Properties

Label 7448.2.a.bt.1.1
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $11$
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] = [7448,2,Mod(1,7448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7448, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7448.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.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: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 25x^{9} - 7x^{8} + 212x^{7} + 112x^{6} - 694x^{5} - 480x^{4} + 740x^{3} + 632x^{2} + 48x - 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.30652\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.30652 q^{3} -1.89470 q^{5} +7.93307 q^{9} +O(q^{10})\) \(q-3.30652 q^{3} -1.89470 q^{5} +7.93307 q^{9} -5.04694 q^{11} -5.48574 q^{13} +6.26487 q^{15} +4.64492 q^{17} -1.00000 q^{19} +1.62087 q^{23} -1.41010 q^{25} -16.3113 q^{27} +6.36766 q^{29} -9.87764 q^{31} +16.6878 q^{33} -2.33543 q^{37} +18.1387 q^{39} -2.07651 q^{41} -0.514880 q^{43} -15.0308 q^{45} -6.51172 q^{47} -15.3585 q^{51} -6.23852 q^{53} +9.56245 q^{55} +3.30652 q^{57} +4.59343 q^{59} -8.61446 q^{61} +10.3938 q^{65} -0.0521628 q^{67} -5.35943 q^{69} -8.16475 q^{71} +12.0580 q^{73} +4.66254 q^{75} -11.9542 q^{79} +30.1344 q^{81} +1.80009 q^{83} -8.80074 q^{85} -21.0548 q^{87} -10.5858 q^{89} +32.6606 q^{93} +1.89470 q^{95} -16.9780 q^{97} -40.0378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 3 q^{5} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 3 q^{5} + 17 q^{9} - 6 q^{11} - 8 q^{13} + 4 q^{15} + 13 q^{17} - 11 q^{19} - 2 q^{23} + 38 q^{25} - 21 q^{27} + 16 q^{29} - 6 q^{31} + 8 q^{33} + 9 q^{37} + q^{39} - 4 q^{41} + 31 q^{43} + 33 q^{45} + 7 q^{47} - 21 q^{51} - 11 q^{55} + 34 q^{59} + 42 q^{65} - 14 q^{67} - 19 q^{69} - 16 q^{71} + 8 q^{73} + 2 q^{75} - 10 q^{79} + 51 q^{81} - 16 q^{83} + 34 q^{85} + 72 q^{87} - 20 q^{89} + 50 q^{93} - 3 q^{95} + 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.30652 −1.90902 −0.954510 0.298179i \(-0.903621\pi\)
−0.954510 + 0.298179i \(0.903621\pi\)
\(4\) 0 0
\(5\) −1.89470 −0.847336 −0.423668 0.905817i \(-0.639258\pi\)
−0.423668 + 0.905817i \(0.639258\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 7.93307 2.64436
\(10\) 0 0
\(11\) −5.04694 −1.52171 −0.760855 0.648922i \(-0.775220\pi\)
−0.760855 + 0.648922i \(0.775220\pi\)
\(12\) 0 0
\(13\) −5.48574 −1.52147 −0.760736 0.649062i \(-0.775162\pi\)
−0.760736 + 0.649062i \(0.775162\pi\)
\(14\) 0 0
\(15\) 6.26487 1.61758
\(16\) 0 0
\(17\) 4.64492 1.12656 0.563279 0.826267i \(-0.309540\pi\)
0.563279 + 0.826267i \(0.309540\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.62087 0.337974 0.168987 0.985618i \(-0.445950\pi\)
0.168987 + 0.985618i \(0.445950\pi\)
\(24\) 0 0
\(25\) −1.41010 −0.282021
\(26\) 0 0
\(27\) −16.3113 −3.13911
\(28\) 0 0
\(29\) 6.36766 1.18245 0.591223 0.806508i \(-0.298645\pi\)
0.591223 + 0.806508i \(0.298645\pi\)
\(30\) 0 0
\(31\) −9.87764 −1.77408 −0.887038 0.461696i \(-0.847241\pi\)
−0.887038 + 0.461696i \(0.847241\pi\)
\(32\) 0 0
\(33\) 16.6878 2.90498
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.33543 −0.383942 −0.191971 0.981401i \(-0.561488\pi\)
−0.191971 + 0.981401i \(0.561488\pi\)
\(38\) 0 0
\(39\) 18.1387 2.90452
\(40\) 0 0
\(41\) −2.07651 −0.324297 −0.162148 0.986766i \(-0.551842\pi\)
−0.162148 + 0.986766i \(0.551842\pi\)
\(42\) 0 0
\(43\) −0.514880 −0.0785185 −0.0392592 0.999229i \(-0.512500\pi\)
−0.0392592 + 0.999229i \(0.512500\pi\)
\(44\) 0 0
\(45\) −15.0308 −2.24066
\(46\) 0 0
\(47\) −6.51172 −0.949832 −0.474916 0.880031i \(-0.657522\pi\)
−0.474916 + 0.880031i \(0.657522\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −15.3585 −2.15062
\(52\) 0 0
\(53\) −6.23852 −0.856926 −0.428463 0.903559i \(-0.640945\pi\)
−0.428463 + 0.903559i \(0.640945\pi\)
\(54\) 0 0
\(55\) 9.56245 1.28940
\(56\) 0 0
\(57\) 3.30652 0.437959
\(58\) 0 0
\(59\) 4.59343 0.598014 0.299007 0.954251i \(-0.403345\pi\)
0.299007 + 0.954251i \(0.403345\pi\)
\(60\) 0 0
\(61\) −8.61446 −1.10297 −0.551484 0.834185i \(-0.685938\pi\)
−0.551484 + 0.834185i \(0.685938\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.3938 1.28920
\(66\) 0 0
\(67\) −0.0521628 −0.00637270 −0.00318635 0.999995i \(-0.501014\pi\)
−0.00318635 + 0.999995i \(0.501014\pi\)
\(68\) 0 0
\(69\) −5.35943 −0.645199
\(70\) 0 0
\(71\) −8.16475 −0.968977 −0.484489 0.874798i \(-0.660994\pi\)
−0.484489 + 0.874798i \(0.660994\pi\)
\(72\) 0 0
\(73\) 12.0580 1.41128 0.705639 0.708571i \(-0.250660\pi\)
0.705639 + 0.708571i \(0.250660\pi\)
\(74\) 0 0
\(75\) 4.66254 0.538383
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.9542 −1.34495 −0.672474 0.740121i \(-0.734768\pi\)
−0.672474 + 0.740121i \(0.734768\pi\)
\(80\) 0 0
\(81\) 30.1344 3.34827
\(82\) 0 0
\(83\) 1.80009 0.197585 0.0987927 0.995108i \(-0.468502\pi\)
0.0987927 + 0.995108i \(0.468502\pi\)
\(84\) 0 0
\(85\) −8.80074 −0.954574
\(86\) 0 0
\(87\) −21.0548 −2.25731
\(88\) 0 0
\(89\) −10.5858 −1.12210 −0.561048 0.827783i \(-0.689602\pi\)
−0.561048 + 0.827783i \(0.689602\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 32.6606 3.38675
\(94\) 0 0
\(95\) 1.89470 0.194392
\(96\) 0 0
\(97\) −16.9780 −1.72386 −0.861929 0.507030i \(-0.830744\pi\)
−0.861929 + 0.507030i \(0.830744\pi\)
\(98\) 0 0
\(99\) −40.0378 −4.02395
\(100\) 0 0
\(101\) −7.65959 −0.762157 −0.381079 0.924543i \(-0.624447\pi\)
−0.381079 + 0.924543i \(0.624447\pi\)
\(102\) 0 0
\(103\) −0.794144 −0.0782493 −0.0391247 0.999234i \(-0.512457\pi\)
−0.0391247 + 0.999234i \(0.512457\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.53622 0.438532 0.219266 0.975665i \(-0.429634\pi\)
0.219266 + 0.975665i \(0.429634\pi\)
\(108\) 0 0
\(109\) 2.31875 0.222096 0.111048 0.993815i \(-0.464579\pi\)
0.111048 + 0.993815i \(0.464579\pi\)
\(110\) 0 0
\(111\) 7.72214 0.732953
\(112\) 0 0
\(113\) −6.48718 −0.610262 −0.305131 0.952310i \(-0.598700\pi\)
−0.305131 + 0.952310i \(0.598700\pi\)
\(114\) 0 0
\(115\) −3.07106 −0.286378
\(116\) 0 0
\(117\) −43.5188 −4.02331
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 14.4716 1.31560
\(122\) 0 0
\(123\) 6.86603 0.619089
\(124\) 0 0
\(125\) 12.1452 1.08630
\(126\) 0 0
\(127\) −10.1971 −0.904845 −0.452423 0.891804i \(-0.649440\pi\)
−0.452423 + 0.891804i \(0.649440\pi\)
\(128\) 0 0
\(129\) 1.70246 0.149893
\(130\) 0 0
\(131\) −12.4185 −1.08501 −0.542503 0.840054i \(-0.682523\pi\)
−0.542503 + 0.840054i \(0.682523\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 30.9050 2.65988
\(136\) 0 0
\(137\) −11.7915 −1.00742 −0.503709 0.863873i \(-0.668032\pi\)
−0.503709 + 0.863873i \(0.668032\pi\)
\(138\) 0 0
\(139\) −13.2774 −1.12617 −0.563085 0.826399i \(-0.690386\pi\)
−0.563085 + 0.826399i \(0.690386\pi\)
\(140\) 0 0
\(141\) 21.5311 1.81325
\(142\) 0 0
\(143\) 27.6862 2.31524
\(144\) 0 0
\(145\) −12.0648 −1.00193
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −12.5942 −1.03176 −0.515880 0.856661i \(-0.672535\pi\)
−0.515880 + 0.856661i \(0.672535\pi\)
\(150\) 0 0
\(151\) 4.51717 0.367602 0.183801 0.982963i \(-0.441160\pi\)
0.183801 + 0.982963i \(0.441160\pi\)
\(152\) 0 0
\(153\) 36.8485 2.97902
\(154\) 0 0
\(155\) 18.7152 1.50324
\(156\) 0 0
\(157\) −6.60949 −0.527495 −0.263747 0.964592i \(-0.584959\pi\)
−0.263747 + 0.964592i \(0.584959\pi\)
\(158\) 0 0
\(159\) 20.6278 1.63589
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −15.5029 −1.21428 −0.607140 0.794595i \(-0.707683\pi\)
−0.607140 + 0.794595i \(0.707683\pi\)
\(164\) 0 0
\(165\) −31.6184 −2.46149
\(166\) 0 0
\(167\) 6.76414 0.523425 0.261712 0.965146i \(-0.415713\pi\)
0.261712 + 0.965146i \(0.415713\pi\)
\(168\) 0 0
\(169\) 17.0934 1.31487
\(170\) 0 0
\(171\) −7.93307 −0.606657
\(172\) 0 0
\(173\) −21.2291 −1.61401 −0.807007 0.590541i \(-0.798914\pi\)
−0.807007 + 0.590541i \(0.798914\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −15.1883 −1.14162
\(178\) 0 0
\(179\) −20.0404 −1.49789 −0.748945 0.662632i \(-0.769440\pi\)
−0.748945 + 0.662632i \(0.769440\pi\)
\(180\) 0 0
\(181\) 2.20042 0.163556 0.0817780 0.996651i \(-0.473940\pi\)
0.0817780 + 0.996651i \(0.473940\pi\)
\(182\) 0 0
\(183\) 28.4839 2.10559
\(184\) 0 0
\(185\) 4.42494 0.325328
\(186\) 0 0
\(187\) −23.4426 −1.71430
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.3726 −0.967607 −0.483803 0.875177i \(-0.660745\pi\)
−0.483803 + 0.875177i \(0.660745\pi\)
\(192\) 0 0
\(193\) 22.0992 1.59074 0.795369 0.606125i \(-0.207277\pi\)
0.795369 + 0.606125i \(0.207277\pi\)
\(194\) 0 0
\(195\) −34.3675 −2.46110
\(196\) 0 0
\(197\) −7.46613 −0.531940 −0.265970 0.963981i \(-0.585692\pi\)
−0.265970 + 0.963981i \(0.585692\pi\)
\(198\) 0 0
\(199\) 5.64006 0.399813 0.199907 0.979815i \(-0.435936\pi\)
0.199907 + 0.979815i \(0.435936\pi\)
\(200\) 0 0
\(201\) 0.172477 0.0121656
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.93437 0.274789
\(206\) 0 0
\(207\) 12.8584 0.893724
\(208\) 0 0
\(209\) 5.04694 0.349104
\(210\) 0 0
\(211\) −3.98185 −0.274122 −0.137061 0.990563i \(-0.543766\pi\)
−0.137061 + 0.990563i \(0.543766\pi\)
\(212\) 0 0
\(213\) 26.9969 1.84980
\(214\) 0 0
\(215\) 0.975544 0.0665316
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −39.8699 −2.69416
\(220\) 0 0
\(221\) −25.4808 −1.71403
\(222\) 0 0
\(223\) −18.3902 −1.23150 −0.615750 0.787941i \(-0.711147\pi\)
−0.615750 + 0.787941i \(0.711147\pi\)
\(224\) 0 0
\(225\) −11.1865 −0.745764
\(226\) 0 0
\(227\) −13.4451 −0.892382 −0.446191 0.894938i \(-0.647220\pi\)
−0.446191 + 0.894938i \(0.647220\pi\)
\(228\) 0 0
\(229\) 9.62234 0.635862 0.317931 0.948114i \(-0.397012\pi\)
0.317931 + 0.948114i \(0.397012\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.8329 1.29930 0.649649 0.760234i \(-0.274916\pi\)
0.649649 + 0.760234i \(0.274916\pi\)
\(234\) 0 0
\(235\) 12.3378 0.804828
\(236\) 0 0
\(237\) 39.5266 2.56753
\(238\) 0 0
\(239\) −1.92198 −0.124323 −0.0621614 0.998066i \(-0.519799\pi\)
−0.0621614 + 0.998066i \(0.519799\pi\)
\(240\) 0 0
\(241\) −4.47923 −0.288532 −0.144266 0.989539i \(-0.546082\pi\)
−0.144266 + 0.989539i \(0.546082\pi\)
\(242\) 0 0
\(243\) −50.7061 −3.25280
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.48574 0.349049
\(248\) 0 0
\(249\) −5.95203 −0.377195
\(250\) 0 0
\(251\) 29.6386 1.87077 0.935385 0.353631i \(-0.115053\pi\)
0.935385 + 0.353631i \(0.115053\pi\)
\(252\) 0 0
\(253\) −8.18042 −0.514299
\(254\) 0 0
\(255\) 29.0998 1.82230
\(256\) 0 0
\(257\) 29.2978 1.82755 0.913773 0.406225i \(-0.133155\pi\)
0.913773 + 0.406225i \(0.133155\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 50.5151 3.12681
\(262\) 0 0
\(263\) −17.1598 −1.05812 −0.529058 0.848586i \(-0.677455\pi\)
−0.529058 + 0.848586i \(0.677455\pi\)
\(264\) 0 0
\(265\) 11.8201 0.726105
\(266\) 0 0
\(267\) 35.0022 2.14210
\(268\) 0 0
\(269\) 5.70864 0.348062 0.174031 0.984740i \(-0.444321\pi\)
0.174031 + 0.984740i \(0.444321\pi\)
\(270\) 0 0
\(271\) −7.46920 −0.453722 −0.226861 0.973927i \(-0.572846\pi\)
−0.226861 + 0.973927i \(0.572846\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.11672 0.429154
\(276\) 0 0
\(277\) 20.3196 1.22088 0.610442 0.792061i \(-0.290992\pi\)
0.610442 + 0.792061i \(0.290992\pi\)
\(278\) 0 0
\(279\) −78.3600 −4.69129
\(280\) 0 0
\(281\) 11.8087 0.704451 0.352225 0.935915i \(-0.385425\pi\)
0.352225 + 0.935915i \(0.385425\pi\)
\(282\) 0 0
\(283\) −4.49546 −0.267228 −0.133614 0.991033i \(-0.542658\pi\)
−0.133614 + 0.991033i \(0.542658\pi\)
\(284\) 0 0
\(285\) −6.26487 −0.371099
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.57528 0.269134
\(290\) 0 0
\(291\) 56.1382 3.29088
\(292\) 0 0
\(293\) −0.163384 −0.00954498 −0.00477249 0.999989i \(-0.501519\pi\)
−0.00477249 + 0.999989i \(0.501519\pi\)
\(294\) 0 0
\(295\) −8.70319 −0.506719
\(296\) 0 0
\(297\) 82.3222 4.77682
\(298\) 0 0
\(299\) −8.89166 −0.514218
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 25.3266 1.45497
\(304\) 0 0
\(305\) 16.3218 0.934586
\(306\) 0 0
\(307\) 26.0828 1.48862 0.744312 0.667832i \(-0.232778\pi\)
0.744312 + 0.667832i \(0.232778\pi\)
\(308\) 0 0
\(309\) 2.62585 0.149380
\(310\) 0 0
\(311\) 1.14375 0.0648563 0.0324281 0.999474i \(-0.489676\pi\)
0.0324281 + 0.999474i \(0.489676\pi\)
\(312\) 0 0
\(313\) 1.40393 0.0793551 0.0396775 0.999213i \(-0.487367\pi\)
0.0396775 + 0.999213i \(0.487367\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.2674 −1.47532 −0.737662 0.675171i \(-0.764070\pi\)
−0.737662 + 0.675171i \(0.764070\pi\)
\(318\) 0 0
\(319\) −32.1372 −1.79934
\(320\) 0 0
\(321\) −14.9991 −0.837167
\(322\) 0 0
\(323\) −4.64492 −0.258450
\(324\) 0 0
\(325\) 7.73547 0.429087
\(326\) 0 0
\(327\) −7.66700 −0.423986
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.93736 −0.381312 −0.190656 0.981657i \(-0.561061\pi\)
−0.190656 + 0.981657i \(0.561061\pi\)
\(332\) 0 0
\(333\) −18.5271 −1.01528
\(334\) 0 0
\(335\) 0.0988329 0.00539982
\(336\) 0 0
\(337\) −15.6914 −0.854762 −0.427381 0.904072i \(-0.640564\pi\)
−0.427381 + 0.904072i \(0.640564\pi\)
\(338\) 0 0
\(339\) 21.4500 1.16500
\(340\) 0 0
\(341\) 49.8519 2.69963
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 10.1545 0.546701
\(346\) 0 0
\(347\) 11.3227 0.607833 0.303917 0.952699i \(-0.401706\pi\)
0.303917 + 0.952699i \(0.401706\pi\)
\(348\) 0 0
\(349\) 17.6771 0.946232 0.473116 0.881000i \(-0.343129\pi\)
0.473116 + 0.881000i \(0.343129\pi\)
\(350\) 0 0
\(351\) 89.4796 4.77607
\(352\) 0 0
\(353\) −5.09677 −0.271273 −0.135637 0.990759i \(-0.543308\pi\)
−0.135637 + 0.990759i \(0.543308\pi\)
\(354\) 0 0
\(355\) 15.4698 0.821050
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.0524 −0.688880 −0.344440 0.938808i \(-0.611931\pi\)
−0.344440 + 0.938808i \(0.611931\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −47.8507 −2.51151
\(364\) 0 0
\(365\) −22.8463 −1.19583
\(366\) 0 0
\(367\) 25.5717 1.33483 0.667416 0.744685i \(-0.267400\pi\)
0.667416 + 0.744685i \(0.267400\pi\)
\(368\) 0 0
\(369\) −16.4731 −0.857557
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 32.2019 1.66735 0.833675 0.552255i \(-0.186233\pi\)
0.833675 + 0.552255i \(0.186233\pi\)
\(374\) 0 0
\(375\) −40.1585 −2.07377
\(376\) 0 0
\(377\) −34.9314 −1.79906
\(378\) 0 0
\(379\) −22.1673 −1.13866 −0.569329 0.822110i \(-0.692797\pi\)
−0.569329 + 0.822110i \(0.692797\pi\)
\(380\) 0 0
\(381\) 33.7169 1.72737
\(382\) 0 0
\(383\) 13.6612 0.698054 0.349027 0.937113i \(-0.386512\pi\)
0.349027 + 0.937113i \(0.386512\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.08458 −0.207631
\(388\) 0 0
\(389\) −14.6997 −0.745303 −0.372651 0.927971i \(-0.621551\pi\)
−0.372651 + 0.927971i \(0.621551\pi\)
\(390\) 0 0
\(391\) 7.52879 0.380747
\(392\) 0 0
\(393\) 41.0619 2.07130
\(394\) 0 0
\(395\) 22.6496 1.13962
\(396\) 0 0
\(397\) −6.60542 −0.331516 −0.165758 0.986166i \(-0.553007\pi\)
−0.165758 + 0.986166i \(0.553007\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 20.6425 1.03084 0.515419 0.856938i \(-0.327636\pi\)
0.515419 + 0.856938i \(0.327636\pi\)
\(402\) 0 0
\(403\) 54.1862 2.69921
\(404\) 0 0
\(405\) −57.0957 −2.83711
\(406\) 0 0
\(407\) 11.7868 0.584249
\(408\) 0 0
\(409\) −11.6301 −0.575070 −0.287535 0.957770i \(-0.592836\pi\)
−0.287535 + 0.957770i \(0.592836\pi\)
\(410\) 0 0
\(411\) 38.9889 1.92318
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −3.41063 −0.167421
\(416\) 0 0
\(417\) 43.9018 2.14988
\(418\) 0 0
\(419\) −9.56954 −0.467502 −0.233751 0.972296i \(-0.575100\pi\)
−0.233751 + 0.972296i \(0.575100\pi\)
\(420\) 0 0
\(421\) −20.8221 −1.01481 −0.507404 0.861708i \(-0.669395\pi\)
−0.507404 + 0.861708i \(0.669395\pi\)
\(422\) 0 0
\(423\) −51.6580 −2.51170
\(424\) 0 0
\(425\) −6.54982 −0.317713
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −91.5450 −4.41984
\(430\) 0 0
\(431\) −28.9972 −1.39675 −0.698373 0.715734i \(-0.746092\pi\)
−0.698373 + 0.715734i \(0.746092\pi\)
\(432\) 0 0
\(433\) −7.17331 −0.344727 −0.172364 0.985033i \(-0.555140\pi\)
−0.172364 + 0.985033i \(0.555140\pi\)
\(434\) 0 0
\(435\) 39.8926 1.91270
\(436\) 0 0
\(437\) −1.62087 −0.0775366
\(438\) 0 0
\(439\) 25.5561 1.21972 0.609862 0.792508i \(-0.291225\pi\)
0.609862 + 0.792508i \(0.291225\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.05961 0.0978548 0.0489274 0.998802i \(-0.484420\pi\)
0.0489274 + 0.998802i \(0.484420\pi\)
\(444\) 0 0
\(445\) 20.0570 0.950792
\(446\) 0 0
\(447\) 41.6431 1.96965
\(448\) 0 0
\(449\) 9.59734 0.452927 0.226463 0.974020i \(-0.427284\pi\)
0.226463 + 0.974020i \(0.427284\pi\)
\(450\) 0 0
\(451\) 10.4800 0.493486
\(452\) 0 0
\(453\) −14.9361 −0.701760
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 29.4947 1.37971 0.689853 0.723950i \(-0.257675\pi\)
0.689853 + 0.723950i \(0.257675\pi\)
\(458\) 0 0
\(459\) −75.7647 −3.53639
\(460\) 0 0
\(461\) −26.2005 −1.22028 −0.610139 0.792294i \(-0.708886\pi\)
−0.610139 + 0.792294i \(0.708886\pi\)
\(462\) 0 0
\(463\) 15.4074 0.716042 0.358021 0.933714i \(-0.383452\pi\)
0.358021 + 0.933714i \(0.383452\pi\)
\(464\) 0 0
\(465\) −61.8821 −2.86971
\(466\) 0 0
\(467\) −13.2036 −0.610990 −0.305495 0.952194i \(-0.598822\pi\)
−0.305495 + 0.952194i \(0.598822\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 21.8544 1.00700
\(472\) 0 0
\(473\) 2.59857 0.119482
\(474\) 0 0
\(475\) 1.41010 0.0647000
\(476\) 0 0
\(477\) −49.4906 −2.26602
\(478\) 0 0
\(479\) 17.3604 0.793217 0.396609 0.917988i \(-0.370187\pi\)
0.396609 + 0.917988i \(0.370187\pi\)
\(480\) 0 0
\(481\) 12.8116 0.584157
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 32.1683 1.46069
\(486\) 0 0
\(487\) 5.03125 0.227988 0.113994 0.993481i \(-0.463636\pi\)
0.113994 + 0.993481i \(0.463636\pi\)
\(488\) 0 0
\(489\) 51.2606 2.31808
\(490\) 0 0
\(491\) −1.32735 −0.0599025 −0.0299512 0.999551i \(-0.509535\pi\)
−0.0299512 + 0.999551i \(0.509535\pi\)
\(492\) 0 0
\(493\) 29.5773 1.33209
\(494\) 0 0
\(495\) 75.8596 3.40964
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 22.9518 1.02746 0.513732 0.857951i \(-0.328263\pi\)
0.513732 + 0.857951i \(0.328263\pi\)
\(500\) 0 0
\(501\) −22.3658 −0.999229
\(502\) 0 0
\(503\) −6.75027 −0.300980 −0.150490 0.988612i \(-0.548085\pi\)
−0.150490 + 0.988612i \(0.548085\pi\)
\(504\) 0 0
\(505\) 14.5126 0.645804
\(506\) 0 0
\(507\) −56.5196 −2.51012
\(508\) 0 0
\(509\) 27.2539 1.20801 0.604005 0.796981i \(-0.293571\pi\)
0.604005 + 0.796981i \(0.293571\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 16.3113 0.720161
\(514\) 0 0
\(515\) 1.50467 0.0663035
\(516\) 0 0
\(517\) 32.8643 1.44537
\(518\) 0 0
\(519\) 70.1943 3.08119
\(520\) 0 0
\(521\) −18.5511 −0.812738 −0.406369 0.913709i \(-0.633205\pi\)
−0.406369 + 0.913709i \(0.633205\pi\)
\(522\) 0 0
\(523\) 37.7813 1.65206 0.826031 0.563625i \(-0.190594\pi\)
0.826031 + 0.563625i \(0.190594\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −45.8808 −1.99860
\(528\) 0 0
\(529\) −20.3728 −0.885774
\(530\) 0 0
\(531\) 36.4400 1.58136
\(532\) 0 0
\(533\) 11.3912 0.493408
\(534\) 0 0
\(535\) −8.59478 −0.371585
\(536\) 0 0
\(537\) 66.2640 2.85950
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9.22642 −0.396675 −0.198337 0.980134i \(-0.563554\pi\)
−0.198337 + 0.980134i \(0.563554\pi\)
\(542\) 0 0
\(543\) −7.27573 −0.312232
\(544\) 0 0
\(545\) −4.39335 −0.188190
\(546\) 0 0
\(547\) 10.3367 0.441966 0.220983 0.975278i \(-0.429074\pi\)
0.220983 + 0.975278i \(0.429074\pi\)
\(548\) 0 0
\(549\) −68.3391 −2.91664
\(550\) 0 0
\(551\) −6.36766 −0.271272
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −14.6312 −0.621058
\(556\) 0 0
\(557\) 7.22359 0.306073 0.153037 0.988220i \(-0.451095\pi\)
0.153037 + 0.988220i \(0.451095\pi\)
\(558\) 0 0
\(559\) 2.82450 0.119464
\(560\) 0 0
\(561\) 77.5135 3.27262
\(562\) 0 0
\(563\) 25.1769 1.06108 0.530539 0.847660i \(-0.321989\pi\)
0.530539 + 0.847660i \(0.321989\pi\)
\(564\) 0 0
\(565\) 12.2913 0.517098
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.5326 −0.567315 −0.283658 0.958926i \(-0.591548\pi\)
−0.283658 + 0.958926i \(0.591548\pi\)
\(570\) 0 0
\(571\) 32.5262 1.36118 0.680589 0.732666i \(-0.261724\pi\)
0.680589 + 0.732666i \(0.261724\pi\)
\(572\) 0 0
\(573\) 44.2167 1.84718
\(574\) 0 0
\(575\) −2.28559 −0.0953157
\(576\) 0 0
\(577\) 37.8021 1.57372 0.786860 0.617131i \(-0.211705\pi\)
0.786860 + 0.617131i \(0.211705\pi\)
\(578\) 0 0
\(579\) −73.0716 −3.03675
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 31.4854 1.30399
\(584\) 0 0
\(585\) 82.4551 3.40910
\(586\) 0 0
\(587\) 3.79306 0.156556 0.0782781 0.996932i \(-0.475058\pi\)
0.0782781 + 0.996932i \(0.475058\pi\)
\(588\) 0 0
\(589\) 9.87764 0.407001
\(590\) 0 0
\(591\) 24.6869 1.01548
\(592\) 0 0
\(593\) 48.3752 1.98653 0.993267 0.115852i \(-0.0369598\pi\)
0.993267 + 0.115852i \(0.0369598\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −18.6490 −0.763251
\(598\) 0 0
\(599\) −11.6858 −0.477470 −0.238735 0.971085i \(-0.576733\pi\)
−0.238735 + 0.971085i \(0.576733\pi\)
\(600\) 0 0
\(601\) −4.06684 −0.165890 −0.0829449 0.996554i \(-0.526433\pi\)
−0.0829449 + 0.996554i \(0.526433\pi\)
\(602\) 0 0
\(603\) −0.413811 −0.0168517
\(604\) 0 0
\(605\) −27.4194 −1.11476
\(606\) 0 0
\(607\) 38.1037 1.54658 0.773290 0.634053i \(-0.218610\pi\)
0.773290 + 0.634053i \(0.218610\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 35.7216 1.44514
\(612\) 0 0
\(613\) 2.69020 0.108656 0.0543281 0.998523i \(-0.482698\pi\)
0.0543281 + 0.998523i \(0.482698\pi\)
\(614\) 0 0
\(615\) −13.0091 −0.524577
\(616\) 0 0
\(617\) −33.1862 −1.33603 −0.668013 0.744150i \(-0.732855\pi\)
−0.668013 + 0.744150i \(0.732855\pi\)
\(618\) 0 0
\(619\) 43.3164 1.74104 0.870518 0.492137i \(-0.163784\pi\)
0.870518 + 0.492137i \(0.163784\pi\)
\(620\) 0 0
\(621\) −26.4384 −1.06094
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −15.9611 −0.638443
\(626\) 0 0
\(627\) −16.6878 −0.666447
\(628\) 0 0
\(629\) −10.8479 −0.432533
\(630\) 0 0
\(631\) 5.63473 0.224315 0.112158 0.993690i \(-0.464224\pi\)
0.112158 + 0.993690i \(0.464224\pi\)
\(632\) 0 0
\(633\) 13.1661 0.523304
\(634\) 0 0
\(635\) 19.3204 0.766708
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −64.7715 −2.56232
\(640\) 0 0
\(641\) −38.5726 −1.52353 −0.761763 0.647855i \(-0.775666\pi\)
−0.761763 + 0.647855i \(0.775666\pi\)
\(642\) 0 0
\(643\) 18.5746 0.732511 0.366255 0.930514i \(-0.380640\pi\)
0.366255 + 0.930514i \(0.380640\pi\)
\(644\) 0 0
\(645\) −3.22566 −0.127010
\(646\) 0 0
\(647\) −3.76936 −0.148189 −0.0740944 0.997251i \(-0.523607\pi\)
−0.0740944 + 0.997251i \(0.523607\pi\)
\(648\) 0 0
\(649\) −23.1828 −0.910004
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 45.9149 1.79679 0.898394 0.439190i \(-0.144735\pi\)
0.898394 + 0.439190i \(0.144735\pi\)
\(654\) 0 0
\(655\) 23.5293 0.919365
\(656\) 0 0
\(657\) 95.6567 3.73192
\(658\) 0 0
\(659\) 11.7263 0.456793 0.228397 0.973568i \(-0.426652\pi\)
0.228397 + 0.973568i \(0.426652\pi\)
\(660\) 0 0
\(661\) 47.2749 1.83878 0.919390 0.393346i \(-0.128683\pi\)
0.919390 + 0.393346i \(0.128683\pi\)
\(662\) 0 0
\(663\) 84.2529 3.27211
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.3211 0.399636
\(668\) 0 0
\(669\) 60.8076 2.35096
\(670\) 0 0
\(671\) 43.4767 1.67840
\(672\) 0 0
\(673\) −14.1187 −0.544237 −0.272119 0.962264i \(-0.587724\pi\)
−0.272119 + 0.962264i \(0.587724\pi\)
\(674\) 0 0
\(675\) 23.0006 0.885295
\(676\) 0 0
\(677\) −39.4869 −1.51760 −0.758802 0.651322i \(-0.774215\pi\)
−0.758802 + 0.651322i \(0.774215\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 44.4565 1.70358
\(682\) 0 0
\(683\) −19.5447 −0.747857 −0.373929 0.927457i \(-0.621989\pi\)
−0.373929 + 0.927457i \(0.621989\pi\)
\(684\) 0 0
\(685\) 22.3414 0.853622
\(686\) 0 0
\(687\) −31.8164 −1.21387
\(688\) 0 0
\(689\) 34.2229 1.30379
\(690\) 0 0
\(691\) −36.4954 −1.38835 −0.694175 0.719806i \(-0.744231\pi\)
−0.694175 + 0.719806i \(0.744231\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 25.1566 0.954246
\(696\) 0 0
\(697\) −9.64524 −0.365339
\(698\) 0 0
\(699\) −65.5780 −2.48039
\(700\) 0 0
\(701\) 0.462695 0.0174757 0.00873787 0.999962i \(-0.497219\pi\)
0.00873787 + 0.999962i \(0.497219\pi\)
\(702\) 0 0
\(703\) 2.33543 0.0880824
\(704\) 0 0
\(705\) −40.7951 −1.53643
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 14.9319 0.560780 0.280390 0.959886i \(-0.409536\pi\)
0.280390 + 0.959886i \(0.409536\pi\)
\(710\) 0 0
\(711\) −94.8331 −3.55652
\(712\) 0 0
\(713\) −16.0103 −0.599592
\(714\) 0 0
\(715\) −52.4571 −1.96179
\(716\) 0 0
\(717\) 6.35507 0.237335
\(718\) 0 0
\(719\) −26.5202 −0.989038 −0.494519 0.869167i \(-0.664656\pi\)
−0.494519 + 0.869167i \(0.664656\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 14.8107 0.550814
\(724\) 0 0
\(725\) −8.97907 −0.333474
\(726\) 0 0
\(727\) −25.1545 −0.932928 −0.466464 0.884540i \(-0.654472\pi\)
−0.466464 + 0.884540i \(0.654472\pi\)
\(728\) 0 0
\(729\) 77.2575 2.86139
\(730\) 0 0
\(731\) −2.39158 −0.0884556
\(732\) 0 0
\(733\) −12.6157 −0.465971 −0.232986 0.972480i \(-0.574850\pi\)
−0.232986 + 0.972480i \(0.574850\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.263263 0.00969740
\(738\) 0 0
\(739\) −52.2690 −1.92275 −0.961374 0.275246i \(-0.911241\pi\)
−0.961374 + 0.275246i \(0.911241\pi\)
\(740\) 0 0
\(741\) −18.1387 −0.666342
\(742\) 0 0
\(743\) −15.3119 −0.561739 −0.280870 0.959746i \(-0.590623\pi\)
−0.280870 + 0.959746i \(0.590623\pi\)
\(744\) 0 0
\(745\) 23.8623 0.874248
\(746\) 0 0
\(747\) 14.2802 0.522487
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4.17115 −0.152207 −0.0761037 0.997100i \(-0.524248\pi\)
−0.0761037 + 0.997100i \(0.524248\pi\)
\(752\) 0 0
\(753\) −98.0005 −3.57134
\(754\) 0 0
\(755\) −8.55870 −0.311483
\(756\) 0 0
\(757\) 31.9386 1.16083 0.580414 0.814321i \(-0.302891\pi\)
0.580414 + 0.814321i \(0.302891\pi\)
\(758\) 0 0
\(759\) 27.0487 0.981806
\(760\) 0 0
\(761\) −36.5252 −1.32404 −0.662019 0.749487i \(-0.730300\pi\)
−0.662019 + 0.749487i \(0.730300\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −69.8169 −2.52423
\(766\) 0 0
\(767\) −25.1984 −0.909861
\(768\) 0 0
\(769\) −50.1274 −1.80764 −0.903820 0.427913i \(-0.859249\pi\)
−0.903820 + 0.427913i \(0.859249\pi\)
\(770\) 0 0
\(771\) −96.8737 −3.48882
\(772\) 0 0
\(773\) 10.9071 0.392301 0.196150 0.980574i \(-0.437156\pi\)
0.196150 + 0.980574i \(0.437156\pi\)
\(774\) 0 0
\(775\) 13.9285 0.500327
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.07651 0.0743988
\(780\) 0 0
\(781\) 41.2070 1.47450
\(782\) 0 0
\(783\) −103.865 −3.71183
\(784\) 0 0
\(785\) 12.5230 0.446966
\(786\) 0 0
\(787\) 19.8247 0.706675 0.353338 0.935496i \(-0.385047\pi\)
0.353338 + 0.935496i \(0.385047\pi\)
\(788\) 0 0
\(789\) 56.7391 2.01996
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 47.2567 1.67814
\(794\) 0 0
\(795\) −39.0835 −1.38615
\(796\) 0 0
\(797\) 7.84489 0.277880 0.138940 0.990301i \(-0.455630\pi\)
0.138940 + 0.990301i \(0.455630\pi\)
\(798\) 0 0
\(799\) −30.2464 −1.07004
\(800\) 0 0
\(801\) −83.9781 −2.96722
\(802\) 0 0
\(803\) −60.8559 −2.14756
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −18.8757 −0.664457
\(808\) 0 0
\(809\) −15.9624 −0.561209 −0.280605 0.959823i \(-0.590535\pi\)
−0.280605 + 0.959823i \(0.590535\pi\)
\(810\) 0 0
\(811\) −36.3313 −1.27576 −0.637882 0.770134i \(-0.720189\pi\)
−0.637882 + 0.770134i \(0.720189\pi\)
\(812\) 0 0
\(813\) 24.6971 0.866164
\(814\) 0 0
\(815\) 29.3733 1.02890
\(816\) 0 0
\(817\) 0.514880 0.0180134
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −43.3963 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(822\) 0 0
\(823\) 29.3173 1.02194 0.510968 0.859600i \(-0.329287\pi\)
0.510968 + 0.859600i \(0.329287\pi\)
\(824\) 0 0
\(825\) −23.5316 −0.819264
\(826\) 0 0
\(827\) −5.76537 −0.200482 −0.100241 0.994963i \(-0.531961\pi\)
−0.100241 + 0.994963i \(0.531961\pi\)
\(828\) 0 0
\(829\) −28.9925 −1.00695 −0.503476 0.864009i \(-0.667946\pi\)
−0.503476 + 0.864009i \(0.667946\pi\)
\(830\) 0 0
\(831\) −67.1870 −2.33069
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −12.8160 −0.443517
\(836\) 0 0
\(837\) 161.117 5.56902
\(838\) 0 0
\(839\) 20.3629 0.703006 0.351503 0.936187i \(-0.385671\pi\)
0.351503 + 0.936187i \(0.385671\pi\)
\(840\) 0 0
\(841\) 11.5471 0.398177
\(842\) 0 0
\(843\) −39.0458 −1.34481
\(844\) 0 0
\(845\) −32.3868 −1.11414
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 14.8643 0.510143
\(850\) 0 0
\(851\) −3.78542 −0.129762
\(852\) 0 0
\(853\) 2.28329 0.0781783 0.0390892 0.999236i \(-0.487554\pi\)
0.0390892 + 0.999236i \(0.487554\pi\)
\(854\) 0 0
\(855\) 15.0308 0.514043
\(856\) 0 0
\(857\) 3.08593 0.105413 0.0527067 0.998610i \(-0.483215\pi\)
0.0527067 + 0.998610i \(0.483215\pi\)
\(858\) 0 0
\(859\) −24.6801 −0.842074 −0.421037 0.907044i \(-0.638334\pi\)
−0.421037 + 0.907044i \(0.638334\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −22.5213 −0.766633 −0.383316 0.923617i \(-0.625218\pi\)
−0.383316 + 0.923617i \(0.625218\pi\)
\(864\) 0 0
\(865\) 40.2227 1.36761
\(866\) 0 0
\(867\) −15.1282 −0.513782
\(868\) 0 0
\(869\) 60.3319 2.04662
\(870\) 0 0
\(871\) 0.286152 0.00969588
\(872\) 0 0
\(873\) −134.688 −4.55849
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −17.5225 −0.591692 −0.295846 0.955236i \(-0.595601\pi\)
−0.295846 + 0.955236i \(0.595601\pi\)
\(878\) 0 0
\(879\) 0.540231 0.0182216
\(880\) 0 0
\(881\) −44.0772 −1.48500 −0.742499 0.669847i \(-0.766360\pi\)
−0.742499 + 0.669847i \(0.766360\pi\)
\(882\) 0 0
\(883\) 7.84919 0.264146 0.132073 0.991240i \(-0.457837\pi\)
0.132073 + 0.991240i \(0.457837\pi\)
\(884\) 0 0
\(885\) 28.7773 0.967337
\(886\) 0 0
\(887\) −35.6933 −1.19846 −0.599232 0.800576i \(-0.704527\pi\)
−0.599232 + 0.800576i \(0.704527\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −152.087 −5.09509
\(892\) 0 0
\(893\) 6.51172 0.217906
\(894\) 0 0
\(895\) 37.9706 1.26922
\(896\) 0 0
\(897\) 29.4004 0.981652
\(898\) 0 0
\(899\) −62.8975 −2.09775
\(900\) 0 0
\(901\) −28.9774 −0.965378
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.16914 −0.138587
\(906\) 0 0
\(907\) 3.68931 0.122502 0.0612508 0.998122i \(-0.480491\pi\)
0.0612508 + 0.998122i \(0.480491\pi\)
\(908\) 0 0
\(909\) −60.7640 −2.01542
\(910\) 0 0
\(911\) −24.0410 −0.796512 −0.398256 0.917274i \(-0.630385\pi\)
−0.398256 + 0.917274i \(0.630385\pi\)
\(912\) 0 0
\(913\) −9.08495 −0.300668
\(914\) 0 0
\(915\) −53.9685 −1.78414
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 33.6071 1.10859 0.554297 0.832319i \(-0.312987\pi\)
0.554297 + 0.832319i \(0.312987\pi\)
\(920\) 0 0
\(921\) −86.2433 −2.84181
\(922\) 0 0
\(923\) 44.7897 1.47427
\(924\) 0 0
\(925\) 3.29320 0.108280
\(926\) 0 0
\(927\) −6.30000 −0.206919
\(928\) 0 0
\(929\) 56.4161 1.85095 0.925477 0.378804i \(-0.123665\pi\)
0.925477 + 0.378804i \(0.123665\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −3.78184 −0.123812
\(934\) 0 0
\(935\) 44.4168 1.45259
\(936\) 0 0
\(937\) 21.9970 0.718610 0.359305 0.933220i \(-0.383014\pi\)
0.359305 + 0.933220i \(0.383014\pi\)
\(938\) 0 0
\(939\) −4.64214 −0.151490
\(940\) 0 0
\(941\) −41.8094 −1.36295 −0.681473 0.731843i \(-0.738660\pi\)
−0.681473 + 0.731843i \(0.738660\pi\)
\(942\) 0 0
\(943\) −3.36575 −0.109604
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 34.5469 1.12262 0.561311 0.827605i \(-0.310297\pi\)
0.561311 + 0.827605i \(0.310297\pi\)
\(948\) 0 0
\(949\) −66.1469 −2.14722
\(950\) 0 0
\(951\) 86.8536 2.81642
\(952\) 0 0
\(953\) −5.43332 −0.176002 −0.0880012 0.996120i \(-0.528048\pi\)
−0.0880012 + 0.996120i \(0.528048\pi\)
\(954\) 0 0
\(955\) 25.3371 0.819888
\(956\) 0 0
\(957\) 106.262 3.43497
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 66.5677 2.14735
\(962\) 0 0
\(963\) 35.9861 1.15964
\(964\) 0 0
\(965\) −41.8715 −1.34789
\(966\) 0 0
\(967\) −4.65268 −0.149620 −0.0748101 0.997198i \(-0.523835\pi\)
−0.0748101 + 0.997198i \(0.523835\pi\)
\(968\) 0 0
\(969\) 15.3585 0.493387
\(970\) 0 0
\(971\) 31.9044 1.02386 0.511930 0.859027i \(-0.328931\pi\)
0.511930 + 0.859027i \(0.328931\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −25.5775 −0.819135
\(976\) 0 0
\(977\) −2.58747 −0.0827805 −0.0413903 0.999143i \(-0.513179\pi\)
−0.0413903 + 0.999143i \(0.513179\pi\)
\(978\) 0 0
\(979\) 53.4261 1.70750
\(980\) 0 0
\(981\) 18.3948 0.587302
\(982\) 0 0
\(983\) −33.9203 −1.08189 −0.540945 0.841058i \(-0.681933\pi\)
−0.540945 + 0.841058i \(0.681933\pi\)
\(984\) 0 0
\(985\) 14.1461 0.450732
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.834552 −0.0265372
\(990\) 0 0
\(991\) −52.2547 −1.65993 −0.829963 0.557818i \(-0.811639\pi\)
−0.829963 + 0.557818i \(0.811639\pi\)
\(992\) 0 0
\(993\) 22.9385 0.727932
\(994\) 0 0
\(995\) −10.6862 −0.338776
\(996\) 0 0
\(997\) −43.3576 −1.37315 −0.686575 0.727059i \(-0.740887\pi\)
−0.686575 + 0.727059i \(0.740887\pi\)
\(998\) 0 0
\(999\) 38.0939 1.20524
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 7448.2.a.bt.1.1 11
7.2 even 3 1064.2.q.o.305.11 22
7.4 even 3 1064.2.q.o.457.11 yes 22
7.6 odd 2 7448.2.a.bs.1.11 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.o.305.11 22 7.2 even 3
1064.2.q.o.457.11 yes 22 7.4 even 3
7448.2.a.bs.1.11 11 7.6 odd 2
7448.2.a.bt.1.1 11 1.1 even 1 trivial