Properties

Label 2001.2.a.i.1.1
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.9780654445\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 5 x^{5} + 18 x^{4} + 4 x^{3} - 26 x^{2} + x + 8\)
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 1.1
Root \(2.37349\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37349 q^{2} +1.00000 q^{3} +3.63344 q^{4} -1.31800 q^{5} -2.37349 q^{6} -0.859291 q^{7} -3.87694 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.37349 q^{2} +1.00000 q^{3} +3.63344 q^{4} -1.31800 q^{5} -2.37349 q^{6} -0.859291 q^{7} -3.87694 q^{8} +1.00000 q^{9} +3.12824 q^{10} +4.30847 q^{11} +3.63344 q^{12} -4.15542 q^{13} +2.03951 q^{14} -1.31800 q^{15} +1.93498 q^{16} +2.08920 q^{17} -2.37349 q^{18} -2.45615 q^{19} -4.78885 q^{20} -0.859291 q^{21} -10.2261 q^{22} +1.00000 q^{23} -3.87694 q^{24} -3.26289 q^{25} +9.86283 q^{26} +1.00000 q^{27} -3.12218 q^{28} -1.00000 q^{29} +3.12824 q^{30} -4.70746 q^{31} +3.16122 q^{32} +4.30847 q^{33} -4.95870 q^{34} +1.13254 q^{35} +3.63344 q^{36} -3.94232 q^{37} +5.82963 q^{38} -4.15542 q^{39} +5.10979 q^{40} -3.17442 q^{41} +2.03951 q^{42} +11.0153 q^{43} +15.6545 q^{44} -1.31800 q^{45} -2.37349 q^{46} +11.1103 q^{47} +1.93498 q^{48} -6.26162 q^{49} +7.74442 q^{50} +2.08920 q^{51} -15.0984 q^{52} -14.0165 q^{53} -2.37349 q^{54} -5.67854 q^{55} +3.33142 q^{56} -2.45615 q^{57} +2.37349 q^{58} +8.47222 q^{59} -4.78885 q^{60} -6.39249 q^{61} +11.1731 q^{62} -0.859291 q^{63} -11.3731 q^{64} +5.47682 q^{65} -10.2261 q^{66} +4.74715 q^{67} +7.59099 q^{68} +1.00000 q^{69} -2.68807 q^{70} -12.4909 q^{71} -3.87694 q^{72} +8.54106 q^{73} +9.35703 q^{74} -3.26289 q^{75} -8.92426 q^{76} -3.70223 q^{77} +9.86283 q^{78} -13.0092 q^{79} -2.55030 q^{80} +1.00000 q^{81} +7.53445 q^{82} -14.2415 q^{83} -3.12218 q^{84} -2.75356 q^{85} -26.1447 q^{86} -1.00000 q^{87} -16.7037 q^{88} +0.795808 q^{89} +3.12824 q^{90} +3.57071 q^{91} +3.63344 q^{92} -4.70746 q^{93} -26.3702 q^{94} +3.23719 q^{95} +3.16122 q^{96} +3.92369 q^{97} +14.8619 q^{98} +4.30847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{2} + 7q^{3} + 5q^{4} - 3q^{5} - 3q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 3q^{2} + 7q^{3} + 5q^{4} - 3q^{5} - 3q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + 3q^{10} - 4q^{11} + 5q^{12} - 18q^{13} - 2q^{14} - 3q^{15} - 7q^{16} - 3q^{17} - 3q^{18} - 4q^{19} - 2q^{20} - 5q^{21} - 26q^{22} + 7q^{23} - 6q^{24} - 8q^{25} - 7q^{26} + 7q^{27} - 6q^{28} - 7q^{29} + 3q^{30} - 22q^{31} + 5q^{32} - 4q^{33} + 9q^{34} + 3q^{35} + 5q^{36} - 25q^{37} + 14q^{38} - 18q^{39} - 10q^{40} - 13q^{41} - 2q^{42} - 2q^{43} + 4q^{44} - 3q^{45} - 3q^{46} - 25q^{47} - 7q^{48} - 8q^{49} + 19q^{50} - 3q^{51} - 12q^{52} - 5q^{53} - 3q^{54} - 15q^{55} + 18q^{56} - 4q^{57} + 3q^{58} + 11q^{59} - 2q^{60} - 33q^{61} + 28q^{62} - 5q^{63} - 14q^{64} - 2q^{65} - 26q^{66} + 8q^{67} + 12q^{68} + 7q^{69} - 22q^{70} - 6q^{71} - 6q^{72} + 15q^{73} + 34q^{74} - 8q^{75} - 28q^{76} - q^{77} - 7q^{78} - 15q^{79} - 12q^{80} + 7q^{81} - 14q^{82} + 21q^{83} - 6q^{84} - 28q^{85} - 12q^{86} - 7q^{87} - 13q^{88} + 8q^{89} + 3q^{90} + 6q^{91} + 5q^{92} - 22q^{93} - 35q^{94} - 25q^{95} + 5q^{96} + 13q^{97} + q^{98} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37349 −1.67831 −0.839154 0.543894i \(-0.816949\pi\)
−0.839154 + 0.543894i \(0.816949\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.63344 1.81672
\(5\) −1.31800 −0.589426 −0.294713 0.955586i \(-0.595224\pi\)
−0.294713 + 0.955586i \(0.595224\pi\)
\(6\) −2.37349 −0.968972
\(7\) −0.859291 −0.324781 −0.162391 0.986727i \(-0.551920\pi\)
−0.162391 + 0.986727i \(0.551920\pi\)
\(8\) −3.87694 −1.37070
\(9\) 1.00000 0.333333
\(10\) 3.12824 0.989238
\(11\) 4.30847 1.29905 0.649526 0.760339i \(-0.274967\pi\)
0.649526 + 0.760339i \(0.274967\pi\)
\(12\) 3.63344 1.04888
\(13\) −4.15542 −1.15251 −0.576253 0.817272i \(-0.695486\pi\)
−0.576253 + 0.817272i \(0.695486\pi\)
\(14\) 2.03951 0.545083
\(15\) −1.31800 −0.340305
\(16\) 1.93498 0.483746
\(17\) 2.08920 0.506706 0.253353 0.967374i \(-0.418467\pi\)
0.253353 + 0.967374i \(0.418467\pi\)
\(18\) −2.37349 −0.559436
\(19\) −2.45615 −0.563479 −0.281740 0.959491i \(-0.590911\pi\)
−0.281740 + 0.959491i \(0.590911\pi\)
\(20\) −4.78885 −1.07082
\(21\) −0.859291 −0.187513
\(22\) −10.2261 −2.18021
\(23\) 1.00000 0.208514
\(24\) −3.87694 −0.791376
\(25\) −3.26289 −0.652577
\(26\) 9.86283 1.93426
\(27\) 1.00000 0.192450
\(28\) −3.12218 −0.590036
\(29\) −1.00000 −0.185695
\(30\) 3.12824 0.571137
\(31\) −4.70746 −0.845484 −0.422742 0.906250i \(-0.638932\pi\)
−0.422742 + 0.906250i \(0.638932\pi\)
\(32\) 3.16122 0.558830
\(33\) 4.30847 0.750008
\(34\) −4.95870 −0.850409
\(35\) 1.13254 0.191434
\(36\) 3.63344 0.605573
\(37\) −3.94232 −0.648113 −0.324056 0.946038i \(-0.605047\pi\)
−0.324056 + 0.946038i \(0.605047\pi\)
\(38\) 5.82963 0.945692
\(39\) −4.15542 −0.665399
\(40\) 5.10979 0.807928
\(41\) −3.17442 −0.495762 −0.247881 0.968791i \(-0.579734\pi\)
−0.247881 + 0.968791i \(0.579734\pi\)
\(42\) 2.03951 0.314704
\(43\) 11.0153 1.67982 0.839909 0.542727i \(-0.182608\pi\)
0.839909 + 0.542727i \(0.182608\pi\)
\(44\) 15.6545 2.36001
\(45\) −1.31800 −0.196475
\(46\) −2.37349 −0.349951
\(47\) 11.1103 1.62061 0.810303 0.586012i \(-0.199303\pi\)
0.810303 + 0.586012i \(0.199303\pi\)
\(48\) 1.93498 0.279291
\(49\) −6.26162 −0.894517
\(50\) 7.74442 1.09523
\(51\) 2.08920 0.292547
\(52\) −15.0984 −2.09378
\(53\) −14.0165 −1.92531 −0.962657 0.270723i \(-0.912737\pi\)
−0.962657 + 0.270723i \(0.912737\pi\)
\(54\) −2.37349 −0.322991
\(55\) −5.67854 −0.765695
\(56\) 3.33142 0.445179
\(57\) −2.45615 −0.325325
\(58\) 2.37349 0.311654
\(59\) 8.47222 1.10299 0.551495 0.834178i \(-0.314058\pi\)
0.551495 + 0.834178i \(0.314058\pi\)
\(60\) −4.78885 −0.618238
\(61\) −6.39249 −0.818475 −0.409237 0.912428i \(-0.634205\pi\)
−0.409237 + 0.912428i \(0.634205\pi\)
\(62\) 11.1731 1.41898
\(63\) −0.859291 −0.108260
\(64\) −11.3731 −1.42163
\(65\) 5.47682 0.679316
\(66\) −10.2261 −1.25874
\(67\) 4.74715 0.579956 0.289978 0.957033i \(-0.406352\pi\)
0.289978 + 0.957033i \(0.406352\pi\)
\(68\) 7.59099 0.920542
\(69\) 1.00000 0.120386
\(70\) −2.68807 −0.321286
\(71\) −12.4909 −1.48240 −0.741201 0.671283i \(-0.765743\pi\)
−0.741201 + 0.671283i \(0.765743\pi\)
\(72\) −3.87694 −0.456901
\(73\) 8.54106 0.999655 0.499827 0.866125i \(-0.333397\pi\)
0.499827 + 0.866125i \(0.333397\pi\)
\(74\) 9.35703 1.08773
\(75\) −3.26289 −0.376766
\(76\) −8.92426 −1.02368
\(77\) −3.70223 −0.421908
\(78\) 9.86283 1.11675
\(79\) −13.0092 −1.46365 −0.731827 0.681491i \(-0.761332\pi\)
−0.731827 + 0.681491i \(0.761332\pi\)
\(80\) −2.55030 −0.285132
\(81\) 1.00000 0.111111
\(82\) 7.53445 0.832041
\(83\) −14.2415 −1.56321 −0.781606 0.623772i \(-0.785599\pi\)
−0.781606 + 0.623772i \(0.785599\pi\)
\(84\) −3.12218 −0.340657
\(85\) −2.75356 −0.298666
\(86\) −26.1447 −2.81925
\(87\) −1.00000 −0.107211
\(88\) −16.7037 −1.78062
\(89\) 0.795808 0.0843554 0.0421777 0.999110i \(-0.486570\pi\)
0.0421777 + 0.999110i \(0.486570\pi\)
\(90\) 3.12824 0.329746
\(91\) 3.57071 0.374312
\(92\) 3.63344 0.378812
\(93\) −4.70746 −0.488141
\(94\) −26.3702 −2.71988
\(95\) 3.23719 0.332129
\(96\) 3.16122 0.322640
\(97\) 3.92369 0.398390 0.199195 0.979960i \(-0.436167\pi\)
0.199195 + 0.979960i \(0.436167\pi\)
\(98\) 14.8619 1.50128
\(99\) 4.30847 0.433017
\(100\) −11.8555 −1.18555
\(101\) 3.90652 0.388713 0.194357 0.980931i \(-0.437738\pi\)
0.194357 + 0.980931i \(0.437738\pi\)
\(102\) −4.95870 −0.490984
\(103\) 1.68054 0.165589 0.0827944 0.996567i \(-0.473616\pi\)
0.0827944 + 0.996567i \(0.473616\pi\)
\(104\) 16.1103 1.57974
\(105\) 1.13254 0.110525
\(106\) 33.2680 3.23127
\(107\) 11.2977 1.09219 0.546096 0.837722i \(-0.316113\pi\)
0.546096 + 0.837722i \(0.316113\pi\)
\(108\) 3.63344 0.349627
\(109\) −17.5897 −1.68479 −0.842394 0.538863i \(-0.818854\pi\)
−0.842394 + 0.538863i \(0.818854\pi\)
\(110\) 13.4779 1.28507
\(111\) −3.94232 −0.374188
\(112\) −1.66271 −0.157112
\(113\) −3.98253 −0.374645 −0.187323 0.982298i \(-0.559981\pi\)
−0.187323 + 0.982298i \(0.559981\pi\)
\(114\) 5.82963 0.545995
\(115\) −1.31800 −0.122904
\(116\) −3.63344 −0.337356
\(117\) −4.15542 −0.384169
\(118\) −20.1087 −1.85116
\(119\) −1.79523 −0.164569
\(120\) 5.10979 0.466458
\(121\) 7.56290 0.687537
\(122\) 15.1725 1.37365
\(123\) −3.17442 −0.286228
\(124\) −17.1042 −1.53601
\(125\) 10.8905 0.974072
\(126\) 2.03951 0.181694
\(127\) 16.7386 1.48531 0.742654 0.669675i \(-0.233567\pi\)
0.742654 + 0.669675i \(0.233567\pi\)
\(128\) 20.6714 1.82711
\(129\) 11.0153 0.969844
\(130\) −12.9992 −1.14010
\(131\) −22.3630 −1.95386 −0.976930 0.213559i \(-0.931494\pi\)
−0.976930 + 0.213559i \(0.931494\pi\)
\(132\) 15.6545 1.36255
\(133\) 2.11055 0.183008
\(134\) −11.2673 −0.973345
\(135\) −1.31800 −0.113435
\(136\) −8.09971 −0.694544
\(137\) −12.8745 −1.09995 −0.549973 0.835182i \(-0.685362\pi\)
−0.549973 + 0.835182i \(0.685362\pi\)
\(138\) −2.37349 −0.202045
\(139\) 12.8067 1.08625 0.543123 0.839653i \(-0.317242\pi\)
0.543123 + 0.839653i \(0.317242\pi\)
\(140\) 4.11502 0.347782
\(141\) 11.1103 0.935657
\(142\) 29.6471 2.48793
\(143\) −17.9035 −1.49716
\(144\) 1.93498 0.161249
\(145\) 1.31800 0.109454
\(146\) −20.2721 −1.67773
\(147\) −6.26162 −0.516450
\(148\) −14.3242 −1.17744
\(149\) 11.7517 0.962740 0.481370 0.876518i \(-0.340139\pi\)
0.481370 + 0.876518i \(0.340139\pi\)
\(150\) 7.74442 0.632329
\(151\) −11.1096 −0.904086 −0.452043 0.891996i \(-0.649305\pi\)
−0.452043 + 0.891996i \(0.649305\pi\)
\(152\) 9.52233 0.772363
\(153\) 2.08920 0.168902
\(154\) 8.78718 0.708091
\(155\) 6.20441 0.498350
\(156\) −15.0984 −1.20884
\(157\) −19.4984 −1.55614 −0.778072 0.628175i \(-0.783802\pi\)
−0.778072 + 0.628175i \(0.783802\pi\)
\(158\) 30.8772 2.45646
\(159\) −14.0165 −1.11158
\(160\) −4.16647 −0.329389
\(161\) −0.859291 −0.0677216
\(162\) −2.37349 −0.186479
\(163\) 21.4125 1.67716 0.838579 0.544779i \(-0.183387\pi\)
0.838579 + 0.544779i \(0.183387\pi\)
\(164\) −11.5341 −0.900659
\(165\) −5.67854 −0.442074
\(166\) 33.8021 2.62355
\(167\) −3.76831 −0.291600 −0.145800 0.989314i \(-0.546576\pi\)
−0.145800 + 0.989314i \(0.546576\pi\)
\(168\) 3.33142 0.257024
\(169\) 4.26750 0.328269
\(170\) 6.53554 0.501253
\(171\) −2.45615 −0.187826
\(172\) 40.0234 3.05176
\(173\) 18.5637 1.41137 0.705686 0.708525i \(-0.250639\pi\)
0.705686 + 0.708525i \(0.250639\pi\)
\(174\) 2.37349 0.179934
\(175\) 2.80377 0.211945
\(176\) 8.33681 0.628411
\(177\) 8.47222 0.636811
\(178\) −1.88884 −0.141574
\(179\) −21.5082 −1.60760 −0.803798 0.594902i \(-0.797191\pi\)
−0.803798 + 0.594902i \(0.797191\pi\)
\(180\) −4.78885 −0.356940
\(181\) −12.8583 −0.955754 −0.477877 0.878427i \(-0.658593\pi\)
−0.477877 + 0.878427i \(0.658593\pi\)
\(182\) −8.47503 −0.628211
\(183\) −6.39249 −0.472547
\(184\) −3.87694 −0.285812
\(185\) 5.19596 0.382014
\(186\) 11.1731 0.819250
\(187\) 9.00127 0.658238
\(188\) 40.3686 2.94418
\(189\) −0.859291 −0.0625042
\(190\) −7.68344 −0.557415
\(191\) 1.67695 0.121340 0.0606700 0.998158i \(-0.480676\pi\)
0.0606700 + 0.998158i \(0.480676\pi\)
\(192\) −11.3731 −0.820781
\(193\) −13.8369 −0.996002 −0.498001 0.867177i \(-0.665932\pi\)
−0.498001 + 0.867177i \(0.665932\pi\)
\(194\) −9.31282 −0.668622
\(195\) 5.47682 0.392204
\(196\) −22.7512 −1.62509
\(197\) −27.8816 −1.98648 −0.993241 0.116074i \(-0.962969\pi\)
−0.993241 + 0.116074i \(0.962969\pi\)
\(198\) −10.2261 −0.726737
\(199\) −17.7635 −1.25922 −0.629609 0.776912i \(-0.716785\pi\)
−0.629609 + 0.776912i \(0.716785\pi\)
\(200\) 12.6500 0.894490
\(201\) 4.74715 0.334838
\(202\) −9.27207 −0.652380
\(203\) 0.859291 0.0603104
\(204\) 7.59099 0.531475
\(205\) 4.18388 0.292215
\(206\) −3.98875 −0.277909
\(207\) 1.00000 0.0695048
\(208\) −8.04066 −0.557520
\(209\) −10.5822 −0.731989
\(210\) −2.68807 −0.185495
\(211\) −21.7285 −1.49585 −0.747926 0.663783i \(-0.768950\pi\)
−0.747926 + 0.663783i \(0.768950\pi\)
\(212\) −50.9281 −3.49775
\(213\) −12.4909 −0.855865
\(214\) −26.8150 −1.83304
\(215\) −14.5181 −0.990128
\(216\) −3.87694 −0.263792
\(217\) 4.04507 0.274598
\(218\) 41.7489 2.82759
\(219\) 8.54106 0.577151
\(220\) −20.6326 −1.39105
\(221\) −8.68152 −0.583982
\(222\) 9.35703 0.628003
\(223\) −0.162927 −0.0109104 −0.00545520 0.999985i \(-0.501736\pi\)
−0.00545520 + 0.999985i \(0.501736\pi\)
\(224\) −2.71641 −0.181497
\(225\) −3.26289 −0.217526
\(226\) 9.45248 0.628770
\(227\) −14.9422 −0.991752 −0.495876 0.868393i \(-0.665153\pi\)
−0.495876 + 0.868393i \(0.665153\pi\)
\(228\) −8.92426 −0.591023
\(229\) −9.10145 −0.601441 −0.300720 0.953712i \(-0.597227\pi\)
−0.300720 + 0.953712i \(0.597227\pi\)
\(230\) 3.12824 0.206270
\(231\) −3.70223 −0.243589
\(232\) 3.87694 0.254533
\(233\) −12.6237 −0.827007 −0.413504 0.910502i \(-0.635695\pi\)
−0.413504 + 0.910502i \(0.635695\pi\)
\(234\) 9.86283 0.644753
\(235\) −14.6433 −0.955227
\(236\) 30.7833 2.00382
\(237\) −13.0092 −0.845041
\(238\) 4.26096 0.276197
\(239\) 16.8514 1.09003 0.545013 0.838428i \(-0.316525\pi\)
0.545013 + 0.838428i \(0.316525\pi\)
\(240\) −2.55030 −0.164621
\(241\) −17.4282 −1.12265 −0.561323 0.827597i \(-0.689708\pi\)
−0.561323 + 0.827597i \(0.689708\pi\)
\(242\) −17.9504 −1.15390
\(243\) 1.00000 0.0641500
\(244\) −23.2267 −1.48694
\(245\) 8.25279 0.527251
\(246\) 7.53445 0.480379
\(247\) 10.2063 0.649413
\(248\) 18.2505 1.15891
\(249\) −14.2415 −0.902521
\(250\) −25.8483 −1.63479
\(251\) 10.2885 0.649407 0.324703 0.945816i \(-0.394736\pi\)
0.324703 + 0.945816i \(0.394736\pi\)
\(252\) −3.12218 −0.196679
\(253\) 4.30847 0.270871
\(254\) −39.7288 −2.49280
\(255\) −2.75356 −0.172435
\(256\) −26.3171 −1.64482
\(257\) −5.27151 −0.328827 −0.164414 0.986391i \(-0.552573\pi\)
−0.164414 + 0.986391i \(0.552573\pi\)
\(258\) −26.1447 −1.62770
\(259\) 3.38760 0.210495
\(260\) 19.8997 1.23413
\(261\) −1.00000 −0.0618984
\(262\) 53.0782 3.27918
\(263\) −4.72941 −0.291628 −0.145814 0.989312i \(-0.546580\pi\)
−0.145814 + 0.989312i \(0.546580\pi\)
\(264\) −16.7037 −1.02804
\(265\) 18.4737 1.13483
\(266\) −5.00935 −0.307143
\(267\) 0.795808 0.0487026
\(268\) 17.2485 1.05362
\(269\) −21.2129 −1.29338 −0.646688 0.762754i \(-0.723846\pi\)
−0.646688 + 0.762754i \(0.723846\pi\)
\(270\) 3.12824 0.190379
\(271\) −11.0667 −0.672253 −0.336127 0.941817i \(-0.609117\pi\)
−0.336127 + 0.941817i \(0.609117\pi\)
\(272\) 4.04257 0.245117
\(273\) 3.57071 0.216109
\(274\) 30.5575 1.84605
\(275\) −14.0580 −0.847732
\(276\) 3.63344 0.218707
\(277\) −7.98577 −0.479818 −0.239909 0.970795i \(-0.577118\pi\)
−0.239909 + 0.970795i \(0.577118\pi\)
\(278\) −30.3964 −1.82306
\(279\) −4.70746 −0.281828
\(280\) −4.39079 −0.262400
\(281\) 6.63114 0.395581 0.197790 0.980244i \(-0.436623\pi\)
0.197790 + 0.980244i \(0.436623\pi\)
\(282\) −26.3702 −1.57032
\(283\) 2.98274 0.177306 0.0886528 0.996063i \(-0.471744\pi\)
0.0886528 + 0.996063i \(0.471744\pi\)
\(284\) −45.3850 −2.69311
\(285\) 3.23719 0.191755
\(286\) 42.4937 2.51270
\(287\) 2.72775 0.161014
\(288\) 3.16122 0.186277
\(289\) −12.6352 −0.743249
\(290\) −3.12824 −0.183697
\(291\) 3.92369 0.230011
\(292\) 31.0334 1.81609
\(293\) 13.4117 0.783521 0.391760 0.920067i \(-0.371866\pi\)
0.391760 + 0.920067i \(0.371866\pi\)
\(294\) 14.8619 0.866762
\(295\) −11.1664 −0.650130
\(296\) 15.2841 0.888371
\(297\) 4.30847 0.250003
\(298\) −27.8926 −1.61577
\(299\) −4.15542 −0.240314
\(300\) −11.8555 −0.684477
\(301\) −9.46535 −0.545574
\(302\) 26.3685 1.51734
\(303\) 3.90652 0.224424
\(304\) −4.75261 −0.272581
\(305\) 8.42528 0.482430
\(306\) −4.95870 −0.283470
\(307\) −7.23125 −0.412709 −0.206355 0.978477i \(-0.566160\pi\)
−0.206355 + 0.978477i \(0.566160\pi\)
\(308\) −13.4518 −0.766488
\(309\) 1.68054 0.0956028
\(310\) −14.7261 −0.836385
\(311\) 0.648787 0.0367894 0.0183947 0.999831i \(-0.494144\pi\)
0.0183947 + 0.999831i \(0.494144\pi\)
\(312\) 16.1103 0.912066
\(313\) 18.3081 1.03483 0.517416 0.855734i \(-0.326894\pi\)
0.517416 + 0.855734i \(0.326894\pi\)
\(314\) 46.2793 2.61169
\(315\) 1.13254 0.0638115
\(316\) −47.2682 −2.65905
\(317\) −21.4173 −1.20292 −0.601458 0.798904i \(-0.705413\pi\)
−0.601458 + 0.798904i \(0.705413\pi\)
\(318\) 33.2680 1.86558
\(319\) −4.30847 −0.241228
\(320\) 14.9897 0.837948
\(321\) 11.2977 0.630578
\(322\) 2.03951 0.113658
\(323\) −5.13140 −0.285518
\(324\) 3.63344 0.201858
\(325\) 13.5587 0.752099
\(326\) −50.8223 −2.81479
\(327\) −17.5897 −0.972712
\(328\) 12.3070 0.679542
\(329\) −9.54699 −0.526342
\(330\) 13.4779 0.741936
\(331\) 2.79629 0.153698 0.0768490 0.997043i \(-0.475514\pi\)
0.0768490 + 0.997043i \(0.475514\pi\)
\(332\) −51.7457 −2.83992
\(333\) −3.94232 −0.216038
\(334\) 8.94403 0.489395
\(335\) −6.25672 −0.341841
\(336\) −1.66271 −0.0907084
\(337\) −31.0998 −1.69411 −0.847057 0.531501i \(-0.821628\pi\)
−0.847057 + 0.531501i \(0.821628\pi\)
\(338\) −10.1288 −0.550937
\(339\) −3.98253 −0.216301
\(340\) −10.0049 −0.542591
\(341\) −20.2819 −1.09833
\(342\) 5.82963 0.315231
\(343\) 11.3956 0.615304
\(344\) −42.7056 −2.30253
\(345\) −1.31800 −0.0709585
\(346\) −44.0607 −2.36872
\(347\) 34.9752 1.87757 0.938785 0.344504i \(-0.111953\pi\)
0.938785 + 0.344504i \(0.111953\pi\)
\(348\) −3.63344 −0.194773
\(349\) 28.8052 1.54191 0.770953 0.636892i \(-0.219780\pi\)
0.770953 + 0.636892i \(0.219780\pi\)
\(350\) −6.65470 −0.355709
\(351\) −4.15542 −0.221800
\(352\) 13.6200 0.725949
\(353\) −11.5890 −0.616819 −0.308409 0.951254i \(-0.599797\pi\)
−0.308409 + 0.951254i \(0.599797\pi\)
\(354\) −20.1087 −1.06877
\(355\) 16.4630 0.873766
\(356\) 2.89152 0.153250
\(357\) −1.79523 −0.0950138
\(358\) 51.0493 2.69804
\(359\) 35.7439 1.88649 0.943246 0.332095i \(-0.107755\pi\)
0.943246 + 0.332095i \(0.107755\pi\)
\(360\) 5.10979 0.269309
\(361\) −12.9673 −0.682491
\(362\) 30.5191 1.60405
\(363\) 7.56290 0.396949
\(364\) 12.9740 0.680020
\(365\) −11.2571 −0.589222
\(366\) 15.1725 0.793079
\(367\) −27.4350 −1.43209 −0.716046 0.698053i \(-0.754050\pi\)
−0.716046 + 0.698053i \(0.754050\pi\)
\(368\) 1.93498 0.100868
\(369\) −3.17442 −0.165254
\(370\) −12.3325 −0.641138
\(371\) 12.0443 0.625306
\(372\) −17.1042 −0.886814
\(373\) 13.3266 0.690027 0.345013 0.938598i \(-0.387874\pi\)
0.345013 + 0.938598i \(0.387874\pi\)
\(374\) −21.3644 −1.10473
\(375\) 10.8905 0.562380
\(376\) −43.0740 −2.22137
\(377\) 4.15542 0.214015
\(378\) 2.03951 0.104901
\(379\) −5.84883 −0.300434 −0.150217 0.988653i \(-0.547997\pi\)
−0.150217 + 0.988653i \(0.547997\pi\)
\(380\) 11.7621 0.603385
\(381\) 16.7386 0.857543
\(382\) −3.98022 −0.203646
\(383\) 13.9417 0.712388 0.356194 0.934412i \(-0.384074\pi\)
0.356194 + 0.934412i \(0.384074\pi\)
\(384\) 20.6714 1.05488
\(385\) 4.87952 0.248683
\(386\) 32.8417 1.67160
\(387\) 11.0153 0.559940
\(388\) 14.2565 0.723763
\(389\) 24.2834 1.23122 0.615608 0.788052i \(-0.288910\pi\)
0.615608 + 0.788052i \(0.288910\pi\)
\(390\) −12.9992 −0.658238
\(391\) 2.08920 0.105656
\(392\) 24.2759 1.22612
\(393\) −22.3630 −1.12806
\(394\) 66.1766 3.33393
\(395\) 17.1461 0.862715
\(396\) 15.6545 0.786670
\(397\) −33.5680 −1.68473 −0.842364 0.538909i \(-0.818837\pi\)
−0.842364 + 0.538909i \(0.818837\pi\)
\(398\) 42.1613 2.11336
\(399\) 2.11055 0.105659
\(400\) −6.31363 −0.315681
\(401\) 16.7895 0.838426 0.419213 0.907888i \(-0.362306\pi\)
0.419213 + 0.907888i \(0.362306\pi\)
\(402\) −11.2673 −0.561961
\(403\) 19.5615 0.974425
\(404\) 14.1941 0.706182
\(405\) −1.31800 −0.0654917
\(406\) −2.03951 −0.101219
\(407\) −16.9854 −0.841933
\(408\) −8.09971 −0.400995
\(409\) 33.9540 1.67892 0.839458 0.543424i \(-0.182872\pi\)
0.839458 + 0.543424i \(0.182872\pi\)
\(410\) −9.93037 −0.490426
\(411\) −12.8745 −0.635054
\(412\) 6.10615 0.300828
\(413\) −7.28010 −0.358230
\(414\) −2.37349 −0.116650
\(415\) 18.7703 0.921398
\(416\) −13.1362 −0.644054
\(417\) 12.8067 0.627145
\(418\) 25.1168 1.22850
\(419\) 1.25305 0.0612157 0.0306079 0.999531i \(-0.490256\pi\)
0.0306079 + 0.999531i \(0.490256\pi\)
\(420\) 4.11502 0.200792
\(421\) 19.7566 0.962880 0.481440 0.876479i \(-0.340114\pi\)
0.481440 + 0.876479i \(0.340114\pi\)
\(422\) 51.5723 2.51050
\(423\) 11.1103 0.540202
\(424\) 54.3411 2.63904
\(425\) −6.81684 −0.330665
\(426\) 29.6471 1.43640
\(427\) 5.49301 0.265825
\(428\) 41.0496 1.98421
\(429\) −17.9035 −0.864389
\(430\) 34.4586 1.66174
\(431\) −28.0855 −1.35283 −0.676416 0.736520i \(-0.736468\pi\)
−0.676416 + 0.736520i \(0.736468\pi\)
\(432\) 1.93498 0.0930969
\(433\) −37.9606 −1.82427 −0.912135 0.409890i \(-0.865567\pi\)
−0.912135 + 0.409890i \(0.865567\pi\)
\(434\) −9.60093 −0.460859
\(435\) 1.31800 0.0631931
\(436\) −63.9110 −3.06078
\(437\) −2.45615 −0.117494
\(438\) −20.2721 −0.968637
\(439\) 33.0666 1.57818 0.789091 0.614277i \(-0.210552\pi\)
0.789091 + 0.614277i \(0.210552\pi\)
\(440\) 22.0154 1.04954
\(441\) −6.26162 −0.298172
\(442\) 20.6055 0.980101
\(443\) −4.67818 −0.222267 −0.111134 0.993805i \(-0.535448\pi\)
−0.111134 + 0.993805i \(0.535448\pi\)
\(444\) −14.3242 −0.679794
\(445\) −1.04887 −0.0497213
\(446\) 0.386705 0.0183110
\(447\) 11.7517 0.555838
\(448\) 9.77278 0.461720
\(449\) 0.0578209 0.00272873 0.00136437 0.999999i \(-0.499566\pi\)
0.00136437 + 0.999999i \(0.499566\pi\)
\(450\) 7.74442 0.365075
\(451\) −13.6769 −0.644020
\(452\) −14.4703 −0.680624
\(453\) −11.1096 −0.521974
\(454\) 35.4652 1.66446
\(455\) −4.70618 −0.220629
\(456\) 9.52233 0.445924
\(457\) −9.68884 −0.453225 −0.226612 0.973985i \(-0.572765\pi\)
−0.226612 + 0.973985i \(0.572765\pi\)
\(458\) 21.6022 1.00940
\(459\) 2.08920 0.0975157
\(460\) −4.78885 −0.223281
\(461\) 13.9639 0.650365 0.325182 0.945651i \(-0.394574\pi\)
0.325182 + 0.945651i \(0.394574\pi\)
\(462\) 8.78718 0.408817
\(463\) 31.3995 1.45926 0.729629 0.683844i \(-0.239693\pi\)
0.729629 + 0.683844i \(0.239693\pi\)
\(464\) −1.93498 −0.0898293
\(465\) 6.20441 0.287723
\(466\) 29.9622 1.38797
\(467\) −20.9278 −0.968422 −0.484211 0.874951i \(-0.660893\pi\)
−0.484211 + 0.874951i \(0.660893\pi\)
\(468\) −15.0984 −0.697926
\(469\) −4.07918 −0.188359
\(470\) 34.7558 1.60316
\(471\) −19.4984 −0.898440
\(472\) −32.8463 −1.51187
\(473\) 47.4591 2.18217
\(474\) 30.8772 1.41824
\(475\) 8.01414 0.367714
\(476\) −6.52286 −0.298975
\(477\) −14.0165 −0.641772
\(478\) −39.9965 −1.82940
\(479\) 41.1688 1.88105 0.940525 0.339724i \(-0.110334\pi\)
0.940525 + 0.339724i \(0.110334\pi\)
\(480\) −4.16647 −0.190173
\(481\) 16.3820 0.746954
\(482\) 41.3655 1.88415
\(483\) −0.859291 −0.0390991
\(484\) 27.4793 1.24906
\(485\) −5.17141 −0.234821
\(486\) −2.37349 −0.107664
\(487\) −16.7097 −0.757190 −0.378595 0.925562i \(-0.623593\pi\)
−0.378595 + 0.925562i \(0.623593\pi\)
\(488\) 24.7833 1.12189
\(489\) 21.4125 0.968308
\(490\) −19.5879 −0.884890
\(491\) 18.7578 0.846526 0.423263 0.906007i \(-0.360885\pi\)
0.423263 + 0.906007i \(0.360885\pi\)
\(492\) −11.5341 −0.519996
\(493\) −2.08920 −0.0940930
\(494\) −24.2246 −1.08991
\(495\) −5.67854 −0.255232
\(496\) −9.10885 −0.408999
\(497\) 10.7333 0.481456
\(498\) 33.8021 1.51471
\(499\) 4.60344 0.206078 0.103039 0.994677i \(-0.467143\pi\)
0.103039 + 0.994677i \(0.467143\pi\)
\(500\) 39.5698 1.76961
\(501\) −3.76831 −0.168356
\(502\) −24.4197 −1.08990
\(503\) −10.6369 −0.474276 −0.237138 0.971476i \(-0.576209\pi\)
−0.237138 + 0.971476i \(0.576209\pi\)
\(504\) 3.33142 0.148393
\(505\) −5.14878 −0.229117
\(506\) −10.2261 −0.454605
\(507\) 4.26750 0.189526
\(508\) 60.8185 2.69839
\(509\) 12.0067 0.532186 0.266093 0.963947i \(-0.414267\pi\)
0.266093 + 0.963947i \(0.414267\pi\)
\(510\) 6.53554 0.289399
\(511\) −7.33925 −0.324669
\(512\) 21.1205 0.933404
\(513\) −2.45615 −0.108442
\(514\) 12.5118 0.551874
\(515\) −2.21495 −0.0976023
\(516\) 40.0234 1.76193
\(517\) 47.8684 2.10525
\(518\) −8.04041 −0.353275
\(519\) 18.5637 0.814856
\(520\) −21.2333 −0.931142
\(521\) 11.2329 0.492123 0.246061 0.969254i \(-0.420864\pi\)
0.246061 + 0.969254i \(0.420864\pi\)
\(522\) 2.37349 0.103885
\(523\) −30.6342 −1.33954 −0.669770 0.742569i \(-0.733607\pi\)
−0.669770 + 0.742569i \(0.733607\pi\)
\(524\) −81.2544 −3.54961
\(525\) 2.80377 0.122366
\(526\) 11.2252 0.489442
\(527\) −9.83484 −0.428412
\(528\) 8.33681 0.362813
\(529\) 1.00000 0.0434783
\(530\) −43.8471 −1.90459
\(531\) 8.47222 0.367663
\(532\) 7.66853 0.332473
\(533\) 13.1911 0.571368
\(534\) −1.88884 −0.0817380
\(535\) −14.8904 −0.643766
\(536\) −18.4044 −0.794948
\(537\) −21.5082 −0.928146
\(538\) 50.3486 2.17068
\(539\) −26.9780 −1.16202
\(540\) −4.78885 −0.206079
\(541\) −24.1023 −1.03624 −0.518119 0.855308i \(-0.673368\pi\)
−0.518119 + 0.855308i \(0.673368\pi\)
\(542\) 26.2666 1.12825
\(543\) −12.8583 −0.551805
\(544\) 6.60443 0.283163
\(545\) 23.1831 0.993057
\(546\) −8.47503 −0.362698
\(547\) 13.8709 0.593075 0.296538 0.955021i \(-0.404168\pi\)
0.296538 + 0.955021i \(0.404168\pi\)
\(548\) −46.7788 −1.99829
\(549\) −6.39249 −0.272825
\(550\) 33.3666 1.42276
\(551\) 2.45615 0.104635
\(552\) −3.87694 −0.165013
\(553\) 11.1787 0.475367
\(554\) 18.9541 0.805283
\(555\) 5.19596 0.220556
\(556\) 46.5322 1.97340
\(557\) 33.6906 1.42752 0.713758 0.700392i \(-0.246991\pi\)
0.713758 + 0.700392i \(0.246991\pi\)
\(558\) 11.1731 0.472994
\(559\) −45.7732 −1.93600
\(560\) 2.19145 0.0926056
\(561\) 9.00127 0.380034
\(562\) −15.7389 −0.663906
\(563\) 41.3582 1.74304 0.871520 0.490360i \(-0.163135\pi\)
0.871520 + 0.490360i \(0.163135\pi\)
\(564\) 40.3686 1.69982
\(565\) 5.24896 0.220825
\(566\) −7.07949 −0.297573
\(567\) −0.859291 −0.0360868
\(568\) 48.4266 2.03193
\(569\) 14.0644 0.589612 0.294806 0.955557i \(-0.404745\pi\)
0.294806 + 0.955557i \(0.404745\pi\)
\(570\) −7.68344 −0.321824
\(571\) −5.85298 −0.244940 −0.122470 0.992472i \(-0.539081\pi\)
−0.122470 + 0.992472i \(0.539081\pi\)
\(572\) −65.0512 −2.71993
\(573\) 1.67695 0.0700556
\(574\) −6.47428 −0.270231
\(575\) −3.26289 −0.136072
\(576\) −11.3731 −0.473878
\(577\) −27.3870 −1.14014 −0.570069 0.821597i \(-0.693083\pi\)
−0.570069 + 0.821597i \(0.693083\pi\)
\(578\) 29.9895 1.24740
\(579\) −13.8369 −0.575042
\(580\) 4.78885 0.198846
\(581\) 12.2376 0.507702
\(582\) −9.31282 −0.386029
\(583\) −60.3897 −2.50108
\(584\) −33.1131 −1.37023
\(585\) 5.47682 0.226439
\(586\) −31.8325 −1.31499
\(587\) −45.3687 −1.87257 −0.936284 0.351245i \(-0.885758\pi\)
−0.936284 + 0.351245i \(0.885758\pi\)
\(588\) −22.7512 −0.938243
\(589\) 11.5622 0.476413
\(590\) 26.5032 1.09112
\(591\) −27.8816 −1.14690
\(592\) −7.62832 −0.313522
\(593\) 17.9412 0.736756 0.368378 0.929676i \(-0.379913\pi\)
0.368378 + 0.929676i \(0.379913\pi\)
\(594\) −10.2261 −0.419582
\(595\) 2.36611 0.0970011
\(596\) 42.6992 1.74903
\(597\) −17.7635 −0.727010
\(598\) 9.86283 0.403321
\(599\) −38.0747 −1.55569 −0.777845 0.628456i \(-0.783687\pi\)
−0.777845 + 0.628456i \(0.783687\pi\)
\(600\) 12.6500 0.516434
\(601\) −25.1262 −1.02492 −0.512461 0.858711i \(-0.671266\pi\)
−0.512461 + 0.858711i \(0.671266\pi\)
\(602\) 22.4659 0.915641
\(603\) 4.74715 0.193319
\(604\) −40.3660 −1.64247
\(605\) −9.96787 −0.405252
\(606\) −9.27207 −0.376652
\(607\) 19.6470 0.797447 0.398723 0.917071i \(-0.369453\pi\)
0.398723 + 0.917071i \(0.369453\pi\)
\(608\) −7.76442 −0.314889
\(609\) 0.859291 0.0348202
\(610\) −19.9973 −0.809666
\(611\) −46.1680 −1.86776
\(612\) 7.59099 0.306847
\(613\) 17.5314 0.708086 0.354043 0.935229i \(-0.384807\pi\)
0.354043 + 0.935229i \(0.384807\pi\)
\(614\) 17.1633 0.692653
\(615\) 4.18388 0.168710
\(616\) 14.3533 0.578311
\(617\) 28.1894 1.13486 0.567430 0.823421i \(-0.307938\pi\)
0.567430 + 0.823421i \(0.307938\pi\)
\(618\) −3.98875 −0.160451
\(619\) 12.6807 0.509680 0.254840 0.966983i \(-0.417977\pi\)
0.254840 + 0.966983i \(0.417977\pi\)
\(620\) 22.5433 0.905362
\(621\) 1.00000 0.0401286
\(622\) −1.53989 −0.0617439
\(623\) −0.683830 −0.0273971
\(624\) −8.04066 −0.321884
\(625\) 1.96086 0.0784345
\(626\) −43.4539 −1.73677
\(627\) −10.5822 −0.422614
\(628\) −70.8463 −2.82708
\(629\) −8.23630 −0.328403
\(630\) −2.68807 −0.107095
\(631\) 24.4176 0.972050 0.486025 0.873945i \(-0.338446\pi\)
0.486025 + 0.873945i \(0.338446\pi\)
\(632\) 50.4360 2.00624
\(633\) −21.7285 −0.863630
\(634\) 50.8337 2.01886
\(635\) −22.0614 −0.875479
\(636\) −50.9281 −2.01943
\(637\) 26.0196 1.03094
\(638\) 10.2261 0.404855
\(639\) −12.4909 −0.494134
\(640\) −27.2448 −1.07695
\(641\) −39.9966 −1.57977 −0.789886 0.613254i \(-0.789860\pi\)
−0.789886 + 0.613254i \(0.789860\pi\)
\(642\) −26.8150 −1.05830
\(643\) −21.9596 −0.866002 −0.433001 0.901393i \(-0.642545\pi\)
−0.433001 + 0.901393i \(0.642545\pi\)
\(644\) −3.12218 −0.123031
\(645\) −14.5181 −0.571651
\(646\) 12.1793 0.479188
\(647\) 5.75236 0.226149 0.113074 0.993587i \(-0.463930\pi\)
0.113074 + 0.993587i \(0.463930\pi\)
\(648\) −3.87694 −0.152300
\(649\) 36.5023 1.43284
\(650\) −32.1813 −1.26225
\(651\) 4.04507 0.158539
\(652\) 77.8010 3.04692
\(653\) −16.3800 −0.640998 −0.320499 0.947249i \(-0.603851\pi\)
−0.320499 + 0.947249i \(0.603851\pi\)
\(654\) 41.7489 1.63251
\(655\) 29.4743 1.15166
\(656\) −6.14245 −0.239823
\(657\) 8.54106 0.333218
\(658\) 22.6596 0.883365
\(659\) −7.33501 −0.285731 −0.142866 0.989742i \(-0.545632\pi\)
−0.142866 + 0.989742i \(0.545632\pi\)
\(660\) −20.6326 −0.803124
\(661\) 23.2593 0.904681 0.452340 0.891845i \(-0.350589\pi\)
0.452340 + 0.891845i \(0.350589\pi\)
\(662\) −6.63695 −0.257953
\(663\) −8.68152 −0.337162
\(664\) 55.2136 2.14270
\(665\) −2.78169 −0.107869
\(666\) 9.35703 0.362578
\(667\) −1.00000 −0.0387202
\(668\) −13.6919 −0.529756
\(669\) −0.162927 −0.00629913
\(670\) 14.8502 0.573715
\(671\) −27.5418 −1.06324
\(672\) −2.71641 −0.104788
\(673\) 28.8875 1.11353 0.556766 0.830670i \(-0.312042\pi\)
0.556766 + 0.830670i \(0.312042\pi\)
\(674\) 73.8150 2.84325
\(675\) −3.26289 −0.125589
\(676\) 15.5057 0.596372
\(677\) 27.0586 1.03995 0.519974 0.854182i \(-0.325942\pi\)
0.519974 + 0.854182i \(0.325942\pi\)
\(678\) 9.45248 0.363020
\(679\) −3.37159 −0.129390
\(680\) 10.6754 0.409382
\(681\) −14.9422 −0.572588
\(682\) 48.1389 1.84333
\(683\) 33.2775 1.27333 0.636664 0.771141i \(-0.280314\pi\)
0.636664 + 0.771141i \(0.280314\pi\)
\(684\) −8.92426 −0.341228
\(685\) 16.9686 0.648337
\(686\) −27.0473 −1.03267
\(687\) −9.10145 −0.347242
\(688\) 21.3144 0.812605
\(689\) 58.2444 2.21894
\(690\) 3.12824 0.119090
\(691\) 13.0933 0.498093 0.249046 0.968492i \(-0.419883\pi\)
0.249046 + 0.968492i \(0.419883\pi\)
\(692\) 67.4500 2.56406
\(693\) −3.70223 −0.140636
\(694\) −83.0133 −3.15114
\(695\) −16.8791 −0.640262
\(696\) 3.87694 0.146955
\(697\) −6.63202 −0.251206
\(698\) −68.3687 −2.58779
\(699\) −12.6237 −0.477473
\(700\) 10.1873 0.385044
\(701\) −5.48506 −0.207168 −0.103584 0.994621i \(-0.533031\pi\)
−0.103584 + 0.994621i \(0.533031\pi\)
\(702\) 9.86283 0.372248
\(703\) 9.68292 0.365198
\(704\) −49.0005 −1.84678
\(705\) −14.6433 −0.551500
\(706\) 27.5063 1.03521
\(707\) −3.35683 −0.126247
\(708\) 30.7833 1.15691
\(709\) 9.81311 0.368539 0.184270 0.982876i \(-0.441008\pi\)
0.184270 + 0.982876i \(0.441008\pi\)
\(710\) −39.0747 −1.46645
\(711\) −13.0092 −0.487885
\(712\) −3.08530 −0.115626
\(713\) −4.70746 −0.176296
\(714\) 4.26096 0.159462
\(715\) 23.5967 0.882467
\(716\) −78.1485 −2.92055
\(717\) 16.8514 0.629327
\(718\) −84.8377 −3.16611
\(719\) −24.9155 −0.929193 −0.464596 0.885522i \(-0.653801\pi\)
−0.464596 + 0.885522i \(0.653801\pi\)
\(720\) −2.55030 −0.0950440
\(721\) −1.44408 −0.0537802
\(722\) 30.7778 1.14543
\(723\) −17.4282 −0.648160
\(724\) −46.7200 −1.73633
\(725\) 3.26289 0.121181
\(726\) −17.9504 −0.666203
\(727\) 36.6602 1.35965 0.679825 0.733374i \(-0.262056\pi\)
0.679825 + 0.733374i \(0.262056\pi\)
\(728\) −13.8434 −0.513071
\(729\) 1.00000 0.0370370
\(730\) 26.7185 0.988897
\(731\) 23.0132 0.851175
\(732\) −23.2267 −0.858484
\(733\) 18.9303 0.699206 0.349603 0.936898i \(-0.386317\pi\)
0.349603 + 0.936898i \(0.386317\pi\)
\(734\) 65.1165 2.40349
\(735\) 8.25279 0.304409
\(736\) 3.16122 0.116524
\(737\) 20.4529 0.753393
\(738\) 7.53445 0.277347
\(739\) 8.84818 0.325485 0.162743 0.986669i \(-0.447966\pi\)
0.162743 + 0.986669i \(0.447966\pi\)
\(740\) 18.8792 0.694012
\(741\) 10.2063 0.374939
\(742\) −28.5869 −1.04946
\(743\) 4.67217 0.171405 0.0857026 0.996321i \(-0.472687\pi\)
0.0857026 + 0.996321i \(0.472687\pi\)
\(744\) 18.2505 0.669096
\(745\) −15.4887 −0.567464
\(746\) −31.6306 −1.15808
\(747\) −14.2415 −0.521071
\(748\) 32.7055 1.19583
\(749\) −9.70803 −0.354724
\(750\) −25.8483 −0.943848
\(751\) −23.8022 −0.868555 −0.434277 0.900779i \(-0.642996\pi\)
−0.434277 + 0.900779i \(0.642996\pi\)
\(752\) 21.4983 0.783961
\(753\) 10.2885 0.374935
\(754\) −9.86283 −0.359183
\(755\) 14.6424 0.532892
\(756\) −3.12218 −0.113552
\(757\) −0.980413 −0.0356337 −0.0178169 0.999841i \(-0.505672\pi\)
−0.0178169 + 0.999841i \(0.505672\pi\)
\(758\) 13.8821 0.504221
\(759\) 4.30847 0.156388
\(760\) −12.5504 −0.455251
\(761\) 28.6974 1.04028 0.520140 0.854081i \(-0.325880\pi\)
0.520140 + 0.854081i \(0.325880\pi\)
\(762\) −39.7288 −1.43922
\(763\) 15.1147 0.547187
\(764\) 6.09309 0.220440
\(765\) −2.75356 −0.0995553
\(766\) −33.0904 −1.19561
\(767\) −35.2056 −1.27120
\(768\) −26.3171 −0.949637
\(769\) 34.6389 1.24911 0.624556 0.780980i \(-0.285280\pi\)
0.624556 + 0.780980i \(0.285280\pi\)
\(770\) −11.5815 −0.417367
\(771\) −5.27151 −0.189849
\(772\) −50.2755 −1.80945
\(773\) 3.18514 0.114561 0.0572807 0.998358i \(-0.481757\pi\)
0.0572807 + 0.998358i \(0.481757\pi\)
\(774\) −26.1447 −0.939751
\(775\) 15.3599 0.551744
\(776\) −15.2119 −0.546075
\(777\) 3.38760 0.121529
\(778\) −57.6363 −2.06636
\(779\) 7.79686 0.279351
\(780\) 19.8997 0.712523
\(781\) −53.8168 −1.92572
\(782\) −4.95870 −0.177323
\(783\) −1.00000 −0.0357371
\(784\) −12.1161 −0.432719
\(785\) 25.6989 0.917232
\(786\) 53.0782 1.89324
\(787\) 47.6246 1.69764 0.848818 0.528686i \(-0.177315\pi\)
0.848818 + 0.528686i \(0.177315\pi\)
\(788\) −101.306 −3.60888
\(789\) −4.72941 −0.168371
\(790\) −40.6961 −1.44790
\(791\) 3.42215 0.121678
\(792\) −16.7037 −0.593539
\(793\) 26.5635 0.943297
\(794\) 79.6731 2.82749
\(795\) 18.4737 0.655194
\(796\) −64.5424 −2.28764
\(797\) 44.5050 1.57645 0.788223 0.615389i \(-0.211001\pi\)
0.788223 + 0.615389i \(0.211001\pi\)
\(798\) −5.00935 −0.177329
\(799\) 23.2117 0.821171
\(800\) −10.3147 −0.364680
\(801\) 0.795808 0.0281185
\(802\) −39.8496 −1.40714
\(803\) 36.7989 1.29860
\(804\) 17.2485 0.608306
\(805\) 1.13254 0.0399168
\(806\) −46.4288 −1.63539
\(807\) −21.2129 −0.746731
\(808\) −15.1453 −0.532811
\(809\) −34.0983 −1.19883 −0.599416 0.800438i \(-0.704600\pi\)
−0.599416 + 0.800438i \(0.704600\pi\)
\(810\) 3.12824 0.109915
\(811\) −10.5525 −0.370550 −0.185275 0.982687i \(-0.559318\pi\)
−0.185275 + 0.982687i \(0.559318\pi\)
\(812\) 3.12218 0.109567
\(813\) −11.0667 −0.388126
\(814\) 40.3145 1.41302
\(815\) −28.2216 −0.988561
\(816\) 4.04257 0.141518
\(817\) −27.0552 −0.946543
\(818\) −80.5893 −2.81774
\(819\) 3.57071 0.124771
\(820\) 15.2018 0.530872
\(821\) 30.2775 1.05669 0.528345 0.849030i \(-0.322813\pi\)
0.528345 + 0.849030i \(0.322813\pi\)
\(822\) 30.5575 1.06582
\(823\) −40.7346 −1.41992 −0.709960 0.704242i \(-0.751287\pi\)
−0.709960 + 0.704242i \(0.751287\pi\)
\(824\) −6.51536 −0.226973
\(825\) −14.0580 −0.489438
\(826\) 17.2792 0.601221
\(827\) 7.88557 0.274208 0.137104 0.990557i \(-0.456221\pi\)
0.137104 + 0.990557i \(0.456221\pi\)
\(828\) 3.63344 0.126271
\(829\) 8.87941 0.308395 0.154197 0.988040i \(-0.450721\pi\)
0.154197 + 0.988040i \(0.450721\pi\)
\(830\) −44.5510 −1.54639
\(831\) −7.98577 −0.277023
\(832\) 47.2599 1.63844
\(833\) −13.0818 −0.453257
\(834\) −30.3964 −1.05254
\(835\) 4.96662 0.171877
\(836\) −38.4499 −1.32982
\(837\) −4.70746 −0.162714
\(838\) −2.97411 −0.102739
\(839\) −0.405359 −0.0139946 −0.00699728 0.999976i \(-0.502227\pi\)
−0.00699728 + 0.999976i \(0.502227\pi\)
\(840\) −4.39079 −0.151497
\(841\) 1.00000 0.0344828
\(842\) −46.8921 −1.61601
\(843\) 6.63114 0.228389
\(844\) −78.9491 −2.71754
\(845\) −5.62455 −0.193490
\(846\) −26.3702 −0.906625
\(847\) −6.49873 −0.223299
\(848\) −27.1217 −0.931363
\(849\) 2.98274 0.102367
\(850\) 16.1797 0.554958
\(851\) −3.94232 −0.135141
\(852\) −45.3850 −1.55486
\(853\) 38.4556 1.31669 0.658347 0.752715i \(-0.271256\pi\)
0.658347 + 0.752715i \(0.271256\pi\)
\(854\) −13.0376 −0.446137
\(855\) 3.23719 0.110710
\(856\) −43.8006 −1.49707
\(857\) −4.08648 −0.139592 −0.0697958 0.997561i \(-0.522235\pi\)
−0.0697958 + 0.997561i \(0.522235\pi\)
\(858\) 42.4937 1.45071
\(859\) −26.7695 −0.913362 −0.456681 0.889631i \(-0.650962\pi\)
−0.456681 + 0.889631i \(0.650962\pi\)
\(860\) −52.7507 −1.79878
\(861\) 2.72775 0.0929615
\(862\) 66.6606 2.27047
\(863\) 26.1278 0.889402 0.444701 0.895679i \(-0.353310\pi\)
0.444701 + 0.895679i \(0.353310\pi\)
\(864\) 3.16122 0.107547
\(865\) −24.4669 −0.831899
\(866\) 90.0989 3.06169
\(867\) −12.6352 −0.429115
\(868\) 14.6975 0.498866
\(869\) −56.0499 −1.90136
\(870\) −3.12824 −0.106057
\(871\) −19.7264 −0.668403
\(872\) 68.1941 2.30934
\(873\) 3.92369 0.132797
\(874\) 5.82963 0.197190
\(875\) −9.35806 −0.316360
\(876\) 31.0334 1.04852
\(877\) −4.82414 −0.162900 −0.0814498 0.996677i \(-0.525955\pi\)
−0.0814498 + 0.996677i \(0.525955\pi\)
\(878\) −78.4831 −2.64867
\(879\) 13.4117 0.452366
\(880\) −10.9879 −0.370402
\(881\) −24.2045 −0.815469 −0.407734 0.913101i \(-0.633681\pi\)
−0.407734 + 0.913101i \(0.633681\pi\)
\(882\) 14.8619 0.500425
\(883\) 18.1602 0.611139 0.305570 0.952170i \(-0.401153\pi\)
0.305570 + 0.952170i \(0.401153\pi\)
\(884\) −31.5437 −1.06093
\(885\) −11.1664 −0.375353
\(886\) 11.1036 0.373033
\(887\) −40.7965 −1.36981 −0.684907 0.728630i \(-0.740157\pi\)
−0.684907 + 0.728630i \(0.740157\pi\)
\(888\) 15.2841 0.512901
\(889\) −14.3833 −0.482400
\(890\) 2.48948 0.0834476
\(891\) 4.30847 0.144339
\(892\) −0.591985 −0.0198211
\(893\) −27.2886 −0.913177
\(894\) −27.8926 −0.932867
\(895\) 28.3477 0.947558
\(896\) −17.7627 −0.593411
\(897\) −4.15542 −0.138745
\(898\) −0.137237 −0.00457966
\(899\) 4.70746 0.157002
\(900\) −11.8555 −0.395183
\(901\) −29.2833 −0.975569
\(902\) 32.4619 1.08086
\(903\) −9.46535 −0.314987
\(904\) 15.4400 0.513528
\(905\) 16.9473 0.563346
\(906\) 26.3685 0.876034
\(907\) 20.5919 0.683744 0.341872 0.939747i \(-0.388939\pi\)
0.341872 + 0.939747i \(0.388939\pi\)
\(908\) −54.2917 −1.80173
\(909\) 3.90652 0.129571
\(910\) 11.1701 0.370284
\(911\) 0.555205 0.0183948 0.00919738 0.999958i \(-0.497072\pi\)
0.00919738 + 0.999958i \(0.497072\pi\)
\(912\) −4.75261 −0.157374
\(913\) −61.3593 −2.03069
\(914\) 22.9963 0.760651
\(915\) 8.42528 0.278531
\(916\) −33.0695 −1.09265
\(917\) 19.2163 0.634577
\(918\) −4.95870 −0.163661
\(919\) 51.8269 1.70961 0.854805 0.518949i \(-0.173676\pi\)
0.854805 + 0.518949i \(0.173676\pi\)
\(920\) 5.10979 0.168465
\(921\) −7.23125 −0.238278
\(922\) −33.1432 −1.09151
\(923\) 51.9051 1.70848
\(924\) −13.4518 −0.442532
\(925\) 12.8633 0.422944
\(926\) −74.5262 −2.44908
\(927\) 1.68054 0.0551963
\(928\) −3.16122 −0.103772
\(929\) 24.3448 0.798727 0.399364 0.916793i \(-0.369231\pi\)
0.399364 + 0.916793i \(0.369231\pi\)
\(930\) −14.7261 −0.482887
\(931\) 15.3795 0.504042
\(932\) −45.8675 −1.50244
\(933\) 0.648787 0.0212403
\(934\) 49.6718 1.62531
\(935\) −11.8636 −0.387982
\(936\) 16.1103 0.526581
\(937\) 2.62171 0.0856475 0.0428237 0.999083i \(-0.486365\pi\)
0.0428237 + 0.999083i \(0.486365\pi\)
\(938\) 9.68187 0.316124
\(939\) 18.3081 0.597461
\(940\) −53.2057 −1.73538
\(941\) −27.1040 −0.883566 −0.441783 0.897122i \(-0.645654\pi\)
−0.441783 + 0.897122i \(0.645654\pi\)
\(942\) 46.2793 1.50786
\(943\) −3.17442 −0.103373
\(944\) 16.3936 0.533566
\(945\) 1.13254 0.0368416
\(946\) −112.644 −3.66236
\(947\) 1.67384 0.0543924 0.0271962 0.999630i \(-0.491342\pi\)
0.0271962 + 0.999630i \(0.491342\pi\)
\(948\) −47.2682 −1.53520
\(949\) −35.4917 −1.15211
\(950\) −19.0214 −0.617137
\(951\) −21.4173 −0.694504
\(952\) 6.96001 0.225575
\(953\) −39.1266 −1.26743 −0.633717 0.773565i \(-0.718472\pi\)
−0.633717 + 0.773565i \(0.718472\pi\)
\(954\) 33.2680 1.07709
\(955\) −2.21021 −0.0715209
\(956\) 61.2284 1.98027
\(957\) −4.30847 −0.139273
\(958\) −97.7136 −3.15698
\(959\) 11.0630 0.357242
\(960\) 14.9897 0.483789
\(961\) −8.83984 −0.285156
\(962\) −38.8824 −1.25362
\(963\) 11.2977 0.364064
\(964\) −63.3241 −2.03953
\(965\) 18.2370 0.587069
\(966\) 2.03951 0.0656203
\(967\) −46.2331 −1.48676 −0.743378 0.668872i \(-0.766777\pi\)
−0.743378 + 0.668872i \(0.766777\pi\)
\(968\) −29.3209 −0.942409
\(969\) −5.13140 −0.164844
\(970\) 12.2743 0.394103
\(971\) 39.1168 1.25532 0.627660 0.778488i \(-0.284013\pi\)
0.627660 + 0.778488i \(0.284013\pi\)
\(972\) 3.63344 0.116542
\(973\) −11.0046 −0.352793
\(974\) 39.6603 1.27080
\(975\) 13.5587 0.434225
\(976\) −12.3694 −0.395934
\(977\) −11.4002 −0.364725 −0.182363 0.983231i \(-0.558374\pi\)
−0.182363 + 0.983231i \(0.558374\pi\)
\(978\) −50.8223 −1.62512
\(979\) 3.42871 0.109582
\(980\) 29.9860 0.957867
\(981\) −17.5897 −0.561596
\(982\) −44.5213 −1.42073
\(983\) 47.4586 1.51369 0.756846 0.653593i \(-0.226739\pi\)
0.756846 + 0.653593i \(0.226739\pi\)
\(984\) 12.3070 0.392334
\(985\) 36.7478 1.17088
\(986\) 4.95870 0.157917
\(987\) −9.54699 −0.303884
\(988\) 37.0840 1.17980
\(989\) 11.0153 0.350266
\(990\) 13.4779 0.428357
\(991\) 52.3146 1.66183 0.830914 0.556401i \(-0.187818\pi\)
0.830914 + 0.556401i \(0.187818\pi\)
\(992\) −14.8813 −0.472482
\(993\) 2.79629 0.0887376
\(994\) −25.4754 −0.808032
\(995\) 23.4122 0.742215
\(996\) −51.7457 −1.63963
\(997\) −46.9541 −1.48705 −0.743525 0.668708i \(-0.766848\pi\)
−0.743525 + 0.668708i \(0.766848\pi\)
\(998\) −10.9262 −0.345863
\(999\) −3.94232 −0.124729
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 2001.2.a.i.1.1 7
3.2 odd 2 6003.2.a.j.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.i.1.1 7 1.1 even 1 trivial
6003.2.a.j.1.7 7 3.2 odd 2