Properties

Label 5290.2.a.q.1.2
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1509.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.551929\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.551929 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.551929 q^{6} -3.69537 q^{7} +1.00000 q^{8} -2.69537 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.551929 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.551929 q^{6} -3.69537 q^{7} +1.00000 q^{8} -2.69537 q^{9} +1.00000 q^{10} +1.44807 q^{11} -0.551929 q^{12} -5.69537 q^{13} -3.69537 q^{14} -0.551929 q^{15} +1.00000 q^{16} +4.55193 q^{17} -2.69537 q^{18} -6.79923 q^{19} +1.00000 q^{20} +2.03959 q^{21} +1.44807 q^{22} -0.551929 q^{24} +1.00000 q^{25} -5.69537 q^{26} +3.14344 q^{27} -3.69537 q^{28} +10.4946 q^{29} -0.551929 q^{30} -2.59152 q^{31} +1.00000 q^{32} -0.799233 q^{33} +4.55193 q^{34} -3.69537 q^{35} -2.69537 q^{36} +0.207718 q^{37} -6.79923 q^{38} +3.14344 q^{39} +1.00000 q^{40} +1.44807 q^{41} +2.03959 q^{42} +10.4946 q^{43} +1.44807 q^{44} -2.69537 q^{45} -10.2869 q^{47} -0.551929 q^{48} +6.65579 q^{49} +1.00000 q^{50} -2.51234 q^{51} -5.69537 q^{52} +13.3907 q^{53} +3.14344 q^{54} +1.44807 q^{55} -3.69537 q^{56} +3.75270 q^{57} +10.4946 q^{58} +4.49461 q^{59} -0.551929 q^{60} +11.7350 q^{61} -2.59152 q^{62} +9.96041 q^{63} +1.00000 q^{64} -5.69537 q^{65} -0.799233 q^{66} -3.10386 q^{67} +4.55193 q^{68} -3.69537 q^{70} -4.55193 q^{71} -2.69537 q^{72} +2.49461 q^{73} +0.207718 q^{74} -0.551929 q^{75} -6.79923 q^{76} -5.35116 q^{77} +3.14344 q^{78} +10.2869 q^{79} +1.00000 q^{80} +6.35116 q^{81} +1.44807 q^{82} +7.59847 q^{83} +2.03959 q^{84} +4.55193 q^{85} +10.4946 q^{86} -5.79228 q^{87} +1.44807 q^{88} -7.39075 q^{89} -2.69537 q^{90} +21.0465 q^{91} +1.43033 q^{93} -10.2869 q^{94} -6.79923 q^{95} -0.551929 q^{96} -10.3442 q^{97} +6.65579 q^{98} -3.90309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99} + O(q^{100}) \)

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
\(3\) −0.551929 −0.318657 −0.159328 0.987226i \(-0.550933\pi\)
−0.159328 + 0.987226i \(0.550933\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −0.551929 −0.225324
\(7\) −3.69537 −1.39672 −0.698360 0.715747i \(-0.746087\pi\)
−0.698360 + 0.715747i \(0.746087\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.69537 −0.898458
\(10\) 1.00000 0.316228
\(11\) 1.44807 0.436610 0.218305 0.975881i \(-0.429947\pi\)
0.218305 + 0.975881i \(0.429947\pi\)
\(12\) −0.551929 −0.159328
\(13\) −5.69537 −1.57961 −0.789806 0.613356i \(-0.789819\pi\)
−0.789806 + 0.613356i \(0.789819\pi\)
\(14\) −3.69537 −0.987630
\(15\) −0.551929 −0.142508
\(16\) 1.00000 0.250000
\(17\) 4.55193 1.10401 0.552003 0.833842i \(-0.313864\pi\)
0.552003 + 0.833842i \(0.313864\pi\)
\(18\) −2.69537 −0.635306
\(19\) −6.79923 −1.55985 −0.779925 0.625872i \(-0.784743\pi\)
−0.779925 + 0.625872i \(0.784743\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.03959 0.445074
\(22\) 1.44807 0.308730
\(23\) 0 0
\(24\) −0.551929 −0.112662
\(25\) 1.00000 0.200000
\(26\) −5.69537 −1.11695
\(27\) 3.14344 0.604956
\(28\) −3.69537 −0.698360
\(29\) 10.4946 1.94880 0.974400 0.224822i \(-0.0721802\pi\)
0.974400 + 0.224822i \(0.0721802\pi\)
\(30\) −0.551929 −0.100768
\(31\) −2.59152 −0.465450 −0.232725 0.972543i \(-0.574764\pi\)
−0.232725 + 0.972543i \(0.574764\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.799233 −0.139129
\(34\) 4.55193 0.780649
\(35\) −3.69537 −0.624632
\(36\) −2.69537 −0.449229
\(37\) 0.207718 0.0341486 0.0170743 0.999854i \(-0.494565\pi\)
0.0170743 + 0.999854i \(0.494565\pi\)
\(38\) −6.79923 −1.10298
\(39\) 3.14344 0.503354
\(40\) 1.00000 0.158114
\(41\) 1.44807 0.226151 0.113075 0.993586i \(-0.463930\pi\)
0.113075 + 0.993586i \(0.463930\pi\)
\(42\) 2.03959 0.314715
\(43\) 10.4946 1.60041 0.800206 0.599725i \(-0.204723\pi\)
0.800206 + 0.599725i \(0.204723\pi\)
\(44\) 1.44807 0.218305
\(45\) −2.69537 −0.401803
\(46\) 0 0
\(47\) −10.2869 −1.50050 −0.750248 0.661156i \(-0.770066\pi\)
−0.750248 + 0.661156i \(0.770066\pi\)
\(48\) −0.551929 −0.0796642
\(49\) 6.65579 0.950827
\(50\) 1.00000 0.141421
\(51\) −2.51234 −0.351799
\(52\) −5.69537 −0.789806
\(53\) 13.3907 1.83936 0.919680 0.392668i \(-0.128448\pi\)
0.919680 + 0.392668i \(0.128448\pi\)
\(54\) 3.14344 0.427769
\(55\) 1.44807 0.195258
\(56\) −3.69537 −0.493815
\(57\) 3.75270 0.497057
\(58\) 10.4946 1.37801
\(59\) 4.49461 0.585148 0.292574 0.956243i \(-0.405488\pi\)
0.292574 + 0.956243i \(0.405488\pi\)
\(60\) −0.551929 −0.0712538
\(61\) 11.7350 1.50251 0.751254 0.660013i \(-0.229449\pi\)
0.751254 + 0.660013i \(0.229449\pi\)
\(62\) −2.59152 −0.329123
\(63\) 9.96041 1.25489
\(64\) 1.00000 0.125000
\(65\) −5.69537 −0.706424
\(66\) −0.799233 −0.0983788
\(67\) −3.10386 −0.379197 −0.189598 0.981862i \(-0.560719\pi\)
−0.189598 + 0.981862i \(0.560719\pi\)
\(68\) 4.55193 0.552003
\(69\) 0 0
\(70\) −3.69537 −0.441682
\(71\) −4.55193 −0.540215 −0.270107 0.962830i \(-0.587059\pi\)
−0.270107 + 0.962830i \(0.587059\pi\)
\(72\) −2.69537 −0.317653
\(73\) 2.49461 0.291972 0.145986 0.989287i \(-0.453365\pi\)
0.145986 + 0.989287i \(0.453365\pi\)
\(74\) 0.207718 0.0241467
\(75\) −0.551929 −0.0637313
\(76\) −6.79923 −0.779925
\(77\) −5.35116 −0.609822
\(78\) 3.14344 0.355925
\(79\) 10.2869 1.15737 0.578683 0.815553i \(-0.303567\pi\)
0.578683 + 0.815553i \(0.303567\pi\)
\(80\) 1.00000 0.111803
\(81\) 6.35116 0.705685
\(82\) 1.44807 0.159913
\(83\) 7.59847 0.834040 0.417020 0.908897i \(-0.363075\pi\)
0.417020 + 0.908897i \(0.363075\pi\)
\(84\) 2.03959 0.222537
\(85\) 4.55193 0.493726
\(86\) 10.4946 1.13166
\(87\) −5.79228 −0.620998
\(88\) 1.44807 0.154365
\(89\) −7.39075 −0.783418 −0.391709 0.920089i \(-0.628116\pi\)
−0.391709 + 0.920089i \(0.628116\pi\)
\(90\) −2.69537 −0.284117
\(91\) 21.0465 2.20628
\(92\) 0 0
\(93\) 1.43033 0.148319
\(94\) −10.2869 −1.06101
\(95\) −6.79923 −0.697587
\(96\) −0.551929 −0.0563311
\(97\) −10.3442 −1.05030 −0.525148 0.851011i \(-0.675990\pi\)
−0.525148 + 0.851011i \(0.675990\pi\)
\(98\) 6.65579 0.672336
\(99\) −3.90309 −0.392275
\(100\) 1.00000 0.100000
\(101\) 0.207718 0.0206687 0.0103343 0.999947i \(-0.496710\pi\)
0.0103343 + 0.999947i \(0.496710\pi\)
\(102\) −2.51234 −0.248759
\(103\) 8.63110 0.850448 0.425224 0.905088i \(-0.360195\pi\)
0.425224 + 0.905088i \(0.360195\pi\)
\(104\) −5.69537 −0.558477
\(105\) 2.03959 0.199043
\(106\) 13.3907 1.30062
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 3.14344 0.302478
\(109\) 18.7992 1.80064 0.900320 0.435229i \(-0.143332\pi\)
0.900320 + 0.435229i \(0.143332\pi\)
\(110\) 1.44807 0.138068
\(111\) −0.114646 −0.0108817
\(112\) −3.69537 −0.349180
\(113\) −4.49461 −0.422817 −0.211409 0.977398i \(-0.567805\pi\)
−0.211409 + 0.977398i \(0.567805\pi\)
\(114\) 3.75270 0.351472
\(115\) 0 0
\(116\) 10.4946 0.974400
\(117\) 15.3512 1.41922
\(118\) 4.49461 0.413762
\(119\) −16.8211 −1.54199
\(120\) −0.551929 −0.0503840
\(121\) −8.90309 −0.809372
\(122\) 11.7350 1.06243
\(123\) −0.799233 −0.0720644
\(124\) −2.59152 −0.232725
\(125\) 1.00000 0.0894427
\(126\) 9.96041 0.887344
\(127\) −15.8062 −1.40257 −0.701286 0.712880i \(-0.747390\pi\)
−0.701286 + 0.712880i \(0.747390\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.79228 −0.509982
\(130\) −5.69537 −0.499517
\(131\) −6.20772 −0.542371 −0.271185 0.962527i \(-0.587416\pi\)
−0.271185 + 0.962527i \(0.587416\pi\)
\(132\) −0.799233 −0.0695643
\(133\) 25.1257 2.17868
\(134\) −3.10386 −0.268133
\(135\) 3.14344 0.270545
\(136\) 4.55193 0.390325
\(137\) 17.2938 1.47751 0.738756 0.673973i \(-0.235413\pi\)
0.738756 + 0.673973i \(0.235413\pi\)
\(138\) 0 0
\(139\) 10.8961 0.924199 0.462099 0.886828i \(-0.347096\pi\)
0.462099 + 0.886828i \(0.347096\pi\)
\(140\) −3.69537 −0.312316
\(141\) 5.67764 0.478143
\(142\) −4.55193 −0.381989
\(143\) −8.24730 −0.689674
\(144\) −2.69537 −0.224614
\(145\) 10.4946 0.871530
\(146\) 2.49461 0.206455
\(147\) −3.67353 −0.302987
\(148\) 0.207718 0.0170743
\(149\) 5.20077 0.426063 0.213032 0.977045i \(-0.431666\pi\)
0.213032 + 0.977045i \(0.431666\pi\)
\(150\) −0.551929 −0.0450648
\(151\) 15.4481 1.25715 0.628573 0.777751i \(-0.283639\pi\)
0.628573 + 0.777751i \(0.283639\pi\)
\(152\) −6.79923 −0.551491
\(153\) −12.2692 −0.991902
\(154\) −5.35116 −0.431209
\(155\) −2.59152 −0.208155
\(156\) 3.14344 0.251677
\(157\) −8.89614 −0.709989 −0.354995 0.934868i \(-0.615517\pi\)
−0.354995 + 0.934868i \(0.615517\pi\)
\(158\) 10.2869 0.818381
\(159\) −7.39075 −0.586124
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 6.35116 0.498994
\(163\) 12.1900 0.954793 0.477396 0.878688i \(-0.341581\pi\)
0.477396 + 0.878688i \(0.341581\pi\)
\(164\) 1.44807 0.113075
\(165\) −0.799233 −0.0622202
\(166\) 7.59847 0.589755
\(167\) −13.5985 −1.05228 −0.526140 0.850398i \(-0.676361\pi\)
−0.526140 + 0.850398i \(0.676361\pi\)
\(168\) 2.03959 0.157357
\(169\) 19.4373 1.49518
\(170\) 4.55193 0.349117
\(171\) 18.3265 1.40146
\(172\) 10.4946 0.800206
\(173\) 1.44807 0.110095 0.0550474 0.998484i \(-0.482469\pi\)
0.0550474 + 0.998484i \(0.482469\pi\)
\(174\) −5.79228 −0.439112
\(175\) −3.69537 −0.279344
\(176\) 1.44807 0.109152
\(177\) −2.48071 −0.186461
\(178\) −7.39075 −0.553960
\(179\) −19.3907 −1.44933 −0.724666 0.689100i \(-0.758006\pi\)
−0.724666 + 0.689100i \(0.758006\pi\)
\(180\) −2.69537 −0.200901
\(181\) −14.1900 −1.05473 −0.527366 0.849638i \(-0.676821\pi\)
−0.527366 + 0.849638i \(0.676821\pi\)
\(182\) 21.0465 1.56007
\(183\) −6.47687 −0.478784
\(184\) 0 0
\(185\) 0.207718 0.0152717
\(186\) 1.43033 0.104877
\(187\) 6.59152 0.482019
\(188\) −10.2869 −0.750248
\(189\) −11.6162 −0.844954
\(190\) −6.79923 −0.493268
\(191\) 4.60925 0.333514 0.166757 0.985998i \(-0.446670\pi\)
0.166757 + 0.985998i \(0.446670\pi\)
\(192\) −0.551929 −0.0398321
\(193\) −0.896141 −0.0645057 −0.0322528 0.999480i \(-0.510268\pi\)
−0.0322528 + 0.999480i \(0.510268\pi\)
\(194\) −10.3442 −0.742671
\(195\) 3.14344 0.225107
\(196\) 6.65579 0.475413
\(197\) −7.65579 −0.545452 −0.272726 0.962092i \(-0.587925\pi\)
−0.272726 + 0.962092i \(0.587925\pi\)
\(198\) −3.90309 −0.277381
\(199\) 6.20772 0.440053 0.220027 0.975494i \(-0.429386\pi\)
0.220027 + 0.975494i \(0.429386\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.71311 0.120834
\(202\) 0.207718 0.0146150
\(203\) −38.7815 −2.72193
\(204\) −2.51234 −0.175899
\(205\) 1.44807 0.101138
\(206\) 8.63110 0.601357
\(207\) 0 0
\(208\) −5.69537 −0.394903
\(209\) −9.84577 −0.681046
\(210\) 2.03959 0.140745
\(211\) 17.1830 1.18293 0.591464 0.806331i \(-0.298550\pi\)
0.591464 + 0.806331i \(0.298550\pi\)
\(212\) 13.3907 0.919680
\(213\) 2.51234 0.172143
\(214\) 6.00000 0.410152
\(215\) 10.4946 0.715726
\(216\) 3.14344 0.213884
\(217\) 9.57662 0.650103
\(218\) 18.7992 1.27324
\(219\) −1.37685 −0.0930387
\(220\) 1.44807 0.0976289
\(221\) −25.9249 −1.74390
\(222\) −0.114646 −0.00769450
\(223\) −15.8854 −1.06376 −0.531881 0.846819i \(-0.678515\pi\)
−0.531881 + 0.846819i \(0.678515\pi\)
\(224\) −3.69537 −0.246908
\(225\) −2.69537 −0.179692
\(226\) −4.49461 −0.298977
\(227\) −19.1830 −1.27322 −0.636611 0.771185i \(-0.719664\pi\)
−0.636611 + 0.771185i \(0.719664\pi\)
\(228\) 3.75270 0.248528
\(229\) 12.2077 0.806709 0.403354 0.915044i \(-0.367844\pi\)
0.403354 + 0.915044i \(0.367844\pi\)
\(230\) 0 0
\(231\) 2.95346 0.194324
\(232\) 10.4946 0.689005
\(233\) 3.10386 0.203341 0.101670 0.994818i \(-0.467581\pi\)
0.101670 + 0.994818i \(0.467581\pi\)
\(234\) 15.3512 1.00354
\(235\) −10.2869 −0.671043
\(236\) 4.49461 0.292574
\(237\) −5.67764 −0.368802
\(238\) −16.8211 −1.09035
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −0.551929 −0.0356269
\(241\) −6.20772 −0.399874 −0.199937 0.979809i \(-0.564074\pi\)
−0.199937 + 0.979809i \(0.564074\pi\)
\(242\) −8.90309 −0.572312
\(243\) −12.9357 −0.829827
\(244\) 11.7350 0.751254
\(245\) 6.65579 0.425223
\(246\) −0.799233 −0.0509572
\(247\) 38.7242 2.46396
\(248\) −2.59152 −0.164561
\(249\) −4.19382 −0.265772
\(250\) 1.00000 0.0632456
\(251\) 27.7884 1.75399 0.876996 0.480498i \(-0.159544\pi\)
0.876996 + 0.480498i \(0.159544\pi\)
\(252\) 9.96041 0.627447
\(253\) 0 0
\(254\) −15.8062 −0.991768
\(255\) −2.51234 −0.157329
\(256\) 1.00000 0.0625000
\(257\) −12.0931 −0.754345 −0.377173 0.926143i \(-0.623104\pi\)
−0.377173 + 0.926143i \(0.623104\pi\)
\(258\) −5.79228 −0.360612
\(259\) −0.767595 −0.0476960
\(260\) −5.69537 −0.353212
\(261\) −28.2869 −1.75091
\(262\) −6.20772 −0.383514
\(263\) −2.83882 −0.175049 −0.0875245 0.996162i \(-0.527896\pi\)
−0.0875245 + 0.996162i \(0.527896\pi\)
\(264\) −0.799233 −0.0491894
\(265\) 13.3907 0.822587
\(266\) 25.1257 1.54056
\(267\) 4.07917 0.249641
\(268\) −3.10386 −0.189598
\(269\) −9.31158 −0.567737 −0.283868 0.958863i \(-0.591618\pi\)
−0.283868 + 0.958863i \(0.591618\pi\)
\(270\) 3.14344 0.191304
\(271\) −3.00695 −0.182659 −0.0913296 0.995821i \(-0.529112\pi\)
−0.0913296 + 0.995821i \(0.529112\pi\)
\(272\) 4.55193 0.276001
\(273\) −11.6162 −0.703045
\(274\) 17.2938 1.04476
\(275\) 1.44807 0.0873219
\(276\) 0 0
\(277\) 25.1969 1.51394 0.756968 0.653451i \(-0.226680\pi\)
0.756968 + 0.653451i \(0.226680\pi\)
\(278\) 10.8961 0.653507
\(279\) 6.98510 0.418187
\(280\) −3.69537 −0.220841
\(281\) −4.07917 −0.243343 −0.121671 0.992570i \(-0.538825\pi\)
−0.121671 + 0.992570i \(0.538825\pi\)
\(282\) 5.67764 0.338098
\(283\) 10.4946 0.623840 0.311920 0.950108i \(-0.399028\pi\)
0.311920 + 0.950108i \(0.399028\pi\)
\(284\) −4.55193 −0.270107
\(285\) 3.75270 0.222291
\(286\) −8.24730 −0.487673
\(287\) −5.35116 −0.315869
\(288\) −2.69537 −0.158826
\(289\) 3.72006 0.218827
\(290\) 10.4946 0.616265
\(291\) 5.70927 0.334684
\(292\) 2.49461 0.145986
\(293\) −6.41544 −0.374794 −0.187397 0.982284i \(-0.560005\pi\)
−0.187397 + 0.982284i \(0.560005\pi\)
\(294\) −3.67353 −0.214244
\(295\) 4.49461 0.261686
\(296\) 0.207718 0.0120733
\(297\) 4.55193 0.264130
\(298\) 5.20077 0.301272
\(299\) 0 0
\(300\) −0.551929 −0.0318657
\(301\) −38.7815 −2.23533
\(302\) 15.4481 0.888937
\(303\) −0.114646 −0.00658621
\(304\) −6.79923 −0.389963
\(305\) 11.7350 0.671942
\(306\) −12.2692 −0.701381
\(307\) −3.86351 −0.220502 −0.110251 0.993904i \(-0.535165\pi\)
−0.110251 + 0.993904i \(0.535165\pi\)
\(308\) −5.35116 −0.304911
\(309\) −4.76376 −0.271001
\(310\) −2.59152 −0.147188
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 3.14344 0.177962
\(313\) −17.2938 −0.977506 −0.488753 0.872422i \(-0.662548\pi\)
−0.488753 + 0.872422i \(0.662548\pi\)
\(314\) −8.89614 −0.502038
\(315\) 9.96041 0.561206
\(316\) 10.2869 0.578683
\(317\) −15.4877 −0.869873 −0.434937 0.900461i \(-0.643229\pi\)
−0.434937 + 0.900461i \(0.643229\pi\)
\(318\) −7.39075 −0.414453
\(319\) 15.1969 0.850865
\(320\) 1.00000 0.0559017
\(321\) −3.31158 −0.184834
\(322\) 0 0
\(323\) −30.9496 −1.72208
\(324\) 6.35116 0.352842
\(325\) −5.69537 −0.315923
\(326\) 12.1900 0.675141
\(327\) −10.3758 −0.573786
\(328\) 1.44807 0.0799563
\(329\) 38.0139 2.09577
\(330\) −0.799233 −0.0439963
\(331\) 11.3907 0.626092 0.313046 0.949738i \(-0.398651\pi\)
0.313046 + 0.949738i \(0.398651\pi\)
\(332\) 7.59847 0.417020
\(333\) −0.559877 −0.0306811
\(334\) −13.5985 −0.744075
\(335\) −3.10386 −0.169582
\(336\) 2.03959 0.111269
\(337\) 2.09691 0.114226 0.0571129 0.998368i \(-0.481810\pi\)
0.0571129 + 0.998368i \(0.481810\pi\)
\(338\) 19.4373 1.05725
\(339\) 2.48071 0.134733
\(340\) 4.55193 0.246863
\(341\) −3.75270 −0.203220
\(342\) 18.3265 0.990982
\(343\) 1.27199 0.0686811
\(344\) 10.4946 0.565831
\(345\) 0 0
\(346\) 1.44807 0.0778488
\(347\) −13.1257 −0.704625 −0.352312 0.935882i \(-0.614605\pi\)
−0.352312 + 0.935882i \(0.614605\pi\)
\(348\) −5.79228 −0.310499
\(349\) 18.3800 0.983857 0.491928 0.870636i \(-0.336292\pi\)
0.491928 + 0.870636i \(0.336292\pi\)
\(350\) −3.69537 −0.197526
\(351\) −17.9031 −0.955596
\(352\) 1.44807 0.0771824
\(353\) 28.1722 1.49946 0.749729 0.661745i \(-0.230184\pi\)
0.749729 + 0.661745i \(0.230184\pi\)
\(354\) −2.48071 −0.131848
\(355\) −4.55193 −0.241591
\(356\) −7.39075 −0.391709
\(357\) 9.28405 0.491364
\(358\) −19.3907 −1.02483
\(359\) 16.0792 0.848626 0.424313 0.905516i \(-0.360516\pi\)
0.424313 + 0.905516i \(0.360516\pi\)
\(360\) −2.69537 −0.142059
\(361\) 27.2296 1.43314
\(362\) −14.1900 −0.745809
\(363\) 4.91388 0.257912
\(364\) 21.0465 1.10314
\(365\) 2.49461 0.130574
\(366\) −6.47687 −0.338551
\(367\) −15.1969 −0.793273 −0.396637 0.917976i \(-0.629823\pi\)
−0.396637 + 0.917976i \(0.629823\pi\)
\(368\) 0 0
\(369\) −3.90309 −0.203187
\(370\) 0.207718 0.0107987
\(371\) −49.4838 −2.56907
\(372\) 1.43033 0.0741593
\(373\) −25.3907 −1.31468 −0.657342 0.753593i \(-0.728319\pi\)
−0.657342 + 0.753593i \(0.728319\pi\)
\(374\) 6.59152 0.340839
\(375\) −0.551929 −0.0285015
\(376\) −10.2869 −0.530506
\(377\) −59.7707 −3.07835
\(378\) −11.6162 −0.597473
\(379\) −25.4481 −1.30718 −0.653590 0.756849i \(-0.726738\pi\)
−0.653590 + 0.756849i \(0.726738\pi\)
\(380\) −6.79923 −0.348793
\(381\) 8.72390 0.446939
\(382\) 4.60925 0.235830
\(383\) 20.5738 1.05127 0.525635 0.850710i \(-0.323828\pi\)
0.525635 + 0.850710i \(0.323828\pi\)
\(384\) −0.551929 −0.0281655
\(385\) −5.35116 −0.272720
\(386\) −0.896141 −0.0456124
\(387\) −28.2869 −1.43790
\(388\) −10.3442 −0.525148
\(389\) 26.6311 1.35025 0.675125 0.737703i \(-0.264090\pi\)
0.675125 + 0.737703i \(0.264090\pi\)
\(390\) 3.14344 0.159174
\(391\) 0 0
\(392\) 6.65579 0.336168
\(393\) 3.42622 0.172830
\(394\) −7.65579 −0.385693
\(395\) 10.2869 0.517590
\(396\) −3.90309 −0.196138
\(397\) 27.1257 1.36140 0.680700 0.732562i \(-0.261676\pi\)
0.680700 + 0.732562i \(0.261676\pi\)
\(398\) 6.20772 0.311165
\(399\) −13.8676 −0.694249
\(400\) 1.00000 0.0500000
\(401\) 26.0139 1.29907 0.649536 0.760331i \(-0.274963\pi\)
0.649536 + 0.760331i \(0.274963\pi\)
\(402\) 1.71311 0.0854422
\(403\) 14.7596 0.735230
\(404\) 0.207718 0.0103343
\(405\) 6.35116 0.315592
\(406\) −38.7815 −1.92469
\(407\) 0.300790 0.0149096
\(408\) −2.51234 −0.124380
\(409\) −7.48766 −0.370241 −0.185120 0.982716i \(-0.559268\pi\)
−0.185120 + 0.982716i \(0.559268\pi\)
\(410\) 1.44807 0.0715151
\(411\) −9.54498 −0.470819
\(412\) 8.63110 0.425224
\(413\) −16.6093 −0.817288
\(414\) 0 0
\(415\) 7.59847 0.372994
\(416\) −5.69537 −0.279239
\(417\) −6.01390 −0.294502
\(418\) −9.84577 −0.481572
\(419\) −4.28689 −0.209428 −0.104714 0.994502i \(-0.533393\pi\)
−0.104714 + 0.994502i \(0.533393\pi\)
\(420\) 2.03959 0.0995216
\(421\) 33.9962 1.65687 0.828436 0.560084i \(-0.189231\pi\)
0.828436 + 0.560084i \(0.189231\pi\)
\(422\) 17.1830 0.836457
\(423\) 27.7270 1.34813
\(424\) 13.3907 0.650312
\(425\) 4.55193 0.220801
\(426\) 2.51234 0.121723
\(427\) −43.3651 −2.09858
\(428\) 6.00000 0.290021
\(429\) 4.55193 0.219769
\(430\) 10.4946 0.506095
\(431\) 17.7923 0.857024 0.428512 0.903536i \(-0.359038\pi\)
0.428512 + 0.903536i \(0.359038\pi\)
\(432\) 3.14344 0.151239
\(433\) 2.51234 0.120736 0.0603678 0.998176i \(-0.480773\pi\)
0.0603678 + 0.998176i \(0.480773\pi\)
\(434\) 9.57662 0.459692
\(435\) −5.79228 −0.277719
\(436\) 18.7992 0.900320
\(437\) 0 0
\(438\) −1.37685 −0.0657883
\(439\) 36.7638 1.75464 0.877319 0.479907i \(-0.159330\pi\)
0.877319 + 0.479907i \(0.159330\pi\)
\(440\) 1.44807 0.0690341
\(441\) −17.9398 −0.854278
\(442\) −25.9249 −1.23312
\(443\) 0.383797 0.0182348 0.00911738 0.999958i \(-0.497098\pi\)
0.00911738 + 0.999958i \(0.497098\pi\)
\(444\) −0.114646 −0.00544084
\(445\) −7.39075 −0.350355
\(446\) −15.8854 −0.752193
\(447\) −2.87046 −0.135768
\(448\) −3.69537 −0.174590
\(449\) −28.6707 −1.35305 −0.676527 0.736418i \(-0.736516\pi\)
−0.676527 + 0.736418i \(0.736516\pi\)
\(450\) −2.69537 −0.127061
\(451\) 2.09691 0.0987396
\(452\) −4.49461 −0.211409
\(453\) −8.52624 −0.400598
\(454\) −19.1830 −0.900304
\(455\) 21.0465 0.986677
\(456\) 3.75270 0.175736
\(457\) 1.71311 0.0801360 0.0400680 0.999197i \(-0.487243\pi\)
0.0400680 + 0.999197i \(0.487243\pi\)
\(458\) 12.2077 0.570429
\(459\) 14.3087 0.667875
\(460\) 0 0
\(461\) 10.6093 0.494122 0.247061 0.969000i \(-0.420535\pi\)
0.247061 + 0.969000i \(0.420535\pi\)
\(462\) 2.95346 0.137408
\(463\) −26.1722 −1.21633 −0.608164 0.793812i \(-0.708094\pi\)
−0.608164 + 0.793812i \(0.708094\pi\)
\(464\) 10.4946 0.487200
\(465\) 1.43033 0.0663301
\(466\) 3.10386 0.143783
\(467\) 7.59847 0.351615 0.175808 0.984425i \(-0.443746\pi\)
0.175808 + 0.984425i \(0.443746\pi\)
\(468\) 15.3512 0.709608
\(469\) 11.4699 0.529632
\(470\) −10.2869 −0.474499
\(471\) 4.91004 0.226243
\(472\) 4.49461 0.206881
\(473\) 15.1969 0.698756
\(474\) −5.67764 −0.260782
\(475\) −6.79923 −0.311970
\(476\) −16.8211 −0.770993
\(477\) −36.0931 −1.65259
\(478\) 12.0000 0.548867
\(479\) −10.8170 −0.494240 −0.247120 0.968985i \(-0.579484\pi\)
−0.247120 + 0.968985i \(0.579484\pi\)
\(480\) −0.551929 −0.0251920
\(481\) −1.18303 −0.0539415
\(482\) −6.20772 −0.282754
\(483\) 0 0
\(484\) −8.90309 −0.404686
\(485\) −10.3442 −0.469706
\(486\) −12.9357 −0.586776
\(487\) 3.39075 0.153649 0.0768247 0.997045i \(-0.475522\pi\)
0.0768247 + 0.997045i \(0.475522\pi\)
\(488\) 11.7350 0.531217
\(489\) −6.72801 −0.304251
\(490\) 6.65579 0.300678
\(491\) −4.60925 −0.208013 −0.104006 0.994577i \(-0.533166\pi\)
−0.104006 + 0.994577i \(0.533166\pi\)
\(492\) −0.799233 −0.0360322
\(493\) 47.7707 2.15148
\(494\) 38.7242 1.74228
\(495\) −3.90309 −0.175431
\(496\) −2.59152 −0.116362
\(497\) 16.8211 0.754529
\(498\) −4.19382 −0.187929
\(499\) −6.70232 −0.300037 −0.150019 0.988683i \(-0.547933\pi\)
−0.150019 + 0.988683i \(0.547933\pi\)
\(500\) 1.00000 0.0447214
\(501\) 7.50539 0.335316
\(502\) 27.7884 1.24026
\(503\) −30.0614 −1.34037 −0.670187 0.742193i \(-0.733786\pi\)
−0.670187 + 0.742193i \(0.733786\pi\)
\(504\) 9.96041 0.443672
\(505\) 0.207718 0.00924332
\(506\) 0 0
\(507\) −10.7280 −0.476448
\(508\) −15.8062 −0.701286
\(509\) 30.3008 1.34306 0.671529 0.740978i \(-0.265638\pi\)
0.671529 + 0.740978i \(0.265638\pi\)
\(510\) −2.51234 −0.111248
\(511\) −9.21850 −0.407803
\(512\) 1.00000 0.0441942
\(513\) −21.3730 −0.943641
\(514\) −12.0931 −0.533403
\(515\) 8.63110 0.380332
\(516\) −5.79228 −0.254991
\(517\) −14.8961 −0.655132
\(518\) −0.767595 −0.0337262
\(519\) −0.799233 −0.0350824
\(520\) −5.69537 −0.249759
\(521\) 21.8715 0.958206 0.479103 0.877759i \(-0.340962\pi\)
0.479103 + 0.877759i \(0.340962\pi\)
\(522\) −28.2869 −1.23808
\(523\) 13.3907 0.585537 0.292768 0.956183i \(-0.405424\pi\)
0.292768 + 0.956183i \(0.405424\pi\)
\(524\) −6.20772 −0.271185
\(525\) 2.03959 0.0890148
\(526\) −2.83882 −0.123778
\(527\) −11.7964 −0.513859
\(528\) −0.799233 −0.0347821
\(529\) 0 0
\(530\) 13.3907 0.581657
\(531\) −12.1146 −0.525731
\(532\) 25.1257 1.08934
\(533\) −8.24730 −0.357230
\(534\) 4.07917 0.176523
\(535\) 6.00000 0.259403
\(536\) −3.10386 −0.134066
\(537\) 10.7023 0.461839
\(538\) −9.31158 −0.401451
\(539\) 9.63805 0.415140
\(540\) 3.14344 0.135272
\(541\) 3.71311 0.159639 0.0798196 0.996809i \(-0.474566\pi\)
0.0798196 + 0.996809i \(0.474566\pi\)
\(542\) −3.00695 −0.129160
\(543\) 7.83187 0.336098
\(544\) 4.55193 0.195162
\(545\) 18.7992 0.805271
\(546\) −11.6162 −0.497128
\(547\) −33.9823 −1.45298 −0.726488 0.687179i \(-0.758849\pi\)
−0.726488 + 0.687179i \(0.758849\pi\)
\(548\) 17.2938 0.738756
\(549\) −31.6301 −1.34994
\(550\) 1.44807 0.0617459
\(551\) −71.3553 −3.03984
\(552\) 0 0
\(553\) −38.0139 −1.61652
\(554\) 25.1969 1.07052
\(555\) −0.114646 −0.00486643
\(556\) 10.8961 0.462099
\(557\) 39.4046 1.66963 0.834814 0.550532i \(-0.185575\pi\)
0.834814 + 0.550532i \(0.185575\pi\)
\(558\) 6.98510 0.295703
\(559\) −59.7707 −2.52803
\(560\) −3.69537 −0.156158
\(561\) −3.63805 −0.153599
\(562\) −4.07917 −0.172069
\(563\) −12.6232 −0.532002 −0.266001 0.963973i \(-0.585703\pi\)
−0.266001 + 0.963973i \(0.585703\pi\)
\(564\) 5.67764 0.239072
\(565\) −4.49461 −0.189090
\(566\) 10.4946 0.441121
\(567\) −23.4699 −0.985644
\(568\) −4.55193 −0.190995
\(569\) 6.09307 0.255435 0.127717 0.991811i \(-0.459235\pi\)
0.127717 + 0.991811i \(0.459235\pi\)
\(570\) 3.75270 0.157183
\(571\) −13.7489 −0.575372 −0.287686 0.957725i \(-0.592886\pi\)
−0.287686 + 0.957725i \(0.592886\pi\)
\(572\) −8.24730 −0.344837
\(573\) −2.54398 −0.106276
\(574\) −5.35116 −0.223353
\(575\) 0 0
\(576\) −2.69537 −0.112307
\(577\) 15.1830 0.632078 0.316039 0.948746i \(-0.397647\pi\)
0.316039 + 0.948746i \(0.397647\pi\)
\(578\) 3.72006 0.154734
\(579\) 0.494607 0.0205552
\(580\) 10.4946 0.435765
\(581\) −28.0792 −1.16492
\(582\) 5.70927 0.236657
\(583\) 19.3907 0.803083
\(584\) 2.49461 0.103228
\(585\) 15.3512 0.634692
\(586\) −6.41544 −0.265019
\(587\) −7.33343 −0.302683 −0.151341 0.988482i \(-0.548359\pi\)
−0.151341 + 0.988482i \(0.548359\pi\)
\(588\) −3.67353 −0.151494
\(589\) 17.6203 0.726032
\(590\) 4.49461 0.185040
\(591\) 4.22545 0.173812
\(592\) 0.207718 0.00853715
\(593\) −2.98921 −0.122752 −0.0613761 0.998115i \(-0.519549\pi\)
−0.0613761 + 0.998115i \(0.519549\pi\)
\(594\) 4.55193 0.186768
\(595\) −16.8211 −0.689597
\(596\) 5.20077 0.213032
\(597\) −3.42622 −0.140226
\(598\) 0 0
\(599\) −13.2404 −0.540986 −0.270493 0.962722i \(-0.587187\pi\)
−0.270493 + 0.962722i \(0.587187\pi\)
\(600\) −0.551929 −0.0225324
\(601\) 1.08612 0.0443038 0.0221519 0.999755i \(-0.492948\pi\)
0.0221519 + 0.999755i \(0.492948\pi\)
\(602\) −38.7815 −1.58062
\(603\) 8.36606 0.340692
\(604\) 15.4481 0.628573
\(605\) −8.90309 −0.361962
\(606\) −0.114646 −0.00465716
\(607\) −14.4015 −0.584540 −0.292270 0.956336i \(-0.594411\pi\)
−0.292270 + 0.956336i \(0.594411\pi\)
\(608\) −6.79923 −0.275745
\(609\) 21.4046 0.867360
\(610\) 11.7350 0.475135
\(611\) 58.5877 2.37020
\(612\) −12.2692 −0.495951
\(613\) 10.4946 0.423873 0.211937 0.977283i \(-0.432023\pi\)
0.211937 + 0.977283i \(0.432023\pi\)
\(614\) −3.86351 −0.155918
\(615\) −0.799233 −0.0322282
\(616\) −5.35116 −0.215604
\(617\) −16.4373 −0.661740 −0.330870 0.943676i \(-0.607342\pi\)
−0.330870 + 0.943676i \(0.607342\pi\)
\(618\) −4.76376 −0.191626
\(619\) −22.9930 −0.924169 −0.462084 0.886836i \(-0.652898\pi\)
−0.462084 + 0.886836i \(0.652898\pi\)
\(620\) −2.59152 −0.104078
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 27.3116 1.09422
\(624\) 3.14344 0.125838
\(625\) 1.00000 0.0400000
\(626\) −17.2938 −0.691201
\(627\) 5.43417 0.217020
\(628\) −8.89614 −0.354995
\(629\) 0.945516 0.0377002
\(630\) 9.96041 0.396832
\(631\) −23.8854 −0.950861 −0.475430 0.879753i \(-0.657708\pi\)
−0.475430 + 0.879753i \(0.657708\pi\)
\(632\) 10.2869 0.409190
\(633\) −9.48382 −0.376948
\(634\) −15.4877 −0.615093
\(635\) −15.8062 −0.627249
\(636\) −7.39075 −0.293062
\(637\) −37.9072 −1.50194
\(638\) 15.1969 0.601652
\(639\) 12.2692 0.485360
\(640\) 1.00000 0.0395285
\(641\) 26.6669 1.05328 0.526639 0.850089i \(-0.323452\pi\)
0.526639 + 0.850089i \(0.323452\pi\)
\(642\) −3.31158 −0.130698
\(643\) 38.4591 1.51668 0.758340 0.651859i \(-0.226011\pi\)
0.758340 + 0.651859i \(0.226011\pi\)
\(644\) 0 0
\(645\) −5.79228 −0.228071
\(646\) −30.9496 −1.21770
\(647\) 44.4591 1.74787 0.873934 0.486044i \(-0.161560\pi\)
0.873934 + 0.486044i \(0.161560\pi\)
\(648\) 6.35116 0.249497
\(649\) 6.50851 0.255481
\(650\) −5.69537 −0.223391
\(651\) −5.28562 −0.207160
\(652\) 12.1900 0.477396
\(653\) 35.2938 1.38115 0.690577 0.723259i \(-0.257357\pi\)
0.690577 + 0.723259i \(0.257357\pi\)
\(654\) −10.3758 −0.405728
\(655\) −6.20772 −0.242556
\(656\) 1.44807 0.0565377
\(657\) −6.72390 −0.262324
\(658\) 38.0139 1.48194
\(659\) −46.2653 −1.80224 −0.901120 0.433569i \(-0.857254\pi\)
−0.901120 + 0.433569i \(0.857254\pi\)
\(660\) −0.799233 −0.0311101
\(661\) −36.0357 −1.40163 −0.700814 0.713344i \(-0.747180\pi\)
−0.700814 + 0.713344i \(0.747180\pi\)
\(662\) 11.3907 0.442714
\(663\) 14.3087 0.555705
\(664\) 7.59847 0.294878
\(665\) 25.1257 0.974333
\(666\) −0.559877 −0.0216948
\(667\) 0 0
\(668\) −13.5985 −0.526140
\(669\) 8.76759 0.338975
\(670\) −3.10386 −0.119913
\(671\) 16.9930 0.656009
\(672\) 2.03959 0.0786787
\(673\) 15.2622 0.588315 0.294157 0.955757i \(-0.404961\pi\)
0.294157 + 0.955757i \(0.404961\pi\)
\(674\) 2.09691 0.0807699
\(675\) 3.14344 0.120991
\(676\) 19.4373 0.747588
\(677\) 24.8607 0.955473 0.477737 0.878503i \(-0.341457\pi\)
0.477737 + 0.878503i \(0.341457\pi\)
\(678\) 2.48071 0.0952709
\(679\) 38.2257 1.46697
\(680\) 4.55193 0.174559
\(681\) 10.5877 0.405721
\(682\) −3.75270 −0.143698
\(683\) 38.3977 1.46925 0.734624 0.678475i \(-0.237359\pi\)
0.734624 + 0.678475i \(0.237359\pi\)
\(684\) 18.3265 0.700730
\(685\) 17.2938 0.660764
\(686\) 1.27199 0.0485648
\(687\) −6.73780 −0.257063
\(688\) 10.4946 0.400103
\(689\) −76.2653 −2.90548
\(690\) 0 0
\(691\) 37.7568 1.43634 0.718168 0.695869i \(-0.244981\pi\)
0.718168 + 0.695869i \(0.244981\pi\)
\(692\) 1.44807 0.0550474
\(693\) 14.4234 0.547899
\(694\) −13.1257 −0.498245
\(695\) 10.8961 0.413314
\(696\) −5.79228 −0.219556
\(697\) 6.59152 0.249671
\(698\) 18.3800 0.695692
\(699\) −1.71311 −0.0647958
\(700\) −3.69537 −0.139672
\(701\) 26.1900 0.989182 0.494591 0.869126i \(-0.335318\pi\)
0.494591 + 0.869126i \(0.335318\pi\)
\(702\) −17.9031 −0.675709
\(703\) −1.41232 −0.0532667
\(704\) 1.44807 0.0545762
\(705\) 5.67764 0.213832
\(706\) 28.1722 1.06028
\(707\) −0.767595 −0.0288684
\(708\) −2.48071 −0.0932306
\(709\) −29.7134 −1.11591 −0.557955 0.829871i \(-0.688414\pi\)
−0.557955 + 0.829871i \(0.688414\pi\)
\(710\) −4.55193 −0.170831
\(711\) −27.7270 −1.03984
\(712\) −7.39075 −0.276980
\(713\) 0 0
\(714\) 9.28405 0.347447
\(715\) −8.24730 −0.308432
\(716\) −19.3907 −0.724666
\(717\) −6.62315 −0.247346
\(718\) 16.0792 0.600069
\(719\) −31.7745 −1.18499 −0.592495 0.805574i \(-0.701857\pi\)
−0.592495 + 0.805574i \(0.701857\pi\)
\(720\) −2.69537 −0.100451
\(721\) −31.8951 −1.18784
\(722\) 27.2296 1.01338
\(723\) 3.42622 0.127423
\(724\) −14.1900 −0.527366
\(725\) 10.4946 0.389760
\(726\) 4.91388 0.182371
\(727\) −8.93189 −0.331265 −0.165633 0.986188i \(-0.552967\pi\)
−0.165633 + 0.986188i \(0.552967\pi\)
\(728\) 21.0465 0.780037
\(729\) −11.9139 −0.441255
\(730\) 2.49461 0.0923295
\(731\) 47.7707 1.76686
\(732\) −6.47687 −0.239392
\(733\) 24.9753 0.922484 0.461242 0.887274i \(-0.347404\pi\)
0.461242 + 0.887274i \(0.347404\pi\)
\(734\) −15.1969 −0.560929
\(735\) −3.67353 −0.135500
\(736\) 0 0
\(737\) −4.49461 −0.165561
\(738\) −3.90309 −0.143675
\(739\) 43.8854 1.61435 0.807174 0.590313i \(-0.200996\pi\)
0.807174 + 0.590313i \(0.200996\pi\)
\(740\) 0.207718 0.00763586
\(741\) −21.3730 −0.785157
\(742\) −49.4838 −1.81661
\(743\) −18.8923 −0.693091 −0.346546 0.938033i \(-0.612645\pi\)
−0.346546 + 0.938033i \(0.612645\pi\)
\(744\) 1.43033 0.0524386
\(745\) 5.20077 0.190541
\(746\) −25.3907 −0.929621
\(747\) −20.4807 −0.749350
\(748\) 6.59152 0.241010
\(749\) −22.1722 −0.810156
\(750\) −0.551929 −0.0201536
\(751\) −1.59847 −0.0583288 −0.0291644 0.999575i \(-0.509285\pi\)
−0.0291644 + 0.999575i \(0.509285\pi\)
\(752\) −10.2869 −0.375124
\(753\) −15.3373 −0.558921
\(754\) −59.7707 −2.17672
\(755\) 15.4481 0.562213
\(756\) −11.6162 −0.422477
\(757\) −13.3907 −0.486695 −0.243348 0.969939i \(-0.578246\pi\)
−0.243348 + 0.969939i \(0.578246\pi\)
\(758\) −25.4481 −0.924316
\(759\) 0 0
\(760\) −6.79923 −0.246634
\(761\) −21.2799 −0.771397 −0.385699 0.922625i \(-0.626040\pi\)
−0.385699 + 0.922625i \(0.626040\pi\)
\(762\) 8.72390 0.316033
\(763\) −69.4702 −2.51499
\(764\) 4.60925 0.166757
\(765\) −12.2692 −0.443592
\(766\) 20.5738 0.743361
\(767\) −25.5985 −0.924307
\(768\) −0.551929 −0.0199160
\(769\) 6.20772 0.223856 0.111928 0.993716i \(-0.464297\pi\)
0.111928 + 0.993716i \(0.464297\pi\)
\(770\) −5.35116 −0.192842
\(771\) 6.67452 0.240377
\(772\) −0.896141 −0.0322528
\(773\) −17.4699 −0.628349 −0.314175 0.949365i \(-0.601728\pi\)
−0.314175 + 0.949365i \(0.601728\pi\)
\(774\) −28.2869 −1.01675
\(775\) −2.59152 −0.0930900
\(776\) −10.3442 −0.371336
\(777\) 0.423658 0.0151986
\(778\) 26.6311 0.954771
\(779\) −9.84577 −0.352761
\(780\) 3.14344 0.112553
\(781\) −6.59152 −0.235863
\(782\) 0 0
\(783\) 32.9892 1.17894
\(784\) 6.65579 0.237707
\(785\) −8.89614 −0.317517
\(786\) 3.42622 0.122209
\(787\) −50.4591 −1.79867 −0.899337 0.437256i \(-0.855950\pi\)
−0.899337 + 0.437256i \(0.855950\pi\)
\(788\) −7.65579 −0.272726
\(789\) 1.56683 0.0557805
\(790\) 10.2869 0.365991
\(791\) 16.6093 0.590557
\(792\) −3.90309 −0.138690
\(793\) −66.8350 −2.37338
\(794\) 27.1257 0.962655
\(795\) −7.39075 −0.262123
\(796\) 6.20772 0.220027
\(797\) 43.5985 1.54434 0.772168 0.635418i \(-0.219172\pi\)
0.772168 + 0.635418i \(0.219172\pi\)
\(798\) −13.8676 −0.490908
\(799\) −46.8252 −1.65656
\(800\) 1.00000 0.0353553
\(801\) 19.9208 0.703868
\(802\) 26.0139 0.918583
\(803\) 3.61237 0.127478
\(804\) 1.71311 0.0604168
\(805\) 0 0
\(806\) 14.7596 0.519886
\(807\) 5.13933 0.180913
\(808\) 0.207718 0.00730748
\(809\) 7.12571 0.250527 0.125263 0.992124i \(-0.460022\pi\)
0.125263 + 0.992124i \(0.460022\pi\)
\(810\) 6.35116 0.223157
\(811\) 41.8993 1.47128 0.735641 0.677372i \(-0.236881\pi\)
0.735641 + 0.677372i \(0.236881\pi\)
\(812\) −38.7815 −1.36096
\(813\) 1.65962 0.0582056
\(814\) 0.300790 0.0105427
\(815\) 12.1900 0.426996
\(816\) −2.51234 −0.0879496
\(817\) −71.3553 −2.49641
\(818\) −7.48766 −0.261800
\(819\) −56.7283 −1.98225
\(820\) 1.44807 0.0505688
\(821\) 41.4699 1.44731 0.723655 0.690162i \(-0.242461\pi\)
0.723655 + 0.690162i \(0.242461\pi\)
\(822\) −9.54498 −0.332919
\(823\) 34.8607 1.21517 0.607583 0.794256i \(-0.292139\pi\)
0.607583 + 0.794256i \(0.292139\pi\)
\(824\) 8.63110 0.300679
\(825\) −0.799233 −0.0278257
\(826\) −16.6093 −0.577910
\(827\) −3.98610 −0.138610 −0.0693051 0.997596i \(-0.522078\pi\)
−0.0693051 + 0.997596i \(0.522078\pi\)
\(828\) 0 0
\(829\) 49.7707 1.72861 0.864304 0.502970i \(-0.167759\pi\)
0.864304 + 0.502970i \(0.167759\pi\)
\(830\) 7.59847 0.263747
\(831\) −13.9069 −0.482426
\(832\) −5.69537 −0.197452
\(833\) 30.2967 1.04972
\(834\) −6.01390 −0.208244
\(835\) −13.5985 −0.470594
\(836\) −9.84577 −0.340523
\(837\) −8.14628 −0.281577
\(838\) −4.28689 −0.148088
\(839\) −27.0823 −0.934984 −0.467492 0.883997i \(-0.654842\pi\)
−0.467492 + 0.883997i \(0.654842\pi\)
\(840\) 2.03959 0.0703724
\(841\) 81.1368 2.79782
\(842\) 33.9962 1.17159
\(843\) 2.25141 0.0775428
\(844\) 17.1830 0.591464
\(845\) 19.4373 0.668663
\(846\) 27.7270 0.953274
\(847\) 32.9003 1.13047
\(848\) 13.3907 0.459840
\(849\) −5.79228 −0.198791
\(850\) 4.55193 0.156130
\(851\) 0 0
\(852\) 2.51234 0.0860715
\(853\) 26.6846 0.913663 0.456831 0.889553i \(-0.348984\pi\)
0.456831 + 0.889553i \(0.348984\pi\)
\(854\) −43.3651 −1.48392
\(855\) 18.3265 0.626752
\(856\) 6.00000 0.205076
\(857\) 7.29768 0.249284 0.124642 0.992202i \(-0.460222\pi\)
0.124642 + 0.992202i \(0.460222\pi\)
\(858\) 4.55193 0.155400
\(859\) 34.0139 1.16054 0.580270 0.814424i \(-0.302947\pi\)
0.580270 + 0.814424i \(0.302947\pi\)
\(860\) 10.4946 0.357863
\(861\) 2.95346 0.100654
\(862\) 17.7923 0.606008
\(863\) −36.4154 −1.23960 −0.619798 0.784761i \(-0.712785\pi\)
−0.619798 + 0.784761i \(0.712785\pi\)
\(864\) 3.14344 0.106942
\(865\) 1.44807 0.0492359
\(866\) 2.51234 0.0853729
\(867\) −2.05321 −0.0697307
\(868\) 9.57662 0.325052
\(869\) 14.8961 0.505317
\(870\) −5.79228 −0.196377
\(871\) 17.6776 0.598984
\(872\) 18.7992 0.636622
\(873\) 27.8815 0.943646
\(874\) 0 0
\(875\) −3.69537 −0.124926
\(876\) −1.37685 −0.0465193
\(877\) −39.4265 −1.33134 −0.665669 0.746247i \(-0.731854\pi\)
−0.665669 + 0.746247i \(0.731854\pi\)
\(878\) 36.7638 1.24072
\(879\) 3.54087 0.119431
\(880\) 1.44807 0.0488144
\(881\) −23.7707 −0.800856 −0.400428 0.916328i \(-0.631138\pi\)
−0.400428 + 0.916328i \(0.631138\pi\)
\(882\) −17.9398 −0.604066
\(883\) −57.7530 −1.94354 −0.971771 0.235926i \(-0.924188\pi\)
−0.971771 + 0.235926i \(0.924188\pi\)
\(884\) −25.9249 −0.871950
\(885\) −2.48071 −0.0833880
\(886\) 0.383797 0.0128939
\(887\) −40.9100 −1.37362 −0.686812 0.726835i \(-0.740991\pi\)
−0.686812 + 0.726835i \(0.740991\pi\)
\(888\) −0.114646 −0.00384725
\(889\) 58.4098 1.95900
\(890\) −7.39075 −0.247738
\(891\) 9.19693 0.308109
\(892\) −15.8854 −0.531881
\(893\) 69.9430 2.34055
\(894\) −2.87046 −0.0960024
\(895\) −19.3907 −0.648161
\(896\) −3.69537 −0.123454
\(897\) 0 0
\(898\) −28.6707 −0.956753
\(899\) −27.1969 −0.907068
\(900\) −2.69537 −0.0898458
\(901\) 60.9537 2.03066
\(902\) 2.09691 0.0698194
\(903\) 21.4046 0.712302
\(904\) −4.49461 −0.149488
\(905\) −14.1900 −0.471691
\(906\) −8.52624 −0.283266
\(907\) −47.9784 −1.59310 −0.796549 0.604574i \(-0.793343\pi\)
−0.796549 + 0.604574i \(0.793343\pi\)
\(908\) −19.1830 −0.636611
\(909\) −0.559877 −0.0185699
\(910\) 21.0465 0.697686
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 3.75270 0.124264
\(913\) 11.0031 0.364150
\(914\) 1.71311 0.0566647
\(915\) −6.47687 −0.214119
\(916\) 12.2077 0.403354
\(917\) 22.9398 0.757540
\(918\) 14.3087 0.472259
\(919\) 18.5085 0.610539 0.305270 0.952266i \(-0.401253\pi\)
0.305270 + 0.952266i \(0.401253\pi\)
\(920\) 0 0
\(921\) 2.13238 0.0702644
\(922\) 10.6093 0.349397
\(923\) 25.9249 0.853330
\(924\) 2.95346 0.0971618
\(925\) 0.207718 0.00682972
\(926\) −26.1722 −0.860073
\(927\) −23.2640 −0.764091
\(928\) 10.4946 0.344502
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 1.43033 0.0469025
\(931\) −45.2543 −1.48315
\(932\) 3.10386 0.101670
\(933\) −6.62315 −0.216832
\(934\) 7.59847 0.248629
\(935\) 6.59152 0.215566
\(936\) 15.3512 0.501768
\(937\) 1.86762 0.0610124 0.0305062 0.999535i \(-0.490288\pi\)
0.0305062 + 0.999535i \(0.490288\pi\)
\(938\) 11.4699 0.374506
\(939\) 9.54498 0.311489
\(940\) −10.2869 −0.335521
\(941\) −35.6203 −1.16119 −0.580595 0.814193i \(-0.697180\pi\)
−0.580595 + 0.814193i \(0.697180\pi\)
\(942\) 4.91004 0.159978
\(943\) 0 0
\(944\) 4.49461 0.146287
\(945\) −11.6162 −0.377875
\(946\) 15.1969 0.494095
\(947\) 15.9962 0.519805 0.259903 0.965635i \(-0.416309\pi\)
0.259903 + 0.965635i \(0.416309\pi\)
\(948\) −5.67764 −0.184401
\(949\) −14.2077 −0.461202
\(950\) −6.79923 −0.220596
\(951\) 8.54809 0.277191
\(952\) −16.8211 −0.545174
\(953\) −16.9674 −0.549627 −0.274813 0.961498i \(-0.588616\pi\)
−0.274813 + 0.961498i \(0.588616\pi\)
\(954\) −36.0931 −1.16856
\(955\) 4.60925 0.149152
\(956\) 12.0000 0.388108
\(957\) −8.38763 −0.271134
\(958\) −10.8170 −0.349480
\(959\) −63.9072 −2.06367
\(960\) −0.551929 −0.0178134
\(961\) −24.2840 −0.783356
\(962\) −1.18303 −0.0381424
\(963\) −16.1722 −0.521143
\(964\) −6.20772 −0.199937
\(965\) −0.896141 −0.0288478
\(966\) 0 0
\(967\) −30.2869 −0.973961 −0.486980 0.873413i \(-0.661902\pi\)
−0.486980 + 0.873413i \(0.661902\pi\)
\(968\) −8.90309 −0.286156
\(969\) 17.0820 0.548753
\(970\) −10.3442 −0.332133
\(971\) 25.5627 0.820347 0.410173 0.912008i \(-0.365468\pi\)
0.410173 + 0.912008i \(0.365468\pi\)
\(972\) −12.9357 −0.414914
\(973\) −40.2653 −1.29085
\(974\) 3.39075 0.108647
\(975\) 3.14344 0.100671
\(976\) 11.7350 0.375627
\(977\) 18.0614 0.577836 0.288918 0.957354i \(-0.406704\pi\)
0.288918 + 0.957354i \(0.406704\pi\)
\(978\) −6.72801 −0.215138
\(979\) −10.7023 −0.342048
\(980\) 6.65579 0.212611
\(981\) −50.6710 −1.61780
\(982\) −4.60925 −0.147087
\(983\) 38.8388 1.23877 0.619383 0.785089i \(-0.287383\pi\)
0.619383 + 0.785089i \(0.287383\pi\)
\(984\) −0.799233 −0.0254786
\(985\) −7.65579 −0.243934
\(986\) 47.7707 1.52133
\(987\) −20.9810 −0.667832
\(988\) 38.7242 1.23198
\(989\) 0 0
\(990\) −3.90309 −0.124048
\(991\) −33.6558 −1.06911 −0.534556 0.845133i \(-0.679521\pi\)
−0.534556 + 0.845133i \(0.679521\pi\)
\(992\) −2.59152 −0.0822807
\(993\) −6.28689 −0.199508
\(994\) 16.8211 0.533532
\(995\) 6.20772 0.196798
\(996\) −4.19382 −0.132886
\(997\) 2.41544 0.0764976 0.0382488 0.999268i \(-0.487822\pi\)
0.0382488 + 0.999268i \(0.487822\pi\)
\(998\) −6.70232 −0.212158
\(999\) 0.652949 0.0206584
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 5290.2.a.q.1.2 yes 3
23.22 odd 2 5290.2.a.p.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.2 3 23.22 odd 2
5290.2.a.q.1.2 yes 3 1.1 even 1 trivial