Properties

Label 7623.2.a.ca.1.1
Level $7623$
Weight $2$
Character 7623.1
Self dual yes
Analytic conductor $60.870$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7623,2,Mod(1,7623)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("7623.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7623.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: \(60.8699614608\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2541)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.34292\) of defining polynomial
Character \(\chi\) \(=\) 7623.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.34292 q^{2} +3.48929 q^{4} +0.146365 q^{5} +1.00000 q^{7} -3.48929 q^{8} +O(q^{10})\) \(q-2.34292 q^{2} +3.48929 q^{4} +0.146365 q^{5} +1.00000 q^{7} -3.48929 q^{8} -0.342923 q^{10} +4.34292 q^{13} -2.34292 q^{14} +1.19656 q^{16} +0.146365 q^{17} -1.83221 q^{19} +0.510711 q^{20} -8.81079 q^{23} -4.97858 q^{25} -10.1751 q^{26} +3.48929 q^{28} -4.34292 q^{29} +0.292731 q^{31} +4.17513 q^{32} -0.342923 q^{34} +0.146365 q^{35} -3.48929 q^{37} +4.29273 q^{38} -0.510711 q^{40} -2.80344 q^{41} -7.86098 q^{43} +20.6430 q^{46} +0.949808 q^{47} +1.00000 q^{49} +11.6644 q^{50} +15.1537 q^{52} +4.51071 q^{53} -3.48929 q^{56} +10.1751 q^{58} -8.02877 q^{59} +5.43910 q^{61} -0.685846 q^{62} -12.1751 q^{64} +0.635654 q^{65} -7.76060 q^{67} +0.510711 q^{68} -0.342923 q^{70} +3.53948 q^{71} +16.1825 q^{73} +8.17513 q^{74} -6.39312 q^{76} +13.0790 q^{79} +0.175135 q^{80} +6.56825 q^{82} +12.9070 q^{83} +0.0214229 q^{85} +18.4177 q^{86} +9.81079 q^{89} +4.34292 q^{91} -30.7434 q^{92} -2.22533 q^{94} -0.268173 q^{95} -17.4219 q^{97} -2.34292 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} + 3 q^{4} - q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} + 3 q^{4} - q^{5} + 3 q^{7} - 3 q^{8} + 5 q^{10} + 7 q^{13} - q^{14} - q^{16} - q^{17} + 8 q^{19} + 9 q^{20} + 2 q^{23} - 11 q^{26} + 3 q^{28} - 7 q^{29} - 2 q^{31} - 7 q^{32} + 5 q^{34} - q^{35} - 3 q^{37} + 10 q^{38} - 9 q^{40} - 13 q^{41} + 8 q^{43} + 20 q^{46} + 6 q^{47} + 3 q^{49} + 8 q^{50} + 11 q^{52} + 21 q^{53} - 3 q^{56} + 11 q^{58} - 6 q^{59} + 12 q^{61} + 10 q^{62} - 17 q^{64} - 7 q^{65} + 2 q^{67} + 9 q^{68} + 5 q^{70} - 4 q^{73} + 5 q^{74} - 10 q^{76} + 18 q^{79} - 19 q^{80} - 9 q^{82} + 12 q^{83} + 15 q^{85} + 36 q^{86} + q^{89} + 7 q^{91} - 44 q^{92} + 16 q^{94} - 8 q^{95} - 25 q^{97} - q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34292 −1.65670 −0.828348 0.560213i \(-0.810719\pi\)
−0.828348 + 0.560213i \(0.810719\pi\)
\(3\) 0 0
\(4\) 3.48929 1.74464
\(5\) 0.146365 0.0654566 0.0327283 0.999464i \(-0.489580\pi\)
0.0327283 + 0.999464i \(0.489580\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −3.48929 −1.23365
\(9\) 0 0
\(10\) −0.342923 −0.108442
\(11\) 0 0
\(12\) 0 0
\(13\) 4.34292 1.20451 0.602255 0.798304i \(-0.294269\pi\)
0.602255 + 0.798304i \(0.294269\pi\)
\(14\) −2.34292 −0.626173
\(15\) 0 0
\(16\) 1.19656 0.299139
\(17\) 0.146365 0.0354988 0.0177494 0.999842i \(-0.494350\pi\)
0.0177494 + 0.999842i \(0.494350\pi\)
\(18\) 0 0
\(19\) −1.83221 −0.420338 −0.210169 0.977665i \(-0.567401\pi\)
−0.210169 + 0.977665i \(0.567401\pi\)
\(20\) 0.510711 0.114199
\(21\) 0 0
\(22\) 0 0
\(23\) −8.81079 −1.83718 −0.918588 0.395216i \(-0.870670\pi\)
−0.918588 + 0.395216i \(0.870670\pi\)
\(24\) 0 0
\(25\) −4.97858 −0.995715
\(26\) −10.1751 −1.99551
\(27\) 0 0
\(28\) 3.48929 0.659414
\(29\) −4.34292 −0.806461 −0.403230 0.915099i \(-0.632113\pi\)
−0.403230 + 0.915099i \(0.632113\pi\)
\(30\) 0 0
\(31\) 0.292731 0.0525760 0.0262880 0.999654i \(-0.491631\pi\)
0.0262880 + 0.999654i \(0.491631\pi\)
\(32\) 4.17513 0.738067
\(33\) 0 0
\(34\) −0.342923 −0.0588108
\(35\) 0.146365 0.0247403
\(36\) 0 0
\(37\) −3.48929 −0.573636 −0.286818 0.957985i \(-0.592597\pi\)
−0.286818 + 0.957985i \(0.592597\pi\)
\(38\) 4.29273 0.696373
\(39\) 0 0
\(40\) −0.510711 −0.0807506
\(41\) −2.80344 −0.437824 −0.218912 0.975745i \(-0.570251\pi\)
−0.218912 + 0.975745i \(0.570251\pi\)
\(42\) 0 0
\(43\) −7.86098 −1.19879 −0.599394 0.800454i \(-0.704592\pi\)
−0.599394 + 0.800454i \(0.704592\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 20.6430 3.04364
\(47\) 0.949808 0.138544 0.0692719 0.997598i \(-0.477932\pi\)
0.0692719 + 0.997598i \(0.477932\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 11.6644 1.64960
\(51\) 0 0
\(52\) 15.1537 2.10144
\(53\) 4.51071 0.619594 0.309797 0.950803i \(-0.399739\pi\)
0.309797 + 0.950803i \(0.399739\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −3.48929 −0.466276
\(57\) 0 0
\(58\) 10.1751 1.33606
\(59\) −8.02877 −1.04526 −0.522628 0.852561i \(-0.675048\pi\)
−0.522628 + 0.852561i \(0.675048\pi\)
\(60\) 0 0
\(61\) 5.43910 0.696405 0.348202 0.937419i \(-0.386792\pi\)
0.348202 + 0.937419i \(0.386792\pi\)
\(62\) −0.685846 −0.0871026
\(63\) 0 0
\(64\) −12.1751 −1.52189
\(65\) 0.635654 0.0788432
\(66\) 0 0
\(67\) −7.76060 −0.948108 −0.474054 0.880496i \(-0.657210\pi\)
−0.474054 + 0.880496i \(0.657210\pi\)
\(68\) 0.510711 0.0619329
\(69\) 0 0
\(70\) −0.342923 −0.0409871
\(71\) 3.53948 0.420059 0.210030 0.977695i \(-0.432644\pi\)
0.210030 + 0.977695i \(0.432644\pi\)
\(72\) 0 0
\(73\) 16.1825 1.89402 0.947008 0.321210i \(-0.104089\pi\)
0.947008 + 0.321210i \(0.104089\pi\)
\(74\) 8.17513 0.950340
\(75\) 0 0
\(76\) −6.39312 −0.733341
\(77\) 0 0
\(78\) 0 0
\(79\) 13.0790 1.47150 0.735749 0.677254i \(-0.236830\pi\)
0.735749 + 0.677254i \(0.236830\pi\)
\(80\) 0.175135 0.0195807
\(81\) 0 0
\(82\) 6.56825 0.725342
\(83\) 12.9070 1.41672 0.708362 0.705850i \(-0.249435\pi\)
0.708362 + 0.705850i \(0.249435\pi\)
\(84\) 0 0
\(85\) 0.0214229 0.00232364
\(86\) 18.4177 1.98603
\(87\) 0 0
\(88\) 0 0
\(89\) 9.81079 1.03994 0.519971 0.854184i \(-0.325943\pi\)
0.519971 + 0.854184i \(0.325943\pi\)
\(90\) 0 0
\(91\) 4.34292 0.455262
\(92\) −30.7434 −3.20522
\(93\) 0 0
\(94\) −2.22533 −0.229525
\(95\) −0.268173 −0.0275139
\(96\) 0 0
\(97\) −17.4219 −1.76892 −0.884462 0.466612i \(-0.845474\pi\)
−0.884462 + 0.466612i \(0.845474\pi\)
\(98\) −2.34292 −0.236671
\(99\) 0 0
\(100\) −17.3717 −1.73717
\(101\) 15.6357 1.55581 0.777903 0.628385i \(-0.216284\pi\)
0.777903 + 0.628385i \(0.216284\pi\)
\(102\) 0 0
\(103\) 4.16779 0.410664 0.205332 0.978692i \(-0.434173\pi\)
0.205332 + 0.978692i \(0.434173\pi\)
\(104\) −15.1537 −1.48594
\(105\) 0 0
\(106\) −10.5682 −1.02648
\(107\) 5.49663 0.531380 0.265690 0.964059i \(-0.414400\pi\)
0.265690 + 0.964059i \(0.414400\pi\)
\(108\) 0 0
\(109\) 5.87819 0.563029 0.281514 0.959557i \(-0.409163\pi\)
0.281514 + 0.959557i \(0.409163\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.19656 0.113064
\(113\) 3.88240 0.365226 0.182613 0.983185i \(-0.441544\pi\)
0.182613 + 0.983185i \(0.441544\pi\)
\(114\) 0 0
\(115\) −1.28960 −0.120255
\(116\) −15.1537 −1.40699
\(117\) 0 0
\(118\) 18.8108 1.73167
\(119\) 0.146365 0.0134173
\(120\) 0 0
\(121\) 0 0
\(122\) −12.7434 −1.15373
\(123\) 0 0
\(124\) 1.02142 0.0917265
\(125\) −1.46052 −0.130633
\(126\) 0 0
\(127\) −17.6686 −1.56784 −0.783919 0.620863i \(-0.786782\pi\)
−0.783919 + 0.620863i \(0.786782\pi\)
\(128\) 20.1751 1.78325
\(129\) 0 0
\(130\) −1.48929 −0.130619
\(131\) −18.0288 −1.57518 −0.787590 0.616199i \(-0.788672\pi\)
−0.787590 + 0.616199i \(0.788672\pi\)
\(132\) 0 0
\(133\) −1.83221 −0.158873
\(134\) 18.1825 1.57073
\(135\) 0 0
\(136\) −0.510711 −0.0437931
\(137\) 21.5542 1.84150 0.920749 0.390156i \(-0.127579\pi\)
0.920749 + 0.390156i \(0.127579\pi\)
\(138\) 0 0
\(139\) 13.5395 1.14840 0.574202 0.818714i \(-0.305312\pi\)
0.574202 + 0.818714i \(0.305312\pi\)
\(140\) 0.510711 0.0431630
\(141\) 0 0
\(142\) −8.29273 −0.695911
\(143\) 0 0
\(144\) 0 0
\(145\) −0.635654 −0.0527882
\(146\) −37.9143 −3.13781
\(147\) 0 0
\(148\) −12.1751 −1.00079
\(149\) −10.3001 −0.843815 −0.421908 0.906639i \(-0.638639\pi\)
−0.421908 + 0.906639i \(0.638639\pi\)
\(150\) 0 0
\(151\) 1.31836 0.107287 0.0536435 0.998560i \(-0.482917\pi\)
0.0536435 + 0.998560i \(0.482917\pi\)
\(152\) 6.39312 0.518550
\(153\) 0 0
\(154\) 0 0
\(155\) 0.0428457 0.00344145
\(156\) 0 0
\(157\) 9.85677 0.786656 0.393328 0.919398i \(-0.371324\pi\)
0.393328 + 0.919398i \(0.371324\pi\)
\(158\) −30.6430 −2.43783
\(159\) 0 0
\(160\) 0.611096 0.0483114
\(161\) −8.81079 −0.694387
\(162\) 0 0
\(163\) −0.292731 −0.0229285 −0.0114642 0.999934i \(-0.503649\pi\)
−0.0114642 + 0.999934i \(0.503649\pi\)
\(164\) −9.78202 −0.763847
\(165\) 0 0
\(166\) −30.2400 −2.34708
\(167\) 15.7360 1.21769 0.608846 0.793289i \(-0.291633\pi\)
0.608846 + 0.793289i \(0.291633\pi\)
\(168\) 0 0
\(169\) 5.86098 0.450845
\(170\) −0.0501921 −0.00384956
\(171\) 0 0
\(172\) −27.4292 −2.09146
\(173\) 17.7360 1.34845 0.674223 0.738528i \(-0.264479\pi\)
0.674223 + 0.738528i \(0.264479\pi\)
\(174\) 0 0
\(175\) −4.97858 −0.376345
\(176\) 0 0
\(177\) 0 0
\(178\) −22.9859 −1.72287
\(179\) 23.2285 1.73618 0.868088 0.496410i \(-0.165349\pi\)
0.868088 + 0.496410i \(0.165349\pi\)
\(180\) 0 0
\(181\) 25.1109 1.86648 0.933238 0.359259i \(-0.116970\pi\)
0.933238 + 0.359259i \(0.116970\pi\)
\(182\) −10.1751 −0.754231
\(183\) 0 0
\(184\) 30.7434 2.26643
\(185\) −0.510711 −0.0375483
\(186\) 0 0
\(187\) 0 0
\(188\) 3.31415 0.241710
\(189\) 0 0
\(190\) 0.628308 0.0455822
\(191\) 17.8898 1.29446 0.647228 0.762296i \(-0.275928\pi\)
0.647228 + 0.762296i \(0.275928\pi\)
\(192\) 0 0
\(193\) −10.3288 −0.743487 −0.371743 0.928336i \(-0.621240\pi\)
−0.371743 + 0.928336i \(0.621240\pi\)
\(194\) 40.8181 2.93057
\(195\) 0 0
\(196\) 3.48929 0.249235
\(197\) −14.8610 −1.05880 −0.529401 0.848372i \(-0.677583\pi\)
−0.529401 + 0.848372i \(0.677583\pi\)
\(198\) 0 0
\(199\) 0.0674041 0.00477815 0.00238908 0.999997i \(-0.499240\pi\)
0.00238908 + 0.999997i \(0.499240\pi\)
\(200\) 17.3717 1.22836
\(201\) 0 0
\(202\) −36.6331 −2.57750
\(203\) −4.34292 −0.304813
\(204\) 0 0
\(205\) −0.410327 −0.0286585
\(206\) −9.76481 −0.680346
\(207\) 0 0
\(208\) 5.19656 0.360316
\(209\) 0 0
\(210\) 0 0
\(211\) −13.1323 −0.904064 −0.452032 0.892002i \(-0.649301\pi\)
−0.452032 + 0.892002i \(0.649301\pi\)
\(212\) 15.7392 1.08097
\(213\) 0 0
\(214\) −12.8782 −0.880335
\(215\) −1.15058 −0.0784687
\(216\) 0 0
\(217\) 0.292731 0.0198719
\(218\) −13.7722 −0.932768
\(219\) 0 0
\(220\) 0 0
\(221\) 0.635654 0.0427587
\(222\) 0 0
\(223\) 5.37169 0.359715 0.179858 0.983693i \(-0.442436\pi\)
0.179858 + 0.983693i \(0.442436\pi\)
\(224\) 4.17513 0.278963
\(225\) 0 0
\(226\) −9.09617 −0.605068
\(227\) 6.85785 0.455171 0.227586 0.973758i \(-0.426917\pi\)
0.227586 + 0.973758i \(0.426917\pi\)
\(228\) 0 0
\(229\) −8.76060 −0.578917 −0.289458 0.957191i \(-0.593475\pi\)
−0.289458 + 0.957191i \(0.593475\pi\)
\(230\) 3.02142 0.199227
\(231\) 0 0
\(232\) 15.1537 0.994890
\(233\) −1.36435 −0.0893813 −0.0446906 0.999001i \(-0.514230\pi\)
−0.0446906 + 0.999001i \(0.514230\pi\)
\(234\) 0 0
\(235\) 0.139019 0.00906861
\(236\) −28.0147 −1.82360
\(237\) 0 0
\(238\) −0.342923 −0.0222284
\(239\) −4.97858 −0.322037 −0.161019 0.986951i \(-0.551478\pi\)
−0.161019 + 0.986951i \(0.551478\pi\)
\(240\) 0 0
\(241\) 14.1678 0.912627 0.456314 0.889819i \(-0.349169\pi\)
0.456314 + 0.889819i \(0.349169\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 18.9786 1.21498
\(245\) 0.146365 0.00935095
\(246\) 0 0
\(247\) −7.95715 −0.506302
\(248\) −1.02142 −0.0648604
\(249\) 0 0
\(250\) 3.42188 0.216419
\(251\) 2.82908 0.178570 0.0892848 0.996006i \(-0.471542\pi\)
0.0892848 + 0.996006i \(0.471542\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 41.3963 2.59743
\(255\) 0 0
\(256\) −22.9185 −1.43241
\(257\) 22.9901 1.43409 0.717043 0.697029i \(-0.245495\pi\)
0.717043 + 0.697029i \(0.245495\pi\)
\(258\) 0 0
\(259\) −3.48929 −0.216814
\(260\) 2.21798 0.137553
\(261\) 0 0
\(262\) 42.2400 2.60960
\(263\) −3.63986 −0.224444 −0.112222 0.993683i \(-0.535797\pi\)
−0.112222 + 0.993683i \(0.535797\pi\)
\(264\) 0 0
\(265\) 0.660212 0.0405565
\(266\) 4.29273 0.263204
\(267\) 0 0
\(268\) −27.0790 −1.65411
\(269\) 7.54683 0.460138 0.230069 0.973174i \(-0.426105\pi\)
0.230069 + 0.973174i \(0.426105\pi\)
\(270\) 0 0
\(271\) 23.6644 1.43751 0.718756 0.695263i \(-0.244712\pi\)
0.718756 + 0.695263i \(0.244712\pi\)
\(272\) 0.175135 0.0106191
\(273\) 0 0
\(274\) −50.4998 −3.05080
\(275\) 0 0
\(276\) 0 0
\(277\) 31.8929 1.91626 0.958129 0.286337i \(-0.0924378\pi\)
0.958129 + 0.286337i \(0.0924378\pi\)
\(278\) −31.7220 −1.90256
\(279\) 0 0
\(280\) −0.510711 −0.0305208
\(281\) 30.5082 1.81997 0.909983 0.414645i \(-0.136094\pi\)
0.909983 + 0.414645i \(0.136094\pi\)
\(282\) 0 0
\(283\) 22.6430 1.34599 0.672993 0.739649i \(-0.265008\pi\)
0.672993 + 0.739649i \(0.265008\pi\)
\(284\) 12.3503 0.732854
\(285\) 0 0
\(286\) 0 0
\(287\) −2.80344 −0.165482
\(288\) 0 0
\(289\) −16.9786 −0.998740
\(290\) 1.48929 0.0874540
\(291\) 0 0
\(292\) 56.4653 3.30438
\(293\) 1.81079 0.105787 0.0528937 0.998600i \(-0.483156\pi\)
0.0528937 + 0.998600i \(0.483156\pi\)
\(294\) 0 0
\(295\) −1.17513 −0.0684190
\(296\) 12.1751 0.707665
\(297\) 0 0
\(298\) 24.1323 1.39795
\(299\) −38.2646 −2.21290
\(300\) 0 0
\(301\) −7.86098 −0.453099
\(302\) −3.08883 −0.177742
\(303\) 0 0
\(304\) −2.19235 −0.125740
\(305\) 0.796096 0.0455843
\(306\) 0 0
\(307\) 29.8469 1.70345 0.851726 0.523987i \(-0.175556\pi\)
0.851726 + 0.523987i \(0.175556\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.100384 −0.00570144
\(311\) 5.09304 0.288800 0.144400 0.989519i \(-0.453875\pi\)
0.144400 + 0.989519i \(0.453875\pi\)
\(312\) 0 0
\(313\) −22.0319 −1.24532 −0.622658 0.782494i \(-0.713947\pi\)
−0.622658 + 0.782494i \(0.713947\pi\)
\(314\) −23.0937 −1.30325
\(315\) 0 0
\(316\) 45.6363 2.56724
\(317\) 7.08883 0.398148 0.199074 0.979984i \(-0.436207\pi\)
0.199074 + 0.979984i \(0.436207\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.78202 −0.0996179
\(321\) 0 0
\(322\) 20.6430 1.15039
\(323\) −0.268173 −0.0149215
\(324\) 0 0
\(325\) −21.6216 −1.19935
\(326\) 0.685846 0.0379855
\(327\) 0 0
\(328\) 9.78202 0.540122
\(329\) 0.949808 0.0523646
\(330\) 0 0
\(331\) −34.6044 −1.90203 −0.951014 0.309148i \(-0.899956\pi\)
−0.951014 + 0.309148i \(0.899956\pi\)
\(332\) 45.0361 2.47168
\(333\) 0 0
\(334\) −36.8683 −2.01735
\(335\) −1.13588 −0.0620599
\(336\) 0 0
\(337\) −12.5254 −0.682302 −0.341151 0.940008i \(-0.610817\pi\)
−0.341151 + 0.940008i \(0.610817\pi\)
\(338\) −13.7318 −0.746913
\(339\) 0 0
\(340\) 0.0747505 0.00405392
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 27.4292 1.47889
\(345\) 0 0
\(346\) −41.5542 −2.23397
\(347\) −27.6461 −1.48412 −0.742061 0.670332i \(-0.766152\pi\)
−0.742061 + 0.670332i \(0.766152\pi\)
\(348\) 0 0
\(349\) −11.2969 −0.604711 −0.302356 0.953195i \(-0.597773\pi\)
−0.302356 + 0.953195i \(0.597773\pi\)
\(350\) 11.6644 0.623490
\(351\) 0 0
\(352\) 0 0
\(353\) −16.8034 −0.894357 −0.447178 0.894445i \(-0.647571\pi\)
−0.447178 + 0.894445i \(0.647571\pi\)
\(354\) 0 0
\(355\) 0.518058 0.0274957
\(356\) 34.2327 1.81433
\(357\) 0 0
\(358\) −54.4225 −2.87632
\(359\) −29.0607 −1.53376 −0.766882 0.641788i \(-0.778193\pi\)
−0.766882 + 0.641788i \(0.778193\pi\)
\(360\) 0 0
\(361\) −15.6430 −0.823316
\(362\) −58.8328 −3.09218
\(363\) 0 0
\(364\) 15.1537 0.794270
\(365\) 2.36856 0.123976
\(366\) 0 0
\(367\) 17.6974 0.923797 0.461898 0.886933i \(-0.347168\pi\)
0.461898 + 0.886933i \(0.347168\pi\)
\(368\) −10.5426 −0.549572
\(369\) 0 0
\(370\) 1.19656 0.0622061
\(371\) 4.51071 0.234184
\(372\) 0 0
\(373\) −12.7820 −0.661828 −0.330914 0.943661i \(-0.607357\pi\)
−0.330914 + 0.943661i \(0.607357\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.31415 −0.170914
\(377\) −18.8610 −0.971390
\(378\) 0 0
\(379\) −19.6258 −1.00811 −0.504055 0.863672i \(-0.668159\pi\)
−0.504055 + 0.863672i \(0.668159\pi\)
\(380\) −0.935731 −0.0480020
\(381\) 0 0
\(382\) −41.9143 −2.14452
\(383\) −29.5500 −1.50993 −0.754966 0.655764i \(-0.772347\pi\)
−0.754966 + 0.655764i \(0.772347\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 24.1997 1.23173
\(387\) 0 0
\(388\) −60.7900 −3.08614
\(389\) 13.0962 0.664002 0.332001 0.943279i \(-0.392276\pi\)
0.332001 + 0.943279i \(0.392276\pi\)
\(390\) 0 0
\(391\) −1.28960 −0.0652176
\(392\) −3.48929 −0.176236
\(393\) 0 0
\(394\) 34.8181 1.75411
\(395\) 1.91431 0.0963193
\(396\) 0 0
\(397\) 24.4679 1.22801 0.614003 0.789303i \(-0.289558\pi\)
0.614003 + 0.789303i \(0.289558\pi\)
\(398\) −0.157923 −0.00791595
\(399\) 0 0
\(400\) −5.95715 −0.297858
\(401\) −24.1751 −1.20725 −0.603624 0.797269i \(-0.706277\pi\)
−0.603624 + 0.797269i \(0.706277\pi\)
\(402\) 0 0
\(403\) 1.27131 0.0633284
\(404\) 54.5573 2.71433
\(405\) 0 0
\(406\) 10.1751 0.504983
\(407\) 0 0
\(408\) 0 0
\(409\) 5.22112 0.258168 0.129084 0.991634i \(-0.458796\pi\)
0.129084 + 0.991634i \(0.458796\pi\)
\(410\) 0.961365 0.0474784
\(411\) 0 0
\(412\) 14.5426 0.716463
\(413\) −8.02877 −0.395070
\(414\) 0 0
\(415\) 1.88913 0.0927339
\(416\) 18.1323 0.889009
\(417\) 0 0
\(418\) 0 0
\(419\) 22.6718 1.10759 0.553794 0.832654i \(-0.313179\pi\)
0.553794 + 0.832654i \(0.313179\pi\)
\(420\) 0 0
\(421\) −2.41454 −0.117677 −0.0588387 0.998268i \(-0.518740\pi\)
−0.0588387 + 0.998268i \(0.518740\pi\)
\(422\) 30.7679 1.49776
\(423\) 0 0
\(424\) −15.7392 −0.764362
\(425\) −0.728692 −0.0353467
\(426\) 0 0
\(427\) 5.43910 0.263216
\(428\) 19.1793 0.927069
\(429\) 0 0
\(430\) 2.69571 0.129999
\(431\) 1.35700 0.0653644 0.0326822 0.999466i \(-0.489595\pi\)
0.0326822 + 0.999466i \(0.489595\pi\)
\(432\) 0 0
\(433\) 20.6503 0.992392 0.496196 0.868210i \(-0.334730\pi\)
0.496196 + 0.868210i \(0.334730\pi\)
\(434\) −0.685846 −0.0329217
\(435\) 0 0
\(436\) 20.5107 0.982285
\(437\) 16.1432 0.772235
\(438\) 0 0
\(439\) −20.3074 −0.969220 −0.484610 0.874730i \(-0.661039\pi\)
−0.484610 + 0.874730i \(0.661039\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.48929 −0.0708382
\(443\) 9.81752 0.466444 0.233222 0.972423i \(-0.425073\pi\)
0.233222 + 0.972423i \(0.425073\pi\)
\(444\) 0 0
\(445\) 1.43596 0.0680711
\(446\) −12.5855 −0.595939
\(447\) 0 0
\(448\) −12.1751 −0.575221
\(449\) −10.0748 −0.475457 −0.237728 0.971332i \(-0.576403\pi\)
−0.237728 + 0.971332i \(0.576403\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 13.5468 0.637189
\(453\) 0 0
\(454\) −16.0674 −0.754081
\(455\) 0.635654 0.0297999
\(456\) 0 0
\(457\) 14.6791 0.686660 0.343330 0.939215i \(-0.388445\pi\)
0.343330 + 0.939215i \(0.388445\pi\)
\(458\) 20.5254 0.959089
\(459\) 0 0
\(460\) −4.49977 −0.209803
\(461\) −27.1396 −1.26402 −0.632009 0.774961i \(-0.717770\pi\)
−0.632009 + 0.774961i \(0.717770\pi\)
\(462\) 0 0
\(463\) 23.2369 1.07991 0.539955 0.841694i \(-0.318441\pi\)
0.539955 + 0.841694i \(0.318441\pi\)
\(464\) −5.19656 −0.241244
\(465\) 0 0
\(466\) 3.19656 0.148078
\(467\) −23.8568 −1.10396 −0.551980 0.833857i \(-0.686127\pi\)
−0.551980 + 0.833857i \(0.686127\pi\)
\(468\) 0 0
\(469\) −7.76060 −0.358351
\(470\) −0.325711 −0.0150239
\(471\) 0 0
\(472\) 28.0147 1.28948
\(473\) 0 0
\(474\) 0 0
\(475\) 9.12181 0.418537
\(476\) 0.510711 0.0234084
\(477\) 0 0
\(478\) 11.6644 0.533518
\(479\) 17.2081 0.786259 0.393129 0.919483i \(-0.371392\pi\)
0.393129 + 0.919483i \(0.371392\pi\)
\(480\) 0 0
\(481\) −15.1537 −0.690950
\(482\) −33.1940 −1.51195
\(483\) 0 0
\(484\) 0 0
\(485\) −2.54996 −0.115788
\(486\) 0 0
\(487\) −3.16044 −0.143213 −0.0716066 0.997433i \(-0.522813\pi\)
−0.0716066 + 0.997433i \(0.522813\pi\)
\(488\) −18.9786 −0.859120
\(489\) 0 0
\(490\) −0.342923 −0.0154917
\(491\) −4.22533 −0.190686 −0.0953432 0.995444i \(-0.530395\pi\)
−0.0953432 + 0.995444i \(0.530395\pi\)
\(492\) 0 0
\(493\) −0.635654 −0.0286284
\(494\) 18.6430 0.838788
\(495\) 0 0
\(496\) 0.350269 0.0157276
\(497\) 3.53948 0.158767
\(498\) 0 0
\(499\) 30.5615 1.36812 0.684061 0.729425i \(-0.260212\pi\)
0.684061 + 0.729425i \(0.260212\pi\)
\(500\) −5.09617 −0.227908
\(501\) 0 0
\(502\) −6.62831 −0.295836
\(503\) 0.513847 0.0229113 0.0114557 0.999934i \(-0.496353\pi\)
0.0114557 + 0.999934i \(0.496353\pi\)
\(504\) 0 0
\(505\) 2.28852 0.101838
\(506\) 0 0
\(507\) 0 0
\(508\) −61.6510 −2.73532
\(509\) −24.9217 −1.10463 −0.552316 0.833635i \(-0.686256\pi\)
−0.552316 + 0.833635i \(0.686256\pi\)
\(510\) 0 0
\(511\) 16.1825 0.715871
\(512\) 13.3461 0.589818
\(513\) 0 0
\(514\) −53.8641 −2.37584
\(515\) 0.610020 0.0268807
\(516\) 0 0
\(517\) 0 0
\(518\) 8.17513 0.359195
\(519\) 0 0
\(520\) −2.21798 −0.0972649
\(521\) 31.8855 1.39693 0.698465 0.715644i \(-0.253867\pi\)
0.698465 + 0.715644i \(0.253867\pi\)
\(522\) 0 0
\(523\) 5.34713 0.233814 0.116907 0.993143i \(-0.462702\pi\)
0.116907 + 0.993143i \(0.462702\pi\)
\(524\) −62.9076 −2.74813
\(525\) 0 0
\(526\) 8.52792 0.371835
\(527\) 0.0428457 0.00186639
\(528\) 0 0
\(529\) 54.6300 2.37522
\(530\) −1.54683 −0.0671899
\(531\) 0 0
\(532\) −6.39312 −0.277177
\(533\) −12.1751 −0.527364
\(534\) 0 0
\(535\) 0.804518 0.0347823
\(536\) 27.0790 1.16963
\(537\) 0 0
\(538\) −17.6816 −0.762309
\(539\) 0 0
\(540\) 0 0
\(541\) 27.8610 1.19784 0.598919 0.800810i \(-0.295597\pi\)
0.598919 + 0.800810i \(0.295597\pi\)
\(542\) −55.4439 −2.38152
\(543\) 0 0
\(544\) 0.611096 0.0262005
\(545\) 0.860365 0.0368540
\(546\) 0 0
\(547\) −30.7005 −1.31266 −0.656330 0.754474i \(-0.727892\pi\)
−0.656330 + 0.754474i \(0.727892\pi\)
\(548\) 75.2087 3.21276
\(549\) 0 0
\(550\) 0 0
\(551\) 7.95715 0.338986
\(552\) 0 0
\(553\) 13.0790 0.556174
\(554\) −74.7226 −3.17466
\(555\) 0 0
\(556\) 47.2432 2.00356
\(557\) −16.7434 −0.709440 −0.354720 0.934973i \(-0.615424\pi\)
−0.354720 + 0.934973i \(0.615424\pi\)
\(558\) 0 0
\(559\) −34.1396 −1.44395
\(560\) 0.175135 0.00740079
\(561\) 0 0
\(562\) −71.4783 −3.01513
\(563\) 27.6932 1.16713 0.583564 0.812067i \(-0.301658\pi\)
0.583564 + 0.812067i \(0.301658\pi\)
\(564\) 0 0
\(565\) 0.568250 0.0239065
\(566\) −53.0508 −2.22989
\(567\) 0 0
\(568\) −12.3503 −0.518206
\(569\) 11.6827 0.489765 0.244882 0.969553i \(-0.421251\pi\)
0.244882 + 0.969553i \(0.421251\pi\)
\(570\) 0 0
\(571\) −24.1151 −1.00918 −0.504592 0.863358i \(-0.668357\pi\)
−0.504592 + 0.863358i \(0.668357\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 6.56825 0.274153
\(575\) 43.8652 1.82930
\(576\) 0 0
\(577\) 44.2572 1.84245 0.921226 0.389027i \(-0.127189\pi\)
0.921226 + 0.389027i \(0.127189\pi\)
\(578\) 39.7795 1.65461
\(579\) 0 0
\(580\) −2.21798 −0.0920966
\(581\) 12.9070 0.535471
\(582\) 0 0
\(583\) 0 0
\(584\) −56.4653 −2.33655
\(585\) 0 0
\(586\) −4.24254 −0.175258
\(587\) −8.42188 −0.347608 −0.173804 0.984780i \(-0.555606\pi\)
−0.173804 + 0.984780i \(0.555606\pi\)
\(588\) 0 0
\(589\) −0.536345 −0.0220997
\(590\) 2.75325 0.113350
\(591\) 0 0
\(592\) −4.17513 −0.171597
\(593\) −1.94560 −0.0798961 −0.0399480 0.999202i \(-0.512719\pi\)
−0.0399480 + 0.999202i \(0.512719\pi\)
\(594\) 0 0
\(595\) 0.0214229 0.000878251 0
\(596\) −35.9399 −1.47216
\(597\) 0 0
\(598\) 89.6510 3.66610
\(599\) −31.0361 −1.26810 −0.634051 0.773292i \(-0.718609\pi\)
−0.634051 + 0.773292i \(0.718609\pi\)
\(600\) 0 0
\(601\) −5.80031 −0.236599 −0.118300 0.992978i \(-0.537744\pi\)
−0.118300 + 0.992978i \(0.537744\pi\)
\(602\) 18.4177 0.750648
\(603\) 0 0
\(604\) 4.60015 0.187178
\(605\) 0 0
\(606\) 0 0
\(607\) 2.57560 0.104540 0.0522701 0.998633i \(-0.483354\pi\)
0.0522701 + 0.998633i \(0.483354\pi\)
\(608\) −7.64973 −0.310238
\(609\) 0 0
\(610\) −1.86519 −0.0755194
\(611\) 4.12494 0.166877
\(612\) 0 0
\(613\) 15.8353 0.639584 0.319792 0.947488i \(-0.396387\pi\)
0.319792 + 0.947488i \(0.396387\pi\)
\(614\) −69.9290 −2.82210
\(615\) 0 0
\(616\) 0 0
\(617\) 1.72448 0.0694250 0.0347125 0.999397i \(-0.488948\pi\)
0.0347125 + 0.999397i \(0.488948\pi\)
\(618\) 0 0
\(619\) −17.3288 −0.696505 −0.348253 0.937401i \(-0.613225\pi\)
−0.348253 + 0.937401i \(0.613225\pi\)
\(620\) 0.149501 0.00600411
\(621\) 0 0
\(622\) −11.9326 −0.478454
\(623\) 9.81079 0.393061
\(624\) 0 0
\(625\) 24.6791 0.987165
\(626\) 51.6191 2.06311
\(627\) 0 0
\(628\) 34.3931 1.37243
\(629\) −0.510711 −0.0203634
\(630\) 0 0
\(631\) 6.54683 0.260625 0.130313 0.991473i \(-0.458402\pi\)
0.130313 + 0.991473i \(0.458402\pi\)
\(632\) −45.6363 −1.81531
\(633\) 0 0
\(634\) −16.6086 −0.659611
\(635\) −2.58608 −0.102625
\(636\) 0 0
\(637\) 4.34292 0.172073
\(638\) 0 0
\(639\) 0 0
\(640\) 2.95294 0.116725
\(641\) −16.0930 −0.635637 −0.317818 0.948152i \(-0.602950\pi\)
−0.317818 + 0.948152i \(0.602950\pi\)
\(642\) 0 0
\(643\) −3.21377 −0.126739 −0.0633694 0.997990i \(-0.520185\pi\)
−0.0633694 + 0.997990i \(0.520185\pi\)
\(644\) −30.7434 −1.21146
\(645\) 0 0
\(646\) 0.628308 0.0247204
\(647\) 37.8083 1.48640 0.743198 0.669071i \(-0.233308\pi\)
0.743198 + 0.669071i \(0.233308\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 50.6577 1.98696
\(651\) 0 0
\(652\) −1.02142 −0.0400020
\(653\) 13.9754 0.546901 0.273451 0.961886i \(-0.411835\pi\)
0.273451 + 0.961886i \(0.411835\pi\)
\(654\) 0 0
\(655\) −2.63879 −0.103106
\(656\) −3.35448 −0.130970
\(657\) 0 0
\(658\) −2.22533 −0.0867523
\(659\) −8.31729 −0.323996 −0.161998 0.986791i \(-0.551794\pi\)
−0.161998 + 0.986791i \(0.551794\pi\)
\(660\) 0 0
\(661\) −38.2474 −1.48765 −0.743825 0.668374i \(-0.766990\pi\)
−0.743825 + 0.668374i \(0.766990\pi\)
\(662\) 81.0754 3.15108
\(663\) 0 0
\(664\) −45.0361 −1.74774
\(665\) −0.268173 −0.0103993
\(666\) 0 0
\(667\) 38.2646 1.48161
\(668\) 54.9076 2.12444
\(669\) 0 0
\(670\) 2.66129 0.102815
\(671\) 0 0
\(672\) 0 0
\(673\) −7.86098 −0.303019 −0.151509 0.988456i \(-0.548413\pi\)
−0.151509 + 0.988456i \(0.548413\pi\)
\(674\) 29.3461 1.13037
\(675\) 0 0
\(676\) 20.4507 0.786564
\(677\) 31.9603 1.22833 0.614167 0.789176i \(-0.289492\pi\)
0.614167 + 0.789176i \(0.289492\pi\)
\(678\) 0 0
\(679\) −17.4219 −0.668591
\(680\) −0.0747505 −0.00286655
\(681\) 0 0
\(682\) 0 0
\(683\) −35.1856 −1.34634 −0.673170 0.739488i \(-0.735068\pi\)
−0.673170 + 0.739488i \(0.735068\pi\)
\(684\) 0 0
\(685\) 3.15479 0.120538
\(686\) −2.34292 −0.0894532
\(687\) 0 0
\(688\) −9.40612 −0.358605
\(689\) 19.5897 0.746307
\(690\) 0 0
\(691\) 2.05754 0.0782725 0.0391362 0.999234i \(-0.487539\pi\)
0.0391362 + 0.999234i \(0.487539\pi\)
\(692\) 61.8862 2.35256
\(693\) 0 0
\(694\) 64.7728 2.45874
\(695\) 1.98171 0.0751706
\(696\) 0 0
\(697\) −0.410327 −0.0155423
\(698\) 26.4679 1.00182
\(699\) 0 0
\(700\) −17.3717 −0.656588
\(701\) 11.1207 0.420024 0.210012 0.977699i \(-0.432650\pi\)
0.210012 + 0.977699i \(0.432650\pi\)
\(702\) 0 0
\(703\) 6.39312 0.241121
\(704\) 0 0
\(705\) 0 0
\(706\) 39.3692 1.48168
\(707\) 15.6357 0.588039
\(708\) 0 0
\(709\) 26.6901 1.00237 0.501183 0.865341i \(-0.332898\pi\)
0.501183 + 0.865341i \(0.332898\pi\)
\(710\) −1.21377 −0.0455520
\(711\) 0 0
\(712\) −34.2327 −1.28292
\(713\) −2.57919 −0.0965915
\(714\) 0 0
\(715\) 0 0
\(716\) 81.0508 3.02901
\(717\) 0 0
\(718\) 68.0869 2.54098
\(719\) −19.8996 −0.742130 −0.371065 0.928607i \(-0.621007\pi\)
−0.371065 + 0.928607i \(0.621007\pi\)
\(720\) 0 0
\(721\) 4.16779 0.155217
\(722\) 36.6503 1.36398
\(723\) 0 0
\(724\) 87.6191 3.25634
\(725\) 21.6216 0.803005
\(726\) 0 0
\(727\) 17.3618 0.643915 0.321957 0.946754i \(-0.395659\pi\)
0.321957 + 0.946754i \(0.395659\pi\)
\(728\) −15.1537 −0.561634
\(729\) 0 0
\(730\) −5.54935 −0.205391
\(731\) −1.15058 −0.0425556
\(732\) 0 0
\(733\) 33.3790 1.23288 0.616441 0.787401i \(-0.288574\pi\)
0.616441 + 0.787401i \(0.288574\pi\)
\(734\) −41.4637 −1.53045
\(735\) 0 0
\(736\) −36.7862 −1.35596
\(737\) 0 0
\(738\) 0 0
\(739\) 15.2369 0.560498 0.280249 0.959927i \(-0.409583\pi\)
0.280249 + 0.959927i \(0.409583\pi\)
\(740\) −1.78202 −0.0655083
\(741\) 0 0
\(742\) −10.5682 −0.387973
\(743\) 23.3387 0.856214 0.428107 0.903728i \(-0.359181\pi\)
0.428107 + 0.903728i \(0.359181\pi\)
\(744\) 0 0
\(745\) −1.50758 −0.0552333
\(746\) 29.9473 1.09645
\(747\) 0 0
\(748\) 0 0
\(749\) 5.49663 0.200843
\(750\) 0 0
\(751\) 29.6174 1.08075 0.540377 0.841423i \(-0.318282\pi\)
0.540377 + 0.841423i \(0.318282\pi\)
\(752\) 1.13650 0.0414439
\(753\) 0 0
\(754\) 44.1898 1.60930
\(755\) 0.192963 0.00702265
\(756\) 0 0
\(757\) −25.4360 −0.924486 −0.462243 0.886753i \(-0.652955\pi\)
−0.462243 + 0.886753i \(0.652955\pi\)
\(758\) 45.9817 1.67013
\(759\) 0 0
\(760\) 0.935731 0.0339425
\(761\) −44.9473 −1.62934 −0.814669 0.579926i \(-0.803081\pi\)
−0.814669 + 0.579926i \(0.803081\pi\)
\(762\) 0 0
\(763\) 5.87819 0.212805
\(764\) 62.4225 2.25837
\(765\) 0 0
\(766\) 69.2333 2.50150
\(767\) −34.8683 −1.25902
\(768\) 0 0
\(769\) −32.6749 −1.17829 −0.589144 0.808028i \(-0.700535\pi\)
−0.589144 + 0.808028i \(0.700535\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −36.0403 −1.29712
\(773\) 49.6222 1.78479 0.892393 0.451259i \(-0.149025\pi\)
0.892393 + 0.451259i \(0.149025\pi\)
\(774\) 0 0
\(775\) −1.45738 −0.0523508
\(776\) 60.7900 2.18223
\(777\) 0 0
\(778\) −30.6833 −1.10005
\(779\) 5.13650 0.184034
\(780\) 0 0
\(781\) 0 0
\(782\) 3.02142 0.108046
\(783\) 0 0
\(784\) 1.19656 0.0427342
\(785\) 1.44269 0.0514918
\(786\) 0 0
\(787\) 40.2583 1.43505 0.717527 0.696531i \(-0.245274\pi\)
0.717527 + 0.696531i \(0.245274\pi\)
\(788\) −51.8543 −1.84723
\(789\) 0 0
\(790\) −4.48508 −0.159572
\(791\) 3.88240 0.138042
\(792\) 0 0
\(793\) 23.6216 0.838827
\(794\) −57.3263 −2.03444
\(795\) 0 0
\(796\) 0.235192 0.00833618
\(797\) −17.4862 −0.619391 −0.309696 0.950836i \(-0.600227\pi\)
−0.309696 + 0.950836i \(0.600227\pi\)
\(798\) 0 0
\(799\) 0.139019 0.00491814
\(800\) −20.7862 −0.734904
\(801\) 0 0
\(802\) 56.6405 2.00004
\(803\) 0 0
\(804\) 0 0
\(805\) −1.28960 −0.0454523
\(806\) −2.97858 −0.104916
\(807\) 0 0
\(808\) −54.5573 −1.91932
\(809\) −25.9473 −0.912258 −0.456129 0.889914i \(-0.650764\pi\)
−0.456129 + 0.889914i \(0.650764\pi\)
\(810\) 0 0
\(811\) −18.2829 −0.641998 −0.320999 0.947079i \(-0.604019\pi\)
−0.320999 + 0.947079i \(0.604019\pi\)
\(812\) −15.1537 −0.531791
\(813\) 0 0
\(814\) 0 0
\(815\) −0.0428457 −0.00150082
\(816\) 0 0
\(817\) 14.4030 0.503897
\(818\) −12.2327 −0.427705
\(819\) 0 0
\(820\) −1.43175 −0.0499989
\(821\) 25.3288 0.883983 0.441991 0.897019i \(-0.354272\pi\)
0.441991 + 0.897019i \(0.354272\pi\)
\(822\) 0 0
\(823\) 39.2713 1.36891 0.684456 0.729054i \(-0.260040\pi\)
0.684456 + 0.729054i \(0.260040\pi\)
\(824\) −14.5426 −0.506616
\(825\) 0 0
\(826\) 18.8108 0.654511
\(827\) 27.4047 0.952954 0.476477 0.879187i \(-0.341914\pi\)
0.476477 + 0.879187i \(0.341914\pi\)
\(828\) 0 0
\(829\) 38.5155 1.33770 0.668850 0.743397i \(-0.266787\pi\)
0.668850 + 0.743397i \(0.266787\pi\)
\(830\) −4.42610 −0.153632
\(831\) 0 0
\(832\) −52.8757 −1.83313
\(833\) 0.146365 0.00507126
\(834\) 0 0
\(835\) 2.30321 0.0797060
\(836\) 0 0
\(837\) 0 0
\(838\) −53.1182 −1.83494
\(839\) 17.7276 0.612025 0.306013 0.952027i \(-0.401005\pi\)
0.306013 + 0.952027i \(0.401005\pi\)
\(840\) 0 0
\(841\) −10.1390 −0.349621
\(842\) 5.65708 0.194956
\(843\) 0 0
\(844\) −45.8223 −1.57727
\(845\) 0.857845 0.0295108
\(846\) 0 0
\(847\) 0 0
\(848\) 5.39733 0.185345
\(849\) 0 0
\(850\) 1.70727 0.0585588
\(851\) 30.7434 1.05387
\(852\) 0 0
\(853\) 15.3032 0.523972 0.261986 0.965072i \(-0.415623\pi\)
0.261986 + 0.965072i \(0.415623\pi\)
\(854\) −12.7434 −0.436070
\(855\) 0 0
\(856\) −19.1793 −0.655537
\(857\) −10.7722 −0.367970 −0.183985 0.982929i \(-0.558900\pi\)
−0.183985 + 0.982929i \(0.558900\pi\)
\(858\) 0 0
\(859\) 47.2516 1.61220 0.806101 0.591777i \(-0.201574\pi\)
0.806101 + 0.591777i \(0.201574\pi\)
\(860\) −4.01469 −0.136900
\(861\) 0 0
\(862\) −3.17935 −0.108289
\(863\) 34.0294 1.15837 0.579187 0.815195i \(-0.303370\pi\)
0.579187 + 0.815195i \(0.303370\pi\)
\(864\) 0 0
\(865\) 2.59594 0.0882647
\(866\) −48.3822 −1.64409
\(867\) 0 0
\(868\) 1.02142 0.0346694
\(869\) 0 0
\(870\) 0 0
\(871\) −33.7037 −1.14201
\(872\) −20.5107 −0.694580
\(873\) 0 0
\(874\) −37.8223 −1.27936
\(875\) −1.46052 −0.0493746
\(876\) 0 0
\(877\) −3.25410 −0.109883 −0.0549415 0.998490i \(-0.517497\pi\)
−0.0549415 + 0.998490i \(0.517497\pi\)
\(878\) 47.5787 1.60570
\(879\) 0 0
\(880\) 0 0
\(881\) 13.3545 0.449924 0.224962 0.974368i \(-0.427774\pi\)
0.224962 + 0.974368i \(0.427774\pi\)
\(882\) 0 0
\(883\) −25.4741 −0.857273 −0.428636 0.903477i \(-0.641006\pi\)
−0.428636 + 0.903477i \(0.641006\pi\)
\(884\) 2.21798 0.0745988
\(885\) 0 0
\(886\) −23.0017 −0.772757
\(887\) −21.6932 −0.728386 −0.364193 0.931323i \(-0.618655\pi\)
−0.364193 + 0.931323i \(0.618655\pi\)
\(888\) 0 0
\(889\) −17.6686 −0.592587
\(890\) −3.36435 −0.112773
\(891\) 0 0
\(892\) 18.7434 0.627575
\(893\) −1.74025 −0.0582352
\(894\) 0 0
\(895\) 3.39985 0.113644
\(896\) 20.1751 0.674004
\(897\) 0 0
\(898\) 23.6044 0.787688
\(899\) −1.27131 −0.0424005
\(900\) 0 0
\(901\) 0.660212 0.0219949
\(902\) 0 0
\(903\) 0 0
\(904\) −13.5468 −0.450561
\(905\) 3.67536 0.122173
\(906\) 0 0
\(907\) 1.21377 0.0403026 0.0201513 0.999797i \(-0.493585\pi\)
0.0201513 + 0.999797i \(0.493585\pi\)
\(908\) 23.9290 0.794112
\(909\) 0 0
\(910\) −1.48929 −0.0493694
\(911\) −57.0080 −1.88876 −0.944379 0.328859i \(-0.893336\pi\)
−0.944379 + 0.328859i \(0.893336\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −34.3920 −1.13759
\(915\) 0 0
\(916\) −30.5682 −1.01000
\(917\) −18.0288 −0.595362
\(918\) 0 0
\(919\) 6.45065 0.212787 0.106394 0.994324i \(-0.466070\pi\)
0.106394 + 0.994324i \(0.466070\pi\)
\(920\) 4.49977 0.148353
\(921\) 0 0
\(922\) 63.5861 2.09410
\(923\) 15.3717 0.505965
\(924\) 0 0
\(925\) 17.3717 0.571178
\(926\) −54.4422 −1.78908
\(927\) 0 0
\(928\) −18.1323 −0.595222
\(929\) −2.74652 −0.0901104 −0.0450552 0.998984i \(-0.514346\pi\)
−0.0450552 + 0.998984i \(0.514346\pi\)
\(930\) 0 0
\(931\) −1.83221 −0.0600483
\(932\) −4.76060 −0.155939
\(933\) 0 0
\(934\) 55.8946 1.82893
\(935\) 0 0
\(936\) 0 0
\(937\) 25.8923 0.845864 0.422932 0.906162i \(-0.361001\pi\)
0.422932 + 0.906162i \(0.361001\pi\)
\(938\) 18.1825 0.593679
\(939\) 0 0
\(940\) 0.485078 0.0158215
\(941\) 9.01890 0.294008 0.147004 0.989136i \(-0.453037\pi\)
0.147004 + 0.989136i \(0.453037\pi\)
\(942\) 0 0
\(943\) 24.7005 0.804360
\(944\) −9.60688 −0.312677
\(945\) 0 0
\(946\) 0 0
\(947\) −39.2003 −1.27384 −0.636919 0.770930i \(-0.719792\pi\)
−0.636919 + 0.770930i \(0.719792\pi\)
\(948\) 0 0
\(949\) 70.2793 2.28136
\(950\) −21.3717 −0.693389
\(951\) 0 0
\(952\) −0.510711 −0.0165523
\(953\) 55.4464 1.79609 0.898043 0.439907i \(-0.144989\pi\)
0.898043 + 0.439907i \(0.144989\pi\)
\(954\) 0 0
\(955\) 2.61844 0.0847308
\(956\) −17.3717 −0.561841
\(957\) 0 0
\(958\) −40.3173 −1.30259
\(959\) 21.5542 0.696021
\(960\) 0 0
\(961\) −30.9143 −0.997236
\(962\) 35.5040 1.14469
\(963\) 0 0
\(964\) 49.4355 1.59221
\(965\) −1.51179 −0.0486661
\(966\) 0 0
\(967\) 23.9467 0.770073 0.385037 0.922901i \(-0.374189\pi\)
0.385037 + 0.922901i \(0.374189\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 5.97437 0.191825
\(971\) 6.42188 0.206088 0.103044 0.994677i \(-0.467142\pi\)
0.103044 + 0.994677i \(0.467142\pi\)
\(972\) 0 0
\(973\) 13.5395 0.434056
\(974\) 7.40467 0.237261
\(975\) 0 0
\(976\) 6.50819 0.208322
\(977\) −38.5584 −1.23359 −0.616796 0.787123i \(-0.711570\pi\)
−0.616796 + 0.787123i \(0.711570\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.510711 0.0163141
\(981\) 0 0
\(982\) 9.89962 0.315909
\(983\) −21.6069 −0.689153 −0.344576 0.938758i \(-0.611977\pi\)
−0.344576 + 0.938758i \(0.611977\pi\)
\(984\) 0 0
\(985\) −2.17513 −0.0693056
\(986\) 1.48929 0.0474286
\(987\) 0 0
\(988\) −27.7648 −0.883316
\(989\) 69.2614 2.20239
\(990\) 0 0
\(991\) 34.4507 1.09436 0.547181 0.837015i \(-0.315701\pi\)
0.547181 + 0.837015i \(0.315701\pi\)
\(992\) 1.22219 0.0388046
\(993\) 0 0
\(994\) −8.29273 −0.263029
\(995\) 0.00986564 0.000312762 0
\(996\) 0 0
\(997\) −7.76733 −0.245994 −0.122997 0.992407i \(-0.539251\pi\)
−0.122997 + 0.992407i \(0.539251\pi\)
\(998\) −71.6033 −2.26656
\(999\) 0 0
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 7623.2.a.ca.1.1 3
3.2 odd 2 2541.2.a.bj.1.3 yes 3
11.10 odd 2 7623.2.a.cc.1.3 3
33.32 even 2 2541.2.a.bh.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2541.2.a.bh.1.1 3 33.32 even 2
2541.2.a.bj.1.3 yes 3 3.2 odd 2
7623.2.a.ca.1.1 3 1.1 even 1 trivial
7623.2.a.cc.1.3 3 11.10 odd 2