Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.5 | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.f.1601.5 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24547 | + | 1.39924i | −0.848707 | + | 0.528863i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.37897 | + | 0.796151i | 0.415776 | + | 0.240049i | 0.693269 | − | 0.720679i | \(-0.256170\pi\) |
−0.277492 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.925091i | − | 0.256574i | −0.991737 | − | 0.128287i | \(-0.959052\pi\) | ||
0.991737 | − | 0.128287i | \(-0.0409479\pi\) | |||||||
\(14\) | 1.24501 | − | 2.33451i | 0.332743 | − | 0.623925i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.97883 | − | 3.42743i | 0.479936 | − | 0.831273i | −0.519799 | − | 0.854288i | \(-0.673993\pi\) |
0.999735 | + | 0.0230153i | \(0.00732664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.541679 | + | 0.312739i | −0.124270 | + | 0.0717472i | −0.560846 | − | 0.827920i | \(-0.689524\pi\) |
0.436577 | + | 0.899667i | \(0.356191\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.59230 | −0.339480 | ||||||||
\(23\) | −6.74256 | + | 3.89282i | −1.40592 | + | 0.811709i | −0.994992 | − | 0.0999578i | \(-0.968129\pi\) |
−0.410930 | + | 0.911667i | \(0.634796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.462546 | + | 0.801153i | 0.0907127 | + | 0.157119i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0890445 | + | 2.64425i | 0.0168278 | + | 0.499717i | ||||
\(29\) | − | 9.34805i | − | 1.73589i | −0.496661 | − | 0.867945i | \(-0.665441\pi\) | ||
0.496661 | − | 0.867945i | \(-0.334559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94618 | + | 5.16508i | 1.60678 | + | 0.927675i | 0.990084 | + | 0.140474i | \(0.0448626\pi\) |
0.616696 | + | 0.787201i | \(0.288471\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.95765i | 0.678732i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.213192 | − | 0.369259i | −0.0350485 | − | 0.0607058i | 0.847969 | − | 0.530046i | \(-0.177825\pi\) |
−0.883018 | + | 0.469340i | \(0.844492\pi\) | |||||||
\(38\) | 0.312739 | − | 0.541679i | 0.0507329 | − | 0.0878720i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.35463 | −1.30477 | −0.652387 | − | 0.757886i | \(-0.726232\pi\) | ||||
−0.652387 | + | 0.757886i | \(0.726232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.27133 | −0.956369 | −0.478184 | − | 0.878259i | \(-0.658705\pi\) | ||||
−0.478184 | + | 0.878259i | \(0.658705\pi\) | |||||||
\(44\) | 1.37897 | − | 0.796151i | 0.207888 | − | 0.120024i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.89282 | − | 6.74256i | 0.573965 | − | 0.994137i | ||||
\(47\) | −1.39065 | − | 2.40868i | −0.202847 | − | 0.351342i | 0.746597 | − | 0.665276i | \(-0.231686\pi\) |
−0.949445 | + | 0.313934i | \(0.898353\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.08425 | − | 6.28390i | 0.440607 | − | 0.897700i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.801153 | − | 0.462546i | −0.111100 | − | 0.0641435i | ||||
\(53\) | −2.90217 | − | 1.67557i | −0.398644 | − | 0.230157i | 0.287255 | − | 0.957854i | \(-0.407257\pi\) |
−0.685899 | + | 0.727697i | \(0.740591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.39924 | − | 2.24547i | −0.186981 | − | 0.300063i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.67403 | + | 8.09565i | 0.613730 | + | 1.06301i | ||||
\(59\) | −3.10680 | + | 5.38113i | −0.404471 | + | 0.700564i | −0.994260 | − | 0.106994i | \(-0.965878\pi\) |
0.589789 | + | 0.807557i | \(0.299211\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.52671 | − | 5.50025i | 1.21977 | − | 0.704235i | 0.254902 | − | 0.966967i | \(-0.417957\pi\) |
0.964869 | + | 0.262732i | \(0.0846236\pi\) | |||||||
\(62\) | −10.3302 | −1.31193 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.178089 | − | 0.308459i | 0.0217570 | − | 0.0376843i | −0.854942 | − | 0.518724i | \(-0.826407\pi\) |
0.876699 | + | 0.481039i | \(0.159741\pi\) | |||||||
\(68\) | −1.97883 | − | 3.42743i | −0.239968 | − | 0.415637i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.07975i | − | 1.07757i | −0.842444 | − | 0.538784i | \(-0.818884\pi\) | ||
0.842444 | − | 0.538784i | \(-0.181116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.91515 | + | 3.41511i | 0.692316 | + | 0.399709i | 0.804479 | − | 0.593981i | \(-0.202445\pi\) |
−0.112163 | + | 0.993690i | \(0.535778\pi\) | |||||||
\(74\) | 0.369259 | + | 0.213192i | 0.0429255 | + | 0.0247830i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.625477i | 0.0717472i | ||||||||
\(77\) | −4.21045 | + | 0.141786i | −0.479825 | + | 0.0161580i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.52582 | + | 7.83895i | 0.509195 | + | 0.881951i | 0.999943 | + | 0.0106498i | \(0.00339001\pi\) |
−0.490749 | + | 0.871301i | \(0.663277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.23532 | − | 4.17731i | 0.799007 | − | 0.461307i | ||||
\(83\) | 0.809898 | 0.0888978 | 0.0444489 | − | 0.999012i | \(-0.485847\pi\) | ||||
0.0444489 | + | 0.999012i | \(0.485847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.43113 | − | 3.13566i | 0.585654 | − | 0.338127i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.796151 | + | 1.37897i | −0.0848700 | + | 0.146999i | ||||
\(89\) | −2.00721 | − | 3.47659i | −0.212764 | − | 0.368518i | 0.739815 | − | 0.672811i | \(-0.234913\pi\) |
−0.952579 | + | 0.304293i | \(0.901580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29443 | + | 2.07726i | 0.135693 | + | 0.217756i | ||||
\(92\) | 7.78564i | 0.811709i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.40868 | + | 1.39065i | 0.248436 | + | 0.143435i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.87721i | 0.799809i | 0.916557 | + | 0.399905i | \(0.130957\pi\) | ||||
−0.916557 | + | 0.399905i | \(0.869043\pi\) | |||||||
\(98\) | 0.470912 | + | 6.98414i | 0.0475693 | + | 0.705505i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.76411 | − | 6.51962i | 0.374543 | − | 0.648727i | −0.615716 | − | 0.787968i | \(-0.711133\pi\) |
0.990258 | + | 0.139241i | \(0.0444664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.44073 | + | 0.831805i | −0.141959 | + | 0.0819601i | −0.569297 | − | 0.822132i | \(-0.692785\pi\) |
0.427338 | + | 0.904092i | \(0.359451\pi\) | |||||||
\(104\) | 0.925091 | 0.0907127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.35114 | 0.325492 | ||||||||
\(107\) | 16.8033 | − | 9.70139i | 1.62444 | − | 0.937869i | 0.638724 | − | 0.769436i | \(-0.279463\pi\) |
0.985713 | − | 0.168433i | \(-0.0538706\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.33451 | + | 1.24501i | 0.220591 | + | 0.117643i | ||||
\(113\) | − | 16.0750i | − | 1.51221i | −0.654451 | − | 0.756104i | \(-0.727100\pi\) | ||
0.654451 | − | 0.756104i | \(-0.272900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.09565 | − | 4.67403i | −0.751662 | − | 0.433972i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.21360i | − | 0.572008i | ||||||
\(119\) | 0.352407 | + | 10.4650i | 0.0323051 | + | 0.959328i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.23229 | − | 7.33053i | −0.384753 | − | 0.666412i | ||||
\(122\) | −5.50025 | + | 9.52671i | −0.497969 | + | 0.862508i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.94618 | − | 5.16508i | 0.803390 | − | 0.463838i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2173 | 1.17285 | 0.586424 | − | 0.810004i | \(-0.300535\pi\) | ||||
0.586424 | + | 0.810004i | \(0.300535\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.70080 | − | 8.14203i | −0.410711 | − | 0.711372i | 0.584257 | − | 0.811569i | \(-0.301386\pi\) |
−0.994968 | + | 0.100197i | \(0.968053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.778726 | − | 1.46018i | 0.0675241 | − | 0.126614i | ||||
\(134\) | 0.356178i | 0.0307691i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.42743 | + | 1.97883i | 0.293899 | + | 0.169683i | ||||
\(137\) | 8.11701 | + | 4.68636i | 0.693483 | + | 0.400382i | 0.804915 | − | 0.593390i | \(-0.202211\pi\) |
−0.111433 | + | 0.993772i | \(0.535544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.1106i | − | 1.19685i | −0.801180 | − | 0.598423i | \(-0.795794\pi\) | ||
0.801180 | − | 0.598423i | \(-0.204206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.53988 | + | 7.86330i | 0.380978 | + | 0.659873i | ||||
\(143\) | 0.736513 | − | 1.27568i | 0.0615903 | − | 0.106678i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.83023 | −0.565274 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.426383 | −0.0350485 | ||||||||
\(149\) | −2.14103 | + | 1.23612i | −0.175400 | + | 0.101267i | −0.585130 | − | 0.810940i | \(-0.698956\pi\) |
0.409730 | + | 0.912207i | \(0.365623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4425 | − | 18.0869i | 0.849796 | − | 1.47189i | −0.0315949 | − | 0.999501i | \(-0.510059\pi\) |
0.881391 | − | 0.472388i | \(-0.156608\pi\) | |||||||
\(152\) | −0.312739 | − | 0.541679i | −0.0253664 | − | 0.0439360i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.57546 | − | 2.22802i | 0.288119 | − | 0.179539i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1722 | − | 12.2238i | −1.68972 | − | 0.975563i | −0.954723 | − | 0.297498i | \(-0.903848\pi\) |
−0.735002 | − | 0.678065i | \(-0.762819\pi\) | |||||||
\(158\) | −7.83895 | − | 4.52582i | −0.623634 | − | 0.360055i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.69321 | − | 18.1757i | 0.763932 | − | 1.43244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.95758 | − | 5.12267i | −0.231655 | − | 0.401239i | 0.726640 | − | 0.687018i | \(-0.241081\pi\) |
−0.958295 | + | 0.285780i | \(0.907747\pi\) | |||||||
\(164\) | −4.17731 | + | 7.23532i | −0.326193 | + | 0.564983i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.701392 | + | 0.404949i | −0.0544386 | + | 0.0314301i | ||||
\(167\) | −12.1440 | −0.939733 | −0.469867 | − | 0.882737i | \(-0.655698\pi\) | ||||
−0.469867 | + | 0.882737i | \(0.655698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1442 | 0.934170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.13566 | + | 5.43113i | −0.239092 | + | 0.414120i | ||||
\(173\) | −8.19918 | − | 14.2014i | −0.623372 | − | 1.07971i | −0.988853 | − | 0.148893i | \(-0.952429\pi\) |
0.365481 | − | 0.930819i | \(-0.380904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.59230i | − | 0.120024i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.47659 | + | 2.00721i | 0.260581 | + | 0.150447i | ||||
\(179\) | −2.73398 | − | 1.57846i | −0.204347 | − | 0.117980i | 0.394334 | − | 0.918967i | \(-0.370975\pi\) |
−0.598682 | + | 0.800987i | \(0.704309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.17916i | 0.607952i | 0.952680 | + | 0.303976i | \(0.0983143\pi\) | ||||
−0.952680 | + | 0.303976i | \(0.901686\pi\) | |||||||
\(182\) | −2.15964 | − | 1.15175i | −0.160083 | − | 0.0853733i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.89282 | − | 6.74256i | −0.286983 | − | 0.497068i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.45750 | − | 3.15089i | 0.399092 | − | 0.230416i | ||||
\(188\) | −2.78130 | −0.202847 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.44949 | − | 1.41421i | 0.177239 | − | 0.102329i | −0.408756 | − | 0.912644i | \(-0.634037\pi\) |
0.585995 | + | 0.810315i | \(0.300704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.85772 | + | 15.3420i | −0.637593 | + | 1.10434i | 0.348367 | + | 0.937358i | \(0.386736\pi\) |
−0.985959 | + | 0.166985i | \(0.946597\pi\) | |||||||
\(194\) | −3.93860 | − | 6.82186i | −0.282775 | − | 0.489781i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.89989 | − | 5.81299i | −0.278564 | − | 0.415213i | ||||
\(197\) | 4.30350i | 0.306612i | 0.988179 | + | 0.153306i | \(0.0489919\pi\) | ||||
−0.988179 | + | 0.153306i | \(0.951008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.00000 | + | 1.73205i | 0.212664 | + | 0.122782i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.52821i | 0.529683i | ||||||||
\(203\) | 13.0802 | + | 20.9907i | 0.918048 | + | 1.47326i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.831805 | − | 1.44073i | 0.0579546 | − | 0.100380i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.801153 | + | 0.462546i | −0.0555499 | + | 0.0320718i | ||||
\(209\) | −0.995949 | −0.0688912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3886 | 0.715183 | 0.357592 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357592 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(212\) | −2.90217 | + | 1.67557i | −0.199322 | + | 0.115079i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.70139 | + | 16.8033i | −0.663173 | + | 1.14865i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.3155 | + | 0.919844i | −1.85430 | + | 0.0624431i | ||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.17068 | − | 1.83059i | −0.213283 | − | 0.123139i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.3555i | − | 1.22918i | −0.788848 | − | 0.614589i | \(-0.789322\pi\) | ||
0.788848 | − | 0.614589i | \(-0.210678\pi\) | |||||||
\(224\) | −2.64425 | + | 0.0890445i | −0.176677 | + | 0.00594954i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.03750 | + | 13.9214i | 0.534646 | + | 0.926035i | ||||
\(227\) | 1.51152 | − | 2.61803i | 0.100323 | − | 0.173765i | −0.811495 | − | 0.584360i | \(-0.801346\pi\) |
0.911818 | + | 0.410595i | \(0.134679\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.22014 | + | 5.32325i | −0.609284 | + | 0.351770i | −0.772685 | − | 0.634789i | \(-0.781087\pi\) |
0.163401 | + | 0.986560i | \(0.447754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.34805 | 0.613730 | ||||||||
\(233\) | 3.45185 | − | 1.99293i | 0.226138 | − | 0.130561i | −0.382651 | − | 0.923893i | \(-0.624989\pi\) |
0.608789 | + | 0.793332i | \(0.291655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.10680 | + | 5.38113i | 0.202235 | + | 0.350282i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.53771 | − | 8.88678i | −0.358956 | − | 0.576044i | ||||
\(239\) | − | 8.24699i | − | 0.533453i | −0.963772 | − | 0.266727i | \(-0.914058\pi\) | ||
0.963772 | − | 0.266727i | \(-0.0859421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.48785 | − | 5.47782i | −0.611166 | − | 0.352857i | 0.162255 | − | 0.986749i | \(-0.448123\pi\) |
−0.773422 | + | 0.633892i | \(0.781456\pi\) | |||||||
\(242\) | 7.33053 | + | 4.23229i | 0.471225 | + | 0.272062i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.0005i | − | 0.704235i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.289312 | + | 0.501103i | 0.0184085 | + | 0.0318844i | ||||
\(248\) | −5.16508 | + | 8.94618i | −0.327983 | + | 0.568083i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.7369 | −1.37202 | −0.686012 | − | 0.727590i | \(-0.740640\pi\) | ||||
−0.686012 | + | 0.727590i | \(0.740640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3971 | −0.779399 | ||||||||
\(254\) | −11.4465 | + | 6.60867i | −0.718220 | + | 0.414665i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.71758 | − | 15.0993i | −0.543787 | − | 0.941868i | −0.998682 | − | 0.0513223i | \(-0.983656\pi\) |
0.454895 | − | 0.890545i | \(-0.349677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.995397 | + | 0.530852i | 0.0618510 | + | 0.0329856i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.14203 | + | 4.70080i | 0.503016 | + | 0.290417i | ||||
\(263\) | 15.8926 | + | 9.17557i | 0.979977 | + | 0.565790i | 0.902263 | − | 0.431186i | \(-0.141905\pi\) |
0.0777137 | + | 0.996976i | \(0.475238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0556953 | + | 1.65392i | 0.00341490 | + | 0.101408i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.178089 | − | 0.308459i | −0.0108785 | − | 0.0188422i | ||||
\(269\) | 12.4185 | − | 21.5095i | 0.757171 | − | 1.31146i | −0.187117 | − | 0.982338i | \(-0.559914\pi\) |
0.944288 | − | 0.329121i | \(-0.106752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1663 | − | 12.2204i | 1.28576 | − | 0.742335i | 0.307867 | − | 0.951430i | \(-0.400385\pi\) |
0.977895 | + | 0.209094i | \(0.0670516\pi\) | |||||||
\(272\) | −3.95765 | −0.239968 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.37271 | −0.566226 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5985 | − | 20.0892i | 0.696888 | − | 1.20704i | −0.272653 | − | 0.962113i | \(-0.587901\pi\) |
0.969540 | − | 0.244932i | \(-0.0787657\pi\) | |||||||
\(278\) | 7.05530 | + | 12.2201i | 0.423149 | + | 0.732915i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0801i | 0.839949i | 0.907536 | + | 0.419974i | \(0.137961\pi\) | ||||
−0.907536 | + | 0.419974i | \(0.862039\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.42331 | − | 1.39910i | −0.144051 | − | 0.0831677i | 0.426242 | − | 0.904609i | \(-0.359837\pi\) |
−0.570293 | + | 0.821441i | \(0.693170\pi\) | |||||||
\(284\) | −7.86330 | − | 4.53988i | −0.466601 | − | 0.269392i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.47303i | 0.0871018i | ||||||||
\(287\) | 18.7600 | − | 11.6901i | 1.10737 | − | 0.690047i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.668498 | + | 1.15787i | 0.0393234 | + | 0.0681101i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.91515 | − | 3.41511i | 0.346158 | − | 0.199854i | ||||
\(293\) | 25.5598 | 1.49322 | 0.746609 | − | 0.665263i | \(-0.231681\pi\) | ||||
0.746609 | + | 0.665263i | \(0.231681\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.369259 | − | 0.213192i | 0.0214627 | − | 0.0123915i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.23612 | − | 2.14103i | 0.0716068 | − | 0.124027i | ||||
\(299\) | 3.60121 | + | 6.23749i | 0.208264 | + | 0.360723i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.0821 | − | 8.77510i | 0.811677 | − | 0.505788i | ||||
\(302\) | 20.8849i | 1.20179i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.541679 | + | 0.312739i | 0.0310674 | + | 0.0179368i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.2860i | − | 1.95681i | −0.206704 | − | 0.978403i | \(-0.566274\pi\) | ||
0.206704 | − | 0.978403i | \(-0.433726\pi\) | |||||||
\(308\) | −1.98243 | + | 3.71725i | −0.112960 | + | 0.211810i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.34021 | + | 7.51746i | −0.246110 | + | 0.426276i | −0.962443 | − | 0.271483i | \(-0.912486\pi\) |
0.716333 | + | 0.697759i | \(0.245819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.9992 | − | 15.0106i | 1.46956 | − | 0.848452i | 0.470145 | − | 0.882589i | \(-0.344202\pi\) |
0.999417 | + | 0.0341376i | \(0.0108684\pi\) | |||||||
\(314\) | 24.4475 | 1.37965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.05164 | 0.509195 | ||||||||
\(317\) | 24.0111 | − | 13.8628i | 1.34860 | − | 0.778613i | 0.360547 | − | 0.932741i | \(-0.382590\pi\) |
0.988051 | + | 0.154128i | \(0.0492567\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.44246 | − | 12.8907i | 0.416698 | − | 0.721742i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.693269 | + | 20.5872i | 0.0386344 | + | 1.14728i | ||||
\(323\) | 2.47542i | 0.137736i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.12267 | + | 2.95758i | 0.283719 | + | 0.163805i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.35463i | − | 0.461307i | ||||||
\(329\) | 6.49298 | + | 3.46275i | 0.357970 | + | 0.190908i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.15175 | − | 5.45899i | −0.173236 | − | 0.300053i | 0.766314 | − | 0.642467i | \(-0.222089\pi\) |
−0.939549 | + | 0.342414i | \(0.888756\pi\) | |||||||
\(332\) | 0.404949 | − | 0.701392i | 0.0222245 | − | 0.0384939i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5170 | − | 6.07201i | 0.575467 | − | 0.332246i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.4097 | −1.49310 | −0.746550 | − | 0.665329i | \(-0.768291\pi\) | ||||
−0.746550 | + | 0.665329i | \(0.768291\pi\) | |||||||
\(338\) | −10.5172 | + | 6.07210i | −0.572060 | + | 0.330279i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.22437 | + | 14.2450i | 0.445374 | + | 0.771411i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.86711 | + | 18.4259i | 0.100815 | + | 0.994905i | ||||
\(344\) | − | 6.27133i | − | 0.338127i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.2014 | + | 8.19918i | 0.763472 | + | 0.440791i | ||||
\(347\) | −7.07258 | − | 4.08336i | −0.379676 | − | 0.219206i | 0.298001 | − | 0.954566i | \(-0.403680\pi\) |
−0.677677 | + | 0.735359i | \(0.737013\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.5885i | 1.47678i | 0.674374 | + | 0.738390i | \(0.264413\pi\) | ||||
−0.674374 | + | 0.738390i | \(0.735587\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.796151 | + | 1.37897i | 0.0424350 | + | 0.0734996i | ||||
\(353\) | 3.52142 | − | 6.09929i | 0.187426 | − | 0.324632i | −0.756965 | − | 0.653455i | \(-0.773319\pi\) |
0.944391 | + | 0.328823i | \(0.106652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.01442 | −0.212764 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.15693 | 0.166849 | ||||||||
\(359\) | 14.1545 | − | 8.17213i | 0.747048 | − | 0.431308i | −0.0775782 | − | 0.996986i | \(-0.524719\pi\) |
0.824626 | + | 0.565678i | \(0.191385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.30439 | + | 16.1157i | −0.489705 | + | 0.848193i | ||||
\(362\) | −4.08958 | − | 7.08336i | −0.214943 | − | 0.372293i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.44618 | − | 0.0823743i | 0.128214 | − | 0.00431759i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.60498 | − | 1.50399i | −0.135979 | − | 0.0785076i | 0.430467 | − | 0.902606i | \(-0.358349\pi\) |
−0.566446 | + | 0.824099i | \(0.691682\pi\) | |||||||
\(368\) | 6.74256 | + | 3.89282i | 0.351480 | + | 0.202927i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.86126 | − | 0.298401i | 0.460054 | − | 0.0154922i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5985 | + | 20.0892i | 0.600549 | + | 1.04018i | 0.992738 | + | 0.120296i | \(0.0383844\pi\) |
−0.392189 | + | 0.919884i | \(0.628282\pi\) | |||||||
\(374\) | −3.15089 | + | 5.45750i | −0.162929 | + | 0.282201i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.40868 | − | 1.39065i | 0.124218 | − | 0.0717174i | ||||
\(377\) | −8.64780 | −0.445384 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.2718 | −1.40086 | −0.700429 | − | 0.713722i | \(-0.747008\pi\) | ||||
−0.700429 | + | 0.713722i | \(0.747008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.41421 | + | 2.44949i | −0.0723575 | + | 0.125327i | ||||
\(383\) | 2.13098 | + | 3.69096i | 0.108888 | + | 0.188599i | 0.915320 | − | 0.402727i | \(-0.131938\pi\) |
−0.806432 | + | 0.591327i | \(0.798604\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 17.7154i | − | 0.901692i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.82186 | + | 3.93860i | 0.346327 | + | 0.199952i | ||||
\(389\) | −1.80282 | − | 1.04086i | −0.0914066 | − | 0.0527736i | 0.453600 | − | 0.891205i | \(-0.350140\pi\) |
−0.545007 | + | 0.838432i | \(0.683473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.8129i | 1.55827i | ||||||||
\(392\) | 6.28390 | + | 3.08425i | 0.317385 | + | 0.155778i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.15175 | − | 3.72694i | −0.108404 | − | 0.187760i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.3791 | − | 11.1885i | 0.972610 | − | 0.561537i | 0.0725790 | − | 0.997363i | \(-0.476877\pi\) |
0.900031 | + | 0.435826i | \(0.143544\pi\) | |||||||
\(398\) | −3.46410 | −0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.0295 | + | 9.83196i | −0.850411 | + | 0.490985i | −0.860789 | − | 0.508961i | \(-0.830030\pi\) |
0.0103787 | + | 0.999946i | \(0.496696\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.77817 | − | 8.27603i | 0.238017 | − | 0.412258i | ||||
\(404\) | −3.76411 | − | 6.51962i | −0.187271 | − | 0.324363i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.8231 | − | 11.6384i | −1.08306 | − | 0.577606i | ||||
\(407\) | − | 0.678932i | − | 0.0336534i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.19932 | − | 1.26978i | −0.108750 | − | 0.0627866i | 0.444639 | − | 0.895710i | \(-0.353332\pi\) |
−0.553388 | + | 0.832923i | \(0.686665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.66361i | 0.0819601i | ||||||||
\(413\) | −0.553287 | − | 16.4303i | −0.0272255 | − | 0.808483i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.462546 | − | 0.801153i | 0.0226782 | − | 0.0392797i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.862517 | − | 0.497974i | 0.0421871 | − | 0.0243567i | ||||
\(419\) | −32.0568 | −1.56608 | −0.783039 | − | 0.621973i | \(-0.786331\pi\) | ||||
−0.783039 | + | 0.621973i | \(0.786331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2201 | −1.22915 | −0.614577 | − | 0.788857i | \(-0.710673\pi\) | ||||
−0.614577 | + | 0.788857i | \(0.710673\pi\) | |||||||
\(422\) | −8.99682 | + | 5.19432i | −0.437959 | + | 0.252855i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.67557 | − | 2.90217i | 0.0813729 | − | 0.140942i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.6957 | + | 25.6808i | −0.662784 | + | 1.24278i | ||||
\(428\) | − | 19.4028i | − | 0.937869i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.1599 | + | 16.8355i | 1.40458 | + | 0.810937i | 0.994859 | − | 0.101271i | \(-0.0322910\pi\) |
0.409726 | + | 0.912209i | \(0.365624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.7610i | − | 1.09382i | −0.837190 | − | 0.546912i | \(-0.815803\pi\) | ||
0.837190 | − | 0.546912i | \(-0.184197\pi\) | |||||||
\(434\) | 23.1960 | − | 14.4544i | 1.11344 | − | 0.693832i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | 2.43487 | − | 4.21732i | 0.116476 | − | 0.201742i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.86282 | + | 1.07550i | −0.0889074 | + | 0.0513307i | −0.543795 | − | 0.839218i | \(-0.683013\pi\) |
0.454887 | + | 0.890549i | \(0.349680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.66119 | 0.174145 | ||||||||
\(443\) | 6.63790 | − | 3.83239i | 0.315376 | − | 0.182082i | −0.333954 | − | 0.942590i | \(-0.608383\pi\) |
0.649330 | + | 0.760507i | \(0.275050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.17777 | + | 15.8964i | 0.434580 | + | 0.752715i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.24547 | − | 1.39924i | 0.106088 | − | 0.0661079i | ||||
\(449\) | − | 18.8337i | − | 0.888817i | −0.895824 | − | 0.444408i | \(-0.853414\pi\) | ||
0.895824 | − | 0.444408i | \(-0.146586\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.5208 | − | 6.65155i | −0.542494 | − | 0.313209i | ||||
\(452\) | −13.9214 | − | 8.03750i | −0.654805 | − | 0.378052i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.02304i | 0.141879i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6325 | + | 25.3442i | 0.684478 | + | 1.18555i | 0.973601 | + | 0.228258i | \(0.0733031\pi\) |
−0.289123 | + | 0.957292i | \(0.593364\pi\) | |||||||
\(458\) | 5.32325 | − | 9.22014i | 0.248739 | − | 0.430829i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1963 | −0.661188 | −0.330594 | − | 0.943773i | \(-0.607249\pi\) | ||||
−0.330594 | + | 0.943773i | \(0.607249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.65787 | 0.355891 | 0.177946 | − | 0.984040i | \(-0.443055\pi\) | ||||
0.177946 | + | 0.984040i | \(0.443055\pi\) | |||||||
\(464\) | −8.09565 | + | 4.67403i | −0.375831 | + | 0.216986i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.99293 | + | 3.45185i | −0.0923206 | + | 0.159904i | ||||
\(467\) | 8.85713 | + | 15.3410i | 0.409859 | + | 0.709897i | 0.994874 | − | 0.101126i | \(-0.0322446\pi\) |
−0.585015 | + | 0.811023i | \(0.698911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0317157 | + | 0.941825i | 0.00146450 | + | 0.0434894i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.38113 | − | 3.10680i | −0.247687 | − | 0.143002i | ||||
\(473\) | −8.64800 | − | 4.99293i | −0.397636 | − | 0.229575i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.23918 | + | 4.92732i | 0.423477 | + | 0.225843i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.12349 | + | 7.14210i | 0.188604 | + | 0.326672i | ||||
\(479\) | −6.41996 | + | 11.1197i | −0.293336 | + | 0.508072i | −0.974596 | − | 0.223969i | \(-0.928099\pi\) |
0.681261 | + | 0.732041i | \(0.261432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.341598 | + | 0.197222i | −0.0155755 | + | 0.00899254i | ||||
\(482\) | 10.9556 | 0.499015 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.46457 | −0.384753 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.88929 | − | 3.27235i | 0.0856119 | − | 0.148284i | −0.820040 | − | 0.572306i | \(-0.806049\pi\) |
0.905652 | + | 0.424022i | \(0.139382\pi\) | |||||||
\(488\) | 5.50025 | + | 9.52671i | 0.248985 | + | 0.431254i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.1664i | − | 1.45165i | −0.687880 | − | 0.725824i | \(-0.741459\pi\) | ||
0.687880 | − | 0.725824i | \(-0.258541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.0398 | − | 18.4982i | −1.44300 | − | 0.833115i | ||||
\(494\) | −0.501103 | − | 0.289312i | −0.0225457 | − | 0.0130168i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 10.3302i | − | 0.463838i | ||||||
\(497\) | 12.7048 | + | 20.3883i | 0.569886 | + | 0.914540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.9683 | + | 27.6579i | 0.714839 | + | 1.23814i | 0.963022 | + | 0.269424i | \(0.0868332\pi\) |
−0.248183 | + | 0.968713i | \(0.579833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.8247 | − | 10.8685i | 0.840190 | − | 0.485084i | ||||
\(503\) | 5.29834 | 0.236241 | 0.118121 | − | 0.992999i | \(-0.462313\pi\) | ||||
0.118121 | + | 0.992999i | \(0.462313\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.7362 | − | 6.19855i | 0.477282 | − | 0.275559i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.60867 | − | 11.4465i | 0.293212 | − | 0.507858i | ||||
\(509\) | 18.6321 | + | 32.2718i | 0.825854 | + | 1.43042i | 0.901265 | + | 0.433269i | \(0.142640\pi\) |
−0.0754100 | + | 0.997153i | \(0.524027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0608 | + | 0.608195i | −0.798965 | + | 0.0269049i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0993 | + | 8.71758i | 0.666001 | + | 0.384516i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.42867i | − | 0.194773i | ||||||
\(518\) | −1.12747 | + | 0.0379671i | −0.0495380 | + | 0.00166818i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00676 | + | 10.4040i | −0.263161 | + | 0.455808i | −0.967080 | − | 0.254472i | \(-0.918098\pi\) |
0.703919 | + | 0.710280i | \(0.251432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.4136 | − | 13.5178i | 1.02380 | − | 0.591093i | 0.108600 | − | 0.994085i | \(-0.465363\pi\) |
0.915203 | + | 0.402992i | \(0.132030\pi\) | |||||||
\(524\) | −9.40160 | −0.410711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.3511 | −0.800148 | ||||||||
\(527\) | 35.4058 | − | 20.4416i | 1.54230 | − | 0.890449i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8081 | − | 32.5766i | 0.817744 | − | 1.41637i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.875193 | − | 1.40449i | −0.0379444 | − | 0.0608923i | ||||
\(533\) | 7.72879i | 0.334771i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.308459 | + | 0.178089i | 0.0133234 | + | 0.00769228i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.8371i | 1.07080i | ||||||||
\(539\) | 9.25604 | − | 6.20981i | 0.398686 | − | 0.267475i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.85450 | + | 10.1403i | 0.251705 | + | 0.435965i | 0.963995 | − | 0.265919i | \(-0.0856755\pi\) |
−0.712291 | + | 0.701885i | \(0.752342\pi\) | |||||||
\(542\) | −12.2204 | + | 21.1663i | −0.524910 | + | 0.909171i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.42743 | − | 1.97883i | 0.146950 | − | 0.0848415i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6050 | −0.752737 | −0.376369 | − | 0.926470i | \(-0.622827\pi\) | ||||
−0.376369 | + | 0.926470i | \(0.622827\pi\) | |||||||
\(548\) | 8.11701 | − | 4.68636i | 0.346741 | − | 0.200191i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.92350 | + | 5.06364i | 0.124545 | + | 0.215718i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.1312 | − | 11.2694i | −0.898589 | − | 0.479224i | ||||
\(554\) | 23.1970i | 0.985548i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.2201 | − | 7.05530i | −0.518249 | − | 0.299211i | ||||
\(557\) | −17.3913 | − | 10.0409i | −0.736892 | − | 0.425445i | 0.0840462 | − | 0.996462i | \(-0.473216\pi\) |
−0.820938 | + | 0.571017i | \(0.806549\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.80155i | 0.245380i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.04005 | − | 12.1937i | −0.296967 | − | 0.514361i | ||||
\(563\) | −11.9038 | + | 20.6180i | −0.501687 | + | 0.868947i | 0.498312 | + | 0.866998i | \(0.333954\pi\) |
−0.999998 | + | 0.00194851i | \(0.999380\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.79820 | 0.117617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.07975 | 0.380978 | ||||||||
\(569\) | −35.8766 | + | 20.7134i | −1.50403 | + | 0.868350i | −0.504037 | + | 0.863682i | \(0.668152\pi\) |
−0.999989 | + | 0.00466765i | \(0.998514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5784 | + | 35.6428i | −0.861177 | + | 1.49160i | 0.00961607 | + | 0.999954i | \(0.496939\pi\) |
−0.870793 | + | 0.491649i | \(0.836394\pi\) | |||||||
\(572\) | −0.736513 | − | 1.27568i | −0.0307951 | − | 0.0533388i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.4016 | + | 19.5040i | −0.434155 | + | 0.814080i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.7532 | − | 6.20835i | −0.447661 | − | 0.258457i | 0.259181 | − | 0.965829i | \(-0.416547\pi\) |
−0.706842 | + | 0.707372i | \(0.749881\pi\) | |||||||
\(578\) | −1.15787 | − | 0.668498i | −0.0481611 | − | 0.0278058i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.81860 | + | 1.13324i | −0.0754482 | + | 0.0470148i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.66802 | − | 4.62114i | −0.110498 | − | 0.191388i | ||||
\(584\) | −3.41511 | + | 5.91515i | −0.141318 | + | 0.244771i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1354 | + | 12.7799i | −0.914406 | + | 0.527932i | ||||
\(587\) | −4.01980 | −0.165915 | −0.0829575 | − | 0.996553i | \(-0.526437\pi\) | ||||
−0.0829575 | + | 0.996553i | \(0.526437\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.46127 | −0.266232 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.213192 | + | 0.369259i | −0.00876213 | + | 0.0151764i | ||||
\(593\) | −21.7667 | − | 37.7010i | −0.893850 | − | 1.54819i | −0.835221 | − | 0.549914i | \(-0.814660\pi\) |
−0.0586292 | − | 0.998280i | \(-0.518673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.47225i | 0.101267i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.23749 | − | 3.60121i | −0.255070 | − | 0.147265i | ||||
\(599\) | 27.8218 | + | 16.0629i | 1.13677 | + | 0.656314i | 0.945629 | − | 0.325249i | \(-0.105448\pi\) |
0.191141 | + | 0.981563i | \(0.438781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.21681i | 0.335171i | 0.985858 | + | 0.167585i | \(0.0535970\pi\) | ||||
−0.985858 | + | 0.167585i | \(0.946403\pi\) | |||||||
\(602\) | −7.80788 | + | 14.6405i | −0.318225 | + | 0.596702i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.4425 | − | 18.0869i | −0.424898 | − | 0.735945i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4532 | − | 14.1180i | 0.992523 | − | 0.573034i | 0.0864957 | − | 0.996252i | \(-0.472433\pi\) |
0.906028 | + | 0.423219i | \(0.139100\pi\) | |||||||
\(608\) | −0.625477 | −0.0253664 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.22825 | + | 1.28648i | −0.0901452 | + | 0.0520454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3962 | + | 26.6670i | −0.621846 | + | 1.07707i | 0.367296 | + | 0.930104i | \(0.380284\pi\) |
−0.989142 | + | 0.146965i | \(0.953050\pi\) | |||||||
\(614\) | 17.1430 | + | 29.6926i | 0.691836 | + | 1.19829i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.141786 | − | 4.21045i | −0.00571272 | − | 0.169644i | ||||
\(617\) | − | 4.42613i | − | 0.178189i | −0.996023 | − | 0.0890947i | \(-0.971603\pi\) | ||
0.996023 | − | 0.0890947i | \(-0.0283974\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.47047 | − | 5.46778i | −0.380650 | − | 0.219768i | 0.297451 | − | 0.954737i | \(-0.403864\pi\) |
−0.678101 | + | 0.734969i | \(0.737197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8.68041i | − | 0.348053i | ||||||
\(623\) | 9.37171 | + | 4.99800i | 0.375470 | + | 0.200241i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.0106 | + | 25.9992i | −0.599946 | + | 1.03914i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.1722 | + | 12.2238i | −0.844862 | + | 0.487781i | ||||
\(629\) | −1.68748 | −0.0672841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.2293 | −1.52189 | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||||
−0.760943 | + | 0.648819i | \(0.775263\pi\) | |||||||
\(632\) | −7.83895 | + | 4.52582i | −0.311817 | + | 0.180028i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.8628 | + | 24.0111i | −0.550563 | + | 0.953603i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.81318 | − | 2.85321i | −0.230327 | − | 0.113048i | ||||
\(638\) | 14.8849i | 0.589300i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.0339 | + | 16.7627i | 1.14677 | + | 0.662088i | 0.948098 | − | 0.317979i | \(-0.103004\pi\) |
0.198671 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4072i | 0.686474i | 0.939249 | + | 0.343237i | \(0.111523\pi\) | ||||
−0.939249 | + | 0.343237i | \(0.888477\pi\) | |||||||
\(644\) | −10.8940 | − | 17.4824i | −0.429283 | − | 0.688903i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.23771 | − | 2.14378i | −0.0486971 | − | 0.0843458i | ||||
\(647\) | −19.1301 | + | 33.1343i | −0.752082 | + | 1.30264i | 0.194730 | + | 0.980857i | \(0.437617\pi\) |
−0.946812 | + | 0.321787i | \(0.895716\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.56839 | + | 4.94696i | −0.336339 | + | 0.194185i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.91515 | −0.231655 | ||||||||
\(653\) | 28.0023 | − | 16.1671i | 1.09581 | − | 0.632669i | 0.160696 | − | 0.987004i | \(-0.448626\pi\) |
0.935119 | + | 0.354335i | \(0.115293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.17731 | + | 7.23532i | 0.163097 | + | 0.282492i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.35446 | + | 0.247660i | −0.286707 | + | 0.00965478i | ||||
\(659\) | 16.4516i | 0.640865i | 0.947271 | + | 0.320433i | \(0.103828\pi\) | ||||
−0.947271 | + | 0.320433i | \(0.896172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.14550 | − | 1.23870i | −0.0834502 | − | 0.0481800i | 0.457694 | − | 0.889110i | \(-0.348675\pi\) |
−0.541144 | + | 0.840930i | \(0.682009\pi\) | |||||||
\(662\) | 5.45899 | + | 3.15175i | 0.212170 | + | 0.122496i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.809898i | 0.0314301i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.3903 | + | 63.0298i | 1.40904 | + | 2.44052i | ||||
\(668\) | −6.07201 | + | 10.5170i | −0.234933 | + | 0.406916i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.5161 | 0.676202 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0784 | −0.658326 | −0.329163 | − | 0.944273i | \(-0.606767\pi\) | ||||
−0.329163 | + | 0.944273i | \(0.606767\pi\) | |||||||
\(674\) | 23.7375 | − | 13.7048i | 0.914333 | − | 0.527891i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.07210 | − | 10.5172i | 0.233542 | − | 0.404507i | ||||
\(677\) | −23.3041 | − | 40.3639i | −0.895650 | − | 1.55131i | −0.832998 | − | 0.553276i | \(-0.813377\pi\) |
−0.0626524 | − | 0.998035i | \(-0.519956\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.0221 | − | 17.6880i | −0.422990 | − | 0.678803i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.2450 | − | 8.22437i | −0.545470 | − | 0.314927i | ||||
\(683\) | 2.04994 | + | 1.18353i | 0.0784388 | + | 0.0452867i | 0.538706 | − | 0.842494i | \(-0.318913\pi\) |
−0.460268 | + | 0.887780i | \(0.652247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.8299 | − | 15.0237i | −0.413488 | − | 0.573609i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.13566 | + | 5.43113i | 0.119546 | + | 0.207060i | ||||
\(689\) | −1.55006 | + | 2.68478i | −0.0590524 | + | 0.102282i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0534 | + | 11.0005i | −0.724826 | + | 0.418479i | −0.816527 | − | 0.577308i | \(-0.804103\pi\) |
0.0917001 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(692\) | −16.3984 | −0.623372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.16672 | 0.310004 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.5323 | + | 28.6349i | −0.626207 | + | 1.08462i | ||||
\(698\) | −13.7943 | − | 23.8924i | −0.522120 | − | 0.904339i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.7909i | − | 1.08742i | −0.839274 | − | 0.543708i | \(-0.817020\pi\) | ||
0.839274 | − | 0.543708i | \(-0.182980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.230963 | + | 0.133347i | 0.00871094 | + | 0.00502926i | ||||
\(704\) | −1.37897 | − | 0.796151i | −0.0519721 | − | 0.0300061i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.04285i | 0.265061i | ||||||||
\(707\) | 0.670346 | + | 19.9065i | 0.0252110 | + | 0.748661i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.64049 | − | 13.2337i | −0.286945 | − | 0.497003i | 0.686134 | − | 0.727475i | \(-0.259306\pi\) |
−0.973079 | + | 0.230472i | \(0.925973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.47659 | − | 2.00721i | 0.130291 | − | 0.0752234i | ||||
\(713\) | −80.4269 | −3.01201 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.73398 | + | 1.57846i | −0.102174 | + | 0.0589900i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.17213 | + | 14.1545i | −0.304981 | + | 0.528243i | ||||
\(719\) | −8.33730 | − | 14.4406i | −0.310929 | − | 0.538545i | 0.667635 | − | 0.744489i | \(-0.267307\pi\) |
−0.978564 | + | 0.205944i | \(0.933973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.07121 | − | 3.88372i | 0.0771360 | − | 0.144637i | ||||
\(722\) | − | 18.6088i | − | 0.692547i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.08336 | + | 4.08958i | 0.263251 | + | 0.151988i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.4228i | − | 1.20250i | −0.799062 | − | 0.601248i | \(-0.794670\pi\) | ||
0.799062 | − | 0.601248i | \(-0.205330\pi\) | |||||||
\(728\) | −2.07726 | + | 1.29443i | −0.0769885 | + | 0.0479746i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4099 | + | 21.4945i | −0.458996 | + | 0.795004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1207 | + | 23.1637i | −1.48189 | + | 0.855570i | −0.999789 | − | 0.0205452i | \(-0.993460\pi\) |
−0.482102 | + | 0.876115i | \(0.660126\pi\) | |||||||
\(734\) | 3.00798 | 0.111026 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.78564 | −0.286983 | ||||||||
\(737\) | 0.491161 | − | 0.283572i | 0.0180921 | − | 0.0104455i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.23689 | + | 14.2667i | −0.302999 | + | 0.524809i | −0.976814 | − | 0.214091i | \(-0.931321\pi\) |
0.673815 | + | 0.738900i | \(0.264655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.52488 | + | 4.68905i | −0.276247 | + | 0.172141i | ||||
\(743\) | 38.4778i | 1.41161i | 0.708405 | + | 0.705806i | \(0.249415\pi\) | ||||
−0.708405 | + | 0.705806i | \(0.750585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.0892 | − | 11.5985i | −0.735519 | − | 0.424652i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 6.30178i | − | 0.230416i | ||||||
\(749\) | −24.1567 | + | 45.2960i | −0.882666 | + | 1.65508i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9145 | − | 32.7608i | −0.690198 | − | 1.19546i | −0.971773 | − | 0.235919i | \(-0.924190\pi\) |
0.281574 | − | 0.959539i | \(-0.409143\pi\) | |||||||
\(752\) | −1.39065 | + | 2.40868i | −0.0507118 | + | 0.0878355i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.48922 | − | 4.32390i | 0.272741 | − | 0.157467i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1485 | 0.405197 | 0.202599 | − | 0.979262i | \(-0.435061\pi\) | ||||
0.202599 | + | 0.979262i | \(0.435061\pi\) | |||||||
\(758\) | 23.6181 | − | 13.6359i | 0.857846 | − | 0.495278i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.6239 | + | 25.3294i | 0.530117 | + | 0.918189i | 0.999383 | + | 0.0351321i | \(0.0111852\pi\) |
−0.469266 | + | 0.883057i | \(0.655481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.178089 | + | 5.28850i | 0.00644726 | + | 0.191457i | ||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.69096 | − | 2.13098i | −0.133360 | − | 0.0769953i | ||||
\(767\) | 4.97804 | + | 2.87407i | 0.179747 | + | 0.103777i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 0.892823i | − | 0.0321960i | −0.999870 | − | 0.0160980i | \(-0.994876\pi\) | ||
0.999870 | − | 0.0160980i | \(-0.00512438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.85772 | + | 15.3420i | 0.318796 | + | 0.552172i | ||||
\(773\) | −9.89011 | + | 17.1302i | −0.355723 | + | 0.616130i | −0.987241 | − | 0.159231i | \(-0.949099\pi\) |
0.631519 | + | 0.775361i | \(0.282432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.87721 | −0.282775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.08172 | 0.0746332 | ||||||||
\(779\) | 4.52553 | − | 2.61281i | 0.162144 | − | 0.0936138i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.22886 | − | 12.5207i | 0.258669 | − | 0.448028i | ||||
\(782\) | −15.4064 | − | 26.6847i | −0.550933 | − | 0.954243i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.98414 | + | 0.470912i | −0.249434 | + | 0.0168183i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0325 | − | 13.2978i | −0.821021 | − | 0.474017i | 0.0297473 | − | 0.999557i | \(-0.490530\pi\) |
−0.850769 | + | 0.525541i | \(0.823863\pi\) | |||||||
\(788\) | 3.72694 | + | 2.15175i | 0.132767 | + | 0.0766529i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.4928 | + | 36.0959i | 0.799752 | + | 1.28342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.08823 | − | 8.81308i | −0.180688 | − | 0.312962i | ||||
\(794\) | −11.1885 | + | 19.3791i | −0.397066 | + | 0.687739i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | − | 1.73205i | 0.106332 | − | 0.0613909i | ||||
\(797\) | 21.4698 | 0.760499 | 0.380250 | − | 0.924884i | \(-0.375838\pi\) | ||||
0.380250 | + | 0.924884i | \(0.375838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.0074 | −0.389415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.83196 | − | 17.0295i | 0.347179 | − | 0.601331i | ||||
\(803\) | 5.43790 | + | 9.41871i | 0.191899 | + | 0.332379i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.55634i | 0.336608i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.51962 | + | 3.76411i | 0.229360 | + | 0.132421i | ||||
\(809\) | 18.2930 | + | 10.5615i | 0.643149 | + | 0.371322i | 0.785827 | − | 0.618447i | \(-0.212238\pi\) |
−0.142677 | + | 0.989769i | \(0.545571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3784i | 0.469779i | 0.972022 | + | 0.234889i | \(0.0754728\pi\) | ||||
−0.972022 | + | 0.234889i | \(0.924527\pi\) | |||||||
\(812\) | 24.7186 | − | 0.832393i | 0.867453 | − | 0.0292113i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.339466 | + | 0.587972i | 0.0118983 | + | 0.0206084i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.39705 | − | 1.96129i | 0.118848 | − | 0.0686167i | ||||
\(818\) | 2.53956 | 0.0887936 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.67591 | + | 3.27699i | −0.198091 | + | 0.114368i | −0.595765 | − | 0.803159i | \(-0.703151\pi\) |
0.397674 | + | 0.917527i | \(0.369818\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.9344 | − | 37.9915i | 0.764585 | − | 1.32430i | −0.175880 | − | 0.984412i | \(-0.556277\pi\) |
0.940466 | − | 0.339889i | \(-0.110389\pi\) | |||||||
\(824\) | −0.831805 | − | 1.44073i | −0.0289773 | − | 0.0501901i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.69432 | + | 13.9524i | 0.302514 | + | 0.485467i | ||||
\(827\) | 19.1611i | 0.666296i | 0.942875 | + | 0.333148i | \(0.108111\pi\) | ||||
−0.942875 | + | 0.333148i | \(0.891889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.6635 | − | 8.46597i | −0.509284 | − | 0.294035i | 0.223255 | − | 0.974760i | \(-0.428332\pi\) |
−0.732539 | + | 0.680725i | \(0.761665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.925091i | 0.0320718i | ||||||||
\(833\) | −15.4344 | − | 23.0058i | −0.534771 | − | 0.797103i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.497974 | + | 0.862517i | −0.0172228 | + | 0.0298308i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.7620 | − | 16.0284i | 0.959023 | − | 0.553692i | ||||
\(839\) | −10.5028 | −0.362596 | −0.181298 | − | 0.983428i | \(-0.558030\pi\) | ||||
−0.181298 | + | 0.983428i | \(0.558030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −58.3861 | −2.01331 | ||||||||
\(842\) | 21.8413 | − | 12.6101i | 0.752700 | − | 0.434572i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.19432 | − | 8.99682i | 0.178796 | − | 0.309683i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.7606 | + | 10.5385i | 0.678984 | + | 0.362107i | ||||
\(848\) | 3.35114i | 0.115079i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.87492 | + | 1.65983i | 0.0985509 | + | 0.0568984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2419i | 1.03546i | 0.855544 | + | 0.517731i | \(0.173223\pi\) | ||||
−0.855544 | + | 0.517731i | \(0.826777\pi\) | |||||||
\(854\) | −0.979534 | − | 29.0881i | −0.0335190 | − | 0.995374i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.70139 | + | 16.8033i | 0.331587 | + | 0.574325i | ||||
\(857\) | −11.1322 | + | 19.2816i | −0.380270 | + | 0.658646i | −0.991101 | − | 0.133115i | \(-0.957502\pi\) |
0.610831 | + | 0.791761i | \(0.290835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.7059 | + | 15.4187i | −0.911195 | + | 0.526078i | −0.880815 | − | 0.473460i | \(-0.843005\pi\) |
−0.0303793 | + | 0.999538i | \(0.509672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.6710 | −1.14684 | ||||||||
\(863\) | −20.0190 | + | 11.5580i | −0.681454 | + | 0.393437i | −0.800403 | − | 0.599463i | \(-0.795381\pi\) |
0.118949 | + | 0.992900i | \(0.462048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.3805 | + | 19.7116i | 0.386725 | + | 0.669828i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.8612 | + | 24.1159i | −0.436536 | + | 0.818546i | ||||
\(869\) | 14.4130i | 0.488926i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.285353 | − | 0.164749i | −0.00966882 | − | 0.00558230i | ||||
\(872\) | 1.73205 | + | 1.00000i | 0.0586546 | + | 0.0338643i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.86974i | 0.164721i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6074 | + | 21.8366i | 0.425720 | + | 0.737369i | 0.996487 | − | 0.0837427i | \(-0.0266874\pi\) |
−0.570767 | + | 0.821112i | \(0.693354\pi\) | |||||||
\(878\) | 1.07550 | − | 1.86282i | 0.0362963 | − | 0.0628670i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5142 | 0.691140 | 0.345570 | − | 0.938393i | \(-0.387686\pi\) | ||||
0.345570 | + | 0.938393i | \(0.387686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0491 | 1.44872 | 0.724358 | − | 0.689424i | \(-0.242136\pi\) | ||||
0.724358 | + | 0.689424i | \(0.242136\pi\) | |||||||
\(884\) | −3.17068 | + | 1.83059i | −0.106642 | + | 0.0615696i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.83239 | + | 6.63790i | −0.128752 | + | 0.223005i | ||||
\(887\) | −16.6952 | − | 28.9170i | −0.560571 | − | 0.970938i | −0.997447 | − | 0.0714156i | \(-0.977248\pi\) |
0.436876 | − | 0.899522i | \(-0.356085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.6791 | + | 18.4942i | −0.995405 | + | 0.620277i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.8964 | − | 9.17777i | −0.532250 | − | 0.307294i | ||||
\(893\) | 1.50657 | + | 0.869820i | 0.0504156 | + | 0.0291074i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.24501 | + | 2.33451i | −0.0415929 | + | 0.0779906i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.41684 | + | 16.3104i | 0.314244 | + | 0.544287i | ||||
\(899\) | 48.2834 | − | 83.6293i | 1.61034 | − | 2.78919i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4858 | + | 6.63132i | −0.382647 | + | 0.220921i | ||||
\(902\) | 13.3031 | 0.442945 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.0750 | 0.534646 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6898 | − | 23.7115i | 0.454563 | − | 0.787327i | −0.544100 | − | 0.839021i | \(-0.683129\pi\) |
0.998663 | + | 0.0516937i | \(0.0164620\pi\) | |||||||
\(908\) | −1.51152 | − | 2.61803i | −0.0501616 | − | 0.0868825i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.0422i | 1.09474i | 0.836892 | + | 0.547368i | \(0.184370\pi\) | ||||
−0.836892 | + | 0.547368i | \(0.815630\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.11683 | + | 0.644801i | 0.0369616 | + | 0.0213398i | ||||
\(914\) | −25.3442 | − | 14.6325i | −0.838311 | − | 0.483999i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.6465i | 0.351770i | ||||||||
\(917\) | 21.9482 | + | 11.7051i | 0.724792 | + | 0.386537i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.2444 | − | 22.9400i | −0.436893 | − | 0.756722i | 0.560555 | − | 0.828117i | \(-0.310588\pi\) |
−0.997448 | + | 0.0713958i | \(0.977255\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.2944 | − | 7.09815i | 0.404893 | − | 0.233765i | ||||
\(923\) | −8.39960 | −0.276476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.63191 | + | 3.82893i | −0.217938 | + | 0.125827i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.67403 | − | 8.09565i | 0.153432 | − | 0.265753i | ||||
\(929\) | −15.5952 | − | 27.0117i | −0.511663 | − | 0.886226i | −0.999909 | − | 0.0135196i | \(-0.995696\pi\) |
0.488246 | − | 0.872706i | \(-0.337637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.294545 | + | 4.36842i | 0.00965332 | + | 0.143169i | ||||
\(932\) | − | 3.98585i | − | 0.130561i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.3410 | − | 8.85713i | −0.501973 | − | 0.289814i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.40017i | 0.209084i | 0.994520 | + | 0.104542i | \(0.0333377\pi\) | ||||
−0.994520 | + | 0.104542i | \(0.966662\pi\) | |||||||
\(938\) | −0.498379 | − | 0.799787i | −0.0162727 | − | 0.0261140i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.56243 | − | 4.43825i | 0.0835327 | − | 0.144683i | −0.821232 | − | 0.570594i | \(-0.806713\pi\) |
0.904765 | + | 0.425911i | \(0.140046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.3316 | − | 32.5231i | 1.83441 | − | 1.05910i | ||||
\(944\) | 6.21360 | 0.202235 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.98585 | 0.324668 | ||||||||
\(947\) | −36.5679 | + | 21.1125i | −1.18830 | + | 0.686064i | −0.957919 | − | 0.287037i | \(-0.907330\pi\) |
−0.230378 | + | 0.973101i | \(0.573996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.15929 | − | 5.47206i | 0.102555 | − | 0.177630i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.4650 | + | 0.352407i | −0.339174 | + | 0.0114216i | ||||
\(953\) | − | 8.12428i | − | 0.263171i | −0.991305 | − | 0.131586i | \(-0.957993\pi\) | ||
0.991305 | − | 0.131586i | \(-0.0420068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.14210 | − | 4.12349i | −0.230992 | − | 0.133363i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 12.8399i | − | 0.414839i | ||||||
\(959\) | −24.7838 | + | 0.834589i | −0.800311 | + | 0.0269503i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8560 | + | 65.5686i | 1.22116 | + | 2.11512i | ||||
\(962\) | 0.197222 | − | 0.341598i | 0.00635869 | − | 0.0110136i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.48785 | + | 5.47782i | −0.305583 | + | 0.176429i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.3097 | −1.68217 | −0.841084 | − | 0.540905i | \(-0.818082\pi\) | ||||
−0.841084 | + | 0.540905i | \(0.818082\pi\) | |||||||
\(968\) | 7.33053 | − | 4.23229i | 0.235612 | − | 0.136031i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.55280 | − | 14.8139i | −0.274473 | − | 0.475400i | 0.695529 | − | 0.718498i | \(-0.255170\pi\) |
−0.970002 | + | 0.243097i | \(0.921837\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.7441 | + | 31.6849i | 0.632968 | + | 1.01577i | ||||
\(974\) | 3.77858i | 0.121073i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.52671 | − | 5.50025i | −0.304943 | − | 0.176059i | ||||
\(977\) | −31.5215 | − | 18.1989i | −1.00846 | − | 0.582235i | −0.0977201 | − | 0.995214i | \(-0.531155\pi\) |
−0.910741 | + | 0.412979i | \(0.864488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.39217i | − | 0.204295i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.0832 | + | 27.8569i | 0.513235 | + | 0.888950i | ||||
\(983\) | 12.8641 | − | 22.2813i | 0.410302 | − | 0.710664i | −0.584621 | − | 0.811307i | \(-0.698757\pi\) |
0.994923 | + | 0.100643i | \(0.0320900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.9963 | 1.17820 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.578623 | 0.0184085 | ||||||||
\(989\) | 42.2848 | − | 24.4132i | 1.34458 | − | 0.776293i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.07375 | − | 10.5200i | 0.192939 | − | 0.334180i | −0.753284 | − | 0.657696i | \(-0.771531\pi\) |
0.946223 | + | 0.323515i | \(0.104865\pi\) | |||||||
\(992\) | 5.16508 | + | 8.94618i | 0.163991 | + | 0.284041i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.1968 | − | 11.3044i | −0.672321 | − | 0.358554i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.8552 | − | 8.57663i | −0.470468 | − | 0.271625i | 0.245968 | − | 0.969278i | \(-0.420894\pi\) |
−0.716435 | + | 0.697653i | \(0.754228\pi\) | |||||||
\(998\) | −27.6579 | − | 15.9683i | −0.875495 | − | 0.505467i | ||||
\(999\) | 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 | 3150.2.bf.f.1151.5 | 32 | ||
3.2 | odd | 2 | inner | 3150.2.bf.f.1151.15 | 32 | ||
5.2 | odd | 4 | 630.2.bo.a.269.5 | yes | 16 | ||
5.3 | odd | 4 | 630.2.bo.b.269.7 | yes | 16 | ||
5.4 | even | 2 | inner | 3150.2.bf.f.1151.16 | 32 | ||
7.5 | odd | 6 | inner | 3150.2.bf.f.1601.13 | 32 | ||
15.2 | even | 4 | 630.2.bo.b.269.4 | yes | 16 | ||
15.8 | even | 4 | 630.2.bo.a.269.2 | yes | 16 | ||
15.14 | odd | 2 | inner | 3150.2.bf.f.1151.6 | 32 | ||
21.5 | even | 6 | inner | 3150.2.bf.f.1601.5 | 32 | ||
35.3 | even | 12 | 4410.2.d.a.4409.13 | 16 | |||
35.12 | even | 12 | 630.2.bo.a.89.2 | ✓ | 16 | ||
35.17 | even | 12 | 4410.2.d.b.4409.14 | 16 | |||
35.18 | odd | 12 | 4410.2.d.a.4409.4 | 16 | |||
35.19 | odd | 6 | inner | 3150.2.bf.f.1601.6 | 32 | ||
35.32 | odd | 12 | 4410.2.d.b.4409.3 | 16 | |||
35.33 | even | 12 | 630.2.bo.b.89.4 | yes | 16 | ||
105.17 | odd | 12 | 4410.2.d.a.4409.3 | 16 | |||
105.32 | even | 12 | 4410.2.d.a.4409.14 | 16 | |||
105.38 | odd | 12 | 4410.2.d.b.4409.4 | 16 | |||
105.47 | odd | 12 | 630.2.bo.b.89.7 | yes | 16 | ||
105.53 | even | 12 | 4410.2.d.b.4409.13 | 16 | |||
105.68 | odd | 12 | 630.2.bo.a.89.5 | yes | 16 | ||
105.89 | even | 6 | inner | 3150.2.bf.f.1601.14 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.2 | ✓ | 16 | 35.12 | even | 12 | ||
630.2.bo.a.89.5 | yes | 16 | 105.68 | odd | 12 | ||
630.2.bo.a.269.2 | yes | 16 | 15.8 | even | 4 | ||
630.2.bo.a.269.5 | yes | 16 | 5.2 | odd | 4 | ||
630.2.bo.b.89.4 | yes | 16 | 35.33 | even | 12 | ||
630.2.bo.b.89.7 | yes | 16 | 105.47 | odd | 12 | ||
630.2.bo.b.269.4 | yes | 16 | 15.2 | even | 4 | ||
630.2.bo.b.269.7 | yes | 16 | 5.3 | odd | 4 | ||
3150.2.bf.f.1151.5 | 32 | 1.1 | even | 1 | trivial | ||
3150.2.bf.f.1151.6 | 32 | 15.14 | odd | 2 | inner | ||
3150.2.bf.f.1151.15 | 32 | 3.2 | odd | 2 | inner | ||
3150.2.bf.f.1151.16 | 32 | 5.4 | even | 2 | inner | ||
3150.2.bf.f.1601.5 | 32 | 21.5 | even | 6 | inner | ||
3150.2.bf.f.1601.6 | 32 | 35.19 | odd | 6 | inner | ||
3150.2.bf.f.1601.13 | 32 | 7.5 | odd | 6 | inner | ||
3150.2.bf.f.1601.14 | 32 | 105.89 | even | 6 | inner | ||
4410.2.d.a.4409.3 | 16 | 105.17 | odd | 12 | |||
4410.2.d.a.4409.4 | 16 | 35.18 | odd | 12 | |||
4410.2.d.a.4409.13 | 16 | 35.3 | even | 12 | |||
4410.2.d.a.4409.14 | 16 | 105.32 | even | 12 | |||
4410.2.d.b.4409.3 | 16 | 35.32 | odd | 12 | |||
4410.2.d.b.4409.4 | 16 | 105.38 | odd | 12 | |||
4410.2.d.b.4409.13 | 16 | 105.53 | even | 12 | |||
4410.2.d.b.4409.14 | 16 | 35.17 | even | 12 |