Properties

Label 819.2.fm.f.370.7
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(370,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.370");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 370.7
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.f.622.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500642 + 1.86842i) q^{2} +(-1.50830 + 0.870817i) q^{4} +(2.44068 + 2.44068i) q^{5} +(-2.60515 + 0.461729i) q^{7} +(0.353388 + 0.353388i) q^{8} +O(q^{10})\) \(q+(0.500642 + 1.86842i) q^{2} +(-1.50830 + 0.870817i) q^{4} +(2.44068 + 2.44068i) q^{5} +(-2.60515 + 0.461729i) q^{7} +(0.353388 + 0.353388i) q^{8} +(-3.33831 + 5.78213i) q^{10} +(-2.85290 + 0.764433i) q^{11} +(-3.60488 + 0.0697642i) q^{13} +(-2.16695 - 4.63635i) q^{14} +(-2.22499 + 3.85380i) q^{16} +(-0.667729 - 1.15654i) q^{17} +(1.32547 - 4.94673i) q^{19} +(-5.80667 - 1.55589i) q^{20} +(-2.85656 - 4.94771i) q^{22} +(7.61450 + 4.39623i) q^{23} +6.91386i q^{25} +(-1.93510 - 6.70049i) q^{26} +(3.52726 - 2.96503i) q^{28} +(-3.97913 + 6.89205i) q^{29} +(2.04259 + 2.04259i) q^{31} +(-7.34896 - 1.96915i) q^{32} +(1.82661 - 1.82661i) q^{34} +(-7.48528 - 5.23141i) q^{35} +(4.73577 - 1.26895i) q^{37} +9.90616 q^{38} +1.72501i q^{40} +(-1.45657 + 0.390287i) q^{41} +(-0.212417 + 0.122639i) q^{43} +(3.63735 - 3.63735i) q^{44} +(-4.40187 + 16.4280i) q^{46} +(-1.13049 + 1.13049i) q^{47} +(6.57361 - 2.40574i) q^{49} +(-12.9180 + 3.46137i) q^{50} +(5.37648 - 3.24441i) q^{52} -2.62146 q^{53} +(-8.82877 - 5.09729i) q^{55} +(-1.08380 - 0.757458i) q^{56} +(-14.8694 - 3.98423i) q^{58} +(3.96915 + 1.06353i) q^{59} +(7.82911 - 4.52014i) q^{61} +(-2.79382 + 4.83903i) q^{62} -5.81681i q^{64} +(-8.96863 - 8.62809i) q^{65} +(-2.97553 - 11.1048i) q^{67} +(2.01427 + 1.16294i) q^{68} +(6.02703 - 16.6047i) q^{70} +(11.0479 + 2.96028i) q^{71} +(-1.06136 + 1.06136i) q^{73} +(4.74184 + 8.21311i) q^{74} +(2.30849 + 8.61540i) q^{76} +(7.07928 - 3.30873i) q^{77} +7.65266 q^{79} +(-14.8364 + 3.97540i) q^{80} +(-1.45844 - 2.52609i) q^{82} +(-10.1314 - 10.1314i) q^{83} +(1.19303 - 4.45246i) q^{85} +(-0.335486 - 0.335486i) q^{86} +(-1.27832 - 0.738039i) q^{88} +(4.11486 + 15.3569i) q^{89} +(9.35903 - 1.84622i) q^{91} -15.3133 q^{92} +(-2.67819 - 1.54626i) q^{94} +(15.3085 - 8.83835i) q^{95} +(-3.28484 + 12.2592i) q^{97} +(7.78596 + 11.0779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500642 + 1.86842i 0.354007 + 1.32117i 0.881729 + 0.471755i \(0.156379\pi\)
−0.527722 + 0.849417i \(0.676954\pi\)
\(3\) 0 0
\(4\) −1.50830 + 0.870817i −0.754150 + 0.435408i
\(5\) 2.44068 + 2.44068i 1.09151 + 1.09151i 0.995368 + 0.0961385i \(0.0306492\pi\)
0.0961385 + 0.995368i \(0.469351\pi\)
\(6\) 0 0
\(7\) −2.60515 + 0.461729i −0.984654 + 0.174517i
\(8\) 0.353388 + 0.353388i 0.124941 + 0.124941i
\(9\) 0 0
\(10\) −3.33831 + 5.78213i −1.05567 + 1.82847i
\(11\) −2.85290 + 0.764433i −0.860183 + 0.230485i −0.661838 0.749647i \(-0.730223\pi\)
−0.198345 + 0.980132i \(0.563557\pi\)
\(12\) 0 0
\(13\) −3.60488 + 0.0697642i −0.999813 + 0.0193491i
\(14\) −2.16695 4.63635i −0.579142 1.23912i
\(15\) 0 0
\(16\) −2.22499 + 3.85380i −0.556247 + 0.963449i
\(17\) −0.667729 1.15654i −0.161948 0.280502i 0.773619 0.633651i \(-0.218444\pi\)
−0.935567 + 0.353149i \(0.885111\pi\)
\(18\) 0 0
\(19\) 1.32547 4.94673i 0.304084 1.13486i −0.629646 0.776882i \(-0.716800\pi\)
0.933731 0.357977i \(-0.116533\pi\)
\(20\) −5.80667 1.55589i −1.29841 0.347908i
\(21\) 0 0
\(22\) −2.85656 4.94771i −0.609022 1.05486i
\(23\) 7.61450 + 4.39623i 1.58773 + 0.916678i 0.993680 + 0.112253i \(0.0358066\pi\)
0.594053 + 0.804426i \(0.297527\pi\)
\(24\) 0 0
\(25\) 6.91386i 1.38277i
\(26\) −1.93510 6.70049i −0.379504 1.31408i
\(27\) 0 0
\(28\) 3.52726 2.96503i 0.666590 0.560339i
\(29\) −3.97913 + 6.89205i −0.738905 + 1.27982i 0.214084 + 0.976815i \(0.431323\pi\)
−0.952989 + 0.303006i \(0.902010\pi\)
\(30\) 0 0
\(31\) 2.04259 + 2.04259i 0.366861 + 0.366861i 0.866331 0.499470i \(-0.166472\pi\)
−0.499470 + 0.866331i \(0.666472\pi\)
\(32\) −7.34896 1.96915i −1.29912 0.348099i
\(33\) 0 0
\(34\) 1.82661 1.82661i 0.313261 0.313261i
\(35\) −7.48528 5.23141i −1.26524 0.884270i
\(36\) 0 0
\(37\) 4.73577 1.26895i 0.778555 0.208613i 0.152408 0.988318i \(-0.451297\pi\)
0.626148 + 0.779704i \(0.284631\pi\)
\(38\) 9.90616 1.60699
\(39\) 0 0
\(40\) 1.72501i 0.272749i
\(41\) −1.45657 + 0.390287i −0.227478 + 0.0609527i −0.370758 0.928730i \(-0.620902\pi\)
0.143279 + 0.989682i \(0.454235\pi\)
\(42\) 0 0
\(43\) −0.212417 + 0.122639i −0.0323933 + 0.0187023i −0.516109 0.856523i \(-0.672620\pi\)
0.483716 + 0.875225i \(0.339287\pi\)
\(44\) 3.63735 3.63735i 0.548351 0.548351i
\(45\) 0 0
\(46\) −4.40187 + 16.4280i −0.649021 + 2.42218i
\(47\) −1.13049 + 1.13049i −0.164899 + 0.164899i −0.784733 0.619834i \(-0.787200\pi\)
0.619834 + 0.784733i \(0.287200\pi\)
\(48\) 0 0
\(49\) 6.57361 2.40574i 0.939088 0.343678i
\(50\) −12.9180 + 3.46137i −1.82688 + 0.489511i
\(51\) 0 0
\(52\) 5.37648 3.24441i 0.745584 0.449919i
\(53\) −2.62146 −0.360085 −0.180043 0.983659i \(-0.557624\pi\)
−0.180043 + 0.983659i \(0.557624\pi\)
\(54\) 0 0
\(55\) −8.82877 5.09729i −1.19047 0.687319i
\(56\) −1.08380 0.757458i −0.144828 0.101220i
\(57\) 0 0
\(58\) −14.8694 3.98423i −1.95244 0.523155i
\(59\) 3.96915 + 1.06353i 0.516739 + 0.138460i 0.507758 0.861500i \(-0.330474\pi\)
0.00898130 + 0.999960i \(0.497141\pi\)
\(60\) 0 0
\(61\) 7.82911 4.52014i 1.00241 0.578744i 0.0934527 0.995624i \(-0.470210\pi\)
0.908962 + 0.416879i \(0.136876\pi\)
\(62\) −2.79382 + 4.83903i −0.354815 + 0.614558i
\(63\) 0 0
\(64\) 5.81681i 0.727101i
\(65\) −8.96863 8.62809i −1.11242 1.07018i
\(66\) 0 0
\(67\) −2.97553 11.1048i −0.363519 1.35667i −0.869417 0.494079i \(-0.835505\pi\)
0.505898 0.862593i \(-0.331161\pi\)
\(68\) 2.01427 + 1.16294i 0.244266 + 0.141027i
\(69\) 0 0
\(70\) 6.02703 16.6047i 0.720368 1.98464i
\(71\) 11.0479 + 2.96028i 1.31115 + 0.351320i 0.845654 0.533732i \(-0.179211\pi\)
0.465492 + 0.885052i \(0.345877\pi\)
\(72\) 0 0
\(73\) −1.06136 + 1.06136i −0.124222 + 0.124222i −0.766485 0.642262i \(-0.777996\pi\)
0.642262 + 0.766485i \(0.277996\pi\)
\(74\) 4.74184 + 8.21311i 0.551228 + 0.954755i
\(75\) 0 0
\(76\) 2.30849 + 8.61540i 0.264802 + 0.988254i
\(77\) 7.07928 3.30873i 0.806759 0.377065i
\(78\) 0 0
\(79\) 7.65266 0.860992 0.430496 0.902593i \(-0.358339\pi\)
0.430496 + 0.902593i \(0.358339\pi\)
\(80\) −14.8364 + 3.97540i −1.65876 + 0.444463i
\(81\) 0 0
\(82\) −1.45844 2.52609i −0.161058 0.278960i
\(83\) −10.1314 10.1314i −1.11207 1.11207i −0.992871 0.119194i \(-0.961969\pi\)
−0.119194 0.992871i \(-0.538031\pi\)
\(84\) 0 0
\(85\) 1.19303 4.45246i 0.129403 0.482937i
\(86\) −0.335486 0.335486i −0.0361763 0.0361763i
\(87\) 0 0
\(88\) −1.27832 0.738039i −0.136270 0.0786753i
\(89\) 4.11486 + 15.3569i 0.436174 + 1.62782i 0.738241 + 0.674537i \(0.235657\pi\)
−0.302067 + 0.953287i \(0.597677\pi\)
\(90\) 0 0
\(91\) 9.35903 1.84622i 0.981093 0.193537i
\(92\) −15.3133 −1.59652
\(93\) 0 0
\(94\) −2.67819 1.54626i −0.276235 0.159484i
\(95\) 15.3085 8.83835i 1.57062 0.906795i
\(96\) 0 0
\(97\) −3.28484 + 12.2592i −0.333525 + 1.24473i 0.571934 + 0.820300i \(0.306193\pi\)
−0.905459 + 0.424433i \(0.860473\pi\)
\(98\) 7.78596 + 11.0779i 0.786501 + 1.11903i
\(99\) 0 0
\(100\) −6.02071 10.4282i −0.602071 1.04282i
\(101\) −4.49790 + 7.79059i −0.447558 + 0.775192i −0.998226 0.0595314i \(-0.981039\pi\)
0.550669 + 0.834724i \(0.314373\pi\)
\(102\) 0 0
\(103\) 6.31734 0.622466 0.311233 0.950334i \(-0.399258\pi\)
0.311233 + 0.950334i \(0.399258\pi\)
\(104\) −1.29857 1.24926i −0.127335 0.122500i
\(105\) 0 0
\(106\) −1.31241 4.89799i −0.127473 0.475735i
\(107\) 9.52494 16.4977i 0.920810 1.59489i 0.122646 0.992450i \(-0.460862\pi\)
0.798164 0.602440i \(-0.205805\pi\)
\(108\) 0 0
\(109\) −9.27465 + 9.27465i −0.888351 + 0.888351i −0.994365 0.106014i \(-0.966191\pi\)
0.106014 + 0.994365i \(0.466191\pi\)
\(110\) 5.10383 19.0478i 0.486631 1.81613i
\(111\) 0 0
\(112\) 4.01702 11.0671i 0.379573 1.04574i
\(113\) 3.53376 + 6.12066i 0.332429 + 0.575783i 0.982987 0.183673i \(-0.0587986\pi\)
−0.650559 + 0.759456i \(0.725465\pi\)
\(114\) 0 0
\(115\) 7.85477 + 29.3144i 0.732461 + 2.73358i
\(116\) 13.8604i 1.28690i
\(117\) 0 0
\(118\) 7.94848i 0.731717i
\(119\) 2.27354 + 2.70465i 0.208415 + 0.247935i
\(120\) 0 0
\(121\) −1.97158 + 1.13829i −0.179234 + 0.103481i
\(122\) 12.3651 + 12.3651i 1.11948 + 1.11948i
\(123\) 0 0
\(124\) −4.85957 1.30212i −0.436402 0.116934i
\(125\) −4.67113 + 4.67113i −0.417799 + 0.417799i
\(126\) 0 0
\(127\) 12.2515 + 7.07343i 1.08715 + 0.627665i 0.932816 0.360354i \(-0.117344\pi\)
0.154332 + 0.988019i \(0.450677\pi\)
\(128\) −3.82967 + 1.02616i −0.338498 + 0.0907002i
\(129\) 0 0
\(130\) 11.6308 21.0767i 1.02009 1.84855i
\(131\) 9.97987i 0.871945i −0.899960 0.435973i \(-0.856404\pi\)
0.899960 0.435973i \(-0.143596\pi\)
\(132\) 0 0
\(133\) −1.16901 + 13.4990i −0.101366 + 1.17051i
\(134\) 19.2588 11.1191i 1.66371 0.960543i
\(135\) 0 0
\(136\) 0.172740 0.644674i 0.0148123 0.0552803i
\(137\) 0.141310 0.527376i 0.0120729 0.0450567i −0.959627 0.281277i \(-0.909242\pi\)
0.971700 + 0.236220i \(0.0759087\pi\)
\(138\) 0 0
\(139\) 2.89550 1.67172i 0.245593 0.141793i −0.372152 0.928172i \(-0.621380\pi\)
0.617745 + 0.786379i \(0.288047\pi\)
\(140\) 15.8456 + 1.37223i 1.33920 + 0.115974i
\(141\) 0 0
\(142\) 22.1242i 1.85662i
\(143\) 10.2310 2.95472i 0.855562 0.247086i
\(144\) 0 0
\(145\) −26.5331 + 7.10952i −2.20345 + 0.590413i
\(146\) −2.51442 1.45170i −0.208095 0.120144i
\(147\) 0 0
\(148\) −6.03794 + 6.03794i −0.496315 + 0.496315i
\(149\) 8.56339 + 2.29455i 0.701540 + 0.187977i 0.591920 0.805996i \(-0.298370\pi\)
0.109620 + 0.993974i \(0.465037\pi\)
\(150\) 0 0
\(151\) −10.4345 10.4345i −0.849144 0.849144i 0.140882 0.990026i \(-0.455006\pi\)
−0.990026 + 0.140882i \(0.955006\pi\)
\(152\) 2.21652 1.27971i 0.179784 0.103798i
\(153\) 0 0
\(154\) 9.72628 + 11.5706i 0.783766 + 0.932384i
\(155\) 9.97065i 0.800862i
\(156\) 0 0
\(157\) 1.05925i 0.0845376i −0.999106 0.0422688i \(-0.986541\pi\)
0.999106 0.0422688i \(-0.0134586\pi\)
\(158\) 3.83124 + 14.2984i 0.304797 + 1.13752i
\(159\) 0 0
\(160\) −13.1304 22.7425i −1.03805 1.79795i
\(161\) −21.8668 7.93702i −1.72334 0.625525i
\(162\) 0 0
\(163\) 2.76615 10.3234i 0.216661 0.808591i −0.768914 0.639353i \(-0.779202\pi\)
0.985575 0.169239i \(-0.0541309\pi\)
\(164\) 1.85708 1.85708i 0.145013 0.145013i
\(165\) 0 0
\(166\) 13.8575 24.0019i 1.07555 1.86291i
\(167\) −0.203527 0.759573i −0.0157494 0.0587775i 0.957604 0.288088i \(-0.0930196\pi\)
−0.973353 + 0.229310i \(0.926353\pi\)
\(168\) 0 0
\(169\) 12.9903 0.502983i 0.999251 0.0386910i
\(170\) 8.91635 0.683853
\(171\) 0 0
\(172\) 0.213592 0.369952i 0.0162862 0.0282086i
\(173\) 2.78559 + 4.82478i 0.211784 + 0.366821i 0.952273 0.305248i \(-0.0987392\pi\)
−0.740489 + 0.672069i \(0.765406\pi\)
\(174\) 0 0
\(175\) −3.19233 18.0117i −0.241317 1.36155i
\(176\) 3.40171 12.6954i 0.256414 0.956949i
\(177\) 0 0
\(178\) −26.6330 + 15.3766i −1.99623 + 1.15252i
\(179\) 3.04329 + 1.75705i 0.227466 + 0.131328i 0.609403 0.792861i \(-0.291409\pi\)
−0.381936 + 0.924189i \(0.624743\pi\)
\(180\) 0 0
\(181\) 23.3185 1.73325 0.866624 0.498961i \(-0.166285\pi\)
0.866624 + 0.498961i \(0.166285\pi\)
\(182\) 8.13503 + 16.5623i 0.603009 + 1.22768i
\(183\) 0 0
\(184\) 1.13730 + 4.24444i 0.0838425 + 0.312905i
\(185\) 14.6556 + 8.46141i 1.07750 + 0.622096i
\(186\) 0 0
\(187\) 2.78906 + 2.78906i 0.203956 + 0.203956i
\(188\) 0.720666 2.68956i 0.0525599 0.196156i
\(189\) 0 0
\(190\) 24.1778 + 24.1778i 1.75404 + 1.75404i
\(191\) −6.95240 12.0419i −0.503058 0.871322i −0.999994 0.00353445i \(-0.998875\pi\)
0.496936 0.867787i \(-0.334458\pi\)
\(192\) 0 0
\(193\) 2.80644 0.751984i 0.202012 0.0541290i −0.156394 0.987695i \(-0.549987\pi\)
0.358406 + 0.933566i \(0.383320\pi\)
\(194\) −24.5499 −1.76258
\(195\) 0 0
\(196\) −7.82001 + 9.35300i −0.558572 + 0.668071i
\(197\) −0.210804 0.786731i −0.0150192 0.0560523i 0.958010 0.286736i \(-0.0925703\pi\)
−0.973029 + 0.230684i \(0.925904\pi\)
\(198\) 0 0
\(199\) −0.861092 1.49145i −0.0610412 0.105726i 0.833890 0.551931i \(-0.186109\pi\)
−0.894931 + 0.446204i \(0.852775\pi\)
\(200\) −2.44327 + 2.44327i −0.172766 + 0.172766i
\(201\) 0 0
\(202\) −16.8079 4.50367i −1.18260 0.316877i
\(203\) 7.18396 19.7921i 0.504215 1.38913i
\(204\) 0 0
\(205\) −4.50760 2.60246i −0.314824 0.181764i
\(206\) 3.16272 + 11.8034i 0.220357 + 0.822385i
\(207\) 0 0
\(208\) 7.75196 14.0477i 0.537501 0.974031i
\(209\) 15.1258i 1.04627i
\(210\) 0 0
\(211\) −1.84269 + 3.19163i −0.126856 + 0.219721i −0.922457 0.386100i \(-0.873822\pi\)
0.795601 + 0.605821i \(0.207155\pi\)
\(212\) 3.95395 2.28281i 0.271558 0.156784i
\(213\) 0 0
\(214\) 35.5932 + 9.53716i 2.43310 + 0.651947i
\(215\) −0.817765 0.219119i −0.0557711 0.0149438i
\(216\) 0 0
\(217\) −6.26439 4.37814i −0.425254 0.297208i
\(218\) −21.9722 12.6857i −1.48815 0.859182i
\(219\) 0 0
\(220\) 17.7552 1.19706
\(221\) 2.48776 + 4.12260i 0.167345 + 0.277316i
\(222\) 0 0
\(223\) −18.0743 + 4.84300i −1.21035 + 0.324311i −0.806898 0.590691i \(-0.798855\pi\)
−0.403449 + 0.915002i \(0.632189\pi\)
\(224\) 20.0543 + 1.73670i 1.33994 + 0.116038i
\(225\) 0 0
\(226\) −9.66681 + 9.66681i −0.643027 + 0.643027i
\(227\) −0.339915 + 1.26858i −0.0225609 + 0.0841985i −0.976288 0.216474i \(-0.930544\pi\)
0.953727 + 0.300672i \(0.0972111\pi\)
\(228\) 0 0
\(229\) −6.99659 + 6.99659i −0.462348 + 0.462348i −0.899424 0.437077i \(-0.856014\pi\)
0.437077 + 0.899424i \(0.356014\pi\)
\(230\) −50.8392 + 29.3520i −3.35224 + 1.93541i
\(231\) 0 0
\(232\) −3.84174 + 1.02939i −0.252222 + 0.0675828i
\(233\) 24.7335i 1.62035i 0.586189 + 0.810174i \(0.300627\pi\)
−0.586189 + 0.810174i \(0.699373\pi\)
\(234\) 0 0
\(235\) −5.51832 −0.359976
\(236\) −6.91280 + 1.85228i −0.449985 + 0.120573i
\(237\) 0 0
\(238\) −3.91519 + 5.60199i −0.253784 + 0.363123i
\(239\) 7.30351 7.30351i 0.472425 0.472425i −0.430274 0.902698i \(-0.641583\pi\)
0.902698 + 0.430274i \(0.141583\pi\)
\(240\) 0 0
\(241\) 8.63024 + 2.31247i 0.555923 + 0.148959i 0.525833 0.850588i \(-0.323754\pi\)
0.0300903 + 0.999547i \(0.490421\pi\)
\(242\) −3.11386 3.11386i −0.200166 0.200166i
\(243\) 0 0
\(244\) −7.87242 + 13.6354i −0.503980 + 0.872920i
\(245\) 21.9158 + 10.1724i 1.40015 + 0.649894i
\(246\) 0 0
\(247\) −4.43306 + 17.9248i −0.282069 + 1.14053i
\(248\) 1.44365i 0.0916722i
\(249\) 0 0
\(250\) −11.0662 6.38907i −0.699888 0.404081i
\(251\) 6.13739 + 10.6303i 0.387389 + 0.670977i 0.992097 0.125470i \(-0.0400438\pi\)
−0.604709 + 0.796447i \(0.706710\pi\)
\(252\) 0 0
\(253\) −25.0841 6.72126i −1.57702 0.422562i
\(254\) −7.08250 + 26.4323i −0.444396 + 1.65851i
\(255\) 0 0
\(256\) −9.65139 16.7167i −0.603212 1.04479i
\(257\) −2.78870 + 4.83017i −0.173954 + 0.301298i −0.939799 0.341728i \(-0.888988\pi\)
0.765845 + 0.643026i \(0.222321\pi\)
\(258\) 0 0
\(259\) −11.7515 + 5.49243i −0.730201 + 0.341283i
\(260\) 21.0409 + 5.20370i 1.30490 + 0.322720i
\(261\) 0 0
\(262\) 18.6466 4.99634i 1.15199 0.308675i
\(263\) 0.243621 0.421964i 0.0150223 0.0260194i −0.858417 0.512953i \(-0.828551\pi\)
0.873439 + 0.486934i \(0.161885\pi\)
\(264\) 0 0
\(265\) −6.39815 6.39815i −0.393035 0.393035i
\(266\) −25.8070 + 4.57396i −1.58233 + 0.280447i
\(267\) 0 0
\(268\) 14.1583 + 14.1583i 0.864854 + 0.864854i
\(269\) 14.2503 8.22741i 0.868855 0.501634i 0.00188759 0.999998i \(-0.499399\pi\)
0.866968 + 0.498364i \(0.166066\pi\)
\(270\) 0 0
\(271\) 5.62502 + 20.9928i 0.341695 + 1.27522i 0.896426 + 0.443194i \(0.146155\pi\)
−0.554730 + 0.832030i \(0.687178\pi\)
\(272\) 5.94276 0.360333
\(273\) 0 0
\(274\) 1.05610 0.0638016
\(275\) −5.28519 19.7246i −0.318709 1.18944i
\(276\) 0 0
\(277\) 23.9312 13.8167i 1.43789 0.830165i 0.440186 0.897907i \(-0.354913\pi\)
0.997703 + 0.0677412i \(0.0215792\pi\)
\(278\) 4.57307 + 4.57307i 0.274275 + 0.274275i
\(279\) 0 0
\(280\) −0.796488 4.49392i −0.0475993 0.268563i
\(281\) −15.4703 15.4703i −0.922880 0.922880i 0.0743517 0.997232i \(-0.476311\pi\)
−0.997232 + 0.0743517i \(0.976311\pi\)
\(282\) 0 0
\(283\) −2.67677 + 4.63631i −0.159118 + 0.275600i −0.934551 0.355830i \(-0.884198\pi\)
0.775433 + 0.631430i \(0.217532\pi\)
\(284\) −19.2414 + 5.15572i −1.14177 + 0.305936i
\(285\) 0 0
\(286\) 10.6427 + 17.6366i 0.629318 + 1.04287i
\(287\) 3.61438 1.68930i 0.213350 0.0997161i
\(288\) 0 0
\(289\) 7.60828 13.1779i 0.447546 0.775172i
\(290\) −26.5671 46.0156i −1.56008 2.70213i
\(291\) 0 0
\(292\) 0.676596 2.52509i 0.0395948 0.147770i
\(293\) −11.8844 3.18441i −0.694294 0.186035i −0.105620 0.994407i \(-0.533683\pi\)
−0.588673 + 0.808371i \(0.700350\pi\)
\(294\) 0 0
\(295\) 7.09169 + 12.2832i 0.412894 + 0.715154i
\(296\) 2.12199 + 1.22513i 0.123338 + 0.0712093i
\(297\) 0 0
\(298\) 17.1488i 0.993401i
\(299\) −27.7560 15.3167i −1.60517 0.885785i
\(300\) 0 0
\(301\) 0.496752 0.417572i 0.0286323 0.0240684i
\(302\) 14.2720 24.7199i 0.821263 1.42247i
\(303\) 0 0
\(304\) 16.1145 + 16.1145i 0.924232 + 0.924232i
\(305\) 30.1406 + 8.07615i 1.72585 + 0.462439i
\(306\) 0 0
\(307\) 8.36730 8.36730i 0.477547 0.477547i −0.426799 0.904346i \(-0.640359\pi\)
0.904346 + 0.426799i \(0.140359\pi\)
\(308\) −7.79638 + 11.1553i −0.444240 + 0.635633i
\(309\) 0 0
\(310\) −18.6294 + 4.99172i −1.05808 + 0.283511i
\(311\) 2.28494 0.129567 0.0647836 0.997899i \(-0.479364\pi\)
0.0647836 + 0.997899i \(0.479364\pi\)
\(312\) 0 0
\(313\) 24.6656i 1.39418i −0.716982 0.697091i \(-0.754477\pi\)
0.716982 0.697091i \(-0.245523\pi\)
\(314\) 1.97913 0.530306i 0.111689 0.0299269i
\(315\) 0 0
\(316\) −11.5425 + 6.66407i −0.649317 + 0.374883i
\(317\) −3.55562 + 3.55562i −0.199704 + 0.199704i −0.799873 0.600169i \(-0.795100\pi\)
0.600169 + 0.799873i \(0.295100\pi\)
\(318\) 0 0
\(319\) 6.08355 22.7041i 0.340613 1.27119i
\(320\) 14.1970 14.1970i 0.793636 0.793636i
\(321\) 0 0
\(322\) 3.88226 44.8299i 0.216350 2.49827i
\(323\) −6.60615 + 1.77011i −0.367576 + 0.0984917i
\(324\) 0 0
\(325\) −0.482340 24.9236i −0.0267554 1.38251i
\(326\) 20.6733 1.14499
\(327\) 0 0
\(328\) −0.652657 0.376812i −0.0360370 0.0208060i
\(329\) 2.42311 3.46707i 0.133590 0.191146i
\(330\) 0 0
\(331\) 17.6446 + 4.72784i 0.969832 + 0.259866i 0.708757 0.705453i \(-0.249256\pi\)
0.261075 + 0.965318i \(0.415923\pi\)
\(332\) 24.1038 + 6.45858i 1.32287 + 0.354461i
\(333\) 0 0
\(334\) 1.31731 0.760548i 0.0720798 0.0416153i
\(335\) 19.8411 34.3657i 1.08403 1.87760i
\(336\) 0 0
\(337\) 22.3954i 1.21996i −0.792418 0.609978i \(-0.791178\pi\)
0.792418 0.609978i \(-0.208822\pi\)
\(338\) 7.44325 + 24.0195i 0.404859 + 1.30649i
\(339\) 0 0
\(340\) 2.07783 + 7.75456i 0.112686 + 0.420550i
\(341\) −7.38875 4.26590i −0.400123 0.231011i
\(342\) 0 0
\(343\) −16.0144 + 9.30255i −0.864699 + 0.502291i
\(344\) −0.118405 0.0317264i −0.00638394 0.00171057i
\(345\) 0 0
\(346\) −7.62013 + 7.62013i −0.409661 + 0.409661i
\(347\) −7.01258 12.1461i −0.376455 0.652039i 0.614089 0.789237i \(-0.289524\pi\)
−0.990544 + 0.137198i \(0.956190\pi\)
\(348\) 0 0
\(349\) −2.12038 7.91338i −0.113502 0.423594i 0.885669 0.464317i \(-0.153700\pi\)
−0.999170 + 0.0407238i \(0.987034\pi\)
\(350\) 32.0551 14.9820i 1.71342 0.800821i
\(351\) 0 0
\(352\) 22.4711 1.19772
\(353\) −25.1216 + 6.73131i −1.33709 + 0.358271i −0.855353 0.518046i \(-0.826659\pi\)
−0.481734 + 0.876318i \(0.659993\pi\)
\(354\) 0 0
\(355\) 19.7393 + 34.1895i 1.04766 + 1.81459i
\(356\) −19.5794 19.5794i −1.03771 1.03771i
\(357\) 0 0
\(358\) −1.75930 + 6.56579i −0.0929819 + 0.347013i
\(359\) −3.71625 3.71625i −0.196136 0.196136i 0.602205 0.798341i \(-0.294289\pi\)
−0.798341 + 0.602205i \(0.794289\pi\)
\(360\) 0 0
\(361\) −6.25881 3.61353i −0.329411 0.190186i
\(362\) 11.6742 + 43.5687i 0.613582 + 2.28992i
\(363\) 0 0
\(364\) −12.5085 + 10.9347i −0.655623 + 0.573132i
\(365\) −5.18087 −0.271179
\(366\) 0 0
\(367\) −26.8907 15.5253i −1.40368 0.810416i −0.408913 0.912573i \(-0.634092\pi\)
−0.994768 + 0.102157i \(0.967426\pi\)
\(368\) −33.8844 + 19.5632i −1.76634 + 1.01980i
\(369\) 0 0
\(370\) −8.47227 + 31.6189i −0.440452 + 1.64379i
\(371\) 6.82930 1.21040i 0.354559 0.0628410i
\(372\) 0 0
\(373\) −6.35916 11.0144i −0.329265 0.570304i 0.653101 0.757271i \(-0.273468\pi\)
−0.982366 + 0.186967i \(0.940134\pi\)
\(374\) −3.81482 + 6.60746i −0.197260 + 0.341664i
\(375\) 0 0
\(376\) −0.799000 −0.0412053
\(377\) 13.8634 25.1226i 0.714003 1.29388i
\(378\) 0 0
\(379\) −5.03747 18.8001i −0.258757 0.965696i −0.965961 0.258686i \(-0.916710\pi\)
0.707204 0.707010i \(-0.249956\pi\)
\(380\) −15.3932 + 26.6617i −0.789653 + 1.36772i
\(381\) 0 0
\(382\) 19.0187 19.0187i 0.973080 0.973080i
\(383\) −1.38240 + 5.15917i −0.0706372 + 0.263621i −0.992209 0.124587i \(-0.960239\pi\)
0.921572 + 0.388209i \(0.126906\pi\)
\(384\) 0 0
\(385\) 25.3538 + 9.20272i 1.29215 + 0.469014i
\(386\) 2.81004 + 4.86714i 0.143028 + 0.247731i
\(387\) 0 0
\(388\) −5.72099 21.3510i −0.290439 1.08393i
\(389\) 3.01128i 0.152678i −0.997082 0.0763390i \(-0.975677\pi\)
0.997082 0.0763390i \(-0.0243231\pi\)
\(390\) 0 0
\(391\) 11.7420i 0.593817i
\(392\) 3.17319 + 1.47287i 0.160270 + 0.0743913i
\(393\) 0 0
\(394\) 1.36441 0.787740i 0.0687378 0.0396858i
\(395\) 18.6777 + 18.6777i 0.939778 + 0.939778i
\(396\) 0 0
\(397\) 13.7845 + 3.69353i 0.691822 + 0.185373i 0.587565 0.809177i \(-0.300087\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(398\) 2.35556 2.35556i 0.118074 0.118074i
\(399\) 0 0
\(400\) −26.6446 15.3833i −1.33223 0.769164i
\(401\) −29.6397 + 7.94193i −1.48014 + 0.396601i −0.906393 0.422435i \(-0.861176\pi\)
−0.573742 + 0.819036i \(0.694509\pi\)
\(402\) 0 0
\(403\) −7.50580 7.22080i −0.373891 0.359694i
\(404\) 15.6674i 0.779481i
\(405\) 0 0
\(406\) 40.5765 + 3.51391i 2.01378 + 0.174393i
\(407\) −12.5407 + 7.24036i −0.621618 + 0.358891i
\(408\) 0 0
\(409\) 2.88987 10.7851i 0.142895 0.533291i −0.856945 0.515408i \(-0.827641\pi\)
0.999840 0.0178834i \(-0.00569276\pi\)
\(410\) 2.60580 9.72499i 0.128691 0.480283i
\(411\) 0 0
\(412\) −9.52844 + 5.50125i −0.469433 + 0.271027i
\(413\) −10.8313 0.937986i −0.532973 0.0461553i
\(414\) 0 0
\(415\) 49.4550i 2.42765i
\(416\) 26.6295 + 6.58584i 1.30562 + 0.322897i
\(417\) 0 0
\(418\) −28.2613 + 7.57260i −1.38231 + 0.370388i
\(419\) 9.49737 + 5.48331i 0.463977 + 0.267877i 0.713715 0.700436i \(-0.247011\pi\)
−0.249738 + 0.968313i \(0.580345\pi\)
\(420\) 0 0
\(421\) 6.63694 6.63694i 0.323465 0.323465i −0.526630 0.850095i \(-0.676545\pi\)
0.850095 + 0.526630i \(0.176545\pi\)
\(422\) −6.88584 1.84505i −0.335197 0.0898159i
\(423\) 0 0
\(424\) −0.926392 0.926392i −0.0449895 0.0449895i
\(425\) 7.99616 4.61658i 0.387871 0.223937i
\(426\) 0 0
\(427\) −18.3089 + 15.3906i −0.886031 + 0.744801i
\(428\) 33.1779i 1.60371i
\(429\) 0 0
\(430\) 1.63763i 0.0789734i
\(431\) −8.92021 33.2907i −0.429671 1.60355i −0.753506 0.657441i \(-0.771639\pi\)
0.323835 0.946114i \(-0.395028\pi\)
\(432\) 0 0
\(433\) −19.6718 34.0725i −0.945365 1.63742i −0.755019 0.655703i \(-0.772372\pi\)
−0.190346 0.981717i \(-0.560961\pi\)
\(434\) 5.04399 13.8964i 0.242119 0.667048i
\(435\) 0 0
\(436\) 5.91243 22.0655i 0.283154 1.05674i
\(437\) 31.8398 31.8398i 1.52311 1.52311i
\(438\) 0 0
\(439\) 0.862363 1.49366i 0.0411583 0.0712883i −0.844712 0.535220i \(-0.820229\pi\)
0.885871 + 0.463932i \(0.153562\pi\)
\(440\) −1.31866 4.92130i −0.0628645 0.234614i
\(441\) 0 0
\(442\) −6.45727 + 6.71213i −0.307141 + 0.319264i
\(443\) 3.62484 0.172221 0.0861107 0.996286i \(-0.472556\pi\)
0.0861107 + 0.996286i \(0.472556\pi\)
\(444\) 0 0
\(445\) −27.4382 + 47.5243i −1.30069 + 2.25287i
\(446\) −18.0975 31.3458i −0.856943 1.48427i
\(447\) 0 0
\(448\) 2.68579 + 15.1537i 0.126892 + 0.715943i
\(449\) −3.15356 + 11.7692i −0.148826 + 0.555425i 0.850730 + 0.525604i \(0.176160\pi\)
−0.999555 + 0.0298212i \(0.990506\pi\)
\(450\) 0 0
\(451\) 3.85711 2.22690i 0.181624 0.104861i
\(452\) −10.6599 6.15452i −0.501402 0.289484i
\(453\) 0 0
\(454\) −2.54041 −0.119227
\(455\) 27.3485 + 18.3364i 1.28212 + 0.859623i
\(456\) 0 0
\(457\) −4.20527 15.6943i −0.196714 0.734147i −0.991816 0.127672i \(-0.959250\pi\)
0.795102 0.606475i \(-0.207417\pi\)
\(458\) −16.5754 9.56978i −0.774515 0.447167i
\(459\) 0 0
\(460\) −37.3748 37.3748i −1.74261 1.74261i
\(461\) −0.972700 + 3.63017i −0.0453031 + 0.169074i −0.984871 0.173289i \(-0.944561\pi\)
0.939568 + 0.342363i \(0.111227\pi\)
\(462\) 0 0
\(463\) −8.26689 8.26689i −0.384195 0.384195i 0.488416 0.872611i \(-0.337575\pi\)
−0.872611 + 0.488416i \(0.837575\pi\)
\(464\) −17.7070 30.6695i −0.822028 1.42379i
\(465\) 0 0
\(466\) −46.2126 + 12.3826i −2.14076 + 0.573615i
\(467\) −32.1951 −1.48981 −0.744905 0.667170i \(-0.767505\pi\)
−0.744905 + 0.667170i \(0.767505\pi\)
\(468\) 0 0
\(469\) 12.8791 + 27.5559i 0.594703 + 1.27241i
\(470\) −2.76270 10.3105i −0.127434 0.475590i
\(471\) 0 0
\(472\) 1.02681 + 1.77849i 0.0472627 + 0.0818615i
\(473\) 0.512255 0.512255i 0.0235535 0.0235535i
\(474\) 0 0
\(475\) 34.2010 + 9.16414i 1.56925 + 0.420480i
\(476\) −5.78444 2.09958i −0.265129 0.0962343i
\(477\) 0 0
\(478\) 17.3025 + 9.98958i 0.791396 + 0.456913i
\(479\) 0.610243 + 2.27746i 0.0278827 + 0.104060i 0.978465 0.206413i \(-0.0661792\pi\)
−0.950582 + 0.310473i \(0.899513\pi\)
\(480\) 0 0
\(481\) −16.9833 + 4.90478i −0.774373 + 0.223639i
\(482\) 17.2826i 0.787202i
\(483\) 0 0
\(484\) 1.98249 3.43377i 0.0901130 0.156080i
\(485\) −37.9381 + 21.9036i −1.72268 + 0.994589i
\(486\) 0 0
\(487\) −13.0172 3.48794i −0.589864 0.158054i −0.0484729 0.998824i \(-0.515435\pi\)
−0.541391 + 0.840771i \(0.682102\pi\)
\(488\) 4.36407 + 1.16935i 0.197552 + 0.0529339i
\(489\) 0 0
\(490\) −8.03445 + 46.0406i −0.362960 + 2.07990i
\(491\) 24.0166 + 13.8660i 1.08386 + 0.625764i 0.931934 0.362628i \(-0.118121\pi\)
0.151921 + 0.988393i \(0.451454\pi\)
\(492\) 0 0
\(493\) 10.6279 0.478657
\(494\) −35.7105 + 0.691095i −1.60669 + 0.0310938i
\(495\) 0 0
\(496\) −12.4165 + 3.32699i −0.557517 + 0.149386i
\(497\) −30.1483 2.61083i −1.35234 0.117112i
\(498\) 0 0
\(499\) −12.5883 + 12.5883i −0.563529 + 0.563529i −0.930308 0.366779i \(-0.880460\pi\)
0.366779 + 0.930308i \(0.380460\pi\)
\(500\) 2.97776 11.1132i 0.133170 0.496996i
\(501\) 0 0
\(502\) −16.7892 + 16.7892i −0.749338 + 0.749338i
\(503\) −35.8460 + 20.6957i −1.59829 + 0.922776i −0.606479 + 0.795100i \(0.707418\pi\)
−0.991816 + 0.127676i \(0.959248\pi\)
\(504\) 0 0
\(505\) −29.9923 + 8.03641i −1.33464 + 0.357616i
\(506\) 50.2325i 2.23311i
\(507\) 0 0
\(508\) −24.6386 −1.09316
\(509\) −3.60857 + 0.966913i −0.159947 + 0.0428577i −0.337904 0.941181i \(-0.609718\pi\)
0.177957 + 0.984038i \(0.443051\pi\)
\(510\) 0 0
\(511\) 2.27494 3.25505i 0.100637 0.143995i
\(512\) 20.7949 20.7949i 0.919014 0.919014i
\(513\) 0 0
\(514\) −10.4209 2.79228i −0.459647 0.123162i
\(515\) 15.4186 + 15.4186i 0.679426 + 0.679426i
\(516\) 0 0
\(517\) 2.36099 4.08935i 0.103836 0.179850i
\(518\) −16.1454 19.2070i −0.709390 0.843905i
\(519\) 0 0
\(520\) −0.120344 6.21846i −0.00527744 0.272698i
\(521\) 38.7341i 1.69697i −0.529219 0.848486i \(-0.677515\pi\)
0.529219 0.848486i \(-0.322485\pi\)
\(522\) 0 0
\(523\) 30.8201 + 17.7940i 1.34767 + 0.778077i 0.987919 0.154972i \(-0.0495289\pi\)
0.359749 + 0.933049i \(0.382862\pi\)
\(524\) 8.69064 + 15.0526i 0.379652 + 0.657577i
\(525\) 0 0
\(526\) 0.910373 + 0.243934i 0.0396942 + 0.0106360i
\(527\) 0.998443 3.72624i 0.0434929 0.162318i
\(528\) 0 0
\(529\) 27.1537 + 47.0317i 1.18060 + 2.04486i
\(530\) 8.75125 15.1576i 0.380130 0.658405i
\(531\) 0 0
\(532\) −9.99194 21.3785i −0.433205 0.926876i
\(533\) 5.22354 1.50855i 0.226256 0.0653427i
\(534\) 0 0
\(535\) 63.5129 17.0182i 2.74590 0.735763i
\(536\) 2.87280 4.97583i 0.124086 0.214923i
\(537\) 0 0
\(538\) 22.5065 + 22.5065i 0.970326 + 0.970326i
\(539\) −16.9149 + 11.8884i −0.728574 + 0.512072i
\(540\) 0 0
\(541\) 12.2027 + 12.2027i 0.524634 + 0.524634i 0.918967 0.394333i \(-0.129025\pi\)
−0.394333 + 0.918967i \(0.629025\pi\)
\(542\) −36.4073 + 21.0198i −1.56383 + 0.902877i
\(543\) 0 0
\(544\) 2.62971 + 9.81422i 0.112748 + 0.420781i
\(545\) −45.2730 −1.93928
\(546\) 0 0
\(547\) −12.9228 −0.552538 −0.276269 0.961080i \(-0.589098\pi\)
−0.276269 + 0.961080i \(0.589098\pi\)
\(548\) 0.246110 + 0.918495i 0.0105133 + 0.0392362i
\(549\) 0 0
\(550\) 34.2078 19.7499i 1.45863 0.842138i
\(551\) 28.8189 + 28.8189i 1.22773 + 1.22773i
\(552\) 0 0
\(553\) −19.9363 + 3.53345i −0.847779 + 0.150258i
\(554\) 37.7964 + 37.7964i 1.60581 + 1.60581i
\(555\) 0 0
\(556\) −2.91152 + 5.04289i −0.123476 + 0.213866i
\(557\) −5.77693 + 1.54792i −0.244777 + 0.0655877i −0.379121 0.925347i \(-0.623774\pi\)
0.134345 + 0.990935i \(0.457107\pi\)
\(558\) 0 0
\(559\) 0.757180 0.456917i 0.0320253 0.0193255i
\(560\) 36.8155 17.2069i 1.55574 0.727124i
\(561\) 0 0
\(562\) 21.1599 36.6501i 0.892578 1.54599i
\(563\) −3.80484 6.59017i −0.160355 0.277743i 0.774641 0.632401i \(-0.217930\pi\)
−0.934996 + 0.354658i \(0.884597\pi\)
\(564\) 0 0
\(565\) −6.31379 + 23.5634i −0.265623 + 0.991319i
\(566\) −10.0027 2.68021i −0.420443 0.112657i
\(567\) 0 0
\(568\) 2.85807 + 4.95032i 0.119922 + 0.207711i
\(569\) 23.3969 + 13.5082i 0.980848 + 0.566293i 0.902526 0.430635i \(-0.141711\pi\)
0.0783217 + 0.996928i \(0.475044\pi\)
\(570\) 0 0
\(571\) 17.2946i 0.723757i 0.932225 + 0.361878i \(0.117864\pi\)
−0.932225 + 0.361878i \(0.882136\pi\)
\(572\) −12.8584 + 13.3660i −0.537639 + 0.558859i
\(573\) 0 0
\(574\) 4.96583 + 5.90745i 0.207270 + 0.246572i
\(575\) −30.3950 + 52.6456i −1.26756 + 2.19547i
\(576\) 0 0
\(577\) 1.06958 + 1.06958i 0.0445272 + 0.0445272i 0.729020 0.684493i \(-0.239976\pi\)
−0.684493 + 0.729020i \(0.739976\pi\)
\(578\) 28.4309 + 7.61804i 1.18257 + 0.316869i
\(579\) 0 0
\(580\) 33.8287 33.8287i 1.40466 1.40466i
\(581\) 31.0718 + 21.7158i 1.28907 + 0.900925i
\(582\) 0 0
\(583\) 7.47878 2.00393i 0.309739 0.0829944i
\(584\) −0.750141 −0.0310410
\(585\) 0 0
\(586\) 23.7993i 0.983139i
\(587\) 42.5402 11.3986i 1.75582 0.470471i 0.769967 0.638083i \(-0.220272\pi\)
0.985853 + 0.167613i \(0.0536058\pi\)
\(588\) 0 0
\(589\) 12.8116 7.39677i 0.527892 0.304778i
\(590\) −19.3997 + 19.3997i −0.798674 + 0.798674i
\(591\) 0 0
\(592\) −5.64678 + 21.0741i −0.232081 + 0.866139i
\(593\) −14.9496 + 14.9496i −0.613907 + 0.613907i −0.943962 0.330055i \(-0.892933\pi\)
0.330055 + 0.943962i \(0.392933\pi\)
\(594\) 0 0
\(595\) −1.05220 + 12.1502i −0.0431361 + 0.498109i
\(596\) −14.9143 + 3.99627i −0.610913 + 0.163694i
\(597\) 0 0
\(598\) 14.7221 59.5281i 0.602033 2.43428i
\(599\) −22.8397 −0.933203 −0.466601 0.884468i \(-0.654522\pi\)
−0.466601 + 0.884468i \(0.654522\pi\)
\(600\) 0 0
\(601\) −24.7100 14.2663i −1.00794 0.581936i −0.0973547 0.995250i \(-0.531038\pi\)
−0.910589 + 0.413313i \(0.864371\pi\)
\(602\) 1.02889 + 0.719087i 0.0419346 + 0.0293078i
\(603\) 0 0
\(604\) 24.8248 + 6.65178i 1.01011 + 0.270657i
\(605\) −7.59020 2.03379i −0.308586 0.0826852i
\(606\) 0 0
\(607\) −22.6642 + 13.0852i −0.919913 + 0.531112i −0.883607 0.468229i \(-0.844892\pi\)
−0.0363055 + 0.999341i \(0.511559\pi\)
\(608\) −19.4817 + 33.7433i −0.790087 + 1.36847i
\(609\) 0 0
\(610\) 60.3585i 2.44385i
\(611\) 3.99640 4.15413i 0.161677 0.168058i
\(612\) 0 0
\(613\) 7.15174 + 26.6907i 0.288856 + 1.07803i 0.945975 + 0.324239i \(0.105108\pi\)
−0.657119 + 0.753787i \(0.728225\pi\)
\(614\) 19.8226 + 11.4446i 0.799977 + 0.461867i
\(615\) 0 0
\(616\) 3.67099 + 1.33247i 0.147909 + 0.0536866i
\(617\) −18.4697 4.94894i −0.743562 0.199237i −0.132901 0.991129i \(-0.542429\pi\)
−0.610660 + 0.791893i \(0.709096\pi\)
\(618\) 0 0
\(619\) −5.80624 + 5.80624i −0.233373 + 0.233373i −0.814099 0.580726i \(-0.802769\pi\)
0.580726 + 0.814099i \(0.302769\pi\)
\(620\) −8.68261 15.0387i −0.348702 0.603970i
\(621\) 0 0
\(622\) 1.14394 + 4.26923i 0.0458677 + 0.171180i
\(623\) −17.8105 38.1070i −0.713563 1.52672i
\(624\) 0 0
\(625\) 11.7678 0.470712
\(626\) 46.0857 12.3486i 1.84196 0.493550i
\(627\) 0 0
\(628\) 0.922415 + 1.59767i 0.0368084 + 0.0637540i
\(629\) −4.62979 4.62979i −0.184602 0.184602i
\(630\) 0 0
\(631\) 1.64802 6.15049i 0.0656065 0.244847i −0.925333 0.379155i \(-0.876215\pi\)
0.990940 + 0.134308i \(0.0428813\pi\)
\(632\) 2.70436 + 2.70436i 0.107573 + 0.107573i
\(633\) 0 0
\(634\) −8.42348 4.86330i −0.334539 0.193146i
\(635\) 12.6381 + 47.1661i 0.501529 + 1.87173i
\(636\) 0 0
\(637\) −23.5292 + 9.13101i −0.932262 + 0.361784i
\(638\) 45.4665 1.80004
\(639\) 0 0
\(640\) −11.8515 6.84248i −0.468473 0.270473i
\(641\) 12.5318 7.23523i 0.494976 0.285774i −0.231660 0.972797i \(-0.574416\pi\)
0.726636 + 0.687022i \(0.241083\pi\)
\(642\) 0 0
\(643\) 7.35905 27.4644i 0.290213 1.08309i −0.654733 0.755861i \(-0.727219\pi\)
0.944945 0.327228i \(-0.106115\pi\)
\(644\) 39.8933 7.07057i 1.57202 0.278620i
\(645\) 0 0
\(646\) −6.61463 11.4569i −0.260249 0.450765i
\(647\) −4.83456 + 8.37370i −0.190066 + 0.329204i −0.945272 0.326284i \(-0.894204\pi\)
0.755206 + 0.655488i \(0.227537\pi\)
\(648\) 0 0
\(649\) −12.1366 −0.476403
\(650\) 46.3263 13.3790i 1.81707 0.524768i
\(651\) 0 0
\(652\) 4.81762 + 17.9796i 0.188672 + 0.704135i
\(653\) 16.6586 28.8535i 0.651900 1.12912i −0.330762 0.943714i \(-0.607306\pi\)
0.982661 0.185409i \(-0.0593610\pi\)
\(654\) 0 0
\(655\) 24.3577 24.3577i 0.951734 0.951734i
\(656\) 1.73677 6.48172i 0.0678095 0.253069i
\(657\) 0 0
\(658\) 7.69105 + 2.79163i 0.299828 + 0.108829i
\(659\) −13.4367 23.2730i −0.523418 0.906586i −0.999629 0.0272549i \(-0.991323\pi\)
0.476211 0.879331i \(-0.342010\pi\)
\(660\) 0 0
\(661\) −4.30948 16.0832i −0.167619 0.625564i −0.997692 0.0679081i \(-0.978368\pi\)
0.830072 0.557656i \(-0.188299\pi\)
\(662\) 35.3344i 1.37331i
\(663\) 0 0
\(664\) 7.16062i 0.277886i
\(665\) −35.7999 + 30.0936i −1.38826 + 1.16698i
\(666\) 0 0
\(667\) −60.5981 + 34.9863i −2.34637 + 1.35468i
\(668\) 0.968429 + 0.968429i 0.0374696 + 0.0374696i
\(669\) 0 0
\(670\) 74.1428 + 19.8665i 2.86439 + 0.767510i
\(671\) −18.8803 + 18.8803i −0.728868 + 0.728868i
\(672\) 0 0
\(673\) 22.1779 + 12.8044i 0.854896 + 0.493574i 0.862300 0.506398i \(-0.169023\pi\)
−0.00740398 + 0.999973i \(0.502357\pi\)
\(674\) 41.8440 11.2121i 1.61177 0.431873i
\(675\) 0 0
\(676\) −19.1552 + 12.0708i −0.736739 + 0.464261i
\(677\) 11.4036i 0.438275i −0.975694 0.219138i \(-0.929676\pi\)
0.975694 0.219138i \(-0.0703244\pi\)
\(678\) 0 0
\(679\) 2.89708 33.4538i 0.111180 1.28384i
\(680\) 1.99505 1.15184i 0.0765066 0.0441711i
\(681\) 0 0
\(682\) 4.27137 15.9410i 0.163559 0.610412i
\(683\) −9.10656 + 33.9861i −0.348453 + 1.30044i 0.540073 + 0.841618i \(0.318396\pi\)
−0.888526 + 0.458826i \(0.848270\pi\)
\(684\) 0 0
\(685\) 1.63205 0.942264i 0.0623574 0.0360021i
\(686\) −25.3986 25.2645i −0.969722 0.964602i
\(687\) 0 0
\(688\) 1.09148i 0.0416123i
\(689\) 9.45004 0.182884i 0.360018 0.00696733i
\(690\) 0 0
\(691\) −40.2685 + 10.7899i −1.53189 + 0.410468i −0.923634 0.383276i \(-0.874796\pi\)
−0.608252 + 0.793744i \(0.708129\pi\)
\(692\) −8.40300 4.85147i −0.319434 0.184425i
\(693\) 0 0
\(694\) 19.1833 19.1833i 0.728188 0.728188i
\(695\) 11.1471 + 2.98686i 0.422834 + 0.113298i
\(696\) 0 0
\(697\) 1.42398 + 1.42398i 0.0539370 + 0.0539370i
\(698\) 13.7240 7.92353i 0.519460 0.299910i
\(699\) 0 0
\(700\) 20.4998 + 24.3870i 0.774821 + 0.921743i
\(701\) 8.53135i 0.322225i −0.986936 0.161112i \(-0.948492\pi\)
0.986936 0.161112i \(-0.0515081\pi\)
\(702\) 0 0
\(703\) 25.1085i 0.946986i
\(704\) 4.44656 + 16.5948i 0.167586 + 0.625440i
\(705\) 0 0
\(706\) −25.1538 43.5677i −0.946676 1.63969i
\(707\) 8.12056 22.3725i 0.305405 0.841403i
\(708\) 0 0
\(709\) −0.424499 + 1.58425i −0.0159424 + 0.0594978i −0.973439 0.228947i \(-0.926472\pi\)
0.957496 + 0.288445i \(0.0931383\pi\)
\(710\) −53.9981 + 53.9981i −2.02651 + 2.02651i
\(711\) 0 0
\(712\) −3.97278 + 6.88106i −0.148886 + 0.257879i
\(713\) 6.57361 + 24.5331i 0.246184 + 0.918770i
\(714\) 0 0
\(715\) 32.1822 + 17.7592i 1.20355 + 0.664156i
\(716\) −6.12026 −0.228725
\(717\) 0 0
\(718\) 5.08300 8.80401i 0.189696 0.328563i
\(719\) 7.35184 + 12.7338i 0.274177 + 0.474889i 0.969927 0.243395i \(-0.0782611\pi\)
−0.695750 + 0.718284i \(0.744928\pi\)
\(720\) 0 0
\(721\) −16.4576 + 2.91690i −0.612914 + 0.108631i
\(722\) 3.61816 13.5032i 0.134654 0.502536i
\(723\) 0 0
\(724\) −35.1712 + 20.3061i −1.30713 + 0.754671i
\(725\) −47.6507 27.5111i −1.76970 1.02174i
\(726\) 0 0
\(727\) −26.9644 −1.00005 −0.500026 0.866010i \(-0.666676\pi\)
−0.500026 + 0.866010i \(0.666676\pi\)
\(728\) 3.95980 + 2.65493i 0.146760 + 0.0983984i
\(729\) 0 0
\(730\) −2.59376 9.68004i −0.0959993 0.358274i
\(731\) 0.283674 + 0.163779i 0.0104920 + 0.00605759i
\(732\) 0 0
\(733\) 27.0088 + 27.0088i 0.997593 + 0.997593i 0.999997 0.00240406i \(-0.000765238\pi\)
−0.00240406 + 0.999997i \(0.500765\pi\)
\(734\) 15.5453 58.0157i 0.573786 2.14140i
\(735\) 0 0
\(736\) −47.3018 47.3018i −1.74357 1.74357i
\(737\) 16.9778 + 29.4064i 0.625386 + 1.08320i
\(738\) 0 0
\(739\) 45.4039 12.1659i 1.67021 0.447532i 0.705043 0.709165i \(-0.250928\pi\)
0.965167 + 0.261633i \(0.0842610\pi\)
\(740\) −29.4734 −1.08346
\(741\) 0 0
\(742\) 5.68057 + 12.1540i 0.208540 + 0.446188i
\(743\) −7.20187 26.8777i −0.264211 0.986049i −0.962732 0.270459i \(-0.912825\pi\)
0.698521 0.715590i \(-0.253842\pi\)
\(744\) 0 0
\(745\) 15.3002 + 26.5008i 0.560557 + 0.970914i
\(746\) 17.3958 17.3958i 0.636907 0.636907i
\(747\) 0 0
\(748\) −6.63550 1.77798i −0.242618 0.0650093i
\(749\) −17.1964 + 47.3769i −0.628344 + 1.73111i
\(750\) 0 0
\(751\) 35.2503 + 20.3518i 1.28630 + 0.742647i 0.977993 0.208639i \(-0.0669034\pi\)
0.308310 + 0.951286i \(0.400237\pi\)
\(752\) −1.84134 6.87199i −0.0671469 0.250596i
\(753\) 0 0
\(754\) 53.8801 + 13.3253i 1.96220 + 0.485279i
\(755\) 50.9344i 1.85369i
\(756\) 0 0
\(757\) 6.21461 10.7640i 0.225874 0.391225i −0.730707 0.682691i \(-0.760810\pi\)
0.956581 + 0.291466i \(0.0941430\pi\)
\(758\) 32.6045 18.8242i 1.18425 0.683726i
\(759\) 0 0
\(760\) 8.53318 + 2.28646i 0.309531 + 0.0829386i
\(761\) −9.99508 2.67817i −0.362322 0.0970838i 0.0730655 0.997327i \(-0.476722\pi\)
−0.435387 + 0.900243i \(0.643388\pi\)
\(762\) 0 0
\(763\) 19.8795 28.4442i 0.719686 1.02975i
\(764\) 20.9726 + 12.1085i 0.758762 + 0.438071i
\(765\) 0 0
\(766\) −10.3316 −0.373295
\(767\) −14.3825 3.55699i −0.519322 0.128435i
\(768\) 0 0
\(769\) −12.9631 + 3.47345i −0.467461 + 0.125256i −0.484858 0.874593i \(-0.661129\pi\)
0.0173970 + 0.999849i \(0.494462\pi\)
\(770\) −4.50135 + 51.9789i −0.162218 + 1.87319i
\(771\) 0 0
\(772\) −3.57812 + 3.57812i −0.128779 + 0.128779i
\(773\) 8.80996 32.8792i 0.316872 1.18258i −0.605362 0.795950i \(-0.706972\pi\)
0.922234 0.386632i \(-0.126362\pi\)
\(774\) 0 0
\(775\) −14.1222 + 14.1222i −0.507285 + 0.507285i
\(776\) −5.49307 + 3.17143i −0.197190 + 0.113848i
\(777\) 0 0
\(778\) 5.62633 1.50757i 0.201714 0.0540491i
\(779\) 7.72259i 0.276691i
\(780\) 0 0
\(781\) −33.7816 −1.20880
\(782\) 21.9389 5.87852i 0.784534 0.210215i
\(783\) 0 0
\(784\) −5.35497 + 30.6861i −0.191249 + 1.09593i
\(785\) 2.58530 2.58530i 0.0922733 0.0922733i
\(786\) 0 0
\(787\) −44.0881 11.8134i −1.57157 0.421101i −0.635267 0.772293i \(-0.719110\pi\)
−0.936303 + 0.351192i \(0.885776\pi\)
\(788\) 1.00305 + 1.00305i 0.0357323 + 0.0357323i
\(789\) 0 0
\(790\) −25.5470 + 44.2487i −0.908921 + 1.57430i
\(791\) −12.0321 14.3136i −0.427811 0.508933i
\(792\) 0 0
\(793\) −27.9076 + 16.8407i −0.991029 + 0.598032i
\(794\) 27.6043i 0.979639i
\(795\) 0 0
\(796\) 2.59757 + 1.49971i 0.0920683 + 0.0531557i
\(797\) −2.38876 4.13745i −0.0846141 0.146556i 0.820613 0.571485i \(-0.193632\pi\)
−0.905227 + 0.424929i \(0.860299\pi\)
\(798\) 0 0
\(799\) 2.06231 + 0.552595i 0.0729594 + 0.0195494i
\(800\) 13.6144 50.8097i 0.481342 1.79639i
\(801\) 0 0
\(802\) −29.6777 51.4033i −1.04796 1.81511i
\(803\) 2.21661 3.83929i 0.0782226 0.135485i
\(804\) 0 0
\(805\) −33.9981 72.7416i −1.19828 2.56381i
\(806\) 9.73377 17.6390i 0.342857 0.621308i
\(807\) 0 0
\(808\) −4.34260 + 1.16360i −0.152772 + 0.0409351i
\(809\) −15.3742 + 26.6289i −0.540529 + 0.936224i 0.458345 + 0.888775i \(0.348443\pi\)
−0.998874 + 0.0474491i \(0.984891\pi\)
\(810\) 0 0
\(811\) 27.1910 + 27.1910i 0.954806 + 0.954806i 0.999022 0.0442157i \(-0.0140789\pi\)
−0.0442157 + 0.999022i \(0.514079\pi\)
\(812\) 6.39972 + 36.1083i 0.224586 + 1.26715i
\(813\) 0 0
\(814\) −19.8064 19.8064i −0.694214 0.694214i
\(815\) 31.9474 18.4449i 1.11907 0.646095i
\(816\) 0 0
\(817\) 0.325109 + 1.21332i 0.0113741 + 0.0424488i
\(818\) 21.5980 0.755155
\(819\) 0 0
\(820\) 9.06508 0.316566
\(821\) −0.190347 0.710386i −0.00664317 0.0247926i 0.962525 0.271194i \(-0.0874185\pi\)
−0.969168 + 0.246401i \(0.920752\pi\)
\(822\) 0 0
\(823\) −29.7715 + 17.1886i −1.03777 + 0.599157i −0.919201 0.393789i \(-0.871164\pi\)
−0.118570 + 0.992946i \(0.537831\pi\)
\(824\) 2.23247 + 2.23247i 0.0777718 + 0.0777718i
\(825\) 0 0
\(826\) −3.67004 20.7070i −0.127697 0.720488i
\(827\) −17.5703 17.5703i −0.610979 0.610979i 0.332222 0.943201i \(-0.392202\pi\)
−0.943201 + 0.332222i \(0.892202\pi\)
\(828\) 0 0
\(829\) 0.225668 0.390869i 0.00783778 0.0135754i −0.862080 0.506772i \(-0.830838\pi\)
0.869918 + 0.493197i \(0.164172\pi\)
\(830\) 92.4028 24.7592i 3.20735 0.859406i
\(831\) 0 0
\(832\) 0.405805 + 20.9689i 0.0140688 + 0.726965i
\(833\) −7.17173 5.99626i −0.248486 0.207758i
\(834\) 0 0
\(835\) 1.35713 2.35062i 0.0469655 0.0813466i
\(836\) −13.1718 22.8142i −0.455556 0.789046i
\(837\) 0 0
\(838\) −5.49034 + 20.4902i −0.189661 + 0.707824i
\(839\) 42.5808 + 11.4095i 1.47005 + 0.393899i 0.902949 0.429748i \(-0.141398\pi\)
0.567102 + 0.823647i \(0.308064\pi\)
\(840\) 0 0
\(841\) −17.1669 29.7339i −0.591961 1.02531i
\(842\) 15.7233 + 9.07786i 0.541861 + 0.312844i
\(843\) 0 0
\(844\) 6.41858i 0.220937i
\(845\) 32.9327 + 30.4775i 1.13292 + 1.04846i
\(846\) 0 0
\(847\) 4.61067 3.87575i 0.158425 0.133172i
\(848\) 5.83272 10.1026i 0.200297 0.346924i
\(849\) 0 0
\(850\) 12.6289 + 12.6289i 0.433169 + 0.433169i
\(851\) 41.6391 + 11.1572i 1.42737 + 0.382463i
\(852\) 0 0
\(853\) −3.63181 + 3.63181i −0.124351 + 0.124351i −0.766543 0.642193i \(-0.778025\pi\)
0.642193 + 0.766543i \(0.278025\pi\)
\(854\) −37.9222 26.5036i −1.29767 0.906934i
\(855\) 0 0
\(856\) 9.19607 2.46408i 0.314315 0.0842205i
\(857\) −12.7961 −0.437106 −0.218553 0.975825i \(-0.570134\pi\)
−0.218553 + 0.975825i \(0.570134\pi\)
\(858\) 0 0
\(859\) 8.61431i 0.293917i −0.989143 0.146958i \(-0.953052\pi\)
0.989143 0.146958i \(-0.0469483\pi\)
\(860\) 1.42425 0.381626i 0.0485664 0.0130133i
\(861\) 0 0
\(862\) 57.7351 33.3334i 1.96647 1.13534i
\(863\) −36.6611 + 36.6611i −1.24796 + 1.24796i −0.291338 + 0.956620i \(0.594101\pi\)
−0.956620 + 0.291338i \(0.905899\pi\)
\(864\) 0 0
\(865\) −4.97702 + 18.5745i −0.169224 + 0.631552i
\(866\) 53.8132 53.8132i 1.82865 1.82865i
\(867\) 0 0
\(868\) 13.2611 + 1.14841i 0.450112 + 0.0389796i
\(869\) −21.8323 + 5.84995i −0.740610 + 0.198446i
\(870\) 0 0
\(871\) 11.5011 + 39.8240i 0.389701 + 1.34938i
\(872\) −6.55509 −0.221983
\(873\) 0 0
\(874\) 75.4305 + 43.5498i 2.55147 + 1.47309i
\(875\) 10.0122 14.3258i 0.338474 0.484300i
\(876\) 0 0
\(877\) −8.12066 2.17593i −0.274215 0.0734758i 0.119091 0.992883i \(-0.462002\pi\)
−0.393306 + 0.919408i \(0.628669\pi\)
\(878\) 3.22251 + 0.863470i 0.108755 + 0.0291407i
\(879\) 0 0
\(880\) 39.2879 22.6829i 1.32439 0.764639i
\(881\) 24.2720 42.0404i 0.817745 1.41638i −0.0895951 0.995978i \(-0.528557\pi\)
0.907340 0.420397i \(-0.138109\pi\)
\(882\) 0 0
\(883\) 41.4666i 1.39546i 0.716359 + 0.697731i \(0.245807\pi\)
−0.716359 + 0.697731i \(0.754193\pi\)
\(884\) −7.34232 4.05173i −0.246949 0.136274i
\(885\) 0 0
\(886\) 1.81475 + 6.77273i 0.0609676 + 0.227534i
\(887\) 35.6698 + 20.5940i 1.19768 + 0.691479i 0.960037 0.279875i \(-0.0902929\pi\)
0.237640 + 0.971353i \(0.423626\pi\)
\(888\) 0 0
\(889\) −35.1831 12.7705i −1.18000 0.428307i
\(890\) −102.532 27.4734i −3.43688 0.920909i
\(891\) 0 0
\(892\) 23.0441 23.0441i 0.771575 0.771575i
\(893\) 4.09379 + 7.09065i 0.136993 + 0.237280i
\(894\) 0 0
\(895\) 3.13932 + 11.7161i 0.104936 + 0.391626i
\(896\) 9.50305 4.44156i 0.317475 0.148382i
\(897\) 0 0
\(898\) −23.5687 −0.786497
\(899\) −22.2054 + 5.94992i −0.740591 + 0.198441i
\(900\) 0 0
\(901\) 1.75042 + 3.03182i 0.0583151 + 0.101005i
\(902\) 6.09182 + 6.09182i 0.202836 + 0.202836i
\(903\) 0 0
\(904\) −0.914177 + 3.41175i −0.0304051 + 0.113473i
\(905\) 56.9130 + 56.9130i 1.89185 + 1.89185i
\(906\) 0 0
\(907\) −11.7828 6.80280i −0.391241 0.225883i 0.291456 0.956584i \(-0.405860\pi\)
−0.682698 + 0.730701i \(0.739193\pi\)
\(908\) −0.592007 2.20940i −0.0196464 0.0733215i
\(909\) 0 0
\(910\) −20.5683 + 60.2784i −0.681832 + 1.99821i
\(911\) 4.82402 0.159827 0.0799135 0.996802i \(-0.474536\pi\)
0.0799135 + 0.996802i \(0.474536\pi\)
\(912\) 0 0
\(913\) 36.6487 + 21.1591i 1.21289 + 0.700265i
\(914\) 27.2181 15.7144i 0.900296 0.519786i
\(915\) 0 0
\(916\) 4.46020 16.6457i 0.147369 0.549989i
\(917\) 4.60799 + 25.9991i 0.152169 + 0.858564i
\(918\) 0 0
\(919\) 26.8960 + 46.5852i 0.887216 + 1.53670i 0.843153 + 0.537674i \(0.180697\pi\)
0.0440628 + 0.999029i \(0.485970\pi\)
\(920\) −7.58356 + 13.1351i −0.250023 + 0.433052i
\(921\) 0 0
\(922\) −7.26965 −0.239413
\(923\) −40.0329 9.90069i −1.31770 0.325885i
\(924\) 0 0
\(925\) 8.77331 + 32.7425i 0.288465 + 1.07657i
\(926\) 11.3073 19.5848i 0.371580 0.643596i
\(927\) 0 0
\(928\) 42.8139 42.8139i 1.40543 1.40543i
\(929\) 1.83189 6.83673i 0.0601025 0.224306i −0.929341 0.369221i \(-0.879624\pi\)
0.989444 + 0.144916i \(0.0462911\pi\)
\(930\) 0 0
\(931\) −3.18743 35.7067i −0.104464 1.17024i
\(932\) −21.5384 37.3056i −0.705513 1.22198i
\(933\) 0 0
\(934\) −16.1182 60.1539i −0.527403 1.96830i
\(935\) 13.6144i 0.445240i
\(936\) 0 0
\(937\) 17.4831i 0.571147i −0.958357 0.285574i \(-0.907816\pi\)
0.958357 0.285574i \(-0.0921841\pi\)
\(938\) −45.0381 + 37.8592i −1.47055 + 1.23615i
\(939\) 0 0
\(940\) 8.32328 4.80545i 0.271475 0.156736i
\(941\) 11.1218 + 11.1218i 0.362560 + 0.362560i 0.864754 0.502195i \(-0.167474\pi\)
−0.502195 + 0.864754i \(0.667474\pi\)
\(942\) 0 0
\(943\) −12.8069 3.43159i −0.417049 0.111748i
\(944\) −12.9299 + 12.9299i −0.420834 + 0.420834i
\(945\) 0 0
\(946\) 1.21356 + 0.700652i 0.0394564 + 0.0227802i
\(947\) 42.7851 11.4642i 1.39033 0.372537i 0.515466 0.856910i \(-0.327619\pi\)
0.874862 + 0.484373i \(0.160952\pi\)
\(948\) 0 0
\(949\) 3.75202 3.90011i 0.121796 0.126603i
\(950\) 68.4899i 2.22210i
\(951\) 0 0
\(952\) −0.152349 + 1.75923i −0.00493765 + 0.0570170i
\(953\) 46.1967 26.6717i 1.49646 0.863980i 0.496465 0.868057i \(-0.334631\pi\)
0.999992 + 0.00407700i \(0.00129775\pi\)
\(954\) 0 0
\(955\) 12.4219 46.3591i 0.401962 1.50014i
\(956\) −4.65586 + 17.3759i −0.150581 + 0.561976i
\(957\) 0 0
\(958\) −3.94974 + 2.28038i −0.127610 + 0.0736758i
\(959\) −0.124629 + 1.43914i −0.00402448 + 0.0464722i
\(960\) 0 0
\(961\) 22.6556i 0.730826i
\(962\) −17.6667 29.2765i −0.569599 0.943911i
\(963\) 0 0
\(964\) −15.0307 + 4.02747i −0.484107 + 0.129716i
\(965\) 8.68499 + 5.01428i 0.279580 + 0.161415i
\(966\) 0 0
\(967\) 8.45160 8.45160i 0.271785 0.271785i −0.558033 0.829819i \(-0.688444\pi\)
0.829819 + 0.558033i \(0.188444\pi\)
\(968\) −1.09899 0.294473i −0.0353228 0.00946472i
\(969\) 0 0
\(970\) −59.9184 59.9184i −1.92386 1.92386i
\(971\) −14.8642 + 8.58184i −0.477014 + 0.275404i −0.719171 0.694833i \(-0.755478\pi\)
0.242157 + 0.970237i \(0.422145\pi\)
\(972\) 0 0
\(973\) −6.77132 + 5.69200i −0.217079 + 0.182477i
\(974\) 26.0677i 0.835264i
\(975\) 0 0
\(976\) 40.2290i 1.28770i
\(977\) 0.601718 + 2.24564i 0.0192507 + 0.0718444i 0.974883 0.222718i \(-0.0714928\pi\)
−0.955632 + 0.294562i \(0.904826\pi\)
\(978\) 0 0
\(979\) −23.4786 40.6661i −0.750379 1.29969i
\(980\) −41.9139 + 3.74153i −1.33889 + 0.119519i
\(981\) 0 0
\(982\) −13.8838 + 51.8150i −0.443050 + 1.65348i
\(983\) 28.2865 28.2865i 0.902198 0.902198i −0.0934279 0.995626i \(-0.529782\pi\)
0.995626 + 0.0934279i \(0.0297825\pi\)
\(984\) 0 0
\(985\) 1.40566 2.43467i 0.0447879 0.0775749i
\(986\) 5.32077 + 19.8574i 0.169448 + 0.632388i
\(987\) 0 0
\(988\) −8.92286 30.8964i −0.283874 0.982945i
\(989\) −2.15660 −0.0685758
\(990\) 0 0
\(991\) 19.2831 33.3993i 0.612549 1.06097i −0.378261 0.925699i \(-0.623478\pi\)
0.990809 0.135266i \(-0.0431889\pi\)
\(992\) −10.9888 19.0331i −0.348894 0.604302i
\(993\) 0 0
\(994\) −10.2154 57.6368i −0.324012 1.82813i
\(995\) 1.53852 5.74182i 0.0487742 0.182028i
\(996\) 0 0
\(997\) 27.3485 15.7897i 0.866136 0.500064i 7.37730e−5 1.00000i \(-0.499977\pi\)
0.866062 + 0.499936i \(0.166643\pi\)
\(998\) −29.8224 17.2180i −0.944012 0.545026i
\(999\) 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 819.2.fm.f.370.7 32
3.2 odd 2 273.2.by.c.97.2 yes 32
7.6 odd 2 819.2.fm.e.370.7 32
13.11 odd 12 819.2.fm.e.622.7 32
21.20 even 2 273.2.by.d.97.2 yes 32
39.11 even 12 273.2.by.d.76.2 yes 32
91.76 even 12 inner 819.2.fm.f.622.7 32
273.167 odd 12 273.2.by.c.76.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.by.c.76.2 32 273.167 odd 12
273.2.by.c.97.2 yes 32 3.2 odd 2
273.2.by.d.76.2 yes 32 39.11 even 12
273.2.by.d.97.2 yes 32 21.20 even 2
819.2.fm.e.370.7 32 7.6 odd 2
819.2.fm.e.622.7 32 13.11 odd 12
819.2.fm.f.370.7 32 1.1 even 1 trivial
819.2.fm.f.622.7 32 91.76 even 12 inner