Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(407,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.407");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.j (of order \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 743.5 | ||
Root | \(-1.85804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.743 |
Dual form | 1050.2.j.c.407.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.510256 | − | 1.65519i | −0.294597 | − | 0.955622i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.809587 | − | 1.53120i | 0.330513 | − | 0.625109i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.47928 | + | 1.68914i | −0.826426 | + | 0.563046i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.598662i | 0.180503i | 0.995919 | + | 0.0902516i | \(0.0287671\pi\) | ||||
−0.995919 | + | 0.0902516i | \(0.971233\pi\) | |||||||
\(12\) | 1.65519 | − | 0.510256i | 0.477811 | − | 0.147298i | ||||
\(13\) | −2.55914 | − | 2.55914i | −0.709778 | − | 0.709778i | 0.256710 | − | 0.966488i | \(-0.417361\pi\) |
−0.966488 | + | 0.256710i | \(0.917361\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.20435 | − | 4.20435i | −1.01971 | − | 1.01971i | −0.999802 | − | 0.0199035i | \(-0.993664\pi\) |
−0.0199035 | − | 0.999802i | \(-0.506336\pi\) | |||||||
\(18\) | −2.94751 | − | 0.558713i | −0.694736 | − | 0.131690i | ||||
\(19\) | − | 5.70208i | − | 1.30815i | −0.756431 | − | 0.654074i | \(-0.773059\pi\) | ||
0.756431 | − | 0.654074i | \(-0.226941\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.53120 | + | 0.809587i | 0.334135 | + | 0.176666i | ||||
\(22\) | −0.423318 | + | 0.423318i | −0.0902516 | + | 0.0902516i | ||||
\(23\) | 2.23887 | − | 2.23887i | 0.466837 | − | 0.466837i | −0.434051 | − | 0.900888i | \(-0.642916\pi\) |
0.900888 | + | 0.434051i | \(0.142916\pi\) | |||||||
\(24\) | 1.53120 | + | 0.809587i | 0.312555 | + | 0.165256i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.61917i | − | 0.709778i | ||||||
\(27\) | 4.06090 | + | 3.24177i | 0.781521 | + | 0.623879i | ||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | −0.0410252 | −0.00761819 | −0.00380909 | − | 0.999993i | \(-0.501212\pi\) | ||||
−0.00380909 | + | 0.999993i | \(0.501212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.68243 | −1.55941 | −0.779705 | − | 0.626147i | \(-0.784631\pi\) | ||||
−0.779705 | + | 0.626147i | \(0.784631\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0.990896 | − | 0.305471i | 0.172493 | − | 0.0531756i | ||||
\(34\) | − | 5.94585i | − | 1.01971i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.68914 | − | 2.47928i | −0.281523 | − | 0.413213i | ||||
\(37\) | −1.56975 | + | 1.56975i | −0.258066 | + | 0.258066i | −0.824267 | − | 0.566201i | \(-0.808413\pi\) |
0.566201 | + | 0.824267i | \(0.308413\pi\) | |||||||
\(38\) | 4.03198 | − | 4.03198i | 0.654074 | − | 0.654074i | ||||
\(39\) | −2.93004 | + | 5.54167i | −0.469181 | + | 0.887378i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.79231i | − | 0.904608i | −0.891864 | − | 0.452304i | \(-0.850602\pi\) | ||
0.891864 | − | 0.452304i | \(-0.149398\pi\) | |||||||
\(42\) | 0.510256 | + | 1.65519i | 0.0787343 | + | 0.255401i | ||||
\(43\) | −0.325797 | − | 0.325797i | −0.0496835 | − | 0.0496835i | 0.681829 | − | 0.731512i | \(-0.261185\pi\) |
−0.731512 | + | 0.681829i | \(0.761185\pi\) | |||||||
\(44\) | −0.598662 | −0.0902516 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.16624 | 0.466837 | ||||||||
\(47\) | 1.56415 | + | 1.56415i | 0.228154 | + | 0.228154i | 0.811921 | − | 0.583767i | \(-0.198422\pi\) |
−0.583767 | + | 0.811921i | \(0.698422\pi\) | |||||||
\(48\) | 0.510256 | + | 1.65519i | 0.0736492 | + | 0.238905i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.81369 | + | 9.10428i | −0.674051 | + | 1.27485i | ||||
\(52\) | 2.55914 | − | 2.55914i | 0.354889 | − | 0.354889i | ||||
\(53\) | 2.01202 | − | 2.01202i | 0.276372 | − | 0.276372i | −0.555287 | − | 0.831659i | \(-0.687392\pi\) |
0.831659 | + | 0.555287i | \(0.187392\pi\) | |||||||
\(54\) | 0.579214 | + | 5.16377i | 0.0788210 | + | 0.702700i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | −9.43801 | + | 2.90952i | −1.25009 | + | 0.385376i | ||||
\(58\) | −0.0290092 | − | 0.0290092i | −0.00380909 | − | 0.00380909i | ||||
\(59\) | −9.35820 | −1.21833 | −0.609167 | − | 0.793042i | \(-0.708496\pi\) | ||||
−0.609167 | + | 0.793042i | \(0.708496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.8424 | −1.90038 | −0.950190 | − | 0.311670i | \(-0.899112\pi\) | ||||
−0.950190 | + | 0.311670i | \(0.899112\pi\) | |||||||
\(62\) | −6.13941 | − | 6.13941i | −0.779705 | − | 0.779705i | ||||
\(63\) | 0.558713 | − | 2.94751i | 0.0703912 | − | 0.371352i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.916670 | + | 0.484669i | 0.112834 | + | 0.0596586i | ||||
\(67\) | −5.89503 | + | 5.89503i | −0.720192 | + | 0.720192i | −0.968644 | − | 0.248452i | \(-0.920078\pi\) |
0.248452 | + | 0.968644i | \(0.420078\pi\) | |||||||
\(68\) | 4.20435 | − | 4.20435i | 0.509853 | − | 0.509853i | ||||
\(69\) | −4.84814 | − | 2.56335i | −0.583648 | − | 0.308591i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4437i | − | 1.71415i | −0.515194 | − | 0.857074i | \(-0.672280\pi\) | ||
0.515194 | − | 0.857074i | \(-0.327720\pi\) | |||||||
\(72\) | 0.558713 | − | 2.94751i | 0.0658450 | − | 0.347368i | ||||
\(73\) | 9.67606 | + | 9.67606i | 1.13250 | + | 1.13250i | 0.989761 | + | 0.142737i | \(0.0455903\pi\) |
0.142737 | + | 0.989761i | \(0.454410\pi\) | |||||||
\(74\) | −2.21997 | −0.258066 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.70208 | 0.654074 | ||||||||
\(77\) | −0.423318 | − | 0.423318i | −0.0482415 | − | 0.0482415i | ||||
\(78\) | −5.99040 | + | 1.84671i | −0.678280 | + | 0.209098i | ||||
\(79\) | 11.7772i | 1.32504i | 0.749046 | + | 0.662518i | \(0.230512\pi\) | ||||
−0.749046 | + | 0.662518i | \(0.769488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.29363 | − | 8.37568i | 0.365959 | − | 0.930631i | ||||
\(82\) | 4.09578 | − | 4.09578i | 0.452304 | − | 0.452304i | ||||
\(83\) | 1.04802 | − | 1.04802i | 0.115035 | − | 0.115035i | −0.647246 | − | 0.762281i | \(-0.724079\pi\) |
0.762281 | + | 0.647246i | \(0.224079\pi\) | |||||||
\(84\) | −0.809587 | + | 1.53120i | −0.0883332 | + | 0.167067i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.460746i | − | 0.0496835i | ||||||
\(87\) | 0.0209334 | + | 0.0679043i | 0.00224429 | + | 0.00728010i | ||||
\(88\) | −0.423318 | − | 0.423318i | −0.0451258 | − | 0.0451258i | ||||
\(89\) | 18.1407 | 1.92292 | 0.961458 | − | 0.274953i | \(-0.0886624\pi\) | ||||
0.961458 | + | 0.274953i | \(0.0886624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.61917 | 0.379393 | ||||||||
\(92\) | 2.23887 | + | 2.23887i | 0.233418 | + | 0.233418i | ||||
\(93\) | 4.43026 | + | 14.3710i | 0.459397 | + | 1.49021i | ||||
\(94\) | 2.21204i | 0.228154i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.809587 | + | 1.53120i | −0.0826281 | + | 0.156277i | ||||
\(97\) | 4.69359 | − | 4.69359i | 0.476562 | − | 0.476562i | −0.427469 | − | 0.904030i | \(-0.640595\pi\) |
0.904030 | + | 0.427469i | \(0.140595\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | −1.01122 | − | 1.48425i | −0.101632 | − | 0.149173i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.02663i | − | 0.798680i | −0.916803 | − | 0.399340i | \(-0.869239\pi\) | ||
0.916803 | − | 0.399340i | \(-0.130761\pi\) | |||||||
\(102\) | −9.84149 | + | 3.03391i | −0.974453 | + | 0.300402i | ||||
\(103\) | −9.14232 | − | 9.14232i | −0.900819 | − | 0.900819i | 0.0946877 | − | 0.995507i | \(-0.469815\pi\) |
−0.995507 | + | 0.0946877i | \(0.969815\pi\) | |||||||
\(104\) | 3.61917 | 0.354889 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.84542 | 0.276372 | ||||||||
\(107\) | 0.372768 | + | 0.372768i | 0.0360368 | + | 0.0360368i | 0.724896 | − | 0.688859i | \(-0.241888\pi\) |
−0.688859 | + | 0.724896i | \(0.741888\pi\) | |||||||
\(108\) | −3.24177 | + | 4.06090i | −0.311939 | + | 0.390761i | ||||
\(109\) | 8.37785i | 0.802453i | 0.915979 | + | 0.401226i | \(0.131416\pi\) | ||||
−0.915979 | + | 0.401226i | \(0.868584\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.39921 | + | 1.79726i | 0.322639 | + | 0.170588i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | 4.65789 | − | 4.65789i | 0.438178 | − | 0.438178i | −0.453221 | − | 0.891398i | \(-0.649725\pi\) |
0.891398 | + | 0.453221i | \(0.149725\pi\) | |||||||
\(114\) | −8.73102 | − | 4.61633i | −0.817735 | − | 0.432359i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 0.0410252i | − | 0.00380909i | ||||||
\(117\) | 10.6676 | + | 2.02208i | 0.986217 | + | 0.186941i | ||||
\(118\) | −6.61725 | − | 6.61725i | −0.609167 | − | 0.609167i | ||||
\(119\) | 5.94585 | 0.545055 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6416 | 0.967419 | ||||||||
\(122\) | −10.4952 | − | 10.4952i | −0.950190 | − | 0.950190i | ||||
\(123\) | −9.58735 | + | 2.95556i | −0.864463 | + | 0.266494i | ||||
\(124\) | − | 8.68243i | − | 0.779705i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.47928 | − | 1.68914i | 0.220872 | − | 0.150480i | ||||
\(127\) | −2.75150 | + | 2.75150i | −0.244157 | + | 0.244157i | −0.818567 | − | 0.574411i | \(-0.805231\pi\) |
0.574411 | + | 0.818567i | \(0.305231\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −0.373014 | + | 0.705494i | −0.0328421 | + | 0.0621153i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2622i | 1.33346i | 0.745298 | + | 0.666731i | \(0.232307\pi\) | ||||
−0.745298 | + | 0.666731i | \(0.767693\pi\) | |||||||
\(132\) | 0.305471 | + | 0.990896i | 0.0265878 | + | 0.0862464i | ||||
\(133\) | 4.03198 | + | 4.03198i | 0.349617 | + | 0.349617i | ||||
\(134\) | −8.33683 | −0.720192 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.94585 | 0.509853 | ||||||||
\(137\) | −3.68517 | − | 3.68517i | −0.314845 | − | 0.314845i | 0.531938 | − | 0.846783i | \(-0.321464\pi\) |
−0.846783 | + | 0.531938i | \(0.821464\pi\) | |||||||
\(138\) | −1.61559 | − | 5.24071i | −0.137528 | − | 0.446119i | ||||
\(139\) | 10.4104i | 0.883003i | 0.897261 | + | 0.441501i | \(0.145554\pi\) | ||||
−0.897261 | + | 0.441501i | \(0.854446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.79084 | − | 3.38706i | 0.150816 | − | 0.285242i | ||||
\(142\) | 10.2132 | − | 10.2132i | 0.857074 | − | 0.857074i | ||||
\(143\) | 1.53206 | − | 1.53206i | 0.128117 | − | 0.128117i | ||||
\(144\) | 2.47928 | − | 1.68914i | 0.206606 | − | 0.140761i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.6840i | 1.13250i | ||||||||
\(147\) | −1.65519 | + | 0.510256i | −0.136517 | + | 0.0420852i | ||||
\(148\) | −1.56975 | − | 1.56975i | −0.129033 | − | 0.129033i | ||||
\(149\) | 12.7565 | 1.04506 | 0.522529 | − | 0.852622i | \(-0.324989\pi\) | ||||
0.522529 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.5026 | −1.50572 | −0.752862 | − | 0.658178i | \(-0.771327\pi\) | ||||
−0.752862 | + | 0.658178i | \(0.771327\pi\) | |||||||
\(152\) | 4.03198 | + | 4.03198i | 0.327037 | + | 0.327037i | ||||
\(153\) | 17.5255 | + | 3.32203i | 1.41685 | + | 0.268570i | ||||
\(154\) | − | 0.598662i | − | 0.0482415i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.54167 | − | 2.93004i | −0.443689 | − | 0.234591i | ||||
\(157\) | 0.0325033 | − | 0.0325033i | 0.00259405 | − | 0.00259405i | −0.705809 | − | 0.708403i | \(-0.749416\pi\) |
0.708403 | + | 0.705809i | \(0.249416\pi\) | |||||||
\(158\) | −8.32772 | + | 8.32772i | −0.662518 | + | 0.662518i | ||||
\(159\) | −4.35690 | − | 2.30362i | −0.345525 | − | 0.182689i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.16624i | 0.249535i | ||||||||
\(162\) | 8.25145 | − | 3.59355i | 0.648295 | − | 0.282336i | ||||
\(163\) | −9.48125 | − | 9.48125i | −0.742629 | − | 0.742629i | 0.230454 | − | 0.973083i | \(-0.425979\pi\) |
−0.973083 | + | 0.230454i | \(0.925979\pi\) | |||||||
\(164\) | 5.79231 | 0.452304 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.48212 | 0.115035 | ||||||||
\(167\) | 14.2927 | + | 14.2927i | 1.10600 | + | 1.10600i | 0.993671 | + | 0.112330i | \(0.0358315\pi\) |
0.112330 | + | 0.993671i | \(0.464168\pi\) | |||||||
\(168\) | −1.65519 | + | 0.510256i | −0.127700 | + | 0.0393671i | ||||
\(169\) | 0.0984218i | 0.00757091i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.63160 | + | 14.1370i | 0.736547 | + | 1.08109i | ||||
\(172\) | 0.325797 | − | 0.325797i | 0.0248418 | − | 0.0248418i | ||||
\(173\) | 13.1681 | − | 13.1681i | 1.00115 | − | 1.00115i | 0.00115154 | − | 0.999999i | \(-0.499633\pi\) |
0.999999 | − | 0.00115154i | \(-0.000366547\pi\) | |||||||
\(174\) | −0.0332135 | + | 0.0628177i | −0.00251791 | + | 0.00476220i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.598662i | − | 0.0451258i | ||||||
\(177\) | 4.77508 | + | 15.4896i | 0.358917 | + | 1.16427i | ||||
\(178\) | 12.8274 | + | 12.8274i | 0.961458 | + | 0.961458i | ||||
\(179\) | 3.19365 | 0.238705 | 0.119352 | − | 0.992852i | \(-0.461918\pi\) | ||||
0.119352 | + | 0.992852i | \(0.461918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7718 | 1.09798 | 0.548990 | − | 0.835829i | \(-0.315012\pi\) | ||||
0.548990 | + | 0.835829i | \(0.315012\pi\) | |||||||
\(182\) | 2.55914 | + | 2.55914i | 0.189696 | + | 0.189696i | ||||
\(183\) | 7.57345 | + | 24.5670i | 0.559846 | + | 1.81605i | ||||
\(184\) | 3.16624i | 0.233418i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.02918 | + | 13.2945i | −0.515405 | + | 0.974802i | ||||
\(187\) | 2.51698 | − | 2.51698i | 0.184060 | − | 0.184060i | ||||
\(188\) | −1.56415 | + | 1.56415i | −0.114077 | + | 0.114077i | ||||
\(189\) | −5.16377 | + | 0.579214i | −0.375609 | + | 0.0421316i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6699i | 0.772049i | 0.922489 | + | 0.386024i | \(0.126152\pi\) | ||||
−0.922489 | + | 0.386024i | \(0.873848\pi\) | |||||||
\(192\) | −1.65519 | + | 0.510256i | −0.119453 | + | 0.0368246i | ||||
\(193\) | −0.840964 | − | 0.840964i | −0.0605339 | − | 0.0605339i | 0.676192 | − | 0.736726i | \(-0.263629\pi\) |
−0.736726 | + | 0.676192i | \(0.763629\pi\) | |||||||
\(194\) | 6.63773 | 0.476562 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −18.2786 | − | 18.2786i | −1.30230 | − | 1.30230i | −0.926840 | − | 0.375456i | \(-0.877486\pi\) |
−0.375456 | − | 0.926840i | \(-0.622514\pi\) | |||||||
\(198\) | 0.334480 | − | 1.76456i | 0.0237705 | − | 0.125402i | ||||
\(199\) | − | 11.0697i | − | 0.784713i | −0.919813 | − | 0.392356i | \(-0.871660\pi\) | ||
0.919813 | − | 0.392356i | \(-0.128340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.7653 | + | 6.74939i | 0.900398 | + | 0.476065i | ||||
\(202\) | 5.67569 | − | 5.67569i | 0.399340 | − | 0.399340i | ||||
\(203\) | 0.0290092 | − | 0.0290092i | 0.00203605 | − | 0.00203605i | ||||
\(204\) | −9.10428 | − | 4.81369i | −0.637427 | − | 0.337025i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 12.9292i | − | 0.900819i | ||||||
\(207\) | −1.76902 | + | 9.33254i | −0.122955 | + | 0.648656i | ||||
\(208\) | 2.55914 | + | 2.55914i | 0.177445 | + | 0.177445i | ||||
\(209\) | 3.41362 | 0.236125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.97584 | −0.480236 | −0.240118 | − | 0.970744i | \(-0.577186\pi\) | ||||
−0.240118 | + | 0.970744i | \(0.577186\pi\) | |||||||
\(212\) | 2.01202 | + | 2.01202i | 0.138186 | + | 0.138186i | ||||
\(213\) | −23.9069 | + | 7.36997i | −1.63808 | + | 0.504982i | ||||
\(214\) | 0.527173i | 0.0360368i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.16377 | + | 0.579214i | −0.351350 | + | 0.0394105i | ||||
\(217\) | 6.13941 | − | 6.13941i | 0.416770 | − | 0.416770i | ||||
\(218\) | −5.92404 | + | 5.92404i | −0.401226 | + | 0.401226i | ||||
\(219\) | 11.0784 | − | 20.9530i | 0.748609 | − | 1.41587i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.5191i | 1.44753i | ||||||||
\(222\) | 1.13275 | + | 3.67445i | 0.0760253 | + | 0.246613i | ||||
\(223\) | 6.44180 | + | 6.44180i | 0.431375 | + | 0.431375i | 0.889096 | − | 0.457721i | \(-0.151334\pi\) |
−0.457721 | + | 0.889096i | \(0.651334\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.58726 | 0.438178 | ||||||||
\(227\) | 3.80409 | + | 3.80409i | 0.252487 | + | 0.252487i | 0.821989 | − | 0.569503i | \(-0.192864\pi\) |
−0.569503 | + | 0.821989i | \(0.692864\pi\) | |||||||
\(228\) | −2.90952 | − | 9.43801i | −0.192688 | − | 0.625047i | ||||
\(229\) | − | 16.2301i | − | 1.07252i | −0.844054 | − | 0.536258i | \(-0.819837\pi\) | ||
0.844054 | − | 0.536258i | \(-0.180163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.484669 | + | 0.916670i | −0.0318889 | + | 0.0603124i | ||||
\(232\) | 0.0290092 | − | 0.0290092i | 0.00190455 | − | 0.00190455i | ||||
\(233\) | 1.42491 | − | 1.42491i | 0.0933492 | − | 0.0933492i | −0.658890 | − | 0.752239i | \(-0.728974\pi\) |
0.752239 | + | 0.658890i | \(0.228974\pi\) | |||||||
\(234\) | 6.11328 | + | 8.97294i | 0.399638 | + | 0.586579i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 9.35820i | − | 0.609167i | ||||||
\(237\) | 19.4934 | − | 6.00938i | 1.26623 | − | 0.390351i | ||||
\(238\) | 4.20435 | + | 4.20435i | 0.272528 | + | 0.272528i | ||||
\(239\) | 10.0287 | 0.648706 | 0.324353 | − | 0.945936i | \(-0.394854\pi\) | ||||
0.324353 | + | 0.945936i | \(0.394854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.87963 | −0.185493 | −0.0927465 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927465 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(242\) | 7.52475 | + | 7.52475i | 0.483709 | + | 0.483709i | ||||
\(243\) | −15.5439 | − | 1.17782i | −0.997141 | − | 0.0755574i | ||||
\(244\) | − | 14.8424i | − | 0.950190i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.86918 | − | 4.68938i | −0.565478 | − | 0.298984i | ||||
\(247\) | −14.5924 | + | 14.5924i | −0.928495 | + | 0.928495i | ||||
\(248\) | 6.13941 | − | 6.13941i | 0.389853 | − | 0.389853i | ||||
\(249\) | −2.26942 | − | 1.19990i | −0.143818 | − | 0.0760408i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.73681i | 0.235865i | 0.993022 | + | 0.117933i | \(0.0376267\pi\) | ||||
−0.993022 | + | 0.117933i | \(0.962373\pi\) | |||||||
\(252\) | 2.94751 | + | 0.558713i | 0.185676 | + | 0.0351956i | ||||
\(253\) | 1.34033 | + | 1.34033i | 0.0842655 | + | 0.0842655i | ||||
\(254\) | −3.89122 | −0.244157 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.77237 | + | 9.77237i | 0.609584 | + | 0.609584i | 0.942837 | − | 0.333254i | \(-0.108147\pi\) |
−0.333254 | + | 0.942837i | \(0.608147\pi\) | |||||||
\(258\) | −0.762620 | + | 0.235099i | −0.0474787 | + | 0.0146366i | ||||
\(259\) | − | 2.21997i | − | 0.137942i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.101713 | − | 0.0692972i | 0.00629586 | − | 0.00428939i | ||||
\(262\) | −10.7920 | + | 10.7920i | −0.666731 | + | 0.666731i | ||||
\(263\) | −3.45891 | + | 3.45891i | −0.213285 | + | 0.213285i | −0.805662 | − | 0.592376i | \(-0.798190\pi\) |
0.592376 | + | 0.805662i | \(0.298190\pi\) | |||||||
\(264\) | −0.484669 | + | 0.916670i | −0.0298293 | + | 0.0564171i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.70208i | 0.349617i | ||||||||
\(267\) | −9.25643 | − | 30.0263i | −0.566484 | − | 1.83758i | ||||
\(268\) | −5.89503 | − | 5.89503i | −0.360096 | − | 0.360096i | ||||
\(269\) | −15.6157 | −0.952106 | −0.476053 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.76022 | 0.289163 | 0.144581 | − | 0.989493i | \(-0.453816\pi\) | ||||
0.144581 | + | 0.989493i | \(0.453816\pi\) | |||||||
\(272\) | 4.20435 | + | 4.20435i | 0.254926 | + | 0.254926i | ||||
\(273\) | −1.84671 | − | 5.99040i | −0.111768 | − | 0.362556i | ||||
\(274\) | − | 5.21161i | − | 0.314845i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.56335 | − | 4.84814i | 0.154295 | − | 0.291824i | ||||
\(277\) | 8.63721 | − | 8.63721i | 0.518960 | − | 0.518960i | −0.398297 | − | 0.917257i | \(-0.630399\pi\) |
0.917257 | + | 0.398297i | \(0.130399\pi\) | |||||||
\(278\) | −7.36130 | + | 7.36130i | −0.441501 | + | 0.441501i | ||||
\(279\) | 21.5261 | − | 14.6658i | 1.28874 | − | 0.878020i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.1403i | 0.664577i | 0.943178 | + | 0.332289i | \(0.107821\pi\) | ||||
−0.943178 | + | 0.332289i | \(0.892179\pi\) | |||||||
\(282\) | 3.66133 | − | 1.12870i | 0.218029 | − | 0.0672134i | ||||
\(283\) | −12.7294 | − | 12.7294i | −0.756686 | − | 0.756686i | 0.219032 | − | 0.975718i | \(-0.429710\pi\) |
−0.975718 | + | 0.219032i | \(0.929710\pi\) | |||||||
\(284\) | 14.4437 | 0.857074 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.16666 | 0.128117 | ||||||||
\(287\) | 4.09578 | + | 4.09578i | 0.241767 | + | 0.241767i | ||||
\(288\) | 2.94751 | + | 0.558713i | 0.173684 | + | 0.0329225i | ||||
\(289\) | 18.3532i | 1.07960i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1637 | − | 5.37382i | −0.595806 | − | 0.315019i | ||||
\(292\) | −9.67606 | + | 9.67606i | −0.566249 | + | 0.566249i | ||||
\(293\) | 12.1490 | − | 12.1490i | 0.709750 | − | 0.709750i | −0.256732 | − | 0.966483i | \(-0.582646\pi\) |
0.966483 | + | 0.256732i | \(0.0826459\pi\) | |||||||
\(294\) | −1.53120 | − | 0.809587i | −0.0893013 | − | 0.0472161i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.21997i | − | 0.129033i | ||||||
\(297\) | −1.94072 | + | 2.43111i | −0.112612 | + | 0.141067i | ||||
\(298\) | 9.02024 | + | 9.02024i | 0.522529 | + | 0.522529i | ||||
\(299\) | −11.4592 | −0.662701 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.460746 | 0.0265570 | ||||||||
\(302\) | −13.0833 | − | 13.0833i | −0.752862 | − | 0.752862i | ||||
\(303\) | −13.2856 | + | 4.09564i | −0.763236 | + | 0.235288i | ||||
\(304\) | 5.70208i | 0.327037i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.0434 | + | 14.7414i | 0.574141 | + | 0.842711i | ||||
\(307\) | −11.2499 | + | 11.2499i | −0.642067 | + | 0.642067i | −0.951063 | − | 0.308996i | \(-0.900007\pi\) |
0.308996 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(308\) | 0.423318 | − | 0.423318i | 0.0241208 | − | 0.0241208i | ||||
\(309\) | −10.4673 | + | 19.7972i | −0.595464 | + | 1.12622i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.1891i | − | 1.14482i | −0.819967 | − | 0.572411i | \(-0.806008\pi\) | ||
0.819967 | − | 0.572411i | \(-0.193992\pi\) | |||||||
\(312\) | −1.84671 | − | 5.99040i | −0.104549 | − | 0.339140i | ||||
\(313\) | 2.05777 | + | 2.05777i | 0.116312 | + | 0.116312i | 0.762867 | − | 0.646555i | \(-0.223791\pi\) |
−0.646555 | + | 0.762867i | \(0.723791\pi\) | |||||||
\(314\) | 0.0459667 | 0.00259405 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7772 | −0.662518 | ||||||||
\(317\) | −2.75877 | − | 2.75877i | −0.154948 | − | 0.154948i | 0.625376 | − | 0.780324i | \(-0.284946\pi\) |
−0.780324 | + | 0.625376i | \(0.784946\pi\) | |||||||
\(318\) | −1.45189 | − | 4.70970i | −0.0814182 | − | 0.264107i | ||||
\(319\) | − | 0.0245602i | − | 0.00137511i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.426792 | − | 0.807207i | 0.0238212 | − | 0.0450539i | ||||
\(322\) | −2.23887 | + | 2.23887i | −0.124767 | + | 0.124767i | ||||
\(323\) | −23.9736 | + | 23.9736i | −1.33393 | + | 1.33393i | ||||
\(324\) | 8.37568 | + | 3.29363i | 0.465316 | + | 0.182979i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.4085i | − | 0.742629i | ||||||
\(327\) | 13.8669 | − | 4.27485i | 0.766841 | − | 0.236400i | ||||
\(328\) | 4.09578 | + | 4.09578i | 0.226152 | + | 0.226152i | ||||
\(329\) | −2.21204 | −0.121953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.8209 | 1.58414 | 0.792070 | − | 0.610430i | \(-0.209004\pi\) | ||||
0.792070 | + | 0.610430i | \(0.209004\pi\) | |||||||
\(332\) | 1.04802 | + | 1.04802i | 0.0575173 | + | 0.0575173i | ||||
\(333\) | 1.24032 | − | 6.54338i | 0.0679693 | − | 0.358575i | ||||
\(334\) | 20.2129i | 1.10600i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.53120 | − | 0.809587i | −0.0835337 | − | 0.0441666i | ||||
\(337\) | −9.09298 | + | 9.09298i | −0.495326 | + | 0.495326i | −0.909980 | − | 0.414653i | \(-0.863903\pi\) |
0.414653 | + | 0.909980i | \(0.363903\pi\) | |||||||
\(338\) | −0.0695947 | + | 0.0695947i | −0.00378545 | + | 0.00378545i | ||||
\(339\) | −10.0864 | − | 5.33296i | −0.547818 | − | 0.289647i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.19784i | − | 0.281479i | ||||||
\(342\) | −3.18583 | + | 16.8070i | −0.172270 | + | 0.908817i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0.460746 | 0.0248418 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.6225 | 1.00115 | ||||||||
\(347\) | −13.3263 | − | 13.3263i | −0.715396 | − | 0.715396i | 0.252263 | − | 0.967659i | \(-0.418825\pi\) |
−0.967659 | + | 0.252263i | \(0.918825\pi\) | |||||||
\(348\) | −0.0679043 | + | 0.0209334i | −0.00364005 | + | 0.00112215i | ||||
\(349\) | 3.86507i | 0.206893i | 0.994635 | + | 0.103446i | \(0.0329870\pi\) | ||||
−0.994635 | + | 0.103446i | \(0.967013\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.09628 | − | 18.6886i | −0.111891 | − | 0.997523i | ||||
\(352\) | 0.423318 | − | 0.423318i | 0.0225629 | − | 0.0225629i | ||||
\(353\) | −21.9705 | + | 21.9705i | −1.16937 | + | 1.16937i | −0.187018 | + | 0.982357i | \(0.559882\pi\) |
−0.982357 | + | 0.187018i | \(0.940118\pi\) | |||||||
\(354\) | −7.57628 | + | 14.3293i | −0.402675 | + | 0.761592i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.1407i | 0.961458i | ||||||||
\(357\) | −3.03391 | − | 9.84149i | −0.160571 | − | 0.520867i | ||||
\(358\) | 2.25825 | + | 2.25825i | 0.119352 | + | 0.119352i | ||||
\(359\) | −14.8406 | −0.783254 | −0.391627 | − | 0.920124i | \(-0.628088\pi\) | ||||
−0.391627 | + | 0.920124i | \(0.628088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5138 | −0.711250 | ||||||||
\(362\) | 10.4453 | + | 10.4453i | 0.548990 | + | 0.548990i | ||||
\(363\) | −5.42995 | − | 17.6138i | −0.284998 | − | 0.924486i | ||||
\(364\) | 3.61917i | 0.189696i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.0163 | + | 22.7267i | −0.628100 | + | 1.18795i | ||||
\(367\) | −14.0652 | + | 14.0652i | −0.734196 | + | 0.734196i | −0.971448 | − | 0.237252i | \(-0.923753\pi\) |
0.237252 | + | 0.971448i | \(0.423753\pi\) | |||||||
\(368\) | −2.23887 | + | 2.23887i | −0.116709 | + | 0.116709i | ||||
\(369\) | 9.78402 | + | 14.3608i | 0.509335 | + | 0.747591i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.84542i | 0.147727i | ||||||||
\(372\) | −14.3710 | + | 4.43026i | −0.745103 | + | 0.229699i | ||||
\(373\) | −3.13757 | − | 3.13757i | −0.162457 | − | 0.162457i | 0.621197 | − | 0.783654i | \(-0.286647\pi\) |
−0.783654 | + | 0.621197i | \(0.786647\pi\) | |||||||
\(374\) | 3.55955 | 0.184060 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.21204 | −0.114077 | ||||||||
\(377\) | 0.104989 | + | 0.104989i | 0.00540722 | + | 0.00540722i | ||||
\(378\) | −4.06090 | − | 3.24177i | −0.208870 | − | 0.166739i | ||||
\(379\) | − | 2.17092i | − | 0.111513i | −0.998444 | − | 0.0557564i | \(-0.982243\pi\) | ||
0.998444 | − | 0.0557564i | \(-0.0177570\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.95822 | + | 3.15028i | 0.305249 | + | 0.161394i | ||||
\(382\) | −7.54478 | + | 7.54478i | −0.386024 | + | 0.386024i | ||||
\(383\) | −8.83769 | + | 8.83769i | −0.451585 | + | 0.451585i | −0.895880 | − | 0.444295i | \(-0.853454\pi\) |
0.444295 | + | 0.895880i | \(0.353454\pi\) | |||||||
\(384\) | −1.53120 | − | 0.809587i | −0.0781386 | − | 0.0413141i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.18930i | − | 0.0605339i | ||||||
\(387\) | 1.35806 | + | 0.257425i | 0.0690338 | + | 0.0130856i | ||||
\(388\) | 4.69359 | + | 4.69359i | 0.238281 | + | 0.238281i | ||||
\(389\) | −2.07217 | −0.105063 | −0.0525315 | − | 0.998619i | \(-0.516729\pi\) | ||||
−0.0525315 | + | 0.998619i | \(0.516729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8260 | −0.952072 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 25.2617 | − | 7.78762i | 1.27429 | − | 0.392833i | ||||
\(394\) | − | 25.8498i | − | 1.30230i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.48425 | − | 1.01122i | 0.0745863 | − | 0.0508158i | ||||
\(397\) | 1.16067 | − | 1.16067i | 0.0582524 | − | 0.0582524i | −0.677380 | − | 0.735633i | \(-0.736885\pi\) |
0.735633 | + | 0.677380i | \(0.236885\pi\) | |||||||
\(398\) | 7.82749 | − | 7.82749i | 0.392356 | − | 0.392356i | ||||
\(399\) | 4.61633 | − | 8.73102i | 0.231106 | − | 0.437098i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 34.3593i | − | 1.71582i | −0.513797 | − | 0.857912i | \(-0.671762\pi\) | ||
0.513797 | − | 0.857912i | \(-0.328238\pi\) | |||||||
\(402\) | 4.25392 | + | 13.7990i | 0.212166 | + | 0.688231i | ||||
\(403\) | 22.2196 | + | 22.2196i | 1.10684 | + | 1.10684i | ||||
\(404\) | 8.02663 | 0.399340 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0410252 | 0.00203605 | ||||||||
\(407\) | −0.939751 | − | 0.939751i | −0.0465817 | − | 0.0465817i | ||||
\(408\) | −3.03391 | − | 9.84149i | −0.150201 | − | 0.487226i | ||||
\(409\) | − | 9.04629i | − | 0.447310i | −0.974668 | − | 0.223655i | \(-0.928201\pi\) | ||
0.974668 | − | 0.223655i | \(-0.0717989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.21926 | + | 7.98002i | −0.208121 | + | 0.393625i | ||||
\(412\) | 9.14232 | − | 9.14232i | 0.450410 | − | 0.450410i | ||||
\(413\) | 6.61725 | − | 6.61725i | 0.325613 | − | 0.325613i | ||||
\(414\) | −7.84999 | + | 5.34821i | −0.385806 | + | 0.262850i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.61917i | 0.177445i | ||||||||
\(417\) | 17.2312 | − | 5.31200i | 0.843816 | − | 0.260130i | ||||
\(418\) | 2.41379 | + | 2.41379i | 0.118062 | + | 0.118062i | ||||
\(419\) | 6.31612 | 0.308563 | 0.154281 | − | 0.988027i | \(-0.450694\pi\) | ||||
0.154281 | + | 0.988027i | \(0.450694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7613 | −0.670683 | −0.335341 | − | 0.942097i | \(-0.608852\pi\) | ||||
−0.335341 | + | 0.942097i | \(0.608852\pi\) | |||||||
\(422\) | −4.93266 | − | 4.93266i | −0.240118 | − | 0.240118i | ||||
\(423\) | −6.52000 | − | 1.23589i | −0.317013 | − | 0.0600912i | ||||
\(424\) | 2.84542i | 0.138186i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.1161 | − | 11.6934i | −1.07153 | − | 0.566547i | ||||
\(427\) | 10.4952 | − | 10.4952i | 0.507898 | − | 0.507898i | ||||
\(428\) | −0.372768 | + | 0.372768i | −0.0180184 | + | 0.0180184i | ||||
\(429\) | −3.31759 | − | 1.75410i | −0.160175 | − | 0.0846888i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1437i | 0.729448i | 0.931116 | + | 0.364724i | \(0.118837\pi\) | ||||
−0.931116 | + | 0.364724i | \(0.881163\pi\) | |||||||
\(432\) | −4.06090 | − | 3.24177i | −0.195380 | − | 0.155970i | ||||
\(433\) | −7.32819 | − | 7.32819i | −0.352170 | − | 0.352170i | 0.508746 | − | 0.860916i | \(-0.330109\pi\) |
−0.860916 | + | 0.508746i | \(0.830109\pi\) | |||||||
\(434\) | 8.68243 | 0.416770 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.37785 | −0.401226 | ||||||||
\(437\) | −12.7662 | − | 12.7662i | −0.610691 | − | 0.610691i | ||||
\(438\) | 22.6496 | − | 6.98236i | 1.08224 | − | 0.333630i | ||||
\(439\) | − | 4.14139i | − | 0.197658i | −0.995104 | − | 0.0988288i | \(-0.968490\pi\) | ||
0.995104 | − | 0.0988288i | \(-0.0315096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.68914 | + | 2.47928i | 0.0804351 | + | 0.118061i | ||||
\(442\) | −15.2163 | + | 15.2163i | −0.723765 | + | 0.723765i | ||||
\(443\) | 28.1456 | − | 28.1456i | 1.33724 | − | 1.33724i | 0.438517 | − | 0.898723i | \(-0.355504\pi\) |
0.898723 | − | 0.438517i | \(-0.144496\pi\) | |||||||
\(444\) | −1.79726 | + | 3.39921i | −0.0852940 | + | 0.161319i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.11008i | 0.431375i | ||||||||
\(447\) | −6.50911 | − | 21.1145i | −0.307870 | − | 0.998679i | ||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | −2.90662 | −0.137172 | −0.0685860 | − | 0.997645i | \(-0.521849\pi\) | ||||
−0.0685860 | + | 0.997645i | \(0.521849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.46764 | 0.163285 | ||||||||
\(452\) | 4.65789 | + | 4.65789i | 0.219089 | + | 0.219089i | ||||
\(453\) | 9.44109 | + | 30.6253i | 0.443581 | + | 1.43890i | ||||
\(454\) | 5.37980i | 0.252487i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.61633 | − | 8.73102i | 0.216180 | − | 0.408868i | ||||
\(457\) | 28.5766 | − | 28.5766i | 1.33676 | − | 1.33676i | 0.437578 | − | 0.899181i | \(-0.355837\pi\) |
0.899181 | − | 0.437578i | \(-0.144163\pi\) | |||||||
\(458\) | 11.4764 | − | 11.4764i | 0.536258 | − | 0.536258i | ||||
\(459\) | −3.44392 | − | 30.7030i | −0.160748 | − | 1.43309i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8861i | 1.48508i | 0.669800 | + | 0.742542i | \(0.266380\pi\) | ||||
−0.669800 | + | 0.742542i | \(0.733620\pi\) | |||||||
\(462\) | −0.990896 | + | 0.305471i | −0.0461006 | + | 0.0142118i | ||||
\(463\) | 1.03747 | + | 1.03747i | 0.0482153 | + | 0.0482153i | 0.730803 | − | 0.682588i | \(-0.239146\pi\) |
−0.682588 | + | 0.730803i | \(0.739146\pi\) | |||||||
\(464\) | 0.0410252 | 0.00190455 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.01513 | 0.0933492 | ||||||||
\(467\) | −17.9187 | − | 17.9187i | −0.829178 | − | 0.829178i | 0.158226 | − | 0.987403i | \(-0.449423\pi\) |
−0.987403 | + | 0.158226i | \(0.949423\pi\) | |||||||
\(468\) | −2.02208 | + | 10.6676i | −0.0934707 | + | 0.493108i | ||||
\(469\) | − | 8.33683i | − | 0.384959i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0703841 | − | 0.0372140i | −0.00324313 | − | 0.00171473i | ||||
\(472\) | 6.61725 | − | 6.61725i | 0.304583 | − | 0.304583i | ||||
\(473\) | 0.195042 | − | 0.195042i | 0.00896804 | − | 0.00896804i | ||||
\(474\) | 18.0332 | + | 9.53465i | 0.828292 | + | 0.437941i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.94585i | 0.272528i | ||||||||
\(477\) | −1.58977 | + | 8.38692i | −0.0727907 | + | 0.384011i | ||||
\(478\) | 7.09139 | + | 7.09139i | 0.324353 | + | 0.324353i | ||||
\(479\) | −17.9344 | −0.819446 | −0.409723 | − | 0.912210i | \(-0.634375\pi\) | ||||
−0.409723 | + | 0.912210i | \(0.634375\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.03444 | 0.366339 | ||||||||
\(482\) | −2.03620 | − | 2.03620i | −0.0927465 | − | 0.0927465i | ||||
\(483\) | 5.24071 | − | 1.61559i | 0.238461 | − | 0.0735121i | ||||
\(484\) | 10.6416i | 0.483709i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.1583 | − | 11.8240i | −0.460792 | − | 0.536349i | ||||
\(487\) | 17.7003 | − | 17.7003i | 0.802078 | − | 0.802078i | −0.181342 | − | 0.983420i | \(-0.558044\pi\) |
0.983420 | + | 0.181342i | \(0.0580441\pi\) | |||||||
\(488\) | 10.4952 | − | 10.4952i | 0.475095 | − | 0.475095i | ||||
\(489\) | −10.8554 | + | 20.5311i | −0.490896 | + | 0.928448i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.5352i | − | 1.46829i | −0.678990 | − | 0.734147i | \(-0.737582\pi\) | ||
0.678990 | − | 0.734147i | \(-0.262418\pi\) | |||||||
\(492\) | −2.95556 | − | 9.58735i | −0.133247 | − | 0.432231i | ||||
\(493\) | 0.172484 | + | 0.172484i | 0.00776830 | + | 0.00776830i | ||||
\(494\) | −20.6368 | −0.928495 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.68243 | 0.389853 | ||||||||
\(497\) | 10.2132 | + | 10.2132i | 0.458125 | + | 0.458125i | ||||
\(498\) | −0.756260 | − | 2.45318i | −0.0338888 | − | 0.109930i | ||||
\(499\) | 17.2851i | 0.773788i | 0.922124 | + | 0.386894i | \(0.126452\pi\) | ||||
−0.922124 | + | 0.386894i | \(0.873548\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.3641 | − | 30.9500i | 0.731095 | − | 1.38274i | ||||
\(502\) | −2.64232 | + | 2.64232i | −0.117933 | + | 0.117933i | ||||
\(503\) | −9.37011 | + | 9.37011i | −0.417793 | + | 0.417793i | −0.884442 | − | 0.466650i | \(-0.845461\pi\) |
0.466650 | + | 0.884442i | \(0.345461\pi\) | |||||||
\(504\) | 1.68914 | + | 2.47928i | 0.0752402 | + | 0.110436i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.89551i | 0.0842655i | ||||||||
\(507\) | 0.162906 | − | 0.0502203i | 0.00723492 | − | 0.00223036i | ||||
\(508\) | −2.75150 | − | 2.75150i | −0.122078 | − | 0.122078i | ||||
\(509\) | −37.6289 | −1.66787 | −0.833937 | − | 0.551860i | \(-0.813918\pi\) | ||||
−0.833937 | + | 0.551860i | \(0.813918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.6840 | −0.605345 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 18.4848 | − | 23.1556i | 0.816126 | − | 1.02234i | ||||
\(514\) | 13.8202i | 0.609584i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.705494 | − | 0.373014i | −0.0310576 | − | 0.0164210i | ||||
\(517\) | −0.936394 | + | 0.936394i | −0.0411825 | + | 0.0411825i | ||||
\(518\) | 1.56975 | − | 1.56975i | 0.0689710 | − | 0.0689710i | ||||
\(519\) | −28.5147 | − | 15.0765i | −1.25166 | − | 0.661786i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 38.1318i | − | 1.67059i | −0.549805 | − | 0.835293i | \(-0.685298\pi\) | ||
0.549805 | − | 0.835293i | \(-0.314702\pi\) | |||||||
\(522\) | 0.120922 | + | 0.0229213i | 0.00529263 | + | 0.00100324i | ||||
\(523\) | −24.0284 | − | 24.0284i | −1.05069 | − | 1.05069i | −0.998645 | − | 0.0520439i | \(-0.983426\pi\) |
−0.0520439 | − | 0.998645i | \(-0.516574\pi\) | |||||||
\(524\) | −15.2622 | −0.666731 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.89164 | −0.213285 | ||||||||
\(527\) | 36.5040 | + | 36.5040i | 1.59014 | + | 1.59014i | ||||
\(528\) | −0.990896 | + | 0.305471i | −0.0431232 | + | 0.0132939i | ||||
\(529\) | 12.9749i | 0.564127i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.2016 | − | 15.8073i | 1.00686 | − | 0.685978i | ||||
\(532\) | −4.03198 | + | 4.03198i | −0.174809 | + | 0.174809i | ||||
\(533\) | −14.8234 | + | 14.8234i | −0.642071 | + | 0.642071i | ||||
\(534\) | 14.6865 | − | 27.7771i | 0.635548 | − | 1.20203i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 8.33683i | − | 0.360096i | ||||||
\(537\) | −1.62958 | − | 5.28609i | −0.0703216 | − | 0.228111i | ||||
\(538\) | −11.0420 | − | 11.0420i | −0.476053 | − | 0.476053i | ||||
\(539\) | 0.598662 | 0.0257862 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.81137 | −0.249850 | −0.124925 | − | 0.992166i | \(-0.539869\pi\) | ||||
−0.124925 | + | 0.992166i | \(0.539869\pi\) | |||||||
\(542\) | 3.36598 | + | 3.36598i | 0.144581 | + | 0.144581i | ||||
\(543\) | −7.53741 | − | 24.4501i | −0.323461 | − | 1.04925i | ||||
\(544\) | 5.94585i | 0.254926i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.93004 | − | 5.54167i | 0.125394 | − | 0.237162i | ||||
\(547\) | −12.9045 | + | 12.9045i | −0.551755 | + | 0.551755i | −0.926947 | − | 0.375192i | \(-0.877577\pi\) |
0.375192 | + | 0.926947i | \(0.377577\pi\) | |||||||
\(548\) | 3.68517 | − | 3.68517i | 0.157423 | − | 0.157423i | ||||
\(549\) | 36.7985 | − | 25.0709i | 1.57052 | − | 1.07000i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.233929i | 0.00996571i | ||||||||
\(552\) | 5.24071 | − | 1.61559i | 0.223060 | − | 0.0687642i | ||||
\(553\) | −8.32772 | − | 8.32772i | −0.354131 | − | 0.354131i | ||||
\(554\) | 12.2149 | 0.518960 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.4104 | −0.441501 | ||||||||
\(557\) | −20.2842 | − | 20.2842i | −0.859467 | − | 0.859467i | 0.131808 | − | 0.991275i | \(-0.457922\pi\) |
−0.991275 | + | 0.131808i | \(0.957922\pi\) | |||||||
\(558\) | 25.5916 | + | 4.85099i | 1.08338 | + | 0.205359i | ||||
\(559\) | 1.66752i | 0.0705286i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.45038 | − | 2.88177i | −0.230115 | − | 0.121668i | ||||
\(562\) | −7.87742 | + | 7.87742i | −0.332289 | + | 0.332289i | ||||
\(563\) | 21.4141 | − | 21.4141i | 0.902497 | − | 0.902497i | −0.0931543 | − | 0.995652i | \(-0.529695\pi\) |
0.995652 | + | 0.0931543i | \(0.0296950\pi\) | |||||||
\(564\) | 3.38706 | + | 1.79084i | 0.142621 | + | 0.0754078i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 18.0021i | − | 0.756686i | ||||||
\(567\) | 3.59355 | + | 8.25145i | 0.150915 | + | 0.346528i | ||||
\(568\) | 10.2132 | + | 10.2132i | 0.428537 | + | 0.428537i | ||||
\(569\) | 36.8247 | 1.54377 | 0.771885 | − | 0.635762i | \(-0.219314\pi\) | ||||
0.771885 | + | 0.635762i | \(0.219314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8712 | 1.25007 | 0.625036 | − | 0.780596i | \(-0.285084\pi\) | ||||
0.625036 | + | 0.780596i | \(0.285084\pi\) | |||||||
\(572\) | 1.53206 | + | 1.53206i | 0.0640587 | + | 0.0640587i | ||||
\(573\) | 17.6607 | − | 5.44440i | 0.737787 | − | 0.227443i | ||||
\(574\) | 5.79231i | 0.241767i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.68914 | + | 2.47928i | 0.0703807 | + | 0.103303i | ||||
\(577\) | 19.6893 | − | 19.6893i | 0.819678 | − | 0.819678i | −0.166383 | − | 0.986061i | \(-0.553209\pi\) |
0.986061 | + | 0.166383i | \(0.0532088\pi\) | |||||||
\(578\) | −12.9777 | + | 12.9777i | −0.539799 | + | 0.539799i | ||||
\(579\) | −0.962845 | + | 1.82106i | −0.0400145 | + | 0.0756806i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.48212i | 0.0614886i | ||||||||
\(582\) | −3.38695 | − | 10.9867i | −0.140393 | − | 0.455413i | ||||
\(583\) | 1.20452 | + | 1.20452i | 0.0498860 | + | 0.0498860i | ||||
\(584\) | −13.6840 | −0.566249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.1812 | 0.709750 | ||||||||
\(587\) | −1.33177 | − | 1.33177i | −0.0549679 | − | 0.0549679i | 0.679088 | − | 0.734056i | \(-0.262375\pi\) |
−0.734056 | + | 0.679088i | \(0.762375\pi\) | |||||||
\(588\) | −0.510256 | − | 1.65519i | −0.0210426 | − | 0.0682587i | ||||
\(589\) | 49.5079i | 2.03994i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.9277 | + | 39.5812i | −0.860850 | + | 1.62815i | ||||
\(592\) | 1.56975 | − | 1.56975i | 0.0645164 | − | 0.0645164i | ||||
\(593\) | 15.2499 | − | 15.2499i | 0.626239 | − | 0.626239i | −0.320881 | − | 0.947120i | \(-0.603979\pi\) |
0.947120 | + | 0.320881i | \(0.103979\pi\) | |||||||
\(594\) | −3.09135 | + | 0.346753i | −0.126840 | + | 0.0142275i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.7565i | 0.522529i | ||||||||
\(597\) | −18.3225 | + | 5.64840i | −0.749889 | + | 0.231174i | ||||
\(598\) | −8.10286 | − | 8.10286i | −0.331351 | − | 0.331351i | ||||
\(599\) | 5.47995 | 0.223905 | 0.111952 | − | 0.993714i | \(-0.464290\pi\) | ||||
0.111952 | + | 0.993714i | \(0.464290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7009 | 0.762825 | 0.381412 | − | 0.924405i | \(-0.375438\pi\) | ||||
0.381412 | + | 0.924405i | \(0.375438\pi\) | |||||||
\(602\) | 0.325797 | + | 0.325797i | 0.0132785 | + | 0.0132785i | ||||
\(603\) | 4.65789 | − | 24.5729i | 0.189684 | − | 1.00069i | ||||
\(604\) | − | 18.5026i | − | 0.752862i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.2904 | − | 6.49826i | −0.499262 | − | 0.263974i | ||||
\(607\) | 1.74605 | − | 1.74605i | 0.0708699 | − | 0.0708699i | −0.670783 | − | 0.741653i | \(-0.734042\pi\) |
0.741653 | + | 0.670783i | \(0.234042\pi\) | |||||||
\(608\) | −4.03198 | + | 4.03198i | −0.163518 | + | 0.163518i | ||||
\(609\) | −0.0628177 | − | 0.0332135i | −0.00254550 | − | 0.00134588i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8.00574i | − | 0.323878i | ||||||
\(612\) | −3.32203 | + | 17.5255i | −0.134285 | + | 0.708426i | ||||
\(613\) | −11.8503 | − | 11.8503i | −0.478628 | − | 0.478628i | 0.426064 | − | 0.904693i | \(-0.359900\pi\) |
−0.904693 | + | 0.426064i | \(0.859900\pi\) | |||||||
\(614\) | −15.9098 | −0.642067 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.598662 | 0.0241208 | ||||||||
\(617\) | 8.20715 | + | 8.20715i | 0.330407 | + | 0.330407i | 0.852741 | − | 0.522334i | \(-0.174938\pi\) |
−0.522334 | + | 0.852741i | \(0.674938\pi\) | |||||||
\(618\) | −21.4002 | + | 6.59720i | −0.860842 | + | 0.265378i | ||||
\(619\) | 17.6445i | 0.709194i | 0.935019 | + | 0.354597i | \(0.115382\pi\) | ||||
−0.935019 | + | 0.354597i | \(0.884618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.3497 | − | 1.83393i | 0.656092 | − | 0.0735931i | ||||
\(622\) | 14.2759 | − | 14.2759i | 0.572411 | − | 0.572411i | ||||
\(623\) | −12.8274 | + | 12.8274i | −0.513921 | + | 0.513921i | ||||
\(624\) | 2.93004 | − | 5.54167i | 0.117295 | − | 0.221845i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.91013i | 0.116312i | ||||||||
\(627\) | −1.74182 | − | 5.65017i | −0.0695616 | − | 0.225646i | ||||
\(628\) | 0.0325033 | + | 0.0325033i | 0.00129702 | + | 0.00129702i | ||||
\(629\) | 13.1996 | 0.526302 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6697 | 1.02190 | 0.510948 | − | 0.859612i | \(-0.329295\pi\) | ||||
0.510948 | + | 0.859612i | \(0.329295\pi\) | |||||||
\(632\) | −8.32772 | − | 8.32772i | −0.331259 | − | 0.331259i | ||||
\(633\) | 3.55946 | + | 11.5463i | 0.141476 | + | 0.458924i | ||||
\(634\) | − | 3.90148i | − | 0.154948i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.30362 | − | 4.35690i | 0.0913443 | − | 0.172762i | ||||
\(637\) | −2.55914 | + | 2.55914i | −0.101397 | + | 0.101397i | ||||
\(638\) | 0.0173667 | − | 0.0173667i | 0.000687554 | − | 0.000687554i | ||||
\(639\) | 24.3973 | + | 35.8098i | 0.965143 | + | 1.41662i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.3415i | − | 0.487459i | −0.969843 | − | 0.243729i | \(-0.921629\pi\) | ||
0.969843 | − | 0.243729i | \(-0.0783709\pi\) | |||||||
\(642\) | 0.872569 | − | 0.268993i | 0.0344376 | − | 0.0106163i | ||||
\(643\) | −17.1538 | − | 17.1538i | −0.676482 | − | 0.676482i | 0.282721 | − | 0.959202i | \(-0.408763\pi\) |
−0.959202 | + | 0.282721i | \(0.908763\pi\) | |||||||
\(644\) | −3.16624 | −0.124767 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −33.9038 | −1.33393 | ||||||||
\(647\) | −27.7839 | − | 27.7839i | −1.09230 | − | 1.09230i | −0.995283 | − | 0.0970159i | \(-0.969070\pi\) |
−0.0970159 | − | 0.995283i | \(-0.530930\pi\) | |||||||
\(648\) | 3.59355 | + | 8.25145i | 0.141168 | + | 0.324147i | ||||
\(649\) | − | 5.60240i | − | 0.219913i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2945 | − | 7.02918i | −0.521053 | − | 0.275495i | ||||
\(652\) | 9.48125 | − | 9.48125i | 0.371315 | − | 0.371315i | ||||
\(653\) | −12.4080 | + | 12.4080i | −0.485561 | + | 0.485561i | −0.906902 | − | 0.421341i | \(-0.861559\pi\) |
0.421341 | + | 0.906902i | \(0.361559\pi\) | |||||||
\(654\) | 12.8282 | + | 6.78260i | 0.501621 | + | 0.265221i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.79231i | 0.226152i | ||||||||
\(657\) | −40.3338 | − | 7.64544i | −1.57357 | − | 0.298277i | ||||
\(658\) | −1.56415 | − | 1.56415i | −0.0609767 | − | 0.0609767i | ||||
\(659\) | −3.40992 | −0.132832 | −0.0664158 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664158 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.9472 | −1.90382 | −0.951912 | − | 0.306372i | \(-0.900885\pi\) | ||||
−0.951912 | + | 0.306372i | \(0.900885\pi\) | |||||||
\(662\) | 20.3795 | + | 20.3795i | 0.792070 | + | 0.792070i | ||||
\(663\) | 35.6181 | − | 10.9802i | 1.38329 | − | 0.426437i | ||||
\(664\) | 1.48212i | 0.0575173i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.50391 | − | 3.74983i | 0.213272 | − | 0.145303i | ||||
\(667\) | −0.0918500 | + | 0.0918500i | −0.00355645 | + | 0.00355645i | ||||
\(668\) | −14.2927 | + | 14.2927i | −0.553001 | + | 0.553001i | ||||
\(669\) | 7.37540 | − | 13.9493i | 0.285150 | − | 0.539313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.88560i | − | 0.343025i | ||||||
\(672\) | −0.510256 | − | 1.65519i | −0.0196836 | − | 0.0638502i | ||||
\(673\) | −13.0130 | − | 13.0130i | −0.501615 | − | 0.501615i | 0.410325 | − | 0.911940i | \(-0.365415\pi\) |
−0.911940 | + | 0.410325i | \(0.865415\pi\) | |||||||
\(674\) | −12.8594 | −0.495326 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.0984218 | −0.00378545 | ||||||||
\(677\) | 23.6302 | + | 23.6302i | 0.908184 | + | 0.908184i | 0.996126 | − | 0.0879415i | \(-0.0280289\pi\) |
−0.0879415 | + | 0.996126i | \(0.528029\pi\) | |||||||
\(678\) | −3.36119 | − | 10.9031i | −0.129086 | − | 0.418732i | ||||
\(679\) | 6.63773i | 0.254733i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.35542 | − | 8.23755i | 0.166900 | − | 0.315663i | ||||
\(682\) | 3.67543 | − | 3.67543i | 0.140739 | − | 0.140739i | ||||
\(683\) | −20.7794 | + | 20.7794i | −0.795100 | + | 0.795100i | −0.982318 | − | 0.187218i | \(-0.940053\pi\) |
0.187218 | + | 0.982318i | \(0.440053\pi\) | |||||||
\(684\) | −14.1370 | + | 9.63160i | −0.540543 | + | 0.368274i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | −26.8638 | + | 8.28152i | −1.02492 | + | 0.315960i | ||||
\(688\) | 0.325797 | + | 0.325797i | 0.0124209 | + | 0.0124209i | ||||
\(689\) | −10.2981 | −0.392325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.314417 | 0.0119610 | 0.00598048 | − | 0.999982i | \(-0.498096\pi\) | ||||
0.00598048 | + | 0.999982i | \(0.498096\pi\) | |||||||
\(692\) | 13.1681 | + | 13.1681i | 0.500575 | + | 0.500575i | ||||
\(693\) | 1.76456 | + | 0.334480i | 0.0670302 | + | 0.0127058i | ||||
\(694\) | − | 18.8463i | − | 0.715396i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.0628177 | − | 0.0332135i | −0.00238110 | − | 0.00125895i | ||||
\(697\) | −24.3529 | + | 24.3529i | −0.922433 | + | 0.922433i | ||||
\(698\) | −2.73302 | + | 2.73302i | −0.103446 | + | 0.103446i | ||||
\(699\) | −3.08557 | − | 1.63143i | −0.116707 | − | 0.0617062i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0199i | 0.756143i | 0.925776 | + | 0.378071i | \(0.123413\pi\) | ||||
−0.925776 | + | 0.378071i | \(0.876587\pi\) | |||||||
\(702\) | 11.7325 | − | 14.6971i | 0.442816 | − | 0.554707i | ||||
\(703\) | 8.95086 | + | 8.95086i | 0.337588 | + | 0.337588i | ||||
\(704\) | 0.598662 | 0.0225629 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.0710 | −1.16937 | ||||||||
\(707\) | 5.67569 | + | 5.67569i | 0.213456 | + | 0.213456i | ||||
\(708\) | −15.4896 | + | 4.77508i | −0.582133 | + | 0.179459i | ||||
\(709\) | − | 30.4538i | − | 1.14372i | −0.820352 | − | 0.571858i | \(-0.806223\pi\) | ||
0.820352 | − | 0.571858i | \(-0.193777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.8933 | − | 29.1989i | −0.746056 | − | 1.09504i | ||||
\(712\) | −12.8274 | + | 12.8274i | −0.480729 | + | 0.480729i | ||||
\(713\) | −19.4388 | + | 19.4388i | −0.727990 | + | 0.727990i | ||||
\(714\) | 4.81369 | − | 9.10428i | 0.180148 | − | 0.340719i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.19365i | 0.119352i | ||||||||
\(717\) | −5.11723 | − | 16.5994i | −0.191106 | − | 0.619917i | ||||
\(718\) | −10.4939 | − | 10.4939i | −0.391627 | − | 0.391627i | ||||
\(719\) | −23.5199 | −0.877145 | −0.438573 | − | 0.898696i | \(-0.644516\pi\) | ||||
−0.438573 | + | 0.898696i | \(0.644516\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.9292 | 0.481508 | ||||||||
\(722\) | −9.55567 | − | 9.55567i | −0.355625 | − | 0.355625i | ||||
\(723\) | 1.46935 | + | 4.76631i | 0.0546456 | + | 0.177261i | ||||
\(724\) | 14.7718i | 0.548990i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.61531 | − | 16.2944i | 0.319744 | − | 0.604742i | ||||
\(727\) | −25.7430 | + | 25.7430i | −0.954754 | + | 0.954754i | −0.999020 | − | 0.0442655i | \(-0.985905\pi\) |
0.0442655 | + | 0.999020i | \(0.485905\pi\) | |||||||
\(728\) | −2.55914 | + | 2.55914i | −0.0948481 | + | 0.0948481i | ||||
\(729\) | 5.98186 | + | 26.3290i | 0.221550 | + | 0.975149i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.73953i | 0.101325i | ||||||||
\(732\) | −24.5670 | + | 7.57345i | −0.908023 | + | 0.279923i | ||||
\(733\) | −7.70481 | − | 7.70481i | −0.284584 | − | 0.284584i | 0.550350 | − | 0.834934i | \(-0.314494\pi\) |
−0.834934 | + | 0.550350i | \(0.814494\pi\) | |||||||
\(734\) | −19.8912 | −0.734196 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.16624 | −0.116709 | ||||||||
\(737\) | −3.52913 | − | 3.52913i | −0.129997 | − | 0.129997i | ||||
\(738\) | −3.23624 | + | 17.0729i | −0.119128 | + | 0.628463i | ||||
\(739\) | − | 37.0585i | − | 1.36322i | −0.731716 | − | 0.681610i | \(-0.761280\pi\) | ||
0.731716 | − | 0.681610i | \(-0.238720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.5991 | + | 16.7073i | 1.16082 | + | 0.613759i | ||||
\(742\) | −2.01202 | + | 2.01202i | −0.0738634 | + | 0.0738634i | ||||
\(743\) | −7.81755 | + | 7.81755i | −0.286798 | + | 0.286798i | −0.835813 | − | 0.549015i | \(-0.815003\pi\) |
0.549015 | + | 0.835813i | \(0.315003\pi\) | |||||||
\(744\) | −13.2945 | − | 7.02918i | −0.487401 | − | 0.257702i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 4.43719i | − | 0.162457i | ||||||
\(747\) | −0.828079 | + | 4.36856i | −0.0302978 | + | 0.159837i | ||||
\(748\) | 2.51698 | + | 2.51698i | 0.0920301 | + | 0.0920301i | ||||
\(749\) | −0.527173 | −0.0192625 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.7592 | −1.15891 | −0.579455 | − | 0.815004i | \(-0.696735\pi\) | ||||
−0.579455 | + | 0.815004i | \(0.696735\pi\) | |||||||
\(752\) | −1.56415 | − | 1.56415i | −0.0570385 | − | 0.0570385i | ||||
\(753\) | 6.18511 | − | 1.90673i | 0.225398 | − | 0.0694851i | ||||
\(754\) | 0.148477i | 0.00540722i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.579214 | − | 5.16377i | −0.0210658 | − | 0.187804i | ||||
\(757\) | 1.94012 | − | 1.94012i | 0.0705150 | − | 0.0705150i | −0.670970 | − | 0.741485i | \(-0.734122\pi\) |
0.741485 | + | 0.670970i | \(0.234122\pi\) | |||||||
\(758\) | 1.53507 | − | 1.53507i | 0.0557564 | − | 0.0557564i | ||||
\(759\) | 1.53458 | − | 2.90240i | 0.0557016 | − | 0.105350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.3779i | 1.49995i | 0.661467 | + | 0.749974i | \(0.269934\pi\) | ||||
−0.661467 | + | 0.749974i | \(0.730066\pi\) | |||||||
\(762\) | 1.98552 | + | 6.44068i | 0.0719277 | + | 0.233321i | ||||
\(763\) | −5.92404 | − | 5.92404i | −0.214465 | − | 0.214465i | ||||
\(764\) | −10.6699 | −0.386024 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.4984 | −0.451585 | ||||||||
\(767\) | 23.9490 | + | 23.9490i | 0.864747 | + | 0.864747i | ||||
\(768\) | −0.510256 | − | 1.65519i | −0.0184123 | − | 0.0597264i | ||||
\(769\) | − | 9.04505i | − | 0.326173i | −0.986612 | − | 0.163086i | \(-0.947855\pi\) | ||
0.986612 | − | 0.163086i | \(-0.0521449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1887 | − | 21.1615i | 0.402950 | − | 0.762113i | ||||
\(772\) | 0.840964 | − | 0.840964i | 0.0302670 | − | 0.0302670i | ||||
\(773\) | −1.06409 | + | 1.06409i | −0.0382726 | + | 0.0382726i | −0.725984 | − | 0.687711i | \(-0.758615\pi\) |
0.687711 | + | 0.725984i | \(0.258615\pi\) | |||||||
\(774\) | 0.778264 | + | 1.14232i | 0.0279741 | + | 0.0410597i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.63773i | 0.238281i | ||||||||
\(777\) | −3.67445 | + | 1.13275i | −0.131820 | + | 0.0406372i | ||||
\(778\) | −1.46524 | − | 1.46524i | −0.0525315 | − | 0.0525315i | ||||
\(779\) | −33.0283 | −1.18336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.64687 | 0.309409 | ||||||||
\(782\) | −13.3120 | − | 13.3120i | −0.476036 | − | 0.476036i | ||||
\(783\) | −0.166599 | − | 0.132994i | −0.00595377 | − | 0.00475283i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23.3694 | + | 12.3561i | 0.833559 | + | 0.440726i | ||||
\(787\) | 29.2527 | − | 29.2527i | 1.04275 | − | 1.04275i | 0.0437024 | − | 0.999045i | \(-0.486085\pi\) |
0.999045 | − | 0.0437024i | \(-0.0139153\pi\) | |||||||
\(788\) | 18.2786 | − | 18.2786i | 0.651148 | − | 0.651148i | ||||
\(789\) | 7.49007 | + | 3.96021i | 0.266653 | + | 0.140987i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.58726i | 0.234216i | ||||||||
\(792\) | 1.76456 | + | 0.334480i | 0.0627010 | + | 0.0118852i | ||||
\(793\) | 37.9839 | + | 37.9839i | 1.34885 | + | 1.34885i | ||||
\(794\) | 1.64144 | 0.0582524 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0697 | 0.392356 | ||||||||
\(797\) | 27.0449 | + | 27.0449i | 0.957979 | + | 0.957979i | 0.999152 | − | 0.0411732i | \(-0.0131095\pi\) |
−0.0411732 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(798\) | 9.43801 | − | 2.90952i | 0.334102 | − | 0.102996i | ||||
\(799\) | − | 13.1524i | − | 0.465300i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.9759 | + | 30.6422i | −1.58915 | + | 1.08269i | ||||
\(802\) | 24.2957 | − | 24.2957i | 0.857912 | − | 0.857912i | ||||
\(803\) | −5.79269 | + | 5.79269i | −0.204420 | + | 0.204420i | ||||
\(804\) | −6.74939 | + | 12.7653i | −0.238033 | + | 0.450199i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.4232i | 1.10684i | ||||||||
\(807\) | 7.96801 | + | 25.8469i | 0.280487 | + | 0.909853i | ||||
\(808\) | 5.67569 | + | 5.67569i | 0.199670 | + | 0.199670i | ||||
\(809\) | 0.344140 | 0.0120993 | 0.00604965 | − | 0.999982i | \(-0.498074\pi\) | ||||
0.00604965 | + | 0.999982i | \(0.498074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.2804 | −0.641911 | −0.320955 | − | 0.947094i | \(-0.604004\pi\) | ||||
−0.320955 | + | 0.947094i | \(0.604004\pi\) | |||||||
\(812\) | 0.0290092 | + | 0.0290092i | 0.00101802 | + | 0.00101802i | ||||
\(813\) | −2.42893 | − | 7.87905i | −0.0851864 | − | 0.276330i | ||||
\(814\) | − | 1.32901i | − | 0.0465817i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.81369 | − | 9.10428i | 0.168513 | − | 0.318714i | ||||
\(817\) | −1.85772 | + | 1.85772i | −0.0649934 | + | 0.0649934i | ||||
\(818\) | 6.39669 | − | 6.39669i | 0.223655 | − | 0.223655i | ||||
\(819\) | −8.97294 | + | 6.11328i | −0.313540 | + | 0.213615i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.8883i | 0.484704i | 0.970188 | + | 0.242352i | \(0.0779189\pi\) | ||||
−0.970188 | + | 0.242352i | \(0.922081\pi\) | |||||||
\(822\) | −8.62619 | + | 2.65926i | −0.300873 | + | 0.0927523i | ||||
\(823\) | 6.37913 | + | 6.37913i | 0.222362 | + | 0.222362i | 0.809493 | − | 0.587130i | \(-0.199742\pi\) |
−0.587130 | + | 0.809493i | \(0.699742\pi\) | |||||||
\(824\) | 12.9292 | 0.450410 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.35820 | 0.325613 | ||||||||
\(827\) | 2.61168 | + | 2.61168i | 0.0908170 | + | 0.0908170i | 0.751056 | − | 0.660239i | \(-0.229545\pi\) |
−0.660239 | + | 0.751056i | \(0.729545\pi\) | |||||||
\(828\) | −9.33254 | − | 1.76902i | −0.324328 | − | 0.0614777i | ||||
\(829\) | − | 9.12880i | − | 0.317056i | −0.987354 | − | 0.158528i | \(-0.949325\pi\) | ||
0.987354 | − | 0.158528i | \(-0.0506749\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.7034 | − | 9.88900i | −0.648813 | − | 0.343045i | ||||
\(832\) | −2.55914 | + | 2.55914i | −0.0887223 | + | 0.0887223i | ||||
\(833\) | −4.20435 | + | 4.20435i | −0.145672 | + | 0.145672i | ||||
\(834\) | 15.9405 | + | 8.42816i | 0.551973 | + | 0.291843i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.41362i | 0.118062i | ||||||||
\(837\) | −35.2585 | − | 28.1464i | −1.21871 | − | 0.972883i | ||||
\(838\) | 4.46617 | + | 4.46617i | 0.154281 | + | 0.154281i | ||||
\(839\) | 11.1650 | 0.385458 | 0.192729 | − | 0.981252i | \(-0.438266\pi\) | ||||
0.192729 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9983 | −0.999942 | ||||||||
\(842\) | −9.73068 | − | 9.73068i | −0.335341 | − | 0.335341i | ||||
\(843\) | 18.4393 | − | 5.68443i | 0.635085 | − | 0.195782i | ||||
\(844\) | − | 6.97584i | − | 0.240118i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.73643 | − | 5.48425i | −0.128461 | − | 0.188552i | ||||
\(847\) | −7.52475 | + | 7.52475i | −0.258553 | + | 0.258553i | ||||
\(848\) | −2.01202 | + | 2.01202i | −0.0690929 | + | 0.0690929i | ||||
\(849\) | −14.5743 | + | 27.5648i | −0.500188 | + | 0.946023i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.02894i | 0.240949i | ||||||||
\(852\) | −7.36997 | − | 23.9069i | −0.252491 | − | 0.819038i | ||||
\(853\) | 25.4088 | + | 25.4088i | 0.869980 | + | 0.869980i | 0.992470 | − | 0.122490i | \(-0.0390878\pi\) |
−0.122490 | + | 0.992470i | \(0.539088\pi\) | |||||||
\(854\) | 14.8424 | 0.507898 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.527173 | −0.0180184 | ||||||||
\(857\) | 5.49909 | + | 5.49909i | 0.187845 | + | 0.187845i | 0.794764 | − | 0.606919i | \(-0.207595\pi\) |
−0.606919 | + | 0.794764i | \(0.707595\pi\) | |||||||
\(858\) | −1.10555 | − | 3.58622i | −0.0377429 | − | 0.122432i | ||||
\(859\) | − | 17.8783i | − | 0.610000i | −0.952352 | − | 0.305000i | \(-0.901343\pi\) | ||
0.952352 | − | 0.305000i | \(-0.0986565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.68938 | − | 8.86918i | 0.159814 | − | 0.302261i | ||||
\(862\) | −10.7082 | + | 10.7082i | −0.364724 | + | 0.364724i | ||||
\(863\) | 3.20549 | − | 3.20549i | 0.109116 | − | 0.109116i | −0.650441 | − | 0.759557i | \(-0.725416\pi\) |
0.759557 | + | 0.650441i | \(0.225416\pi\) | |||||||
\(864\) | −0.579214 | − | 5.16377i | −0.0197053 | − | 0.175675i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 10.3636i | − | 0.352170i | ||||||
\(867\) | 30.3779 | − | 9.36482i | 1.03169 | − | 0.318046i | ||||
\(868\) | 6.13941 | + | 6.13941i | 0.208385 | + | 0.208385i | ||||
\(869\) | −7.05055 | −0.239173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.1724 | 1.02235 | ||||||||
\(872\) | −5.92404 | − | 5.92404i | −0.200613 | − | 0.200613i | ||||
\(873\) | −3.70859 | + | 19.5648i | −0.125517 | + | 0.662169i | ||||
\(874\) | − | 18.0542i | − | 0.610691i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.9530 | + | 11.0784i | 0.707935 | + | 0.374305i | ||||
\(877\) | 11.2393 | − | 11.2393i | 0.379526 | − | 0.379526i | −0.491405 | − | 0.870931i | \(-0.663517\pi\) |
0.870931 | + | 0.491405i | \(0.163517\pi\) | |||||||
\(878\) | 2.92840 | − | 2.92840i | 0.0988288 | − | 0.0988288i | ||||
\(879\) | −26.3079 | − | 13.9097i | −0.887343 | − | 0.469163i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.11008i | − | 0.239545i | −0.992801 | − | 0.119772i | \(-0.961784\pi\) | ||
0.992801 | − | 0.119772i | \(-0.0382165\pi\) | |||||||
\(882\) | −0.558713 | + | 2.94751i | −0.0188128 | + | 0.0992480i | ||||
\(883\) | 9.93919 | + | 9.93919i | 0.334480 | + | 0.334480i | 0.854285 | − | 0.519805i | \(-0.173995\pi\) |
−0.519805 | + | 0.854285i | \(0.673995\pi\) | |||||||
\(884\) | −21.5191 | −0.723765 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.8040 | 1.33724 | ||||||||
\(887\) | −14.3454 | − | 14.3454i | −0.481672 | − | 0.481672i | 0.423993 | − | 0.905665i | \(-0.360628\pi\) |
−0.905665 | + | 0.423993i | \(0.860628\pi\) | |||||||
\(888\) | −3.67445 | + | 1.13275i | −0.123307 | + | 0.0380127i | ||||
\(889\) | − | 3.89122i | − | 0.130507i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.01420 | + | 1.97177i | 0.167982 | + | 0.0660568i | ||||
\(892\) | −6.44180 | + | 6.44180i | −0.215687 | + | 0.215687i | ||||
\(893\) | 8.91889 | − | 8.91889i | 0.298459 | − | 0.298459i | ||||
\(894\) | 10.3275 | − | 19.5328i | 0.345405 | − | 0.653275i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 5.84712 | + | 18.9671i | 0.195229 | + | 0.633292i | ||||
\(898\) | −2.05529 | − | 2.05529i | −0.0685860 | − | 0.0685860i | ||||
\(899\) | 0.356198 | 0.0118799 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.9185 | −0.563635 | ||||||||
\(902\) | 2.45199 | + | 2.45199i | 0.0816423 | + | 0.0816423i | ||||
\(903\) | −0.235099 | − | 0.762620i | −0.00782359 | − | 0.0253784i | ||||
\(904\) | 6.58726i | 0.219089i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.9795 | + | 28.3312i | −0.497661 | + | 0.941242i | ||||
\(907\) | −7.56005 | + | 7.56005i | −0.251027 | + | 0.251027i | −0.821392 | − | 0.570364i | \(-0.806802\pi\) |
0.570364 | + | 0.821392i | \(0.306802\pi\) | |||||||
\(908\) | −3.80409 | + | 3.80409i | −0.126243 | + | 0.126243i | ||||
\(909\) | 13.5581 | + | 19.9002i | 0.449693 | + | 0.660049i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3383i | 1.03829i | 0.854688 | + | 0.519143i | \(0.173749\pi\) | ||||
−0.854688 | + | 0.519143i | \(0.826251\pi\) | |||||||
\(912\) | 9.43801 | − | 2.90952i | 0.312524 | − | 0.0963440i | ||||
\(913\) | 0.627407 | + | 0.627407i | 0.0207641 | + | 0.0207641i | ||||
\(914\) | 40.4135 | 1.33676 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.2301 | 0.536258 | ||||||||
\(917\) | −10.7920 | − | 10.7920i | −0.356383 | − | 0.356383i | ||||
\(918\) | 19.2751 | − | 24.1455i | 0.636173 | − | 0.796921i | ||||
\(919\) | 6.42200i | 0.211842i | 0.994375 | + | 0.105921i | \(0.0337791\pi\) | ||||
−0.994375 | + | 0.105921i | \(0.966221\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.3610 | + | 12.8804i | 0.802724 | + | 0.424422i | ||||
\(922\) | −22.5469 | + | 22.5469i | −0.742542 | + | 0.742542i | ||||
\(923\) | −36.9634 | + | 36.9634i | −1.21666 | + | 1.21666i | ||||
\(924\) | −0.916670 | − | 0.484669i | −0.0301562 | − | 0.0159444i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.46720i | 0.0482153i | ||||||||
\(927\) | 38.1090 | + | 7.22371i | 1.25166 | + | 0.237258i | ||||
\(928\) | 0.0290092 | + | 0.0290092i | 0.000952273 | + | 0.000952273i | ||||
\(929\) | 34.6015 | 1.13524 | 0.567619 | − | 0.823291i | \(-0.307865\pi\) | ||||
0.567619 | + | 0.823291i | \(0.307865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.70208 | −0.186878 | ||||||||
\(932\) | 1.42491 | + | 1.42491i | 0.0466746 | + | 0.0466746i | ||||
\(933\) | −33.4168 | + | 10.3016i | −1.09402 | + | 0.337260i | ||||
\(934\) | − | 25.3408i | − | 0.829178i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.97294 | + | 6.11328i | −0.293290 | + | 0.199819i | ||||
\(937\) | −27.1028 | + | 27.1028i | −0.885410 | + | 0.885410i | −0.994078 | − | 0.108669i | \(-0.965341\pi\) |
0.108669 | + | 0.994078i | \(0.465341\pi\) | |||||||
\(938\) | 5.89503 | − | 5.89503i | 0.192479 | − | 0.192479i | ||||
\(939\) | 2.35600 | − | 4.45598i | 0.0768852 | − | 0.145416i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 11.0796i | − | 0.361184i | −0.983558 | − | 0.180592i | \(-0.942199\pi\) | ||
0.983558 | − | 0.180592i | \(-0.0578014\pi\) | |||||||
\(942\) | −0.0234548 | − | 0.0760833i | −0.000764198 | − | 0.00247893i | ||||
\(943\) | −12.9682 | − | 12.9682i | −0.422304 | − | 0.422304i | ||||
\(944\) | 9.35820 | 0.304583 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.275831 | 0.00896804 | ||||||||
\(947\) | −8.57908 | − | 8.57908i | −0.278783 | − | 0.278783i | 0.553840 | − | 0.832623i | \(-0.313162\pi\) |
−0.832623 | + | 0.553840i | \(0.813162\pi\) | |||||||
\(948\) | 6.00938 | + | 19.4934i | 0.195176 | + | 0.633117i | ||||
\(949\) | − | 49.5249i | − | 1.60764i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.15859 | + | 5.97395i | −0.102424 | + | 0.193719i | ||||
\(952\) | −4.20435 | + | 4.20435i | −0.136264 | + | 0.136264i | ||||
\(953\) | −32.2510 | + | 32.2510i | −1.04471 | + | 1.04471i | −0.0457608 | + | 0.998952i | \(0.514571\pi\) |
−0.998952 | + | 0.0457608i | \(0.985429\pi\) | |||||||
\(954\) | −7.05459 | + | 4.80631i | −0.228401 | + | 0.155610i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.0287i | 0.324353i | ||||||||
\(957\) | −0.0406517 | + | 0.0125320i | −0.00131408 | + | 0.000405102i | ||||
\(958\) | −12.6816 | − | 12.6816i | −0.409723 | − | 0.409723i | ||||
\(959\) | 5.21161 | 0.168292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.3846 | 1.43176 | ||||||||
\(962\) | 5.68121 | + | 5.68121i | 0.183170 | + | 0.183170i | ||||
\(963\) | −1.55385 | − | 0.294538i | −0.0500721 | − | 0.00949137i | ||||
\(964\) | − | 2.87963i | − | 0.0927465i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.84814 | + | 2.56335i | 0.155986 | + | 0.0824743i | ||||
\(967\) | 11.6969 | − | 11.6969i | 0.376148 | − | 0.376148i | −0.493563 | − | 0.869710i | \(-0.664306\pi\) |
0.869710 | + | 0.493563i | \(0.164306\pi\) | |||||||
\(968\) | −7.52475 | + | 7.52475i | −0.241855 | + | 0.241855i | ||||
\(969\) | 51.9134 | + | 27.4480i | 1.66770 | + | 0.881758i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 36.2562i | − | 1.16352i | −0.813361 | − | 0.581759i | \(-0.802365\pi\) | ||
0.813361 | − | 0.581759i | \(-0.197635\pi\) | |||||||
\(972\) | 1.17782 | − | 15.5439i | 0.0377787 | − | 0.498571i | ||||
\(973\) | −7.36130 | − | 7.36130i | −0.235992 | − | 0.235992i | ||||
\(974\) | 25.0320 | 0.802078 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.8424 | 0.475095 | ||||||||
\(977\) | 29.9247 | + | 29.9247i | 0.957377 | + | 0.957377i | 0.999128 | − | 0.0417515i | \(-0.0132938\pi\) |
−0.0417515 | + | 0.999128i | \(0.513294\pi\) | |||||||
\(978\) | −22.1936 | + | 6.84178i | −0.709672 | + | 0.218776i | ||||
\(979\) | 10.8602i | 0.347092i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1513 | − | 20.7710i | −0.451818 | − | 0.663168i | ||||
\(982\) | 23.0059 | − | 23.0059i | 0.734147 | − | 0.734147i | ||||
\(983\) | 35.8103 | − | 35.8103i | 1.14217 | − | 1.14217i | 0.154121 | − | 0.988052i | \(-0.450746\pi\) |
0.988052 | − | 0.154121i | \(-0.0492545\pi\) | |||||||
\(984\) | 4.68938 | − | 8.86918i | 0.149492 | − | 0.282739i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.243930i | 0.00776830i | ||||||||
\(987\) | 1.12870 | + | 3.66133i | 0.0359271 | + | 0.116541i | ||||
\(988\) | −14.5924 | − | 14.5924i | −0.464248 | − | 0.464248i | ||||
\(989\) | −1.45883 | −0.0463882 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9238 | 0.791731 | 0.395866 | − | 0.918308i | \(-0.370445\pi\) | ||||
0.395866 | + | 0.918308i | \(0.370445\pi\) | |||||||
\(992\) | 6.13941 | + | 6.13941i | 0.194926 | + | 0.194926i | ||||
\(993\) | −14.7060 | − | 47.7039i | −0.466682 | − | 1.51384i | ||||
\(994\) | 14.4437i | 0.458125i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.19990 | − | 2.26942i | 0.0380204 | − | 0.0719092i | ||||
\(997\) | −8.94298 | + | 8.94298i | −0.283227 | + | 0.283227i | −0.834395 | − | 0.551168i | \(-0.814182\pi\) |
0.551168 | + | 0.834395i | \(0.314182\pi\) | |||||||
\(998\) | −12.2224 | + | 12.2224i | −0.386894 | + | 0.386894i | ||||
\(999\) | −11.4634 | + | 1.28584i | −0.362686 | + | 0.0406820i |
(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 | 1050.2.j.c.743.5 | 12 | ||
3.2 | odd | 2 | 1050.2.j.d.743.1 | 12 | |||
5.2 | odd | 4 | 1050.2.j.d.407.1 | 12 | |||
5.3 | odd | 4 | 210.2.j.b.197.6 | yes | 12 | ||
5.4 | even | 2 | 210.2.j.a.113.2 | ✓ | 12 | ||
15.2 | even | 4 | inner | 1050.2.j.c.407.5 | 12 | ||
15.8 | even | 4 | 210.2.j.a.197.2 | yes | 12 | ||
15.14 | odd | 2 | 210.2.j.b.113.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.j.a.113.2 | ✓ | 12 | 5.4 | even | 2 | ||
210.2.j.a.197.2 | yes | 12 | 15.8 | even | 4 | ||
210.2.j.b.113.6 | yes | 12 | 15.14 | odd | 2 | ||
210.2.j.b.197.6 | yes | 12 | 5.3 | odd | 4 | ||
1050.2.j.c.407.5 | 12 | 15.2 | even | 4 | inner | ||
1050.2.j.c.743.5 | 12 | 1.1 | even | 1 | trivial | ||
1050.2.j.d.407.1 | 12 | 5.2 | odd | 4 | |||
1050.2.j.d.743.1 | 12 | 3.2 | odd | 2 |