Properties

Label 1260.2.c.d.811.13
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1260,2,Mod(811,1260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1260.811");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), 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: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.13
Root \(-0.947441 - 1.04993i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.d.811.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.947441 - 1.04993i) q^{2} +(-0.204711 - 1.98950i) q^{4} +1.00000i q^{5} +(-2.29670 - 1.31346i) q^{7} +(-2.28279 - 1.67000i) q^{8} +O(q^{10})\) \(q+(0.947441 - 1.04993i) q^{2} +(-0.204711 - 1.98950i) q^{4} +1.00000i q^{5} +(-2.29670 - 1.31346i) q^{7} +(-2.28279 - 1.67000i) q^{8} +(1.04993 + 0.947441i) q^{10} -0.477147i q^{11} +2.96271i q^{13} +(-3.55503 + 1.16694i) q^{14} +(-3.91619 + 0.814543i) q^{16} -3.83353i q^{17} -5.31262 q^{19} +(1.98950 - 0.204711i) q^{20} +(-0.500972 - 0.452069i) q^{22} -7.60808i q^{23} -1.00000 q^{25} +(3.11064 + 2.80699i) q^{26} +(-2.14297 + 4.83815i) q^{28} -6.17752 q^{29} -3.38789 q^{31} +(-2.85514 + 4.88346i) q^{32} +(-4.02494 - 3.63204i) q^{34} +(1.31346 - 2.29670i) q^{35} -8.62867 q^{37} +(-5.03339 + 5.57788i) q^{38} +(1.67000 - 2.28279i) q^{40} +1.01125i q^{41} +6.85412i q^{43} +(-0.949282 + 0.0976772i) q^{44} +(-7.98796 - 7.20820i) q^{46} +6.21838 q^{47} +(3.54963 + 6.03325i) q^{49} +(-0.947441 + 1.04993i) q^{50} +(5.89430 - 0.606499i) q^{52} +9.30380 q^{53} +0.477147 q^{55} +(3.04938 + 6.83383i) q^{56} +(-5.85284 + 6.48597i) q^{58} -4.88854 q^{59} -4.75818i q^{61} +(-3.20982 + 3.55705i) q^{62} +(2.42221 + 7.62449i) q^{64} -2.96271 q^{65} -1.30610i q^{67} +(-7.62679 + 0.784764i) q^{68} +(-1.16694 - 3.55503i) q^{70} -9.18700i q^{71} +4.49766i q^{73} +(-8.17516 + 9.05951i) q^{74} +(1.08755 + 10.5694i) q^{76} +(-0.626715 + 1.09586i) q^{77} -8.80833i q^{79} +(-0.814543 - 3.91619i) q^{80} +(1.06174 + 0.958097i) q^{82} -10.9520 q^{83} +3.83353 q^{85} +(7.19635 + 6.49388i) q^{86} +(-0.796835 + 1.08922i) q^{88} -13.1208i q^{89} +(3.89141 - 6.80445i) q^{91} +(-15.1362 + 1.55746i) q^{92} +(5.89154 - 6.52887i) q^{94} -5.31262i q^{95} +1.60612i q^{97} +(9.69756 + 1.98928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.947441 1.04993i 0.669942 0.742413i
\(3\) 0 0
\(4\) −0.204711 1.98950i −0.102355 0.994748i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.29670 1.31346i −0.868070 0.496442i
\(8\) −2.28279 1.67000i −0.807086 0.590433i
\(9\) 0 0
\(10\) 1.04993 + 0.947441i 0.332017 + 0.299607i
\(11\) 0.477147i 0.143865i −0.997409 0.0719326i \(-0.977083\pi\)
0.997409 0.0719326i \(-0.0229167\pi\)
\(12\) 0 0
\(13\) 2.96271i 0.821708i 0.911701 + 0.410854i \(0.134769\pi\)
−0.911701 + 0.410854i \(0.865231\pi\)
\(14\) −3.55503 + 1.16694i −0.950122 + 0.311879i
\(15\) 0 0
\(16\) −3.91619 + 0.814543i −0.979047 + 0.203636i
\(17\) 3.83353i 0.929767i −0.885372 0.464883i \(-0.846096\pi\)
0.885372 0.464883i \(-0.153904\pi\)
\(18\) 0 0
\(19\) −5.31262 −1.21880 −0.609399 0.792864i \(-0.708589\pi\)
−0.609399 + 0.792864i \(0.708589\pi\)
\(20\) 1.98950 0.204711i 0.444865 0.0457747i
\(21\) 0 0
\(22\) −0.500972 0.452069i −0.106808 0.0963814i
\(23\) 7.60808i 1.58639i −0.608965 0.793197i \(-0.708415\pi\)
0.608965 0.793197i \(-0.291585\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.11064 + 2.80699i 0.610047 + 0.550497i
\(27\) 0 0
\(28\) −2.14297 + 4.83815i −0.404983 + 0.914324i
\(29\) −6.17752 −1.14714 −0.573569 0.819158i \(-0.694441\pi\)
−0.573569 + 0.819158i \(0.694441\pi\)
\(30\) 0 0
\(31\) −3.38789 −0.608482 −0.304241 0.952595i \(-0.598403\pi\)
−0.304241 + 0.952595i \(0.598403\pi\)
\(32\) −2.85514 + 4.88346i −0.504723 + 0.863282i
\(33\) 0 0
\(34\) −4.02494 3.63204i −0.690271 0.622890i
\(35\) 1.31346 2.29670i 0.222016 0.388213i
\(36\) 0 0
\(37\) −8.62867 −1.41854 −0.709272 0.704935i \(-0.750976\pi\)
−0.709272 + 0.704935i \(0.750976\pi\)
\(38\) −5.03339 + 5.57788i −0.816524 + 0.904852i
\(39\) 0 0
\(40\) 1.67000 2.28279i 0.264050 0.360940i
\(41\) 1.01125i 0.157930i 0.996877 + 0.0789651i \(0.0251616\pi\)
−0.996877 + 0.0789651i \(0.974838\pi\)
\(42\) 0 0
\(43\) 6.85412i 1.04524i 0.852565 + 0.522622i \(0.175046\pi\)
−0.852565 + 0.522622i \(0.824954\pi\)
\(44\) −0.949282 + 0.0976772i −0.143110 + 0.0147254i
\(45\) 0 0
\(46\) −7.98796 7.20820i −1.17776 1.06279i
\(47\) 6.21838 0.907043 0.453522 0.891245i \(-0.350167\pi\)
0.453522 + 0.891245i \(0.350167\pi\)
\(48\) 0 0
\(49\) 3.54963 + 6.03325i 0.507090 + 0.861893i
\(50\) −0.947441 + 1.04993i −0.133988 + 0.148483i
\(51\) 0 0
\(52\) 5.89430 0.606499i 0.817392 0.0841063i
\(53\) 9.30380 1.27797 0.638987 0.769217i \(-0.279354\pi\)
0.638987 + 0.769217i \(0.279354\pi\)
\(54\) 0 0
\(55\) 0.477147 0.0643385
\(56\) 3.04938 + 6.83383i 0.407491 + 0.913209i
\(57\) 0 0
\(58\) −5.85284 + 6.48597i −0.768515 + 0.851650i
\(59\) −4.88854 −0.636433 −0.318217 0.948018i \(-0.603084\pi\)
−0.318217 + 0.948018i \(0.603084\pi\)
\(60\) 0 0
\(61\) 4.75818i 0.609222i −0.952477 0.304611i \(-0.901474\pi\)
0.952477 0.304611i \(-0.0985264\pi\)
\(62\) −3.20982 + 3.55705i −0.407648 + 0.451745i
\(63\) 0 0
\(64\) 2.42221 + 7.62449i 0.302777 + 0.953061i
\(65\) −2.96271 −0.367479
\(66\) 0 0
\(67\) 1.30610i 0.159565i −0.996812 0.0797826i \(-0.974577\pi\)
0.996812 0.0797826i \(-0.0254226\pi\)
\(68\) −7.62679 + 0.784764i −0.924884 + 0.0951667i
\(69\) 0 0
\(70\) −1.16694 3.55503i −0.139477 0.424907i
\(71\) 9.18700i 1.09030i −0.838340 0.545148i \(-0.816473\pi\)
0.838340 0.545148i \(-0.183527\pi\)
\(72\) 0 0
\(73\) 4.49766i 0.526411i 0.964740 + 0.263206i \(0.0847797\pi\)
−0.964740 + 0.263206i \(0.915220\pi\)
\(74\) −8.17516 + 9.05951i −0.950343 + 1.05315i
\(75\) 0 0
\(76\) 1.08755 + 10.5694i 0.124751 + 1.21240i
\(77\) −0.626715 + 1.09586i −0.0714208 + 0.124885i
\(78\) 0 0
\(79\) 8.80833i 0.991015i −0.868604 0.495507i \(-0.834982\pi\)
0.868604 0.495507i \(-0.165018\pi\)
\(80\) −0.814543 3.91619i −0.0910686 0.437843i
\(81\) 0 0
\(82\) 1.06174 + 0.958097i 0.117249 + 0.105804i
\(83\) −10.9520 −1.20214 −0.601068 0.799198i \(-0.705258\pi\)
−0.601068 + 0.799198i \(0.705258\pi\)
\(84\) 0 0
\(85\) 3.83353 0.415804
\(86\) 7.19635 + 6.49388i 0.776003 + 0.700253i
\(87\) 0 0
\(88\) −0.796835 + 1.08922i −0.0849429 + 0.116112i
\(89\) 13.1208i 1.39080i −0.718621 0.695402i \(-0.755226\pi\)
0.718621 0.695402i \(-0.244774\pi\)
\(90\) 0 0
\(91\) 3.89141 6.80445i 0.407931 0.713300i
\(92\) −15.1362 + 1.55746i −1.57806 + 0.162376i
\(93\) 0 0
\(94\) 5.89154 6.52887i 0.607666 0.673401i
\(95\) 5.31262i 0.545063i
\(96\) 0 0
\(97\) 1.60612i 0.163077i 0.996670 + 0.0815384i \(0.0259833\pi\)
−0.996670 + 0.0815384i \(0.974017\pi\)
\(98\) 9.69756 + 1.98928i 0.979602 + 0.200948i
\(99\) 0 0
\(100\) 0.204711 + 1.98950i 0.0204711 + 0.198950i
\(101\) 6.17664i 0.614599i −0.951613 0.307299i \(-0.900575\pi\)
0.951613 0.307299i \(-0.0994253\pi\)
\(102\) 0 0
\(103\) 16.8145 1.65678 0.828390 0.560151i \(-0.189257\pi\)
0.828390 + 0.560151i \(0.189257\pi\)
\(104\) 4.94772 6.76323i 0.485164 0.663189i
\(105\) 0 0
\(106\) 8.81480 9.76835i 0.856169 0.948786i
\(107\) 9.15824i 0.885360i 0.896680 + 0.442680i \(0.145972\pi\)
−0.896680 + 0.442680i \(0.854028\pi\)
\(108\) 0 0
\(109\) −15.2477 −1.46046 −0.730230 0.683201i \(-0.760587\pi\)
−0.730230 + 0.683201i \(0.760587\pi\)
\(110\) 0.452069 0.500972i 0.0431031 0.0477658i
\(111\) 0 0
\(112\) 10.0642 + 3.27301i 0.950974 + 0.309270i
\(113\) 4.04995 0.380987 0.190493 0.981688i \(-0.438991\pi\)
0.190493 + 0.981688i \(0.438991\pi\)
\(114\) 0 0
\(115\) 7.60808 0.709457
\(116\) 1.26461 + 12.2902i 0.117416 + 1.14111i
\(117\) 0 0
\(118\) −4.63160 + 5.13263i −0.426373 + 0.472496i
\(119\) −5.03519 + 8.80445i −0.461576 + 0.807102i
\(120\) 0 0
\(121\) 10.7723 0.979303
\(122\) −4.99576 4.50809i −0.452295 0.408143i
\(123\) 0 0
\(124\) 0.693537 + 6.74018i 0.0622814 + 0.605286i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 12.9949i 1.15311i −0.817059 0.576554i \(-0.804397\pi\)
0.817059 0.576554i \(-0.195603\pi\)
\(128\) 10.3001 + 4.68060i 0.910409 + 0.413710i
\(129\) 0 0
\(130\) −2.80699 + 3.11064i −0.246190 + 0.272821i
\(131\) 1.77552 0.155128 0.0775640 0.996987i \(-0.475286\pi\)
0.0775640 + 0.996987i \(0.475286\pi\)
\(132\) 0 0
\(133\) 12.2015 + 6.97792i 1.05800 + 0.605063i
\(134\) −1.37131 1.23745i −0.118463 0.106899i
\(135\) 0 0
\(136\) −6.40198 + 8.75112i −0.548965 + 0.750402i
\(137\) 15.1622 1.29539 0.647695 0.761900i \(-0.275733\pi\)
0.647695 + 0.761900i \(0.275733\pi\)
\(138\) 0 0
\(139\) −18.8544 −1.59921 −0.799607 0.600524i \(-0.794959\pi\)
−0.799607 + 0.600524i \(0.794959\pi\)
\(140\) −4.83815 2.14297i −0.408898 0.181114i
\(141\) 0 0
\(142\) −9.64571 8.70414i −0.809450 0.730435i
\(143\) 1.41365 0.118215
\(144\) 0 0
\(145\) 6.17752i 0.513015i
\(146\) 4.72223 + 4.26127i 0.390815 + 0.352665i
\(147\) 0 0
\(148\) 1.76638 + 17.1667i 0.145196 + 1.41109i
\(149\) 18.8439 1.54376 0.771878 0.635771i \(-0.219318\pi\)
0.771878 + 0.635771i \(0.219318\pi\)
\(150\) 0 0
\(151\) 18.6462i 1.51741i 0.651435 + 0.758704i \(0.274167\pi\)
−0.651435 + 0.758704i \(0.725833\pi\)
\(152\) 12.1276 + 8.87206i 0.983675 + 0.719619i
\(153\) 0 0
\(154\) 0.556804 + 1.69627i 0.0448686 + 0.136690i
\(155\) 3.38789i 0.272121i
\(156\) 0 0
\(157\) 22.6941i 1.81118i −0.424149 0.905592i \(-0.639427\pi\)
0.424149 0.905592i \(-0.360573\pi\)
\(158\) −9.24814 8.34538i −0.735743 0.663922i
\(159\) 0 0
\(160\) −4.88346 2.85514i −0.386071 0.225719i
\(161\) −9.99293 + 17.4734i −0.787553 + 1.37710i
\(162\) 0 0
\(163\) 9.17980i 0.719017i −0.933142 0.359509i \(-0.882944\pi\)
0.933142 0.359509i \(-0.117056\pi\)
\(164\) 2.01187 0.207013i 0.157101 0.0161650i
\(165\) 0 0
\(166\) −10.3764 + 11.4988i −0.805362 + 0.892483i
\(167\) −14.8751 −1.15107 −0.575535 0.817777i \(-0.695206\pi\)
−0.575535 + 0.817777i \(0.695206\pi\)
\(168\) 0 0
\(169\) 4.22235 0.324796
\(170\) 3.63204 4.02494i 0.278565 0.308699i
\(171\) 0 0
\(172\) 13.6362 1.40311i 1.03975 0.106986i
\(173\) 18.2211i 1.38532i 0.721262 + 0.692662i \(0.243562\pi\)
−0.721262 + 0.692662i \(0.756438\pi\)
\(174\) 0 0
\(175\) 2.29670 + 1.31346i 0.173614 + 0.0992885i
\(176\) 0.388657 + 1.86860i 0.0292961 + 0.140851i
\(177\) 0 0
\(178\) −13.7760 12.4312i −1.03255 0.931758i
\(179\) 5.02780i 0.375796i −0.982189 0.187898i \(-0.939833\pi\)
0.982189 0.187898i \(-0.0601674\pi\)
\(180\) 0 0
\(181\) 14.6503i 1.08895i −0.838777 0.544476i \(-0.816729\pi\)
0.838777 0.544476i \(-0.183271\pi\)
\(182\) −3.45732 10.5325i −0.256274 0.780723i
\(183\) 0 0
\(184\) −12.7055 + 17.3676i −0.936660 + 1.28036i
\(185\) 8.62867i 0.634393i
\(186\) 0 0
\(187\) −1.82916 −0.133761
\(188\) −1.27297 12.3714i −0.0928408 0.902279i
\(189\) 0 0
\(190\) −5.57788 5.03339i −0.404662 0.365161i
\(191\) 6.84692i 0.495426i 0.968833 + 0.247713i \(0.0796790\pi\)
−0.968833 + 0.247713i \(0.920321\pi\)
\(192\) 0 0
\(193\) 7.47575 0.538116 0.269058 0.963124i \(-0.413288\pi\)
0.269058 + 0.963124i \(0.413288\pi\)
\(194\) 1.68632 + 1.52170i 0.121070 + 0.109252i
\(195\) 0 0
\(196\) 11.2765 8.29705i 0.805463 0.592646i
\(197\) 14.2749 1.01705 0.508523 0.861048i \(-0.330192\pi\)
0.508523 + 0.861048i \(0.330192\pi\)
\(198\) 0 0
\(199\) 1.60743 0.113948 0.0569739 0.998376i \(-0.481855\pi\)
0.0569739 + 0.998376i \(0.481855\pi\)
\(200\) 2.28279 + 1.67000i 0.161417 + 0.118087i
\(201\) 0 0
\(202\) −6.48505 5.85200i −0.456286 0.411745i
\(203\) 14.1879 + 8.11395i 0.995795 + 0.569487i
\(204\) 0 0
\(205\) −1.01125 −0.0706285
\(206\) 15.9307 17.6541i 1.10995 1.23002i
\(207\) 0 0
\(208\) −2.41325 11.6025i −0.167329 0.804491i
\(209\) 2.53490i 0.175343i
\(210\) 0 0
\(211\) 1.32588i 0.0912770i 0.998958 + 0.0456385i \(0.0145322\pi\)
−0.998958 + 0.0456385i \(0.985468\pi\)
\(212\) −1.90459 18.5099i −0.130808 1.27126i
\(213\) 0 0
\(214\) 9.61552 + 8.67689i 0.657303 + 0.593140i
\(215\) −6.85412 −0.467447
\(216\) 0 0
\(217\) 7.78094 + 4.44986i 0.528205 + 0.302076i
\(218\) −14.4463 + 16.0090i −0.978424 + 1.08427i
\(219\) 0 0
\(220\) −0.0976772 0.949282i −0.00658539 0.0640006i
\(221\) 11.3576 0.763997
\(222\) 0 0
\(223\) −21.5307 −1.44180 −0.720902 0.693037i \(-0.756272\pi\)
−0.720902 + 0.693037i \(0.756272\pi\)
\(224\) 12.9716 7.46570i 0.866704 0.498823i
\(225\) 0 0
\(226\) 3.83709 4.25216i 0.255239 0.282850i
\(227\) 14.0514 0.932625 0.466313 0.884620i \(-0.345582\pi\)
0.466313 + 0.884620i \(0.345582\pi\)
\(228\) 0 0
\(229\) 17.1949i 1.13627i −0.822934 0.568136i \(-0.807665\pi\)
0.822934 0.568136i \(-0.192335\pi\)
\(230\) 7.20820 7.98796i 0.475295 0.526710i
\(231\) 0 0
\(232\) 14.1020 + 10.3164i 0.925839 + 0.677308i
\(233\) 11.5500 0.756668 0.378334 0.925669i \(-0.376497\pi\)
0.378334 + 0.925669i \(0.376497\pi\)
\(234\) 0 0
\(235\) 6.21838i 0.405642i
\(236\) 1.00074 + 9.72572i 0.0651424 + 0.633091i
\(237\) 0 0
\(238\) 4.47351 + 13.6283i 0.289975 + 0.883392i
\(239\) 13.5047i 0.873549i −0.899571 0.436774i \(-0.856121\pi\)
0.899571 0.436774i \(-0.143879\pi\)
\(240\) 0 0
\(241\) 6.07807i 0.391523i 0.980652 + 0.195761i \(0.0627178\pi\)
−0.980652 + 0.195761i \(0.937282\pi\)
\(242\) 10.2061 11.3102i 0.656076 0.727048i
\(243\) 0 0
\(244\) −9.46637 + 0.974050i −0.606022 + 0.0623572i
\(245\) −6.03325 + 3.54963i −0.385450 + 0.226778i
\(246\) 0 0
\(247\) 15.7397i 1.00150i
\(248\) 7.73381 + 5.65776i 0.491098 + 0.359268i
\(249\) 0 0
\(250\) −1.04993 0.947441i −0.0664035 0.0599214i
\(251\) −25.9947 −1.64077 −0.820385 0.571812i \(-0.806241\pi\)
−0.820385 + 0.571812i \(0.806241\pi\)
\(252\) 0 0
\(253\) −3.63017 −0.228227
\(254\) −13.6437 12.3119i −0.856083 0.772516i
\(255\) 0 0
\(256\) 14.6730 6.37980i 0.917065 0.398738i
\(257\) 26.1382i 1.63045i −0.579141 0.815227i \(-0.696612\pi\)
0.579141 0.815227i \(-0.303388\pi\)
\(258\) 0 0
\(259\) 19.8174 + 11.3334i 1.23140 + 0.704226i
\(260\) 0.606499 + 5.89430i 0.0376135 + 0.365549i
\(261\) 0 0
\(262\) 1.68220 1.86417i 0.103927 0.115169i
\(263\) 20.1419i 1.24200i −0.783809 0.621001i \(-0.786726\pi\)
0.783809 0.621001i \(-0.213274\pi\)
\(264\) 0 0
\(265\) 9.30380i 0.571528i
\(266\) 18.8865 6.19953i 1.15801 0.380118i
\(267\) 0 0
\(268\) −2.59848 + 0.267372i −0.158727 + 0.0163324i
\(269\) 25.1731i 1.53483i −0.641151 0.767415i \(-0.721543\pi\)
0.641151 0.767415i \(-0.278457\pi\)
\(270\) 0 0
\(271\) −9.13276 −0.554776 −0.277388 0.960758i \(-0.589469\pi\)
−0.277388 + 0.960758i \(0.589469\pi\)
\(272\) 3.12257 + 15.0128i 0.189334 + 0.910285i
\(273\) 0 0
\(274\) 14.3652 15.9192i 0.867836 0.961715i
\(275\) 0.477147i 0.0287731i
\(276\) 0 0
\(277\) −17.2069 −1.03386 −0.516931 0.856027i \(-0.672926\pi\)
−0.516931 + 0.856027i \(0.672926\pi\)
\(278\) −17.8635 + 19.7959i −1.07138 + 1.18728i
\(279\) 0 0
\(280\) −6.83383 + 3.04938i −0.408400 + 0.182236i
\(281\) −10.6360 −0.634490 −0.317245 0.948344i \(-0.602758\pi\)
−0.317245 + 0.948344i \(0.602758\pi\)
\(282\) 0 0
\(283\) 19.3615 1.15092 0.575462 0.817828i \(-0.304822\pi\)
0.575462 + 0.817828i \(0.304822\pi\)
\(284\) −18.2775 + 1.88068i −1.08457 + 0.111598i
\(285\) 0 0
\(286\) 1.33935 1.48423i 0.0791974 0.0877646i
\(287\) 1.32823 2.32253i 0.0784032 0.137094i
\(288\) 0 0
\(289\) 2.30407 0.135534
\(290\) −6.48597 5.85284i −0.380869 0.343690i
\(291\) 0 0
\(292\) 8.94807 0.920719i 0.523646 0.0538810i
\(293\) 24.5856i 1.43631i 0.695885 + 0.718153i \(0.255012\pi\)
−0.695885 + 0.718153i \(0.744988\pi\)
\(294\) 0 0
\(295\) 4.88854i 0.284622i
\(296\) 19.6974 + 14.4099i 1.14489 + 0.837556i
\(297\) 0 0
\(298\) 17.8535 19.7848i 1.03423 1.14611i
\(299\) 22.5405 1.30355
\(300\) 0 0
\(301\) 9.00263 15.7418i 0.518903 0.907344i
\(302\) 19.5773 + 17.6662i 1.12654 + 1.01658i
\(303\) 0 0
\(304\) 20.8052 4.32735i 1.19326 0.248191i
\(305\) 4.75818 0.272452
\(306\) 0 0
\(307\) −3.23094 −0.184399 −0.0921997 0.995741i \(-0.529390\pi\)
−0.0921997 + 0.995741i \(0.529390\pi\)
\(308\) 2.30851 + 1.02251i 0.131539 + 0.0582630i
\(309\) 0 0
\(310\) −3.55705 3.20982i −0.202027 0.182306i
\(311\) −9.34597 −0.529962 −0.264981 0.964254i \(-0.585366\pi\)
−0.264981 + 0.964254i \(0.585366\pi\)
\(312\) 0 0
\(313\) 16.6495i 0.941085i 0.882377 + 0.470543i \(0.155942\pi\)
−0.882377 + 0.470543i \(0.844058\pi\)
\(314\) −23.8272 21.5013i −1.34465 1.21339i
\(315\) 0 0
\(316\) −17.5241 + 1.80316i −0.985810 + 0.101436i
\(317\) −25.7874 −1.44836 −0.724182 0.689609i \(-0.757782\pi\)
−0.724182 + 0.689609i \(0.757782\pi\)
\(318\) 0 0
\(319\) 2.94759i 0.165033i
\(320\) −7.62449 + 2.42221i −0.426222 + 0.135406i
\(321\) 0 0
\(322\) 8.87821 + 27.0469i 0.494763 + 1.50727i
\(323\) 20.3661i 1.13320i
\(324\) 0 0
\(325\) 2.96271i 0.164342i
\(326\) −9.63816 8.69732i −0.533808 0.481700i
\(327\) 0 0
\(328\) 1.68878 2.30846i 0.0932473 0.127463i
\(329\) −14.2817 8.16760i −0.787377 0.450295i
\(330\) 0 0
\(331\) 33.4834i 1.84041i 0.391432 + 0.920207i \(0.371980\pi\)
−0.391432 + 0.920207i \(0.628020\pi\)
\(332\) 2.24199 + 21.7889i 0.123045 + 1.19582i
\(333\) 0 0
\(334\) −14.0933 + 15.6178i −0.771151 + 0.854571i
\(335\) 1.30610 0.0713598
\(336\) 0 0
\(337\) −4.98366 −0.271477 −0.135739 0.990745i \(-0.543341\pi\)
−0.135739 + 0.990745i \(0.543341\pi\)
\(338\) 4.00042 4.43317i 0.217594 0.241133i
\(339\) 0 0
\(340\) −0.784764 7.62679i −0.0425598 0.413620i
\(341\) 1.61652i 0.0875395i
\(342\) 0 0
\(343\) −0.227975 18.5189i −0.0123095 0.999924i
\(344\) 11.4464 15.6465i 0.617147 0.843602i
\(345\) 0 0
\(346\) 19.1309 + 17.2634i 1.02848 + 0.928087i
\(347\) 2.96693i 0.159273i −0.996824 0.0796367i \(-0.974624\pi\)
0.996824 0.0796367i \(-0.0253760\pi\)
\(348\) 0 0
\(349\) 15.7698i 0.844139i −0.906563 0.422070i \(-0.861304\pi\)
0.906563 0.422070i \(-0.138696\pi\)
\(350\) 3.55503 1.16694i 0.190024 0.0623758i
\(351\) 0 0
\(352\) 2.33013 + 1.36232i 0.124196 + 0.0726121i
\(353\) 9.20491i 0.489928i 0.969532 + 0.244964i \(0.0787761\pi\)
−0.969532 + 0.244964i \(0.921224\pi\)
\(354\) 0 0
\(355\) 9.18700 0.487595
\(356\) −26.1038 + 2.68597i −1.38350 + 0.142356i
\(357\) 0 0
\(358\) −5.27885 4.76355i −0.278996 0.251761i
\(359\) 20.9031i 1.10322i 0.834102 + 0.551611i \(0.185987\pi\)
−0.834102 + 0.551611i \(0.814013\pi\)
\(360\) 0 0
\(361\) 9.22390 0.485468
\(362\) −15.3819 13.8803i −0.808452 0.729534i
\(363\) 0 0
\(364\) −14.3340 6.34900i −0.751308 0.332778i
\(365\) −4.49766 −0.235418
\(366\) 0 0
\(367\) 4.79845 0.250477 0.125239 0.992127i \(-0.460030\pi\)
0.125239 + 0.992127i \(0.460030\pi\)
\(368\) 6.19710 + 29.7947i 0.323046 + 1.55315i
\(369\) 0 0
\(370\) −9.05951 8.17516i −0.470982 0.425006i
\(371\) −21.3680 12.2202i −1.10937 0.634441i
\(372\) 0 0
\(373\) 28.9408 1.49850 0.749250 0.662287i \(-0.230414\pi\)
0.749250 + 0.662287i \(0.230414\pi\)
\(374\) −1.73302 + 1.92049i −0.0896122 + 0.0993061i
\(375\) 0 0
\(376\) −14.1952 10.3847i −0.732062 0.535549i
\(377\) 18.3022i 0.942612i
\(378\) 0 0
\(379\) 4.73908i 0.243430i 0.992565 + 0.121715i \(0.0388394\pi\)
−0.992565 + 0.121715i \(0.961161\pi\)
\(380\) −10.5694 + 1.08755i −0.542200 + 0.0557901i
\(381\) 0 0
\(382\) 7.18880 + 6.48706i 0.367811 + 0.331907i
\(383\) 11.9795 0.612125 0.306063 0.952011i \(-0.400988\pi\)
0.306063 + 0.952011i \(0.400988\pi\)
\(384\) 0 0
\(385\) −1.09586 0.626715i −0.0558503 0.0319404i
\(386\) 7.08283 7.84902i 0.360507 0.399505i
\(387\) 0 0
\(388\) 3.19537 0.328790i 0.162220 0.0166918i
\(389\) −24.1871 −1.22633 −0.613167 0.789953i \(-0.710105\pi\)
−0.613167 + 0.789953i \(0.710105\pi\)
\(390\) 0 0
\(391\) −29.1658 −1.47498
\(392\) 1.97247 19.7005i 0.0996249 0.995025i
\(393\) 0 0
\(394\) 13.5246 14.9877i 0.681362 0.755069i
\(395\) 8.80833 0.443195
\(396\) 0 0
\(397\) 37.1405i 1.86403i 0.362420 + 0.932015i \(0.381951\pi\)
−0.362420 + 0.932015i \(0.618049\pi\)
\(398\) 1.52295 1.68769i 0.0763384 0.0845964i
\(399\) 0 0
\(400\) 3.91619 0.814543i 0.195809 0.0407271i
\(401\) −20.4040 −1.01893 −0.509464 0.860492i \(-0.670156\pi\)
−0.509464 + 0.860492i \(0.670156\pi\)
\(402\) 0 0
\(403\) 10.0373i 0.499995i
\(404\) −12.2884 + 1.26442i −0.611371 + 0.0629075i
\(405\) 0 0
\(406\) 21.9613 7.20883i 1.08992 0.357768i
\(407\) 4.11715i 0.204079i
\(408\) 0 0
\(409\) 4.69204i 0.232007i −0.993249 0.116003i \(-0.962992\pi\)
0.993249 0.116003i \(-0.0370083\pi\)
\(410\) −0.958097 + 1.06174i −0.0473170 + 0.0524356i
\(411\) 0 0
\(412\) −3.44211 33.4523i −0.169580 1.64808i
\(413\) 11.2275 + 6.42091i 0.552468 + 0.315952i
\(414\) 0 0
\(415\) 10.9520i 0.537612i
\(416\) −14.4683 8.45896i −0.709365 0.414735i
\(417\) 0 0
\(418\) 2.66147 + 2.40167i 0.130177 + 0.117469i
\(419\) 10.4551 0.510766 0.255383 0.966840i \(-0.417798\pi\)
0.255383 + 0.966840i \(0.417798\pi\)
\(420\) 0 0
\(421\) −29.0598 −1.41629 −0.708144 0.706068i \(-0.750467\pi\)
−0.708144 + 0.706068i \(0.750467\pi\)
\(422\) 1.39208 + 1.25619i 0.0677653 + 0.0611503i
\(423\) 0 0
\(424\) −21.2386 15.5373i −1.03144 0.754559i
\(425\) 3.83353i 0.185953i
\(426\) 0 0
\(427\) −6.24969 + 10.9281i −0.302444 + 0.528847i
\(428\) 18.2203 1.87479i 0.880710 0.0906214i
\(429\) 0 0
\(430\) −6.49388 + 7.19635i −0.313162 + 0.347039i
\(431\) 11.8497i 0.570779i −0.958412 0.285389i \(-0.907877\pi\)
0.958412 0.285389i \(-0.0921229\pi\)
\(432\) 0 0
\(433\) 37.2566i 1.79044i 0.445625 + 0.895220i \(0.352981\pi\)
−0.445625 + 0.895220i \(0.647019\pi\)
\(434\) 12.0440 3.95347i 0.578132 0.189773i
\(435\) 0 0
\(436\) 3.12136 + 30.3352i 0.149486 + 1.45279i
\(437\) 40.4188i 1.93349i
\(438\) 0 0
\(439\) 2.20068 0.105033 0.0525163 0.998620i \(-0.483276\pi\)
0.0525163 + 0.998620i \(0.483276\pi\)
\(440\) −1.08922 0.796835i −0.0519267 0.0379876i
\(441\) 0 0
\(442\) 10.7607 11.9247i 0.511834 0.567202i
\(443\) 5.86101i 0.278465i −0.990260 0.139233i \(-0.955536\pi\)
0.990260 0.139233i \(-0.0444636\pi\)
\(444\) 0 0
\(445\) 13.1208 0.621987
\(446\) −20.3991 + 22.6058i −0.965925 + 1.07041i
\(447\) 0 0
\(448\) 4.45139 20.6926i 0.210309 0.977635i
\(449\) 11.2784 0.532259 0.266129 0.963937i \(-0.414255\pi\)
0.266129 + 0.963937i \(0.414255\pi\)
\(450\) 0 0
\(451\) 0.482513 0.0227207
\(452\) −0.829068 8.05735i −0.0389961 0.378986i
\(453\) 0 0
\(454\) 13.3129 14.7530i 0.624805 0.692394i
\(455\) 6.80445 + 3.89141i 0.318997 + 0.182432i
\(456\) 0 0
\(457\) 10.5671 0.494307 0.247153 0.968976i \(-0.420505\pi\)
0.247153 + 0.968976i \(0.420505\pi\)
\(458\) −18.0535 16.2912i −0.843584 0.761237i
\(459\) 0 0
\(460\) −1.55746 15.1362i −0.0726167 0.705731i
\(461\) 0.502682i 0.0234122i −0.999931 0.0117061i \(-0.996274\pi\)
0.999931 0.0117061i \(-0.00372626\pi\)
\(462\) 0 0
\(463\) 16.5694i 0.770044i −0.922907 0.385022i \(-0.874194\pi\)
0.922907 0.385022i \(-0.125806\pi\)
\(464\) 24.1923 5.03185i 1.12310 0.233598i
\(465\) 0 0
\(466\) 10.9430 12.1267i 0.506924 0.561761i
\(467\) 17.1182 0.792137 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(468\) 0 0
\(469\) −1.71551 + 2.99971i −0.0792149 + 0.138514i
\(470\) 6.52887 + 5.89154i 0.301154 + 0.271757i
\(471\) 0 0
\(472\) 11.1595 + 8.16384i 0.513657 + 0.375771i
\(473\) 3.27042 0.150374
\(474\) 0 0
\(475\) 5.31262 0.243760
\(476\) 18.5472 + 8.21513i 0.850108 + 0.376540i
\(477\) 0 0
\(478\) −14.1790 12.7949i −0.648534 0.585227i
\(479\) −7.51289 −0.343272 −0.171636 0.985160i \(-0.554905\pi\)
−0.171636 + 0.985160i \(0.554905\pi\)
\(480\) 0 0
\(481\) 25.5643i 1.16563i
\(482\) 6.38155 + 5.75861i 0.290672 + 0.262298i
\(483\) 0 0
\(484\) −2.20521 21.4315i −0.100237 0.974159i
\(485\) −1.60612 −0.0729302
\(486\) 0 0
\(487\) 18.3725i 0.832537i 0.909242 + 0.416269i \(0.136662\pi\)
−0.909242 + 0.416269i \(0.863338\pi\)
\(488\) −7.94614 + 10.8619i −0.359705 + 0.491695i
\(489\) 0 0
\(490\) −1.98928 + 9.69756i −0.0898666 + 0.438091i
\(491\) 12.3732i 0.558395i 0.960234 + 0.279197i \(0.0900684\pi\)
−0.960234 + 0.279197i \(0.909932\pi\)
\(492\) 0 0
\(493\) 23.6817i 1.06657i
\(494\) −16.5257 14.9125i −0.743524 0.670944i
\(495\) 0 0
\(496\) 13.2676 2.75958i 0.595732 0.123909i
\(497\) −12.0668 + 21.0997i −0.541269 + 0.946453i
\(498\) 0 0
\(499\) 3.90928i 0.175003i −0.996164 0.0875017i \(-0.972112\pi\)
0.996164 0.0875017i \(-0.0278883\pi\)
\(500\) −1.98950 + 0.204711i −0.0889730 + 0.00915495i
\(501\) 0 0
\(502\) −24.6284 + 27.2926i −1.09922 + 1.21813i
\(503\) 20.7397 0.924738 0.462369 0.886688i \(-0.347000\pi\)
0.462369 + 0.886688i \(0.347000\pi\)
\(504\) 0 0
\(505\) 6.17664 0.274857
\(506\) −3.43937 + 3.81143i −0.152899 + 0.169439i
\(507\) 0 0
\(508\) −25.8532 + 2.66019i −1.14705 + 0.118027i
\(509\) 19.9445i 0.884025i −0.897009 0.442012i \(-0.854265\pi\)
0.897009 0.442012i \(-0.145735\pi\)
\(510\) 0 0
\(511\) 5.90751 10.3298i 0.261333 0.456962i
\(512\) 7.20349 21.4502i 0.318352 0.947972i
\(513\) 0 0
\(514\) −27.4433 24.7644i −1.21047 1.09231i
\(515\) 16.8145i 0.740935i
\(516\) 0 0
\(517\) 2.96708i 0.130492i
\(518\) 30.6752 10.0692i 1.34779 0.442414i
\(519\) 0 0
\(520\) 6.76323 + 4.94772i 0.296587 + 0.216972i
\(521\) 37.8103i 1.65650i −0.560361 0.828249i \(-0.689338\pi\)
0.560361 0.828249i \(-0.310662\pi\)
\(522\) 0 0
\(523\) 16.5206 0.722398 0.361199 0.932489i \(-0.382368\pi\)
0.361199 + 0.932489i \(0.382368\pi\)
\(524\) −0.363468 3.53239i −0.0158782 0.154313i
\(525\) 0 0
\(526\) −21.1476 19.0833i −0.922080 0.832070i
\(527\) 12.9875i 0.565746i
\(528\) 0 0
\(529\) −34.8828 −1.51664
\(530\) 9.76835 + 8.81480i 0.424310 + 0.382890i
\(531\) 0 0
\(532\) 11.3848 25.7032i 0.493593 1.11438i
\(533\) −2.99603 −0.129773
\(534\) 0 0
\(535\) −9.15824 −0.395945
\(536\) −2.18118 + 2.98154i −0.0942127 + 0.128783i
\(537\) 0 0
\(538\) −26.4300 23.8500i −1.13948 1.02825i
\(539\) 2.87875 1.69370i 0.123996 0.0729527i
\(540\) 0 0
\(541\) −32.6251 −1.40266 −0.701331 0.712836i \(-0.747411\pi\)
−0.701331 + 0.712836i \(0.747411\pi\)
\(542\) −8.65275 + 9.58877i −0.371668 + 0.411873i
\(543\) 0 0
\(544\) 18.7209 + 10.9453i 0.802650 + 0.469274i
\(545\) 15.2477i 0.653138i
\(546\) 0 0
\(547\) 35.9526i 1.53722i 0.639716 + 0.768612i \(0.279052\pi\)
−0.639716 + 0.768612i \(0.720948\pi\)
\(548\) −3.10386 30.1650i −0.132590 1.28859i
\(549\) 0 0
\(550\) 0.500972 + 0.452069i 0.0213615 + 0.0192763i
\(551\) 32.8188 1.39813
\(552\) 0 0
\(553\) −11.5694 + 20.2301i −0.491982 + 0.860270i
\(554\) −16.3025 + 18.0661i −0.692628 + 0.767553i
\(555\) 0 0
\(556\) 3.85971 + 37.5108i 0.163688 + 1.59081i
\(557\) 8.84229 0.374660 0.187330 0.982297i \(-0.440017\pi\)
0.187330 + 0.982297i \(0.440017\pi\)
\(558\) 0 0
\(559\) −20.3068 −0.858885
\(560\) −3.27301 + 10.0642i −0.138310 + 0.425289i
\(561\) 0 0
\(562\) −10.0770 + 11.1671i −0.425072 + 0.471054i
\(563\) 17.7594 0.748471 0.374235 0.927334i \(-0.377905\pi\)
0.374235 + 0.927334i \(0.377905\pi\)
\(564\) 0 0
\(565\) 4.04995i 0.170383i
\(566\) 18.3439 20.3283i 0.771052 0.854462i
\(567\) 0 0
\(568\) −15.3423 + 20.9719i −0.643747 + 0.879963i
\(569\) −36.7269 −1.53967 −0.769835 0.638243i \(-0.779661\pi\)
−0.769835 + 0.638243i \(0.779661\pi\)
\(570\) 0 0
\(571\) 17.1069i 0.715902i 0.933740 + 0.357951i \(0.116524\pi\)
−0.933740 + 0.357951i \(0.883476\pi\)
\(572\) −0.289389 2.81245i −0.0121000 0.117594i
\(573\) 0 0
\(574\) −1.18007 3.59501i −0.0492551 0.150053i
\(575\) 7.60808i 0.317279i
\(576\) 0 0
\(577\) 37.9794i 1.58110i −0.612395 0.790552i \(-0.709794\pi\)
0.612395 0.790552i \(-0.290206\pi\)
\(578\) 2.18297 2.41912i 0.0907998 0.100622i
\(579\) 0 0
\(580\) −12.2902 + 1.26461i −0.510321 + 0.0525099i
\(581\) 25.1534 + 14.3850i 1.04354 + 0.596792i
\(582\) 0 0
\(583\) 4.43928i 0.183856i
\(584\) 7.51108 10.2672i 0.310811 0.424859i
\(585\) 0 0
\(586\) 25.8132 + 23.2934i 1.06633 + 0.962242i
\(587\) −40.1743 −1.65817 −0.829085 0.559122i \(-0.811138\pi\)
−0.829085 + 0.559122i \(0.811138\pi\)
\(588\) 0 0
\(589\) 17.9985 0.741617
\(590\) −5.13263 4.63160i −0.211307 0.190680i
\(591\) 0 0
\(592\) 33.7915 7.02842i 1.38882 0.288866i
\(593\) 2.80855i 0.115333i −0.998336 0.0576667i \(-0.981634\pi\)
0.998336 0.0576667i \(-0.0183661\pi\)
\(594\) 0 0
\(595\) −8.80445 5.03519i −0.360947 0.206423i
\(596\) −3.85756 37.4899i −0.158012 1.53565i
\(597\) 0 0
\(598\) 21.3558 23.6660i 0.873305 0.967775i
\(599\) 10.0933i 0.412399i 0.978510 + 0.206200i \(0.0661097\pi\)
−0.978510 + 0.206200i \(0.933890\pi\)
\(600\) 0 0
\(601\) 8.17083i 0.333295i 0.986017 + 0.166648i \(0.0532942\pi\)
−0.986017 + 0.166648i \(0.946706\pi\)
\(602\) −7.99838 24.3666i −0.325990 0.993109i
\(603\) 0 0
\(604\) 37.0966 3.81708i 1.50944 0.155315i
\(605\) 10.7723i 0.437958i
\(606\) 0 0
\(607\) −20.7112 −0.840642 −0.420321 0.907375i \(-0.638083\pi\)
−0.420321 + 0.907375i \(0.638083\pi\)
\(608\) 15.1683 25.9439i 0.615155 1.05217i
\(609\) 0 0
\(610\) 4.50809 4.99576i 0.182527 0.202272i
\(611\) 18.4232i 0.745325i
\(612\) 0 0
\(613\) 4.61369 0.186345 0.0931726 0.995650i \(-0.470299\pi\)
0.0931726 + 0.995650i \(0.470299\pi\)
\(614\) −3.06112 + 3.39226i −0.123537 + 0.136901i
\(615\) 0 0
\(616\) 3.26074 1.45501i 0.131379 0.0586238i
\(617\) −13.3799 −0.538655 −0.269328 0.963049i \(-0.586801\pi\)
−0.269328 + 0.963049i \(0.586801\pi\)
\(618\) 0 0
\(619\) 36.4215 1.46390 0.731951 0.681357i \(-0.238610\pi\)
0.731951 + 0.681357i \(0.238610\pi\)
\(620\) −6.74018 + 0.693537i −0.270692 + 0.0278531i
\(621\) 0 0
\(622\) −8.85476 + 9.81263i −0.355044 + 0.393451i
\(623\) −17.2337 + 30.1345i −0.690454 + 1.20732i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 17.4808 + 15.7744i 0.698674 + 0.630473i
\(627\) 0 0
\(628\) −45.1498 + 4.64572i −1.80167 + 0.185385i
\(629\) 33.0782i 1.31892i
\(630\) 0 0
\(631\) 23.3976i 0.931442i 0.884932 + 0.465721i \(0.154205\pi\)
−0.884932 + 0.465721i \(0.845795\pi\)
\(632\) −14.7099 + 20.1075i −0.585128 + 0.799835i
\(633\) 0 0
\(634\) −24.4320 + 27.0750i −0.970320 + 1.07528i
\(635\) 12.9949 0.515686
\(636\) 0 0
\(637\) −17.8748 + 10.5165i −0.708224 + 0.416680i
\(638\) 3.09476 + 2.79267i 0.122523 + 0.110563i
\(639\) 0 0
\(640\) −4.68060 + 10.3001i −0.185017 + 0.407147i
\(641\) −14.4482 −0.570668 −0.285334 0.958428i \(-0.592104\pi\)
−0.285334 + 0.958428i \(0.592104\pi\)
\(642\) 0 0
\(643\) −14.1004 −0.556065 −0.278033 0.960572i \(-0.589682\pi\)
−0.278033 + 0.960572i \(0.589682\pi\)
\(644\) 36.8090 + 16.3039i 1.45048 + 0.642463i
\(645\) 0 0
\(646\) 21.3830 + 19.2956i 0.841301 + 0.759177i
\(647\) 13.1557 0.517205 0.258602 0.965984i \(-0.416738\pi\)
0.258602 + 0.965984i \(0.416738\pi\)
\(648\) 0 0
\(649\) 2.33255i 0.0915606i
\(650\) −3.11064 2.80699i −0.122009 0.110099i
\(651\) 0 0
\(652\) −18.2632 + 1.87920i −0.715241 + 0.0735953i
\(653\) −34.5944 −1.35378 −0.676892 0.736083i \(-0.736673\pi\)
−0.676892 + 0.736083i \(0.736673\pi\)
\(654\) 0 0
\(655\) 1.77552i 0.0693753i
\(656\) −0.823703 3.96023i −0.0321602 0.154621i
\(657\) 0 0
\(658\) −22.1065 + 7.25650i −0.861802 + 0.282888i
\(659\) 8.35962i 0.325644i −0.986655 0.162822i \(-0.947940\pi\)
0.986655 0.162822i \(-0.0520597\pi\)
\(660\) 0 0
\(661\) 45.6469i 1.77546i 0.460366 + 0.887729i \(0.347718\pi\)
−0.460366 + 0.887729i \(0.652282\pi\)
\(662\) 35.1553 + 31.7235i 1.36635 + 1.23297i
\(663\) 0 0
\(664\) 25.0010 + 18.2898i 0.970228 + 0.709782i
\(665\) −6.97792 + 12.2015i −0.270592 + 0.473153i
\(666\) 0 0
\(667\) 46.9991i 1.81981i
\(668\) 3.04510 + 29.5940i 0.117818 + 1.14503i
\(669\) 0 0
\(670\) 1.23745 1.37131i 0.0478069 0.0529784i
\(671\) −2.27035 −0.0876459
\(672\) 0 0
\(673\) −39.4155 −1.51936 −0.759678 0.650299i \(-0.774644\pi\)
−0.759678 + 0.650299i \(0.774644\pi\)
\(674\) −4.72173 + 5.23250i −0.181874 + 0.201548i
\(675\) 0 0
\(676\) −0.864360 8.40034i −0.0332446 0.323090i
\(677\) 19.6704i 0.755995i −0.925807 0.377997i \(-0.876613\pi\)
0.925807 0.377997i \(-0.123387\pi\)
\(678\) 0 0
\(679\) 2.10958 3.68877i 0.0809582 0.141562i
\(680\) −8.75112 6.40198i −0.335590 0.245505i
\(681\) 0 0
\(682\) 1.69723 + 1.53156i 0.0649905 + 0.0586464i
\(683\) 5.27739i 0.201934i 0.994890 + 0.100967i \(0.0321936\pi\)
−0.994890 + 0.100967i \(0.967806\pi\)
\(684\) 0 0
\(685\) 15.1622i 0.579316i
\(686\) −19.6595 17.3062i −0.750604 0.660753i
\(687\) 0 0
\(688\) −5.58297 26.8420i −0.212849 1.02334i
\(689\) 27.5645i 1.05012i
\(690\) 0 0
\(691\) −8.48775 −0.322889 −0.161445 0.986882i \(-0.551615\pi\)
−0.161445 + 0.986882i \(0.551615\pi\)
\(692\) 36.2508 3.73005i 1.37805 0.141795i
\(693\) 0 0
\(694\) −3.11508 2.81100i −0.118247 0.106704i
\(695\) 18.8544i 0.715190i
\(696\) 0 0
\(697\) 3.87664 0.146838
\(698\) −16.5572 14.9410i −0.626700 0.565524i
\(699\) 0 0
\(700\) 2.14297 4.83815i 0.0809967 0.182865i
\(701\) 10.1888 0.384825 0.192412 0.981314i \(-0.438369\pi\)
0.192412 + 0.981314i \(0.438369\pi\)
\(702\) 0 0
\(703\) 45.8408 1.72892
\(704\) 3.63800 1.15575i 0.137112 0.0435591i
\(705\) 0 0
\(706\) 9.66452 + 8.72111i 0.363729 + 0.328223i
\(707\) −8.11279 + 14.1859i −0.305113 + 0.533514i
\(708\) 0 0
\(709\) 3.99960 0.150208 0.0751041 0.997176i \(-0.476071\pi\)
0.0751041 + 0.997176i \(0.476071\pi\)
\(710\) 8.70414 9.64571i 0.326660 0.361997i
\(711\) 0 0
\(712\) −21.9117 + 29.9520i −0.821177 + 1.12250i
\(713\) 25.7753i 0.965292i
\(714\) 0 0
\(715\) 1.41365i 0.0528675i
\(716\) −10.0028 + 1.02925i −0.373822 + 0.0384647i
\(717\) 0 0
\(718\) 21.9468 + 19.8044i 0.819046 + 0.739094i
\(719\) 8.22659 0.306800 0.153400 0.988164i \(-0.450978\pi\)
0.153400 + 0.988164i \(0.450978\pi\)
\(720\) 0 0
\(721\) −38.6178 22.0852i −1.43820 0.822496i
\(722\) 8.73910 9.68446i 0.325236 0.360418i
\(723\) 0 0
\(724\) −29.1468 + 2.99908i −1.08323 + 0.111460i
\(725\) 6.17752 0.229427
\(726\) 0 0
\(727\) 2.05684 0.0762839 0.0381419 0.999272i \(-0.487856\pi\)
0.0381419 + 0.999272i \(0.487856\pi\)
\(728\) −20.2467 + 9.03444i −0.750391 + 0.334839i
\(729\) 0 0
\(730\) −4.26127 + 4.72223i −0.157717 + 0.174778i
\(731\) 26.2755 0.971833
\(732\) 0 0
\(733\) 24.8578i 0.918145i −0.888399 0.459072i \(-0.848182\pi\)
0.888399 0.459072i \(-0.151818\pi\)
\(734\) 4.54625 5.03804i 0.167805 0.185958i
\(735\) 0 0
\(736\) 37.1537 + 21.7221i 1.36950 + 0.800689i
\(737\) −0.623201 −0.0229559
\(738\) 0 0
\(739\) 1.48614i 0.0546686i 0.999626 + 0.0273343i \(0.00870186\pi\)
−0.999626 + 0.0273343i \(0.991298\pi\)
\(740\) −17.1667 + 1.76638i −0.631061 + 0.0649335i
\(741\) 0 0
\(742\) −33.0753 + 10.8570i −1.21423 + 0.398574i
\(743\) 4.73363i 0.173660i 0.996223 + 0.0868299i \(0.0276737\pi\)
−0.996223 + 0.0868299i \(0.972326\pi\)
\(744\) 0 0
\(745\) 18.8439i 0.690389i
\(746\) 27.4197 30.3859i 1.00391 1.11251i
\(747\) 0 0
\(748\) 0.374448 + 3.63910i 0.0136912 + 0.133059i
\(749\) 12.0290 21.0337i 0.439530 0.768555i
\(750\) 0 0
\(751\) 49.1841i 1.79475i −0.441266 0.897376i \(-0.645470\pi\)
0.441266 0.897376i \(-0.354530\pi\)
\(752\) −24.3523 + 5.06513i −0.888038 + 0.184706i
\(753\) 0 0
\(754\) −19.2161 17.3403i −0.699808 0.631495i
\(755\) −18.6462 −0.678606
\(756\) 0 0
\(757\) −6.41551 −0.233176 −0.116588 0.993180i \(-0.537196\pi\)
−0.116588 + 0.993180i \(0.537196\pi\)
\(758\) 4.97571 + 4.49000i 0.180726 + 0.163084i
\(759\) 0 0
\(760\) −8.87206 + 12.1276i −0.321823 + 0.439913i
\(761\) 1.23026i 0.0445970i −0.999751 0.0222985i \(-0.992902\pi\)
0.999751 0.0222985i \(-0.00709843\pi\)
\(762\) 0 0
\(763\) 35.0192 + 20.0272i 1.26778 + 0.725035i
\(764\) 13.6219 1.40164i 0.492824 0.0507095i
\(765\) 0 0
\(766\) 11.3499 12.5777i 0.410088 0.454450i
\(767\) 14.4833i 0.522962i
\(768\) 0 0
\(769\) 28.9327i 1.04334i −0.853147 0.521670i \(-0.825309\pi\)
0.853147 0.521670i \(-0.174691\pi\)
\(770\) −1.69627 + 0.556804i −0.0611294 + 0.0200658i
\(771\) 0 0
\(772\) −1.53037 14.8730i −0.0550791 0.535290i
\(773\) 12.9773i 0.466761i 0.972385 + 0.233380i \(0.0749788\pi\)
−0.972385 + 0.233380i \(0.925021\pi\)
\(774\) 0 0
\(775\) 3.38789 0.121696
\(776\) 2.68222 3.66643i 0.0962860 0.131617i
\(777\) 0 0
\(778\) −22.9158 + 25.3948i −0.821573 + 0.910447i
\(779\) 5.37237i 0.192485i
\(780\) 0 0
\(781\) −4.38355 −0.156856
\(782\) −27.6328 + 30.6220i −0.988148 + 1.09504i
\(783\) 0 0
\(784\) −18.8154 20.7360i −0.671977 0.740572i
\(785\) 22.6941 0.809986
\(786\) 0 0
\(787\) −16.7024 −0.595377 −0.297688 0.954663i \(-0.596216\pi\)
−0.297688 + 0.954663i \(0.596216\pi\)
\(788\) −2.92223 28.3999i −0.104100 1.01170i
\(789\) 0 0
\(790\) 8.34538 9.24814i 0.296915 0.329034i
\(791\) −9.30150 5.31945i −0.330723 0.189138i
\(792\) 0 0
\(793\) 14.0971 0.500603
\(794\) 38.9950 + 35.1885i 1.38388 + 1.24879i
\(795\) 0 0
\(796\) −0.329059 3.19798i −0.0116632 0.113349i
\(797\) 7.59395i 0.268992i 0.990914 + 0.134496i \(0.0429415\pi\)
−0.990914 + 0.134496i \(0.957059\pi\)
\(798\) 0 0
\(799\) 23.8383i 0.843339i
\(800\) 2.85514 4.88346i 0.100945 0.172656i
\(801\) 0 0
\(802\) −19.3316 + 21.4228i −0.682622 + 0.756465i
\(803\) 2.14604 0.0757323
\(804\) 0 0
\(805\) −17.4734 9.99293i −0.615858 0.352204i
\(806\) −10.5385 9.50977i −0.371203 0.334967i
\(807\) 0 0
\(808\) −10.3150 + 14.0999i −0.362880 + 0.496034i
\(809\) −26.4140 −0.928665 −0.464333 0.885661i \(-0.653706\pi\)
−0.464333 + 0.885661i \(0.653706\pi\)
\(810\) 0 0
\(811\) −2.20334 −0.0773697 −0.0386848 0.999251i \(-0.512317\pi\)
−0.0386848 + 0.999251i \(0.512317\pi\)
\(812\) 13.2382 29.8878i 0.464571 1.04886i
\(813\) 0 0
\(814\) 4.32272 + 3.90075i 0.151511 + 0.136721i
\(815\) 9.17980 0.321554
\(816\) 0 0
\(817\) 36.4133i 1.27394i
\(818\) −4.92632 4.44544i −0.172245 0.155431i
\(819\) 0 0
\(820\) 0.207013 + 2.01187i 0.00722921 + 0.0702576i
\(821\) −8.94895 −0.312321 −0.156160 0.987732i \(-0.549912\pi\)
−0.156160 + 0.987732i \(0.549912\pi\)
\(822\) 0 0
\(823\) 40.8135i 1.42267i −0.702853 0.711335i \(-0.748091\pi\)
0.702853 0.711335i \(-0.251909\pi\)
\(824\) −38.3839 28.0802i −1.33716 0.978218i
\(825\) 0 0
\(826\) 17.3789 5.70465i 0.604689 0.198490i
\(827\) 4.55874i 0.158523i −0.996854 0.0792615i \(-0.974744\pi\)
0.996854 0.0792615i \(-0.0252562\pi\)
\(828\) 0 0
\(829\) 0.872606i 0.0303069i 0.999885 + 0.0151534i \(0.00482367\pi\)
−0.999885 + 0.0151534i \(0.995176\pi\)
\(830\) −11.4988 10.3764i −0.399130 0.360169i
\(831\) 0 0
\(832\) −22.5892 + 7.17632i −0.783138 + 0.248794i
\(833\) 23.1286 13.6076i 0.801359 0.471476i
\(834\) 0 0
\(835\) 14.8751i 0.514775i
\(836\) 5.04317 0.518921i 0.174422 0.0179473i
\(837\) 0 0
\(838\) 9.90561 10.9772i 0.342184 0.379200i
\(839\) −48.9005 −1.68823 −0.844117 0.536160i \(-0.819874\pi\)
−0.844117 + 0.536160i \(0.819874\pi\)
\(840\) 0 0
\(841\) 9.16178 0.315923
\(842\) −27.5324 + 30.5108i −0.948831 + 1.05147i
\(843\) 0 0
\(844\) 2.63782 0.271421i 0.0907976 0.00934270i
\(845\) 4.22235i 0.145253i
\(846\) 0 0
\(847\) −24.7408 14.1491i −0.850103 0.486167i
\(848\) −36.4354 + 7.57834i −1.25120 + 0.260241i
\(849\) 0 0
\(850\) 4.02494 + 3.63204i 0.138054 + 0.124578i
\(851\) 65.6476i 2.25037i
\(852\) 0 0
\(853\) 46.6995i 1.59896i −0.600692 0.799480i \(-0.705108\pi\)
0.600692 0.799480i \(-0.294892\pi\)
\(854\) 5.55253 + 16.9155i 0.190004 + 0.578835i
\(855\) 0 0
\(856\) 15.2942 20.9063i 0.522746 0.714562i
\(857\) 42.6029i 1.45529i 0.685955 + 0.727644i \(0.259385\pi\)
−0.685955 + 0.727644i \(0.740615\pi\)
\(858\) 0 0
\(859\) 33.0255 1.12682 0.563408 0.826179i \(-0.309490\pi\)
0.563408 + 0.826179i \(0.309490\pi\)
\(860\) 1.40311 + 13.6362i 0.0478457 + 0.464992i
\(861\) 0 0
\(862\) −12.4413 11.2269i −0.423754 0.382389i
\(863\) 50.3282i 1.71319i −0.515989 0.856595i \(-0.672575\pi\)
0.515989 0.856595i \(-0.327425\pi\)
\(864\) 0 0
\(865\) −18.2211 −0.619536
\(866\) 39.1169 + 35.2985i 1.32925 + 1.19949i
\(867\) 0 0
\(868\) 7.26014 16.3911i 0.246425 0.556350i
\(869\) −4.20287 −0.142573
\(870\) 0 0
\(871\) 3.86959 0.131116
\(872\) 34.8071 + 25.4636i 1.17872 + 0.862305i
\(873\) 0 0
\(874\) 42.4370 + 38.2944i 1.43545 + 1.29533i
\(875\) −1.31346 + 2.29670i −0.0444031 + 0.0776425i
\(876\) 0 0
\(877\) 18.9157 0.638738 0.319369 0.947630i \(-0.396529\pi\)
0.319369 + 0.947630i \(0.396529\pi\)
\(878\) 2.08501 2.31056i 0.0703658 0.0779776i
\(879\) 0 0
\(880\) −1.86860 + 0.388657i −0.0629904 + 0.0131016i
\(881\) 18.9884i 0.639736i 0.947462 + 0.319868i \(0.103639\pi\)
−0.947462 + 0.319868i \(0.896361\pi\)
\(882\) 0 0
\(883\) 35.4843i 1.19414i 0.802188 + 0.597072i \(0.203669\pi\)
−0.802188 + 0.597072i \(0.796331\pi\)
\(884\) −2.32503 22.5960i −0.0781992 0.759984i
\(885\) 0 0
\(886\) −6.15366 5.55296i −0.206736 0.186555i
\(887\) −53.4487 −1.79463 −0.897315 0.441390i \(-0.854485\pi\)
−0.897315 + 0.441390i \(0.854485\pi\)
\(888\) 0 0
\(889\) −17.0683 + 29.8453i −0.572452 + 1.00098i
\(890\) 12.4312 13.7760i 0.416695 0.461771i
\(891\) 0 0
\(892\) 4.40757 + 42.8353i 0.147576 + 1.43423i
\(893\) −33.0358 −1.10550
\(894\) 0 0
\(895\) 5.02780 0.168061
\(896\) −17.5084 24.2787i −0.584915 0.811095i
\(897\) 0 0
\(898\) 10.6856 11.8415i 0.356583 0.395156i
\(899\) 20.9287 0.698012
\(900\) 0 0
\(901\) 35.6664i 1.18822i
\(902\) 0.457153 0.506606i 0.0152215 0.0168681i
\(903\) 0 0
\(904\) −9.24516 6.76340i −0.307489 0.224947i
\(905\) 14.6503 0.486994
\(906\) 0 0
\(907\) 48.4656i 1.60927i −0.593768 0.804636i \(-0.702360\pi\)
0.593768 0.804636i \(-0.297640\pi\)
\(908\) −2.87648 27.9552i −0.0954592 0.927727i
\(909\) 0 0
\(910\) 10.5325 3.45732i 0.349150 0.114609i
\(911\) 1.00067i 0.0331538i 0.999863 + 0.0165769i \(0.00527684\pi\)
−0.999863 + 0.0165769i \(0.994723\pi\)
\(912\) 0 0
\(913\) 5.22571i 0.172946i
\(914\) 10.0117 11.0947i 0.331157 0.366980i
\(915\) 0 0
\(916\) −34.2092 + 3.51999i −1.13030 + 0.116304i
\(917\) −4.07783 2.33208i −0.134662 0.0770121i
\(918\) 0 0
\(919\) 6.71273i 0.221433i 0.993852 + 0.110716i \(0.0353145\pi\)
−0.993852 + 0.110716i \(0.964686\pi\)
\(920\) −17.3676 12.7055i −0.572593 0.418887i
\(921\) 0 0
\(922\) −0.527782 0.476262i −0.0173816 0.0156848i
\(923\) 27.2184 0.895905
\(924\) 0 0
\(925\) 8.62867 0.283709
\(926\) −17.3967 15.6985i −0.571691 0.515885i
\(927\) 0 0
\(928\) 17.6377 30.1677i 0.578986 0.990302i
\(929\) 12.9220i 0.423957i −0.977274 0.211979i \(-0.932009\pi\)
0.977274 0.211979i \(-0.0679907\pi\)
\(930\) 0 0
\(931\) −18.8578 32.0524i −0.618040 1.05047i
\(932\) −2.36442 22.9788i −0.0774491 0.752694i
\(933\) 0 0
\(934\) 16.2185 17.9730i 0.530686 0.588093i
\(935\) 1.82916i 0.0598198i
\(936\) 0 0
\(937\) 55.1955i 1.80316i 0.432615 + 0.901579i \(0.357591\pi\)
−0.432615 + 0.901579i \(0.642409\pi\)
\(938\) 1.52414 + 4.64322i 0.0497651 + 0.151606i
\(939\) 0 0
\(940\) 12.3714 1.27297i 0.403512 0.0415197i
\(941\) 41.8089i 1.36293i −0.731851 0.681465i \(-0.761343\pi\)
0.731851 0.681465i \(-0.238657\pi\)
\(942\) 0 0
\(943\) 7.69364 0.250539
\(944\) 19.1444 3.98192i 0.623098 0.129600i
\(945\) 0 0
\(946\) 3.09853 3.43372i 0.100742 0.111640i
\(947\) 29.9634i 0.973679i −0.873491 0.486839i \(-0.838150\pi\)
0.873491 0.486839i \(-0.161850\pi\)
\(948\) 0 0
\(949\) −13.3253 −0.432556
\(950\) 5.03339 5.57788i 0.163305 0.180970i
\(951\) 0 0
\(952\) 26.1977 11.6899i 0.849072 0.378872i
\(953\) −4.49708 −0.145675 −0.0728373 0.997344i \(-0.523205\pi\)
−0.0728373 + 0.997344i \(0.523205\pi\)
\(954\) 0 0
\(955\) −6.84692 −0.221561
\(956\) −26.8676 + 2.76457i −0.868961 + 0.0894125i
\(957\) 0 0
\(958\) −7.11802 + 7.88801i −0.229973 + 0.254850i
\(959\) −34.8229 19.9149i −1.12449 0.643086i
\(960\) 0 0
\(961\) −19.5222 −0.629749
\(962\) −26.8407 24.2206i −0.865379 0.780904i
\(963\) 0 0
\(964\) 12.0923 1.24425i 0.389467 0.0400745i
\(965\) 7.47575i 0.240653i
\(966\) 0 0
\(967\) 15.3198i 0.492651i −0.969187 0.246326i \(-0.920777\pi\)
0.969187 0.246326i \(-0.0792232\pi\)
\(968\) −24.5909 17.9898i −0.790382 0.578213i
\(969\) 0 0
\(970\) −1.52170 + 1.68632i −0.0488590 + 0.0541443i
\(971\) −2.95293 −0.0947641 −0.0473821 0.998877i \(-0.515088\pi\)
−0.0473821 + 0.998877i \(0.515088\pi\)
\(972\) 0 0
\(973\) 43.3029 + 24.7646i 1.38823 + 0.793917i
\(974\) 19.2899 + 17.4069i 0.618087 + 0.557752i
\(975\) 0 0
\(976\) 3.87574 + 18.6339i 0.124059 + 0.596457i
\(977\) −32.6707 −1.04523 −0.522615 0.852569i \(-0.675043\pi\)
−0.522615 + 0.852569i \(0.675043\pi\)
\(978\) 0 0
\(979\) −6.26056 −0.200088
\(980\) 8.29705 + 11.2765i 0.265039 + 0.360214i
\(981\) 0 0
\(982\) 12.9910 + 11.7229i 0.414560 + 0.374092i
\(983\) −12.7915 −0.407986 −0.203993 0.978972i \(-0.565392\pi\)
−0.203993 + 0.978972i \(0.565392\pi\)
\(984\) 0 0
\(985\) 14.2749i 0.454837i
\(986\) 24.8641 + 22.4370i 0.791836 + 0.714540i
\(987\) 0 0
\(988\) −31.3142 + 3.22210i −0.996236 + 0.102509i
\(989\) 52.1467 1.65817
\(990\) 0 0
\(991\) 29.8437i 0.948015i −0.880521 0.474008i \(-0.842807\pi\)
0.880521 0.474008i \(-0.157193\pi\)
\(992\) 9.67290 16.5446i 0.307115 0.525291i
\(993\) 0 0
\(994\) 10.7207 + 32.6601i 0.340041 + 1.03591i
\(995\) 1.60743i 0.0509590i
\(996\) 0 0
\(997\) 16.0457i 0.508172i −0.967182 0.254086i \(-0.918225\pi\)
0.967182 0.254086i \(-0.0817746\pi\)
\(998\) −4.10448 3.70381i −0.129925 0.117242i
\(999\) 0 0
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 1260.2.c.d.811.13 16
3.2 odd 2 420.2.c.a.391.4 yes 16
4.3 odd 2 1260.2.c.e.811.14 16
7.6 odd 2 1260.2.c.e.811.13 16
12.11 even 2 420.2.c.b.391.3 yes 16
21.20 even 2 420.2.c.b.391.4 yes 16
28.27 even 2 inner 1260.2.c.d.811.14 16
84.83 odd 2 420.2.c.a.391.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
420.2.c.a.391.3 16 84.83 odd 2
420.2.c.a.391.4 yes 16 3.2 odd 2
420.2.c.b.391.3 yes 16 12.11 even 2
420.2.c.b.391.4 yes 16 21.20 even 2
1260.2.c.d.811.13 16 1.1 even 1 trivial
1260.2.c.d.811.14 16 28.27 even 2 inner
1260.2.c.e.811.13 16 7.6 odd 2
1260.2.c.e.811.14 16 4.3 odd 2