Properties

Label 392.3.k.i.67.3
Level $392$
Weight $3$
Character 392.67
Analytic conductor $10.681$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,3,Mod(67,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.67");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not 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: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.796594176.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 67.3
Root \(-0.207107 - 2.54762i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.i.275.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26663 - 1.54779i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(-1.34221 + 0.774923i) q^{5} +(2.41421 + 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +O(q^{10})\) \(q+(1.26663 - 1.54779i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(-1.34221 + 0.774923i) q^{5} +(2.41421 + 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +(-0.500665 + 3.05899i) q^{10} +(2.24264 - 3.88437i) q^{11} +(12.9443 + 4.35381i) q^{12} +1.54985i q^{13} -5.29150i q^{15} +(-14.7477 + 6.20520i) q^{16} +(-11.8284 + 20.4874i) q^{17} +(-5.24394 - 0.858275i) q^{18} +(12.4350 + 21.5381i) q^{19} +(4.10051 + 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +(-30.5055 + 17.6124i) q^{23} +(23.1344 - 14.5203i) q^{24} +(-11.2990 + 19.5704i) q^{25} +(2.39883 + 1.96308i) q^{26} -21.6569 q^{27} +22.4499i q^{29} +(-8.19012 - 6.70239i) q^{30} +(-40.4569 - 23.3578i) q^{31} +(-9.07561 + 30.6860i) q^{32} +(7.65685 + 13.2621i) q^{33} +(16.7279 + 44.2579i) q^{34} +(-7.97056 + 7.02938i) q^{36} +(50.7340 - 29.2913i) q^{37} +(49.0870 + 8.03407i) q^{38} +(-4.58258 - 2.64575i) q^{39} +(12.3903 - 0.457458i) q^{40} -26.9706 q^{41} -17.1716 q^{43} +(-17.0050 - 5.71963i) q^{44} +(3.56604 + 2.05886i) q^{45} +(-11.3791 + 69.5245i) q^{46} +(31.2918 - 18.0663i) q^{47} +(6.82843 - 54.1990i) q^{48} +(15.9792 + 42.2769i) q^{50} +(-40.3848 - 69.9485i) q^{51} +(6.07687 - 1.22637i) q^{52} +(84.7102 + 48.9075i) q^{53} +(-27.4313 + 33.5202i) q^{54} +6.95149i q^{55} -84.9117 q^{57} +(34.7477 + 28.4358i) q^{58} +(-30.7782 + 53.3094i) q^{59} +(-20.7477 + 4.18710i) q^{60} +(32.6340 - 18.8412i) q^{61} +(-87.3970 + 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-1.20101 - 2.08021i) q^{65} +(30.2253 + 4.94697i) q^{66} +(16.6863 - 28.9015i) q^{67} +(89.6899 + 30.1672i) q^{68} -120.265i q^{69} -102.199i q^{71} +(0.784207 + 21.2404i) q^{72} +(-34.6569 + 60.0274i) q^{73} +(18.9246 - 115.627i) q^{74} +(-38.5772 - 66.8176i) q^{75} +(74.6102 - 65.8000i) q^{76} +(-9.89949 + 3.74166i) q^{78} +(-33.5156 + 19.3503i) q^{79} +(14.9859 - 19.7570i) q^{80} +(48.9264 - 84.7430i) q^{81} +(-34.1618 + 41.7447i) q^{82} +3.61522 q^{83} -36.6645i q^{85} +(-21.7501 + 26.5779i) q^{86} +(-66.3799 - 38.3245i) q^{87} +(-30.3918 + 19.0754i) q^{88} +(-22.0294 - 38.1561i) q^{89} +(7.70354 - 2.91166i) q^{90} +(93.1960 + 105.674i) q^{92} +(138.129 - 79.7486i) q^{93} +(11.6724 - 71.3164i) q^{94} +(-33.3807 - 19.2724i) q^{95} +(-75.2393 - 79.2191i) q^{96} +96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{3} + 12 q^{4} + 8 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{3} + 12 q^{4} + 8 q^{6} + 12 q^{9} + 28 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{16} - 72 q^{17} - 16 q^{18} - 8 q^{19} + 112 q^{20} - 48 q^{22} + 40 q^{24} + 68 q^{25} - 28 q^{26} - 128 q^{27} + 16 q^{33} + 32 q^{34} + 72 q^{36} + 76 q^{38} - 56 q^{40} - 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} + 32 q^{48} + 224 q^{50} - 176 q^{51} + 56 q^{52} + 16 q^{54} - 272 q^{57} + 168 q^{58} - 184 q^{59} - 56 q^{60} - 224 q^{62} + 288 q^{64} - 168 q^{65} + 32 q^{66} + 224 q^{67} + 216 q^{68} + 160 q^{72} - 232 q^{73} + 280 q^{74} - 88 q^{75} - 48 q^{76} + 336 q^{80} + 52 q^{81} + 48 q^{82} + 176 q^{83} - 8 q^{86} - 240 q^{88} - 312 q^{89} + 616 q^{90} + 112 q^{92} + 112 q^{94} - 176 q^{96} - 272 q^{97} - 480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26663 1.54779i 0.633316 0.773893i
\(3\) −1.70711 + 2.95680i −0.569036 + 0.985599i 0.427626 + 0.903956i \(0.359350\pi\)
−0.996662 + 0.0816428i \(0.973983\pi\)
\(4\) −0.791288 3.92095i −0.197822 0.980238i
\(5\) −1.34221 + 0.774923i −0.268441 + 0.154985i −0.628179 0.778069i \(-0.716199\pi\)
0.359738 + 0.933053i \(0.382866\pi\)
\(6\) 2.41421 + 6.38741i 0.402369 + 1.06457i
\(7\) 0 0
\(8\) −7.07107 3.74166i −0.883883 0.467707i
\(9\) −1.32843 2.30090i −0.147603 0.255656i
\(10\) −0.500665 + 3.05899i −0.0500665 + 0.305899i
\(11\) 2.24264 3.88437i 0.203876 0.353124i −0.745898 0.666060i \(-0.767979\pi\)
0.949774 + 0.312936i \(0.101313\pi\)
\(12\) 12.9443 + 4.35381i 1.07869 + 0.362817i
\(13\) 1.54985i 0.119219i 0.998222 + 0.0596094i \(0.0189855\pi\)
−0.998222 + 0.0596094i \(0.981014\pi\)
\(14\) 0 0
\(15\) 5.29150i 0.352767i
\(16\) −14.7477 + 6.20520i −0.921733 + 0.387825i
\(17\) −11.8284 + 20.4874i −0.695790 + 1.20514i 0.274124 + 0.961694i \(0.411612\pi\)
−0.969914 + 0.243449i \(0.921721\pi\)
\(18\) −5.24394 0.858275i −0.291330 0.0476820i
\(19\) 12.4350 + 21.5381i 0.654475 + 1.13358i 0.982025 + 0.188750i \(0.0604437\pi\)
−0.327550 + 0.944834i \(0.606223\pi\)
\(20\) 4.10051 + 4.64954i 0.205025 + 0.232477i
\(21\) 0 0
\(22\) −3.17157 8.39119i −0.144162 0.381418i
\(23\) −30.5055 + 17.6124i −1.32633 + 0.765756i −0.984730 0.174090i \(-0.944301\pi\)
−0.341598 + 0.939846i \(0.610968\pi\)
\(24\) 23.1344 14.5203i 0.963933 0.605012i
\(25\) −11.2990 + 19.5704i −0.451960 + 0.782817i
\(26\) 2.39883 + 1.96308i 0.0922627 + 0.0755032i
\(27\) −21.6569 −0.802106
\(28\) 0 0
\(29\) 22.4499i 0.774136i 0.922051 + 0.387068i \(0.126512\pi\)
−0.922051 + 0.387068i \(0.873488\pi\)
\(30\) −8.19012 6.70239i −0.273004 0.223413i
\(31\) −40.4569 23.3578i −1.30506 0.753478i −0.323795 0.946127i \(-0.604959\pi\)
−0.981268 + 0.192649i \(0.938292\pi\)
\(32\) −9.07561 + 30.6860i −0.283613 + 0.958939i
\(33\) 7.65685 + 13.2621i 0.232026 + 0.401881i
\(34\) 16.7279 + 44.2579i 0.491998 + 1.30170i
\(35\) 0 0
\(36\) −7.97056 + 7.02938i −0.221405 + 0.195260i
\(37\) 50.7340 29.2913i 1.37119 0.791657i 0.380111 0.924941i \(-0.375886\pi\)
0.991078 + 0.133284i \(0.0425523\pi\)
\(38\) 49.0870 + 8.03407i 1.29176 + 0.211423i
\(39\) −4.58258 2.64575i −0.117502 0.0678398i
\(40\) 12.3903 0.457458i 0.309758 0.0114364i
\(41\) −26.9706 −0.657819 −0.328909 0.944362i \(-0.606681\pi\)
−0.328909 + 0.944362i \(0.606681\pi\)
\(42\) 0 0
\(43\) −17.1716 −0.399339 −0.199669 0.979863i \(-0.563987\pi\)
−0.199669 + 0.979863i \(0.563987\pi\)
\(44\) −17.0050 5.71963i −0.386477 0.129992i
\(45\) 3.56604 + 2.05886i 0.0792454 + 0.0457524i
\(46\) −11.3791 + 69.5245i −0.247371 + 1.51140i
\(47\) 31.2918 18.0663i 0.665783 0.384390i −0.128694 0.991684i \(-0.541079\pi\)
0.794477 + 0.607295i \(0.207745\pi\)
\(48\) 6.82843 54.1990i 0.142259 1.12915i
\(49\) 0 0
\(50\) 15.9792 + 42.2769i 0.319584 + 0.845539i
\(51\) −40.3848 69.9485i −0.791858 1.37154i
\(52\) 6.07687 1.22637i 0.116863 0.0235841i
\(53\) 84.7102 + 48.9075i 1.59831 + 0.922782i 0.991814 + 0.127693i \(0.0407571\pi\)
0.606492 + 0.795090i \(0.292576\pi\)
\(54\) −27.4313 + 33.5202i −0.507986 + 0.620744i
\(55\) 6.95149i 0.126391i
\(56\) 0 0
\(57\) −84.9117 −1.48968
\(58\) 34.7477 + 28.4358i 0.599099 + 0.490273i
\(59\) −30.7782 + 53.3094i −0.521664 + 0.903549i 0.478018 + 0.878350i \(0.341355\pi\)
−0.999682 + 0.0251987i \(0.991978\pi\)
\(60\) −20.7477 + 4.18710i −0.345795 + 0.0697850i
\(61\) 32.6340 18.8412i 0.534983 0.308873i −0.208060 0.978116i \(-0.566715\pi\)
0.743043 + 0.669243i \(0.233382\pi\)
\(62\) −87.3970 + 33.0329i −1.40963 + 0.532790i
\(63\) 0 0
\(64\) 36.0000 + 52.9150i 0.562500 + 0.826797i
\(65\) −1.20101 2.08021i −0.0184771 0.0320032i
\(66\) 30.2253 + 4.94697i 0.457958 + 0.0749541i
\(67\) 16.6863 28.9015i 0.249049 0.431366i −0.714213 0.699928i \(-0.753215\pi\)
0.963262 + 0.268563i \(0.0865486\pi\)
\(68\) 89.6899 + 30.1672i 1.31897 + 0.443636i
\(69\) 120.265i 1.74297i
\(70\) 0 0
\(71\) 102.199i 1.43942i −0.694277 0.719708i \(-0.744276\pi\)
0.694277 0.719708i \(-0.255724\pi\)
\(72\) 0.784207 + 21.2404i 0.0108918 + 0.295005i
\(73\) −34.6569 + 60.0274i −0.474751 + 0.822294i −0.999582 0.0289132i \(-0.990795\pi\)
0.524830 + 0.851207i \(0.324129\pi\)
\(74\) 18.9246 115.627i 0.255738 1.56252i
\(75\) −38.5772 66.8176i −0.514362 0.890901i
\(76\) 74.6102 65.8000i 0.981713 0.865789i
\(77\) 0 0
\(78\) −9.89949 + 3.74166i −0.126917 + 0.0479700i
\(79\) −33.5156 + 19.3503i −0.424248 + 0.244940i −0.696893 0.717175i \(-0.745435\pi\)
0.272645 + 0.962115i \(0.412102\pi\)
\(80\) 14.9859 19.7570i 0.187324 0.246963i
\(81\) 48.9264 84.7430i 0.604030 1.04621i
\(82\) −34.1618 + 41.7447i −0.416607 + 0.509081i
\(83\) 3.61522 0.0435569 0.0217785 0.999763i \(-0.493067\pi\)
0.0217785 + 0.999763i \(0.493067\pi\)
\(84\) 0 0
\(85\) 36.6645i 0.431347i
\(86\) −21.7501 + 26.5779i −0.252908 + 0.309046i
\(87\) −66.3799 38.3245i −0.762987 0.440511i
\(88\) −30.3918 + 19.0754i −0.345362 + 0.216766i
\(89\) −22.0294 38.1561i −0.247522 0.428720i 0.715316 0.698801i \(-0.246283\pi\)
−0.962838 + 0.270081i \(0.912950\pi\)
\(90\) 7.70354 2.91166i 0.0855948 0.0323518i
\(91\) 0 0
\(92\) 93.1960 + 105.674i 1.01300 + 1.14863i
\(93\) 138.129 79.7486i 1.48525 0.857512i
\(94\) 11.6724 71.3164i 0.124174 0.758685i
\(95\) −33.3807 19.2724i −0.351376 0.202867i
\(96\) −75.2393 79.2191i −0.783743 0.825199i
\(97\) 96.1076 0.990800 0.495400 0.868665i \(-0.335021\pi\)
0.495400 + 0.868665i \(0.335021\pi\)
\(98\) 0 0
\(99\) −11.9167 −0.120371
\(100\) 85.6754 + 28.8170i 0.856754 + 0.288170i
\(101\) 16.9881 + 9.80808i 0.168199 + 0.0971097i 0.581736 0.813377i \(-0.302374\pi\)
−0.413537 + 0.910487i \(0.635707\pi\)
\(102\) −159.418 26.0920i −1.56292 0.255803i
\(103\) −37.3120 + 21.5421i −0.362252 + 0.209146i −0.670068 0.742300i \(-0.733735\pi\)
0.307816 + 0.951446i \(0.400402\pi\)
\(104\) 5.79899 10.9591i 0.0557595 0.105376i
\(105\) 0 0
\(106\) 182.995 69.1656i 1.72637 0.652506i
\(107\) −7.79899 13.5082i −0.0728878 0.126245i 0.827278 0.561793i \(-0.189888\pi\)
−0.900166 + 0.435547i \(0.856555\pi\)
\(108\) 17.1368 + 84.9155i 0.158674 + 0.786254i
\(109\) 3.33576 + 1.92590i 0.0306033 + 0.0176688i 0.515224 0.857056i \(-0.327709\pi\)
−0.484620 + 0.874725i \(0.661042\pi\)
\(110\) 10.7594 + 8.80498i 0.0978130 + 0.0800453i
\(111\) 200.013i 1.80192i
\(112\) 0 0
\(113\) −13.7746 −0.121899 −0.0609496 0.998141i \(-0.519413\pi\)
−0.0609496 + 0.998141i \(0.519413\pi\)
\(114\) −107.552 + 131.425i −0.943437 + 1.15285i
\(115\) 27.2965 47.2789i 0.237361 0.411121i
\(116\) 88.0252 17.7644i 0.758838 0.153141i
\(117\) 3.56604 2.05886i 0.0304790 0.0175971i
\(118\) 43.5269 + 115.161i 0.368872 + 0.975944i
\(119\) 0 0
\(120\) −19.7990 + 37.4166i −0.164992 + 0.311805i
\(121\) 50.4411 + 87.3666i 0.416869 + 0.722038i
\(122\) 12.1730 74.3754i 0.0997789 0.609634i
\(123\) 46.0416 79.7464i 0.374322 0.648345i
\(124\) −59.5718 + 177.112i −0.480418 + 1.42833i
\(125\) 73.7695i 0.590156i
\(126\) 0 0
\(127\) 125.025i 0.984445i −0.870469 0.492223i \(-0.836185\pi\)
0.870469 0.492223i \(-0.163815\pi\)
\(128\) 127.500 + 11.3035i 0.996093 + 0.0883088i
\(129\) 29.3137 50.7728i 0.227238 0.393588i
\(130\) −4.74096 0.775953i −0.0364689 0.00596887i
\(131\) −50.1751 86.9059i −0.383016 0.663404i 0.608475 0.793573i \(-0.291781\pi\)
−0.991492 + 0.130169i \(0.958448\pi\)
\(132\) 45.9411 40.5163i 0.348039 0.306941i
\(133\) 0 0
\(134\) −23.5980 62.4344i −0.176104 0.465928i
\(135\) 29.0679 16.7824i 0.215318 0.124314i
\(136\) 160.297 100.610i 1.17865 0.739780i
\(137\) −28.6569 + 49.6351i −0.209174 + 0.362300i −0.951455 0.307789i \(-0.900411\pi\)
0.742280 + 0.670089i \(0.233744\pi\)
\(138\) −186.144 152.331i −1.34887 1.10385i
\(139\) −183.664 −1.32132 −0.660662 0.750684i \(-0.729724\pi\)
−0.660662 + 0.750684i \(0.729724\pi\)
\(140\) 0 0
\(141\) 123.365i 0.874926i
\(142\) −158.182 129.448i −1.11395 0.911605i
\(143\) 6.02017 + 3.47575i 0.0420991 + 0.0243059i
\(144\) 33.8689 + 25.6899i 0.235200 + 0.178402i
\(145\) −17.3970 30.1324i −0.119979 0.207810i
\(146\) 49.0122 + 129.674i 0.335700 + 0.888179i
\(147\) 0 0
\(148\) −154.995 175.748i −1.04726 1.18748i
\(149\) −166.545 + 96.1549i −1.11775 + 0.645335i −0.940826 0.338889i \(-0.889949\pi\)
−0.176927 + 0.984224i \(0.556616\pi\)
\(150\) −152.282 24.9241i −1.01522 0.166161i
\(151\) −99.3791 57.3765i −0.658140 0.379977i 0.133428 0.991058i \(-0.457401\pi\)
−0.791568 + 0.611081i \(0.790735\pi\)
\(152\) −7.34073 198.825i −0.0482943 1.30806i
\(153\) 62.8528 0.410803
\(154\) 0 0
\(155\) 72.4020 0.467110
\(156\) −6.74773 + 20.0616i −0.0432547 + 0.128600i
\(157\) −183.724 106.073i −1.17022 0.675625i −0.216486 0.976286i \(-0.569460\pi\)
−0.953731 + 0.300661i \(0.902793\pi\)
\(158\) −12.5019 + 76.3847i −0.0791259 + 0.483447i
\(159\) −289.219 + 166.981i −1.81899 + 1.05019i
\(160\) −11.5980 48.2199i −0.0724874 0.301374i
\(161\) 0 0
\(162\) −69.1924 183.066i −0.427114 1.13004i
\(163\) 120.267 + 208.309i 0.737835 + 1.27797i 0.953469 + 0.301493i \(0.0974849\pi\)
−0.215634 + 0.976474i \(0.569182\pi\)
\(164\) 21.3415 + 105.750i 0.130131 + 0.644819i
\(165\) −20.5541 11.8669i −0.124571 0.0719208i
\(166\) 4.57916 5.59560i 0.0275853 0.0337084i
\(167\) 212.101i 1.27006i 0.772486 + 0.635032i \(0.219013\pi\)
−0.772486 + 0.635032i \(0.780987\pi\)
\(168\) 0 0
\(169\) 166.598 0.985787
\(170\) −56.7488 46.4404i −0.333816 0.273179i
\(171\) 33.0381 57.2236i 0.193205 0.334641i
\(172\) 13.5877 + 67.3289i 0.0789980 + 0.391447i
\(173\) 157.801 91.1065i 0.912145 0.526627i 0.0310245 0.999519i \(-0.490123\pi\)
0.881121 + 0.472891i \(0.156790\pi\)
\(174\) −143.397 + 54.1990i −0.824121 + 0.311488i
\(175\) 0 0
\(176\) −8.97056 + 71.2016i −0.0509691 + 0.404555i
\(177\) −105.083 182.010i −0.593691 1.02830i
\(178\) −86.9607 14.2329i −0.488543 0.0799599i
\(179\) −28.6030 + 49.5419i −0.159793 + 0.276770i −0.934794 0.355190i \(-0.884416\pi\)
0.775001 + 0.631960i \(0.217749\pi\)
\(180\) 5.25091 15.6114i 0.0291717 0.0867302i
\(181\) 326.212i 1.80228i −0.433533 0.901138i \(-0.642733\pi\)
0.433533 0.901138i \(-0.357267\pi\)
\(182\) 0 0
\(183\) 128.656i 0.703039i
\(184\) 281.606 10.3971i 1.53047 0.0565058i
\(185\) −45.3970 + 78.6299i −0.245389 + 0.425026i
\(186\) 51.5243 314.806i 0.277012 1.69250i
\(187\) 53.0538 + 91.8919i 0.283710 + 0.491401i
\(188\) −95.5980 108.398i −0.508500 0.576585i
\(189\) 0 0
\(190\) −72.1106 + 27.2552i −0.379530 + 0.143449i
\(191\) −84.0589 + 48.5314i −0.440099 + 0.254091i −0.703639 0.710557i \(-0.748443\pi\)
0.263541 + 0.964648i \(0.415110\pi\)
\(192\) −217.915 + 16.1130i −1.13497 + 0.0839221i
\(193\) −78.6518 + 136.229i −0.407522 + 0.705849i −0.994611 0.103673i \(-0.966940\pi\)
0.587089 + 0.809522i \(0.300274\pi\)
\(194\) 121.733 148.754i 0.627490 0.766774i
\(195\) 8.20101 0.0420565
\(196\) 0 0
\(197\) 124.117i 0.630034i 0.949086 + 0.315017i \(0.102010\pi\)
−0.949086 + 0.315017i \(0.897990\pi\)
\(198\) −15.0941 + 18.4446i −0.0762329 + 0.0931544i
\(199\) 156.729 + 90.4874i 0.787581 + 0.454710i 0.839110 0.543961i \(-0.183076\pi\)
−0.0515289 + 0.998672i \(0.516409\pi\)
\(200\) 153.122 96.1069i 0.765609 0.480534i
\(201\) 56.9706 + 98.6759i 0.283436 + 0.490925i
\(202\) 36.6985 13.8707i 0.181676 0.0686669i
\(203\) 0 0
\(204\) −242.309 + 213.696i −1.18779 + 1.04753i
\(205\) 36.2000 20.9001i 0.176586 0.101952i
\(206\) −13.9180 + 85.0368i −0.0675630 + 0.412800i
\(207\) 81.0488 + 46.7935i 0.391540 + 0.226056i
\(208\) −9.61710 22.8567i −0.0462361 0.109888i
\(209\) 111.549 0.533728
\(210\) 0 0
\(211\) 164.049 0.777482 0.388741 0.921347i \(-0.372910\pi\)
0.388741 + 0.921347i \(0.372910\pi\)
\(212\) 124.734 370.844i 0.588366 1.74927i
\(213\) 302.180 + 174.464i 1.41869 + 0.819079i
\(214\) −30.7863 5.03880i −0.143861 0.0235458i
\(215\) 23.0478 13.3066i 0.107199 0.0618913i
\(216\) 153.137 + 81.0325i 0.708968 + 0.375151i
\(217\) 0 0
\(218\) 7.20606 2.72363i 0.0330553 0.0124937i
\(219\) −118.326 204.946i −0.540301 0.935829i
\(220\) 27.2565 5.50063i 0.123893 0.0250029i
\(221\) −31.7524 18.3322i −0.143676 0.0829513i
\(222\) 309.578 + 253.343i 1.39450 + 1.14119i
\(223\) 10.5830i 0.0474574i −0.999718 0.0237287i \(-0.992446\pi\)
0.999718 0.0237287i \(-0.00755379\pi\)
\(224\) 0 0
\(225\) 60.0395 0.266842
\(226\) −17.4474 + 21.3201i −0.0772007 + 0.0943369i
\(227\) −52.9031 + 91.6308i −0.233053 + 0.403660i −0.958705 0.284402i \(-0.908205\pi\)
0.725652 + 0.688062i \(0.241538\pi\)
\(228\) 67.1896 + 332.935i 0.294691 + 1.46024i
\(229\) −64.8469 + 37.4394i −0.283174 + 0.163491i −0.634860 0.772628i \(-0.718942\pi\)
0.351685 + 0.936118i \(0.385609\pi\)
\(230\) −38.6030 102.134i −0.167839 0.444061i
\(231\) 0 0
\(232\) 84.0000 158.745i 0.362069 0.684246i
\(233\) 209.569 + 362.983i 0.899436 + 1.55787i 0.828217 + 0.560408i \(0.189356\pi\)
0.0712190 + 0.997461i \(0.477311\pi\)
\(234\) 1.33019 8.12729i 0.00568459 0.0347320i
\(235\) −28.0000 + 48.4974i −0.119149 + 0.206372i
\(236\) 233.378 + 78.4967i 0.988889 + 0.332613i
\(237\) 132.132i 0.557518i
\(238\) 0 0
\(239\) 148.318i 0.620577i 0.950642 + 0.310288i \(0.100426\pi\)
−0.950642 + 0.310288i \(0.899574\pi\)
\(240\) 32.8348 + 78.0376i 0.136812 + 0.325157i
\(241\) 229.936 398.261i 0.954092 1.65254i 0.217658 0.976025i \(-0.430158\pi\)
0.736433 0.676510i \(-0.236508\pi\)
\(242\) 199.115 + 32.5892i 0.822790 + 0.134666i
\(243\) 69.5894 + 120.532i 0.286376 + 0.496018i
\(244\) −99.6985 113.047i −0.408600 0.463309i
\(245\) 0 0
\(246\) −65.1127 172.272i −0.264686 0.700293i
\(247\) −33.3807 + 19.2724i −0.135145 + 0.0780258i
\(248\) 198.677 + 316.541i 0.801116 + 1.27637i
\(249\) −6.17157 + 10.6895i −0.0247854 + 0.0429296i
\(250\) −114.179 93.4388i −0.456718 0.373755i
\(251\) 124.919 0.497685 0.248842 0.968544i \(-0.419950\pi\)
0.248842 + 0.968544i \(0.419950\pi\)
\(252\) 0 0
\(253\) 157.993i 0.624478i
\(254\) −193.511 158.360i −0.761856 0.623465i
\(255\) 108.409 + 62.5902i 0.425135 + 0.245452i
\(256\) 178.991 183.025i 0.699183 0.714943i
\(257\) 213.676 + 370.098i 0.831425 + 1.44007i 0.896908 + 0.442216i \(0.145808\pi\)
−0.0654835 + 0.997854i \(0.520859\pi\)
\(258\) −41.4558 109.682i −0.160682 0.425123i
\(259\) 0 0
\(260\) −7.20606 + 6.35515i −0.0277156 + 0.0244429i
\(261\) 51.6552 29.8231i 0.197912 0.114265i
\(262\) −198.065 32.4173i −0.755974 0.123730i
\(263\) −223.109 128.812i −0.848322 0.489779i 0.0117625 0.999931i \(-0.496256\pi\)
−0.860084 + 0.510152i \(0.829589\pi\)
\(264\) −4.52005 122.426i −0.0171214 0.463736i
\(265\) −151.598 −0.572068
\(266\) 0 0
\(267\) 150.426 0.563395
\(268\) −126.525 42.5567i −0.472108 0.158794i
\(269\) 186.408 + 107.623i 0.692968 + 0.400085i 0.804723 0.593650i \(-0.202314\pi\)
−0.111755 + 0.993736i \(0.535647\pi\)
\(270\) 10.8428 66.2481i 0.0401586 0.245363i
\(271\) 327.833 189.275i 1.20972 0.698431i 0.247020 0.969010i \(-0.420549\pi\)
0.962698 + 0.270580i \(0.0872154\pi\)
\(272\) 47.3137 375.541i 0.173947 1.38067i
\(273\) 0 0
\(274\) 40.5269 + 107.224i 0.147908 + 0.391329i
\(275\) 50.6791 + 87.7789i 0.184288 + 0.319196i
\(276\) −471.553 + 95.1641i −1.70852 + 0.344798i
\(277\) 144.149 + 83.2243i 0.520393 + 0.300449i 0.737095 0.675789i \(-0.236197\pi\)
−0.216703 + 0.976238i \(0.569530\pi\)
\(278\) −232.635 + 284.273i −0.836815 + 1.02256i
\(279\) 124.117i 0.444863i
\(280\) 0 0
\(281\) −421.765 −1.50094 −0.750471 0.660904i \(-0.770173\pi\)
−0.750471 + 0.660904i \(0.770173\pi\)
\(282\) 190.942 + 156.257i 0.677099 + 0.554104i
\(283\) 172.719 299.159i 0.610316 1.05710i −0.380872 0.924628i \(-0.624376\pi\)
0.991187 0.132470i \(-0.0422907\pi\)
\(284\) −400.716 + 80.8685i −1.41097 + 0.284748i
\(285\) 113.969 65.8000i 0.399891 0.230877i
\(286\) 13.0051 4.91545i 0.0454722 0.0171869i
\(287\) 0 0
\(288\) 82.6619 19.8821i 0.287021 0.0690350i
\(289\) −135.323 234.387i −0.468247 0.811028i
\(290\) −68.6741 11.2399i −0.236807 0.0387583i
\(291\) −164.066 + 284.171i −0.563801 + 0.976532i
\(292\) 262.788 + 88.3889i 0.899960 + 0.302702i
\(293\) 511.038i 1.74416i 0.489365 + 0.872079i \(0.337229\pi\)
−0.489365 + 0.872079i \(0.662771\pi\)
\(294\) 0 0
\(295\) 95.4028i 0.323399i
\(296\) −468.342 + 17.2914i −1.58224 + 0.0584170i
\(297\) −48.5685 + 84.1232i −0.163530 + 0.283243i
\(298\) −62.1241 + 379.569i −0.208470 + 1.27372i
\(299\) −27.2965 47.2789i −0.0912925 0.158123i
\(300\) −231.463 + 204.131i −0.771543 + 0.680437i
\(301\) 0 0
\(302\) −214.683 + 81.1427i −0.710872 + 0.268684i
\(303\) −58.0010 + 33.4869i −0.191422 + 0.110518i
\(304\) −317.037 240.476i −1.04288 0.791040i
\(305\) −29.2010 + 50.5776i −0.0957410 + 0.165828i
\(306\) 79.6114 97.2828i 0.260168 0.317917i
\(307\) 223.331 0.727462 0.363731 0.931504i \(-0.381503\pi\)
0.363731 + 0.931504i \(0.381503\pi\)
\(308\) 0 0
\(309\) 147.098i 0.476047i
\(310\) 91.7067 112.063i 0.295828 0.361493i
\(311\) 10.7376 + 6.19938i 0.0345262 + 0.0199337i 0.517164 0.855886i \(-0.326988\pi\)
−0.482638 + 0.875820i \(0.660321\pi\)
\(312\) 22.5042 + 35.8547i 0.0721289 + 0.114919i
\(313\) −205.024 355.113i −0.655030 1.13455i −0.981886 0.189471i \(-0.939323\pi\)
0.326856 0.945074i \(-0.394011\pi\)
\(314\) −396.889 + 150.010i −1.26398 + 0.477739i
\(315\) 0 0
\(316\) 102.392 + 116.102i 0.324025 + 0.367410i
\(317\) −112.857 + 65.1580i −0.356016 + 0.205546i −0.667332 0.744761i \(-0.732564\pi\)
0.311316 + 0.950306i \(0.399230\pi\)
\(318\) −107.883 + 659.152i −0.339256 + 2.07280i
\(319\) 87.2038 + 50.3472i 0.273366 + 0.157828i
\(320\) −89.3244 43.1256i −0.279139 0.134768i
\(321\) 53.2548 0.165903
\(322\) 0 0
\(323\) −588.347 −1.82151
\(324\) −370.988 124.782i −1.14503 0.385130i
\(325\) −30.3311 17.5117i −0.0933266 0.0538821i
\(326\) 474.751 + 77.7026i 1.45629 + 0.238351i
\(327\) −11.3890 + 6.57544i −0.0348287 + 0.0201084i
\(328\) 190.711 + 100.915i 0.581435 + 0.307666i
\(329\) 0 0
\(330\) −44.4020 + 16.7824i −0.134552 + 0.0508557i
\(331\) −107.130 185.555i −0.323655 0.560588i 0.657584 0.753381i \(-0.271579\pi\)
−0.981239 + 0.192794i \(0.938245\pi\)
\(332\) −2.86068 14.1751i −0.00861651 0.0426961i
\(333\) −134.793 77.8227i −0.404783 0.233702i
\(334\) 328.287 + 268.653i 0.982894 + 0.804352i
\(335\) 51.7223i 0.154395i
\(336\) 0 0
\(337\) 164.049 0.486792 0.243396 0.969927i \(-0.421739\pi\)
0.243396 + 0.969927i \(0.421739\pi\)
\(338\) 211.018 257.858i 0.624314 0.762894i
\(339\) 23.5147 40.7287i 0.0693650 0.120144i
\(340\) −143.760 + 29.0121i −0.422822 + 0.0853298i
\(341\) −181.461 + 104.766i −0.532143 + 0.307233i
\(342\) −46.7229 123.617i −0.136617 0.361454i
\(343\) 0 0
\(344\) 121.421 + 64.2501i 0.352969 + 0.186774i
\(345\) 93.1960 + 161.420i 0.270133 + 0.467884i
\(346\) 58.8625 359.641i 0.170123 1.03942i
\(347\) 54.8457 94.9955i 0.158057 0.273762i −0.776111 0.630596i \(-0.782810\pi\)
0.934168 + 0.356834i \(0.116144\pi\)
\(348\) −97.7427 + 290.598i −0.280870 + 0.835052i
\(349\) 463.479i 1.32802i 0.747723 + 0.664010i \(0.231147\pi\)
−0.747723 + 0.664010i \(0.768853\pi\)
\(350\) 0 0
\(351\) 33.5648i 0.0956261i
\(352\) 98.8425 + 104.071i 0.280803 + 0.295656i
\(353\) −39.0488 + 67.6345i −0.110620 + 0.191599i −0.916020 0.401132i \(-0.868617\pi\)
0.805401 + 0.592731i \(0.201950\pi\)
\(354\) −414.814 67.8926i −1.17179 0.191787i
\(355\) 79.1960 + 137.171i 0.223087 + 0.386398i
\(356\) −132.177 + 116.569i −0.371283 + 0.327441i
\(357\) 0 0
\(358\) 40.4508 + 107.023i 0.112991 + 0.298946i
\(359\) −316.198 + 182.557i −0.880774 + 0.508515i −0.870913 0.491437i \(-0.836472\pi\)
−0.00986020 + 0.999951i \(0.503139\pi\)
\(360\) −17.5122 27.9012i −0.0486450 0.0775034i
\(361\) −128.760 + 223.019i −0.356676 + 0.617780i
\(362\) −504.906 413.190i −1.39477 1.14141i
\(363\) −344.434 −0.948853
\(364\) 0 0
\(365\) 107.426i 0.294316i
\(366\) 199.132 + 162.960i 0.544077 + 0.445245i
\(367\) −191.165 110.369i −0.520887 0.300734i 0.216411 0.976302i \(-0.430565\pi\)
−0.737297 + 0.675568i \(0.763898\pi\)
\(368\) 340.599 449.036i 0.925541 1.22021i
\(369\) 35.8284 + 62.0567i 0.0970960 + 0.168175i
\(370\) 64.2010 + 169.860i 0.173516 + 0.459081i
\(371\) 0 0
\(372\) −421.990 478.492i −1.13438 1.28627i
\(373\) 217.852 125.777i 0.584052 0.337203i −0.178690 0.983905i \(-0.557186\pi\)
0.762742 + 0.646703i \(0.223853\pi\)
\(374\) 209.429 + 34.2772i 0.559970 + 0.0916503i
\(375\) 218.121 + 125.932i 0.581657 + 0.335820i
\(376\) −288.864 + 10.6650i −0.768256 + 0.0283645i
\(377\) −34.7939 −0.0922916
\(378\) 0 0
\(379\) 286.024 0.754682 0.377341 0.926074i \(-0.376839\pi\)
0.377341 + 0.926074i \(0.376839\pi\)
\(380\) −49.1523 + 146.134i −0.129348 + 0.384564i
\(381\) 369.672 + 213.430i 0.970268 + 0.560184i
\(382\) −31.3554 + 191.577i −0.0820821 + 0.501509i
\(383\) −92.5727 + 53.4468i −0.241704 + 0.139548i −0.615960 0.787778i \(-0.711232\pi\)
0.374256 + 0.927326i \(0.377898\pi\)
\(384\) −251.078 + 357.695i −0.653850 + 0.931497i
\(385\) 0 0
\(386\) 111.230 + 294.288i 0.288162 + 0.762404i
\(387\) 22.8112 + 39.5101i 0.0589436 + 0.102093i
\(388\) −76.0488 376.833i −0.196002 0.971220i
\(389\) −66.8405 38.5904i −0.171826 0.0992040i 0.411620 0.911355i \(-0.364963\pi\)
−0.583447 + 0.812151i \(0.698296\pi\)
\(390\) 10.3877 12.6934i 0.0266350 0.0325472i
\(391\) 833.307i 2.13122i
\(392\) 0 0
\(393\) 342.617 0.871800
\(394\) 192.106 + 157.210i 0.487579 + 0.399010i
\(395\) 29.9899 51.9440i 0.0759238 0.131504i
\(396\) 9.42957 + 46.7250i 0.0238120 + 0.117992i
\(397\) −569.424 + 328.757i −1.43432 + 0.828103i −0.997446 0.0714218i \(-0.977246\pi\)
−0.436870 + 0.899525i \(0.643913\pi\)
\(398\) 338.573 127.968i 0.850685 0.321529i
\(399\) 0 0
\(400\) 45.1960 358.732i 0.112990 0.896830i
\(401\) −159.397 276.084i −0.397499 0.688488i 0.595918 0.803045i \(-0.296788\pi\)
−0.993417 + 0.114557i \(0.963455\pi\)
\(402\) 224.890 + 36.8078i 0.559428 + 0.0915616i
\(403\) 36.2010 62.7020i 0.0898288 0.155588i
\(404\) 25.0145 74.3705i 0.0619172 0.184085i
\(405\) 151.657i 0.374461i
\(406\) 0 0
\(407\) 262.759i 0.645600i
\(408\) 23.8402 + 645.716i 0.0584319 + 1.58264i
\(409\) −72.6325 + 125.803i −0.177585 + 0.307587i −0.941053 0.338259i \(-0.890162\pi\)
0.763468 + 0.645846i \(0.223495\pi\)
\(410\) 13.5032 82.5027i 0.0329347 0.201226i
\(411\) −97.8406 169.465i −0.238055 0.412323i
\(412\) 113.990 + 129.252i 0.276675 + 0.313719i
\(413\) 0 0
\(414\) 175.085 66.1760i 0.422911 0.159846i
\(415\) −4.85237 + 2.80152i −0.0116925 + 0.00675065i
\(416\) −47.5586 14.0658i −0.114324 0.0338120i
\(417\) 313.534 543.057i 0.751880 1.30229i
\(418\) 141.292 172.654i 0.338019 0.413049i
\(419\) 707.012 1.68738 0.843690 0.536831i \(-0.180379\pi\)
0.843690 + 0.536831i \(0.180379\pi\)
\(420\) 0 0
\(421\) 121.989i 0.289761i −0.989449 0.144880i \(-0.953720\pi\)
0.989449 0.144880i \(-0.0462798\pi\)
\(422\) 207.789 253.913i 0.492392 0.601688i
\(423\) −83.1377 47.9996i −0.196543 0.113474i
\(424\) −415.997 662.784i −0.981124 1.56317i
\(425\) −267.299 462.975i −0.628938 1.08935i
\(426\) 652.784 246.729i 1.53236 0.579176i
\(427\) 0 0
\(428\) −46.7939 + 41.2684i −0.109332 + 0.0964214i
\(429\) −20.5541 + 11.8669i −0.0479118 + 0.0276619i
\(430\) 8.59720 52.5277i 0.0199935 0.122157i
\(431\) −509.969 294.431i −1.18322 0.683133i −0.226464 0.974020i \(-0.572717\pi\)
−0.956758 + 0.290886i \(0.906050\pi\)
\(432\) 319.389 134.385i 0.739327 0.311077i
\(433\) 137.696 0.318004 0.159002 0.987278i \(-0.449172\pi\)
0.159002 + 0.987278i \(0.449172\pi\)
\(434\) 0 0
\(435\) 118.794 0.273090
\(436\) 4.91182 14.6033i 0.0112656 0.0334938i
\(437\) −758.675 438.021i −1.73610 1.00234i
\(438\) −467.089 76.4485i −1.06641 0.174540i
\(439\) 381.522 220.272i 0.869070 0.501758i 0.00203069 0.999998i \(-0.499354\pi\)
0.867039 + 0.498240i \(0.166020\pi\)
\(440\) 26.0101 49.1545i 0.0591139 0.111715i
\(441\) 0 0
\(442\) −68.5929 + 25.9257i −0.155188 + 0.0586554i
\(443\) 243.529 + 421.805i 0.549727 + 0.952155i 0.998293 + 0.0584052i \(0.0186015\pi\)
−0.448566 + 0.893750i \(0.648065\pi\)
\(444\) 784.243 158.268i 1.76631 0.356460i
\(445\) 59.1361 + 34.1422i 0.132890 + 0.0767241i
\(446\) −16.3802 13.4048i −0.0367270 0.0300555i
\(447\) 656.587i 1.46887i
\(448\) 0 0
\(449\) 264.039 0.588059 0.294030 0.955796i \(-0.405004\pi\)
0.294030 + 0.955796i \(0.405004\pi\)
\(450\) 76.0480 92.9284i 0.168996 0.206508i
\(451\) −60.4853 + 104.764i −0.134114 + 0.232292i
\(452\) 10.8997 + 54.0096i 0.0241143 + 0.119490i
\(453\) 339.301 195.896i 0.749010 0.432441i
\(454\) 74.8162 + 197.945i 0.164793 + 0.436003i
\(455\) 0 0
\(456\) 600.416 + 317.710i 1.31670 + 0.696733i
\(457\) 257.161 + 445.417i 0.562717 + 0.974654i 0.997258 + 0.0740019i \(0.0235771\pi\)
−0.434542 + 0.900652i \(0.643090\pi\)
\(458\) −24.1890 + 147.791i −0.0528144 + 0.322688i
\(459\) 256.167 443.693i 0.558097 0.966652i
\(460\) −206.978 69.6169i −0.449951 0.151341i
\(461\) 202.224i 0.438664i 0.975650 + 0.219332i \(0.0703878\pi\)
−0.975650 + 0.219332i \(0.929612\pi\)
\(462\) 0 0
\(463\) 722.653i 1.56081i 0.625277 + 0.780403i \(0.284986\pi\)
−0.625277 + 0.780403i \(0.715014\pi\)
\(464\) −139.306 331.086i −0.300229 0.713547i
\(465\) −123.598 + 214.078i −0.265802 + 0.460383i
\(466\) 827.267 + 135.399i 1.77525 + 0.290555i
\(467\) 173.641 + 300.755i 0.371822 + 0.644015i 0.989846 0.142144i \(-0.0453997\pi\)
−0.618023 + 0.786160i \(0.712066\pi\)
\(468\) −10.8944 12.3531i −0.0232787 0.0263956i
\(469\) 0 0
\(470\) 39.5980 + 104.766i 0.0842510 + 0.222907i
\(471\) 627.273 362.156i 1.33179 0.768910i
\(472\) 417.100 261.793i 0.883686 0.554646i
\(473\) −38.5097 + 66.7007i −0.0814158 + 0.141016i
\(474\) −204.512 167.362i −0.431460 0.353085i
\(475\) −562.013 −1.18319
\(476\) 0 0
\(477\) 259.880i 0.544822i
\(478\) 229.564 + 187.864i 0.480260 + 0.393021i
\(479\) 25.2716 + 14.5906i 0.0527591 + 0.0304605i 0.526148 0.850393i \(-0.323636\pi\)
−0.473388 + 0.880854i \(0.656969\pi\)
\(480\) 162.375 + 48.0236i 0.338282 + 0.100049i
\(481\) 45.3970 + 78.6299i 0.0943804 + 0.163472i
\(482\) −325.179 860.342i −0.674645 1.78494i
\(483\) 0 0
\(484\) 302.647 266.909i 0.625303 0.551466i
\(485\) −128.996 + 74.4760i −0.265972 + 0.153559i
\(486\) 274.702 + 44.9606i 0.565231 + 0.0925114i
\(487\) 607.640 + 350.821i 1.24772 + 0.720372i 0.970654 0.240478i \(-0.0773043\pi\)
0.277067 + 0.960851i \(0.410638\pi\)
\(488\) −301.255 + 11.1225i −0.617325 + 0.0227920i
\(489\) −821.235 −1.67942
\(490\) 0 0
\(491\) −59.9512 −0.122100 −0.0610501 0.998135i \(-0.519445\pi\)
−0.0610501 + 0.998135i \(0.519445\pi\)
\(492\) −349.114 117.425i −0.709582 0.238668i
\(493\) −459.942 265.548i −0.932945 0.538636i
\(494\) −12.4516 + 76.0772i −0.0252056 + 0.154003i
\(495\) 15.9947 9.23455i 0.0323125 0.0186557i
\(496\) 741.588 + 93.4313i 1.49514 + 0.188370i
\(497\) 0 0
\(498\) 8.72792 + 23.0919i 0.0175259 + 0.0463693i
\(499\) 42.1421 + 72.9923i 0.0844532 + 0.146277i 0.905158 0.425075i \(-0.139752\pi\)
−0.820705 + 0.571352i \(0.806419\pi\)
\(500\) −289.247 + 58.3729i −0.578493 + 0.116746i
\(501\) −627.138 362.079i −1.25177 0.722712i
\(502\) 158.226 193.348i 0.315192 0.385155i
\(503\) 409.987i 0.815083i −0.913187 0.407542i \(-0.866386\pi\)
0.913187 0.407542i \(-0.133614\pi\)
\(504\) 0 0
\(505\) −30.4020 −0.0602020
\(506\) 244.539 + 200.119i 0.483280 + 0.395492i
\(507\) −284.401 + 492.596i −0.560948 + 0.971590i
\(508\) −490.215 + 98.9304i −0.964991 + 0.194745i
\(509\) −413.123 + 238.516i −0.811636 + 0.468598i −0.847524 0.530758i \(-0.821907\pi\)
0.0358878 + 0.999356i \(0.488574\pi\)
\(510\) 234.191 88.5158i 0.459198 0.173560i
\(511\) 0 0
\(512\) −56.5685 508.865i −0.110485 0.993878i
\(513\) −269.304 466.448i −0.524958 0.909254i
\(514\) 843.482 + 138.053i 1.64102 + 0.268585i
\(515\) 33.3869 57.8278i 0.0648289 0.112287i
\(516\) −222.273 74.7617i −0.430762 0.144887i
\(517\) 162.065i 0.313472i
\(518\) 0 0
\(519\) 622.114i 1.19868i
\(520\) 0.708989 + 19.2031i 0.00136344 + 0.0369290i
\(521\) −105.437 + 182.621i −0.202373 + 0.350521i −0.949293 0.314394i \(-0.898199\pi\)
0.746919 + 0.664915i \(0.231532\pi\)
\(522\) 19.2682 117.726i 0.0369123 0.225529i
\(523\) −255.783 443.030i −0.489069 0.847093i 0.510852 0.859669i \(-0.329330\pi\)
−0.999921 + 0.0125761i \(0.995997\pi\)
\(524\) −301.051 + 265.502i −0.574525 + 0.506683i
\(525\) 0 0
\(526\) −481.970 + 182.167i −0.916292 + 0.346326i
\(527\) 957.084 552.573i 1.81610 1.04852i
\(528\) −195.215 148.073i −0.369725 0.280441i
\(529\) 355.892 616.423i 0.672764 1.16526i
\(530\) −192.019 + 234.641i −0.362300 + 0.442720i
\(531\) 163.546 0.307997
\(532\) 0 0
\(533\) 41.8002i 0.0784244i
\(534\) 190.535 232.828i 0.356807 0.436007i
\(535\) 20.9357 + 12.0872i 0.0391321 + 0.0225929i
\(536\) −226.129 + 141.930i −0.421883 + 0.264795i
\(537\) −97.6569 169.147i −0.181856 0.314984i
\(538\) 402.688 152.202i 0.748491 0.282903i
\(539\) 0 0
\(540\) −88.8040 100.694i −0.164452 0.186471i
\(541\) −296.542 + 171.208i −0.548136 + 0.316466i −0.748370 0.663282i \(-0.769163\pi\)
0.200234 + 0.979748i \(0.435830\pi\)
\(542\) 122.287 747.157i 0.225622 1.37852i
\(543\) 964.542 + 556.878i 1.77632 + 1.02556i
\(544\) −521.328 548.904i −0.958324 1.00901i
\(545\) −5.96970 −0.0109536
\(546\) 0 0
\(547\) −441.976 −0.807999 −0.404000 0.914759i \(-0.632380\pi\)
−0.404000 + 0.914759i \(0.632380\pi\)
\(548\) 217.293 + 73.0865i 0.396520 + 0.133369i
\(549\) −86.7038 50.0584i −0.157930 0.0911811i
\(550\) 200.055 + 32.7430i 0.363736 + 0.0595327i
\(551\) −483.529 + 279.166i −0.877548 + 0.506653i
\(552\) −449.990 + 850.401i −0.815199 + 1.54058i
\(553\) 0 0
\(554\) 311.397 117.697i 0.562088 0.212449i
\(555\) −154.995 268.459i −0.279270 0.483710i
\(556\) 145.331 + 720.138i 0.261387 + 1.29521i
\(557\) 316.714 + 182.855i 0.568607 + 0.328285i 0.756593 0.653886i \(-0.226863\pi\)
−0.187986 + 0.982172i \(0.560196\pi\)
\(558\) 192.106 + 157.210i 0.344276 + 0.281739i
\(559\) 26.6133i 0.0476087i
\(560\) 0 0
\(561\) −362.274 −0.645765
\(562\) −534.220 + 652.802i −0.950570 + 1.16157i
\(563\) −403.194 + 698.353i −0.716154 + 1.24041i 0.246359 + 0.969179i \(0.420766\pi\)
−0.962513 + 0.271236i \(0.912568\pi\)
\(564\) 483.706 97.6169i 0.857636 0.173080i
\(565\) 18.4883 10.6743i 0.0327227 0.0188925i
\(566\) −244.262 646.256i −0.431558 1.14180i
\(567\) 0 0
\(568\) −382.392 + 722.653i −0.673225 + 1.27228i
\(569\) −111.446 193.030i −0.195862 0.339244i 0.751320 0.659938i \(-0.229417\pi\)
−0.947183 + 0.320694i \(0.896084\pi\)
\(570\) 42.5123 259.744i 0.0745830 0.455691i
\(571\) −286.541 + 496.304i −0.501823 + 0.869184i 0.498174 + 0.867077i \(0.334004\pi\)
−0.999998 + 0.00210683i \(0.999329\pi\)
\(572\) 8.86455 26.3551i 0.0154975 0.0460754i
\(573\) 331.393i 0.578348i
\(574\) 0 0
\(575\) 796.008i 1.38436i
\(576\) 73.9290 153.126i 0.128349 0.265844i
\(577\) 361.950 626.916i 0.627297 1.08651i −0.360795 0.932645i \(-0.617495\pi\)
0.988092 0.153865i \(-0.0491721\pi\)
\(578\) −534.186 87.4302i −0.924197 0.151263i
\(579\) −268.534 465.115i −0.463789 0.803307i
\(580\) −104.382 + 92.0561i −0.179969 + 0.158717i
\(581\) 0 0
\(582\) 232.024 + 613.879i 0.398667 + 1.05477i
\(583\) 379.949 219.364i 0.651714 0.376267i
\(584\) 469.663 294.784i 0.804218 0.504767i
\(585\) −3.19091 + 5.52682i −0.00545455 + 0.00944755i
\(586\) 790.978 + 647.297i 1.34979 + 1.10460i
\(587\) 21.1198 0.0359793 0.0179896 0.999838i \(-0.494273\pi\)
0.0179896 + 0.999838i \(0.494273\pi\)
\(588\) 0 0
\(589\) 1161.82i 1.97253i
\(590\) −147.663 120.840i −0.250277 0.204814i
\(591\) −366.988 211.880i −0.620960 0.358512i
\(592\) −566.453 + 746.795i −0.956846 + 1.26148i
\(593\) 64.3726 + 111.497i 0.108554 + 0.188021i 0.915185 0.403035i \(-0.132045\pi\)
−0.806631 + 0.591056i \(0.798711\pi\)
\(594\) 68.6863 + 181.727i 0.115633 + 0.305937i
\(595\) 0 0
\(596\) 508.804 + 576.930i 0.853698 + 0.968003i
\(597\) −535.105 + 308.943i −0.896324 + 0.517493i
\(598\) −107.752 17.6358i −0.180188 0.0294913i
\(599\) −280.705 162.065i −0.468623 0.270559i 0.247040 0.969005i \(-0.420542\pi\)
−0.715663 + 0.698446i \(0.753875\pi\)
\(600\) 22.7731 + 616.814i 0.0379552 + 1.02802i
\(601\) −721.862 −1.20110 −0.600551 0.799587i \(-0.705052\pi\)
−0.600551 + 0.799587i \(0.705052\pi\)
\(602\) 0 0
\(603\) −88.6661 −0.147042
\(604\) −146.333 + 435.062i −0.242273 + 0.720301i
\(605\) −135.405 78.1759i −0.223809 0.129216i
\(606\) −21.6353 + 132.189i −0.0357019 + 0.218133i
\(607\) 611.413 353.000i 1.00727 0.581548i 0.0968795 0.995296i \(-0.469114\pi\)
0.910391 + 0.413748i \(0.135781\pi\)
\(608\) −773.775 + 186.110i −1.27266 + 0.306103i
\(609\) 0 0
\(610\) 41.2965 + 109.260i 0.0676991 + 0.179115i
\(611\) 28.0000 + 48.4974i 0.0458265 + 0.0793739i
\(612\) −49.7347 246.443i −0.0812658 0.402684i
\(613\) −18.9026 10.9134i −0.0308363 0.0178033i 0.484503 0.874790i \(-0.339001\pi\)
−0.515339 + 0.856986i \(0.672334\pi\)
\(614\) 282.878 345.669i 0.460713 0.562978i
\(615\) 142.715i 0.232057i
\(616\) 0 0
\(617\) −699.578 −1.13384 −0.566919 0.823774i \(-0.691865\pi\)
−0.566919 + 0.823774i \(0.691865\pi\)
\(618\) −227.677 186.320i −0.368409 0.301488i
\(619\) −48.0990 + 83.3100i −0.0777044 + 0.134588i −0.902259 0.431194i \(-0.858092\pi\)
0.824555 + 0.565782i \(0.191426\pi\)
\(620\) −57.2908 283.885i −0.0924046 0.457879i
\(621\) 660.654 381.429i 1.06386 0.614217i
\(622\) 23.1960 8.76725i 0.0372925 0.0140953i
\(623\) 0 0
\(624\) 84.0000 + 10.5830i 0.134615 + 0.0169599i
\(625\) −225.309 390.247i −0.360495 0.624395i
\(626\) −809.329 132.463i −1.29286 0.211602i
\(627\) −190.426 + 329.828i −0.303710 + 0.526042i
\(628\) −270.529 + 804.308i −0.430779 + 1.28074i
\(629\) 1385.88i 2.20331i
\(630\) 0 0
\(631\) 269.399i 0.426940i 0.976950 + 0.213470i \(0.0684766\pi\)
−0.976950 + 0.213470i \(0.931523\pi\)
\(632\) 309.393 11.4230i 0.489546 0.0180743i
\(633\) −280.049 + 485.059i −0.442415 + 0.766285i
\(634\) −42.0975 + 257.210i −0.0663999 + 0.405694i
\(635\) 96.8843 + 167.809i 0.152574 + 0.264266i
\(636\) 883.578 + 1001.88i 1.38927 + 1.57529i
\(637\) 0 0
\(638\) 188.382 71.2016i 0.295269 0.111601i
\(639\) −235.149 + 135.763i −0.367995 + 0.212462i
\(640\) −179.890 + 83.6309i −0.281079 + 0.130673i
\(641\) −317.907 + 550.630i −0.495954 + 0.859018i −0.999989 0.00466541i \(-0.998515\pi\)
0.504035 + 0.863683i \(0.331848\pi\)
\(642\) 67.4543 82.4271i 0.105069 0.128391i
\(643\) 1281.70 1.99332 0.996658 0.0816828i \(-0.0260295\pi\)
0.996658 + 0.0816828i \(0.0260295\pi\)
\(644\) 0 0
\(645\) 90.8634i 0.140874i
\(646\) −745.219 + 910.636i −1.15359 + 1.40965i
\(647\) 225.826 + 130.381i 0.349035 + 0.201516i 0.664260 0.747501i \(-0.268747\pi\)
−0.315225 + 0.949017i \(0.602080\pi\)
\(648\) −663.041 + 416.158i −1.02321 + 0.642219i
\(649\) 138.049 + 239.107i 0.212710 + 0.368424i
\(650\) −65.5227 + 24.7653i −0.100804 + 0.0381004i
\(651\) 0 0
\(652\) 721.602 636.393i 1.10675 0.976063i
\(653\) −944.471 + 545.291i −1.44636 + 0.835055i −0.998262 0.0589313i \(-0.981231\pi\)
−0.448095 + 0.893986i \(0.647897\pi\)
\(654\) −4.24828 + 25.9564i −0.00649585 + 0.0396887i
\(655\) 134.691 + 77.7637i 0.205635 + 0.118723i
\(656\) 397.754 167.358i 0.606333 0.255119i
\(657\) 184.156 0.280299
\(658\) 0 0
\(659\) −362.780 −0.550500 −0.275250 0.961373i \(-0.588761\pi\)
−0.275250 + 0.961373i \(0.588761\pi\)
\(660\) −30.2655 + 89.9820i −0.0458567 + 0.136336i
\(661\) −102.047 58.9169i −0.154383 0.0891330i 0.420818 0.907145i \(-0.361743\pi\)
−0.575201 + 0.818012i \(0.695076\pi\)
\(662\) −422.893 69.2149i −0.638811 0.104554i
\(663\) 108.409 62.5902i 0.163513 0.0944045i
\(664\) −25.5635 13.5269i −0.0384992 0.0203719i
\(665\) 0 0
\(666\) −291.186 + 110.058i −0.437216 + 0.165252i
\(667\) −395.397 684.848i −0.592799 1.02676i
\(668\) 831.637 167.833i 1.24496 0.251247i
\(669\) 31.2918 + 18.0663i 0.0467740 + 0.0270050i
\(670\) 80.0552 + 65.5132i 0.119485 + 0.0977808i
\(671\) 169.017i 0.251888i
\(672\) 0 0
\(673\) −6.56854 −0.00976009 −0.00488005 0.999988i \(-0.501553\pi\)
−0.00488005 + 0.999988i \(0.501553\pi\)
\(674\) 207.789 253.913i 0.308293 0.376725i
\(675\) 244.701 423.834i 0.362519 0.627902i
\(676\) −131.827 653.223i −0.195010 0.966306i
\(677\) 108.942 62.8978i 0.160919 0.0929066i −0.417378 0.908733i \(-0.637051\pi\)
0.578297 + 0.815826i \(0.303718\pi\)
\(678\) −33.2548 87.9840i −0.0490484 0.129770i
\(679\) 0 0
\(680\) −137.186 + 259.257i −0.201744 + 0.381260i
\(681\) −180.622 312.847i −0.265231 0.459394i
\(682\) −67.6879 + 413.563i −0.0992491 + 0.606397i
\(683\) 276.887 479.583i 0.405399 0.702171i −0.588969 0.808156i \(-0.700466\pi\)
0.994368 + 0.105984i \(0.0337994\pi\)
\(684\) −250.514 84.2603i −0.366248 0.123188i
\(685\) 88.8274i 0.129675i
\(686\) 0 0
\(687\) 255.652i 0.372128i
\(688\) 253.242 106.553i 0.368084 0.154874i
\(689\) −75.7990 + 131.288i −0.110013 + 0.190548i
\(690\) 367.889 + 60.2124i 0.533172 + 0.0872644i
\(691\) 523.413 + 906.577i 0.757471 + 1.31198i 0.944136 + 0.329555i \(0.106899\pi\)
−0.186665 + 0.982424i \(0.559768\pi\)
\(692\) −482.090 546.639i −0.696662 0.789941i
\(693\) 0 0
\(694\) −77.5635 205.214i −0.111763 0.295697i
\(695\) 246.515 142.325i 0.354698 0.204785i
\(696\) 325.980 + 519.366i 0.468362 + 0.746215i
\(697\) 319.019 552.558i 0.457703 0.792766i
\(698\) 717.367 + 587.058i 1.02775 + 0.841057i
\(699\) −1431.02 −2.04724
\(700\) 0 0
\(701\) 625.993i 0.893000i −0.894784 0.446500i \(-0.852670\pi\)
0.894784 0.446500i \(-0.147330\pi\)
\(702\) −51.9511 42.5142i −0.0740044 0.0605615i
\(703\) 1261.76 + 728.476i 1.79482 + 1.03624i
\(704\) 286.276 21.1678i 0.406643 0.0300680i
\(705\) −95.5980 165.581i −0.135600 0.234866i
\(706\) 55.2233 + 146.107i 0.0782200 + 0.206951i
\(707\) 0 0
\(708\) −630.500 + 556.048i −0.890536 + 0.785379i
\(709\) 513.979 296.746i 0.724935 0.418541i −0.0916314 0.995793i \(-0.529208\pi\)
0.816566 + 0.577252i \(0.195875\pi\)
\(710\) 312.624 + 51.1672i 0.440316 + 0.0720665i
\(711\) 89.0461 + 51.4108i 0.125241 + 0.0723077i
\(712\) 13.0046 + 352.231i 0.0182649 + 0.494706i
\(713\) 1645.55 2.30792
\(714\) 0 0
\(715\) −10.7737 −0.0150682
\(716\) 216.885 + 72.9492i 0.302912 + 0.101884i
\(717\) −438.546 253.194i −0.611640 0.353130i
\(718\) −117.947 + 720.639i −0.164272 + 1.00368i
\(719\) −529.578 + 305.752i −0.736549 + 0.425247i −0.820813 0.571197i \(-0.806479\pi\)
0.0842645 + 0.996443i \(0.473146\pi\)
\(720\) −65.3667 8.23543i −0.0907870 0.0114381i
\(721\) 0 0
\(722\) 182.094 + 481.775i 0.252208 + 0.667279i
\(723\) 785.051 + 1359.75i 1.08582 + 1.88070i
\(724\) −1279.06 + 258.127i −1.76666 + 0.356530i
\(725\) −439.355 253.662i −0.606007 0.349878i
\(726\) −436.270 + 533.110i −0.600924 + 0.734311i
\(727\) 944.144i 1.29868i 0.760496 + 0.649342i \(0.224956\pi\)
−0.760496 + 0.649342i \(0.775044\pi\)
\(728\) 0 0
\(729\) 405.489 0.556227
\(730\) −166.272 136.069i −0.227770 0.186395i
\(731\) 203.113 351.802i 0.277856 0.481261i
\(732\) 504.454 101.804i 0.689145 0.139076i
\(733\) −189.014 + 109.127i −0.257863 + 0.148878i −0.623360 0.781935i \(-0.714233\pi\)
0.365496 + 0.930813i \(0.380899\pi\)
\(734\) −412.965 + 156.086i −0.562622 + 0.212651i
\(735\) 0 0
\(736\) −263.598 1095.94i −0.358149 1.48905i
\(737\) −74.8427 129.631i −0.101550 0.175891i
\(738\) 141.432 + 23.1482i 0.191642 + 0.0313661i
\(739\) 3.64971 6.32149i 0.00493872 0.00855411i −0.863545 0.504271i \(-0.831761\pi\)
0.868484 + 0.495717i \(0.165095\pi\)
\(740\) 344.226 + 115.780i 0.465170 + 0.156460i
\(741\) 131.600i 0.177598i
\(742\) 0 0
\(743\) 106.867i 0.143832i −0.997411 0.0719159i \(-0.977089\pi\)
0.997411 0.0719159i \(-0.0229113\pi\)
\(744\) −1275.11 + 47.0778i −1.71386 + 0.0632766i
\(745\) 149.025 258.119i 0.200034 0.346469i
\(746\) 81.2623 496.500i 0.108931 0.665550i
\(747\) −4.80256 8.31828i −0.00642913 0.0111356i
\(748\) 318.323 280.734i 0.425565 0.375313i
\(749\) 0 0
\(750\) 471.196 178.095i 0.628261 0.237460i
\(751\) 110.387 63.7317i 0.146986 0.0848624i −0.424703 0.905333i \(-0.639622\pi\)
0.571689 + 0.820470i \(0.306288\pi\)
\(752\) −349.378 + 460.609i −0.464598 + 0.612512i
\(753\) −213.250 + 369.359i −0.283200 + 0.490517i
\(754\) −44.0711 + 53.8536i −0.0584497 + 0.0714239i
\(755\) 177.849 0.235562
\(756\) 0 0
\(757\) 704.275i 0.930350i 0.885219 + 0.465175i \(0.154009\pi\)
−0.885219 + 0.465175i \(0.845991\pi\)
\(758\) 362.288 442.705i 0.477952 0.584043i
\(759\) −467.153 269.711i −0.615485 0.355350i
\(760\) 163.927 + 261.175i 0.215693 + 0.343652i
\(761\) 501.465 + 868.563i 0.658955 + 1.14134i 0.980886 + 0.194581i \(0.0623348\pi\)
−0.321931 + 0.946763i \(0.604332\pi\)
\(762\) 798.583 301.836i 1.04801 0.396110i
\(763\) 0 0
\(764\) 256.804 + 291.188i 0.336131 + 0.381137i
\(765\) −84.3614 + 48.7061i −0.110276 + 0.0636681i
\(766\) −34.5311 + 210.980i −0.0450798 + 0.275431i
\(767\) −82.6213 47.7014i −0.107720 0.0621922i
\(768\) 235.612 + 841.683i 0.306786 + 1.09594i
\(769\) −646.950 −0.841288 −0.420644 0.907226i \(-0.638196\pi\)
−0.420644 + 0.907226i \(0.638196\pi\)
\(770\) 0 0
\(771\) −1459.07 −1.89244
\(772\) 596.383 + 200.594i 0.772517 + 0.259836i
\(773\) 488.668 + 282.132i 0.632170 + 0.364984i 0.781592 0.623790i \(-0.214408\pi\)
−0.149422 + 0.988774i \(0.547741\pi\)
\(774\) 90.0466 + 14.7379i 0.116339 + 0.0190413i
\(775\) 914.245 527.840i 1.17967 0.681083i
\(776\) −679.584 359.602i −0.875752 0.463404i
\(777\) 0 0
\(778\) −144.392 + 54.5750i −0.185594 + 0.0701478i
\(779\) −335.380 580.895i −0.430526 0.745693i
\(780\) −6.48936 32.1558i −0.00831969 0.0412253i
\(781\) −396.977 229.195i −0.508293 0.293463i
\(782\) −1289.78 1055.49i −1.64934 1.34974i
\(783\) 486.195i 0.620939i
\(784\) 0 0
\(785\) 328.794 0.418846
\(786\) 433.970 530.299i 0.552125 0.674680i
\(787\) −461.673 + 799.640i −0.586623 + 1.01606i 0.408048 + 0.912961i \(0.366210\pi\)
−0.994671 + 0.103101i \(0.967124\pi\)
\(788\) 486.655 98.2120i 0.617583 0.124635i
\(789\) 761.740 439.791i 0.965451 0.557403i
\(790\) −42.4121 112.212i −0.0536862 0.142040i
\(791\) 0 0
\(792\) 84.2641 + 44.5884i 0.106394 + 0.0562984i
\(793\) 29.2010 + 50.5776i 0.0368235 + 0.0637801i
\(794\) −212.404 + 1297.76i −0.267512 + 1.63446i
\(795\) 258.794 448.244i 0.325527 0.563829i
\(796\) 230.779 686.127i 0.289923 0.861969i
\(797\) 207.983i 0.260957i −0.991451 0.130479i \(-0.958349\pi\)
0.991451 0.130479i \(-0.0416514\pi\)
\(798\) 0 0
\(799\) 854.785i 1.06982i
\(800\) −497.994 524.335i −0.622492 0.655419i
\(801\) −58.5290 + 101.375i −0.0730699 + 0.126561i
\(802\) −629.216 102.984i −0.784558 0.128409i
\(803\) 155.446 + 269.240i 0.193581 + 0.335293i
\(804\) 341.823 301.460i 0.425153 0.374950i
\(805\) 0 0
\(806\) −51.1960 135.452i −0.0635186 0.168054i
\(807\) −636.438 + 367.448i −0.788647 + 0.455326i
\(808\) −83.4255 132.917i −0.103249 0.164502i
\(809\) −170.270 + 294.916i −0.210470 + 0.364544i −0.951862 0.306528i \(-0.900833\pi\)
0.741392 + 0.671072i \(0.234166\pi\)
\(810\) 234.732 + 192.093i 0.289793 + 0.237152i
\(811\) −907.380 −1.11884 −0.559420 0.828884i \(-0.688976\pi\)
−0.559420 + 0.828884i \(0.688976\pi\)
\(812\) 0 0
\(813\) 1292.45i 1.58973i
\(814\) −406.695 332.819i −0.499626 0.408869i
\(815\) −322.846 186.395i −0.396130 0.228706i
\(816\) 1029.63 + 780.985i 1.26180 + 0.957090i
\(817\) −213.529 369.843i −0.261357 0.452684i
\(818\) 102.718 + 271.766i 0.125572 + 0.332232i
\(819\) 0 0
\(820\) −110.593 125.401i −0.134869 0.152928i
\(821\) 548.560 316.711i 0.668161 0.385763i −0.127219 0.991875i \(-0.540605\pi\)
0.795379 + 0.606112i \(0.207272\pi\)
\(822\) −386.224 63.2132i −0.469858 0.0769018i
\(823\) 124.404 + 71.8247i 0.151159 + 0.0872718i 0.573672 0.819085i \(-0.305518\pi\)
−0.422513 + 0.906357i \(0.638852\pi\)
\(824\) 344.438 12.7169i 0.418008 0.0154331i
\(825\) −346.059 −0.419465
\(826\) 0 0
\(827\) 1545.57 1.86888 0.934442 0.356114i \(-0.115899\pi\)
0.934442 + 0.356114i \(0.115899\pi\)
\(828\) 119.342 354.815i 0.144133 0.428521i
\(829\) 644.285 + 371.978i 0.777183 + 0.448707i 0.835431 0.549595i \(-0.185218\pi\)
−0.0582482 + 0.998302i \(0.518551\pi\)
\(830\) −1.81002 + 11.0589i −0.00218074 + 0.0133240i
\(831\) −492.155 + 284.146i −0.592244 + 0.341932i
\(832\) −82.0101 + 55.7944i −0.0985698 + 0.0670606i
\(833\) 0 0
\(834\) −443.404 1173.14i −0.531660 1.40664i
\(835\) −164.362 284.683i −0.196840 0.340937i
\(836\) −88.2675 437.379i −0.105583 0.523181i
\(837\) 876.170 + 505.857i 1.04680 + 0.604369i
\(838\) 895.524 1094.30i 1.06864 1.30585i
\(839\) 96.3107i 0.114792i 0.998351 + 0.0573961i \(0.0182798\pi\)
−0.998351 + 0.0573961i \(0.981720\pi\)
\(840\) 0 0
\(841\) 337.000 0.400713
\(842\) −188.814 154.516i −0.224244 0.183510i
\(843\) 719.997 1247.07i 0.854089 1.47933i
\(844\) −129.810 643.227i −0.153803 0.762118i
\(845\) −223.609 + 129.101i −0.264626 + 0.152782i
\(846\) −179.598 + 67.8817i −0.212291 + 0.0802384i
\(847\) 0 0
\(848\) −1552.76 195.630i −1.83109 0.230696i
\(849\) 589.701 + 1021.39i 0.694583 + 1.20305i
\(850\) −1055.15 172.697i −1.24136 0.203173i
\(851\) −1031.78 + 1787.09i −1.21243 + 2.09999i
\(852\) 444.953 1322.89i 0.522245 1.55268i
\(853\) 904.866i 1.06080i −0.847746 0.530402i \(-0.822041\pi\)
0.847746 0.530402i \(-0.177959\pi\)
\(854\) 0 0
\(855\) 102.408i 0.119775i
\(856\) 4.60396 + 124.699i 0.00537845 + 0.145676i
\(857\) −80.4659 + 139.371i −0.0938926 + 0.162627i −0.909146 0.416478i \(-0.863264\pi\)
0.815253 + 0.579105i \(0.196598\pi\)
\(858\) −7.66704 + 46.8445i −0.00893594 + 0.0545973i
\(859\) −115.846 200.652i −0.134862 0.233587i 0.790683 0.612226i \(-0.209726\pi\)
−0.925545 + 0.378638i \(0.876392\pi\)
\(860\) −70.4121 79.8398i −0.0818746 0.0928370i
\(861\) 0 0
\(862\) −1101.66 + 416.388i −1.27803 + 0.483048i
\(863\) −1158.18 + 668.674i −1.34204 + 0.774825i −0.987106 0.160068i \(-0.948829\pi\)
−0.354931 + 0.934893i \(0.615495\pi\)
\(864\) 196.549 664.563i 0.227487 0.769170i
\(865\) −141.201 + 244.567i −0.163238 + 0.282737i
\(866\) 174.410 213.123i 0.201397 0.246101i
\(867\) 924.046 1.06580
\(868\) 0 0
\(869\) 173.583i 0.199750i
\(870\) 150.468 183.868i 0.172952 0.211342i
\(871\) 44.7929 + 25.8612i 0.0514269 + 0.0296914i
\(872\) −16.3813 26.0994i −0.0187859 0.0299305i
\(873\) −127.672 221.134i −0.146245 0.253304i
\(874\) −1638.92 + 619.455i −1.87520 + 0.708759i
\(875\) 0 0
\(876\) −709.955 + 626.122i −0.810451 + 0.714751i
\(877\) 1243.73 718.068i 1.41816 0.818777i 0.422026 0.906584i \(-0.361319\pi\)
0.996138 + 0.0878061i \(0.0279856\pi\)
\(878\) 142.314 869.517i 0.162089 0.990338i
\(879\) −1511.04 872.397i −1.71904 0.992488i
\(880\) −43.1354 102.519i −0.0490175 0.116499i
\(881\) −186.706 −0.211926 −0.105963 0.994370i \(-0.533792\pi\)
−0.105963 + 0.994370i \(0.533792\pi\)
\(882\) 0 0
\(883\) 1277.99 1.44733 0.723664 0.690153i \(-0.242457\pi\)
0.723664 + 0.690153i \(0.242457\pi\)
\(884\) −46.7545 + 139.006i −0.0528898 + 0.157246i
\(885\) 282.087 + 162.863i 0.318742 + 0.184026i
\(886\) 961.325 + 157.340i 1.08502 + 0.177585i
\(887\) −849.326 + 490.359i −0.957526 + 0.552828i −0.895411 0.445241i \(-0.853118\pi\)
−0.0621155 + 0.998069i \(0.519785\pi\)
\(888\) 748.382 1414.31i 0.842772 1.59269i
\(889\) 0 0
\(890\) 127.748 48.2844i 0.143538 0.0542521i
\(891\) −219.449 380.096i −0.246295 0.426595i
\(892\) −41.4955 + 8.37420i −0.0465196 + 0.00938812i
\(893\) 778.228 + 449.310i 0.871476 + 0.503147i
\(894\) −1016.26 831.654i −1.13675 0.930262i
\(895\) 88.6605i 0.0990621i
\(896\) 0 0
\(897\) 186.392 0.207795
\(898\) 334.440 408.676i 0.372427 0.455095i
\(899\) 524.382 908.256i 0.583295 1.01030i
\(900\) −47.5086 235.412i −0.0527873 0.261569i
\(901\) −2003.98 + 1157.00i −2.22417 + 1.28412i
\(902\) 85.5391 + 226.315i 0.0948327 + 0.250904i
\(903\) 0 0
\(904\) 97.4012 + 51.5398i 0.107745 + 0.0570131i
\(905\) 252.789 + 437.843i 0.279325 + 0.483805i
\(906\) 126.565 773.294i 0.139697 0.853525i
\(907\) 329.186 570.167i 0.362939 0.628629i −0.625504 0.780221i \(-0.715107\pi\)
0.988443 + 0.151592i \(0.0484399\pi\)
\(908\) 401.142 + 134.924i 0.441786 + 0.148595i
\(909\) 52.1173i 0.0573348i
\(910\) 0 0
\(911\) 276.507i 0.303520i −0.988417 0.151760i \(-0.951506\pi\)
0.988417 0.151760i \(-0.0484941\pi\)
\(912\) 1252.25 526.894i 1.37309 0.577735i
\(913\) 8.10765 14.0429i 0.00888023 0.0153810i
\(914\) 1015.14 + 166.148i 1.11066 + 0.181781i
\(915\) −99.6985 172.683i −0.108960 0.188724i
\(916\) 198.111 + 224.636i 0.216278 + 0.245236i
\(917\) 0 0
\(918\) −362.274 958.487i −0.394634 1.04410i
\(919\) −1160.24 + 669.867i −1.26251 + 0.728908i −0.973559 0.228437i \(-0.926639\pi\)
−0.288948 + 0.957345i \(0.593305\pi\)
\(920\) −369.916 + 232.178i −0.402083 + 0.252367i
\(921\) −381.250 + 660.344i −0.413952 + 0.716986i
\(922\) 313.000 + 256.144i 0.339479 + 0.277813i
\(923\) 158.392 0.171606
\(924\) 0 0
\(925\) 1323.85i 1.43119i
\(926\) 1118.51 + 915.335i 1.20790 + 0.988483i
\(927\) 99.1324 + 57.2341i 0.106939 + 0.0617412i
\(928\) −688.900 203.747i −0.742349 0.219555i
\(929\) −17.7006 30.6583i −0.0190534 0.0330014i 0.856342 0.516410i \(-0.172732\pi\)
−0.875395 + 0.483409i \(0.839399\pi\)
\(930\) 174.794 + 462.461i 0.187950 + 0.497270i
\(931\) 0 0
\(932\) 1257.41 1108.93i 1.34915 1.18984i
\(933\) −36.6606 + 21.1660i −0.0392933 + 0.0226860i
\(934\) 685.444 + 112.187i 0.733880 + 0.120114i
\(935\) −142.418 82.2252i −0.152319 0.0879414i
\(936\) −32.9193 + 1.21540i −0.0351702 + 0.00129850i
\(937\) 610.235 0.651265 0.325633 0.945496i \(-0.394423\pi\)
0.325633 + 0.945496i \(0.394423\pi\)
\(938\) 0 0
\(939\) 1399.99 1.49094
\(940\) 212.312 + 71.4112i 0.225864 + 0.0759694i
\(941\) 1604.66 + 926.450i 1.70527 + 0.984537i 0.940222 + 0.340563i \(0.110618\pi\)
0.765047 + 0.643975i \(0.222716\pi\)
\(942\) 233.983 1429.60i 0.248390 1.51763i
\(943\) 822.752 475.016i 0.872483 0.503728i
\(944\) 123.113 977.177i 0.130416 1.03514i
\(945\) 0 0
\(946\) 54.4609 + 144.090i 0.0575697 + 0.152315i
\(947\) 916.448 + 1587.33i 0.967738 + 1.67617i 0.702072 + 0.712106i \(0.252259\pi\)
0.265666 + 0.964065i \(0.414408\pi\)
\(948\) −518.082 + 104.554i −0.546500 + 0.110289i
\(949\) −93.0332 53.7128i −0.0980329 0.0565993i
\(950\) −711.864 + 869.876i −0.749330 + 0.915659i
\(951\) 444.927i 0.467852i
\(952\) 0 0
\(953\) 349.687 0.366933 0.183467 0.983026i \(-0.441268\pi\)
0.183467 + 0.983026i \(0.441268\pi\)
\(954\) −402.239 329.172i −0.421634 0.345044i
\(955\) 75.2162 130.278i 0.0787604 0.136417i
\(956\) 581.547 117.362i 0.608313 0.122764i
\(957\) −297.733 + 171.896i −0.311110 + 0.179620i
\(958\) 54.5929 20.6342i 0.0569864 0.0215388i
\(959\) 0 0
\(960\) 280.000 190.494i 0.291667 0.198431i
\(961\) 610.676 + 1057.72i 0.635459 + 1.10065i
\(962\) 179.203 + 29.3302i 0.186282 + 0.0304888i
\(963\) −20.7208 + 35.8894i −0.0215169 + 0.0372684i
\(964\) −1743.51 586.429i −1.80862 0.608329i
\(965\) 243.796i 0.252639i
\(966\) 0 0
\(967\) 632.128i 0.653700i −0.945076 0.326850i \(-0.894013\pi\)
0.945076 0.326850i \(-0.105987\pi\)
\(968\) −29.7768 806.509i −0.0307611 0.833170i
\(969\) 1004.37 1739.62i 1.03650 1.79528i
\(970\) −48.1177 + 293.992i −0.0496059 + 0.303085i
\(971\) −328.248 568.543i −0.338052 0.585523i 0.646014 0.763325i \(-0.276435\pi\)
−0.984066 + 0.177802i \(0.943101\pi\)
\(972\) 417.536 368.232i 0.429564 0.378840i
\(973\) 0 0
\(974\) 1312.65 496.136i 1.34769 0.509380i
\(975\) 103.557 59.7886i 0.106212 0.0613217i
\(976\) −364.363 + 480.366i −0.373323 + 0.492178i
\(977\) −84.6569 + 146.630i −0.0866498 + 0.150082i −0.906093 0.423078i \(-0.860949\pi\)
0.819443 + 0.573160i \(0.194283\pi\)
\(978\) −1040.20 + 1271.10i −1.06360 + 1.29969i
\(979\) −197.616 −0.201855
\(980\) 0 0
\(981\) 10.2337i 0.0104319i
\(982\) −75.9361 + 92.7917i −0.0773280 + 0.0944926i
\(983\) −605.012 349.304i −0.615475 0.355345i 0.159630 0.987177i \(-0.448970\pi\)
−0.775105 + 0.631832i \(0.782303\pi\)
\(984\) −623.947 + 391.621i −0.634093 + 0.397988i
\(985\) −96.1808 166.590i −0.0976455 0.169127i
\(986\) −993.588 + 375.541i −1.00770 + 0.380873i
\(987\) 0 0
\(988\) 101.980 + 115.634i 0.103218 + 0.117039i
\(989\) 523.828 302.432i 0.529654 0.305796i
\(990\) 5.96629 36.4532i 0.00602656 0.0368214i
\(991\) −372.133 214.851i −0.375513 0.216802i 0.300352 0.953829i \(-0.402896\pi\)
−0.675864 + 0.737026i \(0.736229\pi\)
\(992\) 1083.93 1029.48i 1.09267 1.03778i
\(993\) 731.529 0.736686
\(994\) 0 0
\(995\) −280.483 −0.281892
\(996\) 46.7964 + 15.7400i 0.0469844 + 0.0158032i
\(997\) 45.3720 + 26.1955i 0.0455085 + 0.0262743i 0.522582 0.852589i \(-0.324969\pi\)
−0.477073 + 0.878864i \(0.658302\pi\)
\(998\) 166.355 + 27.2274i 0.166688 + 0.0272819i
\(999\) −1098.74 + 634.357i −1.09984 + 0.634992i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 392.3.k.i.67.3 8
7.2 even 3 inner 392.3.k.i.275.1 8
7.3 odd 6 392.3.g.h.99.4 4
7.4 even 3 56.3.g.a.43.4 yes 4
7.5 odd 6 392.3.k.j.275.1 8
7.6 odd 2 392.3.k.j.67.3 8
8.3 odd 2 inner 392.3.k.i.67.1 8
21.11 odd 6 504.3.g.a.379.1 4
28.3 even 6 1568.3.g.h.687.4 4
28.11 odd 6 224.3.g.a.15.1 4
56.3 even 6 392.3.g.h.99.3 4
56.11 odd 6 56.3.g.a.43.3 4
56.19 even 6 392.3.k.j.275.3 8
56.27 even 2 392.3.k.j.67.1 8
56.45 odd 6 1568.3.g.h.687.3 4
56.51 odd 6 inner 392.3.k.i.275.3 8
56.53 even 6 224.3.g.a.15.2 4
84.11 even 6 2016.3.g.a.1135.3 4
112.11 odd 12 1792.3.d.g.1023.8 8
112.53 even 12 1792.3.d.g.1023.2 8
112.67 odd 12 1792.3.d.g.1023.1 8
112.109 even 12 1792.3.d.g.1023.7 8
168.11 even 6 504.3.g.a.379.2 4
168.53 odd 6 2016.3.g.a.1135.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.g.a.43.3 4 56.11 odd 6
56.3.g.a.43.4 yes 4 7.4 even 3
224.3.g.a.15.1 4 28.11 odd 6
224.3.g.a.15.2 4 56.53 even 6
392.3.g.h.99.3 4 56.3 even 6
392.3.g.h.99.4 4 7.3 odd 6
392.3.k.i.67.1 8 8.3 odd 2 inner
392.3.k.i.67.3 8 1.1 even 1 trivial
392.3.k.i.275.1 8 7.2 even 3 inner
392.3.k.i.275.3 8 56.51 odd 6 inner
392.3.k.j.67.1 8 56.27 even 2
392.3.k.j.67.3 8 7.6 odd 2
392.3.k.j.275.1 8 7.5 odd 6
392.3.k.j.275.3 8 56.19 even 6
504.3.g.a.379.1 4 21.11 odd 6
504.3.g.a.379.2 4 168.11 even 6
1568.3.g.h.687.3 4 56.45 odd 6
1568.3.g.h.687.4 4 28.3 even 6
1792.3.d.g.1023.1 8 112.67 odd 12
1792.3.d.g.1023.2 8 112.53 even 12
1792.3.d.g.1023.7 8 112.109 even 12
1792.3.d.g.1023.8 8 112.11 odd 12
2016.3.g.a.1135.2 4 168.53 odd 6
2016.3.g.a.1135.3 4 84.11 even 6