Properties

Label 4730.2.a.be.1.8
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 12
CM no
Inner twists 1

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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 1.8
Root \(2.14541\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.14541 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.14541 q^{6} -4.86538 q^{7} +1.00000 q^{8} +1.60277 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.14541 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.14541 q^{6} -4.86538 q^{7} +1.00000 q^{8} +1.60277 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.14541 q^{12} +0.772928 q^{13} -4.86538 q^{14} +2.14541 q^{15} +1.00000 q^{16} +3.64772 q^{17} +1.60277 q^{18} +6.17757 q^{19} +1.00000 q^{20} -10.4382 q^{21} -1.00000 q^{22} +1.22707 q^{23} +2.14541 q^{24} +1.00000 q^{25} +0.772928 q^{26} -2.99763 q^{27} -4.86538 q^{28} +8.75395 q^{29} +2.14541 q^{30} -1.82359 q^{31} +1.00000 q^{32} -2.14541 q^{33} +3.64772 q^{34} -4.86538 q^{35} +1.60277 q^{36} +10.5210 q^{37} +6.17757 q^{38} +1.65824 q^{39} +1.00000 q^{40} +1.71235 q^{41} -10.4382 q^{42} +1.00000 q^{43} -1.00000 q^{44} +1.60277 q^{45} +1.22707 q^{46} -0.956221 q^{47} +2.14541 q^{48} +16.6719 q^{49} +1.00000 q^{50} +7.82585 q^{51} +0.772928 q^{52} +12.8969 q^{53} -2.99763 q^{54} -1.00000 q^{55} -4.86538 q^{56} +13.2534 q^{57} +8.75395 q^{58} -10.8365 q^{59} +2.14541 q^{60} -1.28503 q^{61} -1.82359 q^{62} -7.79807 q^{63} +1.00000 q^{64} +0.772928 q^{65} -2.14541 q^{66} -13.6755 q^{67} +3.64772 q^{68} +2.63257 q^{69} -4.86538 q^{70} +6.58014 q^{71} +1.60277 q^{72} +12.0544 q^{73} +10.5210 q^{74} +2.14541 q^{75} +6.17757 q^{76} +4.86538 q^{77} +1.65824 q^{78} -2.42150 q^{79} +1.00000 q^{80} -11.2394 q^{81} +1.71235 q^{82} -4.52346 q^{83} -10.4382 q^{84} +3.64772 q^{85} +1.00000 q^{86} +18.7808 q^{87} -1.00000 q^{88} -3.19651 q^{89} +1.60277 q^{90} -3.76059 q^{91} +1.22707 q^{92} -3.91233 q^{93} -0.956221 q^{94} +6.17757 q^{95} +2.14541 q^{96} -9.25991 q^{97} +16.6719 q^{98} -1.60277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + O(q^{10}) \) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + 12q^{10} - 12q^{11} + 3q^{12} + 16q^{13} + 8q^{14} + 3q^{15} + 12q^{16} + 18q^{17} + 25q^{18} - 4q^{19} + 12q^{20} + 4q^{21} - 12q^{22} + 8q^{23} + 3q^{24} + 12q^{25} + 16q^{26} + 6q^{27} + 8q^{28} + 20q^{29} + 3q^{30} + 5q^{31} + 12q^{32} - 3q^{33} + 18q^{34} + 8q^{35} + 25q^{36} + 19q^{37} - 4q^{38} + 6q^{39} + 12q^{40} + 16q^{41} + 4q^{42} + 12q^{43} - 12q^{44} + 25q^{45} + 8q^{46} - q^{47} + 3q^{48} + 52q^{49} + 12q^{50} + q^{51} + 16q^{52} + 11q^{53} + 6q^{54} - 12q^{55} + 8q^{56} + 9q^{57} + 20q^{58} - 11q^{59} + 3q^{60} + 18q^{61} + 5q^{62} + 15q^{63} + 12q^{64} + 16q^{65} - 3q^{66} - 10q^{67} + 18q^{68} + 8q^{70} - 2q^{71} + 25q^{72} + 29q^{73} + 19q^{74} + 3q^{75} - 4q^{76} - 8q^{77} + 6q^{78} + 2q^{79} + 12q^{80} - 8q^{81} + 16q^{82} + 26q^{83} + 4q^{84} + 18q^{85} + 12q^{86} - 4q^{87} - 12q^{88} + 41q^{89} + 25q^{90} - 4q^{91} + 8q^{92} + 5q^{93} - q^{94} - 4q^{95} + 3q^{96} - 7q^{97} + 52q^{98} - 25q^{99} + O(q^{100}) \)

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
\(3\) 2.14541 1.23865 0.619325 0.785134i \(-0.287406\pi\)
0.619325 + 0.785134i \(0.287406\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.14541 0.875858
\(7\) −4.86538 −1.83894 −0.919470 0.393159i \(-0.871382\pi\)
−0.919470 + 0.393159i \(0.871382\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.60277 0.534255
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 2.14541 0.619325
\(13\) 0.772928 0.214372 0.107186 0.994239i \(-0.465816\pi\)
0.107186 + 0.994239i \(0.465816\pi\)
\(14\) −4.86538 −1.30033
\(15\) 2.14541 0.553941
\(16\) 1.00000 0.250000
\(17\) 3.64772 0.884703 0.442351 0.896842i \(-0.354144\pi\)
0.442351 + 0.896842i \(0.354144\pi\)
\(18\) 1.60277 0.377776
\(19\) 6.17757 1.41723 0.708616 0.705594i \(-0.249320\pi\)
0.708616 + 0.705594i \(0.249320\pi\)
\(20\) 1.00000 0.223607
\(21\) −10.4382 −2.27781
\(22\) −1.00000 −0.213201
\(23\) 1.22707 0.255862 0.127931 0.991783i \(-0.459166\pi\)
0.127931 + 0.991783i \(0.459166\pi\)
\(24\) 2.14541 0.437929
\(25\) 1.00000 0.200000
\(26\) 0.772928 0.151584
\(27\) −2.99763 −0.576895
\(28\) −4.86538 −0.919470
\(29\) 8.75395 1.62557 0.812784 0.582566i \(-0.197951\pi\)
0.812784 + 0.582566i \(0.197951\pi\)
\(30\) 2.14541 0.391696
\(31\) −1.82359 −0.327526 −0.163763 0.986500i \(-0.552363\pi\)
−0.163763 + 0.986500i \(0.552363\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.14541 −0.373467
\(34\) 3.64772 0.625579
\(35\) −4.86538 −0.822399
\(36\) 1.60277 0.267128
\(37\) 10.5210 1.72965 0.864824 0.502076i \(-0.167430\pi\)
0.864824 + 0.502076i \(0.167430\pi\)
\(38\) 6.17757 1.00213
\(39\) 1.65824 0.265532
\(40\) 1.00000 0.158114
\(41\) 1.71235 0.267425 0.133712 0.991020i \(-0.457310\pi\)
0.133712 + 0.991020i \(0.457310\pi\)
\(42\) −10.4382 −1.61065
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 1.60277 0.238926
\(46\) 1.22707 0.180922
\(47\) −0.956221 −0.139479 −0.0697396 0.997565i \(-0.522217\pi\)
−0.0697396 + 0.997565i \(0.522217\pi\)
\(48\) 2.14541 0.309663
\(49\) 16.6719 2.38170
\(50\) 1.00000 0.141421
\(51\) 7.82585 1.09584
\(52\) 0.772928 0.107186
\(53\) 12.8969 1.77153 0.885763 0.464138i \(-0.153636\pi\)
0.885763 + 0.464138i \(0.153636\pi\)
\(54\) −2.99763 −0.407926
\(55\) −1.00000 −0.134840
\(56\) −4.86538 −0.650164
\(57\) 13.2534 1.75546
\(58\) 8.75395 1.14945
\(59\) −10.8365 −1.41079 −0.705396 0.708813i \(-0.749231\pi\)
−0.705396 + 0.708813i \(0.749231\pi\)
\(60\) 2.14541 0.276971
\(61\) −1.28503 −0.164531 −0.0822654 0.996610i \(-0.526216\pi\)
−0.0822654 + 0.996610i \(0.526216\pi\)
\(62\) −1.82359 −0.231596
\(63\) −7.79807 −0.982464
\(64\) 1.00000 0.125000
\(65\) 0.772928 0.0958699
\(66\) −2.14541 −0.264081
\(67\) −13.6755 −1.67072 −0.835362 0.549700i \(-0.814742\pi\)
−0.835362 + 0.549700i \(0.814742\pi\)
\(68\) 3.64772 0.442351
\(69\) 2.63257 0.316924
\(70\) −4.86538 −0.581524
\(71\) 6.58014 0.780919 0.390459 0.920620i \(-0.372316\pi\)
0.390459 + 0.920620i \(0.372316\pi\)
\(72\) 1.60277 0.188888
\(73\) 12.0544 1.41086 0.705429 0.708781i \(-0.250754\pi\)
0.705429 + 0.708781i \(0.250754\pi\)
\(74\) 10.5210 1.22305
\(75\) 2.14541 0.247730
\(76\) 6.17757 0.708616
\(77\) 4.86538 0.554462
\(78\) 1.65824 0.187759
\(79\) −2.42150 −0.272440 −0.136220 0.990679i \(-0.543495\pi\)
−0.136220 + 0.990679i \(0.543495\pi\)
\(80\) 1.00000 0.111803
\(81\) −11.2394 −1.24883
\(82\) 1.71235 0.189098
\(83\) −4.52346 −0.496515 −0.248257 0.968694i \(-0.579858\pi\)
−0.248257 + 0.968694i \(0.579858\pi\)
\(84\) −10.4382 −1.13890
\(85\) 3.64772 0.395651
\(86\) 1.00000 0.107833
\(87\) 18.7808 2.01351
\(88\) −1.00000 −0.106600
\(89\) −3.19651 −0.338829 −0.169415 0.985545i \(-0.554188\pi\)
−0.169415 + 0.985545i \(0.554188\pi\)
\(90\) 1.60277 0.168946
\(91\) −3.76059 −0.394217
\(92\) 1.22707 0.127931
\(93\) −3.91233 −0.405690
\(94\) −0.956221 −0.0986267
\(95\) 6.17757 0.633806
\(96\) 2.14541 0.218965
\(97\) −9.25991 −0.940201 −0.470101 0.882613i \(-0.655782\pi\)
−0.470101 + 0.882613i \(0.655782\pi\)
\(98\) 16.6719 1.68412
\(99\) −1.60277 −0.161084
\(100\) 1.00000 0.100000
\(101\) −19.6223 −1.95249 −0.976247 0.216661i \(-0.930483\pi\)
−0.976247 + 0.216661i \(0.930483\pi\)
\(102\) 7.82585 0.774874
\(103\) −1.16390 −0.114682 −0.0573410 0.998355i \(-0.518262\pi\)
−0.0573410 + 0.998355i \(0.518262\pi\)
\(104\) 0.772928 0.0757918
\(105\) −10.4382 −1.01867
\(106\) 12.8969 1.25266
\(107\) 10.5763 1.02245 0.511227 0.859446i \(-0.329191\pi\)
0.511227 + 0.859446i \(0.329191\pi\)
\(108\) −2.99763 −0.288447
\(109\) 14.6577 1.40395 0.701977 0.712199i \(-0.252301\pi\)
0.701977 + 0.712199i \(0.252301\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 22.5719 2.14243
\(112\) −4.86538 −0.459735
\(113\) −5.58684 −0.525565 −0.262783 0.964855i \(-0.584640\pi\)
−0.262783 + 0.964855i \(0.584640\pi\)
\(114\) 13.2534 1.24130
\(115\) 1.22707 0.114425
\(116\) 8.75395 0.812784
\(117\) 1.23882 0.114529
\(118\) −10.8365 −0.997581
\(119\) −17.7476 −1.62692
\(120\) 2.14541 0.195848
\(121\) 1.00000 0.0909091
\(122\) −1.28503 −0.116341
\(123\) 3.67370 0.331246
\(124\) −1.82359 −0.163763
\(125\) 1.00000 0.0894427
\(126\) −7.79807 −0.694707
\(127\) −10.6963 −0.949147 −0.474574 0.880216i \(-0.657398\pi\)
−0.474574 + 0.880216i \(0.657398\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.14541 0.188892
\(130\) 0.772928 0.0677903
\(131\) 2.05074 0.179174 0.0895871 0.995979i \(-0.471445\pi\)
0.0895871 + 0.995979i \(0.471445\pi\)
\(132\) −2.14541 −0.186734
\(133\) −30.0562 −2.60621
\(134\) −13.6755 −1.18138
\(135\) −2.99763 −0.257995
\(136\) 3.64772 0.312790
\(137\) 18.6621 1.59441 0.797207 0.603706i \(-0.206310\pi\)
0.797207 + 0.603706i \(0.206310\pi\)
\(138\) 2.63257 0.224099
\(139\) 16.5332 1.40233 0.701163 0.713001i \(-0.252664\pi\)
0.701163 + 0.713001i \(0.252664\pi\)
\(140\) −4.86538 −0.411200
\(141\) −2.05148 −0.172766
\(142\) 6.58014 0.552193
\(143\) −0.772928 −0.0646355
\(144\) 1.60277 0.133564
\(145\) 8.75395 0.726976
\(146\) 12.0544 0.997627
\(147\) 35.7680 2.95010
\(148\) 10.5210 0.864824
\(149\) 14.4421 1.18315 0.591573 0.806252i \(-0.298507\pi\)
0.591573 + 0.806252i \(0.298507\pi\)
\(150\) 2.14541 0.175172
\(151\) 5.43320 0.442147 0.221074 0.975257i \(-0.429044\pi\)
0.221074 + 0.975257i \(0.429044\pi\)
\(152\) 6.17757 0.501067
\(153\) 5.84645 0.472657
\(154\) 4.86538 0.392063
\(155\) −1.82359 −0.146474
\(156\) 1.65824 0.132766
\(157\) 2.32998 0.185953 0.0929765 0.995668i \(-0.470362\pi\)
0.0929765 + 0.995668i \(0.470362\pi\)
\(158\) −2.42150 −0.192644
\(159\) 27.6691 2.19430
\(160\) 1.00000 0.0790569
\(161\) −5.97017 −0.470515
\(162\) −11.2394 −0.883054
\(163\) −1.87279 −0.146688 −0.0733441 0.997307i \(-0.523367\pi\)
−0.0733441 + 0.997307i \(0.523367\pi\)
\(164\) 1.71235 0.133712
\(165\) −2.14541 −0.167020
\(166\) −4.52346 −0.351089
\(167\) 12.7269 0.984834 0.492417 0.870359i \(-0.336113\pi\)
0.492417 + 0.870359i \(0.336113\pi\)
\(168\) −10.4382 −0.805326
\(169\) −12.4026 −0.954045
\(170\) 3.64772 0.279768
\(171\) 9.90121 0.757164
\(172\) 1.00000 0.0762493
\(173\) −18.8851 −1.43580 −0.717902 0.696144i \(-0.754898\pi\)
−0.717902 + 0.696144i \(0.754898\pi\)
\(174\) 18.7808 1.42377
\(175\) −4.86538 −0.367788
\(176\) −1.00000 −0.0753778
\(177\) −23.2487 −1.74748
\(178\) −3.19651 −0.239589
\(179\) −5.52325 −0.412827 −0.206414 0.978465i \(-0.566179\pi\)
−0.206414 + 0.978465i \(0.566179\pi\)
\(180\) 1.60277 0.119463
\(181\) −12.7201 −0.945479 −0.472740 0.881202i \(-0.656735\pi\)
−0.472740 + 0.881202i \(0.656735\pi\)
\(182\) −3.76059 −0.278753
\(183\) −2.75690 −0.203796
\(184\) 1.22707 0.0904609
\(185\) 10.5210 0.773522
\(186\) −3.91233 −0.286866
\(187\) −3.64772 −0.266748
\(188\) −0.956221 −0.0697396
\(189\) 14.5846 1.06088
\(190\) 6.17757 0.448168
\(191\) 1.51319 0.109491 0.0547453 0.998500i \(-0.482565\pi\)
0.0547453 + 0.998500i \(0.482565\pi\)
\(192\) 2.14541 0.154831
\(193\) −0.480458 −0.0345842 −0.0172921 0.999850i \(-0.505505\pi\)
−0.0172921 + 0.999850i \(0.505505\pi\)
\(194\) −9.25991 −0.664823
\(195\) 1.65824 0.118749
\(196\) 16.6719 1.19085
\(197\) 25.3554 1.80650 0.903248 0.429118i \(-0.141176\pi\)
0.903248 + 0.429118i \(0.141176\pi\)
\(198\) −1.60277 −0.113904
\(199\) −22.0088 −1.56017 −0.780083 0.625676i \(-0.784823\pi\)
−0.780083 + 0.625676i \(0.784823\pi\)
\(200\) 1.00000 0.0707107
\(201\) −29.3394 −2.06944
\(202\) −19.6223 −1.38062
\(203\) −42.5913 −2.98932
\(204\) 7.82585 0.547919
\(205\) 1.71235 0.119596
\(206\) −1.16390 −0.0810924
\(207\) 1.96671 0.136696
\(208\) 0.772928 0.0535929
\(209\) −6.17757 −0.427312
\(210\) −10.4382 −0.720305
\(211\) −16.1348 −1.11076 −0.555382 0.831595i \(-0.687428\pi\)
−0.555382 + 0.831595i \(0.687428\pi\)
\(212\) 12.8969 0.885763
\(213\) 14.1171 0.967286
\(214\) 10.5763 0.722984
\(215\) 1.00000 0.0681994
\(216\) −2.99763 −0.203963
\(217\) 8.87244 0.602301
\(218\) 14.6577 0.992746
\(219\) 25.8615 1.74756
\(220\) −1.00000 −0.0674200
\(221\) 2.81943 0.189655
\(222\) 22.5719 1.51493
\(223\) 19.6717 1.31732 0.658658 0.752443i \(-0.271124\pi\)
0.658658 + 0.752443i \(0.271124\pi\)
\(224\) −4.86538 −0.325082
\(225\) 1.60277 0.106851
\(226\) −5.58684 −0.371631
\(227\) 7.76226 0.515200 0.257600 0.966252i \(-0.417068\pi\)
0.257600 + 0.966252i \(0.417068\pi\)
\(228\) 13.2534 0.877728
\(229\) −14.9929 −0.990759 −0.495380 0.868677i \(-0.664971\pi\)
−0.495380 + 0.868677i \(0.664971\pi\)
\(230\) 1.22707 0.0809107
\(231\) 10.4382 0.686784
\(232\) 8.75395 0.574725
\(233\) 7.01617 0.459644 0.229822 0.973233i \(-0.426186\pi\)
0.229822 + 0.973233i \(0.426186\pi\)
\(234\) 1.23882 0.0809844
\(235\) −0.956221 −0.0623770
\(236\) −10.8365 −0.705396
\(237\) −5.19510 −0.337458
\(238\) −17.7476 −1.15040
\(239\) −6.58603 −0.426015 −0.213007 0.977051i \(-0.568326\pi\)
−0.213007 + 0.977051i \(0.568326\pi\)
\(240\) 2.14541 0.138485
\(241\) −20.3260 −1.30931 −0.654656 0.755927i \(-0.727187\pi\)
−0.654656 + 0.755927i \(0.727187\pi\)
\(242\) 1.00000 0.0642824
\(243\) −15.1203 −0.969965
\(244\) −1.28503 −0.0822654
\(245\) 16.6719 1.06513
\(246\) 3.67370 0.234226
\(247\) 4.77482 0.303815
\(248\) −1.82359 −0.115798
\(249\) −9.70466 −0.615008
\(250\) 1.00000 0.0632456
\(251\) −3.62591 −0.228866 −0.114433 0.993431i \(-0.536505\pi\)
−0.114433 + 0.993431i \(0.536505\pi\)
\(252\) −7.79807 −0.491232
\(253\) −1.22707 −0.0771453
\(254\) −10.6963 −0.671148
\(255\) 7.82585 0.490074
\(256\) 1.00000 0.0625000
\(257\) 7.21242 0.449899 0.224949 0.974370i \(-0.427778\pi\)
0.224949 + 0.974370i \(0.427778\pi\)
\(258\) 2.14541 0.133567
\(259\) −51.1888 −3.18072
\(260\) 0.772928 0.0479350
\(261\) 14.0305 0.868468
\(262\) 2.05074 0.126695
\(263\) −18.5653 −1.14479 −0.572393 0.819979i \(-0.693985\pi\)
−0.572393 + 0.819979i \(0.693985\pi\)
\(264\) −2.14541 −0.132041
\(265\) 12.8969 0.792250
\(266\) −30.0562 −1.84287
\(267\) −6.85781 −0.419691
\(268\) −13.6755 −0.835362
\(269\) −23.5234 −1.43425 −0.717123 0.696947i \(-0.754541\pi\)
−0.717123 + 0.696947i \(0.754541\pi\)
\(270\) −2.99763 −0.182430
\(271\) 10.8571 0.659522 0.329761 0.944064i \(-0.393032\pi\)
0.329761 + 0.944064i \(0.393032\pi\)
\(272\) 3.64772 0.221176
\(273\) −8.06799 −0.488297
\(274\) 18.6621 1.12742
\(275\) −1.00000 −0.0603023
\(276\) 2.63257 0.158462
\(277\) 11.1316 0.668832 0.334416 0.942426i \(-0.391461\pi\)
0.334416 + 0.942426i \(0.391461\pi\)
\(278\) 16.5332 0.991595
\(279\) −2.92278 −0.174982
\(280\) −4.86538 −0.290762
\(281\) −7.18944 −0.428886 −0.214443 0.976737i \(-0.568794\pi\)
−0.214443 + 0.976737i \(0.568794\pi\)
\(282\) −2.05148 −0.122164
\(283\) −15.0195 −0.892817 −0.446408 0.894829i \(-0.647297\pi\)
−0.446408 + 0.894829i \(0.647297\pi\)
\(284\) 6.58014 0.390459
\(285\) 13.2534 0.785064
\(286\) −0.772928 −0.0457042
\(287\) −8.33126 −0.491779
\(288\) 1.60277 0.0944439
\(289\) −3.69411 −0.217301
\(290\) 8.75395 0.514050
\(291\) −19.8663 −1.16458
\(292\) 12.0544 0.705429
\(293\) −19.1081 −1.11631 −0.558154 0.829737i \(-0.688490\pi\)
−0.558154 + 0.829737i \(0.688490\pi\)
\(294\) 35.7680 2.08603
\(295\) −10.8365 −0.630926
\(296\) 10.5210 0.611523
\(297\) 2.99763 0.173940
\(298\) 14.4421 0.836610
\(299\) 0.948438 0.0548496
\(300\) 2.14541 0.123865
\(301\) −4.86538 −0.280436
\(302\) 5.43320 0.312645
\(303\) −42.0978 −2.41846
\(304\) 6.17757 0.354308
\(305\) −1.28503 −0.0735804
\(306\) 5.84645 0.334219
\(307\) −15.6944 −0.895729 −0.447865 0.894101i \(-0.647815\pi\)
−0.447865 + 0.894101i \(0.647815\pi\)
\(308\) 4.86538 0.277231
\(309\) −2.49703 −0.142051
\(310\) −1.82359 −0.103573
\(311\) −17.4073 −0.987077 −0.493538 0.869724i \(-0.664297\pi\)
−0.493538 + 0.869724i \(0.664297\pi\)
\(312\) 1.65824 0.0938796
\(313\) −5.94600 −0.336088 −0.168044 0.985780i \(-0.553745\pi\)
−0.168044 + 0.985780i \(0.553745\pi\)
\(314\) 2.32998 0.131489
\(315\) −7.79807 −0.439371
\(316\) −2.42150 −0.136220
\(317\) 10.1749 0.571477 0.285739 0.958308i \(-0.407761\pi\)
0.285739 + 0.958308i \(0.407761\pi\)
\(318\) 27.6691 1.55161
\(319\) −8.75395 −0.490127
\(320\) 1.00000 0.0559017
\(321\) 22.6906 1.26646
\(322\) −5.97017 −0.332705
\(323\) 22.5341 1.25383
\(324\) −11.2394 −0.624413
\(325\) 0.772928 0.0428743
\(326\) −1.87279 −0.103724
\(327\) 31.4467 1.73901
\(328\) 1.71235 0.0945490
\(329\) 4.65238 0.256494
\(330\) −2.14541 −0.118101
\(331\) 21.5396 1.18392 0.591961 0.805967i \(-0.298354\pi\)
0.591961 + 0.805967i \(0.298354\pi\)
\(332\) −4.52346 −0.248257
\(333\) 16.8628 0.924073
\(334\) 12.7269 0.696383
\(335\) −13.6755 −0.747171
\(336\) −10.4382 −0.569451
\(337\) −7.28531 −0.396856 −0.198428 0.980115i \(-0.563584\pi\)
−0.198428 + 0.980115i \(0.563584\pi\)
\(338\) −12.4026 −0.674612
\(339\) −11.9860 −0.650992
\(340\) 3.64772 0.197826
\(341\) 1.82359 0.0987527
\(342\) 9.90121 0.535396
\(343\) −47.0576 −2.54087
\(344\) 1.00000 0.0539164
\(345\) 2.63257 0.141733
\(346\) −18.8851 −1.01527
\(347\) −8.13671 −0.436802 −0.218401 0.975859i \(-0.570084\pi\)
−0.218401 + 0.975859i \(0.570084\pi\)
\(348\) 18.7808 1.00676
\(349\) −29.8617 −1.59846 −0.799229 0.601026i \(-0.794759\pi\)
−0.799229 + 0.601026i \(0.794759\pi\)
\(350\) −4.86538 −0.260065
\(351\) −2.31695 −0.123670
\(352\) −1.00000 −0.0533002
\(353\) 6.05373 0.322207 0.161104 0.986937i \(-0.448495\pi\)
0.161104 + 0.986937i \(0.448495\pi\)
\(354\) −23.2487 −1.23565
\(355\) 6.58014 0.349238
\(356\) −3.19651 −0.169415
\(357\) −38.0757 −2.01518
\(358\) −5.52325 −0.291913
\(359\) 20.3069 1.07176 0.535878 0.844296i \(-0.319981\pi\)
0.535878 + 0.844296i \(0.319981\pi\)
\(360\) 1.60277 0.0844732
\(361\) 19.1624 1.00855
\(362\) −12.7201 −0.668555
\(363\) 2.14541 0.112605
\(364\) −3.76059 −0.197108
\(365\) 12.0544 0.630955
\(366\) −2.75690 −0.144106
\(367\) −5.38172 −0.280924 −0.140462 0.990086i \(-0.544859\pi\)
−0.140462 + 0.990086i \(0.544859\pi\)
\(368\) 1.22707 0.0639655
\(369\) 2.74451 0.142873
\(370\) 10.5210 0.546962
\(371\) −62.7483 −3.25773
\(372\) −3.91233 −0.202845
\(373\) 32.0733 1.66069 0.830346 0.557248i \(-0.188143\pi\)
0.830346 + 0.557248i \(0.188143\pi\)
\(374\) −3.64772 −0.188619
\(375\) 2.14541 0.110788
\(376\) −0.956221 −0.0493134
\(377\) 6.76617 0.348476
\(378\) 14.5846 0.750152
\(379\) −25.8241 −1.32649 −0.663247 0.748400i \(-0.730822\pi\)
−0.663247 + 0.748400i \(0.730822\pi\)
\(380\) 6.17757 0.316903
\(381\) −22.9480 −1.17566
\(382\) 1.51319 0.0774215
\(383\) −19.1585 −0.978953 −0.489476 0.872017i \(-0.662812\pi\)
−0.489476 + 0.872017i \(0.662812\pi\)
\(384\) 2.14541 0.109482
\(385\) 4.86538 0.247963
\(386\) −0.480458 −0.0244547
\(387\) 1.60277 0.0814732
\(388\) −9.25991 −0.470101
\(389\) 19.0935 0.968077 0.484039 0.875047i \(-0.339169\pi\)
0.484039 + 0.875047i \(0.339169\pi\)
\(390\) 1.65824 0.0839685
\(391\) 4.47602 0.226362
\(392\) 16.6719 0.842059
\(393\) 4.39968 0.221934
\(394\) 25.3554 1.27739
\(395\) −2.42150 −0.121839
\(396\) −1.60277 −0.0805420
\(397\) 4.23712 0.212655 0.106327 0.994331i \(-0.466091\pi\)
0.106327 + 0.994331i \(0.466091\pi\)
\(398\) −22.0088 −1.10320
\(399\) −64.4829 −3.22818
\(400\) 1.00000 0.0500000
\(401\) −22.0131 −1.09928 −0.549642 0.835400i \(-0.685236\pi\)
−0.549642 + 0.835400i \(0.685236\pi\)
\(402\) −29.3394 −1.46332
\(403\) −1.40950 −0.0702123
\(404\) −19.6223 −0.976247
\(405\) −11.2394 −0.558492
\(406\) −42.5913 −2.11377
\(407\) −10.5210 −0.521508
\(408\) 7.82585 0.387437
\(409\) −16.4216 −0.811995 −0.405998 0.913874i \(-0.633076\pi\)
−0.405998 + 0.913874i \(0.633076\pi\)
\(410\) 1.71235 0.0845672
\(411\) 40.0379 1.97492
\(412\) −1.16390 −0.0573410
\(413\) 52.7237 2.59436
\(414\) 1.96671 0.0966585
\(415\) −4.52346 −0.222048
\(416\) 0.772928 0.0378959
\(417\) 35.4704 1.73699
\(418\) −6.17757 −0.302155
\(419\) 21.6506 1.05770 0.528851 0.848715i \(-0.322623\pi\)
0.528851 + 0.848715i \(0.322623\pi\)
\(420\) −10.4382 −0.509333
\(421\) −1.30156 −0.0634340 −0.0317170 0.999497i \(-0.510098\pi\)
−0.0317170 + 0.999497i \(0.510098\pi\)
\(422\) −16.1348 −0.785429
\(423\) −1.53260 −0.0745175
\(424\) 12.8969 0.626329
\(425\) 3.64772 0.176941
\(426\) 14.1171 0.683974
\(427\) 6.25214 0.302562
\(428\) 10.5763 0.511227
\(429\) −1.65824 −0.0800608
\(430\) 1.00000 0.0482243
\(431\) 24.6994 1.18973 0.594864 0.803827i \(-0.297206\pi\)
0.594864 + 0.803827i \(0.297206\pi\)
\(432\) −2.99763 −0.144224
\(433\) 2.38419 0.114577 0.0572885 0.998358i \(-0.481755\pi\)
0.0572885 + 0.998358i \(0.481755\pi\)
\(434\) 8.87244 0.425891
\(435\) 18.7808 0.900469
\(436\) 14.6577 0.701977
\(437\) 7.58033 0.362616
\(438\) 25.8615 1.23571
\(439\) 18.0871 0.863252 0.431626 0.902053i \(-0.357940\pi\)
0.431626 + 0.902053i \(0.357940\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 26.7212 1.27244
\(442\) 2.81943 0.134107
\(443\) −18.9713 −0.901352 −0.450676 0.892687i \(-0.648817\pi\)
−0.450676 + 0.892687i \(0.648817\pi\)
\(444\) 22.5719 1.07121
\(445\) −3.19651 −0.151529
\(446\) 19.6717 0.931483
\(447\) 30.9842 1.46550
\(448\) −4.86538 −0.229868
\(449\) −36.1825 −1.70756 −0.853779 0.520636i \(-0.825695\pi\)
−0.853779 + 0.520636i \(0.825695\pi\)
\(450\) 1.60277 0.0755551
\(451\) −1.71235 −0.0806316
\(452\) −5.58684 −0.262783
\(453\) 11.6564 0.547666
\(454\) 7.76226 0.364301
\(455\) −3.76059 −0.176299
\(456\) 13.2534 0.620648
\(457\) −40.0930 −1.87547 −0.937736 0.347349i \(-0.887082\pi\)
−0.937736 + 0.347349i \(0.887082\pi\)
\(458\) −14.9929 −0.700573
\(459\) −10.9345 −0.510381
\(460\) 1.22707 0.0572125
\(461\) 35.4116 1.64928 0.824641 0.565656i \(-0.191377\pi\)
0.824641 + 0.565656i \(0.191377\pi\)
\(462\) 10.4382 0.485630
\(463\) 26.9926 1.25445 0.627225 0.778838i \(-0.284191\pi\)
0.627225 + 0.778838i \(0.284191\pi\)
\(464\) 8.75395 0.406392
\(465\) −3.91233 −0.181430
\(466\) 7.01617 0.325018
\(467\) −24.0272 −1.11185 −0.555923 0.831234i \(-0.687635\pi\)
−0.555923 + 0.831234i \(0.687635\pi\)
\(468\) 1.23882 0.0572646
\(469\) 66.5363 3.07236
\(470\) −0.956221 −0.0441072
\(471\) 4.99876 0.230331
\(472\) −10.8365 −0.498791
\(473\) −1.00000 −0.0459800
\(474\) −5.19510 −0.238619
\(475\) 6.17757 0.283447
\(476\) −17.7476 −0.813458
\(477\) 20.6707 0.946447
\(478\) −6.58603 −0.301238
\(479\) −10.9421 −0.499960 −0.249980 0.968251i \(-0.580424\pi\)
−0.249980 + 0.968251i \(0.580424\pi\)
\(480\) 2.14541 0.0979239
\(481\) 8.13200 0.370787
\(482\) −20.3260 −0.925824
\(483\) −12.8084 −0.582804
\(484\) 1.00000 0.0454545
\(485\) −9.25991 −0.420471
\(486\) −15.1203 −0.685869
\(487\) −5.20402 −0.235817 −0.117908 0.993024i \(-0.537619\pi\)
−0.117908 + 0.993024i \(0.537619\pi\)
\(488\) −1.28503 −0.0581704
\(489\) −4.01789 −0.181695
\(490\) 16.6719 0.753161
\(491\) 13.6038 0.613931 0.306966 0.951721i \(-0.400686\pi\)
0.306966 + 0.951721i \(0.400686\pi\)
\(492\) 3.67370 0.165623
\(493\) 31.9320 1.43814
\(494\) 4.77482 0.214829
\(495\) −1.60277 −0.0720390
\(496\) −1.82359 −0.0818814
\(497\) −32.0149 −1.43606
\(498\) −9.70466 −0.434876
\(499\) 29.2689 1.31026 0.655129 0.755517i \(-0.272614\pi\)
0.655129 + 0.755517i \(0.272614\pi\)
\(500\) 1.00000 0.0447214
\(501\) 27.3043 1.21987
\(502\) −3.62591 −0.161832
\(503\) 34.2338 1.52641 0.763204 0.646157i \(-0.223625\pi\)
0.763204 + 0.646157i \(0.223625\pi\)
\(504\) −7.79807 −0.347354
\(505\) −19.6223 −0.873182
\(506\) −1.22707 −0.0545500
\(507\) −26.6086 −1.18173
\(508\) −10.6963 −0.474574
\(509\) −42.7379 −1.89432 −0.947162 0.320756i \(-0.896063\pi\)
−0.947162 + 0.320756i \(0.896063\pi\)
\(510\) 7.82585 0.346534
\(511\) −58.6491 −2.59448
\(512\) 1.00000 0.0441942
\(513\) −18.5181 −0.817594
\(514\) 7.21242 0.318126
\(515\) −1.16390 −0.0512874
\(516\) 2.14541 0.0944462
\(517\) 0.956221 0.0420546
\(518\) −51.1888 −2.24911
\(519\) −40.5161 −1.77846
\(520\) 0.772928 0.0338951
\(521\) −18.1284 −0.794219 −0.397109 0.917771i \(-0.629987\pi\)
−0.397109 + 0.917771i \(0.629987\pi\)
\(522\) 14.0305 0.614100
\(523\) −24.2328 −1.05963 −0.529813 0.848114i \(-0.677738\pi\)
−0.529813 + 0.848114i \(0.677738\pi\)
\(524\) 2.05074 0.0895871
\(525\) −10.4382 −0.455561
\(526\) −18.5653 −0.809486
\(527\) −6.65194 −0.289763
\(528\) −2.14541 −0.0933668
\(529\) −21.4943 −0.934535
\(530\) 12.8969 0.560205
\(531\) −17.3684 −0.753724
\(532\) −30.0562 −1.30310
\(533\) 1.32353 0.0573283
\(534\) −6.85781 −0.296767
\(535\) 10.5763 0.457255
\(536\) −13.6755 −0.590690
\(537\) −11.8496 −0.511349
\(538\) −23.5234 −1.01416
\(539\) −16.6719 −0.718111
\(540\) −2.99763 −0.128998
\(541\) −8.36896 −0.359810 −0.179905 0.983684i \(-0.557579\pi\)
−0.179905 + 0.983684i \(0.557579\pi\)
\(542\) 10.8571 0.466352
\(543\) −27.2898 −1.17112
\(544\) 3.64772 0.156395
\(545\) 14.6577 0.627867
\(546\) −8.06799 −0.345278
\(547\) 16.7353 0.715550 0.357775 0.933808i \(-0.383536\pi\)
0.357775 + 0.933808i \(0.383536\pi\)
\(548\) 18.6621 0.797207
\(549\) −2.05960 −0.0879014
\(550\) −1.00000 −0.0426401
\(551\) 54.0782 2.30381
\(552\) 2.63257 0.112050
\(553\) 11.7815 0.501001
\(554\) 11.1316 0.472935
\(555\) 22.5719 0.958123
\(556\) 16.5332 0.701163
\(557\) 7.35292 0.311553 0.155777 0.987792i \(-0.450212\pi\)
0.155777 + 0.987792i \(0.450212\pi\)
\(558\) −2.92278 −0.123731
\(559\) 0.772928 0.0326914
\(560\) −4.86538 −0.205600
\(561\) −7.82585 −0.330408
\(562\) −7.18944 −0.303268
\(563\) −9.88663 −0.416672 −0.208336 0.978057i \(-0.566805\pi\)
−0.208336 + 0.978057i \(0.566805\pi\)
\(564\) −2.05148 −0.0863830
\(565\) −5.58684 −0.235040
\(566\) −15.0195 −0.631317
\(567\) 54.6841 2.29652
\(568\) 6.58014 0.276097
\(569\) 46.3023 1.94110 0.970548 0.240909i \(-0.0774457\pi\)
0.970548 + 0.240909i \(0.0774457\pi\)
\(570\) 13.2534 0.555124
\(571\) −1.12415 −0.0470444 −0.0235222 0.999723i \(-0.507488\pi\)
−0.0235222 + 0.999723i \(0.507488\pi\)
\(572\) −0.772928 −0.0323177
\(573\) 3.24641 0.135621
\(574\) −8.33126 −0.347740
\(575\) 1.22707 0.0511724
\(576\) 1.60277 0.0667819
\(577\) −3.80465 −0.158390 −0.0791948 0.996859i \(-0.525235\pi\)
−0.0791948 + 0.996859i \(0.525235\pi\)
\(578\) −3.69411 −0.153655
\(579\) −1.03078 −0.0428377
\(580\) 8.75395 0.363488
\(581\) 22.0084 0.913061
\(582\) −19.8663 −0.823483
\(583\) −12.8969 −0.534135
\(584\) 12.0544 0.498814
\(585\) 1.23882 0.0512190
\(586\) −19.1081 −0.789349
\(587\) 13.2532 0.547019 0.273510 0.961869i \(-0.411815\pi\)
0.273510 + 0.961869i \(0.411815\pi\)
\(588\) 35.7680 1.47505
\(589\) −11.2653 −0.464180
\(590\) −10.8365 −0.446132
\(591\) 54.3976 2.23762
\(592\) 10.5210 0.432412
\(593\) 24.5509 1.00819 0.504093 0.863650i \(-0.331827\pi\)
0.504093 + 0.863650i \(0.331827\pi\)
\(594\) 2.99763 0.122994
\(595\) −17.7476 −0.727579
\(596\) 14.4421 0.591573
\(597\) −47.2179 −1.93250
\(598\) 0.948438 0.0387845
\(599\) −12.6605 −0.517295 −0.258648 0.965972i \(-0.583277\pi\)
−0.258648 + 0.965972i \(0.583277\pi\)
\(600\) 2.14541 0.0875858
\(601\) 7.39922 0.301820 0.150910 0.988547i \(-0.451780\pi\)
0.150910 + 0.988547i \(0.451780\pi\)
\(602\) −4.86538 −0.198298
\(603\) −21.9186 −0.892594
\(604\) 5.43320 0.221074
\(605\) 1.00000 0.0406558
\(606\) −42.0978 −1.71011
\(607\) −11.2387 −0.456163 −0.228081 0.973642i \(-0.573245\pi\)
−0.228081 + 0.973642i \(0.573245\pi\)
\(608\) 6.17757 0.250534
\(609\) −91.3756 −3.70273
\(610\) −1.28503 −0.0520292
\(611\) −0.739090 −0.0299004
\(612\) 5.84645 0.236329
\(613\) −5.91644 −0.238963 −0.119481 0.992836i \(-0.538123\pi\)
−0.119481 + 0.992836i \(0.538123\pi\)
\(614\) −15.6944 −0.633376
\(615\) 3.67370 0.148138
\(616\) 4.86538 0.196032
\(617\) −41.8120 −1.68329 −0.841644 0.540033i \(-0.818412\pi\)
−0.841644 + 0.540033i \(0.818412\pi\)
\(618\) −2.49703 −0.100445
\(619\) 17.9307 0.720697 0.360349 0.932818i \(-0.382658\pi\)
0.360349 + 0.932818i \(0.382658\pi\)
\(620\) −1.82359 −0.0732370
\(621\) −3.67831 −0.147606
\(622\) −17.4073 −0.697969
\(623\) 15.5522 0.623087
\(624\) 1.65824 0.0663829
\(625\) 1.00000 0.0400000
\(626\) −5.94600 −0.237650
\(627\) −13.2534 −0.529290
\(628\) 2.32998 0.0929765
\(629\) 38.3778 1.53022
\(630\) −7.79807 −0.310682
\(631\) −5.71163 −0.227377 −0.113688 0.993516i \(-0.536267\pi\)
−0.113688 + 0.993516i \(0.536267\pi\)
\(632\) −2.42150 −0.0963221
\(633\) −34.6156 −1.37585
\(634\) 10.1749 0.404096
\(635\) −10.6963 −0.424471
\(636\) 27.6691 1.09715
\(637\) 12.8862 0.510570
\(638\) −8.75395 −0.346572
\(639\) 10.5464 0.417210
\(640\) 1.00000 0.0395285
\(641\) −21.7733 −0.859994 −0.429997 0.902830i \(-0.641485\pi\)
−0.429997 + 0.902830i \(0.641485\pi\)
\(642\) 22.6906 0.895525
\(643\) 31.6164 1.24683 0.623414 0.781892i \(-0.285745\pi\)
0.623414 + 0.781892i \(0.285745\pi\)
\(644\) −5.97017 −0.235258
\(645\) 2.14541 0.0844753
\(646\) 22.5341 0.886592
\(647\) 33.3862 1.31255 0.656273 0.754523i \(-0.272132\pi\)
0.656273 + 0.754523i \(0.272132\pi\)
\(648\) −11.2394 −0.441527
\(649\) 10.8365 0.425370
\(650\) 0.772928 0.0303167
\(651\) 19.0350 0.746040
\(652\) −1.87279 −0.0733441
\(653\) 8.49962 0.332616 0.166308 0.986074i \(-0.446815\pi\)
0.166308 + 0.986074i \(0.446815\pi\)
\(654\) 31.4467 1.22967
\(655\) 2.05074 0.0801292
\(656\) 1.71235 0.0668562
\(657\) 19.3204 0.753759
\(658\) 4.65238 0.181369
\(659\) −31.0343 −1.20892 −0.604462 0.796634i \(-0.706612\pi\)
−0.604462 + 0.796634i \(0.706612\pi\)
\(660\) −2.14541 −0.0835098
\(661\) 3.33299 0.129638 0.0648191 0.997897i \(-0.479353\pi\)
0.0648191 + 0.997897i \(0.479353\pi\)
\(662\) 21.5396 0.837159
\(663\) 6.04882 0.234917
\(664\) −4.52346 −0.175544
\(665\) −30.0562 −1.16553
\(666\) 16.8628 0.653419
\(667\) 10.7417 0.415921
\(668\) 12.7269 0.492417
\(669\) 42.2038 1.63169
\(670\) −13.6755 −0.528329
\(671\) 1.28503 0.0496079
\(672\) −10.4382 −0.402663
\(673\) −34.9119 −1.34575 −0.672877 0.739755i \(-0.734942\pi\)
−0.672877 + 0.739755i \(0.734942\pi\)
\(674\) −7.28531 −0.280620
\(675\) −2.99763 −0.115379
\(676\) −12.4026 −0.477022
\(677\) 18.6517 0.716842 0.358421 0.933560i \(-0.383315\pi\)
0.358421 + 0.933560i \(0.383315\pi\)
\(678\) −11.9860 −0.460321
\(679\) 45.0530 1.72897
\(680\) 3.64772 0.139884
\(681\) 16.6532 0.638152
\(682\) 1.82359 0.0698287
\(683\) −10.8277 −0.414310 −0.207155 0.978308i \(-0.566421\pi\)
−0.207155 + 0.978308i \(0.566421\pi\)
\(684\) 9.90121 0.378582
\(685\) 18.6621 0.713044
\(686\) −47.0576 −1.79667
\(687\) −32.1659 −1.22720
\(688\) 1.00000 0.0381246
\(689\) 9.96838 0.379765
\(690\) 2.63257 0.100220
\(691\) 11.5977 0.441197 0.220598 0.975365i \(-0.429199\pi\)
0.220598 + 0.975365i \(0.429199\pi\)
\(692\) −18.8851 −0.717902
\(693\) 7.79807 0.296224
\(694\) −8.13671 −0.308865
\(695\) 16.5332 0.627140
\(696\) 18.7808 0.711883
\(697\) 6.24620 0.236592
\(698\) −29.8617 −1.13028
\(699\) 15.0525 0.569339
\(700\) −4.86538 −0.183894
\(701\) 44.7904 1.69171 0.845855 0.533412i \(-0.179091\pi\)
0.845855 + 0.533412i \(0.179091\pi\)
\(702\) −2.31695 −0.0874478
\(703\) 64.9945 2.45131
\(704\) −1.00000 −0.0376889
\(705\) −2.05148 −0.0772633
\(706\) 6.05373 0.227835
\(707\) 95.4700 3.59052
\(708\) −23.2487 −0.873740
\(709\) 12.7391 0.478426 0.239213 0.970967i \(-0.423110\pi\)
0.239213 + 0.970967i \(0.423110\pi\)
\(710\) 6.58014 0.246948
\(711\) −3.88110 −0.145553
\(712\) −3.19651 −0.119794
\(713\) −2.23767 −0.0838015
\(714\) −38.0757 −1.42495
\(715\) −0.772928 −0.0289059
\(716\) −5.52325 −0.206414
\(717\) −14.1297 −0.527684
\(718\) 20.3069 0.757846
\(719\) 13.8359 0.515992 0.257996 0.966146i \(-0.416938\pi\)
0.257996 + 0.966146i \(0.416938\pi\)
\(720\) 1.60277 0.0597316
\(721\) 5.66279 0.210893
\(722\) 19.1624 0.713152
\(723\) −43.6075 −1.62178
\(724\) −12.7201 −0.472740
\(725\) 8.75395 0.325113
\(726\) 2.14541 0.0796235
\(727\) −0.669168 −0.0248181 −0.0124090 0.999923i \(-0.503950\pi\)
−0.0124090 + 0.999923i \(0.503950\pi\)
\(728\) −3.76059 −0.139377
\(729\) 1.27922 0.0473786
\(730\) 12.0544 0.446153
\(731\) 3.64772 0.134916
\(732\) −2.75690 −0.101898
\(733\) −48.5314 −1.79255 −0.896273 0.443502i \(-0.853736\pi\)
−0.896273 + 0.443502i \(0.853736\pi\)
\(734\) −5.38172 −0.198643
\(735\) 35.7680 1.31932
\(736\) 1.22707 0.0452305
\(737\) 13.6755 0.503742
\(738\) 2.74451 0.101027
\(739\) −10.9944 −0.404434 −0.202217 0.979341i \(-0.564815\pi\)
−0.202217 + 0.979341i \(0.564815\pi\)
\(740\) 10.5210 0.386761
\(741\) 10.2439 0.376320
\(742\) −62.7483 −2.30356
\(743\) 42.3391 1.55327 0.776635 0.629951i \(-0.216925\pi\)
0.776635 + 0.629951i \(0.216925\pi\)
\(744\) −3.91233 −0.143433
\(745\) 14.4421 0.529119
\(746\) 32.0733 1.17429
\(747\) −7.25006 −0.265266
\(748\) −3.64772 −0.133374
\(749\) −51.4579 −1.88023
\(750\) 2.14541 0.0783391
\(751\) 8.53646 0.311500 0.155750 0.987797i \(-0.450221\pi\)
0.155750 + 0.987797i \(0.450221\pi\)
\(752\) −0.956221 −0.0348698
\(753\) −7.77906 −0.283485
\(754\) 6.76617 0.246409
\(755\) 5.43320 0.197734
\(756\) 14.5846 0.530438
\(757\) 11.3872 0.413876 0.206938 0.978354i \(-0.433650\pi\)
0.206938 + 0.978354i \(0.433650\pi\)
\(758\) −25.8241 −0.937973
\(759\) −2.63257 −0.0955561
\(760\) 6.17757 0.224084
\(761\) 41.8331 1.51645 0.758225 0.651993i \(-0.226067\pi\)
0.758225 + 0.651993i \(0.226067\pi\)
\(762\) −22.9480 −0.831318
\(763\) −71.3153 −2.58179
\(764\) 1.51319 0.0547453
\(765\) 5.84645 0.211379
\(766\) −19.1585 −0.692224
\(767\) −8.37584 −0.302434
\(768\) 2.14541 0.0774157
\(769\) 44.4811 1.60403 0.802015 0.597303i \(-0.203761\pi\)
0.802015 + 0.597303i \(0.203761\pi\)
\(770\) 4.86538 0.175336
\(771\) 15.4736 0.557267
\(772\) −0.480458 −0.0172921
\(773\) 6.19609 0.222858 0.111429 0.993772i \(-0.464457\pi\)
0.111429 + 0.993772i \(0.464457\pi\)
\(774\) 1.60277 0.0576103
\(775\) −1.82359 −0.0655052
\(776\) −9.25991 −0.332411
\(777\) −109.821 −3.93980
\(778\) 19.0935 0.684534
\(779\) 10.5782 0.379003
\(780\) 1.65824 0.0593747
\(781\) −6.58014 −0.235456
\(782\) 4.47602 0.160062
\(783\) −26.2411 −0.937781
\(784\) 16.6719 0.595426
\(785\) 2.32998 0.0831607
\(786\) 4.39968 0.156931
\(787\) −29.7402 −1.06012 −0.530062 0.847959i \(-0.677831\pi\)
−0.530062 + 0.847959i \(0.677831\pi\)
\(788\) 25.3554 0.903248
\(789\) −39.8301 −1.41799
\(790\) −2.42150 −0.0861531
\(791\) 27.1821 0.966484
\(792\) −1.60277 −0.0569518
\(793\) −0.993233 −0.0352707
\(794\) 4.23712 0.150370
\(795\) 27.6691 0.981321
\(796\) −22.0088 −0.780083
\(797\) 1.14408 0.0405254 0.0202627 0.999795i \(-0.493550\pi\)
0.0202627 + 0.999795i \(0.493550\pi\)
\(798\) −64.4829 −2.28267
\(799\) −3.48803 −0.123398
\(800\) 1.00000 0.0353553
\(801\) −5.12326 −0.181021
\(802\) −22.0131 −0.777311
\(803\) −12.0544 −0.425390
\(804\) −29.3394 −1.03472
\(805\) −5.97017 −0.210421
\(806\) −1.40950 −0.0496476
\(807\) −50.4672 −1.77653
\(808\) −19.6223 −0.690311
\(809\) −15.6089 −0.548781 −0.274390 0.961618i \(-0.588476\pi\)
−0.274390 + 0.961618i \(0.588476\pi\)
\(810\) −11.2394 −0.394914
\(811\) −28.4191 −0.997928 −0.498964 0.866623i \(-0.666286\pi\)
−0.498964 + 0.866623i \(0.666286\pi\)
\(812\) −42.5913 −1.49466
\(813\) 23.2929 0.816917
\(814\) −10.5210 −0.368762
\(815\) −1.87279 −0.0656009
\(816\) 7.82585 0.273959
\(817\) 6.17757 0.216126
\(818\) −16.4216 −0.574167
\(819\) −6.02735 −0.210613
\(820\) 1.71235 0.0597980
\(821\) 22.0333 0.768966 0.384483 0.923132i \(-0.374380\pi\)
0.384483 + 0.923132i \(0.374380\pi\)
\(822\) 40.0379 1.39648
\(823\) −3.16142 −0.110200 −0.0551002 0.998481i \(-0.517548\pi\)
−0.0551002 + 0.998481i \(0.517548\pi\)
\(824\) −1.16390 −0.0405462
\(825\) −2.14541 −0.0746934
\(826\) 52.7237 1.83449
\(827\) 31.7908 1.10547 0.552737 0.833355i \(-0.313583\pi\)
0.552737 + 0.833355i \(0.313583\pi\)
\(828\) 1.96671 0.0683479
\(829\) 10.0201 0.348014 0.174007 0.984744i \(-0.444328\pi\)
0.174007 + 0.984744i \(0.444328\pi\)
\(830\) −4.52346 −0.157012
\(831\) 23.8817 0.828449
\(832\) 0.772928 0.0267965
\(833\) 60.8146 2.10710
\(834\) 35.4704 1.22824
\(835\) 12.7269 0.440431
\(836\) −6.17757 −0.213656
\(837\) 5.46644 0.188948
\(838\) 21.6506 0.747908
\(839\) 1.53509 0.0529973 0.0264986 0.999649i \(-0.491564\pi\)
0.0264986 + 0.999649i \(0.491564\pi\)
\(840\) −10.4382 −0.360153
\(841\) 47.6316 1.64247
\(842\) −1.30156 −0.0448546
\(843\) −15.4243 −0.531240
\(844\) −16.1348 −0.555382
\(845\) −12.4026 −0.426662
\(846\) −1.53260 −0.0526919
\(847\) −4.86538 −0.167176
\(848\) 12.8969 0.442881
\(849\) −32.2229 −1.10589
\(850\) 3.64772 0.125116
\(851\) 12.9101 0.442551
\(852\) 14.1171 0.483643
\(853\) −20.2927 −0.694808 −0.347404 0.937716i \(-0.612937\pi\)
−0.347404 + 0.937716i \(0.612937\pi\)
\(854\) 6.25214 0.213944
\(855\) 9.90121 0.338614
\(856\) 10.5763 0.361492
\(857\) −54.4394 −1.85961 −0.929807 0.368048i \(-0.880026\pi\)
−0.929807 + 0.368048i \(0.880026\pi\)
\(858\) −1.65824 −0.0566115
\(859\) 33.0740 1.12847 0.564236 0.825614i \(-0.309171\pi\)
0.564236 + 0.825614i \(0.309171\pi\)
\(860\) 1.00000 0.0340997
\(861\) −17.8739 −0.609142
\(862\) 24.6994 0.841264
\(863\) 11.0252 0.375304 0.187652 0.982236i \(-0.439912\pi\)
0.187652 + 0.982236i \(0.439912\pi\)
\(864\) −2.99763 −0.101982
\(865\) −18.8851 −0.642111
\(866\) 2.38419 0.0810182
\(867\) −7.92537 −0.269160
\(868\) 8.87244 0.301150
\(869\) 2.42150 0.0821438
\(870\) 18.7808 0.636728
\(871\) −10.5702 −0.358156
\(872\) 14.6577 0.496373
\(873\) −14.8415 −0.502308
\(874\) 7.58033 0.256408
\(875\) −4.86538 −0.164480
\(876\) 25.8615 0.873780
\(877\) −8.09361 −0.273302 −0.136651 0.990619i \(-0.543634\pi\)
−0.136651 + 0.990619i \(0.543634\pi\)
\(878\) 18.0871 0.610411
\(879\) −40.9947 −1.38272
\(880\) −1.00000 −0.0337100
\(881\) −24.5156 −0.825951 −0.412975 0.910742i \(-0.635510\pi\)
−0.412975 + 0.910742i \(0.635510\pi\)
\(882\) 26.7212 0.899750
\(883\) −57.6361 −1.93961 −0.969805 0.243882i \(-0.921579\pi\)
−0.969805 + 0.243882i \(0.921579\pi\)
\(884\) 2.81943 0.0948276
\(885\) −23.2487 −0.781497
\(886\) −18.9713 −0.637352
\(887\) 30.9153 1.03804 0.519018 0.854764i \(-0.326298\pi\)
0.519018 + 0.854764i \(0.326298\pi\)
\(888\) 22.5719 0.757463
\(889\) 52.0418 1.74543
\(890\) −3.19651 −0.107147
\(891\) 11.2394 0.376535
\(892\) 19.6717 0.658658
\(893\) −5.90713 −0.197675
\(894\) 30.9842 1.03627
\(895\) −5.52325 −0.184622
\(896\) −4.86538 −0.162541
\(897\) 2.03479 0.0679395
\(898\) −36.1825 −1.20743
\(899\) −15.9636 −0.532415
\(900\) 1.60277 0.0534255
\(901\) 47.0443 1.56727
\(902\) −1.71235 −0.0570152
\(903\) −10.4382 −0.347362
\(904\) −5.58684 −0.185815
\(905\) −12.7201 −0.422831
\(906\) 11.6564 0.387259
\(907\) 3.77120 0.125221 0.0626104 0.998038i \(-0.480057\pi\)
0.0626104 + 0.998038i \(0.480057\pi\)
\(908\) 7.76226 0.257600
\(909\) −31.4500 −1.04313
\(910\) −3.76059 −0.124662
\(911\) −42.2902 −1.40114 −0.700569 0.713585i \(-0.747070\pi\)
−0.700569 + 0.713585i \(0.747070\pi\)
\(912\) 13.2534 0.438864
\(913\) 4.52346 0.149705
\(914\) −40.0930 −1.32616
\(915\) −2.75690 −0.0911404
\(916\) −14.9929 −0.495380
\(917\) −9.97764 −0.329491
\(918\) −10.9345 −0.360894
\(919\) −59.6592 −1.96797 −0.983987 0.178241i \(-0.942959\pi\)
−0.983987 + 0.178241i \(0.942959\pi\)
\(920\) 1.22707 0.0404554
\(921\) −33.6709 −1.10950
\(922\) 35.4116 1.16622
\(923\) 5.08598 0.167407
\(924\) 10.4382 0.343392
\(925\) 10.5210 0.345929
\(926\) 26.9926 0.887030
\(927\) −1.86545 −0.0612695
\(928\) 8.75395 0.287362
\(929\) −4.27682 −0.140318 −0.0701589 0.997536i \(-0.522351\pi\)
−0.0701589 + 0.997536i \(0.522351\pi\)
\(930\) −3.91233 −0.128290
\(931\) 102.992 3.37543
\(932\) 7.01617 0.229822
\(933\) −37.3457 −1.22264
\(934\) −24.0272 −0.786194
\(935\) −3.64772 −0.119293
\(936\) 1.23882 0.0404922
\(937\) 35.6833 1.16572 0.582862 0.812571i \(-0.301933\pi\)
0.582862 + 0.812571i \(0.301933\pi\)
\(938\) 66.5363 2.17249
\(939\) −12.7566 −0.416295
\(940\) −0.956221 −0.0311885
\(941\) 57.1676 1.86361 0.931805 0.362959i \(-0.118233\pi\)
0.931805 + 0.362959i \(0.118233\pi\)
\(942\) 4.99876 0.162868
\(943\) 2.10118 0.0684239
\(944\) −10.8365 −0.352698
\(945\) 14.5846 0.474438
\(946\) −1.00000 −0.0325128
\(947\) 27.0875 0.880225 0.440112 0.897943i \(-0.354939\pi\)
0.440112 + 0.897943i \(0.354939\pi\)
\(948\) −5.19510 −0.168729
\(949\) 9.31717 0.302448
\(950\) 6.17757 0.200427
\(951\) 21.8292 0.707861
\(952\) −17.7476 −0.575202
\(953\) −16.3172 −0.528566 −0.264283 0.964445i \(-0.585135\pi\)
−0.264283 + 0.964445i \(0.585135\pi\)
\(954\) 20.6707 0.669239
\(955\) 1.51319 0.0489657
\(956\) −6.58603 −0.213007
\(957\) −18.7808 −0.607096
\(958\) −10.9421 −0.353525
\(959\) −90.7984 −2.93203
\(960\) 2.14541 0.0692427
\(961\) −27.6745 −0.892727
\(962\) 8.13200 0.262186
\(963\) 16.9514 0.546252
\(964\) −20.3260 −0.654656
\(965\) −0.480458 −0.0154665
\(966\) −12.8084 −0.412105
\(967\) 40.3368 1.29714 0.648572 0.761154i \(-0.275367\pi\)
0.648572 + 0.761154i \(0.275367\pi\)
\(968\) 1.00000 0.0321412
\(969\) 48.3448 1.55306
\(970\) −9.25991 −0.297318
\(971\) −57.4012 −1.84209 −0.921046 0.389453i \(-0.872664\pi\)
−0.921046 + 0.389453i \(0.872664\pi\)
\(972\) −15.1203 −0.484983
\(973\) −80.4403 −2.57880
\(974\) −5.20402 −0.166748
\(975\) 1.65824 0.0531063
\(976\) −1.28503 −0.0411327
\(977\) 10.4168 0.333264 0.166632 0.986019i \(-0.446711\pi\)
0.166632 + 0.986019i \(0.446711\pi\)
\(978\) −4.01789 −0.128478
\(979\) 3.19651 0.102161
\(980\) 16.6719 0.532565
\(981\) 23.4929 0.750070
\(982\) 13.6038 0.434115
\(983\) 25.3456 0.808398 0.404199 0.914671i \(-0.367550\pi\)
0.404199 + 0.914671i \(0.367550\pi\)
\(984\) 3.67370 0.117113
\(985\) 25.3554 0.807890
\(986\) 31.9320 1.01692
\(987\) 9.98124 0.317707
\(988\) 4.77482 0.151907
\(989\) 1.22707 0.0390186
\(990\) −1.60277 −0.0509393
\(991\) −57.8547 −1.83781 −0.918907 0.394474i \(-0.870927\pi\)
−0.918907 + 0.394474i \(0.870927\pi\)
\(992\) −1.82359 −0.0578989
\(993\) 46.2111 1.46646
\(994\) −32.0149 −1.01545
\(995\) −22.0088 −0.697727
\(996\) −9.70466 −0.307504
\(997\) 40.9105 1.29565 0.647824 0.761790i \(-0.275679\pi\)
0.647824 + 0.761790i \(0.275679\pi\)
\(998\) 29.2689 0.926492
\(999\) −31.5382 −0.997824
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.1.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.be.1.8 12 1.1 even 1 trivial