Properties

Label 189.2.o.a.125.1
Level $189$
Weight $2$
Character 189.125
Analytic conductor $1.509$
Analytic rank $0$
Dimension $12$
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] = [189,2,Mod(62,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.62");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 125.1
Root \(-1.82904 - 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 189.125
Dual form 189.2.o.a.62.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.02704 + 0.592963i) q^{2} +(-0.296790 + 0.514055i) q^{4} +(-1.41899 + 2.45776i) q^{5} +(-2.07253 - 1.64457i) q^{7} -3.07579i q^{8} +O(q^{10})\) \(q+(-1.02704 + 0.592963i) q^{2} +(-0.296790 + 0.514055i) q^{4} +(-1.41899 + 2.45776i) q^{5} +(-2.07253 - 1.64457i) q^{7} -3.07579i q^{8} -3.36562i q^{10} +(-0.136673 + 0.0789082i) q^{11} +(-3.41468 - 1.97146i) q^{13} +(3.10375 + 0.460106i) q^{14} +(1.23025 + 2.13086i) q^{16} -4.14487 q^{17} +6.33597i q^{19} +(-0.842281 - 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} +(-0.472958 - 0.273062i) q^{23} +(-1.52704 - 2.64491i) q^{25} +4.67602 q^{26} +(1.46050 - 0.577305i) q^{28} +(-4.02704 + 2.32501i) q^{29} +(0.112086 + 0.0647129i) q^{31} +(2.80039 + 1.61680i) q^{32} +(4.25696 - 2.45776i) q^{34} +(6.98284 - 2.76016i) q^{35} -2.46050 q^{37} +(-3.75700 - 6.50731i) q^{38} +(7.55955 + 4.36451i) q^{40} +(1.99569 - 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} -0.0936766i q^{44} +0.647664 q^{46} +(4.33370 + 7.50619i) q^{47} +(1.59079 + 6.81685i) q^{49} +(3.13667 + 1.81096i) q^{50} +(2.02688 - 1.17022i) q^{52} +2.60234i q^{53} -0.447879i q^{55} +(-5.05835 + 6.37468i) q^{56} +(2.75729 - 4.77577i) q^{58} +(-1.80686 + 3.12957i) q^{59} +(-2.91472 + 1.68281i) q^{61} -0.153489 q^{62} -8.75583 q^{64} +(9.69076 - 5.59496i) q^{65} +(-0.663715 + 1.14959i) q^{67} +(1.23016 - 2.13069i) q^{68} +(-5.53500 + 6.97537i) q^{70} +0.409310i q^{71} -15.0124i q^{73} +(2.52704 - 1.45899i) q^{74} +(-3.25704 - 1.88045i) q^{76} +(0.413030 + 0.0612283i) q^{77} +(-2.16372 - 3.74766i) q^{79} -6.98284 q^{80} +4.73348i q^{82} +(-3.22585 - 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} +(-6.74630 - 3.89498i) q^{86} +(0.242705 + 0.420378i) q^{88} -5.05368 q^{89} +(3.83482 + 9.70160i) q^{91} +(0.280738 - 0.162084i) q^{92} +(-8.90179 - 5.13945i) q^{94} +(-15.5723 - 8.99066i) q^{95} +(-2.18452 + 1.26123i) q^{97} +(-5.67594 - 6.05791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64} + 78 q^{65} + 12 q^{67} + 18 q^{70} + 12 q^{74} + 24 q^{77} - 6 q^{79} - 6 q^{85} - 96 q^{86} + 34 q^{88} - 24 q^{91} - 30 q^{92} - 72 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02704 + 0.592963i −0.726228 + 0.419288i −0.817041 0.576580i \(-0.804387\pi\)
0.0908124 + 0.995868i \(0.471054\pi\)
\(3\) 0 0
\(4\) −0.296790 + 0.514055i −0.148395 + 0.257027i
\(5\) −1.41899 + 2.45776i −0.634590 + 1.09914i 0.352012 + 0.935995i \(0.385498\pi\)
−0.986602 + 0.163146i \(0.947836\pi\)
\(6\) 0 0
\(7\) −2.07253 1.64457i −0.783344 0.621589i
\(8\) 3.07579i 1.08746i
\(9\) 0 0
\(10\) 3.36562i 1.06430i
\(11\) −0.136673 + 0.0789082i −0.0412085 + 0.0237917i −0.520463 0.853884i \(-0.674241\pi\)
0.479254 + 0.877676i \(0.340907\pi\)
\(12\) 0 0
\(13\) −3.41468 1.97146i −0.947061 0.546786i −0.0548943 0.998492i \(-0.517482\pi\)
−0.892167 + 0.451706i \(0.850816\pi\)
\(14\) 3.10375 + 0.460106i 0.829511 + 0.122968i
\(15\) 0 0
\(16\) 1.23025 + 2.13086i 0.307563 + 0.532715i
\(17\) −4.14487 −1.00528 −0.502640 0.864496i \(-0.667638\pi\)
−0.502640 + 0.864496i \(0.667638\pi\)
\(18\) 0 0
\(19\) 6.33597i 1.45357i 0.686864 + 0.726786i \(0.258987\pi\)
−0.686864 + 0.726786i \(0.741013\pi\)
\(20\) −0.842281 1.45887i −0.188340 0.326214i
\(21\) 0 0
\(22\) 0.0935793 0.162084i 0.0199512 0.0345565i
\(23\) −0.472958 0.273062i −0.0986185 0.0569374i 0.449880 0.893089i \(-0.351467\pi\)
−0.548498 + 0.836152i \(0.684800\pi\)
\(24\) 0 0
\(25\) −1.52704 2.64491i −0.305408 0.528983i
\(26\) 4.67602 0.917044
\(27\) 0 0
\(28\) 1.46050 0.577305i 0.276009 0.109100i
\(29\) −4.02704 + 2.32501i −0.747803 + 0.431744i −0.824900 0.565279i \(-0.808768\pi\)
0.0770966 + 0.997024i \(0.475435\pi\)
\(30\) 0 0
\(31\) 0.112086 + 0.0647129i 0.0201313 + 0.0116228i 0.510032 0.860156i \(-0.329634\pi\)
−0.489901 + 0.871778i \(0.662967\pi\)
\(32\) 2.80039 + 1.61680i 0.495043 + 0.285813i
\(33\) 0 0
\(34\) 4.25696 2.45776i 0.730062 0.421502i
\(35\) 6.98284 2.76016i 1.18032 0.466552i
\(36\) 0 0
\(37\) −2.46050 −0.404505 −0.202252 0.979333i \(-0.564826\pi\)
−0.202252 + 0.979333i \(0.564826\pi\)
\(38\) −3.75700 6.50731i −0.609465 1.05563i
\(39\) 0 0
\(40\) 7.55955 + 4.36451i 1.19527 + 0.690089i
\(41\) 1.99569 3.45664i 0.311675 0.539836i −0.667050 0.745013i \(-0.732443\pi\)
0.978725 + 0.205176i \(0.0657768\pi\)
\(42\) 0 0
\(43\) 3.28434 + 5.68864i 0.500857 + 0.867509i 1.00000 0.000989450i \(0.000314952\pi\)
−0.499143 + 0.866520i \(0.666352\pi\)
\(44\) 0.0936766i 0.0141223i
\(45\) 0 0
\(46\) 0.647664 0.0954928
\(47\) 4.33370 + 7.50619i 0.632135 + 1.09489i 0.987114 + 0.160016i \(0.0511547\pi\)
−0.354979 + 0.934874i \(0.615512\pi\)
\(48\) 0 0
\(49\) 1.59079 + 6.81685i 0.227255 + 0.973835i
\(50\) 3.13667 + 1.81096i 0.443593 + 0.256108i
\(51\) 0 0
\(52\) 2.02688 1.17022i 0.281078 0.162280i
\(53\) 2.60234i 0.357459i 0.983898 + 0.178730i \(0.0571988\pi\)
−0.983898 + 0.178730i \(0.942801\pi\)
\(54\) 0 0
\(55\) 0.447879i 0.0603920i
\(56\) −5.05835 + 6.37468i −0.675951 + 0.851853i
\(57\) 0 0
\(58\) 2.75729 4.77577i 0.362051 0.627090i
\(59\) −1.80686 + 3.12957i −0.235233 + 0.407436i −0.959340 0.282252i \(-0.908919\pi\)
0.724107 + 0.689687i \(0.242252\pi\)
\(60\) 0 0
\(61\) −2.91472 + 1.68281i −0.373191 + 0.215462i −0.674852 0.737953i \(-0.735792\pi\)
0.301660 + 0.953415i \(0.402459\pi\)
\(62\) −0.153489 −0.0194932
\(63\) 0 0
\(64\) −8.75583 −1.09448
\(65\) 9.69076 5.59496i 1.20199 0.693970i
\(66\) 0 0
\(67\) −0.663715 + 1.14959i −0.0810857 + 0.140445i −0.903717 0.428131i \(-0.859172\pi\)
0.822631 + 0.568576i \(0.192505\pi\)
\(68\) 1.23016 2.13069i 0.149178 0.258384i
\(69\) 0 0
\(70\) −5.53500 + 6.97537i −0.661559 + 0.833716i
\(71\) 0.409310i 0.0485761i 0.999705 + 0.0242881i \(0.00773189\pi\)
−0.999705 + 0.0242881i \(0.992268\pi\)
\(72\) 0 0
\(73\) 15.0124i 1.75707i −0.477681 0.878533i \(-0.658522\pi\)
0.477681 0.878533i \(-0.341478\pi\)
\(74\) 2.52704 1.45899i 0.293763 0.169604i
\(75\) 0 0
\(76\) −3.25704 1.88045i −0.373608 0.215703i
\(77\) 0.413030 + 0.0612283i 0.0470691 + 0.00697762i
\(78\) 0 0
\(79\) −2.16372 3.74766i −0.243437 0.421645i 0.718254 0.695781i \(-0.244942\pi\)
−0.961691 + 0.274136i \(0.911608\pi\)
\(80\) −6.98284 −0.780706
\(81\) 0 0
\(82\) 4.73348i 0.522726i
\(83\) −3.22585 5.58733i −0.354083 0.613289i 0.632878 0.774252i \(-0.281874\pi\)
−0.986961 + 0.160963i \(0.948540\pi\)
\(84\) 0 0
\(85\) 5.88151 10.1871i 0.637940 1.10494i
\(86\) −6.74630 3.89498i −0.727473 0.420007i
\(87\) 0 0
\(88\) 0.242705 + 0.420378i 0.0258725 + 0.0448125i
\(89\) −5.05368 −0.535689 −0.267845 0.963462i \(-0.586311\pi\)
−0.267845 + 0.963462i \(0.586311\pi\)
\(90\) 0 0
\(91\) 3.83482 + 9.70160i 0.401999 + 1.01700i
\(92\) 0.280738 0.162084i 0.0292690 0.0168984i
\(93\) 0 0
\(94\) −8.90179 5.13945i −0.918150 0.530094i
\(95\) −15.5723 8.99066i −1.59768 0.922422i
\(96\) 0 0
\(97\) −2.18452 + 1.26123i −0.221805 + 0.128059i −0.606786 0.794866i \(-0.707541\pi\)
0.384981 + 0.922925i \(0.374208\pi\)
\(98\) −5.67594 6.05791i −0.573357 0.611941i
\(99\) 0 0
\(100\) 1.81284 0.181284
\(101\) −1.49573 2.59068i −0.148831 0.257782i 0.781965 0.623323i \(-0.214218\pi\)
−0.930796 + 0.365540i \(0.880884\pi\)
\(102\) 0 0
\(103\) −11.4286 6.59832i −1.12610 0.650152i −0.183146 0.983086i \(-0.558628\pi\)
−0.942950 + 0.332934i \(0.891962\pi\)
\(104\) −6.06382 + 10.5028i −0.594606 + 1.02989i
\(105\) 0 0
\(106\) −1.54309 2.67272i −0.149879 0.259597i
\(107\) 19.5555i 1.89051i 0.326339 + 0.945253i \(0.394185\pi\)
−0.326339 + 0.945253i \(0.605815\pi\)
\(108\) 0 0
\(109\) 13.2484 1.26897 0.634485 0.772935i \(-0.281212\pi\)
0.634485 + 0.772935i \(0.281212\pi\)
\(110\) 0.265576 + 0.459990i 0.0253216 + 0.0438584i
\(111\) 0 0
\(112\) 0.954606 6.43951i 0.0902018 0.608477i
\(113\) 8.72665 + 5.03834i 0.820935 + 0.473967i 0.850739 0.525589i \(-0.176155\pi\)
−0.0298041 + 0.999556i \(0.509488\pi\)
\(114\) 0 0
\(115\) 1.34224 0.774943i 0.125165 0.0722638i
\(116\) 2.76016i 0.256274i
\(117\) 0 0
\(118\) 4.28561i 0.394522i
\(119\) 8.59038 + 6.81653i 0.787479 + 0.624870i
\(120\) 0 0
\(121\) −5.48755 + 9.50471i −0.498868 + 0.864065i
\(122\) 1.99569 3.45664i 0.180681 0.312949i
\(123\) 0 0
\(124\) −0.0665320 + 0.0384123i −0.00597475 + 0.00344952i
\(125\) −5.52245 −0.493943
\(126\) 0 0
\(127\) −12.4897 −1.10828 −0.554140 0.832423i \(-0.686953\pi\)
−0.554140 + 0.832423i \(0.686953\pi\)
\(128\) 3.39183 1.95827i 0.299798 0.173089i
\(129\) 0 0
\(130\) −6.63521 + 11.4925i −0.581946 + 1.00796i
\(131\) 5.02249 8.69921i 0.438817 0.760054i −0.558781 0.829315i \(-0.688731\pi\)
0.997599 + 0.0692612i \(0.0220642\pi\)
\(132\) 0 0
\(133\) 10.4199 13.1315i 0.903524 1.13865i
\(134\) 1.57423i 0.135993i
\(135\) 0 0
\(136\) 12.7488i 1.09320i
\(137\) 6.96410 4.02073i 0.594984 0.343514i −0.172082 0.985083i \(-0.555049\pi\)
0.767066 + 0.641569i \(0.221716\pi\)
\(138\) 0 0
\(139\) 16.3702 + 9.45136i 1.38850 + 0.801654i 0.993147 0.116873i \(-0.0372872\pi\)
0.395358 + 0.918527i \(0.370621\pi\)
\(140\) −0.653562 + 4.40875i −0.0552361 + 0.372607i
\(141\) 0 0
\(142\) −0.242705 0.420378i −0.0203674 0.0352774i
\(143\) 0.622259 0.0520359
\(144\) 0 0
\(145\) 13.1966i 1.09592i
\(146\) 8.90179 + 15.4184i 0.736717 + 1.27603i
\(147\) 0 0
\(148\) 0.730252 1.26483i 0.0600264 0.103969i
\(149\) −16.8063 9.70313i −1.37683 0.794912i −0.385051 0.922895i \(-0.625816\pi\)
−0.991776 + 0.127984i \(0.959149\pi\)
\(150\) 0 0
\(151\) 0.893968 + 1.54840i 0.0727501 + 0.126007i 0.900106 0.435672i \(-0.143489\pi\)
−0.827356 + 0.561678i \(0.810156\pi\)
\(152\) 19.4881 1.58070
\(153\) 0 0
\(154\) −0.460505 + 0.182027i −0.0371085 + 0.0146682i
\(155\) −0.318097 + 0.183653i −0.0255502 + 0.0147514i
\(156\) 0 0
\(157\) 3.80255 + 2.19540i 0.303477 + 0.175212i 0.644004 0.765022i \(-0.277272\pi\)
−0.340527 + 0.940235i \(0.610605\pi\)
\(158\) 4.44445 + 2.56601i 0.353582 + 0.204140i
\(159\) 0 0
\(160\) −7.94742 + 4.58845i −0.628299 + 0.362749i
\(161\) 0.531151 + 1.34374i 0.0418606 + 0.105902i
\(162\) 0 0
\(163\) 5.43560 0.425749 0.212874 0.977080i \(-0.431717\pi\)
0.212874 + 0.977080i \(0.431717\pi\)
\(164\) 1.18460 + 2.05179i 0.0925018 + 0.160218i
\(165\) 0 0
\(166\) 6.62616 + 3.82562i 0.514290 + 0.296925i
\(167\) 5.25273 9.09799i 0.406468 0.704024i −0.588023 0.808844i \(-0.700093\pi\)
0.994491 + 0.104821i \(0.0334268\pi\)
\(168\) 0 0
\(169\) 1.27335 + 2.20550i 0.0979497 + 0.169654i
\(170\) 13.9501i 1.06992i
\(171\) 0 0
\(172\) −3.89903 −0.297298
\(173\) −8.77949 15.2065i −0.667492 1.15613i −0.978603 0.205757i \(-0.934034\pi\)
0.311111 0.950374i \(-0.399299\pi\)
\(174\) 0 0
\(175\) −1.18490 + 7.99300i −0.0895699 + 0.604214i
\(176\) −0.336285 0.194154i −0.0253484 0.0146349i
\(177\) 0 0
\(178\) 5.19035 2.99665i 0.389033 0.224608i
\(179\) 18.2033i 1.36058i 0.732945 + 0.680288i \(0.238145\pi\)
−0.732945 + 0.680288i \(0.761855\pi\)
\(180\) 0 0
\(181\) 6.60182i 0.490710i 0.969433 + 0.245355i \(0.0789045\pi\)
−0.969433 + 0.245355i \(0.921096\pi\)
\(182\) −9.69121 7.69004i −0.718360 0.570024i
\(183\) 0 0
\(184\) −0.839883 + 1.45472i −0.0619170 + 0.107243i
\(185\) 3.49142 6.04732i 0.256694 0.444608i
\(186\) 0 0
\(187\) 0.566492 0.327065i 0.0414260 0.0239173i
\(188\) −5.14479 −0.375223
\(189\) 0 0
\(190\) 21.3245 1.54704
\(191\) 12.3063 7.10506i 0.890454 0.514104i 0.0163630 0.999866i \(-0.494791\pi\)
0.874091 + 0.485762i \(0.161458\pi\)
\(192\) 0 0
\(193\) 5.00214 8.66395i 0.360062 0.623645i −0.627909 0.778287i \(-0.716089\pi\)
0.987971 + 0.154642i \(0.0494223\pi\)
\(194\) 1.49573 2.59068i 0.107387 0.186000i
\(195\) 0 0
\(196\) −3.97636 1.20542i −0.284026 0.0861013i
\(197\) 20.1017i 1.43218i −0.698006 0.716092i \(-0.745929\pi\)
0.698006 0.716092i \(-0.254071\pi\)
\(198\) 0 0
\(199\) 12.9378i 0.917136i 0.888659 + 0.458568i \(0.151637\pi\)
−0.888659 + 0.458568i \(0.848363\pi\)
\(200\) −8.13521 + 4.69687i −0.575246 + 0.332119i
\(201\) 0 0
\(202\) 3.07236 + 1.77383i 0.216170 + 0.124806i
\(203\) 12.1698 + 1.80408i 0.854154 + 0.126622i
\(204\) 0 0
\(205\) 5.66372 + 9.80984i 0.395571 + 0.685149i
\(206\) 15.6502 1.09040
\(207\) 0 0
\(208\) 9.70160i 0.672685i
\(209\) −0.499960 0.865957i −0.0345830 0.0598995i
\(210\) 0 0
\(211\) −4.50720 + 7.80669i −0.310288 + 0.537435i −0.978425 0.206604i \(-0.933759\pi\)
0.668136 + 0.744039i \(0.267092\pi\)
\(212\) −1.33775 0.772349i −0.0918769 0.0530451i
\(213\) 0 0
\(214\) −11.5957 20.0844i −0.792667 1.37294i
\(215\) −18.6417 −1.27135
\(216\) 0 0
\(217\) −0.125877 0.318453i −0.00854510 0.0216180i
\(218\) −13.6067 + 7.85584i −0.921562 + 0.532064i
\(219\) 0 0
\(220\) 0.230234 + 0.132926i 0.0155224 + 0.00896185i
\(221\) 14.1534 + 8.17147i 0.952061 + 0.549672i
\(222\) 0 0
\(223\) −1.95429 + 1.12831i −0.130869 + 0.0755571i −0.564005 0.825771i \(-0.690740\pi\)
0.433136 + 0.901328i \(0.357407\pi\)
\(224\) −3.14495 7.95631i −0.210131 0.531604i
\(225\) 0 0
\(226\) −11.9502 −0.794915
\(227\) 9.32085 + 16.1442i 0.618647 + 1.07153i 0.989733 + 0.142929i \(0.0456522\pi\)
−0.371086 + 0.928598i \(0.621015\pi\)
\(228\) 0 0
\(229\) −12.3891 7.15283i −0.818692 0.472672i 0.0312731 0.999511i \(-0.490044\pi\)
−0.849965 + 0.526839i \(0.823377\pi\)
\(230\) −0.919025 + 1.59180i −0.0605987 + 0.104960i
\(231\) 0 0
\(232\) 7.15126 + 12.3863i 0.469503 + 0.813204i
\(233\) 17.0679i 1.11815i −0.829116 0.559077i \(-0.811156\pi\)
0.829116 0.559077i \(-0.188844\pi\)
\(234\) 0 0
\(235\) −24.5979 −1.60459
\(236\) −1.07251 1.85765i −0.0698148 0.120923i
\(237\) 0 0
\(238\) −12.8646 1.90708i −0.833890 0.123618i
\(239\) −1.93560 1.11752i −0.125203 0.0722863i 0.436090 0.899903i \(-0.356363\pi\)
−0.561294 + 0.827617i \(0.689696\pi\)
\(240\) 0 0
\(241\) −3.91464 + 2.26012i −0.252164 + 0.145587i −0.620755 0.784005i \(-0.713174\pi\)
0.368591 + 0.929592i \(0.379840\pi\)
\(242\) 13.0157i 0.836678i
\(243\) 0 0
\(244\) 1.99777i 0.127894i
\(245\) −19.0114 5.76324i −1.21460 0.368200i
\(246\) 0 0
\(247\) 12.4911 21.6353i 0.794793 1.37662i
\(248\) 0.199044 0.344754i 0.0126393 0.0218919i
\(249\) 0 0
\(250\) 5.67179 3.27461i 0.358716 0.207105i
\(251\) 21.1727 1.33641 0.668205 0.743978i \(-0.267063\pi\)
0.668205 + 0.743978i \(0.267063\pi\)
\(252\) 0 0
\(253\) 0.0861875 0.00541856
\(254\) 12.8274 7.40592i 0.804865 0.464689i
\(255\) 0 0
\(256\) 6.43346 11.1431i 0.402091 0.696443i
\(257\) −15.6502 + 27.1070i −0.976236 + 1.69089i −0.300440 + 0.953801i \(0.597134\pi\)
−0.675796 + 0.737089i \(0.736200\pi\)
\(258\) 0 0
\(259\) 5.09948 + 4.04647i 0.316866 + 0.251435i
\(260\) 6.64211i 0.411926i
\(261\) 0 0
\(262\) 11.9126i 0.735964i
\(263\) 5.78220 3.33836i 0.356546 0.205852i −0.311019 0.950404i \(-0.600670\pi\)
0.667564 + 0.744552i \(0.267337\pi\)
\(264\) 0 0
\(265\) −6.39593 3.69269i −0.392899 0.226840i
\(266\) −2.91522 + 19.6653i −0.178743 + 1.20575i
\(267\) 0 0
\(268\) −0.393968 0.682372i −0.0240654 0.0416825i
\(269\) 10.6589 0.649887 0.324944 0.945733i \(-0.394655\pi\)
0.324944 + 0.945733i \(0.394655\pi\)
\(270\) 0 0
\(271\) 7.44498i 0.452250i −0.974098 0.226125i \(-0.927394\pi\)
0.974098 0.226125i \(-0.0726058\pi\)
\(272\) −5.09924 8.83214i −0.309187 0.535527i
\(273\) 0 0
\(274\) −4.76829 + 8.25891i −0.288063 + 0.498939i
\(275\) 0.417411 + 0.240992i 0.0251708 + 0.0145324i
\(276\) 0 0
\(277\) 13.2793 + 23.0004i 0.797874 + 1.38196i 0.920998 + 0.389568i \(0.127376\pi\)
−0.123124 + 0.992391i \(0.539291\pi\)
\(278\) −22.4172 −1.34450
\(279\) 0 0
\(280\) −8.48968 21.4778i −0.507356 1.28354i
\(281\) −21.0993 + 12.1817i −1.25868 + 0.726699i −0.972818 0.231572i \(-0.925613\pi\)
−0.285862 + 0.958271i \(0.592280\pi\)
\(282\) 0 0
\(283\) 7.49302 + 4.32610i 0.445414 + 0.257160i 0.705891 0.708320i \(-0.250547\pi\)
−0.260478 + 0.965480i \(0.583880\pi\)
\(284\) −0.210408 0.121479i −0.0124854 0.00720844i
\(285\) 0 0
\(286\) −0.639086 + 0.368977i −0.0377900 + 0.0218181i
\(287\) −9.82082 + 3.88195i −0.579704 + 0.229144i
\(288\) 0 0
\(289\) 0.179961 0.0105860
\(290\) 7.82512 + 13.5535i 0.459507 + 0.795890i
\(291\) 0 0
\(292\) 7.71719 + 4.45552i 0.451614 + 0.260740i
\(293\) −4.40023 + 7.62143i −0.257064 + 0.445249i −0.965454 0.260573i \(-0.916089\pi\)
0.708390 + 0.705821i \(0.249422\pi\)
\(294\) 0 0
\(295\) −5.12782 8.88164i −0.298553 0.517109i
\(296\) 7.56800i 0.439881i
\(297\) 0 0
\(298\) 23.0144 1.33319
\(299\) 1.07667 + 1.86484i 0.0622652 + 0.107846i
\(300\) 0 0
\(301\) 2.54846 17.1912i 0.146891 0.990885i
\(302\) −1.83628 1.06018i −0.105666 0.0610065i
\(303\) 0 0
\(304\) −13.5011 + 7.79485i −0.774339 + 0.447065i
\(305\) 9.55155i 0.546920i
\(306\) 0 0
\(307\) 11.1747i 0.637771i −0.947793 0.318886i \(-0.896691\pi\)
0.947793 0.318886i \(-0.103309\pi\)
\(308\) −0.154058 + 0.194148i −0.00877825 + 0.0110626i
\(309\) 0 0
\(310\) 0.217799 0.377240i 0.0123702 0.0214258i
\(311\) −8.20279 + 14.2076i −0.465137 + 0.805641i −0.999208 0.0397985i \(-0.987328\pi\)
0.534070 + 0.845440i \(0.320662\pi\)
\(312\) 0 0
\(313\) −7.10514 + 4.10216i −0.401606 + 0.231868i −0.687177 0.726490i \(-0.741150\pi\)
0.285570 + 0.958358i \(0.407817\pi\)
\(314\) −5.20717 −0.293858
\(315\) 0 0
\(316\) 2.56867 0.144499
\(317\) −19.8427 + 11.4562i −1.11448 + 0.643443i −0.939985 0.341215i \(-0.889161\pi\)
−0.174491 + 0.984659i \(0.555828\pi\)
\(318\) 0 0
\(319\) 0.366926 0.635534i 0.0205439 0.0355831i
\(320\) 12.4244 21.5197i 0.694545 1.20299i
\(321\) 0 0
\(322\) −1.34230 1.06513i −0.0748037 0.0593572i
\(323\) 26.2618i 1.46125i
\(324\) 0 0
\(325\) 12.0420i 0.667972i
\(326\) −5.58259 + 3.22311i −0.309191 + 0.178512i
\(327\) 0 0
\(328\) −10.6319 6.13833i −0.587049 0.338933i
\(329\) 3.36271 22.6839i 0.185392 1.25060i
\(330\) 0 0
\(331\) −9.63161 16.6824i −0.529401 0.916950i −0.999412 0.0342892i \(-0.989083\pi\)
0.470011 0.882661i \(-0.344250\pi\)
\(332\) 3.82959 0.210176
\(333\) 0 0
\(334\) 12.4587i 0.681709i
\(335\) −1.88361 3.26250i −0.102912 0.178249i
\(336\) 0 0
\(337\) −2.26829 + 3.92878i −0.123561 + 0.214015i −0.921170 0.389161i \(-0.872765\pi\)
0.797608 + 0.603176i \(0.206098\pi\)
\(338\) −2.61556 1.51009i −0.142268 0.0821383i
\(339\) 0 0
\(340\) 3.49115 + 6.04684i 0.189334 + 0.327936i
\(341\) −0.0204255 −0.00110610
\(342\) 0 0
\(343\) 7.91381 16.7443i 0.427306 0.904107i
\(344\) 17.4971 10.1019i 0.943379 0.544660i
\(345\) 0 0
\(346\) 18.0338 + 10.4118i 0.969504 + 0.559743i
\(347\) −7.56294 4.36646i −0.406000 0.234404i 0.283070 0.959099i \(-0.408647\pi\)
−0.689070 + 0.724695i \(0.741981\pi\)
\(348\) 0 0
\(349\) 7.82927 4.52023i 0.419091 0.241963i −0.275597 0.961273i \(-0.588876\pi\)
0.694689 + 0.719311i \(0.255542\pi\)
\(350\) −3.52261 8.91175i −0.188292 0.476353i
\(351\) 0 0
\(352\) −0.510317 −0.0272000
\(353\) −0.607896 1.05291i −0.0323550 0.0560406i 0.849394 0.527758i \(-0.176967\pi\)
−0.881750 + 0.471718i \(0.843634\pi\)
\(354\) 0 0
\(355\) −1.00598 0.580805i −0.0533920 0.0308259i
\(356\) 1.49988 2.59787i 0.0794936 0.137687i
\(357\) 0 0
\(358\) −10.7939 18.6955i −0.570473 0.988089i
\(359\) 17.3069i 0.913424i 0.889615 + 0.456712i \(0.150973\pi\)
−0.889615 + 0.456712i \(0.849027\pi\)
\(360\) 0 0
\(361\) −21.1445 −1.11287
\(362\) −3.91464 6.78035i −0.205749 0.356367i
\(363\) 0 0
\(364\) −6.12529 0.908025i −0.321052 0.0475934i
\(365\) 36.8968 + 21.3024i 1.93127 + 1.11502i
\(366\) 0 0
\(367\) −24.4297 + 14.1045i −1.27522 + 0.736250i −0.975966 0.217923i \(-0.930072\pi\)
−0.299256 + 0.954173i \(0.596738\pi\)
\(368\) 1.34374i 0.0700474i
\(369\) 0 0
\(370\) 8.28114i 0.430516i
\(371\) 4.27973 5.39344i 0.222193 0.280014i
\(372\) 0 0
\(373\) −14.1264 + 24.4676i −0.731435 + 1.26688i 0.224835 + 0.974397i \(0.427816\pi\)
−0.956270 + 0.292486i \(0.905518\pi\)
\(374\) −0.387874 + 0.671818i −0.0200565 + 0.0347389i
\(375\) 0 0
\(376\) 23.0875 13.3296i 1.19065 0.687420i
\(377\) 18.3347 0.944287
\(378\) 0 0
\(379\) 14.6447 0.752250 0.376125 0.926569i \(-0.377256\pi\)
0.376125 + 0.926569i \(0.377256\pi\)
\(380\) 9.24338 5.33667i 0.474175 0.273765i
\(381\) 0 0
\(382\) −8.42607 + 14.5944i −0.431115 + 0.746714i
\(383\) −12.3932 + 21.4657i −0.633264 + 1.09684i 0.353617 + 0.935390i \(0.384952\pi\)
−0.986880 + 0.161454i \(0.948382\pi\)
\(384\) 0 0
\(385\) −0.736567 + 0.928244i −0.0375390 + 0.0473077i
\(386\) 11.8643i 0.603878i
\(387\) 0 0
\(388\) 1.49729i 0.0760131i
\(389\) −4.43706 + 2.56174i −0.224968 + 0.129885i −0.608248 0.793747i \(-0.708128\pi\)
0.383281 + 0.923632i \(0.374794\pi\)
\(390\) 0 0
\(391\) 1.96035 + 1.13181i 0.0991391 + 0.0572380i
\(392\) 20.9672 4.89293i 1.05900 0.247130i
\(393\) 0 0
\(394\) 11.9195 + 20.6453i 0.600498 + 1.04009i
\(395\) 12.2811 0.617930
\(396\) 0 0
\(397\) 1.92094i 0.0964093i 0.998837 + 0.0482046i \(0.0153500\pi\)
−0.998837 + 0.0482046i \(0.984650\pi\)
\(398\) −7.67163 13.2877i −0.384544 0.666050i
\(399\) 0 0
\(400\) 3.75729 6.50783i 0.187865 0.325391i
\(401\) 12.4612 + 7.19446i 0.622282 + 0.359274i 0.777757 0.628565i \(-0.216358\pi\)
−0.155475 + 0.987840i \(0.549691\pi\)
\(402\) 0 0
\(403\) −0.255158 0.441947i −0.0127103 0.0220150i
\(404\) 1.77567 0.0883429
\(405\) 0 0
\(406\) −13.5687 + 5.36339i −0.673402 + 0.266181i
\(407\) 0.336285 0.194154i 0.0166690 0.00962386i
\(408\) 0 0
\(409\) 8.42281 + 4.86291i 0.416481 + 0.240455i 0.693571 0.720389i \(-0.256037\pi\)
−0.277090 + 0.960844i \(0.589370\pi\)
\(410\) −11.6337 6.71675i −0.574550 0.331717i
\(411\) 0 0
\(412\) 6.78380 3.91663i 0.334214 0.192958i
\(413\) 8.89158 3.51464i 0.437526 0.172944i
\(414\) 0 0
\(415\) 18.3097 0.898789
\(416\) −6.37495 11.0417i −0.312558 0.541366i
\(417\) 0 0
\(418\) 1.02696 + 0.592916i 0.0502303 + 0.0290005i
\(419\) 14.9512 25.8963i 0.730416 1.26512i −0.226289 0.974060i \(-0.572660\pi\)
0.956706 0.291058i \(-0.0940072\pi\)
\(420\) 0 0
\(421\) −12.5452 21.7290i −0.611417 1.05901i −0.991002 0.133848i \(-0.957266\pi\)
0.379585 0.925157i \(-0.376067\pi\)
\(422\) 10.6904i 0.520401i
\(423\) 0 0
\(424\) 8.00427 0.388722
\(425\) 6.32939 + 10.9628i 0.307021 + 0.531775i
\(426\) 0 0
\(427\) 8.80835 + 1.30577i 0.426266 + 0.0631905i
\(428\) −10.0526 5.80388i −0.485912 0.280541i
\(429\) 0 0
\(430\) 19.1458 11.0538i 0.923293 0.533064i
\(431\) 6.39061i 0.307825i 0.988084 + 0.153913i \(0.0491874\pi\)
−0.988084 + 0.153913i \(0.950813\pi\)
\(432\) 0 0
\(433\) 33.1771i 1.59439i 0.603721 + 0.797196i \(0.293684\pi\)
−0.603721 + 0.797196i \(0.706316\pi\)
\(434\) 0.318112 + 0.252424i 0.0152699 + 0.0121167i
\(435\) 0 0
\(436\) −3.93200 + 6.81042i −0.188309 + 0.326160i
\(437\) 1.73012 2.99665i 0.0827627 0.143349i
\(438\) 0 0
\(439\) 7.32931 4.23158i 0.349809 0.201962i −0.314792 0.949161i \(-0.601935\pi\)
0.664601 + 0.747198i \(0.268601\pi\)
\(440\) −1.37758 −0.0656737
\(441\) 0 0
\(442\) −19.3815 −0.921885
\(443\) −16.1082 + 9.30006i −0.765322 + 0.441859i −0.831203 0.555969i \(-0.812348\pi\)
0.0658812 + 0.997827i \(0.479014\pi\)
\(444\) 0 0
\(445\) 7.17111 12.4207i 0.339943 0.588799i
\(446\) 1.33809 2.31764i 0.0633604 0.109743i
\(447\) 0 0
\(448\) 18.1468 + 14.3996i 0.857353 + 0.680316i
\(449\) 20.3100i 0.958489i 0.877681 + 0.479245i \(0.159089\pi\)
−0.877681 + 0.479245i \(0.840911\pi\)
\(450\) 0 0
\(451\) 0.629906i 0.0296611i
\(452\) −5.17996 + 2.99065i −0.243645 + 0.140668i
\(453\) 0 0
\(454\) −19.1458 11.0538i −0.898558 0.518783i
\(455\) −29.2857 4.34137i −1.37294 0.203527i
\(456\) 0 0
\(457\) −5.67830 9.83511i −0.265620 0.460067i 0.702106 0.712072i \(-0.252243\pi\)
−0.967726 + 0.252005i \(0.918910\pi\)
\(458\) 16.9654 0.792743
\(459\) 0 0
\(460\) 0.919981i 0.0428943i
\(461\) 19.4984 + 33.7721i 0.908129 + 1.57293i 0.816661 + 0.577117i \(0.195822\pi\)
0.0914676 + 0.995808i \(0.470844\pi\)
\(462\) 0 0
\(463\) −5.03443 + 8.71990i −0.233970 + 0.405248i −0.958973 0.283498i \(-0.908505\pi\)
0.725003 + 0.688746i \(0.241838\pi\)
\(464\) −9.90856 5.72071i −0.459993 0.265577i
\(465\) 0 0
\(466\) 10.1206 + 17.5294i 0.468829 + 0.812035i
\(467\) −3.59330 −0.166278 −0.0831389 0.996538i \(-0.526495\pi\)
−0.0831389 + 0.996538i \(0.526495\pi\)
\(468\) 0 0
\(469\) 3.26615 1.29103i 0.150817 0.0596145i
\(470\) 25.2630 14.5856i 1.16530 0.672784i
\(471\) 0 0
\(472\) 9.62592 + 5.55753i 0.443069 + 0.255806i
\(473\) −0.897761 0.518322i −0.0412791 0.0238325i
\(474\) 0 0
\(475\) 16.7581 9.67530i 0.768915 0.443933i
\(476\) −6.05361 + 2.39285i −0.277467 + 0.109676i
\(477\) 0 0
\(478\) 2.65059 0.121235
\(479\) −0.811090 1.40485i −0.0370597 0.0641892i 0.846901 0.531751i \(-0.178466\pi\)
−0.883960 + 0.467562i \(0.845132\pi\)
\(480\) 0 0
\(481\) 8.40183 + 4.85080i 0.383090 + 0.221177i
\(482\) 2.68033 4.64247i 0.122086 0.211459i
\(483\) 0 0
\(484\) −3.25729 5.64180i −0.148059 0.256445i
\(485\) 7.15869i 0.325060i
\(486\) 0 0
\(487\) 7.99573 0.362321 0.181161 0.983454i \(-0.442015\pi\)
0.181161 + 0.983454i \(0.442015\pi\)
\(488\) 5.17598 + 8.96507i 0.234306 + 0.405829i
\(489\) 0 0
\(490\) 22.9429 5.35399i 1.03646 0.241869i
\(491\) −9.30632 5.37300i −0.419988 0.242480i 0.275084 0.961420i \(-0.411294\pi\)
−0.695072 + 0.718940i \(0.744628\pi\)
\(492\) 0 0
\(493\) 16.6916 9.63688i 0.751751 0.434023i
\(494\) 29.6272i 1.33299i
\(495\) 0 0
\(496\) 0.318453i 0.0142990i
\(497\) 0.673138 0.848308i 0.0301944 0.0380518i
\(498\) 0 0
\(499\) −8.46050 + 14.6540i −0.378744 + 0.656004i −0.990880 0.134749i \(-0.956977\pi\)
0.612136 + 0.790753i \(0.290311\pi\)
\(500\) 1.63901 2.83884i 0.0732986 0.126957i
\(501\) 0 0
\(502\) −21.7453 + 12.5546i −0.970538 + 0.560341i
\(503\) −33.9226 −1.51253 −0.756267 0.654263i \(-0.772979\pi\)
−0.756267 + 0.654263i \(0.772979\pi\)
\(504\) 0 0
\(505\) 8.48968 0.377786
\(506\) −0.0885182 + 0.0511060i −0.00393511 + 0.00227194i
\(507\) 0 0
\(508\) 3.70681 6.42038i 0.164463 0.284858i
\(509\) 5.06805 8.77812i 0.224637 0.389083i −0.731573 0.681763i \(-0.761214\pi\)
0.956211 + 0.292680i \(0.0945469\pi\)
\(510\) 0 0
\(511\) −24.6889 + 31.1137i −1.09217 + 1.37639i
\(512\) 23.0923i 1.02055i
\(513\) 0 0
\(514\) 37.1201i 1.63730i
\(515\) 32.4341 18.7259i 1.42922 0.825160i
\(516\) 0 0
\(517\) −1.18460 0.683930i −0.0520987 0.0300792i
\(518\) −7.63679 1.13209i −0.335541 0.0497413i
\(519\) 0 0
\(520\) −17.2089 29.8068i −0.754662 1.30711i
\(521\) −31.6986 −1.38874 −0.694370 0.719618i \(-0.744317\pi\)
−0.694370 + 0.719618i \(0.744317\pi\)
\(522\) 0 0
\(523\) 8.09911i 0.354149i 0.984197 + 0.177075i \(0.0566634\pi\)
−0.984197 + 0.177075i \(0.943337\pi\)
\(524\) 2.98125 + 5.16367i 0.130236 + 0.225576i
\(525\) 0 0
\(526\) −3.95904 + 6.85726i −0.172622 + 0.298991i
\(527\) −0.464582 0.268227i −0.0202375 0.0116841i
\(528\) 0 0
\(529\) −11.3509 19.6603i −0.493516 0.854795i
\(530\) 8.75851 0.380446
\(531\) 0 0
\(532\) 3.65779 + 9.25372i 0.158585 + 0.401200i
\(533\) −13.6293 + 7.86887i −0.590350 + 0.340839i
\(534\) 0 0
\(535\) −48.0628 27.7490i −2.07793 1.19970i
\(536\) 3.53590 + 2.04145i 0.152727 + 0.0881772i
\(537\) 0 0
\(538\) −10.9472 + 6.32036i −0.471967 + 0.272490i
\(539\) −0.755323 0.806153i −0.0325341 0.0347235i
\(540\) 0 0
\(541\) 1.21634 0.0522944 0.0261472 0.999658i \(-0.491676\pi\)
0.0261472 + 0.999658i \(0.491676\pi\)
\(542\) 4.41460 + 7.64631i 0.189623 + 0.328437i
\(543\) 0 0
\(544\) −11.6073 6.70145i −0.497657 0.287322i
\(545\) −18.7994 + 32.5614i −0.805276 + 1.39478i
\(546\) 0 0
\(547\) 13.1278 + 22.7380i 0.561305 + 0.972209i 0.997383 + 0.0722999i \(0.0230339\pi\)
−0.436078 + 0.899909i \(0.643633\pi\)
\(548\) 4.77324i 0.203903i
\(549\) 0 0
\(550\) −0.571598 −0.0243730
\(551\) −14.7312 25.5152i −0.627571 1.08699i
\(552\) 0 0
\(553\) −1.67892 + 11.3255i −0.0713950 + 0.481611i
\(554\) −27.2768 15.7482i −1.15888 0.669079i
\(555\) 0 0
\(556\) −9.71703 + 5.61013i −0.412094 + 0.237923i
\(557\) 27.2172i 1.15323i −0.817016 0.576615i \(-0.804373\pi\)
0.817016 0.576615i \(-0.195627\pi\)
\(558\) 0 0
\(559\) 25.8998i 1.09545i
\(560\) 14.4722 + 11.4838i 0.611561 + 0.485278i
\(561\) 0 0
\(562\) 14.4466 25.0222i 0.609393 1.05550i
\(563\) 4.68017 8.10630i 0.197246 0.341640i −0.750389 0.660997i \(-0.770134\pi\)
0.947634 + 0.319357i \(0.103467\pi\)
\(564\) 0 0
\(565\) −24.7660 + 14.2987i −1.04191 + 0.601549i
\(566\) −10.2609 −0.431296
\(567\) 0 0
\(568\) 1.25895 0.0528244
\(569\) 30.2424 17.4605i 1.26783 0.731980i 0.293251 0.956036i \(-0.405263\pi\)
0.974576 + 0.224055i \(0.0719296\pi\)
\(570\) 0 0
\(571\) 0.735987 1.27477i 0.0308001 0.0533473i −0.850214 0.526436i \(-0.823528\pi\)
0.881015 + 0.473089i \(0.156861\pi\)
\(572\) −0.184680 + 0.319875i −0.00772186 + 0.0133747i
\(573\) 0 0
\(574\) 7.78454 9.81030i 0.324920 0.409474i
\(575\) 1.66791i 0.0695567i
\(576\) 0 0
\(577\) 18.6196i 0.775146i −0.921839 0.387573i \(-0.873314\pi\)
0.921839 0.387573i \(-0.126686\pi\)
\(578\) −0.184828 + 0.106710i −0.00768783 + 0.00443857i
\(579\) 0 0
\(580\) 6.78380 + 3.91663i 0.281682 + 0.162629i
\(581\) −2.50307 + 16.8851i −0.103845 + 0.700510i
\(582\) 0 0
\(583\) −0.205346 0.355670i −0.00850458 0.0147304i
\(584\) −46.1750 −1.91073
\(585\) 0 0
\(586\) 10.4367i 0.431136i
\(587\) −9.28551 16.0830i −0.383254 0.663816i 0.608271 0.793729i \(-0.291863\pi\)
−0.991525 + 0.129914i \(0.958530\pi\)
\(588\) 0 0
\(589\) −0.410019 + 0.710174i −0.0168945 + 0.0292622i
\(590\) 10.5330 + 6.08121i 0.433636 + 0.250360i
\(591\) 0 0
\(592\) −3.02704 5.24299i −0.124411 0.215486i
\(593\) 30.9228 1.26985 0.634924 0.772574i \(-0.281031\pi\)
0.634924 + 0.772574i \(0.281031\pi\)
\(594\) 0 0
\(595\) −28.9430 + 11.4405i −1.18655 + 0.469015i
\(596\) 9.97588 5.75958i 0.408628 0.235922i
\(597\) 0 0
\(598\) −2.21156 1.27685i −0.0904375 0.0522141i
\(599\) −11.8741 6.85553i −0.485164 0.280109i 0.237402 0.971411i \(-0.423704\pi\)
−0.722566 + 0.691302i \(0.757037\pi\)
\(600\) 0 0
\(601\) −17.1065 + 9.87644i −0.697788 + 0.402868i −0.806523 0.591203i \(-0.798653\pi\)
0.108735 + 0.994071i \(0.465320\pi\)
\(602\) 7.57638 + 19.1672i 0.308790 + 0.781198i
\(603\) 0 0
\(604\) −1.06128 −0.0431829
\(605\) −15.5735 26.9741i −0.633153 1.09665i
\(606\) 0 0
\(607\) −15.5219 8.96157i −0.630014 0.363739i 0.150744 0.988573i \(-0.451833\pi\)
−0.780757 + 0.624834i \(0.785167\pi\)
\(608\) −10.2440 + 17.7432i −0.415450 + 0.719581i
\(609\) 0 0
\(610\) 5.66372 + 9.80984i 0.229317 + 0.397189i
\(611\) 34.1750i 1.38257i
\(612\) 0 0
\(613\) −41.4327 −1.67345 −0.836725 0.547623i \(-0.815533\pi\)
−0.836725 + 0.547623i \(0.815533\pi\)
\(614\) 6.62616 + 11.4768i 0.267410 + 0.463168i
\(615\) 0 0
\(616\) 0.188326 1.27039i 0.00758786 0.0511856i
\(617\) −19.9686 11.5289i −0.803904 0.464134i 0.0409302 0.999162i \(-0.486968\pi\)
−0.844835 + 0.535028i \(0.820301\pi\)
\(618\) 0 0
\(619\) 1.67850 0.969082i 0.0674646 0.0389507i −0.465888 0.884844i \(-0.654265\pi\)
0.533353 + 0.845893i \(0.320932\pi\)
\(620\) 0.218026i 0.00875613i
\(621\) 0 0
\(622\) 19.4558i 0.780106i
\(623\) 10.4739 + 8.31113i 0.419629 + 0.332978i
\(624\) 0 0
\(625\) 15.4715 26.7974i 0.618860 1.07190i
\(626\) 4.86485 8.42617i 0.194439 0.336778i
\(627\) 0 0
\(628\) −2.25712 + 1.30315i −0.0900687 + 0.0520012i
\(629\) 10.1985 0.406640
\(630\) 0 0
\(631\) 23.5831 0.938827 0.469414 0.882978i \(-0.344465\pi\)
0.469414 + 0.882978i \(0.344465\pi\)
\(632\) −11.5270 + 6.65514i −0.458521 + 0.264727i
\(633\) 0 0
\(634\) 13.5862 23.5320i 0.539576 0.934574i
\(635\) 17.7227 30.6966i 0.703303 1.21816i
\(636\) 0 0
\(637\) 8.00715 26.4135i 0.317255 1.04654i
\(638\) 0.870293i 0.0344552i
\(639\) 0 0
\(640\) 11.1151i 0.439361i
\(641\) −21.5093 + 12.4184i −0.849568 + 0.490498i −0.860505 0.509442i \(-0.829852\pi\)
0.0109373 + 0.999940i \(0.496518\pi\)
\(642\) 0 0
\(643\) 37.9247 + 21.8959i 1.49561 + 0.863489i 0.999987 0.00505169i \(-0.00160801\pi\)
0.495619 + 0.868540i \(0.334941\pi\)
\(644\) −0.848397 0.125768i −0.0334315 0.00495596i
\(645\) 0 0
\(646\) 15.5723 + 26.9720i 0.612683 + 1.06120i
\(647\) −29.3713 −1.15471 −0.577353 0.816494i \(-0.695914\pi\)
−0.577353 + 0.816494i \(0.695914\pi\)
\(648\) 0 0
\(649\) 0.570305i 0.0223864i
\(650\) −7.14048 12.3677i −0.280073 0.485100i
\(651\) 0 0
\(652\) −1.61323 + 2.79420i −0.0631789 + 0.109429i
\(653\) 28.0816 + 16.2129i 1.09892 + 0.634461i 0.935937 0.352168i \(-0.114556\pi\)
0.162981 + 0.986629i \(0.447889\pi\)
\(654\) 0 0
\(655\) 14.2537 + 24.6881i 0.556938 + 0.964645i
\(656\) 9.82082 0.383438
\(657\) 0 0
\(658\) 9.99707 + 25.2913i 0.389727 + 0.985957i
\(659\) 0.203016 0.117211i 0.00790837 0.00456590i −0.496041 0.868299i \(-0.665213\pi\)
0.503949 + 0.863733i \(0.331880\pi\)
\(660\) 0 0
\(661\) −3.05138 1.76171i −0.118685 0.0685227i 0.439482 0.898251i \(-0.355162\pi\)
−0.558167 + 0.829728i \(0.688495\pi\)
\(662\) 19.7841 + 11.4224i 0.768933 + 0.443943i
\(663\) 0 0
\(664\) −17.1855 + 9.92204i −0.666926 + 0.385050i
\(665\) 17.4883 + 44.2431i 0.678167 + 1.71567i
\(666\) 0 0
\(667\) 2.53950 0.0983296
\(668\) 3.11791 + 5.40038i 0.120636 + 0.208947i
\(669\) 0 0
\(670\) 3.86908 + 2.23382i 0.149476 + 0.0862999i
\(671\) 0.265576 0.459990i 0.0102524 0.0177577i
\(672\) 0 0
\(673\) 9.16585 + 15.8757i 0.353318 + 0.611964i 0.986829 0.161770i \(-0.0517202\pi\)
−0.633511 + 0.773734i \(0.718387\pi\)
\(674\) 5.38004i 0.207231i
\(675\) 0 0
\(676\) −1.51166 −0.0581409
\(677\) 16.9260 + 29.3166i 0.650517 + 1.12673i 0.982998 + 0.183619i \(0.0587812\pi\)
−0.332480 + 0.943110i \(0.607885\pi\)
\(678\) 0 0
\(679\) 6.60168 + 0.978646i 0.253349 + 0.0375570i
\(680\) −31.3334 18.0903i −1.20158 0.693732i
\(681\) 0 0
\(682\) 0.0209779 0.0121116i 0.000803285 0.000463777i
\(683\) 28.0284i 1.07248i 0.844066 + 0.536239i \(0.180156\pi\)
−0.844066 + 0.536239i \(0.819844\pi\)
\(684\) 0 0
\(685\) 22.8214i 0.871962i
\(686\) 1.80093 + 21.8897i 0.0687599 + 0.835753i
\(687\) 0 0
\(688\) −8.08113 + 13.9969i −0.308090 + 0.533628i
\(689\) 5.13043 8.88616i 0.195454 0.338536i
\(690\) 0 0
\(691\) 42.7393 24.6756i 1.62588 0.938703i 0.640577 0.767894i \(-0.278695\pi\)
0.985304 0.170809i \(-0.0546381\pi\)
\(692\) 10.4226 0.396210
\(693\) 0 0
\(694\) 10.3566 0.393131
\(695\) −46.4583 + 26.8227i −1.76226 + 1.01744i
\(696\) 0 0
\(697\) −8.27188 + 14.3273i −0.313320 + 0.542686i
\(698\) −5.36066 + 9.28494i −0.202904 + 0.351440i
\(699\) 0 0
\(700\) −3.75717 2.98134i −0.142008 0.112684i
\(701\) 26.3889i 0.996696i −0.866977 0.498348i \(-0.833940\pi\)
0.866977 0.498348i \(-0.166060\pi\)
\(702\) 0 0
\(703\) 15.5897i 0.587976i
\(704\) 1.19669 0.690907i 0.0451018 0.0260396i
\(705\) 0 0
\(706\) 1.24867 + 0.720920i 0.0469943 + 0.0271322i
\(707\) −1.16060 + 7.82911i −0.0436489 + 0.294444i
\(708\) 0 0
\(709\) 5.35661 + 9.27792i 0.201172 + 0.348440i 0.948906 0.315558i \(-0.102192\pi\)
−0.747735 + 0.663998i \(0.768858\pi\)
\(710\) 1.37758 0.0516998
\(711\) 0 0
\(712\) 15.5441i 0.582539i
\(713\) −0.0353413 0.0612130i −0.00132354 0.00229244i
\(714\) 0 0
\(715\) −0.882977 + 1.52936i −0.0330215 + 0.0571949i
\(716\) −9.35748 5.40254i −0.349705 0.201902i
\(717\) 0 0
\(718\) −10.2624 17.7749i −0.382988 0.663354i
\(719\) 17.5794 0.655601 0.327801 0.944747i \(-0.393693\pi\)
0.327801 + 0.944747i \(0.393693\pi\)
\(720\) 0 0
\(721\) 12.8348 + 32.4704i 0.477994 + 1.20926i
\(722\) 21.7163 12.5379i 0.808198 0.466614i
\(723\) 0 0
\(724\) −3.39370 1.95935i −0.126126 0.0728188i
\(725\) 12.2989 + 7.10079i 0.456771 + 0.263717i
\(726\) 0 0
\(727\) 43.4695 25.0971i 1.61220 0.930802i 0.623336 0.781954i \(-0.285777\pi\)
0.988860 0.148847i \(-0.0475563\pi\)
\(728\) 29.8401 11.7951i 1.10595 0.437156i
\(729\) 0 0
\(730\) −50.5261 −1.87005
\(731\) −13.6132 23.5787i −0.503501 0.872089i
\(732\) 0 0
\(733\) 34.5617 + 19.9542i 1.27656 + 0.737025i 0.976215 0.216804i \(-0.0695633\pi\)
0.300350 + 0.953829i \(0.402897\pi\)
\(734\) 16.7269 28.9719i 0.617402 1.06937i
\(735\) 0 0
\(736\) −0.882977 1.52936i −0.0325470 0.0563730i
\(737\) 0.209490i 0.00771668i
\(738\) 0 0
\(739\) 30.3432 1.11619 0.558096 0.829777i \(-0.311532\pi\)
0.558096 + 0.829777i \(0.311532\pi\)
\(740\) 2.07244 + 3.58956i 0.0761843 + 0.131955i
\(741\) 0 0
\(742\) −1.19735 + 8.07702i −0.0439562 + 0.296517i
\(743\) 39.5861 + 22.8550i 1.45227 + 0.838470i 0.998610 0.0527041i \(-0.0167840\pi\)
0.453662 + 0.891174i \(0.350117\pi\)
\(744\) 0 0
\(745\) 47.6959 27.5372i 1.74744 1.00889i
\(746\) 33.5056i 1.22673i
\(747\) 0 0
\(748\) 0.388278i 0.0141968i
\(749\) 32.1604 40.5295i 1.17512 1.48092i
\(750\) 0 0
\(751\) −6.07753 + 10.5266i −0.221772 + 0.384121i −0.955346 0.295489i \(-0.904517\pi\)
0.733574 + 0.679610i \(0.237851\pi\)
\(752\) −10.6631 + 18.4690i −0.388843 + 0.673496i
\(753\) 0 0
\(754\) −18.8305 + 10.8718i −0.685768 + 0.395928i
\(755\) −5.07411 −0.184666
\(756\) 0 0
\(757\) −9.71614 −0.353139 −0.176570 0.984288i \(-0.556500\pi\)
−0.176570 + 0.984288i \(0.556500\pi\)
\(758\) −15.0408 + 8.68379i −0.546305 + 0.315409i
\(759\) 0 0
\(760\) −27.6534 + 47.8971i −1.00309 + 1.73741i
\(761\) 19.4175 33.6320i 0.703882 1.21916i −0.263211 0.964738i \(-0.584782\pi\)
0.967093 0.254422i \(-0.0818851\pi\)
\(762\) 0 0
\(763\) −27.4578 21.7880i −0.994040 0.788777i
\(764\) 8.43483i 0.305161i
\(765\) 0 0
\(766\) 29.3949i 1.06208i
\(767\) 12.3397 7.12432i 0.445560 0.257244i
\(768\) 0 0
\(769\) −9.42879 5.44371i −0.340011 0.196305i 0.320266 0.947328i \(-0.396228\pi\)
−0.660277 + 0.751022i \(0.729561\pi\)
\(770\) 0.206072 1.39010i 0.00742630 0.0500958i
\(771\) 0 0
\(772\) 2.96916 + 5.14274i 0.106863 + 0.185091i
\(773\) 37.3337 1.34280 0.671400 0.741096i \(-0.265693\pi\)
0.671400 + 0.741096i \(0.265693\pi\)
\(774\) 0 0
\(775\) 0.395277i 0.0141988i
\(776\) 3.87930 + 6.71914i 0.139259 + 0.241203i
\(777\) 0 0
\(778\) 3.03803 5.26203i 0.108919 0.188653i
\(779\) 21.9012 + 12.6446i 0.784691 + 0.453041i
\(780\) 0 0
\(781\) −0.0322979 0.0559416i −0.00115571 0.00200175i
\(782\) −2.68448 −0.0959969
\(783\) 0 0
\(784\) −12.5687 + 11.7762i −0.448881 + 0.420578i
\(785\) −10.7915 + 6.23049i −0.385166 + 0.222376i
\(786\) 0 0
\(787\) −15.4554 8.92315i −0.550924 0.318076i 0.198571 0.980087i \(-0.436370\pi\)
−0.749495 + 0.662011i \(0.769703\pi\)
\(788\) 10.3334 + 5.96597i 0.368111 + 0.212529i
\(789\) 0 0
\(790\) −12.6132 + 7.28225i −0.448759 + 0.259091i
\(791\) −9.80039 24.7937i −0.348462 0.881562i
\(792\) 0 0
\(793\) 13.2704 0.471246
\(794\) −1.13905 1.97289i −0.0404233 0.0700151i
\(795\) 0 0
\(796\) −6.65074 3.83980i −0.235729 0.136098i
\(797\) −5.74854 + 9.95676i −0.203624 + 0.352687i −0.949693 0.313181i \(-0.898605\pi\)
0.746070 + 0.665868i \(0.231939\pi\)
\(798\) 0 0
\(799\) −17.9626 31.1122i −0.635473 1.10067i
\(800\) 9.87572i 0.349159i
\(801\) 0 0
\(802\) −17.0642 −0.602558
\(803\) 1.18460 + 2.05179i 0.0418037 + 0.0724061i
\(804\) 0 0
\(805\) −4.05629 0.601312i −0.142965 0.0211935i
\(806\) 0.524117 + 0.302599i 0.0184612 + 0.0106586i
\(807\) 0 0
\(808\) −7.96840 + 4.60056i −0.280327 + 0.161847i
\(809\) 13.1945i 0.463893i 0.972729 + 0.231946i \(0.0745094\pi\)
−0.972729 + 0.231946i \(0.925491\pi\)
\(810\) 0 0
\(811\) 46.5800i 1.63565i −0.575469 0.817823i \(-0.695181\pi\)
0.575469 0.817823i \(-0.304819\pi\)
\(812\) −4.53927 + 5.72052i −0.159297 + 0.200751i
\(813\) 0 0
\(814\) −0.230252 + 0.398809i −0.00807034 + 0.0139782i
\(815\) −7.71304 + 13.3594i −0.270176 + 0.467958i
\(816\) 0 0
\(817\) −36.0431 + 20.8095i −1.26099 + 0.728031i
\(818\) −11.5341 −0.403280
\(819\) 0 0
\(820\) −6.72373 −0.234803
\(821\) −34.3623 + 19.8391i −1.19925 + 0.692390i −0.960389 0.278663i \(-0.910109\pi\)
−0.238865 + 0.971053i \(0.576775\pi\)
\(822\) 0 0
\(823\) 19.6156 33.9751i 0.683755 1.18430i −0.290071 0.957005i \(-0.593679\pi\)
0.973826 0.227294i \(-0.0729878\pi\)
\(824\) −20.2951 + 35.1521i −0.707013 + 1.22458i
\(825\) 0 0
\(826\) −7.04797 + 8.88206i −0.245230 + 0.309046i
\(827\) 21.0827i 0.733118i 0.930395 + 0.366559i \(0.119464\pi\)
−0.930395 + 0.366559i \(0.880536\pi\)
\(828\) 0 0
\(829\) 13.3261i 0.462834i 0.972855 + 0.231417i \(0.0743361\pi\)
−0.972855 + 0.231417i \(0.925664\pi\)
\(830\) −18.8049 + 10.8570i −0.652726 + 0.376852i
\(831\) 0 0
\(832\) 29.8983 + 17.2618i 1.03654 + 0.598446i
\(833\) −6.59361 28.2550i −0.228455 0.978976i
\(834\) 0 0
\(835\) 14.9071 + 25.8198i 0.515881 + 0.893533i
\(836\) 0.593532 0.0205277
\(837\) 0 0
\(838\) 35.4621i 1.22502i
\(839\) −8.39768 14.5452i −0.289920 0.502156i 0.683870 0.729604i \(-0.260295\pi\)
−0.973790 + 0.227447i \(0.926962\pi\)
\(840\) 0 0
\(841\) −3.68862 + 6.38888i −0.127194 + 0.220306i
\(842\) 25.7690 + 14.8777i 0.888057 + 0.512720i
\(843\) 0 0
\(844\) −2.67538 4.63389i −0.0920903 0.159505i
\(845\) −7.22744 −0.248632
\(846\) 0 0
\(847\) 27.0043 10.6742i 0.927878 0.366769i
\(848\) −5.54523 + 3.20154i −0.190424 + 0.109941i
\(849\) 0 0
\(850\) −13.0011 7.50619i −0.445934 0.257460i
\(851\) 1.16372 + 0.671871i 0.0398916 + 0.0230315i
\(852\) 0 0
\(853\) −35.5011 + 20.4966i −1.21554 + 0.701790i −0.963960 0.266048i \(-0.914282\pi\)
−0.251576 + 0.967838i \(0.580949\pi\)
\(854\) −9.82082 + 3.88195i −0.336061 + 0.132837i
\(855\) 0 0
\(856\) 60.1488 2.05584
\(857\) −20.8718 36.1510i −0.712967 1.23489i −0.963739 0.266848i \(-0.914018\pi\)
0.250772 0.968046i \(-0.419316\pi\)
\(858\) 0 0
\(859\) 24.0479 + 13.8841i 0.820505 + 0.473719i 0.850590 0.525829i \(-0.176245\pi\)
−0.0300858 + 0.999547i \(0.509578\pi\)
\(860\) 5.53267 9.58286i 0.188662 0.326773i
\(861\) 0 0
\(862\) −3.78940 6.56343i −0.129067 0.223551i
\(863\) 45.6090i 1.55255i −0.630396 0.776274i \(-0.717107\pi\)
0.630396 0.776274i \(-0.282893\pi\)
\(864\) 0 0
\(865\) 49.8319 1.69434
\(866\) −19.6728 34.0743i −0.668510 1.15789i
\(867\) 0 0
\(868\) 0.201061 + 0.0298057i 0.00682447 + 0.00101167i
\(869\) 0.591443 + 0.341470i 0.0200633 + 0.0115836i
\(870\) 0 0
\(871\) 4.53275 2.61698i 0.153586 0.0886731i
\(872\) 40.7495i 1.37995i
\(873\) 0 0
\(874\) 4.10358i 0.138806i
\(875\) 11.4455 + 9.08206i 0.386927 + 0.307030i
\(876\) 0 0
\(877\) −8.84368 + 15.3177i −0.298630 + 0.517242i −0.975823 0.218564i \(-0.929863\pi\)
0.677193 + 0.735805i \(0.263196\pi\)
\(878\) −5.01834 + 8.69203i −0.169361 + 0.293342i
\(879\) 0 0
\(880\) 0.954367 0.551004i 0.0321717 0.0185743i
\(881\) 11.6169 0.391384 0.195692 0.980665i \(-0.437305\pi\)
0.195692 + 0.980665i \(0.437305\pi\)
\(882\) 0 0
\(883\) −35.5480 −1.19629 −0.598143 0.801389i \(-0.704095\pi\)
−0.598143 + 0.801389i \(0.704095\pi\)
\(884\) −8.40116 + 4.85041i −0.282562 + 0.163137i
\(885\) 0 0
\(886\) 11.0292 19.1031i 0.370532 0.641781i
\(887\) −12.2751 + 21.2610i −0.412156 + 0.713876i −0.995125 0.0986188i \(-0.968558\pi\)
0.582969 + 0.812494i \(0.301891\pi\)
\(888\) 0 0
\(889\) 25.8853 + 20.5401i 0.868165 + 0.688894i
\(890\) 17.0088i 0.570136i
\(891\) 0 0
\(892\) 1.33948i 0.0448492i
\(893\) −47.5590 + 27.4582i −1.59150 + 0.918854i
\(894\) 0 0
\(895\) −44.7392 25.8302i −1.49547 0.863408i
\(896\) −10.2502 1.51951i −0.342435 0.0507633i
\(897\) 0 0
\(898\) −12.0431 20.8593i −0.401883 0.696082i
\(899\) −0.601834 −0.0200723
\(900\) 0 0
\(901\) 10.7864i 0.359346i
\(902\) −0.373511 0.646940i −0.0124366 0.0215407i
\(903\) 0 0
\(904\) 15.4969 26.8414i 0.515419 0.892731i
\(905\) −16.2257 9.36790i −0.539360 0.311399i
\(906\) 0 0
\(907\) −18.4502 31.9567i −0.612628 1.06110i −0.990796 0.135366i \(-0.956779\pi\)
0.378167 0.925737i \(-0.376554\pi\)
\(908\) −11.0653 −0.367216
\(909\) 0 0
\(910\) 32.6519 12.9066i 1.08240 0.427849i
\(911\) 34.4774 19.9056i 1.14229 0.659500i 0.195292 0.980745i \(-0.437435\pi\)
0.946996 + 0.321245i \(0.104101\pi\)
\(912\) 0 0
\(913\) 0.881773 + 0.509092i 0.0291824 + 0.0168485i
\(914\) 11.6637 + 6.73405i 0.385801 + 0.222743i
\(915\) 0 0
\(916\) 7.35389 4.24577i 0.242979 0.140284i
\(917\) −24.7157 + 9.76957i −0.816186 + 0.322620i
\(918\) 0 0
\(919\) −56.8725 −1.87605 −0.938026 0.346565i \(-0.887348\pi\)
−0.938026 + 0.346565i \(0.887348\pi\)
\(920\) −2.38357 4.12846i −0.0785838 0.136111i
\(921\) 0 0
\(922\) −40.0513 23.1236i −1.31902 0.761535i
\(923\) 0.806939 1.39766i 0.0265607 0.0460045i
\(924\) 0 0
\(925\) 3.75729 + 6.50783i 0.123539 + 0.213976i
\(926\) 11.9409i 0.392403i
\(927\) 0 0
\(928\) −15.0364 −0.493593
\(929\) 22.8885 + 39.6440i 0.750946 + 1.30068i 0.947365 + 0.320156i \(0.103735\pi\)
−0.196419 + 0.980520i \(0.562931\pi\)
\(930\) 0 0
\(931\) −43.1913 + 10.0792i −1.41554 + 0.330332i
\(932\) 8.77383 + 5.06557i 0.287396 + 0.165928i
\(933\) 0 0
\(934\) 3.69047 2.13069i 0.120756 0.0697183i
\(935\) 1.85640i 0.0607108i
\(936\) 0 0
\(937\) 24.0003i 0.784054i −0.919954 0.392027i \(-0.871774\pi\)
0.919954 0.392027i \(-0.128226\pi\)
\(938\) −2.58894 + 3.26265i −0.0845318 + 0.106529i
\(939\) 0 0
\(940\) 7.30039 12.6446i 0.238112 0.412423i
\(941\) −1.64316 + 2.84603i −0.0535654 + 0.0927780i −0.891565 0.452893i \(-0.850392\pi\)
0.837999 + 0.545671i \(0.183725\pi\)
\(942\) 0 0
\(943\) −1.88776 + 1.08990i −0.0614738 + 0.0354919i
\(944\) −8.89158 −0.289396
\(945\) 0 0
\(946\) 1.22938 0.0399707
\(947\) 25.9420 14.9776i 0.843002 0.486707i −0.0152815 0.999883i \(-0.504864\pi\)
0.858284 + 0.513176i \(0.171531\pi\)
\(948\) 0 0
\(949\) −29.5964 + 51.2624i −0.960739 + 1.66405i
\(950\) −11.4742 + 19.8739i −0.372272 + 0.644794i
\(951\) 0 0
\(952\) 20.9662 26.4222i 0.679519 0.856350i
\(953\) 16.0580i 0.520169i −0.965586 0.260084i \(-0.916250\pi\)
0.965586 0.260084i \(-0.0837504\pi\)
\(954\) 0 0
\(955\) 40.3279i 1.30498i
\(956\) 1.14893 0.663336i 0.0371591 0.0214538i
\(957\) 0 0
\(958\) 1.66605 + 0.961893i 0.0538275 + 0.0310773i
\(959\) −21.0457 3.11986i −0.679601 0.100745i
\(960\) 0 0
\(961\) −15.4916 26.8323i −0.499730 0.865557i
\(962\) −11.5054 −0.370948
\(963\) 0 0
\(964\) 2.68312i 0.0864174i
\(965\) 14.1959 + 24.5881i 0.456983 + 0.791518i
\(966\) 0 0
\(967\) 25.0275 43.3489i 0.804831 1.39401i −0.111574 0.993756i \(-0.535589\pi\)
0.916405 0.400252i \(-0.131077\pi\)
\(968\) 29.2345 + 16.8786i 0.939633 + 0.542497i
\(969\) 0 0
\(970\) 4.24484 + 7.35228i 0.136294 + 0.236068i
\(971\) 1.04188 0.0334354 0.0167177 0.999860i \(-0.494678\pi\)
0.0167177 + 0.999860i \(0.494678\pi\)
\(972\) 0 0
\(973\) −18.3844 46.5102i −0.589378 1.49105i
\(974\) −8.21195 + 4.74117i −0.263128 + 0.151917i
\(975\) 0 0
\(976\) −7.17167 4.14057i −0.229560 0.132536i
\(977\) −21.1765 12.2262i −0.677495 0.391152i 0.121416 0.992602i \(-0.461257\pi\)
−0.798910 + 0.601450i \(0.794590\pi\)
\(978\) 0 0
\(979\) 0.690703 0.398777i 0.0220750 0.0127450i
\(980\) 8.60502 8.06246i 0.274877 0.257546i
\(981\) 0 0
\(982\) 12.7440 0.406677
\(983\) 28.0788 + 48.6339i 0.895575 + 1.55118i 0.833092 + 0.553135i \(0.186569\pi\)
0.0624829 + 0.998046i \(0.480098\pi\)
\(984\) 0 0
\(985\) 49.4050 + 28.5240i 1.57417 + 0.908850i
\(986\) −11.4286 + 19.7950i −0.363962 + 0.630400i
\(987\) 0 0
\(988\) 7.41449 + 12.8423i 0.235886 + 0.408567i
\(989\) 3.58731i 0.114070i
\(990\) 0 0
\(991\) 18.2278 0.579025 0.289513 0.957174i \(-0.406507\pi\)
0.289513 + 0.957174i \(0.406507\pi\)
\(992\) 0.209256 + 0.362443i 0.00664390 + 0.0115076i
\(993\) 0 0
\(994\) −0.188326 + 1.27039i −0.00597333 + 0.0402944i
\(995\) −31.7979 18.3586i −1.00806 0.582005i
\(996\) 0 0
\(997\) −29.8197 + 17.2164i −0.944399 + 0.545249i −0.891337 0.453342i \(-0.850232\pi\)
−0.0530623 + 0.998591i \(0.516898\pi\)
\(998\) 20.0671i 0.635212i
\(999\) 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 189.2.o.a.125.1 12
3.2 odd 2 63.2.o.a.41.5 yes 12
4.3 odd 2 3024.2.cc.a.881.1 12
7.2 even 3 1323.2.s.c.962.6 12
7.3 odd 6 1323.2.i.c.1097.2 12
7.4 even 3 1323.2.i.c.1097.1 12
7.5 odd 6 1323.2.s.c.962.5 12
7.6 odd 2 inner 189.2.o.a.125.2 12
9.2 odd 6 inner 189.2.o.a.62.2 12
9.4 even 3 567.2.c.c.566.4 12
9.5 odd 6 567.2.c.c.566.9 12
9.7 even 3 63.2.o.a.20.6 yes 12
12.11 even 2 1008.2.cc.a.545.4 12
21.2 odd 6 441.2.s.c.374.1 12
21.5 even 6 441.2.s.c.374.2 12
21.11 odd 6 441.2.i.c.68.6 12
21.17 even 6 441.2.i.c.68.5 12
21.20 even 2 63.2.o.a.41.6 yes 12
28.27 even 2 3024.2.cc.a.881.6 12
36.7 odd 6 1008.2.cc.a.209.3 12
36.11 even 6 3024.2.cc.a.2897.6 12
63.2 odd 6 1323.2.i.c.521.6 12
63.11 odd 6 1323.2.s.c.656.5 12
63.13 odd 6 567.2.c.c.566.3 12
63.16 even 3 441.2.i.c.227.1 12
63.20 even 6 inner 189.2.o.a.62.1 12
63.25 even 3 441.2.s.c.362.2 12
63.34 odd 6 63.2.o.a.20.5 12
63.38 even 6 1323.2.s.c.656.6 12
63.41 even 6 567.2.c.c.566.10 12
63.47 even 6 1323.2.i.c.521.5 12
63.52 odd 6 441.2.s.c.362.1 12
63.61 odd 6 441.2.i.c.227.2 12
84.83 odd 2 1008.2.cc.a.545.3 12
252.83 odd 6 3024.2.cc.a.2897.1 12
252.223 even 6 1008.2.cc.a.209.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.o.a.20.5 12 63.34 odd 6
63.2.o.a.20.6 yes 12 9.7 even 3
63.2.o.a.41.5 yes 12 3.2 odd 2
63.2.o.a.41.6 yes 12 21.20 even 2
189.2.o.a.62.1 12 63.20 even 6 inner
189.2.o.a.62.2 12 9.2 odd 6 inner
189.2.o.a.125.1 12 1.1 even 1 trivial
189.2.o.a.125.2 12 7.6 odd 2 inner
441.2.i.c.68.5 12 21.17 even 6
441.2.i.c.68.6 12 21.11 odd 6
441.2.i.c.227.1 12 63.16 even 3
441.2.i.c.227.2 12 63.61 odd 6
441.2.s.c.362.1 12 63.52 odd 6
441.2.s.c.362.2 12 63.25 even 3
441.2.s.c.374.1 12 21.2 odd 6
441.2.s.c.374.2 12 21.5 even 6
567.2.c.c.566.3 12 63.13 odd 6
567.2.c.c.566.4 12 9.4 even 3
567.2.c.c.566.9 12 9.5 odd 6
567.2.c.c.566.10 12 63.41 even 6
1008.2.cc.a.209.3 12 36.7 odd 6
1008.2.cc.a.209.4 12 252.223 even 6
1008.2.cc.a.545.3 12 84.83 odd 2
1008.2.cc.a.545.4 12 12.11 even 2
1323.2.i.c.521.5 12 63.47 even 6
1323.2.i.c.521.6 12 63.2 odd 6
1323.2.i.c.1097.1 12 7.4 even 3
1323.2.i.c.1097.2 12 7.3 odd 6
1323.2.s.c.656.5 12 63.11 odd 6
1323.2.s.c.656.6 12 63.38 even 6
1323.2.s.c.962.5 12 7.5 odd 6
1323.2.s.c.962.6 12 7.2 even 3
3024.2.cc.a.881.1 12 4.3 odd 2
3024.2.cc.a.881.6 12 28.27 even 2
3024.2.cc.a.2897.1 12 252.83 odd 6
3024.2.cc.a.2897.6 12 36.11 even 6