Properties

Label 700.6.e.g.449.1
Level $700$
Weight $6$
Character 700.449
Analytic conductor $112.269$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,6,Mod(449,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.449");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 700.e (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(112.268673869\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 998x^{4} + 249001x^{2} + 44100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.1
Root \(-22.5458i\) of defining polynomial
Character \(\chi\) \(=\) 700.449
Dual form 700.6.e.g.449.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-24.5458i q^{3} +49.0000i q^{7} -359.498 q^{9} +O(q^{10})\) \(q-24.5458i q^{3} +49.0000i q^{7} -359.498 q^{9} +90.2356 q^{11} +14.4413i q^{13} +407.384i q^{17} -2289.19 q^{19} +1202.75 q^{21} +505.976i q^{23} +2859.53i q^{27} +3164.56 q^{29} -6231.43 q^{31} -2214.91i q^{33} +5388.70i q^{37} +354.474 q^{39} +11764.3 q^{41} +5824.58i q^{43} +7349.38i q^{47} -2401.00 q^{49} +9999.57 q^{51} -14971.6i q^{53} +56190.1i q^{57} +47153.5 q^{59} -4289.61 q^{61} -17615.4i q^{63} +48898.3i q^{67} +12419.6 q^{69} +58567.6 q^{71} +1599.07i q^{73} +4421.54i q^{77} +79121.1 q^{79} -17168.4 q^{81} +71472.1i q^{83} -77676.9i q^{87} +77165.9 q^{89} -707.624 q^{91} +152956. i q^{93} +11559.6i q^{97} -32439.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 562 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 562 q^{9} - 28 q^{11} - 4656 q^{19} + 588 q^{21} - 8184 q^{29} + 11776 q^{31} - 27404 q^{39} + 22900 q^{41} - 14406 q^{49} + 63524 q^{51} - 24776 q^{59} + 54364 q^{61} + 124280 q^{69} + 163984 q^{71} + 31852 q^{79} - 64202 q^{81} + 191420 q^{89} - 392 q^{91} + 228736 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) − 24.5458i − 1.57462i −0.616560 0.787308i \(-0.711474\pi\)
0.616560 0.787308i \(-0.288526\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 49.0000i 0.377964i
\(8\) 0 0
\(9\) −359.498 −1.47941
\(10\) 0 0
\(11\) 90.2356 0.224852 0.112426 0.993660i \(-0.464138\pi\)
0.112426 + 0.993660i \(0.464138\pi\)
\(12\) 0 0
\(13\) 14.4413i 0.0237000i 0.999930 + 0.0118500i \(0.00377206\pi\)
−0.999930 + 0.0118500i \(0.996228\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 407.384i 0.341886i 0.985281 + 0.170943i \(0.0546814\pi\)
−0.985281 + 0.170943i \(0.945319\pi\)
\(18\) 0 0
\(19\) −2289.19 −1.45478 −0.727391 0.686223i \(-0.759268\pi\)
−0.727391 + 0.686223i \(0.759268\pi\)
\(20\) 0 0
\(21\) 1202.75 0.595149
\(22\) 0 0
\(23\) 505.976i 0.199439i 0.995016 + 0.0997197i \(0.0317946\pi\)
−0.995016 + 0.0997197i \(0.968205\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2859.53i 0.754893i
\(28\) 0 0
\(29\) 3164.56 0.698745 0.349373 0.936984i \(-0.386395\pi\)
0.349373 + 0.936984i \(0.386395\pi\)
\(30\) 0 0
\(31\) −6231.43 −1.16462 −0.582309 0.812968i \(-0.697851\pi\)
−0.582309 + 0.812968i \(0.697851\pi\)
\(32\) 0 0
\(33\) − 2214.91i − 0.354055i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5388.70i 0.647113i 0.946209 + 0.323556i \(0.104879\pi\)
−0.946209 + 0.323556i \(0.895121\pi\)
\(38\) 0 0
\(39\) 354.474 0.0373184
\(40\) 0 0
\(41\) 11764.3 1.09297 0.546484 0.837469i \(-0.315966\pi\)
0.546484 + 0.837469i \(0.315966\pi\)
\(42\) 0 0
\(43\) 5824.58i 0.480390i 0.970725 + 0.240195i \(0.0772113\pi\)
−0.970725 + 0.240195i \(0.922789\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7349.38i 0.485295i 0.970114 + 0.242648i \(0.0780159\pi\)
−0.970114 + 0.242648i \(0.921984\pi\)
\(48\) 0 0
\(49\) −2401.00 −0.142857
\(50\) 0 0
\(51\) 9999.57 0.538339
\(52\) 0 0
\(53\) − 14971.6i − 0.732114i −0.930592 0.366057i \(-0.880707\pi\)
0.930592 0.366057i \(-0.119293\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 56190.1i 2.29072i
\(58\) 0 0
\(59\) 47153.5 1.76353 0.881767 0.471685i \(-0.156354\pi\)
0.881767 + 0.471685i \(0.156354\pi\)
\(60\) 0 0
\(61\) −4289.61 −0.147602 −0.0738011 0.997273i \(-0.523513\pi\)
−0.0738011 + 0.997273i \(0.523513\pi\)
\(62\) 0 0
\(63\) − 17615.4i − 0.559166i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 48898.3i 1.33078i 0.746496 + 0.665390i \(0.231735\pi\)
−0.746496 + 0.665390i \(0.768265\pi\)
\(68\) 0 0
\(69\) 12419.6 0.314040
\(70\) 0 0
\(71\) 58567.6 1.37883 0.689417 0.724365i \(-0.257867\pi\)
0.689417 + 0.724365i \(0.257867\pi\)
\(72\) 0 0
\(73\) 1599.07i 0.0351206i 0.999846 + 0.0175603i \(0.00558990\pi\)
−0.999846 + 0.0175603i \(0.994410\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4421.54i 0.0849859i
\(78\) 0 0
\(79\) 79121.1 1.42634 0.713172 0.700989i \(-0.247258\pi\)
0.713172 + 0.700989i \(0.247258\pi\)
\(80\) 0 0
\(81\) −17168.4 −0.290748
\(82\) 0 0
\(83\) 71472.1i 1.13878i 0.822066 + 0.569392i \(0.192821\pi\)
−0.822066 + 0.569392i \(0.807179\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 77676.9i − 1.10026i
\(88\) 0 0
\(89\) 77165.9 1.03264 0.516322 0.856395i \(-0.327301\pi\)
0.516322 + 0.856395i \(0.327301\pi\)
\(90\) 0 0
\(91\) −707.624 −0.00895775
\(92\) 0 0
\(93\) 152956.i 1.83383i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 11559.6i 0.124743i 0.998053 + 0.0623713i \(0.0198663\pi\)
−0.998053 + 0.0623713i \(0.980134\pi\)
\(98\) 0 0
\(99\) −32439.5 −0.332649
\(100\) 0 0
\(101\) −171423. −1.67211 −0.836057 0.548642i \(-0.815145\pi\)
−0.836057 + 0.548642i \(0.815145\pi\)
\(102\) 0 0
\(103\) 182469.i 1.69471i 0.531024 + 0.847357i \(0.321807\pi\)
−0.531024 + 0.847357i \(0.678193\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 76696.7i − 0.647616i −0.946123 0.323808i \(-0.895037\pi\)
0.946123 0.323808i \(-0.104963\pi\)
\(108\) 0 0
\(109\) 13146.0 0.105981 0.0529904 0.998595i \(-0.483125\pi\)
0.0529904 + 0.998595i \(0.483125\pi\)
\(110\) 0 0
\(111\) 132270. 1.01895
\(112\) 0 0
\(113\) − 5996.97i − 0.0441811i −0.999756 0.0220905i \(-0.992968\pi\)
0.999756 0.0220905i \(-0.00703221\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) − 5191.61i − 0.0350621i
\(118\) 0 0
\(119\) −19961.8 −0.129221
\(120\) 0 0
\(121\) −152909. −0.949442
\(122\) 0 0
\(123\) − 288765.i − 1.72101i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 109534.i − 0.602613i −0.953527 0.301306i \(-0.902577\pi\)
0.953527 0.301306i \(-0.0974227\pi\)
\(128\) 0 0
\(129\) 142969. 0.756429
\(130\) 0 0
\(131\) 385186. 1.96107 0.980533 0.196354i \(-0.0629101\pi\)
0.980533 + 0.196354i \(0.0629101\pi\)
\(132\) 0 0
\(133\) − 112170.i − 0.549856i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 315816.i − 1.43758i −0.695226 0.718791i \(-0.744696\pi\)
0.695226 0.718791i \(-0.255304\pi\)
\(138\) 0 0
\(139\) −95433.5 −0.418952 −0.209476 0.977814i \(-0.567176\pi\)
−0.209476 + 0.977814i \(0.567176\pi\)
\(140\) 0 0
\(141\) 180397. 0.764154
\(142\) 0 0
\(143\) 1303.12i 0.00532898i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 58934.5i 0.224945i
\(148\) 0 0
\(149\) 151387. 0.558629 0.279315 0.960200i \(-0.409893\pi\)
0.279315 + 0.960200i \(0.409893\pi\)
\(150\) 0 0
\(151\) 300641. 1.07301 0.536507 0.843896i \(-0.319743\pi\)
0.536507 + 0.843896i \(0.319743\pi\)
\(152\) 0 0
\(153\) − 146453.i − 0.505791i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 306110.i − 0.991125i −0.868572 0.495563i \(-0.834962\pi\)
0.868572 0.495563i \(-0.165038\pi\)
\(158\) 0 0
\(159\) −367491. −1.15280
\(160\) 0 0
\(161\) −24792.8 −0.0753810
\(162\) 0 0
\(163\) − 373022.i − 1.09968i −0.835271 0.549839i \(-0.814689\pi\)
0.835271 0.549839i \(-0.185311\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 317441.i − 0.880789i −0.897804 0.440394i \(-0.854839\pi\)
0.897804 0.440394i \(-0.145161\pi\)
\(168\) 0 0
\(169\) 371084. 0.999438
\(170\) 0 0
\(171\) 822959. 2.15223
\(172\) 0 0
\(173\) 354815.i 0.901335i 0.892692 + 0.450668i \(0.148814\pi\)
−0.892692 + 0.450668i \(0.851186\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) − 1.15742e6i − 2.77689i
\(178\) 0 0
\(179\) −356294. −0.831144 −0.415572 0.909560i \(-0.636419\pi\)
−0.415572 + 0.909560i \(0.636419\pi\)
\(180\) 0 0
\(181\) 9772.82 0.0221729 0.0110865 0.999939i \(-0.496471\pi\)
0.0110865 + 0.999939i \(0.496471\pi\)
\(182\) 0 0
\(183\) 105292.i 0.232417i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 36760.5i 0.0768736i
\(188\) 0 0
\(189\) −140117. −0.285323
\(190\) 0 0
\(191\) −302267. −0.599525 −0.299762 0.954014i \(-0.596907\pi\)
−0.299762 + 0.954014i \(0.596907\pi\)
\(192\) 0 0
\(193\) − 267712.i − 0.517339i −0.965966 0.258669i \(-0.916716\pi\)
0.965966 0.258669i \(-0.0832840\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 151930.i − 0.278920i −0.990228 0.139460i \(-0.955463\pi\)
0.990228 0.139460i \(-0.0445366\pi\)
\(198\) 0 0
\(199\) −825686. −1.47803 −0.739013 0.673691i \(-0.764708\pi\)
−0.739013 + 0.673691i \(0.764708\pi\)
\(200\) 0 0
\(201\) 1.20025e6 2.09547
\(202\) 0 0
\(203\) 155064.i 0.264101i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 181897.i − 0.295053i
\(208\) 0 0
\(209\) −206567. −0.327110
\(210\) 0 0
\(211\) 972289. 1.50345 0.751726 0.659476i \(-0.229222\pi\)
0.751726 + 0.659476i \(0.229222\pi\)
\(212\) 0 0
\(213\) − 1.43759e6i − 2.17113i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 305340.i − 0.440184i
\(218\) 0 0
\(219\) 39250.6 0.0553014
\(220\) 0 0
\(221\) −5883.15 −0.00810269
\(222\) 0 0
\(223\) 1.35209e6i 1.82073i 0.413811 + 0.910363i \(0.364197\pi\)
−0.413811 + 0.910363i \(0.635803\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 876401.i 1.12885i 0.825483 + 0.564427i \(0.190903\pi\)
−0.825483 + 0.564427i \(0.809097\pi\)
\(228\) 0 0
\(229\) −1.10402e6 −1.39119 −0.695597 0.718433i \(-0.744860\pi\)
−0.695597 + 0.718433i \(0.744860\pi\)
\(230\) 0 0
\(231\) 108530. 0.133820
\(232\) 0 0
\(233\) − 81858.7i − 0.0987814i −0.998780 0.0493907i \(-0.984272\pi\)
0.998780 0.0493907i \(-0.0157279\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 1.94209e6i − 2.24594i
\(238\) 0 0
\(239\) 1.45239e6 1.64471 0.822354 0.568977i \(-0.192661\pi\)
0.822354 + 0.568977i \(0.192661\pi\)
\(240\) 0 0
\(241\) 1.11432e6 1.23586 0.617929 0.786234i \(-0.287972\pi\)
0.617929 + 0.786234i \(0.287972\pi\)
\(242\) 0 0
\(243\) 1.11628e6i 1.21271i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 33058.9i − 0.0344783i
\(248\) 0 0
\(249\) 1.75434e6 1.79315
\(250\) 0 0
\(251\) −157265. −0.157560 −0.0787801 0.996892i \(-0.525102\pi\)
−0.0787801 + 0.996892i \(0.525102\pi\)
\(252\) 0 0
\(253\) 45657.1i 0.0448443i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 655000.i 0.618598i 0.950965 + 0.309299i \(0.100094\pi\)
−0.950965 + 0.309299i \(0.899906\pi\)
\(258\) 0 0
\(259\) −264046. −0.244586
\(260\) 0 0
\(261\) −1.13765e6 −1.03373
\(262\) 0 0
\(263\) 498514.i 0.444414i 0.975000 + 0.222207i \(0.0713261\pi\)
−0.975000 + 0.222207i \(0.928674\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 1.89410e6i − 1.62602i
\(268\) 0 0
\(269\) 1.00547e6 0.847202 0.423601 0.905849i \(-0.360766\pi\)
0.423601 + 0.905849i \(0.360766\pi\)
\(270\) 0 0
\(271\) 93641.4 0.0774541 0.0387271 0.999250i \(-0.487670\pi\)
0.0387271 + 0.999250i \(0.487670\pi\)
\(272\) 0 0
\(273\) 17369.2i 0.0141050i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12211.8i 0.00956271i 0.999989 + 0.00478135i \(0.00152196\pi\)
−0.999989 + 0.00478135i \(0.998478\pi\)
\(278\) 0 0
\(279\) 2.24018e6 1.72295
\(280\) 0 0
\(281\) −389424. −0.294210 −0.147105 0.989121i \(-0.546996\pi\)
−0.147105 + 0.989121i \(0.546996\pi\)
\(282\) 0 0
\(283\) − 1.23856e6i − 0.919283i −0.888105 0.459642i \(-0.847978\pi\)
0.888105 0.459642i \(-0.152022\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 576452.i 0.413103i
\(288\) 0 0
\(289\) 1.25390e6 0.883114
\(290\) 0 0
\(291\) 283741. 0.196422
\(292\) 0 0
\(293\) 1.36915e6i 0.931716i 0.884860 + 0.465858i \(0.154254\pi\)
−0.884860 + 0.465858i \(0.845746\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 258032.i 0.169739i
\(298\) 0 0
\(299\) −7306.96 −0.00472671
\(300\) 0 0
\(301\) −285404. −0.181570
\(302\) 0 0
\(303\) 4.20772e6i 2.63294i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.15266e6i 1.30356i 0.758409 + 0.651778i \(0.225977\pi\)
−0.758409 + 0.651778i \(0.774023\pi\)
\(308\) 0 0
\(309\) 4.47885e6 2.66852
\(310\) 0 0
\(311\) 2.58326e6 1.51449 0.757245 0.653131i \(-0.226545\pi\)
0.757245 + 0.653131i \(0.226545\pi\)
\(312\) 0 0
\(313\) − 3.07474e6i − 1.77398i −0.461793 0.886988i \(-0.652794\pi\)
0.461793 0.886988i \(-0.347206\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 1.04850e6i − 0.586031i −0.956108 0.293015i \(-0.905341\pi\)
0.956108 0.293015i \(-0.0946587\pi\)
\(318\) 0 0
\(319\) 285556. 0.157114
\(320\) 0 0
\(321\) −1.88258e6 −1.01975
\(322\) 0 0
\(323\) − 932579.i − 0.497370i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 322680.i − 0.166879i
\(328\) 0 0
\(329\) −360120. −0.183424
\(330\) 0 0
\(331\) 2.26689e6 1.13726 0.568631 0.822592i \(-0.307473\pi\)
0.568631 + 0.822592i \(0.307473\pi\)
\(332\) 0 0
\(333\) − 1.93723e6i − 0.957348i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2.78963e6i 1.33805i 0.743240 + 0.669024i \(0.233288\pi\)
−0.743240 + 0.669024i \(0.766712\pi\)
\(338\) 0 0
\(339\) −147201. −0.0695682
\(340\) 0 0
\(341\) −562297. −0.261866
\(342\) 0 0
\(343\) − 117649.i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.74629e6i 0.778562i 0.921119 + 0.389281i \(0.127277\pi\)
−0.921119 + 0.389281i \(0.872723\pi\)
\(348\) 0 0
\(349\) −3.21671e6 −1.41367 −0.706836 0.707377i \(-0.749878\pi\)
−0.706836 + 0.707377i \(0.749878\pi\)
\(350\) 0 0
\(351\) −41295.4 −0.0178910
\(352\) 0 0
\(353\) − 507518.i − 0.216778i −0.994109 0.108389i \(-0.965431\pi\)
0.994109 0.108389i \(-0.0345691\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 489979.i 0.203473i
\(358\) 0 0
\(359\) −804256. −0.329350 −0.164675 0.986348i \(-0.552658\pi\)
−0.164675 + 0.986348i \(0.552658\pi\)
\(360\) 0 0
\(361\) 2.76430e6 1.11639
\(362\) 0 0
\(363\) 3.75327e6i 1.49501i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.60921e6i 0.623658i 0.950138 + 0.311829i \(0.100942\pi\)
−0.950138 + 0.311829i \(0.899058\pi\)
\(368\) 0 0
\(369\) −4.22925e6 −1.61695
\(370\) 0 0
\(371\) 733609. 0.276713
\(372\) 0 0
\(373\) 5.19298e6i 1.93261i 0.257397 + 0.966306i \(0.417135\pi\)
−0.257397 + 0.966306i \(0.582865\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 45700.4i 0.0165603i
\(378\) 0 0
\(379\) 114187. 0.0408337 0.0204169 0.999792i \(-0.493501\pi\)
0.0204169 + 0.999792i \(0.493501\pi\)
\(380\) 0 0
\(381\) −2.68859e6 −0.948884
\(382\) 0 0
\(383\) 3.03725e6i 1.05799i 0.848624 + 0.528997i \(0.177432\pi\)
−0.848624 + 0.528997i \(0.822568\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 2.09392e6i − 0.710695i
\(388\) 0 0
\(389\) −1.75485e6 −0.587985 −0.293993 0.955808i \(-0.594984\pi\)
−0.293993 + 0.955808i \(0.594984\pi\)
\(390\) 0 0
\(391\) −206127. −0.0681855
\(392\) 0 0
\(393\) − 9.45471e6i − 3.08793i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) − 411623.i − 0.131076i −0.997850 0.0655380i \(-0.979124\pi\)
0.997850 0.0655380i \(-0.0208764\pi\)
\(398\) 0 0
\(399\) −2.75332e6 −0.865812
\(400\) 0 0
\(401\) −3.34807e6 −1.03976 −0.519881 0.854238i \(-0.674024\pi\)
−0.519881 + 0.854238i \(0.674024\pi\)
\(402\) 0 0
\(403\) − 89990.0i − 0.0276014i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 486253.i 0.145504i
\(408\) 0 0
\(409\) 1.67438e6 0.494933 0.247467 0.968896i \(-0.420402\pi\)
0.247467 + 0.968896i \(0.420402\pi\)
\(410\) 0 0
\(411\) −7.75197e6 −2.26364
\(412\) 0 0
\(413\) 2.31052e6i 0.666553i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.34249e6i 0.659688i
\(418\) 0 0
\(419\) −2.61117e6 −0.726608 −0.363304 0.931671i \(-0.618351\pi\)
−0.363304 + 0.931671i \(0.618351\pi\)
\(420\) 0 0
\(421\) 3.20146e6 0.880324 0.440162 0.897918i \(-0.354921\pi\)
0.440162 + 0.897918i \(0.354921\pi\)
\(422\) 0 0
\(423\) − 2.64209e6i − 0.717953i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 210191.i − 0.0557884i
\(428\) 0 0
\(429\) 31986.1 0.00839109
\(430\) 0 0
\(431\) 5.57601e6 1.44587 0.722937 0.690914i \(-0.242792\pi\)
0.722937 + 0.690914i \(0.242792\pi\)
\(432\) 0 0
\(433\) − 5.12039e6i − 1.31245i −0.754564 0.656226i \(-0.772152\pi\)
0.754564 0.656226i \(-0.227848\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 1.15828e6i − 0.290141i
\(438\) 0 0
\(439\) −3.83173e6 −0.948930 −0.474465 0.880274i \(-0.657358\pi\)
−0.474465 + 0.880274i \(0.657358\pi\)
\(440\) 0 0
\(441\) 863154. 0.211345
\(442\) 0 0
\(443\) 2.70686e6i 0.655325i 0.944795 + 0.327662i \(0.106261\pi\)
−0.944795 + 0.327662i \(0.893739\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 3.71592e6i − 0.879626i
\(448\) 0 0
\(449\) 7.55860e6 1.76940 0.884699 0.466164i \(-0.154364\pi\)
0.884699 + 0.466164i \(0.154364\pi\)
\(450\) 0 0
\(451\) 1.06156e6 0.245756
\(452\) 0 0
\(453\) − 7.37948e6i − 1.68959i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 2.67340e6i − 0.598790i −0.954129 0.299395i \(-0.903215\pi\)
0.954129 0.299395i \(-0.0967848\pi\)
\(458\) 0 0
\(459\) −1.16493e6 −0.258087
\(460\) 0 0
\(461\) −792744. −0.173732 −0.0868661 0.996220i \(-0.527685\pi\)
−0.0868661 + 0.996220i \(0.527685\pi\)
\(462\) 0 0
\(463\) − 6.72717e6i − 1.45841i −0.684294 0.729206i \(-0.739890\pi\)
0.684294 0.729206i \(-0.260110\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 7.79719e6i − 1.65442i −0.561892 0.827211i \(-0.689926\pi\)
0.561892 0.827211i \(-0.310074\pi\)
\(468\) 0 0
\(469\) −2.39601e6 −0.502988
\(470\) 0 0
\(471\) −7.51373e6 −1.56064
\(472\) 0 0
\(473\) 525584.i 0.108016i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.38226e6i 1.08310i
\(478\) 0 0
\(479\) 2.99000e6 0.595433 0.297717 0.954654i \(-0.403775\pi\)
0.297717 + 0.954654i \(0.403775\pi\)
\(480\) 0 0
\(481\) −77819.9 −0.0153366
\(482\) 0 0
\(483\) 608561.i 0.118696i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.01844e7i 1.94587i 0.231082 + 0.972934i \(0.425774\pi\)
−0.231082 + 0.972934i \(0.574226\pi\)
\(488\) 0 0
\(489\) −9.15614e6 −1.73157
\(490\) 0 0
\(491\) −2.36159e6 −0.442079 −0.221040 0.975265i \(-0.570945\pi\)
−0.221040 + 0.975265i \(0.570945\pi\)
\(492\) 0 0
\(493\) 1.28919e6i 0.238891i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.86981e6i 0.521150i
\(498\) 0 0
\(499\) −1.04692e7 −1.88219 −0.941096 0.338141i \(-0.890202\pi\)
−0.941096 + 0.338141i \(0.890202\pi\)
\(500\) 0 0
\(501\) −7.79185e6 −1.38690
\(502\) 0 0
\(503\) 5.05909e6i 0.891565i 0.895141 + 0.445782i \(0.147074\pi\)
−0.895141 + 0.445782i \(0.852926\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 9.10858e6i − 1.57373i
\(508\) 0 0
\(509\) −8.22380e6 −1.40695 −0.703474 0.710721i \(-0.748369\pi\)
−0.703474 + 0.710721i \(0.748369\pi\)
\(510\) 0 0
\(511\) −78354.6 −0.0132743
\(512\) 0 0
\(513\) − 6.54602e6i − 1.09821i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 663176.i 0.109119i
\(518\) 0 0
\(519\) 8.70922e6 1.41926
\(520\) 0 0
\(521\) 1.91440e6 0.308985 0.154493 0.987994i \(-0.450626\pi\)
0.154493 + 0.987994i \(0.450626\pi\)
\(522\) 0 0
\(523\) 1.13982e7i 1.82215i 0.412245 + 0.911073i \(0.364745\pi\)
−0.412245 + 0.911073i \(0.635255\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 2.53858e6i − 0.398167i
\(528\) 0 0
\(529\) 6.18033e6 0.960224
\(530\) 0 0
\(531\) −1.69516e7 −2.60900
\(532\) 0 0
\(533\) 169892.i 0.0259033i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 8.74554e6i 1.30873i
\(538\) 0 0
\(539\) −216656. −0.0321217
\(540\) 0 0
\(541\) −2.18345e6 −0.320738 −0.160369 0.987057i \(-0.551268\pi\)
−0.160369 + 0.987057i \(0.551268\pi\)
\(542\) 0 0
\(543\) − 239882.i − 0.0349139i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 3.45056e6i − 0.493084i −0.969132 0.246542i \(-0.920706\pi\)
0.969132 0.246542i \(-0.0792944\pi\)
\(548\) 0 0
\(549\) 1.54210e6 0.218365
\(550\) 0 0
\(551\) −7.24430e6 −1.01652
\(552\) 0 0
\(553\) 3.87693e6i 0.539108i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 1.17331e7i − 1.60241i −0.598391 0.801204i \(-0.704193\pi\)
0.598391 0.801204i \(-0.295807\pi\)
\(558\) 0 0
\(559\) −84114.5 −0.0113852
\(560\) 0 0
\(561\) 902317. 0.121046
\(562\) 0 0
\(563\) 604258.i 0.0803436i 0.999193 + 0.0401718i \(0.0127905\pi\)
−0.999193 + 0.0401718i \(0.987209\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 841250.i − 0.109892i
\(568\) 0 0
\(569\) −1.22306e6 −0.158368 −0.0791842 0.996860i \(-0.525232\pi\)
−0.0791842 + 0.996860i \(0.525232\pi\)
\(570\) 0 0
\(571\) −6.34785e6 −0.814772 −0.407386 0.913256i \(-0.633560\pi\)
−0.407386 + 0.913256i \(0.633560\pi\)
\(572\) 0 0
\(573\) 7.41939e6i 0.944021i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 5.02896e6i 0.628838i 0.949284 + 0.314419i \(0.101810\pi\)
−0.949284 + 0.314419i \(0.898190\pi\)
\(578\) 0 0
\(579\) −6.57122e6 −0.814610
\(580\) 0 0
\(581\) −3.50213e6 −0.430420
\(582\) 0 0
\(583\) − 1.35097e6i − 0.164617i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.24089e7i 1.48641i 0.669063 + 0.743206i \(0.266696\pi\)
−0.669063 + 0.743206i \(0.733304\pi\)
\(588\) 0 0
\(589\) 1.42649e7 1.69427
\(590\) 0 0
\(591\) −3.72926e6 −0.439191
\(592\) 0 0
\(593\) 1.60941e7i 1.87945i 0.341932 + 0.939725i \(0.388919\pi\)
−0.341932 + 0.939725i \(0.611081\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.02671e7i 2.32732i
\(598\) 0 0
\(599\) −2.42343e6 −0.275971 −0.137986 0.990434i \(-0.544063\pi\)
−0.137986 + 0.990434i \(0.544063\pi\)
\(600\) 0 0
\(601\) 7.84941e6 0.886443 0.443222 0.896412i \(-0.353835\pi\)
0.443222 + 0.896412i \(0.353835\pi\)
\(602\) 0 0
\(603\) − 1.75788e7i − 1.96878i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.84175e6i 0.753695i 0.926275 + 0.376847i \(0.122992\pi\)
−0.926275 + 0.376847i \(0.877008\pi\)
\(608\) 0 0
\(609\) 3.80617e6 0.415858
\(610\) 0 0
\(611\) −106135. −0.0115015
\(612\) 0 0
\(613\) 1.16723e6i 0.125460i 0.998031 + 0.0627302i \(0.0199808\pi\)
−0.998031 + 0.0627302i \(0.980019\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.05925e6i 0.852279i 0.904657 + 0.426140i \(0.140127\pi\)
−0.904657 + 0.426140i \(0.859873\pi\)
\(618\) 0 0
\(619\) −5.10346e6 −0.535350 −0.267675 0.963509i \(-0.586255\pi\)
−0.267675 + 0.963509i \(0.586255\pi\)
\(620\) 0 0
\(621\) −1.44686e6 −0.150555
\(622\) 0 0
\(623\) 3.78113e6i 0.390303i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 5.07035e6i 0.515073i
\(628\) 0 0
\(629\) −2.19527e6 −0.221239
\(630\) 0 0
\(631\) 6.01731e6 0.601630 0.300815 0.953683i \(-0.402741\pi\)
0.300815 + 0.953683i \(0.402741\pi\)
\(632\) 0 0
\(633\) − 2.38656e7i − 2.36736i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 34673.6i − 0.00338571i
\(638\) 0 0
\(639\) −2.10549e7 −2.03987
\(640\) 0 0
\(641\) 6.28323e6 0.604002 0.302001 0.953308i \(-0.402345\pi\)
0.302001 + 0.953308i \(0.402345\pi\)
\(642\) 0 0
\(643\) 7.65315e6i 0.729983i 0.931011 + 0.364991i \(0.118928\pi\)
−0.931011 + 0.364991i \(0.881072\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.00172e7i 1.87994i 0.341260 + 0.939969i \(0.389146\pi\)
−0.341260 + 0.939969i \(0.610854\pi\)
\(648\) 0 0
\(649\) 4.25492e6 0.396534
\(650\) 0 0
\(651\) −7.49483e6 −0.693121
\(652\) 0 0
\(653\) 2.94459e6i 0.270236i 0.990830 + 0.135118i \(0.0431413\pi\)
−0.990830 + 0.135118i \(0.956859\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 574863.i − 0.0519579i
\(658\) 0 0
\(659\) 6.11116e6 0.548164 0.274082 0.961706i \(-0.411626\pi\)
0.274082 + 0.961706i \(0.411626\pi\)
\(660\) 0 0
\(661\) 6.81315e6 0.606518 0.303259 0.952908i \(-0.401925\pi\)
0.303259 + 0.952908i \(0.401925\pi\)
\(662\) 0 0
\(663\) 144407.i 0.0127586i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.60120e6i 0.139357i
\(668\) 0 0
\(669\) 3.31882e7 2.86694
\(670\) 0 0
\(671\) −387075. −0.0331886
\(672\) 0 0
\(673\) 1.02171e7i 0.869540i 0.900541 + 0.434770i \(0.143170\pi\)
−0.900541 + 0.434770i \(0.856830\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.09917e6i 0.259881i 0.991522 + 0.129940i \(0.0414786\pi\)
−0.991522 + 0.129940i \(0.958521\pi\)
\(678\) 0 0
\(679\) −566422. −0.0471483
\(680\) 0 0
\(681\) 2.15120e7 1.77751
\(682\) 0 0
\(683\) − 1.08480e7i − 0.889814i −0.895577 0.444907i \(-0.853237\pi\)
0.895577 0.444907i \(-0.146763\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.70990e7i 2.19059i
\(688\) 0 0
\(689\) 216210. 0.0173511
\(690\) 0 0
\(691\) 1.27049e6 0.101222 0.0506112 0.998718i \(-0.483883\pi\)
0.0506112 + 0.998718i \(0.483883\pi\)
\(692\) 0 0
\(693\) − 1.58953e6i − 0.125729i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 4.79260e6i 0.373671i
\(698\) 0 0
\(699\) −2.00929e6 −0.155543
\(700\) 0 0
\(701\) 2.34177e6 0.179990 0.0899952 0.995942i \(-0.471315\pi\)
0.0899952 + 0.995942i \(0.471315\pi\)
\(702\) 0 0
\(703\) − 1.23358e7i − 0.941408i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 8.39973e6i − 0.632000i
\(708\) 0 0
\(709\) 7.30501e6 0.545764 0.272882 0.962048i \(-0.412023\pi\)
0.272882 + 0.962048i \(0.412023\pi\)
\(710\) 0 0
\(711\) −2.84438e7 −2.11015
\(712\) 0 0
\(713\) − 3.15296e6i − 0.232271i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) − 3.56501e7i − 2.58978i
\(718\) 0 0
\(719\) −1.26261e7 −0.910850 −0.455425 0.890274i \(-0.650513\pi\)
−0.455425 + 0.890274i \(0.650513\pi\)
\(720\) 0 0
\(721\) −8.94098e6 −0.640541
\(722\) 0 0
\(723\) − 2.73520e7i − 1.94600i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.43022e7i 1.00361i 0.864980 + 0.501806i \(0.167331\pi\)
−0.864980 + 0.501806i \(0.832669\pi\)
\(728\) 0 0
\(729\) 2.32281e7 1.61880
\(730\) 0 0
\(731\) −2.37284e6 −0.164238
\(732\) 0 0
\(733\) 2.32911e7i 1.60114i 0.599237 + 0.800572i \(0.295471\pi\)
−0.599237 + 0.800572i \(0.704529\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.41236e6i 0.299228i
\(738\) 0 0
\(739\) 1.00700e7 0.678293 0.339146 0.940734i \(-0.389862\pi\)
0.339146 + 0.940734i \(0.389862\pi\)
\(740\) 0 0
\(741\) −811458. −0.0542901
\(742\) 0 0
\(743\) 1.66744e7i 1.10810i 0.832484 + 0.554049i \(0.186918\pi\)
−0.832484 + 0.554049i \(0.813082\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 2.56940e7i − 1.68473i
\(748\) 0 0
\(749\) 3.75814e6 0.244776
\(750\) 0 0
\(751\) 39313.6 0.00254356 0.00127178 0.999999i \(-0.499595\pi\)
0.00127178 + 0.999999i \(0.499595\pi\)
\(752\) 0 0
\(753\) 3.86019e6i 0.248097i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 4.77082e6i − 0.302589i −0.988489 0.151295i \(-0.951656\pi\)
0.988489 0.151295i \(-0.0483442\pi\)
\(758\) 0 0
\(759\) 1.12069e6 0.0706125
\(760\) 0 0
\(761\) 1.58376e7 0.991350 0.495675 0.868508i \(-0.334921\pi\)
0.495675 + 0.868508i \(0.334921\pi\)
\(762\) 0 0
\(763\) 644154.i 0.0400570i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 680958.i 0.0417957i
\(768\) 0 0
\(769\) −1.80265e7 −1.09925 −0.549624 0.835412i \(-0.685229\pi\)
−0.549624 + 0.835412i \(0.685229\pi\)
\(770\) 0 0
\(771\) 1.60775e7 0.974055
\(772\) 0 0
\(773\) 7.60103e6i 0.457534i 0.973481 + 0.228767i \(0.0734694\pi\)
−0.973481 + 0.228767i \(0.926531\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.48124e6i 0.385128i
\(778\) 0 0
\(779\) −2.69308e7 −1.59003
\(780\) 0 0
\(781\) 5.28488e6 0.310033
\(782\) 0 0
\(783\) 9.04917e6i 0.527478i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 3.13160e7i − 1.80231i −0.433498 0.901155i \(-0.642721\pi\)
0.433498 0.901155i \(-0.357279\pi\)
\(788\) 0 0
\(789\) 1.22364e7 0.699781
\(790\) 0 0
\(791\) 293852. 0.0166989
\(792\) 0 0
\(793\) − 61947.5i − 0.00349817i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.51589e6i 0.419117i 0.977796 + 0.209558i \(0.0672026\pi\)
−0.977796 + 0.209558i \(0.932797\pi\)
\(798\) 0 0
\(799\) −2.99402e6 −0.165916
\(800\) 0 0
\(801\) −2.77410e7 −1.52771
\(802\) 0 0
\(803\) 144293.i 0.00789691i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) − 2.46800e7i − 1.33402i
\(808\) 0 0
\(809\) −3.23042e7 −1.73535 −0.867676 0.497130i \(-0.834387\pi\)
−0.867676 + 0.497130i \(0.834387\pi\)
\(810\) 0 0
\(811\) 3.53053e7 1.88490 0.942448 0.334354i \(-0.108518\pi\)
0.942448 + 0.334354i \(0.108518\pi\)
\(812\) 0 0
\(813\) − 2.29851e6i − 0.121960i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 1.33336e7i − 0.698862i
\(818\) 0 0
\(819\) 254389. 0.0132522
\(820\) 0 0
\(821\) 1.06861e7 0.553299 0.276650 0.960971i \(-0.410776\pi\)
0.276650 + 0.960971i \(0.410776\pi\)
\(822\) 0 0
\(823\) 1.14692e7i 0.590246i 0.955459 + 0.295123i \(0.0953607\pi\)
−0.955459 + 0.295123i \(0.904639\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 3.29781e6i − 0.167673i −0.996480 0.0838363i \(-0.973283\pi\)
0.996480 0.0838363i \(-0.0267173\pi\)
\(828\) 0 0
\(829\) 7.63786e6 0.385998 0.192999 0.981199i \(-0.438179\pi\)
0.192999 + 0.981199i \(0.438179\pi\)
\(830\) 0 0
\(831\) 299749. 0.0150576
\(832\) 0 0
\(833\) − 978128.i − 0.0488408i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 1.78190e7i − 0.879162i
\(838\) 0 0
\(839\) −2.15181e6 −0.105536 −0.0527678 0.998607i \(-0.516804\pi\)
−0.0527678 + 0.998607i \(0.516804\pi\)
\(840\) 0 0
\(841\) −1.04967e7 −0.511755
\(842\) 0 0
\(843\) 9.55874e6i 0.463267i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 7.49252e6i − 0.358855i
\(848\) 0 0
\(849\) −3.04014e7 −1.44752
\(850\) 0 0
\(851\) −2.72656e6 −0.129060
\(852\) 0 0
\(853\) − 6.77711e6i − 0.318913i −0.987205 0.159456i \(-0.949026\pi\)
0.987205 0.159456i \(-0.0509741\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 2.76782e7i − 1.28732i −0.765313 0.643658i \(-0.777416\pi\)
0.765313 0.643658i \(-0.222584\pi\)
\(858\) 0 0
\(859\) −9.64843e6 −0.446143 −0.223071 0.974802i \(-0.571608\pi\)
−0.223071 + 0.974802i \(0.571608\pi\)
\(860\) 0 0
\(861\) 1.41495e7 0.650479
\(862\) 0 0
\(863\) 1.44710e7i 0.661413i 0.943734 + 0.330707i \(0.107287\pi\)
−0.943734 + 0.330707i \(0.892713\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 3.07779e7i − 1.39057i
\(868\) 0 0
\(869\) 7.13954e6 0.320716
\(870\) 0 0
\(871\) −706154. −0.0315395
\(872\) 0 0
\(873\) − 4.15566e6i − 0.184546i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 1.65012e7i − 0.724463i −0.932088 0.362231i \(-0.882015\pi\)
0.932088 0.362231i \(-0.117985\pi\)
\(878\) 0 0
\(879\) 3.36070e7 1.46709
\(880\) 0 0
\(881\) 2.14305e7 0.930236 0.465118 0.885249i \(-0.346012\pi\)
0.465118 + 0.885249i \(0.346012\pi\)
\(882\) 0 0
\(883\) − 2.06482e7i − 0.891213i −0.895229 0.445606i \(-0.852988\pi\)
0.895229 0.445606i \(-0.147012\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 2.33225e7i − 0.995326i −0.867370 0.497663i \(-0.834192\pi\)
0.867370 0.497663i \(-0.165808\pi\)
\(888\) 0 0
\(889\) 5.36715e6 0.227766
\(890\) 0 0
\(891\) −1.54920e6 −0.0653751
\(892\) 0 0
\(893\) − 1.68241e7i − 0.705999i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 179355.i 0.00744275i
\(898\) 0 0
\(899\) −1.97198e7 −0.813772
\(900\) 0 0
\(901\) 6.09919e6 0.250300
\(902\) 0 0
\(903\) 7.00549e6i 0.285903i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 3.53172e6i 0.142550i 0.997457 + 0.0712752i \(0.0227069\pi\)
−0.997457 + 0.0712752i \(0.977293\pi\)
\(908\) 0 0
\(909\) 6.16262e7 2.47375
\(910\) 0 0
\(911\) 4.09852e7 1.63618 0.818091 0.575089i \(-0.195033\pi\)
0.818091 + 0.575089i \(0.195033\pi\)
\(912\) 0 0
\(913\) 6.44932e6i 0.256057i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.88741e7i 0.741213i
\(918\) 0 0
\(919\) 4.53948e7 1.77304 0.886518 0.462693i \(-0.153117\pi\)
0.886518 + 0.462693i \(0.153117\pi\)
\(920\) 0 0
\(921\) 5.28389e7 2.05260
\(922\) 0 0
\(923\) 845793.i 0.0326783i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 6.55972e7i − 2.50718i
\(928\) 0 0
\(929\) 3.26640e7 1.24174 0.620869 0.783914i \(-0.286780\pi\)
0.620869 + 0.783914i \(0.286780\pi\)
\(930\) 0 0
\(931\) 5.49635e6 0.207826
\(932\) 0 0
\(933\) − 6.34082e7i − 2.38474i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1.27944e7i 0.476068i 0.971257 + 0.238034i \(0.0765030\pi\)
−0.971257 + 0.238034i \(0.923497\pi\)
\(938\) 0 0
\(939\) −7.54720e7 −2.79333
\(940\) 0 0
\(941\) 1.71929e7 0.632957 0.316479 0.948600i \(-0.397499\pi\)
0.316479 + 0.948600i \(0.397499\pi\)
\(942\) 0 0
\(943\) 5.95248e6i 0.217981i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 4.33455e7i − 1.57061i −0.619107 0.785307i \(-0.712505\pi\)
0.619107 0.785307i \(-0.287495\pi\)
\(948\) 0 0
\(949\) −23092.7 −0.000832356 0
\(950\) 0 0
\(951\) −2.57363e7 −0.922773
\(952\) 0 0
\(953\) 6.85588e6i 0.244529i 0.992498 + 0.122265i \(0.0390157\pi\)
−0.992498 + 0.122265i \(0.960984\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) − 7.00922e6i − 0.247394i
\(958\) 0 0
\(959\) 1.54750e7 0.543355
\(960\) 0 0
\(961\) 1.02016e7 0.356335
\(962\) 0 0
\(963\) 2.75723e7i 0.958092i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.81761e7i 0.625080i 0.949905 + 0.312540i \(0.101180\pi\)
−0.949905 + 0.312540i \(0.898820\pi\)
\(968\) 0 0
\(969\) −2.28909e7 −0.783166
\(970\) 0 0
\(971\) −2.09710e7 −0.713790 −0.356895 0.934144i \(-0.616165\pi\)
−0.356895 + 0.934144i \(0.616165\pi\)
\(972\) 0 0
\(973\) − 4.67624e6i − 0.158349i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.72323e7i 0.912742i 0.889790 + 0.456371i \(0.150851\pi\)
−0.889790 + 0.456371i \(0.849149\pi\)
\(978\) 0 0
\(979\) 6.96311e6 0.232192
\(980\) 0 0
\(981\) −4.72596e6 −0.156790
\(982\) 0 0
\(983\) 3.97759e7i 1.31291i 0.754363 + 0.656457i \(0.227946\pi\)
−0.754363 + 0.656457i \(0.772054\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 8.83944e6i 0.288823i
\(988\) 0 0
\(989\) −2.94710e6 −0.0958086
\(990\) 0 0
\(991\) −9.12673e6 −0.295210 −0.147605 0.989046i \(-0.547156\pi\)
−0.147605 + 0.989046i \(0.547156\pi\)
\(992\) 0 0
\(993\) − 5.56427e7i − 1.79075i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 1.68299e7i − 0.536221i −0.963388 0.268110i \(-0.913601\pi\)
0.963388 0.268110i \(-0.0863992\pi\)
\(998\) 0 0
\(999\) −1.54092e7 −0.488501
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 700.6.e.g.449.1 6
5.2 odd 4 700.6.a.i.1.1 3
5.3 odd 4 140.6.a.d.1.3 3
5.4 even 2 inner 700.6.e.g.449.6 6
20.3 even 4 560.6.a.t.1.1 3
35.13 even 4 980.6.a.h.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.6.a.d.1.3 3 5.3 odd 4
560.6.a.t.1.1 3 20.3 even 4
700.6.a.i.1.1 3 5.2 odd 4
700.6.e.g.449.1 6 1.1 even 1 trivial
700.6.e.g.449.6 6 5.4 even 2 inner
980.6.a.h.1.1 3 35.13 even 4