Properties

Label 4730.2.a.z.1.8
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
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 1.8
Root \(-1.53249\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.53249 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53249 q^{6} -0.583820 q^{7} -1.00000 q^{8} +3.41349 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.53249 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53249 q^{6} -0.583820 q^{7} -1.00000 q^{8} +3.41349 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.53249 q^{12} -4.55520 q^{13} +0.583820 q^{14} +2.53249 q^{15} +1.00000 q^{16} +5.04549 q^{17} -3.41349 q^{18} -4.92944 q^{19} +1.00000 q^{20} -1.47852 q^{21} -1.00000 q^{22} -0.815754 q^{23} -2.53249 q^{24} +1.00000 q^{25} +4.55520 q^{26} +1.04716 q^{27} -0.583820 q^{28} +7.94882 q^{29} -2.53249 q^{30} -2.45826 q^{31} -1.00000 q^{32} +2.53249 q^{33} -5.04549 q^{34} -0.583820 q^{35} +3.41349 q^{36} +3.39751 q^{37} +4.92944 q^{38} -11.5360 q^{39} -1.00000 q^{40} +10.9373 q^{41} +1.47852 q^{42} +1.00000 q^{43} +1.00000 q^{44} +3.41349 q^{45} +0.815754 q^{46} +7.21973 q^{47} +2.53249 q^{48} -6.65915 q^{49} -1.00000 q^{50} +12.7776 q^{51} -4.55520 q^{52} +11.9243 q^{53} -1.04716 q^{54} +1.00000 q^{55} +0.583820 q^{56} -12.4837 q^{57} -7.94882 q^{58} +9.88656 q^{59} +2.53249 q^{60} -7.37908 q^{61} +2.45826 q^{62} -1.99286 q^{63} +1.00000 q^{64} -4.55520 q^{65} -2.53249 q^{66} +9.44673 q^{67} +5.04549 q^{68} -2.06589 q^{69} +0.583820 q^{70} +11.2834 q^{71} -3.41349 q^{72} -1.95228 q^{73} -3.39751 q^{74} +2.53249 q^{75} -4.92944 q^{76} -0.583820 q^{77} +11.5360 q^{78} +16.0023 q^{79} +1.00000 q^{80} -7.58855 q^{81} -10.9373 q^{82} +0.0176475 q^{83} -1.47852 q^{84} +5.04549 q^{85} -1.00000 q^{86} +20.1303 q^{87} -1.00000 q^{88} -4.04716 q^{89} -3.41349 q^{90} +2.65942 q^{91} -0.815754 q^{92} -6.22551 q^{93} -7.21973 q^{94} -4.92944 q^{95} -2.53249 q^{96} +3.09439 q^{97} +6.65915 q^{98} +3.41349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 10q^{11} + 8q^{12} + 7q^{13} - 3q^{14} + 8q^{15} + 10q^{16} + 2q^{17} - 14q^{18} - 7q^{19} + 10q^{20} - 2q^{21} - 10q^{22} + 12q^{23} - 8q^{24} + 10q^{25} - 7q^{26} + 23q^{27} + 3q^{28} - 12q^{29} - 8q^{30} + 16q^{31} - 10q^{32} + 8q^{33} - 2q^{34} + 3q^{35} + 14q^{36} + 19q^{37} + 7q^{38} + 6q^{39} - 10q^{40} + 9q^{41} + 2q^{42} + 10q^{43} + 10q^{44} + 14q^{45} - 12q^{46} + 29q^{47} + 8q^{48} + 23q^{49} - 10q^{50} - 7q^{51} + 7q^{52} + 6q^{53} - 23q^{54} + 10q^{55} - 3q^{56} + 23q^{57} + 12q^{58} + 29q^{59} + 8q^{60} - 4q^{61} - 16q^{62} + 10q^{64} + 7q^{65} - 8q^{66} + 45q^{67} + 2q^{68} + 24q^{69} - 3q^{70} - 18q^{71} - 14q^{72} + 3q^{73} - 19q^{74} + 8q^{75} - 7q^{76} + 3q^{77} - 6q^{78} - 14q^{79} + 10q^{80} + 6q^{81} - 9q^{82} + 23q^{83} - 2q^{84} + 2q^{85} - 10q^{86} + 25q^{87} - 10q^{88} + q^{89} - 14q^{90} + q^{91} + 12q^{92} + 35q^{93} - 29q^{94} - 7q^{95} - 8q^{96} + 30q^{97} - 23q^{98} + 14q^{99} + O(q^{100}) \)

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
\(3\) 2.53249 1.46213 0.731066 0.682307i \(-0.239023\pi\)
0.731066 + 0.682307i \(0.239023\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.53249 −1.03388
\(7\) −0.583820 −0.220663 −0.110332 0.993895i \(-0.535191\pi\)
−0.110332 + 0.993895i \(0.535191\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.41349 1.13783
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 2.53249 0.731066
\(13\) −4.55520 −1.26338 −0.631692 0.775219i \(-0.717639\pi\)
−0.631692 + 0.775219i \(0.717639\pi\)
\(14\) 0.583820 0.156032
\(15\) 2.53249 0.653885
\(16\) 1.00000 0.250000
\(17\) 5.04549 1.22371 0.611856 0.790969i \(-0.290423\pi\)
0.611856 + 0.790969i \(0.290423\pi\)
\(18\) −3.41349 −0.804567
\(19\) −4.92944 −1.13089 −0.565445 0.824786i \(-0.691296\pi\)
−0.565445 + 0.824786i \(0.691296\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.47852 −0.322639
\(22\) −1.00000 −0.213201
\(23\) −0.815754 −0.170096 −0.0850482 0.996377i \(-0.527104\pi\)
−0.0850482 + 0.996377i \(0.527104\pi\)
\(24\) −2.53249 −0.516942
\(25\) 1.00000 0.200000
\(26\) 4.55520 0.893348
\(27\) 1.04716 0.201526
\(28\) −0.583820 −0.110332
\(29\) 7.94882 1.47606 0.738029 0.674769i \(-0.235757\pi\)
0.738029 + 0.674769i \(0.235757\pi\)
\(30\) −2.53249 −0.462367
\(31\) −2.45826 −0.441516 −0.220758 0.975329i \(-0.570853\pi\)
−0.220758 + 0.975329i \(0.570853\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.53249 0.440849
\(34\) −5.04549 −0.865294
\(35\) −0.583820 −0.0986836
\(36\) 3.41349 0.568915
\(37\) 3.39751 0.558547 0.279274 0.960212i \(-0.409906\pi\)
0.279274 + 0.960212i \(0.409906\pi\)
\(38\) 4.92944 0.799660
\(39\) −11.5360 −1.84724
\(40\) −1.00000 −0.158114
\(41\) 10.9373 1.70812 0.854059 0.520177i \(-0.174134\pi\)
0.854059 + 0.520177i \(0.174134\pi\)
\(42\) 1.47852 0.228140
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 3.41349 0.508853
\(46\) 0.815754 0.120276
\(47\) 7.21973 1.05311 0.526553 0.850143i \(-0.323484\pi\)
0.526553 + 0.850143i \(0.323484\pi\)
\(48\) 2.53249 0.365533
\(49\) −6.65915 −0.951308
\(50\) −1.00000 −0.141421
\(51\) 12.7776 1.78923
\(52\) −4.55520 −0.631692
\(53\) 11.9243 1.63793 0.818964 0.573845i \(-0.194549\pi\)
0.818964 + 0.573845i \(0.194549\pi\)
\(54\) −1.04716 −0.142500
\(55\) 1.00000 0.134840
\(56\) 0.583820 0.0780162
\(57\) −12.4837 −1.65351
\(58\) −7.94882 −1.04373
\(59\) 9.88656 1.28712 0.643560 0.765395i \(-0.277457\pi\)
0.643560 + 0.765395i \(0.277457\pi\)
\(60\) 2.53249 0.326943
\(61\) −7.37908 −0.944794 −0.472397 0.881386i \(-0.656611\pi\)
−0.472397 + 0.881386i \(0.656611\pi\)
\(62\) 2.45826 0.312199
\(63\) −1.99286 −0.251077
\(64\) 1.00000 0.125000
\(65\) −4.55520 −0.565003
\(66\) −2.53249 −0.311728
\(67\) 9.44673 1.15410 0.577051 0.816708i \(-0.304203\pi\)
0.577051 + 0.816708i \(0.304203\pi\)
\(68\) 5.04549 0.611856
\(69\) −2.06589 −0.248703
\(70\) 0.583820 0.0697799
\(71\) 11.2834 1.33909 0.669547 0.742770i \(-0.266488\pi\)
0.669547 + 0.742770i \(0.266488\pi\)
\(72\) −3.41349 −0.402284
\(73\) −1.95228 −0.228497 −0.114249 0.993452i \(-0.536446\pi\)
−0.114249 + 0.993452i \(0.536446\pi\)
\(74\) −3.39751 −0.394952
\(75\) 2.53249 0.292426
\(76\) −4.92944 −0.565445
\(77\) −0.583820 −0.0665325
\(78\) 11.5360 1.30619
\(79\) 16.0023 1.80040 0.900200 0.435476i \(-0.143420\pi\)
0.900200 + 0.435476i \(0.143420\pi\)
\(80\) 1.00000 0.111803
\(81\) −7.58855 −0.843173
\(82\) −10.9373 −1.20782
\(83\) 0.0176475 0.00193706 0.000968530 1.00000i \(-0.499692\pi\)
0.000968530 1.00000i \(0.499692\pi\)
\(84\) −1.47852 −0.161319
\(85\) 5.04549 0.547260
\(86\) −1.00000 −0.107833
\(87\) 20.1303 2.15819
\(88\) −1.00000 −0.106600
\(89\) −4.04716 −0.428998 −0.214499 0.976724i \(-0.568812\pi\)
−0.214499 + 0.976724i \(0.568812\pi\)
\(90\) −3.41349 −0.359813
\(91\) 2.65942 0.278783
\(92\) −0.815754 −0.0850482
\(93\) −6.22551 −0.645555
\(94\) −7.21973 −0.744658
\(95\) −4.92944 −0.505750
\(96\) −2.53249 −0.258471
\(97\) 3.09439 0.314188 0.157094 0.987584i \(-0.449787\pi\)
0.157094 + 0.987584i \(0.449787\pi\)
\(98\) 6.65915 0.672676
\(99\) 3.41349 0.343069
\(100\) 1.00000 0.100000
\(101\) −16.2277 −1.61472 −0.807360 0.590060i \(-0.799104\pi\)
−0.807360 + 0.590060i \(0.799104\pi\)
\(102\) −12.7776 −1.26517
\(103\) 15.8775 1.56445 0.782227 0.622994i \(-0.214084\pi\)
0.782227 + 0.622994i \(0.214084\pi\)
\(104\) 4.55520 0.446674
\(105\) −1.47852 −0.144288
\(106\) −11.9243 −1.15819
\(107\) 1.99047 0.192426 0.0962129 0.995361i \(-0.469327\pi\)
0.0962129 + 0.995361i \(0.469327\pi\)
\(108\) 1.04716 0.100763
\(109\) 5.94794 0.569710 0.284855 0.958571i \(-0.408055\pi\)
0.284855 + 0.958571i \(0.408055\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 8.60415 0.816670
\(112\) −0.583820 −0.0551658
\(113\) 1.56740 0.147448 0.0737241 0.997279i \(-0.476512\pi\)
0.0737241 + 0.997279i \(0.476512\pi\)
\(114\) 12.4837 1.16921
\(115\) −0.815754 −0.0760694
\(116\) 7.94882 0.738029
\(117\) −15.5491 −1.43752
\(118\) −9.88656 −0.910132
\(119\) −2.94566 −0.270028
\(120\) −2.53249 −0.231183
\(121\) 1.00000 0.0909091
\(122\) 7.37908 0.668070
\(123\) 27.6985 2.49749
\(124\) −2.45826 −0.220758
\(125\) 1.00000 0.0894427
\(126\) 1.99286 0.177538
\(127\) −14.2359 −1.26323 −0.631616 0.775281i \(-0.717608\pi\)
−0.631616 + 0.775281i \(0.717608\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.53249 0.222973
\(130\) 4.55520 0.399517
\(131\) −9.61130 −0.839743 −0.419871 0.907584i \(-0.637925\pi\)
−0.419871 + 0.907584i \(0.637925\pi\)
\(132\) 2.53249 0.220425
\(133\) 2.87790 0.249546
\(134\) −9.44673 −0.816073
\(135\) 1.04716 0.0901251
\(136\) −5.04549 −0.432647
\(137\) 14.6263 1.24961 0.624803 0.780782i \(-0.285179\pi\)
0.624803 + 0.780782i \(0.285179\pi\)
\(138\) 2.06589 0.175860
\(139\) 11.7412 0.995879 0.497939 0.867212i \(-0.334090\pi\)
0.497939 + 0.867212i \(0.334090\pi\)
\(140\) −0.583820 −0.0493418
\(141\) 18.2839 1.53978
\(142\) −11.2834 −0.946882
\(143\) −4.55520 −0.380925
\(144\) 3.41349 0.284458
\(145\) 7.94882 0.660113
\(146\) 1.95228 0.161572
\(147\) −16.8642 −1.39094
\(148\) 3.39751 0.279274
\(149\) −23.6217 −1.93516 −0.967581 0.252560i \(-0.918728\pi\)
−0.967581 + 0.252560i \(0.918728\pi\)
\(150\) −2.53249 −0.206777
\(151\) −5.02949 −0.409294 −0.204647 0.978836i \(-0.565605\pi\)
−0.204647 + 0.978836i \(0.565605\pi\)
\(152\) 4.92944 0.399830
\(153\) 17.2227 1.39238
\(154\) 0.583820 0.0470456
\(155\) −2.45826 −0.197452
\(156\) −11.5360 −0.923618
\(157\) −14.0823 −1.12389 −0.561943 0.827176i \(-0.689946\pi\)
−0.561943 + 0.827176i \(0.689946\pi\)
\(158\) −16.0023 −1.27308
\(159\) 30.1981 2.39487
\(160\) −1.00000 −0.0790569
\(161\) 0.476254 0.0375340
\(162\) 7.58855 0.596213
\(163\) 18.3786 1.43952 0.719760 0.694223i \(-0.244252\pi\)
0.719760 + 0.694223i \(0.244252\pi\)
\(164\) 10.9373 0.854059
\(165\) 2.53249 0.197154
\(166\) −0.0176475 −0.00136971
\(167\) −4.93771 −0.382091 −0.191046 0.981581i \(-0.561188\pi\)
−0.191046 + 0.981581i \(0.561188\pi\)
\(168\) 1.47852 0.114070
\(169\) 7.74983 0.596141
\(170\) −5.04549 −0.386971
\(171\) −16.8266 −1.28676
\(172\) 1.00000 0.0762493
\(173\) 4.02612 0.306100 0.153050 0.988218i \(-0.451090\pi\)
0.153050 + 0.988218i \(0.451090\pi\)
\(174\) −20.1303 −1.52607
\(175\) −0.583820 −0.0441327
\(176\) 1.00000 0.0753778
\(177\) 25.0376 1.88194
\(178\) 4.04716 0.303347
\(179\) 22.7886 1.70330 0.851649 0.524112i \(-0.175603\pi\)
0.851649 + 0.524112i \(0.175603\pi\)
\(180\) 3.41349 0.254427
\(181\) 14.6773 1.09095 0.545477 0.838126i \(-0.316348\pi\)
0.545477 + 0.838126i \(0.316348\pi\)
\(182\) −2.65942 −0.197129
\(183\) −18.6874 −1.38141
\(184\) 0.815754 0.0601382
\(185\) 3.39751 0.249790
\(186\) 6.22551 0.456477
\(187\) 5.04549 0.368963
\(188\) 7.21973 0.526553
\(189\) −0.611352 −0.0444693
\(190\) 4.92944 0.357619
\(191\) −15.6918 −1.13542 −0.567708 0.823230i \(-0.692170\pi\)
−0.567708 + 0.823230i \(0.692170\pi\)
\(192\) 2.53249 0.182767
\(193\) 16.6265 1.19680 0.598400 0.801197i \(-0.295803\pi\)
0.598400 + 0.801197i \(0.295803\pi\)
\(194\) −3.09439 −0.222164
\(195\) −11.5360 −0.826109
\(196\) −6.65915 −0.475654
\(197\) −17.0689 −1.21611 −0.608056 0.793894i \(-0.708050\pi\)
−0.608056 + 0.793894i \(0.708050\pi\)
\(198\) −3.41349 −0.242586
\(199\) 2.64964 0.187828 0.0939142 0.995580i \(-0.470062\pi\)
0.0939142 + 0.995580i \(0.470062\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 23.9237 1.68745
\(202\) 16.2277 1.14178
\(203\) −4.64068 −0.325712
\(204\) 12.7776 0.894614
\(205\) 10.9373 0.763893
\(206\) −15.8775 −1.10624
\(207\) −2.78457 −0.193541
\(208\) −4.55520 −0.315846
\(209\) −4.92944 −0.340976
\(210\) 1.47852 0.102027
\(211\) −12.3084 −0.847344 −0.423672 0.905816i \(-0.639259\pi\)
−0.423672 + 0.905816i \(0.639259\pi\)
\(212\) 11.9243 0.818964
\(213\) 28.5751 1.95793
\(214\) −1.99047 −0.136066
\(215\) 1.00000 0.0681994
\(216\) −1.04716 −0.0712501
\(217\) 1.43518 0.0974265
\(218\) −5.94794 −0.402846
\(219\) −4.94413 −0.334093
\(220\) 1.00000 0.0674200
\(221\) −22.9832 −1.54602
\(222\) −8.60415 −0.577473
\(223\) −20.1134 −1.34690 −0.673448 0.739235i \(-0.735187\pi\)
−0.673448 + 0.739235i \(0.735187\pi\)
\(224\) 0.583820 0.0390081
\(225\) 3.41349 0.227566
\(226\) −1.56740 −0.104262
\(227\) −7.14194 −0.474027 −0.237014 0.971506i \(-0.576169\pi\)
−0.237014 + 0.971506i \(0.576169\pi\)
\(228\) −12.4837 −0.826756
\(229\) −8.41493 −0.556074 −0.278037 0.960570i \(-0.589684\pi\)
−0.278037 + 0.960570i \(0.589684\pi\)
\(230\) 0.815754 0.0537892
\(231\) −1.47852 −0.0972793
\(232\) −7.94882 −0.521865
\(233\) −26.0543 −1.70687 −0.853437 0.521196i \(-0.825486\pi\)
−0.853437 + 0.521196i \(0.825486\pi\)
\(234\) 15.5491 1.01648
\(235\) 7.21973 0.470963
\(236\) 9.88656 0.643560
\(237\) 40.5256 2.63242
\(238\) 2.94566 0.190939
\(239\) 17.1905 1.11196 0.555980 0.831195i \(-0.312343\pi\)
0.555980 + 0.831195i \(0.312343\pi\)
\(240\) 2.53249 0.163471
\(241\) −26.0696 −1.67929 −0.839644 0.543137i \(-0.817236\pi\)
−0.839644 + 0.543137i \(0.817236\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −22.3594 −1.43436
\(244\) −7.37908 −0.472397
\(245\) −6.65915 −0.425438
\(246\) −27.6985 −1.76599
\(247\) 22.4546 1.42875
\(248\) 2.45826 0.156100
\(249\) 0.0446920 0.00283224
\(250\) −1.00000 −0.0632456
\(251\) −19.8815 −1.25491 −0.627454 0.778654i \(-0.715903\pi\)
−0.627454 + 0.778654i \(0.715903\pi\)
\(252\) −1.99286 −0.125539
\(253\) −0.815754 −0.0512860
\(254\) 14.2359 0.893240
\(255\) 12.7776 0.800167
\(256\) 1.00000 0.0625000
\(257\) 9.58725 0.598036 0.299018 0.954247i \(-0.403341\pi\)
0.299018 + 0.954247i \(0.403341\pi\)
\(258\) −2.53249 −0.157666
\(259\) −1.98353 −0.123251
\(260\) −4.55520 −0.282501
\(261\) 27.1332 1.67950
\(262\) 9.61130 0.593788
\(263\) −1.68571 −0.103946 −0.0519728 0.998649i \(-0.516551\pi\)
−0.0519728 + 0.998649i \(0.516551\pi\)
\(264\) −2.53249 −0.155864
\(265\) 11.9243 0.732504
\(266\) −2.87790 −0.176456
\(267\) −10.2494 −0.627252
\(268\) 9.44673 0.577051
\(269\) 1.64644 0.100385 0.0501927 0.998740i \(-0.484016\pi\)
0.0501927 + 0.998740i \(0.484016\pi\)
\(270\) −1.04716 −0.0637281
\(271\) −2.11722 −0.128612 −0.0643060 0.997930i \(-0.520483\pi\)
−0.0643060 + 0.997930i \(0.520483\pi\)
\(272\) 5.04549 0.305928
\(273\) 6.73494 0.407617
\(274\) −14.6263 −0.883605
\(275\) 1.00000 0.0603023
\(276\) −2.06589 −0.124352
\(277\) 11.7728 0.707357 0.353678 0.935367i \(-0.384931\pi\)
0.353678 + 0.935367i \(0.384931\pi\)
\(278\) −11.7412 −0.704193
\(279\) −8.39125 −0.502371
\(280\) 0.583820 0.0348899
\(281\) 6.18333 0.368867 0.184433 0.982845i \(-0.440955\pi\)
0.184433 + 0.982845i \(0.440955\pi\)
\(282\) −18.2839 −1.08879
\(283\) −29.0060 −1.72422 −0.862112 0.506717i \(-0.830859\pi\)
−0.862112 + 0.506717i \(0.830859\pi\)
\(284\) 11.2834 0.669547
\(285\) −12.4837 −0.739473
\(286\) 4.55520 0.269355
\(287\) −6.38541 −0.376919
\(288\) −3.41349 −0.201142
\(289\) 8.45697 0.497469
\(290\) −7.94882 −0.466771
\(291\) 7.83651 0.459384
\(292\) −1.95228 −0.114249
\(293\) 31.7771 1.85644 0.928220 0.372033i \(-0.121339\pi\)
0.928220 + 0.372033i \(0.121339\pi\)
\(294\) 16.8642 0.983541
\(295\) 9.88656 0.575618
\(296\) −3.39751 −0.197476
\(297\) 1.04716 0.0607623
\(298\) 23.6217 1.36837
\(299\) 3.71592 0.214897
\(300\) 2.53249 0.146213
\(301\) −0.583820 −0.0336508
\(302\) 5.02949 0.289415
\(303\) −41.0965 −2.36093
\(304\) −4.92944 −0.282723
\(305\) −7.37908 −0.422525
\(306\) −17.2227 −0.984558
\(307\) 29.9260 1.70797 0.853984 0.520299i \(-0.174180\pi\)
0.853984 + 0.520299i \(0.174180\pi\)
\(308\) −0.583820 −0.0332662
\(309\) 40.2095 2.28744
\(310\) 2.45826 0.139620
\(311\) −33.8063 −1.91698 −0.958490 0.285127i \(-0.907964\pi\)
−0.958490 + 0.285127i \(0.907964\pi\)
\(312\) 11.5360 0.653096
\(313\) −10.0501 −0.568065 −0.284032 0.958815i \(-0.591672\pi\)
−0.284032 + 0.958815i \(0.591672\pi\)
\(314\) 14.0823 0.794708
\(315\) −1.99286 −0.112285
\(316\) 16.0023 0.900200
\(317\) −5.78777 −0.325074 −0.162537 0.986702i \(-0.551968\pi\)
−0.162537 + 0.986702i \(0.551968\pi\)
\(318\) −30.1981 −1.69343
\(319\) 7.94882 0.445048
\(320\) 1.00000 0.0559017
\(321\) 5.04083 0.281352
\(322\) −0.476254 −0.0265406
\(323\) −24.8714 −1.38388
\(324\) −7.58855 −0.421586
\(325\) −4.55520 −0.252677
\(326\) −18.3786 −1.01789
\(327\) 15.0631 0.832991
\(328\) −10.9373 −0.603911
\(329\) −4.21502 −0.232382
\(330\) −2.53249 −0.139409
\(331\) −2.60786 −0.143341 −0.0716704 0.997428i \(-0.522833\pi\)
−0.0716704 + 0.997428i \(0.522833\pi\)
\(332\) 0.0176475 0.000968530 0
\(333\) 11.5974 0.635532
\(334\) 4.93771 0.270179
\(335\) 9.44673 0.516130
\(336\) −1.47852 −0.0806597
\(337\) −3.61378 −0.196855 −0.0984277 0.995144i \(-0.531381\pi\)
−0.0984277 + 0.995144i \(0.531381\pi\)
\(338\) −7.74983 −0.421535
\(339\) 3.96941 0.215589
\(340\) 5.04549 0.273630
\(341\) −2.45826 −0.133122
\(342\) 16.8266 0.909878
\(343\) 7.97449 0.430582
\(344\) −1.00000 −0.0539164
\(345\) −2.06589 −0.111224
\(346\) −4.02612 −0.216445
\(347\) −16.2439 −0.872016 −0.436008 0.899943i \(-0.643608\pi\)
−0.436008 + 0.899943i \(0.643608\pi\)
\(348\) 20.1303 1.07910
\(349\) −36.5970 −1.95899 −0.979495 0.201468i \(-0.935429\pi\)
−0.979495 + 0.201468i \(0.935429\pi\)
\(350\) 0.583820 0.0312065
\(351\) −4.77002 −0.254605
\(352\) −1.00000 −0.0533002
\(353\) −3.60517 −0.191884 −0.0959419 0.995387i \(-0.530586\pi\)
−0.0959419 + 0.995387i \(0.530586\pi\)
\(354\) −25.0376 −1.33073
\(355\) 11.2834 0.598861
\(356\) −4.04716 −0.214499
\(357\) −7.45984 −0.394817
\(358\) −22.7886 −1.20441
\(359\) −0.996118 −0.0525731 −0.0262865 0.999654i \(-0.508368\pi\)
−0.0262865 + 0.999654i \(0.508368\pi\)
\(360\) −3.41349 −0.179907
\(361\) 5.29936 0.278913
\(362\) −14.6773 −0.771421
\(363\) 2.53249 0.132921
\(364\) 2.65942 0.139391
\(365\) −1.95228 −0.102187
\(366\) 18.6874 0.976807
\(367\) −1.64638 −0.0859402 −0.0429701 0.999076i \(-0.513682\pi\)
−0.0429701 + 0.999076i \(0.513682\pi\)
\(368\) −0.815754 −0.0425241
\(369\) 37.3343 1.94355
\(370\) −3.39751 −0.176628
\(371\) −6.96164 −0.361431
\(372\) −6.22551 −0.322778
\(373\) −14.5695 −0.754381 −0.377190 0.926136i \(-0.623110\pi\)
−0.377190 + 0.926136i \(0.623110\pi\)
\(374\) −5.04549 −0.260896
\(375\) 2.53249 0.130777
\(376\) −7.21973 −0.372329
\(377\) −36.2084 −1.86483
\(378\) 0.611352 0.0314446
\(379\) 17.4192 0.894765 0.447383 0.894343i \(-0.352356\pi\)
0.447383 + 0.894343i \(0.352356\pi\)
\(380\) −4.92944 −0.252875
\(381\) −36.0523 −1.84701
\(382\) 15.6918 0.802861
\(383\) −30.5126 −1.55912 −0.779559 0.626328i \(-0.784557\pi\)
−0.779559 + 0.626328i \(0.784557\pi\)
\(384\) −2.53249 −0.129235
\(385\) −0.583820 −0.0297542
\(386\) −16.6265 −0.846266
\(387\) 3.41349 0.173517
\(388\) 3.09439 0.157094
\(389\) 16.1307 0.817858 0.408929 0.912566i \(-0.365902\pi\)
0.408929 + 0.912566i \(0.365902\pi\)
\(390\) 11.5360 0.584147
\(391\) −4.11588 −0.208149
\(392\) 6.65915 0.336338
\(393\) −24.3405 −1.22782
\(394\) 17.0689 0.859920
\(395\) 16.0023 0.805163
\(396\) 3.41349 0.171534
\(397\) −20.6024 −1.03401 −0.517003 0.855983i \(-0.672952\pi\)
−0.517003 + 0.855983i \(0.672952\pi\)
\(398\) −2.64964 −0.132815
\(399\) 7.28826 0.364869
\(400\) 1.00000 0.0500000
\(401\) 7.69504 0.384272 0.192136 0.981368i \(-0.438459\pi\)
0.192136 + 0.981368i \(0.438459\pi\)
\(402\) −23.9237 −1.19321
\(403\) 11.1979 0.557805
\(404\) −16.2277 −0.807360
\(405\) −7.58855 −0.377078
\(406\) 4.64068 0.230313
\(407\) 3.39751 0.168408
\(408\) −12.7776 −0.632587
\(409\) −35.5918 −1.75990 −0.879950 0.475066i \(-0.842424\pi\)
−0.879950 + 0.475066i \(0.842424\pi\)
\(410\) −10.9373 −0.540154
\(411\) 37.0408 1.82709
\(412\) 15.8775 0.782227
\(413\) −5.77197 −0.284020
\(414\) 2.78457 0.136854
\(415\) 0.0176475 0.000866280 0
\(416\) 4.55520 0.223337
\(417\) 29.7345 1.45611
\(418\) 4.92944 0.241107
\(419\) 23.2886 1.13772 0.568861 0.822434i \(-0.307384\pi\)
0.568861 + 0.822434i \(0.307384\pi\)
\(420\) −1.47852 −0.0721442
\(421\) −27.6647 −1.34830 −0.674148 0.738596i \(-0.735489\pi\)
−0.674148 + 0.738596i \(0.735489\pi\)
\(422\) 12.3084 0.599163
\(423\) 24.6445 1.19825
\(424\) −11.9243 −0.579095
\(425\) 5.04549 0.244742
\(426\) −28.5751 −1.38447
\(427\) 4.30805 0.208481
\(428\) 1.99047 0.0962129
\(429\) −11.5360 −0.556962
\(430\) −1.00000 −0.0482243
\(431\) −31.7418 −1.52895 −0.764473 0.644656i \(-0.777001\pi\)
−0.764473 + 0.644656i \(0.777001\pi\)
\(432\) 1.04716 0.0503815
\(433\) −3.14451 −0.151116 −0.0755579 0.997141i \(-0.524074\pi\)
−0.0755579 + 0.997141i \(0.524074\pi\)
\(434\) −1.43518 −0.0688909
\(435\) 20.1303 0.965173
\(436\) 5.94794 0.284855
\(437\) 4.02121 0.192360
\(438\) 4.94413 0.236240
\(439\) −1.21375 −0.0579292 −0.0289646 0.999580i \(-0.509221\pi\)
−0.0289646 + 0.999580i \(0.509221\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −22.7310 −1.08243
\(442\) 22.9832 1.09320
\(443\) 14.3917 0.683771 0.341886 0.939742i \(-0.388934\pi\)
0.341886 + 0.939742i \(0.388934\pi\)
\(444\) 8.60415 0.408335
\(445\) −4.04716 −0.191854
\(446\) 20.1134 0.952399
\(447\) −59.8216 −2.82946
\(448\) −0.583820 −0.0275829
\(449\) 37.0597 1.74896 0.874478 0.485065i \(-0.161204\pi\)
0.874478 + 0.485065i \(0.161204\pi\)
\(450\) −3.41349 −0.160913
\(451\) 10.9373 0.515017
\(452\) 1.56740 0.0737241
\(453\) −12.7371 −0.598442
\(454\) 7.14194 0.335188
\(455\) 2.65942 0.124675
\(456\) 12.4837 0.584605
\(457\) 26.5804 1.24338 0.621690 0.783263i \(-0.286446\pi\)
0.621690 + 0.783263i \(0.286446\pi\)
\(458\) 8.41493 0.393204
\(459\) 5.28343 0.246609
\(460\) −0.815754 −0.0380347
\(461\) 20.9312 0.974865 0.487433 0.873161i \(-0.337933\pi\)
0.487433 + 0.873161i \(0.337933\pi\)
\(462\) 1.47852 0.0687868
\(463\) −15.7816 −0.733434 −0.366717 0.930333i \(-0.619518\pi\)
−0.366717 + 0.930333i \(0.619518\pi\)
\(464\) 7.94882 0.369015
\(465\) −6.22551 −0.288701
\(466\) 26.0543 1.20694
\(467\) −14.4659 −0.669400 −0.334700 0.942325i \(-0.608635\pi\)
−0.334700 + 0.942325i \(0.608635\pi\)
\(468\) −15.5491 −0.718759
\(469\) −5.51519 −0.254668
\(470\) −7.21973 −0.333021
\(471\) −35.6631 −1.64327
\(472\) −9.88656 −0.455066
\(473\) 1.00000 0.0459800
\(474\) −40.5256 −1.86140
\(475\) −4.92944 −0.226178
\(476\) −2.94566 −0.135014
\(477\) 40.7035 1.86368
\(478\) −17.1905 −0.786275
\(479\) 0.630533 0.0288098 0.0144049 0.999896i \(-0.495415\pi\)
0.0144049 + 0.999896i \(0.495415\pi\)
\(480\) −2.53249 −0.115592
\(481\) −15.4763 −0.705660
\(482\) 26.0696 1.18744
\(483\) 1.20611 0.0548797
\(484\) 1.00000 0.0454545
\(485\) 3.09439 0.140509
\(486\) 22.3594 1.01424
\(487\) −26.5453 −1.20288 −0.601442 0.798916i \(-0.705407\pi\)
−0.601442 + 0.798916i \(0.705407\pi\)
\(488\) 7.37908 0.334035
\(489\) 46.5435 2.10477
\(490\) 6.65915 0.300830
\(491\) 11.5756 0.522401 0.261200 0.965285i \(-0.415882\pi\)
0.261200 + 0.965285i \(0.415882\pi\)
\(492\) 27.6985 1.24875
\(493\) 40.1057 1.80627
\(494\) −22.4546 −1.01028
\(495\) 3.41349 0.153425
\(496\) −2.45826 −0.110379
\(497\) −6.58748 −0.295489
\(498\) −0.0446920 −0.00200269
\(499\) 38.0328 1.70258 0.851291 0.524693i \(-0.175820\pi\)
0.851291 + 0.524693i \(0.175820\pi\)
\(500\) 1.00000 0.0447214
\(501\) −12.5047 −0.558668
\(502\) 19.8815 0.887354
\(503\) 14.6478 0.653112 0.326556 0.945178i \(-0.394112\pi\)
0.326556 + 0.945178i \(0.394112\pi\)
\(504\) 1.99286 0.0887692
\(505\) −16.2277 −0.722124
\(506\) 0.815754 0.0362647
\(507\) 19.6264 0.871637
\(508\) −14.2359 −0.631616
\(509\) 22.6830 1.00541 0.502703 0.864459i \(-0.332339\pi\)
0.502703 + 0.864459i \(0.332339\pi\)
\(510\) −12.7776 −0.565803
\(511\) 1.13978 0.0504210
\(512\) −1.00000 −0.0441942
\(513\) −5.16190 −0.227904
\(514\) −9.58725 −0.422876
\(515\) 15.8775 0.699645
\(516\) 2.53249 0.111487
\(517\) 7.21973 0.317523
\(518\) 1.98353 0.0871515
\(519\) 10.1961 0.447559
\(520\) 4.55520 0.199759
\(521\) 6.33354 0.277478 0.138739 0.990329i \(-0.455695\pi\)
0.138739 + 0.990329i \(0.455695\pi\)
\(522\) −27.1332 −1.18759
\(523\) 35.8448 1.56738 0.783691 0.621151i \(-0.213335\pi\)
0.783691 + 0.621151i \(0.213335\pi\)
\(524\) −9.61130 −0.419871
\(525\) −1.47852 −0.0645278
\(526\) 1.68571 0.0735007
\(527\) −12.4031 −0.540289
\(528\) 2.53249 0.110212
\(529\) −22.3345 −0.971067
\(530\) −11.9243 −0.517958
\(531\) 33.7477 1.46452
\(532\) 2.87790 0.124773
\(533\) −49.8215 −2.15801
\(534\) 10.2494 0.443534
\(535\) 1.99047 0.0860554
\(536\) −9.44673 −0.408037
\(537\) 57.7118 2.49045
\(538\) −1.64644 −0.0709832
\(539\) −6.65915 −0.286830
\(540\) 1.04716 0.0450625
\(541\) −33.6136 −1.44516 −0.722580 0.691287i \(-0.757044\pi\)
−0.722580 + 0.691287i \(0.757044\pi\)
\(542\) 2.11722 0.0909424
\(543\) 37.1700 1.59512
\(544\) −5.04549 −0.216324
\(545\) 5.94794 0.254782
\(546\) −6.73494 −0.288229
\(547\) −8.36898 −0.357832 −0.178916 0.983864i \(-0.557259\pi\)
−0.178916 + 0.983864i \(0.557259\pi\)
\(548\) 14.6263 0.624803
\(549\) −25.1884 −1.07502
\(550\) −1.00000 −0.0426401
\(551\) −39.1832 −1.66926
\(552\) 2.06589 0.0879299
\(553\) −9.34247 −0.397282
\(554\) −11.7728 −0.500177
\(555\) 8.60415 0.365226
\(556\) 11.7412 0.497939
\(557\) 4.53983 0.192359 0.0961793 0.995364i \(-0.469338\pi\)
0.0961793 + 0.995364i \(0.469338\pi\)
\(558\) 8.39125 0.355230
\(559\) −4.55520 −0.192664
\(560\) −0.583820 −0.0246709
\(561\) 12.7776 0.539472
\(562\) −6.18333 −0.260828
\(563\) 17.1652 0.723427 0.361714 0.932289i \(-0.382192\pi\)
0.361714 + 0.932289i \(0.382192\pi\)
\(564\) 18.2839 0.769889
\(565\) 1.56740 0.0659408
\(566\) 29.0060 1.21921
\(567\) 4.43035 0.186057
\(568\) −11.2834 −0.473441
\(569\) −40.6384 −1.70365 −0.851824 0.523828i \(-0.824504\pi\)
−0.851824 + 0.523828i \(0.824504\pi\)
\(570\) 12.4837 0.522886
\(571\) 34.0159 1.42352 0.711761 0.702422i \(-0.247898\pi\)
0.711761 + 0.702422i \(0.247898\pi\)
\(572\) −4.55520 −0.190462
\(573\) −39.7392 −1.66013
\(574\) 6.38541 0.266522
\(575\) −0.815754 −0.0340193
\(576\) 3.41349 0.142229
\(577\) 0.948124 0.0394709 0.0197355 0.999805i \(-0.493718\pi\)
0.0197355 + 0.999805i \(0.493718\pi\)
\(578\) −8.45697 −0.351764
\(579\) 42.1064 1.74988
\(580\) 7.94882 0.330057
\(581\) −0.0103029 −0.000427438 0
\(582\) −7.83651 −0.324834
\(583\) 11.9243 0.493854
\(584\) 1.95228 0.0807860
\(585\) −15.5491 −0.642877
\(586\) −31.7771 −1.31270
\(587\) 9.62369 0.397212 0.198606 0.980079i \(-0.436359\pi\)
0.198606 + 0.980079i \(0.436359\pi\)
\(588\) −16.8642 −0.695469
\(589\) 12.1178 0.499307
\(590\) −9.88656 −0.407023
\(591\) −43.2269 −1.77812
\(592\) 3.39751 0.139637
\(593\) 17.5234 0.719599 0.359800 0.933030i \(-0.382845\pi\)
0.359800 + 0.933030i \(0.382845\pi\)
\(594\) −1.04716 −0.0429654
\(595\) −2.94566 −0.120760
\(596\) −23.6217 −0.967581
\(597\) 6.71019 0.274630
\(598\) −3.71592 −0.151955
\(599\) 1.17796 0.0481300 0.0240650 0.999710i \(-0.492339\pi\)
0.0240650 + 0.999710i \(0.492339\pi\)
\(600\) −2.53249 −0.103388
\(601\) 4.94523 0.201720 0.100860 0.994901i \(-0.467841\pi\)
0.100860 + 0.994901i \(0.467841\pi\)
\(602\) 0.583820 0.0237947
\(603\) 32.2463 1.31317
\(604\) −5.02949 −0.204647
\(605\) 1.00000 0.0406558
\(606\) 41.0965 1.66943
\(607\) 47.2175 1.91650 0.958250 0.285932i \(-0.0923031\pi\)
0.958250 + 0.285932i \(0.0923031\pi\)
\(608\) 4.92944 0.199915
\(609\) −11.7525 −0.476234
\(610\) 7.37908 0.298770
\(611\) −32.8873 −1.33048
\(612\) 17.2227 0.696188
\(613\) −11.0345 −0.445679 −0.222839 0.974855i \(-0.571533\pi\)
−0.222839 + 0.974855i \(0.571533\pi\)
\(614\) −29.9260 −1.20772
\(615\) 27.6985 1.11691
\(616\) 0.583820 0.0235228
\(617\) 18.0283 0.725791 0.362895 0.931830i \(-0.381788\pi\)
0.362895 + 0.931830i \(0.381788\pi\)
\(618\) −40.2095 −1.61746
\(619\) 15.4212 0.619830 0.309915 0.950764i \(-0.399699\pi\)
0.309915 + 0.950764i \(0.399699\pi\)
\(620\) −2.45826 −0.0987261
\(621\) −0.854224 −0.0342788
\(622\) 33.8063 1.35551
\(623\) 2.36281 0.0946641
\(624\) −11.5360 −0.461809
\(625\) 1.00000 0.0400000
\(626\) 10.0501 0.401682
\(627\) −12.4837 −0.498552
\(628\) −14.0823 −0.561943
\(629\) 17.1421 0.683500
\(630\) 1.99286 0.0793976
\(631\) −19.0201 −0.757180 −0.378590 0.925564i \(-0.623591\pi\)
−0.378590 + 0.925564i \(0.623591\pi\)
\(632\) −16.0023 −0.636538
\(633\) −31.1708 −1.23893
\(634\) 5.78777 0.229862
\(635\) −14.2359 −0.564935
\(636\) 30.1981 1.19743
\(637\) 30.3338 1.20187
\(638\) −7.94882 −0.314697
\(639\) 38.5158 1.52366
\(640\) −1.00000 −0.0395285
\(641\) −18.1488 −0.716836 −0.358418 0.933561i \(-0.616684\pi\)
−0.358418 + 0.933561i \(0.616684\pi\)
\(642\) −5.04083 −0.198946
\(643\) 23.5214 0.927593 0.463796 0.885942i \(-0.346487\pi\)
0.463796 + 0.885942i \(0.346487\pi\)
\(644\) 0.476254 0.0187670
\(645\) 2.53249 0.0997166
\(646\) 24.8714 0.978553
\(647\) −8.30021 −0.326315 −0.163157 0.986600i \(-0.552168\pi\)
−0.163157 + 0.986600i \(0.552168\pi\)
\(648\) 7.58855 0.298107
\(649\) 9.88656 0.388081
\(650\) 4.55520 0.178670
\(651\) 3.63458 0.142450
\(652\) 18.3786 0.719760
\(653\) −35.7957 −1.40079 −0.700396 0.713754i \(-0.746993\pi\)
−0.700396 + 0.713754i \(0.746993\pi\)
\(654\) −15.0631 −0.589013
\(655\) −9.61130 −0.375544
\(656\) 10.9373 0.427029
\(657\) −6.66410 −0.259991
\(658\) 4.21502 0.164319
\(659\) 8.74484 0.340651 0.170325 0.985388i \(-0.445518\pi\)
0.170325 + 0.985388i \(0.445518\pi\)
\(660\) 2.53249 0.0985769
\(661\) −24.4400 −0.950607 −0.475304 0.879822i \(-0.657662\pi\)
−0.475304 + 0.879822i \(0.657662\pi\)
\(662\) 2.60786 0.101357
\(663\) −58.2047 −2.26048
\(664\) −0.0176475 −0.000684854 0
\(665\) 2.87790 0.111600
\(666\) −11.5974 −0.449389
\(667\) −6.48428 −0.251072
\(668\) −4.93771 −0.191046
\(669\) −50.9370 −1.96934
\(670\) −9.44673 −0.364959
\(671\) −7.37908 −0.284866
\(672\) 1.47852 0.0570350
\(673\) 33.8166 1.30354 0.651768 0.758419i \(-0.274028\pi\)
0.651768 + 0.758419i \(0.274028\pi\)
\(674\) 3.61378 0.139198
\(675\) 1.04716 0.0403052
\(676\) 7.74983 0.298070
\(677\) −27.9108 −1.07270 −0.536349 0.843996i \(-0.680197\pi\)
−0.536349 + 0.843996i \(0.680197\pi\)
\(678\) −3.96941 −0.152444
\(679\) −1.80657 −0.0693297
\(680\) −5.04549 −0.193486
\(681\) −18.0869 −0.693090
\(682\) 2.45826 0.0941316
\(683\) 51.8370 1.98349 0.991745 0.128228i \(-0.0409289\pi\)
0.991745 + 0.128228i \(0.0409289\pi\)
\(684\) −16.8266 −0.643381
\(685\) 14.6263 0.558841
\(686\) −7.97449 −0.304467
\(687\) −21.3107 −0.813054
\(688\) 1.00000 0.0381246
\(689\) −54.3175 −2.06933
\(690\) 2.06589 0.0786469
\(691\) 15.0849 0.573856 0.286928 0.957952i \(-0.407366\pi\)
0.286928 + 0.957952i \(0.407366\pi\)
\(692\) 4.02612 0.153050
\(693\) −1.99286 −0.0757027
\(694\) 16.2439 0.616608
\(695\) 11.7412 0.445371
\(696\) −20.1303 −0.763036
\(697\) 55.1840 2.09024
\(698\) 36.5970 1.38522
\(699\) −65.9822 −2.49568
\(700\) −0.583820 −0.0220663
\(701\) 19.8774 0.750760 0.375380 0.926871i \(-0.377512\pi\)
0.375380 + 0.926871i \(0.377512\pi\)
\(702\) 4.77002 0.180033
\(703\) −16.7478 −0.631656
\(704\) 1.00000 0.0376889
\(705\) 18.2839 0.688610
\(706\) 3.60517 0.135682
\(707\) 9.47407 0.356309
\(708\) 25.0376 0.940970
\(709\) 35.4530 1.33147 0.665734 0.746190i \(-0.268119\pi\)
0.665734 + 0.746190i \(0.268119\pi\)
\(710\) −11.2834 −0.423458
\(711\) 54.6237 2.04855
\(712\) 4.04716 0.151674
\(713\) 2.00533 0.0751004
\(714\) 7.45984 0.279178
\(715\) −4.55520 −0.170355
\(716\) 22.7886 0.851649
\(717\) 43.5347 1.62583
\(718\) 0.996118 0.0371748
\(719\) −17.9118 −0.667998 −0.333999 0.942573i \(-0.608398\pi\)
−0.333999 + 0.942573i \(0.608398\pi\)
\(720\) 3.41349 0.127213
\(721\) −9.26959 −0.345217
\(722\) −5.29936 −0.197222
\(723\) −66.0208 −2.45534
\(724\) 14.6773 0.545477
\(725\) 7.94882 0.295212
\(726\) −2.53249 −0.0939894
\(727\) −41.4357 −1.53677 −0.768383 0.639991i \(-0.778938\pi\)
−0.768383 + 0.639991i \(0.778938\pi\)
\(728\) −2.65942 −0.0985645
\(729\) −33.8592 −1.25404
\(730\) 1.95228 0.0722572
\(731\) 5.04549 0.186614
\(732\) −18.6874 −0.690707
\(733\) 31.1540 1.15070 0.575349 0.817908i \(-0.304866\pi\)
0.575349 + 0.817908i \(0.304866\pi\)
\(734\) 1.64638 0.0607689
\(735\) −16.8642 −0.622046
\(736\) 0.815754 0.0300691
\(737\) 9.44673 0.347975
\(738\) −37.3343 −1.37430
\(739\) 50.0623 1.84157 0.920786 0.390068i \(-0.127549\pi\)
0.920786 + 0.390068i \(0.127549\pi\)
\(740\) 3.39751 0.124895
\(741\) 56.8659 2.08902
\(742\) 6.96164 0.255570
\(743\) 43.2272 1.58585 0.792926 0.609318i \(-0.208557\pi\)
0.792926 + 0.609318i \(0.208557\pi\)
\(744\) 6.22551 0.228238
\(745\) −23.6217 −0.865431
\(746\) 14.5695 0.533428
\(747\) 0.0602394 0.00220405
\(748\) 5.04549 0.184481
\(749\) −1.16207 −0.0424613
\(750\) −2.53249 −0.0924733
\(751\) −29.8808 −1.09037 −0.545183 0.838317i \(-0.683540\pi\)
−0.545183 + 0.838317i \(0.683540\pi\)
\(752\) 7.21973 0.263276
\(753\) −50.3496 −1.83484
\(754\) 36.2084 1.31863
\(755\) −5.02949 −0.183042
\(756\) −0.611352 −0.0222347
\(757\) 28.0307 1.01879 0.509397 0.860532i \(-0.329869\pi\)
0.509397 + 0.860532i \(0.329869\pi\)
\(758\) −17.4192 −0.632695
\(759\) −2.06589 −0.0749869
\(760\) 4.92944 0.178809
\(761\) 10.4620 0.379247 0.189624 0.981857i \(-0.439273\pi\)
0.189624 + 0.981857i \(0.439273\pi\)
\(762\) 36.0523 1.30604
\(763\) −3.47253 −0.125714
\(764\) −15.6918 −0.567708
\(765\) 17.2227 0.622689
\(766\) 30.5126 1.10246
\(767\) −45.0352 −1.62613
\(768\) 2.53249 0.0913833
\(769\) 16.1772 0.583366 0.291683 0.956515i \(-0.405785\pi\)
0.291683 + 0.956515i \(0.405785\pi\)
\(770\) 0.583820 0.0210394
\(771\) 24.2796 0.874408
\(772\) 16.6265 0.598400
\(773\) −29.7787 −1.07106 −0.535532 0.844515i \(-0.679889\pi\)
−0.535532 + 0.844515i \(0.679889\pi\)
\(774\) −3.41349 −0.122695
\(775\) −2.45826 −0.0883033
\(776\) −3.09439 −0.111082
\(777\) −5.02327 −0.180209
\(778\) −16.1307 −0.578313
\(779\) −53.9147 −1.93169
\(780\) −11.5360 −0.413054
\(781\) 11.2834 0.403752
\(782\) 4.11588 0.147184
\(783\) 8.32367 0.297464
\(784\) −6.65915 −0.237827
\(785\) −14.0823 −0.502617
\(786\) 24.3405 0.868196
\(787\) 9.30091 0.331542 0.165771 0.986164i \(-0.446989\pi\)
0.165771 + 0.986164i \(0.446989\pi\)
\(788\) −17.0689 −0.608056
\(789\) −4.26905 −0.151982
\(790\) −16.0023 −0.569337
\(791\) −0.915077 −0.0325364
\(792\) −3.41349 −0.121293
\(793\) 33.6132 1.19364
\(794\) 20.6024 0.731153
\(795\) 30.1981 1.07102
\(796\) 2.64964 0.0939142
\(797\) 29.8483 1.05728 0.528641 0.848845i \(-0.322702\pi\)
0.528641 + 0.848845i \(0.322702\pi\)
\(798\) −7.28826 −0.258001
\(799\) 36.4271 1.28870
\(800\) −1.00000 −0.0353553
\(801\) −13.8149 −0.488127
\(802\) −7.69504 −0.271721
\(803\) −1.95228 −0.0688946
\(804\) 23.9237 0.843725
\(805\) 0.476254 0.0167857
\(806\) −11.1979 −0.394428
\(807\) 4.16960 0.146777
\(808\) 16.2277 0.570890
\(809\) −25.3798 −0.892305 −0.446153 0.894957i \(-0.647206\pi\)
−0.446153 + 0.894957i \(0.647206\pi\)
\(810\) 7.58855 0.266635
\(811\) 25.9330 0.910632 0.455316 0.890330i \(-0.349526\pi\)
0.455316 + 0.890330i \(0.349526\pi\)
\(812\) −4.64068 −0.162856
\(813\) −5.36184 −0.188048
\(814\) −3.39751 −0.119083
\(815\) 18.3786 0.643773
\(816\) 12.7776 0.447307
\(817\) −4.92944 −0.172459
\(818\) 35.5918 1.24444
\(819\) 9.07789 0.317207
\(820\) 10.9373 0.381947
\(821\) 10.6854 0.372924 0.186462 0.982462i \(-0.440298\pi\)
0.186462 + 0.982462i \(0.440298\pi\)
\(822\) −37.0408 −1.29195
\(823\) −39.8524 −1.38917 −0.694583 0.719413i \(-0.744411\pi\)
−0.694583 + 0.719413i \(0.744411\pi\)
\(824\) −15.8775 −0.553118
\(825\) 2.53249 0.0881699
\(826\) 5.77197 0.200833
\(827\) 34.0616 1.18444 0.592218 0.805778i \(-0.298252\pi\)
0.592218 + 0.805778i \(0.298252\pi\)
\(828\) −2.78457 −0.0967704
\(829\) −39.6901 −1.37849 −0.689247 0.724526i \(-0.742058\pi\)
−0.689247 + 0.724526i \(0.742058\pi\)
\(830\) −0.0176475 −0.000612552 0
\(831\) 29.8144 1.03425
\(832\) −4.55520 −0.157923
\(833\) −33.5987 −1.16413
\(834\) −29.7345 −1.02962
\(835\) −4.93771 −0.170876
\(836\) −4.92944 −0.170488
\(837\) −2.57419 −0.0889770
\(838\) −23.2886 −0.804490
\(839\) −24.2538 −0.837333 −0.418667 0.908140i \(-0.637502\pi\)
−0.418667 + 0.908140i \(0.637502\pi\)
\(840\) 1.47852 0.0510137
\(841\) 34.1837 1.17875
\(842\) 27.6647 0.953390
\(843\) 15.6592 0.539332
\(844\) −12.3084 −0.423672
\(845\) 7.74983 0.266602
\(846\) −24.6445 −0.847294
\(847\) −0.583820 −0.0200603
\(848\) 11.9243 0.409482
\(849\) −73.4572 −2.52104
\(850\) −5.04549 −0.173059
\(851\) −2.77153 −0.0950069
\(852\) 28.5751 0.978966
\(853\) 42.6761 1.46120 0.730600 0.682805i \(-0.239240\pi\)
0.730600 + 0.682805i \(0.239240\pi\)
\(854\) −4.30805 −0.147419
\(855\) −16.8266 −0.575457
\(856\) −1.99047 −0.0680328
\(857\) 40.1740 1.37232 0.686160 0.727451i \(-0.259295\pi\)
0.686160 + 0.727451i \(0.259295\pi\)
\(858\) 11.5360 0.393832
\(859\) −54.1225 −1.84663 −0.923317 0.384038i \(-0.874533\pi\)
−0.923317 + 0.384038i \(0.874533\pi\)
\(860\) 1.00000 0.0340997
\(861\) −16.1710 −0.551105
\(862\) 31.7418 1.08113
\(863\) −12.4671 −0.424385 −0.212192 0.977228i \(-0.568060\pi\)
−0.212192 + 0.977228i \(0.568060\pi\)
\(864\) −1.04716 −0.0356251
\(865\) 4.02612 0.136892
\(866\) 3.14451 0.106855
\(867\) 21.4172 0.727365
\(868\) 1.43518 0.0487132
\(869\) 16.0023 0.542841
\(870\) −20.1303 −0.682480
\(871\) −43.0317 −1.45807
\(872\) −5.94794 −0.201423
\(873\) 10.5627 0.357492
\(874\) −4.02121 −0.136019
\(875\) −0.583820 −0.0197367
\(876\) −4.94413 −0.167047
\(877\) 13.5911 0.458940 0.229470 0.973316i \(-0.426301\pi\)
0.229470 + 0.973316i \(0.426301\pi\)
\(878\) 1.21375 0.0409621
\(879\) 80.4751 2.71436
\(880\) 1.00000 0.0337100
\(881\) −43.5037 −1.46568 −0.732839 0.680402i \(-0.761805\pi\)
−0.732839 + 0.680402i \(0.761805\pi\)
\(882\) 22.7310 0.765391
\(883\) −33.3274 −1.12156 −0.560778 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(884\) −22.9832 −0.773009
\(885\) 25.0376 0.841629
\(886\) −14.3917 −0.483499
\(887\) 6.15054 0.206515 0.103257 0.994655i \(-0.467073\pi\)
0.103257 + 0.994655i \(0.467073\pi\)
\(888\) −8.60415 −0.288736
\(889\) 8.31121 0.278749
\(890\) 4.04716 0.135661
\(891\) −7.58855 −0.254226
\(892\) −20.1134 −0.673448
\(893\) −35.5892 −1.19095
\(894\) 59.8216 2.00073
\(895\) 22.7886 0.761738
\(896\) 0.583820 0.0195041
\(897\) 9.41052 0.314208
\(898\) −37.0597 −1.23670
\(899\) −19.5403 −0.651704
\(900\) 3.41349 0.113783
\(901\) 60.1639 2.00435
\(902\) −10.9373 −0.364172
\(903\) −1.47852 −0.0492020
\(904\) −1.56740 −0.0521308
\(905\) 14.6773 0.487890
\(906\) 12.7371 0.423163
\(907\) 0.695483 0.0230931 0.0115466 0.999933i \(-0.496325\pi\)
0.0115466 + 0.999933i \(0.496325\pi\)
\(908\) −7.14194 −0.237014
\(909\) −55.3932 −1.83728
\(910\) −2.65942 −0.0881588
\(911\) 3.77664 0.125126 0.0625629 0.998041i \(-0.480073\pi\)
0.0625629 + 0.998041i \(0.480073\pi\)
\(912\) −12.4837 −0.413378
\(913\) 0.0176475 0.000584046 0
\(914\) −26.5804 −0.879202
\(915\) −18.6874 −0.617787
\(916\) −8.41493 −0.278037
\(917\) 5.61127 0.185300
\(918\) −5.28343 −0.174379
\(919\) 53.9165 1.77854 0.889271 0.457381i \(-0.151212\pi\)
0.889271 + 0.457381i \(0.151212\pi\)
\(920\) 0.815754 0.0268946
\(921\) 75.7873 2.49728
\(922\) −20.9312 −0.689334
\(923\) −51.3981 −1.69179
\(924\) −1.47852 −0.0486396
\(925\) 3.39751 0.111709
\(926\) 15.7816 0.518616
\(927\) 54.1976 1.78008
\(928\) −7.94882 −0.260933
\(929\) 3.14341 0.103132 0.0515659 0.998670i \(-0.483579\pi\)
0.0515659 + 0.998670i \(0.483579\pi\)
\(930\) 6.22551 0.204143
\(931\) 32.8259 1.07582
\(932\) −26.0543 −0.853437
\(933\) −85.6140 −2.80288
\(934\) 14.4659 0.473337
\(935\) 5.04549 0.165005
\(936\) 15.5491 0.508239
\(937\) −6.42862 −0.210014 −0.105007 0.994471i \(-0.533486\pi\)
−0.105007 + 0.994471i \(0.533486\pi\)
\(938\) 5.51519 0.180077
\(939\) −25.4517 −0.830586
\(940\) 7.21973 0.235481
\(941\) −17.2433 −0.562115 −0.281058 0.959691i \(-0.590685\pi\)
−0.281058 + 0.959691i \(0.590685\pi\)
\(942\) 35.6631 1.16197
\(943\) −8.92214 −0.290545
\(944\) 9.88656 0.321780
\(945\) −0.611352 −0.0198873
\(946\) −1.00000 −0.0325128
\(947\) 1.87122 0.0608066 0.0304033 0.999538i \(-0.490321\pi\)
0.0304033 + 0.999538i \(0.490321\pi\)
\(948\) 40.5256 1.31621
\(949\) 8.89304 0.288680
\(950\) 4.92944 0.159932
\(951\) −14.6575 −0.475301
\(952\) 2.94566 0.0954694
\(953\) 51.3865 1.66457 0.832285 0.554347i \(-0.187032\pi\)
0.832285 + 0.554347i \(0.187032\pi\)
\(954\) −40.7035 −1.31782
\(955\) −15.6918 −0.507774
\(956\) 17.1905 0.555980
\(957\) 20.1303 0.650719
\(958\) −0.630533 −0.0203716
\(959\) −8.53911 −0.275742
\(960\) 2.53249 0.0817357
\(961\) −24.9570 −0.805063
\(962\) 15.4763 0.498977
\(963\) 6.79444 0.218948
\(964\) −26.0696 −0.839644
\(965\) 16.6265 0.535226
\(966\) −1.20611 −0.0388058
\(967\) 16.4900 0.530284 0.265142 0.964209i \(-0.414581\pi\)
0.265142 + 0.964209i \(0.414581\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −62.9866 −2.02342
\(970\) −3.09439 −0.0993549
\(971\) −34.4893 −1.10681 −0.553407 0.832911i \(-0.686673\pi\)
−0.553407 + 0.832911i \(0.686673\pi\)
\(972\) −22.3594 −0.717178
\(973\) −6.85477 −0.219754
\(974\) 26.5453 0.850568
\(975\) −11.5360 −0.369447
\(976\) −7.37908 −0.236198
\(977\) 32.0527 1.02546 0.512729 0.858551i \(-0.328635\pi\)
0.512729 + 0.858551i \(0.328635\pi\)
\(978\) −46.5435 −1.48830
\(979\) −4.04716 −0.129348
\(980\) −6.65915 −0.212719
\(981\) 20.3033 0.648233
\(982\) −11.5756 −0.369393
\(983\) 33.0705 1.05478 0.527392 0.849622i \(-0.323170\pi\)
0.527392 + 0.849622i \(0.323170\pi\)
\(984\) −27.6985 −0.882997
\(985\) −17.0689 −0.543861
\(986\) −40.1057 −1.27723
\(987\) −10.6745 −0.339773
\(988\) 22.4546 0.714375
\(989\) −0.815754 −0.0259395
\(990\) −3.41349 −0.108488
\(991\) 17.7451 0.563693 0.281846 0.959460i \(-0.409053\pi\)
0.281846 + 0.959460i \(0.409053\pi\)
\(992\) 2.45826 0.0780498
\(993\) −6.60436 −0.209583
\(994\) 6.58748 0.208942
\(995\) 2.64964 0.0839994
\(996\) 0.0446920 0.00141612
\(997\) −17.4927 −0.553998 −0.276999 0.960870i \(-0.589340\pi\)
−0.276999 + 0.960870i \(0.589340\pi\)
\(998\) −38.0328 −1.20391
\(999\) 3.55773 0.112562
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 4730.2.a.z.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.z.1.8 10 1.1 even 1 trivial