Properties

Label 6025.2.a.p.1.14
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.30874 q^{2} -1.88426 q^{3} -0.287190 q^{4} +2.46601 q^{6} +1.28779 q^{7} +2.99335 q^{8} +0.550432 q^{9} +O(q^{10})\) \(q-1.30874 q^{2} -1.88426 q^{3} -0.287190 q^{4} +2.46601 q^{6} +1.28779 q^{7} +2.99335 q^{8} +0.550432 q^{9} +0.698979 q^{11} +0.541141 q^{12} -5.53802 q^{13} -1.68539 q^{14} -3.34314 q^{16} +3.43199 q^{17} -0.720375 q^{18} -3.98407 q^{19} -2.42653 q^{21} -0.914784 q^{22} +6.27054 q^{23} -5.64024 q^{24} +7.24785 q^{26} +4.61562 q^{27} -0.369841 q^{28} +6.15912 q^{29} -0.212499 q^{31} -1.61138 q^{32} -1.31706 q^{33} -4.49160 q^{34} -0.158079 q^{36} -5.91052 q^{37} +5.21413 q^{38} +10.4351 q^{39} -9.65382 q^{41} +3.17571 q^{42} -7.78957 q^{43} -0.200740 q^{44} -8.20652 q^{46} +3.86035 q^{47} +6.29934 q^{48} -5.34159 q^{49} -6.46676 q^{51} +1.59047 q^{52} +10.2480 q^{53} -6.04066 q^{54} +3.85481 q^{56} +7.50702 q^{57} -8.06070 q^{58} -9.54071 q^{59} +8.82214 q^{61} +0.278107 q^{62} +0.708842 q^{63} +8.79516 q^{64} +1.72369 q^{66} +7.38392 q^{67} -0.985635 q^{68} -11.8153 q^{69} -6.00088 q^{71} +1.64763 q^{72} -2.96121 q^{73} +7.73535 q^{74} +1.14419 q^{76} +0.900139 q^{77} -13.6568 q^{78} -6.80832 q^{79} -10.3483 q^{81} +12.6344 q^{82} +16.1202 q^{83} +0.696877 q^{84} +10.1946 q^{86} -11.6054 q^{87} +2.09228 q^{88} +1.74849 q^{89} -7.13182 q^{91} -1.80084 q^{92} +0.400404 q^{93} -5.05221 q^{94} +3.03625 q^{96} +0.714461 q^{97} +6.99077 q^{98} +0.384741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30874 −0.925421 −0.462711 0.886509i \(-0.653123\pi\)
−0.462711 + 0.886509i \(0.653123\pi\)
\(3\) −1.88426 −1.08788 −0.543939 0.839125i \(-0.683068\pi\)
−0.543939 + 0.839125i \(0.683068\pi\)
\(4\) −0.287190 −0.143595
\(5\) 0 0
\(6\) 2.46601 1.00675
\(7\) 1.28779 0.486739 0.243370 0.969934i \(-0.421747\pi\)
0.243370 + 0.969934i \(0.421747\pi\)
\(8\) 2.99335 1.05831
\(9\) 0.550432 0.183477
\(10\) 0 0
\(11\) 0.698979 0.210750 0.105375 0.994433i \(-0.466396\pi\)
0.105375 + 0.994433i \(0.466396\pi\)
\(12\) 0.541141 0.156214
\(13\) −5.53802 −1.53597 −0.767985 0.640468i \(-0.778741\pi\)
−0.767985 + 0.640468i \(0.778741\pi\)
\(14\) −1.68539 −0.450439
\(15\) 0 0
\(16\) −3.34314 −0.835785
\(17\) 3.43199 0.832380 0.416190 0.909278i \(-0.363365\pi\)
0.416190 + 0.909278i \(0.363365\pi\)
\(18\) −0.720375 −0.169794
\(19\) −3.98407 −0.914009 −0.457004 0.889464i \(-0.651078\pi\)
−0.457004 + 0.889464i \(0.651078\pi\)
\(20\) 0 0
\(21\) −2.42653 −0.529513
\(22\) −0.914784 −0.195033
\(23\) 6.27054 1.30750 0.653749 0.756712i \(-0.273195\pi\)
0.653749 + 0.756712i \(0.273195\pi\)
\(24\) −5.64024 −1.15131
\(25\) 0 0
\(26\) 7.24785 1.42142
\(27\) 4.61562 0.888276
\(28\) −0.369841 −0.0698935
\(29\) 6.15912 1.14372 0.571859 0.820352i \(-0.306222\pi\)
0.571859 + 0.820352i \(0.306222\pi\)
\(30\) 0 0
\(31\) −0.212499 −0.0381660 −0.0190830 0.999818i \(-0.506075\pi\)
−0.0190830 + 0.999818i \(0.506075\pi\)
\(32\) −1.61138 −0.284854
\(33\) −1.31706 −0.229270
\(34\) −4.49160 −0.770302
\(35\) 0 0
\(36\) −0.158079 −0.0263465
\(37\) −5.91052 −0.971683 −0.485841 0.874047i \(-0.661487\pi\)
−0.485841 + 0.874047i \(0.661487\pi\)
\(38\) 5.21413 0.845843
\(39\) 10.4351 1.67095
\(40\) 0 0
\(41\) −9.65382 −1.50767 −0.753837 0.657062i \(-0.771799\pi\)
−0.753837 + 0.657062i \(0.771799\pi\)
\(42\) 3.17571 0.490023
\(43\) −7.78957 −1.18790 −0.593949 0.804502i \(-0.702432\pi\)
−0.593949 + 0.804502i \(0.702432\pi\)
\(44\) −0.200740 −0.0302627
\(45\) 0 0
\(46\) −8.20652 −1.20999
\(47\) 3.86035 0.563090 0.281545 0.959548i \(-0.409153\pi\)
0.281545 + 0.959548i \(0.409153\pi\)
\(48\) 6.29934 0.909232
\(49\) −5.34159 −0.763085
\(50\) 0 0
\(51\) −6.46676 −0.905527
\(52\) 1.59047 0.220558
\(53\) 10.2480 1.40767 0.703837 0.710361i \(-0.251468\pi\)
0.703837 + 0.710361i \(0.251468\pi\)
\(54\) −6.04066 −0.822030
\(55\) 0 0
\(56\) 3.85481 0.515120
\(57\) 7.50702 0.994329
\(58\) −8.06070 −1.05842
\(59\) −9.54071 −1.24209 −0.621047 0.783773i \(-0.713293\pi\)
−0.621047 + 0.783773i \(0.713293\pi\)
\(60\) 0 0
\(61\) 8.82214 1.12956 0.564779 0.825242i \(-0.308961\pi\)
0.564779 + 0.825242i \(0.308961\pi\)
\(62\) 0.278107 0.0353196
\(63\) 0.708842 0.0893057
\(64\) 8.79516 1.09940
\(65\) 0 0
\(66\) 1.72369 0.212172
\(67\) 7.38392 0.902089 0.451045 0.892501i \(-0.351052\pi\)
0.451045 + 0.892501i \(0.351052\pi\)
\(68\) −0.985635 −0.119526
\(69\) −11.8153 −1.42240
\(70\) 0 0
\(71\) −6.00088 −0.712174 −0.356087 0.934453i \(-0.615889\pi\)
−0.356087 + 0.934453i \(0.615889\pi\)
\(72\) 1.64763 0.194176
\(73\) −2.96121 −0.346584 −0.173292 0.984870i \(-0.555440\pi\)
−0.173292 + 0.984870i \(0.555440\pi\)
\(74\) 7.73535 0.899216
\(75\) 0 0
\(76\) 1.14419 0.131247
\(77\) 0.900139 0.102580
\(78\) −13.6568 −1.54633
\(79\) −6.80832 −0.765996 −0.382998 0.923749i \(-0.625108\pi\)
−0.382998 + 0.923749i \(0.625108\pi\)
\(80\) 0 0
\(81\) −10.3483 −1.14981
\(82\) 12.6344 1.39523
\(83\) 16.1202 1.76942 0.884709 0.466144i \(-0.154357\pi\)
0.884709 + 0.466144i \(0.154357\pi\)
\(84\) 0.696877 0.0760355
\(85\) 0 0
\(86\) 10.1946 1.09931
\(87\) −11.6054 −1.24423
\(88\) 2.09228 0.223038
\(89\) 1.74849 0.185340 0.0926698 0.995697i \(-0.470460\pi\)
0.0926698 + 0.995697i \(0.470460\pi\)
\(90\) 0 0
\(91\) −7.13182 −0.747617
\(92\) −1.80084 −0.187750
\(93\) 0.400404 0.0415199
\(94\) −5.05221 −0.521096
\(95\) 0 0
\(96\) 3.03625 0.309886
\(97\) 0.714461 0.0725425 0.0362713 0.999342i \(-0.488452\pi\)
0.0362713 + 0.999342i \(0.488452\pi\)
\(98\) 6.99077 0.706175
\(99\) 0.384741 0.0386679
\(100\) 0 0
\(101\) −2.31355 −0.230207 −0.115104 0.993353i \(-0.536720\pi\)
−0.115104 + 0.993353i \(0.536720\pi\)
\(102\) 8.46333 0.837994
\(103\) −2.90751 −0.286485 −0.143243 0.989688i \(-0.545753\pi\)
−0.143243 + 0.989688i \(0.545753\pi\)
\(104\) −16.5772 −1.62553
\(105\) 0 0
\(106\) −13.4120 −1.30269
\(107\) 14.8579 1.43637 0.718186 0.695851i \(-0.244973\pi\)
0.718186 + 0.695851i \(0.244973\pi\)
\(108\) −1.32556 −0.127552
\(109\) −11.2125 −1.07396 −0.536980 0.843595i \(-0.680435\pi\)
−0.536980 + 0.843595i \(0.680435\pi\)
\(110\) 0 0
\(111\) 11.1369 1.05707
\(112\) −4.30527 −0.406810
\(113\) 15.7753 1.48402 0.742009 0.670390i \(-0.233873\pi\)
0.742009 + 0.670390i \(0.233873\pi\)
\(114\) −9.82477 −0.920174
\(115\) 0 0
\(116\) −1.76884 −0.164233
\(117\) −3.04831 −0.281816
\(118\) 12.4863 1.14946
\(119\) 4.41969 0.405152
\(120\) 0 0
\(121\) −10.5114 −0.955584
\(122\) −11.5459 −1.04532
\(123\) 18.1903 1.64016
\(124\) 0.0610277 0.00548045
\(125\) 0 0
\(126\) −0.927693 −0.0826454
\(127\) −12.8024 −1.13603 −0.568016 0.823018i \(-0.692289\pi\)
−0.568016 + 0.823018i \(0.692289\pi\)
\(128\) −8.28786 −0.732550
\(129\) 14.6776 1.29229
\(130\) 0 0
\(131\) −1.22476 −0.107008 −0.0535039 0.998568i \(-0.517039\pi\)
−0.0535039 + 0.998568i \(0.517039\pi\)
\(132\) 0.378246 0.0329221
\(133\) −5.13065 −0.444884
\(134\) −9.66366 −0.834813
\(135\) 0 0
\(136\) 10.2731 0.880914
\(137\) −2.83614 −0.242308 −0.121154 0.992634i \(-0.538659\pi\)
−0.121154 + 0.992634i \(0.538659\pi\)
\(138\) 15.4632 1.31632
\(139\) 2.03279 0.172419 0.0862095 0.996277i \(-0.472525\pi\)
0.0862095 + 0.996277i \(0.472525\pi\)
\(140\) 0 0
\(141\) −7.27390 −0.612573
\(142\) 7.85362 0.659061
\(143\) −3.87096 −0.323706
\(144\) −1.84017 −0.153348
\(145\) 0 0
\(146\) 3.87547 0.320736
\(147\) 10.0649 0.830143
\(148\) 1.69744 0.139529
\(149\) 21.0260 1.72252 0.861259 0.508166i \(-0.169676\pi\)
0.861259 + 0.508166i \(0.169676\pi\)
\(150\) 0 0
\(151\) 5.32656 0.433469 0.216735 0.976231i \(-0.430459\pi\)
0.216735 + 0.976231i \(0.430459\pi\)
\(152\) −11.9257 −0.967302
\(153\) 1.88908 0.152723
\(154\) −1.17805 −0.0949300
\(155\) 0 0
\(156\) −2.99685 −0.239940
\(157\) −16.8020 −1.34094 −0.670471 0.741936i \(-0.733908\pi\)
−0.670471 + 0.741936i \(0.733908\pi\)
\(158\) 8.91035 0.708869
\(159\) −19.3099 −1.53138
\(160\) 0 0
\(161\) 8.07514 0.636410
\(162\) 13.5433 1.06406
\(163\) −6.28719 −0.492450 −0.246225 0.969213i \(-0.579190\pi\)
−0.246225 + 0.969213i \(0.579190\pi\)
\(164\) 2.77249 0.216495
\(165\) 0 0
\(166\) −21.0972 −1.63746
\(167\) 15.4202 1.19325 0.596626 0.802519i \(-0.296508\pi\)
0.596626 + 0.802519i \(0.296508\pi\)
\(168\) −7.26345 −0.560387
\(169\) 17.6697 1.35921
\(170\) 0 0
\(171\) −2.19296 −0.167700
\(172\) 2.23709 0.170577
\(173\) 3.72835 0.283461 0.141731 0.989905i \(-0.454733\pi\)
0.141731 + 0.989905i \(0.454733\pi\)
\(174\) 15.1885 1.15143
\(175\) 0 0
\(176\) −2.33678 −0.176142
\(177\) 17.9772 1.35125
\(178\) −2.28833 −0.171517
\(179\) 10.9282 0.816811 0.408405 0.912801i \(-0.366085\pi\)
0.408405 + 0.912801i \(0.366085\pi\)
\(180\) 0 0
\(181\) 12.6140 0.937590 0.468795 0.883307i \(-0.344688\pi\)
0.468795 + 0.883307i \(0.344688\pi\)
\(182\) 9.33372 0.691861
\(183\) −16.6232 −1.22882
\(184\) 18.7699 1.38373
\(185\) 0 0
\(186\) −0.524026 −0.0384234
\(187\) 2.39889 0.175424
\(188\) −1.10866 −0.0808571
\(189\) 5.94396 0.432359
\(190\) 0 0
\(191\) 14.4657 1.04670 0.523349 0.852118i \(-0.324682\pi\)
0.523349 + 0.852118i \(0.324682\pi\)
\(192\) −16.5724 −1.19601
\(193\) 8.80554 0.633837 0.316918 0.948453i \(-0.397352\pi\)
0.316918 + 0.948453i \(0.397352\pi\)
\(194\) −0.935046 −0.0671324
\(195\) 0 0
\(196\) 1.53405 0.109575
\(197\) −20.3391 −1.44910 −0.724552 0.689220i \(-0.757953\pi\)
−0.724552 + 0.689220i \(0.757953\pi\)
\(198\) −0.503527 −0.0357841
\(199\) 18.6435 1.32160 0.660800 0.750562i \(-0.270217\pi\)
0.660800 + 0.750562i \(0.270217\pi\)
\(200\) 0 0
\(201\) −13.9132 −0.981363
\(202\) 3.02785 0.213039
\(203\) 7.93166 0.556693
\(204\) 1.85719 0.130029
\(205\) 0 0
\(206\) 3.80518 0.265120
\(207\) 3.45151 0.239896
\(208\) 18.5144 1.28374
\(209\) −2.78478 −0.192627
\(210\) 0 0
\(211\) −9.60455 −0.661205 −0.330602 0.943770i \(-0.607252\pi\)
−0.330602 + 0.943770i \(0.607252\pi\)
\(212\) −2.94314 −0.202135
\(213\) 11.3072 0.774758
\(214\) −19.4452 −1.32925
\(215\) 0 0
\(216\) 13.8161 0.940070
\(217\) −0.273655 −0.0185769
\(218\) 14.6743 0.993866
\(219\) 5.57970 0.377041
\(220\) 0 0
\(221\) −19.0064 −1.27851
\(222\) −14.5754 −0.978237
\(223\) 21.8910 1.46593 0.732967 0.680265i \(-0.238135\pi\)
0.732967 + 0.680265i \(0.238135\pi\)
\(224\) −2.07512 −0.138650
\(225\) 0 0
\(226\) −20.6459 −1.37334
\(227\) 25.5764 1.69757 0.848783 0.528742i \(-0.177336\pi\)
0.848783 + 0.528742i \(0.177336\pi\)
\(228\) −2.15595 −0.142781
\(229\) 17.6417 1.16580 0.582899 0.812544i \(-0.301918\pi\)
0.582899 + 0.812544i \(0.301918\pi\)
\(230\) 0 0
\(231\) −1.69609 −0.111595
\(232\) 18.4364 1.21041
\(233\) 9.74499 0.638416 0.319208 0.947685i \(-0.396583\pi\)
0.319208 + 0.947685i \(0.396583\pi\)
\(234\) 3.98945 0.260799
\(235\) 0 0
\(236\) 2.74000 0.178359
\(237\) 12.8286 0.833310
\(238\) −5.78424 −0.374936
\(239\) −29.1323 −1.88441 −0.942205 0.335037i \(-0.891251\pi\)
−0.942205 + 0.335037i \(0.891251\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 13.7568 0.884318
\(243\) 5.65206 0.362580
\(244\) −2.53363 −0.162199
\(245\) 0 0
\(246\) −23.8064 −1.51784
\(247\) 22.0639 1.40389
\(248\) −0.636084 −0.0403913
\(249\) −30.3746 −1.92491
\(250\) 0 0
\(251\) 17.9810 1.13495 0.567474 0.823391i \(-0.307921\pi\)
0.567474 + 0.823391i \(0.307921\pi\)
\(252\) −0.203573 −0.0128239
\(253\) 4.38297 0.275555
\(254\) 16.7551 1.05131
\(255\) 0 0
\(256\) −6.74365 −0.421478
\(257\) −20.0744 −1.25221 −0.626105 0.779739i \(-0.715352\pi\)
−0.626105 + 0.779739i \(0.715352\pi\)
\(258\) −19.2092 −1.19591
\(259\) −7.61151 −0.472956
\(260\) 0 0
\(261\) 3.39018 0.209847
\(262\) 1.60290 0.0990273
\(263\) −15.6319 −0.963906 −0.481953 0.876197i \(-0.660072\pi\)
−0.481953 + 0.876197i \(0.660072\pi\)
\(264\) −3.94241 −0.242638
\(265\) 0 0
\(266\) 6.71471 0.411705
\(267\) −3.29461 −0.201627
\(268\) −2.12059 −0.129536
\(269\) 22.2853 1.35876 0.679379 0.733787i \(-0.262249\pi\)
0.679379 + 0.733787i \(0.262249\pi\)
\(270\) 0 0
\(271\) −19.6867 −1.19588 −0.597939 0.801541i \(-0.704014\pi\)
−0.597939 + 0.801541i \(0.704014\pi\)
\(272\) −11.4736 −0.695691
\(273\) 13.4382 0.813316
\(274\) 3.71178 0.224237
\(275\) 0 0
\(276\) 3.39325 0.204249
\(277\) −19.8218 −1.19097 −0.595487 0.803365i \(-0.703041\pi\)
−0.595487 + 0.803365i \(0.703041\pi\)
\(278\) −2.66040 −0.159560
\(279\) −0.116966 −0.00700260
\(280\) 0 0
\(281\) −25.1818 −1.50222 −0.751111 0.660176i \(-0.770482\pi\)
−0.751111 + 0.660176i \(0.770482\pi\)
\(282\) 9.51967 0.566888
\(283\) 1.69555 0.100790 0.0503950 0.998729i \(-0.483952\pi\)
0.0503950 + 0.998729i \(0.483952\pi\)
\(284\) 1.72340 0.102265
\(285\) 0 0
\(286\) 5.06609 0.299564
\(287\) −12.4321 −0.733844
\(288\) −0.886955 −0.0522643
\(289\) −5.22144 −0.307144
\(290\) 0 0
\(291\) −1.34623 −0.0789174
\(292\) 0.850433 0.0497678
\(293\) 21.2874 1.24362 0.621811 0.783167i \(-0.286397\pi\)
0.621811 + 0.783167i \(0.286397\pi\)
\(294\) −13.1724 −0.768232
\(295\) 0 0
\(296\) −17.6922 −1.02834
\(297\) 3.22622 0.187204
\(298\) −27.5177 −1.59405
\(299\) −34.7264 −2.00828
\(300\) 0 0
\(301\) −10.0313 −0.578197
\(302\) −6.97110 −0.401142
\(303\) 4.35933 0.250437
\(304\) 13.3193 0.763915
\(305\) 0 0
\(306\) −2.47232 −0.141333
\(307\) −17.5022 −0.998901 −0.499450 0.866342i \(-0.666465\pi\)
−0.499450 + 0.866342i \(0.666465\pi\)
\(308\) −0.258511 −0.0147300
\(309\) 5.47850 0.311661
\(310\) 0 0
\(311\) −27.1108 −1.53732 −0.768658 0.639661i \(-0.779075\pi\)
−0.768658 + 0.639661i \(0.779075\pi\)
\(312\) 31.2358 1.76838
\(313\) −5.43613 −0.307268 −0.153634 0.988128i \(-0.549098\pi\)
−0.153634 + 0.988128i \(0.549098\pi\)
\(314\) 21.9894 1.24094
\(315\) 0 0
\(316\) 1.95528 0.109993
\(317\) 1.24021 0.0696573 0.0348287 0.999393i \(-0.488911\pi\)
0.0348287 + 0.999393i \(0.488911\pi\)
\(318\) 25.2718 1.41717
\(319\) 4.30509 0.241039
\(320\) 0 0
\(321\) −27.9962 −1.56260
\(322\) −10.5683 −0.588948
\(323\) −13.6733 −0.760802
\(324\) 2.97194 0.165108
\(325\) 0 0
\(326\) 8.22831 0.455724
\(327\) 21.1272 1.16834
\(328\) −28.8972 −1.59558
\(329\) 4.97133 0.274078
\(330\) 0 0
\(331\) −13.6324 −0.749307 −0.374654 0.927165i \(-0.622238\pi\)
−0.374654 + 0.927165i \(0.622238\pi\)
\(332\) −4.62956 −0.254080
\(333\) −3.25334 −0.178282
\(334\) −20.1811 −1.10426
\(335\) 0 0
\(336\) 8.11224 0.442559
\(337\) −9.45300 −0.514938 −0.257469 0.966287i \(-0.582888\pi\)
−0.257469 + 0.966287i \(0.582888\pi\)
\(338\) −23.1251 −1.25784
\(339\) −29.7248 −1.61443
\(340\) 0 0
\(341\) −0.148532 −0.00804348
\(342\) 2.87002 0.155193
\(343\) −15.8934 −0.858163
\(344\) −23.3169 −1.25716
\(345\) 0 0
\(346\) −4.87945 −0.262321
\(347\) −25.8641 −1.38846 −0.694230 0.719754i \(-0.744255\pi\)
−0.694230 + 0.719754i \(0.744255\pi\)
\(348\) 3.33295 0.178665
\(349\) 10.7675 0.576372 0.288186 0.957575i \(-0.406948\pi\)
0.288186 + 0.957575i \(0.406948\pi\)
\(350\) 0 0
\(351\) −25.5614 −1.36437
\(352\) −1.12632 −0.0600330
\(353\) −29.7801 −1.58504 −0.792518 0.609848i \(-0.791230\pi\)
−0.792518 + 0.609848i \(0.791230\pi\)
\(354\) −23.5275 −1.25047
\(355\) 0 0
\(356\) −0.502150 −0.0266139
\(357\) −8.32784 −0.440756
\(358\) −14.3022 −0.755894
\(359\) 9.88958 0.521952 0.260976 0.965345i \(-0.415956\pi\)
0.260976 + 0.965345i \(0.415956\pi\)
\(360\) 0 0
\(361\) −3.12718 −0.164588
\(362\) −16.5085 −0.867666
\(363\) 19.8063 1.03956
\(364\) 2.04819 0.107354
\(365\) 0 0
\(366\) 21.7555 1.13718
\(367\) 24.3156 1.26926 0.634631 0.772815i \(-0.281152\pi\)
0.634631 + 0.772815i \(0.281152\pi\)
\(368\) −20.9633 −1.09279
\(369\) −5.31378 −0.276624
\(370\) 0 0
\(371\) 13.1973 0.685171
\(372\) −0.114992 −0.00596206
\(373\) −6.98503 −0.361671 −0.180836 0.983513i \(-0.557880\pi\)
−0.180836 + 0.983513i \(0.557880\pi\)
\(374\) −3.13953 −0.162341
\(375\) 0 0
\(376\) 11.5554 0.595923
\(377\) −34.1093 −1.75672
\(378\) −7.77911 −0.400114
\(379\) 24.8142 1.27462 0.637309 0.770608i \(-0.280047\pi\)
0.637309 + 0.770608i \(0.280047\pi\)
\(380\) 0 0
\(381\) 24.1231 1.23586
\(382\) −18.9318 −0.968637
\(383\) −7.88965 −0.403142 −0.201571 0.979474i \(-0.564605\pi\)
−0.201571 + 0.979474i \(0.564605\pi\)
\(384\) 15.6165 0.796924
\(385\) 0 0
\(386\) −11.5242 −0.586566
\(387\) −4.28763 −0.217953
\(388\) −0.205186 −0.0104168
\(389\) −18.8488 −0.955670 −0.477835 0.878450i \(-0.658578\pi\)
−0.477835 + 0.878450i \(0.658578\pi\)
\(390\) 0 0
\(391\) 21.5204 1.08833
\(392\) −15.9892 −0.807578
\(393\) 2.30776 0.116411
\(394\) 26.6187 1.34103
\(395\) 0 0
\(396\) −0.110494 −0.00555252
\(397\) 0.758306 0.0380583 0.0190292 0.999819i \(-0.493942\pi\)
0.0190292 + 0.999819i \(0.493942\pi\)
\(398\) −24.3995 −1.22304
\(399\) 9.66748 0.483979
\(400\) 0 0
\(401\) −34.8303 −1.73934 −0.869672 0.493629i \(-0.835670\pi\)
−0.869672 + 0.493629i \(0.835670\pi\)
\(402\) 18.2088 0.908174
\(403\) 1.17682 0.0586218
\(404\) 0.664431 0.0330567
\(405\) 0 0
\(406\) −10.3805 −0.515176
\(407\) −4.13132 −0.204782
\(408\) −19.3572 −0.958326
\(409\) 17.3471 0.857760 0.428880 0.903361i \(-0.358908\pi\)
0.428880 + 0.903361i \(0.358908\pi\)
\(410\) 0 0
\(411\) 5.34402 0.263601
\(412\) 0.835008 0.0411379
\(413\) −12.2864 −0.604576
\(414\) −4.51714 −0.222005
\(415\) 0 0
\(416\) 8.92384 0.437527
\(417\) −3.83031 −0.187571
\(418\) 3.64456 0.178261
\(419\) −22.5895 −1.10357 −0.551786 0.833986i \(-0.686053\pi\)
−0.551786 + 0.833986i \(0.686053\pi\)
\(420\) 0 0
\(421\) −27.8005 −1.35491 −0.677457 0.735563i \(-0.736918\pi\)
−0.677457 + 0.735563i \(0.736918\pi\)
\(422\) 12.5699 0.611893
\(423\) 2.12486 0.103314
\(424\) 30.6759 1.48975
\(425\) 0 0
\(426\) −14.7982 −0.716977
\(427\) 11.3611 0.549801
\(428\) −4.26706 −0.206256
\(429\) 7.29389 0.352152
\(430\) 0 0
\(431\) −17.6040 −0.847957 −0.423978 0.905672i \(-0.639367\pi\)
−0.423978 + 0.905672i \(0.639367\pi\)
\(432\) −15.4307 −0.742408
\(433\) −7.38130 −0.354723 −0.177361 0.984146i \(-0.556756\pi\)
−0.177361 + 0.984146i \(0.556756\pi\)
\(434\) 0.358144 0.0171915
\(435\) 0 0
\(436\) 3.22012 0.154216
\(437\) −24.9823 −1.19506
\(438\) −7.30239 −0.348922
\(439\) 2.17048 0.103591 0.0517956 0.998658i \(-0.483506\pi\)
0.0517956 + 0.998658i \(0.483506\pi\)
\(440\) 0 0
\(441\) −2.94019 −0.140009
\(442\) 24.8745 1.18316
\(443\) 12.7026 0.603518 0.301759 0.953384i \(-0.402426\pi\)
0.301759 + 0.953384i \(0.402426\pi\)
\(444\) −3.19842 −0.151790
\(445\) 0 0
\(446\) −28.6498 −1.35661
\(447\) −39.6185 −1.87389
\(448\) 11.3263 0.535119
\(449\) −4.30823 −0.203318 −0.101659 0.994819i \(-0.532415\pi\)
−0.101659 + 0.994819i \(0.532415\pi\)
\(450\) 0 0
\(451\) −6.74781 −0.317742
\(452\) −4.53052 −0.213098
\(453\) −10.0366 −0.471561
\(454\) −33.4730 −1.57096
\(455\) 0 0
\(456\) 22.4711 1.05231
\(457\) −3.68356 −0.172310 −0.0861548 0.996282i \(-0.527458\pi\)
−0.0861548 + 0.996282i \(0.527458\pi\)
\(458\) −23.0885 −1.07886
\(459\) 15.8408 0.739384
\(460\) 0 0
\(461\) 37.3221 1.73826 0.869131 0.494582i \(-0.164679\pi\)
0.869131 + 0.494582i \(0.164679\pi\)
\(462\) 2.21975 0.103272
\(463\) −12.4345 −0.577880 −0.288940 0.957347i \(-0.593303\pi\)
−0.288940 + 0.957347i \(0.593303\pi\)
\(464\) −20.5908 −0.955903
\(465\) 0 0
\(466\) −12.7537 −0.590804
\(467\) 3.71254 0.171796 0.0858980 0.996304i \(-0.472624\pi\)
0.0858980 + 0.996304i \(0.472624\pi\)
\(468\) 0.875444 0.0404674
\(469\) 9.50895 0.439082
\(470\) 0 0
\(471\) 31.6592 1.45878
\(472\) −28.5586 −1.31452
\(473\) −5.44475 −0.250350
\(474\) −16.7894 −0.771163
\(475\) 0 0
\(476\) −1.26929 −0.0581779
\(477\) 5.64085 0.258277
\(478\) 38.1267 1.74387
\(479\) −32.8371 −1.50036 −0.750182 0.661231i \(-0.770034\pi\)
−0.750182 + 0.661231i \(0.770034\pi\)
\(480\) 0 0
\(481\) 32.7326 1.49248
\(482\) −1.30874 −0.0596116
\(483\) −15.2157 −0.692337
\(484\) 3.01878 0.137217
\(485\) 0 0
\(486\) −7.39710 −0.335539
\(487\) −27.1109 −1.22851 −0.614256 0.789107i \(-0.710544\pi\)
−0.614256 + 0.789107i \(0.710544\pi\)
\(488\) 26.4077 1.19542
\(489\) 11.8467 0.535726
\(490\) 0 0
\(491\) −6.70831 −0.302742 −0.151371 0.988477i \(-0.548369\pi\)
−0.151371 + 0.988477i \(0.548369\pi\)
\(492\) −5.22408 −0.235520
\(493\) 21.1380 0.952009
\(494\) −28.8759 −1.29919
\(495\) 0 0
\(496\) 0.710415 0.0318986
\(497\) −7.72789 −0.346643
\(498\) 39.7525 1.78135
\(499\) −33.9775 −1.52104 −0.760520 0.649314i \(-0.775056\pi\)
−0.760520 + 0.649314i \(0.775056\pi\)
\(500\) 0 0
\(501\) −29.0557 −1.29811
\(502\) −23.5325 −1.05031
\(503\) −6.74907 −0.300926 −0.150463 0.988616i \(-0.548076\pi\)
−0.150463 + 0.988616i \(0.548076\pi\)
\(504\) 2.12181 0.0945129
\(505\) 0 0
\(506\) −5.73618 −0.255005
\(507\) −33.2942 −1.47865
\(508\) 3.67674 0.163129
\(509\) −5.20927 −0.230897 −0.115448 0.993313i \(-0.536831\pi\)
−0.115448 + 0.993313i \(0.536831\pi\)
\(510\) 0 0
\(511\) −3.81343 −0.168696
\(512\) 25.4014 1.12259
\(513\) −18.3890 −0.811892
\(514\) 26.2723 1.15882
\(515\) 0 0
\(516\) −4.21526 −0.185566
\(517\) 2.69830 0.118671
\(518\) 9.96152 0.437684
\(519\) −7.02518 −0.308371
\(520\) 0 0
\(521\) 4.39792 0.192676 0.0963382 0.995349i \(-0.469287\pi\)
0.0963382 + 0.995349i \(0.469287\pi\)
\(522\) −4.43687 −0.194197
\(523\) −28.7186 −1.25578 −0.627889 0.778303i \(-0.716081\pi\)
−0.627889 + 0.778303i \(0.716081\pi\)
\(524\) 0.351739 0.0153658
\(525\) 0 0
\(526\) 20.4582 0.892019
\(527\) −0.729295 −0.0317686
\(528\) 4.40311 0.191621
\(529\) 16.3196 0.709549
\(530\) 0 0
\(531\) −5.25152 −0.227896
\(532\) 1.47347 0.0638832
\(533\) 53.4631 2.31574
\(534\) 4.31180 0.186590
\(535\) 0 0
\(536\) 22.1026 0.954688
\(537\) −20.5915 −0.888590
\(538\) −29.1657 −1.25742
\(539\) −3.73366 −0.160820
\(540\) 0 0
\(541\) −11.5157 −0.495099 −0.247549 0.968875i \(-0.579625\pi\)
−0.247549 + 0.968875i \(0.579625\pi\)
\(542\) 25.7648 1.10669
\(543\) −23.7680 −1.01998
\(544\) −5.53023 −0.237107
\(545\) 0 0
\(546\) −17.5871 −0.752660
\(547\) 1.46564 0.0626662 0.0313331 0.999509i \(-0.490025\pi\)
0.0313331 + 0.999509i \(0.490025\pi\)
\(548\) 0.814512 0.0347942
\(549\) 4.85599 0.207249
\(550\) 0 0
\(551\) −24.5384 −1.04537
\(552\) −35.3673 −1.50533
\(553\) −8.76770 −0.372840
\(554\) 25.9416 1.10215
\(555\) 0 0
\(556\) −0.583798 −0.0247586
\(557\) 9.02751 0.382508 0.191254 0.981541i \(-0.438745\pi\)
0.191254 + 0.981541i \(0.438745\pi\)
\(558\) 0.153079 0.00648035
\(559\) 43.1388 1.82458
\(560\) 0 0
\(561\) −4.52013 −0.190840
\(562\) 32.9566 1.39019
\(563\) −1.03855 −0.0437698 −0.0218849 0.999760i \(-0.506967\pi\)
−0.0218849 + 0.999760i \(0.506967\pi\)
\(564\) 2.08900 0.0879626
\(565\) 0 0
\(566\) −2.21904 −0.0932732
\(567\) −13.3265 −0.559660
\(568\) −17.9627 −0.753699
\(569\) −16.4700 −0.690458 −0.345229 0.938519i \(-0.612199\pi\)
−0.345229 + 0.938519i \(0.612199\pi\)
\(570\) 0 0
\(571\) 34.2521 1.43341 0.716703 0.697378i \(-0.245650\pi\)
0.716703 + 0.697378i \(0.245650\pi\)
\(572\) 1.11170 0.0464826
\(573\) −27.2570 −1.13868
\(574\) 16.2704 0.679115
\(575\) 0 0
\(576\) 4.84114 0.201714
\(577\) −3.72767 −0.155185 −0.0775924 0.996985i \(-0.524723\pi\)
−0.0775924 + 0.996985i \(0.524723\pi\)
\(578\) 6.83353 0.284237
\(579\) −16.5919 −0.689537
\(580\) 0 0
\(581\) 20.7594 0.861245
\(582\) 1.76187 0.0730318
\(583\) 7.16315 0.296667
\(584\) −8.86394 −0.366792
\(585\) 0 0
\(586\) −27.8597 −1.15088
\(587\) −29.8715 −1.23293 −0.616464 0.787383i \(-0.711435\pi\)
−0.616464 + 0.787383i \(0.711435\pi\)
\(588\) −2.89056 −0.119205
\(589\) 0.846612 0.0348840
\(590\) 0 0
\(591\) 38.3242 1.57645
\(592\) 19.7597 0.812118
\(593\) −37.2358 −1.52909 −0.764546 0.644569i \(-0.777037\pi\)
−0.764546 + 0.644569i \(0.777037\pi\)
\(594\) −4.22229 −0.173243
\(595\) 0 0
\(596\) −6.03847 −0.247345
\(597\) −35.1291 −1.43774
\(598\) 45.4479 1.85850
\(599\) −14.2870 −0.583753 −0.291877 0.956456i \(-0.594280\pi\)
−0.291877 + 0.956456i \(0.594280\pi\)
\(600\) 0 0
\(601\) −5.96440 −0.243293 −0.121647 0.992573i \(-0.538817\pi\)
−0.121647 + 0.992573i \(0.538817\pi\)
\(602\) 13.1285 0.535076
\(603\) 4.06435 0.165513
\(604\) −1.52974 −0.0622441
\(605\) 0 0
\(606\) −5.70525 −0.231760
\(607\) 2.52516 0.102493 0.0512466 0.998686i \(-0.483681\pi\)
0.0512466 + 0.998686i \(0.483681\pi\)
\(608\) 6.41984 0.260359
\(609\) −14.9453 −0.605614
\(610\) 0 0
\(611\) −21.3787 −0.864890
\(612\) −0.542525 −0.0219303
\(613\) 9.04094 0.365160 0.182580 0.983191i \(-0.441555\pi\)
0.182580 + 0.983191i \(0.441555\pi\)
\(614\) 22.9058 0.924404
\(615\) 0 0
\(616\) 2.69443 0.108562
\(617\) −38.5569 −1.55224 −0.776120 0.630585i \(-0.782815\pi\)
−0.776120 + 0.630585i \(0.782815\pi\)
\(618\) −7.16995 −0.288418
\(619\) −18.0419 −0.725166 −0.362583 0.931951i \(-0.618105\pi\)
−0.362583 + 0.931951i \(0.618105\pi\)
\(620\) 0 0
\(621\) 28.9424 1.16142
\(622\) 35.4811 1.42266
\(623\) 2.25169 0.0902121
\(624\) −34.8859 −1.39655
\(625\) 0 0
\(626\) 7.11449 0.284352
\(627\) 5.24725 0.209555
\(628\) 4.82536 0.192553
\(629\) −20.2848 −0.808809
\(630\) 0 0
\(631\) −4.00131 −0.159290 −0.0796448 0.996823i \(-0.525379\pi\)
−0.0796448 + 0.996823i \(0.525379\pi\)
\(632\) −20.3797 −0.810659
\(633\) 18.0975 0.719310
\(634\) −1.62312 −0.0644624
\(635\) 0 0
\(636\) 5.54563 0.219899
\(637\) 29.5818 1.17208
\(638\) −5.63426 −0.223062
\(639\) −3.30308 −0.130668
\(640\) 0 0
\(641\) 48.4959 1.91547 0.957736 0.287650i \(-0.0928741\pi\)
0.957736 + 0.287650i \(0.0928741\pi\)
\(642\) 36.6399 1.44606
\(643\) −24.8486 −0.979935 −0.489967 0.871741i \(-0.662991\pi\)
−0.489967 + 0.871741i \(0.662991\pi\)
\(644\) −2.31910 −0.0913855
\(645\) 0 0
\(646\) 17.8948 0.704063
\(647\) −43.2159 −1.69899 −0.849496 0.527595i \(-0.823094\pi\)
−0.849496 + 0.527595i \(0.823094\pi\)
\(648\) −30.9761 −1.21686
\(649\) −6.66875 −0.261771
\(650\) 0 0
\(651\) 0.515636 0.0202094
\(652\) 1.80562 0.0707135
\(653\) −1.40884 −0.0551323 −0.0275662 0.999620i \(-0.508776\pi\)
−0.0275662 + 0.999620i \(0.508776\pi\)
\(654\) −27.6501 −1.08120
\(655\) 0 0
\(656\) 32.2741 1.26009
\(657\) −1.62995 −0.0635904
\(658\) −6.50619 −0.253638
\(659\) −4.34247 −0.169158 −0.0845792 0.996417i \(-0.526955\pi\)
−0.0845792 + 0.996417i \(0.526955\pi\)
\(660\) 0 0
\(661\) 26.3595 1.02527 0.512633 0.858608i \(-0.328670\pi\)
0.512633 + 0.858608i \(0.328670\pi\)
\(662\) 17.8414 0.693425
\(663\) 35.8130 1.39086
\(664\) 48.2532 1.87259
\(665\) 0 0
\(666\) 4.25779 0.164986
\(667\) 38.6210 1.49541
\(668\) −4.42854 −0.171345
\(669\) −41.2484 −1.59476
\(670\) 0 0
\(671\) 6.16648 0.238054
\(672\) 3.91006 0.150834
\(673\) −1.88857 −0.0727989 −0.0363995 0.999337i \(-0.511589\pi\)
−0.0363995 + 0.999337i \(0.511589\pi\)
\(674\) 12.3716 0.476534
\(675\) 0 0
\(676\) −5.07456 −0.195175
\(677\) 40.6860 1.56369 0.781845 0.623473i \(-0.214279\pi\)
0.781845 + 0.623473i \(0.214279\pi\)
\(678\) 38.9021 1.49403
\(679\) 0.920077 0.0353093
\(680\) 0 0
\(681\) −48.1926 −1.84674
\(682\) 0.194391 0.00744361
\(683\) −13.1902 −0.504710 −0.252355 0.967635i \(-0.581205\pi\)
−0.252355 + 0.967635i \(0.581205\pi\)
\(684\) 0.629798 0.0240809
\(685\) 0 0
\(686\) 20.8004 0.794162
\(687\) −33.2416 −1.26825
\(688\) 26.0416 0.992828
\(689\) −56.7538 −2.16215
\(690\) 0 0
\(691\) −21.4420 −0.815692 −0.407846 0.913051i \(-0.633720\pi\)
−0.407846 + 0.913051i \(0.633720\pi\)
\(692\) −1.07075 −0.0407037
\(693\) 0.495466 0.0188212
\(694\) 33.8495 1.28491
\(695\) 0 0
\(696\) −34.7389 −1.31677
\(697\) −33.1318 −1.25496
\(698\) −14.0919 −0.533387
\(699\) −18.3621 −0.694518
\(700\) 0 0
\(701\) 15.8950 0.600348 0.300174 0.953885i \(-0.402955\pi\)
0.300174 + 0.953885i \(0.402955\pi\)
\(702\) 33.4533 1.26261
\(703\) 23.5479 0.888126
\(704\) 6.14763 0.231698
\(705\) 0 0
\(706\) 38.9746 1.46683
\(707\) −2.97937 −0.112051
\(708\) −5.16287 −0.194033
\(709\) −38.8392 −1.45864 −0.729318 0.684175i \(-0.760162\pi\)
−0.729318 + 0.684175i \(0.760162\pi\)
\(710\) 0 0
\(711\) −3.74752 −0.140543
\(712\) 5.23384 0.196146
\(713\) −1.33248 −0.0499019
\(714\) 10.8990 0.407885
\(715\) 0 0
\(716\) −3.13847 −0.117290
\(717\) 54.8927 2.05001
\(718\) −12.9429 −0.483025
\(719\) −1.15150 −0.0429436 −0.0214718 0.999769i \(-0.506835\pi\)
−0.0214718 + 0.999769i \(0.506835\pi\)
\(720\) 0 0
\(721\) −3.74426 −0.139444
\(722\) 4.09267 0.152314
\(723\) −1.88426 −0.0700764
\(724\) −3.62262 −0.134634
\(725\) 0 0
\(726\) −25.9213 −0.962030
\(727\) −2.07741 −0.0770469 −0.0385234 0.999258i \(-0.512265\pi\)
−0.0385234 + 0.999258i \(0.512265\pi\)
\(728\) −21.3480 −0.791209
\(729\) 20.3950 0.755371
\(730\) 0 0
\(731\) −26.7337 −0.988783
\(732\) 4.77402 0.176453
\(733\) −0.247310 −0.00913459 −0.00456729 0.999990i \(-0.501454\pi\)
−0.00456729 + 0.999990i \(0.501454\pi\)
\(734\) −31.8228 −1.17460
\(735\) 0 0
\(736\) −10.1042 −0.372446
\(737\) 5.16120 0.190115
\(738\) 6.95437 0.255994
\(739\) −41.8038 −1.53778 −0.768889 0.639382i \(-0.779190\pi\)
−0.768889 + 0.639382i \(0.779190\pi\)
\(740\) 0 0
\(741\) −41.5740 −1.52726
\(742\) −17.2719 −0.634072
\(743\) −16.1617 −0.592916 −0.296458 0.955046i \(-0.595805\pi\)
−0.296458 + 0.955046i \(0.595805\pi\)
\(744\) 1.19855 0.0439408
\(745\) 0 0
\(746\) 9.14162 0.334698
\(747\) 8.87306 0.324648
\(748\) −0.688938 −0.0251901
\(749\) 19.1339 0.699139
\(750\) 0 0
\(751\) −8.92639 −0.325729 −0.162864 0.986648i \(-0.552073\pi\)
−0.162864 + 0.986648i \(0.552073\pi\)
\(752\) −12.9057 −0.470622
\(753\) −33.8808 −1.23468
\(754\) 44.6403 1.62570
\(755\) 0 0
\(756\) −1.70705 −0.0620847
\(757\) −2.30487 −0.0837720 −0.0418860 0.999122i \(-0.513337\pi\)
−0.0418860 + 0.999122i \(0.513337\pi\)
\(758\) −32.4754 −1.17956
\(759\) −8.25865 −0.299770
\(760\) 0 0
\(761\) −5.45934 −0.197901 −0.0989505 0.995092i \(-0.531549\pi\)
−0.0989505 + 0.995092i \(0.531549\pi\)
\(762\) −31.5709 −1.14369
\(763\) −14.4393 −0.522739
\(764\) −4.15440 −0.150301
\(765\) 0 0
\(766\) 10.3255 0.373076
\(767\) 52.8366 1.90782
\(768\) 12.7068 0.458516
\(769\) 20.6287 0.743890 0.371945 0.928255i \(-0.378691\pi\)
0.371945 + 0.928255i \(0.378691\pi\)
\(770\) 0 0
\(771\) 37.8254 1.36225
\(772\) −2.52887 −0.0910159
\(773\) 36.9986 1.33075 0.665374 0.746510i \(-0.268272\pi\)
0.665374 + 0.746510i \(0.268272\pi\)
\(774\) 5.61141 0.201698
\(775\) 0 0
\(776\) 2.13863 0.0767723
\(777\) 14.3421 0.514519
\(778\) 24.6682 0.884398
\(779\) 38.4615 1.37803
\(780\) 0 0
\(781\) −4.19449 −0.150091
\(782\) −28.1647 −1.00717
\(783\) 28.4281 1.01594
\(784\) 17.8577 0.637775
\(785\) 0 0
\(786\) −3.02027 −0.107730
\(787\) 9.55601 0.340635 0.170317 0.985389i \(-0.445521\pi\)
0.170317 + 0.985389i \(0.445521\pi\)
\(788\) 5.84121 0.208084
\(789\) 29.4546 1.04861
\(790\) 0 0
\(791\) 20.3153 0.722330
\(792\) 1.15166 0.0409225
\(793\) −48.8572 −1.73497
\(794\) −0.992428 −0.0352200
\(795\) 0 0
\(796\) −5.35423 −0.189776
\(797\) 31.5410 1.11724 0.558620 0.829424i \(-0.311331\pi\)
0.558620 + 0.829424i \(0.311331\pi\)
\(798\) −12.6523 −0.447885
\(799\) 13.2487 0.468705
\(800\) 0 0
\(801\) 0.962426 0.0340056
\(802\) 45.5840 1.60963
\(803\) −2.06983 −0.0730426
\(804\) 3.99574 0.140919
\(805\) 0 0
\(806\) −1.54016 −0.0542499
\(807\) −41.9913 −1.47816
\(808\) −6.92527 −0.243630
\(809\) 26.1016 0.917685 0.458842 0.888518i \(-0.348264\pi\)
0.458842 + 0.888518i \(0.348264\pi\)
\(810\) 0 0
\(811\) −34.3946 −1.20776 −0.603880 0.797076i \(-0.706379\pi\)
−0.603880 + 0.797076i \(0.706379\pi\)
\(812\) −2.27790 −0.0799385
\(813\) 37.0948 1.30097
\(814\) 5.40684 0.189510
\(815\) 0 0
\(816\) 21.6193 0.756826
\(817\) 31.0342 1.08575
\(818\) −22.7029 −0.793790
\(819\) −3.92558 −0.137171
\(820\) 0 0
\(821\) 52.9922 1.84944 0.924720 0.380647i \(-0.124299\pi\)
0.924720 + 0.380647i \(0.124299\pi\)
\(822\) −6.99395 −0.243942
\(823\) −20.4286 −0.712095 −0.356047 0.934468i \(-0.615876\pi\)
−0.356047 + 0.934468i \(0.615876\pi\)
\(824\) −8.70318 −0.303189
\(825\) 0 0
\(826\) 16.0798 0.559488
\(827\) 40.8210 1.41949 0.709743 0.704461i \(-0.248811\pi\)
0.709743 + 0.704461i \(0.248811\pi\)
\(828\) −0.991240 −0.0344480
\(829\) 7.89986 0.274374 0.137187 0.990545i \(-0.456194\pi\)
0.137187 + 0.990545i \(0.456194\pi\)
\(830\) 0 0
\(831\) 37.3494 1.29563
\(832\) −48.7078 −1.68864
\(833\) −18.3323 −0.635176
\(834\) 5.01289 0.173582
\(835\) 0 0
\(836\) 0.799762 0.0276604
\(837\) −0.980816 −0.0339019
\(838\) 29.5639 1.02127
\(839\) 45.1697 1.55943 0.779716 0.626133i \(-0.215363\pi\)
0.779716 + 0.626133i \(0.215363\pi\)
\(840\) 0 0
\(841\) 8.93470 0.308093
\(842\) 36.3837 1.25387
\(843\) 47.4491 1.63423
\(844\) 2.75834 0.0949458
\(845\) 0 0
\(846\) −2.78090 −0.0956093
\(847\) −13.5365 −0.465121
\(848\) −34.2606 −1.17651
\(849\) −3.19486 −0.109647
\(850\) 0 0
\(851\) −37.0621 −1.27047
\(852\) −3.24732 −0.111252
\(853\) 33.8378 1.15859 0.579293 0.815120i \(-0.303329\pi\)
0.579293 + 0.815120i \(0.303329\pi\)
\(854\) −14.8687 −0.508797
\(855\) 0 0
\(856\) 44.4750 1.52012
\(857\) 22.0350 0.752701 0.376351 0.926477i \(-0.377179\pi\)
0.376351 + 0.926477i \(0.377179\pi\)
\(858\) −9.54583 −0.325889
\(859\) −43.0953 −1.47039 −0.735197 0.677853i \(-0.762910\pi\)
−0.735197 + 0.677853i \(0.762910\pi\)
\(860\) 0 0
\(861\) 23.4253 0.798333
\(862\) 23.0392 0.784717
\(863\) −41.5592 −1.41469 −0.707347 0.706867i \(-0.750108\pi\)
−0.707347 + 0.706867i \(0.750108\pi\)
\(864\) −7.43751 −0.253029
\(865\) 0 0
\(866\) 9.66022 0.328268
\(867\) 9.83855 0.334135
\(868\) 0.0785910 0.00266755
\(869\) −4.75887 −0.161434
\(870\) 0 0
\(871\) −40.8923 −1.38558
\(872\) −33.5628 −1.13658
\(873\) 0.393263 0.0133099
\(874\) 32.6954 1.10594
\(875\) 0 0
\(876\) −1.60244 −0.0541413
\(877\) 41.5051 1.40153 0.700763 0.713394i \(-0.252843\pi\)
0.700763 + 0.713394i \(0.252843\pi\)
\(878\) −2.84060 −0.0958655
\(879\) −40.1110 −1.35291
\(880\) 0 0
\(881\) 5.22392 0.175998 0.0879991 0.996121i \(-0.471953\pi\)
0.0879991 + 0.996121i \(0.471953\pi\)
\(882\) 3.84795 0.129567
\(883\) −31.9624 −1.07562 −0.537810 0.843066i \(-0.680748\pi\)
−0.537810 + 0.843066i \(0.680748\pi\)
\(884\) 5.45847 0.183588
\(885\) 0 0
\(886\) −16.6244 −0.558509
\(887\) 26.7513 0.898222 0.449111 0.893476i \(-0.351741\pi\)
0.449111 + 0.893476i \(0.351741\pi\)
\(888\) 33.3367 1.11871
\(889\) −16.4869 −0.552952
\(890\) 0 0
\(891\) −7.23326 −0.242323
\(892\) −6.28690 −0.210501
\(893\) −15.3799 −0.514669
\(894\) 51.8504 1.73414
\(895\) 0 0
\(896\) −10.6730 −0.356561
\(897\) 65.4335 2.18476
\(898\) 5.63837 0.188155
\(899\) −1.30881 −0.0436512
\(900\) 0 0
\(901\) 35.1711 1.17172
\(902\) 8.83116 0.294045
\(903\) 18.9017 0.629008
\(904\) 47.2210 1.57055
\(905\) 0 0
\(906\) 13.1354 0.436393
\(907\) −23.1619 −0.769078 −0.384539 0.923109i \(-0.625640\pi\)
−0.384539 + 0.923109i \(0.625640\pi\)
\(908\) −7.34530 −0.243762
\(909\) −1.27346 −0.0422378
\(910\) 0 0
\(911\) 49.1366 1.62797 0.813984 0.580888i \(-0.197294\pi\)
0.813984 + 0.580888i \(0.197294\pi\)
\(912\) −25.0970 −0.831046
\(913\) 11.2676 0.372905
\(914\) 4.82083 0.159459
\(915\) 0 0
\(916\) −5.06654 −0.167403
\(917\) −1.57724 −0.0520849
\(918\) −20.7315 −0.684241
\(919\) −52.6144 −1.73559 −0.867794 0.496923i \(-0.834463\pi\)
−0.867794 + 0.496923i \(0.834463\pi\)
\(920\) 0 0
\(921\) 32.9786 1.08668
\(922\) −48.8450 −1.60862
\(923\) 33.2330 1.09388
\(924\) 0.487102 0.0160245
\(925\) 0 0
\(926\) 16.2736 0.534782
\(927\) −1.60039 −0.0525636
\(928\) −9.92466 −0.325793
\(929\) 11.0619 0.362930 0.181465 0.983397i \(-0.441916\pi\)
0.181465 + 0.983397i \(0.441916\pi\)
\(930\) 0 0
\(931\) 21.2813 0.697466
\(932\) −2.79867 −0.0916735
\(933\) 51.0839 1.67241
\(934\) −4.85877 −0.158984
\(935\) 0 0
\(936\) −9.12463 −0.298248
\(937\) 47.7232 1.55905 0.779525 0.626371i \(-0.215461\pi\)
0.779525 + 0.626371i \(0.215461\pi\)
\(938\) −12.4448 −0.406336
\(939\) 10.2431 0.334270
\(940\) 0 0
\(941\) −7.26848 −0.236946 −0.118473 0.992957i \(-0.537800\pi\)
−0.118473 + 0.992957i \(0.537800\pi\)
\(942\) −41.4338 −1.34999
\(943\) −60.5346 −1.97128
\(944\) 31.8959 1.03812
\(945\) 0 0
\(946\) 7.12577 0.231679
\(947\) −42.4508 −1.37947 −0.689734 0.724063i \(-0.742272\pi\)
−0.689734 + 0.724063i \(0.742272\pi\)
\(948\) −3.68426 −0.119659
\(949\) 16.3993 0.532343
\(950\) 0 0
\(951\) −2.33688 −0.0757787
\(952\) 13.2297 0.428776
\(953\) −31.8336 −1.03119 −0.515596 0.856832i \(-0.672429\pi\)
−0.515596 + 0.856832i \(0.672429\pi\)
\(954\) −7.38242 −0.239015
\(955\) 0 0
\(956\) 8.36651 0.270592
\(957\) −8.11190 −0.262221
\(958\) 42.9753 1.38847
\(959\) −3.65236 −0.117941
\(960\) 0 0
\(961\) −30.9548 −0.998543
\(962\) −42.8385 −1.38117
\(963\) 8.17830 0.263542
\(964\) −0.287190 −0.00924978
\(965\) 0 0
\(966\) 19.9134 0.640703
\(967\) 1.98161 0.0637242 0.0318621 0.999492i \(-0.489856\pi\)
0.0318621 + 0.999492i \(0.489856\pi\)
\(968\) −31.4643 −1.01130
\(969\) 25.7640 0.827660
\(970\) 0 0
\(971\) −24.3073 −0.780057 −0.390029 0.920803i \(-0.627535\pi\)
−0.390029 + 0.920803i \(0.627535\pi\)
\(972\) −1.62322 −0.0520647
\(973\) 2.61781 0.0839232
\(974\) 35.4812 1.13689
\(975\) 0 0
\(976\) −29.4936 −0.944068
\(977\) −22.5696 −0.722064 −0.361032 0.932553i \(-0.617576\pi\)
−0.361032 + 0.932553i \(0.617576\pi\)
\(978\) −15.5043 −0.495772
\(979\) 1.22216 0.0390603
\(980\) 0 0
\(981\) −6.17171 −0.197048
\(982\) 8.77946 0.280164
\(983\) −27.4009 −0.873953 −0.436976 0.899473i \(-0.643951\pi\)
−0.436976 + 0.899473i \(0.643951\pi\)
\(984\) 54.4499 1.73580
\(985\) 0 0
\(986\) −27.6643 −0.881009
\(987\) −9.36727 −0.298164
\(988\) −6.33653 −0.201592
\(989\) −48.8448 −1.55317
\(990\) 0 0
\(991\) −39.0711 −1.24114 −0.620568 0.784153i \(-0.713098\pi\)
−0.620568 + 0.784153i \(0.713098\pi\)
\(992\) 0.342416 0.0108717
\(993\) 25.6871 0.815154
\(994\) 10.1138 0.320791
\(995\) 0 0
\(996\) 8.72329 0.276408
\(997\) 55.0824 1.74448 0.872239 0.489080i \(-0.162667\pi\)
0.872239 + 0.489080i \(0.162667\pi\)
\(998\) 44.4678 1.40760
\(999\) −27.2807 −0.863123
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 6025.2.a.p.1.14 46
5.2 odd 4 1205.2.b.c.724.14 46
5.3 odd 4 1205.2.b.c.724.33 yes 46
5.4 even 2 inner 6025.2.a.p.1.33 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.14 46 5.2 odd 4
1205.2.b.c.724.33 yes 46 5.3 odd 4
6025.2.a.p.1.14 46 1.1 even 1 trivial
6025.2.a.p.1.33 46 5.4 even 2 inner