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 | 49.14 | ||
Character | \(\chi\) | \(=\) | 360.49 |
Dual form | 360.2.bi.b.169.14 |
$q$-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 | ||||||||
\(3\) | 1.54437 | + | 0.784174i | 0.891641 | + | 0.452743i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.59892 | − | 1.56315i | 0.715061 | − | 0.699062i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.608912 | − | 0.351555i | 0.230147 | − | 0.132875i | −0.380493 | − | 0.924784i | \(-0.624246\pi\) |
0.610640 | + | 0.791908i | \(0.290912\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.77014 | + | 2.42211i | 0.590047 | + | 0.807369i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.80274 | − | 3.12243i | −0.543546 | − | 0.941449i | −0.998697 | − | 0.0510348i | \(-0.983748\pi\) |
0.455151 | − | 0.890414i | \(-0.349585\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.97952 | + | 1.14288i | 0.549020 | + | 0.316977i | 0.748726 | − | 0.662879i | \(-0.230666\pi\) |
−0.199707 | + | 0.979856i | \(0.563999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.69511 | − | 1.16024i | 0.954073 | − | 0.299574i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.471334i | 0.114315i | 0.998365 | + | 0.0571576i | \(0.0182038\pi\) | ||||
−0.998365 | + | 0.0571576i | \(0.981796\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.51095 | −1.26430 | −0.632149 | − | 0.774847i | \(-0.717827\pi\) | ||||
−0.632149 | + | 0.774847i | \(0.717827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.21606 | − | 0.0654377i | 0.265367 | − | 0.0142797i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.68816 | + | 1.55201i | 0.560520 | + | 0.323617i | 0.753354 | − | 0.657615i | \(-0.228435\pi\) |
−0.192834 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.113116 | − | 4.99872i | 0.0226233 | − | 0.999744i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.834394 | + | 5.12872i | 0.160579 | + | 0.987023i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.195925 | + | 0.339352i | 0.0363823 | + | 0.0630161i | 0.883643 | − | 0.468161i | \(-0.155083\pi\) |
−0.847261 | + | 0.531177i | \(0.821750\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.10681 | + | 5.38116i | −0.558000 | + | 0.966484i | 0.439663 | + | 0.898163i | \(0.355098\pi\) |
−0.997663 | + | 0.0683218i | \(0.978236\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.335557 | − | 6.23584i | −0.0584130 | − | 1.08552i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.424070 | − | 1.51393i | 0.0716808 | − | 0.255901i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1237i | 1.66432i | 0.554537 | + | 0.832159i | \(0.312896\pi\) | ||||
−0.554537 | + | 0.832159i | \(0.687104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.16089 | + | 3.31731i | 0.346019 | + | 0.531194i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.18197 | − | 8.97544i | 0.809288 | − | 1.40173i | −0.104069 | − | 0.994570i | \(-0.533186\pi\) |
0.913358 | − | 0.407159i | \(-0.133480\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.279206 | + | 0.161200i | −0.0425786 | + | 0.0245827i | −0.521138 | − | 0.853472i | \(-0.674492\pi\) |
0.478560 | + | 0.878055i | \(0.341159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.61644 | + | 1.10577i | 0.986321 | + | 0.164838i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.51687 | + | 5.49457i | −1.38818 | + | 0.801465i | −0.993110 | − | 0.117187i | \(-0.962612\pi\) |
−0.395068 | + | 0.918652i | \(0.629279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.25282 | + | 5.63405i | −0.464688 | + | 0.804864i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.369608 | + | 0.727913i | −0.0517555 | + | 0.101928i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.0166i | − | 1.65060i | −0.564691 | − | 0.825302i | \(-0.691005\pi\) | ||
0.564691 | − | 0.825302i | \(-0.308995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.76328 | − | 2.17458i | −1.04680 | − | 0.293221i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.51093 | − | 4.32154i | −1.12730 | − | 0.572402i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.13487 | − | 5.42975i | 0.408125 | − | 0.706893i | −0.586555 | − | 0.809910i | \(-0.699516\pi\) |
0.994680 | + | 0.103017i | \(0.0328495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.09437 | + | 1.89551i | 0.140120 | + | 0.242695i | 0.927542 | − | 0.373720i | \(-0.121918\pi\) |
−0.787422 | + | 0.616415i | \(0.788585\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.92936 | + | 0.852547i | 0.243077 | + | 0.107411i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.95159 | − | 1.26692i | 0.614169 | − | 0.157142i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.04913 | − | 5.22452i | −1.10553 | − | 0.638277i | −0.167860 | − | 0.985811i | \(-0.553686\pi\) |
−0.937667 | + | 0.347534i | \(0.887019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.93446 | + | 4.50486i | 0.353268 | + | 0.542322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.13506 | 0.372064 | 0.186032 | − | 0.982544i | \(-0.440437\pi\) | ||||
0.186032 | + | 0.982544i | \(0.440437\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.39185i | − | 0.396986i | −0.980102 | − | 0.198493i | \(-0.936395\pi\) | ||
0.980102 | − | 0.198493i | \(-0.0636047\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.09456 | − | 7.63116i | 0.472799 | − | 0.881170i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.19542 | − | 1.26752i | −0.250191 | − | 0.144448i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.66578 | − | 2.88522i | −0.187415 | − | 0.324613i | 0.756972 | − | 0.653447i | \(-0.226678\pi\) |
−0.944388 | + | 0.328834i | \(0.893344\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.73320 | + | 8.57494i | −0.303689 | + | 0.952771i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2334 | + | 7.06296i | −1.34279 | + | 0.775260i | −0.987216 | − | 0.159388i | \(-0.949048\pi\) |
−0.355574 | + | 0.934648i | \(0.615715\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.736766 | + | 0.753627i | 0.0799135 | + | 0.0817423i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0364690 | + | 0.677723i | 0.00390989 | + | 0.0726596i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.11521 | −0.436212 | −0.218106 | − | 0.975925i | \(-0.569988\pi\) | ||||
−0.218106 | + | 0.975925i | \(0.569988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.60714 | 0.168474 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.01783 | + | 5.87420i | −0.935105 | + | 0.609126i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.81159 | + | 8.61444i | −0.904050 | + | 0.883823i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.4831 | + | 6.62975i | −1.16593 | + | 0.673149i | −0.952718 | − | 0.303857i | \(-0.901725\pi\) |
−0.213211 | + | 0.977006i | \(0.568392\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.37177 | − | 9.89357i | 0.439379 | − | 0.994341i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.07080 | − | 8.78289i | −0.504564 | − | 0.873930i | −0.999986 | − | 0.00527795i | \(-0.998320\pi\) |
0.495422 | − | 0.868652i | \(-0.335013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.21663 | + | 1.85712i | 0.316944 | + | 0.182988i | 0.650030 | − | 0.759909i | \(-0.274756\pi\) |
−0.333085 | + | 0.942897i | \(0.608090\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.84211 | − | 2.00552i | 0.179771 | − | 0.195719i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.93731i | 0.283961i | 0.989869 | + | 0.141980i | \(0.0453470\pi\) | ||||
−0.989869 | + | 0.141980i | \(0.954653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21238 | −0.211907 | −0.105954 | − | 0.994371i | \(-0.533790\pi\) | ||||
−0.105954 | + | 0.994371i | \(0.533790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.93871 | + | 15.6346i | −0.753509 | + | 1.48397i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4513 | + | 6.61142i | 1.07725 | + | 0.621950i | 0.930153 | − | 0.367172i | \(-0.119674\pi\) |
0.147097 | + | 0.989122i | \(0.453007\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.72419 | − | 1.72046i | 0.627034 | − | 0.160433i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.735861 | + | 6.81765i | 0.0680303 | + | 0.630292i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.165700 | + | 0.287001i | 0.0151897 | + | 0.0263093i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.999726 | + | 1.73158i | −0.0908842 | + | 0.157416i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.0412 | − | 9.79781i | 1.35622 | − | 0.883439i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.63289 | − | 8.16939i | −0.682707 | − | 0.730693i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.68855i | − | 0.682249i | −0.940018 | − | 0.341124i | \(-0.889192\pi\) | ||
0.940018 | − | 0.341124i | \(-0.110808\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.557606 | + | 0.0300053i | −0.0490945 | + | 0.00264182i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.30649 | − | 14.3873i | 0.725741 | − | 1.25702i | −0.232927 | − | 0.972494i | \(-0.574830\pi\) |
0.958668 | − | 0.284526i | \(-0.0918363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.35568 | + | 1.93740i | −0.290974 | + | 0.167994i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.35110 | + | 6.89615i | 0.804815 | + | 0.593526i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4297 | + | 6.02160i | −0.891071 | + | 0.514460i | −0.874293 | − | 0.485399i | \(-0.838674\pi\) |
−0.0167781 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0834 | − | 19.1970i | 0.940079 | − | 1.62827i | 0.174763 | − | 0.984610i | \(-0.444084\pi\) |
0.765316 | − | 0.643655i | \(-0.222583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.0062 | + | 1.02275i | −1.60061 | + | 0.0861307i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.24122i | − | 0.689165i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.843727 | + | 0.236338i | 0.0700678 | + | 0.0196268i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.44162 | + | 6.15026i | −0.778732 | + | 0.507265i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.95157 | + | 12.0405i | −0.569495 | + | 0.986394i | 0.427121 | + | 0.904194i | \(0.359528\pi\) |
−0.996616 | + | 0.0821996i | \(0.973805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2513 | + | 19.4879i | 0.915620 | + | 1.58590i | 0.805991 | + | 0.591927i | \(0.201633\pi\) |
0.109628 | + | 0.993973i | \(0.465034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.14162 | + | 0.834327i | −0.0922946 | + | 0.0674514i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.44401 | + | 13.4605i | 0.276629 | + | 1.08117i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9128 | + | 10.3420i | 1.42960 | + | 0.825380i | 0.997089 | − | 0.0762487i | \(-0.0242943\pi\) |
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.42310 | − | 18.5580i | 0.747300 | − | 1.47175i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.18247 | 0.172003 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.2797i | − | 1.04015i | −0.854121 | − | 0.520074i | \(-0.825904\pi\) | ||
0.854121 | − | 0.520074i | \(-0.174096\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.2841 | − | 9.44612i | −0.800616 | − | 0.735379i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7831 | + | 10.8444i | 1.45348 | + | 0.839166i | 0.998677 | − | 0.0514271i | \(-0.0163770\pi\) |
0.454801 | + | 0.890593i | \(0.349710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.88767 | − | 6.73365i | −0.299052 | − | 0.517973i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.75515 | − | 13.3481i | −0.745995 | − | 1.02075i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.80171 | − | 3.92697i | 0.517124 | − | 0.298562i | −0.218633 | − | 0.975807i | \(-0.570160\pi\) |
0.735757 | + | 0.677245i | \(0.236826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.68845 | − | 3.08355i | −0.127635 | − | 0.233094i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.09925 | − | 5.92724i | 0.683942 | − | 0.445519i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.01228 | 0.225149 | 0.112574 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112574 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4261 | 1.74125 | 0.870625 | − | 0.491947i | \(-0.163715\pi\) | ||||
0.870625 | + | 0.491947i | \(0.163715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.203704 | + | 3.78554i | 0.0150582 | + | 0.279835i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.8248 | + | 16.1870i | 1.16346 | + | 1.19009i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.47171 | − | 0.849691i | 0.107622 | − | 0.0621356i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.31110 | + | 2.82960i | 0.168108 | + | 0.205823i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.68264 | + | 8.11057i | 0.338824 | + | 0.586860i | 0.984212 | − | 0.176995i | \(-0.0566376\pi\) |
−0.645388 | + | 0.763855i | \(0.723304\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.14899 | + | 5.28217i | 0.658559 | + | 0.380219i | 0.791728 | − | 0.610874i | \(-0.209182\pi\) |
−0.133169 | + | 0.991093i | \(0.542515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.64055 | + | 1.92632i | 0.618763 | + | 0.137947i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.8747i | − | 1.27352i | −0.771061 | − | 0.636761i | \(-0.780274\pi\) | ||
0.771061 | − | 0.636761i | \(-0.219726\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.91876 | −0.136017 | −0.0680087 | − | 0.997685i | \(-0.521665\pi\) | ||||
−0.0680087 | + | 0.997685i | \(0.521665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.87825 | − | 15.1647i | −0.696758 | − | 1.06963i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.238602 | + | 0.137757i | 0.0167466 | + | 0.00966864i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.74439 | − | 22.4513i | −0.401206 | − | 1.56806i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.999290 | + | 9.25829i | 0.0694554 | + | 0.643496i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.93479 | + | 17.2076i | 0.687204 | + | 1.19027i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.17779 | − | 8.96820i | 0.356454 | − | 0.617396i | −0.630912 | − | 0.775855i | \(-0.717319\pi\) |
0.987366 | + | 0.158458i | \(0.0506524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.84169 | + | 2.45844i | 0.331747 | + | 0.168449i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.194450 | + | 0.694188i | −0.0132614 | + | 0.0473432i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.36887i | 0.296578i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.65980 | − | 5.23826i | 0.179733 | − | 0.353969i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.538676 | + | 0.933014i | −0.0362353 | + | 0.0627613i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.82440 | + | 2.78537i | −0.323066 | + | 0.186522i | −0.652758 | − | 0.757566i | \(-0.726388\pi\) |
0.329692 | + | 0.944088i | \(0.393055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.3077 | − | 8.57446i | 0.820511 | − | 0.571631i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2675 | − | 7.65998i | 0.880593 | − | 0.508411i | 0.00973922 | − | 0.999953i | \(-0.496900\pi\) |
0.870854 | + | 0.491542i | \(0.163567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.77489 | + | 4.80624i | −0.183370 | + | 0.317606i | −0.943026 | − | 0.332719i | \(-0.892034\pi\) |
0.759656 | + | 0.650325i | \(0.225367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.39657 | − | 3.67911i | −0.157683 | − | 0.242068i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.1929i | 1.19186i | 0.803037 | + | 0.595929i | \(0.203216\pi\) | ||||
−0.803037 | + | 0.595929i | \(0.796784\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.62791 | + | 23.6617i | −0.432357 | + | 1.54352i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.310065 | − | 5.76211i | −0.0201409 | − | 0.374289i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.76278 | + | 9.98142i | −0.372763 | + | 0.645644i | −0.989989 | − | 0.141141i | \(-0.954923\pi\) |
0.617226 | + | 0.786786i | \(0.288256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.68563 | + | 15.0440i | 0.559491 | + | 0.969067i | 0.997539 | + | 0.0701150i | \(0.0223366\pi\) |
−0.438048 | + | 0.898952i | \(0.644330\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.9453 | + | 11.0996i | −0.702142 | + | 0.712037i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.60586 | + | 14.0931i | 0.230370 | + | 0.900372i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9090 | − | 6.29832i | −0.694124 | − | 0.400753i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.4315 | + | 1.31468i | −1.54828 | + | 0.0833146i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8501 | −1.25293 | −0.626463 | − | 0.779451i | \(-0.715498\pi\) | ||||
−0.626463 | + | 0.779451i | \(0.715498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.1915i | − | 0.703602i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.546863 | + | 1.74163i | 0.0342459 | + | 0.109065i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.78010 | − | 3.33714i | −0.360553 | − | 0.208165i | 0.308770 | − | 0.951137i | \(-0.400083\pi\) |
−0.669323 | + | 0.742971i | \(0.733416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.55903 | + | 6.16441i | 0.221147 | + | 0.383038i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.475132 | + | 1.07525i | −0.0294099 | + | 0.0665564i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.11719 | − | 1.22236i | 0.130551 | − | 0.0753739i | −0.433302 | − | 0.901249i | \(-0.642652\pi\) |
0.563853 | + | 0.825875i | \(0.309318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.7837 | − | 19.2136i | −1.15388 | − | 1.18028i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.35540 | − | 3.22704i | −0.388944 | − | 0.197492i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0675 | −0.613828 | −0.306914 | − | 0.951737i | \(-0.599296\pi\) | ||||
−0.306914 | + | 0.951737i | \(0.599296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5777 | 1.31075 | 0.655376 | − | 0.755303i | \(-0.272510\pi\) | ||||
0.655376 | + | 0.755303i | \(0.272510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.48201 | + | 1.26027i | 0.150218 | + | 0.0762753i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.8121 | + | 8.65818i | −0.953505 | + | 0.522108i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1935 | − | 14.5455i | 1.51373 | − | 0.873954i | 0.513862 | − | 0.857873i | \(-0.328214\pi\) |
0.999871 | − | 0.0160814i | \(-0.00511910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.5332 | + | 2.00038i | −1.10956 | + | 0.119759i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.84998 | − | 15.3286i | −0.527946 | − | 0.914429i | −0.999469 | − | 0.0325754i | \(-0.989629\pi\) |
0.471524 | − | 0.881853i | \(-0.343704\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.936723 | + | 0.540817i | 0.0556824 | + | 0.0321482i | 0.527583 | − | 0.849504i | \(-0.323098\pi\) |
−0.471900 | + | 0.881652i | \(0.656432\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20.3636 | + | 6.39405i | −1.20623 | + | 0.378751i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.28700i | − | 0.430138i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7778 | 0.986932 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.9329 | + | 1.23405i | −1.34435 | + | 0.0723410i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.96683 | − | 1.71290i | −0.173324 | − | 0.100069i | 0.410828 | − | 0.911713i | \(-0.365240\pi\) |
−0.584152 | + | 0.811644i | \(0.698573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.47510 | − | 13.5820i | −0.202328 | − | 0.790776i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.5099 | − | 11.8511i | 0.841950 | − | 0.687669i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.54751 | + | 6.14447i | 0.205158 | + | 0.355344i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.113341 | + | 0.196313i | −0.00653289 | + | 0.0113153i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.943867 | − | 17.5404i | −0.0542237 | − | 1.00767i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.71278 | + | 1.32010i | 0.269853 | + | 0.0755890i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.76092i | − | 0.385866i | −0.981212 | − | 0.192933i | \(-0.938200\pi\) | ||
0.981212 | − | 0.192933i | \(-0.0618000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.51136 | + | 5.39049i | 0.199754 | + | 0.306654i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.54403 | − | 7.87049i | 0.257668 | − | 0.446295i | −0.707948 | − | 0.706264i | \(-0.750379\pi\) |
0.965617 | + | 0.259969i | \(0.0837124\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0630 | + | 12.7381i | −1.24707 | + | 0.719999i | −0.970525 | − | 0.241001i | \(-0.922524\pi\) |
−0.276550 | + | 0.961000i | \(0.589191\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.41757 | − | 1.65273i | 0.248902 | − | 0.0931209i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0926 | + | 6.40430i | −0.623021 | + | 0.359701i | −0.778044 | − | 0.628209i | \(-0.783788\pi\) |
0.155023 | + | 0.987911i | \(0.450455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.706402 | − | 1.22352i | 0.0395509 | − | 0.0685042i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.30337 | + | 4.53629i | −0.128561 | + | 0.253191i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.59750i | − | 0.144529i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.93683 | − | 9.76578i | 0.329316 | − | 0.541708i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.41672 | − | 1.73489i | −0.188945 | − | 0.0959396i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.86329 | + | 6.69142i | −0.212990 | + | 0.368910i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.63447 | + | 14.9553i | 0.474594 | + | 0.822020i | 0.999577 | − | 0.0290924i | \(-0.00926172\pi\) |
−0.524983 | + | 0.851113i | \(0.675928\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.5206 | + | 17.9203i | −1.34372 | + | 0.982026i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.6356 | + | 5.79155i | −1.23671 | + | 0.316426i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.5275 | − | 15.3157i | −1.44505 | − | 0.834298i | −0.446867 | − | 0.894600i | \(-0.647460\pi\) |
−0.998180 | + | 0.0603018i | \(0.980794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5005 | + | 19.1903i | 0.678936 | + | 1.04227i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.4031 | 1.21319 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.49596i | 0.512734i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.7338 | + | 2.61592i | 0.631724 | + | 0.140837i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.4143 | + | 7.74476i | 0.720118 | + | 0.415760i | 0.814796 | − | 0.579748i | \(-0.196849\pi\) |
−0.0946781 | + | 0.995508i | \(0.530182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.70955 | − | 8.15717i | −0.252096 | − | 0.436643i | 0.712007 | − | 0.702173i | \(-0.247787\pi\) |
−0.964103 | + | 0.265529i | \(0.914453\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.20979 | + | 11.1060i | −0.224702 | + | 0.592795i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1570 | + | 8.75092i | −0.806728 | + | 0.465765i | −0.845818 | − | 0.533471i | \(-0.820887\pi\) |
0.0390902 | + | 0.999236i | \(0.487554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.01273 | − | 4.90058i | 0.266048 | − | 0.260096i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0308430 | + | 0.573172i | 0.00163238 | + | 0.0303355i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.81160 | −0.465059 | −0.232529 | − | 0.972589i | \(-0.574700\pi\) | ||||
−0.232529 | + | 0.972589i | \(0.574700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3705 | 0.598449 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.90180 | + | 1.89023i | −0.152305 | + | 0.0992114i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.30197 | − | 5.42331i | −0.277518 | − | 0.283869i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5888 | − | 9.57753i | 0.865927 | − | 0.499943i | −6.57031e−5 | − | 1.00000i | \(-0.500021\pi\) |
0.865993 | + | 0.500057i | \(0.166688\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.9123 | − | 3.33651i | 1.60923 | − | 0.173692i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.22449 | − | 7.31704i | −0.219325 | − | 0.379882i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.80045 | + | 1.03949i | 0.0932237 | + | 0.0538227i | 0.545887 | − | 0.837859i | \(-0.316193\pi\) |
−0.452663 | + | 0.891681i | \(0.649526\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.38176 | − | 18.6021i | −0.277913 | − | 0.960606i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.895671i | 0.0461294i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.8021 | −0.708966 | −0.354483 | − | 0.935063i | \(-0.615343\pi\) | ||||
−0.354483 | + | 0.935063i | \(0.615343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.02917 | − | 11.8739i | 0.308884 | − | 0.608321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4234 | − | 9.48208i | −0.839199 | − | 0.484512i | 0.0177929 | − | 0.999842i | \(-0.494336\pi\) |
−0.856992 | + | 0.515330i | \(0.827669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.49164 | + | 1.40509i | −0.279880 | + | 0.0716102i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.884678 | − | 0.390921i | −0.0449707 | − | 0.0198716i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.71567 | + | 11.6319i | 0.340498 | + | 0.589760i | 0.984525 | − | 0.175243i | \(-0.0560710\pi\) |
−0.644027 | + | 0.765002i | \(0.722738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.731515 | + | 1.26702i | −0.0369943 | + | 0.0640760i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.1104 | − | 15.7055i | 1.21621 | − | 0.792237i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.17350 | − | 2.00938i | −0.360938 | − | 0.101103i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.78992i | 0.491342i | 0.969353 | + | 0.245671i | \(0.0790083\pi\) | ||||
−0.969353 | + | 0.245671i | \(0.920992\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.70167 | + | 0.360623i | −0.335503 | + | 0.0180538i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.06224 | − | 7.03601i | 0.202859 | − | 0.351361i | −0.746590 | − | 0.665285i | \(-0.768310\pi\) |
0.949448 | + | 0.313923i | \(0.101643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.3000 | + | 7.10140i | −0.612706 | + | 0.353746i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.03375 | + | 17.9831i | 0.448891 | + | 0.893587i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.6104 | − | 18.2503i | 1.56687 | − | 0.904633i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1670 | + | 19.3418i | −0.552171 | + | 0.956388i | 0.445947 | + | 0.895060i | \(0.352867\pi\) |
−0.998118 | + | 0.0613286i | \(0.980466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.8293 | + | 1.12085i | −1.02743 | + | 0.0552872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.40832i | − | 0.216919i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.51981 | + | 30.4158i | −0.418221 | + | 1.49305i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.1706 | − | 20.9559i | 1.57540 | − | 1.02621i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.90806 | + | 11.9651i | −0.337481 | + | 0.584534i | −0.983958 | − | 0.178399i | \(-0.942908\pi\) |
0.646477 | + | 0.762933i | \(0.276241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.04704 | − | 7.00968i | −0.197241 | − | 0.341631i | 0.750392 | − | 0.660993i | \(-0.229865\pi\) |
−0.947633 | + | 0.319362i | \(0.896531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.1546 | − | 13.3247i | −1.46617 | − | 0.647870i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.35607 | + | 0.0533156i | 0.114286 | + | 0.00258619i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.33275 | + | 0.769465i | 0.0644964 | + | 0.0372370i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.46255 | − | 12.7275i | 0.312015 | − | 0.614488i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5943 | 0.654814 | 0.327407 | − | 0.944883i | \(-0.393825\pi\) | ||||
0.327407 | + | 0.944883i | \(0.393825\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 37.9830i | − | 1.82535i | −0.408688 | − | 0.912674i | \(-0.634014\pi\) | ||
0.408688 | − | 0.912674i | \(-0.365986\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.11770 | + | 1.02662i | 0.0535894 | + | 0.0492227i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.8143 | − | 8.55305i | −0.708665 | − | 0.409148i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.29167 | − | 16.0936i | −0.443467 | − | 0.768108i | 0.554477 | − | 0.832199i | \(-0.312918\pi\) |
−0.997944 | + | 0.0640914i | \(0.979585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.4042 | + | 2.09438i | −0.924010 | + | 0.0997326i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5829 | − | 7.84211i | 0.645345 | − | 0.372590i | −0.141326 | − | 0.989963i | \(-0.545136\pi\) |
0.786670 | + | 0.617373i | \(0.211803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.57991 | + | 6.43270i | −0.311918 | + | 0.304939i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.1776 | + | 13.1437i | −0.954368 | + | 0.621674i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.59068 | 0.405419 | 0.202710 | − | 0.979239i | \(-0.435025\pi\) | ||||
0.202710 | + | 0.979239i | \(0.435025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.3670 | −1.75954 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.09429 | + | 38.9194i | 0.0983985 | + | 1.82859i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.56969 | − | 2.51220i | 0.120469 | − | 0.117774i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.89306 | + | 2.82501i | −0.228888 | + | 0.132148i | −0.610059 | − | 0.792356i | \(-0.708854\pi\) |
0.381171 | + | 0.924505i | \(0.375521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.41734 | + | 0.393278i | −0.112832 | + | 0.0183567i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6423 | − | 18.4329i | −0.495659 | − | 0.858507i | 0.504328 | − | 0.863512i | \(-0.331740\pi\) |
−0.999987 | + | 0.00500482i | \(0.998407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.9615 | + | 21.3397i | 1.71775 | + | 0.991741i | 0.923003 | + | 0.384794i | \(0.125727\pi\) |
0.794743 | + | 0.606947i | \(0.207606\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.23655 | + | 23.4886i | −0.242839 | + | 1.08926i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.709510i | 0.0328322i | 0.999865 | + | 0.0164161i | \(0.00522564\pi\) | ||||
−0.999865 | + | 0.0164161i | \(0.994774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.34683 | −0.339245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.5541 | + | 30.0186i | 0.901005 | + | 1.38318i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00667 | + | 0.581202i | 0.0462868 | + | 0.0267237i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.623378 | + | 27.5477i | −0.0286026 | + | 1.26397i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.1054 | − | 21.2710i | 1.33265 | − | 0.973934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5274 | − | 23.4301i | −0.618083 | − | 1.07055i | −0.989835 | − | 0.142219i | \(-0.954576\pi\) |
0.371753 | − | 0.928332i | \(-0.378757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.5701 | + | 20.0400i | −0.527550 | + | 0.913743i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.37054 | + | 1.71144i | 0.153365 | + | 0.0778731i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.99724 | + | 28.5502i | −0.363136 | + | 1.29640i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.04139i | − | 0.273761i | −0.990588 | − | 0.136881i | \(-0.956292\pi\) | ||
0.990588 | − | 0.136881i | \(-0.0437077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.4136 | − | 20.5088i | 0.470920 | − | 0.927438i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0042 | − | 24.2559i | 0.631999 | − | 1.09465i | −0.355144 | − | 0.934812i | \(-0.615568\pi\) |
0.987143 | − | 0.159842i | \(-0.0510986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.159948 | + | 0.0923460i | −0.00720370 | + | 0.00415906i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.47503 | − | 22.6528i | −0.380924 | − | 1.01817i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.90898 | − | 1.10215i | 0.0856293 | − | 0.0494381i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.67425 | + | 8.09604i | −0.209248 | + | 0.362429i | −0.951478 | − | 0.307717i | \(-0.900435\pi\) |
0.742230 | + | 0.670146i | \(0.233768\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.5041 | + | 31.4770i | 0.916054 | + | 1.40629i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9461i | 0.755588i | 0.925890 | + | 0.377794i | \(0.123317\pi\) | ||||
−0.925890 | + | 0.377794i | \(0.876683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.8368 | − | 6.11674i | −0.971726 | − | 0.272191i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.723642 | − | 13.4478i | −0.0321381 | − | 0.597239i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7973 | − | 27.3617i | 0.700203 | − | 1.21279i | −0.268192 | − | 0.963365i | \(-0.586426\pi\) |
0.968395 | − | 0.249422i | \(-0.0802405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.19242 | − | 2.06534i | −0.0527497 | − | 0.0913652i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.59830 | − | 28.2641i | −0.203020 | − | 1.24789i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.04612 | − | 2.05868i | 0.354554 | − | 0.0907165i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.3128 | + | 19.8105i | 1.50908 | + | 0.871266i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5838 | − | 0.730956i | 0.596261 | − | 0.0320854i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.2592 | 0.756138 | 0.378069 | − | 0.925777i | \(-0.376588\pi\) | ||||
0.378069 | + | 0.925777i | \(0.376588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.1076i | 1.40397i | 0.712194 | + | 0.701983i | \(0.247702\pi\) | ||||
−0.712194 | + | 0.701983i | \(0.752298\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.189548 | − | 6.08617i | −0.00827254 | − | 0.265622i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.53632 | − | 1.46435i | −0.110484 | − | 0.0637879i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.68253 | − | 11.5745i | −0.290545 | − | 0.503238i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.7006 | − | 2.01844i | 0.811536 | − | 0.0875928i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.5156 | − | 11.8447i | 0.888630 | − | 0.513051i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.59146 | + | 4.69654i | 0.198506 | + | 0.203049i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.65207 | + | 2.36215i | 0.200752 | + | 0.101934i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.4559 | 1.01032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7891 | −0.807806 | −0.403903 | − | 0.914802i | \(-0.632347\pi\) | ||||
−0.403903 | + | 0.914802i | \(0.632347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.1785 | + | 18.3702i | 1.55257 | + | 0.788339i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.53742 | + | 3.45828i | −0.151527 | + | 0.148136i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.5936 | − | 19.3953i | 1.43636 | − | 0.829283i | 0.438766 | − | 0.898601i | \(-0.355416\pi\) |
0.997595 | + | 0.0693181i | \(0.0220823\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.65393 | + | 6.00600i | −0.113267 | + | 0.256330i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.07973 | − | 1.87015i | −0.0459981 | − | 0.0796711i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.02863 | − | 1.17123i | −0.0862662 | − | 0.0498058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.7459 | + | 37.4080i | 0.498586 | + | 1.58788i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.50060i | 0.317811i | 0.987294 | + | 0.158905i | \(0.0507964\pi\) | ||||
−0.987294 | + | 0.158905i | \(0.949204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.736925 | −0.0311686 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.93916 | − | 0.158159i | 0.124092 | − | 0.00667750i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.47802 | − | 3.16273i | −0.230871 | − | 0.133293i | 0.380103 | − | 0.924944i | \(-0.375889\pi\) |
−0.610974 | + | 0.791651i | \(0.709222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.6445 | − | 7.32898i | 1.20508 | − | 0.308333i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.35029 | + | 6.18225i | 0.0567068 | + | 0.259630i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.3447 | − | 31.7739i | −0.769049 | − | 1.33203i | −0.938079 | − | 0.346420i | \(-0.887397\pi\) |
0.169031 | − | 0.985611i | \(-0.445936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.98496 | − | 13.8304i | 0.334160 | − | 0.578782i | −0.649163 | − | 0.760649i | \(-0.724881\pi\) |
0.983323 | + | 0.181867i | \(0.0582140\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.871615 | + | 16.1977i | 0.0364122 | + | 0.676669i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.06214 | − | 13.2618i | 0.336215 | − | 0.553056i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.8972i | 0.745071i | 0.928018 | + | 0.372535i | \(0.121511\pi\) | ||||
−0.928018 | + | 0.372535i | \(0.878489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.98726 | + | 15.3320i | 0.415056 | + | 0.637177i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.96604 | + | 8.60144i | −0.206026 | + | 0.356848i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.5210 | + | 21.6627i | −1.55396 | + | 0.897179i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.8336 | + | 9.75065i | 0.489260 | + | 0.403140i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.9853 | − | 10.3838i | 0.742334 | − | 0.428587i | −0.0805831 | − | 0.996748i | \(-0.525678\pi\) |
0.822917 | + | 0.568161i | \(0.192345\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1215 | − | 29.6553i | 0.705478 | − | 1.22192i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.0169 | − | 27.6052i | 0.576579 | − | 1.13552i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.5422i | 1.54167i | 0.637032 | + | 0.770837i | \(0.280162\pi\) | ||||
−0.637032 | + | 0.770837i | \(0.719838\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.713567 | + | 0.199878i | 0.0292534 | + | 0.00819421i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.96327 | − | 1.50464i | −0.121279 | − | 0.0615810i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6773 | − | 21.9577i | 0.517981 | − | 0.897169i | −0.481801 | − | 0.876281i | \(-0.660017\pi\) |
0.999782 | − | 0.0208884i | \(-0.00664946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.87584 | − | 15.3734i | −0.362053 | − | 0.627095i | 0.626245 | − | 0.779626i | \(-0.284591\pi\) |
−0.988299 | + | 0.152531i | \(0.951257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.36390 | − | 31.1661i | −0.136989 | − | 1.26918i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.10823 | + | 4.33138i | 0.0450560 | + | 0.176096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.3197 | − | 12.3090i | −0.865342 | − | 0.499605i | 0.000455621 | − | 1.00000i | \(-0.499855\pi\) |
−0.865798 | + | 0.500395i | \(0.833188\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.260464 | + | 0.399853i | 0.0105545 | + | 0.0162029i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.1184 | −1.01618 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27.6596i | − | 1.11716i | −0.829450 | − | 0.558580i | \(-0.811346\pi\) | ||
0.829450 | − | 0.558580i | \(-0.188654\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.73425 | − | 39.1776i | 0.352199 | − | 1.57979i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8187 | − | 8.55558i | −0.596578 | − | 0.344435i | 0.171116 | − | 0.985251i | \(-0.445263\pi\) |
−0.767694 | + | 0.640816i | \(0.778596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2301 | + | 29.8435i | 0.692538 | + | 1.19951i | 0.971004 | + | 0.239064i | \(0.0768407\pi\) |
−0.278466 | + | 0.960446i | \(0.589826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.71684 | + | 15.0818i | −0.229409 | + | 0.605213i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.50580 | + | 1.44673i | −0.100393 | + | 0.0579618i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9744 | − | 1.13087i | −0.998976 | − | 0.0452350i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.84924 | + | 34.3654i | 0.0738514 | + | 1.37242i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.77162 | −0.190257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.7172 | 0.705311 | 0.352655 | − | 0.935753i | \(-0.385279\pi\) | ||||
0.352655 | + | 0.935753i | \(0.385279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.0290 | − | 9.78990i | 0.597351 | − | 0.389114i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0184 | − | 12.2934i | −0.476934 | − | 0.487849i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.8780 | + | 7.43513i | −0.510246 | + | 0.294591i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.54950 | + | 7.59346i | 0.219535 | + | 0.300393i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.42149 | + | 14.5864i | 0.332629 | + | 0.576130i | 0.983026 | − | 0.183464i | \(-0.0587310\pi\) |
−0.650398 | + | 0.759594i | \(0.725398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.5655 | + | 17.6470i | 1.20538 | + | 0.695929i | 0.961748 | − | 0.273937i | \(-0.0883261\pi\) |
0.243637 | + | 0.969867i | \(0.421659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.844667 | + | 0.919599i | −0.0332587 | + | 0.0362092i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 0.447554i | − | 0.0175952i | −0.999961 | − | 0.00879758i | \(-0.997200\pi\) | ||
0.999961 | − | 0.00879758i | \(-0.00280039\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.6054 | −0.887338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.42595 | + | 6.74714i | −0.134274 | + | 0.264441i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.5161 | − | 10.6903i | −0.724592 | − | 0.418343i | 0.0918485 | − | 0.995773i | \(-0.470722\pi\) |
−0.816440 | + | 0.577430i | \(0.804056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.20802 | − | 35.9884i | −0.359787 | − | 1.40618i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.21542 | − | 6.00405i | 0.320514 | − | 0.234240i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.20807 | − | 5.55655i | −0.124969 | − | 0.216452i | 0.796752 | − | 0.604306i | \(-0.206550\pi\) |
−0.921721 | + | 0.387854i | \(0.873216\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8800 | + | 29.2370i | −0.656555 | + | 1.13719i | 0.324946 | + | 0.945732i | \(0.394654\pi\) |
−0.981502 | + | 0.191454i | \(0.938680\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.56356 | + | 1.01850i | −0.0607236 | + | 0.0395553i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.33702 | + | 8.34320i | −0.0906259 | + | 0.323535i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.21631i | 0.0470957i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.63487 | + | 0.518462i | −0.372506 | + | 0.0200449i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.94573 | − | 6.83421i | 0.152323 | − | 0.263832i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.28190 | − | 4.78156i | 0.319244 | − | 0.184315i | −0.331812 | − | 0.943346i | \(-0.607660\pi\) |
0.651055 | + | 0.759030i | \(0.274327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.7314 | − | 3.59076i | 0.990403 | − | 0.138208i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.0593 | + | 11.0039i | −0.732508 | + | 0.422914i | −0.819339 | − | 0.573309i | \(-0.805659\pi\) |
0.0868307 | + | 0.996223i | \(0.472326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.66145 | + | 8.07387i | −0.178890 | + | 0.309847i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.4966 | − | 1.42581i | 1.01535 | − | 0.0546371i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 13.1585i | − | 0.503497i | −0.967793 | − | 0.251749i | \(-0.918994\pi\) | ||
0.967793 | − | 0.251749i | \(-0.0810057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.26365 | + | 25.9313i | −0.277530 | + | 0.990784i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.05438 | + | 5.24661i | −0.307294 | + | 0.200171i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7335 | − | 23.7870i | 0.523203 | − | 0.906214i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.03103 | + | 1.78579i | 0.0392221 | + | 0.0679346i | 0.884970 | − | 0.465648i | \(-0.154179\pi\) |
−0.845748 | + | 0.533583i | \(0.820845\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.816118 | − | 7.56123i | −0.0310018 | − | 0.287227i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.2863 | − | 48.0195i | −0.466045 | − | 1.82148i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.23043 | + | 2.44244i | 0.160239 | + | 0.0925140i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.2664 | + | 28.0965i | −0.539606 | + | 1.06271i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.9923 | −0.868406 | −0.434203 | − | 0.900815i | \(-0.642970\pi\) | ||||
−0.434203 | + | 0.900815i | \(0.642970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 55.7909i | − | 2.10419i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.7908 | + | 31.3449i | −1.08433 | + | 1.18052i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.17535 | − | 3.56534i | −0.232248 | − | 0.134088i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.82791 | + | 6.63014i | 0.143760 | + | 0.249000i | 0.928910 | − | 0.370306i | \(-0.120747\pi\) |
−0.785149 | + | 0.619306i | \(0.787414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.03964 | − | 9.14196i | 0.151498 | − | 0.342850i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.7032 | + | 9.64361i | −0.625541 | + | 0.361156i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.8823 | − | 13.1771i | −0.481770 | − | 0.492795i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.7270 | + | 10.8960i | −0.624682 | + | 0.406917i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.52489 | 0.0941625 | 0.0470812 | − | 0.998891i | \(-0.485008\pi\) | ||||
0.0470812 | + | 0.998891i | \(0.485008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.61153 | 0.0972584 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.61672 | + | 30.0444i | 0.0601266 | + | 1.11737i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.71849 | − | 0.940988i | 0.0638230 | − | 0.0349474i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1826 | + | 16.8486i | −1.08232 | + | 0.624880i | −0.931522 | − | 0.363684i | \(-0.881519\pi\) |
−0.150802 | + | 0.988564i | \(0.548186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.6076 | + | 8.55875i | −0.948429 | + | 0.316991i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0759789 | − | 0.131599i | −0.00281018 | − | 0.00486738i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.243044 | + | 0.140321i | 0.00897702 | + | 0.00518289i | 0.504482 | − | 0.863422i | \(-0.331684\pi\) |
−0.495505 | + | 0.868605i | \(0.665017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.48265 | + | 24.5925i | −0.202230 | + | 0.907107i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.6738i | 1.38773i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.119448 | −0.00439396 | −0.00219698 | − | 0.999998i | \(-0.500699\pi\) | ||||
−0.00219698 | + | 0.999998i | \(0.500699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.9085 | − | 18.2815i | −0.437471 | − | 0.671588i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.45547 | + | 2.57237i | 0.163455 | + | 0.0943711i | 0.579496 | − | 0.814975i | \(-0.303249\pi\) |
−0.416041 | + | 0.909346i | \(0.636583\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.70605 | + | 30.1182i | 0.282328 | + | 1.10344i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38.7621 | − | 17.1282i | −1.41823 | − | 0.626687i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.03263 | + | 1.78856i | 0.0377314 | + | 0.0653527i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.19703 | + | 5.53743i | −0.116661 | + | 0.202064i | −0.918443 | − | 0.395554i | \(-0.870553\pi\) |
0.801781 | + | 0.597618i | \(0.203886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.6558 | − | 15.5659i | −1.11716 | − | 0.567254i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.4525 | + | 13.5721i | 1.76337 | + | 0.493939i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9405i | 0.433985i | 0.976173 | + | 0.216992i | \(0.0696247\pi\) | ||||
−0.976173 | + | 0.216992i | \(0.930375\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.77606 | − | 17.2837i | 0.318551 | − | 0.627360i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.7055 | + | 41.0591i | −0.859323 | + | 1.48839i | 0.0132529 | + | 0.999912i | \(0.495781\pi\) |
−0.872576 | + | 0.488479i | \(0.837552\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.34714 | + | 0.777773i | −0.0487698 | + | 0.0281573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.521185 | + | 3.11855i | −0.0188435 | + | 0.112751i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4110 | − | 7.16552i | 0.448137 | − | 0.258732i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.763036 | − | 1.32162i | 0.0275158 | − | 0.0476587i | −0.851940 | − | 0.523640i | \(-0.824574\pi\) |
0.879455 | + | 0.475981i | \(0.157907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.30970 | − | 9.68638i | −0.227238 | − | 0.348847i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 33.3154i | − | 1.19827i | −0.800648 | − | 0.599136i | \(-0.795511\pi\) | ||
0.800648 | − | 0.599136i | \(-0.204489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.5475 | + | 16.1388i | 0.953613 | + | 0.579722i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.662468 | + | 12.3110i | 0.0237659 | + | 0.441655i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.5576 | + | 49.4632i | −1.02318 | + | 1.77220i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.65170 | − | 9.78902i | −0.202234 | − | 0.350279i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.57696 | + | 1.28800i | −0.0563561 | + | 0.0460293i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.8073 | − | 11.4644i | 1.59924 | − | 0.409183i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.3702 | − | 10.6060i | −0.654826 | − | 0.378064i | 0.135477 | − | 0.990781i | \(-0.456743\pi\) |
−0.790303 | + | 0.612717i | \(0.790077\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.22826 | − | 0.227527i | 0.150530 | − | 0.00810017i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.29713 | 0.330568 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.00292i | 0.177659i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.9422 | − | 44.4026i | −0.494478 | − | 1.57480i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.7281 | − | 24.0917i | −1.47809 | − | 0.853373i | −0.478393 | − | 0.878146i | \(-0.658780\pi\) |
−0.999693 | + | 0.0247730i | \(0.992114\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.58978 | − | 4.48562i | −0.0916197 | − | 0.158690i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.28451 | − | 9.96748i | −0.257385 | − | 0.352184i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.5908 | + | 6.11462i | −0.373742 | + | 0.215780i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.48961 | − | 3.41153i | 0.122992 | − | 0.120241i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.5480 | − | 7.89470i | −0.547314 | − | 0.277907i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.97117 | 0.174777 | 0.0873886 | − | 0.996174i | \(-0.472148\pi\) | ||||
0.0873886 | + | 0.996174i | \(0.472148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.5332 | −1.07216 | −0.536082 | − | 0.844166i | \(-0.680096\pi\) | ||||
−0.536082 | + | 0.844166i | \(0.680096\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.3239 | + | 16.9207i | 1.16872 | + | 0.593434i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.7582 | − | 21.2333i | −0.727128 | − | 0.743768i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.53869 | − | 0.888364i | 0.0538320 | − | 0.0310799i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.84486 | + | 3.89265i | 0.0994074 | + | 0.136020i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.542675 | + | 0.939941i | 0.0189395 | + | 0.0328042i | 0.875340 | − | 0.483508i | \(-0.160638\pi\) |
−0.856400 | + | 0.516312i | \(0.827304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.4886 | − | 10.6744i | −0.644471 | − | 0.372085i | 0.141864 | − | 0.989886i | \(-0.454690\pi\) |
−0.786335 | + | 0.617801i | \(0.788024\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.2092 | + | 0.971980i | −1.08656 | + | 0.0338400i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.1458i | 1.22214i | 0.791577 | + | 0.611070i | \(0.209260\pi\) | ||||
−0.791577 | + | 0.611070i | \(0.790740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.53738 | 0.0881269 | 0.0440635 | − | 0.999029i | \(-0.485970\pi\) | ||||
0.0440635 | + | 0.999029i | \(0.485970\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.3143 | − | 2.70746i | 1.74538 | − | 0.0939208i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.65552 | − | 1.53316i | −0.0920082 | − | 0.0531210i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.9842 | − | 12.0214i | 1.62595 | − | 0.416017i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.1908 | − | 11.4440i | −1.04355 | − | 0.395561i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.1583 | + | 34.9153i | 0.695943 | + | 1.20541i | 0.969862 | + | 0.243656i | \(0.0783469\pi\) |
−0.273918 | + | 0.961753i | \(0.588320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4232 | − | 24.9818i | 0.497353 | − | 0.861440i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.64731 | − | 30.6130i | −0.0567365 | − | 1.05437i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.7418 | − | 4.68957i | −0.575935 | − | 0.161326i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.40584i | 0.0483051i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.02255 | + | 1.56977i | 0.0350938 | + | 0.0538745i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.7120 | + | 27.2140i | −0.538601 | + | 0.932884i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.5861 | + | 28.6285i | −1.69780 | + | 0.980223i | −0.749949 | + | 0.661495i | \(0.769922\pi\) |
−0.947846 | + | 0.318728i | \(0.896744\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.4628 | − | 6.09382i | −1.24700 | − | 0.208404i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4224 | − | 7.17208i | 0.424341 | − | 0.244994i | −0.272592 | − | 0.962130i | \(-0.587881\pi\) |
0.696933 | + | 0.717136i | \(0.254547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.8559 | + | 25.7312i | −0.506877 | + | 0.877937i | 0.493091 | + | 0.869978i | \(0.335867\pi\) |
−0.999968 | + | 0.00795944i | \(0.997466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.71428 | − | 11.2538i | 0.194742 | − | 0.383529i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.60851i | 0.0547544i | 0.999625 | + | 0.0273772i | \(0.00871552\pi\) | ||||
−0.999625 | + | 0.0273772i | \(0.991284\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.73697 | − | 16.9110i | 0.161062 | − | 0.574992i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.9112 | + | 13.1568i | 0.879989 | + | 0.446827i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00594 | + | 10.4026i | −0.203738 | + | 0.352884i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9419 | − | 20.6841i | −0.404637 | − | 0.700853i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.3846 | − | 16.0776i | −1.23143 | − | 0.544145i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.51975 | − | 2.29106i | −0.254214 | − | 0.0774518i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.5499 | − | 15.3286i | −0.896525 | − | 0.517609i | −0.0204539 | − | 0.999791i | \(-0.506511\pi\) |
−0.876071 | + | 0.482182i | \(0.839844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.23867 | − | 4.97187i | −0.109238 | − | 0.167697i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.69932 | 0.326778 | 0.163389 | − | 0.986562i | \(-0.447757\pi\) | ||||
0.163389 | + | 0.986562i | \(0.447757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.2156i | − | 0.512047i | −0.966671 | − | 0.256023i | \(-0.917588\pi\) | ||
0.966671 | − | 0.256023i | \(-0.0824124\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.28384 | − | 23.7007i | 0.177614 | − | 0.796691i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9037 | − | 7.44993i | −0.433262 | − | 0.250144i | 0.267473 | − | 0.963565i | \(-0.413811\pi\) |
−0.700735 | + | 0.713421i | \(0.747145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.70295 | − | 4.68165i | −0.0906541 | − | 0.157018i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.7019 | − | 6.92413i | 1.06205 | − | 0.231967i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.4470 | − | 30.2803i | 1.75507 | − | 1.01329i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.81641 | − | 4.70865i | 0.160995 | − | 0.157393i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.660325 | + | 12.2712i | 0.0220476 | + | 0.409723i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.43481 | −0.0812054 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.66382 | 0.188689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.328984 | + | 0.214300i | −0.0109479 | + | 0.00713146i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.4566 | − | 36.6186i | 1.24510 | − | 1.21724i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.9280 | + | 18.4336i | −1.06015 | + | 0.612078i | −0.925474 | − | 0.378812i | \(-0.876333\pi\) |
−0.134676 | + | 0.990890i | \(0.543000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.2971 | − | 27.8290i | 0.407868 | − | 0.923029i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6246 | + | 46.1151i | 0.882111 | + | 1.52786i | 0.848989 | + | 0.528411i | \(0.177212\pi\) |
0.0331224 | + | 0.999451i | \(0.489455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.1072 | + | 25.4653i | 1.45974 | + | 0.842779i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.24308 | + | 5.73437i | 0.206390 | + | 0.189572i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 11.6808i | − | 0.385733i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.4511 | 1.13644 | 0.568218 | − | 0.822878i | \(-0.307633\pi\) | ||||
0.568218 | + | 0.822878i | \(0.307633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.30174 | − | 10.4413i | 0.174698 | − | 0.344054i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.20591 | + | 3.58299i | 0.204270 | + | 0.117935i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.6053 | + | 1.14515i | 1.66389 | + | 0.0376523i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.19574 | + | 11.0784i | 0.0392733 | + | 0.363863i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.25536 | + | 10.8346i | 0.205232 | + | 0.355472i | 0.950207 | − | 0.311621i | \(-0.100872\pi\) |
−0.744975 | + | 0.667093i | \(0.767539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.9261 | − | 31.0489i | 0.587504 | − | 1.01759i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.1895 | − | 8.59162i | 0.431805 | − | 0.281277i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.02495 | − | 3.65909i | 0.0335196 | − | 0.119665i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9334i | 0.781870i | 0.920418 | + | 0.390935i | \(0.127848\pi\) | ||||
−0.920418 | + | 0.390935i | \(0.872152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44.0623 | + | 2.37104i | −1.43792 | + | 0.0773758i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.4502 | + | 37.1528i | −0.699256 | + | 1.21115i | 0.269469 | + | 0.963009i | \(0.413152\pi\) |
−0.968725 | + | 0.248138i | \(0.920181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.8600 | − | 16.0850i | 0.907245 | − | 0.523798i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.11838 | + | 0.911719i | 0.264091 | + | 0.0296582i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.0803 | + | 19.6763i | −1.10746 | + | 0.639393i | −0.938171 | − | 0.346173i | \(-0.887481\pi\) |
−0.169291 | + | 0.985566i | \(0.554148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.87646 | − | 6.71423i | 0.125835 | − | 0.217953i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.1531 | + | 1.19208i | −0.718364 | + | 0.0386559i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.66984i | 0.313237i | 0.987659 | + | 0.156618i | \(0.0500593\pi\) | ||||
−0.987659 | + | 0.156618i | \(0.949941\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.1652 | + | 5.64851i | 0.652531 | + | 0.182781i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.05040 | − | 1.33563i | 0.0662801 | − | 0.0431748i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.23385 | + | 7.33325i | −0.136718 | + | 0.236803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.80457 | − | 6.58971i | −0.122728 | − | 0.212571i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.11448 | + | 5.19946i | −0.229261 | + | 0.167550i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8854 | − | 5.85546i | 0.736706 | − | 0.188494i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.6478 | + | 9.03427i | 0.503200 | + | 0.290522i | 0.730034 | − | 0.683411i | \(-0.239504\pi\) |
−0.226834 | + | 0.973933i | \(0.572838\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.03689 | − | 4.01149i | 0.0654343 | − | 0.128868i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.9590 | −0.447966 | −0.223983 | − | 0.974593i | \(-0.571906\pi\) | ||||
−0.223983 | + | 0.974593i | \(0.571906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.5857i | − | 0.499654i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.8267 | − | 10.4264i | 0.538886 | − | 0.333913i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.2970 | + | 12.8732i | 0.713344 | + | 0.411849i | 0.812298 | − | 0.583243i | \(-0.198216\pi\) |
−0.0989538 | + | 0.995092i | \(0.531550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.41865 | + | 12.8495i | 0.237101 | + | 0.410671i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.91622 | − | 5.35861i | −0.125035 | − | 0.171087i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.7056 | + | 6.18090i | −0.341457 | + | 0.197140i | −0.660916 | − | 0.750460i | \(-0.729832\pi\) |
0.319459 | + | 0.947600i | \(0.396499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.9409 | − | 28.5803i | −0.890272 | − | 0.910645i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.2136 | + | 7.30451i | −0.356932 | + | 0.232505i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.00074 | −0.0318215 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5181 | 0.620014 | 0.310007 | − | 0.950734i | \(-0.399669\pi\) | ||||
0.310007 | + | 0.950734i | \(0.399669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.60720 | + | 29.8675i | 0.0510029 | + | 0.947816i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.06796 | + | 2.99932i | −0.0972607 | + | 0.0950847i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.39885 | + | 1.38497i | −0.0759722 | + | 0.0438626i | −0.537505 | − | 0.843261i | \(-0.680633\pi\) |
0.461533 | + | 0.887123i | \(0.347300\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.9214 | + | 8.44712i | −1.64272 | + | 0.267255i |
(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.49.14 | yes | 32 | |
3.2 | odd | 2 | 1080.2.bi.b.1009.3 | 32 | |||
4.3 | odd | 2 | 720.2.by.f.49.3 | 32 | |||
5.4 | even | 2 | inner | 360.2.bi.b.49.3 | ✓ | 32 | |
9.2 | odd | 6 | 1080.2.bi.b.289.8 | 32 | |||
9.4 | even | 3 | 3240.2.f.k.649.3 | 16 | |||
9.5 | odd | 6 | 3240.2.f.i.649.14 | 16 | |||
9.7 | even | 3 | inner | 360.2.bi.b.169.3 | yes | 32 | |
12.11 | even | 2 | 2160.2.by.f.1009.3 | 32 | |||
15.14 | odd | 2 | 1080.2.bi.b.1009.8 | 32 | |||
20.19 | odd | 2 | 720.2.by.f.49.14 | 32 | |||
36.7 | odd | 6 | 720.2.by.f.529.14 | 32 | |||
36.11 | even | 6 | 2160.2.by.f.289.8 | 32 | |||
45.4 | even | 6 | 3240.2.f.k.649.4 | 16 | |||
45.14 | odd | 6 | 3240.2.f.i.649.13 | 16 | |||
45.29 | odd | 6 | 1080.2.bi.b.289.3 | 32 | |||
45.34 | even | 6 | inner | 360.2.bi.b.169.14 | yes | 32 | |
60.59 | even | 2 | 2160.2.by.f.1009.8 | 32 | |||
180.79 | odd | 6 | 720.2.by.f.529.3 | 32 | |||
180.119 | even | 6 | 2160.2.by.f.289.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bi.b.49.3 | ✓ | 32 | 5.4 | even | 2 | inner | |
360.2.bi.b.49.14 | yes | 32 | 1.1 | even | 1 | trivial | |
360.2.bi.b.169.3 | yes | 32 | 9.7 | even | 3 | inner | |
360.2.bi.b.169.14 | yes | 32 | 45.34 | even | 6 | inner | |
720.2.by.f.49.3 | 32 | 4.3 | odd | 2 | |||
720.2.by.f.49.14 | 32 | 20.19 | odd | 2 | |||
720.2.by.f.529.3 | 32 | 180.79 | odd | 6 | |||
720.2.by.f.529.14 | 32 | 36.7 | odd | 6 | |||
1080.2.bi.b.289.3 | 32 | 45.29 | odd | 6 | |||
1080.2.bi.b.289.8 | 32 | 9.2 | odd | 6 | |||
1080.2.bi.b.1009.3 | 32 | 3.2 | odd | 2 | |||
1080.2.bi.b.1009.8 | 32 | 15.14 | odd | 2 | |||
2160.2.by.f.289.3 | 32 | 180.119 | even | 6 | |||
2160.2.by.f.289.8 | 32 | 36.11 | even | 6 | |||
2160.2.by.f.1009.3 | 32 | 12.11 | even | 2 | |||
2160.2.by.f.1009.8 | 32 | 60.59 | even | 2 | |||
3240.2.f.i.649.13 | 16 | 45.14 | odd | 6 | |||
3240.2.f.i.649.14 | 16 | 9.5 | odd | 6 | |||
3240.2.f.k.649.3 | 16 | 9.4 | even | 3 | |||
3240.2.f.k.649.4 | 16 | 45.4 | even | 6 |