Properties

Label 5577.2.a.y.1.5
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.5325692073\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 21 x^{4} + 13 x^{3} - 33 x^{2} - 7 x + 7\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.42819\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.42819 q^{2} +1.00000 q^{3} +0.0397381 q^{4} +0.0606573 q^{5} +1.42819 q^{6} -1.70646 q^{7} -2.79963 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.42819 q^{2} +1.00000 q^{3} +0.0397381 q^{4} +0.0606573 q^{5} +1.42819 q^{6} -1.70646 q^{7} -2.79963 q^{8} +1.00000 q^{9} +0.0866304 q^{10} +1.00000 q^{11} +0.0397381 q^{12} -2.43715 q^{14} +0.0606573 q^{15} -4.07790 q^{16} +3.75599 q^{17} +1.42819 q^{18} +2.02597 q^{19} +0.00241041 q^{20} -1.70646 q^{21} +1.42819 q^{22} +0.704722 q^{23} -2.79963 q^{24} -4.99632 q^{25} +1.00000 q^{27} -0.0678114 q^{28} -0.0346842 q^{29} +0.0866304 q^{30} +1.85987 q^{31} -0.224760 q^{32} +1.00000 q^{33} +5.36429 q^{34} -0.103509 q^{35} +0.0397381 q^{36} +8.82674 q^{37} +2.89348 q^{38} -0.169818 q^{40} +3.32960 q^{41} -2.43715 q^{42} +5.29022 q^{43} +0.0397381 q^{44} +0.0606573 q^{45} +1.00648 q^{46} +6.04622 q^{47} -4.07790 q^{48} -4.08800 q^{49} -7.13572 q^{50} +3.75599 q^{51} -10.6694 q^{53} +1.42819 q^{54} +0.0606573 q^{55} +4.77746 q^{56} +2.02597 q^{57} -0.0495358 q^{58} +3.34547 q^{59} +0.00241041 q^{60} +3.26757 q^{61} +2.65625 q^{62} -1.70646 q^{63} +7.83479 q^{64} +1.42819 q^{66} -10.9701 q^{67} +0.149256 q^{68} +0.704722 q^{69} -0.147831 q^{70} +1.96928 q^{71} -2.79963 q^{72} +15.3057 q^{73} +12.6063 q^{74} -4.99632 q^{75} +0.0805084 q^{76} -1.70646 q^{77} +10.5938 q^{79} -0.247354 q^{80} +1.00000 q^{81} +4.75532 q^{82} +4.19820 q^{83} -0.0678114 q^{84} +0.227828 q^{85} +7.55546 q^{86} -0.0346842 q^{87} -2.79963 q^{88} +14.3643 q^{89} +0.0866304 q^{90} +0.0280043 q^{92} +1.85987 q^{93} +8.63517 q^{94} +0.122890 q^{95} -0.224760 q^{96} +5.86228 q^{97} -5.83846 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + 7q^{11} + 9q^{12} + 8q^{14} + 6q^{15} + 17q^{16} - 2q^{17} + 3q^{18} + 8q^{19} - 2q^{20} + 6q^{21} + 3q^{22} + 4q^{23} + 15q^{24} + 13q^{25} + 7q^{27} + 12q^{28} - 12q^{29} - 10q^{31} + 33q^{32} + 7q^{33} + 28q^{34} - 4q^{35} + 9q^{36} + 6q^{37} + 16q^{38} - 10q^{40} + 2q^{41} + 8q^{42} - 16q^{43} + 9q^{44} + 6q^{45} - 26q^{46} + 18q^{47} + 17q^{48} + 23q^{49} + 39q^{50} - 2q^{51} + 10q^{53} + 3q^{54} + 6q^{55} + 16q^{56} + 8q^{57} + 10q^{58} + 2q^{59} - 2q^{60} - 10q^{61} - 36q^{62} + 6q^{63} + 29q^{64} + 3q^{66} + 8q^{67} - 10q^{68} + 4q^{69} - 20q^{70} + 36q^{71} + 15q^{72} + 20q^{73} + 13q^{75} + 10q^{76} + 6q^{77} + 6q^{79} - 20q^{80} + 7q^{81} - 10q^{82} + 30q^{83} + 12q^{84} - 40q^{85} + 6q^{86} - 12q^{87} + 15q^{88} + 34q^{89} - 12q^{92} - 10q^{93} + 32q^{94} + 18q^{95} + 33q^{96} + 16q^{97} + q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.42819 1.00989 0.504943 0.863153i \(-0.331514\pi\)
0.504943 + 0.863153i \(0.331514\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.0397381 0.0198691
\(5\) 0.0606573 0.0271268 0.0135634 0.999908i \(-0.495683\pi\)
0.0135634 + 0.999908i \(0.495683\pi\)
\(6\) 1.42819 0.583058
\(7\) −1.70646 −0.644980 −0.322490 0.946573i \(-0.604520\pi\)
−0.322490 + 0.946573i \(0.604520\pi\)
\(8\) −2.79963 −0.989820
\(9\) 1.00000 0.333333
\(10\) 0.0866304 0.0273949
\(11\) 1.00000 0.301511
\(12\) 0.0397381 0.0114714
\(13\) 0 0
\(14\) −2.43715 −0.651356
\(15\) 0.0606573 0.0156616
\(16\) −4.07790 −1.01947
\(17\) 3.75599 0.910962 0.455481 0.890246i \(-0.349467\pi\)
0.455481 + 0.890246i \(0.349467\pi\)
\(18\) 1.42819 0.336629
\(19\) 2.02597 0.464790 0.232395 0.972621i \(-0.425344\pi\)
0.232395 + 0.972621i \(0.425344\pi\)
\(20\) 0.00241041 0.000538983 0
\(21\) −1.70646 −0.372379
\(22\) 1.42819 0.304492
\(23\) 0.704722 0.146945 0.0734723 0.997297i \(-0.476592\pi\)
0.0734723 + 0.997297i \(0.476592\pi\)
\(24\) −2.79963 −0.571473
\(25\) −4.99632 −0.999264
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −0.0678114 −0.0128151
\(29\) −0.0346842 −0.00644069 −0.00322035 0.999995i \(-0.501025\pi\)
−0.00322035 + 0.999995i \(0.501025\pi\)
\(30\) 0.0866304 0.0158165
\(31\) 1.85987 0.334042 0.167021 0.985953i \(-0.446585\pi\)
0.167021 + 0.985953i \(0.446585\pi\)
\(32\) −0.224760 −0.0397323
\(33\) 1.00000 0.174078
\(34\) 5.36429 0.919967
\(35\) −0.103509 −0.0174962
\(36\) 0.0397381 0.00662302
\(37\) 8.82674 1.45111 0.725553 0.688166i \(-0.241584\pi\)
0.725553 + 0.688166i \(0.241584\pi\)
\(38\) 2.89348 0.469385
\(39\) 0 0
\(40\) −0.169818 −0.0268506
\(41\) 3.32960 0.519996 0.259998 0.965609i \(-0.416278\pi\)
0.259998 + 0.965609i \(0.416278\pi\)
\(42\) −2.43715 −0.376061
\(43\) 5.29022 0.806751 0.403376 0.915035i \(-0.367837\pi\)
0.403376 + 0.915035i \(0.367837\pi\)
\(44\) 0.0397381 0.00599075
\(45\) 0.0606573 0.00904225
\(46\) 1.00648 0.148397
\(47\) 6.04622 0.881931 0.440966 0.897524i \(-0.354636\pi\)
0.440966 + 0.897524i \(0.354636\pi\)
\(48\) −4.07790 −0.588594
\(49\) −4.08800 −0.584001
\(50\) −7.13572 −1.00914
\(51\) 3.75599 0.525944
\(52\) 0 0
\(53\) −10.6694 −1.46555 −0.732775 0.680471i \(-0.761775\pi\)
−0.732775 + 0.680471i \(0.761775\pi\)
\(54\) 1.42819 0.194353
\(55\) 0.0606573 0.00817903
\(56\) 4.77746 0.638414
\(57\) 2.02597 0.268347
\(58\) −0.0495358 −0.00650436
\(59\) 3.34547 0.435543 0.217771 0.976000i \(-0.430121\pi\)
0.217771 + 0.976000i \(0.430121\pi\)
\(60\) 0.00241041 0.000311182 0
\(61\) 3.26757 0.418369 0.209185 0.977876i \(-0.432919\pi\)
0.209185 + 0.977876i \(0.432919\pi\)
\(62\) 2.65625 0.337344
\(63\) −1.70646 −0.214993
\(64\) 7.83479 0.979349
\(65\) 0 0
\(66\) 1.42819 0.175799
\(67\) −10.9701 −1.34021 −0.670103 0.742268i \(-0.733750\pi\)
−0.670103 + 0.742268i \(0.733750\pi\)
\(68\) 0.149256 0.0181000
\(69\) 0.704722 0.0848385
\(70\) −0.147831 −0.0176692
\(71\) 1.96928 0.233711 0.116855 0.993149i \(-0.462719\pi\)
0.116855 + 0.993149i \(0.462719\pi\)
\(72\) −2.79963 −0.329940
\(73\) 15.3057 1.79140 0.895700 0.444659i \(-0.146675\pi\)
0.895700 + 0.444659i \(0.146675\pi\)
\(74\) 12.6063 1.46545
\(75\) −4.99632 −0.576925
\(76\) 0.0805084 0.00923494
\(77\) −1.70646 −0.194469
\(78\) 0 0
\(79\) 10.5938 1.19190 0.595951 0.803021i \(-0.296775\pi\)
0.595951 + 0.803021i \(0.296775\pi\)
\(80\) −0.247354 −0.0276550
\(81\) 1.00000 0.111111
\(82\) 4.75532 0.525137
\(83\) 4.19820 0.460812 0.230406 0.973095i \(-0.425994\pi\)
0.230406 + 0.973095i \(0.425994\pi\)
\(84\) −0.0678114 −0.00739883
\(85\) 0.227828 0.0247114
\(86\) 7.55546 0.814726
\(87\) −0.0346842 −0.00371854
\(88\) −2.79963 −0.298442
\(89\) 14.3643 1.52261 0.761305 0.648393i \(-0.224559\pi\)
0.761305 + 0.648393i \(0.224559\pi\)
\(90\) 0.0866304 0.00913164
\(91\) 0 0
\(92\) 0.0280043 0.00291965
\(93\) 1.85987 0.192859
\(94\) 8.63517 0.890650
\(95\) 0.122890 0.0126082
\(96\) −0.224760 −0.0229394
\(97\) 5.86228 0.595224 0.297612 0.954687i \(-0.403810\pi\)
0.297612 + 0.954687i \(0.403810\pi\)
\(98\) −5.83846 −0.589774
\(99\) 1.00000 0.100504
\(100\) −0.198544 −0.0198544
\(101\) −12.3706 −1.23092 −0.615460 0.788168i \(-0.711030\pi\)
−0.615460 + 0.788168i \(0.711030\pi\)
\(102\) 5.36429 0.531143
\(103\) 10.0788 0.993094 0.496547 0.868010i \(-0.334601\pi\)
0.496547 + 0.868010i \(0.334601\pi\)
\(104\) 0 0
\(105\) −0.103509 −0.0101014
\(106\) −15.2379 −1.48004
\(107\) 6.17793 0.597243 0.298622 0.954372i \(-0.403473\pi\)
0.298622 + 0.954372i \(0.403473\pi\)
\(108\) 0.0397381 0.00382380
\(109\) 4.64928 0.445320 0.222660 0.974896i \(-0.428526\pi\)
0.222660 + 0.974896i \(0.428526\pi\)
\(110\) 0.0866304 0.00825988
\(111\) 8.82674 0.837797
\(112\) 6.95876 0.657541
\(113\) 8.99146 0.845846 0.422923 0.906166i \(-0.361004\pi\)
0.422923 + 0.906166i \(0.361004\pi\)
\(114\) 2.89348 0.270999
\(115\) 0.0427465 0.00398613
\(116\) −0.00137828 −0.000127971 0
\(117\) 0 0
\(118\) 4.77798 0.439848
\(119\) −6.40944 −0.587552
\(120\) −0.169818 −0.0155022
\(121\) 1.00000 0.0909091
\(122\) 4.66672 0.422505
\(123\) 3.32960 0.300220
\(124\) 0.0739076 0.00663710
\(125\) −0.606350 −0.0542336
\(126\) −2.43715 −0.217119
\(127\) 1.74493 0.154837 0.0774187 0.996999i \(-0.475332\pi\)
0.0774187 + 0.996999i \(0.475332\pi\)
\(128\) 11.6391 1.02876
\(129\) 5.29022 0.465778
\(130\) 0 0
\(131\) −13.8961 −1.21411 −0.607054 0.794661i \(-0.707649\pi\)
−0.607054 + 0.794661i \(0.707649\pi\)
\(132\) 0.0397381 0.00345876
\(133\) −3.45724 −0.299780
\(134\) −15.6674 −1.35345
\(135\) 0.0606573 0.00522055
\(136\) −10.5154 −0.901689
\(137\) 3.08818 0.263841 0.131921 0.991260i \(-0.457886\pi\)
0.131921 + 0.991260i \(0.457886\pi\)
\(138\) 1.00648 0.0856772
\(139\) 1.92887 0.163605 0.0818023 0.996649i \(-0.473932\pi\)
0.0818023 + 0.996649i \(0.473932\pi\)
\(140\) −0.00411325 −0.000347633 0
\(141\) 6.04622 0.509183
\(142\) 2.81252 0.236021
\(143\) 0 0
\(144\) −4.07790 −0.339825
\(145\) −0.00210385 −0.000174715 0
\(146\) 21.8595 1.80911
\(147\) −4.08800 −0.337173
\(148\) 0.350758 0.0288321
\(149\) 9.05192 0.741563 0.370781 0.928720i \(-0.379090\pi\)
0.370781 + 0.928720i \(0.379090\pi\)
\(150\) −7.13572 −0.582629
\(151\) 2.44462 0.198940 0.0994702 0.995041i \(-0.468285\pi\)
0.0994702 + 0.995041i \(0.468285\pi\)
\(152\) −5.67198 −0.460059
\(153\) 3.75599 0.303654
\(154\) −2.43715 −0.196391
\(155\) 0.112814 0.00906147
\(156\) 0 0
\(157\) −8.42793 −0.672622 −0.336311 0.941751i \(-0.609179\pi\)
−0.336311 + 0.941751i \(0.609179\pi\)
\(158\) 15.1301 1.20368
\(159\) −10.6694 −0.846135
\(160\) −0.0136333 −0.00107781
\(161\) −1.20258 −0.0947763
\(162\) 1.42819 0.112210
\(163\) −17.3969 −1.36263 −0.681316 0.731990i \(-0.738592\pi\)
−0.681316 + 0.731990i \(0.738592\pi\)
\(164\) 0.132312 0.0103318
\(165\) 0.0606573 0.00472216
\(166\) 5.99585 0.465368
\(167\) 1.05104 0.0813320 0.0406660 0.999173i \(-0.487052\pi\)
0.0406660 + 0.999173i \(0.487052\pi\)
\(168\) 4.77746 0.368589
\(169\) 0 0
\(170\) 0.325383 0.0249557
\(171\) 2.02597 0.154930
\(172\) 0.210223 0.0160294
\(173\) 18.6654 1.41910 0.709552 0.704653i \(-0.248897\pi\)
0.709552 + 0.704653i \(0.248897\pi\)
\(174\) −0.0495358 −0.00375530
\(175\) 8.52601 0.644505
\(176\) −4.07790 −0.307383
\(177\) 3.34547 0.251461
\(178\) 20.5150 1.53766
\(179\) −24.2443 −1.81210 −0.906051 0.423168i \(-0.860918\pi\)
−0.906051 + 0.423168i \(0.860918\pi\)
\(180\) 0.00241041 0.000179661 0
\(181\) 20.9251 1.55535 0.777675 0.628666i \(-0.216399\pi\)
0.777675 + 0.628666i \(0.216399\pi\)
\(182\) 0 0
\(183\) 3.26757 0.241545
\(184\) −1.97296 −0.145449
\(185\) 0.535406 0.0393638
\(186\) 2.65625 0.194766
\(187\) 3.75599 0.274665
\(188\) 0.240265 0.0175231
\(189\) −1.70646 −0.124126
\(190\) 0.175511 0.0127329
\(191\) 2.77108 0.200508 0.100254 0.994962i \(-0.468034\pi\)
0.100254 + 0.994962i \(0.468034\pi\)
\(192\) 7.83479 0.565428
\(193\) −8.50742 −0.612378 −0.306189 0.951971i \(-0.599054\pi\)
−0.306189 + 0.951971i \(0.599054\pi\)
\(194\) 8.37247 0.601108
\(195\) 0 0
\(196\) −0.162450 −0.0116035
\(197\) −14.4278 −1.02794 −0.513968 0.857810i \(-0.671825\pi\)
−0.513968 + 0.857810i \(0.671825\pi\)
\(198\) 1.42819 0.101497
\(199\) 15.9351 1.12961 0.564806 0.825224i \(-0.308951\pi\)
0.564806 + 0.825224i \(0.308951\pi\)
\(200\) 13.9879 0.989092
\(201\) −10.9701 −0.773768
\(202\) −17.6676 −1.24309
\(203\) 0.0591871 0.00415412
\(204\) 0.149256 0.0104500
\(205\) 0.201965 0.0141058
\(206\) 14.3945 1.00291
\(207\) 0.704722 0.0489815
\(208\) 0 0
\(209\) 2.02597 0.140139
\(210\) −0.147831 −0.0102013
\(211\) −16.6404 −1.14557 −0.572786 0.819705i \(-0.694138\pi\)
−0.572786 + 0.819705i \(0.694138\pi\)
\(212\) −0.423980 −0.0291191
\(213\) 1.96928 0.134933
\(214\) 8.82329 0.603147
\(215\) 0.320890 0.0218845
\(216\) −2.79963 −0.190491
\(217\) −3.17378 −0.215450
\(218\) 6.64007 0.449722
\(219\) 15.3057 1.03427
\(220\) 0.00241041 0.000162510 0
\(221\) 0 0
\(222\) 12.6063 0.846079
\(223\) 29.6492 1.98546 0.992729 0.120372i \(-0.0384088\pi\)
0.992729 + 0.120372i \(0.0384088\pi\)
\(224\) 0.383543 0.0256265
\(225\) −4.99632 −0.333088
\(226\) 12.8416 0.854208
\(227\) −2.17847 −0.144590 −0.0722951 0.997383i \(-0.523032\pi\)
−0.0722951 + 0.997383i \(0.523032\pi\)
\(228\) 0.0805084 0.00533180
\(229\) −2.89071 −0.191024 −0.0955118 0.995428i \(-0.530449\pi\)
−0.0955118 + 0.995428i \(0.530449\pi\)
\(230\) 0.0610503 0.00402554
\(231\) −1.70646 −0.112277
\(232\) 0.0971031 0.00637513
\(233\) 8.88961 0.582377 0.291189 0.956666i \(-0.405949\pi\)
0.291189 + 0.956666i \(0.405949\pi\)
\(234\) 0 0
\(235\) 0.366747 0.0239239
\(236\) 0.132943 0.00865382
\(237\) 10.5938 0.688144
\(238\) −9.15392 −0.593361
\(239\) 28.4940 1.84313 0.921563 0.388229i \(-0.126913\pi\)
0.921563 + 0.388229i \(0.126913\pi\)
\(240\) −0.247354 −0.0159666
\(241\) −15.6266 −1.00660 −0.503299 0.864112i \(-0.667881\pi\)
−0.503299 + 0.864112i \(0.667881\pi\)
\(242\) 1.42819 0.0918078
\(243\) 1.00000 0.0641500
\(244\) 0.129847 0.00831260
\(245\) −0.247967 −0.0158420
\(246\) 4.75532 0.303188
\(247\) 0 0
\(248\) −5.20695 −0.330641
\(249\) 4.19820 0.266050
\(250\) −0.865985 −0.0547697
\(251\) 20.7286 1.30838 0.654189 0.756331i \(-0.273010\pi\)
0.654189 + 0.756331i \(0.273010\pi\)
\(252\) −0.0678114 −0.00427172
\(253\) 0.704722 0.0443055
\(254\) 2.49210 0.156368
\(255\) 0.227828 0.0142672
\(256\) 0.953341 0.0595838
\(257\) −1.38511 −0.0864008 −0.0432004 0.999066i \(-0.513755\pi\)
−0.0432004 + 0.999066i \(0.513755\pi\)
\(258\) 7.55546 0.470383
\(259\) −15.0624 −0.935935
\(260\) 0 0
\(261\) −0.0346842 −0.00214690
\(262\) −19.8463 −1.22611
\(263\) −17.4668 −1.07705 −0.538524 0.842610i \(-0.681018\pi\)
−0.538524 + 0.842610i \(0.681018\pi\)
\(264\) −2.79963 −0.172306
\(265\) −0.647174 −0.0397556
\(266\) −4.93760 −0.302744
\(267\) 14.3643 0.879080
\(268\) −0.435929 −0.0266286
\(269\) 0.559556 0.0341167 0.0170584 0.999854i \(-0.494570\pi\)
0.0170584 + 0.999854i \(0.494570\pi\)
\(270\) 0.0866304 0.00527216
\(271\) −13.2324 −0.803810 −0.401905 0.915681i \(-0.631652\pi\)
−0.401905 + 0.915681i \(0.631652\pi\)
\(272\) −15.3166 −0.928702
\(273\) 0 0
\(274\) 4.41053 0.266450
\(275\) −4.99632 −0.301289
\(276\) 0.0280043 0.00168566
\(277\) −18.4921 −1.11108 −0.555541 0.831489i \(-0.687489\pi\)
−0.555541 + 0.831489i \(0.687489\pi\)
\(278\) 2.75480 0.165222
\(279\) 1.85987 0.111347
\(280\) 0.289787 0.0173181
\(281\) 25.8276 1.54075 0.770373 0.637593i \(-0.220070\pi\)
0.770373 + 0.637593i \(0.220070\pi\)
\(282\) 8.63517 0.514217
\(283\) 6.19965 0.368531 0.184265 0.982877i \(-0.441009\pi\)
0.184265 + 0.982877i \(0.441009\pi\)
\(284\) 0.0782556 0.00464362
\(285\) 0.122890 0.00727938
\(286\) 0 0
\(287\) −5.68182 −0.335387
\(288\) −0.224760 −0.0132441
\(289\) −2.89252 −0.170148
\(290\) −0.00300470 −0.000176442 0
\(291\) 5.86228 0.343653
\(292\) 0.608221 0.0355934
\(293\) −8.49366 −0.496205 −0.248102 0.968734i \(-0.579807\pi\)
−0.248102 + 0.968734i \(0.579807\pi\)
\(294\) −5.83846 −0.340506
\(295\) 0.202927 0.0118149
\(296\) −24.7116 −1.43633
\(297\) 1.00000 0.0580259
\(298\) 12.9279 0.748893
\(299\) 0 0
\(300\) −0.198544 −0.0114630
\(301\) −9.02753 −0.520338
\(302\) 3.49139 0.200907
\(303\) −12.3706 −0.710672
\(304\) −8.26171 −0.473842
\(305\) 0.198202 0.0113490
\(306\) 5.36429 0.306656
\(307\) −10.6196 −0.606095 −0.303047 0.952976i \(-0.598004\pi\)
−0.303047 + 0.952976i \(0.598004\pi\)
\(308\) −0.0678114 −0.00386391
\(309\) 10.0788 0.573363
\(310\) 0.161121 0.00915105
\(311\) −27.5052 −1.55968 −0.779838 0.625981i \(-0.784699\pi\)
−0.779838 + 0.625981i \(0.784699\pi\)
\(312\) 0 0
\(313\) 0.791246 0.0447239 0.0223619 0.999750i \(-0.492881\pi\)
0.0223619 + 0.999750i \(0.492881\pi\)
\(314\) −12.0367 −0.679271
\(315\) −0.103509 −0.00583207
\(316\) 0.420980 0.0236820
\(317\) −10.4687 −0.587983 −0.293991 0.955808i \(-0.594984\pi\)
−0.293991 + 0.955808i \(0.594984\pi\)
\(318\) −15.2379 −0.854500
\(319\) −0.0346842 −0.00194194
\(320\) 0.475237 0.0265666
\(321\) 6.17793 0.344819
\(322\) −1.71751 −0.0957133
\(323\) 7.60954 0.423406
\(324\) 0.0397381 0.00220767
\(325\) 0 0
\(326\) −24.8462 −1.37610
\(327\) 4.64928 0.257106
\(328\) −9.32167 −0.514703
\(329\) −10.3176 −0.568828
\(330\) 0.0866304 0.00476884
\(331\) 21.1531 1.16268 0.581339 0.813661i \(-0.302529\pi\)
0.581339 + 0.813661i \(0.302529\pi\)
\(332\) 0.166829 0.00915591
\(333\) 8.82674 0.483702
\(334\) 1.50109 0.0821361
\(335\) −0.665414 −0.0363554
\(336\) 6.95876 0.379631
\(337\) −4.33688 −0.236245 −0.118123 0.992999i \(-0.537688\pi\)
−0.118123 + 0.992999i \(0.537688\pi\)
\(338\) 0 0
\(339\) 8.99146 0.488349
\(340\) 0.00905347 0.000490993 0
\(341\) 1.85987 0.100717
\(342\) 2.89348 0.156462
\(343\) 18.9212 1.02165
\(344\) −14.8107 −0.798539
\(345\) 0.0427465 0.00230139
\(346\) 26.6578 1.43313
\(347\) −10.5906 −0.568532 −0.284266 0.958745i \(-0.591750\pi\)
−0.284266 + 0.958745i \(0.591750\pi\)
\(348\) −0.00137828 −7.38838e−5 0
\(349\) 24.3761 1.30482 0.652412 0.757864i \(-0.273757\pi\)
0.652412 + 0.757864i \(0.273757\pi\)
\(350\) 12.1768 0.650877
\(351\) 0 0
\(352\) −0.224760 −0.0119797
\(353\) −21.4564 −1.14201 −0.571004 0.820947i \(-0.693446\pi\)
−0.571004 + 0.820947i \(0.693446\pi\)
\(354\) 4.77798 0.253947
\(355\) 0.119451 0.00633982
\(356\) 0.570810 0.0302528
\(357\) −6.40944 −0.339224
\(358\) −34.6255 −1.83002
\(359\) −33.2863 −1.75679 −0.878393 0.477939i \(-0.841384\pi\)
−0.878393 + 0.477939i \(0.841384\pi\)
\(360\) −0.169818 −0.00895020
\(361\) −14.8954 −0.783970
\(362\) 29.8851 1.57073
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 0.928404 0.0485949
\(366\) 4.66672 0.243933
\(367\) 15.3463 0.801073 0.400536 0.916281i \(-0.368824\pi\)
0.400536 + 0.916281i \(0.368824\pi\)
\(368\) −2.87378 −0.149806
\(369\) 3.32960 0.173332
\(370\) 0.764663 0.0397529
\(371\) 18.2068 0.945250
\(372\) 0.0739076 0.00383193
\(373\) −22.1576 −1.14728 −0.573638 0.819109i \(-0.694469\pi\)
−0.573638 + 0.819109i \(0.694469\pi\)
\(374\) 5.36429 0.277381
\(375\) −0.606350 −0.0313118
\(376\) −16.9272 −0.872954
\(377\) 0 0
\(378\) −2.43715 −0.125354
\(379\) −21.0884 −1.08324 −0.541619 0.840624i \(-0.682188\pi\)
−0.541619 + 0.840624i \(0.682188\pi\)
\(380\) 0.00488342 0.000250514 0
\(381\) 1.74493 0.0893955
\(382\) 3.95764 0.202490
\(383\) 6.90976 0.353072 0.176536 0.984294i \(-0.443511\pi\)
0.176536 + 0.984294i \(0.443511\pi\)
\(384\) 11.6391 0.593957
\(385\) −0.103509 −0.00527531
\(386\) −12.1502 −0.618431
\(387\) 5.29022 0.268917
\(388\) 0.232956 0.0118265
\(389\) −32.7232 −1.65913 −0.829565 0.558410i \(-0.811412\pi\)
−0.829565 + 0.558410i \(0.811412\pi\)
\(390\) 0 0
\(391\) 2.64693 0.133861
\(392\) 11.4449 0.578056
\(393\) −13.8961 −0.700966
\(394\) −20.6056 −1.03810
\(395\) 0.642594 0.0323324
\(396\) 0.0397381 0.00199692
\(397\) −10.1016 −0.506987 −0.253494 0.967337i \(-0.581580\pi\)
−0.253494 + 0.967337i \(0.581580\pi\)
\(398\) 22.7585 1.14078
\(399\) −3.45724 −0.173078
\(400\) 20.3745 1.01872
\(401\) 18.3377 0.915739 0.457870 0.889019i \(-0.348613\pi\)
0.457870 + 0.889019i \(0.348613\pi\)
\(402\) −15.6674 −0.781417
\(403\) 0 0
\(404\) −0.491584 −0.0244572
\(405\) 0.0606573 0.00301408
\(406\) 0.0845306 0.00419518
\(407\) 8.82674 0.437525
\(408\) −10.5154 −0.520590
\(409\) −5.60283 −0.277042 −0.138521 0.990359i \(-0.544235\pi\)
−0.138521 + 0.990359i \(0.544235\pi\)
\(410\) 0.288445 0.0142453
\(411\) 3.08818 0.152329
\(412\) 0.400513 0.0197318
\(413\) −5.70890 −0.280916
\(414\) 1.00648 0.0494657
\(415\) 0.254651 0.0125003
\(416\) 0 0
\(417\) 1.92887 0.0944572
\(418\) 2.89348 0.141525
\(419\) −24.6413 −1.20380 −0.601902 0.798570i \(-0.705590\pi\)
−0.601902 + 0.798570i \(0.705590\pi\)
\(420\) −0.00411325 −0.000200706 0
\(421\) 25.4002 1.23793 0.618964 0.785419i \(-0.287553\pi\)
0.618964 + 0.785419i \(0.287553\pi\)
\(422\) −23.7657 −1.15690
\(423\) 6.04622 0.293977
\(424\) 29.8703 1.45063
\(425\) −18.7661 −0.910292
\(426\) 2.81252 0.136267
\(427\) −5.57596 −0.269840
\(428\) 0.245499 0.0118667
\(429\) 0 0
\(430\) 0.458294 0.0221009
\(431\) 33.6254 1.61968 0.809838 0.586653i \(-0.199555\pi\)
0.809838 + 0.586653i \(0.199555\pi\)
\(432\) −4.07790 −0.196198
\(433\) 9.72637 0.467420 0.233710 0.972306i \(-0.424913\pi\)
0.233710 + 0.972306i \(0.424913\pi\)
\(434\) −4.53278 −0.217580
\(435\) −0.00210385 −0.000100872 0
\(436\) 0.184754 0.00884809
\(437\) 1.42775 0.0682984
\(438\) 21.8595 1.04449
\(439\) 17.0758 0.814986 0.407493 0.913208i \(-0.366403\pi\)
0.407493 + 0.913208i \(0.366403\pi\)
\(440\) −0.169818 −0.00809576
\(441\) −4.08800 −0.194667
\(442\) 0 0
\(443\) 21.8637 1.03878 0.519389 0.854538i \(-0.326160\pi\)
0.519389 + 0.854538i \(0.326160\pi\)
\(444\) 0.350758 0.0166462
\(445\) 0.871298 0.0413035
\(446\) 42.3448 2.00509
\(447\) 9.05192 0.428141
\(448\) −13.3697 −0.631661
\(449\) −8.95803 −0.422755 −0.211378 0.977404i \(-0.567795\pi\)
−0.211378 + 0.977404i \(0.567795\pi\)
\(450\) −7.13572 −0.336381
\(451\) 3.32960 0.156785
\(452\) 0.357304 0.0168062
\(453\) 2.44462 0.114858
\(454\) −3.11128 −0.146020
\(455\) 0 0
\(456\) −5.67198 −0.265615
\(457\) −37.7837 −1.76744 −0.883722 0.468011i \(-0.844971\pi\)
−0.883722 + 0.468011i \(0.844971\pi\)
\(458\) −4.12850 −0.192912
\(459\) 3.75599 0.175315
\(460\) 0.00169867 7.92007e−5 0
\(461\) −6.10348 −0.284268 −0.142134 0.989847i \(-0.545396\pi\)
−0.142134 + 0.989847i \(0.545396\pi\)
\(462\) −2.43715 −0.113387
\(463\) −37.1501 −1.72651 −0.863255 0.504768i \(-0.831578\pi\)
−0.863255 + 0.504768i \(0.831578\pi\)
\(464\) 0.141439 0.00656612
\(465\) 0.112814 0.00523164
\(466\) 12.6961 0.588135
\(467\) −10.3642 −0.479598 −0.239799 0.970823i \(-0.577081\pi\)
−0.239799 + 0.970823i \(0.577081\pi\)
\(468\) 0 0
\(469\) 18.7199 0.864406
\(470\) 0.523786 0.0241604
\(471\) −8.42793 −0.388338
\(472\) −9.36608 −0.431109
\(473\) 5.29022 0.243245
\(474\) 15.1301 0.694947
\(475\) −10.1224 −0.464448
\(476\) −0.254699 −0.0116741
\(477\) −10.6694 −0.488516
\(478\) 40.6950 1.86135
\(479\) 20.4038 0.932273 0.466136 0.884713i \(-0.345646\pi\)
0.466136 + 0.884713i \(0.345646\pi\)
\(480\) −0.0136333 −0.000622273 0
\(481\) 0 0
\(482\) −22.3178 −1.01655
\(483\) −1.20258 −0.0547191
\(484\) 0.0397381 0.00180628
\(485\) 0.355590 0.0161465
\(486\) 1.42819 0.0647842
\(487\) 18.1762 0.823644 0.411822 0.911264i \(-0.364893\pi\)
0.411822 + 0.911264i \(0.364893\pi\)
\(488\) −9.14799 −0.414110
\(489\) −17.3969 −0.786716
\(490\) −0.354145 −0.0159987
\(491\) −19.2029 −0.866613 −0.433307 0.901247i \(-0.642653\pi\)
−0.433307 + 0.901247i \(0.642653\pi\)
\(492\) 0.132312 0.00596509
\(493\) −0.130274 −0.00586723
\(494\) 0 0
\(495\) 0.0606573 0.00272634
\(496\) −7.58434 −0.340547
\(497\) −3.36050 −0.150739
\(498\) 5.99585 0.268680
\(499\) −6.46441 −0.289387 −0.144693 0.989477i \(-0.546220\pi\)
−0.144693 + 0.989477i \(0.546220\pi\)
\(500\) −0.0240952 −0.00107757
\(501\) 1.05104 0.0469571
\(502\) 29.6045 1.32131
\(503\) −23.6756 −1.05564 −0.527821 0.849355i \(-0.676991\pi\)
−0.527821 + 0.849355i \(0.676991\pi\)
\(504\) 4.77746 0.212805
\(505\) −0.750367 −0.0333909
\(506\) 1.00648 0.0447435
\(507\) 0 0
\(508\) 0.0693402 0.00307648
\(509\) 29.5632 1.31037 0.655183 0.755470i \(-0.272591\pi\)
0.655183 + 0.755470i \(0.272591\pi\)
\(510\) 0.325383 0.0144082
\(511\) −26.1186 −1.15542
\(512\) −21.9167 −0.968590
\(513\) 2.02597 0.0894489
\(514\) −1.97821 −0.0872550
\(515\) 0.611353 0.0269394
\(516\) 0.210223 0.00925457
\(517\) 6.04622 0.265912
\(518\) −21.5121 −0.945187
\(519\) 18.6654 0.819320
\(520\) 0 0
\(521\) 35.0790 1.53684 0.768420 0.639946i \(-0.221043\pi\)
0.768420 + 0.639946i \(0.221043\pi\)
\(522\) −0.0495358 −0.00216812
\(523\) 12.7792 0.558797 0.279399 0.960175i \(-0.409865\pi\)
0.279399 + 0.960175i \(0.409865\pi\)
\(524\) −0.552205 −0.0241232
\(525\) 8.52601 0.372105
\(526\) −24.9459 −1.08769
\(527\) 6.98564 0.304299
\(528\) −4.07790 −0.177468
\(529\) −22.5034 −0.978407
\(530\) −0.924290 −0.0401486
\(531\) 3.34547 0.145181
\(532\) −0.137384 −0.00595635
\(533\) 0 0
\(534\) 20.5150 0.887770
\(535\) 0.374737 0.0162013
\(536\) 30.7121 1.32656
\(537\) −24.2443 −1.04622
\(538\) 0.799155 0.0344540
\(539\) −4.08800 −0.176083
\(540\) 0.00241041 0.000103727 0
\(541\) 16.4144 0.705711 0.352856 0.935678i \(-0.385211\pi\)
0.352856 + 0.935678i \(0.385211\pi\)
\(542\) −18.8984 −0.811756
\(543\) 20.9251 0.897982
\(544\) −0.844196 −0.0361946
\(545\) 0.282013 0.0120801
\(546\) 0 0
\(547\) −30.0865 −1.28640 −0.643202 0.765696i \(-0.722395\pi\)
−0.643202 + 0.765696i \(0.722395\pi\)
\(548\) 0.122719 0.00524228
\(549\) 3.26757 0.139456
\(550\) −7.13572 −0.304268
\(551\) −0.0702692 −0.00299357
\(552\) −1.97296 −0.0839749
\(553\) −18.0779 −0.768753
\(554\) −26.4103 −1.12207
\(555\) 0.535406 0.0227267
\(556\) 0.0766497 0.00325067
\(557\) −9.18200 −0.389054 −0.194527 0.980897i \(-0.562317\pi\)
−0.194527 + 0.980897i \(0.562317\pi\)
\(558\) 2.65625 0.112448
\(559\) 0 0
\(560\) 0.422099 0.0178369
\(561\) 3.75599 0.158578
\(562\) 36.8868 1.55598
\(563\) −15.8217 −0.666804 −0.333402 0.942785i \(-0.608197\pi\)
−0.333402 + 0.942785i \(0.608197\pi\)
\(564\) 0.240265 0.0101170
\(565\) 0.545398 0.0229451
\(566\) 8.85430 0.372174
\(567\) −1.70646 −0.0716645
\(568\) −5.51327 −0.231332
\(569\) −35.8645 −1.50352 −0.751760 0.659437i \(-0.770795\pi\)
−0.751760 + 0.659437i \(0.770795\pi\)
\(570\) 0.175511 0.00735134
\(571\) 0.130007 0.00544063 0.00272032 0.999996i \(-0.499134\pi\)
0.00272032 + 0.999996i \(0.499134\pi\)
\(572\) 0 0
\(573\) 2.77108 0.115763
\(574\) −8.11474 −0.338703
\(575\) −3.52101 −0.146836
\(576\) 7.83479 0.326450
\(577\) −24.3812 −1.01500 −0.507502 0.861650i \(-0.669431\pi\)
−0.507502 + 0.861650i \(0.669431\pi\)
\(578\) −4.13108 −0.171830
\(579\) −8.50742 −0.353556
\(580\) −8.36030e−5 0 −3.47143e−6 0
\(581\) −7.16405 −0.297215
\(582\) 8.37247 0.347050
\(583\) −10.6694 −0.441880
\(584\) −42.8504 −1.77316
\(585\) 0 0
\(586\) −12.1306 −0.501110
\(587\) 6.61208 0.272910 0.136455 0.990646i \(-0.456429\pi\)
0.136455 + 0.990646i \(0.456429\pi\)
\(588\) −0.162450 −0.00669931
\(589\) 3.76804 0.155259
\(590\) 0.289819 0.0119317
\(591\) −14.4278 −0.593479
\(592\) −35.9945 −1.47937
\(593\) −26.4128 −1.08464 −0.542322 0.840170i \(-0.682455\pi\)
−0.542322 + 0.840170i \(0.682455\pi\)
\(594\) 1.42819 0.0585995
\(595\) −0.388779 −0.0159384
\(596\) 0.359706 0.0147342
\(597\) 15.9351 0.652182
\(598\) 0 0
\(599\) 21.4702 0.877248 0.438624 0.898671i \(-0.355466\pi\)
0.438624 + 0.898671i \(0.355466\pi\)
\(600\) 13.9879 0.571052
\(601\) −9.57861 −0.390720 −0.195360 0.980732i \(-0.562587\pi\)
−0.195360 + 0.980732i \(0.562587\pi\)
\(602\) −12.8931 −0.525482
\(603\) −10.9701 −0.446735
\(604\) 0.0971446 0.00395276
\(605\) 0.0606573 0.00246607
\(606\) −17.6676 −0.717698
\(607\) −28.5549 −1.15901 −0.579504 0.814969i \(-0.696754\pi\)
−0.579504 + 0.814969i \(0.696754\pi\)
\(608\) −0.455357 −0.0184672
\(609\) 0.0591871 0.00239838
\(610\) 0.283070 0.0114612
\(611\) 0 0
\(612\) 0.149256 0.00603332
\(613\) −25.5390 −1.03151 −0.515755 0.856736i \(-0.672488\pi\)
−0.515755 + 0.856736i \(0.672488\pi\)
\(614\) −15.1669 −0.612086
\(615\) 0.201965 0.00814400
\(616\) 4.77746 0.192489
\(617\) 33.4193 1.34541 0.672706 0.739910i \(-0.265132\pi\)
0.672706 + 0.739910i \(0.265132\pi\)
\(618\) 14.3945 0.579031
\(619\) 34.5887 1.39024 0.695119 0.718895i \(-0.255352\pi\)
0.695119 + 0.718895i \(0.255352\pi\)
\(620\) 0.00448303 0.000180043 0
\(621\) 0.704722 0.0282795
\(622\) −39.2827 −1.57509
\(623\) −24.5120 −0.982054
\(624\) 0 0
\(625\) 24.9448 0.997793
\(626\) 1.13005 0.0451660
\(627\) 2.02597 0.0809096
\(628\) −0.334910 −0.0133644
\(629\) 33.1532 1.32190
\(630\) −0.147831 −0.00588973
\(631\) −12.7021 −0.505662 −0.252831 0.967510i \(-0.581362\pi\)
−0.252831 + 0.967510i \(0.581362\pi\)
\(632\) −29.6589 −1.17977
\(633\) −16.6404 −0.661397
\(634\) −14.9514 −0.593796
\(635\) 0.105843 0.00420024
\(636\) −0.423980 −0.0168119
\(637\) 0 0
\(638\) −0.0495358 −0.00196114
\(639\) 1.96928 0.0779036
\(640\) 0.705998 0.0279070
\(641\) −25.9825 −1.02625 −0.513124 0.858314i \(-0.671512\pi\)
−0.513124 + 0.858314i \(0.671512\pi\)
\(642\) 8.82329 0.348227
\(643\) 32.8848 1.29685 0.648425 0.761278i \(-0.275428\pi\)
0.648425 + 0.761278i \(0.275428\pi\)
\(644\) −0.0477881 −0.00188312
\(645\) 0.320890 0.0126350
\(646\) 10.8679 0.427592
\(647\) 2.75086 0.108148 0.0540738 0.998537i \(-0.482779\pi\)
0.0540738 + 0.998537i \(0.482779\pi\)
\(648\) −2.79963 −0.109980
\(649\) 3.34547 0.131321
\(650\) 0 0
\(651\) −3.17378 −0.124390
\(652\) −0.691321 −0.0270742
\(653\) 27.4851 1.07557 0.537787 0.843081i \(-0.319260\pi\)
0.537787 + 0.843081i \(0.319260\pi\)
\(654\) 6.64007 0.259647
\(655\) −0.842900 −0.0329348
\(656\) −13.5778 −0.530123
\(657\) 15.3057 0.597133
\(658\) −14.7355 −0.574451
\(659\) 17.2631 0.672474 0.336237 0.941777i \(-0.390846\pi\)
0.336237 + 0.941777i \(0.390846\pi\)
\(660\) 0.00241041 9.38249e−5 0
\(661\) −2.44386 −0.0950551 −0.0475276 0.998870i \(-0.515134\pi\)
−0.0475276 + 0.998870i \(0.515134\pi\)
\(662\) 30.2107 1.17417
\(663\) 0 0
\(664\) −11.7534 −0.456122
\(665\) −0.209706 −0.00813207
\(666\) 12.6063 0.488484
\(667\) −0.0244427 −0.000946425 0
\(668\) 0.0417664 0.00161599
\(669\) 29.6492 1.14630
\(670\) −0.950340 −0.0367148
\(671\) 3.26757 0.126143
\(672\) 0.383543 0.0147955
\(673\) 26.7842 1.03246 0.516228 0.856451i \(-0.327336\pi\)
0.516228 + 0.856451i \(0.327336\pi\)
\(674\) −6.19391 −0.238581
\(675\) −4.99632 −0.192308
\(676\) 0 0
\(677\) −25.7769 −0.990687 −0.495343 0.868697i \(-0.664958\pi\)
−0.495343 + 0.868697i \(0.664958\pi\)
\(678\) 12.8416 0.493177
\(679\) −10.0037 −0.383908
\(680\) −0.637836 −0.0244599
\(681\) −2.17847 −0.0834792
\(682\) 2.65625 0.101713
\(683\) 12.8667 0.492329 0.246165 0.969228i \(-0.420830\pi\)
0.246165 + 0.969228i \(0.420830\pi\)
\(684\) 0.0805084 0.00307831
\(685\) 0.187321 0.00715716
\(686\) 27.0231 1.03175
\(687\) −2.89071 −0.110288
\(688\) −21.5730 −0.822462
\(689\) 0 0
\(690\) 0.0610503 0.00232414
\(691\) −33.9707 −1.29230 −0.646152 0.763208i \(-0.723623\pi\)
−0.646152 + 0.763208i \(0.723623\pi\)
\(692\) 0.741728 0.0281963
\(693\) −1.70646 −0.0648229
\(694\) −15.1254 −0.574152
\(695\) 0.117000 0.00443806
\(696\) 0.0971031 0.00368068
\(697\) 12.5060 0.473697
\(698\) 34.8138 1.31772
\(699\) 8.88961 0.336236
\(700\) 0.338807 0.0128057
\(701\) −18.4719 −0.697675 −0.348837 0.937183i \(-0.613423\pi\)
−0.348837 + 0.937183i \(0.613423\pi\)
\(702\) 0 0
\(703\) 17.8827 0.674460
\(704\) 7.83479 0.295285
\(705\) 0.366747 0.0138125
\(706\) −30.6439 −1.15330
\(707\) 21.1099 0.793919
\(708\) 0.132943 0.00499629
\(709\) 33.8830 1.27250 0.636251 0.771482i \(-0.280484\pi\)
0.636251 + 0.771482i \(0.280484\pi\)
\(710\) 0.170600 0.00640249
\(711\) 10.5938 0.397300
\(712\) −40.2147 −1.50711
\(713\) 1.31069 0.0490856
\(714\) −9.15392 −0.342577
\(715\) 0 0
\(716\) −0.963422 −0.0360048
\(717\) 28.4940 1.06413
\(718\) −47.5393 −1.77415
\(719\) 31.1501 1.16170 0.580851 0.814010i \(-0.302720\pi\)
0.580851 + 0.814010i \(0.302720\pi\)
\(720\) −0.247354 −0.00921834
\(721\) −17.1990 −0.640526
\(722\) −21.2736 −0.791720
\(723\) −15.6266 −0.581160
\(724\) 0.831524 0.0309034
\(725\) 0.173293 0.00643595
\(726\) 1.42819 0.0530053
\(727\) 1.50815 0.0559341 0.0279671 0.999609i \(-0.491097\pi\)
0.0279671 + 0.999609i \(0.491097\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.32594 0.0490753
\(731\) 19.8700 0.734920
\(732\) 0.129847 0.00479928
\(733\) −4.42002 −0.163257 −0.0816285 0.996663i \(-0.526012\pi\)
−0.0816285 + 0.996663i \(0.526012\pi\)
\(734\) 21.9176 0.808992
\(735\) −0.247967 −0.00914641
\(736\) −0.158393 −0.00583844
\(737\) −10.9701 −0.404087
\(738\) 4.75532 0.175046
\(739\) −13.7640 −0.506317 −0.253159 0.967425i \(-0.581469\pi\)
−0.253159 + 0.967425i \(0.581469\pi\)
\(740\) 0.0212760 0.000782122 0
\(741\) 0 0
\(742\) 26.0028 0.954594
\(743\) 52.1763 1.91416 0.957081 0.289819i \(-0.0935952\pi\)
0.957081 + 0.289819i \(0.0935952\pi\)
\(744\) −5.20695 −0.190896
\(745\) 0.549065 0.0201162
\(746\) −31.6453 −1.15862
\(747\) 4.19820 0.153604
\(748\) 0.149256 0.00545734
\(749\) −10.5424 −0.385210
\(750\) −0.865985 −0.0316213
\(751\) 13.4236 0.489836 0.244918 0.969544i \(-0.421239\pi\)
0.244918 + 0.969544i \(0.421239\pi\)
\(752\) −24.6559 −0.899106
\(753\) 20.7286 0.755393
\(754\) 0 0
\(755\) 0.148284 0.00539661
\(756\) −0.0678114 −0.00246628
\(757\) 12.9431 0.470426 0.235213 0.971944i \(-0.424421\pi\)
0.235213 + 0.971944i \(0.424421\pi\)
\(758\) −30.1183 −1.09395
\(759\) 0.704722 0.0255798
\(760\) −0.344047 −0.0124799
\(761\) 24.5952 0.891576 0.445788 0.895139i \(-0.352923\pi\)
0.445788 + 0.895139i \(0.352923\pi\)
\(762\) 2.49210 0.0902792
\(763\) −7.93379 −0.287223
\(764\) 0.110117 0.00398391
\(765\) 0.227828 0.00823715
\(766\) 9.86847 0.356562
\(767\) 0 0
\(768\) 0.953341 0.0344007
\(769\) −48.0101 −1.73129 −0.865644 0.500660i \(-0.833091\pi\)
−0.865644 + 0.500660i \(0.833091\pi\)
\(770\) −0.147831 −0.00532746
\(771\) −1.38511 −0.0498835
\(772\) −0.338069 −0.0121674
\(773\) −20.9744 −0.754398 −0.377199 0.926132i \(-0.623113\pi\)
−0.377199 + 0.926132i \(0.623113\pi\)
\(774\) 7.55546 0.271575
\(775\) −9.29249 −0.333796
\(776\) −16.4122 −0.589165
\(777\) −15.0624 −0.540362
\(778\) −46.7350 −1.67553
\(779\) 6.74568 0.241689
\(780\) 0 0
\(781\) 1.96928 0.0704665
\(782\) 3.78033 0.135184
\(783\) −0.0346842 −0.00123951
\(784\) 16.6705 0.595374
\(785\) −0.511215 −0.0182460
\(786\) −19.8463 −0.707895
\(787\) 42.1206 1.50144 0.750719 0.660622i \(-0.229707\pi\)
0.750719 + 0.660622i \(0.229707\pi\)
\(788\) −0.573332 −0.0204241
\(789\) −17.4668 −0.621834
\(790\) 0.917749 0.0326520
\(791\) −15.3435 −0.545554
\(792\) −2.79963 −0.0994807
\(793\) 0 0
\(794\) −14.4271 −0.511999
\(795\) −0.647174 −0.0229529
\(796\) 0.633232 0.0224443
\(797\) 24.5853 0.870855 0.435428 0.900224i \(-0.356597\pi\)
0.435428 + 0.900224i \(0.356597\pi\)
\(798\) −4.93760 −0.174789
\(799\) 22.7095 0.803406
\(800\) 1.12297 0.0397030
\(801\) 14.3643 0.507537
\(802\) 26.1897 0.924792
\(803\) 15.3057 0.540127
\(804\) −0.435929 −0.0153740
\(805\) −0.0729450 −0.00257097
\(806\) 0 0
\(807\) 0.559556 0.0196973
\(808\) 34.6332 1.21839
\(809\) −23.9067 −0.840516 −0.420258 0.907405i \(-0.638060\pi\)
−0.420258 + 0.907405i \(0.638060\pi\)
\(810\) 0.0866304 0.00304388
\(811\) −13.7011 −0.481110 −0.240555 0.970636i \(-0.577329\pi\)
−0.240555 + 0.970636i \(0.577329\pi\)
\(812\) 0.00235198 8.25384e−5 0
\(813\) −13.2324 −0.464080
\(814\) 12.6063 0.441850
\(815\) −1.05525 −0.0369638
\(816\) −15.3166 −0.536187
\(817\) 10.7178 0.374970
\(818\) −8.00193 −0.279781
\(819\) 0 0
\(820\) 0.00802569 0.000280269 0
\(821\) −35.5107 −1.23933 −0.619666 0.784866i \(-0.712732\pi\)
−0.619666 + 0.784866i \(0.712732\pi\)
\(822\) 4.41053 0.153835
\(823\) −33.6096 −1.17156 −0.585778 0.810471i \(-0.699211\pi\)
−0.585778 + 0.810471i \(0.699211\pi\)
\(824\) −28.2170 −0.982984
\(825\) −4.99632 −0.173950
\(826\) −8.15341 −0.283693
\(827\) 33.8892 1.17844 0.589221 0.807972i \(-0.299435\pi\)
0.589221 + 0.807972i \(0.299435\pi\)
\(828\) 0.0280043 0.000973217 0
\(829\) 1.03923 0.0360941 0.0180470 0.999837i \(-0.494255\pi\)
0.0180470 + 0.999837i \(0.494255\pi\)
\(830\) 0.363692 0.0126239
\(831\) −18.4921 −0.641484
\(832\) 0 0
\(833\) −15.3545 −0.532002
\(834\) 2.75480 0.0953909
\(835\) 0.0637533 0.00220627
\(836\) 0.0805084 0.00278444
\(837\) 1.85987 0.0642864
\(838\) −35.1925 −1.21570
\(839\) 53.9422 1.86229 0.931146 0.364646i \(-0.118810\pi\)
0.931146 + 0.364646i \(0.118810\pi\)
\(840\) 0.289787 0.00999862
\(841\) −28.9988 −0.999959
\(842\) 36.2764 1.25017
\(843\) 25.8276 0.889550
\(844\) −0.661258 −0.0227615
\(845\) 0 0
\(846\) 8.63517 0.296883
\(847\) −1.70646 −0.0586346
\(848\) 43.5085 1.49409
\(849\) 6.19965 0.212771
\(850\) −26.8017 −0.919291
\(851\) 6.22039 0.213232
\(852\) 0.0782556 0.00268099
\(853\) 20.4632 0.700647 0.350324 0.936629i \(-0.386072\pi\)
0.350324 + 0.936629i \(0.386072\pi\)
\(854\) −7.96355 −0.272507
\(855\) 0.122890 0.00420275
\(856\) −17.2959 −0.591163
\(857\) 24.3582 0.832059 0.416029 0.909351i \(-0.363421\pi\)
0.416029 + 0.909351i \(0.363421\pi\)
\(858\) 0 0
\(859\) 14.8900 0.508042 0.254021 0.967199i \(-0.418247\pi\)
0.254021 + 0.967199i \(0.418247\pi\)
\(860\) 0.0127516 0.000434825 0
\(861\) −5.68182 −0.193636
\(862\) 48.0235 1.63569
\(863\) −7.78442 −0.264985 −0.132492 0.991184i \(-0.542298\pi\)
−0.132492 + 0.991184i \(0.542298\pi\)
\(864\) −0.224760 −0.00764648
\(865\) 1.13219 0.0384957
\(866\) 13.8911 0.472040
\(867\) −2.89252 −0.0982351
\(868\) −0.126120 −0.00428080
\(869\) 10.5938 0.359372
\(870\) −0.00300470 −0.000101869 0
\(871\) 0 0
\(872\) −13.0163 −0.440787
\(873\) 5.86228 0.198408
\(874\) 2.03910 0.0689736
\(875\) 1.03471 0.0349796
\(876\) 0.608221 0.0205499
\(877\) 26.9967 0.911614 0.455807 0.890079i \(-0.349351\pi\)
0.455807 + 0.890079i \(0.349351\pi\)
\(878\) 24.3876 0.823042
\(879\) −8.49366 −0.286484
\(880\) −0.247354 −0.00833831
\(881\) 18.7865 0.632934 0.316467 0.948603i \(-0.397503\pi\)
0.316467 + 0.948603i \(0.397503\pi\)
\(882\) −5.83846 −0.196591
\(883\) 34.5728 1.16347 0.581734 0.813379i \(-0.302375\pi\)
0.581734 + 0.813379i \(0.302375\pi\)
\(884\) 0 0
\(885\) 0.202927 0.00682131
\(886\) 31.2257 1.04905
\(887\) −32.8755 −1.10385 −0.551926 0.833893i \(-0.686107\pi\)
−0.551926 + 0.833893i \(0.686107\pi\)
\(888\) −24.7116 −0.829268
\(889\) −2.97765 −0.0998671
\(890\) 1.24438 0.0417118
\(891\) 1.00000 0.0335013
\(892\) 1.17820 0.0394492
\(893\) 12.2495 0.409913
\(894\) 12.9279 0.432374
\(895\) −1.47059 −0.0491565
\(896\) −19.8617 −0.663532
\(897\) 0 0
\(898\) −12.7938 −0.426935
\(899\) −0.0645080 −0.00215146
\(900\) −0.198544 −0.00661815
\(901\) −40.0740 −1.33506
\(902\) 4.75532 0.158335
\(903\) −9.02753 −0.300418
\(904\) −25.1728 −0.837235
\(905\) 1.26926 0.0421916
\(906\) 3.49139 0.115994
\(907\) −5.02982 −0.167013 −0.0835063 0.996507i \(-0.526612\pi\)
−0.0835063 + 0.996507i \(0.526612\pi\)
\(908\) −0.0865684 −0.00287287
\(909\) −12.3706 −0.410307
\(910\) 0 0
\(911\) 22.8563 0.757263 0.378632 0.925547i \(-0.376395\pi\)
0.378632 + 0.925547i \(0.376395\pi\)
\(912\) −8.26171 −0.273573
\(913\) 4.19820 0.138940
\(914\) −53.9624 −1.78492
\(915\) 0.198202 0.00655235
\(916\) −0.114871 −0.00379546
\(917\) 23.7131 0.783075
\(918\) 5.36429 0.177048
\(919\) 2.37935 0.0784875 0.0392437 0.999230i \(-0.487505\pi\)
0.0392437 + 0.999230i \(0.487505\pi\)
\(920\) −0.119675 −0.00394555
\(921\) −10.6196 −0.349929
\(922\) −8.71696 −0.287078
\(923\) 0 0
\(924\) −0.0678114 −0.00223083
\(925\) −44.1012 −1.45004
\(926\) −53.0575 −1.74358
\(927\) 10.0788 0.331031
\(928\) 0.00779561 0.000255903 0
\(929\) 8.06120 0.264480 0.132240 0.991218i \(-0.457783\pi\)
0.132240 + 0.991218i \(0.457783\pi\)
\(930\) 0.161121 0.00528336
\(931\) −8.28219 −0.271438
\(932\) 0.353256 0.0115713
\(933\) −27.5052 −0.900479
\(934\) −14.8021 −0.484339
\(935\) 0.227828 0.00745078
\(936\) 0 0
\(937\) −24.3236 −0.794618 −0.397309 0.917685i \(-0.630056\pi\)
−0.397309 + 0.917685i \(0.630056\pi\)
\(938\) 26.7357 0.872951
\(939\) 0.791246 0.0258213
\(940\) 0.0145738 0.000475346 0
\(941\) 17.0623 0.556215 0.278107 0.960550i \(-0.410293\pi\)
0.278107 + 0.960550i \(0.410293\pi\)
\(942\) −12.0367 −0.392177
\(943\) 2.34644 0.0764107
\(944\) −13.6425 −0.444025
\(945\) −0.103509 −0.00336715
\(946\) 7.55546 0.245649
\(947\) 57.1623 1.85753 0.928763 0.370673i \(-0.120873\pi\)
0.928763 + 0.370673i \(0.120873\pi\)
\(948\) 0.420980 0.0136728
\(949\) 0 0
\(950\) −14.4568 −0.469039
\(951\) −10.4687 −0.339472
\(952\) 17.9441 0.581571
\(953\) −2.88446 −0.0934370 −0.0467185 0.998908i \(-0.514876\pi\)
−0.0467185 + 0.998908i \(0.514876\pi\)
\(954\) −15.2379 −0.493346
\(955\) 0.168086 0.00543914
\(956\) 1.13230 0.0366212
\(957\) −0.0346842 −0.00112118
\(958\) 29.1406 0.941489
\(959\) −5.26985 −0.170172
\(960\) 0.475237 0.0153382
\(961\) −27.5409 −0.888416
\(962\) 0 0
\(963\) 6.17793 0.199081
\(964\) −0.620972 −0.0200002
\(965\) −0.516037 −0.0166118
\(966\) −1.71751 −0.0552601
\(967\) −44.8041 −1.44080 −0.720402 0.693557i \(-0.756043\pi\)
−0.720402 + 0.693557i \(0.756043\pi\)
\(968\) −2.79963 −0.0899837
\(969\) 7.60954 0.244454
\(970\) 0.507851 0.0163061
\(971\) 36.2237 1.16247 0.581237 0.813735i \(-0.302569\pi\)
0.581237 + 0.813735i \(0.302569\pi\)
\(972\) 0.0397381 0.00127460
\(973\) −3.29153 −0.105522
\(974\) 25.9592 0.831786
\(975\) 0 0
\(976\) −13.3248 −0.426516
\(977\) 8.12311 0.259881 0.129941 0.991522i \(-0.458521\pi\)
0.129941 + 0.991522i \(0.458521\pi\)
\(978\) −24.8462 −0.794493
\(979\) 14.3643 0.459084
\(980\) −0.00985375 −0.000314767 0
\(981\) 4.64928 0.148440
\(982\) −27.4254 −0.875180
\(983\) 16.3355 0.521020 0.260510 0.965471i \(-0.416109\pi\)
0.260510 + 0.965471i \(0.416109\pi\)
\(984\) −9.32167 −0.297164
\(985\) −0.875149 −0.0278846
\(986\) −0.186056 −0.00592523
\(987\) −10.3176 −0.328413
\(988\) 0 0
\(989\) 3.72813 0.118548
\(990\) 0.0866304 0.00275329
\(991\) 19.8188 0.629565 0.314783 0.949164i \(-0.398068\pi\)
0.314783 + 0.949164i \(0.398068\pi\)
\(992\) −0.418023 −0.0132722
\(993\) 21.1531 0.671273
\(994\) −4.79944 −0.152229
\(995\) 0.966582 0.0306427
\(996\) 0.166829 0.00528617
\(997\) 37.6595 1.19269 0.596344 0.802729i \(-0.296619\pi\)
0.596344 + 0.802729i \(0.296619\pi\)
\(998\) −9.23243 −0.292248
\(999\) 8.82674 0.279266
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 5577.2.a.y.1.5 7
13.5 odd 4 429.2.b.b.298.4 14
13.8 odd 4 429.2.b.b.298.11 yes 14
13.12 even 2 5577.2.a.x.1.3 7
39.5 even 4 1287.2.b.c.298.11 14
39.8 even 4 1287.2.b.c.298.4 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.4 14 13.5 odd 4
429.2.b.b.298.11 yes 14 13.8 odd 4
1287.2.b.c.298.4 14 39.8 even 4
1287.2.b.c.298.11 14 39.5 even 4
5577.2.a.x.1.3 7 13.12 even 2
5577.2.a.y.1.5 7 1.1 even 1 trivial