Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{10} + 112x^{8} - 368x^{6} + 928x^{4} - 256x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.12 | ||
Root | \(1.61829 + 0.934317i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.4.b.a.107.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72087 | + | 0.772562i | 0.961974 | + | 0.273142i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.80630 | + | 4.20408i | 0.850787 | + | 0.525510i | ||||
\(5\) | 3.33155i | 0.297983i | 0.988838 | + | 0.148992i | \(0.0476027\pi\) | ||||
−0.988838 | + | 0.148992i | \(0.952397\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.9016i | 0.912600i | 0.889826 | + | 0.456300i | \(0.150826\pi\) | ||||
−0.889826 | + | 0.456300i | \(0.849174\pi\) | |||||||
\(8\) | 15.2712 | + | 16.6971i | 0.674896 | + | 0.737913i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.57383 | + | 9.06473i | −0.0813917 | + | 0.286652i | ||||
\(11\) | 16.8325 | 0.461380 | 0.230690 | − | 0.973027i | \(-0.425902\pi\) | ||||
0.230690 | + | 0.973027i | \(0.425902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.0775 | 0.535020 | 0.267510 | − | 0.963555i | \(-0.413799\pi\) | ||||
0.267510 | + | 0.963555i | \(0.413799\pi\) | |||||||
\(14\) | −13.0575 | + | 45.9871i | −0.249269 | + | 0.877897i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 28.6514 | + | 57.2285i | 0.447677 | + | 0.894195i | ||||
\(17\) | − | 116.919i | − | 1.66806i | −0.551722 | − | 0.834028i | \(-0.686029\pi\) | ||
0.551722 | − | 0.834028i | \(-0.313971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 85.4801i | 1.03213i | 0.856549 | + | 0.516065i | \(0.172604\pi\) | ||||
−0.856549 | + | 0.516065i | \(0.827396\pi\) | |||||||
\(20\) | −14.0061 | + | 22.6755i | −0.156593 | + | 0.253520i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 45.7990 | + | 13.0041i | 0.443836 | + | 0.126022i | ||||
\(23\) | −158.740 | −1.43911 | −0.719555 | − | 0.694436i | \(-0.755654\pi\) | ||||
−0.719555 | + | 0.694436i | \(0.755654\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 113.901 | 0.911206 | ||||||||
\(26\) | 68.2328 | + | 19.3739i | 0.514675 | + | 0.146136i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −71.0557 | + | 115.037i | −0.479581 | + | 0.776428i | ||||
\(29\) | − | 269.955i | − | 1.72860i | −0.502976 | − | 0.864300i | \(-0.667762\pi\) | ||
0.502976 | − | 0.864300i | \(-0.332238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 36.0884i | − | 0.209086i | −0.994520 | − | 0.104543i | \(-0.966662\pi\) | ||
0.994520 | − | 0.104543i | \(-0.0333380\pi\) | |||||||
\(32\) | 33.7442 | + | 177.846i | 0.186412 | + | 0.982472i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 90.3269 | − | 318.121i | 0.455616 | − | 1.60463i | ||||
\(35\) | −56.3085 | −0.271939 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −353.780 | −1.57192 | −0.785960 | − | 0.618277i | \(-0.787831\pi\) | ||||
−0.785960 | + | 0.618277i | \(0.787831\pi\) | |||||||
\(38\) | −66.0386 | + | 232.580i | −0.281918 | + | 0.992882i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −55.6272 | + | 50.8767i | −0.219886 | + | 0.201108i | ||||
\(41\) | − | 144.415i | − | 0.550093i | −0.961431 | − | 0.275046i | \(-0.911307\pi\) | ||
0.961431 | − | 0.275046i | \(-0.0886932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 368.186i | − | 1.30576i | −0.757460 | − | 0.652881i | \(-0.773560\pi\) | ||
0.757460 | − | 0.652881i | \(-0.226440\pi\) | |||||||
\(44\) | 114.567 | + | 70.7651i | 0.392536 | + | 0.242460i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −431.911 | − | 122.636i | −1.38439 | − | 0.393081i | ||||
\(47\) | 397.333 | 1.23313 | 0.616563 | − | 0.787305i | \(-0.288524\pi\) | ||||
0.616563 | + | 0.787305i | \(0.288524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.3363 | 0.167161 | ||||||||
\(50\) | 309.909 | + | 87.9954i | 0.876556 | + | 0.248888i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 170.685 | + | 105.428i | 0.455188 | + | 0.281158i | ||||
\(53\) | 96.0857i | 0.249026i | 0.992218 | + | 0.124513i | \(0.0397369\pi\) | ||||
−0.992218 | + | 0.124513i | \(0.960263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.0783i | 0.137484i | ||||||||
\(56\) | −282.207 | + | 258.107i | −0.673419 | + | 0.615910i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 208.557 | − | 734.514i | 0.472153 | − | 1.66287i | ||||
\(59\) | −294.902 | −0.650727 | −0.325364 | − | 0.945589i | \(-0.605487\pi\) | ||||
−0.325364 | + | 0.945589i | \(0.605487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 146.724 | 0.307969 | 0.153984 | − | 0.988073i | \(-0.450789\pi\) | ||||
0.153984 | + | 0.988073i | \(0.450789\pi\) | |||||||
\(62\) | 27.8805 | − | 98.1920i | 0.0571102 | − | 0.201135i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −45.5837 | + | 509.967i | −0.0890307 | + | 0.996029i | ||||
\(65\) | 83.5471i | 0.159427i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 301.433i | − | 0.549641i | −0.961496 | − | 0.274820i | \(-0.911382\pi\) | ||
0.961496 | − | 0.274820i | \(-0.0886184\pi\) | |||||||
\(68\) | 491.536 | − | 795.784i | 0.876581 | − | 1.41916i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −153.208 | − | 43.5018i | −0.261599 | − | 0.0742780i | ||||
\(71\) | −687.794 | −1.14966 | −0.574832 | − | 0.818272i | \(-0.694933\pi\) | ||||
−0.574832 | + | 0.818272i | \(0.694933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −312.138 | −0.500452 | −0.250226 | − | 0.968187i | \(-0.580505\pi\) | ||||
−0.250226 | + | 0.968187i | \(0.580505\pi\) | |||||||
\(74\) | −962.590 | − | 273.317i | −1.51215 | − | 0.429357i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −359.365 | + | 581.803i | −0.542395 | + | 0.878123i | ||||
\(77\) | 284.496i | 0.421056i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 602.063i | 0.857436i | 0.903438 | + | 0.428718i | \(0.141035\pi\) | ||||
−0.903438 | + | 0.428718i | \(0.858965\pi\) | |||||||
\(80\) | −190.660 | + | 95.4535i | −0.266455 | + | 0.133400i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 111.569 | − | 392.934i | 0.150253 | − | 0.529175i | ||||
\(83\) | 1334.44 | 1.76475 | 0.882373 | − | 0.470551i | \(-0.155945\pi\) | ||||
0.882373 | + | 0.470551i | \(0.155945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 389.521 | 0.497053 | ||||||||
\(86\) | 284.446 | − | 1001.79i | 0.356658 | − | 1.25611i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 257.051 | + | 281.053i | 0.311384 | + | 0.340458i | ||||
\(89\) | 856.292i | 1.01985i | 0.860218 | + | 0.509926i | \(0.170327\pi\) | ||||
−0.860218 | + | 0.509926i | \(0.829673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 423.850i | 0.488259i | ||||||||
\(92\) | −1080.43 | − | 667.355i | −1.22438 | − | 0.756267i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1081.09 | + | 306.964i | 1.18624 | + | 0.336818i | ||||
\(95\) | −284.781 | −0.307557 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 218.564 | 0.228782 | 0.114391 | − | 0.993436i | \(-0.463508\pi\) | ||||
0.114391 | + | 0.993436i | \(0.463508\pi\) | |||||||
\(98\) | 156.005 | + | 44.2959i | 0.160805 | + | 0.0456587i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 775.242 | + | 478.848i | 0.775242 | + | 0.478848i | ||||
\(101\) | 793.625i | 0.781868i | 0.920419 | + | 0.390934i | \(0.127848\pi\) | ||||
−0.920419 | + | 0.390934i | \(0.872152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1245.59i | 1.19157i | 0.803145 | + | 0.595784i | \(0.203159\pi\) | ||||
−0.803145 | + | 0.595784i | \(0.796841\pi\) | |||||||
\(104\) | 382.963 | + | 418.721i | 0.361083 | + | 0.394798i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −74.2321 | + | 261.437i | −0.0680194 | + | 0.239557i | ||||
\(107\) | 95.7189 | 0.0864813 | 0.0432406 | − | 0.999065i | \(-0.486232\pi\) | ||||
0.0432406 | + | 0.999065i | \(0.486232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1349.09 | 1.18550 | 0.592749 | − | 0.805387i | \(-0.298043\pi\) | ||||
0.592749 | + | 0.805387i | \(0.298043\pi\) | |||||||
\(110\) | −43.3239 | + | 152.582i | −0.0375525 | + | 0.132256i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −967.252 | + | 484.253i | −0.816042 | + | 0.408550i | ||||
\(113\) | 1885.41i | 1.56960i | 0.619750 | + | 0.784799i | \(0.287234\pi\) | ||||
−0.619750 | + | 0.784799i | \(0.712766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 528.850i | − | 0.428831i | ||||||
\(116\) | 1134.91 | − | 1837.40i | 0.908398 | − | 1.47067i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −802.390 | − | 227.830i | −0.625983 | − | 0.177741i | ||||
\(119\) | 1976.11 | 1.52227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1047.67 | −0.787128 | ||||||||
\(122\) | 399.217 | + | 113.353i | 0.296258 | + | 0.0841191i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 151.719 | − | 245.629i | 0.109877 | − | 0.177888i | ||||
\(125\) | 795.911i | 0.569507i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 714.330i | − | 0.499106i | −0.968361 | − | 0.249553i | \(-0.919716\pi\) | ||
0.968361 | − | 0.249553i | \(-0.0802838\pi\) | |||||||
\(128\) | −518.008 | + | 1352.34i | −0.357702 | + | 0.933836i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −64.5453 | + | 227.321i | −0.0435461 | + | 0.153364i | ||||
\(131\) | −2153.89 | −1.43654 | −0.718268 | − | 0.695766i | \(-0.755065\pi\) | ||||
−0.718268 | + | 0.695766i | \(0.755065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1444.75 | −0.941922 | ||||||||
\(134\) | 232.876 | − | 820.161i | 0.150130 | − | 0.528740i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1952.20 | − | 1785.48i | 1.23088 | − | 1.12576i | ||||
\(137\) | − | 2053.68i | − | 1.28071i | −0.768079 | − | 0.640356i | \(-0.778787\pi\) | ||
0.768079 | − | 0.640356i | \(-0.221213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2000.40i | − | 1.22066i | −0.792148 | − | 0.610329i | \(-0.791037\pi\) | ||
0.792148 | − | 0.610329i | \(-0.208963\pi\) | |||||||
\(140\) | −383.253 | − | 236.726i | −0.231363 | − | 0.142907i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1871.40 | − | 531.363i | −1.10595 | − | 0.314021i | ||||
\(143\) | 422.117 | 0.246847 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 899.370 | 0.515094 | ||||||||
\(146\) | −849.287 | − | 241.146i | −0.481421 | − | 0.136694i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2407.93 | − | 1487.32i | −1.33737 | − | 0.826060i | ||||
\(149\) | − | 988.026i | − | 0.543236i | −0.962405 | − | 0.271618i | \(-0.912441\pi\) | ||
0.962405 | − | 0.271618i | \(-0.0875588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1630.56i | 0.878764i | 0.898300 | + | 0.439382i | \(0.144803\pi\) | ||||
−0.898300 | + | 0.439382i | \(0.855197\pi\) | |||||||
\(152\) | −1427.27 | + | 1305.38i | −0.761622 | + | 0.696580i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −219.790 | + | 774.076i | −0.115008 | + | 0.405044i | ||||
\(155\) | 120.231 | 0.0623042 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −690.002 | −0.350752 | −0.175376 | − | 0.984501i | \(-0.556114\pi\) | ||||
−0.175376 | + | 0.984501i | \(0.556114\pi\) | |||||||
\(158\) | −465.131 | + | 1638.14i | −0.234202 | + | 0.824831i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −592.505 | + | 112.420i | −0.292760 | + | 0.0555476i | ||||
\(161\) | − | 2682.95i | − | 1.31333i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3414.58i | − | 1.64080i | −0.571790 | − | 0.820400i | \(-0.693751\pi\) | ||
0.571790 | − | 0.820400i | \(-0.306249\pi\) | |||||||
\(164\) | 607.132 | − | 982.930i | 0.289080 | − | 0.468012i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3630.84 | + | 1030.94i | 1.69764 | + | 0.482026i | ||||
\(167\) | −1372.95 | −0.636180 | −0.318090 | − | 0.948061i | \(-0.603041\pi\) | ||||
−0.318090 | + | 0.948061i | \(0.603041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1568.12 | −0.713754 | ||||||||
\(170\) | 1059.84 | + | 300.929i | 0.478152 | + | 0.135766i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1547.88 | − | 2505.98i | 0.686192 | − | 1.11093i | ||||
\(173\) | − | 1118.25i | − | 0.491441i | −0.969341 | − | 0.245721i | \(-0.920975\pi\) | ||
0.969341 | − | 0.245721i | \(-0.0790246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1925.10i | 0.831567i | ||||||||
\(176\) | 482.273 | + | 963.297i | 0.206549 | + | 0.412564i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −661.539 | + | 2329.86i | −0.278564 | + | 0.981071i | ||||
\(179\) | −1755.59 | −0.733067 | −0.366534 | − | 0.930405i | \(-0.619456\pi\) | ||||
−0.366534 | + | 0.930405i | \(0.619456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 312.973 | 0.128525 | 0.0642626 | − | 0.997933i | \(-0.479530\pi\) | ||||
0.0642626 | + | 0.997933i | \(0.479530\pi\) | |||||||
\(182\) | −327.450 | + | 1153.24i | −0.133364 | + | 0.469692i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2424.14 | − | 2650.49i | −0.971249 | − | 1.06194i | ||||
\(185\) | − | 1178.64i | − | 0.468406i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1968.03i | − | 0.769608i | ||||||
\(188\) | 2704.36 | + | 1670.42i | 1.04913 | + | 0.648021i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −774.854 | − | 220.011i | −0.295862 | − | 0.0840068i | ||||
\(191\) | −2024.40 | −0.766915 | −0.383457 | − | 0.923559i | \(-0.625267\pi\) | ||||
−0.383457 | + | 0.923559i | \(0.625267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1138.00 | 0.424431 | 0.212216 | − | 0.977223i | \(-0.431932\pi\) | ||||
0.212216 | + | 0.977223i | \(0.431932\pi\) | |||||||
\(194\) | 594.686 | + | 168.854i | 0.220082 | + | 0.0624899i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 390.248 | + | 241.047i | 0.142219 | + | 0.0878450i | ||||
\(197\) | − | 2345.77i | − | 0.848370i | −0.905576 | − | 0.424185i | \(-0.860561\pi\) | ||
0.905576 | − | 0.424185i | \(-0.139439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2839.16i | 1.01137i | 0.862718 | + | 0.505686i | \(0.168760\pi\) | ||||
−0.862718 | + | 0.505686i | \(0.831240\pi\) | |||||||
\(200\) | 1739.40 | + | 1901.81i | 0.614969 | + | 0.672391i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −613.124 | + | 2159.35i | −0.213561 | + | 0.752136i | ||||
\(203\) | 4562.67 | 1.57752 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 481.126 | 0.163918 | ||||||||
\(206\) | −962.294 | + | 3389.09i | −0.325467 | + | 1.14626i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 718.505 | + | 1435.15i | 0.239516 | + | 0.478412i | ||||
\(209\) | 1438.84i | 0.476204i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 256.564i | − | 0.0837091i | −0.999124 | − | 0.0418545i | \(-0.986673\pi\) | ||
0.999124 | − | 0.0418545i | \(-0.0133266\pi\) | |||||||
\(212\) | −403.952 | + | 653.988i | −0.130866 | + | 0.211868i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 260.439 | + | 73.9488i | 0.0831927 | + | 0.0236217i | ||||
\(215\) | 1226.63 | 0.389095 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 609.952 | 0.190812 | ||||||||
\(218\) | 3670.70 | + | 1042.25i | 1.14042 | + | 0.323809i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −235.758 | + | 381.685i | −0.0722490 | + | 0.116969i | ||||
\(221\) | − | 2932.03i | − | 0.892443i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4020.58i | 1.20734i | 0.797233 | + | 0.603672i | \(0.206296\pi\) | ||||
−0.797233 | + | 0.603672i | \(0.793704\pi\) | |||||||
\(224\) | −3005.89 | + | 570.330i | −0.896604 | + | 0.170120i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1456.60 | + | 5129.97i | −0.428723 | + | 1.50991i | ||||
\(227\) | −2958.44 | −0.865016 | −0.432508 | − | 0.901630i | \(-0.642371\pi\) | ||||
−0.432508 | + | 0.901630i | \(0.642371\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 226.069 | 0.0652360 | 0.0326180 | − | 0.999468i | \(-0.489616\pi\) | ||||
0.0326180 | + | 0.999468i | \(0.489616\pi\) | |||||||
\(230\) | 408.569 | − | 1438.93i | 0.117132 | − | 0.412524i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4507.46 | − | 4122.53i | 1.27556 | − | 1.16663i | ||||
\(233\) | 2356.56i | 0.662591i | 0.943527 | + | 0.331295i | \(0.107486\pi\) | ||||
−0.943527 | + | 0.331295i | \(0.892514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1323.74i | 0.367451i | ||||||||
\(236\) | −2007.19 | − | 1239.79i | −0.553630 | − | 0.341964i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5376.75 | + | 1526.67i | 1.46438 | + | 0.415795i | ||||
\(239\) | 2191.70 | 0.593176 | 0.296588 | − | 0.955006i | \(-0.404151\pi\) | ||||
0.296588 | + | 0.955006i | \(0.404151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6532.08 | 1.74593 | 0.872963 | − | 0.487787i | \(-0.162196\pi\) | ||||
0.872963 | + | 0.487787i | \(0.162196\pi\) | |||||||
\(242\) | −2850.57 | − | 809.388i | −0.757197 | − | 0.214998i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 998.647 | + | 616.840i | 0.262016 | + | 0.161841i | ||||
\(245\) | 191.019i | 0.0498113i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2143.63i | 0.552210i | ||||||||
\(248\) | 602.571 | − | 551.112i | 0.154287 | − | 0.141111i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −614.890 | + | 2165.57i | −0.155556 | + | 0.547851i | ||||
\(251\) | 34.6697 | 0.00871844 | 0.00435922 | − | 0.999990i | \(-0.498612\pi\) | ||||
0.00435922 | + | 0.999990i | \(0.498612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2671.98 | −0.663977 | ||||||||
\(254\) | 551.864 | − | 1943.60i | 0.136327 | − | 0.480127i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2454.20 | + | 3279.35i | −0.599170 | + | 0.800622i | ||||
\(257\) | − | 3945.92i | − | 0.957742i | −0.877885 | − | 0.478871i | \(-0.841046\pi\) | ||
0.877885 | − | 0.478871i | \(-0.158954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5979.44i | − | 1.43453i | ||||||
\(260\) | −351.239 | + | 568.647i | −0.0837805 | + | 0.135638i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5860.46 | − | 1664.01i | −1.38191 | − | 0.392378i | ||||
\(263\) | −6558.79 | −1.53777 | −0.768883 | − | 0.639390i | \(-0.779187\pi\) | ||||
−0.768883 | + | 0.639390i | \(0.779187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −320.115 | −0.0742056 | ||||||||
\(266\) | −3930.98 | − | 1116.16i | −0.906104 | − | 0.257278i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1267.25 | − | 2051.64i | 0.288842 | − | 0.467627i | ||||
\(269\) | 3741.27i | 0.847991i | 0.905664 | + | 0.423995i | \(0.139373\pi\) | ||||
−0.905664 | + | 0.423995i | \(0.860627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6011.98i | 1.34761i | 0.738910 | + | 0.673804i | \(0.235341\pi\) | ||||
−0.738910 | + | 0.673804i | \(0.764659\pi\) | |||||||
\(272\) | 6691.08 | − | 3349.88i | 1.49157 | − | 0.746751i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1586.59 | − | 5587.79i | 0.349816 | − | 1.23201i | ||||
\(275\) | 1917.23 | 0.420412 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4524.48 | −0.981407 | −0.490704 | − | 0.871327i | \(-0.663260\pi\) | ||||
−0.490704 | + | 0.871327i | \(0.663260\pi\) | |||||||
\(278\) | 1545.43 | − | 5442.83i | 0.333413 | − | 1.17424i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −859.896 | − | 940.187i | −0.183531 | − | 0.200668i | ||||
\(281\) | 4251.22i | 0.902514i | 0.892394 | + | 0.451257i | \(0.149024\pi\) | ||||
−0.892394 | + | 0.451257i | \(0.850976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4433.04i | − | 0.931154i | −0.885007 | − | 0.465577i | \(-0.845847\pi\) | ||
0.885007 | − | 0.465577i | \(-0.154153\pi\) | |||||||
\(284\) | −4681.33 | − | 2891.54i | −0.978119 | − | 0.604160i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1148.53 | + | 326.111i | 0.237461 | + | 0.0674243i | ||||
\(287\) | 2440.84 | 0.502015 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8756.99 | −1.78241 | ||||||||
\(290\) | 2447.07 | + | 694.819i | 0.495507 | + | 0.140694i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2124.50 | − | 1312.25i | −0.425778 | − | 0.262993i | ||||
\(293\) | 7734.73i | 1.54221i | 0.636708 | + | 0.771105i | \(0.280296\pi\) | ||||
−0.636708 | + | 0.771105i | \(0.719704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 982.480i | − | 0.193906i | ||||||
\(296\) | −5402.63 | − | 5907.08i | −1.06088 | − | 1.15994i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 763.311 | − | 2688.29i | 0.148381 | − | 0.522579i | ||||
\(299\) | −3980.80 | −0.769952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6222.92 | 1.19164 | ||||||||
\(302\) | −1259.71 | + | 4436.56i | −0.240027 | + | 0.845348i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4891.89 | + | 2449.12i | −0.922926 | + | 0.462061i | ||||
\(305\) | 488.819i | 0.0917694i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8510.18i | − | 1.58209i | −0.611759 | − | 0.791045i | \(-0.709538\pi\) | ||
0.611759 | − | 0.791045i | \(-0.290462\pi\) | |||||||
\(308\) | −1196.04 | + | 1936.36i | −0.221269 | + | 0.358229i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 327.132 | + | 92.8855i | 0.0599350 | + | 0.0170179i | ||||
\(311\) | 8133.65 | 1.48301 | 0.741507 | − | 0.670945i | \(-0.234112\pi\) | ||||
0.741507 | + | 0.670945i | \(0.234112\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5066.73 | 0.914979 | 0.457489 | − | 0.889215i | \(-0.348749\pi\) | ||||
0.457489 | + | 0.889215i | \(0.348749\pi\) | |||||||
\(314\) | −1877.41 | − | 533.069i | −0.337415 | − | 0.0958052i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2531.13 | + | 4097.82i | −0.450591 | + | 0.729495i | ||||
\(317\) | 4122.54i | 0.730425i | 0.930924 | + | 0.365212i | \(0.119004\pi\) | ||||
−0.930924 | + | 0.365212i | \(0.880996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4544.01i | − | 0.797542i | ||||||
\(320\) | −1698.98 | − | 151.865i | −0.296800 | − | 0.0265296i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2072.75 | − | 7299.98i | 0.358726 | − | 1.26339i | ||||
\(323\) | 9994.22 | 1.72165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2856.35 | 0.487513 | ||||||||
\(326\) | 2637.97 | − | 9290.63i | 0.448171 | − | 1.57841i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2411.30 | − | 2205.38i | 0.405921 | − | 0.371256i | ||||
\(329\) | 6715.55i | 1.12535i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3819.96i | 0.634332i | 0.948370 | + | 0.317166i | \(0.102731\pi\) | ||||
−0.948370 | + | 0.317166i | \(0.897269\pi\) | |||||||
\(332\) | 9082.60 | + | 5610.10i | 1.50142 | + | 0.927392i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3735.62 | − | 1060.69i | −0.611988 | − | 0.173767i | ||||
\(335\) | 1004.24 | 0.163784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9712.35 | −1.56993 | −0.784963 | − | 0.619542i | \(-0.787318\pi\) | ||||
−0.784963 | + | 0.619542i | \(0.787318\pi\) | |||||||
\(338\) | −4266.65 | − | 1211.47i | −0.686613 | − | 0.194956i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2651.20 | + | 1637.58i | 0.422886 | + | 0.261206i | ||||
\(341\) | − | 607.457i | − | 0.0964682i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6766.32i | 1.06515i | ||||||||
\(344\) | 6147.62 | − | 5622.62i | 0.963539 | − | 0.881254i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 863.921 | − | 3042.63i | 0.134233 | − | 0.472754i | ||||
\(347\) | −3315.20 | −0.512880 | −0.256440 | − | 0.966560i | \(-0.582550\pi\) | ||||
−0.256440 | + | 0.966560i | \(0.582550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2864.88 | −0.439408 | −0.219704 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219704 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(350\) | −1487.26 | + | 5237.96i | −0.227136 | + | 0.799945i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 567.998 | + | 2993.59i | 0.0860068 | + | 0.453293i | ||||
\(353\) | 4904.72i | 0.739523i | 0.929127 | + | 0.369762i | \(0.120561\pi\) | ||||
−0.929127 | + | 0.369762i | \(0.879439\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2291.42i | − | 0.342580i | ||||||
\(356\) | −3599.92 | + | 5828.18i | −0.535943 | + | 0.867677i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4776.74 | − | 1356.30i | −0.705191 | − | 0.200231i | ||||
\(359\) | −4185.24 | −0.615288 | −0.307644 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307644 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −447.841 | −0.0652924 | ||||||||
\(362\) | 851.559 | + | 241.791i | 0.123638 | + | 0.0351056i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1781.90 | + | 2884.85i | −0.256585 | + | 0.415404i | ||||
\(365\) | − | 1039.90i | − | 0.149126i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4979.97i | − | 0.708317i | −0.935185 | − | 0.354158i | \(-0.884767\pi\) | ||
0.935185 | − | 0.354158i | \(-0.115233\pi\) | |||||||
\(368\) | −4548.11 | − | 9084.44i | −0.644257 | − | 1.28684i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 910.569 | − | 3206.92i | 0.127941 | − | 0.450594i | ||||
\(371\) | −1624.00 | −0.227261 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6411.84 | 0.890060 | 0.445030 | − | 0.895516i | \(-0.353193\pi\) | ||||
0.445030 | + | 0.895516i | \(0.353193\pi\) | |||||||
\(374\) | 1520.43 | − | 5354.76i | 0.210212 | − | 0.740343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6067.73 | + | 6634.29i | 0.832232 | + | 0.909940i | ||||
\(377\) | − | 6769.81i | − | 0.924835i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5294.51i | − | 0.717574i | −0.933419 | − | 0.358787i | \(-0.883190\pi\) | ||
0.933419 | − | 0.358787i | \(-0.116810\pi\) | |||||||
\(380\) | −1938.31 | − | 1197.24i | −0.261666 | − | 0.161625i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5508.14 | − | 1563.98i | −0.737752 | − | 0.209476i | ||||
\(383\) | −5923.23 | −0.790242 | −0.395121 | − | 0.918629i | \(-0.629297\pi\) | ||||
−0.395121 | + | 0.918629i | \(0.629297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −947.812 | −0.125467 | ||||||||
\(386\) | 3096.36 | + | 879.177i | 0.408292 | + | 0.115930i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1487.61 | + | 918.863i | 0.194645 | + | 0.120227i | ||||
\(389\) | − | 4084.92i | − | 0.532426i | −0.963914 | − | 0.266213i | \(-0.914228\pi\) | ||
0.963914 | − | 0.266213i | \(-0.0857724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18559.6i | 2.40052i | ||||||||
\(392\) | 875.592 | + | 957.348i | 0.112817 | + | 0.123350i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1812.25 | − | 6382.53i | 0.231725 | − | 0.816110i | ||||
\(395\) | −2005.81 | −0.255501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2821.56 | 0.356700 | 0.178350 | − | 0.983967i | \(-0.442924\pi\) | ||||
0.178350 | + | 0.983967i | \(0.442924\pi\) | |||||||
\(398\) | −2193.43 | + | 7725.00i | −0.276248 | + | 0.972912i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3263.41 | + | 6518.37i | 0.407926 | + | 0.814796i | ||||
\(401\) | − | 4215.14i | − | 0.524923i | −0.964942 | − | 0.262461i | \(-0.915466\pi\) | ||
0.964942 | − | 0.262461i | \(-0.0845343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 905.009i | − | 0.111865i | ||||||
\(404\) | −3336.47 | + | 5401.65i | −0.410880 | + | 0.665203i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12414.4 | + | 3524.94i | 1.51753 | + | 0.430887i | ||||
\(407\) | −5954.99 | −0.725253 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 605.285 | 0.0731771 | 0.0365885 | − | 0.999330i | \(-0.488351\pi\) | ||||
0.0365885 | + | 0.999330i | \(0.488351\pi\) | |||||||
\(410\) | 1309.08 | + | 371.699i | 0.157685 | + | 0.0447730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5236.56 | + | 8477.85i | −0.626181 | + | 1.01377i | ||||
\(413\) | − | 4984.30i | − | 0.593854i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4445.76i | 0.525865i | ||||||||
\(416\) | 846.220 | + | 4459.95i | 0.0997340 | + | 0.525642i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1111.59 | + | 3914.90i | −0.130071 | + | 0.458096i | ||||
\(419\) | 6479.90 | 0.755523 | 0.377761 | − | 0.925903i | \(-0.376694\pi\) | ||||
0.377761 | + | 0.925903i | \(0.376694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −363.812 | −0.0421166 | −0.0210583 | − | 0.999778i | \(-0.506704\pi\) | ||||
−0.0210583 | + | 0.999778i | \(0.506704\pi\) | |||||||
\(422\) | 198.212 | − | 698.079i | 0.0228645 | − | 0.0805260i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1604.35 | + | 1467.34i | −0.183760 | + | 0.168067i | ||||
\(425\) | − | 13317.1i | − | 1.51994i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2479.87i | 0.281052i | ||||||||
\(428\) | 651.491 | + | 402.410i | 0.0735772 | + | 0.0454468i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3337.50 | + | 947.647i | 0.374299 | + | 0.106278i | ||||
\(431\) | 1486.97 | 0.166182 | 0.0830912 | − | 0.996542i | \(-0.473521\pi\) | ||||
0.0830912 | + | 0.996542i | \(0.473521\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12322.8 | 1.36765 | 0.683827 | − | 0.729644i | \(-0.260314\pi\) | ||||
0.683827 | + | 0.729644i | \(0.260314\pi\) | |||||||
\(434\) | 1659.60 | + | 471.225i | 0.183556 | + | 0.0521188i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9182.30 | + | 5671.69i | 1.00861 | + | 0.622992i | ||||
\(437\) | − | 13569.1i | − | 1.48535i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10918.0i | 1.18698i | 0.804840 | + | 0.593492i | \(0.202251\pi\) | ||||
−0.804840 | + | 0.593492i | \(0.797749\pi\) | |||||||
\(440\) | −936.343 | + | 856.380i | −0.101451 | + | 0.0927871i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2265.18 | − | 7977.69i | 0.243763 | − | 0.858507i | ||||
\(443\) | 3934.04 | 0.421923 | 0.210961 | − | 0.977494i | \(-0.432341\pi\) | ||||
0.210961 | + | 0.977494i | \(0.432341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2852.78 | −0.303899 | ||||||||
\(446\) | −3106.14 | + | 10939.5i | −0.329776 | + | 1.16143i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8619.25 | − | 770.437i | −0.908976 | − | 0.0812494i | ||||
\(449\) | 9560.84i | 1.00491i | 0.864604 | + | 0.502454i | \(0.167570\pi\) | ||||
−0.864604 | + | 0.502454i | \(0.832430\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2430.86i | − | 0.253802i | ||||||
\(452\) | −7926.43 | + | 12832.7i | −0.824840 | + | 1.33539i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8049.54 | − | 2285.58i | −0.832123 | − | 0.236272i | ||||
\(455\) | −1412.08 | −0.145493 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6479.90 | 0.663276 | 0.331638 | − | 0.943407i | \(-0.392399\pi\) | ||||
0.331638 | + | 0.943407i | \(0.392399\pi\) | |||||||
\(458\) | 615.105 | + | 174.652i | 0.0627553 | + | 0.0178187i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2223.33 | − | 3599.51i | 0.225355 | − | 0.364843i | ||||
\(461\) | 3560.77i | 0.359743i | 0.983690 | + | 0.179872i | \(0.0575682\pi\) | ||||
−0.983690 | + | 0.179872i | \(0.942432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15775.3i | − | 1.58346i | −0.610874 | − | 0.791728i | \(-0.709182\pi\) | ||
0.610874 | − | 0.791728i | \(-0.290818\pi\) | |||||||
\(464\) | 15449.1 | − | 7734.58i | 1.54571 | − | 0.773856i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1820.59 | + | 6411.91i | −0.180981 | + | 0.637395i | ||||
\(467\) | −14291.6 | −1.41614 | −0.708071 | − | 0.706141i | \(-0.750434\pi\) | ||||
−0.708071 | + | 0.706141i | \(0.750434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5094.70 | 0.501602 | ||||||||
\(470\) | −1022.67 | + | 3601.72i | −0.100366 | + | 0.353478i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4503.49 | − | 4923.99i | −0.439173 | − | 0.480180i | ||||
\(473\) | − | 6197.48i | − | 0.602453i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9736.24i | 0.940483i | ||||||||
\(476\) | 13450.0 | + | 8307.74i | 1.29513 | + | 0.799968i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5963.32 | + | 1693.22i | 0.570619 | + | 0.162021i | ||||
\(479\) | 14630.0 | 1.39553 | 0.697766 | − | 0.716326i | \(-0.254178\pi\) | ||||
0.697766 | + | 0.716326i | \(0.254178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8871.92 | −0.841008 | ||||||||
\(482\) | 17772.9 | + | 5046.43i | 1.67953 | + | 0.476885i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7130.74 | − | 4404.48i | −0.669679 | − | 0.413644i | ||||
\(485\) | 728.159i | 0.0681732i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16742.7i | − | 1.55787i | −0.627102 | − | 0.778937i | \(-0.715759\pi\) | ||
0.627102 | − | 0.778937i | \(-0.284241\pi\) | |||||||
\(488\) | 2240.64 | + | 2449.86i | 0.207847 | + | 0.227254i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −147.574 | + | 519.739i | −0.0136055 | + | 0.0479171i | ||||
\(491\) | −7342.23 | −0.674847 | −0.337424 | − | 0.941353i | \(-0.609555\pi\) | ||||
−0.337424 | + | 0.941353i | \(0.609555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31562.8 | −2.88340 | ||||||||
\(494\) | −1656.09 | + | 5832.54i | −0.150832 | + | 0.531211i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2065.29 | − | 1033.98i | 0.186964 | − | 0.0936032i | ||||
\(497\) | − | 11624.8i | − | 1.04918i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1565.06i | − | 0.140404i | −0.997533 | − | 0.0702020i | \(-0.977636\pi\) | ||
0.997533 | − | 0.0702020i | \(-0.0223644\pi\) | |||||||
\(500\) | −3346.07 | + | 5417.20i | −0.299282 | + | 0.484529i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 94.3317 | + | 26.7844i | 0.00838691 | + | 0.00238137i | ||||
\(503\) | 1257.87 | 0.111503 | 0.0557513 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557513 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2644.00 | −0.232983 | ||||||||
\(506\) | −7270.12 | − | 2064.27i | −0.638728 | − | 0.181360i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3003.10 | − | 4861.94i | 0.262286 | − | 0.424633i | ||||
\(509\) | 3160.96i | 0.275260i | 0.990484 | + | 0.137630i | \(0.0439484\pi\) | ||||
−0.990484 | + | 0.137630i | \(0.956052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5275.63i | − | 0.456712i | ||||||
\(512\) | −9211.06 | + | 7026.67i | −0.795069 | + | 0.606519i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3048.47 | − | 10736.3i | 0.261599 | − | 0.921323i | ||||
\(515\) | −4149.75 | −0.355067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6688.09 | 0.568940 | ||||||||
\(518\) | 4619.49 | − | 16269.3i | 0.391831 | − | 1.37998i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1394.99 | + | 1275.86i | −0.117643 | + | 0.107597i | ||||
\(521\) | 2973.62i | 0.250051i | 0.992154 | + | 0.125026i | \(0.0399013\pi\) | ||||
−0.992154 | + | 0.125026i | \(0.960099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8019.43i | 0.670488i | 0.942131 | + | 0.335244i | \(0.108819\pi\) | ||||
−0.942131 | + | 0.335244i | \(0.891181\pi\) | |||||||
\(524\) | −14660.0 | − | 9055.14i | −1.22219 | − | 0.754915i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17845.6 | − | 5067.07i | −1.47929 | − | 0.420028i | ||||
\(527\) | −4219.41 | −0.348768 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13031.3 | 1.07104 | ||||||||
\(530\) | −870.991 | − | 247.308i | −0.0713838 | − | 0.0202687i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9833.39 | − | 6073.84i | −0.801375 | − | 0.494990i | ||||
\(533\) | − | 3621.57i | − | 0.294311i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 318.893i | 0.0257700i | ||||||||
\(536\) | 5033.05 | − | 4603.23i | 0.405587 | − | 0.370950i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2890.36 | + | 10179.5i | −0.231622 | + | 0.815745i | ||||
\(539\) | 965.112 | 0.0771249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11815.3 | 0.938961 | 0.469480 | − | 0.882943i | \(-0.344441\pi\) | ||||
0.469480 | + | 0.882943i | \(0.344441\pi\) | |||||||
\(542\) | −4644.63 | + | 16357.8i | −0.368088 | + | 1.29636i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20793.6 | − | 3945.32i | 1.63882 | − | 0.310946i | ||||
\(545\) | 4494.56i | 0.353259i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15596.6i | − | 1.21913i | −0.792737 | − | 0.609564i | \(-0.791345\pi\) | ||
0.792737 | − | 0.609564i | \(-0.208655\pi\) | |||||||
\(548\) | 8633.83 | − | 13977.9i | 0.673027 | − | 1.08961i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5216.54 | + | 1481.18i | 0.404426 | + | 0.114832i | ||||
\(551\) | 23075.8 | 1.78414 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10175.8 | −0.782496 | ||||||||
\(554\) | −12310.5 | − | 3495.44i | −0.944088 | − | 0.268063i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8409.84 | − | 13615.3i | 0.641469 | − | 1.03852i | ||||
\(557\) | − | 19104.3i | − | 1.45327i | −0.687022 | − | 0.726637i | \(-0.741082\pi\) | ||
0.687022 | − | 0.726637i | \(-0.258918\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9233.19i | − | 0.698608i | ||||||
\(560\) | −1613.32 | − | 3222.45i | −0.121741 | − | 0.243167i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3284.33 | + | 11567.0i | −0.246514 | + | 0.868195i | ||||
\(563\) | −13747.5 | −1.02911 | −0.514555 | − | 0.857458i | \(-0.672043\pi\) | ||||
−0.514555 | + | 0.857458i | \(0.672043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6281.35 | −0.467714 | ||||||||
\(566\) | 3424.79 | − | 12061.7i | 0.254337 | − | 0.895746i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10503.4 | − | 11484.1i | −0.775903 | − | 0.848352i | ||||
\(569\) | 18303.4i | 1.34854i | 0.738486 | + | 0.674269i | \(0.235541\pi\) | ||||
−0.738486 | + | 0.674269i | \(0.764459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8345.58i | 0.611649i | 0.952088 | + | 0.305824i | \(0.0989320\pi\) | ||||
−0.952088 | + | 0.305824i | \(0.901068\pi\) | |||||||
\(572\) | 2873.05 | + | 1774.61i | 0.210015 | + | 0.129721i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6641.22 | + | 1885.70i | 0.482925 | + | 0.137121i | ||||
\(575\) | −18080.6 | −1.31133 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21336.5 | −1.53943 | −0.769713 | − | 0.638390i | \(-0.779601\pi\) | ||||
−0.769713 | + | 0.638390i | \(0.779601\pi\) | |||||||
\(578\) | −23826.6 | − | 6765.31i | −1.71463 | − | 0.486851i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6121.38 | + | 3781.03i | 0.438235 | + | 0.270687i | ||||
\(581\) | 22554.2i | 1.61051i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1617.36i | 0.114896i | ||||||||
\(584\) | −4766.71 | − | 5211.78i | −0.337753 | − | 0.369290i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5975.55 | + | 21045.2i | −0.421242 | + | 1.48357i | ||||
\(587\) | 26431.2 | 1.85849 | 0.929244 | − | 0.369467i | \(-0.120460\pi\) | ||||
0.929244 | + | 0.369467i | \(0.120460\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3084.84 | 0.215804 | ||||||||
\(590\) | 759.027 | − | 2673.20i | 0.0529638 | − | 0.186532i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10136.3 | − | 20246.3i | −0.703713 | − | 1.40560i | ||||
\(593\) | − | 248.904i | − | 0.0172366i | −0.999963 | − | 0.00861828i | \(-0.997257\pi\) | ||
0.999963 | − | 0.00861828i | \(-0.00274332\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6583.52i | 0.453610i | ||||||||
\(596\) | 4153.74 | − | 6724.80i | 0.285476 | − | 0.462179i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10831.3 | − | 3075.41i | −0.740674 | − | 0.210306i | ||||
\(599\) | −14995.9 | −1.02290 | −0.511449 | − | 0.859313i | \(-0.670891\pi\) | ||||
−0.511449 | + | 0.859313i | \(0.670891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23747.1 | 1.61175 | 0.805876 | − | 0.592085i | \(-0.201695\pi\) | ||||
0.805876 | + | 0.592085i | \(0.201695\pi\) | |||||||
\(602\) | 16931.8 | + | 4807.59i | 1.14633 | + | 0.325486i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6855.03 | + | 11098.1i | −0.461800 | + | 0.747641i | ||||
\(605\) | − | 3490.36i | − | 0.234551i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6539.02i | − | 0.437250i | −0.975809 | − | 0.218625i | \(-0.929843\pi\) | ||
0.975809 | − | 0.218625i | \(-0.0701571\pi\) | |||||||
\(608\) | −15202.3 | + | 2884.45i | −1.01404 | + | 0.192401i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −377.643 | + | 1330.01i | −0.0250661 | + | 0.0882798i | ||||
\(611\) | 9964.12 | 0.659747 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5985.95 | −0.394405 | −0.197202 | − | 0.980363i | \(-0.563186\pi\) | ||||
−0.197202 | + | 0.980363i | \(0.563186\pi\) | |||||||
\(614\) | 6574.64 | − | 23155.1i | 0.432135 | − | 1.52193i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4750.24 | + | 4344.57i | −0.310702 | + | 0.284169i | ||||
\(617\) | 6168.16i | 0.402465i | 0.979544 | + | 0.201232i | \(0.0644947\pi\) | ||||
−0.979544 | + | 0.201232i | \(0.935505\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6667.31i | 0.432927i | 0.976291 | + | 0.216464i | \(0.0694523\pi\) | ||||
−0.976291 | + | 0.216464i | \(0.930548\pi\) | |||||||
\(620\) | 818.325 | + | 505.459i | 0.0530076 | + | 0.0327415i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22130.6 | + | 6283.75i | 1.42662 | + | 0.405073i | ||||
\(623\) | −14472.7 | −0.930717 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11586.0 | 0.741502 | ||||||||
\(626\) | 13785.9 | + | 3914.36i | 0.880186 | + | 0.249919i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4696.36 | − | 2900.83i | −0.298416 | − | 0.184324i | ||||
\(629\) | 41363.5i | 2.62205i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8168.49i | 0.515344i | 0.966232 | + | 0.257672i | \(0.0829554\pi\) | ||||
−0.966232 | + | 0.257672i | \(0.917045\pi\) | |||||||
\(632\) | −10052.7 | + | 9194.20i | −0.632713 | + | 0.578680i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3184.91 | + | 11216.9i | −0.199510 | + | 0.702649i | ||||
\(635\) | 2379.83 | 0.148725 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1437.85 | 0.0894346 | ||||||||
\(638\) | 3510.53 | − | 12363.7i | 0.217842 | − | 0.767215i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4505.39 | − | 1725.77i | −0.278267 | − | 0.106589i | ||||
\(641\) | 6332.36i | 0.390192i | 0.980784 | + | 0.195096i | \(0.0625018\pi\) | ||||
−0.980784 | + | 0.195096i | \(0.937498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9433.98i | 0.578600i | 0.957239 | + | 0.289300i | \(0.0934225\pi\) | ||||
−0.957239 | + | 0.289300i | \(0.906578\pi\) | |||||||
\(644\) | 11279.4 | − | 18261.0i | 0.690169 | − | 1.11737i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27193.0 | + | 7721.15i | 1.65618 | + | 0.470255i | ||||
\(647\) | 20479.8 | 1.24442 | 0.622212 | − | 0.782848i | \(-0.286234\pi\) | ||||
0.622212 | + | 0.782848i | \(0.286234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4963.92 | −0.300233 | ||||||||
\(650\) | 7771.76 | + | 2206.71i | 0.468975 | + | 0.133160i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14355.2 | − | 23240.6i | 0.862258 | − | 1.39597i | ||||
\(653\) | 24435.7i | 1.46438i | 0.681099 | + | 0.732192i | \(0.261502\pi\) | ||||
−0.681099 | + | 0.732192i | \(0.738498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7175.80i | − | 0.428064i | ||||||
\(656\) | 8264.64 | − | 4137.68i | 0.491890 | − | 0.246264i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5188.18 | + | 18272.2i | −0.307380 | + | 1.08256i | ||||
\(659\) | 32183.0 | 1.90238 | 0.951192 | − | 0.308601i | \(-0.0998607\pi\) | ||||
0.951192 | + | 0.308601i | \(0.0998607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13990.4 | 0.823245 | 0.411622 | − | 0.911355i | \(-0.364962\pi\) | ||||
0.411622 | + | 0.911355i | \(0.364962\pi\) | |||||||
\(662\) | −2951.15 | + | 10393.6i | −0.173263 | + | 0.610211i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20378.5 | + | 22281.2i | 1.19102 | + | 1.30223i | ||||
\(665\) | − | 4813.26i | − | 0.280677i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42852.6i | 2.48765i | ||||||||
\(668\) | −9344.71 | − | 5772.00i | −0.541254 | − | 0.334319i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2732.41 | + | 775.838i | 0.157556 | + | 0.0447362i | ||||
\(671\) | 2469.73 | 0.142091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12289.9 | 0.703923 | 0.351961 | − | 0.936014i | \(-0.385515\pi\) | ||||
0.351961 | + | 0.936014i | \(0.385515\pi\) | |||||||
\(674\) | −26426.1 | − | 7503.39i | −1.51023 | − | 0.428813i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10673.1 | − | 6592.50i | −0.607253 | − | 0.375085i | ||||
\(677\) | − | 16303.5i | − | 0.925548i | −0.886476 | − | 0.462774i | \(-0.846854\pi\) | ||
0.886476 | − | 0.462774i | \(-0.153146\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3694.09i | 0.208786i | ||||||||
\(680\) | 5948.43 | + | 6503.86i | 0.335459 | + | 0.366782i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 469.298 | − | 1652.81i | 0.0263495 | − | 0.0927999i | ||||
\(683\) | −9720.93 | −0.544599 | −0.272299 | − | 0.962213i | \(-0.587784\pi\) | ||||
−0.272299 | + | 0.962213i | \(0.587784\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6841.93 | 0.381630 | ||||||||
\(686\) | −5227.40 | + | 18410.3i | −0.290937 | + | 1.02465i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21070.7 | − | 10549.0i | 1.16761 | − | 0.584560i | ||||
\(689\) | 2409.59i | 0.133234i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 80.4083i | 0.00442674i | 0.999998 | + | 0.00221337i | \(0.000704538\pi\) | ||||
−0.999998 | + | 0.00221337i | \(0.999295\pi\) | |||||||
\(692\) | 4701.24 | − | 7611.17i | 0.258257 | − | 0.418112i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9020.24 | − | 2561.20i | −0.493377 | − | 0.140089i | ||||
\(695\) | 6664.43 | 0.363736 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16884.8 | −0.917586 | ||||||||
\(698\) | −7794.97 | − | 2213.29i | −0.422699 | − | 0.120021i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8093.30 | + | 13102.8i | −0.436997 | + | 0.707486i | ||||
\(701\) | 4285.46i | 0.230898i | 0.993313 | + | 0.115449i | \(0.0368307\pi\) | ||||
−0.993313 | + | 0.115449i | \(0.963169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30241.1i | − | 1.62243i | ||||||
\(704\) | −767.287 | + | 8584.00i | −0.0410770 | + | 0.459548i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3789.19 | + | 13345.1i | −0.201995 | + | 0.711402i | ||||
\(707\) | −13413.5 | −0.713532 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8587.44 | −0.454878 | −0.227439 | − | 0.973792i | \(-0.573035\pi\) | ||||
−0.227439 | + | 0.973792i | \(0.573035\pi\) | |||||||
\(710\) | 1770.26 | − | 6234.67i | 0.0935730 | − | 0.329553i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14297.6 | + | 13076.6i | −0.752562 | + | 0.688294i | ||||
\(713\) | 5728.67i | 0.300898i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1406.30i | 0.0735564i | ||||||||
\(716\) | −11949.1 | − | 7380.65i | −0.623684 | − | 0.385234i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11387.5 | − | 3233.36i | −0.591891 | − | 0.168061i | ||||
\(719\) | 665.197 | 0.0345030 | 0.0172515 | − | 0.999851i | \(-0.494508\pi\) | ||||
0.0172515 | + | 0.999851i | \(0.494508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21052.4 | −1.08742 | ||||||||
\(722\) | −1218.52 | − | 345.984i | −0.0628096 | − | 0.0178341i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2130.18 | + | 1315.76i | 0.109348 | + | 0.0675414i | ||||
\(725\) | − | 30748.1i | − | 1.57511i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1269.94i | 0.0647860i | 0.999475 | + | 0.0323930i | \(0.0103128\pi\) | ||||
−0.999475 | + | 0.0323930i | \(0.989687\pi\) | |||||||
\(728\) | −7077.05 | + | 6472.68i | −0.360292 | + | 0.329524i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 803.390 | − | 2829.45i | 0.0407326 | − | 0.143455i | ||||
\(731\) | −43047.8 | −2.17809 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26425.0 | 1.33155 | 0.665777 | − | 0.746151i | \(-0.268100\pi\) | ||||
0.665777 | + | 0.746151i | \(0.268100\pi\) | |||||||
\(734\) | 3847.33 | − | 13549.9i | 0.193471 | − | 0.681382i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5356.54 | − | 28231.3i | −0.268267 | − | 1.41388i | ||||
\(737\) | − | 5073.87i | − | 0.253593i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4732.65i | − | 0.235579i | −0.993039 | − | 0.117790i | \(-0.962419\pi\) | ||
0.993039 | − | 0.117790i | \(-0.0375809\pi\) | |||||||
\(740\) | 4955.09 | − | 8022.15i | 0.246152 | − | 0.398514i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4418.70 | − | 1254.64i | −0.218619 | − | 0.0620745i | ||||
\(743\) | 14771.2 | 0.729346 | 0.364673 | − | 0.931136i | \(-0.381181\pi\) | ||||
0.364673 | + | 0.931136i | \(0.381181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3291.66 | 0.161875 | ||||||||
\(746\) | 17445.8 | + | 4953.54i | 0.856214 | + | 0.243113i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8273.77 | − | 13395.0i | 0.404437 | − | 0.654773i | ||||
\(749\) | 1617.80i | 0.0789228i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27071.9i | − | 1.31540i | −0.753280 | − | 0.657700i | \(-0.771529\pi\) | ||
0.753280 | − | 0.657700i | \(-0.228471\pi\) | |||||||
\(752\) | 11384.1 | + | 22738.8i | 0.552043 | + | 1.10266i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5230.09 | − | 18419.8i | 0.252611 | − | 0.889667i | ||||
\(755\) | −5432.31 | −0.261857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12404.5 | −0.595576 | −0.297788 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297788 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(758\) | 4090.33 | − | 14405.7i | 0.196000 | − | 0.690288i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4348.94 | − | 4755.01i | −0.207569 | − | 0.226951i | ||||
\(761\) | − | 8564.67i | − | 0.407975i | −0.978973 | − | 0.203988i | \(-0.934610\pi\) | ||
0.978973 | − | 0.203988i | \(-0.0653902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22801.8i | 1.08189i | ||||||||
\(764\) | −13778.7 | − | 8510.76i | −0.652481 | − | 0.403022i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16116.4 | − | 4576.06i | −0.760193 | − | 0.215848i | ||||
\(767\) | −7395.40 | −0.348152 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19117.5 | −0.896483 | −0.448241 | − | 0.893913i | \(-0.647949\pi\) | ||||
−0.448241 | + | 0.893913i | \(0.647949\pi\) | |||||||
\(770\) | −2578.88 | − | 732.243i | −0.120696 | − | 0.0342704i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7745.58 | + | 4784.26i | 0.361101 | + | 0.223043i | ||||
\(773\) | − | 28145.2i | − | 1.30959i | −0.755807 | − | 0.654794i | \(-0.772755\pi\) | ||
0.755807 | − | 0.654794i | \(-0.227245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4110.50i | − | 0.190521i | ||||||
\(776\) | 3337.73 | + | 3649.38i | 0.154404 | + | 0.168821i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3155.85 | − | 11114.5i | 0.145428 | − | 0.512180i | ||||
\(779\) | 12344.6 | 0.567767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11577.3 | −0.530432 | ||||||||
\(782\) | −14338.5 | + | 50498.4i | −0.655681 | + | 2.30923i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1642.76 | + | 3281.27i | 0.0748344 | + | 0.149475i | ||||
\(785\) | − | 2298.78i | − | 0.104518i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15895.3i | − | 0.719959i | −0.932960 | − | 0.359979i | \(-0.882784\pi\) | ||
0.932960 | − | 0.359979i | \(-0.117216\pi\) | |||||||
\(788\) | 9861.80 | − | 15966.0i | 0.445827 | − | 0.721782i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5457.54 | − | 1549.61i | −0.245786 | − | 0.0697881i | ||||
\(791\) | −31866.4 | −1.43242 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3679.47 | 0.164769 | ||||||||
\(794\) | 7677.09 | + | 2179.83i | 0.343136 | + | 0.0974296i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11936.1 | + | 19324.2i | −0.531486 | + | 0.860461i | ||||
\(797\) | − | 39051.2i | − | 1.73559i | −0.496924 | − | 0.867794i | \(-0.665537\pi\) | ||
0.496924 | − | 0.867794i | \(-0.334463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 46455.6i | − | 2.05692i | ||||||
\(800\) | 3843.49 | + | 20256.8i | 0.169860 | + | 0.895234i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3256.46 | − | 11468.9i | 0.143378 | − | 0.504962i | ||||
\(803\) | −5254.05 | −0.230898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8938.40 | 0.391351 | ||||||||
\(806\) | 699.175 | − | 2462.41i | 0.0305551 | − | 0.107611i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13251.2 | + | 12119.6i | −0.576950 | + | 0.527679i | ||||
\(809\) | − | 67.6844i | − | 0.00294148i | −0.999999 | − | 0.00147074i | \(-0.999532\pi\) | ||
0.999999 | − | 0.00147074i | \(-0.000468151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26390.7i | 1.14267i | 0.820718 | + | 0.571334i | \(0.193574\pi\) | ||||
−0.820718 | + | 0.571334i | \(0.806426\pi\) | |||||||
\(812\) | 31054.9 | + | 19181.9i | 1.34213 | + | 0.829004i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16202.8 | − | 4600.60i | −0.697674 | − | 0.198097i | ||||
\(815\) | 11375.9 | 0.488931 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31472.5 | 1.34772 | ||||||||
\(818\) | 1646.90 | + | 467.620i | 0.0703944 | + | 0.0199877i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3274.69 | + | 2022.69i | 0.139460 | + | 0.0861409i | ||||
\(821\) | 15840.6i | 0.673374i | 0.941617 | + | 0.336687i | \(0.109306\pi\) | ||||
−0.941617 | + | 0.336687i | \(0.890694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 227.779i | − | 0.00964747i | −0.999988 | − | 0.00482373i | \(-0.998465\pi\) | ||
0.999988 | − | 0.00482373i | \(-0.00153545\pi\) | |||||||
\(824\) | −20797.7 | + | 19021.6i | −0.879273 | + | 0.804185i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3850.68 | − | 13561.7i | 0.162206 | − | 0.571272i | ||||
\(827\) | 11468.2 | 0.482209 | 0.241105 | − | 0.970499i | \(-0.422490\pi\) | ||||
0.241105 | + | 0.970499i | \(0.422490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15188.4 | 0.636327 | 0.318164 | − | 0.948036i | \(-0.396934\pi\) | ||||
0.318164 | + | 0.948036i | \(0.396934\pi\) | |||||||
\(830\) | −3434.62 | + | 12096.3i | −0.143636 | + | 0.505868i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1143.13 | + | 12788.7i | −0.0476332 | + | 0.532895i | ||||
\(833\) | − | 6703.69i | − | 0.278835i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4574.06i | − | 0.189571i | ||||||
\(836\) | −6049.01 | + | 9793.18i | −0.250250 | + | 0.405149i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17631.0 | + | 5006.12i | 0.726793 | + | 0.206365i | ||||
\(839\) | −28109.4 | −1.15667 | −0.578334 | − | 0.815800i | \(-0.696297\pi\) | ||||
−0.578334 | + | 0.815800i | \(0.696297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −48486.8 | −1.98806 | ||||||||
\(842\) | −989.886 | − | 281.067i | −0.0405151 | − | 0.0115038i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1078.62 | − | 1746.25i | 0.0439900 | − | 0.0712186i | ||||
\(845\) | − | 5224.27i | − | 0.212687i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 17707.2i | − | 0.718333i | ||||||
\(848\) | −5498.84 | + | 2752.99i | −0.222678 | + | 0.111483i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10288.3 | − | 36234.2i | 0.415160 | − | 1.46215i | ||||
\(851\) | 56158.9 | 2.26217 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41817.8 | −1.67856 | −0.839281 | − | 0.543699i | \(-0.817023\pi\) | ||||
−0.839281 | + | 0.543699i | \(0.817023\pi\) | |||||||
\(854\) | −1915.85 | + | 6747.41i | −0.0767671 | + | 0.270365i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1461.74 | + | 1598.22i | 0.0583659 | + | 0.0638156i | ||||
\(857\) | − | 38510.6i | − | 1.53500i | −0.641048 | − | 0.767501i | \(-0.721500\pi\) | ||
0.641048 | − | 0.767501i | \(-0.278500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43912.4i | 1.74421i | 0.489322 | + | 0.872103i | \(0.337244\pi\) | ||||
−0.489322 | + | 0.872103i | \(0.662756\pi\) | |||||||
\(860\) | 8348.81 | + | 5156.86i | 0.331037 | + | 0.204474i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4045.84 | + | 1148.77i | 0.159863 | + | 0.0453913i | ||||
\(863\) | 40298.8 | 1.58956 | 0.794779 | − | 0.606899i | \(-0.207587\pi\) | ||||
0.794779 | + | 0.606899i | \(0.207587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3725.52 | 0.146441 | ||||||||
\(866\) | 33528.7 | + | 9520.09i | 1.31565 | + | 0.373563i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4151.51 | + | 2564.29i | 0.162340 | + | 0.100274i | ||||
\(869\) | 10134.2i | 0.395604i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7559.20i | − | 0.294069i | ||||||
\(872\) | 20602.2 | + | 22525.8i | 0.800088 | + | 0.874795i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10483.0 | − | 36919.7i | 0.405711 | − | 1.42887i | ||||
\(875\) | −13452.2 | −0.519732 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17806.9 | 0.685629 | 0.342814 | − | 0.939403i | \(-0.388620\pi\) | ||||
0.342814 | + | 0.939403i | \(0.388620\pi\) | |||||||
\(878\) | −8434.79 | + | 29706.4i | −0.324215 | + | 1.14185i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3209.28 | + | 1606.72i | −0.122937 | + | 0.0615483i | ||||
\(881\) | − | 4232.13i | − | 0.161843i | −0.996720 | − | 0.0809217i | \(-0.974214\pi\) | ||
0.996720 | − | 0.0809217i | \(-0.0257864\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36881.3i | − | 1.40561i | −0.711382 | − | 0.702806i | \(-0.751930\pi\) | ||
0.711382 | − | 0.702806i | \(-0.248070\pi\) | |||||||
\(884\) | 12326.5 | − | 19956.3i | 0.468988 | − | 0.759279i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10704.0 | + | 3039.29i | 0.405879 | + | 0.115245i | ||||
\(887\) | −31760.2 | −1.20226 | −0.601128 | − | 0.799152i | \(-0.705282\pi\) | ||||
−0.601128 | + | 0.799152i | \(0.705282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12073.3 | 0.455485 | ||||||||
\(890\) | −7762.06 | − | 2203.95i | −0.292343 | − | 0.0830074i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16902.8 | + | 27365.3i | −0.634472 | + | 1.02719i | ||||
\(893\) | 33964.0i | 1.27275i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5848.84i | − | 0.218442i | ||||||
\(896\) | −22856.7 | − | 8755.16i | −0.852218 | − | 0.326439i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7386.34 | + | 26013.8i | −0.274483 | + | 0.966696i | ||||
\(899\) | −9742.26 | −0.361427 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11234.2 | 0.415390 | ||||||||
\(902\) | 1877.99 | − | 6614.06i | 0.0693239 | − | 0.244151i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31480.8 | + | 28792.4i | −1.15823 | + | 1.05932i | ||||
\(905\) | 1042.68i | 0.0382984i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50257.3i | 1.83987i | 0.392066 | + | 0.919937i | \(0.371760\pi\) | ||||
−0.392066 | + | 0.919937i | \(0.628240\pi\) | |||||||
\(908\) | −20136.0 | − | 12437.5i | −0.735945 | − | 0.454575i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3842.09 | − | 1090.92i | −0.139960 | − | 0.0397402i | ||||
\(911\) | −22485.6 | −0.817763 | −0.408881 | − | 0.912588i | \(-0.634081\pi\) | ||||
−0.408881 | + | 0.912588i | \(0.634081\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22461.9 | 0.814219 | ||||||||
\(914\) | 17631.0 | + | 5006.13i | 0.638054 | + | 0.181168i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1538.69 | + | 950.412i | 0.0555020 | + | 0.0342822i | ||||
\(917\) | − | 36404.2i | − | 1.31098i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26918.9i | 0.966240i | 0.875554 | + | 0.483120i | \(0.160496\pi\) | ||||
−0.875554 | + | 0.483120i | \(0.839504\pi\) | |||||||
\(920\) | 8830.24 | − | 8076.15i | 0.316440 | − | 0.289416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2750.91 | + | 9688.40i | −0.0982609 | + | 0.346063i | ||||
\(923\) | −17248.2 | −0.615093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40295.8 | −1.43234 | ||||||||
\(926\) | 12187.4 | − | 42922.6i | 0.432508 | − | 1.52324i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 48010.5 | − | 9109.41i | 1.69830 | − | 0.322232i | ||||
\(929\) | − | 11212.4i | − | 0.395983i | −0.980204 | − | 0.197991i | \(-0.936558\pi\) | ||
0.980204 | − | 0.197991i | \(-0.0634418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4901.11i | 0.172532i | ||||||||
\(932\) | −9907.19 | + | 16039.5i | −0.348198 | + | 0.563724i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38885.8 | − | 11041.2i | −1.36229 | − | 0.386808i | ||||
\(935\) | 6556.60 | 0.229330 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38358.1 | 1.33736 | 0.668679 | − | 0.743551i | \(-0.266860\pi\) | ||||
0.668679 | + | 0.743551i | \(0.266860\pi\) | |||||||
\(938\) | 13862.0 | + | 3935.97i | 0.482528 | + | 0.137008i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5565.09 | + | 9009.74i | −0.193099 | + | 0.312623i | ||||
\(941\) | − | 7558.00i | − | 0.261832i | −0.991393 | − | 0.130916i | \(-0.958208\pi\) | ||
0.991393 | − | 0.130916i | \(-0.0417918\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22924.4i | 0.791644i | ||||||||
\(944\) | −8449.33 | − | 16876.8i | −0.291316 | − | 0.581877i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4787.93 | − | 16862.5i | 0.164555 | − | 0.579544i | ||||
\(947\) | −50708.7 | −1.74003 | −0.870016 | − | 0.493023i | \(-0.835892\pi\) | ||||
−0.870016 | + | 0.493023i | \(0.835892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7827.65 | −0.267751 | ||||||||
\(950\) | −7521.85 | + | 26491.1i | −0.256885 | + | 0.904720i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30177.5 | + | 32995.3i | 1.02737 | + | 1.12330i | ||||
\(953\) | 16440.9i | 0.558837i | 0.960169 | + | 0.279419i | \(0.0901417\pi\) | ||||
−0.960169 | + | 0.279419i | \(0.909858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 6744.41i | − | 0.228528i | ||||||
\(956\) | 14917.3 | + | 9214.07i | 0.504666 | + | 0.311720i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39806.2 | + | 11302.5i | 1.34247 | + | 0.381178i | ||||
\(959\) | 34710.4 | 1.16878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28488.6 | 0.956283 | ||||||||
\(962\) | −24139.4 | − | 6854.11i | −0.809028 | − | 0.229714i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 44459.3 | + | 27461.4i | 1.48541 | + | 0.917502i | ||||
\(965\) | 3791.32i | 0.126473i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 488.917i | 0.0162591i | 0.999967 | + | 0.00812953i | \(0.00258774\pi\) | ||||
−0.999967 | + | 0.00812953i | \(0.997412\pi\) | |||||||
\(968\) | −15999.1 | − | 17493.0i | −0.531230 | − | 0.580832i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −562.548 | + | 1981.23i | −0.0186209 | + | 0.0655808i | ||||
\(971\) | 31950.1 | 1.05595 | 0.527975 | − | 0.849260i | \(-0.322951\pi\) | ||||
0.527975 | + | 0.849260i | \(0.322951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33809.9 | 1.11397 | ||||||||
\(974\) | 12934.8 | − | 45554.8i | 0.425521 | − | 1.49863i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4203.84 | + | 8396.79i | 0.137871 | + | 0.275384i | ||||
\(977\) | 5271.73i | 0.172628i | 0.996268 | + | 0.0863140i | \(0.0275088\pi\) | ||||
−0.996268 | + | 0.0863140i | \(0.972491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14413.5i | 0.470539i | ||||||||
\(980\) | −803.060 | + | 1300.13i | −0.0261763 | + | 0.0423788i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19977.3 | − | 5672.32i | −0.649185 | − | 0.184329i | ||||
\(983\) | 11052.1 | 0.358603 | 0.179302 | − | 0.983794i | \(-0.442616\pi\) | ||||
0.179302 | + | 0.983794i | \(0.442616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7815.04 | 0.252800 | ||||||||
\(986\) | −85878.4 | − | 24384.2i | −2.77376 | − | 0.787578i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9011.99 | + | 14590.2i | −0.290192 | + | 0.469813i | ||||
\(989\) | 58445.7i | 1.87914i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 41203.4i | − | 1.32076i | −0.750933 | − | 0.660378i | \(-0.770396\pi\) | ||
0.750933 | − | 0.660378i | \(-0.229604\pi\) | |||||||
\(992\) | 6418.20 | − | 1217.77i | 0.205421 | − | 0.0389762i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8980.88 | − | 31629.6i | 0.286576 | − | 1.00929i | ||||
\(995\) | −9458.82 | −0.301372 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14951.3 | −0.474938 | −0.237469 | − | 0.971395i | \(-0.576318\pi\) | ||||
−0.237469 | + | 0.971395i | \(0.576318\pi\) | |||||||
\(998\) | 1209.10 | − | 4258.32i | 0.0383502 | − | 0.135065i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 108.4.b.a.107.12 | yes | 12 | |
3.2 | odd | 2 | inner | 108.4.b.a.107.1 | ✓ | 12 | |
4.3 | odd | 2 | inner | 108.4.b.a.107.2 | yes | 12 | |
8.3 | odd | 2 | 1728.4.c.i.1727.5 | 12 | |||
8.5 | even | 2 | 1728.4.c.i.1727.6 | 12 | |||
12.11 | even | 2 | inner | 108.4.b.a.107.11 | yes | 12 | |
24.5 | odd | 2 | 1728.4.c.i.1727.8 | 12 | |||
24.11 | even | 2 | 1728.4.c.i.1727.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.a.107.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
108.4.b.a.107.2 | yes | 12 | 4.3 | odd | 2 | inner | |
108.4.b.a.107.11 | yes | 12 | 12.11 | even | 2 | inner | |
108.4.b.a.107.12 | yes | 12 | 1.1 | even | 1 | trivial | |
1728.4.c.i.1727.5 | 12 | 8.3 | odd | 2 | |||
1728.4.c.i.1727.6 | 12 | 8.5 | even | 2 | |||
1728.4.c.i.1727.7 | 12 | 24.11 | even | 2 | |||
1728.4.c.i.1727.8 | 12 | 24.5 | odd | 2 |