Properties

Label 4026.2.a.u.1.1
Level 4026
Weight 2
Character 4026.1
Self dual yes
Analytic conductor 32.148
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.9176805.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.32361\) of \(x^{5} - x^{4} - 12 x^{3} + 7 x^{2} + 30 x - 20\)
Character \(\chi\) \(=\) 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.32361 q^{5} -1.00000 q^{6} -3.91566 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.32361 q^{5} -1.00000 q^{6} -3.91566 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.32361 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.77487 q^{13} +3.91566 q^{14} -3.32361 q^{15} +1.00000 q^{16} +0.807136 q^{17} -1.00000 q^{18} -7.13386 q^{19} -3.32361 q^{20} -3.91566 q^{21} +1.00000 q^{22} -5.96773 q^{23} -1.00000 q^{24} +6.04641 q^{25} +2.77487 q^{26} +1.00000 q^{27} -3.91566 q^{28} -8.37002 q^{29} +3.32361 q^{30} -0.644116 q^{31} -1.00000 q^{32} -1.00000 q^{33} -0.807136 q^{34} +13.0141 q^{35} +1.00000 q^{36} -8.31795 q^{37} +7.13386 q^{38} -2.77487 q^{39} +3.32361 q^{40} +9.01414 q^{41} +3.91566 q^{42} +10.4023 q^{43} -1.00000 q^{44} -3.32361 q^{45} +5.96773 q^{46} -2.49766 q^{47} +1.00000 q^{48} +8.33239 q^{49} -6.04641 q^{50} +0.807136 q^{51} -2.77487 q^{52} +0.130750 q^{53} -1.00000 q^{54} +3.32361 q^{55} +3.91566 q^{56} -7.13386 q^{57} +8.37002 q^{58} -14.3533 q^{59} -3.32361 q^{60} -1.00000 q^{61} +0.644116 q^{62} -3.91566 q^{63} +1.00000 q^{64} +9.22258 q^{65} +1.00000 q^{66} +11.9931 q^{67} +0.807136 q^{68} -5.96773 q^{69} -13.0141 q^{70} -12.0031 q^{71} -1.00000 q^{72} +9.98430 q^{73} +8.31795 q^{74} +6.04641 q^{75} -7.13386 q^{76} +3.91566 q^{77} +2.77487 q^{78} +16.7103 q^{79} -3.32361 q^{80} +1.00000 q^{81} -9.01414 q^{82} +3.25047 q^{83} -3.91566 q^{84} -2.68261 q^{85} -10.4023 q^{86} -8.37002 q^{87} +1.00000 q^{88} -14.1282 q^{89} +3.32361 q^{90} +10.8654 q^{91} -5.96773 q^{92} -0.644116 q^{93} +2.49766 q^{94} +23.7102 q^{95} -1.00000 q^{96} -12.4575 q^{97} -8.33239 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + q^{10} - 5q^{11} + 5q^{12} + 2q^{13} + 3q^{14} - q^{15} + 5q^{16} + 6q^{17} - 5q^{18} + 7q^{19} - q^{20} - 3q^{21} + 5q^{22} - 12q^{23} - 5q^{24} - 2q^{26} + 5q^{27} - 3q^{28} + 4q^{29} + q^{30} - q^{31} - 5q^{32} - 5q^{33} - 6q^{34} + 17q^{35} + 5q^{36} + 3q^{37} - 7q^{38} + 2q^{39} + q^{40} - 3q^{41} + 3q^{42} + 24q^{43} - 5q^{44} - q^{45} + 12q^{46} + 18q^{47} + 5q^{48} + 26q^{49} + 6q^{51} + 2q^{52} - 13q^{53} - 5q^{54} + q^{55} + 3q^{56} + 7q^{57} - 4q^{58} - 16q^{59} - q^{60} - 5q^{61} + q^{62} - 3q^{63} + 5q^{64} + 4q^{65} + 5q^{66} + 18q^{67} + 6q^{68} - 12q^{69} - 17q^{70} - 31q^{71} - 5q^{72} + 8q^{73} - 3q^{74} + 7q^{76} + 3q^{77} - 2q^{78} + 32q^{79} - q^{80} + 5q^{81} + 3q^{82} + 8q^{83} - 3q^{84} + 29q^{85} - 24q^{86} + 4q^{87} + 5q^{88} + q^{89} + q^{90} - 3q^{91} - 12q^{92} - q^{93} - 18q^{94} + 33q^{95} - 5q^{96} - 4q^{97} - 26q^{98} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −3.32361 −1.48637 −0.743183 0.669089i \(-0.766685\pi\)
−0.743183 + 0.669089i \(0.766685\pi\)
\(6\) −1.00000 −0.408248
\(7\) −3.91566 −1.47998 −0.739990 0.672618i \(-0.765170\pi\)
−0.739990 + 0.672618i \(0.765170\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.32361 1.05102
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) −2.77487 −0.769609 −0.384805 0.922998i \(-0.625731\pi\)
−0.384805 + 0.922998i \(0.625731\pi\)
\(14\) 3.91566 1.04650
\(15\) −3.32361 −0.858153
\(16\) 1.00000 0.250000
\(17\) 0.807136 0.195759 0.0978797 0.995198i \(-0.468794\pi\)
0.0978797 + 0.995198i \(0.468794\pi\)
\(18\) −1.00000 −0.235702
\(19\) −7.13386 −1.63662 −0.818310 0.574777i \(-0.805089\pi\)
−0.818310 + 0.574777i \(0.805089\pi\)
\(20\) −3.32361 −0.743183
\(21\) −3.91566 −0.854467
\(22\) 1.00000 0.213201
\(23\) −5.96773 −1.24436 −0.622179 0.782875i \(-0.713752\pi\)
−0.622179 + 0.782875i \(0.713752\pi\)
\(24\) −1.00000 −0.204124
\(25\) 6.04641 1.20928
\(26\) 2.77487 0.544196
\(27\) 1.00000 0.192450
\(28\) −3.91566 −0.739990
\(29\) −8.37002 −1.55427 −0.777137 0.629331i \(-0.783329\pi\)
−0.777137 + 0.629331i \(0.783329\pi\)
\(30\) 3.32361 0.606806
\(31\) −0.644116 −0.115687 −0.0578433 0.998326i \(-0.518422\pi\)
−0.0578433 + 0.998326i \(0.518422\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −0.807136 −0.138423
\(35\) 13.0141 2.19979
\(36\) 1.00000 0.166667
\(37\) −8.31795 −1.36746 −0.683732 0.729734i \(-0.739644\pi\)
−0.683732 + 0.729734i \(0.739644\pi\)
\(38\) 7.13386 1.15727
\(39\) −2.77487 −0.444334
\(40\) 3.32361 0.525510
\(41\) 9.01414 1.40777 0.703886 0.710313i \(-0.251447\pi\)
0.703886 + 0.710313i \(0.251447\pi\)
\(42\) 3.91566 0.604199
\(43\) 10.4023 1.58633 0.793167 0.609004i \(-0.208431\pi\)
0.793167 + 0.609004i \(0.208431\pi\)
\(44\) −1.00000 −0.150756
\(45\) −3.32361 −0.495455
\(46\) 5.96773 0.879894
\(47\) −2.49766 −0.364321 −0.182161 0.983269i \(-0.558309\pi\)
−0.182161 + 0.983269i \(0.558309\pi\)
\(48\) 1.00000 0.144338
\(49\) 8.33239 1.19034
\(50\) −6.04641 −0.855091
\(51\) 0.807136 0.113022
\(52\) −2.77487 −0.384805
\(53\) 0.130750 0.0179599 0.00897997 0.999960i \(-0.497142\pi\)
0.00897997 + 0.999960i \(0.497142\pi\)
\(54\) −1.00000 −0.136083
\(55\) 3.32361 0.448156
\(56\) 3.91566 0.523252
\(57\) −7.13386 −0.944903
\(58\) 8.37002 1.09904
\(59\) −14.3533 −1.86865 −0.934323 0.356429i \(-0.883994\pi\)
−0.934323 + 0.356429i \(0.883994\pi\)
\(60\) −3.32361 −0.429077
\(61\) −1.00000 −0.128037
\(62\) 0.644116 0.0818028
\(63\) −3.91566 −0.493327
\(64\) 1.00000 0.125000
\(65\) 9.22258 1.14392
\(66\) 1.00000 0.123091
\(67\) 11.9931 1.46519 0.732593 0.680667i \(-0.238310\pi\)
0.732593 + 0.680667i \(0.238310\pi\)
\(68\) 0.807136 0.0978797
\(69\) −5.96773 −0.718430
\(70\) −13.0141 −1.55549
\(71\) −12.0031 −1.42451 −0.712254 0.701922i \(-0.752325\pi\)
−0.712254 + 0.701922i \(0.752325\pi\)
\(72\) −1.00000 −0.117851
\(73\) 9.98430 1.16857 0.584287 0.811547i \(-0.301374\pi\)
0.584287 + 0.811547i \(0.301374\pi\)
\(74\) 8.31795 0.966942
\(75\) 6.04641 0.698179
\(76\) −7.13386 −0.818310
\(77\) 3.91566 0.446231
\(78\) 2.77487 0.314192
\(79\) 16.7103 1.88006 0.940029 0.341094i \(-0.110797\pi\)
0.940029 + 0.341094i \(0.110797\pi\)
\(80\) −3.32361 −0.371591
\(81\) 1.00000 0.111111
\(82\) −9.01414 −0.995445
\(83\) 3.25047 0.356786 0.178393 0.983959i \(-0.442910\pi\)
0.178393 + 0.983959i \(0.442910\pi\)
\(84\) −3.91566 −0.427233
\(85\) −2.68261 −0.290970
\(86\) −10.4023 −1.12171
\(87\) −8.37002 −0.897361
\(88\) 1.00000 0.106600
\(89\) −14.1282 −1.49759 −0.748793 0.662804i \(-0.769366\pi\)
−0.748793 + 0.662804i \(0.769366\pi\)
\(90\) 3.32361 0.350340
\(91\) 10.8654 1.13901
\(92\) −5.96773 −0.622179
\(93\) −0.644116 −0.0667917
\(94\) 2.49766 0.257614
\(95\) 23.7102 2.43262
\(96\) −1.00000 −0.102062
\(97\) −12.4575 −1.26487 −0.632433 0.774615i \(-0.717943\pi\)
−0.632433 + 0.774615i \(0.717943\pi\)
\(98\) −8.33239 −0.841698
\(99\) −1.00000 −0.100504
\(100\) 6.04641 0.604641
\(101\) −3.04203 −0.302693 −0.151347 0.988481i \(-0.548361\pi\)
−0.151347 + 0.988481i \(0.548361\pi\)
\(102\) −0.807136 −0.0799184
\(103\) −12.4252 −1.22429 −0.612146 0.790745i \(-0.709694\pi\)
−0.612146 + 0.790745i \(0.709694\pi\)
\(104\) 2.77487 0.272098
\(105\) 13.0141 1.27005
\(106\) −0.130750 −0.0126996
\(107\) −0.406685 −0.0393157 −0.0196579 0.999807i \(-0.506258\pi\)
−0.0196579 + 0.999807i \(0.506258\pi\)
\(108\) 1.00000 0.0962250
\(109\) −3.50077 −0.335313 −0.167657 0.985845i \(-0.553620\pi\)
−0.167657 + 0.985845i \(0.553620\pi\)
\(110\) −3.32361 −0.316894
\(111\) −8.31795 −0.789505
\(112\) −3.91566 −0.369995
\(113\) −16.9353 −1.59314 −0.796571 0.604545i \(-0.793355\pi\)
−0.796571 + 0.604545i \(0.793355\pi\)
\(114\) 7.13386 0.668147
\(115\) 19.8344 1.84957
\(116\) −8.37002 −0.777137
\(117\) −2.77487 −0.256536
\(118\) 14.3533 1.32133
\(119\) −3.16047 −0.289720
\(120\) 3.32361 0.303403
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 9.01414 0.812778
\(124\) −0.644116 −0.0578433
\(125\) −3.47786 −0.311069
\(126\) 3.91566 0.348835
\(127\) 0.0833558 0.00739663 0.00369831 0.999993i \(-0.498823\pi\)
0.00369831 + 0.999993i \(0.498823\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.4023 0.915871
\(130\) −9.22258 −0.808874
\(131\) 18.1194 1.58310 0.791551 0.611103i \(-0.209274\pi\)
0.791551 + 0.611103i \(0.209274\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 27.9338 2.42217
\(134\) −11.9931 −1.03604
\(135\) −3.32361 −0.286051
\(136\) −0.807136 −0.0692114
\(137\) −10.0875 −0.861829 −0.430915 0.902393i \(-0.641809\pi\)
−0.430915 + 0.902393i \(0.641809\pi\)
\(138\) 5.96773 0.508007
\(139\) −2.57409 −0.218331 −0.109166 0.994024i \(-0.534818\pi\)
−0.109166 + 0.994024i \(0.534818\pi\)
\(140\) 13.0141 1.09990
\(141\) −2.49766 −0.210341
\(142\) 12.0031 1.00728
\(143\) 2.77487 0.232046
\(144\) 1.00000 0.0833333
\(145\) 27.8187 2.31022
\(146\) −9.98430 −0.826306
\(147\) 8.33239 0.687244
\(148\) −8.31795 −0.683732
\(149\) 19.3798 1.58765 0.793827 0.608144i \(-0.208086\pi\)
0.793827 + 0.608144i \(0.208086\pi\)
\(150\) −6.04641 −0.493687
\(151\) 11.6305 0.946480 0.473240 0.880934i \(-0.343084\pi\)
0.473240 + 0.880934i \(0.343084\pi\)
\(152\) 7.13386 0.578633
\(153\) 0.807136 0.0652531
\(154\) −3.91566 −0.315533
\(155\) 2.14079 0.171953
\(156\) −2.77487 −0.222167
\(157\) 12.0906 0.964932 0.482466 0.875915i \(-0.339741\pi\)
0.482466 + 0.875915i \(0.339741\pi\)
\(158\) −16.7103 −1.32940
\(159\) 0.130750 0.0103692
\(160\) 3.32361 0.262755
\(161\) 23.3676 1.84162
\(162\) −1.00000 −0.0785674
\(163\) 23.4030 1.83306 0.916531 0.399963i \(-0.130977\pi\)
0.916531 + 0.399963i \(0.130977\pi\)
\(164\) 9.01414 0.703886
\(165\) 3.32361 0.258743
\(166\) −3.25047 −0.252286
\(167\) 9.58638 0.741817 0.370908 0.928669i \(-0.379046\pi\)
0.370908 + 0.928669i \(0.379046\pi\)
\(168\) 3.91566 0.302100
\(169\) −5.30012 −0.407701
\(170\) 2.68261 0.205747
\(171\) −7.13386 −0.545540
\(172\) 10.4023 0.793167
\(173\) −12.3525 −0.939141 −0.469571 0.882895i \(-0.655591\pi\)
−0.469571 + 0.882895i \(0.655591\pi\)
\(174\) 8.37002 0.634530
\(175\) −23.6757 −1.78971
\(176\) −1.00000 −0.0753778
\(177\) −14.3533 −1.07886
\(178\) 14.1282 1.05895
\(179\) −4.78053 −0.357313 −0.178657 0.983911i \(-0.557175\pi\)
−0.178657 + 0.983911i \(0.557175\pi\)
\(180\) −3.32361 −0.247728
\(181\) 22.0037 1.63552 0.817760 0.575559i \(-0.195216\pi\)
0.817760 + 0.575559i \(0.195216\pi\)
\(182\) −10.8654 −0.805399
\(183\) −1.00000 −0.0739221
\(184\) 5.96773 0.439947
\(185\) 27.6457 2.03255
\(186\) 0.644116 0.0472289
\(187\) −0.807136 −0.0590237
\(188\) −2.49766 −0.182161
\(189\) −3.91566 −0.284822
\(190\) −23.7102 −1.72012
\(191\) −7.89570 −0.571313 −0.285656 0.958332i \(-0.592212\pi\)
−0.285656 + 0.958332i \(0.592212\pi\)
\(192\) 1.00000 0.0721688
\(193\) −8.24919 −0.593790 −0.296895 0.954910i \(-0.595951\pi\)
−0.296895 + 0.954910i \(0.595951\pi\)
\(194\) 12.4575 0.894395
\(195\) 9.22258 0.660443
\(196\) 8.33239 0.595170
\(197\) −3.26843 −0.232866 −0.116433 0.993199i \(-0.537146\pi\)
−0.116433 + 0.993199i \(0.537146\pi\)
\(198\) 1.00000 0.0710669
\(199\) 12.1108 0.858510 0.429255 0.903183i \(-0.358776\pi\)
0.429255 + 0.903183i \(0.358776\pi\)
\(200\) −6.04641 −0.427546
\(201\) 11.9931 0.845926
\(202\) 3.04203 0.214036
\(203\) 32.7742 2.30030
\(204\) 0.807136 0.0565109
\(205\) −29.9595 −2.09246
\(206\) 12.4252 0.865705
\(207\) −5.96773 −0.414786
\(208\) −2.77487 −0.192402
\(209\) 7.13386 0.493460
\(210\) −13.0141 −0.898061
\(211\) 1.11333 0.0766446 0.0383223 0.999265i \(-0.487799\pi\)
0.0383223 + 0.999265i \(0.487799\pi\)
\(212\) 0.130750 0.00897997
\(213\) −12.0031 −0.822440
\(214\) 0.406685 0.0278004
\(215\) −34.5732 −2.35787
\(216\) −1.00000 −0.0680414
\(217\) 2.52214 0.171214
\(218\) 3.50077 0.237102
\(219\) 9.98430 0.674676
\(220\) 3.32361 0.224078
\(221\) −2.23970 −0.150658
\(222\) 8.31795 0.558264
\(223\) −23.2289 −1.55552 −0.777762 0.628559i \(-0.783645\pi\)
−0.777762 + 0.628559i \(0.783645\pi\)
\(224\) 3.91566 0.261626
\(225\) 6.04641 0.403094
\(226\) 16.9353 1.12652
\(227\) 11.1327 0.738904 0.369452 0.929250i \(-0.379545\pi\)
0.369452 + 0.929250i \(0.379545\pi\)
\(228\) −7.13386 −0.472452
\(229\) 13.8435 0.914804 0.457402 0.889260i \(-0.348780\pi\)
0.457402 + 0.889260i \(0.348780\pi\)
\(230\) −19.8344 −1.30784
\(231\) 3.91566 0.257631
\(232\) 8.37002 0.549519
\(233\) −23.9928 −1.57182 −0.785909 0.618342i \(-0.787805\pi\)
−0.785909 + 0.618342i \(0.787805\pi\)
\(234\) 2.77487 0.181399
\(235\) 8.30126 0.541515
\(236\) −14.3533 −0.934323
\(237\) 16.7103 1.08545
\(238\) 3.16047 0.204863
\(239\) −18.2856 −1.18279 −0.591397 0.806380i \(-0.701423\pi\)
−0.591397 + 0.806380i \(0.701423\pi\)
\(240\) −3.32361 −0.214538
\(241\) −15.7631 −1.01539 −0.507696 0.861536i \(-0.669503\pi\)
−0.507696 + 0.861536i \(0.669503\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −27.6936 −1.76928
\(246\) −9.01414 −0.574721
\(247\) 19.7955 1.25956
\(248\) 0.644116 0.0409014
\(249\) 3.25047 0.205990
\(250\) 3.47786 0.219959
\(251\) 13.6086 0.858968 0.429484 0.903074i \(-0.358695\pi\)
0.429484 + 0.903074i \(0.358695\pi\)
\(252\) −3.91566 −0.246663
\(253\) 5.96773 0.375188
\(254\) −0.0833558 −0.00523021
\(255\) −2.68261 −0.167992
\(256\) 1.00000 0.0625000
\(257\) 22.9018 1.42857 0.714287 0.699852i \(-0.246751\pi\)
0.714287 + 0.699852i \(0.246751\pi\)
\(258\) −10.4023 −0.647619
\(259\) 32.5703 2.02382
\(260\) 9.22258 0.571960
\(261\) −8.37002 −0.518091
\(262\) −18.1194 −1.11942
\(263\) −19.2813 −1.18894 −0.594468 0.804120i \(-0.702637\pi\)
−0.594468 + 0.804120i \(0.702637\pi\)
\(264\) 1.00000 0.0615457
\(265\) −0.434564 −0.0266950
\(266\) −27.9338 −1.71273
\(267\) −14.1282 −0.864632
\(268\) 11.9931 0.732593
\(269\) 30.4439 1.85620 0.928099 0.372334i \(-0.121443\pi\)
0.928099 + 0.372334i \(0.121443\pi\)
\(270\) 3.32361 0.202269
\(271\) 14.8369 0.901275 0.450637 0.892707i \(-0.351197\pi\)
0.450637 + 0.892707i \(0.351197\pi\)
\(272\) 0.807136 0.0489398
\(273\) 10.8654 0.657606
\(274\) 10.0875 0.609405
\(275\) −6.04641 −0.364612
\(276\) −5.96773 −0.359215
\(277\) −20.0794 −1.20645 −0.603226 0.797570i \(-0.706118\pi\)
−0.603226 + 0.797570i \(0.706118\pi\)
\(278\) 2.57409 0.154383
\(279\) −0.644116 −0.0385622
\(280\) −13.0141 −0.777744
\(281\) 9.91566 0.591519 0.295759 0.955262i \(-0.404427\pi\)
0.295759 + 0.955262i \(0.404427\pi\)
\(282\) 2.49766 0.148734
\(283\) 22.2578 1.32309 0.661544 0.749906i \(-0.269901\pi\)
0.661544 + 0.749906i \(0.269901\pi\)
\(284\) −12.0031 −0.712254
\(285\) 23.7102 1.40447
\(286\) −2.77487 −0.164081
\(287\) −35.2963 −2.08347
\(288\) −1.00000 −0.0589256
\(289\) −16.3485 −0.961678
\(290\) −27.8187 −1.63357
\(291\) −12.4575 −0.730270
\(292\) 9.98430 0.584287
\(293\) 0.943253 0.0551054 0.0275527 0.999620i \(-0.491229\pi\)
0.0275527 + 0.999620i \(0.491229\pi\)
\(294\) −8.33239 −0.485955
\(295\) 47.7049 2.77749
\(296\) 8.31795 0.483471
\(297\) −1.00000 −0.0580259
\(298\) −19.3798 −1.12264
\(299\) 16.5597 0.957669
\(300\) 6.04641 0.349090
\(301\) −40.7318 −2.34774
\(302\) −11.6305 −0.669262
\(303\) −3.04203 −0.174760
\(304\) −7.13386 −0.409155
\(305\) 3.32361 0.190310
\(306\) −0.807136 −0.0461409
\(307\) 18.0430 1.02977 0.514884 0.857260i \(-0.327835\pi\)
0.514884 + 0.857260i \(0.327835\pi\)
\(308\) 3.91566 0.223115
\(309\) −12.4252 −0.706845
\(310\) −2.14079 −0.121589
\(311\) 15.0514 0.853485 0.426742 0.904373i \(-0.359661\pi\)
0.426742 + 0.904373i \(0.359661\pi\)
\(312\) 2.77487 0.157096
\(313\) 13.1048 0.740729 0.370364 0.928887i \(-0.379233\pi\)
0.370364 + 0.928887i \(0.379233\pi\)
\(314\) −12.0906 −0.682310
\(315\) 13.0141 0.733264
\(316\) 16.7103 0.940029
\(317\) −3.78844 −0.212780 −0.106390 0.994324i \(-0.533929\pi\)
−0.106390 + 0.994324i \(0.533929\pi\)
\(318\) −0.130750 −0.00733211
\(319\) 8.37002 0.468631
\(320\) −3.32361 −0.185796
\(321\) −0.406685 −0.0226990
\(322\) −23.3676 −1.30223
\(323\) −5.75800 −0.320384
\(324\) 1.00000 0.0555556
\(325\) −16.7780 −0.930675
\(326\) −23.4030 −1.29617
\(327\) −3.50077 −0.193593
\(328\) −9.01414 −0.497723
\(329\) 9.77999 0.539188
\(330\) −3.32361 −0.182959
\(331\) −33.4307 −1.83752 −0.918760 0.394817i \(-0.870808\pi\)
−0.918760 + 0.394817i \(0.870808\pi\)
\(332\) 3.25047 0.178393
\(333\) −8.31795 −0.455821
\(334\) −9.58638 −0.524544
\(335\) −39.8603 −2.17780
\(336\) −3.91566 −0.213617
\(337\) −6.57265 −0.358035 −0.179017 0.983846i \(-0.557292\pi\)
−0.179017 + 0.983846i \(0.557292\pi\)
\(338\) 5.30012 0.288288
\(339\) −16.9353 −0.919801
\(340\) −2.68261 −0.145485
\(341\) 0.644116 0.0348808
\(342\) 7.13386 0.385755
\(343\) −5.21717 −0.281701
\(344\) −10.4023 −0.560854
\(345\) 19.8344 1.06785
\(346\) 12.3525 0.664073
\(347\) −13.6625 −0.733442 −0.366721 0.930331i \(-0.619520\pi\)
−0.366721 + 0.930331i \(0.619520\pi\)
\(348\) −8.37002 −0.448680
\(349\) 15.5871 0.834359 0.417180 0.908824i \(-0.363019\pi\)
0.417180 + 0.908824i \(0.363019\pi\)
\(350\) 23.6757 1.26552
\(351\) −2.77487 −0.148111
\(352\) 1.00000 0.0533002
\(353\) −27.3100 −1.45357 −0.726783 0.686867i \(-0.758986\pi\)
−0.726783 + 0.686867i \(0.758986\pi\)
\(354\) 14.3533 0.762871
\(355\) 39.8937 2.11734
\(356\) −14.1282 −0.748793
\(357\) −3.16047 −0.167270
\(358\) 4.78053 0.252659
\(359\) 2.41656 0.127541 0.0637705 0.997965i \(-0.479687\pi\)
0.0637705 + 0.997965i \(0.479687\pi\)
\(360\) 3.32361 0.175170
\(361\) 31.8920 1.67853
\(362\) −22.0037 −1.15649
\(363\) 1.00000 0.0524864
\(364\) 10.8654 0.569503
\(365\) −33.1839 −1.73693
\(366\) 1.00000 0.0522708
\(367\) −19.6890 −1.02776 −0.513878 0.857864i \(-0.671791\pi\)
−0.513878 + 0.857864i \(0.671791\pi\)
\(368\) −5.96773 −0.311089
\(369\) 9.01414 0.469257
\(370\) −27.6457 −1.43723
\(371\) −0.511974 −0.0265804
\(372\) −0.644116 −0.0333959
\(373\) −3.71020 −0.192107 −0.0960535 0.995376i \(-0.530622\pi\)
−0.0960535 + 0.995376i \(0.530622\pi\)
\(374\) 0.807136 0.0417360
\(375\) −3.47786 −0.179596
\(376\) 2.49766 0.128807
\(377\) 23.2257 1.19618
\(378\) 3.91566 0.201400
\(379\) 2.53813 0.130375 0.0651875 0.997873i \(-0.479235\pi\)
0.0651875 + 0.997873i \(0.479235\pi\)
\(380\) 23.7102 1.21631
\(381\) 0.0833558 0.00427044
\(382\) 7.89570 0.403979
\(383\) −31.5793 −1.61363 −0.806813 0.590807i \(-0.798809\pi\)
−0.806813 + 0.590807i \(0.798809\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −13.0141 −0.663262
\(386\) 8.24919 0.419873
\(387\) 10.4023 0.528778
\(388\) −12.4575 −0.632433
\(389\) −4.45252 −0.225752 −0.112876 0.993609i \(-0.536006\pi\)
−0.112876 + 0.993609i \(0.536006\pi\)
\(390\) −9.22258 −0.467004
\(391\) −4.81677 −0.243595
\(392\) −8.33239 −0.420849
\(393\) 18.1194 0.914004
\(394\) 3.26843 0.164661
\(395\) −55.5387 −2.79445
\(396\) −1.00000 −0.0502519
\(397\) −24.1293 −1.21102 −0.605508 0.795839i \(-0.707030\pi\)
−0.605508 + 0.795839i \(0.707030\pi\)
\(398\) −12.1108 −0.607058
\(399\) 27.9338 1.39844
\(400\) 6.04641 0.302320
\(401\) 20.9175 1.04457 0.522285 0.852771i \(-0.325080\pi\)
0.522285 + 0.852771i \(0.325080\pi\)
\(402\) −11.9931 −0.598160
\(403\) 1.78734 0.0890335
\(404\) −3.04203 −0.151347
\(405\) −3.32361 −0.165152
\(406\) −32.7742 −1.62655
\(407\) 8.31795 0.412306
\(408\) −0.807136 −0.0399592
\(409\) −31.6698 −1.56597 −0.782987 0.622039i \(-0.786305\pi\)
−0.782987 + 0.622039i \(0.786305\pi\)
\(410\) 29.9595 1.47960
\(411\) −10.0875 −0.497577
\(412\) −12.4252 −0.612146
\(413\) 56.2028 2.76556
\(414\) 5.96773 0.293298
\(415\) −10.8033 −0.530314
\(416\) 2.77487 0.136049
\(417\) −2.57409 −0.126054
\(418\) −7.13386 −0.348929
\(419\) 14.9639 0.731035 0.365517 0.930804i \(-0.380892\pi\)
0.365517 + 0.930804i \(0.380892\pi\)
\(420\) 13.0141 0.635025
\(421\) 23.1925 1.13033 0.565166 0.824977i \(-0.308812\pi\)
0.565166 + 0.824977i \(0.308812\pi\)
\(422\) −1.11333 −0.0541959
\(423\) −2.49766 −0.121440
\(424\) −0.130750 −0.00634980
\(425\) 4.88028 0.236728
\(426\) 12.0031 0.581553
\(427\) 3.91566 0.189492
\(428\) −0.406685 −0.0196579
\(429\) 2.77487 0.133972
\(430\) 34.5732 1.66727
\(431\) 31.4330 1.51407 0.757037 0.653372i \(-0.226646\pi\)
0.757037 + 0.653372i \(0.226646\pi\)
\(432\) 1.00000 0.0481125
\(433\) −23.8895 −1.14806 −0.574028 0.818836i \(-0.694620\pi\)
−0.574028 + 0.818836i \(0.694620\pi\)
\(434\) −2.52214 −0.121067
\(435\) 27.8187 1.33381
\(436\) −3.50077 −0.167657
\(437\) 42.5730 2.03654
\(438\) −9.98430 −0.477068
\(439\) −24.3409 −1.16173 −0.580863 0.814001i \(-0.697285\pi\)
−0.580863 + 0.814001i \(0.697285\pi\)
\(440\) −3.32361 −0.158447
\(441\) 8.33239 0.396780
\(442\) 2.23970 0.106531
\(443\) −24.7483 −1.17583 −0.587913 0.808924i \(-0.700050\pi\)
−0.587913 + 0.808924i \(0.700050\pi\)
\(444\) −8.31795 −0.394753
\(445\) 46.9567 2.22596
\(446\) 23.2289 1.09992
\(447\) 19.3798 0.916632
\(448\) −3.91566 −0.184998
\(449\) 6.44772 0.304287 0.152143 0.988358i \(-0.451382\pi\)
0.152143 + 0.988358i \(0.451382\pi\)
\(450\) −6.04641 −0.285030
\(451\) −9.01414 −0.424459
\(452\) −16.9353 −0.796571
\(453\) 11.6305 0.546450
\(454\) −11.1327 −0.522484
\(455\) −36.1125 −1.69298
\(456\) 7.13386 0.334074
\(457\) −8.49877 −0.397556 −0.198778 0.980045i \(-0.563697\pi\)
−0.198778 + 0.980045i \(0.563697\pi\)
\(458\) −13.8435 −0.646864
\(459\) 0.807136 0.0376739
\(460\) 19.8344 0.924785
\(461\) 3.36904 0.156912 0.0784559 0.996918i \(-0.475001\pi\)
0.0784559 + 0.996918i \(0.475001\pi\)
\(462\) −3.91566 −0.182173
\(463\) 7.77444 0.361309 0.180655 0.983547i \(-0.442178\pi\)
0.180655 + 0.983547i \(0.442178\pi\)
\(464\) −8.37002 −0.388569
\(465\) 2.14079 0.0992769
\(466\) 23.9928 1.11144
\(467\) 5.06904 0.234567 0.117284 0.993098i \(-0.462581\pi\)
0.117284 + 0.993098i \(0.462581\pi\)
\(468\) −2.77487 −0.128268
\(469\) −46.9608 −2.16845
\(470\) −8.30126 −0.382909
\(471\) 12.0906 0.557104
\(472\) 14.3533 0.660666
\(473\) −10.4023 −0.478298
\(474\) −16.7103 −0.767531
\(475\) −43.1343 −1.97914
\(476\) −3.16047 −0.144860
\(477\) 0.130750 0.00598665
\(478\) 18.2856 0.836362
\(479\) 2.62190 0.119798 0.0598988 0.998204i \(-0.480922\pi\)
0.0598988 + 0.998204i \(0.480922\pi\)
\(480\) 3.32361 0.151702
\(481\) 23.0812 1.05241
\(482\) 15.7631 0.717991
\(483\) 23.3676 1.06326
\(484\) 1.00000 0.0454545
\(485\) 41.4038 1.88005
\(486\) −1.00000 −0.0453609
\(487\) 5.61653 0.254509 0.127255 0.991870i \(-0.459383\pi\)
0.127255 + 0.991870i \(0.459383\pi\)
\(488\) 1.00000 0.0452679
\(489\) 23.4030 1.05832
\(490\) 27.6936 1.25107
\(491\) −12.3413 −0.556956 −0.278478 0.960443i \(-0.589830\pi\)
−0.278478 + 0.960443i \(0.589830\pi\)
\(492\) 9.01414 0.406389
\(493\) −6.75575 −0.304264
\(494\) −19.7955 −0.890642
\(495\) 3.32361 0.149385
\(496\) −0.644116 −0.0289217
\(497\) 47.0001 2.10824
\(498\) −3.25047 −0.145657
\(499\) −22.5628 −1.01005 −0.505024 0.863105i \(-0.668516\pi\)
−0.505024 + 0.863105i \(0.668516\pi\)
\(500\) −3.47786 −0.155535
\(501\) 9.58638 0.428288
\(502\) −13.6086 −0.607382
\(503\) 4.85240 0.216358 0.108179 0.994131i \(-0.465498\pi\)
0.108179 + 0.994131i \(0.465498\pi\)
\(504\) 3.91566 0.174417
\(505\) 10.1105 0.449913
\(506\) −5.96773 −0.265298
\(507\) −5.30012 −0.235386
\(508\) 0.0833558 0.00369831
\(509\) 11.4961 0.509556 0.254778 0.967000i \(-0.417998\pi\)
0.254778 + 0.967000i \(0.417998\pi\)
\(510\) 2.68261 0.118788
\(511\) −39.0951 −1.72947
\(512\) −1.00000 −0.0441942
\(513\) −7.13386 −0.314968
\(514\) −22.9018 −1.01015
\(515\) 41.2966 1.81975
\(516\) 10.4023 0.457935
\(517\) 2.49766 0.109847
\(518\) −32.5703 −1.43106
\(519\) −12.3525 −0.542214
\(520\) −9.22258 −0.404437
\(521\) 31.6025 1.38453 0.692265 0.721644i \(-0.256613\pi\)
0.692265 + 0.721644i \(0.256613\pi\)
\(522\) 8.37002 0.366346
\(523\) −19.5926 −0.856725 −0.428362 0.903607i \(-0.640909\pi\)
−0.428362 + 0.903607i \(0.640909\pi\)
\(524\) 18.1194 0.791551
\(525\) −23.6757 −1.03329
\(526\) 19.2813 0.840704
\(527\) −0.519889 −0.0226467
\(528\) −1.00000 −0.0435194
\(529\) 12.6138 0.548426
\(530\) 0.434564 0.0188762
\(531\) −14.3533 −0.622882
\(532\) 27.9338 1.21108
\(533\) −25.0130 −1.08343
\(534\) 14.1282 0.611387
\(535\) 1.35166 0.0584376
\(536\) −11.9931 −0.518022
\(537\) −4.78053 −0.206295
\(538\) −30.4439 −1.31253
\(539\) −8.33239 −0.358901
\(540\) −3.32361 −0.143026
\(541\) 26.2198 1.12728 0.563638 0.826022i \(-0.309401\pi\)
0.563638 + 0.826022i \(0.309401\pi\)
\(542\) −14.8369 −0.637298
\(543\) 22.0037 0.944268
\(544\) −0.807136 −0.0346057
\(545\) 11.6352 0.498398
\(546\) −10.8654 −0.464998
\(547\) 1.24847 0.0533807 0.0266903 0.999644i \(-0.491503\pi\)
0.0266903 + 0.999644i \(0.491503\pi\)
\(548\) −10.0875 −0.430915
\(549\) −1.00000 −0.0426790
\(550\) 6.04641 0.257820
\(551\) 59.7106 2.54376
\(552\) 5.96773 0.254003
\(553\) −65.4319 −2.78245
\(554\) 20.0794 0.853090
\(555\) 27.6457 1.17349
\(556\) −2.57409 −0.109166
\(557\) 17.4996 0.741483 0.370741 0.928736i \(-0.379104\pi\)
0.370741 + 0.928736i \(0.379104\pi\)
\(558\) 0.644116 0.0272676
\(559\) −28.8650 −1.22086
\(560\) 13.0141 0.549948
\(561\) −0.807136 −0.0340773
\(562\) −9.91566 −0.418267
\(563\) 7.44473 0.313758 0.156879 0.987618i \(-0.449857\pi\)
0.156879 + 0.987618i \(0.449857\pi\)
\(564\) −2.49766 −0.105171
\(565\) 56.2865 2.36799
\(566\) −22.2578 −0.935565
\(567\) −3.91566 −0.164442
\(568\) 12.0031 0.503639
\(569\) 17.4883 0.733148 0.366574 0.930389i \(-0.380531\pi\)
0.366574 + 0.930389i \(0.380531\pi\)
\(570\) −23.7102 −0.993111
\(571\) 36.6687 1.53454 0.767270 0.641325i \(-0.221615\pi\)
0.767270 + 0.641325i \(0.221615\pi\)
\(572\) 2.77487 0.116023
\(573\) −7.89570 −0.329847
\(574\) 35.2963 1.47324
\(575\) −36.0833 −1.50478
\(576\) 1.00000 0.0416667
\(577\) 23.6678 0.985301 0.492651 0.870227i \(-0.336028\pi\)
0.492651 + 0.870227i \(0.336028\pi\)
\(578\) 16.3485 0.680009
\(579\) −8.24919 −0.342825
\(580\) 27.8187 1.15511
\(581\) −12.7277 −0.528036
\(582\) 12.4575 0.516379
\(583\) −0.130750 −0.00541513
\(584\) −9.98430 −0.413153
\(585\) 9.22258 0.381307
\(586\) −0.943253 −0.0389654
\(587\) −40.3512 −1.66547 −0.832736 0.553670i \(-0.813227\pi\)
−0.832736 + 0.553670i \(0.813227\pi\)
\(588\) 8.33239 0.343622
\(589\) 4.59503 0.189335
\(590\) −47.7049 −1.96398
\(591\) −3.26843 −0.134445
\(592\) −8.31795 −0.341866
\(593\) −20.4508 −0.839816 −0.419908 0.907567i \(-0.637938\pi\)
−0.419908 + 0.907567i \(0.637938\pi\)
\(594\) 1.00000 0.0410305
\(595\) 10.5042 0.430630
\(596\) 19.3798 0.793827
\(597\) 12.1108 0.495661
\(598\) −16.5597 −0.677175
\(599\) 8.00213 0.326958 0.163479 0.986547i \(-0.447728\pi\)
0.163479 + 0.986547i \(0.447728\pi\)
\(600\) −6.04641 −0.246844
\(601\) −38.6988 −1.57856 −0.789279 0.614035i \(-0.789546\pi\)
−0.789279 + 0.614035i \(0.789546\pi\)
\(602\) 40.7318 1.66011
\(603\) 11.9931 0.488396
\(604\) 11.6305 0.473240
\(605\) −3.32361 −0.135124
\(606\) 3.04203 0.123574
\(607\) 16.4545 0.667867 0.333934 0.942597i \(-0.391624\pi\)
0.333934 + 0.942597i \(0.391624\pi\)
\(608\) 7.13386 0.289316
\(609\) 32.7742 1.32808
\(610\) −3.32361 −0.134569
\(611\) 6.93068 0.280385
\(612\) 0.807136 0.0326266
\(613\) −22.9397 −0.926527 −0.463263 0.886221i \(-0.653322\pi\)
−0.463263 + 0.886221i \(0.653322\pi\)
\(614\) −18.0430 −0.728156
\(615\) −29.9595 −1.20808
\(616\) −3.91566 −0.157766
\(617\) −47.6198 −1.91710 −0.958550 0.284924i \(-0.908032\pi\)
−0.958550 + 0.284924i \(0.908032\pi\)
\(618\) 12.4252 0.499815
\(619\) −13.7119 −0.551127 −0.275563 0.961283i \(-0.588864\pi\)
−0.275563 + 0.961283i \(0.588864\pi\)
\(620\) 2.14079 0.0859763
\(621\) −5.96773 −0.239477
\(622\) −15.0514 −0.603505
\(623\) 55.3212 2.21640
\(624\) −2.77487 −0.111084
\(625\) −18.6730 −0.746919
\(626\) −13.1048 −0.523774
\(627\) 7.13386 0.284899
\(628\) 12.0906 0.482466
\(629\) −6.71372 −0.267694
\(630\) −13.0141 −0.518496
\(631\) −29.2950 −1.16622 −0.583108 0.812394i \(-0.698164\pi\)
−0.583108 + 0.812394i \(0.698164\pi\)
\(632\) −16.7103 −0.664701
\(633\) 1.11333 0.0442508
\(634\) 3.78844 0.150458
\(635\) −0.277042 −0.0109941
\(636\) 0.130750 0.00518459
\(637\) −23.1213 −0.916098
\(638\) −8.37002 −0.331372
\(639\) −12.0031 −0.474836
\(640\) 3.32361 0.131377
\(641\) 35.9524 1.42004 0.710018 0.704184i \(-0.248687\pi\)
0.710018 + 0.704184i \(0.248687\pi\)
\(642\) 0.406685 0.0160506
\(643\) −5.34924 −0.210954 −0.105477 0.994422i \(-0.533637\pi\)
−0.105477 + 0.994422i \(0.533637\pi\)
\(644\) 23.3676 0.920812
\(645\) −34.5732 −1.36132
\(646\) 5.75800 0.226545
\(647\) −18.3927 −0.723091 −0.361546 0.932354i \(-0.617751\pi\)
−0.361546 + 0.932354i \(0.617751\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 14.3533 0.563418
\(650\) 16.7780 0.658086
\(651\) 2.52214 0.0988504
\(652\) 23.4030 0.916531
\(653\) 5.98049 0.234035 0.117017 0.993130i \(-0.462667\pi\)
0.117017 + 0.993130i \(0.462667\pi\)
\(654\) 3.50077 0.136891
\(655\) −60.2220 −2.35307
\(656\) 9.01414 0.351943
\(657\) 9.98430 0.389524
\(658\) −9.77999 −0.381264
\(659\) −36.7362 −1.43104 −0.715520 0.698592i \(-0.753810\pi\)
−0.715520 + 0.698592i \(0.753810\pi\)
\(660\) 3.32361 0.129371
\(661\) 8.44202 0.328357 0.164178 0.986431i \(-0.447503\pi\)
0.164178 + 0.986431i \(0.447503\pi\)
\(662\) 33.4307 1.29932
\(663\) −2.23970 −0.0869826
\(664\) −3.25047 −0.126143
\(665\) −92.8411 −3.60022
\(666\) 8.31795 0.322314
\(667\) 49.9500 1.93407
\(668\) 9.58638 0.370908
\(669\) −23.2289 −0.898083
\(670\) 39.8603 1.53994
\(671\) 1.00000 0.0386046
\(672\) 3.91566 0.151050
\(673\) −20.7868 −0.801270 −0.400635 0.916238i \(-0.631211\pi\)
−0.400635 + 0.916238i \(0.631211\pi\)
\(674\) 6.57265 0.253169
\(675\) 6.04641 0.232726
\(676\) −5.30012 −0.203851
\(677\) −23.0018 −0.884032 −0.442016 0.897007i \(-0.645737\pi\)
−0.442016 + 0.897007i \(0.645737\pi\)
\(678\) 16.9353 0.650398
\(679\) 48.7792 1.87198
\(680\) 2.68261 0.102873
\(681\) 11.1327 0.426607
\(682\) −0.644116 −0.0246645
\(683\) −1.35728 −0.0519349 −0.0259675 0.999663i \(-0.508267\pi\)
−0.0259675 + 0.999663i \(0.508267\pi\)
\(684\) −7.13386 −0.272770
\(685\) 33.5268 1.28099
\(686\) 5.21717 0.199193
\(687\) 13.8435 0.528163
\(688\) 10.4023 0.396584
\(689\) −0.362815 −0.0138221
\(690\) −19.8344 −0.755084
\(691\) 29.7747 1.13268 0.566342 0.824170i \(-0.308358\pi\)
0.566342 + 0.824170i \(0.308358\pi\)
\(692\) −12.3525 −0.469571
\(693\) 3.91566 0.148744
\(694\) 13.6625 0.518622
\(695\) 8.55527 0.324520
\(696\) 8.37002 0.317265
\(697\) 7.27564 0.275585
\(698\) −15.5871 −0.589981
\(699\) −23.9928 −0.907490
\(700\) −23.6757 −0.894857
\(701\) −36.3283 −1.37210 −0.686050 0.727554i \(-0.740657\pi\)
−0.686050 + 0.727554i \(0.740657\pi\)
\(702\) 2.77487 0.104731
\(703\) 59.3391 2.23802
\(704\) −1.00000 −0.0376889
\(705\) 8.30126 0.312644
\(706\) 27.3100 1.02783
\(707\) 11.9115 0.447980
\(708\) −14.3533 −0.539431
\(709\) 0.0400134 0.00150274 0.000751368 1.00000i \(-0.499761\pi\)
0.000751368 1.00000i \(0.499761\pi\)
\(710\) −39.8937 −1.49718
\(711\) 16.7103 0.626686
\(712\) 14.1282 0.529477
\(713\) 3.84391 0.143956
\(714\) 3.16047 0.118278
\(715\) −9.22258 −0.344905
\(716\) −4.78053 −0.178657
\(717\) −18.2856 −0.682887
\(718\) −2.41656 −0.0901850
\(719\) 41.6522 1.55336 0.776682 0.629893i \(-0.216901\pi\)
0.776682 + 0.629893i \(0.216901\pi\)
\(720\) −3.32361 −0.123864
\(721\) 48.6529 1.81193
\(722\) −31.8920 −1.18690
\(723\) −15.7631 −0.586237
\(724\) 22.0037 0.817760
\(725\) −50.6086 −1.87956
\(726\) −1.00000 −0.0371135
\(727\) −8.83076 −0.327515 −0.163757 0.986501i \(-0.552361\pi\)
−0.163757 + 0.986501i \(0.552361\pi\)
\(728\) −10.8654 −0.402700
\(729\) 1.00000 0.0370370
\(730\) 33.1839 1.22819
\(731\) 8.39607 0.310540
\(732\) −1.00000 −0.0369611
\(733\) −5.35801 −0.197903 −0.0989513 0.995092i \(-0.531549\pi\)
−0.0989513 + 0.995092i \(0.531549\pi\)
\(734\) 19.6890 0.726733
\(735\) −27.6936 −1.02150
\(736\) 5.96773 0.219973
\(737\) −11.9931 −0.441770
\(738\) −9.01414 −0.331815
\(739\) 16.4781 0.606158 0.303079 0.952965i \(-0.401985\pi\)
0.303079 + 0.952965i \(0.401985\pi\)
\(740\) 27.6457 1.01627
\(741\) 19.7955 0.727206
\(742\) 0.511974 0.0187951
\(743\) −30.8241 −1.13083 −0.565413 0.824808i \(-0.691283\pi\)
−0.565413 + 0.824808i \(0.691283\pi\)
\(744\) 0.644116 0.0236144
\(745\) −64.4109 −2.35983
\(746\) 3.71020 0.135840
\(747\) 3.25047 0.118929
\(748\) −0.807136 −0.0295118
\(749\) 1.59244 0.0581865
\(750\) 3.47786 0.126994
\(751\) −0.0567469 −0.00207072 −0.00103536 0.999999i \(-0.500330\pi\)
−0.00103536 + 0.999999i \(0.500330\pi\)
\(752\) −2.49766 −0.0910804
\(753\) 13.6086 0.495925
\(754\) −23.2257 −0.845830
\(755\) −38.6554 −1.40681
\(756\) −3.91566 −0.142411
\(757\) 51.8773 1.88551 0.942756 0.333484i \(-0.108224\pi\)
0.942756 + 0.333484i \(0.108224\pi\)
\(758\) −2.53813 −0.0921891
\(759\) 5.96773 0.216615
\(760\) −23.7102 −0.860059
\(761\) −10.5467 −0.382319 −0.191160 0.981559i \(-0.561225\pi\)
−0.191160 + 0.981559i \(0.561225\pi\)
\(762\) −0.0833558 −0.00301966
\(763\) 13.7078 0.496257
\(764\) −7.89570 −0.285656
\(765\) −2.68261 −0.0969900
\(766\) 31.5793 1.14101
\(767\) 39.8286 1.43813
\(768\) 1.00000 0.0360844
\(769\) 22.2267 0.801514 0.400757 0.916184i \(-0.368747\pi\)
0.400757 + 0.916184i \(0.368747\pi\)
\(770\) 13.0141 0.468997
\(771\) 22.9018 0.824788
\(772\) −8.24919 −0.296895
\(773\) 21.0215 0.756090 0.378045 0.925787i \(-0.376596\pi\)
0.378045 + 0.925787i \(0.376596\pi\)
\(774\) −10.4023 −0.373903
\(775\) −3.89459 −0.139898
\(776\) 12.4575 0.447197
\(777\) 32.5703 1.16845
\(778\) 4.45252 0.159631
\(779\) −64.3056 −2.30399
\(780\) 9.22258 0.330221
\(781\) 12.0031 0.429505
\(782\) 4.81677 0.172247
\(783\) −8.37002 −0.299120
\(784\) 8.33239 0.297585
\(785\) −40.1844 −1.43424
\(786\) −18.1194 −0.646299
\(787\) −5.60095 −0.199652 −0.0998261 0.995005i \(-0.531829\pi\)
−0.0998261 + 0.995005i \(0.531829\pi\)
\(788\) −3.26843 −0.116433
\(789\) −19.2813 −0.686432
\(790\) 55.5387 1.97598
\(791\) 66.3130 2.35782
\(792\) 1.00000 0.0355335
\(793\) 2.77487 0.0985384
\(794\) 24.1293 0.856317
\(795\) −0.434564 −0.0154124
\(796\) 12.1108 0.429255
\(797\) −6.58795 −0.233357 −0.116679 0.993170i \(-0.537225\pi\)
−0.116679 + 0.993170i \(0.537225\pi\)
\(798\) −27.9338 −0.988845
\(799\) −2.01595 −0.0713193
\(800\) −6.04641 −0.213773
\(801\) −14.1282 −0.499195
\(802\) −20.9175 −0.738622
\(803\) −9.98430 −0.352338
\(804\) 11.9931 0.422963
\(805\) −77.6649 −2.73733
\(806\) −1.78734 −0.0629562
\(807\) 30.4439 1.07168
\(808\) 3.04203 0.107018
\(809\) −25.7442 −0.905116 −0.452558 0.891735i \(-0.649488\pi\)
−0.452558 + 0.891735i \(0.649488\pi\)
\(810\) 3.32361 0.116780
\(811\) 39.4129 1.38397 0.691987 0.721910i \(-0.256736\pi\)
0.691987 + 0.721910i \(0.256736\pi\)
\(812\) 32.7742 1.15015
\(813\) 14.8369 0.520351
\(814\) −8.31795 −0.291544
\(815\) −77.7825 −2.72460
\(816\) 0.807136 0.0282554
\(817\) −74.2085 −2.59623
\(818\) 31.6698 1.10731
\(819\) 10.8654 0.379669
\(820\) −29.9595 −1.04623
\(821\) 21.0603 0.735009 0.367505 0.930022i \(-0.380212\pi\)
0.367505 + 0.930022i \(0.380212\pi\)
\(822\) 10.0875 0.351840
\(823\) 17.3989 0.606487 0.303244 0.952913i \(-0.401930\pi\)
0.303244 + 0.952913i \(0.401930\pi\)
\(824\) 12.4252 0.432853
\(825\) −6.04641 −0.210509
\(826\) −56.2028 −1.95554
\(827\) −15.2596 −0.530630 −0.265315 0.964162i \(-0.585476\pi\)
−0.265315 + 0.964162i \(0.585476\pi\)
\(828\) −5.96773 −0.207393
\(829\) −35.3149 −1.22654 −0.613268 0.789875i \(-0.710145\pi\)
−0.613268 + 0.789875i \(0.710145\pi\)
\(830\) 10.8033 0.374989
\(831\) −20.0794 −0.696545
\(832\) −2.77487 −0.0962012
\(833\) 6.72537 0.233020
\(834\) 2.57409 0.0891333
\(835\) −31.8614 −1.10261
\(836\) 7.13386 0.246730
\(837\) −0.644116 −0.0222639
\(838\) −14.9639 −0.516920
\(839\) −55.9965 −1.93321 −0.966606 0.256266i \(-0.917508\pi\)
−0.966606 + 0.256266i \(0.917508\pi\)
\(840\) −13.0141 −0.449030
\(841\) 41.0573 1.41577
\(842\) −23.1925 −0.799265
\(843\) 9.91566 0.341513
\(844\) 1.11333 0.0383223
\(845\) 17.6155 0.605993
\(846\) 2.49766 0.0858714
\(847\) −3.91566 −0.134544
\(848\) 0.130750 0.00448998
\(849\) 22.2578 0.763886
\(850\) −4.88028 −0.167392
\(851\) 49.6393 1.70161
\(852\) −12.0031 −0.411220
\(853\) −54.4324 −1.86373 −0.931865 0.362805i \(-0.881819\pi\)
−0.931865 + 0.362805i \(0.881819\pi\)
\(854\) −3.91566 −0.133991
\(855\) 23.7102 0.810872
\(856\) 0.406685 0.0139002
\(857\) −18.1084 −0.618570 −0.309285 0.950969i \(-0.600090\pi\)
−0.309285 + 0.950969i \(0.600090\pi\)
\(858\) −2.77487 −0.0947324
\(859\) 17.1123 0.583865 0.291932 0.956439i \(-0.405702\pi\)
0.291932 + 0.956439i \(0.405702\pi\)
\(860\) −34.5732 −1.17894
\(861\) −35.2963 −1.20289
\(862\) −31.4330 −1.07061
\(863\) 22.4227 0.763276 0.381638 0.924312i \(-0.375360\pi\)
0.381638 + 0.924312i \(0.375360\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 41.0549 1.39591
\(866\) 23.8895 0.811798
\(867\) −16.3485 −0.555225
\(868\) 2.52214 0.0856070
\(869\) −16.7103 −0.566859
\(870\) −27.8187 −0.943143
\(871\) −33.2792 −1.12762
\(872\) 3.50077 0.118551
\(873\) −12.4575 −0.421622
\(874\) −42.5730 −1.44005
\(875\) 13.6181 0.460376
\(876\) 9.98430 0.337338
\(877\) −12.6452 −0.426999 −0.213499 0.976943i \(-0.568486\pi\)
−0.213499 + 0.976943i \(0.568486\pi\)
\(878\) 24.3409 0.821464
\(879\) 0.943253 0.0318151
\(880\) 3.32361 0.112039
\(881\) −19.8657 −0.669292 −0.334646 0.942344i \(-0.608617\pi\)
−0.334646 + 0.942344i \(0.608617\pi\)
\(882\) −8.33239 −0.280566
\(883\) −37.4856 −1.26149 −0.630746 0.775990i \(-0.717251\pi\)
−0.630746 + 0.775990i \(0.717251\pi\)
\(884\) −2.23970 −0.0753291
\(885\) 47.7049 1.60358
\(886\) 24.7483 0.831434
\(887\) 46.3574 1.55653 0.778265 0.627936i \(-0.216100\pi\)
0.778265 + 0.627936i \(0.216100\pi\)
\(888\) 8.31795 0.279132
\(889\) −0.326393 −0.0109469
\(890\) −46.9567 −1.57399
\(891\) −1.00000 −0.0335013
\(892\) −23.2289 −0.777762
\(893\) 17.8180 0.596256
\(894\) −19.3798 −0.648157
\(895\) 15.8886 0.531098
\(896\) 3.91566 0.130813
\(897\) 16.5597 0.552911
\(898\) −6.44772 −0.215163
\(899\) 5.39127 0.179809
\(900\) 6.04641 0.201547
\(901\) 0.105533 0.00351583
\(902\) 9.01414 0.300138
\(903\) −40.7318 −1.35547
\(904\) 16.9353 0.563261
\(905\) −73.1317 −2.43098
\(906\) −11.6305 −0.386399
\(907\) 32.1322 1.06693 0.533466 0.845822i \(-0.320889\pi\)
0.533466 + 0.845822i \(0.320889\pi\)
\(908\) 11.1327 0.369452
\(909\) −3.04203 −0.100898
\(910\) 36.1125 1.19712
\(911\) 18.0275 0.597276 0.298638 0.954366i \(-0.403468\pi\)
0.298638 + 0.954366i \(0.403468\pi\)
\(912\) −7.13386 −0.236226
\(913\) −3.25047 −0.107575
\(914\) 8.49877 0.281114
\(915\) 3.32361 0.109875
\(916\) 13.8435 0.457402
\(917\) −70.9495 −2.34296
\(918\) −0.807136 −0.0266395
\(919\) 2.88312 0.0951052 0.0475526 0.998869i \(-0.484858\pi\)
0.0475526 + 0.998869i \(0.484858\pi\)
\(920\) −19.8344 −0.653922
\(921\) 18.0430 0.594537
\(922\) −3.36904 −0.110953
\(923\) 33.3070 1.09631
\(924\) 3.91566 0.128816
\(925\) −50.2937 −1.65365
\(926\) −7.77444 −0.255484
\(927\) −12.4252 −0.408097
\(928\) 8.37002 0.274759
\(929\) −36.0073 −1.18136 −0.590681 0.806905i \(-0.701141\pi\)
−0.590681 + 0.806905i \(0.701141\pi\)
\(930\) −2.14079 −0.0701994
\(931\) −59.4421 −1.94814
\(932\) −23.9928 −0.785909
\(933\) 15.0514 0.492760
\(934\) −5.06904 −0.165864
\(935\) 2.68261 0.0877307
\(936\) 2.77487 0.0906993
\(937\) −47.6008 −1.55505 −0.777525 0.628851i \(-0.783525\pi\)
−0.777525 + 0.628851i \(0.783525\pi\)
\(938\) 46.9608 1.53332
\(939\) 13.1048 0.427660
\(940\) 8.30126 0.270757
\(941\) 19.2111 0.626264 0.313132 0.949710i \(-0.398622\pi\)
0.313132 + 0.949710i \(0.398622\pi\)
\(942\) −12.0906 −0.393932
\(943\) −53.7939 −1.75177
\(944\) −14.3533 −0.467161
\(945\) 13.0141 0.423350
\(946\) 10.4023 0.338208
\(947\) −25.5746 −0.831063 −0.415531 0.909579i \(-0.636404\pi\)
−0.415531 + 0.909579i \(0.636404\pi\)
\(948\) 16.7103 0.542726
\(949\) −27.7051 −0.899345
\(950\) 43.1343 1.39946
\(951\) −3.78844 −0.122849
\(952\) 3.16047 0.102431
\(953\) −24.8695 −0.805603 −0.402801 0.915287i \(-0.631963\pi\)
−0.402801 + 0.915287i \(0.631963\pi\)
\(954\) −0.130750 −0.00423320
\(955\) 26.2422 0.849179
\(956\) −18.2856 −0.591397
\(957\) 8.37002 0.270564
\(958\) −2.62190 −0.0847097
\(959\) 39.4990 1.27549
\(960\) −3.32361 −0.107269
\(961\) −30.5851 −0.986617
\(962\) −23.0812 −0.744168
\(963\) −0.406685 −0.0131052
\(964\) −15.7631 −0.507696
\(965\) 27.4171 0.882589
\(966\) −23.3676 −0.751840
\(967\) 13.5029 0.434223 0.217111 0.976147i \(-0.430336\pi\)
0.217111 + 0.976147i \(0.430336\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −5.75800 −0.184974
\(970\) −41.4038 −1.32940
\(971\) 44.2459 1.41992 0.709959 0.704243i \(-0.248713\pi\)
0.709959 + 0.704243i \(0.248713\pi\)
\(972\) 1.00000 0.0320750
\(973\) 10.0792 0.323126
\(974\) −5.61653 −0.179965
\(975\) −16.7780 −0.537325
\(976\) −1.00000 −0.0320092
\(977\) 20.0638 0.641898 0.320949 0.947096i \(-0.395998\pi\)
0.320949 + 0.947096i \(0.395998\pi\)
\(978\) −23.4030 −0.748345
\(979\) 14.1282 0.451539
\(980\) −27.6936 −0.884641
\(981\) −3.50077 −0.111771
\(982\) 12.3413 0.393828
\(983\) −4.55400 −0.145250 −0.0726251 0.997359i \(-0.523138\pi\)
−0.0726251 + 0.997359i \(0.523138\pi\)
\(984\) −9.01414 −0.287360
\(985\) 10.8630 0.346124
\(986\) 6.75575 0.215147
\(987\) 9.77999 0.311301
\(988\) 19.7955 0.629779
\(989\) −62.0781 −1.97397
\(990\) −3.32361 −0.105631
\(991\) −24.7967 −0.787692 −0.393846 0.919176i \(-0.628856\pi\)
−0.393846 + 0.919176i \(0.628856\pi\)
\(992\) 0.644116 0.0204507
\(993\) −33.4307 −1.06089
\(994\) −47.0001 −1.49075
\(995\) −40.2515 −1.27606
\(996\) 3.25047 0.102995
\(997\) −27.5577 −0.872761 −0.436381 0.899762i \(-0.643740\pi\)
−0.436381 + 0.899762i \(0.643740\pi\)
\(998\) 22.5628 0.714212
\(999\) −8.31795 −0.263168
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 4026.2.a.u.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.u.1.1 5 1.1 even 1 trivial