Properties

Label 7623.2.a.cx.1.2
Level $7623$
Weight $2$
Character 7623.1
Self dual yes
Analytic conductor $60.870$
Analytic rank $0$
Dimension $10$
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 231)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.63994\) 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)
 
\(f(q)\) \(=\) \(q-2.63994 q^{2} +4.96928 q^{4} -3.08369 q^{5} -1.00000 q^{7} -7.83871 q^{8} +O(q^{10})\) \(q-2.63994 q^{2} +4.96928 q^{4} -3.08369 q^{5} -1.00000 q^{7} -7.83871 q^{8} +8.14075 q^{10} -5.64097 q^{13} +2.63994 q^{14} +10.7552 q^{16} +5.60085 q^{17} +0.122652 q^{19} -15.3237 q^{20} -1.67325 q^{23} +4.50913 q^{25} +14.8918 q^{26} -4.96928 q^{28} -8.85038 q^{29} +1.59773 q^{31} -12.7156 q^{32} -14.7859 q^{34} +3.08369 q^{35} +4.17268 q^{37} -0.323795 q^{38} +24.1721 q^{40} -3.48859 q^{41} -5.10698 q^{43} +4.41727 q^{46} +1.59400 q^{47} +1.00000 q^{49} -11.9038 q^{50} -28.0316 q^{52} +11.8564 q^{53} +7.83871 q^{56} +23.3645 q^{58} -6.61445 q^{59} -8.48918 q^{61} -4.21790 q^{62} +12.0580 q^{64} +17.3950 q^{65} -8.04949 q^{67} +27.8322 q^{68} -8.14075 q^{70} -6.24379 q^{71} +3.51005 q^{73} -11.0156 q^{74} +0.609494 q^{76} -9.39769 q^{79} -33.1656 q^{80} +9.20967 q^{82} +9.43386 q^{83} -17.2713 q^{85} +13.4821 q^{86} +8.45556 q^{89} +5.64097 q^{91} -8.31482 q^{92} -4.20807 q^{94} -0.378222 q^{95} -5.68478 q^{97} -2.63994 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 18 q^{4} - 5 q^{5} - 10 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 18 q^{4} - 5 q^{5} - 10 q^{7} - 3 q^{8} + 6 q^{10} - 6 q^{13} + 38 q^{16} + 8 q^{17} - 7 q^{20} + 31 q^{25} - q^{26} - 18 q^{28} - 14 q^{29} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 24 q^{37} - 8 q^{38} + 5 q^{40} + 19 q^{41} + 6 q^{43} + q^{46} - 15 q^{47} + 10 q^{49} - q^{50} + 25 q^{52} + q^{53} + 3 q^{56} + 11 q^{58} - 23 q^{59} + 11 q^{62} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} - 26 q^{71} + q^{73} - 39 q^{74} + 2 q^{76} - 5 q^{79} - 6 q^{80} + 5 q^{82} + 6 q^{83} + q^{85} + 41 q^{86} + 9 q^{89} + 6 q^{91} + 48 q^{92} - 42 q^{95} + 24 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63994 −1.86672 −0.933359 0.358943i \(-0.883137\pi\)
−0.933359 + 0.358943i \(0.883137\pi\)
\(3\) 0 0
\(4\) 4.96928 2.48464
\(5\) −3.08369 −1.37907 −0.689534 0.724254i \(-0.742184\pi\)
−0.689534 + 0.724254i \(0.742184\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −7.83871 −2.77140
\(9\) 0 0
\(10\) 8.14075 2.57433
\(11\) 0 0
\(12\) 0 0
\(13\) −5.64097 −1.56452 −0.782262 0.622949i \(-0.785934\pi\)
−0.782262 + 0.622949i \(0.785934\pi\)
\(14\) 2.63994 0.705553
\(15\) 0 0
\(16\) 10.7552 2.68879
\(17\) 5.60085 1.35841 0.679203 0.733951i \(-0.262326\pi\)
0.679203 + 0.733951i \(0.262326\pi\)
\(18\) 0 0
\(19\) 0.122652 0.0281384 0.0140692 0.999901i \(-0.495521\pi\)
0.0140692 + 0.999901i \(0.495521\pi\)
\(20\) −15.3237 −3.42648
\(21\) 0 0
\(22\) 0 0
\(23\) −1.67325 −0.348896 −0.174448 0.984666i \(-0.555814\pi\)
−0.174448 + 0.984666i \(0.555814\pi\)
\(24\) 0 0
\(25\) 4.50913 0.901826
\(26\) 14.8918 2.92053
\(27\) 0 0
\(28\) −4.96928 −0.939105
\(29\) −8.85038 −1.64347 −0.821737 0.569867i \(-0.806995\pi\)
−0.821737 + 0.569867i \(0.806995\pi\)
\(30\) 0 0
\(31\) 1.59773 0.286960 0.143480 0.989653i \(-0.454171\pi\)
0.143480 + 0.989653i \(0.454171\pi\)
\(32\) −12.7156 −2.24782
\(33\) 0 0
\(34\) −14.7859 −2.53576
\(35\) 3.08369 0.521238
\(36\) 0 0
\(37\) 4.17268 0.685984 0.342992 0.939338i \(-0.388560\pi\)
0.342992 + 0.939338i \(0.388560\pi\)
\(38\) −0.323795 −0.0525265
\(39\) 0 0
\(40\) 24.1721 3.82195
\(41\) −3.48859 −0.544827 −0.272413 0.962180i \(-0.587822\pi\)
−0.272413 + 0.962180i \(0.587822\pi\)
\(42\) 0 0
\(43\) −5.10698 −0.778807 −0.389403 0.921067i \(-0.627319\pi\)
−0.389403 + 0.921067i \(0.627319\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.41727 0.651290
\(47\) 1.59400 0.232509 0.116255 0.993219i \(-0.462911\pi\)
0.116255 + 0.993219i \(0.462911\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −11.9038 −1.68346
\(51\) 0 0
\(52\) −28.0316 −3.88728
\(53\) 11.8564 1.62861 0.814303 0.580440i \(-0.197119\pi\)
0.814303 + 0.580440i \(0.197119\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 7.83871 1.04749
\(57\) 0 0
\(58\) 23.3645 3.06790
\(59\) −6.61445 −0.861128 −0.430564 0.902560i \(-0.641685\pi\)
−0.430564 + 0.902560i \(0.641685\pi\)
\(60\) 0 0
\(61\) −8.48918 −1.08693 −0.543464 0.839432i \(-0.682888\pi\)
−0.543464 + 0.839432i \(0.682888\pi\)
\(62\) −4.21790 −0.535674
\(63\) 0 0
\(64\) 12.0580 1.50725
\(65\) 17.3950 2.15758
\(66\) 0 0
\(67\) −8.04949 −0.983402 −0.491701 0.870764i \(-0.663625\pi\)
−0.491701 + 0.870764i \(0.663625\pi\)
\(68\) 27.8322 3.37515
\(69\) 0 0
\(70\) −8.14075 −0.973006
\(71\) −6.24379 −0.741001 −0.370501 0.928832i \(-0.620814\pi\)
−0.370501 + 0.928832i \(0.620814\pi\)
\(72\) 0 0
\(73\) 3.51005 0.410820 0.205410 0.978676i \(-0.434147\pi\)
0.205410 + 0.978676i \(0.434147\pi\)
\(74\) −11.0156 −1.28054
\(75\) 0 0
\(76\) 0.609494 0.0699138
\(77\) 0 0
\(78\) 0 0
\(79\) −9.39769 −1.05732 −0.528661 0.848833i \(-0.677306\pi\)
−0.528661 + 0.848833i \(0.677306\pi\)
\(80\) −33.1656 −3.70803
\(81\) 0 0
\(82\) 9.20967 1.01704
\(83\) 9.43386 1.03550 0.517750 0.855532i \(-0.326770\pi\)
0.517750 + 0.855532i \(0.326770\pi\)
\(84\) 0 0
\(85\) −17.2713 −1.87333
\(86\) 13.4821 1.45381
\(87\) 0 0
\(88\) 0 0
\(89\) 8.45556 0.896288 0.448144 0.893961i \(-0.352085\pi\)
0.448144 + 0.893961i \(0.352085\pi\)
\(90\) 0 0
\(91\) 5.64097 0.591335
\(92\) −8.31482 −0.866880
\(93\) 0 0
\(94\) −4.20807 −0.434030
\(95\) −0.378222 −0.0388047
\(96\) 0 0
\(97\) −5.68478 −0.577202 −0.288601 0.957449i \(-0.593190\pi\)
−0.288601 + 0.957449i \(0.593190\pi\)
\(98\) −2.63994 −0.266674
\(99\) 0 0
\(100\) 22.4071 2.24071
\(101\) −16.8776 −1.67938 −0.839690 0.543066i \(-0.817263\pi\)
−0.839690 + 0.543066i \(0.817263\pi\)
\(102\) 0 0
\(103\) −13.2172 −1.30233 −0.651163 0.758938i \(-0.725719\pi\)
−0.651163 + 0.758938i \(0.725719\pi\)
\(104\) 44.2180 4.33593
\(105\) 0 0
\(106\) −31.3003 −3.04015
\(107\) −11.0745 −1.07061 −0.535307 0.844658i \(-0.679804\pi\)
−0.535307 + 0.844658i \(0.679804\pi\)
\(108\) 0 0
\(109\) −4.87369 −0.466815 −0.233407 0.972379i \(-0.574988\pi\)
−0.233407 + 0.972379i \(0.574988\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −10.7552 −1.01627
\(113\) 5.28263 0.496948 0.248474 0.968639i \(-0.420071\pi\)
0.248474 + 0.968639i \(0.420071\pi\)
\(114\) 0 0
\(115\) 5.15977 0.481151
\(116\) −43.9800 −4.08344
\(117\) 0 0
\(118\) 17.4617 1.60748
\(119\) −5.60085 −0.513429
\(120\) 0 0
\(121\) 0 0
\(122\) 22.4109 2.02899
\(123\) 0 0
\(124\) 7.93955 0.712992
\(125\) 1.51368 0.135388
\(126\) 0 0
\(127\) −11.3400 −1.00627 −0.503133 0.864209i \(-0.667819\pi\)
−0.503133 + 0.864209i \(0.667819\pi\)
\(128\) −6.40120 −0.565792
\(129\) 0 0
\(130\) −45.9217 −4.02760
\(131\) 0.970284 0.0847741 0.0423870 0.999101i \(-0.486504\pi\)
0.0423870 + 0.999101i \(0.486504\pi\)
\(132\) 0 0
\(133\) −0.122652 −0.0106353
\(134\) 21.2502 1.83574
\(135\) 0 0
\(136\) −43.9035 −3.76469
\(137\) 0.125101 0.0106881 0.00534403 0.999986i \(-0.498299\pi\)
0.00534403 + 0.999986i \(0.498299\pi\)
\(138\) 0 0
\(139\) −1.67835 −0.142355 −0.0711777 0.997464i \(-0.522676\pi\)
−0.0711777 + 0.997464i \(0.522676\pi\)
\(140\) 15.3237 1.29509
\(141\) 0 0
\(142\) 16.4832 1.38324
\(143\) 0 0
\(144\) 0 0
\(145\) 27.2918 2.26646
\(146\) −9.26631 −0.766885
\(147\) 0 0
\(148\) 20.7352 1.70442
\(149\) −14.1791 −1.16160 −0.580800 0.814046i \(-0.697260\pi\)
−0.580800 + 0.814046i \(0.697260\pi\)
\(150\) 0 0
\(151\) 15.8823 1.29249 0.646243 0.763132i \(-0.276339\pi\)
0.646243 + 0.763132i \(0.276339\pi\)
\(152\) −0.961437 −0.0779829
\(153\) 0 0
\(154\) 0 0
\(155\) −4.92689 −0.395737
\(156\) 0 0
\(157\) −9.19854 −0.734124 −0.367062 0.930197i \(-0.619636\pi\)
−0.367062 + 0.930197i \(0.619636\pi\)
\(158\) 24.8093 1.97372
\(159\) 0 0
\(160\) 39.2108 3.09989
\(161\) 1.67325 0.131870
\(162\) 0 0
\(163\) 9.76942 0.765200 0.382600 0.923914i \(-0.375029\pi\)
0.382600 + 0.923914i \(0.375029\pi\)
\(164\) −17.3358 −1.35370
\(165\) 0 0
\(166\) −24.9048 −1.93299
\(167\) −6.10236 −0.472215 −0.236107 0.971727i \(-0.575872\pi\)
−0.236107 + 0.971727i \(0.575872\pi\)
\(168\) 0 0
\(169\) 18.8206 1.44774
\(170\) 45.5951 3.49699
\(171\) 0 0
\(172\) −25.3780 −1.93505
\(173\) −6.73818 −0.512294 −0.256147 0.966638i \(-0.582453\pi\)
−0.256147 + 0.966638i \(0.582453\pi\)
\(174\) 0 0
\(175\) −4.50913 −0.340858
\(176\) 0 0
\(177\) 0 0
\(178\) −22.3222 −1.67312
\(179\) −12.9936 −0.971184 −0.485592 0.874186i \(-0.661396\pi\)
−0.485592 + 0.874186i \(0.661396\pi\)
\(180\) 0 0
\(181\) −4.09819 −0.304616 −0.152308 0.988333i \(-0.548671\pi\)
−0.152308 + 0.988333i \(0.548671\pi\)
\(182\) −14.8918 −1.10386
\(183\) 0 0
\(184\) 13.1161 0.966931
\(185\) −12.8672 −0.946018
\(186\) 0 0
\(187\) 0 0
\(188\) 7.92105 0.577702
\(189\) 0 0
\(190\) 0.998483 0.0724375
\(191\) −21.5036 −1.55595 −0.777973 0.628297i \(-0.783752\pi\)
−0.777973 + 0.628297i \(0.783752\pi\)
\(192\) 0 0
\(193\) 17.7964 1.28101 0.640506 0.767953i \(-0.278725\pi\)
0.640506 + 0.767953i \(0.278725\pi\)
\(194\) 15.0075 1.07747
\(195\) 0 0
\(196\) 4.96928 0.354948
\(197\) −18.1083 −1.29016 −0.645080 0.764115i \(-0.723176\pi\)
−0.645080 + 0.764115i \(0.723176\pi\)
\(198\) 0 0
\(199\) 2.67139 0.189370 0.0946848 0.995507i \(-0.469816\pi\)
0.0946848 + 0.995507i \(0.469816\pi\)
\(200\) −35.3458 −2.49933
\(201\) 0 0
\(202\) 44.5557 3.13493
\(203\) 8.85038 0.621175
\(204\) 0 0
\(205\) 10.7577 0.751352
\(206\) 34.8925 2.43108
\(207\) 0 0
\(208\) −60.6696 −4.20668
\(209\) 0 0
\(210\) 0 0
\(211\) −8.15447 −0.561377 −0.280688 0.959799i \(-0.590563\pi\)
−0.280688 + 0.959799i \(0.590563\pi\)
\(212\) 58.9179 4.04650
\(213\) 0 0
\(214\) 29.2360 1.99853
\(215\) 15.7483 1.07403
\(216\) 0 0
\(217\) −1.59773 −0.108461
\(218\) 12.8662 0.871412
\(219\) 0 0
\(220\) 0 0
\(221\) −31.5942 −2.12526
\(222\) 0 0
\(223\) 8.48763 0.568374 0.284187 0.958769i \(-0.408276\pi\)
0.284187 + 0.958769i \(0.408276\pi\)
\(224\) 12.7156 0.849595
\(225\) 0 0
\(226\) −13.9458 −0.927662
\(227\) 22.1524 1.47031 0.735154 0.677900i \(-0.237110\pi\)
0.735154 + 0.677900i \(0.237110\pi\)
\(228\) 0 0
\(229\) −8.98014 −0.593424 −0.296712 0.954967i \(-0.595890\pi\)
−0.296712 + 0.954967i \(0.595890\pi\)
\(230\) −13.6215 −0.898173
\(231\) 0 0
\(232\) 69.3756 4.55473
\(233\) −19.8909 −1.30309 −0.651547 0.758608i \(-0.725880\pi\)
−0.651547 + 0.758608i \(0.725880\pi\)
\(234\) 0 0
\(235\) −4.91541 −0.320646
\(236\) −32.8690 −2.13959
\(237\) 0 0
\(238\) 14.7859 0.958428
\(239\) 9.21976 0.596377 0.298188 0.954507i \(-0.403618\pi\)
0.298188 + 0.954507i \(0.403618\pi\)
\(240\) 0 0
\(241\) −0.802919 −0.0517206 −0.0258603 0.999666i \(-0.508233\pi\)
−0.0258603 + 0.999666i \(0.508233\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −42.1851 −2.70062
\(245\) −3.08369 −0.197010
\(246\) 0 0
\(247\) −0.691879 −0.0440232
\(248\) −12.5241 −0.795282
\(249\) 0 0
\(250\) −3.99603 −0.252731
\(251\) −0.459277 −0.0289893 −0.0144947 0.999895i \(-0.504614\pi\)
−0.0144947 + 0.999895i \(0.504614\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 29.9370 1.87842
\(255\) 0 0
\(256\) −7.21718 −0.451073
\(257\) 23.3574 1.45699 0.728496 0.685050i \(-0.240220\pi\)
0.728496 + 0.685050i \(0.240220\pi\)
\(258\) 0 0
\(259\) −4.17268 −0.259277
\(260\) 86.4406 5.36082
\(261\) 0 0
\(262\) −2.56149 −0.158249
\(263\) 4.96169 0.305951 0.152975 0.988230i \(-0.451114\pi\)
0.152975 + 0.988230i \(0.451114\pi\)
\(264\) 0 0
\(265\) −36.5615 −2.24596
\(266\) 0.323795 0.0198531
\(267\) 0 0
\(268\) −40.0002 −2.44340
\(269\) −1.03203 −0.0629239 −0.0314620 0.999505i \(-0.510016\pi\)
−0.0314620 + 0.999505i \(0.510016\pi\)
\(270\) 0 0
\(271\) 15.1427 0.919856 0.459928 0.887956i \(-0.347875\pi\)
0.459928 + 0.887956i \(0.347875\pi\)
\(272\) 60.2381 3.65247
\(273\) 0 0
\(274\) −0.330258 −0.0199516
\(275\) 0 0
\(276\) 0 0
\(277\) −1.07001 −0.0642909 −0.0321455 0.999483i \(-0.510234\pi\)
−0.0321455 + 0.999483i \(0.510234\pi\)
\(278\) 4.43073 0.265737
\(279\) 0 0
\(280\) −24.1721 −1.44456
\(281\) 31.3090 1.86774 0.933868 0.357617i \(-0.116411\pi\)
0.933868 + 0.357617i \(0.116411\pi\)
\(282\) 0 0
\(283\) 31.9651 1.90013 0.950063 0.312059i \(-0.101019\pi\)
0.950063 + 0.312059i \(0.101019\pi\)
\(284\) −31.0271 −1.84112
\(285\) 0 0
\(286\) 0 0
\(287\) 3.48859 0.205925
\(288\) 0 0
\(289\) 14.3695 0.845266
\(290\) −72.0487 −4.23085
\(291\) 0 0
\(292\) 17.4424 1.02074
\(293\) 0.472963 0.0276308 0.0138154 0.999905i \(-0.495602\pi\)
0.0138154 + 0.999905i \(0.495602\pi\)
\(294\) 0 0
\(295\) 20.3969 1.18755
\(296\) −32.7084 −1.90114
\(297\) 0 0
\(298\) 37.4321 2.16838
\(299\) 9.43873 0.545856
\(300\) 0 0
\(301\) 5.10698 0.294361
\(302\) −41.9284 −2.41271
\(303\) 0 0
\(304\) 1.31915 0.0756583
\(305\) 26.1780 1.49895
\(306\) 0 0
\(307\) −22.3522 −1.27571 −0.637854 0.770158i \(-0.720177\pi\)
−0.637854 + 0.770158i \(0.720177\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 13.0067 0.738730
\(311\) −21.9838 −1.24659 −0.623293 0.781988i \(-0.714206\pi\)
−0.623293 + 0.781988i \(0.714206\pi\)
\(312\) 0 0
\(313\) −7.95027 −0.449376 −0.224688 0.974431i \(-0.572136\pi\)
−0.224688 + 0.974431i \(0.572136\pi\)
\(314\) 24.2836 1.37040
\(315\) 0 0
\(316\) −46.6997 −2.62707
\(317\) 15.1227 0.849374 0.424687 0.905340i \(-0.360384\pi\)
0.424687 + 0.905340i \(0.360384\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −37.1831 −2.07860
\(321\) 0 0
\(322\) −4.41727 −0.246165
\(323\) 0.686958 0.0382234
\(324\) 0 0
\(325\) −25.4359 −1.41093
\(326\) −25.7907 −1.42841
\(327\) 0 0
\(328\) 27.3461 1.50993
\(329\) −1.59400 −0.0878803
\(330\) 0 0
\(331\) −6.02542 −0.331187 −0.165594 0.986194i \(-0.552954\pi\)
−0.165594 + 0.986194i \(0.552954\pi\)
\(332\) 46.8795 2.57285
\(333\) 0 0
\(334\) 16.1099 0.881492
\(335\) 24.8221 1.35618
\(336\) 0 0
\(337\) 20.8494 1.13574 0.567869 0.823119i \(-0.307768\pi\)
0.567869 + 0.823119i \(0.307768\pi\)
\(338\) −49.6851 −2.70252
\(339\) 0 0
\(340\) −85.8258 −4.65456
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 40.0321 2.15839
\(345\) 0 0
\(346\) 17.7884 0.956309
\(347\) −1.49329 −0.0801643 −0.0400821 0.999196i \(-0.512762\pi\)
−0.0400821 + 0.999196i \(0.512762\pi\)
\(348\) 0 0
\(349\) −21.4795 −1.14977 −0.574886 0.818234i \(-0.694954\pi\)
−0.574886 + 0.818234i \(0.694954\pi\)
\(350\) 11.9038 0.636287
\(351\) 0 0
\(352\) 0 0
\(353\) −11.4760 −0.610808 −0.305404 0.952223i \(-0.598792\pi\)
−0.305404 + 0.952223i \(0.598792\pi\)
\(354\) 0 0
\(355\) 19.2539 1.02189
\(356\) 42.0180 2.22695
\(357\) 0 0
\(358\) 34.3022 1.81293
\(359\) 5.72481 0.302144 0.151072 0.988523i \(-0.451727\pi\)
0.151072 + 0.988523i \(0.451727\pi\)
\(360\) 0 0
\(361\) −18.9850 −0.999208
\(362\) 10.8190 0.568632
\(363\) 0 0
\(364\) 28.0316 1.46925
\(365\) −10.8239 −0.566548
\(366\) 0 0
\(367\) 17.4991 0.913445 0.456723 0.889609i \(-0.349023\pi\)
0.456723 + 0.889609i \(0.349023\pi\)
\(368\) −17.9960 −0.938109
\(369\) 0 0
\(370\) 33.9687 1.76595
\(371\) −11.8564 −0.615555
\(372\) 0 0
\(373\) −9.54362 −0.494150 −0.247075 0.968996i \(-0.579469\pi\)
−0.247075 + 0.968996i \(0.579469\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −12.4949 −0.644377
\(377\) 49.9247 2.57126
\(378\) 0 0
\(379\) 31.9605 1.64170 0.820850 0.571144i \(-0.193500\pi\)
0.820850 + 0.571144i \(0.193500\pi\)
\(380\) −1.87949 −0.0964158
\(381\) 0 0
\(382\) 56.7682 2.90452
\(383\) 9.82236 0.501899 0.250950 0.968000i \(-0.419257\pi\)
0.250950 + 0.968000i \(0.419257\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −46.9814 −2.39129
\(387\) 0 0
\(388\) −28.2493 −1.43414
\(389\) −33.1998 −1.68330 −0.841648 0.540027i \(-0.818414\pi\)
−0.841648 + 0.540027i \(0.818414\pi\)
\(390\) 0 0
\(391\) −9.37160 −0.473942
\(392\) −7.83871 −0.395915
\(393\) 0 0
\(394\) 47.8047 2.40837
\(395\) 28.9795 1.45812
\(396\) 0 0
\(397\) 23.6535 1.18713 0.593566 0.804785i \(-0.297719\pi\)
0.593566 + 0.804785i \(0.297719\pi\)
\(398\) −7.05230 −0.353500
\(399\) 0 0
\(400\) 48.4965 2.42482
\(401\) −25.2737 −1.26211 −0.631054 0.775739i \(-0.717377\pi\)
−0.631054 + 0.775739i \(0.717377\pi\)
\(402\) 0 0
\(403\) −9.01273 −0.448956
\(404\) −83.8693 −4.17265
\(405\) 0 0
\(406\) −23.3645 −1.15956
\(407\) 0 0
\(408\) 0 0
\(409\) 13.9735 0.690947 0.345474 0.938428i \(-0.387718\pi\)
0.345474 + 0.938428i \(0.387718\pi\)
\(410\) −28.3998 −1.40256
\(411\) 0 0
\(412\) −65.6798 −3.23581
\(413\) 6.61445 0.325476
\(414\) 0 0
\(415\) −29.0911 −1.42803
\(416\) 71.7282 3.51676
\(417\) 0 0
\(418\) 0 0
\(419\) −29.7445 −1.45311 −0.726556 0.687107i \(-0.758880\pi\)
−0.726556 + 0.687107i \(0.758880\pi\)
\(420\) 0 0
\(421\) 36.2675 1.76757 0.883786 0.467892i \(-0.154986\pi\)
0.883786 + 0.467892i \(0.154986\pi\)
\(422\) 21.5273 1.04793
\(423\) 0 0
\(424\) −92.9392 −4.51353
\(425\) 25.2550 1.22505
\(426\) 0 0
\(427\) 8.48918 0.410820
\(428\) −55.0323 −2.66009
\(429\) 0 0
\(430\) −41.5746 −2.00491
\(431\) −35.8066 −1.72474 −0.862372 0.506275i \(-0.831022\pi\)
−0.862372 + 0.506275i \(0.831022\pi\)
\(432\) 0 0
\(433\) −23.0958 −1.10992 −0.554958 0.831879i \(-0.687266\pi\)
−0.554958 + 0.831879i \(0.687266\pi\)
\(434\) 4.21790 0.202466
\(435\) 0 0
\(436\) −24.2187 −1.15987
\(437\) −0.205228 −0.00981737
\(438\) 0 0
\(439\) 24.7837 1.18286 0.591431 0.806356i \(-0.298563\pi\)
0.591431 + 0.806356i \(0.298563\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 83.4069 3.96726
\(443\) −13.2945 −0.631642 −0.315821 0.948819i \(-0.602280\pi\)
−0.315821 + 0.948819i \(0.602280\pi\)
\(444\) 0 0
\(445\) −26.0743 −1.23604
\(446\) −22.4068 −1.06099
\(447\) 0 0
\(448\) −12.0580 −0.569686
\(449\) −20.8714 −0.984981 −0.492490 0.870318i \(-0.663913\pi\)
−0.492490 + 0.870318i \(0.663913\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 26.2509 1.23474
\(453\) 0 0
\(454\) −58.4810 −2.74465
\(455\) −17.3950 −0.815490
\(456\) 0 0
\(457\) −28.2344 −1.32075 −0.660375 0.750936i \(-0.729603\pi\)
−0.660375 + 0.750936i \(0.729603\pi\)
\(458\) 23.7070 1.10776
\(459\) 0 0
\(460\) 25.6403 1.19549
\(461\) 13.5432 0.630770 0.315385 0.948964i \(-0.397866\pi\)
0.315385 + 0.948964i \(0.397866\pi\)
\(462\) 0 0
\(463\) −33.9584 −1.57818 −0.789090 0.614277i \(-0.789448\pi\)
−0.789090 + 0.614277i \(0.789448\pi\)
\(464\) −95.1873 −4.41896
\(465\) 0 0
\(466\) 52.5107 2.43251
\(467\) −12.5809 −0.582172 −0.291086 0.956697i \(-0.594017\pi\)
−0.291086 + 0.956697i \(0.594017\pi\)
\(468\) 0 0
\(469\) 8.04949 0.371691
\(470\) 12.9764 0.598556
\(471\) 0 0
\(472\) 51.8488 2.38653
\(473\) 0 0
\(474\) 0 0
\(475\) 0.553056 0.0253759
\(476\) −27.8322 −1.27569
\(477\) 0 0
\(478\) −24.3396 −1.11327
\(479\) −28.8916 −1.32009 −0.660046 0.751225i \(-0.729463\pi\)
−0.660046 + 0.751225i \(0.729463\pi\)
\(480\) 0 0
\(481\) −23.5380 −1.07324
\(482\) 2.11966 0.0965478
\(483\) 0 0
\(484\) 0 0
\(485\) 17.5301 0.796001
\(486\) 0 0
\(487\) 25.5077 1.15586 0.577932 0.816085i \(-0.303860\pi\)
0.577932 + 0.816085i \(0.303860\pi\)
\(488\) 66.5443 3.01232
\(489\) 0 0
\(490\) 8.14075 0.367762
\(491\) −4.66598 −0.210573 −0.105286 0.994442i \(-0.533576\pi\)
−0.105286 + 0.994442i \(0.533576\pi\)
\(492\) 0 0
\(493\) −49.5697 −2.23250
\(494\) 1.82652 0.0821789
\(495\) 0 0
\(496\) 17.1838 0.771576
\(497\) 6.24379 0.280072
\(498\) 0 0
\(499\) −18.4958 −0.827987 −0.413994 0.910280i \(-0.635866\pi\)
−0.413994 + 0.910280i \(0.635866\pi\)
\(500\) 7.52191 0.336390
\(501\) 0 0
\(502\) 1.21246 0.0541149
\(503\) 23.1076 1.03032 0.515159 0.857094i \(-0.327733\pi\)
0.515159 + 0.857094i \(0.327733\pi\)
\(504\) 0 0
\(505\) 52.0451 2.31598
\(506\) 0 0
\(507\) 0 0
\(508\) −56.3518 −2.50021
\(509\) 28.6541 1.27007 0.635036 0.772483i \(-0.280985\pi\)
0.635036 + 0.772483i \(0.280985\pi\)
\(510\) 0 0
\(511\) −3.51005 −0.155275
\(512\) 31.8553 1.40782
\(513\) 0 0
\(514\) −61.6620 −2.71979
\(515\) 40.7576 1.79600
\(516\) 0 0
\(517\) 0 0
\(518\) 11.0156 0.483998
\(519\) 0 0
\(520\) −136.354 −5.97954
\(521\) 7.99220 0.350144 0.175072 0.984556i \(-0.443984\pi\)
0.175072 + 0.984556i \(0.443984\pi\)
\(522\) 0 0
\(523\) 37.2399 1.62839 0.814194 0.580592i \(-0.197179\pi\)
0.814194 + 0.580592i \(0.197179\pi\)
\(524\) 4.82161 0.210633
\(525\) 0 0
\(526\) −13.0986 −0.571124
\(527\) 8.94863 0.389808
\(528\) 0 0
\(529\) −20.2002 −0.878272
\(530\) 96.5202 4.19257
\(531\) 0 0
\(532\) −0.609494 −0.0264249
\(533\) 19.6791 0.852394
\(534\) 0 0
\(535\) 34.1503 1.47645
\(536\) 63.0977 2.72541
\(537\) 0 0
\(538\) 2.72449 0.117461
\(539\) 0 0
\(540\) 0 0
\(541\) −22.9890 −0.988376 −0.494188 0.869355i \(-0.664535\pi\)
−0.494188 + 0.869355i \(0.664535\pi\)
\(542\) −39.9759 −1.71711
\(543\) 0 0
\(544\) −71.2180 −3.05345
\(545\) 15.0289 0.643769
\(546\) 0 0
\(547\) 30.4285 1.30103 0.650515 0.759493i \(-0.274553\pi\)
0.650515 + 0.759493i \(0.274553\pi\)
\(548\) 0.621660 0.0265560
\(549\) 0 0
\(550\) 0 0
\(551\) −1.08552 −0.0462447
\(552\) 0 0
\(553\) 9.39769 0.399630
\(554\) 2.82477 0.120013
\(555\) 0 0
\(556\) −8.34016 −0.353702
\(557\) 42.4812 1.79998 0.899992 0.435906i \(-0.143572\pi\)
0.899992 + 0.435906i \(0.143572\pi\)
\(558\) 0 0
\(559\) 28.8083 1.21846
\(560\) 33.1656 1.40150
\(561\) 0 0
\(562\) −82.6538 −3.48654
\(563\) −12.0958 −0.509777 −0.254888 0.966971i \(-0.582039\pi\)
−0.254888 + 0.966971i \(0.582039\pi\)
\(564\) 0 0
\(565\) −16.2900 −0.685325
\(566\) −84.3858 −3.54700
\(567\) 0 0
\(568\) 48.9433 2.05361
\(569\) 34.0054 1.42558 0.712789 0.701378i \(-0.247432\pi\)
0.712789 + 0.701378i \(0.247432\pi\)
\(570\) 0 0
\(571\) 16.0762 0.672767 0.336383 0.941725i \(-0.390796\pi\)
0.336383 + 0.941725i \(0.390796\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −9.20967 −0.384404
\(575\) −7.54489 −0.314643
\(576\) 0 0
\(577\) 3.94068 0.164053 0.0820264 0.996630i \(-0.473861\pi\)
0.0820264 + 0.996630i \(0.473861\pi\)
\(578\) −37.9347 −1.57787
\(579\) 0 0
\(580\) 135.621 5.63134
\(581\) −9.43386 −0.391383
\(582\) 0 0
\(583\) 0 0
\(584\) −27.5142 −1.13855
\(585\) 0 0
\(586\) −1.24859 −0.0515789
\(587\) −9.92820 −0.409781 −0.204890 0.978785i \(-0.565684\pi\)
−0.204890 + 0.978785i \(0.565684\pi\)
\(588\) 0 0
\(589\) 0.195965 0.00807460
\(590\) −53.8466 −2.21683
\(591\) 0 0
\(592\) 44.8778 1.84447
\(593\) −1.35512 −0.0556480 −0.0278240 0.999613i \(-0.508858\pi\)
−0.0278240 + 0.999613i \(0.508858\pi\)
\(594\) 0 0
\(595\) 17.2713 0.708053
\(596\) −70.4601 −2.88616
\(597\) 0 0
\(598\) −24.9177 −1.01896
\(599\) 30.7682 1.25716 0.628578 0.777747i \(-0.283637\pi\)
0.628578 + 0.777747i \(0.283637\pi\)
\(600\) 0 0
\(601\) −13.2165 −0.539113 −0.269557 0.962985i \(-0.586877\pi\)
−0.269557 + 0.962985i \(0.586877\pi\)
\(602\) −13.4821 −0.549490
\(603\) 0 0
\(604\) 78.9237 3.21136
\(605\) 0 0
\(606\) 0 0
\(607\) −5.83308 −0.236757 −0.118379 0.992969i \(-0.537770\pi\)
−0.118379 + 0.992969i \(0.537770\pi\)
\(608\) −1.55960 −0.0632499
\(609\) 0 0
\(610\) −69.1083 −2.79811
\(611\) −8.99173 −0.363767
\(612\) 0 0
\(613\) 6.67731 0.269694 0.134847 0.990866i \(-0.456946\pi\)
0.134847 + 0.990866i \(0.456946\pi\)
\(614\) 59.0084 2.38139
\(615\) 0 0
\(616\) 0 0
\(617\) −15.1716 −0.610785 −0.305392 0.952227i \(-0.598788\pi\)
−0.305392 + 0.952227i \(0.598788\pi\)
\(618\) 0 0
\(619\) 27.9902 1.12502 0.562510 0.826790i \(-0.309836\pi\)
0.562510 + 0.826790i \(0.309836\pi\)
\(620\) −24.4831 −0.983264
\(621\) 0 0
\(622\) 58.0359 2.32703
\(623\) −8.45556 −0.338765
\(624\) 0 0
\(625\) −27.2134 −1.08854
\(626\) 20.9882 0.838858
\(627\) 0 0
\(628\) −45.7101 −1.82403
\(629\) 23.3705 0.931844
\(630\) 0 0
\(631\) −5.58035 −0.222150 −0.111075 0.993812i \(-0.535429\pi\)
−0.111075 + 0.993812i \(0.535429\pi\)
\(632\) 73.6658 2.93027
\(633\) 0 0
\(634\) −39.9230 −1.58554
\(635\) 34.9692 1.38771
\(636\) 0 0
\(637\) −5.64097 −0.223503
\(638\) 0 0
\(639\) 0 0
\(640\) 19.7393 0.780265
\(641\) −10.9667 −0.433158 −0.216579 0.976265i \(-0.569490\pi\)
−0.216579 + 0.976265i \(0.569490\pi\)
\(642\) 0 0
\(643\) 0.399143 0.0157406 0.00787032 0.999969i \(-0.497495\pi\)
0.00787032 + 0.999969i \(0.497495\pi\)
\(644\) 8.31482 0.327650
\(645\) 0 0
\(646\) −1.81353 −0.0713523
\(647\) −31.2956 −1.23036 −0.615178 0.788389i \(-0.710916\pi\)
−0.615178 + 0.788389i \(0.710916\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 67.1492 2.63381
\(651\) 0 0
\(652\) 48.5470 1.90125
\(653\) 26.1788 1.02446 0.512228 0.858849i \(-0.328820\pi\)
0.512228 + 0.858849i \(0.328820\pi\)
\(654\) 0 0
\(655\) −2.99205 −0.116909
\(656\) −37.5204 −1.46493
\(657\) 0 0
\(658\) 4.20807 0.164048
\(659\) 5.84482 0.227682 0.113841 0.993499i \(-0.463685\pi\)
0.113841 + 0.993499i \(0.463685\pi\)
\(660\) 0 0
\(661\) −6.32811 −0.246135 −0.123067 0.992398i \(-0.539273\pi\)
−0.123067 + 0.992398i \(0.539273\pi\)
\(662\) 15.9067 0.618233
\(663\) 0 0
\(664\) −73.9494 −2.86979
\(665\) 0.378222 0.0146668
\(666\) 0 0
\(667\) 14.8089 0.573401
\(668\) −30.3243 −1.17328
\(669\) 0 0
\(670\) −65.5289 −2.53160
\(671\) 0 0
\(672\) 0 0
\(673\) 4.21912 0.162635 0.0813176 0.996688i \(-0.474087\pi\)
0.0813176 + 0.996688i \(0.474087\pi\)
\(674\) −55.0411 −2.12010
\(675\) 0 0
\(676\) 93.5246 3.59710
\(677\) −17.9247 −0.688902 −0.344451 0.938804i \(-0.611935\pi\)
−0.344451 + 0.938804i \(0.611935\pi\)
\(678\) 0 0
\(679\) 5.68478 0.218162
\(680\) 135.385 5.19176
\(681\) 0 0
\(682\) 0 0
\(683\) 5.96513 0.228249 0.114125 0.993466i \(-0.463594\pi\)
0.114125 + 0.993466i \(0.463594\pi\)
\(684\) 0 0
\(685\) −0.385771 −0.0147396
\(686\) 2.63994 0.100793
\(687\) 0 0
\(688\) −54.9264 −2.09405
\(689\) −66.8818 −2.54799
\(690\) 0 0
\(691\) −39.4084 −1.49917 −0.749583 0.661910i \(-0.769746\pi\)
−0.749583 + 0.661910i \(0.769746\pi\)
\(692\) −33.4839 −1.27287
\(693\) 0 0
\(694\) 3.94221 0.149644
\(695\) 5.17549 0.196318
\(696\) 0 0
\(697\) −19.5391 −0.740096
\(698\) 56.7046 2.14630
\(699\) 0 0
\(700\) −22.4071 −0.846910
\(701\) 25.4284 0.960417 0.480208 0.877154i \(-0.340561\pi\)
0.480208 + 0.877154i \(0.340561\pi\)
\(702\) 0 0
\(703\) 0.511789 0.0193025
\(704\) 0 0
\(705\) 0 0
\(706\) 30.2961 1.14021
\(707\) 16.8776 0.634746
\(708\) 0 0
\(709\) 7.08068 0.265921 0.132960 0.991121i \(-0.457552\pi\)
0.132960 + 0.991121i \(0.457552\pi\)
\(710\) −50.8291 −1.90758
\(711\) 0 0
\(712\) −66.2807 −2.48398
\(713\) −2.67339 −0.100119
\(714\) 0 0
\(715\) 0 0
\(716\) −64.5686 −2.41304
\(717\) 0 0
\(718\) −15.1132 −0.564018
\(719\) 21.5811 0.804840 0.402420 0.915455i \(-0.368169\pi\)
0.402420 + 0.915455i \(0.368169\pi\)
\(720\) 0 0
\(721\) 13.2172 0.492233
\(722\) 50.1191 1.86524
\(723\) 0 0
\(724\) −20.3650 −0.756861
\(725\) −39.9075 −1.48213
\(726\) 0 0
\(727\) 35.7114 1.32446 0.662231 0.749300i \(-0.269610\pi\)
0.662231 + 0.749300i \(0.269610\pi\)
\(728\) −44.2180 −1.63883
\(729\) 0 0
\(730\) 28.5744 1.05759
\(731\) −28.6034 −1.05794
\(732\) 0 0
\(733\) 6.34501 0.234358 0.117179 0.993111i \(-0.462615\pi\)
0.117179 + 0.993111i \(0.462615\pi\)
\(734\) −46.1965 −1.70515
\(735\) 0 0
\(736\) 21.2763 0.784254
\(737\) 0 0
\(738\) 0 0
\(739\) 10.9804 0.403922 0.201961 0.979394i \(-0.435269\pi\)
0.201961 + 0.979394i \(0.435269\pi\)
\(740\) −63.9409 −2.35051
\(741\) 0 0
\(742\) 31.3003 1.14907
\(743\) 18.4186 0.675711 0.337856 0.941198i \(-0.390298\pi\)
0.337856 + 0.941198i \(0.390298\pi\)
\(744\) 0 0
\(745\) 43.7240 1.60192
\(746\) 25.1946 0.922438
\(747\) 0 0
\(748\) 0 0
\(749\) 11.0745 0.404654
\(750\) 0 0
\(751\) 4.96566 0.181200 0.0905998 0.995887i \(-0.471122\pi\)
0.0905998 + 0.995887i \(0.471122\pi\)
\(752\) 17.1438 0.625170
\(753\) 0 0
\(754\) −131.798 −4.79981
\(755\) −48.9761 −1.78242
\(756\) 0 0
\(757\) −1.04107 −0.0378384 −0.0189192 0.999821i \(-0.506023\pi\)
−0.0189192 + 0.999821i \(0.506023\pi\)
\(758\) −84.3737 −3.06459
\(759\) 0 0
\(760\) 2.96477 0.107544
\(761\) 42.0282 1.52352 0.761760 0.647860i \(-0.224336\pi\)
0.761760 + 0.647860i \(0.224336\pi\)
\(762\) 0 0
\(763\) 4.87369 0.176439
\(764\) −106.857 −3.86597
\(765\) 0 0
\(766\) −25.9304 −0.936905
\(767\) 37.3119 1.34726
\(768\) 0 0
\(769\) 44.1300 1.59137 0.795684 0.605712i \(-0.207112\pi\)
0.795684 + 0.605712i \(0.207112\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 88.4352 3.18285
\(773\) 37.3027 1.34168 0.670842 0.741600i \(-0.265933\pi\)
0.670842 + 0.741600i \(0.265933\pi\)
\(774\) 0 0
\(775\) 7.20436 0.258788
\(776\) 44.5614 1.59966
\(777\) 0 0
\(778\) 87.6454 3.14224
\(779\) −0.427884 −0.0153305
\(780\) 0 0
\(781\) 0 0
\(782\) 24.7404 0.884717
\(783\) 0 0
\(784\) 10.7552 0.384113
\(785\) 28.3654 1.01241
\(786\) 0 0
\(787\) 7.35809 0.262288 0.131144 0.991363i \(-0.458135\pi\)
0.131144 + 0.991363i \(0.458135\pi\)
\(788\) −89.9850 −3.20558
\(789\) 0 0
\(790\) −76.5042 −2.72190
\(791\) −5.28263 −0.187829
\(792\) 0 0
\(793\) 47.8872 1.70053
\(794\) −62.4437 −2.21604
\(795\) 0 0
\(796\) 13.2749 0.470515
\(797\) −6.00177 −0.212594 −0.106297 0.994334i \(-0.533899\pi\)
−0.106297 + 0.994334i \(0.533899\pi\)
\(798\) 0 0
\(799\) 8.92778 0.315842
\(800\) −57.3362 −2.02714
\(801\) 0 0
\(802\) 66.7210 2.35600
\(803\) 0 0
\(804\) 0 0
\(805\) −5.15977 −0.181858
\(806\) 23.7931 0.838075
\(807\) 0 0
\(808\) 132.298 4.65424
\(809\) 28.3939 0.998278 0.499139 0.866522i \(-0.333650\pi\)
0.499139 + 0.866522i \(0.333650\pi\)
\(810\) 0 0
\(811\) 31.9066 1.12039 0.560196 0.828360i \(-0.310726\pi\)
0.560196 + 0.828360i \(0.310726\pi\)
\(812\) 43.9800 1.54340
\(813\) 0 0
\(814\) 0 0
\(815\) −30.1259 −1.05526
\(816\) 0 0
\(817\) −0.626383 −0.0219144
\(818\) −36.8893 −1.28980
\(819\) 0 0
\(820\) 53.4582 1.86684
\(821\) 4.55941 0.159125 0.0795623 0.996830i \(-0.474648\pi\)
0.0795623 + 0.996830i \(0.474648\pi\)
\(822\) 0 0
\(823\) 46.5932 1.62414 0.812069 0.583562i \(-0.198341\pi\)
0.812069 + 0.583562i \(0.198341\pi\)
\(824\) 103.606 3.60927
\(825\) 0 0
\(826\) −17.4617 −0.607572
\(827\) 1.00246 0.0348589 0.0174294 0.999848i \(-0.494452\pi\)
0.0174294 + 0.999848i \(0.494452\pi\)
\(828\) 0 0
\(829\) −50.4845 −1.75340 −0.876699 0.481039i \(-0.840260\pi\)
−0.876699 + 0.481039i \(0.840260\pi\)
\(830\) 76.7987 2.66572
\(831\) 0 0
\(832\) −68.0187 −2.35813
\(833\) 5.60085 0.194058
\(834\) 0 0
\(835\) 18.8178 0.651216
\(836\) 0 0
\(837\) 0 0
\(838\) 78.5236 2.71255
\(839\) 26.0614 0.899739 0.449869 0.893094i \(-0.351471\pi\)
0.449869 + 0.893094i \(0.351471\pi\)
\(840\) 0 0
\(841\) 49.3292 1.70101
\(842\) −95.7441 −3.29956
\(843\) 0 0
\(844\) −40.5218 −1.39482
\(845\) −58.0368 −1.99652
\(846\) 0 0
\(847\) 0 0
\(848\) 127.518 4.37898
\(849\) 0 0
\(850\) −66.6716 −2.28682
\(851\) −6.98191 −0.239337
\(852\) 0 0
\(853\) −30.1888 −1.03364 −0.516822 0.856093i \(-0.672885\pi\)
−0.516822 + 0.856093i \(0.672885\pi\)
\(854\) −22.4109 −0.766886
\(855\) 0 0
\(856\) 86.8099 2.96710
\(857\) 25.3151 0.864748 0.432374 0.901694i \(-0.357676\pi\)
0.432374 + 0.901694i \(0.357676\pi\)
\(858\) 0 0
\(859\) −10.7680 −0.367399 −0.183699 0.982982i \(-0.558807\pi\)
−0.183699 + 0.982982i \(0.558807\pi\)
\(860\) 78.2578 2.66857
\(861\) 0 0
\(862\) 94.5273 3.21961
\(863\) 35.3003 1.20163 0.600817 0.799386i \(-0.294842\pi\)
0.600817 + 0.799386i \(0.294842\pi\)
\(864\) 0 0
\(865\) 20.7784 0.706488
\(866\) 60.9716 2.07190
\(867\) 0 0
\(868\) −7.93955 −0.269486
\(869\) 0 0
\(870\) 0 0
\(871\) 45.4070 1.53856
\(872\) 38.2035 1.29373
\(873\) 0 0
\(874\) 0.541788 0.0183263
\(875\) −1.51368 −0.0511718
\(876\) 0 0
\(877\) −4.16706 −0.140712 −0.0703558 0.997522i \(-0.522413\pi\)
−0.0703558 + 0.997522i \(0.522413\pi\)
\(878\) −65.4275 −2.20807
\(879\) 0 0
\(880\) 0 0
\(881\) 40.6561 1.36974 0.684870 0.728665i \(-0.259859\pi\)
0.684870 + 0.728665i \(0.259859\pi\)
\(882\) 0 0
\(883\) −19.1697 −0.645113 −0.322556 0.946550i \(-0.604542\pi\)
−0.322556 + 0.946550i \(0.604542\pi\)
\(884\) −157.001 −5.28050
\(885\) 0 0
\(886\) 35.0967 1.17910
\(887\) 37.0380 1.24362 0.621808 0.783170i \(-0.286398\pi\)
0.621808 + 0.783170i \(0.286398\pi\)
\(888\) 0 0
\(889\) 11.3400 0.380333
\(890\) 68.8346 2.30734
\(891\) 0 0
\(892\) 42.1774 1.41220
\(893\) 0.195508 0.00654244
\(894\) 0 0
\(895\) 40.0681 1.33933
\(896\) 6.40120 0.213849
\(897\) 0 0
\(898\) 55.0992 1.83868
\(899\) −14.1405 −0.471612
\(900\) 0 0
\(901\) 66.4061 2.21231
\(902\) 0 0
\(903\) 0 0
\(904\) −41.4090 −1.37724
\(905\) 12.6375 0.420086
\(906\) 0 0
\(907\) −28.7583 −0.954905 −0.477452 0.878658i \(-0.658440\pi\)
−0.477452 + 0.878658i \(0.658440\pi\)
\(908\) 110.082 3.65318
\(909\) 0 0
\(910\) 45.9217 1.52229
\(911\) −44.7716 −1.48335 −0.741675 0.670759i \(-0.765968\pi\)
−0.741675 + 0.670759i \(0.765968\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 74.5371 2.46547
\(915\) 0 0
\(916\) −44.6248 −1.47445
\(917\) −0.970284 −0.0320416
\(918\) 0 0
\(919\) 19.3392 0.637943 0.318971 0.947764i \(-0.396663\pi\)
0.318971 + 0.947764i \(0.396663\pi\)
\(920\) −40.4459 −1.33346
\(921\) 0 0
\(922\) −35.7533 −1.17747
\(923\) 35.2210 1.15931
\(924\) 0 0
\(925\) 18.8152 0.618638
\(926\) 89.6481 2.94602
\(927\) 0 0
\(928\) 112.538 3.69423
\(929\) 26.9129 0.882985 0.441493 0.897265i \(-0.354449\pi\)
0.441493 + 0.897265i \(0.354449\pi\)
\(930\) 0 0
\(931\) 0.122652 0.00401977
\(932\) −98.8433 −3.23772
\(933\) 0 0
\(934\) 33.2127 1.08675
\(935\) 0 0
\(936\) 0 0
\(937\) 42.5349 1.38956 0.694778 0.719224i \(-0.255503\pi\)
0.694778 + 0.719224i \(0.255503\pi\)
\(938\) −21.2502 −0.693843
\(939\) 0 0
\(940\) −24.4260 −0.796690
\(941\) 48.7704 1.58987 0.794934 0.606695i \(-0.207505\pi\)
0.794934 + 0.606695i \(0.207505\pi\)
\(942\) 0 0
\(943\) 5.83727 0.190088
\(944\) −71.1395 −2.31540
\(945\) 0 0
\(946\) 0 0
\(947\) −0.641845 −0.0208572 −0.0104286 0.999946i \(-0.503320\pi\)
−0.0104286 + 0.999946i \(0.503320\pi\)
\(948\) 0 0
\(949\) −19.8001 −0.642738
\(950\) −1.46003 −0.0473698
\(951\) 0 0
\(952\) 43.9035 1.42292
\(953\) −7.65944 −0.248114 −0.124057 0.992275i \(-0.539591\pi\)
−0.124057 + 0.992275i \(0.539591\pi\)
\(954\) 0 0
\(955\) 66.3104 2.14576
\(956\) 45.8156 1.48178
\(957\) 0 0
\(958\) 76.2721 2.46424
\(959\) −0.125101 −0.00403971
\(960\) 0 0
\(961\) −28.4473 −0.917654
\(962\) 62.1388 2.00343
\(963\) 0 0
\(964\) −3.98993 −0.128507
\(965\) −54.8785 −1.76660
\(966\) 0 0
\(967\) −29.7387 −0.956333 −0.478166 0.878269i \(-0.658698\pi\)
−0.478166 + 0.878269i \(0.658698\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −46.2784 −1.48591
\(971\) 34.9188 1.12060 0.560299 0.828291i \(-0.310686\pi\)
0.560299 + 0.828291i \(0.310686\pi\)
\(972\) 0 0
\(973\) 1.67835 0.0538053
\(974\) −67.3388 −2.15767
\(975\) 0 0
\(976\) −91.3026 −2.92253
\(977\) −31.9341 −1.02166 −0.510832 0.859681i \(-0.670662\pi\)
−0.510832 + 0.859681i \(0.670662\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −15.3237 −0.489498
\(981\) 0 0
\(982\) 12.3179 0.393080
\(983\) 33.9111 1.08159 0.540797 0.841153i \(-0.318123\pi\)
0.540797 + 0.841153i \(0.318123\pi\)
\(984\) 0 0
\(985\) 55.8402 1.77922
\(986\) 130.861 4.16746
\(987\) 0 0
\(988\) −3.43814 −0.109382
\(989\) 8.54523 0.271722
\(990\) 0 0
\(991\) −13.3101 −0.422809 −0.211404 0.977399i \(-0.567804\pi\)
−0.211404 + 0.977399i \(0.567804\pi\)
\(992\) −20.3160 −0.645034
\(993\) 0 0
\(994\) −16.4832 −0.522816
\(995\) −8.23772 −0.261153
\(996\) 0 0
\(997\) −2.95257 −0.0935088 −0.0467544 0.998906i \(-0.514888\pi\)
−0.0467544 + 0.998906i \(0.514888\pi\)
\(998\) 48.8279 1.54562
\(999\) 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.cx.1.2 10
3.2 odd 2 2541.2.a.bq.1.9 10
11.5 even 5 693.2.m.j.190.5 20
11.9 even 5 693.2.m.j.631.5 20
11.10 odd 2 7623.2.a.cy.1.9 10
33.5 odd 10 231.2.j.g.190.1 yes 20
33.20 odd 10 231.2.j.g.169.1 20
33.32 even 2 2541.2.a.br.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.g.169.1 20 33.20 odd 10
231.2.j.g.190.1 yes 20 33.5 odd 10
693.2.m.j.190.5 20 11.5 even 5
693.2.m.j.631.5 20 11.9 even 5
2541.2.a.bq.1.9 10 3.2 odd 2
2541.2.a.br.1.2 10 33.32 even 2
7623.2.a.cx.1.2 10 1.1 even 1 trivial
7623.2.a.cy.1.9 10 11.10 odd 2