Properties

Label 882.3.s.e.863.1
Level $882$
Weight $3$
Character 882.863
Analytic conductor $24.033$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,3,Mod(557,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.557");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), 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: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12745506816.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.1
Root \(-1.00781 + 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.e.557.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} -2.82843i q^{8} +(4.29150 + 7.43310i) q^{10} +(10.5120 - 6.06910i) q^{11} -18.5830 q^{13} +(-2.00000 + 3.46410i) q^{16} +(9.44094 - 5.45073i) q^{17} +(-10.0000 + 17.3205i) q^{19} -12.1382i q^{20} -17.1660 q^{22} +(-10.5120 - 6.06910i) q^{23} +(5.91699 + 10.2485i) q^{25} +(22.7594 + 13.1402i) q^{26} -41.8367i q^{29} +(-12.5830 - 21.7944i) q^{31} +(4.89898 - 2.82843i) q^{32} -15.4170 q^{34} +(-19.0000 + 32.9090i) q^{37} +(24.4949 - 14.1421i) q^{38} +(-8.58301 + 14.8662i) q^{40} +60.6337i q^{41} +83.4980 q^{43} +(21.0240 + 12.1382i) q^{44} +(8.58301 + 14.8662i) q^{46} +(-14.6969 - 8.48528i) q^{47} -16.7358i q^{50} +(-18.5830 - 32.1867i) q^{52} +(-81.4431 + 47.0212i) q^{53} -73.6680 q^{55} +(-29.5830 + 51.2393i) q^{58} +(50.4179 - 29.1088i) q^{59} +(-7.83399 + 13.5689i) q^{61} +35.5901i q^{62} -8.00000 q^{64} +(97.6722 + 56.3911i) q^{65} +(66.3320 + 114.890i) q^{67} +(18.8819 + 10.9015i) q^{68} +12.1382i q^{71} +(38.4575 + 66.6104i) q^{73} +(46.5403 - 26.8701i) q^{74} -40.0000 q^{76} +(-16.8340 + 29.1573i) q^{79} +(21.0240 - 12.1382i) q^{80} +(42.8745 - 74.2608i) q^{82} +60.5764i q^{83} -66.1621 q^{85} +(-102.264 - 59.0420i) q^{86} +(-17.1660 - 29.7324i) q^{88} +(-4.13532 - 2.38753i) q^{89} -24.2764i q^{92} +(12.0000 + 20.7846i) q^{94} +(105.120 - 60.6910i) q^{95} -188.413 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 8 q^{10} - 64 q^{13} - 16 q^{16} - 80 q^{19} + 32 q^{22} + 132 q^{25} - 16 q^{31} - 208 q^{34} - 152 q^{37} + 16 q^{40} + 160 q^{43} - 16 q^{46} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} + 96 q^{73} - 320 q^{76} - 304 q^{79} + 216 q^{82} + 656 q^{85} + 32 q^{88} + 96 q^{94} - 576 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −5.25600 3.03455i −1.05120 0.606910i −0.128214 0.991746i \(-0.540925\pi\)
−0.922985 + 0.384836i \(0.874258\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 4.29150 + 7.43310i 0.429150 + 0.743310i
\(11\) 10.5120 6.06910i 0.955636 0.551736i 0.0608086 0.998149i \(-0.480632\pi\)
0.894827 + 0.446413i \(0.147299\pi\)
\(12\) 0 0
\(13\) −18.5830 −1.42946 −0.714731 0.699399i \(-0.753451\pi\)
−0.714731 + 0.699399i \(0.753451\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 9.44094 5.45073i 0.555350 0.320631i −0.195927 0.980618i \(-0.562772\pi\)
0.751277 + 0.659987i \(0.229438\pi\)
\(18\) 0 0
\(19\) −10.0000 + 17.3205i −0.526316 + 0.911606i 0.473214 + 0.880947i \(0.343094\pi\)
−0.999530 + 0.0306583i \(0.990240\pi\)
\(20\) 12.1382i 0.606910i
\(21\) 0 0
\(22\) −17.1660 −0.780273
\(23\) −10.5120 6.06910i −0.457043 0.263874i 0.253757 0.967268i \(-0.418334\pi\)
−0.710800 + 0.703394i \(0.751667\pi\)
\(24\) 0 0
\(25\) 5.91699 + 10.2485i 0.236680 + 0.409941i
\(26\) 22.7594 + 13.1402i 0.875363 + 0.505391i
\(27\) 0 0
\(28\) 0 0
\(29\) 41.8367i 1.44264i −0.692600 0.721322i \(-0.743535\pi\)
0.692600 0.721322i \(-0.256465\pi\)
\(30\) 0 0
\(31\) −12.5830 21.7944i −0.405903 0.703045i 0.588523 0.808481i \(-0.299710\pi\)
−0.994426 + 0.105435i \(0.966376\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −15.4170 −0.453441
\(35\) 0 0
\(36\) 0 0
\(37\) −19.0000 + 32.9090i −0.513514 + 0.889431i 0.486364 + 0.873757i \(0.338323\pi\)
−0.999877 + 0.0156750i \(0.995010\pi\)
\(38\) 24.4949 14.1421i 0.644603 0.372161i
\(39\) 0 0
\(40\) −8.58301 + 14.8662i −0.214575 + 0.371655i
\(41\) 60.6337i 1.47887i 0.673227 + 0.739435i \(0.264908\pi\)
−0.673227 + 0.739435i \(0.735092\pi\)
\(42\) 0 0
\(43\) 83.4980 1.94181 0.970907 0.239455i \(-0.0769689\pi\)
0.970907 + 0.239455i \(0.0769689\pi\)
\(44\) 21.0240 + 12.1382i 0.477818 + 0.275868i
\(45\) 0 0
\(46\) 8.58301 + 14.8662i 0.186587 + 0.323178i
\(47\) −14.6969 8.48528i −0.312701 0.180538i 0.335434 0.942064i \(-0.391117\pi\)
−0.648134 + 0.761526i \(0.724451\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 16.7358i 0.334716i
\(51\) 0 0
\(52\) −18.5830 32.1867i −0.357365 0.618975i
\(53\) −81.4431 + 47.0212i −1.53666 + 0.887193i −0.537632 + 0.843180i \(0.680681\pi\)
−0.999031 + 0.0440129i \(0.985986\pi\)
\(54\) 0 0
\(55\) −73.6680 −1.33942
\(56\) 0 0
\(57\) 0 0
\(58\) −29.5830 + 51.2393i −0.510052 + 0.883436i
\(59\) 50.4179 29.1088i 0.854540 0.493369i −0.00764008 0.999971i \(-0.502432\pi\)
0.862180 + 0.506602i \(0.169099\pi\)
\(60\) 0 0
\(61\) −7.83399 + 13.5689i −0.128426 + 0.222440i −0.923067 0.384639i \(-0.874326\pi\)
0.794641 + 0.607080i \(0.207659\pi\)
\(62\) 35.5901i 0.574034i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 97.6722 + 56.3911i 1.50265 + 0.867555i
\(66\) 0 0
\(67\) 66.3320 + 114.890i 0.990030 + 1.71478i 0.617000 + 0.786964i \(0.288348\pi\)
0.373031 + 0.927819i \(0.378319\pi\)
\(68\) 18.8819 + 10.9015i 0.277675 + 0.160316i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.1382i 0.170961i 0.996340 + 0.0854803i \(0.0272425\pi\)
−0.996340 + 0.0854803i \(0.972758\pi\)
\(72\) 0 0
\(73\) 38.4575 + 66.6104i 0.526815 + 0.912471i 0.999512 + 0.0312455i \(0.00994736\pi\)
−0.472696 + 0.881225i \(0.656719\pi\)
\(74\) 46.5403 26.8701i 0.628923 0.363109i
\(75\) 0 0
\(76\) −40.0000 −0.526316
\(77\) 0 0
\(78\) 0 0
\(79\) −16.8340 + 29.1573i −0.213088 + 0.369080i −0.952680 0.303976i \(-0.901686\pi\)
0.739591 + 0.673056i \(0.235019\pi\)
\(80\) 21.0240 12.1382i 0.262800 0.151728i
\(81\) 0 0
\(82\) 42.8745 74.2608i 0.522860 0.905620i
\(83\) 60.5764i 0.729836i 0.931040 + 0.364918i \(0.118903\pi\)
−0.931040 + 0.364918i \(0.881097\pi\)
\(84\) 0 0
\(85\) −66.1621 −0.778377
\(86\) −102.264 59.0420i −1.18911 0.686535i
\(87\) 0 0
\(88\) −17.1660 29.7324i −0.195068 0.337868i
\(89\) −4.13532 2.38753i −0.0464643 0.0268262i 0.476588 0.879127i \(-0.341873\pi\)
−0.523052 + 0.852301i \(0.675207\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 24.2764i 0.263874i
\(93\) 0 0
\(94\) 12.0000 + 20.7846i 0.127660 + 0.221113i
\(95\) 105.120 60.6910i 1.10653 0.638853i
\(96\) 0 0
\(97\) −188.413 −1.94240 −0.971201 0.238260i \(-0.923423\pi\)
−0.971201 + 0.238260i \(0.923423\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −11.8340 + 20.4971i −0.118340 + 0.204971i
\(101\) −92.4162 + 53.3565i −0.915012 + 0.528282i −0.882040 0.471174i \(-0.843830\pi\)
−0.0329716 + 0.999456i \(0.510497\pi\)
\(102\) 0 0
\(103\) −65.7490 + 113.881i −0.638340 + 1.10564i 0.347457 + 0.937696i \(0.387045\pi\)
−0.985797 + 0.167941i \(0.946288\pi\)
\(104\) 52.5607i 0.505391i
\(105\) 0 0
\(106\) 132.996 1.25468
\(107\) 71.3426 + 41.1897i 0.666753 + 0.384950i 0.794845 0.606812i \(-0.207552\pi\)
−0.128092 + 0.991762i \(0.540885\pi\)
\(108\) 0 0
\(109\) −16.9150 29.2977i −0.155184 0.268786i 0.777942 0.628336i \(-0.216264\pi\)
−0.933126 + 0.359550i \(0.882930\pi\)
\(110\) 90.2245 + 52.0911i 0.820223 + 0.473556i
\(111\) 0 0
\(112\) 0 0
\(113\) 28.5190i 0.252381i 0.992006 + 0.126190i \(0.0402750\pi\)
−0.992006 + 0.126190i \(0.959725\pi\)
\(114\) 0 0
\(115\) 36.8340 + 63.7983i 0.320296 + 0.554768i
\(116\) 72.4633 41.8367i 0.624683 0.360661i
\(117\) 0 0
\(118\) −82.3320 −0.697729
\(119\) 0 0
\(120\) 0 0
\(121\) 13.1680 22.8076i 0.108826 0.188493i
\(122\) 19.1893 11.0789i 0.157289 0.0908109i
\(123\) 0 0
\(124\) 25.1660 43.5888i 0.202952 0.351523i
\(125\) 79.9059i 0.639247i
\(126\) 0 0
\(127\) 129.668 1.02101 0.510504 0.859875i \(-0.329459\pi\)
0.510504 + 0.859875i \(0.329459\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −79.7490 138.129i −0.613454 1.06253i
\(131\) −128.187 74.0087i −0.978525 0.564952i −0.0767004 0.997054i \(-0.524438\pi\)
−0.901824 + 0.432103i \(0.857772\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 187.615i 1.40011i
\(135\) 0 0
\(136\) −15.4170 26.7030i −0.113360 0.196346i
\(137\) 66.6469 38.4786i 0.486474 0.280866i −0.236637 0.971598i \(-0.576045\pi\)
0.723111 + 0.690732i \(0.242712\pi\)
\(138\) 0 0
\(139\) 217.328 1.56351 0.781756 0.623585i \(-0.214324\pi\)
0.781756 + 0.623585i \(0.214324\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.58301 14.8662i 0.0604437 0.104692i
\(143\) −195.344 + 112.782i −1.36604 + 0.788686i
\(144\) 0 0
\(145\) −126.956 + 219.893i −0.875555 + 1.51651i
\(146\) 108.774i 0.745029i
\(147\) 0 0
\(148\) −76.0000 −0.513514
\(149\) 140.231 + 80.9623i 0.941147 + 0.543371i 0.890320 0.455336i \(-0.150481\pi\)
0.0508272 + 0.998707i \(0.483814\pi\)
\(150\) 0 0
\(151\) 46.5830 + 80.6841i 0.308497 + 0.534332i 0.978034 0.208447i \(-0.0668408\pi\)
−0.669537 + 0.742779i \(0.733507\pi\)
\(152\) 48.9898 + 28.2843i 0.322301 + 0.186081i
\(153\) 0 0
\(154\) 0 0
\(155\) 152.735i 0.985388i
\(156\) 0 0
\(157\) 92.4980 + 160.211i 0.589159 + 1.02045i 0.994343 + 0.106219i \(0.0338743\pi\)
−0.405183 + 0.914235i \(0.632792\pi\)
\(158\) 41.2347 23.8069i 0.260979 0.150676i
\(159\) 0 0
\(160\) −34.3320 −0.214575
\(161\) 0 0
\(162\) 0 0
\(163\) −43.4980 + 75.3408i −0.266859 + 0.462214i −0.968049 0.250761i \(-0.919319\pi\)
0.701190 + 0.712975i \(0.252652\pi\)
\(164\) −105.021 + 60.6337i −0.640370 + 0.369718i
\(165\) 0 0
\(166\) 42.8340 74.1906i 0.258036 0.446932i
\(167\) 60.5764i 0.362733i −0.983416 0.181366i \(-0.941948\pi\)
0.983416 0.181366i \(-0.0580520\pi\)
\(168\) 0 0
\(169\) 176.328 1.04336
\(170\) 81.0317 + 46.7837i 0.476657 + 0.275198i
\(171\) 0 0
\(172\) 83.4980 + 144.623i 0.485454 + 0.840830i
\(173\) 140.791 + 81.2858i 0.813822 + 0.469860i 0.848281 0.529546i \(-0.177638\pi\)
−0.0344594 + 0.999406i \(0.510971\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 48.5528i 0.275868i
\(177\) 0 0
\(178\) 3.37648 + 5.84823i 0.0189690 + 0.0328552i
\(179\) −193.202 + 111.545i −1.07934 + 0.623159i −0.930719 0.365735i \(-0.880818\pi\)
−0.148623 + 0.988894i \(0.547484\pi\)
\(180\) 0 0
\(181\) 188.915 1.04373 0.521865 0.853028i \(-0.325237\pi\)
0.521865 + 0.853028i \(0.325237\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −17.1660 + 29.7324i −0.0932935 + 0.161589i
\(185\) 199.728 115.313i 1.07961 0.623313i
\(186\) 0 0
\(187\) 66.1621 114.596i 0.353808 0.612813i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) −171.660 −0.903474
\(191\) −197.486 114.019i −1.03396 0.596957i −0.115844 0.993267i \(-0.536957\pi\)
−0.918117 + 0.396310i \(0.870291\pi\)
\(192\) 0 0
\(193\) −67.0000 116.047i −0.347150 0.601282i 0.638592 0.769546i \(-0.279517\pi\)
−0.985742 + 0.168264i \(0.946184\pi\)
\(194\) 230.758 + 133.228i 1.18947 + 0.686743i
\(195\) 0 0
\(196\) 0 0
\(197\) 188.560i 0.957157i 0.878045 + 0.478579i \(0.158848\pi\)
−0.878045 + 0.478579i \(0.841152\pi\)
\(198\) 0 0
\(199\) −51.2470 88.7625i −0.257523 0.446043i 0.708055 0.706157i \(-0.249573\pi\)
−0.965578 + 0.260115i \(0.916240\pi\)
\(200\) 28.9872 16.7358i 0.144936 0.0836789i
\(201\) 0 0
\(202\) 150.915 0.747104
\(203\) 0 0
\(204\) 0 0
\(205\) 183.996 318.691i 0.897542 1.55459i
\(206\) 161.052 92.9831i 0.781804 0.451375i
\(207\) 0 0
\(208\) 37.1660 64.3734i 0.178683 0.309488i
\(209\) 242.764i 1.16155i
\(210\) 0 0
\(211\) −84.5020 −0.400483 −0.200242 0.979747i \(-0.564173\pi\)
−0.200242 + 0.979747i \(0.564173\pi\)
\(212\) −162.886 94.0424i −0.768331 0.443596i
\(213\) 0 0
\(214\) −58.2510 100.894i −0.272201 0.471466i
\(215\) −438.865 253.379i −2.04123 1.17851i
\(216\) 0 0
\(217\) 0 0
\(218\) 47.8429i 0.219463i
\(219\) 0 0
\(220\) −73.6680 127.597i −0.334854 0.579985i
\(221\) −175.441 + 101.291i −0.793851 + 0.458330i
\(222\) 0 0
\(223\) −158.494 −0.710736 −0.355368 0.934727i \(-0.615644\pi\)
−0.355368 + 0.934727i \(0.615644\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 20.1660 34.9286i 0.0892301 0.154551i
\(227\) −88.1816 + 50.9117i −0.388465 + 0.224281i −0.681495 0.731823i \(-0.738670\pi\)
0.293030 + 0.956103i \(0.405337\pi\)
\(228\) 0 0
\(229\) 134.458 232.887i 0.587151 1.01697i −0.407453 0.913226i \(-0.633583\pi\)
0.994604 0.103749i \(-0.0330837\pi\)
\(230\) 104.182i 0.452966i
\(231\) 0 0
\(232\) −118.332 −0.510052
\(233\) −22.7546 13.1374i −0.0976593 0.0563836i 0.450375 0.892840i \(-0.351290\pi\)
−0.548034 + 0.836456i \(0.684624\pi\)
\(234\) 0 0
\(235\) 51.4980 + 89.1972i 0.219141 + 0.379563i
\(236\) 100.836 + 58.2175i 0.427270 + 0.246684i
\(237\) 0 0
\(238\) 0 0
\(239\) 92.2733i 0.386081i −0.981191 0.193040i \(-0.938165\pi\)
0.981191 0.193040i \(-0.0618348\pi\)
\(240\) 0 0
\(241\) −171.624 297.261i −0.712131 1.23345i −0.964056 0.265700i \(-0.914397\pi\)
0.251925 0.967747i \(-0.418936\pi\)
\(242\) −32.2548 + 18.6223i −0.133284 + 0.0769518i
\(243\) 0 0
\(244\) −31.3360 −0.128426
\(245\) 0 0
\(246\) 0 0
\(247\) 185.830 321.867i 0.752348 1.30311i
\(248\) −61.6439 + 35.5901i −0.248564 + 0.143509i
\(249\) 0 0
\(250\) 56.5020 97.8643i 0.226008 0.391457i
\(251\) 356.382i 1.41985i −0.704278 0.709924i \(-0.748729\pi\)
0.704278 0.709924i \(-0.251271\pi\)
\(252\) 0 0
\(253\) −147.336 −0.582356
\(254\) −158.810 91.6891i −0.625237 0.360981i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −220.603 127.365i −0.858377 0.495584i 0.00509129 0.999987i \(-0.498379\pi\)
−0.863469 + 0.504403i \(0.831713\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 225.564i 0.867555i
\(261\) 0 0
\(262\) 104.664 + 181.283i 0.399481 + 0.691922i
\(263\) −226.880 + 130.989i −0.862663 + 0.498059i −0.864903 0.501939i \(-0.832620\pi\)
0.00224015 + 0.999997i \(0.499287\pi\)
\(264\) 0 0
\(265\) 570.753 2.15378
\(266\) 0 0
\(267\) 0 0
\(268\) −132.664 + 229.781i −0.495015 + 0.857391i
\(269\) −81.0813 + 46.8123i −0.301417 + 0.174023i −0.643079 0.765799i \(-0.722344\pi\)
0.341662 + 0.939823i \(0.389010\pi\)
\(270\) 0 0
\(271\) −0.583005 + 1.00979i −0.00215131 + 0.00372618i −0.867099 0.498136i \(-0.834018\pi\)
0.864948 + 0.501862i \(0.167351\pi\)
\(272\) 43.6058i 0.160316i
\(273\) 0 0
\(274\) −108.834 −0.397204
\(275\) 124.399 + 71.8217i 0.452359 + 0.261170i
\(276\) 0 0
\(277\) −16.0000 27.7128i −0.0577617 0.100046i 0.835699 0.549188i \(-0.185063\pi\)
−0.893460 + 0.449142i \(0.851730\pi\)
\(278\) −266.171 153.674i −0.957451 0.552785i
\(279\) 0 0
\(280\) 0 0
\(281\) 166.757i 0.593441i −0.954964 0.296721i \(-0.904107\pi\)
0.954964 0.296721i \(-0.0958930\pi\)
\(282\) 0 0
\(283\) −8.16995 14.1508i −0.0288691 0.0500027i 0.851230 0.524793i \(-0.175857\pi\)
−0.880099 + 0.474790i \(0.842524\pi\)
\(284\) −21.0240 + 12.1382i −0.0740281 + 0.0427401i
\(285\) 0 0
\(286\) 318.996 1.11537
\(287\) 0 0
\(288\) 0 0
\(289\) −85.0791 + 147.361i −0.294391 + 0.509901i
\(290\) 310.976 179.542i 1.07233 0.619111i
\(291\) 0 0
\(292\) −76.9150 + 133.221i −0.263408 + 0.456235i
\(293\) 368.921i 1.25912i −0.776953 0.629558i \(-0.783236\pi\)
0.776953 0.629558i \(-0.216764\pi\)
\(294\) 0 0
\(295\) −353.328 −1.19772
\(296\) 93.0806 + 53.7401i 0.314462 + 0.181554i
\(297\) 0 0
\(298\) −114.498 198.316i −0.384222 0.665491i
\(299\) 195.344 + 112.782i 0.653326 + 0.377198i
\(300\) 0 0
\(301\) 0 0
\(302\) 131.757i 0.436280i
\(303\) 0 0
\(304\) −40.0000 69.2820i −0.131579 0.227901i
\(305\) 82.3508 47.5453i 0.270003 0.155886i
\(306\) 0 0
\(307\) −192.664 −0.627570 −0.313785 0.949494i \(-0.601597\pi\)
−0.313785 + 0.949494i \(0.601597\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 108.000 187.061i 0.348387 0.603424i
\(311\) −113.688 + 65.6380i −0.365557 + 0.211055i −0.671516 0.740990i \(-0.734356\pi\)
0.305959 + 0.952045i \(0.401023\pi\)
\(312\) 0 0
\(313\) −21.6640 + 37.5232i −0.0692142 + 0.119882i −0.898556 0.438860i \(-0.855383\pi\)
0.829341 + 0.558742i \(0.188716\pi\)
\(314\) 261.624i 0.833197i
\(315\) 0 0
\(316\) −67.3360 −0.213088
\(317\) −218.000 125.862i −0.687696 0.397042i 0.115052 0.993359i \(-0.463297\pi\)
−0.802748 + 0.596318i \(0.796630\pi\)
\(318\) 0 0
\(319\) −253.911 439.787i −0.795960 1.37864i
\(320\) 42.0480 + 24.2764i 0.131400 + 0.0758638i
\(321\) 0 0
\(322\) 0 0
\(323\) 218.029i 0.675013i
\(324\) 0 0
\(325\) −109.956 190.449i −0.338325 0.585996i
\(326\) 106.548 61.5155i 0.326834 0.188698i
\(327\) 0 0
\(328\) 171.498 0.522860
\(329\) 0 0
\(330\) 0 0
\(331\) −180.745 + 313.060i −0.546058 + 0.945800i 0.452482 + 0.891774i \(0.350539\pi\)
−0.998540 + 0.0540260i \(0.982795\pi\)
\(332\) −104.921 + 60.5764i −0.316028 + 0.182459i
\(333\) 0 0
\(334\) −42.8340 + 74.1906i −0.128245 + 0.222128i
\(335\) 805.151i 2.40344i
\(336\) 0 0
\(337\) −298.834 −0.886748 −0.443374 0.896337i \(-0.646219\pi\)
−0.443374 + 0.896337i \(0.646219\pi\)
\(338\) −215.957 124.683i −0.638926 0.368884i
\(339\) 0 0
\(340\) −66.1621 114.596i −0.194594 0.337047i
\(341\) −264.545 152.735i −0.775791 0.447903i
\(342\) 0 0
\(343\) 0 0
\(344\) 236.168i 0.686535i
\(345\) 0 0
\(346\) −114.956 199.109i −0.332241 0.575459i
\(347\) −178.505 + 103.060i −0.514425 + 0.297003i −0.734651 0.678446i \(-0.762654\pi\)
0.220226 + 0.975449i \(0.429321\pi\)
\(348\) 0 0
\(349\) 434.324 1.24448 0.622241 0.782826i \(-0.286222\pi\)
0.622241 + 0.782826i \(0.286222\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 34.3320 59.4648i 0.0975342 0.168934i
\(353\) 160.595 92.7197i 0.454944 0.262662i −0.254972 0.966948i \(-0.582066\pi\)
0.709916 + 0.704286i \(0.248733\pi\)
\(354\) 0 0
\(355\) 36.8340 63.7983i 0.103758 0.179714i
\(356\) 9.55012i 0.0268262i
\(357\) 0 0
\(358\) 315.498 0.881279
\(359\) −447.533 258.383i −1.24661 0.719731i −0.276178 0.961106i \(-0.589068\pi\)
−0.970432 + 0.241376i \(0.922401\pi\)
\(360\) 0 0
\(361\) −19.5000 33.7750i −0.0540166 0.0935595i
\(362\) −231.373 133.583i −0.639151 0.369014i
\(363\) 0 0
\(364\) 0 0
\(365\) 466.805i 1.27892i
\(366\) 0 0
\(367\) 58.7451 + 101.749i 0.160068 + 0.277246i 0.934893 0.354930i \(-0.115495\pi\)
−0.774825 + 0.632176i \(0.782162\pi\)
\(368\) 42.0480 24.2764i 0.114261 0.0659685i
\(369\) 0 0
\(370\) −326.154 −0.881498
\(371\) 0 0
\(372\) 0 0
\(373\) 201.332 348.717i 0.539764 0.934899i −0.459152 0.888358i \(-0.651847\pi\)
0.998916 0.0465413i \(-0.0148199\pi\)
\(374\) −162.063 + 93.5673i −0.433324 + 0.250180i
\(375\) 0 0
\(376\) −24.0000 + 41.5692i −0.0638298 + 0.110556i
\(377\) 777.451i 2.06221i
\(378\) 0 0
\(379\) 398.834 1.05233 0.526166 0.850382i \(-0.323629\pi\)
0.526166 + 0.850382i \(0.323629\pi\)
\(380\) 210.240 + 121.382i 0.553263 + 0.319426i
\(381\) 0 0
\(382\) 161.247 + 279.288i 0.422113 + 0.731121i
\(383\) 645.019 + 372.402i 1.68412 + 0.972329i 0.958869 + 0.283849i \(0.0916114\pi\)
0.725255 + 0.688481i \(0.241722\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 189.505i 0.490945i
\(387\) 0 0
\(388\) −188.413 326.341i −0.485601 0.841085i
\(389\) 463.464 267.581i 1.19142 0.687869i 0.232795 0.972526i \(-0.425213\pi\)
0.958630 + 0.284656i \(0.0918795\pi\)
\(390\) 0 0
\(391\) −132.324 −0.338425
\(392\) 0 0
\(393\) 0 0
\(394\) 133.332 230.938i 0.338406 0.586137i
\(395\) 176.959 102.167i 0.447997 0.258651i
\(396\) 0 0
\(397\) 47.1621 81.6871i 0.118796 0.205761i −0.800495 0.599340i \(-0.795430\pi\)
0.919291 + 0.393579i \(0.128763\pi\)
\(398\) 144.949i 0.364192i
\(399\) 0 0
\(400\) −47.3360 −0.118340
\(401\) −89.7138 51.7963i −0.223725 0.129168i 0.383949 0.923354i \(-0.374564\pi\)
−0.607674 + 0.794187i \(0.707897\pi\)
\(402\) 0 0
\(403\) 233.830 + 405.006i 0.580223 + 1.00498i
\(404\) −184.832 106.713i −0.457506 0.264141i
\(405\) 0 0
\(406\) 0 0
\(407\) 461.252i 1.13330i
\(408\) 0 0
\(409\) 4.87844 + 8.44971i 0.0119277 + 0.0206594i 0.871928 0.489635i \(-0.162870\pi\)
−0.860000 + 0.510294i \(0.829537\pi\)
\(410\) −450.696 + 260.210i −1.09926 + 0.634658i
\(411\) 0 0
\(412\) −262.996 −0.638340
\(413\) 0 0
\(414\) 0 0
\(415\) 183.822 318.389i 0.442945 0.767203i
\(416\) −91.0378 + 52.5607i −0.218841 + 0.126348i
\(417\) 0 0
\(418\) 171.660 297.324i 0.410670 0.711301i
\(419\) 339.411i 0.810051i −0.914305 0.405025i \(-0.867263\pi\)
0.914305 0.405025i \(-0.132737\pi\)
\(420\) 0 0
\(421\) −599.320 −1.42356 −0.711782 0.702401i \(-0.752111\pi\)
−0.711782 + 0.702401i \(0.752111\pi\)
\(422\) 103.493 + 59.7519i 0.245245 + 0.141592i
\(423\) 0 0
\(424\) 132.996 + 230.356i 0.313670 + 0.543292i
\(425\) 111.724 + 64.5039i 0.262880 + 0.151774i
\(426\) 0 0
\(427\) 0 0
\(428\) 164.759i 0.384950i
\(429\) 0 0
\(430\) 358.332 + 620.649i 0.833330 + 1.44337i
\(431\) −615.725 + 355.489i −1.42860 + 0.824800i −0.997010 0.0772717i \(-0.975379\pi\)
−0.431586 + 0.902072i \(0.642046\pi\)
\(432\) 0 0
\(433\) 377.984 0.872943 0.436471 0.899718i \(-0.356228\pi\)
0.436471 + 0.899718i \(0.356228\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 33.8301 58.5954i 0.0775919 0.134393i
\(437\) 210.240 121.382i 0.481098 0.277762i
\(438\) 0 0
\(439\) −264.073 + 457.388i −0.601533 + 1.04189i 0.391056 + 0.920367i \(0.372110\pi\)
−0.992589 + 0.121519i \(0.961223\pi\)
\(440\) 208.365i 0.473556i
\(441\) 0 0
\(442\) 286.494 0.648177
\(443\) 31.7345 + 18.3219i 0.0716354 + 0.0413587i 0.535390 0.844605i \(-0.320165\pi\)
−0.463754 + 0.885964i \(0.653498\pi\)
\(444\) 0 0
\(445\) 14.4902 + 25.0977i 0.0325622 + 0.0563993i
\(446\) 194.115 + 112.072i 0.435235 + 0.251283i
\(447\) 0 0
\(448\) 0 0
\(449\) 397.612i 0.885550i 0.896633 + 0.442775i \(0.146006\pi\)
−0.896633 + 0.442775i \(0.853994\pi\)
\(450\) 0 0
\(451\) 367.992 + 637.381i 0.815947 + 1.41326i
\(452\) −49.3964 + 28.5190i −0.109284 + 0.0630952i
\(453\) 0 0
\(454\) 144.000 0.317181
\(455\) 0 0
\(456\) 0 0
\(457\) −172.162 + 298.193i −0.376722 + 0.652502i −0.990583 0.136912i \(-0.956282\pi\)
0.613861 + 0.789414i \(0.289616\pi\)
\(458\) −329.352 + 190.152i −0.719110 + 0.415178i
\(459\) 0 0
\(460\) −73.6680 + 127.597i −0.160148 + 0.277384i
\(461\) 370.936i 0.804634i 0.915500 + 0.402317i \(0.131795\pi\)
−0.915500 + 0.402317i \(0.868205\pi\)
\(462\) 0 0
\(463\) 78.3320 0.169184 0.0845918 0.996416i \(-0.473041\pi\)
0.0845918 + 0.996416i \(0.473041\pi\)
\(464\) 144.927 + 83.6734i 0.312342 + 0.180331i
\(465\) 0 0
\(466\) 18.5791 + 32.1799i 0.0398692 + 0.0690556i
\(467\) −346.201 199.879i −0.741330 0.428007i 0.0812229 0.996696i \(-0.474117\pi\)
−0.822553 + 0.568689i \(0.807451\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 145.658i 0.309912i
\(471\) 0 0
\(472\) −82.3320 142.603i −0.174432 0.302126i
\(473\) 877.731 506.758i 1.85567 1.07137i
\(474\) 0 0
\(475\) −236.680 −0.498273
\(476\) 0 0
\(477\) 0 0
\(478\) −65.2470 + 113.011i −0.136500 + 0.236425i
\(479\) 609.100 351.664i 1.27161 0.734163i 0.296317 0.955090i \(-0.404241\pi\)
0.975290 + 0.220927i \(0.0709081\pi\)
\(480\) 0 0
\(481\) 353.077 611.547i 0.734048 1.27141i
\(482\) 485.425i 1.00711i
\(483\) 0 0
\(484\) 52.6719 0.108826
\(485\) 990.298 + 571.749i 2.04185 + 1.17886i
\(486\) 0 0
\(487\) 41.2549 + 71.4556i 0.0847124 + 0.146726i 0.905269 0.424840i \(-0.139670\pi\)
−0.820556 + 0.571566i \(0.806336\pi\)
\(488\) 38.3786 + 22.1579i 0.0786446 + 0.0454055i
\(489\) 0 0
\(490\) 0 0
\(491\) 184.203i 0.375158i 0.982249 + 0.187579i \(0.0600641\pi\)
−0.982249 + 0.187579i \(0.939936\pi\)
\(492\) 0 0
\(493\) −228.041 394.978i −0.462557 0.801172i
\(494\) −455.189 + 262.803i −0.921435 + 0.531991i
\(495\) 0 0
\(496\) 100.664 0.202952
\(497\) 0 0
\(498\) 0 0
\(499\) −376.405 + 651.953i −0.754319 + 1.30652i 0.191393 + 0.981513i \(0.438699\pi\)
−0.945712 + 0.325005i \(0.894634\pi\)
\(500\) −138.401 + 79.9059i −0.276802 + 0.159812i
\(501\) 0 0
\(502\) −252.000 + 436.477i −0.501992 + 0.869476i
\(503\) 662.540i 1.31718i 0.752504 + 0.658588i \(0.228846\pi\)
−0.752504 + 0.658588i \(0.771154\pi\)
\(504\) 0 0
\(505\) 647.652 1.28248
\(506\) 180.449 + 104.182i 0.356618 + 0.205894i
\(507\) 0 0
\(508\) 129.668 + 224.592i 0.255252 + 0.442109i
\(509\) 821.958 + 474.557i 1.61485 + 0.932333i 0.988225 + 0.153010i \(0.0488968\pi\)
0.626623 + 0.779322i \(0.284437\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 180.122 + 311.980i 0.350431 + 0.606964i
\(515\) 691.153 399.037i 1.34204 0.774830i
\(516\) 0 0
\(517\) −205.992 −0.398437
\(518\) 0 0
\(519\) 0 0
\(520\) 159.498 276.259i 0.306727 0.531267i
\(521\) −618.640 + 357.172i −1.18741 + 0.685551i −0.957717 0.287712i \(-0.907105\pi\)
−0.229692 + 0.973263i \(0.573772\pi\)
\(522\) 0 0
\(523\) 116.000 200.918i 0.221797 0.384164i −0.733556 0.679629i \(-0.762141\pi\)
0.955354 + 0.295464i \(0.0954743\pi\)
\(524\) 296.035i 0.564952i
\(525\) 0 0
\(526\) 370.494 0.704361
\(527\) −237.591 137.173i −0.450837 0.260291i
\(528\) 0 0
\(529\) −190.832 330.531i −0.360741 0.624822i
\(530\) −699.027 403.583i −1.31892 0.761478i
\(531\) 0 0
\(532\) 0 0
\(533\) 1126.76i 2.11399i
\(534\) 0 0
\(535\) −249.984 432.985i −0.467260 0.809319i
\(536\) 324.959 187.615i 0.606267 0.350029i
\(537\) 0 0
\(538\) 132.405 0.246106
\(539\) 0 0
\(540\) 0 0
\(541\) −82.8340 + 143.473i −0.153113 + 0.265199i −0.932370 0.361505i \(-0.882263\pi\)
0.779257 + 0.626704i \(0.215596\pi\)
\(542\) 1.42807 0.824494i 0.00263481 0.00152121i
\(543\) 0 0
\(544\) 30.8340 53.4060i 0.0566801 0.0981729i
\(545\) 205.318i 0.376730i
\(546\) 0 0
\(547\) 295.676 0.540541 0.270270 0.962784i \(-0.412887\pi\)
0.270270 + 0.962784i \(0.412887\pi\)
\(548\) 133.294 + 76.9573i 0.243237 + 0.140433i
\(549\) 0 0
\(550\) −101.571 175.926i −0.184675 0.319866i
\(551\) 724.633 + 418.367i 1.31512 + 0.759287i
\(552\) 0 0
\(553\) 0 0
\(554\) 45.2548i 0.0816874i
\(555\) 0 0
\(556\) 217.328 + 376.423i 0.390878 + 0.677020i
\(557\) −66.5477 + 38.4213i −0.119475 + 0.0689790i −0.558547 0.829473i \(-0.688641\pi\)
0.439071 + 0.898452i \(0.355307\pi\)
\(558\) 0 0
\(559\) −1551.64 −2.77575
\(560\) 0 0
\(561\) 0 0
\(562\) −117.915 + 204.235i −0.209813 + 0.363407i
\(563\) −880.170 + 508.167i −1.56336 + 0.902605i −0.566444 + 0.824100i \(0.691681\pi\)
−0.996914 + 0.0785049i \(0.974985\pi\)
\(564\) 0 0
\(565\) 86.5425 149.896i 0.153173 0.265303i
\(566\) 23.1081i 0.0408270i
\(567\) 0 0
\(568\) 34.3320 0.0604437
\(569\) −507.952 293.266i −0.892710 0.515406i −0.0178822 0.999840i \(-0.505692\pi\)
−0.874828 + 0.484434i \(0.839026\pi\)
\(570\) 0 0
\(571\) −475.822 824.148i −0.833314 1.44334i −0.895396 0.445271i \(-0.853107\pi\)
0.0620822 0.998071i \(-0.480226\pi\)
\(572\) −390.689 225.564i −0.683022 0.394343i
\(573\) 0 0
\(574\) 0 0
\(575\) 143.643i 0.249815i
\(576\) 0 0
\(577\) 74.3360 + 128.754i 0.128832 + 0.223143i 0.923224 0.384262i \(-0.125544\pi\)
−0.794392 + 0.607405i \(0.792211\pi\)
\(578\) 208.400 120.320i 0.360554 0.208166i
\(579\) 0 0
\(580\) −507.822 −0.875555
\(581\) 0 0
\(582\) 0 0
\(583\) −570.753 + 988.573i −0.978993 + 1.69567i
\(584\) 188.403 108.774i 0.322607 0.186257i
\(585\) 0 0
\(586\) −260.867 + 451.834i −0.445165 + 0.771048i
\(587\) 332.564i 0.566548i −0.959039 0.283274i \(-0.908579\pi\)
0.959039 0.283274i \(-0.0914206\pi\)
\(588\) 0 0
\(589\) 503.320 0.854533
\(590\) 432.737 + 249.841i 0.733452 + 0.423459i
\(591\) 0 0
\(592\) −76.0000 131.636i −0.128378 0.222358i
\(593\) 188.145 + 108.625i 0.317276 + 0.183180i 0.650178 0.759782i \(-0.274694\pi\)
−0.332902 + 0.942962i \(0.608028\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 323.849i 0.543371i
\(597\) 0 0
\(598\) −159.498 276.259i −0.266719 0.461971i
\(599\) 149.111 86.0896i 0.248934 0.143722i −0.370342 0.928895i \(-0.620760\pi\)
0.619276 + 0.785173i \(0.287426\pi\)
\(600\) 0 0
\(601\) −418.000 −0.695507 −0.347754 0.937586i \(-0.613055\pi\)
−0.347754 + 0.937586i \(0.613055\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −93.1660 + 161.368i −0.154248 + 0.267166i
\(605\) −138.422 + 79.9178i −0.228796 + 0.132096i
\(606\) 0 0
\(607\) −313.579 + 543.135i −0.516605 + 0.894786i 0.483209 + 0.875505i \(0.339471\pi\)
−0.999814 + 0.0192808i \(0.993862\pi\)
\(608\) 113.137i 0.186081i
\(609\) 0 0
\(610\) −134.478 −0.220456
\(611\) 273.113 + 157.682i 0.446994 + 0.258072i
\(612\) 0 0
\(613\) 139.664 + 241.905i 0.227837 + 0.394625i 0.957167 0.289537i \(-0.0935014\pi\)
−0.729330 + 0.684162i \(0.760168\pi\)
\(614\) 235.964 + 136.234i 0.384307 + 0.221880i
\(615\) 0 0
\(616\) 0 0
\(617\) 358.380i 0.580843i −0.956899 0.290422i \(-0.906204\pi\)
0.956899 0.290422i \(-0.0937955\pi\)
\(618\) 0 0
\(619\) 491.822 + 851.861i 0.794543 + 1.37619i 0.923129 + 0.384491i \(0.125623\pi\)
−0.128586 + 0.991698i \(0.541044\pi\)
\(620\) −264.545 + 152.735i −0.426685 + 0.246347i
\(621\) 0 0
\(622\) 185.652 0.298476
\(623\) 0 0
\(624\) 0 0
\(625\) 390.403 676.198i 0.624645 1.08192i
\(626\) 53.0658 30.6376i 0.0847697 0.0489418i
\(627\) 0 0
\(628\) −184.996 + 320.423i −0.294580 + 0.510227i
\(629\) 414.256i 0.658594i
\(630\) 0 0
\(631\) −298.996 −0.473845 −0.236922 0.971529i \(-0.576139\pi\)
−0.236922 + 0.971529i \(0.576139\pi\)
\(632\) 82.4694 + 47.6137i 0.130490 + 0.0753382i
\(633\) 0 0
\(634\) 177.996 + 308.298i 0.280751 + 0.486275i
\(635\) −681.534 393.484i −1.07328 0.619660i
\(636\) 0 0
\(637\) 0 0
\(638\) 718.169i 1.12566i
\(639\) 0 0
\(640\) −34.3320 59.4648i −0.0536438 0.0929138i
\(641\) 270.163 155.979i 0.421471 0.243336i −0.274236 0.961663i \(-0.588425\pi\)
0.695706 + 0.718326i \(0.255091\pi\)
\(642\) 0 0
\(643\) −604.000 −0.939347 −0.469673 0.882840i \(-0.655628\pi\)
−0.469673 + 0.882840i \(0.655628\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 154.170 267.030i 0.238653 0.413359i
\(647\) −155.538 + 89.7998i −0.240398 + 0.138794i −0.615360 0.788246i \(-0.710989\pi\)
0.374961 + 0.927040i \(0.377656\pi\)
\(648\) 0 0
\(649\) 353.328 611.982i 0.544419 0.942962i
\(650\) 311.001i 0.478463i
\(651\) 0 0
\(652\) −173.992 −0.266859
\(653\) 417.331 + 240.946i 0.639097 + 0.368983i 0.784267 0.620424i \(-0.213039\pi\)
−0.145169 + 0.989407i \(0.546373\pi\)
\(654\) 0 0
\(655\) 449.166 + 777.978i 0.685750 + 1.18775i
\(656\) −210.041 121.267i −0.320185 0.184859i
\(657\) 0 0
\(658\) 0 0
\(659\) 877.408i 1.33142i −0.746209 0.665711i \(-0.768128\pi\)
0.746209 0.665711i \(-0.231872\pi\)
\(660\) 0 0
\(661\) 260.822 + 451.757i 0.394587 + 0.683445i 0.993048 0.117707i \(-0.0375543\pi\)
−0.598461 + 0.801152i \(0.704221\pi\)
\(662\) 442.733 255.612i 0.668781 0.386121i
\(663\) 0 0
\(664\) 171.336 0.258036
\(665\) 0 0
\(666\) 0 0
\(667\) −253.911 + 439.787i −0.380676 + 0.659351i
\(668\) 104.921 60.5764i 0.157068 0.0906832i
\(669\) 0 0
\(670\) −569.328 + 986.105i −0.849743 + 1.47180i
\(671\) 190.181i 0.283429i
\(672\) 0 0
\(673\) −659.992 −0.980672 −0.490336 0.871534i \(-0.663126\pi\)
−0.490336 + 0.871534i \(0.663126\pi\)
\(674\) 365.995 + 211.308i 0.543020 + 0.313513i
\(675\) 0 0
\(676\) 176.328 + 305.409i 0.260840 + 0.451789i
\(677\) 880.121 + 508.138i 1.30003 + 0.750573i 0.980409 0.196972i \(-0.0631108\pi\)
0.319622 + 0.947545i \(0.396444\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 187.135i 0.275198i
\(681\) 0 0
\(682\) 216.000 + 374.123i 0.316716 + 0.548567i
\(683\) 203.615 117.557i 0.298119 0.172119i −0.343479 0.939160i \(-0.611605\pi\)
0.641597 + 0.767042i \(0.278272\pi\)
\(684\) 0 0
\(685\) −467.061 −0.681841
\(686\) 0 0
\(687\) 0 0
\(688\) −166.996 + 289.246i −0.242727 + 0.420415i
\(689\) 1513.46 873.795i 2.19660 1.26821i
\(690\) 0 0
\(691\) 25.4902 44.1502i 0.0368888 0.0638933i −0.846992 0.531606i \(-0.821589\pi\)
0.883880 + 0.467713i \(0.154922\pi\)
\(692\) 325.143i 0.469860i
\(693\) 0 0
\(694\) 291.498 0.420026
\(695\) −1142.28 659.493i −1.64356 0.948911i
\(696\) 0 0
\(697\) 330.498 + 572.439i 0.474172 + 0.821290i
\(698\) −531.936 307.114i −0.762086 0.439991i
\(699\) 0 0
\(700\) 0 0
\(701\) 141.530i 0.201898i −0.994892 0.100949i \(-0.967812\pi\)
0.994892 0.100949i \(-0.0321879\pi\)
\(702\) 0 0
\(703\) −380.000 658.179i −0.540541 0.936244i
\(704\) −84.0959 + 48.5528i −0.119454 + 0.0689671i
\(705\) 0 0
\(706\) −262.251 −0.371460
\(707\) 0 0
\(708\) 0 0
\(709\) 27.7490 48.0627i 0.0391382 0.0677894i −0.845793 0.533512i \(-0.820872\pi\)
0.884931 + 0.465722i \(0.154205\pi\)
\(710\) −90.2245 + 52.0911i −0.127077 + 0.0733678i
\(711\) 0 0
\(712\) −6.75295 + 11.6965i −0.00948448 + 0.0164276i
\(713\) 305.470i 0.428429i
\(714\) 0 0
\(715\) 1368.97 1.91465
\(716\) −386.405 223.091i −0.539671 0.311579i
\(717\) 0 0
\(718\) 365.409 + 632.907i 0.508926 + 0.881486i
\(719\) −873.843 504.514i −1.21536 0.701688i −0.251438 0.967874i \(-0.580903\pi\)
−0.963922 + 0.266185i \(0.914237\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 55.1543i 0.0763910i
\(723\) 0 0
\(724\) 188.915 + 327.210i 0.260932 + 0.451948i
\(725\) 428.765 247.547i 0.591400 0.341445i
\(726\) 0 0
\(727\) −365.182 −0.502313 −0.251157 0.967946i \(-0.580811\pi\)
−0.251157 + 0.967946i \(0.580811\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −330.081 + 571.717i −0.452166 + 0.783174i
\(731\) 788.300 455.125i 1.07839 0.622606i
\(732\) 0 0
\(733\) 176.539 305.774i 0.240844 0.417154i −0.720111 0.693859i \(-0.755909\pi\)
0.960955 + 0.276705i \(0.0892425\pi\)
\(734\) 166.156i 0.226371i
\(735\) 0 0
\(736\) −68.6640 −0.0932935
\(737\) 1394.56 + 805.151i 1.89222 + 1.09247i
\(738\) 0 0
\(739\) −164.842 285.514i −0.223061 0.386352i 0.732675 0.680579i \(-0.238271\pi\)
−0.955736 + 0.294226i \(0.904938\pi\)
\(740\) 399.456 + 230.626i 0.539805 + 0.311657i
\(741\) 0 0
\(742\) 0 0
\(743\) 112.061i 0.150822i 0.997153 + 0.0754112i \(0.0240270\pi\)
−0.997153 + 0.0754112i \(0.975973\pi\)
\(744\) 0 0
\(745\) −491.369 851.075i −0.659555 1.14238i
\(746\) −493.161 + 284.726i −0.661073 + 0.381671i
\(747\) 0 0
\(748\) 264.648 0.353808
\(749\) 0 0
\(750\) 0 0
\(751\) 72.4131 125.423i 0.0964222 0.167008i −0.813779 0.581174i \(-0.802593\pi\)
0.910201 + 0.414166i \(0.135927\pi\)
\(752\) 58.7878 33.9411i 0.0781752 0.0451345i
\(753\) 0 0
\(754\) 549.741 952.180i 0.729100 1.26284i
\(755\) 565.434i 0.748919i
\(756\) 0 0
\(757\) 78.1699 0.103263 0.0516314 0.998666i \(-0.483558\pi\)
0.0516314 + 0.998666i \(0.483558\pi\)
\(758\) −488.470 282.018i −0.644419 0.372056i
\(759\) 0 0
\(760\) −171.660 297.324i −0.225869 0.391216i
\(761\) 1269.16 + 732.752i 1.66776 + 0.962880i 0.968843 + 0.247676i \(0.0796667\pi\)
0.698915 + 0.715205i \(0.253667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 456.076i 0.596957i
\(765\) 0 0
\(766\) −526.656 912.195i −0.687541 1.19086i
\(767\) −936.915 + 540.928i −1.22153 + 0.705252i
\(768\) 0 0
\(769\) 729.320 0.948401 0.474200 0.880417i \(-0.342737\pi\)
0.474200 + 0.880417i \(0.342737\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 134.000 232.095i 0.173575 0.300641i
\(773\) 376.339 217.280i 0.486855 0.281086i −0.236414 0.971653i \(-0.575972\pi\)
0.723269 + 0.690566i \(0.242639\pi\)
\(774\) 0 0
\(775\) 148.907 257.915i 0.192138 0.332793i
\(776\) 532.913i 0.686743i
\(777\) 0 0
\(778\) −756.834 −0.972794
\(779\) −1050.21 606.337i −1.34815 0.778353i
\(780\) 0 0
\(781\) 73.6680 + 127.597i 0.0943252 + 0.163376i
\(782\) 162.063 + 93.5673i 0.207242 + 0.119651i
\(783\) 0 0
\(784\) 0 0
\(785\) 1122.76i 1.43027i
\(786\) 0 0
\(787\) 7.67585 + 13.2950i 0.00975331 + 0.0168932i 0.870861 0.491530i \(-0.163562\pi\)
−0.861108 + 0.508423i \(0.830229\pi\)
\(788\) −326.595 + 188.560i −0.414461 + 0.239289i
\(789\) 0 0
\(790\) −288.972 −0.365788
\(791\) 0 0
\(792\) 0 0
\(793\) 145.579 252.150i 0.183580 0.317970i
\(794\) −115.523 + 66.6972i −0.145495 + 0.0840016i
\(795\) 0 0
\(796\) 102.494 177.525i 0.128761 0.223021i
\(797\) 1043.48i 1.30927i 0.755947 + 0.654633i \(0.227177\pi\)
−0.755947 + 0.654633i \(0.772823\pi\)
\(798\) 0 0
\(799\) −185.004 −0.231544
\(800\) 57.9745 + 33.4716i 0.0724681 + 0.0418395i
\(801\) 0 0
\(802\) 73.2510 + 126.874i 0.0913354 + 0.158198i
\(803\) 808.530 + 466.805i 1.00689 + 0.581326i
\(804\) 0 0
\(805\) 0 0
\(806\) 661.371i 0.820560i
\(807\) 0 0
\(808\) 150.915 + 261.392i 0.186776 + 0.323506i
\(809\) −901.804 + 520.657i −1.11471 + 0.643581i −0.940046 0.341046i \(-0.889219\pi\)
−0.174668 + 0.984627i \(0.555885\pi\)
\(810\) 0 0
\(811\) 502.316 0.619379 0.309689 0.950838i \(-0.399775\pi\)
0.309689 + 0.950838i \(0.399775\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 326.154 564.916i 0.400681 0.694000i
\(815\) 457.251 263.994i 0.561044 0.323919i
\(816\) 0 0
\(817\) −834.980 + 1446.23i −1.02201 + 1.77017i
\(818\) 13.7983i 0.0168684i
\(819\) 0 0
\(820\) 735.984 0.897542
\(821\) −20.0170 11.5568i −0.0243813 0.0140765i 0.487760 0.872978i \(-0.337814\pi\)
−0.512141 + 0.858901i \(0.671148\pi\)
\(822\) 0 0
\(823\) 300.332 + 520.190i 0.364923 + 0.632066i 0.988764 0.149486i \(-0.0477618\pi\)
−0.623840 + 0.781552i \(0.714428\pi\)
\(824\) 322.103 + 185.966i 0.390902 + 0.225687i
\(825\) 0 0
\(826\) 0 0
\(827\) 1309.21i 1.58308i 0.611118 + 0.791540i \(0.290720\pi\)
−0.611118 + 0.791540i \(0.709280\pi\)
\(828\) 0 0
\(829\) 310.959 + 538.598i 0.375102 + 0.649696i 0.990342 0.138644i \(-0.0442744\pi\)
−0.615240 + 0.788340i \(0.710941\pi\)
\(830\) −450.271 + 259.964i −0.542495 + 0.313209i
\(831\) 0 0
\(832\) 148.664 0.178683
\(833\) 0 0
\(834\) 0 0
\(835\) −183.822 + 318.389i −0.220146 + 0.381305i
\(836\) −420.480 + 242.764i −0.502966 + 0.290388i
\(837\) 0 0
\(838\) −240.000 + 415.692i −0.286396 + 0.496053i
\(839\) 1190.30i 1.41871i −0.704851 0.709355i \(-0.748986\pi\)
0.704851 0.709355i \(-0.251014\pi\)
\(840\) 0 0
\(841\) −909.308 −1.08122
\(842\) 734.014 + 423.783i 0.871751 + 0.503306i
\(843\) 0 0
\(844\) −84.5020 146.362i −0.100121 0.173414i
\(845\) −926.780 535.076i −1.09678 0.633227i
\(846\) 0 0
\(847\) 0 0
\(848\) 376.170i 0.443596i
\(849\) 0 0
\(850\) −91.2223 158.002i −0.107320 0.185884i
\(851\) 399.456 230.626i 0.469396 0.271006i
\(852\) 0 0
\(853\) 137.012 0.160623 0.0803117 0.996770i \(-0.474408\pi\)
0.0803117 + 0.996770i \(0.474408\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 116.502 201.787i 0.136100 0.235733i
\(857\) −403.690 + 233.071i −0.471050 + 0.271961i −0.716679 0.697403i \(-0.754339\pi\)
0.245629 + 0.969364i \(0.421006\pi\)
\(858\) 0 0
\(859\) −11.9921 + 20.7710i −0.0139606 + 0.0241804i −0.872921 0.487861i \(-0.837777\pi\)
0.858961 + 0.512041i \(0.171111\pi\)
\(860\) 1013.52i 1.17851i
\(861\) 0 0
\(862\) 1005.47 1.16644
\(863\) 0.0992493 + 0.0573016i 0.000115005 + 6.63982e-5i 0.500058 0.865992i \(-0.333312\pi\)
−0.499942 + 0.866059i \(0.666646\pi\)
\(864\) 0 0
\(865\) −493.332 854.476i −0.570326 0.987834i
\(866\) −462.934 267.275i −0.534566 0.308632i
\(867\) 0 0
\(868\) 0 0
\(869\) 408.669i 0.470275i
\(870\) 0 0
\(871\) −1232.65 2135.01i −1.41521 2.45122i
\(872\) −82.8664 + 47.8429i −0.0950302 + 0.0548657i
\(873\) 0 0
\(874\) −343.320 −0.392815
\(875\) 0 0
\(876\) 0 0
\(877\) −498.652 + 863.691i −0.568589 + 0.984824i 0.428117 + 0.903723i \(0.359177\pi\)
−0.996706 + 0.0811012i \(0.974156\pi\)
\(878\) 646.845 373.456i 0.736725 0.425348i
\(879\) 0 0
\(880\) 147.336 255.193i 0.167427 0.289992i
\(881\) 935.649i 1.06203i −0.847362 0.531015i \(-0.821811\pi\)
0.847362 0.531015i \(-0.178189\pi\)
\(882\) 0 0
\(883\) −1549.47 −1.75478 −0.877392 0.479774i \(-0.840719\pi\)
−0.877392 + 0.479774i \(0.840719\pi\)
\(884\) −350.882 202.582i −0.396926 0.229165i
\(885\) 0 0
\(886\) −25.9111 44.8793i −0.0292450 0.0506539i
\(887\) −774.654 447.246i −0.873341 0.504224i −0.00488401 0.999988i \(-0.501555\pi\)
−0.868457 + 0.495764i \(0.834888\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 40.9844i 0.0460498i
\(891\) 0 0
\(892\) −158.494 274.520i −0.177684 0.307758i
\(893\) 293.939 169.706i 0.329159 0.190040i
\(894\) 0 0
\(895\) 1353.96 1.51281
\(896\) 0 0
\(897\) 0 0
\(898\) 281.154 486.973i 0.313089 0.542287i
\(899\) −911.806 + 526.431i −1.01424 + 0.585574i
\(900\) 0 0
\(901\) −512.600 + 887.849i −0.568923 + 0.985404i
\(902\) 1040.84i 1.15392i
\(903\) 0 0
\(904\) 80.6640 0.0892301
\(905\) −992.937 573.272i −1.09717 0.633450i
\(906\) 0 0
\(907\) 67.9190 + 117.639i 0.0748831 + 0.129701i 0.901035 0.433746i \(-0.142808\pi\)
−0.826152 + 0.563447i \(0.809475\pi\)
\(908\) −176.363 101.823i −0.194233 0.112140i
\(909\) 0 0
\(910\) 0 0
\(911\) 1242.01i 1.36335i 0.731655 + 0.681675i \(0.238748\pi\)
−0.731655 + 0.681675i \(0.761252\pi\)
\(912\) 0 0
\(913\) 367.644 + 636.779i 0.402677 + 0.697458i
\(914\) 421.709 243.474i 0.461389 0.266383i
\(915\) 0 0
\(916\) 537.830 0.587151
\(917\) 0 0
\(918\) 0 0
\(919\) 194.081 336.158i 0.211187 0.365787i −0.740899 0.671616i \(-0.765600\pi\)
0.952086 + 0.305829i \(0.0989337\pi\)
\(920\) 180.449 104.182i 0.196140 0.113242i
\(921\) 0 0
\(922\) 262.292 454.302i 0.284481 0.492736i
\(923\) 225.564i 0.244382i
\(924\) 0 0
\(925\) −449.692 −0.486153
\(926\) −95.9367 55.3891i −0.103603 0.0598154i
\(927\) 0 0
\(928\) −118.332 204.957i −0.127513 0.220859i
\(929\) −538.403 310.847i −0.579551 0.334604i 0.181404 0.983409i \(-0.441936\pi\)
−0.760955 + 0.648805i \(0.775269\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 52.5495i 0.0563836i
\(933\) 0 0
\(934\) 282.672 + 489.602i 0.302647 + 0.524199i
\(935\) −695.495 + 401.544i −0.743845 + 0.429459i
\(936\) 0 0
\(937\) 1262.00 1.34685 0.673426 0.739255i \(-0.264822\pi\)
0.673426 + 0.739255i \(0.264822\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −102.996 + 178.394i −0.109570 + 0.189781i
\(941\) −582.324 + 336.205i −0.618835 + 0.357285i −0.776415 0.630222i \(-0.782964\pi\)
0.157580 + 0.987506i \(0.449631\pi\)
\(942\) 0 0
\(943\) 367.992 637.381i 0.390236 0.675908i
\(944\) 232.870i 0.246684i
\(945\) 0 0
\(946\) −1433.33 −1.51515
\(947\) 1004.37 + 579.874i 1.06058 + 0.612327i 0.925593 0.378520i \(-0.123567\pi\)
0.134989 + 0.990847i \(0.456900\pi\)
\(948\) 0 0
\(949\) −714.656 1237.82i −0.753062 1.30434i
\(950\) 289.872 + 167.358i 0.305129 + 0.176166i
\(951\) 0 0
\(952\) 0 0
\(953\) 163.104i 0.171148i 0.996332 + 0.0855740i \(0.0272724\pi\)
−0.996332 + 0.0855740i \(0.972728\pi\)
\(954\) 0 0
\(955\) 691.992 + 1198.57i 0.724599 + 1.25504i
\(956\) 159.822 92.2733i 0.167178 0.0965201i
\(957\) 0 0
\(958\) −994.656 −1.03826
\(959\) 0 0
\(960\) 0 0
\(961\) 163.836 283.772i 0.170485 0.295288i
\(962\) −864.859 + 499.326i −0.899022 + 0.519050i
\(963\) 0 0
\(964\) 343.247 594.521i 0.356065 0.616723i
\(965\) 813.260i 0.842756i
\(966\) 0 0
\(967\) 887.012 0.917282 0.458641 0.888622i \(-0.348336\pi\)
0.458641 + 0.888622i \(0.348336\pi\)
\(968\) −64.5097 37.2447i −0.0666422 0.0384759i
\(969\) 0 0
\(970\) −808.575 1400.49i −0.833583 1.44381i
\(971\) −1226.57 708.160i −1.26320 0.729310i −0.289510 0.957175i \(-0.593492\pi\)
−0.973693 + 0.227865i \(0.926826\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 116.687i 0.119801i
\(975\) 0 0
\(976\) −31.3360 54.2755i −0.0321065 0.0556101i
\(977\) −293.627 + 169.525i −0.300539 + 0.173516i −0.642685 0.766131i \(-0.722180\pi\)
0.342146 + 0.939647i \(0.388846\pi\)
\(978\) 0 0
\(979\) −57.9606 −0.0592039
\(980\) 0 0
\(981\) 0 0
\(982\) 130.251 225.601i 0.132638 0.229737i
\(983\) 422.523 243.943i 0.429830 0.248162i −0.269444 0.963016i \(-0.586840\pi\)
0.699274 + 0.714854i \(0.253507\pi\)
\(984\) 0 0
\(985\) 572.195 991.070i 0.580908 1.00616i
\(986\) 644.996i 0.654154i
\(987\) 0 0
\(988\) 743.320 0.752348
\(989\) −877.731 506.758i −0.887493 0.512394i
\(990\) 0 0
\(991\) 468.737 + 811.877i 0.472994 + 0.819250i 0.999522 0.0309078i \(-0.00983984\pi\)
−0.526528 + 0.850158i \(0.676507\pi\)
\(992\) −123.288 71.1802i −0.124282 0.0717543i
\(993\) 0 0
\(994\) 0 0
\(995\) 622.047i 0.625173i
\(996\) 0 0
\(997\) −230.506 399.248i −0.231200 0.400449i 0.726962 0.686678i \(-0.240932\pi\)
−0.958161 + 0.286229i \(0.907598\pi\)
\(998\) 922.001 532.317i 0.923848 0.533384i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 882.3.s.e.863.1 8
3.2 odd 2 inner 882.3.s.e.863.4 8
7.2 even 3 126.3.b.a.71.4 yes 4
7.3 odd 6 882.3.s.i.557.3 8
7.4 even 3 inner 882.3.s.e.557.4 8
7.5 odd 6 882.3.b.f.197.3 4
7.6 odd 2 882.3.s.i.863.2 8
21.2 odd 6 126.3.b.a.71.1 4
21.5 even 6 882.3.b.f.197.2 4
21.11 odd 6 inner 882.3.s.e.557.1 8
21.17 even 6 882.3.s.i.557.2 8
21.20 even 2 882.3.s.i.863.3 8
28.23 odd 6 1008.3.d.a.449.3 4
35.2 odd 12 3150.3.c.b.449.1 8
35.9 even 6 3150.3.e.e.701.2 4
35.23 odd 12 3150.3.c.b.449.7 8
56.37 even 6 4032.3.d.i.449.2 4
56.51 odd 6 4032.3.d.j.449.2 4
63.2 odd 6 1134.3.q.c.701.2 8
63.16 even 3 1134.3.q.c.701.3 8
63.23 odd 6 1134.3.q.c.1079.3 8
63.58 even 3 1134.3.q.c.1079.2 8
84.23 even 6 1008.3.d.a.449.2 4
105.2 even 12 3150.3.c.b.449.6 8
105.23 even 12 3150.3.c.b.449.4 8
105.44 odd 6 3150.3.e.e.701.4 4
168.107 even 6 4032.3.d.j.449.3 4
168.149 odd 6 4032.3.d.i.449.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.b.a.71.1 4 21.2 odd 6
126.3.b.a.71.4 yes 4 7.2 even 3
882.3.b.f.197.2 4 21.5 even 6
882.3.b.f.197.3 4 7.5 odd 6
882.3.s.e.557.1 8 21.11 odd 6 inner
882.3.s.e.557.4 8 7.4 even 3 inner
882.3.s.e.863.1 8 1.1 even 1 trivial
882.3.s.e.863.4 8 3.2 odd 2 inner
882.3.s.i.557.2 8 21.17 even 6
882.3.s.i.557.3 8 7.3 odd 6
882.3.s.i.863.2 8 7.6 odd 2
882.3.s.i.863.3 8 21.20 even 2
1008.3.d.a.449.2 4 84.23 even 6
1008.3.d.a.449.3 4 28.23 odd 6
1134.3.q.c.701.2 8 63.2 odd 6
1134.3.q.c.701.3 8 63.16 even 3
1134.3.q.c.1079.2 8 63.58 even 3
1134.3.q.c.1079.3 8 63.23 odd 6
3150.3.c.b.449.1 8 35.2 odd 12
3150.3.c.b.449.4 8 105.23 even 12
3150.3.c.b.449.6 8 105.2 even 12
3150.3.c.b.449.7 8 35.23 odd 12
3150.3.e.e.701.2 4 35.9 even 6
3150.3.e.e.701.4 4 105.44 odd 6
4032.3.d.i.449.2 4 56.37 even 6
4032.3.d.i.449.3 4 168.149 odd 6
4032.3.d.j.449.2 4 56.51 odd 6
4032.3.d.j.449.3 4 168.107 even 6