Properties

Label 7605.2.a.cl.1.1
Level $7605$
Weight $2$
Character 7605.1
Self dual yes
Analytic conductor $60.726$
Analytic rank $1$
Dimension $5$
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] = [7605,2,Mod(1,7605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7605, 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("7605.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.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: \(60.7262307372\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.3352656.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 6x - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.63209\) of defining polynomial
Character \(\chi\) \(=\) 7605.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.63209 q^{2} +4.92789 q^{4} -1.00000 q^{5} -1.08975 q^{7} -7.70645 q^{8} +O(q^{10})\) \(q-2.63209 q^{2} +4.92789 q^{4} -1.00000 q^{5} -1.08975 q^{7} -7.70645 q^{8} +2.63209 q^{10} -4.72184 q^{11} +2.86832 q^{14} +10.4283 q^{16} +5.22369 q^{17} -2.92789 q^{19} -4.92789 q^{20} +12.4283 q^{22} -7.70645 q^{23} +1.00000 q^{25} -5.37017 q^{28} +1.31118 q^{29} +2.32091 q^{31} -12.0353 q^{32} -13.7492 q^{34} +1.08975 q^{35} +10.4283 q^{37} +7.70645 q^{38} +7.70645 q^{40} -4.98745 q^{41} +5.96838 q^{43} -23.2687 q^{44} +20.2841 q^{46} +8.51804 q^{47} -5.81244 q^{49} -2.63209 q^{50} -9.67627 q^{53} +4.72184 q^{55} +8.39811 q^{56} -3.45115 q^{58} +3.16696 q^{59} +6.32091 q^{61} -6.10883 q^{62} +10.8213 q^{64} +1.57536 q^{67} +25.7417 q^{68} -2.86832 q^{70} +6.00225 q^{71} -12.3098 q^{73} -27.4482 q^{74} -14.4283 q^{76} +5.14562 q^{77} -3.04333 q^{79} -10.4283 q^{80} +13.1274 q^{82} +1.40782 q^{83} -5.22369 q^{85} -15.7093 q^{86} +36.3886 q^{88} +8.67483 q^{89} -37.9765 q^{92} -22.4202 q^{94} +2.92789 q^{95} +11.0324 q^{97} +15.2989 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{2} + 6 q^{4} - 5 q^{5} - q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{2} + 6 q^{4} - 5 q^{5} - q^{7} - 6 q^{8} + 2 q^{10} - 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} - 6 q^{20} + 14 q^{22} - 6 q^{23} + 5 q^{25} + 2 q^{28} + 16 q^{29} - 9 q^{31} - 14 q^{32} + q^{35} + 4 q^{37} + 6 q^{38} + 6 q^{40} - 6 q^{41} + 15 q^{43} - 14 q^{44} + 16 q^{46} - 10 q^{47} + 10 q^{49} - 2 q^{50} - 20 q^{53} + 8 q^{55} - 2 q^{56} + 4 q^{58} - 12 q^{59} + 11 q^{61} - 22 q^{62} + 4 q^{64} - 5 q^{67} + 50 q^{68} + 4 q^{70} - 10 q^{71} - q^{73} - 26 q^{74} - 24 q^{76} + 42 q^{77} - 17 q^{79} - 4 q^{80} + 16 q^{82} - 16 q^{83} - 44 q^{86} + 20 q^{88} - 4 q^{89} - 34 q^{92} - 16 q^{94} - 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63209 −1.86117 −0.930584 0.366079i \(-0.880700\pi\)
−0.930584 + 0.366079i \(0.880700\pi\)
\(3\) 0 0
\(4\) 4.92789 2.46394
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.08975 −0.411887 −0.205943 0.978564i \(-0.566026\pi\)
−0.205943 + 0.978564i \(0.566026\pi\)
\(8\) −7.70645 −2.72464
\(9\) 0 0
\(10\) 2.63209 0.832339
\(11\) −4.72184 −1.42369 −0.711844 0.702338i \(-0.752140\pi\)
−0.711844 + 0.702338i \(0.752140\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 2.86832 0.766590
\(15\) 0 0
\(16\) 10.4283 2.60707
\(17\) 5.22369 1.26693 0.633465 0.773771i \(-0.281632\pi\)
0.633465 + 0.773771i \(0.281632\pi\)
\(18\) 0 0
\(19\) −2.92789 −0.671703 −0.335852 0.941915i \(-0.609024\pi\)
−0.335852 + 0.941915i \(0.609024\pi\)
\(20\) −4.92789 −1.10191
\(21\) 0 0
\(22\) 12.4283 2.64972
\(23\) −7.70645 −1.60691 −0.803453 0.595368i \(-0.797006\pi\)
−0.803453 + 0.595368i \(0.797006\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) −5.37017 −1.01487
\(29\) 1.31118 0.243480 0.121740 0.992562i \(-0.461153\pi\)
0.121740 + 0.992562i \(0.461153\pi\)
\(30\) 0 0
\(31\) 2.32091 0.416847 0.208423 0.978039i \(-0.433167\pi\)
0.208423 + 0.978039i \(0.433167\pi\)
\(32\) −12.0353 −2.12756
\(33\) 0 0
\(34\) −13.7492 −2.35797
\(35\) 1.08975 0.184201
\(36\) 0 0
\(37\) 10.4283 1.71440 0.857200 0.514983i \(-0.172202\pi\)
0.857200 + 0.514983i \(0.172202\pi\)
\(38\) 7.70645 1.25015
\(39\) 0 0
\(40\) 7.70645 1.21850
\(41\) −4.98745 −0.778910 −0.389455 0.921046i \(-0.627337\pi\)
−0.389455 + 0.921046i \(0.627337\pi\)
\(42\) 0 0
\(43\) 5.96838 0.910169 0.455084 0.890448i \(-0.349609\pi\)
0.455084 + 0.890448i \(0.349609\pi\)
\(44\) −23.2687 −3.50789
\(45\) 0 0
\(46\) 20.2841 2.99072
\(47\) 8.51804 1.24248 0.621242 0.783619i \(-0.286628\pi\)
0.621242 + 0.783619i \(0.286628\pi\)
\(48\) 0 0
\(49\) −5.81244 −0.830349
\(50\) −2.63209 −0.372233
\(51\) 0 0
\(52\) 0 0
\(53\) −9.67627 −1.32914 −0.664569 0.747227i \(-0.731385\pi\)
−0.664569 + 0.747227i \(0.731385\pi\)
\(54\) 0 0
\(55\) 4.72184 0.636693
\(56\) 8.39811 1.12224
\(57\) 0 0
\(58\) −3.45115 −0.453158
\(59\) 3.16696 0.412302 0.206151 0.978520i \(-0.433906\pi\)
0.206151 + 0.978520i \(0.433906\pi\)
\(60\) 0 0
\(61\) 6.32091 0.809309 0.404655 0.914470i \(-0.367392\pi\)
0.404655 + 0.914470i \(0.367392\pi\)
\(62\) −6.10883 −0.775822
\(63\) 0 0
\(64\) 10.8213 1.35266
\(65\) 0 0
\(66\) 0 0
\(67\) 1.57536 0.192461 0.0962303 0.995359i \(-0.469321\pi\)
0.0962303 + 0.995359i \(0.469321\pi\)
\(68\) 25.7417 3.12164
\(69\) 0 0
\(70\) −2.86832 −0.342830
\(71\) 6.00225 0.712336 0.356168 0.934422i \(-0.384083\pi\)
0.356168 + 0.934422i \(0.384083\pi\)
\(72\) 0 0
\(73\) −12.3098 −1.44075 −0.720374 0.693586i \(-0.756030\pi\)
−0.720374 + 0.693586i \(0.756030\pi\)
\(74\) −27.4482 −3.19079
\(75\) 0 0
\(76\) −14.4283 −1.65504
\(77\) 5.14562 0.586398
\(78\) 0 0
\(79\) −3.04333 −0.342401 −0.171201 0.985236i \(-0.554765\pi\)
−0.171201 + 0.985236i \(0.554765\pi\)
\(80\) −10.4283 −1.16592
\(81\) 0 0
\(82\) 13.1274 1.44968
\(83\) 1.40782 0.154528 0.0772640 0.997011i \(-0.475382\pi\)
0.0772640 + 0.997011i \(0.475382\pi\)
\(84\) 0 0
\(85\) −5.22369 −0.566588
\(86\) −15.7093 −1.69398
\(87\) 0 0
\(88\) 36.3886 3.87904
\(89\) 8.67483 0.919530 0.459765 0.888041i \(-0.347934\pi\)
0.459765 + 0.888041i \(0.347934\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −37.9765 −3.95933
\(93\) 0 0
\(94\) −22.4202 −2.31247
\(95\) 2.92789 0.300395
\(96\) 0 0
\(97\) 11.0324 1.12017 0.560087 0.828434i \(-0.310768\pi\)
0.560087 + 0.828434i \(0.310768\pi\)
\(98\) 15.2989 1.54542
\(99\) 0 0
\(100\) 4.92789 0.492789
\(101\) −9.21492 −0.916918 −0.458459 0.888715i \(-0.651598\pi\)
−0.458459 + 0.888715i \(0.651598\pi\)
\(102\) 0 0
\(103\) 14.8586 1.46406 0.732031 0.681271i \(-0.238572\pi\)
0.732031 + 0.681271i \(0.238572\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 25.4688 2.47375
\(107\) 6.89487 0.666552 0.333276 0.942829i \(-0.391846\pi\)
0.333276 + 0.942829i \(0.391846\pi\)
\(108\) 0 0
\(109\) 14.5790 1.39642 0.698208 0.715895i \(-0.253981\pi\)
0.698208 + 0.715895i \(0.253981\pi\)
\(110\) −12.4283 −1.18499
\(111\) 0 0
\(112\) −11.3642 −1.07382
\(113\) 13.2938 1.25057 0.625286 0.780395i \(-0.284982\pi\)
0.625286 + 0.780395i \(0.284982\pi\)
\(114\) 0 0
\(115\) 7.70645 0.718631
\(116\) 6.46136 0.599922
\(117\) 0 0
\(118\) −8.33570 −0.767364
\(119\) −5.69251 −0.521832
\(120\) 0 0
\(121\) 11.2958 1.02689
\(122\) −16.6372 −1.50626
\(123\) 0 0
\(124\) 11.4372 1.02709
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 15.4548 1.37139 0.685696 0.727888i \(-0.259498\pi\)
0.685696 + 0.727888i \(0.259498\pi\)
\(128\) −4.41210 −0.389978
\(129\) 0 0
\(130\) 0 0
\(131\) −8.48870 −0.741661 −0.370831 0.928701i \(-0.620927\pi\)
−0.370831 + 0.928701i \(0.620927\pi\)
\(132\) 0 0
\(133\) 3.19067 0.276666
\(134\) −4.14648 −0.358201
\(135\) 0 0
\(136\) −40.2561 −3.45193
\(137\) 5.72185 0.488851 0.244426 0.969668i \(-0.421401\pi\)
0.244426 + 0.969668i \(0.421401\pi\)
\(138\) 0 0
\(139\) −18.3938 −1.56014 −0.780072 0.625689i \(-0.784818\pi\)
−0.780072 + 0.625689i \(0.784818\pi\)
\(140\) 5.37017 0.453862
\(141\) 0 0
\(142\) −15.7985 −1.32578
\(143\) 0 0
\(144\) 0 0
\(145\) −1.31118 −0.108888
\(146\) 32.4004 2.68147
\(147\) 0 0
\(148\) 51.3894 4.22419
\(149\) −22.6603 −1.85640 −0.928202 0.372076i \(-0.878646\pi\)
−0.928202 + 0.372076i \(0.878646\pi\)
\(150\) 0 0
\(151\) 2.26871 0.184625 0.0923125 0.995730i \(-0.470574\pi\)
0.0923125 + 0.995730i \(0.470574\pi\)
\(152\) 22.5636 1.83015
\(153\) 0 0
\(154\) −13.5437 −1.09139
\(155\) −2.32091 −0.186420
\(156\) 0 0
\(157\) −13.8934 −1.10882 −0.554409 0.832245i \(-0.687056\pi\)
−0.554409 + 0.832245i \(0.687056\pi\)
\(158\) 8.01031 0.637266
\(159\) 0 0
\(160\) 12.0353 0.951472
\(161\) 8.39811 0.661864
\(162\) 0 0
\(163\) −24.6218 −1.92853 −0.964264 0.264943i \(-0.914647\pi\)
−0.964264 + 0.264943i \(0.914647\pi\)
\(164\) −24.5776 −1.91919
\(165\) 0 0
\(166\) −3.70550 −0.287603
\(167\) −3.79988 −0.294044 −0.147022 0.989133i \(-0.546969\pi\)
−0.147022 + 0.989133i \(0.546969\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 13.7492 1.05452
\(171\) 0 0
\(172\) 29.4115 2.24260
\(173\) 18.0803 1.37462 0.687309 0.726365i \(-0.258792\pi\)
0.687309 + 0.726365i \(0.258792\pi\)
\(174\) 0 0
\(175\) −1.08975 −0.0823774
\(176\) −49.2407 −3.71166
\(177\) 0 0
\(178\) −22.8329 −1.71140
\(179\) 25.6449 1.91679 0.958394 0.285448i \(-0.0921425\pi\)
0.958394 + 0.285448i \(0.0921425\pi\)
\(180\) 0 0
\(181\) −19.0957 −1.41937 −0.709686 0.704518i \(-0.751163\pi\)
−0.709686 + 0.704518i \(0.751163\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 59.3894 4.37825
\(185\) −10.4283 −0.766703
\(186\) 0 0
\(187\) −24.6654 −1.80371
\(188\) 41.9759 3.06141
\(189\) 0 0
\(190\) −7.70645 −0.559085
\(191\) −24.1538 −1.74771 −0.873853 0.486190i \(-0.838386\pi\)
−0.873853 + 0.486190i \(0.838386\pi\)
\(192\) 0 0
\(193\) −12.7956 −0.921049 −0.460524 0.887647i \(-0.652339\pi\)
−0.460524 + 0.887647i \(0.652339\pi\)
\(194\) −29.0383 −2.08483
\(195\) 0 0
\(196\) −28.6431 −2.04593
\(197\) −0.652546 −0.0464920 −0.0232460 0.999730i \(-0.507400\pi\)
−0.0232460 + 0.999730i \(0.507400\pi\)
\(198\) 0 0
\(199\) −6.38779 −0.452818 −0.226409 0.974032i \(-0.572699\pi\)
−0.226409 + 0.974032i \(0.572699\pi\)
\(200\) −7.70645 −0.544929
\(201\) 0 0
\(202\) 24.2545 1.70654
\(203\) −1.42886 −0.100286
\(204\) 0 0
\(205\) 4.98745 0.348339
\(206\) −39.1092 −2.72487
\(207\) 0 0
\(208\) 0 0
\(209\) 13.8250 0.956296
\(210\) 0 0
\(211\) −17.4976 −1.20458 −0.602292 0.798276i \(-0.705746\pi\)
−0.602292 + 0.798276i \(0.705746\pi\)
\(212\) −47.6836 −3.27492
\(213\) 0 0
\(214\) −18.1479 −1.24056
\(215\) −5.96838 −0.407040
\(216\) 0 0
\(217\) −2.52921 −0.171694
\(218\) −38.3732 −2.59896
\(219\) 0 0
\(220\) 23.2687 1.56877
\(221\) 0 0
\(222\) 0 0
\(223\) 2.65350 0.177692 0.0888458 0.996045i \(-0.471682\pi\)
0.0888458 + 0.996045i \(0.471682\pi\)
\(224\) 13.1154 0.876312
\(225\) 0 0
\(226\) −34.9904 −2.32753
\(227\) 5.10964 0.339139 0.169569 0.985518i \(-0.445762\pi\)
0.169569 + 0.985518i \(0.445762\pi\)
\(228\) 0 0
\(229\) −17.2929 −1.14275 −0.571375 0.820689i \(-0.693590\pi\)
−0.571375 + 0.820689i \(0.693590\pi\)
\(230\) −20.2841 −1.33749
\(231\) 0 0
\(232\) −10.1046 −0.663397
\(233\) 2.40701 0.157688 0.0788441 0.996887i \(-0.474877\pi\)
0.0788441 + 0.996887i \(0.474877\pi\)
\(234\) 0 0
\(235\) −8.51804 −0.555656
\(236\) 15.6064 1.01589
\(237\) 0 0
\(238\) 14.9832 0.971216
\(239\) −8.83530 −0.571508 −0.285754 0.958303i \(-0.592244\pi\)
−0.285754 + 0.958303i \(0.592244\pi\)
\(240\) 0 0
\(241\) 8.54054 0.550145 0.275072 0.961424i \(-0.411298\pi\)
0.275072 + 0.961424i \(0.411298\pi\)
\(242\) −29.7314 −1.91121
\(243\) 0 0
\(244\) 31.1487 1.99409
\(245\) 5.81244 0.371343
\(246\) 0 0
\(247\) 0 0
\(248\) −17.8860 −1.13576
\(249\) 0 0
\(250\) 2.63209 0.166468
\(251\) 2.54513 0.160647 0.0803237 0.996769i \(-0.474405\pi\)
0.0803237 + 0.996769i \(0.474405\pi\)
\(252\) 0 0
\(253\) 36.3886 2.28773
\(254\) −40.6784 −2.55239
\(255\) 0 0
\(256\) −10.0296 −0.626850
\(257\) 12.0513 0.751737 0.375868 0.926673i \(-0.377344\pi\)
0.375868 + 0.926673i \(0.377344\pi\)
\(258\) 0 0
\(259\) −11.3642 −0.706139
\(260\) 0 0
\(261\) 0 0
\(262\) 22.3430 1.38036
\(263\) −10.4729 −0.645788 −0.322894 0.946435i \(-0.604656\pi\)
−0.322894 + 0.946435i \(0.604656\pi\)
\(264\) 0 0
\(265\) 9.67627 0.594409
\(266\) −8.39811 −0.514921
\(267\) 0 0
\(268\) 7.76318 0.474212
\(269\) 8.92325 0.544060 0.272030 0.962289i \(-0.412305\pi\)
0.272030 + 0.962289i \(0.412305\pi\)
\(270\) 0 0
\(271\) −6.77479 −0.411539 −0.205770 0.978600i \(-0.565970\pi\)
−0.205770 + 0.978600i \(0.565970\pi\)
\(272\) 54.4741 3.30298
\(273\) 0 0
\(274\) −15.0604 −0.909834
\(275\) −4.72184 −0.284738
\(276\) 0 0
\(277\) −5.63658 −0.338669 −0.169335 0.985559i \(-0.554162\pi\)
−0.169335 + 0.985559i \(0.554162\pi\)
\(278\) 48.4142 2.90369
\(279\) 0 0
\(280\) −8.39811 −0.501883
\(281\) 12.5297 0.747456 0.373728 0.927538i \(-0.378079\pi\)
0.373728 + 0.927538i \(0.378079\pi\)
\(282\) 0 0
\(283\) 25.3442 1.50656 0.753279 0.657701i \(-0.228471\pi\)
0.753279 + 0.657701i \(0.228471\pi\)
\(284\) 29.5784 1.75516
\(285\) 0 0
\(286\) 0 0
\(287\) 5.43508 0.320823
\(288\) 0 0
\(289\) 10.2869 0.605111
\(290\) 3.45115 0.202658
\(291\) 0 0
\(292\) −60.6611 −3.54992
\(293\) −17.8455 −1.04254 −0.521272 0.853391i \(-0.674542\pi\)
−0.521272 + 0.853391i \(0.674542\pi\)
\(294\) 0 0
\(295\) −3.16696 −0.184387
\(296\) −80.3652 −4.67113
\(297\) 0 0
\(298\) 59.6439 3.45508
\(299\) 0 0
\(300\) 0 0
\(301\) −6.50404 −0.374887
\(302\) −5.97144 −0.343618
\(303\) 0 0
\(304\) −30.5329 −1.75118
\(305\) −6.32091 −0.361934
\(306\) 0 0
\(307\) −10.0377 −0.572880 −0.286440 0.958098i \(-0.592472\pi\)
−0.286440 + 0.958098i \(0.592472\pi\)
\(308\) 25.3571 1.44485
\(309\) 0 0
\(310\) 6.10883 0.346958
\(311\) 8.76317 0.496914 0.248457 0.968643i \(-0.420077\pi\)
0.248457 + 0.968643i \(0.420077\pi\)
\(312\) 0 0
\(313\) 4.37893 0.247512 0.123756 0.992313i \(-0.460506\pi\)
0.123756 + 0.992313i \(0.460506\pi\)
\(314\) 36.5688 2.06369
\(315\) 0 0
\(316\) −14.9972 −0.843657
\(317\) −11.7036 −0.657338 −0.328669 0.944445i \(-0.606600\pi\)
−0.328669 + 0.944445i \(0.606600\pi\)
\(318\) 0 0
\(319\) −6.19119 −0.346640
\(320\) −10.8213 −0.604930
\(321\) 0 0
\(322\) −22.1046 −1.23184
\(323\) −15.2944 −0.851001
\(324\) 0 0
\(325\) 0 0
\(326\) 64.8067 3.58931
\(327\) 0 0
\(328\) 38.4356 2.12225
\(329\) −9.28254 −0.511763
\(330\) 0 0
\(331\) 12.7232 0.699332 0.349666 0.936874i \(-0.386295\pi\)
0.349666 + 0.936874i \(0.386295\pi\)
\(332\) 6.93757 0.380748
\(333\) 0 0
\(334\) 10.0016 0.547265
\(335\) −1.57536 −0.0860710
\(336\) 0 0
\(337\) −4.03730 −0.219926 −0.109963 0.993936i \(-0.535073\pi\)
−0.109963 + 0.993936i \(0.535073\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −25.7417 −1.39604
\(341\) −10.9589 −0.593460
\(342\) 0 0
\(343\) 13.9624 0.753897
\(344\) −45.9950 −2.47989
\(345\) 0 0
\(346\) −47.5889 −2.55839
\(347\) 0.344344 0.0184854 0.00924268 0.999957i \(-0.497058\pi\)
0.00924268 + 0.999957i \(0.497058\pi\)
\(348\) 0 0
\(349\) 34.6402 1.85425 0.927125 0.374752i \(-0.122272\pi\)
0.927125 + 0.374752i \(0.122272\pi\)
\(350\) 2.86832 0.153318
\(351\) 0 0
\(352\) 56.8286 3.02898
\(353\) 17.8402 0.949541 0.474770 0.880110i \(-0.342531\pi\)
0.474770 + 0.880110i \(0.342531\pi\)
\(354\) 0 0
\(355\) −6.00225 −0.318567
\(356\) 42.7486 2.26567
\(357\) 0 0
\(358\) −67.4996 −3.56746
\(359\) 7.22285 0.381207 0.190604 0.981667i \(-0.438955\pi\)
0.190604 + 0.981667i \(0.438955\pi\)
\(360\) 0 0
\(361\) −10.4275 −0.548815
\(362\) 50.2616 2.64169
\(363\) 0 0
\(364\) 0 0
\(365\) 12.3098 0.644322
\(366\) 0 0
\(367\) −29.7505 −1.55296 −0.776481 0.630141i \(-0.782997\pi\)
−0.776481 + 0.630141i \(0.782997\pi\)
\(368\) −80.3652 −4.18932
\(369\) 0 0
\(370\) 27.4482 1.42696
\(371\) 10.5447 0.547455
\(372\) 0 0
\(373\) 3.84177 0.198919 0.0994597 0.995042i \(-0.468289\pi\)
0.0994597 + 0.995042i \(0.468289\pi\)
\(374\) 64.9215 3.35701
\(375\) 0 0
\(376\) −65.6439 −3.38533
\(377\) 0 0
\(378\) 0 0
\(379\) −31.1026 −1.59763 −0.798816 0.601576i \(-0.794540\pi\)
−0.798816 + 0.601576i \(0.794540\pi\)
\(380\) 14.4283 0.740156
\(381\) 0 0
\(382\) 63.5749 3.25277
\(383\) −12.9609 −0.662271 −0.331136 0.943583i \(-0.607432\pi\)
−0.331136 + 0.943583i \(0.607432\pi\)
\(384\) 0 0
\(385\) −5.14562 −0.262245
\(386\) 33.6792 1.71423
\(387\) 0 0
\(388\) 54.3666 2.76005
\(389\) 14.1302 0.716432 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(390\) 0 0
\(391\) −40.2561 −2.03584
\(392\) 44.7933 2.26241
\(393\) 0 0
\(394\) 1.71756 0.0865294
\(395\) 3.04333 0.153126
\(396\) 0 0
\(397\) 28.3100 1.42084 0.710419 0.703779i \(-0.248505\pi\)
0.710419 + 0.703779i \(0.248505\pi\)
\(398\) 16.8132 0.842770
\(399\) 0 0
\(400\) 10.4283 0.521415
\(401\) −4.43551 −0.221499 −0.110749 0.993848i \(-0.535325\pi\)
−0.110749 + 0.993848i \(0.535325\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −45.4101 −2.25923
\(405\) 0 0
\(406\) 3.76089 0.186650
\(407\) −49.2407 −2.44077
\(408\) 0 0
\(409\) 8.96839 0.443459 0.221729 0.975108i \(-0.428830\pi\)
0.221729 + 0.975108i \(0.428830\pi\)
\(410\) −13.1274 −0.648317
\(411\) 0 0
\(412\) 73.2216 3.60737
\(413\) −3.45119 −0.169822
\(414\) 0 0
\(415\) −1.40782 −0.0691071
\(416\) 0 0
\(417\) 0 0
\(418\) −36.3886 −1.77983
\(419\) −34.3921 −1.68016 −0.840081 0.542461i \(-0.817493\pi\)
−0.840081 + 0.542461i \(0.817493\pi\)
\(420\) 0 0
\(421\) −20.1940 −0.984198 −0.492099 0.870539i \(-0.663770\pi\)
−0.492099 + 0.870539i \(0.663770\pi\)
\(422\) 46.0552 2.24193
\(423\) 0 0
\(424\) 74.5698 3.62143
\(425\) 5.22369 0.253386
\(426\) 0 0
\(427\) −6.88821 −0.333344
\(428\) 33.9771 1.64235
\(429\) 0 0
\(430\) 15.7093 0.757569
\(431\) −20.7692 −1.00042 −0.500208 0.865905i \(-0.666743\pi\)
−0.500208 + 0.865905i \(0.666743\pi\)
\(432\) 0 0
\(433\) 36.6923 1.76332 0.881661 0.471884i \(-0.156426\pi\)
0.881661 + 0.471884i \(0.156426\pi\)
\(434\) 6.65710 0.319551
\(435\) 0 0
\(436\) 71.8437 3.44069
\(437\) 22.5636 1.07936
\(438\) 0 0
\(439\) −20.2986 −0.968800 −0.484400 0.874847i \(-0.660962\pi\)
−0.484400 + 0.874847i \(0.660962\pi\)
\(440\) −36.3886 −1.73476
\(441\) 0 0
\(442\) 0 0
\(443\) −10.0068 −0.475439 −0.237720 0.971334i \(-0.576400\pi\)
−0.237720 + 0.971334i \(0.576400\pi\)
\(444\) 0 0
\(445\) −8.67483 −0.411226
\(446\) −6.98425 −0.330714
\(447\) 0 0
\(448\) −11.7925 −0.557145
\(449\) 10.5636 0.498528 0.249264 0.968436i \(-0.419811\pi\)
0.249264 + 0.968436i \(0.419811\pi\)
\(450\) 0 0
\(451\) 23.5500 1.10892
\(452\) 65.5102 3.08134
\(453\) 0 0
\(454\) −13.4490 −0.631194
\(455\) 0 0
\(456\) 0 0
\(457\) 4.81290 0.225138 0.112569 0.993644i \(-0.464092\pi\)
0.112569 + 0.993644i \(0.464092\pi\)
\(458\) 45.5165 2.12685
\(459\) 0 0
\(460\) 37.9765 1.77067
\(461\) 19.5639 0.911181 0.455591 0.890189i \(-0.349428\pi\)
0.455591 + 0.890189i \(0.349428\pi\)
\(462\) 0 0
\(463\) −1.03118 −0.0479230 −0.0239615 0.999713i \(-0.507628\pi\)
−0.0239615 + 0.999713i \(0.507628\pi\)
\(464\) 13.6734 0.634771
\(465\) 0 0
\(466\) −6.33545 −0.293484
\(467\) 12.4884 0.577896 0.288948 0.957345i \(-0.406694\pi\)
0.288948 + 0.957345i \(0.406694\pi\)
\(468\) 0 0
\(469\) −1.71675 −0.0792720
\(470\) 22.4202 1.03417
\(471\) 0 0
\(472\) −24.4060 −1.12338
\(473\) −28.1817 −1.29580
\(474\) 0 0
\(475\) −2.92789 −0.134341
\(476\) −28.0521 −1.28576
\(477\) 0 0
\(478\) 23.2553 1.06367
\(479\) −6.64403 −0.303574 −0.151787 0.988413i \(-0.548503\pi\)
−0.151787 + 0.988413i \(0.548503\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −22.4795 −1.02391
\(483\) 0 0
\(484\) 55.6642 2.53019
\(485\) −11.0324 −0.500957
\(486\) 0 0
\(487\) −0.826873 −0.0374692 −0.0187346 0.999824i \(-0.505964\pi\)
−0.0187346 + 0.999824i \(0.505964\pi\)
\(488\) −48.7118 −2.20508
\(489\) 0 0
\(490\) −15.2989 −0.691132
\(491\) 12.8198 0.578550 0.289275 0.957246i \(-0.406586\pi\)
0.289275 + 0.957246i \(0.406586\pi\)
\(492\) 0 0
\(493\) 6.84920 0.308473
\(494\) 0 0
\(495\) 0 0
\(496\) 24.2031 1.08675
\(497\) −6.54096 −0.293402
\(498\) 0 0
\(499\) −19.8651 −0.889283 −0.444642 0.895709i \(-0.646669\pi\)
−0.444642 + 0.895709i \(0.646669\pi\)
\(500\) −4.92789 −0.220382
\(501\) 0 0
\(502\) −6.69901 −0.298992
\(503\) 18.7090 0.834194 0.417097 0.908862i \(-0.363048\pi\)
0.417097 + 0.908862i \(0.363048\pi\)
\(504\) 0 0
\(505\) 9.21492 0.410058
\(506\) −95.7781 −4.25785
\(507\) 0 0
\(508\) 76.1595 3.37903
\(509\) 10.0362 0.444848 0.222424 0.974950i \(-0.428603\pi\)
0.222424 + 0.974950i \(0.428603\pi\)
\(510\) 0 0
\(511\) 13.4146 0.593425
\(512\) 35.2230 1.55665
\(513\) 0 0
\(514\) −31.7200 −1.39911
\(515\) −14.8586 −0.654749
\(516\) 0 0
\(517\) −40.2208 −1.76891
\(518\) 29.9117 1.31424
\(519\) 0 0
\(520\) 0 0
\(521\) −2.06270 −0.0903687 −0.0451844 0.998979i \(-0.514388\pi\)
−0.0451844 + 0.998979i \(0.514388\pi\)
\(522\) 0 0
\(523\) −32.0369 −1.40088 −0.700438 0.713713i \(-0.747012\pi\)
−0.700438 + 0.713713i \(0.747012\pi\)
\(524\) −41.8314 −1.82741
\(525\) 0 0
\(526\) 27.5656 1.20192
\(527\) 12.1237 0.528116
\(528\) 0 0
\(529\) 36.3894 1.58215
\(530\) −25.4688 −1.10629
\(531\) 0 0
\(532\) 15.7232 0.681689
\(533\) 0 0
\(534\) 0 0
\(535\) −6.89487 −0.298091
\(536\) −12.1404 −0.524386
\(537\) 0 0
\(538\) −23.4868 −1.01259
\(539\) 27.4454 1.18216
\(540\) 0 0
\(541\) 11.1795 0.480644 0.240322 0.970693i \(-0.422747\pi\)
0.240322 + 0.970693i \(0.422747\pi\)
\(542\) 17.8318 0.765943
\(543\) 0 0
\(544\) −62.8685 −2.69546
\(545\) −14.5790 −0.624496
\(546\) 0 0
\(547\) −0.0903080 −0.00386129 −0.00193064 0.999998i \(-0.500615\pi\)
−0.00193064 + 0.999998i \(0.500615\pi\)
\(548\) 28.1967 1.20450
\(549\) 0 0
\(550\) 12.4283 0.529944
\(551\) −3.83899 −0.163547
\(552\) 0 0
\(553\) 3.31647 0.141031
\(554\) 14.8360 0.630320
\(555\) 0 0
\(556\) −90.6427 −3.84411
\(557\) 28.1241 1.19166 0.595829 0.803111i \(-0.296824\pi\)
0.595829 + 0.803111i \(0.296824\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 11.3642 0.480227
\(561\) 0 0
\(562\) −32.9791 −1.39114
\(563\) −23.6557 −0.996967 −0.498484 0.866899i \(-0.666110\pi\)
−0.498484 + 0.866899i \(0.666110\pi\)
\(564\) 0 0
\(565\) −13.2938 −0.559273
\(566\) −66.7082 −2.80396
\(567\) 0 0
\(568\) −46.2561 −1.94086
\(569\) −9.76686 −0.409448 −0.204724 0.978820i \(-0.565630\pi\)
−0.204724 + 0.978820i \(0.565630\pi\)
\(570\) 0 0
\(571\) −20.9688 −0.877518 −0.438759 0.898605i \(-0.644582\pi\)
−0.438759 + 0.898605i \(0.644582\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −14.3056 −0.597105
\(575\) −7.70645 −0.321381
\(576\) 0 0
\(577\) 7.22602 0.300823 0.150412 0.988623i \(-0.451940\pi\)
0.150412 + 0.988623i \(0.451940\pi\)
\(578\) −27.0760 −1.12621
\(579\) 0 0
\(580\) −6.46136 −0.268293
\(581\) −1.53417 −0.0636481
\(582\) 0 0
\(583\) 45.6898 1.89228
\(584\) 94.8646 3.92552
\(585\) 0 0
\(586\) 46.9708 1.94035
\(587\) −24.1904 −0.998443 −0.499221 0.866475i \(-0.666381\pi\)
−0.499221 + 0.866475i \(0.666381\pi\)
\(588\) 0 0
\(589\) −6.79535 −0.279997
\(590\) 8.33570 0.343176
\(591\) 0 0
\(592\) 108.749 4.46957
\(593\) −10.5786 −0.434410 −0.217205 0.976126i \(-0.569694\pi\)
−0.217205 + 0.976126i \(0.569694\pi\)
\(594\) 0 0
\(595\) 5.69251 0.233370
\(596\) −111.667 −4.57408
\(597\) 0 0
\(598\) 0 0
\(599\) 25.8978 1.05816 0.529078 0.848573i \(-0.322538\pi\)
0.529078 + 0.848573i \(0.322538\pi\)
\(600\) 0 0
\(601\) −15.3046 −0.624289 −0.312144 0.950035i \(-0.601047\pi\)
−0.312144 + 0.950035i \(0.601047\pi\)
\(602\) 17.1192 0.697727
\(603\) 0 0
\(604\) 11.1799 0.454905
\(605\) −11.2958 −0.459238
\(606\) 0 0
\(607\) −38.9448 −1.58072 −0.790360 0.612643i \(-0.790107\pi\)
−0.790360 + 0.612643i \(0.790107\pi\)
\(608\) 35.2379 1.42909
\(609\) 0 0
\(610\) 16.6372 0.673620
\(611\) 0 0
\(612\) 0 0
\(613\) −40.5599 −1.63820 −0.819100 0.573651i \(-0.805527\pi\)
−0.819100 + 0.573651i \(0.805527\pi\)
\(614\) 26.4200 1.06623
\(615\) 0 0
\(616\) −39.6545 −1.59773
\(617\) −31.6607 −1.27461 −0.637307 0.770610i \(-0.719952\pi\)
−0.637307 + 0.770610i \(0.719952\pi\)
\(618\) 0 0
\(619\) −18.4523 −0.741661 −0.370831 0.928700i \(-0.620927\pi\)
−0.370831 + 0.928700i \(0.620927\pi\)
\(620\) −11.4372 −0.459327
\(621\) 0 0
\(622\) −23.0654 −0.924839
\(623\) −9.45340 −0.378742
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −11.5257 −0.460661
\(627\) 0 0
\(628\) −68.4653 −2.73206
\(629\) 54.4741 2.17203
\(630\) 0 0
\(631\) −33.5073 −1.33390 −0.666952 0.745101i \(-0.732401\pi\)
−0.666952 + 0.745101i \(0.732401\pi\)
\(632\) 23.4533 0.932921
\(633\) 0 0
\(634\) 30.8048 1.22342
\(635\) −15.4548 −0.613305
\(636\) 0 0
\(637\) 0 0
\(638\) 16.2958 0.645155
\(639\) 0 0
\(640\) 4.41210 0.174403
\(641\) 15.9434 0.629726 0.314863 0.949137i \(-0.398041\pi\)
0.314863 + 0.949137i \(0.398041\pi\)
\(642\) 0 0
\(643\) 14.7201 0.580506 0.290253 0.956950i \(-0.406261\pi\)
0.290253 + 0.956950i \(0.406261\pi\)
\(644\) 41.3849 1.63079
\(645\) 0 0
\(646\) 40.2561 1.58385
\(647\) −37.0838 −1.45791 −0.728957 0.684559i \(-0.759995\pi\)
−0.728957 + 0.684559i \(0.759995\pi\)
\(648\) 0 0
\(649\) −14.9538 −0.586990
\(650\) 0 0
\(651\) 0 0
\(652\) −121.333 −4.75178
\(653\) −20.5706 −0.804988 −0.402494 0.915423i \(-0.631857\pi\)
−0.402494 + 0.915423i \(0.631857\pi\)
\(654\) 0 0
\(655\) 8.48870 0.331681
\(656\) −52.0106 −2.03067
\(657\) 0 0
\(658\) 24.4325 0.952476
\(659\) 29.6632 1.15552 0.577758 0.816208i \(-0.303928\pi\)
0.577758 + 0.816208i \(0.303928\pi\)
\(660\) 0 0
\(661\) 16.1054 0.626427 0.313213 0.949683i \(-0.398595\pi\)
0.313213 + 0.949683i \(0.398595\pi\)
\(662\) −33.4887 −1.30157
\(663\) 0 0
\(664\) −10.8493 −0.421034
\(665\) −3.19067 −0.123729
\(666\) 0 0
\(667\) −10.1046 −0.391250
\(668\) −18.7254 −0.724507
\(669\) 0 0
\(670\) 4.14648 0.160193
\(671\) −29.8463 −1.15220
\(672\) 0 0
\(673\) 7.06634 0.272387 0.136194 0.990682i \(-0.456513\pi\)
0.136194 + 0.990682i \(0.456513\pi\)
\(674\) 10.6265 0.409319
\(675\) 0 0
\(676\) 0 0
\(677\) −23.6740 −0.909866 −0.454933 0.890526i \(-0.650337\pi\)
−0.454933 + 0.890526i \(0.650337\pi\)
\(678\) 0 0
\(679\) −12.0226 −0.461385
\(680\) 40.2561 1.54375
\(681\) 0 0
\(682\) 28.8449 1.10453
\(683\) 20.1994 0.772909 0.386454 0.922309i \(-0.373700\pi\)
0.386454 + 0.922309i \(0.373700\pi\)
\(684\) 0 0
\(685\) −5.72185 −0.218621
\(686\) −36.7502 −1.40313
\(687\) 0 0
\(688\) 62.2400 2.37288
\(689\) 0 0
\(690\) 0 0
\(691\) 31.1378 1.18454 0.592269 0.805740i \(-0.298232\pi\)
0.592269 + 0.805740i \(0.298232\pi\)
\(692\) 89.0975 3.38698
\(693\) 0 0
\(694\) −0.906344 −0.0344044
\(695\) 18.3938 0.697718
\(696\) 0 0
\(697\) −26.0529 −0.986824
\(698\) −91.1762 −3.45107
\(699\) 0 0
\(700\) −5.37017 −0.202973
\(701\) 24.0928 0.909974 0.454987 0.890498i \(-0.349644\pi\)
0.454987 + 0.890498i \(0.349644\pi\)
\(702\) 0 0
\(703\) −30.5329 −1.15157
\(704\) −51.0965 −1.92577
\(705\) 0 0
\(706\) −46.9571 −1.76725
\(707\) 10.0420 0.377667
\(708\) 0 0
\(709\) −4.78080 −0.179547 −0.0897734 0.995962i \(-0.528614\pi\)
−0.0897734 + 0.995962i \(0.528614\pi\)
\(710\) 15.7985 0.592906
\(711\) 0 0
\(712\) −66.8522 −2.50539
\(713\) −17.8860 −0.669834
\(714\) 0 0
\(715\) 0 0
\(716\) 126.375 4.72286
\(717\) 0 0
\(718\) −19.0112 −0.709490
\(719\) −13.5084 −0.503779 −0.251889 0.967756i \(-0.581052\pi\)
−0.251889 + 0.967756i \(0.581052\pi\)
\(720\) 0 0
\(721\) −16.1922 −0.603028
\(722\) 27.4460 1.02144
\(723\) 0 0
\(724\) −94.1014 −3.49725
\(725\) 1.31118 0.0486961
\(726\) 0 0
\(727\) −6.06108 −0.224793 −0.112397 0.993663i \(-0.535853\pi\)
−0.112397 + 0.993663i \(0.535853\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −32.4004 −1.19919
\(731\) 31.1769 1.15312
\(732\) 0 0
\(733\) −5.63897 −0.208280 −0.104140 0.994563i \(-0.533209\pi\)
−0.104140 + 0.994563i \(0.533209\pi\)
\(734\) 78.3059 2.89032
\(735\) 0 0
\(736\) 92.7493 3.41878
\(737\) −7.43858 −0.274004
\(738\) 0 0
\(739\) 3.12716 0.115035 0.0575173 0.998345i \(-0.481682\pi\)
0.0575173 + 0.998345i \(0.481682\pi\)
\(740\) −51.3894 −1.88911
\(741\) 0 0
\(742\) −27.7546 −1.01890
\(743\) −48.7893 −1.78991 −0.894953 0.446161i \(-0.852791\pi\)
−0.894953 + 0.446161i \(0.852791\pi\)
\(744\) 0 0
\(745\) 22.6603 0.830209
\(746\) −10.1119 −0.370222
\(747\) 0 0
\(748\) −121.548 −4.44425
\(749\) −7.51368 −0.274544
\(750\) 0 0
\(751\) −44.6808 −1.63042 −0.815212 0.579163i \(-0.803380\pi\)
−0.815212 + 0.579163i \(0.803380\pi\)
\(752\) 88.8286 3.23925
\(753\) 0 0
\(754\) 0 0
\(755\) −2.26871 −0.0825668
\(756\) 0 0
\(757\) −9.09782 −0.330666 −0.165333 0.986238i \(-0.552870\pi\)
−0.165333 + 0.986238i \(0.552870\pi\)
\(758\) 81.8647 2.97346
\(759\) 0 0
\(760\) −22.5636 −0.818469
\(761\) −30.5748 −1.10833 −0.554167 0.832405i \(-0.686963\pi\)
−0.554167 + 0.832405i \(0.686963\pi\)
\(762\) 0 0
\(763\) −15.8875 −0.575165
\(764\) −119.027 −4.30625
\(765\) 0 0
\(766\) 34.1142 1.23260
\(767\) 0 0
\(768\) 0 0
\(769\) 27.2459 0.982514 0.491257 0.871015i \(-0.336538\pi\)
0.491257 + 0.871015i \(0.336538\pi\)
\(770\) 13.5437 0.488082
\(771\) 0 0
\(772\) −63.0554 −2.26941
\(773\) 7.33531 0.263833 0.131916 0.991261i \(-0.457887\pi\)
0.131916 + 0.991261i \(0.457887\pi\)
\(774\) 0 0
\(775\) 2.32091 0.0833694
\(776\) −85.0210 −3.05207
\(777\) 0 0
\(778\) −37.1920 −1.33340
\(779\) 14.6027 0.523196
\(780\) 0 0
\(781\) −28.3417 −1.01414
\(782\) 105.958 3.78904
\(783\) 0 0
\(784\) −60.6139 −2.16478
\(785\) 13.8934 0.495878
\(786\) 0 0
\(787\) −51.3755 −1.83134 −0.915669 0.401933i \(-0.868338\pi\)
−0.915669 + 0.401933i \(0.868338\pi\)
\(788\) −3.21567 −0.114554
\(789\) 0 0
\(790\) −8.01031 −0.284994
\(791\) −14.4869 −0.515095
\(792\) 0 0
\(793\) 0 0
\(794\) −74.5144 −2.64442
\(795\) 0 0
\(796\) −31.4783 −1.11572
\(797\) 35.3318 1.25152 0.625758 0.780017i \(-0.284790\pi\)
0.625758 + 0.780017i \(0.284790\pi\)
\(798\) 0 0
\(799\) 44.4956 1.57414
\(800\) −12.0353 −0.425511
\(801\) 0 0
\(802\) 11.6746 0.412246
\(803\) 58.1247 2.05118
\(804\) 0 0
\(805\) −8.39811 −0.295995
\(806\) 0 0
\(807\) 0 0
\(808\) 71.0143 2.49828
\(809\) 31.0435 1.09143 0.545715 0.837971i \(-0.316258\pi\)
0.545715 + 0.837971i \(0.316258\pi\)
\(810\) 0 0
\(811\) 9.39427 0.329878 0.164939 0.986304i \(-0.447257\pi\)
0.164939 + 0.986304i \(0.447257\pi\)
\(812\) −7.04126 −0.247100
\(813\) 0 0
\(814\) 129.606 4.54268
\(815\) 24.6218 0.862464
\(816\) 0 0
\(817\) −17.4747 −0.611363
\(818\) −23.6056 −0.825350
\(819\) 0 0
\(820\) 24.5776 0.858287
\(821\) −6.18635 −0.215905 −0.107952 0.994156i \(-0.534429\pi\)
−0.107952 + 0.994156i \(0.534429\pi\)
\(822\) 0 0
\(823\) 22.6710 0.790263 0.395131 0.918625i \(-0.370699\pi\)
0.395131 + 0.918625i \(0.370699\pi\)
\(824\) −114.507 −3.98905
\(825\) 0 0
\(826\) 9.08384 0.316067
\(827\) 11.1599 0.388066 0.194033 0.980995i \(-0.437843\pi\)
0.194033 + 0.980995i \(0.437843\pi\)
\(828\) 0 0
\(829\) −19.7966 −0.687564 −0.343782 0.939049i \(-0.611708\pi\)
−0.343782 + 0.939049i \(0.611708\pi\)
\(830\) 3.70550 0.128620
\(831\) 0 0
\(832\) 0 0
\(833\) −30.3624 −1.05199
\(834\) 0 0
\(835\) 3.79988 0.131500
\(836\) 68.1281 2.35626
\(837\) 0 0
\(838\) 90.5229 3.12706
\(839\) 1.28267 0.0442826 0.0221413 0.999755i \(-0.492952\pi\)
0.0221413 + 0.999755i \(0.492952\pi\)
\(840\) 0 0
\(841\) −27.2808 −0.940717
\(842\) 53.1525 1.83176
\(843\) 0 0
\(844\) −86.2261 −2.96803
\(845\) 0 0
\(846\) 0 0
\(847\) −12.3096 −0.422961
\(848\) −100.907 −3.46516
\(849\) 0 0
\(850\) −13.7492 −0.471594
\(851\) −80.3652 −2.75488
\(852\) 0 0
\(853\) 12.0390 0.412208 0.206104 0.978530i \(-0.433922\pi\)
0.206104 + 0.978530i \(0.433922\pi\)
\(854\) 18.1304 0.620408
\(855\) 0 0
\(856\) −53.1350 −1.81612
\(857\) 28.1181 0.960497 0.480248 0.877133i \(-0.340547\pi\)
0.480248 + 0.877133i \(0.340547\pi\)
\(858\) 0 0
\(859\) −50.0048 −1.70614 −0.853071 0.521795i \(-0.825263\pi\)
−0.853071 + 0.521795i \(0.825263\pi\)
\(860\) −29.4115 −1.00292
\(861\) 0 0
\(862\) 54.6663 1.86194
\(863\) −41.7180 −1.42010 −0.710048 0.704153i \(-0.751327\pi\)
−0.710048 + 0.704153i \(0.751327\pi\)
\(864\) 0 0
\(865\) −18.0803 −0.614748
\(866\) −96.5775 −3.28184
\(867\) 0 0
\(868\) −12.4636 −0.423044
\(869\) 14.3701 0.487472
\(870\) 0 0
\(871\) 0 0
\(872\) −112.352 −3.80473
\(873\) 0 0
\(874\) −59.3894 −2.00888
\(875\) 1.08975 0.0368403
\(876\) 0 0
\(877\) 42.2045 1.42515 0.712573 0.701598i \(-0.247530\pi\)
0.712573 + 0.701598i \(0.247530\pi\)
\(878\) 53.4277 1.80310
\(879\) 0 0
\(880\) 49.2407 1.65990
\(881\) −49.4623 −1.66643 −0.833214 0.552950i \(-0.813502\pi\)
−0.833214 + 0.552950i \(0.813502\pi\)
\(882\) 0 0
\(883\) −7.24684 −0.243876 −0.121938 0.992538i \(-0.538911\pi\)
−0.121938 + 0.992538i \(0.538911\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 26.3389 0.884872
\(887\) −26.4616 −0.888492 −0.444246 0.895905i \(-0.646528\pi\)
−0.444246 + 0.895905i \(0.646528\pi\)
\(888\) 0 0
\(889\) −16.8419 −0.564858
\(890\) 22.8329 0.765361
\(891\) 0 0
\(892\) 13.0762 0.437822
\(893\) −24.9399 −0.834581
\(894\) 0 0
\(895\) −25.6449 −0.857214
\(896\) 4.80808 0.160627
\(897\) 0 0
\(898\) −27.8044 −0.927844
\(899\) 3.04313 0.101494
\(900\) 0 0
\(901\) −50.5458 −1.68392
\(902\) −61.9855 −2.06389
\(903\) 0 0
\(904\) −102.448 −3.40737
\(905\) 19.0957 0.634762
\(906\) 0 0
\(907\) −10.8327 −0.359695 −0.179848 0.983694i \(-0.557561\pi\)
−0.179848 + 0.983694i \(0.557561\pi\)
\(908\) 25.1797 0.835619
\(909\) 0 0
\(910\) 0 0
\(911\) 1.47923 0.0490092 0.0245046 0.999700i \(-0.492199\pi\)
0.0245046 + 0.999700i \(0.492199\pi\)
\(912\) 0 0
\(913\) −6.64749 −0.220000
\(914\) −12.6680 −0.419020
\(915\) 0 0
\(916\) −85.2176 −2.81567
\(917\) 9.25056 0.305481
\(918\) 0 0
\(919\) −24.8120 −0.818472 −0.409236 0.912428i \(-0.634205\pi\)
−0.409236 + 0.912428i \(0.634205\pi\)
\(920\) −59.3894 −1.95801
\(921\) 0 0
\(922\) −51.4939 −1.69586
\(923\) 0 0
\(924\) 0 0
\(925\) 10.4283 0.342880
\(926\) 2.71416 0.0891927
\(927\) 0 0
\(928\) −15.7804 −0.518018
\(929\) 0.603656 0.0198053 0.00990266 0.999951i \(-0.496848\pi\)
0.00990266 + 0.999951i \(0.496848\pi\)
\(930\) 0 0
\(931\) 17.0182 0.557748
\(932\) 11.8614 0.388535
\(933\) 0 0
\(934\) −32.8707 −1.07556
\(935\) 24.6654 0.806645
\(936\) 0 0
\(937\) −1.64793 −0.0538355 −0.0269178 0.999638i \(-0.508569\pi\)
−0.0269178 + 0.999638i \(0.508569\pi\)
\(938\) 4.51863 0.147538
\(939\) 0 0
\(940\) −41.9759 −1.36910
\(941\) −47.2291 −1.53962 −0.769812 0.638271i \(-0.779650\pi\)
−0.769812 + 0.638271i \(0.779650\pi\)
\(942\) 0 0
\(943\) 38.4356 1.25164
\(944\) 33.0259 1.07490
\(945\) 0 0
\(946\) 74.1767 2.41169
\(947\) −32.1407 −1.04443 −0.522217 0.852813i \(-0.674895\pi\)
−0.522217 + 0.852813i \(0.674895\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 7.70645 0.250030
\(951\) 0 0
\(952\) 43.8691 1.42181
\(953\) 14.6590 0.474853 0.237427 0.971405i \(-0.423696\pi\)
0.237427 + 0.971405i \(0.423696\pi\)
\(954\) 0 0
\(955\) 24.1538 0.781598
\(956\) −43.5393 −1.40816
\(957\) 0 0
\(958\) 17.4877 0.565001
\(959\) −6.23539 −0.201351
\(960\) 0 0
\(961\) −25.6134 −0.826239
\(962\) 0 0
\(963\) 0 0
\(964\) 42.0868 1.35553
\(965\) 12.7956 0.411906
\(966\) 0 0
\(967\) −8.77101 −0.282057 −0.141028 0.990006i \(-0.545041\pi\)
−0.141028 + 0.990006i \(0.545041\pi\)
\(968\) −87.0502 −2.79790
\(969\) 0 0
\(970\) 29.0383 0.932365
\(971\) 5.29481 0.169919 0.0849593 0.996384i \(-0.472924\pi\)
0.0849593 + 0.996384i \(0.472924\pi\)
\(972\) 0 0
\(973\) 20.0447 0.642603
\(974\) 2.17640 0.0697365
\(975\) 0 0
\(976\) 65.9163 2.10993
\(977\) −23.2334 −0.743303 −0.371651 0.928372i \(-0.621208\pi\)
−0.371651 + 0.928372i \(0.621208\pi\)
\(978\) 0 0
\(979\) −40.9612 −1.30912
\(980\) 28.6431 0.914969
\(981\) 0 0
\(982\) −33.7429 −1.07678
\(983\) −41.7741 −1.33239 −0.666194 0.745779i \(-0.732078\pi\)
−0.666194 + 0.745779i \(0.732078\pi\)
\(984\) 0 0
\(985\) 0.652546 0.0207919
\(986\) −18.0277 −0.574119
\(987\) 0 0
\(988\) 0 0
\(989\) −45.9950 −1.46256
\(990\) 0 0
\(991\) 27.6286 0.877650 0.438825 0.898573i \(-0.355395\pi\)
0.438825 + 0.898573i \(0.355395\pi\)
\(992\) −27.9327 −0.886865
\(993\) 0 0
\(994\) 17.2164 0.546070
\(995\) 6.38779 0.202506
\(996\) 0 0
\(997\) −9.14898 −0.289751 −0.144876 0.989450i \(-0.546278\pi\)
−0.144876 + 0.989450i \(0.546278\pi\)
\(998\) 52.2866 1.65510
\(999\) 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 7605.2.a.cl.1.1 5
3.2 odd 2 7605.2.a.cn.1.5 5
13.4 even 6 585.2.j.h.406.1 10
13.10 even 6 585.2.j.h.451.1 yes 10
13.12 even 2 7605.2.a.co.1.5 5
39.17 odd 6 585.2.j.i.406.5 yes 10
39.23 odd 6 585.2.j.i.451.5 yes 10
39.38 odd 2 7605.2.a.cm.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.j.h.406.1 10 13.4 even 6
585.2.j.h.451.1 yes 10 13.10 even 6
585.2.j.i.406.5 yes 10 39.17 odd 6
585.2.j.i.451.5 yes 10 39.23 odd 6
7605.2.a.cl.1.1 5 1.1 even 1 trivial
7605.2.a.cm.1.1 5 39.38 odd 2
7605.2.a.cn.1.5 5 3.2 odd 2
7605.2.a.co.1.5 5 13.12 even 2