Properties

Label 195.2.a.e.1.1
Level $195$
Weight $2$
Character 195.1
Self dual yes
Analytic conductor $1.557$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.55708283941\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Defining polynomial: \( x^{3} - x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.34292\) of defining polynomial
Character \(\chi\) \(=\) 195.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.48929 q^{2} -1.00000 q^{3} +4.19656 q^{4} -1.00000 q^{5} +2.48929 q^{6} -1.19656 q^{7} -5.46787 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.48929 q^{2} -1.00000 q^{3} +4.19656 q^{4} -1.00000 q^{5} +2.48929 q^{6} -1.19656 q^{7} -5.46787 q^{8} +1.00000 q^{9} +2.48929 q^{10} -1.19656 q^{11} -4.19656 q^{12} +1.00000 q^{13} +2.97858 q^{14} +1.00000 q^{15} +5.21798 q^{16} +6.17513 q^{17} -2.48929 q^{18} +6.97858 q^{19} -4.19656 q^{20} +1.19656 q^{21} +2.97858 q^{22} +4.17513 q^{23} +5.46787 q^{24} +1.00000 q^{25} -2.48929 q^{26} -1.00000 q^{27} -5.02142 q^{28} +6.00000 q^{29} -2.48929 q^{30} -2.97858 q^{31} -2.05333 q^{32} +1.19656 q^{33} -15.3717 q^{34} +1.19656 q^{35} +4.19656 q^{36} +7.78202 q^{37} -17.3717 q^{38} -1.00000 q^{39} +5.46787 q^{40} -6.17513 q^{41} -2.97858 q^{42} -9.95715 q^{43} -5.02142 q^{44} -1.00000 q^{45} -10.3931 q^{46} -1.02142 q^{47} -5.21798 q^{48} -5.56825 q^{49} -2.48929 q^{50} -6.17513 q^{51} +4.19656 q^{52} +10.1751 q^{53} +2.48929 q^{54} +1.19656 q^{55} +6.54262 q^{56} -6.97858 q^{57} -14.9357 q^{58} +5.37169 q^{59} +4.19656 q^{60} +12.5682 q^{61} +7.41454 q^{62} -1.19656 q^{63} -5.32464 q^{64} -1.00000 q^{65} -2.97858 q^{66} +9.37169 q^{67} +25.9143 q^{68} -4.17513 q^{69} -2.97858 q^{70} -5.19656 q^{71} -5.46787 q^{72} -11.9572 q^{73} -19.3717 q^{74} -1.00000 q^{75} +29.2860 q^{76} +1.43175 q^{77} +2.48929 q^{78} -1.78202 q^{79} -5.21798 q^{80} +1.00000 q^{81} +15.3717 q^{82} -5.37169 q^{83} +5.02142 q^{84} -6.17513 q^{85} +24.7862 q^{86} -6.00000 q^{87} +6.54262 q^{88} +10.1751 q^{89} +2.48929 q^{90} -1.19656 q^{91} +17.5212 q^{92} +2.97858 q^{93} +2.54262 q^{94} -6.97858 q^{95} +2.05333 q^{96} -1.82487 q^{97} +13.8610 q^{98} -1.19656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + q^{11} - 8 q^{12} + 3 q^{13} - 6 q^{14} + 3 q^{15} + 26 q^{16} - q^{17} + 6 q^{19} - 8 q^{20} - q^{21} - 6 q^{22} - 7 q^{23} - 6 q^{24} + 3 q^{25} - 3 q^{27} - 30 q^{28} + 18 q^{29} + 6 q^{31} + 22 q^{32} - q^{33} - 22 q^{34} - q^{35} + 8 q^{36} + 13 q^{37} - 28 q^{38} - 3 q^{39} - 6 q^{40} + q^{41} + 6 q^{42} - 30 q^{44} - 3 q^{45} - 22 q^{46} - 18 q^{47} - 26 q^{48} + 12 q^{49} + q^{51} + 8 q^{52} + 11 q^{53} - q^{55} - 16 q^{56} - 6 q^{57} - 8 q^{59} + 8 q^{60} + 9 q^{61} + 28 q^{62} + q^{63} + 30 q^{64} - 3 q^{65} + 6 q^{66} + 4 q^{67} + 18 q^{68} + 7 q^{69} + 6 q^{70} - 11 q^{71} + 6 q^{72} - 6 q^{73} - 34 q^{74} - 3 q^{75} + 4 q^{76} + 33 q^{77} + 5 q^{79} - 26 q^{80} + 3 q^{81} + 22 q^{82} + 8 q^{83} + 30 q^{84} + q^{85} + 56 q^{86} - 18 q^{87} - 16 q^{88} + 11 q^{89} + q^{91} + 2 q^{92} - 6 q^{93} - 28 q^{94} - 6 q^{95} - 22 q^{96} - 25 q^{97} + 10 q^{98} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48929 −1.76019 −0.880096 0.474795i \(-0.842522\pi\)
−0.880096 + 0.474795i \(0.842522\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.19656 2.09828
\(5\) −1.00000 −0.447214
\(6\) 2.48929 1.01625
\(7\) −1.19656 −0.452256 −0.226128 0.974098i \(-0.572607\pi\)
−0.226128 + 0.974098i \(0.572607\pi\)
\(8\) −5.46787 −1.93318
\(9\) 1.00000 0.333333
\(10\) 2.48929 0.787182
\(11\) −1.19656 −0.360776 −0.180388 0.983596i \(-0.557735\pi\)
−0.180388 + 0.983596i \(0.557735\pi\)
\(12\) −4.19656 −1.21144
\(13\) 1.00000 0.277350
\(14\) 2.97858 0.796058
\(15\) 1.00000 0.258199
\(16\) 5.21798 1.30450
\(17\) 6.17513 1.49769 0.748845 0.662745i \(-0.230609\pi\)
0.748845 + 0.662745i \(0.230609\pi\)
\(18\) −2.48929 −0.586731
\(19\) 6.97858 1.60100 0.800498 0.599336i \(-0.204569\pi\)
0.800498 + 0.599336i \(0.204569\pi\)
\(20\) −4.19656 −0.938379
\(21\) 1.19656 0.261110
\(22\) 2.97858 0.635035
\(23\) 4.17513 0.870576 0.435288 0.900291i \(-0.356647\pi\)
0.435288 + 0.900291i \(0.356647\pi\)
\(24\) 5.46787 1.11612
\(25\) 1.00000 0.200000
\(26\) −2.48929 −0.488190
\(27\) −1.00000 −0.192450
\(28\) −5.02142 −0.948960
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −2.48929 −0.454480
\(31\) −2.97858 −0.534968 −0.267484 0.963562i \(-0.586192\pi\)
−0.267484 + 0.963562i \(0.586192\pi\)
\(32\) −2.05333 −0.362980
\(33\) 1.19656 0.208294
\(34\) −15.3717 −2.63622
\(35\) 1.19656 0.202255
\(36\) 4.19656 0.699426
\(37\) 7.78202 1.27936 0.639678 0.768643i \(-0.279068\pi\)
0.639678 + 0.768643i \(0.279068\pi\)
\(38\) −17.3717 −2.81806
\(39\) −1.00000 −0.160128
\(40\) 5.46787 0.864545
\(41\) −6.17513 −0.964394 −0.482197 0.876063i \(-0.660161\pi\)
−0.482197 + 0.876063i \(0.660161\pi\)
\(42\) −2.97858 −0.459604
\(43\) −9.95715 −1.51845 −0.759226 0.650827i \(-0.774422\pi\)
−0.759226 + 0.650827i \(0.774422\pi\)
\(44\) −5.02142 −0.757008
\(45\) −1.00000 −0.149071
\(46\) −10.3931 −1.53238
\(47\) −1.02142 −0.148990 −0.0744949 0.997221i \(-0.523734\pi\)
−0.0744949 + 0.997221i \(0.523734\pi\)
\(48\) −5.21798 −0.753151
\(49\) −5.56825 −0.795464
\(50\) −2.48929 −0.352039
\(51\) −6.17513 −0.864692
\(52\) 4.19656 0.581958
\(53\) 10.1751 1.39766 0.698831 0.715287i \(-0.253704\pi\)
0.698831 + 0.715287i \(0.253704\pi\)
\(54\) 2.48929 0.338749
\(55\) 1.19656 0.161344
\(56\) 6.54262 0.874294
\(57\) −6.97858 −0.924335
\(58\) −14.9357 −1.96116
\(59\) 5.37169 0.699335 0.349667 0.936874i \(-0.386295\pi\)
0.349667 + 0.936874i \(0.386295\pi\)
\(60\) 4.19656 0.541773
\(61\) 12.5682 1.60920 0.804600 0.593818i \(-0.202380\pi\)
0.804600 + 0.593818i \(0.202380\pi\)
\(62\) 7.41454 0.941647
\(63\) −1.19656 −0.150752
\(64\) −5.32464 −0.665579
\(65\) −1.00000 −0.124035
\(66\) −2.97858 −0.366638
\(67\) 9.37169 1.14493 0.572467 0.819928i \(-0.305986\pi\)
0.572467 + 0.819928i \(0.305986\pi\)
\(68\) 25.9143 3.14257
\(69\) −4.17513 −0.502627
\(70\) −2.97858 −0.356008
\(71\) −5.19656 −0.616718 −0.308359 0.951270i \(-0.599780\pi\)
−0.308359 + 0.951270i \(0.599780\pi\)
\(72\) −5.46787 −0.644394
\(73\) −11.9572 −1.39948 −0.699740 0.714398i \(-0.746701\pi\)
−0.699740 + 0.714398i \(0.746701\pi\)
\(74\) −19.3717 −2.25191
\(75\) −1.00000 −0.115470
\(76\) 29.2860 3.35933
\(77\) 1.43175 0.163163
\(78\) 2.48929 0.281856
\(79\) −1.78202 −0.200493 −0.100246 0.994963i \(-0.531963\pi\)
−0.100246 + 0.994963i \(0.531963\pi\)
\(80\) −5.21798 −0.583388
\(81\) 1.00000 0.111111
\(82\) 15.3717 1.69752
\(83\) −5.37169 −0.589620 −0.294810 0.955556i \(-0.595256\pi\)
−0.294810 + 0.955556i \(0.595256\pi\)
\(84\) 5.02142 0.547882
\(85\) −6.17513 −0.669787
\(86\) 24.7862 2.67277
\(87\) −6.00000 −0.643268
\(88\) 6.54262 0.697445
\(89\) 10.1751 1.07856 0.539281 0.842126i \(-0.318696\pi\)
0.539281 + 0.842126i \(0.318696\pi\)
\(90\) 2.48929 0.262394
\(91\) −1.19656 −0.125433
\(92\) 17.5212 1.82671
\(93\) 2.97858 0.308864
\(94\) 2.54262 0.262251
\(95\) −6.97858 −0.715987
\(96\) 2.05333 0.209567
\(97\) −1.82487 −0.185287 −0.0926435 0.995699i \(-0.529532\pi\)
−0.0926435 + 0.995699i \(0.529532\pi\)
\(98\) 13.8610 1.40017
\(99\) −1.19656 −0.120259
\(100\) 4.19656 0.419656
\(101\) −10.3503 −1.02989 −0.514945 0.857223i \(-0.672188\pi\)
−0.514945 + 0.857223i \(0.672188\pi\)
\(102\) 15.3717 1.52202
\(103\) 18.7434 1.84684 0.923420 0.383790i \(-0.125381\pi\)
0.923420 + 0.383790i \(0.125381\pi\)
\(104\) −5.46787 −0.536168
\(105\) −1.19656 −0.116772
\(106\) −25.3288 −2.46016
\(107\) −18.5682 −1.79506 −0.897530 0.440953i \(-0.854641\pi\)
−0.897530 + 0.440953i \(0.854641\pi\)
\(108\) −4.19656 −0.403814
\(109\) 8.39312 0.803915 0.401957 0.915658i \(-0.368330\pi\)
0.401957 + 0.915658i \(0.368330\pi\)
\(110\) −2.97858 −0.283996
\(111\) −7.78202 −0.738637
\(112\) −6.24361 −0.589966
\(113\) 7.95715 0.748546 0.374273 0.927319i \(-0.377892\pi\)
0.374273 + 0.927319i \(0.377892\pi\)
\(114\) 17.3717 1.62701
\(115\) −4.17513 −0.389333
\(116\) 25.1793 2.33784
\(117\) 1.00000 0.0924500
\(118\) −13.3717 −1.23096
\(119\) −7.38890 −0.677340
\(120\) −5.46787 −0.499146
\(121\) −9.56825 −0.869841
\(122\) −31.2860 −2.83250
\(123\) 6.17513 0.556793
\(124\) −12.4998 −1.12251
\(125\) −1.00000 −0.0894427
\(126\) 2.97858 0.265353
\(127\) −10.3931 −0.922240 −0.461120 0.887338i \(-0.652552\pi\)
−0.461120 + 0.887338i \(0.652552\pi\)
\(128\) 17.3612 1.53453
\(129\) 9.95715 0.876679
\(130\) 2.48929 0.218325
\(131\) −6.39312 −0.558569 −0.279285 0.960208i \(-0.590097\pi\)
−0.279285 + 0.960208i \(0.590097\pi\)
\(132\) 5.02142 0.437059
\(133\) −8.35027 −0.724060
\(134\) −23.3288 −2.01531
\(135\) 1.00000 0.0860663
\(136\) −33.7648 −2.89531
\(137\) 16.7434 1.43048 0.715242 0.698877i \(-0.246316\pi\)
0.715242 + 0.698877i \(0.246316\pi\)
\(138\) 10.3931 0.884721
\(139\) 5.78202 0.490424 0.245212 0.969469i \(-0.421142\pi\)
0.245212 + 0.969469i \(0.421142\pi\)
\(140\) 5.02142 0.424388
\(141\) 1.02142 0.0860193
\(142\) 12.9357 1.08554
\(143\) −1.19656 −0.100061
\(144\) 5.21798 0.434832
\(145\) −6.00000 −0.498273
\(146\) 29.7648 2.46335
\(147\) 5.56825 0.459262
\(148\) 32.6577 2.68445
\(149\) 15.3461 1.25720 0.628599 0.777730i \(-0.283629\pi\)
0.628599 + 0.777730i \(0.283629\pi\)
\(150\) 2.48929 0.203250
\(151\) −8.58546 −0.698675 −0.349337 0.936997i \(-0.613593\pi\)
−0.349337 + 0.936997i \(0.613593\pi\)
\(152\) −38.1579 −3.09502
\(153\) 6.17513 0.499230
\(154\) −3.56404 −0.287198
\(155\) 2.97858 0.239245
\(156\) −4.19656 −0.335994
\(157\) 2.78623 0.222365 0.111183 0.993800i \(-0.464536\pi\)
0.111183 + 0.993800i \(0.464536\pi\)
\(158\) 4.43596 0.352906
\(159\) −10.1751 −0.806941
\(160\) 2.05333 0.162330
\(161\) −4.99579 −0.393723
\(162\) −2.48929 −0.195577
\(163\) 8.76060 0.686183 0.343091 0.939302i \(-0.388526\pi\)
0.343091 + 0.939302i \(0.388526\pi\)
\(164\) −25.9143 −2.02357
\(165\) −1.19656 −0.0931519
\(166\) 13.3717 1.03784
\(167\) −17.3717 −1.34426 −0.672131 0.740432i \(-0.734621\pi\)
−0.672131 + 0.740432i \(0.734621\pi\)
\(168\) −6.54262 −0.504774
\(169\) 1.00000 0.0769231
\(170\) 15.3717 1.17895
\(171\) 6.97858 0.533665
\(172\) −41.7858 −3.18614
\(173\) −7.95715 −0.604971 −0.302486 0.953154i \(-0.597816\pi\)
−0.302486 + 0.953154i \(0.597816\pi\)
\(174\) 14.9357 1.13227
\(175\) −1.19656 −0.0904513
\(176\) −6.24361 −0.470630
\(177\) −5.37169 −0.403761
\(178\) −25.3288 −1.89848
\(179\) −15.5640 −1.16331 −0.581655 0.813435i \(-0.697595\pi\)
−0.581655 + 0.813435i \(0.697595\pi\)
\(180\) −4.19656 −0.312793
\(181\) 15.7820 1.17307 0.586534 0.809925i \(-0.300492\pi\)
0.586534 + 0.809925i \(0.300492\pi\)
\(182\) 2.97858 0.220787
\(183\) −12.5682 −0.929072
\(184\) −22.8291 −1.68298
\(185\) −7.78202 −0.572145
\(186\) −7.41454 −0.543660
\(187\) −7.38890 −0.540330
\(188\) −4.28646 −0.312622
\(189\) 1.19656 0.0870368
\(190\) 17.3717 1.26028
\(191\) 10.7434 0.777364 0.388682 0.921372i \(-0.372930\pi\)
0.388682 + 0.921372i \(0.372930\pi\)
\(192\) 5.32464 0.384272
\(193\) 9.73917 0.701041 0.350521 0.936555i \(-0.386005\pi\)
0.350521 + 0.936555i \(0.386005\pi\)
\(194\) 4.54262 0.326141
\(195\) 1.00000 0.0716115
\(196\) −23.3675 −1.66911
\(197\) −9.56404 −0.681410 −0.340705 0.940170i \(-0.610666\pi\)
−0.340705 + 0.940170i \(0.610666\pi\)
\(198\) 2.97858 0.211678
\(199\) 5.95715 0.422291 0.211146 0.977455i \(-0.432281\pi\)
0.211146 + 0.977455i \(0.432281\pi\)
\(200\) −5.46787 −0.386636
\(201\) −9.37169 −0.661028
\(202\) 25.7648 1.81281
\(203\) −7.17935 −0.503891
\(204\) −25.9143 −1.81436
\(205\) 6.17513 0.431290
\(206\) −46.6577 −3.25080
\(207\) 4.17513 0.290192
\(208\) 5.21798 0.361802
\(209\) −8.35027 −0.577600
\(210\) 2.97858 0.205541
\(211\) 23.9143 1.64633 0.823164 0.567803i \(-0.192206\pi\)
0.823164 + 0.567803i \(0.192206\pi\)
\(212\) 42.7005 2.93269
\(213\) 5.19656 0.356062
\(214\) 46.2217 3.15965
\(215\) 9.95715 0.679072
\(216\) 5.46787 0.372041
\(217\) 3.56404 0.241943
\(218\) −20.8929 −1.41504
\(219\) 11.9572 0.807990
\(220\) 5.02142 0.338544
\(221\) 6.17513 0.415385
\(222\) 19.3717 1.30014
\(223\) 2.62831 0.176004 0.0880022 0.996120i \(-0.471952\pi\)
0.0880022 + 0.996120i \(0.471952\pi\)
\(224\) 2.45692 0.164160
\(225\) 1.00000 0.0666667
\(226\) −19.8077 −1.31759
\(227\) 15.7648 1.04635 0.523174 0.852226i \(-0.324748\pi\)
0.523174 + 0.852226i \(0.324748\pi\)
\(228\) −29.2860 −1.93951
\(229\) 8.74338 0.577779 0.288890 0.957362i \(-0.406714\pi\)
0.288890 + 0.957362i \(0.406714\pi\)
\(230\) 10.3931 0.685302
\(231\) −1.43175 −0.0942022
\(232\) −32.8072 −2.15390
\(233\) −2.17513 −0.142498 −0.0712489 0.997459i \(-0.522698\pi\)
−0.0712489 + 0.997459i \(0.522698\pi\)
\(234\) −2.48929 −0.162730
\(235\) 1.02142 0.0666303
\(236\) 22.5426 1.46740
\(237\) 1.78202 0.115755
\(238\) 18.3931 1.19225
\(239\) 2.80344 0.181340 0.0906698 0.995881i \(-0.471099\pi\)
0.0906698 + 0.995881i \(0.471099\pi\)
\(240\) 5.21798 0.336819
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 23.8181 1.53109
\(243\) −1.00000 −0.0641500
\(244\) 52.7434 3.37655
\(245\) 5.56825 0.355742
\(246\) −15.3717 −0.980063
\(247\) 6.97858 0.444036
\(248\) 16.2865 1.03419
\(249\) 5.37169 0.340417
\(250\) 2.48929 0.157436
\(251\) −23.9143 −1.50946 −0.754729 0.656037i \(-0.772232\pi\)
−0.754729 + 0.656037i \(0.772232\pi\)
\(252\) −5.02142 −0.316320
\(253\) −4.99579 −0.314083
\(254\) 25.8715 1.62332
\(255\) 6.17513 0.386702
\(256\) −32.5678 −2.03549
\(257\) −19.9572 −1.24489 −0.622447 0.782662i \(-0.713861\pi\)
−0.622447 + 0.782662i \(0.713861\pi\)
\(258\) −24.7862 −1.54312
\(259\) −9.31163 −0.578597
\(260\) −4.19656 −0.260259
\(261\) 6.00000 0.371391
\(262\) 15.9143 0.983189
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) −6.54262 −0.402670
\(265\) −10.1751 −0.625054
\(266\) 20.7862 1.27449
\(267\) −10.1751 −0.622708
\(268\) 39.3288 2.40239
\(269\) −2.35027 −0.143298 −0.0716492 0.997430i \(-0.522826\pi\)
−0.0716492 + 0.997430i \(0.522826\pi\)
\(270\) −2.48929 −0.151493
\(271\) 10.9786 0.666901 0.333451 0.942768i \(-0.391787\pi\)
0.333451 + 0.942768i \(0.391787\pi\)
\(272\) 32.2217 1.95373
\(273\) 1.19656 0.0724190
\(274\) −41.6791 −2.51793
\(275\) −1.19656 −0.0721551
\(276\) −17.5212 −1.05465
\(277\) 1.21377 0.0729283 0.0364642 0.999335i \(-0.488391\pi\)
0.0364642 + 0.999335i \(0.488391\pi\)
\(278\) −14.3931 −0.863242
\(279\) −2.97858 −0.178323
\(280\) −6.54262 −0.390996
\(281\) 11.9572 0.713304 0.356652 0.934237i \(-0.383918\pi\)
0.356652 + 0.934237i \(0.383918\pi\)
\(282\) −2.54262 −0.151411
\(283\) −29.8715 −1.77567 −0.887837 0.460158i \(-0.847793\pi\)
−0.887837 + 0.460158i \(0.847793\pi\)
\(284\) −21.8077 −1.29405
\(285\) 6.97858 0.413375
\(286\) 2.97858 0.176127
\(287\) 7.38890 0.436153
\(288\) −2.05333 −0.120993
\(289\) 21.1323 1.24308
\(290\) 14.9357 0.877056
\(291\) 1.82487 0.106975
\(292\) −50.1789 −2.93650
\(293\) 0.777809 0.0454401 0.0227200 0.999742i \(-0.492767\pi\)
0.0227200 + 0.999742i \(0.492767\pi\)
\(294\) −13.8610 −0.808389
\(295\) −5.37169 −0.312752
\(296\) −42.5510 −2.47323
\(297\) 1.19656 0.0694313
\(298\) −38.2008 −2.21291
\(299\) 4.17513 0.241454
\(300\) −4.19656 −0.242288
\(301\) 11.9143 0.686729
\(302\) 21.3717 1.22980
\(303\) 10.3503 0.594607
\(304\) 36.4141 2.08849
\(305\) −12.5682 −0.719656
\(306\) −15.3717 −0.878741
\(307\) 0.760597 0.0434095 0.0217048 0.999764i \(-0.493091\pi\)
0.0217048 + 0.999764i \(0.493091\pi\)
\(308\) 6.00842 0.342362
\(309\) −18.7434 −1.06627
\(310\) −7.41454 −0.421117
\(311\) −23.1281 −1.31147 −0.655736 0.754990i \(-0.727642\pi\)
−0.655736 + 0.754990i \(0.727642\pi\)
\(312\) 5.46787 0.309557
\(313\) −33.9143 −1.91695 −0.958475 0.285176i \(-0.907948\pi\)
−0.958475 + 0.285176i \(0.907948\pi\)
\(314\) −6.93573 −0.391406
\(315\) 1.19656 0.0674184
\(316\) −7.47835 −0.420690
\(317\) 9.64973 0.541983 0.270991 0.962582i \(-0.412648\pi\)
0.270991 + 0.962582i \(0.412648\pi\)
\(318\) 25.3288 1.42037
\(319\) −7.17935 −0.401966
\(320\) 5.32464 0.297656
\(321\) 18.5682 1.03638
\(322\) 12.4360 0.693029
\(323\) 43.0937 2.39780
\(324\) 4.19656 0.233142
\(325\) 1.00000 0.0554700
\(326\) −21.8077 −1.20781
\(327\) −8.39312 −0.464140
\(328\) 33.7648 1.86435
\(329\) 1.22219 0.0673816
\(330\) 2.97858 0.163965
\(331\) 15.3288 0.842550 0.421275 0.906933i \(-0.361583\pi\)
0.421275 + 0.906933i \(0.361583\pi\)
\(332\) −22.5426 −1.23719
\(333\) 7.78202 0.426452
\(334\) 43.2432 2.36616
\(335\) −9.37169 −0.512030
\(336\) 6.24361 0.340617
\(337\) −22.3503 −1.21750 −0.608748 0.793363i \(-0.708328\pi\)
−0.608748 + 0.793363i \(0.708328\pi\)
\(338\) −2.48929 −0.135399
\(339\) −7.95715 −0.432173
\(340\) −25.9143 −1.40540
\(341\) 3.56404 0.193004
\(342\) −17.3717 −0.939354
\(343\) 15.0386 0.812010
\(344\) 54.4444 2.93544
\(345\) 4.17513 0.224782
\(346\) 19.8077 1.06487
\(347\) −5.78202 −0.310395 −0.155198 0.987883i \(-0.549601\pi\)
−0.155198 + 0.987883i \(0.549601\pi\)
\(348\) −25.1793 −1.34975
\(349\) −27.5212 −1.47318 −0.736588 0.676342i \(-0.763564\pi\)
−0.736588 + 0.676342i \(0.763564\pi\)
\(350\) 2.97858 0.159212
\(351\) −1.00000 −0.0533761
\(352\) 2.45692 0.130955
\(353\) −28.7434 −1.52986 −0.764928 0.644116i \(-0.777225\pi\)
−0.764928 + 0.644116i \(0.777225\pi\)
\(354\) 13.3717 0.710697
\(355\) 5.19656 0.275805
\(356\) 42.7005 2.26312
\(357\) 7.38890 0.391062
\(358\) 38.7434 2.04765
\(359\) −12.5855 −0.664235 −0.332118 0.943238i \(-0.607763\pi\)
−0.332118 + 0.943238i \(0.607763\pi\)
\(360\) 5.46787 0.288182
\(361\) 29.7005 1.56319
\(362\) −39.2860 −2.06483
\(363\) 9.56825 0.502203
\(364\) −5.02142 −0.263194
\(365\) 11.9572 0.625866
\(366\) 31.2860 1.63535
\(367\) −27.9143 −1.45712 −0.728558 0.684985i \(-0.759809\pi\)
−0.728558 + 0.684985i \(0.759809\pi\)
\(368\) 21.7858 1.13566
\(369\) −6.17513 −0.321465
\(370\) 19.3717 1.00709
\(371\) −12.1751 −0.632102
\(372\) 12.4998 0.648083
\(373\) −2.35027 −0.121692 −0.0608462 0.998147i \(-0.519380\pi\)
−0.0608462 + 0.998147i \(0.519380\pi\)
\(374\) 18.3931 0.951085
\(375\) 1.00000 0.0516398
\(376\) 5.58500 0.288025
\(377\) 6.00000 0.309016
\(378\) −2.97858 −0.153201
\(379\) 24.5510 1.26110 0.630551 0.776148i \(-0.282829\pi\)
0.630551 + 0.776148i \(0.282829\pi\)
\(380\) −29.2860 −1.50234
\(381\) 10.3931 0.532455
\(382\) −26.7434 −1.36831
\(383\) 5.80765 0.296757 0.148379 0.988931i \(-0.452595\pi\)
0.148379 + 0.988931i \(0.452595\pi\)
\(384\) −17.3612 −0.885961
\(385\) −1.43175 −0.0729687
\(386\) −24.2436 −1.23397
\(387\) −9.95715 −0.506151
\(388\) −7.65815 −0.388784
\(389\) 13.6497 0.692069 0.346034 0.938222i \(-0.387528\pi\)
0.346034 + 0.938222i \(0.387528\pi\)
\(390\) −2.48929 −0.126050
\(391\) 25.7820 1.30385
\(392\) 30.4464 1.53778
\(393\) 6.39312 0.322490
\(394\) 23.8077 1.19941
\(395\) 1.78202 0.0896631
\(396\) −5.02142 −0.252336
\(397\) −12.1323 −0.608902 −0.304451 0.952528i \(-0.598473\pi\)
−0.304451 + 0.952528i \(0.598473\pi\)
\(398\) −14.8291 −0.743314
\(399\) 8.35027 0.418036
\(400\) 5.21798 0.260899
\(401\) −37.4439 −1.86986 −0.934930 0.354832i \(-0.884538\pi\)
−0.934930 + 0.354832i \(0.884538\pi\)
\(402\) 23.3288 1.16354
\(403\) −2.97858 −0.148373
\(404\) −43.4355 −2.16100
\(405\) −1.00000 −0.0496904
\(406\) 17.8715 0.886946
\(407\) −9.31163 −0.461561
\(408\) 33.7648 1.67161
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) −15.3717 −0.759154
\(411\) −16.7434 −0.825890
\(412\) 78.6577 3.87519
\(413\) −6.42754 −0.316279
\(414\) −10.3931 −0.510794
\(415\) 5.37169 0.263686
\(416\) −2.05333 −0.100673
\(417\) −5.78202 −0.283147
\(418\) 20.7862 1.01669
\(419\) 3.17935 0.155321 0.0776606 0.996980i \(-0.475255\pi\)
0.0776606 + 0.996980i \(0.475255\pi\)
\(420\) −5.02142 −0.245020
\(421\) −16.3074 −0.794775 −0.397388 0.917651i \(-0.630083\pi\)
−0.397388 + 0.917651i \(0.630083\pi\)
\(422\) −59.5296 −2.89786
\(423\) −1.02142 −0.0496633
\(424\) −55.6363 −2.70194
\(425\) 6.17513 0.299538
\(426\) −12.9357 −0.626738
\(427\) −15.0386 −0.727771
\(428\) −77.9227 −3.76654
\(429\) 1.19656 0.0577703
\(430\) −24.7862 −1.19530
\(431\) 4.58546 0.220874 0.110437 0.993883i \(-0.464775\pi\)
0.110437 + 0.993883i \(0.464775\pi\)
\(432\) −5.21798 −0.251050
\(433\) −38.3503 −1.84300 −0.921498 0.388383i \(-0.873034\pi\)
−0.921498 + 0.388383i \(0.873034\pi\)
\(434\) −8.87192 −0.425866
\(435\) 6.00000 0.287678
\(436\) 35.2222 1.68684
\(437\) 29.1365 1.39379
\(438\) −29.7648 −1.42222
\(439\) 7.73917 0.369371 0.184685 0.982798i \(-0.440873\pi\)
0.184685 + 0.982798i \(0.440873\pi\)
\(440\) −6.54262 −0.311907
\(441\) −5.56825 −0.265155
\(442\) −15.3717 −0.731157
\(443\) 34.9185 1.65903 0.829514 0.558485i \(-0.188617\pi\)
0.829514 + 0.558485i \(0.188617\pi\)
\(444\) −32.6577 −1.54987
\(445\) −10.1751 −0.482348
\(446\) −6.54262 −0.309802
\(447\) −15.3461 −0.725844
\(448\) 6.37123 0.301012
\(449\) −6.17513 −0.291423 −0.145711 0.989327i \(-0.546547\pi\)
−0.145711 + 0.989327i \(0.546547\pi\)
\(450\) −2.48929 −0.117346
\(451\) 7.38890 0.347930
\(452\) 33.3927 1.57066
\(453\) 8.58546 0.403380
\(454\) −39.2432 −1.84177
\(455\) 1.19656 0.0560955
\(456\) 38.1579 1.78691
\(457\) 1.38890 0.0649702 0.0324851 0.999472i \(-0.489658\pi\)
0.0324851 + 0.999472i \(0.489658\pi\)
\(458\) −21.7648 −1.01700
\(459\) −6.17513 −0.288231
\(460\) −17.5212 −0.816930
\(461\) 28.4826 1.32657 0.663283 0.748369i \(-0.269163\pi\)
0.663283 + 0.748369i \(0.269163\pi\)
\(462\) 3.56404 0.165814
\(463\) 16.3759 0.761053 0.380526 0.924770i \(-0.375743\pi\)
0.380526 + 0.924770i \(0.375743\pi\)
\(464\) 31.3079 1.45343
\(465\) −2.97858 −0.138128
\(466\) 5.41454 0.250824
\(467\) 25.7476 1.19146 0.595728 0.803186i \(-0.296864\pi\)
0.595728 + 0.803186i \(0.296864\pi\)
\(468\) 4.19656 0.193986
\(469\) −11.2138 −0.517804
\(470\) −2.54262 −0.117282
\(471\) −2.78623 −0.128383
\(472\) −29.3717 −1.35194
\(473\) 11.9143 0.547820
\(474\) −4.43596 −0.203750
\(475\) 6.97858 0.320199
\(476\) −31.0080 −1.42125
\(477\) 10.1751 0.465887
\(478\) −6.97858 −0.319193
\(479\) −7.58967 −0.346781 −0.173391 0.984853i \(-0.555472\pi\)
−0.173391 + 0.984853i \(0.555472\pi\)
\(480\) −2.05333 −0.0937212
\(481\) 7.78202 0.354830
\(482\) 14.9357 0.680304
\(483\) 4.99579 0.227316
\(484\) −40.1537 −1.82517
\(485\) 1.82487 0.0828629
\(486\) 2.48929 0.112916
\(487\) 4.41033 0.199851 0.0999255 0.994995i \(-0.468140\pi\)
0.0999255 + 0.994995i \(0.468140\pi\)
\(488\) −68.7215 −3.11088
\(489\) −8.76060 −0.396168
\(490\) −13.8610 −0.626175
\(491\) −0.0856914 −0.00386720 −0.00193360 0.999998i \(-0.500615\pi\)
−0.00193360 + 0.999998i \(0.500615\pi\)
\(492\) 25.9143 1.16831
\(493\) 37.0508 1.66868
\(494\) −17.3717 −0.781589
\(495\) 1.19656 0.0537813
\(496\) −15.5422 −0.697863
\(497\) 6.21798 0.278915
\(498\) −13.3717 −0.599200
\(499\) −17.7220 −0.793344 −0.396672 0.917960i \(-0.629835\pi\)
−0.396672 + 0.917960i \(0.629835\pi\)
\(500\) −4.19656 −0.187676
\(501\) 17.3717 0.776110
\(502\) 59.5296 2.65694
\(503\) −8.70054 −0.387938 −0.193969 0.981008i \(-0.562136\pi\)
−0.193969 + 0.981008i \(0.562136\pi\)
\(504\) 6.54262 0.291431
\(505\) 10.3503 0.460581
\(506\) 12.4360 0.552846
\(507\) −1.00000 −0.0444116
\(508\) −43.6153 −1.93512
\(509\) −33.3545 −1.47841 −0.739206 0.673480i \(-0.764799\pi\)
−0.739206 + 0.673480i \(0.764799\pi\)
\(510\) −15.3717 −0.680670
\(511\) 14.3074 0.632923
\(512\) 46.3482 2.04832
\(513\) −6.97858 −0.308112
\(514\) 49.6791 2.19125
\(515\) −18.7434 −0.825932
\(516\) 41.7858 1.83952
\(517\) 1.22219 0.0537519
\(518\) 23.1793 1.01844
\(519\) 7.95715 0.349280
\(520\) 5.46787 0.239782
\(521\) 18.7005 0.819285 0.409643 0.912246i \(-0.365653\pi\)
0.409643 + 0.912246i \(0.365653\pi\)
\(522\) −14.9357 −0.653719
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −26.8291 −1.17203
\(525\) 1.19656 0.0522221
\(526\) −19.9143 −0.868305
\(527\) −18.3931 −0.801217
\(528\) 6.24361 0.271718
\(529\) −5.56825 −0.242098
\(530\) 25.3288 1.10021
\(531\) 5.37169 0.233112
\(532\) −35.0424 −1.51928
\(533\) −6.17513 −0.267475
\(534\) 25.3288 1.09609
\(535\) 18.5682 0.802775
\(536\) −51.2432 −2.21337
\(537\) 15.5640 0.671638
\(538\) 5.85050 0.252233
\(539\) 6.66273 0.286984
\(540\) 4.19656 0.180591
\(541\) −41.5296 −1.78550 −0.892749 0.450555i \(-0.851226\pi\)
−0.892749 + 0.450555i \(0.851226\pi\)
\(542\) −27.3288 −1.17387
\(543\) −15.7820 −0.677271
\(544\) −12.6796 −0.543632
\(545\) −8.39312 −0.359522
\(546\) −2.97858 −0.127471
\(547\) −7.91431 −0.338391 −0.169196 0.985582i \(-0.554117\pi\)
−0.169196 + 0.985582i \(0.554117\pi\)
\(548\) 70.2646 3.00155
\(549\) 12.5682 0.536400
\(550\) 2.97858 0.127007
\(551\) 41.8715 1.78378
\(552\) 22.8291 0.971670
\(553\) 2.13229 0.0906742
\(554\) −3.02142 −0.128368
\(555\) 7.78202 0.330328
\(556\) 24.2646 1.02905
\(557\) 42.7005 1.80928 0.904640 0.426177i \(-0.140140\pi\)
0.904640 + 0.426177i \(0.140140\pi\)
\(558\) 7.41454 0.313882
\(559\) −9.95715 −0.421143
\(560\) 6.24361 0.263841
\(561\) 7.38890 0.311960
\(562\) −29.7648 −1.25555
\(563\) 1.04706 0.0441282 0.0220641 0.999757i \(-0.492976\pi\)
0.0220641 + 0.999757i \(0.492976\pi\)
\(564\) 4.28646 0.180493
\(565\) −7.95715 −0.334760
\(566\) 74.3587 3.12553
\(567\) −1.19656 −0.0502507
\(568\) 28.4141 1.19223
\(569\) 16.7778 0.703362 0.351681 0.936120i \(-0.385610\pi\)
0.351681 + 0.936120i \(0.385610\pi\)
\(570\) −17.3717 −0.727620
\(571\) −20.6111 −0.862548 −0.431274 0.902221i \(-0.641936\pi\)
−0.431274 + 0.902221i \(0.641936\pi\)
\(572\) −5.02142 −0.209956
\(573\) −10.7434 −0.448811
\(574\) −18.3931 −0.767714
\(575\) 4.17513 0.174115
\(576\) −5.32464 −0.221860
\(577\) 1.38890 0.0578208 0.0289104 0.999582i \(-0.490796\pi\)
0.0289104 + 0.999582i \(0.490796\pi\)
\(578\) −52.6044 −2.18805
\(579\) −9.73917 −0.404746
\(580\) −25.1793 −1.04552
\(581\) 6.42754 0.266659
\(582\) −4.54262 −0.188298
\(583\) −12.1751 −0.504243
\(584\) 65.3801 2.70545
\(585\) −1.00000 −0.0413449
\(586\) −1.93619 −0.0799833
\(587\) −0.935731 −0.0386218 −0.0193109 0.999814i \(-0.506147\pi\)
−0.0193109 + 0.999814i \(0.506147\pi\)
\(588\) 23.3675 0.963659
\(589\) −20.7862 −0.856482
\(590\) 13.3717 0.550504
\(591\) 9.56404 0.393412
\(592\) 40.6064 1.66891
\(593\) −0.478807 −0.0196622 −0.00983112 0.999952i \(-0.503129\pi\)
−0.00983112 + 0.999952i \(0.503129\pi\)
\(594\) −2.97858 −0.122213
\(595\) 7.38890 0.302916
\(596\) 64.4006 2.63795
\(597\) −5.95715 −0.243810
\(598\) −10.3931 −0.425006
\(599\) 29.0852 1.18839 0.594195 0.804321i \(-0.297471\pi\)
0.594195 + 0.804321i \(0.297471\pi\)
\(600\) 5.46787 0.223225
\(601\) 11.4318 0.466311 0.233155 0.972439i \(-0.425095\pi\)
0.233155 + 0.972439i \(0.425095\pi\)
\(602\) −29.6582 −1.20878
\(603\) 9.37169 0.381645
\(604\) −36.0294 −1.46601
\(605\) 9.56825 0.389005
\(606\) −25.7648 −1.04662
\(607\) 27.9143 1.13301 0.566503 0.824059i \(-0.308296\pi\)
0.566503 + 0.824059i \(0.308296\pi\)
\(608\) −14.3293 −0.581130
\(609\) 7.17935 0.290922
\(610\) 31.2860 1.26673
\(611\) −1.02142 −0.0413223
\(612\) 25.9143 1.04752
\(613\) −4.65394 −0.187971 −0.0939855 0.995574i \(-0.529961\pi\)
−0.0939855 + 0.995574i \(0.529961\pi\)
\(614\) −1.89334 −0.0764092
\(615\) −6.17513 −0.249005
\(616\) −7.82862 −0.315424
\(617\) −15.9572 −0.642411 −0.321205 0.947010i \(-0.604088\pi\)
−0.321205 + 0.947010i \(0.604088\pi\)
\(618\) 46.6577 1.87685
\(619\) 1.02142 0.0410545 0.0205272 0.999789i \(-0.493466\pi\)
0.0205272 + 0.999789i \(0.493466\pi\)
\(620\) 12.4998 0.502003
\(621\) −4.17513 −0.167542
\(622\) 57.5725 2.30845
\(623\) −12.1751 −0.487786
\(624\) −5.21798 −0.208886
\(625\) 1.00000 0.0400000
\(626\) 84.4225 3.37420
\(627\) 8.35027 0.333478
\(628\) 11.6926 0.466585
\(629\) 48.0550 1.91608
\(630\) −2.97858 −0.118669
\(631\) −20.4998 −0.816083 −0.408041 0.912963i \(-0.633788\pi\)
−0.408041 + 0.912963i \(0.633788\pi\)
\(632\) 9.74384 0.387589
\(633\) −23.9143 −0.950508
\(634\) −24.0210 −0.953994
\(635\) 10.3931 0.412438
\(636\) −42.7005 −1.69319
\(637\) −5.56825 −0.220622
\(638\) 17.8715 0.707538
\(639\) −5.19656 −0.205573
\(640\) −17.3612 −0.686262
\(641\) 38.2646 1.51136 0.755680 0.654941i \(-0.227307\pi\)
0.755680 + 0.654941i \(0.227307\pi\)
\(642\) −46.2217 −1.82423
\(643\) −33.1109 −1.30577 −0.652883 0.757459i \(-0.726440\pi\)
−0.652883 + 0.757459i \(0.726440\pi\)
\(644\) −20.9651 −0.826141
\(645\) −9.95715 −0.392063
\(646\) −107.273 −4.22058
\(647\) −16.9614 −0.666820 −0.333410 0.942782i \(-0.608199\pi\)
−0.333410 + 0.942782i \(0.608199\pi\)
\(648\) −5.46787 −0.214798
\(649\) −6.42754 −0.252303
\(650\) −2.48929 −0.0976379
\(651\) −3.56404 −0.139686
\(652\) 36.7643 1.43980
\(653\) −19.1709 −0.750216 −0.375108 0.926981i \(-0.622394\pi\)
−0.375108 + 0.926981i \(0.622394\pi\)
\(654\) 20.8929 0.816976
\(655\) 6.39312 0.249800
\(656\) −32.2217 −1.25805
\(657\) −11.9572 −0.466493
\(658\) −3.04239 −0.118605
\(659\) 37.8715 1.47526 0.737631 0.675204i \(-0.235944\pi\)
0.737631 + 0.675204i \(0.235944\pi\)
\(660\) −5.02142 −0.195459
\(661\) 24.3931 0.948782 0.474391 0.880314i \(-0.342668\pi\)
0.474391 + 0.880314i \(0.342668\pi\)
\(662\) −38.1579 −1.48305
\(663\) −6.17513 −0.239822
\(664\) 29.3717 1.13984
\(665\) 8.35027 0.323810
\(666\) −19.3717 −0.750638
\(667\) 25.0508 0.969971
\(668\) −72.9013 −2.82064
\(669\) −2.62831 −0.101616
\(670\) 23.3288 0.901272
\(671\) −15.0386 −0.580560
\(672\) −2.45692 −0.0947779
\(673\) −21.1281 −0.814428 −0.407214 0.913333i \(-0.633500\pi\)
−0.407214 + 0.913333i \(0.633500\pi\)
\(674\) 55.6363 2.14303
\(675\) −1.00000 −0.0384900
\(676\) 4.19656 0.161406
\(677\) −15.3973 −0.591767 −0.295884 0.955224i \(-0.595614\pi\)
−0.295884 + 0.955224i \(0.595614\pi\)
\(678\) 19.8077 0.760708
\(679\) 2.18356 0.0837972
\(680\) 33.7648 1.29482
\(681\) −15.7648 −0.604109
\(682\) −8.87192 −0.339723
\(683\) 30.0722 1.15068 0.575341 0.817914i \(-0.304869\pi\)
0.575341 + 0.817914i \(0.304869\pi\)
\(684\) 29.2860 1.11978
\(685\) −16.7434 −0.639732
\(686\) −37.4355 −1.42929
\(687\) −8.74338 −0.333581
\(688\) −51.9562 −1.98081
\(689\) 10.1751 0.387642
\(690\) −10.3931 −0.395659
\(691\) −8.14950 −0.310022 −0.155011 0.987913i \(-0.549541\pi\)
−0.155011 + 0.987913i \(0.549541\pi\)
\(692\) −33.3927 −1.26940
\(693\) 1.43175 0.0543877
\(694\) 14.3931 0.546355
\(695\) −5.78202 −0.219325
\(696\) 32.8072 1.24355
\(697\) −38.1323 −1.44436
\(698\) 68.5082 2.59307
\(699\) 2.17513 0.0822712
\(700\) −5.02142 −0.189792
\(701\) −28.6921 −1.08369 −0.541843 0.840480i \(-0.682273\pi\)
−0.541843 + 0.840480i \(0.682273\pi\)
\(702\) 2.48929 0.0939521
\(703\) 54.3074 2.04824
\(704\) 6.37123 0.240125
\(705\) −1.02142 −0.0384690
\(706\) 71.5506 2.69284
\(707\) 12.3847 0.465774
\(708\) −22.5426 −0.847203
\(709\) 12.3074 0.462215 0.231108 0.972928i \(-0.425765\pi\)
0.231108 + 0.972928i \(0.425765\pi\)
\(710\) −12.9357 −0.485469
\(711\) −1.78202 −0.0668310
\(712\) −55.6363 −2.08506
\(713\) −12.4360 −0.465730
\(714\) −18.3931 −0.688345
\(715\) 1.19656 0.0447487
\(716\) −65.3154 −2.44095
\(717\) −2.80344 −0.104696
\(718\) 31.3288 1.16918
\(719\) −28.7862 −1.07355 −0.536773 0.843727i \(-0.680357\pi\)
−0.536773 + 0.843727i \(0.680357\pi\)
\(720\) −5.21798 −0.194463
\(721\) −22.4275 −0.835245
\(722\) −73.9332 −2.75151
\(723\) 6.00000 0.223142
\(724\) 66.2302 2.46142
\(725\) 6.00000 0.222834
\(726\) −23.8181 −0.883974
\(727\) 34.3931 1.27557 0.637785 0.770214i \(-0.279851\pi\)
0.637785 + 0.770214i \(0.279851\pi\)
\(728\) 6.54262 0.242485
\(729\) 1.00000 0.0370370
\(730\) −29.7648 −1.10164
\(731\) −61.4868 −2.27417
\(732\) −52.7434 −1.94945
\(733\) −29.0042 −1.07129 −0.535647 0.844442i \(-0.679932\pi\)
−0.535647 + 0.844442i \(0.679932\pi\)
\(734\) 69.4868 2.56480
\(735\) −5.56825 −0.205388
\(736\) −8.57292 −0.316002
\(737\) −11.2138 −0.413065
\(738\) 15.3717 0.565840
\(739\) −6.27804 −0.230941 −0.115471 0.993311i \(-0.536838\pi\)
−0.115471 + 0.993311i \(0.536838\pi\)
\(740\) −32.6577 −1.20052
\(741\) −6.97858 −0.256364
\(742\) 30.3074 1.11262
\(743\) 12.2352 0.448866 0.224433 0.974490i \(-0.427947\pi\)
0.224433 + 0.974490i \(0.427947\pi\)
\(744\) −16.2865 −0.597091
\(745\) −15.3461 −0.562236
\(746\) 5.85050 0.214202
\(747\) −5.37169 −0.196540
\(748\) −31.0080 −1.13376
\(749\) 22.2180 0.811827
\(750\) −2.48929 −0.0908960
\(751\) −28.8757 −1.05369 −0.526844 0.849962i \(-0.676625\pi\)
−0.526844 + 0.849962i \(0.676625\pi\)
\(752\) −5.32976 −0.194357
\(753\) 23.9143 0.871486
\(754\) −14.9357 −0.543927
\(755\) 8.58546 0.312457
\(756\) 5.02142 0.182627
\(757\) 30.3503 1.10310 0.551550 0.834142i \(-0.314037\pi\)
0.551550 + 0.834142i \(0.314037\pi\)
\(758\) −61.1146 −2.21978
\(759\) 4.99579 0.181336
\(760\) 38.1579 1.38413
\(761\) −27.1709 −0.984945 −0.492473 0.870328i \(-0.663907\pi\)
−0.492473 + 0.870328i \(0.663907\pi\)
\(762\) −25.8715 −0.937224
\(763\) −10.0428 −0.363575
\(764\) 45.0852 1.63113
\(765\) −6.17513 −0.223262
\(766\) −14.4569 −0.522350
\(767\) 5.37169 0.193961
\(768\) 32.5678 1.17519
\(769\) −38.3503 −1.38295 −0.691473 0.722402i \(-0.743038\pi\)
−0.691473 + 0.722402i \(0.743038\pi\)
\(770\) 3.56404 0.128439
\(771\) 19.9572 0.718739
\(772\) 40.8710 1.47098
\(773\) −50.2646 −1.80789 −0.903946 0.427647i \(-0.859342\pi\)
−0.903946 + 0.427647i \(0.859342\pi\)
\(774\) 24.7862 0.890923
\(775\) −2.97858 −0.106994
\(776\) 9.97812 0.358194
\(777\) 9.31163 0.334053
\(778\) −33.9781 −1.21817
\(779\) −43.0937 −1.54399
\(780\) 4.19656 0.150261
\(781\) 6.21798 0.222497
\(782\) −64.1789 −2.29503
\(783\) −6.00000 −0.214423
\(784\) −29.0550 −1.03768
\(785\) −2.78623 −0.0994448
\(786\) −15.9143 −0.567645
\(787\) −13.2860 −0.473595 −0.236797 0.971559i \(-0.576098\pi\)
−0.236797 + 0.971559i \(0.576098\pi\)
\(788\) −40.1360 −1.42979
\(789\) −8.00000 −0.284808
\(790\) −4.43596 −0.157824
\(791\) −9.52119 −0.338535
\(792\) 6.54262 0.232482
\(793\) 12.5682 0.446312
\(794\) 30.2008 1.07179
\(795\) 10.1751 0.360875
\(796\) 24.9995 0.886085
\(797\) 9.82487 0.348015 0.174007 0.984744i \(-0.444328\pi\)
0.174007 + 0.984744i \(0.444328\pi\)
\(798\) −20.7862 −0.735825
\(799\) −6.30742 −0.223141
\(800\) −2.05333 −0.0725961
\(801\) 10.1751 0.359521
\(802\) 93.2087 3.29131
\(803\) 14.3074 0.504898
\(804\) −39.3288 −1.38702
\(805\) 4.99579 0.176078
\(806\) 7.41454 0.261166
\(807\) 2.35027 0.0827334
\(808\) 56.5939 1.99097
\(809\) −9.91431 −0.348569 −0.174284 0.984695i \(-0.555761\pi\)
−0.174284 + 0.984695i \(0.555761\pi\)
\(810\) 2.48929 0.0874647
\(811\) −36.5855 −1.28469 −0.642345 0.766416i \(-0.722038\pi\)
−0.642345 + 0.766416i \(0.722038\pi\)
\(812\) −30.1285 −1.05730
\(813\) −10.9786 −0.385036
\(814\) 23.1793 0.812436
\(815\) −8.76060 −0.306870
\(816\) −32.2217 −1.12799
\(817\) −69.4868 −2.43103
\(818\) 34.8500 1.21850
\(819\) −1.19656 −0.0418111
\(820\) 25.9143 0.904967
\(821\) −34.4741 −1.20316 −0.601578 0.798814i \(-0.705461\pi\)
−0.601578 + 0.798814i \(0.705461\pi\)
\(822\) 41.6791 1.45373
\(823\) 13.2566 0.462097 0.231048 0.972942i \(-0.425784\pi\)
0.231048 + 0.972942i \(0.425784\pi\)
\(824\) −102.486 −3.57028
\(825\) 1.19656 0.0416588
\(826\) 16.0000 0.556711
\(827\) 28.1495 0.978854 0.489427 0.872044i \(-0.337206\pi\)
0.489427 + 0.872044i \(0.337206\pi\)
\(828\) 17.5212 0.608904
\(829\) 16.3418 0.567576 0.283788 0.958887i \(-0.408409\pi\)
0.283788 + 0.958887i \(0.408409\pi\)
\(830\) −13.3717 −0.464138
\(831\) −1.21377 −0.0421052
\(832\) −5.32464 −0.184599
\(833\) −34.3847 −1.19136
\(834\) 14.3931 0.498393
\(835\) 17.3717 0.601172
\(836\) −35.0424 −1.21197
\(837\) 2.97858 0.102955
\(838\) −7.91431 −0.273395
\(839\) −30.3675 −1.04840 −0.524201 0.851595i \(-0.675636\pi\)
−0.524201 + 0.851595i \(0.675636\pi\)
\(840\) 6.54262 0.225742
\(841\) 7.00000 0.241379
\(842\) 40.5939 1.39896
\(843\) −11.9572 −0.411826
\(844\) 100.358 3.45446
\(845\) −1.00000 −0.0344010
\(846\) 2.54262 0.0874169
\(847\) 11.4490 0.393391
\(848\) 53.0937 1.82324
\(849\) 29.8715 1.02519
\(850\) −15.3717 −0.527245
\(851\) 32.4910 1.11378
\(852\) 21.8077 0.747118
\(853\) −42.1407 −1.44287 −0.721435 0.692482i \(-0.756517\pi\)
−0.721435 + 0.692482i \(0.756517\pi\)
\(854\) 37.4355 1.28102
\(855\) −6.97858 −0.238662
\(856\) 101.529 3.47018
\(857\) −2.17513 −0.0743012 −0.0371506 0.999310i \(-0.511828\pi\)
−0.0371506 + 0.999310i \(0.511828\pi\)
\(858\) −2.97858 −0.101687
\(859\) 18.5682 0.633541 0.316770 0.948502i \(-0.397402\pi\)
0.316770 + 0.948502i \(0.397402\pi\)
\(860\) 41.7858 1.42488
\(861\) −7.38890 −0.251813
\(862\) −11.4145 −0.388781
\(863\) 33.7220 1.14791 0.573954 0.818887i \(-0.305409\pi\)
0.573954 + 0.818887i \(0.305409\pi\)
\(864\) 2.05333 0.0698556
\(865\) 7.95715 0.270551
\(866\) 95.4649 3.24403
\(867\) −21.1323 −0.717690
\(868\) 14.9567 0.507663
\(869\) 2.13229 0.0723330
\(870\) −14.9357 −0.506369
\(871\) 9.37169 0.317548
\(872\) −45.8924 −1.55411
\(873\) −1.82487 −0.0617623
\(874\) −72.5292 −2.45334
\(875\) 1.19656 0.0404510
\(876\) 50.1789 1.69539
\(877\) 43.4868 1.46844 0.734222 0.678910i \(-0.237547\pi\)
0.734222 + 0.678910i \(0.237547\pi\)
\(878\) −19.2650 −0.650164
\(879\) −0.777809 −0.0262348
\(880\) 6.24361 0.210472
\(881\) 26.7005 0.899564 0.449782 0.893138i \(-0.351502\pi\)
0.449782 + 0.893138i \(0.351502\pi\)
\(882\) 13.8610 0.466724
\(883\) 20.2990 0.683116 0.341558 0.939861i \(-0.389045\pi\)
0.341558 + 0.939861i \(0.389045\pi\)
\(884\) 25.9143 0.871593
\(885\) 5.37169 0.180567
\(886\) −86.9223 −2.92021
\(887\) 36.0550 1.21061 0.605305 0.795994i \(-0.293051\pi\)
0.605305 + 0.795994i \(0.293051\pi\)
\(888\) 42.5510 1.42792
\(889\) 12.4360 0.417089
\(890\) 25.3288 0.849025
\(891\) −1.19656 −0.0400862
\(892\) 11.0298 0.369307
\(893\) −7.12808 −0.238532
\(894\) 38.2008 1.27762
\(895\) 15.5640 0.520248
\(896\) −20.7737 −0.694000
\(897\) −4.17513 −0.139404
\(898\) 15.3717 0.512960
\(899\) −17.8715 −0.596047
\(900\) 4.19656 0.139885
\(901\) 62.8328 2.09326
\(902\) −18.3931 −0.612424
\(903\) −11.9143 −0.396483
\(904\) −43.5087 −1.44708
\(905\) −15.7820 −0.524612
\(906\) −21.3717 −0.710027
\(907\) −7.26504 −0.241232 −0.120616 0.992699i \(-0.538487\pi\)
−0.120616 + 0.992699i \(0.538487\pi\)
\(908\) 66.1579 2.19553
\(909\) −10.3503 −0.343297
\(910\) −2.97858 −0.0987389
\(911\) −6.65769 −0.220579 −0.110290 0.993899i \(-0.535178\pi\)
−0.110290 + 0.993899i \(0.535178\pi\)
\(912\) −36.4141 −1.20579
\(913\) 6.42754 0.212721
\(914\) −3.45738 −0.114360
\(915\) 12.5682 0.415494
\(916\) 36.6921 1.21234
\(917\) 7.64973 0.252616
\(918\) 15.3717 0.507341
\(919\) −27.1831 −0.896688 −0.448344 0.893861i \(-0.647986\pi\)
−0.448344 + 0.893861i \(0.647986\pi\)
\(920\) 22.8291 0.752652
\(921\) −0.760597 −0.0250625
\(922\) −70.9013 −2.33501
\(923\) −5.19656 −0.171047
\(924\) −6.00842 −0.197663
\(925\) 7.78202 0.255871
\(926\) −40.7643 −1.33960
\(927\) 18.7434 0.615614
\(928\) −12.3200 −0.404423
\(929\) −15.3973 −0.505170 −0.252585 0.967575i \(-0.581281\pi\)
−0.252585 + 0.967575i \(0.581281\pi\)
\(930\) 7.41454 0.243132
\(931\) −38.8585 −1.27353
\(932\) −9.12808 −0.299000
\(933\) 23.1281 0.757179
\(934\) −64.0932 −2.09719
\(935\) 7.38890 0.241643
\(936\) −5.46787 −0.178723
\(937\) 1.12808 0.0368527 0.0184264 0.999830i \(-0.494134\pi\)
0.0184264 + 0.999830i \(0.494134\pi\)
\(938\) 27.9143 0.911434
\(939\) 33.9143 1.10675
\(940\) 4.28646 0.139809
\(941\) −30.1407 −0.982559 −0.491280 0.871002i \(-0.663471\pi\)
−0.491280 + 0.871002i \(0.663471\pi\)
\(942\) 6.93573 0.225978
\(943\) −25.7820 −0.839578
\(944\) 28.0294 0.912279
\(945\) −1.19656 −0.0389240
\(946\) −29.6582 −0.964270
\(947\) −20.0294 −0.650868 −0.325434 0.945565i \(-0.605510\pi\)
−0.325434 + 0.945565i \(0.605510\pi\)
\(948\) 7.47835 0.242885
\(949\) −11.9572 −0.388146
\(950\) −17.3717 −0.563612
\(951\) −9.64973 −0.312914
\(952\) 40.4015 1.30942
\(953\) −43.2259 −1.40023 −0.700113 0.714032i \(-0.746867\pi\)
−0.700113 + 0.714032i \(0.746867\pi\)
\(954\) −25.3288 −0.820052
\(955\) −10.7434 −0.347648
\(956\) 11.7648 0.380501
\(957\) 7.17935 0.232075
\(958\) 18.8929 0.610401
\(959\) −20.0344 −0.646945
\(960\) −5.32464 −0.171852
\(961\) −22.1281 −0.713809
\(962\) −19.3717 −0.624568
\(963\) −18.5682 −0.598353
\(964\) −25.1793 −0.810972
\(965\) −9.73917 −0.313515
\(966\) −12.4360 −0.400120
\(967\) 57.6875 1.85511 0.927553 0.373691i \(-0.121908\pi\)
0.927553 + 0.373691i \(0.121908\pi\)
\(968\) 52.3179 1.68156
\(969\) −43.0937 −1.38437
\(970\) −4.54262 −0.145855
\(971\) −19.5296 −0.626735 −0.313368 0.949632i \(-0.601457\pi\)
−0.313368 + 0.949632i \(0.601457\pi\)
\(972\) −4.19656 −0.134605
\(973\) −6.91852 −0.221798
\(974\) −10.9786 −0.351776
\(975\) −1.00000 −0.0320256
\(976\) 65.5809 2.09919
\(977\) −40.3074 −1.28955 −0.644774 0.764373i \(-0.723049\pi\)
−0.644774 + 0.764373i \(0.723049\pi\)
\(978\) 21.8077 0.697332
\(979\) −12.1751 −0.389119
\(980\) 23.3675 0.746447
\(981\) 8.39312 0.267972
\(982\) 0.213311 0.00680702
\(983\) 32.2008 1.02705 0.513523 0.858076i \(-0.328340\pi\)
0.513523 + 0.858076i \(0.328340\pi\)
\(984\) −33.7648 −1.07638
\(985\) 9.56404 0.304736
\(986\) −92.2302 −2.93721
\(987\) −1.22219 −0.0389028
\(988\) 29.2860 0.931712
\(989\) −41.5725 −1.32193
\(990\) −2.97858 −0.0946654
\(991\) 26.4826 0.841246 0.420623 0.907235i \(-0.361811\pi\)
0.420623 + 0.907235i \(0.361811\pi\)
\(992\) 6.11599 0.194183
\(993\) −15.3288 −0.486446
\(994\) −15.4783 −0.490943
\(995\) −5.95715 −0.188854
\(996\) 22.5426 0.714290
\(997\) 35.1365 1.11278 0.556392 0.830920i \(-0.312185\pi\)
0.556392 + 0.830920i \(0.312185\pi\)
\(998\) 44.1151 1.39644
\(999\) −7.78202 −0.246212
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 195.2.a.e.1.1 3
3.2 odd 2 585.2.a.n.1.3 3
4.3 odd 2 3120.2.a.bj.1.2 3
5.2 odd 4 975.2.c.i.274.2 6
5.3 odd 4 975.2.c.i.274.5 6
5.4 even 2 975.2.a.o.1.3 3
7.6 odd 2 9555.2.a.bq.1.1 3
12.11 even 2 9360.2.a.dd.1.2 3
13.12 even 2 2535.2.a.bc.1.3 3
15.2 even 4 2925.2.c.w.2224.5 6
15.8 even 4 2925.2.c.w.2224.2 6
15.14 odd 2 2925.2.a.bh.1.1 3
39.38 odd 2 7605.2.a.bx.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.e.1.1 3 1.1 even 1 trivial
585.2.a.n.1.3 3 3.2 odd 2
975.2.a.o.1.3 3 5.4 even 2
975.2.c.i.274.2 6 5.2 odd 4
975.2.c.i.274.5 6 5.3 odd 4
2535.2.a.bc.1.3 3 13.12 even 2
2925.2.a.bh.1.1 3 15.14 odd 2
2925.2.c.w.2224.2 6 15.8 even 4
2925.2.c.w.2224.5 6 15.2 even 4
3120.2.a.bj.1.2 3 4.3 odd 2
7605.2.a.bx.1.1 3 39.38 odd 2
9360.2.a.dd.1.2 3 12.11 even 2
9555.2.a.bq.1.1 3 7.6 odd 2