Properties

Label 3630.2.a.bo.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: \(\Q(\zeta_{12})^+\)
Defining polynomial: \(x^{2} - 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 3630.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +2.46410 q^{13} -3.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.73205 q^{17} +1.00000 q^{18} -7.00000 q^{19} -1.00000 q^{20} -3.73205 q^{21} -3.26795 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.46410 q^{26} +1.00000 q^{27} -3.73205 q^{28} -5.00000 q^{29} -1.00000 q^{30} -4.19615 q^{31} +1.00000 q^{32} +1.73205 q^{34} +3.73205 q^{35} +1.00000 q^{36} +3.19615 q^{37} -7.00000 q^{38} +2.46410 q^{39} -1.00000 q^{40} -6.19615 q^{41} -3.73205 q^{42} -8.19615 q^{43} -1.00000 q^{45} -3.26795 q^{46} -8.92820 q^{47} +1.00000 q^{48} +6.92820 q^{49} +1.00000 q^{50} +1.73205 q^{51} +2.46410 q^{52} -2.73205 q^{53} +1.00000 q^{54} -3.73205 q^{56} -7.00000 q^{57} -5.00000 q^{58} +5.66025 q^{59} -1.00000 q^{60} +9.12436 q^{61} -4.19615 q^{62} -3.73205 q^{63} +1.00000 q^{64} -2.46410 q^{65} +11.4641 q^{67} +1.73205 q^{68} -3.26795 q^{69} +3.73205 q^{70} +4.46410 q^{71} +1.00000 q^{72} -7.66025 q^{73} +3.19615 q^{74} +1.00000 q^{75} -7.00000 q^{76} +2.46410 q^{78} -10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.19615 q^{82} -16.4641 q^{83} -3.73205 q^{84} -1.73205 q^{85} -8.19615 q^{86} -5.00000 q^{87} +2.53590 q^{89} -1.00000 q^{90} -9.19615 q^{91} -3.26795 q^{92} -4.19615 q^{93} -8.92820 q^{94} +7.00000 q^{95} +1.00000 q^{96} +5.26795 q^{97} +6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{3} + 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{3} + 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} + 2q^{8} + 2q^{9} - 2q^{10} + 2q^{12} - 2q^{13} - 4q^{14} - 2q^{15} + 2q^{16} + 2q^{18} - 14q^{19} - 2q^{20} - 4q^{21} - 10q^{23} + 2q^{24} + 2q^{25} - 2q^{26} + 2q^{27} - 4q^{28} - 10q^{29} - 2q^{30} + 2q^{31} + 2q^{32} + 4q^{35} + 2q^{36} - 4q^{37} - 14q^{38} - 2q^{39} - 2q^{40} - 2q^{41} - 4q^{42} - 6q^{43} - 2q^{45} - 10q^{46} - 4q^{47} + 2q^{48} + 2q^{50} - 2q^{52} - 2q^{53} + 2q^{54} - 4q^{56} - 14q^{57} - 10q^{58} - 6q^{59} - 2q^{60} - 6q^{61} + 2q^{62} - 4q^{63} + 2q^{64} + 2q^{65} + 16q^{67} - 10q^{69} + 4q^{70} + 2q^{71} + 2q^{72} + 2q^{73} - 4q^{74} + 2q^{75} - 14q^{76} - 2q^{78} - 2q^{80} + 2q^{81} - 2q^{82} - 26q^{83} - 4q^{84} - 6q^{86} - 10q^{87} + 12q^{89} - 2q^{90} - 8q^{91} - 10q^{92} + 2q^{93} - 4q^{94} + 14q^{95} + 2q^{96} + 14q^{97} + O(q^{100}) \)

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
\(7\) −3.73205 −1.41058 −0.705291 0.708918i \(-0.749184\pi\)
−0.705291 + 0.708918i \(0.749184\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) 2.46410 0.683419 0.341709 0.939806i \(-0.388994\pi\)
0.341709 + 0.939806i \(0.388994\pi\)
\(14\) −3.73205 −0.997433
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 1.73205 0.420084 0.210042 0.977692i \(-0.432640\pi\)
0.210042 + 0.977692i \(0.432640\pi\)
\(18\) 1.00000 0.235702
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.73205 −0.814400
\(22\) 0 0
\(23\) −3.26795 −0.681415 −0.340707 0.940169i \(-0.610666\pi\)
−0.340707 + 0.940169i \(0.610666\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 2.46410 0.483250
\(27\) 1.00000 0.192450
\(28\) −3.73205 −0.705291
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.19615 −0.753651 −0.376826 0.926284i \(-0.622984\pi\)
−0.376826 + 0.926284i \(0.622984\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 1.73205 0.297044
\(35\) 3.73205 0.630832
\(36\) 1.00000 0.166667
\(37\) 3.19615 0.525444 0.262722 0.964872i \(-0.415380\pi\)
0.262722 + 0.964872i \(0.415380\pi\)
\(38\) −7.00000 −1.13555
\(39\) 2.46410 0.394572
\(40\) −1.00000 −0.158114
\(41\) −6.19615 −0.967676 −0.483838 0.875157i \(-0.660758\pi\)
−0.483838 + 0.875157i \(0.660758\pi\)
\(42\) −3.73205 −0.575868
\(43\) −8.19615 −1.24990 −0.624951 0.780664i \(-0.714881\pi\)
−0.624951 + 0.780664i \(0.714881\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) −3.26795 −0.481833
\(47\) −8.92820 −1.30231 −0.651156 0.758944i \(-0.725716\pi\)
−0.651156 + 0.758944i \(0.725716\pi\)
\(48\) 1.00000 0.144338
\(49\) 6.92820 0.989743
\(50\) 1.00000 0.141421
\(51\) 1.73205 0.242536
\(52\) 2.46410 0.341709
\(53\) −2.73205 −0.375276 −0.187638 0.982238i \(-0.560083\pi\)
−0.187638 + 0.982238i \(0.560083\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −3.73205 −0.498716
\(57\) −7.00000 −0.927173
\(58\) −5.00000 −0.656532
\(59\) 5.66025 0.736902 0.368451 0.929647i \(-0.379888\pi\)
0.368451 + 0.929647i \(0.379888\pi\)
\(60\) −1.00000 −0.129099
\(61\) 9.12436 1.16825 0.584127 0.811662i \(-0.301437\pi\)
0.584127 + 0.811662i \(0.301437\pi\)
\(62\) −4.19615 −0.532912
\(63\) −3.73205 −0.470194
\(64\) 1.00000 0.125000
\(65\) −2.46410 −0.305634
\(66\) 0 0
\(67\) 11.4641 1.40056 0.700281 0.713867i \(-0.253058\pi\)
0.700281 + 0.713867i \(0.253058\pi\)
\(68\) 1.73205 0.210042
\(69\) −3.26795 −0.393415
\(70\) 3.73205 0.446065
\(71\) 4.46410 0.529791 0.264896 0.964277i \(-0.414662\pi\)
0.264896 + 0.964277i \(0.414662\pi\)
\(72\) 1.00000 0.117851
\(73\) −7.66025 −0.896565 −0.448282 0.893892i \(-0.647964\pi\)
−0.448282 + 0.893892i \(0.647964\pi\)
\(74\) 3.19615 0.371545
\(75\) 1.00000 0.115470
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 2.46410 0.279005
\(79\) −10.3923 −1.16923 −0.584613 0.811312i \(-0.698754\pi\)
−0.584613 + 0.811312i \(0.698754\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −6.19615 −0.684251
\(83\) −16.4641 −1.80717 −0.903585 0.428409i \(-0.859074\pi\)
−0.903585 + 0.428409i \(0.859074\pi\)
\(84\) −3.73205 −0.407200
\(85\) −1.73205 −0.187867
\(86\) −8.19615 −0.883814
\(87\) −5.00000 −0.536056
\(88\) 0 0
\(89\) 2.53590 0.268805 0.134402 0.990927i \(-0.457089\pi\)
0.134402 + 0.990927i \(0.457089\pi\)
\(90\) −1.00000 −0.105409
\(91\) −9.19615 −0.964019
\(92\) −3.26795 −0.340707
\(93\) −4.19615 −0.435121
\(94\) −8.92820 −0.920874
\(95\) 7.00000 0.718185
\(96\) 1.00000 0.102062
\(97\) 5.26795 0.534879 0.267440 0.963575i \(-0.413822\pi\)
0.267440 + 0.963575i \(0.413822\pi\)
\(98\) 6.92820 0.699854
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 8.46410 0.842210 0.421105 0.907012i \(-0.361642\pi\)
0.421105 + 0.907012i \(0.361642\pi\)
\(102\) 1.73205 0.171499
\(103\) −17.3923 −1.71371 −0.856857 0.515554i \(-0.827586\pi\)
−0.856857 + 0.515554i \(0.827586\pi\)
\(104\) 2.46410 0.241625
\(105\) 3.73205 0.364211
\(106\) −2.73205 −0.265360
\(107\) 14.3923 1.39136 0.695678 0.718353i \(-0.255104\pi\)
0.695678 + 0.718353i \(0.255104\pi\)
\(108\) 1.00000 0.0962250
\(109\) 12.3923 1.18697 0.593484 0.804846i \(-0.297752\pi\)
0.593484 + 0.804846i \(0.297752\pi\)
\(110\) 0 0
\(111\) 3.19615 0.303365
\(112\) −3.73205 −0.352646
\(113\) −13.8564 −1.30350 −0.651751 0.758433i \(-0.725965\pi\)
−0.651751 + 0.758433i \(0.725965\pi\)
\(114\) −7.00000 −0.655610
\(115\) 3.26795 0.304738
\(116\) −5.00000 −0.464238
\(117\) 2.46410 0.227806
\(118\) 5.66025 0.521069
\(119\) −6.46410 −0.592563
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) 9.12436 0.826080
\(123\) −6.19615 −0.558688
\(124\) −4.19615 −0.376826
\(125\) −1.00000 −0.0894427
\(126\) −3.73205 −0.332478
\(127\) −13.4641 −1.19475 −0.597373 0.801964i \(-0.703789\pi\)
−0.597373 + 0.801964i \(0.703789\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.19615 −0.721631
\(130\) −2.46410 −0.216116
\(131\) −21.1244 −1.84564 −0.922822 0.385227i \(-0.874123\pi\)
−0.922822 + 0.385227i \(0.874123\pi\)
\(132\) 0 0
\(133\) 26.1244 2.26527
\(134\) 11.4641 0.990348
\(135\) −1.00000 −0.0860663
\(136\) 1.73205 0.148522
\(137\) 10.4641 0.894009 0.447004 0.894532i \(-0.352491\pi\)
0.447004 + 0.894532i \(0.352491\pi\)
\(138\) −3.26795 −0.278186
\(139\) −7.00000 −0.593732 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 3.73205 0.315416
\(141\) −8.92820 −0.751890
\(142\) 4.46410 0.374619
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 5.00000 0.415227
\(146\) −7.66025 −0.633967
\(147\) 6.92820 0.571429
\(148\) 3.19615 0.262722
\(149\) 8.39230 0.687524 0.343762 0.939057i \(-0.388299\pi\)
0.343762 + 0.939057i \(0.388299\pi\)
\(150\) 1.00000 0.0816497
\(151\) −20.1962 −1.64354 −0.821770 0.569820i \(-0.807013\pi\)
−0.821770 + 0.569820i \(0.807013\pi\)
\(152\) −7.00000 −0.567775
\(153\) 1.73205 0.140028
\(154\) 0 0
\(155\) 4.19615 0.337043
\(156\) 2.46410 0.197286
\(157\) −14.6603 −1.17002 −0.585008 0.811028i \(-0.698909\pi\)
−0.585008 + 0.811028i \(0.698909\pi\)
\(158\) −10.3923 −0.826767
\(159\) −2.73205 −0.216666
\(160\) −1.00000 −0.0790569
\(161\) 12.1962 0.961191
\(162\) 1.00000 0.0785674
\(163\) 8.19615 0.641972 0.320986 0.947084i \(-0.395986\pi\)
0.320986 + 0.947084i \(0.395986\pi\)
\(164\) −6.19615 −0.483838
\(165\) 0 0
\(166\) −16.4641 −1.27786
\(167\) 6.53590 0.505763 0.252882 0.967497i \(-0.418622\pi\)
0.252882 + 0.967497i \(0.418622\pi\)
\(168\) −3.73205 −0.287934
\(169\) −6.92820 −0.532939
\(170\) −1.73205 −0.132842
\(171\) −7.00000 −0.535303
\(172\) −8.19615 −0.624951
\(173\) −23.6603 −1.79886 −0.899428 0.437069i \(-0.856016\pi\)
−0.899428 + 0.437069i \(0.856016\pi\)
\(174\) −5.00000 −0.379049
\(175\) −3.73205 −0.282117
\(176\) 0 0
\(177\) 5.66025 0.425451
\(178\) 2.53590 0.190074
\(179\) −12.5885 −0.940905 −0.470453 0.882425i \(-0.655909\pi\)
−0.470453 + 0.882425i \(0.655909\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −20.1962 −1.50117 −0.750584 0.660775i \(-0.770228\pi\)
−0.750584 + 0.660775i \(0.770228\pi\)
\(182\) −9.19615 −0.681664
\(183\) 9.12436 0.674492
\(184\) −3.26795 −0.240916
\(185\) −3.19615 −0.234986
\(186\) −4.19615 −0.307677
\(187\) 0 0
\(188\) −8.92820 −0.651156
\(189\) −3.73205 −0.271467
\(190\) 7.00000 0.507833
\(191\) 0.0717968 0.00519503 0.00259752 0.999997i \(-0.499173\pi\)
0.00259752 + 0.999997i \(0.499173\pi\)
\(192\) 1.00000 0.0721688
\(193\) 11.3205 0.814868 0.407434 0.913235i \(-0.366424\pi\)
0.407434 + 0.913235i \(0.366424\pi\)
\(194\) 5.26795 0.378217
\(195\) −2.46410 −0.176458
\(196\) 6.92820 0.494872
\(197\) −9.46410 −0.674289 −0.337145 0.941453i \(-0.609461\pi\)
−0.337145 + 0.941453i \(0.609461\pi\)
\(198\) 0 0
\(199\) 19.3205 1.36959 0.684797 0.728734i \(-0.259891\pi\)
0.684797 + 0.728734i \(0.259891\pi\)
\(200\) 1.00000 0.0707107
\(201\) 11.4641 0.808615
\(202\) 8.46410 0.595532
\(203\) 18.6603 1.30969
\(204\) 1.73205 0.121268
\(205\) 6.19615 0.432758
\(206\) −17.3923 −1.21178
\(207\) −3.26795 −0.227138
\(208\) 2.46410 0.170855
\(209\) 0 0
\(210\) 3.73205 0.257536
\(211\) −6.60770 −0.454892 −0.227446 0.973791i \(-0.573038\pi\)
−0.227446 + 0.973791i \(0.573038\pi\)
\(212\) −2.73205 −0.187638
\(213\) 4.46410 0.305875
\(214\) 14.3923 0.983838
\(215\) 8.19615 0.558973
\(216\) 1.00000 0.0680414
\(217\) 15.6603 1.06309
\(218\) 12.3923 0.839313
\(219\) −7.66025 −0.517632
\(220\) 0 0
\(221\) 4.26795 0.287093
\(222\) 3.19615 0.214512
\(223\) 29.2487 1.95864 0.979319 0.202321i \(-0.0648484\pi\)
0.979319 + 0.202321i \(0.0648484\pi\)
\(224\) −3.73205 −0.249358
\(225\) 1.00000 0.0666667
\(226\) −13.8564 −0.921714
\(227\) 27.4641 1.82286 0.911428 0.411459i \(-0.134981\pi\)
0.911428 + 0.411459i \(0.134981\pi\)
\(228\) −7.00000 −0.463586
\(229\) −5.85641 −0.387002 −0.193501 0.981100i \(-0.561984\pi\)
−0.193501 + 0.981100i \(0.561984\pi\)
\(230\) 3.26795 0.215482
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) 9.07180 0.594313 0.297157 0.954829i \(-0.403962\pi\)
0.297157 + 0.954829i \(0.403962\pi\)
\(234\) 2.46410 0.161083
\(235\) 8.92820 0.582412
\(236\) 5.66025 0.368451
\(237\) −10.3923 −0.675053
\(238\) −6.46410 −0.419005
\(239\) −3.19615 −0.206742 −0.103371 0.994643i \(-0.532963\pi\)
−0.103371 + 0.994643i \(0.532963\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −0.803848 −0.0517804 −0.0258902 0.999665i \(-0.508242\pi\)
−0.0258902 + 0.999665i \(0.508242\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 9.12436 0.584127
\(245\) −6.92820 −0.442627
\(246\) −6.19615 −0.395052
\(247\) −17.2487 −1.09751
\(248\) −4.19615 −0.266456
\(249\) −16.4641 −1.04337
\(250\) −1.00000 −0.0632456
\(251\) 31.3205 1.97693 0.988466 0.151440i \(-0.0483910\pi\)
0.988466 + 0.151440i \(0.0483910\pi\)
\(252\) −3.73205 −0.235097
\(253\) 0 0
\(254\) −13.4641 −0.844813
\(255\) −1.73205 −0.108465
\(256\) 1.00000 0.0625000
\(257\) 19.7846 1.23413 0.617065 0.786912i \(-0.288322\pi\)
0.617065 + 0.786912i \(0.288322\pi\)
\(258\) −8.19615 −0.510270
\(259\) −11.9282 −0.741182
\(260\) −2.46410 −0.152817
\(261\) −5.00000 −0.309492
\(262\) −21.1244 −1.30507
\(263\) 3.26795 0.201510 0.100755 0.994911i \(-0.467874\pi\)
0.100755 + 0.994911i \(0.467874\pi\)
\(264\) 0 0
\(265\) 2.73205 0.167829
\(266\) 26.1244 1.60179
\(267\) 2.53590 0.155194
\(268\) 11.4641 0.700281
\(269\) 21.9808 1.34019 0.670095 0.742275i \(-0.266253\pi\)
0.670095 + 0.742275i \(0.266253\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −23.8564 −1.44917 −0.724587 0.689184i \(-0.757969\pi\)
−0.724587 + 0.689184i \(0.757969\pi\)
\(272\) 1.73205 0.105021
\(273\) −9.19615 −0.556576
\(274\) 10.4641 0.632159
\(275\) 0 0
\(276\) −3.26795 −0.196707
\(277\) 2.14359 0.128796 0.0643980 0.997924i \(-0.479487\pi\)
0.0643980 + 0.997924i \(0.479487\pi\)
\(278\) −7.00000 −0.419832
\(279\) −4.19615 −0.251217
\(280\) 3.73205 0.223033
\(281\) 3.12436 0.186383 0.0931917 0.995648i \(-0.470293\pi\)
0.0931917 + 0.995648i \(0.470293\pi\)
\(282\) −8.92820 −0.531667
\(283\) 8.39230 0.498871 0.249435 0.968391i \(-0.419755\pi\)
0.249435 + 0.968391i \(0.419755\pi\)
\(284\) 4.46410 0.264896
\(285\) 7.00000 0.414644
\(286\) 0 0
\(287\) 23.1244 1.36499
\(288\) 1.00000 0.0589256
\(289\) −14.0000 −0.823529
\(290\) 5.00000 0.293610
\(291\) 5.26795 0.308813
\(292\) −7.66025 −0.448282
\(293\) 14.9282 0.872115 0.436057 0.899919i \(-0.356374\pi\)
0.436057 + 0.899919i \(0.356374\pi\)
\(294\) 6.92820 0.404061
\(295\) −5.66025 −0.329553
\(296\) 3.19615 0.185773
\(297\) 0 0
\(298\) 8.39230 0.486153
\(299\) −8.05256 −0.465692
\(300\) 1.00000 0.0577350
\(301\) 30.5885 1.76309
\(302\) −20.1962 −1.16216
\(303\) 8.46410 0.486250
\(304\) −7.00000 −0.401478
\(305\) −9.12436 −0.522459
\(306\) 1.73205 0.0990148
\(307\) 16.5885 0.946753 0.473377 0.880860i \(-0.343035\pi\)
0.473377 + 0.880860i \(0.343035\pi\)
\(308\) 0 0
\(309\) −17.3923 −0.989414
\(310\) 4.19615 0.238325
\(311\) 13.0718 0.741234 0.370617 0.928786i \(-0.379146\pi\)
0.370617 + 0.928786i \(0.379146\pi\)
\(312\) 2.46410 0.139502
\(313\) 11.8038 0.667193 0.333596 0.942716i \(-0.391738\pi\)
0.333596 + 0.942716i \(0.391738\pi\)
\(314\) −14.6603 −0.827326
\(315\) 3.73205 0.210277
\(316\) −10.3923 −0.584613
\(317\) 8.19615 0.460342 0.230171 0.973150i \(-0.426071\pi\)
0.230171 + 0.973150i \(0.426071\pi\)
\(318\) −2.73205 −0.153206
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 14.3923 0.803300
\(322\) 12.1962 0.679665
\(323\) −12.1244 −0.674617
\(324\) 1.00000 0.0555556
\(325\) 2.46410 0.136684
\(326\) 8.19615 0.453943
\(327\) 12.3923 0.685296
\(328\) −6.19615 −0.342125
\(329\) 33.3205 1.83702
\(330\) 0 0
\(331\) 5.87564 0.322955 0.161477 0.986876i \(-0.448374\pi\)
0.161477 + 0.986876i \(0.448374\pi\)
\(332\) −16.4641 −0.903585
\(333\) 3.19615 0.175148
\(334\) 6.53590 0.357628
\(335\) −11.4641 −0.626351
\(336\) −3.73205 −0.203600
\(337\) 30.1962 1.64489 0.822445 0.568845i \(-0.192610\pi\)
0.822445 + 0.568845i \(0.192610\pi\)
\(338\) −6.92820 −0.376845
\(339\) −13.8564 −0.752577
\(340\) −1.73205 −0.0939336
\(341\) 0 0
\(342\) −7.00000 −0.378517
\(343\) 0.267949 0.0144679
\(344\) −8.19615 −0.441907
\(345\) 3.26795 0.175940
\(346\) −23.6603 −1.27198
\(347\) 14.4641 0.776474 0.388237 0.921560i \(-0.373084\pi\)
0.388237 + 0.921560i \(0.373084\pi\)
\(348\) −5.00000 −0.268028
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) −3.73205 −0.199487
\(351\) 2.46410 0.131524
\(352\) 0 0
\(353\) 1.85641 0.0988065 0.0494033 0.998779i \(-0.484268\pi\)
0.0494033 + 0.998779i \(0.484268\pi\)
\(354\) 5.66025 0.300839
\(355\) −4.46410 −0.236930
\(356\) 2.53590 0.134402
\(357\) −6.46410 −0.342117
\(358\) −12.5885 −0.665321
\(359\) 31.1769 1.64545 0.822727 0.568436i \(-0.192451\pi\)
0.822727 + 0.568436i \(0.192451\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 30.0000 1.57895
\(362\) −20.1962 −1.06149
\(363\) 0 0
\(364\) −9.19615 −0.482009
\(365\) 7.66025 0.400956
\(366\) 9.12436 0.476938
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) −3.26795 −0.170354
\(369\) −6.19615 −0.322559
\(370\) −3.19615 −0.166160
\(371\) 10.1962 0.529358
\(372\) −4.19615 −0.217560
\(373\) −17.3923 −0.900539 −0.450270 0.892893i \(-0.648672\pi\)
−0.450270 + 0.892893i \(0.648672\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −8.92820 −0.460437
\(377\) −12.3205 −0.634538
\(378\) −3.73205 −0.191956
\(379\) 6.12436 0.314587 0.157294 0.987552i \(-0.449723\pi\)
0.157294 + 0.987552i \(0.449723\pi\)
\(380\) 7.00000 0.359092
\(381\) −13.4641 −0.689787
\(382\) 0.0717968 0.00367344
\(383\) −4.14359 −0.211728 −0.105864 0.994381i \(-0.533761\pi\)
−0.105864 + 0.994381i \(0.533761\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 11.3205 0.576199
\(387\) −8.19615 −0.416634
\(388\) 5.26795 0.267440
\(389\) −19.7128 −0.999479 −0.499740 0.866176i \(-0.666571\pi\)
−0.499740 + 0.866176i \(0.666571\pi\)
\(390\) −2.46410 −0.124775
\(391\) −5.66025 −0.286251
\(392\) 6.92820 0.349927
\(393\) −21.1244 −1.06558
\(394\) −9.46410 −0.476795
\(395\) 10.3923 0.522894
\(396\) 0 0
\(397\) 27.9808 1.40431 0.702157 0.712022i \(-0.252220\pi\)
0.702157 + 0.712022i \(0.252220\pi\)
\(398\) 19.3205 0.968450
\(399\) 26.1244 1.30785
\(400\) 1.00000 0.0500000
\(401\) 34.7321 1.73444 0.867218 0.497929i \(-0.165906\pi\)
0.867218 + 0.497929i \(0.165906\pi\)
\(402\) 11.4641 0.571777
\(403\) −10.3397 −0.515059
\(404\) 8.46410 0.421105
\(405\) −1.00000 −0.0496904
\(406\) 18.6603 0.926093
\(407\) 0 0
\(408\) 1.73205 0.0857493
\(409\) −12.9282 −0.639259 −0.319629 0.947543i \(-0.603558\pi\)
−0.319629 + 0.947543i \(0.603558\pi\)
\(410\) 6.19615 0.306006
\(411\) 10.4641 0.516156
\(412\) −17.3923 −0.856857
\(413\) −21.1244 −1.03946
\(414\) −3.26795 −0.160611
\(415\) 16.4641 0.808191
\(416\) 2.46410 0.120813
\(417\) −7.00000 −0.342791
\(418\) 0 0
\(419\) −20.2487 −0.989214 −0.494607 0.869117i \(-0.664688\pi\)
−0.494607 + 0.869117i \(0.664688\pi\)
\(420\) 3.73205 0.182105
\(421\) −15.6603 −0.763234 −0.381617 0.924321i \(-0.624633\pi\)
−0.381617 + 0.924321i \(0.624633\pi\)
\(422\) −6.60770 −0.321658
\(423\) −8.92820 −0.434104
\(424\) −2.73205 −0.132680
\(425\) 1.73205 0.0840168
\(426\) 4.46410 0.216286
\(427\) −34.0526 −1.64792
\(428\) 14.3923 0.695678
\(429\) 0 0
\(430\) 8.19615 0.395254
\(431\) −21.4449 −1.03296 −0.516481 0.856298i \(-0.672758\pi\)
−0.516481 + 0.856298i \(0.672758\pi\)
\(432\) 1.00000 0.0481125
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 15.6603 0.751716
\(435\) 5.00000 0.239732
\(436\) 12.3923 0.593484
\(437\) 22.8756 1.09429
\(438\) −7.66025 −0.366021
\(439\) 14.0000 0.668184 0.334092 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 0 0
\(441\) 6.92820 0.329914
\(442\) 4.26795 0.203006
\(443\) 10.8038 0.513306 0.256653 0.966504i \(-0.417380\pi\)
0.256653 + 0.966504i \(0.417380\pi\)
\(444\) 3.19615 0.151683
\(445\) −2.53590 −0.120213
\(446\) 29.2487 1.38497
\(447\) 8.39230 0.396942
\(448\) −3.73205 −0.176323
\(449\) 5.32051 0.251090 0.125545 0.992088i \(-0.459932\pi\)
0.125545 + 0.992088i \(0.459932\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −13.8564 −0.651751
\(453\) −20.1962 −0.948898
\(454\) 27.4641 1.28895
\(455\) 9.19615 0.431122
\(456\) −7.00000 −0.327805
\(457\) 21.2679 0.994873 0.497436 0.867500i \(-0.334275\pi\)
0.497436 + 0.867500i \(0.334275\pi\)
\(458\) −5.85641 −0.273652
\(459\) 1.73205 0.0808452
\(460\) 3.26795 0.152369
\(461\) −5.39230 −0.251145 −0.125572 0.992084i \(-0.540077\pi\)
−0.125572 + 0.992084i \(0.540077\pi\)
\(462\) 0 0
\(463\) −24.2487 −1.12693 −0.563467 0.826139i \(-0.690533\pi\)
−0.563467 + 0.826139i \(0.690533\pi\)
\(464\) −5.00000 −0.232119
\(465\) 4.19615 0.194592
\(466\) 9.07180 0.420243
\(467\) 28.8038 1.33288 0.666442 0.745557i \(-0.267817\pi\)
0.666442 + 0.745557i \(0.267817\pi\)
\(468\) 2.46410 0.113903
\(469\) −42.7846 −1.97561
\(470\) 8.92820 0.411827
\(471\) −14.6603 −0.675509
\(472\) 5.66025 0.260534
\(473\) 0 0
\(474\) −10.3923 −0.477334
\(475\) −7.00000 −0.321182
\(476\) −6.46410 −0.296282
\(477\) −2.73205 −0.125092
\(478\) −3.19615 −0.146189
\(479\) −25.9808 −1.18709 −0.593546 0.804800i \(-0.702272\pi\)
−0.593546 + 0.804800i \(0.702272\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 7.87564 0.359098
\(482\) −0.803848 −0.0366143
\(483\) 12.1962 0.554944
\(484\) 0 0
\(485\) −5.26795 −0.239205
\(486\) 1.00000 0.0453609
\(487\) −5.67949 −0.257362 −0.128681 0.991686i \(-0.541074\pi\)
−0.128681 + 0.991686i \(0.541074\pi\)
\(488\) 9.12436 0.413040
\(489\) 8.19615 0.370643
\(490\) −6.92820 −0.312984
\(491\) 1.26795 0.0572217 0.0286109 0.999591i \(-0.490892\pi\)
0.0286109 + 0.999591i \(0.490892\pi\)
\(492\) −6.19615 −0.279344
\(493\) −8.66025 −0.390038
\(494\) −17.2487 −0.776056
\(495\) 0 0
\(496\) −4.19615 −0.188413
\(497\) −16.6603 −0.747315
\(498\) −16.4641 −0.737774
\(499\) −27.1962 −1.21747 −0.608733 0.793375i \(-0.708322\pi\)
−0.608733 + 0.793375i \(0.708322\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 6.53590 0.292002
\(502\) 31.3205 1.39790
\(503\) 23.9090 1.06605 0.533024 0.846100i \(-0.321056\pi\)
0.533024 + 0.846100i \(0.321056\pi\)
\(504\) −3.73205 −0.166239
\(505\) −8.46410 −0.376648
\(506\) 0 0
\(507\) −6.92820 −0.307692
\(508\) −13.4641 −0.597373
\(509\) 11.8564 0.525526 0.262763 0.964860i \(-0.415366\pi\)
0.262763 + 0.964860i \(0.415366\pi\)
\(510\) −1.73205 −0.0766965
\(511\) 28.5885 1.26468
\(512\) 1.00000 0.0441942
\(513\) −7.00000 −0.309058
\(514\) 19.7846 0.872662
\(515\) 17.3923 0.766397
\(516\) −8.19615 −0.360815
\(517\) 0 0
\(518\) −11.9282 −0.524095
\(519\) −23.6603 −1.03857
\(520\) −2.46410 −0.108058
\(521\) −18.5885 −0.814375 −0.407188 0.913345i \(-0.633490\pi\)
−0.407188 + 0.913345i \(0.633490\pi\)
\(522\) −5.00000 −0.218844
\(523\) 2.87564 0.125743 0.0628716 0.998022i \(-0.479974\pi\)
0.0628716 + 0.998022i \(0.479974\pi\)
\(524\) −21.1244 −0.922822
\(525\) −3.73205 −0.162880
\(526\) 3.26795 0.142489
\(527\) −7.26795 −0.316597
\(528\) 0 0
\(529\) −12.3205 −0.535674
\(530\) 2.73205 0.118673
\(531\) 5.66025 0.245634
\(532\) 26.1244 1.13263
\(533\) −15.2679 −0.661328
\(534\) 2.53590 0.109739
\(535\) −14.3923 −0.622234
\(536\) 11.4641 0.495174
\(537\) −12.5885 −0.543232
\(538\) 21.9808 0.947658
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) −30.7321 −1.32127 −0.660637 0.750705i \(-0.729714\pi\)
−0.660637 + 0.750705i \(0.729714\pi\)
\(542\) −23.8564 −1.02472
\(543\) −20.1962 −0.866700
\(544\) 1.73205 0.0742611
\(545\) −12.3923 −0.530828
\(546\) −9.19615 −0.393559
\(547\) 23.8564 1.02003 0.510013 0.860167i \(-0.329641\pi\)
0.510013 + 0.860167i \(0.329641\pi\)
\(548\) 10.4641 0.447004
\(549\) 9.12436 0.389418
\(550\) 0 0
\(551\) 35.0000 1.49105
\(552\) −3.26795 −0.139093
\(553\) 38.7846 1.64929
\(554\) 2.14359 0.0910726
\(555\) −3.19615 −0.135669
\(556\) −7.00000 −0.296866
\(557\) 37.3205 1.58132 0.790660 0.612255i \(-0.209737\pi\)
0.790660 + 0.612255i \(0.209737\pi\)
\(558\) −4.19615 −0.177637
\(559\) −20.1962 −0.854206
\(560\) 3.73205 0.157708
\(561\) 0 0
\(562\) 3.12436 0.131793
\(563\) −5.53590 −0.233310 −0.116655 0.993172i \(-0.537217\pi\)
−0.116655 + 0.993172i \(0.537217\pi\)
\(564\) −8.92820 −0.375945
\(565\) 13.8564 0.582943
\(566\) 8.39230 0.352755
\(567\) −3.73205 −0.156731
\(568\) 4.46410 0.187310
\(569\) −23.6603 −0.991889 −0.495945 0.868354i \(-0.665178\pi\)
−0.495945 + 0.868354i \(0.665178\pi\)
\(570\) 7.00000 0.293198
\(571\) −4.53590 −0.189821 −0.0949107 0.995486i \(-0.530257\pi\)
−0.0949107 + 0.995486i \(0.530257\pi\)
\(572\) 0 0
\(573\) 0.0717968 0.00299935
\(574\) 23.1244 0.965192
\(575\) −3.26795 −0.136283
\(576\) 1.00000 0.0416667
\(577\) −45.0333 −1.87476 −0.937381 0.348306i \(-0.886757\pi\)
−0.937381 + 0.348306i \(0.886757\pi\)
\(578\) −14.0000 −0.582323
\(579\) 11.3205 0.470464
\(580\) 5.00000 0.207614
\(581\) 61.4449 2.54916
\(582\) 5.26795 0.218364
\(583\) 0 0
\(584\) −7.66025 −0.316984
\(585\) −2.46410 −0.101878
\(586\) 14.9282 0.616678
\(587\) −1.87564 −0.0774161 −0.0387081 0.999251i \(-0.512324\pi\)
−0.0387081 + 0.999251i \(0.512324\pi\)
\(588\) 6.92820 0.285714
\(589\) 29.3731 1.21030
\(590\) −5.66025 −0.233029
\(591\) −9.46410 −0.389301
\(592\) 3.19615 0.131361
\(593\) −34.7846 −1.42843 −0.714216 0.699925i \(-0.753217\pi\)
−0.714216 + 0.699925i \(0.753217\pi\)
\(594\) 0 0
\(595\) 6.46410 0.265002
\(596\) 8.39230 0.343762
\(597\) 19.3205 0.790736
\(598\) −8.05256 −0.329294
\(599\) 40.2487 1.64452 0.822259 0.569114i \(-0.192714\pi\)
0.822259 + 0.569114i \(0.192714\pi\)
\(600\) 1.00000 0.0408248
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 30.5885 1.24669
\(603\) 11.4641 0.466854
\(604\) −20.1962 −0.821770
\(605\) 0 0
\(606\) 8.46410 0.343831
\(607\) −28.1244 −1.14153 −0.570766 0.821113i \(-0.693354\pi\)
−0.570766 + 0.821113i \(0.693354\pi\)
\(608\) −7.00000 −0.283887
\(609\) 18.6603 0.756152
\(610\) −9.12436 −0.369434
\(611\) −22.0000 −0.890025
\(612\) 1.73205 0.0700140
\(613\) 15.5359 0.627489 0.313745 0.949507i \(-0.398416\pi\)
0.313745 + 0.949507i \(0.398416\pi\)
\(614\) 16.5885 0.669456
\(615\) 6.19615 0.249853
\(616\) 0 0
\(617\) −41.1051 −1.65483 −0.827415 0.561591i \(-0.810189\pi\)
−0.827415 + 0.561591i \(0.810189\pi\)
\(618\) −17.3923 −0.699621
\(619\) −11.8756 −0.477322 −0.238661 0.971103i \(-0.576709\pi\)
−0.238661 + 0.971103i \(0.576709\pi\)
\(620\) 4.19615 0.168522
\(621\) −3.26795 −0.131138
\(622\) 13.0718 0.524131
\(623\) −9.46410 −0.379171
\(624\) 2.46410 0.0986430
\(625\) 1.00000 0.0400000
\(626\) 11.8038 0.471777
\(627\) 0 0
\(628\) −14.6603 −0.585008
\(629\) 5.53590 0.220731
\(630\) 3.73205 0.148688
\(631\) 26.9808 1.07409 0.537044 0.843554i \(-0.319541\pi\)
0.537044 + 0.843554i \(0.319541\pi\)
\(632\) −10.3923 −0.413384
\(633\) −6.60770 −0.262632
\(634\) 8.19615 0.325511
\(635\) 13.4641 0.534307
\(636\) −2.73205 −0.108333
\(637\) 17.0718 0.676409
\(638\) 0 0
\(639\) 4.46410 0.176597
\(640\) −1.00000 −0.0395285
\(641\) 31.8564 1.25825 0.629126 0.777303i \(-0.283413\pi\)
0.629126 + 0.777303i \(0.283413\pi\)
\(642\) 14.3923 0.568019
\(643\) 44.7846 1.76613 0.883066 0.469248i \(-0.155475\pi\)
0.883066 + 0.469248i \(0.155475\pi\)
\(644\) 12.1962 0.480596
\(645\) 8.19615 0.322723
\(646\) −12.1244 −0.477026
\(647\) −26.5359 −1.04323 −0.521617 0.853180i \(-0.674671\pi\)
−0.521617 + 0.853180i \(0.674671\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 2.46410 0.0966500
\(651\) 15.6603 0.613774
\(652\) 8.19615 0.320986
\(653\) −5.51666 −0.215884 −0.107942 0.994157i \(-0.534426\pi\)
−0.107942 + 0.994157i \(0.534426\pi\)
\(654\) 12.3923 0.484577
\(655\) 21.1244 0.825397
\(656\) −6.19615 −0.241919
\(657\) −7.66025 −0.298855
\(658\) 33.3205 1.29897
\(659\) 16.2487 0.632960 0.316480 0.948599i \(-0.397499\pi\)
0.316480 + 0.948599i \(0.397499\pi\)
\(660\) 0 0
\(661\) −40.4449 −1.57312 −0.786561 0.617512i \(-0.788141\pi\)
−0.786561 + 0.617512i \(0.788141\pi\)
\(662\) 5.87564 0.228363
\(663\) 4.26795 0.165753
\(664\) −16.4641 −0.638931
\(665\) −26.1244 −1.01306
\(666\) 3.19615 0.123848
\(667\) 16.3397 0.632677
\(668\) 6.53590 0.252882
\(669\) 29.2487 1.13082
\(670\) −11.4641 −0.442897
\(671\) 0 0
\(672\) −3.73205 −0.143967
\(673\) −17.0718 −0.658069 −0.329035 0.944318i \(-0.606723\pi\)
−0.329035 + 0.944318i \(0.606723\pi\)
\(674\) 30.1962 1.16311
\(675\) 1.00000 0.0384900
\(676\) −6.92820 −0.266469
\(677\) 27.1244 1.04247 0.521237 0.853412i \(-0.325471\pi\)
0.521237 + 0.853412i \(0.325471\pi\)
\(678\) −13.8564 −0.532152
\(679\) −19.6603 −0.754491
\(680\) −1.73205 −0.0664211
\(681\) 27.4641 1.05243
\(682\) 0 0
\(683\) −42.3731 −1.62136 −0.810680 0.585489i \(-0.800902\pi\)
−0.810680 + 0.585489i \(0.800902\pi\)
\(684\) −7.00000 −0.267652
\(685\) −10.4641 −0.399813
\(686\) 0.267949 0.0102303
\(687\) −5.85641 −0.223436
\(688\) −8.19615 −0.312475
\(689\) −6.73205 −0.256471
\(690\) 3.26795 0.124409
\(691\) 12.5167 0.476156 0.238078 0.971246i \(-0.423483\pi\)
0.238078 + 0.971246i \(0.423483\pi\)
\(692\) −23.6603 −0.899428
\(693\) 0 0
\(694\) 14.4641 0.549050
\(695\) 7.00000 0.265525
\(696\) −5.00000 −0.189525
\(697\) −10.7321 −0.406505
\(698\) −34.0000 −1.28692
\(699\) 9.07180 0.343127
\(700\) −3.73205 −0.141058
\(701\) −3.24871 −0.122702 −0.0613511 0.998116i \(-0.519541\pi\)
−0.0613511 + 0.998116i \(0.519541\pi\)
\(702\) 2.46410 0.0930015
\(703\) −22.3731 −0.843816
\(704\) 0 0
\(705\) 8.92820 0.336256
\(706\) 1.85641 0.0698668
\(707\) −31.5885 −1.18801
\(708\) 5.66025 0.212725
\(709\) −24.7321 −0.928832 −0.464416 0.885617i \(-0.653736\pi\)
−0.464416 + 0.885617i \(0.653736\pi\)
\(710\) −4.46410 −0.167535
\(711\) −10.3923 −0.389742
\(712\) 2.53590 0.0950368
\(713\) 13.7128 0.513549
\(714\) −6.46410 −0.241913
\(715\) 0 0
\(716\) −12.5885 −0.470453
\(717\) −3.19615 −0.119362
\(718\) 31.1769 1.16351
\(719\) −46.3923 −1.73014 −0.865071 0.501650i \(-0.832726\pi\)
−0.865071 + 0.501650i \(0.832726\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 64.9090 2.41734
\(722\) 30.0000 1.11648
\(723\) −0.803848 −0.0298954
\(724\) −20.1962 −0.750584
\(725\) −5.00000 −0.185695
\(726\) 0 0
\(727\) −21.1436 −0.784172 −0.392086 0.919928i \(-0.628247\pi\)
−0.392086 + 0.919928i \(0.628247\pi\)
\(728\) −9.19615 −0.340832
\(729\) 1.00000 0.0370370
\(730\) 7.66025 0.283519
\(731\) −14.1962 −0.525064
\(732\) 9.12436 0.337246
\(733\) 4.78461 0.176724 0.0883618 0.996088i \(-0.471837\pi\)
0.0883618 + 0.996088i \(0.471837\pi\)
\(734\) −17.0000 −0.627481
\(735\) −6.92820 −0.255551
\(736\) −3.26795 −0.120458
\(737\) 0 0
\(738\) −6.19615 −0.228084
\(739\) 19.0000 0.698926 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(740\) −3.19615 −0.117493
\(741\) −17.2487 −0.633647
\(742\) 10.1962 0.374313
\(743\) 5.26795 0.193262 0.0966312 0.995320i \(-0.469193\pi\)
0.0966312 + 0.995320i \(0.469193\pi\)
\(744\) −4.19615 −0.153838
\(745\) −8.39230 −0.307470
\(746\) −17.3923 −0.636778
\(747\) −16.4641 −0.602390
\(748\) 0 0
\(749\) −53.7128 −1.96262
\(750\) −1.00000 −0.0365148
\(751\) −1.66025 −0.0605835 −0.0302918 0.999541i \(-0.509644\pi\)
−0.0302918 + 0.999541i \(0.509644\pi\)
\(752\) −8.92820 −0.325578
\(753\) 31.3205 1.14138
\(754\) −12.3205 −0.448686
\(755\) 20.1962 0.735013
\(756\) −3.73205 −0.135733
\(757\) 8.53590 0.310243 0.155121 0.987895i \(-0.450423\pi\)
0.155121 + 0.987895i \(0.450423\pi\)
\(758\) 6.12436 0.222447
\(759\) 0 0
\(760\) 7.00000 0.253917
\(761\) 46.2487 1.67651 0.838257 0.545275i \(-0.183575\pi\)
0.838257 + 0.545275i \(0.183575\pi\)
\(762\) −13.4641 −0.487753
\(763\) −46.2487 −1.67432
\(764\) 0.0717968 0.00259752
\(765\) −1.73205 −0.0626224
\(766\) −4.14359 −0.149714
\(767\) 13.9474 0.503613
\(768\) 1.00000 0.0360844
\(769\) −47.8372 −1.72505 −0.862526 0.506012i \(-0.831119\pi\)
−0.862526 + 0.506012i \(0.831119\pi\)
\(770\) 0 0
\(771\) 19.7846 0.712525
\(772\) 11.3205 0.407434
\(773\) −29.6603 −1.06681 −0.533403 0.845861i \(-0.679087\pi\)
−0.533403 + 0.845861i \(0.679087\pi\)
\(774\) −8.19615 −0.294605
\(775\) −4.19615 −0.150730
\(776\) 5.26795 0.189108
\(777\) −11.9282 −0.427922
\(778\) −19.7128 −0.706739
\(779\) 43.3731 1.55400
\(780\) −2.46410 −0.0882290
\(781\) 0 0
\(782\) −5.66025 −0.202410
\(783\) −5.00000 −0.178685
\(784\) 6.92820 0.247436
\(785\) 14.6603 0.523247
\(786\) −21.1244 −0.753481
\(787\) 38.1962 1.36155 0.680773 0.732495i \(-0.261644\pi\)
0.680773 + 0.732495i \(0.261644\pi\)
\(788\) −9.46410 −0.337145
\(789\) 3.26795 0.116342
\(790\) 10.3923 0.369742
\(791\) 51.7128 1.83870
\(792\) 0 0
\(793\) 22.4833 0.798407
\(794\) 27.9808 0.993000
\(795\) 2.73205 0.0968959
\(796\) 19.3205 0.684797
\(797\) −51.1244 −1.81092 −0.905459 0.424434i \(-0.860473\pi\)
−0.905459 + 0.424434i \(0.860473\pi\)
\(798\) 26.1244 0.924792
\(799\) −15.4641 −0.547081
\(800\) 1.00000 0.0353553
\(801\) 2.53590 0.0896016
\(802\) 34.7321 1.22643
\(803\) 0 0
\(804\) 11.4641 0.404308
\(805\) −12.1962 −0.429858
\(806\) −10.3397 −0.364202
\(807\) 21.9808 0.773759
\(808\) 8.46410 0.297766
\(809\) −2.19615 −0.0772126 −0.0386063 0.999254i \(-0.512292\pi\)
−0.0386063 + 0.999254i \(0.512292\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 44.1769 1.55126 0.775631 0.631187i \(-0.217432\pi\)
0.775631 + 0.631187i \(0.217432\pi\)
\(812\) 18.6603 0.654847
\(813\) −23.8564 −0.836681
\(814\) 0 0
\(815\) −8.19615 −0.287099
\(816\) 1.73205 0.0606339
\(817\) 57.3731 2.00723
\(818\) −12.9282 −0.452024
\(819\) −9.19615 −0.321340
\(820\) 6.19615 0.216379
\(821\) 23.6077 0.823914 0.411957 0.911203i \(-0.364845\pi\)
0.411957 + 0.911203i \(0.364845\pi\)
\(822\) 10.4641 0.364977
\(823\) −1.67949 −0.0585434 −0.0292717 0.999571i \(-0.509319\pi\)
−0.0292717 + 0.999571i \(0.509319\pi\)
\(824\) −17.3923 −0.605890
\(825\) 0 0
\(826\) −21.1244 −0.735010
\(827\) 21.0000 0.730242 0.365121 0.930960i \(-0.381028\pi\)
0.365121 + 0.930960i \(0.381028\pi\)
\(828\) −3.26795 −0.113569
\(829\) −20.5885 −0.715067 −0.357533 0.933900i \(-0.616382\pi\)
−0.357533 + 0.933900i \(0.616382\pi\)
\(830\) 16.4641 0.571477
\(831\) 2.14359 0.0743604
\(832\) 2.46410 0.0854274
\(833\) 12.0000 0.415775
\(834\) −7.00000 −0.242390
\(835\) −6.53590 −0.226184
\(836\) 0 0
\(837\) −4.19615 −0.145040
\(838\) −20.2487 −0.699480
\(839\) −15.5359 −0.536359 −0.268179 0.963369i \(-0.586422\pi\)
−0.268179 + 0.963369i \(0.586422\pi\)
\(840\) 3.73205 0.128768
\(841\) −4.00000 −0.137931
\(842\) −15.6603 −0.539688
\(843\) 3.12436 0.107609
\(844\) −6.60770 −0.227446
\(845\) 6.92820 0.238337
\(846\) −8.92820 −0.306958
\(847\) 0 0
\(848\) −2.73205 −0.0938190
\(849\) 8.39230 0.288023
\(850\) 1.73205 0.0594089
\(851\) −10.4449 −0.358045
\(852\) 4.46410 0.152938
\(853\) 26.7128 0.914629 0.457315 0.889305i \(-0.348811\pi\)
0.457315 + 0.889305i \(0.348811\pi\)
\(854\) −34.0526 −1.16525
\(855\) 7.00000 0.239395
\(856\) 14.3923 0.491919
\(857\) 8.51666 0.290924 0.145462 0.989364i \(-0.453533\pi\)
0.145462 + 0.989364i \(0.453533\pi\)
\(858\) 0 0
\(859\) −37.3205 −1.27336 −0.636680 0.771128i \(-0.719693\pi\)
−0.636680 + 0.771128i \(0.719693\pi\)
\(860\) 8.19615 0.279486
\(861\) 23.1244 0.788076
\(862\) −21.4449 −0.730415
\(863\) −4.53590 −0.154404 −0.0772019 0.997015i \(-0.524599\pi\)
−0.0772019 + 0.997015i \(0.524599\pi\)
\(864\) 1.00000 0.0340207
\(865\) 23.6603 0.804473
\(866\) 4.00000 0.135926
\(867\) −14.0000 −0.475465
\(868\) 15.6603 0.531544
\(869\) 0 0
\(870\) 5.00000 0.169516
\(871\) 28.2487 0.957171
\(872\) 12.3923 0.419656
\(873\) 5.26795 0.178293
\(874\) 22.8756 0.773780
\(875\) 3.73205 0.126166
\(876\) −7.66025 −0.258816
\(877\) 15.5359 0.524610 0.262305 0.964985i \(-0.415517\pi\)
0.262305 + 0.964985i \(0.415517\pi\)
\(878\) 14.0000 0.472477
\(879\) 14.9282 0.503516
\(880\) 0 0
\(881\) 4.58846 0.154589 0.0772945 0.997008i \(-0.475372\pi\)
0.0772945 + 0.997008i \(0.475372\pi\)
\(882\) 6.92820 0.233285
\(883\) −12.0526 −0.405601 −0.202800 0.979220i \(-0.565004\pi\)
−0.202800 + 0.979220i \(0.565004\pi\)
\(884\) 4.26795 0.143547
\(885\) −5.66025 −0.190267
\(886\) 10.8038 0.362962
\(887\) −4.78461 −0.160651 −0.0803257 0.996769i \(-0.525596\pi\)
−0.0803257 + 0.996769i \(0.525596\pi\)
\(888\) 3.19615 0.107256
\(889\) 50.2487 1.68529
\(890\) −2.53590 −0.0850035
\(891\) 0 0
\(892\) 29.2487 0.979319
\(893\) 62.4974 2.09140
\(894\) 8.39230 0.280681
\(895\) 12.5885 0.420786
\(896\) −3.73205 −0.124679
\(897\) −8.05256 −0.268867
\(898\) 5.32051 0.177548
\(899\) 20.9808 0.699748
\(900\) 1.00000 0.0333333
\(901\) −4.73205 −0.157647
\(902\) 0 0
\(903\) 30.5885 1.01792
\(904\) −13.8564 −0.460857
\(905\) 20.1962 0.671343
\(906\) −20.1962 −0.670972
\(907\) −35.0718 −1.16454 −0.582270 0.812996i \(-0.697835\pi\)
−0.582270 + 0.812996i \(0.697835\pi\)
\(908\) 27.4641 0.911428
\(909\) 8.46410 0.280737
\(910\) 9.19615 0.304849
\(911\) −31.1051 −1.03056 −0.515279 0.857022i \(-0.672312\pi\)
−0.515279 + 0.857022i \(0.672312\pi\)
\(912\) −7.00000 −0.231793
\(913\) 0 0
\(914\) 21.2679 0.703481
\(915\) −9.12436 −0.301642
\(916\) −5.85641 −0.193501
\(917\) 78.8372 2.60343
\(918\) 1.73205 0.0571662
\(919\) 2.05256 0.0677077 0.0338538 0.999427i \(-0.489222\pi\)
0.0338538 + 0.999427i \(0.489222\pi\)
\(920\) 3.26795 0.107741
\(921\) 16.5885 0.546608
\(922\) −5.39230 −0.177586
\(923\) 11.0000 0.362069
\(924\) 0 0
\(925\) 3.19615 0.105089
\(926\) −24.2487 −0.796862
\(927\) −17.3923 −0.571238
\(928\) −5.00000 −0.164133
\(929\) −6.87564 −0.225583 −0.112791 0.993619i \(-0.535979\pi\)
−0.112791 + 0.993619i \(0.535979\pi\)
\(930\) 4.19615 0.137597
\(931\) −48.4974 −1.58944
\(932\) 9.07180 0.297157
\(933\) 13.0718 0.427951
\(934\) 28.8038 0.942491
\(935\) 0 0
\(936\) 2.46410 0.0805417
\(937\) 4.92820 0.160997 0.0804987 0.996755i \(-0.474349\pi\)
0.0804987 + 0.996755i \(0.474349\pi\)
\(938\) −42.7846 −1.39697
\(939\) 11.8038 0.385204
\(940\) 8.92820 0.291206
\(941\) 6.07180 0.197935 0.0989675 0.995091i \(-0.468446\pi\)
0.0989675 + 0.995091i \(0.468446\pi\)
\(942\) −14.6603 −0.477657
\(943\) 20.2487 0.659389
\(944\) 5.66025 0.184226
\(945\) 3.73205 0.121404
\(946\) 0 0
\(947\) 44.3731 1.44193 0.720965 0.692971i \(-0.243699\pi\)
0.720965 + 0.692971i \(0.243699\pi\)
\(948\) −10.3923 −0.337526
\(949\) −18.8756 −0.612729
\(950\) −7.00000 −0.227110
\(951\) 8.19615 0.265778
\(952\) −6.46410 −0.209503
\(953\) −10.7846 −0.349348 −0.174674 0.984626i \(-0.555887\pi\)
−0.174674 + 0.984626i \(0.555887\pi\)
\(954\) −2.73205 −0.0884534
\(955\) −0.0717968 −0.00232329
\(956\) −3.19615 −0.103371
\(957\) 0 0
\(958\) −25.9808 −0.839400
\(959\) −39.0526 −1.26107
\(960\) −1.00000 −0.0322749
\(961\) −13.3923 −0.432010
\(962\) 7.87564 0.253921
\(963\) 14.3923 0.463786
\(964\) −0.803848 −0.0258902
\(965\) −11.3205 −0.364420
\(966\) 12.1962 0.392405
\(967\) −47.1769 −1.51711 −0.758554 0.651611i \(-0.774094\pi\)
−0.758554 + 0.651611i \(0.774094\pi\)
\(968\) 0 0
\(969\) −12.1244 −0.389490
\(970\) −5.26795 −0.169144
\(971\) −39.6077 −1.27107 −0.635536 0.772071i \(-0.719221\pi\)
−0.635536 + 0.772071i \(0.719221\pi\)
\(972\) 1.00000 0.0320750
\(973\) 26.1244 0.837508
\(974\) −5.67949 −0.181983
\(975\) 2.46410 0.0789144
\(976\) 9.12436 0.292064
\(977\) 28.1436 0.900393 0.450197 0.892929i \(-0.351354\pi\)
0.450197 + 0.892929i \(0.351354\pi\)
\(978\) 8.19615 0.262084
\(979\) 0 0
\(980\) −6.92820 −0.221313
\(981\) 12.3923 0.395656
\(982\) 1.26795 0.0404619
\(983\) 23.9090 0.762578 0.381289 0.924456i \(-0.375480\pi\)
0.381289 + 0.924456i \(0.375480\pi\)
\(984\) −6.19615 −0.197526
\(985\) 9.46410 0.301551
\(986\) −8.66025 −0.275799
\(987\) 33.3205 1.06060
\(988\) −17.2487 −0.548755
\(989\) 26.7846 0.851701
\(990\) 0 0
\(991\) −42.7846 −1.35910 −0.679549 0.733630i \(-0.737824\pi\)
−0.679549 + 0.733630i \(0.737824\pi\)
\(992\) −4.19615 −0.133228
\(993\) 5.87564 0.186458
\(994\) −16.6603 −0.528431
\(995\) −19.3205 −0.612501
\(996\) −16.4641 −0.521685
\(997\) −6.71281 −0.212597 −0.106298 0.994334i \(-0.533900\pi\)
−0.106298 + 0.994334i \(0.533900\pi\)
\(998\) −27.1962 −0.860879
\(999\) 3.19615 0.101122
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.bo.1.1 yes 2
11.10 odd 2 3630.2.a.bg.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.bg.1.2 2 11.10 odd 2
3630.2.a.bo.1.1 yes 2 1.1 even 1 trivial