Properties

Label 6025.2.a.f.1.3
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.31056073.1
Defining polynomial: \(x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + x^{3} - 9 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 241)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.27758\) of defining polynomial
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.277577 q^{2} +0.494846 q^{3} -1.92295 q^{4} -0.137358 q^{6} -1.36627 q^{7} +1.08892 q^{8} -2.75513 q^{9} +O(q^{10})\) \(q-0.277577 q^{2} +0.494846 q^{3} -1.92295 q^{4} -0.137358 q^{6} -1.36627 q^{7} +1.08892 q^{8} -2.75513 q^{9} -4.69806 q^{11} -0.951564 q^{12} +0.0431968 q^{13} +0.379244 q^{14} +3.54364 q^{16} +7.31430 q^{17} +0.764761 q^{18} -0.697489 q^{19} -0.676090 q^{21} +1.30407 q^{22} -1.41195 q^{23} +0.538848 q^{24} -0.0119904 q^{26} -2.84790 q^{27} +2.62726 q^{28} +8.30334 q^{29} +3.39655 q^{31} -3.16148 q^{32} -2.32481 q^{33} -2.03028 q^{34} +5.29798 q^{36} -7.15948 q^{37} +0.193607 q^{38} +0.0213757 q^{39} +5.45541 q^{41} +0.187667 q^{42} +11.7568 q^{43} +9.03414 q^{44} +0.391925 q^{46} +5.24836 q^{47} +1.75356 q^{48} -5.13332 q^{49} +3.61945 q^{51} -0.0830653 q^{52} +8.57769 q^{53} +0.790512 q^{54} -1.48776 q^{56} -0.345149 q^{57} -2.30482 q^{58} -12.9925 q^{59} +10.1636 q^{61} -0.942804 q^{62} +3.76423 q^{63} -6.20973 q^{64} +0.645315 q^{66} -10.1259 q^{67} -14.0650 q^{68} -0.698697 q^{69} +1.86703 q^{71} -3.00012 q^{72} -6.47826 q^{73} +1.98731 q^{74} +1.34124 q^{76} +6.41880 q^{77} -0.00593342 q^{78} -12.9436 q^{79} +6.85611 q^{81} -1.51430 q^{82} +2.32915 q^{83} +1.30009 q^{84} -3.26342 q^{86} +4.10887 q^{87} -5.11582 q^{88} -14.5180 q^{89} -0.0590183 q^{91} +2.71511 q^{92} +1.68077 q^{93} -1.45682 q^{94} -1.56444 q^{96} +2.23725 q^{97} +1.42489 q^{98} +12.9438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} - 18q^{11} - q^{12} + q^{13} - 6q^{14} + 4q^{16} + 2q^{17} - 8q^{18} - 6q^{19} - 2q^{21} - 10q^{22} + 22q^{23} - 3q^{24} + 8q^{26} - 3q^{27} - 9q^{28} - 16q^{29} - 18q^{31} + 6q^{32} - 4q^{33} + 11q^{34} - 7q^{36} - 8q^{37} - 16q^{38} - 9q^{39} - 15q^{41} - 19q^{42} - 14q^{43} - 4q^{44} + 11q^{46} + 10q^{47} - 31q^{48} + 6q^{49} + 13q^{51} - 27q^{52} - 15q^{53} + 16q^{54} + 13q^{56} - 14q^{57} - 17q^{58} - 18q^{59} + 4q^{61} - 13q^{62} + 16q^{63} + 2q^{64} + 16q^{66} - 18q^{67} + 15q^{68} + 26q^{69} - 50q^{71} - 30q^{72} + 10q^{74} - 20q^{76} - 17q^{77} + 32q^{78} - 15q^{79} - 9q^{81} - 45q^{82} + 24q^{83} + 6q^{84} - 23q^{86} - 12q^{87} - 8q^{88} - 13q^{89} - 12q^{91} + 10q^{92} - 14q^{93} - 32q^{94} - 15q^{96} - q^{97} - 9q^{98} - 20q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.277577 −0.196277 −0.0981383 0.995173i \(-0.531289\pi\)
−0.0981383 + 0.995173i \(0.531289\pi\)
\(3\) 0.494846 0.285699 0.142850 0.989744i \(-0.454373\pi\)
0.142850 + 0.989744i \(0.454373\pi\)
\(4\) −1.92295 −0.961475
\(5\) 0 0
\(6\) −0.137358 −0.0560761
\(7\) −1.36627 −0.516400 −0.258200 0.966092i \(-0.583129\pi\)
−0.258200 + 0.966092i \(0.583129\pi\)
\(8\) 1.08892 0.384992
\(9\) −2.75513 −0.918376
\(10\) 0 0
\(11\) −4.69806 −1.41652 −0.708259 0.705952i \(-0.750519\pi\)
−0.708259 + 0.705952i \(0.750519\pi\)
\(12\) −0.951564 −0.274693
\(13\) 0.0431968 0.0119806 0.00599032 0.999982i \(-0.498093\pi\)
0.00599032 + 0.999982i \(0.498093\pi\)
\(14\) 0.379244 0.101357
\(15\) 0 0
\(16\) 3.54364 0.885911
\(17\) 7.31430 1.77398 0.886989 0.461790i \(-0.152793\pi\)
0.886989 + 0.461790i \(0.152793\pi\)
\(18\) 0.764761 0.180256
\(19\) −0.697489 −0.160015 −0.0800075 0.996794i \(-0.525494\pi\)
−0.0800075 + 0.996794i \(0.525494\pi\)
\(20\) 0 0
\(21\) −0.676090 −0.147535
\(22\) 1.30407 0.278030
\(23\) −1.41195 −0.294412 −0.147206 0.989106i \(-0.547028\pi\)
−0.147206 + 0.989106i \(0.547028\pi\)
\(24\) 0.538848 0.109992
\(25\) 0 0
\(26\) −0.0119904 −0.00235152
\(27\) −2.84790 −0.548078
\(28\) 2.62726 0.496506
\(29\) 8.30334 1.54189 0.770946 0.636901i \(-0.219784\pi\)
0.770946 + 0.636901i \(0.219784\pi\)
\(30\) 0 0
\(31\) 3.39655 0.610038 0.305019 0.952346i \(-0.401337\pi\)
0.305019 + 0.952346i \(0.401337\pi\)
\(32\) −3.16148 −0.558875
\(33\) −2.32481 −0.404698
\(34\) −2.03028 −0.348191
\(35\) 0 0
\(36\) 5.29798 0.882996
\(37\) −7.15948 −1.17701 −0.588506 0.808493i \(-0.700284\pi\)
−0.588506 + 0.808493i \(0.700284\pi\)
\(38\) 0.193607 0.0314072
\(39\) 0.0213757 0.00342286
\(40\) 0 0
\(41\) 5.45541 0.851992 0.425996 0.904725i \(-0.359924\pi\)
0.425996 + 0.904725i \(0.359924\pi\)
\(42\) 0.187667 0.0289577
\(43\) 11.7568 1.79290 0.896448 0.443149i \(-0.146139\pi\)
0.896448 + 0.443149i \(0.146139\pi\)
\(44\) 9.03414 1.36195
\(45\) 0 0
\(46\) 0.391925 0.0577862
\(47\) 5.24836 0.765551 0.382776 0.923841i \(-0.374968\pi\)
0.382776 + 0.923841i \(0.374968\pi\)
\(48\) 1.75356 0.253104
\(49\) −5.13332 −0.733331
\(50\) 0 0
\(51\) 3.61945 0.506824
\(52\) −0.0830653 −0.0115191
\(53\) 8.57769 1.17824 0.589118 0.808047i \(-0.299475\pi\)
0.589118 + 0.808047i \(0.299475\pi\)
\(54\) 0.790512 0.107575
\(55\) 0 0
\(56\) −1.48776 −0.198810
\(57\) −0.345149 −0.0457162
\(58\) −2.30482 −0.302637
\(59\) −12.9925 −1.69148 −0.845738 0.533598i \(-0.820840\pi\)
−0.845738 + 0.533598i \(0.820840\pi\)
\(60\) 0 0
\(61\) 10.1636 1.30132 0.650658 0.759371i \(-0.274493\pi\)
0.650658 + 0.759371i \(0.274493\pi\)
\(62\) −0.942804 −0.119736
\(63\) 3.76423 0.474249
\(64\) −6.20973 −0.776216
\(65\) 0 0
\(66\) 0.645315 0.0794328
\(67\) −10.1259 −1.23707 −0.618536 0.785757i \(-0.712274\pi\)
−0.618536 + 0.785757i \(0.712274\pi\)
\(68\) −14.0650 −1.70564
\(69\) −0.698697 −0.0841132
\(70\) 0 0
\(71\) 1.86703 0.221576 0.110788 0.993844i \(-0.464663\pi\)
0.110788 + 0.993844i \(0.464663\pi\)
\(72\) −3.00012 −0.353567
\(73\) −6.47826 −0.758223 −0.379111 0.925351i \(-0.623770\pi\)
−0.379111 + 0.925351i \(0.623770\pi\)
\(74\) 1.98731 0.231020
\(75\) 0 0
\(76\) 1.34124 0.153850
\(77\) 6.41880 0.731490
\(78\) −0.00593342 −0.000671827 0
\(79\) −12.9436 −1.45627 −0.728136 0.685432i \(-0.759613\pi\)
−0.728136 + 0.685432i \(0.759613\pi\)
\(80\) 0 0
\(81\) 6.85611 0.761790
\(82\) −1.51430 −0.167226
\(83\) 2.32915 0.255657 0.127829 0.991796i \(-0.459199\pi\)
0.127829 + 0.991796i \(0.459199\pi\)
\(84\) 1.30009 0.141851
\(85\) 0 0
\(86\) −3.26342 −0.351904
\(87\) 4.10887 0.440517
\(88\) −5.11582 −0.545348
\(89\) −14.5180 −1.53890 −0.769450 0.638707i \(-0.779470\pi\)
−0.769450 + 0.638707i \(0.779470\pi\)
\(90\) 0 0
\(91\) −0.0590183 −0.00618680
\(92\) 2.71511 0.283070
\(93\) 1.68077 0.174287
\(94\) −1.45682 −0.150260
\(95\) 0 0
\(96\) −1.56444 −0.159670
\(97\) 2.23725 0.227158 0.113579 0.993529i \(-0.463769\pi\)
0.113579 + 0.993529i \(0.463769\pi\)
\(98\) 1.42489 0.143936
\(99\) 12.9438 1.30090
\(100\) 0 0
\(101\) −4.01607 −0.399614 −0.199807 0.979835i \(-0.564031\pi\)
−0.199807 + 0.979835i \(0.564031\pi\)
\(102\) −1.00468 −0.0994778
\(103\) 5.25187 0.517482 0.258741 0.965947i \(-0.416692\pi\)
0.258741 + 0.965947i \(0.416692\pi\)
\(104\) 0.0470379 0.00461245
\(105\) 0 0
\(106\) −2.38097 −0.231260
\(107\) −5.60385 −0.541745 −0.270873 0.962615i \(-0.587312\pi\)
−0.270873 + 0.962615i \(0.587312\pi\)
\(108\) 5.47637 0.526964
\(109\) −4.77557 −0.457416 −0.228708 0.973495i \(-0.573450\pi\)
−0.228708 + 0.973495i \(0.573450\pi\)
\(110\) 0 0
\(111\) −3.54284 −0.336271
\(112\) −4.84155 −0.457484
\(113\) 12.6186 1.18706 0.593531 0.804811i \(-0.297733\pi\)
0.593531 + 0.804811i \(0.297733\pi\)
\(114\) 0.0958056 0.00897301
\(115\) 0 0
\(116\) −15.9669 −1.48249
\(117\) −0.119013 −0.0110027
\(118\) 3.60642 0.331997
\(119\) −9.99327 −0.916082
\(120\) 0 0
\(121\) 11.0718 1.00653
\(122\) −2.82118 −0.255418
\(123\) 2.69959 0.243413
\(124\) −6.53139 −0.586536
\(125\) 0 0
\(126\) −1.04487 −0.0930840
\(127\) −0.427651 −0.0379479 −0.0189740 0.999820i \(-0.506040\pi\)
−0.0189740 + 0.999820i \(0.506040\pi\)
\(128\) 8.04663 0.711229
\(129\) 5.81780 0.512229
\(130\) 0 0
\(131\) −13.3633 −1.16756 −0.583780 0.811912i \(-0.698427\pi\)
−0.583780 + 0.811912i \(0.698427\pi\)
\(132\) 4.47050 0.389107
\(133\) 0.952955 0.0826317
\(134\) 2.81071 0.242808
\(135\) 0 0
\(136\) 7.96470 0.682967
\(137\) −11.2702 −0.962874 −0.481437 0.876481i \(-0.659885\pi\)
−0.481437 + 0.876481i \(0.659885\pi\)
\(138\) 0.193942 0.0165095
\(139\) −0.927184 −0.0786427 −0.0393214 0.999227i \(-0.512520\pi\)
−0.0393214 + 0.999227i \(0.512520\pi\)
\(140\) 0 0
\(141\) 2.59713 0.218717
\(142\) −0.518245 −0.0434902
\(143\) −0.202941 −0.0169708
\(144\) −9.76319 −0.813599
\(145\) 0 0
\(146\) 1.79822 0.148821
\(147\) −2.54020 −0.209512
\(148\) 13.7673 1.13167
\(149\) 12.8757 1.05481 0.527407 0.849612i \(-0.323164\pi\)
0.527407 + 0.849612i \(0.323164\pi\)
\(150\) 0 0
\(151\) −21.2436 −1.72878 −0.864390 0.502823i \(-0.832295\pi\)
−0.864390 + 0.502823i \(0.832295\pi\)
\(152\) −0.759511 −0.0616045
\(153\) −20.1518 −1.62918
\(154\) −1.78171 −0.143574
\(155\) 0 0
\(156\) −0.0411045 −0.00329099
\(157\) −17.1798 −1.37110 −0.685550 0.728026i \(-0.740438\pi\)
−0.685550 + 0.728026i \(0.740438\pi\)
\(158\) 3.59286 0.285832
\(159\) 4.24463 0.336621
\(160\) 0 0
\(161\) 1.92910 0.152034
\(162\) −1.90310 −0.149522
\(163\) −11.1081 −0.870055 −0.435028 0.900417i \(-0.643261\pi\)
−0.435028 + 0.900417i \(0.643261\pi\)
\(164\) −10.4905 −0.819170
\(165\) 0 0
\(166\) −0.646519 −0.0501796
\(167\) 22.3791 1.73174 0.865872 0.500266i \(-0.166764\pi\)
0.865872 + 0.500266i \(0.166764\pi\)
\(168\) −0.736209 −0.0567998
\(169\) −12.9981 −0.999856
\(170\) 0 0
\(171\) 1.92167 0.146954
\(172\) −22.6078 −1.72383
\(173\) −4.16100 −0.316355 −0.158178 0.987411i \(-0.550562\pi\)
−0.158178 + 0.987411i \(0.550562\pi\)
\(174\) −1.14053 −0.0864633
\(175\) 0 0
\(176\) −16.6482 −1.25491
\(177\) −6.42927 −0.483254
\(178\) 4.02985 0.302050
\(179\) −5.79009 −0.432772 −0.216386 0.976308i \(-0.569427\pi\)
−0.216386 + 0.976308i \(0.569427\pi\)
\(180\) 0 0
\(181\) 17.4917 1.30015 0.650076 0.759869i \(-0.274737\pi\)
0.650076 + 0.759869i \(0.274737\pi\)
\(182\) 0.0163821 0.00121432
\(183\) 5.02941 0.371785
\(184\) −1.53750 −0.113346
\(185\) 0 0
\(186\) −0.466542 −0.0342085
\(187\) −34.3630 −2.51287
\(188\) −10.0923 −0.736059
\(189\) 3.89099 0.283028
\(190\) 0 0
\(191\) −21.6074 −1.56346 −0.781728 0.623620i \(-0.785661\pi\)
−0.781728 + 0.623620i \(0.785661\pi\)
\(192\) −3.07286 −0.221764
\(193\) −2.30886 −0.166195 −0.0830977 0.996541i \(-0.526481\pi\)
−0.0830977 + 0.996541i \(0.526481\pi\)
\(194\) −0.621008 −0.0445858
\(195\) 0 0
\(196\) 9.87112 0.705080
\(197\) −1.91876 −0.136706 −0.0683531 0.997661i \(-0.521774\pi\)
−0.0683531 + 0.997661i \(0.521774\pi\)
\(198\) −3.59289 −0.255336
\(199\) 21.2430 1.50588 0.752938 0.658091i \(-0.228636\pi\)
0.752938 + 0.658091i \(0.228636\pi\)
\(200\) 0 0
\(201\) −5.01074 −0.353430
\(202\) 1.11477 0.0784349
\(203\) −11.3446 −0.796232
\(204\) −6.96002 −0.487299
\(205\) 0 0
\(206\) −1.45780 −0.101570
\(207\) 3.89010 0.270381
\(208\) 0.153074 0.0106138
\(209\) 3.27685 0.226664
\(210\) 0 0
\(211\) −19.0961 −1.31463 −0.657314 0.753616i \(-0.728308\pi\)
−0.657314 + 0.753616i \(0.728308\pi\)
\(212\) −16.4945 −1.13285
\(213\) 0.923892 0.0633040
\(214\) 1.55550 0.106332
\(215\) 0 0
\(216\) −3.10114 −0.211006
\(217\) −4.64058 −0.315023
\(218\) 1.32559 0.0897802
\(219\) −3.20574 −0.216624
\(220\) 0 0
\(221\) 0.315954 0.0212534
\(222\) 0.983410 0.0660022
\(223\) −8.41781 −0.563698 −0.281849 0.959459i \(-0.590948\pi\)
−0.281849 + 0.959459i \(0.590948\pi\)
\(224\) 4.31942 0.288603
\(225\) 0 0
\(226\) −3.50265 −0.232993
\(227\) −1.82854 −0.121364 −0.0606821 0.998157i \(-0.519328\pi\)
−0.0606821 + 0.998157i \(0.519328\pi\)
\(228\) 0.663705 0.0439550
\(229\) 2.52038 0.166551 0.0832756 0.996527i \(-0.473462\pi\)
0.0832756 + 0.996527i \(0.473462\pi\)
\(230\) 0 0
\(231\) 3.17631 0.208986
\(232\) 9.04169 0.593616
\(233\) −16.3812 −1.07317 −0.536585 0.843847i \(-0.680286\pi\)
−0.536585 + 0.843847i \(0.680286\pi\)
\(234\) 0.0330352 0.00215958
\(235\) 0 0
\(236\) 24.9839 1.62631
\(237\) −6.40510 −0.416056
\(238\) 2.77390 0.179805
\(239\) −10.7430 −0.694909 −0.347455 0.937697i \(-0.612954\pi\)
−0.347455 + 0.937697i \(0.612954\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −3.07327 −0.197557
\(243\) 11.9364 0.765721
\(244\) −19.5441 −1.25118
\(245\) 0 0
\(246\) −0.749343 −0.0477764
\(247\) −0.0301293 −0.00191708
\(248\) 3.69857 0.234860
\(249\) 1.15257 0.0730411
\(250\) 0 0
\(251\) 23.8819 1.50741 0.753706 0.657212i \(-0.228264\pi\)
0.753706 + 0.657212i \(0.228264\pi\)
\(252\) −7.23844 −0.455979
\(253\) 6.63342 0.417040
\(254\) 0.118706 0.00744829
\(255\) 0 0
\(256\) 10.1859 0.636619
\(257\) −5.25407 −0.327740 −0.163870 0.986482i \(-0.552398\pi\)
−0.163870 + 0.986482i \(0.552398\pi\)
\(258\) −1.61489 −0.100539
\(259\) 9.78175 0.607808
\(260\) 0 0
\(261\) −22.8768 −1.41604
\(262\) 3.70936 0.229165
\(263\) 1.10964 0.0684235 0.0342118 0.999415i \(-0.489108\pi\)
0.0342118 + 0.999415i \(0.489108\pi\)
\(264\) −2.53154 −0.155806
\(265\) 0 0
\(266\) −0.264519 −0.0162187
\(267\) −7.18414 −0.439662
\(268\) 19.4715 1.18941
\(269\) −2.84634 −0.173544 −0.0867722 0.996228i \(-0.527655\pi\)
−0.0867722 + 0.996228i \(0.527655\pi\)
\(270\) 0 0
\(271\) 13.1029 0.795946 0.397973 0.917397i \(-0.369714\pi\)
0.397973 + 0.917397i \(0.369714\pi\)
\(272\) 25.9193 1.57159
\(273\) −0.0292049 −0.00176756
\(274\) 3.12834 0.188990
\(275\) 0 0
\(276\) 1.34356 0.0808728
\(277\) 23.4634 1.40978 0.704888 0.709318i \(-0.250997\pi\)
0.704888 + 0.709318i \(0.250997\pi\)
\(278\) 0.257365 0.0154357
\(279\) −9.35792 −0.560244
\(280\) 0 0
\(281\) 8.91165 0.531625 0.265812 0.964025i \(-0.414360\pi\)
0.265812 + 0.964025i \(0.414360\pi\)
\(282\) −0.720903 −0.0429291
\(283\) 15.8040 0.939453 0.469726 0.882812i \(-0.344353\pi\)
0.469726 + 0.882812i \(0.344353\pi\)
\(284\) −3.59021 −0.213040
\(285\) 0 0
\(286\) 0.0563318 0.00333097
\(287\) −7.45354 −0.439968
\(288\) 8.71027 0.513258
\(289\) 36.4990 2.14700
\(290\) 0 0
\(291\) 1.10709 0.0648988
\(292\) 12.4574 0.729013
\(293\) −32.9425 −1.92452 −0.962261 0.272127i \(-0.912273\pi\)
−0.962261 + 0.272127i \(0.912273\pi\)
\(294\) 0.705102 0.0411224
\(295\) 0 0
\(296\) −7.79611 −0.453140
\(297\) 13.3796 0.776363
\(298\) −3.57399 −0.207036
\(299\) −0.0609917 −0.00352724
\(300\) 0 0
\(301\) −16.0629 −0.925851
\(302\) 5.89674 0.339319
\(303\) −1.98733 −0.114169
\(304\) −2.47165 −0.141759
\(305\) 0 0
\(306\) 5.59369 0.319770
\(307\) −20.2343 −1.15483 −0.577416 0.816450i \(-0.695939\pi\)
−0.577416 + 0.816450i \(0.695939\pi\)
\(308\) −12.3430 −0.703309
\(309\) 2.59886 0.147844
\(310\) 0 0
\(311\) 2.27289 0.128884 0.0644420 0.997921i \(-0.479473\pi\)
0.0644420 + 0.997921i \(0.479473\pi\)
\(312\) 0.0232765 0.00131777
\(313\) −13.1142 −0.741257 −0.370629 0.928781i \(-0.620858\pi\)
−0.370629 + 0.928781i \(0.620858\pi\)
\(314\) 4.76873 0.269115
\(315\) 0 0
\(316\) 24.8900 1.40017
\(317\) 7.86525 0.441757 0.220878 0.975301i \(-0.429108\pi\)
0.220878 + 0.975301i \(0.429108\pi\)
\(318\) −1.17821 −0.0660709
\(319\) −39.0096 −2.18412
\(320\) 0 0
\(321\) −2.77304 −0.154776
\(322\) −0.535473 −0.0298407
\(323\) −5.10164 −0.283863
\(324\) −13.1840 −0.732443
\(325\) 0 0
\(326\) 3.08336 0.170772
\(327\) −2.36317 −0.130683
\(328\) 5.94051 0.328010
\(329\) −7.17065 −0.395331
\(330\) 0 0
\(331\) −19.3752 −1.06496 −0.532480 0.846443i \(-0.678740\pi\)
−0.532480 + 0.846443i \(0.678740\pi\)
\(332\) −4.47884 −0.245808
\(333\) 19.7253 1.08094
\(334\) −6.21192 −0.339901
\(335\) 0 0
\(336\) −2.39582 −0.130703
\(337\) 26.2459 1.42970 0.714852 0.699276i \(-0.246494\pi\)
0.714852 + 0.699276i \(0.246494\pi\)
\(338\) 3.60798 0.196249
\(339\) 6.24428 0.339143
\(340\) 0 0
\(341\) −15.9572 −0.864130
\(342\) −0.533412 −0.0288436
\(343\) 16.5773 0.895092
\(344\) 12.8022 0.690250
\(345\) 0 0
\(346\) 1.15500 0.0620931
\(347\) 3.65189 0.196044 0.0980219 0.995184i \(-0.468748\pi\)
0.0980219 + 0.995184i \(0.468748\pi\)
\(348\) −7.90116 −0.423547
\(349\) −0.818652 −0.0438214 −0.0219107 0.999760i \(-0.506975\pi\)
−0.0219107 + 0.999760i \(0.506975\pi\)
\(350\) 0 0
\(351\) −0.123020 −0.00656633
\(352\) 14.8528 0.791658
\(353\) 28.5367 1.51886 0.759428 0.650591i \(-0.225479\pi\)
0.759428 + 0.650591i \(0.225479\pi\)
\(354\) 1.78462 0.0948514
\(355\) 0 0
\(356\) 27.9173 1.47961
\(357\) −4.94513 −0.261724
\(358\) 1.60720 0.0849430
\(359\) −15.8623 −0.837180 −0.418590 0.908175i \(-0.637476\pi\)
−0.418590 + 0.908175i \(0.637476\pi\)
\(360\) 0 0
\(361\) −18.5135 −0.974395
\(362\) −4.85531 −0.255189
\(363\) 5.47882 0.287563
\(364\) 0.113489 0.00594845
\(365\) 0 0
\(366\) −1.39605 −0.0729727
\(367\) −13.9937 −0.730463 −0.365232 0.930917i \(-0.619010\pi\)
−0.365232 + 0.930917i \(0.619010\pi\)
\(368\) −5.00344 −0.260822
\(369\) −15.0304 −0.782449
\(370\) 0 0
\(371\) −11.7194 −0.608441
\(372\) −3.23203 −0.167573
\(373\) −12.2336 −0.633434 −0.316717 0.948520i \(-0.602581\pi\)
−0.316717 + 0.948520i \(0.602581\pi\)
\(374\) 9.53839 0.493218
\(375\) 0 0
\(376\) 5.71505 0.294731
\(377\) 0.358678 0.0184728
\(378\) −1.08005 −0.0555517
\(379\) 0.284829 0.0146307 0.00731535 0.999973i \(-0.497671\pi\)
0.00731535 + 0.999973i \(0.497671\pi\)
\(380\) 0 0
\(381\) −0.211621 −0.0108417
\(382\) 5.99772 0.306870
\(383\) −29.8268 −1.52408 −0.762038 0.647532i \(-0.775801\pi\)
−0.762038 + 0.647532i \(0.775801\pi\)
\(384\) 3.98184 0.203197
\(385\) 0 0
\(386\) 0.640887 0.0326203
\(387\) −32.3915 −1.64655
\(388\) −4.30211 −0.218407
\(389\) −8.88544 −0.450510 −0.225255 0.974300i \(-0.572321\pi\)
−0.225255 + 0.974300i \(0.572321\pi\)
\(390\) 0 0
\(391\) −10.3274 −0.522280
\(392\) −5.58978 −0.282327
\(393\) −6.61279 −0.333571
\(394\) 0.532605 0.0268322
\(395\) 0 0
\(396\) −24.8902 −1.25078
\(397\) 29.5831 1.48473 0.742367 0.669993i \(-0.233703\pi\)
0.742367 + 0.669993i \(0.233703\pi\)
\(398\) −5.89657 −0.295569
\(399\) 0.471566 0.0236078
\(400\) 0 0
\(401\) 6.30306 0.314760 0.157380 0.987538i \(-0.449695\pi\)
0.157380 + 0.987538i \(0.449695\pi\)
\(402\) 1.39087 0.0693701
\(403\) 0.146720 0.00730864
\(404\) 7.72270 0.384219
\(405\) 0 0
\(406\) 3.14899 0.156282
\(407\) 33.6357 1.66726
\(408\) 3.94130 0.195123
\(409\) −7.63163 −0.377360 −0.188680 0.982039i \(-0.560421\pi\)
−0.188680 + 0.982039i \(0.560421\pi\)
\(410\) 0 0
\(411\) −5.57699 −0.275092
\(412\) −10.0991 −0.497546
\(413\) 17.7512 0.873478
\(414\) −1.07980 −0.0530694
\(415\) 0 0
\(416\) −0.136566 −0.00669568
\(417\) −0.458813 −0.0224682
\(418\) −0.909578 −0.0444889
\(419\) 2.34760 0.114688 0.0573439 0.998354i \(-0.481737\pi\)
0.0573439 + 0.998354i \(0.481737\pi\)
\(420\) 0 0
\(421\) 8.61693 0.419963 0.209982 0.977705i \(-0.432660\pi\)
0.209982 + 0.977705i \(0.432660\pi\)
\(422\) 5.30064 0.258031
\(423\) −14.4599 −0.703064
\(424\) 9.34043 0.453611
\(425\) 0 0
\(426\) −0.256451 −0.0124251
\(427\) −13.8862 −0.671999
\(428\) 10.7759 0.520875
\(429\) −0.100425 −0.00484854
\(430\) 0 0
\(431\) −2.73295 −0.131641 −0.0658207 0.997831i \(-0.520967\pi\)
−0.0658207 + 0.997831i \(0.520967\pi\)
\(432\) −10.0919 −0.485549
\(433\) −14.8768 −0.714934 −0.357467 0.933926i \(-0.616360\pi\)
−0.357467 + 0.933926i \(0.616360\pi\)
\(434\) 1.28812 0.0618317
\(435\) 0 0
\(436\) 9.18318 0.439795
\(437\) 0.984819 0.0471103
\(438\) 0.889839 0.0425182
\(439\) −19.8115 −0.945552 −0.472776 0.881183i \(-0.656748\pi\)
−0.472776 + 0.881183i \(0.656748\pi\)
\(440\) 0 0
\(441\) 14.1430 0.673474
\(442\) −0.0877017 −0.00417154
\(443\) 39.5818 1.88059 0.940293 0.340366i \(-0.110551\pi\)
0.940293 + 0.340366i \(0.110551\pi\)
\(444\) 6.81270 0.323316
\(445\) 0 0
\(446\) 2.33659 0.110641
\(447\) 6.37146 0.301360
\(448\) 8.48414 0.400838
\(449\) −22.9205 −1.08169 −0.540843 0.841124i \(-0.681895\pi\)
−0.540843 + 0.841124i \(0.681895\pi\)
\(450\) 0 0
\(451\) −25.6299 −1.20686
\(452\) −24.2650 −1.14133
\(453\) −10.5123 −0.493911
\(454\) 0.507560 0.0238210
\(455\) 0 0
\(456\) −0.375841 −0.0176003
\(457\) 9.66494 0.452107 0.226053 0.974115i \(-0.427418\pi\)
0.226053 + 0.974115i \(0.427418\pi\)
\(458\) −0.699599 −0.0326901
\(459\) −20.8304 −0.972279
\(460\) 0 0
\(461\) 6.28046 0.292510 0.146255 0.989247i \(-0.453278\pi\)
0.146255 + 0.989247i \(0.453278\pi\)
\(462\) −0.881672 −0.0410191
\(463\) 7.64337 0.355218 0.177609 0.984101i \(-0.443164\pi\)
0.177609 + 0.984101i \(0.443164\pi\)
\(464\) 29.4241 1.36598
\(465\) 0 0
\(466\) 4.54705 0.210638
\(467\) −25.8943 −1.19824 −0.599122 0.800658i \(-0.704484\pi\)
−0.599122 + 0.800658i \(0.704484\pi\)
\(468\) 0.228856 0.0105789
\(469\) 13.8346 0.638823
\(470\) 0 0
\(471\) −8.50136 −0.391722
\(472\) −14.1478 −0.651205
\(473\) −55.2342 −2.53967
\(474\) 1.77791 0.0816621
\(475\) 0 0
\(476\) 19.2166 0.880790
\(477\) −23.6326 −1.08206
\(478\) 2.98202 0.136394
\(479\) 12.6131 0.576309 0.288155 0.957584i \(-0.406958\pi\)
0.288155 + 0.957584i \(0.406958\pi\)
\(480\) 0 0
\(481\) −0.309267 −0.0141013
\(482\) 0.277577 0.0126433
\(483\) 0.954605 0.0434360
\(484\) −21.2905 −0.967749
\(485\) 0 0
\(486\) −3.31328 −0.150293
\(487\) −31.7807 −1.44012 −0.720061 0.693910i \(-0.755886\pi\)
−0.720061 + 0.693910i \(0.755886\pi\)
\(488\) 11.0674 0.500996
\(489\) −5.49680 −0.248574
\(490\) 0 0
\(491\) −10.2151 −0.461001 −0.230500 0.973072i \(-0.574036\pi\)
−0.230500 + 0.973072i \(0.574036\pi\)
\(492\) −5.19117 −0.234036
\(493\) 60.7331 2.73528
\(494\) 0.00836321 0.000376278 0
\(495\) 0 0
\(496\) 12.0361 0.540439
\(497\) −2.55086 −0.114422
\(498\) −0.319927 −0.0143363
\(499\) −9.35390 −0.418738 −0.209369 0.977837i \(-0.567141\pi\)
−0.209369 + 0.977837i \(0.567141\pi\)
\(500\) 0 0
\(501\) 11.0742 0.494758
\(502\) −6.62907 −0.295870
\(503\) 13.7659 0.613792 0.306896 0.951743i \(-0.400710\pi\)
0.306896 + 0.951743i \(0.400710\pi\)
\(504\) 4.09896 0.182582
\(505\) 0 0
\(506\) −1.84129 −0.0818552
\(507\) −6.43207 −0.285658
\(508\) 0.822353 0.0364860
\(509\) 22.6367 1.00335 0.501677 0.865055i \(-0.332717\pi\)
0.501677 + 0.865055i \(0.332717\pi\)
\(510\) 0 0
\(511\) 8.85102 0.391546
\(512\) −18.9206 −0.836182
\(513\) 1.98638 0.0877008
\(514\) 1.45841 0.0643277
\(515\) 0 0
\(516\) −11.1873 −0.492496
\(517\) −24.6571 −1.08442
\(518\) −2.71519 −0.119299
\(519\) −2.05905 −0.0903824
\(520\) 0 0
\(521\) −10.8738 −0.476389 −0.238194 0.971218i \(-0.576555\pi\)
−0.238194 + 0.971218i \(0.576555\pi\)
\(522\) 6.35007 0.277935
\(523\) 3.43232 0.150085 0.0750424 0.997180i \(-0.476091\pi\)
0.0750424 + 0.997180i \(0.476091\pi\)
\(524\) 25.6970 1.12258
\(525\) 0 0
\(526\) −0.308011 −0.0134299
\(527\) 24.8434 1.08219
\(528\) −8.23831 −0.358526
\(529\) −21.0064 −0.913322
\(530\) 0 0
\(531\) 35.7959 1.55341
\(532\) −1.83249 −0.0794483
\(533\) 0.235656 0.0102074
\(534\) 1.99415 0.0862955
\(535\) 0 0
\(536\) −11.0263 −0.476263
\(537\) −2.86520 −0.123643
\(538\) 0.790079 0.0340627
\(539\) 24.1167 1.03878
\(540\) 0 0
\(541\) −1.00758 −0.0433193 −0.0216597 0.999765i \(-0.506895\pi\)
−0.0216597 + 0.999765i \(0.506895\pi\)
\(542\) −3.63707 −0.156226
\(543\) 8.65571 0.371452
\(544\) −23.1240 −0.991433
\(545\) 0 0
\(546\) 0.00810662 0.000346931 0
\(547\) −10.6391 −0.454894 −0.227447 0.973791i \(-0.573038\pi\)
−0.227447 + 0.973791i \(0.573038\pi\)
\(548\) 21.6720 0.925780
\(549\) −28.0020 −1.19510
\(550\) 0 0
\(551\) −5.79149 −0.246726
\(552\) −0.760826 −0.0323829
\(553\) 17.6844 0.752019
\(554\) −6.51289 −0.276706
\(555\) 0 0
\(556\) 1.78293 0.0756130
\(557\) −18.9092 −0.801207 −0.400603 0.916252i \(-0.631199\pi\)
−0.400603 + 0.916252i \(0.631199\pi\)
\(558\) 2.59755 0.109963
\(559\) 0.507856 0.0214800
\(560\) 0 0
\(561\) −17.0044 −0.717926
\(562\) −2.47367 −0.104346
\(563\) −28.1768 −1.18751 −0.593756 0.804645i \(-0.702356\pi\)
−0.593756 + 0.804645i \(0.702356\pi\)
\(564\) −4.99415 −0.210291
\(565\) 0 0
\(566\) −4.38684 −0.184393
\(567\) −9.36727 −0.393388
\(568\) 2.03305 0.0853049
\(569\) −0.499818 −0.0209534 −0.0104767 0.999945i \(-0.503335\pi\)
−0.0104767 + 0.999945i \(0.503335\pi\)
\(570\) 0 0
\(571\) −28.2303 −1.18140 −0.590702 0.806890i \(-0.701149\pi\)
−0.590702 + 0.806890i \(0.701149\pi\)
\(572\) 0.390246 0.0163170
\(573\) −10.6923 −0.446678
\(574\) 2.06893 0.0863555
\(575\) 0 0
\(576\) 17.1086 0.712858
\(577\) 36.3728 1.51422 0.757111 0.653287i \(-0.226610\pi\)
0.757111 + 0.653287i \(0.226610\pi\)
\(578\) −10.1313 −0.421406
\(579\) −1.14253 −0.0474819
\(580\) 0 0
\(581\) −3.18224 −0.132021
\(582\) −0.307303 −0.0127381
\(583\) −40.2985 −1.66899
\(584\) −7.05432 −0.291910
\(585\) 0 0
\(586\) 9.14409 0.377739
\(587\) −16.1223 −0.665437 −0.332718 0.943026i \(-0.607966\pi\)
−0.332718 + 0.943026i \(0.607966\pi\)
\(588\) 4.88468 0.201441
\(589\) −2.36905 −0.0976152
\(590\) 0 0
\(591\) −0.949491 −0.0390569
\(592\) −25.3706 −1.04273
\(593\) −24.8487 −1.02041 −0.510207 0.860052i \(-0.670431\pi\)
−0.510207 + 0.860052i \(0.670431\pi\)
\(594\) −3.71387 −0.152382
\(595\) 0 0
\(596\) −24.7593 −1.01418
\(597\) 10.5120 0.430228
\(598\) 0.0169299 0.000692315 0
\(599\) −1.50155 −0.0613517 −0.0306759 0.999529i \(-0.509766\pi\)
−0.0306759 + 0.999529i \(0.509766\pi\)
\(600\) 0 0
\(601\) −24.0828 −0.982356 −0.491178 0.871059i \(-0.663434\pi\)
−0.491178 + 0.871059i \(0.663434\pi\)
\(602\) 4.45870 0.181723
\(603\) 27.8981 1.13610
\(604\) 40.8504 1.66218
\(605\) 0 0
\(606\) 0.551638 0.0224088
\(607\) −16.0760 −0.652506 −0.326253 0.945283i \(-0.605786\pi\)
−0.326253 + 0.945283i \(0.605786\pi\)
\(608\) 2.20510 0.0894284
\(609\) −5.61381 −0.227483
\(610\) 0 0
\(611\) 0.226712 0.00917179
\(612\) 38.7510 1.56642
\(613\) −43.5233 −1.75789 −0.878945 0.476923i \(-0.841752\pi\)
−0.878945 + 0.476923i \(0.841752\pi\)
\(614\) 5.61658 0.226667
\(615\) 0 0
\(616\) 6.98957 0.281618
\(617\) 3.82544 0.154006 0.0770032 0.997031i \(-0.475465\pi\)
0.0770032 + 0.997031i \(0.475465\pi\)
\(618\) −0.721385 −0.0290183
\(619\) 8.69881 0.349635 0.174817 0.984601i \(-0.444066\pi\)
0.174817 + 0.984601i \(0.444066\pi\)
\(620\) 0 0
\(621\) 4.02109 0.161361
\(622\) −0.630903 −0.0252969
\(623\) 19.8354 0.794687
\(624\) 0.0757480 0.00303235
\(625\) 0 0
\(626\) 3.64020 0.145492
\(627\) 1.62153 0.0647578
\(628\) 33.0360 1.31828
\(629\) −52.3666 −2.08799
\(630\) 0 0
\(631\) −28.0264 −1.11571 −0.557856 0.829938i \(-0.688376\pi\)
−0.557856 + 0.829938i \(0.688376\pi\)
\(632\) −14.0946 −0.560653
\(633\) −9.44961 −0.375588
\(634\) −2.18321 −0.0867065
\(635\) 0 0
\(636\) −8.16222 −0.323653
\(637\) −0.221743 −0.00878578
\(638\) 10.8282 0.428692
\(639\) −5.14391 −0.203490
\(640\) 0 0
\(641\) 22.7621 0.899048 0.449524 0.893268i \(-0.351594\pi\)
0.449524 + 0.893268i \(0.351594\pi\)
\(642\) 0.769733 0.0303789
\(643\) −35.9559 −1.41796 −0.708981 0.705228i \(-0.750845\pi\)
−0.708981 + 0.705228i \(0.750845\pi\)
\(644\) −3.70956 −0.146177
\(645\) 0 0
\(646\) 1.41610 0.0557157
\(647\) 1.94619 0.0765127 0.0382564 0.999268i \(-0.487820\pi\)
0.0382564 + 0.999268i \(0.487820\pi\)
\(648\) 7.46577 0.293283
\(649\) 61.0395 2.39601
\(650\) 0 0
\(651\) −2.29637 −0.0900019
\(652\) 21.3604 0.836537
\(653\) −24.3392 −0.952467 −0.476233 0.879319i \(-0.657998\pi\)
−0.476233 + 0.879319i \(0.657998\pi\)
\(654\) 0.655961 0.0256501
\(655\) 0 0
\(656\) 19.3320 0.754789
\(657\) 17.8484 0.696334
\(658\) 1.99041 0.0775942
\(659\) −6.16907 −0.240313 −0.120156 0.992755i \(-0.538340\pi\)
−0.120156 + 0.992755i \(0.538340\pi\)
\(660\) 0 0
\(661\) −48.1704 −1.87361 −0.936807 0.349848i \(-0.886233\pi\)
−0.936807 + 0.349848i \(0.886233\pi\)
\(662\) 5.37812 0.209027
\(663\) 0.156349 0.00607208
\(664\) 2.53626 0.0984260
\(665\) 0 0
\(666\) −5.47529 −0.212163
\(667\) −11.7239 −0.453951
\(668\) −43.0338 −1.66503
\(669\) −4.16551 −0.161048
\(670\) 0 0
\(671\) −47.7492 −1.84334
\(672\) 2.13744 0.0824537
\(673\) 19.2071 0.740381 0.370190 0.928956i \(-0.379292\pi\)
0.370190 + 0.928956i \(0.379292\pi\)
\(674\) −7.28525 −0.280617
\(675\) 0 0
\(676\) 24.9948 0.961337
\(677\) 14.9094 0.573014 0.286507 0.958078i \(-0.407506\pi\)
0.286507 + 0.958078i \(0.407506\pi\)
\(678\) −1.73327 −0.0665658
\(679\) −3.05667 −0.117304
\(680\) 0 0
\(681\) −0.904843 −0.0346737
\(682\) 4.42935 0.169609
\(683\) 22.8682 0.875029 0.437515 0.899211i \(-0.355859\pi\)
0.437515 + 0.899211i \(0.355859\pi\)
\(684\) −3.69528 −0.141293
\(685\) 0 0
\(686\) −4.60149 −0.175686
\(687\) 1.24720 0.0475835
\(688\) 41.6619 1.58835
\(689\) 0.370529 0.0141160
\(690\) 0 0
\(691\) −35.5210 −1.35128 −0.675641 0.737231i \(-0.736133\pi\)
−0.675641 + 0.737231i \(0.736133\pi\)
\(692\) 8.00140 0.304168
\(693\) −17.6846 −0.671783
\(694\) −1.01368 −0.0384788
\(695\) 0 0
\(696\) 4.47424 0.169596
\(697\) 39.9025 1.51142
\(698\) 0.227239 0.00860112
\(699\) −8.10617 −0.306604
\(700\) 0 0
\(701\) 9.22303 0.348349 0.174175 0.984715i \(-0.444274\pi\)
0.174175 + 0.984715i \(0.444274\pi\)
\(702\) 0.0341476 0.00128882
\(703\) 4.99366 0.188339
\(704\) 29.1737 1.09952
\(705\) 0 0
\(706\) −7.92114 −0.298116
\(707\) 5.48701 0.206360
\(708\) 12.3632 0.464636
\(709\) 28.7763 1.08072 0.540358 0.841435i \(-0.318289\pi\)
0.540358 + 0.841435i \(0.318289\pi\)
\(710\) 0 0
\(711\) 35.6614 1.33741
\(712\) −15.8089 −0.592464
\(713\) −4.79575 −0.179602
\(714\) 1.37265 0.0513703
\(715\) 0 0
\(716\) 11.1341 0.416100
\(717\) −5.31614 −0.198535
\(718\) 4.40301 0.164319
\(719\) −24.1878 −0.902055 −0.451027 0.892510i \(-0.648942\pi\)
−0.451027 + 0.892510i \(0.648942\pi\)
\(720\) 0 0
\(721\) −7.17544 −0.267227
\(722\) 5.13893 0.191251
\(723\) −0.494846 −0.0184035
\(724\) −33.6358 −1.25006
\(725\) 0 0
\(726\) −1.52080 −0.0564420
\(727\) −9.73994 −0.361235 −0.180617 0.983553i \(-0.557810\pi\)
−0.180617 + 0.983553i \(0.557810\pi\)
\(728\) −0.0642663 −0.00238187
\(729\) −14.6617 −0.543024
\(730\) 0 0
\(731\) 85.9928 3.18056
\(732\) −9.67131 −0.357462
\(733\) 4.38060 0.161801 0.0809006 0.996722i \(-0.474220\pi\)
0.0809006 + 0.996722i \(0.474220\pi\)
\(734\) 3.88432 0.143373
\(735\) 0 0
\(736\) 4.46384 0.164539
\(737\) 47.5719 1.75234
\(738\) 4.17208 0.153577
\(739\) −6.21520 −0.228630 −0.114315 0.993445i \(-0.536467\pi\)
−0.114315 + 0.993445i \(0.536467\pi\)
\(740\) 0 0
\(741\) −0.0149094 −0.000547709 0
\(742\) 3.25304 0.119423
\(743\) −26.7097 −0.979885 −0.489942 0.871755i \(-0.662982\pi\)
−0.489942 + 0.871755i \(0.662982\pi\)
\(744\) 1.83022 0.0670992
\(745\) 0 0
\(746\) 3.39578 0.124328
\(747\) −6.41710 −0.234790
\(748\) 66.0784 2.41607
\(749\) 7.65635 0.279757
\(750\) 0 0
\(751\) 46.9924 1.71478 0.857388 0.514670i \(-0.172085\pi\)
0.857388 + 0.514670i \(0.172085\pi\)
\(752\) 18.5983 0.678210
\(753\) 11.8178 0.430666
\(754\) −0.0995608 −0.00362579
\(755\) 0 0
\(756\) −7.48217 −0.272124
\(757\) 35.2425 1.28091 0.640456 0.767995i \(-0.278745\pi\)
0.640456 + 0.767995i \(0.278745\pi\)
\(758\) −0.0790621 −0.00287166
\(759\) 3.28252 0.119148
\(760\) 0 0
\(761\) −47.1109 −1.70777 −0.853885 0.520461i \(-0.825760\pi\)
−0.853885 + 0.520461i \(0.825760\pi\)
\(762\) 0.0587413 0.00212797
\(763\) 6.52469 0.236210
\(764\) 41.5499 1.50322
\(765\) 0 0
\(766\) 8.27923 0.299141
\(767\) −0.561234 −0.0202650
\(768\) 5.04045 0.181881
\(769\) −53.8827 −1.94306 −0.971530 0.236915i \(-0.923864\pi\)
−0.971530 + 0.236915i \(0.923864\pi\)
\(770\) 0 0
\(771\) −2.59995 −0.0936350
\(772\) 4.43983 0.159793
\(773\) 7.33241 0.263728 0.131864 0.991268i \(-0.457904\pi\)
0.131864 + 0.991268i \(0.457904\pi\)
\(774\) 8.99114 0.323180
\(775\) 0 0
\(776\) 2.43618 0.0874539
\(777\) 4.84045 0.173650
\(778\) 2.46639 0.0884245
\(779\) −3.80509 −0.136332
\(780\) 0 0
\(781\) −8.77143 −0.313866
\(782\) 2.86666 0.102511
\(783\) −23.6471 −0.845078
\(784\) −18.1906 −0.649666
\(785\) 0 0
\(786\) 1.83556 0.0654722
\(787\) 0.274880 0.00979841 0.00489921 0.999988i \(-0.498441\pi\)
0.00489921 + 0.999988i \(0.498441\pi\)
\(788\) 3.68969 0.131440
\(789\) 0.549102 0.0195485
\(790\) 0 0
\(791\) −17.2404 −0.612998
\(792\) 14.0947 0.500835
\(793\) 0.439035 0.0155906
\(794\) −8.21160 −0.291419
\(795\) 0 0
\(796\) −40.8493 −1.44786
\(797\) 7.42858 0.263134 0.131567 0.991307i \(-0.457999\pi\)
0.131567 + 0.991307i \(0.457999\pi\)
\(798\) −0.130896 −0.00463366
\(799\) 38.3881 1.35807
\(800\) 0 0
\(801\) 39.9988 1.41329
\(802\) −1.74958 −0.0617800
\(803\) 30.4353 1.07404
\(804\) 9.63541 0.339815
\(805\) 0 0
\(806\) −0.0407261 −0.00143452
\(807\) −1.40850 −0.0495815
\(808\) −4.37318 −0.153848
\(809\) 42.6491 1.49946 0.749730 0.661743i \(-0.230183\pi\)
0.749730 + 0.661743i \(0.230183\pi\)
\(810\) 0 0
\(811\) 25.6139 0.899425 0.449713 0.893173i \(-0.351526\pi\)
0.449713 + 0.893173i \(0.351526\pi\)
\(812\) 21.8150 0.765558
\(813\) 6.48392 0.227401
\(814\) −9.33649 −0.327244
\(815\) 0 0
\(816\) 12.8260 0.449001
\(817\) −8.20024 −0.286890
\(818\) 2.11837 0.0740669
\(819\) 0.162603 0.00568181
\(820\) 0 0
\(821\) 21.8573 0.762826 0.381413 0.924405i \(-0.375438\pi\)
0.381413 + 0.924405i \(0.375438\pi\)
\(822\) 1.54804 0.0539942
\(823\) −1.58270 −0.0551693 −0.0275847 0.999619i \(-0.508782\pi\)
−0.0275847 + 0.999619i \(0.508782\pi\)
\(824\) 5.71887 0.199226
\(825\) 0 0
\(826\) −4.92732 −0.171443
\(827\) −36.2198 −1.25949 −0.629743 0.776803i \(-0.716840\pi\)
−0.629743 + 0.776803i \(0.716840\pi\)
\(828\) −7.48047 −0.259964
\(829\) 30.5957 1.06263 0.531316 0.847174i \(-0.321698\pi\)
0.531316 + 0.847174i \(0.321698\pi\)
\(830\) 0 0
\(831\) 11.6107 0.402772
\(832\) −0.268241 −0.00929957
\(833\) −37.5466 −1.30091
\(834\) 0.127356 0.00440998
\(835\) 0 0
\(836\) −6.30122 −0.217932
\(837\) −9.67303 −0.334349
\(838\) −0.651640 −0.0225105
\(839\) −9.85906 −0.340373 −0.170186 0.985412i \(-0.554437\pi\)
−0.170186 + 0.985412i \(0.554437\pi\)
\(840\) 0 0
\(841\) 39.9455 1.37743
\(842\) −2.39186 −0.0824290
\(843\) 4.40989 0.151885
\(844\) 36.7208 1.26398
\(845\) 0 0
\(846\) 4.01374 0.137995
\(847\) −15.1270 −0.519769
\(848\) 30.3963 1.04381
\(849\) 7.82056 0.268401
\(850\) 0 0
\(851\) 10.1088 0.346526
\(852\) −1.77660 −0.0608653
\(853\) −20.6701 −0.707730 −0.353865 0.935296i \(-0.615133\pi\)
−0.353865 + 0.935296i \(0.615133\pi\)
\(854\) 3.85448 0.131898
\(855\) 0 0
\(856\) −6.10216 −0.208567
\(857\) −36.0858 −1.23267 −0.616334 0.787485i \(-0.711383\pi\)
−0.616334 + 0.787485i \(0.711383\pi\)
\(858\) 0.0278756 0.000951656 0
\(859\) 40.7566 1.39060 0.695299 0.718720i \(-0.255272\pi\)
0.695299 + 0.718720i \(0.255272\pi\)
\(860\) 0 0
\(861\) −3.68835 −0.125699
\(862\) 0.758604 0.0258381
\(863\) −21.5125 −0.732295 −0.366148 0.930557i \(-0.619323\pi\)
−0.366148 + 0.930557i \(0.619323\pi\)
\(864\) 9.00357 0.306308
\(865\) 0 0
\(866\) 4.12947 0.140325
\(867\) 18.0614 0.613396
\(868\) 8.92362 0.302887
\(869\) 60.8100 2.06284
\(870\) 0 0
\(871\) −0.437405 −0.0148209
\(872\) −5.20022 −0.176102
\(873\) −6.16390 −0.208616
\(874\) −0.273363 −0.00924665
\(875\) 0 0
\(876\) 6.16448 0.208278
\(877\) 47.8912 1.61717 0.808586 0.588378i \(-0.200233\pi\)
0.808586 + 0.588378i \(0.200233\pi\)
\(878\) 5.49922 0.185590
\(879\) −16.3015 −0.549835
\(880\) 0 0
\(881\) −18.2689 −0.615496 −0.307748 0.951468i \(-0.599575\pi\)
−0.307748 + 0.951468i \(0.599575\pi\)
\(882\) −3.92576 −0.132187
\(883\) 37.0354 1.24634 0.623170 0.782087i \(-0.285845\pi\)
0.623170 + 0.782087i \(0.285845\pi\)
\(884\) −0.607565 −0.0204346
\(885\) 0 0
\(886\) −10.9870 −0.369115
\(887\) 13.7619 0.462080 0.231040 0.972944i \(-0.425787\pi\)
0.231040 + 0.972944i \(0.425787\pi\)
\(888\) −3.85787 −0.129462
\(889\) 0.584285 0.0195963
\(890\) 0 0
\(891\) −32.2104 −1.07909
\(892\) 16.1870 0.541982
\(893\) −3.66067 −0.122500
\(894\) −1.76857 −0.0591499
\(895\) 0 0
\(896\) −10.9938 −0.367278
\(897\) −0.0301815 −0.00100773
\(898\) 6.36221 0.212310
\(899\) 28.2027 0.940613
\(900\) 0 0
\(901\) 62.7398 2.09017
\(902\) 7.11426 0.236879
\(903\) −7.94866 −0.264515
\(904\) 13.7407 0.457009
\(905\) 0 0
\(906\) 2.91797 0.0969432
\(907\) 27.1842 0.902637 0.451319 0.892363i \(-0.350954\pi\)
0.451319 + 0.892363i \(0.350954\pi\)
\(908\) 3.51619 0.116689
\(909\) 11.0648 0.366996
\(910\) 0 0
\(911\) 29.4894 0.977027 0.488513 0.872556i \(-0.337539\pi\)
0.488513 + 0.872556i \(0.337539\pi\)
\(912\) −1.22309 −0.0405004
\(913\) −10.9425 −0.362143
\(914\) −2.68277 −0.0887380
\(915\) 0 0
\(916\) −4.84656 −0.160135
\(917\) 18.2579 0.602928
\(918\) 5.78204 0.190836
\(919\) −44.2354 −1.45919 −0.729596 0.683878i \(-0.760292\pi\)
−0.729596 + 0.683878i \(0.760292\pi\)
\(920\) 0 0
\(921\) −10.0128 −0.329935
\(922\) −1.74331 −0.0574130
\(923\) 0.0806498 0.00265462
\(924\) −6.10789 −0.200935
\(925\) 0 0
\(926\) −2.12163 −0.0697210
\(927\) −14.4696 −0.475243
\(928\) −26.2508 −0.861726
\(929\) 17.7425 0.582112 0.291056 0.956706i \(-0.405993\pi\)
0.291056 + 0.956706i \(0.405993\pi\)
\(930\) 0 0
\(931\) 3.58043 0.117344
\(932\) 31.5003 1.03183
\(933\) 1.12473 0.0368220
\(934\) 7.18766 0.235187
\(935\) 0 0
\(936\) −0.129596 −0.00423596
\(937\) −46.1680 −1.50824 −0.754121 0.656735i \(-0.771937\pi\)
−0.754121 + 0.656735i \(0.771937\pi\)
\(938\) −3.84017 −0.125386
\(939\) −6.48949 −0.211777
\(940\) 0 0
\(941\) −22.0383 −0.718428 −0.359214 0.933255i \(-0.616955\pi\)
−0.359214 + 0.933255i \(0.616955\pi\)
\(942\) 2.35978 0.0768859
\(943\) −7.70276 −0.250836
\(944\) −46.0407 −1.49850
\(945\) 0 0
\(946\) 15.3317 0.498478
\(947\) 34.5940 1.12416 0.562078 0.827085i \(-0.310002\pi\)
0.562078 + 0.827085i \(0.310002\pi\)
\(948\) 12.3167 0.400028
\(949\) −0.279840 −0.00908399
\(950\) 0 0
\(951\) 3.89209 0.126210
\(952\) −10.8819 −0.352684
\(953\) 20.9799 0.679607 0.339803 0.940496i \(-0.389639\pi\)
0.339803 + 0.940496i \(0.389639\pi\)
\(954\) 6.55988 0.212384
\(955\) 0 0
\(956\) 20.6583 0.668138
\(957\) −19.3037 −0.624001
\(958\) −3.50112 −0.113116
\(959\) 15.3980 0.497228
\(960\) 0 0
\(961\) −19.4635 −0.627854
\(962\) 0.0858453 0.00276777
\(963\) 15.4393 0.497526
\(964\) 1.92295 0.0619341
\(965\) 0 0
\(966\) −0.264976 −0.00852548
\(967\) 0.0716187 0.00230310 0.00115155 0.999999i \(-0.499633\pi\)
0.00115155 + 0.999999i \(0.499633\pi\)
\(968\) 12.0563 0.387504
\(969\) −2.52453 −0.0810995
\(970\) 0 0
\(971\) −8.18205 −0.262575 −0.131287 0.991344i \(-0.541911\pi\)
−0.131287 + 0.991344i \(0.541911\pi\)
\(972\) −22.9531 −0.736222
\(973\) 1.26678 0.0406111
\(974\) 8.82161 0.282663
\(975\) 0 0
\(976\) 36.0162 1.15285
\(977\) −22.6886 −0.725872 −0.362936 0.931814i \(-0.618226\pi\)
−0.362936 + 0.931814i \(0.618226\pi\)
\(978\) 1.52579 0.0487893
\(979\) 68.2062 2.17988
\(980\) 0 0
\(981\) 13.1573 0.420080
\(982\) 2.83548 0.0904837
\(983\) 18.8463 0.601103 0.300551 0.953766i \(-0.402829\pi\)
0.300551 + 0.953766i \(0.402829\pi\)
\(984\) 2.93964 0.0937122
\(985\) 0 0
\(986\) −16.8581 −0.536872
\(987\) −3.54836 −0.112946
\(988\) 0.0579372 0.00184323
\(989\) −16.6000 −0.527850
\(990\) 0 0
\(991\) −16.8310 −0.534655 −0.267328 0.963606i \(-0.586141\pi\)
−0.267328 + 0.963606i \(0.586141\pi\)
\(992\) −10.7381 −0.340935
\(993\) −9.58775 −0.304258
\(994\) 0.708060 0.0224583
\(995\) 0 0
\(996\) −2.21633 −0.0702272
\(997\) −60.1343 −1.90447 −0.952236 0.305363i \(-0.901222\pi\)
−0.952236 + 0.305363i \(0.901222\pi\)
\(998\) 2.59643 0.0821885
\(999\) 20.3895 0.645095
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 6025.2.a.f.1.3 7
5.4 even 2 241.2.a.a.1.5 7
15.14 odd 2 2169.2.a.e.1.3 7
20.19 odd 2 3856.2.a.j.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.5 7 5.4 even 2
2169.2.a.e.1.3 7 15.14 odd 2
3856.2.a.j.1.4 7 20.19 odd 2
6025.2.a.f.1.3 7 1.1 even 1 trivial