Properties

Label 3630.2.a.bi.1.1
Level $3630$
Weight $2$
Character 3630.1
Self dual yes
Analytic conductor $28.986$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.9856959337\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 330)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 3630.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} -0.618034 q^{13} -3.61803 q^{14} +1.00000 q^{15} +1.00000 q^{16} +6.47214 q^{17} +1.00000 q^{18} +0.618034 q^{19} -1.00000 q^{20} +3.61803 q^{21} +4.85410 q^{23} -1.00000 q^{24} +1.00000 q^{25} -0.618034 q^{26} -1.00000 q^{27} -3.61803 q^{28} -3.70820 q^{29} +1.00000 q^{30} -9.23607 q^{31} +1.00000 q^{32} +6.47214 q^{34} +3.61803 q^{35} +1.00000 q^{36} -0.618034 q^{37} +0.618034 q^{38} +0.618034 q^{39} -1.00000 q^{40} +9.32624 q^{41} +3.61803 q^{42} -0.763932 q^{43} -1.00000 q^{45} +4.85410 q^{46} -2.61803 q^{47} -1.00000 q^{48} +6.09017 q^{49} +1.00000 q^{50} -6.47214 q^{51} -0.618034 q^{52} -6.09017 q^{53} -1.00000 q^{54} -3.61803 q^{56} -0.618034 q^{57} -3.70820 q^{58} -14.6180 q^{59} +1.00000 q^{60} -11.2361 q^{61} -9.23607 q^{62} -3.61803 q^{63} +1.00000 q^{64} +0.618034 q^{65} -8.18034 q^{67} +6.47214 q^{68} -4.85410 q^{69} +3.61803 q^{70} -0.291796 q^{71} +1.00000 q^{72} -10.9443 q^{73} -0.618034 q^{74} -1.00000 q^{75} +0.618034 q^{76} +0.618034 q^{78} +4.47214 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.32624 q^{82} +4.94427 q^{83} +3.61803 q^{84} -6.47214 q^{85} -0.763932 q^{86} +3.70820 q^{87} -5.14590 q^{89} -1.00000 q^{90} +2.23607 q^{91} +4.85410 q^{92} +9.23607 q^{93} -2.61803 q^{94} -0.618034 q^{95} -1.00000 q^{96} +14.9443 q^{97} +6.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + 2q^{8} + 2q^{9} - 2q^{10} - 2q^{12} + q^{13} - 5q^{14} + 2q^{15} + 2q^{16} + 4q^{17} + 2q^{18} - q^{19} - 2q^{20} + 5q^{21} + 3q^{23} - 2q^{24} + 2q^{25} + q^{26} - 2q^{27} - 5q^{28} + 6q^{29} + 2q^{30} - 14q^{31} + 2q^{32} + 4q^{34} + 5q^{35} + 2q^{36} + q^{37} - q^{38} - q^{39} - 2q^{40} + 3q^{41} + 5q^{42} - 6q^{43} - 2q^{45} + 3q^{46} - 3q^{47} - 2q^{48} + q^{49} + 2q^{50} - 4q^{51} + q^{52} - q^{53} - 2q^{54} - 5q^{56} + q^{57} + 6q^{58} - 27q^{59} + 2q^{60} - 18q^{61} - 14q^{62} - 5q^{63} + 2q^{64} - q^{65} + 6q^{67} + 4q^{68} - 3q^{69} + 5q^{70} - 14q^{71} + 2q^{72} - 4q^{73} + q^{74} - 2q^{75} - q^{76} - q^{78} - 2q^{80} + 2q^{81} + 3q^{82} - 8q^{83} + 5q^{84} - 4q^{85} - 6q^{86} - 6q^{87} - 17q^{89} - 2q^{90} + 3q^{92} + 14q^{93} - 3q^{94} + q^{95} - 2q^{96} + 12q^{97} + q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.00000 −0.408248
\(7\) −3.61803 −1.36749 −0.683744 0.729722i \(-0.739650\pi\)
−0.683744 + 0.729722i \(0.739650\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) −0.618034 −0.171412 −0.0857059 0.996320i \(-0.527315\pi\)
−0.0857059 + 0.996320i \(0.527315\pi\)
\(14\) −3.61803 −0.966960
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 6.47214 1.56972 0.784862 0.619671i \(-0.212734\pi\)
0.784862 + 0.619671i \(0.212734\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.618034 0.141787 0.0708934 0.997484i \(-0.477415\pi\)
0.0708934 + 0.997484i \(0.477415\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.61803 0.789520
\(22\) 0 0
\(23\) 4.85410 1.01215 0.506075 0.862489i \(-0.331096\pi\)
0.506075 + 0.862489i \(0.331096\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −0.618034 −0.121206
\(27\) −1.00000 −0.192450
\(28\) −3.61803 −0.683744
\(29\) −3.70820 −0.688596 −0.344298 0.938860i \(-0.611883\pi\)
−0.344298 + 0.938860i \(0.611883\pi\)
\(30\) 1.00000 0.182574
\(31\) −9.23607 −1.65885 −0.829423 0.558620i \(-0.811331\pi\)
−0.829423 + 0.558620i \(0.811331\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.47214 1.10996
\(35\) 3.61803 0.611559
\(36\) 1.00000 0.166667
\(37\) −0.618034 −0.101604 −0.0508021 0.998709i \(-0.516178\pi\)
−0.0508021 + 0.998709i \(0.516178\pi\)
\(38\) 0.618034 0.100258
\(39\) 0.618034 0.0989646
\(40\) −1.00000 −0.158114
\(41\) 9.32624 1.45651 0.728257 0.685304i \(-0.240331\pi\)
0.728257 + 0.685304i \(0.240331\pi\)
\(42\) 3.61803 0.558275
\(43\) −0.763932 −0.116499 −0.0582493 0.998302i \(-0.518552\pi\)
−0.0582493 + 0.998302i \(0.518552\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 4.85410 0.715698
\(47\) −2.61803 −0.381880 −0.190940 0.981602i \(-0.561154\pi\)
−0.190940 + 0.981602i \(0.561154\pi\)
\(48\) −1.00000 −0.144338
\(49\) 6.09017 0.870024
\(50\) 1.00000 0.141421
\(51\) −6.47214 −0.906280
\(52\) −0.618034 −0.0857059
\(53\) −6.09017 −0.836549 −0.418275 0.908321i \(-0.637365\pi\)
−0.418275 + 0.908321i \(0.637365\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −3.61803 −0.483480
\(57\) −0.618034 −0.0818606
\(58\) −3.70820 −0.486911
\(59\) −14.6180 −1.90311 −0.951553 0.307485i \(-0.900513\pi\)
−0.951553 + 0.307485i \(0.900513\pi\)
\(60\) 1.00000 0.129099
\(61\) −11.2361 −1.43863 −0.719316 0.694683i \(-0.755544\pi\)
−0.719316 + 0.694683i \(0.755544\pi\)
\(62\) −9.23607 −1.17298
\(63\) −3.61803 −0.455829
\(64\) 1.00000 0.125000
\(65\) 0.618034 0.0766577
\(66\) 0 0
\(67\) −8.18034 −0.999388 −0.499694 0.866202i \(-0.666554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) 6.47214 0.784862
\(69\) −4.85410 −0.584365
\(70\) 3.61803 0.432438
\(71\) −0.291796 −0.0346298 −0.0173149 0.999850i \(-0.505512\pi\)
−0.0173149 + 0.999850i \(0.505512\pi\)
\(72\) 1.00000 0.117851
\(73\) −10.9443 −1.28093 −0.640465 0.767987i \(-0.721258\pi\)
−0.640465 + 0.767987i \(0.721258\pi\)
\(74\) −0.618034 −0.0718450
\(75\) −1.00000 −0.115470
\(76\) 0.618034 0.0708934
\(77\) 0 0
\(78\) 0.618034 0.0699786
\(79\) 4.47214 0.503155 0.251577 0.967837i \(-0.419051\pi\)
0.251577 + 0.967837i \(0.419051\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 9.32624 1.02991
\(83\) 4.94427 0.542704 0.271352 0.962480i \(-0.412529\pi\)
0.271352 + 0.962480i \(0.412529\pi\)
\(84\) 3.61803 0.394760
\(85\) −6.47214 −0.702002
\(86\) −0.763932 −0.0823769
\(87\) 3.70820 0.397561
\(88\) 0 0
\(89\) −5.14590 −0.545464 −0.272732 0.962090i \(-0.587927\pi\)
−0.272732 + 0.962090i \(0.587927\pi\)
\(90\) −1.00000 −0.105409
\(91\) 2.23607 0.234404
\(92\) 4.85410 0.506075
\(93\) 9.23607 0.957736
\(94\) −2.61803 −0.270030
\(95\) −0.618034 −0.0634089
\(96\) −1.00000 −0.102062
\(97\) 14.9443 1.51736 0.758680 0.651463i \(-0.225844\pi\)
0.758680 + 0.651463i \(0.225844\pi\)
\(98\) 6.09017 0.615200
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) −6.47214 −0.640837
\(103\) −9.85410 −0.970954 −0.485477 0.874250i \(-0.661354\pi\)
−0.485477 + 0.874250i \(0.661354\pi\)
\(104\) −0.618034 −0.0606032
\(105\) −3.61803 −0.353084
\(106\) −6.09017 −0.591530
\(107\) −17.8885 −1.72935 −0.864675 0.502331i \(-0.832476\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) 0.618034 0.0586612
\(112\) −3.61803 −0.341872
\(113\) −12.4721 −1.17328 −0.586640 0.809848i \(-0.699550\pi\)
−0.586640 + 0.809848i \(0.699550\pi\)
\(114\) −0.618034 −0.0578842
\(115\) −4.85410 −0.452647
\(116\) −3.70820 −0.344298
\(117\) −0.618034 −0.0571373
\(118\) −14.6180 −1.34570
\(119\) −23.4164 −2.14658
\(120\) 1.00000 0.0912871
\(121\) 0 0
\(122\) −11.2361 −1.01727
\(123\) −9.32624 −0.840919
\(124\) −9.23607 −0.829423
\(125\) −1.00000 −0.0894427
\(126\) −3.61803 −0.322320
\(127\) −12.6180 −1.11967 −0.559835 0.828604i \(-0.689135\pi\)
−0.559835 + 0.828604i \(0.689135\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.763932 0.0672605
\(130\) 0.618034 0.0542052
\(131\) −20.9443 −1.82991 −0.914955 0.403556i \(-0.867774\pi\)
−0.914955 + 0.403556i \(0.867774\pi\)
\(132\) 0 0
\(133\) −2.23607 −0.193892
\(134\) −8.18034 −0.706674
\(135\) 1.00000 0.0860663
\(136\) 6.47214 0.554981
\(137\) 15.4164 1.31711 0.658556 0.752531i \(-0.271167\pi\)
0.658556 + 0.752531i \(0.271167\pi\)
\(138\) −4.85410 −0.413209
\(139\) 7.61803 0.646153 0.323077 0.946373i \(-0.395283\pi\)
0.323077 + 0.946373i \(0.395283\pi\)
\(140\) 3.61803 0.305780
\(141\) 2.61803 0.220478
\(142\) −0.291796 −0.0244870
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 3.70820 0.307950
\(146\) −10.9443 −0.905754
\(147\) −6.09017 −0.502309
\(148\) −0.618034 −0.0508021
\(149\) 8.94427 0.732743 0.366372 0.930469i \(-0.380600\pi\)
0.366372 + 0.930469i \(0.380600\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 12.4721 1.01497 0.507484 0.861661i \(-0.330576\pi\)
0.507484 + 0.861661i \(0.330576\pi\)
\(152\) 0.618034 0.0501292
\(153\) 6.47214 0.523241
\(154\) 0 0
\(155\) 9.23607 0.741859
\(156\) 0.618034 0.0494823
\(157\) −5.61803 −0.448368 −0.224184 0.974547i \(-0.571972\pi\)
−0.224184 + 0.974547i \(0.571972\pi\)
\(158\) 4.47214 0.355784
\(159\) 6.09017 0.482982
\(160\) −1.00000 −0.0790569
\(161\) −17.5623 −1.38410
\(162\) 1.00000 0.0785674
\(163\) 17.8885 1.40114 0.700569 0.713584i \(-0.252929\pi\)
0.700569 + 0.713584i \(0.252929\pi\)
\(164\) 9.32624 0.728257
\(165\) 0 0
\(166\) 4.94427 0.383750
\(167\) 11.5623 0.894718 0.447359 0.894354i \(-0.352365\pi\)
0.447359 + 0.894354i \(0.352365\pi\)
\(168\) 3.61803 0.279137
\(169\) −12.6180 −0.970618
\(170\) −6.47214 −0.496390
\(171\) 0.618034 0.0472622
\(172\) −0.763932 −0.0582493
\(173\) 24.5623 1.86744 0.933719 0.358007i \(-0.116544\pi\)
0.933719 + 0.358007i \(0.116544\pi\)
\(174\) 3.70820 0.281118
\(175\) −3.61803 −0.273498
\(176\) 0 0
\(177\) 14.6180 1.09876
\(178\) −5.14590 −0.385701
\(179\) −11.1459 −0.833084 −0.416542 0.909117i \(-0.636758\pi\)
−0.416542 + 0.909117i \(0.636758\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −24.3607 −1.81072 −0.905358 0.424650i \(-0.860397\pi\)
−0.905358 + 0.424650i \(0.860397\pi\)
\(182\) 2.23607 0.165748
\(183\) 11.2361 0.830594
\(184\) 4.85410 0.357849
\(185\) 0.618034 0.0454388
\(186\) 9.23607 0.677221
\(187\) 0 0
\(188\) −2.61803 −0.190940
\(189\) 3.61803 0.263173
\(190\) −0.618034 −0.0448369
\(191\) −13.7082 −0.991891 −0.495945 0.868354i \(-0.665178\pi\)
−0.495945 + 0.868354i \(0.665178\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 3.70820 0.266922 0.133461 0.991054i \(-0.457391\pi\)
0.133461 + 0.991054i \(0.457391\pi\)
\(194\) 14.9443 1.07294
\(195\) −0.618034 −0.0442583
\(196\) 6.09017 0.435012
\(197\) −3.61803 −0.257774 −0.128887 0.991659i \(-0.541140\pi\)
−0.128887 + 0.991659i \(0.541140\pi\)
\(198\) 0 0
\(199\) −12.9443 −0.917595 −0.458798 0.888541i \(-0.651720\pi\)
−0.458798 + 0.888541i \(0.651720\pi\)
\(200\) 1.00000 0.0707107
\(201\) 8.18034 0.576997
\(202\) −4.00000 −0.281439
\(203\) 13.4164 0.941647
\(204\) −6.47214 −0.453140
\(205\) −9.32624 −0.651373
\(206\) −9.85410 −0.686568
\(207\) 4.85410 0.337383
\(208\) −0.618034 −0.0428529
\(209\) 0 0
\(210\) −3.61803 −0.249668
\(211\) 23.4164 1.61205 0.806026 0.591880i \(-0.201614\pi\)
0.806026 + 0.591880i \(0.201614\pi\)
\(212\) −6.09017 −0.418275
\(213\) 0.291796 0.0199935
\(214\) −17.8885 −1.22284
\(215\) 0.763932 0.0520997
\(216\) −1.00000 −0.0680414
\(217\) 33.4164 2.26845
\(218\) −4.00000 −0.270914
\(219\) 10.9443 0.739545
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 0.618034 0.0414797
\(223\) 7.61803 0.510141 0.255071 0.966922i \(-0.417901\pi\)
0.255071 + 0.966922i \(0.417901\pi\)
\(224\) −3.61803 −0.241740
\(225\) 1.00000 0.0666667
\(226\) −12.4721 −0.829634
\(227\) 4.18034 0.277459 0.138729 0.990330i \(-0.455698\pi\)
0.138729 + 0.990330i \(0.455698\pi\)
\(228\) −0.618034 −0.0409303
\(229\) −11.5279 −0.761783 −0.380891 0.924620i \(-0.624383\pi\)
−0.380891 + 0.924620i \(0.624383\pi\)
\(230\) −4.85410 −0.320070
\(231\) 0 0
\(232\) −3.70820 −0.243456
\(233\) 16.2918 1.06731 0.533656 0.845702i \(-0.320818\pi\)
0.533656 + 0.845702i \(0.320818\pi\)
\(234\) −0.618034 −0.0404021
\(235\) 2.61803 0.170782
\(236\) −14.6180 −0.951553
\(237\) −4.47214 −0.290496
\(238\) −23.4164 −1.51786
\(239\) −22.1803 −1.43473 −0.717363 0.696699i \(-0.754651\pi\)
−0.717363 + 0.696699i \(0.754651\pi\)
\(240\) 1.00000 0.0645497
\(241\) 25.6180 1.65020 0.825101 0.564985i \(-0.191118\pi\)
0.825101 + 0.564985i \(0.191118\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) −11.2361 −0.719316
\(245\) −6.09017 −0.389087
\(246\) −9.32624 −0.594619
\(247\) −0.381966 −0.0243039
\(248\) −9.23607 −0.586491
\(249\) −4.94427 −0.313331
\(250\) −1.00000 −0.0632456
\(251\) 11.5066 0.726289 0.363144 0.931733i \(-0.381703\pi\)
0.363144 + 0.931733i \(0.381703\pi\)
\(252\) −3.61803 −0.227915
\(253\) 0 0
\(254\) −12.6180 −0.791726
\(255\) 6.47214 0.405301
\(256\) 1.00000 0.0625000
\(257\) −5.05573 −0.315368 −0.157684 0.987490i \(-0.550403\pi\)
−0.157684 + 0.987490i \(0.550403\pi\)
\(258\) 0.763932 0.0475603
\(259\) 2.23607 0.138943
\(260\) 0.618034 0.0383288
\(261\) −3.70820 −0.229532
\(262\) −20.9443 −1.29394
\(263\) 8.14590 0.502298 0.251149 0.967948i \(-0.419192\pi\)
0.251149 + 0.967948i \(0.419192\pi\)
\(264\) 0 0
\(265\) 6.09017 0.374116
\(266\) −2.23607 −0.137102
\(267\) 5.14590 0.314924
\(268\) −8.18034 −0.499694
\(269\) −24.7639 −1.50988 −0.754942 0.655792i \(-0.772335\pi\)
−0.754942 + 0.655792i \(0.772335\pi\)
\(270\) 1.00000 0.0608581
\(271\) −0.652476 −0.0396351 −0.0198175 0.999804i \(-0.506309\pi\)
−0.0198175 + 0.999804i \(0.506309\pi\)
\(272\) 6.47214 0.392431
\(273\) −2.23607 −0.135333
\(274\) 15.4164 0.931339
\(275\) 0 0
\(276\) −4.85410 −0.292183
\(277\) 8.27051 0.496927 0.248463 0.968641i \(-0.420074\pi\)
0.248463 + 0.968641i \(0.420074\pi\)
\(278\) 7.61803 0.456899
\(279\) −9.23607 −0.552949
\(280\) 3.61803 0.216219
\(281\) −7.88854 −0.470591 −0.235296 0.971924i \(-0.575606\pi\)
−0.235296 + 0.971924i \(0.575606\pi\)
\(282\) 2.61803 0.155902
\(283\) −3.70820 −0.220430 −0.110215 0.993908i \(-0.535154\pi\)
−0.110215 + 0.993908i \(0.535154\pi\)
\(284\) −0.291796 −0.0173149
\(285\) 0.618034 0.0366092
\(286\) 0 0
\(287\) −33.7426 −1.99177
\(288\) 1.00000 0.0589256
\(289\) 24.8885 1.46403
\(290\) 3.70820 0.217753
\(291\) −14.9443 −0.876049
\(292\) −10.9443 −0.640465
\(293\) −11.0344 −0.644639 −0.322319 0.946631i \(-0.604463\pi\)
−0.322319 + 0.946631i \(0.604463\pi\)
\(294\) −6.09017 −0.355186
\(295\) 14.6180 0.851095
\(296\) −0.618034 −0.0359225
\(297\) 0 0
\(298\) 8.94427 0.518128
\(299\) −3.00000 −0.173494
\(300\) −1.00000 −0.0577350
\(301\) 2.76393 0.159310
\(302\) 12.4721 0.717691
\(303\) 4.00000 0.229794
\(304\) 0.618034 0.0354467
\(305\) 11.2361 0.643375
\(306\) 6.47214 0.369987
\(307\) −26.8328 −1.53143 −0.765715 0.643180i \(-0.777615\pi\)
−0.765715 + 0.643180i \(0.777615\pi\)
\(308\) 0 0
\(309\) 9.85410 0.560580
\(310\) 9.23607 0.524573
\(311\) −27.8885 −1.58141 −0.790707 0.612195i \(-0.790287\pi\)
−0.790707 + 0.612195i \(0.790287\pi\)
\(312\) 0.618034 0.0349893
\(313\) 5.70820 0.322647 0.161323 0.986902i \(-0.448424\pi\)
0.161323 + 0.986902i \(0.448424\pi\)
\(314\) −5.61803 −0.317044
\(315\) 3.61803 0.203853
\(316\) 4.47214 0.251577
\(317\) 10.9098 0.612757 0.306379 0.951910i \(-0.400883\pi\)
0.306379 + 0.951910i \(0.400883\pi\)
\(318\) 6.09017 0.341520
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 17.8885 0.998441
\(322\) −17.5623 −0.978709
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) −0.618034 −0.0342824
\(326\) 17.8885 0.990755
\(327\) 4.00000 0.221201
\(328\) 9.32624 0.514955
\(329\) 9.47214 0.522216
\(330\) 0 0
\(331\) 7.67376 0.421788 0.210894 0.977509i \(-0.432362\pi\)
0.210894 + 0.977509i \(0.432362\pi\)
\(332\) 4.94427 0.271352
\(333\) −0.618034 −0.0338681
\(334\) 11.5623 0.632661
\(335\) 8.18034 0.446940
\(336\) 3.61803 0.197380
\(337\) 20.0000 1.08947 0.544735 0.838608i \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) −12.6180 −0.686331
\(339\) 12.4721 0.677393
\(340\) −6.47214 −0.351001
\(341\) 0 0
\(342\) 0.618034 0.0334195
\(343\) 3.29180 0.177740
\(344\) −0.763932 −0.0411885
\(345\) 4.85410 0.261336
\(346\) 24.5623 1.32048
\(347\) −3.81966 −0.205050 −0.102525 0.994730i \(-0.532692\pi\)
−0.102525 + 0.994730i \(0.532692\pi\)
\(348\) 3.70820 0.198781
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −3.61803 −0.193392
\(351\) 0.618034 0.0329882
\(352\) 0 0
\(353\) −24.6525 −1.31212 −0.656059 0.754709i \(-0.727778\pi\)
−0.656059 + 0.754709i \(0.727778\pi\)
\(354\) 14.6180 0.776940
\(355\) 0.291796 0.0154869
\(356\) −5.14590 −0.272732
\(357\) 23.4164 1.23933
\(358\) −11.1459 −0.589079
\(359\) −25.2361 −1.33191 −0.665954 0.745992i \(-0.731975\pi\)
−0.665954 + 0.745992i \(0.731975\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −18.6180 −0.979897
\(362\) −24.3607 −1.28037
\(363\) 0 0
\(364\) 2.23607 0.117202
\(365\) 10.9443 0.572849
\(366\) 11.2361 0.587319
\(367\) 8.36068 0.436424 0.218212 0.975901i \(-0.429978\pi\)
0.218212 + 0.975901i \(0.429978\pi\)
\(368\) 4.85410 0.253038
\(369\) 9.32624 0.485505
\(370\) 0.618034 0.0321301
\(371\) 22.0344 1.14397
\(372\) 9.23607 0.478868
\(373\) 13.8541 0.717338 0.358669 0.933465i \(-0.383231\pi\)
0.358669 + 0.933465i \(0.383231\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) −2.61803 −0.135015
\(377\) 2.29180 0.118034
\(378\) 3.61803 0.186092
\(379\) −32.7426 −1.68188 −0.840938 0.541131i \(-0.817996\pi\)
−0.840938 + 0.541131i \(0.817996\pi\)
\(380\) −0.618034 −0.0317045
\(381\) 12.6180 0.646441
\(382\) −13.7082 −0.701373
\(383\) −28.4508 −1.45377 −0.726885 0.686759i \(-0.759033\pi\)
−0.726885 + 0.686759i \(0.759033\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 3.70820 0.188743
\(387\) −0.763932 −0.0388328
\(388\) 14.9443 0.758680
\(389\) 3.52786 0.178870 0.0894349 0.995993i \(-0.471494\pi\)
0.0894349 + 0.995993i \(0.471494\pi\)
\(390\) −0.618034 −0.0312954
\(391\) 31.4164 1.58880
\(392\) 6.09017 0.307600
\(393\) 20.9443 1.05650
\(394\) −3.61803 −0.182274
\(395\) −4.47214 −0.225018
\(396\) 0 0
\(397\) 12.6738 0.636078 0.318039 0.948078i \(-0.396976\pi\)
0.318039 + 0.948078i \(0.396976\pi\)
\(398\) −12.9443 −0.648838
\(399\) 2.23607 0.111943
\(400\) 1.00000 0.0500000
\(401\) −1.67376 −0.0835837 −0.0417918 0.999126i \(-0.513307\pi\)
−0.0417918 + 0.999126i \(0.513307\pi\)
\(402\) 8.18034 0.407998
\(403\) 5.70820 0.284346
\(404\) −4.00000 −0.199007
\(405\) −1.00000 −0.0496904
\(406\) 13.4164 0.665845
\(407\) 0 0
\(408\) −6.47214 −0.320418
\(409\) −14.2148 −0.702876 −0.351438 0.936211i \(-0.614307\pi\)
−0.351438 + 0.936211i \(0.614307\pi\)
\(410\) −9.32624 −0.460590
\(411\) −15.4164 −0.760435
\(412\) −9.85410 −0.485477
\(413\) 52.8885 2.60248
\(414\) 4.85410 0.238566
\(415\) −4.94427 −0.242705
\(416\) −0.618034 −0.0303016
\(417\) −7.61803 −0.373057
\(418\) 0 0
\(419\) −11.2016 −0.547235 −0.273618 0.961839i \(-0.588220\pi\)
−0.273618 + 0.961839i \(0.588220\pi\)
\(420\) −3.61803 −0.176542
\(421\) 26.9443 1.31318 0.656592 0.754246i \(-0.271997\pi\)
0.656592 + 0.754246i \(0.271997\pi\)
\(422\) 23.4164 1.13989
\(423\) −2.61803 −0.127293
\(424\) −6.09017 −0.295765
\(425\) 6.47214 0.313945
\(426\) 0.291796 0.0141376
\(427\) 40.6525 1.96731
\(428\) −17.8885 −0.864675
\(429\) 0 0
\(430\) 0.763932 0.0368401
\(431\) −2.18034 −0.105023 −0.0525116 0.998620i \(-0.516723\pi\)
−0.0525116 + 0.998620i \(0.516723\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −33.1246 −1.59187 −0.795934 0.605384i \(-0.793020\pi\)
−0.795934 + 0.605384i \(0.793020\pi\)
\(434\) 33.4164 1.60404
\(435\) −3.70820 −0.177795
\(436\) −4.00000 −0.191565
\(437\) 3.00000 0.143509
\(438\) 10.9443 0.522938
\(439\) −20.1803 −0.963155 −0.481578 0.876403i \(-0.659936\pi\)
−0.481578 + 0.876403i \(0.659936\pi\)
\(440\) 0 0
\(441\) 6.09017 0.290008
\(442\) −4.00000 −0.190261
\(443\) 28.8328 1.36989 0.684944 0.728596i \(-0.259827\pi\)
0.684944 + 0.728596i \(0.259827\pi\)
\(444\) 0.618034 0.0293306
\(445\) 5.14590 0.243939
\(446\) 7.61803 0.360724
\(447\) −8.94427 −0.423050
\(448\) −3.61803 −0.170936
\(449\) −18.6180 −0.878639 −0.439320 0.898331i \(-0.644780\pi\)
−0.439320 + 0.898331i \(0.644780\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −12.4721 −0.586640
\(453\) −12.4721 −0.585992
\(454\) 4.18034 0.196193
\(455\) −2.23607 −0.104828
\(456\) −0.618034 −0.0289421
\(457\) −9.88854 −0.462567 −0.231283 0.972886i \(-0.574292\pi\)
−0.231283 + 0.972886i \(0.574292\pi\)
\(458\) −11.5279 −0.538662
\(459\) −6.47214 −0.302093
\(460\) −4.85410 −0.226324
\(461\) 24.7639 1.15337 0.576686 0.816966i \(-0.304346\pi\)
0.576686 + 0.816966i \(0.304346\pi\)
\(462\) 0 0
\(463\) −3.38197 −0.157173 −0.0785866 0.996907i \(-0.525041\pi\)
−0.0785866 + 0.996907i \(0.525041\pi\)
\(464\) −3.70820 −0.172149
\(465\) −9.23607 −0.428312
\(466\) 16.2918 0.754703
\(467\) 7.05573 0.326500 0.163250 0.986585i \(-0.447802\pi\)
0.163250 + 0.986585i \(0.447802\pi\)
\(468\) −0.618034 −0.0285686
\(469\) 29.5967 1.36665
\(470\) 2.61803 0.120761
\(471\) 5.61803 0.258865
\(472\) −14.6180 −0.672850
\(473\) 0 0
\(474\) −4.47214 −0.205412
\(475\) 0.618034 0.0283573
\(476\) −23.4164 −1.07329
\(477\) −6.09017 −0.278850
\(478\) −22.1803 −1.01451
\(479\) 39.0132 1.78256 0.891278 0.453457i \(-0.149809\pi\)
0.891278 + 0.453457i \(0.149809\pi\)
\(480\) 1.00000 0.0456435
\(481\) 0.381966 0.0174162
\(482\) 25.6180 1.16687
\(483\) 17.5623 0.799113
\(484\) 0 0
\(485\) −14.9443 −0.678584
\(486\) −1.00000 −0.0453609
\(487\) 40.3607 1.82892 0.914458 0.404680i \(-0.132617\pi\)
0.914458 + 0.404680i \(0.132617\pi\)
\(488\) −11.2361 −0.508633
\(489\) −17.8885 −0.808948
\(490\) −6.09017 −0.275126
\(491\) 2.32624 0.104982 0.0524908 0.998621i \(-0.483284\pi\)
0.0524908 + 0.998621i \(0.483284\pi\)
\(492\) −9.32624 −0.420459
\(493\) −24.0000 −1.08091
\(494\) −0.381966 −0.0171855
\(495\) 0 0
\(496\) −9.23607 −0.414712
\(497\) 1.05573 0.0473559
\(498\) −4.94427 −0.221558
\(499\) −33.6869 −1.50803 −0.754017 0.656855i \(-0.771886\pi\)
−0.754017 + 0.656855i \(0.771886\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −11.5623 −0.516566
\(502\) 11.5066 0.513564
\(503\) 4.79837 0.213949 0.106974 0.994262i \(-0.465884\pi\)
0.106974 + 0.994262i \(0.465884\pi\)
\(504\) −3.61803 −0.161160
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 12.6180 0.560387
\(508\) −12.6180 −0.559835
\(509\) −25.4164 −1.12656 −0.563281 0.826265i \(-0.690461\pi\)
−0.563281 + 0.826265i \(0.690461\pi\)
\(510\) 6.47214 0.286591
\(511\) 39.5967 1.75166
\(512\) 1.00000 0.0441942
\(513\) −0.618034 −0.0272869
\(514\) −5.05573 −0.222999
\(515\) 9.85410 0.434224
\(516\) 0.763932 0.0336302
\(517\) 0 0
\(518\) 2.23607 0.0982472
\(519\) −24.5623 −1.07817
\(520\) 0.618034 0.0271026
\(521\) 37.3262 1.63529 0.817646 0.575721i \(-0.195279\pi\)
0.817646 + 0.575721i \(0.195279\pi\)
\(522\) −3.70820 −0.162304
\(523\) −2.29180 −0.100213 −0.0501066 0.998744i \(-0.515956\pi\)
−0.0501066 + 0.998744i \(0.515956\pi\)
\(524\) −20.9443 −0.914955
\(525\) 3.61803 0.157904
\(526\) 8.14590 0.355178
\(527\) −59.7771 −2.60393
\(528\) 0 0
\(529\) 0.562306 0.0244481
\(530\) 6.09017 0.264540
\(531\) −14.6180 −0.634369
\(532\) −2.23607 −0.0969458
\(533\) −5.76393 −0.249664
\(534\) 5.14590 0.222685
\(535\) 17.8885 0.773389
\(536\) −8.18034 −0.353337
\(537\) 11.1459 0.480981
\(538\) −24.7639 −1.06765
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 15.0557 0.647296 0.323648 0.946178i \(-0.395091\pi\)
0.323648 + 0.946178i \(0.395091\pi\)
\(542\) −0.652476 −0.0280262
\(543\) 24.3607 1.04542
\(544\) 6.47214 0.277491
\(545\) 4.00000 0.171341
\(546\) −2.23607 −0.0956949
\(547\) 19.2361 0.822475 0.411237 0.911528i \(-0.365097\pi\)
0.411237 + 0.911528i \(0.365097\pi\)
\(548\) 15.4164 0.658556
\(549\) −11.2361 −0.479544
\(550\) 0 0
\(551\) −2.29180 −0.0976338
\(552\) −4.85410 −0.206604
\(553\) −16.1803 −0.688058
\(554\) 8.27051 0.351380
\(555\) −0.618034 −0.0262341
\(556\) 7.61803 0.323077
\(557\) −13.6738 −0.579376 −0.289688 0.957121i \(-0.593552\pi\)
−0.289688 + 0.957121i \(0.593552\pi\)
\(558\) −9.23607 −0.390994
\(559\) 0.472136 0.0199692
\(560\) 3.61803 0.152890
\(561\) 0 0
\(562\) −7.88854 −0.332758
\(563\) −45.3050 −1.90938 −0.954688 0.297608i \(-0.903811\pi\)
−0.954688 + 0.297608i \(0.903811\pi\)
\(564\) 2.61803 0.110239
\(565\) 12.4721 0.524707
\(566\) −3.70820 −0.155867
\(567\) −3.61803 −0.151943
\(568\) −0.291796 −0.0122435
\(569\) −14.8541 −0.622716 −0.311358 0.950293i \(-0.600784\pi\)
−0.311358 + 0.950293i \(0.600784\pi\)
\(570\) 0.618034 0.0258866
\(571\) 21.5066 0.900022 0.450011 0.893023i \(-0.351420\pi\)
0.450011 + 0.893023i \(0.351420\pi\)
\(572\) 0 0
\(573\) 13.7082 0.572668
\(574\) −33.7426 −1.40839
\(575\) 4.85410 0.202430
\(576\) 1.00000 0.0416667
\(577\) −7.12461 −0.296601 −0.148301 0.988942i \(-0.547380\pi\)
−0.148301 + 0.988942i \(0.547380\pi\)
\(578\) 24.8885 1.03523
\(579\) −3.70820 −0.154108
\(580\) 3.70820 0.153975
\(581\) −17.8885 −0.742142
\(582\) −14.9443 −0.619460
\(583\) 0 0
\(584\) −10.9443 −0.452877
\(585\) 0.618034 0.0255526
\(586\) −11.0344 −0.455829
\(587\) 34.8328 1.43770 0.718852 0.695163i \(-0.244668\pi\)
0.718852 + 0.695163i \(0.244668\pi\)
\(588\) −6.09017 −0.251154
\(589\) −5.70820 −0.235202
\(590\) 14.6180 0.601815
\(591\) 3.61803 0.148826
\(592\) −0.618034 −0.0254010
\(593\) 2.58359 0.106095 0.0530477 0.998592i \(-0.483106\pi\)
0.0530477 + 0.998592i \(0.483106\pi\)
\(594\) 0 0
\(595\) 23.4164 0.959979
\(596\) 8.94427 0.366372
\(597\) 12.9443 0.529774
\(598\) −3.00000 −0.122679
\(599\) −4.29180 −0.175358 −0.0876790 0.996149i \(-0.527945\pi\)
−0.0876790 + 0.996149i \(0.527945\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 35.0902 1.43136 0.715679 0.698429i \(-0.246117\pi\)
0.715679 + 0.698429i \(0.246117\pi\)
\(602\) 2.76393 0.112649
\(603\) −8.18034 −0.333129
\(604\) 12.4721 0.507484
\(605\) 0 0
\(606\) 4.00000 0.162489
\(607\) 16.3607 0.664060 0.332030 0.943269i \(-0.392267\pi\)
0.332030 + 0.943269i \(0.392267\pi\)
\(608\) 0.618034 0.0250646
\(609\) −13.4164 −0.543660
\(610\) 11.2361 0.454935
\(611\) 1.61803 0.0654586
\(612\) 6.47214 0.261621
\(613\) −45.4164 −1.83435 −0.917176 0.398483i \(-0.869537\pi\)
−0.917176 + 0.398483i \(0.869537\pi\)
\(614\) −26.8328 −1.08288
\(615\) 9.32624 0.376070
\(616\) 0 0
\(617\) 23.0557 0.928189 0.464094 0.885786i \(-0.346380\pi\)
0.464094 + 0.885786i \(0.346380\pi\)
\(618\) 9.85410 0.396390
\(619\) 23.7426 0.954298 0.477149 0.878823i \(-0.341670\pi\)
0.477149 + 0.878823i \(0.341670\pi\)
\(620\) 9.23607 0.370929
\(621\) −4.85410 −0.194788
\(622\) −27.8885 −1.11823
\(623\) 18.6180 0.745916
\(624\) 0.618034 0.0247412
\(625\) 1.00000 0.0400000
\(626\) 5.70820 0.228146
\(627\) 0 0
\(628\) −5.61803 −0.224184
\(629\) −4.00000 −0.159490
\(630\) 3.61803 0.144146
\(631\) 1.70820 0.0680025 0.0340013 0.999422i \(-0.489175\pi\)
0.0340013 + 0.999422i \(0.489175\pi\)
\(632\) 4.47214 0.177892
\(633\) −23.4164 −0.930719
\(634\) 10.9098 0.433285
\(635\) 12.6180 0.500731
\(636\) 6.09017 0.241491
\(637\) −3.76393 −0.149132
\(638\) 0 0
\(639\) −0.291796 −0.0115433
\(640\) −1.00000 −0.0395285
\(641\) 37.4508 1.47922 0.739610 0.673036i \(-0.235010\pi\)
0.739610 + 0.673036i \(0.235010\pi\)
\(642\) 17.8885 0.706005
\(643\) −3.41641 −0.134730 −0.0673650 0.997728i \(-0.521459\pi\)
−0.0673650 + 0.997728i \(0.521459\pi\)
\(644\) −17.5623 −0.692052
\(645\) −0.763932 −0.0300798
\(646\) 4.00000 0.157378
\(647\) −30.8328 −1.21216 −0.606082 0.795403i \(-0.707259\pi\)
−0.606082 + 0.795403i \(0.707259\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −0.618034 −0.0242413
\(651\) −33.4164 −1.30969
\(652\) 17.8885 0.700569
\(653\) −15.8541 −0.620419 −0.310209 0.950668i \(-0.600399\pi\)
−0.310209 + 0.950668i \(0.600399\pi\)
\(654\) 4.00000 0.156412
\(655\) 20.9443 0.818360
\(656\) 9.32624 0.364128
\(657\) −10.9443 −0.426977
\(658\) 9.47214 0.369262
\(659\) −28.2705 −1.10126 −0.550631 0.834749i \(-0.685613\pi\)
−0.550631 + 0.834749i \(0.685613\pi\)
\(660\) 0 0
\(661\) 41.4853 1.61359 0.806795 0.590831i \(-0.201200\pi\)
0.806795 + 0.590831i \(0.201200\pi\)
\(662\) 7.67376 0.298249
\(663\) 4.00000 0.155347
\(664\) 4.94427 0.191875
\(665\) 2.23607 0.0867110
\(666\) −0.618034 −0.0239483
\(667\) −18.0000 −0.696963
\(668\) 11.5623 0.447359
\(669\) −7.61803 −0.294530
\(670\) 8.18034 0.316034
\(671\) 0 0
\(672\) 3.61803 0.139569
\(673\) 45.5967 1.75763 0.878813 0.477167i \(-0.158336\pi\)
0.878813 + 0.477167i \(0.158336\pi\)
\(674\) 20.0000 0.770371
\(675\) −1.00000 −0.0384900
\(676\) −12.6180 −0.485309
\(677\) −14.3607 −0.551926 −0.275963 0.961168i \(-0.588997\pi\)
−0.275963 + 0.961168i \(0.588997\pi\)
\(678\) 12.4721 0.478989
\(679\) −54.0689 −2.07497
\(680\) −6.47214 −0.248195
\(681\) −4.18034 −0.160191
\(682\) 0 0
\(683\) 31.1246 1.19095 0.595475 0.803374i \(-0.296964\pi\)
0.595475 + 0.803374i \(0.296964\pi\)
\(684\) 0.618034 0.0236311
\(685\) −15.4164 −0.589031
\(686\) 3.29180 0.125681
\(687\) 11.5279 0.439815
\(688\) −0.763932 −0.0291246
\(689\) 3.76393 0.143394
\(690\) 4.85410 0.184793
\(691\) −1.50658 −0.0573129 −0.0286565 0.999589i \(-0.509123\pi\)
−0.0286565 + 0.999589i \(0.509123\pi\)
\(692\) 24.5623 0.933719
\(693\) 0 0
\(694\) −3.81966 −0.144992
\(695\) −7.61803 −0.288969
\(696\) 3.70820 0.140559
\(697\) 60.3607 2.28632
\(698\) −10.0000 −0.378506
\(699\) −16.2918 −0.616212
\(700\) −3.61803 −0.136749
\(701\) 20.0689 0.757991 0.378996 0.925398i \(-0.376270\pi\)
0.378996 + 0.925398i \(0.376270\pi\)
\(702\) 0.618034 0.0233262
\(703\) −0.381966 −0.0144061
\(704\) 0 0
\(705\) −2.61803 −0.0986009
\(706\) −24.6525 −0.927808
\(707\) 14.4721 0.544281
\(708\) 14.6180 0.549379
\(709\) −24.6525 −0.925843 −0.462922 0.886399i \(-0.653199\pi\)
−0.462922 + 0.886399i \(0.653199\pi\)
\(710\) 0.291796 0.0109509
\(711\) 4.47214 0.167718
\(712\) −5.14590 −0.192851
\(713\) −44.8328 −1.67900
\(714\) 23.4164 0.876337
\(715\) 0 0
\(716\) −11.1459 −0.416542
\(717\) 22.1803 0.828340
\(718\) −25.2361 −0.941802
\(719\) −23.8885 −0.890892 −0.445446 0.895309i \(-0.646955\pi\)
−0.445446 + 0.895309i \(0.646955\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 35.6525 1.32777
\(722\) −18.6180 −0.692891
\(723\) −25.6180 −0.952745
\(724\) −24.3607 −0.905358
\(725\) −3.70820 −0.137719
\(726\) 0 0
\(727\) −46.6312 −1.72946 −0.864728 0.502241i \(-0.832509\pi\)
−0.864728 + 0.502241i \(0.832509\pi\)
\(728\) 2.23607 0.0828742
\(729\) 1.00000 0.0370370
\(730\) 10.9443 0.405066
\(731\) −4.94427 −0.182871
\(732\) 11.2361 0.415297
\(733\) 28.4721 1.05164 0.525821 0.850595i \(-0.323758\pi\)
0.525821 + 0.850595i \(0.323758\pi\)
\(734\) 8.36068 0.308598
\(735\) 6.09017 0.224639
\(736\) 4.85410 0.178925
\(737\) 0 0
\(738\) 9.32624 0.343304
\(739\) −27.6180 −1.01595 −0.507973 0.861373i \(-0.669605\pi\)
−0.507973 + 0.861373i \(0.669605\pi\)
\(740\) 0.618034 0.0227194
\(741\) 0.381966 0.0140319
\(742\) 22.0344 0.808910
\(743\) 7.14590 0.262158 0.131079 0.991372i \(-0.458156\pi\)
0.131079 + 0.991372i \(0.458156\pi\)
\(744\) 9.23607 0.338611
\(745\) −8.94427 −0.327693
\(746\) 13.8541 0.507235
\(747\) 4.94427 0.180901
\(748\) 0 0
\(749\) 64.7214 2.36487
\(750\) 1.00000 0.0365148
\(751\) −30.2492 −1.10381 −0.551905 0.833907i \(-0.686099\pi\)
−0.551905 + 0.833907i \(0.686099\pi\)
\(752\) −2.61803 −0.0954699
\(753\) −11.5066 −0.419323
\(754\) 2.29180 0.0834623
\(755\) −12.4721 −0.453908
\(756\) 3.61803 0.131587
\(757\) 1.85410 0.0673885 0.0336942 0.999432i \(-0.489273\pi\)
0.0336942 + 0.999432i \(0.489273\pi\)
\(758\) −32.7426 −1.18927
\(759\) 0 0
\(760\) −0.618034 −0.0224184
\(761\) 7.88854 0.285959 0.142980 0.989726i \(-0.454332\pi\)
0.142980 + 0.989726i \(0.454332\pi\)
\(762\) 12.6180 0.457103
\(763\) 14.4721 0.523926
\(764\) −13.7082 −0.495945
\(765\) −6.47214 −0.234001
\(766\) −28.4508 −1.02797
\(767\) 9.03444 0.326215
\(768\) −1.00000 −0.0360844
\(769\) 34.7984 1.25486 0.627431 0.778672i \(-0.284107\pi\)
0.627431 + 0.778672i \(0.284107\pi\)
\(770\) 0 0
\(771\) 5.05573 0.182078
\(772\) 3.70820 0.133461
\(773\) 3.79837 0.136618 0.0683090 0.997664i \(-0.478240\pi\)
0.0683090 + 0.997664i \(0.478240\pi\)
\(774\) −0.763932 −0.0274590
\(775\) −9.23607 −0.331769
\(776\) 14.9443 0.536468
\(777\) −2.23607 −0.0802185
\(778\) 3.52786 0.126480
\(779\) 5.76393 0.206514
\(780\) −0.618034 −0.0221292
\(781\) 0 0
\(782\) 31.4164 1.12345
\(783\) 3.70820 0.132520
\(784\) 6.09017 0.217506
\(785\) 5.61803 0.200516
\(786\) 20.9443 0.747057
\(787\) 18.1803 0.648059 0.324030 0.946047i \(-0.394962\pi\)
0.324030 + 0.946047i \(0.394962\pi\)
\(788\) −3.61803 −0.128887
\(789\) −8.14590 −0.290002
\(790\) −4.47214 −0.159111
\(791\) 45.1246 1.60445
\(792\) 0 0
\(793\) 6.94427 0.246598
\(794\) 12.6738 0.449775
\(795\) −6.09017 −0.215996
\(796\) −12.9443 −0.458798
\(797\) 13.7426 0.486789 0.243395 0.969927i \(-0.421739\pi\)
0.243395 + 0.969927i \(0.421739\pi\)
\(798\) 2.23607 0.0791559
\(799\) −16.9443 −0.599445
\(800\) 1.00000 0.0353553
\(801\) −5.14590 −0.181821
\(802\) −1.67376 −0.0591026
\(803\) 0 0
\(804\) 8.18034 0.288498
\(805\) 17.5623 0.618990
\(806\) 5.70820 0.201063
\(807\) 24.7639 0.871732
\(808\) −4.00000 −0.140720
\(809\) 3.49342 0.122822 0.0614111 0.998113i \(-0.480440\pi\)
0.0614111 + 0.998113i \(0.480440\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −26.2705 −0.922482 −0.461241 0.887275i \(-0.652596\pi\)
−0.461241 + 0.887275i \(0.652596\pi\)
\(812\) 13.4164 0.470824
\(813\) 0.652476 0.0228833
\(814\) 0 0
\(815\) −17.8885 −0.626608
\(816\) −6.47214 −0.226570
\(817\) −0.472136 −0.0165179
\(818\) −14.2148 −0.497008
\(819\) 2.23607 0.0781345
\(820\) −9.32624 −0.325686
\(821\) −12.7639 −0.445464 −0.222732 0.974880i \(-0.571498\pi\)
−0.222732 + 0.974880i \(0.571498\pi\)
\(822\) −15.4164 −0.537709
\(823\) 32.9098 1.14716 0.573582 0.819148i \(-0.305553\pi\)
0.573582 + 0.819148i \(0.305553\pi\)
\(824\) −9.85410 −0.343284
\(825\) 0 0
\(826\) 52.8885 1.84023
\(827\) 9.70820 0.337587 0.168794 0.985651i \(-0.446013\pi\)
0.168794 + 0.985651i \(0.446013\pi\)
\(828\) 4.85410 0.168692
\(829\) −23.3050 −0.809414 −0.404707 0.914446i \(-0.632627\pi\)
−0.404707 + 0.914446i \(0.632627\pi\)
\(830\) −4.94427 −0.171618
\(831\) −8.27051 −0.286901
\(832\) −0.618034 −0.0214265
\(833\) 39.4164 1.36570
\(834\) −7.61803 −0.263791
\(835\) −11.5623 −0.400130
\(836\) 0 0
\(837\) 9.23607 0.319245
\(838\) −11.2016 −0.386954
\(839\) 33.1246 1.14359 0.571794 0.820397i \(-0.306248\pi\)
0.571794 + 0.820397i \(0.306248\pi\)
\(840\) −3.61803 −0.124834
\(841\) −15.2492 −0.525835
\(842\) 26.9443 0.928561
\(843\) 7.88854 0.271696
\(844\) 23.4164 0.806026
\(845\) 12.6180 0.434074
\(846\) −2.61803 −0.0900099
\(847\) 0 0
\(848\) −6.09017 −0.209137
\(849\) 3.70820 0.127265
\(850\) 6.47214 0.221992
\(851\) −3.00000 −0.102839
\(852\) 0.291796 0.00999677
\(853\) −48.8115 −1.67127 −0.835637 0.549281i \(-0.814902\pi\)
−0.835637 + 0.549281i \(0.814902\pi\)
\(854\) 40.6525 1.39110
\(855\) −0.618034 −0.0211363
\(856\) −17.8885 −0.611418
\(857\) −55.2361 −1.88683 −0.943414 0.331617i \(-0.892406\pi\)
−0.943414 + 0.331617i \(0.892406\pi\)
\(858\) 0 0
\(859\) 51.0344 1.74127 0.870636 0.491927i \(-0.163707\pi\)
0.870636 + 0.491927i \(0.163707\pi\)
\(860\) 0.763932 0.0260499
\(861\) 33.7426 1.14995
\(862\) −2.18034 −0.0742627
\(863\) −0.145898 −0.00496643 −0.00248321 0.999997i \(-0.500790\pi\)
−0.00248321 + 0.999997i \(0.500790\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −24.5623 −0.835143
\(866\) −33.1246 −1.12562
\(867\) −24.8885 −0.845259
\(868\) 33.4164 1.13423
\(869\) 0 0
\(870\) −3.70820 −0.125720
\(871\) 5.05573 0.171307
\(872\) −4.00000 −0.135457
\(873\) 14.9443 0.505787
\(874\) 3.00000 0.101477
\(875\) 3.61803 0.122312
\(876\) 10.9443 0.369773
\(877\) 23.3820 0.789553 0.394776 0.918777i \(-0.370822\pi\)
0.394776 + 0.918777i \(0.370822\pi\)
\(878\) −20.1803 −0.681053
\(879\) 11.0344 0.372182
\(880\) 0 0
\(881\) 7.79837 0.262734 0.131367 0.991334i \(-0.458063\pi\)
0.131367 + 0.991334i \(0.458063\pi\)
\(882\) 6.09017 0.205067
\(883\) 25.3050 0.851579 0.425790 0.904822i \(-0.359996\pi\)
0.425790 + 0.904822i \(0.359996\pi\)
\(884\) −4.00000 −0.134535
\(885\) −14.6180 −0.491380
\(886\) 28.8328 0.968657
\(887\) −1.25735 −0.0422178 −0.0211089 0.999777i \(-0.506720\pi\)
−0.0211089 + 0.999777i \(0.506720\pi\)
\(888\) 0.618034 0.0207399
\(889\) 45.6525 1.53113
\(890\) 5.14590 0.172491
\(891\) 0 0
\(892\) 7.61803 0.255071
\(893\) −1.61803 −0.0541454
\(894\) −8.94427 −0.299141
\(895\) 11.1459 0.372566
\(896\) −3.61803 −0.120870
\(897\) 3.00000 0.100167
\(898\) −18.6180 −0.621292
\(899\) 34.2492 1.14228
\(900\) 1.00000 0.0333333
\(901\) −39.4164 −1.31315
\(902\) 0 0
\(903\) −2.76393 −0.0919779
\(904\) −12.4721 −0.414817
\(905\) 24.3607 0.809776
\(906\) −12.4721 −0.414359
\(907\) 29.8885 0.992433 0.496216 0.868199i \(-0.334722\pi\)
0.496216 + 0.868199i \(0.334722\pi\)
\(908\) 4.18034 0.138729
\(909\) −4.00000 −0.132672
\(910\) −2.23607 −0.0741249
\(911\) −10.6525 −0.352932 −0.176466 0.984307i \(-0.556467\pi\)
−0.176466 + 0.984307i \(0.556467\pi\)
\(912\) −0.618034 −0.0204652
\(913\) 0 0
\(914\) −9.88854 −0.327084
\(915\) −11.2361 −0.371453
\(916\) −11.5279 −0.380891
\(917\) 75.7771 2.50238
\(918\) −6.47214 −0.213612
\(919\) 18.0689 0.596037 0.298019 0.954560i \(-0.403674\pi\)
0.298019 + 0.954560i \(0.403674\pi\)
\(920\) −4.85410 −0.160035
\(921\) 26.8328 0.884171
\(922\) 24.7639 0.815557
\(923\) 0.180340 0.00593596
\(924\) 0 0
\(925\) −0.618034 −0.0203208
\(926\) −3.38197 −0.111138
\(927\) −9.85410 −0.323651
\(928\) −3.70820 −0.121728
\(929\) −7.03444 −0.230793 −0.115396 0.993320i \(-0.536814\pi\)
−0.115396 + 0.993320i \(0.536814\pi\)
\(930\) −9.23607 −0.302863
\(931\) 3.76393 0.123358
\(932\) 16.2918 0.533656
\(933\) 27.8885 0.913030
\(934\) 7.05573 0.230870
\(935\) 0 0
\(936\) −0.618034 −0.0202011
\(937\) −48.3607 −1.57987 −0.789937 0.613188i \(-0.789887\pi\)
−0.789937 + 0.613188i \(0.789887\pi\)
\(938\) 29.5967 0.966368
\(939\) −5.70820 −0.186280
\(940\) 2.61803 0.0853909
\(941\) −11.0557 −0.360406 −0.180203 0.983629i \(-0.557676\pi\)
−0.180203 + 0.983629i \(0.557676\pi\)
\(942\) 5.61803 0.183045
\(943\) 45.2705 1.47421
\(944\) −14.6180 −0.475776
\(945\) −3.61803 −0.117695
\(946\) 0 0
\(947\) −3.30495 −0.107396 −0.0536982 0.998557i \(-0.517101\pi\)
−0.0536982 + 0.998557i \(0.517101\pi\)
\(948\) −4.47214 −0.145248
\(949\) 6.76393 0.219567
\(950\) 0.618034 0.0200517
\(951\) −10.9098 −0.353775
\(952\) −23.4164 −0.758930
\(953\) 44.7639 1.45005 0.725023 0.688725i \(-0.241829\pi\)
0.725023 + 0.688725i \(0.241829\pi\)
\(954\) −6.09017 −0.197177
\(955\) 13.7082 0.443587
\(956\) −22.1803 −0.717363
\(957\) 0 0
\(958\) 39.0132 1.26046
\(959\) −55.7771 −1.80114
\(960\) 1.00000 0.0322749
\(961\) 54.3050 1.75177
\(962\) 0.381966 0.0123151
\(963\) −17.8885 −0.576450
\(964\) 25.6180 0.825101
\(965\) −3.70820 −0.119371
\(966\) 17.5623 0.565058
\(967\) 4.25735 0.136907 0.0684536 0.997654i \(-0.478193\pi\)
0.0684536 + 0.997654i \(0.478193\pi\)
\(968\) 0 0
\(969\) −4.00000 −0.128499
\(970\) −14.9443 −0.479832
\(971\) 5.79837 0.186079 0.0930393 0.995662i \(-0.470342\pi\)
0.0930393 + 0.995662i \(0.470342\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −27.5623 −0.883607
\(974\) 40.3607 1.29324
\(975\) 0.618034 0.0197929
\(976\) −11.2361 −0.359658
\(977\) −24.8328 −0.794472 −0.397236 0.917716i \(-0.630031\pi\)
−0.397236 + 0.917716i \(0.630031\pi\)
\(978\) −17.8885 −0.572013
\(979\) 0 0
\(980\) −6.09017 −0.194543
\(981\) −4.00000 −0.127710
\(982\) 2.32624 0.0742332
\(983\) −33.0344 −1.05364 −0.526818 0.849978i \(-0.676615\pi\)
−0.526818 + 0.849978i \(0.676615\pi\)
\(984\) −9.32624 −0.297310
\(985\) 3.61803 0.115280
\(986\) −24.0000 −0.764316
\(987\) −9.47214 −0.301501
\(988\) −0.381966 −0.0121520
\(989\) −3.70820 −0.117914
\(990\) 0 0
\(991\) 8.94427 0.284124 0.142062 0.989858i \(-0.454627\pi\)
0.142062 + 0.989858i \(0.454627\pi\)
\(992\) −9.23607 −0.293245
\(993\) −7.67376 −0.243519
\(994\) 1.05573 0.0334857
\(995\) 12.9443 0.410361
\(996\) −4.94427 −0.156665
\(997\) 13.7771 0.436325 0.218162 0.975912i \(-0.429994\pi\)
0.218162 + 0.975912i \(0.429994\pi\)
\(998\) −33.6869 −1.06634
\(999\) 0.618034 0.0195537
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 3630.2.a.bi.1.1 2
11.7 odd 10 330.2.m.d.181.1 yes 4
11.8 odd 10 330.2.m.d.31.1 4
11.10 odd 2 3630.2.a.bc.1.2 2
33.8 even 10 990.2.n.a.361.1 4
33.29 even 10 990.2.n.a.181.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
330.2.m.d.31.1 4 11.8 odd 10
330.2.m.d.181.1 yes 4 11.7 odd 10
990.2.n.a.181.1 4 33.29 even 10
990.2.n.a.361.1 4 33.8 even 10
3630.2.a.bc.1.2 2 11.10 odd 2
3630.2.a.bi.1.1 2 1.1 even 1 trivial