Properties

Label 360.2.x.a.53.20
Level $360$
Weight $2$
Character 360.53
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(53,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.x (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 53.20
Character \(\chi\) \(=\) 360.53
Dual form 360.2.x.a.197.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.19248 - 0.760261i) q^{2} +(0.844006 - 1.81319i) q^{4} +(2.23604 - 0.0113158i) q^{5} +(0.471963 - 0.471963i) q^{7} +(-0.372039 - 2.80385i) q^{8} +O(q^{10})\) \(q+(1.19248 - 0.760261i) q^{2} +(0.844006 - 1.81319i) q^{4} +(2.23604 - 0.0113158i) q^{5} +(0.471963 - 0.471963i) q^{7} +(-0.372039 - 2.80385i) q^{8} +(2.65782 - 1.71347i) q^{10} -0.335652 q^{11} +(-3.50404 + 3.50404i) q^{13} +(0.203990 - 0.921620i) q^{14} +(-2.57531 - 3.06068i) q^{16} +(2.53299 + 2.53299i) q^{17} -4.07474 q^{19} +(1.86671 - 4.06391i) q^{20} +(-0.400257 + 0.255183i) q^{22} +(6.20627 - 6.20627i) q^{23} +(4.99974 - 0.0506050i) q^{25} +(-1.51450 + 6.84248i) q^{26} +(-0.457418 - 1.25410i) q^{28} +2.42367i q^{29} -6.41004 q^{31} +(-5.39792 - 1.69189i) q^{32} +(4.94626 + 1.09480i) q^{34} +(1.04999 - 1.06067i) q^{35} +(-2.24893 - 2.24893i) q^{37} +(-4.85903 + 3.09787i) q^{38} +(-0.863622 - 6.26531i) q^{40} +5.80736i q^{41} +(-4.87603 + 4.87603i) q^{43} +(-0.283292 + 0.608600i) q^{44} +(2.68245 - 12.1192i) q^{46} +(-1.68276 - 1.68276i) q^{47} +6.55450i q^{49} +(5.92361 - 3.86146i) q^{50} +(3.39606 + 9.31092i) q^{52} +(3.05444 + 3.05444i) q^{53} +(-0.750530 + 0.00379815i) q^{55} +(-1.49890 - 1.14772i) q^{56} +(1.84263 + 2.89018i) q^{58} +12.2950i q^{59} -7.49787i q^{61} +(-7.64383 + 4.87331i) q^{62} +(-7.72317 + 2.08629i) q^{64} +(-7.79553 + 7.87483i) q^{65} +(5.55519 + 5.55519i) q^{67} +(6.73064 - 2.45493i) q^{68} +(0.445701 - 2.06309i) q^{70} -13.4793i q^{71} +(5.05035 + 5.05035i) q^{73} +(-4.39157 - 0.972023i) q^{74} +(-3.43910 + 7.38827i) q^{76} +(-0.158415 + 0.158415i) q^{77} +8.85503i q^{79} +(-5.79313 - 6.81467i) q^{80} +(4.41511 + 6.92515i) q^{82} +(-4.78510 - 4.78510i) q^{83} +(5.69252 + 5.63520i) q^{85} +(-2.10750 + 9.52162i) q^{86} +(0.124876 + 0.941117i) q^{88} -8.33405 q^{89} +3.30755i q^{91} +(-6.01502 - 16.4913i) q^{92} +(-3.28598 - 0.727315i) q^{94} +(-9.11128 + 0.0461088i) q^{95} +(10.1367 - 10.1367i) q^{97} +(4.98313 + 7.81610i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19248 0.760261i 0.843209 0.537586i
\(3\) 0 0
\(4\) 0.844006 1.81319i 0.422003 0.906594i
\(5\) 2.23604 0.0113158i 0.999987 0.00506057i
\(6\) 0 0
\(7\) 0.471963 0.471963i 0.178385 0.178385i −0.612266 0.790652i \(-0.709742\pi\)
0.790652 + 0.612266i \(0.209742\pi\)
\(8\) −0.372039 2.80385i −0.131536 0.991311i
\(9\) 0 0
\(10\) 2.65782 1.71347i 0.840478 0.541846i
\(11\) −0.335652 −0.101203 −0.0506014 0.998719i \(-0.516114\pi\)
−0.0506014 + 0.998719i \(0.516114\pi\)
\(12\) 0 0
\(13\) −3.50404 + 3.50404i −0.971846 + 0.971846i −0.999614 0.0277680i \(-0.991160\pi\)
0.0277680 + 0.999614i \(0.491160\pi\)
\(14\) 0.203990 0.921620i 0.0545186 0.246313i
\(15\) 0 0
\(16\) −2.57531 3.06068i −0.643827 0.765171i
\(17\) 2.53299 + 2.53299i 0.614340 + 0.614340i 0.944074 0.329734i \(-0.106959\pi\)
−0.329734 + 0.944074i \(0.606959\pi\)
\(18\) 0 0
\(19\) −4.07474 −0.934809 −0.467405 0.884044i \(-0.654811\pi\)
−0.467405 + 0.884044i \(0.654811\pi\)
\(20\) 1.86671 4.06391i 0.417410 0.908718i
\(21\) 0 0
\(22\) −0.400257 + 0.255183i −0.0853351 + 0.0544052i
\(23\) 6.20627 6.20627i 1.29410 1.29410i 0.361868 0.932229i \(-0.382139\pi\)
0.932229 0.361868i \(-0.117861\pi\)
\(24\) 0 0
\(25\) 4.99974 0.0506050i 0.999949 0.0101210i
\(26\) −1.51450 + 6.84248i −0.297019 + 1.34192i
\(27\) 0 0
\(28\) −0.457418 1.25410i −0.0864439 0.237002i
\(29\) 2.42367i 0.450065i 0.974351 + 0.225032i \(0.0722488\pi\)
−0.974351 + 0.225032i \(0.927751\pi\)
\(30\) 0 0
\(31\) −6.41004 −1.15128 −0.575639 0.817704i \(-0.695247\pi\)
−0.575639 + 0.817704i \(0.695247\pi\)
\(32\) −5.39792 1.69189i −0.954226 0.299087i
\(33\) 0 0
\(34\) 4.94626 + 1.09480i 0.848277 + 0.187756i
\(35\) 1.04999 1.06067i 0.177480 0.179286i
\(36\) 0 0
\(37\) −2.24893 2.24893i −0.369721 0.369721i 0.497654 0.867375i \(-0.334195\pi\)
−0.867375 + 0.497654i \(0.834195\pi\)
\(38\) −4.85903 + 3.09787i −0.788239 + 0.502540i
\(39\) 0 0
\(40\) −0.863622 6.26531i −0.136551 0.990633i
\(41\) 5.80736i 0.906957i 0.891267 + 0.453479i \(0.149817\pi\)
−0.891267 + 0.453479i \(0.850183\pi\)
\(42\) 0 0
\(43\) −4.87603 + 4.87603i −0.743588 + 0.743588i −0.973267 0.229678i \(-0.926233\pi\)
0.229678 + 0.973267i \(0.426233\pi\)
\(44\) −0.283292 + 0.608600i −0.0427078 + 0.0917498i
\(45\) 0 0
\(46\) 2.68245 12.1192i 0.395506 1.78688i
\(47\) −1.68276 1.68276i −0.245455 0.245455i 0.573647 0.819102i \(-0.305528\pi\)
−0.819102 + 0.573647i \(0.805528\pi\)
\(48\) 0 0
\(49\) 6.55450i 0.936358i
\(50\) 5.92361 3.86146i 0.837725 0.546092i
\(51\) 0 0
\(52\) 3.39606 + 9.31092i 0.470949 + 1.29119i
\(53\) 3.05444 + 3.05444i 0.419560 + 0.419560i 0.885052 0.465492i \(-0.154123\pi\)
−0.465492 + 0.885052i \(0.654123\pi\)
\(54\) 0 0
\(55\) −0.750530 + 0.00379815i −0.101201 + 0.000512143i
\(56\) −1.49890 1.14772i −0.200299 0.153371i
\(57\) 0 0
\(58\) 1.84263 + 2.89018i 0.241949 + 0.379499i
\(59\) 12.2950i 1.60067i 0.599553 + 0.800335i \(0.295345\pi\)
−0.599553 + 0.800335i \(0.704655\pi\)
\(60\) 0 0
\(61\) 7.49787i 0.960004i −0.877267 0.480002i \(-0.840636\pi\)
0.877267 0.480002i \(-0.159364\pi\)
\(62\) −7.64383 + 4.87331i −0.970767 + 0.618910i
\(63\) 0 0
\(64\) −7.72317 + 2.08629i −0.965397 + 0.260786i
\(65\) −7.79553 + 7.87483i −0.966916 + 0.976752i
\(66\) 0 0
\(67\) 5.55519 + 5.55519i 0.678674 + 0.678674i 0.959700 0.281026i \(-0.0906748\pi\)
−0.281026 + 0.959700i \(0.590675\pi\)
\(68\) 6.73064 2.45493i 0.816210 0.297704i
\(69\) 0 0
\(70\) 0.445701 2.06309i 0.0532714 0.246586i
\(71\) 13.4793i 1.59970i −0.600199 0.799851i \(-0.704912\pi\)
0.600199 0.799851i \(-0.295088\pi\)
\(72\) 0 0
\(73\) 5.05035 + 5.05035i 0.591099 + 0.591099i 0.937928 0.346830i \(-0.112742\pi\)
−0.346830 + 0.937928i \(0.612742\pi\)
\(74\) −4.39157 0.972023i −0.510509 0.112995i
\(75\) 0 0
\(76\) −3.43910 + 7.38827i −0.394492 + 0.847493i
\(77\) −0.158415 + 0.158415i −0.0180531 + 0.0180531i
\(78\) 0 0
\(79\) 8.85503i 0.996268i 0.867100 + 0.498134i \(0.165981\pi\)
−0.867100 + 0.498134i \(0.834019\pi\)
\(80\) −5.79313 6.81467i −0.647691 0.761903i
\(81\) 0 0
\(82\) 4.41511 + 6.92515i 0.487567 + 0.764755i
\(83\) −4.78510 4.78510i −0.525233 0.525233i 0.393914 0.919147i \(-0.371121\pi\)
−0.919147 + 0.393914i \(0.871121\pi\)
\(84\) 0 0
\(85\) 5.69252 + 5.63520i 0.617441 + 0.611223i
\(86\) −2.10750 + 9.52162i −0.227258 + 1.02674i
\(87\) 0 0
\(88\) 0.124876 + 0.941117i 0.0133118 + 0.100323i
\(89\) −8.33405 −0.883408 −0.441704 0.897161i \(-0.645626\pi\)
−0.441704 + 0.897161i \(0.645626\pi\)
\(90\) 0 0
\(91\) 3.30755i 0.346726i
\(92\) −6.01502 16.4913i −0.627109 1.71933i
\(93\) 0 0
\(94\) −3.28598 0.727315i −0.338923 0.0750168i
\(95\) −9.11128 + 0.0461088i −0.934797 + 0.00473066i
\(96\) 0 0
\(97\) 10.1367 10.1367i 1.02922 1.02922i 0.0296647 0.999560i \(-0.490556\pi\)
0.999560 0.0296647i \(-0.00944397\pi\)
\(98\) 4.98313 + 7.81610i 0.503373 + 0.789545i
\(99\) 0 0
\(100\) 4.12806 9.10819i 0.412806 0.910819i
\(101\) −9.88830 −0.983922 −0.491961 0.870617i \(-0.663720\pi\)
−0.491961 + 0.870617i \(0.663720\pi\)
\(102\) 0 0
\(103\) −10.0033 10.0033i −0.985653 0.985653i 0.0142455 0.999899i \(-0.495465\pi\)
−0.999899 + 0.0142455i \(0.995465\pi\)
\(104\) 11.1285 + 8.52117i 1.09124 + 0.835570i
\(105\) 0 0
\(106\) 5.96453 + 1.32018i 0.579326 + 0.128227i
\(107\) 10.2013 10.2013i 0.986198 0.986198i −0.0137076 0.999906i \(-0.504363\pi\)
0.999906 + 0.0137076i \(0.00436339\pi\)
\(108\) 0 0
\(109\) 11.0144 1.05498 0.527492 0.849560i \(-0.323133\pi\)
0.527492 + 0.849560i \(0.323133\pi\)
\(110\) −0.892103 + 0.575128i −0.0850586 + 0.0548363i
\(111\) 0 0
\(112\) −2.65998 0.229079i −0.251344 0.0216459i
\(113\) 2.45369 2.45369i 0.230823 0.230823i −0.582213 0.813036i \(-0.697813\pi\)
0.813036 + 0.582213i \(0.197813\pi\)
\(114\) 0 0
\(115\) 13.8072 13.9477i 1.28753 1.30063i
\(116\) 4.39458 + 2.04559i 0.408026 + 0.189929i
\(117\) 0 0
\(118\) 9.34740 + 14.6615i 0.860498 + 1.34970i
\(119\) 2.39095 0.219178
\(120\) 0 0
\(121\) −10.8873 −0.989758
\(122\) −5.70034 8.94105i −0.516085 0.809484i
\(123\) 0 0
\(124\) −5.41011 + 11.6226i −0.485842 + 1.04374i
\(125\) 11.1791 0.169731i 0.999885 0.0151812i
\(126\) 0 0
\(127\) 6.00329 6.00329i 0.532705 0.532705i −0.388671 0.921377i \(-0.627066\pi\)
0.921377 + 0.388671i \(0.127066\pi\)
\(128\) −7.62359 + 8.35948i −0.673836 + 0.738881i
\(129\) 0 0
\(130\) −3.30906 + 15.3172i −0.290224 + 1.34341i
\(131\) −11.3345 −0.990301 −0.495151 0.868807i \(-0.664887\pi\)
−0.495151 + 0.868807i \(0.664887\pi\)
\(132\) 0 0
\(133\) −1.92312 + 1.92312i −0.166756 + 0.166756i
\(134\) 10.8478 + 2.40104i 0.937109 + 0.207418i
\(135\) 0 0
\(136\) 6.15975 8.04449i 0.528194 0.689809i
\(137\) 10.8670 + 10.8670i 0.928434 + 0.928434i 0.997605 0.0691711i \(-0.0220354\pi\)
−0.0691711 + 0.997605i \(0.522035\pi\)
\(138\) 0 0
\(139\) −13.3432 −1.13176 −0.565878 0.824489i \(-0.691463\pi\)
−0.565878 + 0.824489i \(0.691463\pi\)
\(140\) −1.03700 2.79903i −0.0876422 0.236561i
\(141\) 0 0
\(142\) −10.2478 16.0738i −0.859977 1.34888i
\(143\) 1.17614 1.17614i 0.0983535 0.0983535i
\(144\) 0 0
\(145\) 0.0274257 + 5.41943i 0.00227758 + 0.450059i
\(146\) 9.86201 + 2.18284i 0.816186 + 0.180653i
\(147\) 0 0
\(148\) −5.97583 + 2.17962i −0.491211 + 0.179164i
\(149\) 13.5961i 1.11384i −0.830566 0.556919i \(-0.811983\pi\)
0.830566 0.556919i \(-0.188017\pi\)
\(150\) 0 0
\(151\) −9.64289 −0.784727 −0.392364 0.919810i \(-0.628343\pi\)
−0.392364 + 0.919810i \(0.628343\pi\)
\(152\) 1.51596 + 11.4250i 0.122961 + 0.926687i
\(153\) 0 0
\(154\) −0.0684695 + 0.309343i −0.00551743 + 0.0249276i
\(155\) −14.3331 + 0.0725345i −1.15126 + 0.00582611i
\(156\) 0 0
\(157\) −7.62403 7.62403i −0.608464 0.608464i 0.334080 0.942545i \(-0.391574\pi\)
−0.942545 + 0.334080i \(0.891574\pi\)
\(158\) 6.73213 + 10.5594i 0.535580 + 0.840062i
\(159\) 0 0
\(160\) −12.0891 3.72205i −0.955727 0.294254i
\(161\) 5.85826i 0.461695i
\(162\) 0 0
\(163\) 16.2490 16.2490i 1.27272 1.27272i 0.328065 0.944655i \(-0.393603\pi\)
0.944655 0.328065i \(-0.106397\pi\)
\(164\) 10.5298 + 4.90145i 0.822242 + 0.382739i
\(165\) 0 0
\(166\) −9.34405 2.06820i −0.725239 0.160523i
\(167\) 13.7067 + 13.7067i 1.06066 + 1.06066i 0.998037 + 0.0626204i \(0.0199458\pi\)
0.0626204 + 0.998037i \(0.480054\pi\)
\(168\) 0 0
\(169\) 11.5566i 0.888971i
\(170\) 11.0724 + 2.39204i 0.849216 + 0.183461i
\(171\) 0 0
\(172\) 4.72577 + 12.9566i 0.360337 + 0.987929i
\(173\) −3.35678 3.35678i −0.255211 0.255211i 0.567892 0.823103i \(-0.307759\pi\)
−0.823103 + 0.567892i \(0.807759\pi\)
\(174\) 0 0
\(175\) 2.33581 2.38358i 0.176571 0.180181i
\(176\) 0.864406 + 1.02732i 0.0651571 + 0.0774374i
\(177\) 0 0
\(178\) −9.93817 + 6.33606i −0.744897 + 0.474907i
\(179\) 10.7537i 0.803772i −0.915690 0.401886i \(-0.868355\pi\)
0.915690 0.401886i \(-0.131645\pi\)
\(180\) 0 0
\(181\) 10.1290i 0.752883i −0.926440 0.376441i \(-0.877148\pi\)
0.926440 0.376441i \(-0.122852\pi\)
\(182\) 2.51460 + 3.94418i 0.186395 + 0.292362i
\(183\) 0 0
\(184\) −19.7104 15.0925i −1.45307 1.11263i
\(185\) −5.05414 5.00324i −0.371587 0.367845i
\(186\) 0 0
\(187\) −0.850201 0.850201i −0.0621728 0.0621728i
\(188\) −4.47141 + 1.63090i −0.326111 + 0.118946i
\(189\) 0 0
\(190\) −10.8299 + 6.98193i −0.785686 + 0.506523i
\(191\) 4.32194i 0.312725i 0.987700 + 0.156362i \(0.0499768\pi\)
−0.987700 + 0.156362i \(0.950023\pi\)
\(192\) 0 0
\(193\) −7.97419 7.97419i −0.573995 0.573995i 0.359248 0.933242i \(-0.383033\pi\)
−0.933242 + 0.359248i \(0.883033\pi\)
\(194\) 4.38124 19.7943i 0.314555 1.42115i
\(195\) 0 0
\(196\) 11.8846 + 5.53204i 0.848897 + 0.395146i
\(197\) 4.30206 4.30206i 0.306509 0.306509i −0.537045 0.843554i \(-0.680459\pi\)
0.843554 + 0.537045i \(0.180459\pi\)
\(198\) 0 0
\(199\) 3.02113i 0.214162i −0.994250 0.107081i \(-0.965850\pi\)
0.994250 0.107081i \(-0.0341505\pi\)
\(200\) −2.00199 13.9997i −0.141562 0.989929i
\(201\) 0 0
\(202\) −11.7916 + 7.51769i −0.829652 + 0.528943i
\(203\) 1.14388 + 1.14388i 0.0802849 + 0.0802849i
\(204\) 0 0
\(205\) 0.0657147 + 12.9855i 0.00458972 + 0.906946i
\(206\) −19.5338 4.32358i −1.36098 0.301238i
\(207\) 0 0
\(208\) 19.7488 + 1.70078i 1.36933 + 0.117928i
\(209\) 1.36769 0.0946052
\(210\) 0 0
\(211\) 8.87754i 0.611155i 0.952167 + 0.305577i \(0.0988495\pi\)
−0.952167 + 0.305577i \(0.901151\pi\)
\(212\) 8.11625 2.96031i 0.557426 0.203315i
\(213\) 0 0
\(214\) 4.40918 19.9205i 0.301405 1.36174i
\(215\) −10.8478 + 10.9582i −0.739816 + 0.747342i
\(216\) 0 0
\(217\) −3.02530 + 3.02530i −0.205371 + 0.205371i
\(218\) 13.1344 8.37379i 0.889572 0.567144i
\(219\) 0 0
\(220\) −0.626565 + 1.36406i −0.0422430 + 0.0919648i
\(221\) −17.7514 −1.19409
\(222\) 0 0
\(223\) 9.93808 + 9.93808i 0.665503 + 0.665503i 0.956672 0.291169i \(-0.0940441\pi\)
−0.291169 + 0.956672i \(0.594044\pi\)
\(224\) −3.34612 + 1.74911i −0.223572 + 0.116867i
\(225\) 0 0
\(226\) 1.06052 4.79141i 0.0705449 0.318720i
\(227\) 7.21442 7.21442i 0.478838 0.478838i −0.425922 0.904760i \(-0.640050\pi\)
0.904760 + 0.425922i \(0.140050\pi\)
\(228\) 0 0
\(229\) 21.8687 1.44512 0.722562 0.691306i \(-0.242965\pi\)
0.722562 + 0.691306i \(0.242965\pi\)
\(230\) 5.86093 27.1294i 0.386458 1.78886i
\(231\) 0 0
\(232\) 6.79562 0.901702i 0.446154 0.0591996i
\(233\) 6.78300 6.78300i 0.444369 0.444369i −0.449108 0.893477i \(-0.648258\pi\)
0.893477 + 0.449108i \(0.148258\pi\)
\(234\) 0 0
\(235\) −3.78175 3.74367i −0.246694 0.244210i
\(236\) 22.2931 + 10.3770i 1.45116 + 0.675488i
\(237\) 0 0
\(238\) 2.85115 1.81775i 0.184813 0.117827i
\(239\) −4.63287 −0.299676 −0.149838 0.988711i \(-0.547875\pi\)
−0.149838 + 0.988711i \(0.547875\pi\)
\(240\) 0 0
\(241\) −9.72150 −0.626217 −0.313109 0.949717i \(-0.601370\pi\)
−0.313109 + 0.949717i \(0.601370\pi\)
\(242\) −12.9829 + 8.27722i −0.834573 + 0.532080i
\(243\) 0 0
\(244\) −13.5951 6.32825i −0.870335 0.405125i
\(245\) 0.0741692 + 14.6561i 0.00473850 + 0.936346i
\(246\) 0 0
\(247\) 14.2781 14.2781i 0.908491 0.908491i
\(248\) 2.38479 + 17.9728i 0.151434 + 1.14127i
\(249\) 0 0
\(250\) 13.2017 8.70140i 0.834951 0.550325i
\(251\) 30.6190 1.93265 0.966327 0.257316i \(-0.0828382\pi\)
0.966327 + 0.257316i \(0.0828382\pi\)
\(252\) 0 0
\(253\) −2.08314 + 2.08314i −0.130966 + 0.130966i
\(254\) 2.59472 11.7228i 0.162807 0.735557i
\(255\) 0 0
\(256\) −2.73557 + 15.7644i −0.170973 + 0.985276i
\(257\) 1.63773 + 1.63773i 0.102158 + 0.102158i 0.756339 0.654180i \(-0.226986\pi\)
−0.654180 + 0.756339i \(0.726986\pi\)
\(258\) 0 0
\(259\) −2.12282 −0.131905
\(260\) 7.69908 + 20.7812i 0.477477 + 1.28879i
\(261\) 0 0
\(262\) −13.5162 + 8.61719i −0.835031 + 0.532372i
\(263\) −7.77099 + 7.77099i −0.479180 + 0.479180i −0.904869 0.425689i \(-0.860032\pi\)
0.425689 + 0.904869i \(0.360032\pi\)
\(264\) 0 0
\(265\) 6.86441 + 6.79529i 0.421678 + 0.417431i
\(266\) −0.831206 + 3.75536i −0.0509645 + 0.230256i
\(267\) 0 0
\(268\) 14.7612 5.38399i 0.901684 0.328880i
\(269\) 16.1341i 0.983714i −0.870676 0.491857i \(-0.836318\pi\)
0.870676 0.491857i \(-0.163682\pi\)
\(270\) 0 0
\(271\) 16.8474 1.02341 0.511704 0.859162i \(-0.329014\pi\)
0.511704 + 0.859162i \(0.329014\pi\)
\(272\) 1.22945 14.2759i 0.0745463 0.865603i
\(273\) 0 0
\(274\) 21.2205 + 4.69691i 1.28198 + 0.283751i
\(275\) −1.67817 + 0.0169856i −0.101198 + 0.00102427i
\(276\) 0 0
\(277\) −16.3206 16.3206i −0.980611 0.980611i 0.0192042 0.999816i \(-0.493887\pi\)
−0.999816 + 0.0192042i \(0.993887\pi\)
\(278\) −15.9115 + 10.1443i −0.954307 + 0.608416i
\(279\) 0 0
\(280\) −3.36459 2.54940i −0.201073 0.152356i
\(281\) 31.2898i 1.86659i −0.359106 0.933297i \(-0.616918\pi\)
0.359106 0.933297i \(-0.383082\pi\)
\(282\) 0 0
\(283\) −9.97554 + 9.97554i −0.592984 + 0.592984i −0.938436 0.345452i \(-0.887726\pi\)
0.345452 + 0.938436i \(0.387726\pi\)
\(284\) −24.4406 11.3766i −1.45028 0.675079i
\(285\) 0 0
\(286\) 0.508346 2.29669i 0.0300591 0.135806i
\(287\) 2.74086 + 2.74086i 0.161788 + 0.161788i
\(288\) 0 0
\(289\) 4.16795i 0.245174i
\(290\) 4.15289 + 6.44170i 0.243866 + 0.378270i
\(291\) 0 0
\(292\) 13.4198 4.89471i 0.785332 0.286441i
\(293\) 5.26253 + 5.26253i 0.307440 + 0.307440i 0.843916 0.536476i \(-0.180245\pi\)
−0.536476 + 0.843916i \(0.680245\pi\)
\(294\) 0 0
\(295\) 0.139127 + 27.4921i 0.00810030 + 1.60065i
\(296\) −5.46897 + 7.14235i −0.317877 + 0.415140i
\(297\) 0 0
\(298\) −10.3366 16.2131i −0.598784 0.939199i
\(299\) 43.4941i 2.51533i
\(300\) 0 0
\(301\) 4.60261i 0.265290i
\(302\) −11.4989 + 7.33112i −0.661689 + 0.421858i
\(303\) 0 0
\(304\) 10.4937 + 12.4715i 0.601855 + 0.715289i
\(305\) −0.0848442 16.7655i −0.00485816 0.959992i
\(306\) 0 0
\(307\) 9.54586 + 9.54586i 0.544811 + 0.544811i 0.924935 0.380124i \(-0.124119\pi\)
−0.380124 + 0.924935i \(0.624119\pi\)
\(308\) 0.153533 + 0.420939i 0.00874836 + 0.0239852i
\(309\) 0 0
\(310\) −17.0368 + 10.9834i −0.967623 + 0.623815i
\(311\) 4.08587i 0.231688i 0.993267 + 0.115844i \(0.0369573\pi\)
−0.993267 + 0.115844i \(0.963043\pi\)
\(312\) 0 0
\(313\) −14.4004 14.4004i −0.813958 0.813958i 0.171266 0.985225i \(-0.445214\pi\)
−0.985225 + 0.171266i \(0.945214\pi\)
\(314\) −14.8877 3.29523i −0.840164 0.185961i
\(315\) 0 0
\(316\) 16.0558 + 7.47369i 0.903211 + 0.420428i
\(317\) −12.0841 + 12.0841i −0.678710 + 0.678710i −0.959708 0.280998i \(-0.909334\pi\)
0.280998 + 0.959708i \(0.409334\pi\)
\(318\) 0 0
\(319\) 0.813510i 0.0455478i
\(320\) −17.2457 + 4.75241i −0.964065 + 0.265668i
\(321\) 0 0
\(322\) −4.45381 6.98584i −0.248201 0.389306i
\(323\) −10.3213 10.3213i −0.574290 0.574290i
\(324\) 0 0
\(325\) −17.3420 + 17.6966i −0.961961 + 0.981633i
\(326\) 7.02309 31.7301i 0.388973 1.75737i
\(327\) 0 0
\(328\) 16.2830 2.16057i 0.899077 0.119297i
\(329\) −1.58840 −0.0875711
\(330\) 0 0
\(331\) 33.6119i 1.84747i 0.383027 + 0.923737i \(0.374882\pi\)
−0.383027 + 0.923737i \(0.625118\pi\)
\(332\) −12.7149 + 4.63764i −0.697823 + 0.254523i
\(333\) 0 0
\(334\) 26.7656 + 5.92427i 1.46455 + 0.324162i
\(335\) 12.4845 + 12.3588i 0.682100 + 0.675231i
\(336\) 0 0
\(337\) −20.2142 + 20.2142i −1.10114 + 1.10114i −0.106864 + 0.994274i \(0.534081\pi\)
−0.994274 + 0.106864i \(0.965919\pi\)
\(338\) −8.78605 13.7810i −0.477898 0.749588i
\(339\) 0 0
\(340\) 15.0222 5.56548i 0.814693 0.301830i
\(341\) 2.15154 0.116512
\(342\) 0 0
\(343\) 6.39722 + 6.39722i 0.345417 + 0.345417i
\(344\) 15.4858 + 11.8576i 0.834936 + 0.639319i
\(345\) 0 0
\(346\) −6.55492 1.45086i −0.352394 0.0779985i
\(347\) −0.443163 + 0.443163i −0.0237903 + 0.0237903i −0.718902 0.695112i \(-0.755355\pi\)
0.695112 + 0.718902i \(0.255355\pi\)
\(348\) 0 0
\(349\) 10.8766 0.582212 0.291106 0.956691i \(-0.405977\pi\)
0.291106 + 0.956691i \(0.405977\pi\)
\(350\) 0.973259 4.61819i 0.0520229 0.246852i
\(351\) 0 0
\(352\) 1.81182 + 0.567885i 0.0965703 + 0.0302684i
\(353\) 10.0437 10.0437i 0.534572 0.534572i −0.387357 0.921930i \(-0.626612\pi\)
0.921930 + 0.387357i \(0.126612\pi\)
\(354\) 0 0
\(355\) −0.152529 30.1403i −0.00809540 1.59968i
\(356\) −7.03399 + 15.1112i −0.372801 + 0.800893i
\(357\) 0 0
\(358\) −8.17565 12.8236i −0.432097 0.677748i
\(359\) −19.6724 −1.03827 −0.519136 0.854692i \(-0.673746\pi\)
−0.519136 + 0.854692i \(0.673746\pi\)
\(360\) 0 0
\(361\) −2.39651 −0.126132
\(362\) −7.70069 12.0786i −0.404739 0.634837i
\(363\) 0 0
\(364\) 5.99722 + 2.79159i 0.314340 + 0.146319i
\(365\) 11.3499 + 11.2356i 0.594082 + 0.588100i
\(366\) 0 0
\(367\) −9.86005 + 9.86005i −0.514690 + 0.514690i −0.915960 0.401270i \(-0.868569\pi\)
0.401270 + 0.915960i \(0.368569\pi\)
\(368\) −34.9785 3.01237i −1.82338 0.157031i
\(369\) 0 0
\(370\) −9.83071 2.12379i −0.511074 0.110410i
\(371\) 2.88316 0.149686
\(372\) 0 0
\(373\) −12.6526 + 12.6526i −0.655127 + 0.655127i −0.954223 0.299096i \(-0.903315\pi\)
0.299096 + 0.954223i \(0.403315\pi\)
\(374\) −1.66022 0.367471i −0.0858480 0.0190015i
\(375\) 0 0
\(376\) −4.09215 + 5.34425i −0.211036 + 0.275609i
\(377\) −8.49265 8.49265i −0.437394 0.437394i
\(378\) 0 0
\(379\) −37.9577 −1.94975 −0.974877 0.222743i \(-0.928499\pi\)
−0.974877 + 0.222743i \(0.928499\pi\)
\(380\) −7.60636 + 16.5594i −0.390198 + 0.849478i
\(381\) 0 0
\(382\) 3.28581 + 5.15382i 0.168116 + 0.263692i
\(383\) −9.18320 + 9.18320i −0.469240 + 0.469240i −0.901668 0.432428i \(-0.857657\pi\)
0.432428 + 0.901668i \(0.357657\pi\)
\(384\) 0 0
\(385\) −0.352429 + 0.356015i −0.0179615 + 0.0181442i
\(386\) −15.5715 3.44657i −0.792569 0.175426i
\(387\) 0 0
\(388\) −9.82431 26.9352i −0.498754 1.36743i
\(389\) 4.22258i 0.214093i 0.994254 + 0.107047i \(0.0341394\pi\)
−0.994254 + 0.107047i \(0.965861\pi\)
\(390\) 0 0
\(391\) 31.4408 1.59003
\(392\) 18.3779 2.43853i 0.928222 0.123165i
\(393\) 0 0
\(394\) 1.85942 8.40081i 0.0936764 0.423227i
\(395\) 0.100201 + 19.8002i 0.00504168 + 0.996256i
\(396\) 0 0
\(397\) 1.27679 + 1.27679i 0.0640801 + 0.0640801i 0.738421 0.674340i \(-0.235572\pi\)
−0.674340 + 0.738421i \(0.735572\pi\)
\(398\) −2.29685 3.60263i −0.115131 0.180584i
\(399\) 0 0
\(400\) −13.0308 15.1723i −0.651538 0.758616i
\(401\) 0.899990i 0.0449434i −0.999747 0.0224717i \(-0.992846\pi\)
0.999747 0.0224717i \(-0.00715356\pi\)
\(402\) 0 0
\(403\) 22.4611 22.4611i 1.11886 1.11886i
\(404\) −8.34578 + 17.9294i −0.415218 + 0.892019i
\(405\) 0 0
\(406\) 2.23371 + 0.494405i 0.110857 + 0.0245369i
\(407\) 0.754855 + 0.754855i 0.0374168 + 0.0374168i
\(408\) 0 0
\(409\) 24.1722i 1.19524i 0.801781 + 0.597618i \(0.203886\pi\)
−0.801781 + 0.597618i \(0.796114\pi\)
\(410\) 9.95072 + 15.4349i 0.491431 + 0.762277i
\(411\) 0 0
\(412\) −26.5807 + 9.69502i −1.30954 + 0.477639i
\(413\) 5.80277 + 5.80277i 0.285536 + 0.285536i
\(414\) 0 0
\(415\) −10.7538 10.6455i −0.527884 0.522568i
\(416\) 24.8430 12.9861i 1.21803 0.636695i
\(417\) 0 0
\(418\) 1.63094 1.03980i 0.0797720 0.0508584i
\(419\) 8.45513i 0.413060i −0.978440 0.206530i \(-0.933783\pi\)
0.978440 0.206530i \(-0.0662171\pi\)
\(420\) 0 0
\(421\) 13.8561i 0.675307i 0.941270 + 0.337654i \(0.109633\pi\)
−0.941270 + 0.337654i \(0.890367\pi\)
\(422\) 6.74925 + 10.5863i 0.328548 + 0.515331i
\(423\) 0 0
\(424\) 7.42783 9.70057i 0.360727 0.471102i
\(425\) 12.7925 + 12.5361i 0.620526 + 0.608090i
\(426\) 0 0
\(427\) −3.53872 3.53872i −0.171250 0.171250i
\(428\) −9.88694 27.1069i −0.477904 1.31026i
\(429\) 0 0
\(430\) −4.60471 + 21.3146i −0.222059 + 1.02788i
\(431\) 5.84351i 0.281472i 0.990047 + 0.140736i \(0.0449469\pi\)
−0.990047 + 0.140736i \(0.955053\pi\)
\(432\) 0 0
\(433\) 10.0632 + 10.0632i 0.483605 + 0.483605i 0.906281 0.422676i \(-0.138909\pi\)
−0.422676 + 0.906281i \(0.638909\pi\)
\(434\) −1.30758 + 5.90762i −0.0627660 + 0.283575i
\(435\) 0 0
\(436\) 9.29618 19.9711i 0.445206 0.956442i
\(437\) −25.2889 + 25.2889i −1.20973 + 1.20973i
\(438\) 0 0
\(439\) 34.0222i 1.62379i 0.583802 + 0.811896i \(0.301564\pi\)
−0.583802 + 0.811896i \(0.698436\pi\)
\(440\) 0.289876 + 2.10296i 0.0138193 + 0.100255i
\(441\) 0 0
\(442\) −21.1681 + 13.4957i −1.00687 + 0.641925i
\(443\) 6.45259 + 6.45259i 0.306572 + 0.306572i 0.843578 0.537006i \(-0.180445\pi\)
−0.537006 + 0.843578i \(0.680445\pi\)
\(444\) 0 0
\(445\) −18.6353 + 0.0943062i −0.883396 + 0.00447054i
\(446\) 19.4065 + 4.29540i 0.918923 + 0.203393i
\(447\) 0 0
\(448\) −2.66040 + 4.62970i −0.125692 + 0.218733i
\(449\) −5.72541 −0.270199 −0.135099 0.990832i \(-0.543135\pi\)
−0.135099 + 0.990832i \(0.543135\pi\)
\(450\) 0 0
\(451\) 1.94925i 0.0917866i
\(452\) −2.37807 6.51992i −0.111855 0.306671i
\(453\) 0 0
\(454\) 3.11819 14.0879i 0.146344 0.661177i
\(455\) 0.0374275 + 7.39582i 0.00175463 + 0.346721i
\(456\) 0 0
\(457\) 14.9718 14.9718i 0.700352 0.700352i −0.264134 0.964486i \(-0.585086\pi\)
0.964486 + 0.264134i \(0.0850862\pi\)
\(458\) 26.0779 16.6259i 1.21854 0.776878i
\(459\) 0 0
\(460\) −13.6364 36.8071i −0.635802 1.71614i
\(461\) 25.8187 1.20250 0.601249 0.799062i \(-0.294670\pi\)
0.601249 + 0.799062i \(0.294670\pi\)
\(462\) 0 0
\(463\) −20.5140 20.5140i −0.953368 0.953368i 0.0455925 0.998960i \(-0.485482\pi\)
−0.998960 + 0.0455925i \(0.985482\pi\)
\(464\) 7.41810 6.24171i 0.344377 0.289764i
\(465\) 0 0
\(466\) 2.93172 13.2454i 0.135810 0.613583i
\(467\) 3.07112 3.07112i 0.142114 0.142114i −0.632470 0.774585i \(-0.717959\pi\)
0.774585 + 0.632470i \(0.217959\pi\)
\(468\) 0 0
\(469\) 5.24368 0.242131
\(470\) −7.35582 1.58912i −0.339299 0.0733007i
\(471\) 0 0
\(472\) 34.4733 4.57422i 1.58676 0.210545i
\(473\) 1.63665 1.63665i 0.0752532 0.0752532i
\(474\) 0 0
\(475\) −20.3726 + 0.206202i −0.934761 + 0.00946120i
\(476\) 2.01798 4.33524i 0.0924938 0.198706i
\(477\) 0 0
\(478\) −5.52460 + 3.52219i −0.252689 + 0.161101i
\(479\) 33.2621 1.51979 0.759893 0.650049i \(-0.225252\pi\)
0.759893 + 0.650049i \(0.225252\pi\)
\(480\) 0 0
\(481\) 15.7607 0.718624
\(482\) −11.5927 + 7.39088i −0.528032 + 0.336645i
\(483\) 0 0
\(484\) −9.18898 + 19.7408i −0.417681 + 0.897309i
\(485\) 22.5513 22.7807i 1.02400 1.03442i
\(486\) 0 0
\(487\) 1.39322 1.39322i 0.0631329 0.0631329i −0.674835 0.737968i \(-0.735785\pi\)
0.737968 + 0.674835i \(0.235785\pi\)
\(488\) −21.0229 + 2.78950i −0.951663 + 0.126275i
\(489\) 0 0
\(490\) 11.2309 + 17.4207i 0.507362 + 0.786988i
\(491\) 14.4709 0.653061 0.326530 0.945187i \(-0.394120\pi\)
0.326530 + 0.945187i \(0.394120\pi\)
\(492\) 0 0
\(493\) −6.13913 + 6.13913i −0.276493 + 0.276493i
\(494\) 6.17121 27.8813i 0.277656 1.25444i
\(495\) 0 0
\(496\) 16.5078 + 19.6191i 0.741224 + 0.880924i
\(497\) −6.36174 6.36174i −0.285363 0.285363i
\(498\) 0 0
\(499\) 20.4107 0.913710 0.456855 0.889541i \(-0.348976\pi\)
0.456855 + 0.889541i \(0.348976\pi\)
\(500\) 9.12743 20.4130i 0.408191 0.912897i
\(501\) 0 0
\(502\) 36.5125 23.2784i 1.62963 1.03897i
\(503\) 2.54697 2.54697i 0.113564 0.113564i −0.648041 0.761605i \(-0.724412\pi\)
0.761605 + 0.648041i \(0.224412\pi\)
\(504\) 0 0
\(505\) −22.1106 + 0.111894i −0.983910 + 0.00497920i
\(506\) −0.900369 + 4.06784i −0.0400263 + 0.180837i
\(507\) 0 0
\(508\) −5.81828 15.9519i −0.258145 0.707751i
\(509\) 13.5045i 0.598575i −0.954163 0.299288i \(-0.903251\pi\)
0.954163 0.299288i \(-0.0967490\pi\)
\(510\) 0 0
\(511\) 4.76715 0.210886
\(512\) 8.72296 + 20.8785i 0.385504 + 0.922706i
\(513\) 0 0
\(514\) 3.19805 + 0.707852i 0.141060 + 0.0312220i
\(515\) −22.4809 22.2545i −0.990628 0.980652i
\(516\) 0 0
\(517\) 0.564820 + 0.564820i 0.0248407 + 0.0248407i
\(518\) −2.53141 + 1.61390i −0.111224 + 0.0709105i
\(519\) 0 0
\(520\) 24.9801 + 18.9278i 1.09545 + 0.830037i
\(521\) 13.5151i 0.592108i 0.955171 + 0.296054i \(0.0956708\pi\)
−0.955171 + 0.296054i \(0.904329\pi\)
\(522\) 0 0
\(523\) −12.6641 + 12.6641i −0.553760 + 0.553760i −0.927524 0.373764i \(-0.878067\pi\)
0.373764 + 0.927524i \(0.378067\pi\)
\(524\) −9.56640 + 20.5516i −0.417910 + 0.897802i
\(525\) 0 0
\(526\) −3.35875 + 15.1747i −0.146448 + 0.661649i
\(527\) −16.2365 16.2365i −0.707275 0.707275i
\(528\) 0 0
\(529\) 54.0356i 2.34938i
\(530\) 13.3519 + 2.88448i 0.579968 + 0.125294i
\(531\) 0 0
\(532\) 1.86386 + 5.11011i 0.0808086 + 0.221552i
\(533\) −20.3492 20.3492i −0.881423 0.881423i
\(534\) 0 0
\(535\) 22.6951 22.9260i 0.981195 0.991177i
\(536\) 13.5092 17.6427i 0.583507 0.762047i
\(537\) 0 0
\(538\) −12.2661 19.2396i −0.528831 0.829476i
\(539\) 2.20003i 0.0947619i
\(540\) 0 0
\(541\) 17.1804i 0.738644i −0.929301 0.369322i \(-0.879590\pi\)
0.929301 0.369322i \(-0.120410\pi\)
\(542\) 20.0902 12.8084i 0.862947 0.550170i
\(543\) 0 0
\(544\) −9.38732 17.9584i −0.402478 0.769960i
\(545\) 24.6285 0.124636i 1.05497 0.00533881i
\(546\) 0 0
\(547\) 17.4105 + 17.4105i 0.744417 + 0.744417i 0.973425 0.229007i \(-0.0735480\pi\)
−0.229007 + 0.973425i \(0.573548\pi\)
\(548\) 28.8758 10.5322i 1.23351 0.449911i
\(549\) 0 0
\(550\) −1.98827 + 1.29610i −0.0847801 + 0.0552661i
\(551\) 9.87584i 0.420725i
\(552\) 0 0
\(553\) 4.17924 + 4.17924i 0.177719 + 0.177719i
\(554\) −31.8699 7.05404i −1.35402 0.299698i
\(555\) 0 0
\(556\) −11.2617 + 24.1938i −0.477604 + 1.02604i
\(557\) 9.22732 9.22732i 0.390974 0.390974i −0.484060 0.875035i \(-0.660838\pi\)
0.875035 + 0.484060i \(0.160838\pi\)
\(558\) 0 0
\(559\) 34.1717i 1.44531i
\(560\) −5.95041 0.482130i −0.251451 0.0203737i
\(561\) 0 0
\(562\) −23.7884 37.3124i −1.00345 1.57393i
\(563\) −19.8727 19.8727i −0.837535 0.837535i 0.150999 0.988534i \(-0.451751\pi\)
−0.988534 + 0.150999i \(0.951751\pi\)
\(564\) 0 0
\(565\) 5.45877 5.51430i 0.229652 0.231988i
\(566\) −4.31159 + 19.4796i −0.181230 + 0.818790i
\(567\) 0 0
\(568\) −37.7940 + 5.01484i −1.58580 + 0.210418i
\(569\) 4.73031 0.198305 0.0991524 0.995072i \(-0.468387\pi\)
0.0991524 + 0.995072i \(0.468387\pi\)
\(570\) 0 0
\(571\) 5.54039i 0.231858i 0.993257 + 0.115929i \(0.0369845\pi\)
−0.993257 + 0.115929i \(0.963015\pi\)
\(572\) −1.13989 3.12523i −0.0476613 0.130672i
\(573\) 0 0
\(574\) 5.35218 + 1.18464i 0.223396 + 0.0494460i
\(575\) 30.7157 31.3438i 1.28093 1.30713i
\(576\) 0 0
\(577\) −12.9105 + 12.9105i −0.537472 + 0.537472i −0.922786 0.385314i \(-0.874093\pi\)
0.385314 + 0.922786i \(0.374093\pi\)
\(578\) −3.16873 4.97019i −0.131802 0.206733i
\(579\) 0 0
\(580\) 9.84960 + 4.52430i 0.408982 + 0.187861i
\(581\) −4.51677 −0.187387
\(582\) 0 0
\(583\) −1.02523 1.02523i −0.0424606 0.0424606i
\(584\) 12.2815 16.0394i 0.508212 0.663713i
\(585\) 0 0
\(586\) 10.2763 + 2.27455i 0.424512 + 0.0939609i
\(587\) −1.90309 + 1.90309i −0.0785487 + 0.0785487i −0.745290 0.666741i \(-0.767689\pi\)
0.666741 + 0.745290i \(0.267689\pi\)
\(588\) 0 0
\(589\) 26.1192 1.07622
\(590\) 21.0671 + 32.6779i 0.867317 + 1.34533i
\(591\) 0 0
\(592\) −1.09157 + 12.6749i −0.0448634 + 0.520936i
\(593\) −11.7312 + 11.7312i −0.481745 + 0.481745i −0.905688 0.423944i \(-0.860645\pi\)
0.423944 + 0.905688i \(0.360645\pi\)
\(594\) 0 0
\(595\) 5.34626 0.0270554i 0.219175 0.00110916i
\(596\) −24.6524 11.4752i −1.00980 0.470043i
\(597\) 0 0
\(598\) 33.0669 + 51.8657i 1.35220 + 2.12095i
\(599\) −2.61594 −0.106884 −0.0534422 0.998571i \(-0.517019\pi\)
−0.0534422 + 0.998571i \(0.517019\pi\)
\(600\) 0 0
\(601\) 20.1722 0.822840 0.411420 0.911446i \(-0.365033\pi\)
0.411420 + 0.911446i \(0.365033\pi\)
\(602\) 3.49919 + 5.48851i 0.142616 + 0.223695i
\(603\) 0 0
\(604\) −8.13865 + 17.4844i −0.331157 + 0.711429i
\(605\) −24.3445 + 0.123199i −0.989745 + 0.00500873i
\(606\) 0 0
\(607\) −17.3218 + 17.3218i −0.703069 + 0.703069i −0.965068 0.261999i \(-0.915618\pi\)
0.261999 + 0.965068i \(0.415618\pi\)
\(608\) 21.9951 + 6.89401i 0.892019 + 0.279589i
\(609\) 0 0
\(610\) −12.8474 19.9280i −0.520175 0.806862i
\(611\) 11.7929 0.477090
\(612\) 0 0
\(613\) 16.8299 16.8299i 0.679754 0.679754i −0.280191 0.959944i \(-0.590398\pi\)
0.959944 + 0.280191i \(0.0903977\pi\)
\(614\) 18.6406 + 4.12588i 0.752273 + 0.166507i
\(615\) 0 0
\(616\) 0.503109 + 0.385236i 0.0202708 + 0.0155216i
\(617\) 2.56139 + 2.56139i 0.103118 + 0.103118i 0.756783 0.653666i \(-0.226770\pi\)
−0.653666 + 0.756783i \(0.726770\pi\)
\(618\) 0 0
\(619\) −16.9662 −0.681931 −0.340965 0.940076i \(-0.610754\pi\)
−0.340965 + 0.940076i \(0.610754\pi\)
\(620\) −11.9657 + 26.0498i −0.480554 + 1.04619i
\(621\) 0 0
\(622\) 3.10633 + 4.87231i 0.124552 + 0.195362i
\(623\) −3.93336 + 3.93336i −0.157587 + 0.157587i
\(624\) 0 0
\(625\) 24.9949 0.506024i 0.999795 0.0202410i
\(626\) −28.1202 6.22409i −1.12391 0.248765i
\(627\) 0 0
\(628\) −20.2585 + 7.38909i −0.808404 + 0.294857i
\(629\) 11.3930i 0.454269i
\(630\) 0 0
\(631\) −39.5630 −1.57498 −0.787488 0.616330i \(-0.788619\pi\)
−0.787488 + 0.616330i \(0.788619\pi\)
\(632\) 24.8282 3.29442i 0.987612 0.131045i
\(633\) 0 0
\(634\) −5.22294 + 23.5971i −0.207429 + 0.937159i
\(635\) 13.3557 13.4915i 0.530003 0.535394i
\(636\) 0 0
\(637\) −22.9673 22.9673i −0.909996 0.909996i
\(638\) −0.618480 0.970092i −0.0244859 0.0384063i
\(639\) 0 0
\(640\) −16.9521 + 18.7784i −0.670089 + 0.742281i
\(641\) 47.3441i 1.86998i 0.354676 + 0.934989i \(0.384591\pi\)
−0.354676 + 0.934989i \(0.615409\pi\)
\(642\) 0 0
\(643\) 14.8250 14.8250i 0.584639 0.584639i −0.351535 0.936175i \(-0.614340\pi\)
0.936175 + 0.351535i \(0.114340\pi\)
\(644\) −10.6221 4.94440i −0.418570 0.194837i
\(645\) 0 0
\(646\) −20.1547 4.46102i −0.792977 0.175516i
\(647\) −4.86574 4.86574i −0.191292 0.191292i 0.604962 0.796254i \(-0.293188\pi\)
−0.796254 + 0.604962i \(0.793188\pi\)
\(648\) 0 0
\(649\) 4.12683i 0.161992i
\(650\) −7.22587 + 34.2873i −0.283422 + 1.34486i
\(651\) 0 0
\(652\) −15.7483 43.1768i −0.616750 1.69093i
\(653\) 11.8214 + 11.8214i 0.462609 + 0.462609i 0.899510 0.436901i \(-0.143924\pi\)
−0.436901 + 0.899510i \(0.643924\pi\)
\(654\) 0 0
\(655\) −25.3444 + 0.128259i −0.990289 + 0.00501149i
\(656\) 17.7745 14.9557i 0.693977 0.583924i
\(657\) 0 0
\(658\) −1.89413 + 1.20760i −0.0738408 + 0.0470770i
\(659\) 6.02230i 0.234595i 0.993097 + 0.117298i \(0.0374232\pi\)
−0.993097 + 0.117298i \(0.962577\pi\)
\(660\) 0 0
\(661\) 37.9790i 1.47721i −0.674137 0.738606i \(-0.735484\pi\)
0.674137 0.738606i \(-0.264516\pi\)
\(662\) 25.5538 + 40.0814i 0.993176 + 1.55781i
\(663\) 0 0
\(664\) −11.6365 + 15.1970i −0.451582 + 0.589756i
\(665\) −4.27842 + 4.32194i −0.165910 + 0.167598i
\(666\) 0 0
\(667\) 15.0420 + 15.0420i 0.582428 + 0.582428i
\(668\) 36.4214 13.2843i 1.40919 0.513986i
\(669\) 0 0
\(670\) 24.2833 + 5.24607i 0.938147 + 0.202673i
\(671\) 2.51667i 0.0971551i
\(672\) 0 0
\(673\) 7.99686 + 7.99686i 0.308256 + 0.308256i 0.844233 0.535977i \(-0.180057\pi\)
−0.535977 + 0.844233i \(0.680057\pi\)
\(674\) −8.73691 + 39.4731i −0.336533 + 1.52045i
\(675\) 0 0
\(676\) −20.9543 9.75386i −0.805936 0.375148i
\(677\) 7.11103 7.11103i 0.273299 0.273299i −0.557128 0.830427i \(-0.688097\pi\)
0.830427 + 0.557128i \(0.188097\pi\)
\(678\) 0 0
\(679\) 9.56827i 0.367197i
\(680\) 13.6824 18.0575i 0.524697 0.692474i
\(681\) 0 0
\(682\) 2.56566 1.63573i 0.0982443 0.0626354i
\(683\) 7.99061 + 7.99061i 0.305752 + 0.305752i 0.843259 0.537507i \(-0.180634\pi\)
−0.537507 + 0.843259i \(0.680634\pi\)
\(684\) 0 0
\(685\) 24.4221 + 24.1762i 0.933120 + 0.923723i
\(686\) 12.4921 + 2.76498i 0.476950 + 0.105568i
\(687\) 0 0
\(688\) 27.4813 + 2.36671i 1.04771 + 0.0902298i
\(689\) −21.4058 −0.815495
\(690\) 0 0
\(691\) 32.5931i 1.23990i −0.784641 0.619951i \(-0.787152\pi\)
0.784641 0.619951i \(-0.212848\pi\)
\(692\) −8.91962 + 3.25334i −0.339073 + 0.123673i
\(693\) 0 0
\(694\) −0.191542 + 0.865382i −0.00727085 + 0.0328495i
\(695\) −29.8359 + 0.150989i −1.13174 + 0.00572732i
\(696\) 0 0
\(697\) −14.7100 + 14.7100i −0.557180 + 0.557180i
\(698\) 12.9701 8.26907i 0.490927 0.312989i
\(699\) 0 0
\(700\) −2.35044 6.24701i −0.0888382 0.236115i
\(701\) −42.9064 −1.62055 −0.810277 0.586047i \(-0.800683\pi\)
−0.810277 + 0.586047i \(0.800683\pi\)
\(702\) 0 0
\(703\) 9.16379 + 9.16379i 0.345619 + 0.345619i
\(704\) 2.59229 0.700265i 0.0977008 0.0263922i
\(705\) 0 0
\(706\) 4.34105 19.6127i 0.163378 0.738135i
\(707\) −4.66691 + 4.66691i −0.175517 + 0.175517i
\(708\) 0 0
\(709\) 10.3299 0.387949 0.193975 0.981007i \(-0.437862\pi\)
0.193975 + 0.981007i \(0.437862\pi\)
\(710\) −23.0964 35.8257i −0.866792 1.34451i
\(711\) 0 0
\(712\) 3.10059 + 23.3674i 0.116200 + 0.875732i
\(713\) −39.7825 + 39.7825i −1.48986 + 1.48986i
\(714\) 0 0
\(715\) 2.61658 2.64320i 0.0978545 0.0988500i
\(716\) −19.4986 9.07622i −0.728696 0.339194i
\(717\) 0 0
\(718\) −23.4589 + 14.9562i −0.875480 + 0.558160i
\(719\) 6.49219 0.242118 0.121059 0.992645i \(-0.461371\pi\)
0.121059 + 0.992645i \(0.461371\pi\)
\(720\) 0 0
\(721\) −9.44235 −0.351652
\(722\) −2.85778 + 1.82197i −0.106356 + 0.0678067i
\(723\) 0 0
\(724\) −18.3658 8.54893i −0.682559 0.317719i
\(725\) 0.122650 + 12.1177i 0.00455511 + 0.450042i
\(726\) 0 0
\(727\) −11.0479 + 11.0479i −0.409744 + 0.409744i −0.881649 0.471905i \(-0.843566\pi\)
0.471905 + 0.881649i \(0.343566\pi\)
\(728\) 9.27389 1.23054i 0.343713 0.0456068i
\(729\) 0 0
\(730\) 22.0765 + 4.76933i 0.817090 + 0.176521i
\(731\) −24.7019 −0.913631
\(732\) 0 0
\(733\) 19.5376 19.5376i 0.721636 0.721636i −0.247302 0.968938i \(-0.579544\pi\)
0.968938 + 0.247302i \(0.0795441\pi\)
\(734\) −4.26167 + 19.2541i −0.157301 + 0.710682i
\(735\) 0 0
\(736\) −44.0013 + 23.0006i −1.62191 + 0.847814i
\(737\) −1.86461 1.86461i −0.0686837 0.0686837i
\(738\) 0 0
\(739\) 24.8980 0.915890 0.457945 0.888981i \(-0.348586\pi\)
0.457945 + 0.888981i \(0.348586\pi\)
\(740\) −13.3375 + 4.94134i −0.490298 + 0.181647i
\(741\) 0 0
\(742\) 3.43811 2.19196i 0.126217 0.0804693i
\(743\) 15.8961 15.8961i 0.583171 0.583171i −0.352602 0.935773i \(-0.614703\pi\)
0.935773 + 0.352602i \(0.114703\pi\)
\(744\) 0 0
\(745\) −0.153851 30.4015i −0.00563665 1.11382i
\(746\) −5.46866 + 24.7072i −0.200222 + 0.904595i
\(747\) 0 0
\(748\) −2.25915 + 0.824000i −0.0826027 + 0.0301284i
\(749\) 9.62928i 0.351846i
\(750\) 0 0
\(751\) 11.5535 0.421594 0.210797 0.977530i \(-0.432394\pi\)
0.210797 + 0.977530i \(0.432394\pi\)
\(752\) −0.816768 + 9.48400i −0.0297845 + 0.345846i
\(753\) 0 0
\(754\) −16.5839 3.67066i −0.603951 0.133678i
\(755\) −21.5619 + 0.109117i −0.784717 + 0.00397116i
\(756\) 0 0
\(757\) 18.8612 + 18.8612i 0.685524 + 0.685524i 0.961239 0.275716i \(-0.0889148\pi\)
−0.275716 + 0.961239i \(0.588915\pi\)
\(758\) −45.2637 + 28.8577i −1.64405 + 1.04816i
\(759\) 0 0
\(760\) 3.51904 + 25.5295i 0.127649 + 0.926053i
\(761\) 33.0567i 1.19830i 0.800636 + 0.599151i \(0.204495\pi\)
−0.800636 + 0.599151i \(0.795505\pi\)
\(762\) 0 0
\(763\) 5.19836 5.19836i 0.188193 0.188193i
\(764\) 7.83650 + 3.64774i 0.283515 + 0.131971i
\(765\) 0 0
\(766\) −3.96913 + 17.9324i −0.143411 + 0.647924i
\(767\) −43.0821 43.0821i −1.55561 1.55561i
\(768\) 0 0
\(769\) 44.9240i 1.62000i 0.586429 + 0.810001i \(0.300533\pi\)
−0.586429 + 0.810001i \(0.699467\pi\)
\(770\) −0.149600 + 0.692478i −0.00539121 + 0.0249552i
\(771\) 0 0
\(772\) −21.1890 + 7.72845i −0.762608 + 0.278153i
\(773\) 28.3672 + 28.3672i 1.02030 + 1.02030i 0.999790 + 0.0205060i \(0.00652772\pi\)
0.0205060 + 0.999790i \(0.493472\pi\)
\(774\) 0 0
\(775\) −32.0486 + 0.324380i −1.15122 + 0.0116521i
\(776\) −32.1930 24.6505i −1.15566 0.884902i
\(777\) 0 0
\(778\) 3.21026 + 5.03533i 0.115093 + 0.180525i
\(779\) 23.6635i 0.847832i
\(780\) 0 0
\(781\) 4.52436i 0.161894i
\(782\) 37.4925 23.9032i 1.34073 0.854778i
\(783\) 0 0
\(784\) 20.0613 16.8799i 0.716474 0.602852i
\(785\) −17.1339 16.9614i −0.611536 0.605377i
\(786\) 0 0
\(787\) −4.79302 4.79302i −0.170853 0.170853i 0.616501 0.787354i \(-0.288550\pi\)
−0.787354 + 0.616501i \(0.788550\pi\)
\(788\) −4.16949 11.4314i −0.148532 0.407228i
\(789\) 0 0
\(790\) 15.1728 + 23.5351i 0.539824 + 0.837341i
\(791\) 2.31610i 0.0823509i
\(792\) 0 0
\(793\) 26.2729 + 26.2729i 0.932977 + 0.932977i
\(794\) 2.49323 + 0.551849i 0.0884815 + 0.0195844i
\(795\) 0 0
\(796\) −5.47788 2.54985i −0.194158 0.0903771i
\(797\) −7.30136 + 7.30136i −0.258627 + 0.258627i −0.824496 0.565868i \(-0.808541\pi\)
0.565868 + 0.824496i \(0.308541\pi\)
\(798\) 0 0
\(799\) 8.52480i 0.301586i
\(800\) −27.0738 8.18585i −0.957204 0.289414i
\(801\) 0 0
\(802\) −0.684228 1.07322i −0.0241609 0.0378966i
\(803\) −1.69516 1.69516i −0.0598208 0.0598208i
\(804\) 0 0
\(805\) −0.0662907 13.0993i −0.00233644 0.461689i
\(806\) 9.70804 43.8606i 0.341951 1.54492i
\(807\) 0 0
\(808\) 3.67884 + 27.7253i 0.129421 + 0.975373i
\(809\) 26.9078 0.946026 0.473013 0.881055i \(-0.343166\pi\)
0.473013 + 0.881055i \(0.343166\pi\)
\(810\) 0 0
\(811\) 4.38227i 0.153882i 0.997036 + 0.0769412i \(0.0245154\pi\)
−0.997036 + 0.0769412i \(0.975485\pi\)
\(812\) 3.03952 1.10863i 0.106666 0.0389054i
\(813\) 0 0
\(814\) 1.47404 + 0.326261i 0.0516649 + 0.0114354i
\(815\) 36.1495 36.5173i 1.26626 1.27914i
\(816\) 0 0
\(817\) 19.8686 19.8686i 0.695113 0.695113i
\(818\) 18.3772 + 28.8248i 0.642542 + 1.00783i
\(819\) 0 0
\(820\) 23.6006 + 10.8407i 0.824169 + 0.378573i
\(821\) 34.5890 1.20716 0.603582 0.797301i \(-0.293739\pi\)
0.603582 + 0.797301i \(0.293739\pi\)
\(822\) 0 0
\(823\) −5.63496 5.63496i −0.196422 0.196422i 0.602042 0.798464i \(-0.294354\pi\)
−0.798464 + 0.602042i \(0.794354\pi\)
\(824\) −24.3261 + 31.7694i −0.847441 + 1.10674i
\(825\) 0 0
\(826\) 11.3313 + 2.50805i 0.394266 + 0.0872663i
\(827\) −29.8906 + 29.8906i −1.03940 + 1.03940i −0.0402073 + 0.999191i \(0.512802\pi\)
−0.999191 + 0.0402073i \(0.987198\pi\)
\(828\) 0 0
\(829\) −45.0207 −1.56363 −0.781817 0.623508i \(-0.785707\pi\)
−0.781817 + 0.623508i \(0.785707\pi\)
\(830\) −20.9171 4.51884i −0.726042 0.156851i
\(831\) 0 0
\(832\) 19.7519 34.3728i 0.684774 1.19166i
\(833\) −16.6025 + 16.6025i −0.575241 + 0.575241i
\(834\) 0 0
\(835\) 30.8039 + 30.4937i 1.06601 + 1.05528i
\(836\) 1.15434 2.47988i 0.0399237 0.0857686i
\(837\) 0 0
\(838\) −6.42811 10.0826i −0.222055 0.348296i
\(839\) 6.14853 0.212271 0.106135 0.994352i \(-0.466152\pi\)
0.106135 + 0.994352i \(0.466152\pi\)
\(840\) 0 0
\(841\) 23.1258 0.797442
\(842\) 10.5343 + 16.5231i 0.363036 + 0.569425i
\(843\) 0 0
\(844\) 16.0966 + 7.49269i 0.554070 + 0.257909i
\(845\) −0.130772 25.8411i −0.00449870 0.888960i
\(846\) 0 0
\(847\) −5.13842 + 5.13842i −0.176558 + 0.176558i
\(848\) 1.48255 17.2148i 0.0509110 0.591159i
\(849\) 0 0
\(850\) 24.7854 + 5.22341i 0.850134 + 0.179161i
\(851\) −27.9149 −0.956910
\(852\) 0 0
\(853\) −11.5962 + 11.5962i −0.397046 + 0.397046i −0.877190 0.480144i \(-0.840585\pi\)
0.480144 + 0.877190i \(0.340585\pi\)
\(854\) −6.91019 1.52949i −0.236462 0.0523381i
\(855\) 0 0
\(856\) −32.3983 24.8077i −1.10735 0.847909i
\(857\) −23.8521 23.8521i −0.814772 0.814772i 0.170573 0.985345i \(-0.445438\pi\)
−0.985345 + 0.170573i \(0.945438\pi\)
\(858\) 0 0
\(859\) −31.3817 −1.07073 −0.535365 0.844621i \(-0.679826\pi\)
−0.535365 + 0.844621i \(0.679826\pi\)
\(860\) 10.7136 + 28.9179i 0.365331 + 0.986093i
\(861\) 0 0
\(862\) 4.44259 + 6.96825i 0.151315 + 0.237340i
\(863\) −12.4212 + 12.4212i −0.422823 + 0.422823i −0.886175 0.463351i \(-0.846647\pi\)
0.463351 + 0.886175i \(0.346647\pi\)
\(864\) 0 0
\(865\) −7.54388 7.46791i −0.256500 0.253917i
\(866\) 19.6507 + 4.34946i 0.667759 + 0.147801i
\(867\) 0 0
\(868\) 2.93207 + 8.03881i 0.0995209 + 0.272855i
\(869\) 2.97220i 0.100825i
\(870\) 0 0
\(871\) −38.9312 −1.31913
\(872\) −4.09777 30.8826i −0.138768 1.04582i
\(873\) 0 0
\(874\) −10.9303 + 49.3827i −0.369723 + 1.67039i
\(875\) 5.19599 5.35620i 0.175656 0.181073i
\(876\) 0 0
\(877\) 38.0074 + 38.0074i 1.28342 + 1.28342i 0.938710 + 0.344708i \(0.112022\pi\)
0.344708 + 0.938710i \(0.387978\pi\)
\(878\) 25.8658 + 40.5707i 0.872928 + 1.36920i
\(879\) 0 0
\(880\) 1.94447 + 2.28735i 0.0655481 + 0.0771067i
\(881\) 10.9118i 0.367626i 0.982961 + 0.183813i \(0.0588442\pi\)
−0.982961 + 0.183813i \(0.941156\pi\)
\(882\) 0 0
\(883\) 1.85770 1.85770i 0.0625165 0.0625165i −0.675157 0.737674i \(-0.735924\pi\)
0.737674 + 0.675157i \(0.235924\pi\)
\(884\) −14.9823 + 32.1866i −0.503908 + 1.08255i
\(885\) 0 0
\(886\) 12.6002 + 2.78891i 0.423313 + 0.0936954i
\(887\) 3.17163 + 3.17163i 0.106493 + 0.106493i 0.758346 0.651853i \(-0.226008\pi\)
−0.651853 + 0.758346i \(0.726008\pi\)
\(888\) 0 0
\(889\) 5.66665i 0.190053i
\(890\) −22.1504 + 14.2801i −0.742484 + 0.478671i
\(891\) 0 0
\(892\) 26.4074 9.63182i 0.884185 0.322497i
\(893\) 6.85679 + 6.85679i 0.229454 + 0.229454i
\(894\) 0 0
\(895\) −0.121687 24.0458i −0.00406754 0.803762i
\(896\) 0.347313 + 7.54341i 0.0116029 + 0.252008i
\(897\) 0 0
\(898\) −6.82743 + 4.35281i −0.227834 + 0.145255i
\(899\) 15.5358i 0.518150i
\(900\) 0 0
\(901\) 15.4737i 0.515504i
\(902\) −1.48194 2.32444i −0.0493432 0.0773953i
\(903\) 0 0
\(904\) −7.79264 5.96690i −0.259179 0.198456i
\(905\) −0.114617 22.6488i −0.00381001 0.752873i
\(906\) 0 0
\(907\) −5.88501 5.88501i −0.195408 0.195408i 0.602620 0.798028i \(-0.294124\pi\)
−0.798028 + 0.602620i \(0.794124\pi\)
\(908\) −6.99209 19.1701i −0.232041 0.636183i
\(909\) 0 0
\(910\) 5.66739 + 8.79089i 0.187872 + 0.291415i
\(911\) 10.3886i 0.344188i 0.985080 + 0.172094i \(0.0550534\pi\)
−0.985080 + 0.172094i \(0.944947\pi\)
\(912\) 0 0
\(913\) 1.60613 + 1.60613i 0.0531550 + 0.0531550i
\(914\) 6.47106 29.2360i 0.214044 0.967042i
\(915\) 0 0
\(916\) 18.4573 39.6521i 0.609846 1.31014i
\(917\) −5.34947 + 5.34947i −0.176655 + 0.176655i
\(918\) 0 0
\(919\) 14.5186i 0.478924i −0.970906 0.239462i \(-0.923029\pi\)
0.970906 0.239462i \(-0.0769710\pi\)
\(920\) −44.2441 33.5244i −1.45869 1.10527i
\(921\) 0 0
\(922\) 30.7883 19.6290i 1.01396 0.646446i
\(923\) 47.2321 + 47.2321i 1.55466 + 1.55466i
\(924\) 0 0
\(925\) −11.3579 11.1302i −0.373444 0.365960i
\(926\) −40.0585 8.86650i −1.31641 0.291371i
\(927\) 0 0
\(928\) 4.10059 13.0828i 0.134608 0.429464i
\(929\) 44.3689 1.45570 0.727848 0.685738i \(-0.240520\pi\)
0.727848 + 0.685738i \(0.240520\pi\)
\(930\) 0 0
\(931\) 26.7079i 0.875316i
\(932\) −6.57397 18.0238i −0.215338 0.590388i
\(933\) 0 0
\(934\) 1.32739 5.99709i 0.0434335 0.196231i
\(935\) −1.91070 1.89146i −0.0624867 0.0618574i
\(936\) 0 0
\(937\) −2.66665 + 2.66665i −0.0871157 + 0.0871157i −0.749322 0.662206i \(-0.769620\pi\)
0.662206 + 0.749322i \(0.269620\pi\)
\(938\) 6.25297 3.98657i 0.204167 0.130166i
\(939\) 0 0
\(940\) −9.97980 + 3.69735i −0.325505 + 0.120594i
\(941\) 41.4675 1.35180 0.675901 0.736992i \(-0.263755\pi\)
0.675901 + 0.736992i \(0.263755\pi\)
\(942\) 0 0
\(943\) 36.0421 + 36.0421i 1.17369 + 1.17369i
\(944\) 37.6311 31.6634i 1.22479 1.03056i
\(945\) 0 0
\(946\) 0.707386 3.19595i 0.0229991 0.103909i
\(947\) 34.3858 34.3858i 1.11739 1.11739i 0.125264 0.992123i \(-0.460022\pi\)
0.992123 0.125264i \(-0.0399779\pi\)
\(948\) 0 0
\(949\) −35.3933 −1.14891
\(950\) −24.1372 + 15.7344i −0.783113 + 0.510492i
\(951\) 0 0
\(952\) −0.889527 6.70387i −0.0288298 0.217274i
\(953\) 5.82947 5.82947i 0.188835 0.188835i −0.606357 0.795192i \(-0.707370\pi\)
0.795192 + 0.606357i \(0.207370\pi\)
\(954\) 0 0
\(955\) 0.0489061 + 9.66403i 0.00158256 + 0.312721i
\(956\) −3.91017 + 8.40027i −0.126464 + 0.271684i
\(957\) 0 0
\(958\) 39.6643 25.2879i 1.28150 0.817015i
\(959\) 10.2577 0.331237
\(960\) 0 0
\(961\) 10.0886 0.325439
\(962\) 18.7942 11.9822i 0.605951 0.386322i
\(963\) 0 0
\(964\) −8.20501 + 17.6269i −0.264265 + 0.567725i
\(965\) −17.9208 17.7404i −0.576892 0.571083i
\(966\) 0 0
\(967\) 18.1550 18.1550i 0.583826 0.583826i −0.352126 0.935952i \(-0.614541\pi\)
0.935952 + 0.352126i \(0.114541\pi\)
\(968\) 4.05052 + 30.5265i 0.130189 + 0.981158i
\(969\) 0 0
\(970\) 9.57264 44.3104i 0.307359 1.42272i
\(971\) −6.87264 −0.220554 −0.110277 0.993901i \(-0.535174\pi\)
−0.110277 + 0.993901i \(0.535174\pi\)
\(972\) 0 0
\(973\) −6.29749 + 6.29749i −0.201888 + 0.201888i
\(974\) 0.602173 2.72060i 0.0192949 0.0871735i
\(975\) 0 0
\(976\) −22.9486 + 19.3093i −0.734567 + 0.618077i
\(977\) 14.8533 + 14.8533i 0.475200 + 0.475200i 0.903593 0.428393i \(-0.140920\pi\)
−0.428393 + 0.903593i \(0.640920\pi\)
\(978\) 0 0
\(979\) 2.79734 0.0894033
\(980\) 26.6369 + 12.2354i 0.850885 + 0.390845i
\(981\) 0 0
\(982\) 17.2562 11.0016i 0.550667 0.351076i
\(983\) 21.3770 21.3770i 0.681822 0.681822i −0.278589 0.960410i \(-0.589867\pi\)
0.960410 + 0.278589i \(0.0898667\pi\)
\(984\) 0 0
\(985\) 9.57090 9.66827i 0.304954 0.308057i
\(986\) −2.65343 + 11.9881i −0.0845026 + 0.381780i
\(987\) 0 0
\(988\) −13.8381 37.9396i −0.440247 1.20702i
\(989\) 60.5240i 1.92455i
\(990\) 0 0
\(991\) 27.1515 0.862497 0.431249 0.902233i \(-0.358073\pi\)
0.431249 + 0.902233i \(0.358073\pi\)
\(992\) 34.6009 + 10.8451i 1.09858 + 0.344332i
\(993\) 0 0
\(994\) −12.4228 2.74965i −0.394028 0.0872135i
\(995\) −0.0341864 6.75537i −0.00108378 0.214160i
\(996\) 0 0
\(997\) 16.8850 + 16.8850i 0.534754 + 0.534754i 0.921983 0.387230i \(-0.126568\pi\)
−0.387230 + 0.921983i \(0.626568\pi\)
\(998\) 24.3393 15.5175i 0.770448 0.491198i
\(999\) 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 360.2.x.a.53.20 yes 48
3.2 odd 2 inner 360.2.x.a.53.5 48
4.3 odd 2 1440.2.bj.a.593.23 48
5.2 odd 4 inner 360.2.x.a.197.17 yes 48
8.3 odd 2 1440.2.bj.a.593.1 48
8.5 even 2 inner 360.2.x.a.53.8 yes 48
12.11 even 2 1440.2.bj.a.593.2 48
15.2 even 4 inner 360.2.x.a.197.8 yes 48
20.7 even 4 1440.2.bj.a.17.24 48
24.5 odd 2 inner 360.2.x.a.53.17 yes 48
24.11 even 2 1440.2.bj.a.593.24 48
40.27 even 4 1440.2.bj.a.17.2 48
40.37 odd 4 inner 360.2.x.a.197.5 yes 48
60.47 odd 4 1440.2.bj.a.17.1 48
120.77 even 4 inner 360.2.x.a.197.20 yes 48
120.107 odd 4 1440.2.bj.a.17.23 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.x.a.53.5 48 3.2 odd 2 inner
360.2.x.a.53.8 yes 48 8.5 even 2 inner
360.2.x.a.53.17 yes 48 24.5 odd 2 inner
360.2.x.a.53.20 yes 48 1.1 even 1 trivial
360.2.x.a.197.5 yes 48 40.37 odd 4 inner
360.2.x.a.197.8 yes 48 15.2 even 4 inner
360.2.x.a.197.17 yes 48 5.2 odd 4 inner
360.2.x.a.197.20 yes 48 120.77 even 4 inner
1440.2.bj.a.17.1 48 60.47 odd 4
1440.2.bj.a.17.2 48 40.27 even 4
1440.2.bj.a.17.23 48 120.107 odd 4
1440.2.bj.a.17.24 48 20.7 even 4
1440.2.bj.a.593.1 48 8.3 odd 2
1440.2.bj.a.593.2 48 12.11 even 2
1440.2.bj.a.593.23 48 4.3 odd 2
1440.2.bj.a.593.24 48 24.11 even 2