Properties

Label 1225.4.a.bi.1.3
Level $1225$
Weight $4$
Character 1225.1
Self dual yes
Analytic conductor $72.277$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.2773397570\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.1163891200.1
Defining polynomial: \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 7 \)
Twist minimal: no (minimal twist has level 245)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.05886\) of defining polynomial
Character \(\chi\) \(=\) 1225.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.644648 q^{2} +4.18687 q^{3} -7.58443 q^{4} -2.69906 q^{6} +10.0465 q^{8} -9.47008 q^{9} +O(q^{10})\) \(q-0.644648 q^{2} +4.18687 q^{3} -7.58443 q^{4} -2.69906 q^{6} +10.0465 q^{8} -9.47008 q^{9} -47.7013 q^{11} -31.7550 q^{12} -57.2256 q^{13} +54.1990 q^{16} +36.9686 q^{17} +6.10487 q^{18} +30.7659 q^{19} +30.7506 q^{22} -53.1282 q^{23} +42.0633 q^{24} +36.8904 q^{26} -152.696 q^{27} -195.663 q^{29} +257.870 q^{31} -115.311 q^{32} -199.719 q^{33} -23.8317 q^{34} +71.8252 q^{36} -346.423 q^{37} -19.8332 q^{38} -239.596 q^{39} +267.050 q^{41} +176.859 q^{43} +361.787 q^{44} +34.2490 q^{46} +311.598 q^{47} +226.924 q^{48} +154.783 q^{51} +434.024 q^{52} +492.270 q^{53} +98.4349 q^{54} +128.813 q^{57} +126.134 q^{58} +98.7653 q^{59} +82.1682 q^{61} -166.235 q^{62} -359.257 q^{64} +128.749 q^{66} -654.668 q^{67} -280.386 q^{68} -222.441 q^{69} +779.658 q^{71} -95.1409 q^{72} +829.673 q^{73} +223.321 q^{74} -233.342 q^{76} +154.455 q^{78} -769.426 q^{79} -383.625 q^{81} -172.153 q^{82} -613.203 q^{83} -114.012 q^{86} -819.215 q^{87} -479.230 q^{88} -457.666 q^{89} +402.947 q^{92} +1079.67 q^{93} -200.871 q^{94} -482.793 q^{96} +1412.11 q^{97} +451.736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} - 16 q^{3} + 14 q^{4} + 24 q^{6} + 66 q^{8} + 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} - 16 q^{3} + 14 q^{4} + 24 q^{6} + 66 q^{8} + 70 q^{9} - 16 q^{11} - 160 q^{12} - 168 q^{13} + 298 q^{16} + 4 q^{17} - 354 q^{18} + 308 q^{19} + 236 q^{22} + 336 q^{23} - 92 q^{24} + 56 q^{26} - 964 q^{27} + 176 q^{29} + 392 q^{31} + 770 q^{32} - 188 q^{33} + 812 q^{34} + 230 q^{36} + 140 q^{37} - 20 q^{38} + 140 q^{39} + 656 q^{41} + 388 q^{43} - 160 q^{44} - 388 q^{46} - 628 q^{47} - 1396 q^{48} + 744 q^{51} - 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 1468 q^{57} + 2012 q^{58} + 996 q^{59} + 740 q^{61} + 364 q^{62} + 1426 q^{64} - 3620 q^{66} - 1768 q^{67} + 2940 q^{68} - 1048 q^{69} - 224 q^{71} - 2858 q^{72} - 2640 q^{73} + 928 q^{74} - 1340 q^{76} - 8 q^{78} + 1636 q^{79} + 4442 q^{81} + 1756 q^{82} - 140 q^{83} + 1180 q^{86} - 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 1952 q^{92} + 1592 q^{93} - 3332 q^{94} - 6460 q^{96} - 516 q^{97} - 2804 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.644648 −0.227917 −0.113959 0.993485i \(-0.536353\pi\)
−0.113959 + 0.993485i \(0.536353\pi\)
\(3\) 4.18687 0.805764 0.402882 0.915252i \(-0.368008\pi\)
0.402882 + 0.915252i \(0.368008\pi\)
\(4\) −7.58443 −0.948054
\(5\) 0 0
\(6\) −2.69906 −0.183648
\(7\) 0 0
\(8\) 10.0465 0.443995
\(9\) −9.47008 −0.350744
\(10\) 0 0
\(11\) −47.7013 −1.30750 −0.653750 0.756711i \(-0.726805\pi\)
−0.653750 + 0.756711i \(0.726805\pi\)
\(12\) −31.7550 −0.763908
\(13\) −57.2256 −1.22089 −0.610443 0.792060i \(-0.709009\pi\)
−0.610443 + 0.792060i \(0.709009\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 54.1990 0.846859
\(17\) 36.9686 0.527423 0.263712 0.964602i \(-0.415053\pi\)
0.263712 + 0.964602i \(0.415053\pi\)
\(18\) 6.10487 0.0799407
\(19\) 30.7659 0.371484 0.185742 0.982599i \(-0.440531\pi\)
0.185742 + 0.982599i \(0.440531\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 30.7506 0.298002
\(23\) −53.1282 −0.481652 −0.240826 0.970568i \(-0.577418\pi\)
−0.240826 + 0.970568i \(0.577418\pi\)
\(24\) 42.0633 0.357756
\(25\) 0 0
\(26\) 36.8904 0.278261
\(27\) −152.696 −1.08838
\(28\) 0 0
\(29\) −195.663 −1.25288 −0.626442 0.779468i \(-0.715490\pi\)
−0.626442 + 0.779468i \(0.715490\pi\)
\(30\) 0 0
\(31\) 257.870 1.49403 0.747014 0.664809i \(-0.231487\pi\)
0.747014 + 0.664809i \(0.231487\pi\)
\(32\) −115.311 −0.637010
\(33\) −199.719 −1.05354
\(34\) −23.8317 −0.120209
\(35\) 0 0
\(36\) 71.8252 0.332524
\(37\) −346.423 −1.53923 −0.769616 0.638507i \(-0.779553\pi\)
−0.769616 + 0.638507i \(0.779553\pi\)
\(38\) −19.8332 −0.0846676
\(39\) −239.596 −0.983747
\(40\) 0 0
\(41\) 267.050 1.01722 0.508611 0.860996i \(-0.330159\pi\)
0.508611 + 0.860996i \(0.330159\pi\)
\(42\) 0 0
\(43\) 176.859 0.627227 0.313614 0.949551i \(-0.398460\pi\)
0.313614 + 0.949551i \(0.398460\pi\)
\(44\) 361.787 1.23958
\(45\) 0 0
\(46\) 34.2490 0.109777
\(47\) 311.598 0.967049 0.483524 0.875331i \(-0.339356\pi\)
0.483524 + 0.875331i \(0.339356\pi\)
\(48\) 226.924 0.682369
\(49\) 0 0
\(50\) 0 0
\(51\) 154.783 0.424979
\(52\) 434.024 1.15747
\(53\) 492.270 1.27582 0.637910 0.770111i \(-0.279799\pi\)
0.637910 + 0.770111i \(0.279799\pi\)
\(54\) 98.4349 0.248061
\(55\) 0 0
\(56\) 0 0
\(57\) 128.813 0.299328
\(58\) 126.134 0.285554
\(59\) 98.7653 0.217935 0.108967 0.994045i \(-0.465246\pi\)
0.108967 + 0.994045i \(0.465246\pi\)
\(60\) 0 0
\(61\) 82.1682 0.172468 0.0862340 0.996275i \(-0.472517\pi\)
0.0862340 + 0.996275i \(0.472517\pi\)
\(62\) −166.235 −0.340515
\(63\) 0 0
\(64\) −359.257 −0.701674
\(65\) 0 0
\(66\) 128.749 0.240119
\(67\) −654.668 −1.19374 −0.596869 0.802339i \(-0.703589\pi\)
−0.596869 + 0.802339i \(0.703589\pi\)
\(68\) −280.386 −0.500026
\(69\) −222.441 −0.388098
\(70\) 0 0
\(71\) 779.658 1.30322 0.651608 0.758556i \(-0.274095\pi\)
0.651608 + 0.758556i \(0.274095\pi\)
\(72\) −95.1409 −0.155729
\(73\) 829.673 1.33022 0.665109 0.746747i \(-0.268385\pi\)
0.665109 + 0.746747i \(0.268385\pi\)
\(74\) 223.321 0.350818
\(75\) 0 0
\(76\) −233.342 −0.352186
\(77\) 0 0
\(78\) 154.455 0.224213
\(79\) −769.426 −1.09579 −0.547894 0.836548i \(-0.684570\pi\)
−0.547894 + 0.836548i \(0.684570\pi\)
\(80\) 0 0
\(81\) −383.625 −0.526235
\(82\) −172.153 −0.231843
\(83\) −613.203 −0.810937 −0.405469 0.914109i \(-0.632892\pi\)
−0.405469 + 0.914109i \(0.632892\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −114.012 −0.142956
\(87\) −819.215 −1.00953
\(88\) −479.230 −0.580524
\(89\) −457.666 −0.545084 −0.272542 0.962144i \(-0.587864\pi\)
−0.272542 + 0.962144i \(0.587864\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 402.947 0.456632
\(93\) 1079.67 1.20383
\(94\) −200.871 −0.220407
\(95\) 0 0
\(96\) −482.793 −0.513280
\(97\) 1412.11 1.47813 0.739063 0.673636i \(-0.235268\pi\)
0.739063 + 0.673636i \(0.235268\pi\)
\(98\) 0 0
\(99\) 451.736 0.458597
\(100\) 0 0
\(101\) 1823.79 1.79677 0.898386 0.439208i \(-0.144741\pi\)
0.898386 + 0.439208i \(0.144741\pi\)
\(102\) −99.7804 −0.0968601
\(103\) −407.775 −0.390090 −0.195045 0.980794i \(-0.562485\pi\)
−0.195045 + 0.980794i \(0.562485\pi\)
\(104\) −574.915 −0.542068
\(105\) 0 0
\(106\) −317.341 −0.290782
\(107\) 370.109 0.334390 0.167195 0.985924i \(-0.446529\pi\)
0.167195 + 0.985924i \(0.446529\pi\)
\(108\) 1158.11 1.03184
\(109\) 975.570 0.857272 0.428636 0.903477i \(-0.358994\pi\)
0.428636 + 0.903477i \(0.358994\pi\)
\(110\) 0 0
\(111\) −1450.43 −1.24026
\(112\) 0 0
\(113\) −1978.85 −1.64739 −0.823693 0.567036i \(-0.808090\pi\)
−0.823693 + 0.567036i \(0.808090\pi\)
\(114\) −83.0391 −0.0682221
\(115\) 0 0
\(116\) 1483.99 1.18780
\(117\) 541.931 0.428219
\(118\) −63.6689 −0.0496711
\(119\) 0 0
\(120\) 0 0
\(121\) 944.416 0.709554
\(122\) −52.9695 −0.0393085
\(123\) 1118.10 0.819642
\(124\) −1955.80 −1.41642
\(125\) 0 0
\(126\) 0 0
\(127\) −1392.38 −0.972867 −0.486433 0.873718i \(-0.661702\pi\)
−0.486433 + 0.873718i \(0.661702\pi\)
\(128\) 1154.08 0.796933
\(129\) 740.487 0.505397
\(130\) 0 0
\(131\) −1777.02 −1.18518 −0.592591 0.805504i \(-0.701895\pi\)
−0.592591 + 0.805504i \(0.701895\pi\)
\(132\) 1514.76 0.998809
\(133\) 0 0
\(134\) 422.031 0.272074
\(135\) 0 0
\(136\) 371.404 0.234174
\(137\) 1980.48 1.23506 0.617532 0.786545i \(-0.288132\pi\)
0.617532 + 0.786545i \(0.288132\pi\)
\(138\) 143.396 0.0884543
\(139\) 2182.09 1.33153 0.665763 0.746163i \(-0.268106\pi\)
0.665763 + 0.746163i \(0.268106\pi\)
\(140\) 0 0
\(141\) 1304.62 0.779213
\(142\) −502.605 −0.297026
\(143\) 2729.74 1.59631
\(144\) −513.269 −0.297031
\(145\) 0 0
\(146\) −534.847 −0.303180
\(147\) 0 0
\(148\) 2627.42 1.45928
\(149\) 670.154 0.368464 0.184232 0.982883i \(-0.441020\pi\)
0.184232 + 0.982883i \(0.441020\pi\)
\(150\) 0 0
\(151\) 3348.84 1.80480 0.902401 0.430898i \(-0.141803\pi\)
0.902401 + 0.430898i \(0.141803\pi\)
\(152\) 309.089 0.164937
\(153\) −350.096 −0.184990
\(154\) 0 0
\(155\) 0 0
\(156\) 1817.20 0.932645
\(157\) −2408.41 −1.22428 −0.612140 0.790749i \(-0.709691\pi\)
−0.612140 + 0.790749i \(0.709691\pi\)
\(158\) 496.009 0.249749
\(159\) 2061.07 1.02801
\(160\) 0 0
\(161\) 0 0
\(162\) 247.303 0.119938
\(163\) 3811.03 1.83131 0.915654 0.401968i \(-0.131674\pi\)
0.915654 + 0.401968i \(0.131674\pi\)
\(164\) −2025.42 −0.964382
\(165\) 0 0
\(166\) 395.300 0.184827
\(167\) −1207.15 −0.559354 −0.279677 0.960094i \(-0.590227\pi\)
−0.279677 + 0.960094i \(0.590227\pi\)
\(168\) 0 0
\(169\) 1077.77 0.490564
\(170\) 0 0
\(171\) −291.356 −0.130296
\(172\) −1341.38 −0.594645
\(173\) −3243.28 −1.42533 −0.712665 0.701505i \(-0.752512\pi\)
−0.712665 + 0.701505i \(0.752512\pi\)
\(174\) 528.105 0.230089
\(175\) 0 0
\(176\) −2585.36 −1.10727
\(177\) 413.518 0.175604
\(178\) 295.034 0.124234
\(179\) 859.728 0.358989 0.179495 0.983759i \(-0.442554\pi\)
0.179495 + 0.983759i \(0.442554\pi\)
\(180\) 0 0
\(181\) −290.504 −0.119298 −0.0596491 0.998219i \(-0.518998\pi\)
−0.0596491 + 0.998219i \(0.518998\pi\)
\(182\) 0 0
\(183\) 344.028 0.138969
\(184\) −533.751 −0.213851
\(185\) 0 0
\(186\) −696.007 −0.274375
\(187\) −1763.45 −0.689605
\(188\) −2363.30 −0.916814
\(189\) 0 0
\(190\) 0 0
\(191\) 4895.61 1.85463 0.927315 0.374282i \(-0.122111\pi\)
0.927315 + 0.374282i \(0.122111\pi\)
\(192\) −1504.16 −0.565384
\(193\) 3548.73 1.32354 0.661770 0.749707i \(-0.269806\pi\)
0.661770 + 0.749707i \(0.269806\pi\)
\(194\) −910.315 −0.336891
\(195\) 0 0
\(196\) 0 0
\(197\) 650.107 0.235118 0.117559 0.993066i \(-0.462493\pi\)
0.117559 + 0.993066i \(0.462493\pi\)
\(198\) −291.210 −0.104522
\(199\) 4055.09 1.44451 0.722256 0.691626i \(-0.243105\pi\)
0.722256 + 0.691626i \(0.243105\pi\)
\(200\) 0 0
\(201\) −2741.01 −0.961871
\(202\) −1175.70 −0.409516
\(203\) 0 0
\(204\) −1173.94 −0.402903
\(205\) 0 0
\(206\) 262.871 0.0889083
\(207\) 503.128 0.168936
\(208\) −3101.57 −1.03392
\(209\) −1467.58 −0.485714
\(210\) 0 0
\(211\) −1569.67 −0.512134 −0.256067 0.966659i \(-0.582427\pi\)
−0.256067 + 0.966659i \(0.582427\pi\)
\(212\) −3733.59 −1.20955
\(213\) 3264.33 1.05008
\(214\) −238.590 −0.0762134
\(215\) 0 0
\(216\) −1534.05 −0.483236
\(217\) 0 0
\(218\) −628.900 −0.195387
\(219\) 3473.74 1.07184
\(220\) 0 0
\(221\) −2115.55 −0.643924
\(222\) 935.017 0.282677
\(223\) −4723.86 −1.41853 −0.709267 0.704940i \(-0.750974\pi\)
−0.709267 + 0.704940i \(0.750974\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1275.66 0.375468
\(227\) −3685.02 −1.07746 −0.538730 0.842479i \(-0.681096\pi\)
−0.538730 + 0.842479i \(0.681096\pi\)
\(228\) −976.973 −0.283779
\(229\) 3356.78 0.968656 0.484328 0.874887i \(-0.339064\pi\)
0.484328 + 0.874887i \(0.339064\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1965.72 −0.556275
\(233\) −2314.01 −0.650627 −0.325314 0.945606i \(-0.605470\pi\)
−0.325314 + 0.945606i \(0.605470\pi\)
\(234\) −349.355 −0.0975985
\(235\) 0 0
\(236\) −749.079 −0.206614
\(237\) −3221.49 −0.882946
\(238\) 0 0
\(239\) 941.179 0.254727 0.127364 0.991856i \(-0.459348\pi\)
0.127364 + 0.991856i \(0.459348\pi\)
\(240\) 0 0
\(241\) 5638.24 1.50702 0.753509 0.657438i \(-0.228360\pi\)
0.753509 + 0.657438i \(0.228360\pi\)
\(242\) −608.816 −0.161720
\(243\) 2516.59 0.664360
\(244\) −623.199 −0.163509
\(245\) 0 0
\(246\) −720.783 −0.186811
\(247\) −1760.60 −0.453539
\(248\) 2590.69 0.663341
\(249\) −2567.40 −0.653424
\(250\) 0 0
\(251\) 365.822 0.0919940 0.0459970 0.998942i \(-0.485354\pi\)
0.0459970 + 0.998942i \(0.485354\pi\)
\(252\) 0 0
\(253\) 2534.28 0.629759
\(254\) 897.598 0.221733
\(255\) 0 0
\(256\) 2130.08 0.520039
\(257\) 6276.46 1.52340 0.761702 0.647928i \(-0.224364\pi\)
0.761702 + 0.647928i \(0.224364\pi\)
\(258\) −477.353 −0.115189
\(259\) 0 0
\(260\) 0 0
\(261\) 1852.94 0.439442
\(262\) 1145.55 0.270124
\(263\) 4225.97 0.990817 0.495408 0.868660i \(-0.335018\pi\)
0.495408 + 0.868660i \(0.335018\pi\)
\(264\) −2006.48 −0.467765
\(265\) 0 0
\(266\) 0 0
\(267\) −1916.19 −0.439210
\(268\) 4965.28 1.13173
\(269\) 981.591 0.222486 0.111243 0.993793i \(-0.464517\pi\)
0.111243 + 0.993793i \(0.464517\pi\)
\(270\) 0 0
\(271\) 3884.42 0.870708 0.435354 0.900259i \(-0.356623\pi\)
0.435354 + 0.900259i \(0.356623\pi\)
\(272\) 2003.66 0.446653
\(273\) 0 0
\(274\) −1276.71 −0.281493
\(275\) 0 0
\(276\) 1687.09 0.367938
\(277\) −3614.93 −0.784116 −0.392058 0.919941i \(-0.628237\pi\)
−0.392058 + 0.919941i \(0.628237\pi\)
\(278\) −1406.68 −0.303478
\(279\) −2442.05 −0.524021
\(280\) 0 0
\(281\) 72.6835 0.0154304 0.00771518 0.999970i \(-0.497544\pi\)
0.00771518 + 0.999970i \(0.497544\pi\)
\(282\) −841.023 −0.177596
\(283\) −1743.04 −0.366125 −0.183062 0.983101i \(-0.558601\pi\)
−0.183062 + 0.983101i \(0.558601\pi\)
\(284\) −5913.26 −1.23552
\(285\) 0 0
\(286\) −1759.72 −0.363827
\(287\) 0 0
\(288\) 1092.01 0.223427
\(289\) −3546.32 −0.721825
\(290\) 0 0
\(291\) 5912.34 1.19102
\(292\) −6292.59 −1.26112
\(293\) 4989.29 0.994804 0.497402 0.867520i \(-0.334287\pi\)
0.497402 + 0.867520i \(0.334287\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −3480.33 −0.683412
\(297\) 7283.78 1.42306
\(298\) −432.013 −0.0839794
\(299\) 3040.29 0.588042
\(300\) 0 0
\(301\) 0 0
\(302\) −2158.82 −0.411346
\(303\) 7635.98 1.44777
\(304\) 1667.48 0.314594
\(305\) 0 0
\(306\) 225.688 0.0421626
\(307\) −1664.61 −0.309461 −0.154731 0.987957i \(-0.549451\pi\)
−0.154731 + 0.987957i \(0.549451\pi\)
\(308\) 0 0
\(309\) −1707.30 −0.314320
\(310\) 0 0
\(311\) 545.623 0.0994838 0.0497419 0.998762i \(-0.484160\pi\)
0.0497419 + 0.998762i \(0.484160\pi\)
\(312\) −2407.10 −0.436779
\(313\) −213.564 −0.0385667 −0.0192833 0.999814i \(-0.506138\pi\)
−0.0192833 + 0.999814i \(0.506138\pi\)
\(314\) 1552.58 0.279035
\(315\) 0 0
\(316\) 5835.66 1.03887
\(317\) 2683.93 0.475535 0.237767 0.971322i \(-0.423584\pi\)
0.237767 + 0.971322i \(0.423584\pi\)
\(318\) −1328.67 −0.234302
\(319\) 9333.37 1.63815
\(320\) 0 0
\(321\) 1549.60 0.269440
\(322\) 0 0
\(323\) 1137.37 0.195929
\(324\) 2909.58 0.498899
\(325\) 0 0
\(326\) −2456.77 −0.417387
\(327\) 4084.59 0.690760
\(328\) 2682.91 0.451642
\(329\) 0 0
\(330\) 0 0
\(331\) −5067.52 −0.841500 −0.420750 0.907177i \(-0.638233\pi\)
−0.420750 + 0.907177i \(0.638233\pi\)
\(332\) 4650.80 0.768812
\(333\) 3280.66 0.539876
\(334\) 778.187 0.127487
\(335\) 0 0
\(336\) 0 0
\(337\) 9353.21 1.51187 0.755937 0.654644i \(-0.227182\pi\)
0.755937 + 0.654644i \(0.227182\pi\)
\(338\) −694.782 −0.111808
\(339\) −8285.20 −1.32741
\(340\) 0 0
\(341\) −12300.7 −1.95344
\(342\) 187.822 0.0296966
\(343\) 0 0
\(344\) 1776.81 0.278486
\(345\) 0 0
\(346\) 2090.77 0.324858
\(347\) −2349.34 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(348\) 6213.28 0.957088
\(349\) −10472.6 −1.60626 −0.803128 0.595806i \(-0.796833\pi\)
−0.803128 + 0.595806i \(0.796833\pi\)
\(350\) 0 0
\(351\) 8738.10 1.32879
\(352\) 5500.49 0.832889
\(353\) 7174.63 1.08178 0.540888 0.841095i \(-0.318088\pi\)
0.540888 + 0.841095i \(0.318088\pi\)
\(354\) −266.574 −0.0400232
\(355\) 0 0
\(356\) 3471.14 0.516769
\(357\) 0 0
\(358\) −554.222 −0.0818199
\(359\) −7534.13 −1.10762 −0.553811 0.832643i \(-0.686827\pi\)
−0.553811 + 0.832643i \(0.686827\pi\)
\(360\) 0 0
\(361\) −5912.46 −0.862000
\(362\) 187.273 0.0271902
\(363\) 3954.15 0.571733
\(364\) 0 0
\(365\) 0 0
\(366\) −221.777 −0.0316734
\(367\) −5453.06 −0.775606 −0.387803 0.921742i \(-0.626766\pi\)
−0.387803 + 0.921742i \(0.626766\pi\)
\(368\) −2879.49 −0.407891
\(369\) −2528.98 −0.356785
\(370\) 0 0
\(371\) 0 0
\(372\) −8188.68 −1.14130
\(373\) −8231.29 −1.14263 −0.571314 0.820732i \(-0.693566\pi\)
−0.571314 + 0.820732i \(0.693566\pi\)
\(374\) 1136.80 0.157173
\(375\) 0 0
\(376\) 3130.46 0.429365
\(377\) 11196.9 1.52963
\(378\) 0 0
\(379\) 1670.06 0.226346 0.113173 0.993575i \(-0.463898\pi\)
0.113173 + 0.993575i \(0.463898\pi\)
\(380\) 0 0
\(381\) −5829.74 −0.783901
\(382\) −3155.95 −0.422703
\(383\) −3220.14 −0.429612 −0.214806 0.976657i \(-0.568912\pi\)
−0.214806 + 0.976657i \(0.568912\pi\)
\(384\) 4832.00 0.642140
\(385\) 0 0
\(386\) −2287.68 −0.301658
\(387\) −1674.87 −0.219996
\(388\) −10710.1 −1.40134
\(389\) 3522.23 0.459085 0.229543 0.973299i \(-0.426277\pi\)
0.229543 + 0.973299i \(0.426277\pi\)
\(390\) 0 0
\(391\) −1964.07 −0.254034
\(392\) 0 0
\(393\) −7440.15 −0.954977
\(394\) −419.090 −0.0535875
\(395\) 0 0
\(396\) −3426.16 −0.434775
\(397\) 5455.16 0.689639 0.344819 0.938669i \(-0.387940\pi\)
0.344819 + 0.938669i \(0.387940\pi\)
\(398\) −2614.11 −0.329229
\(399\) 0 0
\(400\) 0 0
\(401\) −1161.80 −0.144682 −0.0723409 0.997380i \(-0.523047\pi\)
−0.0723409 + 0.997380i \(0.523047\pi\)
\(402\) 1766.99 0.219227
\(403\) −14756.8 −1.82404
\(404\) −13832.4 −1.70344
\(405\) 0 0
\(406\) 0 0
\(407\) 16524.8 2.01255
\(408\) 1555.02 0.188689
\(409\) −7398.65 −0.894473 −0.447237 0.894416i \(-0.647592\pi\)
−0.447237 + 0.894416i \(0.647592\pi\)
\(410\) 0 0
\(411\) 8292.02 0.995171
\(412\) 3092.74 0.369826
\(413\) 0 0
\(414\) −324.341 −0.0385036
\(415\) 0 0
\(416\) 6598.74 0.777716
\(417\) 9136.12 1.07290
\(418\) 946.069 0.110703
\(419\) 2134.46 0.248867 0.124433 0.992228i \(-0.460289\pi\)
0.124433 + 0.992228i \(0.460289\pi\)
\(420\) 0 0
\(421\) −3902.36 −0.451756 −0.225878 0.974156i \(-0.572525\pi\)
−0.225878 + 0.974156i \(0.572525\pi\)
\(422\) 1011.88 0.116724
\(423\) −2950.86 −0.339186
\(424\) 4945.58 0.566459
\(425\) 0 0
\(426\) −2104.34 −0.239333
\(427\) 0 0
\(428\) −2807.06 −0.317020
\(429\) 11429.1 1.28625
\(430\) 0 0
\(431\) −3618.13 −0.404360 −0.202180 0.979348i \(-0.564803\pi\)
−0.202180 + 0.979348i \(0.564803\pi\)
\(432\) −8275.95 −0.921706
\(433\) −4222.37 −0.468624 −0.234312 0.972161i \(-0.575284\pi\)
−0.234312 + 0.972161i \(0.575284\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7399.14 −0.812740
\(437\) −1634.54 −0.178926
\(438\) −2239.34 −0.244291
\(439\) 13518.0 1.46965 0.734826 0.678256i \(-0.237264\pi\)
0.734826 + 0.678256i \(0.237264\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1363.78 0.146762
\(443\) −16591.2 −1.77939 −0.889695 0.456555i \(-0.849083\pi\)
−0.889695 + 0.456555i \(0.849083\pi\)
\(444\) 11000.7 1.17583
\(445\) 0 0
\(446\) 3045.23 0.323309
\(447\) 2805.85 0.296895
\(448\) 0 0
\(449\) 8354.32 0.878095 0.439048 0.898464i \(-0.355316\pi\)
0.439048 + 0.898464i \(0.355316\pi\)
\(450\) 0 0
\(451\) −12738.6 −1.33002
\(452\) 15008.5 1.56181
\(453\) 14021.2 1.45424
\(454\) 2375.54 0.245572
\(455\) 0 0
\(456\) 1294.12 0.132900
\(457\) 1280.34 0.131054 0.0655269 0.997851i \(-0.479127\pi\)
0.0655269 + 0.997851i \(0.479127\pi\)
\(458\) −2163.94 −0.220774
\(459\) −5644.94 −0.574038
\(460\) 0 0
\(461\) 6986.72 0.705865 0.352932 0.935649i \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(462\) 0 0
\(463\) 5587.32 0.560831 0.280416 0.959879i \(-0.409528\pi\)
0.280416 + 0.959879i \(0.409528\pi\)
\(464\) −10604.7 −1.06102
\(465\) 0 0
\(466\) 1491.73 0.148289
\(467\) −9933.83 −0.984332 −0.492166 0.870501i \(-0.663795\pi\)
−0.492166 + 0.870501i \(0.663795\pi\)
\(468\) −4110.24 −0.405974
\(469\) 0 0
\(470\) 0 0
\(471\) −10083.7 −0.986481
\(472\) 992.243 0.0967620
\(473\) −8436.41 −0.820099
\(474\) 2076.73 0.201239
\(475\) 0 0
\(476\) 0 0
\(477\) −4661.84 −0.447486
\(478\) −606.729 −0.0580568
\(479\) −5068.62 −0.483489 −0.241744 0.970340i \(-0.577720\pi\)
−0.241744 + 0.970340i \(0.577720\pi\)
\(480\) 0 0
\(481\) 19824.3 1.87923
\(482\) −3634.68 −0.343476
\(483\) 0 0
\(484\) −7162.86 −0.672695
\(485\) 0 0
\(486\) −1622.32 −0.151419
\(487\) −264.353 −0.0245975 −0.0122988 0.999924i \(-0.503915\pi\)
−0.0122988 + 0.999924i \(0.503915\pi\)
\(488\) 825.500 0.0765751
\(489\) 15956.3 1.47560
\(490\) 0 0
\(491\) −7459.47 −0.685623 −0.342812 0.939404i \(-0.611379\pi\)
−0.342812 + 0.939404i \(0.611379\pi\)
\(492\) −8480.17 −0.777064
\(493\) −7233.37 −0.660800
\(494\) 1134.97 0.103370
\(495\) 0 0
\(496\) 13976.3 1.26523
\(497\) 0 0
\(498\) 1655.07 0.148927
\(499\) 7206.67 0.646523 0.323261 0.946310i \(-0.395221\pi\)
0.323261 + 0.946310i \(0.395221\pi\)
\(500\) 0 0
\(501\) −5054.19 −0.450707
\(502\) −235.827 −0.0209670
\(503\) 10886.7 0.965037 0.482519 0.875886i \(-0.339722\pi\)
0.482519 + 0.875886i \(0.339722\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1633.72 −0.143533
\(507\) 4512.49 0.395279
\(508\) 10560.4 0.922330
\(509\) −7504.97 −0.653540 −0.326770 0.945104i \(-0.605960\pi\)
−0.326770 + 0.945104i \(0.605960\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −10605.8 −0.915459
\(513\) −4697.82 −0.404316
\(514\) −4046.11 −0.347210
\(515\) 0 0
\(516\) −5616.17 −0.479144
\(517\) −14863.7 −1.26442
\(518\) 0 0
\(519\) −13579.2 −1.14848
\(520\) 0 0
\(521\) −22264.8 −1.87224 −0.936120 0.351681i \(-0.885610\pi\)
−0.936120 + 0.351681i \(0.885610\pi\)
\(522\) −1194.50 −0.100156
\(523\) −11286.7 −0.943655 −0.471828 0.881691i \(-0.656405\pi\)
−0.471828 + 0.881691i \(0.656405\pi\)
\(524\) 13477.7 1.12362
\(525\) 0 0
\(526\) −2724.27 −0.225824
\(527\) 9533.09 0.787985
\(528\) −10824.6 −0.892197
\(529\) −9344.40 −0.768012
\(530\) 0 0
\(531\) −935.316 −0.0764393
\(532\) 0 0
\(533\) −15282.1 −1.24191
\(534\) 1235.27 0.100104
\(535\) 0 0
\(536\) −6577.10 −0.530014
\(537\) 3599.57 0.289261
\(538\) −632.781 −0.0507084
\(539\) 0 0
\(540\) 0 0
\(541\) 16406.8 1.30385 0.651924 0.758284i \(-0.273962\pi\)
0.651924 + 0.758284i \(0.273962\pi\)
\(542\) −2504.08 −0.198450
\(543\) −1216.30 −0.0961263
\(544\) −4262.88 −0.335974
\(545\) 0 0
\(546\) 0 0
\(547\) 8692.48 0.679458 0.339729 0.940523i \(-0.389665\pi\)
0.339729 + 0.940523i \(0.389665\pi\)
\(548\) −15020.8 −1.17091
\(549\) −778.139 −0.0604921
\(550\) 0 0
\(551\) −6019.74 −0.465426
\(552\) −2234.75 −0.172314
\(553\) 0 0
\(554\) 2330.36 0.178714
\(555\) 0 0
\(556\) −16549.9 −1.26236
\(557\) 13935.7 1.06010 0.530049 0.847967i \(-0.322174\pi\)
0.530049 + 0.847967i \(0.322174\pi\)
\(558\) 1574.26 0.119434
\(559\) −10120.9 −0.765773
\(560\) 0 0
\(561\) −7383.34 −0.555659
\(562\) −46.8553 −0.00351685
\(563\) −22263.6 −1.66661 −0.833304 0.552815i \(-0.813553\pi\)
−0.833304 + 0.552815i \(0.813553\pi\)
\(564\) −9894.82 −0.738736
\(565\) 0 0
\(566\) 1123.65 0.0834462
\(567\) 0 0
\(568\) 7832.81 0.578622
\(569\) 9525.66 0.701822 0.350911 0.936409i \(-0.385872\pi\)
0.350911 + 0.936409i \(0.385872\pi\)
\(570\) 0 0
\(571\) 7669.99 0.562135 0.281068 0.959688i \(-0.409311\pi\)
0.281068 + 0.959688i \(0.409311\pi\)
\(572\) −20703.5 −1.51339
\(573\) 20497.3 1.49439
\(574\) 0 0
\(575\) 0 0
\(576\) 3402.19 0.246108
\(577\) 3907.15 0.281901 0.140950 0.990017i \(-0.454984\pi\)
0.140950 + 0.990017i \(0.454984\pi\)
\(578\) 2286.13 0.164516
\(579\) 14858.1 1.06646
\(580\) 0 0
\(581\) 0 0
\(582\) −3811.38 −0.271455
\(583\) −23481.9 −1.66813
\(584\) 8335.28 0.590610
\(585\) 0 0
\(586\) −3216.34 −0.226733
\(587\) −19891.6 −1.39866 −0.699331 0.714798i \(-0.746519\pi\)
−0.699331 + 0.714798i \(0.746519\pi\)
\(588\) 0 0
\(589\) 7933.61 0.555007
\(590\) 0 0
\(591\) 2721.92 0.189450
\(592\) −18775.8 −1.30351
\(593\) 4780.36 0.331038 0.165519 0.986207i \(-0.447070\pi\)
0.165519 + 0.986207i \(0.447070\pi\)
\(594\) −4695.48 −0.324340
\(595\) 0 0
\(596\) −5082.74 −0.349324
\(597\) 16978.2 1.16394
\(598\) −1959.92 −0.134025
\(599\) 11085.6 0.756170 0.378085 0.925771i \(-0.376583\pi\)
0.378085 + 0.925771i \(0.376583\pi\)
\(600\) 0 0
\(601\) 1573.44 0.106792 0.0533958 0.998573i \(-0.482995\pi\)
0.0533958 + 0.998573i \(0.482995\pi\)
\(602\) 0 0
\(603\) 6199.76 0.418696
\(604\) −25399.1 −1.71105
\(605\) 0 0
\(606\) −4922.52 −0.329973
\(607\) 8542.73 0.571233 0.285617 0.958344i \(-0.407802\pi\)
0.285617 + 0.958344i \(0.407802\pi\)
\(608\) −3547.65 −0.236639
\(609\) 0 0
\(610\) 0 0
\(611\) −17831.4 −1.18066
\(612\) 2655.27 0.175381
\(613\) −15068.2 −0.992817 −0.496409 0.868089i \(-0.665348\pi\)
−0.496409 + 0.868089i \(0.665348\pi\)
\(614\) 1073.09 0.0705316
\(615\) 0 0
\(616\) 0 0
\(617\) −2524.58 −0.164725 −0.0823627 0.996602i \(-0.526247\pi\)
−0.0823627 + 0.996602i \(0.526247\pi\)
\(618\) 1100.61 0.0716391
\(619\) 21238.9 1.37910 0.689551 0.724237i \(-0.257808\pi\)
0.689551 + 0.724237i \(0.257808\pi\)
\(620\) 0 0
\(621\) 8112.44 0.524221
\(622\) −351.735 −0.0226741
\(623\) 0 0
\(624\) −12985.9 −0.833095
\(625\) 0 0
\(626\) 137.674 0.00879002
\(627\) −6144.55 −0.391371
\(628\) 18266.4 1.16068
\(629\) −12806.8 −0.811827
\(630\) 0 0
\(631\) −8885.83 −0.560601 −0.280300 0.959912i \(-0.590434\pi\)
−0.280300 + 0.959912i \(0.590434\pi\)
\(632\) −7730.02 −0.486525
\(633\) −6571.99 −0.412659
\(634\) −1730.19 −0.108383
\(635\) 0 0
\(636\) −15632.1 −0.974609
\(637\) 0 0
\(638\) −6016.74 −0.373362
\(639\) −7383.42 −0.457095
\(640\) 0 0
\(641\) 3655.63 0.225255 0.112628 0.993637i \(-0.464073\pi\)
0.112628 + 0.993637i \(0.464073\pi\)
\(642\) −998.946 −0.0614100
\(643\) 4221.22 0.258894 0.129447 0.991586i \(-0.458680\pi\)
0.129447 + 0.991586i \(0.458680\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −733.205 −0.0446557
\(647\) 103.679 0.00629989 0.00314995 0.999995i \(-0.498997\pi\)
0.00314995 + 0.999995i \(0.498997\pi\)
\(648\) −3854.08 −0.233646
\(649\) −4711.24 −0.284949
\(650\) 0 0
\(651\) 0 0
\(652\) −28904.5 −1.73618
\(653\) −4476.11 −0.268245 −0.134122 0.990965i \(-0.542821\pi\)
−0.134122 + 0.990965i \(0.542821\pi\)
\(654\) −2633.12 −0.157436
\(655\) 0 0
\(656\) 14473.8 0.861445
\(657\) −7857.07 −0.466566
\(658\) 0 0
\(659\) 12022.0 0.710641 0.355321 0.934745i \(-0.384372\pi\)
0.355321 + 0.934745i \(0.384372\pi\)
\(660\) 0 0
\(661\) −13451.0 −0.791504 −0.395752 0.918357i \(-0.629516\pi\)
−0.395752 + 0.918357i \(0.629516\pi\)
\(662\) 3266.77 0.191792
\(663\) −8857.54 −0.518851
\(664\) −6160.53 −0.360053
\(665\) 0 0
\(666\) −2114.87 −0.123047
\(667\) 10395.2 0.603454
\(668\) 9155.55 0.530297
\(669\) −19778.2 −1.14300
\(670\) 0 0
\(671\) −3919.53 −0.225502
\(672\) 0 0
\(673\) −9774.83 −0.559869 −0.279935 0.960019i \(-0.590313\pi\)
−0.279935 + 0.960019i \(0.590313\pi\)
\(674\) −6029.53 −0.344583
\(675\) 0 0
\(676\) −8174.27 −0.465081
\(677\) 23857.4 1.35438 0.677190 0.735808i \(-0.263198\pi\)
0.677190 + 0.735808i \(0.263198\pi\)
\(678\) 5341.04 0.302539
\(679\) 0 0
\(680\) 0 0
\(681\) −15428.7 −0.868179
\(682\) 7929.65 0.445223
\(683\) −11919.4 −0.667763 −0.333881 0.942615i \(-0.608358\pi\)
−0.333881 + 0.942615i \(0.608358\pi\)
\(684\) 2209.77 0.123527
\(685\) 0 0
\(686\) 0 0
\(687\) 14054.4 0.780508
\(688\) 9585.59 0.531173
\(689\) −28170.5 −1.55763
\(690\) 0 0
\(691\) 8203.58 0.451634 0.225817 0.974170i \(-0.427495\pi\)
0.225817 + 0.974170i \(0.427495\pi\)
\(692\) 24598.4 1.35129
\(693\) 0 0
\(694\) 1514.50 0.0828380
\(695\) 0 0
\(696\) −8230.22 −0.448227
\(697\) 9872.44 0.536507
\(698\) 6751.12 0.366094
\(699\) −9688.49 −0.524252
\(700\) 0 0
\(701\) 449.084 0.0241964 0.0120982 0.999927i \(-0.496149\pi\)
0.0120982 + 0.999927i \(0.496149\pi\)
\(702\) −5633.00 −0.302855
\(703\) −10658.0 −0.571800
\(704\) 17137.0 0.917438
\(705\) 0 0
\(706\) −4625.11 −0.246556
\(707\) 0 0
\(708\) −3136.30 −0.166482
\(709\) 1897.64 0.100518 0.0502590 0.998736i \(-0.483995\pi\)
0.0502590 + 0.998736i \(0.483995\pi\)
\(710\) 0 0
\(711\) 7286.53 0.384341
\(712\) −4597.93 −0.242015
\(713\) −13700.2 −0.719601
\(714\) 0 0
\(715\) 0 0
\(716\) −6520.54 −0.340341
\(717\) 3940.60 0.205250
\(718\) 4856.86 0.252446
\(719\) −6494.70 −0.336873 −0.168436 0.985713i \(-0.553872\pi\)
−0.168436 + 0.985713i \(0.553872\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3811.45 0.196465
\(723\) 23606.6 1.21430
\(724\) 2203.31 0.113101
\(725\) 0 0
\(726\) −2549.04 −0.130308
\(727\) −18311.2 −0.934148 −0.467074 0.884218i \(-0.654692\pi\)
−0.467074 + 0.884218i \(0.654692\pi\)
\(728\) 0 0
\(729\) 20894.5 1.06155
\(730\) 0 0
\(731\) 6538.23 0.330814
\(732\) −2609.25 −0.131750
\(733\) 21233.3 1.06994 0.534972 0.844870i \(-0.320322\pi\)
0.534972 + 0.844870i \(0.320322\pi\)
\(734\) 3515.30 0.176774
\(735\) 0 0
\(736\) 6126.27 0.306817
\(737\) 31228.5 1.56081
\(738\) 1630.30 0.0813175
\(739\) −22023.5 −1.09628 −0.548138 0.836388i \(-0.684663\pi\)
−0.548138 + 0.836388i \(0.684663\pi\)
\(740\) 0 0
\(741\) −7371.40 −0.365446
\(742\) 0 0
\(743\) −9436.77 −0.465951 −0.232975 0.972483i \(-0.574846\pi\)
−0.232975 + 0.972483i \(0.574846\pi\)
\(744\) 10846.9 0.534497
\(745\) 0 0
\(746\) 5306.29 0.260425
\(747\) 5807.09 0.284431
\(748\) 13374.8 0.653783
\(749\) 0 0
\(750\) 0 0
\(751\) −39161.8 −1.90284 −0.951421 0.307893i \(-0.900376\pi\)
−0.951421 + 0.307893i \(0.900376\pi\)
\(752\) 16888.3 0.818954
\(753\) 1531.65 0.0741255
\(754\) −7218.07 −0.348629
\(755\) 0 0
\(756\) 0 0
\(757\) −20340.6 −0.976607 −0.488303 0.872674i \(-0.662384\pi\)
−0.488303 + 0.872674i \(0.662384\pi\)
\(758\) −1076.60 −0.0515883
\(759\) 10610.7 0.507438
\(760\) 0 0
\(761\) −3307.90 −0.157570 −0.0787852 0.996892i \(-0.525104\pi\)
−0.0787852 + 0.996892i \(0.525104\pi\)
\(762\) 3758.13 0.178665
\(763\) 0 0
\(764\) −37130.4 −1.75829
\(765\) 0 0
\(766\) 2075.85 0.0979160
\(767\) −5651.91 −0.266074
\(768\) 8918.37 0.419029
\(769\) −17234.0 −0.808159 −0.404079 0.914724i \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(770\) 0 0
\(771\) 26278.7 1.22750
\(772\) −26915.1 −1.25479
\(773\) −8726.33 −0.406034 −0.203017 0.979175i \(-0.565075\pi\)
−0.203017 + 0.979175i \(0.565075\pi\)
\(774\) 1079.70 0.0501409
\(775\) 0 0
\(776\) 14186.7 0.656281
\(777\) 0 0
\(778\) −2270.60 −0.104634
\(779\) 8216.03 0.377882
\(780\) 0 0
\(781\) −37190.7 −1.70395
\(782\) 1266.14 0.0578989
\(783\) 29876.8 1.36362
\(784\) 0 0
\(785\) 0 0
\(786\) 4796.28 0.217656
\(787\) −10642.1 −0.482018 −0.241009 0.970523i \(-0.577478\pi\)
−0.241009 + 0.970523i \(0.577478\pi\)
\(788\) −4930.69 −0.222904
\(789\) 17693.6 0.798365
\(790\) 0 0
\(791\) 0 0
\(792\) 4538.35 0.203615
\(793\) −4702.12 −0.210564
\(794\) −3516.66 −0.157181
\(795\) 0 0
\(796\) −30755.5 −1.36947
\(797\) 29234.1 1.29928 0.649640 0.760242i \(-0.274920\pi\)
0.649640 + 0.760242i \(0.274920\pi\)
\(798\) 0 0
\(799\) 11519.3 0.510044
\(800\) 0 0
\(801\) 4334.14 0.191185
\(802\) 748.950 0.0329755
\(803\) −39576.5 −1.73926
\(804\) 20789.0 0.911906
\(805\) 0 0
\(806\) 9512.93 0.415730
\(807\) 4109.80 0.179271
\(808\) 18322.7 0.797758
\(809\) 36211.2 1.57369 0.786846 0.617150i \(-0.211713\pi\)
0.786846 + 0.617150i \(0.211713\pi\)
\(810\) 0 0
\(811\) 27995.2 1.21214 0.606069 0.795412i \(-0.292746\pi\)
0.606069 + 0.795412i \(0.292746\pi\)
\(812\) 0 0
\(813\) 16263.6 0.701585
\(814\) −10652.7 −0.458694
\(815\) 0 0
\(816\) 8389.07 0.359897
\(817\) 5441.23 0.233005
\(818\) 4769.52 0.203866
\(819\) 0 0
\(820\) 0 0
\(821\) 44805.7 1.90467 0.952333 0.305060i \(-0.0986766\pi\)
0.952333 + 0.305060i \(0.0986766\pi\)
\(822\) −5345.44 −0.226817
\(823\) 15850.9 0.671360 0.335680 0.941976i \(-0.391034\pi\)
0.335680 + 0.941976i \(0.391034\pi\)
\(824\) −4096.70 −0.173198
\(825\) 0 0
\(826\) 0 0
\(827\) 45013.9 1.89273 0.946363 0.323104i \(-0.104726\pi\)
0.946363 + 0.323104i \(0.104726\pi\)
\(828\) −3815.94 −0.160161
\(829\) −5655.83 −0.236954 −0.118477 0.992957i \(-0.537801\pi\)
−0.118477 + 0.992957i \(0.537801\pi\)
\(830\) 0 0
\(831\) −15135.3 −0.631812
\(832\) 20558.7 0.856664
\(833\) 0 0
\(834\) −5889.58 −0.244532
\(835\) 0 0
\(836\) 11130.7 0.460483
\(837\) −39375.7 −1.62607
\(838\) −1375.97 −0.0567211
\(839\) 22037.0 0.906797 0.453398 0.891308i \(-0.350211\pi\)
0.453398 + 0.891308i \(0.350211\pi\)
\(840\) 0 0
\(841\) 13894.9 0.569719
\(842\) 2515.65 0.102963
\(843\) 304.317 0.0124332
\(844\) 11905.0 0.485530
\(845\) 0 0
\(846\) 1902.27 0.0773065
\(847\) 0 0
\(848\) 26680.5 1.08044
\(849\) −7297.91 −0.295010
\(850\) 0 0
\(851\) 18404.8 0.741374
\(852\) −24758.1 −0.995537
\(853\) −44486.7 −1.78569 −0.892846 0.450362i \(-0.851295\pi\)
−0.892846 + 0.450362i \(0.851295\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 3718.29 0.148468
\(857\) −38559.6 −1.53696 −0.768478 0.639877i \(-0.778985\pi\)
−0.768478 + 0.639877i \(0.778985\pi\)
\(858\) −7367.72 −0.293158
\(859\) −8426.01 −0.334682 −0.167341 0.985899i \(-0.553518\pi\)
−0.167341 + 0.985899i \(0.553518\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2332.42 0.0921608
\(863\) 20054.3 0.791029 0.395514 0.918460i \(-0.370566\pi\)
0.395514 + 0.918460i \(0.370566\pi\)
\(864\) 17607.5 0.693309
\(865\) 0 0
\(866\) 2721.94 0.106808
\(867\) −14848.0 −0.581621
\(868\) 0 0
\(869\) 36702.6 1.43274
\(870\) 0 0
\(871\) 37463.8 1.45742
\(872\) 9801.04 0.380625
\(873\) −13372.8 −0.518444
\(874\) 1053.70 0.0407803
\(875\) 0 0
\(876\) −26346.3 −1.01616
\(877\) −47082.1 −1.81283 −0.906414 0.422391i \(-0.861191\pi\)
−0.906414 + 0.422391i \(0.861191\pi\)
\(878\) −8714.32 −0.334959
\(879\) 20889.5 0.801577
\(880\) 0 0
\(881\) 9467.24 0.362042 0.181021 0.983479i \(-0.442060\pi\)
0.181021 + 0.983479i \(0.442060\pi\)
\(882\) 0 0
\(883\) 3049.49 0.116221 0.0581106 0.998310i \(-0.481492\pi\)
0.0581106 + 0.998310i \(0.481492\pi\)
\(884\) 16045.2 0.610475
\(885\) 0 0
\(886\) 10695.5 0.405554
\(887\) −19468.6 −0.736968 −0.368484 0.929634i \(-0.620123\pi\)
−0.368484 + 0.929634i \(0.620123\pi\)
\(888\) −14571.7 −0.550669
\(889\) 0 0
\(890\) 0 0
\(891\) 18299.4 0.688052
\(892\) 35827.8 1.34485
\(893\) 9586.61 0.359243
\(894\) −1808.79 −0.0676676
\(895\) 0 0
\(896\) 0 0
\(897\) 12729.3 0.473823
\(898\) −5385.60 −0.200133
\(899\) −50455.6 −1.87184
\(900\) 0 0
\(901\) 18198.5 0.672898
\(902\) 8211.92 0.303134
\(903\) 0 0
\(904\) −19880.5 −0.731432
\(905\) 0 0
\(906\) −9038.73 −0.331448
\(907\) 32014.2 1.17201 0.586006 0.810307i \(-0.300699\pi\)
0.586006 + 0.810307i \(0.300699\pi\)
\(908\) 27948.8 1.02149
\(909\) −17271.4 −0.630206
\(910\) 0 0
\(911\) 20921.1 0.760866 0.380433 0.924809i \(-0.375775\pi\)
0.380433 + 0.924809i \(0.375775\pi\)
\(912\) 6981.54 0.253489
\(913\) 29250.6 1.06030
\(914\) −825.366 −0.0298694
\(915\) 0 0
\(916\) −25459.2 −0.918337
\(917\) 0 0
\(918\) 3639.00 0.130833
\(919\) 43467.4 1.56024 0.780118 0.625632i \(-0.215159\pi\)
0.780118 + 0.625632i \(0.215159\pi\)
\(920\) 0 0
\(921\) −6969.53 −0.249353
\(922\) −4503.97 −0.160879
\(923\) −44616.4 −1.59108
\(924\) 0 0
\(925\) 0 0
\(926\) −3601.85 −0.127823
\(927\) 3861.66 0.136822
\(928\) 22562.1 0.798099
\(929\) 18542.1 0.654840 0.327420 0.944879i \(-0.393821\pi\)
0.327420 + 0.944879i \(0.393821\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 17550.5 0.616830
\(933\) 2284.46 0.0801605
\(934\) 6403.82 0.224346
\(935\) 0 0
\(936\) 5444.50 0.190127
\(937\) 13842.5 0.482619 0.241309 0.970448i \(-0.422423\pi\)
0.241309 + 0.970448i \(0.422423\pi\)
\(938\) 0 0
\(939\) −894.167 −0.0310757
\(940\) 0 0
\(941\) 53393.2 1.84970 0.924850 0.380333i \(-0.124191\pi\)
0.924850 + 0.380333i \(0.124191\pi\)
\(942\) 6500.44 0.224836
\(943\) −14187.9 −0.489947
\(944\) 5352.98 0.184560
\(945\) 0 0
\(946\) 5438.52 0.186915
\(947\) −22344.2 −0.766727 −0.383364 0.923598i \(-0.625234\pi\)
−0.383364 + 0.923598i \(0.625234\pi\)
\(948\) 24433.2 0.837081
\(949\) −47478.5 −1.62404
\(950\) 0 0
\(951\) 11237.3 0.383169
\(952\) 0 0
\(953\) 8902.63 0.302607 0.151304 0.988487i \(-0.451653\pi\)
0.151304 + 0.988487i \(0.451653\pi\)
\(954\) 3005.25 0.101990
\(955\) 0 0
\(956\) −7138.31 −0.241495
\(957\) 39077.6 1.31996
\(958\) 3267.48 0.110196
\(959\) 0 0
\(960\) 0 0
\(961\) 36706.0 1.23212
\(962\) −12779.7 −0.428309
\(963\) −3504.96 −0.117285
\(964\) −42762.8 −1.42873
\(965\) 0 0
\(966\) 0 0
\(967\) 2225.57 0.0740119 0.0370059 0.999315i \(-0.488218\pi\)
0.0370059 + 0.999315i \(0.488218\pi\)
\(968\) 9488.05 0.315039
\(969\) 4762.03 0.157873
\(970\) 0 0
\(971\) 11324.8 0.374285 0.187143 0.982333i \(-0.440077\pi\)
0.187143 + 0.982333i \(0.440077\pi\)
\(972\) −19086.9 −0.629849
\(973\) 0 0
\(974\) 170.415 0.00560621
\(975\) 0 0
\(976\) 4453.43 0.146056
\(977\) 57695.9 1.88931 0.944654 0.328067i \(-0.106397\pi\)
0.944654 + 0.328067i \(0.106397\pi\)
\(978\) −10286.2 −0.336315
\(979\) 21831.3 0.712697
\(980\) 0 0
\(981\) −9238.73 −0.300683
\(982\) 4808.73 0.156266
\(983\) 59657.3 1.93568 0.967839 0.251570i \(-0.0809469\pi\)
0.967839 + 0.251570i \(0.0809469\pi\)
\(984\) 11233.0 0.363917
\(985\) 0 0
\(986\) 4662.98 0.150608
\(987\) 0 0
\(988\) 13353.1 0.429980
\(989\) −9396.20 −0.302105
\(990\) 0 0
\(991\) 2890.60 0.0926568 0.0463284 0.998926i \(-0.485248\pi\)
0.0463284 + 0.998926i \(0.485248\pi\)
\(992\) −29735.3 −0.951710
\(993\) −21217.1 −0.678050
\(994\) 0 0
\(995\) 0 0
\(996\) 19472.3 0.619481
\(997\) −10619.6 −0.337337 −0.168669 0.985673i \(-0.553947\pi\)
−0.168669 + 0.985673i \(0.553947\pi\)
\(998\) −4645.77 −0.147354
\(999\) 52897.3 1.67527
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 1225.4.a.bi.1.3 6
5.4 even 2 245.4.a.p.1.4 yes 6
7.6 odd 2 1225.4.a.bj.1.3 6
15.14 odd 2 2205.4.a.ca.1.3 6
35.4 even 6 245.4.e.p.226.3 12
35.9 even 6 245.4.e.p.116.3 12
35.19 odd 6 245.4.e.q.116.3 12
35.24 odd 6 245.4.e.q.226.3 12
35.34 odd 2 245.4.a.o.1.4 6
105.104 even 2 2205.4.a.bz.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.4 6 35.34 odd 2
245.4.a.p.1.4 yes 6 5.4 even 2
245.4.e.p.116.3 12 35.9 even 6
245.4.e.p.226.3 12 35.4 even 6
245.4.e.q.116.3 12 35.19 odd 6
245.4.e.q.226.3 12 35.24 odd 6
1225.4.a.bi.1.3 6 1.1 even 1 trivial
1225.4.a.bj.1.3 6 7.6 odd 2
2205.4.a.bz.1.3 6 105.104 even 2
2205.4.a.ca.1.3 6 15.14 odd 2