Properties

Label 1183.2.a.p.1.6
Level $1183$
Weight $2$
Character 1183.1
Self dual yes
Analytic conductor $9.446$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.7674048.1
Defining polynomial: \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.70320\) of defining polynomial
Character \(\chi\) \(=\) 1183.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -1.00000 q^{7} +8.94020 q^{8} -2.88032 q^{9} +O(q^{10})\) \(q+2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -1.00000 q^{7} +8.94020 q^{8} -2.88032 q^{9} +8.80735 q^{10} -1.84603 q^{11} -1.83605 q^{12} -2.70320 q^{14} -1.12715 q^{15} +13.5526 q^{16} +2.15314 q^{17} -7.78607 q^{18} -2.40096 q^{19} +17.2917 q^{20} +0.345949 q^{21} -4.99017 q^{22} +1.81263 q^{23} -3.09285 q^{24} +5.61537 q^{25} +2.03429 q^{27} -5.30727 q^{28} -2.73406 q^{29} -3.04689 q^{30} +1.74236 q^{31} +18.7549 q^{32} +0.638632 q^{33} +5.82036 q^{34} -3.25812 q^{35} -15.2866 q^{36} -5.93565 q^{37} -6.49025 q^{38} +29.1283 q^{40} -4.22131 q^{41} +0.935168 q^{42} -8.68223 q^{43} -9.79737 q^{44} -9.38444 q^{45} +4.89989 q^{46} +5.87774 q^{47} -4.68850 q^{48} +1.00000 q^{49} +15.1794 q^{50} -0.744877 q^{51} -9.30628 q^{53} +5.49909 q^{54} -6.01459 q^{55} -8.94020 q^{56} +0.830609 q^{57} -7.39071 q^{58} -10.7523 q^{59} -5.98206 q^{60} +10.1101 q^{61} +4.70994 q^{62} +2.88032 q^{63} +23.5929 q^{64} +1.72635 q^{66} -0.826916 q^{67} +11.4273 q^{68} -0.627077 q^{69} -8.80735 q^{70} -2.35425 q^{71} -25.7506 q^{72} +3.19482 q^{73} -16.0452 q^{74} -1.94263 q^{75} -12.7425 q^{76} +1.84603 q^{77} +0.801911 q^{79} +44.1559 q^{80} +7.93720 q^{81} -11.4110 q^{82} +9.97031 q^{83} +1.83605 q^{84} +7.01520 q^{85} -23.4698 q^{86} +0.945847 q^{87} -16.5039 q^{88} +15.1135 q^{89} -25.3680 q^{90} +9.62010 q^{92} -0.602768 q^{93} +15.8887 q^{94} -7.82261 q^{95} -6.48823 q^{96} +9.23171 q^{97} +2.70320 q^{98} +5.31715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{14} + 20 q^{15} + 8 q^{16} - 4 q^{17} - 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} + 6 q^{27} - 4 q^{28} - 8 q^{29} + 8 q^{30} - 14 q^{31} + 8 q^{32} + 16 q^{33} - 2 q^{34} - 6 q^{35} - 10 q^{36} + 12 q^{37} - 2 q^{38} + 46 q^{40} + 28 q^{41} - 4 q^{42} + 2 q^{43} - 20 q^{44} + 16 q^{45} + 20 q^{46} + 14 q^{47} + 2 q^{48} + 6 q^{49} + 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} + 6 q^{55} - 12 q^{56} + 4 q^{58} - 2 q^{59} - 14 q^{61} - 4 q^{62} - 4 q^{63} + 26 q^{64} - 26 q^{66} + 24 q^{67} + 8 q^{68} + 4 q^{69} - 12 q^{70} + 4 q^{71} + 8 q^{72} + 36 q^{73} - 6 q^{74} + 46 q^{75} - 26 q^{76} - 4 q^{77} - 28 q^{79} + 36 q^{80} - 2 q^{81} + 14 q^{82} + 26 q^{83} - 2 q^{84} - 20 q^{85} - 24 q^{86} + 2 q^{87} - 14 q^{88} + 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70320 1.91145 0.955724 0.294264i \(-0.0950745\pi\)
0.955724 + 0.294264i \(0.0950745\pi\)
\(3\) −0.345949 −0.199734 −0.0998669 0.995001i \(-0.531842\pi\)
−0.0998669 + 0.995001i \(0.531842\pi\)
\(4\) 5.30727 2.65363
\(5\) 3.25812 1.45708 0.728539 0.685005i \(-0.240200\pi\)
0.728539 + 0.685005i \(0.240200\pi\)
\(6\) −0.935168 −0.381781
\(7\) −1.00000 −0.377964
\(8\) 8.94020 3.16084
\(9\) −2.88032 −0.960106
\(10\) 8.80735 2.78513
\(11\) −1.84603 −0.556598 −0.278299 0.960494i \(-0.589771\pi\)
−0.278299 + 0.960494i \(0.589771\pi\)
\(12\) −1.83605 −0.530021
\(13\) 0 0
\(14\) −2.70320 −0.722460
\(15\) −1.12715 −0.291028
\(16\) 13.5526 3.38814
\(17\) 2.15314 0.522213 0.261107 0.965310i \(-0.415913\pi\)
0.261107 + 0.965310i \(0.415913\pi\)
\(18\) −7.78607 −1.83519
\(19\) −2.40096 −0.550817 −0.275408 0.961327i \(-0.588813\pi\)
−0.275408 + 0.961327i \(0.588813\pi\)
\(20\) 17.2917 3.86655
\(21\) 0.345949 0.0754923
\(22\) −4.99017 −1.06391
\(23\) 1.81263 0.377959 0.188979 0.981981i \(-0.439482\pi\)
0.188979 + 0.981981i \(0.439482\pi\)
\(24\) −3.09285 −0.631326
\(25\) 5.61537 1.12307
\(26\) 0 0
\(27\) 2.03429 0.391500
\(28\) −5.30727 −1.00298
\(29\) −2.73406 −0.507703 −0.253851 0.967243i \(-0.581697\pi\)
−0.253851 + 0.967243i \(0.581697\pi\)
\(30\) −3.04689 −0.556284
\(31\) 1.74236 0.312937 0.156468 0.987683i \(-0.449989\pi\)
0.156468 + 0.987683i \(0.449989\pi\)
\(32\) 18.7549 3.31542
\(33\) 0.638632 0.111172
\(34\) 5.82036 0.998183
\(35\) −3.25812 −0.550723
\(36\) −15.2866 −2.54777
\(37\) −5.93565 −0.975815 −0.487908 0.872895i \(-0.662240\pi\)
−0.487908 + 0.872895i \(0.662240\pi\)
\(38\) −6.49025 −1.05286
\(39\) 0 0
\(40\) 29.1283 4.60558
\(41\) −4.22131 −0.659259 −0.329629 0.944110i \(-0.606924\pi\)
−0.329629 + 0.944110i \(0.606924\pi\)
\(42\) 0.935168 0.144300
\(43\) −8.68223 −1.32403 −0.662014 0.749492i \(-0.730298\pi\)
−0.662014 + 0.749492i \(0.730298\pi\)
\(44\) −9.79737 −1.47701
\(45\) −9.38444 −1.39895
\(46\) 4.89989 0.722449
\(47\) 5.87774 0.857357 0.428678 0.903457i \(-0.358979\pi\)
0.428678 + 0.903457i \(0.358979\pi\)
\(48\) −4.68850 −0.676727
\(49\) 1.00000 0.142857
\(50\) 15.1794 2.14670
\(51\) −0.744877 −0.104304
\(52\) 0 0
\(53\) −9.30628 −1.27832 −0.639158 0.769076i \(-0.720717\pi\)
−0.639158 + 0.769076i \(0.720717\pi\)
\(54\) 5.49909 0.748331
\(55\) −6.01459 −0.811007
\(56\) −8.94020 −1.19468
\(57\) 0.830609 0.110017
\(58\) −7.39071 −0.970447
\(59\) −10.7523 −1.39982 −0.699912 0.714229i \(-0.746778\pi\)
−0.699912 + 0.714229i \(0.746778\pi\)
\(60\) −5.98206 −0.772281
\(61\) 10.1101 1.29446 0.647231 0.762294i \(-0.275927\pi\)
0.647231 + 0.762294i \(0.275927\pi\)
\(62\) 4.70994 0.598163
\(63\) 2.88032 0.362886
\(64\) 23.5929 2.94911
\(65\) 0 0
\(66\) 1.72635 0.212499
\(67\) −0.826916 −0.101024 −0.0505119 0.998723i \(-0.516085\pi\)
−0.0505119 + 0.998723i \(0.516085\pi\)
\(68\) 11.4273 1.38576
\(69\) −0.627077 −0.0754912
\(70\) −8.80735 −1.05268
\(71\) −2.35425 −0.279398 −0.139699 0.990194i \(-0.544613\pi\)
−0.139699 + 0.990194i \(0.544613\pi\)
\(72\) −25.7506 −3.03474
\(73\) 3.19482 0.373925 0.186963 0.982367i \(-0.440136\pi\)
0.186963 + 0.982367i \(0.440136\pi\)
\(74\) −16.0452 −1.86522
\(75\) −1.94263 −0.224316
\(76\) −12.7425 −1.46167
\(77\) 1.84603 0.210374
\(78\) 0 0
\(79\) 0.801911 0.0902220 0.0451110 0.998982i \(-0.485636\pi\)
0.0451110 + 0.998982i \(0.485636\pi\)
\(80\) 44.1559 4.93678
\(81\) 7.93720 0.881911
\(82\) −11.4110 −1.26014
\(83\) 9.97031 1.09438 0.547192 0.837007i \(-0.315697\pi\)
0.547192 + 0.837007i \(0.315697\pi\)
\(84\) 1.83605 0.200329
\(85\) 7.01520 0.760905
\(86\) −23.4698 −2.53081
\(87\) 0.945847 0.101405
\(88\) −16.5039 −1.75932
\(89\) 15.1135 1.60202 0.801012 0.598648i \(-0.204295\pi\)
0.801012 + 0.598648i \(0.204295\pi\)
\(90\) −25.3680 −2.67402
\(91\) 0 0
\(92\) 9.62010 1.00296
\(93\) −0.602768 −0.0625041
\(94\) 15.8887 1.63879
\(95\) −7.82261 −0.802583
\(96\) −6.48823 −0.662202
\(97\) 9.23171 0.937338 0.468669 0.883374i \(-0.344734\pi\)
0.468669 + 0.883374i \(0.344734\pi\)
\(98\) 2.70320 0.273064
\(99\) 5.31715 0.534394
\(100\) 29.8023 2.98023
\(101\) 14.8234 1.47498 0.737491 0.675357i \(-0.236011\pi\)
0.737491 + 0.675357i \(0.236011\pi\)
\(102\) −2.01355 −0.199371
\(103\) −4.28286 −0.422003 −0.211001 0.977486i \(-0.567672\pi\)
−0.211001 + 0.977486i \(0.567672\pi\)
\(104\) 0 0
\(105\) 1.12715 0.109998
\(106\) −25.1567 −2.44343
\(107\) −19.1258 −1.84896 −0.924479 0.381233i \(-0.875500\pi\)
−0.924479 + 0.381233i \(0.875500\pi\)
\(108\) 10.7965 1.03890
\(109\) 4.27153 0.409139 0.204569 0.978852i \(-0.434421\pi\)
0.204569 + 0.978852i \(0.434421\pi\)
\(110\) −16.2586 −1.55020
\(111\) 2.05343 0.194903
\(112\) −13.5526 −1.28060
\(113\) 2.74976 0.258676 0.129338 0.991601i \(-0.458715\pi\)
0.129338 + 0.991601i \(0.458715\pi\)
\(114\) 2.24530 0.210291
\(115\) 5.90576 0.550715
\(116\) −14.5104 −1.34726
\(117\) 0 0
\(118\) −29.0655 −2.67569
\(119\) −2.15314 −0.197378
\(120\) −10.0769 −0.919891
\(121\) −7.59218 −0.690198
\(122\) 27.3295 2.47430
\(123\) 1.46036 0.131676
\(124\) 9.24717 0.830420
\(125\) 2.00495 0.179329
\(126\) 7.78607 0.693638
\(127\) −9.73438 −0.863786 −0.431893 0.901925i \(-0.642154\pi\)
−0.431893 + 0.901925i \(0.642154\pi\)
\(128\) 26.2666 2.32166
\(129\) 3.00361 0.264453
\(130\) 0 0
\(131\) −18.6615 −1.63046 −0.815230 0.579138i \(-0.803389\pi\)
−0.815230 + 0.579138i \(0.803389\pi\)
\(132\) 3.38939 0.295009
\(133\) 2.40096 0.208189
\(134\) −2.23532 −0.193102
\(135\) 6.62797 0.570445
\(136\) 19.2495 1.65063
\(137\) 8.42156 0.719502 0.359751 0.933048i \(-0.382862\pi\)
0.359751 + 0.933048i \(0.382862\pi\)
\(138\) −1.69511 −0.144298
\(139\) −17.6362 −1.49588 −0.747941 0.663765i \(-0.768957\pi\)
−0.747941 + 0.663765i \(0.768957\pi\)
\(140\) −17.2917 −1.46142
\(141\) −2.03340 −0.171243
\(142\) −6.36399 −0.534054
\(143\) 0 0
\(144\) −39.0357 −3.25298
\(145\) −8.90791 −0.739762
\(146\) 8.63623 0.714739
\(147\) −0.345949 −0.0285334
\(148\) −31.5021 −2.58946
\(149\) −4.02104 −0.329416 −0.164708 0.986342i \(-0.552668\pi\)
−0.164708 + 0.986342i \(0.552668\pi\)
\(150\) −5.25132 −0.428768
\(151\) 18.9010 1.53814 0.769069 0.639165i \(-0.220720\pi\)
0.769069 + 0.639165i \(0.220720\pi\)
\(152\) −21.4650 −1.74104
\(153\) −6.20173 −0.501380
\(154\) 4.99017 0.402120
\(155\) 5.67682 0.455973
\(156\) 0 0
\(157\) −11.5735 −0.923670 −0.461835 0.886966i \(-0.652809\pi\)
−0.461835 + 0.886966i \(0.652809\pi\)
\(158\) 2.16772 0.172455
\(159\) 3.21950 0.255323
\(160\) 61.1056 4.83082
\(161\) −1.81263 −0.142855
\(162\) 21.4558 1.68573
\(163\) 4.40542 0.345059 0.172529 0.985004i \(-0.444806\pi\)
0.172529 + 0.985004i \(0.444806\pi\)
\(164\) −22.4037 −1.74943
\(165\) 2.08074 0.161985
\(166\) 26.9517 2.09186
\(167\) −9.01909 −0.697918 −0.348959 0.937138i \(-0.613465\pi\)
−0.348959 + 0.937138i \(0.613465\pi\)
\(168\) 3.09285 0.238619
\(169\) 0 0
\(170\) 18.9635 1.45443
\(171\) 6.91552 0.528843
\(172\) −46.0789 −3.51349
\(173\) 6.09200 0.463166 0.231583 0.972815i \(-0.425609\pi\)
0.231583 + 0.972815i \(0.425609\pi\)
\(174\) 2.55681 0.193831
\(175\) −5.61537 −0.424482
\(176\) −25.0184 −1.88583
\(177\) 3.71974 0.279592
\(178\) 40.8547 3.06219
\(179\) 3.87964 0.289978 0.144989 0.989433i \(-0.453685\pi\)
0.144989 + 0.989433i \(0.453685\pi\)
\(180\) −49.8057 −3.71230
\(181\) 6.58392 0.489379 0.244690 0.969601i \(-0.421314\pi\)
0.244690 + 0.969601i \(0.421314\pi\)
\(182\) 0 0
\(183\) −3.49757 −0.258548
\(184\) 16.2052 1.19467
\(185\) −19.3391 −1.42184
\(186\) −1.62940 −0.119473
\(187\) −3.97476 −0.290663
\(188\) 31.1948 2.27511
\(189\) −2.03429 −0.147973
\(190\) −21.1460 −1.53410
\(191\) −13.7434 −0.994435 −0.497218 0.867626i \(-0.665645\pi\)
−0.497218 + 0.867626i \(0.665645\pi\)
\(192\) −8.16195 −0.589038
\(193\) 22.7530 1.63780 0.818899 0.573937i \(-0.194585\pi\)
0.818899 + 0.573937i \(0.194585\pi\)
\(194\) 24.9551 1.79167
\(195\) 0 0
\(196\) 5.30727 0.379091
\(197\) 14.5272 1.03502 0.517509 0.855678i \(-0.326859\pi\)
0.517509 + 0.855678i \(0.326859\pi\)
\(198\) 14.3733 1.02147
\(199\) 23.8404 1.69000 0.845001 0.534765i \(-0.179600\pi\)
0.845001 + 0.534765i \(0.179600\pi\)
\(200\) 50.2025 3.54985
\(201\) 0.286071 0.0201779
\(202\) 40.0705 2.81935
\(203\) 2.73406 0.191894
\(204\) −3.95326 −0.276784
\(205\) −13.7536 −0.960591
\(206\) −11.5774 −0.806637
\(207\) −5.22095 −0.362881
\(208\) 0 0
\(209\) 4.43223 0.306584
\(210\) 3.04689 0.210256
\(211\) 4.31527 0.297076 0.148538 0.988907i \(-0.452543\pi\)
0.148538 + 0.988907i \(0.452543\pi\)
\(212\) −49.3909 −3.39218
\(213\) 0.814450 0.0558052
\(214\) −51.7007 −3.53419
\(215\) −28.2878 −1.92921
\(216\) 18.1870 1.23747
\(217\) −1.74236 −0.118279
\(218\) 11.5468 0.782047
\(219\) −1.10525 −0.0746856
\(220\) −31.9210 −2.15212
\(221\) 0 0
\(222\) 5.55083 0.372548
\(223\) 23.3947 1.56662 0.783312 0.621629i \(-0.213529\pi\)
0.783312 + 0.621629i \(0.213529\pi\)
\(224\) −18.7549 −1.25311
\(225\) −16.1741 −1.07827
\(226\) 7.43315 0.494446
\(227\) −26.7229 −1.77366 −0.886829 0.462097i \(-0.847097\pi\)
−0.886829 + 0.462097i \(0.847097\pi\)
\(228\) 4.40826 0.291944
\(229\) −3.00670 −0.198688 −0.0993442 0.995053i \(-0.531674\pi\)
−0.0993442 + 0.995053i \(0.531674\pi\)
\(230\) 15.9644 1.05266
\(231\) −0.638632 −0.0420189
\(232\) −24.4431 −1.60477
\(233\) −11.7148 −0.767462 −0.383731 0.923445i \(-0.625361\pi\)
−0.383731 + 0.923445i \(0.625361\pi\)
\(234\) 0 0
\(235\) 19.1504 1.24924
\(236\) −57.0651 −3.71462
\(237\) −0.277420 −0.0180204
\(238\) −5.82036 −0.377278
\(239\) −1.42797 −0.0923677 −0.0461838 0.998933i \(-0.514706\pi\)
−0.0461838 + 0.998933i \(0.514706\pi\)
\(240\) −15.2757 −0.986043
\(241\) 2.67969 0.172614 0.0863069 0.996269i \(-0.472493\pi\)
0.0863069 + 0.996269i \(0.472493\pi\)
\(242\) −20.5232 −1.31928
\(243\) −8.84874 −0.567647
\(244\) 53.6569 3.43503
\(245\) 3.25812 0.208154
\(246\) 3.94764 0.251692
\(247\) 0 0
\(248\) 15.5770 0.989143
\(249\) −3.44922 −0.218586
\(250\) 5.41978 0.342777
\(251\) 10.9339 0.690143 0.345072 0.938576i \(-0.387855\pi\)
0.345072 + 0.938576i \(0.387855\pi\)
\(252\) 15.2866 0.962967
\(253\) −3.34616 −0.210371
\(254\) −26.3139 −1.65108
\(255\) −2.42690 −0.151978
\(256\) 23.8178 1.48861
\(257\) 4.15138 0.258956 0.129478 0.991582i \(-0.458670\pi\)
0.129478 + 0.991582i \(0.458670\pi\)
\(258\) 8.11935 0.505488
\(259\) 5.93565 0.368823
\(260\) 0 0
\(261\) 7.87497 0.487448
\(262\) −50.4456 −3.11654
\(263\) 4.05360 0.249955 0.124978 0.992160i \(-0.460114\pi\)
0.124978 + 0.992160i \(0.460114\pi\)
\(264\) 5.70949 0.351395
\(265\) −30.3210 −1.86260
\(266\) 6.49025 0.397943
\(267\) −5.22849 −0.319979
\(268\) −4.38866 −0.268080
\(269\) 4.00022 0.243898 0.121949 0.992536i \(-0.461086\pi\)
0.121949 + 0.992536i \(0.461086\pi\)
\(270\) 17.9167 1.09038
\(271\) −2.78502 −0.169178 −0.0845888 0.996416i \(-0.526958\pi\)
−0.0845888 + 0.996416i \(0.526958\pi\)
\(272\) 29.1806 1.76933
\(273\) 0 0
\(274\) 22.7651 1.37529
\(275\) −10.3661 −0.625101
\(276\) −3.32807 −0.200326
\(277\) 16.6924 1.00295 0.501474 0.865173i \(-0.332791\pi\)
0.501474 + 0.865173i \(0.332791\pi\)
\(278\) −47.6741 −2.85930
\(279\) −5.01855 −0.300453
\(280\) −29.1283 −1.74075
\(281\) 13.3731 0.797774 0.398887 0.917000i \(-0.369397\pi\)
0.398887 + 0.917000i \(0.369397\pi\)
\(282\) −5.49668 −0.327322
\(283\) −18.8862 −1.12267 −0.561335 0.827589i \(-0.689712\pi\)
−0.561335 + 0.827589i \(0.689712\pi\)
\(284\) −12.4946 −0.741419
\(285\) 2.70623 0.160303
\(286\) 0 0
\(287\) 4.22131 0.249176
\(288\) −54.0200 −3.18316
\(289\) −12.3640 −0.727293
\(290\) −24.0798 −1.41402
\(291\) −3.19370 −0.187218
\(292\) 16.9558 0.992262
\(293\) 3.41790 0.199676 0.0998380 0.995004i \(-0.468168\pi\)
0.0998380 + 0.995004i \(0.468168\pi\)
\(294\) −0.935168 −0.0545401
\(295\) −35.0322 −2.03965
\(296\) −53.0659 −3.08439
\(297\) −3.75536 −0.217908
\(298\) −10.8697 −0.629663
\(299\) 0 0
\(300\) −10.3101 −0.595252
\(301\) 8.68223 0.500435
\(302\) 51.0930 2.94007
\(303\) −5.12814 −0.294604
\(304\) −32.5391 −1.86625
\(305\) 32.9399 1.88613
\(306\) −16.7645 −0.958362
\(307\) −16.3679 −0.934165 −0.467083 0.884214i \(-0.654695\pi\)
−0.467083 + 0.884214i \(0.654695\pi\)
\(308\) 9.79737 0.558257
\(309\) 1.48165 0.0842883
\(310\) 15.3456 0.871569
\(311\) 23.6979 1.34378 0.671891 0.740650i \(-0.265482\pi\)
0.671891 + 0.740650i \(0.265482\pi\)
\(312\) 0 0
\(313\) −5.18025 −0.292805 −0.146403 0.989225i \(-0.546769\pi\)
−0.146403 + 0.989225i \(0.546769\pi\)
\(314\) −31.2856 −1.76555
\(315\) 9.38444 0.528753
\(316\) 4.25596 0.239416
\(317\) 6.06537 0.340665 0.170332 0.985387i \(-0.445516\pi\)
0.170332 + 0.985387i \(0.445516\pi\)
\(318\) 8.70294 0.488037
\(319\) 5.04715 0.282586
\(320\) 76.8686 4.29709
\(321\) 6.61655 0.369300
\(322\) −4.89989 −0.273060
\(323\) −5.16959 −0.287644
\(324\) 42.1248 2.34027
\(325\) 0 0
\(326\) 11.9087 0.659562
\(327\) −1.47773 −0.0817188
\(328\) −37.7394 −2.08381
\(329\) −5.87774 −0.324050
\(330\) 5.62465 0.309627
\(331\) 17.2749 0.949512 0.474756 0.880118i \(-0.342536\pi\)
0.474756 + 0.880118i \(0.342536\pi\)
\(332\) 52.9151 2.90410
\(333\) 17.0966 0.936886
\(334\) −24.3804 −1.33403
\(335\) −2.69419 −0.147200
\(336\) 4.68850 0.255779
\(337\) 8.35464 0.455106 0.227553 0.973766i \(-0.426927\pi\)
0.227553 + 0.973766i \(0.426927\pi\)
\(338\) 0 0
\(339\) −0.951279 −0.0516664
\(340\) 37.2315 2.01916
\(341\) −3.21644 −0.174180
\(342\) 18.6940 1.01086
\(343\) −1.00000 −0.0539949
\(344\) −77.6208 −4.18504
\(345\) −2.04309 −0.109997
\(346\) 16.4679 0.885318
\(347\) 28.8220 1.54725 0.773623 0.633646i \(-0.218443\pi\)
0.773623 + 0.633646i \(0.218443\pi\)
\(348\) 5.01986 0.269093
\(349\) −11.7221 −0.627467 −0.313734 0.949511i \(-0.601580\pi\)
−0.313734 + 0.949511i \(0.601580\pi\)
\(350\) −15.1794 −0.811376
\(351\) 0 0
\(352\) −34.6220 −1.84536
\(353\) −17.8362 −0.949326 −0.474663 0.880168i \(-0.657430\pi\)
−0.474663 + 0.880168i \(0.657430\pi\)
\(354\) 10.0552 0.534426
\(355\) −7.67043 −0.407104
\(356\) 80.2113 4.25119
\(357\) 0.744877 0.0394231
\(358\) 10.4874 0.554278
\(359\) −5.68162 −0.299864 −0.149932 0.988696i \(-0.547906\pi\)
−0.149932 + 0.988696i \(0.547906\pi\)
\(360\) −83.8987 −4.42185
\(361\) −13.2354 −0.696601
\(362\) 17.7976 0.935423
\(363\) 2.62651 0.137856
\(364\) 0 0
\(365\) 10.4091 0.544838
\(366\) −9.45462 −0.494201
\(367\) −19.6316 −1.02476 −0.512381 0.858758i \(-0.671236\pi\)
−0.512381 + 0.858758i \(0.671236\pi\)
\(368\) 24.5658 1.28058
\(369\) 12.1587 0.632958
\(370\) −52.2773 −2.71777
\(371\) 9.30628 0.483158
\(372\) −3.19905 −0.165863
\(373\) 32.0645 1.66024 0.830119 0.557586i \(-0.188272\pi\)
0.830119 + 0.557586i \(0.188272\pi\)
\(374\) −10.7445 −0.555587
\(375\) −0.693612 −0.0358180
\(376\) 52.5482 2.70997
\(377\) 0 0
\(378\) −5.49909 −0.282843
\(379\) 19.0231 0.977150 0.488575 0.872522i \(-0.337517\pi\)
0.488575 + 0.872522i \(0.337517\pi\)
\(380\) −41.5167 −2.12976
\(381\) 3.36760 0.172527
\(382\) −37.1510 −1.90081
\(383\) 0.699829 0.0357596 0.0178798 0.999840i \(-0.494308\pi\)
0.0178798 + 0.999840i \(0.494308\pi\)
\(384\) −9.08689 −0.463714
\(385\) 6.01459 0.306532
\(386\) 61.5059 3.13057
\(387\) 25.0076 1.27121
\(388\) 48.9951 2.48735
\(389\) −20.0547 −1.01681 −0.508407 0.861117i \(-0.669765\pi\)
−0.508407 + 0.861117i \(0.669765\pi\)
\(390\) 0 0
\(391\) 3.90284 0.197375
\(392\) 8.94020 0.451548
\(393\) 6.45592 0.325658
\(394\) 39.2698 1.97838
\(395\) 2.61272 0.131460
\(396\) 28.2195 1.41809
\(397\) 22.2803 1.11822 0.559108 0.829095i \(-0.311144\pi\)
0.559108 + 0.829095i \(0.311144\pi\)
\(398\) 64.4453 3.23035
\(399\) −0.830609 −0.0415824
\(400\) 76.1027 3.80513
\(401\) −4.80749 −0.240074 −0.120037 0.992769i \(-0.538301\pi\)
−0.120037 + 0.992769i \(0.538301\pi\)
\(402\) 0.773306 0.0385690
\(403\) 0 0
\(404\) 78.6717 3.91406
\(405\) 25.8604 1.28501
\(406\) 7.39071 0.366795
\(407\) 10.9574 0.543137
\(408\) −6.65935 −0.329687
\(409\) 36.8035 1.81981 0.909907 0.414811i \(-0.136152\pi\)
0.909907 + 0.414811i \(0.136152\pi\)
\(410\) −37.1786 −1.83612
\(411\) −2.91343 −0.143709
\(412\) −22.7303 −1.11984
\(413\) 10.7523 0.529084
\(414\) −14.1132 −0.693628
\(415\) 32.4845 1.59460
\(416\) 0 0
\(417\) 6.10122 0.298778
\(418\) 11.9812 0.586019
\(419\) 29.2667 1.42977 0.714887 0.699240i \(-0.246478\pi\)
0.714887 + 0.699240i \(0.246478\pi\)
\(420\) 5.98206 0.291895
\(421\) 7.53862 0.367410 0.183705 0.982981i \(-0.441191\pi\)
0.183705 + 0.982981i \(0.441191\pi\)
\(422\) 11.6650 0.567845
\(423\) −16.9298 −0.823154
\(424\) −83.2000 −4.04055
\(425\) 12.0907 0.586484
\(426\) 2.20162 0.106669
\(427\) −10.1101 −0.489261
\(428\) −101.506 −4.90646
\(429\) 0 0
\(430\) −76.4674 −3.68759
\(431\) 31.2261 1.50411 0.752055 0.659101i \(-0.229063\pi\)
0.752055 + 0.659101i \(0.229063\pi\)
\(432\) 27.5699 1.32646
\(433\) 5.88404 0.282769 0.141384 0.989955i \(-0.454845\pi\)
0.141384 + 0.989955i \(0.454845\pi\)
\(434\) −4.70994 −0.226084
\(435\) 3.08169 0.147755
\(436\) 22.6702 1.08570
\(437\) −4.35204 −0.208186
\(438\) −2.98770 −0.142758
\(439\) −9.95642 −0.475194 −0.237597 0.971364i \(-0.576360\pi\)
−0.237597 + 0.971364i \(0.576360\pi\)
\(440\) −53.7716 −2.56346
\(441\) −2.88032 −0.137158
\(442\) 0 0
\(443\) −35.8813 −1.70477 −0.852385 0.522915i \(-0.824845\pi\)
−0.852385 + 0.522915i \(0.824845\pi\)
\(444\) 10.8981 0.517202
\(445\) 49.2416 2.33427
\(446\) 63.2404 2.99452
\(447\) 1.39108 0.0657956
\(448\) −23.5929 −1.11466
\(449\) −3.99528 −0.188549 −0.0942744 0.995546i \(-0.530053\pi\)
−0.0942744 + 0.995546i \(0.530053\pi\)
\(450\) −43.7217 −2.06106
\(451\) 7.79266 0.366942
\(452\) 14.5937 0.686432
\(453\) −6.53877 −0.307218
\(454\) −72.2371 −3.39026
\(455\) 0 0
\(456\) 7.42580 0.347745
\(457\) −41.2222 −1.92829 −0.964147 0.265369i \(-0.914506\pi\)
−0.964147 + 0.265369i \(0.914506\pi\)
\(458\) −8.12770 −0.379783
\(459\) 4.38011 0.204446
\(460\) 31.3435 1.46140
\(461\) 24.7266 1.15163 0.575816 0.817579i \(-0.304684\pi\)
0.575816 + 0.817579i \(0.304684\pi\)
\(462\) −1.72635 −0.0803169
\(463\) −24.4057 −1.13423 −0.567115 0.823639i \(-0.691940\pi\)
−0.567115 + 0.823639i \(0.691940\pi\)
\(464\) −37.0536 −1.72017
\(465\) −1.96389 −0.0910733
\(466\) −31.6674 −1.46696
\(467\) −4.44860 −0.205857 −0.102928 0.994689i \(-0.532821\pi\)
−0.102928 + 0.994689i \(0.532821\pi\)
\(468\) 0 0
\(469\) 0.826916 0.0381834
\(470\) 51.7673 2.38785
\(471\) 4.00386 0.184488
\(472\) −96.1273 −4.42462
\(473\) 16.0276 0.736951
\(474\) −0.749922 −0.0344450
\(475\) −13.4823 −0.618608
\(476\) −11.4273 −0.523769
\(477\) 26.8051 1.22732
\(478\) −3.86008 −0.176556
\(479\) −31.6766 −1.44734 −0.723671 0.690145i \(-0.757547\pi\)
−0.723671 + 0.690145i \(0.757547\pi\)
\(480\) −21.1394 −0.964879
\(481\) 0 0
\(482\) 7.24372 0.329942
\(483\) 0.627077 0.0285330
\(484\) −40.2938 −1.83153
\(485\) 30.0780 1.36577
\(486\) −23.9199 −1.08503
\(487\) 26.9156 1.21966 0.609832 0.792531i \(-0.291237\pi\)
0.609832 + 0.792531i \(0.291237\pi\)
\(488\) 90.3860 4.09158
\(489\) −1.52405 −0.0689200
\(490\) 8.80735 0.397875
\(491\) 9.72716 0.438980 0.219490 0.975615i \(-0.429561\pi\)
0.219490 + 0.975615i \(0.429561\pi\)
\(492\) 7.75052 0.349421
\(493\) −5.88682 −0.265129
\(494\) 0 0
\(495\) 17.3239 0.778653
\(496\) 23.6134 1.06027
\(497\) 2.35425 0.105602
\(498\) −9.32392 −0.417815
\(499\) −7.87525 −0.352545 −0.176272 0.984341i \(-0.556404\pi\)
−0.176272 + 0.984341i \(0.556404\pi\)
\(500\) 10.6408 0.475872
\(501\) 3.12015 0.139398
\(502\) 29.5565 1.31917
\(503\) −9.75206 −0.434823 −0.217411 0.976080i \(-0.569761\pi\)
−0.217411 + 0.976080i \(0.569761\pi\)
\(504\) 25.7506 1.14702
\(505\) 48.2964 2.14916
\(506\) −9.04533 −0.402114
\(507\) 0 0
\(508\) −51.6630 −2.29217
\(509\) 23.0256 1.02059 0.510295 0.859999i \(-0.329536\pi\)
0.510295 + 0.859999i \(0.329536\pi\)
\(510\) −6.56039 −0.290499
\(511\) −3.19482 −0.141331
\(512\) 11.8512 0.523752
\(513\) −4.88424 −0.215645
\(514\) 11.2220 0.494981
\(515\) −13.9541 −0.614891
\(516\) 15.9410 0.701762
\(517\) −10.8505 −0.477203
\(518\) 16.0452 0.704987
\(519\) −2.10752 −0.0925100
\(520\) 0 0
\(521\) 0.486481 0.0213131 0.0106566 0.999943i \(-0.496608\pi\)
0.0106566 + 0.999943i \(0.496608\pi\)
\(522\) 21.2876 0.931733
\(523\) −34.6270 −1.51413 −0.757065 0.653339i \(-0.773368\pi\)
−0.757065 + 0.653339i \(0.773368\pi\)
\(524\) −99.0414 −4.32664
\(525\) 1.94263 0.0847834
\(526\) 10.9577 0.477777
\(527\) 3.75154 0.163420
\(528\) 8.65510 0.376665
\(529\) −19.7144 −0.857147
\(530\) −81.9636 −3.56027
\(531\) 30.9699 1.34398
\(532\) 12.7425 0.552458
\(533\) 0 0
\(534\) −14.1336 −0.611622
\(535\) −62.3141 −2.69408
\(536\) −7.39279 −0.319320
\(537\) −1.34216 −0.0579185
\(538\) 10.8134 0.466198
\(539\) −1.84603 −0.0795140
\(540\) 35.1764 1.51375
\(541\) 22.5384 0.969002 0.484501 0.874791i \(-0.339001\pi\)
0.484501 + 0.874791i \(0.339001\pi\)
\(542\) −7.52844 −0.323374
\(543\) −2.27770 −0.0977456
\(544\) 40.3818 1.73136
\(545\) 13.9172 0.596146
\(546\) 0 0
\(547\) 39.3716 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(548\) 44.6955 1.90930
\(549\) −29.1202 −1.24282
\(550\) −28.0217 −1.19485
\(551\) 6.56436 0.279651
\(552\) −5.60619 −0.238615
\(553\) −0.801911 −0.0341007
\(554\) 45.1227 1.91708
\(555\) 6.69034 0.283989
\(556\) −93.6000 −3.96952
\(557\) 0.726975 0.0308029 0.0154015 0.999881i \(-0.495097\pi\)
0.0154015 + 0.999881i \(0.495097\pi\)
\(558\) −13.5661 −0.574300
\(559\) 0 0
\(560\) −44.1559 −1.86593
\(561\) 1.37506 0.0580552
\(562\) 36.1502 1.52490
\(563\) 41.6077 1.75355 0.876777 0.480897i \(-0.159689\pi\)
0.876777 + 0.480897i \(0.159689\pi\)
\(564\) −10.7918 −0.454417
\(565\) 8.95907 0.376911
\(566\) −51.0532 −2.14593
\(567\) −7.93720 −0.333331
\(568\) −21.0474 −0.883130
\(569\) −25.3888 −1.06435 −0.532177 0.846633i \(-0.678626\pi\)
−0.532177 + 0.846633i \(0.678626\pi\)
\(570\) 7.31546 0.306411
\(571\) 16.9992 0.711393 0.355697 0.934602i \(-0.384244\pi\)
0.355697 + 0.934602i \(0.384244\pi\)
\(572\) 0 0
\(573\) 4.75451 0.198622
\(574\) 11.4110 0.476288
\(575\) 10.1786 0.424476
\(576\) −67.9551 −2.83146
\(577\) 15.9759 0.665084 0.332542 0.943088i \(-0.392094\pi\)
0.332542 + 0.943088i \(0.392094\pi\)
\(578\) −33.4223 −1.39018
\(579\) −7.87139 −0.327124
\(580\) −47.2767 −1.96306
\(581\) −9.97031 −0.413638
\(582\) −8.63320 −0.357858
\(583\) 17.1796 0.711508
\(584\) 28.5623 1.18192
\(585\) 0 0
\(586\) 9.23926 0.381670
\(587\) 15.9815 0.659627 0.329814 0.944046i \(-0.393014\pi\)
0.329814 + 0.944046i \(0.393014\pi\)
\(588\) −1.83605 −0.0757172
\(589\) −4.18333 −0.172371
\(590\) −94.6989 −3.89869
\(591\) −5.02566 −0.206728
\(592\) −80.4433 −3.30620
\(593\) −29.0532 −1.19307 −0.596536 0.802586i \(-0.703457\pi\)
−0.596536 + 0.802586i \(0.703457\pi\)
\(594\) −10.1515 −0.416520
\(595\) −7.01520 −0.287595
\(596\) −21.3407 −0.874151
\(597\) −8.24757 −0.337551
\(598\) 0 0
\(599\) 3.45554 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(600\) −17.3675 −0.709026
\(601\) 15.5304 0.633497 0.316748 0.948510i \(-0.397409\pi\)
0.316748 + 0.948510i \(0.397409\pi\)
\(602\) 23.4698 0.956556
\(603\) 2.38178 0.0969936
\(604\) 100.313 4.08166
\(605\) −24.7363 −1.00567
\(606\) −13.8624 −0.563120
\(607\) 15.4784 0.628250 0.314125 0.949382i \(-0.398289\pi\)
0.314125 + 0.949382i \(0.398289\pi\)
\(608\) −45.0296 −1.82619
\(609\) −0.945847 −0.0383276
\(610\) 89.0429 3.60524
\(611\) 0 0
\(612\) −32.9142 −1.33048
\(613\) 7.13223 0.288068 0.144034 0.989573i \(-0.453993\pi\)
0.144034 + 0.989573i \(0.453993\pi\)
\(614\) −44.2456 −1.78561
\(615\) 4.75803 0.191862
\(616\) 16.5039 0.664959
\(617\) −4.96685 −0.199958 −0.0999789 0.994990i \(-0.531878\pi\)
−0.0999789 + 0.994990i \(0.531878\pi\)
\(618\) 4.00520 0.161113
\(619\) −42.3570 −1.70247 −0.851235 0.524784i \(-0.824146\pi\)
−0.851235 + 0.524784i \(0.824146\pi\)
\(620\) 30.1284 1.20999
\(621\) 3.68741 0.147971
\(622\) 64.0600 2.56857
\(623\) −15.1135 −0.605508
\(624\) 0 0
\(625\) −21.5445 −0.861779
\(626\) −14.0032 −0.559682
\(627\) −1.53333 −0.0612352
\(628\) −61.4239 −2.45108
\(629\) −12.7803 −0.509583
\(630\) 25.3680 1.01068
\(631\) 6.26775 0.249515 0.124758 0.992187i \(-0.460185\pi\)
0.124758 + 0.992187i \(0.460185\pi\)
\(632\) 7.16924 0.285177
\(633\) −1.49286 −0.0593361
\(634\) 16.3959 0.651163
\(635\) −31.7158 −1.25860
\(636\) 17.0868 0.677534
\(637\) 0 0
\(638\) 13.6434 0.540149
\(639\) 6.78098 0.268251
\(640\) 85.5797 3.38283
\(641\) −31.5637 −1.24669 −0.623345 0.781947i \(-0.714227\pi\)
−0.623345 + 0.781947i \(0.714227\pi\)
\(642\) 17.8858 0.705897
\(643\) 18.2504 0.719725 0.359863 0.933005i \(-0.382824\pi\)
0.359863 + 0.933005i \(0.382824\pi\)
\(644\) −9.62010 −0.379085
\(645\) 9.78613 0.385329
\(646\) −13.9744 −0.549816
\(647\) 23.0273 0.905298 0.452649 0.891689i \(-0.350479\pi\)
0.452649 + 0.891689i \(0.350479\pi\)
\(648\) 70.9601 2.78758
\(649\) 19.8490 0.779140
\(650\) 0 0
\(651\) 0.602768 0.0236243
\(652\) 23.3807 0.915660
\(653\) 28.8124 1.12752 0.563759 0.825939i \(-0.309355\pi\)
0.563759 + 0.825939i \(0.309355\pi\)
\(654\) −3.99460 −0.156201
\(655\) −60.8014 −2.37571
\(656\) −57.2096 −2.23366
\(657\) −9.20210 −0.359008
\(658\) −15.8887 −0.619406
\(659\) −31.2228 −1.21627 −0.608134 0.793835i \(-0.708082\pi\)
−0.608134 + 0.793835i \(0.708082\pi\)
\(660\) 11.0431 0.429850
\(661\) −26.5582 −1.03299 −0.516496 0.856289i \(-0.672764\pi\)
−0.516496 + 0.856289i \(0.672764\pi\)
\(662\) 46.6973 1.81494
\(663\) 0 0
\(664\) 89.1366 3.45917
\(665\) 7.82261 0.303348
\(666\) 46.2154 1.79081
\(667\) −4.95584 −0.191891
\(668\) −47.8667 −1.85202
\(669\) −8.09337 −0.312908
\(670\) −7.28293 −0.281364
\(671\) −18.6635 −0.720495
\(672\) 6.48823 0.250289
\(673\) −19.7386 −0.760867 −0.380434 0.924808i \(-0.624225\pi\)
−0.380434 + 0.924808i \(0.624225\pi\)
\(674\) 22.5842 0.869912
\(675\) 11.4233 0.439683
\(676\) 0 0
\(677\) −13.1440 −0.505163 −0.252582 0.967576i \(-0.581280\pi\)
−0.252582 + 0.967576i \(0.581280\pi\)
\(678\) −2.57149 −0.0987576
\(679\) −9.23171 −0.354280
\(680\) 62.7172 2.40510
\(681\) 9.24475 0.354260
\(682\) −8.69468 −0.332936
\(683\) 6.76255 0.258762 0.129381 0.991595i \(-0.458701\pi\)
0.129381 + 0.991595i \(0.458701\pi\)
\(684\) 36.7025 1.40336
\(685\) 27.4385 1.04837
\(686\) −2.70320 −0.103209
\(687\) 1.04017 0.0396848
\(688\) −117.666 −4.48599
\(689\) 0 0
\(690\) −5.52288 −0.210253
\(691\) −9.17090 −0.348877 −0.174439 0.984668i \(-0.555811\pi\)
−0.174439 + 0.984668i \(0.555811\pi\)
\(692\) 32.3319 1.22907
\(693\) −5.31715 −0.201982
\(694\) 77.9115 2.95748
\(695\) −57.4609 −2.17962
\(696\) 8.45605 0.320526
\(697\) −9.08908 −0.344273
\(698\) −31.6870 −1.19937
\(699\) 4.05272 0.153288
\(700\) −29.8023 −1.12642
\(701\) −47.4700 −1.79292 −0.896459 0.443127i \(-0.853869\pi\)
−0.896459 + 0.443127i \(0.853869\pi\)
\(702\) 0 0
\(703\) 14.2512 0.537495
\(704\) −43.5532 −1.64147
\(705\) −6.62507 −0.249515
\(706\) −48.2148 −1.81459
\(707\) −14.8234 −0.557491
\(708\) 19.7416 0.741936
\(709\) −34.9719 −1.31340 −0.656699 0.754153i \(-0.728048\pi\)
−0.656699 + 0.754153i \(0.728048\pi\)
\(710\) −20.7347 −0.778158
\(711\) −2.30976 −0.0866227
\(712\) 135.117 5.06374
\(713\) 3.15825 0.118277
\(714\) 2.01355 0.0753552
\(715\) 0 0
\(716\) 20.5903 0.769496
\(717\) 0.494005 0.0184490
\(718\) −15.3585 −0.573175
\(719\) −8.36101 −0.311813 −0.155907 0.987772i \(-0.549830\pi\)
−0.155907 + 0.987772i \(0.549830\pi\)
\(720\) −127.183 −4.73984
\(721\) 4.28286 0.159502
\(722\) −35.7779 −1.33152
\(723\) −0.927035 −0.0344768
\(724\) 34.9427 1.29863
\(725\) −15.3528 −0.570188
\(726\) 7.09997 0.263505
\(727\) 27.4014 1.01626 0.508131 0.861280i \(-0.330337\pi\)
0.508131 + 0.861280i \(0.330337\pi\)
\(728\) 0 0
\(729\) −20.7504 −0.768532
\(730\) 28.1379 1.04143
\(731\) −18.6941 −0.691425
\(732\) −18.5625 −0.686092
\(733\) 12.1569 0.449026 0.224513 0.974471i \(-0.427921\pi\)
0.224513 + 0.974471i \(0.427921\pi\)
\(734\) −53.0681 −1.95878
\(735\) −1.12715 −0.0415754
\(736\) 33.9956 1.25309
\(737\) 1.52651 0.0562297
\(738\) 32.8674 1.20987
\(739\) −48.4439 −1.78204 −0.891019 0.453966i \(-0.850009\pi\)
−0.891019 + 0.453966i \(0.850009\pi\)
\(740\) −102.638 −3.77304
\(741\) 0 0
\(742\) 25.1567 0.923531
\(743\) 16.9906 0.623326 0.311663 0.950193i \(-0.399114\pi\)
0.311663 + 0.950193i \(0.399114\pi\)
\(744\) −5.38886 −0.197565
\(745\) −13.1010 −0.479985
\(746\) 86.6767 3.17346
\(747\) −28.7177 −1.05073
\(748\) −21.0951 −0.771313
\(749\) 19.1258 0.698841
\(750\) −1.87497 −0.0684642
\(751\) 43.0323 1.57027 0.785136 0.619323i \(-0.212593\pi\)
0.785136 + 0.619323i \(0.212593\pi\)
\(752\) 79.6585 2.90485
\(753\) −3.78258 −0.137845
\(754\) 0 0
\(755\) 61.5817 2.24119
\(756\) −10.7965 −0.392666
\(757\) 29.1785 1.06051 0.530255 0.847838i \(-0.322096\pi\)
0.530255 + 0.847838i \(0.322096\pi\)
\(758\) 51.4231 1.86777
\(759\) 1.15760 0.0420183
\(760\) −69.9357 −2.53683
\(761\) 29.4251 1.06666 0.533330 0.845907i \(-0.320941\pi\)
0.533330 + 0.845907i \(0.320941\pi\)
\(762\) 9.10328 0.329777
\(763\) −4.27153 −0.154640
\(764\) −72.9398 −2.63887
\(765\) −20.2060 −0.730550
\(766\) 1.89178 0.0683526
\(767\) 0 0
\(768\) −8.23976 −0.297327
\(769\) −17.1864 −0.619759 −0.309879 0.950776i \(-0.600289\pi\)
−0.309879 + 0.950776i \(0.600289\pi\)
\(770\) 16.2586 0.585920
\(771\) −1.43617 −0.0517223
\(772\) 120.756 4.34612
\(773\) 21.9601 0.789851 0.394926 0.918713i \(-0.370770\pi\)
0.394926 + 0.918713i \(0.370770\pi\)
\(774\) 67.6004 2.42985
\(775\) 9.78399 0.351451
\(776\) 82.5333 2.96277
\(777\) −2.05343 −0.0736665
\(778\) −54.2118 −1.94359
\(779\) 10.1352 0.363131
\(780\) 0 0
\(781\) 4.34600 0.155512
\(782\) 10.5501 0.377272
\(783\) −5.56188 −0.198765
\(784\) 13.5526 0.484020
\(785\) −37.7081 −1.34586
\(786\) 17.4516 0.622478
\(787\) 2.33567 0.0832578 0.0416289 0.999133i \(-0.486745\pi\)
0.0416289 + 0.999133i \(0.486745\pi\)
\(788\) 77.0996 2.74656
\(789\) −1.40234 −0.0499246
\(790\) 7.06271 0.251280
\(791\) −2.74976 −0.0977704
\(792\) 47.5364 1.68913
\(793\) 0 0
\(794\) 60.2280 2.13741
\(795\) 10.4895 0.372025
\(796\) 126.527 4.48465
\(797\) 27.8040 0.984869 0.492434 0.870350i \(-0.336107\pi\)
0.492434 + 0.870350i \(0.336107\pi\)
\(798\) −2.24530 −0.0794827
\(799\) 12.6556 0.447723
\(800\) 105.315 3.72346
\(801\) −43.5316 −1.53811
\(802\) −12.9956 −0.458890
\(803\) −5.89773 −0.208126
\(804\) 1.51825 0.0535447
\(805\) −5.90576 −0.208151
\(806\) 0 0
\(807\) −1.38387 −0.0487147
\(808\) 132.524 4.66218
\(809\) 15.0203 0.528087 0.264043 0.964511i \(-0.414944\pi\)
0.264043 + 0.964511i \(0.414944\pi\)
\(810\) 69.9056 2.45623
\(811\) −43.6933 −1.53428 −0.767139 0.641481i \(-0.778320\pi\)
−0.767139 + 0.641481i \(0.778320\pi\)
\(812\) 14.5104 0.509215
\(813\) 0.963474 0.0337905
\(814\) 29.6199 1.03818
\(815\) 14.3534 0.502778
\(816\) −10.0950 −0.353395
\(817\) 20.8456 0.729297
\(818\) 99.4870 3.47848
\(819\) 0 0
\(820\) −72.9939 −2.54906
\(821\) −18.0701 −0.630651 −0.315326 0.948984i \(-0.602114\pi\)
−0.315326 + 0.948984i \(0.602114\pi\)
\(822\) −7.87557 −0.274692
\(823\) 4.45550 0.155309 0.0776544 0.996980i \(-0.475257\pi\)
0.0776544 + 0.996980i \(0.475257\pi\)
\(824\) −38.2896 −1.33388
\(825\) 3.58615 0.124854
\(826\) 29.0655 1.01132
\(827\) 11.8352 0.411549 0.205774 0.978599i \(-0.434029\pi\)
0.205774 + 0.978599i \(0.434029\pi\)
\(828\) −27.7090 −0.962953
\(829\) −3.53894 −0.122913 −0.0614563 0.998110i \(-0.519574\pi\)
−0.0614563 + 0.998110i \(0.519574\pi\)
\(830\) 87.8120 3.04800
\(831\) −5.77471 −0.200323
\(832\) 0 0
\(833\) 2.15314 0.0746019
\(834\) 16.4928 0.571099
\(835\) −29.3853 −1.01692
\(836\) 23.5230 0.813561
\(837\) 3.54447 0.122515
\(838\) 79.1137 2.73294
\(839\) 33.4853 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(840\) 10.0769 0.347686
\(841\) −21.5249 −0.742238
\(842\) 20.3784 0.702285
\(843\) −4.62642 −0.159343
\(844\) 22.9023 0.788330
\(845\) 0 0
\(846\) −45.7645 −1.57342
\(847\) 7.59218 0.260870
\(848\) −126.124 −4.33112
\(849\) 6.53368 0.224235
\(850\) 32.6835 1.12103
\(851\) −10.7591 −0.368818
\(852\) 4.32250 0.148087
\(853\) 22.0871 0.756248 0.378124 0.925755i \(-0.376569\pi\)
0.378124 + 0.925755i \(0.376569\pi\)
\(854\) −27.3295 −0.935196
\(855\) 22.5316 0.770565
\(856\) −170.988 −5.84426
\(857\) −6.89363 −0.235482 −0.117741 0.993044i \(-0.537565\pi\)
−0.117741 + 0.993044i \(0.537565\pi\)
\(858\) 0 0
\(859\) −37.4834 −1.27892 −0.639459 0.768825i \(-0.720842\pi\)
−0.639459 + 0.768825i \(0.720842\pi\)
\(860\) −150.131 −5.11942
\(861\) −1.46036 −0.0497689
\(862\) 84.4103 2.87503
\(863\) 17.5248 0.596552 0.298276 0.954480i \(-0.403588\pi\)
0.298276 + 0.954480i \(0.403588\pi\)
\(864\) 38.1528 1.29799
\(865\) 19.8485 0.674869
\(866\) 15.9057 0.540498
\(867\) 4.27731 0.145265
\(868\) −9.24717 −0.313869
\(869\) −1.48035 −0.0502174
\(870\) 8.33040 0.282427
\(871\) 0 0
\(872\) 38.1883 1.29322
\(873\) −26.5903 −0.899944
\(874\) −11.7644 −0.397937
\(875\) −2.00495 −0.0677798
\(876\) −5.86584 −0.198188
\(877\) −46.7491 −1.57860 −0.789302 0.614005i \(-0.789557\pi\)
−0.789302 + 0.614005i \(0.789557\pi\)
\(878\) −26.9142 −0.908309
\(879\) −1.18242 −0.0398821
\(880\) −81.5131 −2.74781
\(881\) −2.91875 −0.0983350 −0.0491675 0.998791i \(-0.515657\pi\)
−0.0491675 + 0.998791i \(0.515657\pi\)
\(882\) −7.78607 −0.262171
\(883\) −28.5505 −0.960801 −0.480400 0.877049i \(-0.659509\pi\)
−0.480400 + 0.877049i \(0.659509\pi\)
\(884\) 0 0
\(885\) 12.1194 0.407388
\(886\) −96.9941 −3.25858
\(887\) 0.422914 0.0142001 0.00710004 0.999975i \(-0.497740\pi\)
0.00710004 + 0.999975i \(0.497740\pi\)
\(888\) 18.3581 0.616058
\(889\) 9.73438 0.326480
\(890\) 133.110 4.46184
\(891\) −14.6523 −0.490870
\(892\) 124.162 4.15725
\(893\) −14.1122 −0.472247
\(894\) 3.76035 0.125765
\(895\) 12.6404 0.422521
\(896\) −26.2666 −0.877504
\(897\) 0 0
\(898\) −10.8000 −0.360401
\(899\) −4.76372 −0.158879
\(900\) −85.8401 −2.86134
\(901\) −20.0377 −0.667553
\(902\) 21.0651 0.701391
\(903\) −3.00361 −0.0999539
\(904\) 24.5834 0.817633
\(905\) 21.4512 0.713063
\(906\) −17.6756 −0.587232
\(907\) −22.4284 −0.744723 −0.372361 0.928088i \(-0.621452\pi\)
−0.372361 + 0.928088i \(0.621452\pi\)
\(908\) −141.825 −4.70664
\(909\) −42.6961 −1.41614
\(910\) 0 0
\(911\) −32.5788 −1.07938 −0.539692 0.841863i \(-0.681459\pi\)
−0.539692 + 0.841863i \(0.681459\pi\)
\(912\) 11.2569 0.372752
\(913\) −18.4055 −0.609132
\(914\) −111.432 −3.68583
\(915\) −11.3955 −0.376724
\(916\) −15.9574 −0.527247
\(917\) 18.6615 0.616256
\(918\) 11.8403 0.390788
\(919\) −9.87913 −0.325883 −0.162941 0.986636i \(-0.552098\pi\)
−0.162941 + 0.986636i \(0.552098\pi\)
\(920\) 52.7987 1.74072
\(921\) 5.66246 0.186584
\(922\) 66.8408 2.20129
\(923\) 0 0
\(924\) −3.38939 −0.111503
\(925\) −33.3309 −1.09591
\(926\) −65.9734 −2.16802
\(927\) 12.3360 0.405168
\(928\) −51.2769 −1.68325
\(929\) 29.9136 0.981434 0.490717 0.871319i \(-0.336735\pi\)
0.490717 + 0.871319i \(0.336735\pi\)
\(930\) −5.30878 −0.174082
\(931\) −2.40096 −0.0786881
\(932\) −62.1736 −2.03656
\(933\) −8.19826 −0.268399
\(934\) −12.0255 −0.393485
\(935\) −12.9502 −0.423518
\(936\) 0 0
\(937\) −31.8296 −1.03983 −0.519914 0.854219i \(-0.674036\pi\)
−0.519914 + 0.854219i \(0.674036\pi\)
\(938\) 2.23532 0.0729856
\(939\) 1.79210 0.0584831
\(940\) 101.636 3.31501
\(941\) 42.0885 1.37205 0.686023 0.727580i \(-0.259355\pi\)
0.686023 + 0.727580i \(0.259355\pi\)
\(942\) 10.8232 0.352640
\(943\) −7.65167 −0.249173
\(944\) −145.721 −4.74280
\(945\) −6.62797 −0.215608
\(946\) 43.3258 1.40864
\(947\) 60.3377 1.96071 0.980357 0.197234i \(-0.0631958\pi\)
0.980357 + 0.197234i \(0.0631958\pi\)
\(948\) −1.47234 −0.0478195
\(949\) 0 0
\(950\) −36.4452 −1.18244
\(951\) −2.09831 −0.0680423
\(952\) −19.2495 −0.623880
\(953\) −17.3754 −0.562844 −0.281422 0.959584i \(-0.590806\pi\)
−0.281422 + 0.959584i \(0.590806\pi\)
\(954\) 72.4593 2.34596
\(955\) −44.7776 −1.44897
\(956\) −7.57862 −0.245110
\(957\) −1.74606 −0.0564421
\(958\) −85.6281 −2.76652
\(959\) −8.42156 −0.271946
\(960\) −26.5926 −0.858274
\(961\) −27.9642 −0.902070
\(962\) 0 0
\(963\) 55.0883 1.77520
\(964\) 14.2218 0.458054
\(965\) 74.1322 2.38640
\(966\) 1.69511 0.0545393
\(967\) −18.8630 −0.606594 −0.303297 0.952896i \(-0.598087\pi\)
−0.303297 + 0.952896i \(0.598087\pi\)
\(968\) −67.8756 −2.18160
\(969\) 1.78842 0.0574522
\(970\) 81.3068 2.61061
\(971\) −1.56446 −0.0502060 −0.0251030 0.999685i \(-0.507991\pi\)
−0.0251030 + 0.999685i \(0.507991\pi\)
\(972\) −46.9626 −1.50633
\(973\) 17.6362 0.565390
\(974\) 72.7582 2.33132
\(975\) 0 0
\(976\) 137.017 4.38582
\(977\) 27.8755 0.891817 0.445909 0.895078i \(-0.352881\pi\)
0.445909 + 0.895078i \(0.352881\pi\)
\(978\) −4.11981 −0.131737
\(979\) −27.8999 −0.891684
\(980\) 17.2917 0.552364
\(981\) −12.3034 −0.392817
\(982\) 26.2944 0.839088
\(983\) 33.4239 1.06606 0.533029 0.846097i \(-0.321054\pi\)
0.533029 + 0.846097i \(0.321054\pi\)
\(984\) 13.0559 0.416207
\(985\) 47.3313 1.50810
\(986\) −15.9132 −0.506780
\(987\) 2.03340 0.0647238
\(988\) 0 0
\(989\) −15.7376 −0.500428
\(990\) 46.8300 1.48835
\(991\) −18.9110 −0.600726 −0.300363 0.953825i \(-0.597108\pi\)
−0.300363 + 0.953825i \(0.597108\pi\)
\(992\) 32.6777 1.03752
\(993\) −5.97622 −0.189650
\(994\) 6.36399 0.201853
\(995\) 77.6750 2.46246
\(996\) −18.3059 −0.580046
\(997\) 43.5775 1.38011 0.690057 0.723755i \(-0.257585\pi\)
0.690057 + 0.723755i \(0.257585\pi\)
\(998\) −21.2884 −0.673871
\(999\) −12.0748 −0.382031
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 1183.2.a.p.1.6 6
7.6 odd 2 8281.2.a.ch.1.6 6
13.5 odd 4 1183.2.c.i.337.1 12
13.6 odd 12 91.2.q.a.36.1 12
13.8 odd 4 1183.2.c.i.337.12 12
13.11 odd 12 91.2.q.a.43.1 yes 12
13.12 even 2 1183.2.a.m.1.1 6
39.11 even 12 819.2.ct.a.316.6 12
39.32 even 12 819.2.ct.a.127.6 12
52.11 even 12 1456.2.cc.c.225.4 12
52.19 even 12 1456.2.cc.c.673.4 12
91.6 even 12 637.2.q.h.491.1 12
91.11 odd 12 637.2.u.h.30.6 12
91.19 even 12 637.2.u.i.361.6 12
91.24 even 12 637.2.u.i.30.6 12
91.32 odd 12 637.2.k.h.569.1 12
91.37 odd 12 637.2.k.h.459.6 12
91.45 even 12 637.2.k.g.569.1 12
91.58 odd 12 637.2.u.h.361.6 12
91.76 even 12 637.2.q.h.589.1 12
91.89 even 12 637.2.k.g.459.6 12
91.90 odd 2 8281.2.a.by.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.1 12 13.6 odd 12
91.2.q.a.43.1 yes 12 13.11 odd 12
637.2.k.g.459.6 12 91.89 even 12
637.2.k.g.569.1 12 91.45 even 12
637.2.k.h.459.6 12 91.37 odd 12
637.2.k.h.569.1 12 91.32 odd 12
637.2.q.h.491.1 12 91.6 even 12
637.2.q.h.589.1 12 91.76 even 12
637.2.u.h.30.6 12 91.11 odd 12
637.2.u.h.361.6 12 91.58 odd 12
637.2.u.i.30.6 12 91.24 even 12
637.2.u.i.361.6 12 91.19 even 12
819.2.ct.a.127.6 12 39.32 even 12
819.2.ct.a.316.6 12 39.11 even 12
1183.2.a.m.1.1 6 13.12 even 2
1183.2.a.p.1.6 6 1.1 even 1 trivial
1183.2.c.i.337.1 12 13.5 odd 4
1183.2.c.i.337.12 12 13.8 odd 4
1456.2.cc.c.225.4 12 52.11 even 12
1456.2.cc.c.673.4 12 52.19 even 12
8281.2.a.by.1.1 6 91.90 odd 2
8281.2.a.ch.1.6 6 7.6 odd 2