Properties

Label 5290.2.a.p.1.2
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $1$
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: \(1\)
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

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

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 \(-0.253913\pi\)
0.698360 + 0.715747i \(0.253913\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.69537 −0.898458
\(10\) −1.00000 −0.316228
\(11\) −1.44807 −0.436610 −0.218305 0.975881i \(-0.570053\pi\)
−0.218305 + 0.975881i \(0.570053\pi\)
\(12\) −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 \(-0.686136\pi\)
−0.552003 + 0.833842i \(0.686136\pi\)
\(18\) −2.69537 −0.635306
\(19\) 6.79923 1.55985 0.779925 0.625872i \(-0.215257\pi\)
0.779925 + 0.625872i \(0.215257\pi\)
\(20\) −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 \(-0.505435\pi\)
−0.0170743 + 0.999854i \(0.505435\pi\)
\(38\) 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 \(-0.795277\pi\)
−0.800206 + 0.599725i \(0.795277\pi\)
\(44\) −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 \(-0.871552\pi\)
−0.919680 + 0.392668i \(0.871552\pi\)
\(54\) 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 \(-0.770551\pi\)
−0.751254 + 0.660013i \(0.770551\pi\)
\(62\) −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 \(-0.439281\pi\)
0.189598 + 0.981862i \(0.439281\pi\)
\(68\) −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 \(-0.696433\pi\)
−0.578683 + 0.815553i \(0.696433\pi\)
\(80\) −1.00000 −0.111803
\(81\) 6.35116 0.705685
\(82\) 1.44807 0.159913
\(83\) −7.59847 −0.834040 −0.417020 0.908897i \(-0.636925\pi\)
−0.417020 + 0.908897i \(0.636925\pi\)
\(84\) −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 \(-0.371884\pi\)
0.391709 + 0.920089i \(0.371884\pi\)
\(90\) 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 \(-0.324010\pi\)
0.525148 + 0.851011i \(0.324010\pi\)
\(98\) 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 \(-0.639805\pi\)
−0.425224 + 0.905088i \(0.639805\pi\)
\(104\) −5.69537 −0.558477
\(105\) 2.03959 0.199043
\(106\) −13.3907 −1.30062
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 3.14344 0.302478
\(109\) −18.7992 −1.80064 −0.900320 0.435229i \(-0.856668\pi\)
−0.900320 + 0.435229i \(0.856668\pi\)
\(110\) 1.44807 0.138068
\(111\) 0.114646 0.0108817
\(112\) 3.69537 0.349180
\(113\) 4.49461 0.422817 0.211409 0.977398i \(-0.432195\pi\)
0.211409 + 0.977398i \(0.432195\pi\)
\(114\) −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 \(-0.764587\pi\)
−0.738756 + 0.673973i \(0.764587\pi\)
\(138\) 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 \(-0.568334\pi\)
−0.213032 + 0.977045i \(0.568334\pi\)
\(150\) −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 \(-0.384483\pi\)
0.354995 + 0.934868i \(0.384483\pi\)
\(158\) −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 \(-0.323179\pi\)
0.527366 + 0.849638i \(0.323179\pi\)
\(182\) −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 \(-0.553330\pi\)
−0.166757 + 0.985998i \(0.553330\pi\)
\(192\) −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 \(-0.570614\pi\)
−0.220027 + 0.975494i \(0.570614\pi\)
\(200\) 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 \(-0.280336\pi\)
0.636611 + 0.771185i \(0.280336\pi\)
\(228\) −3.75270 −0.248528
\(229\) −12.2077 −0.806709 −0.403354 0.915044i \(-0.632156\pi\)
−0.403354 + 0.915044i \(0.632156\pi\)
\(230\) 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 \(-0.435926\pi\)
0.199937 + 0.979809i \(0.435926\pi\)
\(242\) −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 \(-0.840456\pi\)
−0.876996 + 0.480498i \(0.840456\pi\)
\(252\) −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 \(-0.472104\pi\)
0.0875245 + 0.996162i \(0.472104\pi\)
\(264\) 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 \(-0.461175\pi\)
0.121671 + 0.992570i \(0.461175\pi\)
\(282\) 5.67764 0.338098
\(283\) −10.4946 −0.623840 −0.311920 0.950108i \(-0.600972\pi\)
−0.311920 + 0.950108i \(0.600972\pi\)
\(284\) −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 \(-0.439995\pi\)
0.187397 + 0.982284i \(0.439995\pi\)
\(294\) −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 \(-0.337452\pi\)
0.488753 + 0.872422i \(0.337452\pi\)
\(314\) 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 \(-0.518190\pi\)
−0.0571129 + 0.998368i \(0.518190\pi\)
\(338\) 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 \(-0.639484\pi\)
−0.424313 + 0.905516i \(0.639484\pi\)
\(360\) 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 \(-0.370177\pi\)
0.396637 + 0.917976i \(0.370177\pi\)
\(368\) 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 \(-0.271681\pi\)
0.657342 + 0.753593i \(0.271681\pi\)
\(374\) 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 \(-0.273262\pi\)
0.653590 + 0.756849i \(0.273262\pi\)
\(380\) −6.79923 −0.348793
\(381\) 8.72390 0.446939
\(382\) −4.60925 −0.235830
\(383\) −20.5738 −1.05127 −0.525635 0.850710i \(-0.676172\pi\)
−0.525635 + 0.850710i \(0.676172\pi\)
\(384\) −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 \(-0.735910\pi\)
−0.675125 + 0.737703i \(0.735910\pi\)
\(390\) −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 \(-0.725037\pi\)
−0.649536 + 0.760331i \(0.725037\pi\)
\(402\) −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 \(-0.466607\pi\)
0.104714 + 0.994502i \(0.466607\pi\)
\(420\) 2.03959 0.0995216
\(421\) −33.9962 −1.65687 −0.828436 0.560084i \(-0.810769\pi\)
−0.828436 + 0.560084i \(0.810769\pi\)
\(422\) 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 \(-0.640962\pi\)
−0.428512 + 0.903536i \(0.640962\pi\)
\(432\) 3.14344 0.151239
\(433\) −2.51234 −0.120736 −0.0603678 0.998176i \(-0.519227\pi\)
−0.0603678 + 0.998176i \(0.519227\pi\)
\(434\) −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 \(-0.512757\pi\)
−0.0400680 + 0.999197i \(0.512757\pi\)
\(458\) −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 \(-0.556254\pi\)
−0.175808 + 0.984425i \(0.556254\pi\)
\(468\) 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 \(-0.420516\pi\)
0.247120 + 0.968985i \(0.420516\pi\)
\(480\) 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 \(-0.266214\pi\)
0.670187 + 0.742193i \(0.266214\pi\)
\(504\) −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 \(-0.659038\pi\)
−0.479103 + 0.877759i \(0.659038\pi\)
\(522\) −28.2869 −1.23808
\(523\) −13.3907 −0.585537 −0.292768 0.956183i \(-0.594576\pi\)
−0.292768 + 0.956183i \(0.594576\pi\)
\(524\) −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 \(-0.814425\pi\)
−0.834814 + 0.550532i \(0.814425\pi\)
\(558\) 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 \(-0.414297\pi\)
0.266001 + 0.963973i \(0.414297\pi\)
\(564\) 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 \(-0.540765\pi\)
−0.127717 + 0.991811i \(0.540765\pi\)
\(570\) 3.75270 0.157183
\(571\) 13.7489 0.575372 0.287686 0.957725i \(-0.407114\pi\)
0.287686 + 0.957725i \(0.407114\pi\)
\(572\) 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 \(-0.567977\pi\)
−0.211937 + 0.977283i \(0.567977\pi\)
\(614\) −3.86351 −0.155918
\(615\) 0.799233 0.0322282
\(616\) −5.35116 −0.215604
\(617\) 16.4373 0.661740 0.330870 0.943676i \(-0.392658\pi\)
0.330870 + 0.943676i \(0.392658\pi\)
\(618\) 4.76376 0.191626
\(619\) 22.9930 0.924169 0.462084 0.886836i \(-0.347102\pi\)
0.462084 + 0.886836i \(0.347102\pi\)
\(620\) 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 \(-0.342292\pi\)
0.475430 + 0.879753i \(0.342292\pi\)
\(632\) −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 \(-0.676548\pi\)
−0.526639 + 0.850089i \(0.676548\pi\)
\(642\) 3.31158 0.130698
\(643\) −38.4591 −1.51668 −0.758340 0.651859i \(-0.773989\pi\)
−0.758340 + 0.651859i \(0.773989\pi\)
\(644\) 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 \(-0.142746\pi\)
0.901120 + 0.433569i \(0.142746\pi\)
\(660\) −0.799233 −0.0311101
\(661\) 36.0357 1.40163 0.700814 0.713344i \(-0.252820\pi\)
0.700814 + 0.713344i \(0.252820\pi\)
\(662\) 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 \(-0.658543\pi\)
−0.477737 + 0.878503i \(0.658543\pi\)
\(678\) −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 \(-0.664682\pi\)
−0.494591 + 0.869126i \(0.664682\pi\)
\(702\) −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 \(-0.311586\pi\)
0.557955 + 0.829871i \(0.311586\pi\)
\(710\) 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 \(-0.447033\pi\)
0.165633 + 0.986188i \(0.447033\pi\)
\(728\) −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 \(-0.652596\pi\)
−0.461242 + 0.887274i \(0.652596\pi\)
\(734\) 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 \(-0.387355\pi\)
0.346546 + 0.938033i \(0.387355\pi\)
\(744\) 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 \(-0.490715\pi\)
0.0291644 + 0.999575i \(0.490715\pi\)
\(752\) −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 \(-0.421754\pi\)
0.243348 + 0.969939i \(0.421754\pi\)
\(758\) 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 \(-0.535703\pi\)
−0.111928 + 0.993716i \(0.535703\pi\)
\(770\) 5.35116 0.192842
\(771\) 6.67452 0.240377
\(772\) −0.896141 −0.0322528
\(773\) 17.4699 0.628349 0.314175 0.949365i \(-0.398272\pi\)
0.314175 + 0.949365i \(0.398272\pi\)
\(774\) 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 \(-0.144050\pi\)
0.899337 + 0.437256i \(0.144050\pi\)
\(788\) −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 \(-0.780828\pi\)
−0.772168 + 0.635418i \(0.780828\pi\)
\(798\) −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 \(-0.477922\pi\)
0.0693051 + 0.997596i \(0.477922\pi\)
\(828\) 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 \(-0.345158\pi\)
0.467492 + 0.883997i \(0.345158\pi\)
\(840\) 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 \(-0.368862\pi\)
0.400428 + 0.916328i \(0.368862\pi\)
\(882\) −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 \(-0.206657\pi\)
0.796549 + 0.604574i \(0.206657\pi\)
\(908\) 19.1830 0.636611
\(909\) −0.559877 −0.0185699
\(910\) 21.0465 0.697686
\(911\) −36.0000 −1.19273 −0.596367 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) −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 \(-0.598747\pi\)
−0.305270 + 0.952266i \(0.598747\pi\)
\(920\) 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 \(-0.509712\pi\)
−0.0305062 + 0.999535i \(0.509712\pi\)
\(938\) 11.4699 0.374506
\(939\) −9.54498 −0.311489
\(940\) 10.2869 0.335521
\(941\) 35.6203 1.16119 0.580595 0.814193i \(-0.302820\pi\)
0.580595 + 0.814193i \(0.302820\pi\)
\(942\) −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 \(-0.411384\pi\)
0.274813 + 0.961498i \(0.411384\pi\)
\(954\) 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 \(-0.634532\pi\)
−0.410173 + 0.912008i \(0.634532\pi\)
\(972\) −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 \(-0.593296\pi\)
−0.288918 + 0.957354i \(0.593296\pi\)
\(978\) −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 \(-0.712617\pi\)
−0.619383 + 0.785089i \(0.712617\pi\)
\(984\) −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.p.1.2 3
23.22 odd 2 5290.2.a.q.1.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.2 3 1.1 even 1 trivial
5290.2.a.q.1.2 yes 3 23.22 odd 2