\pi\)
0.380853 + 0.924636i \(0.375630\pi\)
\(132\) −1.32408 −0.115246
\(133\) 1.86822 0.161996
\(134\) 17.4408 1.50666
\(135\) −3.33400 −0.286945
\(136\) −16.1507 −1.38491
\(137\) −4.66285 −0.398374 −0.199187 0.979962i \(-0.563830\pi\)
−0.199187 + 0.979962i \(0.563830\pi\)
\(138\) −6.25356 −0.532339
\(139\) −19.7441 −1.67467 −0.837334 0.546691i \(-0.815887\pi\)
−0.837334 + 0.546691i \(0.815887\pi\)
\(140\) 1.51848 0.128335
\(141\) 7.34702 0.618731
\(142\) −12.2856 −1.03098
\(143\) −13.3513 −1.11649
\(144\) −2.88166 −0.240138
\(145\) −12.3337 −1.02426
\(146\) 3.19675 0.264565
\(147\) 1.00000 0.0824786
\(148\) 4.79962 0.394526
\(149\) −5.49864 −0.450467 −0.225233 0.974305i \(-0.572314\pi\)
−0.225233 + 0.974305i \(0.572314\pi\)
\(150\) −7.60043 −0.620572
\(151\) −11.8169 −0.961645 −0.480822 0.876818i \(-0.659662\pi\)
−0.480822 + 0.876818i \(0.659662\pi\)
\(152\) 5.70113 0.462423
\(153\) −5.29249 −0.427873
\(154\) −3.61302 −0.291146
\(155\) −3.22931 −0.259384
\(156\) 2.09168 0.167469
\(157\) 3.77762 0.301487 0.150744 0.988573i \(-0.451833\pi\)
0.150744 + 0.988573i \(0.451833\pi\)
\(158\) −18.1083 −1.44062
\(159\) −11.2837 −0.894854
\(160\) 8.40817 0.664724
\(161\) 5.03184 0.396565
\(162\) −1.24280 −0.0976435
\(163\) −20.0111 −1.56739 −0.783694 0.621147i \(-0.786667\pi\)
−0.783694 + 0.621147i \(0.786667\pi\)
\(164\) −5.26530 −0.411151
\(165\) −9.69250 −0.754560
\(166\) −0.613249 −0.0475973
\(167\) −16.4295 −1.27135 −0.635675 0.771957i \(-0.719278\pi\)
−0.635675 + 0.771957i \(0.719278\pi\)
\(168\) 3.05163 0.235439
\(169\) 8.09145 0.622419
\(170\) −21.9294 −1.68191
\(171\) 1.86822 0.142867
\(172\) −1.16080 −0.0885103
\(173\) −16.2436 −1.23498 −0.617489 0.786580i \(-0.711850\pi\)
−0.617489 + 0.786580i \(0.711850\pi\)
\(174\) −4.59758 −0.348541
\(175\) 6.11557 0.462294
\(176\) −8.37746 −0.631475
\(177\) −13.3410 −1.00277
\(178\) −15.1189 −1.13321
\(179\) −4.00381 −0.299259 −0.149630 0.988742i \(-0.547808\pi\)
−0.149630 + 0.988742i \(0.547808\pi\)
\(180\) 1.51848 0.113181
\(181\) −24.4061 −1.81409 −0.907044 0.421035i \(-0.861667\pi\)
−0.907044 + 0.421035i \(0.861667\pi\)
\(182\) 5.70761 0.423076
\(183\) 0.666722 0.0492855
\(184\) 15.3553 1.13201
\(185\) 35.1342 2.58312
\(186\) −1.20377 −0.0882648
\(187\) −15.3862 −1.12515
\(188\) −3.34622 −0.244048
\(189\) 1.00000 0.0727393
\(190\) 7.74097 0.561589
\(191\) −22.5671 −1.63290 −0.816450 0.577416i \(-0.804061\pi\)
−0.816450 + 0.577416i \(0.804061\pi\)
\(192\) 8.89758 0.642128
\(193\) 20.7333 1.49242 0.746208 0.665713i \(-0.231873\pi\)
0.746208 + 0.665713i \(0.231873\pi\)
\(194\) 18.2699 1.31170
\(195\) 15.3116 1.09648
\(196\) −0.455452 −0.0325323
\(197\) −3.77768 −0.269148 −0.134574 0.990904i \(-0.542967\pi\)
−0.134574 + 0.990904i \(0.542967\pi\)
\(198\) −3.61302 −0.256766
\(199\) −9.73569 −0.690145 −0.345072 0.938576i \(-0.612146\pi\)
−0.345072 + 0.938576i \(0.612146\pi\)
\(200\) 18.6625 1.31964
\(201\) −14.0335 −0.989847
\(202\) 9.56583 0.673050
\(203\) 3.69938 0.259645
\(204\) 2.41048 0.168767
\(205\) −38.5431 −2.69196
\(206\) 22.4887 1.56686
\(207\) 5.03184 0.349737
\(208\) 13.2341 0.917623
\(209\) 5.43124 0.375687
\(210\) 4.14349 0.285928
\(211\) 4.66669 0.321268 0.160634 0.987014i \(-0.448646\pi\)
0.160634 + 0.987014i \(0.448646\pi\)
\(212\) 5.13918 0.352960
\(213\) 9.88541 0.677337
\(214\) 2.86662 0.195958
\(215\) −8.49730 −0.579511
\(216\) 3.05163 0.207637
\(217\) 0.968597 0.0657527
\(218\) 1.10867 0.0750889
\(219\) −2.57222 −0.173815
\(220\) 4.41447 0.297624
\(221\) 24.3060 1.63500
\(222\) 13.0968 0.878999
\(223\) 5.37863 0.360180 0.180090 0.983650i \(-0.442361\pi\)
0.180090 + 0.983650i \(0.442361\pi\)
\(224\) −2.52194 −0.168504
\(225\) 6.11557 0.407705
\(226\) −5.41486 −0.360191
\(227\) −11.5084 −0.763837 −0.381918 0.924196i \(-0.624736\pi\)
−0.381918 + 0.924196i \(0.624736\pi\)
\(228\) −0.850887 −0.0563514
\(229\) −1.87862 −0.124142 −0.0620712 0.998072i \(-0.519771\pi\)
−0.0620712 + 0.998072i \(0.519771\pi\)
\(230\) 20.8494 1.37477
\(231\) 2.90717 0.191278
\(232\) 11.2891 0.741168
\(233\) 13.5663 0.888755 0.444378 0.895840i \(-0.353425\pi\)
0.444378 + 0.895840i \(0.353425\pi\)
\(234\) 5.70761 0.373118
\(235\) −24.4950 −1.59788
\(236\) 6.07619 0.395526
\(237\) 14.5706 0.946463
\(238\) 6.57750 0.426356
\(239\) 22.4619 1.45294 0.726468 0.687200i \(-0.241160\pi\)
0.726468 + 0.687200i \(0.241160\pi\)
\(240\) 9.60746 0.620159
\(241\) 12.0289 0.774848 0.387424 0.921902i \(-0.373365\pi\)
0.387424 + 0.921902i \(0.373365\pi\)
\(242\) 3.16712 0.203590
\(243\) 1.00000 0.0641500
\(244\) −0.303660 −0.0194399
\(245\) −3.33400 −0.213002
\(246\) −14.3675 −0.916038
\(247\) −8.57990 −0.545926
\(248\) 2.95580 0.187694
\(249\) 0.493442 0.0312706
\(250\) 4.62237 0.292345
\(251\) 5.27452 0.332924 0.166462 0.986048i \(-0.446766\pi\)
0.166462 + 0.986048i \(0.446766\pi\)
\(252\) −0.455452 −0.0286908
\(253\) 14.6284 0.919680
\(254\) 1.24280 0.0779801
\(255\) 17.6452 1.10498
\(256\) −10.3210 −0.645060
\(257\) −28.6479 −1.78701 −0.893504 0.449055i \(-0.851761\pi\)
−0.893504 + 0.449055i \(0.851761\pi\)
\(258\) −3.16749 −0.197199
\(259\) −10.5381 −0.654808
\(260\) −6.97368 −0.432489
\(261\) 3.69938 0.228986
\(262\) −10.8349 −0.669380
\(263\) −6.33902 −0.390881 −0.195440 0.980716i \(-0.562614\pi\)
−0.195440 + 0.980716i \(0.562614\pi\)
\(264\) 8.87160 0.546010
\(265\) 37.6198 2.31097
\(266\) −2.32183 −0.142360
\(267\) 12.1652 0.744497
\(268\) 6.39159 0.390429
\(269\) 1.26346 0.0770348 0.0385174 0.999258i \(-0.487736\pi\)
0.0385174 + 0.999258i \(0.487736\pi\)
\(270\) 4.14349 0.252165
\(271\) −5.15641 −0.313230 −0.156615 0.987660i \(-0.550058\pi\)
−0.156615 + 0.987660i \(0.550058\pi\)
\(272\) 15.2512 0.924737
\(273\) −4.59254 −0.277953
\(274\) 5.79498 0.350087
\(275\) 17.7790 1.07211
\(276\) −2.29176 −0.137948
\(277\) 2.77471 0.166716 0.0833580 0.996520i \(-0.473435\pi\)
0.0833580 + 0.996520i \(0.473435\pi\)
\(278\) 24.5379 1.47168
\(279\) 0.968597 0.0579884
\(280\) −10.1741 −0.608022
\(281\) 5.01385 0.299101 0.149551 0.988754i \(-0.452217\pi\)
0.149551 + 0.988754i \(0.452217\pi\)
\(282\) −9.13087 −0.543735
\(283\) −8.84064 −0.525521 −0.262761 0.964861i \(-0.584633\pi\)
−0.262761 + 0.964861i \(0.584633\pi\)
\(284\) −4.50233 −0.267164
\(285\) −6.22866 −0.368954
\(286\) 16.5930 0.981162
\(287\) 11.5606 0.682401
\(288\) −2.52194 −0.148607
\(289\) 11.0105 0.647674
\(290\) 15.3283 0.900111
\(291\) −14.7006 −0.861767
\(292\) 1.17152 0.0685583
\(293\) −16.5617 −0.967545 −0.483772 0.875194i \(-0.660734\pi\)
−0.483772 + 0.875194i \(0.660734\pi\)
\(294\) −1.24280 −0.0724815
\(295\) 44.4789 2.58966
\(296\) −32.1585 −1.86918
\(297\) 2.90717 0.168691
\(298\) 6.83371 0.395866
\(299\) −23.1089 −1.33643
\(300\) −2.78535 −0.160812
\(301\) 2.54868 0.146903
\(302\) 14.6860 0.845085
\(303\) −7.69701 −0.442182
\(304\) −5.38358 −0.308770
\(305\) −2.22285 −0.127280
\(306\) 6.57750 0.376011
\(307\) −23.4209 −1.33670 −0.668352 0.743845i \(-0.733000\pi\)
−0.668352 + 0.743845i \(0.733000\pi\)
\(308\) −1.32408 −0.0754462
\(309\) −18.0952 −1.02940
\(310\) 4.01338 0.227944
\(311\) −19.5726 −1.10986 −0.554929 0.831898i \(-0.687255\pi\)
−0.554929 + 0.831898i \(0.687255\pi\)
\(312\) −14.0148 −0.793429
\(313\) 5.10217 0.288392 0.144196 0.989549i \(-0.453940\pi\)
0.144196 + 0.989549i \(0.453940\pi\)
\(314\) −4.69483 −0.264944
\(315\) −3.33400 −0.187850
\(316\) −6.63622 −0.373316
\(317\) −19.6691 −1.10472 −0.552362 0.833604i \(-0.686273\pi\)
−0.552362 + 0.833604i \(0.686273\pi\)
\(318\) 14.0233 0.786390
\(319\) 10.7547 0.602148
\(320\) −29.6646 −1.65830
\(321\) −2.30658 −0.128741
\(322\) −6.25356 −0.348497
\(323\) −9.88756 −0.550158
\(324\) −0.455452 −0.0253029
\(325\) −28.0860 −1.55793
\(326\) 24.8697 1.37741
\(327\) −0.892079 −0.0493321
\(328\) 35.2787 1.94794
\(329\) 7.34702 0.405055
\(330\) 12.0458 0.663101
\(331\) 15.1305 0.831648 0.415824 0.909445i \(-0.363493\pi\)
0.415824 + 0.909445i \(0.363493\pi\)
\(332\) −0.224739 −0.0123342
\(333\) −10.5381 −0.577487
\(334\) 20.4185 1.11725
\(335\) 46.7877 2.55629
\(336\) −2.88166 −0.157207
\(337\) −7.21235 −0.392882 −0.196441 0.980516i \(-0.562938\pi\)
−0.196441 + 0.980516i \(0.562938\pi\)
\(338\) −10.0560 −0.546977
\(339\) 4.35699 0.236639
\(340\) −8.03654 −0.435842
\(341\) 2.81587 0.152488
\(342\) −2.32183 −0.125550
\(343\) 1.00000 0.0539949
\(344\) 7.77763 0.419342
\(345\) −16.7762 −0.903199
\(346\) 20.1875 1.08529
\(347\) 28.7813 1.54506 0.772531 0.634977i \(-0.218990\pi\)
0.772531 + 0.634977i \(0.218990\pi\)
\(348\) −1.68489 −0.0903195
\(349\) −28.8201 −1.54270 −0.771352 0.636409i \(-0.780419\pi\)
−0.771352 + 0.636409i \(0.780419\pi\)
\(350\) −7.60043 −0.406260
\(351\) −4.59254 −0.245132
\(352\) −7.33171 −0.390782
\(353\) 26.6489 1.41838 0.709188 0.705019i \(-0.249062\pi\)
0.709188 + 0.705019i \(0.249062\pi\)
\(354\) 16.5802 0.881226
\(355\) −32.9580 −1.74923
\(356\) −5.54066 −0.293655
\(357\) −5.29249 −0.280108
\(358\) 4.97593 0.262986
\(359\) −14.4278 −0.761469 −0.380734 0.924684i \(-0.624329\pi\)
−0.380734 + 0.924684i \(0.624329\pi\)
\(360\) −10.1741 −0.536225
\(361\) −15.5097 −0.816302
\(362\) 30.3318 1.59421
\(363\) −2.54838 −0.133755
\(364\) 2.09168 0.109634
\(365\) 8.57580 0.448878
\(366\) −0.828601 −0.0433117
\(367\) −8.35795 −0.436282 −0.218141 0.975917i \(-0.569999\pi\)
−0.218141 + 0.975917i \(0.569999\pi\)
\(368\) −14.5000 −0.755867
\(369\) 11.5606 0.601821
\(370\) −43.6647 −2.27002
\(371\) −11.2837 −0.585819
\(372\) −0.441150 −0.0228726
\(373\) 30.3153 1.56966 0.784832 0.619708i \(-0.212749\pi\)
0.784832 + 0.619708i \(0.212749\pi\)
\(374\) 19.1219 0.988769
\(375\) −3.71933 −0.192065
\(376\) 22.4204 1.15624
\(377\) −16.9895 −0.875006
\(378\) −1.24280 −0.0639226
\(379\) 2.57847 0.132447 0.0662235 0.997805i \(-0.478905\pi\)
0.0662235 + 0.997805i \(0.478905\pi\)
\(380\) 2.83686 0.145528
\(381\) −1.00000 −0.0512316
\(382\) 28.0464 1.43498
\(383\) −14.6277 −0.747438 −0.373719 0.927542i \(-0.621918\pi\)
−0.373719 + 0.927542i \(0.621918\pi\)
\(384\) −6.01402 −0.306901
\(385\) −9.69250 −0.493976
\(386\) −25.7673 −1.31152
\(387\) 2.54868 0.129557
\(388\) 6.69544 0.339909
\(389\) 19.5586 0.991663 0.495831 0.868419i \(-0.334863\pi\)
0.495831 + 0.868419i \(0.334863\pi\)
\(390\) −19.0292 −0.963580
\(391\) −26.6310 −1.34679
\(392\) 3.05163 0.154131
\(393\) 8.71812 0.439771
\(394\) 4.69489 0.236525
\(395\) −48.5784 −2.44425
\(396\) −1.32408 −0.0665373
\(397\) −8.35455 −0.419303 −0.209651 0.977776i \(-0.567233\pi\)
−0.209651 + 0.977776i \(0.567233\pi\)
\(398\) 12.0995 0.606493
\(399\) 1.86822 0.0935282
\(400\) −17.6230 −0.881150
\(401\) 7.25894 0.362494 0.181247 0.983438i \(-0.441987\pi\)
0.181247 + 0.983438i \(0.441987\pi\)
\(402\) 17.4408 0.869869
\(403\) −4.44832 −0.221587
\(404\) 3.50562 0.174411
\(405\) −3.33400 −0.165668
\(406\) −4.59758 −0.228174
\(407\) −30.6361 −1.51858
\(408\) −16.1507 −0.799581
\(409\) 8.46320 0.418478 0.209239 0.977864i \(-0.432901\pi\)
0.209239 + 0.977864i \(0.432901\pi\)
\(410\) 47.9013 2.36567
\(411\) −4.66285 −0.230001
\(412\) 8.24150 0.406029
\(413\) −13.3410 −0.656468
\(414\) −6.25356 −0.307346
\(415\) −1.64514 −0.0807566
\(416\) 11.5821 0.567861
\(417\) −19.7441 −0.966870
\(418\) −6.74994 −0.330150
\(419\) 26.7971 1.30912 0.654561 0.756009i \(-0.272854\pi\)
0.654561 + 0.756009i \(0.272854\pi\)
\(420\) 1.51848 0.0740942
\(421\) 14.1261 0.688463 0.344231 0.938885i \(-0.388140\pi\)
0.344231 + 0.938885i \(0.388140\pi\)
\(422\) −5.79976 −0.282328
\(423\) 7.34702 0.357225
\(424\) −34.4336 −1.67225
\(425\) −32.3666 −1.57001
\(426\) −12.2856 −0.595238
\(427\) 0.666722 0.0322650
\(428\) 1.05054 0.0507797
\(429\) −13.3513 −0.644606
\(430\) 10.5604 0.509269
\(431\) −16.6128 −0.800211 −0.400105 0.916469i \(-0.631026\pi\)
−0.400105 + 0.916469i \(0.631026\pi\)
\(432\) −2.88166 −0.138644
\(433\) 24.5878 1.18161 0.590807 0.806813i \(-0.298810\pi\)
0.590807 + 0.806813i \(0.298810\pi\)
\(434\) −1.20377 −0.0577829
\(435\) −12.3337 −0.591357
\(436\) 0.406300 0.0194582
\(437\) 9.40061 0.449692
\(438\) 3.19675 0.152747
\(439\) −38.1271 −1.81971 −0.909853 0.414930i \(-0.863806\pi\)
−0.909853 + 0.414930i \(0.863806\pi\)
\(440\) −29.5780 −1.41007
\(441\) 1.00000 0.0476190
\(442\) −30.2074 −1.43682
\(443\) 22.7120 1.07908 0.539541 0.841959i \(-0.318598\pi\)
0.539541 + 0.841959i \(0.318598\pi\)
\(444\) 4.79962 0.227780
\(445\) −40.5588 −1.92267
\(446\) −6.68455 −0.316523
\(447\) −5.49864 −0.260077
\(448\) 8.89758 0.420371
\(449\) −29.0754 −1.37215 −0.686075 0.727531i \(-0.740668\pi\)
−0.686075 + 0.727531i \(0.740668\pi\)
\(450\) −7.60043 −0.358287
\(451\) 33.6086 1.58257
\(452\) −1.98440 −0.0933385
\(453\) −11.8169 −0.555206
\(454\) 14.3026 0.671253
\(455\) 15.3116 0.717817
\(456\) 5.70113 0.266980
\(457\) 25.5196 1.19376 0.596879 0.802332i \(-0.296407\pi\)
0.596879 + 0.802332i \(0.296407\pi\)
\(458\) 2.33474 0.109095
\(459\) −5.29249 −0.247032
\(460\) 7.64075 0.356252
\(461\) −10.8134 −0.503631 −0.251815 0.967775i \(-0.581028\pi\)
−0.251815 + 0.967775i \(0.581028\pi\)
\(462\) −3.61302 −0.168093
\(463\) 5.98793 0.278283 0.139141 0.990273i \(-0.455566\pi\)
0.139141 + 0.990273i \(0.455566\pi\)
\(464\) −10.6603 −0.494894
\(465\) −3.22931 −0.149755
\(466\) −16.8601 −0.781030
\(467\) 41.9564 1.94151 0.970755 0.240074i \(-0.0771717\pi\)
0.970755 + 0.240074i \(0.0771717\pi\)
\(468\) 2.09168 0.0966881
\(469\) −14.0335 −0.648007
\(470\) 30.4423 1.40420
\(471\) 3.77762 0.174064
\(472\) −40.7118 −1.87391
\(473\) 7.40943 0.340686
\(474\) −18.1083 −0.831743
\(475\) 11.4253 0.524227
\(476\) 2.41048 0.110484
\(477\) −11.2837 −0.516644
\(478\) −27.9156 −1.27683
\(479\) −9.65088 −0.440960 −0.220480 0.975392i \(-0.570762\pi\)
−0.220480 + 0.975392i \(0.570762\pi\)
\(480\) 8.40817 0.383779
\(481\) 48.3969 2.20671
\(482\) −14.9495 −0.680930
\(483\) 5.03184 0.228957
\(484\) 1.16067 0.0527575
\(485\) 49.0120 2.22552
\(486\) −1.24280 −0.0563745
\(487\) −17.7189 −0.802920 −0.401460 0.915877i \(-0.631497\pi\)
−0.401460 + 0.915877i \(0.631497\pi\)
\(488\) 2.03459 0.0921016
\(489\) −20.0111 −0.904932
\(490\) 4.14349 0.187184
\(491\) −4.97599 −0.224563 −0.112282 0.993676i \(-0.535816\pi\)
−0.112282 + 0.993676i \(0.535816\pi\)
\(492\) −5.26530 −0.237378
\(493\) −19.5789 −0.881790
\(494\) 10.6631 0.479755
\(495\) −9.69250 −0.435646
\(496\) −2.79117 −0.125327
\(497\) 9.88541 0.443421
\(498\) −0.613249 −0.0274803
\(499\) 44.0654 1.97264 0.986318 0.164851i \(-0.0527143\pi\)
0.986318 + 0.164851i \(0.0527143\pi\)
\(500\) 1.69398 0.0757569
\(501\) −16.4295 −0.734014
\(502\) −6.55516 −0.292571
\(503\) 5.31840 0.237136 0.118568 0.992946i \(-0.462170\pi\)
0.118568 + 0.992946i \(0.462170\pi\)
\(504\) 3.05163 0.135930
\(505\) 25.6619 1.14194
\(506\) −18.1802 −0.808207
\(507\) 8.09145 0.359354
\(508\) 0.455452 0.0202074
\(509\) 10.4607 0.463661 0.231830 0.972756i \(-0.425529\pi\)
0.231830 + 0.972756i \(0.425529\pi\)
\(510\) −21.9294 −0.971050
\(511\) −2.57222 −0.113788
\(512\) 24.8549 1.09844
\(513\) 1.86822 0.0824841
\(514\) 35.6036 1.57041
\(515\) 60.3294 2.65843
\(516\) −1.16080 −0.0511014
\(517\) 21.3590 0.939369
\(518\) 13.0968 0.575440
\(519\) −16.2436 −0.713015
\(520\) 46.7252 2.04904
\(521\) 35.6052 1.55989 0.779947 0.625846i \(-0.215246\pi\)
0.779947 + 0.625846i \(0.215246\pi\)
\(522\) −4.59758 −0.201230
\(523\) 23.5608 1.03024 0.515120 0.857118i \(-0.327747\pi\)
0.515120 + 0.857118i \(0.327747\pi\)
\(524\) −3.97069 −0.173460
\(525\) 6.11557 0.266906
\(526\) 7.87813 0.343503
\(527\) −5.12629 −0.223305
\(528\) −8.37746 −0.364582
\(529\) 2.31943 0.100845
\(530\) −46.7538 −2.03086
\(531\) −13.3410 −0.578950
\(532\) −0.850887 −0.0368906
\(533\) −53.0926 −2.29969
\(534\) −15.1189 −0.654258
\(535\) 7.69015 0.332474
\(536\) −42.8251 −1.84976
\(537\) −4.00381 −0.172777
\(538\) −1.57023 −0.0676975
\(539\) 2.90717 0.125221
\(540\) 1.51848 0.0653449
\(541\) 7.71667 0.331765 0.165883 0.986145i \(-0.446953\pi\)
0.165883 + 0.986145i \(0.446953\pi\)
\(542\) 6.40838 0.275264
\(543\) −24.4061 −1.04736
\(544\) 13.3474 0.572263
\(545\) 2.97419 0.127400
\(546\) 5.70761 0.244263
\(547\) −15.9737 −0.682987 −0.341494 0.939884i \(-0.610933\pi\)
−0.341494 + 0.939884i \(0.610933\pi\)
\(548\) 2.12370 0.0907201
\(549\) 0.666722 0.0284550
\(550\) −22.0957 −0.942164
\(551\) 6.91126 0.294430
\(552\) 15.3553 0.653566
\(553\) 14.5706 0.619605
\(554\) −3.44840 −0.146509
\(555\) 35.1342 1.49136
\(556\) 8.99247 0.381366
\(557\) 0.464136 0.0196661 0.00983304 0.999952i \(-0.496870\pi\)
0.00983304 + 0.999952i \(0.496870\pi\)
\(558\) −1.20377 −0.0509597
\(559\) −11.7049 −0.495065
\(560\) 9.60746 0.405989
\(561\) −15.3862 −0.649604
\(562\) −6.23121 −0.262848
\(563\) 35.9885 1.51673 0.758367 0.651828i \(-0.225998\pi\)
0.758367 + 0.651828i \(0.225998\pi\)
\(564\) −3.34622 −0.140901
\(565\) −14.5262 −0.611123
\(566\) 10.9871 0.461824
\(567\) 1.00000 0.0419961
\(568\) 30.1666 1.26576
\(569\) −11.1032 −0.465469 −0.232735 0.972540i \(-0.574767\pi\)
−0.232735 + 0.972540i \(0.574767\pi\)
\(570\) 7.74097 0.324234
\(571\) 10.2214 0.427753 0.213877 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(572\) 6.08088 0.254254
\(573\) −22.5671 −0.942755
\(574\) −14.3675 −0.599688
\(575\) 30.7726 1.28331
\(576\) 8.89758 0.370733
\(577\) 10.4490 0.434999 0.217500 0.976060i \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(578\) −13.6838 −0.569170
\(579\) 20.7333 0.861646
\(580\) 5.61742 0.233251
\(581\) 0.493442 0.0204714
\(582\) 18.2699 0.757313
\(583\) −32.8035 −1.35858
\(584\) −7.84948 −0.324814
\(585\) 15.3116 0.633055
\(586\) 20.5829 0.850270
\(587\) 37.8825 1.56358 0.781789 0.623543i \(-0.214307\pi\)
0.781789 + 0.623543i \(0.214307\pi\)
\(588\) −0.455452 −0.0187825
\(589\) 1.80956 0.0745615
\(590\) −55.2783 −2.27577
\(591\) −3.77768 −0.155393
\(592\) 30.3673 1.24809
\(593\) −43.2711 −1.77693 −0.888466 0.458942i \(-0.848228\pi\)
−0.888466 + 0.458942i \(0.848228\pi\)
\(594\) −3.61302 −0.148244
\(595\) 17.6452 0.723382
\(596\) 2.50437 0.102583
\(597\) −9.73569 −0.398455
\(598\) 28.7198 1.17444
\(599\) −28.8279 −1.17787 −0.588937 0.808179i \(-0.700453\pi\)
−0.588937 + 0.808179i \(0.700453\pi\)
\(600\) 18.6625 0.761893
\(601\) 29.8137 1.21612 0.608062 0.793889i \(-0.291947\pi\)
0.608062 + 0.793889i \(0.291947\pi\)
\(602\) −3.16749 −0.129097
\(603\) −14.0335 −0.571489
\(604\) 5.38203 0.218992
\(605\) 8.49630 0.345424
\(606\) 9.56583 0.388585
\(607\) −15.0035 −0.608974 −0.304487 0.952516i \(-0.598485\pi\)
−0.304487 + 0.952516i \(0.598485\pi\)
\(608\) −4.71156 −0.191079
\(609\) 3.69938 0.149906
\(610\) 2.76256 0.111853
\(611\) −33.7415 −1.36504
\(612\) 2.41048 0.0974378
\(613\) −5.68365 −0.229561 −0.114780 0.993391i \(-0.536616\pi\)
−0.114780 + 0.993391i \(0.536616\pi\)
\(614\) 29.1075 1.17468
\(615\) −38.5431 −1.55421
\(616\) 8.87160 0.357447
\(617\) 13.5363 0.544952 0.272476 0.962163i \(-0.412158\pi\)
0.272476 + 0.962163i \(0.412158\pi\)
\(618\) 22.4887 0.904627
\(619\) −27.0321 −1.08651 −0.543256 0.839567i \(-0.682809\pi\)
−0.543256 + 0.839567i \(0.682809\pi\)
\(620\) 1.47079 0.0590685
\(621\) 5.03184 0.201921
\(622\) 24.3247 0.975334
\(623\) 12.1652 0.487388
\(624\) 13.2341 0.529790
\(625\) −18.1776 −0.727105
\(626\) −6.34097 −0.253436
\(627\) 5.43124 0.216903
\(628\) −1.72053 −0.0686565
\(629\) 55.7730 2.22382
\(630\) 4.14349 0.165081
\(631\) 2.75817 0.109801 0.0549004 0.998492i \(-0.482516\pi\)
0.0549004 + 0.998492i \(0.482516\pi\)
\(632\) 44.4641 1.76869
\(633\) 4.66669 0.185484
\(634\) 24.4447 0.970822
\(635\) 3.33400 0.132306
\(636\) 5.13918 0.203782
\(637\) −4.59254 −0.181963
\(638\) −13.3659 −0.529162
\(639\) 9.88541 0.391061
\(640\) 20.0507 0.792575
\(641\) −10.2155 −0.403489 −0.201744 0.979438i \(-0.564661\pi\)
−0.201744 + 0.979438i \(0.564661\pi\)
\(642\) 2.86662 0.113136
\(643\) −25.3762 −1.00074 −0.500370 0.865812i \(-0.666803\pi\)
−0.500370 + 0.865812i \(0.666803\pi\)
\(644\) −2.29176 −0.0903081
\(645\) −8.49730 −0.334581
\(646\) 12.2882 0.483474
\(647\) −22.1567 −0.871068 −0.435534 0.900172i \(-0.643440\pi\)
−0.435534 + 0.900172i \(0.643440\pi\)
\(648\) 3.05163 0.119879
\(649\) −38.7845 −1.52243
\(650\) 34.9053 1.36910
\(651\) 0.968597 0.0379623
\(652\) 9.11409 0.356935
\(653\) −9.65817 −0.377954 −0.188977 0.981982i \(-0.560517\pi\)
−0.188977 + 0.981982i \(0.560517\pi\)
\(654\) 1.10867 0.0433526
\(655\) −29.0662 −1.13571
\(656\) −33.3137 −1.30068
\(657\) −2.57222 −0.100352
\(658\) −9.13087 −0.355958
\(659\) −14.6717 −0.571527 −0.285764 0.958300i \(-0.592247\pi\)
−0.285764 + 0.958300i \(0.592247\pi\)
\(660\) 4.41447 0.171833
\(661\) 33.3172 1.29589 0.647945 0.761687i \(-0.275629\pi\)
0.647945 + 0.761687i \(0.275629\pi\)
\(662\) −18.8042 −0.730845
\(663\) 24.3060 0.943967
\(664\) 1.50580 0.0584365
\(665\) −6.22866 −0.241537
\(666\) 13.0968 0.507490
\(667\) 18.6147 0.720763
\(668\) 7.48283 0.289519
\(669\) 5.37863 0.207950
\(670\) −58.1477 −2.24644
\(671\) 1.93827 0.0748262
\(672\) −2.52194 −0.0972861
\(673\) 1.32670 0.0511404 0.0255702 0.999673i \(-0.491860\pi\)
0.0255702 + 0.999673i \(0.491860\pi\)
\(674\) 8.96350 0.345261
\(675\) 6.11557 0.235389
\(676\) −3.68527 −0.141741
\(677\) 11.9106 0.457761 0.228881 0.973454i \(-0.426493\pi\)
0.228881 + 0.973454i \(0.426493\pi\)
\(678\) −5.41486 −0.207957
\(679\) −14.7006 −0.564159
\(680\) 53.8466 2.06492
\(681\) −11.5084 −0.441001
\(682\) −3.49956 −0.134005
\(683\) −6.04534 −0.231318 −0.115659 0.993289i \(-0.536898\pi\)
−0.115659 + 0.993289i \(0.536898\pi\)
\(684\) −0.850887 −0.0325345
\(685\) 15.5459 0.593980
\(686\) −1.24280 −0.0474503
\(687\) −1.87862 −0.0716737
\(688\) −7.34442 −0.280003
\(689\) 51.8208 1.97421
\(690\) 20.8494 0.793723
\(691\) −26.4623 −1.00667 −0.503336 0.864090i \(-0.667894\pi\)
−0.503336 + 0.864090i \(0.667894\pi\)
\(692\) 7.39818 0.281237
\(693\) 2.90717 0.110434
\(694\) −35.7694 −1.35779
\(695\) 65.8267 2.49695
\(696\) 11.2891 0.427913
\(697\) −61.1844 −2.31752
\(698\) 35.8176 1.35571
\(699\) 13.5663 0.513123
\(700\) −2.78535 −0.105276
\(701\) 27.8873 1.05329 0.526645 0.850085i \(-0.323450\pi\)
0.526645 + 0.850085i \(0.323450\pi\)
\(702\) 5.70761 0.215420
\(703\) −19.6876 −0.742532
\(704\) 25.8668 0.974890
\(705\) −24.4950 −0.922535
\(706\) −33.1192 −1.24646
\(707\) −7.69701 −0.289476
\(708\) 6.07619 0.228357
\(709\) −21.7892 −0.818312 −0.409156 0.912465i \(-0.634177\pi\)
−0.409156 + 0.912465i \(0.634177\pi\)
\(710\) 40.9601 1.53721
\(711\) 14.5706 0.546440
\(712\) 37.1237 1.39127
\(713\) 4.87383 0.182526
\(714\) 6.57750 0.246157
\(715\) 44.5132 1.66470
\(716\) 1.82355 0.0681491
\(717\) 22.4619 0.838853
\(718\) 17.9308 0.669172
\(719\) 0.503768 0.0187874 0.00939368 0.999956i \(-0.497010\pi\)
0.00939368 + 0.999956i \(0.497010\pi\)
\(720\) 9.60746 0.358049
\(721\) −18.0952 −0.673900
\(722\) 19.2755 0.717359
\(723\) 12.0289 0.447359
\(724\) 11.1158 0.413115
\(725\) 22.6238 0.840227
\(726\) 3.16712 0.117543
\(727\) 23.4153 0.868427 0.434213 0.900810i \(-0.357026\pi\)
0.434213 + 0.900810i \(0.357026\pi\)
\(728\) −14.0148 −0.519421
\(729\) 1.00000 0.0370370
\(730\) −10.6580 −0.394470
\(731\) −13.4889 −0.498903
\(732\) −0.303660 −0.0112236
\(733\) 52.3311 1.93289 0.966446 0.256871i \(-0.0826915\pi\)
0.966446 + 0.256871i \(0.0826915\pi\)
\(734\) 10.3872 0.383400
\(735\) −3.33400 −0.122977
\(736\) −12.6900 −0.467760
\(737\) −40.7978 −1.50280
\(738\) −14.3675 −0.528875
\(739\) −11.4312 −0.420504 −0.210252 0.977647i \(-0.567429\pi\)
−0.210252 + 0.977647i \(0.567429\pi\)
\(740\) −16.0020 −0.588243
\(741\) −8.57990 −0.315190
\(742\) 14.0233 0.514813
\(743\) 33.8238 1.24087 0.620437 0.784256i \(-0.286955\pi\)
0.620437 + 0.784256i \(0.286955\pi\)
\(744\) 2.95580 0.108365
\(745\) 18.3325 0.671651
\(746\) −37.6758 −1.37941
\(747\) 0.493442 0.0180541
\(748\) 7.00766 0.256225
\(749\) −2.30658 −0.0842807
\(750\) 4.62237 0.168785
\(751\) −50.0895 −1.82779 −0.913896 0.405949i \(-0.866941\pi\)
−0.913896 + 0.405949i \(0.866941\pi\)
\(752\) −21.1716 −0.772049
\(753\) 5.27452 0.192214
\(754\) 21.1146 0.768947
\(755\) 39.3975 1.43382
\(756\) −0.455452 −0.0165646
\(757\) 16.9391 0.615663 0.307831 0.951441i \(-0.400397\pi\)
0.307831 + 0.951441i \(0.400397\pi\)
\(758\) −3.20451 −0.116393
\(759\) 14.6284 0.530977
\(760\) −19.0076 −0.689478
\(761\) −32.7577 −1.18747 −0.593734 0.804662i \(-0.702347\pi\)
−0.593734 + 0.804662i \(0.702347\pi\)
\(762\) 1.24280 0.0450218
\(763\) −0.892079 −0.0322954
\(764\) 10.2783 0.371854
\(765\) 17.6452 0.637963
\(766\) 18.1792 0.656842
\(767\) 61.2691 2.21230
\(768\) −10.3210 −0.372426
\(769\) 47.6458 1.71815 0.859075 0.511850i \(-0.171040\pi\)
0.859075 + 0.511850i \(0.171040\pi\)
\(770\) 12.0458 0.434101
\(771\) −28.6479 −1.03173
\(772\) −9.44303 −0.339862
\(773\) −47.1769 −1.69683 −0.848417 0.529328i \(-0.822444\pi\)
−0.848417 + 0.529328i \(0.822444\pi\)
\(774\) −3.16749 −0.113853
\(775\) 5.92353 0.212779
\(776\) −44.8609 −1.61041
\(777\) −10.5381 −0.378054
\(778\) −24.3075 −0.871464
\(779\) 21.5978 0.773821
\(780\) −6.97368 −0.249698
\(781\) 28.7385 1.02835
\(782\) 33.0969 1.18354
\(783\) 3.69938 0.132205
\(784\) −2.88166 −0.102916
\(785\) −12.5946 −0.449521
\(786\) −10.8349 −0.386467
\(787\) −15.6611 −0.558257 −0.279129 0.960254i \(-0.590046\pi\)
−0.279129 + 0.960254i \(0.590046\pi\)
\(788\) 1.72055 0.0612921
\(789\) −6.33902 −0.225675
\(790\) 60.3732 2.14798
\(791\) 4.35699 0.154917
\(792\) 8.87160 0.315239
\(793\) −3.06195 −0.108733
\(794\) 10.3830 0.368479
\(795\) 37.6198 1.33424
\(796\) 4.43414 0.157164
\(797\) −2.11085 −0.0747702 −0.0373851 0.999301i \(-0.511903\pi\)
−0.0373851 + 0.999301i \(0.511903\pi\)
\(798\) −2.32183 −0.0821917
\(799\) −38.8841 −1.37562
\(800\) −15.4231 −0.545290
\(801\) 12.1652 0.429836
\(802\) −9.02139 −0.318556
\(803\) −7.47788 −0.263889
\(804\) 6.39159 0.225414
\(805\) −16.7762 −0.591282
\(806\) 5.52837 0.194729
\(807\) 1.26346 0.0444761
\(808\) −23.4884 −0.826321
\(809\) −10.8674 −0.382079 −0.191039 0.981582i \(-0.561186\pi\)
−0.191039 + 0.981582i \(0.561186\pi\)
\(810\) 4.14349 0.145588
\(811\) −46.4996 −1.63282 −0.816411 0.577472i \(-0.804039\pi\)
−0.816411 + 0.577472i \(0.804039\pi\)
\(812\) −1.68489 −0.0591280
\(813\) −5.15641 −0.180843
\(814\) 38.0746 1.33451
\(815\) 66.7170 2.33699
\(816\) 15.2512 0.533897
\(817\) 4.76150 0.166584
\(818\) −10.5181 −0.367755
\(819\) −4.59254 −0.160476
\(820\) 17.5545 0.613031
\(821\) −26.4225 −0.922152 −0.461076 0.887361i \(-0.652536\pi\)
−0.461076 + 0.887361i \(0.652536\pi\)
\(822\) 5.79498 0.202123
\(823\) −26.4500 −0.921989 −0.460995 0.887403i \(-0.652507\pi\)
−0.460995 + 0.887403i \(0.652507\pi\)
\(824\) −55.2199 −1.92368
\(825\) 17.7790 0.618985
\(826\) 16.5802 0.576898
\(827\) 31.2695 1.08735 0.543673 0.839297i \(-0.317033\pi\)
0.543673 + 0.839297i \(0.317033\pi\)
\(828\) −2.29176 −0.0796443
\(829\) −52.6203 −1.82758 −0.913790 0.406187i \(-0.866858\pi\)
−0.913790 + 0.406187i \(0.866858\pi\)
\(830\) 2.04457 0.0709682
\(831\) 2.77471 0.0962536
\(832\) −40.8625 −1.41665
\(833\) −5.29249 −0.183374
\(834\) 24.5379 0.849677
\(835\) 54.7758 1.89560
\(836\) −2.47367 −0.0855537
\(837\) 0.968597 0.0334796
\(838\) −33.3033 −1.15044
\(839\) −29.2755 −1.01070 −0.505352 0.862913i \(-0.668637\pi\)
−0.505352 + 0.862913i \(0.668637\pi\)
\(840\) −10.1741 −0.351042
\(841\) −15.3146 −0.528090
\(842\) −17.5559 −0.605015
\(843\) 5.01385 0.172686
\(844\) −2.12546 −0.0731612
\(845\) −26.9769 −0.928034
\(846\) −9.13087 −0.313926
\(847\) −2.54838 −0.0875633
\(848\) 32.5157 1.11659
\(849\) −8.84064 −0.303410
\(850\) 40.2252 1.37971
\(851\) −53.0263 −1.81772
\(852\) −4.50233 −0.154247
\(853\) −22.4780 −0.769631 −0.384816 0.922994i \(-0.625735\pi\)
−0.384816 + 0.922994i \(0.625735\pi\)
\(854\) −0.828601 −0.0283542
\(855\) −6.22866 −0.213016
\(856\) −7.03884 −0.240583
\(857\) −35.5634 −1.21482 −0.607412 0.794387i \(-0.707792\pi\)
−0.607412 + 0.794387i \(0.707792\pi\)
\(858\) 16.5930 0.566474
\(859\) 38.2979 1.30671 0.653354 0.757053i \(-0.273361\pi\)
0.653354 + 0.757053i \(0.273361\pi\)
\(860\) 3.87011 0.131970
\(861\) 11.5606 0.393984
\(862\) 20.6464 0.703218
\(863\) 47.7198 1.62440 0.812201 0.583378i \(-0.198270\pi\)
0.812201 + 0.583378i \(0.198270\pi\)
\(864\) −2.52194 −0.0857983
\(865\) 54.1562 1.84137
\(866\) −30.5577 −1.03839
\(867\) 11.0105 0.373935
\(868\) −0.441150 −0.0149736
\(869\) 42.3592 1.43694
\(870\) 15.3283 0.519679
\(871\) 64.4495 2.18379
\(872\) −2.72230 −0.0921886
\(873\) −14.7006 −0.497541
\(874\) −11.6831 −0.395185
\(875\) −3.71933 −0.125736
\(876\) 1.17152 0.0395821
\(877\) −20.9916 −0.708837 −0.354418 0.935087i \(-0.615321\pi\)
−0.354418 + 0.935087i \(0.615321\pi\)
\(878\) 47.3843 1.59914
\(879\) −16.5617 −0.558612
\(880\) 27.9305 0.941536
\(881\) −47.8891 −1.61343 −0.806713 0.590943i \(-0.798756\pi\)
−0.806713 + 0.590943i \(0.798756\pi\)
\(882\) −1.24280 −0.0418472
\(883\) 10.1634 0.342026 0.171013 0.985269i \(-0.445296\pi\)
0.171013 + 0.985269i \(0.445296\pi\)
\(884\) −11.0702 −0.372332
\(885\) 44.4789 1.49514
\(886\) −28.2265 −0.948287
\(887\) −49.2135 −1.65243 −0.826213 0.563357i \(-0.809510\pi\)
−0.826213 + 0.563357i \(0.809510\pi\)
\(888\) −32.1585 −1.07917
\(889\) −1.00000 −0.0335389
\(890\) 50.4064 1.68963
\(891\) 2.90717 0.0973938
\(892\) −2.44971 −0.0820223
\(893\) 13.7259 0.459319
\(894\) 6.83371 0.228553
\(895\) 13.3487 0.446199
\(896\) −6.01402 −0.200914
\(897\) −23.1089 −0.771585
\(898\) 36.1348 1.20583
\(899\) 3.58320 0.119507
\(900\) −2.78535 −0.0928451
\(901\) 59.7188 1.98952
\(902\) −41.7687 −1.39075
\(903\) 2.54868 0.0848147
\(904\) 13.2959 0.442216
\(905\) 81.3699 2.70483
\(906\) 14.6860 0.487910
\(907\) 50.4233 1.67428 0.837139 0.546991i \(-0.184227\pi\)
0.837139 + 0.546991i \(0.184227\pi\)
\(908\) 5.24151 0.173946
\(909\) −7.69701 −0.255294
\(910\) −19.0292 −0.630811
\(911\) 19.4045 0.642899 0.321449 0.946927i \(-0.395830\pi\)
0.321449 + 0.946927i \(0.395830\pi\)
\(912\) −5.38358 −0.178268
\(913\) 1.43452 0.0474756
\(914\) −31.7157 −1.04906
\(915\) −2.22285 −0.0734853
\(916\) 0.855620 0.0282705
\(917\) 8.71812 0.287898
\(918\) 6.57750 0.217090
\(919\) −38.9767 −1.28572 −0.642861 0.765983i \(-0.722253\pi\)
−0.642861 + 0.765983i \(0.722253\pi\)
\(920\) −51.1947 −1.68784
\(921\) −23.4209 −0.771746
\(922\) 13.4389 0.442586
\(923\) −45.3992 −1.49433
\(924\) −1.32408 −0.0435589
\(925\) −64.4468 −2.11900
\(926\) −7.44179 −0.244552
\(927\) −18.0952 −0.594324
\(928\) −9.32962 −0.306260
\(929\) −2.48794 −0.0816266 −0.0408133 0.999167i \(-0.512995\pi\)
−0.0408133 + 0.999167i \(0.512995\pi\)
\(930\) 4.01338 0.131604
\(931\) 1.86822 0.0612286
\(932\) −6.17878 −0.202393
\(933\) −19.5726 −0.640777
\(934\) −52.1433 −1.70618
\(935\) 51.2975 1.67761
\(936\) −14.0148 −0.458086
\(937\) 42.9656 1.40362 0.701812 0.712362i \(-0.252375\pi\)
0.701812 + 0.712362i \(0.252375\pi\)
\(938\) 17.4408 0.569463
\(939\) 5.10217 0.166503
\(940\) 11.1563 0.363878
\(941\) 49.3601 1.60909 0.804547 0.593889i \(-0.202408\pi\)
0.804547 + 0.593889i \(0.202408\pi\)
\(942\) −4.69483 −0.152966
\(943\) 58.1711 1.89431
\(944\) 38.4442 1.25125
\(945\) −3.33400 −0.108455
\(946\) −9.20843 −0.299392
\(947\) −7.03435 −0.228586 −0.114293 0.993447i \(-0.536460\pi\)
−0.114293 + 0.993447i \(0.536460\pi\)
\(948\) −6.63622 −0.215534
\(949\) 11.8130 0.383468
\(950\) −14.1993 −0.460686
\(951\) −19.6691 −0.637813
\(952\) −16.1507 −0.523448
\(953\) 12.7667 0.413553 0.206777 0.978388i \(-0.433703\pi\)
0.206777 + 0.978388i \(0.433703\pi\)
\(954\) 14.0233 0.454022
\(955\) 75.2389 2.43467
\(956\) −10.2303 −0.330872
\(957\) 10.7547 0.347650
\(958\) 11.9941 0.387512
\(959\) −4.66285 −0.150571
\(960\) −29.6646 −0.957420
\(961\) −30.0618 −0.969736
\(962\) −60.1476 −1.93924
\(963\) −2.30658 −0.0743286
\(964\) −5.47858 −0.176453
\(965\) −69.1249 −2.22521
\(966\) −6.25356 −0.201205
\(967\) 53.8825 1.73274 0.866372 0.499400i \(-0.166446\pi\)
0.866372 + 0.499400i \(0.166446\pi\)
\(968\) −7.77671 −0.249953
\(969\) −9.88756 −0.317634
\(970\) −60.9120 −1.95577
\(971\) −55.2100 −1.77177 −0.885887 0.463901i \(-0.846449\pi\)
−0.885887 + 0.463901i \(0.846449\pi\)
\(972\) −0.455452 −0.0146086
\(973\) −19.7441 −0.632965
\(974\) 22.0210 0.705599
\(975\) −28.0860 −0.899473
\(976\) −1.92127 −0.0614982
\(977\) −38.3352 −1.22645 −0.613226 0.789908i \(-0.710128\pi\)
−0.613226 + 0.789908i \(0.710128\pi\)
\(978\) 24.8697 0.795246
\(979\) 35.3662 1.13031
\(980\) 1.51848 0.0485060
\(981\) −0.892079 −0.0284819
\(982\) 6.18415 0.197344
\(983\) −19.8976 −0.634635 −0.317317 0.948319i \(-0.602782\pi\)
−0.317317 + 0.948319i \(0.602782\pi\)
\(984\) 35.2787 1.12464
\(985\) 12.5948 0.401303
\(986\) 24.3326 0.774909
\(987\) 7.34702 0.233858
\(988\) 3.90774 0.124322
\(989\) 12.8245 0.407797
\(990\) 12.0458 0.382842
\(991\) 5.55649 0.176508 0.0882538 0.996098i \(-0.471871\pi\)
0.0882538 + 0.996098i \(0.471871\pi\)
\(992\) −2.44275 −0.0775573
\(993\) 15.1305 0.480152
\(994\) −12.2856 −0.389675
\(995\) 32.4588 1.02901
\(996\) −0.224739 −0.00712114
\(997\) 4.32640 0.137019 0.0685093 0.997650i \(-0.478176\pi\)
0.0685093 + 0.997650i \(0.478176\pi\)
\(998\) −54.7644 −1.73354
\(999\) −10.5381 −0.333412
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 2667.2.a.j.1.3 7
3.2 odd 2 8001.2.a.l.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.3 7 1.1 even 1 trivial
8001.2.a.l.1.5 7 3.2 odd 2