Properties

Label 1305.2.a.t.1.7
Level $1305$
Weight $2$
Character 1305.1
Self dual yes
Analytic conductor $10.420$
Analytic rank $0$
Dimension $7$
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] = [1305,2,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, 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("1305.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1305.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: \(10.4204774638\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 13x^{5} + 12x^{4} + 47x^{3} - 37x^{2} - 35x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(2.57501\) of defining polynomial
Character \(\chi\) \(=\) 1305.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.57501 q^{2} +4.63069 q^{4} +1.00000 q^{5} -2.24826 q^{7} +6.77405 q^{8} +O(q^{10})\) \(q+2.57501 q^{2} +4.63069 q^{4} +1.00000 q^{5} -2.24826 q^{7} +6.77405 q^{8} +2.57501 q^{10} +3.75744 q^{11} -1.55119 q^{13} -5.78930 q^{14} +8.18188 q^{16} +3.55119 q^{17} -1.18909 q^{19} +4.63069 q^{20} +9.67546 q^{22} +3.67991 q^{23} +1.00000 q^{25} -3.99434 q^{26} -10.4110 q^{28} -1.00000 q^{29} +5.18909 q^{31} +7.52034 q^{32} +9.14436 q^{34} -2.24826 q^{35} +0.969518 q^{37} -3.06193 q^{38} +6.77405 q^{40} -11.3809 q^{41} -0.884393 q^{43} +17.3995 q^{44} +9.47581 q^{46} -11.2251 q^{47} -1.94533 q^{49} +2.57501 q^{50} -7.18308 q^{52} +10.6567 q^{53} +3.75744 q^{55} -15.2298 q^{56} -2.57501 q^{58} -8.49652 q^{59} -10.8743 q^{61} +13.3620 q^{62} +3.00121 q^{64} -1.55119 q^{65} -4.05179 q^{67} +16.4445 q^{68} -5.78930 q^{70} -6.37818 q^{71} -3.26017 q^{73} +2.49652 q^{74} -5.50631 q^{76} -8.44770 q^{77} +6.32579 q^{79} +8.18188 q^{80} -29.3060 q^{82} +9.03930 q^{83} +3.55119 q^{85} -2.27732 q^{86} +25.4531 q^{88} -1.46717 q^{89} +3.48748 q^{91} +17.0405 q^{92} -28.9047 q^{94} -1.18909 q^{95} +12.3993 q^{97} -5.00924 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{2} + 13 q^{4} + 7 q^{5} + 10 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + q^{2} + 13 q^{4} + 7 q^{5} + 10 q^{7} + q^{10} - 3 q^{11} + 6 q^{13} - 9 q^{14} + 21 q^{16} + 8 q^{17} + 10 q^{19} + 13 q^{20} + 9 q^{22} + 11 q^{23} + 7 q^{25} + 3 q^{26} + 25 q^{28} - 7 q^{29} + 18 q^{31} + q^{32} - q^{34} + 10 q^{35} + 13 q^{37} + 12 q^{38} - 13 q^{41} + 9 q^{43} - 37 q^{44} - 8 q^{46} + 2 q^{47} + 21 q^{49} + q^{50} - q^{52} + 5 q^{53} - 3 q^{55} - 30 q^{56} - q^{58} - 8 q^{59} + 14 q^{61} - 8 q^{62} + 8 q^{64} + 6 q^{65} + 14 q^{67} + 27 q^{68} - 9 q^{70} - 8 q^{71} + 3 q^{73} - 34 q^{74} + 4 q^{76} - 28 q^{77} + 4 q^{79} + 21 q^{80} - 20 q^{82} + 17 q^{83} + 8 q^{85} + 4 q^{86} + 26 q^{88} - 20 q^{89} + 12 q^{91} + 60 q^{92} - 21 q^{94} + 10 q^{95} + 13 q^{97} - 20 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.57501 1.82081 0.910404 0.413720i \(-0.135771\pi\)
0.910404 + 0.413720i \(0.135771\pi\)
\(3\) 0 0
\(4\) 4.63069 2.31534
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.24826 −0.849762 −0.424881 0.905249i \(-0.639684\pi\)
−0.424881 + 0.905249i \(0.639684\pi\)
\(8\) 6.77405 2.39499
\(9\) 0 0
\(10\) 2.57501 0.814290
\(11\) 3.75744 1.13291 0.566456 0.824092i \(-0.308314\pi\)
0.566456 + 0.824092i \(0.308314\pi\)
\(12\) 0 0
\(13\) −1.55119 −0.430223 −0.215112 0.976589i \(-0.569012\pi\)
−0.215112 + 0.976589i \(0.569012\pi\)
\(14\) −5.78930 −1.54725
\(15\) 0 0
\(16\) 8.18188 2.04547
\(17\) 3.55119 0.861291 0.430645 0.902521i \(-0.358286\pi\)
0.430645 + 0.902521i \(0.358286\pi\)
\(18\) 0 0
\(19\) −1.18909 −0.272796 −0.136398 0.990654i \(-0.543553\pi\)
−0.136398 + 0.990654i \(0.543553\pi\)
\(20\) 4.63069 1.03545
\(21\) 0 0
\(22\) 9.67546 2.06281
\(23\) 3.67991 0.767314 0.383657 0.923476i \(-0.374664\pi\)
0.383657 + 0.923476i \(0.374664\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −3.99434 −0.783354
\(27\) 0 0
\(28\) −10.4110 −1.96749
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 5.18909 0.931988 0.465994 0.884788i \(-0.345697\pi\)
0.465994 + 0.884788i \(0.345697\pi\)
\(32\) 7.52034 1.32942
\(33\) 0 0
\(34\) 9.14436 1.56825
\(35\) −2.24826 −0.380025
\(36\) 0 0
\(37\) 0.969518 0.159388 0.0796939 0.996819i \(-0.474606\pi\)
0.0796939 + 0.996819i \(0.474606\pi\)
\(38\) −3.06193 −0.496710
\(39\) 0 0
\(40\) 6.77405 1.07107
\(41\) −11.3809 −1.77740 −0.888700 0.458489i \(-0.848391\pi\)
−0.888700 + 0.458489i \(0.848391\pi\)
\(42\) 0 0
\(43\) −0.884393 −0.134869 −0.0674343 0.997724i \(-0.521481\pi\)
−0.0674343 + 0.997724i \(0.521481\pi\)
\(44\) 17.3995 2.62308
\(45\) 0 0
\(46\) 9.47581 1.39713
\(47\) −11.2251 −1.63734 −0.818672 0.574262i \(-0.805289\pi\)
−0.818672 + 0.574262i \(0.805289\pi\)
\(48\) 0 0
\(49\) −1.94533 −0.277904
\(50\) 2.57501 0.364162
\(51\) 0 0
\(52\) −7.18308 −0.996115
\(53\) 10.6567 1.46381 0.731906 0.681406i \(-0.238631\pi\)
0.731906 + 0.681406i \(0.238631\pi\)
\(54\) 0 0
\(55\) 3.75744 0.506653
\(56\) −15.2298 −2.03517
\(57\) 0 0
\(58\) −2.57501 −0.338116
\(59\) −8.49652 −1.10615 −0.553076 0.833131i \(-0.686546\pi\)
−0.553076 + 0.833131i \(0.686546\pi\)
\(60\) 0 0
\(61\) −10.8743 −1.39231 −0.696154 0.717892i \(-0.745107\pi\)
−0.696154 + 0.717892i \(0.745107\pi\)
\(62\) 13.3620 1.69697
\(63\) 0 0
\(64\) 3.00121 0.375151
\(65\) −1.55119 −0.192402
\(66\) 0 0
\(67\) −4.05179 −0.495005 −0.247502 0.968887i \(-0.579610\pi\)
−0.247502 + 0.968887i \(0.579610\pi\)
\(68\) 16.4445 1.99418
\(69\) 0 0
\(70\) −5.78930 −0.691953
\(71\) −6.37818 −0.756951 −0.378476 0.925611i \(-0.623552\pi\)
−0.378476 + 0.925611i \(0.623552\pi\)
\(72\) 0 0
\(73\) −3.26017 −0.381573 −0.190787 0.981632i \(-0.561104\pi\)
−0.190787 + 0.981632i \(0.561104\pi\)
\(74\) 2.49652 0.290215
\(75\) 0 0
\(76\) −5.50631 −0.631617
\(77\) −8.44770 −0.962705
\(78\) 0 0
\(79\) 6.32579 0.711707 0.355854 0.934542i \(-0.384190\pi\)
0.355854 + 0.934542i \(0.384190\pi\)
\(80\) 8.18188 0.914762
\(81\) 0 0
\(82\) −29.3060 −3.23630
\(83\) 9.03930 0.992193 0.496096 0.868268i \(-0.334766\pi\)
0.496096 + 0.868268i \(0.334766\pi\)
\(84\) 0 0
\(85\) 3.55119 0.385181
\(86\) −2.27732 −0.245570
\(87\) 0 0
\(88\) 25.4531 2.71331
\(89\) −1.46717 −0.155520 −0.0777599 0.996972i \(-0.524777\pi\)
−0.0777599 + 0.996972i \(0.524777\pi\)
\(90\) 0 0
\(91\) 3.48748 0.365588
\(92\) 17.0405 1.77660
\(93\) 0 0
\(94\) −28.9047 −2.98129
\(95\) −1.18909 −0.121998
\(96\) 0 0
\(97\) 12.3993 1.25896 0.629478 0.777018i \(-0.283269\pi\)
0.629478 + 0.777018i \(0.283269\pi\)
\(98\) −5.00924 −0.506010
\(99\) 0 0
\(100\) 4.63069 0.463069
\(101\) −3.45196 −0.343483 −0.171742 0.985142i \(-0.554939\pi\)
−0.171742 + 0.985142i \(0.554939\pi\)
\(102\) 0 0
\(103\) 18.1975 1.79306 0.896528 0.442988i \(-0.146082\pi\)
0.896528 + 0.442988i \(0.146082\pi\)
\(104\) −10.5078 −1.03038
\(105\) 0 0
\(106\) 27.4412 2.66532
\(107\) −8.07919 −0.781044 −0.390522 0.920594i \(-0.627706\pi\)
−0.390522 + 0.920594i \(0.627706\pi\)
\(108\) 0 0
\(109\) −14.0114 −1.34205 −0.671026 0.741434i \(-0.734146\pi\)
−0.671026 + 0.741434i \(0.734146\pi\)
\(110\) 9.67546 0.922518
\(111\) 0 0
\(112\) −18.3950 −1.73816
\(113\) 0.678491 0.0638270 0.0319135 0.999491i \(-0.489840\pi\)
0.0319135 + 0.999491i \(0.489840\pi\)
\(114\) 0 0
\(115\) 3.67991 0.343153
\(116\) −4.63069 −0.429948
\(117\) 0 0
\(118\) −21.8786 −2.01409
\(119\) −7.98400 −0.731892
\(120\) 0 0
\(121\) 3.11836 0.283488
\(122\) −28.0014 −2.53513
\(123\) 0 0
\(124\) 24.0291 2.15787
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.39928 −0.745315 −0.372658 0.927969i \(-0.621553\pi\)
−0.372658 + 0.927969i \(0.621553\pi\)
\(128\) −7.31254 −0.646343
\(129\) 0 0
\(130\) −3.99434 −0.350327
\(131\) −7.34298 −0.641559 −0.320779 0.947154i \(-0.603945\pi\)
−0.320779 + 0.947154i \(0.603945\pi\)
\(132\) 0 0
\(133\) 2.67339 0.231812
\(134\) −10.4334 −0.901308
\(135\) 0 0
\(136\) 24.0559 2.06278
\(137\) −1.80353 −0.154086 −0.0770429 0.997028i \(-0.524548\pi\)
−0.0770429 + 0.997028i \(0.524548\pi\)
\(138\) 0 0
\(139\) 0.707451 0.0600052 0.0300026 0.999550i \(-0.490448\pi\)
0.0300026 + 0.999550i \(0.490448\pi\)
\(140\) −10.4110 −0.879889
\(141\) 0 0
\(142\) −16.4239 −1.37826
\(143\) −5.82851 −0.487405
\(144\) 0 0
\(145\) −1.00000 −0.0830455
\(146\) −8.39496 −0.694772
\(147\) 0 0
\(148\) 4.48953 0.369037
\(149\) −16.9930 −1.39212 −0.696062 0.717982i \(-0.745066\pi\)
−0.696062 + 0.717982i \(0.745066\pi\)
\(150\) 0 0
\(151\) 7.86646 0.640163 0.320082 0.947390i \(-0.396290\pi\)
0.320082 + 0.947390i \(0.396290\pi\)
\(152\) −8.05497 −0.653344
\(153\) 0 0
\(154\) −21.7529 −1.75290
\(155\) 5.18909 0.416798
\(156\) 0 0
\(157\) 9.85591 0.786588 0.393294 0.919413i \(-0.371336\pi\)
0.393294 + 0.919413i \(0.371336\pi\)
\(158\) 16.2890 1.29588
\(159\) 0 0
\(160\) 7.52034 0.594535
\(161\) −8.27340 −0.652035
\(162\) 0 0
\(163\) 16.5786 1.29853 0.649267 0.760560i \(-0.275076\pi\)
0.649267 + 0.760560i \(0.275076\pi\)
\(164\) −52.7014 −4.11529
\(165\) 0 0
\(166\) 23.2763 1.80659
\(167\) −4.74360 −0.367071 −0.183536 0.983013i \(-0.558754\pi\)
−0.183536 + 0.983013i \(0.558754\pi\)
\(168\) 0 0
\(169\) −10.5938 −0.814908
\(170\) 9.14436 0.701341
\(171\) 0 0
\(172\) −4.09534 −0.312267
\(173\) −19.8201 −1.50689 −0.753446 0.657510i \(-0.771610\pi\)
−0.753446 + 0.657510i \(0.771610\pi\)
\(174\) 0 0
\(175\) −2.24826 −0.169952
\(176\) 30.7429 2.31734
\(177\) 0 0
\(178\) −3.77798 −0.283172
\(179\) 7.42036 0.554624 0.277312 0.960780i \(-0.410557\pi\)
0.277312 + 0.960780i \(0.410557\pi\)
\(180\) 0 0
\(181\) 19.8411 1.47478 0.737390 0.675468i \(-0.236058\pi\)
0.737390 + 0.675468i \(0.236058\pi\)
\(182\) 8.98031 0.665665
\(183\) 0 0
\(184\) 24.9279 1.83771
\(185\) 0.969518 0.0712804
\(186\) 0 0
\(187\) 13.3434 0.975766
\(188\) −51.9797 −3.79101
\(189\) 0 0
\(190\) −3.06193 −0.222136
\(191\) 5.66409 0.409839 0.204920 0.978779i \(-0.434307\pi\)
0.204920 + 0.978779i \(0.434307\pi\)
\(192\) 0 0
\(193\) 14.7896 1.06458 0.532289 0.846563i \(-0.321332\pi\)
0.532289 + 0.846563i \(0.321332\pi\)
\(194\) 31.9283 2.29232
\(195\) 0 0
\(196\) −9.00820 −0.643443
\(197\) 27.1349 1.93328 0.966640 0.256139i \(-0.0824504\pi\)
0.966640 + 0.256139i \(0.0824504\pi\)
\(198\) 0 0
\(199\) −9.53523 −0.675934 −0.337967 0.941158i \(-0.609739\pi\)
−0.337967 + 0.941158i \(0.609739\pi\)
\(200\) 6.77405 0.478997
\(201\) 0 0
\(202\) −8.88885 −0.625417
\(203\) 2.24826 0.157797
\(204\) 0 0
\(205\) −11.3809 −0.794877
\(206\) 46.8588 3.26481
\(207\) 0 0
\(208\) −12.6917 −0.880009
\(209\) −4.46794 −0.309054
\(210\) 0 0
\(211\) 21.5727 1.48513 0.742564 0.669775i \(-0.233609\pi\)
0.742564 + 0.669775i \(0.233609\pi\)
\(212\) 49.3479 3.38923
\(213\) 0 0
\(214\) −20.8040 −1.42213
\(215\) −0.884393 −0.0603151
\(216\) 0 0
\(217\) −11.6664 −0.791969
\(218\) −36.0796 −2.44362
\(219\) 0 0
\(220\) 17.3995 1.17308
\(221\) −5.50858 −0.370547
\(222\) 0 0
\(223\) 22.5140 1.50765 0.753824 0.657076i \(-0.228207\pi\)
0.753824 + 0.657076i \(0.228207\pi\)
\(224\) −16.9077 −1.12969
\(225\) 0 0
\(226\) 1.74712 0.116217
\(227\) 8.38063 0.556242 0.278121 0.960546i \(-0.410288\pi\)
0.278121 + 0.960546i \(0.410288\pi\)
\(228\) 0 0
\(229\) −11.5492 −0.763192 −0.381596 0.924329i \(-0.624625\pi\)
−0.381596 + 0.924329i \(0.624625\pi\)
\(230\) 9.47581 0.624817
\(231\) 0 0
\(232\) −6.77405 −0.444738
\(233\) −8.85319 −0.579991 −0.289996 0.957028i \(-0.593654\pi\)
−0.289996 + 0.957028i \(0.593654\pi\)
\(234\) 0 0
\(235\) −11.2251 −0.732242
\(236\) −39.3447 −2.56112
\(237\) 0 0
\(238\) −20.5589 −1.33264
\(239\) 13.9536 0.902584 0.451292 0.892376i \(-0.350963\pi\)
0.451292 + 0.892376i \(0.350963\pi\)
\(240\) 0 0
\(241\) −24.2138 −1.55975 −0.779874 0.625937i \(-0.784717\pi\)
−0.779874 + 0.625937i \(0.784717\pi\)
\(242\) 8.02983 0.516177
\(243\) 0 0
\(244\) −50.3554 −3.22367
\(245\) −1.94533 −0.124282
\(246\) 0 0
\(247\) 1.84451 0.117363
\(248\) 35.1512 2.23210
\(249\) 0 0
\(250\) 2.57501 0.162858
\(251\) −10.1141 −0.638397 −0.319198 0.947688i \(-0.603414\pi\)
−0.319198 + 0.947688i \(0.603414\pi\)
\(252\) 0 0
\(253\) 13.8270 0.869299
\(254\) −21.6282 −1.35708
\(255\) 0 0
\(256\) −24.8323 −1.55202
\(257\) −18.2290 −1.13709 −0.568546 0.822652i \(-0.692494\pi\)
−0.568546 + 0.822652i \(0.692494\pi\)
\(258\) 0 0
\(259\) −2.17973 −0.135442
\(260\) −7.18308 −0.445476
\(261\) 0 0
\(262\) −18.9083 −1.16816
\(263\) 4.26573 0.263036 0.131518 0.991314i \(-0.458015\pi\)
0.131518 + 0.991314i \(0.458015\pi\)
\(264\) 0 0
\(265\) 10.6567 0.654637
\(266\) 6.88401 0.422086
\(267\) 0 0
\(268\) −18.7626 −1.14611
\(269\) 8.10868 0.494395 0.247197 0.968965i \(-0.420490\pi\)
0.247197 + 0.968965i \(0.420490\pi\)
\(270\) 0 0
\(271\) 26.9259 1.63563 0.817815 0.575481i \(-0.195185\pi\)
0.817815 + 0.575481i \(0.195185\pi\)
\(272\) 29.0554 1.76174
\(273\) 0 0
\(274\) −4.64410 −0.280561
\(275\) 3.75744 0.226582
\(276\) 0 0
\(277\) 29.1380 1.75073 0.875367 0.483459i \(-0.160620\pi\)
0.875367 + 0.483459i \(0.160620\pi\)
\(278\) 1.82169 0.109258
\(279\) 0 0
\(280\) −15.2298 −0.910156
\(281\) 21.6594 1.29209 0.646047 0.763298i \(-0.276421\pi\)
0.646047 + 0.763298i \(0.276421\pi\)
\(282\) 0 0
\(283\) −16.1608 −0.960660 −0.480330 0.877088i \(-0.659483\pi\)
−0.480330 + 0.877088i \(0.659483\pi\)
\(284\) −29.5354 −1.75260
\(285\) 0 0
\(286\) −15.0085 −0.887471
\(287\) 25.5872 1.51037
\(288\) 0 0
\(289\) −4.38903 −0.258178
\(290\) −2.57501 −0.151210
\(291\) 0 0
\(292\) −15.0968 −0.883473
\(293\) 16.5348 0.965975 0.482988 0.875627i \(-0.339552\pi\)
0.482988 + 0.875627i \(0.339552\pi\)
\(294\) 0 0
\(295\) −8.49652 −0.494687
\(296\) 6.56756 0.381732
\(297\) 0 0
\(298\) −43.7573 −2.53479
\(299\) −5.70825 −0.330117
\(300\) 0 0
\(301\) 1.98834 0.114606
\(302\) 20.2562 1.16561
\(303\) 0 0
\(304\) −9.72901 −0.557997
\(305\) −10.8743 −0.622659
\(306\) 0 0
\(307\) −25.3923 −1.44922 −0.724608 0.689161i \(-0.757979\pi\)
−0.724608 + 0.689161i \(0.757979\pi\)
\(308\) −39.1187 −2.22899
\(309\) 0 0
\(310\) 13.3620 0.758909
\(311\) 16.8950 0.958030 0.479015 0.877807i \(-0.340994\pi\)
0.479015 + 0.877807i \(0.340994\pi\)
\(312\) 0 0
\(313\) −22.1978 −1.25469 −0.627347 0.778740i \(-0.715859\pi\)
−0.627347 + 0.778740i \(0.715859\pi\)
\(314\) 25.3791 1.43223
\(315\) 0 0
\(316\) 29.2927 1.64785
\(317\) −26.1161 −1.46683 −0.733414 0.679783i \(-0.762074\pi\)
−0.733414 + 0.679783i \(0.762074\pi\)
\(318\) 0 0
\(319\) −3.75744 −0.210376
\(320\) 3.00121 0.167773
\(321\) 0 0
\(322\) −21.3041 −1.18723
\(323\) −4.22270 −0.234957
\(324\) 0 0
\(325\) −1.55119 −0.0860447
\(326\) 42.6900 2.36438
\(327\) 0 0
\(328\) −77.0948 −4.25685
\(329\) 25.2369 1.39135
\(330\) 0 0
\(331\) 24.3439 1.33806 0.669030 0.743236i \(-0.266710\pi\)
0.669030 + 0.743236i \(0.266710\pi\)
\(332\) 41.8582 2.29727
\(333\) 0 0
\(334\) −12.2148 −0.668366
\(335\) −4.05179 −0.221373
\(336\) 0 0
\(337\) −23.5099 −1.28067 −0.640333 0.768098i \(-0.721204\pi\)
−0.640333 + 0.768098i \(0.721204\pi\)
\(338\) −27.2792 −1.48379
\(339\) 0 0
\(340\) 16.4445 0.891826
\(341\) 19.4977 1.05586
\(342\) 0 0
\(343\) 20.1114 1.08591
\(344\) −5.99092 −0.323009
\(345\) 0 0
\(346\) −51.0369 −2.74376
\(347\) −29.9492 −1.60776 −0.803879 0.594793i \(-0.797234\pi\)
−0.803879 + 0.594793i \(0.797234\pi\)
\(348\) 0 0
\(349\) −17.0927 −0.914951 −0.457476 0.889222i \(-0.651246\pi\)
−0.457476 + 0.889222i \(0.651246\pi\)
\(350\) −5.78930 −0.309451
\(351\) 0 0
\(352\) 28.2572 1.50612
\(353\) −6.40124 −0.340704 −0.170352 0.985383i \(-0.554490\pi\)
−0.170352 + 0.985383i \(0.554490\pi\)
\(354\) 0 0
\(355\) −6.37818 −0.338519
\(356\) −6.79400 −0.360082
\(357\) 0 0
\(358\) 19.1075 1.00986
\(359\) −29.2509 −1.54380 −0.771902 0.635741i \(-0.780694\pi\)
−0.771902 + 0.635741i \(0.780694\pi\)
\(360\) 0 0
\(361\) −17.5861 −0.925582
\(362\) 51.0911 2.68529
\(363\) 0 0
\(364\) 16.1494 0.846461
\(365\) −3.26017 −0.170645
\(366\) 0 0
\(367\) −13.2919 −0.693832 −0.346916 0.937896i \(-0.612771\pi\)
−0.346916 + 0.937896i \(0.612771\pi\)
\(368\) 30.1086 1.56952
\(369\) 0 0
\(370\) 2.49652 0.129788
\(371\) −23.9591 −1.24389
\(372\) 0 0
\(373\) −19.7309 −1.02163 −0.510814 0.859691i \(-0.670656\pi\)
−0.510814 + 0.859691i \(0.670656\pi\)
\(374\) 34.3594 1.77668
\(375\) 0 0
\(376\) −76.0391 −3.92142
\(377\) 1.55119 0.0798905
\(378\) 0 0
\(379\) 25.4806 1.30885 0.654424 0.756128i \(-0.272911\pi\)
0.654424 + 0.756128i \(0.272911\pi\)
\(380\) −5.50631 −0.282468
\(381\) 0 0
\(382\) 14.5851 0.746239
\(383\) −0.542784 −0.0277350 −0.0138675 0.999904i \(-0.504414\pi\)
−0.0138675 + 0.999904i \(0.504414\pi\)
\(384\) 0 0
\(385\) −8.44770 −0.430535
\(386\) 38.0833 1.93839
\(387\) 0 0
\(388\) 57.4171 2.91491
\(389\) 19.9301 1.01050 0.505249 0.862974i \(-0.331401\pi\)
0.505249 + 0.862974i \(0.331401\pi\)
\(390\) 0 0
\(391\) 13.0681 0.660881
\(392\) −13.1777 −0.665576
\(393\) 0 0
\(394\) 69.8726 3.52013
\(395\) 6.32579 0.318285
\(396\) 0 0
\(397\) 9.40286 0.471916 0.235958 0.971763i \(-0.424177\pi\)
0.235958 + 0.971763i \(0.424177\pi\)
\(398\) −24.5533 −1.23075
\(399\) 0 0
\(400\) 8.18188 0.409094
\(401\) −9.37578 −0.468204 −0.234102 0.972212i \(-0.575215\pi\)
−0.234102 + 0.972212i \(0.575215\pi\)
\(402\) 0 0
\(403\) −8.04928 −0.400963
\(404\) −15.9850 −0.795282
\(405\) 0 0
\(406\) 5.78930 0.287318
\(407\) 3.64291 0.180572
\(408\) 0 0
\(409\) 19.7204 0.975111 0.487556 0.873092i \(-0.337889\pi\)
0.487556 + 0.873092i \(0.337889\pi\)
\(410\) −29.3060 −1.44732
\(411\) 0 0
\(412\) 84.2670 4.15154
\(413\) 19.1024 0.939967
\(414\) 0 0
\(415\) 9.03930 0.443722
\(416\) −11.6655 −0.571948
\(417\) 0 0
\(418\) −11.5050 −0.562728
\(419\) 6.24026 0.304857 0.152428 0.988315i \(-0.451291\pi\)
0.152428 + 0.988315i \(0.451291\pi\)
\(420\) 0 0
\(421\) 6.31722 0.307882 0.153941 0.988080i \(-0.450803\pi\)
0.153941 + 0.988080i \(0.450803\pi\)
\(422\) 55.5500 2.70413
\(423\) 0 0
\(424\) 72.1891 3.50581
\(425\) 3.55119 0.172258
\(426\) 0 0
\(427\) 24.4482 1.18313
\(428\) −37.4122 −1.80839
\(429\) 0 0
\(430\) −2.27732 −0.109822
\(431\) 37.8006 1.82079 0.910396 0.413737i \(-0.135777\pi\)
0.910396 + 0.413737i \(0.135777\pi\)
\(432\) 0 0
\(433\) 37.8447 1.81870 0.909350 0.416032i \(-0.136580\pi\)
0.909350 + 0.416032i \(0.136580\pi\)
\(434\) −30.0412 −1.44202
\(435\) 0 0
\(436\) −64.8825 −3.10731
\(437\) −4.37575 −0.209321
\(438\) 0 0
\(439\) −15.5318 −0.741291 −0.370646 0.928774i \(-0.620864\pi\)
−0.370646 + 0.928774i \(0.620864\pi\)
\(440\) 25.4531 1.21343
\(441\) 0 0
\(442\) −14.1847 −0.674696
\(443\) 5.24223 0.249066 0.124533 0.992215i \(-0.460257\pi\)
0.124533 + 0.992215i \(0.460257\pi\)
\(444\) 0 0
\(445\) −1.46717 −0.0695505
\(446\) 57.9738 2.74514
\(447\) 0 0
\(448\) −6.74749 −0.318789
\(449\) 28.0123 1.32198 0.660992 0.750393i \(-0.270136\pi\)
0.660992 + 0.750393i \(0.270136\pi\)
\(450\) 0 0
\(451\) −42.7631 −2.01364
\(452\) 3.14188 0.147781
\(453\) 0 0
\(454\) 21.5802 1.01281
\(455\) 3.48748 0.163496
\(456\) 0 0
\(457\) 1.90391 0.0890610 0.0445305 0.999008i \(-0.485821\pi\)
0.0445305 + 0.999008i \(0.485821\pi\)
\(458\) −29.7393 −1.38963
\(459\) 0 0
\(460\) 17.0405 0.794518
\(461\) −30.5294 −1.42190 −0.710949 0.703244i \(-0.751734\pi\)
−0.710949 + 0.703244i \(0.751734\pi\)
\(462\) 0 0
\(463\) 32.9230 1.53006 0.765030 0.643995i \(-0.222724\pi\)
0.765030 + 0.643995i \(0.222724\pi\)
\(464\) −8.18188 −0.379834
\(465\) 0 0
\(466\) −22.7971 −1.05605
\(467\) 4.42775 0.204892 0.102446 0.994739i \(-0.467333\pi\)
0.102446 + 0.994739i \(0.467333\pi\)
\(468\) 0 0
\(469\) 9.10947 0.420636
\(470\) −28.9047 −1.33327
\(471\) 0 0
\(472\) −57.5558 −2.64922
\(473\) −3.32305 −0.152794
\(474\) 0 0
\(475\) −1.18909 −0.0545593
\(476\) −36.9714 −1.69458
\(477\) 0 0
\(478\) 35.9307 1.64343
\(479\) 8.27071 0.377898 0.188949 0.981987i \(-0.439492\pi\)
0.188949 + 0.981987i \(0.439492\pi\)
\(480\) 0 0
\(481\) −1.50391 −0.0685723
\(482\) −62.3508 −2.84000
\(483\) 0 0
\(484\) 14.4402 0.656371
\(485\) 12.3993 0.563022
\(486\) 0 0
\(487\) 39.9284 1.80933 0.904665 0.426124i \(-0.140121\pi\)
0.904665 + 0.426124i \(0.140121\pi\)
\(488\) −73.6628 −3.33456
\(489\) 0 0
\(490\) −5.00924 −0.226294
\(491\) 33.3896 1.50685 0.753427 0.657532i \(-0.228399\pi\)
0.753427 + 0.657532i \(0.228399\pi\)
\(492\) 0 0
\(493\) −3.55119 −0.159938
\(494\) 4.74964 0.213696
\(495\) 0 0
\(496\) 42.4565 1.90635
\(497\) 14.3398 0.643229
\(498\) 0 0
\(499\) −3.12737 −0.140000 −0.0700002 0.997547i \(-0.522300\pi\)
−0.0700002 + 0.997547i \(0.522300\pi\)
\(500\) 4.63069 0.207091
\(501\) 0 0
\(502\) −26.0439 −1.16240
\(503\) 17.2563 0.769419 0.384710 0.923038i \(-0.374302\pi\)
0.384710 + 0.923038i \(0.374302\pi\)
\(504\) 0 0
\(505\) −3.45196 −0.153610
\(506\) 35.6048 1.58283
\(507\) 0 0
\(508\) −38.8944 −1.72566
\(509\) 4.71879 0.209157 0.104578 0.994517i \(-0.466651\pi\)
0.104578 + 0.994517i \(0.466651\pi\)
\(510\) 0 0
\(511\) 7.32970 0.324247
\(512\) −49.3183 −2.17958
\(513\) 0 0
\(514\) −46.9398 −2.07043
\(515\) 18.1975 0.801879
\(516\) 0 0
\(517\) −42.1775 −1.85496
\(518\) −5.61283 −0.246613
\(519\) 0 0
\(520\) −10.5078 −0.460800
\(521\) −40.0385 −1.75412 −0.877060 0.480381i \(-0.840498\pi\)
−0.877060 + 0.480381i \(0.840498\pi\)
\(522\) 0 0
\(523\) −5.38694 −0.235555 −0.117777 0.993040i \(-0.537577\pi\)
−0.117777 + 0.993040i \(0.537577\pi\)
\(524\) −34.0030 −1.48543
\(525\) 0 0
\(526\) 10.9843 0.478939
\(527\) 18.4275 0.802713
\(528\) 0 0
\(529\) −9.45826 −0.411229
\(530\) 27.4412 1.19197
\(531\) 0 0
\(532\) 12.3796 0.536725
\(533\) 17.6540 0.764679
\(534\) 0 0
\(535\) −8.07919 −0.349294
\(536\) −27.4470 −1.18553
\(537\) 0 0
\(538\) 20.8799 0.900198
\(539\) −7.30945 −0.314840
\(540\) 0 0
\(541\) 35.9892 1.54730 0.773649 0.633614i \(-0.218429\pi\)
0.773649 + 0.633614i \(0.218429\pi\)
\(542\) 69.3345 2.97817
\(543\) 0 0
\(544\) 26.7062 1.14502
\(545\) −14.0114 −0.600184
\(546\) 0 0
\(547\) 24.2745 1.03790 0.518951 0.854804i \(-0.326323\pi\)
0.518951 + 0.854804i \(0.326323\pi\)
\(548\) −8.35157 −0.356761
\(549\) 0 0
\(550\) 9.67546 0.412563
\(551\) 1.18909 0.0506570
\(552\) 0 0
\(553\) −14.2220 −0.604782
\(554\) 75.0307 3.18775
\(555\) 0 0
\(556\) 3.27598 0.138933
\(557\) 4.93097 0.208932 0.104466 0.994528i \(-0.466687\pi\)
0.104466 + 0.994528i \(0.466687\pi\)
\(558\) 0 0
\(559\) 1.37186 0.0580236
\(560\) −18.3950 −0.777330
\(561\) 0 0
\(562\) 55.7733 2.35266
\(563\) 34.7020 1.46252 0.731258 0.682101i \(-0.238933\pi\)
0.731258 + 0.682101i \(0.238933\pi\)
\(564\) 0 0
\(565\) 0.678491 0.0285443
\(566\) −41.6142 −1.74918
\(567\) 0 0
\(568\) −43.2061 −1.81289
\(569\) −19.9633 −0.836903 −0.418452 0.908239i \(-0.637427\pi\)
−0.418452 + 0.908239i \(0.637427\pi\)
\(570\) 0 0
\(571\) −7.22542 −0.302375 −0.151187 0.988505i \(-0.548310\pi\)
−0.151187 + 0.988505i \(0.548310\pi\)
\(572\) −26.9900 −1.12851
\(573\) 0 0
\(574\) 65.8875 2.75009
\(575\) 3.67991 0.153463
\(576\) 0 0
\(577\) 17.6693 0.735581 0.367791 0.929909i \(-0.380114\pi\)
0.367791 + 0.929909i \(0.380114\pi\)
\(578\) −11.3018 −0.470093
\(579\) 0 0
\(580\) −4.63069 −0.192279
\(581\) −20.3227 −0.843128
\(582\) 0 0
\(583\) 40.0420 1.65837
\(584\) −22.0845 −0.913864
\(585\) 0 0
\(586\) 42.5774 1.75886
\(587\) 13.1365 0.542203 0.271102 0.962551i \(-0.412612\pi\)
0.271102 + 0.962551i \(0.412612\pi\)
\(588\) 0 0
\(589\) −6.17031 −0.254243
\(590\) −21.8786 −0.900729
\(591\) 0 0
\(592\) 7.93248 0.326023
\(593\) 11.3675 0.466807 0.233403 0.972380i \(-0.425014\pi\)
0.233403 + 0.972380i \(0.425014\pi\)
\(594\) 0 0
\(595\) −7.98400 −0.327312
\(596\) −78.6894 −3.22324
\(597\) 0 0
\(598\) −14.6988 −0.601079
\(599\) −8.98828 −0.367251 −0.183626 0.982996i \(-0.558783\pi\)
−0.183626 + 0.982996i \(0.558783\pi\)
\(600\) 0 0
\(601\) −5.15704 −0.210360 −0.105180 0.994453i \(-0.533542\pi\)
−0.105180 + 0.994453i \(0.533542\pi\)
\(602\) 5.12001 0.208676
\(603\) 0 0
\(604\) 36.4271 1.48220
\(605\) 3.11836 0.126780
\(606\) 0 0
\(607\) −36.3436 −1.47514 −0.737570 0.675271i \(-0.764027\pi\)
−0.737570 + 0.675271i \(0.764027\pi\)
\(608\) −8.94238 −0.362661
\(609\) 0 0
\(610\) −28.0014 −1.13374
\(611\) 17.4122 0.704423
\(612\) 0 0
\(613\) 18.9943 0.767171 0.383585 0.923505i \(-0.374689\pi\)
0.383585 + 0.923505i \(0.374689\pi\)
\(614\) −65.3855 −2.63874
\(615\) 0 0
\(616\) −57.2251 −2.30567
\(617\) −24.5060 −0.986574 −0.493287 0.869867i \(-0.664205\pi\)
−0.493287 + 0.869867i \(0.664205\pi\)
\(618\) 0 0
\(619\) 12.5314 0.503680 0.251840 0.967769i \(-0.418964\pi\)
0.251840 + 0.967769i \(0.418964\pi\)
\(620\) 24.0291 0.965030
\(621\) 0 0
\(622\) 43.5049 1.74439
\(623\) 3.29858 0.132155
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −57.1596 −2.28456
\(627\) 0 0
\(628\) 45.6396 1.82122
\(629\) 3.44294 0.137279
\(630\) 0 0
\(631\) 17.8019 0.708681 0.354340 0.935116i \(-0.384705\pi\)
0.354340 + 0.935116i \(0.384705\pi\)
\(632\) 42.8512 1.70453
\(633\) 0 0
\(634\) −67.2493 −2.67081
\(635\) −8.39928 −0.333315
\(636\) 0 0
\(637\) 3.01758 0.119561
\(638\) −9.67546 −0.383055
\(639\) 0 0
\(640\) −7.31254 −0.289053
\(641\) 20.3973 0.805644 0.402822 0.915278i \(-0.368029\pi\)
0.402822 + 0.915278i \(0.368029\pi\)
\(642\) 0 0
\(643\) −23.6531 −0.932787 −0.466394 0.884577i \(-0.654447\pi\)
−0.466394 + 0.884577i \(0.654447\pi\)
\(644\) −38.3115 −1.50968
\(645\) 0 0
\(646\) −10.8735 −0.427812
\(647\) −17.5789 −0.691096 −0.345548 0.938401i \(-0.612307\pi\)
−0.345548 + 0.938401i \(0.612307\pi\)
\(648\) 0 0
\(649\) −31.9252 −1.25317
\(650\) −3.99434 −0.156671
\(651\) 0 0
\(652\) 76.7702 3.00655
\(653\) 10.4035 0.407121 0.203560 0.979062i \(-0.434749\pi\)
0.203560 + 0.979062i \(0.434749\pi\)
\(654\) 0 0
\(655\) −7.34298 −0.286914
\(656\) −93.1172 −3.63562
\(657\) 0 0
\(658\) 64.9852 2.53339
\(659\) −43.5638 −1.69700 −0.848502 0.529192i \(-0.822495\pi\)
−0.848502 + 0.529192i \(0.822495\pi\)
\(660\) 0 0
\(661\) 18.2404 0.709469 0.354734 0.934967i \(-0.384571\pi\)
0.354734 + 0.934967i \(0.384571\pi\)
\(662\) 62.6857 2.43635
\(663\) 0 0
\(664\) 61.2327 2.37629
\(665\) 2.67339 0.103670
\(666\) 0 0
\(667\) −3.67991 −0.142487
\(668\) −21.9661 −0.849895
\(669\) 0 0
\(670\) −10.4334 −0.403077
\(671\) −40.8595 −1.57736
\(672\) 0 0
\(673\) −25.8626 −0.996929 −0.498464 0.866910i \(-0.666103\pi\)
−0.498464 + 0.866910i \(0.666103\pi\)
\(674\) −60.5383 −2.33185
\(675\) 0 0
\(676\) −49.0566 −1.88679
\(677\) 30.3287 1.16563 0.582813 0.812606i \(-0.301952\pi\)
0.582813 + 0.812606i \(0.301952\pi\)
\(678\) 0 0
\(679\) −27.8768 −1.06981
\(680\) 24.0559 0.922503
\(681\) 0 0
\(682\) 50.2068 1.92252
\(683\) 39.4637 1.51004 0.755018 0.655704i \(-0.227628\pi\)
0.755018 + 0.655704i \(0.227628\pi\)
\(684\) 0 0
\(685\) −1.80353 −0.0689092
\(686\) 51.7871 1.97724
\(687\) 0 0
\(688\) −7.23599 −0.275870
\(689\) −16.5306 −0.629766
\(690\) 0 0
\(691\) −24.5853 −0.935269 −0.467635 0.883922i \(-0.654894\pi\)
−0.467635 + 0.883922i \(0.654894\pi\)
\(692\) −91.7805 −3.48897
\(693\) 0 0
\(694\) −77.1196 −2.92742
\(695\) 0.707451 0.0268351
\(696\) 0 0
\(697\) −40.4158 −1.53086
\(698\) −44.0139 −1.66595
\(699\) 0 0
\(700\) −10.4110 −0.393498
\(701\) 34.8635 1.31678 0.658388 0.752678i \(-0.271238\pi\)
0.658388 + 0.752678i \(0.271238\pi\)
\(702\) 0 0
\(703\) −1.15285 −0.0434804
\(704\) 11.2769 0.425012
\(705\) 0 0
\(706\) −16.4833 −0.620356
\(707\) 7.76091 0.291879
\(708\) 0 0
\(709\) −24.4622 −0.918698 −0.459349 0.888256i \(-0.651917\pi\)
−0.459349 + 0.888256i \(0.651917\pi\)
\(710\) −16.4239 −0.616378
\(711\) 0 0
\(712\) −9.93868 −0.372468
\(713\) 19.0954 0.715128
\(714\) 0 0
\(715\) −5.82851 −0.217974
\(716\) 34.3613 1.28414
\(717\) 0 0
\(718\) −75.3214 −2.81097
\(719\) 27.1333 1.01190 0.505951 0.862562i \(-0.331142\pi\)
0.505951 + 0.862562i \(0.331142\pi\)
\(720\) 0 0
\(721\) −40.9128 −1.52367
\(722\) −45.2843 −1.68531
\(723\) 0 0
\(724\) 91.8780 3.41462
\(725\) −1.00000 −0.0371391
\(726\) 0 0
\(727\) 33.9854 1.26045 0.630224 0.776413i \(-0.282963\pi\)
0.630224 + 0.776413i \(0.282963\pi\)
\(728\) 23.6244 0.875578
\(729\) 0 0
\(730\) −8.39496 −0.310712
\(731\) −3.14065 −0.116161
\(732\) 0 0
\(733\) 17.2131 0.635779 0.317889 0.948128i \(-0.397026\pi\)
0.317889 + 0.948128i \(0.397026\pi\)
\(734\) −34.2268 −1.26333
\(735\) 0 0
\(736\) 27.6742 1.02008
\(737\) −15.2244 −0.560796
\(738\) 0 0
\(739\) −12.5603 −0.462039 −0.231019 0.972949i \(-0.574206\pi\)
−0.231019 + 0.972949i \(0.574206\pi\)
\(740\) 4.48953 0.165038
\(741\) 0 0
\(742\) −61.6949 −2.26489
\(743\) −43.0323 −1.57870 −0.789350 0.613943i \(-0.789582\pi\)
−0.789350 + 0.613943i \(0.789582\pi\)
\(744\) 0 0
\(745\) −16.9930 −0.622577
\(746\) −50.8073 −1.86019
\(747\) 0 0
\(748\) 61.7891 2.25923
\(749\) 18.1641 0.663702
\(750\) 0 0
\(751\) −12.4133 −0.452969 −0.226485 0.974015i \(-0.572723\pi\)
−0.226485 + 0.974015i \(0.572723\pi\)
\(752\) −91.8421 −3.34914
\(753\) 0 0
\(754\) 3.99434 0.145465
\(755\) 7.86646 0.286290
\(756\) 0 0
\(757\) 18.0439 0.655815 0.327907 0.944710i \(-0.393657\pi\)
0.327907 + 0.944710i \(0.393657\pi\)
\(758\) 65.6127 2.38316
\(759\) 0 0
\(760\) −8.05497 −0.292184
\(761\) 8.20477 0.297423 0.148711 0.988881i \(-0.452487\pi\)
0.148711 + 0.988881i \(0.452487\pi\)
\(762\) 0 0
\(763\) 31.5013 1.14043
\(764\) 26.2286 0.948919
\(765\) 0 0
\(766\) −1.39768 −0.0505001
\(767\) 13.1797 0.475893
\(768\) 0 0
\(769\) −23.5524 −0.849320 −0.424660 0.905353i \(-0.639606\pi\)
−0.424660 + 0.905353i \(0.639606\pi\)
\(770\) −21.7529 −0.783921
\(771\) 0 0
\(772\) 68.4859 2.46486
\(773\) 27.2326 0.979487 0.489743 0.871867i \(-0.337090\pi\)
0.489743 + 0.871867i \(0.337090\pi\)
\(774\) 0 0
\(775\) 5.18909 0.186398
\(776\) 83.9933 3.01518
\(777\) 0 0
\(778\) 51.3203 1.83992
\(779\) 13.5330 0.484868
\(780\) 0 0
\(781\) −23.9657 −0.857559
\(782\) 33.6504 1.20334
\(783\) 0 0
\(784\) −15.9164 −0.568444
\(785\) 9.85591 0.351773
\(786\) 0 0
\(787\) 20.2585 0.722137 0.361069 0.932539i \(-0.382412\pi\)
0.361069 + 0.932539i \(0.382412\pi\)
\(788\) 125.653 4.47621
\(789\) 0 0
\(790\) 16.2890 0.579536
\(791\) −1.52542 −0.0542378
\(792\) 0 0
\(793\) 16.8681 0.599004
\(794\) 24.2125 0.859269
\(795\) 0 0
\(796\) −44.1546 −1.56502
\(797\) −27.8574 −0.986761 −0.493381 0.869814i \(-0.664239\pi\)
−0.493381 + 0.869814i \(0.664239\pi\)
\(798\) 0 0
\(799\) −39.8624 −1.41023
\(800\) 7.52034 0.265884
\(801\) 0 0
\(802\) −24.1427 −0.852510
\(803\) −12.2499 −0.432289
\(804\) 0 0
\(805\) −8.27340 −0.291599
\(806\) −20.7270 −0.730077
\(807\) 0 0
\(808\) −23.3838 −0.822638
\(809\) 17.5060 0.615477 0.307739 0.951471i \(-0.400428\pi\)
0.307739 + 0.951471i \(0.400428\pi\)
\(810\) 0 0
\(811\) 39.1690 1.37541 0.687704 0.725991i \(-0.258619\pi\)
0.687704 + 0.725991i \(0.258619\pi\)
\(812\) 10.4110 0.365354
\(813\) 0 0
\(814\) 9.38053 0.328787
\(815\) 16.5786 0.580722
\(816\) 0 0
\(817\) 1.05162 0.0367917
\(818\) 50.7803 1.77549
\(819\) 0 0
\(820\) −52.7014 −1.84041
\(821\) −19.8338 −0.692203 −0.346101 0.938197i \(-0.612495\pi\)
−0.346101 + 0.938197i \(0.612495\pi\)
\(822\) 0 0
\(823\) 10.3727 0.361568 0.180784 0.983523i \(-0.442136\pi\)
0.180784 + 0.983523i \(0.442136\pi\)
\(824\) 123.271 4.29434
\(825\) 0 0
\(826\) 49.1889 1.71150
\(827\) 3.35272 0.116586 0.0582928 0.998300i \(-0.481434\pi\)
0.0582928 + 0.998300i \(0.481434\pi\)
\(828\) 0 0
\(829\) −43.0572 −1.49544 −0.747719 0.664015i \(-0.768851\pi\)
−0.747719 + 0.664015i \(0.768851\pi\)
\(830\) 23.2763 0.807933
\(831\) 0 0
\(832\) −4.65545 −0.161399
\(833\) −6.90823 −0.239356
\(834\) 0 0
\(835\) −4.74360 −0.164159
\(836\) −20.6896 −0.715566
\(837\) 0 0
\(838\) 16.0688 0.555086
\(839\) −39.3736 −1.35933 −0.679664 0.733523i \(-0.737875\pi\)
−0.679664 + 0.733523i \(0.737875\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 16.2669 0.560595
\(843\) 0 0
\(844\) 99.8965 3.43858
\(845\) −10.5938 −0.364438
\(846\) 0 0
\(847\) −7.01089 −0.240897
\(848\) 87.1919 2.99418
\(849\) 0 0
\(850\) 9.14436 0.313649
\(851\) 3.56774 0.122301
\(852\) 0 0
\(853\) −45.2743 −1.55016 −0.775081 0.631862i \(-0.782291\pi\)
−0.775081 + 0.631862i \(0.782291\pi\)
\(854\) 62.9544 2.15426
\(855\) 0 0
\(856\) −54.7288 −1.87059
\(857\) 24.1619 0.825353 0.412677 0.910878i \(-0.364594\pi\)
0.412677 + 0.910878i \(0.364594\pi\)
\(858\) 0 0
\(859\) −22.3680 −0.763185 −0.381593 0.924331i \(-0.624624\pi\)
−0.381593 + 0.924331i \(0.624624\pi\)
\(860\) −4.09534 −0.139650
\(861\) 0 0
\(862\) 97.3371 3.31531
\(863\) −2.98467 −0.101599 −0.0507997 0.998709i \(-0.516177\pi\)
−0.0507997 + 0.998709i \(0.516177\pi\)
\(864\) 0 0
\(865\) −19.8201 −0.673902
\(866\) 97.4505 3.31150
\(867\) 0 0
\(868\) −54.0236 −1.83368
\(869\) 23.7688 0.806301
\(870\) 0 0
\(871\) 6.28510 0.212963
\(872\) −94.9141 −3.21420
\(873\) 0 0
\(874\) −11.2676 −0.381133
\(875\) −2.24826 −0.0760051
\(876\) 0 0
\(877\) 29.5037 0.996269 0.498135 0.867100i \(-0.334019\pi\)
0.498135 + 0.867100i \(0.334019\pi\)
\(878\) −39.9945 −1.34975
\(879\) 0 0
\(880\) 30.7429 1.03634
\(881\) −52.0937 −1.75508 −0.877541 0.479502i \(-0.840817\pi\)
−0.877541 + 0.479502i \(0.840817\pi\)
\(882\) 0 0
\(883\) 22.2221 0.747832 0.373916 0.927463i \(-0.378015\pi\)
0.373916 + 0.927463i \(0.378015\pi\)
\(884\) −25.5085 −0.857944
\(885\) 0 0
\(886\) 13.4988 0.453502
\(887\) −38.6220 −1.29680 −0.648400 0.761300i \(-0.724562\pi\)
−0.648400 + 0.761300i \(0.724562\pi\)
\(888\) 0 0
\(889\) 18.8838 0.633341
\(890\) −3.77798 −0.126638
\(891\) 0 0
\(892\) 104.255 3.49072
\(893\) 13.3476 0.446662
\(894\) 0 0
\(895\) 7.42036 0.248035
\(896\) 16.4405 0.549238
\(897\) 0 0
\(898\) 72.1321 2.40708
\(899\) −5.18909 −0.173066
\(900\) 0 0
\(901\) 37.8440 1.26077
\(902\) −110.116 −3.66645
\(903\) 0 0
\(904\) 4.59613 0.152865
\(905\) 19.8411 0.659541
\(906\) 0 0
\(907\) −29.7861 −0.989030 −0.494515 0.869169i \(-0.664654\pi\)
−0.494515 + 0.869169i \(0.664654\pi\)
\(908\) 38.8080 1.28789
\(909\) 0 0
\(910\) 8.98031 0.297694
\(911\) −53.7163 −1.77970 −0.889850 0.456254i \(-0.849191\pi\)
−0.889850 + 0.456254i \(0.849191\pi\)
\(912\) 0 0
\(913\) 33.9647 1.12407
\(914\) 4.90258 0.162163
\(915\) 0 0
\(916\) −53.4807 −1.76705
\(917\) 16.5089 0.545173
\(918\) 0 0
\(919\) 52.0358 1.71650 0.858251 0.513231i \(-0.171551\pi\)
0.858251 + 0.513231i \(0.171551\pi\)
\(920\) 24.9279 0.821848
\(921\) 0 0
\(922\) −78.6137 −2.58900
\(923\) 9.89379 0.325658
\(924\) 0 0
\(925\) 0.969518 0.0318775
\(926\) 84.7770 2.78595
\(927\) 0 0
\(928\) −7.52034 −0.246867
\(929\) 52.5081 1.72273 0.861367 0.507982i \(-0.169609\pi\)
0.861367 + 0.507982i \(0.169609\pi\)
\(930\) 0 0
\(931\) 2.31317 0.0758112
\(932\) −40.9963 −1.34288
\(933\) 0 0
\(934\) 11.4015 0.373068
\(935\) 13.3434 0.436376
\(936\) 0 0
\(937\) 46.1947 1.50912 0.754558 0.656233i \(-0.227851\pi\)
0.754558 + 0.656233i \(0.227851\pi\)
\(938\) 23.4570 0.765898
\(939\) 0 0
\(940\) −51.9797 −1.69539
\(941\) −29.8642 −0.973545 −0.486773 0.873529i \(-0.661826\pi\)
−0.486773 + 0.873529i \(0.661826\pi\)
\(942\) 0 0
\(943\) −41.8807 −1.36382
\(944\) −69.5175 −2.26260
\(945\) 0 0
\(946\) −8.55690 −0.278209
\(947\) −11.7523 −0.381898 −0.190949 0.981600i \(-0.561157\pi\)
−0.190949 + 0.981600i \(0.561157\pi\)
\(948\) 0 0
\(949\) 5.05714 0.164162
\(950\) −3.06193 −0.0993420
\(951\) 0 0
\(952\) −54.0840 −1.75287
\(953\) 17.1653 0.556040 0.278020 0.960575i \(-0.410322\pi\)
0.278020 + 0.960575i \(0.410322\pi\)
\(954\) 0 0
\(955\) 5.66409 0.183286
\(956\) 64.6147 2.08979
\(957\) 0 0
\(958\) 21.2972 0.688081
\(959\) 4.05480 0.130936
\(960\) 0 0
\(961\) −4.07332 −0.131397
\(962\) −3.87258 −0.124857
\(963\) 0 0
\(964\) −112.126 −3.61135
\(965\) 14.7896 0.476093
\(966\) 0 0
\(967\) 20.2076 0.649831 0.324916 0.945743i \(-0.394664\pi\)
0.324916 + 0.945743i \(0.394664\pi\)
\(968\) 21.1239 0.678949
\(969\) 0 0
\(970\) 31.9283 1.02516
\(971\) −24.7827 −0.795315 −0.397658 0.917534i \(-0.630177\pi\)
−0.397658 + 0.917534i \(0.630177\pi\)
\(972\) 0 0
\(973\) −1.59053 −0.0509902
\(974\) 102.816 3.29444
\(975\) 0 0
\(976\) −88.9720 −2.84792
\(977\) −38.5423 −1.23308 −0.616539 0.787324i \(-0.711466\pi\)
−0.616539 + 0.787324i \(0.711466\pi\)
\(978\) 0 0
\(979\) −5.51281 −0.176190
\(980\) −9.00820 −0.287756
\(981\) 0 0
\(982\) 85.9787 2.74369
\(983\) −13.0762 −0.417065 −0.208532 0.978015i \(-0.566869\pi\)
−0.208532 + 0.978015i \(0.566869\pi\)
\(984\) 0 0
\(985\) 27.1349 0.864589
\(986\) −9.14436 −0.291216
\(987\) 0 0
\(988\) 8.54135 0.271737
\(989\) −3.25449 −0.103487
\(990\) 0 0
\(991\) −36.8186 −1.16958 −0.584791 0.811184i \(-0.698823\pi\)
−0.584791 + 0.811184i \(0.698823\pi\)
\(992\) 39.0237 1.23900
\(993\) 0 0
\(994\) 36.9252 1.17120
\(995\) −9.53523 −0.302287
\(996\) 0 0
\(997\) −18.5570 −0.587707 −0.293854 0.955850i \(-0.594938\pi\)
−0.293854 + 0.955850i \(0.594938\pi\)
\(998\) −8.05302 −0.254914
\(999\) 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 1305.2.a.t.1.7 yes 7
3.2 odd 2 1305.2.a.s.1.1 7
5.4 even 2 6525.2.a.bv.1.1 7
15.14 odd 2 6525.2.a.bw.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1305.2.a.s.1.1 7 3.2 odd 2
1305.2.a.t.1.7 yes 7 1.1 even 1 trivial
6525.2.a.bv.1.1 7 5.4 even 2
6525.2.a.bw.1.7 7 15.14 odd 2