Properties

Label 14.5.b.a.13.2
Level $14$
Weight $5$
Character 14.13
Analytic conductor $1.447$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [14,5,Mod(13,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.13");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 14.b (of order \(2\), degree \(1\), 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: \(1.44717948317\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.1308672.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 72x^{2} + 1278 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 13.2
Root \(-6.34371i\) of defining polynomial
Character \(\chi\) \(=\) 14.13
Dual form 14.5.b.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.82843 q^{2} +12.6874i q^{3} +8.00000 q^{4} +23.1980i q^{5} -35.8854i q^{6} +(6.45584 - 48.5729i) q^{7} -22.6274 q^{8} -79.9706 q^{9} +O(q^{10})\) \(q-2.82843 q^{2} +12.6874i q^{3} +8.00000 q^{4} +23.1980i q^{5} -35.8854i q^{6} +(6.45584 - 48.5729i) q^{7} -22.6274 q^{8} -79.9706 q^{9} -65.6139i q^{10} +191.823 q^{11} +101.499i q^{12} +48.5729i q^{13} +(-18.2599 + 137.385i) q^{14} -294.323 q^{15} +64.0000 q^{16} +181.977i q^{17} +226.191 q^{18} -599.915i q^{19} +185.584i q^{20} +(616.264 + 81.9080i) q^{21} -542.558 q^{22} -469.529 q^{23} -287.083i q^{24} +86.8519 q^{25} -137.385i q^{26} +13.0609i q^{27} +(51.6468 - 388.583i) q^{28} -338.881 q^{29} +832.471 q^{30} -267.556i q^{31} -181.019 q^{32} +2433.74i q^{33} -514.710i q^{34} +(1126.79 + 149.763i) q^{35} -639.765 q^{36} -668.530 q^{37} +1696.82i q^{38} -616.264 q^{39} -524.911i q^{40} -1323.85i q^{41} +(-1743.06 - 231.671i) q^{42} +1940.23 q^{43} +1534.59 q^{44} -1855.16i q^{45} +1328.03 q^{46} -2936.89i q^{47} +811.995i q^{48} +(-2317.64 - 627.158i) q^{49} -245.654 q^{50} -2308.82 q^{51} +388.583i q^{52} -1460.94 q^{53} -36.9418i q^{54} +4449.92i q^{55} +(-146.079 + 1099.08i) q^{56} +7611.38 q^{57} +958.501 q^{58} +1730.83i q^{59} -2354.58 q^{60} -246.343i q^{61} +756.763i q^{62} +(-516.277 + 3884.40i) q^{63} +512.000 q^{64} -1126.79 q^{65} -6883.67i q^{66} -1076.59 q^{67} +1455.82i q^{68} -5957.11i q^{69} +(-3187.05 - 423.593i) q^{70} -2276.39 q^{71} +1809.53 q^{72} +7106.94i q^{73} +1890.89 q^{74} +1101.93i q^{75} -4799.32i q^{76} +(1238.38 - 9317.41i) q^{77} +1743.06 q^{78} +7012.38 q^{79} +1484.67i q^{80} -6643.32 q^{81} +3744.40i q^{82} +1448.36i q^{83} +(4930.11 + 655.264i) q^{84} -4221.52 q^{85} -5487.81 q^{86} -4299.53i q^{87} -4340.47 q^{88} +2133.73i q^{89} +5247.18i q^{90} +(2359.32 + 313.579i) q^{91} -3756.23 q^{92} +3394.60 q^{93} +8306.77i q^{94} +13916.8 q^{95} -2296.67i q^{96} +5898.76i q^{97} +(6555.29 + 1773.87i) q^{98} -15340.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9} + 360 q^{11} - 288 q^{14} + 384 q^{15} + 256 q^{16} + 192 q^{18} + 768 q^{21} - 1152 q^{22} - 792 q^{23} - 2300 q^{25} - 608 q^{28} + 1224 q^{29} + 4416 q^{30} + 4032 q^{35} - 2016 q^{36} - 3896 q^{37} - 768 q^{39} - 4800 q^{42} + 3688 q^{43} + 2880 q^{44} + 3072 q^{46} - 1532 q^{49} - 7488 q^{50} - 11136 q^{51} + 5832 q^{53} - 2304 q^{56} + 12864 q^{57} + 7296 q^{58} + 3072 q^{60} + 3060 q^{63} + 2048 q^{64} - 4032 q^{65} - 1048 q^{67} - 1344 q^{70} - 21528 q^{71} + 1536 q^{72} - 3456 q^{74} + 3528 q^{77} + 4800 q^{78} + 12776 q^{79} - 29628 q^{81} + 6144 q^{84} + 16512 q^{85} - 11520 q^{86} - 9216 q^{88} + 5568 q^{91} - 6336 q^{92} + 38016 q^{93} + 36864 q^{95} + 21888 q^{98} - 29592 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82843 −0.707107
\(3\) 12.6874i 1.40971i 0.709350 + 0.704857i \(0.248989\pi\)
−0.709350 + 0.704857i \(0.751011\pi\)
\(4\) 8.00000 0.500000
\(5\) 23.1980i 0.927921i 0.885856 + 0.463960i \(0.153572\pi\)
−0.885856 + 0.463960i \(0.846428\pi\)
\(6\) 35.8854i 0.996818i
\(7\) 6.45584 48.5729i 0.131752 0.991283i
\(8\) −22.6274 −0.353553
\(9\) −79.9706 −0.987291
\(10\) 65.6139i 0.656139i
\(11\) 191.823 1.58532 0.792659 0.609666i \(-0.208696\pi\)
0.792659 + 0.609666i \(0.208696\pi\)
\(12\) 101.499i 0.704857i
\(13\) 48.5729i 0.287413i 0.989620 + 0.143707i \(0.0459022\pi\)
−0.989620 + 0.143707i \(0.954098\pi\)
\(14\) −18.2599 + 137.385i −0.0931627 + 0.700943i
\(15\) −294.323 −1.30810
\(16\) 64.0000 0.250000
\(17\) 181.977i 0.629680i 0.949145 + 0.314840i \(0.101951\pi\)
−0.949145 + 0.314840i \(0.898049\pi\)
\(18\) 226.191 0.698120
\(19\) 599.915i 1.66182i −0.556410 0.830908i \(-0.687822\pi\)
0.556410 0.830908i \(-0.312178\pi\)
\(20\) 185.584i 0.463960i
\(21\) 616.264 + 81.9080i 1.39742 + 0.185732i
\(22\) −542.558 −1.12099
\(23\) −469.529 −0.887578 −0.443789 0.896131i \(-0.646366\pi\)
−0.443789 + 0.896131i \(0.646366\pi\)
\(24\) 287.083i 0.498409i
\(25\) 86.8519 0.138963
\(26\) 137.385i 0.203232i
\(27\) 13.0609i 0.0179162i
\(28\) 51.6468 388.583i 0.0658760 0.495641i
\(29\) −338.881 −0.402951 −0.201475 0.979494i \(-0.564574\pi\)
−0.201475 + 0.979494i \(0.564574\pi\)
\(30\) 832.471 0.924968
\(31\) 267.556i 0.278414i −0.990263 0.139207i \(-0.955545\pi\)
0.990263 0.139207i \(-0.0444554\pi\)
\(32\) −181.019 −0.176777
\(33\) 2433.74i 2.23484i
\(34\) 514.710i 0.445251i
\(35\) 1126.79 + 149.763i 0.919832 + 0.122255i
\(36\) −639.765 −0.493645
\(37\) −668.530 −0.488334 −0.244167 0.969733i \(-0.578515\pi\)
−0.244167 + 0.969733i \(0.578515\pi\)
\(38\) 1696.82i 1.17508i
\(39\) −616.264 −0.405170
\(40\) 524.911i 0.328070i
\(41\) 1323.85i 0.787534i −0.919210 0.393767i \(-0.871172\pi\)
0.919210 0.393767i \(-0.128828\pi\)
\(42\) −1743.06 231.671i −0.988128 0.131333i
\(43\) 1940.23 1.04934 0.524671 0.851305i \(-0.324188\pi\)
0.524671 + 0.851305i \(0.324188\pi\)
\(44\) 1534.59 0.792659
\(45\) 1855.16i 0.916128i
\(46\) 1328.03 0.627613
\(47\) 2936.89i 1.32951i −0.747062 0.664755i \(-0.768536\pi\)
0.747062 0.664755i \(-0.231464\pi\)
\(48\) 811.995i 0.352428i
\(49\) −2317.64 627.158i −0.965283 0.261207i
\(50\) −245.654 −0.0982618
\(51\) −2308.82 −0.887668
\(52\) 388.583i 0.143707i
\(53\) −1460.94 −0.520091 −0.260046 0.965596i \(-0.583738\pi\)
−0.260046 + 0.965596i \(0.583738\pi\)
\(54\) 36.9418i 0.0126687i
\(55\) 4449.92i 1.47105i
\(56\) −146.079 + 1099.08i −0.0465813 + 0.350471i
\(57\) 7611.38 2.34268
\(58\) 958.501 0.284929
\(59\) 1730.83i 0.497223i 0.968603 + 0.248612i \(0.0799743\pi\)
−0.968603 + 0.248612i \(0.920026\pi\)
\(60\) −2354.58 −0.654051
\(61\) 246.343i 0.0662034i −0.999452 0.0331017i \(-0.989461\pi\)
0.999452 0.0331017i \(-0.0105385\pi\)
\(62\) 756.763i 0.196869i
\(63\) −516.277 + 3884.40i −0.130077 + 0.978684i
\(64\) 512.000 0.125000
\(65\) −1126.79 −0.266697
\(66\) 6883.67i 1.58027i
\(67\) −1076.59 −0.239828 −0.119914 0.992784i \(-0.538262\pi\)
−0.119914 + 0.992784i \(0.538262\pi\)
\(68\) 1455.82i 0.314840i
\(69\) 5957.11i 1.25123i
\(70\) −3187.05 423.593i −0.650419 0.0864476i
\(71\) −2276.39 −0.451574 −0.225787 0.974177i \(-0.572495\pi\)
−0.225787 + 0.974177i \(0.572495\pi\)
\(72\) 1809.53 0.349060
\(73\) 7106.94i 1.33363i 0.745221 + 0.666817i \(0.232344\pi\)
−0.745221 + 0.666817i \(0.767656\pi\)
\(74\) 1890.89 0.345305
\(75\) 1101.93i 0.195898i
\(76\) 4799.32i 0.830908i
\(77\) 1238.38 9317.41i 0.208869 1.57150i
\(78\) 1743.06 0.286499
\(79\) 7012.38 1.12360 0.561799 0.827274i \(-0.310109\pi\)
0.561799 + 0.827274i \(0.310109\pi\)
\(80\) 1484.67i 0.231980i
\(81\) −6643.32 −1.01255
\(82\) 3744.40i 0.556871i
\(83\) 1448.36i 0.210243i 0.994459 + 0.105121i \(0.0335231\pi\)
−0.994459 + 0.105121i \(0.966477\pi\)
\(84\) 4930.11 + 655.264i 0.698712 + 0.0928662i
\(85\) −4221.52 −0.584293
\(86\) −5487.81 −0.741997
\(87\) 4299.53i 0.568045i
\(88\) −4340.47 −0.560494
\(89\) 2133.73i 0.269376i 0.990888 + 0.134688i \(0.0430032\pi\)
−0.990888 + 0.134688i \(0.956997\pi\)
\(90\) 5247.18i 0.647800i
\(91\) 2359.32 + 313.579i 0.284908 + 0.0378673i
\(92\) −3756.23 −0.443789
\(93\) 3394.60 0.392484
\(94\) 8306.77i 0.940105i
\(95\) 13916.8 1.54203
\(96\) 2296.67i 0.249204i
\(97\) 5898.76i 0.626928i 0.949600 + 0.313464i \(0.101489\pi\)
−0.949600 + 0.313464i \(0.898511\pi\)
\(98\) 6555.29 + 1773.87i 0.682558 + 0.184701i
\(99\) −15340.2 −1.56517
\(100\) 694.816 0.0694816
\(101\) 9172.07i 0.899135i −0.893246 0.449567i \(-0.851578\pi\)
0.893246 0.449567i \(-0.148422\pi\)
\(102\) 6530.34 0.627676
\(103\) 3906.46i 0.368222i −0.982905 0.184111i \(-0.941059\pi\)
0.982905 0.184111i \(-0.0589406\pi\)
\(104\) 1099.08i 0.101616i
\(105\) −1900.10 + 14296.1i −0.172345 + 1.29670i
\(106\) 4132.15 0.367760
\(107\) −12141.3 −1.06047 −0.530233 0.847852i \(-0.677896\pi\)
−0.530233 + 0.847852i \(0.677896\pi\)
\(108\) 104.487i 0.00895809i
\(109\) 6808.34 0.573044 0.286522 0.958074i \(-0.407501\pi\)
0.286522 + 0.958074i \(0.407501\pi\)
\(110\) 12586.3i 1.04019i
\(111\) 8481.92i 0.688411i
\(112\) 413.174 3108.66i 0.0329380 0.247821i
\(113\) −4764.20 −0.373107 −0.186553 0.982445i \(-0.559732\pi\)
−0.186553 + 0.982445i \(0.559732\pi\)
\(114\) −21528.2 −1.65653
\(115\) 10892.1i 0.823602i
\(116\) −2711.05 −0.201475
\(117\) 3884.40i 0.283761i
\(118\) 4895.54i 0.351590i
\(119\) 8839.17 + 1174.82i 0.624191 + 0.0829615i
\(120\) 6659.77 0.462484
\(121\) 22155.2 1.51323
\(122\) 696.763i 0.0468129i
\(123\) 16796.2 1.11020
\(124\) 2140.45i 0.139207i
\(125\) 16513.6i 1.05687i
\(126\) 1460.25 10986.7i 0.0919787 0.692034i
\(127\) −27968.9 −1.73408 −0.867038 0.498242i \(-0.833979\pi\)
−0.867038 + 0.498242i \(0.833979\pi\)
\(128\) −1448.15 −0.0883883
\(129\) 24616.6i 1.47927i
\(130\) 3187.05 0.188583
\(131\) 24016.5i 1.39948i 0.714397 + 0.699741i \(0.246701\pi\)
−0.714397 + 0.699741i \(0.753299\pi\)
\(132\) 19469.9i 1.11742i
\(133\) −29139.6 3872.96i −1.64733 0.218947i
\(134\) 3045.05 0.169584
\(135\) −302.987 −0.0166248
\(136\) 4117.68i 0.222625i
\(137\) −4162.00 −0.221748 −0.110874 0.993834i \(-0.535365\pi\)
−0.110874 + 0.993834i \(0.535365\pi\)
\(138\) 16849.3i 0.884754i
\(139\) 26365.8i 1.36462i −0.731064 0.682309i \(-0.760976\pi\)
0.731064 0.682309i \(-0.239024\pi\)
\(140\) 9014.35 + 1198.10i 0.459916 + 0.0611277i
\(141\) 37261.5 1.87423
\(142\) 6438.59 0.319311
\(143\) 9317.41i 0.455641i
\(144\) −5118.12 −0.246823
\(145\) 7861.38i 0.373906i
\(146\) 20101.5i 0.943022i
\(147\) 7957.01 29404.9i 0.368227 1.36077i
\(148\) −5348.24 −0.244167
\(149\) −6576.57 −0.296229 −0.148114 0.988970i \(-0.547320\pi\)
−0.148114 + 0.988970i \(0.547320\pi\)
\(150\) 3116.72i 0.138521i
\(151\) −22930.4 −1.00568 −0.502839 0.864380i \(-0.667711\pi\)
−0.502839 + 0.864380i \(0.667711\pi\)
\(152\) 13574.5i 0.587540i
\(153\) 14552.8i 0.621677i
\(154\) −3502.67 + 26353.6i −0.147692 + 1.11122i
\(155\) 6206.77 0.258346
\(156\) −4930.11 −0.202585
\(157\) 37292.9i 1.51296i −0.654017 0.756480i \(-0.726918\pi\)
0.654017 0.756480i \(-0.273082\pi\)
\(158\) −19834.0 −0.794504
\(159\) 18535.5i 0.733180i
\(160\) 4199.29i 0.164035i
\(161\) −3031.21 + 22806.4i −0.116940 + 0.879841i
\(162\) 18790.2 0.715979
\(163\) 40854.0 1.53766 0.768828 0.639455i \(-0.220840\pi\)
0.768828 + 0.639455i \(0.220840\pi\)
\(164\) 10590.8i 0.393767i
\(165\) −56458.0 −2.07376
\(166\) 4096.58i 0.148664i
\(167\) 34774.9i 1.24690i 0.781862 + 0.623452i \(0.214270\pi\)
−0.781862 + 0.623452i \(0.785730\pi\)
\(168\) −13944.5 1853.37i −0.494064 0.0656663i
\(169\) 26201.7 0.917394
\(170\) 11940.3 0.413158
\(171\) 47975.6i 1.64070i
\(172\) 15521.9 0.524671
\(173\) 31600.1i 1.05583i −0.849296 0.527917i \(-0.822973\pi\)
0.849296 0.527917i \(-0.177027\pi\)
\(174\) 12160.9i 0.401668i
\(175\) 560.703 4218.65i 0.0183087 0.137752i
\(176\) 12276.7 0.396329
\(177\) −21959.8 −0.700942
\(178\) 6035.09i 0.190478i
\(179\) 22750.7 0.710048 0.355024 0.934857i \(-0.384473\pi\)
0.355024 + 0.934857i \(0.384473\pi\)
\(180\) 14841.3i 0.458064i
\(181\) 55434.4i 1.69208i 0.533116 + 0.846042i \(0.321021\pi\)
−0.533116 + 0.846042i \(0.678979\pi\)
\(182\) −6673.17 886.935i −0.201460 0.0267762i
\(183\) 3125.45 0.0933278
\(184\) 10624.2 0.313806
\(185\) 15508.6i 0.453136i
\(186\) −9601.37 −0.277528
\(187\) 34907.5i 0.998242i
\(188\) 23495.1i 0.664755i
\(189\) 634.405 + 84.3191i 0.0177600 + 0.00236049i
\(190\) −39362.8 −1.09038
\(191\) −50817.6 −1.39299 −0.696494 0.717562i \(-0.745258\pi\)
−0.696494 + 0.717562i \(0.745258\pi\)
\(192\) 6495.96i 0.176214i
\(193\) −1248.34 −0.0335134 −0.0167567 0.999860i \(-0.505334\pi\)
−0.0167567 + 0.999860i \(0.505334\pi\)
\(194\) 16684.2i 0.443305i
\(195\) 14296.1i 0.375966i
\(196\) −18541.2 5017.26i −0.482641 0.130603i
\(197\) 64454.6 1.66082 0.830408 0.557155i \(-0.188107\pi\)
0.830408 + 0.557155i \(0.188107\pi\)
\(198\) 43388.7 1.10674
\(199\) 2352.60i 0.0594076i 0.999559 + 0.0297038i \(0.00945641\pi\)
−0.999559 + 0.0297038i \(0.990544\pi\)
\(200\) −1965.24 −0.0491309
\(201\) 13659.1i 0.338088i
\(202\) 25942.5i 0.635784i
\(203\) −2187.77 + 16460.4i −0.0530895 + 0.399438i
\(204\) −18470.6 −0.443834
\(205\) 30710.6 0.730769
\(206\) 11049.2i 0.260372i
\(207\) 37548.5 0.876298
\(208\) 3108.66i 0.0718533i
\(209\) 115078.i 2.63450i
\(210\) 5374.30 40435.5i 0.121866 0.916905i
\(211\) −65056.4 −1.46125 −0.730626 0.682778i \(-0.760772\pi\)
−0.730626 + 0.682778i \(0.760772\pi\)
\(212\) −11687.5 −0.260046
\(213\) 28881.5i 0.636590i
\(214\) 34340.7 0.749863
\(215\) 45009.6i 0.973706i
\(216\) 295.534i 0.00633433i
\(217\) −12996.0 1727.30i −0.275987 0.0366816i
\(218\) −19256.9 −0.405203
\(219\) −90168.7 −1.88004
\(220\) 35599.4i 0.735524i
\(221\) −8839.17 −0.180978
\(222\) 23990.5i 0.486780i
\(223\) 30412.4i 0.611563i −0.952102 0.305781i \(-0.901082\pi\)
0.952102 0.305781i \(-0.0989177\pi\)
\(224\) −1168.63 + 8792.63i −0.0232907 + 0.175236i
\(225\) −6945.60 −0.137197
\(226\) 13475.2 0.263826
\(227\) 52125.5i 1.01158i −0.862658 0.505788i \(-0.831202\pi\)
0.862658 0.505788i \(-0.168798\pi\)
\(228\) 60891.0 1.17134
\(229\) 81280.2i 1.54994i 0.632000 + 0.774968i \(0.282234\pi\)
−0.632000 + 0.774968i \(0.717766\pi\)
\(230\) 30807.6i 0.582375i
\(231\) 118214. + 15711.9i 2.21536 + 0.294445i
\(232\) 7668.01 0.142465
\(233\) −41718.9 −0.768459 −0.384229 0.923238i \(-0.625533\pi\)
−0.384229 + 0.923238i \(0.625533\pi\)
\(234\) 10986.7i 0.200649i
\(235\) 68129.9 1.23368
\(236\) 13846.7i 0.248612i
\(237\) 88968.9i 1.58395i
\(238\) −25000.9 3322.89i −0.441370 0.0586627i
\(239\) −3936.55 −0.0689160 −0.0344580 0.999406i \(-0.510970\pi\)
−0.0344580 + 0.999406i \(0.510970\pi\)
\(240\) −18836.7 −0.327025
\(241\) 70511.5i 1.21402i 0.794694 + 0.607010i \(0.207631\pi\)
−0.794694 + 0.607010i \(0.792369\pi\)
\(242\) −62664.4 −1.07002
\(243\) 83228.7i 1.40949i
\(244\) 1970.74i 0.0331017i
\(245\) 14548.8 53764.8i 0.242379 0.895706i
\(246\) −47506.8 −0.785028
\(247\) 29139.6 0.477628
\(248\) 6054.11i 0.0984343i
\(249\) −18376.0 −0.296382
\(250\) 46707.4i 0.747318i
\(251\) 72042.3i 1.14351i 0.820424 + 0.571755i \(0.193737\pi\)
−0.820424 + 0.571755i \(0.806263\pi\)
\(252\) −4130.22 + 31075.2i −0.0650387 + 0.489342i
\(253\) −90066.6 −1.40709
\(254\) 79108.1 1.22618
\(255\) 53560.1i 0.823685i
\(256\) 4096.00 0.0625000
\(257\) 65615.5i 0.993436i −0.867912 0.496718i \(-0.834538\pi\)
0.867912 0.496718i \(-0.165462\pi\)
\(258\) 69626.1i 1.04600i
\(259\) −4315.92 + 32472.4i −0.0643390 + 0.484078i
\(260\) −9014.35 −0.133348
\(261\) 27100.5 0.397829
\(262\) 67929.0i 0.989583i
\(263\) −38706.1 −0.559588 −0.279794 0.960060i \(-0.590266\pi\)
−0.279794 + 0.960060i \(0.590266\pi\)
\(264\) 55069.3i 0.790136i
\(265\) 33890.8i 0.482604i
\(266\) 82419.2 + 10954.4i 1.16484 + 0.154819i
\(267\) −27071.5 −0.379743
\(268\) −8612.70 −0.119914
\(269\) 87226.9i 1.20544i 0.797952 + 0.602721i \(0.205917\pi\)
−0.797952 + 0.602721i \(0.794083\pi\)
\(270\) 856.977 0.0117555
\(271\) 105362.i 1.43465i −0.696739 0.717324i \(-0.745367\pi\)
0.696739 0.717324i \(-0.254633\pi\)
\(272\) 11646.6i 0.157420i
\(273\) −3978.50 + 29933.7i −0.0533820 + 0.401638i
\(274\) 11771.9 0.156800
\(275\) 16660.2 0.220301
\(276\) 47656.9i 0.625615i
\(277\) 36178.9 0.471515 0.235758 0.971812i \(-0.424243\pi\)
0.235758 + 0.971812i \(0.424243\pi\)
\(278\) 74573.7i 0.964931i
\(279\) 21396.6i 0.274876i
\(280\) −25496.4 3388.75i −0.325210 0.0432238i
\(281\) 99142.2 1.25558 0.627792 0.778381i \(-0.283959\pi\)
0.627792 + 0.778381i \(0.283959\pi\)
\(282\) −105391. −1.32528
\(283\) 4153.27i 0.0518581i 0.999664 + 0.0259291i \(0.00825441\pi\)
−0.999664 + 0.0259291i \(0.991746\pi\)
\(284\) −18211.1 −0.225787
\(285\) 176569.i 2.17382i
\(286\) 26353.6i 0.322187i
\(287\) −64302.9 8546.54i −0.780669 0.103759i
\(288\) 14476.2 0.174530
\(289\) 50405.2 0.603503
\(290\) 22235.3i 0.264392i
\(291\) −74840.1 −0.883788
\(292\) 56855.5i 0.666817i
\(293\) 20239.4i 0.235756i 0.993028 + 0.117878i \(0.0376092\pi\)
−0.993028 + 0.117878i \(0.962391\pi\)
\(294\) −22505.8 + 83169.7i −0.260376 + 0.962211i
\(295\) −40151.9 −0.461384
\(296\) 15127.1 0.172652
\(297\) 2505.39i 0.0284028i
\(298\) 18601.3 0.209465
\(299\) 22806.4i 0.255102i
\(300\) 8815.42i 0.0979491i
\(301\) 12525.8 94242.7i 0.138253 1.04019i
\(302\) 64857.1 0.711121
\(303\) 116370. 1.26752
\(304\) 38394.6i 0.415454i
\(305\) 5714.66 0.0614315
\(306\) 41161.7i 0.439592i
\(307\) 63269.8i 0.671305i −0.941986 0.335652i \(-0.891043\pi\)
0.941986 0.335652i \(-0.108957\pi\)
\(308\) 9907.05 74539.3i 0.104434 0.785749i
\(309\) 49563.0 0.519087
\(310\) −17555.4 −0.182679
\(311\) 14375.4i 0.148627i 0.997235 + 0.0743137i \(0.0236766\pi\)
−0.997235 + 0.0743137i \(0.976323\pi\)
\(312\) 13944.5 0.143249
\(313\) 36763.0i 0.375252i −0.982241 0.187626i \(-0.939921\pi\)
0.982241 0.187626i \(-0.0600792\pi\)
\(314\) 105480.i 1.06982i
\(315\) −90110.3 11976.6i −0.908142 0.120702i
\(316\) 56099.0 0.561799
\(317\) −125556. −1.24945 −0.624726 0.780844i \(-0.714789\pi\)
−0.624726 + 0.780844i \(0.714789\pi\)
\(318\) 52426.4i 0.518436i
\(319\) −65005.4 −0.638804
\(320\) 11877.4i 0.115990i
\(321\) 154041.i 1.49495i
\(322\) 8573.55 64506.1i 0.0826892 0.622142i
\(323\) 109171. 1.04641
\(324\) −53146.6 −0.506274
\(325\) 4218.65i 0.0399399i
\(326\) −115553. −1.08729
\(327\) 86380.2i 0.807828i
\(328\) 29955.2i 0.278435i
\(329\) −142653. 18960.1i −1.31792 0.175165i
\(330\) 159687. 1.46637
\(331\) 5376.54 0.0490735 0.0245367 0.999699i \(-0.492189\pi\)
0.0245367 + 0.999699i \(0.492189\pi\)
\(332\) 11586.9i 0.105121i
\(333\) 53462.7 0.482128
\(334\) 98358.3i 0.881694i
\(335\) 24974.7i 0.222541i
\(336\) 39440.9 + 5242.11i 0.349356 + 0.0464331i
\(337\) 2202.27 0.0193914 0.00969572 0.999953i \(-0.496914\pi\)
0.00969572 + 0.999953i \(0.496914\pi\)
\(338\) −74109.5 −0.648695
\(339\) 60445.4i 0.525974i
\(340\) −33772.1 −0.292146
\(341\) 51323.5i 0.441375i
\(342\) 135695.i 1.16015i
\(343\) −45425.2 + 108526.i −0.386108 + 0.922454i
\(344\) −43902.5 −0.370998
\(345\) 138193. 1.16104
\(346\) 89378.5i 0.746587i
\(347\) 222201. 1.84538 0.922691 0.385541i \(-0.125985\pi\)
0.922691 + 0.385541i \(0.125985\pi\)
\(348\) 34396.2i 0.284022i
\(349\) 102679.i 0.843006i 0.906827 + 0.421503i \(0.138497\pi\)
−0.906827 + 0.421503i \(0.861503\pi\)
\(350\) −1585.91 + 11932.1i −0.0129462 + 0.0974052i
\(351\) −634.405 −0.00514935
\(352\) −34723.7 −0.280247
\(353\) 62595.6i 0.502336i −0.967943 0.251168i \(-0.919185\pi\)
0.967943 0.251168i \(-0.0808147\pi\)
\(354\) 62111.8 0.495641
\(355\) 52807.7i 0.419025i
\(356\) 17069.8i 0.134688i
\(357\) −14905.4 + 112146.i −0.116952 + 0.879930i
\(358\) −64348.6 −0.502080
\(359\) 95505.9 0.741040 0.370520 0.928825i \(-0.379180\pi\)
0.370520 + 0.928825i \(0.379180\pi\)
\(360\) 41977.4i 0.323900i
\(361\) −229577. −1.76163
\(362\) 156792.i 1.19648i
\(363\) 281092.i 2.13322i
\(364\) 18874.6 + 2508.63i 0.142454 + 0.0189336i
\(365\) −164867. −1.23751
\(366\) −8840.12 −0.0659927
\(367\) 82330.9i 0.611267i 0.952149 + 0.305633i \(0.0988682\pi\)
−0.952149 + 0.305633i \(0.901132\pi\)
\(368\) −30049.9 −0.221895
\(369\) 105869.i 0.777525i
\(370\) 43864.9i 0.320415i
\(371\) −9431.58 + 70961.9i −0.0685230 + 0.515558i
\(372\) 27156.8 0.196242
\(373\) 130223. 0.935991 0.467995 0.883731i \(-0.344976\pi\)
0.467995 + 0.883731i \(0.344976\pi\)
\(374\) 98733.4i 0.705864i
\(375\) −209514. −1.48988
\(376\) 66454.2i 0.470053i
\(377\) 16460.4i 0.115813i
\(378\) −1794.37 238.491i −0.0125582 0.00166912i
\(379\) 192349. 1.33909 0.669546 0.742770i \(-0.266489\pi\)
0.669546 + 0.742770i \(0.266489\pi\)
\(380\) 111335. 0.771016
\(381\) 354853.i 2.44455i
\(382\) 143734. 0.984992
\(383\) 101933.i 0.694891i 0.937700 + 0.347446i \(0.112951\pi\)
−0.937700 + 0.347446i \(0.887049\pi\)
\(384\) 18373.3i 0.124602i
\(385\) 216145. + 28728.0i 1.45823 + 0.193813i
\(386\) 3530.84 0.0236975
\(387\) −155162. −1.03601
\(388\) 47190.1i 0.313464i
\(389\) 191074. 1.26271 0.631353 0.775495i \(-0.282500\pi\)
0.631353 + 0.775495i \(0.282500\pi\)
\(390\) 40435.5i 0.265848i
\(391\) 85443.7i 0.558890i
\(392\) 52442.3 + 14191.0i 0.341279 + 0.0923506i
\(393\) −304708. −1.97287
\(394\) −182305. −1.17437
\(395\) 162673.i 1.04261i
\(396\) −122722. −0.782585
\(397\) 201143.i 1.27622i −0.769947 0.638108i \(-0.779717\pi\)
0.769947 0.638108i \(-0.220283\pi\)
\(398\) 6654.16i 0.0420076i
\(399\) 49137.9 369706.i 0.308653 2.32226i
\(400\) 5558.52 0.0347408
\(401\) −39978.4 −0.248621 −0.124310 0.992243i \(-0.539672\pi\)
−0.124310 + 0.992243i \(0.539672\pi\)
\(402\) 38633.8i 0.239065i
\(403\) 12996.0 0.0800200
\(404\) 73376.6i 0.449567i
\(405\) 154112.i 0.939564i
\(406\) 6187.93 46557.1i 0.0375399 0.282445i
\(407\) −128240. −0.774165
\(408\) 52242.7 0.313838
\(409\) 80655.7i 0.482157i 0.970506 + 0.241078i \(0.0775011\pi\)
−0.970506 + 0.241078i \(0.922499\pi\)
\(410\) −86862.6 −0.516732
\(411\) 52805.0i 0.312602i
\(412\) 31251.7i 0.184111i
\(413\) 84071.6 + 11174.0i 0.492889 + 0.0655101i
\(414\) −106203. −0.619636
\(415\) −33599.1 −0.195088
\(416\) 8792.63i 0.0508080i
\(417\) 334514. 1.92372
\(418\) 325489.i 1.86288i
\(419\) 252034.i 1.43559i −0.696254 0.717795i \(-0.745151\pi\)
0.696254 0.717795i \(-0.254849\pi\)
\(420\) −15200.8 + 114369.i −0.0861725 + 0.648349i
\(421\) −84439.3 −0.476410 −0.238205 0.971215i \(-0.576559\pi\)
−0.238205 + 0.971215i \(0.576559\pi\)
\(422\) 184007. 1.03326
\(423\) 234864.i 1.31261i
\(424\) 33057.2 0.183880
\(425\) 15805.1i 0.0875023i
\(426\) 81689.1i 0.450137i
\(427\) −11965.6 1590.35i −0.0656263 0.00872242i
\(428\) −97130.2 −0.530233
\(429\) −118214. −0.642323
\(430\) 127306.i 0.688514i
\(431\) −127512. −0.686431 −0.343215 0.939257i \(-0.611516\pi\)
−0.343215 + 0.939257i \(0.611516\pi\)
\(432\) 835.898i 0.00447905i
\(433\) 233539.i 1.24562i 0.782375 + 0.622808i \(0.214008\pi\)
−0.782375 + 0.622808i \(0.785992\pi\)
\(434\) 36758.2 + 4885.55i 0.195153 + 0.0259378i
\(435\) 99740.6 0.527100
\(436\) 54466.7 0.286522
\(437\) 281678.i 1.47499i
\(438\) 255036. 1.32939
\(439\) 304238.i 1.57864i 0.613980 + 0.789322i \(0.289568\pi\)
−0.613980 + 0.789322i \(0.710432\pi\)
\(440\) 100690.i 0.520094i
\(441\) 185343. + 50154.1i 0.953015 + 0.257887i
\(442\) 25000.9 0.127971
\(443\) −87061.0 −0.443625 −0.221813 0.975089i \(-0.571197\pi\)
−0.221813 + 0.975089i \(0.571197\pi\)
\(444\) 67855.3i 0.344206i
\(445\) −49498.2 −0.249960
\(446\) 86019.3i 0.432440i
\(447\) 83439.7i 0.417597i
\(448\) 3305.39 24869.3i 0.0164690 0.123910i
\(449\) −91141.4 −0.452088 −0.226044 0.974117i \(-0.572579\pi\)
−0.226044 + 0.974117i \(0.572579\pi\)
\(450\) 19645.1 0.0970129
\(451\) 253944.i 1.24849i
\(452\) −38113.6 −0.186553
\(453\) 290928.i 1.41772i
\(454\) 147433.i 0.715292i
\(455\) −7274.41 + 54731.6i −0.0351378 + 0.264372i
\(456\) −172226. −0.828263
\(457\) −411928. −1.97237 −0.986187 0.165634i \(-0.947033\pi\)
−0.986187 + 0.165634i \(0.947033\pi\)
\(458\) 229895.i 1.09597i
\(459\) −2376.79 −0.0112815
\(460\) 87137.1i 0.411801i
\(461\) 157397.i 0.740617i 0.928909 + 0.370309i \(0.120748\pi\)
−0.928909 + 0.370309i \(0.879252\pi\)
\(462\) −334359. 44439.9i −1.56650 0.208204i
\(463\) 245557. 1.14549 0.572745 0.819734i \(-0.305879\pi\)
0.572745 + 0.819734i \(0.305879\pi\)
\(464\) −21688.4 −0.100738
\(465\) 78747.9i 0.364194i
\(466\) 117999. 0.543383
\(467\) 33069.2i 0.151632i 0.997122 + 0.0758158i \(0.0241561\pi\)
−0.997122 + 0.0758158i \(0.975844\pi\)
\(468\) 31075.2i 0.141880i
\(469\) −6950.28 + 52292.9i −0.0315978 + 0.237737i
\(470\) −192701. −0.872343
\(471\) 473151. 2.13284
\(472\) 39164.3i 0.175795i
\(473\) 372182. 1.66354
\(474\) 251642.i 1.12002i
\(475\) 52103.8i 0.230931i
\(476\) 70713.3 + 9398.55i 0.312095 + 0.0414808i
\(477\) 116832. 0.513482
\(478\) 11134.2 0.0487309
\(479\) 384277.i 1.67484i −0.546559 0.837421i \(-0.684063\pi\)
0.546559 0.837421i \(-0.315937\pi\)
\(480\) 53278.1 0.231242
\(481\) 32472.4i 0.140354i
\(482\) 199437.i 0.858442i
\(483\) −289354. 38458.2i −1.24032 0.164852i
\(484\) 177242. 0.756615
\(485\) −136840. −0.581739
\(486\) 235406.i 0.996657i
\(487\) −173526. −0.731657 −0.365829 0.930682i \(-0.619214\pi\)
−0.365829 + 0.930682i \(0.619214\pi\)
\(488\) 5574.10i 0.0234064i
\(489\) 518332.i 2.16765i
\(490\) −41150.3 + 152070.i −0.171388 + 0.633360i
\(491\) −20006.3 −0.0829858 −0.0414929 0.999139i \(-0.513211\pi\)
−0.0414929 + 0.999139i \(0.513211\pi\)
\(492\) 134369. 0.555099
\(493\) 61668.8i 0.253730i
\(494\) −82419.2 −0.337734
\(495\) 355863.i 1.45235i
\(496\) 17123.6i 0.0696036i
\(497\) −14696.0 + 110571.i −0.0594958 + 0.447638i
\(498\) 51975.1 0.209574
\(499\) −428368. −1.72035 −0.860174 0.510000i \(-0.829645\pi\)
−0.860174 + 0.510000i \(0.829645\pi\)
\(500\) 132108.i 0.528434i
\(501\) −441204. −1.75778
\(502\) 203766.i 0.808584i
\(503\) 36793.4i 0.145423i −0.997353 0.0727116i \(-0.976835\pi\)
0.997353 0.0727116i \(-0.0231653\pi\)
\(504\) 11682.0 87893.9i 0.0459893 0.346017i
\(505\) 212774. 0.834326
\(506\) 254747. 0.994965
\(507\) 332432.i 1.29326i
\(508\) −223751. −0.867038
\(509\) 137334.i 0.530080i 0.964237 + 0.265040i \(0.0853852\pi\)
−0.964237 + 0.265040i \(0.914615\pi\)
\(510\) 151491.i 0.582434i
\(511\) 345204. + 45881.3i 1.32201 + 0.175709i
\(512\) −11585.2 −0.0441942
\(513\) 7835.43 0.0297734
\(514\) 185589.i 0.702466i
\(515\) 90622.2 0.341681
\(516\) 196932.i 0.739636i
\(517\) 563363.i 2.10769i
\(518\) 12207.3 91845.8i 0.0454945 0.342294i
\(519\) 400923. 1.48842
\(520\) 25496.4 0.0942916
\(521\) 102775.i 0.378629i −0.981916 0.189315i \(-0.939373\pi\)
0.981916 0.189315i \(-0.0606266\pi\)
\(522\) −76651.9 −0.281308
\(523\) 314194.i 1.14867i 0.818621 + 0.574334i \(0.194739\pi\)
−0.818621 + 0.574334i \(0.805261\pi\)
\(524\) 192132.i 0.699741i
\(525\) 53523.7 + 7113.87i 0.194190 + 0.0258100i
\(526\) 109478. 0.395689
\(527\) 48689.2 0.175312
\(528\) 155760.i 0.558711i
\(529\) −59383.5 −0.212204
\(530\) 95857.8i 0.341252i
\(531\) 138416.i 0.490904i
\(532\) −233117. 30983.7i −0.823664 0.109474i
\(533\) 64302.9 0.226348
\(534\) 76569.7 0.268519
\(535\) 281654.i 0.984029i
\(536\) 24360.4 0.0847919
\(537\) 288647.i 1.00096i
\(538\) 246715.i 0.852376i
\(539\) −444578. 120303.i −1.53028 0.414096i
\(540\) −2423.90 −0.00831240
\(541\) 298384. 1.01948 0.509742 0.860327i \(-0.329741\pi\)
0.509742 + 0.860327i \(0.329741\pi\)
\(542\) 298009.i 1.01445i
\(543\) −703319. −2.38535
\(544\) 32941.4i 0.111313i
\(545\) 157940.i 0.531740i
\(546\) 11252.9 84665.3i 0.0377468 0.284001i
\(547\) 361462. 1.20806 0.604029 0.796963i \(-0.293561\pi\)
0.604029 + 0.796963i \(0.293561\pi\)
\(548\) −33296.0 −0.110874
\(549\) 19700.2i 0.0653620i
\(550\) −47122.3 −0.155776
\(551\) 203300.i 0.669629i
\(552\) 134794.i 0.442377i
\(553\) 45270.8 340611.i 0.148036 1.11380i
\(554\) −102329. −0.333412
\(555\) 196764. 0.638791
\(556\) 210926.i 0.682309i
\(557\) 112424. 0.362367 0.181183 0.983449i \(-0.442007\pi\)
0.181183 + 0.983449i \(0.442007\pi\)
\(558\) 60518.8i 0.194367i
\(559\) 94242.7i 0.301595i
\(560\) 72114.8 + 9584.82i 0.229958 + 0.0305638i
\(561\) −442886. −1.40724
\(562\) −280416. −0.887832
\(563\) 441530.i 1.39298i −0.717569 0.696488i \(-0.754745\pi\)
0.717569 0.696488i \(-0.245255\pi\)
\(564\) 298092. 0.937113
\(565\) 110520.i 0.346214i
\(566\) 11747.2i 0.0366692i
\(567\) −42888.3 + 322685.i −0.133405 + 1.00372i
\(568\) 51508.8 0.159656
\(569\) 397273. 1.22706 0.613529 0.789673i \(-0.289750\pi\)
0.613529 + 0.789673i \(0.289750\pi\)
\(570\) 499412.i 1.53713i
\(571\) −67235.8 −0.206219 −0.103109 0.994670i \(-0.532879\pi\)
−0.103109 + 0.994670i \(0.532879\pi\)
\(572\) 74539.3i 0.227821i
\(573\) 644744.i 1.96371i
\(574\) 181876. + 24173.3i 0.552016 + 0.0733688i
\(575\) −40779.5 −0.123341
\(576\) −40944.9 −0.123411
\(577\) 64756.1i 0.194504i 0.995260 + 0.0972521i \(0.0310053\pi\)
−0.995260 + 0.0972521i \(0.968995\pi\)
\(578\) −142567. −0.426741
\(579\) 15838.2i 0.0472443i
\(580\) 62891.0i 0.186953i
\(581\) 70351.0 + 9350.39i 0.208410 + 0.0276999i
\(582\) 211680. 0.624933
\(583\) −280242. −0.824510
\(584\) 160812.i 0.471511i
\(585\) 90110.3 0.263307
\(586\) 57245.8i 0.166705i
\(587\) 338967.i 0.983741i 0.870668 + 0.491870i \(0.163687\pi\)
−0.870668 + 0.491870i \(0.836313\pi\)
\(588\) 63656.1 235239.i 0.184113 0.680386i
\(589\) −160511. −0.462673
\(590\) 113567. 0.326248
\(591\) 817763.i 2.34128i
\(592\) −42785.9 −0.122084
\(593\) 255668.i 0.727054i −0.931584 0.363527i \(-0.881572\pi\)
0.931584 0.363527i \(-0.118428\pi\)
\(594\) 7086.30i 0.0200838i
\(595\) −27253.5 + 205051.i −0.0769817 + 0.579200i
\(596\) −52612.6 −0.148114
\(597\) −29848.4 −0.0837477
\(598\) 64506.1i 0.180384i
\(599\) 129521. 0.360982 0.180491 0.983577i \(-0.442231\pi\)
0.180491 + 0.983577i \(0.442231\pi\)
\(600\) 24933.8i 0.0692604i
\(601\) 377277.i 1.04451i 0.852790 + 0.522254i \(0.174909\pi\)
−0.852790 + 0.522254i \(0.825091\pi\)
\(602\) −35428.4 + 266559.i −0.0977595 + 0.735529i
\(603\) 86095.3 0.236780
\(604\) −183444. −0.502839
\(605\) 513957.i 1.40416i
\(606\) −329144. −0.896274
\(607\) 421091.i 1.14287i −0.820646 0.571437i \(-0.806386\pi\)
0.820646 0.571437i \(-0.193614\pi\)
\(608\) 108596.i 0.293770i
\(609\) −208840. 27757.1i −0.563093 0.0748410i
\(610\) −16163.5 −0.0434386
\(611\) 142653. 0.382119
\(612\) 116423.i 0.310839i
\(613\) 412173. 1.09688 0.548440 0.836190i \(-0.315222\pi\)
0.548440 + 0.836190i \(0.315222\pi\)
\(614\) 178954.i 0.474684i
\(615\) 389638.i 1.03018i
\(616\) −28021.4 + 210829.i −0.0738462 + 0.555608i
\(617\) −262676. −0.690002 −0.345001 0.938602i \(-0.612121\pi\)
−0.345001 + 0.938602i \(0.612121\pi\)
\(618\) −140185. −0.367050
\(619\) 373975.i 0.976026i 0.872836 + 0.488013i \(0.162278\pi\)
−0.872836 + 0.488013i \(0.837722\pi\)
\(620\) 49654.2 0.129173
\(621\) 6132.47i 0.0159020i
\(622\) 40659.7i 0.105095i
\(623\) 103641. + 13775.0i 0.267028 + 0.0354908i
\(624\) −39440.9 −0.101293
\(625\) −328799. −0.841726
\(626\) 103982.i 0.265343i
\(627\) 1.46004e6 3.71389
\(628\) 298344.i 0.756480i
\(629\) 121657.i 0.307494i
\(630\) 254871. + 33875.0i 0.642153 + 0.0853489i
\(631\) −408746. −1.02659 −0.513293 0.858214i \(-0.671574\pi\)
−0.513293 + 0.858214i \(0.671574\pi\)
\(632\) −158672. −0.397252
\(633\) 825397.i 2.05995i
\(634\) 355126. 0.883495
\(635\) 648824.i 1.60909i
\(636\) 148284.i 0.366590i
\(637\) 30462.8 112575.i 0.0750743 0.277435i
\(638\) 183863. 0.451703
\(639\) 182044. 0.445835
\(640\) 33594.3i 0.0820174i
\(641\) −528074. −1.28522 −0.642612 0.766192i \(-0.722149\pi\)
−0.642612 + 0.766192i \(0.722149\pi\)
\(642\) 435695.i 1.05709i
\(643\) 323445.i 0.782310i 0.920325 + 0.391155i \(0.127924\pi\)
−0.920325 + 0.391155i \(0.872076\pi\)
\(644\) −24249.6 + 182451.i −0.0584701 + 0.439921i
\(645\) −571055. −1.37265
\(646\) −308782. −0.739925
\(647\) 592372.i 1.41510i −0.706665 0.707548i \(-0.749801\pi\)
0.706665 0.707548i \(-0.250199\pi\)
\(648\) 150321. 0.357990
\(649\) 332015.i 0.788257i
\(650\) 11932.1i 0.0282417i
\(651\) 21915.0 164885.i 0.0517106 0.389063i
\(652\) 326832. 0.768828
\(653\) −329810. −0.773459 −0.386730 0.922193i \(-0.626395\pi\)
−0.386730 + 0.922193i \(0.626395\pi\)
\(654\) 244320.i 0.571221i
\(655\) −557135. −1.29861
\(656\) 84726.1i 0.196884i
\(657\) 568346.i 1.31669i
\(658\) 403483. + 53627.2i 0.931910 + 0.123861i
\(659\) −526737. −1.21290 −0.606448 0.795123i \(-0.707406\pi\)
−0.606448 + 0.795123i \(0.707406\pi\)
\(660\) −451664. −1.03688
\(661\) 144047.i 0.329686i 0.986320 + 0.164843i \(0.0527117\pi\)
−0.986320 + 0.164843i \(0.947288\pi\)
\(662\) −15207.2 −0.0347002
\(663\) 112146.i 0.255128i
\(664\) 32772.7i 0.0743320i
\(665\) 89845.0 675981.i 0.203166 1.52859i
\(666\) −151215. −0.340916
\(667\) 159115. 0.357650
\(668\) 278199.i 0.623452i
\(669\) 385855. 0.862128
\(670\) 70639.1i 0.157360i
\(671\) 47254.3i 0.104953i
\(672\) −111556. 14826.9i −0.247032 0.0328332i
\(673\) 620117. 1.36913 0.684563 0.728953i \(-0.259993\pi\)
0.684563 + 0.728953i \(0.259993\pi\)
\(674\) −6228.95 −0.0137118
\(675\) 1134.36i 0.00248969i
\(676\) 209613. 0.458697
\(677\) 626172.i 1.36621i 0.730322 + 0.683103i \(0.239370\pi\)
−0.730322 + 0.683103i \(0.760630\pi\)
\(678\) 170965.i 0.371920i
\(679\) 286520. + 38081.5i 0.621463 + 0.0825989i
\(680\) 95522.0 0.206579
\(681\) 661338. 1.42603
\(682\) 145165.i 0.312099i
\(683\) 185558. 0.397775 0.198888 0.980022i \(-0.436267\pi\)
0.198888 + 0.980022i \(0.436267\pi\)
\(684\) 383805.i 0.820348i
\(685\) 96550.1i 0.205765i
\(686\) 128482. 306957.i 0.273019 0.652273i
\(687\) −1.03124e6 −2.18497
\(688\) 124175. 0.262336
\(689\) 70961.9i 0.149481i
\(690\) −390869. −0.820981
\(691\) 548881.i 1.14953i 0.818317 + 0.574767i \(0.194907\pi\)
−0.818317 + 0.574767i \(0.805093\pi\)
\(692\) 252800.i 0.527917i
\(693\) −99034.1 + 745118.i −0.206214 + 1.55153i
\(694\) −628478. −1.30488
\(695\) 611634. 1.26626
\(696\) 97287.2i 0.200834i
\(697\) 240910. 0.495894
\(698\) 290420.i 0.596095i
\(699\) 529305.i 1.08331i
\(700\) 4485.62 33749.2i 0.00915433 0.0688759i
\(701\) 517501. 1.05311 0.526556 0.850140i \(-0.323483\pi\)
0.526556 + 0.850140i \(0.323483\pi\)
\(702\) 1794.37 0.00364114
\(703\) 401061.i 0.811522i
\(704\) 98213.6 0.198165
\(705\) 864393.i 1.73913i
\(706\) 177047.i 0.355205i
\(707\) −445514. 59213.5i −0.891297 0.118463i
\(708\) −175679. −0.350471
\(709\) 6035.96 0.0120075 0.00600377 0.999982i \(-0.498089\pi\)
0.00600377 + 0.999982i \(0.498089\pi\)
\(710\) 149363.i 0.296296i
\(711\) −560784. −1.10932
\(712\) 48280.7i 0.0952388i
\(713\) 125625.i 0.247115i
\(714\) 42158.9 317197.i 0.0826975 0.622204i
\(715\) −216145. −0.422799
\(716\) 182005. 0.355024
\(717\) 49944.6i 0.0971517i
\(718\) −270132. −0.523994
\(719\) 748658.i 1.44819i −0.689700 0.724095i \(-0.742258\pi\)
0.689700 0.724095i \(-0.257742\pi\)
\(720\) 118730.i 0.229032i
\(721\) −189748. 25219.5i −0.365012 0.0485139i
\(722\) 649343. 1.24566
\(723\) −894609. −1.71142
\(724\) 443475.i 0.846042i
\(725\) −29432.5 −0.0559953
\(726\) 795049.i 1.50841i
\(727\) 370335.i 0.700691i 0.936621 + 0.350345i \(0.113936\pi\)
−0.936621 + 0.350345i \(0.886064\pi\)
\(728\) −53385.4 7095.48i −0.100730 0.0133881i
\(729\) 517848. 0.974422
\(730\) 466314. 0.875050
\(731\) 353079.i 0.660750i
\(732\) 25003.6 0.0466639
\(733\) 144545.i 0.269027i −0.990912 0.134513i \(-0.957053\pi\)
0.990912 0.134513i \(-0.0429471\pi\)
\(734\) 232867.i 0.432231i
\(735\) 682136. + 184587.i 1.26269 + 0.341685i
\(736\) 84993.8 0.156903
\(737\) −206515. −0.380203
\(738\) 299442.i 0.549793i
\(739\) 4650.26 0.00851506 0.00425753 0.999991i \(-0.498645\pi\)
0.00425753 + 0.999991i \(0.498645\pi\)
\(740\) 124069.i 0.226568i
\(741\) 369706.i 0.673318i
\(742\) 26676.5 200710.i 0.0484531 0.364554i
\(743\) 500204. 0.906087 0.453043 0.891489i \(-0.350338\pi\)
0.453043 + 0.891489i \(0.350338\pi\)
\(744\) −76811.0 −0.138764
\(745\) 152563.i 0.274877i
\(746\) −368327. −0.661845
\(747\) 115826.i 0.207571i
\(748\) 279260.i 0.499121i
\(749\) −78382.2 + 589737.i −0.139718 + 1.05122i
\(750\) 592596. 1.05350
\(751\) 944576. 1.67478 0.837389 0.546608i \(-0.184081\pi\)
0.837389 + 0.546608i \(0.184081\pi\)
\(752\) 187961.i 0.332377i
\(753\) −914031. −1.61202
\(754\) 46557.1i 0.0818924i
\(755\) 531941.i 0.933189i
\(756\) 5075.24 + 674.553i 0.00888000 + 0.00118025i
\(757\) −654028. −1.14131 −0.570656 0.821189i \(-0.693311\pi\)
−0.570656 + 0.821189i \(0.693311\pi\)
\(758\) −544044. −0.946881
\(759\) 1.14271e6i 1.98360i
\(760\) −314902. −0.545191
\(761\) 643673.i 1.11147i −0.831361 0.555733i \(-0.812438\pi\)
0.831361 0.555733i \(-0.187562\pi\)
\(762\) 1.00368e6i 1.72856i
\(763\) 43953.6 330700.i 0.0754997 0.568049i
\(764\) −406541. −0.696494
\(765\) 337597. 0.576867
\(766\) 288310.i 0.491362i
\(767\) −84071.6 −0.142909
\(768\) 51967.7i 0.0881071i
\(769\) 103697.i 0.175354i 0.996149 + 0.0876768i \(0.0279443\pi\)
−0.996149 + 0.0876768i \(0.972056\pi\)
\(770\) −611352. 81255.1i −1.03112 0.137047i
\(771\) 832491. 1.40046
\(772\) −9986.72 −0.0167567
\(773\) 796380.i 1.33279i 0.745599 + 0.666394i \(0.232163\pi\)
−0.745599 + 0.666394i \(0.767837\pi\)
\(774\) 438863. 0.732567
\(775\) 23237.8i 0.0386893i
\(776\) 133474.i 0.221652i
\(777\) −411991. 54757.9i −0.682410 0.0906995i
\(778\) −540439. −0.892868
\(779\) −794195. −1.30874
\(780\) 114369.i 0.187983i
\(781\) −436664. −0.715889
\(782\) 241671.i 0.395195i
\(783\) 4426.10i 0.00721934i
\(784\) −148329. 40138.1i −0.241321 0.0653017i
\(785\) 865122. 1.40391
\(786\) 861843. 1.39503
\(787\) 1.16895e6i 1.88733i −0.330905 0.943664i \(-0.607354\pi\)
0.330905 0.943664i \(-0.392646\pi\)
\(788\) 515637. 0.830408
\(789\) 491081.i 0.788859i
\(790\) 460109.i 0.737237i
\(791\) −30756.9 + 231411.i −0.0491575 + 0.369854i
\(792\) 347110. 0.553371
\(793\) 11965.6 0.0190277
\(794\) 568919.i 0.902421i
\(795\) 429987. 0.680333
\(796\) 18820.8i 0.0297038i
\(797\) 808048.i 1.27210i 0.771649 + 0.636049i \(0.219432\pi\)
−0.771649 + 0.636049i \(0.780568\pi\)
\(798\) −138983. + 1.04569e6i −0.218251 + 1.64209i
\(799\) 534447. 0.837165
\(800\) −15721.9 −0.0245654
\(801\) 170635.i 0.265952i
\(802\) 113076. 0.175801
\(803\) 1.36328e6i 2.11423i
\(804\) 109273.i 0.169044i
\(805\) −529062. 70318.0i −0.816423 0.108511i
\(806\) −36758.2 −0.0565827
\(807\) −1.10668e6 −1.69933
\(808\) 207540.i 0.317892i
\(809\) −692708. −1.05841 −0.529204 0.848495i \(-0.677509\pi\)
−0.529204 + 0.848495i \(0.677509\pi\)
\(810\) 435894.i 0.664372i
\(811\) 382267.i 0.581200i −0.956845 0.290600i \(-0.906145\pi\)
0.956845 0.290600i \(-0.0938548\pi\)
\(812\) −17502.1 + 131683.i −0.0265448 + 0.199719i
\(813\) 1.33677e6 2.02244
\(814\) 362717. 0.547417
\(815\) 947732.i 1.42682i
\(816\) −147765. −0.221917
\(817\) 1.16398e6i 1.74381i
\(818\) 228129.i 0.340936i
\(819\) −188676. 25077.1i −0.281287 0.0373860i
\(820\) 245685. 0.365385
\(821\) 116392. 0.172678 0.0863392 0.996266i \(-0.472483\pi\)
0.0863392 + 0.996266i \(0.472483\pi\)
\(822\) 149355.i 0.221043i
\(823\) 640526. 0.945665 0.472832 0.881152i \(-0.343232\pi\)
0.472832 + 0.881152i \(0.343232\pi\)
\(824\) 88393.2i 0.130186i
\(825\) 211375.i 0.310561i
\(826\) −237790. 31604.8i −0.348525 0.0463227i
\(827\) −158299. −0.231455 −0.115727 0.993281i \(-0.536920\pi\)
−0.115727 + 0.993281i \(0.536920\pi\)
\(828\) 300388. 0.438149
\(829\) 680501.i 0.990192i 0.868838 + 0.495096i \(0.164867\pi\)
−0.868838 + 0.495096i \(0.835133\pi\)
\(830\) 95032.6 0.137948
\(831\) 459017.i 0.664701i
\(832\) 24869.3i 0.0359267i
\(833\) 114129. 421759.i 0.164477 0.607819i
\(834\) −946148. −1.36028
\(835\) −806709. −1.15703
\(836\) 920622.i 1.31725i
\(837\) 3494.53 0.00498812
\(838\) 712859.i 1.01512i
\(839\) 622397.i 0.884186i −0.896969 0.442093i \(-0.854236\pi\)
0.896969 0.442093i \(-0.145764\pi\)
\(840\) 42994.4 323484.i 0.0609331 0.458452i
\(841\) −592440. −0.837631
\(842\) 238831. 0.336873
\(843\) 1.25786e6i 1.77001i
\(844\) −520451. −0.730626
\(845\) 607827.i 0.851269i
\(846\) 664297.i 0.928157i
\(847\) 143031. 1.07614e6i 0.199371 1.50004i
\(848\) −93500.0 −0.130023
\(849\) −52694.2 −0.0731051
\(850\) 44703.6i 0.0618735i
\(851\) 313894. 0.433435
\(852\) 231052.i 0.318295i
\(853\) 826596.i 1.13604i −0.823013 0.568022i \(-0.807709\pi\)
0.823013 0.568022i \(-0.192291\pi\)
\(854\) 33843.7 + 4498.19i 0.0464048 + 0.00616768i
\(855\) −1.11294e6 −1.52243
\(856\) 274726. 0.374931
\(857\) 539076.i 0.733987i −0.930223 0.366994i \(-0.880387\pi\)
0.930223 0.366994i \(-0.119613\pi\)
\(858\) 334359. 0.454191
\(859\) 499964.i 0.677567i −0.940864 0.338783i \(-0.889985\pi\)
0.940864 0.338783i \(-0.110015\pi\)
\(860\) 360077.i 0.486853i
\(861\) 108433. 815838.i 0.146271 1.10052i
\(862\) 360659. 0.485380
\(863\) 1.16944e6 1.57021 0.785103 0.619365i \(-0.212610\pi\)
0.785103 + 0.619365i \(0.212610\pi\)
\(864\) 2364.28i 0.00316716i
\(865\) 733059. 0.979730
\(866\) 660548.i 0.880783i
\(867\) 639512.i 0.850766i
\(868\) −103968. 13818.4i −0.137994 0.0183408i
\(869\) 1.34514e6 1.78126
\(870\) −282109. −0.372716
\(871\) 52292.9i 0.0689297i
\(872\) −154055. −0.202602
\(873\) 471727.i 0.618960i
\(874\) 796705.i 1.04298i
\(875\) 802110. + 106609.i 1.04765 + 0.139244i
\(876\) −721350. −0.940021
\(877\) 187496. 0.243777 0.121888 0.992544i \(-0.461105\pi\)
0.121888 + 0.992544i \(0.461105\pi\)
\(878\) 860515.i 1.11627i
\(879\) −256786. −0.332349
\(880\) 284795.i 0.367762i
\(881\) 179673.i 0.231489i 0.993279 + 0.115745i \(0.0369254\pi\)
−0.993279 + 0.115745i \(0.963075\pi\)
\(882\) −524230. 141857.i −0.673883 0.182354i
\(883\) −1.04658e6 −1.34231 −0.671155 0.741317i \(-0.734201\pi\)
−0.671155 + 0.741317i \(0.734201\pi\)
\(884\) −70713.3 −0.0904892
\(885\) 509424.i 0.650419i
\(886\) 246246. 0.313691
\(887\) 1.30029e6i 1.65270i 0.563158 + 0.826349i \(0.309586\pi\)
−0.563158 + 0.826349i \(0.690414\pi\)
\(888\) 191924.i 0.243390i
\(889\) −180563. + 1.35853e6i −0.228468 + 1.71896i
\(890\) 140002. 0.176748
\(891\) −1.27434e6 −1.60521
\(892\) 243299.i 0.305781i
\(893\) −1.76188e6 −2.20940
\(894\) 236003.i 0.295286i
\(895\) 527770.i 0.658868i
\(896\) −9349.06 + 70341.0i −0.0116453 + 0.0876178i
\(897\) 289354. 0.359620
\(898\) 257787. 0.319675
\(899\) 90669.8i 0.112187i
\(900\) −55564.8 −0.0685985
\(901\) 265858.i 0.327491i
\(902\) 718263.i 0.882817i
\(903\) 1.19570e6 + 158921.i 1.46638 + 0.194897i
\(904\) 107802. 0.131913
\(905\) −1.28597e6 −1.57012
\(906\) 822869.i 1.00248i
\(907\) 1.18388e6 1.43911 0.719556 0.694435i \(-0.244346\pi\)
0.719556 + 0.694435i \(0.244346\pi\)
\(908\) 417004.i 0.505788i
\(909\) 733496.i 0.887708i
\(910\) 20575.1 154804.i 0.0248462 0.186939i
\(911\) −1.30731e6 −1.57522 −0.787612 0.616172i \(-0.788683\pi\)
−0.787612 + 0.616172i \(0.788683\pi\)
\(912\) 487128. 0.585671
\(913\) 277830.i 0.333301i
\(914\) 1.16511e6 1.39468
\(915\) 72504.3i 0.0866008i
\(916\) 650242.i 0.774968i
\(917\) 1.16655e6 + 155047.i 1.38728 + 0.184384i
\(918\) 6722.58 0.00797720
\(919\) 698775. 0.827382 0.413691 0.910417i \(-0.364239\pi\)
0.413691 + 0.910417i \(0.364239\pi\)
\(920\) 246461.i 0.291187i
\(921\) 802730. 0.946347
\(922\) 445185.i 0.523696i
\(923\) 110571.i 0.129789i
\(924\) 945711. + 125695.i 1.10768 + 0.147222i
\(925\) −58063.1 −0.0678605
\(926\) −694541. −0.809984
\(927\) 312402.i 0.363542i
\(928\) 61344.1 0.0712323
\(929\) 1.39460e6i 1.61591i −0.589244 0.807955i \(-0.700574\pi\)
0.589244 0.807955i \(-0.299426\pi\)
\(930\) 222733.i 0.257524i
\(931\) −376241. + 1.39039e6i −0.434077 + 1.60412i
\(932\) −333751. −0.384229
\(933\) −182387. −0.209522
\(934\) 93533.8i 0.107220i
\(935\) −809786. −0.926290
\(936\) 87893.9i 0.100325i
\(937\) 509380.i 0.580180i −0.956999 0.290090i \(-0.906315\pi\)
0.956999 0.290090i \(-0.0936852\pi\)
\(938\) 19658.4 147907.i 0.0223430 0.168106i
\(939\) 466428. 0.528997
\(940\) 545040. 0.616840
\(941\) 1.62505e6i 1.83522i −0.397486 0.917608i \(-0.630117\pi\)
0.397486 0.917608i \(-0.369883\pi\)
\(942\) −1.33827e6 −1.50814
\(943\) 621584.i 0.698998i
\(944\) 110773.i 0.124306i
\(945\) −1956.04 + 14716.9i −0.00219035 + 0.0164799i
\(946\) −1.05269e6 −1.17630
\(947\) 1.22462e6 1.36553 0.682763 0.730640i \(-0.260778\pi\)
0.682763 + 0.730640i \(0.260778\pi\)
\(948\) 711752.i 0.791976i
\(949\) −345204. −0.383304
\(950\) 147372.i 0.163293i
\(951\) 1.59298e6i 1.76137i
\(952\) −200007. 26583.1i −0.220685 0.0293313i
\(953\) −1.14847e6 −1.26454 −0.632269 0.774749i \(-0.717876\pi\)
−0.632269 + 0.774749i \(0.717876\pi\)
\(954\) −330451. −0.363086
\(955\) 1.17887e6i 1.29258i
\(956\) −31492.4 −0.0344580
\(957\) 824750.i 0.900531i
\(958\) 1.08690e6i 1.18429i
\(959\) −26869.2 + 202160.i −0.0292158 + 0.219815i
\(960\) −150693. −0.163513
\(961\) 851935. 0.922485
\(962\) 91845.8i 0.0992451i
\(963\) 970945. 1.04699
\(964\) 564092.i 0.607010i
\(965\) 28959.0i 0.0310978i
\(966\) 818416. + 108776.i 0.877041 + 0.116568i
\(967\) −733668. −0.784597 −0.392298 0.919838i \(-0.628320\pi\)
−0.392298 + 0.919838i \(0.628320\pi\)
\(968\) −501315. −0.535008
\(969\) 1.38510e6i 1.47514i
\(970\) 387041. 0.411352
\(971\) 786749.i 0.834445i −0.908804 0.417223i \(-0.863004\pi\)
0.908804 0.417223i \(-0.136996\pi\)
\(972\) 665830.i 0.704743i
\(973\) −1.28066e6 170213.i −1.35272 0.179791i
\(974\) 490807. 0.517360
\(975\) −53523.7 −0.0563037
\(976\) 15765.9i 0.0165508i
\(977\) 837039. 0.876913 0.438457 0.898752i \(-0.355525\pi\)
0.438457 + 0.898752i \(0.355525\pi\)
\(978\) 1.46606e6i 1.53276i
\(979\) 409299.i 0.427046i
\(980\) 116390. 430118.i 0.121190 0.447853i
\(981\) −544467. −0.565761
\(982\) 56586.3 0.0586798
\(983\) 644129.i 0.666600i −0.942821 0.333300i \(-0.891838\pi\)
0.942821 0.333300i \(-0.108162\pi\)
\(984\) −380054. −0.392514
\(985\) 1.49522e6i 1.54111i
\(986\) 174426.i 0.179414i
\(987\) 240554. 1.80990e6i 0.246933 1.85789i
\(988\) 233117. 0.238814
\(989\) −910996. −0.931374
\(990\) 1.00653e6i 1.02697i
\(991\) 92517.5 0.0942056 0.0471028 0.998890i \(-0.485001\pi\)
0.0471028 + 0.998890i \(0.485001\pi\)
\(992\) 48432.8i 0.0492172i
\(993\) 68214.4i 0.0691795i
\(994\) 41566.6 312741.i 0.0420699 0.316528i
\(995\) −54575.7 −0.0551256
\(996\) −147008. −0.148191
\(997\) 366383.i 0.368591i −0.982871 0.184295i \(-0.941000\pi\)
0.982871 0.184295i \(-0.0590003\pi\)
\(998\) 1.21161e6 1.21647
\(999\) 8731.60i 0.00874909i
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 14.5.b.a.13.2 yes 4
3.2 odd 2 126.5.c.a.55.3 4
4.3 odd 2 112.5.c.c.97.1 4
5.2 odd 4 350.5.d.a.349.4 8
5.3 odd 4 350.5.d.a.349.5 8
5.4 even 2 350.5.b.a.251.3 4
7.2 even 3 98.5.d.d.31.3 8
7.3 odd 6 98.5.d.d.19.3 8
7.4 even 3 98.5.d.d.19.4 8
7.5 odd 6 98.5.d.d.31.4 8
7.6 odd 2 inner 14.5.b.a.13.1 4
8.3 odd 2 448.5.c.f.321.4 4
8.5 even 2 448.5.c.e.321.1 4
12.11 even 2 1008.5.f.h.433.2 4
21.20 even 2 126.5.c.a.55.4 4
28.27 even 2 112.5.c.c.97.4 4
35.13 even 4 350.5.d.a.349.8 8
35.27 even 4 350.5.d.a.349.1 8
35.34 odd 2 350.5.b.a.251.4 4
56.13 odd 2 448.5.c.e.321.4 4
56.27 even 2 448.5.c.f.321.1 4
84.83 odd 2 1008.5.f.h.433.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.5.b.a.13.1 4 7.6 odd 2 inner
14.5.b.a.13.2 yes 4 1.1 even 1 trivial
98.5.d.d.19.3 8 7.3 odd 6
98.5.d.d.19.4 8 7.4 even 3
98.5.d.d.31.3 8 7.2 even 3
98.5.d.d.31.4 8 7.5 odd 6
112.5.c.c.97.1 4 4.3 odd 2
112.5.c.c.97.4 4 28.27 even 2
126.5.c.a.55.3 4 3.2 odd 2
126.5.c.a.55.4 4 21.20 even 2
350.5.b.a.251.3 4 5.4 even 2
350.5.b.a.251.4 4 35.34 odd 2
350.5.d.a.349.1 8 35.27 even 4
350.5.d.a.349.4 8 5.2 odd 4
350.5.d.a.349.5 8 5.3 odd 4
350.5.d.a.349.8 8 35.13 even 4
448.5.c.e.321.1 4 8.5 even 2
448.5.c.e.321.4 4 56.13 odd 2
448.5.c.f.321.1 4 56.27 even 2
448.5.c.f.321.4 4 8.3 odd 2
1008.5.f.h.433.2 4 12.11 even 2
1008.5.f.h.433.3 4 84.83 odd 2