Properties

Label 9025.2.a.bx.1.2
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.0649878242\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.66064384.1
Defining polynomial: \(x^{6} - 9 x^{4} + 13 x^{2} - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.68667\) of defining polynomial
Character \(\chi\) \(=\) 9025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.82254 q^{2} -2.31446 q^{3} +1.32164 q^{4} +4.21819 q^{6} +1.45033 q^{7} +1.23634 q^{8} +2.35673 q^{9} +O(q^{10})\) \(q-1.82254 q^{2} -2.31446 q^{3} +1.32164 q^{4} +4.21819 q^{6} +1.45033 q^{7} +1.23634 q^{8} +2.35673 q^{9} -3.89655 q^{11} -3.05888 q^{12} -3.05888 q^{13} -2.64327 q^{14} -4.89655 q^{16} +3.92301 q^{17} -4.29522 q^{18} -3.35673 q^{21} +7.10160 q^{22} -5.37334 q^{23} -2.86146 q^{24} +5.57491 q^{26} +1.48883 q^{27} +1.91681 q^{28} -6.00000 q^{29} +8.43637 q^{31} +6.45146 q^{32} +9.01841 q^{33} -7.14982 q^{34} +3.11474 q^{36} +5.95953 q^{37} +7.07965 q^{39} -10.4364 q^{41} +6.11775 q^{42} -1.45033 q^{43} -5.14982 q^{44} +9.79310 q^{46} +4.90686 q^{47} +11.3329 q^{48} -4.89655 q^{49} -9.07965 q^{51} -4.04272 q^{52} +4.23127 q^{53} -2.71345 q^{54} +1.79310 q^{56} +10.9352 q^{58} -3.35673 q^{59} +10.3329 q^{61} -15.3756 q^{62} +3.41802 q^{63} -1.96491 q^{64} -16.4364 q^{66} +9.84404 q^{67} +5.18479 q^{68} +12.4364 q^{69} -8.64327 q^{71} +2.91372 q^{72} -2.43418 q^{73} -10.8615 q^{74} -5.65127 q^{77} -12.9029 q^{78} +12.4364 q^{79} -10.5160 q^{81} +19.0207 q^{82} +12.6635 q^{83} -4.43637 q^{84} +2.64327 q^{86} +13.8868 q^{87} -4.81746 q^{88} -12.3662 q^{89} -4.43637 q^{91} -7.10160 q^{92} -19.5256 q^{93} -8.94292 q^{94} -14.9316 q^{96} -3.05888 q^{97} +8.92414 q^{98} -9.18310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 8 q^{4} + 14 q^{9} + O(q^{10}) \) \( 6 q + 8 q^{4} + 14 q^{9} + 2 q^{11} - 16 q^{14} - 4 q^{16} - 20 q^{21} + 8 q^{24} + 8 q^{26} - 36 q^{29} + 8 q^{34} - 32 q^{36} - 8 q^{39} - 12 q^{41} + 20 q^{44} + 8 q^{46} - 4 q^{49} - 4 q^{51} - 16 q^{54} - 40 q^{56} - 20 q^{59} - 14 q^{61} - 12 q^{64} - 48 q^{66} + 24 q^{69} - 52 q^{71} - 40 q^{74} + 24 q^{79} + 38 q^{81} + 24 q^{84} + 16 q^{86} - 24 q^{89} + 24 q^{91} + 48 q^{94} - 64 q^{96} - 30 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82254 −1.28873 −0.644364 0.764719i \(-0.722878\pi\)
−0.644364 + 0.764719i \(0.722878\pi\)
\(3\) −2.31446 −1.33625 −0.668127 0.744047i \(-0.732904\pi\)
−0.668127 + 0.744047i \(0.732904\pi\)
\(4\) 1.32164 0.660819
\(5\) 0 0
\(6\) 4.21819 1.72207
\(7\) 1.45033 0.548172 0.274086 0.961705i \(-0.411625\pi\)
0.274086 + 0.961705i \(0.411625\pi\)
\(8\) 1.23634 0.437112
\(9\) 2.35673 0.785575
\(10\) 0 0
\(11\) −3.89655 −1.17485 −0.587427 0.809277i \(-0.699859\pi\)
−0.587427 + 0.809277i \(0.699859\pi\)
\(12\) −3.05888 −0.883022
\(13\) −3.05888 −0.848380 −0.424190 0.905573i \(-0.639441\pi\)
−0.424190 + 0.905573i \(0.639441\pi\)
\(14\) −2.64327 −0.706445
\(15\) 0 0
\(16\) −4.89655 −1.22414
\(17\) 3.92301 0.951469 0.475735 0.879589i \(-0.342182\pi\)
0.475735 + 0.879589i \(0.342182\pi\)
\(18\) −4.29522 −1.01239
\(19\) 0 0
\(20\) 0 0
\(21\) −3.35673 −0.732498
\(22\) 7.10160 1.51407
\(23\) −5.37334 −1.12042 −0.560209 0.828351i \(-0.689279\pi\)
−0.560209 + 0.828351i \(0.689279\pi\)
\(24\) −2.86146 −0.584093
\(25\) 0 0
\(26\) 5.57491 1.09333
\(27\) 1.48883 0.286526
\(28\) 1.91681 0.362242
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 8.43637 1.51522 0.757609 0.652709i \(-0.226368\pi\)
0.757609 + 0.652709i \(0.226368\pi\)
\(32\) 6.45146 1.14047
\(33\) 9.01841 1.56990
\(34\) −7.14982 −1.22618
\(35\) 0 0
\(36\) 3.11474 0.519123
\(37\) 5.95953 0.979741 0.489871 0.871795i \(-0.337044\pi\)
0.489871 + 0.871795i \(0.337044\pi\)
\(38\) 0 0
\(39\) 7.07965 1.13365
\(40\) 0 0
\(41\) −10.4364 −1.62989 −0.814944 0.579540i \(-0.803232\pi\)
−0.814944 + 0.579540i \(0.803232\pi\)
\(42\) 6.11775 0.943990
\(43\) −1.45033 −0.221173 −0.110586 0.993867i \(-0.535273\pi\)
−0.110586 + 0.993867i \(0.535273\pi\)
\(44\) −5.14982 −0.776365
\(45\) 0 0
\(46\) 9.79310 1.44391
\(47\) 4.90686 0.715739 0.357869 0.933772i \(-0.383503\pi\)
0.357869 + 0.933772i \(0.383503\pi\)
\(48\) 11.3329 1.63576
\(49\) −4.89655 −0.699507
\(50\) 0 0
\(51\) −9.07965 −1.27140
\(52\) −4.04272 −0.560625
\(53\) 4.23127 0.581209 0.290605 0.956843i \(-0.406144\pi\)
0.290605 + 0.956843i \(0.406144\pi\)
\(54\) −2.71345 −0.369254
\(55\) 0 0
\(56\) 1.79310 0.239613
\(57\) 0 0
\(58\) 10.9352 1.43586
\(59\) −3.35673 −0.437008 −0.218504 0.975836i \(-0.570118\pi\)
−0.218504 + 0.975836i \(0.570118\pi\)
\(60\) 0 0
\(61\) 10.3329 1.32300 0.661498 0.749947i \(-0.269921\pi\)
0.661498 + 0.749947i \(0.269921\pi\)
\(62\) −15.3756 −1.95270
\(63\) 3.41802 0.430631
\(64\) −1.96491 −0.245614
\(65\) 0 0
\(66\) −16.4364 −2.02318
\(67\) 9.84404 1.20264 0.601320 0.799008i \(-0.294642\pi\)
0.601320 + 0.799008i \(0.294642\pi\)
\(68\) 5.18479 0.628749
\(69\) 12.4364 1.49716
\(70\) 0 0
\(71\) −8.64327 −1.02577 −0.512884 0.858458i \(-0.671423\pi\)
−0.512884 + 0.858458i \(0.671423\pi\)
\(72\) 2.91372 0.343385
\(73\) −2.43418 −0.284899 −0.142449 0.989802i \(-0.545498\pi\)
−0.142449 + 0.989802i \(0.545498\pi\)
\(74\) −10.8615 −1.26262
\(75\) 0 0
\(76\) 0 0
\(77\) −5.65127 −0.644022
\(78\) −12.9029 −1.46097
\(79\) 12.4364 1.39920 0.699601 0.714534i \(-0.253361\pi\)
0.699601 + 0.714534i \(0.253361\pi\)
\(80\) 0 0
\(81\) −10.5160 −1.16845
\(82\) 19.0207 2.10048
\(83\) 12.6635 1.39000 0.694999 0.719011i \(-0.255405\pi\)
0.694999 + 0.719011i \(0.255405\pi\)
\(84\) −4.43637 −0.484048
\(85\) 0 0
\(86\) 2.64327 0.285032
\(87\) 13.8868 1.48882
\(88\) −4.81746 −0.513543
\(89\) −12.3662 −1.31081 −0.655407 0.755276i \(-0.727503\pi\)
−0.655407 + 0.755276i \(0.727503\pi\)
\(90\) 0 0
\(91\) −4.43637 −0.465058
\(92\) −7.10160 −0.740393
\(93\) −19.5256 −2.02472
\(94\) −8.94292 −0.922392
\(95\) 0 0
\(96\) −14.9316 −1.52395
\(97\) −3.05888 −0.310582 −0.155291 0.987869i \(-0.549631\pi\)
−0.155291 + 0.987869i \(0.549631\pi\)
\(98\) 8.92414 0.901474
\(99\) −9.18310 −0.922936
\(100\) 0 0
\(101\) 3.35673 0.334007 0.167003 0.985956i \(-0.446591\pi\)
0.167003 + 0.985956i \(0.446591\pi\)
\(102\) 16.5480 1.63849
\(103\) −13.0611 −1.28695 −0.643476 0.765466i \(-0.722508\pi\)
−0.643476 + 0.765466i \(0.722508\pi\)
\(104\) −3.78181 −0.370837
\(105\) 0 0
\(106\) −7.71164 −0.749020
\(107\) 5.77099 0.557903 0.278951 0.960305i \(-0.410013\pi\)
0.278951 + 0.960305i \(0.410013\pi\)
\(108\) 1.96770 0.189342
\(109\) −6.64327 −0.636310 −0.318155 0.948039i \(-0.603063\pi\)
−0.318155 + 0.948039i \(0.603063\pi\)
\(110\) 0 0
\(111\) −13.7931 −1.30918
\(112\) −7.10160 −0.671038
\(113\) 9.41606 0.885789 0.442894 0.896574i \(-0.353952\pi\)
0.442894 + 0.896574i \(0.353952\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −7.92982 −0.736266
\(117\) −7.20893 −0.666466
\(118\) 6.11775 0.563185
\(119\) 5.68965 0.521569
\(120\) 0 0
\(121\) 4.18310 0.380282
\(122\) −18.8321 −1.70498
\(123\) 24.1546 2.17794
\(124\) 11.1498 1.00128
\(125\) 0 0
\(126\) −6.22947 −0.554966
\(127\) −11.0934 −0.984383 −0.492192 0.870487i \(-0.663804\pi\)
−0.492192 + 0.870487i \(0.663804\pi\)
\(128\) −9.32179 −0.823938
\(129\) 3.35673 0.295543
\(130\) 0 0
\(131\) 4.61000 0.402778 0.201389 0.979511i \(-0.435455\pi\)
0.201389 + 0.979511i \(0.435455\pi\)
\(132\) 11.9191 1.03742
\(133\) 0 0
\(134\) −17.9411 −1.54988
\(135\) 0 0
\(136\) 4.85018 0.415899
\(137\) −13.1808 −1.12612 −0.563058 0.826417i \(-0.690375\pi\)
−0.563058 + 0.826417i \(0.690375\pi\)
\(138\) −22.6657 −1.92944
\(139\) 1.18310 0.100349 0.0501745 0.998740i \(-0.484022\pi\)
0.0501745 + 0.998740i \(0.484022\pi\)
\(140\) 0 0
\(141\) −11.3567 −0.956409
\(142\) 15.7527 1.32194
\(143\) 11.9191 0.996722
\(144\) −11.5398 −0.961652
\(145\) 0 0
\(146\) 4.43637 0.367157
\(147\) 11.3329 0.934719
\(148\) 7.87634 0.647431
\(149\) 5.46018 0.447315 0.223658 0.974668i \(-0.428200\pi\)
0.223658 + 0.974668i \(0.428200\pi\)
\(150\) 0 0
\(151\) 5.07965 0.413376 0.206688 0.978407i \(-0.433732\pi\)
0.206688 + 0.978407i \(0.433732\pi\)
\(152\) 0 0
\(153\) 9.24546 0.747451
\(154\) 10.2996 0.829969
\(155\) 0 0
\(156\) 9.35673 0.749138
\(157\) 6.11775 0.488250 0.244125 0.969744i \(-0.421499\pi\)
0.244125 + 0.969744i \(0.421499\pi\)
\(158\) −22.6657 −1.80319
\(159\) −9.79310 −0.776643
\(160\) 0 0
\(161\) −7.79310 −0.614182
\(162\) 19.1658 1.50581
\(163\) −16.4365 −1.28740 −0.643701 0.765277i \(-0.722602\pi\)
−0.643701 + 0.765277i \(0.722602\pi\)
\(164\) −13.7931 −1.07706
\(165\) 0 0
\(166\) −23.0796 −1.79133
\(167\) 3.80329 0.294308 0.147154 0.989114i \(-0.452989\pi\)
0.147154 + 0.989114i \(0.452989\pi\)
\(168\) −4.15006 −0.320184
\(169\) −3.64327 −0.280252
\(170\) 0 0
\(171\) 0 0
\(172\) −1.91681 −0.146155
\(173\) 11.3838 0.865491 0.432746 0.901516i \(-0.357545\pi\)
0.432746 + 0.901516i \(0.357545\pi\)
\(174\) −25.3091 −1.91868
\(175\) 0 0
\(176\) 19.0796 1.43818
\(177\) 7.76901 0.583954
\(178\) 22.5378 1.68928
\(179\) −10.0702 −0.752680 −0.376340 0.926482i \(-0.622818\pi\)
−0.376340 + 0.926482i \(0.622818\pi\)
\(180\) 0 0
\(181\) −0.573097 −0.0425980 −0.0212990 0.999773i \(-0.506780\pi\)
−0.0212990 + 0.999773i \(0.506780\pi\)
\(182\) 8.08545 0.599333
\(183\) −23.9151 −1.76786
\(184\) −6.64327 −0.489749
\(185\) 0 0
\(186\) 35.5862 2.60931
\(187\) −15.2862 −1.11784
\(188\) 6.48509 0.472973
\(189\) 2.15930 0.157066
\(190\) 0 0
\(191\) −3.18310 −0.230321 −0.115160 0.993347i \(-0.536738\pi\)
−0.115160 + 0.993347i \(0.536738\pi\)
\(192\) 4.54771 0.328203
\(193\) −3.05888 −0.220183 −0.110091 0.993921i \(-0.535114\pi\)
−0.110091 + 0.993921i \(0.535114\pi\)
\(194\) 5.57491 0.400255
\(195\) 0 0
\(196\) −6.47146 −0.462247
\(197\) 21.4933 1.53134 0.765669 0.643235i \(-0.222408\pi\)
0.765669 + 0.643235i \(0.222408\pi\)
\(198\) 16.7365 1.18941
\(199\) −4.81690 −0.341461 −0.170731 0.985318i \(-0.554613\pi\)
−0.170731 + 0.985318i \(0.554613\pi\)
\(200\) 0 0
\(201\) −22.7836 −1.60703
\(202\) −6.11775 −0.430444
\(203\) −8.70197 −0.610758
\(204\) −12.0000 −0.840168
\(205\) 0 0
\(206\) 23.8044 1.65853
\(207\) −12.6635 −0.880173
\(208\) 14.9779 1.03853
\(209\) 0 0
\(210\) 0 0
\(211\) −10.5066 −0.723301 −0.361650 0.932314i \(-0.617787\pi\)
−0.361650 + 0.932314i \(0.617787\pi\)
\(212\) 5.59220 0.384074
\(213\) 20.0045 1.37069
\(214\) −10.5178 −0.718984
\(215\) 0 0
\(216\) 1.84070 0.125244
\(217\) 12.2355 0.830600
\(218\) 12.1076 0.820031
\(219\) 5.63380 0.380697
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 25.1384 1.68718
\(223\) 16.8947 1.13136 0.565678 0.824626i \(-0.308615\pi\)
0.565678 + 0.824626i \(0.308615\pi\)
\(224\) 9.35673 0.625173
\(225\) 0 0
\(226\) −17.1611 −1.14154
\(227\) −17.1342 −1.13724 −0.568618 0.822602i \(-0.692522\pi\)
−0.568618 + 0.822602i \(0.692522\pi\)
\(228\) 0 0
\(229\) 25.0464 1.65511 0.827555 0.561384i \(-0.189731\pi\)
0.827555 + 0.561384i \(0.189731\pi\)
\(230\) 0 0
\(231\) 13.0796 0.860578
\(232\) −7.41804 −0.487018
\(233\) 19.2986 1.26429 0.632147 0.774849i \(-0.282174\pi\)
0.632147 + 0.774849i \(0.282174\pi\)
\(234\) 13.1385 0.858893
\(235\) 0 0
\(236\) −4.43637 −0.288783
\(237\) −28.7835 −1.86969
\(238\) −10.3696 −0.672161
\(239\) 18.7693 1.21408 0.607042 0.794669i \(-0.292356\pi\)
0.607042 + 0.794669i \(0.292356\pi\)
\(240\) 0 0
\(241\) 14.4364 0.929929 0.464964 0.885329i \(-0.346067\pi\)
0.464964 + 0.885329i \(0.346067\pi\)
\(242\) −7.62385 −0.490079
\(243\) 19.8724 1.27482
\(244\) 13.6564 0.874260
\(245\) 0 0
\(246\) −44.0226 −2.80678
\(247\) 0 0
\(248\) 10.4302 0.662320
\(249\) −29.3091 −1.85739
\(250\) 0 0
\(251\) −10.9762 −0.692811 −0.346406 0.938085i \(-0.612598\pi\)
−0.346406 + 0.938085i \(0.612598\pi\)
\(252\) 4.51739 0.284569
\(253\) 20.9375 1.31633
\(254\) 20.2182 1.26860
\(255\) 0 0
\(256\) 20.9191 1.30745
\(257\) 17.6392 1.10030 0.550150 0.835066i \(-0.314570\pi\)
0.550150 + 0.835066i \(0.314570\pi\)
\(258\) −6.11775 −0.380875
\(259\) 8.64327 0.537067
\(260\) 0 0
\(261\) −14.1404 −0.875266
\(262\) −8.40189 −0.519071
\(263\) −1.68976 −0.104195 −0.0520975 0.998642i \(-0.516591\pi\)
−0.0520975 + 0.998642i \(0.516591\pi\)
\(264\) 11.1498 0.686224
\(265\) 0 0
\(266\) 0 0
\(267\) 28.6211 1.75158
\(268\) 13.0102 0.794727
\(269\) 27.1022 1.65245 0.826226 0.563339i \(-0.190484\pi\)
0.826226 + 0.563339i \(0.190484\pi\)
\(270\) 0 0
\(271\) 23.9524 1.45500 0.727502 0.686105i \(-0.240681\pi\)
0.727502 + 0.686105i \(0.240681\pi\)
\(272\) −19.2092 −1.16473
\(273\) 10.2678 0.621436
\(274\) 24.0226 1.45126
\(275\) 0 0
\(276\) 16.4364 0.989353
\(277\) 8.23549 0.494822 0.247411 0.968911i \(-0.420420\pi\)
0.247411 + 0.968911i \(0.420420\pi\)
\(278\) −2.15624 −0.129323
\(279\) 19.8822 1.19032
\(280\) 0 0
\(281\) 10.4364 0.622582 0.311291 0.950315i \(-0.399239\pi\)
0.311291 + 0.950315i \(0.399239\pi\)
\(282\) 20.6980 1.23255
\(283\) −10.4687 −0.622302 −0.311151 0.950361i \(-0.600714\pi\)
−0.311151 + 0.950361i \(0.600714\pi\)
\(284\) −11.4233 −0.677847
\(285\) 0 0
\(286\) −21.7229 −1.28450
\(287\) −15.1362 −0.893459
\(288\) 15.2043 0.895923
\(289\) −1.61000 −0.0947059
\(290\) 0 0
\(291\) 7.07965 0.415016
\(292\) −3.21710 −0.188266
\(293\) 16.4668 0.961999 0.481000 0.876721i \(-0.340274\pi\)
0.481000 + 0.876721i \(0.340274\pi\)
\(294\) −20.6546 −1.20460
\(295\) 0 0
\(296\) 7.36801 0.428257
\(297\) −5.80131 −0.336626
\(298\) −9.95137 −0.576467
\(299\) 16.4364 0.950540
\(300\) 0 0
\(301\) −2.10345 −0.121241
\(302\) −9.25784 −0.532729
\(303\) −7.76901 −0.446318
\(304\) 0 0
\(305\) 0 0
\(306\) −16.8502 −0.963260
\(307\) −7.87634 −0.449526 −0.224763 0.974413i \(-0.572161\pi\)
−0.224763 + 0.974413i \(0.572161\pi\)
\(308\) −7.46893 −0.425582
\(309\) 30.2295 1.71969
\(310\) 0 0
\(311\) 3.89655 0.220953 0.110477 0.993879i \(-0.464762\pi\)
0.110477 + 0.993879i \(0.464762\pi\)
\(312\) 8.75286 0.495533
\(313\) 7.76901 0.439130 0.219565 0.975598i \(-0.429536\pi\)
0.219565 + 0.975598i \(0.429536\pi\)
\(314\) −11.1498 −0.629221
\(315\) 0 0
\(316\) 16.4364 0.924618
\(317\) −19.0510 −1.07001 −0.535005 0.844849i \(-0.679690\pi\)
−0.535005 + 0.844849i \(0.679690\pi\)
\(318\) 17.8483 1.00088
\(319\) 23.3793 1.30899
\(320\) 0 0
\(321\) −13.3567 −0.745500
\(322\) 14.2032 0.791514
\(323\) 0 0
\(324\) −13.8984 −0.772131
\(325\) 0 0
\(326\) 29.9560 1.65911
\(327\) 15.3756 0.850272
\(328\) −12.9029 −0.712444
\(329\) 7.11655 0.392348
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 16.7365 0.918536
\(333\) 14.0450 0.769660
\(334\) −6.93164 −0.379282
\(335\) 0 0
\(336\) 16.4364 0.896678
\(337\) 6.89249 0.375458 0.187729 0.982221i \(-0.439887\pi\)
0.187729 + 0.982221i \(0.439887\pi\)
\(338\) 6.64000 0.361168
\(339\) −21.7931 −1.18364
\(340\) 0 0
\(341\) −32.8727 −1.78016
\(342\) 0 0
\(343\) −17.2539 −0.931623
\(344\) −1.79310 −0.0966774
\(345\) 0 0
\(346\) −20.7473 −1.11538
\(347\) −30.5503 −1.64002 −0.820012 0.572346i \(-0.806033\pi\)
−0.820012 + 0.572346i \(0.806033\pi\)
\(348\) 18.3533 0.983838
\(349\) 16.7693 0.897640 0.448820 0.893622i \(-0.351844\pi\)
0.448820 + 0.893622i \(0.351844\pi\)
\(350\) 0 0
\(351\) −4.55416 −0.243083
\(352\) −25.1384 −1.33988
\(353\) 29.0999 1.54883 0.774417 0.632676i \(-0.218044\pi\)
0.774417 + 0.632676i \(0.218044\pi\)
\(354\) −14.1593 −0.752558
\(355\) 0 0
\(356\) −16.3436 −0.866210
\(357\) −13.1685 −0.696949
\(358\) 18.3533 0.970000
\(359\) −11.6896 −0.616956 −0.308478 0.951231i \(-0.599820\pi\)
−0.308478 + 0.951231i \(0.599820\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 1.04449 0.0548972
\(363\) −9.68161 −0.508153
\(364\) −5.86328 −0.307319
\(365\) 0 0
\(366\) 43.5862 2.27829
\(367\) −4.20095 −0.219288 −0.109644 0.993971i \(-0.534971\pi\)
−0.109644 + 0.993971i \(0.534971\pi\)
\(368\) 26.3108 1.37155
\(369\) −24.5957 −1.28040
\(370\) 0 0
\(371\) 6.13672 0.318603
\(372\) −25.8058 −1.33797
\(373\) 16.9456 0.877412 0.438706 0.898631i \(-0.355437\pi\)
0.438706 + 0.898631i \(0.355437\pi\)
\(374\) 27.8596 1.44059
\(375\) 0 0
\(376\) 6.06655 0.312858
\(377\) 18.3533 0.945241
\(378\) −3.93539 −0.202415
\(379\) −10.3662 −0.532476 −0.266238 0.963907i \(-0.585781\pi\)
−0.266238 + 0.963907i \(0.585781\pi\)
\(380\) 0 0
\(381\) 25.6753 1.31539
\(382\) 5.80131 0.296821
\(383\) −20.5907 −1.05214 −0.526068 0.850442i \(-0.676334\pi\)
−0.526068 + 0.850442i \(0.676334\pi\)
\(384\) 21.5749 1.10099
\(385\) 0 0
\(386\) 5.57491 0.283756
\(387\) −3.41802 −0.173748
\(388\) −4.04272 −0.205238
\(389\) 8.10345 0.410861 0.205431 0.978672i \(-0.434141\pi\)
0.205431 + 0.978672i \(0.434141\pi\)
\(390\) 0 0
\(391\) −21.0796 −1.06604
\(392\) −6.05380 −0.305763
\(393\) −10.6697 −0.538213
\(394\) −39.1724 −1.97348
\(395\) 0 0
\(396\) −12.1367 −0.609893
\(397\) 3.46891 0.174100 0.0870499 0.996204i \(-0.472256\pi\)
0.0870499 + 0.996204i \(0.472256\pi\)
\(398\) 8.77898 0.440050
\(399\) 0 0
\(400\) 0 0
\(401\) 15.9524 0.796625 0.398312 0.917250i \(-0.369596\pi\)
0.398312 + 0.917250i \(0.369596\pi\)
\(402\) 41.5240 2.07103
\(403\) −25.8058 −1.28548
\(404\) 4.43637 0.220718
\(405\) 0 0
\(406\) 15.8596 0.787101
\(407\) −23.2216 −1.15105
\(408\) −11.2255 −0.555747
\(409\) 3.92982 0.194317 0.0971586 0.995269i \(-0.469025\pi\)
0.0971586 + 0.995269i \(0.469025\pi\)
\(410\) 0 0
\(411\) 30.5066 1.50478
\(412\) −17.2621 −0.850442
\(413\) −4.86835 −0.239556
\(414\) 23.0796 1.13430
\(415\) 0 0
\(416\) −19.7342 −0.967549
\(417\) −2.73823 −0.134092
\(418\) 0 0
\(419\) −34.2996 −1.67565 −0.837824 0.545941i \(-0.816172\pi\)
−0.837824 + 0.545941i \(0.816172\pi\)
\(420\) 0 0
\(421\) 26.0891 1.27151 0.635753 0.771893i \(-0.280690\pi\)
0.635753 + 0.771893i \(0.280690\pi\)
\(422\) 19.1486 0.932138
\(423\) 11.5641 0.562267
\(424\) 5.23129 0.254054
\(425\) 0 0
\(426\) −36.4589 −1.76644
\(427\) 14.9861 0.725229
\(428\) 7.62715 0.368672
\(429\) −27.5862 −1.33187
\(430\) 0 0
\(431\) −10.2996 −0.496117 −0.248058 0.968745i \(-0.579792\pi\)
−0.248058 + 0.968745i \(0.579792\pi\)
\(432\) −7.29014 −0.350747
\(433\) 36.2319 1.74119 0.870596 0.491999i \(-0.163734\pi\)
0.870596 + 0.491999i \(0.163734\pi\)
\(434\) −22.2996 −1.07042
\(435\) 0 0
\(436\) −8.78000 −0.420486
\(437\) 0 0
\(438\) −10.2678 −0.490615
\(439\) 24.0891 1.14971 0.574855 0.818255i \(-0.305058\pi\)
0.574855 + 0.818255i \(0.305058\pi\)
\(440\) 0 0
\(441\) −11.5398 −0.549515
\(442\) 21.8704 1.04027
\(443\) −5.52337 −0.262423 −0.131212 0.991354i \(-0.541887\pi\)
−0.131212 + 0.991354i \(0.541887\pi\)
\(444\) −18.2295 −0.865132
\(445\) 0 0
\(446\) −30.7913 −1.45801
\(447\) −12.6374 −0.597727
\(448\) −2.84977 −0.134639
\(449\) −7.92982 −0.374231 −0.187116 0.982338i \(-0.559914\pi\)
−0.187116 + 0.982338i \(0.559914\pi\)
\(450\) 0 0
\(451\) 40.6658 1.91488
\(452\) 12.4446 0.585346
\(453\) −11.7566 −0.552375
\(454\) 31.2277 1.46559
\(455\) 0 0
\(456\) 0 0
\(457\) −22.6534 −1.05968 −0.529840 0.848098i \(-0.677748\pi\)
−0.529840 + 0.848098i \(0.677748\pi\)
\(458\) −45.6479 −2.13299
\(459\) 5.84070 0.272621
\(460\) 0 0
\(461\) 13.3900 0.623634 0.311817 0.950142i \(-0.399062\pi\)
0.311817 + 0.950142i \(0.399062\pi\)
\(462\) −23.8381 −1.10905
\(463\) −16.9029 −0.785546 −0.392773 0.919635i \(-0.628484\pi\)
−0.392773 + 0.919635i \(0.628484\pi\)
\(464\) 29.3793 1.36390
\(465\) 0 0
\(466\) −35.1724 −1.62933
\(467\) −22.2501 −1.02961 −0.514807 0.857306i \(-0.672136\pi\)
−0.514807 + 0.857306i \(0.672136\pi\)
\(468\) −9.52759 −0.440413
\(469\) 14.2771 0.659254
\(470\) 0 0
\(471\) −14.1593 −0.652426
\(472\) −4.15006 −0.191022
\(473\) 5.65127 0.259846
\(474\) 52.4589 2.40952
\(475\) 0 0
\(476\) 7.51965 0.344663
\(477\) 9.97194 0.456584
\(478\) −34.2077 −1.56462
\(479\) 0.366196 0.0167319 0.00836597 0.999965i \(-0.497337\pi\)
0.00836597 + 0.999965i \(0.497337\pi\)
\(480\) 0 0
\(481\) −18.2295 −0.831192
\(482\) −26.3108 −1.19842
\(483\) 18.0368 0.820704
\(484\) 5.52854 0.251297
\(485\) 0 0
\(486\) −36.2182 −1.64289
\(487\) 26.8461 1.21651 0.608257 0.793740i \(-0.291869\pi\)
0.608257 + 0.793740i \(0.291869\pi\)
\(488\) 12.7750 0.578298
\(489\) 38.0415 1.72030
\(490\) 0 0
\(491\) −23.7266 −1.07076 −0.535382 0.844610i \(-0.679832\pi\)
−0.535382 + 0.844610i \(0.679832\pi\)
\(492\) 31.9236 1.43923
\(493\) −23.5381 −1.06010
\(494\) 0 0
\(495\) 0 0
\(496\) −41.3091 −1.85483
\(497\) −12.5356 −0.562298
\(498\) 53.4169 2.39367
\(499\) 6.81690 0.305166 0.152583 0.988291i \(-0.451241\pi\)
0.152583 + 0.988291i \(0.451241\pi\)
\(500\) 0 0
\(501\) −8.80257 −0.393270
\(502\) 20.0045 0.892845
\(503\) −23.4102 −1.04381 −0.521904 0.853004i \(-0.674778\pi\)
−0.521904 + 0.853004i \(0.674778\pi\)
\(504\) 4.22584 0.188234
\(505\) 0 0
\(506\) −38.1593 −1.69639
\(507\) 8.43221 0.374488
\(508\) −14.6615 −0.650499
\(509\) −16.9204 −0.749981 −0.374991 0.927029i \(-0.622354\pi\)
−0.374991 + 0.927029i \(0.622354\pi\)
\(510\) 0 0
\(511\) −3.53035 −0.156174
\(512\) −19.4823 −0.861003
\(513\) 0 0
\(514\) −32.1480 −1.41799
\(515\) 0 0
\(516\) 4.43637 0.195300
\(517\) −19.1198 −0.840888
\(518\) −15.7527 −0.692133
\(519\) −26.3473 −1.15652
\(520\) 0 0
\(521\) 3.49345 0.153051 0.0765254 0.997068i \(-0.475617\pi\)
0.0765254 + 0.997068i \(0.475617\pi\)
\(522\) 25.7713 1.12798
\(523\) 14.9271 0.652714 0.326357 0.945247i \(-0.394179\pi\)
0.326357 + 0.945247i \(0.394179\pi\)
\(524\) 6.09275 0.266163
\(525\) 0 0
\(526\) 3.07965 0.134279
\(527\) 33.0960 1.44168
\(528\) −44.1591 −1.92178
\(529\) 5.87275 0.255337
\(530\) 0 0
\(531\) −7.91088 −0.343303
\(532\) 0 0
\(533\) 31.9236 1.38276
\(534\) −52.1629 −2.25731
\(535\) 0 0
\(536\) 12.1706 0.525689
\(537\) 23.3070 1.00577
\(538\) −49.3948 −2.12956
\(539\) 19.0796 0.821819
\(540\) 0 0
\(541\) −12.6991 −0.545978 −0.272989 0.962017i \(-0.588012\pi\)
−0.272989 + 0.962017i \(0.588012\pi\)
\(542\) −43.6541 −1.87510
\(543\) 1.32641 0.0569217
\(544\) 25.3091 1.08512
\(545\) 0 0
\(546\) −18.7135 −0.800862
\(547\) 31.8162 1.36036 0.680182 0.733043i \(-0.261901\pi\)
0.680182 + 0.733043i \(0.261901\pi\)
\(548\) −17.4203 −0.744158
\(549\) 24.3519 1.03931
\(550\) 0 0
\(551\) 0 0
\(552\) 15.3756 0.654429
\(553\) 18.0368 0.767003
\(554\) −15.0095 −0.637691
\(555\) 0 0
\(556\) 1.56363 0.0663125
\(557\) −9.64731 −0.408770 −0.204385 0.978891i \(-0.565519\pi\)
−0.204385 + 0.978891i \(0.565519\pi\)
\(558\) −36.2361 −1.53399
\(559\) 4.43637 0.187639
\(560\) 0 0
\(561\) 35.3793 1.49372
\(562\) −19.0207 −0.802338
\(563\) 4.28216 0.180471 0.0902357 0.995920i \(-0.471238\pi\)
0.0902357 + 0.995920i \(0.471238\pi\)
\(564\) −15.0095 −0.632013
\(565\) 0 0
\(566\) 19.0796 0.801977
\(567\) −15.2517 −0.640510
\(568\) −10.6860 −0.448376
\(569\) −42.2295 −1.77035 −0.885176 0.465257i \(-0.845962\pi\)
−0.885176 + 0.465257i \(0.845962\pi\)
\(570\) 0 0
\(571\) −19.2200 −0.804332 −0.402166 0.915567i \(-0.631743\pi\)
−0.402166 + 0.915567i \(0.631743\pi\)
\(572\) 15.7527 0.658653
\(573\) 7.36715 0.307767
\(574\) 27.5862 1.15143
\(575\) 0 0
\(576\) −4.63076 −0.192948
\(577\) −40.7919 −1.69819 −0.849096 0.528239i \(-0.822852\pi\)
−0.849096 + 0.528239i \(0.822852\pi\)
\(578\) 2.93428 0.122050
\(579\) 7.07965 0.294220
\(580\) 0 0
\(581\) 18.3662 0.761958
\(582\) −12.9029 −0.534843
\(583\) −16.4873 −0.682836
\(584\) −3.00947 −0.124533
\(585\) 0 0
\(586\) −30.0113 −1.23975
\(587\) −31.8851 −1.31604 −0.658019 0.753001i \(-0.728605\pi\)
−0.658019 + 0.753001i \(0.728605\pi\)
\(588\) 14.9779 0.617680
\(589\) 0 0
\(590\) 0 0
\(591\) −49.7455 −2.04626
\(592\) −29.1811 −1.19934
\(593\) −38.8973 −1.59732 −0.798660 0.601783i \(-0.794457\pi\)
−0.798660 + 0.601783i \(0.794457\pi\)
\(594\) 10.5731 0.433819
\(595\) 0 0
\(596\) 7.21637 0.295594
\(597\) 11.1485 0.456279
\(598\) −29.9559 −1.22499
\(599\) −28.1629 −1.15071 −0.575353 0.817905i \(-0.695135\pi\)
−0.575353 + 0.817905i \(0.695135\pi\)
\(600\) 0 0
\(601\) 5.56363 0.226945 0.113473 0.993541i \(-0.463803\pi\)
0.113473 + 0.993541i \(0.463803\pi\)
\(602\) 3.83361 0.156246
\(603\) 23.1997 0.944764
\(604\) 6.71345 0.273166
\(605\) 0 0
\(606\) 14.1593 0.575182
\(607\) −33.9986 −1.37996 −0.689980 0.723828i \(-0.742381\pi\)
−0.689980 + 0.723828i \(0.742381\pi\)
\(608\) 0 0
\(609\) 20.1404 0.816128
\(610\) 0 0
\(611\) −15.0095 −0.607218
\(612\) 12.2191 0.493929
\(613\) 17.5703 0.709659 0.354830 0.934931i \(-0.384539\pi\)
0.354830 + 0.934931i \(0.384539\pi\)
\(614\) 14.3549 0.579317
\(615\) 0 0
\(616\) −6.98690 −0.281510
\(617\) −13.0791 −0.526544 −0.263272 0.964722i \(-0.584802\pi\)
−0.263272 + 0.964722i \(0.584802\pi\)
\(618\) −55.0943 −2.21622
\(619\) −18.9393 −0.761234 −0.380617 0.924733i \(-0.624288\pi\)
−0.380617 + 0.924733i \(0.624288\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) −7.10160 −0.284748
\(623\) −17.9350 −0.718552
\(624\) −34.6658 −1.38774
\(625\) 0 0
\(626\) −14.1593 −0.565919
\(627\) 0 0
\(628\) 8.08545 0.322645
\(629\) 23.3793 0.932194
\(630\) 0 0
\(631\) 31.6896 1.26154 0.630772 0.775968i \(-0.282738\pi\)
0.630772 + 0.775968i \(0.282738\pi\)
\(632\) 15.3756 0.611608
\(633\) 24.3170 0.966514
\(634\) 34.7211 1.37895
\(635\) 0 0
\(636\) −12.9429 −0.513220
\(637\) 14.9779 0.593448
\(638\) −42.6096 −1.68693
\(639\) −20.3698 −0.805818
\(640\) 0 0
\(641\) −47.9750 −1.89490 −0.947449 0.319908i \(-0.896348\pi\)
−0.947449 + 0.319908i \(0.896348\pi\)
\(642\) 24.3431 0.960746
\(643\) −0.200927 −0.00792378 −0.00396189 0.999992i \(-0.501261\pi\)
−0.00396189 + 0.999992i \(0.501261\pi\)
\(644\) −10.2996 −0.405863
\(645\) 0 0
\(646\) 0 0
\(647\) 1.58798 0.0624299 0.0312150 0.999513i \(-0.490062\pi\)
0.0312150 + 0.999513i \(0.490062\pi\)
\(648\) −13.0014 −0.510743
\(649\) 13.0796 0.513421
\(650\) 0 0
\(651\) −28.3186 −1.10989
\(652\) −21.7230 −0.850739
\(653\) −33.5624 −1.31340 −0.656700 0.754152i \(-0.728048\pi\)
−0.656700 + 0.754152i \(0.728048\pi\)
\(654\) −28.0226 −1.09577
\(655\) 0 0
\(656\) 51.1022 1.99521
\(657\) −5.73669 −0.223809
\(658\) −12.9702 −0.505630
\(659\) −15.3567 −0.598213 −0.299107 0.954220i \(-0.596689\pi\)
−0.299107 + 0.954220i \(0.596689\pi\)
\(660\) 0 0
\(661\) −12.8026 −0.497962 −0.248981 0.968508i \(-0.580096\pi\)
−0.248981 + 0.968508i \(0.580096\pi\)
\(662\) 14.5803 0.566679
\(663\) 27.7735 1.07863
\(664\) 15.6564 0.607585
\(665\) 0 0
\(666\) −25.5975 −0.991882
\(667\) 32.2400 1.24834
\(668\) 5.02657 0.194484
\(669\) −39.1022 −1.51178
\(670\) 0 0
\(671\) −40.2627 −1.55433
\(672\) −21.6558 −0.835389
\(673\) −7.82545 −0.301649 −0.150824 0.988561i \(-0.548193\pi\)
−0.150824 + 0.988561i \(0.548193\pi\)
\(674\) −12.5618 −0.483863
\(675\) 0 0
\(676\) −4.81509 −0.185196
\(677\) −21.6516 −0.832137 −0.416069 0.909333i \(-0.636592\pi\)
−0.416069 + 0.909333i \(0.636592\pi\)
\(678\) 39.7187 1.52539
\(679\) −4.43637 −0.170252
\(680\) 0 0
\(681\) 39.6564 1.51964
\(682\) 59.9118 2.29414
\(683\) −6.38751 −0.244411 −0.122206 0.992505i \(-0.538997\pi\)
−0.122206 + 0.992505i \(0.538997\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 31.4458 1.20061
\(687\) −57.9688 −2.21165
\(688\) 7.10160 0.270746
\(689\) −12.9429 −0.493086
\(690\) 0 0
\(691\) 44.4958 1.69270 0.846351 0.532626i \(-0.178795\pi\)
0.846351 + 0.532626i \(0.178795\pi\)
\(692\) 15.0452 0.571933
\(693\) −13.3185 −0.505928
\(694\) 55.6789 2.11354
\(695\) 0 0
\(696\) 17.1688 0.650780
\(697\) −40.9420 −1.55079
\(698\) −30.5626 −1.15681
\(699\) −44.6658 −1.68942
\(700\) 0 0
\(701\) 17.5160 0.661571 0.330785 0.943706i \(-0.392686\pi\)
0.330785 + 0.943706i \(0.392686\pi\)
\(702\) 8.30011 0.313268
\(703\) 0 0
\(704\) 7.65638 0.288560
\(705\) 0 0
\(706\) −53.0357 −1.99602
\(707\) 4.86835 0.183093
\(708\) 10.2678 0.385888
\(709\) 11.4269 0.429146 0.214573 0.976708i \(-0.431164\pi\)
0.214573 + 0.976708i \(0.431164\pi\)
\(710\) 0 0
\(711\) 29.3091 1.09918
\(712\) −15.2888 −0.572973
\(713\) −45.3315 −1.69768
\(714\) 24.0000 0.898177
\(715\) 0 0
\(716\) −13.3091 −0.497385
\(717\) −43.4408 −1.62233
\(718\) 21.3048 0.795088
\(719\) 15.8965 0.592841 0.296421 0.955057i \(-0.404207\pi\)
0.296421 + 0.955057i \(0.404207\pi\)
\(720\) 0 0
\(721\) −18.9429 −0.705471
\(722\) 0 0
\(723\) −33.4124 −1.24262
\(724\) −0.757427 −0.0281495
\(725\) 0 0
\(726\) 17.6451 0.654871
\(727\) 41.9905 1.55734 0.778670 0.627434i \(-0.215895\pi\)
0.778670 + 0.627434i \(0.215895\pi\)
\(728\) −5.48487 −0.203283
\(729\) −14.4458 −0.535031
\(730\) 0 0
\(731\) −5.68965 −0.210439
\(732\) −31.6071 −1.16823
\(733\) −0.632884 −0.0233761 −0.0116881 0.999932i \(-0.503721\pi\)
−0.0116881 + 0.999932i \(0.503721\pi\)
\(734\) 7.65638 0.282602
\(735\) 0 0
\(736\) −34.6658 −1.27780
\(737\) −38.3578 −1.41293
\(738\) 44.8265 1.65009
\(739\) −29.5493 −1.08699 −0.543494 0.839413i \(-0.682899\pi\)
−0.543494 + 0.839413i \(0.682899\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −11.1844 −0.410592
\(743\) 31.3374 1.14966 0.574829 0.818274i \(-0.305069\pi\)
0.574829 + 0.818274i \(0.305069\pi\)
\(744\) −24.1404 −0.885028
\(745\) 0 0
\(746\) −30.8840 −1.13074
\(747\) 29.8443 1.09195
\(748\) −20.2028 −0.738688
\(749\) 8.36983 0.305827
\(750\) 0 0
\(751\) −25.0131 −0.912741 −0.456371 0.889790i \(-0.650851\pi\)
−0.456371 + 0.889790i \(0.650851\pi\)
\(752\) −24.0267 −0.876163
\(753\) 25.4040 0.925772
\(754\) −33.4495 −1.21816
\(755\) 0 0
\(756\) 2.85381 0.103792
\(757\) −32.0900 −1.16633 −0.583165 0.812354i \(-0.698186\pi\)
−0.583165 + 0.812354i \(0.698186\pi\)
\(758\) 18.8928 0.686216
\(759\) −48.4589 −1.75895
\(760\) 0 0
\(761\) −40.4922 −1.46784 −0.733921 0.679235i \(-0.762312\pi\)
−0.733921 + 0.679235i \(0.762312\pi\)
\(762\) −46.7942 −1.69517
\(763\) −9.63492 −0.348808
\(764\) −4.20690 −0.152200
\(765\) 0 0
\(766\) 37.5273 1.35592
\(767\) 10.2678 0.370749
\(768\) −48.4165 −1.74708
\(769\) 3.09398 0.111572 0.0557859 0.998443i \(-0.482234\pi\)
0.0557859 + 0.998443i \(0.482234\pi\)
\(770\) 0 0
\(771\) −40.8251 −1.47028
\(772\) −4.04272 −0.145501
\(773\) 1.96350 0.0706220 0.0353110 0.999376i \(-0.488758\pi\)
0.0353110 + 0.999376i \(0.488758\pi\)
\(774\) 6.22947 0.223914
\(775\) 0 0
\(776\) −3.78181 −0.135759
\(777\) −20.0045 −0.717658
\(778\) −14.7688 −0.529488
\(779\) 0 0
\(780\) 0 0
\(781\) 33.6789 1.20513
\(782\) 38.4184 1.37384
\(783\) −8.93300 −0.319239
\(784\) 23.9762 0.856293
\(785\) 0 0
\(786\) 19.4458 0.693610
\(787\) 0.107331 0.00382595 0.00191297 0.999998i \(-0.499391\pi\)
0.00191297 + 0.999998i \(0.499391\pi\)
\(788\) 28.4064 1.01194
\(789\) 3.91088 0.139231
\(790\) 0 0
\(791\) 13.6564 0.485565
\(792\) −11.3534 −0.403427
\(793\) −31.6071 −1.12240
\(794\) −6.32222 −0.224367
\(795\) 0 0
\(796\) −6.36620 −0.225644
\(797\) 8.32068 0.294734 0.147367 0.989082i \(-0.452920\pi\)
0.147367 + 0.989082i \(0.452920\pi\)
\(798\) 0 0
\(799\) 19.2496 0.681003
\(800\) 0 0
\(801\) −29.1437 −1.02974
\(802\) −29.0738 −1.02663
\(803\) 9.48489 0.334714
\(804\) −30.1117 −1.06196
\(805\) 0 0
\(806\) 47.0320 1.65663
\(807\) −62.7270 −2.20810
\(808\) 4.15006 0.145998
\(809\) −27.6231 −0.971177 −0.485588 0.874188i \(-0.661395\pi\)
−0.485588 + 0.874188i \(0.661395\pi\)
\(810\) 0 0
\(811\) −23.0095 −0.807972 −0.403986 0.914765i \(-0.632376\pi\)
−0.403986 + 0.914765i \(0.632376\pi\)
\(812\) −11.5008 −0.403600
\(813\) −55.4369 −1.94426
\(814\) 42.3222 1.48339
\(815\) 0 0
\(816\) 44.4589 1.55637
\(817\) 0 0
\(818\) −7.16224 −0.250422
\(819\) −10.4553 −0.365338
\(820\) 0 0
\(821\) 31.1355 1.08664 0.543318 0.839527i \(-0.317168\pi\)
0.543318 + 0.839527i \(0.317168\pi\)
\(822\) −55.5993 −1.93925
\(823\) 20.4201 0.711800 0.355900 0.934524i \(-0.384174\pi\)
0.355900 + 0.934524i \(0.384174\pi\)
\(824\) −16.1480 −0.562543
\(825\) 0 0
\(826\) 8.87275 0.308722
\(827\) 0.902638 0.0313878 0.0156939 0.999877i \(-0.495004\pi\)
0.0156939 + 0.999877i \(0.495004\pi\)
\(828\) −16.7365 −0.581634
\(829\) 13.4971 0.468773 0.234386 0.972143i \(-0.424692\pi\)
0.234386 + 0.972143i \(0.424692\pi\)
\(830\) 0 0
\(831\) −19.0607 −0.661209
\(832\) 6.01042 0.208374
\(833\) −19.2092 −0.665560
\(834\) 4.99053 0.172808
\(835\) 0 0
\(836\) 0 0
\(837\) 12.5603 0.434149
\(838\) 62.5123 2.15945
\(839\) −33.1022 −1.14282 −0.571408 0.820666i \(-0.693603\pi\)
−0.571408 + 0.820666i \(0.693603\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −47.5484 −1.63862
\(843\) −24.1546 −0.831928
\(844\) −13.8858 −0.477971
\(845\) 0 0
\(846\) −21.0760 −0.724608
\(847\) 6.06686 0.208460
\(848\) −20.7186 −0.711480
\(849\) 24.2295 0.831553
\(850\) 0 0
\(851\) −32.0226 −1.09772
\(852\) 26.4387 0.905775
\(853\) 50.9097 1.74312 0.871558 0.490293i \(-0.163110\pi\)
0.871558 + 0.490293i \(0.163110\pi\)
\(854\) −27.3128 −0.934623
\(855\) 0 0
\(856\) 7.13491 0.243866
\(857\) −21.2333 −0.725317 −0.362659 0.931922i \(-0.618131\pi\)
−0.362659 + 0.931922i \(0.618131\pi\)
\(858\) 50.2768 1.71642
\(859\) 29.4827 1.00594 0.502969 0.864304i \(-0.332241\pi\)
0.502969 + 0.864304i \(0.332241\pi\)
\(860\) 0 0
\(861\) 35.0320 1.19389
\(862\) 18.7715 0.639359
\(863\) −25.7755 −0.877408 −0.438704 0.898632i \(-0.644562\pi\)
−0.438704 + 0.898632i \(0.644562\pi\)
\(864\) 9.60514 0.326773
\(865\) 0 0
\(866\) −66.0339 −2.24392
\(867\) 3.72628 0.126551
\(868\) 16.1709 0.548876
\(869\) −48.4589 −1.64386
\(870\) 0 0
\(871\) −30.1117 −1.02030
\(872\) −8.21335 −0.278139
\(873\) −7.20893 −0.243985
\(874\) 0 0
\(875\) 0 0
\(876\) 7.44584 0.251572
\(877\) −54.2687 −1.83252 −0.916261 0.400581i \(-0.868808\pi\)
−0.916261 + 0.400581i \(0.868808\pi\)
\(878\) −43.9033 −1.48166
\(879\) −38.1117 −1.28548
\(880\) 0 0
\(881\) −28.4922 −0.959927 −0.479964 0.877288i \(-0.659350\pi\)
−0.479964 + 0.877288i \(0.659350\pi\)
\(882\) 21.0317 0.708176
\(883\) 40.5264 1.36382 0.681911 0.731435i \(-0.261149\pi\)
0.681911 + 0.731435i \(0.261149\pi\)
\(884\) −15.8596 −0.533418
\(885\) 0 0
\(886\) 10.0665 0.338192
\(887\) 11.4705 0.385142 0.192571 0.981283i \(-0.438317\pi\)
0.192571 + 0.981283i \(0.438317\pi\)
\(888\) −17.0530 −0.572260
\(889\) −16.0891 −0.539612
\(890\) 0 0
\(891\) 40.9762 1.37275
\(892\) 22.3287 0.747621
\(893\) 0 0
\(894\) 23.0320 0.770307
\(895\) 0 0
\(896\) −13.5197 −0.451660
\(897\) −38.0413 −1.27016
\(898\) 14.4524 0.482282
\(899\) −50.6182 −1.68821
\(900\) 0 0
\(901\) 16.5993 0.553003
\(902\) −74.1150 −2.46776
\(903\) 4.86835 0.162009
\(904\) 11.6415 0.387189
\(905\) 0 0
\(906\) 21.4269 0.711861
\(907\) 48.1000 1.59714 0.798568 0.601905i \(-0.205591\pi\)
0.798568 + 0.601905i \(0.205591\pi\)
\(908\) −22.6452 −0.751506
\(909\) 7.91088 0.262387
\(910\) 0 0
\(911\) 12.8062 0.424288 0.212144 0.977238i \(-0.431955\pi\)
0.212144 + 0.977238i \(0.431955\pi\)
\(912\) 0 0
\(913\) −49.3439 −1.63304
\(914\) 41.2865 1.36564
\(915\) 0 0
\(916\) 33.1022 1.09373
\(917\) 6.68601 0.220792
\(918\) −10.6449 −0.351334
\(919\) −38.7135 −1.27704 −0.638519 0.769606i \(-0.720453\pi\)
−0.638519 + 0.769606i \(0.720453\pi\)
\(920\) 0 0
\(921\) 18.2295 0.600682
\(922\) −24.4038 −0.803695
\(923\) 26.4387 0.870241
\(924\) 17.2865 0.568686
\(925\) 0 0
\(926\) 30.8062 1.01235
\(927\) −30.7815 −1.01100
\(928\) −38.7087 −1.27068
\(929\) −36.0189 −1.18174 −0.590872 0.806766i \(-0.701216\pi\)
−0.590872 + 0.806766i \(0.701216\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 25.5058 0.835469
\(933\) −9.01841 −0.295249
\(934\) 40.5517 1.32689
\(935\) 0 0
\(936\) −8.91270 −0.291321
\(937\) 45.2421 1.47799 0.738997 0.673709i \(-0.235300\pi\)
0.738997 + 0.673709i \(0.235300\pi\)
\(938\) −26.0205 −0.849599
\(939\) −17.9811 −0.586790
\(940\) 0 0
\(941\) 11.7455 0.382892 0.191446 0.981503i \(-0.438682\pi\)
0.191446 + 0.981503i \(0.438682\pi\)
\(942\) 25.8058 0.840799
\(943\) 56.0781 1.82616
\(944\) 16.4364 0.534958
\(945\) 0 0
\(946\) −10.2996 −0.334870
\(947\) 13.7752 0.447635 0.223817 0.974631i \(-0.428148\pi\)
0.223817 + 0.974631i \(0.428148\pi\)
\(948\) −38.0413 −1.23552
\(949\) 7.44584 0.241702
\(950\) 0 0
\(951\) 44.0927 1.42981
\(952\) 7.03434 0.227984
\(953\) 9.01421 0.291999 0.145999 0.989285i \(-0.453360\pi\)
0.145999 + 0.989285i \(0.453360\pi\)
\(954\) −18.1742 −0.588412
\(955\) 0 0
\(956\) 24.8062 0.802290
\(957\) −54.1105 −1.74914
\(958\) −0.667406 −0.0215629
\(959\) −19.1166 −0.617306
\(960\) 0 0
\(961\) 40.1724 1.29588
\(962\) 33.2239 1.07118
\(963\) 13.6006 0.438274
\(964\) 19.0796 0.614514
\(965\) 0 0
\(966\) −32.8727 −1.05766
\(967\) −30.3232 −0.975129 −0.487564 0.873087i \(-0.662115\pi\)
−0.487564 + 0.873087i \(0.662115\pi\)
\(968\) 5.17173 0.166226
\(969\) 0 0
\(970\) 0 0
\(971\) 31.5636 1.01292 0.506462 0.862262i \(-0.330953\pi\)
0.506462 + 0.862262i \(0.330953\pi\)
\(972\) 26.2641 0.842422
\(973\) 1.71588 0.0550086
\(974\) −48.9280 −1.56775
\(975\) 0 0
\(976\) −50.5957 −1.61953
\(977\) 43.1285 1.37980 0.689902 0.723903i \(-0.257654\pi\)
0.689902 + 0.723903i \(0.257654\pi\)
\(978\) −69.3320 −2.21699
\(979\) 48.1855 1.54002
\(980\) 0 0
\(981\) −15.6564 −0.499870
\(982\) 43.2425 1.37992
\(983\) 7.81570 0.249282 0.124641 0.992202i \(-0.460222\pi\)
0.124641 + 0.992202i \(0.460222\pi\)
\(984\) 29.8633 0.952006
\(985\) 0 0
\(986\) 42.8989 1.36618
\(987\) −16.4710 −0.524277
\(988\) 0 0
\(989\) 7.79310 0.247806
\(990\) 0 0
\(991\) 23.5197 0.747126 0.373563 0.927605i \(-0.378136\pi\)
0.373563 + 0.927605i \(0.378136\pi\)
\(992\) 54.4269 1.72806
\(993\) 18.5157 0.587577
\(994\) 22.8465 0.724648
\(995\) 0 0
\(996\) −38.7360 −1.22740
\(997\) 33.6395 1.06537 0.532686 0.846313i \(-0.321183\pi\)
0.532686 + 0.846313i \(0.321183\pi\)
\(998\) −12.4240 −0.393276
\(999\) 8.87275 0.280721
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 9025.2.a.bx.1.2 6
5.2 odd 4 1805.2.b.e.1084.2 6
5.3 odd 4 1805.2.b.e.1084.5 6
5.4 even 2 inner 9025.2.a.bx.1.5 6
19.18 odd 2 475.2.a.j.1.5 6
57.56 even 2 4275.2.a.br.1.2 6
76.75 even 2 7600.2.a.ck.1.2 6
95.18 even 4 95.2.b.b.39.2 6
95.37 even 4 95.2.b.b.39.5 yes 6
95.94 odd 2 475.2.a.j.1.2 6
285.113 odd 4 855.2.c.d.514.5 6
285.227 odd 4 855.2.c.d.514.2 6
285.284 even 2 4275.2.a.br.1.5 6
380.227 odd 4 1520.2.d.h.609.5 6
380.303 odd 4 1520.2.d.h.609.2 6
380.379 even 2 7600.2.a.ck.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.b.b.39.2 6 95.18 even 4
95.2.b.b.39.5 yes 6 95.37 even 4
475.2.a.j.1.2 6 95.94 odd 2
475.2.a.j.1.5 6 19.18 odd 2
855.2.c.d.514.2 6 285.227 odd 4
855.2.c.d.514.5 6 285.113 odd 4
1520.2.d.h.609.2 6 380.303 odd 4
1520.2.d.h.609.5 6 380.227 odd 4
1805.2.b.e.1084.2 6 5.2 odd 4
1805.2.b.e.1084.5 6 5.3 odd 4
4275.2.a.br.1.2 6 57.56 even 2
4275.2.a.br.1.5 6 285.284 even 2
7600.2.a.ck.1.2 6 76.75 even 2
7600.2.a.ck.1.5 6 380.379 even 2
9025.2.a.bx.1.2 6 1.1 even 1 trivial
9025.2.a.bx.1.5 6 5.4 even 2 inner