Properties

Label 1100.6.a.b.1.2
Level $1100$
Weight $6$
Character 1100.1
Self dual yes
Analytic conductor $176.422$
Analytic rank $0$
Dimension $2$
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] = [1100,6,Mod(1,1100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1100.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1100.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: \(176.422201794\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{31}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 31 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 44)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(5.56776\) of defining polynomial
Character \(\chi\) \(=\) 1100.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+25.2711 q^{3} -200.813 q^{7} +395.626 q^{9} +O(q^{10})\) \(q+25.2711 q^{3} -200.813 q^{7} +395.626 q^{9} -121.000 q^{11} -727.355 q^{13} +1108.74 q^{17} +1662.40 q^{19} -5074.76 q^{21} -2986.99 q^{23} +3857.03 q^{27} -1550.86 q^{29} +9511.56 q^{31} -3057.80 q^{33} +9430.48 q^{37} -18381.0 q^{39} +7371.29 q^{41} +8528.56 q^{43} -30033.5 q^{47} +23518.9 q^{49} +28019.0 q^{51} -23965.7 q^{53} +42010.7 q^{57} -6965.57 q^{59} +49080.3 q^{61} -79447.0 q^{63} +23928.7 q^{67} -75484.5 q^{69} -1881.22 q^{71} +13674.6 q^{73} +24298.4 q^{77} +11584.9 q^{79} +1334.00 q^{81} +55143.4 q^{83} -39191.8 q^{87} -2372.81 q^{89} +146063. q^{91} +240367. q^{93} +7919.13 q^{97} -47870.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{3} - 268 q^{7} + 524 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{3} - 268 q^{7} + 524 q^{9} - 242 q^{11} - 1232 q^{13} + 124 q^{17} + 1944 q^{19} - 3780 q^{21} - 3346 q^{23} + 6066 q^{27} - 6576 q^{29} + 2498 q^{31} - 726 q^{33} + 14674 q^{37} - 8656 q^{39} - 6504 q^{41} - 11628 q^{43} - 36816 q^{47} + 11226 q^{49} + 46996 q^{51} + 3292 q^{53} + 36584 q^{57} + 12126 q^{59} + 73128 q^{61} - 88072 q^{63} - 29334 q^{67} - 68566 q^{69} - 46122 q^{71} - 8240 q^{73} + 32428 q^{77} - 14780 q^{79} - 72430 q^{81} + 74564 q^{83} + 57648 q^{87} - 33698 q^{89} + 179968 q^{91} + 375526 q^{93} - 126162 q^{97} - 63404 q^{99}+O(q^{100}) \) 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
\(3\) 25.2711 1.62114 0.810570 0.585642i \(-0.199158\pi\)
0.810570 + 0.585642i \(0.199158\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −200.813 −1.54898 −0.774492 0.632583i \(-0.781995\pi\)
−0.774492 + 0.632583i \(0.781995\pi\)
\(8\) 0 0
\(9\) 395.626 1.62809
\(10\) 0 0
\(11\) −121.000 −0.301511
\(12\) 0 0
\(13\) −727.355 −1.19368 −0.596840 0.802360i \(-0.703577\pi\)
−0.596840 + 0.802360i \(0.703577\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1108.74 0.930481 0.465240 0.885184i \(-0.345968\pi\)
0.465240 + 0.885184i \(0.345968\pi\)
\(18\) 0 0
\(19\) 1662.40 1.05646 0.528229 0.849102i \(-0.322856\pi\)
0.528229 + 0.849102i \(0.322856\pi\)
\(20\) 0 0
\(21\) −5074.76 −2.51112
\(22\) 0 0
\(23\) −2986.99 −1.17737 −0.588687 0.808361i \(-0.700355\pi\)
−0.588687 + 0.808361i \(0.700355\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3857.03 1.01822
\(28\) 0 0
\(29\) −1550.86 −0.342434 −0.171217 0.985233i \(-0.554770\pi\)
−0.171217 + 0.985233i \(0.554770\pi\)
\(30\) 0 0
\(31\) 9511.56 1.77766 0.888828 0.458241i \(-0.151520\pi\)
0.888828 + 0.458241i \(0.151520\pi\)
\(32\) 0 0
\(33\) −3057.80 −0.488792
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9430.48 1.13248 0.566239 0.824241i \(-0.308398\pi\)
0.566239 + 0.824241i \(0.308398\pi\)
\(38\) 0 0
\(39\) −18381.0 −1.93512
\(40\) 0 0
\(41\) 7371.29 0.684832 0.342416 0.939548i \(-0.388755\pi\)
0.342416 + 0.939548i \(0.388755\pi\)
\(42\) 0 0
\(43\) 8528.56 0.703404 0.351702 0.936112i \(-0.385603\pi\)
0.351702 + 0.936112i \(0.385603\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −30033.5 −1.98318 −0.991588 0.129436i \(-0.958683\pi\)
−0.991588 + 0.129436i \(0.958683\pi\)
\(48\) 0 0
\(49\) 23518.9 1.39935
\(50\) 0 0
\(51\) 28019.0 1.50844
\(52\) 0 0
\(53\) −23965.7 −1.17193 −0.585964 0.810337i \(-0.699284\pi\)
−0.585964 + 0.810337i \(0.699284\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 42010.7 1.71267
\(58\) 0 0
\(59\) −6965.57 −0.260511 −0.130256 0.991480i \(-0.541580\pi\)
−0.130256 + 0.991480i \(0.541580\pi\)
\(60\) 0 0
\(61\) 49080.3 1.68882 0.844409 0.535699i \(-0.179952\pi\)
0.844409 + 0.535699i \(0.179952\pi\)
\(62\) 0 0
\(63\) −79447.0 −2.52189
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 23928.7 0.651228 0.325614 0.945503i \(-0.394429\pi\)
0.325614 + 0.945503i \(0.394429\pi\)
\(68\) 0 0
\(69\) −75484.5 −1.90869
\(70\) 0 0
\(71\) −1881.22 −0.0442889 −0.0221444 0.999755i \(-0.507049\pi\)
−0.0221444 + 0.999755i \(0.507049\pi\)
\(72\) 0 0
\(73\) 13674.6 0.300336 0.150168 0.988661i \(-0.452019\pi\)
0.150168 + 0.988661i \(0.452019\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 24298.4 0.467036
\(78\) 0 0
\(79\) 11584.9 0.208846 0.104423 0.994533i \(-0.466700\pi\)
0.104423 + 0.994533i \(0.466700\pi\)
\(80\) 0 0
\(81\) 1334.00 0.0225915
\(82\) 0 0
\(83\) 55143.4 0.878614 0.439307 0.898337i \(-0.355224\pi\)
0.439307 + 0.898337i \(0.355224\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −39191.8 −0.555133
\(88\) 0 0
\(89\) −2372.81 −0.0317533 −0.0158766 0.999874i \(-0.505054\pi\)
−0.0158766 + 0.999874i \(0.505054\pi\)
\(90\) 0 0
\(91\) 146063. 1.84899
\(92\) 0 0
\(93\) 240367. 2.88183
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7919.13 0.0854571 0.0427286 0.999087i \(-0.486395\pi\)
0.0427286 + 0.999087i \(0.486395\pi\)
\(98\) 0 0
\(99\) −47870.8 −0.490888
\(100\) 0 0
\(101\) −45021.1 −0.439150 −0.219575 0.975596i \(-0.570467\pi\)
−0.219575 + 0.975596i \(0.570467\pi\)
\(102\) 0 0
\(103\) 112625. 1.04603 0.523013 0.852325i \(-0.324808\pi\)
0.523013 + 0.852325i \(0.324808\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 207255. 1.75003 0.875015 0.484096i \(-0.160851\pi\)
0.875015 + 0.484096i \(0.160851\pi\)
\(108\) 0 0
\(109\) 94995.8 0.765840 0.382920 0.923781i \(-0.374918\pi\)
0.382920 + 0.923781i \(0.374918\pi\)
\(110\) 0 0
\(111\) 238318. 1.83590
\(112\) 0 0
\(113\) −84333.5 −0.621304 −0.310652 0.950524i \(-0.600547\pi\)
−0.310652 + 0.950524i \(0.600547\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −287761. −1.94342
\(118\) 0 0
\(119\) −222650. −1.44130
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) 0 0
\(123\) 186280. 1.11021
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −33416.9 −0.183847 −0.0919236 0.995766i \(-0.529302\pi\)
−0.0919236 + 0.995766i \(0.529302\pi\)
\(128\) 0 0
\(129\) 215526. 1.14032
\(130\) 0 0
\(131\) 353269. 1.79857 0.899286 0.437362i \(-0.144087\pi\)
0.899286 + 0.437362i \(0.144087\pi\)
\(132\) 0 0
\(133\) −333832. −1.63644
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 195043. 0.887829 0.443915 0.896069i \(-0.353589\pi\)
0.443915 + 0.896069i \(0.353589\pi\)
\(138\) 0 0
\(139\) 297644. 1.30665 0.653326 0.757077i \(-0.273373\pi\)
0.653326 + 0.757077i \(0.273373\pi\)
\(140\) 0 0
\(141\) −758978. −3.21500
\(142\) 0 0
\(143\) 88010.0 0.359908
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 594348. 2.26855
\(148\) 0 0
\(149\) 32976.3 0.121685 0.0608423 0.998147i \(-0.480621\pi\)
0.0608423 + 0.998147i \(0.480621\pi\)
\(150\) 0 0
\(151\) 325852. 1.16299 0.581497 0.813548i \(-0.302467\pi\)
0.581497 + 0.813548i \(0.302467\pi\)
\(152\) 0 0
\(153\) 438647. 1.51491
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 362988. 1.17528 0.587642 0.809121i \(-0.300056\pi\)
0.587642 + 0.809121i \(0.300056\pi\)
\(158\) 0 0
\(159\) −605639. −1.89986
\(160\) 0 0
\(161\) 599827. 1.82373
\(162\) 0 0
\(163\) −597696. −1.76202 −0.881011 0.473095i \(-0.843137\pi\)
−0.881011 + 0.473095i \(0.843137\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 474413. 1.31633 0.658166 0.752873i \(-0.271333\pi\)
0.658166 + 0.752873i \(0.271333\pi\)
\(168\) 0 0
\(169\) 157753. 0.424874
\(170\) 0 0
\(171\) 657690. 1.72001
\(172\) 0 0
\(173\) −48727.9 −0.123783 −0.0618917 0.998083i \(-0.519713\pi\)
−0.0618917 + 0.998083i \(0.519713\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −176027. −0.422325
\(178\) 0 0
\(179\) 615070. 1.43480 0.717401 0.696660i \(-0.245332\pi\)
0.717401 + 0.696660i \(0.245332\pi\)
\(180\) 0 0
\(181\) 101539. 0.230374 0.115187 0.993344i \(-0.463253\pi\)
0.115187 + 0.993344i \(0.463253\pi\)
\(182\) 0 0
\(183\) 1.24031e6 2.73781
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −134158. −0.280550
\(188\) 0 0
\(189\) −774542. −1.57721
\(190\) 0 0
\(191\) 41311.8 0.0819389 0.0409695 0.999160i \(-0.486955\pi\)
0.0409695 + 0.999160i \(0.486955\pi\)
\(192\) 0 0
\(193\) 487524. 0.942111 0.471056 0.882103i \(-0.343873\pi\)
0.471056 + 0.882103i \(0.343873\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 393575. 0.722539 0.361270 0.932461i \(-0.382343\pi\)
0.361270 + 0.932461i \(0.382343\pi\)
\(198\) 0 0
\(199\) −295187. −0.528401 −0.264201 0.964468i \(-0.585108\pi\)
−0.264201 + 0.964468i \(0.585108\pi\)
\(200\) 0 0
\(201\) 604705. 1.05573
\(202\) 0 0
\(203\) 311433. 0.530425
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.18173e6 −1.91687
\(208\) 0 0
\(209\) −201151. −0.318534
\(210\) 0 0
\(211\) −481974. −0.745276 −0.372638 0.927977i \(-0.621547\pi\)
−0.372638 + 0.927977i \(0.621547\pi\)
\(212\) 0 0
\(213\) −47540.5 −0.0717984
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.91005e6 −2.75356
\(218\) 0 0
\(219\) 345571. 0.486886
\(220\) 0 0
\(221\) −806448. −1.11070
\(222\) 0 0
\(223\) −233896. −0.314964 −0.157482 0.987522i \(-0.550338\pi\)
−0.157482 + 0.987522i \(0.550338\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.10273e6 −1.42038 −0.710191 0.704009i \(-0.751391\pi\)
−0.710191 + 0.704009i \(0.751391\pi\)
\(228\) 0 0
\(229\) 46621.7 0.0587489 0.0293744 0.999568i \(-0.490648\pi\)
0.0293744 + 0.999568i \(0.490648\pi\)
\(230\) 0 0
\(231\) 614046. 0.757131
\(232\) 0 0
\(233\) −995577. −1.20139 −0.600696 0.799477i \(-0.705110\pi\)
−0.600696 + 0.799477i \(0.705110\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 292764. 0.338568
\(238\) 0 0
\(239\) −1.40120e6 −1.58674 −0.793372 0.608738i \(-0.791676\pi\)
−0.793372 + 0.608738i \(0.791676\pi\)
\(240\) 0 0
\(241\) −1.51280e6 −1.67780 −0.838899 0.544287i \(-0.816800\pi\)
−0.838899 + 0.544287i \(0.816800\pi\)
\(242\) 0 0
\(243\) −903546. −0.981601
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.20916e6 −1.26107
\(248\) 0 0
\(249\) 1.39353e6 1.42436
\(250\) 0 0
\(251\) 39179.9 0.0392536 0.0196268 0.999807i \(-0.493752\pi\)
0.0196268 + 0.999807i \(0.493752\pi\)
\(252\) 0 0
\(253\) 361426. 0.354992
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −341829. −0.322831 −0.161416 0.986887i \(-0.551606\pi\)
−0.161416 + 0.986887i \(0.551606\pi\)
\(258\) 0 0
\(259\) −1.89376e6 −1.75419
\(260\) 0 0
\(261\) −613560. −0.557514
\(262\) 0 0
\(263\) 751539. 0.669980 0.334990 0.942222i \(-0.391267\pi\)
0.334990 + 0.942222i \(0.391267\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −59963.5 −0.0514765
\(268\) 0 0
\(269\) −50498.3 −0.0425497 −0.0212748 0.999774i \(-0.506772\pi\)
−0.0212748 + 0.999774i \(0.506772\pi\)
\(270\) 0 0
\(271\) 447260. 0.369944 0.184972 0.982744i \(-0.440780\pi\)
0.184972 + 0.982744i \(0.440780\pi\)
\(272\) 0 0
\(273\) 3.69115e6 2.99748
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −363369. −0.284543 −0.142272 0.989828i \(-0.545441\pi\)
−0.142272 + 0.989828i \(0.545441\pi\)
\(278\) 0 0
\(279\) 3.76302e6 2.89419
\(280\) 0 0
\(281\) 607636. 0.459069 0.229535 0.973301i \(-0.426280\pi\)
0.229535 + 0.973301i \(0.426280\pi\)
\(282\) 0 0
\(283\) 1.08363e6 0.804293 0.402147 0.915575i \(-0.368264\pi\)
0.402147 + 0.915575i \(0.368264\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.48025e6 −1.06079
\(288\) 0 0
\(289\) −190553. −0.134206
\(290\) 0 0
\(291\) 200125. 0.138538
\(292\) 0 0
\(293\) 384971. 0.261974 0.130987 0.991384i \(-0.458185\pi\)
0.130987 + 0.991384i \(0.458185\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −466701. −0.307006
\(298\) 0 0
\(299\) 2.17260e6 1.40541
\(300\) 0 0
\(301\) −1.71265e6 −1.08956
\(302\) 0 0
\(303\) −1.13773e6 −0.711924
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −76125.6 −0.0460983 −0.0230492 0.999734i \(-0.507337\pi\)
−0.0230492 + 0.999734i \(0.507337\pi\)
\(308\) 0 0
\(309\) 2.84616e6 1.69575
\(310\) 0 0
\(311\) 1.25747e6 0.737219 0.368610 0.929584i \(-0.379834\pi\)
0.368610 + 0.929584i \(0.379834\pi\)
\(312\) 0 0
\(313\) 1.31816e6 0.760516 0.380258 0.924881i \(-0.375835\pi\)
0.380258 + 0.924881i \(0.375835\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.56055e6 −1.43115 −0.715574 0.698536i \(-0.753835\pi\)
−0.715574 + 0.698536i \(0.753835\pi\)
\(318\) 0 0
\(319\) 187654. 0.103248
\(320\) 0 0
\(321\) 5.23755e6 2.83704
\(322\) 0 0
\(323\) 1.84317e6 0.983014
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 2.40064e6 1.24153
\(328\) 0 0
\(329\) 6.03112e6 3.07191
\(330\) 0 0
\(331\) −355258. −0.178227 −0.0891135 0.996021i \(-0.528403\pi\)
−0.0891135 + 0.996021i \(0.528403\pi\)
\(332\) 0 0
\(333\) 3.73095e6 1.84378
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.46585e6 0.703095 0.351548 0.936170i \(-0.385656\pi\)
0.351548 + 0.936170i \(0.385656\pi\)
\(338\) 0 0
\(339\) −2.13120e6 −1.00722
\(340\) 0 0
\(341\) −1.15090e6 −0.535983
\(342\) 0 0
\(343\) −1.34784e6 −0.618592
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.14456e6 0.956126 0.478063 0.878326i \(-0.341339\pi\)
0.478063 + 0.878326i \(0.341339\pi\)
\(348\) 0 0
\(349\) −3.12653e6 −1.37404 −0.687019 0.726640i \(-0.741081\pi\)
−0.687019 + 0.726640i \(0.741081\pi\)
\(350\) 0 0
\(351\) −2.80543e6 −1.21543
\(352\) 0 0
\(353\) −368782. −0.157519 −0.0787594 0.996894i \(-0.525096\pi\)
−0.0787594 + 0.996894i \(0.525096\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −5.62659e6 −2.33655
\(358\) 0 0
\(359\) −2.36501e6 −0.968496 −0.484248 0.874931i \(-0.660907\pi\)
−0.484248 + 0.874931i \(0.660907\pi\)
\(360\) 0 0
\(361\) 287484. 0.116104
\(362\) 0 0
\(363\) 369994. 0.147376
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.98689e6 −0.770032 −0.385016 0.922910i \(-0.625804\pi\)
−0.385016 + 0.922910i \(0.625804\pi\)
\(368\) 0 0
\(369\) 2.91628e6 1.11497
\(370\) 0 0
\(371\) 4.81263e6 1.81530
\(372\) 0 0
\(373\) −100049. −0.0372339 −0.0186170 0.999827i \(-0.505926\pi\)
−0.0186170 + 0.999827i \(0.505926\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.12802e6 0.408757
\(378\) 0 0
\(379\) 271345. 0.0970340 0.0485170 0.998822i \(-0.484550\pi\)
0.0485170 + 0.998822i \(0.484550\pi\)
\(380\) 0 0
\(381\) −844481. −0.298042
\(382\) 0 0
\(383\) 3.35065e6 1.16717 0.583583 0.812054i \(-0.301650\pi\)
0.583583 + 0.812054i \(0.301650\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.37412e6 1.14521
\(388\) 0 0
\(389\) −1.57219e6 −0.526782 −0.263391 0.964689i \(-0.584841\pi\)
−0.263391 + 0.964689i \(0.584841\pi\)
\(390\) 0 0
\(391\) −3.31180e6 −1.09552
\(392\) 0 0
\(393\) 8.92749e6 2.91573
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2.94505e6 0.937813 0.468907 0.883248i \(-0.344648\pi\)
0.468907 + 0.883248i \(0.344648\pi\)
\(398\) 0 0
\(399\) −8.43630e6 −2.65289
\(400\) 0 0
\(401\) −480807. −0.149317 −0.0746586 0.997209i \(-0.523787\pi\)
−0.0746586 + 0.997209i \(0.523787\pi\)
\(402\) 0 0
\(403\) −6.91829e6 −2.12195
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.14109e6 −0.341455
\(408\) 0 0
\(409\) 2.80073e6 0.827872 0.413936 0.910306i \(-0.364154\pi\)
0.413936 + 0.910306i \(0.364154\pi\)
\(410\) 0 0
\(411\) 4.92895e6 1.43930
\(412\) 0 0
\(413\) 1.39878e6 0.403528
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7.52177e6 2.11826
\(418\) 0 0
\(419\) −4.58561e6 −1.27603 −0.638017 0.770022i \(-0.720245\pi\)
−0.638017 + 0.770022i \(0.720245\pi\)
\(420\) 0 0
\(421\) 3.65111e6 1.00397 0.501984 0.864877i \(-0.332604\pi\)
0.501984 + 0.864877i \(0.332604\pi\)
\(422\) 0 0
\(423\) −1.18820e7 −3.22879
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −9.85598e6 −2.61595
\(428\) 0 0
\(429\) 2.22411e6 0.583461
\(430\) 0 0
\(431\) 3.90343e6 1.01217 0.506085 0.862484i \(-0.331092\pi\)
0.506085 + 0.862484i \(0.331092\pi\)
\(432\) 0 0
\(433\) 6.51560e6 1.67007 0.835035 0.550196i \(-0.185447\pi\)
0.835035 + 0.550196i \(0.185447\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.96558e6 −1.24385
\(438\) 0 0
\(439\) 2.51459e6 0.622738 0.311369 0.950289i \(-0.399213\pi\)
0.311369 + 0.950289i \(0.399213\pi\)
\(440\) 0 0
\(441\) 9.30471e6 2.27828
\(442\) 0 0
\(443\) −1.09010e6 −0.263910 −0.131955 0.991256i \(-0.542126\pi\)
−0.131955 + 0.991256i \(0.542126\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 833345. 0.197268
\(448\) 0 0
\(449\) −2.03880e6 −0.477265 −0.238633 0.971110i \(-0.576699\pi\)
−0.238633 + 0.971110i \(0.576699\pi\)
\(450\) 0 0
\(451\) −891927. −0.206485
\(452\) 0 0
\(453\) 8.23462e6 1.88538
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.74124e6 1.73388 0.866942 0.498410i \(-0.166082\pi\)
0.866942 + 0.498410i \(0.166082\pi\)
\(458\) 0 0
\(459\) 4.27644e6 0.947438
\(460\) 0 0
\(461\) 5.59266e6 1.22565 0.612824 0.790219i \(-0.290033\pi\)
0.612824 + 0.790219i \(0.290033\pi\)
\(462\) 0 0
\(463\) 796538. 0.172685 0.0863423 0.996266i \(-0.472482\pi\)
0.0863423 + 0.996266i \(0.472482\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.88198e6 −0.399322 −0.199661 0.979865i \(-0.563984\pi\)
−0.199661 + 0.979865i \(0.563984\pi\)
\(468\) 0 0
\(469\) −4.80521e6 −1.00874
\(470\) 0 0
\(471\) 9.17309e6 1.90530
\(472\) 0 0
\(473\) −1.03196e6 −0.212084
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.48147e6 −1.90801
\(478\) 0 0
\(479\) −7.39299e6 −1.47225 −0.736125 0.676846i \(-0.763346\pi\)
−0.736125 + 0.676846i \(0.763346\pi\)
\(480\) 0 0
\(481\) −6.85931e6 −1.35182
\(482\) 0 0
\(483\) 1.51583e7 2.95653
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 2.44572e6 0.467288 0.233644 0.972322i \(-0.424935\pi\)
0.233644 + 0.972322i \(0.424935\pi\)
\(488\) 0 0
\(489\) −1.51044e7 −2.85648
\(490\) 0 0
\(491\) 555739. 0.104032 0.0520160 0.998646i \(-0.483435\pi\)
0.0520160 + 0.998646i \(0.483435\pi\)
\(492\) 0 0
\(493\) −1.71950e6 −0.318628
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 377775. 0.0686028
\(498\) 0 0
\(499\) 8.28233e6 1.48902 0.744511 0.667610i \(-0.232683\pi\)
0.744511 + 0.667610i \(0.232683\pi\)
\(500\) 0 0
\(501\) 1.19889e7 2.13396
\(502\) 0 0
\(503\) −2.15819e6 −0.380337 −0.190169 0.981751i \(-0.560903\pi\)
−0.190169 + 0.981751i \(0.560903\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.98658e6 0.688780
\(508\) 0 0
\(509\) −7.95956e6 −1.36174 −0.680870 0.732404i \(-0.738398\pi\)
−0.680870 + 0.732404i \(0.738398\pi\)
\(510\) 0 0
\(511\) −2.74603e6 −0.465215
\(512\) 0 0
\(513\) 6.41194e6 1.07571
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 3.63405e6 0.597950
\(518\) 0 0
\(519\) −1.23140e6 −0.200670
\(520\) 0 0
\(521\) −3.85570e6 −0.622312 −0.311156 0.950359i \(-0.600716\pi\)
−0.311156 + 0.950359i \(0.600716\pi\)
\(522\) 0 0
\(523\) −7.82125e6 −1.25032 −0.625161 0.780496i \(-0.714967\pi\)
−0.625161 + 0.780496i \(0.714967\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.05458e7 1.65407
\(528\) 0 0
\(529\) 2.48578e6 0.386210
\(530\) 0 0
\(531\) −2.75576e6 −0.424136
\(532\) 0 0
\(533\) −5.36155e6 −0.817471
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.55435e7 2.32601
\(538\) 0 0
\(539\) −2.84579e6 −0.421921
\(540\) 0 0
\(541\) 1.17121e6 0.172044 0.0860221 0.996293i \(-0.472584\pi\)
0.0860221 + 0.996293i \(0.472584\pi\)
\(542\) 0 0
\(543\) 2.56599e6 0.373469
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −4.98116e6 −0.711807 −0.355904 0.934523i \(-0.615827\pi\)
−0.355904 + 0.934523i \(0.615827\pi\)
\(548\) 0 0
\(549\) 1.94175e7 2.74955
\(550\) 0 0
\(551\) −2.57815e6 −0.361767
\(552\) 0 0
\(553\) −2.32641e6 −0.323499
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.59988e6 1.03793 0.518966 0.854795i \(-0.326317\pi\)
0.518966 + 0.854795i \(0.326317\pi\)
\(558\) 0 0
\(559\) −6.20329e6 −0.839639
\(560\) 0 0
\(561\) −3.39030e6 −0.454811
\(562\) 0 0
\(563\) −4.85731e6 −0.645840 −0.322920 0.946426i \(-0.604664\pi\)
−0.322920 + 0.946426i \(0.604664\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −267885. −0.0349938
\(568\) 0 0
\(569\) 4.86673e6 0.630169 0.315084 0.949064i \(-0.397967\pi\)
0.315084 + 0.949064i \(0.397967\pi\)
\(570\) 0 0
\(571\) 647211. 0.0830722 0.0415361 0.999137i \(-0.486775\pi\)
0.0415361 + 0.999137i \(0.486775\pi\)
\(572\) 0 0
\(573\) 1.04399e6 0.132834
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −6.28194e6 −0.785515 −0.392757 0.919642i \(-0.628479\pi\)
−0.392757 + 0.919642i \(0.628479\pi\)
\(578\) 0 0
\(579\) 1.23202e7 1.52729
\(580\) 0 0
\(581\) −1.10735e7 −1.36096
\(582\) 0 0
\(583\) 2.89985e6 0.353349
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.43029e7 1.71328 0.856638 0.515917i \(-0.172549\pi\)
0.856638 + 0.515917i \(0.172549\pi\)
\(588\) 0 0
\(589\) 1.58120e7 1.87802
\(590\) 0 0
\(591\) 9.94604e6 1.17134
\(592\) 0 0
\(593\) −1.11657e7 −1.30392 −0.651960 0.758254i \(-0.726053\pi\)
−0.651960 + 0.758254i \(0.726053\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.45968e6 −0.856612
\(598\) 0 0
\(599\) −2.22282e6 −0.253126 −0.126563 0.991959i \(-0.540395\pi\)
−0.126563 + 0.991959i \(0.540395\pi\)
\(600\) 0 0
\(601\) 1.25195e7 1.41384 0.706920 0.707294i \(-0.250084\pi\)
0.706920 + 0.707294i \(0.250084\pi\)
\(602\) 0 0
\(603\) 9.46684e6 1.06026
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −9.80774e6 −1.08043 −0.540216 0.841527i \(-0.681657\pi\)
−0.540216 + 0.841527i \(0.681657\pi\)
\(608\) 0 0
\(609\) 7.87023e6 0.859893
\(610\) 0 0
\(611\) 2.18450e7 2.36728
\(612\) 0 0
\(613\) 1.04278e7 1.12084 0.560418 0.828210i \(-0.310641\pi\)
0.560418 + 0.828210i \(0.310641\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.83918e6 0.194497 0.0972483 0.995260i \(-0.468996\pi\)
0.0972483 + 0.995260i \(0.468996\pi\)
\(618\) 0 0
\(619\) 185199. 0.0194272 0.00971362 0.999953i \(-0.496908\pi\)
0.00971362 + 0.999953i \(0.496908\pi\)
\(620\) 0 0
\(621\) −1.15209e7 −1.19883
\(622\) 0 0
\(623\) 476492. 0.0491853
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −5.08329e6 −0.516388
\(628\) 0 0
\(629\) 1.04559e7 1.05375
\(630\) 0 0
\(631\) −6.47412e6 −0.647303 −0.323651 0.946176i \(-0.604910\pi\)
−0.323651 + 0.946176i \(0.604910\pi\)
\(632\) 0 0
\(633\) −1.21800e7 −1.20820
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.71066e7 −1.67038
\(638\) 0 0
\(639\) −744262. −0.0721064
\(640\) 0 0
\(641\) 4.64672e6 0.446685 0.223343 0.974740i \(-0.428303\pi\)
0.223343 + 0.974740i \(0.428303\pi\)
\(642\) 0 0
\(643\) 1.28549e7 1.22614 0.613072 0.790027i \(-0.289933\pi\)
0.613072 + 0.790027i \(0.289933\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.61104e7 −1.51302 −0.756510 0.653982i \(-0.773097\pi\)
−0.756510 + 0.653982i \(0.773097\pi\)
\(648\) 0 0
\(649\) 842834. 0.0785471
\(650\) 0 0
\(651\) −4.82689e7 −4.46391
\(652\) 0 0
\(653\) −4.72189e6 −0.433344 −0.216672 0.976244i \(-0.569520\pi\)
−0.216672 + 0.976244i \(0.569520\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.41002e6 0.488974
\(658\) 0 0
\(659\) −6.08366e6 −0.545697 −0.272848 0.962057i \(-0.587966\pi\)
−0.272848 + 0.962057i \(0.587966\pi\)
\(660\) 0 0
\(661\) 1.01649e6 0.0904897 0.0452448 0.998976i \(-0.485593\pi\)
0.0452448 + 0.998976i \(0.485593\pi\)
\(662\) 0 0
\(663\) −2.03798e7 −1.80059
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4.63240e6 0.403173
\(668\) 0 0
\(669\) −5.91080e6 −0.510600
\(670\) 0 0
\(671\) −5.93872e6 −0.509198
\(672\) 0 0
\(673\) −1.00418e7 −0.854619 −0.427310 0.904105i \(-0.640539\pi\)
−0.427310 + 0.904105i \(0.640539\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.12734e7 −0.945331 −0.472665 0.881242i \(-0.656708\pi\)
−0.472665 + 0.881242i \(0.656708\pi\)
\(678\) 0 0
\(679\) −1.59027e6 −0.132372
\(680\) 0 0
\(681\) −2.78672e7 −2.30264
\(682\) 0 0
\(683\) 2.74328e6 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.17818e6 0.0952401
\(688\) 0 0
\(689\) 1.74316e7 1.39891
\(690\) 0 0
\(691\) −1.31710e7 −1.04936 −0.524680 0.851300i \(-0.675815\pi\)
−0.524680 + 0.851300i \(0.675815\pi\)
\(692\) 0 0
\(693\) 9.61308e6 0.760378
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 8.17285e6 0.637223
\(698\) 0 0
\(699\) −2.51593e7 −1.94763
\(700\) 0 0
\(701\) 1.76568e7 1.35712 0.678558 0.734546i \(-0.262605\pi\)
0.678558 + 0.734546i \(0.262605\pi\)
\(702\) 0 0
\(703\) 1.56773e7 1.19641
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.04084e6 0.680237
\(708\) 0 0
\(709\) −1.58423e7 −1.18360 −0.591798 0.806086i \(-0.701582\pi\)
−0.591798 + 0.806086i \(0.701582\pi\)
\(710\) 0 0
\(711\) 4.58331e6 0.340020
\(712\) 0 0
\(713\) −2.84110e7 −2.09297
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.54099e7 −2.57233
\(718\) 0 0
\(719\) 1.10799e7 0.799305 0.399652 0.916667i \(-0.369131\pi\)
0.399652 + 0.916667i \(0.369131\pi\)
\(720\) 0 0
\(721\) −2.26166e7 −1.62028
\(722\) 0 0
\(723\) −3.82301e7 −2.71994
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 9.71158e6 0.681481 0.340741 0.940157i \(-0.389322\pi\)
0.340741 + 0.940157i \(0.389322\pi\)
\(728\) 0 0
\(729\) −2.31577e7 −1.61390
\(730\) 0 0
\(731\) 9.45595e6 0.654503
\(732\) 0 0
\(733\) −2.45714e6 −0.168916 −0.0844580 0.996427i \(-0.526916\pi\)
−0.0844580 + 0.996427i \(0.526916\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.89538e6 −0.196353
\(738\) 0 0
\(739\) 2.22772e6 0.150055 0.0750273 0.997181i \(-0.476096\pi\)
0.0750273 + 0.997181i \(0.476096\pi\)
\(740\) 0 0
\(741\) −3.05567e7 −2.04438
\(742\) 0 0
\(743\) −1.01867e7 −0.676960 −0.338480 0.940974i \(-0.609913\pi\)
−0.338480 + 0.940974i \(0.609913\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.18162e7 1.43046
\(748\) 0 0
\(749\) −4.16195e7 −2.71077
\(750\) 0 0
\(751\) 6.45437e6 0.417594 0.208797 0.977959i \(-0.433045\pi\)
0.208797 + 0.977959i \(0.433045\pi\)
\(752\) 0 0
\(753\) 990119. 0.0636355
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.46247e7 0.927571 0.463785 0.885948i \(-0.346491\pi\)
0.463785 + 0.885948i \(0.346491\pi\)
\(758\) 0 0
\(759\) 9.13362e6 0.575491
\(760\) 0 0
\(761\) −2.73756e7 −1.71357 −0.856784 0.515675i \(-0.827541\pi\)
−0.856784 + 0.515675i \(0.827541\pi\)
\(762\) 0 0
\(763\) −1.90764e7 −1.18627
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.06644e6 0.310967
\(768\) 0 0
\(769\) −1.18927e7 −0.725213 −0.362607 0.931942i \(-0.618113\pi\)
−0.362607 + 0.931942i \(0.618113\pi\)
\(770\) 0 0
\(771\) −8.63837e6 −0.523354
\(772\) 0 0
\(773\) 1.16963e7 0.704042 0.352021 0.935992i \(-0.385495\pi\)
0.352021 + 0.935992i \(0.385495\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −4.78574e7 −2.84379
\(778\) 0 0
\(779\) 1.22541e7 0.723496
\(780\) 0 0
\(781\) 227628. 0.0133536
\(782\) 0 0
\(783\) −5.98170e6 −0.348675
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.48828e6 −0.143206 −0.0716031 0.997433i \(-0.522811\pi\)
−0.0716031 + 0.997433i \(0.522811\pi\)
\(788\) 0 0
\(789\) 1.89922e7 1.08613
\(790\) 0 0
\(791\) 1.69353e7 0.962390
\(792\) 0 0
\(793\) −3.56988e7 −2.01591
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.98889e7 −1.66673 −0.833363 0.552726i \(-0.813588\pi\)
−0.833363 + 0.552726i \(0.813588\pi\)
\(798\) 0 0
\(799\) −3.32993e7 −1.84531
\(800\) 0 0
\(801\) −938747. −0.0516972
\(802\) 0 0
\(803\) −1.65462e6 −0.0905546
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.27615e6 −0.0689789
\(808\) 0 0
\(809\) −2.61207e7 −1.40318 −0.701590 0.712581i \(-0.747526\pi\)
−0.701590 + 0.712581i \(0.747526\pi\)
\(810\) 0 0
\(811\) 2.19410e7 1.17140 0.585699 0.810529i \(-0.300820\pi\)
0.585699 + 0.810529i \(0.300820\pi\)
\(812\) 0 0
\(813\) 1.13027e7 0.599731
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.41779e7 0.743116
\(818\) 0 0
\(819\) 5.77862e7 3.01033
\(820\) 0 0
\(821\) 4.75760e6 0.246337 0.123169 0.992386i \(-0.460694\pi\)
0.123169 + 0.992386i \(0.460694\pi\)
\(822\) 0 0
\(823\) −6.19431e6 −0.318782 −0.159391 0.987216i \(-0.550953\pi\)
−0.159391 + 0.987216i \(0.550953\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.41552e7 0.719699 0.359850 0.933010i \(-0.382828\pi\)
0.359850 + 0.933010i \(0.382828\pi\)
\(828\) 0 0
\(829\) −1.19032e7 −0.601556 −0.300778 0.953694i \(-0.597246\pi\)
−0.300778 + 0.953694i \(0.597246\pi\)
\(830\) 0 0
\(831\) −9.18271e6 −0.461284
\(832\) 0 0
\(833\) 2.60764e7 1.30207
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3.66864e7 1.81005
\(838\) 0 0
\(839\) 3.80619e7 1.86675 0.933374 0.358904i \(-0.116850\pi\)
0.933374 + 0.358904i \(0.116850\pi\)
\(840\) 0 0
\(841\) −1.81060e7 −0.882739
\(842\) 0 0
\(843\) 1.53556e7 0.744215
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.94011e6 −0.140817
\(848\) 0 0
\(849\) 2.73844e7 1.30387
\(850\) 0 0
\(851\) −2.81688e7 −1.33335
\(852\) 0 0
\(853\) −8.91252e6 −0.419400 −0.209700 0.977766i \(-0.567249\pi\)
−0.209700 + 0.977766i \(0.567249\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.38385e7 −1.10873 −0.554366 0.832273i \(-0.687039\pi\)
−0.554366 + 0.832273i \(0.687039\pi\)
\(858\) 0 0
\(859\) −7.15819e6 −0.330994 −0.165497 0.986210i \(-0.552923\pi\)
−0.165497 + 0.986210i \(0.552923\pi\)
\(860\) 0 0
\(861\) −3.74076e7 −1.71970
\(862\) 0 0
\(863\) −2.33903e7 −1.06908 −0.534539 0.845144i \(-0.679515\pi\)
−0.534539 + 0.845144i \(0.679515\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −4.81548e6 −0.217567
\(868\) 0 0
\(869\) −1.40178e6 −0.0629694
\(870\) 0 0
\(871\) −1.74047e7 −0.777358
\(872\) 0 0
\(873\) 3.13302e6 0.139132
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 4.19751e7 1.84286 0.921431 0.388543i \(-0.127021\pi\)
0.921431 + 0.388543i \(0.127021\pi\)
\(878\) 0 0
\(879\) 9.72862e6 0.424697
\(880\) 0 0
\(881\) −7.55945e6 −0.328134 −0.164067 0.986449i \(-0.552461\pi\)
−0.164067 + 0.986449i \(0.552461\pi\)
\(882\) 0 0
\(883\) 2.89794e7 1.25080 0.625400 0.780304i \(-0.284936\pi\)
0.625400 + 0.780304i \(0.284936\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 4.19301e7 1.78944 0.894719 0.446629i \(-0.147376\pi\)
0.894719 + 0.446629i \(0.147376\pi\)
\(888\) 0 0
\(889\) 6.71056e6 0.284776
\(890\) 0 0
\(891\) −161414. −0.00681158
\(892\) 0 0
\(893\) −4.99278e7 −2.09514
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 5.49040e7 2.27836
\(898\) 0 0
\(899\) −1.47511e7 −0.608730
\(900\) 0 0
\(901\) −2.65717e7 −1.09046
\(902\) 0 0
\(903\) −4.32804e7 −1.76633
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 7.79438e6 0.314603 0.157302 0.987551i \(-0.449721\pi\)
0.157302 + 0.987551i \(0.449721\pi\)
\(908\) 0 0
\(909\) −1.78116e7 −0.714977
\(910\) 0 0
\(911\) −2.09270e7 −0.835431 −0.417715 0.908578i \(-0.637169\pi\)
−0.417715 + 0.908578i \(0.637169\pi\)
\(912\) 0 0
\(913\) −6.67235e6 −0.264912
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.09411e7 −2.78596
\(918\) 0 0
\(919\) 6.21354e6 0.242689 0.121344 0.992610i \(-0.461279\pi\)
0.121344 + 0.992610i \(0.461279\pi\)
\(920\) 0 0
\(921\) −1.92378e6 −0.0747318
\(922\) 0 0
\(923\) 1.36832e6 0.0528668
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 4.45575e7 1.70303
\(928\) 0 0
\(929\) 1.86038e7 0.707234 0.353617 0.935390i \(-0.384952\pi\)
0.353617 + 0.935390i \(0.384952\pi\)
\(930\) 0 0
\(931\) 3.90979e7 1.47836
\(932\) 0 0
\(933\) 3.17776e7 1.19514
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −5.27518e7 −1.96286 −0.981428 0.191832i \(-0.938557\pi\)
−0.981428 + 0.191832i \(0.938557\pi\)
\(938\) 0 0
\(939\) 3.33114e7 1.23290
\(940\) 0 0
\(941\) 3.67919e7 1.35450 0.677249 0.735754i \(-0.263172\pi\)
0.677249 + 0.735754i \(0.263172\pi\)
\(942\) 0 0
\(943\) −2.20180e7 −0.806304
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.70930e7 −1.34406 −0.672028 0.740526i \(-0.734576\pi\)
−0.672028 + 0.740526i \(0.734576\pi\)
\(948\) 0 0
\(949\) −9.94627e6 −0.358505
\(950\) 0 0
\(951\) −6.47078e7 −2.32009
\(952\) 0 0
\(953\) 1.77859e7 0.634373 0.317187 0.948363i \(-0.397262\pi\)
0.317187 + 0.948363i \(0.397262\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 4.74221e6 0.167379
\(958\) 0 0
\(959\) −3.91673e7 −1.37523
\(960\) 0 0
\(961\) 6.18407e7 2.16006
\(962\) 0 0
\(963\) 8.19955e7 2.84921
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.30531e7 0.448897 0.224448 0.974486i \(-0.427942\pi\)
0.224448 + 0.974486i \(0.427942\pi\)
\(968\) 0 0
\(969\) 4.65789e7 1.59360
\(970\) 0 0
\(971\) 1.33944e7 0.455908 0.227954 0.973672i \(-0.426796\pi\)
0.227954 + 0.973672i \(0.426796\pi\)
\(972\) 0 0
\(973\) −5.97708e7 −2.02398
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.84912e7 1.96044 0.980221 0.197905i \(-0.0634139\pi\)
0.980221 + 0.197905i \(0.0634139\pi\)
\(978\) 0 0
\(979\) 287110. 0.00957397
\(980\) 0 0
\(981\) 3.75828e7 1.24686
\(982\) 0 0
\(983\) −2.61534e7 −0.863265 −0.431632 0.902050i \(-0.642062\pi\)
−0.431632 + 0.902050i \(0.642062\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.52413e8 4.97999
\(988\) 0 0
\(989\) −2.54747e7 −0.828169
\(990\) 0 0
\(991\) 5.29034e7 1.71119 0.855597 0.517643i \(-0.173190\pi\)
0.855597 + 0.517643i \(0.173190\pi\)
\(992\) 0 0
\(993\) −8.97774e6 −0.288931
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 4.23746e7 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(998\) 0 0
\(999\) 3.63736e7 1.15312
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 1100.6.a.b.1.2 2
5.2 odd 4 1100.6.b.c.749.1 4
5.3 odd 4 1100.6.b.c.749.4 4
5.4 even 2 44.6.a.b.1.1 2
15.14 odd 2 396.6.a.f.1.2 2
20.19 odd 2 176.6.a.g.1.2 2
40.19 odd 2 704.6.a.m.1.1 2
40.29 even 2 704.6.a.n.1.2 2
55.54 odd 2 484.6.a.d.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
44.6.a.b.1.1 2 5.4 even 2
176.6.a.g.1.2 2 20.19 odd 2
396.6.a.f.1.2 2 15.14 odd 2
484.6.a.d.1.1 2 55.54 odd 2
704.6.a.m.1.1 2 40.19 odd 2
704.6.a.n.1.2 2 40.29 even 2
1100.6.a.b.1.2 2 1.1 even 1 trivial
1100.6.b.c.749.1 4 5.2 odd 4
1100.6.b.c.749.4 4 5.3 odd 4