Properties

Label 4730.2.a.be.1.9
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 12
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.38729\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.38729 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.38729 q^{6} +3.92530 q^{7} +1.00000 q^{8} +2.69915 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.38729 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.38729 q^{6} +3.92530 q^{7} +1.00000 q^{8} +2.69915 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.38729 q^{12} +0.812933 q^{13} +3.92530 q^{14} +2.38729 q^{15} +1.00000 q^{16} -5.34911 q^{17} +2.69915 q^{18} -0.405790 q^{19} +1.00000 q^{20} +9.37084 q^{21} -1.00000 q^{22} +1.18707 q^{23} +2.38729 q^{24} +1.00000 q^{25} +0.812933 q^{26} -0.718217 q^{27} +3.92530 q^{28} +1.86640 q^{29} +2.38729 q^{30} -10.0613 q^{31} +1.00000 q^{32} -2.38729 q^{33} -5.34911 q^{34} +3.92530 q^{35} +2.69915 q^{36} +6.13412 q^{37} -0.405790 q^{38} +1.94071 q^{39} +1.00000 q^{40} +11.7137 q^{41} +9.37084 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.69915 q^{45} +1.18707 q^{46} +8.05997 q^{47} +2.38729 q^{48} +8.40801 q^{49} +1.00000 q^{50} -12.7699 q^{51} +0.812933 q^{52} +9.24636 q^{53} -0.718217 q^{54} -1.00000 q^{55} +3.92530 q^{56} -0.968738 q^{57} +1.86640 q^{58} +7.78548 q^{59} +2.38729 q^{60} +11.1613 q^{61} -10.0613 q^{62} +10.5950 q^{63} +1.00000 q^{64} +0.812933 q^{65} -2.38729 q^{66} -1.05981 q^{67} -5.34911 q^{68} +2.83387 q^{69} +3.92530 q^{70} -11.7969 q^{71} +2.69915 q^{72} -2.94467 q^{73} +6.13412 q^{74} +2.38729 q^{75} -0.405790 q^{76} -3.92530 q^{77} +1.94071 q^{78} -7.82323 q^{79} +1.00000 q^{80} -9.81204 q^{81} +11.7137 q^{82} -14.2689 q^{83} +9.37084 q^{84} -5.34911 q^{85} +1.00000 q^{86} +4.45565 q^{87} -1.00000 q^{88} +0.276107 q^{89} +2.69915 q^{90} +3.19101 q^{91} +1.18707 q^{92} -24.0193 q^{93} +8.05997 q^{94} -0.405790 q^{95} +2.38729 q^{96} +3.54637 q^{97} +8.40801 q^{98} -2.69915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + O(q^{10}) \) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + 12q^{10} - 12q^{11} + 3q^{12} + 16q^{13} + 8q^{14} + 3q^{15} + 12q^{16} + 18q^{17} + 25q^{18} - 4q^{19} + 12q^{20} + 4q^{21} - 12q^{22} + 8q^{23} + 3q^{24} + 12q^{25} + 16q^{26} + 6q^{27} + 8q^{28} + 20q^{29} + 3q^{30} + 5q^{31} + 12q^{32} - 3q^{33} + 18q^{34} + 8q^{35} + 25q^{36} + 19q^{37} - 4q^{38} + 6q^{39} + 12q^{40} + 16q^{41} + 4q^{42} + 12q^{43} - 12q^{44} + 25q^{45} + 8q^{46} - q^{47} + 3q^{48} + 52q^{49} + 12q^{50} + q^{51} + 16q^{52} + 11q^{53} + 6q^{54} - 12q^{55} + 8q^{56} + 9q^{57} + 20q^{58} - 11q^{59} + 3q^{60} + 18q^{61} + 5q^{62} + 15q^{63} + 12q^{64} + 16q^{65} - 3q^{66} - 10q^{67} + 18q^{68} + 8q^{70} - 2q^{71} + 25q^{72} + 29q^{73} + 19q^{74} + 3q^{75} - 4q^{76} - 8q^{77} + 6q^{78} + 2q^{79} + 12q^{80} - 8q^{81} + 16q^{82} + 26q^{83} + 4q^{84} + 18q^{85} + 12q^{86} - 4q^{87} - 12q^{88} + 41q^{89} + 25q^{90} - 4q^{91} + 8q^{92} + 5q^{93} - q^{94} - 4q^{95} + 3q^{96} - 7q^{97} + 52q^{98} - 25q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.38729 1.37830 0.689151 0.724618i \(-0.257984\pi\)
0.689151 + 0.724618i \(0.257984\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.38729 0.974607
\(7\) 3.92530 1.48363 0.741813 0.670607i \(-0.233966\pi\)
0.741813 + 0.670607i \(0.233966\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.69915 0.899717
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 2.38729 0.689151
\(13\) 0.812933 0.225467 0.112734 0.993625i \(-0.464039\pi\)
0.112734 + 0.993625i \(0.464039\pi\)
\(14\) 3.92530 1.04908
\(15\) 2.38729 0.616395
\(16\) 1.00000 0.250000
\(17\) −5.34911 −1.29735 −0.648675 0.761065i \(-0.724677\pi\)
−0.648675 + 0.761065i \(0.724677\pi\)
\(18\) 2.69915 0.636196
\(19\) −0.405790 −0.0930946 −0.0465473 0.998916i \(-0.514822\pi\)
−0.0465473 + 0.998916i \(0.514822\pi\)
\(20\) 1.00000 0.223607
\(21\) 9.37084 2.04488
\(22\) −1.00000 −0.213201
\(23\) 1.18707 0.247521 0.123760 0.992312i \(-0.460505\pi\)
0.123760 + 0.992312i \(0.460505\pi\)
\(24\) 2.38729 0.487303
\(25\) 1.00000 0.200000
\(26\) 0.812933 0.159429
\(27\) −0.718217 −0.138221
\(28\) 3.92530 0.741813
\(29\) 1.86640 0.346582 0.173291 0.984871i \(-0.444560\pi\)
0.173291 + 0.984871i \(0.444560\pi\)
\(30\) 2.38729 0.435857
\(31\) −10.0613 −1.80707 −0.903535 0.428513i \(-0.859037\pi\)
−0.903535 + 0.428513i \(0.859037\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.38729 −0.415574
\(34\) −5.34911 −0.917365
\(35\) 3.92530 0.663497
\(36\) 2.69915 0.449858
\(37\) 6.13412 1.00844 0.504221 0.863575i \(-0.331780\pi\)
0.504221 + 0.863575i \(0.331780\pi\)
\(38\) −0.405790 −0.0658279
\(39\) 1.94071 0.310762
\(40\) 1.00000 0.158114
\(41\) 11.7137 1.82938 0.914689 0.404159i \(-0.132436\pi\)
0.914689 + 0.404159i \(0.132436\pi\)
\(42\) 9.37084 1.44595
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 2.69915 0.402365
\(46\) 1.18707 0.175023
\(47\) 8.05997 1.17567 0.587834 0.808982i \(-0.299981\pi\)
0.587834 + 0.808982i \(0.299981\pi\)
\(48\) 2.38729 0.344576
\(49\) 8.40801 1.20114
\(50\) 1.00000 0.141421
\(51\) −12.7699 −1.78814
\(52\) 0.812933 0.112734
\(53\) 9.24636 1.27009 0.635043 0.772477i \(-0.280983\pi\)
0.635043 + 0.772477i \(0.280983\pi\)
\(54\) −0.718217 −0.0977369
\(55\) −1.00000 −0.134840
\(56\) 3.92530 0.524541
\(57\) −0.968738 −0.128313
\(58\) 1.86640 0.245071
\(59\) 7.78548 1.01358 0.506792 0.862068i \(-0.330831\pi\)
0.506792 + 0.862068i \(0.330831\pi\)
\(60\) 2.38729 0.308198
\(61\) 11.1613 1.42905 0.714526 0.699608i \(-0.246642\pi\)
0.714526 + 0.699608i \(0.246642\pi\)
\(62\) −10.0613 −1.27779
\(63\) 10.5950 1.33484
\(64\) 1.00000 0.125000
\(65\) 0.812933 0.100832
\(66\) −2.38729 −0.293855
\(67\) −1.05981 −0.129476 −0.0647380 0.997902i \(-0.520621\pi\)
−0.0647380 + 0.997902i \(0.520621\pi\)
\(68\) −5.34911 −0.648675
\(69\) 2.83387 0.341158
\(70\) 3.92530 0.469164
\(71\) −11.7969 −1.40004 −0.700018 0.714126i \(-0.746825\pi\)
−0.700018 + 0.714126i \(0.746825\pi\)
\(72\) 2.69915 0.318098
\(73\) −2.94467 −0.344647 −0.172324 0.985040i \(-0.555127\pi\)
−0.172324 + 0.985040i \(0.555127\pi\)
\(74\) 6.13412 0.713076
\(75\) 2.38729 0.275660
\(76\) −0.405790 −0.0465473
\(77\) −3.92530 −0.447330
\(78\) 1.94071 0.219742
\(79\) −7.82323 −0.880182 −0.440091 0.897953i \(-0.645054\pi\)
−0.440091 + 0.897953i \(0.645054\pi\)
\(80\) 1.00000 0.111803
\(81\) −9.81204 −1.09023
\(82\) 11.7137 1.29357
\(83\) −14.2689 −1.56622 −0.783109 0.621884i \(-0.786367\pi\)
−0.783109 + 0.621884i \(0.786367\pi\)
\(84\) 9.37084 1.02244
\(85\) −5.34911 −0.580193
\(86\) 1.00000 0.107833
\(87\) 4.45565 0.477695
\(88\) −1.00000 −0.106600
\(89\) 0.276107 0.0292673 0.0146336 0.999893i \(-0.495342\pi\)
0.0146336 + 0.999893i \(0.495342\pi\)
\(90\) 2.69915 0.284515
\(91\) 3.19101 0.334509
\(92\) 1.18707 0.123760
\(93\) −24.0193 −2.49069
\(94\) 8.05997 0.831322
\(95\) −0.405790 −0.0416332
\(96\) 2.38729 0.243652
\(97\) 3.54637 0.360079 0.180040 0.983659i \(-0.442377\pi\)
0.180040 + 0.983659i \(0.442377\pi\)
\(98\) 8.40801 0.849338
\(99\) −2.69915 −0.271275
\(100\) 1.00000 0.100000
\(101\) −11.9091 −1.18500 −0.592499 0.805571i \(-0.701858\pi\)
−0.592499 + 0.805571i \(0.701858\pi\)
\(102\) −12.7699 −1.26441
\(103\) −16.4288 −1.61878 −0.809388 0.587274i \(-0.800201\pi\)
−0.809388 + 0.587274i \(0.800201\pi\)
\(104\) 0.812933 0.0797147
\(105\) 9.37084 0.914500
\(106\) 9.24636 0.898086
\(107\) 8.32995 0.805287 0.402644 0.915357i \(-0.368091\pi\)
0.402644 + 0.915357i \(0.368091\pi\)
\(108\) −0.718217 −0.0691104
\(109\) −15.7533 −1.50889 −0.754447 0.656361i \(-0.772095\pi\)
−0.754447 + 0.656361i \(0.772095\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 14.6439 1.38994
\(112\) 3.92530 0.370906
\(113\) 4.83624 0.454955 0.227477 0.973783i \(-0.426952\pi\)
0.227477 + 0.973783i \(0.426952\pi\)
\(114\) −0.968738 −0.0907307
\(115\) 1.18707 0.110695
\(116\) 1.86640 0.173291
\(117\) 2.19423 0.202856
\(118\) 7.78548 0.716712
\(119\) −20.9969 −1.92478
\(120\) 2.38729 0.217929
\(121\) 1.00000 0.0909091
\(122\) 11.1613 1.01049
\(123\) 27.9641 2.52143
\(124\) −10.0613 −0.903535
\(125\) 1.00000 0.0894427
\(126\) 10.5950 0.943876
\(127\) 10.1467 0.900371 0.450185 0.892935i \(-0.351358\pi\)
0.450185 + 0.892935i \(0.351358\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.38729 0.210189
\(130\) 0.812933 0.0712990
\(131\) 4.88758 0.427029 0.213515 0.976940i \(-0.431509\pi\)
0.213515 + 0.976940i \(0.431509\pi\)
\(132\) −2.38729 −0.207787
\(133\) −1.59285 −0.138118
\(134\) −1.05981 −0.0915533
\(135\) −0.718217 −0.0618143
\(136\) −5.34911 −0.458683
\(137\) −15.7894 −1.34898 −0.674492 0.738283i \(-0.735637\pi\)
−0.674492 + 0.738283i \(0.735637\pi\)
\(138\) 2.83387 0.241235
\(139\) −14.0825 −1.19446 −0.597232 0.802068i \(-0.703733\pi\)
−0.597232 + 0.802068i \(0.703733\pi\)
\(140\) 3.92530 0.331749
\(141\) 19.2415 1.62042
\(142\) −11.7969 −0.989975
\(143\) −0.812933 −0.0679809
\(144\) 2.69915 0.224929
\(145\) 1.86640 0.154996
\(146\) −2.94467 −0.243702
\(147\) 20.0724 1.65554
\(148\) 6.13412 0.504221
\(149\) 5.70949 0.467740 0.233870 0.972268i \(-0.424861\pi\)
0.233870 + 0.972268i \(0.424861\pi\)
\(150\) 2.38729 0.194921
\(151\) −6.67469 −0.543178 −0.271589 0.962413i \(-0.587549\pi\)
−0.271589 + 0.962413i \(0.587549\pi\)
\(152\) −0.405790 −0.0329139
\(153\) −14.4381 −1.16725
\(154\) −3.92530 −0.316310
\(155\) −10.0613 −0.808147
\(156\) 1.94071 0.155381
\(157\) −20.2095 −1.61290 −0.806448 0.591305i \(-0.798613\pi\)
−0.806448 + 0.591305i \(0.798613\pi\)
\(158\) −7.82323 −0.622383
\(159\) 22.0737 1.75056
\(160\) 1.00000 0.0790569
\(161\) 4.65960 0.367228
\(162\) −9.81204 −0.770907
\(163\) 7.78522 0.609785 0.304893 0.952387i \(-0.401379\pi\)
0.304893 + 0.952387i \(0.401379\pi\)
\(164\) 11.7137 0.914689
\(165\) −2.38729 −0.185850
\(166\) −14.2689 −1.10748
\(167\) −23.0156 −1.78100 −0.890502 0.454979i \(-0.849647\pi\)
−0.890502 + 0.454979i \(0.849647\pi\)
\(168\) 9.37084 0.722976
\(169\) −12.3391 −0.949165
\(170\) −5.34911 −0.410258
\(171\) −1.09529 −0.0837588
\(172\) 1.00000 0.0762493
\(173\) 4.79082 0.364239 0.182119 0.983276i \(-0.441704\pi\)
0.182119 + 0.983276i \(0.441704\pi\)
\(174\) 4.45565 0.337782
\(175\) 3.92530 0.296725
\(176\) −1.00000 −0.0753778
\(177\) 18.5862 1.39702
\(178\) 0.276107 0.0206951
\(179\) 12.9298 0.966421 0.483211 0.875504i \(-0.339470\pi\)
0.483211 + 0.875504i \(0.339470\pi\)
\(180\) 2.69915 0.201183
\(181\) −0.164956 −0.0122611 −0.00613053 0.999981i \(-0.501951\pi\)
−0.00613053 + 0.999981i \(0.501951\pi\)
\(182\) 3.19101 0.236533
\(183\) 26.6452 1.96967
\(184\) 1.18707 0.0875117
\(185\) 6.13412 0.450989
\(186\) −24.0193 −1.76118
\(187\) 5.34911 0.391166
\(188\) 8.05997 0.587834
\(189\) −2.81922 −0.205068
\(190\) −0.405790 −0.0294391
\(191\) −25.0988 −1.81608 −0.908042 0.418878i \(-0.862423\pi\)
−0.908042 + 0.418878i \(0.862423\pi\)
\(192\) 2.38729 0.172288
\(193\) 8.07002 0.580893 0.290446 0.956891i \(-0.406196\pi\)
0.290446 + 0.956891i \(0.406196\pi\)
\(194\) 3.54637 0.254614
\(195\) 1.94071 0.138977
\(196\) 8.40801 0.600572
\(197\) −18.0918 −1.28899 −0.644493 0.764610i \(-0.722932\pi\)
−0.644493 + 0.764610i \(0.722932\pi\)
\(198\) −2.69915 −0.191820
\(199\) 9.19769 0.652007 0.326003 0.945369i \(-0.394298\pi\)
0.326003 + 0.945369i \(0.394298\pi\)
\(200\) 1.00000 0.0707107
\(201\) −2.53006 −0.178457
\(202\) −11.9091 −0.837920
\(203\) 7.32620 0.514199
\(204\) −12.7699 −0.894070
\(205\) 11.7137 0.818122
\(206\) −16.4288 −1.14465
\(207\) 3.20407 0.222698
\(208\) 0.812933 0.0563668
\(209\) 0.405790 0.0280691
\(210\) 9.37084 0.646649
\(211\) 2.78371 0.191638 0.0958191 0.995399i \(-0.469453\pi\)
0.0958191 + 0.995399i \(0.469453\pi\)
\(212\) 9.24636 0.635043
\(213\) −28.1626 −1.92967
\(214\) 8.32995 0.569424
\(215\) 1.00000 0.0681994
\(216\) −0.718217 −0.0488685
\(217\) −39.4938 −2.68102
\(218\) −15.7533 −1.06695
\(219\) −7.02977 −0.475028
\(220\) −1.00000 −0.0674200
\(221\) −4.34847 −0.292510
\(222\) 14.6439 0.982835
\(223\) 10.5184 0.704366 0.352183 0.935931i \(-0.385440\pi\)
0.352183 + 0.935931i \(0.385440\pi\)
\(224\) 3.92530 0.262270
\(225\) 2.69915 0.179943
\(226\) 4.83624 0.321702
\(227\) −17.8730 −1.18627 −0.593135 0.805103i \(-0.702110\pi\)
−0.593135 + 0.805103i \(0.702110\pi\)
\(228\) −0.968738 −0.0641563
\(229\) 13.1275 0.867491 0.433746 0.901035i \(-0.357192\pi\)
0.433746 + 0.901035i \(0.357192\pi\)
\(230\) 1.18707 0.0782729
\(231\) −9.37084 −0.616556
\(232\) 1.86640 0.122535
\(233\) −24.2231 −1.58691 −0.793453 0.608632i \(-0.791719\pi\)
−0.793453 + 0.608632i \(0.791719\pi\)
\(234\) 2.19423 0.143441
\(235\) 8.05997 0.525774
\(236\) 7.78548 0.506792
\(237\) −18.6763 −1.21316
\(238\) −20.9969 −1.36103
\(239\) 6.88492 0.445348 0.222674 0.974893i \(-0.428521\pi\)
0.222674 + 0.974893i \(0.428521\pi\)
\(240\) 2.38729 0.154099
\(241\) 28.1350 1.81234 0.906168 0.422919i \(-0.138994\pi\)
0.906168 + 0.422919i \(0.138994\pi\)
\(242\) 1.00000 0.0642824
\(243\) −21.2695 −1.36444
\(244\) 11.1613 0.714526
\(245\) 8.40801 0.537168
\(246\) 27.9641 1.78292
\(247\) −0.329880 −0.0209898
\(248\) −10.0613 −0.638896
\(249\) −34.0641 −2.15872
\(250\) 1.00000 0.0632456
\(251\) 2.91600 0.184056 0.0920280 0.995756i \(-0.470665\pi\)
0.0920280 + 0.995756i \(0.470665\pi\)
\(252\) 10.5950 0.667421
\(253\) −1.18707 −0.0746302
\(254\) 10.1467 0.636658
\(255\) −12.7699 −0.799681
\(256\) 1.00000 0.0625000
\(257\) −22.6806 −1.41477 −0.707387 0.706826i \(-0.750126\pi\)
−0.707387 + 0.706826i \(0.750126\pi\)
\(258\) 2.38729 0.148626
\(259\) 24.0783 1.49615
\(260\) 0.812933 0.0504160
\(261\) 5.03770 0.311826
\(262\) 4.88758 0.301955
\(263\) −31.0321 −1.91352 −0.956761 0.290875i \(-0.906054\pi\)
−0.956761 + 0.290875i \(0.906054\pi\)
\(264\) −2.38729 −0.146927
\(265\) 9.24636 0.567999
\(266\) −1.59285 −0.0976639
\(267\) 0.659147 0.0403391
\(268\) −1.05981 −0.0647380
\(269\) −17.5504 −1.07006 −0.535032 0.844832i \(-0.679700\pi\)
−0.535032 + 0.844832i \(0.679700\pi\)
\(270\) −0.718217 −0.0437093
\(271\) 21.3862 1.29912 0.649561 0.760310i \(-0.274953\pi\)
0.649561 + 0.760310i \(0.274953\pi\)
\(272\) −5.34911 −0.324338
\(273\) 7.61786 0.461054
\(274\) −15.7894 −0.953875
\(275\) −1.00000 −0.0603023
\(276\) 2.83387 0.170579
\(277\) 29.2162 1.75543 0.877715 0.479183i \(-0.159067\pi\)
0.877715 + 0.479183i \(0.159067\pi\)
\(278\) −14.0825 −0.844614
\(279\) −27.1571 −1.62585
\(280\) 3.92530 0.234582
\(281\) 20.3275 1.21264 0.606320 0.795221i \(-0.292645\pi\)
0.606320 + 0.795221i \(0.292645\pi\)
\(282\) 19.2415 1.14581
\(283\) 29.9954 1.78304 0.891520 0.452982i \(-0.149640\pi\)
0.891520 + 0.452982i \(0.149640\pi\)
\(284\) −11.7969 −0.700018
\(285\) −0.968738 −0.0573831
\(286\) −0.812933 −0.0480698
\(287\) 45.9800 2.71411
\(288\) 2.69915 0.159049
\(289\) 11.6130 0.683119
\(290\) 1.86640 0.109599
\(291\) 8.46621 0.496298
\(292\) −2.94467 −0.172324
\(293\) −19.8554 −1.15997 −0.579983 0.814628i \(-0.696941\pi\)
−0.579983 + 0.814628i \(0.696941\pi\)
\(294\) 20.0724 1.17064
\(295\) 7.78548 0.453288
\(296\) 6.13412 0.356538
\(297\) 0.718217 0.0416752
\(298\) 5.70949 0.330742
\(299\) 0.965006 0.0558077
\(300\) 2.38729 0.137830
\(301\) 3.92530 0.226251
\(302\) −6.67469 −0.384085
\(303\) −28.4304 −1.63328
\(304\) −0.405790 −0.0232737
\(305\) 11.1613 0.639092
\(306\) −14.4381 −0.825369
\(307\) 11.1521 0.636486 0.318243 0.948009i \(-0.396907\pi\)
0.318243 + 0.948009i \(0.396907\pi\)
\(308\) −3.92530 −0.223665
\(309\) −39.2202 −2.23116
\(310\) −10.0613 −0.571446
\(311\) −5.42995 −0.307904 −0.153952 0.988078i \(-0.549200\pi\)
−0.153952 + 0.988078i \(0.549200\pi\)
\(312\) 1.94071 0.109871
\(313\) −5.87031 −0.331809 −0.165905 0.986142i \(-0.553054\pi\)
−0.165905 + 0.986142i \(0.553054\pi\)
\(314\) −20.2095 −1.14049
\(315\) 10.5950 0.596960
\(316\) −7.82323 −0.440091
\(317\) 17.0584 0.958095 0.479048 0.877789i \(-0.340982\pi\)
0.479048 + 0.877789i \(0.340982\pi\)
\(318\) 22.0737 1.23783
\(319\) −1.86640 −0.104499
\(320\) 1.00000 0.0559017
\(321\) 19.8860 1.10993
\(322\) 4.65960 0.259669
\(323\) 2.17062 0.120776
\(324\) −9.81204 −0.545113
\(325\) 0.812933 0.0450934
\(326\) 7.78522 0.431183
\(327\) −37.6077 −2.07971
\(328\) 11.7137 0.646783
\(329\) 31.6378 1.74425
\(330\) −2.38729 −0.131416
\(331\) −9.13065 −0.501866 −0.250933 0.968004i \(-0.580737\pi\)
−0.250933 + 0.968004i \(0.580737\pi\)
\(332\) −14.2689 −0.783109
\(333\) 16.5569 0.907312
\(334\) −23.0156 −1.25936
\(335\) −1.05981 −0.0579034
\(336\) 9.37084 0.511221
\(337\) 29.1566 1.58826 0.794129 0.607749i \(-0.207927\pi\)
0.794129 + 0.607749i \(0.207927\pi\)
\(338\) −12.3391 −0.671161
\(339\) 11.5455 0.627065
\(340\) −5.34911 −0.290096
\(341\) 10.0613 0.544852
\(342\) −1.09529 −0.0592264
\(343\) 5.52688 0.298423
\(344\) 1.00000 0.0539164
\(345\) 2.83387 0.152571
\(346\) 4.79082 0.257556
\(347\) 3.01791 0.162010 0.0810049 0.996714i \(-0.474187\pi\)
0.0810049 + 0.996714i \(0.474187\pi\)
\(348\) 4.45565 0.238848
\(349\) 5.69395 0.304790 0.152395 0.988320i \(-0.451301\pi\)
0.152395 + 0.988320i \(0.451301\pi\)
\(350\) 3.92530 0.209816
\(351\) −0.583862 −0.0311643
\(352\) −1.00000 −0.0533002
\(353\) −22.5135 −1.19827 −0.599136 0.800648i \(-0.704489\pi\)
−0.599136 + 0.800648i \(0.704489\pi\)
\(354\) 18.5862 0.987846
\(355\) −11.7969 −0.626115
\(356\) 0.276107 0.0146336
\(357\) −50.1257 −2.65293
\(358\) 12.9298 0.683363
\(359\) 23.1603 1.22235 0.611176 0.791495i \(-0.290697\pi\)
0.611176 + 0.791495i \(0.290697\pi\)
\(360\) 2.69915 0.142258
\(361\) −18.8353 −0.991333
\(362\) −0.164956 −0.00866988
\(363\) 2.38729 0.125300
\(364\) 3.19101 0.167254
\(365\) −2.94467 −0.154131
\(366\) 26.6452 1.39276
\(367\) 10.8593 0.566851 0.283425 0.958994i \(-0.408529\pi\)
0.283425 + 0.958994i \(0.408529\pi\)
\(368\) 1.18707 0.0618801
\(369\) 31.6171 1.64592
\(370\) 6.13412 0.318898
\(371\) 36.2948 1.88433
\(372\) −24.0193 −1.24534
\(373\) −18.9180 −0.979535 −0.489768 0.871853i \(-0.662918\pi\)
−0.489768 + 0.871853i \(0.662918\pi\)
\(374\) 5.34911 0.276596
\(375\) 2.38729 0.123279
\(376\) 8.05997 0.415661
\(377\) 1.51726 0.0781429
\(378\) −2.81922 −0.145005
\(379\) −5.27705 −0.271064 −0.135532 0.990773i \(-0.543274\pi\)
−0.135532 + 0.990773i \(0.543274\pi\)
\(380\) −0.405790 −0.0208166
\(381\) 24.2230 1.24098
\(382\) −25.0988 −1.28417
\(383\) −36.4918 −1.86465 −0.932323 0.361627i \(-0.882221\pi\)
−0.932323 + 0.361627i \(0.882221\pi\)
\(384\) 2.38729 0.121826
\(385\) −3.92530 −0.200052
\(386\) 8.07002 0.410753
\(387\) 2.69915 0.137205
\(388\) 3.54637 0.180040
\(389\) 4.06976 0.206345 0.103172 0.994663i \(-0.467101\pi\)
0.103172 + 0.994663i \(0.467101\pi\)
\(390\) 1.94071 0.0982715
\(391\) −6.34975 −0.321121
\(392\) 8.40801 0.424669
\(393\) 11.6681 0.588576
\(394\) −18.0918 −0.911451
\(395\) −7.82323 −0.393630
\(396\) −2.69915 −0.135637
\(397\) 7.75558 0.389242 0.194621 0.980879i \(-0.437652\pi\)
0.194621 + 0.980879i \(0.437652\pi\)
\(398\) 9.19769 0.461038
\(399\) −3.80259 −0.190368
\(400\) 1.00000 0.0500000
\(401\) 12.4546 0.621953 0.310976 0.950418i \(-0.399344\pi\)
0.310976 + 0.950418i \(0.399344\pi\)
\(402\) −2.53006 −0.126188
\(403\) −8.17920 −0.407435
\(404\) −11.9091 −0.592499
\(405\) −9.81204 −0.487564
\(406\) 7.32620 0.363593
\(407\) −6.13412 −0.304057
\(408\) −12.7699 −0.632203
\(409\) −19.2547 −0.952083 −0.476042 0.879423i \(-0.657929\pi\)
−0.476042 + 0.879423i \(0.657929\pi\)
\(410\) 11.7137 0.578500
\(411\) −37.6940 −1.85931
\(412\) −16.4288 −0.809388
\(413\) 30.5604 1.50378
\(414\) 3.20407 0.157471
\(415\) −14.2689 −0.700434
\(416\) 0.812933 0.0398573
\(417\) −33.6191 −1.64633
\(418\) 0.405790 0.0198478
\(419\) −28.1001 −1.37278 −0.686390 0.727234i \(-0.740806\pi\)
−0.686390 + 0.727234i \(0.740806\pi\)
\(420\) 9.37084 0.457250
\(421\) 16.8136 0.819444 0.409722 0.912211i \(-0.365626\pi\)
0.409722 + 0.912211i \(0.365626\pi\)
\(422\) 2.78371 0.135509
\(423\) 21.7551 1.05777
\(424\) 9.24636 0.449043
\(425\) −5.34911 −0.259470
\(426\) −28.1626 −1.36448
\(427\) 43.8113 2.12018
\(428\) 8.32995 0.402644
\(429\) −1.94071 −0.0936982
\(430\) 1.00000 0.0482243
\(431\) −16.5619 −0.797760 −0.398880 0.917003i \(-0.630601\pi\)
−0.398880 + 0.917003i \(0.630601\pi\)
\(432\) −0.718217 −0.0345552
\(433\) −24.0005 −1.15339 −0.576696 0.816959i \(-0.695658\pi\)
−0.576696 + 0.816959i \(0.695658\pi\)
\(434\) −39.4938 −1.89576
\(435\) 4.45565 0.213632
\(436\) −15.7533 −0.754447
\(437\) −0.481700 −0.0230428
\(438\) −7.02977 −0.335895
\(439\) 16.7666 0.800228 0.400114 0.916465i \(-0.368970\pi\)
0.400114 + 0.916465i \(0.368970\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 22.6945 1.08069
\(442\) −4.34847 −0.206836
\(443\) −7.53930 −0.358203 −0.179101 0.983831i \(-0.557319\pi\)
−0.179101 + 0.983831i \(0.557319\pi\)
\(444\) 14.6439 0.694969
\(445\) 0.276107 0.0130887
\(446\) 10.5184 0.498062
\(447\) 13.6302 0.644687
\(448\) 3.92530 0.185453
\(449\) −29.5577 −1.39492 −0.697458 0.716626i \(-0.745686\pi\)
−0.697458 + 0.716626i \(0.745686\pi\)
\(450\) 2.69915 0.127239
\(451\) −11.7137 −0.551578
\(452\) 4.83624 0.227477
\(453\) −15.9344 −0.748664
\(454\) −17.8730 −0.838820
\(455\) 3.19101 0.149597
\(456\) −0.968738 −0.0453653
\(457\) 33.4690 1.56561 0.782806 0.622266i \(-0.213788\pi\)
0.782806 + 0.622266i \(0.213788\pi\)
\(458\) 13.1275 0.613409
\(459\) 3.84182 0.179321
\(460\) 1.18707 0.0553473
\(461\) 1.75000 0.0815056 0.0407528 0.999169i \(-0.487024\pi\)
0.0407528 + 0.999169i \(0.487024\pi\)
\(462\) −9.37084 −0.435971
\(463\) −5.58904 −0.259745 −0.129872 0.991531i \(-0.541457\pi\)
−0.129872 + 0.991531i \(0.541457\pi\)
\(464\) 1.86640 0.0866456
\(465\) −24.0193 −1.11387
\(466\) −24.2231 −1.12211
\(467\) −8.21645 −0.380212 −0.190106 0.981764i \(-0.560883\pi\)
−0.190106 + 0.981764i \(0.560883\pi\)
\(468\) 2.19423 0.101428
\(469\) −4.16006 −0.192094
\(470\) 8.05997 0.371779
\(471\) −48.2460 −2.22306
\(472\) 7.78548 0.358356
\(473\) −1.00000 −0.0459800
\(474\) −18.6763 −0.857832
\(475\) −0.405790 −0.0186189
\(476\) −20.9969 −0.962391
\(477\) 24.9573 1.14272
\(478\) 6.88492 0.314909
\(479\) −20.6013 −0.941297 −0.470649 0.882321i \(-0.655980\pi\)
−0.470649 + 0.882321i \(0.655980\pi\)
\(480\) 2.38729 0.108964
\(481\) 4.98663 0.227371
\(482\) 28.1350 1.28151
\(483\) 11.1238 0.506151
\(484\) 1.00000 0.0454545
\(485\) 3.54637 0.161032
\(486\) −21.2695 −0.964805
\(487\) 12.5620 0.569239 0.284620 0.958640i \(-0.408133\pi\)
0.284620 + 0.958640i \(0.408133\pi\)
\(488\) 11.1613 0.505246
\(489\) 18.5856 0.840468
\(490\) 8.40801 0.379835
\(491\) −15.5086 −0.699895 −0.349948 0.936769i \(-0.613801\pi\)
−0.349948 + 0.936769i \(0.613801\pi\)
\(492\) 27.9641 1.26072
\(493\) −9.98360 −0.449639
\(494\) −0.329880 −0.0148420
\(495\) −2.69915 −0.121318
\(496\) −10.0613 −0.451768
\(497\) −46.3065 −2.07713
\(498\) −34.0641 −1.52645
\(499\) 18.3476 0.821350 0.410675 0.911782i \(-0.365293\pi\)
0.410675 + 0.911782i \(0.365293\pi\)
\(500\) 1.00000 0.0447214
\(501\) −54.9450 −2.45476
\(502\) 2.91600 0.130147
\(503\) −11.9948 −0.534820 −0.267410 0.963583i \(-0.586168\pi\)
−0.267410 + 0.963583i \(0.586168\pi\)
\(504\) 10.5950 0.471938
\(505\) −11.9091 −0.529947
\(506\) −1.18707 −0.0527716
\(507\) −29.4571 −1.30824
\(508\) 10.1467 0.450185
\(509\) 20.1205 0.891825 0.445912 0.895077i \(-0.352879\pi\)
0.445912 + 0.895077i \(0.352879\pi\)
\(510\) −12.7699 −0.565460
\(511\) −11.5587 −0.511327
\(512\) 1.00000 0.0441942
\(513\) 0.291445 0.0128676
\(514\) −22.6806 −1.00040
\(515\) −16.4288 −0.723939
\(516\) 2.38729 0.105095
\(517\) −8.05997 −0.354477
\(518\) 24.0783 1.05794
\(519\) 11.4371 0.502031
\(520\) 0.812933 0.0356495
\(521\) 24.7788 1.08558 0.542790 0.839868i \(-0.317368\pi\)
0.542790 + 0.839868i \(0.317368\pi\)
\(522\) 5.03770 0.220494
\(523\) 17.1383 0.749406 0.374703 0.927145i \(-0.377745\pi\)
0.374703 + 0.927145i \(0.377745\pi\)
\(524\) 4.88758 0.213515
\(525\) 9.37084 0.408977
\(526\) −31.0321 −1.35306
\(527\) 53.8193 2.34440
\(528\) −2.38729 −0.103893
\(529\) −21.5909 −0.938734
\(530\) 9.24636 0.401636
\(531\) 21.0142 0.911938
\(532\) −1.59285 −0.0690588
\(533\) 9.52248 0.412464
\(534\) 0.659147 0.0285241
\(535\) 8.32995 0.360135
\(536\) −1.05981 −0.0457767
\(537\) 30.8673 1.33202
\(538\) −17.5504 −0.756650
\(539\) −8.40801 −0.362159
\(540\) −0.718217 −0.0309071
\(541\) 29.4682 1.26694 0.633468 0.773769i \(-0.281631\pi\)
0.633468 + 0.773769i \(0.281631\pi\)
\(542\) 21.3862 0.918617
\(543\) −0.393797 −0.0168994
\(544\) −5.34911 −0.229341
\(545\) −15.7533 −0.674798
\(546\) 7.61786 0.326014
\(547\) 38.7145 1.65531 0.827657 0.561235i \(-0.189674\pi\)
0.827657 + 0.561235i \(0.189674\pi\)
\(548\) −15.7894 −0.674492
\(549\) 30.1259 1.28574
\(550\) −1.00000 −0.0426401
\(551\) −0.757368 −0.0322650
\(552\) 2.83387 0.120618
\(553\) −30.7086 −1.30586
\(554\) 29.2162 1.24128
\(555\) 14.6439 0.621599
\(556\) −14.0825 −0.597232
\(557\) 16.3853 0.694267 0.347133 0.937816i \(-0.387155\pi\)
0.347133 + 0.937816i \(0.387155\pi\)
\(558\) −27.1571 −1.14965
\(559\) 0.812933 0.0343834
\(560\) 3.92530 0.165874
\(561\) 12.7699 0.539145
\(562\) 20.3275 0.857465
\(563\) −23.1756 −0.976735 −0.488368 0.872638i \(-0.662407\pi\)
−0.488368 + 0.872638i \(0.662407\pi\)
\(564\) 19.2415 0.810212
\(565\) 4.83624 0.203462
\(566\) 29.9954 1.26080
\(567\) −38.5152 −1.61749
\(568\) −11.7969 −0.494987
\(569\) 45.3924 1.90295 0.951475 0.307727i \(-0.0995682\pi\)
0.951475 + 0.307727i \(0.0995682\pi\)
\(570\) −0.968738 −0.0405760
\(571\) 46.1854 1.93280 0.966400 0.257044i \(-0.0827484\pi\)
0.966400 + 0.257044i \(0.0827484\pi\)
\(572\) −0.812933 −0.0339904
\(573\) −59.9181 −2.50311
\(574\) 45.9800 1.91917
\(575\) 1.18707 0.0495041
\(576\) 2.69915 0.112465
\(577\) −32.7305 −1.36259 −0.681295 0.732009i \(-0.738583\pi\)
−0.681295 + 0.732009i \(0.738583\pi\)
\(578\) 11.6130 0.483038
\(579\) 19.2655 0.800645
\(580\) 1.86640 0.0774982
\(581\) −56.0099 −2.32368
\(582\) 8.46621 0.350935
\(583\) −9.24636 −0.382945
\(584\) −2.94467 −0.121851
\(585\) 2.19423 0.0907202
\(586\) −19.8554 −0.820220
\(587\) 13.7346 0.566889 0.283444 0.958989i \(-0.408523\pi\)
0.283444 + 0.958989i \(0.408523\pi\)
\(588\) 20.0724 0.827770
\(589\) 4.08279 0.168229
\(590\) 7.78548 0.320523
\(591\) −43.1903 −1.77661
\(592\) 6.13412 0.252111
\(593\) 10.0242 0.411646 0.205823 0.978589i \(-0.434013\pi\)
0.205823 + 0.978589i \(0.434013\pi\)
\(594\) 0.718217 0.0294688
\(595\) −20.9969 −0.860789
\(596\) 5.70949 0.233870
\(597\) 21.9575 0.898662
\(598\) 0.965006 0.0394620
\(599\) 20.6244 0.842689 0.421344 0.906901i \(-0.361558\pi\)
0.421344 + 0.906901i \(0.361558\pi\)
\(600\) 2.38729 0.0974607
\(601\) 44.4507 1.81318 0.906590 0.422012i \(-0.138676\pi\)
0.906590 + 0.422012i \(0.138676\pi\)
\(602\) 3.92530 0.159983
\(603\) −2.86058 −0.116492
\(604\) −6.67469 −0.271589
\(605\) 1.00000 0.0406558
\(606\) −28.4304 −1.15491
\(607\) −18.3201 −0.743591 −0.371796 0.928315i \(-0.621258\pi\)
−0.371796 + 0.928315i \(0.621258\pi\)
\(608\) −0.405790 −0.0164570
\(609\) 17.4898 0.708721
\(610\) 11.1613 0.451906
\(611\) 6.55222 0.265074
\(612\) −14.4381 −0.583624
\(613\) −22.0525 −0.890694 −0.445347 0.895358i \(-0.646920\pi\)
−0.445347 + 0.895358i \(0.646920\pi\)
\(614\) 11.1521 0.450063
\(615\) 27.9641 1.12762
\(616\) −3.92530 −0.158155
\(617\) 20.3489 0.819215 0.409607 0.912262i \(-0.365666\pi\)
0.409607 + 0.912262i \(0.365666\pi\)
\(618\) −39.2202 −1.57767
\(619\) −43.6503 −1.75446 −0.877228 0.480075i \(-0.840610\pi\)
−0.877228 + 0.480075i \(0.840610\pi\)
\(620\) −10.0613 −0.404073
\(621\) −0.852571 −0.0342125
\(622\) −5.42995 −0.217721
\(623\) 1.08380 0.0434217
\(624\) 1.94071 0.0776904
\(625\) 1.00000 0.0400000
\(626\) −5.87031 −0.234625
\(627\) 0.968738 0.0386877
\(628\) −20.2095 −0.806448
\(629\) −32.8121 −1.30830
\(630\) 10.5950 0.422114
\(631\) −0.442788 −0.0176271 −0.00881355 0.999961i \(-0.502805\pi\)
−0.00881355 + 0.999961i \(0.502805\pi\)
\(632\) −7.82323 −0.311191
\(633\) 6.64551 0.264135
\(634\) 17.0584 0.677476
\(635\) 10.1467 0.402658
\(636\) 22.0737 0.875281
\(637\) 6.83515 0.270819
\(638\) −1.86640 −0.0738916
\(639\) −31.8416 −1.25964
\(640\) 1.00000 0.0395285
\(641\) −15.0798 −0.595616 −0.297808 0.954626i \(-0.596256\pi\)
−0.297808 + 0.954626i \(0.596256\pi\)
\(642\) 19.8860 0.784838
\(643\) −10.5018 −0.414151 −0.207076 0.978325i \(-0.566395\pi\)
−0.207076 + 0.978325i \(0.566395\pi\)
\(644\) 4.65960 0.183614
\(645\) 2.38729 0.0939994
\(646\) 2.17062 0.0854018
\(647\) 49.9513 1.96379 0.981893 0.189435i \(-0.0606656\pi\)
0.981893 + 0.189435i \(0.0606656\pi\)
\(648\) −9.81204 −0.385453
\(649\) −7.78548 −0.305607
\(650\) 0.812933 0.0318859
\(651\) −94.2832 −3.69525
\(652\) 7.78522 0.304893
\(653\) −0.741876 −0.0290318 −0.0145159 0.999895i \(-0.504621\pi\)
−0.0145159 + 0.999895i \(0.504621\pi\)
\(654\) −37.6077 −1.47058
\(655\) 4.88758 0.190973
\(656\) 11.7137 0.457344
\(657\) −7.94810 −0.310085
\(658\) 31.6378 1.23337
\(659\) 1.03186 0.0401955 0.0200978 0.999798i \(-0.493602\pi\)
0.0200978 + 0.999798i \(0.493602\pi\)
\(660\) −2.38729 −0.0929251
\(661\) 17.8340 0.693661 0.346831 0.937928i \(-0.387258\pi\)
0.346831 + 0.937928i \(0.387258\pi\)
\(662\) −9.13065 −0.354873
\(663\) −10.3811 −0.403167
\(664\) −14.2689 −0.553742
\(665\) −1.59285 −0.0617681
\(666\) 16.5569 0.641567
\(667\) 2.21555 0.0857863
\(668\) −23.0156 −0.890502
\(669\) 25.1105 0.970829
\(670\) −1.05981 −0.0409439
\(671\) −11.1613 −0.430876
\(672\) 9.37084 0.361488
\(673\) −20.3742 −0.785369 −0.392684 0.919673i \(-0.628453\pi\)
−0.392684 + 0.919673i \(0.628453\pi\)
\(674\) 29.1566 1.12307
\(675\) −0.718217 −0.0276442
\(676\) −12.3391 −0.474582
\(677\) −10.7885 −0.414638 −0.207319 0.978273i \(-0.566474\pi\)
−0.207319 + 0.978273i \(0.566474\pi\)
\(678\) 11.5455 0.443402
\(679\) 13.9206 0.534223
\(680\) −5.34911 −0.205129
\(681\) −42.6679 −1.63504
\(682\) 10.0613 0.385269
\(683\) −33.0968 −1.26641 −0.633207 0.773982i \(-0.718262\pi\)
−0.633207 + 0.773982i \(0.718262\pi\)
\(684\) −1.09529 −0.0418794
\(685\) −15.7894 −0.603284
\(686\) 5.52688 0.211017
\(687\) 31.3392 1.19567
\(688\) 1.00000 0.0381246
\(689\) 7.51667 0.286362
\(690\) 2.83387 0.107884
\(691\) 25.0195 0.951788 0.475894 0.879503i \(-0.342125\pi\)
0.475894 + 0.879503i \(0.342125\pi\)
\(692\) 4.79082 0.182119
\(693\) −10.5950 −0.402470
\(694\) 3.01791 0.114558
\(695\) −14.0825 −0.534181
\(696\) 4.45565 0.168891
\(697\) −62.6581 −2.37334
\(698\) 5.69395 0.215519
\(699\) −57.8274 −2.18723
\(700\) 3.92530 0.148363
\(701\) −12.9498 −0.489109 −0.244554 0.969636i \(-0.578642\pi\)
−0.244554 + 0.969636i \(0.578642\pi\)
\(702\) −0.583862 −0.0220365
\(703\) −2.48916 −0.0938806
\(704\) −1.00000 −0.0376889
\(705\) 19.2415 0.724676
\(706\) −22.5135 −0.847306
\(707\) −46.7467 −1.75809
\(708\) 18.5862 0.698512
\(709\) −1.17477 −0.0441195 −0.0220598 0.999757i \(-0.507022\pi\)
−0.0220598 + 0.999757i \(0.507022\pi\)
\(710\) −11.7969 −0.442730
\(711\) −21.1161 −0.791915
\(712\) 0.276107 0.0103475
\(713\) −11.9435 −0.447287
\(714\) −50.1257 −1.87591
\(715\) −0.812933 −0.0304020
\(716\) 12.9298 0.483211
\(717\) 16.4363 0.613824
\(718\) 23.1603 0.864334
\(719\) −15.5216 −0.578857 −0.289428 0.957200i \(-0.593465\pi\)
−0.289428 + 0.957200i \(0.593465\pi\)
\(720\) 2.69915 0.100591
\(721\) −64.4880 −2.40166
\(722\) −18.8353 −0.700979
\(723\) 67.1664 2.49795
\(724\) −0.164956 −0.00613053
\(725\) 1.86640 0.0693165
\(726\) 2.38729 0.0886006
\(727\) 26.1274 0.969011 0.484505 0.874788i \(-0.339000\pi\)
0.484505 + 0.874788i \(0.339000\pi\)
\(728\) 3.19101 0.118267
\(729\) −21.3404 −0.790385
\(730\) −2.94467 −0.108987
\(731\) −5.34911 −0.197844
\(732\) 26.6452 0.984833
\(733\) 48.5419 1.79294 0.896468 0.443109i \(-0.146124\pi\)
0.896468 + 0.443109i \(0.146124\pi\)
\(734\) 10.8593 0.400824
\(735\) 20.0724 0.740380
\(736\) 1.18707 0.0437559
\(737\) 1.05981 0.0390385
\(738\) 31.6171 1.16384
\(739\) −7.99208 −0.293994 −0.146997 0.989137i \(-0.546961\pi\)
−0.146997 + 0.989137i \(0.546961\pi\)
\(740\) 6.13412 0.225495
\(741\) −0.787520 −0.0289303
\(742\) 36.2948 1.33242
\(743\) 37.4068 1.37232 0.686161 0.727450i \(-0.259295\pi\)
0.686161 + 0.727450i \(0.259295\pi\)
\(744\) −24.0193 −0.880592
\(745\) 5.70949 0.209180
\(746\) −18.9180 −0.692636
\(747\) −38.5140 −1.40915
\(748\) 5.34911 0.195583
\(749\) 32.6976 1.19474
\(750\) 2.38729 0.0871715
\(751\) 42.9305 1.56656 0.783278 0.621672i \(-0.213546\pi\)
0.783278 + 0.621672i \(0.213546\pi\)
\(752\) 8.05997 0.293917
\(753\) 6.96133 0.253685
\(754\) 1.51726 0.0552554
\(755\) −6.67469 −0.242917
\(756\) −2.81922 −0.102534
\(757\) −12.6484 −0.459714 −0.229857 0.973224i \(-0.573826\pi\)
−0.229857 + 0.973224i \(0.573826\pi\)
\(758\) −5.27705 −0.191671
\(759\) −2.83387 −0.102863
\(760\) −0.405790 −0.0147196
\(761\) 7.52832 0.272901 0.136451 0.990647i \(-0.456430\pi\)
0.136451 + 0.990647i \(0.456430\pi\)
\(762\) 24.2230 0.877507
\(763\) −61.8366 −2.23863
\(764\) −25.0988 −0.908042
\(765\) −14.4381 −0.522009
\(766\) −36.4918 −1.31850
\(767\) 6.32908 0.228530
\(768\) 2.38729 0.0861439
\(769\) −32.9311 −1.18753 −0.593763 0.804640i \(-0.702358\pi\)
−0.593763 + 0.804640i \(0.702358\pi\)
\(770\) −3.92530 −0.141458
\(771\) −54.1450 −1.94999
\(772\) 8.07002 0.290446
\(773\) −35.8391 −1.28904 −0.644521 0.764587i \(-0.722943\pi\)
−0.644521 + 0.764587i \(0.722943\pi\)
\(774\) 2.69915 0.0970189
\(775\) −10.0613 −0.361414
\(776\) 3.54637 0.127307
\(777\) 57.4818 2.06215
\(778\) 4.06976 0.145908
\(779\) −4.75332 −0.170305
\(780\) 1.94071 0.0694884
\(781\) 11.7969 0.422127
\(782\) −6.34975 −0.227067
\(783\) −1.34048 −0.0479049
\(784\) 8.40801 0.300286
\(785\) −20.2095 −0.721309
\(786\) 11.6681 0.416186
\(787\) −40.5948 −1.44705 −0.723525 0.690299i \(-0.757479\pi\)
−0.723525 + 0.690299i \(0.757479\pi\)
\(788\) −18.0918 −0.644493
\(789\) −74.0826 −2.63741
\(790\) −7.82323 −0.278338
\(791\) 18.9837 0.674982
\(792\) −2.69915 −0.0959101
\(793\) 9.07336 0.322204
\(794\) 7.75558 0.275235
\(795\) 22.0737 0.782875
\(796\) 9.19769 0.326003
\(797\) 34.1345 1.20911 0.604554 0.796565i \(-0.293352\pi\)
0.604554 + 0.796565i \(0.293352\pi\)
\(798\) −3.80259 −0.134610
\(799\) −43.1137 −1.52525
\(800\) 1.00000 0.0353553
\(801\) 0.745254 0.0263322
\(802\) 12.4546 0.439787
\(803\) 2.94467 0.103915
\(804\) −2.53006 −0.0892285
\(805\) 4.65960 0.164229
\(806\) −8.17920 −0.288100
\(807\) −41.8978 −1.47487
\(808\) −11.9091 −0.418960
\(809\) −5.99334 −0.210715 −0.105357 0.994434i \(-0.533599\pi\)
−0.105357 + 0.994434i \(0.533599\pi\)
\(810\) −9.81204 −0.344760
\(811\) 37.2917 1.30949 0.654744 0.755851i \(-0.272776\pi\)
0.654744 + 0.755851i \(0.272776\pi\)
\(812\) 7.32620 0.257099
\(813\) 51.0551 1.79058
\(814\) −6.13412 −0.215001
\(815\) 7.78522 0.272704
\(816\) −12.7699 −0.447035
\(817\) −0.405790 −0.0141968
\(818\) −19.2547 −0.673224
\(819\) 8.61301 0.300963
\(820\) 11.7137 0.409061
\(821\) 20.2387 0.706337 0.353169 0.935560i \(-0.385104\pi\)
0.353169 + 0.935560i \(0.385104\pi\)
\(822\) −37.6940 −1.31473
\(823\) 35.4228 1.23476 0.617381 0.786664i \(-0.288194\pi\)
0.617381 + 0.786664i \(0.288194\pi\)
\(824\) −16.4288 −0.572324
\(825\) −2.38729 −0.0831147
\(826\) 30.5604 1.06333
\(827\) −36.7247 −1.27704 −0.638521 0.769605i \(-0.720453\pi\)
−0.638521 + 0.769605i \(0.720453\pi\)
\(828\) 3.20407 0.111349
\(829\) 1.07736 0.0374183 0.0187092 0.999825i \(-0.494044\pi\)
0.0187092 + 0.999825i \(0.494044\pi\)
\(830\) −14.2689 −0.495282
\(831\) 69.7475 2.41951
\(832\) 0.812933 0.0281834
\(833\) −44.9754 −1.55831
\(834\) −33.6191 −1.16413
\(835\) −23.0156 −0.796489
\(836\) 0.405790 0.0140345
\(837\) 7.22623 0.249775
\(838\) −28.1001 −0.970702
\(839\) 14.4935 0.500371 0.250186 0.968198i \(-0.419508\pi\)
0.250186 + 0.968198i \(0.419508\pi\)
\(840\) 9.37084 0.323325
\(841\) −25.5165 −0.879881
\(842\) 16.8136 0.579434
\(843\) 48.5277 1.67138
\(844\) 2.78371 0.0958191
\(845\) −12.3391 −0.424479
\(846\) 21.7551 0.747954
\(847\) 3.92530 0.134875
\(848\) 9.24636 0.317521
\(849\) 71.6076 2.45757
\(850\) −5.34911 −0.183473
\(851\) 7.28161 0.249610
\(852\) −28.1626 −0.964836
\(853\) 10.4133 0.356545 0.178273 0.983981i \(-0.442949\pi\)
0.178273 + 0.983981i \(0.442949\pi\)
\(854\) 43.8113 1.49919
\(855\) −1.09529 −0.0374581
\(856\) 8.32995 0.284712
\(857\) −17.7157 −0.605158 −0.302579 0.953124i \(-0.597848\pi\)
−0.302579 + 0.953124i \(0.597848\pi\)
\(858\) −1.94071 −0.0662546
\(859\) 14.2764 0.487104 0.243552 0.969888i \(-0.421687\pi\)
0.243552 + 0.969888i \(0.421687\pi\)
\(860\) 1.00000 0.0340997
\(861\) 109.767 3.74086
\(862\) −16.5619 −0.564101
\(863\) 19.0979 0.650101 0.325051 0.945697i \(-0.394619\pi\)
0.325051 + 0.945697i \(0.394619\pi\)
\(864\) −0.718217 −0.0244342
\(865\) 4.79082 0.162893
\(866\) −24.0005 −0.815571
\(867\) 27.7236 0.941544
\(868\) −39.4938 −1.34051
\(869\) 7.82323 0.265385
\(870\) 4.45565 0.151061
\(871\) −0.861552 −0.0291926
\(872\) −15.7533 −0.533475
\(873\) 9.57218 0.323969
\(874\) −0.481700 −0.0162937
\(875\) 3.92530 0.132699
\(876\) −7.02977 −0.237514
\(877\) 1.36115 0.0459627 0.0229813 0.999736i \(-0.492684\pi\)
0.0229813 + 0.999736i \(0.492684\pi\)
\(878\) 16.7666 0.565847
\(879\) −47.4006 −1.59878
\(880\) −1.00000 −0.0337100
\(881\) −21.8139 −0.734927 −0.367464 0.930038i \(-0.619774\pi\)
−0.367464 + 0.930038i \(0.619774\pi\)
\(882\) 22.6945 0.764163
\(883\) 9.99369 0.336315 0.168157 0.985760i \(-0.446218\pi\)
0.168157 + 0.985760i \(0.446218\pi\)
\(884\) −4.34847 −0.146255
\(885\) 18.5862 0.624768
\(886\) −7.53930 −0.253288
\(887\) 4.23285 0.142125 0.0710626 0.997472i \(-0.477361\pi\)
0.0710626 + 0.997472i \(0.477361\pi\)
\(888\) 14.6439 0.491417
\(889\) 39.8287 1.33581
\(890\) 0.276107 0.00925512
\(891\) 9.81204 0.328716
\(892\) 10.5184 0.352183
\(893\) −3.27066 −0.109448
\(894\) 13.6302 0.455862
\(895\) 12.9298 0.432197
\(896\) 3.92530 0.131135
\(897\) 2.30375 0.0769199
\(898\) −29.5577 −0.986354
\(899\) −18.7785 −0.626299
\(900\) 2.69915 0.0899717
\(901\) −49.4598 −1.64775
\(902\) −11.7137 −0.390025
\(903\) 9.37084 0.311842
\(904\) 4.83624 0.160851
\(905\) −0.164956 −0.00548331
\(906\) −15.9344 −0.529385
\(907\) −4.74007 −0.157391 −0.0786957 0.996899i \(-0.525076\pi\)
−0.0786957 + 0.996899i \(0.525076\pi\)
\(908\) −17.8730 −0.593135
\(909\) −32.1444 −1.06616
\(910\) 3.19101 0.105781
\(911\) 2.72992 0.0904464 0.0452232 0.998977i \(-0.485600\pi\)
0.0452232 + 0.998977i \(0.485600\pi\)
\(912\) −0.968738 −0.0320781
\(913\) 14.2689 0.472233
\(914\) 33.4690 1.10705
\(915\) 26.6452 0.880862
\(916\) 13.1275 0.433746
\(917\) 19.1852 0.633552
\(918\) 3.84182 0.126799
\(919\) −14.3248 −0.472531 −0.236265 0.971689i \(-0.575923\pi\)
−0.236265 + 0.971689i \(0.575923\pi\)
\(920\) 1.18707 0.0391364
\(921\) 26.6234 0.877270
\(922\) 1.75000 0.0576331
\(923\) −9.59010 −0.315662
\(924\) −9.37084 −0.308278
\(925\) 6.13412 0.201688
\(926\) −5.58904 −0.183667
\(927\) −44.3437 −1.45644
\(928\) 1.86640 0.0612677
\(929\) −3.43268 −0.112623 −0.0563113 0.998413i \(-0.517934\pi\)
−0.0563113 + 0.998413i \(0.517934\pi\)
\(930\) −24.0193 −0.787625
\(931\) −3.41189 −0.111820
\(932\) −24.2231 −0.793453
\(933\) −12.9629 −0.424385
\(934\) −8.21645 −0.268850
\(935\) 5.34911 0.174935
\(936\) 2.19423 0.0717206
\(937\) 44.7878 1.46315 0.731576 0.681760i \(-0.238785\pi\)
0.731576 + 0.681760i \(0.238785\pi\)
\(938\) −4.16006 −0.135831
\(939\) −14.0141 −0.457333
\(940\) 8.05997 0.262887
\(941\) −10.2556 −0.334322 −0.167161 0.985930i \(-0.553460\pi\)
−0.167161 + 0.985930i \(0.553460\pi\)
\(942\) −48.2460 −1.57194
\(943\) 13.9050 0.452808
\(944\) 7.78548 0.253396
\(945\) −2.81922 −0.0917092
\(946\) −1.00000 −0.0325128
\(947\) −31.1886 −1.01349 −0.506747 0.862095i \(-0.669152\pi\)
−0.506747 + 0.862095i \(0.669152\pi\)
\(948\) −18.6763 −0.606579
\(949\) −2.39382 −0.0777066
\(950\) −0.405790 −0.0131656
\(951\) 40.7233 1.32054
\(952\) −20.9969 −0.680513
\(953\) −24.6453 −0.798338 −0.399169 0.916877i \(-0.630701\pi\)
−0.399169 + 0.916877i \(0.630701\pi\)
\(954\) 24.9573 0.808023
\(955\) −25.0988 −0.812178
\(956\) 6.88492 0.222674
\(957\) −4.45565 −0.144031
\(958\) −20.6013 −0.665598
\(959\) −61.9784 −2.00139
\(960\) 2.38729 0.0770494
\(961\) 70.2307 2.26550
\(962\) 4.98663 0.160775
\(963\) 22.4838 0.724530
\(964\) 28.1350 0.906168
\(965\) 8.07002 0.259783
\(966\) 11.1238 0.357903
\(967\) 28.7288 0.923855 0.461927 0.886918i \(-0.347158\pi\)
0.461927 + 0.886918i \(0.347158\pi\)
\(968\) 1.00000 0.0321412
\(969\) 5.18189 0.166466
\(970\) 3.54637 0.113867
\(971\) 43.6728 1.40153 0.700763 0.713394i \(-0.252843\pi\)
0.700763 + 0.713394i \(0.252843\pi\)
\(972\) −21.2695 −0.682220
\(973\) −55.2782 −1.77214
\(974\) 12.5620 0.402513
\(975\) 1.94071 0.0621524
\(976\) 11.1613 0.357263
\(977\) 56.1895 1.79766 0.898831 0.438296i \(-0.144418\pi\)
0.898831 + 0.438296i \(0.144418\pi\)
\(978\) 18.5856 0.594301
\(979\) −0.276107 −0.00882441
\(980\) 8.40801 0.268584
\(981\) −42.5206 −1.35758
\(982\) −15.5086 −0.494901
\(983\) −18.5707 −0.592313 −0.296157 0.955139i \(-0.595705\pi\)
−0.296157 + 0.955139i \(0.595705\pi\)
\(984\) 27.9641 0.891462
\(985\) −18.0918 −0.576452
\(986\) −9.98360 −0.317943
\(987\) 75.5286 2.40410
\(988\) −0.329880 −0.0104949
\(989\) 1.18707 0.0377465
\(990\) −2.69915 −0.0857846
\(991\) −8.77508 −0.278750 −0.139375 0.990240i \(-0.544509\pi\)
−0.139375 + 0.990240i \(0.544509\pi\)
\(992\) −10.0613 −0.319448
\(993\) −21.7975 −0.691723
\(994\) −46.3065 −1.46875
\(995\) 9.19769 0.291586
\(996\) −34.0641 −1.07936
\(997\) 47.3802 1.50054 0.750272 0.661129i \(-0.229922\pi\)
0.750272 + 0.661129i \(0.229922\pi\)
\(998\) 18.3476 0.580782
\(999\) −4.40562 −0.139388
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 4730.2.a.be.1.9 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.be.1.9 12 1.1 even 1 trivial