Properties

Label 1859.2.a.t.1.4
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 1.4
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32475 q^{2} +2.00106 q^{3} +3.40448 q^{4} +3.04764 q^{5} -4.65197 q^{6} -5.08642 q^{7} -3.26506 q^{8} +1.00425 q^{9} +O(q^{10})\) \(q-2.32475 q^{2} +2.00106 q^{3} +3.40448 q^{4} +3.04764 q^{5} -4.65197 q^{6} -5.08642 q^{7} -3.26506 q^{8} +1.00425 q^{9} -7.08500 q^{10} +1.00000 q^{11} +6.81257 q^{12} +11.8247 q^{14} +6.09851 q^{15} +0.781510 q^{16} +4.98005 q^{17} -2.33463 q^{18} -4.25776 q^{19} +10.3756 q^{20} -10.1782 q^{21} -2.32475 q^{22} +3.33940 q^{23} -6.53359 q^{24} +4.28809 q^{25} -3.99363 q^{27} -17.3166 q^{28} +0.0575180 q^{29} -14.1775 q^{30} +4.65867 q^{31} +4.71331 q^{32} +2.00106 q^{33} -11.5774 q^{34} -15.5016 q^{35} +3.41893 q^{36} -1.03109 q^{37} +9.89823 q^{38} -9.95072 q^{40} +12.3888 q^{41} +23.6619 q^{42} +0.344029 q^{43} +3.40448 q^{44} +3.06058 q^{45} -7.76328 q^{46} +5.15893 q^{47} +1.56385 q^{48} +18.8717 q^{49} -9.96875 q^{50} +9.96538 q^{51} +5.27048 q^{53} +9.28419 q^{54} +3.04764 q^{55} +16.6075 q^{56} -8.52003 q^{57} -0.133715 q^{58} -4.35492 q^{59} +20.7622 q^{60} +13.7147 q^{61} -10.8303 q^{62} -5.10802 q^{63} -12.5203 q^{64} -4.65197 q^{66} -0.194220 q^{67} +16.9544 q^{68} +6.68234 q^{69} +36.0373 q^{70} +13.1520 q^{71} -3.27893 q^{72} +9.71787 q^{73} +2.39703 q^{74} +8.58073 q^{75} -14.4954 q^{76} -5.08642 q^{77} -3.22146 q^{79} +2.38176 q^{80} -11.0042 q^{81} -28.8009 q^{82} +7.54152 q^{83} -34.6516 q^{84} +15.1774 q^{85} -0.799782 q^{86} +0.115097 q^{87} -3.26506 q^{88} -2.89929 q^{89} -7.11509 q^{90} +11.3689 q^{92} +9.32229 q^{93} -11.9932 q^{94} -12.9761 q^{95} +9.43162 q^{96} -3.31003 q^{97} -43.8721 q^{98} +1.00425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32475 −1.64385 −0.821924 0.569597i \(-0.807099\pi\)
−0.821924 + 0.569597i \(0.807099\pi\)
\(3\) 2.00106 1.15531 0.577657 0.816280i \(-0.303967\pi\)
0.577657 + 0.816280i \(0.303967\pi\)
\(4\) 3.40448 1.70224
\(5\) 3.04764 1.36294 0.681472 0.731844i \(-0.261340\pi\)
0.681472 + 0.731844i \(0.261340\pi\)
\(6\) −4.65197 −1.89916
\(7\) −5.08642 −1.92249 −0.961244 0.275700i \(-0.911090\pi\)
−0.961244 + 0.275700i \(0.911090\pi\)
\(8\) −3.26506 −1.15437
\(9\) 1.00425 0.334749
\(10\) −7.08500 −2.24047
\(11\) 1.00000 0.301511
\(12\) 6.81257 1.96662
\(13\) 0 0
\(14\) 11.8247 3.16028
\(15\) 6.09851 1.57463
\(16\) 0.781510 0.195377
\(17\) 4.98005 1.20784 0.603919 0.797046i \(-0.293605\pi\)
0.603919 + 0.797046i \(0.293605\pi\)
\(18\) −2.33463 −0.550276
\(19\) −4.25776 −0.976796 −0.488398 0.872621i \(-0.662419\pi\)
−0.488398 + 0.872621i \(0.662419\pi\)
\(20\) 10.3756 2.32006
\(21\) −10.1782 −2.22108
\(22\) −2.32475 −0.495639
\(23\) 3.33940 0.696313 0.348156 0.937437i \(-0.386808\pi\)
0.348156 + 0.937437i \(0.386808\pi\)
\(24\) −6.53359 −1.33366
\(25\) 4.28809 0.857618
\(26\) 0 0
\(27\) −3.99363 −0.768574
\(28\) −17.3166 −3.27253
\(29\) 0.0575180 0.0106808 0.00534041 0.999986i \(-0.498300\pi\)
0.00534041 + 0.999986i \(0.498300\pi\)
\(30\) −14.1775 −2.58845
\(31\) 4.65867 0.836722 0.418361 0.908281i \(-0.362605\pi\)
0.418361 + 0.908281i \(0.362605\pi\)
\(32\) 4.71331 0.833203
\(33\) 2.00106 0.348340
\(34\) −11.5774 −1.98550
\(35\) −15.5016 −2.62024
\(36\) 3.41893 0.569822
\(37\) −1.03109 −0.169510 −0.0847549 0.996402i \(-0.527011\pi\)
−0.0847549 + 0.996402i \(0.527011\pi\)
\(38\) 9.89823 1.60571
\(39\) 0 0
\(40\) −9.95072 −1.57335
\(41\) 12.3888 1.93481 0.967404 0.253238i \(-0.0814954\pi\)
0.967404 + 0.253238i \(0.0814954\pi\)
\(42\) 23.6619 3.65111
\(43\) 0.344029 0.0524639 0.0262320 0.999656i \(-0.491649\pi\)
0.0262320 + 0.999656i \(0.491649\pi\)
\(44\) 3.40448 0.513244
\(45\) 3.06058 0.456244
\(46\) −7.76328 −1.14463
\(47\) 5.15893 0.752507 0.376253 0.926517i \(-0.377212\pi\)
0.376253 + 0.926517i \(0.377212\pi\)
\(48\) 1.56385 0.225722
\(49\) 18.8717 2.69596
\(50\) −9.96875 −1.40979
\(51\) 9.96538 1.39543
\(52\) 0 0
\(53\) 5.27048 0.723956 0.361978 0.932187i \(-0.382102\pi\)
0.361978 + 0.932187i \(0.382102\pi\)
\(54\) 9.28419 1.26342
\(55\) 3.04764 0.410943
\(56\) 16.6075 2.21927
\(57\) −8.52003 −1.12851
\(58\) −0.133715 −0.0175577
\(59\) −4.35492 −0.566962 −0.283481 0.958978i \(-0.591489\pi\)
−0.283481 + 0.958978i \(0.591489\pi\)
\(60\) 20.7622 2.68039
\(61\) 13.7147 1.75599 0.877994 0.478671i \(-0.158881\pi\)
0.877994 + 0.478671i \(0.158881\pi\)
\(62\) −10.8303 −1.37545
\(63\) −5.10802 −0.643550
\(64\) −12.5203 −1.56504
\(65\) 0 0
\(66\) −4.65197 −0.572618
\(67\) −0.194220 −0.0237277 −0.0118639 0.999930i \(-0.503776\pi\)
−0.0118639 + 0.999930i \(0.503776\pi\)
\(68\) 16.9544 2.05603
\(69\) 6.68234 0.804459
\(70\) 36.0373 4.30728
\(71\) 13.1520 1.56086 0.780430 0.625243i \(-0.215000\pi\)
0.780430 + 0.625243i \(0.215000\pi\)
\(72\) −3.27893 −0.386425
\(73\) 9.71787 1.13739 0.568695 0.822548i \(-0.307448\pi\)
0.568695 + 0.822548i \(0.307448\pi\)
\(74\) 2.39703 0.278649
\(75\) 8.58073 0.990817
\(76\) −14.4954 −1.66274
\(77\) −5.08642 −0.579652
\(78\) 0 0
\(79\) −3.22146 −0.362442 −0.181221 0.983442i \(-0.558005\pi\)
−0.181221 + 0.983442i \(0.558005\pi\)
\(80\) 2.38176 0.266289
\(81\) −11.0042 −1.22269
\(82\) −28.8009 −3.18053
\(83\) 7.54152 0.827789 0.413895 0.910325i \(-0.364168\pi\)
0.413895 + 0.910325i \(0.364168\pi\)
\(84\) −34.6516 −3.78080
\(85\) 15.1774 1.64622
\(86\) −0.799782 −0.0862427
\(87\) 0.115097 0.0123397
\(88\) −3.26506 −0.348057
\(89\) −2.89929 −0.307324 −0.153662 0.988123i \(-0.549107\pi\)
−0.153662 + 0.988123i \(0.549107\pi\)
\(90\) −7.11509 −0.749996
\(91\) 0 0
\(92\) 11.3689 1.18529
\(93\) 9.32229 0.966677
\(94\) −11.9932 −1.23701
\(95\) −12.9761 −1.33132
\(96\) 9.43162 0.962610
\(97\) −3.31003 −0.336083 −0.168041 0.985780i \(-0.553744\pi\)
−0.168041 + 0.985780i \(0.553744\pi\)
\(98\) −43.8721 −4.43175
\(99\) 1.00425 0.100931
\(100\) 14.5987 1.45987
\(101\) −11.7377 −1.16794 −0.583970 0.811775i \(-0.698501\pi\)
−0.583970 + 0.811775i \(0.698501\pi\)
\(102\) −23.1670 −2.29388
\(103\) 3.28198 0.323383 0.161692 0.986841i \(-0.448305\pi\)
0.161692 + 0.986841i \(0.448305\pi\)
\(104\) 0 0
\(105\) −31.0196 −3.02720
\(106\) −12.2526 −1.19007
\(107\) −2.65096 −0.256278 −0.128139 0.991756i \(-0.540900\pi\)
−0.128139 + 0.991756i \(0.540900\pi\)
\(108\) −13.5962 −1.30830
\(109\) 3.20728 0.307202 0.153601 0.988133i \(-0.450913\pi\)
0.153601 + 0.988133i \(0.450913\pi\)
\(110\) −7.08500 −0.675528
\(111\) −2.06327 −0.195837
\(112\) −3.97509 −0.375611
\(113\) −2.96858 −0.279260 −0.139630 0.990204i \(-0.544591\pi\)
−0.139630 + 0.990204i \(0.544591\pi\)
\(114\) 19.8070 1.85509
\(115\) 10.1773 0.949035
\(116\) 0.195819 0.0181813
\(117\) 0 0
\(118\) 10.1241 0.932000
\(119\) −25.3306 −2.32205
\(120\) −19.9120 −1.81771
\(121\) 1.00000 0.0909091
\(122\) −31.8833 −2.88658
\(123\) 24.7908 2.23531
\(124\) 15.8603 1.42430
\(125\) −2.16965 −0.194059
\(126\) 11.8749 1.05790
\(127\) −11.9699 −1.06216 −0.531080 0.847321i \(-0.678214\pi\)
−0.531080 + 0.847321i \(0.678214\pi\)
\(128\) 19.6800 1.73948
\(129\) 0.688423 0.0606122
\(130\) 0 0
\(131\) 6.94560 0.606840 0.303420 0.952857i \(-0.401871\pi\)
0.303420 + 0.952857i \(0.401871\pi\)
\(132\) 6.81257 0.592958
\(133\) 21.6568 1.87788
\(134\) 0.451513 0.0390048
\(135\) −12.1711 −1.04752
\(136\) −16.2602 −1.39430
\(137\) 3.71854 0.317697 0.158848 0.987303i \(-0.449222\pi\)
0.158848 + 0.987303i \(0.449222\pi\)
\(138\) −15.5348 −1.32241
\(139\) −7.03252 −0.596491 −0.298245 0.954489i \(-0.596401\pi\)
−0.298245 + 0.954489i \(0.596401\pi\)
\(140\) −52.7747 −4.46028
\(141\) 10.3233 0.869381
\(142\) −30.5752 −2.56582
\(143\) 0 0
\(144\) 0.784828 0.0654024
\(145\) 0.175294 0.0145574
\(146\) −22.5917 −1.86970
\(147\) 37.7634 3.11468
\(148\) −3.51032 −0.288546
\(149\) 13.3703 1.09533 0.547667 0.836696i \(-0.315516\pi\)
0.547667 + 0.836696i \(0.315516\pi\)
\(150\) −19.9481 −1.62875
\(151\) 11.3479 0.923483 0.461741 0.887015i \(-0.347225\pi\)
0.461741 + 0.887015i \(0.347225\pi\)
\(152\) 13.9018 1.12759
\(153\) 5.00119 0.404323
\(154\) 11.8247 0.952860
\(155\) 14.1979 1.14041
\(156\) 0 0
\(157\) −21.2941 −1.69946 −0.849729 0.527220i \(-0.823234\pi\)
−0.849729 + 0.527220i \(0.823234\pi\)
\(158\) 7.48909 0.595800
\(159\) 10.5465 0.836396
\(160\) 14.3644 1.13561
\(161\) −16.9856 −1.33865
\(162\) 25.5821 2.00992
\(163\) −10.7358 −0.840890 −0.420445 0.907318i \(-0.638126\pi\)
−0.420445 + 0.907318i \(0.638126\pi\)
\(164\) 42.1774 3.29351
\(165\) 6.09851 0.474768
\(166\) −17.5322 −1.36076
\(167\) −15.1963 −1.17592 −0.587961 0.808889i \(-0.700069\pi\)
−0.587961 + 0.808889i \(0.700069\pi\)
\(168\) 33.2326 2.56395
\(169\) 0 0
\(170\) −35.2836 −2.70613
\(171\) −4.27584 −0.326981
\(172\) 1.17124 0.0893061
\(173\) 1.28222 0.0974855 0.0487428 0.998811i \(-0.484479\pi\)
0.0487428 + 0.998811i \(0.484479\pi\)
\(174\) −0.267572 −0.0202846
\(175\) −21.8110 −1.64876
\(176\) 0.781510 0.0589085
\(177\) −8.71446 −0.655019
\(178\) 6.74014 0.505195
\(179\) −10.0223 −0.749099 −0.374549 0.927207i \(-0.622203\pi\)
−0.374549 + 0.927207i \(0.622203\pi\)
\(180\) 10.4197 0.776636
\(181\) 21.9616 1.63239 0.816197 0.577774i \(-0.196079\pi\)
0.816197 + 0.577774i \(0.196079\pi\)
\(182\) 0 0
\(183\) 27.4440 2.02872
\(184\) −10.9033 −0.803805
\(185\) −3.14238 −0.231033
\(186\) −21.6720 −1.58907
\(187\) 4.98005 0.364177
\(188\) 17.5634 1.28095
\(189\) 20.3133 1.47757
\(190\) 30.1662 2.18849
\(191\) −0.205772 −0.0148892 −0.00744458 0.999972i \(-0.502370\pi\)
−0.00744458 + 0.999972i \(0.502370\pi\)
\(192\) −25.0539 −1.80811
\(193\) 4.47205 0.321905 0.160952 0.986962i \(-0.448543\pi\)
0.160952 + 0.986962i \(0.448543\pi\)
\(194\) 7.69500 0.552469
\(195\) 0 0
\(196\) 64.2483 4.58916
\(197\) −9.65570 −0.687940 −0.343970 0.938981i \(-0.611772\pi\)
−0.343970 + 0.938981i \(0.611772\pi\)
\(198\) −2.33463 −0.165915
\(199\) 0.490365 0.0347610 0.0173805 0.999849i \(-0.494467\pi\)
0.0173805 + 0.999849i \(0.494467\pi\)
\(200\) −14.0009 −0.990011
\(201\) −0.388646 −0.0274129
\(202\) 27.2871 1.91992
\(203\) −0.292561 −0.0205337
\(204\) 33.9269 2.37536
\(205\) 37.7566 2.63704
\(206\) −7.62979 −0.531593
\(207\) 3.35358 0.233090
\(208\) 0 0
\(209\) −4.25776 −0.294515
\(210\) 72.1129 4.97626
\(211\) 24.7914 1.70671 0.853356 0.521329i \(-0.174564\pi\)
0.853356 + 0.521329i \(0.174564\pi\)
\(212\) 17.9432 1.23235
\(213\) 26.3180 1.80328
\(214\) 6.16282 0.421282
\(215\) 1.04847 0.0715054
\(216\) 13.0394 0.887221
\(217\) −23.6960 −1.60859
\(218\) −7.45613 −0.504993
\(219\) 19.4461 1.31404
\(220\) 10.3756 0.699523
\(221\) 0 0
\(222\) 4.79660 0.321926
\(223\) −20.9129 −1.40043 −0.700215 0.713932i \(-0.746913\pi\)
−0.700215 + 0.713932i \(0.746913\pi\)
\(224\) −23.9739 −1.60182
\(225\) 4.30630 0.287087
\(226\) 6.90121 0.459062
\(227\) 9.40504 0.624235 0.312117 0.950044i \(-0.398962\pi\)
0.312117 + 0.950044i \(0.398962\pi\)
\(228\) −29.0063 −1.92099
\(229\) 3.22675 0.213229 0.106615 0.994300i \(-0.465999\pi\)
0.106615 + 0.994300i \(0.465999\pi\)
\(230\) −23.6596 −1.56007
\(231\) −10.1782 −0.669679
\(232\) −0.187800 −0.0123297
\(233\) −25.5696 −1.67512 −0.837562 0.546343i \(-0.816020\pi\)
−0.837562 + 0.546343i \(0.816020\pi\)
\(234\) 0 0
\(235\) 15.7225 1.02562
\(236\) −14.8262 −0.965105
\(237\) −6.44633 −0.418734
\(238\) 58.8874 3.81711
\(239\) −18.0533 −1.16777 −0.583885 0.811836i \(-0.698468\pi\)
−0.583885 + 0.811836i \(0.698468\pi\)
\(240\) 4.76604 0.307647
\(241\) −4.45917 −0.287240 −0.143620 0.989633i \(-0.545874\pi\)
−0.143620 + 0.989633i \(0.545874\pi\)
\(242\) −2.32475 −0.149441
\(243\) −10.0393 −0.644019
\(244\) 46.6914 2.98911
\(245\) 57.5141 3.67444
\(246\) −57.6325 −3.67451
\(247\) 0 0
\(248\) −15.2109 −0.965890
\(249\) 15.0910 0.956356
\(250\) 5.04389 0.319004
\(251\) 2.24448 0.141670 0.0708351 0.997488i \(-0.477434\pi\)
0.0708351 + 0.997488i \(0.477434\pi\)
\(252\) −17.3901 −1.09548
\(253\) 3.33940 0.209946
\(254\) 27.8272 1.74603
\(255\) 30.3708 1.90190
\(256\) −20.7105 −1.29441
\(257\) 1.79575 0.112016 0.0560081 0.998430i \(-0.482163\pi\)
0.0560081 + 0.998430i \(0.482163\pi\)
\(258\) −1.60041 −0.0996374
\(259\) 5.24455 0.325881
\(260\) 0 0
\(261\) 0.0577622 0.00357539
\(262\) −16.1468 −0.997553
\(263\) 26.8199 1.65378 0.826892 0.562361i \(-0.190107\pi\)
0.826892 + 0.562361i \(0.190107\pi\)
\(264\) −6.53359 −0.402115
\(265\) 16.0625 0.986711
\(266\) −50.3466 −3.08695
\(267\) −5.80166 −0.355056
\(268\) −0.661217 −0.0403902
\(269\) 14.9673 0.912572 0.456286 0.889833i \(-0.349179\pi\)
0.456286 + 0.889833i \(0.349179\pi\)
\(270\) 28.2948 1.72197
\(271\) 4.90091 0.297709 0.148855 0.988859i \(-0.452441\pi\)
0.148855 + 0.988859i \(0.452441\pi\)
\(272\) 3.89195 0.235984
\(273\) 0 0
\(274\) −8.64470 −0.522245
\(275\) 4.28809 0.258581
\(276\) 22.7499 1.36938
\(277\) −8.61514 −0.517634 −0.258817 0.965926i \(-0.583333\pi\)
−0.258817 + 0.965926i \(0.583333\pi\)
\(278\) 16.3489 0.980540
\(279\) 4.67846 0.280092
\(280\) 50.6136 3.02474
\(281\) 7.50695 0.447827 0.223913 0.974609i \(-0.428117\pi\)
0.223913 + 0.974609i \(0.428117\pi\)
\(282\) −23.9992 −1.42913
\(283\) −22.5526 −1.34061 −0.670306 0.742084i \(-0.733837\pi\)
−0.670306 + 0.742084i \(0.733837\pi\)
\(284\) 44.7758 2.65696
\(285\) −25.9660 −1.53809
\(286\) 0 0
\(287\) −63.0148 −3.71964
\(288\) 4.73332 0.278914
\(289\) 7.80085 0.458874
\(290\) −0.407515 −0.0239301
\(291\) −6.62357 −0.388281
\(292\) 33.0843 1.93611
\(293\) −21.9190 −1.28052 −0.640262 0.768156i \(-0.721174\pi\)
−0.640262 + 0.768156i \(0.721174\pi\)
\(294\) −87.7907 −5.12006
\(295\) −13.2722 −0.772738
\(296\) 3.36657 0.195678
\(297\) −3.99363 −0.231734
\(298\) −31.0826 −1.80056
\(299\) 0 0
\(300\) 29.2129 1.68661
\(301\) −1.74988 −0.100861
\(302\) −26.3812 −1.51807
\(303\) −23.4878 −1.34934
\(304\) −3.32748 −0.190844
\(305\) 41.7975 2.39332
\(306\) −11.6265 −0.664645
\(307\) −22.2819 −1.27169 −0.635846 0.771816i \(-0.719349\pi\)
−0.635846 + 0.771816i \(0.719349\pi\)
\(308\) −17.3166 −0.986706
\(309\) 6.56744 0.373609
\(310\) −33.0067 −1.87466
\(311\) −10.5412 −0.597735 −0.298867 0.954295i \(-0.596609\pi\)
−0.298867 + 0.954295i \(0.596609\pi\)
\(312\) 0 0
\(313\) 24.1202 1.36335 0.681676 0.731654i \(-0.261251\pi\)
0.681676 + 0.731654i \(0.261251\pi\)
\(314\) 49.5036 2.79365
\(315\) −15.5674 −0.877123
\(316\) −10.9674 −0.616963
\(317\) 5.12796 0.288015 0.144007 0.989577i \(-0.454001\pi\)
0.144007 + 0.989577i \(0.454001\pi\)
\(318\) −24.5181 −1.37491
\(319\) 0.0575180 0.00322039
\(320\) −38.1573 −2.13306
\(321\) −5.30473 −0.296081
\(322\) 39.4873 2.20054
\(323\) −21.2038 −1.17981
\(324\) −37.4636 −2.08131
\(325\) 0 0
\(326\) 24.9580 1.38230
\(327\) 6.41796 0.354914
\(328\) −40.4503 −2.23349
\(329\) −26.2405 −1.44668
\(330\) −14.1775 −0.780447
\(331\) −16.2969 −0.895759 −0.447879 0.894094i \(-0.647821\pi\)
−0.447879 + 0.894094i \(0.647821\pi\)
\(332\) 25.6749 1.40909
\(333\) −1.03547 −0.0567432
\(334\) 35.3276 1.93304
\(335\) −0.591911 −0.0323396
\(336\) −7.95440 −0.433948
\(337\) −12.0708 −0.657541 −0.328770 0.944410i \(-0.606634\pi\)
−0.328770 + 0.944410i \(0.606634\pi\)
\(338\) 0 0
\(339\) −5.94031 −0.322633
\(340\) 51.6710 2.80225
\(341\) 4.65867 0.252281
\(342\) 9.94027 0.537508
\(343\) −60.3845 −3.26046
\(344\) −1.12328 −0.0605630
\(345\) 20.3653 1.09643
\(346\) −2.98085 −0.160251
\(347\) 15.4440 0.829079 0.414540 0.910031i \(-0.363943\pi\)
0.414540 + 0.910031i \(0.363943\pi\)
\(348\) 0.391845 0.0210051
\(349\) 16.3111 0.873116 0.436558 0.899676i \(-0.356197\pi\)
0.436558 + 0.899676i \(0.356197\pi\)
\(350\) 50.7053 2.71031
\(351\) 0 0
\(352\) 4.71331 0.251220
\(353\) −13.3191 −0.708905 −0.354453 0.935074i \(-0.615333\pi\)
−0.354453 + 0.935074i \(0.615333\pi\)
\(354\) 20.2590 1.07675
\(355\) 40.0826 2.12737
\(356\) −9.87058 −0.523140
\(357\) −50.6881 −2.68270
\(358\) 23.2993 1.23141
\(359\) 7.76716 0.409935 0.204967 0.978769i \(-0.434291\pi\)
0.204967 + 0.978769i \(0.434291\pi\)
\(360\) −9.99298 −0.526676
\(361\) −0.871506 −0.0458688
\(362\) −51.0553 −2.68341
\(363\) 2.00106 0.105028
\(364\) 0 0
\(365\) 29.6165 1.55020
\(366\) −63.8005 −3.33490
\(367\) 33.5692 1.75230 0.876149 0.482040i \(-0.160104\pi\)
0.876149 + 0.482040i \(0.160104\pi\)
\(368\) 2.60977 0.136044
\(369\) 12.4414 0.647675
\(370\) 7.30526 0.379783
\(371\) −26.8079 −1.39180
\(372\) 31.7375 1.64551
\(373\) 15.6957 0.812693 0.406346 0.913719i \(-0.366803\pi\)
0.406346 + 0.913719i \(0.366803\pi\)
\(374\) −11.5774 −0.598652
\(375\) −4.34160 −0.224199
\(376\) −16.8442 −0.868674
\(377\) 0 0
\(378\) −47.2233 −2.42891
\(379\) −9.90362 −0.508715 −0.254357 0.967110i \(-0.581864\pi\)
−0.254357 + 0.967110i \(0.581864\pi\)
\(380\) −44.1768 −2.26622
\(381\) −23.9526 −1.22713
\(382\) 0.478370 0.0244755
\(383\) 35.1438 1.79577 0.897883 0.440233i \(-0.145104\pi\)
0.897883 + 0.440233i \(0.145104\pi\)
\(384\) 39.3808 2.00965
\(385\) −15.5016 −0.790033
\(386\) −10.3964 −0.529163
\(387\) 0.345490 0.0175622
\(388\) −11.2689 −0.572093
\(389\) 24.8371 1.25929 0.629645 0.776883i \(-0.283200\pi\)
0.629645 + 0.776883i \(0.283200\pi\)
\(390\) 0 0
\(391\) 16.6304 0.841033
\(392\) −61.6173 −3.11214
\(393\) 13.8986 0.701091
\(394\) 22.4471 1.13087
\(395\) −9.81783 −0.493989
\(396\) 3.41893 0.171808
\(397\) 18.4965 0.928313 0.464157 0.885753i \(-0.346357\pi\)
0.464157 + 0.885753i \(0.346357\pi\)
\(398\) −1.13998 −0.0571419
\(399\) 43.3365 2.16954
\(400\) 3.35118 0.167559
\(401\) −5.62259 −0.280779 −0.140389 0.990096i \(-0.544835\pi\)
−0.140389 + 0.990096i \(0.544835\pi\)
\(402\) 0.903505 0.0450627
\(403\) 0 0
\(404\) −39.9606 −1.98811
\(405\) −33.5369 −1.66646
\(406\) 0.680132 0.0337544
\(407\) −1.03109 −0.0511091
\(408\) −32.5376 −1.61085
\(409\) 6.49631 0.321222 0.160611 0.987018i \(-0.448654\pi\)
0.160611 + 0.987018i \(0.448654\pi\)
\(410\) −87.7748 −4.33489
\(411\) 7.44104 0.367039
\(412\) 11.1734 0.550475
\(413\) 22.1510 1.08998
\(414\) −7.79624 −0.383164
\(415\) 22.9838 1.12823
\(416\) 0 0
\(417\) −14.0725 −0.689133
\(418\) 9.89823 0.484138
\(419\) −36.1997 −1.76847 −0.884237 0.467039i \(-0.845321\pi\)
−0.884237 + 0.467039i \(0.845321\pi\)
\(420\) −105.605 −5.15302
\(421\) −10.6708 −0.520061 −0.260030 0.965600i \(-0.583733\pi\)
−0.260030 + 0.965600i \(0.583733\pi\)
\(422\) −57.6339 −2.80558
\(423\) 5.18083 0.251901
\(424\) −17.2084 −0.835715
\(425\) 21.3549 1.03586
\(426\) −61.1829 −2.96432
\(427\) −69.7588 −3.37587
\(428\) −9.02512 −0.436246
\(429\) 0 0
\(430\) −2.43745 −0.117544
\(431\) 0.747781 0.0360193 0.0180097 0.999838i \(-0.494267\pi\)
0.0180097 + 0.999838i \(0.494267\pi\)
\(432\) −3.12106 −0.150162
\(433\) −9.08995 −0.436835 −0.218417 0.975855i \(-0.570089\pi\)
−0.218417 + 0.975855i \(0.570089\pi\)
\(434\) 55.0873 2.64428
\(435\) 0.350774 0.0168183
\(436\) 10.9191 0.522931
\(437\) −14.2183 −0.680156
\(438\) −45.2073 −2.16009
\(439\) 32.2269 1.53810 0.769052 0.639186i \(-0.220729\pi\)
0.769052 + 0.639186i \(0.220729\pi\)
\(440\) −9.95072 −0.474382
\(441\) 18.9518 0.902469
\(442\) 0 0
\(443\) −7.16298 −0.340323 −0.170162 0.985416i \(-0.554429\pi\)
−0.170162 + 0.985416i \(0.554429\pi\)
\(444\) −7.02436 −0.333361
\(445\) −8.83599 −0.418866
\(446\) 48.6173 2.30210
\(447\) 26.7547 1.26545
\(448\) 63.6835 3.00876
\(449\) 14.0670 0.663864 0.331932 0.943303i \(-0.392300\pi\)
0.331932 + 0.943303i \(0.392300\pi\)
\(450\) −10.0111 −0.471927
\(451\) 12.3888 0.583367
\(452\) −10.1065 −0.475368
\(453\) 22.7079 1.06691
\(454\) −21.8644 −1.02615
\(455\) 0 0
\(456\) 27.8184 1.30272
\(457\) −1.76158 −0.0824032 −0.0412016 0.999151i \(-0.513119\pi\)
−0.0412016 + 0.999151i \(0.513119\pi\)
\(458\) −7.50139 −0.350517
\(459\) −19.8884 −0.928313
\(460\) 34.6483 1.61548
\(461\) 35.0354 1.63176 0.815880 0.578221i \(-0.196253\pi\)
0.815880 + 0.578221i \(0.196253\pi\)
\(462\) 23.6619 1.10085
\(463\) −18.0450 −0.838622 −0.419311 0.907843i \(-0.637728\pi\)
−0.419311 + 0.907843i \(0.637728\pi\)
\(464\) 0.0449509 0.00208679
\(465\) 28.4110 1.31753
\(466\) 59.4431 2.75365
\(467\) 10.2052 0.472242 0.236121 0.971724i \(-0.424124\pi\)
0.236121 + 0.971724i \(0.424124\pi\)
\(468\) 0 0
\(469\) 0.987884 0.0456162
\(470\) −36.5510 −1.68597
\(471\) −42.6109 −1.96341
\(472\) 14.2191 0.654486
\(473\) 0.344029 0.0158185
\(474\) 14.9861 0.688336
\(475\) −18.2576 −0.837718
\(476\) −86.2375 −3.95269
\(477\) 5.29286 0.242343
\(478\) 41.9694 1.91964
\(479\) −39.0076 −1.78230 −0.891151 0.453706i \(-0.850102\pi\)
−0.891151 + 0.453706i \(0.850102\pi\)
\(480\) 28.7441 1.31198
\(481\) 0 0
\(482\) 10.3665 0.472179
\(483\) −33.9892 −1.54656
\(484\) 3.40448 0.154749
\(485\) −10.0878 −0.458062
\(486\) 23.3388 1.05867
\(487\) −31.7323 −1.43793 −0.718963 0.695048i \(-0.755383\pi\)
−0.718963 + 0.695048i \(0.755383\pi\)
\(488\) −44.7794 −2.02707
\(489\) −21.4829 −0.971492
\(490\) −133.706 −6.04022
\(491\) 19.6523 0.886898 0.443449 0.896300i \(-0.353755\pi\)
0.443449 + 0.896300i \(0.353755\pi\)
\(492\) 84.3997 3.80503
\(493\) 0.286442 0.0129007
\(494\) 0 0
\(495\) 3.06058 0.137563
\(496\) 3.64080 0.163477
\(497\) −66.8968 −3.00073
\(498\) −35.0829 −1.57210
\(499\) 30.1913 1.35155 0.675774 0.737109i \(-0.263809\pi\)
0.675774 + 0.737109i \(0.263809\pi\)
\(500\) −7.38651 −0.330335
\(501\) −30.4087 −1.35856
\(502\) −5.21786 −0.232884
\(503\) −32.6853 −1.45737 −0.728683 0.684851i \(-0.759867\pi\)
−0.728683 + 0.684851i \(0.759867\pi\)
\(504\) 16.6780 0.742898
\(505\) −35.7721 −1.59184
\(506\) −7.76328 −0.345120
\(507\) 0 0
\(508\) −40.7514 −1.80805
\(509\) 27.5311 1.22029 0.610147 0.792288i \(-0.291111\pi\)
0.610147 + 0.792288i \(0.291111\pi\)
\(510\) −70.6047 −3.12643
\(511\) −49.4292 −2.18662
\(512\) 8.78685 0.388328
\(513\) 17.0039 0.750740
\(514\) −4.17469 −0.184138
\(515\) 10.0023 0.440753
\(516\) 2.34372 0.103176
\(517\) 5.15893 0.226889
\(518\) −12.1923 −0.535698
\(519\) 2.56580 0.112626
\(520\) 0 0
\(521\) 16.0836 0.704634 0.352317 0.935881i \(-0.385394\pi\)
0.352317 + 0.935881i \(0.385394\pi\)
\(522\) −0.134283 −0.00587740
\(523\) −2.15081 −0.0940485 −0.0470243 0.998894i \(-0.514974\pi\)
−0.0470243 + 0.998894i \(0.514974\pi\)
\(524\) 23.6461 1.03299
\(525\) −43.6452 −1.90483
\(526\) −62.3496 −2.71857
\(527\) 23.2004 1.01063
\(528\) 1.56385 0.0680578
\(529\) −11.8484 −0.515149
\(530\) −37.3413 −1.62200
\(531\) −4.37341 −0.189790
\(532\) 73.7299 3.19660
\(533\) 0 0
\(534\) 13.4874 0.583658
\(535\) −8.07915 −0.349292
\(536\) 0.634139 0.0273907
\(537\) −20.0552 −0.865444
\(538\) −34.7952 −1.50013
\(539\) 18.8717 0.812862
\(540\) −41.4363 −1.78313
\(541\) −14.8583 −0.638808 −0.319404 0.947619i \(-0.603483\pi\)
−0.319404 + 0.947619i \(0.603483\pi\)
\(542\) −11.3934 −0.489389
\(543\) 43.9465 1.88593
\(544\) 23.4725 1.00637
\(545\) 9.77462 0.418699
\(546\) 0 0
\(547\) −27.1548 −1.16105 −0.580527 0.814241i \(-0.697153\pi\)
−0.580527 + 0.814241i \(0.697153\pi\)
\(548\) 12.6597 0.540796
\(549\) 13.7730 0.587815
\(550\) −9.96875 −0.425069
\(551\) −0.244898 −0.0104330
\(552\) −21.8183 −0.928647
\(553\) 16.3857 0.696791
\(554\) 20.0281 0.850911
\(555\) −6.28810 −0.266915
\(556\) −23.9421 −1.01537
\(557\) −1.56382 −0.0662613 −0.0331307 0.999451i \(-0.510548\pi\)
−0.0331307 + 0.999451i \(0.510548\pi\)
\(558\) −10.8763 −0.460429
\(559\) 0 0
\(560\) −12.1146 −0.511936
\(561\) 9.96538 0.420739
\(562\) −17.4518 −0.736160
\(563\) 22.1420 0.933172 0.466586 0.884476i \(-0.345484\pi\)
0.466586 + 0.884476i \(0.345484\pi\)
\(564\) 35.1455 1.47989
\(565\) −9.04715 −0.380616
\(566\) 52.4292 2.20376
\(567\) 55.9722 2.35061
\(568\) −42.9422 −1.80182
\(569\) −19.4029 −0.813412 −0.406706 0.913559i \(-0.633323\pi\)
−0.406706 + 0.913559i \(0.633323\pi\)
\(570\) 60.3645 2.52839
\(571\) 6.21755 0.260196 0.130098 0.991501i \(-0.458471\pi\)
0.130098 + 0.991501i \(0.458471\pi\)
\(572\) 0 0
\(573\) −0.411763 −0.0172017
\(574\) 146.494 6.11453
\(575\) 14.3196 0.597170
\(576\) −12.5735 −0.523894
\(577\) −38.5071 −1.60307 −0.801535 0.597948i \(-0.795983\pi\)
−0.801535 + 0.597948i \(0.795983\pi\)
\(578\) −18.1351 −0.754319
\(579\) 8.94884 0.371901
\(580\) 0.596784 0.0247801
\(581\) −38.3594 −1.59141
\(582\) 15.3982 0.638275
\(583\) 5.27048 0.218281
\(584\) −31.7295 −1.31297
\(585\) 0 0
\(586\) 50.9564 2.10499
\(587\) −36.5181 −1.50726 −0.753632 0.657297i \(-0.771700\pi\)
−0.753632 + 0.657297i \(0.771700\pi\)
\(588\) 128.565 5.30192
\(589\) −19.8355 −0.817307
\(590\) 30.8546 1.27026
\(591\) −19.3216 −0.794786
\(592\) −0.805805 −0.0331184
\(593\) −39.6301 −1.62741 −0.813707 0.581275i \(-0.802554\pi\)
−0.813707 + 0.581275i \(0.802554\pi\)
\(594\) 9.28419 0.380935
\(595\) −77.1985 −3.16483
\(596\) 45.5187 1.86452
\(597\) 0.981250 0.0401599
\(598\) 0 0
\(599\) −16.3326 −0.667332 −0.333666 0.942691i \(-0.608286\pi\)
−0.333666 + 0.942691i \(0.608286\pi\)
\(600\) −28.0166 −1.14377
\(601\) −20.6168 −0.840975 −0.420488 0.907298i \(-0.638141\pi\)
−0.420488 + 0.907298i \(0.638141\pi\)
\(602\) 4.06803 0.165801
\(603\) −0.195044 −0.00794282
\(604\) 38.6338 1.57199
\(605\) 3.04764 0.123904
\(606\) 54.6032 2.21811
\(607\) 27.2740 1.10702 0.553508 0.832844i \(-0.313289\pi\)
0.553508 + 0.832844i \(0.313289\pi\)
\(608\) −20.0681 −0.813870
\(609\) −0.585432 −0.0237229
\(610\) −97.1688 −3.93425
\(611\) 0 0
\(612\) 17.0264 0.688253
\(613\) 22.7881 0.920401 0.460201 0.887815i \(-0.347777\pi\)
0.460201 + 0.887815i \(0.347777\pi\)
\(614\) 51.7998 2.09047
\(615\) 75.5533 3.04660
\(616\) 16.6075 0.669135
\(617\) −1.28652 −0.0517933 −0.0258967 0.999665i \(-0.508244\pi\)
−0.0258967 + 0.999665i \(0.508244\pi\)
\(618\) −15.2677 −0.614156
\(619\) −16.7525 −0.673339 −0.336669 0.941623i \(-0.609300\pi\)
−0.336669 + 0.941623i \(0.609300\pi\)
\(620\) 48.3366 1.94124
\(621\) −13.3363 −0.535167
\(622\) 24.5056 0.982585
\(623\) 14.7470 0.590827
\(624\) 0 0
\(625\) −28.0527 −1.12211
\(626\) −56.0734 −2.24114
\(627\) −8.52003 −0.340257
\(628\) −72.4954 −2.89288
\(629\) −5.13487 −0.204741
\(630\) 36.1904 1.44186
\(631\) 39.1631 1.55906 0.779529 0.626366i \(-0.215458\pi\)
0.779529 + 0.626366i \(0.215458\pi\)
\(632\) 10.5183 0.418394
\(633\) 49.6091 1.97179
\(634\) −11.9212 −0.473453
\(635\) −36.4800 −1.44767
\(636\) 35.9055 1.42374
\(637\) 0 0
\(638\) −0.133715 −0.00529383
\(639\) 13.2079 0.522496
\(640\) 59.9774 2.37082
\(641\) 6.31152 0.249290 0.124645 0.992201i \(-0.460221\pi\)
0.124645 + 0.992201i \(0.460221\pi\)
\(642\) 12.3322 0.486712
\(643\) 5.47875 0.216061 0.108030 0.994148i \(-0.465546\pi\)
0.108030 + 0.994148i \(0.465546\pi\)
\(644\) −57.8271 −2.27871
\(645\) 2.09806 0.0826111
\(646\) 49.2937 1.93943
\(647\) 7.22980 0.284233 0.142116 0.989850i \(-0.454609\pi\)
0.142116 + 0.989850i \(0.454609\pi\)
\(648\) 35.9295 1.41144
\(649\) −4.35492 −0.170946
\(650\) 0 0
\(651\) −47.4171 −1.85842
\(652\) −36.5497 −1.43140
\(653\) 13.2893 0.520050 0.260025 0.965602i \(-0.416269\pi\)
0.260025 + 0.965602i \(0.416269\pi\)
\(654\) −14.9202 −0.583425
\(655\) 21.1677 0.827090
\(656\) 9.68198 0.378018
\(657\) 9.75914 0.380740
\(658\) 61.0026 2.37813
\(659\) −4.15593 −0.161892 −0.0809461 0.996718i \(-0.525794\pi\)
−0.0809461 + 0.996718i \(0.525794\pi\)
\(660\) 20.7622 0.808169
\(661\) −35.1591 −1.36753 −0.683765 0.729702i \(-0.739659\pi\)
−0.683765 + 0.729702i \(0.739659\pi\)
\(662\) 37.8863 1.47249
\(663\) 0 0
\(664\) −24.6235 −0.955578
\(665\) 66.0019 2.55944
\(666\) 2.40720 0.0932773
\(667\) 0.192075 0.00743719
\(668\) −51.7354 −2.00170
\(669\) −41.8480 −1.61794
\(670\) 1.37605 0.0531613
\(671\) 13.7147 0.529451
\(672\) −47.9732 −1.85061
\(673\) 5.17495 0.199479 0.0997397 0.995014i \(-0.468199\pi\)
0.0997397 + 0.995014i \(0.468199\pi\)
\(674\) 28.0617 1.08090
\(675\) −17.1250 −0.659142
\(676\) 0 0
\(677\) 8.11284 0.311802 0.155901 0.987773i \(-0.450172\pi\)
0.155901 + 0.987773i \(0.450172\pi\)
\(678\) 13.8098 0.530360
\(679\) 16.8362 0.646115
\(680\) −49.5551 −1.90035
\(681\) 18.8201 0.721187
\(682\) −10.8303 −0.414712
\(683\) −18.6591 −0.713969 −0.356985 0.934110i \(-0.616195\pi\)
−0.356985 + 0.934110i \(0.616195\pi\)
\(684\) −14.5570 −0.556600
\(685\) 11.3328 0.433003
\(686\) 140.379 5.35970
\(687\) 6.45692 0.246347
\(688\) 0.268862 0.0102503
\(689\) 0 0
\(690\) −47.3444 −1.80237
\(691\) 29.5207 1.12302 0.561510 0.827470i \(-0.310221\pi\)
0.561510 + 0.827470i \(0.310221\pi\)
\(692\) 4.36529 0.165944
\(693\) −5.10802 −0.194038
\(694\) −35.9036 −1.36288
\(695\) −21.4326 −0.812983
\(696\) −0.375799 −0.0142446
\(697\) 61.6969 2.33694
\(698\) −37.9194 −1.43527
\(699\) −51.1664 −1.93529
\(700\) −74.2552 −2.80658
\(701\) 32.4406 1.22526 0.612632 0.790368i \(-0.290111\pi\)
0.612632 + 0.790368i \(0.290111\pi\)
\(702\) 0 0
\(703\) 4.39012 0.165577
\(704\) −12.5203 −0.471876
\(705\) 31.4617 1.18492
\(706\) 30.9637 1.16533
\(707\) 59.7027 2.24535
\(708\) −29.6682 −1.11500
\(709\) −47.2300 −1.77376 −0.886880 0.462000i \(-0.847132\pi\)
−0.886880 + 0.462000i \(0.847132\pi\)
\(710\) −93.1822 −3.49707
\(711\) −3.23514 −0.121327
\(712\) 9.46637 0.354767
\(713\) 15.5572 0.582620
\(714\) 117.837 4.40995
\(715\) 0 0
\(716\) −34.1206 −1.27515
\(717\) −36.1257 −1.34914
\(718\) −18.0567 −0.673871
\(719\) 39.5065 1.47334 0.736672 0.676250i \(-0.236396\pi\)
0.736672 + 0.676250i \(0.236396\pi\)
\(720\) 2.39187 0.0891398
\(721\) −16.6935 −0.621700
\(722\) 2.02604 0.0754013
\(723\) −8.92307 −0.331852
\(724\) 74.7678 2.77872
\(725\) 0.246642 0.00916006
\(726\) −4.65197 −0.172651
\(727\) −1.94811 −0.0722515 −0.0361258 0.999347i \(-0.511502\pi\)
−0.0361258 + 0.999347i \(0.511502\pi\)
\(728\) 0 0
\(729\) 12.9235 0.478648
\(730\) −68.8511 −2.54830
\(731\) 1.71328 0.0633679
\(732\) 93.4324 3.45336
\(733\) −41.7816 −1.54324 −0.771618 0.636086i \(-0.780552\pi\)
−0.771618 + 0.636086i \(0.780552\pi\)
\(734\) −78.0401 −2.88051
\(735\) 115.089 4.24513
\(736\) 15.7396 0.580170
\(737\) −0.194220 −0.00715417
\(738\) −28.9232 −1.06468
\(739\) 10.6578 0.392054 0.196027 0.980598i \(-0.437196\pi\)
0.196027 + 0.980598i \(0.437196\pi\)
\(740\) −10.6982 −0.393272
\(741\) 0 0
\(742\) 62.3217 2.28790
\(743\) 12.3377 0.452626 0.226313 0.974055i \(-0.427333\pi\)
0.226313 + 0.974055i \(0.427333\pi\)
\(744\) −30.4379 −1.11591
\(745\) 40.7477 1.49288
\(746\) −36.4886 −1.33594
\(747\) 7.57354 0.277101
\(748\) 16.9544 0.619916
\(749\) 13.4839 0.492691
\(750\) 10.0931 0.368549
\(751\) −28.8574 −1.05302 −0.526511 0.850168i \(-0.676500\pi\)
−0.526511 + 0.850168i \(0.676500\pi\)
\(752\) 4.03175 0.147023
\(753\) 4.49134 0.163674
\(754\) 0 0
\(755\) 34.5844 1.25866
\(756\) 69.1561 2.51518
\(757\) 6.38475 0.232058 0.116029 0.993246i \(-0.462983\pi\)
0.116029 + 0.993246i \(0.462983\pi\)
\(758\) 23.0235 0.836250
\(759\) 6.68234 0.242554
\(760\) 42.3678 1.53684
\(761\) 9.99134 0.362186 0.181093 0.983466i \(-0.442037\pi\)
0.181093 + 0.983466i \(0.442037\pi\)
\(762\) 55.6839 2.01721
\(763\) −16.3136 −0.590591
\(764\) −0.700547 −0.0253449
\(765\) 15.2418 0.551069
\(766\) −81.7008 −2.95197
\(767\) 0 0
\(768\) −41.4430 −1.49545
\(769\) 14.2532 0.513982 0.256991 0.966414i \(-0.417269\pi\)
0.256991 + 0.966414i \(0.417269\pi\)
\(770\) 36.0373 1.29869
\(771\) 3.59342 0.129414
\(772\) 15.2250 0.547959
\(773\) −20.1973 −0.726445 −0.363222 0.931702i \(-0.618323\pi\)
−0.363222 + 0.931702i \(0.618323\pi\)
\(774\) −0.803178 −0.0288696
\(775\) 19.9768 0.717588
\(776\) 10.8075 0.387965
\(777\) 10.4947 0.376494
\(778\) −57.7401 −2.07008
\(779\) −52.7486 −1.88991
\(780\) 0 0
\(781\) 13.1520 0.470617
\(782\) −38.6615 −1.38253
\(783\) −0.229705 −0.00820900
\(784\) 14.7484 0.526729
\(785\) −64.8968 −2.31627
\(786\) −32.3108 −1.15249
\(787\) −32.9401 −1.17419 −0.587093 0.809519i \(-0.699728\pi\)
−0.587093 + 0.809519i \(0.699728\pi\)
\(788\) −32.8726 −1.17104
\(789\) 53.6682 1.91064
\(790\) 22.8240 0.812043
\(791\) 15.0994 0.536875
\(792\) −3.27893 −0.116512
\(793\) 0 0
\(794\) −42.9998 −1.52601
\(795\) 32.1420 1.13996
\(796\) 1.66943 0.0591716
\(797\) 10.2184 0.361953 0.180977 0.983487i \(-0.442074\pi\)
0.180977 + 0.983487i \(0.442074\pi\)
\(798\) −100.747 −3.56639
\(799\) 25.6917 0.908906
\(800\) 20.2111 0.714570
\(801\) −2.91161 −0.102877
\(802\) 13.0711 0.461558
\(803\) 9.71787 0.342936
\(804\) −1.32313 −0.0466634
\(805\) −51.7659 −1.82451
\(806\) 0 0
\(807\) 29.9505 1.05431
\(808\) 38.3242 1.34824
\(809\) −46.1097 −1.62113 −0.810565 0.585649i \(-0.800840\pi\)
−0.810565 + 0.585649i \(0.800840\pi\)
\(810\) 77.9650 2.73941
\(811\) 25.9692 0.911904 0.455952 0.890004i \(-0.349299\pi\)
0.455952 + 0.890004i \(0.349299\pi\)
\(812\) −0.996017 −0.0349533
\(813\) 9.80702 0.343947
\(814\) 2.39703 0.0840157
\(815\) −32.7187 −1.14609
\(816\) 7.78804 0.272636
\(817\) −1.46479 −0.0512466
\(818\) −15.1023 −0.528040
\(819\) 0 0
\(820\) 128.542 4.48886
\(821\) −37.0459 −1.29291 −0.646455 0.762952i \(-0.723749\pi\)
−0.646455 + 0.762952i \(0.723749\pi\)
\(822\) −17.2986 −0.603357
\(823\) −20.7517 −0.723360 −0.361680 0.932302i \(-0.617797\pi\)
−0.361680 + 0.932302i \(0.617797\pi\)
\(824\) −10.7159 −0.373305
\(825\) 8.58073 0.298743
\(826\) −51.4955 −1.79176
\(827\) 16.7564 0.582675 0.291338 0.956620i \(-0.405900\pi\)
0.291338 + 0.956620i \(0.405900\pi\)
\(828\) 11.4172 0.396774
\(829\) −16.9103 −0.587317 −0.293659 0.955910i \(-0.594873\pi\)
−0.293659 + 0.955910i \(0.594873\pi\)
\(830\) −53.4317 −1.85464
\(831\) −17.2394 −0.598029
\(832\) 0 0
\(833\) 93.9819 3.25628
\(834\) 32.7151 1.13283
\(835\) −46.3127 −1.60272
\(836\) −14.4954 −0.501335
\(837\) −18.6050 −0.643083
\(838\) 84.1555 2.90710
\(839\) −8.60829 −0.297191 −0.148596 0.988898i \(-0.547475\pi\)
−0.148596 + 0.988898i \(0.547475\pi\)
\(840\) 101.281 3.49452
\(841\) −28.9967 −0.999886
\(842\) 24.8069 0.854901
\(843\) 15.0219 0.517380
\(844\) 84.4018 2.90523
\(845\) 0 0
\(846\) −12.0442 −0.414087
\(847\) −5.08642 −0.174772
\(848\) 4.11893 0.141445
\(849\) −45.1291 −1.54883
\(850\) −49.6448 −1.70280
\(851\) −3.44321 −0.118032
\(852\) 89.5992 3.06962
\(853\) −15.7832 −0.540407 −0.270204 0.962803i \(-0.587091\pi\)
−0.270204 + 0.962803i \(0.587091\pi\)
\(854\) 162.172 5.54941
\(855\) −13.0312 −0.445658
\(856\) 8.65554 0.295840
\(857\) 18.2640 0.623887 0.311944 0.950101i \(-0.399020\pi\)
0.311944 + 0.950101i \(0.399020\pi\)
\(858\) 0 0
\(859\) 2.02303 0.0690248 0.0345124 0.999404i \(-0.489012\pi\)
0.0345124 + 0.999404i \(0.489012\pi\)
\(860\) 3.56951 0.121719
\(861\) −126.096 −4.29735
\(862\) −1.73841 −0.0592103
\(863\) 32.2203 1.09679 0.548395 0.836219i \(-0.315239\pi\)
0.548395 + 0.836219i \(0.315239\pi\)
\(864\) −18.8232 −0.640378
\(865\) 3.90775 0.132867
\(866\) 21.1319 0.718091
\(867\) 15.6100 0.530143
\(868\) −80.6724 −2.73820
\(869\) −3.22146 −0.109280
\(870\) −0.815463 −0.0276468
\(871\) 0 0
\(872\) −10.4720 −0.354626
\(873\) −3.32409 −0.112503
\(874\) 33.0541 1.11807
\(875\) 11.0357 0.373076
\(876\) 66.2036 2.23681
\(877\) 24.0953 0.813640 0.406820 0.913508i \(-0.366638\pi\)
0.406820 + 0.913508i \(0.366638\pi\)
\(878\) −74.9195 −2.52841
\(879\) −43.8614 −1.47941
\(880\) 2.38176 0.0802890
\(881\) −37.1187 −1.25056 −0.625280 0.780400i \(-0.715015\pi\)
−0.625280 + 0.780400i \(0.715015\pi\)
\(882\) −44.0584 −1.48352
\(883\) 31.7603 1.06882 0.534409 0.845226i \(-0.320534\pi\)
0.534409 + 0.845226i \(0.320534\pi\)
\(884\) 0 0
\(885\) −26.5585 −0.892754
\(886\) 16.6522 0.559440
\(887\) 22.8376 0.766813 0.383406 0.923580i \(-0.374751\pi\)
0.383406 + 0.923580i \(0.374751\pi\)
\(888\) 6.73671 0.226069
\(889\) 60.8842 2.04199
\(890\) 20.5415 0.688553
\(891\) −11.0042 −0.368656
\(892\) −71.1975 −2.38387
\(893\) −21.9655 −0.735046
\(894\) −62.1981 −2.08022
\(895\) −30.5442 −1.02098
\(896\) −100.101 −3.34413
\(897\) 0 0
\(898\) −32.7023 −1.09129
\(899\) 0.267958 0.00893688
\(900\) 14.6607 0.488690
\(901\) 26.2472 0.874421
\(902\) −28.8009 −0.958966
\(903\) −3.50161 −0.116526
\(904\) 9.69259 0.322371
\(905\) 66.9310 2.22486
\(906\) −52.7903 −1.75384
\(907\) 0.817669 0.0271502 0.0135751 0.999908i \(-0.495679\pi\)
0.0135751 + 0.999908i \(0.495679\pi\)
\(908\) 32.0193 1.06260
\(909\) −11.7875 −0.390967
\(910\) 0 0
\(911\) −27.0495 −0.896191 −0.448095 0.893986i \(-0.647897\pi\)
−0.448095 + 0.893986i \(0.647897\pi\)
\(912\) −6.65849 −0.220485
\(913\) 7.54152 0.249588
\(914\) 4.09524 0.135458
\(915\) 83.6393 2.76503
\(916\) 10.9854 0.362967
\(917\) −35.3283 −1.16664
\(918\) 46.2357 1.52601
\(919\) 1.21525 0.0400874 0.0200437 0.999799i \(-0.493619\pi\)
0.0200437 + 0.999799i \(0.493619\pi\)
\(920\) −33.2294 −1.09554
\(921\) −44.5874 −1.46920
\(922\) −81.4486 −2.68237
\(923\) 0 0
\(924\) −34.6516 −1.13995
\(925\) −4.42140 −0.145375
\(926\) 41.9502 1.37857
\(927\) 3.29592 0.108252
\(928\) 0.271100 0.00889929
\(929\) −6.38753 −0.209568 −0.104784 0.994495i \(-0.533415\pi\)
−0.104784 + 0.994495i \(0.533415\pi\)
\(930\) −66.0485 −2.16581
\(931\) −80.3511 −2.63340
\(932\) −87.0513 −2.85146
\(933\) −21.0935 −0.690571
\(934\) −23.7246 −0.776294
\(935\) 15.1774 0.496353
\(936\) 0 0
\(937\) −2.36713 −0.0773308 −0.0386654 0.999252i \(-0.512311\pi\)
−0.0386654 + 0.999252i \(0.512311\pi\)
\(938\) −2.29659 −0.0749862
\(939\) 48.2659 1.57510
\(940\) 53.5270 1.74586
\(941\) −39.7672 −1.29637 −0.648187 0.761481i \(-0.724472\pi\)
−0.648187 + 0.761481i \(0.724472\pi\)
\(942\) 99.0598 3.22754
\(943\) 41.3712 1.34723
\(944\) −3.40341 −0.110772
\(945\) 61.9075 2.01385
\(946\) −0.799782 −0.0260032
\(947\) 20.3615 0.661659 0.330830 0.943690i \(-0.392671\pi\)
0.330830 + 0.943690i \(0.392671\pi\)
\(948\) −21.9464 −0.712786
\(949\) 0 0
\(950\) 42.4445 1.37708
\(951\) 10.2614 0.332747
\(952\) 82.7060 2.68052
\(953\) −46.3605 −1.50176 −0.750882 0.660437i \(-0.770371\pi\)
−0.750882 + 0.660437i \(0.770371\pi\)
\(954\) −12.3046 −0.398376
\(955\) −0.627119 −0.0202931
\(956\) −61.4620 −1.98782
\(957\) 0.115097 0.00372056
\(958\) 90.6830 2.92984
\(959\) −18.9141 −0.610768
\(960\) −76.3551 −2.46435
\(961\) −9.29676 −0.299896
\(962\) 0 0
\(963\) −2.66221 −0.0857887
\(964\) −15.1811 −0.488951
\(965\) 13.6292 0.438739
\(966\) 79.0165 2.54231
\(967\) −25.9505 −0.834511 −0.417256 0.908789i \(-0.637008\pi\)
−0.417256 + 0.908789i \(0.637008\pi\)
\(968\) −3.26506 −0.104943
\(969\) −42.4301 −1.36305
\(970\) 23.4516 0.752985
\(971\) −33.0430 −1.06040 −0.530200 0.847873i \(-0.677883\pi\)
−0.530200 + 0.847873i \(0.677883\pi\)
\(972\) −34.1784 −1.09627
\(973\) 35.7704 1.14675
\(974\) 73.7697 2.36373
\(975\) 0 0
\(976\) 10.7182 0.343081
\(977\) 49.6432 1.58823 0.794113 0.607770i \(-0.207936\pi\)
0.794113 + 0.607770i \(0.207936\pi\)
\(978\) 49.9425 1.59699
\(979\) −2.89929 −0.0926618
\(980\) 195.805 6.25477
\(981\) 3.22090 0.102835
\(982\) −45.6868 −1.45793
\(983\) 9.33920 0.297874 0.148937 0.988847i \(-0.452415\pi\)
0.148937 + 0.988847i \(0.452415\pi\)
\(984\) −80.9435 −2.58038
\(985\) −29.4271 −0.937624
\(986\) −0.665907 −0.0212068
\(987\) −52.5088 −1.67137
\(988\) 0 0
\(989\) 1.14885 0.0365313
\(990\) −7.11509 −0.226132
\(991\) −0.819686 −0.0260382 −0.0130191 0.999915i \(-0.504144\pi\)
−0.0130191 + 0.999915i \(0.504144\pi\)
\(992\) 21.9578 0.697160
\(993\) −32.6111 −1.03488
\(994\) 155.519 4.93275
\(995\) 1.49445 0.0473773
\(996\) 51.3771 1.62795
\(997\) 42.0034 1.33026 0.665130 0.746728i \(-0.268376\pi\)
0.665130 + 0.746728i \(0.268376\pi\)
\(998\) −70.1873 −2.22174
\(999\) 4.11778 0.130281
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.1.4 yes 21
13.12 even 2 1859.2.a.s.1.18 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.18 21 13.12 even 2
1859.2.a.t.1.4 yes 21 1.1 even 1 trivial