Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(49,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bi (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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.9 | ||
Character | \(\chi\) | \(=\) | 360.49 |
Dual form | 360.2.bi.b.169.9 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.284761 | + | 1.70848i | 0.164407 | + | 0.986393i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.07259 | − | 1.96203i | 0.479677 | − | 0.877445i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.55262 | + | 2.05111i | −1.34276 | + | 0.775245i | −0.987212 | − | 0.159411i | \(-0.949040\pi\) |
−0.355552 | + | 0.934657i | \(0.615707\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.83782 | + | 0.973019i | −0.945941 | + | 0.324340i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.04732 | + | 5.27812i | 0.918802 | + | 1.59141i | 0.801237 | + | 0.598347i | \(0.204175\pi\) |
0.117565 | + | 0.993065i | \(0.462491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.45043 | + | 2.56946i | 1.23433 | + | 0.712639i | 0.967929 | − | 0.251224i | \(-0.0808330\pi\) |
0.266398 | + | 0.963863i | \(0.414166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.65752 | + | 1.27379i | 0.944368 | + | 0.328891i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.73647i | 0.663692i | 0.943334 | + | 0.331846i | \(0.107671\pi\) | ||||
−0.943334 | + | 0.331846i | \(0.892329\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80595 | −0.414313 | −0.207156 | − | 0.978308i | \(-0.566421\pi\) | ||||
−0.207156 | + | 0.978308i | \(0.566421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.51593 | − | 5.48551i | −0.985456 | − | 1.19704i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.582439 | − | 0.336271i | −0.121447 | − | 0.0701174i | 0.438046 | − | 0.898953i | \(-0.355671\pi\) |
−0.559493 | + | 0.828835i | \(0.689004\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.69910 | − | 4.20890i | −0.539821 | − | 0.841780i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.47049 | − | 4.57129i | −0.475446 | − | 0.879745i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75334 | + | 3.03688i | 0.325588 | + | 0.563935i | 0.981631 | − | 0.190789i | \(-0.0611045\pi\) |
−0.656043 | + | 0.754723i | \(0.727771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.30067 | − | 5.71692i | 0.592817 | − | 1.02679i | −0.401034 | − | 0.916063i | \(-0.631349\pi\) |
0.993851 | − | 0.110726i | \(-0.0353176\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.14981 | + | 6.70930i | −1.41870 | + | 1.16794i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.213823 | + | 9.17033i | 0.0361426 | + | 1.55007i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.44214i | − | 0.730283i | −0.930952 | − | 0.365141i | \(-0.881021\pi\) | ||
0.930952 | − | 0.365141i | \(-0.118979\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.12256 | + | 8.33516i | −0.500010 | + | 1.33469i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.08923 | + | 3.61865i | −0.326283 | + | 0.565138i | −0.981771 | − | 0.190067i | \(-0.939130\pi\) |
0.655488 | + | 0.755205i | \(0.272463\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.01162 | − | 2.31611i | 0.611767 | − | 0.353204i | −0.161890 | − | 0.986809i | \(-0.551759\pi\) |
0.773657 | + | 0.633605i | \(0.218426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.13473 | + | 6.61153i | −0.169155 | + | 0.985589i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.38258 | − | 0.798234i | 0.201670 | − | 0.116434i | −0.395764 | − | 0.918352i | \(-0.629520\pi\) |
0.597434 | + | 0.801918i | \(0.296187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.91407 | − | 8.51143i | 0.702011 | − | 1.21592i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.67521 | + | 0.779242i | −0.654661 | + | 0.109116i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.02220i | − | 1.10193i | −0.834527 | − | 0.550967i | \(-0.814259\pi\) | ||
0.834527 | − | 0.550967i | \(-0.185741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.6243 | − | 0.317676i | 1.83710 | − | 0.0428354i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.514264 | − | 3.08543i | −0.0681159 | − | 0.408675i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.65011 | + | 4.59012i | −0.345015 | + | 0.597583i | −0.985356 | − | 0.170507i | \(-0.945459\pi\) |
0.640342 | + | 0.768090i | \(0.278793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.38942 | − | 5.87064i | −0.433970 | − | 0.751659i | 0.563241 | − | 0.826293i | \(-0.309554\pi\) |
−0.997211 | + | 0.0746344i | \(0.976221\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.08594 | − | 9.27744i | 1.01873 | − | 1.16885i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.81483 | − | 5.97589i | 1.21738 | − | 0.741218i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.82638 | − | 5.67327i | −1.20048 | − | 0.693100i | −0.239821 | − | 0.970817i | \(-0.577089\pi\) |
−0.960663 | + | 0.277717i | \(0.910422\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.408657 | − | 1.09084i | 0.0491966 | − | 0.131322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3686 | 1.58656 | 0.793280 | − | 0.608857i | \(-0.208372\pi\) | ||||
0.793280 | + | 0.608857i | \(0.208372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50669i | 0.761550i | 0.924668 | + | 0.380775i | \(0.124343\pi\) | ||||
−0.924668 | + | 0.380775i | \(0.875657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.42223 | − | 5.80990i | 0.741575 | − | 0.670870i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.6520 | − | 12.5008i | −2.46747 | − | 1.42459i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.49502 | + | 2.58946i | 0.168203 | + | 0.291337i | 0.937788 | − | 0.347208i | \(-0.112870\pi\) |
−0.769585 | + | 0.638545i | \(0.779537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.10647 | − | 5.52251i | 0.789607 | − | 0.613612i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.71043 | − | 2.14222i | 0.407273 | − | 0.235139i | −0.282344 | − | 0.959313i | \(-0.591112\pi\) |
0.689617 | + | 0.724174i | \(0.257779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.36903 | + | 2.93511i | 0.582354 | + | 0.318358i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.68917 | + | 3.86034i | −0.502732 | + | 0.413872i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.19878 | 0.763070 | 0.381535 | − | 0.924354i | \(-0.375396\pi\) | ||||
0.381535 | + | 0.924354i | \(0.375396\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.0809 | −2.20988 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.7072 | + | 4.01117i | 1.11028 | + | 0.415939i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.93704 | + | 3.54332i | −0.198736 | + | 0.363537i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.33696 | − | 1.92659i | 0.338817 | − | 0.195616i | −0.320932 | − | 0.947102i | \(-0.603996\pi\) |
0.659749 | + | 0.751486i | \(0.270663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.7835 | − | 12.0133i | −1.38529 | − | 1.20738i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.87483 | + | 8.44346i | 0.485064 | + | 0.840155i | 0.999853 | − | 0.0171617i | \(-0.00546301\pi\) |
−0.514789 | + | 0.857317i | \(0.672130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.64658 | − | 5.56946i | −0.950506 | − | 0.548775i | −0.0572679 | − | 0.998359i | \(-0.518239\pi\) |
−0.893238 | + | 0.449584i | \(0.851572\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.6065 | + | 2.97667i | −1.52303 | + | 0.290493i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.19494i | 0.115519i | 0.998331 | + | 0.0577595i | \(0.0183956\pi\) | ||||
−0.998331 | + | 0.0577595i | \(0.981604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.05323 | 0.867143 | 0.433571 | − | 0.901119i | \(-0.357253\pi\) | ||||
0.433571 | + | 0.901119i | \(0.357253\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.58931 | − | 1.26495i | 0.720346 | − | 0.120064i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.85715 | + | 3.95898i | 0.645066 | + | 0.372429i | 0.786563 | − | 0.617510i | \(-0.211858\pi\) |
−0.141497 | + | 0.989939i | \(0.545192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.28449 | + | 0.782080i | −0.119779 | + | 0.0729293i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.1297 | − | 2.96131i | −1.39874 | − | 0.273773i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.61280 | − | 9.72165i | −0.514524 | − | 0.891182i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0723 | + | 22.6420i | −1.18839 | + | 2.05836i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.77733 | − | 2.53896i | −0.611092 | − | 0.228930i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1530 | + | 0.781290i | −0.997555 | + | 0.0698807i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.00959i | − | 0.799471i | −0.916630 | − | 0.399736i | \(-0.869102\pi\) | ||
0.916630 | − | 0.399736i | \(-0.130898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.09939 | + | 6.19425i | 0.448976 | + | 0.545373i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.26972 | − | 2.19922i | 0.110936 | − | 0.192147i | −0.805212 | − | 0.592987i | \(-0.797948\pi\) |
0.916148 | + | 0.400840i | \(0.131282\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.41585 | − | 3.70419i | 0.556324 | − | 0.321194i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.6188 | − | 0.0559540i | −0.999988 | − | 0.00481575i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.67867 | − | 4.43328i | 0.656033 | − | 0.378761i | −0.134731 | − | 0.990882i | \(-0.543017\pi\) |
0.790764 | + | 0.612121i | \(0.209684\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.49731 | − | 12.9857i | 0.635913 | − | 1.10143i | −0.350408 | − | 0.936597i | \(-0.613957\pi\) |
0.986321 | − | 0.164837i | \(-0.0527098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.75747 | + | 2.13481i | 0.148006 | + | 0.179783i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.3198i | 2.61910i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.83906 | − | 0.182782i | 0.650999 | − | 0.0151792i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.9410 | + | 5.97188i | 1.31479 | + | 0.492553i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.89813 | − | 11.9479i | 0.565117 | − | 0.978811i | −0.431922 | − | 0.901911i | \(-0.642164\pi\) |
0.997039 | − | 0.0769000i | \(-0.0245022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.30312 | + | 2.25708i | 0.106047 | + | 0.183678i | 0.914165 | − | 0.405341i | \(-0.132847\pi\) |
−0.808119 | + | 0.589020i | \(0.799514\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.66264 | − | 7.76562i | −0.215262 | − | 0.627813i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.67650 | − | 12.6079i | −0.616591 | − | 1.01269i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9478 | + | 7.47543i | 1.03335 | + | 0.596604i | 0.917942 | − | 0.396714i | \(-0.129850\pi\) |
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.7058 | − | 2.28441i | 1.08694 | − | 0.181166i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.75891 | 0.217433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.49019i | 0.743329i | 0.928367 | + | 0.371664i | \(0.121213\pi\) | ||||
−0.928367 | + | 0.371664i | \(0.878787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.42243 | + | 23.1865i | 0.344285 | + | 1.80506i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.325986 | + | 0.188208i | 0.0252256 | + | 0.0145640i | 0.512560 | − | 0.858652i | \(-0.328697\pi\) |
−0.487334 | + | 0.873216i | \(0.662031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.70422 | + | 11.6120i | 0.515709 | + | 0.893234i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.12496 | − | 1.75722i | 0.391915 | − | 0.134378i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.253324 | + | 0.146257i | −0.0192598 | + | 0.0111197i | −0.509599 | − | 0.860412i | \(-0.670206\pi\) |
0.490339 | + | 0.871532i | \(0.336873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.2218 | + | 9.41648i | 1.37744 | + | 0.711819i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.59679 | − | 3.22057i | −0.646175 | − | 0.242073i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.4931 | −1.75596 | −0.877978 | − | 0.478702i | \(-0.841108\pi\) | ||||
−0.877978 | + | 0.478702i | \(0.841108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.37931 | −0.176853 | −0.0884263 | − | 0.996083i | \(-0.528184\pi\) | ||||
−0.0884263 | + | 0.996083i | \(0.528184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.06471 | − | 7.46249i | 0.670083 | − | 0.551643i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.71559 | − | 4.76459i | −0.640783 | − | 0.350300i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.4434 | + | 8.33891i | −1.05621 | + | 0.609802i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.1529 | + | 11.1728i | 1.32043 | + | 0.812703i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.68671 | + | 9.84967i | 0.411476 | + | 0.712697i | 0.995051 | − | 0.0993618i | \(-0.0316801\pi\) |
−0.583576 | + | 0.812059i | \(0.698347\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7831 | − | 10.8444i | −1.35204 | − | 0.780600i | −0.363504 | − | 0.931593i | \(-0.618420\pi\) |
−0.988535 | + | 0.150993i | \(0.951753\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.0046 | + | 15.0668i | 0.931278 | + | 1.07895i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2214i | 1.01323i | 0.862171 | + | 0.506617i | \(0.169104\pi\) | ||||
−0.862171 | + | 0.506617i | \(0.830896\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3820 | −1.30306 | −0.651532 | − | 0.758621i | \(-0.725873\pi\) | ||||
−0.651532 | + | 0.758621i | \(0.725873\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.89450 | − | 18.4037i | 0.486300 | − | 1.29810i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.4579 | − | 7.19259i | −0.874376 | − | 0.504821i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.85901 | + | 7.98045i | 0.339368 | + | 0.557379i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.98006 | + | 0.387554i | 0.137623 | + | 0.0269368i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.50330 | − | 9.53200i | −0.380671 | − | 0.659342i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.11683 | + | 12.3267i | −0.489943 | + | 0.848606i | −0.999933 | − | 0.0115745i | \(-0.996316\pi\) |
0.509990 | + | 0.860180i | \(0.329649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.80686 | + | 22.8400i | 0.260842 | + | 1.56497i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.241449 | − | 10.3552i | −0.0164667 | − | 0.706216i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.0801i | 1.83831i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.1166 | + | 1.85285i | −0.751188 | + | 0.125204i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.03125 | + | 12.1785i | −0.472973 | + | 0.819213i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.04188 | + | 1.75623i | −0.203699 | + | 0.117606i | −0.598380 | − | 0.801213i | \(-0.704189\pi\) |
0.394680 | + | 0.918818i | \(0.370855\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7549 | + | 9.31783i | 0.783661 | + | 0.621189i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.99580 | − | 4.03903i | 0.464328 | − | 0.268080i | −0.249535 | − | 0.968366i | \(-0.580278\pi\) |
0.713862 | + | 0.700286i | \(0.246944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97185 | + | 12.0756i | −0.460713 | + | 0.797978i | −0.998997 | − | 0.0447858i | \(-0.985739\pi\) |
0.538284 | + | 0.842764i | \(0.319073\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.1917 | − | 40.5517i | 0.999540 | − | 2.66811i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.09746i | 0.333946i | 0.985961 | + | 0.166973i | \(0.0533992\pi\) | ||||
−0.985961 | + | 0.166973i | \(0.946601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0832139 | − | 3.56884i | −0.00542828 | − | 0.232805i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.99832 | + | 3.29160i | −0.259719 | + | 0.213812i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.80932 | − | 8.32999i | 0.311089 | − | 0.538822i | −0.667509 | − | 0.744601i | \(-0.732640\pi\) |
0.978598 | + | 0.205779i | \(0.0659729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3198 | − | 21.3385i | −0.793586 | − | 1.37453i | −0.923733 | − | 0.383036i | \(-0.874878\pi\) |
0.130147 | − | 0.991495i | \(-0.458455\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.4588 | + | 10.5687i | 0.735080 | + | 0.677981i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.4289 | − | 18.7708i | −0.730163 | − | 1.19922i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.03724 | − | 4.64030i | −0.511398 | − | 0.295256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.71653 | + | 5.72919i | 0.298898 | + | 0.363072i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.2882 | −1.02810 | −0.514052 | − | 0.857759i | \(-0.671856\pi\) | ||||
−0.514052 | + | 0.857759i | \(0.671856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.09891i | − | 0.257696i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.48569 | + | 10.0087i | −0.218283 | + | 0.626769i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7891 | + | 8.53851i | 0.922521 | + | 0.532618i | 0.884439 | − | 0.466657i | \(-0.154542\pi\) |
0.0380828 | + | 0.999275i | \(0.487875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.11129 | + | 15.7812i | 0.566148 | + | 0.980598i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.93062 | − | 6.91209i | −0.490893 | − | 0.427848i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2639 | − | 8.81262i | 0.941213 | − | 0.543409i | 0.0508724 | − | 0.998705i | \(-0.483800\pi\) |
0.890340 | + | 0.455296i | \(0.150467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.7398 | − | 8.60453i | −0.966887 | − | 0.528572i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.04994 | + | 12.2990i | 0.125454 | + | 0.752686i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9751 | −0.730132 | −0.365066 | − | 0.930982i | \(-0.618954\pi\) | ||||
−0.365066 | + | 0.930982i | \(0.618954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.08606 | −0.0659734 | −0.0329867 | − | 0.999456i | \(-0.510502\pi\) | ||||
−0.0329867 | + | 0.999456i | \(0.510502\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00303 | − | 36.0164i | −0.363320 | − | 2.17981i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.9900 | − | 27.0721i | 0.843631 | − | 1.63251i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6902 | − | 7.90405i | 0.822565 | − | 0.474908i | −0.0287349 | − | 0.999587i | \(-0.509148\pi\) |
0.851300 | + | 0.524679i | \(0.175815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.80403 | + | 19.4352i | −0.227741 | + | 1.16356i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.731476 | − | 1.26695i | −0.0436362 | − | 0.0755801i | 0.843382 | − | 0.537314i | \(-0.180561\pi\) |
−0.887019 | + | 0.461734i | \(0.847228\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1349 | + | 7.00608i | 0.721344 | + | 0.416468i | 0.815247 | − | 0.579113i | \(-0.196601\pi\) |
−0.0939029 | + | 0.995581i | \(0.529934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.60529 | − | 2.30040i | −0.391264 | − | 0.136264i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 17.1409i | − | 1.01180i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.51172 | 0.559513 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.24179 | + | 5.15251i | 0.248658 | + | 0.302046i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.0624 | − | 9.85101i | −0.996799 | − | 0.575502i | −0.0894991 | − | 0.995987i | \(-0.528527\pi\) |
−0.907300 | + | 0.420485i | \(0.861860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.16347 | + | 10.1229i | 0.358851 | + | 0.589378i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.5994 | − | 26.9697i | 0.963196 | − | 1.56494i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.72807 | − | 2.99310i | −0.0999368 | − | 0.173096i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.50119 | + | 16.4565i | −0.547639 | + | 0.948539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.0373 | + | 10.7329i | −0.748975 | + | 0.616591i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1538 | + | 0.353338i | −0.867705 | + | 0.0202321i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.0537i | − | 1.20160i | −0.799400 | − | 0.600799i | \(-0.794849\pi\) | ||
0.799400 | − | 0.600799i | \(-0.205151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.76834 | − | 18.0670i | 0.385038 | − | 1.02779i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.261873 | − | 0.453578i | 0.0148495 | − | 0.0257200i | −0.858505 | − | 0.512805i | \(-0.828606\pi\) |
0.873355 | + | 0.487085i | \(0.161940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.90085 | − | 4.56156i | 0.446582 | − | 0.257834i | −0.259803 | − | 0.965662i | \(-0.583658\pi\) |
0.706386 | + | 0.707827i | \(0.250324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.52970 | − | 25.8157i | −0.536938 | − | 1.45455i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5322 | + | 7.81279i | −0.760041 | + | 0.438810i | −0.829311 | − | 0.558788i | \(-0.811267\pi\) |
0.0692693 | + | 0.997598i | \(0.477933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.6860 | + | 18.5087i | −0.598302 | + | 1.03629i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.04153 | + | 0.340272i | −0.113947 | + | 0.0189921i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.94193i | − | 0.274976i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.19758 | − | 25.6666i | −0.0664297 | − | 1.42373i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.57801 | + | 15.4673i | 0.142564 | + | 0.855343i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.27452 | + | 5.67164i | −0.180530 | + | 0.312688i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1692 | + | 22.8097i | 0.723845 | + | 1.25374i | 0.959448 | + | 0.281887i | \(0.0909604\pi\) |
−0.235602 | + | 0.971850i | \(0.575706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.32228 | + | 12.6060i | 0.236860 | + | 0.690804i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.6708 | + | 13.1945i | −1.18400 | + | 0.720895i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.5926 | + | 13.6212i | 1.28517 | + | 0.741994i | 0.977789 | − | 0.209592i | \(-0.0672135\pi\) |
0.307383 | + | 0.951586i | \(0.400547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.81119 | + | 12.8427i | −0.261308 | + | 0.697518i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.2328 | 2.17873 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.6017i | 0.626431i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.70194 | − | 1.97182i | −0.0916295 | − | 0.106159i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.1764 | + | 8.18475i | 0.761029 | + | 0.439380i | 0.829665 | − | 0.558261i | \(-0.188531\pi\) |
−0.0686360 | + | 0.997642i | \(0.521865\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.14725 | − | 15.8435i | −0.489641 | − | 0.848083i | 0.510288 | − | 0.860004i | \(-0.329539\pi\) |
−0.999929 | + | 0.0119207i | \(0.996205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.751000 | − | 26.6920i | 0.0400854 | − | 1.42471i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.6650 | − | 10.1989i | 0.940215 | − | 0.542833i | 0.0501873 | − | 0.998740i | \(-0.484018\pi\) |
0.890028 | + | 0.455906i | \(0.150685\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.3390 | − | 26.2295i | 0.761036 | − | 1.39212i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.0110 | − | 12.3577i | 0.794464 | − | 0.654039i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.33006 | 0.492422 | 0.246211 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246211 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7386 | −0.828345 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −42.4059 | − | 15.8863i | −2.22573 | − | 0.833815i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.7663 | + | 6.97901i | 0.668219 | + | 0.365298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.93529 | − | 4.58144i | 0.414219 | − | 0.239149i | −0.278382 | − | 0.960470i | \(-0.589798\pi\) |
0.692601 | + | 0.721321i | \(0.256465\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.40784 | − | 12.3020i | 0.125347 | − | 0.640414i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4544 | + | 28.4998i | 0.854269 | + | 1.47964i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0965 | − | 12.1801i | −1.09233 | − | 0.630659i | −0.158137 | − | 0.987417i | \(-0.550549\pi\) |
−0.934197 | + | 0.356758i | \(0.883882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.51076 | − | 18.8322i | −0.232935 | − | 0.972492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.0206i | 0.928107i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.84198 | 0.402815 | 0.201408 | − | 0.979508i | \(-0.435448\pi\) | ||||
0.201408 | + | 0.979508i | \(0.435448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3927 | − | 2.56558i | 0.788593 | − | 0.131439i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.6868 | − | 15.4076i | −1.36363 | − | 0.787292i | −0.373525 | − | 0.927620i | \(-0.621851\pi\) |
−0.990105 | + | 0.140328i | \(0.955184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −47.7505 | + | 29.0735i | −2.43359 | + | 1.48172i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.13065 | + | 10.4761i | −0.464137 | + | 0.532530i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.37020 | − | 4.10531i | −0.120174 | − | 0.208147i | 0.799662 | − | 0.600450i | \(-0.205012\pi\) |
−0.919836 | + | 0.392303i | \(0.871679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.920197 | − | 1.59383i | 0.0465364 | − | 0.0806033i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.11890 | + | 1.54304i | 0.207771 | + | 0.0778363i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.68413 | − | 0.155853i | 0.336315 | − | 0.00784179i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 36.8417i | − | 1.84903i | −0.381146 | − | 0.924515i | \(-0.624471\pi\) | ||
0.381146 | − | 0.924515i | \(-0.375529\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.15553 | + | 9.90655i | 0.408287 | + | 0.495948i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.70249 | − | 6.41289i | 0.184893 | − | 0.320245i | −0.758647 | − | 0.651502i | \(-0.774139\pi\) |
0.943541 | + | 0.331257i | \(0.107473\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.3788 | − | 16.9618i | 1.46346 | − | 0.844929i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.21299 | − | 19.8665i | −0.159655 | − | 0.987173i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.4461 | − | 13.5366i | 1.16218 | − | 0.670985i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.304008 | + | 0.526557i | −0.0150322 | + | 0.0260366i | −0.873444 | − | 0.486925i | \(-0.838118\pi\) |
0.858411 | + | 0.512962i | \(0.171452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.76077 | + | 11.8564i | 0.481463 | + | 0.584835i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 21.7426i | − | 1.06988i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.223321 | − | 9.57769i | −0.0109624 | − | 0.470150i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.3208 | + | 9.11119i | 1.19100 | + | 0.446177i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.18339 | + | 10.7099i | −0.302078 | + | 0.523215i | −0.976607 | − | 0.215034i | \(-0.931014\pi\) |
0.674528 | + | 0.738249i | \(0.264347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.49789 | − | 11.2547i | −0.316688 | − | 0.548519i | 0.663107 | − | 0.748524i | \(-0.269237\pi\) |
−0.979795 | + | 0.200005i | \(0.935904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.14682 | + | 3.61052i | −0.153004 | + | 0.175550i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.5175 | − | 7.38602i | 0.558683 | − | 0.358275i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0826 | + | 13.9041i | 1.16544 | + | 0.672867i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −53.5094 | + | 8.91868i | −2.58346 | + | 0.430598i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.47990 | −0.215789 | −0.107895 | − | 0.994162i | \(-0.534411\pi\) | ||||
−0.107895 | + | 0.994162i | \(0.534411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.5313i | 0.794443i | 0.917723 | + | 0.397222i | \(0.130026\pi\) | ||||
−0.917723 | + | 0.397222i | \(0.869974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.54454 | + | 13.3409i | 0.122001 | + | 0.639645i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.05185 | + | 0.607288i | 0.0503170 | + | 0.0290505i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.6927 | − | 20.2523i | −0.558060 | − | 0.966588i | −0.997658 | − | 0.0683936i | \(-0.978213\pi\) |
0.439599 | − | 0.898194i | \(-0.355121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.66349 | + | 28.9354i | −0.269690 | + | 1.37788i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.8422 | + | 10.3012i | −0.847709 | + | 0.489425i | −0.859877 | − | 0.510501i | \(-0.829460\pi\) |
0.0121681 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.72134 | − | 14.1242i | 0.366027 | − | 0.669552i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.3771 | + | 8.38303i | 1.05840 | + | 0.396504i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.1837 | −0.622177 | −0.311088 | − | 0.950381i | \(-0.600694\pi\) | ||||
−0.311088 | + | 0.950381i | \(0.600694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.4662 | −1.19916 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.48510 | + | 2.86909i | −0.163744 | + | 0.134802i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.6112 | + | 41.3613i | −1.06003 | + | 1.93905i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.7886 | + | 18.3532i | −1.48701 | + | 0.858525i | −0.999890 | − | 0.0148107i | \(-0.995285\pi\) |
−0.487119 | + | 0.873336i | \(0.661952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.5092 | − | 6.76042i | 0.583880 | − | 0.315549i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.68518 | − | 13.3111i | −0.357934 | − | 0.619961i | 0.629681 | − | 0.776854i | \(-0.283186\pi\) |
−0.987616 | + | 0.156893i | \(0.949852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.704658 | + | 0.406834i | 0.0327482 | + | 0.0189072i | 0.516285 | − | 0.856417i | \(-0.327315\pi\) |
−0.483537 | + | 0.875324i | \(0.660648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.3544 | − | 16.7054i | 0.897540 | − | 0.774694i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.2103i | − | 0.703850i | −0.936028 | − | 0.351925i | \(-0.885527\pi\) | ||
0.936028 | − | 0.351925i | \(-0.114473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.5459 | 2.14929 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.08460 | + | 24.2498i | −0.418596 | + | 1.11737i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.4494 | + | 14.1159i | 1.12419 | + | 0.649049i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.87444 | + | 7.60105i | 0.223655 | + | 0.348760i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.80575 | + | 22.7656i | 0.357401 | + | 1.04236i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.70488 | − | 6.41703i | −0.169280 | − | 0.293202i | 0.768887 | − | 0.639385i | \(-0.220811\pi\) |
−0.938167 | + | 0.346183i | \(0.887478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.4139 | − | 19.7694i | 0.520428 | − | 0.901408i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.785631 | + | 4.71355i | 0.0357475 | + | 0.214474i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.200843 | − | 8.61365i | −0.00911979 | − | 0.391126i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.0092i | 1.90362i | 0.306692 | + | 0.951809i | \(0.400778\pi\) | ||||
−0.306692 | + | 0.951809i | \(0.599222\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2138 | + | 2.70244i | −0.733214 | + | 0.122208i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.84004 | + | 6.65115i | −0.173299 | + | 0.300162i | −0.939571 | − | 0.342354i | \(-0.888776\pi\) |
0.766272 | + | 0.642516i | \(0.222109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.31034 | + | 4.79798i | −0.374279 | + | 0.216090i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −38.3543 | + | 14.1582i | −1.72390 | + | 0.636366i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −47.4935 | + | 27.4204i | −2.13038 | + | 1.22997i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.8363 | − | 34.3574i | 0.887993 | − | 1.53805i | 0.0457495 | − | 0.998953i | \(-0.485432\pi\) |
0.842244 | − | 0.539097i | \(-0.181234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.228722 | + | 0.610536i | −0.0102186 | + | 0.0272767i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 26.0215i | − | 1.16024i | −0.814530 | − | 0.580121i | \(-0.803005\pi\) | ||
0.814530 | − | 0.580121i | \(-0.196995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.7950 | − | 0.508189i | 0.969864 | − | 0.0226141i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.9299 | + | 14.7607i | −0.796294 | + | 0.655546i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.06530 | + | 12.2375i | −0.313164 | + | 0.542416i | −0.979046 | − | 0.203641i | \(-0.934722\pi\) |
0.665881 | + | 0.746058i | \(0.268056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.3459 | − | 23.1158i | −0.590388 | − | 1.02258i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.46157 | + | 8.25551i | 0.196983 | + | 0.364490i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.2743 | + | 12.9531i | −0.937456 | + | 0.570783i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.42634 | + | 4.86495i | 0.370590 | + | 0.213960i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.322013 | − | 0.391151i | −0.0141348 | − | 0.0171696i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0285 | 0.570788 | 0.285394 | − | 0.958410i | \(-0.407876\pi\) | ||||
0.285394 | + | 0.958410i | \(0.407876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.9922i | 0.961651i | 0.876816 | + | 0.480826i | \(0.159663\pi\) | ||||
−0.876816 | + | 0.480826i | \(0.840337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.8990 | + | 33.8130i | −0.475672 | + | 1.47572i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.6442 | + | 9.03218i | 0.681472 | + | 0.393448i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2738 | − | 19.5269i | −0.490167 | − | 0.848994i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.05426 | − | 15.6046i | 0.132544 | − | 0.677180i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.5959 | + | 10.7364i | −0.805480 | + | 0.465044i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.34450 | + | 1.28168i | 0.101362 | + | 0.0554117i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.68992 | − | 40.1375i | −0.288691 | − | 1.73206i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 59.8991 | 2.58003 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7006 | −1.06196 | −0.530981 | − | 0.847384i | \(-0.678177\pi\) | ||||
−0.530981 | + | 0.847384i | \(0.678177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.677535 | − | 4.06501i | −0.0290758 | − | 0.174446i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.71041 | − | 17.7627i | 0.415948 | − | 0.760870i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.78713 | + | 5.65060i | −0.418467 | + | 0.241602i | −0.694421 | − | 0.719569i | \(-0.744340\pi\) |
0.275954 | + | 0.961171i | \(0.411006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3308 | + | 13.3619i | 0.654303 | + | 0.570271i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.16645 | − | 5.48445i | −0.134895 | − | 0.233645i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.6225 | − | 6.13291i | −0.451715 | − | 0.260798i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.65835 | − | 16.2472i | 0.240184 | − | 0.689656i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0264i | 1.06040i | 0.847872 | + | 0.530201i | \(0.177884\pi\) | ||||
−0.847872 | + | 0.530201i | \(0.822116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.8046 | 1.00683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.3598 | − | 22.3017i | −0.775152 | − | 0.941580i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.7163 | + | 13.6926i | 0.999522 | + | 0.577074i | 0.908107 | − | 0.418739i | \(-0.137528\pi\) |
0.0914149 | + | 0.995813i | \(0.470861\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.1225 | − | 9.20755i | 0.636209 | − | 0.387365i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.9193 | + | 34.1955i | −0.584557 | + | 1.43608i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.1180 | + | 31.3813i | 0.759545 | + | 1.31557i | 0.943083 | + | 0.332558i | \(0.107912\pi\) |
−0.183538 | + | 0.983013i | \(0.558755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.89985 | − | 10.2188i | 0.246901 | − | 0.427645i | −0.715763 | − | 0.698343i | \(-0.753921\pi\) |
0.962664 | + | 0.270698i | \(0.0872543\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2086 | + | 12.5204i | −0.635350 | + | 0.523049i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.156730 | + | 3.35906i | 0.00653610 | + | 0.140082i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 8.24270i | − | 0.343148i | −0.985171 | − | 0.171574i | \(-0.945115\pi\) | ||
0.985171 | − | 0.171574i | \(-0.0548853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1788 | − | 35.1787i | 0.547693 | − | 1.46198i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.78784 | + | 15.2210i | −0.364581 | + | 0.631473i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.3421 | − | 24.4462i | 1.75363 | − | 1.01246i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.0381 | + | 26.5085i | −0.911163 | + | 1.09599i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.3803 | − | 21.5815i | 1.54285 | − | 0.890764i | 0.544191 | − | 0.838961i | \(-0.316837\pi\) |
0.998657 | − | 0.0518030i | \(-0.0164968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.96083 | + | 10.3245i | −0.245612 | + | 0.425412i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.2971 | + | 4.04971i | −0.999447 | + | 0.166583i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.9976i | 1.72464i | 0.506367 | + | 0.862318i | \(0.330988\pi\) | ||||
−0.506367 | + | 0.862318i | \(0.669012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.0944 | + | 0.585120i | −1.02877 | + | 0.0239876i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.23447 | − | 31.4053i | −0.214233 | − | 1.28533i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.845089 | + | 1.46374i | −0.0345294 | + | 0.0598067i | −0.882774 | − | 0.469799i | \(-0.844327\pi\) |
0.848244 | + | 0.529605i | \(0.177660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1126 | + | 24.4438i | 0.575666 | + | 0.997083i | 0.995969 | + | 0.0896992i | \(0.0285906\pi\) |
−0.420303 | + | 0.907384i | \(0.638076\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.4057 | + | 6.53846i | 1.36039 | + | 0.266267i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.4029 | + | 49.9338i | 1.23605 | + | 2.03010i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.0986 | − | 7.56250i | −0.531657 | − | 0.306952i | 0.210034 | − | 0.977694i | \(-0.432643\pi\) |
−0.741691 | + | 0.670742i | \(0.765976\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.74088 | − | 23.3323i | 0.354198 | − | 0.945474i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.20411 | 0.331903 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.1010i | 1.33694i | 0.743741 | + | 0.668468i | \(0.233050\pi\) | ||||
−0.743741 | + | 0.668468i | \(0.766950\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.2508 | + | 10.5741i | −0.494000 | + | 0.426387i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.4974 | + | 22.8039i | 1.59011 | + | 0.918048i | 0.993287 | + | 0.115673i | \(0.0369024\pi\) |
0.596819 | + | 0.802376i | \(0.296431\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.819595 | + | 1.41958i | 0.0329423 | + | 0.0570578i | 0.882027 | − | 0.471200i | \(-0.156179\pi\) |
−0.849084 | + | 0.528258i | \(0.822846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0982852 | + | 3.49325i | −0.00394405 | + | 0.140179i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.5745 | + | 14.7655i | −1.02462 | + | 0.591566i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4297 | + | 22.7205i | −0.417188 | + | 0.908820i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.7181 | − | 12.1166i | 0.587785 | − | 0.483892i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.1558 | 0.484683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.4741 | 1.13354 | 0.566769 | − | 0.823877i | \(-0.308193\pi\) | ||||
0.566769 | + | 0.823877i | \(0.308193\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.0866 | − | 8.64880i | −0.917608 | − | 0.343759i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.6771 | − | 9.66359i | −0.701492 | − | 0.383488i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.7395 | − | 25.2530i | 1.73302 | − | 1.00056i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.9377 | + | 13.0079i | −1.50079 | + | 0.514584i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.4614 | + | 37.1722i | 0.847674 | + | 1.46821i | 0.883278 | + | 0.468849i | \(0.155331\pi\) |
−0.0356042 | + | 0.999366i | \(0.511336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.7060 | − | 25.2337i | −1.72360 | − | 0.995118i | −0.911142 | − | 0.412093i | \(-0.864798\pi\) |
−0.812454 | − | 0.583025i | \(-0.801869\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.6228 | − | 3.36126i | 0.693899 | − | 0.132349i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.8898i | − | 0.546064i | −0.962005 | − | 0.273032i | \(-0.911974\pi\) | ||
0.962005 | − | 0.273032i | \(-0.0880265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.3029 | −1.26800 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −46.2658 | + | 7.71135i | −1.81330 | + | 0.302232i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.60198 | + | 5.54371i | 0.375755 | + | 0.216942i | 0.675970 | − | 0.736930i | \(-0.263725\pi\) |
−0.300215 | + | 0.953872i | \(0.597058\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.95305 | − | 4.85010i | −0.115385 | − | 0.189509i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.33113 | − | 18.4648i | −0.247001 | − | 0.720381i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.32773 | + | 4.03175i | 0.0906755 | + | 0.157055i | 0.907796 | − | 0.419413i | \(-0.137764\pi\) |
−0.817120 | + | 0.576468i | \(0.804431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0556 | − | 36.4693i | 0.818966 | − | 1.41849i | −0.0874783 | − | 0.996166i | \(-0.527881\pi\) |
0.906445 | − | 0.422325i | \(-0.138786\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.8089 | − | 8.54480i | −0.885826 | − | 0.331853i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.386153 | − | 16.5611i | −0.0149744 | − | 0.642214i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.35840i | − | 0.0913175i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.86670 | − | 4.69689i | −0.149495 | − | 0.181592i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.6573 | − | 35.7795i | 0.797465 | − | 1.38125i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.89063 | − | 4.55566i | 0.304161 | − | 0.175608i | −0.340149 | − | 0.940371i | \(-0.610478\pi\) |
0.644311 | + | 0.764764i | \(0.277144\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.5720 | + | 22.7364i | −0.483897 | + | 0.875125i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.1996 | + | 8.19813i | −0.545734 | + | 0.315080i | −0.747400 | − | 0.664375i | \(-0.768698\pi\) |
0.201665 | + | 0.979454i | \(0.435365\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.90330 | + | 13.6889i | −0.303301 | + | 0.525332i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.89274 | + | 10.8020i | 0.340771 | + | 0.413935i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31.3665i | − | 1.20021i | −0.799923 | − | 0.600103i | \(-0.795126\pi\) | ||
0.799923 | − | 0.600103i | \(-0.204874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.462159 | − | 19.8209i | −0.0176582 | − | 0.757316i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.6163 | − | 8.47262i | −0.862864 | − | 0.323250i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.6127 | − | 35.7022i | 0.785281 | − | 1.36015i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.56088 | + | 2.70353i | 0.0593788 | + | 0.102847i | 0.894187 | − | 0.447694i | \(-0.147755\pi\) |
−0.834808 | + | 0.550541i | \(0.814421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 73.6079 | + | 14.4072i | 2.79613 | + | 0.547283i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.4368 | − | 28.6383i | −0.661415 | − | 1.08631i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.90234 | − | 5.71712i | −0.375078 | − | 0.216551i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.70892 | + | 1.45156i | −0.329402 | + | 0.0549030i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.9206 | −1.39447 | −0.697236 | − | 0.716841i | \(-0.745587\pi\) | ||||
−0.697236 | + | 0.716841i | \(0.745587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.02227i | 0.302566i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.07360 | − | 1.15844i | 0.228745 | − | 0.0436293i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.6369 | − | 19.9976i | −1.30265 | − | 0.752087i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.6544 | − | 28.8463i | −0.625471 | − | 1.08335i | −0.988450 | − | 0.151550i | \(-0.951574\pi\) |
0.362979 | − | 0.931797i | \(-0.381760\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.76220 | − | 5.89373i | −0.253602 | − | 0.221032i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.84487 | + | 2.21984i | −0.143992 | + | 0.0831336i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.4504 | + | 33.5933i | 2.29811 | + | 1.25632i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.6011 | + | 5.84458i | 0.582635 | + | 0.218270i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.6734 | −1.51686 | −0.758431 | − | 0.651753i | \(-0.774034\pi\) | ||||
−0.758431 | + | 0.651753i | \(0.774034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.6942 | 1.70174 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.9482 | − | 27.1245i | 1.22536 | − | 1.00877i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.04948 | − | 15.5765i | 0.298950 | − | 0.578497i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9235 | + | 16.6990i | −1.07271 | + | 0.619332i | −0.928922 | − | 0.370276i | \(-0.879263\pi\) |
−0.143793 | + | 0.989608i | \(0.545930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.7934 | + | 22.5866i | −0.547903 | + | 0.836542i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.33798 | + | 10.9777i | 0.234419 | + | 0.406025i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.9504 | − | 26.5295i | −1.69722 | − | 0.979889i | −0.948380 | − | 0.317136i | \(-0.897279\pi\) |
−0.748838 | − | 0.662753i | \(-0.769388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.8151 | − | 24.8712i | 1.06286 | − | 0.917388i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 69.1531i | − | 2.54729i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.18128 | 0.337739 | 0.168869 | − | 0.985638i | \(-0.445988\pi\) | ||||
0.168869 | + | 0.985638i | \(0.445988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.63918 | − | 15.0529i | 0.207161 | − | 0.552981i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4494 | + | 18.1573i | 1.15377 | + | 0.666128i | 0.949802 | − | 0.312850i | \(-0.101284\pi\) |
0.203965 | + | 0.978978i | \(0.434617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.0433 | − | 26.3495i | −0.587780 | − | 0.965372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.44513 | + | 9.68956i | −0.308991 | + | 0.354522i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.45094 | − | 4.24516i | −0.0895555 | − | 0.155115i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.29856 | − | 12.6415i | 0.266328 | − | 0.461294i | −0.701582 | − | 0.712588i | \(-0.747523\pi\) |
0.967911 | + | 0.251294i | \(0.0808561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.63826 | − | 27.8281i | −0.169027 | − | 1.01411i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.82616 | − | 0.135847i | 0.212036 | − | 0.00494399i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.8778i | 1.63111i | 0.578677 | + | 0.815556i | \(0.303569\pi\) | ||||
−0.578677 | + | 0.815556i | \(0.696431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.00291 | − | 1.16721i | 0.254189 | − | 0.0423670i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.4488 | + | 38.8825i | −0.813769 | + | 1.40949i | 0.0964392 | + | 0.995339i | \(0.469255\pi\) |
−0.910208 | + | 0.414151i | \(0.864079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.1627 | + | 18.5691i | −1.16437 | + | 0.672248i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.0923 | − | 3.10515i | −0.654128 | − | 0.112267i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.5883 | + | 13.6187i | −0.851722 | + | 0.491742i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.43182 | + | 14.6043i | −0.304059 | + | 0.526646i | −0.977051 | − | 0.213004i | \(-0.931675\pi\) |
0.672992 | + | 0.739649i | \(0.265009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.3765 | + | 27.6984i | −0.373701 | + | 0.997534i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 41.8399i | − | 1.50488i | −0.658663 | − | 0.752438i | \(-0.728878\pi\) | ||
0.658663 | − | 0.752438i | \(-0.271122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.9708 | + | 1.53838i | −1.18435 | + | 0.0552603i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.3674 | + | 20.0604i | −0.874175 | + | 0.719662i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.77304 | − | 6.53510i | 0.135183 | − | 0.234144i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.7384 | + | 70.5610i | 1.45773 | + | 2.52487i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.55085 | − | 15.5176i | 0.341320 | − | 0.554555i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.5547 | − | 17.3859i | 1.01916 | − | 0.620530i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.1768 | − | 16.2679i | −1.00440 | − | 0.579888i | −0.0948495 | − | 0.995492i | \(-0.530237\pi\) |
−0.909546 | + | 0.415604i | \(0.863570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.4028 | + | 23.5686i | 0.690757 | + | 0.839065i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.4811 | −1.15490 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 34.8358i | − | 1.23706i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.2186 | − | 29.3414i | 0.362417 | − | 1.04063i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.8845 | − | 19.5632i | −1.20025 | − | 0.692965i | −0.239639 | − | 0.970862i | \(-0.577029\pi\) |
−0.960611 | + | 0.277897i | \(0.910363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.18434 | + | 3.78340i | 0.0772766 | + | 0.133847i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.4289 | + | 7.00456i | −0.721819 | + | 0.247494i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.3431 | + | 19.8280i | −1.21194 | + | 0.699714i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.95918 | − | 5.41306i | 0.104297 | − | 0.190785i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.41003 | − | 20.4592i | −0.120039 | − | 0.720197i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.5260 | −1.10840 | −0.554198 | − | 0.832385i | \(-0.686975\pi\) | ||||
−0.554198 | + | 0.832385i | \(0.686975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.54430 | −0.229801 | −0.114901 | − | 0.993377i | \(-0.536655\pi\) | ||||
−0.114901 | + | 0.993377i | \(0.536655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.309268 | − | 1.85551i | −0.0108465 | − | 0.0650757i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.6200 | + | 10.1791i | 0.652230 | + | 0.356557i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.24478 | + | 4.18278i | −0.253463 | + | 0.146337i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 59.8239 | − | 20.5121i | 2.09042 | − | 0.716752i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6905 | − | 46.2293i | −0.931505 | − | 1.61341i | −0.780750 | − | 0.624843i | \(-0.785163\pi\) |
−0.150755 | − | 0.988571i | \(-0.548170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.7001 | + | 18.8794i | 1.13985 | + | 0.658095i | 0.946395 | − | 0.323013i | \(-0.104696\pi\) |
0.193460 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 50.2359 | + | 16.1926i | 1.74899 | + | 0.563756i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.15055i | − | 0.213875i | −0.994266 | − | 0.106938i | \(-0.965895\pi\) | ||
0.994266 | − | 0.106938i | \(-0.0341045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.1456 | −1.49851 | −0.749255 | − | 0.662282i | \(-0.769588\pi\) | ||||
−0.749255 | + | 0.662282i | \(0.769588\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4024 | + | 21.1387i | 0.603682 | + | 0.733294i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.2913 | + | 13.4472i | 0.806995 | + | 0.465919i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.718919 | − | 0.437724i | 0.0248792 | − | 0.0151481i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.2880 | − | 0.964718i | −1.18517 | − | 0.0333455i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.8927 | + | 30.9911i | 0.617726 | + | 1.06993i | 0.989900 | + | 0.141769i | \(0.0452792\pi\) |
−0.372174 | + | 0.928163i | \(0.621388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.35157 | − | 14.4653i | 0.287985 | − | 0.498805i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.95627 | − | 1.61049i | 0.0673776 | − | 0.0554683i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.9740 | − | 0.698898i | 1.03114 | − | 0.0240428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 107.251i | − | 3.68519i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.51422 | + | 22.7273i | −0.292207 | + | 0.779999i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.49376 | + | 2.58727i | −0.0512055 | + | 0.0886906i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.1522 | − | 7.59341i | 0.450322 | − | 0.259993i | −0.257644 | − | 0.966240i | \(-0.582946\pi\) |
0.707966 | + | 0.706246i | \(0.249613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.04926 | − | 11.9401i | 0.0700832 | − | 0.408342i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.919391 | − | 0.530811i | 0.0314058 | − | 0.0181321i | −0.484215 | − | 0.874949i | \(-0.660895\pi\) |
0.515621 | + | 0.856817i | \(0.327561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.604035 | − | 1.04622i | 0.0206094 | − | 0.0356965i | −0.855537 | − | 0.517742i | \(-0.826773\pi\) |
0.876146 | + | 0.482046i | \(0.160106\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.2850 | − | 4.88107i | 0.998029 | − | 0.166347i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 13.2305i | − | 0.450373i | −0.974316 | − | 0.225186i | \(-0.927701\pi\) | ||
0.974316 | − | 0.225186i | \(-0.0722991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0152469 | + | 0.653901i | 0.000518409 | + | 0.0222333i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.70857 | + | 16.2506i | 0.0919878 | + | 0.551899i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.11164 | + | 15.7818i | −0.309091 | + | 0.535361i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.1544 | − | 50.4969i | −0.987860 | − | 1.71102i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.59508 | + | 8.71425i | −0.257055 | + | 0.294933i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.0199 | − | 25.6516i | 1.28531 | − | 0.867183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.4105 | + | 20.4443i | 1.19573 | + | 0.690355i | 0.959600 | − | 0.281367i | \(-0.0907879\pi\) |
0.236129 | + | 0.971722i | \(0.424121\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.9715 | − | 31.9561i | 0.403790 | − | 1.07785i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.2103 | 0.781975 | 0.390988 | − | 0.920396i | \(-0.372133\pi\) | ||||
0.390988 | + | 0.920396i | \(0.372133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.1285i | − | 0.677377i | −0.940899 | − | 0.338689i | \(-0.890017\pi\) | ||
0.940899 | − | 0.338689i | \(-0.109983\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.5397 | + | 13.4128i | −0.522361 | + | 0.450866i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.946216 | + | 0.546298i | 0.0317708 | + | 0.0183429i | 0.515801 | − | 0.856708i | \(-0.327494\pi\) |
−0.484030 | + | 0.875051i | \(0.660828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.4796 | + | 32.0076i | 0.619786 | + | 1.07350i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.8041 | + | 20.6799i | 1.70200 | + | 0.692803i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.49687 | + | 1.44157i | −0.0835546 | + | 0.0482402i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.1984 | + | 46.0941i | −0.842291 | + | 1.54075i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.62158 | − | 3.80469i | 0.154310 | − | 0.127035i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.1488 | 0.772056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.9525 | 0.731345 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.8213 | − | 11.5464i | −1.02567 | − | 0.384241i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.55202 | + | 4.66827i | −0.0848321 | + | 0.155179i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.59622 | − | 2.07628i | 0.119410 | − | 0.0689416i | −0.439105 | − | 0.898436i | \(-0.644704\pi\) |
0.558516 | + | 0.829494i | \(0.311371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.0495 | − | 19.2177i | −0.731337 | − | 0.637412i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.0374 | − | 24.3135i | −0.465080 | − | 0.805542i | 0.534125 | − | 0.845405i | \(-0.320641\pi\) |
−0.999205 | + | 0.0398635i | \(0.987308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.6138 | + | 13.0561i | 0.748406 | + | 0.432093i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.91889 | − | 25.7894i | −0.162614 | − | 0.852571i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.4173i | 0.344011i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0993 | 0.597041 | 0.298520 | − | 0.954403i | \(-0.403507\pi\) | ||||
0.298520 | + | 0.954403i | \(0.403507\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.9698 | − | 5.99528i | 1.18525 | − | 0.197551i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 59.4960 | + | 34.3500i | 1.95833 | + | 1.13064i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.6965 | + | 11.9898i | −0.614738 | + | 0.394222i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.7945 | + | 6.41882i | 1.07711 | + | 0.210822i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5132 | − | 25.1377i | −0.476164 | − | 0.824740i | 0.523463 | − | 0.852048i | \(-0.324640\pi\) |
−0.999627 | + | 0.0273082i | \(0.991306\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.87456 | + | 15.3712i | −0.290852 | + | 0.503770i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.849501 | + | 0.318245i | 0.0278114 | + | 0.0104189i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.869311 | + | 37.2826i | 0.0284295 | + | 1.21927i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.8353i | − | 0.876672i | −0.898811 | − | 0.438336i | \(-0.855568\pi\) | ||
0.898811 | − | 0.438336i | \(-0.144432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0432 | + | 12.1995i | 0.327747 | + | 0.398116i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7696 | − | 35.9741i | 0.677071 | − | 1.17272i | −0.298789 | − | 0.954319i | \(-0.596583\pi\) |
0.975859 | − | 0.218401i | \(-0.0700841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.43370 | − | 1.40510i | 0.0792521 | − | 0.0457562i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.3920 | − | 23.6326i | 1.34648 | − | 0.768770i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.0805 | + | 21.9858i | −1.23745 | + | 0.714443i | −0.968573 | − | 0.248731i | \(-0.919986\pi\) |
−0.268879 | + | 0.963174i | \(0.586653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.7187 | + | 28.9576i | −0.542711 | + | 0.940002i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.2014 | − | 20.8947i | −0.557795 | − | 0.677556i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.3790i | 0.627749i | 0.949465 | + | 0.313874i | \(0.101627\pi\) | ||||
−0.949465 | + | 0.313874i | \(0.898373\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.4248 | − | 0.592825i | 0.822728 | − | 0.0191834i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.6648 | − | 12.9863i | −1.12055 | − | 0.419787i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.1863 | + | 31.4995i | −0.587265 | + | 1.01717i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.28879 | − | 10.8925i | −0.202864 | − | 0.351371i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.16270 | − | 3.39102i | −0.0374674 | − | 0.109274i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.4237 | + | 25.2214i | −1.33347 | + | 0.811904i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.64129 | + | 0.947601i | 0.0527804 | + | 0.0304728i | 0.526158 | − | 0.850387i | \(-0.323632\pi\) |
−0.473378 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.44319 | − | 1.40727i | 0.271234 | − | 0.0452080i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8043 | −1.18111 | −0.590553 | − | 0.806999i | \(-0.701090\pi\) | ||||
−0.590553 | + | 0.806999i | \(0.701090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 61.5111i | 1.97196i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43.5100 | − | 9.35491i | 1.39343 | − | 0.299597i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.2472 | − | 19.7726i | −1.09566 | − | 0.632582i | −0.160585 | − | 0.987022i | \(-0.551338\pi\) |
−0.935079 | + | 0.354440i | \(0.884672\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.9370 | + | 37.9960i | 0.701110 | + | 1.21436i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.6915 | + | 8.80897i | −0.820265 | + | 0.281249i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.4295 | − | 7.75350i | 0.428333 | − | 0.247298i | −0.270303 | − | 0.962775i | \(-0.587124\pi\) |
0.698636 | + | 0.715477i | \(0.253791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.9028 | + | 15.2538i | 0.889058 | + | 0.486025i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.6224 | − | 3.97940i | −0.338113 | − | 0.126666i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.11537 | −0.0990629 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.4814 | 0.745910 | 0.372955 | − | 0.927849i | \(-0.378345\pi\) | ||||
0.372955 | + | 0.927849i | \(0.378345\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.2200 | + | 28.9947i | −1.11767 | + | 0.920119i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.7163 | + | 36.0659i | −0.625049 | + | 1.14337i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.5213 | + | 13.5800i | −0.744928 | + | 0.430084i | −0.823858 | − | 0.566796i | \(-0.808183\pi\) |
0.0789305 | + | 0.996880i | \(0.474849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.3063 | + | 10.9742i | −0.642463 | + | 0.347210i |
(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 | 360.2.bi.b.49.9 | yes | 32 | |
3.2 | odd | 2 | 1080.2.bi.b.1009.6 | 32 | |||
4.3 | odd | 2 | 720.2.by.f.49.8 | 32 | |||
5.4 | even | 2 | inner | 360.2.bi.b.49.8 | ✓ | 32 | |
9.2 | odd | 6 | 1080.2.bi.b.289.5 | 32 | |||
9.4 | even | 3 | 3240.2.f.k.649.2 | 16 | |||
9.5 | odd | 6 | 3240.2.f.i.649.15 | 16 | |||
9.7 | even | 3 | inner | 360.2.bi.b.169.8 | yes | 32 | |
12.11 | even | 2 | 2160.2.by.f.1009.6 | 32 | |||
15.14 | odd | 2 | 1080.2.bi.b.1009.5 | 32 | |||
20.19 | odd | 2 | 720.2.by.f.49.9 | 32 | |||
36.7 | odd | 6 | 720.2.by.f.529.9 | 32 | |||
36.11 | even | 6 | 2160.2.by.f.289.5 | 32 | |||
45.4 | even | 6 | 3240.2.f.k.649.1 | 16 | |||
45.14 | odd | 6 | 3240.2.f.i.649.16 | 16 | |||
45.29 | odd | 6 | 1080.2.bi.b.289.6 | 32 | |||
45.34 | even | 6 | inner | 360.2.bi.b.169.9 | yes | 32 | |
60.59 | even | 2 | 2160.2.by.f.1009.5 | 32 | |||
180.79 | odd | 6 | 720.2.by.f.529.8 | 32 | |||
180.119 | even | 6 | 2160.2.by.f.289.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bi.b.49.8 | ✓ | 32 | 5.4 | even | 2 | inner | |
360.2.bi.b.49.9 | yes | 32 | 1.1 | even | 1 | trivial | |
360.2.bi.b.169.8 | yes | 32 | 9.7 | even | 3 | inner | |
360.2.bi.b.169.9 | yes | 32 | 45.34 | even | 6 | inner | |
720.2.by.f.49.8 | 32 | 4.3 | odd | 2 | |||
720.2.by.f.49.9 | 32 | 20.19 | odd | 2 | |||
720.2.by.f.529.8 | 32 | 180.79 | odd | 6 | |||
720.2.by.f.529.9 | 32 | 36.7 | odd | 6 | |||
1080.2.bi.b.289.5 | 32 | 9.2 | odd | 6 | |||
1080.2.bi.b.289.6 | 32 | 45.29 | odd | 6 | |||
1080.2.bi.b.1009.5 | 32 | 15.14 | odd | 2 | |||
1080.2.bi.b.1009.6 | 32 | 3.2 | odd | 2 | |||
2160.2.by.f.289.5 | 32 | 36.11 | even | 6 | |||
2160.2.by.f.289.6 | 32 | 180.119 | even | 6 | |||
2160.2.by.f.1009.5 | 32 | 60.59 | even | 2 | |||
2160.2.by.f.1009.6 | 32 | 12.11 | even | 2 | |||
3240.2.f.i.649.15 | 16 | 9.5 | odd | 6 | |||
3240.2.f.i.649.16 | 16 | 45.14 | odd | 6 | |||
3240.2.f.k.649.1 | 16 | 45.4 | even | 6 | |||
3240.2.f.k.649.2 | 16 | 9.4 | even | 3 |