Properties

Label 8007.2.a.f.1.16
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.24727 q^{2} -1.00000 q^{3} -0.444326 q^{4} -3.92446 q^{5} +1.24727 q^{6} -1.90187 q^{7} +3.04873 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.24727 q^{2} -1.00000 q^{3} -0.444326 q^{4} -3.92446 q^{5} +1.24727 q^{6} -1.90187 q^{7} +3.04873 q^{8} +1.00000 q^{9} +4.89484 q^{10} +1.97041 q^{11} +0.444326 q^{12} +3.57557 q^{13} +2.37214 q^{14} +3.92446 q^{15} -2.91392 q^{16} -1.00000 q^{17} -1.24727 q^{18} -5.19382 q^{19} +1.74374 q^{20} +1.90187 q^{21} -2.45763 q^{22} -3.01141 q^{23} -3.04873 q^{24} +10.4013 q^{25} -4.45968 q^{26} -1.00000 q^{27} +0.845051 q^{28} -3.31624 q^{29} -4.89484 q^{30} -2.36779 q^{31} -2.46301 q^{32} -1.97041 q^{33} +1.24727 q^{34} +7.46381 q^{35} -0.444326 q^{36} -6.13347 q^{37} +6.47808 q^{38} -3.57557 q^{39} -11.9646 q^{40} -5.59751 q^{41} -2.37214 q^{42} -0.968369 q^{43} -0.875505 q^{44} -3.92446 q^{45} +3.75603 q^{46} +10.0826 q^{47} +2.91392 q^{48} -3.38288 q^{49} -12.9733 q^{50} +1.00000 q^{51} -1.58872 q^{52} +9.56969 q^{53} +1.24727 q^{54} -7.73279 q^{55} -5.79829 q^{56} +5.19382 q^{57} +4.13624 q^{58} -5.13708 q^{59} -1.74374 q^{60} -0.466107 q^{61} +2.95327 q^{62} -1.90187 q^{63} +8.89988 q^{64} -14.0321 q^{65} +2.45763 q^{66} -2.98041 q^{67} +0.444326 q^{68} +3.01141 q^{69} -9.30937 q^{70} +2.55658 q^{71} +3.04873 q^{72} +11.8437 q^{73} +7.65007 q^{74} -10.4013 q^{75} +2.30775 q^{76} -3.74747 q^{77} +4.45968 q^{78} -1.47189 q^{79} +11.4356 q^{80} +1.00000 q^{81} +6.98159 q^{82} +17.0058 q^{83} -0.845051 q^{84} +3.92446 q^{85} +1.20781 q^{86} +3.31624 q^{87} +6.00725 q^{88} -5.04747 q^{89} +4.89484 q^{90} -6.80027 q^{91} +1.33805 q^{92} +2.36779 q^{93} -12.5757 q^{94} +20.3829 q^{95} +2.46301 q^{96} +10.2918 q^{97} +4.21935 q^{98} +1.97041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24727 −0.881951 −0.440975 0.897519i \(-0.645367\pi\)
−0.440975 + 0.897519i \(0.645367\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.444326 −0.222163
\(5\) −3.92446 −1.75507 −0.877535 0.479513i \(-0.840813\pi\)
−0.877535 + 0.479513i \(0.840813\pi\)
\(6\) 1.24727 0.509194
\(7\) −1.90187 −0.718840 −0.359420 0.933176i \(-0.617026\pi\)
−0.359420 + 0.933176i \(0.617026\pi\)
\(8\) 3.04873 1.07789
\(9\) 1.00000 0.333333
\(10\) 4.89484 1.54788
\(11\) 1.97041 0.594101 0.297051 0.954862i \(-0.403997\pi\)
0.297051 + 0.954862i \(0.403997\pi\)
\(12\) 0.444326 0.128266
\(13\) 3.57557 0.991684 0.495842 0.868413i \(-0.334860\pi\)
0.495842 + 0.868413i \(0.334860\pi\)
\(14\) 2.37214 0.633982
\(15\) 3.92446 1.01329
\(16\) −2.91392 −0.728481
\(17\) −1.00000 −0.242536
\(18\) −1.24727 −0.293984
\(19\) −5.19382 −1.19154 −0.595772 0.803153i \(-0.703154\pi\)
−0.595772 + 0.803153i \(0.703154\pi\)
\(20\) 1.74374 0.389911
\(21\) 1.90187 0.415023
\(22\) −2.45763 −0.523968
\(23\) −3.01141 −0.627923 −0.313961 0.949436i \(-0.601656\pi\)
−0.313961 + 0.949436i \(0.601656\pi\)
\(24\) −3.04873 −0.622319
\(25\) 10.4013 2.08027
\(26\) −4.45968 −0.874616
\(27\) −1.00000 −0.192450
\(28\) 0.845051 0.159700
\(29\) −3.31624 −0.615811 −0.307906 0.951417i \(-0.599628\pi\)
−0.307906 + 0.951417i \(0.599628\pi\)
\(30\) −4.89484 −0.893672
\(31\) −2.36779 −0.425268 −0.212634 0.977132i \(-0.568204\pi\)
−0.212634 + 0.977132i \(0.568204\pi\)
\(32\) −2.46301 −0.435403
\(33\) −1.97041 −0.343005
\(34\) 1.24727 0.213904
\(35\) 7.46381 1.26161
\(36\) −0.444326 −0.0740543
\(37\) −6.13347 −1.00834 −0.504168 0.863605i \(-0.668201\pi\)
−0.504168 + 0.863605i \(0.668201\pi\)
\(38\) 6.47808 1.05088
\(39\) −3.57557 −0.572549
\(40\) −11.9646 −1.89177
\(41\) −5.59751 −0.874184 −0.437092 0.899417i \(-0.643992\pi\)
−0.437092 + 0.899417i \(0.643992\pi\)
\(42\) −2.37214 −0.366030
\(43\) −0.968369 −0.147675 −0.0738375 0.997270i \(-0.523525\pi\)
−0.0738375 + 0.997270i \(0.523525\pi\)
\(44\) −0.875505 −0.131987
\(45\) −3.92446 −0.585023
\(46\) 3.75603 0.553797
\(47\) 10.0826 1.47071 0.735353 0.677685i \(-0.237017\pi\)
0.735353 + 0.677685i \(0.237017\pi\)
\(48\) 2.91392 0.420589
\(49\) −3.38288 −0.483269
\(50\) −12.9733 −1.83470
\(51\) 1.00000 0.140028
\(52\) −1.58872 −0.220315
\(53\) 9.56969 1.31450 0.657249 0.753674i \(-0.271720\pi\)
0.657249 + 0.753674i \(0.271720\pi\)
\(54\) 1.24727 0.169731
\(55\) −7.73279 −1.04269
\(56\) −5.79829 −0.774829
\(57\) 5.19382 0.687939
\(58\) 4.13624 0.543115
\(59\) −5.13708 −0.668791 −0.334395 0.942433i \(-0.608532\pi\)
−0.334395 + 0.942433i \(0.608532\pi\)
\(60\) −1.74374 −0.225115
\(61\) −0.466107 −0.0596789 −0.0298395 0.999555i \(-0.509500\pi\)
−0.0298395 + 0.999555i \(0.509500\pi\)
\(62\) 2.95327 0.375065
\(63\) −1.90187 −0.239613
\(64\) 8.89988 1.11249
\(65\) −14.0321 −1.74047
\(66\) 2.45763 0.302513
\(67\) −2.98041 −0.364115 −0.182058 0.983288i \(-0.558276\pi\)
−0.182058 + 0.983288i \(0.558276\pi\)
\(68\) 0.444326 0.0538824
\(69\) 3.01141 0.362531
\(70\) −9.30937 −1.11268
\(71\) 2.55658 0.303410 0.151705 0.988426i \(-0.451524\pi\)
0.151705 + 0.988426i \(0.451524\pi\)
\(72\) 3.04873 0.359296
\(73\) 11.8437 1.38620 0.693101 0.720840i \(-0.256244\pi\)
0.693101 + 0.720840i \(0.256244\pi\)
\(74\) 7.65007 0.889303
\(75\) −10.4013 −1.20104
\(76\) 2.30775 0.264717
\(77\) −3.74747 −0.427064
\(78\) 4.45968 0.504960
\(79\) −1.47189 −0.165600 −0.0828001 0.996566i \(-0.526386\pi\)
−0.0828001 + 0.996566i \(0.526386\pi\)
\(80\) 11.4356 1.27853
\(81\) 1.00000 0.111111
\(82\) 6.98159 0.770987
\(83\) 17.0058 1.86663 0.933314 0.359062i \(-0.116903\pi\)
0.933314 + 0.359062i \(0.116903\pi\)
\(84\) −0.845051 −0.0922027
\(85\) 3.92446 0.425667
\(86\) 1.20781 0.130242
\(87\) 3.31624 0.355539
\(88\) 6.00725 0.640375
\(89\) −5.04747 −0.535031 −0.267516 0.963554i \(-0.586203\pi\)
−0.267516 + 0.963554i \(0.586203\pi\)
\(90\) 4.89484 0.515962
\(91\) −6.80027 −0.712862
\(92\) 1.33805 0.139501
\(93\) 2.36779 0.245528
\(94\) −12.5757 −1.29709
\(95\) 20.3829 2.09124
\(96\) 2.46301 0.251380
\(97\) 10.2918 1.04497 0.522485 0.852648i \(-0.325005\pi\)
0.522485 + 0.852648i \(0.325005\pi\)
\(98\) 4.21935 0.426219
\(99\) 1.97041 0.198034
\(100\) −4.62159 −0.462159
\(101\) 7.25728 0.722127 0.361063 0.932541i \(-0.382414\pi\)
0.361063 + 0.932541i \(0.382414\pi\)
\(102\) −1.24727 −0.123498
\(103\) −9.41904 −0.928086 −0.464043 0.885813i \(-0.653602\pi\)
−0.464043 + 0.885813i \(0.653602\pi\)
\(104\) 10.9009 1.06892
\(105\) −7.46381 −0.728394
\(106\) −11.9360 −1.15932
\(107\) 2.14570 0.207433 0.103717 0.994607i \(-0.466927\pi\)
0.103717 + 0.994607i \(0.466927\pi\)
\(108\) 0.444326 0.0427553
\(109\) −6.67574 −0.639420 −0.319710 0.947515i \(-0.603585\pi\)
−0.319710 + 0.947515i \(0.603585\pi\)
\(110\) 9.64485 0.919601
\(111\) 6.13347 0.582163
\(112\) 5.54191 0.523661
\(113\) 8.91557 0.838706 0.419353 0.907823i \(-0.362257\pi\)
0.419353 + 0.907823i \(0.362257\pi\)
\(114\) −6.47808 −0.606728
\(115\) 11.8181 1.10205
\(116\) 1.47349 0.136810
\(117\) 3.57557 0.330561
\(118\) 6.40731 0.589840
\(119\) 1.90187 0.174344
\(120\) 11.9646 1.09221
\(121\) −7.11748 −0.647043
\(122\) 0.581360 0.0526339
\(123\) 5.59751 0.504710
\(124\) 1.05207 0.0944787
\(125\) −21.1973 −1.89595
\(126\) 2.37214 0.211327
\(127\) −5.94634 −0.527652 −0.263826 0.964570i \(-0.584984\pi\)
−0.263826 + 0.964570i \(0.584984\pi\)
\(128\) −6.17450 −0.545754
\(129\) 0.968369 0.0852602
\(130\) 17.5018 1.53501
\(131\) −12.2907 −1.07384 −0.536920 0.843633i \(-0.680412\pi\)
−0.536920 + 0.843633i \(0.680412\pi\)
\(132\) 0.875505 0.0762029
\(133\) 9.87799 0.856530
\(134\) 3.71737 0.321131
\(135\) 3.92446 0.337763
\(136\) −3.04873 −0.261426
\(137\) −1.39823 −0.119459 −0.0597294 0.998215i \(-0.519024\pi\)
−0.0597294 + 0.998215i \(0.519024\pi\)
\(138\) −3.75603 −0.319735
\(139\) 20.2787 1.72002 0.860009 0.510279i \(-0.170458\pi\)
0.860009 + 0.510279i \(0.170458\pi\)
\(140\) −3.31637 −0.280284
\(141\) −10.0826 −0.849112
\(142\) −3.18874 −0.267593
\(143\) 7.04534 0.589161
\(144\) −2.91392 −0.242827
\(145\) 13.0145 1.08079
\(146\) −14.7723 −1.22256
\(147\) 3.38288 0.279015
\(148\) 2.72526 0.224015
\(149\) 15.4296 1.26404 0.632020 0.774952i \(-0.282226\pi\)
0.632020 + 0.774952i \(0.282226\pi\)
\(150\) 12.9733 1.05926
\(151\) −7.44637 −0.605977 −0.302989 0.952994i \(-0.597984\pi\)
−0.302989 + 0.952994i \(0.597984\pi\)
\(152\) −15.8345 −1.28435
\(153\) −1.00000 −0.0808452
\(154\) 4.67410 0.376649
\(155\) 9.29229 0.746375
\(156\) 1.58872 0.127199
\(157\) −1.00000 −0.0798087
\(158\) 1.83583 0.146051
\(159\) −9.56969 −0.758926
\(160\) 9.66599 0.764163
\(161\) 5.72732 0.451376
\(162\) −1.24727 −0.0979945
\(163\) 15.7613 1.23452 0.617261 0.786758i \(-0.288242\pi\)
0.617261 + 0.786758i \(0.288242\pi\)
\(164\) 2.48712 0.194211
\(165\) 7.73279 0.601997
\(166\) −21.2107 −1.64627
\(167\) 19.0386 1.47325 0.736625 0.676301i \(-0.236418\pi\)
0.736625 + 0.676301i \(0.236418\pi\)
\(168\) 5.79829 0.447348
\(169\) −0.215326 −0.0165635
\(170\) −4.89484 −0.375417
\(171\) −5.19382 −0.397182
\(172\) 0.430271 0.0328079
\(173\) 2.58463 0.196506 0.0982528 0.995161i \(-0.468675\pi\)
0.0982528 + 0.995161i \(0.468675\pi\)
\(174\) −4.13624 −0.313568
\(175\) −19.7820 −1.49538
\(176\) −5.74163 −0.432791
\(177\) 5.13708 0.386126
\(178\) 6.29555 0.471871
\(179\) 3.15247 0.235626 0.117813 0.993036i \(-0.462412\pi\)
0.117813 + 0.993036i \(0.462412\pi\)
\(180\) 1.74374 0.129970
\(181\) 11.2974 0.839730 0.419865 0.907586i \(-0.362077\pi\)
0.419865 + 0.907586i \(0.362077\pi\)
\(182\) 8.48175 0.628709
\(183\) 0.466107 0.0344556
\(184\) −9.18097 −0.676830
\(185\) 24.0705 1.76970
\(186\) −2.95327 −0.216544
\(187\) −1.97041 −0.144091
\(188\) −4.47998 −0.326736
\(189\) 1.90187 0.138341
\(190\) −25.4229 −1.84437
\(191\) 8.75330 0.633367 0.316683 0.948531i \(-0.397431\pi\)
0.316683 + 0.948531i \(0.397431\pi\)
\(192\) −8.89988 −0.642294
\(193\) −3.53395 −0.254379 −0.127189 0.991878i \(-0.540596\pi\)
−0.127189 + 0.991878i \(0.540596\pi\)
\(194\) −12.8366 −0.921613
\(195\) 14.0321 1.00486
\(196\) 1.50310 0.107364
\(197\) −11.6634 −0.830984 −0.415492 0.909597i \(-0.636391\pi\)
−0.415492 + 0.909597i \(0.636391\pi\)
\(198\) −2.45763 −0.174656
\(199\) 6.99995 0.496214 0.248107 0.968733i \(-0.420192\pi\)
0.248107 + 0.968733i \(0.420192\pi\)
\(200\) 31.7109 2.24230
\(201\) 2.98041 0.210222
\(202\) −9.05177 −0.636880
\(203\) 6.30707 0.442670
\(204\) −0.444326 −0.0311090
\(205\) 21.9672 1.53425
\(206\) 11.7481 0.818526
\(207\) −3.01141 −0.209308
\(208\) −10.4189 −0.722422
\(209\) −10.2340 −0.707898
\(210\) 9.30937 0.642407
\(211\) 16.7118 1.15049 0.575245 0.817981i \(-0.304907\pi\)
0.575245 + 0.817981i \(0.304907\pi\)
\(212\) −4.25206 −0.292033
\(213\) −2.55658 −0.175174
\(214\) −2.67626 −0.182946
\(215\) 3.80032 0.259180
\(216\) −3.04873 −0.207440
\(217\) 4.50324 0.305700
\(218\) 8.32643 0.563937
\(219\) −11.8437 −0.800325
\(220\) 3.43588 0.231647
\(221\) −3.57557 −0.240519
\(222\) −7.65007 −0.513439
\(223\) 18.6493 1.24885 0.624425 0.781085i \(-0.285333\pi\)
0.624425 + 0.781085i \(0.285333\pi\)
\(224\) 4.68434 0.312986
\(225\) 10.4013 0.693423
\(226\) −11.1201 −0.739697
\(227\) −12.7841 −0.848513 −0.424256 0.905542i \(-0.639464\pi\)
−0.424256 + 0.905542i \(0.639464\pi\)
\(228\) −2.30775 −0.152834
\(229\) 11.3142 0.747661 0.373831 0.927497i \(-0.378044\pi\)
0.373831 + 0.927497i \(0.378044\pi\)
\(230\) −14.7404 −0.971952
\(231\) 3.74747 0.246566
\(232\) −10.1103 −0.663775
\(233\) −2.67372 −0.175161 −0.0875807 0.996157i \(-0.527914\pi\)
−0.0875807 + 0.996157i \(0.527914\pi\)
\(234\) −4.45968 −0.291539
\(235\) −39.5689 −2.58119
\(236\) 2.28254 0.148580
\(237\) 1.47189 0.0956093
\(238\) −2.37214 −0.153763
\(239\) 24.7445 1.60059 0.800294 0.599608i \(-0.204677\pi\)
0.800294 + 0.599608i \(0.204677\pi\)
\(240\) −11.4356 −0.738162
\(241\) −20.4111 −1.31480 −0.657398 0.753544i \(-0.728343\pi\)
−0.657398 + 0.753544i \(0.728343\pi\)
\(242\) 8.87739 0.570660
\(243\) −1.00000 −0.0641500
\(244\) 0.207104 0.0132584
\(245\) 13.2760 0.848170
\(246\) −6.98159 −0.445130
\(247\) −18.5709 −1.18164
\(248\) −7.21875 −0.458391
\(249\) −17.0058 −1.07770
\(250\) 26.4387 1.67213
\(251\) 17.2616 1.08954 0.544771 0.838585i \(-0.316617\pi\)
0.544771 + 0.838585i \(0.316617\pi\)
\(252\) 0.845051 0.0532332
\(253\) −5.93372 −0.373050
\(254\) 7.41667 0.465363
\(255\) −3.92446 −0.245759
\(256\) −10.0985 −0.631157
\(257\) 4.86988 0.303775 0.151887 0.988398i \(-0.451465\pi\)
0.151887 + 0.988398i \(0.451465\pi\)
\(258\) −1.20781 −0.0751953
\(259\) 11.6651 0.724833
\(260\) 6.23485 0.386669
\(261\) −3.31624 −0.205270
\(262\) 15.3297 0.947074
\(263\) −9.83877 −0.606684 −0.303342 0.952882i \(-0.598103\pi\)
−0.303342 + 0.952882i \(0.598103\pi\)
\(264\) −6.00725 −0.369720
\(265\) −37.5558 −2.30704
\(266\) −12.3205 −0.755417
\(267\) 5.04747 0.308900
\(268\) 1.32427 0.0808929
\(269\) 1.10034 0.0670887 0.0335443 0.999437i \(-0.489321\pi\)
0.0335443 + 0.999437i \(0.489321\pi\)
\(270\) −4.89484 −0.297891
\(271\) −18.8137 −1.14285 −0.571424 0.820655i \(-0.693609\pi\)
−0.571424 + 0.820655i \(0.693609\pi\)
\(272\) 2.91392 0.176683
\(273\) 6.80027 0.411571
\(274\) 1.74396 0.105357
\(275\) 20.4949 1.23589
\(276\) −1.33805 −0.0805410
\(277\) −9.06431 −0.544622 −0.272311 0.962209i \(-0.587788\pi\)
−0.272311 + 0.962209i \(0.587788\pi\)
\(278\) −25.2930 −1.51697
\(279\) −2.36779 −0.141756
\(280\) 22.7551 1.35988
\(281\) 8.60453 0.513303 0.256652 0.966504i \(-0.417381\pi\)
0.256652 + 0.966504i \(0.417381\pi\)
\(282\) 12.5757 0.748875
\(283\) −32.6934 −1.94342 −0.971711 0.236173i \(-0.924107\pi\)
−0.971711 + 0.236173i \(0.924107\pi\)
\(284\) −1.13596 −0.0674066
\(285\) −20.3829 −1.20738
\(286\) −8.78741 −0.519611
\(287\) 10.6457 0.628399
\(288\) −2.46301 −0.145134
\(289\) 1.00000 0.0588235
\(290\) −16.2325 −0.953205
\(291\) −10.2918 −0.603314
\(292\) −5.26247 −0.307963
\(293\) −18.5780 −1.08534 −0.542668 0.839947i \(-0.682586\pi\)
−0.542668 + 0.839947i \(0.682586\pi\)
\(294\) −4.21935 −0.246078
\(295\) 20.1602 1.17377
\(296\) −18.6993 −1.08687
\(297\) −1.97041 −0.114335
\(298\) −19.2448 −1.11482
\(299\) −10.7675 −0.622701
\(300\) 4.62159 0.266828
\(301\) 1.84171 0.106155
\(302\) 9.28761 0.534442
\(303\) −7.25728 −0.416920
\(304\) 15.1344 0.868017
\(305\) 1.82922 0.104741
\(306\) 1.24727 0.0713015
\(307\) −3.35507 −0.191484 −0.0957421 0.995406i \(-0.530522\pi\)
−0.0957421 + 0.995406i \(0.530522\pi\)
\(308\) 1.66510 0.0948778
\(309\) 9.41904 0.535831
\(310\) −11.5900 −0.658266
\(311\) 23.3473 1.32391 0.661953 0.749545i \(-0.269728\pi\)
0.661953 + 0.749545i \(0.269728\pi\)
\(312\) −10.9009 −0.617143
\(313\) −26.0520 −1.47254 −0.736272 0.676685i \(-0.763416\pi\)
−0.736272 + 0.676685i \(0.763416\pi\)
\(314\) 1.24727 0.0703873
\(315\) 7.46381 0.420538
\(316\) 0.653997 0.0367902
\(317\) −16.0610 −0.902076 −0.451038 0.892505i \(-0.648946\pi\)
−0.451038 + 0.892505i \(0.648946\pi\)
\(318\) 11.9360 0.669335
\(319\) −6.53437 −0.365854
\(320\) −34.9272 −1.95249
\(321\) −2.14570 −0.119762
\(322\) −7.14350 −0.398092
\(323\) 5.19382 0.288992
\(324\) −0.444326 −0.0246848
\(325\) 37.1907 2.06297
\(326\) −19.6586 −1.08879
\(327\) 6.67574 0.369169
\(328\) −17.0653 −0.942272
\(329\) −19.1759 −1.05720
\(330\) −9.64485 −0.530932
\(331\) 2.96550 0.162999 0.0814994 0.996673i \(-0.474029\pi\)
0.0814994 + 0.996673i \(0.474029\pi\)
\(332\) −7.55611 −0.414695
\(333\) −6.13347 −0.336112
\(334\) −23.7462 −1.29933
\(335\) 11.6965 0.639047
\(336\) −5.54191 −0.302336
\(337\) −1.29156 −0.0703559 −0.0351780 0.999381i \(-0.511200\pi\)
−0.0351780 + 0.999381i \(0.511200\pi\)
\(338\) 0.268569 0.0146082
\(339\) −8.91557 −0.484227
\(340\) −1.74374 −0.0945674
\(341\) −4.66552 −0.252652
\(342\) 6.47808 0.350295
\(343\) 19.7469 1.06623
\(344\) −2.95229 −0.159177
\(345\) −11.8181 −0.636268
\(346\) −3.22372 −0.173308
\(347\) −27.0891 −1.45422 −0.727109 0.686522i \(-0.759136\pi\)
−0.727109 + 0.686522i \(0.759136\pi\)
\(348\) −1.47349 −0.0789875
\(349\) 32.2067 1.72398 0.861992 0.506922i \(-0.169217\pi\)
0.861992 + 0.506922i \(0.169217\pi\)
\(350\) 24.6735 1.31885
\(351\) −3.57557 −0.190850
\(352\) −4.85315 −0.258674
\(353\) 32.0498 1.70584 0.852919 0.522043i \(-0.174830\pi\)
0.852919 + 0.522043i \(0.174830\pi\)
\(354\) −6.40731 −0.340544
\(355\) −10.0332 −0.532506
\(356\) 2.24272 0.118864
\(357\) −1.90187 −0.100658
\(358\) −3.93196 −0.207811
\(359\) 16.3561 0.863243 0.431622 0.902055i \(-0.357942\pi\)
0.431622 + 0.902055i \(0.357942\pi\)
\(360\) −11.9646 −0.630589
\(361\) 7.97579 0.419778
\(362\) −14.0909 −0.740601
\(363\) 7.11748 0.373571
\(364\) 3.02154 0.158372
\(365\) −46.4802 −2.43288
\(366\) −0.581360 −0.0303882
\(367\) −7.20264 −0.375975 −0.187987 0.982171i \(-0.560196\pi\)
−0.187987 + 0.982171i \(0.560196\pi\)
\(368\) 8.77502 0.457430
\(369\) −5.59751 −0.291395
\(370\) −30.0224 −1.56079
\(371\) −18.2003 −0.944914
\(372\) −1.05207 −0.0545473
\(373\) −27.0862 −1.40247 −0.701234 0.712931i \(-0.747367\pi\)
−0.701234 + 0.712931i \(0.747367\pi\)
\(374\) 2.45763 0.127081
\(375\) 21.1973 1.09463
\(376\) 30.7392 1.58525
\(377\) −11.8574 −0.610690
\(378\) −2.37214 −0.122010
\(379\) −2.74743 −0.141126 −0.0705631 0.997507i \(-0.522480\pi\)
−0.0705631 + 0.997507i \(0.522480\pi\)
\(380\) −9.05666 −0.464597
\(381\) 5.94634 0.304640
\(382\) −10.9177 −0.558598
\(383\) −20.8036 −1.06302 −0.531508 0.847053i \(-0.678374\pi\)
−0.531508 + 0.847053i \(0.678374\pi\)
\(384\) 6.17450 0.315091
\(385\) 14.7068 0.749527
\(386\) 4.40777 0.224350
\(387\) −0.968369 −0.0492250
\(388\) −4.57290 −0.232154
\(389\) 28.3435 1.43707 0.718536 0.695490i \(-0.244812\pi\)
0.718536 + 0.695490i \(0.244812\pi\)
\(390\) −17.5018 −0.886240
\(391\) 3.01141 0.152294
\(392\) −10.3135 −0.520909
\(393\) 12.2907 0.619982
\(394\) 14.5474 0.732887
\(395\) 5.77635 0.290640
\(396\) −0.875505 −0.0439958
\(397\) −15.8047 −0.793217 −0.396609 0.917988i \(-0.629813\pi\)
−0.396609 + 0.917988i \(0.629813\pi\)
\(398\) −8.73081 −0.437636
\(399\) −9.87799 −0.494518
\(400\) −30.3087 −1.51544
\(401\) −17.6425 −0.881026 −0.440513 0.897746i \(-0.645203\pi\)
−0.440513 + 0.897746i \(0.645203\pi\)
\(402\) −3.71737 −0.185405
\(403\) −8.46619 −0.421731
\(404\) −3.22460 −0.160430
\(405\) −3.92446 −0.195008
\(406\) −7.86660 −0.390413
\(407\) −12.0855 −0.599054
\(408\) 3.04873 0.150934
\(409\) −26.2691 −1.29893 −0.649463 0.760393i \(-0.725006\pi\)
−0.649463 + 0.760393i \(0.725006\pi\)
\(410\) −27.3989 −1.35314
\(411\) 1.39823 0.0689695
\(412\) 4.18513 0.206186
\(413\) 9.77007 0.480754
\(414\) 3.75603 0.184599
\(415\) −66.7384 −3.27606
\(416\) −8.80667 −0.431782
\(417\) −20.2787 −0.993052
\(418\) 12.7645 0.624331
\(419\) 26.6647 1.30265 0.651327 0.758797i \(-0.274213\pi\)
0.651327 + 0.758797i \(0.274213\pi\)
\(420\) 3.31637 0.161822
\(421\) 8.61628 0.419932 0.209966 0.977709i \(-0.432665\pi\)
0.209966 + 0.977709i \(0.432665\pi\)
\(422\) −20.8441 −1.01468
\(423\) 10.0826 0.490235
\(424\) 29.1754 1.41688
\(425\) −10.4013 −0.504539
\(426\) 3.18874 0.154495
\(427\) 0.886477 0.0428996
\(428\) −0.953392 −0.0460839
\(429\) −7.04534 −0.340152
\(430\) −4.74001 −0.228584
\(431\) 11.7450 0.565737 0.282868 0.959159i \(-0.408714\pi\)
0.282868 + 0.959159i \(0.408714\pi\)
\(432\) 2.91392 0.140196
\(433\) −4.31157 −0.207201 −0.103601 0.994619i \(-0.533036\pi\)
−0.103601 + 0.994619i \(0.533036\pi\)
\(434\) −5.61674 −0.269612
\(435\) −13.0145 −0.623995
\(436\) 2.96620 0.142055
\(437\) 15.6407 0.748198
\(438\) 14.7723 0.705847
\(439\) −4.25124 −0.202901 −0.101450 0.994841i \(-0.532348\pi\)
−0.101450 + 0.994841i \(0.532348\pi\)
\(440\) −23.5752 −1.12390
\(441\) −3.38288 −0.161090
\(442\) 4.45968 0.212126
\(443\) 16.1584 0.767707 0.383854 0.923394i \(-0.374597\pi\)
0.383854 + 0.923394i \(0.374597\pi\)
\(444\) −2.72526 −0.129335
\(445\) 19.8086 0.939017
\(446\) −23.2607 −1.10142
\(447\) −15.4296 −0.729794
\(448\) −16.9264 −0.799699
\(449\) −27.7060 −1.30753 −0.653764 0.756698i \(-0.726811\pi\)
−0.653764 + 0.756698i \(0.726811\pi\)
\(450\) −12.9733 −0.611565
\(451\) −11.0294 −0.519354
\(452\) −3.96142 −0.186329
\(453\) 7.44637 0.349861
\(454\) 15.9452 0.748346
\(455\) 26.6874 1.25112
\(456\) 15.8345 0.741520
\(457\) 14.1422 0.661545 0.330772 0.943711i \(-0.392691\pi\)
0.330772 + 0.943711i \(0.392691\pi\)
\(458\) −14.1118 −0.659400
\(459\) 1.00000 0.0466760
\(460\) −5.25111 −0.244834
\(461\) −7.22072 −0.336302 −0.168151 0.985761i \(-0.553780\pi\)
−0.168151 + 0.985761i \(0.553780\pi\)
\(462\) −4.67410 −0.217459
\(463\) −38.2507 −1.77766 −0.888831 0.458235i \(-0.848482\pi\)
−0.888831 + 0.458235i \(0.848482\pi\)
\(464\) 9.66328 0.448606
\(465\) −9.29229 −0.430920
\(466\) 3.33485 0.154484
\(467\) 16.2433 0.751652 0.375826 0.926690i \(-0.377359\pi\)
0.375826 + 0.926690i \(0.377359\pi\)
\(468\) −1.58872 −0.0734385
\(469\) 5.66836 0.261741
\(470\) 49.3530 2.27648
\(471\) 1.00000 0.0460776
\(472\) −15.6615 −0.720881
\(473\) −1.90809 −0.0877339
\(474\) −1.83583 −0.0843227
\(475\) −54.0228 −2.47873
\(476\) −0.845051 −0.0387329
\(477\) 9.56969 0.438166
\(478\) −30.8630 −1.41164
\(479\) 19.3167 0.882601 0.441300 0.897359i \(-0.354517\pi\)
0.441300 + 0.897359i \(0.354517\pi\)
\(480\) −9.66599 −0.441190
\(481\) −21.9306 −0.999951
\(482\) 25.4581 1.15958
\(483\) −5.72732 −0.260602
\(484\) 3.16248 0.143749
\(485\) −40.3896 −1.83400
\(486\) 1.24727 0.0565772
\(487\) −3.05857 −0.138597 −0.0692985 0.997596i \(-0.522076\pi\)
−0.0692985 + 0.997596i \(0.522076\pi\)
\(488\) −1.42103 −0.0643272
\(489\) −15.7613 −0.712752
\(490\) −16.5587 −0.748044
\(491\) 26.5879 1.19990 0.599948 0.800039i \(-0.295188\pi\)
0.599948 + 0.800039i \(0.295188\pi\)
\(492\) −2.48712 −0.112128
\(493\) 3.31624 0.149356
\(494\) 23.1628 1.04214
\(495\) −7.73279 −0.347563
\(496\) 6.89956 0.309799
\(497\) −4.86229 −0.218104
\(498\) 21.2107 0.950476
\(499\) −14.3859 −0.644000 −0.322000 0.946740i \(-0.604355\pi\)
−0.322000 + 0.946740i \(0.604355\pi\)
\(500\) 9.41853 0.421209
\(501\) −19.0386 −0.850581
\(502\) −21.5298 −0.960921
\(503\) −16.6156 −0.740851 −0.370425 0.928862i \(-0.620788\pi\)
−0.370425 + 0.928862i \(0.620788\pi\)
\(504\) −5.79829 −0.258276
\(505\) −28.4809 −1.26738
\(506\) 7.40093 0.329012
\(507\) 0.215326 0.00956296
\(508\) 2.64211 0.117225
\(509\) −20.4287 −0.905487 −0.452744 0.891641i \(-0.649555\pi\)
−0.452744 + 0.891641i \(0.649555\pi\)
\(510\) 4.89484 0.216747
\(511\) −22.5253 −0.996459
\(512\) 24.9445 1.10240
\(513\) 5.19382 0.229313
\(514\) −6.07403 −0.267914
\(515\) 36.9646 1.62886
\(516\) −0.430271 −0.0189416
\(517\) 19.8670 0.873748
\(518\) −14.5495 −0.639267
\(519\) −2.58463 −0.113453
\(520\) −42.7802 −1.87604
\(521\) −22.1558 −0.970665 −0.485332 0.874330i \(-0.661301\pi\)
−0.485332 + 0.874330i \(0.661301\pi\)
\(522\) 4.13624 0.181038
\(523\) 0.659750 0.0288489 0.0144244 0.999896i \(-0.495408\pi\)
0.0144244 + 0.999896i \(0.495408\pi\)
\(524\) 5.46106 0.238568
\(525\) 19.7820 0.863359
\(526\) 12.2716 0.535066
\(527\) 2.36779 0.103143
\(528\) 5.74163 0.249872
\(529\) −13.9314 −0.605713
\(530\) 46.8421 2.03469
\(531\) −5.13708 −0.222930
\(532\) −4.38905 −0.190289
\(533\) −20.0143 −0.866914
\(534\) −6.29555 −0.272435
\(535\) −8.42072 −0.364059
\(536\) −9.08645 −0.392475
\(537\) −3.15247 −0.136039
\(538\) −1.37241 −0.0591689
\(539\) −6.66567 −0.287111
\(540\) −1.74374 −0.0750385
\(541\) 2.05421 0.0883172 0.0441586 0.999025i \(-0.485939\pi\)
0.0441586 + 0.999025i \(0.485939\pi\)
\(542\) 23.4657 1.00794
\(543\) −11.2974 −0.484819
\(544\) 2.46301 0.105601
\(545\) 26.1986 1.12223
\(546\) −8.48175 −0.362986
\(547\) −4.35591 −0.186245 −0.0931226 0.995655i \(-0.529685\pi\)
−0.0931226 + 0.995655i \(0.529685\pi\)
\(548\) 0.621269 0.0265393
\(549\) −0.466107 −0.0198930
\(550\) −25.5627 −1.09000
\(551\) 17.2240 0.733766
\(552\) 9.18097 0.390768
\(553\) 2.79934 0.119040
\(554\) 11.3056 0.480329
\(555\) −24.0705 −1.02174
\(556\) −9.01035 −0.382124
\(557\) 7.50545 0.318016 0.159008 0.987277i \(-0.449170\pi\)
0.159008 + 0.987277i \(0.449170\pi\)
\(558\) 2.95327 0.125022
\(559\) −3.46247 −0.146447
\(560\) −21.7490 −0.919062
\(561\) 1.97041 0.0831908
\(562\) −10.7321 −0.452708
\(563\) 43.9796 1.85352 0.926759 0.375656i \(-0.122583\pi\)
0.926759 + 0.375656i \(0.122583\pi\)
\(564\) 4.47998 0.188641
\(565\) −34.9887 −1.47199
\(566\) 40.7774 1.71400
\(567\) −1.90187 −0.0798711
\(568\) 7.79432 0.327042
\(569\) 33.7679 1.41563 0.707813 0.706400i \(-0.249682\pi\)
0.707813 + 0.706400i \(0.249682\pi\)
\(570\) 25.4229 1.06485
\(571\) −24.1461 −1.01048 −0.505241 0.862978i \(-0.668596\pi\)
−0.505241 + 0.862978i \(0.668596\pi\)
\(572\) −3.13043 −0.130890
\(573\) −8.75330 −0.365674
\(574\) −13.2781 −0.554217
\(575\) −31.3227 −1.30625
\(576\) 8.89988 0.370828
\(577\) −7.76858 −0.323410 −0.161705 0.986839i \(-0.551699\pi\)
−0.161705 + 0.986839i \(0.551699\pi\)
\(578\) −1.24727 −0.0518795
\(579\) 3.53395 0.146866
\(580\) −5.78266 −0.240112
\(581\) −32.3428 −1.34181
\(582\) 12.8366 0.532093
\(583\) 18.8562 0.780945
\(584\) 36.1083 1.49417
\(585\) −14.0321 −0.580158
\(586\) 23.1717 0.957213
\(587\) −22.1988 −0.916244 −0.458122 0.888889i \(-0.651478\pi\)
−0.458122 + 0.888889i \(0.651478\pi\)
\(588\) −1.50310 −0.0619868
\(589\) 12.2979 0.506726
\(590\) −25.1452 −1.03521
\(591\) 11.6634 0.479769
\(592\) 17.8725 0.734554
\(593\) 41.5262 1.70527 0.852637 0.522503i \(-0.175002\pi\)
0.852637 + 0.522503i \(0.175002\pi\)
\(594\) 2.45763 0.100838
\(595\) −7.46381 −0.305987
\(596\) −6.85576 −0.280823
\(597\) −6.99995 −0.286489
\(598\) 13.4299 0.549191
\(599\) 27.7525 1.13394 0.566969 0.823739i \(-0.308116\pi\)
0.566969 + 0.823739i \(0.308116\pi\)
\(600\) −31.7109 −1.29459
\(601\) −2.73004 −0.111360 −0.0556802 0.998449i \(-0.517733\pi\)
−0.0556802 + 0.998449i \(0.517733\pi\)
\(602\) −2.29711 −0.0936232
\(603\) −2.98041 −0.121372
\(604\) 3.30862 0.134626
\(605\) 27.9322 1.13561
\(606\) 9.05177 0.367703
\(607\) 40.1308 1.62886 0.814429 0.580263i \(-0.197050\pi\)
0.814429 + 0.580263i \(0.197050\pi\)
\(608\) 12.7925 0.518803
\(609\) −6.30707 −0.255576
\(610\) −2.28152 −0.0923761
\(611\) 36.0512 1.45847
\(612\) 0.444326 0.0179608
\(613\) 13.5023 0.545352 0.272676 0.962106i \(-0.412091\pi\)
0.272676 + 0.962106i \(0.412091\pi\)
\(614\) 4.18467 0.168880
\(615\) −21.9672 −0.885802
\(616\) −11.4250 −0.460327
\(617\) 30.8726 1.24288 0.621442 0.783461i \(-0.286547\pi\)
0.621442 + 0.783461i \(0.286547\pi\)
\(618\) −11.7481 −0.472576
\(619\) −29.2586 −1.17600 −0.588001 0.808860i \(-0.700085\pi\)
−0.588001 + 0.808860i \(0.700085\pi\)
\(620\) −4.12880 −0.165817
\(621\) 3.01141 0.120844
\(622\) −29.1204 −1.16762
\(623\) 9.59965 0.384602
\(624\) 10.4189 0.417091
\(625\) 31.1813 1.24725
\(626\) 32.4938 1.29871
\(627\) 10.2340 0.408705
\(628\) 0.444326 0.0177305
\(629\) 6.13347 0.244557
\(630\) −9.30937 −0.370894
\(631\) 5.77641 0.229955 0.114978 0.993368i \(-0.463320\pi\)
0.114978 + 0.993368i \(0.463320\pi\)
\(632\) −4.48738 −0.178498
\(633\) −16.7118 −0.664236
\(634\) 20.0324 0.795587
\(635\) 23.3361 0.926066
\(636\) 4.25206 0.168605
\(637\) −12.0957 −0.479250
\(638\) 8.15010 0.322665
\(639\) 2.55658 0.101137
\(640\) 24.2315 0.957836
\(641\) −6.62357 −0.261615 −0.130808 0.991408i \(-0.541757\pi\)
−0.130808 + 0.991408i \(0.541757\pi\)
\(642\) 2.67626 0.105624
\(643\) −6.96249 −0.274574 −0.137287 0.990531i \(-0.543838\pi\)
−0.137287 + 0.990531i \(0.543838\pi\)
\(644\) −2.54480 −0.100279
\(645\) −3.80032 −0.149638
\(646\) −6.47808 −0.254877
\(647\) −49.9536 −1.96388 −0.981938 0.189201i \(-0.939410\pi\)
−0.981938 + 0.189201i \(0.939410\pi\)
\(648\) 3.04873 0.119765
\(649\) −10.1222 −0.397329
\(650\) −46.3867 −1.81944
\(651\) −4.50324 −0.176496
\(652\) −7.00317 −0.274265
\(653\) 35.5408 1.39082 0.695410 0.718613i \(-0.255223\pi\)
0.695410 + 0.718613i \(0.255223\pi\)
\(654\) −8.32643 −0.325589
\(655\) 48.2342 1.88466
\(656\) 16.3107 0.636826
\(657\) 11.8437 0.462068
\(658\) 23.9175 0.932400
\(659\) 1.13420 0.0441822 0.0220911 0.999756i \(-0.492968\pi\)
0.0220911 + 0.999756i \(0.492968\pi\)
\(660\) −3.43588 −0.133741
\(661\) 43.9492 1.70943 0.854713 0.519101i \(-0.173733\pi\)
0.854713 + 0.519101i \(0.173733\pi\)
\(662\) −3.69877 −0.143757
\(663\) 3.57557 0.138863
\(664\) 51.8460 2.01201
\(665\) −38.7657 −1.50327
\(666\) 7.65007 0.296434
\(667\) 9.98658 0.386682
\(668\) −8.45934 −0.327302
\(669\) −18.6493 −0.721024
\(670\) −14.5886 −0.563608
\(671\) −0.918423 −0.0354553
\(672\) −4.68434 −0.180702
\(673\) −2.84734 −0.109757 −0.0548784 0.998493i \(-0.517477\pi\)
−0.0548784 + 0.998493i \(0.517477\pi\)
\(674\) 1.61092 0.0620504
\(675\) −10.4013 −0.400348
\(676\) 0.0956749 0.00367980
\(677\) −25.9993 −0.999233 −0.499617 0.866247i \(-0.666526\pi\)
−0.499617 + 0.866247i \(0.666526\pi\)
\(678\) 11.1201 0.427064
\(679\) −19.5736 −0.751167
\(680\) 11.9646 0.458821
\(681\) 12.7841 0.489889
\(682\) 5.81915 0.222827
\(683\) −25.1300 −0.961574 −0.480787 0.876837i \(-0.659649\pi\)
−0.480787 + 0.876837i \(0.659649\pi\)
\(684\) 2.30775 0.0882390
\(685\) 5.48729 0.209658
\(686\) −24.6297 −0.940365
\(687\) −11.3142 −0.431662
\(688\) 2.82175 0.107578
\(689\) 34.2171 1.30357
\(690\) 14.7404 0.561157
\(691\) −23.7764 −0.904498 −0.452249 0.891892i \(-0.649378\pi\)
−0.452249 + 0.891892i \(0.649378\pi\)
\(692\) −1.14842 −0.0436563
\(693\) −3.74747 −0.142355
\(694\) 33.7873 1.28255
\(695\) −79.5829 −3.01875
\(696\) 10.1103 0.383231
\(697\) 5.59751 0.212021
\(698\) −40.1703 −1.52047
\(699\) 2.67372 0.101129
\(700\) 8.78967 0.332218
\(701\) −26.2160 −0.990166 −0.495083 0.868846i \(-0.664862\pi\)
−0.495083 + 0.868846i \(0.664862\pi\)
\(702\) 4.45968 0.168320
\(703\) 31.8562 1.20148
\(704\) 17.5364 0.660929
\(705\) 39.5689 1.49025
\(706\) −39.9746 −1.50447
\(707\) −13.8024 −0.519094
\(708\) −2.28254 −0.0857830
\(709\) −26.3366 −0.989091 −0.494545 0.869152i \(-0.664665\pi\)
−0.494545 + 0.869152i \(0.664665\pi\)
\(710\) 12.5141 0.469644
\(711\) −1.47189 −0.0552001
\(712\) −15.3884 −0.576703
\(713\) 7.13039 0.267035
\(714\) 2.37214 0.0887752
\(715\) −27.6491 −1.03402
\(716\) −1.40072 −0.0523474
\(717\) −24.7445 −0.924100
\(718\) −20.4004 −0.761338
\(719\) −22.2420 −0.829487 −0.414743 0.909938i \(-0.636129\pi\)
−0.414743 + 0.909938i \(0.636129\pi\)
\(720\) 11.4356 0.426178
\(721\) 17.9138 0.667146
\(722\) −9.94794 −0.370224
\(723\) 20.4111 0.759097
\(724\) −5.01973 −0.186557
\(725\) −34.4934 −1.28105
\(726\) −8.87739 −0.329471
\(727\) 41.1899 1.52765 0.763825 0.645423i \(-0.223319\pi\)
0.763825 + 0.645423i \(0.223319\pi\)
\(728\) −20.7322 −0.768385
\(729\) 1.00000 0.0370370
\(730\) 57.9732 2.14568
\(731\) 0.968369 0.0358164
\(732\) −0.207104 −0.00765477
\(733\) 26.9504 0.995435 0.497718 0.867339i \(-0.334172\pi\)
0.497718 + 0.867339i \(0.334172\pi\)
\(734\) 8.98361 0.331591
\(735\) −13.2760 −0.489691
\(736\) 7.41715 0.273400
\(737\) −5.87263 −0.216321
\(738\) 6.98159 0.256996
\(739\) −21.7601 −0.800458 −0.400229 0.916415i \(-0.631069\pi\)
−0.400229 + 0.916415i \(0.631069\pi\)
\(740\) −10.6952 −0.393162
\(741\) 18.5709 0.682217
\(742\) 22.7007 0.833368
\(743\) 32.3414 1.18649 0.593245 0.805022i \(-0.297847\pi\)
0.593245 + 0.805022i \(0.297847\pi\)
\(744\) 7.21875 0.264652
\(745\) −60.5527 −2.21848
\(746\) 33.7837 1.23691
\(747\) 17.0058 0.622209
\(748\) 0.875505 0.0320116
\(749\) −4.08086 −0.149111
\(750\) −26.4387 −0.965406
\(751\) −18.7550 −0.684378 −0.342189 0.939631i \(-0.611168\pi\)
−0.342189 + 0.939631i \(0.611168\pi\)
\(752\) −29.3801 −1.07138
\(753\) −17.2616 −0.629047
\(754\) 14.7894 0.538598
\(755\) 29.2230 1.06353
\(756\) −0.845051 −0.0307342
\(757\) −6.99981 −0.254413 −0.127206 0.991876i \(-0.540601\pi\)
−0.127206 + 0.991876i \(0.540601\pi\)
\(758\) 3.42678 0.124466
\(759\) 5.93372 0.215380
\(760\) 62.1419 2.25413
\(761\) 26.7063 0.968102 0.484051 0.875040i \(-0.339165\pi\)
0.484051 + 0.875040i \(0.339165\pi\)
\(762\) −7.41667 −0.268678
\(763\) 12.6964 0.459641
\(764\) −3.88932 −0.140711
\(765\) 3.92446 0.141889
\(766\) 25.9477 0.937528
\(767\) −18.3680 −0.663229
\(768\) 10.0985 0.364399
\(769\) −24.2992 −0.876251 −0.438126 0.898914i \(-0.644358\pi\)
−0.438126 + 0.898914i \(0.644358\pi\)
\(770\) −18.3433 −0.661046
\(771\) −4.86988 −0.175384
\(772\) 1.57022 0.0565136
\(773\) 14.4433 0.519490 0.259745 0.965677i \(-0.416362\pi\)
0.259745 + 0.965677i \(0.416362\pi\)
\(774\) 1.20781 0.0434140
\(775\) −24.6282 −0.884672
\(776\) 31.3768 1.12636
\(777\) −11.6651 −0.418482
\(778\) −35.3519 −1.26743
\(779\) 29.0725 1.04163
\(780\) −6.23485 −0.223243
\(781\) 5.03752 0.180257
\(782\) −3.75603 −0.134315
\(783\) 3.31624 0.118513
\(784\) 9.85745 0.352052
\(785\) 3.92446 0.140070
\(786\) −15.3297 −0.546794
\(787\) −6.19889 −0.220967 −0.110483 0.993878i \(-0.535240\pi\)
−0.110483 + 0.993878i \(0.535240\pi\)
\(788\) 5.18236 0.184614
\(789\) 9.83877 0.350269
\(790\) −7.20465 −0.256330
\(791\) −16.9563 −0.602896
\(792\) 6.00725 0.213458
\(793\) −1.66660 −0.0591826
\(794\) 19.7127 0.699578
\(795\) 37.5558 1.33197
\(796\) −3.11026 −0.110240
\(797\) −26.5091 −0.939002 −0.469501 0.882932i \(-0.655566\pi\)
−0.469501 + 0.882932i \(0.655566\pi\)
\(798\) 12.3205 0.436140
\(799\) −10.0826 −0.356698
\(800\) −25.6187 −0.905756
\(801\) −5.04747 −0.178344
\(802\) 22.0049 0.777022
\(803\) 23.3370 0.823545
\(804\) −1.32427 −0.0467035
\(805\) −22.4766 −0.792197
\(806\) 10.5596 0.371946
\(807\) −1.10034 −0.0387337
\(808\) 22.1255 0.778371
\(809\) 5.88602 0.206941 0.103471 0.994633i \(-0.467005\pi\)
0.103471 + 0.994633i \(0.467005\pi\)
\(810\) 4.89484 0.171987
\(811\) 40.0906 1.40777 0.703886 0.710313i \(-0.251447\pi\)
0.703886 + 0.710313i \(0.251447\pi\)
\(812\) −2.80240 −0.0983448
\(813\) 18.8137 0.659824
\(814\) 15.0738 0.528336
\(815\) −61.8546 −2.16667
\(816\) −2.91392 −0.102008
\(817\) 5.02954 0.175961
\(818\) 32.7646 1.14559
\(819\) −6.80027 −0.237621
\(820\) −9.76058 −0.340854
\(821\) 2.45614 0.0857199 0.0428600 0.999081i \(-0.486353\pi\)
0.0428600 + 0.999081i \(0.486353\pi\)
\(822\) −1.74396 −0.0608277
\(823\) −20.0340 −0.698342 −0.349171 0.937059i \(-0.613537\pi\)
−0.349171 + 0.937059i \(0.613537\pi\)
\(824\) −28.7161 −1.00037
\(825\) −20.4949 −0.713542
\(826\) −12.1859 −0.424001
\(827\) −38.3989 −1.33526 −0.667630 0.744493i \(-0.732691\pi\)
−0.667630 + 0.744493i \(0.732691\pi\)
\(828\) 1.33805 0.0465004
\(829\) 12.6922 0.440818 0.220409 0.975408i \(-0.429261\pi\)
0.220409 + 0.975408i \(0.429261\pi\)
\(830\) 83.2406 2.88932
\(831\) 9.06431 0.314437
\(832\) 31.8221 1.10323
\(833\) 3.38288 0.117210
\(834\) 25.2930 0.875823
\(835\) −74.7161 −2.58566
\(836\) 4.54722 0.157269
\(837\) 2.36779 0.0818428
\(838\) −33.2580 −1.14888
\(839\) 24.5535 0.847682 0.423841 0.905737i \(-0.360682\pi\)
0.423841 + 0.905737i \(0.360682\pi\)
\(840\) −22.7551 −0.785126
\(841\) −18.0025 −0.620777
\(842\) −10.7468 −0.370359
\(843\) −8.60453 −0.296356
\(844\) −7.42551 −0.255596
\(845\) 0.845037 0.0290701
\(846\) −12.5757 −0.432363
\(847\) 13.5365 0.465121
\(848\) −27.8853 −0.957586
\(849\) 32.6934 1.12204
\(850\) 12.9733 0.444979
\(851\) 18.4704 0.633157
\(852\) 1.13596 0.0389172
\(853\) 13.2362 0.453199 0.226599 0.973988i \(-0.427239\pi\)
0.226599 + 0.973988i \(0.427239\pi\)
\(854\) −1.10567 −0.0378353
\(855\) 20.3829 0.697081
\(856\) 6.54166 0.223589
\(857\) 8.51458 0.290853 0.145426 0.989369i \(-0.453545\pi\)
0.145426 + 0.989369i \(0.453545\pi\)
\(858\) 8.78741 0.299997
\(859\) 2.22619 0.0759566 0.0379783 0.999279i \(-0.487908\pi\)
0.0379783 + 0.999279i \(0.487908\pi\)
\(860\) −1.68858 −0.0575801
\(861\) −10.6457 −0.362806
\(862\) −14.6491 −0.498952
\(863\) −32.6231 −1.11050 −0.555252 0.831682i \(-0.687378\pi\)
−0.555252 + 0.831682i \(0.687378\pi\)
\(864\) 2.46301 0.0837934
\(865\) −10.1433 −0.344881
\(866\) 5.37768 0.182741
\(867\) −1.00000 −0.0339618
\(868\) −2.00090 −0.0679151
\(869\) −2.90022 −0.0983833
\(870\) 16.2325 0.550333
\(871\) −10.6567 −0.361087
\(872\) −20.3525 −0.689223
\(873\) 10.2918 0.348324
\(874\) −19.5082 −0.659874
\(875\) 40.3147 1.36288
\(876\) 5.26247 0.177802
\(877\) 13.8433 0.467456 0.233728 0.972302i \(-0.424908\pi\)
0.233728 + 0.972302i \(0.424908\pi\)
\(878\) 5.30243 0.178948
\(879\) 18.5780 0.626619
\(880\) 22.5328 0.759579
\(881\) −29.5246 −0.994711 −0.497355 0.867547i \(-0.665695\pi\)
−0.497355 + 0.867547i \(0.665695\pi\)
\(882\) 4.21935 0.142073
\(883\) 5.60480 0.188616 0.0943082 0.995543i \(-0.469936\pi\)
0.0943082 + 0.995543i \(0.469936\pi\)
\(884\) 1.58872 0.0534343
\(885\) −20.1602 −0.677679
\(886\) −20.1538 −0.677080
\(887\) 24.3732 0.818370 0.409185 0.912451i \(-0.365813\pi\)
0.409185 + 0.912451i \(0.365813\pi\)
\(888\) 18.6993 0.627507
\(889\) 11.3092 0.379298
\(890\) −24.7066 −0.828167
\(891\) 1.97041 0.0660113
\(892\) −8.28637 −0.277448
\(893\) −52.3675 −1.75241
\(894\) 19.2448 0.643643
\(895\) −12.3717 −0.413541
\(896\) 11.7431 0.392310
\(897\) 10.7675 0.359516
\(898\) 34.5568 1.15318
\(899\) 7.85217 0.261885
\(900\) −4.62159 −0.154053
\(901\) −9.56969 −0.318813
\(902\) 13.7566 0.458045
\(903\) −1.84171 −0.0612884
\(904\) 27.1811 0.904031
\(905\) −44.3362 −1.47379
\(906\) −9.28761 −0.308560
\(907\) 34.7601 1.15419 0.577096 0.816677i \(-0.304186\pi\)
0.577096 + 0.816677i \(0.304186\pi\)
\(908\) 5.68032 0.188508
\(909\) 7.25728 0.240709
\(910\) −33.2863 −1.10343
\(911\) −36.7803 −1.21858 −0.609292 0.792946i \(-0.708546\pi\)
−0.609292 + 0.792946i \(0.708546\pi\)
\(912\) −15.1344 −0.501150
\(913\) 33.5084 1.10897
\(914\) −17.6391 −0.583450
\(915\) −1.82922 −0.0604720
\(916\) −5.02718 −0.166103
\(917\) 23.3753 0.771920
\(918\) −1.24727 −0.0411659
\(919\) −17.5853 −0.580084 −0.290042 0.957014i \(-0.593669\pi\)
−0.290042 + 0.957014i \(0.593669\pi\)
\(920\) 36.0303 1.18788
\(921\) 3.35507 0.110553
\(922\) 9.00616 0.296602
\(923\) 9.14123 0.300887
\(924\) −1.66510 −0.0547777
\(925\) −63.7964 −2.09761
\(926\) 47.7089 1.56781
\(927\) −9.41904 −0.309362
\(928\) 8.16795 0.268126
\(929\) −32.0477 −1.05145 −0.525725 0.850655i \(-0.676206\pi\)
−0.525725 + 0.850655i \(0.676206\pi\)
\(930\) 11.5900 0.380050
\(931\) 17.5701 0.575836
\(932\) 1.18800 0.0389144
\(933\) −23.3473 −0.764358
\(934\) −20.2598 −0.662920
\(935\) 7.73279 0.252889
\(936\) 10.9009 0.356308
\(937\) −46.7479 −1.52719 −0.763594 0.645697i \(-0.776567\pi\)
−0.763594 + 0.645697i \(0.776567\pi\)
\(938\) −7.06996 −0.230842
\(939\) 26.0520 0.850174
\(940\) 17.5815 0.573445
\(941\) 22.6502 0.738377 0.369188 0.929355i \(-0.379636\pi\)
0.369188 + 0.929355i \(0.379636\pi\)
\(942\) −1.24727 −0.0406381
\(943\) 16.8564 0.548920
\(944\) 14.9690 0.487201
\(945\) −7.46381 −0.242798
\(946\) 2.37989 0.0773770
\(947\) −10.1787 −0.330764 −0.165382 0.986230i \(-0.552886\pi\)
−0.165382 + 0.986230i \(0.552886\pi\)
\(948\) −0.653997 −0.0212408
\(949\) 42.3480 1.37467
\(950\) 67.3808 2.18612
\(951\) 16.0610 0.520814
\(952\) 5.79829 0.187924
\(953\) −53.3931 −1.72957 −0.864786 0.502140i \(-0.832546\pi\)
−0.864786 + 0.502140i \(0.832546\pi\)
\(954\) −11.9360 −0.386441
\(955\) −34.3519 −1.11160
\(956\) −10.9946 −0.355591
\(957\) 6.53437 0.211226
\(958\) −24.0930 −0.778410
\(959\) 2.65925 0.0858718
\(960\) 34.9272 1.12727
\(961\) −25.3936 −0.819147
\(962\) 27.3533 0.881907
\(963\) 2.14570 0.0691443
\(964\) 9.06919 0.292099
\(965\) 13.8688 0.446453
\(966\) 7.14350 0.229838
\(967\) −14.1816 −0.456051 −0.228025 0.973655i \(-0.573227\pi\)
−0.228025 + 0.973655i \(0.573227\pi\)
\(968\) −21.6992 −0.697440
\(969\) −5.19382 −0.166850
\(970\) 50.3766 1.61749
\(971\) −41.2432 −1.32356 −0.661778 0.749700i \(-0.730198\pi\)
−0.661778 + 0.749700i \(0.730198\pi\)
\(972\) 0.444326 0.0142518
\(973\) −38.5675 −1.23642
\(974\) 3.81485 0.122236
\(975\) −37.1907 −1.19106
\(976\) 1.35820 0.0434749
\(977\) −32.9117 −1.05294 −0.526470 0.850194i \(-0.676485\pi\)
−0.526470 + 0.850194i \(0.676485\pi\)
\(978\) 19.6586 0.628612
\(979\) −9.94560 −0.317863
\(980\) −5.89885 −0.188432
\(981\) −6.67574 −0.213140
\(982\) −33.1622 −1.05825
\(983\) 36.0394 1.14948 0.574739 0.818336i \(-0.305103\pi\)
0.574739 + 0.818336i \(0.305103\pi\)
\(984\) 17.0653 0.544021
\(985\) 45.7726 1.45844
\(986\) −4.13624 −0.131725
\(987\) 19.1759 0.610376
\(988\) 8.25151 0.262516
\(989\) 2.91616 0.0927284
\(990\) 9.64485 0.306534
\(991\) 38.8020 1.23259 0.616294 0.787516i \(-0.288633\pi\)
0.616294 + 0.787516i \(0.288633\pi\)
\(992\) 5.83190 0.185163
\(993\) −2.96550 −0.0941074
\(994\) 6.06458 0.192357
\(995\) −27.4710 −0.870889
\(996\) 7.55611 0.239424
\(997\) −37.6538 −1.19251 −0.596253 0.802796i \(-0.703345\pi\)
−0.596253 + 0.802796i \(0.703345\pi\)
\(998\) 17.9430 0.567976
\(999\) 6.13347 0.194054
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 8007.2.a.f.1.16 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.16 48 1.1 even 1 trivial