Properties

Label 648.2.v.b.35.18
Level $648$
Weight $2$
Character 648.35
Analytic conductor $5.174$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [648,2,Mod(35,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.v (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 35.18
Character \(\chi\) \(=\) 648.35
Dual form 648.2.v.b.611.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.315008 - 1.37868i) q^{2} +(-1.80154 - 0.868594i) q^{4} +(0.437371 + 0.159190i) q^{5} +(-3.46177 - 0.610403i) q^{7} +(-1.76502 + 2.21014i) q^{8} +O(q^{10})\) \(q+(0.315008 - 1.37868i) q^{2} +(-1.80154 - 0.868594i) q^{4} +(0.437371 + 0.159190i) q^{5} +(-3.46177 - 0.610403i) q^{7} +(-1.76502 + 2.21014i) q^{8} +(0.357248 - 0.552850i) q^{10} +(-0.485871 - 1.33492i) q^{11} +(-1.62110 - 1.93196i) q^{13} +(-1.93204 + 4.58040i) q^{14} +(2.49109 + 3.12961i) q^{16} +(0.667069 - 0.385133i) q^{17} +(-3.66125 + 6.34147i) q^{19} +(-0.649669 - 0.666685i) q^{20} +(-1.99349 + 0.249352i) q^{22} +(1.25561 + 7.12090i) q^{23} +(-3.66427 - 3.07469i) q^{25} +(-3.17422 + 1.62641i) q^{26} +(5.70632 + 4.10653i) q^{28} +(-3.15733 - 2.64931i) q^{29} +(-7.80121 + 1.37556i) q^{31} +(5.09946 - 2.44857i) q^{32} +(-0.320844 - 1.04100i) q^{34} +(-1.41691 - 0.818051i) q^{35} +(-2.79436 + 1.61333i) q^{37} +(7.58956 + 7.04532i) q^{38} +(-1.12380 + 0.685678i) q^{40} +(-1.74280 - 2.07699i) q^{41} +(-1.99564 + 0.726352i) q^{43} +(-0.284188 + 2.82694i) q^{44} +(10.2130 + 0.512058i) q^{46} +(1.82437 - 10.3465i) q^{47} +(5.03339 + 1.83200i) q^{49} +(-5.39330 + 4.08332i) q^{50} +(1.24240 + 4.88858i) q^{52} +8.73592 q^{53} -0.661201i q^{55} +(7.45915 - 6.57361i) q^{56} +(-4.64715 + 3.51840i) q^{58} +(-0.818263 + 2.24816i) q^{59} +(3.02492 + 0.533375i) q^{61} +(-0.560979 + 11.1887i) q^{62} +(-1.76943 - 7.80187i) q^{64} +(-0.401476 - 1.10305i) q^{65} +(-4.04105 + 3.39085i) q^{67} +(-1.53628 + 0.114419i) q^{68} +(-1.57417 + 1.69577i) q^{70} +(-5.70758 - 9.88583i) q^{71} +(2.96144 - 5.12936i) q^{73} +(1.34402 + 4.36075i) q^{74} +(12.1041 - 8.24427i) q^{76} +(0.867134 + 4.91776i) q^{77} +(8.94667 - 10.6622i) q^{79} +(0.591327 + 1.76536i) q^{80} +(-3.41251 + 1.74850i) q^{82} +(-7.41209 + 8.83338i) q^{83} +(0.353066 - 0.0622550i) q^{85} +(0.372768 + 2.98016i) q^{86} +(3.80793 + 1.28231i) q^{88} +(-8.59338 - 4.96139i) q^{89} +(4.43261 + 7.67751i) q^{91} +(3.92315 - 13.9192i) q^{92} +(-13.6899 - 5.77446i) q^{94} +(-2.61082 + 2.19074i) q^{95} +(-1.95198 + 0.710462i) q^{97} +(4.11131 - 6.36235i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.315008 1.37868i 0.222745 0.974877i
\(3\) 0 0
\(4\) −1.80154 0.868594i −0.900770 0.434297i
\(5\) 0.437371 + 0.159190i 0.195598 + 0.0711919i 0.437962 0.898994i \(-0.355700\pi\)
−0.242364 + 0.970185i \(0.577923\pi\)
\(6\) 0 0
\(7\) −3.46177 0.610403i −1.30842 0.230711i −0.524417 0.851462i \(-0.675717\pi\)
−0.784008 + 0.620751i \(0.786828\pi\)
\(8\) −1.76502 + 2.21014i −0.624028 + 0.781402i
\(9\) 0 0
\(10\) 0.357248 0.552850i 0.112972 0.174827i
\(11\) −0.485871 1.33492i −0.146496 0.402494i 0.844642 0.535331i \(-0.179813\pi\)
−0.991138 + 0.132838i \(0.957591\pi\)
\(12\) 0 0
\(13\) −1.62110 1.93196i −0.449614 0.535829i 0.492860 0.870108i \(-0.335951\pi\)
−0.942474 + 0.334280i \(0.891507\pi\)
\(14\) −1.93204 + 4.58040i −0.516359 + 1.22416i
\(15\) 0 0
\(16\) 2.49109 + 3.12961i 0.622772 + 0.782403i
\(17\) 0.667069 0.385133i 0.161788 0.0934084i −0.416920 0.908943i \(-0.636890\pi\)
0.578708 + 0.815535i \(0.303557\pi\)
\(18\) 0 0
\(19\) −3.66125 + 6.34147i −0.839948 + 1.45483i 0.0499885 + 0.998750i \(0.484082\pi\)
−0.889937 + 0.456084i \(0.849252\pi\)
\(20\) −0.649669 0.666685i −0.145271 0.149075i
\(21\) 0 0
\(22\) −1.99349 + 0.249352i −0.425013 + 0.0531620i
\(23\) 1.25561 + 7.12090i 0.261812 + 1.48481i 0.777961 + 0.628312i \(0.216254\pi\)
−0.516149 + 0.856499i \(0.672635\pi\)
\(24\) 0 0
\(25\) −3.66427 3.07469i −0.732854 0.614938i
\(26\) −3.17422 + 1.62641i −0.622516 + 0.318965i
\(27\) 0 0
\(28\) 5.70632 + 4.10653i 1.07839 + 0.776062i
\(29\) −3.15733 2.64931i −0.586301 0.491965i 0.300709 0.953716i \(-0.402777\pi\)
−0.887010 + 0.461751i \(0.847221\pi\)
\(30\) 0 0
\(31\) −7.80121 + 1.37556i −1.40114 + 0.247059i −0.822611 0.568604i \(-0.807484\pi\)
−0.578528 + 0.815663i \(0.696373\pi\)
\(32\) 5.09946 2.44857i 0.901466 0.432850i
\(33\) 0 0
\(34\) −0.320844 1.04100i −0.0550242 0.178530i
\(35\) −1.41691 0.818051i −0.239501 0.138276i
\(36\) 0 0
\(37\) −2.79436 + 1.61333i −0.459390 + 0.265229i −0.711788 0.702394i \(-0.752114\pi\)
0.252397 + 0.967624i \(0.418781\pi\)
\(38\) 7.58956 + 7.04532i 1.23119 + 1.14290i
\(39\) 0 0
\(40\) −1.12380 + 0.685678i −0.177688 + 0.108415i
\(41\) −1.74280 2.07699i −0.272180 0.324371i 0.612589 0.790402i \(-0.290128\pi\)
−0.884769 + 0.466031i \(0.845684\pi\)
\(42\) 0 0
\(43\) −1.99564 + 0.726352i −0.304332 + 0.110768i −0.489672 0.871907i \(-0.662883\pi\)
0.185340 + 0.982674i \(0.440661\pi\)
\(44\) −0.284188 + 2.82694i −0.0428429 + 0.426177i
\(45\) 0 0
\(46\) 10.2130 + 0.512058i 1.50583 + 0.0754989i
\(47\) 1.82437 10.3465i 0.266111 1.50919i −0.499741 0.866175i \(-0.666572\pi\)
0.765852 0.643017i \(-0.222317\pi\)
\(48\) 0 0
\(49\) 5.03339 + 1.83200i 0.719055 + 0.261715i
\(50\) −5.39330 + 4.08332i −0.762728 + 0.577468i
\(51\) 0 0
\(52\) 1.24240 + 4.88858i 0.172290 + 0.677924i
\(53\) 8.73592 1.19997 0.599986 0.800011i \(-0.295173\pi\)
0.599986 + 0.800011i \(0.295173\pi\)
\(54\) 0 0
\(55\) 0.661201i 0.0891564i
\(56\) 7.45915 6.57361i 0.996771 0.878436i
\(57\) 0 0
\(58\) −4.64715 + 3.51840i −0.610201 + 0.461989i
\(59\) −0.818263 + 2.24816i −0.106529 + 0.292685i −0.981492 0.191504i \(-0.938663\pi\)
0.874963 + 0.484190i \(0.160886\pi\)
\(60\) 0 0
\(61\) 3.02492 + 0.533375i 0.387301 + 0.0682916i 0.363908 0.931435i \(-0.381442\pi\)
0.0233926 + 0.999726i \(0.492553\pi\)
\(62\) −0.560979 + 11.1887i −0.0712444 + 1.42097i
\(63\) 0 0
\(64\) −1.76943 7.80187i −0.221179 0.975233i
\(65\) −0.401476 1.10305i −0.0497969 0.136816i
\(66\) 0 0
\(67\) −4.04105 + 3.39085i −0.493693 + 0.414258i −0.855348 0.518054i \(-0.826657\pi\)
0.361654 + 0.932312i \(0.382212\pi\)
\(68\) −1.53628 + 0.114419i −0.186301 + 0.0138754i
\(69\) 0 0
\(70\) −1.57417 + 1.69577i −0.188149 + 0.202684i
\(71\) −5.70758 9.88583i −0.677366 1.17323i −0.975771 0.218793i \(-0.929788\pi\)
0.298406 0.954439i \(-0.403545\pi\)
\(72\) 0 0
\(73\) 2.96144 5.12936i 0.346610 0.600346i −0.639035 0.769178i \(-0.720666\pi\)
0.985645 + 0.168832i \(0.0539994\pi\)
\(74\) 1.34402 + 4.36075i 0.156239 + 0.506927i
\(75\) 0 0
\(76\) 12.1041 8.24427i 1.38843 0.945683i
\(77\) 0.867134 + 4.91776i 0.0988191 + 0.560431i
\(78\) 0 0
\(79\) 8.94667 10.6622i 1.00658 1.19959i 0.0267740 0.999642i \(-0.491477\pi\)
0.979805 0.199953i \(-0.0640790\pi\)
\(80\) 0.591327 + 1.76536i 0.0661123 + 0.197373i
\(81\) 0 0
\(82\) −3.41251 + 1.74850i −0.376848 + 0.193090i
\(83\) −7.41209 + 8.83338i −0.813582 + 0.969590i −0.999917 0.0128968i \(-0.995895\pi\)
0.186335 + 0.982486i \(0.440339\pi\)
\(84\) 0 0
\(85\) 0.353066 0.0622550i 0.0382954 0.00675251i
\(86\) 0.372768 + 2.98016i 0.0401966 + 0.321359i
\(87\) 0 0
\(88\) 3.80793 + 1.28231i 0.405927 + 0.136695i
\(89\) −8.59338 4.96139i −0.910896 0.525906i −0.0301767 0.999545i \(-0.509607\pi\)
−0.880719 + 0.473639i \(0.842940\pi\)
\(90\) 0 0
\(91\) 4.43261 + 7.67751i 0.464664 + 0.804822i
\(92\) 3.92315 13.9192i 0.409016 1.45118i
\(93\) 0 0
\(94\) −13.6899 5.77446i −1.41200 0.595590i
\(95\) −2.61082 + 2.19074i −0.267865 + 0.224765i
\(96\) 0 0
\(97\) −1.95198 + 0.710462i −0.198193 + 0.0721365i −0.439210 0.898385i \(-0.644741\pi\)
0.241016 + 0.970521i \(0.422519\pi\)
\(98\) 4.11131 6.36235i 0.415305 0.642695i
\(99\) 0 0
\(100\) 3.93067 + 8.72193i 0.393067 + 0.872193i
\(101\) 1.48081 8.39808i 0.147346 0.835641i −0.818108 0.575065i \(-0.804977\pi\)
0.965454 0.260575i \(-0.0839123\pi\)
\(102\) 0 0
\(103\) 2.93036 8.05109i 0.288737 0.793298i −0.707507 0.706706i \(-0.750180\pi\)
0.996244 0.0865915i \(-0.0275975\pi\)
\(104\) 7.13117 0.172930i 0.699269 0.0169572i
\(105\) 0 0
\(106\) 2.75189 12.0441i 0.267287 1.16982i
\(107\) 10.8657i 1.05042i 0.850972 + 0.525211i \(0.176014\pi\)
−0.850972 + 0.525211i \(0.823986\pi\)
\(108\) 0 0
\(109\) 8.94866i 0.857126i 0.903512 + 0.428563i \(0.140980\pi\)
−0.903512 + 0.428563i \(0.859020\pi\)
\(110\) −0.911588 0.208284i −0.0869165 0.0198591i
\(111\) 0 0
\(112\) −6.71324 12.3546i −0.634342 1.16740i
\(113\) 1.31870 3.62309i 0.124053 0.340832i −0.862084 0.506765i \(-0.830841\pi\)
0.986137 + 0.165933i \(0.0530635\pi\)
\(114\) 0 0
\(115\) −0.584410 + 3.31436i −0.0544966 + 0.309065i
\(116\) 3.38687 + 7.51528i 0.314463 + 0.697776i
\(117\) 0 0
\(118\) 2.84174 + 1.83631i 0.261603 + 0.169046i
\(119\) −2.54432 + 0.926058i −0.233238 + 0.0848916i
\(120\) 0 0
\(121\) 6.88055 5.77346i 0.625504 0.524860i
\(122\) 1.68823 4.00239i 0.152845 0.362359i
\(123\) 0 0
\(124\) 15.2490 + 4.29795i 1.36940 + 0.385968i
\(125\) −2.27679 3.94351i −0.203642 0.352718i
\(126\) 0 0
\(127\) −9.84084 5.68161i −0.873233 0.504162i −0.00481202 0.999988i \(-0.501532\pi\)
−0.868421 + 0.495827i \(0.834865\pi\)
\(128\) −11.3137 0.0181658i −0.999999 0.00160564i
\(129\) 0 0
\(130\) −1.64722 + 0.206040i −0.144471 + 0.0180709i
\(131\) 19.4659 3.43236i 1.70074 0.299887i 0.762790 0.646647i \(-0.223829\pi\)
0.937954 + 0.346760i \(0.112718\pi\)
\(132\) 0 0
\(133\) 16.5452 19.7179i 1.43465 1.70975i
\(134\) 3.40194 + 6.63948i 0.293883 + 0.573564i
\(135\) 0 0
\(136\) −0.326192 + 2.15408i −0.0279707 + 0.184711i
\(137\) −4.33502 + 5.16628i −0.370366 + 0.441385i −0.918749 0.394843i \(-0.870799\pi\)
0.548383 + 0.836227i \(0.315244\pi\)
\(138\) 0 0
\(139\) −2.54700 14.4448i −0.216034 1.22519i −0.879103 0.476631i \(-0.841858\pi\)
0.663069 0.748558i \(-0.269253\pi\)
\(140\) 1.84206 + 2.70447i 0.155682 + 0.228569i
\(141\) 0 0
\(142\) −15.4274 + 4.75484i −1.29464 + 0.399017i
\(143\) −1.79136 + 3.10273i −0.149801 + 0.259463i
\(144\) 0 0
\(145\) −0.959179 1.66135i −0.0796555 0.137967i
\(146\) −6.13889 5.69868i −0.508058 0.471626i
\(147\) 0 0
\(148\) 6.43548 0.479304i 0.528993 0.0393985i
\(149\) 6.53906 5.48692i 0.535700 0.449506i −0.334364 0.942444i \(-0.608521\pi\)
0.870064 + 0.492938i \(0.164077\pi\)
\(150\) 0 0
\(151\) 1.70566 + 4.68627i 0.138805 + 0.381364i 0.989545 0.144223i \(-0.0460682\pi\)
−0.850740 + 0.525586i \(0.823846\pi\)
\(152\) −7.55337 19.2847i −0.612659 1.56419i
\(153\) 0 0
\(154\) 7.05319 + 0.353632i 0.568362 + 0.0284965i
\(155\) −3.63100 0.640243i −0.291649 0.0514256i
\(156\) 0 0
\(157\) −7.74744 + 21.2859i −0.618313 + 1.69880i 0.0927644 + 0.995688i \(0.470430\pi\)
−0.711078 + 0.703113i \(0.751793\pi\)
\(158\) −11.8816 15.6933i −0.945247 1.24849i
\(159\) 0 0
\(160\) 2.62014 0.259150i 0.207141 0.0204876i
\(161\) 25.4173i 2.00317i
\(162\) 0 0
\(163\) −24.9254 −1.95231 −0.976156 0.217071i \(-0.930350\pi\)
−0.976156 + 0.217071i \(0.930350\pi\)
\(164\) 1.33566 + 5.25556i 0.104298 + 0.410390i
\(165\) 0 0
\(166\) 9.84357 + 13.0015i 0.764009 + 1.00911i
\(167\) −0.989406 0.360114i −0.0765625 0.0278665i 0.303455 0.952846i \(-0.401860\pi\)
−0.380017 + 0.924979i \(0.624082\pi\)
\(168\) 0 0
\(169\) 1.15295 6.53869i 0.0886883 0.502976i
\(170\) 0.0253887 0.506377i 0.00194722 0.0388374i
\(171\) 0 0
\(172\) 4.22612 + 0.424846i 0.322239 + 0.0323942i
\(173\) −3.27836 + 1.19323i −0.249249 + 0.0907192i −0.463623 0.886032i \(-0.653451\pi\)
0.214374 + 0.976752i \(0.431229\pi\)
\(174\) 0 0
\(175\) 10.8080 + 12.8805i 0.817012 + 0.973677i
\(176\) 2.96744 4.84599i 0.223679 0.365281i
\(177\) 0 0
\(178\) −9.54717 + 10.2847i −0.715591 + 0.770869i
\(179\) −11.9338 + 6.89000i −0.891976 + 0.514983i −0.874588 0.484866i \(-0.838868\pi\)
−0.0173878 + 0.999849i \(0.505535\pi\)
\(180\) 0 0
\(181\) −2.04781 1.18231i −0.152213 0.0878801i 0.421959 0.906615i \(-0.361343\pi\)
−0.574172 + 0.818735i \(0.694676\pi\)
\(182\) 11.9812 3.69269i 0.888104 0.273721i
\(183\) 0 0
\(184\) −17.9544 9.79345i −1.32361 0.721982i
\(185\) −1.47900 + 0.260787i −0.108738 + 0.0191735i
\(186\) 0 0
\(187\) −0.838231 0.703359i −0.0612975 0.0514347i
\(188\) −12.2736 + 17.0550i −0.895142 + 1.24386i
\(189\) 0 0
\(190\) 2.19791 + 4.28960i 0.159453 + 0.311200i
\(191\) −8.27044 6.93973i −0.598428 0.502141i 0.292512 0.956262i \(-0.405509\pi\)
−0.890940 + 0.454121i \(0.849953\pi\)
\(192\) 0 0
\(193\) 3.57316 + 20.2644i 0.257201 + 1.45866i 0.790358 + 0.612645i \(0.209894\pi\)
−0.533157 + 0.846016i \(0.678994\pi\)
\(194\) 0.364613 + 2.91496i 0.0261777 + 0.209282i
\(195\) 0 0
\(196\) −7.47658 7.67240i −0.534041 0.548028i
\(197\) 1.27921 2.21565i 0.0911396 0.157858i −0.816851 0.576848i \(-0.804282\pi\)
0.907991 + 0.418990i \(0.137616\pi\)
\(198\) 0 0
\(199\) −18.0736 + 10.4348i −1.28121 + 0.739704i −0.977069 0.212924i \(-0.931701\pi\)
−0.304136 + 0.952628i \(0.598368\pi\)
\(200\) 13.2630 2.67167i 0.937835 0.188916i
\(201\) 0 0
\(202\) −11.1118 4.68703i −0.781826 0.329779i
\(203\) 9.31278 + 11.0985i 0.653629 + 0.778965i
\(204\) 0 0
\(205\) −0.431614 1.18585i −0.0301453 0.0828234i
\(206\) −10.1768 6.57620i −0.709053 0.458185i
\(207\) 0 0
\(208\) 2.00796 9.88611i 0.139227 0.685478i
\(209\) 10.2443 + 1.80634i 0.708610 + 0.124947i
\(210\) 0 0
\(211\) 0.0141986 + 0.00516787i 0.000977473 + 0.000355771i 0.342509 0.939515i \(-0.388723\pi\)
−0.341531 + 0.939870i \(0.610946\pi\)
\(212\) −15.7381 7.58797i −1.08090 0.521144i
\(213\) 0 0
\(214\) 14.9803 + 3.42277i 1.02403 + 0.233976i
\(215\) −0.988461 −0.0674125
\(216\) 0 0
\(217\) 27.8456 1.89028
\(218\) 12.3374 + 2.81890i 0.835592 + 0.190920i
\(219\) 0 0
\(220\) −0.574315 + 1.19118i −0.0387203 + 0.0803093i
\(221\) −1.82545 0.664409i −0.122793 0.0446930i
\(222\) 0 0
\(223\) 2.68574 + 0.473569i 0.179851 + 0.0317125i 0.262848 0.964837i \(-0.415338\pi\)
−0.0829974 + 0.996550i \(0.526449\pi\)
\(224\) −19.1478 + 5.36365i −1.27936 + 0.358374i
\(225\) 0 0
\(226\) −4.57970 2.95937i −0.304637 0.196855i
\(227\) −0.693824 1.90627i −0.0460507 0.126523i 0.914535 0.404506i \(-0.132556\pi\)
−0.960586 + 0.277983i \(0.910334\pi\)
\(228\) 0 0
\(229\) 4.00131 + 4.76857i 0.264414 + 0.315116i 0.881873 0.471487i \(-0.156282\pi\)
−0.617459 + 0.786603i \(0.711838\pi\)
\(230\) 4.38536 + 1.84977i 0.289162 + 0.121970i
\(231\) 0 0
\(232\) 11.4281 2.30205i 0.750291 0.151137i
\(233\) 21.4888 12.4066i 1.40778 0.812783i 0.412607 0.910909i \(-0.364618\pi\)
0.995174 + 0.0981264i \(0.0312850\pi\)
\(234\) 0 0
\(235\) 2.44498 4.23484i 0.159493 0.276250i
\(236\) 3.42687 3.33941i 0.223070 0.217377i
\(237\) 0 0
\(238\) 0.475258 + 3.79953i 0.0308064 + 0.246287i
\(239\) 4.43265 + 25.1388i 0.286725 + 1.62610i 0.699059 + 0.715064i \(0.253602\pi\)
−0.412335 + 0.911032i \(0.635287\pi\)
\(240\) 0 0
\(241\) −12.6387 10.6052i −0.814133 0.683139i 0.137458 0.990508i \(-0.456107\pi\)
−0.951590 + 0.307369i \(0.900551\pi\)
\(242\) −5.79235 11.3048i −0.372347 0.726699i
\(243\) 0 0
\(244\) −4.98622 3.58832i −0.319210 0.229719i
\(245\) 1.90982 + 1.60253i 0.122014 + 0.102382i
\(246\) 0 0
\(247\) 18.1867 3.20681i 1.15719 0.204044i
\(248\) 10.7291 19.6697i 0.681297 1.24902i
\(249\) 0 0
\(250\) −6.15406 + 1.89673i −0.389217 + 0.119960i
\(251\) 3.82463 + 2.20815i 0.241408 + 0.139377i 0.615824 0.787884i \(-0.288823\pi\)
−0.374416 + 0.927261i \(0.622157\pi\)
\(252\) 0 0
\(253\) 8.89578 5.13598i 0.559273 0.322896i
\(254\) −10.9331 + 11.7777i −0.686003 + 0.738996i
\(255\) 0 0
\(256\) −3.58895 + 15.5923i −0.224310 + 0.974518i
\(257\) −12.1155 14.4386i −0.755741 0.900657i 0.241830 0.970319i \(-0.422253\pi\)
−0.997571 + 0.0696615i \(0.977808\pi\)
\(258\) 0 0
\(259\) 10.6582 3.87927i 0.662269 0.241046i
\(260\) −0.234824 + 2.33590i −0.0145632 + 0.144866i
\(261\) 0 0
\(262\) 1.39978 27.9185i 0.0864785 1.72481i
\(263\) −3.00966 + 17.0686i −0.185583 + 1.05250i 0.739620 + 0.673024i \(0.235005\pi\)
−0.925204 + 0.379471i \(0.876106\pi\)
\(264\) 0 0
\(265\) 3.82084 + 1.39067i 0.234712 + 0.0854283i
\(266\) −21.9728 29.0220i −1.34724 1.77945i
\(267\) 0 0
\(268\) 10.2254 2.59871i 0.624615 0.158741i
\(269\) 10.9959 0.670431 0.335215 0.942142i \(-0.391191\pi\)
0.335215 + 0.942142i \(0.391191\pi\)
\(270\) 0 0
\(271\) 19.7167i 1.19770i −0.800861 0.598851i \(-0.795624\pi\)
0.800861 0.598851i \(-0.204376\pi\)
\(272\) 2.86704 + 1.12827i 0.173840 + 0.0684113i
\(273\) 0 0
\(274\) 5.75709 + 7.60404i 0.347799 + 0.459377i
\(275\) −2.32410 + 6.38541i −0.140148 + 0.385055i
\(276\) 0 0
\(277\) −18.3745 3.23992i −1.10402 0.194668i −0.408203 0.912891i \(-0.633845\pi\)
−0.695813 + 0.718223i \(0.744956\pi\)
\(278\) −20.7171 1.03871i −1.24253 0.0622978i
\(279\) 0 0
\(280\) 4.30887 1.68769i 0.257504 0.100859i
\(281\) 8.37613 + 23.0132i 0.499678 + 1.37285i 0.891587 + 0.452850i \(0.149593\pi\)
−0.391909 + 0.920004i \(0.628185\pi\)
\(282\) 0 0
\(283\) 13.4469 11.2833i 0.799338 0.670724i −0.148700 0.988882i \(-0.547509\pi\)
0.948038 + 0.318159i \(0.103064\pi\)
\(284\) 1.69567 + 22.7673i 0.100619 + 1.35099i
\(285\) 0 0
\(286\) 3.71339 + 3.44711i 0.219577 + 0.203832i
\(287\) 4.76537 + 8.25386i 0.281291 + 0.487210i
\(288\) 0 0
\(289\) −8.20335 + 14.2086i −0.482550 + 0.835801i
\(290\) −2.59262 + 0.799067i −0.152244 + 0.0469228i
\(291\) 0 0
\(292\) −9.79048 + 6.66846i −0.572944 + 0.390242i
\(293\) 4.42079 + 25.0715i 0.258265 + 1.46470i 0.787550 + 0.616251i \(0.211349\pi\)
−0.529285 + 0.848444i \(0.677540\pi\)
\(294\) 0 0
\(295\) −0.715769 + 0.853020i −0.0416737 + 0.0496647i
\(296\) 1.36642 9.02348i 0.0794217 0.524479i
\(297\) 0 0
\(298\) −5.50487 10.7437i −0.318889 0.622367i
\(299\) 11.7218 13.9695i 0.677890 0.807878i
\(300\) 0 0
\(301\) 7.35179 1.29632i 0.423750 0.0747186i
\(302\) 6.99819 0.875357i 0.402701 0.0503711i
\(303\) 0 0
\(304\) −28.9669 + 4.33887i −1.66136 + 0.248851i
\(305\) 1.23810 + 0.714819i 0.0708936 + 0.0409304i
\(306\) 0 0
\(307\) 13.7038 + 23.7357i 0.782117 + 1.35467i 0.930706 + 0.365768i \(0.119194\pi\)
−0.148589 + 0.988899i \(0.547473\pi\)
\(308\) 2.70936 9.61273i 0.154380 0.547736i
\(309\) 0 0
\(310\) −2.02649 + 4.80432i −0.115097 + 0.272867i
\(311\) 11.9153 9.99813i 0.675655 0.566942i −0.239078 0.971000i \(-0.576845\pi\)
0.914733 + 0.404058i \(0.132401\pi\)
\(312\) 0 0
\(313\) −9.57684 + 3.48568i −0.541315 + 0.197022i −0.598183 0.801359i \(-0.704111\pi\)
0.0568687 + 0.998382i \(0.481888\pi\)
\(314\) 26.9061 + 17.3865i 1.51840 + 0.981178i
\(315\) 0 0
\(316\) −25.3789 + 11.4374i −1.42768 + 0.643404i
\(317\) −5.74143 + 32.5613i −0.322471 + 1.82882i 0.204410 + 0.978885i \(0.434472\pi\)
−0.526881 + 0.849939i \(0.676639\pi\)
\(318\) 0 0
\(319\) −2.00257 + 5.50201i −0.112122 + 0.308053i
\(320\) 0.468081 3.69399i 0.0261665 0.206500i
\(321\) 0 0
\(322\) −35.0425 8.00667i −1.95284 0.446194i
\(323\) 5.64027i 0.313833i
\(324\) 0 0
\(325\) 12.0636i 0.669168i
\(326\) −7.85172 + 34.3643i −0.434867 + 1.90326i
\(327\) 0 0
\(328\) 7.66651 0.185912i 0.423312 0.0102653i
\(329\) −12.6311 + 34.7035i −0.696373 + 1.91327i
\(330\) 0 0
\(331\) 1.92984 10.9447i 0.106074 0.601574i −0.884712 0.466138i \(-0.845645\pi\)
0.990786 0.135437i \(-0.0432437\pi\)
\(332\) 21.0258 9.47559i 1.15394 0.520041i
\(333\) 0 0
\(334\) −0.808155 + 1.25064i −0.0442203 + 0.0684319i
\(335\) −2.30723 + 0.839763i −0.126057 + 0.0458811i
\(336\) 0 0
\(337\) 4.91071 4.12058i 0.267504 0.224462i −0.499162 0.866509i \(-0.666359\pi\)
0.766666 + 0.642046i \(0.221914\pi\)
\(338\) −8.65160 3.64929i −0.470585 0.198495i
\(339\) 0 0
\(340\) −0.690137 0.194516i −0.0374279 0.0105491i
\(341\) 5.62665 + 9.74565i 0.304700 + 0.527756i
\(342\) 0 0
\(343\) 5.00343 + 2.88873i 0.270160 + 0.155977i
\(344\) 1.91699 5.69266i 0.103357 0.306928i
\(345\) 0 0
\(346\) 0.612370 + 4.89570i 0.0329212 + 0.263194i
\(347\) 31.8049 5.60806i 1.70738 0.301056i 0.767115 0.641510i \(-0.221692\pi\)
0.940261 + 0.340453i \(0.110581\pi\)
\(348\) 0 0
\(349\) −0.166560 + 0.198498i −0.00891573 + 0.0106254i −0.770484 0.637459i \(-0.779985\pi\)
0.761568 + 0.648085i \(0.224430\pi\)
\(350\) 21.1628 10.8434i 1.13120 0.579605i
\(351\) 0 0
\(352\) −5.74633 5.61768i −0.306280 0.299424i
\(353\) 5.28492 6.29832i 0.281288 0.335226i −0.606839 0.794825i \(-0.707563\pi\)
0.888126 + 0.459599i \(0.152007\pi\)
\(354\) 0 0
\(355\) −0.922607 5.23236i −0.0489669 0.277705i
\(356\) 11.1719 + 16.4023i 0.592108 + 0.869320i
\(357\) 0 0
\(358\) 5.73988 + 18.6234i 0.303362 + 0.984276i
\(359\) −0.180226 + 0.312161i −0.00951198 + 0.0164752i −0.870742 0.491740i \(-0.836361\pi\)
0.861230 + 0.508215i \(0.169694\pi\)
\(360\) 0 0
\(361\) −17.3095 29.9810i −0.911027 1.57794i
\(362\) −2.27510 + 2.45085i −0.119577 + 0.128814i
\(363\) 0 0
\(364\) −1.31689 17.6815i −0.0690236 0.926761i
\(365\) 2.11179 1.77200i 0.110536 0.0927508i
\(366\) 0 0
\(367\) 10.6705 + 29.3168i 0.556993 + 1.53033i 0.823975 + 0.566626i \(0.191751\pi\)
−0.266982 + 0.963702i \(0.586026\pi\)
\(368\) −19.1578 + 21.6684i −0.998671 + 1.12954i
\(369\) 0 0
\(370\) −0.106354 + 2.12122i −0.00552906 + 0.110277i
\(371\) −30.2417 5.33243i −1.57007 0.276846i
\(372\) 0 0
\(373\) −2.92591 + 8.03888i −0.151498 + 0.416237i −0.992105 0.125408i \(-0.959976\pi\)
0.840607 + 0.541645i \(0.182198\pi\)
\(374\) −1.23376 + 0.934092i −0.0637962 + 0.0483007i
\(375\) 0 0
\(376\) 19.6472 + 22.2938i 1.01322 + 1.14972i
\(377\) 10.3946i 0.535351i
\(378\) 0 0
\(379\) −11.8737 −0.609912 −0.304956 0.952366i \(-0.598642\pi\)
−0.304956 + 0.952366i \(0.598642\pi\)
\(380\) 6.60637 1.67896i 0.338899 0.0861289i
\(381\) 0 0
\(382\) −12.1729 + 9.21626i −0.622822 + 0.471545i
\(383\) −21.6357 7.87475i −1.10553 0.402381i −0.276179 0.961106i \(-0.589068\pi\)
−0.829353 + 0.558725i \(0.811291\pi\)
\(384\) 0 0
\(385\) −0.403599 + 2.28892i −0.0205693 + 0.116654i
\(386\) 29.0637 + 1.45719i 1.47931 + 0.0741692i
\(387\) 0 0
\(388\) 4.13367 + 0.415551i 0.209855 + 0.0210964i
\(389\) −17.2027 + 6.26126i −0.872210 + 0.317458i −0.739062 0.673638i \(-0.764731\pi\)
−0.133148 + 0.991096i \(0.542509\pi\)
\(390\) 0 0
\(391\) 3.58007 + 4.26656i 0.181052 + 0.215769i
\(392\) −12.9330 + 7.89097i −0.653215 + 0.398554i
\(393\) 0 0
\(394\) −2.65172 2.46157i −0.133592 0.124012i
\(395\) 5.61034 3.23913i 0.282287 0.162978i
\(396\) 0 0
\(397\) −5.79128 3.34360i −0.290656 0.167810i 0.347582 0.937650i \(-0.387003\pi\)
−0.638238 + 0.769839i \(0.720336\pi\)
\(398\) 8.69296 + 28.2049i 0.435739 + 1.41378i
\(399\) 0 0
\(400\) 0.494560 19.1271i 0.0247280 0.956353i
\(401\) 7.86143 1.38618i 0.392581 0.0692226i 0.0261266 0.999659i \(-0.491683\pi\)
0.366454 + 0.930436i \(0.380572\pi\)
\(402\) 0 0
\(403\) 15.3041 + 12.8417i 0.762352 + 0.639689i
\(404\) −9.96226 + 13.8433i −0.495641 + 0.688728i
\(405\) 0 0
\(406\) 18.2350 9.34325i 0.904987 0.463698i
\(407\) 3.51136 + 2.94638i 0.174052 + 0.146047i
\(408\) 0 0
\(409\) −1.04527 5.92801i −0.0516852 0.293121i 0.947998 0.318275i \(-0.103104\pi\)
−0.999684 + 0.0251538i \(0.991992\pi\)
\(410\) −1.77088 + 0.221507i −0.0874573 + 0.0109394i
\(411\) 0 0
\(412\) −12.2723 + 11.9591i −0.604612 + 0.589181i
\(413\) 4.20492 7.28313i 0.206910 0.358379i
\(414\) 0 0
\(415\) −4.64802 + 2.68353i −0.228162 + 0.131729i
\(416\) −12.9973 5.88255i −0.637245 0.288416i
\(417\) 0 0
\(418\) 5.71740 13.5546i 0.279647 0.662976i
\(419\) −17.2811 20.5948i −0.844237 1.00612i −0.999833 0.0183011i \(-0.994174\pi\)
0.155596 0.987821i \(-0.450270\pi\)
\(420\) 0 0
\(421\) 6.51235 + 17.8925i 0.317392 + 0.872029i 0.991111 + 0.133040i \(0.0424739\pi\)
−0.673718 + 0.738988i \(0.735304\pi\)
\(422\) 0.0115975 0.0179475i 0.000564560 0.000873670i
\(423\) 0 0
\(424\) −15.4191 + 19.3076i −0.748815 + 0.937660i
\(425\) −3.62848 0.639800i −0.176007 0.0310348i
\(426\) 0 0
\(427\) −10.1460 3.69284i −0.490999 0.178709i
\(428\) 9.43785 19.5749i 0.456195 0.946189i
\(429\) 0 0
\(430\) −0.311374 + 1.36278i −0.0150158 + 0.0657189i
\(431\) 19.2221 0.925894 0.462947 0.886386i \(-0.346792\pi\)
0.462947 + 0.886386i \(0.346792\pi\)
\(432\) 0 0
\(433\) 13.6658 0.656735 0.328367 0.944550i \(-0.393502\pi\)
0.328367 + 0.944550i \(0.393502\pi\)
\(434\) 8.77160 38.3903i 0.421050 1.84279i
\(435\) 0 0
\(436\) 7.77275 16.1214i 0.372247 0.772073i
\(437\) −49.7541 18.1090i −2.38006 0.866271i
\(438\) 0 0
\(439\) −24.1314 4.25502i −1.15173 0.203081i −0.434999 0.900431i \(-0.643251\pi\)
−0.716731 + 0.697350i \(0.754362\pi\)
\(440\) 1.46135 + 1.16703i 0.0696670 + 0.0556360i
\(441\) 0 0
\(442\) −1.49104 + 2.30742i −0.0709216 + 0.109753i
\(443\) −4.71302 12.9489i −0.223922 0.615222i 0.775956 0.630786i \(-0.217268\pi\)
−0.999879 + 0.0155648i \(0.995045\pi\)
\(444\) 0 0
\(445\) −2.96869 3.53795i −0.140729 0.167715i
\(446\) 1.49893 3.55361i 0.0709765 0.168268i
\(447\) 0 0
\(448\) 1.36308 + 28.0883i 0.0643994 + 1.32705i
\(449\) −15.6709 + 9.04759i −0.739555 + 0.426982i −0.821907 0.569621i \(-0.807090\pi\)
0.0823526 + 0.996603i \(0.473757\pi\)
\(450\) 0 0
\(451\) −1.92584 + 3.33565i −0.0906842 + 0.157070i
\(452\) −5.52268 + 5.38173i −0.259765 + 0.253135i
\(453\) 0 0
\(454\) −2.84670 + 0.356074i −0.133602 + 0.0167114i
\(455\) 0.716513 + 4.06355i 0.0335907 + 0.190502i
\(456\) 0 0
\(457\) −5.09369 4.27411i −0.238273 0.199935i 0.515830 0.856691i \(-0.327484\pi\)
−0.754103 + 0.656756i \(0.771928\pi\)
\(458\) 7.83480 4.01440i 0.366096 0.187581i
\(459\) 0 0
\(460\) 3.93167 5.46333i 0.183315 0.254729i
\(461\) −17.2916 14.5094i −0.805352 0.675771i 0.144141 0.989557i \(-0.453958\pi\)
−0.949494 + 0.313786i \(0.898402\pi\)
\(462\) 0 0
\(463\) 9.30336 1.64043i 0.432364 0.0762374i 0.0467691 0.998906i \(-0.485107\pi\)
0.385594 + 0.922668i \(0.373996\pi\)
\(464\) 0.426139 16.4809i 0.0197830 0.765106i
\(465\) 0 0
\(466\) −10.3356 33.5345i −0.478788 1.55346i
\(467\) −6.76157 3.90380i −0.312888 0.180646i 0.335330 0.942101i \(-0.391152\pi\)
−0.648218 + 0.761455i \(0.724486\pi\)
\(468\) 0 0
\(469\) 16.0590 9.27165i 0.741534 0.428125i
\(470\) −5.06831 4.70487i −0.233784 0.217019i
\(471\) 0 0
\(472\) −3.52450 5.77651i −0.162228 0.265886i
\(473\) 1.93924 + 2.31110i 0.0891666 + 0.106265i
\(474\) 0 0
\(475\) 32.9139 11.9797i 1.51019 0.549665i
\(476\) 5.38807 + 0.541654i 0.246962 + 0.0248267i
\(477\) 0 0
\(478\) 36.0548 + 1.80771i 1.64911 + 0.0826829i
\(479\) 4.13778 23.4665i 0.189060 1.07221i −0.731567 0.681770i \(-0.761211\pi\)
0.920627 0.390444i \(-0.127678\pi\)
\(480\) 0 0
\(481\) 7.64683 + 2.78322i 0.348666 + 0.126904i
\(482\) −18.6025 + 14.0841i −0.847320 + 0.641514i
\(483\) 0 0
\(484\) −17.4104 + 4.42472i −0.791381 + 0.201124i
\(485\) −0.966837 −0.0439018
\(486\) 0 0
\(487\) 5.00210i 0.226667i −0.993557 0.113333i \(-0.963847\pi\)
0.993557 0.113333i \(-0.0361528\pi\)
\(488\) −6.51786 + 5.74407i −0.295050 + 0.260022i
\(489\) 0 0
\(490\) 2.81099 2.12823i 0.126988 0.0961436i
\(491\) 10.7540 29.5462i 0.485319 1.33340i −0.419557 0.907729i \(-0.637815\pi\)
0.904876 0.425674i \(-0.139963\pi\)
\(492\) 0 0
\(493\) −3.12649 0.551285i −0.140810 0.0248286i
\(494\) 1.30779 26.0839i 0.0588404 1.17357i
\(495\) 0 0
\(496\) −23.7385 20.9881i −1.06589 0.942394i
\(497\) 13.7240 + 37.7063i 0.615605 + 1.69136i
\(498\) 0 0
\(499\) 9.47652 7.95175i 0.424227 0.355969i −0.405541 0.914077i \(-0.632917\pi\)
0.829769 + 0.558108i \(0.188472\pi\)
\(500\) 0.676412 + 9.08199i 0.0302500 + 0.406159i
\(501\) 0 0
\(502\) 4.24913 4.57737i 0.189648 0.204298i
\(503\) 0.0403972 + 0.0699700i 0.00180122 + 0.00311981i 0.866925 0.498439i \(-0.166093\pi\)
−0.865123 + 0.501559i \(0.832760\pi\)
\(504\) 0 0
\(505\) 1.98455 3.43735i 0.0883115 0.152960i
\(506\) −4.27865 13.8823i −0.190209 0.617145i
\(507\) 0 0
\(508\) 12.7936 + 18.7833i 0.567626 + 0.833376i
\(509\) −7.45238 42.2646i −0.330321 1.87334i −0.469286 0.883046i \(-0.655489\pi\)
0.138964 0.990297i \(-0.455623\pi\)
\(510\) 0 0
\(511\) −13.3828 + 15.9490i −0.592019 + 0.705541i
\(512\) 20.3663 + 9.85973i 0.900071 + 0.435743i
\(513\) 0 0
\(514\) −23.7228 + 12.1551i −1.04637 + 0.536138i
\(515\) 2.56331 3.05483i 0.112953 0.134612i
\(516\) 0 0
\(517\) −14.6982 + 2.59168i −0.646424 + 0.113982i
\(518\) −1.99086 15.9163i −0.0874735 0.699322i
\(519\) 0 0
\(520\) 3.14650 + 1.05958i 0.137983 + 0.0464655i
\(521\) 8.07399 + 4.66152i 0.353728 + 0.204225i 0.666326 0.745661i \(-0.267866\pi\)
−0.312598 + 0.949886i \(0.601199\pi\)
\(522\) 0 0
\(523\) −2.56968 4.45082i −0.112364 0.194621i 0.804359 0.594144i \(-0.202509\pi\)
−0.916723 + 0.399523i \(0.869176\pi\)
\(524\) −38.0499 10.7244i −1.66222 0.468499i
\(525\) 0 0
\(526\) 22.5841 + 9.52612i 0.984716 + 0.415359i
\(527\) −4.67417 + 3.92210i −0.203610 + 0.170849i
\(528\) 0 0
\(529\) −27.5178 + 10.0157i −1.19643 + 0.435463i
\(530\) 3.12089 4.82966i 0.135563 0.209787i
\(531\) 0 0
\(532\) −46.9337 + 21.1514i −2.03484 + 0.917029i
\(533\) −1.18739 + 6.73403i −0.0514316 + 0.291683i
\(534\) 0 0
\(535\) −1.72970 + 4.75232i −0.0747816 + 0.205461i
\(536\) −0.361716 14.9162i −0.0156238 0.644282i
\(537\) 0 0
\(538\) 3.46379 15.1598i 0.149335 0.653587i
\(539\) 7.60929i 0.327755i
\(540\) 0 0
\(541\) 23.3927i 1.00573i −0.864365 0.502865i \(-0.832279\pi\)
0.864365 0.502865i \(-0.167721\pi\)
\(542\) −27.1830 6.21091i −1.16761 0.266781i
\(543\) 0 0
\(544\) 2.45867 3.59733i 0.105415 0.154234i
\(545\) −1.42454 + 3.91388i −0.0610204 + 0.167652i
\(546\) 0 0
\(547\) −3.87158 + 21.9568i −0.165537 + 0.938806i 0.782972 + 0.622056i \(0.213703\pi\)
−0.948509 + 0.316749i \(0.897409\pi\)
\(548\) 12.2971 5.54188i 0.525306 0.236737i
\(549\) 0 0
\(550\) 8.07135 + 5.21566i 0.344164 + 0.222396i
\(551\) 28.3603 10.3223i 1.20819 0.439745i
\(552\) 0 0
\(553\) −37.4796 + 31.4491i −1.59379 + 1.33735i
\(554\) −10.2549 + 24.3120i −0.435691 + 1.03292i
\(555\) 0 0
\(556\) −7.95811 + 28.2351i −0.337499 + 1.19744i
\(557\) 13.3979 + 23.2059i 0.567688 + 0.983265i 0.996794 + 0.0800105i \(0.0254954\pi\)
−0.429106 + 0.903254i \(0.641171\pi\)
\(558\) 0 0
\(559\) 4.63842 + 2.67799i 0.196184 + 0.113267i
\(560\) −0.969456 6.47220i −0.0409670 0.273501i
\(561\) 0 0
\(562\) 34.3665 4.29868i 1.44966 0.181329i
\(563\) −26.1430 + 4.60972i −1.10180 + 0.194276i −0.694835 0.719169i \(-0.744523\pi\)
−0.406961 + 0.913446i \(0.633411\pi\)
\(564\) 0 0
\(565\) 1.15352 1.37471i 0.0485290 0.0578346i
\(566\) −11.3202 22.0934i −0.475825 0.928656i
\(567\) 0 0
\(568\) 31.9230 + 4.83409i 1.33946 + 0.202834i
\(569\) −4.50444 + 5.36818i −0.188836 + 0.225046i −0.852153 0.523292i \(-0.824704\pi\)
0.663317 + 0.748338i \(0.269148\pi\)
\(570\) 0 0
\(571\) −1.80104 10.2142i −0.0753710 0.427450i −0.999022 0.0442155i \(-0.985921\pi\)
0.923651 0.383235i \(-0.125190\pi\)
\(572\) 5.92222 4.03372i 0.247620 0.168658i
\(573\) 0 0
\(574\) 12.8806 3.96990i 0.537626 0.165700i
\(575\) 17.2937 29.9535i 0.721196 1.24915i
\(576\) 0 0
\(577\) −5.28015 9.14548i −0.219815 0.380731i 0.734936 0.678136i \(-0.237212\pi\)
−0.954751 + 0.297405i \(0.903879\pi\)
\(578\) 17.0051 + 15.7857i 0.707317 + 0.656597i
\(579\) 0 0
\(580\) 0.284963 + 3.82612i 0.0118324 + 0.158871i
\(581\) 31.0508 26.0547i 1.28821 1.08093i
\(582\) 0 0
\(583\) −4.24453 11.6618i −0.175791 0.482981i
\(584\) 6.10961 + 15.5986i 0.252818 + 0.645475i
\(585\) 0 0
\(586\) 35.9583 + 1.80287i 1.48542 + 0.0744760i
\(587\) 23.9487 + 4.22280i 0.988467 + 0.174293i 0.644431 0.764663i \(-0.277094\pi\)
0.344037 + 0.938956i \(0.388206\pi\)
\(588\) 0 0
\(589\) 19.8391 54.5074i 0.817455 2.24594i
\(590\) 0.950572 + 1.25553i 0.0391344 + 0.0516892i
\(591\) 0 0
\(592\) −12.0101 4.72634i −0.493612 0.194251i
\(593\) 3.37367i 0.138540i −0.997598 0.0692700i \(-0.977933\pi\)
0.997598 0.0692700i \(-0.0220670\pi\)
\(594\) 0 0
\(595\) −1.26023 −0.0516645
\(596\) −16.5463 + 4.20512i −0.677762 + 0.172248i
\(597\) 0 0
\(598\) −15.5671 20.5612i −0.636585 0.840809i
\(599\) 5.23313 + 1.90470i 0.213820 + 0.0778241i 0.446709 0.894679i \(-0.352596\pi\)
−0.232889 + 0.972503i \(0.574818\pi\)
\(600\) 0 0
\(601\) −4.92392 + 27.9250i −0.200851 + 1.13908i 0.702985 + 0.711205i \(0.251850\pi\)
−0.903836 + 0.427879i \(0.859261\pi\)
\(602\) 0.528661 10.5442i 0.0215466 0.429748i
\(603\) 0 0
\(604\) 0.997648 9.92404i 0.0405937 0.403803i
\(605\) 3.92843 1.42983i 0.159713 0.0581309i
\(606\) 0 0
\(607\) −12.4758 14.8681i −0.506379 0.603479i 0.450925 0.892562i \(-0.351094\pi\)
−0.957304 + 0.289083i \(0.906650\pi\)
\(608\) −3.14287 + 41.3029i −0.127460 + 1.67505i
\(609\) 0 0
\(610\) 1.37552 1.48178i 0.0556933 0.0599955i
\(611\) −22.9465 + 13.2482i −0.928315 + 0.535963i
\(612\) 0 0
\(613\) −4.17880 2.41263i −0.168780 0.0974452i 0.413230 0.910626i \(-0.364400\pi\)
−0.582010 + 0.813181i \(0.697734\pi\)
\(614\) 37.0408 11.4163i 1.49485 0.460723i
\(615\) 0 0
\(616\) −12.3994 6.76344i −0.499588 0.272507i
\(617\) −21.9486 + 3.87013i −0.883617 + 0.155806i −0.597002 0.802240i \(-0.703641\pi\)
−0.286616 + 0.958046i \(0.592530\pi\)
\(618\) 0 0
\(619\) 7.17245 + 6.01840i 0.288285 + 0.241900i 0.775448 0.631411i \(-0.217524\pi\)
−0.487163 + 0.873311i \(0.661968\pi\)
\(620\) 5.98528 + 4.30729i 0.240374 + 0.172985i
\(621\) 0 0
\(622\) −10.0308 19.5769i −0.402200 0.784964i
\(623\) 26.7198 + 22.4206i 1.07051 + 0.898262i
\(624\) 0 0
\(625\) 3.78508 + 21.4663i 0.151403 + 0.858650i
\(626\) 1.78887 + 14.3014i 0.0714977 + 0.571601i
\(627\) 0 0
\(628\) 32.4461 31.6180i 1.29474 1.26170i
\(629\) −1.24269 + 2.15240i −0.0495493 + 0.0858218i
\(630\) 0 0
\(631\) 27.6553 15.9668i 1.10094 0.635628i 0.164472 0.986382i \(-0.447408\pi\)
0.936468 + 0.350754i \(0.114075\pi\)
\(632\) 7.77399 + 38.5924i 0.309233 + 1.53512i
\(633\) 0 0
\(634\) 43.0831 + 18.1727i 1.71105 + 0.721730i
\(635\) −3.39964 4.05154i −0.134911 0.160780i
\(636\) 0 0
\(637\) −4.62030 12.6942i −0.183063 0.502961i
\(638\) 6.95470 + 4.49408i 0.275339 + 0.177922i
\(639\) 0 0
\(640\) −4.94539 1.80897i −0.195484 0.0715059i
\(641\) 21.6518 + 3.81780i 0.855195 + 0.150794i 0.584023 0.811737i \(-0.301478\pi\)
0.271172 + 0.962531i \(0.412589\pi\)
\(642\) 0 0
\(643\) −21.2821 7.74607i −0.839286 0.305475i −0.113622 0.993524i \(-0.536245\pi\)
−0.725664 + 0.688049i \(0.758467\pi\)
\(644\) −22.0773 + 45.7903i −0.869969 + 1.80439i
\(645\) 0 0
\(646\) 7.77615 + 1.77673i 0.305948 + 0.0699046i
\(647\) −46.7102 −1.83637 −0.918183 0.396157i \(-0.870344\pi\)
−0.918183 + 0.396157i \(0.870344\pi\)
\(648\) 0 0
\(649\) 3.39868 0.133410
\(650\) 16.6319 + 3.80014i 0.652357 + 0.149054i
\(651\) 0 0
\(652\) 44.9042 + 21.6501i 1.75858 + 0.847883i
\(653\) 10.0893 + 3.67221i 0.394825 + 0.143705i 0.531800 0.846870i \(-0.321516\pi\)
−0.136975 + 0.990575i \(0.543738\pi\)
\(654\) 0 0
\(655\) 9.06022 + 1.59756i 0.354012 + 0.0624219i
\(656\) 2.15870 10.6283i 0.0842831 0.414964i
\(657\) 0 0
\(658\) 43.8663 + 28.3461i 1.71009 + 1.10505i
\(659\) −13.5526 37.2355i −0.527935 1.45049i −0.861497 0.507762i \(-0.830473\pi\)
0.333562 0.942728i \(-0.391749\pi\)
\(660\) 0 0
\(661\) −8.48287 10.1095i −0.329945 0.393213i 0.575412 0.817863i \(-0.304842\pi\)
−0.905358 + 0.424650i \(0.860397\pi\)
\(662\) −14.4813 6.10831i −0.562833 0.237406i
\(663\) 0 0
\(664\) −6.44055 31.9728i −0.249942 1.24079i
\(665\) 10.3753 5.99018i 0.402337 0.232289i
\(666\) 0 0
\(667\) 14.9011 25.8095i 0.576974 0.999349i
\(668\) 1.46966 + 1.50815i 0.0568629 + 0.0583521i
\(669\) 0 0
\(670\) 0.430971 + 3.44547i 0.0166499 + 0.133110i
\(671\) −0.757708 4.29718i −0.0292510 0.165891i
\(672\) 0 0
\(673\) −4.00717 3.36241i −0.154465 0.129612i 0.562280 0.826947i \(-0.309924\pi\)
−0.716745 + 0.697335i \(0.754369\pi\)
\(674\) −4.13406 8.06834i −0.159238 0.310781i
\(675\) 0 0
\(676\) −7.75655 + 10.7783i −0.298329 + 0.414549i
\(677\) −0.442568 0.371358i −0.0170093 0.0142725i 0.634243 0.773133i \(-0.281312\pi\)
−0.651253 + 0.758861i \(0.725756\pi\)
\(678\) 0 0
\(679\) 7.19096 1.26796i 0.275964 0.0486598i
\(680\) −0.485575 + 0.890206i −0.0186209 + 0.0341378i
\(681\) 0 0
\(682\) 15.2086 4.68742i 0.582368 0.179490i
\(683\) 0.194169 + 0.112104i 0.00742968 + 0.00428953i 0.503710 0.863873i \(-0.331968\pi\)
−0.496281 + 0.868162i \(0.665301\pi\)
\(684\) 0 0
\(685\) −2.71843 + 1.56949i −0.103866 + 0.0599670i
\(686\) 5.55878 5.98818i 0.212235 0.228630i
\(687\) 0 0
\(688\) −7.24451 4.43616i −0.276194 0.169127i
\(689\) −14.1618 16.8774i −0.539523 0.642979i
\(690\) 0 0
\(691\) −13.3272 + 4.85069i −0.506989 + 0.184529i −0.582835 0.812591i \(-0.698057\pi\)
0.0758457 + 0.997120i \(0.475834\pi\)
\(692\) 6.94252 + 0.697921i 0.263915 + 0.0265310i
\(693\) 0 0
\(694\) 2.28706 45.6155i 0.0868157 1.73154i
\(695\) 1.18548 6.72318i 0.0449677 0.255025i
\(696\) 0 0
\(697\) −1.96248 0.714286i −0.0743344 0.0270555i
\(698\) 0.221198 + 0.292162i 0.00837248 + 0.0110585i
\(699\) 0 0
\(700\) −8.28317 32.5926i −0.313075 1.23188i
\(701\) −5.36891 −0.202781 −0.101391 0.994847i \(-0.532329\pi\)
−0.101391 + 0.994847i \(0.532329\pi\)
\(702\) 0 0
\(703\) 23.6272i 0.891115i
\(704\) −9.55515 + 6.15275i −0.360123 + 0.231891i
\(705\) 0 0
\(706\) −7.01860 9.27026i −0.264149 0.348891i
\(707\) −10.2524 + 28.1683i −0.385582 + 1.05938i
\(708\) 0 0
\(709\) −16.2741 2.86956i −0.611187 0.107769i −0.140517 0.990078i \(-0.544876\pi\)
−0.470670 + 0.882310i \(0.655988\pi\)
\(710\) −7.50441 0.376255i −0.281635 0.0141206i
\(711\) 0 0
\(712\) 26.1328 10.2356i 0.979368 0.383596i
\(713\) −19.5905 53.8245i −0.733671 2.01574i
\(714\) 0 0
\(715\) −1.27741 + 1.07188i −0.0477725 + 0.0400859i
\(716\) 27.4839 2.04695i 1.02712 0.0764982i
\(717\) 0 0
\(718\) 0.373599 + 0.346809i 0.0139426 + 0.0129428i
\(719\) −1.17170 2.02945i −0.0436971 0.0756857i 0.843350 0.537365i \(-0.180580\pi\)
−0.887047 + 0.461680i \(0.847247\pi\)
\(720\) 0 0
\(721\) −15.0586 + 26.0823i −0.560812 + 0.971356i
\(722\) −46.7869 + 14.4201i −1.74123 + 0.536660i
\(723\) 0 0
\(724\) 2.66227 + 3.90869i 0.0989426 + 0.145265i
\(725\) 3.42349 + 19.4156i 0.127145 + 0.721077i
\(726\) 0 0
\(727\) −10.6227 + 12.6596i −0.393974 + 0.469520i −0.926173 0.377099i \(-0.876922\pi\)
0.532198 + 0.846620i \(0.321366\pi\)
\(728\) −24.7920 3.75424i −0.918853 0.139142i
\(729\) 0 0
\(730\) −1.77780 3.46969i −0.0657993 0.128419i
\(731\) −1.05149 + 1.25311i −0.0388906 + 0.0463480i
\(732\) 0 0
\(733\) −35.2664 + 6.21842i −1.30260 + 0.229683i −0.781548 0.623845i \(-0.785570\pi\)
−0.521047 + 0.853528i \(0.674458\pi\)
\(734\) 43.7800 5.47614i 1.61595 0.202128i
\(735\) 0 0
\(736\) 23.8390 + 33.2383i 0.878715 + 1.22518i
\(737\) 6.48994 + 3.74697i 0.239060 + 0.138021i
\(738\) 0 0
\(739\) 15.1448 + 26.2316i 0.557112 + 0.964946i 0.997736 + 0.0672539i \(0.0214238\pi\)
−0.440624 + 0.897692i \(0.645243\pi\)
\(740\) 2.89099 + 0.814831i 0.106275 + 0.0299538i
\(741\) 0 0
\(742\) −16.8781 + 40.0140i −0.619616 + 1.46896i
\(743\) 37.2460 31.2531i 1.36642 1.14657i 0.392485 0.919758i \(-0.371616\pi\)
0.973940 0.226808i \(-0.0728289\pi\)
\(744\) 0 0
\(745\) 3.73346 1.35887i 0.136783 0.0497850i
\(746\) 10.1614 + 6.56622i 0.372035 + 0.240407i
\(747\) 0 0
\(748\) 0.899173 + 1.99521i 0.0328770 + 0.0729522i
\(749\) 6.63243 37.6144i 0.242344 1.37440i
\(750\) 0 0
\(751\) 1.78479 4.90367i 0.0651279 0.178937i −0.902860 0.429935i \(-0.858536\pi\)
0.967988 + 0.250998i \(0.0807586\pi\)
\(752\) 36.9252 20.0645i 1.34652 0.731676i
\(753\) 0 0
\(754\) 14.3309 + 3.27440i 0.521901 + 0.119246i
\(755\) 2.32116i 0.0844758i
\(756\) 0 0
\(757\) 23.5414i 0.855626i 0.903867 + 0.427813i \(0.140716\pi\)
−0.903867 + 0.427813i \(0.859284\pi\)
\(758\) −3.74032 + 16.3701i −0.135855 + 0.594589i
\(759\) 0 0
\(760\) −0.233696 9.63698i −0.00847703 0.349570i
\(761\) −11.0387 + 30.3285i −0.400151 + 1.09941i 0.562059 + 0.827097i \(0.310010\pi\)
−0.962210 + 0.272309i \(0.912213\pi\)
\(762\) 0 0
\(763\) 5.46228 30.9782i 0.197748 1.12148i
\(764\) 8.87173 + 19.6858i 0.320968 + 0.712209i
\(765\) 0 0
\(766\) −17.6722 + 27.3482i −0.638523 + 0.988129i
\(767\) 5.66984 2.06365i 0.204726 0.0745141i
\(768\) 0 0
\(769\) −10.7031 + 8.98096i −0.385964 + 0.323862i −0.815038 0.579407i \(-0.803284\pi\)
0.429075 + 0.903269i \(0.358840\pi\)
\(770\) 3.02857 + 1.27747i 0.109142 + 0.0460367i
\(771\) 0 0
\(772\) 11.1643 39.6107i 0.401813 1.42562i
\(773\) −7.86483 13.6223i −0.282878 0.489959i 0.689214 0.724558i \(-0.257956\pi\)
−0.972092 + 0.234598i \(0.924623\pi\)
\(774\) 0 0
\(775\) 32.8152 + 18.9459i 1.17876 + 0.680555i
\(776\) 1.87505 5.56812i 0.0673105 0.199884i
\(777\) 0 0
\(778\) 3.21331 + 25.6894i 0.115203 + 0.921009i
\(779\) 19.5520 3.44754i 0.700523 0.123521i
\(780\) 0 0
\(781\) −10.4236 + 12.4224i −0.372987 + 0.444509i
\(782\) 7.00999 3.59178i 0.250677 0.128442i
\(783\) 0 0
\(784\) 6.80515 + 20.3162i 0.243041 + 0.725580i
\(785\) −6.77701 + 8.07653i −0.241882 + 0.288264i
\(786\) 0 0
\(787\) 0.897820 + 5.09179i 0.0320038 + 0.181503i 0.996619 0.0821580i \(-0.0261812\pi\)
−0.964616 + 0.263661i \(0.915070\pi\)
\(788\) −4.22904 + 2.88047i −0.150653 + 0.102612i
\(789\) 0 0
\(790\) −2.69843 8.75523i −0.0960059 0.311497i
\(791\) −6.77657 + 11.7374i −0.240947 + 0.417333i
\(792\) 0 0
\(793\) −3.87325 6.70867i −0.137543 0.238232i
\(794\) −6.43407 + 6.93108i −0.228336 + 0.245975i
\(795\) 0 0
\(796\) 41.6240 3.10008i 1.47532 0.109880i
\(797\) −1.73089 + 1.45239i −0.0613111 + 0.0514461i −0.672928 0.739708i \(-0.734964\pi\)
0.611617 + 0.791154i \(0.290519\pi\)
\(798\) 0 0
\(799\) −2.76779 7.60445i −0.0979175 0.269026i
\(800\) −26.2144 6.70703i −0.926819 0.237129i
\(801\) 0 0
\(802\) 0.565309 11.2751i 0.0199617 0.398137i
\(803\) −8.28617 1.46107i −0.292412 0.0515602i
\(804\) 0 0
\(805\) 4.04618 11.1168i 0.142609 0.391816i
\(806\) 22.5255 17.0543i 0.793428 0.600712i
\(807\) 0 0
\(808\) 15.9473 + 18.0956i 0.561024 + 0.636599i
\(809\) 3.55121i 0.124854i 0.998050 + 0.0624270i \(0.0198841\pi\)
−0.998050 + 0.0624270i \(0.980116\pi\)
\(810\) 0 0
\(811\) −24.8246 −0.871710 −0.435855 0.900017i \(-0.643554\pi\)
−0.435855 + 0.900017i \(0.643554\pi\)
\(812\) −7.13722 28.0835i −0.250467 0.985537i
\(813\) 0 0
\(814\) 5.16824 3.91292i 0.181147 0.137148i
\(815\) −10.9017 3.96788i −0.381869 0.138989i
\(816\) 0 0
\(817\) 2.70038 15.3146i 0.0944744 0.535791i
\(818\) −8.50212 0.426278i −0.297270 0.0149045i
\(819\) 0 0
\(820\) −0.252453 + 2.51125i −0.00881603 + 0.0876968i
\(821\) 7.98474 2.90621i 0.278669 0.101427i −0.198905 0.980019i \(-0.563738\pi\)
0.477574 + 0.878591i \(0.341516\pi\)
\(822\) 0 0
\(823\) −21.2355 25.3075i −0.740223 0.882163i 0.256204 0.966623i \(-0.417528\pi\)
−0.996427 + 0.0844593i \(0.973084\pi\)
\(824\) 12.6219 + 20.6868i 0.439705 + 0.720659i
\(825\) 0 0
\(826\) −8.71655 8.09150i −0.303288 0.281539i
\(827\) 27.5962 15.9327i 0.959613 0.554033i 0.0635591 0.997978i \(-0.479755\pi\)
0.896054 + 0.443945i \(0.146422\pi\)
\(828\) 0 0
\(829\) −3.48406 2.01153i −0.121007 0.0698632i 0.438275 0.898841i \(-0.355590\pi\)
−0.559282 + 0.828978i \(0.688923\pi\)
\(830\) 2.23558 + 7.25348i 0.0775982 + 0.251772i
\(831\) 0 0
\(832\) −12.2044 + 16.0661i −0.423113 + 0.556992i
\(833\) 4.06318 0.716448i 0.140781 0.0248235i
\(834\) 0 0
\(835\) −0.375411 0.315007i −0.0129916 0.0109013i
\(836\) −16.8865 12.1523i −0.584030 0.420296i
\(837\) 0 0
\(838\) −33.8374 + 17.3376i −1.16889 + 0.598918i
\(839\) −13.1010 10.9931i −0.452298 0.379523i 0.387990 0.921664i \(-0.373170\pi\)
−0.840288 + 0.542140i \(0.817614\pi\)
\(840\) 0 0
\(841\) −2.08594 11.8299i −0.0719288 0.407929i
\(842\) 26.7196 3.34217i 0.920818 0.115179i
\(843\) 0 0
\(844\) −0.0210906 0.0216430i −0.000725968 0.000744981i
\(845\) 1.54516 2.67630i 0.0531551 0.0920674i
\(846\) 0 0
\(847\) −27.3430 + 15.7865i −0.939516 + 0.542430i
\(848\) 21.7620 + 27.3401i 0.747309 + 0.938861i
\(849\) 0 0
\(850\) −2.02508 + 4.80099i −0.0694598 + 0.164673i
\(851\) −14.9970 17.8727i −0.514089 0.612668i
\(852\) 0 0
\(853\) −4.54120 12.4769i −0.155488 0.427199i 0.837350 0.546667i \(-0.184104\pi\)
−0.992838 + 0.119467i \(0.961881\pi\)
\(854\) −8.28732 + 12.8248i −0.283586 + 0.438857i
\(855\) 0 0
\(856\) −24.0146 19.1781i −0.820803 0.655493i
\(857\) −1.39542 0.246051i −0.0476668 0.00840494i 0.149764 0.988722i \(-0.452149\pi\)
−0.197431 + 0.980317i \(0.563260\pi\)
\(858\) 0 0
\(859\) 13.1020 + 4.76873i 0.447034 + 0.162707i 0.555721 0.831369i \(-0.312442\pi\)
−0.108687 + 0.994076i \(0.534665\pi\)
\(860\) 1.78075 + 0.858572i 0.0607231 + 0.0292770i
\(861\) 0 0
\(862\) 6.05511 26.5011i 0.206238 0.902633i
\(863\) −32.7283 −1.11408 −0.557041 0.830485i \(-0.688064\pi\)
−0.557041 + 0.830485i \(0.688064\pi\)
\(864\) 0 0
\(865\) −1.62381 −0.0552111
\(866\) 4.30483 18.8408i 0.146284 0.640236i
\(867\) 0 0
\(868\) −50.1650 24.1865i −1.70271 0.820945i
\(869\) −18.5802 6.76263i −0.630289 0.229406i
\(870\) 0 0
\(871\) 13.1019 + 2.31023i 0.443942 + 0.0782790i
\(872\) −19.7778 15.7945i −0.669760 0.534870i
\(873\) 0 0
\(874\) −40.6396 + 62.8907i −1.37465 + 2.12731i
\(875\) 5.47457 + 15.0413i 0.185074 + 0.508488i
\(876\) 0 0
\(877\) 16.7454 + 19.9563i 0.565450 + 0.673878i 0.970691 0.240333i \(-0.0772565\pi\)
−0.405240 + 0.914210i \(0.632812\pi\)
\(878\) −13.4679 + 31.9292i −0.454520 + 1.07756i
\(879\) 0 0
\(880\) 2.06930 1.64711i 0.0697562 0.0555241i
\(881\) −32.0686 + 18.5148i −1.08042 + 0.623779i −0.931009 0.364996i \(-0.881070\pi\)
−0.149408 + 0.988776i \(0.547737\pi\)
\(882\) 0 0
\(883\) 15.5793 26.9841i 0.524285 0.908089i −0.475315 0.879816i \(-0.657666\pi\)
0.999600 0.0282731i \(-0.00900081\pi\)
\(884\) 2.71152 + 2.78253i 0.0911981 + 0.0935867i
\(885\) 0 0
\(886\) −19.3371 + 2.41875i −0.649643 + 0.0812595i
\(887\) 1.60872 + 9.12349i 0.0540154 + 0.306337i 0.999831 0.0183666i \(-0.00584661\pi\)
−0.945816 + 0.324703i \(0.894735\pi\)
\(888\) 0 0
\(889\) 30.5986 + 25.6753i 1.02624 + 0.861122i
\(890\) −5.81287 + 2.97840i −0.194848 + 0.0998363i
\(891\) 0 0
\(892\) −4.42713 3.18597i −0.148231 0.106674i
\(893\) 58.9325 + 49.4503i 1.97210 + 1.65479i
\(894\) 0 0
\(895\) −6.31633 + 1.11374i −0.211132 + 0.0372282i
\(896\) 39.1543 + 6.96880i 1.30805 + 0.232811i
\(897\) 0 0
\(898\) 7.53731 + 24.4553i 0.251523 + 0.816083i
\(899\) 28.2753 + 16.3247i 0.943033 + 0.544461i
\(900\) 0 0
\(901\) 5.82747 3.36449i 0.194141 0.112087i
\(902\) 3.99215 + 3.70588i 0.132924 + 0.123392i
\(903\) 0 0
\(904\) 5.68002 + 9.30932i 0.188915 + 0.309624i
\(905\) −0.707443 0.843097i −0.0235162 0.0280255i
\(906\) 0 0
\(907\) 14.1698 5.15740i 0.470502 0.171249i −0.0958780 0.995393i \(-0.530566\pi\)
0.566380 + 0.824145i \(0.308344\pi\)
\(908\) −0.405820 + 4.03686i −0.0134676 + 0.133968i
\(909\) 0 0
\(910\) 5.82806 + 0.292206i 0.193198 + 0.00968655i
\(911\) −2.78022 + 15.7674i −0.0921129 + 0.522398i 0.903481 + 0.428628i \(0.141003\pi\)
−0.995594 + 0.0937702i \(0.970108\pi\)
\(912\) 0 0
\(913\) 15.3932 + 5.60266i 0.509440 + 0.185421i
\(914\) −7.49721 + 5.67621i −0.247986 + 0.187752i
\(915\) 0 0
\(916\) −3.06656 12.0663i −0.101322 0.398681i
\(917\) −69.4815 −2.29448
\(918\) 0 0
\(919\) 35.6444i 1.17580i 0.808934 + 0.587900i \(0.200045\pi\)
−0.808934 + 0.587900i \(0.799955\pi\)
\(920\) −6.29369 7.14152i −0.207497 0.235449i
\(921\) 0 0
\(922\) −25.4509 + 19.2691i −0.838181 + 0.634595i
\(923\) −9.84640 + 27.0528i −0.324098 + 0.890453i
\(924\) 0 0
\(925\) 15.1998 + 2.68013i 0.499766 + 0.0881222i
\(926\) 0.668997 13.3431i 0.0219846 0.438483i
\(927\) 0 0
\(928\) −22.5877 5.77913i −0.741477 0.189709i
\(929\) −5.42788 14.9130i −0.178083 0.489279i 0.818248 0.574866i \(-0.194946\pi\)
−0.996331 + 0.0855870i \(0.972723\pi\)
\(930\) 0 0
\(931\) −30.0461 + 25.2117i −0.984721 + 0.826279i
\(932\) −49.4893 + 3.68588i −1.62108 + 0.120735i
\(933\) 0 0
\(934\) −7.51205 + 8.09234i −0.245802 + 0.264790i
\(935\) −0.254650 0.441067i −0.00832795 0.0144244i
\(936\) 0 0
\(937\) 3.18741 5.52076i 0.104128 0.180355i −0.809253 0.587460i \(-0.800128\pi\)
0.913382 + 0.407104i \(0.133461\pi\)
\(938\) −7.72397 25.0609i −0.252196 0.818267i
\(939\) 0 0
\(940\) −8.08309 + 5.50552i −0.263641 + 0.179570i
\(941\) 3.12587 + 17.7277i 0.101900 + 0.577906i 0.992413 + 0.122948i \(0.0392348\pi\)
−0.890513 + 0.454959i \(0.849654\pi\)
\(942\) 0 0
\(943\) 12.6018 15.0182i 0.410370 0.489060i
\(944\) −9.07423 + 3.03952i −0.295341 + 0.0989278i
\(945\) 0 0
\(946\) 3.79716 1.94559i 0.123456 0.0632566i
\(947\) 3.51808 4.19268i 0.114322 0.136244i −0.705848 0.708363i \(-0.749434\pi\)
0.820171 + 0.572119i \(0.193878\pi\)
\(948\) 0 0
\(949\) −14.7105 + 2.59386i −0.477523 + 0.0842002i
\(950\) −6.14803 49.1515i −0.199468 1.59469i
\(951\) 0 0
\(952\) 2.44406 7.25782i 0.0792123 0.235227i
\(953\) 8.89078 + 5.13310i 0.288001 + 0.166277i 0.637040 0.770831i \(-0.280159\pi\)
−0.349039 + 0.937108i \(0.613492\pi\)
\(954\) 0 0
\(955\) −2.51252 4.35181i −0.0813031 0.140821i
\(956\) 13.8498 49.1388i 0.447936 1.58926i
\(957\) 0 0
\(958\) −31.0495 13.0969i −1.00316 0.423140i
\(959\) 18.1603 15.2383i 0.586428 0.492071i
\(960\) 0 0
\(961\) 29.8362 10.8595i 0.962460 0.350307i
\(962\) 6.24600 9.66583i 0.201379 0.311639i
\(963\) 0 0
\(964\) 13.5576 + 30.0836i 0.436661 + 0.968926i
\(965\) −1.66309 + 9.43186i −0.0535368 + 0.303622i
\(966\) 0 0
\(967\) 1.87573 5.15353i 0.0603195 0.165726i −0.905872 0.423551i \(-0.860783\pi\)
0.966192 + 0.257825i \(0.0830057\pi\)
\(968\) 0.615880 + 25.3972i 0.0197951 + 0.816298i
\(969\) 0 0
\(970\) −0.304562 + 1.33296i −0.00977889 + 0.0427988i
\(971\) 22.2762i 0.714877i 0.933937 + 0.357439i \(0.116350\pi\)
−0.933937 + 0.357439i \(0.883650\pi\)
\(972\) 0 0
\(973\) 51.5591i 1.65291i
\(974\) −6.89631 1.57570i −0.220972 0.0504887i
\(975\) 0 0
\(976\) 5.86608 + 10.7955i 0.187769 + 0.345556i
\(977\) 8.42429 23.1456i 0.269517 0.740492i −0.728920 0.684599i \(-0.759977\pi\)
0.998437 0.0558929i \(-0.0178005\pi\)
\(978\) 0 0
\(979\) −2.44778 + 13.8821i −0.0782315 + 0.443673i
\(980\) −2.04867 4.54588i −0.0654423 0.145213i
\(981\) 0 0
\(982\) −37.3473 24.1336i −1.19180 0.770135i
\(983\) −19.2748 + 7.01545i −0.614771 + 0.223758i −0.630589 0.776117i \(-0.717187\pi\)
0.0158187 + 0.999875i \(0.494965\pi\)
\(984\) 0 0
\(985\) 0.912196 0.765424i 0.0290650 0.0243884i
\(986\) −1.74492 + 4.13679i −0.0555695 + 0.131742i
\(987\) 0 0
\(988\) −35.5495 10.0197i −1.13098 0.318769i
\(989\) −7.67802 13.2987i −0.244147 0.422875i
\(990\) 0 0
\(991\) 19.3983 + 11.1996i 0.616207 + 0.355767i 0.775391 0.631482i \(-0.217553\pi\)
−0.159184 + 0.987249i \(0.550886\pi\)
\(992\) −36.4138 + 26.1164i −1.15614 + 0.829198i
\(993\) 0 0
\(994\) 56.3083 7.04323i 1.78599 0.223398i
\(995\) −9.56599 + 1.68674i −0.303262 + 0.0534733i
\(996\) 0 0
\(997\) −27.6176 + 32.9134i −0.874659 + 1.04238i 0.124085 + 0.992272i \(0.460400\pi\)
−0.998744 + 0.0501062i \(0.984044\pi\)
\(998\) −7.97776 15.5700i −0.252532 0.492860i
\(999\) 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 648.2.v.b.35.18 192
3.2 odd 2 216.2.v.b.11.15 yes 192
8.3 odd 2 inner 648.2.v.b.35.29 192
12.11 even 2 864.2.bh.b.335.21 192
24.5 odd 2 864.2.bh.b.335.22 192
24.11 even 2 216.2.v.b.11.4 192
27.5 odd 18 inner 648.2.v.b.611.29 192
27.22 even 9 216.2.v.b.59.4 yes 192
108.103 odd 18 864.2.bh.b.815.22 192
216.59 even 18 inner 648.2.v.b.611.18 192
216.157 even 18 864.2.bh.b.815.21 192
216.211 odd 18 216.2.v.b.59.15 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.11.4 192 24.11 even 2
216.2.v.b.11.15 yes 192 3.2 odd 2
216.2.v.b.59.4 yes 192 27.22 even 9
216.2.v.b.59.15 yes 192 216.211 odd 18
648.2.v.b.35.18 192 1.1 even 1 trivial
648.2.v.b.35.29 192 8.3 odd 2 inner
648.2.v.b.611.18 192 216.59 even 18 inner
648.2.v.b.611.29 192 27.5 odd 18 inner
864.2.bh.b.335.21 192 12.11 even 2
864.2.bh.b.335.22 192 24.5 odd 2
864.2.bh.b.815.21 192 216.157 even 18
864.2.bh.b.815.22 192 108.103 odd 18