Properties

Label 4033.2.a.f.1.4
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.62495 q^{2} +2.49737 q^{3} +4.89034 q^{4} +0.915854 q^{5} -6.55547 q^{6} +2.77253 q^{7} -7.58698 q^{8} +3.23688 q^{9} +O(q^{10})\) \(q-2.62495 q^{2} +2.49737 q^{3} +4.89034 q^{4} +0.915854 q^{5} -6.55547 q^{6} +2.77253 q^{7} -7.58698 q^{8} +3.23688 q^{9} -2.40407 q^{10} +3.08728 q^{11} +12.2130 q^{12} -5.11135 q^{13} -7.27774 q^{14} +2.28723 q^{15} +10.1347 q^{16} -0.311928 q^{17} -8.49662 q^{18} +5.58279 q^{19} +4.47883 q^{20} +6.92405 q^{21} -8.10393 q^{22} +6.75058 q^{23} -18.9475 q^{24} -4.16121 q^{25} +13.4170 q^{26} +0.591568 q^{27} +13.5586 q^{28} -5.41237 q^{29} -6.00385 q^{30} +8.83960 q^{31} -11.4291 q^{32} +7.71008 q^{33} +0.818793 q^{34} +2.53923 q^{35} +15.8294 q^{36} +1.00000 q^{37} -14.6545 q^{38} -12.7650 q^{39} -6.94856 q^{40} +4.63897 q^{41} -18.1752 q^{42} -11.3400 q^{43} +15.0978 q^{44} +2.96451 q^{45} -17.7199 q^{46} +7.62852 q^{47} +25.3102 q^{48} +0.686928 q^{49} +10.9230 q^{50} -0.779000 q^{51} -24.9962 q^{52} +12.8607 q^{53} -1.55283 q^{54} +2.82749 q^{55} -21.0351 q^{56} +13.9423 q^{57} +14.2072 q^{58} +2.95362 q^{59} +11.1853 q^{60} -7.40494 q^{61} -23.2035 q^{62} +8.97434 q^{63} +9.73142 q^{64} -4.68125 q^{65} -20.2385 q^{66} -4.29048 q^{67} -1.52543 q^{68} +16.8587 q^{69} -6.66535 q^{70} -2.69005 q^{71} -24.5581 q^{72} +3.23107 q^{73} -2.62495 q^{74} -10.3921 q^{75} +27.3017 q^{76} +8.55957 q^{77} +33.5073 q^{78} -2.50044 q^{79} +9.28193 q^{80} -8.23326 q^{81} -12.1771 q^{82} +12.4005 q^{83} +33.8609 q^{84} -0.285680 q^{85} +29.7669 q^{86} -13.5167 q^{87} -23.4231 q^{88} -8.44240 q^{89} -7.78166 q^{90} -14.1714 q^{91} +33.0126 q^{92} +22.0758 q^{93} -20.0244 q^{94} +5.11302 q^{95} -28.5428 q^{96} +0.983838 q^{97} -1.80315 q^{98} +9.99313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62495 −1.85612 −0.928058 0.372435i \(-0.878523\pi\)
−0.928058 + 0.372435i \(0.878523\pi\)
\(3\) 2.49737 1.44186 0.720930 0.693008i \(-0.243715\pi\)
0.720930 + 0.693008i \(0.243715\pi\)
\(4\) 4.89034 2.44517
\(5\) 0.915854 0.409582 0.204791 0.978806i \(-0.434348\pi\)
0.204791 + 0.978806i \(0.434348\pi\)
\(6\) −6.55547 −2.67626
\(7\) 2.77253 1.04792 0.523959 0.851743i \(-0.324454\pi\)
0.523959 + 0.851743i \(0.324454\pi\)
\(8\) −7.58698 −2.68240
\(9\) 3.23688 1.07896
\(10\) −2.40407 −0.760232
\(11\) 3.08728 0.930849 0.465424 0.885088i \(-0.345902\pi\)
0.465424 + 0.885088i \(0.345902\pi\)
\(12\) 12.2130 3.52559
\(13\) −5.11135 −1.41763 −0.708817 0.705393i \(-0.750771\pi\)
−0.708817 + 0.705393i \(0.750771\pi\)
\(14\) −7.27774 −1.94506
\(15\) 2.28723 0.590560
\(16\) 10.1347 2.53368
\(17\) −0.311928 −0.0756536 −0.0378268 0.999284i \(-0.512044\pi\)
−0.0378268 + 0.999284i \(0.512044\pi\)
\(18\) −8.49662 −2.00267
\(19\) 5.58279 1.28078 0.640390 0.768050i \(-0.278773\pi\)
0.640390 + 0.768050i \(0.278773\pi\)
\(20\) 4.47883 1.00150
\(21\) 6.92405 1.51095
\(22\) −8.10393 −1.72776
\(23\) 6.75058 1.40759 0.703796 0.710402i \(-0.251487\pi\)
0.703796 + 0.710402i \(0.251487\pi\)
\(24\) −18.9475 −3.86765
\(25\) −4.16121 −0.832242
\(26\) 13.4170 2.63129
\(27\) 0.591568 0.113847
\(28\) 13.5586 2.56234
\(29\) −5.41237 −1.00505 −0.502526 0.864562i \(-0.667596\pi\)
−0.502526 + 0.864562i \(0.667596\pi\)
\(30\) −6.00385 −1.09615
\(31\) 8.83960 1.58764 0.793820 0.608153i \(-0.208089\pi\)
0.793820 + 0.608153i \(0.208089\pi\)
\(32\) −11.4291 −2.02041
\(33\) 7.71008 1.34215
\(34\) 0.818793 0.140422
\(35\) 2.53923 0.429209
\(36\) 15.8294 2.63824
\(37\) 1.00000 0.164399
\(38\) −14.6545 −2.37728
\(39\) −12.7650 −2.04403
\(40\) −6.94856 −1.09866
\(41\) 4.63897 0.724486 0.362243 0.932084i \(-0.382011\pi\)
0.362243 + 0.932084i \(0.382011\pi\)
\(42\) −18.1752 −2.80450
\(43\) −11.3400 −1.72933 −0.864667 0.502346i \(-0.832471\pi\)
−0.864667 + 0.502346i \(0.832471\pi\)
\(44\) 15.0978 2.27608
\(45\) 2.96451 0.441922
\(46\) −17.7199 −2.61266
\(47\) 7.62852 1.11273 0.556367 0.830937i \(-0.312195\pi\)
0.556367 + 0.830937i \(0.312195\pi\)
\(48\) 25.3102 3.65321
\(49\) 0.686928 0.0981325
\(50\) 10.9230 1.54474
\(51\) −0.779000 −0.109082
\(52\) −24.9962 −3.46635
\(53\) 12.8607 1.76656 0.883278 0.468850i \(-0.155331\pi\)
0.883278 + 0.468850i \(0.155331\pi\)
\(54\) −1.55283 −0.211314
\(55\) 2.82749 0.381259
\(56\) −21.0351 −2.81094
\(57\) 13.9423 1.84671
\(58\) 14.2072 1.86549
\(59\) 2.95362 0.384529 0.192264 0.981343i \(-0.438417\pi\)
0.192264 + 0.981343i \(0.438417\pi\)
\(60\) 11.1853 1.44402
\(61\) −7.40494 −0.948105 −0.474053 0.880496i \(-0.657209\pi\)
−0.474053 + 0.880496i \(0.657209\pi\)
\(62\) −23.2035 −2.94684
\(63\) 8.97434 1.13066
\(64\) 9.73142 1.21643
\(65\) −4.68125 −0.580638
\(66\) −20.2385 −2.49119
\(67\) −4.29048 −0.524166 −0.262083 0.965045i \(-0.584409\pi\)
−0.262083 + 0.965045i \(0.584409\pi\)
\(68\) −1.52543 −0.184986
\(69\) 16.8587 2.02955
\(70\) −6.66535 −0.796661
\(71\) −2.69005 −0.319250 −0.159625 0.987178i \(-0.551028\pi\)
−0.159625 + 0.987178i \(0.551028\pi\)
\(72\) −24.5581 −2.89420
\(73\) 3.23107 0.378168 0.189084 0.981961i \(-0.439448\pi\)
0.189084 + 0.981961i \(0.439448\pi\)
\(74\) −2.62495 −0.305144
\(75\) −10.3921 −1.19998
\(76\) 27.3017 3.13172
\(77\) 8.55957 0.975453
\(78\) 33.5073 3.79395
\(79\) −2.50044 −0.281321 −0.140661 0.990058i \(-0.544923\pi\)
−0.140661 + 0.990058i \(0.544923\pi\)
\(80\) 9.28193 1.03775
\(81\) −8.23326 −0.914807
\(82\) −12.1771 −1.34473
\(83\) 12.4005 1.36113 0.680564 0.732689i \(-0.261735\pi\)
0.680564 + 0.732689i \(0.261735\pi\)
\(84\) 33.8609 3.69453
\(85\) −0.285680 −0.0309864
\(86\) 29.7669 3.20985
\(87\) −13.5167 −1.44914
\(88\) −23.4231 −2.49691
\(89\) −8.44240 −0.894892 −0.447446 0.894311i \(-0.647666\pi\)
−0.447446 + 0.894311i \(0.647666\pi\)
\(90\) −7.78166 −0.820259
\(91\) −14.1714 −1.48556
\(92\) 33.0126 3.44180
\(93\) 22.0758 2.28915
\(94\) −20.0244 −2.06536
\(95\) 5.11302 0.524585
\(96\) −28.5428 −2.91314
\(97\) 0.983838 0.0998937 0.0499468 0.998752i \(-0.484095\pi\)
0.0499468 + 0.998752i \(0.484095\pi\)
\(98\) −1.80315 −0.182145
\(99\) 9.99313 1.00435
\(100\) −20.3497 −2.03497
\(101\) −5.09642 −0.507112 −0.253556 0.967321i \(-0.581600\pi\)
−0.253556 + 0.967321i \(0.581600\pi\)
\(102\) 2.04483 0.202469
\(103\) 6.86124 0.676058 0.338029 0.941136i \(-0.390240\pi\)
0.338029 + 0.941136i \(0.390240\pi\)
\(104\) 38.7797 3.80266
\(105\) 6.34141 0.618859
\(106\) −33.7587 −3.27893
\(107\) 11.8027 1.14101 0.570505 0.821294i \(-0.306747\pi\)
0.570505 + 0.821294i \(0.306747\pi\)
\(108\) 2.89296 0.278376
\(109\) −1.00000 −0.0957826
\(110\) −7.42202 −0.707661
\(111\) 2.49737 0.237040
\(112\) 28.0988 2.65509
\(113\) 20.6389 1.94155 0.970774 0.239996i \(-0.0771462\pi\)
0.970774 + 0.239996i \(0.0771462\pi\)
\(114\) −36.5978 −3.42770
\(115\) 6.18254 0.576525
\(116\) −26.4683 −2.45752
\(117\) −16.5448 −1.52957
\(118\) −7.75309 −0.713730
\(119\) −0.864829 −0.0792788
\(120\) −17.3532 −1.58412
\(121\) −1.46873 −0.133521
\(122\) 19.4376 1.75979
\(123\) 11.5853 1.04461
\(124\) 43.2286 3.88205
\(125\) −8.39033 −0.750454
\(126\) −23.5571 −2.09864
\(127\) 2.69862 0.239464 0.119732 0.992806i \(-0.461797\pi\)
0.119732 + 0.992806i \(0.461797\pi\)
\(128\) −2.68616 −0.237425
\(129\) −28.3202 −2.49346
\(130\) 12.2880 1.07773
\(131\) 6.83118 0.596843 0.298422 0.954434i \(-0.403540\pi\)
0.298422 + 0.954434i \(0.403540\pi\)
\(132\) 37.7049 3.28179
\(133\) 15.4785 1.34215
\(134\) 11.2623 0.972913
\(135\) 0.541789 0.0466298
\(136\) 2.36659 0.202933
\(137\) 5.26696 0.449987 0.224994 0.974360i \(-0.427764\pi\)
0.224994 + 0.974360i \(0.427764\pi\)
\(138\) −44.2532 −3.76708
\(139\) 18.0099 1.52758 0.763789 0.645466i \(-0.223337\pi\)
0.763789 + 0.645466i \(0.223337\pi\)
\(140\) 12.4177 1.04949
\(141\) 19.0513 1.60441
\(142\) 7.06123 0.592565
\(143\) −15.7801 −1.31960
\(144\) 32.8048 2.73374
\(145\) −4.95694 −0.411651
\(146\) −8.48137 −0.701923
\(147\) 1.71552 0.141493
\(148\) 4.89034 0.401983
\(149\) −4.00260 −0.327905 −0.163953 0.986468i \(-0.552424\pi\)
−0.163953 + 0.986468i \(0.552424\pi\)
\(150\) 27.2787 2.22730
\(151\) −12.8623 −1.04672 −0.523361 0.852111i \(-0.675322\pi\)
−0.523361 + 0.852111i \(0.675322\pi\)
\(152\) −42.3565 −3.43557
\(153\) −1.00967 −0.0816271
\(154\) −22.4684 −1.81056
\(155\) 8.09578 0.650269
\(156\) −62.4249 −4.99799
\(157\) 17.1050 1.36513 0.682564 0.730826i \(-0.260865\pi\)
0.682564 + 0.730826i \(0.260865\pi\)
\(158\) 6.56351 0.522165
\(159\) 32.1180 2.54713
\(160\) −10.4674 −0.827522
\(161\) 18.7162 1.47504
\(162\) 21.6119 1.69799
\(163\) −3.00302 −0.235215 −0.117607 0.993060i \(-0.537522\pi\)
−0.117607 + 0.993060i \(0.537522\pi\)
\(164\) 22.6861 1.77149
\(165\) 7.06131 0.549722
\(166\) −32.5505 −2.52641
\(167\) −13.1879 −1.02051 −0.510254 0.860023i \(-0.670449\pi\)
−0.510254 + 0.860023i \(0.670449\pi\)
\(168\) −52.5326 −4.05298
\(169\) 13.1259 1.00968
\(170\) 0.749895 0.0575143
\(171\) 18.0708 1.38191
\(172\) −55.4564 −4.22851
\(173\) 8.80846 0.669695 0.334847 0.942272i \(-0.391315\pi\)
0.334847 + 0.942272i \(0.391315\pi\)
\(174\) 35.4806 2.68978
\(175\) −11.5371 −0.872122
\(176\) 31.2887 2.35847
\(177\) 7.37630 0.554436
\(178\) 22.1608 1.66102
\(179\) −14.6016 −1.09138 −0.545688 0.837988i \(-0.683732\pi\)
−0.545688 + 0.837988i \(0.683732\pi\)
\(180\) 14.4974 1.08057
\(181\) 17.1855 1.27739 0.638693 0.769461i \(-0.279475\pi\)
0.638693 + 0.769461i \(0.279475\pi\)
\(182\) 37.1991 2.75738
\(183\) −18.4929 −1.36703
\(184\) −51.2165 −3.77573
\(185\) 0.915854 0.0673349
\(186\) −57.9477 −4.24893
\(187\) −0.963007 −0.0704220
\(188\) 37.3060 2.72082
\(189\) 1.64014 0.119303
\(190\) −13.4214 −0.973691
\(191\) −20.5170 −1.48456 −0.742279 0.670091i \(-0.766255\pi\)
−0.742279 + 0.670091i \(0.766255\pi\)
\(192\) 24.3030 1.75392
\(193\) 1.47202 0.105958 0.0529792 0.998596i \(-0.483128\pi\)
0.0529792 + 0.998596i \(0.483128\pi\)
\(194\) −2.58252 −0.185414
\(195\) −11.6908 −0.837198
\(196\) 3.35931 0.239951
\(197\) −8.38377 −0.597319 −0.298659 0.954360i \(-0.596539\pi\)
−0.298659 + 0.954360i \(0.596539\pi\)
\(198\) −26.2314 −1.86419
\(199\) −7.88280 −0.558797 −0.279398 0.960175i \(-0.590135\pi\)
−0.279398 + 0.960175i \(0.590135\pi\)
\(200\) 31.5710 2.23241
\(201\) −10.7149 −0.755773
\(202\) 13.3778 0.941260
\(203\) −15.0060 −1.05321
\(204\) −3.80957 −0.266723
\(205\) 4.24862 0.296737
\(206\) −18.0104 −1.25484
\(207\) 21.8508 1.51873
\(208\) −51.8021 −3.59183
\(209\) 17.2356 1.19221
\(210\) −16.6459 −1.14867
\(211\) −1.41650 −0.0975162 −0.0487581 0.998811i \(-0.515526\pi\)
−0.0487581 + 0.998811i \(0.515526\pi\)
\(212\) 62.8933 4.31953
\(213\) −6.71805 −0.460313
\(214\) −30.9815 −2.11785
\(215\) −10.3858 −0.708305
\(216\) −4.48821 −0.305384
\(217\) 24.5081 1.66372
\(218\) 2.62495 0.177784
\(219\) 8.06918 0.545265
\(220\) 13.8274 0.932243
\(221\) 1.59437 0.107249
\(222\) −6.55547 −0.439974
\(223\) 6.32104 0.423288 0.211644 0.977347i \(-0.432118\pi\)
0.211644 + 0.977347i \(0.432118\pi\)
\(224\) −31.6876 −2.11722
\(225\) −13.4693 −0.897955
\(226\) −54.1761 −3.60374
\(227\) 11.4149 0.757634 0.378817 0.925472i \(-0.376331\pi\)
0.378817 + 0.925472i \(0.376331\pi\)
\(228\) 68.1827 4.51551
\(229\) 0.101449 0.00670391 0.00335195 0.999994i \(-0.498933\pi\)
0.00335195 + 0.999994i \(0.498933\pi\)
\(230\) −16.2288 −1.07010
\(231\) 21.3764 1.40647
\(232\) 41.0635 2.69595
\(233\) 20.4082 1.33698 0.668492 0.743719i \(-0.266940\pi\)
0.668492 + 0.743719i \(0.266940\pi\)
\(234\) 43.4292 2.83906
\(235\) 6.98661 0.455756
\(236\) 14.4442 0.940238
\(237\) −6.24453 −0.405626
\(238\) 2.27013 0.147151
\(239\) −10.3833 −0.671642 −0.335821 0.941926i \(-0.609014\pi\)
−0.335821 + 0.941926i \(0.609014\pi\)
\(240\) 23.1804 1.49629
\(241\) 8.52476 0.549128 0.274564 0.961569i \(-0.411467\pi\)
0.274564 + 0.961569i \(0.411467\pi\)
\(242\) 3.85533 0.247830
\(243\) −22.3362 −1.43287
\(244\) −36.2127 −2.31828
\(245\) 0.629125 0.0401934
\(246\) −30.4107 −1.93891
\(247\) −28.5356 −1.81568
\(248\) −67.0658 −4.25869
\(249\) 30.9686 1.96256
\(250\) 22.0242 1.39293
\(251\) −20.0318 −1.26440 −0.632199 0.774806i \(-0.717847\pi\)
−0.632199 + 0.774806i \(0.717847\pi\)
\(252\) 43.8875 2.76466
\(253\) 20.8409 1.31026
\(254\) −7.08372 −0.444472
\(255\) −0.713450 −0.0446780
\(256\) −12.4118 −0.775738
\(257\) 24.9607 1.55700 0.778501 0.627643i \(-0.215980\pi\)
0.778501 + 0.627643i \(0.215980\pi\)
\(258\) 74.3390 4.62815
\(259\) 2.77253 0.172277
\(260\) −22.8929 −1.41976
\(261\) −17.5192 −1.08441
\(262\) −17.9315 −1.10781
\(263\) −26.6623 −1.64407 −0.822035 0.569437i \(-0.807161\pi\)
−0.822035 + 0.569437i \(0.807161\pi\)
\(264\) −58.4962 −3.60019
\(265\) 11.7785 0.723550
\(266\) −40.6301 −2.49119
\(267\) −21.0838 −1.29031
\(268\) −20.9819 −1.28167
\(269\) −18.7869 −1.14545 −0.572727 0.819746i \(-0.694115\pi\)
−0.572727 + 0.819746i \(0.694115\pi\)
\(270\) −1.42217 −0.0865504
\(271\) −1.23039 −0.0747406 −0.0373703 0.999301i \(-0.511898\pi\)
−0.0373703 + 0.999301i \(0.511898\pi\)
\(272\) −3.16130 −0.191682
\(273\) −35.3912 −2.14197
\(274\) −13.8255 −0.835229
\(275\) −12.8468 −0.774692
\(276\) 82.4448 4.96259
\(277\) −17.9773 −1.08015 −0.540074 0.841617i \(-0.681604\pi\)
−0.540074 + 0.841617i \(0.681604\pi\)
\(278\) −47.2750 −2.83536
\(279\) 28.6127 1.71300
\(280\) −19.2651 −1.15131
\(281\) 19.4732 1.16167 0.580837 0.814020i \(-0.302725\pi\)
0.580837 + 0.814020i \(0.302725\pi\)
\(282\) −50.0085 −2.97796
\(283\) −22.2775 −1.32426 −0.662130 0.749389i \(-0.730347\pi\)
−0.662130 + 0.749389i \(0.730347\pi\)
\(284\) −13.1552 −0.780620
\(285\) 12.7691 0.756378
\(286\) 41.4220 2.44934
\(287\) 12.8617 0.759202
\(288\) −36.9947 −2.17993
\(289\) −16.9027 −0.994277
\(290\) 13.0117 0.764073
\(291\) 2.45701 0.144033
\(292\) 15.8010 0.924684
\(293\) −28.3324 −1.65520 −0.827599 0.561319i \(-0.810294\pi\)
−0.827599 + 0.561319i \(0.810294\pi\)
\(294\) −4.50313 −0.262628
\(295\) 2.70509 0.157496
\(296\) −7.58698 −0.440984
\(297\) 1.82633 0.105975
\(298\) 10.5066 0.608631
\(299\) −34.5046 −1.99545
\(300\) −50.8209 −2.93414
\(301\) −31.4405 −1.81220
\(302\) 33.7629 1.94284
\(303\) −12.7277 −0.731185
\(304\) 56.5801 3.24509
\(305\) −6.78184 −0.388327
\(306\) 2.65033 0.151509
\(307\) −1.17159 −0.0668664 −0.0334332 0.999441i \(-0.510644\pi\)
−0.0334332 + 0.999441i \(0.510644\pi\)
\(308\) 41.8592 2.38515
\(309\) 17.1351 0.974781
\(310\) −21.2510 −1.20697
\(311\) −9.62845 −0.545979 −0.272990 0.962017i \(-0.588012\pi\)
−0.272990 + 0.962017i \(0.588012\pi\)
\(312\) 96.8474 5.48290
\(313\) −33.9059 −1.91648 −0.958238 0.285971i \(-0.907684\pi\)
−0.958238 + 0.285971i \(0.907684\pi\)
\(314\) −44.8997 −2.53384
\(315\) 8.21918 0.463098
\(316\) −12.2280 −0.687878
\(317\) −4.74609 −0.266567 −0.133283 0.991078i \(-0.542552\pi\)
−0.133283 + 0.991078i \(0.542552\pi\)
\(318\) −84.3081 −4.72776
\(319\) −16.7095 −0.935551
\(320\) 8.91256 0.498227
\(321\) 29.4758 1.64518
\(322\) −49.1290 −2.73785
\(323\) −1.74143 −0.0968956
\(324\) −40.2634 −2.23686
\(325\) 21.2694 1.17981
\(326\) 7.88277 0.436586
\(327\) −2.49737 −0.138105
\(328\) −35.1958 −1.94336
\(329\) 21.1503 1.16605
\(330\) −18.5355 −1.02035
\(331\) −10.7828 −0.592676 −0.296338 0.955083i \(-0.595765\pi\)
−0.296338 + 0.955083i \(0.595765\pi\)
\(332\) 60.6425 3.32819
\(333\) 3.23688 0.177380
\(334\) 34.6175 1.89418
\(335\) −3.92945 −0.214689
\(336\) 70.1733 3.82827
\(337\) −11.0289 −0.600781 −0.300391 0.953816i \(-0.597117\pi\)
−0.300391 + 0.953816i \(0.597117\pi\)
\(338\) −34.4548 −1.87409
\(339\) 51.5431 2.79944
\(340\) −1.39707 −0.0757669
\(341\) 27.2903 1.47785
\(342\) −47.4349 −2.56498
\(343\) −17.5032 −0.945083
\(344\) 86.0363 4.63877
\(345\) 15.4401 0.831268
\(346\) −23.1217 −1.24303
\(347\) −14.5936 −0.783426 −0.391713 0.920087i \(-0.628117\pi\)
−0.391713 + 0.920087i \(0.628117\pi\)
\(348\) −66.1013 −3.54340
\(349\) −16.4844 −0.882389 −0.441194 0.897412i \(-0.645445\pi\)
−0.441194 + 0.897412i \(0.645445\pi\)
\(350\) 30.2842 1.61876
\(351\) −3.02371 −0.161394
\(352\) −35.2849 −1.88069
\(353\) 3.53753 0.188284 0.0941418 0.995559i \(-0.469989\pi\)
0.0941418 + 0.995559i \(0.469989\pi\)
\(354\) −19.3624 −1.02910
\(355\) −2.46369 −0.130759
\(356\) −41.2862 −2.18816
\(357\) −2.15980 −0.114309
\(358\) 38.3284 2.02572
\(359\) 10.3635 0.546964 0.273482 0.961877i \(-0.411825\pi\)
0.273482 + 0.961877i \(0.411825\pi\)
\(360\) −22.4916 −1.18541
\(361\) 12.1676 0.640399
\(362\) −45.1109 −2.37098
\(363\) −3.66796 −0.192518
\(364\) −69.3028 −3.63245
\(365\) 2.95918 0.154891
\(366\) 48.5429 2.53738
\(367\) 15.7341 0.821311 0.410656 0.911791i \(-0.365300\pi\)
0.410656 + 0.911791i \(0.365300\pi\)
\(368\) 68.4152 3.56639
\(369\) 15.0158 0.781690
\(370\) −2.40407 −0.124981
\(371\) 35.6567 1.85121
\(372\) 107.958 5.59736
\(373\) 31.6788 1.64027 0.820134 0.572171i \(-0.193899\pi\)
0.820134 + 0.572171i \(0.193899\pi\)
\(374\) 2.52784 0.130712
\(375\) −20.9538 −1.08205
\(376\) −57.8774 −2.98480
\(377\) 27.6645 1.42479
\(378\) −4.30528 −0.221440
\(379\) 7.84041 0.402735 0.201367 0.979516i \(-0.435462\pi\)
0.201367 + 0.979516i \(0.435462\pi\)
\(380\) 25.0044 1.28270
\(381\) 6.73946 0.345273
\(382\) 53.8560 2.75551
\(383\) 30.5171 1.55935 0.779675 0.626185i \(-0.215384\pi\)
0.779675 + 0.626185i \(0.215384\pi\)
\(384\) −6.70835 −0.342334
\(385\) 7.83931 0.399528
\(386\) −3.86397 −0.196671
\(387\) −36.7062 −1.86588
\(388\) 4.81130 0.244257
\(389\) 2.60412 0.132034 0.0660171 0.997818i \(-0.478971\pi\)
0.0660171 + 0.997818i \(0.478971\pi\)
\(390\) 30.6878 1.55394
\(391\) −2.10569 −0.106489
\(392\) −5.21170 −0.263231
\(393\) 17.0600 0.860564
\(394\) 22.0069 1.10869
\(395\) −2.29004 −0.115224
\(396\) 48.8698 2.45580
\(397\) −15.0405 −0.754859 −0.377430 0.926038i \(-0.623192\pi\)
−0.377430 + 0.926038i \(0.623192\pi\)
\(398\) 20.6919 1.03719
\(399\) 38.6555 1.93520
\(400\) −42.1727 −2.10864
\(401\) −19.7617 −0.986850 −0.493425 0.869788i \(-0.664255\pi\)
−0.493425 + 0.869788i \(0.664255\pi\)
\(402\) 28.1261 1.40280
\(403\) −45.1823 −2.25069
\(404\) −24.9232 −1.23998
\(405\) −7.54047 −0.374689
\(406\) 39.3898 1.95488
\(407\) 3.08728 0.153031
\(408\) 5.91026 0.292601
\(409\) 10.9404 0.540970 0.270485 0.962724i \(-0.412816\pi\)
0.270485 + 0.962724i \(0.412816\pi\)
\(410\) −11.1524 −0.550778
\(411\) 13.1536 0.648818
\(412\) 33.5538 1.65308
\(413\) 8.18901 0.402955
\(414\) −57.3571 −2.81895
\(415\) 11.3570 0.557494
\(416\) 58.4183 2.86419
\(417\) 44.9774 2.20255
\(418\) −45.2426 −2.21289
\(419\) −2.45686 −0.120026 −0.0600128 0.998198i \(-0.519114\pi\)
−0.0600128 + 0.998198i \(0.519114\pi\)
\(420\) 31.0117 1.51321
\(421\) 30.9934 1.51052 0.755262 0.655423i \(-0.227510\pi\)
0.755262 + 0.655423i \(0.227510\pi\)
\(422\) 3.71825 0.181001
\(423\) 24.6926 1.20059
\(424\) −97.5740 −4.73861
\(425\) 1.29800 0.0629621
\(426\) 17.6345 0.854395
\(427\) −20.5304 −0.993537
\(428\) 57.7192 2.78996
\(429\) −39.4089 −1.90268
\(430\) 27.2621 1.31470
\(431\) 36.5313 1.75965 0.879826 0.475295i \(-0.157659\pi\)
0.879826 + 0.475295i \(0.157659\pi\)
\(432\) 5.99537 0.288453
\(433\) −20.8301 −1.00103 −0.500516 0.865727i \(-0.666856\pi\)
−0.500516 + 0.865727i \(0.666856\pi\)
\(434\) −64.3323 −3.08805
\(435\) −12.3793 −0.593543
\(436\) −4.89034 −0.234205
\(437\) 37.6871 1.80282
\(438\) −21.1812 −1.01207
\(439\) −21.8879 −1.04465 −0.522327 0.852745i \(-0.674936\pi\)
−0.522327 + 0.852745i \(0.674936\pi\)
\(440\) −21.4521 −1.02269
\(441\) 2.22350 0.105881
\(442\) −4.18514 −0.199067
\(443\) 27.5200 1.30752 0.653758 0.756704i \(-0.273192\pi\)
0.653758 + 0.756704i \(0.273192\pi\)
\(444\) 12.2130 0.579603
\(445\) −7.73200 −0.366532
\(446\) −16.5924 −0.785672
\(447\) −9.99598 −0.472794
\(448\) 26.9807 1.27472
\(449\) 20.3484 0.960302 0.480151 0.877186i \(-0.340582\pi\)
0.480151 + 0.877186i \(0.340582\pi\)
\(450\) 35.3562 1.66671
\(451\) 14.3218 0.674387
\(452\) 100.931 4.74741
\(453\) −32.1220 −1.50923
\(454\) −29.9635 −1.40626
\(455\) −12.9789 −0.608461
\(456\) −105.780 −4.95361
\(457\) −4.17012 −0.195070 −0.0975350 0.995232i \(-0.531096\pi\)
−0.0975350 + 0.995232i \(0.531096\pi\)
\(458\) −0.266297 −0.0124432
\(459\) −0.184526 −0.00861295
\(460\) 30.2347 1.40970
\(461\) −28.8920 −1.34564 −0.672818 0.739808i \(-0.734916\pi\)
−0.672818 + 0.739808i \(0.734916\pi\)
\(462\) −56.1120 −2.61057
\(463\) 29.3546 1.36423 0.682113 0.731247i \(-0.261061\pi\)
0.682113 + 0.731247i \(0.261061\pi\)
\(464\) −54.8529 −2.54648
\(465\) 20.2182 0.937596
\(466\) −53.5704 −2.48160
\(467\) 36.5212 1.69000 0.845000 0.534767i \(-0.179600\pi\)
0.845000 + 0.534767i \(0.179600\pi\)
\(468\) −80.9097 −3.74005
\(469\) −11.8955 −0.549283
\(470\) −18.3395 −0.845936
\(471\) 42.7176 1.96832
\(472\) −22.4091 −1.03146
\(473\) −35.0097 −1.60975
\(474\) 16.3915 0.752889
\(475\) −23.2312 −1.06592
\(476\) −4.22931 −0.193850
\(477\) 41.6286 1.90604
\(478\) 27.2557 1.24665
\(479\) 23.1199 1.05638 0.528188 0.849127i \(-0.322871\pi\)
0.528188 + 0.849127i \(0.322871\pi\)
\(480\) −26.1411 −1.19317
\(481\) −5.11135 −0.233057
\(482\) −22.3770 −1.01925
\(483\) 46.7413 2.12680
\(484\) −7.18257 −0.326480
\(485\) 0.901052 0.0409147
\(486\) 58.6314 2.65957
\(487\) 33.4896 1.51756 0.758779 0.651348i \(-0.225796\pi\)
0.758779 + 0.651348i \(0.225796\pi\)
\(488\) 56.1811 2.54320
\(489\) −7.49967 −0.339147
\(490\) −1.65142 −0.0746035
\(491\) 29.3470 1.32441 0.662205 0.749323i \(-0.269621\pi\)
0.662205 + 0.749323i \(0.269621\pi\)
\(492\) 56.6558 2.55424
\(493\) 1.68827 0.0760358
\(494\) 74.9044 3.37011
\(495\) 9.15225 0.411363
\(496\) 89.5869 4.02257
\(497\) −7.45824 −0.334548
\(498\) −81.2909 −3.64273
\(499\) −6.80632 −0.304693 −0.152346 0.988327i \(-0.548683\pi\)
−0.152346 + 0.988327i \(0.548683\pi\)
\(500\) −41.0315 −1.83499
\(501\) −32.9351 −1.47143
\(502\) 52.5824 2.34687
\(503\) 17.5390 0.782027 0.391014 0.920385i \(-0.372125\pi\)
0.391014 + 0.920385i \(0.372125\pi\)
\(504\) −68.0881 −3.03288
\(505\) −4.66757 −0.207704
\(506\) −54.7062 −2.43199
\(507\) 32.7803 1.45582
\(508\) 13.1972 0.585529
\(509\) −10.9100 −0.483577 −0.241788 0.970329i \(-0.577734\pi\)
−0.241788 + 0.970329i \(0.577734\pi\)
\(510\) 1.87277 0.0829276
\(511\) 8.95823 0.396289
\(512\) 37.9526 1.67729
\(513\) 3.30260 0.145813
\(514\) −65.5203 −2.88998
\(515\) 6.28390 0.276902
\(516\) −138.495 −6.09692
\(517\) 23.5513 1.03579
\(518\) −7.27774 −0.319766
\(519\) 21.9980 0.965606
\(520\) 35.5165 1.55750
\(521\) −0.811856 −0.0355681 −0.0177840 0.999842i \(-0.505661\pi\)
−0.0177840 + 0.999842i \(0.505661\pi\)
\(522\) 45.9869 2.01279
\(523\) −44.1589 −1.93093 −0.965466 0.260529i \(-0.916103\pi\)
−0.965466 + 0.260529i \(0.916103\pi\)
\(524\) 33.4068 1.45938
\(525\) −28.8124 −1.25748
\(526\) 69.9872 3.05159
\(527\) −2.75732 −0.120111
\(528\) 78.1395 3.40059
\(529\) 22.5703 0.981318
\(530\) −30.9180 −1.34299
\(531\) 9.56051 0.414891
\(532\) 75.6949 3.28179
\(533\) −23.7114 −1.02706
\(534\) 55.3439 2.39496
\(535\) 10.8096 0.467338
\(536\) 32.5518 1.40602
\(537\) −36.4657 −1.57361
\(538\) 49.3145 2.12610
\(539\) 2.12074 0.0913466
\(540\) 2.64953 0.114018
\(541\) 35.0167 1.50549 0.752743 0.658314i \(-0.228730\pi\)
0.752743 + 0.658314i \(0.228730\pi\)
\(542\) 3.22969 0.138727
\(543\) 42.9186 1.84181
\(544\) 3.56507 0.152851
\(545\) −0.915854 −0.0392309
\(546\) 92.9000 3.97575
\(547\) 7.53892 0.322341 0.161170 0.986927i \(-0.448473\pi\)
0.161170 + 0.986927i \(0.448473\pi\)
\(548\) 25.7572 1.10029
\(549\) −23.9689 −1.02297
\(550\) 33.7222 1.43792
\(551\) −30.2161 −1.28725
\(552\) −127.907 −5.44407
\(553\) −6.93254 −0.294802
\(554\) 47.1893 2.00488
\(555\) 2.28723 0.0970875
\(556\) 88.0744 3.73519
\(557\) −41.9938 −1.77933 −0.889667 0.456609i \(-0.849064\pi\)
−0.889667 + 0.456609i \(0.849064\pi\)
\(558\) −75.1067 −3.17952
\(559\) 57.9627 2.45156
\(560\) 25.7344 1.08748
\(561\) −2.40499 −0.101539
\(562\) −51.1161 −2.15620
\(563\) −10.2205 −0.430742 −0.215371 0.976532i \(-0.569096\pi\)
−0.215371 + 0.976532i \(0.569096\pi\)
\(564\) 93.1671 3.92304
\(565\) 18.9022 0.795224
\(566\) 58.4772 2.45798
\(567\) −22.8270 −0.958643
\(568\) 20.4093 0.856356
\(569\) 7.91378 0.331763 0.165882 0.986146i \(-0.446953\pi\)
0.165882 + 0.986146i \(0.446953\pi\)
\(570\) −33.5183 −1.40393
\(571\) −21.5305 −0.901022 −0.450511 0.892771i \(-0.648758\pi\)
−0.450511 + 0.892771i \(0.648758\pi\)
\(572\) −77.1702 −3.22665
\(573\) −51.2386 −2.14052
\(574\) −33.7613 −1.40917
\(575\) −28.0906 −1.17146
\(576\) 31.4994 1.31247
\(577\) −13.0018 −0.541274 −0.270637 0.962682i \(-0.587234\pi\)
−0.270637 + 0.962682i \(0.587234\pi\)
\(578\) 44.3687 1.84549
\(579\) 3.67618 0.152777
\(580\) −24.2411 −1.00656
\(581\) 34.3807 1.42635
\(582\) −6.44952 −0.267341
\(583\) 39.7046 1.64440
\(584\) −24.5140 −1.01440
\(585\) −15.1526 −0.626484
\(586\) 74.3711 3.07224
\(587\) −38.9953 −1.60951 −0.804754 0.593608i \(-0.797703\pi\)
−0.804754 + 0.593608i \(0.797703\pi\)
\(588\) 8.38945 0.345975
\(589\) 49.3497 2.03342
\(590\) −7.10070 −0.292331
\(591\) −20.9374 −0.861249
\(592\) 10.1347 0.416535
\(593\) −33.7818 −1.38725 −0.693627 0.720334i \(-0.743988\pi\)
−0.693627 + 0.720334i \(0.743988\pi\)
\(594\) −4.79402 −0.196701
\(595\) −0.792057 −0.0324712
\(596\) −19.5740 −0.801784
\(597\) −19.6863 −0.805707
\(598\) 90.5726 3.70379
\(599\) −30.7155 −1.25500 −0.627501 0.778616i \(-0.715922\pi\)
−0.627501 + 0.778616i \(0.715922\pi\)
\(600\) 78.8446 3.21882
\(601\) −42.5521 −1.73574 −0.867868 0.496795i \(-0.834510\pi\)
−0.867868 + 0.496795i \(0.834510\pi\)
\(602\) 82.5296 3.36366
\(603\) −13.8878 −0.565553
\(604\) −62.9011 −2.55941
\(605\) −1.34514 −0.0546877
\(606\) 33.4094 1.35716
\(607\) −0.357441 −0.0145081 −0.00725405 0.999974i \(-0.502309\pi\)
−0.00725405 + 0.999974i \(0.502309\pi\)
\(608\) −63.8065 −2.58770
\(609\) −37.4755 −1.51858
\(610\) 17.8020 0.720780
\(611\) −38.9920 −1.57745
\(612\) −4.93763 −0.199592
\(613\) 42.3848 1.71191 0.855953 0.517054i \(-0.172971\pi\)
0.855953 + 0.517054i \(0.172971\pi\)
\(614\) 3.07537 0.124112
\(615\) 10.6104 0.427853
\(616\) −64.9412 −2.61656
\(617\) −15.5147 −0.624599 −0.312299 0.949984i \(-0.601099\pi\)
−0.312299 + 0.949984i \(0.601099\pi\)
\(618\) −44.9787 −1.80931
\(619\) −25.5528 −1.02705 −0.513527 0.858073i \(-0.671662\pi\)
−0.513527 + 0.858073i \(0.671662\pi\)
\(620\) 39.5911 1.59002
\(621\) 3.99342 0.160251
\(622\) 25.2741 1.01340
\(623\) −23.4068 −0.937774
\(624\) −129.369 −5.17891
\(625\) 13.1217 0.524870
\(626\) 89.0012 3.55720
\(627\) 43.0438 1.71900
\(628\) 83.6492 3.33797
\(629\) −0.311928 −0.0124374
\(630\) −21.5749 −0.859565
\(631\) 0.588235 0.0234173 0.0117086 0.999931i \(-0.496273\pi\)
0.0117086 + 0.999931i \(0.496273\pi\)
\(632\) 18.9708 0.754617
\(633\) −3.53754 −0.140605
\(634\) 12.4582 0.494779
\(635\) 2.47154 0.0980801
\(636\) 157.068 6.22815
\(637\) −3.51113 −0.139116
\(638\) 43.8615 1.73649
\(639\) −8.70735 −0.344457
\(640\) −2.46013 −0.0972452
\(641\) 42.5528 1.68073 0.840367 0.542018i \(-0.182340\pi\)
0.840367 + 0.542018i \(0.182340\pi\)
\(642\) −77.3723 −3.05364
\(643\) −11.3746 −0.448569 −0.224285 0.974524i \(-0.572005\pi\)
−0.224285 + 0.974524i \(0.572005\pi\)
\(644\) 91.5285 3.60673
\(645\) −25.9372 −1.02128
\(646\) 4.57115 0.179850
\(647\) 32.6647 1.28418 0.642091 0.766628i \(-0.278067\pi\)
0.642091 + 0.766628i \(0.278067\pi\)
\(648\) 62.4656 2.45388
\(649\) 9.11864 0.357938
\(650\) −55.8310 −2.18987
\(651\) 61.2058 2.39884
\(652\) −14.6858 −0.575140
\(653\) 36.0416 1.41042 0.705209 0.708999i \(-0.250853\pi\)
0.705209 + 0.708999i \(0.250853\pi\)
\(654\) 6.55547 0.256339
\(655\) 6.25636 0.244456
\(656\) 47.0147 1.83562
\(657\) 10.4586 0.408027
\(658\) −55.5184 −2.16433
\(659\) −14.8904 −0.580050 −0.290025 0.957019i \(-0.593664\pi\)
−0.290025 + 0.957019i \(0.593664\pi\)
\(660\) 34.5322 1.34416
\(661\) −22.6126 −0.879527 −0.439763 0.898114i \(-0.644938\pi\)
−0.439763 + 0.898114i \(0.644938\pi\)
\(662\) 28.3042 1.10008
\(663\) 3.98174 0.154638
\(664\) −94.0821 −3.65109
\(665\) 14.1760 0.549722
\(666\) −8.49662 −0.329237
\(667\) −36.5366 −1.41470
\(668\) −64.4932 −2.49532
\(669\) 15.7860 0.610322
\(670\) 10.3146 0.398488
\(671\) −22.8611 −0.882543
\(672\) −79.1359 −3.05273
\(673\) 39.3898 1.51837 0.759183 0.650878i \(-0.225599\pi\)
0.759183 + 0.650878i \(0.225599\pi\)
\(674\) 28.9502 1.11512
\(675\) −2.46164 −0.0947485
\(676\) 64.1901 2.46885
\(677\) 13.7814 0.529661 0.264830 0.964295i \(-0.414684\pi\)
0.264830 + 0.964295i \(0.414684\pi\)
\(678\) −135.298 −5.19608
\(679\) 2.72772 0.104680
\(680\) 2.16745 0.0831179
\(681\) 28.5073 1.09240
\(682\) −71.6355 −2.74307
\(683\) −15.4366 −0.590666 −0.295333 0.955394i \(-0.595431\pi\)
−0.295333 + 0.955394i \(0.595431\pi\)
\(684\) 88.3723 3.37900
\(685\) 4.82377 0.184307
\(686\) 45.9449 1.75418
\(687\) 0.253355 0.00966609
\(688\) −114.928 −4.38158
\(689\) −65.7356 −2.50433
\(690\) −40.5295 −1.54293
\(691\) −34.2472 −1.30282 −0.651412 0.758724i \(-0.725823\pi\)
−0.651412 + 0.758724i \(0.725823\pi\)
\(692\) 43.0763 1.63752
\(693\) 27.7063 1.05247
\(694\) 38.3074 1.45413
\(695\) 16.4944 0.625669
\(696\) 102.551 3.88718
\(697\) −1.44702 −0.0548100
\(698\) 43.2706 1.63782
\(699\) 50.9669 1.92774
\(700\) −56.4203 −2.13249
\(701\) 30.1425 1.13847 0.569233 0.822177i \(-0.307240\pi\)
0.569233 + 0.822177i \(0.307240\pi\)
\(702\) 7.93707 0.299565
\(703\) 5.58279 0.210559
\(704\) 30.0436 1.13231
\(705\) 17.4482 0.657136
\(706\) −9.28582 −0.349476
\(707\) −14.1300 −0.531412
\(708\) 36.0726 1.35569
\(709\) −37.7185 −1.41655 −0.708274 0.705937i \(-0.750526\pi\)
−0.708274 + 0.705937i \(0.750526\pi\)
\(710\) 6.46705 0.242704
\(711\) −8.09361 −0.303534
\(712\) 64.0523 2.40046
\(713\) 59.6724 2.23475
\(714\) 5.66936 0.212171
\(715\) −14.4523 −0.540486
\(716\) −71.4068 −2.66860
\(717\) −25.9311 −0.968413
\(718\) −27.2036 −1.01523
\(719\) 2.07831 0.0775078 0.0387539 0.999249i \(-0.487661\pi\)
0.0387539 + 0.999249i \(0.487661\pi\)
\(720\) 30.0444 1.11969
\(721\) 19.0230 0.708454
\(722\) −31.9392 −1.18866
\(723\) 21.2895 0.791765
\(724\) 84.0428 3.12343
\(725\) 22.5220 0.836447
\(726\) 9.62819 0.357336
\(727\) −36.8618 −1.36713 −0.683564 0.729890i \(-0.739571\pi\)
−0.683564 + 0.729890i \(0.739571\pi\)
\(728\) 107.518 3.98488
\(729\) −31.0821 −1.15119
\(730\) −7.76770 −0.287495
\(731\) 3.53726 0.130830
\(732\) −90.4365 −3.34263
\(733\) −35.7912 −1.32198 −0.660988 0.750396i \(-0.729863\pi\)
−0.660988 + 0.750396i \(0.729863\pi\)
\(734\) −41.3010 −1.52445
\(735\) 1.57116 0.0579532
\(736\) −77.1533 −2.84391
\(737\) −13.2459 −0.487919
\(738\) −39.4156 −1.45091
\(739\) −34.1041 −1.25454 −0.627269 0.778803i \(-0.715827\pi\)
−0.627269 + 0.778803i \(0.715827\pi\)
\(740\) 4.47883 0.164645
\(741\) −71.2641 −2.61795
\(742\) −93.5970 −3.43605
\(743\) 10.3748 0.380615 0.190308 0.981724i \(-0.439051\pi\)
0.190308 + 0.981724i \(0.439051\pi\)
\(744\) −167.488 −6.14043
\(745\) −3.66579 −0.134304
\(746\) −83.1552 −3.04453
\(747\) 40.1388 1.46860
\(748\) −4.70943 −0.172194
\(749\) 32.7234 1.19569
\(750\) 55.0026 2.00841
\(751\) 40.2692 1.46945 0.734723 0.678367i \(-0.237312\pi\)
0.734723 + 0.678367i \(0.237312\pi\)
\(752\) 77.3129 2.81931
\(753\) −50.0270 −1.82308
\(754\) −72.6178 −2.64459
\(755\) −11.7800 −0.428719
\(756\) 8.02083 0.291715
\(757\) −4.88608 −0.177588 −0.0887938 0.996050i \(-0.528301\pi\)
−0.0887938 + 0.996050i \(0.528301\pi\)
\(758\) −20.5806 −0.747522
\(759\) 52.0475 1.88921
\(760\) −38.7924 −1.40715
\(761\) −27.7179 −1.00477 −0.502387 0.864643i \(-0.667545\pi\)
−0.502387 + 0.864643i \(0.667545\pi\)
\(762\) −17.6907 −0.640867
\(763\) −2.77253 −0.100372
\(764\) −100.335 −3.63000
\(765\) −0.924711 −0.0334330
\(766\) −80.1056 −2.89433
\(767\) −15.0970 −0.545121
\(768\) −30.9969 −1.11851
\(769\) 3.32049 0.119740 0.0598699 0.998206i \(-0.480931\pi\)
0.0598699 + 0.998206i \(0.480931\pi\)
\(770\) −20.5778 −0.741571
\(771\) 62.3361 2.24498
\(772\) 7.19868 0.259086
\(773\) −2.72115 −0.0978729 −0.0489364 0.998802i \(-0.515583\pi\)
−0.0489364 + 0.998802i \(0.515583\pi\)
\(774\) 96.3517 3.46329
\(775\) −36.7835 −1.32130
\(776\) −7.46436 −0.267955
\(777\) 6.92405 0.248399
\(778\) −6.83568 −0.245071
\(779\) 25.8984 0.927908
\(780\) −57.1721 −2.04709
\(781\) −8.30492 −0.297173
\(782\) 5.52733 0.197657
\(783\) −3.20178 −0.114422
\(784\) 6.96182 0.248637
\(785\) 15.6657 0.559132
\(786\) −44.7816 −1.59731
\(787\) −15.5636 −0.554783 −0.277392 0.960757i \(-0.589470\pi\)
−0.277392 + 0.960757i \(0.589470\pi\)
\(788\) −40.9994 −1.46054
\(789\) −66.5858 −2.37052
\(790\) 6.01122 0.213870
\(791\) 57.2221 2.03458
\(792\) −75.8176 −2.69406
\(793\) 37.8492 1.34407
\(794\) 39.4804 1.40111
\(795\) 29.4154 1.04326
\(796\) −38.5496 −1.36635
\(797\) 48.8218 1.72936 0.864679 0.502325i \(-0.167522\pi\)
0.864679 + 0.502325i \(0.167522\pi\)
\(798\) −101.469 −3.59195
\(799\) −2.37955 −0.0841823
\(800\) 47.5591 1.68147
\(801\) −27.3270 −0.965552
\(802\) 51.8733 1.83171
\(803\) 9.97519 0.352017
\(804\) −52.3997 −1.84799
\(805\) 17.1413 0.604151
\(806\) 118.601 4.17754
\(807\) −46.9178 −1.65158
\(808\) 38.6664 1.36028
\(809\) 7.27769 0.255870 0.127935 0.991783i \(-0.459165\pi\)
0.127935 + 0.991783i \(0.459165\pi\)
\(810\) 19.7933 0.695466
\(811\) −35.5030 −1.24668 −0.623339 0.781952i \(-0.714224\pi\)
−0.623339 + 0.781952i \(0.714224\pi\)
\(812\) −73.3842 −2.57528
\(813\) −3.07273 −0.107765
\(814\) −8.10393 −0.284043
\(815\) −2.75033 −0.0963398
\(816\) −7.89495 −0.276379
\(817\) −63.3089 −2.21490
\(818\) −28.7180 −1.00410
\(819\) −45.8710 −1.60286
\(820\) 20.7772 0.725571
\(821\) 8.93883 0.311967 0.155984 0.987760i \(-0.450145\pi\)
0.155984 + 0.987760i \(0.450145\pi\)
\(822\) −34.5274 −1.20428
\(823\) 24.2143 0.844057 0.422028 0.906583i \(-0.361318\pi\)
0.422028 + 0.906583i \(0.361318\pi\)
\(824\) −52.0561 −1.81346
\(825\) −32.0833 −1.11700
\(826\) −21.4957 −0.747931
\(827\) −10.2997 −0.358155 −0.179078 0.983835i \(-0.557311\pi\)
−0.179078 + 0.983835i \(0.557311\pi\)
\(828\) 106.858 3.71356
\(829\) −10.6592 −0.370211 −0.185105 0.982719i \(-0.559263\pi\)
−0.185105 + 0.982719i \(0.559263\pi\)
\(830\) −29.8115 −1.03477
\(831\) −44.8959 −1.55742
\(832\) −49.7407 −1.72445
\(833\) −0.214272 −0.00742408
\(834\) −118.063 −4.08820
\(835\) −12.0782 −0.417982
\(836\) 84.2880 2.91516
\(837\) 5.22922 0.180748
\(838\) 6.44913 0.222781
\(839\) 10.6957 0.369256 0.184628 0.982808i \(-0.440892\pi\)
0.184628 + 0.982808i \(0.440892\pi\)
\(840\) −48.1122 −1.66003
\(841\) 0.293738 0.0101289
\(842\) −81.3558 −2.80371
\(843\) 48.6319 1.67497
\(844\) −6.92719 −0.238444
\(845\) 12.0214 0.413549
\(846\) −64.8166 −2.22844
\(847\) −4.07209 −0.139919
\(848\) 130.340 4.47589
\(849\) −55.6353 −1.90940
\(850\) −3.40717 −0.116865
\(851\) 6.75058 0.231407
\(852\) −32.8535 −1.12554
\(853\) 14.6907 0.502999 0.251499 0.967857i \(-0.419076\pi\)
0.251499 + 0.967857i \(0.419076\pi\)
\(854\) 53.8912 1.84412
\(855\) 16.5502 0.566006
\(856\) −89.5469 −3.06065
\(857\) 11.4796 0.392137 0.196068 0.980590i \(-0.437183\pi\)
0.196068 + 0.980590i \(0.437183\pi\)
\(858\) 103.446 3.53160
\(859\) 39.7116 1.35494 0.677471 0.735550i \(-0.263076\pi\)
0.677471 + 0.735550i \(0.263076\pi\)
\(860\) −50.7900 −1.73192
\(861\) 32.1205 1.09466
\(862\) −95.8928 −3.26612
\(863\) 14.0470 0.478165 0.239082 0.970999i \(-0.423153\pi\)
0.239082 + 0.970999i \(0.423153\pi\)
\(864\) −6.76111 −0.230018
\(865\) 8.06726 0.274295
\(866\) 54.6780 1.85803
\(867\) −42.2124 −1.43361
\(868\) 119.853 4.06807
\(869\) −7.71954 −0.261868
\(870\) 32.4951 1.10169
\(871\) 21.9302 0.743075
\(872\) 7.58698 0.256927
\(873\) 3.18456 0.107781
\(874\) −98.9265 −3.34624
\(875\) −23.2625 −0.786414
\(876\) 39.4610 1.33326
\(877\) 42.3028 1.42847 0.714233 0.699908i \(-0.246776\pi\)
0.714233 + 0.699908i \(0.246776\pi\)
\(878\) 57.4546 1.93900
\(879\) −70.7567 −2.38656
\(880\) 28.6559 0.965989
\(881\) −20.7693 −0.699734 −0.349867 0.936799i \(-0.613773\pi\)
−0.349867 + 0.936799i \(0.613773\pi\)
\(882\) −5.83657 −0.196527
\(883\) 22.4329 0.754927 0.377464 0.926024i \(-0.376796\pi\)
0.377464 + 0.926024i \(0.376796\pi\)
\(884\) 7.79702 0.262242
\(885\) 6.75561 0.227087
\(886\) −72.2385 −2.42690
\(887\) −35.5623 −1.19406 −0.597032 0.802217i \(-0.703654\pi\)
−0.597032 + 0.802217i \(0.703654\pi\)
\(888\) −18.9475 −0.635837
\(889\) 7.48200 0.250938
\(890\) 20.2961 0.680326
\(891\) −25.4184 −0.851547
\(892\) 30.9120 1.03501
\(893\) 42.5884 1.42517
\(894\) 26.2389 0.877560
\(895\) −13.3729 −0.447008
\(896\) −7.44746 −0.248802
\(897\) −86.1708 −2.87716
\(898\) −53.4135 −1.78243
\(899\) −47.8432 −1.59566
\(900\) −65.8695 −2.19565
\(901\) −4.01162 −0.133646
\(902\) −37.5939 −1.25174
\(903\) −78.5187 −2.61294
\(904\) −156.587 −5.20801
\(905\) 15.7394 0.523195
\(906\) 84.3186 2.80130
\(907\) −23.5567 −0.782186 −0.391093 0.920351i \(-0.627903\pi\)
−0.391093 + 0.920351i \(0.627903\pi\)
\(908\) 55.8227 1.85254
\(909\) −16.4965 −0.547153
\(910\) 34.0689 1.12937
\(911\) −53.8620 −1.78453 −0.892264 0.451514i \(-0.850884\pi\)
−0.892264 + 0.451514i \(0.850884\pi\)
\(912\) 141.302 4.67896
\(913\) 38.2837 1.26700
\(914\) 10.9463 0.362073
\(915\) −16.9368 −0.559913
\(916\) 0.496117 0.0163922
\(917\) 18.9397 0.625443
\(918\) 0.484372 0.0159866
\(919\) 48.6339 1.60428 0.802142 0.597133i \(-0.203693\pi\)
0.802142 + 0.597133i \(0.203693\pi\)
\(920\) −46.9068 −1.54647
\(921\) −2.92591 −0.0964119
\(922\) 75.8400 2.49766
\(923\) 13.7498 0.452579
\(924\) 104.538 3.43905
\(925\) −4.16121 −0.136820
\(926\) −77.0543 −2.53216
\(927\) 22.2090 0.729439
\(928\) 61.8587 2.03061
\(929\) −50.8799 −1.66932 −0.834658 0.550769i \(-0.814335\pi\)
−0.834658 + 0.550769i \(0.814335\pi\)
\(930\) −53.0717 −1.74029
\(931\) 3.83498 0.125686
\(932\) 99.8029 3.26915
\(933\) −24.0458 −0.787225
\(934\) −95.8662 −3.13684
\(935\) −0.881974 −0.0288436
\(936\) 125.525 4.10291
\(937\) −37.9815 −1.24080 −0.620400 0.784286i \(-0.713030\pi\)
−0.620400 + 0.784286i \(0.713030\pi\)
\(938\) 31.2250 1.01953
\(939\) −84.6758 −2.76329
\(940\) 34.1669 1.11440
\(941\) 5.15932 0.168189 0.0840946 0.996458i \(-0.473200\pi\)
0.0840946 + 0.996458i \(0.473200\pi\)
\(942\) −112.131 −3.65343
\(943\) 31.3158 1.01978
\(944\) 29.9341 0.974273
\(945\) 1.50213 0.0488642
\(946\) 91.8986 2.98788
\(947\) −19.0304 −0.618406 −0.309203 0.950996i \(-0.600062\pi\)
−0.309203 + 0.950996i \(0.600062\pi\)
\(948\) −30.5379 −0.991823
\(949\) −16.5151 −0.536103
\(950\) 60.9806 1.97847
\(951\) −11.8528 −0.384352
\(952\) 6.56144 0.212657
\(953\) −37.4951 −1.21459 −0.607293 0.794478i \(-0.707745\pi\)
−0.607293 + 0.794478i \(0.707745\pi\)
\(954\) −109.273 −3.53783
\(955\) −18.7906 −0.608049
\(956\) −50.7780 −1.64228
\(957\) −41.7298 −1.34893
\(958\) −60.6886 −1.96076
\(959\) 14.6028 0.471550
\(960\) 22.2580 0.718373
\(961\) 47.1385 1.52060
\(962\) 13.4170 0.432582
\(963\) 38.2039 1.23110
\(964\) 41.6889 1.34271
\(965\) 1.34816 0.0433987
\(966\) −122.693 −3.94760
\(967\) −20.8946 −0.671926 −0.335963 0.941875i \(-0.609062\pi\)
−0.335963 + 0.941875i \(0.609062\pi\)
\(968\) 11.1432 0.358156
\(969\) −4.34900 −0.139710
\(970\) −2.36521 −0.0759424
\(971\) −12.5698 −0.403384 −0.201692 0.979449i \(-0.564644\pi\)
−0.201692 + 0.979449i \(0.564644\pi\)
\(972\) −109.232 −3.50361
\(973\) 49.9330 1.60078
\(974\) −87.9084 −2.81677
\(975\) 53.1177 1.70113
\(976\) −75.0470 −2.40220
\(977\) −17.6853 −0.565803 −0.282901 0.959149i \(-0.591297\pi\)
−0.282901 + 0.959149i \(0.591297\pi\)
\(978\) 19.6862 0.629496
\(979\) −26.0640 −0.833009
\(980\) 3.07664 0.0982795
\(981\) −3.23688 −0.103345
\(982\) −77.0341 −2.45826
\(983\) −43.3426 −1.38241 −0.691207 0.722657i \(-0.742921\pi\)
−0.691207 + 0.722657i \(0.742921\pi\)
\(984\) −87.8970 −2.80206
\(985\) −7.67830 −0.244651
\(986\) −4.43161 −0.141131
\(987\) 52.8202 1.68129
\(988\) −139.549 −4.43964
\(989\) −76.5516 −2.43420
\(990\) −24.0241 −0.763537
\(991\) 13.8247 0.439157 0.219579 0.975595i \(-0.429532\pi\)
0.219579 + 0.975595i \(0.429532\pi\)
\(992\) −101.029 −3.20767
\(993\) −26.9287 −0.854556
\(994\) 19.5775 0.620960
\(995\) −7.21949 −0.228873
\(996\) 151.447 4.79878
\(997\) −27.7601 −0.879172 −0.439586 0.898200i \(-0.644875\pi\)
−0.439586 + 0.898200i \(0.644875\pi\)
\(998\) 17.8662 0.565545
\(999\) 0.591568 0.0187164
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 4033.2.a.f.1.4 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.4 85 1.1 even 1 trivial