Properties

Label 1859.2.a.g.1.2
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.361.1
Defining polynomial: \( x^{3} - x^{2} - 6x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.50702\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.22188 q^{2} -2.50702 q^{3} -0.507019 q^{4} +2.28514 q^{5} -3.06327 q^{6} +0.285142 q^{7} -3.06327 q^{8} +3.28514 q^{9} +O(q^{10})\) \(q+1.22188 q^{2} -2.50702 q^{3} -0.507019 q^{4} +2.28514 q^{5} -3.06327 q^{6} +0.285142 q^{7} -3.06327 q^{8} +3.28514 q^{9} +2.79216 q^{10} -1.00000 q^{11} +1.27111 q^{12} +0.348409 q^{14} -5.72889 q^{15} -2.72889 q^{16} +0.507019 q^{17} +4.01404 q^{18} +3.95077 q^{19} -1.15861 q^{20} -0.714858 q^{21} -1.22188 q^{22} -0.0632663 q^{23} +7.67967 q^{24} +0.221876 q^{25} -0.714858 q^{27} -0.144573 q^{28} -10.7429 q^{29} -7.00000 q^{30} +3.57028 q^{31} +2.79216 q^{32} +2.50702 q^{33} +0.619514 q^{34} +0.651591 q^{35} -1.66563 q^{36} -7.72889 q^{37} +4.82735 q^{38} -7.00000 q^{40} +0.380486 q^{41} -0.873467 q^{42} -5.41168 q^{43} +0.507019 q^{44} +7.50702 q^{45} -0.0773036 q^{46} +11.3624 q^{47} +6.84139 q^{48} -6.91869 q^{49} +0.271105 q^{50} -1.27111 q^{51} -6.72889 q^{53} -0.873467 q^{54} -2.28514 q^{55} -0.873467 q^{56} -9.90466 q^{57} -13.1265 q^{58} -13.7289 q^{59} +2.90466 q^{60} -3.33437 q^{61} +4.36245 q^{62} +0.936734 q^{63} +8.86946 q^{64} +3.06327 q^{66} -0.207839 q^{67} -0.257068 q^{68} +0.158610 q^{69} +0.796164 q^{70} +2.77812 q^{71} -10.0633 q^{72} +2.00000 q^{73} -9.44375 q^{74} -0.556248 q^{75} -2.00311 q^{76} -0.285142 q^{77} -3.45779 q^{79} -6.23591 q^{80} -8.06327 q^{81} +0.464907 q^{82} -4.74293 q^{83} +0.362446 q^{84} +1.15861 q^{85} -6.61240 q^{86} +26.9327 q^{87} +3.06327 q^{88} +3.71486 q^{89} +9.17265 q^{90} +0.0320772 q^{92} -8.95077 q^{93} +13.8835 q^{94} +9.02807 q^{95} -7.00000 q^{96} -15.0281 q^{97} -8.45379 q^{98} -3.28514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9} - 6 q^{10} - 3 q^{11} + 15 q^{12} - 8 q^{14} - 6 q^{15} + 3 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 4 q^{20} - 8 q^{21} - q^{22} + 3 q^{23} - 2 q^{24} - 2 q^{25} - 8 q^{27} - 18 q^{28} - 4 q^{29} - 21 q^{30} - q^{31} - 6 q^{32} - q^{33} + 4 q^{34} + 11 q^{35} + 3 q^{36} - 12 q^{37} + 31 q^{38} - 21 q^{40} - q^{41} - 9 q^{42} - 4 q^{43} - 7 q^{44} + 14 q^{45} + 20 q^{46} + 8 q^{47} + 20 q^{48} + 12 q^{50} - 15 q^{51} - 9 q^{53} - 9 q^{54} - q^{55} - 9 q^{56} - 26 q^{57} - 33 q^{58} - 30 q^{59} + 5 q^{60} - 18 q^{61} - 13 q^{62} + 6 q^{63} - 8 q^{64} + 6 q^{66} - 15 q^{67} - 29 q^{68} + q^{69} + 29 q^{70} + 11 q^{71} - 27 q^{72} + 6 q^{73} - 23 q^{74} - 7 q^{75} - 30 q^{76} + 5 q^{77} + 12 q^{79} + q^{80} - 21 q^{81} + 44 q^{82} + 14 q^{83} - 25 q^{84} + 4 q^{85} + 43 q^{86} + 43 q^{87} + 6 q^{88} + 17 q^{89} + 11 q^{90} + 7 q^{92} - 13 q^{93} - 10 q^{94} - 7 q^{95} - 21 q^{96} - 11 q^{97} + 38 q^{98} - 4 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22188 0.863997 0.431998 0.901874i \(-0.357809\pi\)
0.431998 + 0.901874i \(0.357809\pi\)
\(3\) −2.50702 −1.44743 −0.723714 0.690100i \(-0.757566\pi\)
−0.723714 + 0.690100i \(0.757566\pi\)
\(4\) −0.507019 −0.253509
\(5\) 2.28514 1.02195 0.510973 0.859597i \(-0.329285\pi\)
0.510973 + 0.859597i \(0.329285\pi\)
\(6\) −3.06327 −1.25057
\(7\) 0.285142 0.107774 0.0538869 0.998547i \(-0.482839\pi\)
0.0538869 + 0.998547i \(0.482839\pi\)
\(8\) −3.06327 −1.08303
\(9\) 3.28514 1.09505
\(10\) 2.79216 0.882959
\(11\) −1.00000 −0.301511
\(12\) 1.27111 0.366936
\(13\) 0 0
\(14\) 0.348409 0.0931162
\(15\) −5.72889 −1.47919
\(16\) −2.72889 −0.682224
\(17\) 0.507019 0.122970 0.0614850 0.998108i \(-0.480416\pi\)
0.0614850 + 0.998108i \(0.480416\pi\)
\(18\) 4.01404 0.946118
\(19\) 3.95077 0.906369 0.453185 0.891417i \(-0.350288\pi\)
0.453185 + 0.891417i \(0.350288\pi\)
\(20\) −1.15861 −0.259073
\(21\) −0.714858 −0.155995
\(22\) −1.22188 −0.260505
\(23\) −0.0632663 −0.0131919 −0.00659597 0.999978i \(-0.502100\pi\)
−0.00659597 + 0.999978i \(0.502100\pi\)
\(24\) 7.67967 1.56761
\(25\) 0.221876 0.0443752
\(26\) 0 0
\(27\) −0.714858 −0.137574
\(28\) −0.144573 −0.0273216
\(29\) −10.7429 −1.99491 −0.997456 0.0712820i \(-0.977291\pi\)
−0.997456 + 0.0712820i \(0.977291\pi\)
\(30\) −7.00000 −1.27802
\(31\) 3.57028 0.641242 0.320621 0.947208i \(-0.396108\pi\)
0.320621 + 0.947208i \(0.396108\pi\)
\(32\) 2.79216 0.493589
\(33\) 2.50702 0.436416
\(34\) 0.619514 0.106246
\(35\) 0.651591 0.110139
\(36\) −1.66563 −0.277605
\(37\) −7.72889 −1.27062 −0.635311 0.772256i \(-0.719128\pi\)
−0.635311 + 0.772256i \(0.719128\pi\)
\(38\) 4.82735 0.783100
\(39\) 0 0
\(40\) −7.00000 −1.10680
\(41\) 0.380486 0.0594219 0.0297110 0.999559i \(-0.490541\pi\)
0.0297110 + 0.999559i \(0.490541\pi\)
\(42\) −0.873467 −0.134779
\(43\) −5.41168 −0.825273 −0.412636 0.910896i \(-0.635392\pi\)
−0.412636 + 0.910896i \(0.635392\pi\)
\(44\) 0.507019 0.0764359
\(45\) 7.50702 1.11908
\(46\) −0.0773036 −0.0113978
\(47\) 11.3624 1.65738 0.828692 0.559706i \(-0.189086\pi\)
0.828692 + 0.559706i \(0.189086\pi\)
\(48\) 6.84139 0.987470
\(49\) −6.91869 −0.988385
\(50\) 0.271105 0.0383401
\(51\) −1.27111 −0.177990
\(52\) 0 0
\(53\) −6.72889 −0.924285 −0.462142 0.886806i \(-0.652919\pi\)
−0.462142 + 0.886806i \(0.652919\pi\)
\(54\) −0.873467 −0.118864
\(55\) −2.28514 −0.308129
\(56\) −0.873467 −0.116722
\(57\) −9.90466 −1.31190
\(58\) −13.1265 −1.72360
\(59\) −13.7289 −1.78735 −0.893675 0.448715i \(-0.851882\pi\)
−0.893675 + 0.448715i \(0.851882\pi\)
\(60\) 2.90466 0.374990
\(61\) −3.33437 −0.426923 −0.213461 0.976952i \(-0.568474\pi\)
−0.213461 + 0.976952i \(0.568474\pi\)
\(62\) 4.36245 0.554031
\(63\) 0.936734 0.118017
\(64\) 8.86946 1.10868
\(65\) 0 0
\(66\) 3.06327 0.377062
\(67\) −0.207839 −0.0253916 −0.0126958 0.999919i \(-0.504041\pi\)
−0.0126958 + 0.999919i \(0.504041\pi\)
\(68\) −0.257068 −0.0311741
\(69\) 0.158610 0.0190944
\(70\) 0.796164 0.0951598
\(71\) 2.77812 0.329703 0.164851 0.986318i \(-0.447286\pi\)
0.164851 + 0.986318i \(0.447286\pi\)
\(72\) −10.0633 −1.18597
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −9.44375 −1.09781
\(75\) −0.556248 −0.0642299
\(76\) −2.00311 −0.229773
\(77\) −0.285142 −0.0324950
\(78\) 0 0
\(79\) −3.45779 −0.389032 −0.194516 0.980899i \(-0.562314\pi\)
−0.194516 + 0.980899i \(0.562314\pi\)
\(80\) −6.23591 −0.697196
\(81\) −8.06327 −0.895918
\(82\) 0.464907 0.0513404
\(83\) −4.74293 −0.520604 −0.260302 0.965527i \(-0.583822\pi\)
−0.260302 + 0.965527i \(0.583822\pi\)
\(84\) 0.362446 0.0395461
\(85\) 1.15861 0.125669
\(86\) −6.61240 −0.713033
\(87\) 26.9327 2.88749
\(88\) 3.06327 0.326545
\(89\) 3.71486 0.393774 0.196887 0.980426i \(-0.436917\pi\)
0.196887 + 0.980426i \(0.436917\pi\)
\(90\) 9.17265 0.966882
\(91\) 0 0
\(92\) 0.0320772 0.00334428
\(93\) −8.95077 −0.928152
\(94\) 13.8835 1.43197
\(95\) 9.02807 0.926261
\(96\) −7.00000 −0.714435
\(97\) −15.0281 −1.52587 −0.762935 0.646475i \(-0.776242\pi\)
−0.762935 + 0.646475i \(0.776242\pi\)
\(98\) −8.45379 −0.853961
\(99\) −3.28514 −0.330169
\(100\) −0.112495 −0.0112495
\(101\) 14.9327 1.48586 0.742931 0.669368i \(-0.233435\pi\)
0.742931 + 0.669368i \(0.233435\pi\)
\(102\) −1.55313 −0.153783
\(103\) −17.3905 −1.71354 −0.856769 0.515700i \(-0.827532\pi\)
−0.856769 + 0.515700i \(0.827532\pi\)
\(104\) 0 0
\(105\) −1.63355 −0.159418
\(106\) −8.22188 −0.798579
\(107\) −15.7429 −1.52193 −0.760963 0.648795i \(-0.775273\pi\)
−0.760963 + 0.648795i \(0.775273\pi\)
\(108\) 0.362446 0.0348764
\(109\) −18.9648 −1.81650 −0.908250 0.418429i \(-0.862581\pi\)
−0.908250 + 0.418429i \(0.862581\pi\)
\(110\) −2.79216 −0.266222
\(111\) 19.3765 1.83913
\(112\) −0.778124 −0.0735258
\(113\) −14.6476 −1.37793 −0.688965 0.724795i \(-0.741934\pi\)
−0.688965 + 0.724795i \(0.741934\pi\)
\(114\) −12.1023 −1.13348
\(115\) −0.144573 −0.0134815
\(116\) 5.44687 0.505729
\(117\) 0 0
\(118\) −16.7750 −1.54426
\(119\) 0.144573 0.0132529
\(120\) 17.5491 1.60201
\(121\) 1.00000 0.0909091
\(122\) −4.07419 −0.368860
\(123\) −0.953886 −0.0860090
\(124\) −1.81020 −0.162561
\(125\) −10.9187 −0.976598
\(126\) 1.14457 0.101967
\(127\) 0.841390 0.0746613 0.0373307 0.999303i \(-0.488115\pi\)
0.0373307 + 0.999303i \(0.488115\pi\)
\(128\) 5.25307 0.464310
\(129\) 13.5672 1.19452
\(130\) 0 0
\(131\) 0.299180 0.0261395 0.0130697 0.999915i \(-0.495840\pi\)
0.0130697 + 0.999915i \(0.495840\pi\)
\(132\) −1.27111 −0.110636
\(133\) 1.12653 0.0976828
\(134\) −0.253953 −0.0219382
\(135\) −1.63355 −0.140594
\(136\) −1.55313 −0.133180
\(137\) 10.7922 0.922037 0.461018 0.887391i \(-0.347484\pi\)
0.461018 + 0.887391i \(0.347484\pi\)
\(138\) 0.193802 0.0164975
\(139\) 3.68278 0.312369 0.156185 0.987728i \(-0.450081\pi\)
0.156185 + 0.987728i \(0.450081\pi\)
\(140\) −0.330369 −0.0279213
\(141\) −28.4859 −2.39894
\(142\) 3.39452 0.284862
\(143\) 0 0
\(144\) −8.96481 −0.747067
\(145\) −24.5491 −2.03869
\(146\) 2.44375 0.202246
\(147\) 17.3453 1.43062
\(148\) 3.91869 0.322115
\(149\) −10.8695 −0.890461 −0.445231 0.895416i \(-0.646878\pi\)
−0.445231 + 0.895416i \(0.646878\pi\)
\(150\) −0.679666 −0.0554945
\(151\) −11.4749 −0.933817 −0.466909 0.884306i \(-0.654632\pi\)
−0.466909 + 0.884306i \(0.654632\pi\)
\(152\) −12.1023 −0.981623
\(153\) 1.66563 0.134658
\(154\) −0.348409 −0.0280756
\(155\) 8.15861 0.655315
\(156\) 0 0
\(157\) 16.1234 1.28679 0.643394 0.765535i \(-0.277526\pi\)
0.643394 + 0.765535i \(0.277526\pi\)
\(158\) −4.22499 −0.336122
\(159\) 16.8695 1.33784
\(160\) 6.38049 0.504422
\(161\) −0.0180399 −0.00142174
\(162\) −9.85231 −0.774071
\(163\) 18.3132 1.43440 0.717201 0.696866i \(-0.245423\pi\)
0.717201 + 0.696866i \(0.245423\pi\)
\(164\) −0.192913 −0.0150640
\(165\) 5.72889 0.445994
\(166\) −5.79528 −0.449801
\(167\) 10.7741 0.833727 0.416863 0.908969i \(-0.363129\pi\)
0.416863 + 0.908969i \(0.363129\pi\)
\(168\) 2.18980 0.168947
\(169\) 0 0
\(170\) 1.41568 0.108578
\(171\) 12.9788 0.992517
\(172\) 2.74382 0.209214
\(173\) −21.2500 −1.61560 −0.807802 0.589454i \(-0.799343\pi\)
−0.807802 + 0.589454i \(0.799343\pi\)
\(174\) 32.9085 2.49478
\(175\) 0.0632663 0.00478248
\(176\) 2.72889 0.205698
\(177\) 34.4186 2.58706
\(178\) 4.53910 0.340220
\(179\) 4.14457 0.309780 0.154890 0.987932i \(-0.450498\pi\)
0.154890 + 0.987932i \(0.450498\pi\)
\(180\) −3.80620 −0.283697
\(181\) 20.2811 1.50749 0.753743 0.657170i \(-0.228247\pi\)
0.753743 + 0.657170i \(0.228247\pi\)
\(182\) 0 0
\(183\) 8.35933 0.617940
\(184\) 0.193802 0.0142872
\(185\) −17.6616 −1.29851
\(186\) −10.9367 −0.801920
\(187\) −0.507019 −0.0370769
\(188\) −5.76097 −0.420162
\(189\) −0.203836 −0.0148269
\(190\) 11.0312 0.800287
\(191\) 4.61951 0.334256 0.167128 0.985935i \(-0.446551\pi\)
0.167128 + 0.985935i \(0.446551\pi\)
\(192\) −22.2359 −1.60474
\(193\) 5.69682 0.410066 0.205033 0.978755i \(-0.434270\pi\)
0.205033 + 0.978755i \(0.434270\pi\)
\(194\) −18.3624 −1.31835
\(195\) 0 0
\(196\) 3.50791 0.250565
\(197\) 1.85943 0.132479 0.0662395 0.997804i \(-0.478900\pi\)
0.0662395 + 0.997804i \(0.478900\pi\)
\(198\) −4.01404 −0.285265
\(199\) 8.26710 0.586039 0.293020 0.956106i \(-0.405340\pi\)
0.293020 + 0.956106i \(0.405340\pi\)
\(200\) −0.679666 −0.0480596
\(201\) 0.521056 0.0367525
\(202\) 18.2459 1.28378
\(203\) −3.06327 −0.214999
\(204\) 0.644474 0.0451222
\(205\) 0.869465 0.0607261
\(206\) −21.2491 −1.48049
\(207\) −0.207839 −0.0144458
\(208\) 0 0
\(209\) −3.95077 −0.273281
\(210\) −1.99600 −0.137737
\(211\) 2.81020 0.193462 0.0967311 0.995311i \(-0.469161\pi\)
0.0967311 + 0.995311i \(0.469161\pi\)
\(212\) 3.41168 0.234315
\(213\) −6.96481 −0.477221
\(214\) −19.2359 −1.31494
\(215\) −12.3664 −0.843385
\(216\) 2.18980 0.148997
\(217\) 1.01804 0.0691091
\(218\) −23.1726 −1.56945
\(219\) −5.01404 −0.338817
\(220\) 1.15861 0.0781135
\(221\) 0 0
\(222\) 23.6757 1.58901
\(223\) 14.0602 0.941537 0.470769 0.882257i \(-0.343977\pi\)
0.470769 + 0.882257i \(0.343977\pi\)
\(224\) 0.796164 0.0531959
\(225\) 0.728895 0.0485930
\(226\) −17.8975 −1.19053
\(227\) 19.2038 1.27460 0.637302 0.770614i \(-0.280051\pi\)
0.637302 + 0.770614i \(0.280051\pi\)
\(228\) 5.02185 0.332580
\(229\) −12.4789 −0.824632 −0.412316 0.911041i \(-0.635280\pi\)
−0.412316 + 0.911041i \(0.635280\pi\)
\(230\) −0.176650 −0.0116479
\(231\) 0.714858 0.0470342
\(232\) 32.9085 2.16055
\(233\) −7.97193 −0.522258 −0.261129 0.965304i \(-0.584095\pi\)
−0.261129 + 0.965304i \(0.584095\pi\)
\(234\) 0 0
\(235\) 25.9648 1.69376
\(236\) 6.96081 0.453110
\(237\) 8.66874 0.563095
\(238\) 0.176650 0.0114505
\(239\) 18.9468 1.22556 0.612782 0.790252i \(-0.290050\pi\)
0.612782 + 0.790252i \(0.290050\pi\)
\(240\) 15.6336 1.00914
\(241\) −15.6336 −1.00705 −0.503523 0.863982i \(-0.667963\pi\)
−0.503523 + 0.863982i \(0.667963\pi\)
\(242\) 1.22188 0.0785452
\(243\) 22.3593 1.43435
\(244\) 1.69059 0.108229
\(245\) −15.8102 −1.01008
\(246\) −1.16553 −0.0743115
\(247\) 0 0
\(248\) −10.9367 −0.694483
\(249\) 11.8906 0.753537
\(250\) −13.3413 −0.843777
\(251\) 3.88750 0.245377 0.122689 0.992445i \(-0.460848\pi\)
0.122689 + 0.992445i \(0.460848\pi\)
\(252\) −0.474941 −0.0299185
\(253\) 0.0632663 0.00397752
\(254\) 1.02807 0.0645071
\(255\) −2.90466 −0.181897
\(256\) −11.3203 −0.707521
\(257\) 14.0452 0.876117 0.438059 0.898946i \(-0.355666\pi\)
0.438059 + 0.898946i \(0.355666\pi\)
\(258\) 16.5774 1.03206
\(259\) −2.20384 −0.136940
\(260\) 0 0
\(261\) −35.2921 −2.18452
\(262\) 0.365561 0.0225844
\(263\) 20.1194 1.24062 0.620308 0.784358i \(-0.287008\pi\)
0.620308 + 0.784358i \(0.287008\pi\)
\(264\) −7.67967 −0.472651
\(265\) −15.3765 −0.944570
\(266\) 1.37648 0.0843976
\(267\) −9.31322 −0.569960
\(268\) 0.105378 0.00643700
\(269\) −6.28514 −0.383212 −0.191606 0.981472i \(-0.561370\pi\)
−0.191606 + 0.981472i \(0.561370\pi\)
\(270\) −1.99600 −0.121473
\(271\) −31.7922 −1.93124 −0.965618 0.259965i \(-0.916289\pi\)
−0.965618 + 0.259965i \(0.916289\pi\)
\(272\) −1.38360 −0.0838931
\(273\) 0 0
\(274\) 13.1867 0.796637
\(275\) −0.221876 −0.0133796
\(276\) −0.0804181 −0.00484060
\(277\) 16.8343 1.01147 0.505737 0.862688i \(-0.331221\pi\)
0.505737 + 0.862688i \(0.331221\pi\)
\(278\) 4.49990 0.269886
\(279\) 11.7289 0.702191
\(280\) −1.99600 −0.119284
\(281\) 9.09134 0.542344 0.271172 0.962531i \(-0.412589\pi\)
0.271172 + 0.962531i \(0.412589\pi\)
\(282\) −34.8062 −2.07268
\(283\) 23.1546 1.37640 0.688199 0.725522i \(-0.258401\pi\)
0.688199 + 0.725522i \(0.258401\pi\)
\(284\) −1.40856 −0.0835827
\(285\) −22.6336 −1.34070
\(286\) 0 0
\(287\) 0.108493 0.00640412
\(288\) 9.17265 0.540503
\(289\) −16.7429 −0.984878
\(290\) −29.9960 −1.76143
\(291\) 37.6757 2.20859
\(292\) −1.01404 −0.0593420
\(293\) −22.3734 −1.30707 −0.653533 0.756898i \(-0.726714\pi\)
−0.653533 + 0.756898i \(0.726714\pi\)
\(294\) 21.1938 1.23605
\(295\) −31.3725 −1.82658
\(296\) 23.6757 1.37612
\(297\) 0.714858 0.0414802
\(298\) −13.2811 −0.769356
\(299\) 0 0
\(300\) 0.282028 0.0162829
\(301\) −1.54310 −0.0889427
\(302\) −14.0210 −0.806815
\(303\) −37.4366 −2.15068
\(304\) −10.7812 −0.618346
\(305\) −7.61951 −0.436292
\(306\) 2.03519 0.116344
\(307\) −7.72889 −0.441111 −0.220556 0.975374i \(-0.570787\pi\)
−0.220556 + 0.975374i \(0.570787\pi\)
\(308\) 0.144573 0.00823779
\(309\) 43.5984 2.48022
\(310\) 9.96881 0.566190
\(311\) −23.7218 −1.34514 −0.672569 0.740034i \(-0.734809\pi\)
−0.672569 + 0.740034i \(0.734809\pi\)
\(312\) 0 0
\(313\) 2.48987 0.140736 0.0703678 0.997521i \(-0.477583\pi\)
0.0703678 + 0.997521i \(0.477583\pi\)
\(314\) 19.7008 1.11178
\(315\) 2.14057 0.120607
\(316\) 1.75316 0.0986232
\(317\) 5.53910 0.311107 0.155553 0.987827i \(-0.450284\pi\)
0.155553 + 0.987827i \(0.450284\pi\)
\(318\) 20.6124 1.15589
\(319\) 10.7429 0.601489
\(320\) 20.2680 1.13302
\(321\) 39.4678 2.20288
\(322\) −0.0220425 −0.00122838
\(323\) 2.00311 0.111456
\(324\) 4.08823 0.227124
\(325\) 0 0
\(326\) 22.3765 1.23932
\(327\) 47.5451 2.62925
\(328\) −1.16553 −0.0643556
\(329\) 3.23992 0.178622
\(330\) 7.00000 0.385337
\(331\) 19.7750 1.08693 0.543466 0.839431i \(-0.317112\pi\)
0.543466 + 0.839431i \(0.317112\pi\)
\(332\) 2.40475 0.131978
\(333\) −25.3905 −1.39139
\(334\) 13.1646 0.720337
\(335\) −0.474941 −0.0259488
\(336\) 1.95077 0.106423
\(337\) 19.1858 1.04512 0.522558 0.852603i \(-0.324978\pi\)
0.522558 + 0.852603i \(0.324978\pi\)
\(338\) 0 0
\(339\) 36.7218 1.99445
\(340\) −0.587437 −0.0318582
\(341\) −3.57028 −0.193342
\(342\) 15.8585 0.857532
\(343\) −3.96881 −0.214296
\(344\) 16.5774 0.893794
\(345\) 0.362446 0.0195134
\(346\) −25.9648 −1.39588
\(347\) −1.39452 −0.0748619 −0.0374310 0.999299i \(-0.511917\pi\)
−0.0374310 + 0.999299i \(0.511917\pi\)
\(348\) −13.6554 −0.732006
\(349\) 8.18668 0.438223 0.219112 0.975700i \(-0.429684\pi\)
0.219112 + 0.975700i \(0.429684\pi\)
\(350\) 0.0773036 0.00413205
\(351\) 0 0
\(352\) −2.79216 −0.148823
\(353\) 24.8171 1.32088 0.660441 0.750878i \(-0.270369\pi\)
0.660441 + 0.750878i \(0.270369\pi\)
\(354\) 42.0553 2.23521
\(355\) 6.34841 0.336939
\(356\) −1.88350 −0.0998254
\(357\) −0.362446 −0.0191827
\(358\) 5.06415 0.267649
\(359\) 2.06327 0.108895 0.0544475 0.998517i \(-0.482660\pi\)
0.0544475 + 0.998517i \(0.482660\pi\)
\(360\) −22.9960 −1.21200
\(361\) −3.39141 −0.178495
\(362\) 24.7810 1.30246
\(363\) −2.50702 −0.131584
\(364\) 0 0
\(365\) 4.57028 0.239220
\(366\) 10.2141 0.533898
\(367\) 25.5803 1.33528 0.667641 0.744483i \(-0.267304\pi\)
0.667641 + 0.744483i \(0.267304\pi\)
\(368\) 0.172647 0.00899985
\(369\) 1.24995 0.0650698
\(370\) −21.5803 −1.12191
\(371\) −1.91869 −0.0996136
\(372\) 4.53821 0.235295
\(373\) 12.0913 0.626066 0.313033 0.949742i \(-0.398655\pi\)
0.313033 + 0.949742i \(0.398655\pi\)
\(374\) −0.619514 −0.0320343
\(375\) 27.3734 1.41355
\(376\) −34.8062 −1.79499
\(377\) 0 0
\(378\) −0.249063 −0.0128104
\(379\) −15.7781 −0.810468 −0.405234 0.914213i \(-0.632810\pi\)
−0.405234 + 0.914213i \(0.632810\pi\)
\(380\) −4.57740 −0.234816
\(381\) −2.10938 −0.108067
\(382\) 5.64447 0.288796
\(383\) −21.7601 −1.11189 −0.555944 0.831220i \(-0.687643\pi\)
−0.555944 + 0.831220i \(0.687643\pi\)
\(384\) −13.1695 −0.672055
\(385\) −0.651591 −0.0332082
\(386\) 6.96081 0.354296
\(387\) −17.7781 −0.903713
\(388\) 7.61951 0.386822
\(389\) 4.54913 0.230650 0.115325 0.993328i \(-0.463209\pi\)
0.115325 + 0.993328i \(0.463209\pi\)
\(390\) 0 0
\(391\) −0.0320772 −0.00162221
\(392\) 21.1938 1.07045
\(393\) −0.750049 −0.0378350
\(394\) 2.27199 0.114461
\(395\) −7.90154 −0.397570
\(396\) 1.66563 0.0837010
\(397\) −13.8726 −0.696245 −0.348122 0.937449i \(-0.613181\pi\)
−0.348122 + 0.937449i \(0.613181\pi\)
\(398\) 10.1014 0.506336
\(399\) −2.82424 −0.141389
\(400\) −0.605477 −0.0302738
\(401\) −12.0241 −0.600453 −0.300227 0.953868i \(-0.597062\pi\)
−0.300227 + 0.953868i \(0.597062\pi\)
\(402\) 0.636666 0.0317540
\(403\) 0 0
\(404\) −7.57117 −0.376680
\(405\) −18.4257 −0.915581
\(406\) −3.74293 −0.185759
\(407\) 7.72889 0.383107
\(408\) 3.89373 0.192769
\(409\) 17.4678 0.863728 0.431864 0.901939i \(-0.357856\pi\)
0.431864 + 0.901939i \(0.357856\pi\)
\(410\) 1.06238 0.0524671
\(411\) −27.0561 −1.33458
\(412\) 8.81732 0.434398
\(413\) −3.91469 −0.192629
\(414\) −0.253953 −0.0124811
\(415\) −10.8383 −0.532030
\(416\) 0 0
\(417\) −9.23280 −0.452132
\(418\) −4.82735 −0.236114
\(419\) 23.4999 1.14805 0.574023 0.818839i \(-0.305382\pi\)
0.574023 + 0.818839i \(0.305382\pi\)
\(420\) 0.828241 0.0404140
\(421\) −1.87347 −0.0913072 −0.0456536 0.998957i \(-0.514537\pi\)
−0.0456536 + 0.998957i \(0.514537\pi\)
\(422\) 3.43372 0.167151
\(423\) 37.3273 1.81491
\(424\) 20.6124 1.00103
\(425\) 0.112495 0.00545683
\(426\) −8.51013 −0.412317
\(427\) −0.950771 −0.0460110
\(428\) 7.98196 0.385823
\(429\) 0 0
\(430\) −15.1103 −0.728682
\(431\) −6.15772 −0.296607 −0.148304 0.988942i \(-0.547381\pi\)
−0.148304 + 0.988942i \(0.547381\pi\)
\(432\) 1.95077 0.0938565
\(433\) 22.3624 1.07467 0.537335 0.843369i \(-0.319431\pi\)
0.537335 + 0.843369i \(0.319431\pi\)
\(434\) 1.24392 0.0597100
\(435\) 61.5451 2.95086
\(436\) 9.61551 0.460499
\(437\) −0.249951 −0.0119568
\(438\) −6.12653 −0.292737
\(439\) −38.5632 −1.84052 −0.920260 0.391308i \(-0.872023\pi\)
−0.920260 + 0.391308i \(0.872023\pi\)
\(440\) 7.00000 0.333712
\(441\) −22.7289 −1.08233
\(442\) 0 0
\(443\) −25.4819 −1.21068 −0.605340 0.795967i \(-0.706963\pi\)
−0.605340 + 0.795967i \(0.706963\pi\)
\(444\) −9.82424 −0.466238
\(445\) 8.48898 0.402416
\(446\) 17.1798 0.813485
\(447\) 27.2500 1.28888
\(448\) 2.52906 0.119487
\(449\) −36.3553 −1.71571 −0.857857 0.513888i \(-0.828205\pi\)
−0.857857 + 0.513888i \(0.828205\pi\)
\(450\) 0.890619 0.0419842
\(451\) −0.380486 −0.0179164
\(452\) 7.42660 0.349318
\(453\) 28.7679 1.35163
\(454\) 23.4647 1.10125
\(455\) 0 0
\(456\) 30.3406 1.42083
\(457\) −16.2780 −0.761454 −0.380727 0.924688i \(-0.624326\pi\)
−0.380727 + 0.924688i \(0.624326\pi\)
\(458\) −15.2477 −0.712479
\(459\) −0.362446 −0.0169175
\(460\) 0.0733010 0.00341768
\(461\) −2.80620 −0.130698 −0.0653488 0.997862i \(-0.520816\pi\)
−0.0653488 + 0.997862i \(0.520816\pi\)
\(462\) 0.873467 0.0406374
\(463\) −18.8835 −0.877591 −0.438795 0.898587i \(-0.644595\pi\)
−0.438795 + 0.898587i \(0.644595\pi\)
\(464\) 29.3163 1.36098
\(465\) −20.4538 −0.948522
\(466\) −9.74071 −0.451229
\(467\) −25.6295 −1.18599 −0.592997 0.805205i \(-0.702055\pi\)
−0.592997 + 0.805205i \(0.702055\pi\)
\(468\) 0 0
\(469\) −0.0592637 −0.00273654
\(470\) 31.7258 1.46340
\(471\) −40.4217 −1.86253
\(472\) 42.0553 1.93575
\(473\) 5.41168 0.248829
\(474\) 10.5921 0.486513
\(475\) 0.876582 0.0402203
\(476\) −0.0733010 −0.00335974
\(477\) −22.1054 −1.01214
\(478\) 23.1506 1.05888
\(479\) −4.49298 −0.205290 −0.102645 0.994718i \(-0.532730\pi\)
−0.102645 + 0.994718i \(0.532730\pi\)
\(480\) −15.9960 −0.730114
\(481\) 0 0
\(482\) −19.1023 −0.870084
\(483\) 0.0452264 0.00205787
\(484\) −0.507019 −0.0230463
\(485\) −34.3413 −1.55936
\(486\) 27.3203 1.23928
\(487\) 21.8093 0.988274 0.494137 0.869384i \(-0.335484\pi\)
0.494137 + 0.869384i \(0.335484\pi\)
\(488\) 10.2141 0.462369
\(489\) −45.9116 −2.07619
\(490\) −19.3181 −0.872703
\(491\) 0.359332 0.0162164 0.00810820 0.999967i \(-0.497419\pi\)
0.00810820 + 0.999967i \(0.497419\pi\)
\(492\) 0.483638 0.0218041
\(493\) −5.44687 −0.245315
\(494\) 0 0
\(495\) −7.50702 −0.337415
\(496\) −9.74293 −0.437471
\(497\) 0.792161 0.0355333
\(498\) 14.5289 0.651054
\(499\) 0.394523 0.0176613 0.00883064 0.999961i \(-0.497189\pi\)
0.00883064 + 0.999961i \(0.497189\pi\)
\(500\) 5.53598 0.247577
\(501\) −27.0109 −1.20676
\(502\) 4.75005 0.212005
\(503\) −25.5812 −1.14061 −0.570305 0.821433i \(-0.693175\pi\)
−0.570305 + 0.821433i \(0.693175\pi\)
\(504\) −2.86946 −0.127816
\(505\) 34.1234 1.51847
\(506\) 0.0773036 0.00343656
\(507\) 0 0
\(508\) −0.426600 −0.0189273
\(509\) 8.88350 0.393754 0.196877 0.980428i \(-0.436920\pi\)
0.196877 + 0.980428i \(0.436920\pi\)
\(510\) −3.54913 −0.157158
\(511\) 0.570285 0.0252279
\(512\) −24.3382 −1.07561
\(513\) −2.82424 −0.124693
\(514\) 17.1615 0.756963
\(515\) −39.7398 −1.75115
\(516\) −6.87881 −0.302823
\(517\) −11.3624 −0.499720
\(518\) −2.69281 −0.118315
\(519\) 53.2740 2.33847
\(520\) 0 0
\(521\) 38.5803 1.69023 0.845117 0.534581i \(-0.179531\pi\)
0.845117 + 0.534581i \(0.179531\pi\)
\(522\) −43.1225 −1.88742
\(523\) 24.2359 1.05976 0.529881 0.848072i \(-0.322236\pi\)
0.529881 + 0.848072i \(0.322236\pi\)
\(524\) −0.151690 −0.00662660
\(525\) −0.158610 −0.00692230
\(526\) 24.5834 1.07189
\(527\) 1.81020 0.0788536
\(528\) −6.84139 −0.297733
\(529\) −22.9960 −0.999826
\(530\) −18.7882 −0.816105
\(531\) −45.1014 −1.95723
\(532\) −0.571173 −0.0247635
\(533\) 0 0
\(534\) −11.3796 −0.492443
\(535\) −35.9748 −1.55533
\(536\) 0.636666 0.0274998
\(537\) −10.3905 −0.448384
\(538\) −7.67967 −0.331094
\(539\) 6.91869 0.298009
\(540\) 0.828241 0.0356418
\(541\) −9.10538 −0.391471 −0.195735 0.980657i \(-0.562709\pi\)
−0.195735 + 0.980657i \(0.562709\pi\)
\(542\) −38.8461 −1.66858
\(543\) −50.8452 −2.18198
\(544\) 1.41568 0.0606967
\(545\) −43.3373 −1.85637
\(546\) 0 0
\(547\) −42.0109 −1.79626 −0.898129 0.439733i \(-0.855073\pi\)
−0.898129 + 0.439733i \(0.855073\pi\)
\(548\) −5.47183 −0.233745
\(549\) −10.9539 −0.467500
\(550\) −0.271105 −0.0115600
\(551\) −42.4429 −1.80813
\(552\) −0.485864 −0.0206798
\(553\) −0.985963 −0.0419274
\(554\) 20.5694 0.873910
\(555\) 44.2780 1.87950
\(556\) −1.86724 −0.0791885
\(557\) −10.6124 −0.449662 −0.224831 0.974398i \(-0.572183\pi\)
−0.224831 + 0.974398i \(0.572183\pi\)
\(558\) 14.3313 0.606690
\(559\) 0 0
\(560\) −1.77812 −0.0751394
\(561\) 1.27111 0.0536661
\(562\) 11.1085 0.468583
\(563\) −19.3945 −0.817382 −0.408691 0.912673i \(-0.634015\pi\)
−0.408691 + 0.912673i \(0.634015\pi\)
\(564\) 14.4429 0.608154
\(565\) −33.4718 −1.40817
\(566\) 28.2921 1.18920
\(567\) −2.29918 −0.0965565
\(568\) −8.51013 −0.357077
\(569\) 33.6625 1.41121 0.705603 0.708607i \(-0.250676\pi\)
0.705603 + 0.708607i \(0.250676\pi\)
\(570\) −27.6554 −1.15836
\(571\) −11.0250 −0.461380 −0.230690 0.973027i \(-0.574098\pi\)
−0.230690 + 0.973027i \(0.574098\pi\)
\(572\) 0 0
\(573\) −11.5812 −0.483812
\(574\) 0.132565 0.00553314
\(575\) −0.0140373 −0.000585395 0
\(576\) 29.1375 1.21406
\(577\) −11.1898 −0.465837 −0.232919 0.972496i \(-0.574828\pi\)
−0.232919 + 0.972496i \(0.574828\pi\)
\(578\) −20.4578 −0.850932
\(579\) −14.2820 −0.593541
\(580\) 12.4469 0.516828
\(581\) −1.35241 −0.0561075
\(582\) 46.0350 1.90821
\(583\) 6.72889 0.278682
\(584\) −6.12653 −0.253518
\(585\) 0 0
\(586\) −27.3375 −1.12930
\(587\) −4.45779 −0.183993 −0.0919963 0.995759i \(-0.529325\pi\)
−0.0919963 + 0.995759i \(0.529325\pi\)
\(588\) −8.79439 −0.362674
\(589\) 14.1054 0.581202
\(590\) −38.3333 −1.57816
\(591\) −4.66163 −0.191754
\(592\) 21.0913 0.866849
\(593\) 28.0733 1.15283 0.576416 0.817156i \(-0.304451\pi\)
0.576416 + 0.817156i \(0.304451\pi\)
\(594\) 0.873467 0.0358388
\(595\) 0.330369 0.0135438
\(596\) 5.51102 0.225740
\(597\) −20.7258 −0.848250
\(598\) 0 0
\(599\) 17.6304 0.720360 0.360180 0.932883i \(-0.382715\pi\)
0.360180 + 0.932883i \(0.382715\pi\)
\(600\) 1.70393 0.0695628
\(601\) 6.69771 0.273205 0.136603 0.990626i \(-0.456382\pi\)
0.136603 + 0.990626i \(0.456382\pi\)
\(602\) −1.88548 −0.0768462
\(603\) −0.682780 −0.0278050
\(604\) 5.81801 0.236731
\(605\) 2.28514 0.0929043
\(606\) −45.7429 −1.85818
\(607\) −11.1546 −0.452752 −0.226376 0.974040i \(-0.572688\pi\)
−0.226376 + 0.974040i \(0.572688\pi\)
\(608\) 11.0312 0.447374
\(609\) 7.67967 0.311196
\(610\) −9.31010 −0.376955
\(611\) 0 0
\(612\) −0.844505 −0.0341371
\(613\) 15.3203 0.618782 0.309391 0.950935i \(-0.399875\pi\)
0.309391 + 0.950935i \(0.399875\pi\)
\(614\) −9.44375 −0.381119
\(615\) −2.17976 −0.0878966
\(616\) 0.873467 0.0351930
\(617\) −24.4819 −0.985603 −0.492801 0.870142i \(-0.664027\pi\)
−0.492801 + 0.870142i \(0.664027\pi\)
\(618\) 53.2718 2.14291
\(619\) −14.3624 −0.577275 −0.288638 0.957438i \(-0.593202\pi\)
−0.288638 + 0.957438i \(0.593202\pi\)
\(620\) −4.13657 −0.166129
\(621\) 0.0452264 0.00181487
\(622\) −28.9851 −1.16220
\(623\) 1.05926 0.0424385
\(624\) 0 0
\(625\) −26.0602 −1.04241
\(626\) 3.04231 0.121595
\(627\) 9.90466 0.395554
\(628\) −8.17487 −0.326213
\(629\) −3.91869 −0.156249
\(630\) 2.61551 0.104204
\(631\) −25.4186 −1.01190 −0.505949 0.862563i \(-0.668858\pi\)
−0.505949 + 0.862563i \(0.668858\pi\)
\(632\) 10.5921 0.421332
\(633\) −7.04523 −0.280023
\(634\) 6.76809 0.268795
\(635\) 1.92270 0.0762999
\(636\) −8.55313 −0.339154
\(637\) 0 0
\(638\) 13.1265 0.519684
\(639\) 9.12653 0.361040
\(640\) 12.0040 0.474500
\(641\) −18.6897 −0.738199 −0.369099 0.929390i \(-0.620334\pi\)
−0.369099 + 0.929390i \(0.620334\pi\)
\(642\) 48.2248 1.90328
\(643\) −0.221876 −0.00874994 −0.00437497 0.999990i \(-0.501393\pi\)
−0.00437497 + 0.999990i \(0.501393\pi\)
\(644\) 0.00914657 0.000360425 0
\(645\) 31.0029 1.22074
\(646\) 2.44756 0.0962979
\(647\) −10.0602 −0.395505 −0.197753 0.980252i \(-0.563364\pi\)
−0.197753 + 0.980252i \(0.563364\pi\)
\(648\) 24.6999 0.970305
\(649\) 13.7289 0.538906
\(650\) 0 0
\(651\) −2.55225 −0.100030
\(652\) −9.28514 −0.363634
\(653\) 25.1375 0.983705 0.491852 0.870679i \(-0.336320\pi\)
0.491852 + 0.870679i \(0.336320\pi\)
\(654\) 58.0943 2.27167
\(655\) 0.683668 0.0267131
\(656\) −1.03831 −0.0405390
\(657\) 6.57028 0.256331
\(658\) 3.95878 0.154329
\(659\) −30.7530 −1.19797 −0.598983 0.800762i \(-0.704428\pi\)
−0.598983 + 0.800762i \(0.704428\pi\)
\(660\) −2.90466 −0.113064
\(661\) −44.1335 −1.71659 −0.858296 0.513155i \(-0.828477\pi\)
−0.858296 + 0.513155i \(0.828477\pi\)
\(662\) 24.1626 0.939107
\(663\) 0 0
\(664\) 14.5289 0.563829
\(665\) 2.57429 0.0998266
\(666\) −31.0241 −1.20216
\(667\) 0.679666 0.0263168
\(668\) −5.46268 −0.211357
\(669\) −35.2491 −1.36281
\(670\) −0.580320 −0.0224197
\(671\) 3.33437 0.128722
\(672\) −1.99600 −0.0769973
\(673\) 19.6516 0.757513 0.378757 0.925496i \(-0.376352\pi\)
0.378757 + 0.925496i \(0.376352\pi\)
\(674\) 23.4427 0.902978
\(675\) −0.158610 −0.00610490
\(676\) 0 0
\(677\) 26.0250 1.00022 0.500110 0.865962i \(-0.333293\pi\)
0.500110 + 0.865962i \(0.333293\pi\)
\(678\) 44.8695 1.72320
\(679\) −4.28514 −0.164449
\(680\) −3.54913 −0.136103
\(681\) −48.1444 −1.84490
\(682\) −4.36245 −0.167047
\(683\) −14.4609 −0.553331 −0.276666 0.960966i \(-0.589229\pi\)
−0.276666 + 0.960966i \(0.589229\pi\)
\(684\) −6.58052 −0.251612
\(685\) 24.6616 0.942272
\(686\) −4.84940 −0.185151
\(687\) 31.2849 1.19360
\(688\) 14.7679 0.563021
\(689\) 0 0
\(690\) 0.442864 0.0168596
\(691\) 8.71085 0.331377 0.165688 0.986178i \(-0.447015\pi\)
0.165688 + 0.986178i \(0.447015\pi\)
\(692\) 10.7741 0.409571
\(693\) −0.936734 −0.0355836
\(694\) −1.70393 −0.0646805
\(695\) 8.41568 0.319225
\(696\) −82.5021 −3.12724
\(697\) 0.192913 0.00730712
\(698\) 10.0031 0.378623
\(699\) 19.9858 0.755931
\(700\) −0.0320772 −0.00121240
\(701\) 37.5732 1.41912 0.709560 0.704645i \(-0.248894\pi\)
0.709560 + 0.704645i \(0.248894\pi\)
\(702\) 0 0
\(703\) −30.5351 −1.15165
\(704\) −8.86946 −0.334281
\(705\) −65.0943 −2.45159
\(706\) 30.3234 1.14124
\(707\) 4.25796 0.160137
\(708\) −17.4509 −0.655844
\(709\) −10.9196 −0.410094 −0.205047 0.978752i \(-0.565735\pi\)
−0.205047 + 0.978752i \(0.565735\pi\)
\(710\) 7.75697 0.291114
\(711\) −11.3593 −0.426008
\(712\) −11.3796 −0.426468
\(713\) −0.225879 −0.00845923
\(714\) −0.442864 −0.0165738
\(715\) 0 0
\(716\) −2.10138 −0.0785321
\(717\) −47.4999 −1.77392
\(718\) 2.52106 0.0940850
\(719\) 34.6093 1.29071 0.645354 0.763883i \(-0.276710\pi\)
0.645354 + 0.763883i \(0.276710\pi\)
\(720\) −20.4859 −0.763463
\(721\) −4.95878 −0.184674
\(722\) −4.14388 −0.154219
\(723\) 39.1936 1.45763
\(724\) −10.2829 −0.382162
\(725\) −2.38360 −0.0885247
\(726\) −3.06327 −0.113688
\(727\) 19.3281 0.716841 0.358421 0.933560i \(-0.383315\pi\)
0.358421 + 0.933560i \(0.383315\pi\)
\(728\) 0 0
\(729\) −31.8655 −1.18020
\(730\) 5.58432 0.206685
\(731\) −2.74382 −0.101484
\(732\) −4.23834 −0.156653
\(733\) −8.03519 −0.296787 −0.148393 0.988928i \(-0.547410\pi\)
−0.148393 + 0.988928i \(0.547410\pi\)
\(734\) 31.2560 1.15368
\(735\) 39.6365 1.46201
\(736\) −0.176650 −0.00651140
\(737\) 0.207839 0.00765584
\(738\) 1.52729 0.0562201
\(739\) 15.0290 0.552849 0.276425 0.961036i \(-0.410850\pi\)
0.276425 + 0.961036i \(0.410850\pi\)
\(740\) 8.95477 0.329184
\(741\) 0 0
\(742\) −2.34441 −0.0860659
\(743\) 41.7006 1.52985 0.764924 0.644121i \(-0.222777\pi\)
0.764924 + 0.644121i \(0.222777\pi\)
\(744\) 27.4186 1.00521
\(745\) −24.8383 −0.910004
\(746\) 14.7741 0.540919
\(747\) −15.5812 −0.570087
\(748\) 0.257068 0.00939933
\(749\) −4.48898 −0.164024
\(750\) 33.4469 1.22131
\(751\) −26.1827 −0.955420 −0.477710 0.878518i \(-0.658533\pi\)
−0.477710 + 0.878518i \(0.658533\pi\)
\(752\) −31.0069 −1.13071
\(753\) −9.74605 −0.355166
\(754\) 0 0
\(755\) −26.2219 −0.954312
\(756\) 0.103349 0.00375876
\(757\) 50.3734 1.83085 0.915426 0.402487i \(-0.131854\pi\)
0.915426 + 0.402487i \(0.131854\pi\)
\(758\) −19.2789 −0.700242
\(759\) −0.158610 −0.00575717
\(760\) −27.6554 −1.00317
\(761\) 15.0882 0.546948 0.273474 0.961879i \(-0.411827\pi\)
0.273474 + 0.961879i \(0.411827\pi\)
\(762\) −2.57740 −0.0933694
\(763\) −5.40767 −0.195771
\(764\) −2.34218 −0.0847371
\(765\) 3.80620 0.137613
\(766\) −26.5881 −0.960668
\(767\) 0 0
\(768\) 28.3803 1.02409
\(769\) −34.1094 −1.23002 −0.615008 0.788521i \(-0.710847\pi\)
−0.615008 + 0.788521i \(0.710847\pi\)
\(770\) −0.796164 −0.0286918
\(771\) −35.2116 −1.26812
\(772\) −2.88839 −0.103956
\(773\) −16.5772 −0.596241 −0.298120 0.954528i \(-0.596360\pi\)
−0.298120 + 0.954528i \(0.596360\pi\)
\(774\) −21.7227 −0.780805
\(775\) 0.792161 0.0284553
\(776\) 46.0350 1.65256
\(777\) 5.52506 0.198210
\(778\) 5.55847 0.199281
\(779\) 1.50321 0.0538582
\(780\) 0 0
\(781\) −2.77812 −0.0994091
\(782\) −0.0391944 −0.00140159
\(783\) 7.67967 0.274449
\(784\) 18.8804 0.674300
\(785\) 36.8443 1.31503
\(786\) −0.916467 −0.0326893
\(787\) −21.7670 −0.775910 −0.387955 0.921678i \(-0.626818\pi\)
−0.387955 + 0.921678i \(0.626818\pi\)
\(788\) −0.942766 −0.0335846
\(789\) −50.4397 −1.79570
\(790\) −9.65471 −0.343499
\(791\) −4.17665 −0.148505
\(792\) 10.0633 0.357583
\(793\) 0 0
\(794\) −16.9506 −0.601553
\(795\) 38.5491 1.36720
\(796\) −4.19158 −0.148566
\(797\) −28.9717 −1.02623 −0.513116 0.858319i \(-0.671509\pi\)
−0.513116 + 0.858319i \(0.671509\pi\)
\(798\) −3.45087 −0.122159
\(799\) 5.76097 0.203809
\(800\) 0.619514 0.0219031
\(801\) 12.2038 0.431201
\(802\) −14.6919 −0.518790
\(803\) −2.00000 −0.0705785
\(804\) −0.264185 −0.00931709
\(805\) −0.0412238 −0.00145295
\(806\) 0 0
\(807\) 15.7570 0.554672
\(808\) −45.7429 −1.60923
\(809\) −48.4257 −1.70256 −0.851279 0.524714i \(-0.824172\pi\)
−0.851279 + 0.524714i \(0.824172\pi\)
\(810\) −22.5139 −0.791059
\(811\) −50.7499 −1.78207 −0.891034 0.453936i \(-0.850019\pi\)
−0.891034 + 0.453936i \(0.850019\pi\)
\(812\) 1.55313 0.0545043
\(813\) 79.7035 2.79533
\(814\) 9.44375 0.331003
\(815\) 41.8483 1.46588
\(816\) 3.46871 0.121429
\(817\) −21.3803 −0.748002
\(818\) 21.3435 0.746259
\(819\) 0 0
\(820\) −0.440835 −0.0153946
\(821\) 24.2600 0.846679 0.423340 0.905971i \(-0.360858\pi\)
0.423340 + 0.905971i \(0.360858\pi\)
\(822\) −33.0593 −1.15307
\(823\) 25.5171 0.889469 0.444734 0.895663i \(-0.353298\pi\)
0.444734 + 0.895663i \(0.353298\pi\)
\(824\) 53.2718 1.85581
\(825\) 0.556248 0.0193661
\(826\) −4.78327 −0.166431
\(827\) −8.82112 −0.306741 −0.153370 0.988169i \(-0.549013\pi\)
−0.153370 + 0.988169i \(0.549013\pi\)
\(828\) 0.105378 0.00366215
\(829\) −19.4718 −0.676285 −0.338142 0.941095i \(-0.609799\pi\)
−0.338142 + 0.941095i \(0.609799\pi\)
\(830\) −13.2430 −0.459672
\(831\) −42.2038 −1.46403
\(832\) 0 0
\(833\) −3.50791 −0.121542
\(834\) −11.2813 −0.390641
\(835\) 24.6204 0.852024
\(836\) 2.00311 0.0692792
\(837\) −2.55225 −0.0882185
\(838\) 28.7140 0.991908
\(839\) 24.3905 0.842054 0.421027 0.907048i \(-0.361670\pi\)
0.421027 + 0.907048i \(0.361670\pi\)
\(840\) 5.00400 0.172654
\(841\) 86.4106 2.97968
\(842\) −2.28915 −0.0788892
\(843\) −22.7922 −0.785004
\(844\) −1.42482 −0.0490445
\(845\) 0 0
\(846\) 45.6093 1.56808
\(847\) 0.285142 0.00979761
\(848\) 18.3624 0.630569
\(849\) −58.0490 −1.99224
\(850\) 0.137455 0.00471468
\(851\) 0.488979 0.0167620
\(852\) 3.53129 0.120980
\(853\) 11.8984 0.407394 0.203697 0.979034i \(-0.434704\pi\)
0.203697 + 0.979034i \(0.434704\pi\)
\(854\) −1.16172 −0.0397534
\(855\) 29.6585 1.01430
\(856\) 48.2248 1.64829
\(857\) 38.5030 1.31524 0.657619 0.753351i \(-0.271564\pi\)
0.657619 + 0.753351i \(0.271564\pi\)
\(858\) 0 0
\(859\) 23.8804 0.814788 0.407394 0.913252i \(-0.366438\pi\)
0.407394 + 0.913252i \(0.366438\pi\)
\(860\) 6.27002 0.213806
\(861\) −0.271993 −0.00926951
\(862\) −7.52397 −0.256268
\(863\) 32.7289 1.11410 0.557052 0.830477i \(-0.311932\pi\)
0.557052 + 0.830477i \(0.311932\pi\)
\(864\) −1.99600 −0.0679052
\(865\) −48.5592 −1.65106
\(866\) 27.3241 0.928512
\(867\) 41.9748 1.42554
\(868\) −0.516165 −0.0175198
\(869\) 3.45779 0.117297
\(870\) 75.2005 2.54954
\(871\) 0 0
\(872\) 58.0943 1.96732
\(873\) −49.3694 −1.67090
\(874\) −0.305409 −0.0103306
\(875\) −3.11338 −0.105252
\(876\) 2.54221 0.0858933
\(877\) −26.6344 −0.899381 −0.449691 0.893184i \(-0.648466\pi\)
−0.449691 + 0.893184i \(0.648466\pi\)
\(878\) −47.1194 −1.59020
\(879\) 56.0905 1.89188
\(880\) 6.23591 0.210213
\(881\) 0.349297 0.0117681 0.00588406 0.999983i \(-0.498127\pi\)
0.00588406 + 0.999983i \(0.498127\pi\)
\(882\) −27.7719 −0.935128
\(883\) −32.5039 −1.09384 −0.546922 0.837184i \(-0.684200\pi\)
−0.546922 + 0.837184i \(0.684200\pi\)
\(884\) 0 0
\(885\) 78.6514 2.64384
\(886\) −31.1357 −1.04602
\(887\) 29.1375 0.978340 0.489170 0.872188i \(-0.337300\pi\)
0.489170 + 0.872188i \(0.337300\pi\)
\(888\) −59.3553 −1.99183
\(889\) 0.239916 0.00804653
\(890\) 10.3725 0.347686
\(891\) 8.06327 0.270130
\(892\) −7.12876 −0.238689
\(893\) 44.8904 1.50220
\(894\) 33.2961 1.11359
\(895\) 9.47094 0.316579
\(896\) 1.49787 0.0500404
\(897\) 0 0
\(898\) −44.4217 −1.48237
\(899\) −38.3553 −1.27922
\(900\) −0.369563 −0.0123188
\(901\) −3.41168 −0.113659
\(902\) −0.464907 −0.0154797
\(903\) 3.86858 0.128738
\(904\) 44.8695 1.49234
\(905\) 46.3453 1.54057
\(906\) 35.1508 1.16781
\(907\) −0.664740 −0.0220723 −0.0110362 0.999939i \(-0.503513\pi\)
−0.0110362 + 0.999939i \(0.503513\pi\)
\(908\) −9.73670 −0.323124
\(909\) 49.0561 1.62709
\(910\) 0 0
\(911\) 24.5522 0.813452 0.406726 0.913550i \(-0.366670\pi\)
0.406726 + 0.913550i \(0.366670\pi\)
\(912\) 27.0288 0.895012
\(913\) 4.74293 0.156968
\(914\) −19.8897 −0.657894
\(915\) 19.1023 0.631501
\(916\) 6.32706 0.209052
\(917\) 0.0853089 0.00281715
\(918\) −0.442864 −0.0146167
\(919\) −21.0561 −0.694578 −0.347289 0.937758i \(-0.612898\pi\)
−0.347289 + 0.937758i \(0.612898\pi\)
\(920\) 0.442864 0.0146008
\(921\) 19.3765 0.638477
\(922\) −3.42883 −0.112922
\(923\) 0 0
\(924\) −0.362446 −0.0119236
\(925\) −1.71486 −0.0563842
\(926\) −23.0733 −0.758236
\(927\) −57.1303 −1.87641
\(928\) −29.9960 −0.984667
\(929\) 2.97104 0.0974766 0.0487383 0.998812i \(-0.484480\pi\)
0.0487383 + 0.998812i \(0.484480\pi\)
\(930\) −24.9920 −0.819520
\(931\) −27.3342 −0.895841
\(932\) 4.04191 0.132397
\(933\) 59.4709 1.94699
\(934\) −31.3161 −1.02470
\(935\) −1.15861 −0.0378906
\(936\) 0 0
\(937\) 52.0350 1.69991 0.849955 0.526856i \(-0.176629\pi\)
0.849955 + 0.526856i \(0.176629\pi\)
\(938\) −0.0724129 −0.00236436
\(939\) −6.24214 −0.203705
\(940\) −13.1646 −0.429383
\(941\) 44.2108 1.44123 0.720615 0.693336i \(-0.243860\pi\)
0.720615 + 0.693336i \(0.243860\pi\)
\(942\) −49.3903 −1.60922
\(943\) −0.0240719 −0.000783891 0
\(944\) 37.4647 1.21937
\(945\) −0.465795 −0.0151523
\(946\) 6.61240 0.214988
\(947\) 17.9969 0.584820 0.292410 0.956293i \(-0.405543\pi\)
0.292410 + 0.956293i \(0.405543\pi\)
\(948\) −4.39521 −0.142750
\(949\) 0 0
\(950\) 1.07107 0.0347502
\(951\) −13.8866 −0.450304
\(952\) −0.442864 −0.0143533
\(953\) 6.50390 0.210682 0.105341 0.994436i \(-0.466407\pi\)
0.105341 + 0.994436i \(0.466407\pi\)
\(954\) −27.0100 −0.874482
\(955\) 10.5562 0.341592
\(956\) −9.60636 −0.310692
\(957\) −26.9327 −0.870612
\(958\) −5.48987 −0.177370
\(959\) 3.07730 0.0993713
\(960\) −50.8122 −1.63996
\(961\) −18.2531 −0.588809
\(962\) 0 0
\(963\) −51.7178 −1.66658
\(964\) 7.92650 0.255295
\(965\) 13.0180 0.419066
\(966\) 0.0552611 0.00177800
\(967\) 27.4429 0.882503 0.441252 0.897383i \(-0.354535\pi\)
0.441252 + 0.897383i \(0.354535\pi\)
\(968\) −3.06327 −0.0984571
\(969\) −5.02185 −0.161325
\(970\) −41.9608 −1.34728
\(971\) 27.2780 0.875393 0.437697 0.899123i \(-0.355794\pi\)
0.437697 + 0.899123i \(0.355794\pi\)
\(972\) −11.3366 −0.363622
\(973\) 1.05012 0.0336652
\(974\) 26.6483 0.853866
\(975\) 0 0
\(976\) 9.09915 0.291257
\(977\) 7.17665 0.229601 0.114801 0.993389i \(-0.463377\pi\)
0.114801 + 0.993389i \(0.463377\pi\)
\(978\) −56.0983 −1.79382
\(979\) −3.71486 −0.118727
\(980\) 8.01607 0.256064
\(981\) −62.3021 −1.98915
\(982\) 0.439059 0.0140109
\(983\) 28.4326 0.906860 0.453430 0.891292i \(-0.350200\pi\)
0.453430 + 0.891292i \(0.350200\pi\)
\(984\) 2.92201 0.0931501
\(985\) 4.24906 0.135386
\(986\) −6.65540 −0.211951
\(987\) −8.12253 −0.258543
\(988\) 0 0
\(989\) 0.342377 0.0108869
\(990\) −9.17265 −0.291526
\(991\) 42.7490 1.35797 0.678983 0.734154i \(-0.262421\pi\)
0.678983 + 0.734154i \(0.262421\pi\)
\(992\) 9.96881 0.316510
\(993\) −49.5763 −1.57326
\(994\) 0.967923 0.0307006
\(995\) 18.8915 0.598901
\(996\) −6.02877 −0.191029
\(997\) −28.7859 −0.911660 −0.455830 0.890067i \(-0.650657\pi\)
−0.455830 + 0.890067i \(0.650657\pi\)
\(998\) 0.482059 0.0152593
\(999\) 5.52506 0.174805
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.g.1.2 3
13.4 even 6 143.2.e.b.133.2 yes 6
13.10 even 6 143.2.e.b.100.2 6
13.12 even 2 1859.2.a.f.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.e.b.100.2 6 13.10 even 6
143.2.e.b.133.2 yes 6 13.4 even 6
1859.2.a.f.1.2 3 13.12 even 2
1859.2.a.g.1.2 3 1.1 even 1 trivial