Properties

Label 6025.2.a.f.1.6
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 1.6
Root \(-0.911223\) of defining polynomial
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.91122 q^{2} +0.186202 q^{3} +1.65278 q^{4} +0.355874 q^{6} -3.52970 q^{7} -0.663624 q^{8} -2.96533 q^{9} +O(q^{10})\) \(q+1.91122 q^{2} +0.186202 q^{3} +1.65278 q^{4} +0.355874 q^{6} -3.52970 q^{7} -0.663624 q^{8} -2.96533 q^{9} +0.515564 q^{11} +0.307750 q^{12} +5.38098 q^{13} -6.74604 q^{14} -4.57388 q^{16} +4.16566 q^{17} -5.66741 q^{18} +4.92935 q^{19} -0.657237 q^{21} +0.985358 q^{22} +7.69193 q^{23} -0.123568 q^{24} +10.2843 q^{26} -1.11076 q^{27} -5.83379 q^{28} -8.93755 q^{29} -4.43182 q^{31} -7.41447 q^{32} +0.0959992 q^{33} +7.96151 q^{34} -4.90102 q^{36} -5.99816 q^{37} +9.42110 q^{38} +1.00195 q^{39} -8.99946 q^{41} -1.25613 q^{42} +1.66336 q^{43} +0.852112 q^{44} +14.7010 q^{46} -8.55484 q^{47} -0.851668 q^{48} +5.45876 q^{49} +0.775656 q^{51} +8.89356 q^{52} -13.1736 q^{53} -2.12291 q^{54} +2.34239 q^{56} +0.917857 q^{57} -17.0817 q^{58} +9.25521 q^{59} -10.4203 q^{61} -8.47019 q^{62} +10.4667 q^{63} -5.02293 q^{64} +0.183476 q^{66} +3.91715 q^{67} +6.88490 q^{68} +1.43226 q^{69} -13.6724 q^{71} +1.96786 q^{72} -11.5529 q^{73} -11.4638 q^{74} +8.14711 q^{76} -1.81979 q^{77} +1.91495 q^{78} -1.43448 q^{79} +8.68916 q^{81} -17.2000 q^{82} -1.73047 q^{83} -1.08627 q^{84} +3.17906 q^{86} -1.66419 q^{87} -0.342141 q^{88} -1.07999 q^{89} -18.9932 q^{91} +12.7130 q^{92} -0.825214 q^{93} -16.3502 q^{94} -1.38059 q^{96} +16.0883 q^{97} +10.4329 q^{98} -1.52882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} - 18q^{11} - q^{12} + q^{13} - 6q^{14} + 4q^{16} + 2q^{17} - 8q^{18} - 6q^{19} - 2q^{21} - 10q^{22} + 22q^{23} - 3q^{24} + 8q^{26} - 3q^{27} - 9q^{28} - 16q^{29} - 18q^{31} + 6q^{32} - 4q^{33} + 11q^{34} - 7q^{36} - 8q^{37} - 16q^{38} - 9q^{39} - 15q^{41} - 19q^{42} - 14q^{43} - 4q^{44} + 11q^{46} + 10q^{47} - 31q^{48} + 6q^{49} + 13q^{51} - 27q^{52} - 15q^{53} + 16q^{54} + 13q^{56} - 14q^{57} - 17q^{58} - 18q^{59} + 4q^{61} - 13q^{62} + 16q^{63} + 2q^{64} + 16q^{66} - 18q^{67} + 15q^{68} + 26q^{69} - 50q^{71} - 30q^{72} + 10q^{74} - 20q^{76} - 17q^{77} + 32q^{78} - 15q^{79} - 9q^{81} - 45q^{82} + 24q^{83} + 6q^{84} - 23q^{86} - 12q^{87} - 8q^{88} - 13q^{89} - 12q^{91} + 10q^{92} - 14q^{93} - 32q^{94} - 15q^{96} - q^{97} - 9q^{98} - 20q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.91122 1.35144 0.675720 0.737159i \(-0.263833\pi\)
0.675720 + 0.737159i \(0.263833\pi\)
\(3\) 0.186202 0.107504 0.0537520 0.998554i \(-0.482882\pi\)
0.0537520 + 0.998554i \(0.482882\pi\)
\(4\) 1.65278 0.826388
\(5\) 0 0
\(6\) 0.355874 0.145285
\(7\) −3.52970 −1.33410 −0.667050 0.745013i \(-0.732443\pi\)
−0.667050 + 0.745013i \(0.732443\pi\)
\(8\) −0.663624 −0.234627
\(9\) −2.96533 −0.988443
\(10\) 0 0
\(11\) 0.515564 0.155448 0.0777242 0.996975i \(-0.475235\pi\)
0.0777242 + 0.996975i \(0.475235\pi\)
\(12\) 0.307750 0.0888399
\(13\) 5.38098 1.49242 0.746208 0.665712i \(-0.231872\pi\)
0.746208 + 0.665712i \(0.231872\pi\)
\(14\) −6.74604 −1.80295
\(15\) 0 0
\(16\) −4.57388 −1.14347
\(17\) 4.16566 1.01032 0.505161 0.863025i \(-0.331433\pi\)
0.505161 + 0.863025i \(0.331433\pi\)
\(18\) −5.66741 −1.33582
\(19\) 4.92935 1.13087 0.565436 0.824792i \(-0.308708\pi\)
0.565436 + 0.824792i \(0.308708\pi\)
\(20\) 0 0
\(21\) −0.657237 −0.143421
\(22\) 0.985358 0.210079
\(23\) 7.69193 1.60388 0.801940 0.597405i \(-0.203802\pi\)
0.801940 + 0.597405i \(0.203802\pi\)
\(24\) −0.123568 −0.0252233
\(25\) 0 0
\(26\) 10.2843 2.01691
\(27\) −1.11076 −0.213765
\(28\) −5.83379 −1.10248
\(29\) −8.93755 −1.65966 −0.829831 0.558015i \(-0.811563\pi\)
−0.829831 + 0.558015i \(0.811563\pi\)
\(30\) 0 0
\(31\) −4.43182 −0.795978 −0.397989 0.917390i \(-0.630292\pi\)
−0.397989 + 0.917390i \(0.630292\pi\)
\(32\) −7.41447 −1.31070
\(33\) 0.0959992 0.0167113
\(34\) 7.96151 1.36539
\(35\) 0 0
\(36\) −4.90102 −0.816837
\(37\) −5.99816 −0.986091 −0.493046 0.870003i \(-0.664116\pi\)
−0.493046 + 0.870003i \(0.664116\pi\)
\(38\) 9.42110 1.52830
\(39\) 1.00195 0.160441
\(40\) 0 0
\(41\) −8.99946 −1.40548 −0.702740 0.711447i \(-0.748040\pi\)
−0.702740 + 0.711447i \(0.748040\pi\)
\(42\) −1.25613 −0.193825
\(43\) 1.66336 0.253660 0.126830 0.991924i \(-0.459520\pi\)
0.126830 + 0.991924i \(0.459520\pi\)
\(44\) 0.852112 0.128461
\(45\) 0 0
\(46\) 14.7010 2.16754
\(47\) −8.55484 −1.24785 −0.623926 0.781483i \(-0.714463\pi\)
−0.623926 + 0.781483i \(0.714463\pi\)
\(48\) −0.851668 −0.122928
\(49\) 5.45876 0.779823
\(50\) 0 0
\(51\) 0.775656 0.108614
\(52\) 8.89356 1.23331
\(53\) −13.1736 −1.80954 −0.904769 0.425903i \(-0.859957\pi\)
−0.904769 + 0.425903i \(0.859957\pi\)
\(54\) −2.12291 −0.288891
\(55\) 0 0
\(56\) 2.34239 0.313015
\(57\) 0.917857 0.121573
\(58\) −17.0817 −2.24293
\(59\) 9.25521 1.20493 0.602463 0.798147i \(-0.294186\pi\)
0.602463 + 0.798147i \(0.294186\pi\)
\(60\) 0 0
\(61\) −10.4203 −1.33418 −0.667090 0.744978i \(-0.732460\pi\)
−0.667090 + 0.744978i \(0.732460\pi\)
\(62\) −8.47019 −1.07572
\(63\) 10.4667 1.31868
\(64\) −5.02293 −0.627867
\(65\) 0 0
\(66\) 0.183476 0.0225843
\(67\) 3.91715 0.478555 0.239278 0.970951i \(-0.423089\pi\)
0.239278 + 0.970951i \(0.423089\pi\)
\(68\) 6.88490 0.834917
\(69\) 1.43226 0.172423
\(70\) 0 0
\(71\) −13.6724 −1.62262 −0.811308 0.584619i \(-0.801244\pi\)
−0.811308 + 0.584619i \(0.801244\pi\)
\(72\) 1.96786 0.231915
\(73\) −11.5529 −1.35217 −0.676083 0.736825i \(-0.736324\pi\)
−0.676083 + 0.736825i \(0.736324\pi\)
\(74\) −11.4638 −1.33264
\(75\) 0 0
\(76\) 8.14711 0.934538
\(77\) −1.81979 −0.207384
\(78\) 1.91495 0.216826
\(79\) −1.43448 −0.161391 −0.0806956 0.996739i \(-0.525714\pi\)
−0.0806956 + 0.996739i \(0.525714\pi\)
\(80\) 0 0
\(81\) 8.68916 0.965462
\(82\) −17.2000 −1.89942
\(83\) −1.73047 −0.189944 −0.0949720 0.995480i \(-0.530276\pi\)
−0.0949720 + 0.995480i \(0.530276\pi\)
\(84\) −1.08627 −0.118521
\(85\) 0 0
\(86\) 3.17906 0.342807
\(87\) −1.66419 −0.178420
\(88\) −0.342141 −0.0364724
\(89\) −1.07999 −0.114478 −0.0572392 0.998360i \(-0.518230\pi\)
−0.0572392 + 0.998360i \(0.518230\pi\)
\(90\) 0 0
\(91\) −18.9932 −1.99103
\(92\) 12.7130 1.32543
\(93\) −0.825214 −0.0855707
\(94\) −16.3502 −1.68640
\(95\) 0 0
\(96\) −1.38059 −0.140906
\(97\) 16.0883 1.63352 0.816759 0.576979i \(-0.195769\pi\)
0.816759 + 0.576979i \(0.195769\pi\)
\(98\) 10.4329 1.05388
\(99\) −1.52882 −0.153652
\(100\) 0 0
\(101\) −1.23922 −0.123307 −0.0616536 0.998098i \(-0.519637\pi\)
−0.0616536 + 0.998098i \(0.519637\pi\)
\(102\) 1.48245 0.146785
\(103\) −5.27633 −0.519892 −0.259946 0.965623i \(-0.583705\pi\)
−0.259946 + 0.965623i \(0.583705\pi\)
\(104\) −3.57095 −0.350161
\(105\) 0 0
\(106\) −25.1778 −2.44548
\(107\) −10.7822 −1.04236 −0.521178 0.853448i \(-0.674507\pi\)
−0.521178 + 0.853448i \(0.674507\pi\)
\(108\) −1.83583 −0.176653
\(109\) −1.15255 −0.110394 −0.0551972 0.998475i \(-0.517579\pi\)
−0.0551972 + 0.998475i \(0.517579\pi\)
\(110\) 0 0
\(111\) −1.11687 −0.106009
\(112\) 16.1444 1.52550
\(113\) 8.70999 0.819367 0.409684 0.912228i \(-0.365639\pi\)
0.409684 + 0.912228i \(0.365639\pi\)
\(114\) 1.75423 0.164299
\(115\) 0 0
\(116\) −14.7718 −1.37152
\(117\) −15.9564 −1.47517
\(118\) 17.6888 1.62838
\(119\) −14.7035 −1.34787
\(120\) 0 0
\(121\) −10.7342 −0.975836
\(122\) −19.9155 −1.80306
\(123\) −1.67572 −0.151095
\(124\) −7.32480 −0.657786
\(125\) 0 0
\(126\) 20.0042 1.78212
\(127\) 8.22063 0.729463 0.364732 0.931113i \(-0.381161\pi\)
0.364732 + 0.931113i \(0.381161\pi\)
\(128\) 5.22899 0.462181
\(129\) 0.309722 0.0272695
\(130\) 0 0
\(131\) −7.30323 −0.638086 −0.319043 0.947740i \(-0.603362\pi\)
−0.319043 + 0.947740i \(0.603362\pi\)
\(132\) 0.158665 0.0138100
\(133\) −17.3991 −1.50870
\(134\) 7.48654 0.646739
\(135\) 0 0
\(136\) −2.76444 −0.237048
\(137\) −5.95317 −0.508614 −0.254307 0.967124i \(-0.581847\pi\)
−0.254307 + 0.967124i \(0.581847\pi\)
\(138\) 2.73736 0.233020
\(139\) 14.9650 1.26931 0.634656 0.772795i \(-0.281142\pi\)
0.634656 + 0.772795i \(0.281142\pi\)
\(140\) 0 0
\(141\) −1.59293 −0.134149
\(142\) −26.1310 −2.19287
\(143\) 2.77424 0.231994
\(144\) 13.5631 1.13026
\(145\) 0 0
\(146\) −22.0802 −1.82737
\(147\) 1.01643 0.0838340
\(148\) −9.91361 −0.814894
\(149\) −0.130576 −0.0106972 −0.00534860 0.999986i \(-0.501703\pi\)
−0.00534860 + 0.999986i \(0.501703\pi\)
\(150\) 0 0
\(151\) 0.276102 0.0224688 0.0112344 0.999937i \(-0.496424\pi\)
0.0112344 + 0.999937i \(0.496424\pi\)
\(152\) −3.27124 −0.265333
\(153\) −12.3526 −0.998645
\(154\) −3.47802 −0.280267
\(155\) 0 0
\(156\) 1.65600 0.132586
\(157\) −16.1044 −1.28527 −0.642636 0.766172i \(-0.722159\pi\)
−0.642636 + 0.766172i \(0.722159\pi\)
\(158\) −2.74160 −0.218110
\(159\) −2.45296 −0.194532
\(160\) 0 0
\(161\) −27.1502 −2.13973
\(162\) 16.6069 1.30476
\(163\) 18.5215 1.45071 0.725357 0.688373i \(-0.241675\pi\)
0.725357 + 0.688373i \(0.241675\pi\)
\(164\) −14.8741 −1.16147
\(165\) 0 0
\(166\) −3.30732 −0.256698
\(167\) −15.5017 −1.19956 −0.599779 0.800166i \(-0.704745\pi\)
−0.599779 + 0.800166i \(0.704745\pi\)
\(168\) 0.436159 0.0336504
\(169\) 15.9550 1.22731
\(170\) 0 0
\(171\) −14.6172 −1.11780
\(172\) 2.74916 0.209622
\(173\) 0.366438 0.0278597 0.0139299 0.999903i \(-0.495566\pi\)
0.0139299 + 0.999903i \(0.495566\pi\)
\(174\) −3.18064 −0.241124
\(175\) 0 0
\(176\) −2.35813 −0.177751
\(177\) 1.72334 0.129534
\(178\) −2.06410 −0.154711
\(179\) 12.8719 0.962090 0.481045 0.876696i \(-0.340257\pi\)
0.481045 + 0.876696i \(0.340257\pi\)
\(180\) 0 0
\(181\) −12.2125 −0.907746 −0.453873 0.891066i \(-0.649958\pi\)
−0.453873 + 0.891066i \(0.649958\pi\)
\(182\) −36.3003 −2.69076
\(183\) −1.94028 −0.143429
\(184\) −5.10456 −0.376313
\(185\) 0 0
\(186\) −1.57717 −0.115644
\(187\) 2.14767 0.157053
\(188\) −14.1392 −1.03121
\(189\) 3.92064 0.285184
\(190\) 0 0
\(191\) −3.92400 −0.283930 −0.141965 0.989872i \(-0.545342\pi\)
−0.141965 + 0.989872i \(0.545342\pi\)
\(192\) −0.935281 −0.0674981
\(193\) 1.69319 0.121879 0.0609393 0.998141i \(-0.480590\pi\)
0.0609393 + 0.998141i \(0.480590\pi\)
\(194\) 30.7483 2.20760
\(195\) 0 0
\(196\) 9.02210 0.644436
\(197\) 2.20382 0.157016 0.0785080 0.996913i \(-0.474984\pi\)
0.0785080 + 0.996913i \(0.474984\pi\)
\(198\) −2.92191 −0.207651
\(199\) −15.5533 −1.10255 −0.551274 0.834324i \(-0.685858\pi\)
−0.551274 + 0.834324i \(0.685858\pi\)
\(200\) 0 0
\(201\) 0.729381 0.0514466
\(202\) −2.36843 −0.166642
\(203\) 31.5468 2.21415
\(204\) 1.28198 0.0897569
\(205\) 0 0
\(206\) −10.0842 −0.702603
\(207\) −22.8091 −1.58534
\(208\) −24.6120 −1.70654
\(209\) 2.54140 0.175792
\(210\) 0 0
\(211\) 6.55996 0.451606 0.225803 0.974173i \(-0.427499\pi\)
0.225803 + 0.974173i \(0.427499\pi\)
\(212\) −21.7731 −1.49538
\(213\) −2.54583 −0.174438
\(214\) −20.6072 −1.40868
\(215\) 0 0
\(216\) 0.737126 0.0501551
\(217\) 15.6430 1.06191
\(218\) −2.20278 −0.149191
\(219\) −2.15118 −0.145363
\(220\) 0 0
\(221\) 22.4154 1.50782
\(222\) −2.13459 −0.143264
\(223\) −6.53800 −0.437817 −0.218908 0.975745i \(-0.570250\pi\)
−0.218908 + 0.975745i \(0.570250\pi\)
\(224\) 26.1708 1.74861
\(225\) 0 0
\(226\) 16.6467 1.10732
\(227\) −16.1673 −1.07306 −0.536530 0.843881i \(-0.680265\pi\)
−0.536530 + 0.843881i \(0.680265\pi\)
\(228\) 1.51701 0.100466
\(229\) 0.0208412 0.00137722 0.000688612 1.00000i \(-0.499781\pi\)
0.000688612 1.00000i \(0.499781\pi\)
\(230\) 0 0
\(231\) −0.338848 −0.0222946
\(232\) 5.93118 0.389401
\(233\) 0.651845 0.0427038 0.0213519 0.999772i \(-0.493203\pi\)
0.0213519 + 0.999772i \(0.493203\pi\)
\(234\) −30.4962 −1.99360
\(235\) 0 0
\(236\) 15.2968 0.995736
\(237\) −0.267103 −0.0173502
\(238\) −28.1017 −1.82156
\(239\) −8.99997 −0.582160 −0.291080 0.956699i \(-0.594015\pi\)
−0.291080 + 0.956699i \(0.594015\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −20.5154 −1.31878
\(243\) 4.95021 0.317556
\(244\) −17.2224 −1.10255
\(245\) 0 0
\(246\) −3.20268 −0.204195
\(247\) 26.5248 1.68773
\(248\) 2.94106 0.186758
\(249\) −0.322218 −0.0204197
\(250\) 0 0
\(251\) 16.4986 1.04138 0.520691 0.853745i \(-0.325674\pi\)
0.520691 + 0.853745i \(0.325674\pi\)
\(252\) 17.2991 1.08974
\(253\) 3.96569 0.249321
\(254\) 15.7115 0.985825
\(255\) 0 0
\(256\) 20.0396 1.25248
\(257\) −7.99029 −0.498420 −0.249210 0.968449i \(-0.580171\pi\)
−0.249210 + 0.968449i \(0.580171\pi\)
\(258\) 0.591948 0.0368530
\(259\) 21.1717 1.31554
\(260\) 0 0
\(261\) 26.5028 1.64048
\(262\) −13.9581 −0.862335
\(263\) 5.47488 0.337595 0.168798 0.985651i \(-0.446012\pi\)
0.168798 + 0.985651i \(0.446012\pi\)
\(264\) −0.0637074 −0.00392092
\(265\) 0 0
\(266\) −33.2536 −2.03891
\(267\) −0.201096 −0.0123069
\(268\) 6.47416 0.395472
\(269\) −2.34697 −0.143097 −0.0715486 0.997437i \(-0.522794\pi\)
−0.0715486 + 0.997437i \(0.522794\pi\)
\(270\) 0 0
\(271\) 1.60301 0.0973758 0.0486879 0.998814i \(-0.484496\pi\)
0.0486879 + 0.998814i \(0.484496\pi\)
\(272\) −19.0533 −1.15527
\(273\) −3.53658 −0.214044
\(274\) −11.3778 −0.687360
\(275\) 0 0
\(276\) 2.36720 0.142488
\(277\) 21.6775 1.30247 0.651237 0.758875i \(-0.274250\pi\)
0.651237 + 0.758875i \(0.274250\pi\)
\(278\) 28.6014 1.71540
\(279\) 13.1418 0.786779
\(280\) 0 0
\(281\) 26.9010 1.60478 0.802388 0.596802i \(-0.203562\pi\)
0.802388 + 0.596802i \(0.203562\pi\)
\(282\) −3.04445 −0.181294
\(283\) −3.89230 −0.231373 −0.115687 0.993286i \(-0.536907\pi\)
−0.115687 + 0.993286i \(0.536907\pi\)
\(284\) −22.5974 −1.34091
\(285\) 0 0
\(286\) 5.30220 0.313526
\(287\) 31.7654 1.87505
\(288\) 21.9863 1.29556
\(289\) 0.352752 0.0207501
\(290\) 0 0
\(291\) 2.99567 0.175610
\(292\) −19.0944 −1.11741
\(293\) 5.57389 0.325630 0.162815 0.986657i \(-0.447943\pi\)
0.162815 + 0.986657i \(0.447943\pi\)
\(294\) 1.94263 0.113297
\(295\) 0 0
\(296\) 3.98053 0.231363
\(297\) −0.572667 −0.0332295
\(298\) −0.249560 −0.0144566
\(299\) 41.3902 2.39366
\(300\) 0 0
\(301\) −5.87116 −0.338408
\(302\) 0.527692 0.0303652
\(303\) −0.230746 −0.0132560
\(304\) −22.5463 −1.29312
\(305\) 0 0
\(306\) −23.6085 −1.34961
\(307\) −23.0795 −1.31722 −0.658608 0.752486i \(-0.728854\pi\)
−0.658608 + 0.752486i \(0.728854\pi\)
\(308\) −3.00770 −0.171379
\(309\) −0.982465 −0.0558905
\(310\) 0 0
\(311\) −14.9884 −0.849916 −0.424958 0.905213i \(-0.639711\pi\)
−0.424958 + 0.905213i \(0.639711\pi\)
\(312\) −0.664919 −0.0376437
\(313\) 2.31082 0.130615 0.0653076 0.997865i \(-0.479197\pi\)
0.0653076 + 0.997865i \(0.479197\pi\)
\(314\) −30.7791 −1.73697
\(315\) 0 0
\(316\) −2.37087 −0.133372
\(317\) 18.3630 1.03137 0.515684 0.856779i \(-0.327538\pi\)
0.515684 + 0.856779i \(0.327538\pi\)
\(318\) −4.68816 −0.262899
\(319\) −4.60788 −0.257992
\(320\) 0 0
\(321\) −2.00767 −0.112057
\(322\) −51.8901 −2.89172
\(323\) 20.5340 1.14254
\(324\) 14.3612 0.797846
\(325\) 0 0
\(326\) 35.3987 1.96055
\(327\) −0.214608 −0.0118678
\(328\) 5.97226 0.329763
\(329\) 30.1960 1.66476
\(330\) 0 0
\(331\) −6.47933 −0.356136 −0.178068 0.984018i \(-0.556985\pi\)
−0.178068 + 0.984018i \(0.556985\pi\)
\(332\) −2.86008 −0.156967
\(333\) 17.7865 0.974695
\(334\) −29.6272 −1.62113
\(335\) 0 0
\(336\) 3.00613 0.163998
\(337\) 3.54257 0.192976 0.0964880 0.995334i \(-0.469239\pi\)
0.0964880 + 0.995334i \(0.469239\pi\)
\(338\) 30.4936 1.65863
\(339\) 1.62182 0.0880852
\(340\) 0 0
\(341\) −2.28489 −0.123734
\(342\) −27.9366 −1.51064
\(343\) 5.44011 0.293739
\(344\) −1.10385 −0.0595155
\(345\) 0 0
\(346\) 0.700344 0.0376507
\(347\) 14.4844 0.777566 0.388783 0.921329i \(-0.372896\pi\)
0.388783 + 0.921329i \(0.372896\pi\)
\(348\) −2.75053 −0.147444
\(349\) −23.6287 −1.26482 −0.632408 0.774636i \(-0.717933\pi\)
−0.632408 + 0.774636i \(0.717933\pi\)
\(350\) 0 0
\(351\) −5.97697 −0.319027
\(352\) −3.82263 −0.203747
\(353\) 18.2662 0.972209 0.486105 0.873901i \(-0.338417\pi\)
0.486105 + 0.873901i \(0.338417\pi\)
\(354\) 3.29369 0.175058
\(355\) 0 0
\(356\) −1.78498 −0.0946036
\(357\) −2.73783 −0.144901
\(358\) 24.6010 1.30021
\(359\) −20.3758 −1.07539 −0.537697 0.843138i \(-0.680706\pi\)
−0.537697 + 0.843138i \(0.680706\pi\)
\(360\) 0 0
\(361\) 5.29852 0.278870
\(362\) −23.3408 −1.22676
\(363\) −1.99873 −0.104906
\(364\) −31.3916 −1.64536
\(365\) 0 0
\(366\) −3.70830 −0.193836
\(367\) 1.76412 0.0920862 0.0460431 0.998939i \(-0.485339\pi\)
0.0460431 + 0.998939i \(0.485339\pi\)
\(368\) −35.1820 −1.83399
\(369\) 26.6864 1.38924
\(370\) 0 0
\(371\) 46.4989 2.41410
\(372\) −1.36389 −0.0707146
\(373\) 32.1736 1.66589 0.832943 0.553359i \(-0.186654\pi\)
0.832943 + 0.553359i \(0.186654\pi\)
\(374\) 4.10467 0.212247
\(375\) 0 0
\(376\) 5.67720 0.292779
\(377\) −48.0928 −2.47691
\(378\) 7.49321 0.385409
\(379\) −31.3680 −1.61126 −0.805632 0.592416i \(-0.798174\pi\)
−0.805632 + 0.592416i \(0.798174\pi\)
\(380\) 0 0
\(381\) 1.53070 0.0784201
\(382\) −7.49963 −0.383715
\(383\) −16.8623 −0.861624 −0.430812 0.902442i \(-0.641773\pi\)
−0.430812 + 0.902442i \(0.641773\pi\)
\(384\) 0.973649 0.0496863
\(385\) 0 0
\(386\) 3.23607 0.164712
\(387\) −4.93242 −0.250729
\(388\) 26.5903 1.34992
\(389\) −0.816001 −0.0413729 −0.0206864 0.999786i \(-0.506585\pi\)
−0.0206864 + 0.999786i \(0.506585\pi\)
\(390\) 0 0
\(391\) 32.0420 1.62043
\(392\) −3.62257 −0.182967
\(393\) −1.35988 −0.0685968
\(394\) 4.21200 0.212198
\(395\) 0 0
\(396\) −2.52679 −0.126976
\(397\) 21.8279 1.09551 0.547755 0.836639i \(-0.315483\pi\)
0.547755 + 0.836639i \(0.315483\pi\)
\(398\) −29.7259 −1.49003
\(399\) −3.23976 −0.162191
\(400\) 0 0
\(401\) −15.4857 −0.773321 −0.386661 0.922222i \(-0.626372\pi\)
−0.386661 + 0.922222i \(0.626372\pi\)
\(402\) 1.39401 0.0695269
\(403\) −23.8475 −1.18793
\(404\) −2.04816 −0.101900
\(405\) 0 0
\(406\) 60.2931 2.99229
\(407\) −3.09244 −0.153286
\(408\) −0.514744 −0.0254836
\(409\) 26.0377 1.28748 0.643740 0.765245i \(-0.277382\pi\)
0.643740 + 0.765245i \(0.277382\pi\)
\(410\) 0 0
\(411\) −1.10849 −0.0546780
\(412\) −8.72059 −0.429633
\(413\) −32.6681 −1.60749
\(414\) −43.5933 −2.14249
\(415\) 0 0
\(416\) −39.8971 −1.95612
\(417\) 2.78651 0.136456
\(418\) 4.85718 0.237572
\(419\) −33.2204 −1.62292 −0.811462 0.584406i \(-0.801328\pi\)
−0.811462 + 0.584406i \(0.801328\pi\)
\(420\) 0 0
\(421\) 2.90586 0.141623 0.0708115 0.997490i \(-0.477441\pi\)
0.0708115 + 0.997490i \(0.477441\pi\)
\(422\) 12.5375 0.610318
\(423\) 25.3679 1.23343
\(424\) 8.74235 0.424566
\(425\) 0 0
\(426\) −4.86565 −0.235742
\(427\) 36.7804 1.77993
\(428\) −17.8206 −0.861390
\(429\) 0.516570 0.0249402
\(430\) 0 0
\(431\) −28.4892 −1.37228 −0.686139 0.727471i \(-0.740696\pi\)
−0.686139 + 0.727471i \(0.740696\pi\)
\(432\) 5.08048 0.244435
\(433\) 28.9311 1.39034 0.695169 0.718846i \(-0.255329\pi\)
0.695169 + 0.718846i \(0.255329\pi\)
\(434\) 29.8972 1.43511
\(435\) 0 0
\(436\) −1.90491 −0.0912286
\(437\) 37.9163 1.81378
\(438\) −4.11138 −0.196449
\(439\) −8.92156 −0.425803 −0.212901 0.977074i \(-0.568291\pi\)
−0.212901 + 0.977074i \(0.568291\pi\)
\(440\) 0 0
\(441\) −16.1870 −0.770810
\(442\) 42.8408 2.03773
\(443\) −24.8216 −1.17931 −0.589656 0.807655i \(-0.700736\pi\)
−0.589656 + 0.807655i \(0.700736\pi\)
\(444\) −1.84594 −0.0876042
\(445\) 0 0
\(446\) −12.4956 −0.591683
\(447\) −0.0243136 −0.00114999
\(448\) 17.7294 0.837637
\(449\) 11.9254 0.562793 0.281397 0.959592i \(-0.409202\pi\)
0.281397 + 0.959592i \(0.409202\pi\)
\(450\) 0 0
\(451\) −4.63980 −0.218480
\(452\) 14.3957 0.677115
\(453\) 0.0514107 0.00241549
\(454\) −30.8993 −1.45018
\(455\) 0 0
\(456\) −0.609112 −0.0285243
\(457\) −8.44205 −0.394902 −0.197451 0.980313i \(-0.563266\pi\)
−0.197451 + 0.980313i \(0.563266\pi\)
\(458\) 0.0398321 0.00186123
\(459\) −4.62704 −0.215972
\(460\) 0 0
\(461\) 23.2925 1.08484 0.542419 0.840108i \(-0.317509\pi\)
0.542419 + 0.840108i \(0.317509\pi\)
\(462\) −0.647614 −0.0301297
\(463\) −1.66578 −0.0774152 −0.0387076 0.999251i \(-0.512324\pi\)
−0.0387076 + 0.999251i \(0.512324\pi\)
\(464\) 40.8793 1.89777
\(465\) 0 0
\(466\) 1.24582 0.0577116
\(467\) 6.66428 0.308386 0.154193 0.988041i \(-0.450722\pi\)
0.154193 + 0.988041i \(0.450722\pi\)
\(468\) −26.3723 −1.21906
\(469\) −13.8263 −0.638441
\(470\) 0 0
\(471\) −2.99868 −0.138172
\(472\) −6.14198 −0.282708
\(473\) 0.857570 0.0394311
\(474\) −0.510493 −0.0234477
\(475\) 0 0
\(476\) −24.3016 −1.11386
\(477\) 39.0642 1.78863
\(478\) −17.2010 −0.786753
\(479\) −13.6902 −0.625523 −0.312762 0.949832i \(-0.601254\pi\)
−0.312762 + 0.949832i \(0.601254\pi\)
\(480\) 0 0
\(481\) −32.2760 −1.47166
\(482\) −1.91122 −0.0870538
\(483\) −5.05543 −0.230030
\(484\) −17.7412 −0.806419
\(485\) 0 0
\(486\) 9.46096 0.429158
\(487\) −31.9634 −1.44840 −0.724200 0.689590i \(-0.757791\pi\)
−0.724200 + 0.689590i \(0.757791\pi\)
\(488\) 6.91515 0.313034
\(489\) 3.44874 0.155957
\(490\) 0 0
\(491\) −10.0550 −0.453777 −0.226889 0.973921i \(-0.572855\pi\)
−0.226889 + 0.973921i \(0.572855\pi\)
\(492\) −2.76959 −0.124863
\(493\) −37.2308 −1.67679
\(494\) 50.6948 2.28087
\(495\) 0 0
\(496\) 20.2706 0.910178
\(497\) 48.2594 2.16473
\(498\) −0.615830 −0.0275960
\(499\) 9.14295 0.409295 0.204647 0.978836i \(-0.434395\pi\)
0.204647 + 0.978836i \(0.434395\pi\)
\(500\) 0 0
\(501\) −2.88645 −0.128957
\(502\) 31.5325 1.40736
\(503\) 27.2050 1.21301 0.606506 0.795079i \(-0.292571\pi\)
0.606506 + 0.795079i \(0.292571\pi\)
\(504\) −6.94597 −0.309398
\(505\) 0 0
\(506\) 7.57931 0.336941
\(507\) 2.97086 0.131940
\(508\) 13.5869 0.602819
\(509\) 7.79598 0.345551 0.172775 0.984961i \(-0.444726\pi\)
0.172775 + 0.984961i \(0.444726\pi\)
\(510\) 0 0
\(511\) 40.7783 1.80392
\(512\) 27.8422 1.23046
\(513\) −5.47532 −0.241741
\(514\) −15.2712 −0.673585
\(515\) 0 0
\(516\) 0.511900 0.0225352
\(517\) −4.41057 −0.193977
\(518\) 40.4638 1.77788
\(519\) 0.0682315 0.00299503
\(520\) 0 0
\(521\) 32.6959 1.43243 0.716216 0.697878i \(-0.245872\pi\)
0.716216 + 0.697878i \(0.245872\pi\)
\(522\) 50.6527 2.21701
\(523\) 7.80136 0.341129 0.170565 0.985346i \(-0.445441\pi\)
0.170565 + 0.985346i \(0.445441\pi\)
\(524\) −12.0706 −0.527307
\(525\) 0 0
\(526\) 10.4637 0.456240
\(527\) −18.4615 −0.804194
\(528\) −0.439089 −0.0191089
\(529\) 36.1658 1.57243
\(530\) 0 0
\(531\) −27.4447 −1.19100
\(532\) −28.7568 −1.24677
\(533\) −48.4260 −2.09756
\(534\) −0.384340 −0.0166320
\(535\) 0 0
\(536\) −2.59951 −0.112282
\(537\) 2.39677 0.103428
\(538\) −4.48558 −0.193387
\(539\) 2.81434 0.121222
\(540\) 0 0
\(541\) 22.3971 0.962926 0.481463 0.876467i \(-0.340106\pi\)
0.481463 + 0.876467i \(0.340106\pi\)
\(542\) 3.06371 0.131597
\(543\) −2.27399 −0.0975863
\(544\) −30.8862 −1.32423
\(545\) 0 0
\(546\) −6.75920 −0.289267
\(547\) −37.2322 −1.59193 −0.795966 0.605341i \(-0.793037\pi\)
−0.795966 + 0.605341i \(0.793037\pi\)
\(548\) −9.83925 −0.420312
\(549\) 30.8995 1.31876
\(550\) 0 0
\(551\) −44.0563 −1.87686
\(552\) −0.950480 −0.0404551
\(553\) 5.06326 0.215312
\(554\) 41.4305 1.76021
\(555\) 0 0
\(556\) 24.7337 1.04894
\(557\) 27.6457 1.17139 0.585693 0.810533i \(-0.300823\pi\)
0.585693 + 0.810533i \(0.300823\pi\)
\(558\) 25.1169 1.06328
\(559\) 8.95053 0.378567
\(560\) 0 0
\(561\) 0.399900 0.0168838
\(562\) 51.4138 2.16876
\(563\) 23.3454 0.983891 0.491945 0.870626i \(-0.336286\pi\)
0.491945 + 0.870626i \(0.336286\pi\)
\(564\) −2.63276 −0.110859
\(565\) 0 0
\(566\) −7.43905 −0.312687
\(567\) −30.6701 −1.28802
\(568\) 9.07334 0.380709
\(569\) 2.61346 0.109562 0.0547811 0.998498i \(-0.482554\pi\)
0.0547811 + 0.998498i \(0.482554\pi\)
\(570\) 0 0
\(571\) 16.9259 0.708326 0.354163 0.935184i \(-0.384766\pi\)
0.354163 + 0.935184i \(0.384766\pi\)
\(572\) 4.58520 0.191717
\(573\) −0.730657 −0.0305236
\(574\) 60.7107 2.53402
\(575\) 0 0
\(576\) 14.8946 0.620610
\(577\) −4.67534 −0.194637 −0.0973185 0.995253i \(-0.531027\pi\)
−0.0973185 + 0.995253i \(0.531027\pi\)
\(578\) 0.674188 0.0280425
\(579\) 0.315276 0.0131024
\(580\) 0 0
\(581\) 6.10804 0.253404
\(582\) 5.72540 0.237326
\(583\) −6.79185 −0.281290
\(584\) 7.66680 0.317254
\(585\) 0 0
\(586\) 10.6530 0.440069
\(587\) 3.78940 0.156405 0.0782027 0.996937i \(-0.475082\pi\)
0.0782027 + 0.996937i \(0.475082\pi\)
\(588\) 1.67994 0.0692794
\(589\) −21.8460 −0.900148
\(590\) 0 0
\(591\) 0.410357 0.0168798
\(592\) 27.4349 1.12757
\(593\) 6.81434 0.279831 0.139916 0.990163i \(-0.455317\pi\)
0.139916 + 0.990163i \(0.455317\pi\)
\(594\) −1.09449 −0.0449076
\(595\) 0 0
\(596\) −0.215813 −0.00884004
\(597\) −2.89607 −0.118528
\(598\) 79.1059 3.23488
\(599\) −39.7739 −1.62512 −0.812559 0.582879i \(-0.801926\pi\)
−0.812559 + 0.582879i \(0.801926\pi\)
\(600\) 0 0
\(601\) 27.4256 1.11871 0.559356 0.828927i \(-0.311048\pi\)
0.559356 + 0.828927i \(0.311048\pi\)
\(602\) −11.2211 −0.457338
\(603\) −11.6156 −0.473025
\(604\) 0.456334 0.0185680
\(605\) 0 0
\(606\) −0.441007 −0.0179147
\(607\) −20.6168 −0.836811 −0.418405 0.908260i \(-0.637411\pi\)
−0.418405 + 0.908260i \(0.637411\pi\)
\(608\) −36.5485 −1.48224
\(609\) 5.87409 0.238030
\(610\) 0 0
\(611\) −46.0335 −1.86232
\(612\) −20.4160 −0.825268
\(613\) 12.9127 0.521540 0.260770 0.965401i \(-0.416024\pi\)
0.260770 + 0.965401i \(0.416024\pi\)
\(614\) −44.1100 −1.78014
\(615\) 0 0
\(616\) 1.20765 0.0486578
\(617\) −26.3856 −1.06225 −0.531123 0.847295i \(-0.678230\pi\)
−0.531123 + 0.847295i \(0.678230\pi\)
\(618\) −1.87771 −0.0755326
\(619\) −2.30850 −0.0927866 −0.0463933 0.998923i \(-0.514773\pi\)
−0.0463933 + 0.998923i \(0.514773\pi\)
\(620\) 0 0
\(621\) −8.54387 −0.342854
\(622\) −28.6462 −1.14861
\(623\) 3.81203 0.152726
\(624\) −4.58281 −0.183459
\(625\) 0 0
\(626\) 4.41649 0.176519
\(627\) 0.473214 0.0188983
\(628\) −26.6170 −1.06213
\(629\) −24.9863 −0.996270
\(630\) 0 0
\(631\) −8.60820 −0.342687 −0.171343 0.985211i \(-0.554811\pi\)
−0.171343 + 0.985211i \(0.554811\pi\)
\(632\) 0.951953 0.0378667
\(633\) 1.22148 0.0485494
\(634\) 35.0958 1.39383
\(635\) 0 0
\(636\) −4.05419 −0.160759
\(637\) 29.3735 1.16382
\(638\) −8.80669 −0.348660
\(639\) 40.5432 1.60386
\(640\) 0 0
\(641\) −11.7479 −0.464014 −0.232007 0.972714i \(-0.574529\pi\)
−0.232007 + 0.972714i \(0.574529\pi\)
\(642\) −3.83711 −0.151439
\(643\) −15.0808 −0.594729 −0.297364 0.954764i \(-0.596108\pi\)
−0.297364 + 0.954764i \(0.596108\pi\)
\(644\) −44.8732 −1.76825
\(645\) 0 0
\(646\) 39.2451 1.54408
\(647\) 5.68014 0.223309 0.111655 0.993747i \(-0.464385\pi\)
0.111655 + 0.993747i \(0.464385\pi\)
\(648\) −5.76634 −0.226523
\(649\) 4.77166 0.187304
\(650\) 0 0
\(651\) 2.91276 0.114160
\(652\) 30.6118 1.19885
\(653\) 48.9941 1.91729 0.958644 0.284608i \(-0.0918633\pi\)
0.958644 + 0.284608i \(0.0918633\pi\)
\(654\) −0.410163 −0.0160387
\(655\) 0 0
\(656\) 41.1625 1.60713
\(657\) 34.2582 1.33654
\(658\) 57.7113 2.24982
\(659\) −23.5789 −0.918505 −0.459252 0.888306i \(-0.651883\pi\)
−0.459252 + 0.888306i \(0.651883\pi\)
\(660\) 0 0
\(661\) −38.6322 −1.50262 −0.751310 0.659949i \(-0.770578\pi\)
−0.751310 + 0.659949i \(0.770578\pi\)
\(662\) −12.3835 −0.481296
\(663\) 4.17379 0.162097
\(664\) 1.14838 0.0445659
\(665\) 0 0
\(666\) 33.9940 1.31724
\(667\) −68.7470 −2.66190
\(668\) −25.6208 −0.991300
\(669\) −1.21739 −0.0470670
\(670\) 0 0
\(671\) −5.37232 −0.207396
\(672\) 4.87306 0.187983
\(673\) 37.4530 1.44371 0.721853 0.692047i \(-0.243291\pi\)
0.721853 + 0.692047i \(0.243291\pi\)
\(674\) 6.77064 0.260795
\(675\) 0 0
\(676\) 26.3700 1.01423
\(677\) −16.0616 −0.617297 −0.308649 0.951176i \(-0.599877\pi\)
−0.308649 + 0.951176i \(0.599877\pi\)
\(678\) 3.09966 0.119042
\(679\) −56.7868 −2.17928
\(680\) 0 0
\(681\) −3.01038 −0.115358
\(682\) −4.36693 −0.167218
\(683\) −13.5819 −0.519696 −0.259848 0.965649i \(-0.583673\pi\)
−0.259848 + 0.965649i \(0.583673\pi\)
\(684\) −24.1589 −0.923737
\(685\) 0 0
\(686\) 10.3973 0.396970
\(687\) 0.00388067 0.000148057 0
\(688\) −7.60803 −0.290053
\(689\) −70.8871 −2.70058
\(690\) 0 0
\(691\) −5.72328 −0.217724 −0.108862 0.994057i \(-0.534721\pi\)
−0.108862 + 0.994057i \(0.534721\pi\)
\(692\) 0.605639 0.0230229
\(693\) 5.39626 0.204987
\(694\) 27.6830 1.05083
\(695\) 0 0
\(696\) 1.10440 0.0418621
\(697\) −37.4887 −1.41999
\(698\) −45.1597 −1.70932
\(699\) 0.121375 0.00459083
\(700\) 0 0
\(701\) −20.2921 −0.766421 −0.383211 0.923661i \(-0.625182\pi\)
−0.383211 + 0.923661i \(0.625182\pi\)
\(702\) −11.4233 −0.431146
\(703\) −29.5670 −1.11514
\(704\) −2.58964 −0.0976009
\(705\) 0 0
\(706\) 34.9107 1.31388
\(707\) 4.37408 0.164504
\(708\) 2.84829 0.107045
\(709\) −31.5398 −1.18450 −0.592251 0.805754i \(-0.701761\pi\)
−0.592251 + 0.805754i \(0.701761\pi\)
\(710\) 0 0
\(711\) 4.25369 0.159526
\(712\) 0.716706 0.0268597
\(713\) −34.0892 −1.27665
\(714\) −5.23260 −0.195825
\(715\) 0 0
\(716\) 21.2743 0.795059
\(717\) −1.67581 −0.0625844
\(718\) −38.9427 −1.45333
\(719\) −11.0676 −0.412753 −0.206376 0.978473i \(-0.566167\pi\)
−0.206376 + 0.978473i \(0.566167\pi\)
\(720\) 0 0
\(721\) 18.6238 0.693588
\(722\) 10.1267 0.376875
\(723\) −0.186202 −0.00692494
\(724\) −20.1845 −0.750150
\(725\) 0 0
\(726\) −3.82002 −0.141774
\(727\) 49.5631 1.83819 0.919096 0.394033i \(-0.128921\pi\)
0.919096 + 0.394033i \(0.128921\pi\)
\(728\) 12.6044 0.467149
\(729\) −25.1457 −0.931324
\(730\) 0 0
\(731\) 6.92901 0.256279
\(732\) −3.20684 −0.118528
\(733\) 2.44508 0.0903110 0.0451555 0.998980i \(-0.485622\pi\)
0.0451555 + 0.998980i \(0.485622\pi\)
\(734\) 3.37162 0.124449
\(735\) 0 0
\(736\) −57.0316 −2.10221
\(737\) 2.01954 0.0743907
\(738\) 51.0036 1.87747
\(739\) 36.9067 1.35764 0.678818 0.734307i \(-0.262492\pi\)
0.678818 + 0.734307i \(0.262492\pi\)
\(740\) 0 0
\(741\) 4.93897 0.181438
\(742\) 88.8699 3.26252
\(743\) −40.6188 −1.49016 −0.745079 0.666976i \(-0.767588\pi\)
−0.745079 + 0.666976i \(0.767588\pi\)
\(744\) 0.547632 0.0200772
\(745\) 0 0
\(746\) 61.4909 2.25134
\(747\) 5.13142 0.187749
\(748\) 3.54961 0.129787
\(749\) 38.0579 1.39061
\(750\) 0 0
\(751\) −14.0406 −0.512349 −0.256174 0.966631i \(-0.582462\pi\)
−0.256174 + 0.966631i \(0.582462\pi\)
\(752\) 39.1289 1.42688
\(753\) 3.07207 0.111953
\(754\) −91.9161 −3.34739
\(755\) 0 0
\(756\) 6.47993 0.235673
\(757\) −24.6936 −0.897505 −0.448752 0.893656i \(-0.648131\pi\)
−0.448752 + 0.893656i \(0.648131\pi\)
\(758\) −59.9512 −2.17753
\(759\) 0.738419 0.0268029
\(760\) 0 0
\(761\) 12.6083 0.457051 0.228525 0.973538i \(-0.426610\pi\)
0.228525 + 0.973538i \(0.426610\pi\)
\(762\) 2.92551 0.105980
\(763\) 4.06816 0.147277
\(764\) −6.48548 −0.234636
\(765\) 0 0
\(766\) −32.2276 −1.16443
\(767\) 49.8021 1.79825
\(768\) 3.73142 0.134646
\(769\) 42.1413 1.51965 0.759827 0.650125i \(-0.225283\pi\)
0.759827 + 0.650125i \(0.225283\pi\)
\(770\) 0 0
\(771\) −1.48781 −0.0535821
\(772\) 2.79847 0.100719
\(773\) 9.62659 0.346244 0.173122 0.984900i \(-0.444614\pi\)
0.173122 + 0.984900i \(0.444614\pi\)
\(774\) −9.42695 −0.338845
\(775\) 0 0
\(776\) −10.6766 −0.383267
\(777\) 3.94221 0.141426
\(778\) −1.55956 −0.0559129
\(779\) −44.3615 −1.58942
\(780\) 0 0
\(781\) −7.04900 −0.252233
\(782\) 61.2394 2.18992
\(783\) 9.92745 0.354778
\(784\) −24.9677 −0.891705
\(785\) 0 0
\(786\) −2.59903 −0.0927044
\(787\) −50.4413 −1.79804 −0.899019 0.437909i \(-0.855719\pi\)
−0.899019 + 0.437909i \(0.855719\pi\)
\(788\) 3.64243 0.129756
\(789\) 1.01943 0.0362928
\(790\) 0 0
\(791\) −30.7436 −1.09312
\(792\) 1.01456 0.0360508
\(793\) −56.0713 −1.99115
\(794\) 41.7179 1.48051
\(795\) 0 0
\(796\) −25.7062 −0.911131
\(797\) −34.3043 −1.21512 −0.607561 0.794273i \(-0.707852\pi\)
−0.607561 + 0.794273i \(0.707852\pi\)
\(798\) −6.19190 −0.219191
\(799\) −35.6366 −1.26073
\(800\) 0 0
\(801\) 3.20252 0.113155
\(802\) −29.5967 −1.04510
\(803\) −5.95627 −0.210192
\(804\) 1.20550 0.0425148
\(805\) 0 0
\(806\) −45.5780 −1.60542
\(807\) −0.437011 −0.0153835
\(808\) 0.822378 0.0289312
\(809\) −43.9886 −1.54656 −0.773279 0.634066i \(-0.781385\pi\)
−0.773279 + 0.634066i \(0.781385\pi\)
\(810\) 0 0
\(811\) −43.0270 −1.51088 −0.755440 0.655217i \(-0.772577\pi\)
−0.755440 + 0.655217i \(0.772577\pi\)
\(812\) 52.1398 1.82975
\(813\) 0.298484 0.0104683
\(814\) −5.91034 −0.207157
\(815\) 0 0
\(816\) −3.54776 −0.124196
\(817\) 8.19930 0.286857
\(818\) 49.7638 1.73995
\(819\) 56.3212 1.96802
\(820\) 0 0
\(821\) 18.7704 0.655090 0.327545 0.944836i \(-0.393779\pi\)
0.327545 + 0.944836i \(0.393779\pi\)
\(822\) −2.11858 −0.0738939
\(823\) −27.1588 −0.946695 −0.473348 0.880876i \(-0.656955\pi\)
−0.473348 + 0.880876i \(0.656955\pi\)
\(824\) 3.50150 0.121981
\(825\) 0 0
\(826\) −62.4360 −2.17243
\(827\) −41.5157 −1.44364 −0.721821 0.692079i \(-0.756695\pi\)
−0.721821 + 0.692079i \(0.756695\pi\)
\(828\) −37.6983 −1.31011
\(829\) −30.6349 −1.06399 −0.531997 0.846746i \(-0.678558\pi\)
−0.531997 + 0.846746i \(0.678558\pi\)
\(830\) 0 0
\(831\) 4.03640 0.140021
\(832\) −27.0283 −0.937039
\(833\) 22.7394 0.787872
\(834\) 5.32565 0.184412
\(835\) 0 0
\(836\) 4.20036 0.145272
\(837\) 4.92267 0.170153
\(838\) −63.4916 −2.19328
\(839\) 30.2456 1.04419 0.522097 0.852886i \(-0.325150\pi\)
0.522097 + 0.852886i \(0.325150\pi\)
\(840\) 0 0
\(841\) 50.8798 1.75447
\(842\) 5.55375 0.191395
\(843\) 5.00902 0.172520
\(844\) 10.8421 0.373202
\(845\) 0 0
\(846\) 48.4838 1.66691
\(847\) 37.8884 1.30186
\(848\) 60.2547 2.06915
\(849\) −0.724755 −0.0248735
\(850\) 0 0
\(851\) −46.1374 −1.58157
\(852\) −4.20769 −0.144153
\(853\) −42.7734 −1.46453 −0.732267 0.681018i \(-0.761538\pi\)
−0.732267 + 0.681018i \(0.761538\pi\)
\(854\) 70.2956 2.40546
\(855\) 0 0
\(856\) 7.15534 0.244564
\(857\) 18.8048 0.642361 0.321181 0.947018i \(-0.395920\pi\)
0.321181 + 0.947018i \(0.395920\pi\)
\(858\) 0.987281 0.0337052
\(859\) −8.22676 −0.280693 −0.140347 0.990102i \(-0.544822\pi\)
−0.140347 + 0.990102i \(0.544822\pi\)
\(860\) 0 0
\(861\) 5.91478 0.201575
\(862\) −54.4493 −1.85455
\(863\) 41.8464 1.42447 0.712235 0.701941i \(-0.247683\pi\)
0.712235 + 0.701941i \(0.247683\pi\)
\(864\) 8.23567 0.280183
\(865\) 0 0
\(866\) 55.2937 1.87896
\(867\) 0.0656832 0.00223072
\(868\) 25.8543 0.877552
\(869\) −0.739564 −0.0250880
\(870\) 0 0
\(871\) 21.0781 0.714204
\(872\) 0.764862 0.0259015
\(873\) −47.7071 −1.61464
\(874\) 72.4664 2.45121
\(875\) 0 0
\(876\) −3.55541 −0.120126
\(877\) 6.11483 0.206483 0.103242 0.994656i \(-0.467079\pi\)
0.103242 + 0.994656i \(0.467079\pi\)
\(878\) −17.0511 −0.575446
\(879\) 1.03787 0.0350065
\(880\) 0 0
\(881\) −13.5157 −0.455355 −0.227678 0.973737i \(-0.573113\pi\)
−0.227678 + 0.973737i \(0.573113\pi\)
\(882\) −30.9370 −1.04170
\(883\) −38.5489 −1.29727 −0.648637 0.761098i \(-0.724661\pi\)
−0.648637 + 0.761098i \(0.724661\pi\)
\(884\) 37.0476 1.24604
\(885\) 0 0
\(886\) −47.4397 −1.59377
\(887\) −40.8386 −1.37123 −0.685613 0.727966i \(-0.740466\pi\)
−0.685613 + 0.727966i \(0.740466\pi\)
\(888\) 0.741183 0.0248725
\(889\) −29.0163 −0.973177
\(890\) 0 0
\(891\) 4.47982 0.150080
\(892\) −10.8058 −0.361806
\(893\) −42.1698 −1.41116
\(894\) −0.0464686 −0.00155414
\(895\) 0 0
\(896\) −18.4567 −0.616596
\(897\) 7.70694 0.257327
\(898\) 22.7921 0.760581
\(899\) 39.6096 1.32105
\(900\) 0 0
\(901\) −54.8769 −1.82822
\(902\) −8.86770 −0.295262
\(903\) −1.09322 −0.0363802
\(904\) −5.78016 −0.192245
\(905\) 0 0
\(906\) 0.0982574 0.00326438
\(907\) 34.3321 1.13998 0.569989 0.821652i \(-0.306947\pi\)
0.569989 + 0.821652i \(0.306947\pi\)
\(908\) −26.7209 −0.886763
\(909\) 3.67470 0.121882
\(910\) 0 0
\(911\) 49.0410 1.62480 0.812400 0.583100i \(-0.198160\pi\)
0.812400 + 0.583100i \(0.198160\pi\)
\(912\) −4.19817 −0.139015
\(913\) −0.892169 −0.0295265
\(914\) −16.1346 −0.533686
\(915\) 0 0
\(916\) 0.0344458 0.00113812
\(917\) 25.7782 0.851271
\(918\) −8.84331 −0.291873
\(919\) 48.7329 1.60755 0.803775 0.594934i \(-0.202822\pi\)
0.803775 + 0.594934i \(0.202822\pi\)
\(920\) 0 0
\(921\) −4.29745 −0.141606
\(922\) 44.5171 1.46609
\(923\) −73.5710 −2.42162
\(924\) −0.560040 −0.0184240
\(925\) 0 0
\(926\) −3.18367 −0.104622
\(927\) 15.6461 0.513884
\(928\) 66.2672 2.17533
\(929\) 52.9031 1.73569 0.867847 0.496832i \(-0.165504\pi\)
0.867847 + 0.496832i \(0.165504\pi\)
\(930\) 0 0
\(931\) 26.9081 0.881879
\(932\) 1.07735 0.0352899
\(933\) −2.79088 −0.0913693
\(934\) 12.7369 0.416765
\(935\) 0 0
\(936\) 10.5891 0.346114
\(937\) 16.1310 0.526976 0.263488 0.964663i \(-0.415127\pi\)
0.263488 + 0.964663i \(0.415127\pi\)
\(938\) −26.4252 −0.862814
\(939\) 0.430280 0.0140416
\(940\) 0 0
\(941\) 10.7225 0.349544 0.174772 0.984609i \(-0.444081\pi\)
0.174772 + 0.984609i \(0.444081\pi\)
\(942\) −5.73114 −0.186731
\(943\) −69.2233 −2.25422
\(944\) −42.3323 −1.37780
\(945\) 0 0
\(946\) 1.63901 0.0532887
\(947\) 21.9984 0.714851 0.357426 0.933942i \(-0.383655\pi\)
0.357426 + 0.933942i \(0.383655\pi\)
\(948\) −0.441460 −0.0143380
\(949\) −62.1660 −2.01800
\(950\) 0 0
\(951\) 3.41923 0.110876
\(952\) 9.75762 0.316246
\(953\) 40.5214 1.31262 0.656309 0.754492i \(-0.272117\pi\)
0.656309 + 0.754492i \(0.272117\pi\)
\(954\) 74.6603 2.41722
\(955\) 0 0
\(956\) −14.8749 −0.481090
\(957\) −0.857998 −0.0277351
\(958\) −26.1651 −0.845356
\(959\) 21.0129 0.678542
\(960\) 0 0
\(961\) −11.3590 −0.366419
\(962\) −61.6867 −1.98886
\(963\) 31.9728 1.03031
\(964\) −1.65278 −0.0532323
\(965\) 0 0
\(966\) −9.66205 −0.310871
\(967\) 46.5645 1.49741 0.748706 0.662902i \(-0.230676\pi\)
0.748706 + 0.662902i \(0.230676\pi\)
\(968\) 7.12347 0.228957
\(969\) 3.82348 0.122828
\(970\) 0 0
\(971\) 2.03099 0.0651775 0.0325887 0.999469i \(-0.489625\pi\)
0.0325887 + 0.999469i \(0.489625\pi\)
\(972\) 8.18159 0.262425
\(973\) −52.8218 −1.69339
\(974\) −61.0892 −1.95743
\(975\) 0 0
\(976\) 47.6611 1.52560
\(977\) 45.7170 1.46262 0.731308 0.682047i \(-0.238910\pi\)
0.731308 + 0.682047i \(0.238910\pi\)
\(978\) 6.59131 0.210767
\(979\) −0.556803 −0.0177955
\(980\) 0 0
\(981\) 3.41770 0.109119
\(982\) −19.2174 −0.613252
\(983\) 47.0190 1.49967 0.749837 0.661623i \(-0.230132\pi\)
0.749837 + 0.661623i \(0.230132\pi\)
\(984\) 1.11205 0.0354508
\(985\) 0 0
\(986\) −71.1564 −2.26608
\(987\) 5.62256 0.178968
\(988\) 43.8395 1.39472
\(989\) 12.7945 0.406841
\(990\) 0 0
\(991\) 54.4626 1.73006 0.865031 0.501718i \(-0.167298\pi\)
0.865031 + 0.501718i \(0.167298\pi\)
\(992\) 32.8596 1.04329
\(993\) −1.20647 −0.0382860
\(994\) 92.2346 2.92550
\(995\) 0 0
\(996\) −0.532553 −0.0168746
\(997\) −13.5868 −0.430297 −0.215149 0.976581i \(-0.569024\pi\)
−0.215149 + 0.976581i \(0.569024\pi\)
\(998\) 17.4742 0.553137
\(999\) 6.66250 0.210792
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.1.6 7
5.4 even 2 241.2.a.a.1.2 7
15.14 odd 2 2169.2.a.e.1.6 7
20.19 odd 2 3856.2.a.j.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.2 7 5.4 even 2
2169.2.a.e.1.6 7 15.14 odd 2
3856.2.a.j.1.3 7 20.19 odd 2
6025.2.a.f.1.6 7 1.1 even 1 trivial