Properties

Label 882.3.s.e.863.2
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 863.2
Root \(2.23256 - 1.28897i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.e.557.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(7.70549 + 4.44876i) q^{5} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(7.70549 + 4.44876i) q^{5} -2.82843i q^{8} +(-6.29150 - 10.8972i) q^{10} +(-15.4110 + 8.89753i) q^{11} +2.58301 q^{13} +(-2.00000 + 3.46410i) q^{16} +(22.4024 - 12.9340i) q^{17} +(-10.0000 + 17.3205i) q^{19} +17.7951i q^{20} +25.1660 q^{22} +(15.4110 + 8.89753i) q^{23} +(27.0830 + 46.9091i) q^{25} +(-3.16352 - 1.82646i) q^{26} -11.9034i q^{29} +(8.58301 + 14.8662i) q^{31} +(4.89898 - 2.82843i) q^{32} -36.5830 q^{34} +(-19.0000 + 32.9090i) q^{37} +(24.4949 - 14.1421i) q^{38} +(12.5830 - 21.7944i) q^{40} +15.7338i q^{41} -43.4980 q^{43} +(-30.8219 - 17.7951i) q^{44} +(-12.5830 - 21.7944i) q^{46} +(-14.6969 - 8.48528i) q^{47} -76.6023i q^{50} +(2.58301 + 4.47390i) q^{52} +(74.0947 - 42.7786i) q^{53} -158.332 q^{55} +(-8.41699 + 14.5787i) q^{58} +(-1.42807 + 0.824494i) q^{59} +(-50.1660 + 86.8901i) q^{61} -24.2764i q^{62} -8.00000 q^{64} +(19.9033 + 11.4912i) q^{65} +(-18.3320 - 31.7520i) q^{67} +(44.8048 + 25.8681i) q^{68} -17.7951i q^{71} +(-14.4575 - 25.0411i) q^{73} +(46.5403 - 26.8701i) q^{74} -40.0000 q^{76} +(-59.1660 + 102.479i) q^{79} +(-30.8219 + 17.7951i) q^{80} +(11.1255 - 19.2699i) q^{82} +120.443i q^{83} +230.162 q^{85} +(53.2740 + 30.7578i) q^{86} +(25.1660 + 43.5888i) q^{88} +(-120.789 - 69.7374i) q^{89} +35.5901i q^{92} +(12.0000 + 20.7846i) q^{94} +(-154.110 + 88.9753i) q^{95} +44.4131 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4}+O(q^{10}) \) 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
\(5\) 7.70549 + 4.44876i 1.54110 + 0.889753i 0.998770 + 0.0495855i \(0.0157900\pi\)
0.542327 + 0.840167i \(0.317543\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −6.29150 10.8972i −0.629150 1.08972i
\(11\) −15.4110 + 8.89753i −1.40100 + 0.808866i −0.994495 0.104784i \(-0.966585\pi\)
−0.406502 + 0.913650i \(0.633252\pi\)
\(12\) 0 0
\(13\) 2.58301 0.198693 0.0993464 0.995053i \(-0.468325\pi\)
0.0993464 + 0.995053i \(0.468325\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 22.4024 12.9340i 1.31779 0.760826i 0.334417 0.942425i \(-0.391461\pi\)
0.983373 + 0.181599i \(0.0581273\pi\)
\(18\) 0 0
\(19\) −10.0000 + 17.3205i −0.526316 + 0.911606i 0.473214 + 0.880947i \(0.343094\pi\)
−0.999530 + 0.0306583i \(0.990240\pi\)
\(20\) 17.7951i 0.889753i
\(21\) 0 0
\(22\) 25.1660 1.14391
\(23\) 15.4110 + 8.89753i 0.670042 + 0.386849i 0.796093 0.605175i \(-0.206897\pi\)
−0.126050 + 0.992024i \(0.540230\pi\)
\(24\) 0 0
\(25\) 27.0830 + 46.9091i 1.08332 + 1.87637i
\(26\) −3.16352 1.82646i −0.121674 0.0702485i
\(27\) 0 0
\(28\) 0 0
\(29\) 11.9034i 0.410463i −0.978713 0.205232i \(-0.934205\pi\)
0.978713 0.205232i \(-0.0657947\pi\)
\(30\) 0 0
\(31\) 8.58301 + 14.8662i 0.276871 + 0.479555i 0.970605 0.240676i \(-0.0773692\pi\)
−0.693734 + 0.720231i \(0.744036\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −36.5830 −1.07597
\(35\) 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
\(40\) 12.5830 21.7944i 0.314575 0.544860i
\(41\) 15.7338i 0.383752i 0.981419 + 0.191876i \(0.0614571\pi\)
−0.981419 + 0.191876i \(0.938543\pi\)
\(42\) 0 0
\(43\) −43.4980 −1.01158 −0.505791 0.862656i \(-0.668799\pi\)
−0.505791 + 0.862656i \(0.668799\pi\)
\(44\) −30.8219 17.7951i −0.700499 0.404433i
\(45\) 0 0
\(46\) −12.5830 21.7944i −0.273544 0.473791i
\(47\) −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
\(50\) 76.6023i 1.53205i
\(51\) 0 0
\(52\) 2.58301 + 4.47390i 0.0496732 + 0.0860365i
\(53\) 74.0947 42.7786i 1.39801 0.807143i 0.403828 0.914835i \(-0.367679\pi\)
0.994184 + 0.107692i \(0.0343461\pi\)
\(54\) 0 0
\(55\) −158.332 −2.87876
\(56\) 0 0
\(57\) 0 0
\(58\) −8.41699 + 14.5787i −0.145121 + 0.251356i
\(59\) −1.42807 + 0.824494i −0.0242045 + 0.0139745i −0.512053 0.858954i \(-0.671115\pi\)
0.487849 + 0.872928i \(0.337782\pi\)
\(60\) 0 0
\(61\) −50.1660 + 86.8901i −0.822394 + 1.42443i 0.0815014 + 0.996673i \(0.474028\pi\)
−0.903895 + 0.427754i \(0.859305\pi\)
\(62\) 24.2764i 0.391555i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 19.9033 + 11.4912i 0.306205 + 0.176787i
\(66\) 0 0
\(67\) −18.3320 31.7520i −0.273612 0.473910i 0.696172 0.717875i \(-0.254885\pi\)
−0.969784 + 0.243965i \(0.921552\pi\)
\(68\) 44.8048 + 25.8681i 0.658895 + 0.380413i
\(69\) 0 0
\(70\) 0 0
\(71\) 17.7951i 0.250635i −0.992117 0.125317i \(-0.960005\pi\)
0.992117 0.125317i \(-0.0399949\pi\)
\(72\) 0 0
\(73\) −14.4575 25.0411i −0.198048 0.343029i 0.749847 0.661611i \(-0.230127\pi\)
−0.947895 + 0.318581i \(0.896794\pi\)
\(74\) 46.5403 26.8701i 0.628923 0.363109i
\(75\) 0 0
\(76\) −40.0000 −0.526316
\(77\) 0 0
\(78\) 0 0
\(79\) −59.1660 + 102.479i −0.748937 + 1.29720i 0.199396 + 0.979919i \(0.436102\pi\)
−0.948333 + 0.317278i \(0.897231\pi\)
\(80\) −30.8219 + 17.7951i −0.385274 + 0.222438i
\(81\) 0 0
\(82\) 11.1255 19.2699i 0.135677 0.234999i
\(83\) 120.443i 1.45112i 0.688159 + 0.725560i \(0.258419\pi\)
−0.688159 + 0.725560i \(0.741581\pi\)
\(84\) 0 0
\(85\) 230.162 2.70779
\(86\) 53.2740 + 30.7578i 0.619465 + 0.357648i
\(87\) 0 0
\(88\) 25.1660 + 43.5888i 0.285977 + 0.495327i
\(89\) −120.789 69.7374i −1.35718 0.783566i −0.367934 0.929852i \(-0.619935\pi\)
−0.989242 + 0.146286i \(0.953268\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 35.5901i 0.386849i
\(93\) 0 0
\(94\) 12.0000 + 20.7846i 0.127660 + 0.221113i
\(95\) −154.110 + 88.9753i −1.62221 + 0.936582i
\(96\) 0 0
\(97\) 44.4131 0.457867 0.228933 0.973442i \(-0.426476\pi\)
0.228933 + 0.973442i \(0.426476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −54.1660 + 93.8183i −0.541660 + 0.938183i
\(101\) −27.6088 + 15.9399i −0.273354 + 0.157821i −0.630411 0.776261i \(-0.717114\pi\)
0.357057 + 0.934083i \(0.383780\pi\)
\(102\) 0 0
\(103\) −2.25098 + 3.89882i −0.0218542 + 0.0378526i −0.876746 0.480954i \(-0.840290\pi\)
0.854891 + 0.518807i \(0.173624\pi\)
\(104\) 7.30584i 0.0702485i
\(105\) 0 0
\(106\) −120.996 −1.14147
\(107\) 149.111 + 86.0896i 1.39357 + 0.804575i 0.993708 0.112002i \(-0.0357263\pi\)
0.399857 + 0.916577i \(0.369060\pi\)
\(108\) 0 0
\(109\) 88.9150 + 154.005i 0.815734 + 1.41289i 0.908800 + 0.417233i \(0.137000\pi\)
−0.0930653 + 0.995660i \(0.529667\pi\)
\(110\) 193.916 + 111.958i 1.76288 + 1.01780i
\(111\) 0 0
\(112\) 0 0
\(113\) 31.3475i 0.277411i −0.990334 0.138706i \(-0.955706\pi\)
0.990334 0.138706i \(-0.0442942\pi\)
\(114\) 0 0
\(115\) 79.1660 + 137.120i 0.688400 + 1.19234i
\(116\) 20.6173 11.9034i 0.177736 0.102616i
\(117\) 0 0
\(118\) 2.33202 0.0197629
\(119\) 0 0
\(120\) 0 0
\(121\) 97.8320 169.450i 0.808529 1.40041i
\(122\) 122.881 70.9455i 1.00722 0.581520i
\(123\) 0 0
\(124\) −17.1660 + 29.7324i −0.138436 + 0.239777i
\(125\) 259.505i 2.07604i
\(126\) 0 0
\(127\) 214.332 1.68765 0.843827 0.536616i \(-0.180297\pi\)
0.843827 + 0.536616i \(0.180297\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −16.2510 28.1475i −0.125008 0.216519i
\(131\) 79.1970 + 45.7244i 0.604557 + 0.349041i 0.770832 0.637038i \(-0.219841\pi\)
−0.166275 + 0.986079i \(0.553174\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 51.8508i 0.386946i
\(135\) 0 0
\(136\) −36.5830 63.3636i −0.268993 0.465909i
\(137\) 92.5699 53.4453i 0.675693 0.390111i −0.122537 0.992464i \(-0.539103\pi\)
0.798230 + 0.602353i \(0.205770\pi\)
\(138\) 0 0
\(139\) −121.328 −0.872864 −0.436432 0.899737i \(-0.643758\pi\)
−0.436432 + 0.899737i \(0.643758\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.5830 + 21.7944i −0.0886127 + 0.153482i
\(143\) −39.8066 + 22.9824i −0.278368 + 0.160716i
\(144\) 0 0
\(145\) 52.9555 91.7217i 0.365211 0.632563i
\(146\) 40.8920i 0.280082i
\(147\) 0 0
\(148\) −76.0000 −0.513514
\(149\) −15.3069 8.83744i −0.102731 0.0593117i 0.447754 0.894157i \(-0.352224\pi\)
−0.550485 + 0.834845i \(0.685557\pi\)
\(150\) 0 0
\(151\) 25.4170 + 44.0235i 0.168324 + 0.291547i 0.937831 0.347093i \(-0.112831\pi\)
−0.769506 + 0.638639i \(0.779498\pi\)
\(152\) 48.9898 + 28.2843i 0.322301 + 0.186081i
\(153\) 0 0
\(154\) 0 0
\(155\) 152.735i 0.985388i
\(156\) 0 0
\(157\) −34.4980 59.7523i −0.219733 0.380588i 0.734994 0.678074i \(-0.237185\pi\)
−0.954726 + 0.297486i \(0.903852\pi\)
\(158\) 144.927 83.6734i 0.917257 0.529578i
\(159\) 0 0
\(160\) 50.3320 0.314575
\(161\) 0 0
\(162\) 0 0
\(163\) 83.4980 144.623i 0.512258 0.887257i −0.487641 0.873044i \(-0.662143\pi\)
0.999899 0.0142125i \(-0.00452412\pi\)
\(164\) −27.2518 + 15.7338i −0.166169 + 0.0959379i
\(165\) 0 0
\(166\) 85.1660 147.512i 0.513048 0.888626i
\(167\) 120.443i 0.721215i −0.932718 0.360608i \(-0.882569\pi\)
0.932718 0.360608i \(-0.117431\pi\)
\(168\) 0 0
\(169\) −162.328 −0.960521
\(170\) −281.890 162.749i −1.65818 0.957348i
\(171\) 0 0
\(172\) −43.4980 75.3408i −0.252896 0.438028i
\(173\) −79.5540 45.9305i −0.459850 0.265494i 0.252131 0.967693i \(-0.418868\pi\)
−0.711981 + 0.702199i \(0.752202\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 71.1802i 0.404433i
\(177\) 0 0
\(178\) 98.6235 + 170.821i 0.554065 + 0.959668i
\(179\) −115.433 + 66.6455i −0.644879 + 0.372321i −0.786492 0.617601i \(-0.788105\pi\)
0.141612 + 0.989922i \(0.454771\pi\)
\(180\) 0 0
\(181\) 83.0850 0.459033 0.229517 0.973305i \(-0.426286\pi\)
0.229517 + 0.973305i \(0.426286\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 25.1660 43.5888i 0.136772 0.236896i
\(185\) −292.808 + 169.053i −1.58275 + 0.913800i
\(186\) 0 0
\(187\) −230.162 + 398.652i −1.23081 + 2.13183i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) 251.660 1.32453
\(191\) 35.8202 + 20.6808i 0.187540 + 0.108276i 0.590830 0.806796i \(-0.298800\pi\)
−0.403290 + 0.915072i \(0.632134\pi\)
\(192\) 0 0
\(193\) −67.0000 116.047i −0.347150 0.601282i 0.638592 0.769546i \(-0.279517\pi\)
−0.985742 + 0.168264i \(0.946184\pi\)
\(194\) −54.3947 31.4048i −0.280385 0.161880i
\(195\) 0 0
\(196\) 0 0
\(197\) 68.8269i 0.349375i 0.984624 + 0.174688i \(0.0558916\pi\)
−0.984624 + 0.174688i \(0.944108\pi\)
\(198\) 0 0
\(199\) 139.247 + 241.183i 0.699734 + 1.21197i 0.968559 + 0.248786i \(0.0800314\pi\)
−0.268825 + 0.963189i \(0.586635\pi\)
\(200\) 132.679 76.6023i 0.663395 0.383012i
\(201\) 0 0
\(202\) 45.0850 0.223193
\(203\) 0 0
\(204\) 0 0
\(205\) −69.9961 + 121.237i −0.341444 + 0.591399i
\(206\) 5.51376 3.18337i 0.0267658 0.0154533i
\(207\) 0 0
\(208\) −5.16601 + 8.94779i −0.0248366 + 0.0430182i
\(209\) 355.901i 1.70288i
\(210\) 0 0
\(211\) −211.498 −1.00236 −0.501180 0.865343i \(-0.667101\pi\)
−0.501180 + 0.865343i \(0.667101\pi\)
\(212\) 148.189 + 85.5571i 0.699006 + 0.403571i
\(213\) 0 0
\(214\) −121.749 210.875i −0.568921 0.985399i
\(215\) −335.173 193.512i −1.55895 0.900058i
\(216\) 0 0
\(217\) 0 0
\(218\) 251.490i 1.15362i
\(219\) 0 0
\(220\) −158.332 274.239i −0.719691 1.24654i
\(221\) 57.8656 33.4087i 0.261835 0.151171i
\(222\) 0 0
\(223\) 222.494 0.997731 0.498866 0.866679i \(-0.333750\pi\)
0.498866 + 0.866679i \(0.333750\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −22.1660 + 38.3927i −0.0980797 + 0.169879i
\(227\) −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
\(229\) 81.5425 141.236i 0.356081 0.616750i −0.631222 0.775603i \(-0.717446\pi\)
0.987302 + 0.158853i \(0.0507795\pi\)
\(230\) 223.915i 0.973545i
\(231\) 0 0
\(232\) −33.6680 −0.145121
\(233\) 314.244 + 181.429i 1.34869 + 0.778664i 0.988063 0.154047i \(-0.0492308\pi\)
0.360623 + 0.932712i \(0.382564\pi\)
\(234\) 0 0
\(235\) −75.4980 130.766i −0.321268 0.556453i
\(236\) −2.85613 1.64899i −0.0121022 0.00698724i
\(237\) 0 0
\(238\) 0 0
\(239\) 177.126i 0.741113i 0.928810 + 0.370557i \(0.120833\pi\)
−0.928810 + 0.370557i \(0.879167\pi\)
\(240\) 0 0
\(241\) −76.3765 132.288i −0.316915 0.548913i 0.662928 0.748683i \(-0.269314\pi\)
−0.979843 + 0.199771i \(0.935980\pi\)
\(242\) −239.639 + 138.355i −0.990242 + 0.571716i
\(243\) 0 0
\(244\) −200.664 −0.822394
\(245\) 0 0
\(246\) 0 0
\(247\) −25.8301 + 44.7390i −0.104575 + 0.181129i
\(248\) 42.0480 24.2764i 0.169548 0.0978887i
\(249\) 0 0
\(250\) 183.498 317.828i 0.733992 1.27131i
\(251\) 356.382i 1.41985i −0.704278 0.709924i \(-0.748729\pi\)
0.704278 0.709924i \(-0.251271\pi\)
\(252\) 0 0
\(253\) −316.664 −1.25164
\(254\) −262.502 151.556i −1.03347 0.596676i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 51.5882 + 29.7844i 0.200732 + 0.115893i 0.596997 0.802244i \(-0.296360\pi\)
−0.396265 + 0.918136i \(0.629694\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 45.9647i 0.176787i
\(261\) 0 0
\(262\) −64.6640 112.001i −0.246809 0.427486i
\(263\) 6.42629 3.71022i 0.0244346 0.0141073i −0.487733 0.872993i \(-0.662176\pi\)
0.512168 + 0.858886i \(0.328843\pi\)
\(264\) 0 0
\(265\) 761.247 2.87263
\(266\) 0 0
\(267\) 0 0
\(268\) 36.6640 63.5040i 0.136806 0.236955i
\(269\) 372.571 215.104i 1.38502 0.799642i 0.392272 0.919849i \(-0.371689\pi\)
0.992749 + 0.120207i \(0.0383559\pi\)
\(270\) 0 0
\(271\) 20.5830 35.6508i 0.0759520 0.131553i −0.825548 0.564332i \(-0.809134\pi\)
0.901500 + 0.432779i \(0.142467\pi\)
\(272\) 103.472i 0.380413i
\(273\) 0 0
\(274\) −151.166 −0.551701
\(275\) −834.751 481.944i −3.03546 1.75252i
\(276\) 0 0
\(277\) −16.0000 27.7128i −0.0577617 0.100046i 0.835699 0.549188i \(-0.185063\pi\)
−0.893460 + 0.449142i \(0.851730\pi\)
\(278\) 148.596 + 85.7919i 0.534518 + 0.308604i
\(279\) 0 0
\(280\) 0 0
\(281\) 17.0907i 0.0608211i −0.999537 0.0304106i \(-0.990319\pi\)
0.999537 0.0304106i \(-0.00968147\pi\)
\(282\) 0 0
\(283\) −219.830 380.757i −0.776785 1.34543i −0.933786 0.357832i \(-0.883516\pi\)
0.157001 0.987598i \(-0.449817\pi\)
\(284\) 30.8219 17.7951i 0.108528 0.0626587i
\(285\) 0 0
\(286\) 65.0039 0.227286
\(287\) 0 0
\(288\) 0 0
\(289\) 190.079 329.227i 0.657713 1.13919i
\(290\) −129.714 + 74.8904i −0.447290 + 0.258243i
\(291\) 0 0
\(292\) 28.9150 50.0823i 0.0990241 0.171515i
\(293\) 394.377i 1.34600i 0.739644 + 0.672998i \(0.234994\pi\)
−0.739644 + 0.672998i \(0.765006\pi\)
\(294\) 0 0
\(295\) −14.6719 −0.0497353
\(296\) 93.0806 + 53.7401i 0.314462 + 0.181554i
\(297\) 0 0
\(298\) 12.4980 + 21.6472i 0.0419397 + 0.0726417i
\(299\) 39.8066 + 22.9824i 0.133133 + 0.0768641i
\(300\) 0 0
\(301\) 0 0
\(302\) 71.8901i 0.238047i
\(303\) 0 0
\(304\) −40.0000 69.2820i −0.131579 0.227901i
\(305\) −773.107 + 446.353i −2.53478 + 1.46345i
\(306\) 0 0
\(307\) −23.3360 −0.0760129 −0.0380064 0.999277i \(-0.512101\pi\)
−0.0380064 + 0.999277i \(0.512101\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 108.000 187.061i 0.348387 0.603424i
\(311\) 456.617 263.628i 1.46822 0.847678i 0.468855 0.883275i \(-0.344667\pi\)
0.999366 + 0.0355970i \(0.0113333\pi\)
\(312\) 0 0
\(313\) 147.664 255.762i 0.471770 0.817130i −0.527708 0.849426i \(-0.676949\pi\)
0.999478 + 0.0322959i \(0.0102819\pi\)
\(314\) 97.5752i 0.310749i
\(315\) 0 0
\(316\) −236.664 −0.748937
\(317\) 93.0758 + 53.7373i 0.293614 + 0.169518i 0.639571 0.768732i \(-0.279112\pi\)
−0.345956 + 0.938251i \(0.612445\pi\)
\(318\) 0 0
\(319\) 105.911 + 183.443i 0.332010 + 0.575058i
\(320\) −61.6439 35.5901i −0.192637 0.111219i
\(321\) 0 0
\(322\) 0 0
\(323\) 517.362i 1.60174i
\(324\) 0 0
\(325\) 69.9555 + 121.167i 0.215248 + 0.372820i
\(326\) −204.528 + 118.084i −0.627385 + 0.362221i
\(327\) 0 0
\(328\) 44.5020 0.135677
\(329\) 0 0
\(330\) 0 0
\(331\) 136.745 236.849i 0.413127 0.715557i −0.582103 0.813115i \(-0.697770\pi\)
0.995230 + 0.0975581i \(0.0311032\pi\)
\(332\) −208.613 + 120.443i −0.628353 + 0.362780i
\(333\) 0 0
\(334\) −85.1660 + 147.512i −0.254988 + 0.441652i
\(335\) 326.219i 0.973789i
\(336\) 0 0
\(337\) −341.166 −1.01236 −0.506181 0.862427i \(-0.668943\pi\)
−0.506181 + 0.862427i \(0.668943\pi\)
\(338\) 198.810 + 114.783i 0.588197 + 0.339596i
\(339\) 0 0
\(340\) 230.162 + 398.652i 0.676947 + 1.17251i
\(341\) −264.545 152.735i −0.775791 0.447903i
\(342\) 0 0
\(343\) 0 0
\(344\) 123.031i 0.357648i
\(345\) 0 0
\(346\) 64.9555 + 112.506i 0.187733 + 0.325163i
\(347\) −100.736 + 58.1602i −0.290307 + 0.167609i −0.638080 0.769970i \(-0.720271\pi\)
0.347773 + 0.937579i \(0.386938\pi\)
\(348\) 0 0
\(349\) −158.324 −0.453651 −0.226825 0.973935i \(-0.572835\pi\)
−0.226825 + 0.973935i \(0.572835\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −50.3320 + 87.1776i −0.142989 + 0.247664i
\(353\) 199.480 115.170i 0.565098 0.326260i −0.190091 0.981766i \(-0.560878\pi\)
0.755189 + 0.655507i \(0.227545\pi\)
\(354\) 0 0
\(355\) 79.1660 137.120i 0.223003 0.386252i
\(356\) 278.949i 0.783566i
\(357\) 0 0
\(358\) 188.502 0.526542
\(359\) 148.695 + 85.8492i 0.414193 + 0.239134i 0.692590 0.721332i \(-0.256470\pi\)
−0.278397 + 0.960466i \(0.589803\pi\)
\(360\) 0 0
\(361\) −19.5000 33.7750i −0.0540166 0.0935595i
\(362\) −101.758 58.7499i −0.281099 0.162293i
\(363\) 0 0
\(364\) 0 0
\(365\) 257.272i 0.704856i
\(366\) 0 0
\(367\) −258.745 448.160i −0.705027 1.22114i −0.966682 0.255982i \(-0.917601\pi\)
0.261654 0.965162i \(-0.415732\pi\)
\(368\) −61.6439 + 35.5901i −0.167511 + 0.0967123i
\(369\) 0 0
\(370\) 478.154 1.29231
\(371\) 0 0
\(372\) 0 0
\(373\) 116.668 202.075i 0.312783 0.541756i −0.666181 0.745790i \(-0.732072\pi\)
0.978964 + 0.204035i \(0.0654055\pi\)
\(374\) 563.780 325.498i 1.50743 0.870316i
\(375\) 0 0
\(376\) −24.0000 + 41.5692i −0.0638298 + 0.110556i
\(377\) 30.7466i 0.0815560i
\(378\) 0 0
\(379\) 441.166 1.16403 0.582013 0.813179i \(-0.302265\pi\)
0.582013 + 0.813179i \(0.302265\pi\)
\(380\) −308.219 177.951i −0.811104 0.468291i
\(381\) 0 0
\(382\) −29.2470 50.6574i −0.0765630 0.132611i
\(383\) −184.515 106.530i −0.481763 0.278146i 0.239388 0.970924i \(-0.423053\pi\)
−0.721151 + 0.692778i \(0.756387\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 189.505i 0.490945i
\(387\) 0 0
\(388\) 44.4131 + 76.9257i 0.114467 + 0.198262i
\(389\) 489.387 282.548i 1.25806 0.726344i 0.285367 0.958418i \(-0.407885\pi\)
0.972698 + 0.232074i \(0.0745512\pi\)
\(390\) 0 0
\(391\) 460.324 1.17730
\(392\) 0 0
\(393\) 0 0
\(394\) 48.6680 84.2954i 0.123523 0.213948i
\(395\) −911.806 + 526.431i −2.30837 + 1.33274i
\(396\) 0 0
\(397\) −249.162 + 431.561i −0.627612 + 1.08706i 0.360417 + 0.932791i \(0.382634\pi\)
−0.988029 + 0.154265i \(0.950699\pi\)
\(398\) 393.850i 0.989573i
\(399\) 0 0
\(400\) −216.664 −0.541660
\(401\) −167.483 96.6962i −0.417662 0.241138i 0.276414 0.961039i \(-0.410854\pi\)
−0.694077 + 0.719901i \(0.744187\pi\)
\(402\) 0 0
\(403\) 22.1699 + 38.3995i 0.0550123 + 0.0952841i
\(404\) −55.2176 31.8799i −0.136677 0.0789106i
\(405\) 0 0
\(406\) 0 0
\(407\) 676.212i 1.66145i
\(408\) 0 0
\(409\) 227.122 + 393.386i 0.555309 + 0.961824i 0.997879 + 0.0650902i \(0.0207335\pi\)
−0.442570 + 0.896734i \(0.645933\pi\)
\(410\) 171.455 98.9894i 0.418182 0.241438i
\(411\) 0 0
\(412\) −9.00394 −0.0218542
\(413\) 0 0
\(414\) 0 0
\(415\) −535.822 + 928.071i −1.29114 + 2.23632i
\(416\) 12.6541 7.30584i 0.0304185 0.0175621i
\(417\) 0 0
\(418\) −251.660 + 435.888i −0.602058 + 1.04279i
\(419\) 339.411i 0.810051i −0.914305 0.405025i \(-0.867263\pi\)
0.914305 0.405025i \(-0.132737\pi\)
\(420\) 0 0
\(421\) 247.320 0.587459 0.293729 0.955889i \(-0.405104\pi\)
0.293729 + 0.955889i \(0.405104\pi\)
\(422\) 259.031 + 149.552i 0.613818 + 0.354388i
\(423\) 0 0
\(424\) −120.996 209.571i −0.285368 0.494272i
\(425\) 1213.45 + 700.586i 2.85518 + 1.64844i
\(426\) 0 0
\(427\) 0 0
\(428\) 344.358i 0.804575i
\(429\) 0 0
\(430\) 273.668 + 474.007i 0.636437 + 1.10234i
\(431\) 395.271 228.210i 0.917101 0.529489i 0.0343923 0.999408i \(-0.489050\pi\)
0.882709 + 0.469920i \(0.155717\pi\)
\(432\) 0 0
\(433\) −637.984 −1.47340 −0.736702 0.676217i \(-0.763618\pi\)
−0.736702 + 0.676217i \(0.763618\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −177.830 + 308.011i −0.407867 + 0.706447i
\(437\) −308.219 + 177.951i −0.705308 + 0.407210i
\(438\) 0 0
\(439\) 392.073 679.091i 0.893105 1.54690i 0.0569728 0.998376i \(-0.481855\pi\)
0.836132 0.548528i \(-0.184812\pi\)
\(440\) 447.831i 1.01780i
\(441\) 0 0
\(442\) −94.4941 −0.213788
\(443\) −408.956 236.111i −0.923151 0.532981i −0.0385120 0.999258i \(-0.512262\pi\)
−0.884639 + 0.466277i \(0.845595\pi\)
\(444\) 0 0
\(445\) −620.490 1074.72i −1.39436 2.41510i
\(446\) −272.499 157.327i −0.610983 0.352751i
\(447\) 0 0
\(448\) 0 0
\(449\) 739.852i 1.64778i −0.566752 0.823888i \(-0.691800\pi\)
0.566752 0.823888i \(-0.308200\pi\)
\(450\) 0 0
\(451\) −139.992 242.473i −0.310404 0.537635i
\(452\) 54.2954 31.3475i 0.120123 0.0693528i
\(453\) 0 0
\(454\) 144.000 0.317181
\(455\) 0 0
\(456\) 0 0
\(457\) 124.162 215.055i 0.271689 0.470580i −0.697605 0.716482i \(-0.745751\pi\)
0.969295 + 0.245903i \(0.0790843\pi\)
\(458\) −199.737 + 115.318i −0.436108 + 0.251787i
\(459\) 0 0
\(460\) −158.332 + 274.239i −0.344200 + 0.596172i
\(461\) 355.970i 0.772168i 0.922464 + 0.386084i \(0.126173\pi\)
−0.922464 + 0.386084i \(0.873827\pi\)
\(462\) 0 0
\(463\) −6.33202 −0.0136761 −0.00683804 0.999977i \(-0.502177\pi\)
−0.00683804 + 0.999977i \(0.502177\pi\)
\(464\) 41.2347 + 23.8069i 0.0888679 + 0.0513079i
\(465\) 0 0
\(466\) −256.579 444.408i −0.550599 0.953665i
\(467\) −760.968 439.345i −1.62948 0.940782i −0.984247 0.176799i \(-0.943426\pi\)
−0.645236 0.763984i \(-0.723241\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 213.541i 0.454342i
\(471\) 0 0
\(472\) 2.33202 + 4.03918i 0.00494072 + 0.00855758i
\(473\) 670.347 387.025i 1.41722 0.818235i
\(474\) 0 0
\(475\) −1083.32 −2.28067
\(476\) 0 0
\(477\) 0 0
\(478\) 125.247 216.934i 0.262023 0.453837i
\(479\) 194.333 112.198i 0.405705 0.234234i −0.283238 0.959050i \(-0.591409\pi\)
0.688943 + 0.724816i \(0.258075\pi\)
\(480\) 0 0
\(481\) −49.0771 + 85.0040i −0.102031 + 0.176724i
\(482\) 216.025i 0.448185i
\(483\) 0 0
\(484\) 391.328 0.808529
\(485\) 342.224 + 197.583i 0.705617 + 0.407388i
\(486\) 0 0
\(487\) 358.745 + 621.365i 0.736643 + 1.27590i 0.953999 + 0.299810i \(0.0969234\pi\)
−0.217356 + 0.976092i \(0.569743\pi\)
\(488\) 245.762 + 141.891i 0.503611 + 0.290760i
\(489\) 0 0
\(490\) 0 0
\(491\) 274.002i 0.558050i 0.960284 + 0.279025i \(0.0900112\pi\)
−0.960284 + 0.279025i \(0.909989\pi\)
\(492\) 0 0
\(493\) −153.959 266.666i −0.312291 0.540904i
\(494\) 63.2704 36.5292i 0.128078 0.0739458i
\(495\) 0 0
\(496\) −68.6640 −0.138436
\(497\) 0 0
\(498\) 0 0
\(499\) 364.405 631.168i 0.730271 1.26487i −0.226496 0.974012i \(-0.572727\pi\)
0.956767 0.290854i \(-0.0939395\pi\)
\(500\) −449.477 + 259.505i −0.898953 + 0.519011i
\(501\) 0 0
\(502\) −252.000 + 436.477i −0.501992 + 0.869476i
\(503\) 594.657i 1.18222i −0.806590 0.591111i \(-0.798690\pi\)
0.806590 0.591111i \(-0.201310\pi\)
\(504\) 0 0
\(505\) −283.652 −0.561688
\(506\) 387.833 + 223.915i 0.766468 + 0.442520i
\(507\) 0 0
\(508\) 214.332 + 371.234i 0.421913 + 0.730775i
\(509\) 860.842 + 497.007i 1.69124 + 0.976439i 0.953518 + 0.301336i \(0.0974325\pi\)
0.737723 + 0.675103i \(0.235901\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −42.1216 72.9567i −0.0819486 0.141939i
\(515\) −34.6899 + 20.0282i −0.0673589 + 0.0388897i
\(516\) 0 0
\(517\) 301.992 0.584124
\(518\) 0 0
\(519\) 0 0
\(520\) 32.5020 56.2951i 0.0625038 0.108260i
\(521\) −35.3735 + 20.4229i −0.0678955 + 0.0391995i −0.533563 0.845760i \(-0.679147\pi\)
0.465668 + 0.884960i \(0.345814\pi\)
\(522\) 0 0
\(523\) 116.000 200.918i 0.221797 0.384164i −0.733556 0.679629i \(-0.762141\pi\)
0.955354 + 0.295464i \(0.0954743\pi\)
\(524\) 182.898i 0.349041i
\(525\) 0 0
\(526\) −10.4941 −0.0199507
\(527\) 384.560 + 222.026i 0.729716 + 0.421302i
\(528\) 0 0
\(529\) −106.168 183.888i −0.200696 0.347615i
\(530\) −932.333 538.283i −1.75912 1.01563i
\(531\) 0 0
\(532\) 0 0
\(533\) 40.6405i 0.0762487i
\(534\) 0 0
\(535\) 765.984 + 1326.72i 1.43175 + 2.47986i
\(536\) −89.8082 + 51.8508i −0.167553 + 0.0967365i
\(537\) 0 0
\(538\) −608.405 −1.13086
\(539\) 0 0
\(540\) 0 0
\(541\) −125.166 + 216.794i −0.231360 + 0.400728i −0.958209 0.286070i \(-0.907651\pi\)
0.726848 + 0.686798i \(0.240984\pi\)
\(542\) −50.4179 + 29.1088i −0.0930219 + 0.0537062i
\(543\) 0 0
\(544\) 73.1660 126.727i 0.134496 0.232954i
\(545\) 1582.25i 2.90321i
\(546\) 0 0
\(547\) 888.324 1.62399 0.811996 0.583662i \(-0.198381\pi\)
0.811996 + 0.583662i \(0.198381\pi\)
\(548\) 185.140 + 106.891i 0.337846 + 0.195056i
\(549\) 0 0
\(550\) 681.571 + 1180.52i 1.23922 + 2.14639i
\(551\) 206.173 + 119.034i 0.374180 + 0.216033i
\(552\) 0 0
\(553\) 0 0
\(554\) 45.2548i 0.0816874i
\(555\) 0 0
\(556\) −121.328 210.146i −0.218216 0.377961i
\(557\) −273.931 + 158.154i −0.491798 + 0.283940i −0.725320 0.688412i \(-0.758308\pi\)
0.233522 + 0.972351i \(0.424975\pi\)
\(558\) 0 0
\(559\) −112.356 −0.200994
\(560\) 0 0
\(561\) 0 0
\(562\) −12.0850 + 20.9318i −0.0215035 + 0.0372452i
\(563\) −50.6356 + 29.2345i −0.0899390 + 0.0519263i −0.544295 0.838894i \(-0.683203\pi\)
0.454356 + 0.890820i \(0.349869\pi\)
\(564\) 0 0
\(565\) 139.458 241.547i 0.246827 0.427518i
\(566\) 621.773i 1.09854i
\(567\) 0 0
\(568\) −50.3320 −0.0886127
\(569\) 191.968 + 110.833i 0.337378 + 0.194785i 0.659112 0.752045i \(-0.270932\pi\)
−0.321734 + 0.946830i \(0.604266\pi\)
\(570\) 0 0
\(571\) 243.822 + 422.312i 0.427009 + 0.739601i 0.996606 0.0823230i \(-0.0262339\pi\)
−0.569597 + 0.821924i \(0.692901\pi\)
\(572\) −79.6132 45.9647i −0.139184 0.0803579i
\(573\) 0 0
\(574\) 0 0
\(575\) 963.887i 1.67633i
\(576\) 0 0
\(577\) 243.664 + 422.039i 0.422295 + 0.731436i 0.996164 0.0875114i \(-0.0278914\pi\)
−0.573869 + 0.818947i \(0.694558\pi\)
\(578\) −465.597 + 268.812i −0.805531 + 0.465073i
\(579\) 0 0
\(580\) 211.822 0.365211
\(581\) 0 0
\(582\) 0 0
\(583\) −761.247 + 1318.52i −1.30574 + 2.26161i
\(584\) −70.8271 + 40.8920i −0.121279 + 0.0700206i
\(585\) 0 0
\(586\) 278.867 483.011i 0.475882 0.824251i
\(587\) 445.701i 0.759286i 0.925133 + 0.379643i \(0.123953\pi\)
−0.925133 + 0.379643i \(0.876047\pi\)
\(588\) 0 0
\(589\) −343.320 −0.582887
\(590\) 17.9694 + 10.3746i 0.0304565 + 0.0175841i
\(591\) 0 0
\(592\) −76.0000 131.636i −0.128378 0.222358i
\(593\) −239.584 138.324i −0.404020 0.233261i 0.284197 0.958766i \(-0.408273\pi\)
−0.688217 + 0.725505i \(0.741606\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 35.3498i 0.0593117i
\(597\) 0 0
\(598\) −32.5020 56.2951i −0.0543511 0.0941389i
\(599\) 71.3426 41.1897i 0.119103 0.0687641i −0.439265 0.898358i \(-0.644761\pi\)
0.558368 + 0.829593i \(0.311428\pi\)
\(600\) 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
\(604\) −50.8340 + 88.0471i −0.0841622 + 0.145773i
\(605\) 1507.69 870.463i 2.49204 1.43878i
\(606\) 0 0
\(607\) −38.4209 + 66.5470i −0.0632964 + 0.109633i −0.895937 0.444181i \(-0.853495\pi\)
0.832641 + 0.553814i \(0.186828\pi\)
\(608\) 113.137i 0.186081i
\(609\) 0 0
\(610\) 1262.48 2.06964
\(611\) −37.9623 21.9175i −0.0621314 0.0358716i
\(612\) 0 0
\(613\) −29.6640 51.3796i −0.0483916 0.0838167i 0.840815 0.541323i \(-0.182076\pi\)
−0.889207 + 0.457506i \(0.848743\pi\)
\(614\) 28.5806 + 16.5010i 0.0465482 + 0.0268746i
\(615\) 0 0
\(616\) 0 0
\(617\) 29.1143i 0.0471869i −0.999722 0.0235935i \(-0.992489\pi\)
0.999722 0.0235935i \(-0.00751073\pi\)
\(618\) 0 0
\(619\) −227.822 394.600i −0.368049 0.637479i 0.621212 0.783643i \(-0.286641\pi\)
−0.989260 + 0.146164i \(0.953307\pi\)
\(620\) −264.545 + 152.735i −0.426685 + 0.246347i
\(621\) 0 0
\(622\) −745.652 −1.19880
\(623\) 0 0
\(624\) 0 0
\(625\) −477.403 + 826.887i −0.763845 + 1.32302i
\(626\) −361.702 + 208.828i −0.577798 + 0.333592i
\(627\) 0 0
\(628\) 68.9961 119.505i 0.109866 0.190294i
\(629\) 982.987i 1.56278i
\(630\) 0 0
\(631\) −45.0039 −0.0713216 −0.0356608 0.999364i \(-0.511354\pi\)
−0.0356608 + 0.999364i \(0.511354\pi\)
\(632\) 289.853 + 167.347i 0.458628 + 0.264789i
\(633\) 0 0
\(634\) −75.9961 131.629i −0.119868 0.207617i
\(635\) 1651.53 + 953.513i 2.60084 + 1.50159i
\(636\) 0 0
\(637\) 0 0
\(638\) 299.562i 0.469533i
\(639\) 0 0
\(640\) 50.3320 + 87.1776i 0.0786438 + 0.136215i
\(641\) 555.315 320.611i 0.866327 0.500174i 0.000200774 1.00000i \(-0.499936\pi\)
0.866126 + 0.499826i \(0.166603\pi\)
\(642\) 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
\(646\) 365.830 633.636i 0.566300 0.980861i
\(647\) 155.538 89.7998i 0.240398 0.138794i −0.374961 0.927040i \(-0.622344\pi\)
0.615360 + 0.788246i \(0.289011\pi\)
\(648\) 0 0
\(649\) 14.6719 25.4125i 0.0226070 0.0391564i
\(650\) 197.864i 0.304406i
\(651\) 0 0
\(652\) 333.992 0.512258
\(653\) 339.562 + 196.046i 0.520003 + 0.300224i 0.736936 0.675963i \(-0.236272\pi\)
−0.216933 + 0.976186i \(0.569605\pi\)
\(654\) 0 0
\(655\) 406.834 + 704.657i 0.621121 + 1.07581i
\(656\) −54.5036 31.4676i −0.0830847 0.0479690i
\(657\) 0 0
\(658\) 0 0
\(659\) 1266.54i 1.92191i −0.276701 0.960956i \(-0.589241\pi\)
0.276701 0.960956i \(-0.410759\pi\)
\(660\) 0 0
\(661\) −458.822 794.703i −0.694133 1.20227i −0.970472 0.241214i \(-0.922454\pi\)
0.276339 0.961060i \(-0.410879\pi\)
\(662\) −334.956 + 193.387i −0.505975 + 0.292125i
\(663\) 0 0
\(664\) 340.664 0.513048
\(665\) 0 0
\(666\) 0 0
\(667\) 105.911 183.443i 0.158787 0.275028i
\(668\) 208.613 120.443i 0.312295 0.180304i
\(669\) 0 0
\(670\) −230.672 + 399.535i −0.344286 + 0.596322i
\(671\) 1785.41i 2.66083i
\(672\) 0 0
\(673\) −152.008 −0.225866 −0.112933 0.993603i \(-0.536025\pi\)
−0.112933 + 0.993603i \(0.536025\pi\)
\(674\) 417.841 + 241.241i 0.619943 + 0.357924i
\(675\) 0 0
\(676\) −162.328 281.160i −0.240130 0.415918i
\(677\) 141.316 + 81.5891i 0.208739 + 0.120516i 0.600725 0.799456i \(-0.294879\pi\)
−0.391986 + 0.919971i \(0.628212\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 650.997i 0.957348i
\(681\) 0 0
\(682\) 216.000 + 374.123i 0.316716 + 0.548567i
\(683\) 281.384 162.457i 0.411982 0.237858i −0.279659 0.960099i \(-0.590221\pi\)
0.691641 + 0.722241i \(0.256888\pi\)
\(684\) 0 0
\(685\) 951.061 1.38841
\(686\) 0 0
\(687\) 0 0
\(688\) 86.9961 150.682i 0.126448 0.219014i
\(689\) 191.387 110.497i 0.277775 0.160373i
\(690\) 0 0
\(691\) −609.490 + 1055.67i −0.882041 + 1.52774i −0.0329725 + 0.999456i \(0.510497\pi\)
−0.849068 + 0.528283i \(0.822836\pi\)
\(692\) 183.722i 0.265494i
\(693\) 0 0
\(694\) 164.502 0.237035
\(695\) −934.892 539.760i −1.34517 0.776633i
\(696\) 0 0
\(697\) 203.502 + 352.476i 0.291968 + 0.505704i
\(698\) 193.907 + 111.952i 0.277803 + 0.160390i
\(699\) 0 0
\(700\) 0 0
\(701\) 427.202i 0.609417i 0.952446 + 0.304709i \(0.0985591\pi\)
−0.952446 + 0.304709i \(0.901441\pi\)
\(702\) 0 0
\(703\) −380.000 658.179i −0.540541 0.936244i
\(704\) 123.288 71.1802i 0.175125 0.101108i
\(705\) 0 0
\(706\) −325.749 −0.461401
\(707\) 0 0
\(708\) 0 0
\(709\) −35.7490 + 61.9191i −0.0504217 + 0.0873330i −0.890135 0.455697i \(-0.849390\pi\)
0.839713 + 0.543031i \(0.182723\pi\)
\(710\) −193.916 + 111.958i −0.273122 + 0.157687i
\(711\) 0 0
\(712\) −197.247 + 341.642i −0.277032 + 0.479834i
\(713\) 305.470i 0.428429i
\(714\) 0 0
\(715\) −408.972 −0.571989
\(716\) −230.867 133.291i −0.322440 0.186161i
\(717\) 0 0
\(718\) −121.409 210.287i −0.169093 0.292879i
\(719\) −96.1545 55.5148i −0.133734 0.0772112i 0.431641 0.902046i \(-0.357935\pi\)
−0.565374 + 0.824835i \(0.691268\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 55.1543i 0.0763910i
\(723\) 0 0
\(724\) 83.0850 + 143.907i 0.114758 + 0.198767i
\(725\) 558.380 322.381i 0.770179 0.444663i
\(726\) 0 0
\(727\) −1338.82 −1.84157 −0.920783 0.390076i \(-0.872449\pi\)
−0.920783 + 0.390076i \(0.872449\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −181.919 + 315.093i −0.249204 + 0.431634i
\(731\) −974.461 + 562.606i −1.33305 + 0.769638i
\(732\) 0 0
\(733\) −24.5385 + 42.5020i −0.0334769 + 0.0579836i −0.882278 0.470728i \(-0.843991\pi\)
0.848802 + 0.528712i \(0.177325\pi\)
\(734\) 731.842i 0.997059i
\(735\) 0 0
\(736\) 100.664 0.136772
\(737\) 565.028 + 326.219i 0.766660 + 0.442631i
\(738\) 0 0
\(739\) −715.158 1238.69i −0.967738 1.67617i −0.702073 0.712105i \(-0.747742\pi\)
−0.265665 0.964065i \(-0.585592\pi\)
\(740\) −585.617 338.106i −0.791374 0.456900i
\(741\) 0 0
\(742\) 0 0
\(743\) 875.736i 1.17865i −0.807896 0.589325i \(-0.799394\pi\)
0.807896 0.589325i \(-0.200606\pi\)
\(744\) 0 0
\(745\) −78.6314 136.194i −0.105546 0.182810i
\(746\) −285.777 + 164.993i −0.383079 + 0.221171i
\(747\) 0 0
\(748\) −920.648 −1.23081
\(749\) 0 0
\(750\) 0 0
\(751\) −160.413 + 277.844i −0.213599 + 0.369965i −0.952838 0.303478i \(-0.901852\pi\)
0.739239 + 0.673443i \(0.235185\pi\)
\(752\) 58.7878 33.9411i 0.0781752 0.0451345i
\(753\) 0 0
\(754\) −21.7411 + 37.6568i −0.0288344 + 0.0499427i
\(755\) 452.297i 0.599069i
\(756\) 0 0
\(757\) 289.830 0.382867 0.191433 0.981506i \(-0.438686\pi\)
0.191433 + 0.981506i \(0.438686\pi\)
\(758\) −540.316 311.951i −0.712818 0.411545i
\(759\) 0 0
\(760\) 251.660 + 435.888i 0.331132 + 0.573537i
\(761\) −610.251 352.329i −0.801907 0.462981i 0.0422307 0.999108i \(-0.486554\pi\)
−0.844137 + 0.536127i \(0.819887\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 82.7231i 0.108276i
\(765\) 0 0
\(766\) 150.656 + 260.944i 0.196679 + 0.340658i
\(767\) −3.68870 + 2.12967i −0.00480926 + 0.00277663i
\(768\) 0 0
\(769\) −117.320 −0.152562 −0.0762810 0.997086i \(-0.524305\pi\)
−0.0762810 + 0.997086i \(0.524305\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 134.000 232.095i 0.173575 0.300641i
\(773\) −569.849 + 329.002i −0.737191 + 0.425618i −0.821047 0.570860i \(-0.806610\pi\)
0.0838559 + 0.996478i \(0.473276\pi\)
\(774\) 0 0
\(775\) −464.907 + 805.243i −0.599880 + 1.03902i
\(776\) 125.619i 0.161880i
\(777\) 0 0
\(778\) −799.166 −1.02721
\(779\) −272.518 157.338i −0.349830 0.201975i
\(780\) 0 0
\(781\) 158.332 + 274.239i 0.202730 + 0.351138i
\(782\) −563.780 325.498i −0.720946 0.416238i
\(783\) 0 0
\(784\) 0 0
\(785\) 613.894i 0.782031i
\(786\) 0 0
\(787\) 600.324 + 1039.79i 0.762801 + 1.32121i 0.941402 + 0.337288i \(0.109510\pi\)
−0.178601 + 0.983922i \(0.557157\pi\)
\(788\) −119.212 + 68.8269i −0.151284 + 0.0873438i
\(789\) 0 0
\(790\) 1488.97 1.88478
\(791\) 0 0
\(792\) 0 0
\(793\) −129.579 + 224.438i −0.163404 + 0.283023i
\(794\) 610.320 352.368i 0.768665 0.443789i
\(795\) 0 0
\(796\) −278.494 + 482.366i −0.349867 + 0.605987i
\(797\) 797.411i 1.00052i −0.865876 0.500258i \(-0.833239\pi\)
0.865876 0.500258i \(-0.166761\pi\)
\(798\) 0 0
\(799\) −438.996 −0.549432
\(800\) 265.358 + 153.205i 0.331698 + 0.191506i
\(801\) 0 0
\(802\) 136.749 + 236.856i 0.170510 + 0.295332i
\(803\) 445.609 + 257.272i 0.554930 + 0.320389i
\(804\) 0 0
\(805\) 0 0
\(806\) 62.7061i 0.0777991i
\(807\) 0 0
\(808\) 45.0850 + 78.0895i 0.0557982 + 0.0966454i
\(809\) 135.114 78.0082i 0.167014 0.0964254i −0.414163 0.910203i \(-0.635926\pi\)
0.581177 + 0.813777i \(0.302592\pi\)
\(810\) 0 0
\(811\) −598.316 −0.737751 −0.368876 0.929479i \(-0.620257\pi\)
−0.368876 + 0.929479i \(0.620257\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −478.154 + 828.187i −0.587413 + 1.01743i
\(815\) 1286.79 742.926i 1.57888 0.911566i
\(816\) 0 0
\(817\) 434.980 753.408i 0.532412 0.922164i
\(818\) 642.397i 0.785326i
\(819\) 0 0
\(820\) −279.984 −0.341444
\(821\) −849.552 490.489i −1.03478 0.597429i −0.116427 0.993199i \(-0.537144\pi\)
−0.918349 + 0.395770i \(0.870478\pi\)
\(822\) 0 0
\(823\) 215.668 + 373.548i 0.262051 + 0.453886i 0.966787 0.255584i \(-0.0822678\pi\)
−0.704736 + 0.709470i \(0.748934\pi\)
\(824\) 11.0275 + 6.36674i 0.0133829 + 0.00772663i
\(825\) 0 0
\(826\) 0 0
\(827\) 1219.41i 1.47449i 0.675623 + 0.737247i \(0.263875\pi\)
−0.675623 + 0.737247i \(0.736125\pi\)
\(828\) 0 0
\(829\) 385.041 + 666.910i 0.464464 + 0.804475i 0.999177 0.0405586i \(-0.0129137\pi\)
−0.534713 + 0.845034i \(0.679580\pi\)
\(830\) 1312.49 757.767i 1.58131 0.912972i
\(831\) 0 0
\(832\) −20.6640 −0.0248366
\(833\) 0 0
\(834\) 0 0
\(835\) 535.822 928.071i 0.641703 1.11146i
\(836\) 616.439 355.901i 0.737367 0.425719i
\(837\) 0 0
\(838\) −240.000 + 415.692i −0.286396 + 0.496053i
\(839\) 1310.03i 1.56142i −0.624894 0.780710i \(-0.714858\pi\)
0.624894 0.780710i \(-0.285142\pi\)
\(840\) 0 0
\(841\) 699.308 0.831520
\(842\) −302.904 174.882i −0.359744 0.207698i
\(843\) 0 0
\(844\) −211.498 366.325i −0.250590 0.434035i
\(845\) −1250.82 722.159i −1.48026 0.854626i
\(846\) 0 0
\(847\) 0 0
\(848\) 342.229i 0.403571i
\(849\) 0 0
\(850\) −990.778 1716.08i −1.16562 2.01891i
\(851\) −585.617 + 338.106i −0.688151 + 0.397304i
\(852\) 0 0
\(853\) 898.988 1.05391 0.526957 0.849892i \(-0.323333\pi\)
0.526957 + 0.849892i \(0.323333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 243.498 421.751i 0.284460 0.492700i
\(857\) 646.190 373.078i 0.754014 0.435330i −0.0731286 0.997323i \(-0.523298\pi\)
0.827142 + 0.561993i \(0.189965\pi\)
\(858\) 0 0
\(859\) 495.992 859.084i 0.577406 1.00010i −0.418369 0.908277i \(-0.637398\pi\)
0.995776 0.0918202i \(-0.0292685\pi\)
\(860\) 774.050i 0.900058i
\(861\) 0 0
\(862\) −645.474 −0.748810
\(863\) −181.361 104.709i −0.210152 0.121332i 0.391230 0.920293i \(-0.372050\pi\)
−0.601382 + 0.798961i \(0.705383\pi\)
\(864\) 0 0
\(865\) −408.668 707.834i −0.472449 0.818305i
\(866\) 781.368 + 451.123i 0.902272 + 0.520927i
\(867\) 0 0
\(868\) 0 0
\(869\) 2105.73i 2.42316i
\(870\) 0 0
\(871\) −47.3517 82.0156i −0.0543648 0.0941625i
\(872\) 435.593 251.490i 0.499533 0.288406i
\(873\) 0 0
\(874\) 503.320 0.575881
\(875\) 0 0
\(876\) 0 0
\(877\) 432.652 749.376i 0.493332 0.854476i −0.506638 0.862159i \(-0.669112\pi\)
0.999970 + 0.00768242i \(0.00244541\pi\)
\(878\) −960.379 + 554.475i −1.09383 + 0.631521i
\(879\) 0 0
\(880\) 316.664 548.478i 0.359846 0.623271i
\(881\) 995.046i 1.12945i 0.825279 + 0.564725i \(0.191018\pi\)
−0.825279 + 0.564725i \(0.808982\pi\)
\(882\) 0 0
\(883\) 101.474 0.114920 0.0574600 0.998348i \(-0.481700\pi\)
0.0574600 + 0.998348i \(0.481700\pi\)
\(884\) 115.731 + 66.8174i 0.130918 + 0.0755853i
\(885\) 0 0
\(886\) 333.911 + 578.351i 0.376875 + 0.652766i
\(887\) −930.191 537.046i −1.04869 0.605464i −0.126410 0.991978i \(-0.540346\pi\)
−0.922283 + 0.386514i \(0.873679\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 1755.01i 1.97192i
\(891\) 0 0
\(892\) 222.494 + 385.371i 0.249433 + 0.432030i
\(893\) 293.939 169.706i 0.329159 0.190040i
\(894\) 0 0
\(895\) −1185.96 −1.32510
\(896\) 0 0
\(897\) 0 0
\(898\) −523.154 + 906.130i −0.582577 + 1.00905i
\(899\) 176.959 102.167i 0.196840 0.113645i
\(900\) 0 0
\(901\) 1106.60 1916.69i 1.22819 2.12729i
\(902\) 395.958i 0.438977i
\(903\) 0 0
\(904\) −88.6640 −0.0980797
\(905\) 640.210 + 369.625i 0.707414 + 0.408426i
\(906\) 0 0
\(907\) 216.081 + 374.263i 0.238237 + 0.412639i 0.960209 0.279284i \(-0.0900971\pi\)
−0.721971 + 0.691923i \(0.756764\pi\)
\(908\) −176.363 101.823i −0.194233 0.112140i
\(909\) 0 0
\(910\) 0 0
\(911\) 104.984i 0.115241i −0.998339 0.0576205i \(-0.981649\pi\)
0.998339 0.0576205i \(-0.0183513\pi\)
\(912\) 0 0
\(913\) −1071.64 1856.14i −1.17376 2.03301i
\(914\) −304.134 + 175.592i −0.332750 + 0.192113i
\(915\) 0 0
\(916\) 326.170 0.356081
\(917\) 0 0
\(918\) 0 0
\(919\) 45.9190 79.5340i 0.0499662 0.0865440i −0.839961 0.542647i \(-0.817422\pi\)
0.889927 + 0.456103i \(0.150755\pi\)
\(920\) 387.833 223.915i 0.421557 0.243386i
\(921\) 0 0
\(922\) 251.708 435.972i 0.273003 0.472855i
\(923\) 45.9647i 0.0497993i
\(924\) 0 0
\(925\) −2058.31 −2.22520
\(926\) 7.75511 + 4.47741i 0.00837485 + 0.00483522i
\(927\) 0 0
\(928\) −33.6680 58.3147i −0.0362801 0.0628391i
\(929\) 1133.63 + 654.501i 1.22027 + 0.704522i 0.964975 0.262342i \(-0.0844949\pi\)
0.255293 + 0.966864i \(0.417828\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 725.715i 0.778664i
\(933\) 0 0
\(934\) 621.328 + 1076.17i 0.665233 + 1.15222i
\(935\) −3547.02 + 2047.87i −3.79361 + 2.19024i
\(936\) 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
\(940\) 150.996 261.533i 0.160634 0.278226i
\(941\) −1139.67 + 657.987i −1.21112 + 0.699243i −0.963004 0.269487i \(-0.913146\pi\)
−0.248120 + 0.968729i \(0.579813\pi\)
\(942\) 0 0
\(943\) −139.992 + 242.473i −0.148454 + 0.257130i
\(944\) 6.59595i 0.00698724i
\(945\) 0 0
\(946\) −1094.67 −1.15716
\(947\) −421.392 243.291i −0.444976 0.256907i 0.260730 0.965412i \(-0.416037\pi\)
−0.705706 + 0.708505i \(0.749370\pi\)
\(948\) 0 0
\(949\) −37.3438 64.6814i −0.0393507 0.0681574i
\(950\) 1326.79 + 766.023i 1.39662 + 0.806340i
\(951\) 0 0
\(952\) 0 0
\(953\) 43.3711i 0.0455100i 0.999741 + 0.0227550i \(0.00724377\pi\)
−0.999741 + 0.0227550i \(0.992756\pi\)
\(954\) 0 0
\(955\) 184.008 + 318.711i 0.192678 + 0.333729i
\(956\) −306.791 + 177.126i −0.320911 + 0.185278i
\(957\) 0 0
\(958\) −317.344 −0.331257
\(959\) 0 0
\(960\) 0 0
\(961\) 333.164 577.057i 0.346685 0.600476i
\(962\) 120.214 69.4055i 0.124962 0.0721471i
\(963\) 0 0
\(964\) 152.753 264.576i 0.158457 0.274456i
\(965\) 1192.27i 1.23551i
\(966\) 0 0
\(967\) 1648.99 1.70526 0.852631 0.522514i \(-0.175006\pi\)
0.852631 + 0.522514i \(0.175006\pi\)
\(968\) −479.277 276.711i −0.495121 0.285858i
\(969\) 0 0
\(970\) −279.425 483.978i −0.288067 0.498946i
\(971\) −448.881 259.162i −0.462287 0.266902i 0.250718 0.968060i \(-0.419333\pi\)
−0.713006 + 0.701158i \(0.752667\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1014.68i 1.04177i
\(975\) 0 0
\(976\) −200.664 347.560i −0.205598 0.356107i
\(977\) 95.2179 54.9741i 0.0974595 0.0562682i −0.450478 0.892787i \(-0.648746\pi\)
0.547938 + 0.836519i \(0.315413\pi\)
\(978\) 0 0
\(979\) 2481.96 2.53520
\(980\) 0 0
\(981\) 0 0
\(982\) 193.749 335.583i 0.197300 0.341734i
\(983\) −510.704 + 294.855i −0.519536 + 0.299954i −0.736745 0.676171i \(-0.763638\pi\)
0.217209 + 0.976125i \(0.430305\pi\)
\(984\) 0 0
\(985\) −306.195 + 530.345i −0.310858 + 0.538421i
\(986\) 435.463i 0.441646i
\(987\) 0 0
\(988\) −103.320 −0.104575
\(989\) −670.347 387.025i −0.677803 0.391330i
\(990\) 0 0
\(991\) −356.737 617.887i −0.359977 0.623498i 0.627980 0.778230i \(-0.283882\pi\)
−0.987957 + 0.154731i \(0.950549\pi\)
\(992\) 84.0959 + 48.5528i 0.0847741 + 0.0489444i
\(993\) 0 0
\(994\) 0 0
\(995\) 2477.91i 2.49036i
\(996\) 0 0
\(997\) −611.494 1059.14i −0.613334 1.06233i −0.990674 0.136251i \(-0.956495\pi\)
0.377340 0.926075i \(-0.376839\pi\)
\(998\) −892.607 + 515.347i −0.894396 + 0.516380i
\(999\) 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.863.2 8
3.2 odd 2 inner 882.3.s.e.863.3 8
7.2 even 3 126.3.b.a.71.3 yes 4
7.3 odd 6 882.3.s.i.557.4 8
7.4 even 3 inner 882.3.s.e.557.3 8
7.5 odd 6 882.3.b.f.197.4 4
7.6 odd 2 882.3.s.i.863.1 8
21.2 odd 6 126.3.b.a.71.2 4
21.5 even 6 882.3.b.f.197.1 4
21.11 odd 6 inner 882.3.s.e.557.2 8
21.17 even 6 882.3.s.i.557.1 8
21.20 even 2 882.3.s.i.863.4 8
28.23 odd 6 1008.3.d.a.449.1 4
35.2 odd 12 3150.3.c.b.449.3 8
35.9 even 6 3150.3.e.e.701.1 4
35.23 odd 12 3150.3.c.b.449.5 8
56.37 even 6 4032.3.d.i.449.4 4
56.51 odd 6 4032.3.d.j.449.4 4
63.2 odd 6 1134.3.q.c.701.1 8
63.16 even 3 1134.3.q.c.701.4 8
63.23 odd 6 1134.3.q.c.1079.4 8
63.58 even 3 1134.3.q.c.1079.1 8
84.23 even 6 1008.3.d.a.449.4 4
105.2 even 12 3150.3.c.b.449.8 8
105.23 even 12 3150.3.c.b.449.2 8
105.44 odd 6 3150.3.e.e.701.3 4
168.107 even 6 4032.3.d.j.449.1 4
168.149 odd 6 4032.3.d.i.449.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.b.a.71.2 4 21.2 odd 6
126.3.b.a.71.3 yes 4 7.2 even 3
882.3.b.f.197.1 4 21.5 even 6
882.3.b.f.197.4 4 7.5 odd 6
882.3.s.e.557.2 8 21.11 odd 6 inner
882.3.s.e.557.3 8 7.4 even 3 inner
882.3.s.e.863.2 8 1.1 even 1 trivial
882.3.s.e.863.3 8 3.2 odd 2 inner
882.3.s.i.557.1 8 21.17 even 6
882.3.s.i.557.4 8 7.3 odd 6
882.3.s.i.863.1 8 7.6 odd 2
882.3.s.i.863.4 8 21.20 even 2
1008.3.d.a.449.1 4 28.23 odd 6
1008.3.d.a.449.4 4 84.23 even 6
1134.3.q.c.701.1 8 63.2 odd 6
1134.3.q.c.701.4 8 63.16 even 3
1134.3.q.c.1079.1 8 63.58 even 3
1134.3.q.c.1079.4 8 63.23 odd 6
3150.3.c.b.449.2 8 105.23 even 12
3150.3.c.b.449.3 8 35.2 odd 12
3150.3.c.b.449.5 8 35.23 odd 12
3150.3.c.b.449.8 8 105.2 even 12
3150.3.e.e.701.1 4 35.9 even 6
3150.3.e.e.701.3 4 105.44 odd 6
4032.3.d.i.449.1 4 168.149 odd 6
4032.3.d.i.449.4 4 56.37 even 6
4032.3.d.j.449.1 4 168.107 even 6
4032.3.d.j.449.4 4 56.51 odd 6