Properties

Label 1859.2.a.t.1.15
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.43463 q^{2} +0.655312 q^{3} +0.0581570 q^{4} +1.45609 q^{5} +0.940129 q^{6} +3.21683 q^{7} -2.78582 q^{8} -2.57057 q^{9} +O(q^{10})\) \(q+1.43463 q^{2} +0.655312 q^{3} +0.0581570 q^{4} +1.45609 q^{5} +0.940129 q^{6} +3.21683 q^{7} -2.78582 q^{8} -2.57057 q^{9} +2.08894 q^{10} +1.00000 q^{11} +0.0381110 q^{12} +4.61496 q^{14} +0.954190 q^{15} -4.11293 q^{16} +2.77570 q^{17} -3.68781 q^{18} +6.77395 q^{19} +0.0846816 q^{20} +2.10803 q^{21} +1.43463 q^{22} +7.11072 q^{23} -1.82558 q^{24} -2.87981 q^{25} -3.65046 q^{27} +0.187081 q^{28} -3.39343 q^{29} +1.36891 q^{30} +10.2964 q^{31} -0.328883 q^{32} +0.655312 q^{33} +3.98210 q^{34} +4.68398 q^{35} -0.149497 q^{36} -2.07211 q^{37} +9.71809 q^{38} -4.05640 q^{40} +3.73696 q^{41} +3.02424 q^{42} +5.99390 q^{43} +0.0581570 q^{44} -3.74297 q^{45} +10.2012 q^{46} -10.9686 q^{47} -2.69525 q^{48} +3.34801 q^{49} -4.13146 q^{50} +1.81895 q^{51} -1.46322 q^{53} -5.23705 q^{54} +1.45609 q^{55} -8.96152 q^{56} +4.43905 q^{57} -4.86831 q^{58} +9.94003 q^{59} +0.0554929 q^{60} +2.55646 q^{61} +14.7715 q^{62} -8.26908 q^{63} +7.75404 q^{64} +0.940129 q^{66} -11.6323 q^{67} +0.161426 q^{68} +4.65974 q^{69} +6.71977 q^{70} +9.44195 q^{71} +7.16114 q^{72} -7.67100 q^{73} -2.97271 q^{74} -1.88718 q^{75} +0.393953 q^{76} +3.21683 q^{77} +8.09605 q^{79} -5.98878 q^{80} +5.31951 q^{81} +5.36114 q^{82} -2.39011 q^{83} +0.122597 q^{84} +4.04166 q^{85} +8.59902 q^{86} -2.22376 q^{87} -2.78582 q^{88} -13.1321 q^{89} -5.36976 q^{90} +0.413538 q^{92} +6.74735 q^{93} -15.7358 q^{94} +9.86345 q^{95} -0.215521 q^{96} -9.77821 q^{97} +4.80315 q^{98} -2.57057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.43463 1.01444 0.507218 0.861818i \(-0.330674\pi\)
0.507218 + 0.861818i \(0.330674\pi\)
\(3\) 0.655312 0.378344 0.189172 0.981944i \(-0.439420\pi\)
0.189172 + 0.981944i \(0.439420\pi\)
\(4\) 0.0581570 0.0290785
\(5\) 1.45609 0.651181 0.325591 0.945511i \(-0.394437\pi\)
0.325591 + 0.945511i \(0.394437\pi\)
\(6\) 0.940129 0.383806
\(7\) 3.21683 1.21585 0.607924 0.793995i \(-0.292002\pi\)
0.607924 + 0.793995i \(0.292002\pi\)
\(8\) −2.78582 −0.984937
\(9\) −2.57057 −0.856855
\(10\) 2.08894 0.660581
\(11\) 1.00000 0.301511
\(12\) 0.0381110 0.0110017
\(13\) 0 0
\(14\) 4.61496 1.23340
\(15\) 0.954190 0.246371
\(16\) −4.11293 −1.02823
\(17\) 2.77570 0.673206 0.336603 0.941647i \(-0.390722\pi\)
0.336603 + 0.941647i \(0.390722\pi\)
\(18\) −3.68781 −0.869224
\(19\) 6.77395 1.55405 0.777025 0.629470i \(-0.216728\pi\)
0.777025 + 0.629470i \(0.216728\pi\)
\(20\) 0.0846816 0.0189354
\(21\) 2.10803 0.460009
\(22\) 1.43463 0.305864
\(23\) 7.11072 1.48269 0.741344 0.671125i \(-0.234189\pi\)
0.741344 + 0.671125i \(0.234189\pi\)
\(24\) −1.82558 −0.372645
\(25\) −2.87981 −0.575963
\(26\) 0 0
\(27\) −3.65046 −0.702531
\(28\) 0.187081 0.0353551
\(29\) −3.39343 −0.630145 −0.315072 0.949068i \(-0.602029\pi\)
−0.315072 + 0.949068i \(0.602029\pi\)
\(30\) 1.36891 0.249927
\(31\) 10.2964 1.84929 0.924643 0.380834i \(-0.124363\pi\)
0.924643 + 0.380834i \(0.124363\pi\)
\(32\) −0.328883 −0.0581388
\(33\) 0.655312 0.114075
\(34\) 3.98210 0.682924
\(35\) 4.68398 0.791738
\(36\) −0.149497 −0.0249161
\(37\) −2.07211 −0.340653 −0.170327 0.985388i \(-0.554482\pi\)
−0.170327 + 0.985388i \(0.554482\pi\)
\(38\) 9.71809 1.57648
\(39\) 0 0
\(40\) −4.05640 −0.641372
\(41\) 3.73696 0.583615 0.291807 0.956477i \(-0.405743\pi\)
0.291807 + 0.956477i \(0.405743\pi\)
\(42\) 3.02424 0.466650
\(43\) 5.99390 0.914062 0.457031 0.889451i \(-0.348913\pi\)
0.457031 + 0.889451i \(0.348913\pi\)
\(44\) 0.0581570 0.00876750
\(45\) −3.74297 −0.557968
\(46\) 10.2012 1.50409
\(47\) −10.9686 −1.59993 −0.799965 0.600047i \(-0.795149\pi\)
−0.799965 + 0.600047i \(0.795149\pi\)
\(48\) −2.69525 −0.389026
\(49\) 3.34801 0.478287
\(50\) −4.13146 −0.584277
\(51\) 1.81895 0.254704
\(52\) 0 0
\(53\) −1.46322 −0.200988 −0.100494 0.994938i \(-0.532042\pi\)
−0.100494 + 0.994938i \(0.532042\pi\)
\(54\) −5.23705 −0.712672
\(55\) 1.45609 0.196339
\(56\) −8.96152 −1.19753
\(57\) 4.43905 0.587966
\(58\) −4.86831 −0.639241
\(59\) 9.94003 1.29408 0.647041 0.762455i \(-0.276006\pi\)
0.647041 + 0.762455i \(0.276006\pi\)
\(60\) 0.0554929 0.00716410
\(61\) 2.55646 0.327321 0.163660 0.986517i \(-0.447670\pi\)
0.163660 + 0.986517i \(0.447670\pi\)
\(62\) 14.7715 1.87598
\(63\) −8.26908 −1.04181
\(64\) 7.75404 0.969255
\(65\) 0 0
\(66\) 0.940129 0.115722
\(67\) −11.6323 −1.42111 −0.710555 0.703641i \(-0.751556\pi\)
−0.710555 + 0.703641i \(0.751556\pi\)
\(68\) 0.161426 0.0195758
\(69\) 4.65974 0.560967
\(70\) 6.71977 0.803166
\(71\) 9.44195 1.12055 0.560277 0.828305i \(-0.310695\pi\)
0.560277 + 0.828305i \(0.310695\pi\)
\(72\) 7.16114 0.843949
\(73\) −7.67100 −0.897823 −0.448911 0.893576i \(-0.648188\pi\)
−0.448911 + 0.893576i \(0.648188\pi\)
\(74\) −2.97271 −0.345571
\(75\) −1.88718 −0.217912
\(76\) 0.393953 0.0451895
\(77\) 3.21683 0.366592
\(78\) 0 0
\(79\) 8.09605 0.910877 0.455438 0.890267i \(-0.349483\pi\)
0.455438 + 0.890267i \(0.349483\pi\)
\(80\) −5.98878 −0.669566
\(81\) 5.31951 0.591057
\(82\) 5.36114 0.592039
\(83\) −2.39011 −0.262348 −0.131174 0.991359i \(-0.541875\pi\)
−0.131174 + 0.991359i \(0.541875\pi\)
\(84\) 0.122597 0.0133764
\(85\) 4.04166 0.438379
\(86\) 8.59902 0.927256
\(87\) −2.22376 −0.238412
\(88\) −2.78582 −0.296970
\(89\) −13.1321 −1.39200 −0.696000 0.718041i \(-0.745039\pi\)
−0.696000 + 0.718041i \(0.745039\pi\)
\(90\) −5.36976 −0.566023
\(91\) 0 0
\(92\) 0.413538 0.0431144
\(93\) 6.74735 0.699667
\(94\) −15.7358 −1.62302
\(95\) 9.86345 1.01197
\(96\) −0.215521 −0.0219965
\(97\) −9.77821 −0.992827 −0.496413 0.868086i \(-0.665350\pi\)
−0.496413 + 0.868086i \(0.665350\pi\)
\(98\) 4.80315 0.485191
\(99\) −2.57057 −0.258352
\(100\) −0.167482 −0.0167482
\(101\) −8.08592 −0.804579 −0.402290 0.915512i \(-0.631786\pi\)
−0.402290 + 0.915512i \(0.631786\pi\)
\(102\) 2.60951 0.258380
\(103\) −8.01086 −0.789334 −0.394667 0.918824i \(-0.629140\pi\)
−0.394667 + 0.918824i \(0.629140\pi\)
\(104\) 0 0
\(105\) 3.06947 0.299550
\(106\) −2.09917 −0.203890
\(107\) 3.26352 0.315496 0.157748 0.987479i \(-0.449577\pi\)
0.157748 + 0.987479i \(0.449577\pi\)
\(108\) −0.212300 −0.0204286
\(109\) −17.0047 −1.62876 −0.814378 0.580334i \(-0.802922\pi\)
−0.814378 + 0.580334i \(0.802922\pi\)
\(110\) 2.08894 0.199173
\(111\) −1.35788 −0.128884
\(112\) −13.2306 −1.25018
\(113\) −10.0429 −0.944753 −0.472377 0.881397i \(-0.656604\pi\)
−0.472377 + 0.881397i \(0.656604\pi\)
\(114\) 6.36838 0.596453
\(115\) 10.3538 0.965498
\(116\) −0.197352 −0.0183237
\(117\) 0 0
\(118\) 14.2602 1.31276
\(119\) 8.92896 0.818516
\(120\) −2.65820 −0.242660
\(121\) 1.00000 0.0909091
\(122\) 3.66757 0.332046
\(123\) 2.44887 0.220807
\(124\) 0.598808 0.0537745
\(125\) −11.4737 −1.02624
\(126\) −11.8631 −1.05684
\(127\) −2.23609 −0.198420 −0.0992102 0.995066i \(-0.531632\pi\)
−0.0992102 + 0.995066i \(0.531632\pi\)
\(128\) 11.7819 1.04138
\(129\) 3.92788 0.345830
\(130\) 0 0
\(131\) 1.52746 0.133455 0.0667273 0.997771i \(-0.478744\pi\)
0.0667273 + 0.997771i \(0.478744\pi\)
\(132\) 0.0381110 0.00331714
\(133\) 21.7906 1.88949
\(134\) −16.6880 −1.44162
\(135\) −5.31538 −0.457475
\(136\) −7.73260 −0.663065
\(137\) −6.07861 −0.519331 −0.259665 0.965699i \(-0.583612\pi\)
−0.259665 + 0.965699i \(0.583612\pi\)
\(138\) 6.68499 0.569064
\(139\) 16.8529 1.42944 0.714721 0.699410i \(-0.246554\pi\)
0.714721 + 0.699410i \(0.246554\pi\)
\(140\) 0.272407 0.0230226
\(141\) −7.18783 −0.605325
\(142\) 13.5457 1.13673
\(143\) 0 0
\(144\) 10.5726 0.881047
\(145\) −4.94113 −0.410338
\(146\) −11.0050 −0.910783
\(147\) 2.19399 0.180957
\(148\) −0.120508 −0.00990569
\(149\) −6.57344 −0.538517 −0.269259 0.963068i \(-0.586779\pi\)
−0.269259 + 0.963068i \(0.586779\pi\)
\(150\) −2.70740 −0.221058
\(151\) 19.0261 1.54832 0.774162 0.632988i \(-0.218172\pi\)
0.774162 + 0.632988i \(0.218172\pi\)
\(152\) −18.8710 −1.53064
\(153\) −7.13512 −0.576840
\(154\) 4.61496 0.371884
\(155\) 14.9924 1.20422
\(156\) 0 0
\(157\) −3.54317 −0.282776 −0.141388 0.989954i \(-0.545156\pi\)
−0.141388 + 0.989954i \(0.545156\pi\)
\(158\) 11.6148 0.924025
\(159\) −0.958864 −0.0760429
\(160\) −0.478881 −0.0378589
\(161\) 22.8740 1.80272
\(162\) 7.63152 0.599589
\(163\) 8.25772 0.646795 0.323397 0.946263i \(-0.395175\pi\)
0.323397 + 0.946263i \(0.395175\pi\)
\(164\) 0.217330 0.0169707
\(165\) 0.954190 0.0742836
\(166\) −3.42891 −0.266135
\(167\) −4.90041 −0.379205 −0.189602 0.981861i \(-0.560720\pi\)
−0.189602 + 0.981861i \(0.560720\pi\)
\(168\) −5.87259 −0.453080
\(169\) 0 0
\(170\) 5.79827 0.444707
\(171\) −17.4129 −1.33160
\(172\) 0.348588 0.0265796
\(173\) 0.662919 0.0504008 0.0252004 0.999682i \(-0.491978\pi\)
0.0252004 + 0.999682i \(0.491978\pi\)
\(174\) −3.19026 −0.241853
\(175\) −9.26388 −0.700284
\(176\) −4.11293 −0.310024
\(177\) 6.51382 0.489609
\(178\) −18.8397 −1.41209
\(179\) −10.8625 −0.811901 −0.405950 0.913895i \(-0.633059\pi\)
−0.405950 + 0.913895i \(0.633059\pi\)
\(180\) −0.217680 −0.0162249
\(181\) 13.6608 1.01540 0.507698 0.861535i \(-0.330496\pi\)
0.507698 + 0.861535i \(0.330496\pi\)
\(182\) 0 0
\(183\) 1.67528 0.123840
\(184\) −19.8092 −1.46035
\(185\) −3.01717 −0.221827
\(186\) 9.67993 0.709767
\(187\) 2.77570 0.202979
\(188\) −0.637899 −0.0465236
\(189\) −11.7429 −0.854171
\(190\) 14.1504 1.02658
\(191\) −18.5405 −1.34154 −0.670772 0.741664i \(-0.734037\pi\)
−0.670772 + 0.741664i \(0.734037\pi\)
\(192\) 5.08131 0.366712
\(193\) 7.01456 0.504919 0.252460 0.967607i \(-0.418760\pi\)
0.252460 + 0.967607i \(0.418760\pi\)
\(194\) −14.0281 −1.00716
\(195\) 0 0
\(196\) 0.194710 0.0139079
\(197\) 11.3461 0.808376 0.404188 0.914676i \(-0.367554\pi\)
0.404188 + 0.914676i \(0.367554\pi\)
\(198\) −3.68781 −0.262081
\(199\) 9.41305 0.667273 0.333637 0.942702i \(-0.391724\pi\)
0.333637 + 0.942702i \(0.391724\pi\)
\(200\) 8.02265 0.567287
\(201\) −7.62278 −0.537669
\(202\) −11.6003 −0.816193
\(203\) −10.9161 −0.766160
\(204\) 0.105785 0.00740641
\(205\) 5.44133 0.380039
\(206\) −11.4926 −0.800728
\(207\) −18.2786 −1.27045
\(208\) 0 0
\(209\) 6.77395 0.468564
\(210\) 4.40355 0.303874
\(211\) 5.60589 0.385925 0.192963 0.981206i \(-0.438190\pi\)
0.192963 + 0.981206i \(0.438190\pi\)
\(212\) −0.0850964 −0.00584445
\(213\) 6.18742 0.423955
\(214\) 4.68194 0.320051
\(215\) 8.72764 0.595220
\(216\) 10.1695 0.691949
\(217\) 33.1218 2.24845
\(218\) −24.3954 −1.65227
\(219\) −5.02690 −0.339686
\(220\) 0.0846816 0.00570924
\(221\) 0 0
\(222\) −1.94805 −0.130745
\(223\) −14.8767 −0.996215 −0.498108 0.867115i \(-0.665972\pi\)
−0.498108 + 0.867115i \(0.665972\pi\)
\(224\) −1.05796 −0.0706879
\(225\) 7.40275 0.493517
\(226\) −14.4078 −0.958391
\(227\) −18.6696 −1.23915 −0.619574 0.784938i \(-0.712695\pi\)
−0.619574 + 0.784938i \(0.712695\pi\)
\(228\) 0.258162 0.0170972
\(229\) −2.65371 −0.175362 −0.0876811 0.996149i \(-0.527946\pi\)
−0.0876811 + 0.996149i \(0.527946\pi\)
\(230\) 14.8539 0.979436
\(231\) 2.10803 0.138698
\(232\) 9.45350 0.620653
\(233\) 29.7930 1.95180 0.975902 0.218211i \(-0.0700220\pi\)
0.975902 + 0.218211i \(0.0700220\pi\)
\(234\) 0 0
\(235\) −15.9712 −1.04184
\(236\) 0.578083 0.0376300
\(237\) 5.30544 0.344625
\(238\) 12.8097 0.830332
\(239\) −24.4485 −1.58144 −0.790720 0.612179i \(-0.790293\pi\)
−0.790720 + 0.612179i \(0.790293\pi\)
\(240\) −3.92452 −0.253327
\(241\) −11.8300 −0.762036 −0.381018 0.924568i \(-0.624426\pi\)
−0.381018 + 0.924568i \(0.624426\pi\)
\(242\) 1.43463 0.0922214
\(243\) 14.4373 0.926154
\(244\) 0.148676 0.00951801
\(245\) 4.87499 0.311452
\(246\) 3.51322 0.223995
\(247\) 0 0
\(248\) −28.6839 −1.82143
\(249\) −1.56626 −0.0992580
\(250\) −16.4605 −1.04105
\(251\) 11.2327 0.709001 0.354500 0.935056i \(-0.384651\pi\)
0.354500 + 0.935056i \(0.384651\pi\)
\(252\) −0.480905 −0.0302942
\(253\) 7.11072 0.447047
\(254\) −3.20795 −0.201285
\(255\) 2.64854 0.165858
\(256\) 1.39460 0.0871625
\(257\) −23.0023 −1.43484 −0.717422 0.696639i \(-0.754678\pi\)
−0.717422 + 0.696639i \(0.754678\pi\)
\(258\) 5.63504 0.350822
\(259\) −6.66564 −0.414183
\(260\) 0 0
\(261\) 8.72304 0.539943
\(262\) 2.19133 0.135381
\(263\) 21.9165 1.35143 0.675714 0.737163i \(-0.263835\pi\)
0.675714 + 0.737163i \(0.263835\pi\)
\(264\) −1.82558 −0.112357
\(265\) −2.13057 −0.130880
\(266\) 31.2615 1.91676
\(267\) −8.60563 −0.526656
\(268\) −0.676500 −0.0413238
\(269\) 2.52774 0.154119 0.0770594 0.997027i \(-0.475447\pi\)
0.0770594 + 0.997027i \(0.475447\pi\)
\(270\) −7.62559 −0.464079
\(271\) 10.4276 0.633430 0.316715 0.948521i \(-0.397420\pi\)
0.316715 + 0.948521i \(0.397420\pi\)
\(272\) −11.4163 −0.692213
\(273\) 0 0
\(274\) −8.72054 −0.526827
\(275\) −2.87981 −0.173659
\(276\) 0.270997 0.0163121
\(277\) −17.4391 −1.04781 −0.523907 0.851776i \(-0.675526\pi\)
−0.523907 + 0.851776i \(0.675526\pi\)
\(278\) 24.1776 1.45008
\(279\) −26.4676 −1.58457
\(280\) −13.0487 −0.779812
\(281\) −13.3162 −0.794380 −0.397190 0.917736i \(-0.630015\pi\)
−0.397190 + 0.917736i \(0.630015\pi\)
\(282\) −10.3119 −0.614062
\(283\) −8.64894 −0.514126 −0.257063 0.966395i \(-0.582755\pi\)
−0.257063 + 0.966395i \(0.582755\pi\)
\(284\) 0.549116 0.0325840
\(285\) 6.46363 0.382873
\(286\) 0 0
\(287\) 12.0212 0.709587
\(288\) 0.845415 0.0498165
\(289\) −9.29549 −0.546794
\(290\) −7.08868 −0.416262
\(291\) −6.40778 −0.375631
\(292\) −0.446123 −0.0261074
\(293\) −10.2809 −0.600616 −0.300308 0.953842i \(-0.597089\pi\)
−0.300308 + 0.953842i \(0.597089\pi\)
\(294\) 3.14756 0.183569
\(295\) 14.4735 0.842682
\(296\) 5.77254 0.335522
\(297\) −3.65046 −0.211821
\(298\) −9.43044 −0.546291
\(299\) 0 0
\(300\) −0.109753 −0.00633657
\(301\) 19.2814 1.11136
\(302\) 27.2954 1.57067
\(303\) −5.29880 −0.304408
\(304\) −27.8608 −1.59793
\(305\) 3.72242 0.213145
\(306\) −10.2362 −0.585167
\(307\) −27.4584 −1.56714 −0.783568 0.621307i \(-0.786602\pi\)
−0.783568 + 0.621307i \(0.786602\pi\)
\(308\) 0.187081 0.0106600
\(309\) −5.24961 −0.298640
\(310\) 21.5086 1.22160
\(311\) −30.2258 −1.71395 −0.856974 0.515360i \(-0.827658\pi\)
−0.856974 + 0.515360i \(0.827658\pi\)
\(312\) 0 0
\(313\) −19.7213 −1.11472 −0.557358 0.830272i \(-0.688185\pi\)
−0.557358 + 0.830272i \(0.688185\pi\)
\(314\) −5.08313 −0.286857
\(315\) −12.0405 −0.678405
\(316\) 0.470842 0.0264870
\(317\) 0.586819 0.0329590 0.0164795 0.999864i \(-0.494754\pi\)
0.0164795 + 0.999864i \(0.494754\pi\)
\(318\) −1.37561 −0.0771405
\(319\) −3.39343 −0.189996
\(320\) 11.2905 0.631161
\(321\) 2.13862 0.119366
\(322\) 32.8157 1.82875
\(323\) 18.8024 1.04620
\(324\) 0.309367 0.0171871
\(325\) 0 0
\(326\) 11.8468 0.656131
\(327\) −11.1434 −0.616231
\(328\) −10.4105 −0.574824
\(329\) −35.2840 −1.94527
\(330\) 1.36891 0.0753559
\(331\) 33.7665 1.85598 0.927988 0.372611i \(-0.121537\pi\)
0.927988 + 0.372611i \(0.121537\pi\)
\(332\) −0.139002 −0.00762870
\(333\) 5.32650 0.291891
\(334\) −7.03026 −0.384679
\(335\) −16.9376 −0.925401
\(336\) −8.67018 −0.472997
\(337\) −30.2231 −1.64636 −0.823179 0.567781i \(-0.807802\pi\)
−0.823179 + 0.567781i \(0.807802\pi\)
\(338\) 0 0
\(339\) −6.58121 −0.357442
\(340\) 0.235051 0.0127474
\(341\) 10.2964 0.557581
\(342\) −24.9810 −1.35082
\(343\) −11.7478 −0.634324
\(344\) −16.6979 −0.900293
\(345\) 6.78498 0.365291
\(346\) 0.951042 0.0511283
\(347\) −10.9572 −0.588213 −0.294107 0.955773i \(-0.595022\pi\)
−0.294107 + 0.955773i \(0.595022\pi\)
\(348\) −0.129327 −0.00693266
\(349\) −37.0347 −1.98242 −0.991211 0.132293i \(-0.957766\pi\)
−0.991211 + 0.132293i \(0.957766\pi\)
\(350\) −13.2902 −0.710392
\(351\) 0 0
\(352\) −0.328883 −0.0175295
\(353\) 10.2718 0.546711 0.273356 0.961913i \(-0.411866\pi\)
0.273356 + 0.961913i \(0.411866\pi\)
\(354\) 9.34491 0.496676
\(355\) 13.7483 0.729683
\(356\) −0.763725 −0.0404773
\(357\) 5.85125 0.309681
\(358\) −15.5836 −0.823620
\(359\) −11.6703 −0.615935 −0.307968 0.951397i \(-0.599649\pi\)
−0.307968 + 0.951397i \(0.599649\pi\)
\(360\) 10.4272 0.549563
\(361\) 26.8863 1.41507
\(362\) 19.5981 1.03005
\(363\) 0.655312 0.0343949
\(364\) 0 0
\(365\) −11.1696 −0.584645
\(366\) 2.40340 0.125628
\(367\) −18.8743 −0.985229 −0.492615 0.870248i \(-0.663959\pi\)
−0.492615 + 0.870248i \(0.663959\pi\)
\(368\) −29.2459 −1.52455
\(369\) −9.60610 −0.500074
\(370\) −4.32852 −0.225029
\(371\) −4.70693 −0.244371
\(372\) 0.392406 0.0203453
\(373\) −0.390809 −0.0202353 −0.0101177 0.999949i \(-0.503221\pi\)
−0.0101177 + 0.999949i \(0.503221\pi\)
\(374\) 3.98210 0.205909
\(375\) −7.51884 −0.388271
\(376\) 30.5565 1.57583
\(377\) 0 0
\(378\) −16.8467 −0.866501
\(379\) 26.0803 1.33966 0.669828 0.742516i \(-0.266368\pi\)
0.669828 + 0.742516i \(0.266368\pi\)
\(380\) 0.573629 0.0294265
\(381\) −1.46533 −0.0750713
\(382\) −26.5987 −1.36091
\(383\) −1.49911 −0.0766008 −0.0383004 0.999266i \(-0.512194\pi\)
−0.0383004 + 0.999266i \(0.512194\pi\)
\(384\) 7.72084 0.394002
\(385\) 4.68398 0.238718
\(386\) 10.0633 0.512208
\(387\) −15.4077 −0.783219
\(388\) −0.568672 −0.0288699
\(389\) −5.04180 −0.255630 −0.127815 0.991798i \(-0.540796\pi\)
−0.127815 + 0.991798i \(0.540796\pi\)
\(390\) 0 0
\(391\) 19.7372 0.998154
\(392\) −9.32696 −0.471083
\(393\) 1.00096 0.0504918
\(394\) 16.2774 0.820045
\(395\) 11.7885 0.593146
\(396\) −0.149497 −0.00751248
\(397\) −9.30731 −0.467121 −0.233560 0.972342i \(-0.575038\pi\)
−0.233560 + 0.972342i \(0.575038\pi\)
\(398\) 13.5042 0.676905
\(399\) 14.2797 0.714878
\(400\) 11.8445 0.592224
\(401\) 24.4114 1.21905 0.609523 0.792769i \(-0.291361\pi\)
0.609523 + 0.792769i \(0.291361\pi\)
\(402\) −10.9359 −0.545431
\(403\) 0 0
\(404\) −0.470253 −0.0233960
\(405\) 7.74566 0.384885
\(406\) −15.6605 −0.777220
\(407\) −2.07211 −0.102711
\(408\) −5.06727 −0.250867
\(409\) −6.36177 −0.314569 −0.157285 0.987553i \(-0.550274\pi\)
−0.157285 + 0.987553i \(0.550274\pi\)
\(410\) 7.80629 0.385525
\(411\) −3.98338 −0.196486
\(412\) −0.465888 −0.0229527
\(413\) 31.9754 1.57341
\(414\) −26.2230 −1.28879
\(415\) −3.48020 −0.170836
\(416\) 0 0
\(417\) 11.0439 0.540821
\(418\) 9.71809 0.475327
\(419\) 2.57848 0.125967 0.0629835 0.998015i \(-0.479938\pi\)
0.0629835 + 0.998015i \(0.479938\pi\)
\(420\) 0.178511 0.00871046
\(421\) −24.8155 −1.20943 −0.604716 0.796441i \(-0.706713\pi\)
−0.604716 + 0.796441i \(0.706713\pi\)
\(422\) 8.04236 0.391496
\(423\) 28.1954 1.37091
\(424\) 4.07626 0.197961
\(425\) −7.99350 −0.387742
\(426\) 8.87665 0.430075
\(427\) 8.22370 0.397973
\(428\) 0.189797 0.00917417
\(429\) 0 0
\(430\) 12.5209 0.603812
\(431\) 41.0457 1.97710 0.988550 0.150893i \(-0.0482149\pi\)
0.988550 + 0.150893i \(0.0482149\pi\)
\(432\) 15.0141 0.722365
\(433\) 32.5278 1.56319 0.781593 0.623789i \(-0.214408\pi\)
0.781593 + 0.623789i \(0.214408\pi\)
\(434\) 47.5174 2.28091
\(435\) −3.23798 −0.155249
\(436\) −0.988944 −0.0473618
\(437\) 48.1676 2.30417
\(438\) −7.21173 −0.344590
\(439\) 1.98368 0.0946757 0.0473378 0.998879i \(-0.484926\pi\)
0.0473378 + 0.998879i \(0.484926\pi\)
\(440\) −4.05640 −0.193381
\(441\) −8.60628 −0.409823
\(442\) 0 0
\(443\) −30.0670 −1.42853 −0.714264 0.699877i \(-0.753238\pi\)
−0.714264 + 0.699877i \(0.753238\pi\)
\(444\) −0.0789703 −0.00374776
\(445\) −19.1215 −0.906445
\(446\) −21.3425 −1.01060
\(447\) −4.30765 −0.203745
\(448\) 24.9434 1.17847
\(449\) −17.9192 −0.845659 −0.422829 0.906209i \(-0.638963\pi\)
−0.422829 + 0.906209i \(0.638963\pi\)
\(450\) 10.6202 0.500641
\(451\) 3.73696 0.175967
\(452\) −0.584063 −0.0274720
\(453\) 12.4680 0.585800
\(454\) −26.7840 −1.25704
\(455\) 0 0
\(456\) −12.3664 −0.579109
\(457\) 26.8996 1.25831 0.629156 0.777279i \(-0.283401\pi\)
0.629156 + 0.777279i \(0.283401\pi\)
\(458\) −3.80709 −0.177894
\(459\) −10.1326 −0.472948
\(460\) 0.602147 0.0280753
\(461\) 33.5938 1.56462 0.782310 0.622889i \(-0.214041\pi\)
0.782310 + 0.622889i \(0.214041\pi\)
\(462\) 3.02424 0.140700
\(463\) −19.5065 −0.906543 −0.453271 0.891373i \(-0.649743\pi\)
−0.453271 + 0.891373i \(0.649743\pi\)
\(464\) 13.9570 0.647935
\(465\) 9.82472 0.455610
\(466\) 42.7418 1.97998
\(467\) 32.6367 1.51025 0.755124 0.655582i \(-0.227577\pi\)
0.755124 + 0.655582i \(0.227577\pi\)
\(468\) 0 0
\(469\) −37.4191 −1.72786
\(470\) −22.9127 −1.05688
\(471\) −2.32188 −0.106987
\(472\) −27.6912 −1.27459
\(473\) 5.99390 0.275600
\(474\) 7.61133 0.349600
\(475\) −19.5077 −0.895075
\(476\) 0.519282 0.0238012
\(477\) 3.76130 0.172218
\(478\) −35.0744 −1.60427
\(479\) −2.04138 −0.0932732 −0.0466366 0.998912i \(-0.514850\pi\)
−0.0466366 + 0.998912i \(0.514850\pi\)
\(480\) −0.313817 −0.0143237
\(481\) 0 0
\(482\) −16.9716 −0.773036
\(483\) 14.9896 0.682050
\(484\) 0.0581570 0.00264350
\(485\) −14.2379 −0.646510
\(486\) 20.7122 0.939523
\(487\) 1.42608 0.0646216 0.0323108 0.999478i \(-0.489713\pi\)
0.0323108 + 0.999478i \(0.489713\pi\)
\(488\) −7.12184 −0.322390
\(489\) 5.41138 0.244711
\(490\) 6.99380 0.315947
\(491\) −22.8208 −1.02989 −0.514944 0.857224i \(-0.672187\pi\)
−0.514944 + 0.857224i \(0.672187\pi\)
\(492\) 0.142419 0.00642075
\(493\) −9.41915 −0.424217
\(494\) 0 0
\(495\) −3.74297 −0.168234
\(496\) −42.3484 −1.90150
\(497\) 30.3732 1.36242
\(498\) −2.24701 −0.100691
\(499\) 30.2658 1.35488 0.677441 0.735577i \(-0.263089\pi\)
0.677441 + 0.735577i \(0.263089\pi\)
\(500\) −0.667276 −0.0298415
\(501\) −3.21129 −0.143470
\(502\) 16.1147 0.719235
\(503\) 16.2023 0.722423 0.361212 0.932484i \(-0.382363\pi\)
0.361212 + 0.932484i \(0.382363\pi\)
\(504\) 23.0362 1.02611
\(505\) −11.7738 −0.523927
\(506\) 10.2012 0.453500
\(507\) 0 0
\(508\) −0.130044 −0.00576978
\(509\) 35.6080 1.57830 0.789148 0.614203i \(-0.210522\pi\)
0.789148 + 0.614203i \(0.210522\pi\)
\(510\) 3.79968 0.168252
\(511\) −24.6763 −1.09162
\(512\) −21.5631 −0.952964
\(513\) −24.7280 −1.09177
\(514\) −32.9998 −1.45556
\(515\) −11.6645 −0.513999
\(516\) 0.228434 0.0100562
\(517\) −10.9686 −0.482397
\(518\) −9.56271 −0.420161
\(519\) 0.434419 0.0190689
\(520\) 0 0
\(521\) −22.1588 −0.970794 −0.485397 0.874294i \(-0.661325\pi\)
−0.485397 + 0.874294i \(0.661325\pi\)
\(522\) 12.5143 0.547737
\(523\) 5.06169 0.221332 0.110666 0.993858i \(-0.464702\pi\)
0.110666 + 0.993858i \(0.464702\pi\)
\(524\) 0.0888325 0.00388067
\(525\) −6.07073 −0.264948
\(526\) 31.4420 1.37094
\(527\) 28.5797 1.24495
\(528\) −2.69525 −0.117296
\(529\) 27.5623 1.19836
\(530\) −3.05658 −0.132769
\(531\) −25.5515 −1.10884
\(532\) 1.26728 0.0549435
\(533\) 0 0
\(534\) −12.3459 −0.534258
\(535\) 4.75196 0.205445
\(536\) 32.4055 1.39970
\(537\) −7.11832 −0.307178
\(538\) 3.62636 0.156344
\(539\) 3.34801 0.144209
\(540\) −0.309127 −0.0133027
\(541\) −17.5776 −0.755719 −0.377859 0.925863i \(-0.623340\pi\)
−0.377859 + 0.925863i \(0.623340\pi\)
\(542\) 14.9597 0.642573
\(543\) 8.95206 0.384170
\(544\) −0.912879 −0.0391394
\(545\) −24.7603 −1.06062
\(546\) 0 0
\(547\) 44.3094 1.89453 0.947267 0.320444i \(-0.103832\pi\)
0.947267 + 0.320444i \(0.103832\pi\)
\(548\) −0.353514 −0.0151014
\(549\) −6.57155 −0.280467
\(550\) −4.13146 −0.176166
\(551\) −22.9869 −0.979276
\(552\) −12.9812 −0.552517
\(553\) 26.0436 1.10749
\(554\) −25.0186 −1.06294
\(555\) −1.97719 −0.0839270
\(556\) 0.980113 0.0415661
\(557\) −24.1276 −1.02232 −0.511160 0.859486i \(-0.670784\pi\)
−0.511160 + 0.859486i \(0.670784\pi\)
\(558\) −37.9711 −1.60745
\(559\) 0 0
\(560\) −19.2649 −0.814091
\(561\) 1.81895 0.0767961
\(562\) −19.1038 −0.805847
\(563\) 3.82022 0.161003 0.0805016 0.996754i \(-0.474348\pi\)
0.0805016 + 0.996754i \(0.474348\pi\)
\(564\) −0.418023 −0.0176019
\(565\) −14.6233 −0.615206
\(566\) −12.4080 −0.521548
\(567\) 17.1120 0.718635
\(568\) −26.3036 −1.10367
\(569\) −10.4948 −0.439964 −0.219982 0.975504i \(-0.570600\pi\)
−0.219982 + 0.975504i \(0.570600\pi\)
\(570\) 9.27291 0.388399
\(571\) −40.0219 −1.67487 −0.837433 0.546540i \(-0.815945\pi\)
−0.837433 + 0.546540i \(0.815945\pi\)
\(572\) 0 0
\(573\) −12.1498 −0.507566
\(574\) 17.2459 0.719830
\(575\) −20.4776 −0.853973
\(576\) −19.9323 −0.830511
\(577\) 28.4941 1.18623 0.593113 0.805119i \(-0.297899\pi\)
0.593113 + 0.805119i \(0.297899\pi\)
\(578\) −13.3356 −0.554687
\(579\) 4.59673 0.191033
\(580\) −0.287361 −0.0119320
\(581\) −7.68857 −0.318976
\(582\) −9.19278 −0.381053
\(583\) −1.46322 −0.0606003
\(584\) 21.3700 0.884299
\(585\) 0 0
\(586\) −14.7493 −0.609286
\(587\) 5.30994 0.219165 0.109582 0.993978i \(-0.465049\pi\)
0.109582 + 0.993978i \(0.465049\pi\)
\(588\) 0.127596 0.00526197
\(589\) 69.7472 2.87388
\(590\) 20.7641 0.854846
\(591\) 7.43523 0.305845
\(592\) 8.52246 0.350271
\(593\) 27.5649 1.13195 0.565977 0.824421i \(-0.308499\pi\)
0.565977 + 0.824421i \(0.308499\pi\)
\(594\) −5.23705 −0.214879
\(595\) 13.0013 0.533003
\(596\) −0.382292 −0.0156593
\(597\) 6.16848 0.252459
\(598\) 0 0
\(599\) 37.2112 1.52041 0.760205 0.649683i \(-0.225098\pi\)
0.760205 + 0.649683i \(0.225098\pi\)
\(600\) 5.25734 0.214630
\(601\) 18.4580 0.752919 0.376459 0.926433i \(-0.377141\pi\)
0.376459 + 0.926433i \(0.377141\pi\)
\(602\) 27.6616 1.12740
\(603\) 29.9016 1.21769
\(604\) 1.10650 0.0450230
\(605\) 1.45609 0.0591983
\(606\) −7.60181 −0.308802
\(607\) 25.1059 1.01902 0.509508 0.860466i \(-0.329827\pi\)
0.509508 + 0.860466i \(0.329827\pi\)
\(608\) −2.22783 −0.0903506
\(609\) −7.15345 −0.289872
\(610\) 5.34029 0.216222
\(611\) 0 0
\(612\) −0.414957 −0.0167737
\(613\) −29.3930 −1.18717 −0.593586 0.804771i \(-0.702288\pi\)
−0.593586 + 0.804771i \(0.702288\pi\)
\(614\) −39.3926 −1.58976
\(615\) 3.56577 0.143786
\(616\) −8.96152 −0.361070
\(617\) 27.9655 1.12585 0.562923 0.826509i \(-0.309677\pi\)
0.562923 + 0.826509i \(0.309677\pi\)
\(618\) −7.53124 −0.302951
\(619\) 9.84634 0.395758 0.197879 0.980226i \(-0.436595\pi\)
0.197879 + 0.980226i \(0.436595\pi\)
\(620\) 0.871916 0.0350170
\(621\) −25.9574 −1.04163
\(622\) −43.3628 −1.73869
\(623\) −42.2438 −1.69246
\(624\) 0 0
\(625\) −2.30760 −0.0923039
\(626\) −28.2928 −1.13081
\(627\) 4.43905 0.177278
\(628\) −0.206060 −0.00822270
\(629\) −5.75156 −0.229330
\(630\) −17.2736 −0.688198
\(631\) 6.68062 0.265951 0.132976 0.991119i \(-0.457547\pi\)
0.132976 + 0.991119i \(0.457547\pi\)
\(632\) −22.5542 −0.897156
\(633\) 3.67360 0.146013
\(634\) 0.841867 0.0334348
\(635\) −3.25593 −0.129208
\(636\) −0.0557647 −0.00221121
\(637\) 0 0
\(638\) −4.86831 −0.192738
\(639\) −24.2712 −0.960152
\(640\) 17.1555 0.678130
\(641\) 31.3725 1.23914 0.619570 0.784941i \(-0.287307\pi\)
0.619570 + 0.784941i \(0.287307\pi\)
\(642\) 3.06813 0.121089
\(643\) 35.8394 1.41337 0.706684 0.707529i \(-0.250190\pi\)
0.706684 + 0.707529i \(0.250190\pi\)
\(644\) 1.33028 0.0524205
\(645\) 5.71932 0.225198
\(646\) 26.9745 1.06130
\(647\) −23.3917 −0.919621 −0.459811 0.888017i \(-0.652083\pi\)
−0.459811 + 0.888017i \(0.652083\pi\)
\(648\) −14.8192 −0.582154
\(649\) 9.94003 0.390180
\(650\) 0 0
\(651\) 21.7051 0.850689
\(652\) 0.480245 0.0188078
\(653\) 9.33883 0.365457 0.182728 0.983163i \(-0.441507\pi\)
0.182728 + 0.983163i \(0.441507\pi\)
\(654\) −15.9866 −0.625126
\(655\) 2.22411 0.0869032
\(656\) −15.3699 −0.600092
\(657\) 19.7188 0.769304
\(658\) −50.6195 −1.97335
\(659\) −37.2441 −1.45083 −0.725413 0.688314i \(-0.758351\pi\)
−0.725413 + 0.688314i \(0.758351\pi\)
\(660\) 0.0554929 0.00216006
\(661\) 14.6427 0.569536 0.284768 0.958596i \(-0.408083\pi\)
0.284768 + 0.958596i \(0.408083\pi\)
\(662\) 48.4424 1.88277
\(663\) 0 0
\(664\) 6.65841 0.258396
\(665\) 31.7290 1.23040
\(666\) 7.64155 0.296104
\(667\) −24.1297 −0.934307
\(668\) −0.284993 −0.0110267
\(669\) −9.74886 −0.376913
\(670\) −24.2992 −0.938759
\(671\) 2.55646 0.0986910
\(672\) −0.693294 −0.0267444
\(673\) 35.5677 1.37103 0.685517 0.728057i \(-0.259576\pi\)
0.685517 + 0.728057i \(0.259576\pi\)
\(674\) −43.3589 −1.67012
\(675\) 10.5126 0.404632
\(676\) 0 0
\(677\) 34.4663 1.32465 0.662325 0.749217i \(-0.269570\pi\)
0.662325 + 0.749217i \(0.269570\pi\)
\(678\) −9.44159 −0.362602
\(679\) −31.4549 −1.20713
\(680\) −11.2593 −0.431776
\(681\) −12.2344 −0.468825
\(682\) 14.7715 0.565630
\(683\) −1.02390 −0.0391785 −0.0195893 0.999808i \(-0.506236\pi\)
−0.0195893 + 0.999808i \(0.506236\pi\)
\(684\) −1.01268 −0.0387208
\(685\) −8.85098 −0.338178
\(686\) −16.8538 −0.643480
\(687\) −1.73901 −0.0663473
\(688\) −24.6525 −0.939868
\(689\) 0 0
\(690\) 9.73392 0.370564
\(691\) 6.15763 0.234247 0.117124 0.993117i \(-0.462633\pi\)
0.117124 + 0.993117i \(0.462633\pi\)
\(692\) 0.0385534 0.00146558
\(693\) −8.26908 −0.314116
\(694\) −15.7195 −0.596704
\(695\) 24.5392 0.930826
\(696\) 6.19499 0.234820
\(697\) 10.3727 0.392893
\(698\) −53.1310 −2.01104
\(699\) 19.5237 0.738454
\(700\) −0.538760 −0.0203632
\(701\) 31.0865 1.17412 0.587060 0.809543i \(-0.300285\pi\)
0.587060 + 0.809543i \(0.300285\pi\)
\(702\) 0 0
\(703\) −14.0364 −0.529392
\(704\) 7.75404 0.292241
\(705\) −10.4661 −0.394176
\(706\) 14.7362 0.554603
\(707\) −26.0111 −0.978246
\(708\) 0.378825 0.0142371
\(709\) −21.4453 −0.805395 −0.402698 0.915333i \(-0.631927\pi\)
−0.402698 + 0.915333i \(0.631927\pi\)
\(710\) 19.7237 0.740217
\(711\) −20.8114 −0.780490
\(712\) 36.5837 1.37103
\(713\) 73.2148 2.74191
\(714\) 8.39437 0.314151
\(715\) 0 0
\(716\) −0.631730 −0.0236089
\(717\) −16.0214 −0.598329
\(718\) −16.7426 −0.624826
\(719\) −21.7883 −0.812568 −0.406284 0.913747i \(-0.633176\pi\)
−0.406284 + 0.913747i \(0.633176\pi\)
\(720\) 15.3946 0.573721
\(721\) −25.7696 −0.959710
\(722\) 38.5719 1.43550
\(723\) −7.75233 −0.288312
\(724\) 0.794470 0.0295262
\(725\) 9.77245 0.362940
\(726\) 0.940129 0.0348914
\(727\) 19.3982 0.719441 0.359720 0.933060i \(-0.382872\pi\)
0.359720 + 0.933060i \(0.382872\pi\)
\(728\) 0 0
\(729\) −6.49759 −0.240652
\(730\) −16.0243 −0.593085
\(731\) 16.6373 0.615352
\(732\) 0.0974292 0.00360109
\(733\) −45.1048 −1.66599 −0.832993 0.553284i \(-0.813374\pi\)
−0.832993 + 0.553284i \(0.813374\pi\)
\(734\) −27.0776 −0.999451
\(735\) 3.19464 0.117836
\(736\) −2.33859 −0.0862017
\(737\) −11.6323 −0.428481
\(738\) −13.7812 −0.507292
\(739\) 36.1403 1.32944 0.664722 0.747091i \(-0.268550\pi\)
0.664722 + 0.747091i \(0.268550\pi\)
\(740\) −0.175470 −0.00645040
\(741\) 0 0
\(742\) −6.75269 −0.247899
\(743\) −49.3704 −1.81122 −0.905611 0.424108i \(-0.860588\pi\)
−0.905611 + 0.424108i \(0.860588\pi\)
\(744\) −18.7969 −0.689128
\(745\) −9.57149 −0.350672
\(746\) −0.560665 −0.0205274
\(747\) 6.14393 0.224795
\(748\) 0.161426 0.00590234
\(749\) 10.4982 0.383596
\(750\) −10.7867 −0.393876
\(751\) 7.50381 0.273818 0.136909 0.990584i \(-0.456283\pi\)
0.136909 + 0.990584i \(0.456283\pi\)
\(752\) 45.1130 1.64510
\(753\) 7.36091 0.268246
\(754\) 0 0
\(755\) 27.7037 1.00824
\(756\) −0.682933 −0.0248380
\(757\) 40.2759 1.46385 0.731926 0.681384i \(-0.238621\pi\)
0.731926 + 0.681384i \(0.238621\pi\)
\(758\) 37.4156 1.35899
\(759\) 4.65974 0.169138
\(760\) −27.4778 −0.996725
\(761\) −13.0491 −0.473029 −0.236514 0.971628i \(-0.576005\pi\)
−0.236514 + 0.971628i \(0.576005\pi\)
\(762\) −2.10221 −0.0761550
\(763\) −54.7013 −1.98032
\(764\) −1.07826 −0.0390101
\(765\) −10.3893 −0.375628
\(766\) −2.15066 −0.0777065
\(767\) 0 0
\(768\) 0.913898 0.0329775
\(769\) −28.2107 −1.01730 −0.508652 0.860972i \(-0.669856\pi\)
−0.508652 + 0.860972i \(0.669856\pi\)
\(770\) 6.71977 0.242164
\(771\) −15.0737 −0.542865
\(772\) 0.407946 0.0146823
\(773\) −39.3054 −1.41372 −0.706858 0.707355i \(-0.749888\pi\)
−0.706858 + 0.707355i \(0.749888\pi\)
\(774\) −22.1044 −0.794525
\(775\) −29.6517 −1.06512
\(776\) 27.2404 0.977872
\(777\) −4.36807 −0.156704
\(778\) −7.23311 −0.259320
\(779\) 25.3140 0.906967
\(780\) 0 0
\(781\) 9.44195 0.337860
\(782\) 28.3156 1.01256
\(783\) 12.3876 0.442696
\(784\) −13.7701 −0.491791
\(785\) −5.15916 −0.184138
\(786\) 1.43601 0.0512207
\(787\) 0.462301 0.0164793 0.00823963 0.999966i \(-0.497377\pi\)
0.00823963 + 0.999966i \(0.497377\pi\)
\(788\) 0.659856 0.0235064
\(789\) 14.3621 0.511306
\(790\) 16.9122 0.601708
\(791\) −32.3062 −1.14868
\(792\) 7.16114 0.254460
\(793\) 0 0
\(794\) −13.3525 −0.473863
\(795\) −1.39619 −0.0495177
\(796\) 0.547435 0.0194033
\(797\) 10.4672 0.370766 0.185383 0.982666i \(-0.440647\pi\)
0.185383 + 0.982666i \(0.440647\pi\)
\(798\) 20.4860 0.725197
\(799\) −30.4454 −1.07708
\(800\) 0.947121 0.0334858
\(801\) 33.7570 1.19274
\(802\) 35.0212 1.23664
\(803\) −7.67100 −0.270704
\(804\) −0.443318 −0.0156346
\(805\) 33.3065 1.17390
\(806\) 0 0
\(807\) 1.65646 0.0583100
\(808\) 22.5259 0.792460
\(809\) −12.5180 −0.440108 −0.220054 0.975488i \(-0.570623\pi\)
−0.220054 + 0.975488i \(0.570623\pi\)
\(810\) 11.1121 0.390441
\(811\) −5.70313 −0.200264 −0.100132 0.994974i \(-0.531926\pi\)
−0.100132 + 0.994974i \(0.531926\pi\)
\(812\) −0.634848 −0.0222788
\(813\) 6.83331 0.239655
\(814\) −2.97271 −0.104193
\(815\) 12.0239 0.421181
\(816\) −7.48121 −0.261895
\(817\) 40.6024 1.42050
\(818\) −9.12677 −0.319110
\(819\) 0 0
\(820\) 0.316452 0.0110510
\(821\) −14.1529 −0.493939 −0.246969 0.969023i \(-0.579435\pi\)
−0.246969 + 0.969023i \(0.579435\pi\)
\(822\) −5.71467 −0.199322
\(823\) 26.4939 0.923519 0.461760 0.887005i \(-0.347218\pi\)
0.461760 + 0.887005i \(0.347218\pi\)
\(824\) 22.3168 0.777444
\(825\) −1.88718 −0.0657030
\(826\) 45.8728 1.59612
\(827\) −10.9079 −0.379306 −0.189653 0.981851i \(-0.560736\pi\)
−0.189653 + 0.981851i \(0.560736\pi\)
\(828\) −1.06303 −0.0369428
\(829\) 26.4466 0.918527 0.459263 0.888300i \(-0.348113\pi\)
0.459263 + 0.888300i \(0.348113\pi\)
\(830\) −4.99279 −0.173302
\(831\) −11.4280 −0.396434
\(832\) 0 0
\(833\) 9.29307 0.321986
\(834\) 15.8439 0.548628
\(835\) −7.13541 −0.246931
\(836\) 0.393953 0.0136251
\(837\) −37.5866 −1.29918
\(838\) 3.69916 0.127785
\(839\) −3.76688 −0.130047 −0.0650236 0.997884i \(-0.520712\pi\)
−0.0650236 + 0.997884i \(0.520712\pi\)
\(840\) −8.55100 −0.295037
\(841\) −17.4846 −0.602918
\(842\) −35.6010 −1.22689
\(843\) −8.72628 −0.300549
\(844\) 0.326022 0.0112221
\(845\) 0 0
\(846\) 40.4499 1.39070
\(847\) 3.21683 0.110532
\(848\) 6.01812 0.206663
\(849\) −5.66775 −0.194517
\(850\) −11.4677 −0.393339
\(851\) −14.7342 −0.505082
\(852\) 0.359842 0.0123280
\(853\) 6.21698 0.212865 0.106433 0.994320i \(-0.466057\pi\)
0.106433 + 0.994320i \(0.466057\pi\)
\(854\) 11.7979 0.403717
\(855\) −25.3546 −0.867110
\(856\) −9.09158 −0.310744
\(857\) −19.7791 −0.675643 −0.337821 0.941210i \(-0.609690\pi\)
−0.337821 + 0.941210i \(0.609690\pi\)
\(858\) 0 0
\(859\) 39.4374 1.34559 0.672793 0.739831i \(-0.265095\pi\)
0.672793 + 0.739831i \(0.265095\pi\)
\(860\) 0.507574 0.0173081
\(861\) 7.87761 0.268468
\(862\) 58.8853 2.00564
\(863\) 9.53372 0.324532 0.162266 0.986747i \(-0.448120\pi\)
0.162266 + 0.986747i \(0.448120\pi\)
\(864\) 1.20057 0.0408443
\(865\) 0.965267 0.0328201
\(866\) 46.6652 1.58575
\(867\) −6.09145 −0.206876
\(868\) 1.92626 0.0653817
\(869\) 8.09605 0.274640
\(870\) −4.64530 −0.157490
\(871\) 0 0
\(872\) 47.3721 1.60422
\(873\) 25.1355 0.850709
\(874\) 69.1026 2.33743
\(875\) −36.9089 −1.24775
\(876\) −0.292350 −0.00987758
\(877\) 16.0771 0.542885 0.271443 0.962455i \(-0.412499\pi\)
0.271443 + 0.962455i \(0.412499\pi\)
\(878\) 2.84584 0.0960423
\(879\) −6.73719 −0.227240
\(880\) −5.98878 −0.201882
\(881\) 2.42443 0.0816811 0.0408405 0.999166i \(-0.486996\pi\)
0.0408405 + 0.999166i \(0.486996\pi\)
\(882\) −12.3468 −0.415739
\(883\) 0.684622 0.0230394 0.0115197 0.999934i \(-0.496333\pi\)
0.0115197 + 0.999934i \(0.496333\pi\)
\(884\) 0 0
\(885\) 9.48468 0.318824
\(886\) −43.1350 −1.44915
\(887\) −33.8117 −1.13529 −0.567643 0.823275i \(-0.692145\pi\)
−0.567643 + 0.823275i \(0.692145\pi\)
\(888\) 3.78281 0.126943
\(889\) −7.19311 −0.241249
\(890\) −27.4322 −0.919530
\(891\) 5.31951 0.178210
\(892\) −0.865183 −0.0289685
\(893\) −74.3005 −2.48637
\(894\) −6.17988 −0.206686
\(895\) −15.8167 −0.528694
\(896\) 37.9005 1.26617
\(897\) 0 0
\(898\) −25.7074 −0.857866
\(899\) −34.9401 −1.16532
\(900\) 0.430522 0.0143507
\(901\) −4.06145 −0.135307
\(902\) 5.36114 0.178507
\(903\) 12.6353 0.420477
\(904\) 27.9776 0.930522
\(905\) 19.8912 0.661207
\(906\) 17.8870 0.594256
\(907\) 13.3167 0.442173 0.221086 0.975254i \(-0.429040\pi\)
0.221086 + 0.975254i \(0.429040\pi\)
\(908\) −1.08577 −0.0360326
\(909\) 20.7854 0.689408
\(910\) 0 0
\(911\) 2.04780 0.0678466 0.0339233 0.999424i \(-0.489200\pi\)
0.0339233 + 0.999424i \(0.489200\pi\)
\(912\) −18.2575 −0.604566
\(913\) −2.39011 −0.0791010
\(914\) 38.5909 1.27647
\(915\) 2.43935 0.0806423
\(916\) −0.154332 −0.00509927
\(917\) 4.91358 0.162261
\(918\) −14.5365 −0.479775
\(919\) 53.8585 1.77663 0.888314 0.459237i \(-0.151877\pi\)
0.888314 + 0.459237i \(0.151877\pi\)
\(920\) −28.8439 −0.950955
\(921\) −17.9938 −0.592917
\(922\) 48.1947 1.58721
\(923\) 0 0
\(924\) 0.122597 0.00403314
\(925\) 5.96730 0.196204
\(926\) −27.9845 −0.919629
\(927\) 20.5925 0.676345
\(928\) 1.11604 0.0366358
\(929\) −48.4345 −1.58908 −0.794542 0.607209i \(-0.792289\pi\)
−0.794542 + 0.607209i \(0.792289\pi\)
\(930\) 14.0948 0.462187
\(931\) 22.6792 0.743282
\(932\) 1.73267 0.0567556
\(933\) −19.8073 −0.648463
\(934\) 46.8216 1.53205
\(935\) 4.04166 0.132176
\(936\) 0 0
\(937\) −11.2715 −0.368225 −0.184112 0.982905i \(-0.558941\pi\)
−0.184112 + 0.982905i \(0.558941\pi\)
\(938\) −53.6825 −1.75280
\(939\) −12.9236 −0.421747
\(940\) −0.928836 −0.0302953
\(941\) 9.41907 0.307053 0.153526 0.988145i \(-0.450937\pi\)
0.153526 + 0.988145i \(0.450937\pi\)
\(942\) −3.33103 −0.108531
\(943\) 26.5725 0.865319
\(944\) −40.8827 −1.33062
\(945\) −17.0987 −0.556220
\(946\) 8.59902 0.279578
\(947\) −35.7478 −1.16165 −0.580823 0.814030i \(-0.697269\pi\)
−0.580823 + 0.814030i \(0.697269\pi\)
\(948\) 0.308549 0.0100212
\(949\) 0 0
\(950\) −27.9863 −0.907995
\(951\) 0.384549 0.0124699
\(952\) −24.8745 −0.806187
\(953\) 20.9956 0.680114 0.340057 0.940405i \(-0.389554\pi\)
0.340057 + 0.940405i \(0.389554\pi\)
\(954\) 5.39606 0.174704
\(955\) −26.9966 −0.873588
\(956\) −1.42185 −0.0459859
\(957\) −2.22376 −0.0718838
\(958\) −2.92863 −0.0946196
\(959\) −19.5539 −0.631427
\(960\) 7.39883 0.238796
\(961\) 75.0157 2.41986
\(962\) 0 0
\(963\) −8.38909 −0.270335
\(964\) −0.687997 −0.0221589
\(965\) 10.2138 0.328794
\(966\) 21.5045 0.691896
\(967\) 29.7216 0.955783 0.477891 0.878419i \(-0.341401\pi\)
0.477891 + 0.878419i \(0.341401\pi\)
\(968\) −2.78582 −0.0895397
\(969\) 12.3215 0.395822
\(970\) −20.4261 −0.655843
\(971\) −7.84457 −0.251744 −0.125872 0.992046i \(-0.540173\pi\)
−0.125872 + 0.992046i \(0.540173\pi\)
\(972\) 0.839631 0.0269312
\(973\) 54.2129 1.73798
\(974\) 2.04589 0.0655545
\(975\) 0 0
\(976\) −10.5145 −0.336562
\(977\) −9.57173 −0.306227 −0.153113 0.988209i \(-0.548930\pi\)
−0.153113 + 0.988209i \(0.548930\pi\)
\(978\) 7.76332 0.248244
\(979\) −13.1321 −0.419704
\(980\) 0.283515 0.00905655
\(981\) 43.7118 1.39561
\(982\) −32.7394 −1.04476
\(983\) −39.3971 −1.25657 −0.628285 0.777983i \(-0.716243\pi\)
−0.628285 + 0.777983i \(0.716243\pi\)
\(984\) −6.82212 −0.217481
\(985\) 16.5209 0.526399
\(986\) −13.5130 −0.430341
\(987\) −23.1220 −0.735983
\(988\) 0 0
\(989\) 42.6210 1.35527
\(990\) −5.36976 −0.170662
\(991\) −21.6676 −0.688293 −0.344147 0.938916i \(-0.611832\pi\)
−0.344147 + 0.938916i \(0.611832\pi\)
\(992\) −3.38630 −0.107515
\(993\) 22.1276 0.702198
\(994\) 43.5742 1.38209
\(995\) 13.7062 0.434516
\(996\) −0.0910893 −0.00288628
\(997\) 38.4863 1.21887 0.609437 0.792835i \(-0.291396\pi\)
0.609437 + 0.792835i \(0.291396\pi\)
\(998\) 43.4201 1.37444
\(999\) 7.56416 0.239319
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 1859.2.a.t.1.15 yes 21
13.12 even 2 1859.2.a.s.1.7 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.7 21 13.12 even 2
1859.2.a.t.1.15 yes 21 1.1 even 1 trivial