Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(16,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.e (of order \(3\), 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: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.16 |
Dual form | 65.2.e.a.61.2 |
$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.535233i | 0.218508 | + | 0.378467i | 0.954352 | − | 0.298684i | \(-0.0965477\pi\) |
−0.735844 | + | 0.677151i | \(0.763214\pi\) | |||||||
\(3\) | −1.11803 | − | 1.93649i | −0.645497 | − | 1.11803i | −0.984186 | − | 0.177136i | \(-0.943317\pi\) |
0.338689 | − | 0.940898i | \(-0.390016\pi\) | |||||||
\(4\) | 0.809017 | − | 1.40126i | 0.404508 | − | 0.700629i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.690983 | − | 1.19682i | 0.282093 | − | 0.488599i | ||||
\(7\) | −2.11803 | + | 3.66854i | −0.800542 | + | 1.38658i | 0.118718 | + | 0.992928i | \(0.462121\pi\) |
−0.919260 | + | 0.393651i | \(0.871212\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0.309017 | + | 0.535233i | 0.0977198 | + | 0.169256i | ||||
\(11\) | 0.118034 | + | 0.204441i | 0.0355886 | + | 0.0616412i | 0.883271 | − | 0.468863i | \(-0.155336\pi\) |
−0.847683 | + | 0.530504i | \(0.822003\pi\) | |||||||
\(12\) | −3.61803 | −1.04444 | ||||||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | −1.11803 | − | 1.93649i | −0.288675 | − | 0.500000i | ||||
\(16\) | −0.927051 | − | 1.60570i | −0.231763 | − | 0.401425i | ||||
\(17\) | 1.73607 | − | 3.00696i | 0.421058 | − | 0.729294i | −0.574985 | − | 0.818164i | \(-0.694992\pi\) |
0.996043 | + | 0.0888696i | \(0.0283254\pi\) | |||||||
\(18\) | −1.23607 | −0.291344 | ||||||||
\(19\) | −2.11803 | + | 3.66854i | −0.485910 | + | 0.841621i | −0.999869 | − | 0.0161937i | \(-0.994845\pi\) |
0.513959 | + | 0.857815i | \(0.328179\pi\) | |||||||
\(20\) | 0.809017 | − | 1.40126i | 0.180902 | − | 0.313331i | ||||
\(21\) | 9.47214 | 2.06699 | ||||||||
\(22\) | −0.0729490 | + | 0.126351i | −0.0155528 | + | 0.0269382i | ||||
\(23\) | −1.88197 | − | 3.25966i | −0.392417 | − | 0.679686i | 0.600351 | − | 0.799737i | \(-0.295028\pi\) |
−0.992768 | + | 0.120051i | \(0.961694\pi\) | |||||||
\(24\) | −2.50000 | − | 4.33013i | −0.510310 | − | 0.883883i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.16312 | + | 0.535233i | −0.424223 | + | 0.104968i | ||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 3.42705 | + | 5.93583i | 0.647652 | + | 1.12177i | ||||
\(29\) | 3.73607 | + | 6.47106i | 0.693770 | + | 1.20165i | 0.970593 | + | 0.240725i | \(0.0773851\pi\) |
−0.276823 | + | 0.960921i | \(0.589282\pi\) | |||||||
\(30\) | 0.690983 | − | 1.19682i | 0.126156 | − | 0.218508i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 2.80902 | − | 4.86536i | 0.496569 | − | 0.860082i | ||||
\(33\) | 0.263932 | − | 0.457144i | 0.0459447 | − | 0.0795785i | ||||
\(34\) | 2.14590 | 0.368018 | ||||||||
\(35\) | −2.11803 | + | 3.66854i | −0.358013 | + | 0.620097i | ||||
\(36\) | 1.61803 | + | 2.80252i | 0.269672 | + | 0.467086i | ||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | −2.61803 | −0.424701 | ||||||||
\(39\) | 7.82624 | − | 1.93649i | 1.25320 | − | 0.310087i | ||||
\(40\) | 2.23607 | 0.353553 | ||||||||
\(41\) | −5.97214 | − | 10.3440i | −0.932691 | − | 1.61547i | −0.778701 | − | 0.627396i | \(-0.784121\pi\) |
−0.153990 | − | 0.988072i | \(-0.549212\pi\) | |||||||
\(42\) | 2.92705 | + | 5.06980i | 0.451654 | + | 0.782287i | ||||
\(43\) | 3.11803 | − | 5.40059i | 0.475496 | − | 0.823583i | −0.524110 | − | 0.851650i | \(-0.675602\pi\) |
0.999606 | + | 0.0280676i | \(0.00893538\pi\) | |||||||
\(44\) | 0.381966 | 0.0575835 | ||||||||
\(45\) | −1.00000 | + | 1.73205i | −0.149071 | + | 0.258199i | ||||
\(46\) | 1.16312 | − | 2.01458i | 0.171493 | − | 0.297034i | ||||
\(47\) | −4.94427 | −0.721196 | −0.360598 | − | 0.932721i | \(-0.617427\pi\) | ||||
−0.360598 | + | 0.932721i | \(0.617427\pi\) | |||||||
\(48\) | −2.07295 | + | 3.59045i | −0.299204 | + | 0.518237i | ||||
\(49\) | −5.47214 | − | 9.47802i | −0.781734 | − | 1.35400i | ||||
\(50\) | 0.309017 | + | 0.535233i | 0.0437016 | + | 0.0756934i | ||||
\(51\) | −7.76393 | −1.08717 | ||||||||
\(52\) | 4.04508 | + | 4.20378i | 0.560952 | + | 0.582959i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −0.690983 | − | 1.19682i | −0.0940309 | − | 0.162866i | ||||
\(55\) | 0.118034 | + | 0.204441i | 0.0159157 | + | 0.0275668i | ||||
\(56\) | −4.73607 | + | 8.20311i | −0.632884 | + | 1.09619i | ||||
\(57\) | 9.47214 | 1.25462 | ||||||||
\(58\) | −2.30902 | + | 3.99933i | −0.303189 | + | 0.525138i | ||||
\(59\) | 0.354102 | − | 0.613323i | 0.0461001 | − | 0.0798478i | −0.842055 | − | 0.539392i | \(-0.818654\pi\) |
0.888155 | + | 0.459545i | \(0.151987\pi\) | |||||||
\(60\) | −3.61803 | −0.467086 | ||||||||
\(61\) | −7.20820 | + | 12.4850i | −0.922916 | + | 1.59854i | −0.128037 | + | 0.991769i | \(0.540868\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.23607 | − | 7.33708i | −0.533694 | − | 0.924386i | ||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −1.00000 | + | 3.46410i | −0.124035 | + | 0.429669i | ||||
\(66\) | 0.326238 | 0.0401571 | ||||||||
\(67\) | 1.35410 | + | 2.34537i | 0.165430 | + | 0.286533i | 0.936808 | − | 0.349844i | \(-0.113766\pi\) |
−0.771378 | + | 0.636377i | \(0.780432\pi\) | |||||||
\(68\) | −2.80902 | − | 4.86536i | −0.340643 | − | 0.590012i | ||||
\(69\) | −4.20820 | + | 7.28882i | −0.506608 | + | 0.877471i | ||||
\(70\) | −2.61803 | −0.312915 | ||||||||
\(71\) | 3.11803 | − | 5.40059i | 0.370043 | − | 0.640933i | −0.619529 | − | 0.784974i | \(-0.712676\pi\) |
0.989572 | + | 0.144041i | \(0.0460098\pi\) | |||||||
\(72\) | −2.23607 | + | 3.87298i | −0.263523 | + | 0.456435i | ||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0.927051 | − | 1.60570i | 0.107767 | − | 0.186659i | ||||
\(75\) | −1.11803 | − | 1.93649i | −0.129099 | − | 0.223607i | ||||
\(76\) | 3.42705 | + | 5.93583i | 0.393110 | + | 0.680886i | ||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 3.45492 | + | 3.59045i | 0.391192 | + | 0.406539i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −0.927051 | − | 1.60570i | −0.103647 | − | 0.179523i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 3.69098 | − | 6.39297i | 0.407601 | − | 0.705985i | ||||
\(83\) | 8.94427 | 0.981761 | 0.490881 | − | 0.871227i | \(-0.336675\pi\) | ||||
0.490881 | + | 0.871227i | \(0.336675\pi\) | |||||||
\(84\) | 7.66312 | − | 13.2729i | 0.836115 | − | 1.44819i | ||||
\(85\) | 1.73607 | − | 3.00696i | 0.188303 | − | 0.326150i | ||||
\(86\) | 3.85410 | 0.415599 | ||||||||
\(87\) | 8.35410 | − | 14.4697i | 0.895654 | − | 1.55132i | ||||
\(88\) | 0.263932 | + | 0.457144i | 0.0281352 | + | 0.0487317i | ||||
\(89\) | 4.50000 | + | 7.79423i | 0.476999 | + | 0.826187i | 0.999653 | − | 0.0263586i | \(-0.00839118\pi\) |
−0.522654 | + | 0.852545i | \(0.675058\pi\) | |||||||
\(90\) | −1.23607 | −0.130293 | ||||||||
\(91\) | −10.5902 | − | 11.0056i | −1.11015 | − | 1.15370i | ||||
\(92\) | −6.09017 | −0.634944 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.52786 | − | 2.64634i | −0.157587 | − | 0.272949i | ||||
\(95\) | −2.11803 | + | 3.66854i | −0.217306 | + | 0.376385i | ||||
\(96\) | −12.5623 | −1.28213 | ||||||||
\(97\) | 1.73607 | − | 3.00696i | 0.176271 | − | 0.305310i | −0.764329 | − | 0.644826i | \(-0.776930\pi\) |
0.940600 | + | 0.339516i | \(0.110263\pi\) | |||||||
\(98\) | 3.38197 | − | 5.85774i | 0.341630 | − | 0.591721i | ||||
\(99\) | −0.472136 | −0.0474514 | ||||||||
\(100\) | 0.809017 | − | 1.40126i | 0.0809017 | − | 0.140126i | ||||
\(101\) | −0.263932 | − | 0.457144i | −0.0262622 | − | 0.0454875i | 0.852596 | − | 0.522571i | \(-0.175027\pi\) |
−0.878858 | + | 0.477084i | \(0.841694\pi\) | |||||||
\(102\) | −2.39919 | − | 4.15551i | −0.237555 | − | 0.411457i | ||||
\(103\) | 12.9443 | 1.27544 | 0.637719 | − | 0.770270i | \(-0.279878\pi\) | ||||
0.637719 | + | 0.770270i | \(0.279878\pi\) | |||||||
\(104\) | −2.23607 | + | 7.74597i | −0.219265 | + | 0.759555i | ||||
\(105\) | 9.47214 | 0.924386 | ||||||||
\(106\) | 1.85410 | + | 3.21140i | 0.180086 | + | 0.311919i | ||||
\(107\) | 2.88197 | + | 4.99171i | 0.278610 | + | 0.482567i | 0.971040 | − | 0.238919i | \(-0.0767929\pi\) |
−0.692429 | + | 0.721486i | \(0.743460\pi\) | |||||||
\(108\) | −1.80902 | + | 3.13331i | −0.174073 | + | 0.301503i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −0.0729490 | + | 0.126351i | −0.00695542 | + | 0.0120471i | ||||
\(111\) | −3.35410 | + | 5.80948i | −0.318357 | + | 0.551411i | ||||
\(112\) | 7.85410 | 0.742143 | ||||||||
\(113\) | −0.736068 | + | 1.27491i | −0.0692435 | + | 0.119933i | −0.898568 | − | 0.438833i | \(-0.855392\pi\) |
0.829325 | + | 0.558766i | \(0.188725\pi\) | |||||||
\(114\) | 2.92705 | + | 5.06980i | 0.274143 | + | 0.474830i | ||||
\(115\) | −1.88197 | − | 3.25966i | −0.175494 | − | 0.303965i | ||||
\(116\) | 12.0902 | 1.12254 | ||||||||
\(117\) | −5.00000 | − | 5.19615i | −0.462250 | − | 0.480384i | ||||
\(118\) | 0.437694 | 0.0402930 | ||||||||
\(119\) | 7.35410 | + | 12.7377i | 0.674149 | + | 1.16766i | ||||
\(120\) | −2.50000 | − | 4.33013i | −0.228218 | − | 0.395285i | ||||
\(121\) | 5.47214 | − | 9.47802i | 0.497467 | − | 0.861638i | ||||
\(122\) | −8.90983 | −0.806658 | ||||||||
\(123\) | −13.3541 | + | 23.1300i | −1.20410 | + | 2.08556i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.61803 | − | 4.53457i | 0.233233 | − | 0.403971i | ||||
\(127\) | 2.11803 | + | 3.66854i | 0.187945 | + | 0.325531i | 0.944565 | − | 0.328325i | \(-0.106484\pi\) |
−0.756620 | + | 0.653855i | \(0.773151\pi\) | |||||||
\(128\) | −5.69098 | − | 9.85707i | −0.503017 | − | 0.871250i | ||||
\(129\) | −13.9443 | −1.22772 | ||||||||
\(130\) | −2.16312 | + | 0.535233i | −0.189718 | + | 0.0469431i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | −0.427051 | − | 0.739674i | −0.0371700 | − | 0.0643804i | ||||
\(133\) | −8.97214 | − | 15.5402i | −0.777983 | − | 1.34751i | ||||
\(134\) | −0.836881 | + | 1.44952i | −0.0722955 | + | 0.125219i | ||||
\(135\) | −2.23607 | −0.192450 | ||||||||
\(136\) | 3.88197 | − | 6.72376i | 0.332876 | − | 0.576558i | ||||
\(137\) | −0.736068 | + | 1.27491i | −0.0628865 | + | 0.108923i | −0.895755 | − | 0.444549i | \(-0.853364\pi\) |
0.832868 | + | 0.553472i | \(0.186697\pi\) | |||||||
\(138\) | −5.20163 | −0.442792 | ||||||||
\(139\) | 8.35410 | − | 14.4697i | 0.708586 | − | 1.22731i | −0.256796 | − | 0.966466i | \(-0.582667\pi\) |
0.965382 | − | 0.260841i | \(-0.0839998\pi\) | |||||||
\(140\) | 3.42705 | + | 5.93583i | 0.289639 | + | 0.501669i | ||||
\(141\) | 5.52786 | + | 9.57454i | 0.465530 | + | 0.806322i | ||||
\(142\) | 3.85410 | 0.323429 | ||||||||
\(143\) | −0.826238 | + | 0.204441i | −0.0690935 | + | 0.0170962i | ||||
\(144\) | 3.70820 | 0.309017 | ||||||||
\(145\) | 3.73607 | + | 6.47106i | 0.310264 | + | 0.537392i | ||||
\(146\) | −1.85410 | − | 3.21140i | −0.153447 | − | 0.265777i | ||||
\(147\) | −12.2361 | + | 21.1935i | −1.00921 | + | 1.74801i | ||||
\(148\) | −4.85410 | −0.399005 | ||||||||
\(149\) | −2.26393 | + | 3.92125i | −0.185469 | + | 0.321241i | −0.943734 | − | 0.330705i | \(-0.892714\pi\) |
0.758266 | + | 0.651946i | \(0.226047\pi\) | |||||||
\(150\) | 0.690983 | − | 1.19682i | 0.0564185 | − | 0.0977198i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | −4.73607 | + | 8.20311i | −0.384146 | + | 0.665360i | ||||
\(153\) | 3.47214 | + | 6.01392i | 0.280706 | + | 0.486196i | ||||
\(154\) | −0.309017 | − | 0.535233i | −0.0249013 | − | 0.0431303i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.61803 | − | 12.5332i | 0.289675 | − | 1.00346i | ||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.70820 | − | 11.6190i | −0.531995 | − | 0.921443i | ||||
\(160\) | 2.80902 | − | 4.86536i | 0.222072 | − | 0.384640i | ||||
\(161\) | 15.9443 | 1.25658 | ||||||||
\(162\) | −3.39919 | + | 5.88756i | −0.267065 | + | 0.462571i | ||||
\(163\) | −7.35410 | + | 12.7377i | −0.576018 | + | 0.997692i | 0.419913 | + | 0.907565i | \(0.362061\pi\) |
−0.995930 | + | 0.0901274i | \(0.971273\pi\) | |||||||
\(164\) | −19.3262 | −1.50913 | ||||||||
\(165\) | 0.263932 | − | 0.457144i | 0.0205471 | − | 0.0355886i | ||||
\(166\) | 2.76393 | + | 4.78727i | 0.214523 | + | 0.371564i | ||||
\(167\) | 8.59017 | + | 14.8786i | 0.664727 | + | 1.15134i | 0.979359 | + | 0.202128i | \(0.0647856\pi\) |
−0.314632 | + | 0.949214i | \(0.601881\pi\) | |||||||
\(168\) | 21.1803 | 1.63410 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 2.14590 | 0.164583 | ||||||||
\(171\) | −4.23607 | − | 7.33708i | −0.323940 | − | 0.561081i | ||||
\(172\) | −5.04508 | − | 8.73834i | −0.384684 | − | 0.666292i | ||||
\(173\) | 9.44427 | − | 16.3580i | 0.718035 | − | 1.24367i | −0.243743 | − | 0.969840i | \(-0.578375\pi\) |
0.961777 | − | 0.273833i | \(-0.0882914\pi\) | |||||||
\(174\) | 10.3262 | 0.782830 | ||||||||
\(175\) | −2.11803 | + | 3.66854i | −0.160108 | + | 0.277316i | ||||
\(176\) | 0.218847 | − | 0.379054i | 0.0164962 | − | 0.0285723i | ||||
\(177\) | −1.58359 | −0.119030 | ||||||||
\(178\) | −2.78115 | + | 4.81710i | −0.208456 | + | 0.361057i | ||||
\(179\) | 4.11803 | + | 7.13264i | 0.307796 | + | 0.533119i | 0.977880 | − | 0.209167i | \(-0.0670751\pi\) |
−0.670084 | + | 0.742286i | \(0.733742\pi\) | |||||||
\(180\) | 1.61803 | + | 2.80252i | 0.120601 | + | 0.208887i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 2.61803 | − | 9.06914i | 0.194062 | − | 0.672249i | ||||
\(183\) | 32.2361 | 2.38296 | ||||||||
\(184\) | −4.20820 | − | 7.28882i | −0.310233 | − | 0.537339i | ||||
\(185\) | −1.50000 | − | 2.59808i | −0.110282 | − | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.819660 | 0.0599395 | ||||||||
\(188\) | −4.00000 | + | 6.92820i | −0.291730 | + | 0.505291i | ||||
\(189\) | 4.73607 | − | 8.20311i | 0.344498 | − | 0.596688i | ||||
\(190\) | −2.61803 | −0.189932 | ||||||||
\(191\) | 13.5902 | − | 23.5389i | 0.983350 | − | 1.70321i | 0.334300 | − | 0.942467i | \(-0.391500\pi\) |
0.649050 | − | 0.760746i | \(-0.275167\pi\) | |||||||
\(192\) | 0.263932 | + | 0.457144i | 0.0190477 | + | 0.0329915i | ||||
\(193\) | 1.73607 | + | 3.00696i | 0.124965 | + | 0.216446i | 0.921719 | − | 0.387858i | \(-0.126785\pi\) |
−0.796754 | + | 0.604303i | \(0.793452\pi\) | |||||||
\(194\) | 2.14590 | 0.154067 | ||||||||
\(195\) | 7.82624 | − | 1.93649i | 0.560449 | − | 0.138675i | ||||
\(196\) | −17.7082 | −1.26487 | ||||||||
\(197\) | −1.50000 | − | 2.59808i | −0.106871 | − | 0.185105i | 0.807630 | − | 0.589689i | \(-0.200750\pi\) |
−0.914501 | + | 0.404584i | \(0.867416\pi\) | |||||||
\(198\) | −0.145898 | − | 0.252703i | −0.0103685 | − | 0.0179588i | ||||
\(199\) | 0.645898 | − | 1.11873i | 0.0457865 | − | 0.0793045i | −0.842224 | − | 0.539128i | \(-0.818754\pi\) |
0.888010 | + | 0.459823i | \(0.152087\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | 3.02786 | − | 5.24441i | 0.213569 | − | 0.369912i | ||||
\(202\) | 0.163119 | − | 0.282530i | 0.0114770 | − | 0.0198788i | ||||
\(203\) | −31.6525 | −2.22157 | ||||||||
\(204\) | −6.28115 | + | 10.8793i | −0.439769 | + | 0.761702i | ||||
\(205\) | −5.97214 | − | 10.3440i | −0.417112 | − | 0.722459i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 7.52786 | 0.523223 | ||||||||
\(208\) | 6.48936 | − | 1.60570i | 0.449956 | − | 0.111335i | ||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 2.92705 | + | 5.06980i | 0.201986 | + | 0.349850i | ||||
\(211\) | 6.59017 | + | 11.4145i | 0.453686 | + | 0.785807i | 0.998612 | − | 0.0526772i | \(-0.0167754\pi\) |
−0.544926 | + | 0.838484i | \(0.683442\pi\) | |||||||
\(212\) | 4.85410 | − | 8.40755i | 0.333381 | − | 0.577433i | ||||
\(213\) | −13.9443 | −0.955446 | ||||||||
\(214\) | −1.78115 | + | 3.08505i | −0.121757 | + | 0.210889i | ||||
\(215\) | 3.11803 | − | 5.40059i | 0.212648 | − | 0.368317i | ||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.618034 | − | 1.07047i | −0.0418585 | − | 0.0725011i | ||||
\(219\) | 6.70820 | + | 11.6190i | 0.453298 | + | 0.785136i | ||||
\(220\) | 0.381966 | 0.0257521 | ||||||||
\(221\) | 8.68034 | + | 9.02087i | 0.583903 | + | 0.606810i | ||||
\(222\) | −4.14590 | −0.278254 | ||||||||
\(223\) | −0.354102 | − | 0.613323i | −0.0237124 | − | 0.0410711i | 0.853926 | − | 0.520395i | \(-0.174215\pi\) |
−0.877638 | + | 0.479324i | \(0.840882\pi\) | |||||||
\(224\) | 11.8992 | + | 20.6100i | 0.795048 | + | 1.37706i | ||||
\(225\) | −1.00000 | + | 1.73205i | −0.0666667 | + | 0.115470i | ||||
\(226\) | −0.909830 | −0.0605210 | ||||||||
\(227\) | 3.11803 | − | 5.40059i | 0.206951 | − | 0.358450i | −0.743801 | − | 0.668401i | \(-0.766979\pi\) |
0.950753 | + | 0.309951i | \(0.100313\pi\) | |||||||
\(228\) | 7.66312 | − | 13.2729i | 0.507502 | − | 0.879020i | ||||
\(229\) | 15.8885 | 1.04994 | 0.524972 | − | 0.851119i | \(-0.324076\pi\) | ||||
0.524972 | + | 0.851119i | \(0.324076\pi\) | |||||||
\(230\) | 1.16312 | − | 2.01458i | 0.0766938 | − | 0.132838i | ||||
\(231\) | 1.11803 | + | 1.93649i | 0.0735612 | + | 0.127412i | ||||
\(232\) | 8.35410 | + | 14.4697i | 0.548474 | + | 0.949984i | ||||
\(233\) | −15.8885 | −1.04089 | −0.520447 | − | 0.853894i | \(-0.674235\pi\) | ||||
−0.520447 | + | 0.853894i | \(0.674235\pi\) | |||||||
\(234\) | 1.23607 | − | 4.28187i | 0.0808043 | − | 0.279914i | ||||
\(235\) | −4.94427 | −0.322529 | ||||||||
\(236\) | −0.572949 | − | 0.992377i | −0.0372958 | − | 0.0645982i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.54508 | + | 7.87232i | −0.294614 | + | 0.510287i | ||||
\(239\) | −25.8885 | −1.67459 | −0.837295 | − | 0.546751i | \(-0.815864\pi\) | ||||
−0.837295 | + | 0.546751i | \(0.815864\pi\) | |||||||
\(240\) | −2.07295 | + | 3.59045i | −0.133808 | + | 0.231763i | ||||
\(241\) | −7.50000 | + | 12.9904i | −0.483117 | + | 0.836784i | −0.999812 | − | 0.0193858i | \(-0.993829\pi\) |
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(242\) | 6.76393 | 0.434802 | ||||||||
\(243\) | 8.94427 | − | 15.4919i | 0.573775 | − | 0.993808i | ||||
\(244\) | 11.6631 | + | 20.2011i | 0.746655 | + | 1.29324i | ||||
\(245\) | −5.47214 | − | 9.47802i | −0.349602 | − | 0.605528i | ||||
\(246\) | −16.5066 | −1.05242 | ||||||||
\(247\) | −10.5902 | − | 11.0056i | −0.673836 | − | 0.700271i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | − | 17.3205i | −0.633724 | − | 1.09764i | ||||
\(250\) | 0.309017 | + | 0.535233i | 0.0195440 | + | 0.0338511i | ||||
\(251\) | −10.1180 | + | 17.5249i | −0.638645 | + | 1.10616i | 0.347086 | + | 0.937833i | \(0.387171\pi\) |
−0.985730 | + | 0.168332i | \(0.946162\pi\) | |||||||
\(252\) | −13.7082 | −0.863536 | ||||||||
\(253\) | 0.444272 | − | 0.769502i | 0.0279311 | − | 0.0483781i | ||||
\(254\) | −1.30902 | + | 2.26728i | −0.0821350 | + | 0.142262i | ||||
\(255\) | −7.76393 | −0.486196 | ||||||||
\(256\) | 3.28115 | − | 5.68312i | 0.205072 | − | 0.355195i | ||||
\(257\) | −8.73607 | − | 15.1313i | −0.544941 | − | 0.943865i | −0.998611 | − | 0.0526955i | \(-0.983219\pi\) |
0.453670 | − | 0.891170i | \(-0.350115\pi\) | |||||||
\(258\) | −4.30902 | − | 7.46344i | −0.268268 | − | 0.464653i | ||||
\(259\) | 12.7082 | 0.789649 | ||||||||
\(260\) | 4.04508 | + | 4.20378i | 0.250866 | + | 0.260707i | ||||
\(261\) | −14.9443 | −0.925027 | ||||||||
\(262\) | −3.70820 | − | 6.42280i | −0.229094 | − | 0.396802i | ||||
\(263\) | −1.88197 | − | 3.25966i | −0.116047 | − | 0.200999i | 0.802151 | − | 0.597122i | \(-0.203689\pi\) |
−0.918198 | + | 0.396122i | \(0.870356\pi\) | |||||||
\(264\) | 0.590170 | − | 1.02220i | 0.0363224 | − | 0.0629123i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 5.54508 | − | 9.60437i | 0.339991 | − | 0.588882i | ||||
\(267\) | 10.0623 | − | 17.4284i | 0.615803 | − | 1.06660i | ||||
\(268\) | 4.38197 | 0.267671 | ||||||||
\(269\) | 3.26393 | − | 5.65330i | 0.199005 | − | 0.344688i | −0.749201 | − | 0.662343i | \(-0.769562\pi\) |
0.948206 | + | 0.317655i | \(0.102896\pi\) | |||||||
\(270\) | −0.690983 | − | 1.19682i | −0.0420519 | − | 0.0728360i | ||||
\(271\) | −0.645898 | − | 1.11873i | −0.0392355 | − | 0.0679579i | 0.845741 | − | 0.533594i | \(-0.179159\pi\) |
−0.884976 | + | 0.465636i | \(0.845826\pi\) | |||||||
\(272\) | −6.43769 | −0.390343 | ||||||||
\(273\) | −9.47214 | + | 32.8124i | −0.573280 | + | 1.98590i | ||||
\(274\) | −0.909830 | −0.0549648 | ||||||||
\(275\) | 0.118034 | + | 0.204441i | 0.00711772 | + | 0.0123282i | ||||
\(276\) | 6.80902 | + | 11.7936i | 0.409855 | + | 0.709889i | ||||
\(277\) | −8.44427 | + | 14.6259i | −0.507367 | + | 0.878786i | 0.492597 | + | 0.870258i | \(0.336048\pi\) |
−0.999964 | + | 0.00852782i | \(0.997285\pi\) | |||||||
\(278\) | 10.3262 | 0.619327 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.73607 | + | 8.20311i | −0.283034 | + | 0.490230i | ||||
\(281\) | −15.8885 | −0.947831 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(282\) | −3.41641 | + | 5.91739i | −0.203444 | + | 0.352376i | ||||
\(283\) | 5.35410 | + | 9.27358i | 0.318268 | + | 0.551257i | 0.980127 | − | 0.198372i | \(-0.0635654\pi\) |
−0.661859 | + | 0.749629i | \(0.730232\pi\) | |||||||
\(284\) | −5.04508 | − | 8.73834i | −0.299371 | − | 0.518525i | ||||
\(285\) | 9.47214 | 0.561081 | ||||||||
\(286\) | −0.364745 | − | 0.379054i | −0.0215678 | − | 0.0224139i | ||||
\(287\) | 50.5967 | 2.98663 | ||||||||
\(288\) | 5.61803 | + | 9.73072i | 0.331046 | + | 0.573388i | ||||
\(289\) | 2.47214 | + | 4.28187i | 0.145420 | + | 0.251874i | ||||
\(290\) | −2.30902 | + | 3.99933i | −0.135590 | + | 0.234849i | ||||
\(291\) | −7.76393 | −0.455130 | ||||||||
\(292\) | −4.85410 | + | 8.40755i | −0.284065 | + | 0.492015i | ||||
\(293\) | 14.9721 | − | 25.9325i | 0.874682 | − | 1.51499i | 0.0175799 | − | 0.999845i | \(-0.494404\pi\) |
0.857102 | − | 0.515147i | \(-0.172263\pi\) | |||||||
\(294\) | −15.1246 | −0.882085 | ||||||||
\(295\) | 0.354102 | − | 0.613323i | 0.0206166 | − | 0.0357090i | ||||
\(296\) | −3.35410 | − | 5.80948i | −0.194953 | − | 0.337669i | ||||
\(297\) | −0.263932 | − | 0.457144i | −0.0153149 | − | 0.0265262i | ||||
\(298\) | −2.79837 | −0.162105 | ||||||||
\(299\) | 13.1738 | − | 3.25966i | 0.761858 | − | 0.188511i | ||||
\(300\) | −3.61803 | −0.208887 | ||||||||
\(301\) | 13.2082 | + | 22.8773i | 0.761308 | + | 1.31862i | ||||
\(302\) | 2.47214 | + | 4.28187i | 0.142255 | + | 0.246394i | ||||
\(303\) | −0.590170 | + | 1.02220i | −0.0339044 | + | 0.0587241i | ||||
\(304\) | 7.85410 | 0.450464 | ||||||||
\(305\) | −7.20820 | + | 12.4850i | −0.412741 | + | 0.714888i | ||||
\(306\) | −2.14590 | + | 3.71680i | −0.122673 | + | 0.212476i | ||||
\(307\) | 24.9443 | 1.42364 | 0.711822 | − | 0.702360i | \(-0.247870\pi\) | ||||
0.711822 | + | 0.702360i | \(0.247870\pi\) | |||||||
\(308\) | −0.809017 | + | 1.40126i | −0.0460980 | + | 0.0798441i | ||||
\(309\) | −14.4721 | − | 25.0665i | −0.823291 | − | 1.42598i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 17.5000 | − | 4.33013i | 0.990742 | − | 0.245145i | ||||
\(313\) | 3.88854 | 0.219793 | 0.109897 | − | 0.993943i | \(-0.464948\pi\) | ||||
0.109897 | + | 0.993943i | \(0.464948\pi\) | |||||||
\(314\) | −5.56231 | − | 9.63420i | −0.313899 | − | 0.543689i | ||||
\(315\) | −4.23607 | − | 7.33708i | −0.238675 | − | 0.413398i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.8885 | −0.667727 | −0.333864 | − | 0.942621i | \(-0.608352\pi\) | ||||
−0.333864 | + | 0.942621i | \(0.608352\pi\) | |||||||
\(318\) | 4.14590 | − | 7.18091i | 0.232490 | − | 0.402685i | ||||
\(319\) | −0.881966 | + | 1.52761i | −0.0493806 | + | 0.0855297i | ||||
\(320\) | −0.236068 | −0.0131966 | ||||||||
\(321\) | 6.44427 | − | 11.1618i | 0.359684 | − | 0.622991i | ||||
\(322\) | 4.92705 | + | 8.53390i | 0.274574 | + | 0.475576i | ||||
\(323\) | 7.35410 | + | 12.7377i | 0.409193 | + | 0.708743i | ||||
\(324\) | 17.7984 | 0.988799 | ||||||||
\(325\) | −1.00000 | + | 3.46410i | −0.0554700 | + | 0.192154i | ||||
\(326\) | −9.09017 | −0.503458 | ||||||||
\(327\) | 2.23607 | + | 3.87298i | 0.123655 | + | 0.214176i | ||||
\(328\) | −13.3541 | − | 23.1300i | −0.737357 | − | 1.27714i | ||||
\(329\) | 10.4721 | − | 18.1383i | 0.577348 | − | 0.999995i | ||||
\(330\) | 0.326238 | 0.0179588 | ||||||||
\(331\) | 2.82624 | − | 4.89519i | 0.155344 | − | 0.269064i | −0.777840 | − | 0.628462i | \(-0.783685\pi\) |
0.933184 | + | 0.359398i | \(0.117018\pi\) | |||||||
\(332\) | 7.23607 | − | 12.5332i | 0.397131 | − | 0.687851i | ||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | −5.30902 | + | 9.19549i | −0.290496 | + | 0.503155i | ||||
\(335\) | 1.35410 | + | 2.34537i | 0.0739825 | + | 0.128141i | ||||
\(336\) | −8.78115 | − | 15.2094i | −0.479051 | − | 0.829741i | ||||
\(337\) | −7.88854 | −0.429716 | −0.214858 | − | 0.976645i | \(-0.568929\pi\) | ||||
−0.214858 | + | 0.976645i | \(0.568929\pi\) | |||||||
\(338\) | 0.309017 | − | 8.02850i | 0.0168083 | − | 0.436693i | ||||
\(339\) | 3.29180 | 0.178786 | ||||||||
\(340\) | −2.80902 | − | 4.86536i | −0.152340 | − | 0.263861i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.61803 | − | 4.53457i | 0.141567 | − | 0.245201i | ||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 6.97214 | − | 12.0761i | 0.375912 | − | 0.651099i | ||||
\(345\) | −4.20820 | + | 7.28882i | −0.226562 | + | 0.392417i | ||||
\(346\) | 11.6738 | 0.627585 | ||||||||
\(347\) | −15.3541 | + | 26.5941i | −0.824251 | + | 1.42765i | 0.0782387 | + | 0.996935i | \(0.475070\pi\) |
−0.902490 | + | 0.430711i | \(0.858263\pi\) | |||||||
\(348\) | −13.5172 | − | 23.4125i | −0.724599 | − | 1.25504i | ||||
\(349\) | −1.20820 | − | 2.09267i | −0.0646737 | − | 0.112018i | 0.831876 | − | 0.554962i | \(-0.187267\pi\) |
−0.896549 | + | 0.442944i | \(0.853934\pi\) | |||||||
\(350\) | −2.61803 | −0.139940 | ||||||||
\(351\) | 2.23607 | − | 7.74597i | 0.119352 | − | 0.413449i | ||||
\(352\) | 1.32624 | 0.0706887 | ||||||||
\(353\) | 9.73607 | + | 16.8634i | 0.518199 | + | 0.897546i | 0.999776 | + | 0.0211430i | \(0.00673053\pi\) |
−0.481578 | + | 0.876403i | \(0.659936\pi\) | |||||||
\(354\) | −0.489357 | − | 0.847591i | −0.0260090 | − | 0.0450490i | ||||
\(355\) | 3.11803 | − | 5.40059i | 0.165488 | − | 0.286634i | ||||
\(356\) | 14.5623 | 0.771801 | ||||||||
\(357\) | 16.4443 | − | 28.4823i | 0.870323 | − | 1.50744i | ||||
\(358\) | −2.54508 | + | 4.40822i | −0.134512 | + | 0.232981i | ||||
\(359\) | 17.8885 | 0.944121 | 0.472061 | − | 0.881566i | \(-0.343510\pi\) | ||||
0.472061 | + | 0.881566i | \(0.343510\pi\) | |||||||
\(360\) | −2.23607 | + | 3.87298i | −0.117851 | + | 0.204124i | ||||
\(361\) | 0.527864 | + | 0.914287i | 0.0277823 | + | 0.0481204i | ||||
\(362\) | 1.85410 | + | 3.21140i | 0.0974494 | + | 0.168787i | ||||
\(363\) | −24.4721 | −1.28445 | ||||||||
\(364\) | −23.9894 | + | 5.93583i | −1.25738 | + | 0.311122i | ||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 9.96149 | + | 17.2538i | 0.520696 | + | 0.901871i | ||||
\(367\) | −2.82624 | − | 4.89519i | −0.147528 | − | 0.255527i | 0.782785 | − | 0.622292i | \(-0.213798\pi\) |
−0.930313 | + | 0.366766i | \(0.880465\pi\) | |||||||
\(368\) | −3.48936 | + | 6.04374i | −0.181895 | + | 0.315052i | ||||
\(369\) | 23.8885 | 1.24359 | ||||||||
\(370\) | 0.927051 | − | 1.60570i | 0.0481951 | − | 0.0834763i | ||||
\(371\) | −12.7082 | + | 22.0113i | −0.659777 | + | 1.14277i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9721 | + | 24.2004i | −0.723450 | + | 1.25305i | 0.236159 | + | 0.971714i | \(0.424111\pi\) |
−0.959609 | + | 0.281337i | \(0.909222\pi\) | |||||||
\(374\) | 0.253289 | + | 0.438709i | 0.0130973 | + | 0.0226851i | ||||
\(375\) | −1.11803 | − | 1.93649i | −0.0577350 | − | 0.100000i | ||||
\(376\) | −11.0557 | −0.570156 | ||||||||
\(377\) | −26.1525 | + | 6.47106i | −1.34692 | + | 0.333277i | ||||
\(378\) | 5.85410 | 0.301103 | ||||||||
\(379\) | −5.40983 | − | 9.37010i | −0.277884 | − | 0.481310i | 0.692974 | − | 0.720962i | \(-0.256300\pi\) |
−0.970859 | + | 0.239652i | \(0.922967\pi\) | |||||||
\(380\) | 3.42705 | + | 5.93583i | 0.175804 | + | 0.304501i | ||||
\(381\) | 4.73607 | − | 8.20311i | 0.242636 | − | 0.420258i | ||||
\(382\) | 16.7984 | 0.859480 | ||||||||
\(383\) | −2.11803 | + | 3.66854i | −0.108226 | + | 0.187454i | −0.915052 | − | 0.403336i | \(-0.867851\pi\) |
0.806825 | + | 0.590790i | \(0.201184\pi\) | |||||||
\(384\) | −12.7254 | + | 22.0411i | −0.649392 | + | 1.12478i | ||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −1.07295 | + | 1.85840i | −0.0546117 | + | 0.0945902i | ||||
\(387\) | 6.23607 | + | 10.8012i | 0.316997 | + | 0.549055i | ||||
\(388\) | −2.80902 | − | 4.86536i | −0.142606 | − | 0.247001i | ||||
\(389\) | −0.111456 | −0.00565105 | −0.00282553 | − | 0.999996i | \(-0.500899\pi\) | ||||
−0.00282553 | + | 0.999996i | \(0.500899\pi\) | |||||||
\(390\) | 3.45492 | + | 3.59045i | 0.174946 | + | 0.181810i | ||||
\(391\) | −13.0689 | −0.660922 | ||||||||
\(392\) | −12.2361 | − | 21.1935i | −0.618015 | − | 1.07043i | ||||
\(393\) | 13.4164 | + | 23.2379i | 0.676768 | + | 1.17220i | ||||
\(394\) | 0.927051 | − | 1.60570i | 0.0467042 | − | 0.0808940i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.381966 | + | 0.661585i | −0.0191945 | + | 0.0332459i | ||||
\(397\) | −13.9721 | + | 24.2004i | −0.701241 | + | 1.21459i | 0.266790 | + | 0.963755i | \(0.414037\pi\) |
−0.968031 | + | 0.250831i | \(0.919296\pi\) | |||||||
\(398\) | 0.798374 | 0.0400189 | ||||||||
\(399\) | −20.0623 | + | 34.7489i | −1.00437 | + | 1.73962i | ||||
\(400\) | −0.927051 | − | 1.60570i | −0.0463525 | − | 0.0802850i | ||||
\(401\) | −4.44427 | − | 7.69770i | −0.221936 | − | 0.384405i | 0.733460 | − | 0.679733i | \(-0.237904\pi\) |
−0.955396 | + | 0.295328i | \(0.904571\pi\) | |||||||
\(402\) | 3.74265 | 0.186666 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.854102 | −0.0424932 | ||||||||
\(405\) | 5.50000 | + | 9.52628i | 0.273297 | + | 0.473365i | ||||
\(406\) | −9.78115 | − | 16.9415i | −0.485430 | − | 0.840790i | ||||
\(407\) | 0.354102 | − | 0.613323i | 0.0175522 | − | 0.0304013i | ||||
\(408\) | −17.3607 | −0.859482 | ||||||||
\(409\) | −12.4443 | + | 21.5541i | −0.615330 | + | 1.06578i | 0.374997 | + | 0.927026i | \(0.377644\pi\) |
−0.990327 | + | 0.138756i | \(0.955690\pi\) | |||||||
\(410\) | 3.69098 | − | 6.39297i | 0.182285 | − | 0.315726i | ||||
\(411\) | 3.29180 | 0.162372 | ||||||||
\(412\) | 10.4721 | − | 18.1383i | 0.515925 | − | 0.893609i | ||||
\(413\) | 1.50000 | + | 2.59808i | 0.0738102 | + | 0.127843i | ||||
\(414\) | 2.32624 | + | 4.02916i | 0.114328 | + | 0.198023i | ||||
\(415\) | 8.94427 | 0.439057 | ||||||||
\(416\) | 14.0451 | + | 14.5961i | 0.688617 | + | 0.715632i | ||||
\(417\) | −37.3607 | −1.82956 | ||||||||
\(418\) | −0.309017 | − | 0.535233i | −0.0151145 | − | 0.0261791i | ||||
\(419\) | −8.82624 | − | 15.2875i | −0.431190 | − | 0.746843i | 0.565786 | − | 0.824552i | \(-0.308573\pi\) |
−0.996976 | + | 0.0777091i | \(0.975239\pi\) | |||||||
\(420\) | 7.66312 | − | 13.2729i | 0.373922 | − | 0.647652i | ||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | −4.07295 | + | 7.05455i | −0.198268 | + | 0.343410i | ||||
\(423\) | 4.94427 | − | 8.56373i | 0.240399 | − | 0.416383i | ||||
\(424\) | 13.4164 | 0.651558 | ||||||||
\(425\) | 1.73607 | − | 3.00696i | 0.0842117 | − | 0.145859i | ||||
\(426\) | −4.30902 | − | 7.46344i | −0.208773 | − | 0.361605i | ||||
\(427\) | −30.5344 | − | 52.8872i | −1.47767 | − | 2.55939i | ||||
\(428\) | 9.32624 | 0.450801 | ||||||||
\(429\) | 1.31966 | + | 1.37143i | 0.0637138 | + | 0.0662133i | ||||
\(430\) | 3.85410 | 0.185861 | ||||||||
\(431\) | −13.5902 | − | 23.5389i | −0.654615 | − | 1.13383i | −0.981990 | − | 0.188933i | \(-0.939497\pi\) |
0.327375 | − | 0.944895i | \(-0.393836\pi\) | |||||||
\(432\) | 2.07295 | + | 3.59045i | 0.0997348 | + | 0.172746i | ||||
\(433\) | 7.26393 | − | 12.5815i | 0.349082 | − | 0.604628i | −0.637004 | − | 0.770860i | \(-0.719827\pi\) |
0.986087 | + | 0.166232i | \(0.0531600\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.35410 | − | 14.4697i | 0.400549 | − | 0.693770i | ||||
\(436\) | −1.61803 | + | 2.80252i | −0.0774898 | + | 0.134216i | ||||
\(437\) | 15.9443 | 0.762718 | ||||||||
\(438\) | −4.14590 | + | 7.18091i | −0.198099 | + | 0.343117i | ||||
\(439\) | 11.3541 | + | 19.6659i | 0.541902 | + | 0.938601i | 0.998795 | + | 0.0490797i | \(0.0156288\pi\) |
−0.456893 | + | 0.889522i | \(0.651038\pi\) | |||||||
\(440\) | 0.263932 | + | 0.457144i | 0.0125825 | + | 0.0217935i | ||||
\(441\) | 21.8885 | 1.04231 | ||||||||
\(442\) | −2.14590 | + | 7.43361i | −0.102070 | + | 0.353581i | ||||
\(443\) | 0.944272 | 0.0448637 | 0.0224319 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224319 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(444\) | 5.42705 | + | 9.39993i | 0.257556 | + | 0.446101i | ||||
\(445\) | 4.50000 | + | 7.79423i | 0.213320 | + | 0.369482i | ||||
\(446\) | 0.218847 | − | 0.379054i | 0.0103627 | − | 0.0179487i | ||||
\(447\) | 10.1246 | 0.478878 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | −1.97214 | + | 3.41584i | −0.0930709 | + | 0.161203i | −0.908802 | − | 0.417228i | \(-0.863002\pi\) |
0.815731 | + | 0.578431i | \(0.196335\pi\) | |||||||
\(450\) | −1.23607 | −0.0582688 | ||||||||
\(451\) | 1.40983 | − | 2.44190i | 0.0663863 | − | 0.114984i | ||||
\(452\) | 1.19098 | + | 2.06284i | 0.0560191 | + | 0.0970280i | ||||
\(453\) | −8.94427 | − | 15.4919i | −0.420239 | − | 0.727875i | ||||
\(454\) | 3.85410 | 0.180882 | ||||||||
\(455\) | −10.5902 | − | 11.0056i | −0.496475 | − | 0.515952i | ||||
\(456\) | 21.1803 | 0.991860 | ||||||||
\(457\) | 0.791796 | + | 1.37143i | 0.0370387 | + | 0.0641528i | 0.883950 | − | 0.467580i | \(-0.154874\pi\) |
−0.846912 | + | 0.531733i | \(0.821541\pi\) | |||||||
\(458\) | 4.90983 | + | 8.50408i | 0.229421 | + | 0.397369i | ||||
\(459\) | −3.88197 | + | 6.72376i | −0.181195 | + | 0.313838i | ||||
\(460\) | −6.09017 | −0.283956 | ||||||||
\(461\) | 0.791796 | − | 1.37143i | 0.0368776 | − | 0.0638739i | −0.846998 | − | 0.531597i | \(-0.821592\pi\) |
0.883875 | + | 0.467723i | \(0.154925\pi\) | |||||||
\(462\) | −0.690983 | + | 1.19682i | −0.0321474 | + | 0.0556810i | ||||
\(463\) | 11.0557 | 0.513803 | 0.256902 | − | 0.966438i | \(-0.417298\pi\) | ||||
0.256902 | + | 0.966438i | \(0.417298\pi\) | |||||||
\(464\) | 6.92705 | − | 11.9980i | 0.321580 | − | 0.556993i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.90983 | − | 8.50408i | −0.227443 | − | 0.393944i | ||||
\(467\) | 8.94427 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433648\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433648\pi\) | |||||||
\(468\) | −11.3262 | + | 2.80252i | −0.523556 | + | 0.129546i | ||||
\(469\) | −11.4721 | −0.529734 | ||||||||
\(470\) | −1.52786 | − | 2.64634i | −0.0704751 | − | 0.122066i | ||||
\(471\) | 20.1246 | + | 34.8569i | 0.927293 | + | 1.60612i | ||||
\(472\) | 0.791796 | − | 1.37143i | 0.0364454 | − | 0.0631252i | ||||
\(473\) | 1.47214 | 0.0676889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.11803 | + | 3.66854i | −0.0971821 | + | 0.168324i | ||||
\(476\) | 23.7984 | 1.09080 | ||||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | −8.00000 | − | 13.8564i | −0.365911 | − | 0.633777i | ||||
\(479\) | −16.0623 | − | 27.8207i | −0.733905 | − | 1.27116i | −0.955202 | − | 0.295955i | \(-0.904362\pi\) |
0.221296 | − | 0.975207i | \(-0.428971\pi\) | |||||||
\(480\) | −12.5623 | −0.573388 | ||||||||
\(481\) | 10.5000 | − | 2.59808i | 0.478759 | − | 0.118462i | ||||
\(482\) | −9.27051 | −0.422260 | ||||||||
\(483\) | −17.8262 | − | 30.8759i | −0.811122 | − | 1.40490i | ||||
\(484\) | −8.85410 | − | 15.3358i | −0.402459 | − | 0.697080i | ||||
\(485\) | 1.73607 | − | 3.00696i | 0.0788308 | − | 0.136539i | ||||
\(486\) | 11.0557 | 0.501498 | ||||||||
\(487\) | −7.06231 | + | 12.2323i | −0.320024 | + | 0.554297i | −0.980493 | − | 0.196556i | \(-0.937024\pi\) |
0.660469 | + | 0.750853i | \(0.270358\pi\) | |||||||
\(488\) | −16.1180 | + | 27.9173i | −0.729629 | + | 1.26375i | ||||
\(489\) | 32.8885 | 1.48727 | ||||||||
\(490\) | 3.38197 | − | 5.85774i | 0.152782 | − | 0.264626i | ||||
\(491\) | 0.118034 | + | 0.204441i | 0.00532680 | + | 0.00922629i | 0.868677 | − | 0.495380i | \(-0.164971\pi\) |
−0.863350 | + | 0.504606i | \(0.831638\pi\) | |||||||
\(492\) | 21.6074 | + | 37.4251i | 0.974136 | + | 1.68725i | ||||
\(493\) | 25.9443 | 1.16847 | ||||||||
\(494\) | 2.61803 | − | 9.06914i | 0.117791 | − | 0.408040i | ||||
\(495\) | −0.472136 | −0.0212209 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2082 | + | 22.8773i | 0.592469 | + | 1.02619i | ||||
\(498\) | 6.18034 | − | 10.7047i | 0.276948 | − | 0.479687i | ||||
\(499\) | −21.8885 | −0.979866 | −0.489933 | − | 0.871760i | \(-0.662979\pi\) | ||||
−0.489933 | + | 0.871760i | \(0.662979\pi\) | |||||||
\(500\) | 0.809017 | − | 1.40126i | 0.0361803 | − | 0.0626662i | ||||
\(501\) | 19.2082 | − | 33.2696i | 0.858159 | − | 1.48638i | ||||
\(502\) | −12.5066 | −0.558196 | ||||||||
\(503\) | −4.59017 | + | 7.95041i | −0.204666 | + | 0.354491i | −0.950026 | − | 0.312170i | \(-0.898944\pi\) |
0.745361 | + | 0.666662i | \(0.232277\pi\) | |||||||
\(504\) | −9.47214 | − | 16.4062i | −0.421922 | − | 0.730791i | ||||
\(505\) | −0.263932 | − | 0.457144i | −0.0117448 | − | 0.0203426i | ||||
\(506\) | 0.549150 | 0.0244127 | ||||||||
\(507\) | −1.11803 | + | 29.0474i | −0.0496536 | + | 1.29004i | ||||
\(508\) | 6.85410 | 0.304102 | ||||||||
\(509\) | 16.6803 | + | 28.8912i | 0.739343 | + | 1.28058i | 0.952791 | + | 0.303625i | \(0.0981971\pi\) |
−0.213448 | + | 0.976954i | \(0.568470\pi\) | |||||||
\(510\) | −2.39919 | − | 4.15551i | −0.106238 | − | 0.184009i | ||||
\(511\) | 12.7082 | − | 22.0113i | 0.562178 | − | 0.973721i | ||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 4.73607 | − | 8.20311i | 0.209103 | − | 0.362176i | ||||
\(514\) | 5.39919 | − | 9.35167i | 0.238148 | − | 0.412484i | ||||
\(515\) | 12.9443 | 0.570393 | ||||||||
\(516\) | −11.2812 | + | 19.5395i | −0.496625 | + | 0.860180i | ||||
\(517\) | −0.583592 | − | 1.01081i | −0.0256664 | − | 0.0444554i | ||||
\(518\) | 3.92705 | + | 6.80185i | 0.172545 | + | 0.298856i | ||||
\(519\) | −42.2361 | −1.85396 | ||||||||
\(520\) | −2.23607 | + | 7.74597i | −0.0980581 | + | 0.339683i | ||||
\(521\) | 29.7771 | 1.30456 | 0.652279 | − | 0.757979i | \(-0.273813\pi\) | ||||
0.652279 | + | 0.757979i | \(0.273813\pi\) | |||||||
\(522\) | −4.61803 | − | 7.99867i | −0.202126 | − | 0.350092i | ||||
\(523\) | −2.64590 | − | 4.58283i | −0.115697 | − | 0.200393i | 0.802361 | − | 0.596839i | \(-0.203577\pi\) |
−0.918058 | + | 0.396446i | \(0.870244\pi\) | |||||||
\(524\) | −9.70820 | + | 16.8151i | −0.424105 | + | 0.734571i | ||||
\(525\) | 9.47214 | 0.413398 | ||||||||
\(526\) | 1.16312 | − | 2.01458i | 0.0507144 | − | 0.0878399i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.978714 | −0.0425930 | ||||||||
\(529\) | 4.41641 | − | 7.64944i | 0.192018 | − | 0.332584i | ||||
\(530\) | 1.85410 | + | 3.21140i | 0.0805370 | + | 0.139494i | ||||
\(531\) | 0.708204 | + | 1.22665i | 0.0307334 | + | 0.0532319i | ||||
\(532\) | −29.0344 | −1.25880 | ||||||||
\(533\) | 41.8050 | − | 10.3440i | 1.81077 | − | 0.448050i | ||||
\(534\) | 12.4377 | 0.538232 | ||||||||
\(535\) | 2.88197 | + | 4.99171i | 0.124598 | + | 0.215811i | ||||
\(536\) | 3.02786 | + | 5.24441i | 0.130784 | + | 0.226524i | ||||
\(537\) | 9.20820 | − | 15.9491i | 0.397363 | − | 0.688253i | ||||
\(538\) | 4.03444 | 0.173937 | ||||||||
\(539\) | 1.29180 | − | 2.23746i | 0.0556416 | − | 0.0963741i | ||||
\(540\) | −1.80902 | + | 3.13331i | −0.0778477 | + | 0.134836i | ||||
\(541\) | −27.8885 | −1.19902 | −0.599511 | − | 0.800366i | \(-0.704638\pi\) | ||||
−0.599511 | + | 0.800366i | \(0.704638\pi\) | |||||||
\(542\) | 0.399187 | − | 0.691412i | 0.0171465 | − | 0.0296987i | ||||
\(543\) | −6.70820 | − | 11.6190i | −0.287877 | − | 0.498617i | ||||
\(544\) | −9.75329 | − | 16.8932i | −0.418169 | − | 0.724290i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | −20.4894 | + | 5.06980i | −0.876864 | + | 0.216967i | ||||
\(547\) | 18.8328 | 0.805233 | 0.402617 | − | 0.915369i | \(-0.368101\pi\) | ||||
0.402617 | + | 0.915369i | \(0.368101\pi\) | |||||||
\(548\) | 1.19098 | + | 2.06284i | 0.0508763 | + | 0.0881203i | ||||
\(549\) | −14.4164 | − | 24.9700i | −0.615277 | − | 1.06569i | ||||
\(550\) | −0.0729490 | + | 0.126351i | −0.00311056 | + | 0.00538764i | ||||
\(551\) | −31.6525 | −1.34844 | ||||||||
\(552\) | −9.40983 | + | 16.2983i | −0.400509 | + | 0.693702i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.4377 | −0.443455 | ||||||||
\(555\) | −3.35410 | + | 5.80948i | −0.142374 | + | 0.246598i | ||||
\(556\) | −13.5172 | − | 23.4125i | −0.573258 | − | 0.992912i | ||||
\(557\) | 4.97214 | + | 8.61199i | 0.210676 | + | 0.364902i | 0.951926 | − | 0.306327i | \(-0.0991001\pi\) |
−0.741250 | + | 0.671229i | \(0.765767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.5902 | + | 16.2018i | 0.659394 | + | 0.685262i | ||||
\(560\) | 7.85410 | 0.331896 | ||||||||
\(561\) | −0.916408 | − | 1.58726i | −0.0386908 | − | 0.0670144i | ||||
\(562\) | −4.90983 | − | 8.50408i | −0.207109 | − | 0.358723i | ||||
\(563\) | −15.3541 | + | 26.5941i | −0.647098 | + | 1.12081i | 0.336714 | + | 0.941607i | \(0.390684\pi\) |
−0.983813 | + | 0.179200i | \(0.942649\pi\) | |||||||
\(564\) | 17.8885 | 0.753244 | ||||||||
\(565\) | −0.736068 | + | 1.27491i | −0.0309666 | + | 0.0536357i | ||||
\(566\) | −3.30902 | + | 5.73139i | −0.139088 | + | 0.240908i | ||||
\(567\) | −46.5967 | −1.95688 | ||||||||
\(568\) | 6.97214 | − | 12.0761i | 0.292544 | − | 0.506702i | ||||
\(569\) | −8.44427 | − | 14.6259i | −0.354002 | − | 0.613150i | 0.632944 | − | 0.774197i | \(-0.281846\pi\) |
−0.986947 | + | 0.161047i | \(0.948513\pi\) | |||||||
\(570\) | 2.92705 | + | 5.06980i | 0.122601 | + | 0.212351i | ||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | −0.381966 | + | 1.32317i | −0.0159708 | + | 0.0553245i | ||||
\(573\) | −60.7771 | −2.53900 | ||||||||
\(574\) | 15.6353 | + | 27.0811i | 0.652603 | + | 1.13034i | ||||
\(575\) | −1.88197 | − | 3.25966i | −0.0784834 | − | 0.135937i | ||||
\(576\) | 0.236068 | − | 0.408882i | 0.00983617 | − | 0.0170367i | ||||
\(577\) | 27.8885 | 1.16102 | 0.580508 | − | 0.814255i | \(-0.302854\pi\) | ||||
0.580508 | + | 0.814255i | \(0.302854\pi\) | |||||||
\(578\) | −1.52786 | + | 2.64634i | −0.0635508 | + | 0.110073i | ||||
\(579\) | 3.88197 | − | 6.72376i | 0.161329 | − | 0.279430i | ||||
\(580\) | 12.0902 | 0.502017 | ||||||||
\(581\) | −18.9443 | + | 32.8124i | −0.785941 | + | 1.36129i | ||||
\(582\) | −2.39919 | − | 4.15551i | −0.0994495 | − | 0.172252i | ||||
\(583\) | 0.708204 | + | 1.22665i | 0.0293308 | + | 0.0508025i | ||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | −5.00000 | − | 5.19615i | −0.206725 | − | 0.214834i | ||||
\(586\) | 18.5066 | 0.764500 | ||||||||
\(587\) | −5.11803 | − | 8.86469i | −0.211244 | − | 0.365885i | 0.740860 | − | 0.671659i | \(-0.234418\pi\) |
−0.952104 | + | 0.305774i | \(0.901085\pi\) | |||||||
\(588\) | 19.7984 | + | 34.2918i | 0.816471 | + | 1.41417i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0.437694 | 0.0180196 | ||||||||
\(591\) | −3.35410 | + | 5.80948i | −0.137969 | + | 0.238970i | ||||
\(592\) | −2.78115 | + | 4.81710i | −0.114305 | + | 0.197982i | ||||
\(593\) | −7.88854 | −0.323944 | −0.161972 | − | 0.986795i | \(-0.551785\pi\) | ||||
−0.161972 | + | 0.986795i | \(0.551785\pi\) | |||||||
\(594\) | 0.163119 | − | 0.282530i | 0.00669285 | − | 0.0115924i | ||||
\(595\) | 7.35410 | + | 12.7377i | 0.301489 | + | 0.522194i | ||||
\(596\) | 3.66312 | + | 6.34471i | 0.150047 | + | 0.259889i | ||||
\(597\) | −2.88854 | −0.118220 | ||||||||
\(598\) | 5.81559 | + | 6.04374i | 0.237817 | + | 0.247147i | ||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | −2.50000 | − | 4.33013i | −0.102062 | − | 0.176777i | ||||
\(601\) | −21.9721 | − | 38.0569i | −0.896262 | − | 1.55237i | −0.832235 | − | 0.554423i | \(-0.812939\pi\) |
−0.0640274 | − | 0.997948i | \(-0.520394\pi\) | |||||||
\(602\) | −8.16312 | + | 14.1389i | −0.332704 | + | 0.576260i | ||||
\(603\) | −5.41641 | −0.220573 | ||||||||
\(604\) | 6.47214 | − | 11.2101i | 0.263347 | − | 0.456131i | ||||
\(605\) | 5.47214 | − | 9.47802i | 0.222474 | − | 0.385336i | ||||
\(606\) | −0.729490 | −0.0296335 | ||||||||
\(607\) | 0.354102 | − | 0.613323i | 0.0143726 | − | 0.0248940i | −0.858750 | − | 0.512395i | \(-0.828758\pi\) |
0.873122 | + | 0.487501i | \(0.162092\pi\) | |||||||
\(608\) | 11.8992 | + | 20.6100i | 0.482576 | + | 0.835846i | ||||
\(609\) | 35.3885 | + | 61.2948i | 1.43402 | + | 2.48379i | ||||
\(610\) | −8.90983 | −0.360748 | ||||||||
\(611\) | 4.94427 | − | 17.1275i | 0.200024 | − | 0.692903i | ||||
\(612\) | 11.2361 | 0.454191 | ||||||||
\(613\) | −19.9721 | − | 34.5928i | −0.806667 | − | 1.39719i | −0.915160 | − | 0.403091i | \(-0.867936\pi\) |
0.108493 | − | 0.994097i | \(-0.465398\pi\) | |||||||
\(614\) | 7.70820 | + | 13.3510i | 0.311078 | + | 0.538803i | ||||
\(615\) | −13.3541 | + | 23.1300i | −0.538489 | + | 0.932691i | ||||
\(616\) | −2.23607 | −0.0900937 | ||||||||
\(617\) | 20.2082 | − | 35.0016i | 0.813552 | − | 1.40911i | −0.0968116 | − | 0.995303i | \(-0.530864\pi\) |
0.910363 | − | 0.413810i | \(-0.135802\pi\) | |||||||
\(618\) | 8.94427 | − | 15.4919i | 0.359791 | − | 0.623177i | ||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.20820 | + | 7.28882i | 0.168869 | + | 0.292490i | ||||
\(622\) | −7.41641 | − | 12.8456i | −0.297371 | − | 0.515061i | ||||
\(623\) | −38.1246 | −1.52743 | ||||||||
\(624\) | −10.3647 | − | 10.7714i | −0.414922 | − | 0.431199i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.20163 | + | 2.08128i | 0.0480266 | + | 0.0831846i | ||||
\(627\) | 1.11803 | + | 1.93649i | 0.0446500 | + | 0.0773360i | ||||
\(628\) | −14.5623 | + | 25.2227i | −0.581099 | + | 1.00649i | ||||
\(629\) | −10.4164 | −0.415329 | ||||||||
\(630\) | 2.61803 | − | 4.53457i | 0.104305 | − | 0.180662i | ||||
\(631\) | 8.06231 | − | 13.9643i | 0.320955 | − | 0.555911i | −0.659730 | − | 0.751503i | \(-0.729329\pi\) |
0.980685 | + | 0.195592i | \(0.0626627\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7361 | − | 25.5236i | 0.585706 | − | 1.01447i | ||||
\(634\) | −3.67376 | − | 6.36314i | −0.145904 | − | 0.252713i | ||||
\(635\) | 2.11803 | + | 3.66854i | 0.0840516 | + | 0.145582i | ||||
\(636\) | −21.7082 | −0.860786 | ||||||||
\(637\) | 38.3050 | − | 9.47802i | 1.51770 | − | 0.375533i | ||||
\(638\) | −1.09017 | −0.0431602 | ||||||||
\(639\) | 6.23607 | + | 10.8012i | 0.246695 | + | 0.427288i | ||||
\(640\) | −5.69098 | − | 9.85707i | −0.224956 | − | 0.389635i | ||||
\(641\) | −4.44427 | + | 7.69770i | −0.175538 | + | 0.304041i | −0.940347 | − | 0.340216i | \(-0.889500\pi\) |
0.764809 | + | 0.644257i | \(0.222833\pi\) | |||||||
\(642\) | 7.96556 | 0.314376 | ||||||||
\(643\) | 8.64590 | − | 14.9751i | 0.340961 | − | 0.590562i | −0.643650 | − | 0.765320i | \(-0.722581\pi\) |
0.984611 | + | 0.174758i | \(0.0559143\pi\) | |||||||
\(644\) | 12.8992 | − | 22.3420i | 0.508299 | − | 0.880400i | ||||
\(645\) | −13.9443 | −0.549055 | ||||||||
\(646\) | −4.54508 | + | 7.87232i | −0.178824 | + | 0.309732i | ||||
\(647\) | −1.29837 | − | 2.24885i | −0.0510443 | − | 0.0884114i | 0.839374 | − | 0.543554i | \(-0.182922\pi\) |
−0.890419 | + | 0.455142i | \(0.849588\pi\) | |||||||
\(648\) | 12.2984 | + | 21.3014i | 0.483126 | + | 0.836798i | ||||
\(649\) | 0.167184 | 0.00656256 | ||||||||
\(650\) | −2.16312 | + | 0.535233i | −0.0848445 | + | 0.0209936i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.8992 | + | 20.6100i | 0.466008 | + | 0.807150i | ||||
\(653\) | 10.5000 | + | 18.1865i | 0.410897 | + | 0.711694i | 0.994988 | − | 0.0999939i | \(-0.0318823\pi\) |
−0.584091 | + | 0.811688i | \(0.698549\pi\) | |||||||
\(654\) | −1.38197 | + | 2.39364i | −0.0540391 | + | 0.0935985i | ||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | −11.0729 | + | 19.1789i | −0.432326 | + | 0.748811i | ||||
\(657\) | 6.00000 | − | 10.3923i | 0.234082 | − | 0.405442i | ||||
\(658\) | 12.9443 | 0.504620 | ||||||||
\(659\) | 21.8820 | − | 37.9007i | 0.852400 | − | 1.47640i | −0.0266355 | − | 0.999645i | \(-0.508479\pi\) |
0.879036 | − | 0.476756i | \(-0.158187\pi\) | |||||||
\(660\) | −0.427051 | − | 0.739674i | −0.0166229 | − | 0.0287918i | ||||
\(661\) | 20.6803 | + | 35.8194i | 0.804372 | + | 1.39321i | 0.916714 | + | 0.399544i | \(0.130831\pi\) |
−0.112342 | + | 0.993670i | \(0.535835\pi\) | |||||||
\(662\) | 3.49342 | 0.135776 | ||||||||
\(663\) | 7.76393 | − | 26.8950i | 0.301526 | − | 1.04452i | ||||
\(664\) | 20.0000 | 0.776151 | ||||||||
\(665\) | −8.97214 | − | 15.5402i | −0.347925 | − | 0.602623i | ||||
\(666\) | 1.85410 | + | 3.21140i | 0.0718450 | + | 0.124439i | ||||
\(667\) | 14.0623 | − | 24.3566i | 0.544495 | − | 0.943092i | ||||
\(668\) | 27.7984 | 1.07555 | ||||||||
\(669\) | −0.791796 | + | 1.37143i | −0.0306126 | + | 0.0530226i | ||||
\(670\) | −0.836881 | + | 1.44952i | −0.0323315 | + | 0.0559999i | ||||
\(671\) | −3.40325 | −0.131381 | ||||||||
\(672\) | 26.6074 | − | 46.0854i | 1.02640 | − | 1.77778i | ||||
\(673\) | 4.79180 | + | 8.29963i | 0.184710 | + | 0.319927i | 0.943479 | − | 0.331433i | \(-0.107532\pi\) |
−0.758769 | + | 0.651360i | \(0.774199\pi\) | |||||||
\(674\) | −2.43769 | − | 4.22221i | −0.0938965 | − | 0.162633i | ||||
\(675\) | −2.23607 | −0.0860663 | ||||||||
\(676\) | −18.6074 | + | 9.80881i | −0.715669 | + | 0.377262i | ||||
\(677\) | 12.1115 | 0.465481 | 0.232741 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232741 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(678\) | 1.01722 | + | 1.76188i | 0.0390661 | + | 0.0676645i | ||||
\(679\) | 7.35410 | + | 12.7377i | 0.282225 | + | 0.488827i | ||||
\(680\) | 3.88197 | − | 6.72376i | 0.148867 | − | 0.257845i | ||||
\(681\) | −13.9443 | −0.534346 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.8820 | + | 22.3122i | −0.492915 | + | 0.853753i | −0.999967 | − | 0.00816213i | \(-0.997402\pi\) |
0.507052 | + | 0.861915i | \(0.330735\pi\) | |||||||
\(684\) | −13.7082 | −0.524146 | ||||||||
\(685\) | −0.736068 | + | 1.27491i | −0.0281237 | + | 0.0487117i | ||||
\(686\) | 5.16312 | + | 8.94278i | 0.197129 | + | 0.341437i | ||||
\(687\) | −17.7639 | − | 30.7680i | −0.677736 | − | 1.17387i | ||||
\(688\) | −11.5623 | −0.440809 | ||||||||
\(689\) | −6.00000 | + | 20.7846i | −0.228582 | + | 0.791831i | ||||
\(690\) | −5.20163 | −0.198023 | ||||||||
\(691\) | −19.2984 | − | 33.4258i | −0.734145 | − | 1.27158i | −0.955098 | − | 0.296291i | \(-0.904250\pi\) |
0.220953 | − | 0.975284i | \(-0.429083\pi\) | |||||||
\(692\) | −15.2812 | − | 26.4677i | −0.580902 | − | 1.00615i | ||||
\(693\) | 1.00000 | − | 1.73205i | 0.0379869 | − | 0.0657952i | ||||
\(694\) | −18.9787 | −0.720422 | ||||||||
\(695\) | 8.35410 | − | 14.4697i | 0.316889 | − | 0.548868i | ||||
\(696\) | 18.6803 | − | 32.3553i | 0.708076 | − | 1.22642i | ||||
\(697\) | −41.4721 | −1.57087 | ||||||||
\(698\) | 0.746711 | − | 1.29334i | 0.0282634 | − | 0.0489537i | ||||
\(699\) | 17.7639 | + | 30.7680i | 0.671894 | + | 1.16375i | ||||
\(700\) | 3.42705 | + | 5.93583i | 0.129530 | + | 0.224353i | ||||
\(701\) | 7.88854 | 0.297946 | 0.148973 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148973 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(702\) | 4.83688 | − | 1.19682i | 0.182556 | − | 0.0451710i | ||||
\(703\) | 12.7082 | 0.479299 | ||||||||
\(704\) | −0.0278640 | − | 0.0482619i | −0.00105017 | − | 0.00181894i | ||||
\(705\) | 5.52786 | + | 9.57454i | 0.208191 | + | 0.360598i | ||||
\(706\) | −6.01722 | + | 10.4221i | −0.226461 | + | 0.392242i | ||||
\(707\) | 2.23607 | 0.0840960 | ||||||||
\(708\) | −1.28115 | + | 2.21902i | −0.0481487 | + | 0.0833960i | ||||
\(709\) | −12.1525 | + | 21.0487i | −0.456396 | + | 0.790501i | −0.998767 | − | 0.0496381i | \(-0.984193\pi\) |
0.542371 | + | 0.840139i | \(0.317527\pi\) | |||||||
\(710\) | 3.85410 | 0.144642 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0623 | + | 17.4284i | 0.377101 | + | 0.653158i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 20.3262 | 0.760690 | ||||||||
\(715\) | −0.826238 | + | 0.204441i | −0.0308995 | + | 0.00764565i | ||||
\(716\) | 13.3262 | 0.498025 | ||||||||
\(717\) | 28.9443 | + | 50.1329i | 1.08094 | + | 1.87225i | ||||
\(718\) | 5.52786 | + | 9.57454i | 0.206298 | + | 0.357319i | ||||
\(719\) | 16.0623 | − | 27.8207i | 0.599023 | − | 1.03754i | −0.393943 | − | 0.919135i | \(-0.628889\pi\) |
0.992966 | − | 0.118403i | \(-0.0377775\pi\) | |||||||
\(720\) | 3.70820 | 0.138197 | ||||||||
\(721\) | −27.4164 | + | 47.4866i | −1.02104 | + | 1.76849i | ||||
\(722\) | −0.326238 | + | 0.565061i | −0.0121413 | + | 0.0210294i | ||||
\(723\) | 33.5410 | 1.24740 | ||||||||
\(724\) | 4.85410 | − | 8.40755i | 0.180401 | − | 0.312464i | ||||
\(725\) | 3.73607 | + | 6.47106i | 0.138754 | + | 0.240329i | ||||
\(726\) | −7.56231 | − | 13.0983i | −0.280663 | − | 0.486123i | ||||
\(727\) | 28.9443 | 1.07348 | 0.536742 | − | 0.843747i | \(-0.319655\pi\) | ||||
0.536742 | + | 0.843747i | \(0.319655\pi\) | |||||||
\(728\) | −23.6803 | − | 24.6093i | −0.877652 | − | 0.912082i | ||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | −1.85410 | − | 3.21140i | −0.0686234 | − | 0.118859i | ||||
\(731\) | −10.8262 | − | 18.7516i | −0.400423 | − | 0.693553i | ||||
\(732\) | 26.0795 | − | 45.1711i | 0.963927 | − | 1.66957i | ||||
\(733\) | −43.8885 | −1.62106 | −0.810530 | − | 0.585697i | \(-0.800821\pi\) | ||||
−0.810530 | + | 0.585697i | \(0.800821\pi\) | |||||||
\(734\) | 1.74671 | − | 3.02539i | 0.0644723 | − | 0.111669i | ||||
\(735\) | −12.2361 | + | 21.1935i | −0.451334 | + | 0.781734i | ||||
\(736\) | −21.1459 | −0.779448 | ||||||||
\(737\) | −0.319660 | + | 0.553668i | −0.0117748 | + | 0.0203946i | ||||
\(738\) | 7.38197 | + | 12.7859i | 0.271734 | + | 0.470657i | ||||
\(739\) | −13.7705 | − | 23.8512i | −0.506556 | − | 0.877381i | −0.999971 | − | 0.00758729i | \(-0.997585\pi\) |
0.493415 | − | 0.869794i | \(-0.335748\pi\) | |||||||
\(740\) | −4.85410 | −0.178440 | ||||||||
\(741\) | −9.47214 | + | 32.8124i | −0.347968 | + | 1.20540i | ||||
\(742\) | −15.7082 | −0.576666 | ||||||||
\(743\) | 19.0623 | + | 33.0169i | 0.699328 | + | 1.21127i | 0.968700 | + | 0.248236i | \(0.0798507\pi\) |
−0.269372 | + | 0.963036i | \(0.586816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.26393 | + | 3.92125i | −0.0829441 | + | 0.143663i | ||||
\(746\) | −17.2705 | −0.632318 | ||||||||
\(747\) | −8.94427 | + | 15.4919i | −0.327254 | + | 0.566820i | ||||
\(748\) | 0.663119 | − | 1.14856i | 0.0242460 | − | 0.0419954i | ||||
\(749\) | −24.4164 | −0.892156 | ||||||||
\(750\) | 0.690983 | − | 1.19682i | 0.0252311 | − | 0.0437016i | ||||
\(751\) | 15.3541 | + | 26.5941i | 0.560279 | + | 0.970432i | 0.997472 | + | 0.0710640i | \(0.0226395\pi\) |
−0.437193 | + | 0.899368i | \(0.644027\pi\) | |||||||
\(752\) | 4.58359 | + | 7.93901i | 0.167146 | + | 0.289506i | ||||
\(753\) | 45.2492 | 1.64897 | ||||||||
\(754\) | −11.5451 | − | 11.9980i | −0.420447 | − | 0.436942i | ||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | −7.66312 | − | 13.2729i | −0.278705 | − | 0.482731i | ||||
\(757\) | 3.44427 | + | 5.96565i | 0.125184 | + | 0.216825i | 0.921805 | − | 0.387654i | \(-0.126714\pi\) |
−0.796621 | + | 0.604479i | \(0.793381\pi\) | |||||||
\(758\) | 3.34346 | − | 5.79104i | 0.121440 | − | 0.210340i | ||||
\(759\) | −1.98684 | −0.0721179 | ||||||||
\(760\) | −4.73607 | + | 8.20311i | −0.171795 | + | 0.297558i | ||||
\(761\) | 18.9721 | − | 32.8607i | 0.687739 | − | 1.19120i | −0.284828 | − | 0.958579i | \(-0.591937\pi\) |
0.972567 | − | 0.232621i | \(-0.0747302\pi\) | |||||||
\(762\) | 5.85410 | 0.212072 | ||||||||
\(763\) | 4.23607 | − | 7.33708i | 0.153356 | − | 0.265620i | ||||
\(764\) | −21.9894 | − | 38.0867i | −0.795547 | − | 1.37793i | ||||
\(765\) | 3.47214 | + | 6.01392i | 0.125535 | + | 0.217434i | ||||
\(766\) | −2.61803 | −0.0945934 | ||||||||
\(767\) | 1.77051 | + | 1.83997i | 0.0639294 | + | 0.0664374i | ||||
\(768\) | −14.6738 | −0.529494 | ||||||||
\(769\) | −14.9164 | − | 25.8360i | −0.537899 | − | 0.931669i | −0.999017 | − | 0.0443301i | \(-0.985885\pi\) |
0.461118 | − | 0.887339i | \(-0.347449\pi\) | |||||||
\(770\) | −0.309017 | − | 0.535233i | −0.0111362 | − | 0.0192885i | ||||
\(771\) | −19.5344 | + | 33.8346i | −0.703516 | + | 1.21853i | ||||
\(772\) | 5.61803 | 0.202197 | ||||||||
\(773\) | 10.0279 | − | 17.3688i | 0.360677 | − | 0.624711i | −0.627395 | − | 0.778701i | \(-0.715879\pi\) |
0.988072 | + | 0.153990i | \(0.0492123\pi\) | |||||||
\(774\) | −3.85410 | + | 6.67550i | −0.138533 | + | 0.239946i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.88197 | − | 6.72376i | 0.139354 | − | 0.241369i | ||||
\(777\) | −14.2082 | − | 24.6093i | −0.509716 | − | 0.882855i | ||||
\(778\) | −0.0344419 | − | 0.0596550i | −0.00123480 | − | 0.00213874i | ||||
\(779\) | 50.5967 | 1.81282 | ||||||||
\(780\) | 3.61803 | − | 12.5332i | 0.129546 | − | 0.448762i | ||||
\(781\) | 1.47214 | 0.0526772 | ||||||||
\(782\) | −4.03851 | − | 6.99490i | −0.144417 | − | 0.250137i | ||||
\(783\) | −8.35410 | − | 14.4697i | −0.298551 | − | 0.517106i | ||||
\(784\) | −10.1459 | + | 17.5732i | −0.362354 | + | 0.627615i | ||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | −8.29180 | + | 14.3618i | −0.295759 | + | 0.512269i | ||||
\(787\) | −14.7705 | + | 25.5833i | −0.526512 | + | 0.911945i | 0.473011 | + | 0.881057i | \(0.343167\pi\) |
−0.999523 | + | 0.0308887i | \(0.990166\pi\) | |||||||
\(788\) | −4.85410 | −0.172920 | ||||||||
\(789\) | −4.20820 | + | 7.28882i | −0.149816 | + | 0.259489i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.11803 | − | 5.40059i | −0.110865 | − | 0.192023i | ||||
\(792\) | −1.05573 | −0.0375137 | ||||||||
\(793\) | −36.0410 | − | 37.4549i | −1.27985 | − | 1.33006i | ||||
\(794\) | −17.2705 | −0.612907 | ||||||||
\(795\) | −6.70820 | − | 11.6190i | −0.237915 | − | 0.412082i | ||||
\(796\) | −1.04508 | − | 1.81014i | −0.0370421 | − | 0.0641587i | ||||
\(797\) | −26.9164 | + | 46.6206i | −0.953428 | + | 1.65139i | −0.215503 | + | 0.976503i | \(0.569139\pi\) |
−0.737925 | + | 0.674883i | \(0.764194\pi\) | |||||||
\(798\) | −24.7984 | −0.877853 | ||||||||
\(799\) | −8.58359 | + | 14.8672i | −0.303666 | + | 0.525964i | ||||
\(800\) | 2.80902 | − | 4.86536i | 0.0993137 | − | 0.172016i | ||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | 2.74671 | − | 4.75744i | 0.0969897 | − | 0.167991i | ||||
\(803\) | −0.708204 | − | 1.22665i | −0.0249920 | − | 0.0432874i | ||||
\(804\) | −4.89919 | − | 8.48564i | −0.172781 | − | 0.299265i | ||||
\(805\) | 15.9443 | 0.561962 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.5967 | −0.513830 | ||||||||
\(808\) | −0.590170 | − | 1.02220i | −0.0207621 | − | 0.0359610i | ||||
\(809\) | 1.44427 | + | 2.50155i | 0.0507779 | + | 0.0879499i | 0.890297 | − | 0.455380i | \(-0.150497\pi\) |
−0.839519 | + | 0.543330i | \(0.817163\pi\) | |||||||
\(810\) | −3.39919 | + | 5.88756i | −0.119435 | + | 0.206868i | ||||
\(811\) | 31.7771 | 1.11584 | 0.557922 | − | 0.829893i | \(-0.311599\pi\) | ||||
0.557922 | + | 0.829893i | \(0.311599\pi\) | |||||||
\(812\) | −25.6074 | + | 44.3533i | −0.898643 | + | 1.55650i | ||||
\(813\) | −1.44427 | + | 2.50155i | −0.0506528 | + | 0.0877333i | ||||
\(814\) | 0.437694 | 0.0153412 | ||||||||
\(815\) | −7.35410 | + | 12.7377i | −0.257603 | + | 0.446181i | ||||
\(816\) | 7.19756 | + | 12.4665i | 0.251965 | + | 0.436416i | ||||
\(817\) | 13.2082 | + | 22.8773i | 0.462097 | + | 0.800375i | ||||
\(818\) | −15.3820 | −0.537818 | ||||||||
\(819\) | 29.6525 | − | 7.33708i | 1.03614 | − | 0.256378i | ||||
\(820\) | −19.3262 | −0.674902 | ||||||||
\(821\) | 12.6803 | + | 21.9630i | 0.442547 | + | 0.766514i | 0.997878 | − | 0.0651158i | \(-0.0207417\pi\) |
−0.555331 | + | 0.831630i | \(0.687408\pi\) | |||||||
\(822\) | 1.01722 | + | 1.76188i | 0.0354797 | + | 0.0614526i | ||||
\(823\) | 13.2984 | − | 23.0335i | 0.463552 | − | 0.802896i | −0.535583 | − | 0.844483i | \(-0.679908\pi\) |
0.999135 | + | 0.0415869i | \(0.0132413\pi\) | |||||||
\(824\) | 28.9443 | 1.00832 | ||||||||
\(825\) | 0.263932 | − | 0.457144i | 0.00918893 | − | 0.0159157i | ||||
\(826\) | −0.927051 | + | 1.60570i | −0.0322562 | + | 0.0558694i | ||||
\(827\) | −8.94427 | −0.311023 | −0.155511 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155511 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(828\) | 6.09017 | − | 10.5485i | 0.211648 | − | 0.366585i | ||||
\(829\) | 21.6246 | + | 37.4549i | 0.751054 | + | 1.30086i | 0.947312 | + | 0.320311i | \(0.103787\pi\) |
−0.196259 | + | 0.980552i | \(0.562879\pi\) | |||||||
\(830\) | 2.76393 | + | 4.78727i | 0.0959375 | + | 0.166169i | ||||
\(831\) | 37.7639 | 1.31002 | ||||||||
\(832\) | 0.236068 | − | 0.817763i | 0.00818418 | − | 0.0283508i | ||||
\(833\) | −38.0000 | −1.31662 | ||||||||
\(834\) | −11.5451 | − | 19.9967i | −0.399774 | − | 0.692428i | ||||
\(835\) | 8.59017 | + | 14.8786i | 0.297275 | + | 0.514896i | ||||
\(836\) | −0.809017 | + | 1.40126i | −0.0279804 | + | 0.0484635i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.45492 | − | 9.44819i | 0.188437 | − | 0.326382i | ||||
\(839\) | −15.3541 | + | 26.5941i | −0.530082 | + | 0.918130i | 0.469302 | + | 0.883038i | \(0.344506\pi\) |
−0.999384 | + | 0.0350918i | \(0.988828\pi\) | |||||||
\(840\) | 21.1803 | 0.730791 | ||||||||
\(841\) | −13.4164 | + | 23.2379i | −0.462635 | + | 0.801307i | ||||
\(842\) | 1.85410 | + | 3.21140i | 0.0638966 | + | 0.110672i | ||||
\(843\) | 17.7639 | + | 30.7680i | 0.611822 | + | 1.05971i | ||||
\(844\) | 21.3262 | 0.734079 | ||||||||
\(845\) | −11.0000 | − | 6.92820i | −0.378412 | − | 0.238337i | ||||
\(846\) | 6.11146 | 0.210116 | ||||||||
\(847\) | 23.1803 | + | 40.1495i | 0.796486 | + | 1.37955i | ||||
\(848\) | −5.56231 | − | 9.63420i | −0.191010 | − | 0.330840i | ||||
\(849\) | 11.9721 | − | 20.7363i | 0.410883 | − | 0.711670i | ||||
\(850\) | 2.14590 | 0.0736037 | ||||||||
\(851\) | −5.64590 | + | 9.77898i | −0.193539 | + | 0.335219i | ||||
\(852\) | −11.2812 | + | 19.5395i | −0.386486 | + | 0.669413i | ||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | 18.8713 | − | 32.6861i | 0.645763 | − | 1.11849i | ||||
\(855\) | −4.23607 | − | 7.33708i | −0.144870 | − | 0.250923i | ||||
\(856\) | 6.44427 | + | 11.1618i | 0.220261 | + | 0.381503i | ||||
\(857\) | 35.8885 | 1.22593 | 0.612965 | − | 0.790110i | \(-0.289977\pi\) | ||||
0.612965 | + | 0.790110i | \(0.289977\pi\) | |||||||
\(858\) | −0.326238 | + | 1.13012i | −0.0111376 | + | 0.0385817i | ||||
\(859\) | 21.8885 | 0.746827 | 0.373414 | − | 0.927665i | \(-0.378187\pi\) | ||||
0.373414 | + | 0.927665i | \(0.378187\pi\) | |||||||
\(860\) | −5.04508 | − | 8.73834i | −0.172036 | − | 0.297975i | ||||
\(861\) | −56.5689 | − | 97.9802i | −1.92786 | − | 3.33916i | ||||
\(862\) | 8.39919 | − | 14.5478i | 0.286077 | − | 0.495501i | ||||
\(863\) | 14.8328 | 0.504915 | 0.252457 | − | 0.967608i | \(-0.418761\pi\) | ||||
0.252457 | + | 0.967608i | \(0.418761\pi\) | |||||||
\(864\) | −6.28115 | + | 10.8793i | −0.213689 | + | 0.370120i | ||||
\(865\) | 9.44427 | − | 16.3580i | 0.321115 | − | 0.556187i | ||||
\(866\) | 8.97871 | 0.305109 | ||||||||
\(867\) | 5.52786 | − | 9.57454i | 0.187736 | − | 0.325168i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.3262 | 0.350092 | ||||||||
\(871\) | −9.47871 | + | 2.34537i | −0.321174 | + | 0.0794699i | ||||
\(872\) | −4.47214 | −0.151446 | ||||||||
\(873\) | 3.47214 | + | 6.01392i | 0.117514 | + | 0.203540i | ||||
\(874\) | 4.92705 | + | 8.53390i | 0.166660 | + | 0.288664i | ||||
\(875\) | −2.11803 | + | 3.66854i | −0.0716026 | + | 0.124019i | ||||
\(876\) | 21.7082 | 0.733452 | ||||||||
\(877\) | 16.8607 | − | 29.2036i | 0.569345 | − | 0.986134i | −0.427286 | − | 0.904116i | \(-0.640530\pi\) |
0.996631 | − | 0.0820175i | \(-0.0261363\pi\) | |||||||
\(878\) | −7.01722 | + | 12.1542i | −0.236820 | + | 0.410184i | ||||
\(879\) | −66.9574 | −2.25842 | ||||||||
\(880\) | 0.218847 | − | 0.379054i | 0.00737733 | − | 0.0127779i | ||||
\(881\) | −7.50000 | − | 12.9904i | −0.252681 | − | 0.437657i | 0.711582 | − | 0.702603i | \(-0.247979\pi\) |
−0.964263 | + | 0.264946i | \(0.914646\pi\) | |||||||
\(882\) | 6.76393 | + | 11.7155i | 0.227753 | + | 0.394481i | ||||
\(883\) | −42.8328 | −1.44144 | −0.720720 | − | 0.693227i | \(-0.756188\pi\) | ||||
−0.720720 | + | 0.693227i | \(0.756188\pi\) | |||||||
\(884\) | 19.6631 | − | 4.86536i | 0.661342 | − | 0.163640i | ||||
\(885\) | −1.58359 | −0.0532319 | ||||||||
\(886\) | 0.291796 | + | 0.505406i | 0.00980308 | + | 0.0169794i | ||||
\(887\) | −22.2426 | − | 38.5254i | −0.746835 | − | 1.29356i | −0.949333 | − | 0.314273i | \(-0.898239\pi\) |
0.202498 | − | 0.979283i | \(-0.435094\pi\) | |||||||
\(888\) | −7.50000 | + | 12.9904i | −0.251684 | + | 0.435929i | ||||
\(889\) | −17.9443 | −0.601832 | ||||||||
\(890\) | −2.78115 | + | 4.81710i | −0.0932245 | + | 0.161469i | ||||
\(891\) | −1.29837 | + | 2.24885i | −0.0434972 | + | 0.0753393i | ||||
\(892\) | −1.14590 | −0.0383675 | ||||||||
\(893\) | 10.4721 | − | 18.1383i | 0.350437 | − | 0.606974i | ||||
\(894\) | 3.12868 | + | 5.41903i | 0.104639 | + | 0.181239i | ||||
\(895\) | 4.11803 | + | 7.13264i | 0.137651 | + | 0.238418i | ||||
\(896\) | 48.2148 | 1.61074 | ||||||||
\(897\) | −21.0410 | − | 21.8665i | −0.702539 | − | 0.730100i | ||||
\(898\) | −2.43769 | −0.0813469 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.61803 | + | 2.80252i | 0.0539345 | + | 0.0934172i | ||||
\(901\) | 10.4164 | − | 18.0417i | 0.347021 | − | 0.601058i | ||||
\(902\) | 1.74265 | 0.0580238 | ||||||||
\(903\) | 29.5344 | − | 51.1552i | 0.982845 | − | 1.70234i | ||||
\(904\) | −1.64590 | + | 2.85078i | −0.0547418 | + | 0.0948155i | ||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 5.52786 | − | 9.57454i | 0.183651 | − | 0.318093i | ||||
\(907\) | −10.0623 | − | 17.4284i | −0.334113 | − | 0.578701i | 0.649201 | − | 0.760617i | \(-0.275104\pi\) |
−0.983314 | + | 0.181916i | \(0.941770\pi\) | |||||||
\(908\) | −5.04508 | − | 8.73834i | −0.167427 | − | 0.289992i | ||||
\(909\) | 1.05573 | 0.0350163 | ||||||||
\(910\) | 2.61803 | − | 9.06914i | 0.0867870 | − | 0.300639i | ||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | −8.78115 | − | 15.2094i | −0.290773 | − | 0.503634i | ||||
\(913\) | 1.05573 | + | 1.82857i | 0.0349395 | + | 0.0605170i | ||||
\(914\) | −0.489357 | + | 0.847591i | −0.0161865 | + | 0.0280358i | ||||
\(915\) | 32.2361 | 1.06569 | ||||||||
\(916\) | 12.8541 | − | 22.2640i | 0.424711 | − | 0.735622i | ||||
\(917\) | 25.4164 | − | 44.0225i | 0.839324 | − | 1.45375i | ||||
\(918\) | −4.79837 | −0.158370 | ||||||||
\(919\) | −23.3541 | + | 40.4505i | −0.770381 | + | 1.33434i | 0.166974 | + | 0.985961i | \(0.446601\pi\) |
−0.937354 | + | 0.348377i | \(0.886733\pi\) | |||||||
\(920\) | −4.20820 | − | 7.28882i | −0.138740 | − | 0.240305i | ||||
\(921\) | −27.8885 | − | 48.3044i | −0.918959 | − | 1.59168i | ||||
\(922\) | 0.978714 | 0.0322322 | ||||||||
\(923\) | 15.5902 | + | 16.2018i | 0.513157 | + | 0.533288i | ||||
\(924\) | 3.61803 | 0.119025 | ||||||||
\(925\) | −1.50000 | − | 2.59808i | −0.0493197 | − | 0.0854242i | ||||
\(926\) | 3.41641 | + | 5.91739i | 0.112270 | + | 0.194458i | ||||
\(927\) | −12.9443 | + | 22.4201i | −0.425146 | + | 0.736374i | ||||
\(928\) | 41.9787 | 1.37802 | ||||||||
\(929\) | −9.97214 | + | 17.2722i | −0.327175 | + | 0.566684i | −0.981950 | − | 0.189140i | \(-0.939430\pi\) |
0.654775 | + | 0.755824i | \(0.272763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46.3607 | 1.51941 | ||||||||
\(932\) | −12.8541 | + | 22.2640i | −0.421050 | + | 0.729280i | ||||
\(933\) | 26.8328 | + | 46.4758i | 0.878467 | + | 1.52155i | ||||
\(934\) | 2.76393 | + | 4.78727i | 0.0904386 | + | 0.156644i | ||||
\(935\) | 0.819660 | 0.0268058 | ||||||||
\(936\) | −11.1803 | − | 11.6190i | −0.365441 | − | 0.379777i | ||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | −3.54508 | − | 6.14027i | −0.115751 | − | 0.200487i | ||||
\(939\) | −4.34752 | − | 7.53013i | −0.141876 | − | 0.245737i | ||||
\(940\) | −4.00000 | + | 6.92820i | −0.130466 | + | 0.225973i | ||||
\(941\) | −11.8885 | −0.387555 | −0.193778 | − | 0.981045i | \(-0.562074\pi\) | ||||
−0.193778 | + | 0.981045i | \(0.562074\pi\) | |||||||
\(942\) | −12.4377 | + | 21.5427i | −0.405242 | + | 0.701900i | ||||
\(943\) | −22.4787 | + | 38.9343i | −0.732008 | + | 1.26787i | ||||
\(944\) | −1.31308 | −0.0427372 | ||||||||
\(945\) | 4.73607 | − | 8.20311i | 0.154064 | − | 0.266847i | ||||
\(946\) | 0.454915 | + | 0.787936i | 0.0147906 | + | 0.0256180i | ||||
\(947\) | −19.5902 | − | 33.9312i | −0.636595 | − | 1.10261i | −0.986175 | − | 0.165708i | \(-0.947009\pi\) |
0.349580 | − | 0.936907i | \(-0.386324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | − | 20.7846i | 0.194768 | − | 0.674697i | ||||
\(950\) | −2.61803 | −0.0849402 | ||||||||
\(951\) | 13.2918 | + | 23.0221i | 0.431016 | + | 0.746542i | ||||
\(952\) | 16.4443 | + | 28.4823i | 0.532962 | + | 0.923117i | ||||
\(953\) | −21.0967 | + | 36.5406i | −0.683391 | + | 1.18367i | 0.290549 | + | 0.956860i | \(0.406162\pi\) |
−0.973940 | + | 0.226807i | \(0.927171\pi\) | |||||||
\(954\) | −7.41641 | −0.240115 | ||||||||
\(955\) | 13.5902 | − | 23.5389i | 0.439768 | − | 0.761700i | ||||
\(956\) | −20.9443 | + | 36.2765i | −0.677386 | + | 1.17327i | ||||
\(957\) | 3.94427 | 0.127500 | ||||||||
\(958\) | 9.92705 | − | 17.1942i | 0.320728 | − | 0.555518i | ||||
\(959\) | −3.11803 | − | 5.40059i | −0.100687 | − | 0.174394i | ||||
\(960\) | 0.263932 | + | 0.457144i | 0.00851837 | + | 0.0147542i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 4.63525 | + | 4.81710i | 0.149447 | + | 0.155309i | ||||
\(963\) | −11.5279 | −0.371480 | ||||||||
\(964\) | 12.1353 | + | 21.0189i | 0.390850 | + | 0.676972i | ||||
\(965\) | 1.73607 | + | 3.00696i | 0.0558860 | + | 0.0967974i | ||||
\(966\) | 11.0172 | − | 19.0824i | 0.354473 | − | 0.613966i | ||||
\(967\) | −54.8328 | −1.76330 | −0.881652 | − | 0.471900i | \(-0.843568\pi\) | ||||
−0.881652 | + | 0.471900i | \(0.843568\pi\) | |||||||
\(968\) | 12.2361 | − | 21.1935i | 0.393282 | − | 0.681185i | ||||
\(969\) | 16.4443 | − | 28.4823i | 0.528266 | − | 0.914984i | ||||
\(970\) | 2.14590 | 0.0689006 | ||||||||
\(971\) | 5.88197 | − | 10.1879i | 0.188761 | − | 0.326944i | −0.756076 | − | 0.654484i | \(-0.772886\pi\) |
0.944838 | + | 0.327539i | \(0.106219\pi\) | |||||||
\(972\) | −14.4721 | − | 25.0665i | −0.464194 | − | 0.804008i | ||||
\(973\) | 35.3885 | + | 61.2948i | 1.13450 | + | 1.96502i | ||||
\(974\) | −8.72949 | −0.279711 | ||||||||
\(975\) | 7.82624 | − | 1.93649i | 0.250640 | − | 0.0620174i | ||||
\(976\) | 26.7295 | 0.855590 | ||||||||
\(977\) | −3.79180 | − | 6.56758i | −0.121310 | − | 0.210116i | 0.798974 | − | 0.601365i | \(-0.205376\pi\) |
−0.920285 | + | 0.391250i | \(0.872043\pi\) | |||||||
\(978\) | 10.1631 | + | 17.6030i | 0.324981 | + | 0.562883i | ||||
\(979\) | −1.06231 | + | 1.83997i | −0.0339514 | + | 0.0588056i | ||||
\(980\) | −17.7082 | −0.565668 | ||||||||
\(981\) | 2.00000 | − | 3.46410i | 0.0638551 | − | 0.110600i | ||||
\(982\) | −0.0729490 | + | 0.126351i | −0.00232790 | + | 0.00403204i | ||||
\(983\) | 38.8328 | 1.23857 | 0.619287 | − | 0.785165i | \(-0.287422\pi\) | ||||
0.619287 | + | 0.785165i | \(0.287422\pi\) | |||||||
\(984\) | −29.8607 | + | 51.7202i | −0.951924 | + | 1.64878i | ||||
\(985\) | −1.50000 | − | 2.59808i | −0.0477940 | − | 0.0827816i | ||||
\(986\) | 8.01722 | + | 13.8862i | 0.255320 | + | 0.442228i | ||||
\(987\) | −46.8328 | −1.49070 | ||||||||
\(988\) | −23.9894 | + | 5.93583i | −0.763203 | + | 0.188844i | ||||
\(989\) | −23.4721 | −0.746371 | ||||||||
\(990\) | −0.145898 | − | 0.252703i | −0.00463694 | − | 0.00803142i | ||||
\(991\) | 23.3541 | + | 40.4505i | 0.741867 | + | 1.28495i | 0.951644 | + | 0.307203i | \(0.0993930\pi\) |
−0.209777 | + | 0.977749i | \(0.567274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.6393 | −0.401097 | ||||||||
\(994\) | −8.16312 | + | 14.1389i | −0.258918 | + | 0.448460i | ||||
\(995\) | 0.645898 | − | 1.11873i | 0.0204763 | − | 0.0354661i | ||||
\(996\) | −32.3607 | −1.02539 | ||||||||
\(997\) | 9.44427 | − | 16.3580i | 0.299103 | − | 0.518062i | −0.676828 | − | 0.736141i | \(-0.736646\pi\) |
0.975931 | + | 0.218080i | \(0.0699792\pi\) | |||||||
\(998\) | −6.76393 | − | 11.7155i | −0.214109 | − | 0.370847i | ||||
\(999\) | 3.35410 | + | 5.80948i | 0.106119 | + | 0.183804i |
(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 | 65.2.e.a.16.2 | ✓ | 4 | |
3.2 | odd | 2 | 585.2.j.e.406.1 | 4 | |||
4.3 | odd | 2 | 1040.2.q.n.81.2 | 4 | |||
5.2 | odd | 4 | 325.2.o.a.224.2 | 8 | |||
5.3 | odd | 4 | 325.2.o.a.224.3 | 8 | |||
5.4 | even | 2 | 325.2.e.b.276.1 | 4 | |||
13.2 | odd | 12 | 845.2.c.c.506.3 | 4 | |||
13.3 | even | 3 | 845.2.a.e.1.1 | 2 | |||
13.4 | even | 6 | 845.2.e.g.191.1 | 4 | |||
13.5 | odd | 4 | 845.2.m.e.361.3 | 8 | |||
13.6 | odd | 12 | 845.2.m.e.316.2 | 8 | |||
13.7 | odd | 12 | 845.2.m.e.316.3 | 8 | |||
13.8 | odd | 4 | 845.2.m.e.361.2 | 8 | |||
13.9 | even | 3 | inner | 65.2.e.a.61.2 | yes | 4 | |
13.10 | even | 6 | 845.2.a.b.1.2 | 2 | |||
13.11 | odd | 12 | 845.2.c.c.506.2 | 4 | |||
13.12 | even | 2 | 845.2.e.g.146.1 | 4 | |||
39.23 | odd | 6 | 7605.2.a.bf.1.1 | 2 | |||
39.29 | odd | 6 | 7605.2.a.ba.1.2 | 2 | |||
39.35 | odd | 6 | 585.2.j.e.451.1 | 4 | |||
52.35 | odd | 6 | 1040.2.q.n.321.2 | 4 | |||
65.9 | even | 6 | 325.2.e.b.126.1 | 4 | |||
65.22 | odd | 12 | 325.2.o.a.74.3 | 8 | |||
65.29 | even | 6 | 4225.2.a.u.1.2 | 2 | |||
65.48 | odd | 12 | 325.2.o.a.74.2 | 8 | |||
65.49 | even | 6 | 4225.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.a.16.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
65.2.e.a.61.2 | yes | 4 | 13.9 | even | 3 | inner | |
325.2.e.b.126.1 | 4 | 65.9 | even | 6 | |||
325.2.e.b.276.1 | 4 | 5.4 | even | 2 | |||
325.2.o.a.74.2 | 8 | 65.48 | odd | 12 | |||
325.2.o.a.74.3 | 8 | 65.22 | odd | 12 | |||
325.2.o.a.224.2 | 8 | 5.2 | odd | 4 | |||
325.2.o.a.224.3 | 8 | 5.3 | odd | 4 | |||
585.2.j.e.406.1 | 4 | 3.2 | odd | 2 | |||
585.2.j.e.451.1 | 4 | 39.35 | odd | 6 | |||
845.2.a.b.1.2 | 2 | 13.10 | even | 6 | |||
845.2.a.e.1.1 | 2 | 13.3 | even | 3 | |||
845.2.c.c.506.2 | 4 | 13.11 | odd | 12 | |||
845.2.c.c.506.3 | 4 | 13.2 | odd | 12 | |||
845.2.e.g.146.1 | 4 | 13.12 | even | 2 | |||
845.2.e.g.191.1 | 4 | 13.4 | even | 6 | |||
845.2.m.e.316.2 | 8 | 13.6 | odd | 12 | |||
845.2.m.e.316.3 | 8 | 13.7 | odd | 12 | |||
845.2.m.e.361.2 | 8 | 13.8 | odd | 4 | |||
845.2.m.e.361.3 | 8 | 13.5 | odd | 4 | |||
1040.2.q.n.81.2 | 4 | 4.3 | odd | 2 | |||
1040.2.q.n.321.2 | 4 | 52.35 | odd | 6 | |||
4225.2.a.u.1.2 | 2 | 65.29 | even | 6 | |||
4225.2.a.y.1.1 | 2 | 65.49 | even | 6 | |||
7605.2.a.ba.1.2 | 2 | 39.29 | odd | 6 | |||
7605.2.a.bf.1.1 | 2 | 39.23 | odd | 6 |