Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.2 | ||
Root | \(0.809017 + 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.b.379.1 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11803 | + | 0.866025i | −0.790569 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 1.93649i | 0.250000 | − | 0.968246i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.87298i | 1.46385i | 0.681385 | + | 0.731925i | \(0.261378\pi\) | ||||
−0.681385 | + | 0.731925i | \(0.738622\pi\) | |||||||
\(8\) | 1.11803 | + | 2.59808i | 0.395285 | + | 0.918559i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.23607 | 0.620174 | 0.310087 | − | 0.950708i | \(-0.399642\pi\) | ||||
0.310087 | + | 0.950708i | \(0.399642\pi\) | |||||||
\(14\) | −3.35410 | − | 4.33013i | −0.896421 | − | 1.15728i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.50000 | − | 1.93649i | −0.875000 | − | 0.484123i | ||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | + | 1.73205i | 0.917663 | + | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.47214 | + | 3.46410i | −0.953463 | + | 0.738549i | ||||
\(23\) | − | 3.87298i | − | 0.807573i | −0.914853 | − | 0.403786i | \(-0.867694\pi\) | ||
0.914853 | − | 0.403786i | \(-0.132306\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −2.50000 | + | 1.93649i | −0.490290 | + | 0.379777i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.50000 | + | 1.93649i | 1.41737 | + | 0.365963i | ||||
\(29\) | −2.23607 | −0.415227 | −0.207614 | − | 0.978211i | \(-0.566570\pi\) | ||||
−0.207614 | + | 0.978211i | \(0.566570\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.94427 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(32\) | 5.59017 | − | 0.866025i | 0.988212 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.11803 | + | 0.866025i | −0.191741 | + | 0.148522i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | −5.97214 | + | 1.52761i | −0.968808 | + | 0.247811i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 2.00000 | − | 7.74597i | 0.301511 | − | 1.16775i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.35410 | + | 4.33013i | 0.494535 | + | 0.638442i | ||||
\(47\) | 7.74597i | 1.12987i | 0.825137 | + | 0.564933i | \(0.191098\pi\) | ||||
−0.825137 | + | 0.564933i | \(0.808902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.00000 | −1.14286 | ||||||||
\(50\) | −5.59017 | + | 4.33013i | −0.790569 | + | 0.612372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.11803 | − | 4.33013i | 0.155043 | − | 0.600481i | ||||
\(53\) | 6.70820 | 0.921443 | 0.460721 | − | 0.887545i | \(-0.347591\pi\) | ||||
0.460721 | + | 0.887545i | \(0.347591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.0623 | + | 4.33013i | −1.34463 | + | 0.578638i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | − | 1.93649i | 0.328266 | − | 0.254274i | ||||
\(59\) | 8.66025i | 1.12747i | 0.825956 | + | 0.563735i | \(0.190636\pi\) | ||||
−0.825956 | + | 0.563735i | \(0.809364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 10.0000 | − | 7.74597i | 1.27000 | − | 0.983739i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.50000 | + | 5.80948i | −0.687500 | + | 0.726184i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1244i | 1.48123i | 0.671932 | + | 0.740613i | \(0.265465\pi\) | ||||
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(68\) | 0.500000 | − | 1.93649i | 0.0606339 | − | 0.234834i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | 0.351123 | 0.175562 | − | 0.984468i | \(-0.443826\pi\) | ||||
0.175562 | + | 0.984468i | \(0.443826\pi\) | |||||||
\(74\) | 5.00000 | − | 3.87298i | 0.581238 | − | 0.450225i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.35410 | − | 6.87994i | 0.614158 | − | 0.789183i | ||||
\(77\) | 15.4919i | 1.76547i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | + | 7.74597i | 0.662589 | + | 0.855399i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.47214 | + | 10.3923i | 0.476731 | + | 1.10782i | ||||
\(89\) | 13.8564i | 1.46878i | 0.678730 | + | 0.734388i | \(0.262531\pi\) | ||||
−0.678730 | + | 0.734388i | \(0.737469\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.66025i | 0.907841i | ||||||||
\(92\) | −7.50000 | − | 1.93649i | −0.781929 | − | 0.201893i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.70820 | − | 8.66025i | −0.691898 | − | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | 8.94427 | − | 6.92820i | 0.903508 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.50000 | − | 9.68246i | 0.250000 | − | 0.968246i | ||||
\(101\) | 15.4919i | 1.54150i | 0.637135 | + | 0.770752i | \(0.280120\pi\) | ||||
−0.637135 | + | 0.770752i | \(0.719880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8885 | 1.76261 | 0.881305 | − | 0.472547i | \(-0.156665\pi\) | ||||
0.881305 | + | 0.472547i | \(0.156665\pi\) | |||||||
\(104\) | 2.50000 | + | 5.80948i | 0.245145 | + | 0.569666i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.50000 | + | 5.80948i | −0.728464 | + | 0.564266i | ||||
\(107\) | − | 5.19615i | − | 0.502331i | −0.967944 | − | 0.251166i | \(-0.919186\pi\) | ||
0.967944 | − | 0.251166i | \(-0.0808138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6525 | −1.49924 | −0.749618 | − | 0.661871i | \(-0.769763\pi\) | ||||
−0.749618 | + | 0.661871i | \(0.769763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.50000 | − | 13.5554i | 0.708683 | − | 1.28087i | ||||
\(113\) | − | 6.92820i | − | 0.651751i | −0.945413 | − | 0.325875i | \(-0.894341\pi\) | ||
0.945413 | − | 0.325875i | \(-0.105659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.11803 | + | 4.33013i | −0.103807 | + | 0.402042i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.50000 | − | 9.68246i | −0.690431 | − | 0.891343i | ||||
\(119\) | 3.87298i | 0.355036i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.47214 | + | 17.3205i | −0.401610 | + | 1.55543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8885 | 1.58735 | 0.793676 | − | 0.608341i | \(-0.208165\pi\) | ||||
0.793676 | + | 0.608341i | \(0.208165\pi\) | |||||||
\(128\) | 1.11803 | − | 11.2583i | 0.0988212 | − | 0.995105i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.70820 | + | 15.4919i | −0.581675 | + | 1.34332i | ||||
\(134\) | −10.5000 | − | 13.5554i | −0.907062 | − | 1.17101i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.11803 | + | 2.59808i | 0.0958706 | + | 0.222783i | ||||
\(137\) | −19.0000 | −1.62328 | −0.811640 | − | 0.584158i | \(-0.801425\pi\) | ||||
−0.811640 | + | 0.584158i | \(0.801425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.0000 | + | 7.74597i | −0.839181 | + | 0.650027i | ||||
\(143\) | 8.94427 | 0.747958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.35410 | + | 2.59808i | −0.277587 | + | 0.215018i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.23607 | + | 8.66025i | −0.183804 | + | 0.711868i | ||||
\(149\) | − | 15.4919i | − | 1.26915i | −0.772862 | − | 0.634574i | \(-0.781175\pi\) | ||
0.772862 | − | 0.634574i | \(-0.218825\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | −0.0278640 | + | 12.3288i | −0.00226007 | + | 0.999997i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.4164 | − | 17.3205i | −1.08112 | − | 1.39573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4919i | 1.23639i | 0.786024 | + | 0.618195i | \(0.212136\pi\) | ||||
−0.786024 | + | 0.618195i | \(0.787864\pi\) | |||||||
\(158\) | −10.0000 | + | 7.74597i | −0.795557 | + | 0.616236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0000 | 1.18217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | −13.4164 | − | 3.46410i | −1.04765 | − | 0.270501i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.94427 | + | 6.92820i | −0.694210 | + | 0.537733i | ||||
\(167\) | −8.94427 | −0.692129 | −0.346064 | − | 0.938211i | \(-0.612482\pi\) | ||||
−0.346064 | + | 0.938211i | \(0.612482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.4164 | −1.02003 | −0.510015 | − | 0.860165i | \(-0.670360\pi\) | ||||
−0.510015 | + | 0.860165i | \(0.670360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.3649i | 1.46385i | ||||||||
\(176\) | −14.0000 | − | 7.74597i | −1.05529 | − | 0.583874i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.0000 | − | 15.4919i | −0.899438 | − | 1.16117i | ||||
\(179\) | − | 3.46410i | − | 0.258919i | −0.991585 | − | 0.129460i | \(-0.958676\pi\) | ||
0.991585 | − | 0.129460i | \(-0.0413242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.47214 | −0.332411 | −0.166206 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166206 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(182\) | −7.50000 | − | 9.68246i | −0.555937 | − | 0.717712i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.0623 | − | 4.33013i | 0.741803 | − | 0.319221i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 15.0000 | + | 3.87298i | 1.09399 | + | 0.282466i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6190i | 0.840718i | 0.907358 | + | 0.420359i | \(0.138096\pi\) | ||||
−0.907358 | + | 0.420359i | \(0.861904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.92820i | 0.498703i | 0.968413 | + | 0.249351i | \(0.0802174\pi\) | ||||
−0.968413 | + | 0.249351i | \(0.919783\pi\) | |||||||
\(194\) | 6.00000 | + | 7.74597i | 0.430775 | + | 0.556128i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.00000 | + | 15.4919i | −0.285714 | + | 1.10657i | ||||
\(197\) | 15.4919i | 1.10375i | 0.833925 | + | 0.551877i | \(0.186088\pi\) | ||||
−0.833925 | + | 0.551877i | \(0.813912\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 27.1109i | − | 1.92184i | −0.276827 | − | 0.960920i | \(-0.589283\pi\) | ||
0.276827 | − | 0.960920i | \(-0.410717\pi\) | |||||||
\(200\) | 5.59017 | + | 12.9904i | 0.395285 | + | 0.918559i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.4164 | − | 17.3205i | −0.943975 | − | 1.21867i | ||||
\(203\) | − | 8.66025i | − | 0.607831i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.0000 | + | 15.4919i | −1.39347 | + | 1.07937i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.82624 | − | 4.33013i | −0.542652 | − | 0.300240i | ||||
\(209\) | 16.0000 | + | 6.92820i | 1.10674 | + | 0.479234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.5885i | − | 1.07315i | −0.843851 | − | 0.536577i | \(-0.819717\pi\) | ||
0.843851 | − | 0.536577i | \(-0.180283\pi\) | |||||||
\(212\) | 3.35410 | − | 12.9904i | 0.230361 | − | 0.892183i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.50000 | + | 5.80948i | 0.307614 | + | 0.397128i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 34.6410i | − | 2.35159i | ||||||
\(218\) | 17.5000 | − | 13.5554i | 1.18525 | − | 0.918090i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23607 | 0.150414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8885 | 1.19791 | 0.598953 | − | 0.800784i | \(-0.295584\pi\) | ||||
0.598953 | + | 0.800784i | \(0.295584\pi\) | |||||||
\(224\) | 3.35410 | + | 21.6506i | 0.224105 | + | 1.44659i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | + | 7.74597i | 0.399114 | + | 0.515254i | ||||
\(227\) | 15.5885i | 1.03464i | 0.855791 | + | 0.517321i | \(0.173071\pi\) | ||||
−0.855791 | + | 0.517321i | \(0.826929\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.50000 | − | 5.80948i | −0.164133 | − | 0.381411i | ||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.7705 | + | 4.33013i | 1.09167 | + | 0.281867i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.35410 | − | 4.33013i | −0.217414 | − | 0.280680i | ||||
\(239\) | 11.6190i | 0.751567i | 0.926707 | + | 0.375784i | \(0.122626\pi\) | ||||
−0.926707 | + | 0.375784i | \(0.877374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.92820i | 0.446285i | 0.974786 | + | 0.223142i | \(0.0716315\pi\) | ||||
−0.974786 | + | 0.223142i | \(0.928369\pi\) | |||||||
\(242\) | −5.59017 | + | 4.33013i | −0.359350 | + | 0.278351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427 | + | 3.87298i | 0.569110 | + | 0.246432i | ||||
\(248\) | −10.0000 | − | 23.2379i | −0.635001 | − | 1.47561i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.4919i | − | 0.973970i | ||||||
\(254\) | −20.0000 | + | 15.4919i | −1.25491 | + | 0.972050i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 13.5554i | 0.531250 | + | 0.847215i | ||||
\(257\) | − | 27.7128i | − | 1.72868i | −0.502910 | − | 0.864339i | \(-0.667737\pi\) | ||
0.502910 | − | 0.864339i | \(-0.332263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 17.3205i | − | 1.07624i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.94427 | − | 6.92820i | 0.552579 | − | 0.428026i | ||||
\(263\) | − | 23.2379i | − | 1.43291i | −0.697633 | − | 0.716455i | \(-0.745763\pi\) | ||
0.697633 | − | 0.716455i | \(-0.254237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.91641 | − | 23.1300i | −0.362758 | − | 1.41819i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.4787 | + | 6.06218i | 1.43419 | + | 0.370306i | ||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.6190i | − | 0.705801i | −0.935661 | − | 0.352900i | \(-0.885195\pi\) | ||
0.935661 | − | 0.352900i | \(-0.114805\pi\) | |||||||
\(272\) | −3.50000 | − | 1.93649i | −0.212219 | − | 0.117417i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.2426 | − | 16.4545i | 1.28332 | − | 0.994052i | ||||
\(275\) | 20.0000 | 1.20605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 15.4919i | − | 0.930820i | −0.885095 | − | 0.465410i | \(-0.845907\pi\) | ||
0.885095 | − | 0.465410i | \(-0.154093\pi\) | |||||||
\(278\) | 13.4164 | − | 10.3923i | 0.804663 | − | 0.623289i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | 0.475551 | 0.237775 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237775 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(284\) | 4.47214 | − | 17.3205i | 0.265372 | − | 1.02778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.0000 | + | 7.74597i | −0.591312 | + | 0.458029i | ||||
\(287\) | 26.8328 | 1.58389 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.50000 | − | 5.80948i | 0.0877809 | − | 0.339974i | ||||
\(293\) | 6.70820 | 0.391897 | 0.195949 | − | 0.980614i | \(-0.437221\pi\) | ||||
0.195949 | + | 0.980614i | \(0.437221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.00000 | − | 11.6190i | −0.290619 | − | 0.675338i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.4164 | + | 17.3205i | 0.777192 | + | 1.00335i | ||||
\(299\) | − | 8.66025i | − | 0.500835i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.0000 | − | 7.74597i | 0.575435 | − | 0.445730i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.6459 | − | 13.8081i | −0.610584 | − | 0.791951i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.46410i | 0.197707i | 0.995102 | + | 0.0988534i | \(0.0315175\pi\) | ||||
−0.995102 | + | 0.0988534i | \(0.968483\pi\) | |||||||
\(308\) | 30.0000 | + | 7.74597i | 1.70941 | + | 0.441367i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.87298i | − | 0.219617i | −0.993953 | − | 0.109808i | \(-0.964976\pi\) | ||
0.993953 | − | 0.109808i | \(-0.0350237\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | −0.282617 | −0.141308 | − | 0.989966i | \(-0.545131\pi\) | ||||
−0.141308 | + | 0.989966i | \(0.545131\pi\) | |||||||
\(314\) | −13.4164 | − | 17.3205i | −0.757132 | − | 0.977453i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.47214 | − | 17.3205i | 0.251577 | − | 0.974355i | ||||
\(317\) | 33.5410 | 1.88385 | 0.941926 | − | 0.335821i | \(-0.109014\pi\) | ||||
0.941926 | + | 0.335821i | \(0.109014\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.94427 | −0.500783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.7705 | + | 12.9904i | −0.934584 | + | 0.723926i | ||||
\(323\) | 4.00000 | + | 1.73205i | 0.222566 | + | 0.0963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.1803 | 0.620174 | ||||||||
\(326\) | −13.4164 | + | 10.3923i | −0.743066 | + | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.0000 | − | 7.74597i | 0.993884 | − | 0.427699i | ||||
\(329\) | −30.0000 | −1.65395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.9090i | 1.80884i | 0.426643 | + | 0.904420i | \(0.359696\pi\) | ||||
−0.426643 | + | 0.904420i | \(0.640304\pi\) | |||||||
\(332\) | 4.00000 | − | 15.4919i | 0.219529 | − | 0.850230i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0000 | − | 7.74597i | 0.547176 | − | 0.423840i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.8564i | − | 0.754807i | −0.926049 | − | 0.377403i | \(-0.876817\pi\) | ||
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 8.94427 | − | 6.92820i | 0.486504 | − | 0.376845i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.7771 | −1.93744 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.87298i | − | 0.209121i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.0000 | − | 11.6190i | 0.806405 | − | 0.624639i | ||||
\(347\) | −16.0000 | −0.858925 | −0.429463 | − | 0.903085i | \(-0.641297\pi\) | ||||
−0.429463 | + | 0.903085i | \(0.641297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4919i | 0.829264i | 0.909989 | + | 0.414632i | \(0.136090\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | −16.7705 | − | 21.6506i | −0.896421 | − | 1.15728i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.3607 | − | 3.46410i | 1.19183 | − | 0.184637i | ||||
\(353\) | 25.0000 | 1.33062 | 0.665308 | − | 0.746569i | \(-0.268300\pi\) | ||||
0.665308 | + | 0.746569i | \(0.268300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 26.8328 | + | 6.92820i | 1.42214 | + | 0.367194i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.00000 | + | 3.87298i | 0.158555 | + | 0.204694i | ||||
\(359\) | − | 3.87298i | − | 0.204408i | −0.994763 | − | 0.102204i | \(-0.967411\pi\) | ||
0.994763 | − | 0.102204i | \(-0.0325895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 5.00000 | − | 3.87298i | 0.262794 | − | 0.203559i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.7705 | + | 4.33013i | 0.879014 | + | 0.226960i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.74597i | − | 0.404336i | −0.979351 | − | 0.202168i | \(-0.935201\pi\) | ||
0.979351 | − | 0.202168i | \(-0.0647987\pi\) | |||||||
\(368\) | −7.50000 | + | 13.5554i | −0.390965 | + | 0.706626i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.9808i | 1.34885i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1803 | 0.578896 | 0.289448 | − | 0.957194i | \(-0.406528\pi\) | ||||
0.289448 | + | 0.957194i | \(0.406528\pi\) | |||||||
\(374\) | −4.47214 | + | 3.46410i | −0.231249 | + | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.1246 | + | 8.66025i | −1.03785 | + | 0.446619i | ||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.19615i | 0.266908i | 0.991055 | + | 0.133454i | \(0.0426069\pi\) | ||||
−0.991055 | + | 0.133454i | \(0.957393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.0623 | − | 12.9904i | −0.514832 | − | 0.664646i | ||||
\(383\) | 17.8885 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | − | 7.74597i | −0.305392 | − | 0.394259i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.4164 | − | 3.46410i | −0.681115 | − | 0.175863i | ||||
\(389\) | − | 15.4919i | − | 0.785472i | −0.919651 | − | 0.392736i | \(-0.871529\pi\) | ||
0.919651 | − | 0.392736i | \(-0.128471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.87298i | − | 0.195865i | ||||||
\(392\) | −8.94427 | − | 20.7846i | −0.451754 | − | 1.04978i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.4164 | − | 17.3205i | −0.675909 | − | 0.872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4919i | 0.777518i | 0.921340 | + | 0.388759i | \(0.127096\pi\) | ||||
−0.921340 | + | 0.388759i | \(0.872904\pi\) | |||||||
\(398\) | 23.4787 | + | 30.3109i | 1.17688 | + | 1.51935i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.5000 | − | 9.68246i | −0.875000 | − | 0.484123i | ||||
\(401\) | − | 27.7128i | − | 1.38391i | −0.721940 | − | 0.691956i | \(-0.756749\pi\) | ||
0.721940 | − | 0.691956i | \(-0.243251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0000 | −0.996271 | ||||||||
\(404\) | 30.0000 | + | 7.74597i | 1.49256 | + | 0.385376i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.50000 | + | 9.68246i | 0.372219 | + | 0.480532i | ||||
\(407\) | −17.8885 | −0.886702 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.7846i | − | 1.02773i | −0.857870 | − | 0.513866i | \(-0.828213\pi\) | ||
0.857870 | − | 0.513866i | \(-0.171787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.94427 | − | 34.6410i | 0.440653 | − | 1.70664i | ||||
\(413\) | −33.5410 | −1.65045 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.5000 | − | 1.93649i | 0.612863 | − | 0.0949443i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.8885 | + | 6.11044i | −1.16843 | + | 0.298871i | ||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.1803 | 0.544896 | 0.272448 | − | 0.962170i | \(-0.412167\pi\) | ||||
0.272448 | + | 0.962170i | \(0.412167\pi\) | |||||||
\(422\) | 13.5000 | + | 17.4284i | 0.657170 | + | 0.848402i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.50000 | + | 17.4284i | 0.364232 | + | 0.846399i | ||||
\(425\) | 5.00000 | 0.242536 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.0623 | − | 2.59808i | −0.486380 | − | 0.125583i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.7128i | − | 1.33179i | −0.746044 | − | 0.665896i | \(-0.768049\pi\) | ||
0.746044 | − | 0.665896i | \(-0.231951\pi\) | |||||||
\(434\) | 30.0000 | + | 38.7298i | 1.44005 | + | 1.85909i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.82624 | + | 30.3109i | −0.374809 | + | 1.45163i | ||||
\(437\) | 6.70820 | − | 15.4919i | 0.320897 | − | 0.741080i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.8885 | −0.853774 | −0.426887 | − | 0.904305i | \(-0.640390\pi\) | ||||
−0.426887 | + | 0.904305i | \(0.640390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.50000 | + | 1.93649i | −0.118913 | + | 0.0921095i | ||||
\(443\) | −28.0000 | −1.33032 | −0.665160 | − | 0.746701i | \(-0.731637\pi\) | ||||
−0.665160 | + | 0.746701i | \(0.731637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −20.0000 | + | 15.4919i | −0.947027 | + | 0.733564i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22.5000 | − | 21.3014i | −1.06303 | − | 1.00640i | ||||
\(449\) | − | 20.7846i | − | 0.980886i | −0.871473 | − | 0.490443i | \(-0.836835\pi\) | ||
0.871473 | − | 0.490443i | \(-0.163165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.7128i | − | 1.30495i | ||||||
\(452\) | −13.4164 | − | 3.46410i | −0.631055 | − | 0.162938i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.5000 | − | 17.4284i | −0.633586 | − | 0.817957i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.0000 | −1.35656 | −0.678281 | − | 0.734802i | \(-0.737275\pi\) | ||||
−0.678281 | + | 0.734802i | \(0.737275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.9839i | − | 1.44306i | −0.692382 | − | 0.721531i | \(-0.743439\pi\) | ||
0.692382 | − | 0.721531i | \(-0.256561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.74597i | − | 0.359986i | −0.983668 | − | 0.179993i | \(-0.942393\pi\) | ||
0.983668 | − | 0.179993i | \(-0.0576074\pi\) | |||||||
\(464\) | 7.82624 | + | 4.33013i | 0.363324 | + | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.1803 | − | 8.66025i | 0.517919 | − | 0.401179i | ||||
\(467\) | 20.0000 | 0.925490 | 0.462745 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462745 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −46.9574 | −2.16829 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.5000 | + | 9.68246i | −1.03565 | + | 0.445671i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.0000 | + | 8.66025i | 0.917663 | + | 0.397360i | ||||
\(476\) | 7.50000 | + | 1.93649i | 0.343762 | + | 0.0887590i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.0623 | − | 12.9904i | −0.460239 | − | 0.594166i | ||||
\(479\) | 7.74597i | 0.353922i | 0.984218 | + | 0.176961i | \(0.0566267\pi\) | ||||
−0.984218 | + | 0.176961i | \(0.943373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0000 | −0.455961 | ||||||||
\(482\) | −6.00000 | − | 7.74597i | −0.273293 | − | 0.352819i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.50000 | − | 9.68246i | 0.113636 | − | 0.440112i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.8885 | −0.810607 | −0.405304 | − | 0.914182i | \(-0.632834\pi\) | ||||
−0.405304 | + | 0.914182i | \(0.632834\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0000 | 1.44414 | 0.722070 | − | 0.691820i | \(-0.243191\pi\) | ||||
0.722070 | + | 0.691820i | \(0.243191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.23607 | −0.100707 | ||||||||
\(494\) | −13.3541 | + | 3.41584i | −0.600829 | + | 0.153686i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.3050 | + | 17.3205i | 1.40563 | + | 0.777714i | ||||
\(497\) | 34.6410i | 1.55386i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | 0.716258 | 0.358129 | − | 0.933672i | \(-0.383415\pi\) | ||||
0.358129 | + | 0.933672i | \(0.383415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.47214 | − | 3.46410i | 0.199601 | − | 0.154610i | ||||
\(503\) | − | 34.8569i | − | 1.55419i | −0.629383 | − | 0.777095i | \(-0.716692\pi\) | ||
0.629383 | − | 0.777095i | \(-0.283308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.4164 | + | 17.3205i | 0.596432 | + | 0.769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.94427 | − | 34.6410i | 0.396838 | − | 1.53695i | ||||
\(509\) | 22.3607 | 0.991120 | 0.495560 | − | 0.868574i | \(-0.334963\pi\) | ||||
0.495560 | + | 0.868574i | \(0.334963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6190i | 0.513992i | ||||||||
\(512\) | −21.2426 | − | 7.79423i | −0.938801 | − | 0.344459i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.0000 | + | 30.9839i | 1.05859 | + | 1.36664i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.9839i | 1.36267i | ||||||||
\(518\) | 15.0000 | + | 19.3649i | 0.659062 | + | 0.850846i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.92820i | − | 0.303530i | −0.988417 | − | 0.151765i | \(-0.951504\pi\) | ||
0.988417 | − | 0.151765i | \(-0.0484957\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0526i | 0.833110i | 0.909110 | + | 0.416555i | \(0.136763\pi\) | ||||
−0.909110 | + | 0.416555i | \(0.863237\pi\) | |||||||
\(524\) | −4.00000 | + | 15.4919i | −0.174741 | + | 0.676768i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.1246 | + | 25.9808i | 0.877475 | + | 1.13282i | ||||
\(527\) | −8.94427 | −0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.00000 | 0.347826 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.6459 | + | 20.7363i | 1.15525 | + | 0.899035i | ||||
\(533\) | − | 15.4919i | − | 0.671030i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −31.5000 | + | 13.5554i | −1.36059 | + | 0.585506i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0000 | − | 11.6190i | 0.646696 | − | 0.500929i | ||||
\(539\) | −32.0000 | −1.37834 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.9839i | − | 1.33210i | −0.745907 | − | 0.666050i | \(-0.767984\pi\) | ||
0.745907 | − | 0.666050i | \(-0.232016\pi\) | |||||||
\(542\) | 10.0623 | + | 12.9904i | 0.432213 | + | 0.557985i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.59017 | − | 0.866025i | 0.239677 | − | 0.0371305i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1769i | 1.33303i | 0.745492 | + | 0.666514i | \(0.232214\pi\) | ||||
−0.745492 | + | 0.666514i | \(0.767786\pi\) | |||||||
\(548\) | −9.50000 | + | 36.7933i | −0.405820 | + | 1.57173i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.3607 | + | 17.3205i | −0.953463 | + | 0.738549i | ||||
\(551\) | −8.94427 | − | 3.87298i | −0.381039 | − | 0.164995i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.6410i | 1.47309i | ||||||||
\(554\) | 13.4164 | + | 17.3205i | 0.570009 | + | 0.735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.00000 | + | 23.2379i | −0.254457 | + | 0.985506i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3.46410i | − | 0.145994i | −0.997332 | − | 0.0729972i | \(-0.976744\pi\) | ||
0.997332 | − | 0.0729972i | \(-0.0232564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.94427 | + | 6.92820i | −0.375956 | + | 0.291214i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.0000 | + | 23.2379i | 0.419591 | + | 0.975041i | ||||
\(569\) | 20.7846i | 0.871336i | 0.900107 | + | 0.435668i | \(0.143488\pi\) | ||||
−0.900107 | + | 0.435668i | \(0.856512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 4.47214 | − | 17.3205i | 0.186989 | − | 0.724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −30.0000 | + | 23.2379i | −1.25218 | + | 0.969931i | ||||
\(575\) | − | 19.3649i | − | 0.807573i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00000 | −0.374675 | −0.187337 | − | 0.982296i | \(-0.559986\pi\) | ||||
−0.187337 | + | 0.982296i | \(0.559986\pi\) | |||||||
\(578\) | 17.8885 | − | 13.8564i | 0.744065 | − | 0.576351i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.9839i | 1.28543i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.8328 | 1.11130 | ||||||||
\(584\) | 3.35410 | + | 7.79423i | 0.138794 | + | 0.322527i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.50000 | + | 5.80948i | −0.309822 | + | 0.239987i | ||||
\(587\) | 16.0000 | 0.660391 | 0.330195 | − | 0.943913i | \(-0.392885\pi\) | ||||
0.330195 | + | 0.943913i | \(0.392885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.7771 | − | 15.4919i | −1.47417 | − | 0.638334i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.6525 | + | 8.66025i | 0.643313 | + | 0.355934i | ||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.0000 | − | 7.74597i | −1.22885 | − | 0.317287i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.50000 | + | 9.68246i | 0.306698 | + | 0.395945i | ||||
\(599\) | 17.8885 | 0.730906 | 0.365453 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365453 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.92820i | − | 0.282607i | −0.989966 | − | 0.141304i | \(-0.954871\pi\) | ||
0.989966 | − | 0.141304i | \(-0.0451294\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.47214 | + | 17.3205i | −0.181969 | + | 0.704761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.94427 | 0.363037 | 0.181518 | − | 0.983388i | \(-0.441899\pi\) | ||||
0.181518 | + | 0.983388i | \(0.441899\pi\) | |||||||
\(608\) | 23.8607 | + | 6.21836i | 0.967678 | + | 0.252188i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3205i | 0.700713i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 30.9839i | − | 1.25143i | −0.780053 | − | 0.625713i | \(-0.784808\pi\) | ||
0.780053 | − | 0.625713i | \(-0.215192\pi\) | |||||||
\(614\) | −3.00000 | − | 3.87298i | −0.121070 | − | 0.156301i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −40.2492 | + | 17.3205i | −1.62169 | + | 0.697863i | ||||
\(617\) | −10.0000 | −0.402585 | −0.201292 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201292 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0000 | −0.643094 | −0.321547 | − | 0.946894i | \(-0.604203\pi\) | ||||
−0.321547 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.35410 | + | 4.33013i | 0.134487 | + | 0.173622i | ||||
\(623\) | −53.6656 | −2.15007 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 5.59017 | − | 4.33013i | 0.223428 | − | 0.173067i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.0000 | + | 7.74597i | 1.19713 | + | 0.309098i | ||||
\(629\) | −4.47214 | −0.178316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.7298i | − | 1.54181i | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||
0.636950 | − | 0.770905i | \(-0.280196\pi\) | |||||||
\(632\) | 10.0000 | + | 23.2379i | 0.397779 | + | 0.924354i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.5000 | + | 29.0474i | −1.48932 | + | 1.15362i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.8885 | −0.708770 | ||||||||
\(638\) | 10.0000 | − | 7.74597i | 0.395904 | − | 0.306666i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | 7.50000 | − | 29.0474i | 0.295541 | − | 1.14463i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.97214 | + | 1.52761i | −0.234971 | + | 0.0601030i | ||||
\(647\) | 27.1109i | 1.06584i | 0.846166 | + | 0.532919i | \(0.178905\pi\) | ||||
−0.846166 | + | 0.532919i | \(0.821095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.6410i | 1.35978i | ||||||||
\(650\) | −12.5000 | + | 9.68246i | −0.490290 | + | 0.379777i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000 | − | 23.2379i | 0.234978 | − | 0.910066i | ||||
\(653\) | − | 46.4758i | − | 1.81874i | −0.415990 | − | 0.909369i | \(-0.636565\pi\) | ||
0.415990 | − | 0.909369i | \(-0.363435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.4164 | + | 24.2487i | −0.523823 | + | 0.946753i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 33.5410 | − | 25.9808i | 1.30757 | − | 1.01284i | ||||
\(659\) | − | 39.8372i | − | 1.55184i | −0.630834 | − | 0.775918i | \(-0.717287\pi\) | ||
0.630834 | − | 0.775918i | \(-0.282713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.1803 | 0.434865 | 0.217432 | − | 0.976075i | \(-0.430232\pi\) | ||||
0.217432 | + | 0.976075i | \(0.430232\pi\) | |||||||
\(662\) | −28.5000 | − | 36.7933i | −1.10768 | − | 1.43001i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.94427 | + | 20.7846i | 0.347105 | + | 0.806599i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.66025i | 0.335326i | ||||||||
\(668\) | −4.47214 | + | 17.3205i | −0.173032 | + | 0.670151i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.7846i | − | 0.801188i | −0.916256 | − | 0.400594i | \(-0.868804\pi\) | ||
0.916256 | − | 0.400594i | \(-0.131196\pi\) | |||||||
\(674\) | 12.0000 | + | 15.4919i | 0.462223 | + | 0.596727i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | + | 15.4919i | −0.153846 | + | 0.595844i | ||||
\(677\) | 6.70820 | 0.257817 | 0.128909 | − | 0.991656i | \(-0.458853\pi\) | ||||
0.128909 | + | 0.991656i | \(0.458853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.8328 | 1.02975 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 40.0000 | − | 30.9839i | 1.53168 | − | 1.18643i | ||||
\(683\) | 10.3923i | 0.397650i | 0.980035 | + | 0.198825i | \(0.0637126\pi\) | ||||
−0.980035 | + | 0.198825i | \(0.936287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.35410 | + | 4.33013i | 0.128060 | + | 0.165325i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0000 | 0.571454 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0000 | −0.913003 | −0.456502 | − | 0.889723i | \(-0.650898\pi\) | ||||
−0.456502 | + | 0.889723i | \(0.650898\pi\) | |||||||
\(692\) | −6.70820 | + | 25.9808i | −0.255008 | + | 0.987640i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.8885 | − | 13.8564i | 0.679040 | − | 0.525982i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.92820i | − | 0.262424i | ||||||
\(698\) | −13.4164 | − | 17.3205i | −0.507819 | − | 0.655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 37.5000 | + | 9.68246i | 1.41737 | + | 0.365963i | ||||
\(701\) | 30.9839i | 1.17024i | 0.810945 | + | 0.585122i | \(0.198953\pi\) | ||||
−0.810945 | + | 0.585122i | \(0.801047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.8885 | − | 7.74597i | −0.674679 | − | 0.292145i | ||||
\(704\) | −22.0000 | + | 23.2379i | −0.829156 | + | 0.875811i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.9508 | + | 21.6506i | −1.05194 | + | 0.814832i | ||||
\(707\) | −60.0000 | −2.25653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.9839i | 1.16362i | 0.813323 | + | 0.581812i | \(0.197656\pi\) | ||||
−0.813323 | + | 0.581812i | \(0.802344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −36.0000 | + | 15.4919i | −1.34916 | + | 0.580585i | ||||
\(713\) | 34.6410i | 1.29732i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.70820 | − | 1.73205i | −0.250697 | − | 0.0647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.35410 | + | 4.33013i | 0.125174 | + | 0.161599i | ||||
\(719\) | − | 19.3649i | − | 0.722190i | −0.932529 | − | 0.361095i | \(-0.882403\pi\) | ||
0.932529 | − | 0.361095i | \(-0.117597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 69.2820i | 2.58020i | ||||||||
\(722\) | −26.5344 | − | 4.23360i | −0.987510 | − | 0.157558i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.23607 | + | 8.66025i | −0.0831028 | + | 0.321856i | ||||
\(725\) | −11.1803 | −0.415227 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.87298i | 0.143641i | 0.997418 | + | 0.0718205i | \(0.0228809\pi\) | ||||
−0.997418 | + | 0.0718205i | \(0.977119\pi\) | |||||||
\(728\) | −22.5000 | + | 9.68246i | −0.833905 | + | 0.358856i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.9839i | 1.14442i | 0.820109 | + | 0.572208i | \(0.193913\pi\) | ||||
−0.820109 | + | 0.572208i | \(0.806087\pi\) | |||||||
\(734\) | 6.70820 | + | 8.66025i | 0.247604 | + | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.35410 | − | 21.6506i | −0.123634 | − | 0.798053i | ||||
\(737\) | 48.4974i | 1.78643i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.0000 | −0.882854 | −0.441427 | − | 0.897297i | \(-0.645528\pi\) | ||||
−0.441427 | + | 0.897297i | \(0.645528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.5000 | − | 29.0474i | −0.826001 | − | 1.06636i | ||||
\(743\) | 26.8328 | 0.984401 | 0.492200 | − | 0.870482i | \(-0.336193\pi\) | ||||
0.492200 | + | 0.870482i | \(0.336193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.5000 | + | 9.68246i | −0.457658 | + | 0.354500i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.00000 | − | 7.74597i | 0.0731272 | − | 0.283221i | ||||
\(749\) | 20.1246 | 0.735337 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.94427 | −0.326381 | −0.163191 | − | 0.986595i | \(-0.552179\pi\) | ||||
−0.163191 | + | 0.986595i | \(0.552179\pi\) | |||||||
\(752\) | 15.0000 | − | 27.1109i | 0.546994 | − | 0.988632i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.59017 | − | 4.33013i | 0.203582 | − | 0.157694i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 30.9839i | − | 1.12613i | −0.826413 | − | 0.563064i | \(-0.809622\pi\) | ||
0.826413 | − | 0.563064i | \(-0.190378\pi\) | |||||||
\(758\) | −4.50000 | − | 5.80948i | −0.163447 | − | 0.211010i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0000 | −0.398750 | −0.199375 | − | 0.979923i | \(-0.563891\pi\) | ||||
−0.199375 | + | 0.979923i | \(0.563891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 60.6218i | − | 2.19466i | ||||||
\(764\) | 22.5000 | + | 5.80948i | 0.814021 | + | 0.210179i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.0000 | + | 15.4919i | −0.722629 | + | 0.559746i | ||||
\(767\) | 19.3649i | 0.699227i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.0000 | 1.69486 | 0.847432 | − | 0.530904i | \(-0.178148\pi\) | ||||
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.4164 | + | 3.46410i | 0.482867 | + | 0.124676i | ||||
\(773\) | −29.0689 | −1.04554 | −0.522768 | − | 0.852475i | \(-0.675100\pi\) | ||||
−0.522768 | + | 0.852475i | \(0.675100\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.7214 | −1.60644 | ||||||||
\(776\) | 18.0000 | − | 7.74597i | 0.646162 | − | 0.278064i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.4164 | + | 17.3205i | 0.481002 | + | 0.620970i | ||||
\(779\) | 12.0000 | − | 27.7128i | 0.429945 | − | 0.992915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.7771 | 1.28020 | ||||||||
\(782\) | 3.35410 | + | 4.33013i | 0.119942 | + | 0.154845i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | + | 15.4919i | 1.00000 | + | 0.553283i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.73205i | − | 0.0617409i | −0.999523 | − | 0.0308705i | \(-0.990172\pi\) | ||
0.999523 | − | 0.0308705i | \(-0.00982794\pi\) | |||||||
\(788\) | 30.0000 | + | 7.74597i | 1.06871 | + | 0.275939i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.8328 | 0.954065 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −13.4164 | − | 17.3205i | −0.476130 | − | 0.614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −52.5000 | − | 13.5554i | −1.86081 | − | 0.480460i | ||||
\(797\) | −2.23607 | −0.0792056 | −0.0396028 | − | 0.999216i | \(-0.512609\pi\) | ||||
−0.0396028 | + | 0.999216i | \(0.512609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.74597i | 0.274033i | ||||||||
\(800\) | 27.9508 | − | 4.33013i | 0.988212 | − | 0.153093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.0000 | + | 30.9839i | 0.847469 | + | 1.09408i | ||||
\(803\) | 12.0000 | 0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.3607 | − | 17.3205i | 0.787621 | − | 0.610089i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −40.2492 | + | 17.3205i | −1.41596 | + | 0.609333i | ||||
\(809\) | −11.0000 | −0.386739 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.66025i | − | 0.304103i | −0.988373 | − | 0.152051i | \(-0.951412\pi\) | ||
0.988373 | − | 0.152051i | \(-0.0485879\pi\) | |||||||
\(812\) | −16.7705 | − | 4.33013i | −0.588530 | − | 0.151958i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.0000 | − | 15.4919i | 0.701000 | − | 0.542992i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 18.0000 | + | 23.2379i | 0.629355 | + | 0.812494i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 15.4919i | − | 0.540672i | −0.962766 | − | 0.270336i | \(-0.912865\pi\) | ||
0.962766 | − | 0.270336i | \(-0.0871348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.8569i | 1.21503i | 0.794307 | + | 0.607517i | \(0.207834\pi\) | ||||
−0.794307 | + | 0.607517i | \(0.792166\pi\) | |||||||
\(824\) | 20.0000 | + | 46.4758i | 0.696733 | + | 1.61906i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.5000 | − | 29.0474i | 1.30479 | − | 1.01069i | ||||
\(827\) | 22.5167i | 0.782981i | 0.920182 | + | 0.391491i | \(0.128040\pi\) | ||||
−0.920182 | + | 0.391491i | \(0.871960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0132 | 1.32025 | 0.660126 | − | 0.751155i | \(-0.270503\pi\) | ||||
0.660126 | + | 0.751155i | \(0.270503\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.2984 | + | 12.9904i | −0.426369 | + | 0.450360i | ||||
\(833\) | −8.00000 | −0.277184 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 21.4164 | − | 27.5198i | 0.740702 | − | 0.951791i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.94427 | − | 6.92820i | 0.308975 | − | 0.239331i | ||||
\(839\) | −53.6656 | −1.85274 | −0.926372 | − | 0.376611i | \(-0.877089\pi\) | ||||
−0.926372 | + | 0.376611i | \(0.877089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0000 | −0.827586 | ||||||||
\(842\) | −12.5000 | + | 9.68246i | −0.430778 | + | 0.333680i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.1869 | − | 7.79423i | −1.03908 | − | 0.268288i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.3649i | 0.665386i | ||||||||
\(848\) | −23.4787 | − | 12.9904i | −0.806262 | − | 0.446092i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.59017 | + | 4.33013i | −0.191741 | + | 0.148522i | ||||
\(851\) | 17.3205i | 0.593739i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 30.9839i | − | 1.06087i | −0.847726 | − | 0.530434i | \(-0.822029\pi\) | ||
0.847726 | − | 0.530434i | \(-0.177971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.5000 | − | 5.80948i | 0.461421 | − | 0.198564i | ||||
\(857\) | − | 13.8564i | − | 0.473326i | −0.971592 | − | 0.236663i | \(-0.923946\pi\) | ||
0.971592 | − | 0.236663i | \(-0.0760537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.00000 | 0.272956 | 0.136478 | − | 0.990643i | \(-0.456422\pi\) | ||||
0.136478 | + | 0.990643i | \(0.456422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.6656 | −1.82680 | −0.913400 | − | 0.407064i | \(-0.866553\pi\) | ||||
−0.913400 | + | 0.407064i | \(0.866553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24.0000 | + | 30.9839i | 0.815553 | + | 1.05287i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −67.0820 | − | 17.3205i | −2.27691 | − | 0.587896i | ||||
\(869\) | 35.7771 | 1.21365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.1109i | 0.918617i | ||||||||
\(872\) | −17.5000 | − | 40.6663i | −0.592625 | − | 1.37714i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.91641 | + | 23.1300i | 0.200125 | + | 0.782383i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0132 | 1.28361 | 0.641807 | − | 0.766867i | \(-0.278185\pi\) | ||||
0.641807 | + | 0.766867i | \(0.278185\pi\) | |||||||
\(878\) | 20.0000 | − | 15.4919i | 0.674967 | − | 0.522827i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.0000 | −1.07689 | −0.538443 | − | 0.842662i | \(-0.680987\pi\) | ||||
−0.538443 | + | 0.842662i | \(0.680987\pi\) | |||||||
\(884\) | 1.11803 | − | 4.33013i | 0.0376036 | − | 0.145638i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.3050 | − | 24.2487i | 1.05171 | − | 0.814651i | ||||
\(887\) | −17.8885 | −0.600639 | −0.300319 | − | 0.953839i | \(-0.597093\pi\) | ||||
−0.300319 | + | 0.953839i | \(0.597093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 69.2820i | 2.32364i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.94427 | − | 34.6410i | 0.299476 | − | 1.15987i | ||||
\(893\) | −13.4164 | + | 30.9839i | −0.448963 | + | 1.03684i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 43.6033 | + | 4.33013i | 1.45668 | + | 0.144659i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | + | 23.2379i | 0.600668 | + | 0.775459i | ||||
\(899\) | 20.0000 | 0.667037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.70820 | 0.223483 | ||||||||
\(902\) | 24.0000 | + | 30.9839i | 0.799113 | + | 1.03165i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.0000 | − | 7.74597i | 0.598671 | − | 0.257627i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 36.3731i | − | 1.20775i | −0.797080 | − | 0.603874i | \(-0.793623\pi\) | ||
0.797080 | − | 0.603874i | \(-0.206377\pi\) | |||||||
\(908\) | 30.1869 | + | 7.79423i | 1.00179 | + | 0.258661i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.7771 | 1.18535 | 0.592674 | − | 0.805443i | \(-0.298072\pi\) | ||||
0.592674 | + | 0.805443i | \(0.298072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0000 | 1.05905 | ||||||||
\(914\) | 32.4230 | − | 25.1147i | 1.07246 | − | 0.830722i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 30.9839i | − | 1.02318i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.1109i | − | 0.894306i | −0.894458 | − | 0.447153i | \(-0.852438\pi\) | ||
0.894458 | − | 0.447153i | \(-0.147562\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.8328 | + | 34.6410i | 0.883692 | + | 1.14084i | ||||
\(923\) | 20.0000 | 0.658308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.3607 | −0.735215 | ||||||||
\(926\) | 6.70820 | + | 8.66025i | 0.220445 | + | 0.284594i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.5000 | + | 1.93649i | −0.410333 | + | 0.0635685i | ||||
\(929\) | 1.00000 | 0.0328089 | 0.0164045 | − | 0.999865i | \(-0.494778\pi\) | ||||
0.0164045 | + | 0.999865i | \(0.494778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.0000 | − | 13.8564i | −1.04876 | − | 0.454125i | ||||
\(932\) | −5.00000 | + | 19.3649i | −0.163780 | + | 0.634319i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.3607 | + | 17.3205i | −0.731664 | + | 0.566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0000 | −0.686040 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(938\) | 52.5000 | − | 40.6663i | 1.71419 | − | 1.32780i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.0132 | −1.23919 | −0.619597 | − | 0.784920i | \(-0.712704\pi\) | ||||
−0.619597 | + | 0.784920i | \(0.712704\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.8328 | −0.873797 | ||||||||
\(944\) | 16.7705 | − | 30.3109i | 0.545834 | − | 0.986535i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.0000 | −1.29983 | −0.649913 | − | 0.760009i | \(-0.725195\pi\) | ||||
−0.649913 | + | 0.760009i | \(0.725195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.70820 | 0.217758 | ||||||||
\(950\) | −29.8607 | + | 7.63805i | −0.968808 | + | 0.247811i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.0623 | + | 4.33013i | −0.326121 | + | 0.140340i | ||||
\(953\) | − | 27.7128i | − | 0.897706i | −0.893606 | − | 0.448853i | \(-0.851833\pi\) | ||
0.893606 | − | 0.448853i | \(-0.148167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.5000 | + | 5.80948i | 0.727702 | + | 0.187892i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.70820 | − | 8.66025i | −0.216732 | − | 0.279800i | ||||
\(959\) | − | 73.5867i | − | 2.37624i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.0000 | 1.58065 | ||||||||
\(962\) | 11.1803 | − | 8.66025i | 0.360469 | − | 0.279218i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.4164 | + | 3.46410i | 0.432113 | + | 0.111571i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.2379i | 0.747280i | 0.927574 | + | 0.373640i | \(0.121891\pi\) | ||||
−0.927574 | + | 0.373640i | \(0.878109\pi\) | |||||||
\(968\) | 5.59017 | + | 12.9904i | 0.179675 | + | 0.417527i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.3923i | 0.333505i | 0.985999 | + | 0.166752i | \(0.0533281\pi\) | ||||
−0.985999 | + | 0.166752i | \(0.946672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 46.4758i | − | 1.48995i | ||||||
\(974\) | 20.0000 | − | 15.4919i | 0.640841 | − | 0.496394i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20.7846i | − | 0.664959i | −0.943111 | − | 0.332479i | \(-0.892115\pi\) | ||
0.943111 | − | 0.332479i | \(-0.107885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55.4256i | 1.77141i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.7771 | + | 27.7128i | −1.14169 | + | 0.884351i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.50000 | − | 1.93649i | 0.0796162 | − | 0.0616705i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.9721 | − | 15.3840i | 0.380884 | − | 0.489431i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.8885 | −0.568248 | −0.284124 | − | 0.958787i | \(-0.591703\pi\) | ||||
−0.284124 | + | 0.958787i | \(0.591703\pi\) | |||||||
\(992\) | −50.0000 | + | 7.74597i | −1.58750 | + | 0.245935i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.0000 | − | 38.7298i | −0.951542 | − | 1.22844i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 15.4919i | − | 0.490634i | −0.969443 | − | 0.245317i | \(-0.921108\pi\) | ||
0.969443 | − | 0.245317i | \(-0.0788921\pi\) | |||||||
\(998\) | −17.8885 | + | 13.8564i | −0.566252 | + | 0.438617i | ||||
\(999\) | 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 | 1368.2.e.b.379.2 | 4 | ||
3.2 | odd | 2 | 152.2.b.b.75.3 | yes | 4 | ||
4.3 | odd | 2 | 5472.2.e.b.5167.2 | 4 | |||
8.3 | odd | 2 | inner | 1368.2.e.b.379.4 | 4 | ||
8.5 | even | 2 | 5472.2.e.b.5167.3 | 4 | |||
12.11 | even | 2 | 608.2.b.b.303.3 | 4 | |||
19.18 | odd | 2 | inner | 1368.2.e.b.379.3 | 4 | ||
24.5 | odd | 2 | 608.2.b.b.303.4 | 4 | |||
24.11 | even | 2 | 152.2.b.b.75.1 | ✓ | 4 | ||
57.56 | even | 2 | 152.2.b.b.75.2 | yes | 4 | ||
76.75 | even | 2 | 5472.2.e.b.5167.1 | 4 | |||
152.37 | odd | 2 | 5472.2.e.b.5167.4 | 4 | |||
152.75 | even | 2 | inner | 1368.2.e.b.379.1 | 4 | ||
228.227 | odd | 2 | 608.2.b.b.303.1 | 4 | |||
456.227 | odd | 2 | 152.2.b.b.75.4 | yes | 4 | ||
456.341 | even | 2 | 608.2.b.b.303.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.b.b.75.1 | ✓ | 4 | 24.11 | even | 2 | ||
152.2.b.b.75.2 | yes | 4 | 57.56 | even | 2 | ||
152.2.b.b.75.3 | yes | 4 | 3.2 | odd | 2 | ||
152.2.b.b.75.4 | yes | 4 | 456.227 | odd | 2 | ||
608.2.b.b.303.1 | 4 | 228.227 | odd | 2 | |||
608.2.b.b.303.2 | 4 | 456.341 | even | 2 | |||
608.2.b.b.303.3 | 4 | 12.11 | even | 2 | |||
608.2.b.b.303.4 | 4 | 24.5 | odd | 2 | |||
1368.2.e.b.379.1 | 4 | 152.75 | even | 2 | inner | ||
1368.2.e.b.379.2 | 4 | 1.1 | even | 1 | trivial | ||
1368.2.e.b.379.3 | 4 | 19.18 | odd | 2 | inner | ||
1368.2.e.b.379.4 | 4 | 8.3 | odd | 2 | inner | ||
5472.2.e.b.5167.1 | 4 | 76.75 | even | 2 | |||
5472.2.e.b.5167.2 | 4 | 4.3 | odd | 2 | |||
5472.2.e.b.5167.3 | 4 | 8.5 | even | 2 | |||
5472.2.e.b.5167.4 | 4 | 152.37 | odd | 2 |