Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(32,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.p (of order \(12\), degree \(4\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 218.1 | ||
Root | \(-1.29724 - 0.347596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.218 |
Dual form | 225.2.p.b.32.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29724 | + | 0.347596i | −0.917290 | + | 0.245787i | −0.686427 | − | 0.727199i | \(-0.740822\pi\) |
−0.230863 | + | 0.972986i | \(0.574155\pi\) | |||||||
\(3\) | 1.25897 | + | 1.18953i | 0.726869 | + | 0.686776i | ||||
\(4\) | −0.170031 | + | 0.0981673i | −0.0850154 | + | 0.0490837i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.04667 | − | 1.10550i | −0.835551 | − | 0.451318i | ||||
\(7\) | 0.530190 | + | 1.97869i | 0.200393 | + | 0.747876i | 0.990805 | + | 0.135300i | \(0.0432000\pi\) |
−0.790412 | + | 0.612576i | \(0.790133\pi\) | |||||||
\(8\) | 2.08575 | − | 2.08575i | 0.737423 | − | 0.737423i | ||||
\(9\) | 0.170031 | + | 2.99518i | 0.0566769 | + | 0.998393i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.762281 | − | 0.440103i | −0.229836 | − | 0.132696i | 0.380660 | − | 0.924715i | \(-0.375697\pi\) |
−0.610497 | + | 0.792019i | \(0.709030\pi\) | |||||||
\(12\) | −0.330837 | − | 0.0786668i | −0.0955045 | − | 0.0227092i | ||||
\(13\) | −1.43820 | + | 5.36743i | −0.398885 | + | 1.48866i | 0.416177 | + | 0.909283i | \(0.363370\pi\) |
−0.815062 | + | 0.579374i | \(0.803297\pi\) | |||||||
\(14\) | −1.37557 | − | 2.38256i | −0.367637 | − | 0.636766i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.78439 | + | 3.09066i | −0.446098 | + | 0.772664i | ||||
\(17\) | −1.13610 | − | 1.13610i | −0.275544 | − | 0.275544i | 0.555783 | − | 0.831327i | \(-0.312418\pi\) |
−0.831327 | + | 0.555783i | \(0.812418\pi\) | |||||||
\(18\) | −1.26168 | − | 3.82638i | −0.297381 | − | 0.901885i | ||||
\(19\) | − | 1.52456i | − | 0.349758i | −0.984590 | − | 0.174879i | \(-0.944047\pi\) | ||
0.984590 | − | 0.174879i | \(-0.0559535\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.68622 | + | 3.12180i | −0.367964 | + | 0.681233i | ||||
\(22\) | 1.14184 | + | 0.305956i | 0.243442 | + | 0.0652300i | ||||
\(23\) | −1.53331 | − | 0.410850i | −0.319718 | − | 0.0856682i | 0.0953909 | − | 0.995440i | \(-0.469590\pi\) |
−0.415109 | + | 0.909772i | \(0.636257\pi\) | |||||||
\(24\) | 5.10696 | − | 0.144840i | 1.04245 | − | 0.0295653i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 7.46278i | − | 1.46357i | ||||||
\(27\) | −3.34879 | + | 3.97311i | −0.644476 | + | 0.764625i | ||||
\(28\) | −0.284392 | − | 0.284392i | −0.0537450 | − | 0.0537450i | ||||
\(29\) | −0.796583 | + | 1.37972i | −0.147922 | + | 0.256208i | −0.930459 | − | 0.366396i | \(-0.880592\pi\) |
0.782537 | + | 0.622603i | \(0.213925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.49518 | + | 6.05383i | 0.627752 | + | 1.08730i | 0.988002 | + | 0.154443i | \(0.0493583\pi\) |
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(32\) | −0.286379 | + | 1.06878i | −0.0506251 | + | 0.188936i | ||||
\(33\) | −0.436175 | − | 1.46084i | −0.0759284 | − | 0.254299i | ||||
\(34\) | 1.86870 | + | 1.07889i | 0.320479 | + | 0.185029i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.322939 | − | 0.492581i | −0.0538232 | − | 0.0820968i | ||||
\(37\) | 4.25746 | − | 4.25746i | 0.699922 | − | 0.699922i | −0.264472 | − | 0.964393i | \(-0.585198\pi\) |
0.964393 | + | 0.264472i | \(0.0851975\pi\) | |||||||
\(38\) | 0.529931 | + | 1.97773i | 0.0859661 | + | 0.320830i | ||||
\(39\) | −8.19538 | + | 5.04667i | −1.31231 | + | 0.808114i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.11546 | − | 1.79871i | 0.486552 | − | 0.280911i | −0.236591 | − | 0.971609i | \(-0.576030\pi\) |
0.723143 | + | 0.690698i | \(0.242697\pi\) | |||||||
\(42\) | 1.10232 | − | 4.63586i | 0.170092 | − | 0.715329i | ||||
\(43\) | 1.85841 | − | 0.497959i | 0.283404 | − | 0.0759380i | −0.114317 | − | 0.993444i | \(-0.536468\pi\) |
0.397721 | + | 0.917506i | \(0.369801\pi\) | |||||||
\(44\) | 0.172815 | 0.0260528 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.13189 | 0.314330 | ||||||||
\(47\) | 7.99942 | − | 2.14344i | 1.16683 | − | 0.312652i | 0.377142 | − | 0.926155i | \(-0.376907\pi\) |
0.789693 | + | 0.613503i | \(0.210240\pi\) | |||||||
\(48\) | −5.92294 | + | 1.76847i | −0.854902 | + | 0.255256i | ||||
\(49\) | 2.42805 | − | 1.40183i | 0.346864 | − | 0.200262i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0788937 | − | 2.78174i | −0.0110473 | − | 0.389522i | ||||
\(52\) | −0.282368 | − | 1.05381i | −0.0391574 | − | 0.146137i | ||||
\(53\) | 4.65601 | − | 4.65601i | 0.639552 | − | 0.639552i | −0.310893 | − | 0.950445i | \(-0.600628\pi\) |
0.950445 | + | 0.310893i | \(0.100628\pi\) | |||||||
\(54\) | 2.96317 | − | 6.31812i | 0.403236 | − | 0.859787i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.23290 | + | 3.02121i | 0.699275 | + | 0.403727i | ||||
\(57\) | 1.81351 | − | 1.91938i | 0.240206 | − | 0.254229i | ||||
\(58\) | 0.553777 | − | 2.06672i | 0.0727145 | − | 0.271374i | ||||
\(59\) | −3.81780 | − | 6.61262i | −0.497035 | − | 0.860890i | 0.502959 | − | 0.864310i | \(-0.332245\pi\) |
−0.999994 | + | 0.00342048i | \(0.998911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.64002 | − | 11.5008i | 0.850167 | − | 1.47253i | −0.0308900 | − | 0.999523i | \(-0.509834\pi\) |
0.881057 | − | 0.473010i | \(-0.156833\pi\) | |||||||
\(62\) | −6.63838 | − | 6.63838i | −0.843075 | − | 0.843075i | ||||
\(63\) | −5.83639 | + | 1.92445i | −0.735317 | + | 0.242458i | ||||
\(64\) | − | 8.62358i | − | 1.07795i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.07361 | + | 1.74345i | 0.132152 | + | 0.214604i | ||||
\(67\) | −3.20857 | − | 0.859733i | −0.391989 | − | 0.105033i | 0.0574406 | − | 0.998349i | \(-0.481706\pi\) |
−0.449429 | + | 0.893316i | \(0.648373\pi\) | |||||||
\(68\) | 0.304699 | + | 0.0816439i | 0.0369502 | + | 0.00990078i | ||||
\(69\) | −1.44168 | − | 2.34117i | −0.173558 | − | 0.281844i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.89798i | 0.699961i | 0.936757 | + | 0.349980i | \(0.113812\pi\) | ||||
−0.936757 | + | 0.349980i | \(0.886188\pi\) | |||||||
\(72\) | 6.60182 | + | 5.89254i | 0.778032 | + | 0.694442i | ||||
\(73\) | −1.58900 | − | 1.58900i | −0.185979 | − | 0.185979i | 0.607976 | − | 0.793955i | \(-0.291982\pi\) |
−0.793955 | + | 0.607976i | \(0.791982\pi\) | |||||||
\(74\) | −4.04309 | + | 7.00284i | −0.470000 | + | 0.814063i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.149662 | + | 0.259222i | 0.0171674 | + | 0.0297348i | ||||
\(77\) | 0.466676 | − | 1.74166i | 0.0531827 | − | 0.198480i | ||||
\(78\) | 8.87721 | − | 9.39544i | 1.00515 | − | 1.06382i | ||||
\(79\) | 6.69401 | + | 3.86479i | 0.753135 | + | 0.434823i | 0.826826 | − | 0.562458i | \(-0.190144\pi\) |
−0.0736905 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.94218 | + | 1.01854i | −0.993575 | + | 0.113172i | ||||
\(82\) | −3.41628 | + | 3.41628i | −0.377265 | + | 0.377265i | ||||
\(83\) | 2.57170 | + | 9.59770i | 0.282280 | + | 1.05348i | 0.950804 | + | 0.309794i | \(0.100260\pi\) |
−0.668523 | + | 0.743691i | \(0.733073\pi\) | |||||||
\(84\) | −0.0197489 | − | 0.696335i | −0.00215478 | − | 0.0759763i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.23772 | + | 1.29195i | −0.241299 | + | 0.139314i | ||||
\(87\) | −2.64410 | + | 0.789474i | −0.283477 | + | 0.0846405i | ||||
\(88\) | −2.50787 | + | 0.671981i | −0.267340 | + | 0.0716334i | ||||
\(89\) | 4.62765 | 0.490530 | 0.245265 | − | 0.969456i | \(-0.421125\pi\) | ||||
0.245265 | + | 0.969456i | \(0.421125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3830 | −1.19327 | ||||||||
\(92\) | 0.301043 | − | 0.0806641i | 0.0313859 | − | 0.00840982i | ||||
\(93\) | −2.80088 | + | 11.7792i | −0.290437 | + | 1.22145i | ||||
\(94\) | −9.63215 | + | 5.56112i | −0.993480 | + | 0.573586i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.63189 | + | 1.00491i | −0.166554 | + | 0.102563i | ||||
\(97\) | 1.02621 | + | 3.82988i | 0.104196 | + | 0.388865i | 0.998253 | − | 0.0590888i | \(-0.0188195\pi\) |
−0.894057 | + | 0.447954i | \(0.852153\pi\) | |||||||
\(98\) | −2.66250 | + | 2.66250i | −0.268953 | + | 0.268953i | ||||
\(99\) | 1.18858 | − | 2.35800i | 0.119456 | − | 0.236988i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.23195 | − | 1.28862i | −0.222087 | − | 0.128222i | 0.384829 | − | 0.922988i | \(-0.374260\pi\) |
−0.606916 | + | 0.794766i | \(0.707594\pi\) | |||||||
\(102\) | 1.06927 | + | 3.58117i | 0.105873 | + | 0.354589i | ||||
\(103\) | 3.38106 | − | 12.6183i | 0.333146 | − | 1.24332i | −0.572719 | − | 0.819752i | \(-0.694111\pi\) |
0.905865 | − | 0.423566i | \(-0.139222\pi\) | |||||||
\(104\) | 8.19538 | + | 14.1948i | 0.803623 | + | 1.39192i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.42157 | + | 7.65839i | −0.429461 | + | 0.743848i | ||||
\(107\) | 9.23034 | + | 9.23034i | 0.892331 | + | 0.892331i | 0.994742 | − | 0.102411i | \(-0.0326557\pi\) |
−0.102411 | + | 0.994742i | \(0.532656\pi\) | |||||||
\(108\) | 0.179369 | − | 1.00429i | 0.0172598 | − | 0.0966381i | ||||
\(109\) | 8.05480i | 0.771510i | 0.922601 | + | 0.385755i | \(0.126059\pi\) | ||||
−0.922601 | + | 0.385755i | \(0.873941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4244 | − | 0.295649i | 0.989441 | − | 0.0280618i | ||||
\(112\) | −7.06153 | − | 1.89213i | −0.667252 | − | 0.178790i | ||||
\(113\) | −11.5941 | − | 3.10662i | −1.09068 | − | 0.292246i | −0.331714 | − | 0.943380i | \(-0.607627\pi\) |
−0.758963 | + | 0.651134i | \(0.774294\pi\) | |||||||
\(114\) | −1.68540 | + | 3.12028i | −0.157852 | + | 0.292241i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 0.312794i | − | 0.0290422i | ||||||
\(117\) | −16.3209 | − | 3.39503i | −1.50887 | − | 0.313871i | ||||
\(118\) | 7.25113 | + | 7.25113i | 0.667521 | + | 0.667521i | ||||
\(119\) | 1.64564 | − | 2.85034i | 0.150856 | − | 0.261290i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.11262 | − | 8.85532i | −0.464784 | − | 0.805029i | ||||
\(122\) | −4.61608 | + | 17.2274i | −0.417920 | + | 1.55970i | ||||
\(123\) | 6.06190 | + | 1.44140i | 0.546583 | + | 0.129967i | ||||
\(124\) | −1.18858 | − | 0.686224i | −0.106737 | − | 0.0616248i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.90230 | − | 4.52519i | 0.614906 | − | 0.403136i | ||||
\(127\) | −1.90230 | + | 1.90230i | −0.168802 | + | 0.168802i | −0.786452 | − | 0.617651i | \(-0.788085\pi\) |
0.617651 | + | 0.786452i | \(0.288085\pi\) | |||||||
\(128\) | 2.42476 | + | 9.04933i | 0.214321 | + | 0.799855i | ||||
\(129\) | 2.93202 | + | 1.58372i | 0.258150 | + | 0.139438i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.5109 | + | 10.6873i | −1.61731 | + | 0.933754i | −0.629696 | + | 0.776841i | \(0.716821\pi\) |
−0.987613 | + | 0.156912i | \(0.949846\pi\) | |||||||
\(132\) | 0.217569 | + | 0.205569i | 0.0189370 | + | 0.0178925i | ||||
\(133\) | 3.01664 | − | 0.808307i | 0.261576 | − | 0.0700891i | ||||
\(134\) | 4.46113 | 0.385383 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.73922 | −0.406385 | ||||||||
\(137\) | −6.62594 | + | 1.77541i | −0.566092 | + | 0.151684i | −0.530504 | − | 0.847683i | \(-0.677997\pi\) |
−0.0355883 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(138\) | 2.68400 | + | 2.53595i | 0.228477 | + | 0.215875i | ||||
\(139\) | 1.24863 | − | 0.720896i | 0.105907 | − | 0.0611456i | −0.446111 | − | 0.894978i | \(-0.647191\pi\) |
0.552018 | + | 0.833832i | \(0.313858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6207 | + | 6.81703i | 1.06286 | + | 0.574097i | ||||
\(142\) | −2.05011 | − | 7.65111i | −0.172041 | − | 0.642067i | ||||
\(143\) | 3.45853 | − | 3.45853i | 0.289217 | − | 0.289217i | ||||
\(144\) | −9.56047 | − | 4.81906i | −0.796706 | − | 0.401589i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.61366 | + | 1.50900i | 0.216308 | + | 0.124885i | ||||
\(147\) | 4.72437 | + | 1.12337i | 0.389659 | + | 0.0926536i | ||||
\(148\) | −0.305956 | + | 1.14184i | −0.0251494 | + | 0.0938589i | ||||
\(149\) | −8.28457 | − | 14.3493i | −0.678699 | − | 1.17554i | −0.975373 | − | 0.220562i | \(-0.929211\pi\) |
0.296674 | − | 0.954979i | \(-0.404122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.00283730 | − | 0.00491435i | 0.000230896 | − | 0.000399924i | −0.865910 | − | 0.500200i | \(-0.833260\pi\) |
0.866141 | + | 0.499800i | \(0.166593\pi\) | |||||||
\(152\) | −3.17985 | − | 3.17985i | −0.257920 | − | 0.257920i | ||||
\(153\) | 3.20964 | − | 3.59599i | 0.259484 | − | 0.290718i | ||||
\(154\) | 2.42157i | 0.195136i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.898049 | − | 1.66261i | 0.0719014 | − | 0.133115i | ||||
\(157\) | 8.17112 | + | 2.18944i | 0.652126 | + | 0.174737i | 0.569690 | − | 0.821860i | \(-0.307063\pi\) |
0.0824362 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(158\) | −10.0272 | − | 2.68677i | −0.797717 | − | 0.213748i | ||||
\(159\) | 11.4003 | − | 0.323326i | 0.904099 | − | 0.0256414i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.25179i | − | 0.256277i | ||||||
\(162\) | 11.2461 | − | 4.42956i | 0.883581 | − | 0.348019i | ||||
\(163\) | −4.19302 | − | 4.19302i | −0.328422 | − | 0.328422i | 0.523564 | − | 0.851986i | \(-0.324602\pi\) |
−0.851986 | + | 0.523564i | \(0.824602\pi\) | |||||||
\(164\) | −0.353149 | + | 0.611672i | −0.0275763 | + | 0.0477635i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.67224 | − | 11.5567i | −0.517866 | − | 0.896970i | ||||
\(167\) | 1.54428 | − | 5.76334i | 0.119500 | − | 0.445980i | −0.880084 | − | 0.474818i | \(-0.842514\pi\) |
0.999584 | + | 0.0288375i | \(0.00918054\pi\) | |||||||
\(168\) | 2.99425 | + | 10.0283i | 0.231012 | + | 0.773702i | ||||
\(169\) | −15.4826 | − | 8.93886i | −1.19097 | − | 0.687605i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.56633 | − | 0.259222i | 0.349196 | − | 0.0198232i | ||||
\(172\) | −0.267103 | + | 0.267103i | −0.0203664 | + | 0.0203664i | ||||
\(173\) | −3.53677 | − | 13.1994i | −0.268896 | − | 1.00353i | −0.959822 | − | 0.280608i | \(-0.909464\pi\) |
0.690927 | − | 0.722925i | \(-0.257203\pi\) | |||||||
\(174\) | 3.15562 | − | 1.94322i | 0.239227 | − | 0.147315i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.72042 | − | 1.57063i | 0.205059 | − | 0.118391i | ||||
\(177\) | 3.05941 | − | 12.8665i | 0.229959 | − | 0.967106i | ||||
\(178\) | −6.00319 | + | 1.60855i | −0.449958 | + | 0.120566i | ||||
\(179\) | 17.2370 | 1.28836 | 0.644178 | − | 0.764875i | \(-0.277199\pi\) | ||||
0.644178 | + | 0.764875i | \(0.277199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7708 | 1.09790 | 0.548952 | − | 0.835854i | \(-0.315027\pi\) | ||||
0.548952 | + | 0.835854i | \(0.315027\pi\) | |||||||
\(182\) | 14.7666 | − | 3.95669i | 1.09457 | − | 0.293289i | ||||
\(183\) | 22.0402 | − | 6.58076i | 1.62926 | − | 0.486464i | ||||
\(184\) | −4.05503 | + | 2.34117i | −0.298941 | + | 0.172594i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.460987 | − | 16.2541i | −0.0338012 | − | 1.19181i | ||||
\(187\) | 0.366025 | + | 1.36603i | 0.0267664 | + | 0.0998937i | ||||
\(188\) | −1.14973 | + | 1.14973i | −0.0838528 | + | 0.0838528i | ||||
\(189\) | −9.63706 | − | 4.51974i | −0.700993 | − | 0.328763i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.56792 | + | 2.63729i | 0.330523 | + | 0.190827i | 0.656073 | − | 0.754697i | \(-0.272216\pi\) |
−0.325550 | + | 0.945525i | \(0.605550\pi\) | |||||||
\(192\) | 10.2580 | − | 10.8569i | 0.740309 | − | 0.783527i | ||||
\(193\) | −2.40873 | + | 8.98952i | −0.173384 | + | 0.647080i | 0.823437 | + | 0.567408i | \(0.192054\pi\) |
−0.996821 | + | 0.0796715i | \(0.974613\pi\) | |||||||
\(194\) | −2.66250 | − | 4.61158i | −0.191156 | − | 0.331092i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.275228 | + | 0.476709i | −0.0196592 | + | 0.0340507i | ||||
\(197\) | −9.49539 | − | 9.49539i | −0.676519 | − | 0.676519i | 0.282692 | − | 0.959211i | \(-0.408773\pi\) |
−0.959211 | + | 0.282692i | \(0.908773\pi\) | |||||||
\(198\) | −0.722243 | + | 3.47204i | −0.0513276 | + | 0.246747i | ||||
\(199\) | 17.6342i | 1.25005i | 0.780604 | + | 0.625026i | \(0.214912\pi\) | ||||
−0.780604 | + | 0.625026i | \(0.785088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.01682 | − | 4.89907i | −0.212790 | − | 0.345554i | ||||
\(202\) | 3.34330 | + | 0.895835i | 0.235234 | + | 0.0630307i | ||||
\(203\) | −3.15239 | − | 0.844680i | −0.221254 | − | 0.0592849i | ||||
\(204\) | 0.286490 | + | 0.465237i | 0.0200583 | + | 0.0325731i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.5443i | 1.22237i | ||||||||
\(207\) | 0.969859 | − | 4.66240i | 0.0674098 | − | 0.324060i | ||||
\(208\) | −14.0226 | − | 14.0226i | −0.972291 | − | 0.972291i | ||||
\(209\) | −0.670964 | + | 1.16214i | −0.0464116 | + | 0.0803872i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0616050 | + | 0.106703i | 0.00424106 | + | 0.00734574i | 0.868138 | − | 0.496323i | \(-0.165317\pi\) |
−0.863897 | + | 0.503668i | \(0.831983\pi\) | |||||||
\(212\) | −0.334597 | + | 1.24873i | −0.0229802 | + | 0.0857633i | ||||
\(213\) | −7.01583 | + | 7.42540i | −0.480716 | + | 0.508780i | ||||
\(214\) | −15.1824 | − | 8.76558i | −1.03785 | − | 0.599203i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.30216 | + | 15.2716i | 0.0886009 | + | 1.03910i | ||||
\(217\) | −10.1256 | + | 10.1256i | −0.687368 | + | 0.687368i | ||||
\(218\) | −2.79981 | − | 10.4490i | −0.189627 | − | 0.707698i | ||||
\(219\) | −0.110345 | − | 3.89068i | −0.00745640 | − | 0.262908i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.73186 | − | 4.46399i | 0.520101 | − | 0.300281i | ||||
\(222\) | −13.4202 | + | 4.00701i | −0.900707 | + | 0.268933i | ||||
\(223\) | 2.41842 | − | 0.648014i | 0.161949 | − | 0.0433942i | −0.176933 | − | 0.984223i | \(-0.556618\pi\) |
0.338883 | + | 0.940829i | \(0.389951\pi\) | |||||||
\(224\) | −2.26663 | −0.151445 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.1202 | 1.07230 | ||||||||
\(227\) | −14.7293 | + | 3.94671i | −0.977619 | + | 0.261952i | −0.712042 | − | 0.702137i | \(-0.752229\pi\) |
−0.265577 | + | 0.964090i | \(0.585563\pi\) | |||||||
\(228\) | −0.119932 | + | 0.504382i | −0.00794272 | + | 0.0334035i | ||||
\(229\) | 19.1083 | − | 11.0322i | 1.26271 | − | 0.729029i | 0.289116 | − | 0.957294i | \(-0.406639\pi\) |
0.973599 | + | 0.228265i | \(0.0733054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.65929 | − | 1.63758i | 0.174969 | − | 0.107745i | ||||
\(232\) | 1.21628 | + | 4.53922i | 0.0798527 | + | 0.298014i | ||||
\(233\) | −4.22173 | + | 4.22173i | −0.276575 | + | 0.276575i | −0.831740 | − | 0.555165i | \(-0.812655\pi\) |
0.555165 | + | 0.831740i | \(0.312655\pi\) | |||||||
\(234\) | 22.3524 | − | 1.26890i | 1.46122 | − | 0.0829507i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.29829 | + | 0.749566i | 0.0845112 | + | 0.0487926i | ||||
\(237\) | 3.83030 | + | 12.8284i | 0.248805 | + | 0.833294i | ||||
\(238\) | −1.14404 | + | 4.26960i | −0.0741569 | + | 0.276757i | ||||
\(239\) | 6.79199 | + | 11.7641i | 0.439338 | + | 0.760955i | 0.997639 | − | 0.0686835i | \(-0.0218799\pi\) |
−0.558301 | + | 0.829639i | \(0.688547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.56728 | + | 4.44666i | −0.165373 | + | 0.286434i | −0.936788 | − | 0.349898i | \(-0.886216\pi\) |
0.771415 | + | 0.636333i | \(0.219549\pi\) | |||||||
\(242\) | 9.71038 | + | 9.71038i | 0.624207 | + | 0.624207i | ||||
\(243\) | −12.4696 | − | 9.35468i | −0.799923 | − | 0.600103i | ||||
\(244\) | 2.60733i | 0.166917i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.36479 | + | 0.237236i | −0.533319 | + | 0.0151256i | ||||
\(247\) | 8.18298 | + | 2.19262i | 0.520670 | + | 0.139513i | ||||
\(248\) | 19.9168 | + | 5.33669i | 1.26472 | + | 0.338880i | ||||
\(249\) | −8.17907 | + | 15.1424i | −0.518327 | + | 0.959609i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.60221i | − | 0.164250i | −0.996622 | − | 0.0821251i | \(-0.973829\pi\) | ||
0.996622 | − | 0.0821251i | \(-0.0261707\pi\) | |||||||
\(252\) | 0.803448 | − | 0.900159i | 0.0506125 | − | 0.0567047i | ||||
\(253\) | 0.987999 | + | 0.987999i | 0.0621150 | + | 0.0621150i | ||||
\(254\) | 1.80652 | − | 3.12898i | 0.113351 | − | 0.196329i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.33257 | + | 4.04013i | 0.145786 | + | 0.252508i | ||||
\(257\) | 2.73197 | − | 10.1958i | 0.170415 | − | 0.635999i | −0.826872 | − | 0.562390i | \(-0.809882\pi\) |
0.997287 | − | 0.0736085i | \(-0.0234515\pi\) | |||||||
\(258\) | −4.35404 | − | 1.03531i | −0.271071 | − | 0.0644555i | ||||
\(259\) | 10.6815 | + | 6.16695i | 0.663714 | + | 0.383196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.26796 | − | 2.15131i | −0.264180 | − | 0.133163i | ||||
\(262\) | 20.2984 | − | 20.2984i | 1.25404 | − | 1.25404i | ||||
\(263\) | 2.17720 | + | 8.12541i | 0.134252 | + | 0.501034i | 1.00000 | 0.000554412i | \(0.000176475\pi\) | |
−0.865748 | + | 0.500480i | \(0.833157\pi\) | |||||||
\(264\) | −3.95668 | − | 2.13718i | −0.243517 | − | 0.131534i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.63236 | + | 2.09714i | −0.222714 | + | 0.128584i | ||||
\(267\) | 5.82609 | + | 5.50473i | 0.356551 | + | 0.336884i | ||||
\(268\) | 0.629953 | − | 0.168795i | 0.0384805 | − | 0.0103108i | ||||
\(269\) | −26.7708 | −1.63225 | −0.816123 | − | 0.577878i | \(-0.803881\pi\) | ||||
−0.816123 | + | 0.577878i | \(0.803881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5850 | −1.12896 | −0.564480 | − | 0.825447i | \(-0.690923\pi\) | ||||
−0.564480 | + | 0.825447i | \(0.690923\pi\) | |||||||
\(272\) | 5.53853 | − | 1.48405i | 0.335823 | − | 0.0899834i | ||||
\(273\) | −14.3309 | − | 13.5405i | −0.867347 | − | 0.819506i | ||||
\(274\) | 7.97833 | − | 4.60629i | 0.481989 | − | 0.278276i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.474957 | + | 0.256546i | 0.0285891 | + | 0.0154422i | ||||
\(277\) | −7.05259 | − | 26.3206i | −0.423749 | − | 1.58145i | −0.766640 | − | 0.642078i | \(-0.778073\pi\) |
0.342891 | − | 0.939375i | \(-0.388594\pi\) | |||||||
\(278\) | −1.36920 | + | 1.36920i | −0.0821189 | + | 0.0821189i | ||||
\(279\) | −17.5380 | + | 11.4980i | −1.04997 | + | 0.688368i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.7050 | − | 13.1087i | −1.35447 | − | 0.782002i | −0.365595 | − | 0.930774i | \(-0.619135\pi\) |
−0.988872 | + | 0.148772i | \(0.952468\pi\) | |||||||
\(282\) | −18.7418 | − | 4.45643i | −1.11606 | − | 0.265377i | ||||
\(283\) | 0.921880 | − | 3.44050i | 0.0548001 | − | 0.204517i | −0.933098 | − | 0.359623i | \(-0.882905\pi\) |
0.987898 | + | 0.155106i | \(0.0495720\pi\) | |||||||
\(284\) | −0.578988 | − | 1.00284i | −0.0343566 | − | 0.0595074i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.28439 | + | 5.68873i | −0.194210 | + | 0.336382i | ||||
\(287\) | 5.21088 | + | 5.21088i | 0.307589 | + | 0.307589i | ||||
\(288\) | −3.24988 | − | 0.676030i | −0.191501 | − | 0.0398355i | ||||
\(289\) | − | 14.4186i | − | 0.848151i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.26378 | + | 6.04243i | −0.191326 | + | 0.354213i | ||||
\(292\) | 0.426168 | + | 0.114191i | 0.0249396 | + | 0.00668254i | ||||
\(293\) | −2.87816 | − | 0.771199i | −0.168144 | − | 0.0450539i | 0.173765 | − | 0.984787i | \(-0.444407\pi\) |
−0.341909 | + | 0.939733i | \(0.611073\pi\) | |||||||
\(294\) | −6.51914 | + | 0.184891i | −0.380204 | + | 0.0107831i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 17.7600i | − | 1.03228i | ||||||
\(297\) | 4.30130 | − | 1.55481i | 0.249587 | − | 0.0902192i | ||||
\(298\) | 15.7349 | + | 15.7349i | 0.911496 | + | 0.911496i | ||||
\(299\) | 4.41042 | − | 7.63907i | 0.255061 | − | 0.441779i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.97062 | + | 3.41321i | 0.113584 | + | 0.196734i | ||||
\(302\) | −0.00197247 | + | 0.00736135i | −0.000113503 | + | 0.000423598i | ||||
\(303\) | −1.27712 | − | 4.27731i | −0.0733684 | − | 0.245725i | ||||
\(304\) | 4.71190 | + | 2.72042i | 0.270246 | + | 0.156027i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.91374 | + | 5.78053i | −0.166568 | + | 0.330451i | ||||
\(307\) | −21.8017 | + | 21.8017i | −1.24429 | + | 1.24429i | −0.286081 | + | 0.958205i | \(0.592353\pi\) |
−0.958205 | + | 0.286081i | \(0.907647\pi\) | |||||||
\(308\) | 0.0916247 | + | 0.341948i | 0.00522080 | + | 0.0194843i | ||||
\(309\) | 19.2665 | − | 11.8642i | 1.09603 | − | 0.674933i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.3878 | − | 16.9671i | 1.66643 | − | 0.962114i | 0.696892 | − | 0.717176i | \(-0.254565\pi\) |
0.969539 | − | 0.244939i | \(-0.0787679\pi\) | |||||||
\(312\) | −6.56741 | + | 27.6196i | −0.371806 | + | 1.56365i | ||||
\(313\) | 22.4027 | − | 6.00279i | 1.26628 | − | 0.339298i | 0.437673 | − | 0.899134i | \(-0.355803\pi\) |
0.828603 | + | 0.559836i | \(0.189136\pi\) | |||||||
\(314\) | −11.3610 | −0.641137 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.51758 | −0.0853708 | ||||||||
\(317\) | 3.86401 | − | 1.03536i | 0.217024 | − | 0.0581515i | −0.148669 | − | 0.988887i | \(-0.547499\pi\) |
0.365693 | + | 0.930736i | \(0.380832\pi\) | |||||||
\(318\) | −14.6765 | + | 4.38211i | −0.823019 | + | 0.245737i | ||||
\(319\) | 1.21444 | − | 0.701157i | 0.0679956 | − | 0.0392573i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.640980 | + | 22.6005i | 0.0357760 | + | 1.26144i | ||||
\(322\) | 1.13031 | + | 4.21836i | 0.0629896 | + | 0.235080i | ||||
\(323\) | −1.73205 | + | 1.73205i | −0.0963739 | + | 0.0963739i | ||||
\(324\) | 1.42046 | − | 1.05101i | 0.0789143 | − | 0.0583896i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.89684 | + | 3.98189i | 0.381981 | + | 0.220537i | ||||
\(327\) | −9.58143 | + | 10.1408i | −0.529854 | + | 0.560786i | ||||
\(328\) | 2.74640 | − | 10.2497i | 0.151645 | − | 0.565945i | ||||
\(329\) | 8.48242 | + | 14.6920i | 0.467651 | + | 0.809995i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.98175 | + | 5.16454i | −0.163892 | + | 0.283869i | −0.936261 | − | 0.351305i | \(-0.885738\pi\) |
0.772369 | + | 0.635174i | \(0.219071\pi\) | |||||||
\(332\) | −1.37945 | − | 1.37945i | −0.0757071 | − | 0.0757071i | ||||
\(333\) | 13.4757 | + | 12.0279i | 0.738466 | + | 0.659127i | ||||
\(334\) | 8.01324i | 0.438465i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.63954 | − | 10.7821i | −0.362216 | − | 0.588210i | ||||
\(337\) | −9.56887 | − | 2.56397i | −0.521250 | − | 0.139668i | −0.0114051 | − | 0.999935i | \(-0.503630\pi\) |
−0.509845 | + | 0.860267i | \(0.670297\pi\) | |||||||
\(338\) | 23.1918 | + | 6.21422i | 1.26147 | + | 0.338009i | ||||
\(339\) | −10.9012 | − | 17.7026i | −0.592072 | − | 0.961476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.15295i | − | 0.333201i | ||||||
\(342\) | −5.83354 | + | 1.92351i | −0.315442 | + | 0.104012i | ||||
\(343\) | 14.2007 | + | 14.2007i | 0.766764 | + | 0.766764i | ||||
\(344\) | 2.83755 | − | 4.91478i | 0.152990 | − | 0.264987i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.17611 | + | 15.8935i | 0.493311 | + | 0.854440i | ||||
\(347\) | 2.74569 | − | 10.2471i | 0.147396 | − | 0.550091i | −0.852241 | − | 0.523150i | \(-0.824757\pi\) |
0.999637 | − | 0.0269407i | \(-0.00857654\pi\) | |||||||
\(348\) | 0.372078 | − | 0.393799i | 0.0199455 | − | 0.0211098i | ||||
\(349\) | 8.08831 | + | 4.66979i | 0.432957 | + | 0.249968i | 0.700606 | − | 0.713549i | \(-0.252913\pi\) |
−0.267648 | + | 0.963517i | \(0.586247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.5091 | − | 23.6885i | −0.881193 | − | 1.26440i | ||||
\(352\) | 0.688675 | − | 0.688675i | 0.0367065 | − | 0.0367065i | ||||
\(353\) | 4.96965 | + | 18.5470i | 0.264508 | + | 0.987156i | 0.962551 | + | 0.271100i | \(0.0873876\pi\) |
−0.698043 | + | 0.716055i | \(0.745946\pi\) | |||||||
\(354\) | 0.503538 | + | 17.7544i | 0.0267627 | + | 0.943638i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.786842 | + | 0.454284i | −0.0417026 | + | 0.0240770i | ||||
\(357\) | 5.46239 | − | 1.63096i | 0.289100 | − | 0.0863194i | ||||
\(358\) | −22.3606 | + | 5.99152i | −1.18180 | + | 0.316662i | ||||
\(359\) | −12.5944 | −0.664705 | −0.332352 | − | 0.943155i | \(-0.607842\pi\) | ||||
−0.332352 | + | 0.943155i | \(0.607842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.6757 | 0.877669 | ||||||||
\(362\) | −19.1613 | + | 5.13426i | −1.00710 | + | 0.269851i | ||||
\(363\) | 4.09702 | − | 17.2302i | 0.215038 | − | 0.904353i | ||||
\(364\) | 1.93546 | − | 1.11744i | 0.101446 | − | 0.0585698i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −26.3041 | + | 16.1979i | −1.37494 | + | 0.846680i | ||||
\(367\) | 7.32206 | + | 27.3263i | 0.382209 | + | 1.42642i | 0.842520 | + | 0.538665i | \(0.181071\pi\) |
−0.460312 | + | 0.887757i | \(0.652262\pi\) | |||||||
\(368\) | 4.00583 | − | 4.00583i | 0.208818 | − | 0.208818i | ||||
\(369\) | 5.91718 | + | 9.02551i | 0.308036 | + | 0.469849i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.6814 | + | 6.74425i | 0.606467 | + | 0.350144i | ||||
\(372\) | −0.680100 | − | 2.27779i | −0.0352616 | − | 0.118098i | ||||
\(373\) | −0.604851 | + | 2.25734i | −0.0313180 | + | 0.116880i | −0.979815 | − | 0.199905i | \(-0.935937\pi\) |
0.948497 | + | 0.316785i | \(0.102603\pi\) | |||||||
\(374\) | −0.949649 | − | 1.64484i | −0.0491052 | − | 0.0850526i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.2141 | − | 21.1554i | 0.629894 | − | 1.09101i | ||||
\(377\) | −6.25992 | − | 6.25992i | −0.322402 | − | 0.322402i | ||||
\(378\) | 14.0727 | + | 2.51341i | 0.723820 | + | 0.129276i | ||||
\(379\) | − | 18.4618i | − | 0.948320i | −0.880439 | − | 0.474160i | \(-0.842752\pi\) | ||
0.880439 | − | 0.474160i | \(-0.157248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.65779 | + | 0.132101i | −0.238626 | + | 0.00676772i | ||||
\(382\) | −6.84241 | − | 1.83342i | −0.350088 | − | 0.0938059i | ||||
\(383\) | 23.3806 | + | 6.26481i | 1.19469 | + | 0.320117i | 0.800739 | − | 0.599014i | \(-0.204441\pi\) |
0.393953 | + | 0.919131i | \(0.371107\pi\) | |||||||
\(384\) | −7.71175 | + | 14.2772i | −0.393539 | + | 0.728580i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.4989i | − | 0.636176i | ||||||
\(387\) | 1.80746 | + | 5.48159i | 0.0918784 | + | 0.278645i | ||||
\(388\) | −0.550457 | − | 0.550457i | −0.0279452 | − | 0.0279452i | ||||
\(389\) | −13.5444 | + | 23.4596i | −0.686729 | + | 1.18945i | 0.286161 | + | 0.958182i | \(0.407621\pi\) |
−0.972890 | + | 0.231268i | \(0.925712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.27523 | + | 2.20876i | 0.0644911 | + | 0.111702i | ||||
\(392\) | 2.14042 | − | 7.98815i | 0.108108 | − | 0.403463i | ||||
\(393\) | −36.0177 | − | 8.56432i | −1.81685 | − | 0.432013i | ||||
\(394\) | 15.6184 | + | 9.01729i | 0.786844 | + | 0.454284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0293839 | + | 0.517611i | 0.00147659 | + | 0.0260110i | ||||
\(397\) | 18.2252 | − | 18.2252i | 0.914698 | − | 0.914698i | −0.0819389 | − | 0.996637i | \(-0.526111\pi\) |
0.996637 | + | 0.0819389i | \(0.0261112\pi\) | |||||||
\(398\) | −6.12955 | − | 22.8758i | −0.307247 | − | 1.14666i | ||||
\(399\) | 4.75938 | + | 2.57075i | 0.238267 | + | 0.128699i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1294 | + | 6.42558i | −0.555777 | + | 0.320878i | −0.751449 | − | 0.659791i | \(-0.770645\pi\) |
0.195672 | + | 0.980669i | \(0.437311\pi\) | |||||||
\(402\) | 5.61645 | + | 5.30666i | 0.280123 | + | 0.264672i | ||||
\(403\) | −37.5202 | + | 10.0535i | −1.86902 | + | 0.500801i | ||||
\(404\) | 0.506000 | 0.0251745 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.38302 | 0.217526 | ||||||||
\(407\) | −5.11910 | + | 1.37166i | −0.253744 | + | 0.0679906i | ||||
\(408\) | −5.96656 | − | 5.63745i | −0.295389 | − | 0.279096i | ||||
\(409\) | −22.2450 | + | 12.8431i | −1.09994 | + | 0.635053i | −0.936206 | − | 0.351451i | \(-0.885688\pi\) |
−0.163737 | + | 0.986504i | \(0.552355\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4538 | − | 5.64656i | −0.515648 | − | 0.278524i | ||||
\(412\) | 0.663820 | + | 2.47741i | 0.0327041 | + | 0.122053i | ||||
\(413\) | 11.0602 | − | 11.0602i | 0.544237 | − | 0.544237i | ||||
\(414\) | 0.362487 | + | 6.38540i | 0.0178153 | + | 0.313825i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.32474 | − | 3.07424i | −0.261067 | − | 0.150727i | ||||
\(417\) | 2.42952 | + | 0.577694i | 0.118974 | + | 0.0282898i | ||||
\(418\) | 0.466448 | − | 1.74081i | 0.0228147 | − | 0.0851457i | ||||
\(419\) | −6.13243 | − | 10.6217i | −0.299589 | − | 0.518903i | 0.676453 | − | 0.736486i | \(-0.263516\pi\) |
−0.976042 | + | 0.217583i | \(0.930183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.24056 | + | 12.5410i | −0.352883 | + | 0.611212i | −0.986753 | − | 0.162228i | \(-0.948132\pi\) |
0.633870 | + | 0.773439i | \(0.281465\pi\) | |||||||
\(422\) | −0.117006 | − | 0.117006i | −0.00569577 | − | 0.00569577i | ||||
\(423\) | 7.78012 | + | 23.5952i | 0.378283 | + | 1.14724i | ||||
\(424\) | − | 19.4225i | − | 0.943240i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.52020 | − | 12.0712i | 0.315905 | − | 0.584853i | ||||
\(427\) | 26.2771 | + | 7.04094i | 1.27164 | + | 0.340735i | ||||
\(428\) | −2.47556 | − | 0.663324i | −0.119661 | − | 0.0320630i | ||||
\(429\) | 8.46824 | − | 0.240170i | 0.408850 | − | 0.0115955i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.9660i | 1.73242i | 0.499678 | + | 0.866211i | \(0.333452\pi\) | ||||
−0.499678 | + | 0.866211i | \(0.666548\pi\) | |||||||
\(432\) | −6.30395 | − | 17.4396i | −0.303299 | − | 0.839061i | ||||
\(433\) | 0.331545 | + | 0.331545i | 0.0159331 | + | 0.0159331i | 0.715028 | − | 0.699095i | \(-0.246414\pi\) |
−0.699095 | + | 0.715028i | \(0.746414\pi\) | |||||||
\(434\) | 9.61573 | − | 16.6549i | 0.461570 | − | 0.799462i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.790718 | − | 1.36956i | −0.0378685 | − | 0.0655902i | ||||
\(437\) | −0.626366 | + | 2.33763i | −0.0299632 | + | 0.111824i | ||||
\(438\) | 1.49553 | + | 5.00881i | 0.0714591 | + | 0.239330i | ||||
\(439\) | 1.28953 | + | 0.744511i | 0.0615459 | + | 0.0355336i | 0.530457 | − | 0.847712i | \(-0.322020\pi\) |
−0.468911 | + | 0.883245i | \(0.655354\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.61158 | + | 7.03407i | 0.219599 | + | 0.334956i | ||||
\(442\) | −8.47845 | + | 8.47845i | −0.403279 | + | 0.403279i | ||||
\(443\) | −8.29218 | − | 30.9468i | −0.393973 | − | 1.47033i | −0.823522 | − | 0.567285i | \(-0.807994\pi\) |
0.429548 | − | 0.903044i | \(-0.358673\pi\) | |||||||
\(444\) | −1.74345 | + | 1.07361i | −0.0827403 | + | 0.0509511i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.91203 | + | 1.68126i | −0.137889 | + | 0.0796101i | ||||
\(447\) | 6.63888 | − | 27.9202i | 0.314008 | − | 1.32058i | ||||
\(448\) | 17.0634 | − | 4.57213i | 0.806172 | − | 0.216013i | ||||
\(449\) | 21.8283 | 1.03014 | 0.515071 | − | 0.857147i | \(-0.327766\pi\) | ||||
0.515071 | + | 0.857147i | \(0.327766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.16647 | −0.149103 | ||||||||
\(452\) | 2.27631 | − | 0.609937i | 0.107069 | − | 0.0286890i | ||||
\(453\) | 0.00941786 | − | 0.00281198i | 0.000442490 | − | 0.000132118i | ||||
\(454\) | 17.7357 | − | 10.2397i | 0.832376 | − | 0.480572i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.220817 | − | 7.78588i | −0.0103407 | − | 0.364607i | ||||
\(457\) | 0.235886 | + | 0.880339i | 0.0110343 | + | 0.0411805i | 0.971223 | − | 0.238170i | \(-0.0765475\pi\) |
−0.960189 | + | 0.279351i | \(0.909881\pi\) | |||||||
\(458\) | −20.9534 | + | 20.9534i | −0.979090 | + | 0.979090i | ||||
\(459\) | 8.31839 | − | 0.709282i | 0.388269 | − | 0.0331065i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7320 | − | 10.8149i | −0.872434 | − | 0.503700i | −0.00427761 | − | 0.999991i | \(-0.501362\pi\) |
−0.868156 | + | 0.496291i | \(0.834695\pi\) | |||||||
\(462\) | −2.88054 | + | 3.04870i | −0.134015 | + | 0.141838i | ||||
\(463\) | −4.85644 | + | 18.1245i | −0.225698 | + | 0.842316i | 0.756426 | + | 0.654079i | \(0.226944\pi\) |
−0.982124 | + | 0.188236i | \(0.939723\pi\) | |||||||
\(464\) | −2.84283 | − | 4.92393i | −0.131975 | − | 0.228588i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.00916 | − | 6.94407i | 0.185721 | − | 0.321678i | ||||
\(467\) | 16.8295 | + | 16.8295i | 0.778777 | + | 0.778777i | 0.979623 | − | 0.200846i | \(-0.0643691\pi\) |
−0.200846 | + | 0.979623i | \(0.564369\pi\) | |||||||
\(468\) | 3.10834 | − | 1.02492i | 0.143683 | − | 0.0473771i | ||||
\(469\) | − | 6.80460i | − | 0.314207i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.68281 | + | 12.4763i | 0.354005 | + | 0.574875i | ||||
\(472\) | −21.7552 | − | 5.82929i | −1.00136 | − | 0.268315i | ||||
\(473\) | −1.63578 | − | 0.438306i | −0.0752133 | − | 0.0201533i | ||||
\(474\) | −9.42793 | − | 15.3102i | −0.433039 | − | 0.703220i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.646194i | 0.0296182i | ||||||||
\(477\) | 14.7372 | + | 13.1539i | 0.674772 | + | 0.602276i | ||||
\(478\) | −12.9000 | − | 12.9000i | −0.590033 | − | 0.590033i | ||||
\(479\) | 8.91724 | − | 15.4451i | 0.407439 | − | 0.705705i | −0.587163 | − | 0.809469i | \(-0.699755\pi\) |
0.994602 | + | 0.103764i | \(0.0330886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7285 | + | 28.9747i | 0.762756 | + | 1.32113i | ||||
\(482\) | 1.78475 | − | 6.66078i | 0.0812931 | − | 0.303390i | ||||
\(483\) | 3.86810 | − | 4.09392i | 0.176005 | − | 0.186280i | ||||
\(484\) | 1.73861 | + | 1.00378i | 0.0790275 | + | 0.0456265i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.4277 | + | 7.80094i | 0.881259 | + | 0.353858i | ||||
\(487\) | 21.8232 | − | 21.8232i | 0.988904 | − | 0.988904i | −0.0110354 | − | 0.999939i | \(-0.503513\pi\) |
0.999939 | + | 0.0110354i | \(0.00351274\pi\) | |||||||
\(488\) | −10.1385 | − | 37.8372i | −0.458946 | − | 1.71281i | ||||
\(489\) | −0.291174 | − | 10.2666i | −0.0131674 | − | 0.464273i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1670 | − | 20.3037i | 1.58707 | − | 0.916292i | 0.593278 | − | 0.804998i | \(-0.297834\pi\) |
0.993787 | − | 0.111295i | \(-0.0354997\pi\) | |||||||
\(492\) | −1.17221 | + | 0.349997i | −0.0528472 | + | 0.0157791i | ||||
\(493\) | 2.47249 | − | 0.662503i | 0.111356 | − | 0.0298376i | ||||
\(494\) | −11.3775 | −0.511896 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.9471 | −1.12016 | ||||||||
\(497\) | −11.6703 | + | 3.12705i | −0.523484 | + | 0.140267i | ||||
\(498\) | 5.34683 | − | 22.4864i | 0.239597 | − | 1.00764i | ||||
\(499\) | −37.3397 | + | 21.5581i | −1.67156 | + | 0.965073i | −0.704788 | + | 0.709418i | \(0.748958\pi\) |
−0.966768 | + | 0.255655i | \(0.917709\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.79988 | − | 5.41892i | 0.393150 | − | 0.242100i | ||||
\(502\) | 0.904518 | + | 3.37571i | 0.0403706 | + | 0.150665i | ||||
\(503\) | −28.0936 | + | 28.0936i | −1.25263 | + | 1.25263i | −0.298093 | + | 0.954537i | \(0.596351\pi\) |
−0.954537 | + | 0.298093i | \(0.903649\pi\) | |||||||
\(504\) | −8.15932 | + | 16.1872i | −0.363445 | + | 0.721033i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.62510 | − | 0.938252i | −0.0722445 | − | 0.0417104i | ||||
\(507\) | −8.85909 | − | 29.6708i | −0.393446 | − | 1.31773i | ||||
\(508\) | 0.136706 | − | 0.510193i | 0.00606534 | − | 0.0226361i | ||||
\(509\) | −7.39188 | − | 12.8031i | −0.327639 | − | 0.567488i | 0.654404 | − | 0.756145i | \(-0.272920\pi\) |
−0.982043 | + | 0.188658i | \(0.939586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.30168 | − | 3.98663i | 0.101820 | − | 0.176358i | ||||
\(512\) | −17.6794 | − | 17.6794i | −0.781325 | − | 0.781325i | ||||
\(513\) | 6.05725 | + | 5.10544i | 0.267434 | + | 0.225411i | ||||
\(514\) | 14.1761i | 0.625282i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.654003 | + | 0.0185484i | −0.0287909 | + | 0.000816546i | ||||
\(517\) | −7.04114 | − | 1.88667i | −0.309669 | − | 0.0829755i | ||||
\(518\) | −16.0001 | − | 4.28721i | −0.703003 | − | 0.188369i | ||||
\(519\) | 11.2484 | − | 20.8248i | 0.493750 | − | 0.914108i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.4812i | − | 1.24778i | −0.781511 | − | 0.623892i | \(-0.785551\pi\) | ||
0.781511 | − | 0.623892i | \(-0.214449\pi\) | |||||||
\(522\) | 6.28437 | + | 1.30725i | 0.275059 | + | 0.0572170i | ||||
\(523\) | −15.4076 | − | 15.4076i | −0.673726 | − | 0.673726i | 0.284847 | − | 0.958573i | \(-0.408057\pi\) |
−0.958573 | + | 0.284847i | \(0.908057\pi\) | |||||||
\(524\) | 2.09829 | − | 3.63434i | 0.0916641 | − | 0.158767i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.64872 | − | 9.78386i | −0.246296 | − | 0.426597i | ||||
\(527\) | 2.90687 | − | 10.8486i | 0.126625 | − | 0.472572i | ||||
\(528\) | 5.29325 | + | 1.25863i | 0.230359 | + | 0.0547750i | ||||
\(529\) | −17.7363 | − | 10.2401i | −0.771145 | − | 0.445221i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.1568 | − | 12.5593i | 0.831335 | − | 0.545028i | ||||
\(532\) | −0.433573 | + | 0.433573i | −0.0187978 | + | 0.0187978i | ||||
\(533\) | 5.17380 | + | 19.3089i | 0.224102 | + | 0.836361i | ||||
\(534\) | −9.47128 | − | 5.11586i | −0.409862 | − | 0.221385i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.48544 | + | 4.89907i | −0.366515 | + | 0.211608i | ||||
\(537\) | 21.7010 | + | 20.5040i | 0.936466 | + | 0.884813i | ||||
\(538\) | 34.7283 | − | 9.30542i | 1.49724 | − | 0.401185i | ||||
\(539\) | −2.46780 | −0.106296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.11754 | −0.0480466 | −0.0240233 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240233 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(542\) | 24.1093 | − | 6.46008i | 1.03558 | − | 0.277484i | ||||
\(543\) | 18.5960 | + | 17.5703i | 0.798033 | + | 0.754015i | ||||
\(544\) | 1.53959 | − | 0.888885i | 0.0660096 | − | 0.0381106i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 23.2973 | + | 12.5839i | 0.997033 | + | 0.538542i | ||||
\(547\) | −8.33894 | − | 31.1213i | −0.356547 | − | 1.33065i | −0.878526 | − | 0.477694i | \(-0.841473\pi\) |
0.521979 | − | 0.852958i | \(-0.325194\pi\) | |||||||
\(548\) | 0.952326 | − | 0.952326i | 0.0406813 | − | 0.0406813i | ||||
\(549\) | 35.5761 | + | 17.9325i | 1.51835 | + | 0.765342i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.10347 | + | 1.21444i | 0.0896109 | + | 0.0517369i | ||||
\(552\) | −7.89008 | − | 1.87611i | −0.335824 | − | 0.0798526i | ||||
\(553\) | −4.09814 | + | 15.2945i | −0.174271 | + | 0.650387i | ||||
\(554\) | 18.2979 | + | 31.6928i | 0.777402 | + | 1.34650i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.141537 | + | 0.245149i | −0.00600250 | + | 0.0103966i | ||||
\(557\) | 30.4033 | + | 30.4033i | 1.28823 | + | 1.28823i | 0.935862 | + | 0.352366i | \(0.114623\pi\) |
0.352366 | + | 0.935862i | \(0.385377\pi\) | |||||||
\(558\) | 18.7544 | − | 21.0119i | 0.793937 | − | 0.889503i | ||||
\(559\) | 10.6910i | 0.452182i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.16411 | + | 2.15519i | −0.0491489 | + | 0.0909922i | ||||
\(562\) | 34.0105 | + | 9.11308i | 1.43465 | + | 0.384412i | ||||
\(563\) | −1.12220 | − | 0.300692i | −0.0472950 | − | 0.0126727i | 0.235094 | − | 0.971973i | \(-0.424460\pi\) |
−0.282389 | + | 0.959300i | \(0.591127\pi\) | |||||||
\(564\) | −2.81512 | + | 0.0798405i | −0.118538 | + | 0.00336189i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.78361i | 0.201070i | ||||||||
\(567\) | −6.75644 | − | 17.1538i | −0.283744 | − | 0.720393i | ||||
\(568\) | 12.3017 | + | 12.3017i | 0.516167 | + | 0.516167i | ||||
\(569\) | 0.145367 | − | 0.251784i | 0.00609412 | − | 0.0105553i | −0.862962 | − | 0.505268i | \(-0.831394\pi\) |
0.869056 | + | 0.494713i | \(0.164727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0283 | − | 22.5656i | −0.545215 | − | 0.944341i | −0.998593 | − | 0.0530223i | \(-0.983115\pi\) |
0.453378 | − | 0.891318i | \(-0.350219\pi\) | |||||||
\(572\) | −0.248542 | + | 0.927572i | −0.0103921 | + | 0.0387837i | ||||
\(573\) | 2.61375 | + | 8.75395i | 0.109191 | + | 0.365702i | ||||
\(574\) | −8.57106 | − | 4.94851i | −0.357749 | − | 0.206547i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 25.8292 | − | 1.46627i | 1.07621 | − | 0.0610948i | ||||
\(577\) | 2.52834 | − | 2.52834i | 0.105256 | − | 0.105256i | −0.652517 | − | 0.757774i | \(-0.726287\pi\) |
0.757774 | + | 0.652517i | \(0.226287\pi\) | |||||||
\(578\) | 5.01183 | + | 18.7044i | 0.208465 | + | 0.778000i | ||||
\(579\) | −13.7258 | + | 8.45230i | −0.570427 | + | 0.351266i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.6274 | + | 10.1772i | −0.731309 | + | 0.422222i | ||||
\(582\) | 2.13360 | − | 8.97298i | 0.0884408 | − | 0.371942i | ||||
\(583\) | −5.59831 | + | 1.50006i | −0.231858 | + | 0.0621262i | ||||
\(584\) | −6.62852 | −0.274290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.00174 | 0.165310 | ||||||||
\(587\) | −40.0121 | + | 10.7212i | −1.65147 | + | 0.442511i | −0.960025 | − | 0.279914i | \(-0.909694\pi\) |
−0.691449 | + | 0.722425i | \(0.743027\pi\) | |||||||
\(588\) | −0.913566 | + | 0.272772i | −0.0376748 | + | 0.0112489i | ||||
\(589\) | 9.22943 | − | 5.32861i | 0.380292 | − | 0.219562i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.659386 | − | 23.2495i | −0.0271235 | − | 0.956358i | ||||
\(592\) | 5.56137 | + | 20.7553i | 0.228571 | + | 0.853038i | ||||
\(593\) | 26.6583 | − | 26.6583i | 1.09473 | − | 1.09473i | 0.0997087 | − | 0.995017i | \(-0.468209\pi\) |
0.995017 | − | 0.0997087i | \(-0.0317911\pi\) | |||||||
\(594\) | −5.03939 | + | 3.51208i | −0.206769 | + | 0.144102i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.81726 | + | 1.62655i | 0.115400 | + | 0.0666260i | ||||
\(597\) | −20.9764 | + | 22.2009i | −0.858506 | + | 0.908624i | ||||
\(598\) | −3.06608 | + | 11.4428i | −0.125382 | + | 0.467930i | ||||
\(599\) | 13.2427 | + | 22.9370i | 0.541080 | + | 0.937178i | 0.998842 | + | 0.0481037i | \(0.0153178\pi\) |
−0.457762 | + | 0.889075i | \(0.651349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.26710 | − | 7.39084i | 0.174059 | − | 0.301479i | −0.765776 | − | 0.643107i | \(-0.777645\pi\) |
0.939835 | + | 0.341628i | \(0.110978\pi\) | |||||||
\(602\) | −3.74279 | − | 3.74279i | −0.152545 | − | 0.152545i | ||||
\(603\) | 2.02950 | − | 9.75641i | 0.0826475 | − | 0.397312i | ||||
\(604\) | 0.00111412i | 4.53329e-5i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.14351 | + | 5.10480i | 0.127696 | + | 0.207368i | ||||
\(607\) | −44.4113 | − | 11.9000i | −1.80260 | − | 0.483005i | −0.808220 | − | 0.588881i | \(-0.799569\pi\) |
−0.994379 | + | 0.105876i | \(0.966235\pi\) | |||||||
\(608\) | 1.62942 | + | 0.436602i | 0.0660818 | + | 0.0177066i | ||||
\(609\) | −2.96400 | − | 4.81329i | −0.120107 | − | 0.195045i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.0190i | 1.86173i | ||||||||
\(612\) | −0.192730 | + | 0.926510i | −0.00779064 | + | 0.0374520i | ||||
\(613\) | −17.3219 | − | 17.3219i | −0.699625 | − | 0.699625i | 0.264705 | − | 0.964330i | \(-0.414726\pi\) |
−0.964330 | + | 0.264705i | \(0.914726\pi\) | |||||||
\(614\) | 20.7039 | − | 35.8602i | 0.835542 | − | 1.44720i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.65929 | − | 4.60603i | −0.107146 | − | 0.185582i | ||||
\(617\) | −9.74553 | + | 36.3708i | −0.392340 | + | 1.46423i | 0.433923 | + | 0.900950i | \(0.357129\pi\) |
−0.826263 | + | 0.563284i | \(0.809538\pi\) | |||||||
\(618\) | −20.8694 | + | 22.0878i | −0.839492 | + | 0.888500i | ||||
\(619\) | −8.57434 | − | 4.95040i | −0.344632 | − | 0.198973i | 0.317687 | − | 0.948196i | \(-0.397094\pi\) |
−0.662318 | + | 0.749223i | \(0.730427\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.76710 | − | 4.71617i | 0.271554 | − | 0.189253i | ||||
\(622\) | −32.2255 | + | 32.2255i | −1.29213 | + | 1.29213i | ||||
\(623\) | 2.45353 | + | 9.15670i | 0.0982986 | + | 0.366855i | ||||
\(624\) | −0.973765 | − | 34.3344i | −0.0389818 | − | 1.37447i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26.9753 | + | 15.5742i | −1.07815 | + | 0.622469i | ||||
\(627\) | −2.22713 | + | 0.664976i | −0.0889431 | + | 0.0265566i | ||||
\(628\) | −1.60427 | + | 0.429864i | −0.0640175 | + | 0.0171534i | ||||
\(629\) | −9.67378 | −0.385719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0279 | −0.876918 | −0.438459 | − | 0.898751i | \(-0.644476\pi\) | ||||
−0.438459 | + | 0.898751i | \(0.644476\pi\) | |||||||
\(632\) | 22.0230 | − | 5.90104i | 0.876027 | − | 0.234731i | ||||
\(633\) | −0.0493675 | + | 0.207617i | −0.00196218 | + | 0.00825205i | ||||
\(634\) | −4.65268 | + | 2.68622i | −0.184781 | + | 0.106684i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.90665 | + | 1.17411i | −0.0756038 | + | 0.0465564i | ||||
\(637\) | 4.03223 | + | 15.0485i | 0.159763 | + | 0.596242i | ||||
\(638\) | −1.33171 | + | 1.33171i | −0.0527227 | + | 0.0527227i | ||||
\(639\) | −17.6655 | + | 1.00284i | −0.698836 | + | 0.0396716i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.8054 | + | 12.5894i | 0.861263 | + | 0.497251i | 0.864435 | − | 0.502744i | \(-0.167676\pi\) |
−0.00317173 | + | 0.999995i | \(0.501010\pi\) | |||||||
\(642\) | −8.68736 | − | 29.0956i | −0.342863 | − | 1.14831i | ||||
\(643\) | 8.05166 | − | 30.0492i | 0.317526 | − | 1.18502i | −0.604088 | − | 0.796918i | \(-0.706462\pi\) |
0.921614 | − | 0.388107i | \(-0.126871\pi\) | |||||||
\(644\) | 0.319219 | + | 0.552904i | 0.0125790 | + | 0.0217875i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64484 | − | 2.84895i | 0.0647154 | − | 0.112090i | ||||
\(647\) | −7.86580 | − | 7.86580i | −0.309237 | − | 0.309237i | 0.535377 | − | 0.844613i | \(-0.320170\pi\) |
−0.844613 | + | 0.535377i | \(0.820170\pi\) | |||||||
\(648\) | −16.5267 | + | 20.7755i | −0.649230 | + | 0.816140i | ||||
\(649\) | 6.72090i | 0.263818i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.7925 | + | 0.703147i | −0.971695 | + | 0.0275585i | ||||
\(652\) | 1.12456 | + | 0.301325i | 0.0440411 | + | 0.0118008i | ||||
\(653\) | −0.279676 | − | 0.0749391i | −0.0109446 | − | 0.00293259i | 0.253343 | − | 0.967377i | \(-0.418470\pi\) |
−0.264287 | + | 0.964444i | \(0.585137\pi\) | |||||||
\(654\) | 8.90457 | − | 16.4855i | 0.348196 | − | 0.644635i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.8384i | 0.501256i | ||||||||
\(657\) | 4.48917 | − | 5.02953i | 0.175139 | − | 0.196221i | ||||
\(658\) | −16.1106 | − | 16.1106i | −0.628058 | − | 0.628058i | ||||
\(659\) | −13.4009 | + | 23.2111i | −0.522026 | + | 0.904175i | 0.477646 | + | 0.878552i | \(0.341490\pi\) |
−0.999672 | + | 0.0256228i | \(0.991843\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6438 | − | 21.8997i | −0.491787 | − | 0.851800i | 0.508168 | − | 0.861258i | \(-0.330323\pi\) |
−0.999955 | + | 0.00945786i | \(0.996989\pi\) | |||||||
\(662\) | 2.07289 | − | 7.73611i | 0.0805650 | − | 0.300673i | ||||
\(663\) | 15.0443 | + | 3.57724i | 0.584271 | + | 0.138928i | ||||
\(664\) | 25.3823 | + | 14.6545i | 0.985024 | + | 0.568704i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.6622 | − | 10.9191i | −0.839393 | − | 0.423106i | ||||
\(667\) | 1.78827 | − | 1.78827i | 0.0692421 | − | 0.0692421i | ||||
\(668\) | 0.303196 | + | 1.13154i | 0.0117310 | + | 0.0437807i | ||||
\(669\) | 3.81556 | + | 2.06095i | 0.147518 | + | 0.0796811i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1231 | + | 5.84458i | −0.390799 | + | 0.225628i | ||||
\(672\) | −2.85362 | − | 2.69622i | −0.110081 | − | 0.104009i | ||||
\(673\) | 23.5227 | − | 6.30290i | 0.906735 | − | 0.242959i | 0.224829 | − | 0.974398i | \(-0.427818\pi\) |
0.681906 | + | 0.731439i | \(0.261151\pi\) | |||||||
\(674\) | 13.3044 | 0.512466 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.51002 | 0.135001 | ||||||||
\(677\) | 0.896681 | − | 0.240265i | 0.0344623 | − | 0.00923414i | −0.241547 | − | 0.970389i | \(-0.577655\pi\) |
0.276009 | + | 0.961155i | \(0.410988\pi\) | |||||||
\(678\) | 20.2949 | + | 19.1754i | 0.779420 | + | 0.736429i | ||||
\(679\) | −7.03407 | + | 4.06112i | −0.269943 | + | 0.155852i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2386 | − | 12.5522i | −0.890503 | − | 0.481000i | ||||
\(682\) | 2.13874 | + | 7.98188i | 0.0818966 | + | 0.305642i | ||||
\(683\) | −22.2024 | + | 22.2024i | −0.849550 | + | 0.849550i | −0.990077 | − | 0.140526i | \(-0.955120\pi\) |
0.140526 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(684\) | −0.750970 | + | 0.492340i | −0.0287141 | + | 0.0188251i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −23.3578 | − | 13.4856i | −0.891805 | − | 0.514884i | ||||
\(687\) | 37.1801 | + | 8.84071i | 1.41851 | + | 0.337294i | ||||
\(688\) | −1.77711 | + | 6.63225i | −0.0677515 | + | 0.252852i | ||||
\(689\) | 18.2945 | + | 31.6871i | 0.696966 | + | 1.20718i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.05877 | + | 7.02999i | −0.154403 | + | 0.267433i | −0.932841 | − | 0.360287i | \(-0.882679\pi\) |
0.778439 | + | 0.627721i | \(0.216012\pi\) | |||||||
\(692\) | 1.89711 | + | 1.89711i | 0.0721173 | + | 0.0721173i | ||||
\(693\) | 5.29593 | + | 1.10164i | 0.201176 | + | 0.0418479i | ||||
\(694\) | 14.2473i | 0.540821i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.86828 | + | 7.16156i | −0.146627 | + | 0.271458i | ||||
\(697\) | −5.58297 | − | 1.49595i | −0.211470 | − | 0.0566633i | ||||
\(698\) | −12.1157 | − | 3.24640i | −0.458586 | − | 0.122878i | ||||
\(699\) | −10.3369 | + | 0.293168i | −0.390979 | + | 0.0110887i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6359i | 0.741637i | 0.928705 | + | 0.370819i | \(0.120923\pi\) | ||||
−0.928705 | + | 0.370819i | \(0.879077\pi\) | |||||||
\(702\) | 29.6504 | + | 24.9913i | 1.11908 | + | 0.943236i | ||||
\(703\) | −6.49076 | − | 6.49076i | −0.244804 | − | 0.244804i | ||||
\(704\) | −3.79526 | + | 6.57359i | −0.143039 | + | 0.247752i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.8937 | − | 22.3325i | −0.485260 | − | 0.840496i | ||||
\(707\) | 1.36642 | − | 5.09956i | 0.0513896 | − | 0.191789i | ||||
\(708\) | 0.742876 | + | 2.48804i | 0.0279190 | + | 0.0935061i | ||||
\(709\) | 2.68383 | + | 1.54951i | 0.100793 | + | 0.0581931i | 0.549549 | − | 0.835461i | \(-0.314799\pi\) |
−0.448756 | + | 0.893654i | \(0.648133\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.4375 | + | 20.7069i | −0.391438 | + | 0.776569i | ||||
\(712\) | 9.65210 | − | 9.65210i | 0.361728 | − | 0.361728i | ||||
\(713\) | −2.87199 | − | 10.7184i | −0.107557 | − | 0.401408i | ||||
\(714\) | −6.51914 | + | 4.01445i | −0.243973 | + | 0.150237i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.93083 | + | 1.69211i | −0.109530 | + | 0.0632373i | ||||
\(717\) | −5.44280 | + | 22.8900i | −0.203265 | + | 0.854841i | ||||
\(718\) | 16.3380 | − | 4.37774i | 0.609727 | − | 0.163376i | ||||
\(719\) | 20.3126 | 0.757533 | 0.378767 | − | 0.925492i | \(-0.376348\pi\) | ||||
0.378767 | + | 0.925492i | \(0.376348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.7604 | 0.996608 | ||||||||
\(722\) | −21.6325 | + | 5.79640i | −0.805077 | + | 0.215720i | ||||
\(723\) | −8.52158 | + | 2.54437i | −0.316921 | + | 0.0946261i | ||||
\(724\) | −2.51149 | + | 1.45001i | −0.0933388 | + | 0.0538892i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.674315 | + | 23.7759i | 0.0250262 | + | 0.882407i | ||||
\(727\) | −4.57247 | − | 17.0647i | −0.169584 | − | 0.632895i | −0.997411 | − | 0.0719119i | \(-0.977090\pi\) |
0.827827 | − | 0.560983i | \(-0.189577\pi\) | |||||||
\(728\) | −23.7421 | + | 23.7421i | −0.879941 | + | 0.879941i | ||||
\(729\) | −4.57117 | − | 26.6102i | −0.169303 | − | 0.985564i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.67706 | − | 1.54560i | −0.0990147 | − | 0.0571662i | ||||
\(732\) | −3.10150 | + | 3.28256i | −0.114635 | + | 0.121327i | ||||
\(733\) | 6.82693 | − | 25.4785i | 0.252158 | − | 0.941068i | −0.717491 | − | 0.696568i | \(-0.754709\pi\) |
0.969649 | − | 0.244500i | \(-0.0786239\pi\) | |||||||
\(734\) | −18.9970 | − | 32.9038i | −0.701192 | − | 1.21450i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.878218 | − | 1.52112i | 0.0323715 | − | 0.0560692i | ||||
\(737\) | 2.06746 | + | 2.06746i | 0.0761558 | + | 0.0761558i | ||||
\(738\) | −10.8133 | − | 9.65150i | −0.398041 | − | 0.355277i | ||||
\(739\) | − | 6.41459i | − | 0.235965i | −0.993016 | − | 0.117982i | \(-0.962357\pi\) | ||
0.993016 | − | 0.117982i | \(-0.0376426\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.69396 | + | 12.4944i | 0.282645 | + | 0.458992i | ||||
\(742\) | −17.4979 | − | 4.68854i | −0.642368 | − | 0.172122i | ||||
\(743\) | 18.4970 | + | 4.95625i | 0.678588 | + | 0.181827i | 0.581620 | − | 0.813460i | \(-0.302419\pi\) |
0.0969677 | + | 0.995288i | \(0.469086\pi\) | |||||||
\(744\) | 18.7266 | + | 30.4104i | 0.686549 | + | 1.11490i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 3.13856i | − | 0.114911i | ||||||
\(747\) | −28.3096 | + | 9.33459i | −1.03579 | + | 0.341535i | ||||
\(748\) | −0.196335 | − | 0.196335i | −0.00717870 | − | 0.00717870i | ||||
\(749\) | −13.3702 | + | 23.1579i | −0.488536 | + | 0.846170i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.96958 | − | 3.41141i | −0.0718709 | − | 0.124484i | 0.827850 | − | 0.560949i | \(-0.189564\pi\) |
−0.899721 | + | 0.436465i | \(0.856230\pi\) | |||||||
\(752\) | −7.64946 | + | 28.5482i | −0.278947 | + | 1.04105i | ||||
\(753\) | 3.09541 | − | 3.27612i | 0.112803 | − | 0.119388i | ||||
\(754\) | 10.2966 | + | 5.94472i | 0.374979 | + | 0.216494i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.08229 | − | 0.177550i | 0.0757321 | − | 0.00645743i | ||||
\(757\) | −17.3710 | + | 17.3710i | −0.631361 | + | 0.631361i | −0.948409 | − | 0.317049i | \(-0.897308\pi\) |
0.317049 | + | 0.948409i | \(0.397308\pi\) | |||||||
\(758\) | 6.41725 | + | 23.9495i | 0.233085 | + | 0.869885i | ||||
\(759\) | 0.0686093 | + | 2.41912i | 0.00249036 | + | 0.0878085i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.11860 | − | 4.10993i | 0.258049 | − | 0.148985i | −0.365395 | − | 0.930853i | \(-0.619066\pi\) |
0.623444 | + | 0.781868i | \(0.285733\pi\) | |||||||
\(762\) | 5.99637 | − | 1.79039i | 0.217226 | − | 0.0648591i | ||||
\(763\) | −15.9380 | + | 4.27057i | −0.576994 | + | 0.154605i | ||||
\(764\) | −1.03558 | −0.0374660 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.5079 | −1.17456 | ||||||||
\(767\) | 40.9835 | − | 10.9815i | 1.47983 | − | 0.396519i | ||||
\(768\) | −1.86921 | + | 7.86108i | −0.0674495 | + | 0.283662i | ||||
\(769\) | 1.91615 | − | 1.10629i | 0.0690983 | − | 0.0398939i | −0.465053 | − | 0.885283i | \(-0.653965\pi\) |
0.534151 | + | 0.845389i | \(0.320631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.5677 | − | 9.58654i | 0.560659 | − | 0.345251i | ||||
\(772\) | −0.472918 | − | 1.76495i | −0.0170207 | − | 0.0635221i | ||||
\(773\) | 8.23173 | − | 8.23173i | 0.296075 | − | 0.296075i | −0.543400 | − | 0.839474i | \(-0.682863\pi\) |
0.839474 | + | 0.543400i | \(0.182863\pi\) | |||||||
\(774\) | −4.25009 | − | 6.48270i | −0.152766 | − | 0.233016i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.1286 | + | 5.84773i | 0.363595 | + | 0.209921i | ||||
\(777\) | 6.11191 | + | 20.4700i | 0.219264 | + | 0.734356i | ||||
\(778\) | 9.41596 | − | 35.1408i | 0.337579 | − | 1.25986i | ||||
\(779\) | −2.74224 | − | 4.74970i | −0.0982511 | − | 0.170176i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.59572 | − | 4.49591i | 0.0928820 | − | 0.160876i | ||||
\(782\) | −2.42204 | − | 2.42204i | −0.0866119 | − | 0.0866119i | ||||
\(783\) | −2.81419 | − | 7.78531i | −0.100571 | − | 0.278224i | ||||
\(784\) | 10.0057i | 0.357346i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 49.7006 | − | 1.40957i | 1.77276 | − | 0.0502778i | ||||
\(787\) | −33.8541 | − | 9.07119i | −1.20677 | − | 0.323353i | −0.401276 | − | 0.915957i | \(-0.631433\pi\) |
−0.805494 | + | 0.592604i | \(0.798100\pi\) | |||||||
\(788\) | 2.54665 | + | 0.682372i | 0.0907205 | + | 0.0243085i | ||||
\(789\) | −6.92440 | + | 12.8195i | −0.246515 | + | 0.456387i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24.5882i | − | 0.874256i | ||||||
\(792\) | −2.43912 | − | 7.39725i | −0.0866703 | − | 0.262850i | ||||
\(793\) | 52.1803 | + | 52.1803i | 1.85298 | + | 1.85298i | ||||
\(794\) | −17.3076 | + | 29.9776i | −0.614223 | + | 1.06387i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.73110 | − | 2.99835i | −0.0613571 | − | 0.106274i | ||||
\(797\) | 6.77343 | − | 25.2788i | 0.239927 | − | 0.895421i | −0.735938 | − | 0.677049i | \(-0.763259\pi\) |
0.975866 | − | 0.218372i | \(-0.0700747\pi\) | |||||||
\(798\) | −7.06766 | − | 1.68056i | −0.250192 | − | 0.0594910i | ||||
\(799\) | −11.5233 | − | 6.65297i | −0.407664 | − | 0.235365i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.786842 | + | 13.8606i | 0.0278017 | + | 0.489741i | ||||
\(802\) | 12.2041 | − | 12.2041i | 0.430941 | − | 0.430941i | ||||
\(803\) | 0.511942 | + | 1.91059i | 0.0180660 | + | 0.0674233i | ||||
\(804\) | 0.993882 | + | 0.536840i | 0.0350515 | + | 0.0189329i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 45.1784 | − | 26.0837i | 1.59134 | − | 0.918761i | ||||
\(807\) | −33.7038 | − | 31.8447i | −1.18643 | − | 1.12099i | ||||
\(808\) | −7.34301 | + | 1.96755i | −0.258326 | + | 0.0692183i | ||||
\(809\) | 40.3389 | 1.41824 | 0.709120 | − | 0.705088i | \(-0.249092\pi\) | ||||
0.709120 | + | 0.705088i | \(0.249092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.50040 | −0.158030 | −0.0790152 | − | 0.996873i | \(-0.525178\pi\) | ||||
−0.0790152 | + | 0.996873i | \(0.525178\pi\) | |||||||
\(812\) | 0.618923 | − | 0.165840i | 0.0217199 | − | 0.00581984i | ||||
\(813\) | −23.3981 | − | 22.1075i | −0.820606 | − | 0.775343i | ||||
\(814\) | 6.16394 | − | 3.55875i | 0.216046 | − | 0.124734i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.73818 | + | 4.71988i | 0.305898 | + | 0.165229i | ||||
\(817\) | −0.759168 | − | 2.83326i | −0.0265599 | − | 0.0991231i | ||||
\(818\) | 24.3930 | − | 24.3930i | 0.852880 | − | 0.852880i | ||||
\(819\) | −1.93546 | − | 34.0942i | −0.0676306 | − | 1.19135i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3109 | + | 7.68503i | 0.464552 | + | 0.268209i | 0.713956 | − | 0.700190i | \(-0.246901\pi\) |
−0.249404 | + | 0.968399i | \(0.580235\pi\) | |||||||
\(822\) | 15.5238 | + | 3.69127i | 0.541456 | + | 0.128748i | ||||
\(823\) | −3.77065 | + | 14.0723i | −0.131437 | + | 0.490528i | −0.999987 | − | 0.00507263i | \(-0.998385\pi\) |
0.868551 | + | 0.495601i | \(0.165052\pi\) | |||||||
\(824\) | −19.2665 | − | 33.3706i | −0.671182 | − | 1.16252i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.5033 | + | 18.1923i | −0.365457 | + | 0.632989i | ||||
\(827\) | 3.31824 | + | 3.31824i | 0.115387 | + | 0.115387i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
−0.647056 | + | 0.762443i | \(0.724000\pi\) | |||||||
\(828\) | 0.292790 | + | 0.887961i | 0.0101752 | + | 0.0308588i | ||||
\(829\) | − | 33.9539i | − | 1.17927i | −0.807671 | − | 0.589633i | \(-0.799272\pi\) | ||
0.807671 | − | 0.589633i | \(-0.200728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.4302 | − | 41.5263i | 0.778094 | − | 1.44053i | ||||
\(832\) | 46.2865 | + | 12.4024i | 1.60469 | + | 0.429977i | ||||
\(833\) | −4.35112 | − | 1.16588i | −0.150757 | − | 0.0403953i | ||||
\(834\) | −3.35248 | + | 0.0950807i | −0.116087 | + | 0.00329237i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 0.263467i | − | 0.00911220i | ||||||
\(837\) | −35.7571 | − | 6.38629i | −1.23595 | − | 0.220743i | ||||
\(838\) | 11.6473 | + | 11.6473i | 0.402349 | + | 0.402349i | ||||
\(839\) | 5.71824 | − | 9.90428i | 0.197416 | − | 0.341934i | −0.750274 | − | 0.661127i | \(-0.770079\pi\) |
0.947690 | + | 0.319193i | \(0.103412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2309 | + | 22.9166i | 0.456238 | + | 0.790228i | ||||
\(842\) | 5.03357 | − | 18.7855i | 0.173468 | − | 0.647392i | ||||
\(843\) | −12.9918 | − | 43.5119i | −0.447460 | − | 1.49863i | ||||
\(844\) | −0.0209495 | − | 0.0120952i | −0.000721111 | − | 0.000416334i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.2943 | − | 27.9044i | −0.628972 | − | 0.959374i | ||||
\(847\) | 14.8113 | − | 14.8113i | 0.508923 | − | 0.508923i | ||||
\(848\) | 6.08198 | + | 22.6983i | 0.208856 | + | 0.779462i | ||||
\(849\) | 5.25321 | − | 3.23490i | 0.180290 | − | 0.111021i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.27720 | + | 4.77884i | −0.283739 | + | 0.163817i | ||||
\(852\) | 0.463975 | − | 1.95127i | 0.0158955 | − | 0.0668494i | ||||
\(853\) | −23.0994 | + | 6.18947i | −0.790909 | + | 0.211923i | −0.631589 | − | 0.775304i | \(-0.717597\pi\) |
−0.159320 | + | 0.987227i | \(0.550930\pi\) | |||||||
\(854\) | −36.5353 | −1.25021 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.5043 | 1.31605 | ||||||||
\(857\) | 14.4874 | − | 3.88189i | 0.494881 | − | 0.132603i | −0.00274224 | − | 0.999996i | \(-0.500873\pi\) |
0.497623 | + | 0.867393i | \(0.334206\pi\) | |||||||
\(858\) | −10.9019 | + | 3.25508i | −0.372184 | + | 0.111127i | ||||
\(859\) | 37.5983 | − | 21.7074i | 1.28284 | − | 0.740646i | 0.305471 | − | 0.952201i | \(-0.401186\pi\) |
0.977366 | + | 0.211555i | \(0.0678529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.361857 | + | 12.7589i | 0.0123321 | + | 0.434821i | ||||
\(862\) | −12.5016 | − | 46.6567i | −0.425807 | − | 1.58913i | ||||
\(863\) | 2.78648 | − | 2.78648i | 0.0948527 | − | 0.0948527i | −0.658088 | − | 0.752941i | \(-0.728635\pi\) |
0.752941 | + | 0.658088i | \(0.228635\pi\) | |||||||
\(864\) | −3.28736 | − | 4.71694i | −0.111838 | − | 0.160474i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.545339 | − | 0.314852i | −0.0185314 | − | 0.0106991i | ||||
\(867\) | 17.1513 | − | 18.1526i | 0.582490 | − | 0.616495i | ||||
\(868\) | 0.727658 | − | 2.71566i | 0.0246983 | − | 0.0921754i | ||||
\(869\) | −3.40181 | − | 5.89211i | −0.115399 | − | 0.199876i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.22911 | − | 15.9853i | 0.312717 | − | 0.541641i | ||||
\(872\) | 16.8003 | + | 16.8003i | 0.568929 | + | 0.568929i | ||||
\(873\) | −11.2967 | + | 3.72489i | −0.382335 | + | 0.126068i | ||||
\(874\) | − | 3.25020i | − | 0.109940i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.400700 | + | 0.650704i | 0.0135384 | + | 0.0219852i | ||||
\(877\) | 41.5598 | + | 11.1359i | 1.40338 | + | 0.376033i | 0.879556 | − | 0.475796i | \(-0.157840\pi\) |
0.523820 | + | 0.851829i | \(0.324507\pi\) | |||||||
\(878\) | −1.93163 | − | 0.517577i | −0.0651892 | − | 0.0174674i | ||||
\(879\) | −2.70616 | − | 4.39458i | −0.0912764 | − | 0.148225i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 47.0487i | − | 1.58511i | −0.609801 | − | 0.792555i | \(-0.708751\pi\) | ||
0.609801 | − | 0.792555i | \(-0.291249\pi\) | |||||||
\(882\) | −8.42736 | − | 7.52195i | −0.283764 | − | 0.253277i | ||||
\(883\) | −21.0669 | − | 21.0669i | −0.708957 | − | 0.708957i | 0.257359 | − | 0.966316i | \(-0.417148\pi\) |
−0.966316 | + | 0.257359i | \(0.917148\pi\) | |||||||
\(884\) | −0.876436 | + | 1.51803i | −0.0294777 | + | 0.0510569i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.5140 | + | 37.2633i | 0.722776 | + | 1.25188i | ||||
\(887\) | −0.939801 | + | 3.50739i | −0.0315554 | + | 0.117766i | −0.979907 | − | 0.199454i | \(-0.936083\pi\) |
0.948352 | + | 0.317221i | \(0.102750\pi\) | |||||||
\(888\) | 21.1260 | − | 22.3593i | 0.708943 | − | 0.750330i | ||||
\(889\) | −4.77265 | − | 2.75549i | −0.160069 | − | 0.0924161i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.26472 | + | 3.15906i | 0.243377 | + | 0.105833i | ||||
\(892\) | −0.347592 | + | 0.347592i | −0.0116382 | + | 0.0116382i | ||||
\(893\) | −3.26780 | − | 12.1956i | −0.109353 | − | 0.408110i | ||||
\(894\) | 1.09267 | + | 38.5269i | 0.0365444 | + | 1.28853i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.6203 | + | 9.59572i | −0.555245 | + | 0.320571i | ||||
\(897\) | 14.6395 | − | 4.37106i | 0.488799 | − | 0.145945i | ||||
\(898\) | −28.3167 | + | 7.58743i | −0.944939 | + | 0.253196i | ||||
\(899\) | −11.1368 | −0.371433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5794 | −0.352450 | ||||||||
\(902\) | 4.10768 | − | 1.10065i | 0.136771 | − | 0.0366477i | ||||
\(903\) | −1.57916 | + | 6.64125i | −0.0525512 | + | 0.221007i | ||||
\(904\) | −30.6619 | + | 17.7026i | −1.01980 | + | 0.588781i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.0112398 | + | 0.00692143i | −0.000373419 | + | 0.000229949i | ||||
\(907\) | 2.71600 | + | 10.1363i | 0.0901833 | + | 0.336569i | 0.996245 | − | 0.0865764i | \(-0.0275927\pi\) |
−0.906062 | + | 0.423145i | \(0.860926\pi\) | |||||||
\(908\) | 2.11700 | − | 2.11700i | 0.0702551 | − | 0.0702551i | ||||
\(909\) | 3.48014 | − | 6.90419i | 0.115429 | − | 0.228998i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.77512 | + | 3.91162i | 0.224470 | + | 0.129598i | 0.608018 | − | 0.793923i | \(-0.291965\pi\) |
−0.383548 | + | 0.923521i | \(0.625298\pi\) | |||||||
\(912\) | 2.69614 | + | 9.02988i | 0.0892780 | + | 0.299009i | ||||
\(913\) | 2.26362 | − | 8.44796i | 0.0749150 | − | 0.279587i | ||||
\(914\) | −0.612004 | − | 1.06002i | −0.0202433 | − | 0.0350624i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.16600 | + | 3.75163i | −0.0715668 | + | 0.123957i | ||||
\(917\) | −30.9612 | − | 30.9612i | −1.02243 | − | 1.02243i | ||||
\(918\) | −10.5444 | + | 3.81155i | −0.348019 | + | 0.125800i | ||||
\(919\) | 4.61000i | 0.152070i | 0.997105 | + | 0.0760349i | \(0.0242260\pi\) | ||||
−0.997105 | + | 0.0760349i | \(0.975774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.3815 | + | 1.51397i | −1.75898 | + | 0.0498869i | ||||
\(922\) | 28.0591 | + | 7.51842i | 0.924078 | + | 0.247606i | ||||
\(923\) | −31.6570 | − | 8.48246i | −1.04200 | − | 0.279204i | ||||
\(924\) | −0.291405 | + | 0.539494i | −0.00958651 | + | 0.0177481i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 25.1999i | − | 0.828122i | ||||||
\(927\) | 38.3689 | + | 7.98139i | 1.26020 | + | 0.262143i | ||||
\(928\) | −1.24650 | − | 1.24650i | −0.0409182 | − | 0.0409182i | ||||
\(929\) | 15.7062 | − | 27.2039i | 0.515302 | − | 0.892530i | −0.484540 | − | 0.874769i | \(-0.661013\pi\) |
0.999842 | − | 0.0177609i | \(-0.00565375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.13718 | − | 3.70170i | −0.0700433 | − | 0.121318i | ||||
\(932\) | 0.303388 | − | 1.13226i | 0.00993782 | − | 0.0370884i | ||||
\(933\) | 57.1814 | + | 13.5966i | 1.87203 | + | 0.445134i | ||||
\(934\) | −27.6818 | − | 15.9821i | −0.905778 | − | 0.522951i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −41.1225 | + | 26.9602i | −1.34413 | + | 0.881221i | ||||
\(937\) | 21.3617 | − | 21.3617i | 0.697856 | − | 0.697856i | −0.266092 | − | 0.963948i | \(-0.585732\pi\) |
0.963948 | + | 0.266092i | \(0.0857324\pi\) | |||||||
\(938\) | 2.36525 | + | 8.82722i | 0.0772281 | + | 0.288219i | ||||
\(939\) | 35.3449 | + | 19.0914i | 1.15344 | + | 0.623023i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.77035 | + | 3.33151i | −0.188108 | + | 0.108604i | −0.591096 | − | 0.806601i | \(-0.701305\pi\) |
0.402989 | + | 0.915205i | \(0.367971\pi\) | |||||||
\(942\) | −14.3032 | − | 13.5142i | −0.466023 | − | 0.440318i | ||||
\(943\) | −5.51597 | + | 1.47800i | −0.179625 | + | 0.0481303i | ||||
\(944\) | 27.2498 | 0.886905 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.27436 | 0.0739458 | ||||||||
\(947\) | −3.23873 | + | 0.867814i | −0.105245 | + | 0.0282002i | −0.311057 | − | 0.950391i | \(-0.600683\pi\) |
0.205812 | + | 0.978591i | \(0.434016\pi\) | |||||||
\(948\) | −1.91060 | − | 1.80521i | −0.0620534 | − | 0.0586306i | ||||
\(949\) | 10.8142 | − | 6.24356i | 0.351043 | − | 0.202675i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.09628 | + | 3.29287i | 0.197685 | + | 0.106779i | ||||
\(952\) | −2.51269 | − | 9.37748i | −0.0814367 | − | 0.303926i | ||||
\(953\) | 30.7161 | − | 30.7161i | 0.994992 | − | 0.994992i | −0.00499525 | − | 0.999988i | \(-0.501590\pi\) |
0.999988 | + | 0.00499525i | \(0.00159004\pi\) | |||||||
\(954\) | −23.6900 | − | 11.9412i | −0.766993 | − | 0.386612i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.30970 | − | 1.33350i | −0.0747009 | − | 0.0431286i | ||||
\(957\) | 2.36300 | + | 0.561875i | 0.0763848 | + | 0.0181629i | ||||
\(958\) | −6.19919 | + | 23.1357i | −0.200287 | + | 0.747480i | ||||
\(959\) | −7.02601 | − | 12.1694i | −0.226882 | − | 0.392970i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.93253 | + | 15.4716i | −0.288146 | + | 0.499084i | ||||
\(962\) | −31.7725 | − | 31.7725i | −1.02439 | − | 1.02439i | ||||
\(963\) | −26.0771 | + | 29.2160i | −0.840322 | + | 0.941471i | ||||
\(964\) | − | 1.00809i | − | 0.0324684i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.59485 | + | 6.65535i | −0.115662 | + | 0.214132i | ||||
\(967\) | −5.53906 | − | 1.48419i | −0.178124 | − | 0.0477282i | 0.168654 | − | 0.985675i | \(-0.446058\pi\) |
−0.346779 | + | 0.937947i | \(0.612724\pi\) | |||||||
\(968\) | −29.1336 | − | 7.80632i | −0.936388 | − | 0.250904i | ||||
\(969\) | −4.24094 | + | 0.120278i | −0.136238 | + | 0.00386389i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14.2248i | − | 0.456496i | −0.973603 | − | 0.228248i | \(-0.926700\pi\) | ||
0.973603 | − | 0.228248i | \(-0.0732998\pi\) | |||||||
\(972\) | 3.03853 | + | 0.366480i | 0.0974610 | + | 0.0117549i | ||||
\(973\) | 2.08844 | + | 2.08844i | 0.0669524 | + | 0.0669524i | ||||
\(974\) | −20.7244 | + | 35.8957i | −0.664052 | + | 1.15017i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.6968 | + | 41.0440i | 0.758516 | + | 1.31379i | ||||
\(977\) | −8.07944 | + | 30.1529i | −0.258484 | + | 0.964676i | 0.707635 | + | 0.706578i | \(0.249762\pi\) |
−0.966119 | + | 0.258097i | \(0.916904\pi\) | |||||||
\(978\) | 3.94636 | + | 13.2171i | 0.126191 | + | 0.422636i | ||||
\(979\) | −3.52757 | − | 2.03664i | −0.112742 | − | 0.0650913i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.1256 | + | 1.36956i | −0.770270 | + | 0.0437268i | ||||
\(982\) | −38.5627 | + | 38.5627i | −1.23059 | + | 1.23059i | ||||
\(983\) | −2.66543 | − | 9.94750i | −0.0850139 | − | 0.317276i | 0.910303 | − | 0.413943i | \(-0.135849\pi\) |
−0.995317 | + | 0.0966666i | \(0.969182\pi\) | |||||||
\(984\) | 15.6500 | − | 9.63718i | 0.498903 | − | 0.307222i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.97715 | + | 1.71886i | −0.0948116 | + | 0.0547395i | ||||
\(987\) | −6.79742 | + | 28.5869i | −0.216364 | + | 0.909932i | ||||
\(988\) | −1.60660 | + | 0.430488i | −0.0511128 | + | 0.0136956i | ||||
\(989\) | −3.05411 | −0.0971150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9180 | 1.20450 | 0.602252 | − | 0.798306i | \(-0.294270\pi\) | ||||
0.602252 | + | 0.798306i | \(0.294270\pi\) | |||||||
\(992\) | −7.47116 | + | 2.00189i | −0.237210 | + | 0.0635601i | ||||
\(993\) | −9.89733 | + | 2.95514i | −0.314082 | + | 0.0937785i | ||||
\(994\) | 14.0523 | − | 8.11308i | 0.445711 | − | 0.257331i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0957926 | − | 3.37759i | −0.00303530 | − | 0.107023i | ||||
\(997\) | 8.06937 | + | 30.1153i | 0.255559 | + | 0.953761i | 0.967778 | + | 0.251804i | \(0.0810237\pi\) |
−0.712219 | + | 0.701957i | \(0.752310\pi\) | |||||||
\(998\) | 40.9452 | − | 40.9452i | 1.29610 | − | 1.29610i | ||||
\(999\) | 2.65799 | + | 31.1727i | 0.0840952 | + | 0.986260i |
(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 | 225.2.p.b.218.1 | 16 | ||
3.2 | odd | 2 | 675.2.q.a.143.4 | 16 | |||
5.2 | odd | 4 | inner | 225.2.p.b.182.1 | 16 | ||
5.3 | odd | 4 | 45.2.l.a.2.4 | ✓ | 16 | ||
5.4 | even | 2 | 45.2.l.a.38.4 | yes | 16 | ||
9.4 | even | 3 | 675.2.q.a.368.4 | 16 | |||
9.5 | odd | 6 | inner | 225.2.p.b.68.1 | 16 | ||
15.2 | even | 4 | 675.2.q.a.332.4 | 16 | |||
15.8 | even | 4 | 135.2.m.a.62.1 | 16 | |||
15.14 | odd | 2 | 135.2.m.a.8.1 | 16 | |||
20.3 | even | 4 | 720.2.cu.c.497.3 | 16 | |||
20.19 | odd | 2 | 720.2.cu.c.353.4 | 16 | |||
45.4 | even | 6 | 135.2.m.a.98.1 | 16 | |||
45.13 | odd | 12 | 135.2.m.a.17.1 | 16 | |||
45.14 | odd | 6 | 45.2.l.a.23.4 | yes | 16 | ||
45.22 | odd | 12 | 675.2.q.a.557.4 | 16 | |||
45.23 | even | 12 | 45.2.l.a.32.4 | yes | 16 | ||
45.29 | odd | 6 | 405.2.f.a.323.6 | 16 | |||
45.32 | even | 12 | inner | 225.2.p.b.32.1 | 16 | ||
45.34 | even | 6 | 405.2.f.a.323.3 | 16 | |||
45.38 | even | 12 | 405.2.f.a.242.3 | 16 | |||
45.43 | odd | 12 | 405.2.f.a.242.6 | 16 | |||
180.23 | odd | 12 | 720.2.cu.c.257.4 | 16 | |||
180.59 | even | 6 | 720.2.cu.c.113.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.l.a.2.4 | ✓ | 16 | 5.3 | odd | 4 | ||
45.2.l.a.23.4 | yes | 16 | 45.14 | odd | 6 | ||
45.2.l.a.32.4 | yes | 16 | 45.23 | even | 12 | ||
45.2.l.a.38.4 | yes | 16 | 5.4 | even | 2 | ||
135.2.m.a.8.1 | 16 | 15.14 | odd | 2 | |||
135.2.m.a.17.1 | 16 | 45.13 | odd | 12 | |||
135.2.m.a.62.1 | 16 | 15.8 | even | 4 | |||
135.2.m.a.98.1 | 16 | 45.4 | even | 6 | |||
225.2.p.b.32.1 | 16 | 45.32 | even | 12 | inner | ||
225.2.p.b.68.1 | 16 | 9.5 | odd | 6 | inner | ||
225.2.p.b.182.1 | 16 | 5.2 | odd | 4 | inner | ||
225.2.p.b.218.1 | 16 | 1.1 | even | 1 | trivial | ||
405.2.f.a.242.3 | 16 | 45.38 | even | 12 | |||
405.2.f.a.242.6 | 16 | 45.43 | odd | 12 | |||
405.2.f.a.323.3 | 16 | 45.34 | even | 6 | |||
405.2.f.a.323.6 | 16 | 45.29 | odd | 6 | |||
675.2.q.a.143.4 | 16 | 3.2 | odd | 2 | |||
675.2.q.a.332.4 | 16 | 15.2 | even | 4 | |||
675.2.q.a.368.4 | 16 | 9.4 | even | 3 | |||
675.2.q.a.557.4 | 16 | 45.22 | odd | 12 | |||
720.2.cu.c.113.3 | 16 | 180.59 | even | 6 | |||
720.2.cu.c.257.4 | 16 | 180.23 | odd | 12 | |||
720.2.cu.c.353.4 | 16 | 20.19 | odd | 2 | |||
720.2.cu.c.497.3 | 16 | 20.3 | even | 4 |