Properties

Label 3630.2.a.bi.1.2
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 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 3630.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +1.61803 q^{13} -1.38197 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.47214 q^{17} +1.00000 q^{18} -1.61803 q^{19} -1.00000 q^{20} +1.38197 q^{21} -1.85410 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.61803 q^{26} -1.00000 q^{27} -1.38197 q^{28} +9.70820 q^{29} +1.00000 q^{30} -4.76393 q^{31} +1.00000 q^{32} -2.47214 q^{34} +1.38197 q^{35} +1.00000 q^{36} +1.61803 q^{37} -1.61803 q^{38} -1.61803 q^{39} -1.00000 q^{40} -6.32624 q^{41} +1.38197 q^{42} -5.23607 q^{43} -1.00000 q^{45} -1.85410 q^{46} -0.381966 q^{47} -1.00000 q^{48} -5.09017 q^{49} +1.00000 q^{50} +2.47214 q^{51} +1.61803 q^{52} +5.09017 q^{53} -1.00000 q^{54} -1.38197 q^{56} +1.61803 q^{57} +9.70820 q^{58} -12.3820 q^{59} +1.00000 q^{60} -6.76393 q^{61} -4.76393 q^{62} -1.38197 q^{63} +1.00000 q^{64} -1.61803 q^{65} +14.1803 q^{67} -2.47214 q^{68} +1.85410 q^{69} +1.38197 q^{70} -13.7082 q^{71} +1.00000 q^{72} +6.94427 q^{73} +1.61803 q^{74} -1.00000 q^{75} -1.61803 q^{76} -1.61803 q^{78} -4.47214 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.32624 q^{82} -12.9443 q^{83} +1.38197 q^{84} +2.47214 q^{85} -5.23607 q^{86} -9.70820 q^{87} -11.8541 q^{89} -1.00000 q^{90} -2.23607 q^{91} -1.85410 q^{92} +4.76393 q^{93} -0.381966 q^{94} +1.61803 q^{95} -1.00000 q^{96} -2.94427 q^{97} -5.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + 2q^{8} + 2q^{9} - 2q^{10} - 2q^{12} + q^{13} - 5q^{14} + 2q^{15} + 2q^{16} + 4q^{17} + 2q^{18} - q^{19} - 2q^{20} + 5q^{21} + 3q^{23} - 2q^{24} + 2q^{25} + q^{26} - 2q^{27} - 5q^{28} + 6q^{29} + 2q^{30} - 14q^{31} + 2q^{32} + 4q^{34} + 5q^{35} + 2q^{36} + q^{37} - q^{38} - q^{39} - 2q^{40} + 3q^{41} + 5q^{42} - 6q^{43} - 2q^{45} + 3q^{46} - 3q^{47} - 2q^{48} + q^{49} + 2q^{50} - 4q^{51} + q^{52} - q^{53} - 2q^{54} - 5q^{56} + q^{57} + 6q^{58} - 27q^{59} + 2q^{60} - 18q^{61} - 14q^{62} - 5q^{63} + 2q^{64} - q^{65} + 6q^{67} + 4q^{68} - 3q^{69} + 5q^{70} - 14q^{71} + 2q^{72} - 4q^{73} + q^{74} - 2q^{75} - q^{76} - q^{78} - 2q^{80} + 2q^{81} + 3q^{82} - 8q^{83} + 5q^{84} - 4q^{85} - 6q^{86} - 6q^{87} - 17q^{89} - 2q^{90} + 3q^{92} + 14q^{93} - 3q^{94} + q^{95} - 2q^{96} + 12q^{97} + q^{98} + O(q^{100}) \)

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
\(7\) −1.38197 −0.522334 −0.261167 0.965294i \(-0.584107\pi\)
−0.261167 + 0.965294i \(0.584107\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) 1.61803 0.448762 0.224381 0.974502i \(-0.427964\pi\)
0.224381 + 0.974502i \(0.427964\pi\)
\(14\) −1.38197 −0.369346
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −2.47214 −0.599581 −0.299791 0.954005i \(-0.596917\pi\)
−0.299791 + 0.954005i \(0.596917\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.61803 −0.371202 −0.185601 0.982625i \(-0.559423\pi\)
−0.185601 + 0.982625i \(0.559423\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.38197 0.301570
\(22\) 0 0
\(23\) −1.85410 −0.386607 −0.193303 0.981139i \(-0.561920\pi\)
−0.193303 + 0.981139i \(0.561920\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 1.61803 0.317323
\(27\) −1.00000 −0.192450
\(28\) −1.38197 −0.261167
\(29\) 9.70820 1.80277 0.901384 0.433020i \(-0.142552\pi\)
0.901384 + 0.433020i \(0.142552\pi\)
\(30\) 1.00000 0.182574
\(31\) −4.76393 −0.855627 −0.427814 0.903867i \(-0.640716\pi\)
−0.427814 + 0.903867i \(0.640716\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.47214 −0.423968
\(35\) 1.38197 0.233595
\(36\) 1.00000 0.166667
\(37\) 1.61803 0.266003 0.133002 0.991116i \(-0.457538\pi\)
0.133002 + 0.991116i \(0.457538\pi\)
\(38\) −1.61803 −0.262480
\(39\) −1.61803 −0.259093
\(40\) −1.00000 −0.158114
\(41\) −6.32624 −0.987992 −0.493996 0.869464i \(-0.664464\pi\)
−0.493996 + 0.869464i \(0.664464\pi\)
\(42\) 1.38197 0.213242
\(43\) −5.23607 −0.798493 −0.399246 0.916844i \(-0.630728\pi\)
−0.399246 + 0.916844i \(0.630728\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) −1.85410 −0.273372
\(47\) −0.381966 −0.0557155 −0.0278577 0.999612i \(-0.508869\pi\)
−0.0278577 + 0.999612i \(0.508869\pi\)
\(48\) −1.00000 −0.144338
\(49\) −5.09017 −0.727167
\(50\) 1.00000 0.141421
\(51\) 2.47214 0.346168
\(52\) 1.61803 0.224381
\(53\) 5.09017 0.699189 0.349594 0.936901i \(-0.386319\pi\)
0.349594 + 0.936901i \(0.386319\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −1.38197 −0.184673
\(57\) 1.61803 0.214314
\(58\) 9.70820 1.27475
\(59\) −12.3820 −1.61199 −0.805997 0.591919i \(-0.798370\pi\)
−0.805997 + 0.591919i \(0.798370\pi\)
\(60\) 1.00000 0.129099
\(61\) −6.76393 −0.866033 −0.433016 0.901386i \(-0.642551\pi\)
−0.433016 + 0.901386i \(0.642551\pi\)
\(62\) −4.76393 −0.605020
\(63\) −1.38197 −0.174111
\(64\) 1.00000 0.125000
\(65\) −1.61803 −0.200692
\(66\) 0 0
\(67\) 14.1803 1.73240 0.866202 0.499694i \(-0.166554\pi\)
0.866202 + 0.499694i \(0.166554\pi\)
\(68\) −2.47214 −0.299791
\(69\) 1.85410 0.223208
\(70\) 1.38197 0.165177
\(71\) −13.7082 −1.62686 −0.813432 0.581660i \(-0.802404\pi\)
−0.813432 + 0.581660i \(0.802404\pi\)
\(72\) 1.00000 0.117851
\(73\) 6.94427 0.812766 0.406383 0.913703i \(-0.366790\pi\)
0.406383 + 0.913703i \(0.366790\pi\)
\(74\) 1.61803 0.188093
\(75\) −1.00000 −0.115470
\(76\) −1.61803 −0.185601
\(77\) 0 0
\(78\) −1.61803 −0.183206
\(79\) −4.47214 −0.503155 −0.251577 0.967837i \(-0.580949\pi\)
−0.251577 + 0.967837i \(0.580949\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −6.32624 −0.698616
\(83\) −12.9443 −1.42082 −0.710409 0.703789i \(-0.751490\pi\)
−0.710409 + 0.703789i \(0.751490\pi\)
\(84\) 1.38197 0.150785
\(85\) 2.47214 0.268141
\(86\) −5.23607 −0.564620
\(87\) −9.70820 −1.04083
\(88\) 0 0
\(89\) −11.8541 −1.25653 −0.628266 0.777998i \(-0.716235\pi\)
−0.628266 + 0.777998i \(0.716235\pi\)
\(90\) −1.00000 −0.105409
\(91\) −2.23607 −0.234404
\(92\) −1.85410 −0.193303
\(93\) 4.76393 0.493997
\(94\) −0.381966 −0.0393968
\(95\) 1.61803 0.166007
\(96\) −1.00000 −0.102062
\(97\) −2.94427 −0.298946 −0.149473 0.988766i \(-0.547758\pi\)
−0.149473 + 0.988766i \(0.547758\pi\)
\(98\) −5.09017 −0.514185
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 2.47214 0.244778
\(103\) −3.14590 −0.309975 −0.154987 0.987916i \(-0.549534\pi\)
−0.154987 + 0.987916i \(0.549534\pi\)
\(104\) 1.61803 0.158661
\(105\) −1.38197 −0.134866
\(106\) 5.09017 0.494401
\(107\) 17.8885 1.72935 0.864675 0.502331i \(-0.167524\pi\)
0.864675 + 0.502331i \(0.167524\pi\)
\(108\) −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
\(111\) −1.61803 −0.153577
\(112\) −1.38197 −0.130584
\(113\) −3.52786 −0.331874 −0.165937 0.986136i \(-0.553065\pi\)
−0.165937 + 0.986136i \(0.553065\pi\)
\(114\) 1.61803 0.151543
\(115\) 1.85410 0.172896
\(116\) 9.70820 0.901384
\(117\) 1.61803 0.149587
\(118\) −12.3820 −1.13985
\(119\) 3.41641 0.313182
\(120\) 1.00000 0.0912871
\(121\) 0 0
\(122\) −6.76393 −0.612378
\(123\) 6.32624 0.570418
\(124\) −4.76393 −0.427814
\(125\) −1.00000 −0.0894427
\(126\) −1.38197 −0.123115
\(127\) −10.3820 −0.921251 −0.460625 0.887595i \(-0.652375\pi\)
−0.460625 + 0.887595i \(0.652375\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.23607 0.461010
\(130\) −1.61803 −0.141911
\(131\) −3.05573 −0.266980 −0.133490 0.991050i \(-0.542618\pi\)
−0.133490 + 0.991050i \(0.542618\pi\)
\(132\) 0 0
\(133\) 2.23607 0.193892
\(134\) 14.1803 1.22499
\(135\) 1.00000 0.0860663
\(136\) −2.47214 −0.211984
\(137\) −11.4164 −0.975370 −0.487685 0.873020i \(-0.662158\pi\)
−0.487685 + 0.873020i \(0.662158\pi\)
\(138\) 1.85410 0.157832
\(139\) 5.38197 0.456492 0.228246 0.973603i \(-0.426701\pi\)
0.228246 + 0.973603i \(0.426701\pi\)
\(140\) 1.38197 0.116797
\(141\) 0.381966 0.0321673
\(142\) −13.7082 −1.15037
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −9.70820 −0.806222
\(146\) 6.94427 0.574712
\(147\) 5.09017 0.419830
\(148\) 1.61803 0.133002
\(149\) −8.94427 −0.732743 −0.366372 0.930469i \(-0.619400\pi\)
−0.366372 + 0.930469i \(0.619400\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 3.52786 0.287094 0.143547 0.989644i \(-0.454149\pi\)
0.143547 + 0.989644i \(0.454149\pi\)
\(152\) −1.61803 −0.131240
\(153\) −2.47214 −0.199860
\(154\) 0 0
\(155\) 4.76393 0.382648
\(156\) −1.61803 −0.129546
\(157\) −3.38197 −0.269910 −0.134955 0.990852i \(-0.543089\pi\)
−0.134955 + 0.990852i \(0.543089\pi\)
\(158\) −4.47214 −0.355784
\(159\) −5.09017 −0.403677
\(160\) −1.00000 −0.0790569
\(161\) 2.56231 0.201938
\(162\) 1.00000 0.0785674
\(163\) −17.8885 −1.40114 −0.700569 0.713584i \(-0.747071\pi\)
−0.700569 + 0.713584i \(0.747071\pi\)
\(164\) −6.32624 −0.493996
\(165\) 0 0
\(166\) −12.9443 −1.00467
\(167\) −8.56231 −0.662571 −0.331286 0.943531i \(-0.607482\pi\)
−0.331286 + 0.943531i \(0.607482\pi\)
\(168\) 1.38197 0.106621
\(169\) −10.3820 −0.798613
\(170\) 2.47214 0.189604
\(171\) −1.61803 −0.123734
\(172\) −5.23607 −0.399246
\(173\) 4.43769 0.337392 0.168696 0.985668i \(-0.446044\pi\)
0.168696 + 0.985668i \(0.446044\pi\)
\(174\) −9.70820 −0.735977
\(175\) −1.38197 −0.104467
\(176\) 0 0
\(177\) 12.3820 0.930686
\(178\) −11.8541 −0.888503
\(179\) −17.8541 −1.33448 −0.667239 0.744844i \(-0.732524\pi\)
−0.667239 + 0.744844i \(0.732524\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 20.3607 1.51340 0.756699 0.653764i \(-0.226811\pi\)
0.756699 + 0.653764i \(0.226811\pi\)
\(182\) −2.23607 −0.165748
\(183\) 6.76393 0.500004
\(184\) −1.85410 −0.136686
\(185\) −1.61803 −0.118960
\(186\) 4.76393 0.349308
\(187\) 0 0
\(188\) −0.381966 −0.0278577
\(189\) 1.38197 0.100523
\(190\) 1.61803 0.117385
\(191\) −0.291796 −0.0211136 −0.0105568 0.999944i \(-0.503360\pi\)
−0.0105568 + 0.999944i \(0.503360\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −9.70820 −0.698812 −0.349406 0.936971i \(-0.613617\pi\)
−0.349406 + 0.936971i \(0.613617\pi\)
\(194\) −2.94427 −0.211386
\(195\) 1.61803 0.115870
\(196\) −5.09017 −0.363584
\(197\) −1.38197 −0.0984610 −0.0492305 0.998787i \(-0.515677\pi\)
−0.0492305 + 0.998787i \(0.515677\pi\)
\(198\) 0 0
\(199\) 4.94427 0.350490 0.175245 0.984525i \(-0.443928\pi\)
0.175245 + 0.984525i \(0.443928\pi\)
\(200\) 1.00000 0.0707107
\(201\) −14.1803 −1.00020
\(202\) −4.00000 −0.281439
\(203\) −13.4164 −0.941647
\(204\) 2.47214 0.173084
\(205\) 6.32624 0.441844
\(206\) −3.14590 −0.219185
\(207\) −1.85410 −0.128869
\(208\) 1.61803 0.112190
\(209\) 0 0
\(210\) −1.38197 −0.0953647
\(211\) −3.41641 −0.235195 −0.117598 0.993061i \(-0.537519\pi\)
−0.117598 + 0.993061i \(0.537519\pi\)
\(212\) 5.09017 0.349594
\(213\) 13.7082 0.939271
\(214\) 17.8885 1.22284
\(215\) 5.23607 0.357097
\(216\) −1.00000 −0.0680414
\(217\) 6.58359 0.446923
\(218\) −4.00000 −0.270914
\(219\) −6.94427 −0.469250
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) −1.61803 −0.108595
\(223\) 5.38197 0.360403 0.180202 0.983630i \(-0.442325\pi\)
0.180202 + 0.983630i \(0.442325\pi\)
\(224\) −1.38197 −0.0923365
\(225\) 1.00000 0.0666667
\(226\) −3.52786 −0.234670
\(227\) −18.1803 −1.20667 −0.603336 0.797487i \(-0.706162\pi\)
−0.603336 + 0.797487i \(0.706162\pi\)
\(228\) 1.61803 0.107157
\(229\) −20.4721 −1.35284 −0.676418 0.736518i \(-0.736469\pi\)
−0.676418 + 0.736518i \(0.736469\pi\)
\(230\) 1.85410 0.122256
\(231\) 0 0
\(232\) 9.70820 0.637375
\(233\) 29.7082 1.94625 0.973125 0.230279i \(-0.0739640\pi\)
0.973125 + 0.230279i \(0.0739640\pi\)
\(234\) 1.61803 0.105774
\(235\) 0.381966 0.0249167
\(236\) −12.3820 −0.805997
\(237\) 4.47214 0.290496
\(238\) 3.41641 0.221453
\(239\) 0.180340 0.0116652 0.00583261 0.999983i \(-0.498143\pi\)
0.00583261 + 0.999983i \(0.498143\pi\)
\(240\) 1.00000 0.0645497
\(241\) 23.3820 1.50616 0.753082 0.657926i \(-0.228566\pi\)
0.753082 + 0.657926i \(0.228566\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) −6.76393 −0.433016
\(245\) 5.09017 0.325199
\(246\) 6.32624 0.403346
\(247\) −2.61803 −0.166582
\(248\) −4.76393 −0.302510
\(249\) 12.9443 0.820310
\(250\) −1.00000 −0.0632456
\(251\) −26.5066 −1.67308 −0.836540 0.547906i \(-0.815425\pi\)
−0.836540 + 0.547906i \(0.815425\pi\)
\(252\) −1.38197 −0.0870557
\(253\) 0 0
\(254\) −10.3820 −0.651422
\(255\) −2.47214 −0.154811
\(256\) 1.00000 0.0625000
\(257\) −22.9443 −1.43122 −0.715612 0.698498i \(-0.753852\pi\)
−0.715612 + 0.698498i \(0.753852\pi\)
\(258\) 5.23607 0.325983
\(259\) −2.23607 −0.138943
\(260\) −1.61803 −0.100346
\(261\) 9.70820 0.600923
\(262\) −3.05573 −0.188784
\(263\) 14.8541 0.915943 0.457972 0.888967i \(-0.348576\pi\)
0.457972 + 0.888967i \(0.348576\pi\)
\(264\) 0 0
\(265\) −5.09017 −0.312687
\(266\) 2.23607 0.137102
\(267\) 11.8541 0.725459
\(268\) 14.1803 0.866202
\(269\) −29.2361 −1.78255 −0.891277 0.453459i \(-0.850190\pi\)
−0.891277 + 0.453459i \(0.850190\pi\)
\(270\) 1.00000 0.0608581
\(271\) 30.6525 1.86201 0.931003 0.365012i \(-0.118935\pi\)
0.931003 + 0.365012i \(0.118935\pi\)
\(272\) −2.47214 −0.149895
\(273\) 2.23607 0.135333
\(274\) −11.4164 −0.689690
\(275\) 0 0
\(276\) 1.85410 0.111604
\(277\) −25.2705 −1.51836 −0.759179 0.650882i \(-0.774399\pi\)
−0.759179 + 0.650882i \(0.774399\pi\)
\(278\) 5.38197 0.322789
\(279\) −4.76393 −0.285209
\(280\) 1.38197 0.0825883
\(281\) 27.8885 1.66369 0.831846 0.555007i \(-0.187285\pi\)
0.831846 + 0.555007i \(0.187285\pi\)
\(282\) 0.381966 0.0227457
\(283\) 9.70820 0.577093 0.288546 0.957466i \(-0.406828\pi\)
0.288546 + 0.957466i \(0.406828\pi\)
\(284\) −13.7082 −0.813432
\(285\) −1.61803 −0.0958441
\(286\) 0 0
\(287\) 8.74265 0.516062
\(288\) 1.00000 0.0589256
\(289\) −10.8885 −0.640503
\(290\) −9.70820 −0.570085
\(291\) 2.94427 0.172596
\(292\) 6.94427 0.406383
\(293\) 18.0344 1.05358 0.526792 0.849994i \(-0.323395\pi\)
0.526792 + 0.849994i \(0.323395\pi\)
\(294\) 5.09017 0.296865
\(295\) 12.3820 0.720906
\(296\) 1.61803 0.0940463
\(297\) 0 0
\(298\) −8.94427 −0.518128
\(299\) −3.00000 −0.173494
\(300\) −1.00000 −0.0577350
\(301\) 7.23607 0.417080
\(302\) 3.52786 0.203006
\(303\) 4.00000 0.229794
\(304\) −1.61803 −0.0928006
\(305\) 6.76393 0.387302
\(306\) −2.47214 −0.141323
\(307\) 26.8328 1.53143 0.765715 0.643180i \(-0.222385\pi\)
0.765715 + 0.643180i \(0.222385\pi\)
\(308\) 0 0
\(309\) 3.14590 0.178964
\(310\) 4.76393 0.270573
\(311\) 7.88854 0.447318 0.223659 0.974667i \(-0.428200\pi\)
0.223659 + 0.974667i \(0.428200\pi\)
\(312\) −1.61803 −0.0916031
\(313\) −7.70820 −0.435693 −0.217847 0.975983i \(-0.569903\pi\)
−0.217847 + 0.975983i \(0.569903\pi\)
\(314\) −3.38197 −0.190855
\(315\) 1.38197 0.0778650
\(316\) −4.47214 −0.251577
\(317\) 22.0902 1.24071 0.620354 0.784322i \(-0.286989\pi\)
0.620354 + 0.784322i \(0.286989\pi\)
\(318\) −5.09017 −0.285443
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) −17.8885 −0.998441
\(322\) 2.56231 0.142792
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) 1.61803 0.0897524
\(326\) −17.8885 −0.990755
\(327\) 4.00000 0.221201
\(328\) −6.32624 −0.349308
\(329\) 0.527864 0.0291021
\(330\) 0 0
\(331\) 23.3262 1.28213 0.641063 0.767488i \(-0.278494\pi\)
0.641063 + 0.767488i \(0.278494\pi\)
\(332\) −12.9443 −0.710409
\(333\) 1.61803 0.0886677
\(334\) −8.56231 −0.468509
\(335\) −14.1803 −0.774755
\(336\) 1.38197 0.0753924
\(337\) 20.0000 1.08947 0.544735 0.838608i \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) −10.3820 −0.564705
\(339\) 3.52786 0.191607
\(340\) 2.47214 0.134070
\(341\) 0 0
\(342\) −1.61803 −0.0874933
\(343\) 16.7082 0.902158
\(344\) −5.23607 −0.282310
\(345\) −1.85410 −0.0998215
\(346\) 4.43769 0.238572
\(347\) −26.1803 −1.40543 −0.702717 0.711469i \(-0.748030\pi\)
−0.702717 + 0.711469i \(0.748030\pi\)
\(348\) −9.70820 −0.520414
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −1.38197 −0.0738692
\(351\) −1.61803 −0.0863643
\(352\) 0 0
\(353\) 6.65248 0.354076 0.177038 0.984204i \(-0.443349\pi\)
0.177038 + 0.984204i \(0.443349\pi\)
\(354\) 12.3820 0.658094
\(355\) 13.7082 0.727556
\(356\) −11.8541 −0.628266
\(357\) −3.41641 −0.180815
\(358\) −17.8541 −0.943619
\(359\) −20.7639 −1.09588 −0.547939 0.836518i \(-0.684587\pi\)
−0.547939 + 0.836518i \(0.684587\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −16.3820 −0.862209
\(362\) 20.3607 1.07013
\(363\) 0 0
\(364\) −2.23607 −0.117202
\(365\) −6.94427 −0.363480
\(366\) 6.76393 0.353556
\(367\) −36.3607 −1.89801 −0.949006 0.315258i \(-0.897909\pi\)
−0.949006 + 0.315258i \(0.897909\pi\)
\(368\) −1.85410 −0.0966517
\(369\) −6.32624 −0.329331
\(370\) −1.61803 −0.0841176
\(371\) −7.03444 −0.365210
\(372\) 4.76393 0.246998
\(373\) 7.14590 0.370001 0.185000 0.982738i \(-0.440771\pi\)
0.185000 + 0.982738i \(0.440771\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) −0.381966 −0.0196984
\(377\) 15.7082 0.809014
\(378\) 1.38197 0.0710807
\(379\) 9.74265 0.500446 0.250223 0.968188i \(-0.419496\pi\)
0.250223 + 0.968188i \(0.419496\pi\)
\(380\) 1.61803 0.0830034
\(381\) 10.3820 0.531884
\(382\) −0.291796 −0.0149296
\(383\) 27.4508 1.40267 0.701336 0.712830i \(-0.252587\pi\)
0.701336 + 0.712830i \(0.252587\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −9.70820 −0.494135
\(387\) −5.23607 −0.266164
\(388\) −2.94427 −0.149473
\(389\) 12.4721 0.632362 0.316181 0.948699i \(-0.397599\pi\)
0.316181 + 0.948699i \(0.397599\pi\)
\(390\) 1.61803 0.0819323
\(391\) 4.58359 0.231802
\(392\) −5.09017 −0.257092
\(393\) 3.05573 0.154141
\(394\) −1.38197 −0.0696224
\(395\) 4.47214 0.225018
\(396\) 0 0
\(397\) 28.3262 1.42165 0.710827 0.703367i \(-0.248321\pi\)
0.710827 + 0.703367i \(0.248321\pi\)
\(398\) 4.94427 0.247834
\(399\) −2.23607 −0.111943
\(400\) 1.00000 0.0500000
\(401\) −17.3262 −0.865231 −0.432616 0.901579i \(-0.642409\pi\)
−0.432616 + 0.901579i \(0.642409\pi\)
\(402\) −14.1803 −0.707251
\(403\) −7.70820 −0.383973
\(404\) −4.00000 −0.199007
\(405\) −1.00000 −0.0496904
\(406\) −13.4164 −0.665845
\(407\) 0 0
\(408\) 2.47214 0.122389
\(409\) 37.2148 1.84015 0.920076 0.391739i \(-0.128126\pi\)
0.920076 + 0.391739i \(0.128126\pi\)
\(410\) 6.32624 0.312431
\(411\) 11.4164 0.563130
\(412\) −3.14590 −0.154987
\(413\) 17.1115 0.842000
\(414\) −1.85410 −0.0911241
\(415\) 12.9443 0.635409
\(416\) 1.61803 0.0793306
\(417\) −5.38197 −0.263556
\(418\) 0 0
\(419\) −35.7984 −1.74887 −0.874433 0.485147i \(-0.838766\pi\)
−0.874433 + 0.485147i \(0.838766\pi\)
\(420\) −1.38197 −0.0674330
\(421\) 9.05573 0.441349 0.220675 0.975347i \(-0.429174\pi\)
0.220675 + 0.975347i \(0.429174\pi\)
\(422\) −3.41641 −0.166308
\(423\) −0.381966 −0.0185718
\(424\) 5.09017 0.247201
\(425\) −2.47214 −0.119916
\(426\) 13.7082 0.664165
\(427\) 9.34752 0.452358
\(428\) 17.8885 0.864675
\(429\) 0 0
\(430\) 5.23607 0.252506
\(431\) 20.1803 0.972053 0.486026 0.873944i \(-0.338446\pi\)
0.486026 + 0.873944i \(0.338446\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 7.12461 0.342387 0.171193 0.985237i \(-0.445238\pi\)
0.171193 + 0.985237i \(0.445238\pi\)
\(434\) 6.58359 0.316023
\(435\) 9.70820 0.465473
\(436\) −4.00000 −0.191565
\(437\) 3.00000 0.143509
\(438\) −6.94427 −0.331810
\(439\) 2.18034 0.104062 0.0520310 0.998645i \(-0.483431\pi\)
0.0520310 + 0.998645i \(0.483431\pi\)
\(440\) 0 0
\(441\) −5.09017 −0.242389
\(442\) −4.00000 −0.190261
\(443\) −24.8328 −1.17984 −0.589921 0.807461i \(-0.700841\pi\)
−0.589921 + 0.807461i \(0.700841\pi\)
\(444\) −1.61803 −0.0767885
\(445\) 11.8541 0.561938
\(446\) 5.38197 0.254843
\(447\) 8.94427 0.423050
\(448\) −1.38197 −0.0652918
\(449\) −16.3820 −0.773113 −0.386556 0.922266i \(-0.626336\pi\)
−0.386556 + 0.922266i \(0.626336\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −3.52786 −0.165937
\(453\) −3.52786 −0.165754
\(454\) −18.1803 −0.853246
\(455\) 2.23607 0.104828
\(456\) 1.61803 0.0757714
\(457\) 25.8885 1.21102 0.605508 0.795840i \(-0.292970\pi\)
0.605508 + 0.795840i \(0.292970\pi\)
\(458\) −20.4721 −0.956600
\(459\) 2.47214 0.115389
\(460\) 1.85410 0.0864479
\(461\) 29.2361 1.36166 0.680830 0.732442i \(-0.261619\pi\)
0.680830 + 0.732442i \(0.261619\pi\)
\(462\) 0 0
\(463\) −5.61803 −0.261092 −0.130546 0.991442i \(-0.541673\pi\)
−0.130546 + 0.991442i \(0.541673\pi\)
\(464\) 9.70820 0.450692
\(465\) −4.76393 −0.220922
\(466\) 29.7082 1.37621
\(467\) 24.9443 1.15428 0.577142 0.816644i \(-0.304168\pi\)
0.577142 + 0.816644i \(0.304168\pi\)
\(468\) 1.61803 0.0747936
\(469\) −19.5967 −0.904894
\(470\) 0.381966 0.0176188
\(471\) 3.38197 0.155833
\(472\) −12.3820 −0.569926
\(473\) 0 0
\(474\) 4.47214 0.205412
\(475\) −1.61803 −0.0742405
\(476\) 3.41641 0.156591
\(477\) 5.09017 0.233063
\(478\) 0.180340 0.00824855
\(479\) −37.0132 −1.69117 −0.845587 0.533837i \(-0.820749\pi\)
−0.845587 + 0.533837i \(0.820749\pi\)
\(480\) 1.00000 0.0456435
\(481\) 2.61803 0.119372
\(482\) 23.3820 1.06502
\(483\) −2.56231 −0.116589
\(484\) 0 0
\(485\) 2.94427 0.133693
\(486\) −1.00000 −0.0453609
\(487\) −4.36068 −0.197601 −0.0988006 0.995107i \(-0.531501\pi\)
−0.0988006 + 0.995107i \(0.531501\pi\)
\(488\) −6.76393 −0.306189
\(489\) 17.8885 0.808948
\(490\) 5.09017 0.229950
\(491\) −13.3262 −0.601405 −0.300702 0.953718i \(-0.597221\pi\)
−0.300702 + 0.953718i \(0.597221\pi\)
\(492\) 6.32624 0.285209
\(493\) −24.0000 −1.08091
\(494\) −2.61803 −0.117791
\(495\) 0 0
\(496\) −4.76393 −0.213907
\(497\) 18.9443 0.849767
\(498\) 12.9443 0.580047
\(499\) 26.6869 1.19467 0.597335 0.801992i \(-0.296226\pi\)
0.597335 + 0.801992i \(0.296226\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 8.56231 0.382536
\(502\) −26.5066 −1.18305
\(503\) −19.7984 −0.882766 −0.441383 0.897319i \(-0.645512\pi\)
−0.441383 + 0.897319i \(0.645512\pi\)
\(504\) −1.38197 −0.0615577
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 10.3820 0.461079
\(508\) −10.3820 −0.460625
\(509\) 1.41641 0.0627812 0.0313906 0.999507i \(-0.490006\pi\)
0.0313906 + 0.999507i \(0.490006\pi\)
\(510\) −2.47214 −0.109468
\(511\) −9.59675 −0.424535
\(512\) 1.00000 0.0441942
\(513\) 1.61803 0.0714379
\(514\) −22.9443 −1.01203
\(515\) 3.14590 0.138625
\(516\) 5.23607 0.230505
\(517\) 0 0
\(518\) −2.23607 −0.0982472
\(519\) −4.43769 −0.194793
\(520\) −1.61803 −0.0709555
\(521\) 21.6738 0.949545 0.474772 0.880109i \(-0.342530\pi\)
0.474772 + 0.880109i \(0.342530\pi\)
\(522\) 9.70820 0.424917
\(523\) −15.7082 −0.686872 −0.343436 0.939176i \(-0.611591\pi\)
−0.343436 + 0.939176i \(0.611591\pi\)
\(524\) −3.05573 −0.133490
\(525\) 1.38197 0.0603139
\(526\) 14.8541 0.647670
\(527\) 11.7771 0.513018
\(528\) 0 0
\(529\) −19.5623 −0.850535
\(530\) −5.09017 −0.221103
\(531\) −12.3820 −0.537332
\(532\) 2.23607 0.0969458
\(533\) −10.2361 −0.443373
\(534\) 11.8541 0.512977
\(535\) −17.8885 −0.773389
\(536\) 14.1803 0.612497
\(537\) 17.8541 0.770461
\(538\) −29.2361 −1.26046
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 32.9443 1.41638 0.708192 0.706019i \(-0.249511\pi\)
0.708192 + 0.706019i \(0.249511\pi\)
\(542\) 30.6525 1.31664
\(543\) −20.3607 −0.873760
\(544\) −2.47214 −0.105992
\(545\) 4.00000 0.171341
\(546\) 2.23607 0.0956949
\(547\) 14.7639 0.631260 0.315630 0.948882i \(-0.397784\pi\)
0.315630 + 0.948882i \(0.397784\pi\)
\(548\) −11.4164 −0.487685
\(549\) −6.76393 −0.288678
\(550\) 0 0
\(551\) −15.7082 −0.669192
\(552\) 1.85410 0.0789158
\(553\) 6.18034 0.262815
\(554\) −25.2705 −1.07364
\(555\) 1.61803 0.0686817
\(556\) 5.38197 0.228246
\(557\) −29.3262 −1.24259 −0.621296 0.783576i \(-0.713394\pi\)
−0.621296 + 0.783576i \(0.713394\pi\)
\(558\) −4.76393 −0.201673
\(559\) −8.47214 −0.358333
\(560\) 1.38197 0.0583987
\(561\) 0 0
\(562\) 27.8885 1.17641
\(563\) 17.3050 0.729317 0.364658 0.931141i \(-0.381186\pi\)
0.364658 + 0.931141i \(0.381186\pi\)
\(564\) 0.381966 0.0160837
\(565\) 3.52786 0.148418
\(566\) 9.70820 0.408066
\(567\) −1.38197 −0.0580371
\(568\) −13.7082 −0.575183
\(569\) −8.14590 −0.341494 −0.170747 0.985315i \(-0.554618\pi\)
−0.170747 + 0.985315i \(0.554618\pi\)
\(570\) −1.61803 −0.0677720
\(571\) −16.5066 −0.690779 −0.345389 0.938459i \(-0.612253\pi\)
−0.345389 + 0.938459i \(0.612253\pi\)
\(572\) 0 0
\(573\) 0.291796 0.0121900
\(574\) 8.74265 0.364911
\(575\) −1.85410 −0.0773214
\(576\) 1.00000 0.0416667
\(577\) 33.1246 1.37900 0.689498 0.724288i \(-0.257831\pi\)
0.689498 + 0.724288i \(0.257831\pi\)
\(578\) −10.8885 −0.452904
\(579\) 9.70820 0.403459
\(580\) −9.70820 −0.403111
\(581\) 17.8885 0.742142
\(582\) 2.94427 0.122044
\(583\) 0 0
\(584\) 6.94427 0.287356
\(585\) −1.61803 −0.0668975
\(586\) 18.0344 0.744996
\(587\) −18.8328 −0.777313 −0.388657 0.921383i \(-0.627061\pi\)
−0.388657 + 0.921383i \(0.627061\pi\)
\(588\) 5.09017 0.209915
\(589\) 7.70820 0.317611
\(590\) 12.3820 0.509757
\(591\) 1.38197 0.0568465
\(592\) 1.61803 0.0665008
\(593\) 29.4164 1.20799 0.603994 0.796989i \(-0.293575\pi\)
0.603994 + 0.796989i \(0.293575\pi\)
\(594\) 0 0
\(595\) −3.41641 −0.140059
\(596\) −8.94427 −0.366372
\(597\) −4.94427 −0.202356
\(598\) −3.00000 −0.122679
\(599\) −17.7082 −0.723538 −0.361769 0.932268i \(-0.617827\pi\)
−0.361769 + 0.932268i \(0.617827\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 23.9098 0.975302 0.487651 0.873039i \(-0.337854\pi\)
0.487651 + 0.873039i \(0.337854\pi\)
\(602\) 7.23607 0.294920
\(603\) 14.1803 0.577468
\(604\) 3.52786 0.143547
\(605\) 0 0
\(606\) 4.00000 0.162489
\(607\) −28.3607 −1.15112 −0.575562 0.817758i \(-0.695217\pi\)
−0.575562 + 0.817758i \(0.695217\pi\)
\(608\) −1.61803 −0.0656199
\(609\) 13.4164 0.543660
\(610\) 6.76393 0.273864
\(611\) −0.618034 −0.0250030
\(612\) −2.47214 −0.0999302
\(613\) −18.5836 −0.750584 −0.375292 0.926907i \(-0.622458\pi\)
−0.375292 + 0.926907i \(0.622458\pi\)
\(614\) 26.8328 1.08288
\(615\) −6.32624 −0.255099
\(616\) 0 0
\(617\) 40.9443 1.64835 0.824177 0.566332i \(-0.191638\pi\)
0.824177 + 0.566332i \(0.191638\pi\)
\(618\) 3.14590 0.126547
\(619\) −18.7426 −0.753331 −0.376665 0.926349i \(-0.622929\pi\)
−0.376665 + 0.926349i \(0.622929\pi\)
\(620\) 4.76393 0.191324
\(621\) 1.85410 0.0744025
\(622\) 7.88854 0.316302
\(623\) 16.3820 0.656330
\(624\) −1.61803 −0.0647732
\(625\) 1.00000 0.0400000
\(626\) −7.70820 −0.308082
\(627\) 0 0
\(628\) −3.38197 −0.134955
\(629\) −4.00000 −0.159490
\(630\) 1.38197 0.0550588
\(631\) −11.7082 −0.466096 −0.233048 0.972465i \(-0.574870\pi\)
−0.233048 + 0.972465i \(0.574870\pi\)
\(632\) −4.47214 −0.177892
\(633\) 3.41641 0.135790
\(634\) 22.0902 0.877313
\(635\) 10.3820 0.411996
\(636\) −5.09017 −0.201838
\(637\) −8.23607 −0.326325
\(638\) 0 0
\(639\) −13.7082 −0.542288
\(640\) −1.00000 −0.0395285
\(641\) −18.4508 −0.728765 −0.364382 0.931249i \(-0.618720\pi\)
−0.364382 + 0.931249i \(0.618720\pi\)
\(642\) −17.8885 −0.706005
\(643\) 23.4164 0.923453 0.461726 0.887022i \(-0.347230\pi\)
0.461726 + 0.887022i \(0.347230\pi\)
\(644\) 2.56231 0.100969
\(645\) −5.23607 −0.206170
\(646\) 4.00000 0.157378
\(647\) 22.8328 0.897651 0.448825 0.893620i \(-0.351843\pi\)
0.448825 + 0.893620i \(0.351843\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 1.61803 0.0634645
\(651\) −6.58359 −0.258031
\(652\) −17.8885 −0.700569
\(653\) −9.14590 −0.357907 −0.178953 0.983858i \(-0.557271\pi\)
−0.178953 + 0.983858i \(0.557271\pi\)
\(654\) 4.00000 0.156412
\(655\) 3.05573 0.119397
\(656\) −6.32624 −0.246998
\(657\) 6.94427 0.270922
\(658\) 0.527864 0.0205783
\(659\) 5.27051 0.205310 0.102655 0.994717i \(-0.467266\pi\)
0.102655 + 0.994717i \(0.467266\pi\)
\(660\) 0 0
\(661\) −43.4853 −1.69138 −0.845691 0.533673i \(-0.820811\pi\)
−0.845691 + 0.533673i \(0.820811\pi\)
\(662\) 23.3262 0.906600
\(663\) 4.00000 0.155347
\(664\) −12.9443 −0.502335
\(665\) −2.23607 −0.0867110
\(666\) 1.61803 0.0626975
\(667\) −18.0000 −0.696963
\(668\) −8.56231 −0.331286
\(669\) −5.38197 −0.208079
\(670\) −14.1803 −0.547834
\(671\) 0 0
\(672\) 1.38197 0.0533105
\(673\) −3.59675 −0.138644 −0.0693222 0.997594i \(-0.522084\pi\)
−0.0693222 + 0.997594i \(0.522084\pi\)
\(674\) 20.0000 0.770371
\(675\) −1.00000 −0.0384900
\(676\) −10.3820 −0.399306
\(677\) 30.3607 1.16686 0.583428 0.812165i \(-0.301711\pi\)
0.583428 + 0.812165i \(0.301711\pi\)
\(678\) 3.52786 0.135487
\(679\) 4.06888 0.156149
\(680\) 2.47214 0.0948021
\(681\) 18.1803 0.696672
\(682\) 0 0
\(683\) −9.12461 −0.349144 −0.174572 0.984644i \(-0.555854\pi\)
−0.174572 + 0.984644i \(0.555854\pi\)
\(684\) −1.61803 −0.0618671
\(685\) 11.4164 0.436199
\(686\) 16.7082 0.637922
\(687\) 20.4721 0.781061
\(688\) −5.23607 −0.199623
\(689\) 8.23607 0.313769
\(690\) −1.85410 −0.0705845
\(691\) 36.5066 1.38878 0.694388 0.719601i \(-0.255675\pi\)
0.694388 + 0.719601i \(0.255675\pi\)
\(692\) 4.43769 0.168696
\(693\) 0 0
\(694\) −26.1803 −0.993792
\(695\) −5.38197 −0.204150
\(696\) −9.70820 −0.367989
\(697\) 15.6393 0.592381
\(698\) −10.0000 −0.378506
\(699\) −29.7082 −1.12367
\(700\) −1.38197 −0.0522334
\(701\) −38.0689 −1.43784 −0.718921 0.695092i \(-0.755364\pi\)
−0.718921 + 0.695092i \(0.755364\pi\)
\(702\) −1.61803 −0.0610688
\(703\) −2.61803 −0.0987410
\(704\) 0 0
\(705\) −0.381966 −0.0143857
\(706\) 6.65248 0.250369
\(707\) 5.52786 0.207897
\(708\) 12.3820 0.465343
\(709\) 6.65248 0.249839 0.124919 0.992167i \(-0.460133\pi\)
0.124919 + 0.992167i \(0.460133\pi\)
\(710\) 13.7082 0.514460
\(711\) −4.47214 −0.167718
\(712\) −11.8541 −0.444251
\(713\) 8.83282 0.330792
\(714\) −3.41641 −0.127856
\(715\) 0 0
\(716\) −17.8541 −0.667239
\(717\) −0.180340 −0.00673492
\(718\) −20.7639 −0.774903
\(719\) 11.8885 0.443368 0.221684 0.975119i \(-0.428845\pi\)
0.221684 + 0.975119i \(0.428845\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 4.34752 0.161910
\(722\) −16.3820 −0.609674
\(723\) −23.3820 −0.869585
\(724\) 20.3607 0.756699
\(725\) 9.70820 0.360554
\(726\) 0 0
\(727\) 31.6312 1.17314 0.586568 0.809900i \(-0.300479\pi\)
0.586568 + 0.809900i \(0.300479\pi\)
\(728\) −2.23607 −0.0828742
\(729\) 1.00000 0.0370370
\(730\) −6.94427 −0.257019
\(731\) 12.9443 0.478761
\(732\) 6.76393 0.250002
\(733\) 19.5279 0.721278 0.360639 0.932705i \(-0.382559\pi\)
0.360639 + 0.932705i \(0.382559\pi\)
\(734\) −36.3607 −1.34210
\(735\) −5.09017 −0.187754
\(736\) −1.85410 −0.0683431
\(737\) 0 0
\(738\) −6.32624 −0.232872
\(739\) −25.3820 −0.933691 −0.466845 0.884339i \(-0.654610\pi\)
−0.466845 + 0.884339i \(0.654610\pi\)
\(740\) −1.61803 −0.0594801
\(741\) 2.61803 0.0961759
\(742\) −7.03444 −0.258242
\(743\) 13.8541 0.508258 0.254129 0.967170i \(-0.418211\pi\)
0.254129 + 0.967170i \(0.418211\pi\)
\(744\) 4.76393 0.174654
\(745\) 8.94427 0.327693
\(746\) 7.14590 0.261630
\(747\) −12.9443 −0.473606
\(748\) 0 0
\(749\) −24.7214 −0.903299
\(750\) 1.00000 0.0365148
\(751\) 50.2492 1.83362 0.916810 0.399323i \(-0.130755\pi\)
0.916810 + 0.399323i \(0.130755\pi\)
\(752\) −0.381966 −0.0139289
\(753\) 26.5066 0.965953
\(754\) 15.7082 0.572059
\(755\) −3.52786 −0.128392
\(756\) 1.38197 0.0502616
\(757\) −4.85410 −0.176425 −0.0882127 0.996102i \(-0.528116\pi\)
−0.0882127 + 0.996102i \(0.528116\pi\)
\(758\) 9.74265 0.353869
\(759\) 0 0
\(760\) 1.61803 0.0586923
\(761\) −27.8885 −1.01096 −0.505479 0.862839i \(-0.668684\pi\)
−0.505479 + 0.862839i \(0.668684\pi\)
\(762\) 10.3820 0.376099
\(763\) 5.52786 0.200122
\(764\) −0.291796 −0.0105568
\(765\) 2.47214 0.0893803
\(766\) 27.4508 0.991840
\(767\) −20.0344 −0.723402
\(768\) −1.00000 −0.0360844
\(769\) 10.2016 0.367880 0.183940 0.982937i \(-0.441115\pi\)
0.183940 + 0.982937i \(0.441115\pi\)
\(770\) 0 0
\(771\) 22.9443 0.826318
\(772\) −9.70820 −0.349406
\(773\) −20.7984 −0.748066 −0.374033 0.927415i \(-0.622025\pi\)
−0.374033 + 0.927415i \(0.622025\pi\)
\(774\) −5.23607 −0.188207
\(775\) −4.76393 −0.171125
\(776\) −2.94427 −0.105693
\(777\) 2.23607 0.0802185
\(778\) 12.4721 0.447148
\(779\) 10.2361 0.366745
\(780\) 1.61803 0.0579349
\(781\) 0 0
\(782\) 4.58359 0.163909
\(783\) −9.70820 −0.346943
\(784\) −5.09017 −0.181792
\(785\) 3.38197 0.120708
\(786\) 3.05573 0.108994
\(787\) −4.18034 −0.149013 −0.0745065 0.997221i \(-0.523738\pi\)
−0.0745065 + 0.997221i \(0.523738\pi\)
\(788\) −1.38197 −0.0492305
\(789\) −14.8541 −0.528820
\(790\) 4.47214 0.159111
\(791\) 4.87539 0.173349
\(792\) 0 0
\(793\) −10.9443 −0.388642
\(794\) 28.3262 1.00526
\(795\) 5.09017 0.180530
\(796\) 4.94427 0.175245
\(797\) −28.7426 −1.01812 −0.509058 0.860732i \(-0.670006\pi\)
−0.509058 + 0.860732i \(0.670006\pi\)
\(798\) −2.23607 −0.0791559
\(799\) 0.944272 0.0334059
\(800\) 1.00000 0.0353553
\(801\) −11.8541 −0.418844
\(802\) −17.3262 −0.611811
\(803\) 0 0
\(804\) −14.1803 −0.500102
\(805\) −2.56231 −0.0903094
\(806\) −7.70820 −0.271510
\(807\) 29.2361 1.02916
\(808\) −4.00000 −0.140720
\(809\) 41.5066 1.45929 0.729647 0.683824i \(-0.239684\pi\)
0.729647 + 0.683824i \(0.239684\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 7.27051 0.255302 0.127651 0.991819i \(-0.459256\pi\)
0.127651 + 0.991819i \(0.459256\pi\)
\(812\) −13.4164 −0.470824
\(813\) −30.6525 −1.07503
\(814\) 0 0
\(815\) 17.8885 0.626608
\(816\) 2.47214 0.0865421
\(817\) 8.47214 0.296403
\(818\) 37.2148 1.30118
\(819\) −2.23607 −0.0781345
\(820\) 6.32624 0.220922
\(821\) −17.2361 −0.601543 −0.300771 0.953696i \(-0.597244\pi\)
−0.300771 + 0.953696i \(0.597244\pi\)
\(822\) 11.4164 0.398193
\(823\) 44.0902 1.53689 0.768443 0.639918i \(-0.221032\pi\)
0.768443 + 0.639918i \(0.221032\pi\)
\(824\) −3.14590 −0.109593
\(825\) 0 0
\(826\) 17.1115 0.595384
\(827\) −3.70820 −0.128947 −0.0644734 0.997919i \(-0.520537\pi\)
−0.0644734 + 0.997919i \(0.520537\pi\)
\(828\) −1.85410 −0.0644345
\(829\) 39.3050 1.36512 0.682559 0.730831i \(-0.260867\pi\)
0.682559 + 0.730831i \(0.260867\pi\)
\(830\) 12.9443 0.449302
\(831\) 25.2705 0.876624
\(832\) 1.61803 0.0560952
\(833\) 12.5836 0.435996
\(834\) −5.38197 −0.186362
\(835\) 8.56231 0.296311
\(836\) 0 0
\(837\) 4.76393 0.164666
\(838\) −35.7984 −1.23663
\(839\) −7.12461 −0.245969 −0.122984 0.992409i \(-0.539247\pi\)
−0.122984 + 0.992409i \(0.539247\pi\)
\(840\) −1.38197 −0.0476824
\(841\) 65.2492 2.24997
\(842\) 9.05573 0.312081
\(843\) −27.8885 −0.960532
\(844\) −3.41641 −0.117598
\(845\) 10.3820 0.357150
\(846\) −0.381966 −0.0131323
\(847\) 0 0
\(848\) 5.09017 0.174797
\(849\) −9.70820 −0.333185
\(850\) −2.47214 −0.0847936
\(851\) −3.00000 −0.102839
\(852\) 13.7082 0.469635
\(853\) 51.8115 1.77399 0.886996 0.461776i \(-0.152788\pi\)
0.886996 + 0.461776i \(0.152788\pi\)
\(854\) 9.34752 0.319866
\(855\) 1.61803 0.0553356
\(856\) 17.8885 0.611418
\(857\) −50.7639 −1.73406 −0.867031 0.498253i \(-0.833975\pi\)
−0.867031 + 0.498253i \(0.833975\pi\)
\(858\) 0 0
\(859\) 21.9656 0.749455 0.374728 0.927135i \(-0.377736\pi\)
0.374728 + 0.927135i \(0.377736\pi\)
\(860\) 5.23607 0.178548
\(861\) −8.74265 −0.297949
\(862\) 20.1803 0.687345
\(863\) −6.85410 −0.233316 −0.116658 0.993172i \(-0.537218\pi\)
−0.116658 + 0.993172i \(0.537218\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −4.43769 −0.150886
\(866\) 7.12461 0.242104
\(867\) 10.8885 0.369794
\(868\) 6.58359 0.223462
\(869\) 0 0
\(870\) 9.70820 0.329139
\(871\) 22.9443 0.777437
\(872\) −4.00000 −0.135457
\(873\) −2.94427 −0.0996485
\(874\) 3.00000 0.101477
\(875\) 1.38197 0.0467190
\(876\) −6.94427 −0.234625
\(877\) 25.6180 0.865060 0.432530 0.901620i \(-0.357621\pi\)
0.432530 + 0.901620i \(0.357621\pi\)
\(878\) 2.18034 0.0735829
\(879\) −18.0344 −0.608287
\(880\) 0 0
\(881\) −16.7984 −0.565952 −0.282976 0.959127i \(-0.591322\pi\)
−0.282976 + 0.959127i \(0.591322\pi\)
\(882\) −5.09017 −0.171395
\(883\) −37.3050 −1.25541 −0.627706 0.778451i \(-0.716006\pi\)
−0.627706 + 0.778451i \(0.716006\pi\)
\(884\) −4.00000 −0.134535
\(885\) −12.3820 −0.416215
\(886\) −24.8328 −0.834275
\(887\) −43.7426 −1.46873 −0.734367 0.678752i \(-0.762521\pi\)
−0.734367 + 0.678752i \(0.762521\pi\)
\(888\) −1.61803 −0.0542977
\(889\) 14.3475 0.481201
\(890\) 11.8541 0.397350
\(891\) 0 0
\(892\) 5.38197 0.180202
\(893\) 0.618034 0.0206817
\(894\) 8.94427 0.299141
\(895\) 17.8541 0.596797
\(896\) −1.38197 −0.0461682
\(897\) 3.00000 0.100167
\(898\) −16.3820 −0.546673
\(899\) −46.2492 −1.54250
\(900\) 1.00000 0.0333333
\(901\) −12.5836 −0.419220
\(902\) 0 0
\(903\) −7.23607 −0.240801
\(904\) −3.52786 −0.117335
\(905\) −20.3607 −0.676812
\(906\) −3.52786 −0.117205
\(907\) −5.88854 −0.195526 −0.0977629 0.995210i \(-0.531169\pi\)
−0.0977629 + 0.995210i \(0.531169\pi\)
\(908\) −18.1803 −0.603336
\(909\) −4.00000 −0.132672
\(910\) 2.23607 0.0741249
\(911\) 20.6525 0.684247 0.342124 0.939655i \(-0.388854\pi\)
0.342124 + 0.939655i \(0.388854\pi\)
\(912\) 1.61803 0.0535785
\(913\) 0 0
\(914\) 25.8885 0.856317
\(915\) −6.76393 −0.223609
\(916\) −20.4721 −0.676418
\(917\) 4.22291 0.139453
\(918\) 2.47214 0.0815926
\(919\) −40.0689 −1.32175 −0.660875 0.750496i \(-0.729815\pi\)
−0.660875 + 0.750496i \(0.729815\pi\)
\(920\) 1.85410 0.0611279
\(921\) −26.8328 −0.884171
\(922\) 29.2361 0.962839
\(923\) −22.1803 −0.730075
\(924\) 0 0
\(925\) 1.61803 0.0532006
\(926\) −5.61803 −0.184620
\(927\) −3.14590 −0.103325
\(928\) 9.70820 0.318687
\(929\) 22.0344 0.722927 0.361463 0.932386i \(-0.382277\pi\)
0.361463 + 0.932386i \(0.382277\pi\)
\(930\) −4.76393 −0.156215
\(931\) 8.23607 0.269926
\(932\) 29.7082 0.973125
\(933\) −7.88854 −0.258259
\(934\) 24.9443 0.816202
\(935\) 0 0
\(936\) 1.61803 0.0528871
\(937\) −3.63932 −0.118891 −0.0594457 0.998232i \(-0.518933\pi\)
−0.0594457 + 0.998232i \(0.518933\pi\)
\(938\) −19.5967 −0.639856
\(939\) 7.70820 0.251548
\(940\) 0.381966 0.0124584
\(941\) −28.9443 −0.943556 −0.471778 0.881717i \(-0.656388\pi\)
−0.471778 + 0.881717i \(0.656388\pi\)
\(942\) 3.38197 0.110190
\(943\) 11.7295 0.381965
\(944\) −12.3820 −0.402999
\(945\) −1.38197 −0.0449554
\(946\) 0 0
\(947\) 59.3050 1.92715 0.963576 0.267435i \(-0.0861760\pi\)
0.963576 + 0.267435i \(0.0861760\pi\)
\(948\) 4.47214 0.145248
\(949\) 11.2361 0.364738
\(950\) −1.61803 −0.0524960
\(951\) −22.0902 −0.716323
\(952\) 3.41641 0.110726
\(953\) 49.2361 1.59491 0.797456 0.603377i \(-0.206178\pi\)
0.797456 + 0.603377i \(0.206178\pi\)
\(954\) 5.09017 0.164800
\(955\) 0.291796 0.00944230
\(956\) 0.180340 0.00583261
\(957\) 0 0
\(958\) −37.0132 −1.19584
\(959\) 15.7771 0.509469
\(960\) 1.00000 0.0322749
\(961\) −8.30495 −0.267902
\(962\) 2.61803 0.0844088
\(963\) 17.8885 0.576450
\(964\) 23.3820 0.753082
\(965\) 9.70820 0.312518
\(966\) −2.56231 −0.0824408
\(967\) 46.7426 1.50314 0.751571 0.659652i \(-0.229296\pi\)
0.751571 + 0.659652i \(0.229296\pi\)
\(968\) 0 0
\(969\) −4.00000 −0.128499
\(970\) 2.94427 0.0945349
\(971\) −18.7984 −0.603269 −0.301634 0.953424i \(-0.597532\pi\)
−0.301634 + 0.953424i \(0.597532\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −7.43769 −0.238442
\(974\) −4.36068 −0.139725
\(975\) −1.61803 −0.0518186
\(976\) −6.76393 −0.216508
\(977\) 28.8328 0.922443 0.461222 0.887285i \(-0.347411\pi\)
0.461222 + 0.887285i \(0.347411\pi\)
\(978\) 17.8885 0.572013
\(979\) 0 0
\(980\) 5.09017 0.162600
\(981\) −4.00000 −0.127710
\(982\) −13.3262 −0.425257
\(983\) −3.96556 −0.126482 −0.0632408 0.997998i \(-0.520144\pi\)
−0.0632408 + 0.997998i \(0.520144\pi\)
\(984\) 6.32624 0.201673
\(985\) 1.38197 0.0440331
\(986\) −24.0000 −0.764316
\(987\) −0.527864 −0.0168021
\(988\) −2.61803 −0.0832908
\(989\) 9.70820 0.308703
\(990\) 0 0
\(991\) −8.94427 −0.284124 −0.142062 0.989858i \(-0.545373\pi\)
−0.142062 + 0.989858i \(0.545373\pi\)
\(992\) −4.76393 −0.151255
\(993\) −23.3262 −0.740236
\(994\) 18.9443 0.600876
\(995\) −4.94427 −0.156744
\(996\) 12.9443 0.410155
\(997\) −57.7771 −1.82982 −0.914909 0.403659i \(-0.867738\pi\)
−0.914909 + 0.403659i \(0.867738\pi\)
\(998\) 26.6869 0.844760
\(999\) −1.61803 −0.0511923
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.1.2 2
11.2 odd 10 330.2.m.d.301.1 yes 4
11.6 odd 10 330.2.m.d.91.1 4
11.10 odd 2 3630.2.a.bc.1.1 2
33.2 even 10 990.2.n.a.631.1 4
33.17 even 10 990.2.n.a.91.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
330.2.m.d.91.1 4 11.6 odd 10
330.2.m.d.301.1 yes 4 11.2 odd 10
990.2.n.a.91.1 4 33.17 even 10
990.2.n.a.631.1 4 33.2 even 10
3630.2.a.bc.1.1 2 11.10 odd 2
3630.2.a.bi.1.2 2 1.1 even 1 trivial