Properties

Label 7600.2.a.bm.1.2
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7600,2,Mod(1,7600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 950)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.91223\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.25561 q^{3} -4.22547 q^{7} +2.08777 q^{9} +O(q^{10})\) \(q-2.25561 q^{3} -4.22547 q^{7} +2.08777 q^{9} +5.13770 q^{11} +3.16784 q^{13} -6.48108 q^{17} +1.00000 q^{19} +9.53101 q^{21} -7.56885 q^{23} +2.05763 q^{27} +0.832162 q^{29} +4.51122 q^{31} -11.5886 q^{33} +0.137699 q^{37} -7.14540 q^{39} -11.6489 q^{41} +2.51122 q^{43} +5.96216 q^{47} +10.8546 q^{49} +14.6188 q^{51} +0.225470 q^{53} -2.25561 q^{57} -5.39331 q^{59} +14.4509 q^{61} -8.82181 q^{63} +4.11021 q^{67} +17.0724 q^{69} -3.82446 q^{71} +4.70655 q^{73} -21.7092 q^{77} -10.6265 q^{79} -10.9045 q^{81} +12.0999 q^{83} -1.87703 q^{87} -10.0000 q^{89} -13.3856 q^{91} -10.1755 q^{93} +3.93972 q^{97} +10.7263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - 2 q^{7} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - 2 q^{7} + 13 q^{9} - 2 q^{11} - 2 q^{13} - 4 q^{17} + 3 q^{19} - 11 q^{21} - 14 q^{23} + 7 q^{27} + 14 q^{29} + 4 q^{31} + 4 q^{33} - 17 q^{37} - 29 q^{39} - 8 q^{41} - 2 q^{43} - 13 q^{47} + 25 q^{49} + 11 q^{51} - 10 q^{53} - 2 q^{57} + 6 q^{59} + 22 q^{61} - 2 q^{63} + 8 q^{69} + 2 q^{71} - 12 q^{73} - 50 q^{77} - 24 q^{79} - q^{81} - 12 q^{83} + 21 q^{87} - 30 q^{89} + 7 q^{91} - 44 q^{93} - 24 q^{99}+O(q^{100}) \) 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 0
\(3\) −2.25561 −1.30228 −0.651138 0.758959i \(-0.725708\pi\)
−0.651138 + 0.758959i \(0.725708\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.22547 −1.59708 −0.798539 0.601943i \(-0.794393\pi\)
−0.798539 + 0.601943i \(0.794393\pi\)
\(8\) 0 0
\(9\) 2.08777 0.695924
\(10\) 0 0
\(11\) 5.13770 1.54907 0.774537 0.632528i \(-0.217983\pi\)
0.774537 + 0.632528i \(0.217983\pi\)
\(12\) 0 0
\(13\) 3.16784 0.878600 0.439300 0.898340i \(-0.355226\pi\)
0.439300 + 0.898340i \(0.355226\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.48108 −1.57189 −0.785946 0.618295i \(-0.787824\pi\)
−0.785946 + 0.618295i \(0.787824\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 9.53101 2.07984
\(22\) 0 0
\(23\) −7.56885 −1.57821 −0.789107 0.614256i \(-0.789456\pi\)
−0.789107 + 0.614256i \(0.789456\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.05763 0.395991
\(28\) 0 0
\(29\) 0.832162 0.154529 0.0772643 0.997011i \(-0.475381\pi\)
0.0772643 + 0.997011i \(0.475381\pi\)
\(30\) 0 0
\(31\) 4.51122 0.810239 0.405119 0.914264i \(-0.367230\pi\)
0.405119 + 0.914264i \(0.367230\pi\)
\(32\) 0 0
\(33\) −11.5886 −2.01732
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.137699 0.0226376 0.0113188 0.999936i \(-0.496397\pi\)
0.0113188 + 0.999936i \(0.496397\pi\)
\(38\) 0 0
\(39\) −7.14540 −1.14418
\(40\) 0 0
\(41\) −11.6489 −1.81926 −0.909628 0.415425i \(-0.863633\pi\)
−0.909628 + 0.415425i \(0.863633\pi\)
\(42\) 0 0
\(43\) 2.51122 0.382957 0.191479 0.981497i \(-0.438672\pi\)
0.191479 + 0.981497i \(0.438672\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.96216 0.869670 0.434835 0.900510i \(-0.356807\pi\)
0.434835 + 0.900510i \(0.356807\pi\)
\(48\) 0 0
\(49\) 10.8546 1.55066
\(50\) 0 0
\(51\) 14.6188 2.04704
\(52\) 0 0
\(53\) 0.225470 0.0309707 0.0154853 0.999880i \(-0.495071\pi\)
0.0154853 + 0.999880i \(0.495071\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.25561 −0.298763
\(58\) 0 0
\(59\) −5.39331 −0.702149 −0.351074 0.936348i \(-0.614184\pi\)
−0.351074 + 0.936348i \(0.614184\pi\)
\(60\) 0 0
\(61\) 14.4509 1.85025 0.925127 0.379659i \(-0.123959\pi\)
0.925127 + 0.379659i \(0.123959\pi\)
\(62\) 0 0
\(63\) −8.82181 −1.11144
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.11021 0.502142 0.251071 0.967969i \(-0.419217\pi\)
0.251071 + 0.967969i \(0.419217\pi\)
\(68\) 0 0
\(69\) 17.0724 2.05527
\(70\) 0 0
\(71\) −3.82446 −0.453880 −0.226940 0.973909i \(-0.572872\pi\)
−0.226940 + 0.973909i \(0.572872\pi\)
\(72\) 0 0
\(73\) 4.70655 0.550860 0.275430 0.961321i \(-0.411180\pi\)
0.275430 + 0.961321i \(0.411180\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −21.7092 −2.47399
\(78\) 0 0
\(79\) −10.6265 −1.19557 −0.597786 0.801655i \(-0.703953\pi\)
−0.597786 + 0.801655i \(0.703953\pi\)
\(80\) 0 0
\(81\) −10.9045 −1.21161
\(82\) 0 0
\(83\) 12.0999 1.32813 0.664066 0.747674i \(-0.268829\pi\)
0.664066 + 0.747674i \(0.268829\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.87703 −0.201239
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) −13.3856 −1.40319
\(92\) 0 0
\(93\) −10.1755 −1.05515
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 3.93972 0.400018 0.200009 0.979794i \(-0.435903\pi\)
0.200009 + 0.979794i \(0.435903\pi\)
\(98\) 0 0
\(99\) 10.7263 1.07804
\(100\) 0 0
\(101\) 3.19798 0.318211 0.159105 0.987262i \(-0.449139\pi\)
0.159105 + 0.987262i \(0.449139\pi\)
\(102\) 0 0
\(103\) 10.6868 1.05300 0.526499 0.850176i \(-0.323504\pi\)
0.526499 + 0.850176i \(0.323504\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.8168 −1.04570 −0.522848 0.852426i \(-0.675130\pi\)
−0.522848 + 0.852426i \(0.675130\pi\)
\(108\) 0 0
\(109\) 9.24791 0.885789 0.442894 0.896574i \(-0.353952\pi\)
0.442894 + 0.896574i \(0.353952\pi\)
\(110\) 0 0
\(111\) −0.310596 −0.0294804
\(112\) 0 0
\(113\) 17.6489 1.66027 0.830135 0.557562i \(-0.188263\pi\)
0.830135 + 0.557562i \(0.188263\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 6.61372 0.611439
\(118\) 0 0
\(119\) 27.3856 2.51043
\(120\) 0 0
\(121\) 15.3960 1.39963
\(122\) 0 0
\(123\) 26.2754 2.36917
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.7866 1.13463 0.567314 0.823501i \(-0.307982\pi\)
0.567314 + 0.823501i \(0.307982\pi\)
\(128\) 0 0
\(129\) −5.66432 −0.498716
\(130\) 0 0
\(131\) 2.11526 0.184811 0.0924057 0.995721i \(-0.470544\pi\)
0.0924057 + 0.995721i \(0.470544\pi\)
\(132\) 0 0
\(133\) −4.22547 −0.366395
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.36317 −0.458206 −0.229103 0.973402i \(-0.573579\pi\)
−0.229103 + 0.973402i \(0.573579\pi\)
\(138\) 0 0
\(139\) 10.1601 0.861771 0.430886 0.902407i \(-0.358201\pi\)
0.430886 + 0.902407i \(0.358201\pi\)
\(140\) 0 0
\(141\) −13.4483 −1.13255
\(142\) 0 0
\(143\) 16.2754 1.36102
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −24.4837 −2.01938
\(148\) 0 0
\(149\) −5.93972 −0.486601 −0.243301 0.969951i \(-0.578230\pi\)
−0.243301 + 0.969951i \(0.578230\pi\)
\(150\) 0 0
\(151\) 15.2978 1.24492 0.622460 0.782652i \(-0.286133\pi\)
0.622460 + 0.782652i \(0.286133\pi\)
\(152\) 0 0
\(153\) −13.5310 −1.09392
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.7866 −1.02048 −0.510242 0.860031i \(-0.670444\pi\)
−0.510242 + 0.860031i \(0.670444\pi\)
\(158\) 0 0
\(159\) −0.508572 −0.0403324
\(160\) 0 0
\(161\) 31.9819 2.52053
\(162\) 0 0
\(163\) 11.4734 0.898664 0.449332 0.893365i \(-0.351662\pi\)
0.449332 + 0.893365i \(0.351662\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.4131 −1.50223 −0.751115 0.660171i \(-0.770484\pi\)
−0.751115 + 0.660171i \(0.770484\pi\)
\(168\) 0 0
\(169\) −2.96480 −0.228062
\(170\) 0 0
\(171\) 2.08777 0.159656
\(172\) 0 0
\(173\) 9.78662 0.744063 0.372031 0.928220i \(-0.378661\pi\)
0.372031 + 0.928220i \(0.378661\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.1652 0.914392
\(178\) 0 0
\(179\) 6.82446 0.510084 0.255042 0.966930i \(-0.417911\pi\)
0.255042 + 0.966930i \(0.417911\pi\)
\(180\) 0 0
\(181\) −0.137699 −0.0102351 −0.00511755 0.999987i \(-0.501629\pi\)
−0.00511755 + 0.999987i \(0.501629\pi\)
\(182\) 0 0
\(183\) −32.5957 −2.40954
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −33.2978 −2.43498
\(188\) 0 0
\(189\) −8.69446 −0.632429
\(190\) 0 0
\(191\) −19.3779 −1.40214 −0.701068 0.713095i \(-0.747293\pi\)
−0.701068 + 0.713095i \(0.747293\pi\)
\(192\) 0 0
\(193\) −5.42851 −0.390752 −0.195376 0.980728i \(-0.562593\pi\)
−0.195376 + 0.980728i \(0.562593\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.6489 −1.11494 −0.557470 0.830197i \(-0.688228\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(198\) 0 0
\(199\) −18.0499 −1.27953 −0.639763 0.768572i \(-0.720967\pi\)
−0.639763 + 0.768572i \(0.720967\pi\)
\(200\) 0 0
\(201\) −9.27102 −0.653927
\(202\) 0 0
\(203\) −3.51628 −0.246794
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −15.8020 −1.09832
\(208\) 0 0
\(209\) 5.13770 0.355382
\(210\) 0 0
\(211\) 7.50857 0.516911 0.258456 0.966023i \(-0.416786\pi\)
0.258456 + 0.966023i \(0.416786\pi\)
\(212\) 0 0
\(213\) 8.62648 0.591077
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −19.0620 −1.29401
\(218\) 0 0
\(219\) −10.6161 −0.717372
\(220\) 0 0
\(221\) −20.5310 −1.38106
\(222\) 0 0
\(223\) −27.8091 −1.86223 −0.931116 0.364723i \(-0.881164\pi\)
−0.931116 + 0.364723i \(0.881164\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.91223 −0.591525 −0.295763 0.955261i \(-0.595574\pi\)
−0.295763 + 0.955261i \(0.595574\pi\)
\(228\) 0 0
\(229\) −13.6489 −0.901946 −0.450973 0.892538i \(-0.648923\pi\)
−0.450973 + 0.892538i \(0.648923\pi\)
\(230\) 0 0
\(231\) 48.9674 3.22182
\(232\) 0 0
\(233\) 23.2754 1.52482 0.762411 0.647093i \(-0.224015\pi\)
0.762411 + 0.647093i \(0.224015\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 23.9692 1.55697
\(238\) 0 0
\(239\) −3.72898 −0.241208 −0.120604 0.992701i \(-0.538483\pi\)
−0.120604 + 0.992701i \(0.538483\pi\)
\(240\) 0 0
\(241\) −1.48878 −0.0959009 −0.0479505 0.998850i \(-0.515269\pi\)
−0.0479505 + 0.998850i \(0.515269\pi\)
\(242\) 0 0
\(243\) 18.4234 1.18186
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.16784 0.201565
\(248\) 0 0
\(249\) −27.2925 −1.72959
\(250\) 0 0
\(251\) 8.78662 0.554606 0.277303 0.960782i \(-0.410559\pi\)
0.277303 + 0.960782i \(0.410559\pi\)
\(252\) 0 0
\(253\) −38.8865 −2.44477
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.74175 0.171025 0.0855127 0.996337i \(-0.472747\pi\)
0.0855127 + 0.996337i \(0.472747\pi\)
\(258\) 0 0
\(259\) −0.581844 −0.0361540
\(260\) 0 0
\(261\) 1.73736 0.107540
\(262\) 0 0
\(263\) −2.74704 −0.169390 −0.0846948 0.996407i \(-0.526992\pi\)
−0.0846948 + 0.996407i \(0.526992\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 22.5561 1.38041
\(268\) 0 0
\(269\) −9.74175 −0.593965 −0.296982 0.954883i \(-0.595980\pi\)
−0.296982 + 0.954883i \(0.595980\pi\)
\(270\) 0 0
\(271\) −26.3555 −1.60098 −0.800490 0.599346i \(-0.795427\pi\)
−0.800490 + 0.599346i \(0.795427\pi\)
\(272\) 0 0
\(273\) 30.1927 1.82734
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −0.962158 −0.0578104 −0.0289052 0.999582i \(-0.509202\pi\)
−0.0289052 + 0.999582i \(0.509202\pi\)
\(278\) 0 0
\(279\) 9.41839 0.563864
\(280\) 0 0
\(281\) −14.6714 −0.875219 −0.437610 0.899165i \(-0.644175\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(282\) 0 0
\(283\) 26.1601 1.55506 0.777529 0.628847i \(-0.216473\pi\)
0.777529 + 0.628847i \(0.216473\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 49.2221 2.90549
\(288\) 0 0
\(289\) 25.0044 1.47085
\(290\) 0 0
\(291\) −8.88647 −0.520934
\(292\) 0 0
\(293\) −22.4657 −1.31246 −0.656229 0.754562i \(-0.727850\pi\)
−0.656229 + 0.754562i \(0.727850\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 10.5715 0.613420
\(298\) 0 0
\(299\) −23.9769 −1.38662
\(300\) 0 0
\(301\) −10.6111 −0.611612
\(302\) 0 0
\(303\) −7.21338 −0.414398
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −17.2204 −0.982821 −0.491410 0.870928i \(-0.663518\pi\)
−0.491410 + 0.870928i \(0.663518\pi\)
\(308\) 0 0
\(309\) −24.1051 −1.37129
\(310\) 0 0
\(311\) 7.87439 0.446516 0.223258 0.974759i \(-0.428331\pi\)
0.223258 + 0.974759i \(0.428331\pi\)
\(312\) 0 0
\(313\) −25.1678 −1.42257 −0.711285 0.702904i \(-0.751887\pi\)
−0.711285 + 0.702904i \(0.751887\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.9045 −1.34261 −0.671306 0.741180i \(-0.734266\pi\)
−0.671306 + 0.741180i \(0.734266\pi\)
\(318\) 0 0
\(319\) 4.27540 0.239376
\(320\) 0 0
\(321\) 24.3984 1.36178
\(322\) 0 0
\(323\) −6.48108 −0.360617
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −20.8597 −1.15354
\(328\) 0 0
\(329\) −25.1929 −1.38893
\(330\) 0 0
\(331\) −30.7565 −1.69053 −0.845264 0.534348i \(-0.820557\pi\)
−0.845264 + 0.534348i \(0.820557\pi\)
\(332\) 0 0
\(333\) 0.287484 0.0157540
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 13.4734 0.733942 0.366971 0.930232i \(-0.380395\pi\)
0.366971 + 0.930232i \(0.380395\pi\)
\(338\) 0 0
\(339\) −39.8091 −2.16213
\(340\) 0 0
\(341\) 23.1773 1.25512
\(342\) 0 0
\(343\) −16.2875 −0.879441
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.9468 −1.55394 −0.776971 0.629536i \(-0.783245\pi\)
−0.776971 + 0.629536i \(0.783245\pi\)
\(348\) 0 0
\(349\) 27.9243 1.49475 0.747377 0.664400i \(-0.231313\pi\)
0.747377 + 0.664400i \(0.231313\pi\)
\(350\) 0 0
\(351\) 6.51825 0.347918
\(352\) 0 0
\(353\) 28.3099 1.50678 0.753392 0.657571i \(-0.228416\pi\)
0.753392 + 0.657571i \(0.228416\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −61.7712 −3.26928
\(358\) 0 0
\(359\) −2.60163 −0.137309 −0.0686545 0.997640i \(-0.521871\pi\)
−0.0686545 + 0.997640i \(0.521871\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −34.7272 −1.82271
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −11.6489 −0.608069 −0.304034 0.952661i \(-0.598334\pi\)
−0.304034 + 0.952661i \(0.598334\pi\)
\(368\) 0 0
\(369\) −24.3203 −1.26606
\(370\) 0 0
\(371\) −0.952717 −0.0494626
\(372\) 0 0
\(373\) −12.8064 −0.663091 −0.331545 0.943439i \(-0.607570\pi\)
−0.331545 + 0.943439i \(0.607570\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.63615 0.135769
\(378\) 0 0
\(379\) 20.9122 1.07419 0.537095 0.843522i \(-0.319522\pi\)
0.537095 + 0.843522i \(0.319522\pi\)
\(380\) 0 0
\(381\) −28.8416 −1.47760
\(382\) 0 0
\(383\) −10.3511 −0.528916 −0.264458 0.964397i \(-0.585193\pi\)
−0.264458 + 0.964397i \(0.585193\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.24285 0.266509
\(388\) 0 0
\(389\) 6.56620 0.332920 0.166460 0.986048i \(-0.446766\pi\)
0.166460 + 0.986048i \(0.446766\pi\)
\(390\) 0 0
\(391\) 49.0543 2.48078
\(392\) 0 0
\(393\) −4.77121 −0.240676
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 23.5284 1.18085 0.590427 0.807091i \(-0.298959\pi\)
0.590427 + 0.807091i \(0.298959\pi\)
\(398\) 0 0
\(399\) 9.53101 0.477147
\(400\) 0 0
\(401\) 6.22041 0.310633 0.155316 0.987865i \(-0.450360\pi\)
0.155316 + 0.987865i \(0.450360\pi\)
\(402\) 0 0
\(403\) 14.2908 0.711876
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.707457 0.0350674
\(408\) 0 0
\(409\) −34.4905 −1.70545 −0.852723 0.522363i \(-0.825051\pi\)
−0.852723 + 0.522363i \(0.825051\pi\)
\(410\) 0 0
\(411\) 12.0972 0.596711
\(412\) 0 0
\(413\) 22.7893 1.12139
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −22.9173 −1.12226
\(418\) 0 0
\(419\) 10.6265 0.519138 0.259569 0.965725i \(-0.416420\pi\)
0.259569 + 0.965725i \(0.416420\pi\)
\(420\) 0 0
\(421\) −1.98021 −0.0965095 −0.0482548 0.998835i \(-0.515366\pi\)
−0.0482548 + 0.998835i \(0.515366\pi\)
\(422\) 0 0
\(423\) 12.4476 0.605224
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −61.0620 −2.95500
\(428\) 0 0
\(429\) −36.7109 −1.77242
\(430\) 0 0
\(431\) −15.0774 −0.726254 −0.363127 0.931740i \(-0.618291\pi\)
−0.363127 + 0.931740i \(0.618291\pi\)
\(432\) 0 0
\(433\) 13.5337 0.650386 0.325193 0.945648i \(-0.394571\pi\)
0.325193 + 0.945648i \(0.394571\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.56885 −0.362067
\(438\) 0 0
\(439\) −39.1773 −1.86983 −0.934915 0.354872i \(-0.884524\pi\)
−0.934915 + 0.354872i \(0.884524\pi\)
\(440\) 0 0
\(441\) 22.6619 1.07914
\(442\) 0 0
\(443\) −19.3132 −0.917600 −0.458800 0.888540i \(-0.651721\pi\)
−0.458800 + 0.888540i \(0.651721\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 13.3977 0.633689
\(448\) 0 0
\(449\) 41.4131 1.95440 0.977202 0.212310i \(-0.0680985\pi\)
0.977202 + 0.212310i \(0.0680985\pi\)
\(450\) 0 0
\(451\) −59.8486 −2.81816
\(452\) 0 0
\(453\) −34.5059 −1.62123
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −37.8392 −1.77004 −0.885021 0.465551i \(-0.845856\pi\)
−0.885021 + 0.465551i \(0.845856\pi\)
\(458\) 0 0
\(459\) −13.3357 −0.622456
\(460\) 0 0
\(461\) 1.58864 0.0739903 0.0369952 0.999315i \(-0.488221\pi\)
0.0369952 + 0.999315i \(0.488221\pi\)
\(462\) 0 0
\(463\) −40.3581 −1.87560 −0.937800 0.347175i \(-0.887141\pi\)
−0.937800 + 0.347175i \(0.887141\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 39.5130 1.82844 0.914221 0.405217i \(-0.132804\pi\)
0.914221 + 0.405217i \(0.132804\pi\)
\(468\) 0 0
\(469\) −17.3676 −0.801959
\(470\) 0 0
\(471\) 28.8416 1.32895
\(472\) 0 0
\(473\) 12.9019 0.593229
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.470730 0.0215532
\(478\) 0 0
\(479\) −7.61107 −0.347759 −0.173879 0.984767i \(-0.555630\pi\)
−0.173879 + 0.984767i \(0.555630\pi\)
\(480\) 0 0
\(481\) 0.436209 0.0198894
\(482\) 0 0
\(483\) −72.1388 −3.28243
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 20.3907 0.923989 0.461995 0.886883i \(-0.347134\pi\)
0.461995 + 0.886883i \(0.347134\pi\)
\(488\) 0 0
\(489\) −25.8794 −1.17031
\(490\) 0 0
\(491\) −25.0224 −1.12925 −0.564623 0.825349i \(-0.690979\pi\)
−0.564623 + 0.825349i \(0.690979\pi\)
\(492\) 0 0
\(493\) −5.39331 −0.242902
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 16.1601 0.724881
\(498\) 0 0
\(499\) −22.6111 −1.01221 −0.506105 0.862472i \(-0.668915\pi\)
−0.506105 + 0.862472i \(0.668915\pi\)
\(500\) 0 0
\(501\) 43.7884 1.95632
\(502\) 0 0
\(503\) −11.5035 −0.512916 −0.256458 0.966555i \(-0.582556\pi\)
−0.256458 + 0.966555i \(0.582556\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.68744 0.296999
\(508\) 0 0
\(509\) 9.11526 0.404027 0.202013 0.979383i \(-0.435252\pi\)
0.202013 + 0.979383i \(0.435252\pi\)
\(510\) 0 0
\(511\) −19.8874 −0.879766
\(512\) 0 0
\(513\) 2.05763 0.0908467
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 30.6318 1.34718
\(518\) 0 0
\(519\) −22.0748 −0.968975
\(520\) 0 0
\(521\) 15.4888 0.678576 0.339288 0.940683i \(-0.389814\pi\)
0.339288 + 0.940683i \(0.389814\pi\)
\(522\) 0 0
\(523\) −4.34073 −0.189807 −0.0949035 0.995486i \(-0.530254\pi\)
−0.0949035 + 0.995486i \(0.530254\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −29.2376 −1.27361
\(528\) 0 0
\(529\) 34.2875 1.49076
\(530\) 0 0
\(531\) −11.2600 −0.488642
\(532\) 0 0
\(533\) −36.9019 −1.59840
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −15.3933 −0.664270
\(538\) 0 0
\(539\) 55.7677 2.40208
\(540\) 0 0
\(541\) 19.5491 0.840480 0.420240 0.907413i \(-0.361946\pi\)
0.420240 + 0.907413i \(0.361946\pi\)
\(542\) 0 0
\(543\) 0.310596 0.0133289
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 41.8038 1.78740 0.893700 0.448665i \(-0.148100\pi\)
0.893700 + 0.448665i \(0.148100\pi\)
\(548\) 0 0
\(549\) 30.1703 1.28763
\(550\) 0 0
\(551\) 0.832162 0.0354513
\(552\) 0 0
\(553\) 44.9019 1.90942
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.76418 −0.413722 −0.206861 0.978370i \(-0.566325\pi\)
−0.206861 + 0.978370i \(0.566325\pi\)
\(558\) 0 0
\(559\) 7.95513 0.336466
\(560\) 0 0
\(561\) 75.1069 3.17102
\(562\) 0 0
\(563\) −11.4509 −0.482600 −0.241300 0.970451i \(-0.577574\pi\)
−0.241300 + 0.970451i \(0.577574\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 46.0767 1.93504
\(568\) 0 0
\(569\) −13.4338 −0.563174 −0.281587 0.959536i \(-0.590861\pi\)
−0.281587 + 0.959536i \(0.590861\pi\)
\(570\) 0 0
\(571\) −37.6335 −1.57491 −0.787457 0.616370i \(-0.788603\pi\)
−0.787457 + 0.616370i \(0.788603\pi\)
\(572\) 0 0
\(573\) 43.7090 1.82597
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.56885 0.0653121 0.0326560 0.999467i \(-0.489603\pi\)
0.0326560 + 0.999467i \(0.489603\pi\)
\(578\) 0 0
\(579\) 12.2446 0.508868
\(580\) 0 0
\(581\) −51.1276 −2.12113
\(582\) 0 0
\(583\) 1.15840 0.0479759
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −25.8693 −1.06774 −0.533871 0.845566i \(-0.679263\pi\)
−0.533871 + 0.845566i \(0.679263\pi\)
\(588\) 0 0
\(589\) 4.51122 0.185881
\(590\) 0 0
\(591\) 35.2978 1.45196
\(592\) 0 0
\(593\) −28.9243 −1.18778 −0.593890 0.804547i \(-0.702408\pi\)
−0.593890 + 0.804547i \(0.702408\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 40.7136 1.66630
\(598\) 0 0
\(599\) −41.3581 −1.68985 −0.844923 0.534887i \(-0.820354\pi\)
−0.844923 + 0.534887i \(0.820354\pi\)
\(600\) 0 0
\(601\) 2.68147 0.109379 0.0546897 0.998503i \(-0.482583\pi\)
0.0546897 + 0.998503i \(0.482583\pi\)
\(602\) 0 0
\(603\) 8.58117 0.349452
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −3.31324 −0.134480 −0.0672401 0.997737i \(-0.521419\pi\)
−0.0672401 + 0.997737i \(0.521419\pi\)
\(608\) 0 0
\(609\) 7.93134 0.321394
\(610\) 0 0
\(611\) 18.8871 0.764092
\(612\) 0 0
\(613\) −10.0603 −0.406331 −0.203165 0.979144i \(-0.565123\pi\)
−0.203165 + 0.979144i \(0.565123\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27.6265 −1.11220 −0.556100 0.831115i \(-0.687703\pi\)
−0.556100 + 0.831115i \(0.687703\pi\)
\(618\) 0 0
\(619\) −16.6714 −0.670078 −0.335039 0.942204i \(-0.608750\pi\)
−0.335039 + 0.942204i \(0.608750\pi\)
\(620\) 0 0
\(621\) −15.5739 −0.624959
\(622\) 0 0
\(623\) 42.2547 1.69290
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −11.5886 −0.462806
\(628\) 0 0
\(629\) −0.892439 −0.0355839
\(630\) 0 0
\(631\) 0.709194 0.0282326 0.0141163 0.999900i \(-0.495506\pi\)
0.0141163 + 0.999900i \(0.495506\pi\)
\(632\) 0 0
\(633\) −16.9364 −0.673162
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 34.3856 1.36241
\(638\) 0 0
\(639\) −7.98459 −0.315866
\(640\) 0 0
\(641\) −2.43553 −0.0961978 −0.0480989 0.998843i \(-0.515316\pi\)
−0.0480989 + 0.998843i \(0.515316\pi\)
\(642\) 0 0
\(643\) −7.70390 −0.303812 −0.151906 0.988395i \(-0.548541\pi\)
−0.151906 + 0.988395i \(0.548541\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.0499 0.395103 0.197552 0.980292i \(-0.436701\pi\)
0.197552 + 0.980292i \(0.436701\pi\)
\(648\) 0 0
\(649\) −27.7092 −1.08768
\(650\) 0 0
\(651\) 42.9964 1.68516
\(652\) 0 0
\(653\) −7.09283 −0.277564 −0.138782 0.990323i \(-0.544319\pi\)
−0.138782 + 0.990323i \(0.544319\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 9.82620 0.383356
\(658\) 0 0
\(659\) 1.16346 0.0453218 0.0226609 0.999743i \(-0.492786\pi\)
0.0226609 + 0.999743i \(0.492786\pi\)
\(660\) 0 0
\(661\) 1.79432 0.0697909 0.0348955 0.999391i \(-0.488890\pi\)
0.0348955 + 0.999391i \(0.488890\pi\)
\(662\) 0 0
\(663\) 46.3099 1.79853
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.29851 −0.243879
\(668\) 0 0
\(669\) 62.7263 2.42514
\(670\) 0 0
\(671\) 74.2446 2.86618
\(672\) 0 0
\(673\) −25.2824 −0.974566 −0.487283 0.873244i \(-0.662012\pi\)
−0.487283 + 0.873244i \(0.662012\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4.89682 −0.188200 −0.0941001 0.995563i \(-0.529997\pi\)
−0.0941001 + 0.995563i \(0.529997\pi\)
\(678\) 0 0
\(679\) −16.6472 −0.638860
\(680\) 0 0
\(681\) 20.1025 0.770330
\(682\) 0 0
\(683\) −10.1980 −0.390215 −0.195107 0.980782i \(-0.562506\pi\)
−0.195107 + 0.980782i \(0.562506\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 30.7866 1.17458
\(688\) 0 0
\(689\) 0.714253 0.0272109
\(690\) 0 0
\(691\) 39.9846 1.52109 0.760543 0.649288i \(-0.224933\pi\)
0.760543 + 0.649288i \(0.224933\pi\)
\(692\) 0 0
\(693\) −45.3238 −1.72171
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 75.4975 2.85967
\(698\) 0 0
\(699\) −52.5002 −1.98574
\(700\) 0 0
\(701\) 4.91729 0.185723 0.0928617 0.995679i \(-0.470399\pi\)
0.0928617 + 0.995679i \(0.470399\pi\)
\(702\) 0 0
\(703\) 0.137699 0.00519342
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −13.5130 −0.508207
\(708\) 0 0
\(709\) −36.8865 −1.38530 −0.692650 0.721274i \(-0.743557\pi\)
−0.692650 + 0.721274i \(0.743557\pi\)
\(710\) 0 0
\(711\) −22.1857 −0.832027
\(712\) 0 0
\(713\) −34.1447 −1.27873
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8.41113 0.314119
\(718\) 0 0
\(719\) 23.8891 0.890914 0.445457 0.895303i \(-0.353041\pi\)
0.445457 + 0.895303i \(0.353041\pi\)
\(720\) 0 0
\(721\) −45.1566 −1.68172
\(722\) 0 0
\(723\) 3.35811 0.124889
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −19.6894 −0.730240 −0.365120 0.930961i \(-0.618972\pi\)
−0.365120 + 0.930961i \(0.618972\pi\)
\(728\) 0 0
\(729\) −8.84251 −0.327500
\(730\) 0 0
\(731\) −16.2754 −0.601967
\(732\) 0 0
\(733\) 1.76418 0.0651615 0.0325808 0.999469i \(-0.489627\pi\)
0.0325808 + 0.999469i \(0.489627\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.1170 0.777855
\(738\) 0 0
\(739\) −28.1755 −1.03645 −0.518227 0.855243i \(-0.673408\pi\)
−0.518227 + 0.855243i \(0.673408\pi\)
\(740\) 0 0
\(741\) −7.14540 −0.262493
\(742\) 0 0
\(743\) 5.42851 0.199153 0.0995763 0.995030i \(-0.468251\pi\)
0.0995763 + 0.995030i \(0.468251\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 25.2617 0.924278
\(748\) 0 0
\(749\) 45.7059 1.67006
\(750\) 0 0
\(751\) −25.8640 −0.943792 −0.471896 0.881654i \(-0.656430\pi\)
−0.471896 + 0.881654i \(0.656430\pi\)
\(752\) 0 0
\(753\) −19.8192 −0.722251
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −3.76947 −0.137004 −0.0685019 0.997651i \(-0.521822\pi\)
−0.0685019 + 0.997651i \(0.521822\pi\)
\(758\) 0 0
\(759\) 87.7127 3.18377
\(760\) 0 0
\(761\) 18.3605 0.665568 0.332784 0.943003i \(-0.392012\pi\)
0.332784 + 0.943003i \(0.392012\pi\)
\(762\) 0 0
\(763\) −39.0767 −1.41467
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −17.0851 −0.616908
\(768\) 0 0
\(769\) −38.1300 −1.37500 −0.687501 0.726183i \(-0.741292\pi\)
−0.687501 + 0.726183i \(0.741292\pi\)
\(770\) 0 0
\(771\) −6.18431 −0.222722
\(772\) 0 0
\(773\) −29.1575 −1.04872 −0.524361 0.851496i \(-0.675696\pi\)
−0.524361 + 0.851496i \(0.675696\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.31241 0.0470825
\(778\) 0 0
\(779\) −11.6489 −0.417366
\(780\) 0 0
\(781\) −19.6489 −0.703094
\(782\) 0 0
\(783\) 1.71228 0.0611920
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 47.0165 1.67596 0.837978 0.545704i \(-0.183738\pi\)
0.837978 + 0.545704i \(0.183738\pi\)
\(788\) 0 0
\(789\) 6.19624 0.220592
\(790\) 0 0
\(791\) −74.5750 −2.65158
\(792\) 0 0
\(793\) 45.7782 1.62563
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42.6359 −1.51024 −0.755121 0.655586i \(-0.772422\pi\)
−0.755121 + 0.655586i \(0.772422\pi\)
\(798\) 0 0
\(799\) −38.6412 −1.36703
\(800\) 0 0
\(801\) −20.8777 −0.737678
\(802\) 0 0
\(803\) 24.1808 0.853323
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 21.9736 0.773506
\(808\) 0 0
\(809\) 49.4630 1.73903 0.869514 0.493909i \(-0.164432\pi\)
0.869514 + 0.493909i \(0.164432\pi\)
\(810\) 0 0
\(811\) 16.7816 0.589280 0.294640 0.955608i \(-0.404800\pi\)
0.294640 + 0.955608i \(0.404800\pi\)
\(812\) 0 0
\(813\) 59.4476 2.08492
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.51122 0.0878564
\(818\) 0 0
\(819\) −27.9461 −0.976515
\(820\) 0 0
\(821\) 11.5337 0.402527 0.201264 0.979537i \(-0.435495\pi\)
0.201264 + 0.979537i \(0.435495\pi\)
\(822\) 0 0
\(823\) −32.6309 −1.13744 −0.568720 0.822531i \(-0.692561\pi\)
−0.568720 + 0.822531i \(0.692561\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −6.64650 −0.231122 −0.115561 0.993300i \(-0.536867\pi\)
−0.115561 + 0.993300i \(0.536867\pi\)
\(828\) 0 0
\(829\) −30.9217 −1.07395 −0.536977 0.843597i \(-0.680434\pi\)
−0.536977 + 0.843597i \(0.680434\pi\)
\(830\) 0 0
\(831\) 2.17025 0.0752852
\(832\) 0 0
\(833\) −70.3495 −2.43747
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.28243 0.320848
\(838\) 0 0
\(839\) 48.7109 1.68169 0.840844 0.541277i \(-0.182059\pi\)
0.840844 + 0.541277i \(0.182059\pi\)
\(840\) 0 0
\(841\) −28.3075 −0.976121
\(842\) 0 0
\(843\) 33.0928 1.13978
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −65.0551 −2.23532
\(848\) 0 0
\(849\) −59.0070 −2.02512
\(850\) 0 0
\(851\) −1.04222 −0.0357270
\(852\) 0 0
\(853\) 46.1447 1.57997 0.789983 0.613129i \(-0.210089\pi\)
0.789983 + 0.613129i \(0.210089\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8.40607 −0.287146 −0.143573 0.989640i \(-0.545859\pi\)
−0.143573 + 0.989640i \(0.545859\pi\)
\(858\) 0 0
\(859\) 8.49581 0.289873 0.144937 0.989441i \(-0.453702\pi\)
0.144937 + 0.989441i \(0.453702\pi\)
\(860\) 0 0
\(861\) −111.026 −3.78375
\(862\) 0 0
\(863\) −3.37352 −0.114836 −0.0574179 0.998350i \(-0.518287\pi\)
−0.0574179 + 0.998350i \(0.518287\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −56.4001 −1.91545
\(868\) 0 0
\(869\) −54.5957 −1.85203
\(870\) 0 0
\(871\) 13.0205 0.441182
\(872\) 0 0
\(873\) 8.22524 0.278382
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −13.2780 −0.448368 −0.224184 0.974547i \(-0.571972\pi\)
−0.224184 + 0.974547i \(0.571972\pi\)
\(878\) 0 0
\(879\) 50.6738 1.70918
\(880\) 0 0
\(881\) −26.6489 −0.897825 −0.448912 0.893576i \(-0.648188\pi\)
−0.448912 + 0.893576i \(0.648188\pi\)
\(882\) 0 0
\(883\) 47.7884 1.60821 0.804103 0.594490i \(-0.202646\pi\)
0.804103 + 0.594490i \(0.202646\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36.3304 1.21985 0.609927 0.792457i \(-0.291199\pi\)
0.609927 + 0.792457i \(0.291199\pi\)
\(888\) 0 0
\(889\) −54.0295 −1.81209
\(890\) 0 0
\(891\) −56.0242 −1.87688
\(892\) 0 0
\(893\) 5.96216 0.199516
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 54.0825 1.80576
\(898\) 0 0
\(899\) 3.75406 0.125205
\(900\) 0 0
\(901\) −1.46129 −0.0486826
\(902\) 0 0
\(903\) 23.9344 0.796488
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 39.3873 1.30784 0.653918 0.756566i \(-0.273124\pi\)
0.653918 + 0.756566i \(0.273124\pi\)
\(908\) 0 0
\(909\) 6.67664 0.221450
\(910\) 0 0
\(911\) 20.5561 0.681054 0.340527 0.940235i \(-0.389395\pi\)
0.340527 + 0.940235i \(0.389395\pi\)
\(912\) 0 0
\(913\) 62.1654 2.05738
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.93799 −0.295158
\(918\) 0 0
\(919\) −12.4054 −0.409216 −0.204608 0.978844i \(-0.565592\pi\)
−0.204608 + 0.978844i \(0.565592\pi\)
\(920\) 0 0
\(921\) 38.8425 1.27990
\(922\) 0 0
\(923\) −12.1153 −0.398779
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 22.3115 0.732806
\(928\) 0 0
\(929\) −31.3330 −1.02800 −0.514002 0.857789i \(-0.671838\pi\)
−0.514002 + 0.857789i \(0.671838\pi\)
\(930\) 0 0
\(931\) 10.8546 0.355745
\(932\) 0 0
\(933\) −17.7615 −0.581487
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 7.27299 0.237598 0.118799 0.992918i \(-0.462096\pi\)
0.118799 + 0.992918i \(0.462096\pi\)
\(938\) 0 0
\(939\) 56.7688 1.85258
\(940\) 0 0
\(941\) 6.72128 0.219107 0.109554 0.993981i \(-0.465058\pi\)
0.109554 + 0.993981i \(0.465058\pi\)
\(942\) 0 0
\(943\) 88.1689 2.87117
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −10.0757 −0.327416 −0.163708 0.986509i \(-0.552345\pi\)
−0.163708 + 0.986509i \(0.552345\pi\)
\(948\) 0 0
\(949\) 14.9096 0.483986
\(950\) 0 0
\(951\) 53.9193 1.74845
\(952\) 0 0
\(953\) −8.14473 −0.263834 −0.131917 0.991261i \(-0.542113\pi\)
−0.131917 + 0.991261i \(0.542113\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −9.64363 −0.311734
\(958\) 0 0
\(959\) 22.6619 0.731791
\(960\) 0 0
\(961\) −10.6489 −0.343513
\(962\) 0 0
\(963\) −22.5829 −0.727724
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −47.1773 −1.51712 −0.758560 0.651604i \(-0.774097\pi\)
−0.758560 + 0.651604i \(0.774097\pi\)
\(968\) 0 0
\(969\) 14.6188 0.469623
\(970\) 0 0
\(971\) −0.230528 −0.00739801 −0.00369901 0.999993i \(-0.501177\pi\)
−0.00369901 + 0.999993i \(0.501177\pi\)
\(972\) 0 0
\(973\) −42.9313 −1.37632
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5.80905 −0.185848 −0.0929240 0.995673i \(-0.529621\pi\)
−0.0929240 + 0.995673i \(0.529621\pi\)
\(978\) 0 0
\(979\) −51.3770 −1.64202
\(980\) 0 0
\(981\) 19.3075 0.616441
\(982\) 0 0
\(983\) 22.3511 0.712889 0.356444 0.934317i \(-0.383989\pi\)
0.356444 + 0.934317i \(0.383989\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 56.8254 1.80877
\(988\) 0 0
\(989\) −19.0070 −0.604388
\(990\) 0 0
\(991\) 34.9415 1.10995 0.554976 0.831866i \(-0.312727\pi\)
0.554976 + 0.831866i \(0.312727\pi\)
\(992\) 0 0
\(993\) 69.3746 2.20154
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −9.35282 −0.296207 −0.148103 0.988972i \(-0.547317\pi\)
−0.148103 + 0.988972i \(0.547317\pi\)
\(998\) 0 0
\(999\) 0.283334 0.00896430
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 7600.2.a.bm.1.2 3
4.3 odd 2 950.2.a.m.1.2 yes 3
5.4 even 2 7600.2.a.cb.1.2 3
12.11 even 2 8550.2.a.cj.1.3 3
20.3 even 4 950.2.b.g.799.2 6
20.7 even 4 950.2.b.g.799.5 6
20.19 odd 2 950.2.a.k.1.2 3
60.59 even 2 8550.2.a.co.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.k.1.2 3 20.19 odd 2
950.2.a.m.1.2 yes 3 4.3 odd 2
950.2.b.g.799.2 6 20.3 even 4
950.2.b.g.799.5 6 20.7 even 4
7600.2.a.bm.1.2 3 1.1 even 1 trivial
7600.2.a.cb.1.2 3 5.4 even 2
8550.2.a.cj.1.3 3 12.11 even 2
8550.2.a.co.1.1 3 60.59 even 2